LMFDB - Embedded newform 425.2.p.a.16.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(16,425)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("425.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.p (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$42$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.11
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.46406 - 1.06370i) q^{2} +(-1.47315 + 0.478654i) q^{3} +(0.393974 + 1.21253i) q^{4} +(2.22243 - 0.246559i) q^{5} +(2.66592 + 0.866209i) q^{6} -0.242729i q^{7} +(-0.405475 + 1.24792i) q^{8} +(-0.486001 + 0.353100i) q^{9} +(-3.51604 - 2.00303i) q^{10} +(1.18766 - 1.63468i) q^{11} +(-1.16076 - 1.59765i) q^{12} +(-0.848997 + 0.616833i) q^{13} +(-0.258191 + 0.355369i) q^{14} +(-3.15595 + 1.42699i) q^{15} +(3.98394 - 2.89450i) q^{16} +(-2.57537 + 3.21985i) q^{17} +1.08713 q^{18} +(-1.98369 + 6.10517i) q^{19} +(1.17454 + 2.59763i) q^{20} +(0.116183 + 0.357575i) q^{21} +(-3.47761 + 1.12994i) q^{22} +(-3.87906 + 5.33906i) q^{23} -2.03246i q^{24} +(4.87842 - 1.09592i) q^{25} +1.89911 q^{26} +(3.27830 - 4.51219i) q^{27} +(0.294315 - 0.0956289i) q^{28} +(9.41832 - 3.06020i) q^{29} +(6.13839 + 1.26779i) q^{30} +(1.61534 + 0.524856i) q^{31} -6.28730 q^{32} +(-0.967154 + 2.97660i) q^{33} +(7.19546 - 1.97463i) q^{34} +(-0.0598468 - 0.539448i) q^{35} +(-0.619616 - 0.450178i) q^{36} +(-1.00647 - 1.38529i) q^{37} +(9.39831 - 6.82827i) q^{38} +(0.955447 - 1.31506i) q^{39} +(-0.593455 + 2.87340i) q^{40} +(5.92266 + 8.15184i) q^{41} +(0.210254 - 0.647095i) q^{42} +6.02232 q^{43} +(2.45000 + 0.796053i) q^{44} +(-0.993045 + 0.904570i) q^{45} +(11.3583 - 3.69054i) q^{46} +(2.51500 + 7.74038i) q^{47} +(-4.48346 + 6.17095i) q^{48} +6.94108 q^{49} +(-8.30802 - 3.58469i) q^{50} +(2.25270 - 5.97603i) q^{51} +(-1.08241 - 0.786417i) q^{52} +(1.75644 + 5.40578i) q^{53} +(-9.59925 + 3.11899i) q^{54} +(2.23645 - 3.92579i) q^{55} +(0.302907 + 0.0984205i) q^{56} -9.94331i q^{57} +(-17.0441 - 5.53797i) q^{58} +(-10.7215 + 7.78959i) q^{59} +(-2.97364 - 3.26448i) q^{60} +(3.34286 - 4.60106i) q^{61} +(-1.80666 - 2.48666i) q^{62} +(0.0857076 + 0.117966i) q^{63} +(1.23711 + 0.898816i) q^{64} +(-1.73475 + 1.58020i) q^{65} +(4.58218 - 3.32915i) q^{66} +(2.32205 - 7.14655i) q^{67} +(-4.91880 - 1.85417i) q^{68} +(3.15885 - 9.72194i) q^{69} +(-0.486192 + 0.853443i) q^{70} +(-7.05636 + 2.29275i) q^{71} +(-0.243581 - 0.749666i) q^{72} +(-1.66711 + 2.29458i) q^{73} +3.09872i q^{74} +(-6.66206 + 3.94953i) q^{75} -8.18421 q^{76} +(-0.396783 - 0.288280i) q^{77} +(-2.79766 + 0.909016i) q^{78} +(-1.47964 + 0.480764i) q^{79} +(8.14037 - 7.41510i) q^{80} +(-2.11273 + 6.50231i) q^{81} -18.2347i q^{82} +(-2.82701 + 8.70064i) q^{83} +(-0.387797 + 0.281751i) q^{84} +(-4.92971 + 7.79089i) q^{85} +(-8.81702 - 6.40594i) q^{86} +(-12.4098 + 9.01624i) q^{87} +(1.55838 + 2.14493i) q^{88} +(-8.63047 - 6.27041i) q^{89} +(2.41607 - 0.268041i) q^{90} +(0.149723 + 0.206076i) q^{91} +(-8.00201 - 2.60001i) q^{92} -2.63086 q^{93} +(4.55134 - 14.0076i) q^{94} +(-2.90334 + 14.0574i) q^{95} +(9.26212 - 3.00944i) q^{96} +(9.47382 - 3.07823i) q^{97} +(-10.1622 - 7.38324i) q^{98} +1.21382i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) $ 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.46406	−	1.06370i	−1.03525	−	0.752150i	−0.0658940	−	0.997827i	$-0.520990\pi$
$2$	−1.46406	−	1.06370i	−1.03525	−	0.752150i	−0.969352	+	0.245676i	$0.920990\pi$
$3$	−1.47315	+	0.478654i	−0.850521	+	0.276351i	−0.701664	−	0.712508i	$-0.747559\pi$
$3$	−1.47315	+	0.478654i	−0.850521	+	0.276351i	−0.148857	+	0.988859i	$0.547559\pi$
$4$	0.393974	+	1.21253i	0.196987	+	0.606264i
$5$	2.22243	−	0.246559i	0.993902	−	0.110264i
$5$	2.22243	−	0.246559i	0.993902	−	0.110264i
$6$	2.66592	+	0.866209i	1.08836	+	0.353628i
$7$		−	0.242729i		−	0.0917428i	−0.998947	−	0.0458714i	$-0.985394\pi$
$7$		−	0.242729i		−	0.0917428i	0.998947	−	0.0458714i	$-0.0146065\pi$
$8$	−0.405475	+	1.24792i	−0.143357	+	0.441208i
$9$	−0.486001	+	0.353100i	−0.162000	+	0.117700i
$10$	−3.51604	−	2.00303i	−1.11187	−	0.633413i
$11$	1.18766	−	1.63468i	0.358093	−	0.492873i	−0.591523	−	0.806288i	$-0.701473\pi$
$11$	1.18766	−	1.63468i	0.358093	−	0.492873i	0.949616	+	0.313415i	$0.101473\pi$
$12$	−1.16076	−	1.59765i	−0.335084	−	0.461203i
$13$	−0.848997	+	0.616833i	−0.235469	+	0.171079i	−0.699262	−	0.714865i	$-0.746488\pi$
$13$	−0.848997	+	0.616833i	−0.235469	+	0.171079i	0.463793	+	0.885944i	$0.346488\pi$
$14$	−0.258191	+	0.355369i	−0.0690044	+	0.0949764i
$15$	−3.15595	+	1.42699i	−0.814863	+	0.368448i
$16$	3.98394	−	2.89450i	0.995984	−	0.723625i
$17$	−2.57537	+	3.21985i	−0.624620	+	0.780929i
$17$	−2.57537	+	3.21985i	−0.624620	+	0.780929i
$18$	1.08713			0.256238
$19$	−1.98369	+	6.10517i	−0.455090	+	1.40062i	0.415940	+	0.909392i	$0.363452\pi$
$19$	−1.98369	+	6.10517i	−0.455090	+	1.40062i	−0.871030	+	0.491230i	$0.836548\pi$
$20$	1.17454	+	2.59763i	0.262635	+	0.580847i
$21$	0.116183	+	0.357575i	0.0253532	+	0.0780292i
$22$	−3.47761	+	1.12994i	−0.741429	+	0.240905i
$23$	−3.87906	+	5.33906i	−0.808839	+	1.11327i	0.182663	+	0.983176i	$0.441528\pi$
$23$	−3.87906	+	5.33906i	−0.808839	+	1.11327i	−0.991501	+	0.130096i	$0.958472\pi$
$24$		−	2.03246i		−	0.414874i
$25$	4.87842	−	1.09592i	0.975684	−	0.219184i
$26$	1.89911			0.372446
$27$	3.27830	−	4.51219i	0.630909	−	0.868372i
$28$	0.294315	−	0.0956289i	0.0556204	−	0.0180722i
$29$	9.41832	−	3.06020i	1.74894	−	0.568264i	0.752976	−	0.658047i	$-0.228617\pi$
$29$	9.41832	−	3.06020i	1.74894	−	0.568264i	0.995961	+	0.0897832i	$0.0286174\pi$
$30$	6.13839	+	1.26779i	1.12071	+	0.231465i
$31$	1.61534	+	0.524856i	0.290124	+	0.0942669i	0.450463	−	0.892795i	$-0.351259\pi$
$31$	1.61534	+	0.524856i	0.290124	+	0.0942669i	−0.160339	+	0.987062i	$0.551259\pi$
$32$	−6.28730			−1.11145
$33$	−0.967154	+	2.97660i	−0.168360	+	0.518159i
$34$	7.19546	−	1.97463i	1.23401	−	0.338646i
$35$	−0.0598468	−	0.539448i	−0.0101160	−	0.0911834i
$36$	−0.619616	−	0.450178i	−0.103269	−	0.0750296i
$37$	−1.00647	−	1.38529i	−0.165463	−	0.227740i	0.718232	−	0.695804i	$-0.244952\pi$
$37$	−1.00647	−	1.38529i	−0.165463	−	0.227740i	−0.883695	+	0.468064i	$0.844952\pi$
$38$	9.39831	−	6.82827i	1.52461	−	1.10769i
$39$	0.955447	−	1.31506i	0.152994	−	0.210578i
$40$	−0.593455	+	2.87340i	−0.0938335	+	0.454325i
$41$	5.92266	+	8.15184i	0.924964	+	1.27310i	0.961792	+	0.273783i	$0.0882749\pi$
$41$	5.92266	+	8.15184i	0.924964	+	1.27310i	−0.0368272	+	0.999322i	$0.511725\pi$
$42$	0.210254	−	0.647095i	0.0324429	−	0.0998489i
$43$	6.02232			0.918394			0.459197	−	0.888334i	$-0.348137\pi$
$43$	6.02232			0.918394			0.459197	+	0.888334i	$0.348137\pi$
$44$	2.45000	+	0.796053i	0.369351	+	0.120010i
$45$	−0.993045	+	0.904570i	−0.148034	+	0.134845i
$46$	11.3583	−	3.69054i	1.67469	−	0.544141i
$47$	2.51500	+	7.74038i	0.366851	+	1.12905i	0.948814	+	0.315835i	$0.102285\pi$
$47$	2.51500	+	7.74038i	0.366851	+	1.12905i	−0.581963	+	0.813215i	$0.697715\pi$
$48$	−4.48346	+	6.17095i	−0.647131	+	0.890699i
$49$	6.94108			0.991583
$50$	−8.30802	−	3.58469i	−1.17493	−	0.506951i
$51$	2.25270	−	5.97603i	0.315442	−	0.836811i
$52$	−1.08241	−	0.786417i	−0.150103	−	0.109056i
$53$	1.75644	+	5.40578i	0.241266	+	0.742540i	0.996228	+	0.0867721i	$0.0276552\pi$
$53$	1.75644	+	5.40578i	0.241266	+	0.742540i	−0.754962	+	0.655768i	$0.772345\pi$
$54$	−9.59925	+	3.11899i	−1.30629	+	0.424440i
$55$	2.23645	−	3.92579i	0.301563	−	0.529353i
$56$	0.302907	+	0.0984205i	0.0404777	+	0.0131520i
$57$		−	9.94331i		−	1.31702i
$58$	−17.0441	−	5.53797i	−2.23800	−	0.727171i
$59$	−10.7215	+	7.78959i	−1.39581	+	1.01412i	−0.400616	+	0.916246i	$0.631204\pi$
$59$	−10.7215	+	7.78959i	−1.39581	+	1.01412i	−0.995199	+	0.0978725i	$0.968796\pi$
$60$	−2.97364	−	3.26448i	−0.383895	−	0.421443i
$61$	3.34286	−	4.60106i	0.428010	−	0.589105i	−0.539485	−	0.841995i	$-0.681381\pi$
$61$	3.34286	−	4.60106i	0.428010	−	0.589105i	0.967495	+	0.252890i	$0.0813811\pi$
$62$	−1.80666	−	2.48666i	−0.229446	−	0.315806i
$63$	0.0857076	+	0.117966i	0.0107981	+	0.0148624i
$64$	1.23711	+	0.898816i	0.154639	+	0.112352i
$65$	−1.73475	+	1.58020i	−0.215170	+	0.195999i
$66$	4.58218	−	3.32915i	0.564027	−	0.409790i
$67$	2.32205	−	7.14655i	0.283684	−	0.873090i	−0.703106	−	0.711085i	$-0.748204\pi$
$67$	2.32205	−	7.14655i	0.283684	−	0.873090i	0.986790	−	0.162005i	$-0.0517959\pi$
$68$	−4.91880	−	1.85417i	−0.596492	−	0.224852i
$69$	3.15885	−	9.72194i	0.380281	−	1.17038i
$70$	−0.486192	+	0.853443i	−0.0581111	+	0.102006i
$71$	−7.05636	+	2.29275i	−0.837436	+	0.272099i	−0.696174	−	0.717873i	$-0.745116\pi$
$71$	−7.05636	+	2.29275i	−0.837436	+	0.272099i	−0.141262	+	0.989972i	$0.545116\pi$
$72$	−0.243581	−	0.749666i	−0.0287063	−	0.0883490i
$73$	−1.66711	+	2.29458i	−0.195121	+	0.268561i	−0.895356	−	0.445352i	$-0.853079\pi$
$73$	−1.66711	+	2.29458i	−0.195121	+	0.268561i	0.700235	+	0.713912i	$0.253079\pi$
$74$			3.09872i			0.360219i
$75$	−6.66206	+	3.94953i	−0.769268	+	0.456052i
$76$	−8.18421			−0.938794
$77$	−0.396783	−	0.288280i	−0.0452176	−	0.0328525i
$78$	−2.79766	+	0.909016i	−0.316773	+	0.102926i
$79$	−1.47964	+	0.480764i	−0.166472	+	0.0540902i	−0.391067	−	0.920362i	$-0.627894\pi$
$79$	−1.47964	+	0.480764i	−0.166472	+	0.0540902i	0.224595	+	0.974452i	$0.427894\pi$
$80$	8.14037	−	7.41510i	0.910121	−	0.829034i
$81$	−2.11273	+	6.50231i	−0.234748	+	0.722479i
$82$		−	18.2347i		−	2.01369i
$83$	−2.82701	+	8.70064i	−0.310305	+	0.955020i	0.667340	+	0.744754i	$0.267433\pi$
$83$	−2.82701	+	8.70064i	−0.310305	+	0.955020i	−0.977644	+	0.210266i	$0.932567\pi$
$84$	−0.387797	+	0.281751i	−0.0423121	+	0.0307415i
$85$	−4.92971	+	7.79089i	−0.534702	+	0.845041i
$86$	−8.81702	−	6.40594i	−0.950764	−	0.690771i
$87$	−12.4098	+	9.01624i	−1.33047	+	0.966642i
$88$	1.55838	+	2.14493i	0.166124	+	0.228651i
$89$	−8.63047	−	6.27041i	−0.914828	−	0.664662i	0.0274029	−	0.999624i	$-0.491276\pi$
$89$	−8.63047	−	6.27041i	−0.914828	−	0.664662i	−0.942231	+	0.334963i	$0.891276\pi$
$90$	2.41607	−	0.268041i	0.254676	−	0.0282540i
$91$	0.149723	+	0.206076i	0.0156952	+	0.0216026i
$92$	−8.00201	−	2.60001i	−0.834268	−	0.271070i
$93$	−2.63086			−0.272807
$94$	4.55134	−	14.0076i	0.469435	−	1.44477i
$95$	−2.90334	+	14.0574i	−0.297876	+	1.44226i
$96$	9.26212	−	3.00944i	0.945311	−	0.307150i
$97$	9.47382	−	3.07823i	0.961921	−	0.312547i	0.214371	−	0.976752i	$-0.431230\pi$
$97$	9.47382	−	3.07823i	0.961921	−	0.312547i	0.747550	+	0.664205i	$0.231230\pi$
$98$	−10.1622	−	7.38324i	−1.02653	−	0.745820i
$99$			1.21382i			0.121993i
$100$	3.25081	+	5.48346i	0.325081	+	0.548346i
$101$	−11.8846			−1.18256			−0.591279	−	0.806467i	$-0.701377\pi$
$101$	−11.8846			−1.18256			−0.591279	+	0.806467i	$0.701377\pi$
$102$	−9.65480	+	6.35305i	−0.955967	+	0.629046i
$103$	−2.51099	−	7.72802i	−0.247415	−	0.761464i	−0.995230	−	0.0975574i	$-0.968897\pi$
$103$	−2.51099	−	7.72802i	−0.247415	−	0.761464i	0.747815	−	0.663907i	$-0.231103\pi$
$104$	−0.425513	−	1.30959i	−0.0417250	−	0.128416i
$105$	0.346372	+	0.766040i	0.0338025	+	0.0747579i
$106$	3.17859	−	9.78270i	0.308732	−	0.950180i
$107$		−	4.46593i		−	0.431738i	−0.976422	−	0.215869i	$-0.930742\pi$
$107$		−	4.46593i		−	0.431738i	0.976422	−	0.215869i	$-0.0692584\pi$
$108$	6.76273	+	2.19734i	0.650744	+	0.211440i
$109$	10.9222	+	15.0331i	1.04615	+	1.43991i	0.892097	+	0.451844i	$0.149234\pi$
$109$	10.9222	+	15.0331i	1.04615	+	1.43991i	0.154056	+	0.988062i	$0.450766\pi$
$110$	−7.45016	+	3.36866i	−0.710345	+	0.321189i
$111$	2.14575	+	1.55898i	0.203666	+	0.147972i
$112$	−0.702578	−	0.967015i	−0.0663874	−	0.0913744i
$113$	3.29913	+	4.54086i	0.310356	+	0.427168i	0.935492	−	0.353347i	$-0.114957\pi$
$113$	3.29913	+	4.54086i	0.310356	+	0.427168i	−0.625136	+	0.780516i	$0.714957\pi$
$114$	−10.5767	+	14.5576i	−0.990599	+	1.36344i
$115$	−7.30455	+	12.8221i	−0.681153	+	1.19567i
$116$	7.42115	+	10.2143i	0.689037	+	0.948378i
$117$	0.194810	−	0.599563i	0.0180102	−	0.0554296i
$118$	23.9826			2.20778
$119$	0.781551	+	0.625117i	0.0716446	+	0.0573044i
$120$	−0.501120	−	4.51700i	−0.0457458	−	0.412344i
$121$	2.13756	+	6.57874i	0.194324	+	0.598067i
$122$	−9.78830	+	3.18041i	−0.886191	+	0.287941i
$123$	−12.6269	−	9.17395i	−1.13853	−	0.827187i
$124$			2.16543i			0.194461i
$125$	10.5717	−	3.63842i	0.945566	−	0.325431i
$126$		−	0.263877i		−	0.0235080i
$127$	−4.77080	−	3.46619i	−0.423340	−	0.307575i	0.355640	−	0.934623i	$-0.384263\pi$
$127$	−4.77080	−	3.46619i	−0.423340	−	0.307575i	−0.778980	+	0.627048i	$0.784263\pi$
$128$	3.03063	+	9.32733i	0.267873	+	0.824427i
$129$	−8.87175	+	2.88261i	−0.781114	+	0.253799i
$130$	4.22064	−	0.468241i	0.370175	−	0.0410675i
$131$	−12.5300	−	4.07126i	−1.09476	−	0.355708i	−0.294673	−	0.955598i	$-0.595211\pi$
$131$	−12.5300	−	4.07126i	−1.09476	−	0.355708i	−0.800082	+	0.599890i	$0.795211\pi$
$132$	−3.99024			−0.347306
$133$	1.48190	+	0.481498i	0.128497	+	0.0417512i
$134$	−11.0014	+	7.99299i	−0.950377	+	0.690489i
$135$	6.17328	−	10.8363i	0.531312	−	0.932644i
$136$	−2.97388	−	4.51944i	−0.255008	−	0.387539i
$137$	8.68461	−	6.30974i	0.741976	−	0.539077i	−0.151353	−	0.988480i	$-0.548363\pi$
$137$	8.68461	−	6.30974i	0.741976	−	0.539077i	0.893329	+	0.449402i	$0.148363\pi$
$138$	−14.9660	+	10.8734i	−1.27399	+	0.925607i
$139$	4.65830	−	6.41161i	0.395112	−	0.543825i	−0.564397	−	0.825504i	$-0.690891\pi$
$139$	4.65830	−	6.41161i	0.395112	−	0.543825i	0.959509	+	0.281678i	$0.0908911\pi$
$140$	0.630518	−	0.285095i	0.0532885	−	0.0240949i
$141$	−7.40993	−	10.1989i	−0.624029	−	0.858902i
$142$	12.7697	+	4.14914i	1.07161	+	0.348188i
$143$			2.12042i			0.177319i
$144$	−0.914148	+	2.81346i	−0.0761790	+	0.234455i
$145$	20.1771	−	9.12325i	1.67561	−	0.757645i
$146$	4.88150	−	1.58610i	0.403996	−	0.131266i
$147$	−10.2252	+	3.32238i	−0.843363	+	0.274025i
$148$	1.28318	−	1.76614i	0.105476	−	0.145176i
$149$	14.7776			1.21062			0.605312	−	0.795988i	$-0.293048\pi$
$149$	14.7776			1.21062			0.605312	+	0.795988i	$0.293048\pi$
$150$	13.9548	+	1.30410i	1.13940	+	0.106479i
$151$	−20.9136			−1.70193			−0.850964	−	0.525224i	$-0.823981\pi$
$151$	−20.9136			−1.70193			−0.850964	+	0.525224i	$0.823981\pi$
$152$	−6.81445	−	4.95099i	−0.552725	−	0.401578i
$153$	0.114702	−	2.47422i	0.00927313	−	0.200029i
$154$	0.274270	+	0.844116i	0.0221013	+	0.0680208i
$155$	3.71939	+	0.768181i	0.298749	+	0.0617018i
$156$	1.97097	+	0.640407i	0.157804	+	0.0512736i
$157$	16.2695			1.29845			0.649225	−	0.760596i	$-0.275093\pi$
$157$	16.2695			1.29845			0.649225	+	0.760596i	$0.275093\pi$
$158$	2.67767	+	0.870027i	0.213024	+	0.0692157i
$159$	−5.17499	−	7.12277i	−0.410404	−	0.564872i
$160$	−13.9731	+	1.55019i	−1.10467	+	0.122553i
$161$	1.29594	+	0.941558i	0.102135	+	0.0742052i
$162$	10.0097	−	7.27245i	0.786434	−	0.571378i
$163$	−8.48761	−	11.6822i	−0.664801	−	0.915019i	0.334828	−	0.942279i	$-0.391322\pi$
$163$	−8.48761	−	11.6822i	−0.664801	−	0.915019i	−0.999628	+	0.0272599i	$0.991322\pi$
$164$	−7.55097	+	10.3930i	−0.589632	+	0.811558i
$165$	−1.41553	+	6.85374i	−0.110199	+	0.533563i
$166$	13.3938	−	9.73116i	1.03956	−	0.755284i
$167$	5.49426	+	1.78519i	0.425159	+	0.138142i	0.513778	−	0.857923i	$-0.328245\pi$
$167$	5.49426	+	1.78519i	0.425159	+	0.138142i	−0.0886193	+	0.996066i	$0.528245\pi$
$168$	−0.493336			−0.0380617
$169$	−3.67691	+	11.3164i	−0.282839	+	0.870489i
$170$	15.5046	−	6.16258i	1.18915	−	0.472648i
$171$	−1.19166	−	3.66756i	−0.0911287	−	0.280465i
$172$	2.37264	+	7.30223i	0.180912	+	0.556790i
$173$	−7.28947	+	10.0331i	−0.554208	+	0.762802i	−0.990576	−	0.136967i	$-0.956265\pi$
$173$	−7.28947	+	10.0331i	−0.554208	+	0.762802i	0.436368	+	0.899768i	$0.356265\pi$
$174$	27.7592			2.10442
$175$	−0.266011	−	1.18413i	−0.0201086	−	0.0895120i
$176$		−	9.95013i		−	0.750019i
$177$	12.0657	−	16.6071i	0.906917	−	1.24826i
$178$	5.96568	+	18.3605i	0.447147	+	1.37618i
$179$	−0.829599	−	2.55324i	−0.0620071	−	0.190838i	0.915254	−	0.402877i	$-0.131990\pi$
$179$	−0.829599	−	2.55324i	−0.0620071	−	0.190838i	−0.977261	+	0.212039i	$0.931990\pi$
$180$	−1.48805	−	0.847718i	−0.110913	−	0.0631852i
$181$	−15.0144	−	4.87846i	−1.11601	−	0.362613i	−0.307766	−	0.951462i	$-0.599581\pi$
$181$	−15.0144	−	4.87846i	−1.11601	−	0.362613i	−0.808243	+	0.588849i	$0.799581\pi$
$182$		−	0.460968i		−	0.0341692i
$183$	−2.72221	+	8.37811i	−0.201232	+	0.619328i
$184$	−5.08989	−	7.00563i	−0.375231	−	0.516462i
$185$	−2.57837	−	2.83055i	−0.189565	−	0.208106i
$186$	3.85173	+	2.79844i	0.282422	+	0.205192i
$187$	2.20475	+	8.03399i	0.161227	+	0.587504i
$188$	−8.39458	+	6.09902i	−0.612238	+	0.444817i
$189$	−1.09524	−	0.795738i	−0.0796669	−	0.0578814i
$190$	19.2035	−	17.4926i	1.39317	−	1.26905i
$191$	11.5356	−	8.38110i	0.834686	−	0.606435i	−0.0861950	−	0.996278i	$-0.527471\pi$
$191$	11.5356	−	8.38110i	0.834686	−	0.606435i	0.920881	+	0.389843i	$0.127471\pi$
$192$	−2.25267	−	0.731937i	−0.162573	−	0.0528230i
$193$		−	17.7012i		−	1.27416i	−0.770796	−	0.637082i	$-0.780141\pi$
$193$		−	17.7012i		−	1.27416i	0.770796	−	0.637082i	$-0.219859\pi$
$194$	−17.1445	−	5.57060i	−1.23091	−	0.399946i
$195$	1.79918	−	3.15821i	0.128842	−	0.226164i
$196$	2.73461	+	8.41626i	0.195329	+	0.601162i
$197$	−7.34621	+	2.38693i	−0.523396	+	0.170062i	−0.558786	−	0.829312i	$-0.688733\pi$
$197$	−7.34621	+	2.38693i	−0.523396	+	0.170062i	0.0353902	+	0.999374i	$0.488733\pi$
$198$	1.29114	−	1.77710i	0.0917573	−	0.126293i
$199$			7.56325i			0.536145i	0.963399	+	0.268072i	$0.0863866\pi$
$199$			7.56325i			0.536145i	−0.963399	+	0.268072i	$0.913613\pi$
$200$	−0.610452	+	6.53227i	−0.0431655	+	0.461901i
$201$			11.6394i			0.820978i
$202$	17.3997	+	12.6416i	1.22424	+	0.889461i
$203$	−0.742798	−	2.28610i	−0.0521342	−	0.160452i
$204$	8.13361	+	0.377066i	0.569467	+	0.0263999i
$205$	15.1726	+	16.6566i	1.05970	+	1.16335i
$206$	−4.54407	+	13.9852i	−0.316600	+	0.974396i
$207$		−	3.96449i		−	0.275551i
$208$	−1.59693	+	4.91484i	−0.110727	+	0.340783i
$209$	7.62402	+	10.4936i	0.527364	+	0.725855i
$210$	0.307728	−	1.48996i	0.0212353	−	0.102817i
$211$	−0.0113559	+	0.0156301i	−0.000781773	+	0.00107602i	−0.809408	−	0.587247i	$-0.800212\pi$
$211$	−0.0113559	+	0.0156301i	−0.000781773	+	0.00107602i	0.808626	+	0.588323i	$0.200212\pi$
$212$	−5.86266	+	4.25947i	−0.402649	+	0.292542i
$213$	9.29762	−	6.75511i	0.637062	−	0.462853i
$214$	−4.75041	+	6.53838i	−0.324732	+	0.446955i
$215$	13.3842	−	1.48485i	0.912794	−	0.101266i
$216$	4.30161	+	5.92066i	0.292687	+	0.402850i
$217$	0.127398	−	0.392089i	0.00864831	−	0.0266168i
$218$		−	33.6272i		−	2.27752i
$219$	1.35759	−	4.17823i	0.0917373	−	0.282338i
$220$	5.64123	+	1.16511i	0.380332	+	0.0785514i
$221$	0.200374	−	4.32222i	0.0134786	−	0.290744i
$222$	−1.48322	−	4.56487i	−0.0995470	−	0.306374i
$223$	−14.6658	−	10.6553i	−0.982096	−	0.713534i	−0.0239196	−	0.999714i	$-0.507615\pi$
$223$	−14.6658	−	10.6553i	−0.982096	−	0.713534i	−0.958176	+	0.286180i	$0.907615\pi$
$224$			1.52611i			0.101967i
$225$	−1.98395	+	2.25519i	−0.132263	+	0.150346i
$226$		−	10.1574i		−	0.675658i
$227$	−4.04784	+	5.57138i	−0.268665	+	0.369785i	−0.921938	−	0.387337i	$-0.873395\pi$
$227$	−4.04784	+	5.57138i	−0.268665	+	0.369785i	0.653274	+	0.757122i	$0.273395\pi$
$228$	12.0565	−	3.91741i	0.798464	−	0.259437i
$229$	0.876387	+	2.69724i	0.0579133	+	0.178239i	0.975828	−	0.218538i	$-0.0701287\pi$
$229$	0.876387	+	2.69724i	0.0579133	+	0.178239i	−0.917915	+	0.396777i	$0.870129\pi$
$230$	24.3332	−	11.0025i	1.60448	−	0.725482i
$231$	0.722505	+	0.234756i	0.0475374	+	0.0154458i
$232$			12.9942i			0.853110i
$233$	−3.75445	−	1.21989i	−0.245962	−	0.0799179i	0.183442	−	0.983031i	$-0.441276\pi$
$233$	−3.75445	−	1.21989i	−0.245962	−	0.0799179i	−0.429404	+	0.903113i	$0.641276\pi$
$234$	−0.922968	+	0.670576i	−0.0603363	+	0.0438369i
$235$	7.49788	+	16.5824i	0.489108	+	1.08171i
$236$	−13.6691	−	9.93117i	−0.889782	−	0.646464i
$237$	1.94961	−	1.41647i	0.126641	−	0.0920097i
$238$	−0.479299	−	1.74654i	−0.0310683	−	0.113212i
$239$	11.9610	+	8.69020i	0.773695	+	0.562122i	0.903080	−	0.429472i	$-0.141300\pi$
$239$	11.9610	+	8.69020i	0.773695	+	0.562122i	−0.129385	+	0.991594i	$0.541300\pi$
$240$	−8.44268	+	14.8200i	−0.544973	+	0.956624i
$241$	−17.6599	−	24.3067i	−1.13757	−	1.56573i	−0.772816	−	0.634631i	$-0.781152\pi$
$241$	−17.6599	−	24.3067i	−1.13757	−	1.56573i	−0.364756	−	0.931103i	$-0.618848\pi$
$242$	3.86830	−	11.9054i	0.248663	−	0.765307i
$243$			6.14202i			0.394011i
$244$	6.89592	+	2.24062i	0.441466	+	0.143441i
$245$	15.4261	−	1.71138i	0.985537	−	0.109336i
$246$	8.72813	+	26.8624i	0.556485	+	1.71268i
$247$	−2.08172	−	6.40687i	−0.132457	−	0.407660i
$248$	−1.30996	+	1.80301i	−0.0831826	+	0.114491i
$249$		−	14.1705i		−	0.898018i
$250$	−19.3479	−	5.91831i	−1.22367	−	0.374307i
$251$	2.10539			0.132891			0.0664456	−	0.997790i	$-0.478834\pi$
$251$	2.10539			0.132891			0.0664456	+	0.997790i	$0.478834\pi$
$252$	−0.109271	+	0.150399i	−0.00688343	+	0.00947423i
$253$	4.12063	+	12.6820i	0.259062	+	0.797310i
$254$	3.29775	+	10.1494i	0.206919	+	0.636831i
$255$	3.53304	−	13.8367i	0.221248	−	0.866491i
$256$	6.42953	−	19.7881i	0.401846	−	1.23675i
$257$	−7.72335			−0.481769			−0.240885	−	0.970554i	$-0.577438\pi$
$257$	−7.72335			−0.481769			−0.240885	+	0.970554i	$0.577438\pi$
$258$	16.0550	+	5.21658i	0.999540	+	0.324770i
$259$	−0.336249	+	0.244299i	−0.0208935	+	0.0151800i
$260$	−2.59948	−	1.48088i	−0.161213	−	0.0918404i
$261$	−3.49676	+	4.81287i	−0.216444	+	0.297909i
$262$	14.0141	+	19.2888i	0.865796	+	1.19167i
$263$	6.58068	−	4.78114i	0.405782	−	0.294818i	−0.366110	−	0.930572i	$-0.619311\pi$
$263$	6.58068	−	4.78114i	0.405782	−	0.294818i	0.771892	+	0.635754i	$0.219311\pi$
$264$	−3.32241	−	2.41387i	−0.204480	−	0.148564i
$265$	5.23642	+	11.5809i	0.321671	+	0.711410i
$266$	−1.65742	−	2.28124i	−0.101623	−	0.139872i
$267$	15.7153	+	5.10621i	0.961761	+	0.312495i
$268$	9.58022			0.585205
$269$	−21.7066	−	7.05292i	−1.32348	−	0.430024i	−0.439790	−	0.898101i	$-0.644947\pi$
$269$	−21.7066	−	7.05292i	−1.32348	−	0.430024i	−0.883688	+	0.468077i	$0.844947\pi$
$270$	−20.5647	+	9.29851i	−1.25153	+	0.565890i
$271$	4.73730	+	14.5799i	0.287770	+	0.885666i	0.985555	+	0.169358i	$0.0541694\pi$
$271$	4.73730	+	14.5799i	0.287770	+	0.885666i	−0.697784	+	0.716308i	$0.745831\pi$
$272$	−0.940258	+	20.2821i	−0.0570115	+	1.22978i
$273$	−0.319203	−	0.231915i	−0.0193190	−	0.0140361i
$274$	−19.4265			−1.17360
$275$	4.00243	−	9.27621i	0.241356	−	0.559377i
$276$	13.0326			0.784473
$277$	−7.78048	+	10.7089i	−0.467484	+	0.643436i	−0.976040	−	0.217593i	$-0.930180\pi$
$277$	−7.78048	+	10.7089i	−0.467484	+	0.643436i	0.508556	+	0.861029i	$0.330180\pi$
$278$	−13.6401	+	4.43192i	−0.818077	+	0.265809i
$279$	−0.970384	+	0.315297i	−0.0580953	+	0.0188763i
$280$	0.697457	+	0.144049i	0.0416810	+	0.00860855i
$281$	−0.481752	+	1.48268i	−0.0287389	+	0.0884492i	−0.964397	−	0.264458i	$-0.914807\pi$
$281$	−0.481752	+	1.48268i	−0.0287389	+	0.0884492i	0.935658	+	0.352907i	$0.114807\pi$
$282$			22.8137i			1.35854i
$283$	12.7602	+	4.14604i	0.758514	+	0.246456i	0.662641	−	0.748937i	$-0.269436\pi$
$283$	12.7602	+	4.14604i	0.758514	+	0.246456i	0.0958735	+	0.995394i	$0.469436\pi$
$284$	−5.56005	−	7.65275i	−0.329928	−	0.454107i
$285$	−2.45161	−	22.0983i	−0.145221	−	1.30899i
$286$	2.25550	−	3.10442i	0.133370	−	0.183568i
$287$	1.97869	−	1.43760i	0.116798	−	0.0848589i
$288$	3.05564	−	2.22005i	0.180055	−	0.130818i
$289$	−3.73491	−	16.5846i	−0.219701	−	0.975567i
$290$	−39.2448	−	8.10539i	−2.30454	−	0.475965i
$291$	−12.4829	+	9.06937i	−0.731761	+	0.531656i
$292$	−3.43905	−	1.11741i	−0.201255	−	0.0653917i
$293$	19.8261			1.15825			0.579127	−	0.815238i	$-0.303394\pi$
$293$	19.8261			1.15825			0.579127	+	0.815238i	$0.303394\pi$
$294$	18.5044	+	6.01243i	1.07920	+	0.350652i
$295$	−21.9071	+	19.9553i	−1.27548	+	1.16184i
$296$	2.13683	−	0.694299i	0.124201	−	0.0403553i
$297$	−3.48246	−	10.7179i	−0.202073	−	0.621917i
$298$	−21.6352	−	15.7189i	−1.25329	−	0.910571i
$299$		−	6.92558i		−	0.400516i
$300$	−7.41359	−	6.52192i	−0.428024	−	0.376543i
$301$		−	1.46179i		−	0.0842561i
$302$	30.6188	+	22.2459i	1.76191	+	1.28011i
$303$	17.5077	−	5.68860i	1.00579	−	0.326801i
$304$	9.76851	+	30.0644i	0.560262	+	1.72431i
$305$	6.29486	−	11.0498i	0.360443	−	0.632707i
$306$	−2.79976	+	3.50039i	−0.160052	+	0.200104i
$307$	14.6056			0.833585			0.416793	−	0.909002i	$-0.363154\pi$
$307$	14.6056			0.833585			0.416793	+	0.909002i	$0.363154\pi$
$308$	0.193225	−	0.594685i	0.0110100	−	0.0338853i
$309$	7.39810	+	10.1826i	0.420863	+	0.579268i
$310$	−4.62829	−	5.08098i	−0.262869	−	0.288580i
$311$	−16.6189	+	22.8740i	−0.942373	+	1.29707i	0.0124595	+	0.999922i	$0.496034\pi$
$311$	−16.6189	+	22.8740i	−0.942373	+	1.29707i	−0.954833	+	0.297143i	$0.903966\pi$
$312$	1.25369	+	1.72555i	0.0709760	+	0.0976901i
$313$	−14.6727	−	20.1953i	−0.829351	−	1.14150i	−0.988043	−	0.154176i	$-0.950728\pi$
$313$	−14.6727	−	20.1953i	−0.829351	−	1.14150i	0.158692	−	0.987328i	$-0.449272\pi$
$314$	−23.8196	−	17.3059i	−1.34422	−	0.976630i
$315$	0.219565	+	0.241041i	0.0123711	+	0.0135811i
$316$	−1.16588	−	1.60470i	−0.0655859	−	0.0902712i
$317$	−15.9429	−	5.18017i	−0.895443	−	0.290947i	−0.175088	−	0.984553i	$-0.556021\pi$
$317$	−15.9429	−	5.18017i	−0.895443	−	0.290947i	−0.720355	+	0.693606i	$0.756021\pi$
$318$			15.9328i			0.893467i
$319$	6.18334	−	19.0304i	0.346201	−	1.06550i
$320$	2.97101	+	1.69254i	0.166085	+	0.0946157i
$321$	2.13764	+	6.57897i	0.119311	+	0.367202i
$322$	−0.895801	−	2.75699i	−0.0499211	−	0.153641i
$323$	−14.5490	−	22.1103i	−0.809528	−	1.23025i
$324$	−8.71660			−0.484255
$325$	−3.46576	+	3.93960i	−0.192246	+	0.218530i
$326$			26.1317i			1.44730i
$327$	−23.2856	−	16.9180i	−1.28770	−	0.935565i
$328$	−12.5744	+	4.08566i	−0.694304	+	0.225593i
$329$	1.87881	−	0.610463i	0.103582	−	0.0336559i
$330$	9.36276	−	8.52858i	0.515403	−	0.469483i
$331$	−7.74545	+	23.8381i	−0.425729	+	1.31026i	0.476566	+	0.879139i	$0.341881\pi$
$331$	−7.74545	+	23.8381i	−0.425729	+	1.31026i	−0.902295	+	0.431120i	$0.858119\pi$
$332$	−11.6635			−0.640120
$333$	0.978291	+	0.317866i	0.0536100	+	0.0174189i
$334$	−6.14501	−	8.45788i	−0.336240	−	0.462795i
$335$	3.39857	−	16.4552i	0.185684	−	0.899046i
$336$	1.49787	+	1.08826i	0.0817153	+	0.0593696i
$337$	4.59380	+	6.32282i	0.250240	+	0.344426i	0.915595	−	0.402101i	$-0.131720\pi$
$337$	4.59380	+	6.32282i	0.250240	+	0.344426i	−0.665355	+	0.746527i	$0.731720\pi$
$338$	17.4204	−	12.6567i	0.947546	−	0.688433i
$339$	−7.03360	−	5.11021i	−0.382013	−	0.277548i
$340$	−11.3889	−	2.90800i	−0.617647	−	0.157709i
$341$	2.77645	−	2.01721i	0.150353	−	0.109238i
$342$	−2.15652	+	6.63710i	−0.116611	+	0.358893i
$343$		−	3.38390i		−	0.182713i
$344$	−2.44190	+	7.51540i	−0.131658	+	0.405203i
$345$	4.62331	−	22.3852i	0.248910	−	1.20518i
$346$	21.3444	−	6.93522i	1.14748	−	0.372840i
$347$	19.7437	−	6.41511i	1.05990	−	0.344381i	0.273351	−	0.961914i	$-0.411868\pi$
$347$	19.7437	−	6.41511i	1.05990	−	0.344381i	0.786545	+	0.617533i	$0.211868\pi$
$348$	−15.8216	−	11.4951i	−0.848126	−	0.616199i
$349$	9.65277			0.516701			0.258350	−	0.966051i	$-0.416821\pi$
$349$	9.65277			0.516701			0.258350	+	0.966051i	$0.416821\pi$
$350$	−0.870106	+	2.01660i	−0.0465091	+	0.107792i
$351$			5.85300i			0.312410i
$352$	−7.46719	+	10.2777i	−0.398003	+	0.547803i
$353$	−1.11789	−	3.44051i	−0.0594992	−	0.183120i	0.916889	−	0.399142i	$-0.130692\pi$
$353$	−1.11789	−	3.44051i	−0.0594992	−	0.183120i	−0.976389	+	0.216022i	$0.930692\pi$
$354$	−35.3299	+	11.4794i	−1.87776	+	0.610123i
$355$	−15.1170	+	6.83529i	−0.802327	+	0.362780i
$356$	4.20286	−	12.9351i	0.222751	−	0.685558i
$357$	−1.45055	−	0.546796i	−0.0767714	−	0.0289395i
$358$	−1.50130	+	4.62054i	−0.0793464	+	0.244203i
$359$	1.26563	−	0.919531i	0.0667972	−	0.0485310i	−0.553886	−	0.832593i	$-0.686855\pi$
$359$	1.26563	−	0.919531i	0.0667972	−	0.0485310i	0.620683	+	0.784062i	$0.286855\pi$
$360$	−0.726180	−	1.60603i	−0.0382730	−	0.0846450i
$361$	−17.9667	−	13.0536i	−0.945617	−	0.687031i
$362$	16.7927	+	23.1132i	0.882604	+	1.21480i
$363$	−6.29788	−	8.66829i	−0.330553	−	0.454967i
$364$	−0.190886	+	0.262732i	−0.0100051	+	0.0137709i
$365$	−3.13930	+	5.51060i	−0.164318	+	0.288438i
$366$	12.8973	−	9.37042i	0.674152	−	0.489800i
$367$	21.4374	+	6.96542i	1.11902	+	0.363592i	0.809394	−	0.587266i	$-0.199796\pi$
$367$	21.4374	+	6.96542i	1.11902	+	0.363592i	0.309627	+	0.950858i	$0.399796\pi$
$368$			32.4984i			1.69410i
$369$	−5.75684	−	1.87051i	−0.299689	−	0.0973749i
$370$	0.764017	+	6.88671i	0.0397194	+	0.358023i
$371$	1.31214	−	0.426339i	0.0681228	−	0.0221344i
$372$	−1.03649	−	3.18999i	−0.0537395	−	0.165393i
$373$	7.22701	+	5.25073i	0.374200	+	0.271872i	0.758950	−	0.651148i	$-0.225712\pi$
$373$	7.22701	+	5.25073i	0.374200	+	0.271872i	−0.384750	+	0.923021i	$0.625712\pi$
$374$	5.31789	−	14.1074i	0.274982	−	0.729478i
$375$	−13.8322	+	10.4201i	−0.714291	+	0.538094i
$376$	−10.6792			−0.550737
$377$	−6.10850	+	8.40762i	−0.314604	+	0.433015i
$378$	0.757067	+	2.33001i	0.0389393	+	0.119843i
$379$	34.4804	−	11.2034i	1.77114	−	0.575478i	0.772884	−	0.634547i	$-0.218813\pi$
$379$	34.4804	−	11.2034i	1.77114	−	0.575478i	0.998254	+	0.0590693i	$0.0188133\pi$
$380$	−18.1889	+	2.01789i	−0.933069	+	0.103515i
$381$	8.68720	+	2.82264i	0.445059	+	0.144608i
$382$	−25.8038			−1.32024
$383$	7.54702	−	23.2274i	0.385635	−	1.18686i	−0.550384	−	0.834912i	$-0.685519\pi$
$383$	7.54702	−	23.2274i	0.385635	−	1.18686i	0.936019	−	0.351950i	$-0.114481\pi$
$384$	−8.92913	−	12.2899i	−0.455663	−	0.627166i
$385$	−0.952901	−	0.542852i	−0.0485643	−	0.0276663i
$386$	−18.8288	+	25.9157i	−0.958362	+	1.31907i
$387$	−2.92685	+	2.12648i	−0.148780	+	0.108095i
$388$	7.46489	+	10.2745i	0.378972	+	0.521610i
$389$	3.00212	+	2.18117i	0.152214	+	0.110590i	0.661285	−	0.750134i	$-0.270011\pi$
$389$	3.00212	+	2.18117i	0.152214	+	0.110590i	−0.509072	+	0.860724i	$0.670011\pi$
$390$	−5.99349	+	2.71001i	−0.303492	+	0.137227i
$391$	−7.20098	−	26.2401i	−0.364169	−	1.32702i
$392$	−2.81444	+	8.66195i	−0.142151	+	0.437494i
$393$	20.4073			1.02941
$394$	13.2943	+	4.31957i	0.669755	+	0.217617i
$395$	−3.16986	+	1.43328i	−0.159493	+	0.0721163i
$396$	−1.47179	+	0.478213i	−0.0739602	+	0.0240311i
$397$	−0.0609325	+	0.0197982i	−0.00305812	+	0.000993642i	−0.310546	−	0.950558i	$-0.600512\pi$
$397$	−0.0609325	+	0.0197982i	−0.00305812	+	0.000993642i	0.307488	+	0.951552i	$0.400512\pi$
$398$	8.04504	−	11.0730i	0.403261	−	0.555042i
$399$	−2.41353			−0.120827
$400$	16.2632	−	18.4866i	0.813158	−	0.924332i
$401$		−	19.8302i		−	0.990273i	−0.868815	−	0.495136i	$-0.835118\pi$
$401$		−	19.8302i		−	0.990273i	0.868815	−	0.495136i	$-0.164882\pi$
$402$	12.3808	−	17.0407i	0.617499	−	0.849914i
$403$	−1.69517	+	0.550793i	−0.0844423	+	0.0274370i
$404$	−4.68221	−	14.4104i	−0.232949	−	0.716943i
$405$	−3.09220	+	14.9719i	−0.153653	+	0.743958i
$406$	−1.34422	+	4.13709i	−0.0667127	+	0.205321i
$407$	−3.45984			−0.171498
$408$	6.54422	+	5.23434i	0.323987	+	0.259138i
$409$	−7.26262	+	5.27661i	−0.359114	+	0.260911i	−0.752682	−	0.658384i	$-0.771240\pi$
$409$	−7.26262	+	5.27661i	−0.359114	+	0.260911i	0.393569	+	0.919295i	$0.371240\pi$
$410$	−4.49593	−	40.5254i	−0.222038	−	2.00141i
$411$	−9.77352	+	13.4521i	−0.482092	+	0.663543i
$412$	8.38118	−	6.08928i	0.412911	−	0.299997i
$413$	1.89076	+	2.60241i	0.0930381	+	0.128056i
$414$	−4.21703	+	5.80424i	−0.207256	+	0.285263i
$415$	−4.13762	+	20.0336i	−0.203108	+	0.983412i
$416$	5.33790	−	3.87821i	0.261712	−	0.190145i
$417$	−3.79342	+	11.6749i	−0.185765	+	0.571725i
$418$		−	23.4729i		−	1.14810i
$419$	−5.08187	−	1.65120i	−0.248266	−	0.0806664i	0.182241	−	0.983254i	$-0.441665\pi$
$419$	−5.08187	−	1.65120i	−0.248266	−	0.0806664i	−0.430506	+	0.902588i	$0.641665\pi$
$420$	−0.792384	+	0.721787i	−0.0386644	+	0.0352196i
$421$	−4.02311	−	12.3819i	−0.196074	−	0.603455i	−0.999962	−	0.00867416i	$-0.997239\pi$
$421$	−4.02311	−	12.3819i	−0.196074	−	0.603455i	0.803888	−	0.594781i	$-0.202761\pi$
$422$	0.0332515	−	0.0108041i	0.00161866	−	0.000525933i
$423$	−3.95542	−	2.87378i	−0.192319	−	0.139728i
$424$	−7.45820			−0.362202
$425$	−9.03504	+	18.5302i	−0.438264	+	0.898846i
$426$	−20.7977			−1.00765
$427$	−1.11681	−	0.811409i	−0.0540462	−	0.0392668i
$428$	5.41507	−	1.75946i	0.261747	−	0.0850468i
$429$	−1.01495	−	3.12369i	−0.0490022	−	0.150813i
$430$	−21.1747	−	12.0629i	−1.02113	−	0.581723i
$431$	1.93484	+	0.628669i	0.0931981	+	0.0302819i	0.355245	−	0.934773i	$-0.384397\pi$
$431$	1.93484	+	0.628669i	0.0931981	+	0.0302819i	−0.262047	+	0.965055i	$0.584397\pi$
$432$		−	27.4653i		−	1.32143i
$433$	−1.91926	+	5.90688i	−0.0922338	+	0.283867i	−0.986523	−	0.163623i	$-0.947682\pi$
$433$	−1.91926	+	5.90688i	−0.0922338	+	0.283867i	0.894289	+	0.447490i	$0.147682\pi$
$434$	−0.603583	+	0.438529i	−0.0289729	+	0.0210501i
$435$	−25.3569	+	23.0977i	−1.21577	+	1.10745i
$436$	−13.9250	+	19.1661i	−0.666885	+	0.917888i
$437$	−24.9010	−	34.2733i	−1.19118	−	1.63952i
$438$	−6.43197	+	4.67310i	−0.307331	+	0.223289i
$439$	−2.68141	+	3.69064i	−0.127977	+	0.176145i	−0.868197	−	0.496220i	$-0.834721\pi$
$439$	−2.68141	+	3.69064i	−0.127977	+	0.176145i	0.740220	+	0.672364i	$0.234721\pi$
$440$	3.99226	+	4.38274i	0.190323	+	0.208939i
$441$	−3.37337	+	2.45090i	−0.160637	+	0.116709i
$442$	−4.89091	+	6.11485i	−0.232637	+	0.290854i
$443$	19.4598			0.924563			0.462281	−	0.886733i	$-0.347031\pi$
$443$	19.4598			0.924563			0.462281	+	0.886733i	$0.347031\pi$
$444$	−1.04494	+	3.21598i	−0.0495904	+	0.152624i
$445$	−20.7267	−	11.8076i	−0.982539	−	0.559736i
$446$	10.1375	+	31.2001i	0.480026	+	1.47737i
$447$	−21.7695	+	7.07334i	−1.02966	+	0.334557i
$448$	0.218168	−	0.300283i	0.0103075	−	0.0141870i
$449$		−	2.70954i		−	0.127871i	−0.997954	−	0.0639355i	$-0.979635\pi$
$449$		−	2.70954i		−	0.127871i	0.997954	−	0.0639355i	$-0.0203652\pi$
$450$	5.30346	−	1.19140i	0.250008	−	0.0561634i
$451$	20.3597			0.958703
$452$	−4.20615	+	5.78927i	−0.197841	+	0.272304i
$453$	30.8088	−	10.0104i	1.44753	−	0.470330i
$454$	11.8526	−	3.85113i	0.556268	−	0.180742i
$455$	0.383559	+	0.421075i	0.0179815	+	0.0197403i
$456$	12.4085	+	4.03177i	0.581081	+	0.188805i
$457$	14.1515			0.661977			0.330989	−	0.943635i	$-0.392618\pi$
$457$	14.1515			0.661977			0.330989	+	0.943635i	$0.392618\pi$
$458$	1.58598	−	4.88114i	0.0741079	−	0.228081i
$459$	6.08576	+	22.1762i	0.284059	+	1.03510i
$460$	−18.4250	−	3.80539i	−0.859070	−	0.177427i
$461$	30.1221	+	21.8850i	1.40293	+	1.01929i	0.994304	+	0.106581i	$0.0339904\pi$
$461$	30.1221	+	21.8850i	1.40293	+	1.01929i	0.408622	+	0.912704i	$0.366010\pi$
$462$	−0.808080	−	1.11223i	−0.0375953	−	0.0517455i
$463$	−1.82655	+	1.32707i	−0.0848870	+	0.0616740i	−0.629419	−	0.777066i	$-0.716707\pi$
$463$	−1.82655	+	1.32707i	−0.0848870	+	0.0616740i	0.544532	+	0.838740i	$0.316707\pi$
$464$	28.6642	−	39.4529i	1.33070	−	1.83156i
$465$	−5.84690	+	0.648660i	−0.271144	+	0.0300809i
$466$	4.19913	+	5.77960i	0.194521	+	0.267735i
$467$	0.119157	−	0.366727i	0.00551392	−	0.0169701i	−0.948262	−	0.317490i	$-0.897160\pi$
$467$	0.119157	−	0.366727i	0.00551392	−	0.0169701i	0.953776	+	0.300520i	$0.0971601\pi$
$468$	0.803737			0.0371527
$469$	−1.73467	−	0.563629i	−0.0800997	−	0.0260260i
$470$	6.66136	−	32.2531i	0.307265	−	1.48772i
$471$	−23.9674	+	7.78749i	−1.10436	+	0.358828i
$472$	−5.37354	−	16.5381i	−0.247337	−	0.761226i
$473$	7.15247	−	9.84453i	0.328871	−	0.452652i
$474$	−4.36104			−0.200309
$475$	−2.98649	+	31.9575i	−0.137030	+	1.46631i
$476$	−0.450061	+	1.19393i	−0.0206285	+	0.0547238i
$477$	−2.76242	−	2.00701i	−0.126482	−	0.0918948i
$478$	−8.26788	−	25.4459i	−0.378164	−	1.16387i
$479$	33.7742	−	10.9739i	1.54318	−	0.501410i	0.590929	−	0.806723i	$-0.298761\pi$
$479$	33.7742	−	10.9739i	1.54318	−	0.501410i	0.952252	+	0.305314i	$0.0987613\pi$
$480$	19.8424	−	8.97195i	0.905679	−	0.409511i
$481$	1.70898	+	0.555281i	0.0779228	+	0.0253186i
$482$			54.3713i			2.47654i
$483$	−2.35979	−	0.766744i	−0.107374	−	0.0348881i
$484$	−7.13476	+	5.18371i	−0.324307	+	0.235623i
$485$	20.2960	−	9.17701i	0.921592	−	0.416707i
$486$	6.53327	−	8.99228i	0.296355	−	0.407898i
$487$	−14.1669	−	19.4991i	−0.641963	−	0.883586i	0.356755	−	0.934198i	$-0.383883\pi$
$487$	−14.1669	−	19.4991i	−0.641963	−	0.883586i	−0.998718	+	0.0506115i	$0.983883\pi$
$488$	4.38632	+	6.03726i	0.198560	+	0.273294i
$489$	18.0952	+	13.1469i	0.818294	+	0.594525i
$490$	−24.4051	−	13.9032i	−1.10251	−	0.628082i
$491$	34.1096	−	24.7821i	1.53935	−	1.11840i	0.588601	−	0.808423i	$-0.299679\pi$
$491$	34.1096	−	24.7821i	1.53935	−	1.11840i	0.950744	−	0.309977i	$-0.100321\pi$
$492$	6.14902	−	18.9247i	0.277219	−	0.853193i
$493$	−14.4023	+	38.2068i	−0.648647	+	1.72075i
$494$	−3.76724	+	11.5944i	−0.169496	+	0.521655i
$495$	0.299277	+	2.69763i	0.0134515	+	0.121249i
$496$	7.95460	−	2.58461i	0.357172	−	0.116052i
$497$	0.556516	+	1.71278i	0.0249632	+	0.0768287i
$498$	−15.0732	+	20.7464i	−0.675444	+	0.929669i
$499$		−	1.44082i		−	0.0644999i	−0.999480	−	0.0322499i	$-0.989733\pi$
$499$		−	1.44082i		−	0.0644999i	0.999480	−	0.0322499i	$-0.0102673\pi$
$500$	8.57669	+	11.3851i	0.383561	+	0.509157i
$501$	−8.94834			−0.399782
$502$	−3.08242	−	2.23951i	−0.137575	−	0.0999541i
$503$	27.8337	−	9.04373i	1.24104	−	0.403240i	0.386341	−	0.922356i	$-0.373739\pi$
$503$	27.8337	−	9.04373i	1.24104	−	0.403240i	0.854704	+	0.519116i	$0.173739\pi$
$504$	−0.181966	+	0.0591242i	−0.00810539	+	0.00263360i
$505$	−26.4126	+	2.93024i	−1.17535	+	0.130394i
$506$	7.45701	−	22.9503i	0.331504	−	1.02027i
$507$		−	18.4306i		−	0.818532i
$508$	2.32328	−	7.15033i	0.103079	−	0.317244i
$509$	4.45572	−	3.23727i	0.197496	−	0.143490i	−0.484642	−	0.874713i	$-0.661050\pi$
$509$	4.45572	−	3.23727i	0.197496	−	0.143490i	0.682138	+	0.731223i	$0.261050\pi$
$510$	−19.8907	+	16.4997i	−0.880777	+	0.730619i
$511$	0.556961	+	0.404656i	0.0246385	+	0.0179009i
$512$	−14.5932	+	10.6026i	−0.644935	+	0.468573i
$513$	21.0446	+	28.9654i	0.929141	+	1.27885i
$514$	11.3074	+	8.21533i	0.498749	+	0.362363i
$515$	−7.48591	−	16.5559i	−0.329869	−	0.729540i
$516$	−6.99049	−	9.62158i	−0.307739	−	0.423566i
$517$	15.6400	+	5.08174i	0.687845	+	0.223495i
$518$	0.752149			0.0330475
$519$	5.93607	−	18.2693i	0.260564	−	0.801935i
$520$	−1.26857	−	2.80557i	−0.0556303	−	0.123033i
$521$	0.191085	−	0.0620874i	0.00837160	−	0.00272010i	−0.304828	−	0.952407i	$-0.598599\pi$
$521$	0.191085	−	0.0620874i	0.00837160	−	0.00272010i	0.313200	+	0.949687i	$0.398599\pi$
$522$	10.2389	−	3.32682i	0.448145	−	0.145611i
$523$	−7.98228	−	5.79946i	−0.349041	−	0.253593i	0.399426	−	0.916766i	$-0.369209\pi$
$523$	−7.98228	−	5.79946i	−0.349041	−	0.253593i	−0.748466	+	0.663173i	$0.769209\pi$
$524$		−	16.7970i		−	0.733781i
$525$	0.958663	+	1.61707i	0.0418395	+	0.0705748i
$526$	−14.7202			−0.641831
$527$	−5.85006	+	3.84946i	−0.254833	+	0.167685i
$528$	4.76267	+	14.6580i	0.207269	+	0.637907i
$529$	−6.35112	−	19.5467i	−0.276135	−	0.849858i
$530$	4.65220	−	22.5251i	0.202079	−	0.978428i
$531$	2.46013	−	7.57150i	0.106761	−	0.328575i
$532$			1.98654i			0.0861276i
$533$	−10.0566	−	3.26760i	−0.435602	−	0.141536i
$534$	−17.5767	−	24.1922i	−0.760616	−	1.04690i
$535$	−1.10111	−	9.92523i	−0.0476053	−	0.429105i
$536$	7.97682	+	5.79550i	0.344546	+	0.250327i
$537$	2.44424	+	3.36421i	0.105477	+	0.145176i
$538$	24.2776	+	33.4153i	1.04668	+	1.44063i
$539$	8.24366	−	11.3464i	0.355079	−	0.488725i
$540$	15.5715	+	3.21604i	0.670090	+	0.138396i
$541$	1.49891	+	2.06307i	0.0644431	+	0.0886983i	0.840022	−	0.542552i	$-0.182542\pi$
$541$	1.49891	+	2.06307i	0.0644431	+	0.0886983i	−0.775579	+	0.631251i	$0.782542\pi$
$542$	8.57297	−	26.3849i	0.368241	−	1.13333i
$543$	24.4535			1.04940
$544$	16.1922	−	20.2442i	0.694233	−	0.867963i
$545$	27.9803	+	30.7170i	1.19854	+	1.31577i
$546$	0.220644	+	0.679073i	0.00944270	+	0.0290616i
$547$	13.2995	−	4.32126i	0.568644	−	0.184764i	−0.0105629	−	0.999944i	$-0.503362\pi$
$547$	13.2995	−	4.32126i	0.568644	−	0.184764i	0.579207	+	0.815181i	$0.303362\pi$
$548$	11.0723	+	8.04446i	0.472983	+	0.343642i
$549$			3.41649i			0.145812i
$550$	−15.7269	+	9.32353i	−0.670598	+	0.397557i
$551$			63.5709i			2.70821i
$552$	10.8514	+	7.88402i	0.461867	+	0.335566i
$553$	0.116695	+	0.359151i	0.00496239	+	0.0152727i
$554$	22.7822	−	7.40237i	0.967921	−	0.314497i
$555$	5.15317	+	2.93567i	0.218740	+	0.124612i
$556$	9.60951	+	3.12232i	0.407534	+	0.132416i
$557$	0.897073			0.0380102			0.0190051	−	0.999819i	$-0.493950\pi$
$557$	0.897073			0.0380102			0.0190051	+	0.999819i	$0.493950\pi$
$558$	1.75608	+	0.570585i	0.0743408	+	0.0241548i
$559$	−5.11293	+	3.71476i	−0.216254	+	0.157118i
$560$	−1.79986	−	1.97590i	−0.0760579	−	0.0834970i
$561$	−7.09342	−	10.7799i	−0.299484	−	0.455129i
$562$	2.28244	−	1.65829i	0.0962789	−	0.0699507i
$563$	−30.4778	+	22.1434i	−1.28449	+	0.933234i	−0.999679	−	0.0253512i	$-0.991930\pi$
$563$	−30.4778	+	22.1434i	−1.28449	+	0.933234i	−0.284807	+	0.958585i	$0.591930\pi$
$564$	9.44713	−	13.0029i	0.397796	−	0.547519i
$565$	8.45168	+	9.27833i	0.355565	+	0.390342i
$566$	−14.2715	−	19.6431i	−0.599877	−	0.825660i
$567$	1.57830	+	0.512820i	0.0662822	+	0.0215364i
$568$		−	9.73546i		−	0.408491i
$569$	8.00618	−	24.6405i	0.335637	−	1.03298i	−0.630771	−	0.775969i	$-0.717261\pi$
$569$	8.00618	−	24.6405i	0.335637	−	1.03298i	0.966408	−	0.257014i	$-0.0827387\pi$
$570$	−19.9167	+	34.9610i	−0.834220	+	1.46436i
$571$	16.6317	−	5.40398i	0.696016	−	0.226149i	0.0604223	−	0.998173i	$-0.480755\pi$
$571$	16.6317	−	5.40398i	0.696016	−	0.226149i	0.635594	+	0.772024i	$0.280755\pi$
$572$	−2.57107	+	0.835393i	−0.107502	+	0.0349295i
$573$	−12.9820	+	17.8681i	−0.542329	+	0.746452i
$574$	−4.42609			−0.184741
$575$	−13.0725	+	30.2973i	−0.545160	+	1.26348i
$576$	−0.918611			−0.0382755
$577$	1.26167	+	0.916656i	0.0525240	+	0.0381609i	0.613737	−	0.789510i	$-0.289665\pi$
$577$	1.26167	+	0.916656i	0.0525240	+	0.0381609i	−0.561213	+	0.827671i	$0.689665\pi$
$578$	−12.1730	+	28.2537i	−0.506329	+	1.17520i
$579$	8.47278	+	26.0765i	0.352117	+	1.08370i
$580$	19.0114	+	20.8709i	0.789407	+	0.866619i
$581$	2.11190	+	0.686197i	0.0876162	+	0.0284682i
$582$	27.9228			1.15744
$583$	10.9228	+	3.54902i	0.452374	+	0.146985i
$584$	−2.18749	−	3.01083i	−0.0905191	−	0.124589i
$585$	0.285124	−	1.38052i	0.0117884	−	0.0570775i
$586$	−29.0266	−	21.0890i	−1.19908	−	0.871180i
$587$	−10.7167	+	7.78616i	−0.442327	+	0.321369i	−0.786559	−	0.617515i	$-0.788139\pi$
$587$	−10.7167	+	7.78616i	−0.442327	+	0.321369i	0.344232	+	0.938885i	$0.388139\pi$
$588$	−8.05696	−	11.0895i	−0.332263	−	0.457321i
$589$	−6.40866	+	8.82077i	−0.264064	+	0.363453i
$590$	53.2998	−	5.91313i	2.19432	−	0.243440i
$591$	9.67952	−	7.03259i	0.398162	−	0.289282i
$592$	−8.01942	−	2.60567i	−0.329596	−	0.107092i
$593$	−5.36929			−0.220490			−0.110245	−	0.993904i	$-0.535164\pi$
$593$	−5.36929			−0.220490			−0.110245	+	0.993904i	$0.535164\pi$
$594$	−6.30213	+	19.3960i	−0.258580	+	0.795826i
$595$	1.89107	+	1.19658i	0.0775264	+	0.0490551i
$596$	5.82198	+	17.9182i	0.238478	+	0.733958i
$597$	−3.62018	−	11.1418i	−0.148164	−	0.456003i
$598$	−7.36674	+	10.1394i	−0.301248	+	0.414633i
$599$	−38.1668			−1.55945			−0.779727	−	0.626120i	$-0.784642\pi$
$599$	−38.1668			−1.55945			−0.779727	+	0.626120i	$0.784642\pi$
$600$	−2.22741	−	9.91518i	−0.0909337	−	0.404785i
$601$		−	21.3310i		−	0.870111i	−0.900404	−	0.435055i	$-0.856729\pi$
$601$		−	21.3310i		−	0.870111i	0.900404	−	0.435055i	$-0.143271\pi$
$602$	−1.55491	+	2.14014i	−0.0633732	+	0.0872258i
$603$	1.39493	+	4.29315i	0.0568059	+	0.174830i
$604$	−8.23944	−	25.3584i	−0.335258	−	1.03182i
$605$	6.37263	+	14.0938i	0.259084	+	0.572993i
$606$	−31.6833	−	10.2945i	−1.28704	−	0.418186i
$607$			18.7737i			0.762002i	0.924575	+	0.381001i	$0.124421\pi$
$607$			18.7737i			0.762002i	−0.924575	+	0.381001i	$0.875579\pi$
$608$	12.4721	−	38.3851i	0.505809	−	1.55672i
$609$	2.18850	+	3.01221i	0.0886825	+	0.122061i
$610$	−20.9697	+	9.48164i	−0.849038	+	0.383900i
$611$	−6.90975	−	5.02022i	−0.279538	−	0.203097i
$612$	3.04525	−	0.835699i	0.123097	−	0.0337811i
$613$	−13.3910	+	9.72917i	−0.540859	+	0.392957i	−0.824404	−	0.566002i	$-0.808490\pi$
$613$	−13.3910	+	9.72917i	−0.540859	+	0.392957i	0.283545	+	0.958959i	$0.408490\pi$
$614$	−21.3835	−	15.5360i	−0.862966	−	0.626981i
$615$	−30.3243	−	17.2752i	−1.22279	−	0.696605i
$616$	0.520637	−	0.378265i	0.0209771	−	0.0152407i
$617$	−33.1149	−	10.7597i	−1.33316	−	0.433169i	−0.446164	−	0.894951i	$-0.647210\pi$
$617$	−33.1149	−	10.7597i	−1.33316	−	0.433169i	−0.886993	+	0.461782i	$0.847210\pi$
$618$		−	22.7773i		−	0.916238i
$619$	−21.6527	−	7.03540i	−0.870297	−	0.282776i	−0.160374	−	0.987056i	$-0.551270\pi$
$619$	−21.6527	−	7.03540i	−0.870297	−	0.282776i	−0.709922	+	0.704280i	$0.751270\pi$
$620$	0.533904	+	4.81251i	0.0214421	+	0.193275i
$621$	11.3742	+	35.0061i	0.456430	+	1.40475i
$622$	48.6622	−	15.8113i	1.95118	−	0.633976i
$623$	−1.52201	+	2.09486i	−0.0609780	+	0.0839290i
$624$		−	8.00466i		−	0.320443i
$625$	22.5979	−	10.6927i	0.903917	−	0.427708i
$626$			45.1745i			1.80553i
$627$	−16.2541	−	11.8093i	−0.649125	−	0.471617i
$628$	6.40978	+	19.7273i	0.255778	+	0.787204i
$629$	7.05245	+	0.326945i	0.281200	+	0.0130361i
$630$	−0.0650612	−	0.586449i	−0.00259210	−	0.0233647i
$631$	5.50417	−	16.9401i	0.219117	−	0.674374i	−0.779718	−	0.626131i	$-0.784638\pi$
$631$	5.50417	−	16.9401i	0.219117	−	0.674374i	0.998836	−	0.0482434i	$-0.0153623\pi$
$632$		−	2.04142i		−	0.0812032i
$633$	0.00924752	−	0.0284609i	0.000367556	−	0.00113122i
$634$	17.8312	+	24.5426i	0.708168	+	0.974709i
$635$	−11.4574	−	6.52710i	−0.454674	−	0.259020i
$636$	6.59775	−	9.08102i	0.261618	−	0.360086i
$637$	−5.89296	+	4.28149i	−0.233488	+	0.169639i
$638$	−29.2954	+	21.2844i	−1.15982	+	0.842656i
$639$	2.61983	−	3.60588i	0.103639	−	0.142647i
$640$	9.03511	+	19.9821i	0.357144	+	0.789863i
$641$	0.611110	+	0.841121i	0.0241374	+	0.0332223i	0.820915	−	0.571050i	$-0.193464\pi$
$641$	0.611110	+	0.841121i	0.0241374	+	0.0332223i	−0.796778	+	0.604272i	$0.793464\pi$
$642$	3.86843	−	11.9058i	0.152675	−	0.469884i
$643$		−	2.30605i		−	0.0909416i	−0.998966	−	0.0454708i	$-0.985521\pi$
$643$		−	2.30605i		−	0.0909416i	0.998966	−	0.0454708i	$-0.0144788\pi$
$644$	−0.631097	+	1.94232i	−0.0248687	+	0.0765381i
$645$	−19.0061	+	8.59381i	−0.748366	+	0.338381i
$646$	−2.21812	+	47.8465i	−0.0872707	+	1.88250i
$647$	7.68808	+	23.6615i	0.302250	+	0.930229i	0.980689	+	0.195573i	$0.0626566\pi$
$647$	7.68808	+	23.6615i	0.302250	+	0.930229i	−0.678439	+	0.734656i	$0.737343\pi$
$648$	−7.25773	−	5.27305i	−0.285111	−	0.207145i
$649$			26.7775i			1.05111i
$650$	9.26464	−	2.08127i	0.363389	−	0.0816341i
$651$			0.638584i			0.0250281i
$652$	10.8211	−	14.8939i	0.423786	−	0.583292i
$653$	−26.4902	+	8.60718i	−1.03664	+	0.336825i	−0.777413	−	0.628991i	$-0.783468\pi$
$653$	−26.4902	+	8.60718i	−1.03664	+	0.336825i	−0.259228	+	0.965816i	$0.583468\pi$
$654$	16.0958	+	49.5378i	0.629396	+	1.93708i
$655$	−28.8510	−	5.95871i	−1.12730	−	0.232826i
$656$	47.1910	+	15.3333i	1.84250	+	0.598664i
$657$		−	1.70383i		−	0.0664726i
$658$	−3.40004	−	1.10474i	−0.132547	−	0.0430673i
$659$	18.8509	−	13.6960i	0.734328	−	0.533521i	−0.156601	−	0.987662i	$-0.550054\pi$
$659$	18.8509	−	13.6960i	0.734328	−	0.533521i	0.890930	+	0.454141i	$0.150054\pi$
$660$	−8.86804	+	0.983828i	−0.345188	+	0.0382955i
$661$	−7.66748	−	5.57075i	−0.298230	−	0.216677i	0.428600	−	0.903495i	$-0.359007\pi$
$661$	−7.66748	−	5.57075i	−0.298230	−	0.216677i	−0.726830	+	0.686818i	$0.759007\pi$
$662$	36.6964	−	26.6615i	1.42624	−	1.03623i
$663$	1.77367	+	6.46317i	0.0688836	+	0.251009i
$664$	−9.71146	−	7.05579i	−0.376878	−	0.273818i
$665$	3.41214	+	0.704723i	0.132317	+	0.0273280i
$666$	−1.09416	−	1.50598i	−0.0423979	−	0.0583557i
$667$	−20.1956	+	62.1557i	−0.781977	+	2.40668i
$668$			7.36527i			0.284971i
$669$	26.7051	+	8.67702i	1.03248	+	0.335473i
$670$	−22.4792	+	20.4764i	−0.868446	+	0.791072i
$671$	−3.55105	−	10.9290i	−0.137087	−	0.421909i
$672$	−0.730479	−	2.24818i	−0.0281788	−	0.0867255i
$673$	16.0915	−	22.1480i	0.620281	−	0.853744i	−0.377092	−	0.926176i	$-0.623076\pi$
$673$	16.0915	−	22.1480i	0.620281	−	0.853744i	0.997373	+	0.0724317i	$0.0230759\pi$
$674$		−	14.1434i		−	0.544784i
$675$	11.0479	−	25.6051i	0.425235	−	0.985542i
$676$	−15.1700			−0.583462
$677$	29.2663	−	40.2817i	1.12480	−	1.54815i	0.327205	−	0.944953i	$-0.393893\pi$
$677$	29.2663	−	40.2817i	1.12480	−	1.54815i	0.797592	−	0.603197i	$-0.206107\pi$
$678$	4.86187	+	14.9633i	0.186719	+	0.574662i
$679$	−0.747175	−	2.29957i	−0.0286739	−	0.0882493i
$680$	−7.72357	−	9.31092i	−0.296185	−	0.357058i
$681$	3.29630	−	10.1450i	0.126314	−	0.388756i
$682$	−6.21058			−0.237816
$683$	14.3181	+	4.65224i	0.547867	+	0.178013i	0.569855	−	0.821745i	$-0.306999\pi$
$683$	14.3181	+	4.65224i	0.547867	+	0.178013i	−0.0219876	+	0.999758i	$0.506999\pi$
$684$	3.97754	−	2.88985i	0.152085	−	0.110496i
$685$	17.7452	−	16.1642i	0.678011	−	0.617604i
$686$	−3.59946	+	4.95423i	−0.137428	+	0.189153i
$687$	−2.58209	−	3.55395i	−0.0985130	−	0.135592i
$688$	23.9925	−	17.4316i	0.914706	−	0.664573i
$689$	−4.82567	−	3.50606i	−0.183844	−	0.133570i
$690$	−30.5800	+	27.8555i	−1.16416	+	1.06044i
$691$	12.9694	+	17.8508i	0.493378	+	0.679076i	0.981006	−	0.193975i	$-0.0621381\pi$
$691$	12.9694	+	17.8508i	0.493378	+	0.679076i	−0.487629	+	0.873051i	$0.662138\pi$
$692$	−15.0373	−	4.88590i	−0.571631	−	0.185734i
$693$	0.294628			0.0111920
$694$	−35.7297	−	11.6093i	−1.35628	−	0.440682i
$695$	8.77193	−	15.3979i	0.332738	−	0.584076i
$696$	−6.21972	−	19.1423i	−0.235758	−	0.725588i
$697$	−41.5008	−	1.92394i	−1.57196	−	0.0728743i
$698$	−14.1322	−	10.2677i	−0.534912	−	0.388637i
$699$	6.11475			0.231281
$700$	1.33099	−	0.789064i	0.0503068	−	0.0298238i
$701$	−40.2226			−1.51919			−0.759594	−	0.650397i	$-0.774602\pi$
$701$	−40.2226			−1.51919			−0.759594	+	0.650397i	$0.774602\pi$
$702$	6.22584	−	8.56914i	0.234979	−	0.323421i
$703$	10.4539	−	3.39669i	0.394277	−	0.128109i
$704$	2.93854	−	0.954791i	0.110751	−	0.0359850i
$705$	−18.9827	−	20.8394i	−0.714930	−	0.784856i
$706$	−2.02302	+	6.22621i	−0.0761372	+	0.234326i
$707$			2.88472i			0.108491i
$708$	24.8902	+	8.08730i	0.935429	+	0.303939i
$709$	11.6253	+	16.0008i	0.436597	+	0.600924i	0.969452	−	0.245283i	$-0.0788807\pi$
$709$	11.6253	+	16.0008i	0.436597	+	0.600924i	−0.532855	+	0.846207i	$0.678881\pi$
$710$	29.4029	+	6.07269i	1.10347	+	0.227904i
$711$	0.549349	−	0.756113i	0.0206022	−	0.0283565i
$712$	11.3244	−	8.22769i	0.424401	−	0.308346i
$713$	−9.06823	+	6.58845i	−0.339608	+	0.246740i
$714$	1.54207	+	2.34350i	0.0577105	+	0.0877032i
$715$	0.522809	+	4.71250i	0.0195519	+	0.176237i
$716$	2.76904	−	2.01182i	0.103484	−	0.0751854i
$717$	−21.7799	−	7.07673i	−0.813387	−	0.264285i
$718$	−2.83106			−0.105654
$719$	6.56865	+	2.13428i	0.244969	+	0.0795953i	0.428928	−	0.903339i	$-0.358891\pi$
$719$	6.56865	+	2.13428i	0.244969	+	0.0795953i	−0.183959	+	0.982934i	$0.558891\pi$
$720$	−1.33795	+	6.47811i	−0.0498625	+	0.241425i
$721$	−1.87581	+	0.609488i	−0.0698589	+	0.0226985i
$722$	12.4192	+	38.2225i	0.462196	+	1.42249i
$723$	37.6501	+	27.3544i	1.40022	+	1.01732i
$724$		−	20.1273i		−	0.748027i
$725$	42.5928	−	25.2506i	1.58186	−	0.937785i
$726$			19.3900i			0.719629i
$727$	−1.98037	−	1.43883i	−0.0734480	−	0.0533631i	0.550455	−	0.834865i	$-0.314454\pi$
$727$	−1.98037	−	1.43883i	−0.0734480	−	0.0533631i	−0.623903	+	0.781502i	$0.714454\pi$
$728$	−0.317876	+	0.103284i	−0.0117813	+	0.00382797i
$729$	−9.27809	−	28.5550i	−0.343633	−	1.05759i
$730$	10.4577	−	4.72857i	0.387058	−	0.175012i
$731$	−15.5097	+	19.3910i	−0.573647	+	0.717201i
$732$	−11.2312			−0.415116
$733$	−4.22803	+	13.0125i	−0.156166	+	0.480629i	−0.998277	−	0.0586748i	$-0.981313\pi$
$733$	−4.22803	+	13.0125i	−0.156166	+	0.480629i	0.842111	+	0.539304i	$0.181313\pi$
$734$	−23.9764	−	33.0007i	−0.884986	−	1.21808i
$735$	−21.9057	+	9.90488i	−0.808005	+	0.365347i
$736$	24.3888	−	33.5683i	0.898983	−	1.23734i
$737$	−8.92447	−	12.2835i	−0.328737	−	0.452468i
$738$	6.43869	+	8.86209i	0.237011	+	0.326218i
$739$	6.76499	+	4.91505i	0.248854	+	0.180803i	0.705219	−	0.708990i	$-0.250849\pi$
$739$	6.76499	+	4.91505i	0.248854	+	0.180803i	−0.456365	+	0.889793i	$0.650849\pi$
$740$	2.41632	−	4.24151i	0.0888256	−	0.155921i
$741$	6.13336	+	8.44184i	0.225314	+	0.310119i
$742$	−2.37454	−	0.771536i	−0.0871722	−	0.0283240i
$743$		−	39.8408i		−	1.46162i	−0.682583	−	0.730808i	$-0.739143\pi$
$743$		−	39.8408i		−	1.46162i	0.682583	−	0.730808i	$-0.260857\pi$
$744$	1.06675	−	3.28311i	0.0391088	−	0.120365i
$745$	32.8421	−	3.64353i	1.20324	−	0.133489i
$746$	−4.99556	−	15.3747i	−0.182900	−	0.562909i
$747$	−1.69827	−	5.22674i	−0.0621365	−	0.191236i
$748$	−8.87283	+	5.83850i	−0.324423	+	0.213477i
$749$	−1.08401			−0.0396088
$750$	31.3350	−	0.542395i	1.14419	−	0.0198055i
$751$		−	22.1983i		−	0.810028i	−0.914311	−	0.405014i	$-0.867267\pi$
$751$		−	22.1983i		−	0.810028i	0.914311	−	0.405014i	$-0.132733\pi$
$752$	32.4241	+	23.5575i	1.18239	+	0.859053i
$753$	−3.10155	+	1.00775i	−0.113027	+	0.0367246i
$754$	17.8864	−	5.81164i	0.651384	−	0.211648i
$755$	−46.4792	+	5.15644i	−1.69155	+	0.187662i
$756$	0.533359	−	1.64151i	0.0193981	−	0.0597011i
$757$	30.2086			1.09795			0.548975	−	0.835839i	$-0.315018\pi$
$757$	30.2086			1.09795			0.548975	+	0.835839i	$0.315018\pi$
$758$	−62.3983	−	20.2744i	−2.26641	−	0.736401i
$759$	−12.1406	−	16.7101i	−0.440675	−	0.606537i
$760$	−16.3654	−	9.32308i	−0.593635	−	0.338184i
$761$	30.7817	+	22.3642i	1.11584	+	0.810702i	0.983573	−	0.180512i	$-0.0577756\pi$
$761$	30.7817	+	22.3642i	1.11584	+	0.810702i	0.132263	+	0.991215i	$0.457776\pi$
$762$	−9.71612	−	13.3731i	−0.351978	−	0.484456i
$763$	3.64896	−	2.65112i	0.132101	−	0.0959770i
$764$	14.7071	+	10.6853i	0.532082	+	0.386580i
$765$	−0.355121	−	5.52706i	−0.0128394	−	0.199831i
$766$	−35.7562	+	25.9784i	−1.29193	+	0.938639i
$767$	4.29761	−	13.2267i	0.155178	−	0.477588i
$768$			32.2282i			1.16294i
$769$	5.39412	−	16.6014i	0.194517	−	0.598661i	−0.805465	−	0.592643i	$-0.798084\pi$
$769$	5.39412	−	16.6014i	0.194517	−	0.598661i	0.999982	−	0.00601813i	$-0.00191564\pi$
$770$	0.817671	+	1.80837i	0.0294668	+	0.0651691i
$771$	11.3776	−	3.69681i	0.409755	−	0.133137i

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46406 - 1.06370i) q^{2} +(-1.47315 + 0.478654i) q^{3} +(0.393974 + 1.21253i) q^{4} +(2.22243 - 0.246559i) q^{5} +(2.66592 + 0.866209i) q^{6} -0.242729i q^{7} +(-0.405475 + 1.24792i) q^{8} +(-0.486001 + 0.353100i) q^{9} +(-3.51604 - 2.00303i) q^{10} +(1.18766 - 1.63468i) q^{11} +(-1.16076 - 1.59765i) q^{12} +(-0.848997 + 0.616833i) q^{13} +(-0.258191 + 0.355369i) q^{14} +(-3.15595 + 1.42699i) q^{15} +(3.98394 - 2.89450i) q^{16} +(-2.57537 + 3.21985i) q^{17} +1.08713 q^{18} +(-1.98369 + 6.10517i) q^{19} +(1.17454 + 2.59763i) q^{20} +(0.116183 + 0.357575i) q^{21} +(-3.47761 + 1.12994i) q^{22} +(-3.87906 + 5.33906i) q^{23} -2.03246i q^{24} +(4.87842 - 1.09592i) q^{25} +1.89911 q^{26} +(3.27830 - 4.51219i) q^{27} +(0.294315 - 0.0956289i) q^{28} +(9.41832 - 3.06020i) q^{29} +(6.13839 + 1.26779i) q^{30} +(1.61534 + 0.524856i) q^{31} -6.28730 q^{32} +(-0.967154 + 2.97660i) q^{33} +(7.19546 - 1.97463i) q^{34} +(-0.0598468 - 0.539448i) q^{35} +(-0.619616 - 0.450178i) q^{36} +(-1.00647 - 1.38529i) q^{37} +(9.39831 - 6.82827i) q^{38} +(0.955447 - 1.31506i) q^{39} +(-0.593455 + 2.87340i) q^{40} +(5.92266 + 8.15184i) q^{41} +(0.210254 - 0.647095i) q^{42} +6.02232 q^{43} +(2.45000 + 0.796053i) q^{44} +(-0.993045 + 0.904570i) q^{45} +(11.3583 - 3.69054i) q^{46} +(2.51500 + 7.74038i) q^{47} +(-4.48346 + 6.17095i) q^{48} +6.94108 q^{49} +(-8.30802 - 3.58469i) q^{50} +(2.25270 - 5.97603i) q^{51} +(-1.08241 - 0.786417i) q^{52} +(1.75644 + 5.40578i) q^{53} +(-9.59925 + 3.11899i) q^{54} +(2.23645 - 3.92579i) q^{55} +(0.302907 + 0.0984205i) q^{56} -9.94331i q^{57} +(-17.0441 - 5.53797i) q^{58} +(-10.7215 + 7.78959i) q^{59} +(-2.97364 - 3.26448i) q^{60} +(3.34286 - 4.60106i) q^{61} +(-1.80666 - 2.48666i) q^{62} +(0.0857076 + 0.117966i) q^{63} +(1.23711 + 0.898816i) q^{64} +(-1.73475 + 1.58020i) q^{65} +(4.58218 - 3.32915i) q^{66} +(2.32205 - 7.14655i) q^{67} +(-4.91880 - 1.85417i) q^{68} +(3.15885 - 9.72194i) q^{69} +(-0.486192 + 0.853443i) q^{70} +(-7.05636 + 2.29275i) q^{71} +(-0.243581 - 0.749666i) q^{72} +(-1.66711 + 2.29458i) q^{73} +3.09872i q^{74} +(-6.66206 + 3.94953i) q^{75} -8.18421 q^{76} +(-0.396783 - 0.288280i) q^{77} +(-2.79766 + 0.909016i) q^{78} +(-1.47964 + 0.480764i) q^{79} +(8.14037 - 7.41510i) q^{80} +(-2.11273 + 6.50231i) q^{81} -18.2347i q^{82} +(-2.82701 + 8.70064i) q^{83} +(-0.387797 + 0.281751i) q^{84} +(-4.92971 + 7.79089i) q^{85} +(-8.81702 - 6.40594i) q^{86} +(-12.4098 + 9.01624i) q^{87} +(1.55838 + 2.14493i) q^{88} +(-8.63047 - 6.27041i) q^{89} +(2.41607 - 0.268041i) q^{90} +(0.149723 + 0.206076i) q^{91} +(-8.00201 - 2.60001i) q^{92} -2.63086 q^{93} +(4.55134 - 14.0076i) q^{94} +(-2.90334 + 14.0574i) q^{95} +(9.26212 - 3.00944i) q^{96} +(9.47382 - 3.07823i) q^{97} +(-10.1622 - 7.38324i) q^{98} +1.21382i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) \) 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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