LMFDB - Embedded newform 1197.2.j.d.856.2

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			856.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1197.856
Dual form			1197.2.j.d.172.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(0.914214 - 1.58346i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.58579 q^{8} +(-0.378680 - 0.655892i) q^{10} +(0.914214 + 1.58346i) q^{11} -2.82843 q^{13} +(-0.207107 + 1.07616i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(3.82843 + 6.63103i) q^{17} +(0.500000 - 0.866025i) q^{19} +3.34315 q^{20} +0.757359 q^{22} +(1.91421 - 3.31552i) q^{23} +(0.828427 + 1.43488i) q^{25} +(-0.585786 + 1.01461i) q^{26} +(-3.65685 - 3.16693i) q^{28} -0.828427 q^{29} +(4.41421 + 7.64564i) q^{31} +(2.20711 + 3.82282i) q^{32} +3.17157 q^{34} +(-0.914214 + 4.75039i) q^{35} +(-3.41421 + 5.91359i) q^{37} +(-0.207107 - 0.358719i) q^{38} +(1.44975 - 2.51104i) q^{40} +3.65685 q^{41} -1.34315 q^{43} +(-1.67157 + 2.89525i) q^{44} +(-0.792893 - 1.37333i) q^{46} +(5.91421 - 10.2437i) q^{47} +(5.50000 - 4.33013i) q^{49} +0.686292 q^{50} +(-2.58579 - 4.47871i) q^{52} +(-1.00000 - 1.73205i) q^{53} +3.34315 q^{55} +(-3.96447 + 1.37333i) q^{56} +(-0.171573 + 0.297173i) q^{58} +(2.58579 + 4.47871i) q^{59} +(1.67157 - 2.89525i) q^{61} +3.65685 q^{62} -4.17157 q^{64} +(-2.58579 + 4.47871i) q^{65} +(6.00000 + 10.3923i) q^{67} +(-7.00000 + 12.1244i) q^{68} +(1.51472 + 1.31178i) q^{70} -15.6569 q^{71} +(-6.15685 - 10.6640i) q^{73} +(1.41421 + 2.44949i) q^{74} +1.82843 q^{76} +(-3.65685 - 3.16693i) q^{77} +(-6.82843 + 11.8272i) q^{79} +(2.74264 + 4.75039i) q^{80} +(0.757359 - 1.31178i) q^{82} -9.82843 q^{83} +14.0000 q^{85} +(-0.278175 + 0.481813i) q^{86} +(1.44975 + 2.51104i) q^{88} +(2.58579 - 4.47871i) q^{89} +(7.07107 - 2.44949i) q^{91} +7.00000 q^{92} +(-2.44975 - 4.24309i) q^{94} +(-0.914214 - 1.58346i) q^{95} +11.1716 q^{97} +(-0.414214 - 2.86976i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.207107	−	0.358719i	0.146447	−	0.253653i	−0.783465	−	0.621436i	$-0.786550\pi$
$2$	0.207107	−	0.358719i	0.146447	−	0.253653i	0.929912	+	0.367783i	$0.119883\pi$
$3$		0			0
$3$		0			0
$4$	0.914214	+	1.58346i	0.457107	+	0.791732i
$5$	0.914214	−	1.58346i	0.408849	−	0.708147i	−0.585912	−	0.810374i	$-0.699264\pi$
$5$	0.914214	−	1.58346i	0.408849	−	0.708147i	0.994761	+	0.102228i	$0.0325970\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	1.58579			0.560660
$9$		0			0
$10$	−0.378680	−	0.655892i	−0.119749	−	0.207411i
$11$	0.914214	+	1.58346i	0.275646	+	0.477432i	0.970298	−	0.241913i	$-0.0777750\pi$
$11$	0.914214	+	1.58346i	0.275646	+	0.477432i	−0.694652	+	0.719346i	$0.744442\pi$
$12$		0			0
$13$	−2.82843			−0.784465			−0.392232	−	0.919866i	$-0.628297\pi$
$13$	−2.82843			−0.784465			−0.392232	+	0.919866i	$0.628297\pi$
$14$	−0.207107	+	1.07616i	−0.0553516	+	0.287615i
$15$		0			0
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	3.82843	+	6.63103i	0.928530	+	1.60826i	0.785783	+	0.618502i	$0.212260\pi$
$17$	3.82843	+	6.63103i	0.928530	+	1.60826i	0.142747	+	0.989759i	$0.454407\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$	3.34315			0.747550
$21$		0			0
$22$	0.757359			0.161470
$23$	1.91421	−	3.31552i	0.399141	−	0.691333i	−0.594479	−	0.804111i	$-0.702642\pi$
$23$	1.91421	−	3.31552i	0.399141	−	0.691333i	0.993620	+	0.112778i	$0.0359750\pi$
$24$		0			0
$25$	0.828427	+	1.43488i	0.165685	+	0.286976i
$26$	−0.585786	+	1.01461i	−0.114882	+	0.198982i
$27$		0			0
$28$	−3.65685	−	3.16693i	−0.691080	−	0.598493i
$29$	−0.828427			−0.153835			−0.0769175	−	0.997037i	$-0.524508\pi$
$29$	−0.828427			−0.153835			−0.0769175	+	0.997037i	$0.524508\pi$
$30$		0			0
$31$	4.41421	+	7.64564i	0.792816	+	1.37320i	0.924217	+	0.381869i	$0.124719\pi$
$31$	4.41421	+	7.64564i	0.792816	+	1.37320i	−0.131401	+	0.991329i	$0.541947\pi$
$32$	2.20711	+	3.82282i	0.390165	+	0.675786i
$33$		0			0
$34$	3.17157			0.543920
$35$	−0.914214	+	4.75039i	−0.154530	+	0.802963i
$36$		0			0
$37$	−3.41421	+	5.91359i	−0.561293	+	0.972188i	0.436091	+	0.899903i	$0.356363\pi$
$37$	−3.41421	+	5.91359i	−0.561293	+	0.972188i	−0.997384	+	0.0722857i	$0.976971\pi$
$38$	−0.207107	−	0.358719i	−0.0335972	−	0.0581920i
$39$		0			0
$40$	1.44975	−	2.51104i	0.229225	−	0.397030i
$41$	3.65685			0.571105			0.285552	−	0.958363i	$-0.407823\pi$
$41$	3.65685			0.571105			0.285552	+	0.958363i	$0.407823\pi$
$42$		0			0
$43$	−1.34315			−0.204828			−0.102414	−	0.994742i	$-0.532657\pi$
$43$	−1.34315			−0.204828			−0.102414	+	0.994742i	$0.532657\pi$
$44$	−1.67157	+	2.89525i	−0.251999	+	0.436475i
$45$		0			0
$46$	−0.792893	−	1.37333i	−0.116906	−	0.202487i
$47$	5.91421	−	10.2437i	0.862677	−	1.49420i	−0.00665898	−	0.999978i	$-0.502120\pi$
$47$	5.91421	−	10.2437i	0.862677	−	1.49420i	0.869336	−	0.494222i	$-0.164547\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	0.686292			0.0970563
$51$		0			0
$52$	−2.58579	−	4.47871i	−0.358584	−	0.621086i
$53$	−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
$55$	3.34315			0.450790
$56$	−3.96447	+	1.37333i	−0.529774	+	0.183519i
$57$		0			0
$58$	−0.171573	+	0.297173i	−0.0225286	+	0.0390207i
$59$	2.58579	+	4.47871i	0.336641	+	0.583079i	0.983799	−	0.179277i	$-0.0573759\pi$
$59$	2.58579	+	4.47871i	0.336641	+	0.583079i	−0.647158	+	0.762356i	$0.724043\pi$
$60$		0			0
$61$	1.67157	−	2.89525i	0.214023	−	0.370699i	−0.738947	−	0.673764i	$-0.764677\pi$
$61$	1.67157	−	2.89525i	0.214023	−	0.370699i	0.952970	+	0.303065i	$0.0980099\pi$
$62$	3.65685			0.464421
$63$		0			0
$64$	−4.17157			−0.521447
$65$	−2.58579	+	4.47871i	−0.320727	+	0.555516i
$66$		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
$70$	1.51472	+	1.31178i	0.181044	+	0.156788i
$71$	−15.6569			−1.85813			−0.929063	−	0.369921i	$-0.879385\pi$
$71$	−15.6569			−1.85813			−0.929063	+	0.369921i	$0.879385\pi$
$72$		0			0
$73$	−6.15685	−	10.6640i	−0.720605	−	1.24812i	−0.960757	−	0.277390i	$-0.910531\pi$
$73$	−6.15685	−	10.6640i	−0.720605	−	1.24812i	0.240152	−	0.970735i	$-0.422803\pi$
$74$	1.41421	+	2.44949i	0.164399	+	0.284747i
$75$		0			0
$76$	1.82843			0.209735
$77$	−3.65685	−	3.16693i	−0.416737	−	0.360905i
$78$		0			0
$79$	−6.82843	+	11.8272i	−0.768258	+	1.33066i	0.170249	+	0.985401i	$0.445543\pi$
$79$	−6.82843	+	11.8272i	−0.768258	+	1.33066i	−0.938507	+	0.345261i	$0.887790\pi$
$80$	2.74264	+	4.75039i	0.306637	+	0.531110i
$81$		0			0
$82$	0.757359	−	1.31178i	0.0836363	−	0.144862i
$83$	−9.82843			−1.07881			−0.539405	−	0.842046i	$-0.681351\pi$
$83$	−9.82843			−1.07881			−0.539405	+	0.842046i	$0.681351\pi$
$84$		0			0
$85$	14.0000			1.51851
$86$	−0.278175	+	0.481813i	−0.0299963	+	0.0519552i
$87$		0			0
$88$	1.44975	+	2.51104i	0.154544	+	0.267677i
$89$	2.58579	−	4.47871i	0.274093	−	0.474743i	−0.695813	−	0.718223i	$-0.744956\pi$
$89$	2.58579	−	4.47871i	0.274093	−	0.474743i	0.969906	+	0.243480i	$0.0782891\pi$
$90$		0			0
$91$	7.07107	−	2.44949i	0.741249	−	0.256776i
$92$	7.00000			0.729800
$93$		0			0
$94$	−2.44975	−	4.24309i	−0.252672	−	0.437641i
$95$	−0.914214	−	1.58346i	−0.0937963	−	0.162460i
$96$		0			0
$97$	11.1716			1.13430			0.567151	−	0.823614i	$-0.308046\pi$
$97$	11.1716			1.13430			0.567151	+	0.823614i	$0.308046\pi$
$98$	−0.414214	−	2.86976i	−0.0418419	−	0.289889i
$99$		0			0
$100$	−1.51472	+	2.62357i	−0.151472	+	0.262357i
$101$	6.74264	+	11.6786i	0.670918	+	1.16206i	0.977644	+	0.210266i	$0.0674330\pi$
$101$	6.74264	+	11.6786i	0.670918	+	1.16206i	−0.306726	+	0.951798i	$0.599234\pi$
$102$		0			0
$103$	3.82843	−	6.63103i	0.377226	−	0.653375i	−0.613431	−	0.789748i	$-0.710211\pi$
$103$	3.82843	−	6.63103i	0.377226	−	0.653375i	0.990658	+	0.136373i	$0.0435446\pi$
$104$	−4.48528			−0.439818
$105$		0			0
$106$	−0.828427			−0.0804640
$107$	1.41421	−	2.44949i	0.136717	−	0.236801i	−0.789535	−	0.613706i	$-0.789678\pi$
$107$	1.41421	−	2.44949i	0.136717	−	0.236801i	0.926252	+	0.376905i	$0.123012\pi$
$108$		0			0
$109$	5.07107	+	8.78335i	0.485720	+	0.841292i	0.999865	−	0.0164111i	$-0.00522406\pi$
$109$	5.07107	+	8.78335i	0.485720	+	0.841292i	−0.514145	+	0.857703i	$0.671891\pi$
$110$	0.692388	−	1.19925i	0.0660166	−	0.114344i
$111$		0			0
$112$	1.50000	−	7.79423i	0.141737	−	0.736485i
$113$	7.17157			0.674645			0.337322	−	0.941389i	$-0.390479\pi$
$113$	7.17157			0.674645			0.337322	+	0.941389i	$0.390479\pi$
$114$		0			0
$115$	−3.50000	−	6.06218i	−0.326377	−	0.565301i
$116$	−0.757359	−	1.31178i	−0.0703190	−	0.121796i
$117$		0			0
$118$	2.14214			0.197200
$119$	−15.3137	−	13.2621i	−1.40381	−	1.21573i
$120$		0			0
$121$	3.82843	−	6.63103i	0.348039	−	0.602821i
$122$	−0.692388	−	1.19925i	−0.0626859	−	0.108575i
$123$		0			0
$124$	−8.07107	+	13.9795i	−0.724803	+	1.25540i
$125$	12.1716			1.08866
$126$		0			0
$127$	−16.9706			−1.50589			−0.752947	−	0.658081i	$-0.771368\pi$
$127$	−16.9706			−1.50589			−0.752947	+	0.658081i	$0.771368\pi$
$128$	−5.27817	+	9.14207i	−0.466529	+	0.808052i
$129$		0			0
$130$	1.07107	+	1.85514i	0.0939389	+	0.162707i
$131$	10.8284	−	18.7554i	0.946084	−	1.63867i	0.192518	−	0.981293i	$-0.438335\pi$
$131$	10.8284	−	18.7554i	0.946084	−	1.63867i	0.753566	−	0.657372i	$-0.228332\pi$
$132$		0			0
$133$	−0.500000	+	2.59808i	−0.0433555	+	0.225282i
$134$	4.97056			0.429391
$135$		0			0
$136$	6.07107	+	10.5154i	0.520590	+	0.901688i
$137$	−4.08579	−	7.07679i	−0.349072	−	0.604611i	0.637013	−	0.770853i	$-0.280170\pi$
$137$	−4.08579	−	7.07679i	−0.349072	−	0.604611i	−0.986085	+	0.166242i	$0.946837\pi$
$138$		0			0
$139$	4.65685			0.394989			0.197495	−	0.980304i	$-0.436720\pi$
$139$	4.65685			0.394989			0.197495	+	0.980304i	$0.436720\pi$
$140$	−8.35786	+	2.89525i	−0.706368	+	0.244693i
$141$		0			0
$142$	−3.24264	+	5.61642i	−0.272116	+	0.471319i
$143$	−2.58579	−	4.47871i	−0.216234	−	0.374529i
$144$		0			0
$145$	−0.757359	+	1.31178i	−0.0628953	+	0.108938i
$146$	−5.10051			−0.422121
$147$		0			0
$148$	−12.4853			−1.02628
$149$	−0.914214	+	1.58346i	−0.0748953	+	0.129722i	−0.901041	−	0.433734i	$-0.857196\pi$
$149$	−0.914214	+	1.58346i	−0.0748953	+	0.129722i	0.826145	+	0.563457i	$0.190529\pi$
$150$		0			0
$151$	−6.65685	−	11.5300i	−0.541727	−	0.938299i	−0.998805	−	0.0488722i	$-0.984437\pi$
$151$	−6.65685	−	11.5300i	−0.541727	−	0.938299i	0.457078	−	0.889427i	$-0.348896\pi$
$152$	0.792893	−	1.37333i	0.0643121	−	0.111392i
$153$		0			0
$154$	−1.89340	+	0.655892i	−0.152574	+	0.0528533i
$155$	16.1421			1.29657
$156$		0			0
$157$	0.328427	+	0.568852i	0.0262113	+	0.0453994i	0.878834	−	0.477129i	$-0.158322\pi$
$157$	0.328427	+	0.568852i	0.0262113	+	0.0453994i	−0.852622	+	0.522528i	$0.824989\pi$
$158$	2.82843	+	4.89898i	0.225018	+	0.389742i
$159$		0			0
$160$	8.07107			0.638074
$161$	−1.91421	+	9.94655i	−0.150861	+	0.783898i
$162$		0			0
$163$	5.98528	−	10.3668i	0.468803	−	0.811991i	−0.530561	−	0.847647i	$-0.678019\pi$
$163$	5.98528	−	10.3668i	0.468803	−	0.811991i	0.999364	+	0.0356556i	$0.0113519\pi$
$164$	3.34315	+	5.79050i	0.261056	+	0.452162i
$165$		0			0
$166$	−2.03553	+	3.52565i	−0.157988	+	0.273643i
$167$	−3.17157			−0.245424			−0.122712	−	0.992442i	$-0.539159\pi$
$167$	−3.17157			−0.245424			−0.122712	+	0.992442i	$0.539159\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$	2.89949	−	5.02207i	0.222381	−	0.385175i
$171$		0			0
$172$	−1.22792	−	2.12682i	−0.0936282	−	0.162169i
$173$	−1.41421	+	2.44949i	−0.107521	+	0.186231i	−0.914765	−	0.403986i	$-0.867625\pi$
$173$	−1.41421	+	2.44949i	−0.107521	+	0.186231i	0.807245	+	0.590217i	$0.200958\pi$
$174$		0			0
$175$	−3.31371	−	2.86976i	−0.250493	−	0.216933i
$176$	−5.48528			−0.413469
$177$		0			0
$178$	−1.07107	−	1.85514i	−0.0802799	−	0.139049i
$179$	3.24264	+	5.61642i	0.242366	+	0.419791i	0.961388	−	0.275197i	$-0.0887431\pi$
$179$	3.24264	+	5.61642i	0.242366	+	0.419791i	−0.719022	+	0.694988i	$0.755410\pi$
$180$		0			0
$181$	−0.343146			−0.0255058			−0.0127529	−	0.999919i	$-0.504059\pi$
$181$	−0.343146			−0.0255058			−0.0127529	+	0.999919i	$0.504059\pi$
$182$	0.585786	−	3.04384i	0.0434214	−	0.225624i
$183$		0			0
$184$	3.03553	−	5.25770i	0.223783	−	0.387603i
$185$	6.24264	+	10.8126i	0.458968	+	0.794956i
$186$		0			0
$187$	−7.00000	+	12.1244i	−0.511891	+	0.886621i
$188$	21.6274			1.57734
$189$		0			0
$190$	−0.757359			−0.0549446
$191$	3.08579	−	5.34474i	0.223280	−	0.386732i	−0.732522	−	0.680743i	$-0.761657\pi$
$191$	3.08579	−	5.34474i	0.223280	−	0.386732i	0.955802	+	0.294011i	$0.0949903\pi$
$192$		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	$0.879318\pi$
$194$	2.31371	−	4.00746i	0.166115	−	0.287719i
$195$		0			0
$196$	11.8848	+	4.75039i	0.848913	+	0.339314i
$197$	0.514719			0.0366722			0.0183361	−	0.999832i	$-0.494163\pi$
$197$	0.514719			0.0366722			0.0183361	+	0.999832i	$0.494163\pi$
$198$		0			0
$199$	−7.32843	−	12.6932i	−0.519498	−	0.899798i	−0.999743	−	0.0226631i	$-0.992785\pi$
$199$	−7.32843	−	12.6932i	−0.519498	−	0.899798i	0.480245	−	0.877135i	$-0.340548\pi$
$200$	1.31371	+	2.27541i	0.0928932	+	0.160896i
$201$		0			0
$202$	5.58579			0.393015
$203$	2.07107	−	0.717439i	0.145360	−	0.0503543i
$204$		0			0
$205$	3.34315	−	5.79050i	0.233495	−	0.404426i
$206$	−1.58579	−	2.74666i	−0.110487	−	0.191369i
$207$		0			0
$208$	4.24264	−	7.34847i	0.294174	−	0.509525i
$209$	1.82843			0.126475
$210$		0			0
$211$	−0.485281			−0.0334081			−0.0167041	−	0.999860i	$-0.505317\pi$
$211$	−0.485281			−0.0334081			−0.0167041	+	0.999860i	$0.505317\pi$
$212$	1.82843	−	3.16693i	0.125577	−	0.217506i
$213$		0			0
$214$	−0.585786	−	1.01461i	−0.0400435	−	0.0693574i
$215$	−1.22792	+	2.12682i	−0.0837436	+	0.145048i
$216$		0			0
$217$	−17.6569	−	15.2913i	−1.19863	−	1.03804i
$218$	4.20101			0.284528
$219$		0			0
$220$	3.05635	+	5.29375i	0.206059	+	0.356905i
$221$	−10.8284	−	18.7554i	−0.728399	−	1.26162i
$222$		0			0
$223$	−17.7990			−1.19191			−0.595954	−	0.803018i	$-0.703226\pi$
$223$	−17.7990			−1.19191			−0.595954	+	0.803018i	$0.703226\pi$
$224$	−8.82843	−	7.64564i	−0.589874	−	0.510846i
$225$		0			0
$226$	1.48528	−	2.57258i	0.0987994	−	0.171126i
$227$	−8.82843	−	15.2913i	−0.585963	−	1.01492i	−0.994755	−	0.102290i	$-0.967383\pi$
$227$	−8.82843	−	15.2913i	−0.585963	−	1.01492i	0.408791	−	0.912628i	$-0.365950\pi$
$228$		0			0
$229$	2.17157	−	3.76127i	0.143502	−	0.248552i	−0.785311	−	0.619101i	$-0.787497\pi$
$229$	2.17157	−	3.76127i	0.143502	−	0.248552i	0.928813	+	0.370549i	$0.120830\pi$
$230$	−2.89949			−0.191187
$231$		0			0
$232$	−1.31371			−0.0862492
$233$	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
$235$	−10.8137	−	18.7299i	−0.705409	−	1.22180i
$236$	−4.72792	+	8.18900i	−0.307762	+	0.533059i
$237$		0			0
$238$	−7.92893	+	2.74666i	−0.513956	+	0.178040i
$239$	−13.6569			−0.883388			−0.441694	−	0.897166i	$-0.645622\pi$
$239$	−13.6569			−0.883388			−0.441694	+	0.897166i	$0.645622\pi$
$240$		0			0
$241$	9.89949	+	17.1464i	0.637683	+	1.10450i	0.985940	+	0.167100i	$0.0534402\pi$
$241$	9.89949	+	17.1464i	0.637683	+	1.10450i	−0.348257	+	0.937399i	$0.613227\pi$
$242$	−1.58579	−	2.74666i	−0.101938	−	0.176562i
$243$		0			0
$244$	6.11270			0.391325
$245$	−1.82843	−	12.6677i	−0.116814	−	0.809311i
$246$		0			0
$247$	−1.41421	+	2.44949i	−0.0899843	+	0.155857i
$248$	7.00000	+	12.1244i	0.444500	+	0.769897i
$249$		0			0
$250$	2.52082	−	4.36618i	0.159430	−	0.276141i
$251$	−3.48528			−0.219989			−0.109995	−	0.993932i	$-0.535083\pi$
$251$	−3.48528			−0.219989			−0.109995	+	0.993932i	$0.535083\pi$
$252$		0			0
$253$	7.00000			0.440086
$254$	−3.51472	+	6.08767i	−0.220533	+	0.381974i
$255$		0			0
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	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
$259$	3.41421	−	17.7408i	0.212149	−	1.10236i
$260$	−9.45584			−0.586427
$261$		0			0
$262$	−4.48528	−	7.76874i	−0.277102	−	0.479954i
$263$	−5.65685	−	9.79796i	−0.348817	−	0.604168i	0.637223	−	0.770680i	$-0.280083\pi$
$263$	−5.65685	−	9.79796i	−0.348817	−	0.604168i	−0.986040	+	0.166511i	$0.946750\pi$
$264$		0			0
$265$	−3.65685			−0.224639
$266$	0.828427	+	0.717439i	0.0507941	+	0.0439890i
$267$		0			0
$268$	−10.9706	+	19.0016i	−0.670134	+	1.16071i
$269$	−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
$271$	−12.8137	+	22.1940i	−0.778377	+	1.34819i	0.154499	+	0.987993i	$0.450624\pi$
$271$	−12.8137	+	22.1940i	−0.778377	+	1.34819i	−0.932877	+	0.360196i	$0.882710\pi$
$272$	−22.9706			−1.39279
$273$		0			0
$274$	−3.38478			−0.204482
$275$	−1.51472	+	2.62357i	−0.0913410	+	0.158207i
$276$		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	$0.961047\pi$
$278$	0.964466	−	1.67050i	0.0578448	−	0.100190i
$279$		0			0
$280$	−1.44975	+	7.53311i	−0.0866390	+	0.450189i
$281$	26.9706			1.60893			0.804464	−	0.594001i	$-0.202452\pi$
$281$	26.9706			1.60893			0.804464	+	0.594001i	$0.202452\pi$
$282$		0			0
$283$	6.81371	+	11.8017i	0.405033	+	0.701538i	0.994325	−	0.106382i	$-0.0339267\pi$
$283$	6.81371	+	11.8017i	0.405033	+	0.701538i	−0.589292	+	0.807920i	$0.700593\pi$
$284$	−14.3137	−	24.7921i	−0.849362	−	1.47114i
$285$		0			0
$286$	−2.14214			−0.126667
$287$	−9.14214	+	3.16693i	−0.539643	+	0.186938i
$288$		0			0
$289$	−20.8137	+	36.0504i	−1.22434	+	2.12061i
$290$	0.313708	+	0.543359i	0.0184216	+	0.0319071i
$291$		0			0
$292$	11.2574	−	19.4983i	0.658787	−	1.14105i
$293$	−4.82843			−0.282080			−0.141040	−	0.990004i	$-0.545045\pi$
$293$	−4.82843			−0.282080			−0.141040	+	0.990004i	$0.545045\pi$
$294$		0			0
$295$	9.45584			0.550541
$296$	−5.41421	+	9.37769i	−0.314695	+	0.545067i
$297$		0			0
$298$	0.378680	+	0.655892i	0.0219363	+	0.0379948i
$299$	−5.41421	+	9.37769i	−0.313112	+	0.542326i
$300$		0			0
$301$	3.35786	−	1.16320i	0.193544	−	0.0670456i
$302$	−5.51472			−0.317336
$303$		0			0
$304$	1.50000	+	2.59808i	0.0860309	+	0.149010i
$305$	−3.05635	−	5.29375i	−0.175006	−	0.303119i
$306$		0			0
$307$	−14.4853			−0.826719			−0.413359	−	0.910568i	$-0.635645\pi$
$307$	−14.4853			−0.826719			−0.413359	+	0.910568i	$0.635645\pi$
$308$	1.67157	−	8.68575i	0.0952467	−	0.494916i
$309$		0			0
$310$	3.34315	−	5.79050i	0.189878	−	0.328878i
$311$	−11.3137	−	19.5959i	−0.641542	−	1.11118i	−0.985089	−	0.172047i	$-0.944962\pi$
$311$	−11.3137	−	19.5959i	−0.641542	−	1.11118i	0.343547	−	0.939135i	$-0.388371\pi$
$312$		0			0
$313$	12.6421	−	21.8968i	0.714576	−	1.23768i	−0.248547	−	0.968620i	$-0.579953\pi$
$313$	12.6421	−	21.8968i	0.714576	−	1.23768i	0.963123	−	0.269062i	$-0.0867136\pi$
$314$	0.272078			0.0153542
$315$		0			0
$316$	−24.9706			−1.40470
$317$	−4.89949	+	8.48617i	−0.275183	+	0.476631i	−0.970181	−	0.242380i	$-0.922072\pi$
$317$	−4.89949	+	8.48617i	−0.275183	+	0.476631i	0.694998	+	0.719011i	$0.255405\pi$
$318$		0			0
$319$	−0.757359	−	1.31178i	−0.0424040	−	0.0734458i
$320$	−3.81371	+	6.60554i	−0.213193	+	0.369261i
$321$		0			0
$322$	3.17157	+	2.74666i	0.176745	+	0.153066i
$323$	7.65685			0.426039
$324$		0			0
$325$	−2.34315	−	4.05845i	−0.129974	−	0.225122i
$326$	−2.47918	−	4.29407i	−0.137309	−	0.237827i
$327$		0			0
$328$	5.79899			0.320196
$329$	−5.91421	+	30.7312i	−0.326061	+	1.69426i
$330$		0			0
$331$	11.2426	−	19.4728i	0.617951	−	1.07032i	−0.371908	−	0.928270i	$-0.621296\pi$
$331$	11.2426	−	19.4728i	0.617951	−	1.07032i	0.989859	−	0.142053i	$-0.0453705\pi$
$332$	−8.98528	−	15.5630i	−0.493131	−	0.854129i
$333$		0			0
$334$	−0.656854	+	1.13770i	−0.0359415	+	0.0622524i
$335$	21.9411			1.19877
$336$		0			0
$337$	10.4853			0.571170			0.285585	−	0.958353i	$-0.407812\pi$
$337$	10.4853			0.571170			0.285585	+	0.958353i	$0.407812\pi$
$338$	−1.03553	+	1.79360i	−0.0563256	+	0.0975588i
$339$		0			0
$340$	12.7990	+	22.1685i	0.694123	+	1.20226i
$341$	−8.07107	+	13.9795i	−0.437073	+	0.757032i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−2.12994			−0.114839
$345$		0			0
$346$	0.585786	+	1.01461i	0.0314921	+	0.0545459i
$347$	−15.2279	−	26.3755i	−0.817478	−	1.41591i	−0.907535	−	0.419976i	$-0.862038\pi$
$347$	−15.2279	−	26.3755i	−0.817478	−	1.41591i	0.0900574	−	0.995937i	$-0.471295\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$	−1.71573	+	0.594346i	−0.0917096	+	0.0317691i
$351$		0			0
$352$	−4.03553	+	6.98975i	−0.215095	+	0.372555i
$353$	10.6569	+	18.4582i	0.567207	+	0.982432i	0.996841	+	0.0794282i	$0.0253094\pi$
$353$	10.6569	+	18.4582i	0.567207	+	0.982432i	−0.429633	+	0.903003i	$0.641357\pi$
$354$		0			0
$355$	−14.3137	+	24.7921i	−0.759693	+	1.31583i
$356$	9.45584			0.501159
$357$		0			0
$358$	2.68629			0.141975
$359$	−5.91421	+	10.2437i	−0.312140	+	0.540643i	−0.978825	−	0.204697i	$-0.934379\pi$
$359$	−5.91421	+	10.2437i	−0.312140	+	0.540643i	0.666685	+	0.745339i	$0.267713\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	−0.0710678	+	0.123093i	−0.00373524	+	0.00646963i
$363$		0			0
$364$	10.3431	+	8.95743i	0.542128	+	0.469497i
$365$	−22.5147			−1.17847
$366$		0			0
$367$	−9.17157	−	15.8856i	−0.478752	−	0.829223i	0.520951	−	0.853587i	$-0.325577\pi$
$367$	−9.17157	−	15.8856i	−0.478752	−	0.829223i	−0.999703	+	0.0243635i	$0.992244\pi$
$368$	5.74264	+	9.94655i	0.299356	+	0.518500i
$369$		0			0
$370$	5.17157			0.268857
$371$	4.00000	+	3.46410i	0.207670	+	0.179847i
$372$		0			0
$373$	18.1421	−	31.4231i	0.939364	−	1.62703i	0.172704	−	0.984974i	$-0.444750\pi$
$373$	18.1421	−	31.4231i	0.939364	−	1.62703i	0.766661	−	0.642053i	$-0.221917\pi$
$374$	2.89949	+	5.02207i	0.149929	+	0.259685i
$375$		0			0
$376$	9.37868	−	16.2443i	0.483668	−	0.837738i
$377$	2.34315			0.120678
$378$		0			0
$379$	0.485281			0.0249272			0.0124636	−	0.999922i	$-0.496033\pi$
$379$	0.485281			0.0249272			0.0124636	+	0.999922i	$0.496033\pi$
$380$	1.67157	−	2.89525i	0.0857499	−	0.148523i
$381$		0			0
$382$	−1.27817	−	2.21386i	−0.0653971	−	0.113271i
$383$	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
$385$	−8.35786	+	2.89525i	−0.425956	+	0.147556i
$386$	−1.65685			−0.0843317
$387$		0			0
$388$	10.2132	+	17.6898i	0.518497	+	0.898063i
$389$	7.82843	+	13.5592i	0.396917	+	0.687480i	0.993344	−	0.115187i	$-0.0367467\pi$
$389$	7.82843	+	13.5592i	0.396917	+	0.687480i	−0.596427	+	0.802667i	$0.703413\pi$
$390$		0			0
$391$	29.3137			1.48246
$392$	8.72183	−	6.86666i	0.440519	−	0.346819i
$393$		0			0
$394$	0.106602	−	0.184640i	0.00537052	−	0.00930201i
$395$	12.4853	+	21.6251i	0.628203	+	1.08808i
$396$		0			0
$397$	8.65685	−	14.9941i	0.434475	−	0.752533i	−0.562778	−	0.826608i	$-0.690267\pi$
$397$	8.65685	−	14.9941i	0.434475	−	0.752533i	0.997253	+	0.0740755i	$0.0236006\pi$
$398$	−6.07107			−0.304315
$399$		0			0
$400$	−4.97056			−0.248528
$401$	−11.6569	+	20.1903i	−0.582116	+	1.00825i	0.413113	+	0.910680i	$0.364442\pi$
$401$	−11.6569	+	20.1903i	−0.582116	+	1.00825i	−0.995228	+	0.0975738i	$0.968892\pi$
$402$		0			0
$403$	−12.4853	−	21.6251i	−0.621936	−	1.07723i
$404$	−12.3284	+	21.3535i	−0.613362	+	1.06237i
$405$		0			0
$406$	0.171573	−	0.891519i	0.00851502	−	0.0442453i
$407$	−12.4853			−0.618872
$408$		0			0
$409$	8.65685	+	14.9941i	0.428054	+	0.741411i	0.996700	−	0.0811711i	$-0.0258660\pi$
$409$	8.65685	+	14.9941i	0.428054	+	0.741411i	−0.568646	+	0.822582i	$0.692533\pi$
$410$	−1.38478	−	2.39850i	−0.0683892	−	0.118454i
$411$		0			0
$412$	14.0000			0.689730
$413$	−10.3431	−	8.95743i	−0.508953	−	0.440766i
$414$		0			0
$415$	−8.98528	+	15.5630i	−0.441070	+	0.763956i
$416$	−6.24264	−	10.8126i	−0.306071	−	0.530130i
$417$		0			0
$418$	0.378680	−	0.655892i	0.0185218	−	0.0320807i
$419$	15.8284			0.773269			0.386635	−	0.922233i	$-0.373637\pi$
$419$	15.8284			0.773269			0.386635	+	0.922233i	$0.373637\pi$
$420$		0			0
$421$	24.8284			1.21006			0.605032	−	0.796201i	$-0.293160\pi$
$421$	24.8284			1.21006			0.605032	+	0.796201i	$0.293160\pi$
$422$	−0.100505	+	0.174080i	−0.00489251	+	0.00847408i
$423$		0			0
$424$	−1.58579	−	2.74666i	−0.0770126	−	0.133390i
$425$	−6.34315	+	10.9867i	−0.307688	+	0.532931i
$426$		0			0
$427$	−1.67157	+	8.68575i	−0.0808931	+	0.420333i
$428$	5.17157			0.249977
$429$		0			0
$430$	0.508622	+	0.880959i	0.0245279	+	0.0424836i
$431$	−14.4142	−	24.9662i	−0.694308	−	1.20258i	−0.970413	−	0.241450i	$-0.922377\pi$
$431$	−14.4142	−	24.9662i	−0.694308	−	1.20258i	0.276105	−	0.961127i	$-0.410956\pi$
$432$		0			0
$433$	−8.48528			−0.407777			−0.203888	−	0.978994i	$-0.565358\pi$
$433$	−8.48528			−0.407777			−0.203888	+	0.978994i	$0.565358\pi$
$434$	−9.14214	+	3.16693i	−0.438837	+	0.152017i
$435$		0			0
$436$	−9.27208	+	16.0597i	−0.444052	+	0.769121i
$437$	−1.91421	−	3.31552i	−0.0915693	−	0.158603i
$438$		0			0
$439$	−9.89949	+	17.1464i	−0.472477	+	0.818354i	−0.999504	−	0.0314943i	$-0.989973\pi$
$439$	−9.89949	+	17.1464i	−0.472477	+	0.818354i	0.527027	+	0.849849i	$0.323307\pi$
$440$	5.30152			0.252740
$441$		0			0
$442$	−8.97056			−0.426686
$443$	−11.1716	+	19.3497i	−0.530777	+	0.919334i	0.468578	+	0.883422i	$0.344767\pi$
$443$	−11.1716	+	19.3497i	−0.530777	+	0.919334i	−0.999355	+	0.0359111i	$0.988567\pi$
$444$		0			0
$445$	−4.72792	−	8.18900i	−0.224125	−	0.388196i
$446$	−3.68629	+	6.38484i	−0.174551	+	0.302331i
$447$		0			0
$448$	10.4289	−	3.61269i	0.492721	−	0.170683i
$449$	2.14214			0.101094			0.0505468	−	0.998722i	$-0.483904\pi$
$449$	2.14214			0.101094			0.0505468	+	0.998722i	$0.483904\pi$
$450$		0			0
$451$	3.34315	+	5.79050i	0.157423	+	0.272664i
$452$	6.55635	+	11.3559i	0.308385	+	0.534138i
$453$		0			0
$454$	−7.31371			−0.343249
$455$	2.58579	−	13.4361i	0.121224	−	0.629896i
$456$		0			0
$457$	1.67157	−	2.89525i	0.0781929	−	0.135434i	−0.824277	−	0.566186i	$-0.808418\pi$
$457$	1.67157	−	2.89525i	0.0781929	−	0.135434i	0.902470	+	0.430752i	$0.141752\pi$
$458$	−0.899495	−	1.55797i	−0.0420306	−	0.0727992i
$459$		0			0
$460$	6.39949	−	11.0843i	0.298378	−	0.516806i
$461$	28.4558			1.32532			0.662660	−	0.748920i	$-0.269427\pi$
$461$	28.4558			1.32532			0.662660	+	0.748920i	$0.269427\pi$
$462$		0			0
$463$	−9.34315			−0.434213			−0.217106	−	0.976148i	$-0.569662\pi$
$463$	−9.34315			−0.434213			−0.217106	+	0.976148i	$0.569662\pi$
$464$	1.24264	−	2.15232i	0.0576881	−	0.0999188i
$465$		0			0
$466$	−1.24264	−	2.15232i	−0.0575642	−	0.0997042i
$467$	4.25736	−	7.37396i	0.197007	−	0.341226i	−0.750550	−	0.660814i	$-0.770211\pi$
$467$	4.25736	−	7.37396i	0.197007	−	0.341226i	0.947557	+	0.319588i	$0.103544\pi$
$468$		0			0
$469$	−24.0000	−	20.7846i	−1.10822	−	0.959744i
$470$	−8.95837			−0.413219
$471$		0			0
$472$	4.10051	+	7.10228i	0.188741	+	0.326909i
$473$	−1.22792	−	2.12682i	−0.0564599	−	0.0977914i
$474$		0			0
$475$	1.65685			0.0760217
$476$	7.00000	−	36.3731i	0.320844	−	1.66716i
$477$		0			0
$478$	−2.82843	+	4.89898i	−0.129369	+	0.224074i
$479$	8.91421	+	15.4399i	0.407301	+	0.705466i	0.994586	−	0.103914i	$-0.0331367\pi$
$479$	8.91421	+	15.4399i	0.407301	+	0.705466i	−0.587285	+	0.809380i	$0.699803\pi$
$480$		0			0
$481$	9.65685	−	16.7262i	0.440315	−	0.762647i
$482$	8.20101			0.373546
$483$		0			0
$484$	14.0000			0.636364
$485$	10.2132	−	17.6898i	0.463758	−	0.803252i
$486$		0			0
$487$	5.82843	+	10.0951i	0.264111	+	0.457454i	0.967330	−	0.253519i	$-0.0815881\pi$
$487$	5.82843	+	10.0951i	0.264111	+	0.457454i	−0.703219	+	0.710973i	$0.748255\pi$
$488$	2.65076	−	4.59125i	0.119994	−	0.207836i
$489$		0			0
$490$	−4.92284	−	1.96768i	−0.222391	−	0.0888906i
$491$	25.4853			1.15013			0.575067	−	0.818106i	$-0.304976\pi$
$491$	25.4853			1.15013			0.575067	+	0.818106i	$0.304976\pi$
$492$		0			0
$493$	−3.17157	−	5.49333i	−0.142840	−	0.247407i
$494$	0.585786	+	1.01461i	0.0263558	+	0.0456495i
$495$		0			0
$496$	−26.4853			−1.18922
$497$	39.1421	−	13.5592i	1.75576	−	0.608215i
$498$		0			0
$499$	6.98528	−	12.0989i	0.312704	−	0.541619i	−0.666243	−	0.745735i	$-0.732098\pi$
$499$	6.98528	−	12.0989i	0.312704	−	0.541619i	0.978947	+	0.204116i	$0.0654318\pi$
$500$	11.1274	+	19.2733i	0.497633	+	0.861926i
$501$		0			0
$502$	−0.721825	+	1.25024i	−0.0322166	+	0.0558009i
$503$	42.1127			1.87771			0.938856	−	0.344309i	$-0.111887\pi$
$503$	42.1127			1.87771			0.938856	+	0.344309i	$0.111887\pi$
$504$		0			0
$505$	24.6569			1.09722
$506$	1.44975	−	2.51104i	0.0644491	−	0.111629i
$507$		0			0
$508$	−15.5147	−	26.8723i	−0.688354	−	1.19226i
$509$	3.24264	−	5.61642i	0.143728	−	0.248943i	−0.785170	−	0.619280i	$-0.787424\pi$
$509$	3.24264	−	5.61642i	0.143728	−	0.248943i	0.928897	+	0.370337i	$0.120758\pi$
$510$		0			0
$511$	24.6274	+	21.3280i	1.08945	+	0.943494i
$512$	−22.7574			−1.00574
$513$		0			0
$514$	−5.38478	−	9.32671i	−0.237512	−	0.411383i
$515$	−7.00000	−	12.1244i	−0.308457	−	0.534263i
$516$		0			0
$517$	21.6274			0.951173
$518$	−5.65685	−	4.89898i	−0.248548	−	0.215249i
$519$		0			0
$520$	−4.10051	+	7.10228i	−0.179819	+	0.311456i
$521$	−3.51472	−	6.08767i	−0.153983	−	0.266706i	0.778705	−	0.627390i	$-0.215877\pi$
$521$	−3.51472	−	6.08767i	−0.153983	−	0.266706i	−0.932688	+	0.360684i	$0.882543\pi$
$522$		0			0
$523$	−0.899495	+	1.55797i	−0.0393322	+	0.0681253i	−0.885021	−	0.465550i	$-0.845856\pi$
$523$	−0.899495	+	1.55797i	−0.0393322	+	0.0681253i	0.845689	+	0.533676i	$0.179190\pi$
$524$	39.5980			1.72985
$525$		0			0
$526$	−4.68629			−0.204332
$527$	−33.7990	+	58.5416i	−1.47231	+	2.55011i
$528$		0			0
$529$	4.17157	+	7.22538i	0.181373	+	0.314147i
$530$	−0.757359	+	1.31178i	−0.0328976	+	0.0569803i
$531$		0			0
$532$	−4.57107	+	1.58346i	−0.198181	+	0.0686519i
$533$	−10.3431			−0.448011
$534$		0			0
$535$	−2.58579	−	4.47871i	−0.111793	−	0.193632i
$536$	9.51472	+	16.4800i	0.410973	+	0.711827i
$537$		0			0
$538$	−3.31371			−0.142864
$539$	11.8848	+	4.75039i	0.511914	+	0.204614i
$540$		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	$0.331288\pi$
$542$	5.30761	+	9.19305i	0.227981	+	0.394875i
$543$		0			0
$544$	−16.8995	+	29.2708i	−0.724560	+	1.25497i
$545$	18.5442			0.794344
$546$		0			0
$547$	33.7990			1.44514			0.722570	−	0.691298i	$-0.242961\pi$
$547$	33.7990			1.44514			0.722570	+	0.691298i	$0.242961\pi$
$548$	7.47056	−	12.9394i	0.319127	−	0.552744i
$549$		0			0
$550$	0.627417	+	1.08672i	0.0267532	+	0.0463378i
$551$	−0.414214	+	0.717439i	−0.0176461	+	0.0305639i
$552$		0			0
$553$	6.82843	−	35.4815i	0.290374	−	1.50883i
$554$	−5.38478			−0.228777
$555$		0			0
$556$	4.25736	+	7.37396i	0.180552	+	0.312726i
$557$	−18.2279	−	31.5717i	−0.772342	−	1.33774i	−0.936276	−	0.351264i	$-0.885752\pi$
$557$	−18.2279	−	31.5717i	−0.772342	−	1.33774i	0.163935	−	0.986471i	$-0.447581\pi$
$558$		0			0
$559$	3.79899			0.160680
$560$	−10.9706	−	9.50079i	−0.463591	−	0.401481i
$561$		0			0
$562$	5.58579	−	9.67487i	0.235622	−	0.408110i
$563$	−8.24264	−	14.2767i	−0.347386	−	0.601690i	0.638398	−	0.769706i	$-0.279597\pi$
$563$	−8.24264	−	14.2767i	−0.347386	−	0.601690i	−0.985784	+	0.168016i	$0.946264\pi$
$564$		0			0
$565$	6.55635	−	11.3559i	0.275828	−	0.477748i
$566$	5.64466			0.237263
$567$		0			0
$568$	−24.8284			−1.04178
$569$	−3.10051	+	5.37023i	−0.129980	+	0.225132i	−0.923669	−	0.383192i	$-0.874825\pi$
$569$	−3.10051	+	5.37023i	−0.129980	+	0.225132i	0.793689	+	0.608324i	$0.208158\pi$
$570$		0			0
$571$	14.6421	+	25.3609i	0.612754	+	1.06132i	0.990774	+	0.135524i	$0.0432718\pi$
$571$	14.6421	+	25.3609i	0.612754	+	1.06132i	−0.378020	+	0.925798i	$0.623395\pi$
$572$	4.72792	−	8.18900i	0.197684	−	0.342399i
$573$		0			0
$574$	−0.757359	+	3.93535i	−0.0316116	+	0.164259i
$575$	6.34315			0.264527
$576$		0			0
$577$	2.15685	+	3.73578i	0.0897910	+	0.155523i	0.907423	−	0.420219i	$-0.138047\pi$
$577$	2.15685	+	3.73578i	0.0897910	+	0.155523i	−0.817632	+	0.575742i	$0.804713\pi$
$578$	8.62132	+	14.9326i	0.358600	+	0.621113i
$579$		0			0
$580$	−2.76955			−0.114999
$581$	24.5711	−	8.51167i	1.01938	−	0.353123i
$582$		0			0
$583$	1.82843	−	3.16693i	0.0757257	−	0.131161i
$584$	−9.76346	−	16.9108i	−0.404015	−	0.699774i
$585$		0			0
$586$	−1.00000	+	1.73205i	−0.0413096	+	0.0715504i
$587$	−18.6274			−0.768836			−0.384418	−	0.923159i	$-0.625598\pi$
$587$	−18.6274			−0.768836			−0.384418	+	0.923159i	$0.625598\pi$
$588$		0			0
$589$	8.82843			0.363769
$590$	1.95837	−	3.39200i	0.0806248	−	0.139646i
$591$		0			0
$592$	−10.2426	−	17.7408i	−0.420970	−	0.729141i
$593$	5.25736	−	9.10601i	0.215894	−	0.373939i	−0.737655	−	0.675178i	$-0.764067\pi$
$593$	5.25736	−	9.10601i	0.215894	−	0.373939i	0.953549	+	0.301239i	$0.0974001\pi$
$594$		0			0
$595$	−35.0000	+	12.1244i	−1.43486	+	0.497050i
$596$	−3.34315			−0.136941
$597$		0			0
$598$	2.24264	+	3.88437i	0.0917084	+	0.158844i
$599$	16.5563	+	28.6764i	0.676474	+	1.17169i	0.976036	+	0.217611i	$0.0698263\pi$
$599$	16.5563	+	28.6764i	0.676474	+	1.17169i	−0.299562	+	0.954077i	$0.596840\pi$
$600$		0			0
$601$	−31.3137			−1.27731			−0.638656	−	0.769492i	$-0.720509\pi$
$601$	−31.3137			−1.27731			−0.638656	+	0.769492i	$0.720509\pi$
$602$	0.278175	−	1.44544i	0.0113376	−	0.0589116i
$603$		0			0
$604$	12.1716	−	21.0818i	0.495254	−	0.857806i
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	−21.0711	+	36.4962i	−0.855248	+	1.48133i	0.0211663	+	0.999776i	$0.493262\pi$
$607$	−21.0711	+	36.4962i	−0.855248	+	1.48133i	−0.876415	+	0.481557i	$0.840071\pi$
$608$	4.41421			0.179020
$609$		0			0
$610$	−2.53196			−0.102516
$611$	−16.7279	+	28.9736i	−0.676739	+	1.17215i
$612$		0			0
$613$	−4.31371	−	7.47156i	−0.174229	−	0.301774i	0.765665	−	0.643239i	$-0.222410\pi$
$613$	−4.31371	−	7.47156i	−0.174229	−	0.301774i	−0.939894	+	0.341466i	$0.889077\pi$
$614$	−3.00000	+	5.19615i	−0.121070	+	0.209700i
$615$		0			0
$616$	−5.79899	−	5.02207i	−0.233648	−	0.202345i
$617$	37.8284			1.52292			0.761458	−	0.648215i	$-0.224484\pi$
$617$	37.8284			1.52292			0.761458	+	0.648215i	$0.224484\pi$
$618$		0			0
$619$	−10.3284	−	17.8894i	−0.415135	−	0.719034i	0.580308	−	0.814397i	$-0.302932\pi$
$619$	−10.3284	−	17.8894i	−0.415135	−	0.719034i	−0.995443	+	0.0953630i	$0.969599\pi$
$620$	14.7574	+	25.5605i	0.592670	+	1.02653i
$621$		0			0
$622$	−9.37258			−0.375806
$623$	−2.58579	+	13.4361i	−0.103597	+	0.538308i
$624$		0			0
$625$	6.98528	−	12.0989i	0.279411	−	0.483954i
$626$	−5.23654	−	9.06996i	−0.209294	−	0.362509i
$627$		0			0
$628$	−0.600505	+	1.04011i	−0.0239628	+	0.0415047i
$629$	−52.2843			−2.08471
$630$		0			0
$631$	−5.34315			−0.212707			−0.106354	−	0.994328i	$-0.533918\pi$
$631$	−5.34315			−0.212707			−0.106354	+	0.994328i	$0.533918\pi$
$632$	−10.8284	+	18.7554i	−0.430732	+	0.746049i
$633$		0			0
$634$	2.02944	+	3.51509i	0.0805992	+	0.139602i
$635$	−15.5147	+	26.8723i	−0.615683	+	1.06639i
$636$		0			0
$637$	−15.5563	+	12.2474i	−0.616365	+	0.485262i
$638$	−0.627417			−0.0248397
$639$		0			0
$640$	9.65076	+	16.7156i	0.381480	+	0.660742i
$641$	−5.41421	−	9.37769i	−0.213849	−	0.370397i	0.739067	−	0.673632i	$-0.235267\pi$
$641$	−5.41421	−	9.37769i	−0.213849	−	0.370397i	−0.952916	+	0.303235i	$0.901933\pi$
$642$		0			0
$643$	46.6274			1.83881			0.919403	−	0.393317i	$-0.128673\pi$
$643$	46.6274			1.83881			0.919403	+	0.393317i	$0.128673\pi$
$644$	−17.5000	+	6.06218i	−0.689597	+	0.238883i
$645$		0			0
$646$	1.58579	−	2.74666i	0.0623919	−	0.108066i
$647$	17.5711	+	30.4340i	0.690790	+	1.19648i	0.971579	+	0.236714i	$0.0760704\pi$
$647$	17.5711	+	30.4340i	0.690790	+	1.19648i	−0.280789	+	0.959769i	$0.590596\pi$
$648$		0			0
$649$	−4.72792	+	8.18900i	−0.185587	+	0.321446i
$650$	−1.94113			−0.0761372
$651$		0			0
$652$	21.8873			0.857173
$653$	−13.9706	+	24.1977i	−0.546710	+	0.946930i	0.451787	+	0.892126i	$0.350787\pi$
$653$	−13.9706	+	24.1977i	−0.546710	+	0.946930i	−0.998497	+	0.0548042i	$0.982547\pi$
$654$		0			0
$655$	−19.7990	−	34.2929i	−0.773611	−	1.33993i
$656$	−5.48528	+	9.50079i	−0.214164	+	0.370943i
$657$		0			0
$658$	9.79899	+	8.48617i	0.382004	+	0.330826i
$659$	38.4853			1.49917			0.749587	−	0.661906i	$-0.230252\pi$
$659$	38.4853			1.49917			0.749587	+	0.661906i	$0.230252\pi$
$660$		0			0
$661$	22.1421	+	38.3513i	0.861229	+	1.49169i	0.870743	+	0.491738i	$0.163638\pi$
$661$	22.1421	+	38.3513i	0.861229	+	1.49169i	−0.00951390	+	0.999955i	$0.503028\pi$
$662$	−4.65685	−	8.06591i	−0.180994	−	0.313490i
$663$		0			0
$664$	−15.5858			−0.604846
$665$	3.65685	+	3.16693i	0.141807	+	0.122808i
$666$		0			0
$667$	−1.58579	+	2.74666i	−0.0614019	+	0.106351i
$668$	−2.89949	−	5.02207i	−0.112185	−	0.194310i
$669$		0			0
$670$	4.54416	−	7.87071i	0.175556	−	0.304072i
$671$	6.11270			0.235978
$672$		0			0
$673$	−2.82843			−0.109028			−0.0545139	−	0.998513i	$-0.517361\pi$
$673$	−2.82843			−0.109028			−0.0545139	+	0.998513i	$0.517361\pi$
$674$	2.17157	−	3.76127i	0.0836459	−	0.144879i
$675$		0			0
$676$	−4.57107	−	7.91732i	−0.175810	−	0.304512i
$677$	−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
$679$	−27.9289	+	9.67487i	−1.07181	+	0.371287i
$680$	22.2010			0.851370
$681$		0			0
$682$	3.34315	+	5.79050i	0.128016	+	0.221730i
$683$	19.4853	+	33.7495i	0.745584	+	1.29139i	0.949922	+	0.312488i	$0.101162\pi$
$683$	19.4853	+	33.7495i	0.745584	+	1.29139i	−0.204338	+	0.978900i	$0.565504\pi$
$684$		0			0
$685$	−14.9411			−0.570871
$686$	3.52082	+	6.81567i	0.134425	+	0.260223i
$687$		0			0
$688$	2.01472	−	3.48960i	0.0768104	−	0.133040i
$689$	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	$0.239967\pi$
$692$	−5.17157			−0.196594
$693$		0			0
$694$	−12.6152			−0.478867
$695$	4.25736	−	7.37396i	0.161491	−	0.279710i
$696$		0			0
$697$	14.0000	+	24.2487i	0.530288	+	0.918485i
$698$	2.89949	−	5.02207i	0.109748	−	0.190088i
$699$		0			0
$700$	1.51472	−	7.87071i	0.0572510	−	0.297485i
$701$	48.4558			1.83015			0.915076	−	0.403281i	$-0.132130\pi$
$701$	48.4558			1.83015			0.915076	+	0.403281i	$0.132130\pi$
$702$		0			0
$703$	3.41421	+	5.91359i	0.128770	+	0.223035i
$704$	−3.81371	−	6.60554i	−0.143735	−	0.248956i
$705$		0			0
$706$	8.82843			0.332262
$707$	−26.9706	−	23.3572i	−1.01433	−	0.878438i
$708$		0			0
$709$	−8.98528	+	15.5630i	−0.337449	+	0.584479i	−0.983952	−	0.178432i	$-0.942897\pi$
$709$	−8.98528	+	15.5630i	−0.337449	+	0.584479i	0.646503	+	0.762912i	$0.276231\pi$
$710$	5.92893	+	10.2692i	0.222509	+	0.385397i
$711$		0			0
$712$	4.10051	−	7.10228i	0.153673	−	0.266169i
$713$	33.7990			1.26578
$714$		0			0
$715$	−9.45584			−0.353629
$716$	−5.92893	+	10.2692i	−0.221575	+	0.383778i
$717$		0			0
$718$	2.44975	+	4.24309i	0.0914238	+	0.158351i
$719$	16.4853	−	28.5533i	0.614797	−	1.06486i	−0.375623	−	0.926773i	$-0.622571\pi$
$719$	16.4853	−	28.5533i	0.614797	−	1.06486i	0.990420	−	0.138087i	$-0.0440955\pi$
$720$		0			0
$721$	−3.82843	+	19.8931i	−0.142578	+	0.740857i
$722$	−0.414214			−0.0154154
$723$		0			0
$724$	−0.313708	−	0.543359i	−0.0116589	−	0.0201938i
$725$	−0.686292	−	1.18869i	−0.0254882	−	0.0441469i
$726$		0			0
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$	11.2132	−	3.88437i	0.415589	−	0.143964i
$729$		0			0
$730$	−4.66295	+	8.07647i	−0.172584	+	0.298923i
$731$	−5.14214	−	8.90644i	−0.190189	−	0.329417i
$732$		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	$0.0334875\pi$
$734$	−7.59798			−0.280447
$735$		0			0
$736$	16.8995			0.622924
$737$	−10.9706	+	19.0016i	−0.404106	+	0.699932i
$738$		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	$0.786326\pi$
$740$	−11.4142	+	19.7700i	−0.419595	+	0.726760i
$741$		0			0
$742$	2.07107	−	0.717439i	0.0760313	−	0.0263380i
$743$	−38.8284			−1.42448			−0.712238	−	0.701938i	$-0.752319\pi$
$743$	−38.8284			−1.42448			−0.712238	+	0.701938i	$0.752319\pi$
$744$		0			0
$745$	1.67157	+	2.89525i	0.0612417	+	0.106074i
$746$	−7.51472	−	13.0159i	−0.275133	−	0.476545i
$747$		0			0
$748$	−25.5980			−0.935955
$749$	−1.41421	+	7.34847i	−0.0516742	+	0.268507i
$750$		0			0
$751$	5.31371	−	9.20361i	0.193900	−	0.335845i	−0.752639	−	0.658433i	$-0.771220\pi$
$751$	5.31371	−	9.20361i	0.193900	−	0.335845i	0.946539	+	0.322588i	$0.104553\pi$
$752$	17.7426	+	30.7312i	0.647008	+	1.12065i
$753$		0			0
$754$	0.485281	−	0.840532i	0.0176729	−	0.0306104i
$755$	−24.3431			−0.885938
$756$		0			0
$757$	20.6569			0.750786			0.375393	−	0.926866i	$-0.377508\pi$
$757$	20.6569			0.750786			0.375393	+	0.926866i	$0.377508\pi$
$758$	0.100505	−	0.174080i	0.00365051	−	0.00632287i
$759$		0			0
$760$	−1.44975	−	2.51104i	−0.0525879	−	0.0910849i
$761$	10.3995	−	18.0125i	0.376981	−	0.652951i	−0.613640	−	0.789586i	$-0.710295\pi$
$761$	10.3995	−	18.0125i	0.376981	−	0.652951i	0.990621	+	0.136635i	$0.0436287\pi$
$762$		0			0
$763$	−20.2843	−	17.5667i	−0.734340	−	0.635957i
$764$	11.2843			0.408251
$765$		0			0
$766$	−3.31371	−	5.73951i	−0.119729	−	0.207377i
$767$	−7.31371	−	12.6677i	−0.264083	−	0.457405i
$768$		0			0
$769$	−8.31371			−0.299800			−0.149900	−	0.988701i	$-0.547895\pi$
$769$	−8.31371			−0.299800			−0.149900	+	0.988701i	$0.547895\pi$
$770$	−0.692388	+	3.59775i	−0.0249519	+	0.129654i
$771$		0			0
$772$	3.65685	−	6.33386i	0.131613	−	0.227961i
$773$	−1.41421	−	2.44949i	−0.0508657	−	0.0881020i	0.839471	−	0.543404i	$-0.182865\pi$
$773$	−1.41421	−	2.44949i	−0.0508657	−	0.0881020i	−0.890337	+	0.455302i	$0.849531\pi$
$774$		0			0
$775$	−7.31371	+	12.6677i	−0.262716	+	0.455038i
$776$	17.7157			0.635958
$777$		0			0
$778$	6.48528			0.232509
$779$	1.82843	−	3.16693i	0.0655102	−	0.113467i
$780$		0			0
$781$	−14.3137	−	24.7921i	−0.512185	−	0.887130i
$782$	6.07107	−	10.5154i	0.217101	−	0.376030i
$783$		0			0
$784$	3.00000	+	20.7846i	0.107143	+	0.742307i
$785$	1.20101			0.0428659
$786$		0			0
$787$	20.1421	+	34.8872i	0.717990	+	1.24359i	0.961795	+	0.273770i	$0.0882708\pi$
$787$	20.1421	+	34.8872i	0.717990	+	1.24359i	−0.243806	+	0.969824i	$0.578396\pi$
$788$	0.470563	+	0.815039i	0.0167631	+	0.0290345i
$789$		0			0
$790$	10.3431			0.367993
$791$	−17.9289	+	6.21076i	−0.637479	+	0.220829i
$792$		0			0
$793$	−4.72792	+	8.18900i	−0.167893	+	0.290800i
$794$	−3.58579	−	6.21076i	−0.127255	−	0.220412i
$795$		0			0
$796$	13.3995	−	23.2086i	0.474933	−	0.822607i
$797$	−24.4853			−0.867313			−0.433657	−	0.901078i	$-0.642777\pi$
$797$	−24.4853			−0.867313			−0.433657	+	0.901078i	$0.642777\pi$
$798$		0			0
$799$	90.5685			3.20408
$800$	−3.65685	+	6.33386i	−0.129289	+	0.223936i
$801$		0			0
$802$	4.82843	+	8.36308i	0.170498	+	0.295311i
$803$	11.2574	−	19.4983i	0.397264	−	0.688081i
$804$		0			0
$805$	14.0000	+	12.1244i	0.493435	+	0.427327i
$806$	−10.3431			−0.364322
$807$		0			0
$808$	10.6924	+	18.5198i	0.376157	+	0.651523i
$809$	7.39949	+	12.8163i	0.260152	+	0.450597i	0.966282	−	0.257485i	$-0.0828939\pi$
$809$	7.39949	+	12.8163i	0.260152	+	0.450597i	−0.706130	+	0.708082i	$0.749561\pi$
$810$		0			0
$811$	16.1421			0.566827			0.283414	−	0.958998i	$-0.408533\pi$
$811$	16.1421			0.566827			0.283414	+	0.958998i	$0.408533\pi$
$812$	3.02944	+	2.62357i	0.106312	+	0.0920692i
$813$		0			0
$814$	−2.58579	+	4.47871i	−0.0906318	+	0.156979i
$815$	−10.9437	−	18.9550i	−0.383339	−	0.663963i
$816$		0			0
$817$	−0.671573	+	1.16320i	−0.0234954	+	0.0406952i
$818$	7.17157			0.250748
$819$		0			0
$820$	12.2254			0.426929
$821$	17.5711	−	30.4340i	0.613234	−	1.06215i	−0.377457	−	0.926027i	$-0.623201\pi$
$821$	17.5711	−	30.4340i	0.613234	−	1.06215i	0.990692	−	0.136126i	$-0.0434653\pi$
$822$		0			0
$823$	0.985281	+	1.70656i	0.0343447	+	0.0594869i	0.882687	−	0.469962i	$-0.155732\pi$
$823$	0.985281	+	1.70656i	0.0343447	+	0.0594869i	−0.848342	+	0.529448i	$0.822399\pi$
$824$	6.07107	−	10.5154i	0.211496	−	0.366321i
$825$		0			0
$826$	−5.35534	+	1.85514i	−0.186336	+	0.0645487i
$827$	−47.1127			−1.63827			−0.819135	−	0.573601i	$-0.805546\pi$
$827$	−47.1127			−1.63827			−0.819135	+	0.573601i	$0.805546\pi$
$828$		0			0
$829$	4.92893	+	8.53716i	0.171189	+	0.296508i	0.938836	−	0.344365i	$-0.111906\pi$
$829$	4.92893	+	8.53716i	0.171189	+	0.296508i	−0.767647	+	0.640873i	$0.778572\pi$
$830$	3.72183	+	6.44639i	0.129186	+	0.223757i
$831$		0			0
$832$	11.7990			0.409056
$833$	49.7696	+	19.8931i	1.72441	+	0.689255i
$834$		0			0
$835$	−2.89949	+	5.02207i	−0.100341	+	0.173796i
$836$	1.67157	+	2.89525i	0.0578126	+	0.100134i
$837$		0			0
$838$	3.27817	−	5.67796i	0.113243	−	0.196142i
$839$	−45.2548			−1.56237			−0.781185	−	0.624299i	$-0.785385\pi$
$839$	−45.2548			−1.56237			−0.781185	+	0.624299i	$0.785385\pi$
$840$		0			0
$841$	−28.3137			−0.976335
$842$	5.14214	−	8.90644i	0.177210	−	0.306936i
$843$		0			0
$844$	−0.443651	−	0.768426i	−0.0152711	−	0.0264503i
$845$	−4.57107	+	7.91732i	−0.157250	+	0.272364i
$846$		0			0
$847$	−3.82843	+	19.8931i	−0.131546	+	0.683535i
$848$	6.00000			0.206041
$849$		0			0
$850$	2.62742	+	4.55082i	0.0901197	+	0.156092i
$851$	13.0711	+	22.6398i	0.448070	+	0.776081i
$852$		0			0
$853$	−51.6274			−1.76769			−0.883845	−	0.467781i	$-0.845054\pi$
$853$	−51.6274			−1.76769			−0.883845	+	0.467781i	$0.845054\pi$
$854$	2.76955	+	2.39850i	0.0947721	+	0.0820751i
$855$		0			0
$856$	2.24264	−	3.88437i	0.0766519	−	0.132765i
$857$	−10.5858	−	18.3351i	−0.361604	−	0.626316i	0.626621	−	0.779324i	$-0.284437\pi$
$857$	−10.5858	−	18.3351i	−0.361604	−	0.626316i	−0.988225	+	0.153008i	$0.951104\pi$
$858$		0			0
$859$	18.4706	−	31.9920i	0.630207	−	1.09155i	−0.357302	−	0.933989i	$-0.616303\pi$
$859$	18.4706	−	31.9920i	0.630207	−	1.09155i	0.987509	−	0.157562i	$-0.0503635\pi$
$860$	−4.49033			−0.153119
$861$		0			0
$862$	−11.9411			−0.406716
$863$	6.41421	−	11.1097i	0.218342	−	0.378180i	−0.735959	−	0.677026i	$-0.763268\pi$
$863$	6.41421	−	11.1097i	0.218342	−	0.378180i	0.954301	+	0.298846i	$0.0966017\pi$
$864$		0			0
$865$	2.58579	+	4.47871i	0.0879194	+	0.152281i
$866$	−1.75736	+	3.04384i	−0.0597175	+	0.103434i
$867$		0			0
$868$	8.07107	−	41.9385i	0.273950	−	1.42349i
$869$	−24.9706			−0.847068
$870$		0			0
$871$	−16.9706	−	29.3939i	−0.575026	−	0.995974i
$872$	8.04163	+	13.9285i	0.272324	+	0.471679i
$873$		0			0
$874$	−1.58579			−0.0536400
$875$	−30.4289	+	10.5409i	−1.02869	+	0.356347i
$876$		0			0
$877$	−5.17157	+	8.95743i	−0.174632	+	0.302471i	−0.940034	−	0.341082i	$-0.889207\pi$
$877$	−5.17157	+	8.95743i	−0.174632	+	0.302471i	0.765402	+	0.643552i	$0.222540\pi$
$878$	4.10051	+	7.10228i	0.138385	+	0.239690i
$879$		0			0
$880$	−5.01472	+	8.68575i	−0.169046	+	0.292796i
$881$	−40.6274			−1.36877			−0.684386	−	0.729120i	$-0.739930\pi$
$881$	−40.6274			−1.36877			−0.684386	+	0.729120i	$0.739930\pi$
$882$		0			0
$883$	−11.0294			−0.371170			−0.185585	−	0.982628i	$-0.559418\pi$
$883$	−11.0294			−0.371170			−0.185585	+	0.982628i	$0.559418\pi$
$884$	19.7990	−	34.2929i	0.665912	−	1.15339i
$885$		0			0
$886$	4.62742	+	8.01492i	0.155461	+	0.269267i
$887$	17.7279	−	30.7057i	0.595245	−	1.03100i	−0.398267	−	0.917270i	$-0.630388\pi$
$887$	17.7279	−	30.7057i	0.595245	−	1.03100i	0.993512	−	0.113726i	$-0.0362785\pi$
$888$		0			0
$889$	42.4264	−	14.6969i	1.42294	−	0.492919i
$890$	−3.91674			−0.131289
$891$		0			0
$892$	−16.2721	−	28.1841i	−0.544829	−	0.943672i
$893$	−5.91421	−	10.2437i	−0.197912	−	0.342793i
$894$		0			0
$895$	11.8579			0.396365
$896$	5.27817	−	27.4262i	0.176331	−	0.916245i
$897$		0			0
$898$	0.443651	−	0.768426i	0.0148048	−	0.0256427i
$899$	−3.65685	−	6.33386i	−0.121963	−	0.211246i
$900$		0			0
$901$	7.65685	−	13.2621i	0.255087	−	0.441823i
$902$	2.76955			0.0922160
$903$		0			0
$904$	11.3726			0.378246
$905$	−0.313708	+	0.543359i	−0.0104280	+	0.0180619i
$906$		0			0
$907$	4.17157	+	7.22538i	0.138515	+	0.239915i	0.926935	−	0.375223i	$-0.122434\pi$
$907$	4.17157	+	7.22538i	0.138515	+	0.239915i	−0.788420	+	0.615138i	$0.789100\pi$
$908$	16.1421	−	27.9590i	0.535696	−	0.927852i
$909$		0			0
$910$	−4.28427	−	3.71029i	−0.142022	−	0.122995i
$911$	−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
$913$	−8.98528	−	15.5630i	−0.297369	−	0.515059i
$914$	−0.692388	−	1.19925i	−0.0229022	−	0.0396677i
$915$		0			0
$916$	7.94113			0.262382
$917$	−10.8284	+	56.2662i	−0.357586	+	1.85807i
$918$		0			0
$919$	27.3284	−	47.3342i	0.901482	−	1.56141i	0.0759100	−	0.997115i	$-0.475814\pi$
$919$	27.3284	−	47.3342i	0.901482	−	1.56141i	0.825572	−	0.564297i	$-0.190853\pi$
$920$	−5.55025	−	9.61332i	−0.182986	−	0.316942i
$921$		0			0
$922$	5.89340	−	10.2077i	0.194089	−	0.336172i
$923$	44.2843			1.45763
$924$		0			0
$925$	−11.3137			−0.371992
$926$	−1.93503	+	3.35157i	−0.0635890	+	0.110139i
$927$		0			0
$928$	−1.82843	−	3.16693i	−0.0600211	−	0.103960i
$929$	−17.2279	+	29.8396i	−0.565230	+	0.979007i	0.431798	+	0.901970i	$0.357879\pi$
$929$	−17.2279	+	29.8396i	−0.565230	+	0.979007i	−0.997028	+	0.0770366i	$0.975454\pi$
$930$		0			0
$931$	−1.00000	−	6.92820i	−0.0327737	−	0.227063i
$932$	10.9706			0.359353
$933$		0			0
$934$	−1.76346	−	3.05440i	−0.0577020	−	0.0999429i
$935$	12.7990	+	22.1685i	0.418572	+	0.724987i
$936$		0			0
$937$	−27.0000			−0.882052			−0.441026	−	0.897494i	$-0.645385\pi$
$937$	−27.0000			−0.882052			−0.441026	+	0.897494i	$0.645385\pi$
$938$	−12.4264	+	4.30463i	−0.405737	+	0.140551i
$939$		0			0
$940$	19.7721	−	34.2462i	0.644894	−	1.11699i
$941$	−3.97056	−	6.87722i	−0.129437	−	0.224191i	0.794022	−	0.607889i	$-0.207984\pi$
$941$	−3.97056	−	6.87722i	−0.129437	−	0.224191i	−0.923458	+	0.383698i	$0.874650\pi$
$942$		0			0
$943$	7.00000	−	12.1244i	0.227951	−	0.394823i
$944$	−15.5147			−0.504961
$945$		0			0
$946$	−1.01724			−0.0330735
$947$	−19.6569	+	34.0467i	−0.638762	+	1.10637i	0.346943	+	0.937886i	$0.387220\pi$
$947$	−19.6569	+	34.0467i	−0.638762	+	1.10637i	−0.985705	+	0.168482i	$0.946114\pi$
$948$		0			0
$949$	17.4142	+	30.1623i	0.565289	+	0.979110i
$950$	0.343146	−	0.594346i	0.0111331	−	0.0192831i
$951$		0			0
$952$	−24.2843	−	21.0308i	−0.787058	−	0.681612i
$953$	−18.6274			−0.603401			−0.301701	−	0.953403i	$-0.597554\pi$
$953$	−18.6274			−0.603401			−0.301701	+	0.953403i	$0.597554\pi$
$954$		0			0
$955$	−5.64214	−	9.77247i	−0.182575	−	0.316230i
$956$	−12.4853	−	21.6251i	−0.403803	−	0.699407i
$957$		0			0
$958$	7.38478			0.238591
$959$	16.3431	+	14.1536i	0.527748	+	0.457043i
$960$		0			0
$961$	−23.4706	+	40.6522i	−0.757115	+	1.31136i
$962$	−4.00000	−	6.92820i	−0.128965	−	0.223374i
$963$		0			0
$964$	−18.1005	+	31.3510i	−0.582978	+	1.00975i
$965$	−7.31371			−0.235437
$966$		0			0
$967$	−16.0000			−0.514525			−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000			−0.514525			−0.257263	+	0.966342i	$0.582821\pi$
$968$	6.07107	−	10.5154i	0.195132	−	0.337978i
$969$		0			0
$970$	−4.23045	−	7.32735i	−0.135831	−	0.235267i
$971$	−0.100505	+	0.174080i	−0.00322536	+	0.00558649i	−0.867634	−	0.497204i	$-0.834360\pi$
$971$	−0.100505	+	0.174080i	−0.00322536	+	0.00558649i	0.864408	+	0.502791i	$0.167693\pi$
$972$		0			0
$973$	−11.6421	+	4.03295i	−0.373230	+	0.129291i
$974$	4.82843			0.154713
$975$		0			0
$976$	5.01472	+	8.68575i	0.160517	+	0.278024i
$977$	−19.5563	−	33.8726i	−0.625663	−	1.08368i	−0.988412	−	0.151793i	$-0.951495\pi$
$977$	−19.5563	−	33.8726i	−0.625663	−	1.08368i	0.362749	−	0.931887i	$-0.381838\pi$
$978$		0			0
$979$	9.45584			0.302210
$980$	18.3873	−	14.4762i	0.587361	−	0.462427i
$981$		0			0
$982$	5.27817	−	9.14207i	0.168433	−	0.291735i
$983$	−23.7279	−	41.0980i	−0.756803	−	1.31082i	−0.944473	−	0.328589i	$-0.893427\pi$
$983$	−23.7279	−	41.0980i	−0.756803	−	1.31082i	0.187670	−	0.982232i	$-0.439907\pi$
$984$		0			0
$985$	0.470563	−	0.815039i	0.0149934	−	0.0259693i
$986$	−2.62742			−0.0836740
$987$		0			0
$988$	−5.17157			−0.164530
$989$	−2.57107	+	4.45322i	−0.0817552	+	0.141604i
$990$		0			0
$991$	18.6274	+	32.2636i	0.591719	+	1.02489i	0.994001	+	0.109372i	$0.0348840\pi$
$991$	18.6274	+	32.2636i	0.591719	+	1.02489i	−0.402281	+	0.915516i	$0.631783\pi$
$992$	−19.4853	+	33.7495i	−0.618658	+	1.07155i
$993$		0			0
$994$	3.24264	−	16.8493i	0.102850	−	0.534426i
$995$	−26.7990			−0.849585
$996$		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	$0.675762\pi$
$998$	−2.89340	−	5.01151i	−0.0915889	−	0.158637i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.j.d.856.2		4
3.2	odd	2		399.2.j.c.58.1	✓	4
7.2	even	3		8379.2.a.bm.1.1		2
7.4	even	3	inner	1197.2.j.d.172.2		4
7.5	odd	6		8379.2.a.bh.1.1		2
21.2	odd	6		2793.2.a.o.1.2		2
21.5	even	6		2793.2.a.n.1.2		2
21.11	odd	6		399.2.j.c.172.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.c.58.1	✓	4	3.2	odd	2
399.2.j.c.172.1	yes	4	21.11	odd	6
1197.2.j.d.172.2		4	7.4	even	3	inner
1197.2.j.d.856.2		4	1.1	even	1	trivial
2793.2.a.n.1.2		2	21.5	even	6
2793.2.a.o.1.2		2	21.2	odd	6
8379.2.a.bh.1.1		2	7.5	odd	6
8379.2.a.bm.1.1		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)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(0.914214 - 1.58346i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.58579 q^{8} +(-0.378680 - 0.655892i) q^{10} +(0.914214 + 1.58346i) q^{11} -2.82843 q^{13} +(-0.207107 + 1.07616i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(3.82843 + 6.63103i) q^{17} +(0.500000 - 0.866025i) q^{19} +3.34315 q^{20} +0.757359 q^{22} +(1.91421 - 3.31552i) q^{23} +(0.828427 + 1.43488i) q^{25} +(-0.585786 + 1.01461i) q^{26} +(-3.65685 - 3.16693i) q^{28} -0.828427 q^{29} +(4.41421 + 7.64564i) q^{31} +(2.20711 + 3.82282i) q^{32} +3.17157 q^{34} +(-0.914214 + 4.75039i) q^{35} +(-3.41421 + 5.91359i) q^{37} +(-0.207107 - 0.358719i) q^{38} +(1.44975 - 2.51104i) q^{40} +3.65685 q^{41} -1.34315 q^{43} +(-1.67157 + 2.89525i) q^{44} +(-0.792893 - 1.37333i) q^{46} +(5.91421 - 10.2437i) q^{47} +(5.50000 - 4.33013i) q^{49} +0.686292 q^{50} +(-2.58579 - 4.47871i) q^{52} +(-1.00000 - 1.73205i) q^{53} +3.34315 q^{55} +(-3.96447 + 1.37333i) q^{56} +(-0.171573 + 0.297173i) q^{58} +(2.58579 + 4.47871i) q^{59} +(1.67157 - 2.89525i) q^{61} +3.65685 q^{62} -4.17157 q^{64} +(-2.58579 + 4.47871i) q^{65} +(6.00000 + 10.3923i) q^{67} +(-7.00000 + 12.1244i) q^{68} +(1.51472 + 1.31178i) q^{70} -15.6569 q^{71} +(-6.15685 - 10.6640i) q^{73} +(1.41421 + 2.44949i) q^{74} +1.82843 q^{76} +(-3.65685 - 3.16693i) q^{77} +(-6.82843 + 11.8272i) q^{79} +(2.74264 + 4.75039i) q^{80} +(0.757359 - 1.31178i) q^{82} -9.82843 q^{83} +14.0000 q^{85} +(-0.278175 + 0.481813i) q^{86} +(1.44975 + 2.51104i) q^{88} +(2.58579 - 4.47871i) q^{89} +(7.07107 - 2.44949i) q^{91} +7.00000 q^{92} +(-2.44975 - 4.24309i) q^{94} +(-0.914214 - 1.58346i) q^{95} +11.1716 q^{97} +(-0.414214 - 2.86976i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 10 q^{7} + 12 q^{8} - 10 q^{10} - 2 q^{11} + 2 q^{14} - 6 q^{16} + 4 q^{17} + 2 q^{19} + 36 q^{20} + 20 q^{22} + 2 q^{23} - 8 q^{25} - 8 q^{26} + 8 q^{28} + 8 q^{29}+ \cdots + 4 q^{98}+O(q^{100}) \) 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

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