LMFDB - Embedded newform 820.2.s.c.647.71

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(583,820)] 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, 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("820.583"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.s (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			647.71
Character	$\chi$	$=$	820.647
Dual form			820.2.s.c.583.71

$q$-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} -2.89040 q^{3} +(-1.73571 + 0.993633i) q^{4} +(2.03850 + 0.918980i) q^{5} +(-1.05071 - 3.95030i) q^{6} +3.97005i q^{7} +(-1.98895 - 2.01099i) q^{8} +5.35442 q^{9} +(-0.514937 + 3.12007i) q^{10} +(-2.11810 - 2.11810i) q^{11} +(5.01690 - 2.87200i) q^{12} +5.49792i q^{13} +(-5.42584 + 1.44318i) q^{14} +(-5.89208 - 2.65622i) q^{15} +(2.02539 - 3.44932i) q^{16} +4.67818i q^{17} +(1.94642 + 7.31785i) q^{18} +(4.23103 + 4.23103i) q^{19} +(-4.45137 + 0.430435i) q^{20} -11.4750i q^{21} +(2.12483 - 3.66476i) q^{22} +(-2.64446 - 2.64446i) q^{23} +(5.74887 + 5.81256i) q^{24} +(3.31095 + 3.74668i) q^{25} +(-7.51398 + 1.99859i) q^{26} -6.80520 q^{27} +(-3.94477 - 6.89086i) q^{28} +(-5.09727 - 5.09727i) q^{29} +(1.48838 - 9.01825i) q^{30} +3.94542i q^{31} +(5.45043 + 1.51420i) q^{32} +(6.12215 + 6.12215i) q^{33} +(-6.39365 + 1.70060i) q^{34} +(-3.64839 + 8.09294i) q^{35} +(-9.29372 + 5.32032i) q^{36} +(-3.93647 - 3.93647i) q^{37} +(-4.24448 + 7.32057i) 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} +(5.78101 + 1.57179i) q^{44} +(10.9150 + 4.92060i) q^{45} +(2.65287 - 4.57548i) q^{46} -7.58708 q^{47} +(-5.85418 + 9.96991i) q^{48} -8.76128 q^{49} +(-3.91698 + 5.88704i) q^{50} -13.5218i q^{51} +(-5.46291 - 9.54281i) q^{52} -6.61578i q^{53} +(-2.47380 - 9.30064i) q^{54} +(-2.37125 - 6.26422i) q^{55} +(7.98371 - 7.89624i) q^{56} +(-12.2294 - 12.2294i) q^{57} +(5.11347 - 8.81936i) q^{58} -6.92744 q^{59} +(12.8663 - 1.24413i) q^{60} -6.04740i q^{61} +(-5.39219 + 1.43423i) q^{62} +21.2573i q^{63} +(-0.0881340 + 7.99951i) q^{64} +(-5.05248 + 11.2075i) q^{65} +(-6.14161 + 10.5926i) q^{66} +8.81626 q^{67} +(-4.64839 - 8.11997i) q^{68} +(7.64355 + 7.64355i) q^{69} +(-12.3868 - 2.04433i) 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} +(-9.56998 - 10.8294i) q^{75} +(-11.5479 - 3.13975i) 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} +(6.13243 - 6.66283i) q^{82} +(-1.36790 - 1.36790i) q^{83} +(11.4020 + 19.9173i) q^{84} +(-4.29916 + 9.53647i) q^{85} +(10.1252 + 5.87060i) q^{86} +(14.7332 + 14.7332i) q^{87} +(-0.0466698 + 8.47226i) q^{88} +(-4.94457 - 4.94457i) q^{89} +(-2.75719 + 16.7062i) q^{90} -21.8270 q^{91} +(7.21764 + 1.96240i) q^{92} -11.4038i q^{93} +(-2.75803 - 10.3692i) q^{94} +(4.73671 + 12.5132i) q^{95} +(-15.7539 - 4.37666i) q^{96} +5.20787i 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} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * 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 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Character values

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

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

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
$3$	−2.89040			−1.66877			−0.834387	−	0.551179i	$-0.814178\pi$
$3$	−2.89040			−1.66877			−0.834387	+	0.551179i	$0.814178\pi$
$4$	−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
$6$	−1.05071	−	3.95030i	−0.428950	−	1.61270i
$7$			3.97005i			1.50054i	0.661133	+	0.750268i	$0.270076\pi$
$7$			3.97005i			1.50054i	−0.661133	+	0.750268i	$0.729924\pi$
$8$	−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	$-0.399139\pi$
$11$	−2.11810	−	2.11810i	−0.638630	−	0.638630i	−0.950217	+	0.311587i	$0.899139\pi$
$12$	5.01690	−	2.87200i	1.44825	−	0.829074i
$13$			5.49792i			1.52485i	0.647077	+	0.762425i	$0.275991\pi$
$13$			5.49792i			1.52485i	−0.647077	+	0.762425i	$0.724009\pi$
$14$	−5.42584	+	1.44318i	−1.45012	+	0.385706i
$15$	−5.89208	−	2.65622i	−1.52133	−	0.685833i
$16$	2.02539	−	3.44932i	0.506347	−	0.862330i
$17$			4.67818i			1.13463i	0.823502	+	0.567313i	$0.192017\pi$
$17$			4.67818i			1.13463i	−0.823502	+	0.567313i	$0.807983\pi$
$18$	1.94642	+	7.31785i	0.458775	+	1.72483i
$19$	4.23103	+	4.23103i	0.970664	+	0.970664i	0.999582	−	0.0289178i	$-0.00920611\pi$
$19$	4.23103	+	4.23103i	0.970664	+	0.970664i	−0.0289178	+	0.999582i	$0.509206\pi$
$20$	−4.45137	+	0.430435i	−0.995357	+	0.0962482i
$21$		−	11.4750i		−	2.50406i
$22$	2.12483	−	3.66476i	0.453015	−	0.781328i
$23$	−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	$0.877492\pi$
$24$	5.74887	+	5.81256i	1.17348	+	1.18648i
$25$	3.31095	+	3.74668i	0.662190	+	0.749336i
$26$	−7.51398	+	1.99859i	−1.47361	+	0.391955i
$27$	−6.80520			−1.30966
$28$	−3.94477	−	6.89086i	−0.745491	−	1.30225i
$29$	−5.09727	−	5.09727i	−0.946539	−	0.946539i	0.0521023	−	0.998642i	$-0.483408\pi$
$29$	−5.09727	−	5.09727i	−0.946539	−	0.946539i	−0.998642	+	0.0521023i	$0.983408\pi$
$30$	1.48838	−	9.01825i	0.271739	−	1.64650i
$31$			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
$34$	−6.39365	+	1.70060i	−1.09650	+	0.291650i
$35$	−3.64839	+	8.09294i	−0.616691	+	1.36796i
$36$	−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	$0.901293\pi$
$38$	−4.24448	+	7.32057i	−0.688545	+	1.18755i
$39$		−	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	−0.102329	−	0.994751i	$-0.532629\pi$
$43$	5.85200	−	5.85200i	0.892422	−	0.892422i	0.994751	+	0.102329i	$0.0326294\pi$
$44$	5.78101	+	1.57179i	0.871521	+	0.236957i
$45$	10.9150	+	4.92060i	1.62711	+	0.733520i
$46$	2.65287	−	4.57548i	0.391144	−	0.674617i
$47$	−7.58708			−1.10669			−0.553345	−	0.832952i	$-0.686649\pi$
$47$	−7.58708			−1.10669			−0.553345	+	0.832952i	$0.686649\pi$
$48$	−5.85418	+	9.96991i	−0.844979	+	1.43903i
$49$	−8.76128			−1.25161
$50$	−3.91698	+	5.88704i	−0.553945	+	0.832553i
$51$		−	13.5218i		−	1.89343i
$52$	−5.46291	−	9.54281i	−0.757570	−	1.32335i
$53$		−	6.61578i		−	0.908748i	−0.890811	−	0.454374i	$-0.849863\pi$
$53$		−	6.61578i		−	0.908748i	0.890811	−	0.454374i	$-0.150137\pi$
$54$	−2.47380	−	9.30064i	−0.336642	−	1.26566i
$55$	−2.37125	−	6.26422i	−0.319739	−	0.844668i
$56$	7.98371	−	7.89624i	1.06687	−	1.05518i
$57$	−12.2294	−	12.2294i	−1.61982	−	1.61982i
$58$	5.11347	−	8.81936i	0.671432	−	1.15804i
$59$	−6.92744			−0.901876			−0.450938	−	0.892555i	$-0.648910\pi$
$59$	−6.92744			−0.901876			−0.450938	+	0.892555i	$0.648910\pi$
$60$	12.8663	−	1.24413i	1.66103	−	0.160616i
$61$		−	6.04740i		−	0.774290i	−0.922019	−	0.387145i	$-0.873461\pi$
$61$		−	6.04740i		−	0.774290i	0.922019	−	0.387145i	$-0.126539\pi$
$62$	−5.39219	+	1.43423i	−0.684809	+	0.182147i
$63$			21.2573i			2.67817i
$64$	−0.0881340	+	7.99951i	−0.0110168	+	0.999939i
$65$	−5.05248	+	11.2075i	−0.626683	+	1.39012i
$66$	−6.14161	+	10.5926i	−0.755980	+	1.30386i
$67$	8.81626			1.07708			0.538539	−	0.842601i	$-0.318977\pi$
$67$	8.81626			1.07708			0.538539	+	0.842601i	$0.318977\pi$
$68$	−4.64839	−	8.11997i	−0.563701	−	0.984692i
$69$	7.64355	+	7.64355i	0.920175	+	0.920175i
$70$	−12.3868	−	2.04433i	−1.48051	−	0.244344i
$71$	7.87467	+	7.87467i	0.934552	+	0.934552i	0.997986	−	0.0634342i	$-0.0202053\pi$
$71$	7.87467	+	7.87467i	0.934552	+	0.934552i	−0.0634342	+	0.997986i	$0.520205\pi$
$72$	−10.6497	−	10.7677i	−1.25508	−	1.26898i
$73$	4.97545	+	4.97545i	0.582333	+	0.582333i	0.935544	−	0.353211i	$-0.114910\pi$
$73$	4.97545	+	4.97545i	0.582333	+	0.582333i	−0.353211	+	0.935544i	$0.614910\pi$
$74$	3.94898	−	6.81092i	0.459060	−	0.791754i
$75$	−9.56998	−	10.8294i	−1.10505	−	1.25047i
$76$	−11.5479	−	3.13975i	−1.32464	−	0.360155i
$77$	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	−0.763348	−	0.645988i	$-0.776446\pi$
$79$	−1.04312	+	1.04312i	−0.117360	+	0.117360i	0.645988	+	0.763348i	$0.276446\pi$
$80$	7.29861	−	5.17014i	0.816009	−	0.578039i
$81$	3.60652			0.400724
$82$	6.13243	−	6.66283i	0.677213	−	0.735787i
$83$	−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
$85$	−4.29916	+	9.53647i	−0.466309	+	1.03438i
$86$	10.1252	+	5.87060i	1.09183	+	0.633043i
$87$	14.7332	+	14.7332i	1.57956	+	1.57956i
$88$	−0.0466698	+	8.47226i	−0.00497502	+	0.903146i
$89$	−4.94457	−	4.94457i	−0.524123	−	0.524123i	0.394691	−	0.918814i	$-0.370852\pi$
$89$	−4.94457	−	4.94457i	−0.524123	−	0.524123i	−0.918814	+	0.394691i	$0.870852\pi$
$90$	−2.75719	+	16.7062i	−0.290633	+	1.76098i
$91$	−21.8270			−2.28809
$92$	7.21764	+	1.96240i	0.752491	+	0.204594i
$93$		−	11.4038i		−	1.18252i
$94$	−2.75803	−	10.3692i	−0.284469	−	1.06950i
$95$	4.73671	+	12.5132i	0.485976	+	1.28382i
$96$	−15.7539	−	4.37666i	−1.60788	−	0.446691i
$97$			5.20787i			0.528779i	0.964416	+	0.264389i	$0.0851704\pi$
$97$			5.20787i			0.528779i	−0.964416	+	0.264389i	$0.914830\pi$
$98$	−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	0.999029	−	0.0440648i	$-0.0140308\pi$
$101$	9.59727	+	9.59727i	0.954964	+	0.954964i	−0.0440648	+	0.999029i	$0.514031\pi$
$102$	18.4802	−	4.91541i	1.82981	−	0.486698i
$103$	−4.49066	+	4.49066i	−0.442478	+	0.442478i	−0.892844	−	0.450366i	$-0.851294\pi$
$103$	−4.49066	+	4.49066i	−0.442478	+	0.442478i	0.450366	+	0.892844i	$0.351294\pi$
$104$	11.0562	−	10.9351i	1.08415	−	1.07228i
$105$	10.5453	−	23.3918i	1.02912	−	2.28281i
$106$	9.04176	−	2.40495i	0.878213	−	0.233589i
$107$	−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	$0.438824\pi$
$108$	11.8119	−	6.76187i	1.13660	−	0.650661i
$109$	−9.10583	+	9.10583i	−0.872181	+	0.872181i	−0.992710	−	0.120529i	$-0.961541\pi$
$109$	−9.10583	+	9.10583i	−0.872181	+	0.872181i	0.120529	+	0.992710i	$0.461541\pi$
$110$	7.69930	−	5.51792i	0.734099	−	0.526113i
$111$	11.3780	+	11.3780i	1.07995	+	1.07995i
$112$	13.6940	+	8.04089i	1.29396	+	0.759793i
$113$	−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
$116$	13.9122	+	3.78258i	1.29172	+	0.351203i
$117$			29.4382i			2.72156i
$118$	−2.51824	−	9.46770i	−0.231823	−	0.871572i
$119$	−18.5726			−1.70255
$120$	6.37744	+	17.1320i	0.582178	+	1.56393i
$121$		−	2.02734i		−	0.184303i
$122$	8.26495	−	2.19833i	0.748273	−	0.199027i
$123$	9.93838	+	15.6128i	0.896114	+	1.40776i
$124$	−3.92030	−	6.84811i	−0.352053	−	0.614979i
$125$	3.30625	+	10.6803i	0.295720	+	0.955275i
$126$	−29.0522	+	7.72737i	−2.58818	+	0.688409i
$127$	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
$130$	−17.1539	−	2.83109i	−1.50450	−	0.248303i
$131$	−0.242048			−0.0211478			−0.0105739	−	0.999944i	$-0.503366\pi$
$131$	−0.242048			−0.0211478			−0.0105739	+	0.999944i	$0.503366\pi$
$132$	−16.7094	−	4.54312i	−1.45437	−	0.395427i
$133$	−16.7974	+	16.7974i	−1.45652	+	1.45652i
$134$	3.20486	+	12.0491i	0.276857	+	1.04089i
$135$	−13.8724	−	6.25384i	−1.19395	−	0.538245i
$136$	9.40776	−	9.30468i	0.806709	−	0.797870i
$137$			1.85162i			0.158195i	0.996867	+	0.0790973i	$0.0252038\pi$
$137$			1.85162i			0.158195i	−0.996867	+	0.0790973i	$0.974796\pi$
$138$	−7.66785	+	13.2250i	−0.652730	+	1.12578i
$139$	7.67400			0.650900			0.325450	−	0.945559i	$-0.394484\pi$
$139$	7.67400			0.650900			0.325450	+	0.945559i	$0.394484\pi$
$140$	−1.70885	−	17.6722i	−0.144424	−	1.49357i
$141$	21.9297			1.84681
$142$	−7.89970	+	13.6249i	−0.662928	+	1.14337i
$143$	11.6451	−	11.6451i	0.973815	−	0.973815i
$144$	10.8448	−	18.4691i	0.903731	−	1.53909i
$145$	−5.70649	−	15.0751i	−0.473898	−	1.25192i
$146$	−4.99127	+	8.60859i	−0.413080	+	0.712452i
$147$	25.3236			2.08866
$148$	10.7440	+	2.92117i	0.883149	+	0.240119i
$149$	14.4592	−	14.4592i	1.18455	−	1.18455i	0.205993	−	0.978554i	$-0.433958\pi$
$149$	14.4592	−	14.4592i	1.18455	−	1.18455i	0.978554	−	0.205993i	$-0.0660423\pi$
$150$	11.3216	−	17.0159i	0.924408	−	1.38934i
$151$	10.2588	+	10.2588i	0.834848	+	0.834848i	0.988175	−	0.153328i	$-0.0489990\pi$
$151$	10.2588	+	10.2588i	0.834848	+	0.834848i	−0.153328	+	0.988175i	$0.548999\pi$
$152$	0.0932258	−	16.9238i	0.00756161	−	1.37271i
$153$			25.0489i			2.02509i
$154$	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
$157$	1.71893			0.137185			0.0685926	−	0.997645i	$-0.478149\pi$
$157$	1.71893			0.137185			0.0685926	+	0.997645i	$0.478149\pi$
$158$	−1.80482	−	1.04644i	−0.143584	−	0.0832501i
$159$			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	$0.808971\pi$
$164$	11.3353	+	5.95911i	0.885138	+	0.465328i
$165$	6.85386	+	18.1061i	0.533572	+	1.40956i
$166$	1.37225	−	2.36676i	0.106507	−	0.183696i
$167$			6.72919i			0.520720i	0.965512	+	0.260360i	$0.0838413\pi$
$167$			6.72919i			0.520720i	−0.965512	+	0.260360i	$0.916159\pi$
$168$	−23.0761	+	22.8233i	−1.78036	+	1.76085i
$169$	−17.2271			−1.32516
$170$	−14.5963	−	2.40897i	−1.11948	−	0.184760i
$171$	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	0.731355	−	0.681997i	$-0.238888\pi$
$173$	0.649205	+	0.649205i	0.0493581	+	0.0493581i	−0.681997	+	0.731355i	$0.738888\pi$
$174$	−14.7800	+	25.4915i	−1.12047	+	1.93250i
$175$	−14.8745	+	13.1446i	−1.12441	+	0.993641i
$176$	−11.5960	+	3.01602i	−0.874078	+	0.227341i
$177$	20.0231			1.50503
$178$	4.96029	−	8.55515i	0.371789	−	0.641236i
$179$	−10.8330	−	10.8330i	−0.809700	−	0.809700i	0.174889	−	0.984588i	$-0.444043\pi$
$179$	−10.8330	−	10.8330i	−0.809700	−	0.809700i	−0.984588	+	0.174889i	$0.944043\pi$
$180$	−23.8345	+	2.30473i	−1.77652	+	0.171784i
$181$	−2.35689	−	2.35689i	−0.175186	−	0.175186i	0.614067	−	0.789254i	$-0.289532\pi$
$181$	−2.35689	−	2.35689i	−0.175186	−	0.175186i	−0.789254	+	0.614067i	$0.789532\pi$
$182$	−7.93448	−	29.8309i	−0.588143	−	2.21121i
$183$			17.4794i			1.29211i
$184$	−0.0582676	+	10.5777i	−0.00429555	+	0.779797i
$185$	−4.40695	−	11.6420i	−0.324005	−	0.855938i
$186$	15.5856	−	4.14549i	1.14279	−	0.303962i
$187$	9.90884	−	9.90884i	0.724606	−	0.724606i
$188$	13.1690	−	7.53877i	0.960447	−	0.549821i
$189$		−	27.0170i		−	1.96520i
$190$	−15.3798	+	11.0224i	−1.11577	+	0.799648i
$191$	5.54616	−	5.54616i	0.401306	−	0.401306i	−0.477387	−	0.878693i	$-0.658416\pi$
$191$	5.54616	−	5.54616i	0.401306	−	0.401306i	0.878693	+	0.477387i	$0.158416\pi$
$192$	0.254743	−	23.1218i	0.0183845	−	1.66867i
$193$			19.5306i			1.40584i	0.711267	+	0.702922i	$0.248122\pi$
$193$			19.5306i			1.40584i	−0.711267	+	0.702922i	$0.751878\pi$
$194$	−7.11757	+	1.89315i	−0.511012	+	0.135920i
$195$	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	−0.667932	−	0.744223i	$-0.732820\pi$
$197$	1.07079	−	1.07079i	0.0762910	−	0.0762910i	0.744223	+	0.667932i	$0.232820\pi$
$198$	11.3772	−	19.6226i	0.808544	−	1.39452i
$199$	4.54898	+	4.54898i	0.322469	+	0.322469i	0.849713	−	0.527245i	$-0.176775\pi$
$199$	4.54898	+	4.54898i	0.322469	+	0.322469i	−0.527245	+	0.849713i	$0.676775\pi$
$200$	0.949191	−	14.1102i	0.0671180	−	0.997745i
$201$	−25.4825			−1.79740
$202$	−9.62777	+	16.6053i	−0.677408	+	1.16835i
$203$	20.2364	−	20.2364i	1.42032	−	1.42032i
$204$	13.4357	+	23.4700i	0.940689	+	1.64323i
$205$	−2.04523	−	14.1710i	−0.142845	−	0.989745i
$206$	−7.76980	−	4.50494i	−0.541347	−	0.313874i
$207$	−14.1595	−	14.1595i	−0.984156	−	0.984156i
$208$	18.9641	+	11.1354i	1.31492	+	0.772103i
$209$		−	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	$-0.717805\pi$
$211$	2.07424	−	2.07424i	0.142797	−	0.142797i	0.774891	+	0.632095i	$0.217805\pi$
$212$	6.57366	+	11.4831i	0.451481	+	0.788662i
$213$	−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
$216$	13.5352	+	13.6852i	0.920955	+	0.931158i
$217$	−15.6635			−1.06331
$218$	−15.7550	−	9.13478i	−1.06706	−	0.618685i
$219$	−14.3811	−	14.3811i	−0.971781	−	0.971781i
$220$	10.3401	+	8.51674i	0.697132	+	0.574198i
$221$	−25.7203			−1.73013
$222$	−11.4141	+	19.6863i	−0.766066	+	1.32126i
$223$	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	$0.696107\pi$
$224$	−6.01146	+	21.6385i	−0.401658	+	1.44578i
$225$	17.7282	+	20.0613i	1.18188	+	1.33742i
$226$	−17.4014	−	10.0894i	−1.15752	−	0.671134i
$227$	−6.82130			−0.452746			−0.226373	−	0.974041i	$-0.572687\pi$
$227$	−6.82130			−0.452746			−0.226373	+	0.974041i	$0.572687\pi$
$228$	33.3781	+	9.07515i	2.21052	+	0.601016i
$229$	11.7099	−	11.7099i	0.773814	−	0.773814i	−0.204957	−	0.978771i	$-0.565705\pi$
$229$	11.7099	−	11.7099i	0.773814	−	0.773814i	0.978771	+	0.204957i	$0.0657054\pi$
$230$	9.61263	−	6.88917i	0.633838	−	0.454259i
$231$	−24.3052	+	24.3052i	−1.59917	+	1.59917i
$232$	−0.112312	+	20.3888i	−0.00737367	+	1.33859i
$233$			7.39818i			0.484671i	0.970193	+	0.242335i	$0.0779134\pi$
$233$			7.39818i			0.484671i	−0.970193	+	0.242335i	$0.922087\pi$
$234$	−40.2330	+	10.7013i	−2.63011	+	0.699563i
$235$	−15.4663	−	6.97237i	−1.00891	−	0.454827i
$236$	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	−0.880214	−	0.474577i	$-0.842601\pi$
$239$	−6.27100	+	6.27100i	−0.405637	+	0.405637i	0.474577	+	0.880214i	$0.342601\pi$
$240$	−21.0959	+	14.9438i	−1.36173	+	0.964617i
$241$			22.4409i			1.44554i	0.691086	+	0.722772i	$0.257132\pi$
$241$			22.4409i			1.44554i	−0.691086	+	0.722772i	$0.742868\pi$
$242$	2.77075	−	0.736970i	0.178111	−	0.0473742i
$243$	9.99133			0.640944
$244$	6.00889	+	10.4965i	0.384680	+	0.671972i
$245$	−17.8599	−	8.05144i	−1.14102	−	0.514387i
$246$	−17.7252	+	19.2583i	−1.13012	+	1.22786i
$247$	−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	$-0.527345\pi$
$251$	−2.71865			−0.171600			−0.0857999	+	0.996312i	$0.527345\pi$
$252$	−21.1219	−	36.8965i	−1.33056	−	2.32426i
$253$			11.2024i			0.704292i
$254$	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
$257$	−8.12085			−0.506565			−0.253282	−	0.967392i	$-0.581510\pi$
$257$	−8.12085			−0.506565			−0.253282	+	0.967392i	$0.581510\pi$
$258$	−29.2659	−	16.9684i	−1.82201	−	1.05641i
$259$	15.6280	−	15.6280i	0.971074	−	0.971074i
$260$	−2.36650	−	24.4733i	−0.146764	−	1.51777i
$261$	−27.2929	−	27.2929i	−1.68939	−	1.68939i
$262$	−0.0879883	−	0.330805i	−0.00543594	−	0.0204372i
$263$		−	10.8140i		−	0.666821i	−0.942782	−	0.333410i	$-0.891801\pi$
$263$		−	10.8140i		−	0.666821i	0.942782	−	0.333410i	$-0.108199\pi$
$264$	0.134894	−	24.4882i	0.00830218	−	1.50715i
$265$	6.07977	−	13.4863i	0.373477	−	0.828455i
$266$	−29.0630	−	16.8508i	−1.78197	−	1.03319i
$267$	14.2918	+	14.2918i	0.874643	+	0.874643i
$268$	−15.3025	+	8.76012i	−0.934748	+	0.535110i
$269$			19.3684i			1.18091i	0.807070	+	0.590456i	$0.201052\pi$
$269$			19.3684i			1.18091i	−0.807070	+	0.590456i	$0.798948\pi$
$270$	3.50425	−	21.2327i	0.213262	−	1.29218i
$271$		−	16.7811i		−	1.01938i	−0.860358	−	0.509690i	$-0.829760\pi$
$271$		−	16.7811i		−	1.01938i	0.860358	−	0.509690i	$-0.170240\pi$
$272$	16.1365	+	9.47514i	0.978422	+	0.574515i
$273$	63.0888			3.81831
$274$	−2.53060	+	0.673094i	−0.152879	+	0.0406631i
$275$	0.922909	−	14.9487i	0.0556535	−	0.901443i
$276$	−20.8619	−	5.67212i	−1.25574	−	0.341421i
$277$	−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
$280$	23.5313	−	8.75960i	1.40626	−	0.523486i
$281$	−0.244835	−	0.244835i	−0.0146056	−	0.0146056i	0.699766	−	0.714372i	$-0.253287\pi$
$281$	−0.244835	−	0.244835i	−0.0146056	−	0.0146056i	−0.714372	+	0.699766i	$0.753287\pi$
$282$	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	$0.572403\pi$
$284$	−21.4927	−	5.84363i	−1.27536	−	0.346756i
$285$	−13.6910	−	36.1681i	−0.810985	−	2.14241i
$286$	20.1485	+	11.6821i	1.19141	+	0.690780i
$287$	21.4446	−	13.6507i	1.26584	−	0.805772i
$288$	29.1839	+	8.10768i	1.71968	+	0.477749i
$289$	−4.88539			−0.287376
$290$	18.5286	−	13.2791i	1.08804	−	0.779774i
$291$		−	15.0528i		−	0.882412i
$292$	−13.5797	−	3.69218i	−0.794693	−	0.216068i
$293$	11.1282			0.650117			0.325059	−	0.945694i	$-0.394616\pi$
$293$	11.1282			0.650117			0.325059	+	0.945694i	$0.394616\pi$
$294$	9.20555	+	34.6096i	0.536878	+	2.01848i
$295$	−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
$298$	25.0175	+	14.5052i	1.44923	+	0.840263i
$299$	14.5390	−	14.5390i	0.840814	−	0.840814i
$300$	27.3712	+	9.28767i	1.58027	+	0.536224i
$301$	23.2327	+	23.2327i	1.33911	+	1.33911i
$302$	−10.2914	+	17.7499i	−0.592203	+	1.02139i
$303$	−27.7399	−	27.7399i	−1.59362	−	1.59362i
$304$	23.1636	−	6.02469i	1.32853	−	0.345540i
$305$	5.55743	−	12.3276i	0.318218	−	0.705877i
$306$	−34.2343	+	9.10570i	−1.95704	+	0.520538i
$307$	−5.05107	−	5.05107i	−0.288280	−	0.288280i	0.548120	−	0.836400i	$-0.315344\pi$
$307$	−5.05107	−	5.05107i	−0.288280	−	0.288280i	−0.836400	+	0.548120i	$0.815344\pi$
$308$	−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	$-0.886619\pi$
$311$	−10.3786	+	10.3786i	−0.588516	+	0.588516i	0.348713	+	0.937229i	$0.386619\pi$
$312$	−31.9570	+	31.6068i	−1.80921	+	1.78938i
$313$	−1.55243			−0.0877483			−0.0438741	−	0.999037i	$-0.513970\pi$
$313$	−1.55243			−0.0877483			−0.0438741	+	0.999037i	$0.513970\pi$
$314$	0.624858	+	2.34925i	0.0352628	+	0.132576i
$315$	−19.5350	+	43.3329i	−1.10067	+	2.44153i
$316$	0.774079	−	2.84704i	0.0435453	−	0.160159i
$317$	−5.50774			−0.309346			−0.154673	−	0.987966i	$-0.549432\pi$
$317$	−5.50774			−0.309346			−0.154673	+	0.987966i	$0.549432\pi$
$318$	−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
$322$	18.1649	+	10.5320i	1.01229	+	0.586926i
$323$	−19.7935	+	19.7935i	−1.10134	+	1.10134i
$324$	−6.25987	+	3.58355i	−0.347771	+	0.199086i
$325$	−20.5989	+	18.2034i	−1.14262	+	1.00974i
$326$	3.33649	−	5.75453i	0.184791	−	0.318714i
$327$	26.3195	−	26.3195i	1.45547	−	1.45547i
$328$	−4.02372	+	17.6581i	−0.222173	+	0.975007i
$329$		−	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	$-0.179176\pi$
$331$	5.67764	+	5.67764i	0.312071	+	0.312071i	−0.533640	+	0.845712i	$0.679176\pi$
$332$	3.73348	+	1.01509i	0.204901	+	0.0557104i
$333$	−21.0775	−	21.0775i	−1.15504	−	1.15504i
$334$	−9.19675	+	2.44617i	−0.503224	+	0.133849i
$335$	17.9719	+	8.10196i	0.981912	+	0.442658i
$336$	−39.5810	−	23.2414i	−2.15932	−	1.26792i
$337$	−8.59922	+	8.59922i	−0.468430	+	0.468430i	−0.901405	−	0.432976i	$-0.857464\pi$
$337$	−8.59922	+	8.59922i	−0.468430	+	0.468430i	0.432976	+	0.901405i	$0.357464\pi$
$338$	−6.26235	−	23.5443i	−0.340627	−	1.28064i
$339$	29.0699	−	29.0699i	1.57886	−	1.57886i
$340$	−2.01365	−	20.8243i	−0.109206	−	1.12936i
$341$	8.35678	−	8.35678i	0.452545	−	0.452545i
$342$	−22.7267	+	39.1974i	−1.22892	+	2.11955i
$343$		−	6.99236i		−	0.377552i
$344$	−23.4076	−	0.128942i	−1.26206	−	0.00695209i
$345$	8.55710	+	22.6056i	0.460699	+	1.21705i
$346$	−0.651268	+	1.12326i	−0.0350124	+	0.0603869i
$347$	−25.7265			−1.38107			−0.690536	−	0.723298i	$-0.742625\pi$
$347$	−25.7265			−1.38107			−0.690536	+	0.723298i	$0.742625\pi$
$348$	−40.2118	−	10.9332i	−2.15558	−	0.586079i
$349$	5.38091			0.288034			0.144017	−	0.989575i	$-0.453998\pi$
$349$	5.38091			0.288034			0.144017	+	0.989575i	$0.453998\pi$
$350$	−23.3718	−	15.5506i	−1.24928	−	0.831215i
$351$		−	37.4145i		−	1.99704i
$352$	−8.33731	−	14.7518i	−0.444380	−	0.786272i
$353$	−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	$0.937113\pi$
$354$	7.27872	+	27.3654i	0.386859	+	1.45446i
$355$	8.81584	+	23.2892i	0.467896	+	1.23606i
$356$	13.4954	+	3.66926i	0.715257	+	0.194470i
$357$	53.6823			2.84117
$358$	10.8675	−	18.7435i	0.574364	−	0.990623i
$359$	−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
$362$	2.36438	−	4.07792i	0.124269	−	0.214331i
$363$			5.85981i			0.307560i
$364$	37.8854	−	21.6880i	1.98573	−	1.13676i
$365$	5.57011	+	14.7148i	0.291553	+	0.770208i
$366$	−23.8890	+	6.35405i	−1.24870	+	0.332131i
$367$	6.00019	+	6.00019i	0.313207	+	0.313207i	0.846151	−	0.532944i	$-0.178914\pi$
$367$	6.00019	+	6.00019i	0.313207	+	0.313207i	−0.532944	+	0.846151i	$0.678914\pi$
$368$	−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
$372$	11.3312	+	19.7938i	0.587497	+	1.02626i
$373$	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
$375$	−9.55639	−	30.8703i	−0.493490	−	1.59414i
$376$	15.0903	+	15.2575i	0.778225	+	0.786846i
$377$	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	$0.447592\pi$
$380$	−20.6551	−	17.0127i	−1.05958	−	0.872733i
$381$	−26.2174	+	26.2174i	−1.34316	+	1.34316i
$382$	9.59604	+	5.56379i	0.490976	+	0.284668i
$383$			33.1381i			1.69328i	0.532167	+	0.846640i	$0.321378\pi$
$383$			33.1381i			1.69328i	−0.532167	+	0.846640i	$0.678622\pi$
$384$	31.6931	−	8.05700i	1.61733	−	0.411157i
$385$	24.8693	−	9.41397i	1.26746	−	0.479780i
$386$	−26.6924	+	7.09970i	−1.35861	+	0.361365i
$387$	31.3340	−	31.3340i	1.59280	−	1.59280i
$388$	−5.17471	−	9.03936i	−0.262706	−	0.458904i
$389$	36.2135			1.83610			0.918050	−	0.396465i	$-0.129763\pi$
$389$	36.2135			1.83610			0.918050	+	0.396465i	$0.129763\pi$
$390$	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
$393$	0.699615			0.0352909
$394$	1.85270	+	1.07420i	0.0933378	+	0.0541173i
$395$	−3.08501	+	1.16780i	−0.155224	+	0.0587581i
$396$	30.9539	+	8.41604i	1.55549	+	0.422922i
$397$	7.02431			0.352540			0.176270	−	0.984342i	$-0.443597\pi$
$397$	7.02431			0.352540			0.176270	+	0.984342i	$0.443597\pi$
$398$	−4.56344	+	7.87070i	−0.228745	+	0.394523i
$399$	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	$0.102076\pi$
$401$			12.6243i			0.630427i	−0.949021	+	0.315213i	$0.897924\pi$
$402$	−9.26332	−	34.8268i	−0.462012	−	1.73700i
$403$	−21.6916			−1.08054
$404$	−26.1942	−	7.12193i	−1.30321	−	0.354329i
$405$	7.35188	+	3.31432i	0.365318	+	0.164690i
$406$	35.0133	+	20.3007i	1.73768	+	1.00751i
$407$			16.6756i			0.826580i
$408$	−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	$0.972561\pi$
$410$	18.6240	−	7.94659i	0.919772	−	0.392454i
$411$		−	5.35192i		−	0.263991i
$412$	3.33243	−	12.2566i	0.164177	−	0.603838i
$413$		−	27.5023i		−	1.35330i
$414$	14.2045	−	24.4990i	0.698115	−	1.20406i
$415$	−1.53139	−	4.04554i	−0.0751731	−	0.198588i
$416$	−8.32498	+	29.9660i	−0.408166	+	1.46921i
$417$	−22.1809			−1.08621
$418$	24.4959	−	6.51547i	1.19813	−	0.318682i
$419$		−	1.48835i		−	0.0727107i	−0.999339	−	0.0363553i	$-0.988425\pi$
$419$		−	1.48835i		−	0.0727107i	0.999339	−	0.0363553i	$-0.0115748\pi$
$420$	4.93925	+	51.0796i	0.241011	+	2.49243i
$421$	−5.39787	+	5.39787i	−0.263076	+	0.263076i	−0.826303	−	0.563226i	$-0.809560\pi$
$421$	−5.39787	+	5.39787i	−0.263076	+	0.263076i	0.563226	+	0.826303i	$0.309560\pi$
$422$	3.58887	+	2.08083i	0.174704	+	0.101293i
$423$	−40.6244			−1.97522
$424$	−13.3042	+	13.1585i	−0.646111	+	0.639032i
$425$	−17.5276	+	15.4892i	−0.850216	+	0.751338i
$426$	22.8333	−	39.3813i	1.10628	−	1.90803i
$427$	24.0084			1.16185
$428$	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	$-0.264634\pi$
$431$	27.9795			1.34772			0.673862	+	0.738857i	$0.264634\pi$
$432$	−13.7832	+	23.4733i	−0.663143	+	1.12936i
$433$	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	$-0.0690593\pi$
$434$	−5.69394	−	21.4072i	−0.273318	−	1.02758i
$435$	16.4940	+	43.5730i	0.790829	+	2.08916i
$436$	6.75725	−	24.8530i	0.323613	−	1.19024i
$437$		−	22.3776i		−	1.07046i
$438$	14.4268	−	24.8823i	0.689337	−	1.18892i
$439$	−7.77457	+	7.77457i	−0.371060	+	0.371060i	−0.867863	−	0.496803i	$-0.834507\pi$
$439$	−7.77457	+	7.77457i	−0.371060	+	0.371060i	0.496803	+	0.867863i	$0.334507\pi$
$440$	−7.88097	+	17.2278i	−0.375710	+	0.821303i
$441$	−46.9115			−2.23388
$442$	−9.34975	−	35.1518i	−0.444722	−	1.67200i
$443$	−1.04205	+	1.04205i	−0.0495091	+	0.0495091i	−0.731428	−	0.681919i	$-0.761146\pi$
$443$	−1.04205	+	1.04205i	−0.0495091	+	0.0495091i	0.681919	+	0.731428i	$0.261146\pi$
$444$	−31.0544	−	8.44335i	−1.47378	−	0.400704i
$445$	−5.53554	−	14.6235i	−0.262410	−	0.693218i
$446$	−3.56989	+	6.15709i	−0.169039	+	0.291547i
$447$	−41.7930	+	41.7930i	−1.97674	+	1.97674i
$448$	−31.7585	−	0.349896i	−1.50045	−	0.0165310i
$449$	−2.36619			−0.111667			−0.0558337	−	0.998440i	$-0.517782\pi$
$449$	−2.36619			−0.111667			−0.0558337	+	0.998440i	$0.517782\pi$
$450$	−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
$454$	−2.47966	−	9.32264i	−0.116376	−	0.437533i
$455$	−44.4943	−	20.0586i	−2.08593	−	0.940361i
$456$	−0.269460	+	48.9167i	−0.0126186	+	2.29073i
$457$		−	9.72260i		−	0.454804i	−0.973801	−	0.227402i	$-0.926977\pi$
$457$		−	9.72260i		−	0.454804i	0.973801	−	0.227402i	$-0.0730231\pi$
$458$	20.2607	+	11.7472i	0.946719	+	0.548908i
$459$		−	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	$0.201917\pi$
$462$	−42.0532	−	24.3825i	−1.95649	−	1.13438i
$463$	22.0463			1.02458			0.512290	−	0.858813i	$-0.328797\pi$
$463$	22.0463			1.02458			0.512290	+	0.858813i	$0.328797\pi$
$464$	−27.9061	+	7.25816i	−1.29551	+	0.336952i
$465$	10.4799	−	23.2467i	0.485994	−	1.07804i
$466$	−10.1111	+	2.68936i	−0.468385	+	0.124582i
$467$	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	$0.148966\pi$
$468$	−29.2507	−	51.0961i	−1.35211	−	2.36192i
$469$			35.0010i			1.61619i
$470$	3.90687	−	23.6722i	0.180211	−	1.09192i
$471$	−4.96838			−0.228931
$472$	13.7783	+	13.9310i	0.634200	+	0.641226i
$473$	−24.7902			−1.13985
$474$	5.21666	+	3.02463i	0.239609	+	0.138926i
$475$	−1.84357	+	29.8610i	−0.0845886	+	1.37012i
$476$	32.2367	−	18.4543i	1.47757	−	0.845854i
$477$		−	35.4236i		−	1.62194i
$478$	−10.8502	−	6.29094i	−0.496275	−	0.287741i
$479$	14.2940	−	14.2940i	0.653111	−	0.653111i	−0.300630	−	0.953741i	$-0.597197\pi$
$479$	14.2940	−	14.2940i	0.653111	−	0.653111i	0.953741	+	0.300630i	$0.0971968\pi$
$480$	−28.0923	−	23.3993i	−1.28223	−	1.06803i
$481$	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
$485$	−4.78593	+	10.6162i	−0.217318	+	0.482058i
$486$	3.63201	+	13.6551i	0.164752	+	0.619408i
$487$	−7.77770	−	7.77770i	−0.352441	−	0.352441i	0.508576	−	0.861017i	$-0.330172\pi$
$487$	−7.77770	−	7.77770i	−0.352441	−	0.352441i	−0.861017	+	0.508576i	$0.830172\pi$
$488$	−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	$0.914263\pi$
$492$	−32.7636	−	17.2242i	−1.47710	−	0.776528i
$493$	23.8460	−	23.8460i	1.07397	−	1.07397i
$494$	−40.2479	−	23.3358i	−1.81084	−	1.04993i
$495$	−12.6966	−	33.5413i	−0.570672	−	1.50757i
$496$	13.6090	+	7.99101i	0.611063	+	0.358807i
$497$	−31.2628	+	31.2628i	−1.40233	+	1.40233i
$498$	−3.96635	+	6.84089i	−0.177737	+	0.306547i
$499$	−29.1074	+	29.1074i	−1.30303	+	1.30303i	−0.376684	+	0.926342i	$0.622936\pi$
$499$	−29.1074	+	29.1074i	−1.30303	+	1.30303i	−0.926342	+	0.376684i	$0.877064\pi$
$500$	−16.3510	−	15.2527i	−0.731238	−	0.682122i
$501$		−	19.4501i		−	0.868964i
$502$	−0.988274	−	3.71557i	−0.0441088	−	0.165834i
$503$	−23.5030			−1.04795			−0.523974	−	0.851734i	$-0.675551\pi$
$503$	−23.5030			−1.04795			−0.523974	+	0.851734i	$0.675551\pi$
$504$	42.7481	−	42.2797i	1.90415	−	1.88329i
$505$	10.7443	+	28.3837i	0.478116	+	1.26306i
$506$	−15.3103	+	4.07227i	−0.680627	+	0.181035i
$507$	49.7933			2.21140
$508$	−6.73103	+	24.7565i	−0.298641	+	1.09839i
$509$	−27.3102	+	27.3102i	−1.21050	+	1.21050i	−0.239644	+	0.970861i	$0.577031\pi$
$509$	−27.3102	+	27.3102i	−1.21050	+	1.21050i	−0.970861	+	0.239644i	$0.922969\pi$
$510$	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
$514$	−2.95206	−	11.0987i	−0.130210	−	0.489544i
$515$	−13.2810	+	5.02738i	−0.585232	+	0.221533i
$516$	12.5520	−	46.1658i	0.552570	−	2.03234i
$517$	16.0702	+	16.0702i	0.706765	+	0.706765i
$518$	27.0397	+	15.6776i	1.18806	+	0.688836i
$519$	−1.87646	−	1.87646i	−0.0823675	−	0.0823675i
$520$	32.5873	−	12.1307i	1.42905	−	0.531968i
$521$	−21.4258	+	21.4258i	−0.938680	+	0.938680i	−0.998226	−	0.0595460i	$-0.981035\pi$
$521$	−21.4258	+	21.4258i	−0.938680	+	0.938680i	0.0595460	+	0.998226i	$0.481035\pi$
$522$	27.3797	−	47.2225i	1.19838	−	2.06687i
$523$	−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
$526$	14.7795	−	3.93107i	0.644415	−	0.171403i
$527$	−18.4574			−0.804017
$528$	33.5170	−	8.71751i	1.45864	−	0.379381i
$529$		−	9.01366i		−	0.391898i
$530$	20.6417	+	3.40671i	0.896618	+	0.147978i
$531$	−37.0924			−1.60967
$532$	12.4650	−	45.8458i	0.540425	−	1.98767i
$533$	29.6976	−	18.9041i	1.28635	−	0.818828i
$534$	−14.3372	+	24.7278i	−0.620432	+	1.07008i
$535$	−24.1857	+	9.15521i	−1.04564	+	0.395814i
$536$	−17.5351	−	17.7294i	−0.757402	−	0.765793i
$537$	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
$540$	30.2925	−	2.92920i	1.30358	−	0.126053i
$541$		−	13.1806i		−	0.566680i	−0.959020	−	0.283340i	$-0.908558\pi$
$541$		−	13.1806i		−	0.566680i	0.959020	−	0.283340i	$-0.0914424\pi$
$542$	22.9347	−	6.10021i	0.985128	−	0.262026i
$543$	6.81236	+	6.81236i	0.292346	+	0.292346i
$544$	−7.08372	+	25.4981i	−0.303712	+	1.09322i
$545$	−26.9303	+	10.1942i	−1.15357	+	0.436669i
$546$	22.9338	+	86.2232i	0.981477	+	3.69001i
$547$	−6.34750			−0.271400			−0.135700	−	0.990750i	$-0.543328\pi$
$547$	−6.34750			−0.271400			−0.135700	+	0.990750i	$0.543328\pi$
$548$	−1.83983	−	3.21388i	−0.0785936	−	0.137290i
$549$		−	32.3803i		−	1.38196i
$550$	20.7659	−	4.17278i	0.885459	−	0.177928i
$551$		−	43.1334i		−	1.83754i
$552$	0.168417	−	30.5737i	0.00716829	−	1.30130i
$553$	−4.14125	−	4.14125i	−0.176104	−	0.176104i
$554$	8.45614	−	14.5845i	0.359267	−	0.619638i
$555$	12.7378	+	33.6501i	0.540691	+	1.42837i
$556$	−13.3199	+	7.62514i	−0.564888	+	0.323378i
$557$			5.08673i			0.215532i	0.994176	+	0.107766i	$0.0343697\pi$
$557$			5.08673i			0.215532i	−0.994176	+	0.107766i	$0.965630\pi$
$558$	−28.8720	+	7.67944i	−1.22225	+	0.325097i
$559$	32.1738	+	32.1738i	1.36081	+	1.36081i
$560$	20.5257	+	28.9758i	0.867369	+	1.22445i
$561$	−28.6405	+	28.6405i	−1.20920	+	1.20920i
$562$	0.245613	−	0.423616i	0.0103606	−	0.0178692i
$563$	−25.7047			−1.08333			−0.541663	−	0.840596i	$-0.682205\pi$
$563$	−25.7047			−1.08333			−0.541663	+	0.840596i	$0.682205\pi$
$564$	−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
$567$			14.3180i			0.601301i
$568$	0.173509	−	31.4982i	0.00728029	−	1.32164i
$569$	9.50288			0.398381			0.199191	−	0.979961i	$-0.436169\pi$
$569$	9.50288			0.398381			0.199191	+	0.979961i	$0.436169\pi$
$570$	44.4538	−	31.8591i	1.86197	−	1.33443i
$571$	17.3201	+	17.3201i	0.724823	+	0.724823i	0.969584	−	0.244760i	$-0.0787092\pi$
$571$	17.3201	+	17.3201i	0.724823	+	0.724823i	−0.244760	+	0.969584i	$0.578709\pi$
$572$	−8.64160	+	31.7836i	−0.361324	+	1.32894i
$573$	−16.0306	+	16.0306i	−0.669689	+	0.669689i
$574$	26.4518	+	24.3460i	1.10407	+	1.01618i
$575$	1.15226	−	18.6636i	0.0480525	−	0.778327i
$576$	−0.471906	+	42.8327i	−0.0196628	+	1.78470i
$577$	−40.3754			−1.68085			−0.840425	−	0.541928i	$-0.817695\pi$
$577$	−40.3754			−1.68085			−0.840425	+	0.541928i	$0.817695\pi$
$578$	−1.77592	−	6.67684i	−0.0738686	−	0.277720i
$579$		−	56.4513i		−	2.34603i
$580$	24.8839	+	20.4958i	1.03325	+	0.851042i
$581$	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
$585$	−27.0531	+	60.0096i	−1.11851	+	2.48109i
$586$	4.04529	+	15.2089i	0.167109	+	0.628273i
$587$		−	38.9892i		−	1.60926i	−0.593779	−	0.804628i	$-0.702365\pi$
$587$		−	38.9892i		−	1.60926i	0.593779	−	0.804628i	$-0.297635\pi$
$588$	−43.9545	+	25.1624i	−1.81265	+	1.03768i
$589$	−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
$593$	−21.2839			−0.874023			−0.437012	−	0.899456i	$-0.643963\pi$
$593$	−21.2839			−0.874023			−0.437012	+	0.899456i	$0.643963\pi$
$594$	−14.4599	+	24.9394i	−0.593297	+	1.02328i
$595$	−37.8602	−	17.0679i	−1.55212	−	0.699714i
$596$	−10.7299	+	39.4642i	−0.439513	+	1.61652i
$597$	−13.1484	−	13.1484i	−0.538127	−	0.538127i
$598$	25.1556	+	14.5853i	1.02869	+	0.596435i
$599$	22.8913			0.935312			0.467656	−	0.883911i	$-0.345099\pi$
$599$	22.8913			0.935312			0.467656	+	0.883911i	$0.345099\pi$
$600$	−2.74354	+	40.7843i	−0.112005	+	1.66501i
$601$	−22.2838	−	22.2838i	−0.908977	−	0.908977i	0.0872129	−	0.996190i	$-0.472204\pi$
$601$	−22.2838	−	22.2838i	−0.908977	−	0.908977i	−0.996190	+	0.0872129i	$0.972204\pi$
$602$	−23.3066	+	40.1975i	−0.949905	+	1.63833i
$603$	47.2059			1.92237
$604$	−27.9997	−	7.61283i	−1.13929	−	0.309761i
$605$	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	0.434841	−	0.900507i	$-0.356805\pi$
$607$	−11.4728	−	11.4728i	−0.465666	−	0.465666i	−0.900507	+	0.434841i	$0.856805\pi$
$608$	16.6543	+	29.4675i	0.675420	+	1.19507i
$609$	−58.4913	+	58.4913i	−2.37019	+	2.37019i
$610$	18.8683	+	3.11403i	0.763955	+	0.126083i
$611$		−	41.7132i		−	1.68753i
$612$	−24.8894	−	43.4777i	−1.00610	−	1.75748i
$613$	11.5024	+	11.5024i	0.464577	+	0.464577i	0.900152	−	0.435575i	$-0.143455\pi$
$613$	11.5024	+	11.5024i	0.464577	+	0.464577i	−0.435575	+	0.900152i	$0.643455\pi$
$614$	5.06713	−	8.73943i	0.204493	−	0.352695i
$615$	5.91153	+	40.9598i	0.238376	+	1.65166i
$616$	−33.6353	−	0.185281i	−1.35520	−	0.00746520i
$617$	3.02791	−	3.02791i	0.121899	−	0.121899i	−0.643526	−	0.765425i	$-0.722529\pi$
$617$	3.02791	−	3.02791i	0.121899	−	0.121899i	0.765425	+	0.643526i	$0.222529\pi$
$618$	22.4578	+	13.0211i	0.903386	+	0.523784i
$619$	−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
$622$	−17.9572	−	10.4116i	−0.720017	−	0.417467i
$623$	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
$626$	−0.564332	−	2.12169i	−0.0225553	−	0.0847999i
$627$			51.8059i			2.06893i
$628$	−2.98356	+	1.70798i	−0.119057	+	0.0681559i
$629$	18.4155	−	18.4155i	0.734275	−	0.734275i
$630$	−66.3242	−	10.9462i	−2.64242	−	0.436106i
$631$		−	2.37388i		−	0.0945028i	−0.998883	−	0.0472514i	$-0.984954\pi$
$631$		−	2.37388i		−	0.0945028i	0.998883	−	0.0472514i	$-0.0150462\pi$
$632$	4.17243	+	0.0229840i	0.165970	+	0.000914254i
$633$	−5.99538	+	5.99538i	−0.238295	+	0.238295i
$634$	−2.00216	−	7.52741i	−0.0795158	−	0.298951i
$635$	26.8258	−	10.1546i	1.06455	−	0.402973i
$636$	−19.0005	−	33.1907i	−0.753419	−	1.31610i
$637$		−	48.1688i		−	1.90852i
$638$	−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	0.996476	−	0.0838808i	$-0.0267315\pi$
$641$	23.1051	+	23.1051i	0.912595	+	0.912595i	−0.0838808	+	0.996476i	$0.526732\pi$
$642$	40.8973	+	23.7123i	1.61409	+	0.935849i
$643$	−10.6945			−0.421748			−0.210874	−	0.977513i	$-0.567631\pi$
$643$	−10.6945			−0.421748			−0.210874	+	0.977513i	$0.567631\pi$
$644$	−7.79081	+	28.6544i	−0.307001	+	1.12914i
$645$	−50.0246	+	18.9362i	−1.96972	+	0.745614i
$646$	−34.2470	−	19.8564i	−1.34743	−	0.781241i
$647$	26.7516	+	26.7516i	1.05171	+	1.05171i	0.998588	+	0.0531249i	$0.0169181\pi$
$647$	26.7516	+	26.7516i	1.05171	+	1.05171i	0.0531249	+	0.998588i	$0.483082\pi$
$648$	−7.17319	−	7.25265i	−0.281789	−	0.284911i
$649$	14.6730	+	14.6730i	0.575965	+	0.575965i
$650$	−32.3665	−	21.5353i	−1.26952	−	0.844682i
$651$	45.2738			1.77442
$652$	9.07756	+	2.46809i	0.355505	+	0.0966579i
$653$			19.0085i			0.743860i	0.928261	+	0.371930i	$0.121304\pi$
$653$			19.0085i			0.743860i	−0.928261	+	0.371930i	$0.878696\pi$
$654$	45.5383	+	26.4032i	1.78069	+	1.03245i
$655$	−0.493414	−	0.222437i	−0.0192793	−	0.00869133i
$656$	−25.5960	+	0.919824i	−0.999355	+	0.0359131i
$657$	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	−0.812469	−	0.583004i	$-0.801877\pi$
$659$	−5.89061	+	5.89061i	−0.229466	+	0.229466i	0.583004	+	0.812469i	$0.301877\pi$
$660$	−29.8871	−	24.6168i	−1.16336	−	0.958207i
$661$			15.8159i			0.615166i	0.951521	+	0.307583i	$0.0995202\pi$
$661$			15.8159i			0.615166i	−0.951521	+	0.307583i	$0.900480\pi$
$662$	−5.69569	+	9.82352i	−0.221369	+	0.381802i
$663$	74.3419			2.88720
$664$	−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
$667$			26.9591i			1.04386i
$668$	−6.68634	−	11.6799i	−0.258702	−	0.451910i
$669$	−10.2857	−	10.2857i	−0.397669	−	0.397669i
$670$	−4.53982	+	27.5074i	−0.175389	+	1.06270i
$671$	−12.8090	+	12.8090i	−0.494485	+	0.494485i
$672$	17.3755	−	62.5438i	0.670276	−	2.41268i
$673$	6.60956			0.254780			0.127390	−	0.991853i	$-0.459340\pi$
$673$	6.60956			0.254780			0.127390	+	0.991853i	$0.459340\pi$
$674$	−14.8785	−	8.62656i	−0.573098	−	0.332283i
$675$	−22.5317	−	25.4969i	−0.867246	−	0.981376i
$676$	29.9013	−	17.1174i	1.15005	−	0.658363i
$677$	17.3019	−	17.3019i	0.664966	−	0.664966i	−0.291581	−	0.956546i	$-0.594181\pi$
$677$	17.3019	−	17.3019i	0.664966	−	0.664966i	0.956546	+	0.291581i	$0.0941811\pi$
$678$	50.2971	+	29.1623i	1.93165	+	1.11997i
$679$	−20.6755			−0.793452
$680$	27.7285	−	10.3220i	1.06334	−	0.395832i
$681$	19.7163			0.755530
$682$	14.4590	+	8.38335i	0.553664	+	0.321015i
$683$		−	26.3718i		−	1.00909i	−0.863386	−	0.504544i	$-0.831661\pi$
$683$		−	26.3718i		−	1.00909i	0.863386	−	0.504544i	$-0.168339\pi$
$684$	−61.8324	−	16.8116i	−2.36422	−	0.642806i
$685$	−1.70160	+	3.77452i	−0.0650148	+	0.144217i
$686$	9.55642	−	2.54184i	0.364866	−	0.0970478i
$687$	−33.8464	+	33.8464i	−1.29132	+	1.29132i
$688$	−8.33284	−	32.0380i	−0.317687	−	1.22144i
$689$	36.3731			1.38570
$690$	−27.7844	+	19.9125i	−1.05773	+	0.758055i
$691$	5.58695	−	5.58695i	0.212538	−	0.212538i	−0.592807	−	0.805345i	$-0.701980\pi$
$691$	5.58695	−	5.58695i	0.212538	−	0.212538i	0.805345	+	0.592807i	$0.201980\pi$
$692$	−1.77190	−	0.481761i	−0.0673576	−	0.0183138i
$693$	45.0250	−	45.0250i	1.71036	−	1.71036i
$694$	−9.35201	−	35.1603i	−0.354998	−	1.33467i
$695$	15.6434	+	7.05225i	0.593390	+	0.267507i
$696$	0.324628	−	58.9317i	0.0123050	−	2.23380i
$697$	25.2697	−	16.0855i	0.957158	−	0.609282i
$698$	1.95605	+	7.35407i	0.0740376	+	0.278356i
$699$		−	21.3837i		−	0.808805i
$700$	12.7569	−	37.5951i	0.482165	−	1.42096i
$701$	−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
$703$		−	33.3106i		−	1.25633i
$704$	17.1304	−	16.7571i	0.645627	−	0.631556i
$705$	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
$708$	−34.7543	+	19.8956i	−1.30615	+	0.747722i
$709$	−5.10370	−	5.10370i	−0.191673	−	0.191673i	0.604745	−	0.796419i	$-0.293275\pi$
$709$	−5.10370	−	5.10370i	−0.191673	−	0.191673i	−0.796419	+	0.604745i	$0.793275\pi$
$710$	−28.6245	+	20.5146i	−1.07426	+	0.769898i
$711$	−5.58531	+	5.58531i	−0.209466	+	0.209466i
$712$	−0.108948	+	19.7780i	−0.00408299	+	0.741211i
$713$	10.4335	−	10.4335i	0.390738	−	0.390738i
$714$	19.5144	+	73.3673i	0.730308	+	2.74570i
$715$	34.4402	−	13.0369i	1.28799	−	0.487554i
$716$	29.5671	+	8.03897i	1.10497	+	0.300431i
$717$	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	0.898074	−	0.439845i	$-0.144966\pi$
$719$	12.2870	+	12.2870i	0.458229	+	0.458229i	−0.439845	+	0.898074i	$0.644966\pi$
$720$	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
$723$		−	64.8631i		−	2.41229i
$724$	6.43276	+	1.74900i	0.239072	+	0.0650010i
$725$	2.22101	−	35.9747i	0.0824863	−	1.33607i
$726$	−8.00858	+	2.13014i	−0.297226	+	0.0790569i
$727$		−	41.1680i		−	1.52684i	−0.645904	−	0.763419i	$-0.723519\pi$
$727$		−	41.1680i		−	1.52684i	0.645904	−	0.763419i	$-0.276481\pi$
$728$	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
$732$	−17.3681	−	30.3392i	−0.641943	−	1.12137i
$733$	16.8082	+	16.8082i	0.620826	+	0.620826i	0.945743	−	0.324916i	$-0.105336\pi$
$733$	16.8082	+	16.8082i	0.620826	+	0.620826i	−0.324916	+	0.945743i	$0.605336\pi$
$734$	−6.01926	+	10.3816i	−0.222175	+	0.383192i
$735$	51.6221	+	23.2719i	1.90411	+	0.858396i
$736$	−10.4092	−	18.4177i	−0.383688	−	0.678885i
$737$	−18.6737	−	18.6737i	−0.687854	−	0.687854i
$738$	32.8356	−	35.6756i	1.20869	−	1.31324i
$739$	−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	−0.591814	−	0.806074i	$-0.701588\pi$
$743$	5.84030	−	5.84030i	0.214260	−	0.214260i	0.806074	+	0.591814i	$0.201588\pi$
$744$	−22.9330	+	22.6817i	−0.840764	+	0.831552i
$745$	42.7629	−	16.1874i	1.56671	−	0.593060i
$746$	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
$750$	38.7164	−	24.2825i	1.41372	−	0.886673i
$751$	30.4466	+	30.4466i	1.11101	+	1.11101i	0.993014	+	0.118000i	$0.0376484\pi$
$751$	30.4466	+	30.4466i	1.11101	+	1.11101i	0.118000	+	0.993014i	$0.462352\pi$
$752$	−15.3668	+	26.1703i	−0.560369	+	0.954331i
$753$	7.85799			0.286361
$754$	48.4881	+	28.1135i	1.76583	+	1.02383i
$755$	11.4849	+	30.3401i	0.417978	+	1.10419i
$756$	26.8450	+	46.8937i	0.976341	+	1.70551i
$757$			23.8184i			0.865695i	0.901467	+	0.432847i	$0.142491\pi$
$757$			23.8184i			0.865695i	−0.901467	+	0.432847i	$0.857509\pi$
$758$	2.31982	+	8.72171i	0.0842596	+	0.316787i
$759$		−	32.3796i		−	1.17530i
$760$	15.7427	−	34.4136i	0.571048	−	1.24831i
$761$	−0.854509			−0.0309759			−0.0154880	−	0.999880i	$-0.504930\pi$
$761$	−0.854509			−0.0309759			−0.0154880	+	0.999880i	$0.504930\pi$
$762$	−45.3616	−	26.3007i	−1.64328	−	0.952774i
$763$	−36.1506	−	36.1506i	−1.30874	−	1.30874i
$764$	−4.11569	+	15.1374i	−0.148900	+	0.547651i
$765$	−23.0195	+	51.0622i	−0.832270	+	1.84616i
$766$	−45.2897	+	12.0463i	−1.63638	+	0.435249i
$767$		−	38.0865i		−	1.37522i
$768$	22.5324	+	40.3859i	0.813069	+	1.45730i
$769$			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
$772$	−19.4062	−	33.8995i	−0.698446	−	1.22007i
$773$	27.6369			0.994031			0.497015	−	0.867742i	$-0.334429\pi$
$773$	27.6369			0.994031			0.497015	+	0.867742i	$0.334429\pi$
$774$	54.2145	+	31.4336i	1.94870	+	1.12986i
$775$	−14.7822	+	13.0631i	−0.530993	+	0.469240i
$776$	10.4730	−	10.3582i	0.375957	−	0.371838i
$777$	−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
$782$	21.4049	+	12.4106i	0.765438	+	0.443802i
$783$	34.6880	+	34.6880i	1.23965	+	1.23965i
$784$	−17.7450	+	30.2204i	−0.633750	+	1.07930i
$785$	3.50403	+	1.57966i	0.125064	+	0.0563804i
$786$	0.254322	+	0.956160i	0.00907135	+	0.0341051i
$787$	1.73587	+	1.73587i	0.0618770	+	0.0618770i	0.737368	−	0.675491i	$-0.236068\pi$
$787$	1.73587	+	1.73587i	0.0618770	+	0.0618770i	−0.675491	+	0.737368i	$0.736068\pi$
$788$	−0.794614	+	2.92257i	−0.0283070	+	0.104112i
$789$			31.2568i			1.11277i
$790$	−2.71747	−	3.79176i	−0.0966833	−	0.134905i
$791$	−39.9283	−	39.9283i	−1.41969	−	1.41969i
$792$	−0.249889	+	45.3640i	−0.00887944	+	1.61194i
$793$	33.2481			1.18067
$794$	2.55345	+	9.60010i	0.0906187	+	0.340695i
$795$	−17.5730	+	38.9807i	−0.623249	+	1.38250i
$796$	−12.4157	−	3.37570i	−0.440064	−	0.119649i
$797$	−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	$0.832833\pi$
$798$	84.0038	+	48.7055i	2.97370	+	1.72415i
$799$		−	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
$803$		−	21.0770i		−	0.743790i
$804$	44.2303	−	25.3203i	1.55988	−	0.892977i
$805$	31.0495	−	11.7534i	1.09435	−	0.414254i
$806$	−7.88526	−	29.6458i	−0.277746	−	1.04423i
$807$		−	55.9824i		−	1.97067i
$808$	0.211465	−	38.3885i	0.00743930	−	1.35050i
$809$	38.8381	+	38.8381i	1.36547	+	1.36547i	0.866776	+	0.498697i	$0.166188\pi$
$809$	38.8381	+	38.8381i	1.36547	+	1.36547i	0.498697	+	0.866776i	$0.333812\pi$
$810$	−1.85713	+	11.2526i	−0.0652529	+	0.395375i
$811$	−19.9152			−0.699319			−0.349659	−	0.936877i	$-0.613703\pi$
$811$	−19.9152			−0.699319			−0.349659	+	0.936877i	$0.613703\pi$
$812$	−15.0170	+	55.2321i	−0.526994	+	1.93827i
$813$			48.5041i			1.70111i
$814$	−22.7905	+	6.06187i	−0.798807	+	0.212468i
$815$	−3.72342	−	9.83632i	−0.130426	−	0.344551i
$816$	−46.6411	−	27.3869i	−1.63276	−	0.958735i
$817$	49.5199			1.73248
$818$	−4.75938	+	1.26591i	−0.166408	+	0.0442615i
$819$	−116.871			−4.08380
$820$	17.6307	+	22.5646i	0.615690	+	0.787988i
$821$	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
$823$	−23.2629			−0.810893			−0.405446	−	0.914119i	$-0.632884\pi$
$823$	−23.2629			−0.810893			−0.405446	+	0.914119i	$0.632884\pi$
$824$	17.9624	+	0.0989466i	0.625749	+	0.00344697i
$825$	−2.66758	+	43.2078i	−0.0928731	+	1.50430i
$826$	37.5872	−	9.99753i	1.30783	−	0.347858i
$827$			12.1337i			0.421929i	0.977494	+	0.210964i	$0.0676604\pi$
$827$			12.1337i			0.421929i	−0.977494	+	0.210964i	$0.932340\pi$
$828$	38.6463	+	10.5075i	1.34305	+	0.365161i
$829$	27.7302			0.963108			0.481554	−	0.876416i	$-0.340072\pi$
$829$	27.7302			0.963108			0.481554	+	0.876416i	$0.340072\pi$
$830$	4.97234	−	3.56357i	0.172592	−	0.123693i
$831$	24.3642	+	24.3642i	0.845184	+	0.845184i
$832$	−43.9807	−	0.484554i	−1.52476	−	0.0167989i
$833$		−	40.9869i		−	1.42011i
$834$	−8.06314	−	30.3146i	−0.279204	−	1.04971i
$835$	−6.18399	+	13.7174i	−0.214006	+	0.474712i
$836$	17.8093	+	31.1099i	0.615948	+	1.07596i
$837$		−	26.8494i		−	0.928051i
$838$	2.03412	−	0.541040i	0.0702675	−	0.0186899i
$839$	−33.9785	−	33.9785i	−1.17307	−	1.17307i	−0.981474	−	0.191596i	$-0.938634\pi$
$839$	−33.9785	−	33.9785i	−1.17307	−	1.17307i	−0.191596	−	0.981474i	$-0.561366\pi$
$840$	−68.0148	+	25.3187i	−2.34673	+	0.873580i
$841$			22.9643i			0.791874i
$842$	−9.33946	−	5.41503i	−0.321859	−	0.186614i
$843$	0.707670	+	0.707670i	0.0243735	+	0.0243735i
$844$	−1.53925	+	5.66131i	−0.0529832	+	0.194870i
$845$	−35.1175	−	15.8314i	−1.20808	−	0.544617i
$846$	−14.7676	−	55.5211i	−0.507722	−	1.90886i
$847$	8.04862			0.276554
$848$	−22.8199	−	13.3995i	−0.783640	−	0.460142i
$849$	−36.4066	−	36.4066i	−1.24947	−	1.24947i
$850$	−27.5407	−	18.3244i	−0.944637	−	0.628520i
$851$			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	$0.00529452\pi$
$853$	29.6879	+	29.6879i	1.01649	+	1.01649i	0.0166325	+	0.999862i	$0.494705\pi$
$854$	8.72747	+	32.8122i	0.298648	+	1.12281i
$855$	25.3623	+	67.0007i	0.867373	+	2.29138i
$856$	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	$0.405586\pi$
$858$	−58.2373	−	33.7661i	−1.98819	−	1.15275i
$859$			52.4327i			1.78898i	0.447086	+	0.894491i	$0.352462\pi$
$859$			52.4327i			1.78898i	−0.447086	+	0.894491i	$0.647538\pi$
$860$	−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	−0.995217	−	0.0976910i	$-0.968854\pi$
$863$	−26.3665	+	26.3665i	−0.897526	+	0.897526i	0.0976910	+	0.995217i	$0.468854\pi$
$864$	−37.0913	−	10.3045i	−1.26187	−	0.350565i
$865$	0.726797	+	1.92001i	0.0247118	+	0.0652822i
$866$	42.9094	+	24.8789i	1.45812	+	0.845420i
$867$	14.1207			0.479565
$868$	27.1873	−	15.5638i	0.922798	−	0.528269i
$869$	4.41887			0.149900
$870$	−53.5551	+	38.3818i	−1.81569	+	1.30127i
$871$			48.4711i			1.64238i
$872$	36.4228	+	0.200636i	1.23343	+	0.00679441i
$873$			27.8851i			0.943767i
$874$	30.5833	−	8.13461i	1.03450	−	0.275157i
$875$	−42.4013	+	13.1260i	−1.43342	+	0.443739i
$876$	39.2508	+	10.6719i	1.32616	+	0.360569i
$877$	−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	$0.927075\pi$
$878$	−13.4516	−	7.79928i	−0.453971	−	0.263213i
$879$	−32.1650			−1.08490
$880$	−26.4100	−	4.50829i	−0.890281	−	0.151975i
$881$		−	9.30681i		−	0.313554i	−0.987634	−	0.156777i	$-0.949890\pi$
$881$		−	9.30681i		−	0.313554i	0.987634	−	0.156777i	$-0.0501105\pi$
$882$	−17.0531	−	64.1137i	−0.574208	−	2.15882i
$883$			41.2787i			1.38914i	0.719425	+	0.694570i	$0.244405\pi$
$883$			41.2787i			1.38914i	−0.719425	+	0.694570i	$0.755595\pi$
$884$	44.6430	−	25.5565i	1.50151	−	0.859558i
$885$	40.8170	+	18.4008i	1.37205	+	0.618536i
$886$	−1.80296	−	1.04536i	−0.0605716	−	0.0351195i
$887$	−21.8934			−0.735109			−0.367554	−	0.930002i	$-0.619805\pi$
$887$	−21.8934			−0.735109			−0.367554	+	0.930002i	$0.619805\pi$
$888$	0.250700	−	45.5112i	0.00841295	−	1.52726i
$889$	36.0103	+	36.0103i	1.20775	+	1.20775i
$890$	17.9736	−	12.8813i	0.602475	−	0.431781i
$891$	−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
$895$	−12.1278	−	32.0385i	−0.405387	−	1.07093i
$896$	−11.0665	−	43.5313i	−0.369707	−	1.45428i
$897$	−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
$902$	−27.1016	+	1.12344i	−0.902384	+	0.0374066i
$903$	−67.1519	−	67.1519i	−2.23467	−	2.23467i
$904$	40.2290	+	0.221603i	1.33800	+	0.00737040i
$905$	−2.63858	−	6.97045i	−0.0877094	−	0.231706i
$906$	29.7462	−	51.3042i	0.988253	−	1.70447i
$907$	0.978011	+	0.978011i	0.0324743	+	0.0324743i	0.723157	−	0.690683i	$-0.242690\pi$
$907$	0.978011	+	0.978011i	0.0324743	+	0.0324743i	−0.690683	+	0.723157i	$0.742690\pi$
$908$	11.8398	−	6.77787i	0.392918	−	0.224931i
$909$	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	$-0.219437\pi$
$911$	46.5805			1.54328			0.771640	+	0.636060i	$0.219437\pi$
$912$	−66.9522	+	17.4138i	−2.21701	+	0.576627i
$913$			5.79470i			0.191777i
$914$	13.2878	−	3.53432i	0.439522	−	0.116905i
$915$	−16.0632	+	35.6317i	−0.531033	+	1.17795i
$916$	−8.68969	+	31.9604i	−0.287116	+	1.05600i
$917$		−	0.960941i		−	0.0317331i
$918$	43.5101	−	11.5729i	1.43605	−	0.381963i
$919$	32.4294	+	32.4294i	1.06975	+	1.06975i	0.997378	+	0.0723701i	$0.0230563\pi$
$919$	32.4294	+	32.4294i	1.06975	+	1.06975i	0.0723701	+	0.997378i	$0.476944\pi$
$920$	−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
$924$	18.0364	−	66.3373i	0.593354	−	2.18234i
$925$	1.71522	−	27.7821i	0.0563961	−	0.913471i
$926$	8.01421	+	30.1306i	0.263363	+	0.990154i
$927$	−24.0449	+	24.0449i	−0.789737	+	0.789737i
$928$	−20.0640	−	35.5006i	−0.658633	−	1.16537i
$929$	30.1813	−	30.1813i	0.990218	−	0.990218i	−0.00973503	−	0.999953i	$-0.503099\pi$
$929$	30.1813	−	30.1813i	0.990218	−	0.990218i	0.999953	+	0.00973503i	$0.00309881\pi$
$930$	35.5808	+	5.87227i	1.16674	+	0.192559i
$931$	−37.0692	−	37.0692i	−1.21489	−	1.21489i
$932$	−7.35107	−	12.8411i	−0.240792	−	0.420624i
$933$	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
$936$	59.1997	−	58.5511i	1.93500	−	1.91380i
$937$		−	57.0303i		−	1.86310i	−0.363616	−	0.931549i	$-0.618458\pi$
$937$		−	57.0303i		−	1.86310i	0.363616	−	0.931549i	$-0.381542\pi$
$938$	−47.8357	+	12.7234i	−1.56189	+	0.415435i
$939$	4.48713			0.146432
$940$	33.7729	−	3.26574i	1.10155	−	0.106517i
$941$		−	48.5768i		−	1.58356i	−0.610808	−	0.791778i	$-0.709155\pi$
$941$		−	48.5768i		−	1.58356i	0.610808	−	0.791778i	$-0.290845\pi$
$942$	−1.80609	−	6.79027i	−0.0588456	−	0.221239i
$943$	−5.19159	+	23.3771i	−0.169062	+	0.761262i
$944$	−14.0308	+	23.8949i	−0.456662	+	0.777714i
$945$	24.8281	−	55.0741i	0.807657	−	1.79156i
$946$	−9.01165	−	33.8807i	−0.292994	−	1.10155i
$947$	−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
$950$	−41.4811	+	8.33538i	−1.34582	+	0.270435i
$951$	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	$0.349967\pi$
$954$	48.4133	−	12.8771i	1.56744	−	0.416911i
$955$	16.4027	−	6.20903i	0.530777	−	0.200920i
$956$	4.65358	−	17.1157i	0.150507	−	0.553562i
$957$		−	62.4125i		−	2.01751i
$958$	24.7317	+	14.3395i	0.799045	+	0.463287i
$959$	−7.35102			−0.237377
$960$	21.7678	−	46.8997i	0.702551	−	1.51368i
$961$	15.4337			0.497860
$962$	37.4459	+	21.7112i	1.20730	+	0.699997i
$963$	−43.7874	+	43.7874i	−1.41103	+	1.41103i
$964$	−22.2980	−	38.9509i	−0.718170	−	1.25452i
$965$	−17.9482	+	39.8131i	−0.577774	+	1.28163i
$966$	−52.5037	−	30.4417i	−1.68928	−	0.979446i
$967$	−36.3493			−1.16891			−0.584457	−	0.811425i	$-0.698692\pi$
$967$	−36.3493			−1.16891			−0.584457	+	0.811425i	$0.698692\pi$
$968$	−4.07694	+	4.03227i	−0.131038	+	0.129602i
$969$	57.2112	−	57.2112i	1.83789	−	1.83789i
$970$	−16.2489	−	2.68173i	−0.521721	−	0.0861050i
$971$	40.6018	+	40.6018i	1.30297	+	1.30297i	0.926377	+	0.376597i	$0.122906\pi$
$971$	40.6018	+	40.6018i	1.30297	+	1.30297i	0.376597	+	0.926377i	$0.377094\pi$
$972$	−17.3421	+	9.92771i	−0.556247	+	0.318432i
$973$			30.4662i			0.976700i
$974$	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
$977$	23.4482			0.750176			0.375088	−	0.926989i	$-0.377613\pi$
$977$	23.4482			0.750176			0.375088	+	0.926989i	$0.377613\pi$
$978$	−9.64378	+	16.6329i	−0.308374	+	0.531862i
$979$			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	$0.786220\pi$
$984$	11.6302	−	51.0391i	0.370756	−	1.62707i
$985$	3.16685	−	1.19877i	0.100904	−	0.0381961i
$986$	41.2586	+	23.9218i	1.31394	+	0.761824i
$987$			87.0620i			2.77121i
$988$	17.2621	−	63.4896i	0.549181	−	2.01987i
$989$	−30.9508			−0.984177
$990$	41.2252	−	29.5453i	1.31022	−	0.939010i
$991$	−35.6129	−	35.6129i	−1.13128	−	1.13128i	−0.989964	−	0.141316i	$-0.954867\pi$
$991$	−35.6129	−	35.6129i	−1.13128	−	1.13128i	−0.141316	−	0.989964i	$-0.545133\pi$
$992$	−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
$995$	5.09267	+	13.4535i	0.161448	+	0.426505i
$996$	−10.7912	−	2.93402i	−0.341934	−	0.0929680i
$997$	0.0795810			0.00252036			0.00126018	−	0.999999i	$-0.499599\pi$
$997$	0.0795810			0.00252036			0.00126018	+	0.999999i	$0.499599\pi$
$998$	−50.3619	−	29.1999i	−1.59418	−	0.924307i
$999$	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.s.c.647.71	yes	240
4.3	odd	2	inner	820.2.s.c.647.10	yes	240
5.3	odd	4		820.2.j.c.483.111	yes	240
20.3	even	4		820.2.j.c.483.50	✓	240
41.9	even	4		820.2.j.c.747.50	yes	240
164.91	odd	4		820.2.j.c.747.111	yes	240
205.173	odd	4	inner	820.2.s.c.583.10	yes	240
820.583	even	4	inner	820.2.s.c.583.71	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.50	✓	240	20.3	even	4
820.2.j.c.483.111	yes	240	5.3	odd	4
820.2.j.c.747.50	yes	240	41.9	even	4
820.2.j.c.747.111	yes	240	164.91	odd	4
820.2.s.c.583.10	yes	240	205.173	odd	4	inner
820.2.s.c.583.71	yes	240	820.583	even	4	inner
820.2.s.c.647.10	yes	240	4.3	odd	2	inner
820.2.s.c.647.71	yes	240	1.1	even	1	trivial

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.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.363517 + 1.36670i) q^{2} -2.89040 q^{3} +(-1.73571 + 0.993633i) q^{4} +(2.03850 + 0.918980i) q^{5} +(-1.05071 - 3.95030i) q^{6} +3.97005i q^{7} +(-1.98895 - 2.01099i) q^{8} +5.35442 q^{9} +(-0.514937 + 3.12007i) q^{10} +(-2.11810 - 2.11810i) q^{11} +(5.01690 - 2.87200i) q^{12} +5.49792i q^{13} +(-5.42584 + 1.44318i) q^{14} +(-5.89208 - 2.65622i) q^{15} +(2.02539 - 3.44932i) q^{16} +4.67818i q^{17} +(1.94642 + 7.31785i) q^{18} +(4.23103 + 4.23103i) q^{19} +(-4.45137 + 0.430435i) q^{20} -11.4750i q^{21} +(2.12483 - 3.66476i) q^{22} +(-2.64446 - 2.64446i) q^{23} +(5.74887 + 5.81256i) q^{24} +(3.31095 + 3.74668i) q^{25} +(-7.51398 + 1.99859i) q^{26} -6.80520 q^{27} +(-3.94477 - 6.89086i) q^{28} +(-5.09727 - 5.09727i) q^{29} +(1.48838 - 9.01825i) q^{30} +3.94542i q^{31} +(5.45043 + 1.51420i) q^{32} +(6.12215 + 6.12215i) q^{33} +(-6.39365 + 1.70060i) q^{34} +(-3.64839 + 8.09294i) q^{35} +(-9.29372 + 5.32032i) q^{36} +(-3.93647 - 3.93647i) q^{37} +(-4.24448 + 7.32057i) 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} +(5.78101 + 1.57179i) q^{44} +(10.9150 + 4.92060i) q^{45} +(2.65287 - 4.57548i) q^{46} -7.58708 q^{47} +(-5.85418 + 9.96991i) q^{48} -8.76128 q^{49} +(-3.91698 + 5.88704i) q^{50} -13.5218i q^{51} +(-5.46291 - 9.54281i) q^{52} -6.61578i q^{53} +(-2.47380 - 9.30064i) q^{54} +(-2.37125 - 6.26422i) q^{55} +(7.98371 - 7.89624i) q^{56} +(-12.2294 - 12.2294i) q^{57} +(5.11347 - 8.81936i) q^{58} -6.92744 q^{59} +(12.8663 - 1.24413i) q^{60} -6.04740i q^{61} +(-5.39219 + 1.43423i) q^{62} +21.2573i q^{63} +(-0.0881340 + 7.99951i) q^{64} +(-5.05248 + 11.2075i) q^{65} +(-6.14161 + 10.5926i) q^{66} +8.81626 q^{67} +(-4.64839 - 8.11997i) q^{68} +(7.64355 + 7.64355i) q^{69} +(-12.3868 - 2.04433i) 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} +(-9.56998 - 10.8294i) q^{75} +(-11.5479 - 3.13975i) 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} +(6.13243 - 6.66283i) q^{82} +(-1.36790 - 1.36790i) q^{83} +(11.4020 + 19.9173i) q^{84} +(-4.29916 + 9.53647i) q^{85} +(10.1252 + 5.87060i) q^{86} +(14.7332 + 14.7332i) q^{87} +(-0.0466698 + 8.47226i) q^{88} +(-4.94457 - 4.94457i) q^{89} +(-2.75719 + 16.7062i) q^{90} -21.8270 q^{91} +(7.21764 + 1.96240i) q^{92} -11.4038i q^{93} +(-2.75803 - 10.3692i) q^{94} +(4.73671 + 12.5132i) q^{95} +(-15.7539 - 4.37666i) q^{96} +5.20787i q^{97} +(-3.18487 - 11.9740i) q^{98} +(-11.3412 - 11.3412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * 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 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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