LMFDB - Embedded newform 820.2.j.c.747.50

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(483,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.483"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			747.50
Character	$\chi$	$=$	820.747
Dual form			820.2.j.c.483.50

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.363517 - 1.36670i) q^{2} -2.89040i q^{3} +(-1.73571 + 0.993633i) q^{4} +(-2.03850 - 0.918980i) q^{5} +(-3.95030 + 1.05071i) q^{6} -3.97005 q^{7} +(1.98895 + 2.01099i) q^{8} -5.35442 q^{9} +(-0.514937 + 3.12007i) q^{10} +(2.11810 - 2.11810i) q^{11} +(2.87200 + 5.01690i) q^{12} -5.49792 q^{13} +(1.44318 + 5.42584i) q^{14} +(-2.65622 + 5.89208i) q^{15} +(2.02539 - 3.44932i) q^{16} +4.67818 q^{17} +(1.94642 + 7.31785i) q^{18} +(4.23103 - 4.23103i) q^{19} +(4.45137 - 0.430435i) q^{20} +11.4750i q^{21} +(-3.66476 - 2.12483i) q^{22} +(-2.64446 - 2.64446i) q^{23} +(5.81256 - 5.74887i) q^{24} +(3.31095 + 3.74668i) q^{25} +(1.99859 + 7.51398i) q^{26} +6.80520i q^{27} +(6.89086 - 3.94477i) q^{28} +(5.09727 - 5.09727i) q^{29} +(9.01825 + 1.48838i) q^{30} +3.94542i q^{31} +(-5.45043 - 1.51420i) q^{32} +(-6.12215 - 6.12215i) q^{33} +(-1.70060 - 6.39365i) q^{34} +(8.09294 + 3.64839i) q^{35} +(9.29372 - 5.32032i) q^{36} +(-3.93647 - 3.93647i) q^{37} +(-7.32057 - 4.24448i) q^{38} +15.8912i q^{39} +(-2.20642 - 5.92720i) q^{40} +(-3.43841 + 5.40161i) q^{41} +(15.6829 - 4.17136i) q^{42} +(-5.85200 + 5.85200i) q^{43} +(-1.57179 + 5.78101i) q^{44} +(10.9150 + 4.92060i) q^{45} +(-2.65287 + 4.57548i) q^{46} +7.58708i q^{47} +(-9.96991 - 5.85418i) q^{48} +8.76128 q^{49} +(3.91698 - 5.88704i) q^{50} -13.5218i q^{51} +(9.54281 - 5.46291i) q^{52} +6.61578 q^{53} +(9.30064 - 2.47380i) q^{54} +(-6.26422 + 2.37125i) q^{55} +(-7.89624 - 7.98371i) q^{56} +(-12.2294 - 12.2294i) q^{57} +(-8.81936 - 5.11347i) q^{58} -6.92744 q^{59} +(-1.24413 - 12.8663i) q^{60} +6.04740i q^{61} +(5.39219 - 1.43423i) q^{62} +21.2573 q^{63} +(-0.0881340 + 7.99951i) q^{64} +(11.2075 + 5.05248i) q^{65} +(-6.14161 + 10.5926i) q^{66} -8.81626i q^{67} +(-8.11997 + 4.64839i) q^{68} +(-7.64355 + 7.64355i) q^{69} +(2.04433 - 12.3868i) q^{70} +(-7.87467 + 7.87467i) q^{71} +(-10.6497 - 10.7677i) q^{72} +(-4.97545 - 4.97545i) q^{73} +(-3.94898 + 6.81092i) q^{74} +(10.8294 - 9.56998i) q^{75} +(-3.13975 + 11.5479i) q^{76} +(-8.40894 + 8.40894i) q^{77} +(21.7184 - 5.77671i) q^{78} +(-1.04312 - 1.04312i) q^{79} +(-7.29861 + 5.17014i) q^{80} +3.60652 q^{81} +(8.63227 + 2.73569i) q^{82} +(-1.36790 - 1.36790i) q^{83} +(-11.4020 - 19.9173i) q^{84} +(-9.53647 - 4.29916i) q^{85} +(10.1252 + 5.87060i) q^{86} +(-14.7332 - 14.7332i) q^{87} +(8.47226 + 0.0466698i) q^{88} +(4.94457 - 4.94457i) q^{89} +(2.75719 - 16.7062i) q^{90} +21.8270 q^{91} +(7.21764 + 1.96240i) q^{92} +11.4038 q^{93} +(10.3692 - 2.75803i) q^{94} +(-12.5132 + 4.73671i) q^{95} +(-4.37666 + 15.7539i) q^{96} +5.20787 q^{97} +(-3.18487 - 11.9740i) q^{98} +(-11.3412 + 11.3412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.363517	−	1.36670i	−0.257045	−	0.966399i
$2$	−0.363517	−	1.36670i	−0.257045	−	0.966399i
$3$		−	2.89040i		−	1.66877i	−0.551179	−	0.834387i	$-0.685822\pi$
$3$		−	2.89040i		−	1.66877i	0.551179	−	0.834387i	$-0.314178\pi$
$4$	−1.73571	+	0.993633i	−0.867856	+	0.496816i
$5$	−2.03850	−	0.918980i	−0.911644	−	0.410980i
$5$	−2.03850	−	0.918980i	−0.911644	−	0.410980i
$6$	−3.95030	+	1.05071i	−1.61270	+	0.428950i
$7$	−3.97005			−1.50054			−0.750268	−	0.661133i	$-0.770076\pi$
$7$	−3.97005			−1.50054			−0.750268	+	0.661133i	$0.770076\pi$
$8$	1.98895	+	2.01099i	0.703201	+	0.710991i
$9$	−5.35442			−1.78481
$10$	−0.514937	+	3.12007i	−0.162837	+	0.986653i
$11$	2.11810	−	2.11810i	0.638630	−	0.638630i	−0.311587	−	0.950217i	$-0.600861\pi$
$11$	2.11810	−	2.11810i	0.638630	−	0.638630i	0.950217	+	0.311587i	$0.100861\pi$
$12$	2.87200	+	5.01690i	0.829074	+	1.44825i
$13$	−5.49792			−1.52485			−0.762425	−	0.647077i	$-0.775991\pi$
$13$	−5.49792			−1.52485			−0.762425	+	0.647077i	$0.775991\pi$
$14$	1.44318	+	5.42584i	0.385706	+	1.45012i
$15$	−2.65622	+	5.89208i	−0.685833	+	1.52133i
$16$	2.02539	−	3.44932i	0.506347	−	0.862330i
$17$	4.67818			1.13463			0.567313	−	0.823502i	$-0.307983\pi$
$17$	4.67818			1.13463			0.567313	+	0.823502i	$0.307983\pi$
$18$	1.94642	+	7.31785i	0.458775	+	1.72483i
$19$	4.23103	−	4.23103i	0.970664	−	0.970664i	−0.0289178	−	0.999582i	$-0.509206\pi$
$19$	4.23103	−	4.23103i	0.970664	−	0.970664i	0.999582	+	0.0289178i	$0.00920611\pi$
$20$	4.45137	−	0.430435i	0.995357	−	0.0962482i
$21$			11.4750i			2.50406i
$22$	−3.66476	−	2.12483i	−0.781328	−	0.453015i
$23$	−2.64446	−	2.64446i	−0.551408	−	0.551408i	0.375439	−	0.926847i	$-0.377492\pi$
$23$	−2.64446	−	2.64446i	−0.551408	−	0.551408i	−0.926847	+	0.375439i	$0.877492\pi$
$24$	5.81256	−	5.74887i	1.18648	−	1.17348i
$25$	3.31095	+	3.74668i	0.662190	+	0.749336i
$26$	1.99859	+	7.51398i	0.391955	+	1.47361i
$27$			6.80520i			1.30966i
$28$	6.89086	−	3.94477i	1.30225	−	0.745491i
$29$	5.09727	−	5.09727i	0.946539	−	0.946539i	−0.0521023	−	0.998642i	$-0.516592\pi$
$29$	5.09727	−	5.09727i	0.946539	−	0.946539i	0.998642	+	0.0521023i	$0.0165922\pi$
$30$	9.01825	+	1.48838i	1.64650	+	0.271739i
$31$			3.94542i			0.708619i	0.935128	+	0.354309i	$0.115284\pi$
$31$			3.94542i			0.708619i	−0.935128	+	0.354309i	$0.884716\pi$
$32$	−5.45043	−	1.51420i	−0.963509	−	0.267676i
$33$	−6.12215	−	6.12215i	−1.06573	−	1.06573i
$34$	−1.70060	−	6.39365i	−0.291650	−	1.09650i
$35$	8.09294	+	3.64839i	1.36796	+	0.616691i
$36$	9.29372	−	5.32032i	1.54895	−	0.886720i
$37$	−3.93647	−	3.93647i	−0.647151	−	0.647151i	0.305152	−	0.952304i	$-0.401293\pi$
$37$	−3.93647	−	3.93647i	−0.647151	−	0.647151i	−0.952304	+	0.305152i	$0.901293\pi$
$38$	−7.32057	−	4.24448i	−1.18755	−	0.688545i
$39$			15.8912i			2.54463i
$40$	−2.20642	−	5.92720i	−0.348866	−	0.937173i
$41$	−3.43841	+	5.40161i	−0.536989	+	0.843589i
$41$	−3.43841	+	5.40161i	−0.536989	+	0.843589i
$42$	15.6829	−	4.17136i	2.41992	−	0.643655i
$43$	−5.85200	+	5.85200i	−0.892422	+	0.892422i	−0.994751	−	0.102329i	$-0.967371\pi$
$43$	−5.85200	+	5.85200i	−0.892422	+	0.892422i	0.102329	+	0.994751i	$0.467371\pi$
$44$	−1.57179	+	5.78101i	−0.236957	+	0.871521i
$45$	10.9150	+	4.92060i	1.62711	+	0.733520i
$46$	−2.65287	+	4.57548i	−0.391144	+	0.674617i
$47$			7.58708i			1.10669i	0.832952	+	0.553345i	$0.186649\pi$
$47$			7.58708i			1.10669i	−0.832952	+	0.553345i	$0.813351\pi$
$48$	−9.96991	−	5.85418i	−1.43903	−	0.844979i
$49$	8.76128			1.25161
$50$	3.91698	−	5.88704i	0.553945	−	0.832553i
$51$		−	13.5218i		−	1.89343i
$52$	9.54281	−	5.46291i	1.32335	−	0.757570i
$53$	6.61578			0.908748			0.454374	−	0.890811i	$-0.349863\pi$
$53$	6.61578			0.908748			0.454374	+	0.890811i	$0.349863\pi$
$54$	9.30064	−	2.47380i	1.26566	−	0.336642i
$55$	−6.26422	+	2.37125i	−0.844668	+	0.319739i
$56$	−7.89624	−	7.98371i	−1.05518	−	1.06687i
$57$	−12.2294	−	12.2294i	−1.61982	−	1.61982i
$58$	−8.81936	−	5.11347i	−1.15804	−	0.671432i
$59$	−6.92744			−0.901876			−0.450938	−	0.892555i	$-0.648910\pi$
$59$	−6.92744			−0.901876			−0.450938	+	0.892555i	$0.648910\pi$
$60$	−1.24413	−	12.8663i	−0.160616	−	1.66103i
$61$			6.04740i			0.774290i	0.922019	+	0.387145i	$0.126539\pi$
$61$			6.04740i			0.774290i	−0.922019	+	0.387145i	$0.873461\pi$
$62$	5.39219	−	1.43423i	0.684809	−	0.182147i
$63$	21.2573			2.67817
$64$	−0.0881340	+	7.99951i	−0.0110168	+	0.999939i
$65$	11.2075	+	5.05248i	1.39012	+	0.626683i
$66$	−6.14161	+	10.5926i	−0.755980	+	1.30386i
$67$		−	8.81626i		−	1.07708i	−0.842601	−	0.538539i	$-0.818977\pi$
$67$		−	8.81626i		−	1.07708i	0.842601	−	0.538539i	$-0.181023\pi$
$68$	−8.11997	+	4.64839i	−0.984692	+	0.563701i
$69$	−7.64355	+	7.64355i	−0.920175	+	0.920175i
$70$	2.04433	−	12.3868i	0.244344	−	1.48051i
$71$	−7.87467	+	7.87467i	−0.934552	+	0.934552i	−0.997986	−	0.0634342i	$-0.979795\pi$
$71$	−7.87467	+	7.87467i	−0.934552	+	0.934552i	0.0634342	+	0.997986i	$0.479795\pi$
$72$	−10.6497	−	10.7677i	−1.25508	−	1.26898i
$73$	−4.97545	−	4.97545i	−0.582333	−	0.582333i	0.353211	−	0.935544i	$-0.385090\pi$
$73$	−4.97545	−	4.97545i	−0.582333	−	0.582333i	−0.935544	+	0.353211i	$0.885090\pi$
$74$	−3.94898	+	6.81092i	−0.459060	+	0.791754i
$75$	10.8294	−	9.56998i	1.25047	−	1.10505i
$76$	−3.13975	+	11.5479i	−0.360155	+	1.32464i
$77$	−8.40894	+	8.40894i	−0.958288	+	0.958288i
$78$	21.7184	−	5.77671i	2.45913	−	0.654084i
$79$	−1.04312	−	1.04312i	−0.117360	−	0.117360i	0.645988	−	0.763348i	$-0.276446\pi$
$79$	−1.04312	−	1.04312i	−0.117360	−	0.117360i	−0.763348	+	0.645988i	$0.776446\pi$
$80$	−7.29861	+	5.17014i	−0.816009	+	0.578039i
$81$	3.60652			0.400724
$82$	8.63227	+	2.73569i	0.953274	+	0.302106i
$83$	−1.36790	−	1.36790i	−0.150147	−	0.150147i	0.628037	−	0.778184i	$-0.283859\pi$
$83$	−1.36790	−	1.36790i	−0.150147	−	0.150147i	−0.778184	+	0.628037i	$0.783859\pi$
$84$	−11.4020	−	19.9173i	−1.24406	−	2.17316i
$85$	−9.53647	−	4.29916i	−1.03438	−	0.466309i
$86$	10.1252	+	5.87060i	1.09183	+	0.633043i
$87$	−14.7332	−	14.7332i	−1.57956	−	1.57956i
$88$	8.47226	+	0.0466698i	0.903146	+	0.00497502i
$89$	4.94457	−	4.94457i	0.524123	−	0.524123i	−0.394691	−	0.918814i	$-0.629148\pi$
$89$	4.94457	−	4.94457i	0.524123	−	0.524123i	0.918814	+	0.394691i	$0.129148\pi$
$90$	2.75719	−	16.7062i	0.290633	−	1.76098i
$91$	21.8270			2.28809
$92$	7.21764	+	1.96240i	0.752491	+	0.204594i
$93$	11.4038			1.18252
$94$	10.3692	−	2.75803i	1.06950	−	0.284469i
$95$	−12.5132	+	4.73671i	−1.28382	+	0.485976i
$96$	−4.37666	+	15.7539i	−0.446691	+	1.60788i
$97$	5.20787			0.528779			0.264389	−	0.964416i	$-0.414830\pi$
$97$	5.20787			0.528779			0.264389	+	0.964416i	$0.414830\pi$
$98$	−3.18487	−	11.9740i	−0.321720	−	1.20956i
$99$	−11.3412	+	11.3412i	−1.13983	+	1.13983i
$100$	−9.46968	−	3.21328i	−0.946968	−	0.321328i
$101$	9.59727	−	9.59727i	0.954964	−	0.954964i	−0.0440648	−	0.999029i	$-0.514031\pi$
$101$	9.59727	−	9.59727i	0.954964	−	0.954964i	0.999029	+	0.0440648i	$0.0140308\pi$
$102$	−18.4802	+	4.91541i	−1.82981	+	0.486698i
$103$	4.49066	−	4.49066i	0.442478	−	0.442478i	−0.450366	−	0.892844i	$-0.648706\pi$
$103$	4.49066	−	4.49066i	0.442478	−	0.442478i	0.892844	+	0.450366i	$0.148706\pi$
$104$	−10.9351	−	11.0562i	−1.07228	−	1.08415i
$105$	10.5453	−	23.3918i	1.02912	−	2.28281i
$106$	−2.40495	−	9.04176i	−0.233589	−	0.878213i
$107$	−8.17781	+	8.17781i	−0.790579	+	0.790579i	−0.981588	−	0.191009i	$-0.938824\pi$
$107$	−8.17781	+	8.17781i	−0.790579	+	0.790579i	0.191009	+	0.981588i	$0.438824\pi$
$108$	−6.76187	−	11.8119i	−0.650661	−	1.13660i
$109$	9.10583	+	9.10583i	0.872181	+	0.872181i	0.992710	−	0.120529i	$-0.0384591\pi$
$109$	9.10583	+	9.10583i	0.872181	+	0.872181i	−0.120529	+	0.992710i	$0.538459\pi$
$110$	5.51792	+	7.69930i	0.526113	+	0.734099i
$111$	−11.3780	+	11.3780i	−1.07995	+	1.07995i
$112$	−8.04089	+	13.6940i	−0.759793	+	1.29396i
$113$	−10.0574	+	10.0574i	−0.946120	+	0.946120i	−0.998621	−	0.0525011i	$-0.983281\pi$
$113$	−10.0574	+	10.0574i	−0.946120	+	0.946120i	0.0525011	+	0.998621i	$0.483281\pi$
$114$	−12.2682	+	21.1594i	−1.14903	+	1.98176i
$115$	2.96052	+	7.82093i	0.276070	+	0.729306i
$116$	−3.78258	+	13.9122i	−0.351203	+	1.29172i
$117$	29.4382			2.72156
$118$	2.51824	+	9.46770i	0.231823	+	0.871572i
$119$	−18.5726			−1.70255
$120$	−17.1320	+	6.37744i	−1.56393	+	0.582178i
$121$			2.02734i			0.184303i
$122$	8.26495	−	2.19833i	0.748273	−	0.199027i
$123$	15.6128	+	9.93838i	1.40776	+	0.896114i
$124$	−3.92030	−	6.84811i	−0.352053	−	0.614979i
$125$	−3.30625	−	10.6803i	−0.295720	−	0.955275i
$126$	−7.72737	−	29.0522i	−0.688409	−	2.58818i
$127$	9.07050	−	9.07050i	0.804877	−	0.804877i	−0.178977	−	0.983853i	$-0.557279\pi$
$127$	9.07050	−	9.07050i	0.804877	−	0.804877i	0.983853	+	0.178977i	$0.0572786\pi$
$128$	10.9649	−	2.78750i	0.969173	−	0.246383i
$129$	16.9146	+	16.9146i	1.48925	+	1.48925i
$130$	2.83109	−	17.1539i	0.248303	−	1.50450i
$131$	0.242048			0.0211478			0.0105739	−	0.999944i	$-0.496634\pi$
$131$	0.242048			0.0211478			0.0105739	+	0.999944i	$0.496634\pi$
$132$	16.7094	+	4.54312i	1.45437	+	0.395427i
$133$	−16.7974	+	16.7974i	−1.45652	+	1.45652i
$134$	−12.0491	+	3.20486i	−1.04089	+	0.276857i
$135$	6.25384	−	13.8724i	0.538245	−	1.19395i
$136$	9.30468	+	9.40776i	0.797870	+	0.806709i
$137$	1.85162			0.158195			0.0790973	−	0.996867i	$-0.474796\pi$
$137$	1.85162			0.158195			0.0790973	+	0.996867i	$0.474796\pi$
$138$	13.2250	+	7.66785i	1.12578	+	0.652730i
$139$	7.67400			0.650900			0.325450	−	0.945559i	$-0.394484\pi$
$139$	7.67400			0.650900			0.325450	+	0.945559i	$0.394484\pi$
$140$	−17.6722	+	1.70885i	−1.49357	+	0.144424i
$141$	21.9297			1.84681
$142$	13.6249	+	7.89970i	1.14337	+	0.662928i
$143$	−11.6451	+	11.6451i	−0.973815	+	0.973815i
$144$	−10.8448	+	18.4691i	−0.903731	+	1.53909i
$145$	−15.0751	+	5.70649i	−1.25192	+	0.473898i
$146$	−4.99127	+	8.60859i	−0.413080	+	0.712452i
$147$		−	25.3236i		−	2.08866i
$148$	10.7440	+	2.92117i	0.883149	+	0.240119i
$149$	−14.4592	−	14.4592i	−1.18455	−	1.18455i	−0.978554	−	0.205993i	$-0.933958\pi$
$149$	−14.4592	−	14.4592i	−1.18455	−	1.18455i	−0.205993	−	0.978554i	$-0.566042\pi$
$150$	−17.0159	−	11.3216i	−1.38934	−	0.924408i
$151$	−10.2588	+	10.2588i	−0.834848	+	0.834848i	−0.988175	−	0.153328i	$-0.951001\pi$
$151$	−10.2588	+	10.2588i	−0.834848	+	0.834848i	0.153328	+	0.988175i	$0.451001\pi$
$152$	16.9238	+	0.0932258i	1.37271	+	0.00756161i
$153$	−25.0489			−2.02509
$154$	14.5493	+	8.43567i	1.17241	+	0.679766i
$155$	3.62576	−	8.04273i	0.291228	−	0.646008i
$156$	−15.7900	−	27.5825i	−1.26421	−	2.20837i
$157$			1.71893i			0.137185i	0.997645	+	0.0685926i	$0.0218509\pi$
$157$			1.71893i			0.137185i	−0.997645	+	0.0685926i	$0.978149\pi$
$158$	−1.04644	+	1.80482i	−0.0832501	+	0.143584i
$159$		−	19.1223i		−	1.51649i
$160$	9.71917	+	8.09554i	0.768368	+	0.640008i
$161$	10.4986	+	10.4986i	0.827408	+	0.827408i
$162$	−1.31103	−	4.92901i	−0.103004	−	0.387259i
$163$	−3.32591	−	3.32591i	−0.260506	−	0.260506i	0.564754	−	0.825259i	$-0.308971\pi$
$163$	−3.32591	−	3.32591i	−0.260506	−	0.260506i	−0.825259	+	0.564754i	$0.808971\pi$
$164$	0.600876	−	12.7921i	0.0469206	−	0.998899i
$165$	6.85386	+	18.1061i	0.533572	+	1.40956i
$166$	−1.37225	+	2.36676i	−0.106507	+	0.183696i
$167$	−6.72919			−0.520720			−0.260360	−	0.965512i	$-0.583841\pi$
$167$	−6.72919			−0.520720			−0.260360	+	0.965512i	$0.583841\pi$
$168$	−23.0761	+	22.8233i	−1.78036	+	1.76085i
$169$	17.2271			1.32516
$170$	−2.40897	+	14.5963i	−0.184760	+	1.11948i
$171$	−22.6547	+	22.6547i	−1.73245	+	1.73245i
$172$	4.34265	−	15.9721i	0.331124	−	1.21786i
$173$	−0.649205	−	0.649205i	−0.0493581	−	0.0493581i	0.681997	−	0.731355i	$-0.261112\pi$
$173$	−0.649205	−	0.649205i	−0.0493581	−	0.0493581i	−0.731355	+	0.681997i	$0.761112\pi$
$174$	−14.7800	+	25.4915i	−1.12047	+	1.93250i
$175$	−13.1446	−	14.8745i	−0.993641	−	1.12441i
$176$	−3.01602	−	11.5960i	−0.227341	−	0.874078i
$177$			20.0231i			1.50503i
$178$	−8.55515	−	4.96029i	−0.641236	−	0.371789i
$179$	−10.8330	+	10.8330i	−0.809700	+	0.809700i	−0.984588	−	0.174889i	$-0.944043\pi$
$179$	−10.8330	+	10.8330i	−0.809700	+	0.809700i	0.174889	+	0.984588i	$0.444043\pi$
$180$	−23.8345	+	2.30473i	−1.77652	+	0.171784i
$181$	−2.35689	+	2.35689i	−0.175186	+	0.175186i	−0.789254	−	0.614067i	$-0.789532\pi$
$181$	−2.35689	+	2.35689i	−0.175186	+	0.175186i	0.614067	+	0.789254i	$0.289532\pi$
$182$	−7.93448	−	29.8309i	−0.588143	−	2.21121i
$183$	17.4794			1.29211
$184$	0.0582676	−	10.5777i	0.00429555	−	0.779797i
$185$	4.40695	+	11.6420i	0.324005	+	0.855938i
$186$	−4.14549	−	15.5856i	−0.303962	−	1.14279i
$187$	9.90884	−	9.90884i	0.724606	−	0.724606i
$188$	−7.53877	−	13.1690i	−0.549821	−	0.960447i
$189$		−	27.0170i		−	1.96520i
$190$	11.0224	+	15.3798i	0.799648	+	1.11577i
$191$	−5.54616	−	5.54616i	−0.401306	−	0.401306i	0.477387	−	0.878693i	$-0.341584\pi$
$191$	−5.54616	−	5.54616i	−0.401306	−	0.401306i	−0.878693	+	0.477387i	$0.841584\pi$
$192$	23.1218	+	0.254743i	1.66867	+	0.0183845i
$193$	−19.5306			−1.40584			−0.702922	−	0.711267i	$-0.748122\pi$
$193$	−19.5306			−1.40584			−0.702922	+	0.711267i	$0.748122\pi$
$194$	−1.89315	−	7.11757i	−0.135920	−	0.511012i
$195$	14.6037	−	32.3942i	1.04579	−	2.31980i
$196$	−15.2071	+	8.70549i	−1.08622	+	0.621821i
$197$	−1.07079	+	1.07079i	−0.0762910	+	0.0762910i	−0.744223	−	0.667932i	$-0.767180\pi$
$197$	−1.07079	+	1.07079i	−0.0762910	+	0.0762910i	0.667932	+	0.744223i	$0.267180\pi$
$198$	19.6226	+	11.3772i	1.39452	+	0.808544i
$199$	4.54898	−	4.54898i	0.322469	−	0.322469i	−0.527245	−	0.849713i	$-0.676775\pi$
$199$	4.54898	−	4.54898i	0.322469	−	0.322469i	0.849713	+	0.527245i	$0.176775\pi$
$200$	−0.949191	+	14.1102i	−0.0671180	+	0.997745i
$201$	−25.4825			−1.79740
$202$	−16.6053	−	9.62777i	−1.16835	−	0.677408i
$203$	−20.2364	+	20.2364i	−1.42032	+	1.42032i
$204$	13.4357	+	23.4700i	0.940689	+	1.64323i
$205$	11.9732	−	7.85133i	0.836242	−	0.548361i
$206$	−7.76980	−	4.50494i	−0.541347	−	0.313874i
$207$	14.1595	+	14.1595i	0.984156	+	0.984156i
$208$	−11.1354	+	18.9641i	−0.772103	+	1.31492i
$209$		−	17.9234i		−	1.23979i
$210$	−35.8029	−	5.90892i	−2.47063	−	0.407754i
$211$	−2.07424	−	2.07424i	−0.142797	−	0.142797i	0.632095	−	0.774891i	$-0.282195\pi$
$211$	−2.07424	−	2.07424i	−0.142797	−	0.142797i	−0.774891	+	0.632095i	$0.782195\pi$
$212$	−11.4831	+	6.57366i	−0.788662	+	0.451481i
$213$	22.7610	+	22.7610i	1.55956	+	1.55956i
$214$	14.1493	+	8.20381i	0.967229	+	0.560801i
$215$	17.3072	−	6.55142i	1.18034	−	0.446803i
$216$	−13.6852	+	13.5352i	−0.931158	+	0.920955i
$217$		−	15.6635i		−	1.06331i
$218$	9.13478	−	15.7550i	0.618685	−	1.06706i
$219$	−14.3811	+	14.3811i	−0.971781	+	0.971781i
$220$	8.51674	−	10.3401i	0.574198	−	0.697132i
$221$	−25.7203			−1.73013
$222$	19.6863	+	11.4141i	1.32126	+	0.766066i
$223$	3.55858	+	3.55858i	0.238300	+	0.238300i	0.816146	−	0.577846i	$-0.196107\pi$
$223$	3.55858	+	3.55858i	0.238300	+	0.238300i	−0.577846	+	0.816146i	$0.696107\pi$
$224$	21.6385	+	6.01146i	1.44578	+	0.401658i
$225$	−17.7282	−	20.0613i	−1.18188	−	1.33742i
$226$	17.4014	+	10.0894i	1.15752	+	0.671134i
$227$			6.82130i			0.452746i	0.974041	+	0.226373i	$0.0726868\pi$
$227$			6.82130i			0.452746i	−0.974041	+	0.226373i	$0.927313\pi$
$228$	33.3781	+	9.07515i	2.21052	+	0.601016i
$229$	−11.7099	−	11.7099i	−0.773814	−	0.773814i	0.204957	−	0.978771i	$-0.434295\pi$
$229$	−11.7099	−	11.7099i	−0.773814	−	0.773814i	−0.978771	+	0.204957i	$0.934295\pi$
$230$	9.61263	−	6.88917i	0.633838	−	0.454259i
$231$	24.3052	+	24.3052i	1.59917	+	1.59917i
$232$	20.3888	+	0.112312i	1.33859	+	0.00737367i
$233$	−7.39818			−0.484671			−0.242335	−	0.970193i	$-0.577913\pi$
$233$	−7.39818			−0.484671			−0.242335	+	0.970193i	$0.577913\pi$
$234$	−10.7013	−	40.2330i	−0.699563	−	2.63011i
$235$	6.97237	−	15.4663i	0.454827	−	1.00891i
$236$	12.0240	−	6.88333i	0.782698	−	0.448067i
$237$	−3.01504	+	3.01504i	−0.195848	+	0.195848i
$238$	6.75145	+	25.3831i	0.437632	+	1.64534i
$239$	−6.27100	−	6.27100i	−0.405637	−	0.405637i	0.474577	−	0.880214i	$-0.342601\pi$
$239$	−6.27100	−	6.27100i	−0.405637	−	0.405637i	−0.880214	+	0.474577i	$0.842601\pi$
$240$	14.9438	+	21.0959i	0.964617	+	1.36173i
$241$		−	22.4409i		−	1.44554i	−0.691086	−	0.722772i	$-0.742868\pi$
$241$		−	22.4409i		−	1.44554i	0.691086	−	0.722772i	$-0.257132\pi$
$242$	2.77075	−	0.736970i	0.178111	−	0.0473742i
$243$			9.99133i			0.640944i
$244$	−6.00889	−	10.4965i	−0.384680	−	0.671972i
$245$	−17.8599	−	8.05144i	−1.14102	−	0.514387i
$246$	7.90723	−	24.9507i	0.504146	−	1.59080i
$247$	−23.2618	+	23.2618i	−1.48012	+	1.48012i
$248$	−7.93419	+	7.84726i	−0.503821	+	0.498301i
$249$	−3.95379	+	3.95379i	−0.250561	+	0.250561i
$250$	−13.3948	+	8.40110i	−0.847164	+	0.531332i
$251$	2.71865			0.171600			0.0857999	−	0.996312i	$-0.472655\pi$
$251$	2.71865			0.171600			0.0857999	+	0.996312i	$0.472655\pi$
$252$	−36.8965	+	21.1219i	−2.32426	+	1.33056i
$253$	−11.2024			−0.704292
$254$	−15.6939	−	9.09933i	−0.984722	−	0.570943i
$255$	−12.4263	+	27.5642i	−0.778164	+	1.72614i
$256$	−7.79560	−	13.9724i	−0.487225	−	0.873276i
$257$		−	8.12085i		−	0.506565i	−0.967392	−	0.253282i	$-0.918490\pi$
$257$		−	8.12085i		−	0.506565i	0.967392	−	0.253282i	$-0.0815102\pi$
$258$	16.9684	−	29.2659i	1.05641	−	1.82201i
$259$	15.6280	+	15.6280i	0.971074	+	0.971074i
$260$	−24.4733	+	2.36650i	−1.51777	+	0.146764i
$261$	−27.2929	+	27.2929i	−1.68939	+	1.68939i
$262$	−0.0879883	−	0.330805i	−0.00543594	−	0.0204372i
$263$	−10.8140			−0.666821			−0.333410	−	0.942782i	$-0.608199\pi$
$263$	−10.8140			−0.666821			−0.333410	+	0.942782i	$0.608199\pi$
$264$	0.134894	−	24.4882i	0.00830218	−	1.50715i
$265$	−13.4863	−	6.07977i	−0.828455	−	0.373477i
$266$	29.0630	+	16.8508i	1.78197	+	1.03319i
$267$	−14.2918	−	14.2918i	−0.874643	−	0.874643i
$268$	8.76012	+	15.3025i	0.535110	+	0.934748i
$269$			19.3684i			1.18091i	0.807070	+	0.590456i	$0.201052\pi$
$269$			19.3684i			1.18091i	−0.807070	+	0.590456i	$0.798948\pi$
$270$	−21.2327	−	3.50425i	−1.29218	−	0.213262i
$271$		−	16.7811i		−	1.01938i	−0.860358	−	0.509690i	$-0.829760\pi$
$271$		−	16.7811i		−	1.01938i	0.860358	−	0.509690i	$-0.170240\pi$
$272$	9.47514	−	16.1365i	0.574515	−	0.978422i
$273$		−	63.0888i		−	3.81831i
$274$	−0.673094	−	2.53060i	−0.0406631	−	0.152879i
$275$	14.9487	+	0.922909i	0.901443	+	0.0556535i
$276$	5.67212	−	20.8619i	0.341421	−	1.25574i
$277$	−8.42934	−	8.42934i	−0.506470	−	0.506470i	0.406971	−	0.913441i	$-0.366585\pi$
$277$	−8.42934	−	8.42934i	−0.506470	−	0.506470i	−0.913441	+	0.406971i	$0.866585\pi$
$278$	−2.78963	−	10.4880i	−0.167311	−	0.629030i
$279$		−	21.1254i		−	1.26475i
$280$	8.75960	+	23.5313i	0.523486	+	1.40626i
$281$	−0.244835	+	0.244835i	−0.0146056	+	0.0146056i	−0.714372	−	0.699766i	$-0.753287\pi$
$281$	−0.244835	+	0.244835i	−0.0146056	+	0.0146056i	0.699766	+	0.714372i	$0.253287\pi$
$282$	−7.97181	−	29.9712i	−0.474714	−	1.78476i
$283$	12.5957	+	12.5957i	0.748736	+	0.748736i	0.974242	−	0.225506i	$-0.0724035\pi$
$283$	12.5957	+	12.5957i	0.748736	+	0.748736i	−0.225506	+	0.974242i	$0.572403\pi$
$284$	5.84363	−	21.4927i	0.346756	−	1.27536i
$285$	13.6910	+	36.1681i	0.810985	+	2.14241i
$286$	20.1485	+	11.6821i	1.19141	+	0.690780i
$287$	13.6507	−	21.4446i	0.805772	−	1.26584i
$288$	29.1839	+	8.10768i	1.71968	+	0.477749i
$289$	4.88539			0.287376
$290$	13.2791	+	18.5286i	0.779774	+	1.08804i
$291$		−	15.0528i		−	0.882412i
$292$	13.5797	+	3.69218i	0.794693	+	0.216068i
$293$		−	11.1282i		−	0.650117i	−0.945694	−	0.325059i	$-0.894616\pi$
$293$		−	11.1282i		−	0.650117i	0.945694	−	0.325059i	$-0.105384\pi$
$294$	−34.6096	+	9.20555i	−2.01848	+	0.536878i
$295$	14.1216	+	6.36618i	0.822190	+	0.370653i
$296$	0.0867355	−	15.7456i	0.00504140	−	0.915196i
$297$	14.4141	+	14.4141i	0.836389	+	0.836389i
$298$	−14.5052	+	25.0175i	−0.840263	+	1.44923i
$299$	14.5390	+	14.5390i	0.840814	+	0.840814i
$300$	−9.28767	+	27.3712i	−0.536224	+	1.58027i
$301$	23.2327	−	23.2327i	1.33911	−	1.33911i
$302$	17.7499	+	10.2914i	1.02139	+	0.592203i
$303$	−27.7399	−	27.7399i	−1.59362	−	1.59362i
$304$	−6.02469	−	23.1636i	−0.345540	−	1.32853i
$305$	5.55743	−	12.3276i	0.318218	−	0.705877i
$306$	9.10570	+	34.2343i	0.520538	+	1.95704i
$307$	5.05107	+	5.05107i	0.288280	+	0.288280i	0.836400	−	0.548120i	$-0.184656\pi$
$307$	5.05107	+	5.05107i	0.288280	+	0.288280i	−0.548120	+	0.836400i	$0.684656\pi$
$308$	6.24010	−	22.9509i	0.355563	−	1.30775i
$309$	−12.9798	−	12.9798i	−0.738396	−	0.738396i
$310$	−12.3100	−	2.03164i	−0.699161	−	0.115390i
$311$	10.3786	+	10.3786i	0.588516	+	0.588516i	0.937229	−	0.348713i	$-0.113381\pi$
$311$	10.3786	+	10.3786i	0.588516	+	0.588516i	−0.348713	+	0.937229i	$0.613381\pi$
$312$	−31.9570	+	31.6068i	−1.80921	+	1.78938i
$313$			1.55243i			0.0877483i	0.999037	+	0.0438741i	$0.0139701\pi$
$313$			1.55243i			0.0877483i	−0.999037	+	0.0438741i	$0.986030\pi$
$314$	2.34925	−	0.624858i	0.132576	−	0.0352628i
$315$	−43.3329	−	19.5350i	−2.44153	−	1.10067i
$316$	2.84704	+	0.774079i	0.160159	+	0.0435453i
$317$		−	5.50774i		−	0.309346i	−0.987966	−	0.154673i	$-0.950568\pi$
$317$		−	5.50774i		−	0.309346i	0.987966	−	0.154673i	$-0.0494323\pi$
$318$	−26.1343	+	6.95126i	−1.46554	+	0.389807i
$319$		−	21.5930i		−	1.20898i
$320$	7.53105	−	16.2260i	0.420999	−	0.907061i
$321$	23.6371	+	23.6371i	1.31930	+	1.31930i
$322$	10.5320	−	18.1649i	0.586926	−	1.01229i
$323$	19.7935	−	19.7935i	1.10134	−	1.10134i
$324$	−6.25987	+	3.58355i	−0.347771	+	0.199086i
$325$	−18.2034	−	20.5989i	−1.00974	−	1.14262i
$326$	−3.33649	+	5.75453i	−0.184791	+	0.318714i
$327$	26.3195	−	26.3195i	1.45547	−	1.45547i
$328$	−17.7014	+	3.82894i	−0.977396	+	0.211418i
$329$		−	30.1211i		−	1.66063i
$330$	22.2541	−	15.9490i	1.22505	−	0.877964i
$331$	−5.67764	+	5.67764i	−0.312071	+	0.312071i	−0.845712	−	0.533640i	$-0.820824\pi$
$331$	−5.67764	+	5.67764i	−0.312071	+	0.312071i	0.533640	+	0.845712i	$0.320824\pi$
$332$	3.73348	+	1.01509i	0.204901	+	0.0557104i
$333$	21.0775	+	21.0775i	1.15504	+	1.15504i
$334$	2.44617	+	9.19675i	0.133849	+	0.503224i
$335$	−8.10196	+	17.9719i	−0.442658	+	0.981912i
$336$	39.5810	+	23.2414i	2.15932	+	1.26792i
$337$	8.59922	−	8.59922i	0.468430	−	0.468430i	−0.432976	−	0.901405i	$-0.642536\pi$
$337$	8.59922	−	8.59922i	0.468430	−	0.468430i	0.901405	+	0.432976i	$0.142536\pi$
$338$	−6.26235	−	23.5443i	−0.340627	−	1.28064i
$339$	29.0699	+	29.0699i	1.57886	+	1.57886i
$340$	20.8243	−	2.01365i	1.12936	−	0.109206i
$341$	8.35678	+	8.35678i	0.452545	+	0.452545i
$342$	39.1974	+	22.7267i	2.11955	+	1.22892i
$343$	−6.99236			−0.377552
$344$	−23.4076	−	0.128942i	−1.26206	−	0.00695209i
$345$	22.6056	−	8.55710i	1.21705	−	0.460699i
$346$	−0.651268	+	1.12326i	−0.0350124	+	0.0603869i
$347$			25.7265i			1.38107i	0.723298	+	0.690536i	$0.242625\pi$
$347$			25.7265i			1.38107i	−0.723298	+	0.690536i	$0.757375\pi$
$348$	40.2118	+	10.9332i	2.15558	+	0.586079i
$349$	−5.38091			−0.288034			−0.144017	−	0.989575i	$-0.546002\pi$
$349$	−5.38091			−0.288034			−0.144017	+	0.989575i	$0.546002\pi$
$350$	−15.5506	+	23.3718i	−0.831215	+	1.24928i
$351$		−	37.4145i		−	1.99704i
$352$	−14.7518	+	8.33731i	−0.786272	+	0.444380i
$353$	−22.1106	+	22.1106i	−1.17683	+	1.17683i	−0.196281	+	0.980548i	$0.562887\pi$
$353$	−22.1106	+	22.1106i	−1.17683	+	1.17683i	−0.980548	+	0.196281i	$0.937113\pi$
$354$	27.3654	−	7.27872i	1.45446	−	0.386859i
$355$	23.2892	−	8.81584i	1.23606	−	0.467896i
$356$	−3.66926	+	13.4954i	−0.194470	+	0.715257i
$357$			53.6823i			2.84117i
$358$	18.7435	+	10.8675i	0.990623	+	0.574364i
$359$	−1.25683			−0.0663329			−0.0331664	−	0.999450i	$-0.510559\pi$
$359$	−1.25683			−0.0663329			−0.0331664	+	0.999450i	$0.510559\pi$
$360$	11.8141	+	31.7367i	0.622657	+	1.67267i
$361$		−	16.8032i		−	0.884377i
$362$	4.07792	+	2.36438i	0.214331	+	0.124269i
$363$	5.85981			0.307560
$364$	−37.8854	+	21.6880i	−1.98573	+	1.13676i
$365$	5.57011	+	14.7148i	0.291553	+	0.770208i
$366$	−6.35405	−	23.8890i	−0.332131	−	1.24870i
$367$	−6.00019	−	6.00019i	−0.313207	−	0.313207i	0.532944	−	0.846151i	$-0.321086\pi$
$367$	−6.00019	−	6.00019i	−0.313207	−	0.313207i	−0.846151	+	0.532944i	$0.821086\pi$
$368$	−14.4776	+	3.76553i	−0.754700	+	0.196292i
$369$	18.4107	−	28.9224i	0.958421	−	1.50564i
$370$	14.3091	−	10.2550i	0.743894	−	0.533133i
$371$	−26.2650			−1.36361
$372$	−19.7938	+	11.3312i	−1.02626	+	0.587497i
$373$	1.39112	−	1.39112i	0.0720293	−	0.0720293i	−0.670174	−	0.742204i	$-0.733781\pi$
$373$	1.39112	−	1.39112i	0.0720293	−	0.0720293i	0.742204	+	0.670174i	$0.233781\pi$
$374$	−17.1444	−	9.94034i	−0.886515	−	0.514003i
$375$	−30.8703	+	9.55639i	−1.59414	+	0.493490i
$376$	−15.2575	+	15.0903i	−0.786846	+	0.778225i
$377$	−28.0244	+	28.0244i	−1.44333	+	1.44333i
$378$	−36.9240	+	9.82112i	−1.89916	+	0.505144i
$379$	6.38161			0.327801			0.163901	−	0.986477i	$-0.447592\pi$
$379$	6.38161			0.327801			0.163901	+	0.986477i	$0.447592\pi$
$380$	17.0127	−	20.6551i	0.872733	−	1.05958i
$381$	−26.2174	−	26.2174i	−1.34316	−	1.34316i
$382$	−5.56379	+	9.59604i	−0.284668	+	0.490976i
$383$	33.1381			1.69328			0.846640	−	0.532167i	$-0.178622\pi$
$383$	33.1381			1.69328			0.846640	+	0.532167i	$0.178622\pi$
$384$	−8.05700	−	31.6931i	−0.411157	−	1.61733i
$385$	24.8693	−	9.41397i	1.26746	−	0.479780i
$386$	7.09970	+	26.6924i	0.361365	+	1.35861i
$387$	31.3340	−	31.3340i	1.59280	−	1.59280i
$388$	−9.03936	+	5.17471i	−0.458904	+	0.262706i
$389$	−36.2135			−1.83610			−0.918050	−	0.396465i	$-0.870237\pi$
$389$	−36.2135			−1.83610			−0.918050	+	0.396465i	$0.870237\pi$
$390$	−49.5816	−	8.18297i	−2.51066	−	0.414361i
$391$	−12.3713	−	12.3713i	−0.625642	−	0.625642i
$392$	17.4258	+	17.6188i	0.880134	+	0.889884i
$393$		−	0.699615i		−	0.0352909i
$394$	1.85270	+	1.07420i	0.0933378	+	0.0541173i
$395$	1.16780	+	3.08501i	0.0587581	+	0.155224i
$396$	8.41604	−	30.9539i	0.422922	−	1.55549i
$397$			7.02431i			0.352540i	0.984342	+	0.176270i	$0.0564032\pi$
$397$			7.02431i			0.352540i	−0.984342	+	0.176270i	$0.943597\pi$
$398$	−7.87070	−	4.56344i	−0.394523	−	0.228745i
$399$	48.5511	+	48.5511i	2.43060	+	2.43060i
$400$	19.6295	−	3.83205i	0.981473	−	0.191603i
$401$		−	12.6243i		−	0.630427i	−0.949021	−	0.315213i	$-0.897924\pi$
$401$		−	12.6243i		−	0.630427i	0.949021	−	0.315213i	$-0.102076\pi$
$402$	9.26332	+	34.8268i	0.462012	+	1.73700i
$403$		−	21.6916i		−	1.08054i
$404$	−7.12193	+	26.1942i	−0.354329	+	1.30321i
$405$	−7.35188	−	3.31432i	−0.365318	−	0.164690i
$406$	35.0133	+	20.3007i	1.73768	+	1.00751i
$407$	−16.6756			−0.826580
$408$	27.1922	−	26.8943i	1.34621	−	1.33146i
$409$			3.48240i			0.172194i	0.996287	+	0.0860968i	$0.0274394\pi$
$409$			3.48240i			0.172194i	−0.996287	+	0.0860968i	$0.972561\pi$
$410$	−15.0828	−	13.5096i	−0.744888	−	0.667190i
$411$		−	5.35192i		−	0.263991i
$412$	−3.33243	+	12.2566i	−0.164177	+	0.603838i
$413$	27.5023			1.35330
$414$	14.2045	−	24.4990i	0.698115	−	1.20406i
$415$	1.53139	+	4.04554i	0.0751731	+	0.198588i
$416$	29.9660	+	8.32498i	1.46921	+	0.408166i
$417$		−	22.1809i		−	1.08621i
$418$	−24.4959	+	6.51547i	−1.19813	+	0.318682i
$419$			1.48835i			0.0727107i	0.999339	+	0.0363553i	$0.0115748\pi$
$419$			1.48835i			0.0727107i	−0.999339	+	0.0363553i	$0.988425\pi$
$420$	4.93925	+	51.0796i	0.241011	+	2.49243i
$421$	−5.39787	−	5.39787i	−0.263076	−	0.263076i	0.563226	−	0.826303i	$-0.309560\pi$
$421$	−5.39787	−	5.39787i	−0.263076	−	0.263076i	−0.826303	+	0.563226i	$0.809560\pi$
$422$	−2.08083	+	3.58887i	−0.101293	+	0.174704i
$423$		−	40.6244i		−	1.97522i
$424$	13.1585	+	13.3042i	0.639032	+	0.646111i
$425$	15.4892	+	17.5276i	0.751338	+	0.850216i
$426$	22.8333	−	39.3813i	1.10628	−	1.90803i
$427$		−	24.0084i		−	1.16185i
$428$	6.06858	−	22.3201i	0.293336	−	1.07888i
$429$	33.6591	+	33.6591i	1.62508	+	1.62508i
$430$	−15.2452	−	21.2721i	−0.735191	−	1.02583i
$431$	−27.9795			−1.34772			−0.673862	−	0.738857i	$-0.735366\pi$
$431$	−27.9795			−1.34772			−0.673862	+	0.738857i	$0.735366\pi$
$432$	23.4733	+	13.7832i	1.12936	+	0.663143i
$433$	24.8001	−	24.8001i	1.19182	−	1.19182i	0.215258	−	0.976557i	$-0.430941\pi$
$433$	24.8001	−	24.8001i	1.19182	−	1.19182i	0.976557	−	0.215258i	$-0.0690593\pi$
$434$	−21.4072	+	5.69394i	−1.02758	+	0.273318i
$435$	16.4940	+	43.5730i	0.790829	+	2.08916i
$436$	−24.8530	−	6.75725i	−1.19024	−	0.323613i
$437$	−22.3776			−1.07046
$438$	24.8823	+	14.4268i	1.18892	+	0.689337i
$439$	−7.77457	−	7.77457i	−0.371060	−	0.371060i	0.496803	−	0.867863i	$-0.334507\pi$
$439$	−7.77457	−	7.77457i	−0.371060	−	0.371060i	−0.867863	+	0.496803i	$0.834507\pi$
$440$	−17.2278	−	7.88097i	−0.821303	−	0.375710i
$441$	−46.9115			−2.23388
$442$	9.34975	+	35.1518i	0.444722	+	1.67200i
$443$	1.04205	−	1.04205i	0.0495091	−	0.0495091i	−0.681919	−	0.731428i	$-0.738854\pi$
$443$	1.04205	−	1.04205i	0.0495091	−	0.0495091i	0.731428	+	0.681919i	$0.238854\pi$
$444$	8.44335	−	31.0544i	0.400704	−	1.47378i
$445$	−14.6235	+	5.53554i	−0.693218	+	0.262410i
$446$	3.56989	−	6.15709i	0.169039	−	0.291547i
$447$	−41.7930	+	41.7930i	−1.97674	+	1.97674i
$448$	0.349896	−	31.7585i	0.0165310	−	1.50045i
$449$	2.36619			0.111667			0.0558337	−	0.998440i	$-0.482218\pi$
$449$	2.36619			0.111667			0.0558337	+	0.998440i	$0.482218\pi$
$450$	−20.9731	+	31.5217i	−0.988683	+	1.48595i
$451$	4.15824	+	18.7240i	0.195804	+	0.881679i
$452$	7.46338	−	27.4501i	0.351048	−	1.29114i
$453$	29.6520	+	29.6520i	1.39317	+	1.39317i
$454$	9.32264	−	2.47966i	0.437533	−	0.116376i
$455$	−44.4943	−	20.0586i	−2.08593	−	0.940361i
$456$	0.269460	−	48.9167i	0.0126186	−	2.29073i
$457$	−9.72260			−0.454804			−0.227402	−	0.973801i	$-0.573023\pi$
$457$	−9.72260			−0.454804			−0.227402	+	0.973801i	$0.573023\pi$
$458$	−11.7472	+	20.2607i	−0.548908	+	0.946719i
$459$			31.8360i			1.48598i
$460$	−12.9097	−	10.6332i	−0.601920	−	0.495776i
$461$	34.5880			1.61092			0.805462	−	0.592647i	$-0.201917\pi$
$461$	34.5880			1.61092			0.805462	+	0.592647i	$0.201917\pi$
$462$	24.3825	−	42.0532i	1.13438	−	1.95649i
$463$			22.0463i			1.02458i	0.858813	+	0.512290i	$0.171203\pi$
$463$			22.0463i			1.02458i	−0.858813	+	0.512290i	$0.828797\pi$
$464$	−7.25816	−	27.9061i	−0.336952	−	1.29551i
$465$	−23.2467	−	10.4799i	−1.07804	−	0.485994i
$466$	2.68936	+	10.1111i	0.124582	+	0.468385i
$467$	9.53839	−	9.53839i	0.441384	−	0.441384i	−0.451093	−	0.892477i	$-0.648966\pi$
$467$	9.53839	−	9.53839i	0.441384	−	0.441384i	0.892477	+	0.451093i	$0.148966\pi$
$468$	−51.0961	+	29.2507i	−2.36192	+	1.35211i
$469$			35.0010i			1.61619i
$470$	−23.6722	−	3.90687i	−1.09192	−	0.180211i
$471$	4.96838			0.228931
$472$	−13.7783	−	13.9310i	−0.634200	−	0.641226i
$473$			24.7902i			1.13985i
$474$	5.21666	+	3.02463i	0.239609	+	0.138926i
$475$	29.8610	+	1.84357i	1.37012	+	0.0845886i
$476$	32.2367	−	18.4543i	1.47757	−	0.845854i
$477$	−35.4236			−1.62194
$478$	−6.29094	+	10.8502i	−0.287741	+	0.496275i
$479$	14.2940	+	14.2940i	0.653111	+	0.653111i	0.953741	−	0.300630i	$-0.0971968\pi$
$479$	14.2940	+	14.2940i	0.653111	+	0.653111i	−0.300630	+	0.953741i	$0.597197\pi$
$480$	23.3993	−	28.0923i	1.06803	−	1.28223i
$481$	21.6424	+	21.6424i	0.986808	+	0.986808i
$482$	−30.6698	+	8.15763i	−1.39697	+	0.371570i
$483$	30.3453	−	30.3453i	1.38076	−	1.38076i
$484$	−2.01443	−	3.51887i	−0.0915648	−	0.159949i
$485$	−10.6162	−	4.78593i	−0.482058	−	0.217318i
$486$	13.6551	−	3.63201i	0.619408	−	0.164752i
$487$	7.77770	+	7.77770i	0.352441	+	0.352441i	0.861017	−	0.508576i	$-0.169828\pi$
$487$	7.77770	+	7.77770i	0.352441	+	0.352441i	−0.508576	+	0.861017i	$0.669828\pi$
$488$	−12.1612	+	12.0280i	−0.550513	+	0.544481i
$489$	−9.61322	+	9.61322i	−0.434725	+	0.434725i
$490$	−4.51151	+	27.3358i	−0.203809	+	1.23491i
$491$			11.7930i			0.532210i	0.963944	+	0.266105i	$0.0857369\pi$
$491$			11.7930i			0.532210i	−0.963944	+	0.266105i	$0.914263\pi$
$492$	−36.9744	−	1.73677i	−1.66694	−	0.0782998i
$493$	23.8460	−	23.8460i	1.07397	−	1.07397i
$494$	40.2479	+	23.3358i	1.81084	+	1.04993i
$495$	33.5413	−	12.6966i	1.50757	−	0.570672i
$496$	13.6090	+	7.99101i	0.611063	+	0.358807i
$497$	31.2628	−	31.2628i	1.40233	−	1.40233i
$498$	6.84089	+	3.96635i	0.306547	+	0.177737i
$499$	−29.1074	−	29.1074i	−1.30303	−	1.30303i	−0.926342	−	0.376684i	$-0.877064\pi$
$499$	−29.1074	−	29.1074i	−1.30303	−	1.30303i	−0.376684	−	0.926342i	$-0.622936\pi$
$500$	16.3510	+	15.2527i	0.731238	+	0.682122i
$501$			19.4501i			0.868964i
$502$	−0.988274	−	3.71557i	−0.0441088	−	0.165834i
$503$		−	23.5030i		−	1.04795i	−0.851734	−	0.523974i	$-0.824449\pi$
$503$		−	23.5030i		−	1.04795i	0.851734	−	0.523974i	$-0.175551\pi$
$504$	42.2797	+	42.7481i	1.88329	+	1.90415i
$505$	−28.3837	+	10.7443i	−1.26306	+	0.478116i
$506$	4.07227	+	15.3103i	0.181035	+	0.680627i
$507$		−	49.7933i		−	2.21140i
$508$	−6.73103	+	24.7565i	−0.298641	+	1.09839i
$509$	27.3102	+	27.3102i	1.21050	+	1.21050i	0.970861	+	0.239644i	$0.0770307\pi$
$509$	27.3102	+	27.3102i	1.21050	+	1.21050i	0.239644	+	0.970861i	$0.422969\pi$
$510$	42.1890	+	6.96289i	1.86816	+	0.308322i
$511$	19.7528	+	19.7528i	0.873812	+	0.873812i
$512$	−16.2622	+	15.7334i	−0.718695	+	0.695325i
$513$	28.7930	+	28.7930i	1.27124	+	1.27124i
$514$	−11.0987	+	2.95206i	−0.489544	+	0.130210i
$515$	−13.2810	+	5.02738i	−0.585232	+	0.221533i
$516$	−46.1658	−	12.5520i	−2.03234	−	0.552570i
$517$	16.0702	+	16.0702i	0.706765	+	0.706765i
$518$	15.6776	−	27.0397i	0.688836	−	1.18806i
$519$	−1.87646	+	1.87646i	−0.0823675	+	0.0823675i
$520$	12.1307	+	32.5873i	0.531968	+	1.42905i
$521$	−21.4258	−	21.4258i	−0.938680	−	0.938680i	0.0595460	−	0.998226i	$-0.481035\pi$
$521$	−21.4258	−	21.4258i	−0.938680	−	0.938680i	−0.998226	+	0.0595460i	$0.981035\pi$
$522$	47.2225	+	27.3797i	2.06687	+	1.19838i
$523$	−14.7430	−	14.7430i	−0.644667	−	0.644667i	0.307032	−	0.951699i	$-0.400664\pi$
$523$	−14.7430	−	14.7430i	−0.644667	−	0.644667i	−0.951699	+	0.307032i	$0.900664\pi$
$524$	−0.420125	+	0.240506i	−0.0183532	+	0.0105066i
$525$	−42.9932	+	37.9933i	−1.87638	+	1.65816i
$526$	3.93107	+	14.7795i	0.171403	+	0.644415i
$527$			18.4574i			0.804017i
$528$	−33.5170	+	8.71751i	−1.45864	+	0.379381i
$529$		−	9.01366i		−	0.391898i
$530$	−3.40671	+	20.6417i	−0.147978	+	0.896618i
$531$	37.0924			1.60967
$532$	12.4650	−	45.8458i	0.540425	−	1.98767i
$533$	18.9041	−	29.6976i	0.818828	−	1.28635i
$534$	−14.3372	+	24.7278i	−0.620432	+	1.07008i
$535$	24.1857	−	9.15521i	1.04564	−	0.395814i
$536$	17.7294	−	17.5351i	0.765793	−	0.757402i
$537$	31.3118	+	31.3118i	1.35121	+	1.35121i
$538$	26.4707	−	7.04073i	1.14123	−	0.303547i
$539$	18.5572	−	18.5572i	0.799317	−	0.799317i
$540$	2.92920	+	30.2925i	0.126053	+	1.30358i
$541$			13.1806i			0.566680i	0.959020	+	0.283340i	$0.0914424\pi$
$541$			13.1806i			0.566680i	−0.959020	+	0.283340i	$0.908558\pi$
$542$	−22.9347	+	6.10021i	−0.985128	+	0.262026i
$543$	6.81236	+	6.81236i	0.292346	+	0.292346i
$544$	−25.4981	−	7.08372i	−1.09322	−	0.303712i
$545$	−10.1942	−	26.9303i	−0.436669	−	1.15357i
$546$	−86.2232	+	22.9338i	−3.69001	+	0.981477i
$547$			6.34750i			0.271400i	0.990750	+	0.135700i	$0.0433283\pi$
$547$			6.34750i			0.271400i	−0.990750	+	0.135700i	$0.956672\pi$
$548$	−3.21388	+	1.83983i	−0.137290	+	0.0785936i
$549$		−	32.3803i		−	1.38196i
$550$	−4.17278	−	20.7659i	−0.177928	−	0.885459i
$551$		−	43.1334i		−	1.83754i
$552$	−30.5737	−	0.168417i	−1.30130	−	0.00716829i
$553$	4.14125	+	4.14125i	0.176104	+	0.176104i
$554$	−8.45614	+	14.5845i	−0.359267	+	0.619638i
$555$	33.6501	−	12.7378i	1.42837	−	0.540691i
$556$	−13.3199	+	7.62514i	−0.564888	+	0.323378i
$557$	5.08673			0.215532			0.107766	−	0.994176i	$-0.465630\pi$
$557$	5.08673			0.215532			0.107766	+	0.994176i	$0.465630\pi$
$558$	−28.8720	+	7.67944i	−1.22225	+	0.325097i
$559$	32.1738	−	32.1738i	1.36081	−	1.36081i
$560$	28.9758	−	20.5257i	1.22445	−	0.867369i
$561$	−28.6405	−	28.6405i	−1.20920	−	1.20920i
$562$	0.423616	+	0.245613i	0.0178692	+	0.0103606i
$563$		−	25.7047i		−	1.08333i	−0.840596	−	0.541663i	$-0.817795\pi$
$563$		−	25.7047i		−	1.08333i	0.840596	−	0.541663i	$-0.182205\pi$
$564$	−38.0636	+	21.7901i	−1.60277	+	0.917527i
$565$	29.7445	−	11.2594i	1.25136	−	0.473688i
$566$	12.6357	−	21.7932i	0.531119	−	0.916037i
$567$	−14.3180			−0.601301
$568$	−31.4982	−	0.173509i	−1.32164	−	0.00728029i
$569$	−9.50288			−0.398381			−0.199191	−	0.979961i	$-0.563831\pi$
$569$	−9.50288			−0.398381			−0.199191	+	0.979961i	$0.563831\pi$
$570$	44.4538	−	31.8591i	1.86197	−	1.33443i
$571$	−17.3201	+	17.3201i	−0.724823	+	0.724823i	−0.969584	−	0.244760i	$-0.921291\pi$
$571$	−17.3201	+	17.3201i	−0.724823	+	0.724823i	0.244760	+	0.969584i	$0.421291\pi$
$572$	8.64160	−	31.7836i	0.361324	−	1.32894i
$573$	−16.0306	+	16.0306i	−0.669689	+	0.669689i
$574$	−34.2705	−	10.8608i	−1.43042	−	0.453321i
$575$	1.15226	−	18.6636i	0.0480525	−	0.778327i
$576$	0.471906	−	42.8327i	0.0196628	−	1.78470i
$577$		−	40.3754i		−	1.68085i	−0.541928	−	0.840425i	$-0.682305\pi$
$577$		−	40.3754i		−	1.68085i	0.541928	−	0.840425i	$-0.317695\pi$
$578$	−1.77592	−	6.67684i	−0.0738686	−	0.277720i
$579$			56.4513i			2.34603i
$580$	20.4958	−	24.8839i	0.851042	−	1.03325i
$581$	5.43064	+	5.43064i	0.225301	+	0.225301i
$582$	−20.5726	+	5.47195i	−0.852763	+	0.226820i
$583$	14.0129	−	14.0129i	0.580354	−	0.580354i
$584$	0.109628	−	19.9015i	0.00453645	−	0.823530i
$585$	−60.0096	−	27.0531i	−2.48109	−	1.11851i
$586$	−15.2089	+	4.04529i	−0.628273	+	0.167109i
$587$	38.9892			1.60926			0.804628	−	0.593779i	$-0.202365\pi$
$587$	38.9892			1.60926			0.804628	+	0.593779i	$0.202365\pi$
$588$	25.1624	+	43.9545i	1.03768	+	1.81265i
$589$	16.6932	+	16.6932i	0.687830	+	0.687830i
$590$	3.56720	−	21.6141i	0.146859	−	0.889838i
$591$	3.09503	+	3.09503i	0.127312	+	0.127312i
$592$	−21.5510	+	5.60526i	−0.885741	+	0.230375i
$593$			21.2839i			0.874023i	0.899456	+	0.437012i	$0.143963\pi$
$593$			21.2839i			0.874023i	−0.899456	+	0.437012i	$0.856037\pi$
$594$	14.4599	−	24.9394i	0.593297	−	1.02328i
$595$	37.8602	+	17.0679i	1.55212	+	0.699714i
$596$	39.4642	+	10.7299i	1.61652	+	0.439513i
$597$	−13.1484	−	13.1484i	−0.538127	−	0.538127i
$598$	14.5853	−	25.1556i	0.596435	−	1.02869i
$599$	22.8913			0.935312			0.467656	−	0.883911i	$-0.345099\pi$
$599$	22.8913			0.935312			0.467656	+	0.883911i	$0.345099\pi$
$600$	40.7843	+	2.74354i	1.66501	+	0.112005i
$601$	−22.2838	+	22.2838i	−0.908977	+	0.908977i	−0.996190	−	0.0872129i	$-0.972204\pi$
$601$	−22.2838	+	22.2838i	−0.908977	+	0.908977i	0.0872129	+	0.996190i	$0.472204\pi$
$602$	−40.1975	−	23.3066i	−1.63833	−	0.949905i
$603$			47.2059i			1.92237i
$604$	7.61283	−	27.9997i	0.309761	−	1.13929i
$605$	1.86308	−	4.13272i	0.0757450	−	0.168019i
$606$	−27.8281	+	47.9960i	−1.13044	+	1.94970i
$607$	11.4728	+	11.4728i	0.465666	+	0.465666i	0.900507	−	0.434841i	$-0.143195\pi$
$607$	11.4728	+	11.4728i	0.465666	+	0.465666i	−0.434841	+	0.900507i	$0.643195\pi$
$608$	−29.4675	+	16.6543i	−1.19507	+	0.675420i
$609$	58.4913	+	58.4913i	2.37019	+	2.37019i
$610$	−18.8683	−	3.11403i	−0.763955	−	0.126083i
$611$		−	41.7132i		−	1.68753i
$612$	43.4777	−	24.8894i	1.75748	−	1.00610i
$613$	−11.5024	−	11.5024i	−0.464577	−	0.464577i	0.435575	−	0.900152i	$-0.356545\pi$
$613$	−11.5024	−	11.5024i	−0.464577	−	0.464577i	−0.900152	+	0.435575i	$0.856545\pi$
$614$	5.06713	−	8.73943i	0.204493	−	0.352695i
$615$	−22.6935	−	34.6072i	−0.915090	−	1.39550i
$616$	−33.6353	−	0.185281i	−1.35520	−	0.00746520i
$617$	−3.02791	+	3.02791i	−0.121899	+	0.121899i	−0.765425	−	0.643526i	$-0.777471\pi$
$617$	−3.02791	+	3.02791i	−0.121899	+	0.121899i	0.643526	+	0.765425i	$0.277471\pi$
$618$	−13.0211	+	22.4578i	−0.523784	+	0.903386i
$619$	−26.1115			−1.04951			−0.524755	−	0.851253i	$-0.675843\pi$
$619$	−26.1115			−1.04951			−0.524755	+	0.851253i	$0.675843\pi$
$620$	1.69825	+	17.5625i	0.0682032	+	0.705329i
$621$	17.9961	−	17.9961i	0.722158	−	0.722158i
$622$	10.4116	−	17.9572i	0.417467	−	0.720017i
$623$	−19.6302	+	19.6302i	−0.786467	+	0.786467i
$624$	54.8138	+	32.1858i	2.19431	+	1.28846i
$625$	−3.07519	+	24.8101i	−0.123008	+	0.992406i
$626$	2.12169	−	0.564332i	0.0847999	−	0.0225553i
$627$	−51.8059			−2.06893
$628$	−1.70798	−	2.98356i	−0.0681559	−	0.119057i
$629$	−18.4155	−	18.4155i	−0.734275	−	0.734275i
$630$	−10.9462	+	66.3242i	−0.436106	+	2.64242i
$631$		−	2.37388i		−	0.0945028i	−0.998883	−	0.0472514i	$-0.984954\pi$
$631$		−	2.37388i		−	0.0945028i	0.998883	−	0.0472514i	$-0.0150462\pi$
$632$	0.0229840	−	4.17243i	0.000914254	−	0.165970i
$633$	−5.99538	+	5.99538i	−0.238295	+	0.238295i
$634$	−7.52741	+	2.00216i	−0.298951	+	0.0795158i
$635$	−26.8258	+	10.1546i	−1.06455	+	0.402973i
$636$	19.0005	+	33.1907i	0.753419	+	1.31610i
$637$	−48.1688			−1.90852
$638$	−29.5111	+	7.84942i	−1.16835	+	0.310762i
$639$	42.1643	−	42.1643i	1.66799	−	1.66799i
$640$	−24.9137	−	4.39423i	−0.984799	−	0.173697i
$641$	23.1051	−	23.1051i	0.912595	−	0.912595i	−0.0838808	−	0.996476i	$-0.526732\pi$
$641$	23.1051	−	23.1051i	0.912595	−	0.912595i	0.996476	+	0.0838808i	$0.0267315\pi$
$642$	23.7123	−	40.8973i	0.935849	−	1.61409i
$643$		−	10.6945i		−	0.421748i	−0.977513	−	0.210874i	$-0.932369\pi$
$643$		−	10.6945i		−	0.421748i	0.977513	−	0.210874i	$-0.0676310\pi$
$644$	−28.6544	−	7.79081i	−1.12914	−	0.307001i
$645$	−18.9362	−	50.0246i	−0.745614	−	1.96972i
$646$	−34.2470	−	19.8564i	−1.34743	−	0.781241i
$647$	−26.7516	−	26.7516i	−1.05171	−	1.05171i	−0.998588	−	0.0531249i	$-0.983082\pi$
$647$	−26.7516	−	26.7516i	−1.05171	−	1.05171i	−0.0531249	−	0.998588i	$-0.516918\pi$
$648$	7.17319	+	7.25265i	0.281789	+	0.284911i
$649$	−14.6730	+	14.6730i	−0.575965	+	0.575965i
$650$	−21.5353	+	32.3665i	−0.844682	+	1.26952i
$651$	−45.2738			−1.77442
$652$	9.07756	+	2.46809i	0.355505	+	0.0966579i
$653$	−19.0085			−0.743860			−0.371930	−	0.928261i	$-0.621304\pi$
$653$	−19.0085			−0.743860			−0.371930	+	0.928261i	$0.621304\pi$
$654$	−45.5383	−	26.4032i	−1.78069	−	1.03245i
$655$	−0.493414	−	0.222437i	−0.0192793	−	0.00869133i
$656$	11.6677	+	22.8005i	0.455549	+	0.890211i
$657$	26.6406	+	26.6406i	1.03935	+	1.03935i
$658$	−41.1663	+	10.9495i	−1.60483	+	0.426856i
$659$	−5.89061	−	5.89061i	−0.229466	−	0.229466i	0.583004	−	0.812469i	$-0.301877\pi$
$659$	−5.89061	−	5.89061i	−0.229466	−	0.229466i	−0.812469	+	0.583004i	$0.801877\pi$
$660$	−29.8871	−	24.6168i	−1.16336	−	0.958207i
$661$		−	15.8159i		−	0.615166i	−0.951521	−	0.307583i	$-0.900480\pi$
$661$		−	15.8159i		−	0.615166i	0.951521	−	0.307583i	$-0.0995202\pi$
$662$	9.82352	+	5.69569i	0.381802	+	0.221369i
$663$			74.3419i			2.88720i
$664$	0.0301401	−	5.47153i	0.00116966	−	0.212336i
$665$	49.6779	−	18.8050i	1.92643	−	0.729226i
$666$	21.1445	−	36.4685i	0.819332	−	1.41313i
$667$	−26.9591			−1.04386
$668$	11.6799	−	6.68634i	0.451910	−	0.258702i
$669$	10.2857	−	10.2857i	0.397669	−	0.397669i
$670$	27.5074	+	4.53982i	1.06270	+	0.175389i
$671$	12.8090	+	12.8090i	0.494485	+	0.494485i
$672$	17.3755	−	62.5438i	0.670276	−	2.41268i
$673$		−	6.60956i		−	0.254780i	−0.991853	−	0.127390i	$-0.959340\pi$
$673$		−	6.60956i		−	0.254780i	0.991853	−	0.127390i	$-0.0406599\pi$
$674$	−14.8785	−	8.62656i	−0.573098	−	0.332283i
$675$	−25.4969	+	22.5317i	−0.981376	+	0.867246i
$676$	−29.9013	+	17.1174i	−1.15005	+	0.658363i
$677$	−17.3019	+	17.3019i	−0.664966	+	0.664966i	−0.956546	−	0.291581i	$-0.905819\pi$
$677$	−17.3019	+	17.3019i	−0.664966	+	0.664966i	0.291581	+	0.956546i	$0.405819\pi$
$678$	29.1623	−	50.2971i	1.11997	−	1.93165i
$679$	−20.6755			−0.793452
$680$	−10.3220	−	27.7285i	−0.395832	−	1.06334i
$681$	19.7163			0.755530
$682$	8.38335	−	14.4590i	0.321015	−	0.553664i
$683$	−26.3718			−1.00909			−0.504544	−	0.863386i	$-0.668339\pi$
$683$	−26.3718			−1.00909			−0.504544	+	0.863386i	$0.668339\pi$
$684$	16.8116	−	61.8324i	0.642806	−	2.36422i
$685$	−3.77452	−	1.70160i	−0.144217	−	0.0650148i
$686$	2.54184	+	9.55642i	0.0970478	+	0.364866i
$687$	−33.8464	+	33.8464i	−1.29132	+	1.29132i
$688$	8.33284	+	32.0380i	0.317687	+	1.22144i
$689$	−36.3731			−1.38570
$690$	−19.9125	−	27.7844i	−0.758055	−	1.05773i
$691$	−5.58695	−	5.58695i	−0.212538	−	0.212538i	0.592807	−	0.805345i	$-0.298020\pi$
$691$	−5.58695	−	5.58695i	−0.212538	−	0.212538i	−0.805345	+	0.592807i	$0.798020\pi$
$692$	1.77190	+	0.481761i	0.0673576	+	0.0183138i
$693$	45.0250	−	45.0250i	1.71036	−	1.71036i
$694$	35.1603	−	9.35201i	1.33467	−	0.354998i
$695$	−15.6434	−	7.05225i	−0.593390	−	0.267507i
$696$	0.324628	−	58.9317i	0.0123050	−	2.23380i
$697$	−16.0855	+	25.2697i	−0.609282	+	0.957158i
$698$	1.95605	+	7.35407i	0.0740376	+	0.278356i
$699$			21.3837i			0.808805i
$700$	37.5951	+	12.7569i	1.42096	+	0.482165i
$701$	−4.86224			−0.183644			−0.0918221	−	0.995775i	$-0.529269\pi$
$701$	−4.86224			−0.183644			−0.0918221	+	0.995775i	$0.529269\pi$
$702$	−51.1342	+	13.6008i	−1.92994	+	0.513328i
$703$	−33.3106			−1.25633
$704$	16.7571	+	17.1304i	0.631556	+	0.645627i
$705$	−44.7037	−	20.1530i	−1.68364	−	0.759004i
$706$	38.2560	+	22.1809i	1.43978	+	0.834789i
$707$	−38.1016	+	38.1016i	−1.43296	+	1.43296i
$708$	−19.8956	−	34.7543i	−0.747722	−	1.30615i
$709$	5.10370	−	5.10370i	0.191673	−	0.191673i	−0.604745	−	0.796419i	$-0.706725\pi$
$709$	5.10370	−	5.10370i	0.191673	−	0.191673i	0.796419	+	0.604745i	$0.206725\pi$
$710$	−20.5146	−	28.6245i	−0.769898	−	1.07426i
$711$	5.58531	+	5.58531i	0.209466	+	0.209466i
$712$	19.7780	+	0.108948i	0.741211	+	0.00408299i
$713$	10.4335	−	10.4335i	0.390738	−	0.390738i
$714$	73.3673	−	19.5144i	2.74570	−	0.730308i
$715$	34.4402	−	13.0369i	1.28799	−	0.487554i
$716$	8.03897	−	29.5671i	0.300431	−	1.10497i
$717$	−18.1257	+	18.1257i	−0.676917	+	0.676917i
$718$	0.456878	+	1.71770i	0.0170505	+	0.0641041i
$719$	12.2870	−	12.2870i	0.458229	−	0.458229i	−0.439845	−	0.898074i	$-0.644966\pi$
$719$	12.2870	−	12.2870i	0.458229	−	0.458229i	0.898074	+	0.439845i	$0.144966\pi$
$720$	39.0798	−	27.6831i	1.45642	−	1.03169i
$721$	−17.8281	+	17.8281i	−0.663955	+	0.663955i
$722$	−22.9648	+	6.10823i	−0.854661	+	0.227325i
$723$	−64.8631			−2.41229
$724$	1.74900	−	6.43276i	0.0650010	−	0.239072i
$725$	35.9747	+	2.22101i	1.33607	+	0.0824863i
$726$	−2.13014	−	8.00858i	−0.0790569	−	0.297226i
$727$	41.1680			1.52684			0.763419	−	0.645904i	$-0.223519\pi$
$727$	41.1680			1.52684			0.763419	+	0.645904i	$0.223519\pi$
$728$	43.4129	+	43.8938i	1.60899	+	1.62681i
$729$	39.6985			1.47031
$730$	18.0858	−	12.9617i	0.669386	−	0.479735i
$731$	−27.3767	+	27.3767i	−1.01256	+	1.01256i
$732$	−30.3392	+	17.3681i	−1.12137	+	0.641943i
$733$	−16.8082	−	16.8082i	−0.620826	−	0.620826i	0.324916	−	0.945743i	$-0.394664\pi$
$733$	−16.8082	−	16.8082i	−0.620826	−	0.620826i	−0.945743	+	0.324916i	$0.894664\pi$
$734$	−6.01926	+	10.3816i	−0.222175	+	0.383192i
$735$	−23.2719	+	51.6221i	−0.858396	+	1.90411i
$736$	10.4092	+	18.4177i	0.383688	+	0.678885i
$737$	−18.6737	−	18.6737i	−0.687854	−	0.687854i
$738$	−46.2207	−	14.6480i	−1.70141	−	0.539200i
$739$	−52.1405			−1.91802			−0.959009	−	0.283374i	$-0.908546\pi$
$739$	−52.1405			−1.91802			−0.959009	+	0.283374i	$0.908546\pi$
$740$	−19.2171	−	15.8283i	−0.706434	−	0.581860i
$741$	67.2361	+	67.2361i	2.46998	+	2.46998i
$742$	9.54775	+	35.8962i	0.350509	+	1.31779i
$743$	−5.84030	+	5.84030i	−0.214260	+	0.214260i	−0.806074	−	0.591814i	$-0.798412\pi$
$743$	−5.84030	+	5.84030i	−0.214260	+	0.214260i	0.591814	+	0.806074i	$0.298412\pi$
$744$	22.6817	+	22.9330i	0.831552	+	0.840764i
$745$	16.1874	+	42.7629i	0.593060	+	1.56671i
$746$	−2.40693	−	1.39554i	−0.0881238	−	0.0510943i
$747$	7.32432	+	7.32432i	0.267983	+	0.267983i
$748$	−7.35314	+	27.0446i	−0.268857	+	0.988850i
$749$	32.4663	−	32.4663i	1.18629	−	1.18629i
$750$	24.2825	+	38.7164i	0.886673	+	1.41372i
$751$	−30.4466	+	30.4466i	−1.11101	+	1.11101i	−0.118000	+	0.993014i	$0.537648\pi$
$751$	−30.4466	+	30.4466i	−1.11101	+	1.11101i	−0.993014	+	0.118000i	$0.962352\pi$
$752$	26.1703	+	15.3668i	0.954331	+	0.560369i
$753$		−	7.85799i		−	0.286361i
$754$	48.4881	+	28.1135i	1.76583	+	1.02383i
$755$	30.3401	−	11.4849i	1.10419	−	0.417978i
$756$	26.8450	+	46.8937i	0.976341	+	1.70551i
$757$	23.8184			0.865695			0.432847	−	0.901467i	$-0.357509\pi$
$757$	23.8184			0.865695			0.432847	+	0.901467i	$0.357509\pi$
$758$	−2.31982	−	8.72171i	−0.0842596	−	0.316787i
$759$			32.3796i			1.17530i
$760$	−34.4136	−	15.7427i	−1.24831	−	0.571048i
$761$	−0.854509			−0.0309759			−0.0154880	−	0.999880i	$-0.504930\pi$
$761$	−0.854509			−0.0309759			−0.0154880	+	0.999880i	$0.504930\pi$
$762$	−26.3007	+	45.3616i	−0.952774	+	1.64328i
$763$	−36.1506	−	36.1506i	−1.30874	−	1.30874i
$764$	15.1374	+	4.11569i	0.547651	+	0.148900i
$765$	51.0622	+	23.0195i	1.84616	+	0.832270i
$766$	−12.0463	−	45.2897i	−0.435249	−	1.63638i
$767$	38.0865			1.37522
$768$	−40.3859	+	22.5324i	−1.45730	+	0.813069i
$769$			19.1960i			0.692225i	0.938193	+	0.346112i	$0.112498\pi$
$769$			19.1960i			0.692225i	−0.938193	+	0.346112i	$0.887502\pi$
$770$	−21.9064	−	30.5666i	−0.789452	−	1.10154i
$771$	−23.4725			−0.845342
$772$	33.8995	−	19.4062i	1.22007	−	0.698446i
$773$		−	27.6369i		−	0.994031i	−0.867742	−	0.497015i	$-0.834429\pi$
$773$		−	27.6369i		−	0.994031i	0.867742	−	0.497015i	$-0.165571\pi$
$774$	−54.2145	−	31.4336i	−1.94870	−	1.12986i
$775$	−14.7822	+	13.0631i	−0.530993	+	0.469240i
$776$	10.3582	+	10.4730i	0.371838	+	0.375957i
$777$	45.1711	−	45.1711i	1.62050	−	1.62050i
$778$	13.1642	+	49.4929i	0.471960	+	1.77441i
$779$	8.30633	+	37.4023i	0.297605	+	1.34008i
$780$	6.84012	+	70.7376i	0.244916	+	2.53281i
$781$			33.3586i			1.19367i
$782$	−12.4106	+	21.4049i	−0.443802	+	0.765438i
$783$	34.6880	+	34.6880i	1.23965	+	1.23965i
$784$	17.7450	−	30.2204i	0.633750	−	1.07930i
$785$	1.57966	−	3.50403i	0.0563804	−	0.125064i
$786$	−0.956160	+	0.254322i	−0.0341051	+	0.00907135i
$787$	−1.73587	−	1.73587i	−0.0618770	−	0.0618770i	0.675491	−	0.737368i	$-0.263932\pi$
$787$	−1.73587	−	1.73587i	−0.0618770	−	0.0618770i	−0.737368	+	0.675491i	$0.763932\pi$
$788$	0.794614	−	2.92257i	0.0283070	−	0.104112i
$789$			31.2568i			1.11277i
$790$	3.79176	−	2.71747i	0.134905	−	0.0966833i
$791$	39.9283	−	39.9283i	1.41969	−	1.41969i
$792$	−45.3640	−	0.249889i	−1.61194	−	0.00887944i
$793$		−	33.2481i		−	1.18067i
$794$	9.60010	−	2.55345i	0.340695	−	0.0906187i
$795$	−17.5730	+	38.9807i	−0.623249	+	1.38250i
$796$	−3.37570	+	12.4157i	−0.119649	+	0.440064i
$797$	−10.2727	−	10.2727i	−0.363877	−	0.363877i	0.501361	−	0.865238i	$-0.332833\pi$
$797$	−10.2727	−	10.2727i	−0.363877	−	0.363877i	−0.865238	+	0.501361i	$0.832833\pi$
$798$	48.7055	−	84.0038i	1.72415	−	2.97370i
$799$			35.4937i			1.25568i
$800$	−12.3729	−	25.4345i	−0.437447	−	0.899244i
$801$	−26.4753	+	26.4753i	−0.935458	+	0.935458i
$802$	−17.2535	+	4.58914i	−0.609244	+	0.162048i
$803$	−21.0770			−0.743790
$804$	44.2303	−	25.3203i	1.55988	−	0.892977i
$805$	−11.7534	−	31.0495i	−0.414254	−	1.09435i
$806$	−29.6458	+	7.88526i	−1.04423	+	0.277746i
$807$	55.9824			1.97067
$808$	38.3885	+	0.211465i	1.35050	+	0.00743930i
$809$	−38.8381	+	38.8381i	−1.36547	+	1.36547i	−0.498697	+	0.866776i	$0.666188\pi$
$809$	−38.8381	+	38.8381i	−1.36547	+	1.36547i	−0.866776	+	0.498697i	$0.833812\pi$
$810$	−1.85713	+	11.2526i	−0.0652529	+	0.395375i
$811$	19.9152			0.699319			0.349659	−	0.936877i	$-0.386297\pi$
$811$	19.9152			0.699319			0.349659	+	0.936877i	$0.386297\pi$
$812$	15.0170	−	55.2321i	0.526994	−	1.93827i
$813$	−48.5041			−1.70111
$814$	6.06187	+	22.7905i	0.212468	+	0.798807i
$815$	3.72342	+	9.83632i	0.130426	+	0.344551i
$816$	−46.6411	−	27.3869i	−1.63276	−	0.958735i
$817$			49.5199i			1.73248i
$818$	4.75938	−	1.26591i	0.166408	−	0.0442615i
$819$	−116.871			−4.08380
$820$	−12.9806	+	25.5246i	−0.453302	+	0.891357i
$821$	21.2860			0.742887			0.371444	−	0.928455i	$-0.378863\pi$
$821$	21.2860			0.742887			0.371444	+	0.928455i	$0.378863\pi$
$822$	−7.31445	+	1.94551i	−0.255121	+	0.0678575i
$823$		−	23.2629i		−	0.810893i	−0.914119	−	0.405446i	$-0.867116\pi$
$823$		−	23.2629i		−	0.810893i	0.914119	−	0.405446i	$-0.132884\pi$
$824$	17.9624	+	0.0989466i	0.625749	+	0.00344697i
$825$	2.66758	−	43.2078i	0.0928731	−	1.50430i
$826$	−9.99753	−	37.5872i	−0.347858	−	1.30783i
$827$	−12.1337			−0.421929			−0.210964	−	0.977494i	$-0.567660\pi$
$827$	−12.1337			−0.421929			−0.210964	+	0.977494i	$0.567660\pi$
$828$	−38.6463	−	10.5075i	−1.34305	−	0.365161i
$829$	−27.7302			−0.963108			−0.481554	−	0.876416i	$-0.659928\pi$
$829$	−27.7302			−0.963108			−0.481554	+	0.876416i	$0.659928\pi$
$830$	4.97234	−	3.56357i	0.172592	−	0.123693i
$831$	−24.3642	+	24.3642i	−0.845184	+	0.845184i
$832$	0.484554	−	43.9807i	0.0167989	−	1.52476i
$833$	40.9869			1.42011
$834$	−30.3146	+	8.06314i	−1.04971	+	0.279204i
$835$	13.7174	+	6.18399i	0.474712	+	0.214006i
$836$	17.8093	+	31.1099i	0.615948	+	1.07596i
$837$	−26.8494			−0.928051
$838$	2.03412	−	0.541040i	0.0702675	−	0.0186899i
$839$	−33.9785	+	33.9785i	−1.17307	+	1.17307i	−0.191596	+	0.981474i	$0.561366\pi$
$839$	−33.9785	+	33.9785i	−1.17307	+	1.17307i	−0.981474	+	0.191596i	$0.938634\pi$
$840$	68.0148	−	25.3187i	2.34673	−	0.873580i
$841$		−	22.9643i		−	0.791874i
$842$	−5.41503	+	9.33946i	−0.186614	+	0.321859i
$843$	0.707670	+	0.707670i	0.0243735	+	0.0243735i
$844$	5.66131	+	1.53925i	0.194870	+	0.0529832i
$845$	−35.1175	−	15.8314i	−1.20808	−	0.544617i
$846$	−55.5211	+	14.7676i	−1.90886	+	0.507722i
$847$		−	8.04862i		−	0.276554i
$848$	13.3995	−	22.8199i	0.460142	−	0.783640i
$849$	36.4066	−	36.4066i	1.24947	−	1.24947i
$850$	18.3244	−	27.5407i	0.628520	−	0.944637i
$851$			20.8197i			0.713689i
$852$	−62.1225	−	16.8904i	−2.12828	−	0.578656i
$853$	−29.6879	−	29.6879i	−1.01649	−	1.01649i	−0.999862	−	0.0166325i	$-0.994705\pi$
$853$	−29.6879	−	29.6879i	−1.01649	−	1.01649i	−0.0166325	−	0.999862i	$-0.505295\pi$
$854$	−32.8122	+	8.72747i	−1.12281	+	0.298648i
$855$	67.0007	−	25.3623i	2.29138	−	0.867373i
$856$	−32.7107	−	0.180189i	−1.11803	−	0.00615872i
$857$	36.5526	+	36.5526i	1.24861	+	1.24861i	0.956333	+	0.292281i	$0.0944141\pi$
$857$	36.5526	+	36.5526i	1.24861	+	1.24861i	0.292281	+	0.956333i	$0.405586\pi$
$858$	33.7661	−	58.2373i	1.15275	−	1.98819i
$859$		−	52.4327i		−	1.78898i	−0.447086	−	0.894491i	$-0.647538\pi$
$859$		−	52.4327i		−	1.78898i	0.447086	−	0.894491i	$-0.352462\pi$
$860$	−23.5305	+	28.5683i	−0.802385	+	0.974172i
$861$	−61.9836	−	39.4558i	−2.11239	−	1.34465i
$862$	10.1710	+	38.2394i	0.346426	+	1.30244i
$863$	26.3665	−	26.3665i	0.897526	−	0.897526i	−0.0976910	−	0.995217i	$-0.531146\pi$
$863$	26.3665	−	26.3665i	0.897526	−	0.897526i	0.995217	+	0.0976910i	$0.0311457\pi$
$864$	10.3045	−	37.0913i	0.350565	−	1.26187i
$865$	0.726797	+	1.92001i	0.0247118	+	0.0652822i
$866$	−42.9094	−	24.8789i	−1.45812	−	0.845420i
$867$		−	14.1207i		−	0.479565i
$868$	15.5638	+	27.1873i	0.528269	+	0.922798i
$869$	−4.41887			−0.149900
$870$	53.5551	−	38.3818i	1.81569	−	1.30127i
$871$			48.4711i			1.64238i
$872$	−0.200636	+	36.4228i	−0.00679441	+	1.23343i
$873$	−27.8851			−0.943767
$874$	8.13461	+	30.5833i	0.275157	+	1.03450i
$875$	13.1260	+	42.4013i	0.443739	+	1.43342i
$876$	10.6719	−	39.2508i	0.360569	−	1.32616i
$877$	−22.1149	−	22.1149i	−0.746768	−	0.746768i	0.227102	−	0.973871i	$-0.427075\pi$
$877$	−22.1149	−	22.1149i	−0.746768	−	0.746768i	−0.973871	+	0.227102i	$0.927075\pi$
$878$	−7.79928	+	13.4516i	−0.263213	+	0.453971i
$879$	−32.1650			−1.08490
$880$	−4.50829	+	26.4100i	−0.151975	+	0.890281i
$881$			9.30681i			0.313554i	0.987634	+	0.156777i	$0.0501105\pi$
$881$			9.30681i			0.313554i	−0.987634	+	0.156777i	$0.949890\pi$
$882$	17.0531	+	64.1137i	0.574208	+	2.15882i
$883$	41.2787			1.38914			0.694570	−	0.719425i	$-0.255595\pi$
$883$	41.2787			1.38914			0.694570	+	0.719425i	$0.255595\pi$
$884$	44.6430	−	25.5565i	1.50151	−	0.859558i
$885$	18.4008	−	40.8170i	0.618536	−	1.37205i
$886$	−1.80296	−	1.04536i	−0.0605716	−	0.0351195i
$887$			21.8934i			0.735109i	0.930002	+	0.367554i	$0.119805\pi$
$887$			21.8934i			0.735109i	−0.930002	+	0.367554i	$0.880195\pi$
$888$	−45.5112	−	0.250700i	−1.52726	−	0.00841295i
$889$	−36.0103	+	36.0103i	−1.20775	+	1.20775i
$890$	12.8813	+	17.9736i	0.431781	+	0.602475i
$891$	7.63895	−	7.63895i	0.255914	−	0.255914i
$892$	−9.71258	−	2.64074i	−0.325201	−	0.0884186i
$893$	32.1011	+	32.1011i	1.07422	+	1.07422i
$894$	72.3107	+	41.9258i	2.41843	+	1.40221i
$895$	32.0385	−	12.1278i	1.07093	−	0.405387i
$896$	−43.5313	+	11.0665i	−1.45428	+	0.369707i
$897$	42.0236	−	42.0236i	1.40313	−	1.40313i
$898$	−0.860148	−	3.23386i	−0.0287035	−	0.107915i
$899$	20.1109	+	20.1109i	0.670735	+	0.670735i
$900$	50.7046	+	17.2052i	1.69015	+	0.573508i
$901$	30.9498			1.03109
$902$	24.0784	−	12.4895i	0.801724	−	0.415856i
$903$	−67.1519	−	67.1519i	−2.23467	−	2.23467i
$904$	−40.2290	−	0.221603i	−1.33800	−	0.00737040i
$905$	6.97045	−	2.63858i	0.231706	−	0.0877094i
$906$	29.7462	−	51.3042i	0.988253	−	1.70447i
$907$	−0.978011	−	0.978011i	−0.0324743	−	0.0324743i	0.690683	−	0.723157i	$-0.257310\pi$
$907$	−0.978011	−	0.978011i	−0.0324743	−	0.0324743i	−0.723157	+	0.690683i	$0.757310\pi$
$908$	−6.77787	−	11.8398i	−0.224931	−	0.392918i
$909$	−51.3878	+	51.3878i	−1.70442	+	1.70442i
$910$	−11.2395	+	68.1018i	−0.372587	+	2.25755i
$911$	−46.5805			−1.54328			−0.771640	−	0.636060i	$-0.780563\pi$
$911$	−46.5805			−1.54328			−0.771640	+	0.636060i	$0.780563\pi$
$912$	−66.9522	+	17.4138i	−2.21701	+	0.576627i
$913$	−5.79470			−0.191777
$914$	3.53432	+	13.2878i	0.116905	+	0.439522i
$915$	−35.6317	−	16.0632i	−1.17795	−	0.531033i
$916$	31.9604	+	8.68969i	1.05600	+	0.287116i
$917$	−0.960941			−0.0317331
$918$	43.5101	−	11.5729i	1.43605	−	0.381963i
$919$	32.4294	−	32.4294i	1.06975	−	1.06975i	0.0723701	−	0.997378i	$-0.476944\pi$
$919$	32.4294	−	32.4294i	1.06975	−	1.06975i	0.997378	−	0.0723701i	$-0.0230563\pi$
$920$	−9.83945	+	21.5090i	−0.324397	+	0.709132i
$921$	14.5996	−	14.5996i	0.481074	−	0.481074i
$922$	−12.5733	−	47.2713i	−0.414080	−	1.55680i
$923$	43.2943	−	43.2943i	1.42505	−	1.42505i
$924$	−66.3373	−	18.0364i	−2.18234	−	0.593354i
$925$	1.71522	−	27.7821i	0.0563961	−	0.913471i
$926$	30.1306	−	8.01421i	0.990154	−	0.263363i
$927$	−24.0449	+	24.0449i	−0.789737	+	0.789737i
$928$	−35.5006	+	20.0640i	−1.16537	+	0.658633i
$929$	−30.1813	−	30.1813i	−0.990218	−	0.990218i	0.00973503	−	0.999953i	$-0.496901\pi$
$929$	−30.1813	−	30.1813i	−0.990218	−	0.990218i	−0.999953	+	0.00973503i	$0.996901\pi$
$930$	−5.87227	+	35.5808i	−0.192559	+	1.16674i
$931$	37.0692	−	37.0692i	1.21489	−	1.21489i
$932$	12.8411	−	7.35107i	0.420624	−	0.240792i
$933$	29.9983	−	29.9983i	0.982100	−	0.982100i
$934$	−16.5034	−	9.56871i	−0.540009	−	0.313098i
$935$	−29.3052	+	11.0931i	−0.958382	+	0.362784i
$936$	58.5511	+	59.1997i	1.91380	+	1.93500i
$937$	−57.0303			−1.86310			−0.931549	−	0.363616i	$-0.881542\pi$
$937$	−57.0303			−1.86310			−0.931549	+	0.363616i	$0.881542\pi$
$938$	47.8357	−	12.7234i	1.56189	−	0.415435i
$939$	4.48713			0.146432
$940$	3.26574	+	33.7729i	0.106517	+	1.10155i
$941$			48.5768i			1.58356i	0.610808	+	0.791778i	$0.290845\pi$
$941$			48.5768i			1.58356i	−0.610808	+	0.791778i	$0.709155\pi$
$942$	−1.80609	−	6.79027i	−0.0588456	−	0.221239i
$943$	23.3771	−	5.19159i	0.761262	−	0.169062i
$944$	−14.0308	+	23.8949i	−0.456662	+	0.777714i
$945$	−24.8281	+	55.0741i	−0.807657	+	1.79156i
$946$	33.8807	−	9.01165i	1.10155	−	0.292994i
$947$	−24.4622	+	24.4622i	−0.794913	+	0.794913i	−0.982288	−	0.187375i	$-0.940002\pi$
$947$	−24.4622	+	24.4622i	−0.794913	+	0.794913i	0.187375	+	0.982288i	$0.440002\pi$
$948$	2.23740	−	8.22909i	0.0726673	−	0.267268i
$949$	27.3547	+	27.3547i	0.887970	+	0.887970i
$950$	−8.33538	−	41.4811i	−0.270435	−	1.34582i
$951$	−15.9196			−0.516228
$952$	−36.9400	−	37.3493i	−1.19723	−	1.21050i
$953$	−13.4867	+	13.4867i	−0.436876	+	0.436876i	−0.890959	−	0.454083i	$-0.849967\pi$
$953$	−13.4867	+	13.4867i	−0.436876	+	0.436876i	0.454083	+	0.890959i	$0.349967\pi$
$954$	12.8771	+	48.4133i	0.416911	+	1.56744i
$955$	6.20903	+	16.4027i	0.200920	+	0.530777i
$956$	17.1157	+	4.65358i	0.553562	+	0.150507i
$957$	−62.4125			−2.01751
$958$	14.3395	−	24.7317i	0.463287	−	0.799045i
$959$	−7.35102			−0.237377
$960$	−46.8997	−	21.7678i	−1.51368	−	0.702551i
$961$	15.4337			0.497860
$962$	21.7112	−	37.4459i	0.699997	−	1.20730i
$963$	43.7874	−	43.7874i	1.41103	−	1.41103i
$964$	22.2980	+	38.9509i	0.718170	+	1.25452i
$965$	39.8131	+	17.9482i	1.28163	+	0.577774i
$966$	−52.5037	−	30.4417i	−1.68928	−	0.979446i
$967$			36.3493i			1.16891i	0.811425	+	0.584457i	$0.198692\pi$
$967$			36.3493i			1.16891i	−0.811425	+	0.584457i	$0.801308\pi$
$968$	−4.07694	+	4.03227i	−0.131038	+	0.129602i
$969$	−57.2112	−	57.2112i	−1.83789	−	1.83789i
$970$	−2.68173	+	16.2489i	−0.0861050	+	0.521721i
$971$	−40.6018	+	40.6018i	−1.30297	+	1.30297i	−0.376597	+	0.926377i	$0.622906\pi$
$971$	−40.6018	+	40.6018i	−1.30297	+	1.30297i	−0.926377	+	0.376597i	$0.877094\pi$
$972$	−9.92771	−	17.3421i	−0.318432	−	0.556247i
$973$	−30.4662			−0.976700
$974$	7.80242	−	13.4571i	0.250006	−	0.431192i
$975$	−59.5392	+	52.6150i	−1.90678	+	1.68503i
$976$	20.8594	+	12.2483i	0.667693	+	0.392059i
$977$			23.4482i			0.750176i	0.926989	+	0.375088i	$0.122387\pi$
$977$			23.4482i			0.750176i	−0.926989	+	0.375088i	$0.877613\pi$
$978$	16.6329	+	9.64378i	0.531862	+	0.308374i
$979$		−	20.9462i		−	0.669442i
$980$	38.9997	−	3.77116i	1.24580	−	0.120465i
$981$	−48.7564	−	48.7564i	−1.55667	−	1.55667i
$982$	16.1174	−	4.28695i	0.514328	−	0.136802i
$983$	−5.03443	−	5.03443i	−0.160573	−	0.160573i	0.622247	−	0.782821i	$-0.286220\pi$
$983$	−5.03443	−	5.03443i	−0.160573	−	0.160573i	−0.782821	+	0.622247i	$0.786220\pi$
$984$	11.0672	+	51.1641i	0.352809	+	1.63105i
$985$	3.16685	−	1.19877i	0.100904	−	0.0381961i
$986$	−41.2586	−	23.9218i	−1.31394	−	0.761824i
$987$	−87.0620			−2.77121
$988$	17.2621	−	63.4896i	0.549181	−	2.01987i
$989$	30.9508			0.984177
$990$	−29.5453	−	41.2252i	−0.939010	−	1.31022i
$991$	35.6129	−	35.6129i	1.13128	−	1.13128i	0.141316	−	0.989964i	$-0.454867\pi$
$991$	35.6129	−	35.6129i	1.13128	−	1.13128i	0.989964	−	0.141316i	$-0.0451335\pi$
$992$	5.97417	−	21.5042i	0.189680	−	0.682760i
$993$	16.4107	+	16.4107i	0.520777	+	0.520777i
$994$	−54.0913	−	31.3622i	−1.71567	−	0.994749i
$995$	−13.4535	+	5.09267i	−0.426505	+	0.161448i
$996$	2.93402	−	10.7912i	0.0929680	−	0.341934i
$997$			0.0795810i			0.00252036i	0.999999	+	0.00126018i	$0.000401127\pi$
$997$			0.0795810i			0.00252036i	−0.999999	+	0.00126018i	$0.999599\pi$
$998$	−29.1999	+	50.3619i	−0.924307	+	1.59418i
$999$	26.7885	−	26.7885i	0.847549	−	0.847549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.j.c.747.50	yes	240
4.3	odd	2	inner	820.2.j.c.747.111	yes	240
5.3	odd	4		820.2.s.c.583.10	yes	240
20.3	even	4		820.2.s.c.583.71	yes	240
41.32	even	4		820.2.s.c.647.71	yes	240
164.155	odd	4		820.2.s.c.647.10	yes	240
205.73	odd	4	inner	820.2.j.c.483.111	yes	240
820.483	even	4	inner	820.2.j.c.483.50	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.50	✓	240	820.483	even	4	inner
820.2.j.c.483.111	yes	240	205.73	odd	4	inner
820.2.j.c.747.50	yes	240	1.1	even	1	trivial
820.2.j.c.747.111	yes	240	4.3	odd	2	inner
820.2.s.c.583.10	yes	240	5.3	odd	4
820.2.s.c.583.71	yes	240	20.3	even	4
820.2.s.c.647.10	yes	240	164.155	odd	4
820.2.s.c.647.71	yes	240	41.32	even	4

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.363517 - 1.36670i) q^{2} -2.89040i q^{3} +(-1.73571 + 0.993633i) q^{4} +(-2.03850 - 0.918980i) q^{5} +(-3.95030 + 1.05071i) q^{6} -3.97005 q^{7} +(1.98895 + 2.01099i) q^{8} -5.35442 q^{9} +(-0.514937 + 3.12007i) q^{10} +(2.11810 - 2.11810i) q^{11} +(2.87200 + 5.01690i) q^{12} -5.49792 q^{13} +(1.44318 + 5.42584i) q^{14} +(-2.65622 + 5.89208i) q^{15} +(2.02539 - 3.44932i) q^{16} +4.67818 q^{17} +(1.94642 + 7.31785i) q^{18} +(4.23103 - 4.23103i) q^{19} +(4.45137 - 0.430435i) q^{20} +11.4750i q^{21} +(-3.66476 - 2.12483i) q^{22} +(-2.64446 - 2.64446i) q^{23} +(5.81256 - 5.74887i) q^{24} +(3.31095 + 3.74668i) q^{25} +(1.99859 + 7.51398i) q^{26} +6.80520i q^{27} +(6.89086 - 3.94477i) q^{28} +(5.09727 - 5.09727i) q^{29} +(9.01825 + 1.48838i) q^{30} +3.94542i q^{31} +(-5.45043 - 1.51420i) q^{32} +(-6.12215 - 6.12215i) q^{33} +(-1.70060 - 6.39365i) q^{34} +(8.09294 + 3.64839i) q^{35} +(9.29372 - 5.32032i) q^{36} +(-3.93647 - 3.93647i) q^{37} +(-7.32057 - 4.24448i) q^{38} +15.8912i q^{39} +(-2.20642 - 5.92720i) q^{40} +(-3.43841 + 5.40161i) q^{41} +(15.6829 - 4.17136i) q^{42} +(-5.85200 + 5.85200i) q^{43} +(-1.57179 + 5.78101i) q^{44} +(10.9150 + 4.92060i) q^{45} +(-2.65287 + 4.57548i) q^{46} +7.58708i q^{47} +(-9.96991 - 5.85418i) q^{48} +8.76128 q^{49} +(3.91698 - 5.88704i) q^{50} -13.5218i q^{51} +(9.54281 - 5.46291i) q^{52} +6.61578 q^{53} +(9.30064 - 2.47380i) q^{54} +(-6.26422 + 2.37125i) q^{55} +(-7.89624 - 7.98371i) q^{56} +(-12.2294 - 12.2294i) q^{57} +(-8.81936 - 5.11347i) q^{58} -6.92744 q^{59} +(-1.24413 - 12.8663i) q^{60} +6.04740i q^{61} +(5.39219 - 1.43423i) q^{62} +21.2573 q^{63} +(-0.0881340 + 7.99951i) q^{64} +(11.2075 + 5.05248i) q^{65} +(-6.14161 + 10.5926i) q^{66} -8.81626i q^{67} +(-8.11997 + 4.64839i) q^{68} +(-7.64355 + 7.64355i) q^{69} +(2.04433 - 12.3868i) q^{70} +(-7.87467 + 7.87467i) q^{71} +(-10.6497 - 10.7677i) q^{72} +(-4.97545 - 4.97545i) q^{73} +(-3.94898 + 6.81092i) q^{74} +(10.8294 - 9.56998i) q^{75} +(-3.13975 + 11.5479i) q^{76} +(-8.40894 + 8.40894i) q^{77} +(21.7184 - 5.77671i) q^{78} +(-1.04312 - 1.04312i) q^{79} +(-7.29861 + 5.17014i) q^{80} +3.60652 q^{81} +(8.63227 + 2.73569i) q^{82} +(-1.36790 - 1.36790i) q^{83} +(-11.4020 - 19.9173i) q^{84} +(-9.53647 - 4.29916i) q^{85} +(10.1252 + 5.87060i) q^{86} +(-14.7332 - 14.7332i) q^{87} +(8.47226 + 0.0466698i) q^{88} +(4.94457 - 4.94457i) q^{89} +(2.75719 - 16.7062i) q^{90} +21.8270 q^{91} +(7.21764 + 1.96240i) q^{92} +11.4038 q^{93} +(10.3692 - 2.75803i) q^{94} +(-12.5132 + 4.73671i) q^{95} +(-4.37666 + 15.7539i) q^{96} +5.20787 q^{97} +(-3.18487 - 11.9740i) q^{98} +(-11.3412 + 11.3412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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