LMFDB - Embedded newform 990.2.o.a.329.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(329,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.329"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			329.1
Character	$\chi$	$=$	990.329
Dual form			990.2.o.a.659.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.72505 - 0.155544i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.11767 + 0.717978i) q^{5} +(1.57171 - 0.727821i) q^{6} +(0.0167009 + 0.0289269i) q^{7} +1.00000i q^{8} +(2.95161 + 0.536644i) q^{9} +(1.47496 - 1.68062i) q^{10} +(0.184993 - 3.31146i) q^{11} +(-0.997231 + 1.41617i) q^{12} +(1.22550 - 2.12263i) q^{13} +(-0.0289269 - 0.0167009i) q^{14} +(3.76476 - 0.909160i) q^{15} +(-0.500000 - 0.866025i) q^{16} +5.53187i q^{17} +(-2.82449 + 1.01106i) q^{18} +4.37514i q^{19} +(-0.437045 + 2.19294i) q^{20} +(-0.0243106 - 0.0524981i) q^{21} +(1.49552 + 2.96031i) q^{22} +(-0.601970 + 1.04264i) q^{23} +(0.155544 - 1.72505i) q^{24} +(3.96901 - 3.04088i) q^{25} +2.45100i q^{26} +(-5.00821 - 1.38484i) q^{27} +0.0334019 q^{28} +(1.10043 + 1.90601i) q^{29} +(-2.80580 + 2.66974i) q^{30} +(2.57511 - 4.46023i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.834201 + 5.68367i) q^{33} +(-2.76594 - 4.79074i) q^{34} +(-0.0561359 - 0.0492665i) q^{35} +(1.94055 - 2.28785i) q^{36} -1.65816i q^{37} +(-2.18757 - 3.78898i) q^{38} +(-2.44421 + 3.47102i) q^{39} +(-0.717978 - 2.11767i) q^{40} +(-2.65259 + 4.59443i) q^{41} +(0.0473027 + 0.0333094i) q^{42} +(-0.992257 - 1.71864i) q^{43} +(-2.77531 - 1.81594i) q^{44} +(-6.63583 + 0.982762i) q^{45} -1.20394i q^{46} +(-3.71010 - 6.42609i) q^{47} +(0.727821 + 1.57171i) q^{48} +(3.49944 - 6.06121i) q^{49} +(-1.91683 + 4.61798i) q^{50} +(0.860450 - 9.54277i) q^{51} +(-1.22550 - 2.12263i) q^{52} -10.5837 q^{53} +(5.02966 - 1.30480i) q^{54} +(1.98581 + 7.14539i) q^{55} +(-0.0289269 + 0.0167009i) q^{56} +(0.680527 - 7.54734i) q^{57} +(-1.90601 - 1.10043i) q^{58} +(-11.5273 - 6.65531i) q^{59} +(1.09503 - 3.71496i) q^{60} +(-10.4955 + 6.05960i) q^{61} +5.15023i q^{62} +(0.0337713 + 0.0943434i) q^{63} -1.00000 q^{64} +(-1.07120 + 5.37490i) q^{65} +(-2.11940 - 5.33930i) q^{66} +(2.76761 + 1.59788i) q^{67} +(4.79074 + 2.76594i) q^{68} +(1.20061 - 1.70498i) q^{69} +(0.0732484 + 0.0145981i) q^{70} +9.69421i q^{71} +(-0.536644 + 2.95161i) q^{72} -12.6271 q^{73} +(0.829079 + 1.43601i) q^{74} +(-7.31975 + 4.62831i) q^{75} +(3.78898 + 2.18757i) q^{76} +(0.0988798 - 0.0499533i) q^{77} +(0.381238 - 4.22810i) q^{78} +(-4.60468 + 2.65851i) q^{79} +(1.68062 + 1.47496i) q^{80} +(8.42403 + 3.16793i) q^{81} -5.30519i q^{82} +(-12.3941 + 7.15576i) q^{83} +(-0.0576200 - 0.00519547i) q^{84} +(-3.97176 - 11.7147i) q^{85} +(1.71864 + 0.992257i) q^{86} +(-1.60184 - 3.45913i) q^{87} +(3.31146 + 0.184993i) q^{88} +8.45264i q^{89} +(5.25541 - 4.16901i) q^{90} +0.0818680 q^{91} +(0.601970 + 1.04264i) q^{92} +(-5.13597 + 7.29358i) q^{93} +(6.42609 + 3.71010i) q^{94} +(-3.14125 - 9.26508i) q^{95} +(-1.41617 - 0.997231i) q^{96} +(3.44114 - 1.98674i) q^{97} +6.99888i q^{98} +(2.32310 - 9.67487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) $ 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.72505	−	0.155544i	−0.995960	−	0.0898034i
$3$	−1.72505	−	0.155544i	−0.995960	−	0.0898034i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.11767	+	0.717978i	−0.947049	+	0.321090i
$5$	−2.11767	+	0.717978i	−0.947049	+	0.321090i
$6$	1.57171	−	0.727821i	0.641648	−	0.297132i
$7$	0.0167009	+	0.0289269i	0.00631236	+	0.0109333i	0.869164	−	0.494523i	$-0.164657\pi$
$7$	0.0167009	+	0.0289269i	0.00631236	+	0.0109333i	−0.862852	+	0.505457i	$0.831324\pi$
$8$			1.00000i			0.353553i
$9$	2.95161	+	0.536644i	0.983871	+	0.178881i
$10$	1.47496	−	1.68062i	0.466424	−	0.531459i
$11$	0.184993	−	3.31146i	0.0557774	−	0.998443i
$11$	0.184993	−	3.31146i	0.0557774	−	0.998443i
$12$	−0.997231	+	1.41617i	−0.287876	+	0.408812i
$13$	1.22550	−	2.12263i	0.339892	−	0.588711i	−0.644520	−	0.764588i	$-0.722943\pi$
$13$	1.22550	−	2.12263i	0.339892	−	0.588711i	0.984412	+	0.175877i	$0.0562760\pi$
$14$	−0.0289269	−	0.0167009i	−0.00773103	−	0.00446352i
$15$	3.76476	−	0.909160i	0.972057	−	0.234744i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			5.53187i			1.34168i	0.741604	+	0.670838i	$0.234065\pi$
$17$			5.53187i			1.34168i	−0.741604	+	0.670838i	$0.765935\pi$
$18$	−2.82449	+	1.01106i	−0.665739	+	0.238309i
$19$			4.37514i			1.00373i	0.864947	+	0.501863i	$0.167352\pi$
$19$			4.37514i			1.00373i	−0.864947	+	0.501863i	$0.832648\pi$
$20$	−0.437045	+	2.19294i	−0.0977263	+	0.490357i
$21$	−0.0243106	−	0.0524981i	−0.00530501	−	0.0114560i
$22$	1.49552	+	2.96031i	0.318846	+	0.631139i
$23$	−0.601970	+	1.04264i	−0.125520	+	0.217406i	−0.921936	−	0.387342i	$-0.873393\pi$
$23$	−0.601970	+	1.04264i	−0.125520	+	0.217406i	0.796416	+	0.604749i	$0.206726\pi$
$24$	0.155544	−	1.72505i	0.0317503	−	0.352125i
$25$	3.96901	−	3.04088i	0.793803	−	0.608175i
$26$			2.45100i			0.480680i
$27$	−5.00821	−	1.38484i	−0.963831	−	0.266513i
$28$	0.0334019			0.00631236
$29$	1.10043	+	1.90601i	0.204345	+	0.353937i	0.949924	−	0.312481i	$-0.101160\pi$
$29$	1.10043	+	1.90601i	0.204345	+	0.353937i	−0.745579	+	0.666418i	$0.767827\pi$
$30$	−2.80580	+	2.66974i	−0.512266	+	0.487425i
$31$	2.57511	−	4.46023i	0.462504	−	0.801081i	−0.536581	−	0.843849i	$-0.680284\pi$
$31$	2.57511	−	4.46023i	0.462504	−	0.801081i	0.999085	+	0.0427682i	$0.0136177\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.834201	+	5.68367i	−0.145216	+	0.989400i
$34$	−2.76594	−	4.79074i	−0.474354	−	0.821606i
$35$	−0.0561359	−	0.0492665i	−0.00948870	−	0.00832757i
$36$	1.94055	−	2.28785i	0.323425	−	0.381308i
$37$		−	1.65816i		−	0.272599i	−0.990668	−	0.136300i	$-0.956479\pi$
$37$		−	1.65816i		−	0.272599i	0.990668	−	0.136300i	$-0.0435210\pi$
$38$	−2.18757	−	3.78898i	−0.354871	−	0.614654i
$39$	−2.44421	+	3.47102i	−0.391387	+	0.555809i
$40$	−0.717978	−	2.11767i	−0.113522	−	0.334832i
$41$	−2.65259	+	4.59443i	−0.414266	+	0.717529i	−0.995351	−	0.0963135i	$-0.969295\pi$
$41$	−2.65259	+	4.59443i	−0.414266	+	0.717529i	0.581085	+	0.813843i	$0.302628\pi$
$42$	0.0473027	+	0.0333094i	0.00729896	+	0.00513975i
$43$	−0.992257	−	1.71864i	−0.151318	−	0.262090i	0.780394	−	0.625288i	$-0.215018\pi$
$43$	−0.992257	−	1.71864i	−0.151318	−	0.262090i	−0.931712	+	0.363197i	$0.881685\pi$
$44$	−2.77531	−	1.81594i	−0.418394	−	0.273763i
$45$	−6.63583	+	0.982762i	−0.989210	+	0.146502i
$46$		−	1.20394i		−	0.177511i
$47$	−3.71010	−	6.42609i	−0.541174	−	0.937341i	−0.998837	−	0.0482152i	$-0.984647\pi$
$47$	−3.71010	−	6.42609i	−0.541174	−	0.937341i	0.457663	−	0.889126i	$-0.348687\pi$
$48$	0.727821	+	1.57171i	0.105052	+	0.226857i
$49$	3.49944	−	6.06121i	0.499920	−	0.865887i
$50$	−1.91683	+	4.61798i	−0.271081	+	0.653081i
$51$	0.860450	−	9.54277i	0.120487	−	1.33626i
$52$	−1.22550	−	2.12263i	−0.169946	−	0.294355i
$53$	−10.5837			−1.45379			−0.726894	−	0.686750i	$-0.759037\pi$
$53$	−10.5837			−1.45379			−0.726894	+	0.686750i	$0.759037\pi$
$54$	5.02966	−	1.30480i	0.684450	−	0.177560i
$55$	1.98581	+	7.14539i	0.267766	+	0.963484i
$56$	−0.0289269	+	0.0167009i	−0.00386552	+	0.00223176i
$57$	0.680527	−	7.54734i	0.0901380	−	0.999670i
$58$	−1.90601	−	1.10043i	−0.250271	−	0.144494i
$59$	−11.5273	−	6.65531i	−1.50073	−	0.866447i	−1.00000		0.000844712i	$-0.999731\pi$
$59$	−11.5273	−	6.65531i	−1.50073	−	0.866447i	−0.500731	−	0.865603i	$-0.666936\pi$
$60$	1.09503	−	3.71496i	0.141367	−	0.479599i
$61$	−10.4955	+	6.05960i	−1.34382	+	0.775852i	−0.987365	−	0.158462i	$-0.949346\pi$
$61$	−10.4955	+	6.05960i	−1.34382	+	0.775852i	−0.356450	+	0.934314i	$0.616013\pi$
$62$			5.15023i			0.654080i
$63$	0.0337713	+	0.0943434i	0.00425478	+	0.0118862i
$64$	−1.00000			−0.125000
$65$	−1.07120	+	5.37490i	−0.132866	+	0.666674i
$66$	−2.11940	−	5.33930i	−0.260880	−	0.657223i
$67$	2.76761	+	1.59788i	0.338117	+	0.195212i	0.659439	−	0.751758i	$-0.270794\pi$
$67$	2.76761	+	1.59788i	0.338117	+	0.195212i	−0.321322	+	0.946970i	$0.604127\pi$
$68$	4.79074	+	2.76594i	0.580963	+	0.335419i
$69$	1.20061	−	1.70498i	0.144536	−	0.205256i
$70$	0.0732484	+	0.0145981i	0.00875486	+	0.00174481i
$71$			9.69421i			1.15049i	0.817981	+	0.575246i	$0.195094\pi$
$71$			9.69421i			1.15049i	−0.817981	+	0.575246i	$0.804906\pi$
$72$	−0.536644	+	2.95161i	−0.0632440	+	0.347851i
$73$	−12.6271			−1.47789			−0.738947	−	0.673764i	$-0.764677\pi$
$73$	−12.6271			−1.47789			−0.738947	+	0.673764i	$0.764677\pi$
$74$	0.829079	+	1.43601i	0.0963785	+	0.166932i
$75$	−7.31975	+	4.62831i	−0.845212	+	0.534432i
$76$	3.78898	+	2.18757i	0.434626	+	0.250931i
$77$	0.0988798	−	0.0499533i	0.0112684	−	0.00569270i
$78$	0.381238	−	4.22810i	0.0431668	−	0.478738i
$79$	−4.60468	+	2.65851i	−0.518067	+	0.299106i	−0.736143	−	0.676826i	$-0.763355\pi$
$79$	−4.60468	+	2.65851i	−0.518067	+	0.299106i	0.218076	+	0.975932i	$0.430022\pi$
$80$	1.68062	+	1.47496i	0.187899	+	0.164906i
$81$	8.42403	+	3.16793i	0.936003	+	0.351992i
$82$		−	5.30519i		−	0.585860i
$83$	−12.3941	+	7.15576i	−1.36043	+	0.785447i	−0.989681	−	0.143285i	$-0.954233\pi$
$83$	−12.3941	+	7.15576i	−1.36043	+	0.785447i	−0.370752	+	0.928732i	$0.620900\pi$
$84$	−0.0576200	−	0.00519547i	−0.00628686	−	0.000566872i
$85$	−3.97176	−	11.7147i	−0.430798	−	1.27063i
$86$	1.71864	+	0.992257i	0.185326	+	0.106998i
$87$	−1.60184	−	3.45913i	−0.171735	−	0.370857i
$88$	3.31146	+	0.184993i	0.353003	+	0.0197203i
$89$			8.45264i			0.895978i	0.894039	+	0.447989i	$0.147860\pi$
$89$			8.45264i			0.895978i	−0.894039	+	0.447989i	$0.852140\pi$
$90$	5.25541	−	4.16901i	0.553969	−	0.439452i
$91$	0.0818680			0.00858210
$92$	0.601970	+	1.04264i	0.0627598	+	0.108703i
$93$	−5.13597	+	7.29358i	−0.532575	+	0.756309i
$94$	6.42609	+	3.71010i	0.662800	+	0.382668i
$95$	−3.14125	−	9.26508i	−0.322286	−	0.950577i
$96$	−1.41617	−	0.997231i	−0.144537	−	0.101780i
$97$	3.44114	−	1.98674i	0.349395	−	0.201723i	−0.315024	−	0.949084i	$-0.602012\pi$
$97$	3.44114	−	1.98674i	0.349395	−	0.201723i	0.664419	+	0.747360i	$0.268679\pi$
$98$			6.99888i			0.706994i
$99$	2.32310	−	9.67487i	0.233480	−	0.972361i
$100$	−0.648969	−	4.95771i	−0.0648969	−	0.495771i
$101$	−1.53320	−	2.65558i	−0.152559	−	0.264240i	0.779608	−	0.626267i	$-0.215418\pi$
$101$	−1.53320	−	2.65558i	−0.152559	−	0.264240i	−0.932168	+	0.362027i	$0.882085\pi$
$102$	4.02621	+	8.69451i	0.398655	+	0.860884i
$103$	−12.0081	−	6.93286i	−1.18319	−	0.683115i	−0.226439	−	0.974025i	$-0.572709\pi$
$103$	−12.0081	−	6.93286i	−1.18319	−	0.683115i	−0.956750	+	0.290910i	$0.906042\pi$
$104$	2.12263	+	1.22550i	0.208141	+	0.120170i
$105$	0.0891742	+	0.0937190i	0.00870251	+	0.00914604i
$106$	9.16578	−	5.29186i	0.890259	−	0.513991i
$107$		−	11.5899i		−	1.12044i	−0.828344	−	0.560220i	$-0.810717\pi$
$107$		−	11.5899i		−	1.12044i	0.828344	−	0.560220i	$-0.189283\pi$
$108$	−3.70342	+	3.64482i	−0.356361	+	0.350723i
$109$			6.75462i			0.646976i	0.946232	+	0.323488i	$0.104855\pi$
$109$			6.75462i			0.646976i	−0.946232	+	0.323488i	$0.895145\pi$
$110$	−5.29245	−	5.19519i	−0.504616	−	0.495341i
$111$	−0.257917	+	2.86041i	−0.0244804	+	0.271498i
$112$	0.0167009	−	0.0289269i	0.00157809	−	0.00273333i
$113$	4.86304	−	8.42303i	0.457476	−	0.792372i	−0.541350	−	0.840797i	$-0.682087\pi$
$113$	4.86304	−	8.42303i	0.457476	−	0.792372i	0.998827	+	0.0484247i	$0.0154201\pi$
$114$	3.18432	+	6.87645i	0.298239	+	0.644039i
$115$	0.526177	−	2.64017i	0.0490662	−	0.246197i
$116$	2.20087			0.204345
$117$	4.75629	−	5.60752i	0.439719	−	0.518415i
$118$	13.3106			1.22534
$119$	−0.160020	+	0.0923875i	−0.0146690	+	0.00846915i
$120$	0.909160	+	3.76476i	0.0829946	+	0.343674i
$121$	−10.9316	−	1.22519i	−0.993778	−	0.111381i
$122$	6.05960	−	10.4955i	0.548610	−	0.950221i
$123$	5.29050	−	7.51303i	0.477028	−	0.677427i
$124$	−2.57511	−	4.46023i	−0.231252	−	0.400540i
$125$	−6.22176	+	9.28922i	−0.556491	+	0.830854i
$126$	−0.0764185	−	0.0648181i	−0.00680790	−	0.00577446i
$127$	2.11699			0.187852			0.0939261	−	0.995579i	$-0.470058\pi$
$127$	2.11699			0.187852			0.0939261	+	0.995579i	$0.470058\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	1.44437	+	3.11908i	0.127170	+	0.274620i
$130$	−1.75976	−	5.19040i	−0.154342	−	0.455228i
$131$	8.80936	−	15.2583i	0.769677	−	1.33312i	−0.168061	−	0.985777i	$-0.553750\pi$
$131$	8.80936	−	15.2583i	0.769677	−	1.33312i	0.937738	−	0.347343i	$-0.112916\pi$
$132$	4.50510	+	3.56427i	0.392119	+	0.310230i
$133$	−0.126559	+	0.0730689i	−0.0109741	+	0.00633588i
$134$	−3.19576			−0.276072
$135$	11.6000	−	0.663153i	0.998370	−	0.0570751i
$136$	−5.53187			−0.474354
$137$	1.12601	+	1.95031i	0.0962019	+	0.166627i	0.910110	−	0.414368i	$-0.135997\pi$
$137$	1.12601	+	1.95031i	0.0962019	+	0.166627i	−0.813908	+	0.580994i	$0.802664\pi$
$138$	−0.187266	+	2.07686i	−0.0159411	+	0.176794i
$139$	5.26191	+	3.03797i	0.446310	+	0.257677i	0.706270	−	0.707942i	$-0.250376\pi$
$139$	5.26191	+	3.03797i	0.446310	+	0.257677i	−0.259961	+	0.965619i	$0.583710\pi$
$140$	−0.0707340	+	0.0239818i	−0.00597812	+	0.00202683i
$141$	5.40058	+	11.6624i	0.454811	+	0.982153i
$142$	−4.84711	−	8.39543i	−0.406760	−	0.704529i
$143$	−6.80229	−	4.45086i	−0.568836	−	0.372200i
$144$	−1.01106	−	2.82449i	−0.0842549	−	0.235374i
$145$	−3.69882	−	3.24620i	−0.307170	−	0.269582i
$146$	10.9354	−	6.31356i	0.905021	−	0.522514i
$147$	−6.97951	+	9.91159i	−0.575660	+	0.817494i
$148$	−1.43601	−	0.829079i	−0.118039	−	0.0681499i
$149$	−6.03894	+	10.4598i	−0.494729	+	0.856896i	−0.999982	−	0.00607552i	$-0.998066\pi$
$149$	−6.03894	+	10.4598i	−0.494729	+	0.856896i	0.505252	+	0.862972i	$0.331399\pi$
$150$	4.02493	−	7.66811i	0.328634	−	0.626099i
$151$	2.44157	−	1.40964i	0.198692	−	0.114715i	−0.397353	−	0.917666i	$-0.630071\pi$
$151$	2.44157	−	1.40964i	0.198692	−	0.114715i	0.596045	+	0.802951i	$0.296738\pi$
$152$	−4.37514			−0.354871
$153$	−2.96864	+	16.3279i	−0.240001	+	1.32004i
$154$	−0.0606558	+	0.0927007i	−0.00488778	+	0.00747004i
$155$	−2.25088	+	11.2941i	−0.180795	+	0.907168i
$156$	1.78389	+	3.85226i	0.142825	+	0.308428i
$157$	8.10669	+	4.68040i	0.646984	+	0.373537i	0.787300	−	0.616570i	$-0.211478\pi$
$157$	8.10669	+	4.68040i	0.646984	+	0.373537i	−0.140316	+	0.990107i	$0.544812\pi$
$158$	2.65851	−	4.60468i	0.211500	−	0.366329i
$159$	18.2575	+	1.64624i	1.44791	+	0.130555i
$160$	−2.19294	−	0.437045i	−0.173367	−	0.0345515i
$161$	−0.0402139			−0.00316930
$162$	−8.87939	+	1.46851i	−0.697630	+	0.115377i
$163$		−	4.27031i		−	0.334476i	−0.985917	−	0.167238i	$-0.946515\pi$
$163$		−	4.27031i		−	0.334476i	0.985917	−	0.167238i	$-0.0534849\pi$
$164$	2.65259	+	4.59443i	0.207133	+	0.358765i
$165$	−2.31419	−	12.6351i	−0.180160	−	0.983637i
$166$	7.15576	−	12.3941i	0.555395	−	0.961972i
$167$	15.5309	+	8.96674i	1.20181	+	0.693867i	0.960958	−	0.276694i	$-0.0892387\pi$
$167$	15.5309	+	8.96674i	1.20181	+	0.693867i	0.240855	+	0.970561i	$0.422572\pi$
$168$	0.0524981	−	0.0243106i	0.00405032	−	0.00187560i
$169$	3.49630	+	6.05577i	0.268946	+	0.465829i
$170$	9.29698	+	8.15931i	0.713046	+	0.625790i
$171$	−2.34789	+	12.9137i	−0.179548	+	0.987536i
$172$	−1.98451			−0.151318
$173$	−11.0013	+	6.35163i	−0.836417	+	0.482906i	−0.856045	−	0.516902i	$-0.827085\pi$
$173$	−11.0013	+	6.35163i	−0.836417	+	0.482906i	0.0196277	+	0.999807i	$0.493752\pi$
$174$	3.11680	+	2.19477i	0.236284	+	0.166385i
$175$	0.154249	+	0.0640257i	0.0116602	+	0.00483989i
$176$	−2.96031	+	1.49552i	−0.223141	+	0.112729i
$177$	18.8501	+	13.2738i	1.41686	+	0.997717i
$178$	−4.22632	−	7.32020i	−0.316776	−	0.548672i
$179$		−	4.67611i		−	0.349509i	−0.984612	−	0.174754i	$-0.944087\pi$
$179$		−	4.67611i		−	0.349509i	0.984612	−	0.174754i	$-0.0559131\pi$
$180$	−2.46682	+	6.23817i	−0.183866	+	0.464966i
$181$	−10.1846			−0.757013			−0.378507	−	0.925599i	$-0.623562\pi$
$181$	−10.1846			−0.757013			−0.378507	+	0.925599i	$0.623562\pi$
$182$	−0.0708998	+	0.0409340i	−0.00525544	+	0.00303423i
$183$	19.0479	−	8.82061i	1.40806	−	0.652038i
$184$	−1.04264	−	0.601970i	−0.0768647	−	0.0443779i
$185$	1.19052	+	3.51142i	0.0875289	+	0.258165i
$186$	0.801088	−	8.88441i	0.0587386	−	0.651437i
$187$	18.3186	+	1.02336i	1.33959	+	0.0748352i
$188$	−7.42020			−0.541174
$189$	−0.0435827	−	0.168000i	−0.00317017	−	0.0122202i
$190$	7.35295	+	6.45317i	0.533439	+	0.468162i
$191$	−11.7957	+	6.81026i	−0.853507	+	0.492773i	−0.861833	−	0.507193i	$-0.830683\pi$
$191$	−11.7957	+	6.81026i	−0.853507	+	0.492773i	0.00832528	+	0.999965i	$0.497350\pi$
$192$	1.72505	+	0.155544i	0.124495	+	0.0112254i
$193$	−8.55917	+	14.8249i	−0.616103	+	1.06712i	0.374087	+	0.927394i	$0.377956\pi$
$193$	−8.55917	+	14.8249i	−0.616103	+	1.06712i	−0.990190	+	0.139728i	$0.955377\pi$
$194$	−1.98674	+	3.44114i	−0.142640	+	0.247060i
$195$	2.68390	−	9.10536i	0.192198	−	0.652048i
$196$	−3.49944	−	6.06121i	−0.249960	−	0.432944i
$197$		−	20.5696i		−	1.46553i	−0.680484	−	0.732763i	$-0.738231\pi$
$197$		−	20.5696i		−	1.46553i	0.680484	−	0.732763i	$-0.261769\pi$
$198$	2.82557	+	9.54024i	0.200805	+	0.677995i
$199$	−16.0072			−1.13472			−0.567361	−	0.823469i	$-0.692036\pi$
$199$	−16.0072			−1.13472			−0.567361	+	0.823469i	$0.692036\pi$
$200$	3.04088	+	3.96901i	0.215022	+	0.280652i
$201$	−4.52573	−	3.18691i	−0.319221	−	0.224788i
$202$	2.65558	+	1.53320i	0.186846	+	0.107876i
$203$	−0.0367566	+	0.0636642i	−0.00257980	+	0.00446835i
$204$	−7.83406	−	5.51656i	−0.548494	−	0.386236i
$205$	2.31861	−	11.6340i	0.161939	−	0.812551i
$206$	13.8657			0.966070
$207$	−2.33631	+	2.75444i	−0.162385	+	0.191446i
$208$	−2.45100			−0.169946
$209$	14.4881	+	0.809369i	1.00216	+	0.0559852i
$210$	−0.124087	−	0.0365759i	−0.00856279	−	0.00252398i
$211$	−15.4039	−	8.89346i	−1.06045	−	0.612251i	−0.134893	−	0.990860i	$-0.543069\pi$
$211$	−15.4039	−	8.89346i	−1.06045	−	0.612251i	−0.925557	+	0.378609i	$0.876402\pi$
$212$	−5.29186	+	9.16578i	−0.363447	+	0.629508i
$213$	1.50788	−	16.7230i	0.103318	−	1.14584i
$214$	5.79496	+	10.0372i	0.396135	+	0.686126i
$215$	3.33522	+	2.92709i	0.227460	+	0.199626i
$216$	1.38484	−	5.00821i	0.0942267	−	0.340766i
$217$	0.172027			0.0116780
$218$	−3.37731	−	5.84968i	−0.228740	−	0.396190i
$219$	21.7825	+	1.96408i	1.47192	+	0.132720i
$220$	7.18099	+	1.85294i	0.484142	+	0.124925i
$221$	11.7421	+	6.77931i	0.789859	+	0.456025i
$222$	−1.20684	−	2.60615i	−0.0809980	−	0.174913i
$223$	16.3797	−	9.45684i	1.09687	−	0.633277i	0.161471	−	0.986877i	$-0.448376\pi$
$223$	16.3797	−	9.45684i	1.09687	−	0.633277i	0.935396	+	0.353601i	$0.115043\pi$
$224$			0.0334019i			0.00223176i
$225$	13.3469	−	6.84554i	0.889790	−	0.456369i
$226$			9.72608i			0.646969i
$227$	−3.81496	+	2.20257i	−0.253208	+	0.146190i	−0.621232	−	0.783627i	$-0.713368\pi$
$227$	−3.81496	+	2.20257i	−0.253208	+	0.146190i	0.368024	+	0.929816i	$0.380034\pi$
$228$	−6.19593	−	4.36303i	−0.410335	−	0.288948i
$229$	−12.6515	+	21.9130i	−0.836033	+	1.44805i	0.0571539	+	0.998365i	$0.481797\pi$
$229$	−12.6515	+	21.9130i	−0.836033	+	1.44805i	−0.893187	+	0.449686i	$0.851536\pi$
$230$	0.864404	+	2.54954i	0.0569971	+	0.168112i
$231$	−0.178343	+	0.0707918i	−0.0117341	+	0.00465776i
$232$	−1.90601	+	1.10043i	−0.125135	+	0.0722470i
$233$			16.3680i			1.07231i	0.844121	+	0.536153i	$0.180123\pi$
$233$			16.3680i			1.07231i	−0.844121	+	0.536153i	$0.819877\pi$
$234$	−1.31531	+	7.23440i	−0.0859847	+	0.472927i
$235$	12.4705	+	10.9445i	0.813489	+	0.713942i
$236$	−11.5273	+	6.65531i	−0.750366	+	0.433224i
$237$	8.35683	−	3.86984i	0.542834	−	0.251373i
$238$	0.0923875	−	0.160020i	0.00598859	−	0.0103725i
$239$	14.4405	−	25.0116i	0.934075	−	1.61787i	0.157801	−	0.987471i	$-0.449560\pi$
$239$	14.4405	−	25.0116i	0.934075	−	1.61787i	0.776275	−	0.630395i	$-0.217107\pi$
$240$	−2.66974	−	2.80580i	−0.172331	−	0.181114i
$241$	−3.06432	+	1.76919i	−0.197390	+	0.113963i	−0.595438	−	0.803401i	$-0.703021\pi$
$241$	−3.06432	+	1.76919i	−0.197390	+	0.113963i	0.398047	+	0.917365i	$0.369688\pi$
$242$	10.0796	−	4.40473i	0.647941	−	0.283147i
$243$	−14.0391	−	6.77515i	−0.900611	−	0.434626i
$244$			12.1192i			0.775852i
$245$	−3.05883	+	15.3481i	−0.195421	+	0.980557i
$246$	−0.825191	+	9.15173i	−0.0526122	+	0.583493i
$247$	9.28679	+	5.36173i	0.590904	+	0.341159i
$248$	4.46023	+	2.57511i	0.283225	+	0.163520i
$249$	22.4936	−	10.4162i	1.42547	−	0.660102i
$250$	0.743590	−	11.1556i	0.0470288	−	0.705541i
$251$			10.9707i			0.692463i	0.938149	+	0.346232i	$0.112539\pi$
$251$			10.9707i			0.692463i	−0.938149	+	0.346232i	$0.887461\pi$
$252$	0.0985894	+	0.0179249i	0.00621055	+	0.00112916i
$253$	3.34131	+	2.18628i	0.210067	+	0.137450i
$254$	−1.83336	+	1.05849i	−0.115036	+	0.0664158i
$255$	5.02936	+	20.8262i	0.314951	+	1.30419i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.17557	+	7.23230i	−0.260465	+	0.451138i	−0.966365	−	0.257173i	$-0.917209\pi$
$257$	−4.17557	+	7.23230i	−0.260465	+	0.451138i	0.705901	+	0.708311i	$0.250542\pi$
$258$	−2.81040	−	1.97902i	−0.174968	−	0.123208i
$259$	0.0479653	−	0.0276928i	0.00298042	−	0.00172075i
$260$	4.11920	+	3.61513i	0.255462	+	0.224201i
$261$	2.22521	+	6.21633i	0.137737	+	0.384781i
$262$			17.6187i			1.08849i
$263$	1.43711	−	0.829714i	0.0886158	−	0.0511624i	−0.455037	−	0.890472i	$-0.650374\pi$
$263$	1.43711	−	0.829714i	0.0886158	−	0.0511624i	0.543653	+	0.839310i	$0.317041\pi$
$264$	−5.68367	−	0.834201i	−0.349806	−	0.0513415i
$265$	22.4128	−	7.59889i	1.37681	−	0.466796i
$266$	0.0730689	−	0.126559i	0.00448014	−	0.00775984i
$267$	1.31476	−	14.5812i	0.0804619	−	0.892358i
$268$	2.76761	−	1.59788i	0.169059	−	0.0976061i
$269$		−	15.3726i		−	0.937283i	−0.883389	−	0.468641i	$-0.844744\pi$
$269$		−	15.3726i		−	0.937283i	0.883389	−	0.468641i	$-0.155256\pi$
$270$	−9.71433	+	6.37431i	−0.591195	+	0.387928i
$271$			1.65525i			0.100549i	0.998735	+	0.0502747i	$0.0160097\pi$
$271$			1.65525i			0.100549i	−0.998735	+	0.0502747i	$0.983990\pi$
$272$	4.79074	−	2.76594i	0.290481	−	0.167710i
$273$	−0.141227	−	0.0127341i	−0.00854742	−	0.000770702i
$274$	−1.95031	−	1.12601i	−0.117823	−	0.0680250i
$275$	−9.33551	−	13.7058i	−0.562952	−	0.826489i
$276$	−0.876254	−	1.89225i	−0.0527443	−	0.113900i
$277$	−8.10304	−	14.0349i	−0.486865	−	0.843274i	0.513021	−	0.858376i	$-0.328526\pi$
$277$	−8.10304	−	14.0349i	−0.486865	−	0.843274i	−0.999886	+	0.0151017i	$0.995193\pi$
$278$	−6.07594			−0.364410
$279$	9.99429	−	11.7829i	0.598343	−	0.705427i
$280$	0.0492665	−	0.0561359i	0.00294424	−	0.00335476i
$281$	12.7909	+	22.1545i	0.763042	+	1.32163i	0.941276	+	0.337639i	$0.109628\pi$
$281$	12.7909	+	22.1545i	0.763042	+	1.32163i	−0.178234	+	0.983988i	$0.557038\pi$
$282$	−10.5083	−	7.39966i	−0.625757	−	0.440643i
$283$	2.11681	−	3.66643i	0.125832	−	0.217947i	−0.796226	−	0.604999i	$-0.793173\pi$
$283$	2.11681	−	3.66643i	0.125832	−	0.217947i	0.922058	+	0.387052i	$0.126507\pi$
$284$	8.39543	+	4.84711i	0.498177	+	0.287623i
$285$	3.97770	+	16.4714i	0.235619	+	0.975679i
$286$	8.11639	+	0.453417i	0.479932	+	0.0268111i
$287$	−0.177203			−0.0104600
$288$	2.28785	+	1.94055i	0.134813	+	0.114348i
$289$	−13.6016			−0.800095
$290$	4.82637	+	0.961878i	0.283414	+	0.0564834i
$291$	−6.24518	+	2.89199i	−0.366099	+	0.169531i
$292$	−6.31356	+	10.9354i	−0.369473	+	0.639947i
$293$	−20.3208	−	11.7322i	−1.18715	−	0.685402i	−0.229493	−	0.973310i	$-0.573707\pi$
$293$	−20.3208	−	11.7322i	−1.18715	−	0.685402i	−0.957658	+	0.287908i	$0.907040\pi$
$294$	1.08864	−	12.0734i	0.0634905	−	0.704137i
$295$	29.1894	+	5.81734i	1.69947	+	0.338699i
$296$	1.65816			0.0963785
$297$	−5.51234	+	16.3283i	−0.319858	+	0.947465i
$298$		−	12.0779i		−	0.699653i
$299$	1.47543	+	2.55552i	0.0853263	+	0.147789i
$300$	0.348364	+	8.65324i	0.0201128	+	0.499595i
$301$	0.0331433	−	0.0574058i	0.00191035	−	0.00330882i
$302$	−1.40964	+	2.44157i	−0.0811156	+	0.140496i
$303$	2.23179	+	4.81950i	0.128213	+	0.276873i
$304$	3.78898	−	2.18757i	0.217313	−	0.125466i
$305$	17.8754	−	20.3678i	1.02354	−	1.16626i
$306$	−5.59305	−	15.6247i	−0.319733	−	0.893207i
$307$	1.75861			0.100369			0.0501847	−	0.998740i	$-0.484019\pi$
$307$	1.75861			0.100369			0.0501847	+	0.998740i	$0.484019\pi$
$308$	0.00617911	−	0.110609i	0.000352087	−	0.00630254i
$309$	19.6362	+	13.8273i	1.11706	+	0.786609i
$310$	−3.69775	−	10.9065i	−0.210018	−	0.619445i
$311$	−17.9073	−	10.3388i	−1.01543	−	0.586260i	−0.102655	−	0.994717i	$-0.532734\pi$
$311$	−17.9073	−	10.3388i	−1.01543	−	0.586260i	−0.912778	+	0.408457i	$0.866067\pi$
$312$	−3.47102	−	2.44421i	−0.196508	−	0.138376i
$313$	−12.2556	+	7.07575i	−0.692726	+	0.399945i	−0.804632	−	0.593773i	$-0.797638\pi$
$313$	−12.2556	+	7.07575i	−0.692726	+	0.399945i	0.111907	+	0.993719i	$0.464304\pi$
$314$	−9.36080			−0.528260
$315$	−0.139253	−	0.175541i	−0.00784601	−	0.00989060i
$316$			5.31703i			0.299106i
$317$	−15.1076	−	26.1671i	−0.848525	−	1.46969i	−0.882524	−	0.470267i	$-0.844158\pi$
$317$	−15.1076	−	26.1671i	−0.848525	−	1.46969i	0.0339991	−	0.999422i	$-0.489176\pi$
$318$	−16.6346	+	7.70306i	−0.932820	+	0.431966i
$319$	6.51524	−	3.29145i	0.364783	−	0.184286i
$320$	2.11767	−	0.717978i	0.118381	−	0.0401362i
$321$	−1.80274	+	19.9932i	−0.100619	+	1.11591i
$322$	0.0348263	−	0.0201070i	0.00194079	−	0.00112052i
$323$	−24.2027			−1.34667
$324$	6.95552	−	5.71146i	0.386418	−	0.317303i
$325$	−1.59062	−	12.1513i	−0.0882318	−	0.674034i
$326$	2.13515	+	3.69819i	0.118255	+	0.204824i
$327$	1.05064	−	11.6521i	0.0581006	−	0.644362i
$328$	−4.59443	−	2.65259i	−0.253685	−	0.146465i
$329$	0.123924	−	0.214643i	0.00683217	−	0.0118337i
$330$	8.32168	+	9.78518i	0.458093	+	0.538656i
$331$	1.78633	+	3.09402i	0.0981858	+	0.170063i	0.910934	−	0.412553i	$-0.135363\pi$
$331$	1.78633	+	3.09402i	0.0981858	+	0.170063i	−0.812748	+	0.582615i	$0.802029\pi$
$332$			14.3115i			0.785447i
$333$	0.889840	−	4.89424i	0.0487629	−	0.268203i
$334$	−17.9335			−0.981277
$335$	−7.00812	−	1.39669i	−0.382894	−	0.0763094i
$336$	−0.0333094	+	0.0473027i	−0.00181718	+	0.00258057i
$337$	−16.3061	+	28.2431i	−0.888252	+	1.53850i	−0.0463108	+	0.998927i	$0.514746\pi$
$337$	−16.3061	+	28.2431i	−0.888252	+	1.53850i	−0.841941	+	0.539570i	$0.818587\pi$
$338$	−6.05577	−	3.49630i	−0.329391	−	0.190174i
$339$	−9.69915	+	13.7738i	−0.526786	+	0.748088i
$340$	−12.1311	−	2.41768i	−0.657900	−	0.131117i
$341$	−14.2935	−	9.35250i	−0.774036	−	0.506466i
$342$	−4.42352	−	12.3575i	−0.239197	−	0.668220i
$343$	0.467589			0.0252474
$344$	1.71864	−	0.992257i	0.0926629	−	0.0534989i
$345$	−1.31835	+	4.47259i	−0.0709773	+	0.240796i
$346$	6.35163	−	11.0013i	0.341466	−	0.591436i
$347$	19.9338	+	11.5088i	1.07010	+	0.617822i	0.928209	−	0.372060i	$-0.121348\pi$
$347$	19.9338	+	11.5088i	1.07010	+	0.617822i	0.141891	+	0.989882i	$0.454682\pi$
$348$	−3.79661	−	0.342332i	−0.203520	−	0.0183509i
$349$	14.4890	−	8.36523i	0.775578	−	0.447780i	−0.0592827	−	0.998241i	$-0.518881\pi$
$349$	14.4890	−	8.36523i	0.775578	−	0.447780i	0.834861	+	0.550461i	$0.185548\pi$
$350$	−0.165597	+	0.0216768i	−0.00885152	+	0.00115867i
$351$	−9.07707	+	8.93345i	−0.484498	+	0.476832i
$352$	1.81594	−	2.77531i	0.0967899	−	0.147925i
$353$	13.1583	+	22.7909i	0.700346	+	1.21304i	0.968345	+	0.249616i	$0.0803044\pi$
$353$	13.1583	+	22.7909i	0.700346	+	1.21304i	−0.267999	+	0.963419i	$0.586362\pi$
$354$	−22.9615	−	2.07039i	−1.22039	−	0.110040i
$355$	−6.96023	−	20.5291i	−0.369411	−	1.08957i
$356$	7.32020	+	4.22632i	0.387970	+	0.223995i
$357$	0.290413	−	0.134483i	0.0153703	−	0.00711760i
$358$	2.33805	+	4.04963i	0.123570	+	0.214029i
$359$	−13.1402			−0.693513			−0.346757	−	0.937955i	$-0.612717\pi$
$359$	−13.1402			−0.693513			−0.346757	+	0.937955i	$0.612717\pi$
$360$	−0.982762	−	6.63583i	−0.0517961	−	0.349739i
$361$	−0.141837			−0.00746511
$362$	8.82010	−	5.09229i	0.463574	−	0.267645i
$363$	18.6669	+	3.81386i	0.979760	+	0.200176i
$364$	0.0409340	−	0.0708998i	0.00214552	−	0.00371616i
$365$	26.7400	−	9.06601i	1.39964	−	0.474536i
$366$	−12.0856	+	17.1628i	−0.631727	+	0.897115i
$367$	16.1301	−	9.31270i	0.841982	−	0.486119i	−0.0159551	−	0.999873i	$-0.505079\pi$
$367$	16.1301	−	9.31270i	0.841982	−	0.486119i	0.857938	+	0.513754i	$0.171746\pi$
$368$	1.20394			0.0627598
$369$	−10.2950	+	12.1375i	−0.535936	+	0.631851i
$370$	−2.78673	−	2.44572i	−0.144875	−	0.127147i
$371$	−0.176758	−	0.306154i	−0.00917683	−	0.0158947i
$372$	3.74844	+	8.09467i	0.194348	+	0.419689i
$373$	1.99783	−	3.46034i	0.103444	−	0.179169i	−0.809658	−	0.586902i	$-0.800347\pi$
$373$	1.99783	−	3.46034i	0.103444	−	0.179169i	0.913101	+	0.407733i	$0.133681\pi$
$374$	−16.3760	+	8.27304i	−0.846785	+	0.427789i
$375$	12.1777	−	15.0566i	0.628856	−	0.777522i
$376$	6.42609	−	3.71010i	0.331400	−	0.191334i
$377$	5.39432			0.277822
$378$	0.121744	+	0.123701i	0.00626183	+	0.00636250i
$379$	−33.1954			−1.70513			−0.852566	−	0.522620i	$-0.824955\pi$
$379$	−33.1954			−1.70513			−0.852566	+	0.522620i	$0.824955\pi$
$380$	−9.59442	−	1.91213i	−0.492183	−	0.0980904i
$381$	−3.65191	−	0.329285i	−0.187093	−	0.0168698i
$382$	6.81026	−	11.7957i	0.348443	−	0.603521i
$383$	−0.331325	+	0.573871i	−0.0169299	+	0.0293234i	−0.874366	−	0.485267i	$-0.838723\pi$
$383$	−0.331325	+	0.573871i	−0.0169299	+	0.0293234i	0.857436	+	0.514590i	$0.172056\pi$
$384$	−1.57171	+	0.727821i	−0.0802061	+	0.0371415i
$385$	−0.173529	+	0.176778i	−0.00884386	+	0.00900944i
$386$		−	17.1183i		−	0.871301i
$387$	−2.00646	−	5.60525i	−0.101994	−	0.284931i
$388$		−	3.97349i		−	0.201723i
$389$	23.3956	−	13.5075i	1.18620	−	0.684855i	0.228763	−	0.973482i	$-0.426532\pi$
$389$	23.3956	−	13.5075i	1.18620	−	0.684855i	0.957442	+	0.288627i	$0.0931987\pi$
$390$	2.22835	+	9.22743i	0.112837	+	0.467249i
$391$	−5.76777	−	3.33002i	−0.291689	−	0.168407i
$392$	6.06121	+	3.49944i	0.306137	+	0.176749i
$393$	−17.5699	+	24.9510i	−0.886286	+	1.25861i
$394$	10.2848	+	17.8138i	0.518141	+	0.897447i
$395$	7.84242	−	8.93590i	0.394595	−	0.449614i
$396$	−7.21714	−	6.84930i	−0.362675	−	0.344190i
$397$			28.9297i			1.45194i	0.687727	+	0.725969i	$0.258609\pi$
$397$			28.9297i			1.45194i	−0.687727	+	0.725969i	$0.741391\pi$
$398$	13.8627	−	8.00362i	0.694873	−	0.401185i
$399$	0.229687	−	0.106362i	0.0114987	−	0.00532477i
$400$	−4.61798	−	1.91683i	−0.230899	−	0.0958414i
$401$	−4.51361	−	2.60593i	−0.225399	−	0.130134i	0.383049	−	0.923728i	$-0.374874\pi$
$401$	−4.51361	−	2.60593i	−0.225399	−	0.130134i	−0.608448	+	0.793594i	$0.708207\pi$
$402$	5.51286	+	0.497082i	0.274956	+	0.0247922i
$403$	−6.31160	−	10.9320i	−0.314403	−	0.544562i
$404$	−3.06640			−0.152559
$405$	−20.1138	−	0.660340i	−0.999462	−	0.0328126i
$406$		−	0.0735131i		−	0.00364839i
$407$	−5.49093	−	0.306747i	−0.272175	−	0.0152049i
$408$	9.54277	+	0.860450i	0.472438	+	0.0425986i
$409$	−18.8437	−	10.8794i	−0.931761	−	0.537953i	−0.0443931	−	0.999014i	$-0.514135\pi$
$409$	−18.8437	−	10.8794i	−0.931761	−	0.537953i	−0.887368	+	0.461061i	$0.847469\pi$
$410$	3.80901	+	11.2346i	0.188114	+	0.554838i
$411$	−1.63907	−	3.53954i	−0.0808495	−	0.174593i
$412$	−12.0081	+	6.93286i	−0.591595	+	0.341557i
$413$		−	0.444600i		−	0.0218773i
$414$	0.646087	−	3.55357i	0.0317535	−	0.174648i
$415$	21.1090	−	24.0522i	1.03620	−	1.18068i
$416$	2.12263	−	1.22550i	0.104070	−	0.0600850i
$417$	−8.60454	−	6.05911i	−0.421366	−	0.296716i
$418$	−12.9517	+	6.54312i	−0.633491	+	0.320034i
$419$	−14.8843	−	8.59344i	−0.727145	−	0.419817i	0.0902320	−	0.995921i	$-0.471239\pi$
$419$	−14.8843	−	8.59344i	−0.727145	−	0.419817i	−0.817377	+	0.576104i	$0.804572\pi$
$420$	0.125750	−	0.0303677i	0.00613598	−	0.00148179i
$421$	1.09539	+	1.89728i	0.0533862	+	0.0924676i	0.891483	−	0.453053i	$-0.149665\pi$
$421$	1.09539	+	1.89728i	0.0533862	+	0.0924676i	−0.838097	+	0.545521i	$0.816332\pi$
$422$	17.7869			0.865854
$423$	−7.50227	−	20.9583i	−0.364773	−	1.01903i
$424$		−	10.5837i		−	0.513991i
$425$	16.8217	+	21.9561i	0.815974	+	1.06503i
$426$	7.05565	+	15.2365i	0.341847	+	0.738211i
$427$	−0.350571	−	0.202402i	−0.0169653	−	0.00979492i
$428$	−10.0372	−	5.79496i	−0.485164	−	0.280110i
$429$	11.0420	+	8.73603i	0.533113	+	0.421780i
$430$	−4.35192	−	0.867323i	−0.209868	−	0.0418260i
$431$	−13.7317			−0.661433			−0.330716	−	0.943730i	$-0.607290\pi$
$431$	−13.7317			−0.661433			−0.330716	+	0.943730i	$0.607290\pi$
$432$	1.30480	+	5.02966i	0.0627771	+	0.241990i
$433$			12.0038i			0.576864i	0.957500	+	0.288432i	$0.0931340\pi$
$433$			12.0038i			0.576864i	−0.957500	+	0.288432i	$0.906866\pi$
$434$	−0.148980	+	0.0860137i	−0.00715127	+	0.00412879i
$435$	5.87573	+	6.17519i	0.281720	+	0.296078i
$436$	5.84968	+	3.37731i	0.280149	+	0.161744i
$437$	−4.56171	−	2.63370i	−0.218216	−	0.125987i
$438$	−19.8462	+	9.19029i	−0.948288	+	0.439129i
$439$	−9.30620	+	5.37294i	−0.444161	+	0.256436i	−0.705361	−	0.708848i	$-0.749215\pi$
$439$	−9.30620	+	5.37294i	−0.444161	+	0.256436i	0.261200	+	0.965285i	$0.415882\pi$
$440$	−7.14539	+	1.98581i	−0.340643	+	0.0946695i
$441$	13.5817	−	16.0124i	0.646748	−	0.762495i
$442$	−13.5586			−0.644917
$443$	−2.24739	−	3.89260i	−0.106777	−	0.184943i	0.807686	−	0.589613i	$-0.200720\pi$
$443$	−2.24739	−	3.89260i	−0.106777	−	0.184943i	−0.914463	+	0.404670i	$0.867386\pi$
$444$	2.34823	+	1.65357i	0.111442	+	0.0784748i
$445$	−6.06881	−	17.8999i	−0.287689	−	0.848535i
$446$	−9.45684	+	16.3797i	−0.447794	+	0.775603i
$447$	12.0444	−	17.1043i	0.569682	−	0.809005i
$448$	−0.0167009	−	0.0289269i	−0.000789045	−	0.00136667i
$449$		−	37.5452i		−	1.77187i	−0.463814	−	0.885933i	$-0.653519\pi$
$449$		−	37.5452i		−	1.77187i	0.463814	−	0.885933i	$-0.346481\pi$
$450$	−8.13595	+	12.6018i	−0.383532	+	0.594056i
$451$	14.7236	+	9.63390i	0.693305	+	0.453643i
$452$	−4.86304	−	8.42303i	−0.228738	−	0.396186i
$453$	−4.43109	+	2.05193i	−0.208191	+	0.0964080i
$454$	2.20257	−	3.81496i	0.103372	−	0.179045i
$455$	−0.173369	+	0.0587794i	−0.00812766	+	0.00275562i
$456$	7.54734	+	0.680527i	0.353437	+	0.0318686i
$457$	11.0581	+	19.1532i	0.517275	+	0.895947i	0.999799	+	0.0200640i	$0.00638701\pi$
$457$	11.0581	+	19.1532i	0.517275	+	0.895947i	−0.482523	+	0.875883i	$0.660280\pi$
$458$		−	25.3029i		−	1.18233i
$459$	7.66078	−	27.7048i	0.357575	−	1.29315i
$460$	−2.02337	−	1.77577i	−0.0943400	−	0.0827956i
$461$	−4.53374	−	7.85267i	−0.211157	−	0.365735i	0.740920	−	0.671594i	$-0.234390\pi$
$461$	−4.53374	−	7.85267i	−0.211157	−	0.365735i	−0.952077	+	0.305858i	$0.901057\pi$
$462$	0.119053	−	0.150479i	0.00553887	−	0.00700091i
$463$	−27.1358	−	15.6669i	−1.26111	−	0.728102i	−0.287820	−	0.957684i	$-0.592931\pi$
$463$	−27.1358	−	15.6669i	−1.26111	−	0.728102i	−0.973289	+	0.229582i	$0.926264\pi$
$464$	1.10043	−	1.90601i	0.0510863	−	0.0884841i
$465$	5.63963	−	19.1329i	0.261532	−	0.887266i
$466$	−8.18402	−	14.1751i	−0.379117	−	0.656650i
$467$	21.3678			0.988782			0.494391	−	0.869240i	$-0.335391\pi$
$467$	21.3678			0.988782			0.494391	+	0.869240i	$0.335391\pi$
$468$	−2.47810	−	6.92283i	−0.114550	−	0.320008i
$469$			0.106744i			0.00492900i
$470$	−16.2721	−	3.24296i	−0.750575	−	0.149587i
$471$	−13.2565	−	9.33488i	−0.610825	−	0.430129i
$472$	6.65531	−	11.5273i	0.306335	−	0.530589i
$473$	−5.87477	+	2.96789i	−0.270122	+	0.136464i
$474$	−5.30231	+	7.52980i	−0.243543	+	0.345855i
$475$	13.3043	+	17.3650i	0.610441	+	0.796760i
$476$			0.184775i			0.00846915i
$477$	−31.2391	−	5.67969i	−1.43034	−	0.260055i
$478$			28.8809i			1.32098i
$479$	−15.0074	−	25.9936i	−0.685707	−	1.18768i	−0.973214	−	0.229901i	$-0.926160\pi$
$479$	−15.0074	−	25.9936i	−0.685707	−	1.18768i	0.287507	−	0.957779i	$-0.407174\pi$
$480$	3.71496	+	1.09503i	0.169564	+	0.0499808i
$481$	−3.51965	−	2.03207i	−0.160482	−	0.0926545i
$482$	1.76919	−	3.06432i	0.0805843	−	0.139576i
$483$	0.0693711	+	0.00625504i	0.00315649	+	0.000284614i
$484$	−6.52683	+	8.85441i	−0.296674	+	0.402473i
$485$	−5.86075	+	6.67793i	−0.266123	+	0.303229i
$486$	15.5458	−	1.15212i	0.705173	−	0.0522611i
$487$			14.1627i			0.641775i	0.947117	+	0.320887i	$0.103981\pi$
$487$			14.1627i			0.641775i	−0.947117	+	0.320887i	$0.896019\pi$
$488$	−6.05960	−	10.4955i	−0.274305	−	0.475110i
$489$	−0.664221	+	7.36650i	−0.0300371	+	0.333125i
$490$	−5.02505	−	14.8213i	−0.227009	−	0.669558i
$491$	15.7138	−	27.2172i	0.709156	−	1.22829i	−0.256015	−	0.966673i	$-0.582410\pi$
$491$	15.7138	−	27.2172i	0.709156	−	1.22829i	0.965171	−	0.261621i	$-0.0842571\pi$
$492$	−3.86123	−	8.33822i	−0.174078	−	0.375916i
$493$	−10.5438	+	6.08746i	−0.474868	+	0.274165i
$494$	−10.7235			−0.482471
$495$	2.02680	+	22.1561i	0.0910979	+	0.995842i
$496$	−5.15023			−0.231252
$497$	−0.280423	+	0.161902i	−0.0125787	+	0.00726232i
$498$	−14.2719	+	20.2675i	−0.639539	+	0.908209i
$499$	−0.765415	+	1.32574i	−0.0342647	+	0.0593482i	−0.882649	−	0.470032i	$-0.844242\pi$
$499$	−0.765415	+	1.32574i	−0.0342647	+	0.0593482i	0.848385	+	0.529380i	$0.177576\pi$
$500$	4.93382	+	10.0328i	0.220647	+	0.448681i
$501$	−25.3968	−	17.8838i	−1.13465	−	0.798991i
$502$	−5.48534	−	9.50089i	−0.244823	−	0.424046i
$503$			1.56687i			0.0698631i	0.999390	+	0.0349315i	$0.0111213\pi$
$503$			1.56687i			0.0698631i	−0.999390	+	0.0349315i	$0.988879\pi$
$504$	−0.0943434	+	0.0337713i	−0.00420239	+	0.00150429i
$505$	5.15345	+	4.52283i	0.229326	+	0.201263i
$506$	−3.98680	−	0.222720i	−0.177235	−	0.00990113i
$507$	−5.08937	−	10.9904i	−0.226027	−	0.488099i
$508$	1.05849	−	1.83336i	0.0469631	−	0.0813424i
$509$	−2.74575	−	1.58526i	−0.121703	−	0.0702654i	0.437913	−	0.899018i	$-0.355718\pi$
$509$	−2.74575	−	1.58526i	−0.121703	−	0.0702654i	−0.559616	+	0.828752i	$0.689051\pi$
$510$	−14.7686	−	15.5213i	−0.653966	−	0.687296i
$511$	−0.210885	−	0.365263i	−0.00932900	−	0.0161583i
$512$		−	1.00000i		−	0.0441942i
$513$	6.05889	−	21.9116i	0.267506	−	0.967422i
$514$		−	8.35114i		−	0.368353i
$515$	30.4067	+	6.05995i	1.33988	+	0.267033i
$516$	3.42339	+	0.308680i	0.150706	+	0.0135889i
$517$	−21.9661	+	11.0971i	−0.966067	+	0.488049i
$518$	−0.0276928	+	0.0479653i	−0.00121675	+	0.00210748i
$519$	19.9659	−	9.24570i	0.876404	−	0.405841i
$520$	−5.37490	−	1.07120i	−0.235705	−	0.0469751i
$521$			7.59460i			0.332725i	0.986065	+	0.166363i	$0.0532023\pi$
$521$			7.59460i			0.332725i	−0.986065	+	0.166363i	$0.946798\pi$
$522$	−5.03525	−	4.27090i	−0.220387	−	0.186932i
$523$	24.7588			1.08263			0.541313	−	0.840821i	$-0.317927\pi$
$523$	24.7588			1.08263			0.541313	+	0.840821i	$0.317927\pi$
$524$	−8.80936	−	15.2583i	−0.384839	−	0.666560i
$525$	−0.256129	−	0.134440i	−0.0111784	−	0.00586745i
$526$	−0.829714	+	1.43711i	−0.0361773	+	0.0626609i
$527$	24.6734	+	14.2452i	1.07479	+	0.620531i
$528$	5.33930	−	2.11940i	0.232363	−	0.0922349i
$529$	10.7753	+	18.6633i	0.468490	+	0.811448i
$530$	−15.6106	+	17.7872i	−0.678081	+	0.772628i
$531$	−30.4527	−	25.8300i	−1.32153	−	1.12092i
$532$			0.146138i			0.00633588i
$533$	6.50150	+	11.2609i	0.281611	+	0.487765i
$534$	6.15201	+	13.2851i	0.266224	+	0.574903i
$535$	8.32131	+	24.5436i	0.359762	+	1.06111i
$536$	−1.59788	+	2.76761i	−0.0690179	+	0.119543i
$537$	−0.727341	+	8.06653i	−0.0313871	+	0.348096i
$538$	7.68629	+	13.3130i	0.331379	+	0.573966i
$539$	−19.4241	−	12.7095i	−0.836655	−	0.547439i
$540$	5.22570	−	10.3775i	0.224878	−	0.446576i
$541$			19.8803i			0.854721i	0.904081	+	0.427360i	$0.140556\pi$
$541$			19.8803i			0.854721i	−0.904081	+	0.427360i	$0.859444\pi$
$542$	−0.827626	−	1.43349i	−0.0355496	−	0.0615737i
$543$	17.5689	+	1.58415i	0.753955	+	0.0679824i
$544$	−2.76594	+	4.79074i	−0.118589	+	0.205401i
$545$	−4.84967	−	14.3040i	−0.207737	−	0.612717i
$546$	0.128673	−	0.0595852i	0.00550669	−	0.00255001i
$547$	6.18398	+	10.7110i	0.264408	+	0.457968i	0.967408	−	0.253222i	$-0.0814902\pi$
$547$	6.18398	+	10.7110i	0.264408	+	0.457968i	−0.703001	+	0.711189i	$0.748157\pi$
$548$	2.25203			0.0962019
$549$	−34.2306	+	12.2532i	−1.46093	+	0.522955i
$550$	14.9377	+	7.20180i	0.636945	+	0.307086i
$551$	−8.33904	+	4.81455i	−0.355255	+	0.205107i
$552$	1.70498	+	1.20061i	0.0725688	+	0.0511013i
$553$	−0.153805	−	0.0887994i	−0.00654045	−	0.00377613i
$554$	14.0349	+	8.10304i	0.596285	+	0.344265i
$555$	−1.50753	−	6.24257i	−0.0639911	−	0.264982i
$556$	5.26191	−	3.03797i	0.223155	−	0.128839i
$557$		−	34.9789i		−	1.48210i	−0.671448	−	0.741052i	$-0.734327\pi$
$557$		−	34.9789i		−	1.48210i	0.671448	−	0.741052i	$-0.265673\pi$
$558$	−2.76384	+	15.2015i	−0.117003	+	0.643530i
$559$	−4.86404			−0.205727
$560$	−0.0145981	+	0.0732484i	−0.000616884	+	0.00309531i
$561$	−31.4413	−	4.61469i	−1.32745	−	0.194832i
$562$	−22.1545	−	12.7909i	−0.934532	−	0.539552i
$563$	−0.151409	−	0.0874160i	−0.00638113	−	0.00368415i	0.496806	−	0.867862i	$-0.334506\pi$
$563$	−0.151409	−	0.0874160i	−0.00638113	−	0.00368415i	−0.503187	+	0.864177i	$0.667839\pi$
$564$	12.8002	+	1.15417i	0.538987	+	0.0485993i
$565$	−4.25074	+	21.3287i	−0.178830	+	0.897306i
$566$			4.23363i			0.177953i
$567$	0.0490510	+	0.296588i	0.00205995	+	0.0124555i
$568$	−9.69421			−0.406760
$569$	−4.26559	−	7.38822i	−0.178823	−	0.309730i	0.762655	−	0.646806i	$-0.223896\pi$
$569$	−4.26559	−	7.38822i	−0.178823	−	0.309730i	−0.941478	+	0.337076i	$0.890562\pi$
$570$	−11.6805	−	12.2758i	−0.489241	−	0.514175i
$571$	−39.5692	−	22.8453i	−1.65592	−	0.956046i	−0.974568	−	0.224090i	$-0.928059\pi$
$571$	−39.5692	−	22.8453i	−1.65592	−	0.956046i	−0.681352	−	0.731956i	$-0.738608\pi$
$572$	−7.25571	+	3.66552i	−0.303376	+	0.153263i
$573$	21.4075	−	9.91329i	0.894312	−	0.414134i
$574$	0.153463	−	0.0886016i	0.00640540	−	0.00369816i
$575$	0.781320	+	5.96878i	0.0325833	+	0.248916i
$576$	−2.95161	−	0.536644i	−0.122984	−	0.0223601i
$577$			2.96884i			0.123594i	0.998089	+	0.0617972i	$0.0196832\pi$
$577$			2.96884i			0.123594i	−0.998089	+	0.0617972i	$0.980317\pi$
$578$	11.7793	−	6.80081i	0.489956	−	0.282876i
$579$	17.0710	−	24.2424i	0.709445	−	1.00748i
$580$	−4.66070	+	1.58017i	−0.193525	+	0.0656132i
$581$	−0.413988	−	0.239016i	−0.0171751	−	0.00991605i
$582$	3.96249	−	5.62712i	0.164250	−	0.233252i
$583$	−1.95791	+	35.0476i	−0.0810885	+	1.45152i
$584$		−	12.6271i		−	0.522514i
$585$	−6.04616	+	15.2898i	−0.249978	+	0.632154i
$586$	23.4644			0.969305
$587$	13.2090	+	22.8787i	0.545194	+	0.944304i	0.998595	+	0.0529969i	$0.0168773\pi$
$587$	13.2090	+	22.8787i	0.545194	+	0.944304i	−0.453401	+	0.891307i	$0.649789\pi$
$588$	5.09394	+	11.0002i	0.210070	+	0.453642i
$589$	19.5141	+	11.2665i	0.804065	+	0.464227i
$590$	−28.1874	+	9.55674i	−1.16046	+	0.393445i
$591$	−3.19948	+	35.4837i	−0.131609	+	1.45960i
$592$	−1.43601	+	0.829079i	−0.0590195	+	0.0340749i
$593$			30.4298i			1.24960i	0.780784	+	0.624801i	$0.214820\pi$
$593$			30.4298i			1.24960i	−0.780784	+	0.624801i	$0.785180\pi$
$594$	−3.39033	−	16.8969i	−0.139107	−	0.693289i
$595$	0.272536	−	0.310537i	0.0111729	−	0.0127308i
$596$	6.03894	+	10.4598i	0.247365	+	0.428448i
$597$	27.6133	+	2.48983i	1.13014	+	0.101902i
$598$	−2.55552	−	1.47543i	−0.104503	−	0.0603348i
$599$	−7.57582	−	4.37390i	−0.309539	−	0.178713i	0.337181	−	0.941440i	$-0.390527\pi$
$599$	−7.57582	−	4.37390i	−0.309539	−	0.178713i	−0.646720	+	0.762727i	$0.723860\pi$
$600$	−4.62831	−	7.31975i	−0.188950	−	0.298827i
$601$	39.2835	−	22.6803i	1.60241	−	0.925151i	0.611404	−	0.791319i	$-0.290605\pi$
$601$	39.2835	−	22.6803i	1.60241	−	0.925151i	0.991004	−	0.133832i	$-0.0427282\pi$
$602$			0.0662865i			0.00270164i
$603$	7.31142	+	6.20154i	0.297744	+	0.252546i
$604$		−	2.81928i		−	0.114715i
$605$	24.0290	−	5.25407i	0.976919	−	0.213608i
$606$	−4.34254	−	3.05791i	−0.176403	−	0.124219i
$607$	−17.6685	+	30.6028i	−0.717143	+	1.24213i	0.244984	+	0.969527i	$0.421217\pi$
$607$	−17.6685	+	30.6028i	−0.717143	+	1.24213i	−0.962127	+	0.272601i	$0.912116\pi$
$608$	−2.18757	+	3.78898i	−0.0887176	+	0.153663i
$609$	0.0733096	−	0.104107i	0.00297065	−	0.00421862i
$610$	−5.29664	+	26.5767i	−0.214455	+	1.07606i
$611$	−18.1869			−0.735764
$612$	12.6561	+	10.7349i	0.511592	+	0.433932i
$613$	−4.75354			−0.191993			−0.0959967	−	0.995382i	$-0.530604\pi$
$613$	−4.75354			−0.191993			−0.0959967	+	0.995382i	$0.530604\pi$
$614$	−1.52300	+	0.879306i	−0.0614634	+	0.0354859i
$615$	−5.80931	+	19.7086i	−0.234254	+	0.794726i
$616$	0.0499533	+	0.0988798i	0.00201267	+	0.00398398i
$617$	5.28354	−	9.15136i	0.212707	−	0.368420i	−0.739854	−	0.672768i	$-0.765105\pi$
$617$	5.28354	−	9.15136i	0.212707	−	0.368420i	0.952561	+	0.304348i	$0.0984386\pi$
$618$	−23.9191	−	2.15673i	−0.962167	−	0.0867564i
$619$	12.5082	+	21.6648i	0.502747	+	0.870783i	0.999995	+	0.00317489i	$0.00101060\pi$
$619$	12.5082	+	21.6648i	0.502747	+	0.870783i	−0.497248	+	0.867608i	$0.665656\pi$
$620$	8.65558	+	7.59640i	0.347616	+	0.305079i
$621$	4.45870	−	4.38815i	0.178921	−	0.176090i
$622$	20.6776			0.829097
$623$	−0.244509	+	0.141167i	−0.00979603	+	0.00565574i
$624$	4.22810	+	0.381238i	0.169260	+	0.0152618i
$625$	6.50614	−	24.1386i	0.260246	−	0.965542i
$626$	7.07575	−	12.2556i	0.282804	−	0.489831i
$627$	−24.8668	−	3.64974i	−0.993086	−	0.145757i
$628$	8.10669	−	4.68040i	0.323492	−	0.186768i
$629$	9.17272			0.365740
$630$	0.208367	+	0.0823963i	0.00830153	+	0.00328275i
$631$	27.0452			1.07665			0.538326	−	0.842736i	$-0.319057\pi$
$631$	27.0452			1.07665			0.538326	+	0.842736i	$0.319057\pi$
$632$	−2.65851	−	4.60468i	−0.105750	−	0.183164i
$633$	25.1893	+	17.7377i	1.00118	+	0.705009i
$634$	26.1671	+	15.1076i	1.03923	+	0.599998i
$635$	−4.48307	+	1.51995i	−0.177905	+	0.0603174i
$636$	10.5544	−	14.9883i	0.418510	−	0.594326i
$637$	−8.57713	−	14.8560i	−0.339838	−	0.588617i
$638$	−3.99664	+	6.10810i	−0.158229	+	0.241822i
$639$	−5.20234	+	28.6136i	−0.205801	+	1.13193i
$640$	−1.47496	+	1.68062i	−0.0583030	+	0.0664323i
$641$	15.5143	−	8.95716i	0.612777	−	0.353787i	−0.161275	−	0.986910i	$-0.551561\pi$
$641$	15.5143	−	8.95716i	0.612777	−	0.353787i	0.774051	+	0.633123i	$0.218227\pi$
$642$	−8.43538	−	18.2160i	−0.332918	−	0.718928i
$643$	−16.5825	−	9.57390i	−0.653949	−	0.377558i	0.136018	−	0.990706i	$-0.456569\pi$
$643$	−16.5825	−	9.57390i	−0.653949	−	0.377558i	−0.789968	+	0.613149i	$0.789903\pi$
$644$	−0.0201070	+	0.0348263i	−0.000792325	+	0.00137235i
$645$	−5.29813	−	5.56815i	−0.208614	−	0.219246i
$646$	20.9602	−	12.1014i	0.824666	−	0.476121i
$647$	4.38760			0.172494			0.0862471	−	0.996274i	$-0.472513\pi$
$647$	4.38760			0.172494			0.0862471	+	0.996274i	$0.472513\pi$
$648$	−3.16793	+	8.42403i	−0.124448	+	0.330927i
$649$	−24.1713	+	36.9411i	−0.948805	+	1.45007i
$650$	7.45318	+	9.72805i	0.292338	+	0.381565i
$651$	−0.296756	−	0.0267578i	−0.0116308	−	0.00104872i
$652$	−3.69819	−	2.13515i	−0.144832	−	0.0836190i
$653$	13.2315	−	22.9176i	0.517788	−	0.896835i	−0.481999	−	0.876172i	$-0.660089\pi$
$653$	13.2315	−	22.9176i	0.517788	−	0.896835i	0.999787	−	0.0206627i	$-0.00657762\pi$
$654$	4.91616	+	10.6163i	0.192237	+	0.415131i
$655$	−7.70018	+	38.6368i	−0.300871	+	1.50967i
$656$	5.30519			0.207133
$657$	−37.2704	−	6.77627i	−1.45406	−	0.264367i
$658$			0.247849i			0.00966215i
$659$	−21.0172	−	36.4028i	−0.818713	−	1.41805i	−0.906631	−	0.421924i	$-0.861355\pi$
$659$	−21.0172	−	36.4028i	−0.818713	−	1.41805i	0.0879186	−	0.996128i	$-0.471978\pi$
$660$	−12.0994	−	4.31337i	−0.470967	−	0.167898i
$661$	0.108175	−	0.187364i	0.00420751	−	0.00728762i	−0.863914	−	0.503639i	$-0.831994\pi$
$661$	0.108175	−	0.187364i	0.00420751	−	0.00728762i	0.868121	+	0.496352i	$0.165327\pi$
$662$	−3.09402	−	1.78633i	−0.120253	−	0.0694278i
$663$	−19.2013	−	13.5211i	−0.745715	−	0.525115i
$664$	−7.15576	−	12.3941i	−0.277697	−	0.480986i
$665$	0.215548	−	0.245602i	0.00835859	−	0.00952405i
$666$	1.67650	+	4.68346i	0.0649629	+	0.181480i
$667$	−2.64971			−0.102597
$668$	15.5309	−	8.96674i	0.600907	−	0.346934i
$669$	−29.7268	+	13.7658i	−1.14931	+	0.532216i
$670$	6.76755	−	2.29449i	0.261453	−	0.0886438i
$671$	18.1245	+	35.8765i	0.699690	+	1.38500i
$672$	0.00519547	−	0.0576200i	0.000200420	−	0.00222274i
$673$	−19.8387	−	34.3616i	−0.764726	−	1.32454i	−0.940391	−	0.340094i	$-0.889541\pi$
$673$	−19.8387	−	34.3616i	−0.764726	−	1.32454i	0.175665	−	0.984450i	$-0.443792\pi$
$674$		−	32.6123i		−	1.25618i
$675$	−24.0888	+	9.73289i	−0.927179	+	0.374619i
$676$	6.99261			0.268946
$677$	4.77325	−	2.75584i	0.183451	−	0.105916i	−0.405462	−	0.914112i	$-0.632889\pi$
$677$	4.77325	−	2.75584i	0.183451	−	0.105916i	0.588913	+	0.808196i	$0.299556\pi$
$678$	1.51283	−	16.7780i	0.0581001	−	0.644355i
$679$	0.114941	+	0.0663610i	0.00441102	+	0.00254670i
$680$	11.7147	−	3.97176i	0.449237	−	0.152310i
$681$	6.92360	−	3.20615i	0.265313	−	0.122860i
$682$	17.0548	+	0.952755i	0.653061	+	0.0364829i
$683$	22.8308			0.873597			0.436798	−	0.899559i	$-0.356112\pi$
$683$	22.8308			0.873597			0.436798	+	0.899559i	$0.356112\pi$
$684$	10.0097	+	8.49019i	0.382729	+	0.324630i
$685$	−3.78480	−	3.32166i	−0.144610	−	0.126914i
$686$	−0.404944	+	0.233795i	−0.0154608	+	0.00892632i
$687$	25.2329	−	35.8332i	0.962695	−	1.36712i
$688$	−0.992257	+	1.71864i	−0.0378295	+	0.0655225i
$689$	−12.9704	+	22.4653i	−0.494131	+	0.855860i
$690$	−1.09457	−	4.53255i	−0.0416698	−	0.172551i
$691$	19.6037	+	33.9547i	0.745761	+	1.29170i	0.949838	+	0.312742i	$0.101247\pi$
$691$	19.6037	+	33.9547i	0.745761	+	1.29170i	−0.204077	+	0.978955i	$0.565419\pi$
$692$			12.7033i			0.482906i
$693$	0.318662	−	0.0943795i	0.0121050	−	0.00358518i
$694$	−23.0175			−0.873733
$695$	−13.3242	−	2.65546i	−0.505415	−	0.100727i
$696$	3.45913	−	1.60184i	0.131118	−	0.0607175i
$697$	−25.4158	−	14.6738i	−0.962692	−	0.555810i
$698$	−8.36523	+	14.4890i	−0.316628	+	0.548417i
$699$	2.54595	−	28.2357i	0.0962967	−	1.06797i
$700$	0.132573	−	0.101571i	0.00501077	−	0.00383902i
$701$	41.5142			1.56797			0.783986	−	0.620779i	$-0.213184\pi$
$701$	41.5142			1.56797			0.783986	+	0.620779i	$0.213184\pi$
$702$	3.39425	−	12.2751i	0.128108	−	0.463295i
$703$	7.25467			0.273615
$704$	−0.184993	+	3.31146i	−0.00697218	+	0.124805i
$705$	−19.8100	−	20.8196i	−0.746087	−	0.784112i
$706$	−22.7909	−	13.1583i	−0.857745	−	0.495220i
$707$	0.0512118	−	0.0887014i	0.00192602	−	0.00333596i
$708$	20.9204	−	9.68775i	0.786239	−	0.364088i
$709$	−21.6347	−	37.4724i	−0.812509	−	1.40731i	−0.911103	−	0.412179i	$-0.864768\pi$
$709$	−21.6347	−	37.4724i	−0.812509	−	1.40731i	0.0985934	−	0.995128i	$-0.468566\pi$
$710$	16.2923	+	14.2986i	0.611439	+	0.536617i
$711$	−15.0179	+	5.37583i	−0.563215	+	0.201609i
$712$	−8.45264			−0.316776
$713$	3.10029	+	5.36985i	0.116107	+	0.201103i
$714$	−0.184263	+	0.261672i	−0.00689589	+	0.00979284i
$715$	17.6006	+	4.54154i	0.658225	+	0.169844i
$716$	−4.04963	−	2.33805i	−0.151342	−	0.0873772i
$717$	−28.8009	+	40.9002i	−1.07559	+	1.52745i
$718$	11.3797	−	6.57010i	0.424688	−	0.245194i
$719$		−	27.8648i		−	1.03918i	−0.854416	−	0.519590i	$-0.826085\pi$
$719$		−	27.8648i		−	1.03918i	0.854416	−	0.519590i	$-0.173915\pi$
$720$	4.16901	+	5.25541i	0.155370	+	0.195858i
$721$		−	0.463141i		−	0.0172483i
$722$	0.122834	−	0.0709185i	0.00457143	−	0.00263931i
$723$	5.56131	−	2.57531i	0.206827	−	0.0957766i
$724$	−5.09229	+	8.82010i	−0.189253	+	0.327796i
$725$	10.1636	+	4.21869i	0.377465	+	0.156678i
$726$	−18.0730	+	6.03057i	−0.670751	+	0.223815i
$727$	−28.2059	+	16.2847i	−1.04610	+	0.603966i	−0.921555	−	0.388248i	$-0.873081\pi$
$727$	−28.2059	+	16.2847i	−1.04610	+	0.603966i	−0.124545	+	0.992214i	$0.539747\pi$
$728$			0.0818680i			0.00303423i
$729$	23.1644	+	13.8712i	0.857941	+	0.513748i
$730$	−18.6245	+	21.2214i	−0.689325	+	0.785440i
$731$	9.50730	−	5.48904i	0.351640	−	0.203020i
$732$	1.88507	−	20.9063i	0.0696742	−	0.772717i
$733$	12.4198	−	21.5117i	0.458735	−	0.794553i	−0.540159	−	0.841563i	$-0.681636\pi$
$733$	12.4198	−	21.5117i	0.458735	−	0.794553i	0.998894	+	0.0470101i	$0.0149693\pi$
$734$	−9.31270	+	16.1301i	−0.343738	+	0.595371i
$735$	7.66395	−	26.0006i	0.282689	−	0.959045i
$736$	−1.04264	+	0.601970i	−0.0384323	+	0.0221889i
$737$	5.80331	−	8.86924i	0.213768	−	0.326703i
$738$	2.84699	−	15.6589i	0.104799	−	0.576410i
$739$			24.3252i			0.894817i	0.894330	+	0.447409i	$0.147653\pi$
$739$			24.3252i			0.894817i	−0.894330	+	0.447409i	$0.852347\pi$
$740$	3.63624	+	0.724690i	0.133671	+	0.0266401i
$741$	−15.1862	−	10.6938i	−0.557879	−	0.392845i
$742$	0.306154	+	0.176758i	0.0112393	+	0.00648900i
$743$	−5.62426	−	3.24717i	−0.206334	−	0.119127i	0.393272	−	0.919422i	$-0.371343\pi$
$743$	−5.62426	−	3.24717i	−0.206334	−	0.119127i	−0.599607	+	0.800295i	$0.704676\pi$
$744$	−7.29358	−	5.13597i	−0.267396	−	0.188294i
$745$	5.27858	−	26.4861i	0.193392	−	0.970375i
$746$			3.99565i			0.146291i
$747$	−40.4228	+	14.4698i	−1.47899	+	0.529422i
$748$	10.0455	−	15.3527i	0.367301	−	0.561350i
$749$	0.335260	−	0.193563i	0.0122501	−	0.00707262i
$750$	−3.01792	+	19.1283i	−0.110199	+	0.698467i
$751$	−12.5566	+	21.7487i	−0.458198	+	0.793623i	−0.998866	−	0.0476134i	$-0.984838\pi$
$751$	−12.5566	+	21.7487i	−0.458198	+	0.793623i	0.540667	+	0.841236i	$0.318172\pi$
$752$	−3.71010	+	6.42609i	−0.135294	+	0.234335i
$753$	1.70643	−	18.9250i	0.0621856	−	0.689666i
$754$	−4.67162	+	2.69716i	−0.170130	+	0.0982248i
$755$	−4.15833	+	4.73813i	−0.151337	+	0.172438i
$756$	−0.167284	−	0.0462564i	−0.00608405	−	0.00168233i
$757$		−	29.1880i		−	1.06086i	−0.847730	−	0.530428i	$-0.822031\pi$
$757$		−	29.1880i		−	1.06086i	0.847730	−	0.530428i	$-0.177969\pi$
$758$	28.7480	−	16.5977i	1.04418	−	0.602855i
$759$	−5.42388	−	4.29118i	−0.196874	−	0.155760i
$760$	9.26508	−	3.14125i	0.336080	−	0.113945i
$761$	1.22761	−	2.12628i	0.0445008	−	0.0770776i	−0.842917	−	0.538043i	$-0.819164\pi$
$761$	1.22761	−	2.12628i	0.0445008	−	0.0770776i	0.887418	+	0.460966i	$0.152497\pi$
$762$	3.32729	−	1.54079i	0.120535	−	0.0558169i
$763$	−0.195390	+	0.112809i	−0.00707360	+	0.00408395i
$764$			13.6205i			0.492773i
$765$	−5.43652	−	36.7085i	−0.196558	−	1.32720i
$766$		−	0.662649i		−	0.0239425i
$767$	−28.2535	+	16.3122i	−1.02017	+	0.588998i
$768$	0.997231	−	1.41617i	0.0359845	−	0.0511015i
$769$	26.1139	+	15.0769i	0.941692	+	0.543686i	0.890490	−	0.455002i	$-0.150362\pi$
$769$	26.1139	+	15.0769i	0.941692	+	0.543686i	0.0512014	+	0.998688i	$0.483695\pi$
$770$	0.0618916	−	0.239859i	0.00223042	−	0.00864391i
$771$	8.32802	−	11.8266i	0.299926	−	0.425925i
$772$	8.55917	+	14.8249i	0.308051	+	0.533561i
$773$	33.5150			1.20545			0.602725	−	0.797949i	$-0.294082\pi$
$773$	33.5150			1.20545			0.602725	+	0.797949i	$0.294082\pi$
$774$	4.54027	+	3.85106i	0.163197	+	0.138423i
$775$	−3.34234	−	25.5333i	−0.120060	−	0.917184i
$776$	1.98674	+	3.44114i	0.0713200	+	0.123530i
$777$	−0.0870502	+	0.0403108i	−0.00312291	+	0.00144614i
$778$	−13.5075	+	23.3956i	−0.484266	+	0.838773i
$779$	−20.1013	−	11.6055i	−0.720202	−	0.415809i
$780$	−6.54352	−	6.87701i	−0.234296	−	0.246236i
$781$	32.1020	+	1.79336i	1.14870	+	0.0641714i
$782$	6.66005			0.238163
$783$	−2.87168	−	11.0696i	−0.102626	−	0.395596i
$784$	−6.99888			−0.249960
$785$	−20.5277	−	4.09109i	−0.732664	−	0.146017i
$786$	2.74049	−	30.3932i	0.0977500	−	1.08409i
$787$	4.14163	−	7.17351i	0.147633	−	0.255708i	−0.782719	−	0.622375i	$-0.786168\pi$
$787$	4.14163	−	7.17351i	0.147633	−	0.255708i	0.930352	+	0.366667i	$0.119501\pi$
$788$	−17.8138	−	10.2848i	−0.634591	−	0.366381i
$789$	−2.60814	+	1.20777i	−0.0928523	+	0.0429976i
$790$	−2.32378	+	11.6599i	−0.0826764	+	0.414842i
$791$	0.324869			0.0115510
$792$	9.67487	+	2.32310i	0.343782	+	0.0825478i
$793$			29.7041i			1.05482i
$794$	−14.4648	−	25.0538i	−0.513338	−	0.889127i
$795$	−39.8452	+	9.62230i	−1.41316	+	0.341268i
$796$	−8.00362	+	13.8627i	−0.283681	+	0.491349i
$797$	−13.3468	+	23.1173i	−0.472767	+	0.818857i	−0.999514	−	0.0311652i	$-0.990078\pi$
$797$	−13.3468	+	23.1173i	−0.472767	+	0.818857i	0.526747	+	0.850022i	$0.323412\pi$
$798$	−0.145733	+	0.206956i	−0.00515890	+	0.00732615i
$799$	35.5483	−	20.5238i	1.25761	−	0.726080i
$800$	4.95771	−	0.648969i	0.175281	−	0.0229445i
$801$	−4.53606	+	24.9489i	−0.160274	+	0.881527i
$802$	5.21186			0.184037
$803$	−2.33593	+	41.8142i	−0.0824331	+	1.47559i
$804$	−5.02281	+	2.32594i	−0.177141	+	0.0820297i
$805$	0.0851596	−	0.0288727i	0.00300148	−	0.00101763i
$806$	10.9320	+	6.31160i	0.385064	+	0.222317i
$807$	−2.39111	+	26.5185i	−0.0841712	+	0.933496i
$808$	2.65558	−	1.53320i	0.0934230	−	0.0539378i
$809$	−44.9884			−1.58171			−0.790854	−	0.612005i	$-0.790363\pi$
$809$	−44.9884			−1.58171			−0.790854	+	0.612005i	$0.790363\pi$
$810$	17.7492	−	9.48502i	0.623644	−	0.333270i
$811$			37.4501i			1.31505i	0.753432	+	0.657526i	$0.228397\pi$
$811$			37.4501i			1.31505i	−0.753432	+	0.657526i	$0.771603\pi$
$812$	0.0367566	+	0.0636642i	0.00128990	+	0.00223418i
$813$	0.257465	−	2.85540i	0.00902968	−	0.100143i
$814$	4.90866	−	2.47981i	0.172048	−	0.0869174i
$815$	3.06599	+	9.04308i	0.107397	+	0.316765i
$816$	−8.69451	+	4.02621i	−0.304369	+	0.140946i
$817$	7.51929	−	4.34126i	0.263067	−	0.151882i
$818$	21.7588			0.760780
$819$	0.241643	+	0.0439339i	0.00844367	+	0.00153518i
$820$	−8.91601	−	7.82496i	−0.311360	−	0.273259i
$821$	−3.55867	−	6.16380i	−0.124198	−	0.215118i	0.797221	−	0.603688i	$-0.206303\pi$
$821$	−3.55867	−	6.16380i	−0.124198	−	0.215118i	−0.921419	+	0.388570i	$0.872969\pi$
$822$	3.18925	+	2.24579i	0.111238	+	0.0783310i
$823$	30.1877	+	17.4289i	1.05228	+	0.607532i	0.923286	−	0.384113i	$-0.125493\pi$
$823$	30.1877	+	17.4289i	1.05228	+	0.607532i	0.128991	+	0.991646i	$0.458826\pi$
$824$	6.93286	−	12.0081i	0.241518	−	0.418321i
$825$	13.9724	+	25.0953i	0.486456	+	0.873705i
$826$	0.222300	+	0.385035i	0.00773480	+	0.0133971i
$827$			28.3059i			0.984291i	0.870513	+	0.492146i	$0.163787\pi$
$827$			28.3059i			0.984291i	−0.870513	+	0.492146i	$0.836213\pi$
$828$	1.21726	+	3.40052i	0.0423026	+	0.118176i
$829$	30.4567			1.05780			0.528902	−	0.848683i	$-0.322604\pi$
$829$	30.4567			1.05780			0.528902	+	0.848683i	$0.322604\pi$
$830$	−6.25478	+	31.3843i	−0.217107	+	1.08937i
$831$	11.7951	+	25.4713i	0.409168	+	0.883589i
$832$	−1.22550	+	2.12263i	−0.0424865	+	0.0735889i
$833$	33.5299	+	19.3585i	1.16174	+	0.670731i
$834$	10.4813	+	0.945076i	0.362938	+	0.0327253i
$835$	−39.3271	−	7.83774i	−1.36097	−	0.271236i
$836$	7.94499	−	12.1424i	0.274783	−	0.419953i
$837$	−19.0734	+	18.7716i	−0.659275	+	0.648843i
$838$	17.1869			0.593711
$839$	5.88181	−	3.39586i	0.203063	−	0.117238i	−0.395021	−	0.918672i	$-0.629263\pi$
$839$	5.88181	−	3.39586i	0.203063	−	0.117238i	0.598083	+	0.801434i	$0.295929\pi$
$840$	−0.0937190	+	0.0891742i	−0.00323361	+	0.00307680i
$841$	12.0781	−	20.9199i	0.416486	−	0.721375i
$842$	−1.89728	−	1.09539i	−0.0653844	−	0.0377497i
$843$	−18.6190	−	40.2072i	−0.641272	−	1.38481i
$844$	−15.4039	+	8.89346i	−0.530225	+	0.306126i
$845$	−11.7519	−	10.3138i	−0.404278	−	0.354807i
$846$	16.9763	+	14.3993i	0.583658	+	0.495058i
$847$	−0.147126	−	0.336678i	−0.00505532	−	0.0115684i
$848$	5.29186	+	9.16578i	0.181723	+	0.314754i
$849$	−4.22191	+	5.99553i	−0.144895	+	0.205766i
$850$	−25.5461	−	10.6037i	−0.876224	−	0.363702i
$851$	1.72887	+	0.998162i	0.0592648	+	0.0342166i
$852$	−13.7286	−	9.66737i	−0.470335	−	0.331199i
$853$	−9.05391	−	15.6818i	−0.310000	−	0.536936i	0.668362	−	0.743836i	$-0.266996\pi$
$853$	−9.05391	−	15.6818i	−0.310000	−	0.536936i	−0.978362	+	0.206900i	$0.933662\pi$
$854$	0.404804			0.0138521
$855$	−4.29972	−	29.0327i	−0.147047	−	0.992896i
$856$	11.5899			0.396135
$857$	25.9306	−	14.9710i	0.885772	−	0.511401i	0.0132147	−	0.999913i	$-0.495793\pi$
$857$	25.9306	−	14.9710i	0.885772	−	0.511401i	0.872557	+	0.488512i	$0.162460\pi$
$858$	−13.9307	−	2.04462i	−0.475585	−	0.0698023i
$859$	−21.6492	+	37.4976i	−0.738663	+	1.27940i	0.214435	+	0.976738i	$0.431209\pi$
$859$	−21.6492	+	37.4976i	−0.738663	+	1.27940i	−0.953098	+	0.302663i	$0.902124\pi$
$860$	4.20254	−	1.42484i	0.143305	−	0.0485866i
$861$	0.305685	+	0.0275629i	0.0104177	+	0.000939342i
$862$	11.8920	−	6.86585i	0.405043	−	0.233852i
$863$	20.3451			0.692554			0.346277	−	0.938132i	$-0.387446\pi$
$863$	20.3451			0.692554			0.346277	+	0.938132i	$0.387446\pi$
$864$	−3.64482	−	3.70342i	−0.123999	−	0.125993i
$865$	18.7368	−	21.3494i	0.637072	−	0.725900i
$866$	−6.00189	−	10.3956i	−0.203952	−	0.353256i
$867$	23.4635	+	2.11565i	0.796862	+	0.0718513i
$868$	0.0860137	−	0.148980i	0.00291949	−	0.00505671i
$869$	7.95173	+	15.7400i	0.269744	+	0.533944i
$870$	−8.17613	−	2.41000i	−0.277197	−	0.0817068i
$871$	6.78341	−	3.91640i	0.229847	−	0.132702i
$872$	−6.75462			−0.228740
$873$	11.2231	−	4.01743i	0.379844	−	0.135969i
$874$	5.26741			0.178173
$875$	−0.372618	−	0.0248373i	−0.0125968	−	0.000839655i
$876$	12.5922	−	17.8821i	0.425450	−	0.604181i
$877$	15.4313	−	26.7279i	0.521079	−	0.902535i	−0.478620	−	0.878022i	$-0.658863\pi$
$877$	15.4313	−	26.7279i	0.521079	−	0.902535i	0.999699	−	0.0245135i	$-0.00780366\pi$
$878$	5.37294	−	9.30620i	0.181328	−	0.314069i
$879$	33.2295	+	23.3994i	1.12080	+	0.789243i
$880$	5.19519	−	5.29245i	0.175130	−	0.178409i
$881$			21.5627i			0.726467i	0.931698	+	0.363234i	$0.118327\pi$
$881$			21.5627i			0.726467i	−0.931698	+	0.363234i	$0.881673\pi$
$882$	−3.75591	+	20.6580i	−0.126468	+	0.695591i
$883$			3.41164i			0.114811i	0.998351	+	0.0574054i	$0.0182828\pi$
$883$			3.41164i			0.114811i	−0.998351	+	0.0574054i	$0.981717\pi$
$884$	11.7421	−	6.77931i	0.394930	−	0.228013i
$885$	−49.4484	−	14.5755i	−1.66219	−	0.489949i
$886$	3.89260	+	2.24739i	0.130774	+	0.0755026i
$887$	−33.4690	−	19.3233i	−1.12378	−	0.648813i	−0.181415	−	0.983407i	$-0.558068\pi$
$887$	−33.4690	−	19.3233i	−1.12378	−	0.648813i	−0.942363	+	0.334593i	$0.891401\pi$
$888$	−2.86041	−	0.257917i	−0.0959891	−	0.00865512i
$889$	0.0353557	+	0.0612378i	0.00118579	+	0.00205385i
$890$	14.2057	+	12.4673i	0.476175	+	0.417906i
$891$	12.0489	−	27.3098i	0.403652	−	0.914913i
$892$		−	18.9137i		−	0.633277i
$893$	28.1150	−	16.2322i	0.940833	−	0.543190i
$894$	−1.87864	+	20.8350i	−0.0628312	+	0.696826i
$895$	3.35734	+	9.90243i	0.112224	+	0.331002i
$896$	0.0289269	+	0.0167009i	0.000966379	+	0.000557939i
$897$	−2.14770	−	4.63790i	−0.0717095	−	0.154855i
$898$	18.7726	+	32.5151i	0.626449	+	1.08504i
$899$	11.3350			0.378042
$900$	0.745016	−	14.9815i	0.0248339	−	0.499383i
$901$		−	58.5478i		−	1.95051i
$902$	−17.5679	−	0.981421i	−0.584948	−	0.0326777i
$903$	−0.0661030	+	0.0938728i	−0.00219977	+	0.00312389i
$904$	8.42303	+	4.86304i	0.280146	+	0.161742i
$905$	21.5675	−	7.31230i	0.716929	−	0.243069i
$906$	2.81147	−	3.99257i	0.0934049	−	0.132644i
$907$	2.78442	−	1.60758i	0.0924550	−	0.0533789i	−0.453060	−	0.891480i	$-0.649668\pi$
$907$	2.78442	−	1.60758i	0.0924550	−	0.0533789i	0.545515	+	0.838101i	$0.316334\pi$
$908$			4.40514i			0.146190i
$909$	−3.10031	−	8.66102i	−0.102831	−	0.287268i
$910$	0.120752	−	0.137589i	0.00400290	−	0.00456103i
$911$	−0.964207	+	0.556685i	−0.0319456	+	0.0184438i	−0.515888	−	0.856656i	$-0.672538\pi$
$911$	−0.964207	+	0.556685i	−0.0319456	+	0.0184438i	0.483942	+	0.875100i	$0.339205\pi$
$912$	−6.87645	+	3.18432i	−0.227702	+	0.105443i
$913$	21.4032	+	42.3665i	0.708343	+	1.40213i
$914$	−19.1532	−	11.0581i	−0.633530	−	0.365769i
$915$	−34.0040	+	32.3551i	−1.12414	+	1.06963i
$916$	12.6515	+	21.9130i	0.418016	+	0.724026i
$917$	0.588498			0.0194339
$918$	7.21797	+	27.8235i	0.238228	+	0.918311i
$919$		−	7.49883i		−	0.247363i	−0.992322	−	0.123682i	$-0.960530\pi$
$919$		−	7.49883i		−	0.247363i	0.992322	−	0.123682i	$-0.0394702\pi$
$920$	2.64017	+	0.526177i	0.0870439	+	0.0173475i
$921$	−3.03370	−	0.273542i	−0.0999638	−	0.00901351i
$922$	7.85267	+	4.53374i	0.258614	+	0.149311i
$923$	20.5772	+	11.8802i	0.677307	+	0.391043i
$924$	−0.0278639	+	0.189845i	−0.000916654	+	0.00624545i
$925$	−5.04225	−	6.58125i	−0.165788	−	0.216390i
$926$	31.3338			1.02969
$927$	−31.7227	−	26.9072i	−1.04191	−	0.883747i
$928$			2.20087i			0.0722470i
$929$	0.801934	−	0.462997i	0.0263106	−	0.0151904i	−0.486787	−	0.873521i	$-0.661831\pi$
$929$	0.801934	−	0.462997i	0.0263106	−	0.0151904i	0.513098	+	0.858330i	$0.328498\pi$
$930$	4.68238	+	19.3894i	0.153541	+	0.635803i
$931$	26.5186	+	15.3105i	0.869113	+	0.501783i
$932$	14.1751	+	8.18402i	0.464322	+	0.268076i
$933$	29.2830	+	20.6204i	0.958681	+	0.675080i
$934$	−18.5050	+	10.6839i	−0.605503	+	0.349587i
$935$	−39.5274	+	10.9852i	−1.29268	+	0.359255i
$936$	5.60752	+	4.75629i	0.183287	+	0.155464i
$937$	24.5580			0.802274			0.401137	−	0.916018i	$-0.368615\pi$
$937$	24.5580			0.802274			0.401137	+	0.916018i	$0.368615\pi$
$938$	−0.0533722	−	0.0924434i	−0.00174267	−	0.00301838i
$939$	22.2421	−	10.2998i	0.725843	−	0.336120i
$940$	15.7135	−	5.32755i	0.512518	−	0.173765i
$941$	−24.6804	+	42.7477i	−0.804558	+	1.39354i	0.112031	+	0.993705i	$0.464264\pi$
$941$	−24.6804	+	42.7477i	−0.804558	+	1.39354i	−0.916589	+	0.399831i	$0.869069\pi$
$942$	16.1479	+	1.45602i	0.526126	+	0.0474396i
$943$	−3.19357	−	5.53142i	−0.103997	−	0.180128i
$944$			13.3106i			0.433224i
$945$	0.212914	+	0.324477i	0.00692609	+	0.0105552i
$946$	3.60376	−	5.50765i	0.117168	−	0.179069i
$947$	2.00892	+	3.47955i	0.0652811	+	0.113070i	0.896819	−	0.442398i	$-0.145872\pi$
$947$	2.00892	+	3.47955i	0.0652811	+	0.113070i	−0.831538	+	0.555469i	$0.812539\pi$
$948$	0.827032	−	9.17215i	0.0268608	−	0.297898i
$949$	−15.4745	+	26.8027i	−0.502325	+	0.870052i
$950$	−20.2043	−	8.38639i	−0.655515	−	0.272090i
$951$	21.9912	+	47.4894i	0.713114	+	1.53995i
$952$	−0.0923875	−	0.160020i	−0.00299430	−	0.00518627i
$953$		−	16.4299i		−	0.532218i	−0.963943	−	0.266109i	$-0.914262\pi$
$953$		−	16.4299i		−	0.532218i	0.963943	−	0.266109i	$-0.0857381\pi$
$954$	29.8937	−	10.7008i	0.967843	−	0.346450i
$955$	20.0897	−	22.8909i	0.650089	−	0.740732i
$956$	−14.4405	−	25.0116i	−0.467038	−	0.808933i
$957$	−11.7511	+	4.66451i	−0.379859	+	0.150782i
$958$	25.9936	+	15.0074i	0.839816	+	0.484868i
$959$	−0.0376110	+	0.0651442i	−0.00121452	+	0.00210361i
$960$	−3.76476	+	0.909160i	−0.121507	+	0.0293430i
$961$	2.23757	+	3.87559i	0.0721798	+	0.125019i
$962$	4.06414			0.131033
$963$	6.21965	−	34.2089i	0.200425	−	1.10237i
$964$			3.53838i			0.113963i
$965$	7.48149	−	37.5395i	0.240838	−	1.20844i
$966$	−0.0632046	+	0.0292685i	−0.00203358	+	0.000941699i
$967$	21.7402	−	37.6552i	0.699119	−	1.21091i	−0.269654	−	0.962957i	$-0.586909\pi$
$967$	21.7402	−	37.6552i	0.699119	−	1.21091i	0.968772	−	0.247952i	$-0.0797575\pi$
$968$	1.22519	−	10.9316i	0.0393792	−	0.351353i
$969$	41.7509	+	3.76459i	1.34123	+	0.120936i
$970$	1.73659	−	8.71363i	0.0557587	−	0.279778i
$971$			38.2820i			1.22853i	0.789100	+	0.614265i	$0.210547\pi$
$971$			38.2820i			1.22853i	−0.789100	+	0.614265i	$0.789453\pi$
$972$	−12.8870	+	8.77067i	−0.413351	+	0.281320i
$973$			0.202948i			0.00650621i
$974$	−7.08137	−	12.2653i	−0.226902	−	0.393005i
$975$	0.853839	+	21.2091i	0.0273447	+	0.679235i
$976$	10.4955	+	6.05960i	0.335954	+	0.193963i
$977$	−22.8943	+	39.6541i	−0.732454	+	1.26865i	0.223378	+	0.974732i	$0.428292\pi$
$977$	−22.8943	+	39.6541i	−0.732454	+	1.26865i	−0.955832	+	0.293915i	$0.905042\pi$
$978$	−3.10802	−	6.71169i	−0.0993835	−	0.214616i
$979$	27.9906	+	1.56368i	0.894583	+	0.0499753i
$980$	11.7625	+	10.3231i	0.375738	+	0.329759i
$981$	−3.62483	+	19.9370i	−0.115732	+	0.636540i
$982$			31.4277i			1.00290i
$983$	26.8318	+	46.4741i	0.855802	+	1.48229i	0.875899	+	0.482494i	$0.160269\pi$
$983$	26.8318	+	46.4741i	0.855802	+	1.48229i	−0.0200974	+	0.999798i	$0.506398\pi$
$984$	7.51303	+	5.29050i	0.239507	+	0.168655i
$985$	14.7685	+	43.5596i	0.470565	+	1.38792i
$986$	6.08746	−	10.5438i	0.193864	−	0.335783i
$987$	−0.247163	+	0.350995i	−0.00786727	+	0.0111723i
$988$	9.28679	−	5.36173i	0.295452	−	0.170579i
$989$	2.38924			0.0759734
$990$	−12.8333	−	18.1743i	−0.407869	−	0.577618i
$991$	25.0796			0.796679			0.398340	−	0.917238i	$-0.369587\pi$
$991$	25.0796			0.796679			0.398340	+	0.917238i	$0.369587\pi$
$992$	4.46023	−	2.57511i	0.141612	−	0.0817600i
$993$	−2.60026	−	5.61520i	−0.0825168	−	0.178193i
$994$	0.161902	−	0.280423i	0.00513524	−	0.00889449i
$995$	33.8980	−	11.4928i	1.07464	−	0.364348i
$996$	2.22607	−	24.6881i	0.0705358	−	0.782273i
$997$	16.1736	+	28.0136i	0.512225	+	0.887199i	0.999900	+	0.0141737i	$0.00451179\pi$
$997$	16.1736	+	28.0136i	0.512225	+	0.887199i	−0.487675	+	0.873025i	$0.662155\pi$
$998$		−	1.53083i		−	0.0484576i
$999$	−2.29629	+	8.30441i	−0.0726514	+	0.262740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.o.a.329.1	✓	144
5.4	even	2	inner	990.2.o.a.329.72	yes	144
9.2	odd	6	inner	990.2.o.a.659.36	yes	144
11.10	odd	2	inner	990.2.o.a.329.37	yes	144
45.29	odd	6	inner	990.2.o.a.659.37	yes	144
55.54	odd	2	inner	990.2.o.a.329.36	yes	144
99.65	even	6	inner	990.2.o.a.659.72	yes	144
495.164	even	6	inner	990.2.o.a.659.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.o.a.329.1	✓	144	1.1	even	1	trivial
990.2.o.a.329.36	yes	144	55.54	odd	2	inner
990.2.o.a.329.37	yes	144	11.10	odd	2	inner
990.2.o.a.329.72	yes	144	5.4	even	2	inner
990.2.o.a.659.1	yes	144	495.164	even	6	inner
990.2.o.a.659.36	yes	144	9.2	odd	6	inner
990.2.o.a.659.37	yes	144	45.29	odd	6	inner
990.2.o.a.659.72	yes	144	99.65	even	6	inner

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.72505 - 0.155544i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.11767 + 0.717978i) q^{5} +(1.57171 - 0.727821i) q^{6} +(0.0167009 + 0.0289269i) q^{7} +1.00000i q^{8} +(2.95161 + 0.536644i) q^{9} +(1.47496 - 1.68062i) q^{10} +(0.184993 - 3.31146i) q^{11} +(-0.997231 + 1.41617i) q^{12} +(1.22550 - 2.12263i) q^{13} +(-0.0289269 - 0.0167009i) q^{14} +(3.76476 - 0.909160i) q^{15} +(-0.500000 - 0.866025i) q^{16} +5.53187i q^{17} +(-2.82449 + 1.01106i) q^{18} +4.37514i q^{19} +(-0.437045 + 2.19294i) q^{20} +(-0.0243106 - 0.0524981i) q^{21} +(1.49552 + 2.96031i) q^{22} +(-0.601970 + 1.04264i) q^{23} +(0.155544 - 1.72505i) q^{24} +(3.96901 - 3.04088i) q^{25} +2.45100i q^{26} +(-5.00821 - 1.38484i) q^{27} +0.0334019 q^{28} +(1.10043 + 1.90601i) q^{29} +(-2.80580 + 2.66974i) q^{30} +(2.57511 - 4.46023i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.834201 + 5.68367i) q^{33} +(-2.76594 - 4.79074i) q^{34} +(-0.0561359 - 0.0492665i) q^{35} +(1.94055 - 2.28785i) q^{36} -1.65816i q^{37} +(-2.18757 - 3.78898i) q^{38} +(-2.44421 + 3.47102i) q^{39} +(-0.717978 - 2.11767i) q^{40} +(-2.65259 + 4.59443i) q^{41} +(0.0473027 + 0.0333094i) q^{42} +(-0.992257 - 1.71864i) q^{43} +(-2.77531 - 1.81594i) q^{44} +(-6.63583 + 0.982762i) q^{45} -1.20394i q^{46} +(-3.71010 - 6.42609i) q^{47} +(0.727821 + 1.57171i) q^{48} +(3.49944 - 6.06121i) q^{49} +(-1.91683 + 4.61798i) q^{50} +(0.860450 - 9.54277i) q^{51} +(-1.22550 - 2.12263i) q^{52} -10.5837 q^{53} +(5.02966 - 1.30480i) q^{54} +(1.98581 + 7.14539i) q^{55} +(-0.0289269 + 0.0167009i) q^{56} +(0.680527 - 7.54734i) q^{57} +(-1.90601 - 1.10043i) q^{58} +(-11.5273 - 6.65531i) q^{59} +(1.09503 - 3.71496i) q^{60} +(-10.4955 + 6.05960i) q^{61} +5.15023i q^{62} +(0.0337713 + 0.0943434i) q^{63} -1.00000 q^{64} +(-1.07120 + 5.37490i) q^{65} +(-2.11940 - 5.33930i) q^{66} +(2.76761 + 1.59788i) q^{67} +(4.79074 + 2.76594i) q^{68} +(1.20061 - 1.70498i) q^{69} +(0.0732484 + 0.0145981i) q^{70} +9.69421i q^{71} +(-0.536644 + 2.95161i) q^{72} -12.6271 q^{73} +(0.829079 + 1.43601i) q^{74} +(-7.31975 + 4.62831i) q^{75} +(3.78898 + 2.18757i) q^{76} +(0.0988798 - 0.0499533i) q^{77} +(0.381238 - 4.22810i) q^{78} +(-4.60468 + 2.65851i) q^{79} +(1.68062 + 1.47496i) q^{80} +(8.42403 + 3.16793i) q^{81} -5.30519i q^{82} +(-12.3941 + 7.15576i) q^{83} +(-0.0576200 - 0.00519547i) q^{84} +(-3.97176 - 11.7147i) q^{85} +(1.71864 + 0.992257i) q^{86} +(-1.60184 - 3.45913i) q^{87} +(3.31146 + 0.184993i) q^{88} +8.45264i q^{89} +(5.25541 - 4.16901i) q^{90} +0.0818680 q^{91} +(0.601970 + 1.04264i) q^{92} +(-5.13597 + 7.29358i) q^{93} +(6.42609 + 3.71010i) q^{94} +(-3.14125 - 9.26508i) q^{95} +(-1.41617 - 0.997231i) q^{96} +(3.44114 - 1.98674i) q^{97} +6.99888i q^{98} +(2.32310 - 9.67487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) \) 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Introduction

L-functions

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