LMFDB - Embedded newform 1197.2.j.e.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 133)
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.e.172.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20711 + 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +4.41421 q^{8} +(1.20711 + 2.09077i) q^{10} +(-0.207107 - 0.358719i) q^{11} -2.24264 q^{13} +(-6.32843 + 0.866025i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(0.500000 - 0.866025i) q^{19} -3.82843 q^{20} +1.00000 q^{22} +(-2.79289 + 4.83743i) q^{23} +(2.00000 + 3.46410i) q^{25} +(2.70711 - 4.68885i) q^{26} +(3.82843 - 9.37769i) q^{28} +6.58579 q^{29} +(3.12132 + 5.40629i) q^{31} +(0.792893 + 1.37333i) q^{32} +9.65685 q^{34} +(2.62132 - 0.358719i) q^{35} +(-4.53553 + 7.85578i) q^{37} +(1.20711 + 2.09077i) q^{38} +(2.20711 - 3.82282i) q^{40} +3.17157 q^{41} +8.07107 q^{43} +(-0.792893 + 1.37333i) q^{44} +(-6.74264 - 11.6786i) q^{46} +(-2.20711 + 3.82282i) q^{47} +(-1.74264 + 6.77962i) q^{49} -9.65685 q^{50} +(4.29289 + 7.43551i) q^{52} +(-2.12132 - 3.67423i) q^{53} -0.414214 q^{55} +(7.15685 + 9.22911i) q^{56} +(-7.94975 + 13.7694i) q^{58} +(3.41421 + 5.91359i) q^{59} +(-5.91421 + 10.2437i) q^{61} -15.0711 q^{62} -9.82843 q^{64} +(-1.12132 + 1.94218i) q^{65} +(-0.585786 - 1.01461i) q^{67} +(-7.65685 + 13.2621i) q^{68} +(-2.41421 + 5.91359i) q^{70} +14.2426 q^{71} +(-7.57107 - 13.1135i) q^{73} +(-10.9497 - 18.9655i) q^{74} -3.82843 q^{76} +(0.414214 - 1.01461i) q^{77} +(-0.707107 + 1.22474i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-3.82843 + 6.63103i) q^{82} -9.24264 q^{83} -4.00000 q^{85} +(-9.74264 + 16.8747i) q^{86} +(-0.914214 - 1.58346i) q^{88} +(-5.70711 + 9.88500i) q^{89} +(-3.63604 - 4.68885i) q^{91} +21.3848 q^{92} +(-5.32843 - 9.22911i) q^{94} +(-0.500000 - 0.866025i) q^{95} -3.17157 q^{97} +(-12.0711 - 11.8272i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} + 2 q^{10} + 2 q^{11} + 8 q^{13} - 14 q^{14} - 6 q^{16} - 8 q^{17} + 2 q^{19} - 4 q^{20} + 4 q^{22} - 14 q^{23} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 32 q^{29}+ \cdots - 20 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8 + 2 * q^10 + 2 * q^11 + 8 * q^13 - 14 * q^14 - 6 * q^16 - 8 * q^17 + 2 * q^19 - 4 * q^20 + 4 * q^22 - 14 * q^23 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 32 * q^29 + 4 * q^31 + 6 * q^32 + 16 * q^34 + 2 * q^35 - 4 * q^37 + 2 * q^38 + 6 * q^40 + 24 * q^41 + 4 * q^43 - 6 * q^44 - 10 * q^46 - 6 * q^47 + 10 * q^49 - 16 * q^50 + 20 * q^52 + 4 * q^55 + 6 * q^56 - 12 * q^58 + 8 * q^59 - 18 * q^61 - 32 * q^62 - 28 * q^64 + 4 * q^65 - 8 * q^67 - 8 * q^68 - 4 * q^70 + 40 * q^71 - 2 * q^73 - 24 * q^74 - 4 * q^76 - 4 * q^77 + 6 * q^80 - 4 * q^82 - 20 * q^83 - 16 * q^85 - 22 * q^86 + 2 * q^88 - 20 * q^89 - 40 * q^91 + 12 * q^92 - 10 * q^94 - 2 * q^95 - 24 * q^97 - 20 * 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
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$8$	4.41421			1.56066
$9$		0			0
$10$	1.20711	+	2.09077i	0.381721	+	0.661160i
$11$	−0.207107	−	0.358719i	−0.0624450	−	0.108158i	0.833113	−	0.553103i	$-0.186556\pi$
$11$	−0.207107	−	0.358719i	−0.0624450	−	0.108158i	−0.895558	+	0.444945i	$0.853223\pi$
$12$		0			0
$13$	−2.24264			−0.621997			−0.310998	−	0.950410i	$-0.600663\pi$
$13$	−2.24264			−0.621997			−0.310998	+	0.950410i	$0.600663\pi$
$14$	−6.32843	+	0.866025i	−1.69134	+	0.231455i
$15$		0			0
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$	−3.82843			−0.856062
$21$		0			0
$22$	1.00000			0.213201
$23$	−2.79289	+	4.83743i	−0.582358	+	1.00867i	0.412841	+	0.910803i	$0.364537\pi$
$23$	−2.79289	+	4.83743i	−0.582358	+	1.00867i	−0.995199	+	0.0978712i	$0.968797\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	2.70711	−	4.68885i	0.530907	−	0.919558i
$27$		0			0
$28$	3.82843	−	9.37769i	0.723505	−	1.77222i
$29$	6.58579			1.22295			0.611475	−	0.791264i	$-0.290577\pi$
$29$	6.58579			1.22295			0.611475	+	0.791264i	$0.290577\pi$
$30$		0			0
$31$	3.12132	+	5.40629i	0.560606	+	0.970998i	0.997444	+	0.0714573i	$0.0227650\pi$
$31$	3.12132	+	5.40629i	0.560606	+	0.970998i	−0.436838	+	0.899540i	$0.643902\pi$
$32$	0.792893	+	1.37333i	0.140165	+	0.242773i
$33$		0			0
$34$	9.65685			1.65614
$35$	2.62132	−	0.358719i	0.443084	−	0.0606347i
$36$		0			0
$37$	−4.53553	+	7.85578i	−0.745637	+	1.29148i	0.204259	+	0.978917i	$0.434521\pi$
$37$	−4.53553	+	7.85578i	−0.745637	+	1.29148i	−0.949896	+	0.312565i	$0.898812\pi$
$38$	1.20711	+	2.09077i	0.195819	+	0.339168i
$39$		0			0
$40$	2.20711	−	3.82282i	0.348974	−	0.604441i
$41$	3.17157			0.495316			0.247658	−	0.968847i	$-0.420339\pi$
$41$	3.17157			0.495316			0.247658	+	0.968847i	$0.420339\pi$
$42$		0			0
$43$	8.07107			1.23083			0.615413	−	0.788205i	$-0.288989\pi$
$43$	8.07107			1.23083			0.615413	+	0.788205i	$0.288989\pi$
$44$	−0.792893	+	1.37333i	−0.119533	+	0.207037i
$45$		0			0
$46$	−6.74264	−	11.6786i	−0.994148	−	1.72192i
$47$	−2.20711	+	3.82282i	−0.321940	+	0.557616i	−0.980888	−	0.194572i	$-0.937668\pi$
$47$	−2.20711	+	3.82282i	−0.321940	+	0.557616i	0.658949	+	0.752188i	$0.271001\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$	−9.65685			−1.36569
$51$		0			0
$52$	4.29289	+	7.43551i	0.595317	+	1.03112i
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	0.682752	−	0.730650i	$-0.260783\pi$
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	−0.974138	+	0.225955i	$0.927450\pi$
$54$		0			0
$55$	−0.414214			−0.0558525
$56$	7.15685	+	9.22911i	0.956375	+	1.23329i
$57$		0			0
$58$	−7.94975	+	13.7694i	−1.04385	+	1.80801i
$59$	3.41421	+	5.91359i	0.444493	+	0.769884i	0.998017	−	0.0629492i	$-0.0200506\pi$
$59$	3.41421	+	5.91359i	0.444493	+	0.769884i	−0.553524	+	0.832833i	$0.686717\pi$
$60$		0			0
$61$	−5.91421	+	10.2437i	−0.757237	+	1.31157i	0.187017	+	0.982357i	$0.440118\pi$
$61$	−5.91421	+	10.2437i	−0.757237	+	1.31157i	−0.944254	+	0.329217i	$0.893215\pi$
$62$	−15.0711			−1.91403
$63$		0			0
$64$	−9.82843			−1.22855
$65$	−1.12132	+	1.94218i	−0.139083	+	0.240898i
$66$		0			0
$67$	−0.585786	−	1.01461i	−0.0715652	−	0.123955i	0.828022	−	0.560695i	$-0.189466\pi$
$67$	−0.585786	−	1.01461i	−0.0715652	−	0.123955i	−0.899587	+	0.436741i	$0.856133\pi$
$68$	−7.65685	+	13.2621i	−0.928530	+	1.60826i
$69$		0			0
$70$	−2.41421	+	5.91359i	−0.288554	+	0.706809i
$71$	14.2426			1.69029			0.845145	−	0.534537i	$-0.179514\pi$
$71$	14.2426			1.69029			0.845145	+	0.534537i	$0.179514\pi$
$72$		0			0
$73$	−7.57107	−	13.1135i	−0.886126	−	1.53482i	−0.844417	−	0.535686i	$-0.820053\pi$
$73$	−7.57107	−	13.1135i	−0.886126	−	1.53482i	−0.0417094	−	0.999130i	$-0.513280\pi$
$74$	−10.9497	−	18.9655i	−1.27288	−	2.20470i
$75$		0			0
$76$	−3.82843			−0.439151
$77$	0.414214	−	1.01461i	0.0472040	−	0.115626i
$78$		0			0
$79$	−0.707107	+	1.22474i	−0.0795557	+	0.137795i	−0.903058	−	0.429518i	$-0.858683\pi$
$79$	−0.707107	+	1.22474i	−0.0795557	+	0.137795i	0.823503	+	0.567312i	$0.192017\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$		0			0
$82$	−3.82843	+	6.63103i	−0.422779	+	0.732275i
$83$	−9.24264			−1.01451			−0.507256	−	0.861796i	$-0.669340\pi$
$83$	−9.24264			−1.01451			−0.507256	+	0.861796i	$0.669340\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	−9.74264	+	16.8747i	−1.05058	+	1.81965i
$87$		0			0
$88$	−0.914214	−	1.58346i	−0.0974555	−	0.168798i
$89$	−5.70711	+	9.88500i	−0.604952	+	1.04781i	0.387107	+	0.922035i	$0.373474\pi$
$89$	−5.70711	+	9.88500i	−0.604952	+	1.04781i	−0.992059	+	0.125773i	$0.959859\pi$
$90$		0			0
$91$	−3.63604	−	4.68885i	−0.381160	−	0.491525i
$92$	21.3848			2.22952
$93$		0			0
$94$	−5.32843	−	9.22911i	−0.549585	−	0.951910i
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$		0			0
$97$	−3.17157			−0.322024			−0.161012	−	0.986952i	$-0.551476\pi$
$97$	−3.17157			−0.322024			−0.161012	+	0.986952i	$0.551476\pi$
$98$	−12.0711	−	11.8272i	−1.21936	−	1.19473i
$99$		0			0
$100$	7.65685	−	13.2621i	0.765685	−	1.32621i
$101$	9.15685	+	15.8601i	0.911141	+	1.57814i	0.812455	+	0.583024i	$0.198131\pi$
$101$	9.15685	+	15.8601i	0.911141	+	1.57814i	0.0986861	+	0.995119i	$0.468536\pi$
$102$		0			0
$103$	3.00000	−	5.19615i	0.295599	−	0.511992i	−0.679525	−	0.733652i	$-0.737814\pi$
$103$	3.00000	−	5.19615i	0.295599	−	0.511992i	0.975124	+	0.221660i	$0.0711475\pi$
$104$	−9.89949			−0.970725
$105$		0			0
$106$	10.2426			0.994853
$107$	−6.94975	+	12.0373i	−0.671857	+	1.16369i	0.305519	+	0.952186i	$0.401170\pi$
$107$	−6.94975	+	12.0373i	−0.671857	+	1.16369i	−0.977377	+	0.211505i	$0.932163\pi$
$108$		0			0
$109$	4.82843	+	8.36308i	0.462479	+	0.801038i	0.999084	−	0.0427961i	$-0.0136266\pi$
$109$	4.82843	+	8.36308i	0.462479	+	0.801038i	−0.536604	+	0.843834i	$0.680293\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$		0			0
$112$	−7.86396	+	1.07616i	−0.743074	+	0.101687i
$113$	0.242641			0.0228257			0.0114129	−	0.999935i	$-0.496367\pi$
$113$	0.242641			0.0228257			0.0114129	+	0.999935i	$0.496367\pi$
$114$		0			0
$115$	2.79289	+	4.83743i	0.260439	+	0.451093i
$116$	−12.6066	−	21.8353i	−1.17049	−	2.02735i
$117$		0			0
$118$	−16.4853			−1.51759
$119$	4.00000	−	9.79796i	0.366679	−	0.898177i
$120$		0			0
$121$	5.41421	−	9.37769i	0.492201	−	0.852518i
$122$	−14.2782	−	24.7305i	−1.29269	−	2.23900i
$123$		0			0
$124$	11.9497	−	20.6976i	1.07312	−	1.85870i
$125$	9.00000			0.804984
$126$		0			0
$127$	4.24264			0.376473			0.188237	−	0.982124i	$-0.439723\pi$
$127$	4.24264			0.376473			0.188237	+	0.982124i	$0.439723\pi$
$128$	10.2782	−	17.8023i	0.908471	−	1.57352i
$129$		0			0
$130$	−2.70711	−	4.68885i	−0.237429	−	0.411239i
$131$	1.75736	−	3.04384i	0.153541	−	0.265941i	−0.778986	−	0.627042i	$-0.784266\pi$
$131$	1.75736	−	3.04384i	0.153541	−	0.265941i	0.932527	+	0.361101i	$0.117599\pi$
$132$		0			0
$133$	2.62132	−	0.358719i	0.227297	−	0.0311049i
$134$	2.82843			0.244339
$135$		0			0
$136$	−8.82843	−	15.2913i	−0.757031	−	1.31122i
$137$	−9.91421	−	17.1719i	−0.847028	−	1.46710i	−0.883848	−	0.467774i	$-0.845056\pi$
$137$	−9.91421	−	17.1719i	−0.847028	−	1.46710i	0.0368195	−	0.999322i	$-0.488277\pi$
$138$		0			0
$139$	−6.07107			−0.514941			−0.257471	−	0.966286i	$-0.582889\pi$
$139$	−6.07107			−0.514941			−0.257471	+	0.966286i	$0.582889\pi$
$140$	−6.20711	−	8.00436i	−0.524596	−	0.676492i
$141$		0			0
$142$	−17.1924	+	29.7781i	−1.44275	+	2.49892i
$143$	0.464466	+	0.804479i	0.0388406	+	0.0672739i
$144$		0			0
$145$	3.29289	−	5.70346i	0.273460	−	0.473646i
$146$	36.5563			3.02542
$147$		0			0
$148$	34.7279			2.85462
$149$	−0.0857864	+	0.148586i	−0.00702790	+	0.0121727i	−0.869518	−	0.493901i	$-0.835570\pi$
$149$	−0.0857864	+	0.148586i	−0.00702790	+	0.0121727i	0.862490	+	0.506074i	$0.168904\pi$
$150$		0			0
$151$	8.65685	+	14.9941i	0.704485	+	1.22020i	0.966877	+	0.255242i	$0.0821552\pi$
$151$	8.65685	+	14.9941i	0.704485	+	1.22020i	−0.262392	+	0.964961i	$0.584511\pi$
$152$	2.20711	−	3.82282i	0.179020	−	0.310072i
$153$		0			0
$154$	1.62132	+	2.09077i	0.130650	+	0.168479i
$155$	6.24264			0.501421
$156$		0			0
$157$	−3.08579	−	5.34474i	−0.246273	−	0.426557i	0.716216	−	0.697879i	$-0.245873\pi$
$157$	−3.08579	−	5.34474i	−0.246273	−	0.426557i	−0.962489	+	0.271322i	$0.912539\pi$
$158$	−1.70711	−	2.95680i	−0.135810	−	0.235230i
$159$		0			0
$160$	1.58579			0.125367
$161$	−14.6421	+	2.00373i	−1.15396	+	0.157916i
$162$		0			0
$163$	−1.96447	+	3.40256i	−0.153869	+	0.266509i	−0.932647	−	0.360791i	$-0.882507\pi$
$163$	−1.96447	+	3.40256i	−0.153869	+	0.266509i	0.778778	+	0.627300i	$0.215840\pi$
$164$	−6.07107	−	10.5154i	−0.474071	−	0.821115i
$165$		0			0
$166$	11.1569	−	19.3242i	0.865940	−	1.49985i
$167$	−13.0711			−1.01147			−0.505735	−	0.862689i	$-0.668779\pi$
$167$	−13.0711			−1.01147			−0.505735	+	0.862689i	$0.668779\pi$
$168$		0			0
$169$	−7.97056			−0.613120
$170$	4.82843	−	8.36308i	0.370323	−	0.641419i
$171$		0			0
$172$	−15.4497	−	26.7597i	−1.17803	−	2.04041i
$173$	−3.65685	+	6.33386i	−0.278025	+	0.481554i	−0.970894	−	0.239510i	$-0.923013\pi$
$173$	−3.65685	+	6.33386i	−0.278025	+	0.481554i	0.692868	+	0.721064i	$0.256347\pi$
$174$		0			0
$175$	−4.00000	+	9.79796i	−0.302372	+	0.740656i
$176$	1.24264			0.0936676
$177$		0			0
$178$	−13.7782	−	23.8645i	−1.03272	−	1.78872i
$179$	8.89949	+	15.4144i	0.665179	+	1.15212i	0.979237	+	0.202721i	$0.0649783\pi$
$179$	8.89949	+	15.4144i	0.665179	+	1.15212i	−0.314057	+	0.949404i	$0.601688\pi$
$180$		0			0
$181$	9.89949			0.735824			0.367912	−	0.929861i	$-0.380073\pi$
$181$	9.89949			0.735824			0.367912	+	0.929861i	$0.380073\pi$
$182$	14.1924	−	1.94218i	1.05201	−	0.143964i
$183$		0			0
$184$	−12.3284	+	21.3535i	−0.908864	+	1.57420i
$185$	4.53553	+	7.85578i	0.333459	+	0.577568i
$186$		0			0
$187$	−0.828427	+	1.43488i	−0.0605806	+	0.104929i
$188$	16.8995			1.23252
$189$		0			0
$190$	2.41421			0.175145
$191$	4.20711	−	7.28692i	0.304416	−	0.527263i	−0.672715	−	0.739901i	$-0.734872\pi$
$191$	4.20711	−	7.28692i	0.304416	−	0.527263i	0.977131	+	0.212638i	$0.0682055\pi$
$192$		0			0
$193$	−3.94975	−	6.84116i	−0.284309	−	0.492438i	0.688132	−	0.725585i	$-0.258431\pi$
$193$	−3.94975	−	6.84116i	−0.284309	−	0.492438i	−0.972441	+	0.233147i	$0.925098\pi$
$194$	3.82843	−	6.63103i	0.274865	−	0.476080i
$195$		0			0
$196$	25.8137	−	7.19988i	1.84384	−	0.514277i
$197$	−4.51472			−0.321660			−0.160830	−	0.986982i	$-0.551417\pi$
$197$	−4.51472			−0.321660			−0.160830	+	0.986982i	$0.551417\pi$
$198$		0			0
$199$	−8.03553	−	13.9180i	−0.569624	−	0.986618i	−0.996603	−	0.0823560i	$-0.973756\pi$
$199$	−8.03553	−	13.9180i	−0.569624	−	0.986618i	0.426979	−	0.904262i	$-0.359578\pi$
$200$	8.82843	+	15.2913i	0.624264	+	1.08126i
$201$		0			0
$202$	−44.2132			−3.11083
$203$	10.6777	+	13.7694i	0.749425	+	0.966420i
$204$		0			0
$205$	1.58579	−	2.74666i	0.110756	−	0.191835i
$206$	7.24264	+	12.5446i	0.504619	+	0.874025i
$207$		0			0
$208$	3.36396	−	5.82655i	0.233249	−	0.403999i
$209$	−0.414214			−0.0286518
$210$		0			0
$211$	−1.17157			−0.0806544			−0.0403272	−	0.999187i	$-0.512840\pi$
$211$	−1.17157			−0.0806544			−0.0403272	+	0.999187i	$0.512840\pi$
$212$	−8.12132	+	14.0665i	−0.557775	+	0.966094i
$213$		0			0
$214$	−16.7782	−	29.0607i	−1.14693	−	1.98655i
$215$	4.03553	−	6.98975i	0.275221	−	0.476697i
$216$		0			0
$217$	−6.24264	+	15.2913i	−0.423778	+	1.03804i
$218$	−23.3137			−1.57900
$219$		0			0
$220$	0.792893	+	1.37333i	0.0534568	+	0.0925900i
$221$	4.48528	+	7.76874i	0.301713	+	0.522582i
$222$		0			0
$223$	2.24264			0.150178			0.0750892	−	0.997177i	$-0.476076\pi$
$223$	2.24264			0.150178			0.0750892	+	0.997177i	$0.476076\pi$
$224$	−1.58579	+	3.88437i	−0.105955	+	0.259535i
$225$		0			0
$226$	−0.292893	+	0.507306i	−0.0194830	+	0.0337455i
$227$	−10.1213	−	17.5306i	−0.671776	−	1.16355i	−0.977400	−	0.211397i	$-0.932199\pi$
$227$	−10.1213	−	17.5306i	−0.671776	−	1.16355i	0.305625	−	0.952152i	$-0.401135\pi$
$228$		0			0
$229$	−6.24264	+	10.8126i	−0.412525	+	0.714515i	−0.995165	−	0.0982157i	$-0.968686\pi$
$229$	−6.24264	+	10.8126i	−0.412525	+	0.714515i	0.582640	+	0.812730i	$0.302020\pi$
$230$	−13.4853			−0.889193
$231$		0			0
$232$	29.0711			1.90861
$233$	0.242641	−	0.420266i	0.0158959	−	0.0275325i	−0.857968	−	0.513703i	$-0.828273\pi$
$233$	0.242641	−	0.420266i	0.0158959	−	0.0275325i	0.873864	+	0.486171i	$0.161607\pi$
$234$		0			0
$235$	2.20711	+	3.82282i	0.143976	+	0.249373i
$236$	13.0711	−	22.6398i	0.850854	−	1.47372i
$237$		0			0
$238$	15.6569	+	20.1903i	1.01488	+	1.30874i
$239$	−2.00000			−0.129369			−0.0646846	−	0.997906i	$-0.520604\pi$
$239$	−2.00000			−0.129369			−0.0646846	+	0.997906i	$0.520604\pi$
$240$		0			0
$241$	13.0208	+	22.5527i	0.838744	+	1.45275i	0.890945	+	0.454111i	$0.150043\pi$
$241$	13.0208	+	22.5527i	0.838744	+	1.45275i	−0.0522005	+	0.998637i	$0.516623\pi$
$242$	13.0711	+	22.6398i	0.840240	+	1.45534i
$243$		0			0
$244$	45.2843			2.89903
$245$	5.00000	+	4.89898i	0.319438	+	0.312984i
$246$		0			0
$247$	−1.12132	+	1.94218i	−0.0713479	+	0.123578i
$248$	13.7782	+	23.8645i	0.874915	+	1.51540i
$249$		0			0
$250$	−10.8640	+	18.8169i	−0.687097	+	1.19009i
$251$	13.7279			0.866499			0.433249	−	0.901274i	$-0.357367\pi$
$251$	13.7279			0.866499			0.433249	+	0.901274i	$0.357367\pi$
$252$		0			0
$253$	2.31371			0.145462
$254$	−5.12132	+	8.87039i	−0.321340	+	0.556578i
$255$		0			0
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	4.65685	−	8.06591i	0.290487	−	0.503138i	−0.683438	−	0.730008i	$-0.739516\pi$
$257$	4.65685	−	8.06591i	0.290487	−	0.503138i	0.973925	+	0.226871i	$0.0728495\pi$
$258$		0			0
$259$	−23.7782	+	3.25397i	−1.47750	+	0.202192i
$260$	8.58579			0.532468
$261$		0			0
$262$	4.24264	+	7.34847i	0.262111	+	0.453990i
$263$	8.24264	+	14.2767i	0.508263	+	0.880337i	0.999954	+	0.00956772i	$0.00304554\pi$
$263$	8.24264	+	14.2767i	0.508263	+	0.880337i	−0.491691	+	0.870770i	$0.663621\pi$
$264$		0			0
$265$	−4.24264			−0.260623
$266$	−2.41421	+	5.91359i	−0.148025	+	0.362586i
$267$		0			0
$268$	−2.24264	+	3.88437i	−0.136991	+	0.237276i
$269$	−2.00000	−	3.46410i	−0.121942	−	0.211210i	0.798591	−	0.601874i	$-0.205579\pi$
$269$	−2.00000	−	3.46410i	−0.121942	−	0.211210i	−0.920534	+	0.390664i	$0.872246\pi$
$270$		0			0
$271$	7.62132	−	13.2005i	0.462962	−	0.801874i	−0.536145	−	0.844126i	$-0.680120\pi$
$271$	7.62132	−	13.2005i	0.462962	−	0.801874i	0.999107	+	0.0422519i	$0.0134532\pi$
$272$	12.0000			0.727607
$273$		0			0
$274$	47.8701			2.89194
$275$	0.828427	−	1.43488i	0.0499560	−	0.0865264i
$276$		0			0
$277$	11.2279	+	19.4473i	0.674620	+	1.16848i	0.976580	+	0.215156i	$0.0690260\pi$
$277$	11.2279	+	19.4473i	0.674620	+	1.16848i	−0.301959	+	0.953321i	$0.597641\pi$
$278$	7.32843	−	12.6932i	0.439530	−	0.761288i
$279$		0			0
$280$	11.5711	−	1.58346i	0.691504	−	0.0946301i
$281$	28.2426			1.68481			0.842407	−	0.538841i	$-0.181138\pi$
$281$	28.2426			1.68481			0.842407	+	0.538841i	$0.181138\pi$
$282$		0			0
$283$	−15.0355	−	26.0423i	−0.893770	−	1.54805i	−0.835320	−	0.549764i	$-0.814718\pi$
$283$	−15.0355	−	26.0423i	−0.893770	−	1.54805i	−0.0584498	−	0.998290i	$-0.518616\pi$
$284$	−27.2635	−	47.2217i	−1.61779	−	2.80209i
$285$		0			0
$286$	−2.24264			−0.132610
$287$	5.14214	+	6.63103i	0.303531	+	0.391417i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	7.94975	+	13.7694i	0.466825	+	0.808565i
$291$		0			0
$292$	−28.9853	+	50.2040i	−1.69624	+	2.93797i
$293$	−3.17157			−0.185285			−0.0926426	−	0.995699i	$-0.529531\pi$
$293$	−3.17157			−0.185285			−0.0926426	+	0.995699i	$0.529531\pi$
$294$		0			0
$295$	6.82843			0.397566
$296$	−20.0208	+	34.6771i	−1.16369	+	2.01556i
$297$		0			0
$298$	−0.207107	−	0.358719i	−0.0119974	−	0.0207801i
$299$	6.26346	−	10.8486i	0.362225	−	0.627392i
$300$		0			0
$301$	13.0858	+	16.8747i	0.754252	+	0.972644i
$302$	−41.7990			−2.40526
$303$		0			0
$304$	1.50000	+	2.59808i	0.0860309	+	0.149010i
$305$	5.91421	+	10.2437i	0.338647	+	0.586554i
$306$		0			0
$307$	29.3137			1.67302			0.836511	−	0.547950i	$-0.184592\pi$
$307$	29.3137			1.67302			0.836511	+	0.547950i	$0.184592\pi$
$308$	−4.15685	+	0.568852i	−0.236859	+	0.0324134i
$309$		0			0
$310$	−7.53553	+	13.0519i	−0.427990	+	0.741300i
$311$	−11.8995	−	20.6105i	−0.674758	−	1.16872i	−0.976539	−	0.215339i	$-0.930914\pi$
$311$	−11.8995	−	20.6105i	−0.674758	−	1.16872i	0.301781	−	0.953377i	$-0.402419\pi$
$312$		0			0
$313$	3.32843	−	5.76500i	0.188134	−	0.325857i	−0.756494	−	0.654000i	$-0.773089\pi$
$313$	3.32843	−	5.76500i	0.188134	−	0.325857i	0.944628	+	0.328143i	$0.106423\pi$
$314$	14.8995			0.840827
$315$		0			0
$316$	5.41421			0.304573
$317$	−10.1213	+	17.5306i	−0.568470	+	0.984619i	0.428248	+	0.903661i	$0.359131\pi$
$317$	−10.1213	+	17.5306i	−0.568470	+	0.984619i	−0.996718	+	0.0809574i	$0.974202\pi$
$318$		0			0
$319$	−1.36396	−	2.36245i	−0.0763672	−	0.132272i
$320$	−4.91421	+	8.51167i	−0.274713	+	0.475817i
$321$		0			0
$322$	13.4853	−	33.0321i	0.751505	−	1.84080i
$323$	−4.00000			−0.222566
$324$		0			0
$325$	−4.48528	−	7.76874i	−0.248799	−	0.430932i
$326$	−4.74264	−	8.21449i	−0.262671	−	0.454959i
$327$		0			0
$328$	14.0000			0.773021
$329$	−11.5711	+	1.58346i	−0.637934	+	0.0872992i
$330$		0			0
$331$	15.7279	−	27.2416i	0.864485	−	1.49733i	−0.00307307	−	0.999995i	$-0.500978\pi$
$331$	15.7279	−	27.2416i	0.864485	−	1.49733i	0.867558	−	0.497336i	$-0.165688\pi$
$332$	17.6924	+	30.6441i	0.970996	+	1.68181i
$333$		0			0
$334$	15.7782	−	27.3286i	0.863343	−	1.49535i
$335$	−1.17157			−0.0640099
$336$		0			0
$337$	19.5563			1.06530			0.532651	−	0.846335i	$-0.321196\pi$
$337$	19.5563			1.06530			0.532651	+	0.846335i	$0.321196\pi$
$338$	9.62132	−	16.6646i	0.523331	−	0.906436i
$339$		0			0
$340$	7.65685	+	13.2621i	0.415251	+	0.719236i
$341$	1.29289	−	2.23936i	0.0700141	−	0.121268i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	35.6274			1.92090
$345$		0			0
$346$	−8.82843	−	15.2913i	−0.474619	−	0.822065i
$347$	13.5208	+	23.4187i	0.725835	+	1.25718i	0.958629	+	0.284658i	$0.0918799\pi$
$347$	13.5208	+	23.4187i	0.725835	+	1.25718i	−0.232794	+	0.972526i	$0.574787\pi$
$348$		0			0
$349$	4.48528			0.240092			0.120046	−	0.992768i	$-0.461696\pi$
$349$	4.48528			0.240092			0.120046	+	0.992768i	$0.461696\pi$
$350$	−15.6569	−	20.1903i	−0.836894	−	1.07921i
$351$		0			0
$352$	0.328427	−	0.568852i	0.0175052	−	0.0303199i
$353$	0.242641	+	0.420266i	0.0129145	+	0.0223685i	0.872410	−	0.488774i	$-0.162556\pi$
$353$	0.242641	+	0.420266i	0.0129145	+	0.0223685i	−0.859496	+	0.511143i	$0.829222\pi$
$354$		0			0
$355$	7.12132	−	12.3345i	0.377960	−	0.654647i
$356$	43.6985			2.31602
$357$		0			0
$358$	−42.9706			−2.27106
$359$	2.62132	−	4.54026i	0.138348	−	0.239626i	−0.788523	−	0.615005i	$-0.789154\pi$
$359$	2.62132	−	4.54026i	0.138348	−	0.239626i	0.926871	+	0.375379i	$0.122487\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	−11.9497	+	20.6976i	−0.628065	+	1.08784i
$363$		0			0
$364$	−8.58579	+	21.0308i	−0.450017	+	1.10231i
$365$	−15.1421			−0.792576
$366$		0			0
$367$	12.1716	+	21.0818i	0.635351	+	1.10046i	0.986441	+	0.164118i	$0.0524779\pi$
$367$	12.1716	+	21.0818i	0.635351	+	1.10046i	−0.351090	+	0.936342i	$0.614189\pi$
$368$	−8.37868	−	14.5123i	−0.436769	−	0.756506i
$369$		0			0
$370$	−21.8995			−1.13850
$371$	4.24264	−	10.3923i	0.220267	−	0.539542i
$372$		0			0
$373$	−5.65685	+	9.79796i	−0.292901	+	0.507319i	−0.974494	−	0.224412i	$-0.927954\pi$
$373$	−5.65685	+	9.79796i	−0.292901	+	0.507319i	0.681594	+	0.731731i	$0.261287\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$		0			0
$376$	−9.74264	+	16.8747i	−0.502438	+	0.870249i
$377$	−14.7696			−0.760671
$378$		0			0
$379$	4.24264			0.217930			0.108965	−	0.994046i	$-0.465246\pi$
$379$	4.24264			0.217930			0.108965	+	0.994046i	$0.465246\pi$
$380$	−1.91421	+	3.31552i	−0.0981971	+	0.170082i
$381$		0			0
$382$	10.1569	+	17.5922i	0.519670	+	0.900095i
$383$	9.87868	−	17.1104i	0.504777	−	0.874299i	−0.495208	−	0.868775i	$-0.664908\pi$
$383$	9.87868	−	17.1104i	0.504777	−	0.874299i	0.999985	−	0.00552476i	$-0.00175859\pi$
$384$		0			0
$385$	−0.671573	−	0.866025i	−0.0342265	−	0.0441367i
$386$	19.0711			0.970692
$387$		0			0
$388$	6.07107	+	10.5154i	0.308212	+	0.533838i
$389$	−5.75736	−	9.97204i	−0.291910	−	0.505602i	0.682352	−	0.731024i	$-0.260957\pi$
$389$	−5.75736	−	9.97204i	−0.291910	−	0.505602i	−0.974261	+	0.225422i	$0.927624\pi$
$390$		0			0
$391$	22.3431			1.12994
$392$	−7.69239	+	29.9267i	−0.388524	+	1.51153i
$393$		0			0
$394$	5.44975	−	9.43924i	0.274554	−	0.475542i
$395$	0.707107	+	1.22474i	0.0355784	+	0.0616236i
$396$		0			0
$397$	4.31371	−	7.47156i	0.216499	−	0.374987i	−0.737236	−	0.675635i	$-0.763870\pi$
$397$	4.31371	−	7.47156i	0.216499	−	0.374987i	0.953735	+	0.300648i	$0.0972029\pi$
$398$	38.7990			1.94482
$399$		0			0
$400$	−12.0000			−0.600000
$401$	0.242641	−	0.420266i	0.0121169	−	0.0209871i	−0.859903	−	0.510457i	$-0.829476\pi$
$401$	0.242641	−	0.420266i	0.0121169	−	0.0209871i	0.872020	+	0.489470i	$0.162810\pi$
$402$		0			0
$403$	−7.00000	−	12.1244i	−0.348695	−	0.603957i
$404$	35.0563	−	60.7194i	1.74412	−	3.02090i
$405$		0			0
$406$	−41.6777	+	5.70346i	−2.06843	+	0.283058i
$407$	3.75736			0.186245
$408$		0			0
$409$	1.34315	+	2.32640i	0.0664143	+	0.115033i	0.897320	−	0.441380i	$-0.145511\pi$
$409$	1.34315	+	2.32640i	0.0664143	+	0.115033i	−0.830906	+	0.556413i	$0.812177\pi$
$410$	3.82843	+	6.63103i	0.189073	+	0.327483i
$411$		0			0
$412$	−22.9706			−1.13168
$413$	−6.82843	+	16.7262i	−0.336005	+	0.823041i
$414$		0			0
$415$	−4.62132	+	8.00436i	−0.226852	+	0.392919i
$416$	−1.77817	−	3.07989i	−0.0871822	−	0.151004i
$417$		0			0
$418$	0.500000	−	0.866025i	0.0244558	−	0.0423587i
$419$	−6.07107			−0.296591			−0.148296	−	0.988943i	$-0.547379\pi$
$419$	−6.07107			−0.296591			−0.148296	+	0.988943i	$0.547379\pi$
$420$		0			0
$421$	−37.2132			−1.81366			−0.906830	−	0.421496i	$-0.861505\pi$
$421$	−37.2132			−1.81366			−0.906830	+	0.421496i	$0.861505\pi$
$422$	1.41421	−	2.44949i	0.0688428	−	0.119239i
$423$		0			0
$424$	−9.36396	−	16.2189i	−0.454754	−	0.787657i
$425$	8.00000	−	13.8564i	0.388057	−	0.672134i
$426$		0			0
$427$	−31.0061	+	4.24309i	−1.50049	+	0.205337i
$428$	53.2132			2.57216
$429$		0			0
$430$	9.74264	+	16.8747i	0.469832	+	0.813773i
$431$	−5.02082	−	8.69631i	−0.241844	−	0.418886i	0.719395	−	0.694601i	$-0.244419\pi$
$431$	−5.02082	−	8.69631i	−0.241844	−	0.418886i	−0.961240	+	0.275714i	$0.911086\pi$
$432$		0			0
$433$	28.0000			1.34559			0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000			1.34559			0.672797	+	0.739827i	$0.265093\pi$
$434$	−24.4350	−	31.5101i	−1.17292	−	1.51254i
$435$		0			0
$436$	18.4853	−	32.0174i	0.885284	−	1.53336i
$437$	2.79289	+	4.83743i	0.133602	+	0.231406i
$438$		0			0
$439$	12.2426	−	21.2049i	0.584309	−	1.01205i	−0.410652	−	0.911792i	$-0.634699\pi$
$439$	12.2426	−	21.2049i	0.584309	−	1.01205i	0.994961	−	0.100261i	$-0.0319679\pi$
$440$	−1.82843			−0.0871668
$441$		0			0
$442$	−21.6569			−1.03011
$443$	8.82843	−	15.2913i	0.419451	−	0.726511i	−0.576433	−	0.817144i	$-0.695556\pi$
$443$	8.82843	−	15.2913i	0.419451	−	0.726511i	0.995884	+	0.0906335i	$0.0288892\pi$
$444$		0			0
$445$	5.70711	+	9.88500i	0.270543	+	0.468594i
$446$	−2.70711	+	4.68885i	−0.128185	+	0.222023i
$447$		0			0
$448$	−15.9350	−	20.5490i	−0.752859	−	0.970848i
$449$	−9.65685			−0.455735			−0.227868	−	0.973692i	$-0.573175\pi$
$449$	−9.65685			−0.455735			−0.227868	+	0.973692i	$0.573175\pi$
$450$		0			0
$451$	−0.656854	−	1.13770i	−0.0309301	−	0.0535724i
$452$	−0.464466	−	0.804479i	−0.0218466	−	0.0378395i
$453$		0			0
$454$	48.8701			2.29359
$455$	−5.87868	+	0.804479i	−0.275597	+	0.0377146i
$456$		0			0
$457$	3.91421	−	6.77962i	0.183099	−	0.317137i	−0.759835	−	0.650116i	$-0.774720\pi$
$457$	3.91421	−	6.77962i	0.183099	−	0.317137i	0.942934	+	0.332979i	$0.108054\pi$
$458$	−15.0711	−	26.1039i	−0.704225	−	1.21975i
$459$		0			0
$460$	10.6924	−	18.5198i	0.498535	−	0.863488i
$461$	−29.9706			−1.39587			−0.697934	−	0.716162i	$-0.745897\pi$
$461$	−29.9706			−1.39587			−0.697934	+	0.716162i	$0.745897\pi$
$462$		0			0
$463$	−4.07107			−0.189199			−0.0945993	−	0.995515i	$-0.530157\pi$
$463$	−4.07107			−0.189199			−0.0945993	+	0.995515i	$0.530157\pi$
$464$	−9.87868	+	17.1104i	−0.458606	+	0.794329i
$465$		0			0
$466$	0.585786	+	1.01461i	0.0271360	+	0.0470010i
$467$	9.55025	−	16.5415i	0.441933	−	0.765450i	−0.555900	−	0.831249i	$-0.687626\pi$
$467$	9.55025	−	16.5415i	0.441933	−	0.765450i	0.997833	+	0.0657988i	$0.0209596\pi$
$468$		0			0
$469$	1.17157	−	2.86976i	0.0540982	−	0.132513i
$470$	−10.6569			−0.491564
$471$		0			0
$472$	15.0711	+	26.1039i	0.693702	+	1.20153i
$473$	−1.67157	−	2.89525i	−0.0768590	−	0.133124i
$474$		0			0
$475$	4.00000			0.183533
$476$	−40.1421	+	5.49333i	−1.83991	+	0.251786i
$477$		0			0
$478$	2.41421	−	4.18154i	0.110424	−	0.191259i
$479$	−12.6924	−	21.9839i	−0.579930	−	1.00447i	−0.995487	−	0.0949010i	$-0.969747\pi$
$479$	−12.6924	−	21.9839i	−0.579930	−	1.00447i	0.415557	−	0.909567i	$-0.363587\pi$
$480$		0			0
$481$	10.1716	−	17.6177i	0.463784	−	0.803297i
$482$	−62.8701			−2.86365
$483$		0			0
$484$	−41.4558			−1.88436
$485$	−1.58579	+	2.74666i	−0.0720069	+	0.124720i
$486$		0			0
$487$	−7.58579	−	13.1390i	−0.343745	−	0.595383i	0.641380	−	0.767223i	$-0.278362\pi$
$487$	−7.58579	−	13.1390i	−0.343745	−	0.595383i	−0.985125	+	0.171840i	$0.945029\pi$
$488$	−26.1066	+	45.2180i	−1.18179	+	2.04692i
$489$		0			0
$490$	−16.2782	+	4.54026i	−0.735373	+	0.205108i
$491$	1.44365			0.0651510			0.0325755	−	0.999469i	$-0.489629\pi$
$491$	1.44365			0.0651510			0.0325755	+	0.999469i	$0.489629\pi$
$492$		0			0
$493$	−13.1716	−	22.8138i	−0.593218	−	1.02748i
$494$	−2.70711	−	4.68885i	−0.121798	−	0.210961i
$495$		0			0
$496$	−18.7279			−0.840909
$497$	23.0919	+	29.7781i	1.03581	+	1.33573i
$498$		0			0
$499$	−17.2782	+	29.9267i	−0.773477	+	1.33970i	0.162169	+	0.986763i	$0.448151\pi$
$499$	−17.2782	+	29.9267i	−0.773477	+	1.33970i	−0.935646	+	0.352939i	$0.885182\pi$
$500$	−17.2279	−	29.8396i	−0.770456	−	1.33447i
$501$		0			0
$502$	−16.5711	+	28.7019i	−0.739603	+	1.28103i
$503$	29.0416			1.29490			0.647451	−	0.762107i	$-0.275835\pi$
$503$	29.0416			1.29490			0.647451	+	0.762107i	$0.275835\pi$
$504$		0			0
$505$	18.3137			0.814949
$506$	−2.79289	+	4.83743i	−0.124159	+	0.215050i
$507$		0			0
$508$	−8.12132	−	14.0665i	−0.360325	−	0.624102i
$509$	−7.48528	+	12.9649i	−0.331779	+	0.574659i	−0.982861	−	0.184349i	$-0.940982\pi$
$509$	−7.48528	+	12.9649i	−0.331779	+	0.574659i	0.651082	+	0.759008i	$0.274316\pi$
$510$		0			0
$511$	15.1421	−	37.0905i	0.669849	−	1.64079i
$512$	−31.2426			−1.38074
$513$		0			0
$514$	11.2426	+	19.4728i	0.495892	+	0.858909i
$515$	−3.00000	−	5.19615i	−0.132196	−	0.228970i
$516$		0			0
$517$	1.82843			0.0804141
$518$	21.8995	−	53.6426i	0.962209	−	2.35692i
$519$		0			0
$520$	−4.94975	+	8.57321i	−0.217061	+	0.375960i
$521$	20.7782	+	35.9889i	0.910308	+	1.57670i	0.813629	+	0.581385i	$0.197489\pi$
$521$	20.7782	+	35.9889i	0.910308	+	1.57670i	0.0966796	+	0.995316i	$0.469178\pi$
$522$		0			0
$523$	6.17157	−	10.6895i	0.269864	−	0.467418i	−0.698962	−	0.715158i	$-0.746355\pi$
$523$	6.17157	−	10.6895i	0.269864	−	0.467418i	0.968827	+	0.247740i	$0.0796879\pi$
$524$	−13.4558			−0.587821
$525$		0			0
$526$	−39.7990			−1.73532
$527$	12.4853	−	21.6251i	0.543867	−	0.942006i
$528$		0			0
$529$	−4.10051	−	7.10228i	−0.178283	−	0.308795i
$530$	5.12132	−	8.87039i	0.222456	−	0.385305i
$531$		0			0
$532$	−6.20711	−	8.00436i	−0.269112	−	0.347033i
$533$	−7.11270			−0.308085
$534$		0			0
$535$	6.94975	+	12.0373i	0.300464	+	0.520419i
$536$	−2.58579	−	4.47871i	−0.111689	−	0.193451i
$537$		0			0
$538$	9.65685			0.416337
$539$	2.79289	−	0.778985i	0.120298	−	0.0335533i
$540$		0			0
$541$	11.5711	−	20.0417i	0.497479	−	0.861659i	−0.502517	−	0.864567i	$-0.667592\pi$
$541$	11.5711	−	20.0417i	0.497479	−	0.861659i	0.999996	+	0.00290849i	$0.000925802\pi$
$542$	18.3995	+	31.8689i	0.790326	+	1.36888i
$543$		0			0
$544$	3.17157	−	5.49333i	0.135980	−	0.235524i
$545$	9.65685			0.413654
$546$		0			0
$547$	−1.55635			−0.0665447			−0.0332723	−	0.999446i	$-0.510593\pi$
$547$	−1.55635			−0.0665447			−0.0332723	+	0.999446i	$0.510593\pi$
$548$	−37.9558	+	65.7415i	−1.62139	+	2.80834i
$549$		0			0
$550$	2.00000	+	3.46410i	0.0852803	+	0.147710i
$551$	3.29289	−	5.70346i	0.140282	−	0.242975i
$552$		0			0
$553$	−3.70711	+	0.507306i	−0.157642	+	0.0215728i
$554$	−54.2132			−2.30330
$555$		0			0
$556$	11.6213	+	20.1287i	0.492854	+	0.853648i
$557$	7.91421	+	13.7078i	0.335336	+	0.580819i	0.983549	−	0.180640i	$-0.0578168\pi$
$557$	7.91421	+	13.7078i	0.335336	+	0.580819i	−0.648213	+	0.761459i	$0.724483\pi$
$558$		0			0
$559$	−18.1005			−0.765570
$560$	−3.00000	+	7.34847i	−0.126773	+	0.310530i
$561$		0			0
$562$	−34.0919	+	59.0489i	−1.43808	+	2.49083i
$563$	2.94975	+	5.10911i	0.124317	+	0.215323i	0.921466	−	0.388460i	$-0.126993\pi$
$563$	2.94975	+	5.10911i	0.124317	+	0.215323i	−0.797149	+	0.603783i	$0.793659\pi$
$564$		0			0
$565$	0.121320	−	0.210133i	0.00510399	−	0.00884036i
$566$	72.5980			3.05152
$567$		0			0
$568$	62.8701			2.63797
$569$	−4.51472	+	7.81972i	−0.189267	+	0.327820i	−0.945006	−	0.327053i	$-0.893944\pi$
$569$	−4.51472	+	7.81972i	−0.189267	+	0.327820i	0.755739	+	0.654873i	$0.227278\pi$
$570$		0			0
$571$	−0.449747	−	0.778985i	−0.0188213	−	0.0325995i	0.856461	−	0.516211i	$-0.172658\pi$
$571$	−0.449747	−	0.778985i	−0.0188213	−	0.0325995i	−0.875283	+	0.483612i	$0.839325\pi$
$572$	1.77817	−	3.07989i	0.0743492	−	0.128777i
$573$		0			0
$574$	−20.0711	+	2.74666i	−0.837750	+	0.114643i
$575$	−22.3431			−0.931774
$576$		0			0
$577$	2.98528	+	5.17066i	0.124279	+	0.215257i	0.921451	−	0.388495i	$-0.127005\pi$
$577$	2.98528	+	5.17066i	0.124279	+	0.215257i	−0.797172	+	0.603752i	$0.793672\pi$
$578$	1.20711	+	2.09077i	0.0502090	+	0.0869646i
$579$		0			0
$580$	−25.2132			−1.04692
$581$	−14.9853	−	19.3242i	−0.621694	−	0.801704i
$582$		0			0
$583$	−0.878680	+	1.52192i	−0.0363912	+	0.0630314i
$584$	−33.4203	−	57.8857i	−1.38294	−	2.39533i
$585$		0			0
$586$	3.82843	−	6.63103i	0.158151	−	0.273925i
$587$	−14.0000			−0.577842			−0.288921	−	0.957353i	$-0.593296\pi$
$587$	−14.0000			−0.577842			−0.288921	+	0.957353i	$0.593296\pi$
$588$		0			0
$589$	6.24264			0.257224
$590$	−8.24264	+	14.2767i	−0.339344	+	0.587761i
$591$		0			0
$592$	−13.6066	−	23.5673i	−0.559228	−	0.968611i
$593$	5.91421	−	10.2437i	0.242868	−	0.420659i	−0.718662	−	0.695359i	$-0.755245\pi$
$593$	5.91421	−	10.2437i	0.242868	−	0.420659i	0.961530	+	0.274700i	$0.0885786\pi$
$594$		0			0
$595$	−6.48528	−	8.36308i	−0.265871	−	0.342853i
$596$	0.656854			0.0269058
$597$		0			0
$598$	15.1213	+	26.1909i	0.618357	+	1.07103i
$599$	13.8492	+	23.9876i	0.565865	+	0.980106i	0.996969	+	0.0778042i	$0.0247909\pi$
$599$	13.8492	+	23.9876i	0.565865	+	0.980106i	−0.431104	+	0.902302i	$0.641876\pi$
$600$		0			0
$601$	−34.7279			−1.41658			−0.708291	−	0.705921i	$-0.750533\pi$
$601$	−34.7279			−1.41658			−0.708291	+	0.705921i	$0.750533\pi$
$602$	−51.0772	+	6.98975i	−2.08175	+	0.284881i
$603$		0			0
$604$	33.1421	−	57.4039i	1.34853	−	2.33573i
$605$	−5.41421	−	9.37769i	−0.220119	−	0.381257i
$606$		0			0
$607$	16.2635	−	28.1691i	0.660113	−	1.14335i	−0.320472	−	0.947258i	$-0.603842\pi$
$607$	16.2635	−	28.1691i	0.660113	−	1.14335i	0.980586	−	0.196092i	$-0.0628251\pi$
$608$	1.58579			0.0643121
$609$		0			0
$610$	−28.5563			−1.15621
$611$	4.94975	−	8.57321i	0.200245	−	0.346835i
$612$		0			0
$613$	15.6569	+	27.1185i	0.632374	+	1.09530i	0.987065	+	0.160321i	$0.0512529\pi$
$613$	15.6569	+	27.1185i	0.632374	+	1.09530i	−0.354691	+	0.934984i	$0.615414\pi$
$614$	−35.3848	+	61.2882i	−1.42801	+	2.47339i
$615$		0			0
$616$	1.82843	−	4.47871i	0.0736694	−	0.180453i
$617$	−8.45584			−0.340419			−0.170210	−	0.985408i	$-0.554445\pi$
$617$	−8.45584			−0.340419			−0.170210	+	0.985408i	$0.554445\pi$
$618$		0			0
$619$	−17.2782	−	29.9267i	−0.694468	−	1.20285i	−0.970360	−	0.241666i	$-0.922306\pi$
$619$	−17.2782	−	29.9267i	−0.694468	−	1.20285i	0.275891	−	0.961189i	$-0.411027\pi$
$620$	−11.9497	−	20.6976i	−0.479913	−	0.831234i
$621$		0			0
$622$	57.4558			2.30377
$623$	−29.9203	+	4.09450i	−1.19873	+	0.164043i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	8.03553	+	13.9180i	0.321165	+	0.556273i
$627$		0			0
$628$	−11.8137	+	20.4619i	−0.471418	+	0.816520i
$629$	36.2843			1.44675
$630$		0			0
$631$	−36.5563			−1.45529			−0.727643	−	0.685956i	$-0.759384\pi$
$631$	−36.5563			−1.45529			−0.727643	+	0.685956i	$0.759384\pi$
$632$	−3.12132	+	5.40629i	−0.124159	+	0.215050i
$633$		0			0
$634$	−24.4350	−	42.3227i	−0.970439	−	1.68085i
$635$	2.12132	−	3.67423i	0.0841820	−	0.145808i
$636$		0			0
$637$	3.90812	−	15.2042i	0.154845	−	0.602414i
$638$	6.58579			0.260734
$639$		0			0
$640$	−10.2782	−	17.8023i	−0.406281	−	0.703699i
$641$	−17.8995	−	31.0028i	−0.706988	−	1.22454i	−0.965969	−	0.258656i	$-0.916720\pi$
$641$	−17.8995	−	31.0028i	−0.706988	−	1.22454i	0.258982	−	0.965882i	$-0.416613\pi$
$642$		0			0
$643$	1.85786			0.0732670			0.0366335	−	0.999329i	$-0.488337\pi$
$643$	1.85786			0.0732670			0.0366335	+	0.999329i	$0.488337\pi$
$644$	34.6716	+	44.7107i	1.36625	+	1.76185i
$645$		0			0
$646$	4.82843	−	8.36308i	0.189972	−	0.329041i
$647$	−18.1066	−	31.3616i	−0.711844	−	1.23295i	−0.964164	−	0.265306i	$-0.914527\pi$
$647$	−18.1066	−	31.3616i	−0.711844	−	1.23295i	0.252320	−	0.967644i	$-0.418806\pi$
$648$		0			0
$649$	1.41421	−	2.44949i	0.0555127	−	0.0961509i
$650$	21.6569			0.849452
$651$		0			0
$652$	15.0416			0.589076
$653$	−15.0711	+	26.1039i	−0.589776	+	1.02152i	0.404485	+	0.914545i	$0.367451\pi$
$653$	−15.0711	+	26.1039i	−0.589776	+	1.02152i	−0.994261	+	0.106978i	$0.965883\pi$
$654$		0			0
$655$	−1.75736	−	3.04384i	−0.0686657	−	0.118932i
$656$	−4.75736	+	8.23999i	−0.185744	+	0.321717i
$657$		0			0
$658$	10.6569	−	26.1039i	0.415447	−	1.01763i
$659$	−10.0416			−0.391166			−0.195583	−	0.980687i	$-0.562660\pi$
$659$	−10.0416			−0.391166			−0.195583	+	0.980687i	$0.562660\pi$
$660$		0			0
$661$	−1.36396	−	2.36245i	−0.0530519	−	0.0918886i	0.838280	−	0.545240i	$-0.183562\pi$
$661$	−1.36396	−	2.36245i	−0.0530519	−	0.0918886i	−0.891332	+	0.453352i	$0.850228\pi$
$662$	37.9706	+	65.7669i	1.47577	+	2.55610i
$663$		0			0
$664$	−40.7990			−1.58331
$665$	1.00000	−	2.44949i	0.0387783	−	0.0949871i
$666$		0			0
$667$	−18.3934	+	31.8583i	−0.712195	+	1.23356i
$668$	25.0208	+	43.3373i	0.968084	+	1.67677i
$669$		0			0
$670$	1.41421	−	2.44949i	0.0546358	−	0.0946320i
$671$	4.89949			0.189143
$672$		0			0
$673$	−3.79899			−0.146440			−0.0732201	−	0.997316i	$-0.523328\pi$
$673$	−3.79899			−0.146440			−0.0732201	+	0.997316i	$0.523328\pi$
$674$	−23.6066	+	40.8878i	−0.909292	+	1.57494i
$675$		0			0
$676$	15.2574	+	26.4265i	0.586822	+	1.01640i
$677$	11.6569	−	20.1903i	0.448009	−	0.775975i	−0.550247	−	0.835002i	$-0.685466\pi$
$677$	11.6569	−	20.1903i	0.448009	−	0.775975i	0.998256	+	0.0590270i	$0.0187998\pi$
$678$		0			0
$679$	−5.14214	−	6.63103i	−0.197337	−	0.254476i
$680$	−17.6569			−0.677109
$681$		0			0
$682$	3.12132	+	5.40629i	0.119522	+	0.207017i
$683$	−3.24264	−	5.61642i	−0.124076	−	0.214906i	0.797295	−	0.603589i	$-0.206263\pi$
$683$	−3.24264	−	5.61642i	−0.124076	−	0.214906i	−0.921371	+	0.388683i	$0.872930\pi$
$684$		0			0
$685$	−19.8284			−0.757605
$686$	5.15685	−	44.4135i	0.196890	−	1.69571i
$687$		0			0
$688$	−12.1066	+	20.9692i	−0.461560	+	0.799445i
$689$	4.75736	+	8.23999i	0.181241	+	0.313919i
$690$		0			0
$691$	−15.4853	+	26.8213i	−0.589088	+	1.02033i	0.405264	+	0.914200i	$0.367179\pi$
$691$	−15.4853	+	26.8213i	−0.589088	+	1.02033i	−0.994352	+	0.106131i	$0.966154\pi$
$692$	28.0000			1.06440
$693$		0			0
$694$	−65.2843			−2.47816
$695$	−3.03553	+	5.25770i	−0.115144	+	0.199436i
$696$		0			0
$697$	−6.34315	−	10.9867i	−0.240264	−	0.416149i
$698$	−5.41421	+	9.37769i	−0.204931	+	0.354951i
$699$		0			0
$700$	40.1421	−	5.49333i	1.51723	−	0.207628i
$701$	1.82843			0.0690587			0.0345294	−	0.999404i	$-0.489007\pi$
$701$	1.82843			0.0690587			0.0345294	+	0.999404i	$0.489007\pi$
$702$		0			0
$703$	4.53553	+	7.85578i	0.171061	+	0.296286i
$704$	2.03553	+	3.52565i	0.0767171	+	0.132878i
$705$		0			0
$706$	−1.17157			−0.0440927
$707$	−18.3137	+	44.8592i	−0.688758	+	1.68711i
$708$		0			0
$709$	21.4706	−	37.1881i	0.806344	−	1.39663i	−0.109036	−	0.994038i	$-0.534776\pi$
$709$	21.4706	−	37.1881i	0.806344	−	1.39663i	0.915380	−	0.402591i	$-0.131890\pi$
$710$	17.1924	+	29.7781i	0.645219	+	1.11755i
$711$		0			0
$712$	−25.1924	+	43.6345i	−0.944125	+	1.63527i
$713$	−34.8701			−1.30589
$714$		0			0
$715$	0.928932			0.0347401
$716$	34.0711	−	59.0128i	1.27330	−	2.20541i
$717$		0			0
$718$	6.32843	+	10.9612i	0.236175	+	0.409067i
$719$	26.0416	−	45.1054i	0.971189	−	1.68215i	0.279211	−	0.960230i	$-0.409927\pi$
$719$	26.0416	−	45.1054i	0.971189	−	1.68215i	0.691978	−	0.721919i	$-0.256740\pi$
$720$		0			0
$721$	15.7279	−	2.15232i	0.585738	−	0.0801565i
$722$	2.41421			0.0898477
$723$		0			0
$724$	−18.9497	−	32.8219i	−0.704262	−	1.21982i
$725$	13.1716	+	22.8138i	0.489180	+	0.847285i
$726$		0			0
$727$	20.0711			0.744395			0.372197	−	0.928154i	$-0.378604\pi$
$727$	20.0711			0.744395			0.372197	+	0.928154i	$0.378604\pi$
$728$	−16.0503	−	20.6976i	−0.594862	−	0.767103i
$729$		0			0
$730$	18.2782	−	31.6587i	0.676506	−	1.17174i
$731$	−16.1421	−	27.9590i	−0.597038	−	1.03410i
$732$		0			0
$733$	−10.7279	+	18.5813i	−0.396245	+	0.686316i	−0.993259	−	0.115914i	$-0.963020\pi$
$733$	−10.7279	+	18.5813i	−0.396245	+	0.686316i	0.597014	+	0.802231i	$0.296354\pi$
$734$	−58.7696			−2.16922
$735$		0			0
$736$	−8.85786			−0.326505
$737$	−0.242641	+	0.420266i	−0.00893778	+	0.0154807i
$738$		0			0
$739$	4.17157	+	7.22538i	0.153454	+	0.265790i	0.932495	−	0.361183i	$-0.117627\pi$
$739$	4.17157	+	7.22538i	0.153454	+	0.265790i	−0.779041	+	0.626973i	$0.784294\pi$
$740$	17.3640	−	30.0753i	0.638312	−	1.10559i
$741$		0			0
$742$	16.6066	+	21.4150i	0.609648	+	0.786170i
$743$	2.87006			0.105292			0.0526461	−	0.998613i	$-0.483234\pi$
$743$	2.87006			0.105292			0.0526461	+	0.998613i	$0.483234\pi$
$744$		0			0
$745$	0.0857864	+	0.148586i	0.00314297	+	0.00544379i
$746$	−13.6569	−	23.6544i	−0.500013	−	0.866048i
$747$		0			0
$748$	6.34315			0.231928
$749$	−36.4350	+	4.98602i	−1.33131	+	0.182185i
$750$		0			0
$751$	−4.72792	+	8.18900i	−0.172524	+	0.298821i	−0.939302	−	0.343092i	$-0.888526\pi$
$751$	−4.72792	+	8.18900i	−0.172524	+	0.298821i	0.766777	+	0.641913i	$0.221859\pi$
$752$	−6.62132	−	11.4685i	−0.241455	−	0.418212i
$753$		0			0
$754$	17.8284	−	30.8797i	0.649273	−	1.12457i
$755$	17.3137			0.630110
$756$		0			0
$757$	−5.00000			−0.181728			−0.0908640	−	0.995863i	$-0.528963\pi$
$757$	−5.00000			−0.181728			−0.0908640	+	0.995863i	$0.528963\pi$
$758$	−5.12132	+	8.87039i	−0.186015	+	0.322187i
$759$		0			0
$760$	−2.20711	−	3.82282i	−0.0800602	−	0.138668i
$761$	−17.0563	+	29.5425i	−0.618292	+	1.07091i	0.371505	+	0.928431i	$0.378842\pi$
$761$	−17.0563	+	29.5425i	−0.618292	+	1.07091i	−0.989797	+	0.142483i	$0.954492\pi$
$762$		0			0
$763$	−9.65685	+	23.6544i	−0.349602	+	0.856346i
$764$	−32.2132			−1.16543
$765$		0			0
$766$	23.8492	+	41.3081i	0.861708	+	1.49252i
$767$	−7.65685	−	13.2621i	−0.276473	−	0.478865i
$768$		0			0
$769$	−43.4264			−1.56600			−0.782998	−	0.622024i	$-0.786311\pi$
$769$	−43.4264			−1.56600			−0.782998	+	0.622024i	$0.786311\pi$
$770$	2.62132	−	0.358719i	0.0944658	−	0.0129274i
$771$		0			0
$772$	−15.1213	+	26.1909i	−0.544228	+	0.942631i
$773$	−17.1213	−	29.6550i	−0.615811	−	1.06662i	−0.990242	−	0.139361i	$-0.955495\pi$
$773$	−17.1213	−	29.6550i	−0.615811	−	1.06662i	0.374431	−	0.927255i	$-0.377838\pi$
$774$		0			0
$775$	−12.4853	+	21.6251i	−0.448485	+	0.776798i
$776$	−14.0000			−0.502571
$777$		0			0
$778$	27.7990			0.996642
$779$	1.58579	−	2.74666i	0.0568167	−	0.0984094i
$780$		0			0
$781$	−2.94975	−	5.10911i	−0.105550	−	0.182818i
$782$	−26.9706	+	46.7144i	−0.964465	+	1.67050i
$783$		0			0
$784$	−15.0000	−	14.6969i	−0.535714	−	0.524891i
$785$	−6.17157			−0.220273
$786$		0			0
$787$	−20.5061	−	35.5176i	−0.730963	−	1.26607i	−0.956472	−	0.291825i	$-0.905738\pi$
$787$	−20.5061	−	35.5176i	−0.730963	−	1.26607i	0.225508	−	0.974241i	$-0.427596\pi$
$788$	8.64214	+	14.9686i	0.307863	+	0.533235i
$789$		0			0
$790$	−3.41421			−0.121472
$791$	0.393398	+	0.507306i	0.0139876	+	0.0180377i
$792$		0			0
$793$	13.2635	−	22.9730i	0.470999	−	0.815794i
$794$	10.4142	+	18.0379i	0.369587	+	0.640143i
$795$		0			0
$796$	−30.7635	+	53.2839i	−1.09038	+	1.88860i
$797$	30.2426			1.07125			0.535625	−	0.844456i	$-0.320076\pi$
$797$	30.2426			1.07125			0.535625	+	0.844456i	$0.320076\pi$
$798$		0			0
$799$	17.6569			0.624655
$800$	−3.17157	+	5.49333i	−0.112132	+	0.194218i
$801$		0			0
$802$	0.585786	+	1.01461i	0.0206848	+	0.0358272i
$803$	−3.13604	+	5.43178i	−0.110668	+	0.191683i
$804$		0			0
$805$	−5.58579	+	13.6823i	−0.196873	+	0.482239i
$806$	33.7990			1.19052
$807$		0			0
$808$	40.4203	+	70.0100i	1.42198	+	2.46294i
$809$	15.5711	+	26.9699i	0.547450	+	0.948211i	0.998448	+	0.0556859i	$0.0177346\pi$
$809$	15.5711	+	26.9699i	0.547450	+	0.948211i	−0.450999	+	0.892525i	$0.648932\pi$
$810$		0			0
$811$	−0.544156			−0.0191079			−0.00955395	−	0.999954i	$-0.503041\pi$
$811$	−0.544156			−0.0191079			−0.00955395	+	0.999954i	$0.503041\pi$
$812$	25.2132	−	61.7595i	0.884810	−	2.16733i
$813$		0			0
$814$	−4.53553	+	7.85578i	−0.158970	+	0.275345i
$815$	1.96447	+	3.40256i	0.0688122	+	0.119186i
$816$		0			0
$817$	4.03553	−	6.98975i	0.141185	−	0.244540i
$818$	−6.48528			−0.226753
$819$		0			0
$820$	−12.1421			−0.424022
$821$	5.05635	−	8.75785i	0.176468	−	0.305651i	−0.764200	−	0.644979i	$-0.776866\pi$
$821$	5.05635	−	8.75785i	0.176468	−	0.305651i	0.940668	+	0.339328i	$0.110200\pi$
$822$		0			0
$823$	3.10660	+	5.38079i	0.108289	+	0.187563i	0.915077	−	0.403278i	$-0.132129\pi$
$823$	3.10660	+	5.38079i	0.108289	+	0.187563i	−0.806788	+	0.590841i	$0.798796\pi$
$824$	13.2426	−	22.9369i	0.461329	−	0.799046i
$825$		0			0
$826$	−26.7279	−	34.4669i	−0.929983	−	1.19926i
$827$	−12.2843			−0.427166			−0.213583	−	0.976925i	$-0.568513\pi$
$827$	−12.2843			−0.427166			−0.213583	+	0.976925i	$0.568513\pi$
$828$		0			0
$829$	14.1421	+	24.4949i	0.491177	+	0.850743i	0.999948	−	0.0101585i	$-0.00323361\pi$
$829$	14.1421	+	24.4949i	0.491177	+	0.850743i	−0.508772	+	0.860901i	$0.669900\pi$
$830$	−11.1569	−	19.3242i	−0.387260	−	0.670754i
$831$		0			0
$832$	22.0416			0.764156
$833$	26.9706	−	7.52255i	0.934475	−	0.260641i
$834$		0			0
$835$	−6.53553	+	11.3199i	−0.226171	+	0.391740i
$836$	0.792893	+	1.37333i	0.0274228	+	0.0474977i
$837$		0			0
$838$	7.32843	−	12.6932i	0.253156	−	0.438480i
$839$	19.7990			0.683537			0.341769	−	0.939784i	$-0.388974\pi$
$839$	19.7990			0.683537			0.341769	+	0.939784i	$0.388974\pi$
$840$		0			0
$841$	14.3726			0.495606
$842$	44.9203	−	77.8043i	1.54806	−	2.68131i
$843$		0			0
$844$	2.24264	+	3.88437i	0.0771949	+	0.133705i
$845$	−3.98528	+	6.90271i	−0.137098	+	0.237460i
$846$		0			0
$847$	28.3848	−	3.88437i	0.975312	−	0.133468i
$848$	12.7279			0.437079
$849$		0			0
$850$	19.3137	+	33.4523i	0.662455	+	1.14741i
$851$	−25.3345	−	43.8807i	−0.868456	−	1.50421i
$852$		0			0
$853$	43.9706			1.50552			0.752762	−	0.658293i	$-0.228721\pi$
$853$	43.9706			1.50552			0.752762	+	0.658293i	$0.228721\pi$
$854$	28.5563	−	69.9485i	0.977178	−	2.39359i
$855$		0			0
$856$	−30.6777	+	53.1353i	−1.04854	+	1.81613i
$857$	−6.48528	−	11.2328i	−0.221533	−	0.383706i	0.733741	−	0.679430i	$-0.237773\pi$
$857$	−6.48528	−	11.2328i	−0.221533	−	0.383706i	−0.955274	+	0.295723i	$0.904439\pi$
$858$		0			0
$859$	6.03553	−	10.4539i	0.205930	−	0.356681i	−0.744499	−	0.667624i	$-0.767311\pi$
$859$	6.03553	−	10.4539i	0.205930	−	0.356681i	0.950429	+	0.310943i	$0.100645\pi$
$860$	−30.8995			−1.05366
$861$		0			0
$862$	24.2426			0.825708
$863$	2.29289	−	3.97141i	0.0780510	−	0.135188i	−0.824358	−	0.566069i	$-0.808464\pi$
$863$	2.29289	−	3.97141i	0.0780510	−	0.135188i	0.902409	+	0.430881i	$0.141797\pi$
$864$		0			0
$865$	3.65685	+	6.33386i	0.124337	+	0.215358i
$866$	−33.7990	+	58.5416i	−1.14854	+	1.98932i
$867$		0			0
$868$	62.6482	−	8.57321i	2.12642	−	0.290994i
$869$	0.585786			0.0198714
$870$		0			0
$871$	1.31371	+	2.27541i	0.0445133	+	0.0770993i
$872$	21.3137	+	36.9164i	0.721773	+	1.25015i
$873$		0			0
$874$	−13.4853			−0.456146
$875$	14.5919	+	18.8169i	0.493296	+	0.636128i
$876$		0			0
$877$	13.9497	−	24.1617i	0.471050	−	0.815882i	−0.528402	−	0.848994i	$-0.677209\pi$
$877$	13.9497	−	24.1617i	0.471050	−	0.815882i	0.999452	+	0.0331126i	$0.0105420\pi$
$878$	29.5563	+	51.1931i	0.997478	+	1.72768i
$879$		0			0
$880$	0.621320	−	1.07616i	0.0209447	−	0.0362773i
$881$	52.2843			1.76150			0.880751	−	0.473580i	$-0.157038\pi$
$881$	52.2843			1.76150			0.880751	+	0.473580i	$0.157038\pi$
$882$		0			0
$883$	−5.65685			−0.190368			−0.0951842	−	0.995460i	$-0.530344\pi$
$883$	−5.65685			−0.190368			−0.0951842	+	0.995460i	$0.530344\pi$
$884$	17.1716	−	29.7420i	0.577542	−	1.00033i
$885$		0			0
$886$	21.3137	+	36.9164i	0.716048	+	1.24023i
$887$	−10.6569	+	18.4582i	−0.357822	+	0.619766i	−0.987597	−	0.157012i	$-0.949814\pi$
$887$	−10.6569	+	18.4582i	−0.357822	+	0.619766i	0.629775	+	0.776778i	$0.283147\pi$
$888$		0			0
$889$	6.87868	+	8.87039i	0.230704	+	0.297503i
$890$	−27.5563			−0.923691
$891$		0			0
$892$	−4.29289	−	7.43551i	−0.143737	−	0.248959i
$893$	2.20711	+	3.82282i	0.0738580	+	0.127926i
$894$		0			0
$895$	17.7990			0.594955
$896$	53.8848	−	7.37396i	1.80016	−	0.246347i
$897$		0			0
$898$	11.6569	−	20.1903i	0.388994	−	0.673758i
$899$	20.5563	+	35.6046i	0.685593	+	1.18748i
$900$		0			0
$901$	−8.48528	+	14.6969i	−0.282686	+	0.489626i
$902$	3.17157			0.105602
$903$		0			0
$904$	1.07107			0.0356232
$905$	4.94975	−	8.57321i	0.164535	−	0.284983i
$906$		0			0
$907$	−15.7071	−	27.2055i	−0.521546	−	0.903344i	−0.999686	−	0.0250604i	$-0.992022\pi$
$907$	−15.7071	−	27.2055i	−0.521546	−	0.903344i	0.478140	−	0.878284i	$-0.341311\pi$
$908$	−38.7487	+	67.1148i	−1.28592	+	2.22728i
$909$		0			0
$910$	5.41421	−	13.2621i	0.179479	−	0.439633i
$911$	−9.27208			−0.307198			−0.153599	−	0.988133i	$-0.549086\pi$
$911$	−9.27208			−0.307198			−0.153599	+	0.988133i	$0.549086\pi$
$912$		0			0
$913$	1.91421	+	3.31552i	0.0633512	+	0.109728i
$914$	9.44975	+	16.3674i	0.312570	+	0.541387i
$915$		0			0
$916$	47.7990			1.57932
$917$	9.21320	−	1.26080i	0.304247	−	0.0416352i
$918$		0			0
$919$	9.52082	−	16.4905i	0.314063	−	0.543973i	−0.665175	−	0.746687i	$-0.731643\pi$
$919$	9.52082	−	16.4905i	0.314063	−	0.543973i	0.979238	+	0.202715i	$0.0649764\pi$
$920$	12.3284	+	21.3535i	0.406456	+	0.704003i
$921$		0			0
$922$	36.1777	−	62.6616i	1.19145	−	2.06365i
$923$	−31.9411			−1.05135
$924$		0			0
$925$	−36.2843			−1.19302
$926$	4.91421	−	8.51167i	0.161491	−	0.279711i
$927$		0			0
$928$	5.22183	+	9.04447i	0.171415	+	0.296899i
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	−0.716364	−	0.697727i	$-0.754195\pi$
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	0.962431	+	0.271526i	$0.0875283\pi$
$930$		0			0
$931$	5.00000	+	4.89898i	0.163868	+	0.160558i
$932$	−1.85786			−0.0608564
$933$		0			0
$934$	23.0563	+	39.9348i	0.754427	+	1.30671i
$935$	0.828427	+	1.43488i	0.0270925	+	0.0469255i
$936$		0			0
$937$	−33.6863			−1.10048			−0.550242	−	0.835006i	$-0.685464\pi$
$937$	−33.6863			−1.10048			−0.550242	+	0.835006i	$0.685464\pi$
$938$	4.58579	+	5.91359i	0.149731	+	0.193086i
$939$		0			0
$940$	8.44975	−	14.6354i	0.275600	−	0.477354i
$941$	2.02082	+	3.50015i	0.0658767	+	0.114102i	0.897083	−	0.441863i	$-0.145682\pi$
$941$	2.02082	+	3.50015i	0.0658767	+	0.114102i	−0.831206	+	0.555965i	$0.812349\pi$
$942$		0			0
$943$	−8.85786	+	15.3423i	−0.288452	+	0.499613i
$944$	−20.4853			−0.666739
$945$		0			0
$946$	8.07107			0.262413
$947$	1.82843	−	3.16693i	0.0594159	−	0.102911i	−0.834787	−	0.550572i	$-0.814410\pi$
$947$	1.82843	−	3.16693i	0.0594159	−	0.102911i	0.894203	+	0.447661i	$0.147743\pi$
$948$		0			0
$949$	16.9792	+	29.4088i	0.551168	+	0.954650i
$950$	−4.82843	+	8.36308i	−0.156655	+	0.271334i
$951$		0			0
$952$	17.6569	−	43.2503i	0.572262	−	1.40175i
$953$	3.41421			0.110597			0.0552986	−	0.998470i	$-0.482389\pi$
$953$	3.41421			0.110597			0.0552986	+	0.998470i	$0.482389\pi$
$954$		0			0
$955$	−4.20711	−	7.28692i	−0.136139	−	0.235799i
$956$	3.82843	+	6.63103i	0.123820	+	0.214463i
$957$		0			0
$958$	61.2843			1.98000
$959$	19.8284	−	48.5695i	0.640293	−	1.56839i
$960$		0			0
$961$	−3.98528	+	6.90271i	−0.128557	+	0.222668i
$962$	24.5563	+	42.5328i	0.791728	+	1.37131i
$963$		0			0
$964$	49.8492	−	86.3414i	1.60554	−	2.78087i
$965$	−7.89949			−0.254294
$966$		0			0
$967$	−36.2843			−1.16682			−0.583412	−	0.812177i	$-0.698283\pi$
$967$	−36.2843			−1.16682			−0.583412	+	0.812177i	$0.698283\pi$
$968$	23.8995	−	41.3951i	0.768159	−	1.33049i
$969$		0			0
$970$	−3.82843	−	6.63103i	−0.122923	−	0.212910i
$971$	13.4350	−	23.2702i	0.431151	−	0.746775i	−0.565822	−	0.824527i	$-0.691441\pi$
$971$	13.4350	−	23.2702i	0.431151	−	0.746775i	0.996973	+	0.0777526i	$0.0247744\pi$
$972$		0			0
$973$	−9.84315	−	12.6932i	−0.315557	−	0.406926i
$974$	36.6274			1.17362
$975$		0			0
$976$	−17.7426	−	30.7312i	−0.567928	−	0.983680i
$977$	−22.3848	−	38.7716i	−0.716152	−	1.24041i	−0.962513	−	0.271234i	$-0.912568\pi$
$977$	−22.3848	−	38.7716i	−0.716152	−	1.24041i	0.246361	−	0.969178i	$-0.420765\pi$
$978$		0			0
$979$	4.72792			0.151105
$980$	6.67157	−	25.9553i	0.213116	−	0.829111i
$981$		0			0
$982$	−1.74264	+	3.01834i	−0.0556099	+	0.0963192i
$983$	−23.0000	−	39.8372i	−0.733586	−	1.27061i	−0.955341	−	0.295506i	$-0.904512\pi$
$983$	−23.0000	−	39.8372i	−0.733586	−	1.27061i	0.221755	−	0.975102i	$-0.428822\pi$
$984$		0			0
$985$	−2.25736	+	3.90986i	−0.0719254	+	0.124579i
$986$	63.5980			2.02537
$987$		0			0
$988$	8.58579			0.273150
$989$	−22.5416	+	39.0432i	−0.716782	+	1.24150i
$990$		0			0
$991$	−1.89949	−	3.29002i	−0.0603394	−	0.104511i	0.834278	−	0.551344i	$-0.185885\pi$
$991$	−1.89949	−	3.29002i	−0.0603394	−	0.104511i	−0.894617	+	0.446833i	$0.852552\pi$
$992$	−4.94975	+	8.57321i	−0.157155	+	0.272200i
$993$		0			0
$994$	−90.1335	+	12.3345i	−2.85886	+	0.391226i
$995$	−16.0711			−0.509487
$996$		0			0
$997$	14.1421	+	24.4949i	0.447886	+	0.775761i	0.998248	−	0.0591648i	$-0.0188437\pi$
$997$	14.1421	+	24.4949i	0.447886	+	0.775761i	−0.550362	+	0.834926i	$0.685510\pi$
$998$	−41.7132	−	72.2494i	−1.32041	−	2.28701i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.j.e.856.1		4
3.2	odd	2		133.2.f.c.58.2	yes	4
7.2	even	3		8379.2.a.bi.1.2		2
7.4	even	3	inner	1197.2.j.e.172.1		4
7.5	odd	6		8379.2.a.bl.1.2		2
21.2	odd	6		931.2.a.f.1.1		2
21.5	even	6		931.2.a.e.1.1		2
21.11	odd	6		133.2.f.c.39.2	✓	4
21.17	even	6		931.2.f.i.704.2		4
21.20	even	2		931.2.f.i.324.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.c.39.2	✓	4	21.11	odd	6
133.2.f.c.58.2	yes	4	3.2	odd	2
931.2.a.e.1.1		2	21.5	even	6
931.2.a.f.1.1		2	21.2	odd	6
931.2.f.i.324.2		4	21.20	even	2
931.2.f.i.704.2		4	21.17	even	6
1197.2.j.e.172.1		4	7.4	even	3	inner
1197.2.j.e.856.1		4	1.1	even	1	trivial
8379.2.a.bi.1.2		2	7.2	even	3
8379.2.a.bl.1.2		2	7.5	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-1.20711 + 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +4.41421 q^{8} +(1.20711 + 2.09077i) q^{10} +(-0.207107 - 0.358719i) q^{11} -2.24264 q^{13} +(-6.32843 + 0.866025i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(0.500000 - 0.866025i) q^{19} -3.82843 q^{20} +1.00000 q^{22} +(-2.79289 + 4.83743i) q^{23} +(2.00000 + 3.46410i) q^{25} +(2.70711 - 4.68885i) q^{26} +(3.82843 - 9.37769i) q^{28} +6.58579 q^{29} +(3.12132 + 5.40629i) q^{31} +(0.792893 + 1.37333i) q^{32} +9.65685 q^{34} +(2.62132 - 0.358719i) q^{35} +(-4.53553 + 7.85578i) q^{37} +(1.20711 + 2.09077i) q^{38} +(2.20711 - 3.82282i) q^{40} +3.17157 q^{41} +8.07107 q^{43} +(-0.792893 + 1.37333i) q^{44} +(-6.74264 - 11.6786i) q^{46} +(-2.20711 + 3.82282i) q^{47} +(-1.74264 + 6.77962i) q^{49} -9.65685 q^{50} +(4.29289 + 7.43551i) q^{52} +(-2.12132 - 3.67423i) q^{53} -0.414214 q^{55} +(7.15685 + 9.22911i) q^{56} +(-7.94975 + 13.7694i) q^{58} +(3.41421 + 5.91359i) q^{59} +(-5.91421 + 10.2437i) q^{61} -15.0711 q^{62} -9.82843 q^{64} +(-1.12132 + 1.94218i) q^{65} +(-0.585786 - 1.01461i) q^{67} +(-7.65685 + 13.2621i) q^{68} +(-2.41421 + 5.91359i) q^{70} +14.2426 q^{71} +(-7.57107 - 13.1135i) q^{73} +(-10.9497 - 18.9655i) q^{74} -3.82843 q^{76} +(0.414214 - 1.01461i) q^{77} +(-0.707107 + 1.22474i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-3.82843 + 6.63103i) q^{82} -9.24264 q^{83} -4.00000 q^{85} +(-9.74264 + 16.8747i) q^{86} +(-0.914214 - 1.58346i) q^{88} +(-5.70711 + 9.88500i) q^{89} +(-3.63604 - 4.68885i) q^{91} +21.3848 q^{92} +(-5.32843 - 9.22911i) q^{94} +(-0.500000 - 0.866025i) q^{95} -3.17157 q^{97} +(-12.0711 - 11.8272i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} + 2 q^{10} + 2 q^{11} + 8 q^{13} - 14 q^{14} - 6 q^{16} - 8 q^{17} + 2 q^{19} - 4 q^{20} + 4 q^{22} - 14 q^{23} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 32 q^{29}+ \cdots - 20 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8 + 2 * q^10 + 2 * q^11 + 8 * q^13 - 14 * q^14 - 6 * q^16 - 8 * q^17 + 2 * q^19 - 4 * q^20 + 4 * q^22 - 14 * q^23 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 32 * q^29 + 4 * q^31 + 6 * q^32 + 16 * q^34 + 2 * q^35 - 4 * q^37 + 2 * q^38 + 6 * q^40 + 24 * q^41 + 4 * q^43 - 6 * q^44 - 10 * q^46 - 6 * q^47 + 10 * q^49 - 16 * q^50 + 20 * q^52 + 4 * q^55 + 6 * q^56 - 12 * q^58 + 8 * q^59 - 18 * q^61 - 32 * q^62 - 28 * q^64 + 4 * q^65 - 8 * q^67 - 8 * q^68 - 4 * q^70 + 40 * q^71 - 2 * q^73 - 24 * q^74 - 4 * q^76 - 4 * q^77 + 6 * q^80 - 4 * q^82 - 20 * q^83 - 16 * q^85 - 22 * q^86 + 2 * q^88 - 20 * q^89 - 40 * q^91 + 12 * q^92 - 10 * q^94 - 2 * q^95 - 24 * q^97 - 20 * q^98

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