LMFDB - Embedded newform 425.2.p.a.16.12

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			16.12
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.12

$q$-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} +(0.190938 + 4.11868i) 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} +(4.10150 - 6.23309i) 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} +(-1.43984 - 9.10642i) 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	0.148857	−	0.988859i	$-0.452441\pi$
$3$	1.47315	−	0.478654i	0.850521	−	0.276351i	0.701664	+	0.712508i	$0.252441\pi$
$4$	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	$0.0146065\pi$
$7$			0.242729i			0.0917428i	−0.998947	+	0.0458714i	$0.985394\pi$
$8$	−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	−0.949616	−	0.313415i	$-0.898527\pi$
$11$	−1.18766	+	1.63468i	−0.358093	+	0.492873i	0.591523	+	0.806288i	$0.298527\pi$
$12$	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
$17$	0.190938	+	4.11868i	0.0463093	+	0.998927i
$17$	0.190938	+	4.11868i	0.0463093	+	0.998927i
$18$	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	$-0.558472\pi$
$23$	3.87906	−	5.33906i	0.808839	−	1.11327i	0.991501	−	0.130096i	$-0.0415284\pi$
$24$			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	−0.995961	−	0.0897832i	$-0.971383\pi$
$29$	−9.41832	+	3.06020i	−1.74894	+	0.568264i	−0.752976	+	0.658047i	$0.771383\pi$
$30$	6.13839	+	1.26779i	1.12071	+	0.231465i
$31$	−1.61534	−	0.524856i	−0.290124	−	0.0942669i	0.160339	−	0.987062i	$-0.448741\pi$
$31$	−1.61534	−	0.524856i	−0.290124	−	0.0942669i	−0.450463	+	0.892795i	$0.648741\pi$
$32$	−6.28730			−1.11145
$33$	−0.967154	+	2.97660i	−0.168360	+	0.518159i
$34$	4.10150	−	6.23309i	0.703402	−	1.06897i
$35$	−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	0.883695	−	0.468064i	$-0.155048\pi$
$37$	1.00647	+	1.38529i	0.165463	+	0.227740i	−0.718232	+	0.695804i	$0.755048\pi$
$38$	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	$-0.911725\pi$
$41$	−5.92266	−	8.15184i	−0.924964	−	1.27310i	0.0368272	−	0.999322i	$-0.488275\pi$
$42$	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	−0.967495	−	0.252890i	$-0.918619\pi$
$61$	−3.34286	+	4.60106i	−0.428010	+	0.589105i	0.539485	+	0.841995i	$0.318619\pi$
$62$	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	0.141262	−	0.989972i	$-0.454884\pi$
$71$	7.05636	−	2.29275i	0.837436	−	0.272099i	0.696174	+	0.717873i	$0.254884\pi$
$72$	−0.243581	−	0.749666i	−0.0287063	−	0.0883490i
$73$	1.66711	−	2.29458i	0.195121	−	0.268561i	−0.700235	−	0.713912i	$-0.746921\pi$
$73$	1.66711	−	2.29458i	0.195121	−	0.268561i	0.895356	+	0.445352i	$0.146921\pi$
$74$		−	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	−0.224595	−	0.974452i	$-0.572106\pi$
$79$	1.47964	−	0.480764i	0.166472	−	0.0540902i	0.391067	+	0.920362i	$0.372106\pi$
$80$	−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
$85$	−1.43984	−	9.10642i	−0.156173	−	0.987730i
$86$	−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	−0.747550	−	0.664205i	$-0.768770\pi$
$97$	−9.47382	+	3.07823i	−0.961921	+	0.312547i	−0.214371	+	0.976752i	$0.568770\pi$
$98$	−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	$0.701377\pi$
$102$	3.05862	−	11.1455i	0.302848	−	1.10356i
$103$	−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	$0.0692584\pi$
$107$			4.46593i			0.431738i	−0.976422	+	0.215869i	$0.930742\pi$
$108$	−6.76273	−	2.19734i	−0.650744	−	0.211440i
$109$	−10.9222	−	15.0331i	−1.04615	−	1.43991i	−0.892097	−	0.451844i	$-0.850766\pi$
$109$	−10.9222	−	15.0331i	−1.04615	−	1.43991i	−0.154056	−	0.988062i	$-0.549234\pi$
$110$	−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	0.625136	−	0.780516i	$-0.285043\pi$
$113$	−3.29913	−	4.54086i	−0.310356	−	0.427168i	−0.935492	+	0.353347i	$0.885043\pi$
$114$	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
$119$	−0.999722	+	0.0463461i	−0.0916444	+	0.00424854i
$120$	−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	0.800082	−	0.599890i	$-0.204789\pi$
$131$	12.5300	+	4.07126i	1.09476	+	0.355708i	0.294673	+	0.955598i	$0.404789\pi$
$132$	−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
$136$	−5.21723	−	1.43175i	−0.447373	−	0.122771i
$137$	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	−0.959509	−	0.281678i	$-0.909109\pi$
$139$	−4.65830	+	6.41161i	−0.395112	+	0.543825i	0.564397	+	0.825504i	$0.309109\pi$
$140$	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
$153$	−1.54710	−	1.93426i	−0.125076	−	0.156376i
$154$	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	0.999628	−	0.0272599i	$-0.00867816\pi$
$163$	8.48761	+	11.6822i	0.664801	+	0.915019i	−0.334828	+	0.942279i	$0.608678\pi$
$164$	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	0.0886193	−	0.996066i	$-0.471755\pi$
$167$	−5.49426	−	1.78519i	−0.425159	−	0.138142i	−0.513778	+	0.857923i	$0.671755\pi$
$168$	−0.493336			−0.0380617
$169$	−3.67691	+	11.3164i	−0.282839	+	0.870489i
$170$	−7.57849	+	14.8639i	−0.581244	+	1.14001i
$171$	−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	−0.436368	−	0.899768i	$-0.643735\pi$
$173$	7.28947	−	10.0331i	0.554208	−	0.762802i	0.990576	+	0.136967i	$0.0437354\pi$
$174$	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	0.808243	−	0.588849i	$-0.200419\pi$
$181$	15.0144	+	4.87846i	1.11601	+	0.362613i	0.307766	+	0.951462i	$0.400419\pi$
$182$			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
$187$	−6.95948	−	4.57948i	−0.508928	−	0.334885i
$188$	−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	$0.219859\pi$
$193$			17.7012i			1.27416i	−0.770796	+	0.637082i	$0.780141\pi$
$194$	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	−0.0353902	−	0.999374i	$-0.511267\pi$
$197$	7.34621	−	2.38693i	0.523396	−	0.170062i	0.558786	+	0.829312i	$0.311267\pi$
$198$	−1.29114	+	1.77710i	−0.0917573	+	0.126293i
$199$		−	7.56325i		−	0.536145i	−0.963399	−	0.268072i	$-0.913613\pi$
$199$		−	7.56325i		−	0.536145i	0.963399	−	0.268072i	$-0.0863866\pi$
$200$	−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
$204$	−6.35860	+	5.08587i	−0.445191	+	0.356082i
$205$	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	−0.808626	−	0.588323i	$-0.799788\pi$
$211$	0.0113559	−	0.0156301i	0.000781773	−	0.00107602i	0.809408	+	0.587247i	$0.199788\pi$
$212$	−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
$221$	−2.70264	−	3.37897i	−0.181799	−	0.227294i
$222$	−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	−0.653274	−	0.757122i	$-0.726605\pi$
$227$	4.04784	−	5.57138i	0.268665	−	0.369785i	0.921938	+	0.387337i	$0.126605\pi$
$228$	−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	0.429404	−	0.903113i	$-0.358724\pi$
$233$	3.75445	+	1.21989i	0.245962	+	0.0799179i	−0.183442	+	0.983031i	$0.558724\pi$
$234$	−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
$238$	1.51295	+	0.995552i	0.0980700	+	0.0645321i
$239$	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	$0.218848\pi$
$241$	17.6599	+	24.3067i	1.13757	+	1.56573i	0.364756	+	0.931103i	$0.381152\pi$
$242$	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
$255$	−6.47993	−	12.7259i	−0.405789	−	0.796927i
$256$	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	0.883688	−	0.468077i	$-0.155053\pi$
$269$	21.7066	+	7.05292i	1.32348	+	0.430024i	0.439790	+	0.898101i	$0.355053\pi$
$270$	−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	$0.745831\pi$
$272$	12.6822	+	15.8559i	0.768972	+	0.961405i
$273$	−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	−0.508556	−	0.861029i	$-0.669820\pi$
$277$	7.78048	−	10.7089i	0.467484	−	0.643436i	0.976040	+	0.217593i	$0.0698205\pi$
$278$	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	−0.0958735	−	0.995394i	$-0.530564\pi$
$283$	−12.7602	−	4.14604i	−0.758514	−	0.246456i	−0.662641	+	0.748937i	$0.730564\pi$
$284$	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
$289$	−16.9271	+	1.57283i	−0.995711	+	0.0925192i
$290$	−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
$306$	0.207574	+	4.47753i	0.0118662	+	0.255963i
$307$	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	$-0.503966\pi$
$311$	16.6189	−	22.8740i	0.942373	−	1.29707i	0.954833	−	0.297143i	$-0.0960339\pi$
$312$	−1.25369	−	1.72555i	−0.0709760	−	0.0976901i
$313$	14.6727	+	20.1953i	0.829351	+	1.14150i	0.988043	+	0.154176i	$0.0492723\pi$
$313$	14.6727	+	20.1953i	0.829351	+	1.14150i	−0.158692	+	0.987328i	$0.550728\pi$
$314$	−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	0.720355	−	0.693606i	$-0.243979\pi$
$317$	15.9429	+	5.18017i	0.895443	+	0.290947i	0.175088	+	0.984553i	$0.443979\pi$
$318$		−	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
$323$	−25.5240	−	7.00448i	−1.42019	−	0.389740i
$324$	−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	0.665355	−	0.746527i	$-0.268280\pi$
$337$	−4.59380	−	6.32282i	−0.250240	−	0.344426i	−0.915595	+	0.402101i	$0.868280\pi$
$338$	17.4204	−	12.6567i	0.947546	−	0.688433i
$339$	−7.03360	−	5.11021i	−0.382013	−	0.277548i
$340$	10.4745	−	5.33355i	0.568061	−	0.289252i
$341$	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	−0.786545	−	0.617533i	$-0.788132\pi$
$347$	−19.7437	+	6.41511i	−1.05990	+	0.344381i	−0.273351	+	0.961914i	$0.588132\pi$
$348$	−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	−0.309627	−	0.950858i	$-0.600204\pi$
$367$	−21.4374	−	6.96542i	−1.11902	−	0.363592i	−0.809394	+	0.587266i	$0.800204\pi$
$368$		−	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	−0.998254	−	0.0590693i	$-0.981187\pi$
$379$	−34.4804	+	11.2034i	−1.77114	+	0.575478i	−0.772884	+	0.634547i	$0.781187\pi$
$380$	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
$391$	22.7306	+	14.9572i	1.14953	+	0.756416i
$392$	−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	−0.307488	−	0.951552i	$-0.599488\pi$
$397$	0.0609325	−	0.0197982i	0.00305812	−	0.000993642i	0.310546	+	0.950558i	$0.399488\pi$
$398$	−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	$0.164882\pi$
$401$			19.8302i			0.990273i	−0.868815	+	0.495136i	$0.835118\pi$
$402$	−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
$408$	−8.37105	+	0.388073i	−0.414429	+	0.0192125i
$409$	−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	0.430506	−	0.902588i	$-0.358335\pi$
$419$	5.08187	+	1.65120i	0.248266	+	0.0806664i	−0.182241	+	0.983254i	$0.558335\pi$
$420$	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
$425$	5.44522	+	19.8834i	0.264132	+	0.964487i
$426$	−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	0.262047	−	0.965055i	$-0.415603\pi$
$431$	−1.93484	−	0.628669i	−0.0931981	−	0.0302819i	−0.355245	+	0.934773i	$0.615603\pi$
$432$			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	−0.740220	−	0.672364i	$-0.765279\pi$
$439$	2.68141	−	3.69064i	0.127977	−	0.176145i	0.868197	+	0.496220i	$0.165279\pi$
$440$	3.99226	+	4.38274i	0.190323	+	0.208939i
$441$	−3.37337	+	2.45090i	−0.160637	+	0.116709i
$442$	0.362612	+	7.82182i	0.0172477	+	0.372046i
$443$	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	$0.0203652\pi$
$449$			2.70954i			0.127871i	−0.997954	+	0.0639355i	$0.979635\pi$
$450$	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
$459$	−19.2102	−	12.6407i	−0.896657	−	0.590019i
$460$	−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	−0.952252	−	0.305314i	$-0.901239\pi$
$479$	−33.7742	+	10.9739i	−1.54318	+	0.501410i	−0.590929	+	0.806723i	$0.701239\pi$
$480$	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	0.998718	−	0.0506115i	$-0.0161170\pi$
$487$	14.1669	+	19.4991i	0.641963	+	0.883586i	−0.356755	+	0.934198i	$0.616117\pi$
$488$	−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	$0.0102673\pi$
$499$			1.44082i			0.0644999i	−0.999480	+	0.0322499i	$0.989733\pi$
$500$	−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	−0.854704	−	0.519116i	$-0.826261\pi$
$503$	−27.8337	+	9.04373i	−1.24104	+	0.403240i	−0.386341	+	0.922356i	$0.626261\pi$
$504$	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	$0.261050\pi$
$510$	−4.04956	+	25.5242i	−0.179317	+	1.13023i
$511$	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	−0.313200	−	0.949687i	$-0.601401\pi$
$521$	−0.191085	+	0.0620874i	−0.00837160	+	0.00272010i	0.304828	+	0.952407i	$0.401401\pi$
$522$	−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
$527$	1.85328	−	6.75329i	0.0807303	−	0.294178i
$528$	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	0.775579	−	0.631251i	$-0.217458\pi$
$541$	−1.49891	−	2.06307i	−0.0644431	−	0.0886983i	−0.840022	+	0.542552i	$0.817458\pi$
$542$	8.57297	−	26.3849i	0.368241	−	1.13333i
$543$	24.4535			1.04940
$544$	−1.20049	−	25.8954i	−0.0514704	−	1.11026i
$545$	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	−0.579207	−	0.815181i	$-0.696638\pi$
$547$	−13.2995	+	4.32126i	−0.568644	+	0.184764i	0.0105629	+	0.999944i	$0.496638\pi$
$548$	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
$561$	−12.4443	−	3.41506i	−0.525399	−	0.144184i
$562$	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	−0.635594	−	0.772024i	$-0.719245\pi$
$571$	−16.6317	+	5.40398i	−0.696016	+	0.226149i	−0.0604223	+	0.998173i	$0.519245\pi$
$572$	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	$0.689665\pi$
$578$	26.4553	+	15.7026i	1.10039	+	0.653144i
$579$	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
$595$	2.21039	−	0.349491i	0.0906171	−	0.0143277i
$596$	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	$0.143271\pi$
$601$			21.3310i			0.870111i	−0.900404	+	0.435055i	$0.856729\pi$
$602$	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	$-0.875579\pi$
$607$		−	18.7737i		−	0.762002i	0.924575	−	0.381001i	$-0.124421\pi$
$608$	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
$612$	1.73583	−	2.63796i	0.0701668	−	0.106633i
$613$	−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	0.886993	−	0.461782i	$-0.152790\pi$
$617$	33.1149	+	10.7597i	1.33316	+	0.433169i	0.446164	+	0.894951i	$0.352790\pi$
$618$			22.7773i			0.916238i
$619$	21.6527	+	7.03540i	0.870297	+	0.282776i	0.709922	−	0.704280i	$-0.248730\pi$
$619$	21.6527	+	7.03540i	0.870297	+	0.282776i	0.160374	+	0.987056i	$0.448730\pi$
$620$	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
$629$	−5.51338	+	4.40983i	−0.219833	+	0.175832i
$630$	−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	0.796778	−	0.604272i	$-0.206536\pi$
$641$	−0.611110	−	0.841121i	−0.0241374	−	0.0332223i	−0.820915	+	0.571050i	$0.806536\pi$
$642$	3.86843	−	11.9058i	0.152675	−	0.469884i
$643$			2.30605i			0.0909416i	0.998966	+	0.0454708i	$0.0144788\pi$
$643$			2.30605i			0.0909416i	−0.998966	+	0.0454708i	$0.985521\pi$
$644$	−0.631097	+	1.94232i	−0.0248687	+	0.0765381i
$645$	−19.0061	+	8.59381i	−0.748366	+	0.338381i
$646$	29.9180	+	37.4049i	1.17711	+	1.47168i
$647$	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	0.259228	−	0.965816i	$-0.416532\pi$
$653$	26.4902	−	8.60718i	1.03664	−	0.336825i	0.777413	+	0.628991i	$0.216532\pi$
$654$	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
$663$	−5.59875	−	3.68409i	−0.217437	−	0.143078i
$664$	−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	−0.997373	−	0.0724317i	$-0.976924\pi$
$673$	−16.0915	+	22.1480i	−0.620281	+	0.853744i	0.377092	+	0.926176i	$0.376924\pi$
$674$			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	$0.606107\pi$
$677$	−29.2663	+	40.2817i	−1.12480	+	1.54815i	−0.797592	+	0.603197i	$0.793893\pi$
$678$	4.86187	+	14.9633i	0.186719	+	0.574662i
$679$	−0.747175	−	2.29957i	−0.0286739	−	0.0882493i
$680$	11.9479	+	1.89561i	0.458183	+	0.0726934i
$681$	3.29630	−	10.1450i	0.126314	−	0.388756i
$682$	−6.21058			−0.237816
$683$	−14.3181	−	4.65224i	−0.547867	−	0.178013i	0.0219876	−	0.999758i	$-0.493001\pi$
$683$	−14.3181	−	4.65224i	−0.547867	−	0.178013i	−0.569855	+	0.821745i	$0.693001\pi$
$684$	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	0.487629	−	0.873051i	$-0.337862\pi$
$691$	−12.9694	−	17.8508i	−0.493378	−	0.679076i	−0.981006	+	0.193975i	$0.937862\pi$
$692$	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
$697$	32.4440	−	25.9501i	1.22890	−	0.982929i
$698$	−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	0.532855	−	0.846207i	$-0.321119\pi$
$709$	−11.6253	−	16.0008i	−0.436597	−	0.600924i	−0.969452	+	0.245283i	$0.921119\pi$
$710$	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
$714$	2.70532	+	0.742414i	0.101244	+	0.0277841i
$715$	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	0.183959	−	0.982934i	$-0.441109\pi$
$719$	−6.56865	−	2.13428i	−0.244969	−	0.0795953i	−0.428928	+	0.903339i	$0.641109\pi$
$720$	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
$731$	1.14989	+	24.8040i	0.0425302	+	0.917409i
$732$	−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	$0.260857\pi$
$743$			39.8408i			1.46162i	−0.682583	+	0.730808i	$0.739143\pi$
$744$	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
$748$	2.81089	−	10.2428i	0.102776	−	0.374513i
$749$	−1.08401			−0.0396088
$750$	31.3350	−	0.542395i	1.14419	−	0.0198055i
$751$			22.1983i			0.810028i	0.914311	+	0.405014i	$0.132733\pi$
$751$			22.1983i			0.810028i	−0.914311	+	0.405014i	$0.867267\pi$
$752$	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
$765$	3.91525	+	3.91732i	0.141556	+	0.141631i
$766$	−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} +(0.190938 + 4.11868i) 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} +(4.10150 - 6.23309i) 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} +(-1.43984 - 9.10642i) 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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Representations

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Database

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