LMFDB - Embedded newform 1197.2.j.e.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 133)
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.e.172.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +1.58579 q^{8} +(-0.207107 - 0.358719i) q^{10} +(1.20711 + 2.09077i) q^{11} +6.24264 q^{13} +(-0.671573 + 0.866025i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(0.500000 - 0.866025i) q^{19} +1.82843 q^{20} +1.00000 q^{22} +(-4.20711 + 7.28692i) q^{23} +(2.00000 + 3.46410i) q^{25} +(1.29289 - 2.23936i) q^{26} +(-1.82843 - 4.47871i) q^{28} +9.41421 q^{29} +(-1.12132 - 1.94218i) q^{31} +(2.20711 + 3.82282i) q^{32} -1.65685 q^{34} +(-1.62132 + 2.09077i) q^{35} +(2.53553 - 4.39167i) q^{37} +(-0.207107 - 0.358719i) q^{38} +(0.792893 - 1.37333i) q^{40} +8.82843 q^{41} -6.07107 q^{43} +(-2.20711 + 3.82282i) q^{44} +(1.74264 + 3.01834i) q^{46} +(-0.792893 + 1.37333i) q^{47} +(6.74264 + 1.88064i) q^{49} +1.65685 q^{50} +(5.70711 + 9.88500i) q^{52} +(2.12132 + 3.67423i) q^{53} +2.41421 q^{55} +(-4.15685 - 0.568852i) q^{56} +(1.94975 - 3.37706i) q^{58} +(0.585786 + 1.01461i) q^{59} +(-3.08579 + 5.34474i) q^{61} -0.928932 q^{62} -4.17157 q^{64} +(3.12132 - 5.40629i) q^{65} +(-3.41421 - 5.91359i) q^{67} +(3.65685 - 6.33386i) q^{68} +(0.414214 + 1.01461i) q^{70} +5.75736 q^{71} +(6.57107 + 11.3814i) q^{73} +(-1.05025 - 1.81909i) q^{74} +1.82843 q^{76} +(-2.41421 - 5.91359i) q^{77} +(0.707107 - 1.22474i) q^{79} +(1.50000 + 2.59808i) q^{80} +(1.82843 - 3.16693i) q^{82} -0.757359 q^{83} -4.00000 q^{85} +(-1.25736 + 2.17781i) q^{86} +(1.91421 + 3.31552i) q^{88} +(-4.29289 + 7.43551i) q^{89} +(-16.3640 - 2.23936i) q^{91} -15.3848 q^{92} +(0.328427 + 0.568852i) q^{94} +(-0.500000 - 0.866025i) q^{95} -8.82843 q^{97} +(2.07107 - 2.02922i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	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
$5$	0.500000	−	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
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$8$	1.58579			0.560660
$9$		0			0
$10$	−0.207107	−	0.358719i	−0.0654929	−	0.113437i
$11$	1.20711	+	2.09077i	0.363956	+	0.630391i	0.988608	−	0.150513i	$-0.0480924\pi$
$11$	1.20711	+	2.09077i	0.363956	+	0.630391i	−0.624652	+	0.780903i	$0.714759\pi$
$12$		0			0
$13$	6.24264			1.73140			0.865699	−	0.500566i	$-0.166875\pi$
$13$	6.24264			1.73140			0.865699	+	0.500566i	$0.166875\pi$
$14$	−0.671573	+	0.866025i	−0.179485	+	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
$20$	1.82843			0.408849
$21$		0			0
$22$	1.00000			0.213201
$23$	−4.20711	+	7.28692i	−0.877242	+	1.51943i	−0.0228877	+	0.999738i	$0.507286\pi$
$23$	−4.20711	+	7.28692i	−0.877242	+	1.51943i	−0.854355	+	0.519690i	$0.826047\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	1.29289	−	2.23936i	0.253557	−	0.439174i
$27$		0			0
$28$	−1.82843	−	4.47871i	−0.345540	−	0.846397i
$29$	9.41421			1.74818			0.874088	−	0.485768i	$-0.161460\pi$
$29$	9.41421			1.74818			0.874088	+	0.485768i	$0.161460\pi$
$30$		0			0
$31$	−1.12132	−	1.94218i	−0.201395	−	0.348827i	0.747583	−	0.664168i	$-0.231214\pi$
$31$	−1.12132	−	1.94218i	−0.201395	−	0.348827i	−0.948978	+	0.315342i	$0.897881\pi$
$32$	2.20711	+	3.82282i	0.390165	+	0.675786i
$33$		0			0
$34$	−1.65685			−0.284148
$35$	−1.62132	+	2.09077i	−0.274053	+	0.353405i
$36$		0			0
$37$	2.53553	−	4.39167i	0.416839	−	0.721987i	−0.578780	−	0.815483i	$-0.696471\pi$
$37$	2.53553	−	4.39167i	0.416839	−	0.721987i	0.995620	+	0.0934968i	$0.0298045\pi$
$38$	−0.207107	−	0.358719i	−0.0335972	−	0.0581920i
$39$		0			0
$40$	0.792893	−	1.37333i	0.125367	−	0.217143i
$41$	8.82843			1.37877			0.689384	−	0.724396i	$-0.257881\pi$
$41$	8.82843			1.37877			0.689384	+	0.724396i	$0.257881\pi$
$42$		0			0
$43$	−6.07107			−0.925829			−0.462915	−	0.886403i	$-0.653196\pi$
$43$	−6.07107			−0.925829			−0.462915	+	0.886403i	$0.653196\pi$
$44$	−2.20711	+	3.82282i	−0.332734	+	0.576312i
$45$		0			0
$46$	1.74264	+	3.01834i	0.256938	+	0.445030i
$47$	−0.792893	+	1.37333i	−0.115655	+	0.200321i	−0.918042	−	0.396484i	$-0.870230\pi$
$47$	−0.792893	+	1.37333i	−0.115655	+	0.200321i	0.802386	+	0.596805i	$0.203563\pi$
$48$		0			0
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$	1.65685			0.234315
$51$		0			0
$52$	5.70711	+	9.88500i	0.791433	+	1.37080i
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	0.974138	−	0.225955i	$-0.0725503\pi$
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	−0.682752	+	0.730650i	$0.739217\pi$
$54$		0			0
$55$	2.41421			0.325532
$56$	−4.15685	−	0.568852i	−0.555483	−	0.0760161i
$57$		0			0
$58$	1.94975	−	3.37706i	0.256014	−	0.443430i
$59$	0.585786	+	1.01461i	0.0762629	+	0.132091i	0.901635	−	0.432498i	$-0.142368\pi$
$59$	0.585786	+	1.01461i	0.0762629	+	0.132091i	−0.825372	+	0.564589i	$0.809035\pi$
$60$		0			0
$61$	−3.08579	+	5.34474i	−0.395094	+	0.684324i	−0.993113	−	0.117158i	$-0.962621\pi$
$61$	−3.08579	+	5.34474i	−0.395094	+	0.684324i	0.598019	+	0.801482i	$0.295955\pi$
$62$	−0.928932			−0.117975
$63$		0			0
$64$	−4.17157			−0.521447
$65$	3.12132	−	5.40629i	0.387152	−	0.670567i
$66$		0			0
$67$	−3.41421	−	5.91359i	−0.417113	−	0.722460i	0.578535	−	0.815657i	$-0.303625\pi$
$67$	−3.41421	−	5.91359i	−0.417113	−	0.722460i	−0.995648	+	0.0931973i	$0.970291\pi$
$68$	3.65685	−	6.33386i	0.443459	−	0.768093i
$69$		0			0
$70$	0.414214	+	1.01461i	0.0495080	+	0.121269i
$71$	5.75736			0.683273			0.341636	−	0.939832i	$-0.389019\pi$
$71$	5.75736			0.683273			0.341636	+	0.939832i	$0.389019\pi$
$72$		0			0
$73$	6.57107	+	11.3814i	0.769085	+	1.33209i	0.938059	+	0.346474i	$0.112621\pi$
$73$	6.57107	+	11.3814i	0.769085	+	1.33209i	−0.168974	+	0.985620i	$0.554045\pi$
$74$	−1.05025	−	1.81909i	−0.122089	−	0.211465i
$75$		0			0
$76$	1.82843			0.209735
$77$	−2.41421	−	5.91359i	−0.275125	−	0.673916i
$78$		0			0
$79$	0.707107	−	1.22474i	0.0795557	−	0.137795i	−0.823503	−	0.567312i	$-0.807983\pi$
$79$	0.707107	−	1.22474i	0.0795557	−	0.137795i	0.903058	+	0.429518i	$0.141317\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$		0			0
$82$	1.82843	−	3.16693i	0.201916	−	0.349729i
$83$	−0.757359			−0.0831310			−0.0415655	−	0.999136i	$-0.513235\pi$
$83$	−0.757359			−0.0831310			−0.0415655	+	0.999136i	$0.513235\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	−1.25736	+	2.17781i	−0.135585	+	0.234839i
$87$		0			0
$88$	1.91421	+	3.31552i	0.204056	+	0.353435i
$89$	−4.29289	+	7.43551i	−0.455046	+	0.788162i	−0.998691	−	0.0511528i	$-0.983710\pi$
$89$	−4.29289	+	7.43551i	−0.455046	+	0.788162i	0.543645	+	0.839315i	$0.317044\pi$
$90$		0			0
$91$	−16.3640	−	2.23936i	−1.71541	−	0.234748i
$92$	−15.3848			−1.60397
$93$		0			0
$94$	0.328427	+	0.568852i	0.0338747	+	0.0586727i
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$		0			0
$97$	−8.82843			−0.896391			−0.448195	−	0.893936i	$-0.647933\pi$
$97$	−8.82843			−0.896391			−0.448195	+	0.893936i	$0.647933\pi$
$98$	2.07107	−	2.02922i	0.209209	−	0.204983i
$99$		0			0
$100$	−3.65685	+	6.33386i	−0.365685	+	0.633386i
$101$	−2.15685	−	3.73578i	−0.214615	−	0.371724i	0.738538	−	0.674211i	$-0.235516\pi$
$101$	−2.15685	−	3.73578i	−0.214615	−	0.371724i	−0.953153	+	0.302487i	$0.902183\pi$
$102$		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
$106$	1.75736			0.170690
$107$	2.94975	−	5.10911i	0.285163	−	0.493917i	−0.687486	−	0.726198i	$-0.741286\pi$
$107$	2.94975	−	5.10911i	0.285163	−	0.493917i	0.972649	+	0.232281i	$0.0746190\pi$
$108$		0			0
$109$	−0.828427	−	1.43488i	−0.0793489	−	0.137436i	0.823620	−	0.567142i	$-0.191951\pi$
$109$	−0.828427	−	1.43488i	−0.0793489	−	0.137436i	−0.902969	+	0.429705i	$0.858617\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$		0			0
$112$	4.86396	−	6.27231i	0.459601	−	0.592678i
$113$	−8.24264			−0.775402			−0.387701	−	0.921785i	$-0.626731\pi$
$113$	−8.24264			−0.775402			−0.387701	+	0.921785i	$0.626731\pi$
$114$		0			0
$115$	4.20711	+	7.28692i	0.392315	+	0.679509i
$116$	8.60660	+	14.9071i	0.799103	+	1.38409i
$117$		0			0
$118$	0.485281			0.0446738
$119$	4.00000	+	9.79796i	0.366679	+	0.898177i
$120$		0			0
$121$	2.58579	−	4.47871i	0.235071	−	0.407156i
$122$	1.27817	+	2.21386i	0.115720	+	0.200434i
$123$		0			0
$124$	2.05025	−	3.55114i	0.184118	−	0.318902i
$125$	9.00000			0.804984
$126$		0			0
$127$	−4.24264			−0.376473			−0.188237	−	0.982124i	$-0.560277\pi$
$127$	−4.24264			−0.376473			−0.188237	+	0.982124i	$0.560277\pi$
$128$	−5.27817	+	9.14207i	−0.466529	+	0.808052i
$129$		0			0
$130$	−1.29289	−	2.23936i	−0.113394	−	0.196405i
$131$	10.2426	−	17.7408i	0.894904	−	1.55002i	0.0609799	−	0.998139i	$-0.480577\pi$
$131$	10.2426	−	17.7408i	0.894904	−	1.55002i	0.833924	−	0.551880i	$-0.186089\pi$
$132$		0			0
$133$	−1.62132	+	2.09077i	−0.140586	+	0.181293i
$134$	−2.82843			−0.244339
$135$		0			0
$136$	−3.17157	−	5.49333i	−0.271960	−	0.471049i
$137$	−7.08579	−	12.2729i	−0.605380	−	1.04855i	−0.991991	−	0.126306i	$-0.959688\pi$
$137$	−7.08579	−	12.2729i	−0.605380	−	1.04855i	0.386612	−	0.922243i	$-0.373645\pi$
$138$		0			0
$139$	8.07107			0.684579			0.342290	−	0.939595i	$-0.388798\pi$
$139$	8.07107			0.684579			0.342290	+	0.939595i	$0.388798\pi$
$140$	−4.79289	−	0.655892i	−0.405073	−	0.0554330i
$141$		0			0
$142$	1.19239	−	2.06528i	0.100063	−	0.173314i
$143$	7.53553	+	13.0519i	0.630153	+	1.09146i
$144$		0			0
$145$	4.70711	−	8.15295i	0.390904	−	0.677065i
$146$	5.44365			0.450520
$147$		0			0
$148$	9.27208			0.762160
$149$	−2.91421	+	5.04757i	−0.238742	+	0.413513i	−0.960353	−	0.278785i	$-0.910068\pi$
$149$	−2.91421	+	5.04757i	−0.238742	+	0.413513i	0.721612	+	0.692298i	$0.243402\pi$
$150$		0			0
$151$	−2.65685	−	4.60181i	−0.216212	−	0.374490i	0.737435	−	0.675418i	$-0.236037\pi$
$151$	−2.65685	−	4.60181i	−0.216212	−	0.374490i	−0.953647	+	0.300928i	$0.902703\pi$
$152$	0.792893	−	1.37333i	0.0643121	−	0.111392i
$153$		0			0
$154$	−2.62132	−	0.358719i	−0.211232	−	0.0289064i
$155$	−2.24264			−0.180133
$156$		0			0
$157$	−5.91421	−	10.2437i	−0.472006	−	0.817538i	0.527481	−	0.849567i	$-0.323136\pi$
$157$	−5.91421	−	10.2437i	−0.472006	−	0.817538i	−0.999487	+	0.0320289i	$0.989803\pi$
$158$	−0.292893	−	0.507306i	−0.0233013	−	0.0403591i
$159$		0			0
$160$	4.41421			0.348974
$161$	13.6421	−	17.5922i	1.07515	−	1.38646i
$162$		0			0
$163$	−9.03553	+	15.6500i	−0.707718	+	1.22580i	0.257984	+	0.966149i	$0.416942\pi$
$163$	−9.03553	+	15.6500i	−0.707718	+	1.22580i	−0.965702	+	0.259654i	$0.916392\pi$
$164$	8.07107	+	13.9795i	0.630245	+	1.09162i
$165$		0			0
$166$	−0.156854	+	0.271680i	−0.0121743	+	0.0210864i
$167$	1.07107			0.0828817			0.0414409	−	0.999141i	$-0.486805\pi$
$167$	1.07107			0.0828817			0.0414409	+	0.999141i	$0.486805\pi$
$168$		0			0
$169$	25.9706			1.99774
$170$	−0.828427	+	1.43488i	−0.0635375	+	0.110050i
$171$		0			0
$172$	−5.55025	−	9.61332i	−0.423203	−	0.733009i
$173$	7.65685	−	13.2621i	0.582140	−	1.00830i	−0.413086	−	0.910692i	$-0.635549\pi$
$173$	7.65685	−	13.2621i	0.582140	−	1.00830i	0.995225	−	0.0976036i	$-0.0311177\pi$
$174$		0			0
$175$	−4.00000	−	9.79796i	−0.302372	−	0.740656i
$176$	−7.24264			−0.545935
$177$		0			0
$178$	1.77817	+	3.07989i	0.133280	+	0.230847i
$179$	−10.8995	−	18.8785i	−0.814667	−	1.41104i	−0.909567	−	0.415557i	$-0.863587\pi$
$179$	−10.8995	−	18.8785i	−0.814667	−	1.41104i	0.0949006	−	0.995487i	$-0.469747\pi$
$180$		0			0
$181$	−9.89949			−0.735824			−0.367912	−	0.929861i	$-0.619927\pi$
$181$	−9.89949			−0.735824			−0.367912	+	0.929861i	$0.619927\pi$
$182$	−4.19239	+	5.40629i	−0.310760	+	0.400741i
$183$		0			0
$184$	−6.67157	+	11.5555i	−0.491835	+	0.851883i
$185$	−2.53553	−	4.39167i	−0.186416	−	0.322882i
$186$		0			0
$187$	4.82843	−	8.36308i	0.353090	−	0.611569i
$188$	−2.89949			−0.211467
$189$		0			0
$190$	−0.414214			−0.0300502
$191$	2.79289	−	4.83743i	0.202087	−	0.350024i	−0.747114	−	0.664696i	$-0.768561\pi$
$191$	2.79289	−	4.83743i	0.202087	−	0.350024i	0.949201	+	0.314672i	$0.101894\pi$
$192$		0			0
$193$	5.94975	+	10.3053i	0.428272	+	0.741789i	0.996720	−	0.0809303i	$-0.0257891\pi$
$193$	5.94975	+	10.3053i	0.428272	+	0.741789i	−0.568448	+	0.822719i	$0.692456\pi$
$194$	−1.82843	+	3.16693i	−0.131273	+	0.227372i
$195$		0			0
$196$	3.18629	+	12.3960i	0.227592	+	0.885431i
$197$	−21.4853			−1.53076			−0.765381	−	0.643577i	$-0.777450\pi$
$197$	−21.4853			−1.53076			−0.765381	+	0.643577i	$0.777450\pi$
$198$		0			0
$199$	−0.964466	−	1.67050i	−0.0683692	−	0.118419i	0.829814	−	0.558039i	$-0.188446\pi$
$199$	−0.964466	−	1.67050i	−0.0683692	−	0.118419i	−0.898184	+	0.439621i	$0.855113\pi$
$200$	3.17157	+	5.49333i	0.224264	+	0.388437i
$201$		0			0
$202$	−1.78680			−0.125719
$203$	−24.6777	−	3.37706i	−1.73203	−	0.237023i
$204$		0			0
$205$	4.41421	−	7.64564i	0.308302	−	0.533995i
$206$	−1.24264	−	2.15232i	−0.0865789	−	0.149959i
$207$		0			0
$208$	−9.36396	+	16.2189i	−0.649274	+	1.12458i
$209$	2.41421			0.166995
$210$		0			0
$211$	−6.82843			−0.470088			−0.235044	−	0.971985i	$-0.575523\pi$
$211$	−6.82843			−0.470088			−0.235044	+	0.971985i	$0.575523\pi$
$212$	−3.87868	+	6.71807i	−0.266389	+	0.461399i
$213$		0			0
$214$	−1.22183	−	2.11626i	−0.0835223	−	0.144665i
$215$	−3.03553	+	5.25770i	−0.207022	+	0.358572i
$216$		0			0
$217$	2.24264	+	5.49333i	0.152240	+	0.372911i
$218$	−0.686292			−0.0464815
$219$		0			0
$220$	2.20711	+	3.82282i	0.148803	+	0.257735i
$221$	−12.4853	−	21.6251i	−0.839851	−	1.45466i
$222$		0			0
$223$	−6.24264			−0.418038			−0.209019	−	0.977912i	$-0.567027\pi$
$223$	−6.24264			−0.418038			−0.209019	+	0.977912i	$0.567027\pi$
$224$	−4.41421	−	10.8126i	−0.294937	−	0.722445i
$225$		0			0
$226$	−1.70711	+	2.95680i	−0.113555	+	0.196683i
$227$	−5.87868	−	10.1822i	−0.390182	−	0.675814i	0.602292	−	0.798276i	$-0.294254\pi$
$227$	−5.87868	−	10.1822i	−0.390182	−	0.675814i	−0.992473	+	0.122462i	$0.960921\pi$
$228$		0			0
$229$	2.24264	−	3.88437i	0.148198	−	0.256686i	−0.782364	−	0.622822i	$-0.785986\pi$
$229$	2.24264	−	3.88437i	0.148198	−	0.256686i	0.930561	+	0.366136i	$0.119319\pi$
$230$	3.48528			0.229813
$231$		0			0
$232$	14.9289			0.980132
$233$	−8.24264	+	14.2767i	−0.539993	+	0.935296i	0.458910	+	0.888483i	$0.348240\pi$
$233$	−8.24264	+	14.2767i	−0.539993	+	0.935296i	−0.998904	+	0.0468133i	$0.985093\pi$
$234$		0			0
$235$	0.792893	+	1.37333i	0.0517227	+	0.0895863i
$236$	−1.07107	+	1.85514i	−0.0697206	+	0.120760i
$237$		0			0
$238$	4.34315	+	0.594346i	0.281524	+	0.0385257i
$239$	−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
$241$	−11.0208	−	19.0886i	−0.709913	−	1.22961i	−0.964889	−	0.262658i	$-0.915401\pi$
$241$	−11.0208	−	19.0886i	−0.709913	−	1.22961i	0.254976	−	0.966947i	$-0.417932\pi$
$242$	−1.07107	−	1.85514i	−0.0688508	−	0.119253i
$243$		0			0
$244$	−11.2843			−0.722401
$245$	5.00000	−	4.89898i	0.319438	−	0.312984i
$246$		0			0
$247$	3.12132	−	5.40629i	0.198605	−	0.343994i
$248$	−1.77817	−	3.07989i	−0.112914	−	0.195573i
$249$		0			0
$250$	1.86396	−	3.22848i	0.117887	−	0.204187i
$251$	−11.7279			−0.740260			−0.370130	−	0.928980i	$-0.620687\pi$
$251$	−11.7279			−0.740260			−0.370130	+	0.928980i	$0.620687\pi$
$252$		0			0
$253$	−20.3137			−1.27711
$254$	−0.878680	+	1.52192i	−0.0551333	+	0.0954936i
$255$		0			0
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	−6.65685	+	11.5300i	−0.415243	+	0.719222i	−0.995454	−	0.0952441i	$-0.969637\pi$
$257$	−6.65685	+	11.5300i	−0.415243	+	0.719222i	0.580211	+	0.814466i	$0.302970\pi$
$258$		0			0
$259$	−8.22183	+	10.6024i	−0.510879	+	0.658803i
$260$	11.4142			0.707879
$261$		0			0
$262$	−4.24264	−	7.34847i	−0.262111	−	0.453990i
$263$	−0.242641	−	0.420266i	−0.0149619	−	0.0259147i	0.858448	−	0.512901i	$-0.171429\pi$
$263$	−0.242641	−	0.420266i	−0.0149619	−	0.0259147i	−0.873409	+	0.486987i	$0.838096\pi$
$264$		0			0
$265$	4.24264			0.260623
$266$	0.414214	+	1.01461i	0.0253971	+	0.0622098i
$267$		0			0
$268$	6.24264	−	10.8126i	0.381330	−	0.660483i
$269$	−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
$271$	3.37868	−	5.85204i	0.205240	−	0.355486i	−0.744969	−	0.667099i	$-0.767536\pi$
$271$	3.37868	−	5.85204i	0.205240	−	0.355486i	0.950209	+	0.311613i	$0.100869\pi$
$272$	12.0000			0.727607
$273$		0			0
$274$	−5.87006			−0.354623
$275$	−4.82843	+	8.36308i	−0.291165	+	0.504313i
$276$		0			0
$277$	−14.2279	−	24.6435i	−0.854873	−	1.48068i	−0.876763	−	0.480923i	$-0.840302\pi$
$277$	−14.2279	−	24.6435i	−0.854873	−	1.48068i	0.0218898	−	0.999760i	$-0.493032\pi$
$278$	1.67157	−	2.89525i	0.100254	−	0.173646i
$279$		0			0
$280$	−2.57107	+	3.31552i	−0.153651	+	0.198140i
$281$	19.7574			1.17863			0.589313	−	0.807905i	$-0.299399\pi$
$281$	19.7574			1.17863			0.589313	+	0.807905i	$0.299399\pi$
$282$		0			0
$283$	−7.96447	−	13.7949i	−0.473438	−	0.820019i	0.526099	−	0.850423i	$-0.323654\pi$
$283$	−7.96447	−	13.7949i	−0.473438	−	0.820019i	−0.999538	+	0.0304038i	$0.990321\pi$
$284$	5.26346	+	9.11657i	0.312329	+	0.540969i
$285$		0			0
$286$	6.24264			0.369135
$287$	−23.1421	−	3.16693i	−1.36604	−	0.186938i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−1.94975	−	3.37706i	−0.114493	−	0.198308i
$291$		0			0
$292$	−12.0147	+	20.8101i	−0.703108	+	1.21782i
$293$	−8.82843			−0.515762			−0.257881	−	0.966177i	$-0.583024\pi$
$293$	−8.82843			−0.515762			−0.257881	+	0.966177i	$0.583024\pi$
$294$		0			0
$295$	1.17157			0.0682116
$296$	4.02082	−	6.96426i	0.233705	−	0.404789i
$297$		0			0
$298$	1.20711	+	2.09077i	0.0699258	+	0.121115i
$299$	−26.2635	+	45.4896i	−1.51885	+	2.63073i
$300$		0			0
$301$	15.9142	+	2.17781i	0.917280	+	0.125527i
$302$	−2.20101			−0.126654
$303$		0			0
$304$	1.50000	+	2.59808i	0.0860309	+	0.149010i
$305$	3.08579	+	5.34474i	0.176692	+	0.306039i
$306$		0			0
$307$	6.68629			0.381607			0.190803	−	0.981628i	$-0.438891\pi$
$307$	6.68629			0.381607			0.190803	+	0.981628i	$0.438891\pi$
$308$	7.15685	−	9.22911i	0.407800	−	0.525877i
$309$		0			0
$310$	−0.464466	+	0.804479i	−0.0263799	+	0.0456913i
$311$	7.89949	+	13.6823i	0.447939	+	0.775854i	0.998252	−	0.0591052i	$-0.0188247\pi$
$311$	7.89949	+	13.6823i	0.447939	+	0.775854i	−0.550312	+	0.834959i	$0.685491\pi$
$312$		0			0
$313$	−2.32843	+	4.03295i	−0.131610	+	0.227956i	−0.924298	−	0.381673i	$-0.875348\pi$
$313$	−2.32843	+	4.03295i	−0.131610	+	0.227956i	0.792687	+	0.609629i	$0.208681\pi$
$314$	−4.89949			−0.276494
$315$		0			0
$316$	2.58579			0.145462
$317$	−5.87868	+	10.1822i	−0.330180	+	0.571888i	−0.982547	−	0.186015i	$-0.940443\pi$
$317$	−5.87868	+	10.1822i	−0.330180	+	0.571888i	0.652367	+	0.757903i	$0.273776\pi$
$318$		0			0
$319$	11.3640	+	19.6830i	0.636260	+	1.10203i
$320$	−2.08579	+	3.61269i	−0.116599	+	0.201955i
$321$		0			0
$322$	−3.48528	−	8.53716i	−0.194227	−	0.475757i
$323$	−4.00000			−0.222566
$324$		0			0
$325$	12.4853	+	21.6251i	0.692559	+	1.19955i
$326$	3.74264	+	6.48244i	0.207286	+	0.359029i
$327$		0			0
$328$	14.0000			0.773021
$329$	2.57107	−	3.31552i	0.141748	−	0.182790i
$330$		0			0
$331$	−9.72792	+	16.8493i	−0.534695	+	0.926119i	0.464483	+	0.885582i	$0.346240\pi$
$331$	−9.72792	+	16.8493i	−0.534695	+	0.926119i	−0.999178	+	0.0405368i	$0.987093\pi$
$332$	−0.692388	−	1.19925i	−0.0379997	−	0.0658175i
$333$		0			0
$334$	0.221825	−	0.384213i	0.0121377	−	0.0210232i
$335$	−6.82843			−0.373077
$336$		0			0
$337$	−11.5563			−0.629514			−0.314757	−	0.949172i	$-0.601923\pi$
$337$	−11.5563			−0.629514			−0.314757	+	0.949172i	$0.601923\pi$
$338$	5.37868	−	9.31615i	0.292562	−	0.506732i
$339$		0			0
$340$	−3.65685	−	6.33386i	−0.198321	−	0.343502i
$341$	2.70711	−	4.68885i	0.146598	−	0.253915i
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$	−9.62742			−0.519076
$345$		0			0
$346$	−3.17157	−	5.49333i	−0.170505	−	0.295323i
$347$	−10.5208	−	18.2226i	−0.564787	−	0.978240i	−0.997069	−	0.0765015i	$-0.975625\pi$
$347$	−10.5208	−	18.2226i	−0.564787	−	0.978240i	0.432283	−	0.901738i	$-0.357708\pi$
$348$		0			0
$349$	−12.4853			−0.668322			−0.334161	−	0.942516i	$-0.608453\pi$
$349$	−12.4853			−0.668322			−0.334161	+	0.942516i	$0.608453\pi$
$350$	−4.34315	−	0.594346i	−0.232151	−	0.0317691i
$351$		0			0
$352$	−5.32843	+	9.22911i	−0.284006	+	0.491913i
$353$	−8.24264	−	14.2767i	−0.438711	−	0.759871i	0.558879	−	0.829249i	$-0.311232\pi$
$353$	−8.24264	−	14.2767i	−0.438711	−	0.759871i	−0.997590	+	0.0693787i	$0.977898\pi$
$354$		0			0
$355$	2.87868	−	4.98602i	0.152784	−	0.264630i
$356$	−15.6985			−0.832018
$357$		0			0
$358$	−9.02944			−0.477221
$359$	−1.62132	+	2.80821i	−0.0855700	+	0.148212i	−0.905634	−	0.424060i	$-0.860604\pi$
$359$	−1.62132	+	2.80821i	−0.0855700	+	0.148212i	0.820064	+	0.572272i	$0.193938\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	−2.05025	+	3.55114i	−0.107759	+	0.186644i
$363$		0			0
$364$	−11.4142	−	27.9590i	−0.598267	−	1.46545i
$365$	13.1421			0.687891
$366$		0			0
$367$	17.8284	+	30.8797i	0.930636	+	1.61191i	0.782236	+	0.622982i	$0.214079\pi$
$367$	17.8284	+	30.8797i	0.930636	+	1.61191i	0.148400	+	0.988927i	$0.452588\pi$
$368$	−12.6213	−	21.8608i	−0.657932	−	1.13957i
$369$		0			0
$370$	−2.10051			−0.109200
$371$	−4.24264	−	10.3923i	−0.220267	−	0.539542i
$372$		0			0
$373$	5.65685	−	9.79796i	0.292901	−	0.507319i	−0.681594	−	0.731731i	$-0.738713\pi$
$373$	5.65685	−	9.79796i	0.292901	−	0.507319i	0.974494	+	0.224412i	$0.0720461\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$		0			0
$376$	−1.25736	+	2.17781i	−0.0648434	+	0.112312i
$377$	58.7696			3.02679
$378$		0			0
$379$	−4.24264			−0.217930			−0.108965	−	0.994046i	$-0.534754\pi$
$379$	−4.24264			−0.217930			−0.108965	+	0.994046i	$0.534754\pi$
$380$	0.914214	−	1.58346i	0.0468982	−	0.0812300i
$381$		0			0
$382$	−1.15685	−	2.00373i	−0.0591898	−	0.102520i
$383$	14.1213	−	24.4588i	0.721566	−	1.24979i	−0.238806	−	0.971067i	$-0.576756\pi$
$383$	14.1213	−	24.4588i	0.721566	−	1.24979i	0.960372	−	0.278721i	$-0.0899106\pi$
$384$		0			0
$385$	−6.32843	−	0.866025i	−0.322527	−	0.0441367i
$386$	4.92893			0.250876
$387$		0			0
$388$	−8.07107	−	13.9795i	−0.409746	−	0.709702i
$389$	−14.2426	−	24.6690i	−0.722131	−	1.25077i	−0.960144	−	0.279505i	$-0.909830\pi$
$389$	−14.2426	−	24.6690i	−0.722131	−	1.25077i	0.238014	−	0.971262i	$-0.423504\pi$
$390$		0			0
$391$	33.6569			1.70210
$392$	10.6924	+	2.98229i	0.540047	+	0.150628i
$393$		0			0
$394$	−4.44975	+	7.70719i	−0.224175	+	0.388283i
$395$	−0.707107	−	1.22474i	−0.0355784	−	0.0616236i
$396$		0			0
$397$	−18.3137	+	31.7203i	−0.919139	+	1.59199i	−0.118412	+	0.992965i	$0.537780\pi$
$397$	−18.3137	+	31.7203i	−0.919139	+	1.59199i	−0.800726	+	0.599030i	$0.795553\pi$
$398$	−0.798990			−0.0400497
$399$		0			0
$400$	−12.0000			−0.600000
$401$	−8.24264	+	14.2767i	−0.411618	+	0.712943i	−0.995067	−	0.0992068i	$-0.968369\pi$
$401$	−8.24264	+	14.2767i	−0.411618	+	0.712943i	0.583449	+	0.812150i	$0.301703\pi$
$402$		0			0
$403$	−7.00000	−	12.1244i	−0.348695	−	0.603957i
$404$	3.94365	−	6.83060i	0.196204	−	0.339835i
$405$		0			0
$406$	−6.32233	+	8.15295i	−0.313772	+	0.404624i
$407$	12.2426			0.606845
$408$		0			0
$409$	12.6569	+	21.9223i	0.625841	+	1.08399i	0.988378	+	0.152019i	$0.0485775\pi$
$409$	12.6569	+	21.9223i	0.625841	+	1.08399i	−0.362536	+	0.931970i	$0.618089\pi$
$410$	−1.82843	−	3.16693i	−0.0902996	−	0.156403i
$411$		0			0
$412$	10.9706			0.540481
$413$	−1.17157	−	2.86976i	−0.0576493	−	0.141211i
$414$		0			0
$415$	−0.378680	+	0.655892i	−0.0185887	+	0.0321965i
$416$	13.7782	+	23.8645i	0.675531	+	1.17005i
$417$		0			0
$418$	0.500000	−	0.866025i	0.0244558	−	0.0423587i
$419$	8.07107			0.394297			0.197149	−	0.980374i	$-0.436832\pi$
$419$	8.07107			0.394297			0.197149	+	0.980374i	$0.436832\pi$
$420$		0			0
$421$	5.21320			0.254076			0.127038	−	0.991898i	$-0.459453\pi$
$421$	5.21320			0.254076			0.127038	+	0.991898i	$0.459453\pi$
$422$	−1.41421	+	2.44949i	−0.0688428	+	0.119239i
$423$		0			0
$424$	3.36396	+	5.82655i	0.163368	+	0.282962i
$425$	8.00000	−	13.8564i	0.388057	−	0.672134i
$426$		0			0
$427$	10.0061	−	12.9033i	0.484229	−	0.624436i
$428$	10.7868			0.521399
$429$		0			0
$430$	1.25736	+	2.17781i	0.0606353	+	0.105023i
$431$	19.0208	+	32.9450i	0.916200	+	1.58691i	0.805134	+	0.593093i	$0.202093\pi$
$431$	19.0208	+	32.9450i	0.916200	+	1.58691i	0.111066	+	0.993813i	$0.464573\pi$
$432$		0			0
$433$	28.0000			1.34559			0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000			1.34559			0.672797	+	0.739827i	$0.265093\pi$
$434$	2.43503	+	0.333226i	0.116885	+	0.0159954i
$435$		0			0
$436$	1.51472	−	2.62357i	0.0725419	−	0.125646i
$437$	4.20711	+	7.28692i	0.201253	+	0.348581i
$438$		0			0
$439$	3.75736	−	6.50794i	0.179329	−	0.310607i	−0.762322	−	0.647198i	$-0.775941\pi$
$439$	3.75736	−	6.50794i	0.179329	−	0.310607i	0.941651	+	0.336591i	$0.109274\pi$
$440$	3.82843			0.182513
$441$		0			0
$442$	−10.3431			−0.491973
$443$	3.17157	−	5.49333i	0.150686	−	0.260996i	−0.780794	−	0.624789i	$-0.785185\pi$
$443$	3.17157	−	5.49333i	0.150686	−	0.260996i	0.931480	+	0.363793i	$0.118518\pi$
$444$		0			0
$445$	4.29289	+	7.43551i	0.203503	+	0.352477i
$446$	−1.29289	+	2.23936i	−0.0612203	+	0.106037i
$447$		0			0
$448$	10.9350	+	1.49642i	0.516632	+	0.0706994i
$449$	1.65685			0.0781918			0.0390959	−	0.999235i	$-0.487552\pi$
$449$	1.65685			0.0781918			0.0390959	+	0.999235i	$0.487552\pi$
$450$		0			0
$451$	10.6569	+	18.4582i	0.501812	+	0.869163i
$452$	−7.53553	−	13.0519i	−0.354442	−	0.613911i
$453$		0			0
$454$	−4.87006			−0.228563
$455$	−10.1213	+	13.0519i	−0.474495	+	0.611884i
$456$		0			0
$457$	1.08579	−	1.88064i	0.0507909	−	0.0879725i	−0.839512	−	0.543341i	$-0.817159\pi$
$457$	1.08579	−	1.88064i	0.0507909	−	0.0879725i	0.890303	+	0.455368i	$0.150492\pi$
$458$	−0.928932	−	1.60896i	−0.0434062	−	0.0751817i
$459$		0			0
$460$	−7.69239	+	13.3236i	−0.358659	+	0.621216i
$461$	3.97056			0.184928			0.0924638	−	0.995716i	$-0.470526\pi$
$461$	3.97056			0.184928			0.0924638	+	0.995716i	$0.470526\pi$
$462$		0			0
$463$	10.0711			0.468042			0.234021	−	0.972232i	$-0.424812\pi$
$463$	10.0711			0.468042			0.234021	+	0.972232i	$0.424812\pi$
$464$	−14.1213	+	24.4588i	−0.655566	+	1.13547i
$465$		0			0
$466$	3.41421	+	5.91359i	0.158160	+	0.273942i
$467$	19.4497	−	33.6880i	0.900027	−	1.55889i	0.0725700	−	0.997363i	$-0.476880\pi$
$467$	19.4497	−	33.6880i	0.900027	−	1.55889i	0.827457	−	0.561529i	$-0.189787\pi$
$468$		0			0
$469$	6.82843	+	16.7262i	0.315307	+	0.772342i
$470$	0.656854			0.0302984
$471$		0			0
$472$	0.928932	+	1.60896i	0.0427576	+	0.0740583i
$473$	−7.32843	−	12.6932i	−0.336961	−	0.583634i
$474$		0			0
$475$	4.00000			0.183533
$476$	−11.8579	+	15.2913i	−0.543504	+	0.700875i
$477$		0			0
$478$	−0.414214	+	0.717439i	−0.0189457	+	0.0328149i
$479$	5.69239	+	9.85951i	0.260092	+	0.450492i	0.966266	−	0.257546i	$-0.0829138\pi$
$479$	5.69239	+	9.85951i	0.260092	+	0.450492i	−0.706174	+	0.708038i	$0.749580\pi$
$480$		0			0
$481$	15.8284	−	27.4156i	0.721714	−	1.25005i
$482$	−9.12994			−0.415857
$483$		0			0
$484$	9.45584			0.429811
$485$	−4.41421	+	7.64564i	−0.200439	+	0.347171i
$486$		0			0
$487$	−10.4142	−	18.0379i	−0.471913	−	0.817377i	0.527571	−	0.849511i	$-0.323103\pi$
$487$	−10.4142	−	18.0379i	−0.471913	−	0.817377i	−0.999484	+	0.0321338i	$0.989770\pi$
$488$	−4.89340	+	8.47561i	−0.221514	+	0.383673i
$489$		0			0
$490$	−0.721825	−	2.80821i	−0.0326087	−	0.126862i
$491$	32.5563			1.46925			0.734624	−	0.678475i	$-0.237359\pi$
$491$	32.5563			1.46925			0.734624	+	0.678475i	$0.237359\pi$
$492$		0			0
$493$	−18.8284	−	32.6118i	−0.847990	−	1.46876i
$494$	−1.29289	−	2.23936i	−0.0581700	−	0.100753i
$495$		0			0
$496$	6.72792			0.302093
$497$	−15.0919	−	2.06528i	−0.676963	−	0.0926403i
$498$		0			0
$499$	−1.72183	+	2.98229i	−0.0770795	+	0.133506i	−0.901989	−	0.431760i	$-0.857893\pi$
$499$	−1.72183	+	2.98229i	−0.0770795	+	0.133506i	0.824909	+	0.565265i	$0.191226\pi$
$500$	8.22792	+	14.2512i	0.367964	+	0.637332i
$501$		0			0
$502$	−2.42893	+	4.20703i	−0.108409	+	0.187769i
$503$	−19.0416			−0.849024			−0.424512	−	0.905422i	$-0.639554\pi$
$503$	−19.0416			−0.849024			−0.424512	+	0.905422i	$0.639554\pi$
$504$		0			0
$505$	−4.31371			−0.191958
$506$	−4.20711	+	7.28692i	−0.187029	+	0.323943i
$507$		0			0
$508$	−3.87868	−	6.71807i	−0.172089	−	0.298066i
$509$	9.48528	−	16.4290i	0.420428	−	0.728202i	−0.575554	−	0.817764i	$-0.695213\pi$
$509$	9.48528	−	16.4290i	0.420428	−	0.728202i	0.995981	+	0.0895619i	$0.0285467\pi$
$510$		0			0
$511$	−13.1421	−	32.1915i	−0.581374	−	1.42407i
$512$	−22.7574			−1.00574
$513$		0			0
$514$	2.75736	+	4.77589i	0.121622	+	0.210655i
$515$	−3.00000	−	5.19615i	−0.132196	−	0.228970i
$516$		0			0
$517$	−3.82843			−0.168374
$518$	2.10051	+	5.14517i	0.0922909	+	0.226066i
$519$		0			0
$520$	4.94975	−	8.57321i	0.217061	−	0.375960i
$521$	5.22183	+	9.04447i	0.228772	+	0.396245i	0.957445	−	0.288617i	$-0.0931955\pi$
$521$	5.22183	+	9.04447i	0.228772	+	0.396245i	−0.728672	+	0.684863i	$0.759862\pi$
$522$		0			0
$523$	11.8284	−	20.4874i	0.517221	−	0.895853i	−0.482579	−	0.875852i	$-0.660300\pi$
$523$	11.8284	−	20.4874i	0.517221	−	0.895853i	0.999800	−	0.0200006i	$-0.00636681\pi$
$524$	37.4558			1.63627
$525$		0			0
$526$	−0.201010			−0.00876446
$527$	−4.48528	+	7.76874i	−0.195382	+	0.338411i
$528$		0			0
$529$	−23.8995	−	41.3951i	−1.03911	−	1.79979i
$530$	0.878680	−	1.52192i	0.0381674	−	0.0661079i
$531$		0			0
$532$	−4.79289	−	0.655892i	−0.207798	−	0.0284365i
$533$	55.1127			2.38720
$534$		0			0
$535$	−2.94975	−	5.10911i	−0.127529	−	0.220886i
$536$	−5.41421	−	9.37769i	−0.233858	−	0.405055i
$537$		0			0
$538$	−1.65685			−0.0714321
$539$	4.20711	+	16.3674i	0.181213	+	0.704996i
$540$		0			0
$541$	−2.57107	+	4.45322i	−0.110539	+	0.191459i	−0.915988	−	0.401206i	$-0.868591\pi$
$541$	−2.57107	+	4.45322i	−0.110539	+	0.191459i	0.805449	+	0.592665i	$0.201924\pi$
$542$	−1.39949	−	2.42400i	−0.0601135	−	0.104120i
$543$		0			0
$544$	8.82843	−	15.2913i	0.378516	−	0.655608i
$545$	−1.65685			−0.0709718
$546$		0			0
$547$	29.5563			1.26374			0.631869	−	0.775075i	$-0.282288\pi$
$547$	29.5563			1.26374			0.631869	+	0.775075i	$0.282288\pi$
$548$	12.9558	−	22.4402i	0.553446	−	0.958597i
$549$		0			0
$550$	2.00000	+	3.46410i	0.0852803	+	0.147710i
$551$	4.70711	−	8.15295i	0.200529	−	0.347327i
$552$		0			0
$553$	−2.29289	+	2.95680i	−0.0975037	+	0.125736i
$554$	−11.7868			−0.500773
$555$		0			0
$556$	7.37868	+	12.7802i	0.312926	+	0.542003i
$557$	5.08579	+	8.80884i	0.215492	+	0.373243i	0.953425	−	0.301632i	$-0.0975312\pi$
$557$	5.08579	+	8.80884i	0.215492	+	0.373243i	−0.737933	+	0.674874i	$0.764198\pi$
$558$		0			0
$559$	−37.8995			−1.60298
$560$	−3.00000	−	7.34847i	−0.126773	−	0.310530i
$561$		0			0
$562$	4.09188	−	7.08735i	0.172606	−	0.298962i
$563$	−6.94975	−	12.0373i	−0.292897	−	0.507312i	0.681597	−	0.731728i	$-0.261286\pi$
$563$	−6.94975	−	12.0373i	−0.292897	−	0.507312i	−0.974493	+	0.224416i	$0.927953\pi$
$564$		0			0
$565$	−4.12132	+	7.13834i	−0.173385	+	0.300312i
$566$	−6.59798			−0.277334
$567$		0			0
$568$	9.12994			0.383084
$569$	−21.4853	+	37.2136i	−0.900710	+	1.56008i	−0.0741351	+	0.997248i	$0.523620\pi$
$569$	−21.4853	+	37.2136i	−0.900710	+	1.56008i	−0.826575	+	0.562827i	$0.809714\pi$
$570$		0			0
$571$	9.44975	+	16.3674i	0.395460	+	0.684956i	0.993160	−	0.116764i	$-0.0372520\pi$
$571$	9.44975	+	16.3674i	0.395460	+	0.684956i	−0.597700	+	0.801720i	$0.703919\pi$
$572$	−13.7782	+	23.8645i	−0.576094	+	0.997825i
$573$		0			0
$574$	−5.92893	+	7.64564i	−0.247469	+	0.319123i
$575$	−33.6569			−1.40359
$576$		0			0
$577$	−13.9853	−	24.2232i	−0.582215	−	1.00843i	−0.995216	−	0.0976954i	$-0.968853\pi$
$577$	−13.9853	−	24.2232i	−0.582215	−	1.00843i	0.413001	−	0.910730i	$-0.364480\pi$
$578$	−0.207107	−	0.358719i	−0.00861451	−	0.0149208i
$579$		0			0
$580$	17.2132			0.714739
$581$	1.98528	+	0.271680i	0.0823633	+	0.0112712i
$582$		0			0
$583$	−5.12132	+	8.87039i	−0.212103	+	0.367374i
$584$	10.4203	+	18.0485i	0.431196	+	0.746853i
$585$		0			0
$586$	−1.82843	+	3.16693i	−0.0755316	+	0.130825i
$587$	−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
$589$	−2.24264			−0.0924064
$590$	0.242641	−	0.420266i	0.00998936	−	0.0173021i
$591$		0			0
$592$	7.60660	+	13.1750i	0.312629	+	0.541490i
$593$	3.08579	−	5.34474i	0.126718	−	0.219482i	−0.795685	−	0.605710i	$-0.792889\pi$
$593$	3.08579	−	5.34474i	0.126718	−	0.219482i	0.922403	+	0.386228i	$0.126222\pi$
$594$		0			0
$595$	10.4853	+	1.43488i	0.429855	+	0.0588243i
$596$	−10.6569			−0.436522
$597$		0			0
$598$	10.8787	+	18.8424i	0.444862	+	0.770524i
$599$	−15.8492	−	27.4517i	−0.647582	−	1.12165i	−0.983699	−	0.179825i	$-0.942447\pi$
$599$	−15.8492	−	27.4517i	−0.647582	−	1.12165i	0.336116	−	0.941821i	$-0.390887\pi$
$600$		0			0
$601$	−9.27208			−0.378216			−0.189108	−	0.981956i	$-0.560560\pi$
$601$	−9.27208			−0.378216			−0.189108	+	0.981956i	$0.560560\pi$
$602$	4.07716	−	5.25770i	0.166173	−	0.214288i
$603$		0			0
$604$	4.85786	−	8.41407i	0.197664	−	0.342364i
$605$	−2.58579	−	4.47871i	−0.105127	−	0.182086i
$606$		0			0
$607$	−16.2635	+	28.1691i	−0.660113	+	1.14335i	0.320472	+	0.947258i	$0.396158\pi$
$607$	−16.2635	+	28.1691i	−0.660113	+	1.14335i	−0.980586	+	0.196092i	$0.937175\pi$
$608$	4.41421			0.179020
$609$		0			0
$610$	2.55635			0.103504
$611$	−4.94975	+	8.57321i	−0.200245	+	0.346835i
$612$		0			0
$613$	4.34315	+	7.52255i	0.175418	+	0.303833i	0.940306	−	0.340331i	$-0.110539\pi$
$613$	4.34315	+	7.52255i	0.175418	+	0.303833i	−0.764888	+	0.644163i	$0.777206\pi$
$614$	1.38478	−	2.39850i	0.0558850	−	0.0967957i
$615$		0			0
$616$	−3.82843	−	9.37769i	−0.154252	−	0.377838i
$617$	42.4558			1.70921			0.854604	−	0.519280i	$-0.173800\pi$
$617$	42.4558			1.70921			0.854604	+	0.519280i	$0.173800\pi$
$618$		0			0
$619$	−1.72183	−	2.98229i	−0.0692060	−	0.119868i	0.829346	−	0.558735i	$-0.188713\pi$
$619$	−1.72183	−	2.98229i	−0.0692060	−	0.119868i	−0.898552	+	0.438867i	$0.855380\pi$
$620$	−2.05025	−	3.55114i	−0.0823401	−	0.142617i
$621$		0			0
$622$	6.54416			0.262397
$623$	13.9203	−	17.9509i	0.557705	−	0.719188i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	0.964466	+	1.67050i	0.0385478	+	0.0667668i
$627$		0			0
$628$	10.8137	−	18.7299i	0.431514	−	0.747404i
$629$	−20.2843			−0.808787
$630$		0			0
$631$	−5.44365			−0.216708			−0.108354	−	0.994112i	$-0.534558\pi$
$631$	−5.44365			−0.216708			−0.108354	+	0.994112i	$0.534558\pi$
$632$	1.12132	−	1.94218i	0.0446037	−	0.0772559i
$633$		0			0
$634$	2.43503	+	4.21759i	0.0967073	+	0.167502i
$635$	−2.12132	+	3.67423i	−0.0841820	+	0.145808i
$636$		0			0
$637$	42.0919	+	11.7401i	1.66774	+	0.465161i
$638$	9.41421			0.372712
$639$		0			0
$640$	5.27817	+	9.14207i	0.208638	+	0.361372i
$641$	1.89949	+	3.29002i	0.0750255	+	0.129948i	0.901097	−	0.433617i	$-0.142763\pi$
$641$	1.89949	+	3.29002i	0.0750255	+	0.129948i	−0.826072	+	0.563565i	$0.809430\pi$
$642$		0			0
$643$	30.1421			1.18869			0.594345	−	0.804210i	$-0.297411\pi$
$643$	30.1421			1.18869			0.594345	+	0.804210i	$0.297411\pi$
$644$	40.3284	+	5.51882i	1.58916	+	0.217472i
$645$		0			0
$646$	−0.828427	+	1.43488i	−0.0325940	+	0.0564545i
$647$	3.10660	+	5.38079i	0.122133	+	0.211541i	0.920609	−	0.390486i	$-0.127693\pi$
$647$	3.10660	+	5.38079i	0.122133	+	0.211541i	−0.798476	+	0.602027i	$0.794360\pi$
$648$		0			0
$649$	−1.41421	+	2.44949i	−0.0555127	+	0.0961509i
$650$	10.3431			0.405692
$651$		0			0
$652$	−33.0416			−1.29401
$653$	−0.928932	+	1.60896i	−0.0363519	+	0.0629634i	−0.883629	−	0.468188i	$-0.844907\pi$
$653$	−0.928932	+	1.60896i	−0.0363519	+	0.0629634i	0.847277	+	0.531151i	$0.178240\pi$
$654$		0			0
$655$	−10.2426	−	17.7408i	−0.400213	−	0.693189i
$656$	−13.2426	+	22.9369i	−0.517038	+	0.895537i
$657$		0			0
$658$	−0.656854	−	1.60896i	−0.0256068	−	0.0627237i
$659$	38.0416			1.48189			0.740946	−	0.671565i	$-0.234378\pi$
$659$	38.0416			1.48189			0.740946	+	0.671565i	$0.234378\pi$
$660$		0			0
$661$	11.3640	+	19.6830i	0.442007	+	0.765578i	0.997838	−	0.0657167i	$-0.0209334\pi$
$661$	11.3640	+	19.6830i	0.442007	+	0.765578i	−0.555831	+	0.831295i	$0.687600\pi$
$662$	4.02944	+	6.97919i	0.156609	+	0.271254i
$663$		0			0
$664$	−1.20101			−0.0466082
$665$	1.00000	+	2.44949i	0.0387783	+	0.0949871i
$666$		0			0
$667$	−39.6066	+	68.6006i	−1.53357	+	2.65623i
$668$	0.979185	+	1.69600i	0.0378858	+	0.0656201i
$669$		0			0
$670$	−1.41421	+	2.44949i	−0.0546358	+	0.0946320i
$671$	−14.8995			−0.575189
$672$		0			0
$673$	35.7990			1.37995			0.689975	−	0.723833i	$-0.257622\pi$
$673$	35.7990			1.37995			0.689975	+	0.723833i	$0.257622\pi$
$674$	−2.39340	+	4.14549i	−0.0921903	+	0.159678i
$675$		0			0
$676$	23.7426	+	41.1235i	0.913178	+	1.58167i
$677$	0.343146	−	0.594346i	0.0131882	−	0.0228426i	−0.859356	−	0.511378i	$-0.829135\pi$
$677$	0.343146	−	0.594346i	0.0131882	−	0.0228426i	0.872544	+	0.488535i	$0.162469\pi$
$678$		0			0
$679$	23.1421	+	3.16693i	0.888114	+	0.121536i
$680$	−6.34315			−0.243249
$681$		0			0
$682$	−1.12132	−	1.94218i	−0.0429376	−	0.0743701i
$683$	5.24264	+	9.08052i	0.200604	+	0.347456i	0.948723	−	0.316108i	$-0.102376\pi$
$683$	5.24264	+	9.08052i	0.200604	+	0.347456i	−0.748119	+	0.663564i	$0.769043\pi$
$684$		0			0
$685$	−14.1716			−0.541468
$686$	−6.15685	+	4.57631i	−0.235070	+	0.174724i
$687$		0			0
$688$	9.10660	−	15.7731i	0.347186	−	0.601344i
$689$	13.2426	+	22.9369i	0.504504	+	0.873827i
$690$		0			0
$691$	1.48528	−	2.57258i	0.0565028	−	0.0978657i	−0.836390	−	0.548134i	$-0.815338\pi$
$691$	1.48528	−	2.57258i	0.0565028	−	0.0978657i	0.892893	+	0.450268i	$0.148672\pi$
$692$	28.0000			1.06440
$693$		0			0
$694$	−8.71573			−0.330845
$695$	4.03553	−	6.98975i	0.153077	−	0.265136i
$696$		0			0
$697$	−17.6569	−	30.5826i	−0.668801	−	1.15840i
$698$	−2.58579	+	4.47871i	−0.0978735	+	0.169522i
$699$		0			0
$700$	11.8579	−	15.2913i	0.448185	−	0.577956i
$701$	−3.82843			−0.144598			−0.0722988	−	0.997383i	$-0.523034\pi$
$701$	−3.82843			−0.144598			−0.0722988	+	0.997383i	$0.523034\pi$
$702$		0			0
$703$	−2.53553	−	4.39167i	−0.0956295	−	0.165635i
$704$	−5.03553	−	8.72180i	−0.189784	−	0.328715i
$705$		0			0
$706$	−6.82843			−0.256991
$707$	4.31371	+	10.5664i	0.162234	+	0.397390i
$708$		0			0
$709$	−12.4706	+	21.5996i	−0.468342	+	0.811192i	−0.999345	−	0.0361778i	$-0.988482\pi$
$709$	−12.4706	+	21.5996i	−0.468342	+	0.811192i	0.531004	+	0.847370i	$0.321815\pi$
$710$	−1.19239	−	2.06528i	−0.0447495	−	0.0775085i
$711$		0			0
$712$	−6.80761	+	11.7911i	−0.255126	+	0.441891i
$713$	18.8701			0.706689
$714$		0			0
$715$	15.0711			0.563626
$716$	19.9289	−	34.5179i	0.744779	−	1.29000i
$717$		0			0
$718$	0.671573	+	1.16320i	0.0250629	+	0.0434102i
$719$	−22.0416	+	38.1772i	−0.822014	+	1.42377i	0.0821659	+	0.996619i	$0.473816\pi$
$719$	−22.0416	+	38.1772i	−0.822014	+	1.42377i	−0.904180	+	0.427152i	$0.859517\pi$
$720$		0			0
$721$	−9.72792	+	12.5446i	−0.362287	+	0.467186i
$722$	−0.414214			−0.0154154
$723$		0			0
$724$	−9.05025	−	15.6755i	−0.336350	−	0.582575i
$725$	18.8284	+	32.6118i	0.699270	+	1.21117i
$726$		0			0
$727$	5.92893			0.219892			0.109946	−	0.993938i	$-0.464932\pi$
$727$	5.92893			0.219892			0.109946	+	0.993938i	$0.464932\pi$
$728$	−25.9497	−	3.55114i	−0.961762	−	0.131614i
$729$		0			0
$730$	2.72183	−	4.71434i	0.100739	−	0.174486i
$731$	12.1421	+	21.0308i	0.449093	+	0.777852i
$732$		0			0
$733$	14.7279	−	25.5095i	0.543988	−	0.942215i	−0.454682	−	0.890654i	$-0.650247\pi$
$733$	14.7279	−	25.5095i	0.543988	−	0.942215i	0.998670	−	0.0515612i	$-0.0164197\pi$
$734$	14.7696			0.545154
$735$		0			0
$736$	−37.1421			−1.36908
$737$	8.24264	−	14.2767i	0.303622	−	0.525888i
$738$		0			0
$739$	9.82843	+	17.0233i	0.361545	+	0.626214i	0.988215	−	0.153071i	$-0.0489162\pi$
$739$	9.82843	+	17.0233i	0.361545	+	0.626214i	−0.626671	+	0.779284i	$0.715583\pi$
$740$	4.63604	−	8.02986i	0.170424	−	0.295183i
$741$		0			0
$742$	−4.60660	−	0.630399i	−0.169114	−	0.0231427i
$743$	−50.8701			−1.86624			−0.933121	−	0.359563i	$-0.882926\pi$
$743$	−50.8701			−1.86624			−0.933121	+	0.359563i	$0.882926\pi$
$744$		0			0
$745$	2.91421	+	5.04757i	0.106769	+	0.184929i
$746$	−2.34315	−	4.05845i	−0.0857887	−	0.148590i
$747$		0			0
$748$	17.6569			0.645599
$749$	−9.56497	+	12.3345i	−0.349496	+	0.450692i
$750$		0			0
$751$	20.7279	−	35.9018i	0.756373	−	1.31008i	−0.188316	−	0.982108i	$-0.560303\pi$
$751$	20.7279	−	35.9018i	0.756373	−	1.31008i	0.944689	−	0.327967i	$-0.106364\pi$
$752$	−2.37868	−	4.11999i	−0.0867415	−	0.150241i
$753$		0			0
$754$	12.1716	−	21.0818i	0.443263	−	0.767753i
$755$	−5.31371			−0.193386
$756$		0			0
$757$	−5.00000			−0.181728			−0.0908640	−	0.995863i	$-0.528963\pi$
$757$	−5.00000			−0.181728			−0.0908640	+	0.995863i	$0.528963\pi$
$758$	−0.878680	+	1.52192i	−0.0319151	+	0.0552785i
$759$		0			0
$760$	−0.792893	−	1.37333i	−0.0287613	−	0.0498160i
$761$	14.0563	−	24.3463i	0.509542	−	0.882553i	−0.490397	−	0.871499i	$-0.663148\pi$
$761$	14.0563	−	24.3463i	0.509542	−	0.882553i	0.999939	−	0.0110537i	$-0.00351858\pi$
$762$		0			0
$763$	1.65685	+	4.05845i	0.0599822	+	0.146926i
$764$	10.2132			0.369501
$765$		0			0
$766$	−5.84924	−	10.1312i	−0.211342	−	0.366055i
$767$	3.65685	+	6.33386i	0.132041	+	0.228702i
$768$		0			0
$769$	41.4264			1.49387			0.746937	−	0.664895i	$-0.231524\pi$
$769$	41.4264			1.49387			0.746937	+	0.664895i	$0.231524\pi$
$770$	−1.62132	+	2.09077i	−0.0584283	+	0.0753461i
$771$		0			0
$772$	−10.8787	+	18.8424i	−0.391532	+	0.678154i
$773$	−12.8787	−	22.3065i	−0.463214	−	0.802310i	0.535905	−	0.844278i	$-0.319971\pi$
$773$	−12.8787	−	22.3065i	−0.463214	−	0.802310i	−0.999119	+	0.0419682i	$0.986637\pi$
$774$		0			0
$775$	4.48528	−	7.76874i	0.161116	−	0.279061i
$776$	−14.0000			−0.502571
$777$		0			0
$778$	−11.7990			−0.423014
$779$	4.41421	−	7.64564i	0.158156	−	0.273934i
$780$		0			0
$781$	6.94975	+	12.0373i	0.248682	+	0.430729i
$782$	6.97056	−	12.0734i	0.249267	−	0.431743i
$783$		0			0
$784$	−15.0000	+	14.6969i	−0.535714	+	0.524891i
$785$	−11.8284			−0.422175
$786$		0			0
$787$	20.5061	+	35.5176i	0.730963	+	1.26607i	0.956472	+	0.291825i	$0.0942623\pi$
$787$	20.5061	+	35.5176i	0.730963	+	1.26607i	−0.225508	+	0.974241i	$0.572404\pi$
$788$	−19.6421	−	34.0212i	−0.699722	−	1.21195i
$789$		0			0
$790$	−0.585786			−0.0208413
$791$	21.6066	+	2.95680i	0.768242	+	0.105132i
$792$		0			0
$793$	−19.2635	+	33.3653i	−0.684065	+	1.18484i
$794$	7.58579	+	13.1390i	0.269209	+	0.466285i
$795$		0			0
$796$	1.76346	−	3.05440i	0.0625040	−	0.108260i
$797$	21.7574			0.770685			0.385343	−	0.922774i	$-0.374083\pi$
$797$	21.7574			0.770685			0.385343	+	0.922774i	$0.374083\pi$
$798$		0			0
$799$	6.34315			0.224404
$800$	−8.82843	+	15.2913i	−0.312132	+	0.540629i
$801$		0			0
$802$	3.41421	+	5.91359i	0.120560	+	0.208816i
$803$	−15.8640	+	27.4772i	−0.559827	+	0.969649i
$804$		0			0
$805$	−8.41421	−	20.6105i	−0.296562	−	0.726426i
$806$	−5.79899			−0.204261
$807$		0			0
$808$	−3.42031	−	5.92415i	−0.120326	−	0.208411i
$809$	1.42893	+	2.47498i	0.0502386	+	0.0870158i	0.890051	−	0.455861i	$-0.150668\pi$
$809$	1.42893	+	2.47498i	0.0502386	+	0.0870158i	−0.839813	+	0.542877i	$0.817335\pi$
$810$		0			0
$811$	−51.4558			−1.80686			−0.903430	−	0.428737i	$-0.858959\pi$
$811$	−51.4558			−1.80686			−0.903430	+	0.428737i	$0.858959\pi$
$812$	−17.2132	−	42.1636i	−0.604065	−	1.47965i
$813$		0			0
$814$	2.53553	−	4.39167i	0.0888704	−	0.153928i
$815$	9.03553	+	15.6500i	0.316501	+	0.548196i
$816$		0			0
$817$	−3.03553	+	5.25770i	−0.106200	+	0.183944i
$818$	10.4853			0.366609
$819$		0			0
$820$	16.1421			0.563708
$821$	−26.0563	+	45.1309i	−0.909373	+	1.57508i	−0.0944355	+	0.995531i	$0.530105\pi$
$821$	−26.0563	+	45.1309i	−0.909373	+	1.57508i	−0.814937	+	0.579549i	$0.803229\pi$
$822$		0			0
$823$	−18.1066	−	31.3616i	−0.631156	−	1.09320i	−0.987316	−	0.158770i	$-0.949247\pi$
$823$	−18.1066	−	31.3616i	−0.631156	−	1.09320i	0.356159	−	0.934425i	$-0.384086\pi$
$824$	4.75736	−	8.23999i	0.165730	−	0.287054i
$825$		0			0
$826$	−1.27208	−	0.174080i	−0.0442613	−	0.00605701i
$827$	44.2843			1.53991			0.769957	−	0.638095i	$-0.220277\pi$
$827$	44.2843			1.53991			0.769957	+	0.638095i	$0.220277\pi$
$828$		0			0
$829$	−14.1421	−	24.4949i	−0.491177	−	0.850743i	0.508772	−	0.860901i	$-0.330100\pi$
$829$	−14.1421	−	24.4949i	−0.491177	−	0.850743i	−0.999948	+	0.0101585i	$0.996766\pi$
$830$	0.156854	+	0.271680i	0.00544449	+	0.00943013i
$831$		0			0
$832$	−26.0416			−0.902831
$833$	−6.97056	−	27.1185i	−0.241516	−	0.939599i
$834$		0			0
$835$	0.535534	−	0.927572i	0.0185329	−	0.0321000i
$836$	2.20711	+	3.82282i	0.0763344	+	0.132215i
$837$		0			0
$838$	1.67157	−	2.89525i	0.0577435	−	0.100015i
$839$	−19.7990			−0.683537			−0.341769	−	0.939784i	$-0.611026\pi$
$839$	−19.7990			−0.683537			−0.341769	+	0.939784i	$0.611026\pi$
$840$		0			0
$841$	59.6274			2.05612
$842$	1.07969	−	1.87008i	0.0372086	−	0.0644471i
$843$		0			0
$844$	−6.24264	−	10.8126i	−0.214881	−	0.372184i
$845$	12.9853	−	22.4912i	0.446707	−	0.773720i
$846$		0			0
$847$	−8.38478	+	10.8126i	−0.288104	+	0.371524i
$848$	−12.7279			−0.437079
$849$		0			0
$850$	−3.31371	−	5.73951i	−0.113659	−	0.196864i
$851$	21.3345	+	36.9525i	0.731338	+	1.26671i
$852$		0			0
$853$	10.0294			0.343401			0.171701	−	0.985149i	$-0.445074\pi$
$853$	10.0294			0.343401			0.171701	+	0.985149i	$0.445074\pi$
$854$	−2.55635	−	6.26175i	−0.0874765	−	0.214273i
$855$		0			0
$856$	4.67767	−	8.10196i	0.159879	−	0.276919i
$857$	10.4853	+	18.1610i	0.358170	+	0.620369i	0.987655	−	0.156643i	$-0.0500674\pi$
$857$	10.4853	+	18.1610i	0.358170	+	0.620369i	−0.629485	+	0.777013i	$0.716734\pi$
$858$		0			0
$859$	−1.03553	+	1.79360i	−0.0353320	+	0.0611968i	−0.883151	−	0.469089i	$-0.844582\pi$
$859$	−1.03553	+	1.79360i	−0.0353320	+	0.0611968i	0.847819	+	0.530286i	$0.177916\pi$
$860$	−11.1005			−0.378524
$861$		0			0
$862$	15.7574			0.536698
$863$	3.70711	−	6.42090i	0.126191	−	0.218570i	−0.796007	−	0.605288i	$-0.793058\pi$
$863$	3.70711	−	6.42090i	0.126191	−	0.218570i	0.922198	+	0.386718i	$0.126391\pi$
$864$		0			0
$865$	−7.65685	−	13.2621i	−0.260341	−	0.450924i
$866$	5.79899	−	10.0441i	0.197058	−	0.341314i
$867$		0			0
$868$	−6.64823	+	8.57321i	−0.225656	+	0.290994i
$869$	3.41421			0.115819
$870$		0			0
$871$	−21.3137	−	36.9164i	−0.722187	−	1.25087i
$872$	−1.31371	−	2.27541i	−0.0444878	−	0.0770551i
$873$		0			0
$874$	3.48528			0.117891
$875$	−23.5919	−	3.22848i	−0.797551	−	0.109142i
$876$		0			0
$877$	4.05025	−	7.01524i	0.136767	−	0.236888i	−0.789504	−	0.613746i	$-0.789662\pi$
$877$	4.05025	−	7.01524i	0.136767	−	0.236888i	0.926271	+	0.376858i	$0.122995\pi$
$878$	−1.55635	−	2.69568i	−0.0525242	−	0.0909747i
$879$		0			0
$880$	−3.62132	+	6.27231i	−0.122075	+	0.211440i
$881$	−4.28427			−0.144341			−0.0721704	−	0.997392i	$-0.522993\pi$
$881$	−4.28427			−0.144341			−0.0721704	+	0.997392i	$0.522993\pi$
$882$		0			0
$883$	5.65685			0.190368			0.0951842	−	0.995460i	$-0.469656\pi$
$883$	5.65685			0.190368			0.0951842	+	0.995460i	$0.469656\pi$
$884$	22.8284	−	39.5400i	0.767803	−	1.32987i
$885$		0			0
$886$	−1.31371	−	2.27541i	−0.0441349	−	0.0764439i
$887$	0.656854	−	1.13770i	0.0220550	−	0.0382004i	−0.854787	−	0.518979i	$-0.826312\pi$
$887$	0.656854	−	1.13770i	0.0220550	−	0.0382004i	0.876842	+	0.480778i	$0.159646\pi$
$888$		0			0
$889$	11.1213	+	1.52192i	0.372997	+	0.0510435i
$890$	3.55635			0.119209
$891$		0			0
$892$	−5.70711	−	9.88500i	−0.191088	−	0.330974i
$893$	0.792893	+	1.37333i	0.0265332	+	0.0459568i
$894$		0			0
$895$	−21.7990			−0.728660
$896$	17.1152	−	22.0709i	0.571779	−	0.737337i
$897$		0			0
$898$	0.343146	−	0.594346i	0.0114509	−	0.0198336i
$899$	−10.5563	−	18.2841i	−0.352074	−	0.609810i
$900$		0			0
$901$	8.48528	−	14.6969i	0.282686	−	0.489626i
$902$	8.82843			0.293954
$903$		0			0
$904$	−13.0711			−0.434737
$905$	−4.94975	+	8.57321i	−0.164535	+	0.284983i
$906$		0			0
$907$	−14.2929	−	24.7560i	−0.474588	−	0.822010i	0.524989	−	0.851109i	$-0.324070\pi$
$907$	−14.2929	−	24.7560i	−0.474588	−	0.822010i	−0.999577	+	0.0290991i	$0.990736\pi$
$908$	10.7487	−	18.6174i	0.356709	−	0.617839i
$909$		0			0
$910$	2.58579	+	6.33386i	0.0857180	+	0.209965i
$911$	−34.7279			−1.15059			−0.575294	−	0.817947i	$-0.695112\pi$
$911$	−34.7279			−1.15059			−0.575294	+	0.817947i	$0.695112\pi$
$912$		0			0
$913$	−0.914214	−	1.58346i	−0.0302561	−	0.0524050i
$914$	−0.449747	−	0.778985i	−0.0148763	−	0.0257665i
$915$		0			0
$916$	8.20101			0.270969
$917$	−33.2132	+	42.8300i	−1.09680	+	1.41437i
$918$		0			0
$919$	−14.5208	+	25.1508i	−0.478997	+	0.829648i	−0.999710	−	0.0240841i	$-0.992333\pi$
$919$	−14.5208	+	25.1508i	−0.478997	+	0.829648i	0.520712	+	0.853732i	$0.325666\pi$
$920$	6.67157	+	11.5555i	0.219955	+	0.380974i
$921$		0			0
$922$	0.822330	−	1.42432i	0.0270820	−	0.0469074i
$923$	35.9411			1.18302
$924$		0			0
$925$	20.2843			0.666943
$926$	2.08579	−	3.61269i	0.0685432	−	0.118720i
$927$		0			0
$928$	20.7782	+	35.9889i	0.682077	+	1.18139i
$929$	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
$932$	−30.1421			−0.987338
$933$		0			0
$934$	−8.05635	−	13.9540i	−0.263612	−	0.456589i
$935$	−4.82843	−	8.36308i	−0.157906	−	0.273502i
$936$		0			0
$937$	−56.3137			−1.83969			−0.919844	−	0.392284i	$-0.871685\pi$
$937$	−56.3137			−1.83969			−0.919844	+	0.392284i	$0.871685\pi$
$938$	7.41421	+	1.01461i	0.242083	+	0.0331283i
$939$		0			0
$940$	−1.44975	+	2.51104i	−0.0472855	+	0.0819010i
$941$	−22.0208	−	38.1412i	−0.717858	−	1.24337i	−0.961847	−	0.273589i	$-0.911789\pi$
$941$	−22.0208	−	38.1412i	−0.717858	−	1.24337i	0.243989	−	0.969778i	$-0.421544\pi$
$942$		0			0
$943$	−37.1421	+	64.3321i	−1.20951	+	2.09494i
$944$	−3.51472			−0.114394
$945$		0			0
$946$	−6.07107			−0.197387
$947$	−3.82843	+	6.63103i	−0.124407	+	0.215480i	−0.921501	−	0.388376i	$-0.873036\pi$
$947$	−3.82843	+	6.63103i	−0.124407	+	0.215480i	0.797094	+	0.603855i	$0.206370\pi$
$948$		0			0
$949$	41.0208	+	71.0501i	1.33159	+	2.30639i
$950$	0.828427	−	1.43488i	0.0268777	−	0.0465536i
$951$		0			0
$952$	6.34315	+	15.5375i	0.205583	+	0.503572i
$953$	0.585786			0.0189755			0.00948774	−	0.999955i	$-0.496980\pi$
$953$	0.585786			0.0189755			0.00948774	+	0.999955i	$0.496980\pi$
$954$		0			0
$955$	−2.79289	−	4.83743i	−0.0903759	−	0.156536i
$956$	−1.82843	−	3.16693i	−0.0591356	−	0.102426i
$957$		0			0
$958$	4.71573			0.152358
$959$	14.1716	+	34.7131i	0.457624	+	1.12095i
$960$		0			0
$961$	12.9853	−	22.4912i	0.418880	−	0.725522i
$962$	−6.55635	−	11.3559i	−0.211385	−	0.366130i
$963$		0			0
$964$	20.1508	−	34.9021i	0.649012	−	1.12412i
$965$	11.8995			0.383058
$966$		0			0
$967$	20.2843			0.652298			0.326149	−	0.945318i	$-0.394249\pi$
$967$	20.2843			0.652298			0.326149	+	0.945318i	$0.394249\pi$
$968$	4.10051	−	7.10228i	0.131795	−	0.228276i
$969$		0			0
$970$	1.82843	+	3.16693i	0.0587073	+	0.101684i
$971$	−13.4350	+	23.2702i	−0.431151	+	0.746775i	−0.996973	−	0.0777526i	$-0.975226\pi$
$971$	−13.4350	+	23.2702i	−0.431151	+	0.746775i	0.565822	+	0.824527i	$0.308559\pi$
$972$		0			0
$973$	−21.1569	−	2.89525i	−0.678258	−	0.0928174i
$974$	−8.62742			−0.276440
$975$		0			0
$976$	−9.25736	−	16.0342i	−0.296321	−	0.513243i
$977$	14.3848	+	24.9152i	0.460210	+	0.797107i	0.998971	−	0.0453518i	$-0.0144409\pi$
$977$	14.3848	+	24.9152i	0.460210	+	0.797107i	−0.538761	+	0.842458i	$0.681108\pi$
$978$		0			0
$979$	−20.7279			−0.662467
$980$	12.3284	+	3.43861i	0.393817	+	0.109842i
$981$		0			0
$982$	6.74264	−	11.6786i	0.215166	−	0.372679i
$983$	−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
$985$	−10.7426	+	18.6068i	−0.342289	+	0.592862i
$986$	−15.5980			−0.496741
$987$		0			0
$988$	11.4142			0.363135
$989$	25.5416	−	44.2394i	0.812177	−	1.40673i
$990$		0			0
$991$	17.8995	+	31.0028i	0.568596	+	0.984837i	0.996705	+	0.0811104i	$0.0258466\pi$
$991$	17.8995	+	31.0028i	0.568596	+	0.984837i	−0.428109	+	0.903727i	$0.640820\pi$
$992$	4.94975	−	8.57321i	0.157155	−	0.272200i
$993$		0			0
$994$	−3.86649	+	4.98602i	−0.122638	+	0.158147i
$995$	−1.92893			−0.0611513
$996$		0			0
$997$	−14.1421	−	24.4949i	−0.447886	−	0.775761i	0.550362	−	0.834926i	$-0.314490\pi$
$997$	−14.1421	−	24.4949i	−0.447886	−	0.775761i	−0.998248	+	0.0591648i	$0.981156\pi$
$998$	0.713203	+	1.23530i	0.0225761	+	0.0391029i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.j.e.856.2		4
3.2	odd	2		133.2.f.c.58.1	yes	4
7.2	even	3		8379.2.a.bi.1.1		2
7.4	even	3	inner	1197.2.j.e.172.2		4
7.5	odd	6		8379.2.a.bl.1.1		2
21.2	odd	6		931.2.a.f.1.2		2
21.5	even	6		931.2.a.e.1.2		2
21.11	odd	6		133.2.f.c.39.1	✓	4
21.17	even	6		931.2.f.i.704.1		4
21.20	even	2		931.2.f.i.324.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.c.39.1	✓	4	21.11	odd	6
133.2.f.c.58.1	yes	4	3.2	odd	2
931.2.a.e.1.2		2	21.5	even	6
931.2.a.f.1.2		2	21.2	odd	6
931.2.f.i.324.1		4	21.20	even	2
931.2.f.i.704.1		4	21.17	even	6
1197.2.j.e.172.2		4	7.4	even	3	inner
1197.2.j.e.856.2		4	1.1	even	1	trivial
8379.2.a.bi.1.1		2	7.2	even	3
8379.2.a.bl.1.1		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)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +1.58579 q^{8} +(-0.207107 - 0.358719i) q^{10} +(1.20711 + 2.09077i) q^{11} +6.24264 q^{13} +(-0.671573 + 0.866025i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(0.500000 - 0.866025i) q^{19} +1.82843 q^{20} +1.00000 q^{22} +(-4.20711 + 7.28692i) q^{23} +(2.00000 + 3.46410i) q^{25} +(1.29289 - 2.23936i) q^{26} +(-1.82843 - 4.47871i) q^{28} +9.41421 q^{29} +(-1.12132 - 1.94218i) q^{31} +(2.20711 + 3.82282i) q^{32} -1.65685 q^{34} +(-1.62132 + 2.09077i) q^{35} +(2.53553 - 4.39167i) q^{37} +(-0.207107 - 0.358719i) q^{38} +(0.792893 - 1.37333i) q^{40} +8.82843 q^{41} -6.07107 q^{43} +(-2.20711 + 3.82282i) q^{44} +(1.74264 + 3.01834i) q^{46} +(-0.792893 + 1.37333i) q^{47} +(6.74264 + 1.88064i) q^{49} +1.65685 q^{50} +(5.70711 + 9.88500i) q^{52} +(2.12132 + 3.67423i) q^{53} +2.41421 q^{55} +(-4.15685 - 0.568852i) q^{56} +(1.94975 - 3.37706i) q^{58} +(0.585786 + 1.01461i) q^{59} +(-3.08579 + 5.34474i) q^{61} -0.928932 q^{62} -4.17157 q^{64} +(3.12132 - 5.40629i) q^{65} +(-3.41421 - 5.91359i) q^{67} +(3.65685 - 6.33386i) q^{68} +(0.414214 + 1.01461i) q^{70} +5.75736 q^{71} +(6.57107 + 11.3814i) q^{73} +(-1.05025 - 1.81909i) q^{74} +1.82843 q^{76} +(-2.41421 - 5.91359i) q^{77} +(0.707107 - 1.22474i) q^{79} +(1.50000 + 2.59808i) q^{80} +(1.82843 - 3.16693i) q^{82} -0.757359 q^{83} -4.00000 q^{85} +(-1.25736 + 2.17781i) q^{86} +(1.91421 + 3.31552i) q^{88} +(-4.29289 + 7.43551i) q^{89} +(-16.3640 - 2.23936i) q^{91} -15.3848 q^{92} +(0.328427 + 0.568852i) q^{94} +(-0.500000 - 0.866025i) q^{95} -8.82843 q^{97} +(2.07107 - 2.02922i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} + 2 q^{10} + 2 q^{11} + 8 q^{13} - 14 q^{14} - 6 q^{16} - 8 q^{17} + 2 q^{19} - 4 q^{20} + 4 q^{22} - 14 q^{23} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 32 q^{29}+ \cdots - 20 q^{98}+O(q^{100}) \) 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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