LMFDB - Embedded newform 405.4.e.q.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,4,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, degree $2$, not 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:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.84779568.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 13x^{4} - 4x^{3} + 152x^{2} - 96x + 64 $ x^6 - x^5 + 13x^4 - 4x^3 + 152x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.1
Root			$0.327167 + 0.566669i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.4.e.q.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72938 - 4.72742i) q^{2} +(-10.8990 + 18.8776i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(5.90326 + 10.2247i) q^{7} +75.3201 q^{8} +O(q^{10})$	\(q+(-2.72938 - 4.72742i) q^{2} +(-10.8990 + 18.8776i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(5.90326 + 10.2247i) q^{7} +75.3201 q^{8} +27.2938 q^{10} +(28.1188 + 48.7032i) q^{11} +(-17.2980 + 29.9611i) q^{13} +(32.2245 - 55.8144i) q^{14} +(-118.385 - 205.049i) q^{16} +39.2675 q^{17} -146.561 q^{19} +(-54.4951 - 94.3882i) q^{20} +(153.494 - 265.859i) q^{22} +(11.7889 - 20.4189i) q^{23} +(-12.5000 - 21.6506i) q^{25} +188.851 q^{26} -257.359 q^{28} +(-80.5013 - 139.432i) q^{29} +(14.7733 - 25.5880i) q^{31} +(-344.954 + 597.478i) q^{32} +(-107.176 - 185.634i) q^{34} -59.0326 q^{35} -217.688 q^{37} +(400.020 + 692.855i) q^{38} +(-188.300 + 326.146i) q^{40} +(-71.1449 + 123.227i) q^{41} +(234.015 + 405.326i) q^{43} -1225.87 q^{44} -128.705 q^{46} +(-197.159 - 341.490i) q^{47} +(101.803 - 176.328i) q^{49} +(-68.2345 + 118.186i) q^{50} +(-377.063 - 653.092i) q^{52} -134.780 q^{53} -281.188 q^{55} +(444.634 + 770.129i) q^{56} +(-439.437 + 761.128i) q^{58} +(65.5977 - 113.619i) q^{59} +(-129.901 - 224.994i) q^{61} -161.287 q^{62} +1871.88 q^{64} +(-86.4901 - 149.805i) q^{65} +(-222.622 + 385.593i) q^{67} +(-427.977 + 741.278i) q^{68} +(161.122 + 279.072i) q^{70} +560.841 q^{71} -88.6681 q^{73} +(594.152 + 1029.10i) q^{74} +(1597.37 - 2766.72i) q^{76} +(-331.985 + 575.015i) q^{77} +(-225.171 - 390.008i) q^{79} +1183.85 q^{80} +776.726 q^{82} +(-142.148 - 246.207i) q^{83} +(-98.1687 + 170.033i) q^{85} +(1277.43 - 2212.57i) q^{86} +(2117.91 + 3668.33i) q^{88} +625.305 q^{89} -408.459 q^{91} +(256.974 + 445.092i) q^{92} +(-1076.24 + 1864.11i) q^{94} +(366.402 - 634.627i) q^{95} +(96.6307 + 167.369i) q^{97} -1111.44 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{2} - 17 q^{4} - 15 q^{5} + 4 q^{7} + 150 q^{8}+O(q^{10}) $ 6 * q - 5 * q^2 - 17 * q^4 - 15 * q^5 + 4 * q^7 + 150 * q^8	$ 6 q - 5 q^{2} - 17 q^{4} - 15 q^{5} + 4 q^{7} + 150 q^{8} + 50 q^{10} - 5 q^{11} - 7 q^{13} - 60 q^{14} - 161 q^{16} + 310 q^{17} - 100 q^{19} - 85 q^{20} + 229 q^{22} - 285 q^{23} - 75 q^{25} + 370 q^{26} - 668 q^{28} - 115 q^{29} + 115 q^{31} - 775 q^{32} - 413 q^{34} - 40 q^{35} - 768 q^{37} + 1150 q^{38} - 375 q^{40} - 580 q^{41} + 797 q^{43} - 2830 q^{44} - 570 q^{46} + 145 q^{47} - 577 q^{49} - 125 q^{50} - 825 q^{52} - 800 q^{53} + 50 q^{55} + 2190 q^{56} + 59 q^{58} - 380 q^{59} + 152 q^{61} - 2010 q^{62} + 5874 q^{64} - 35 q^{65} - 2 q^{67} - 475 q^{68} - 300 q^{70} + 80 q^{71} - 1960 q^{73} + 2720 q^{74} + 3276 q^{76} - 1950 q^{77} - 1013 q^{79} + 1610 q^{80} + 8 q^{82} - 270 q^{83} - 775 q^{85} + 1555 q^{86} + 5193 q^{88} + 2040 q^{89} - 1264 q^{91} + 1215 q^{92} - 3833 q^{94} + 250 q^{95} - 720 q^{97} - 610 q^{98}+O(q^{100}) $ 6 * q - 5 * q^2 - 17 * q^4 - 15 * q^5 + 4 * q^7 + 150 * q^8 + 50 * q^10 - 5 * q^11 - 7 * q^13 - 60 * q^14 - 161 * q^16 + 310 * q^17 - 100 * q^19 - 85 * q^20 + 229 * q^22 - 285 * q^23 - 75 * q^25 + 370 * q^26 - 668 * q^28 - 115 * q^29 + 115 * q^31 - 775 * q^32 - 413 * q^34 - 40 * q^35 - 768 * q^37 + 1150 * q^38 - 375 * q^40 - 580 * q^41 + 797 * q^43 - 2830 * q^44 - 570 * q^46 + 145 * q^47 - 577 * q^49 - 125 * q^50 - 825 * q^52 - 800 * q^53 + 50 * q^55 + 2190 * q^56 + 59 * q^58 - 380 * q^59 + 152 * q^61 - 2010 * q^62 + 5874 * q^64 - 35 * q^65 - 2 * q^67 - 475 * q^68 - 300 * q^70 + 80 * q^71 - 1960 * q^73 + 2720 * q^74 + 3276 * q^76 - 1950 * q^77 - 1013 * q^79 + 1610 * q^80 + 8 * q^82 - 270 * q^83 - 775 * q^85 + 1555 * q^86 + 5193 * q^88 + 2040 * q^89 - 1264 * q^91 + 1215 * q^92 - 3833 * q^94 + 250 * q^95 - 720 * q^97 - 610 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.72938	−	4.72742i	−0.964981	−	1.67140i	−0.709666	−	0.704538i	$-0.751154\pi$
$2$	−2.72938	−	4.72742i	−0.964981	−	1.67140i	−0.255315	−	0.966858i	$-0.582179\pi$
$3$		0			0
$3$		0			0
$4$	−10.8990	+	18.8776i	−1.36238	+	2.35971i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	5.90326	+	10.2247i	0.318746	+	0.552084i	0.980227	−	0.197878i	$-0.0634050\pi$
$7$	5.90326	+	10.2247i	0.318746	+	0.552084i	−0.661481	+	0.749962i	$0.730072\pi$
$8$	75.3201			3.32871
$9$		0			0
$10$	27.2938			0.863105
$11$	28.1188	+	48.7032i	0.770740	+	1.33496i	0.937158	+	0.348905i	$0.113446\pi$
$11$	28.1188	+	48.7032i	0.770740	+	1.33496i	−0.166418	+	0.986055i	$0.553220\pi$
$12$		0			0
$13$	−17.2980	+	29.9611i	−0.369047	+	0.639208i	−0.989417	−	0.145101i	$-0.953649\pi$
$13$	−17.2980	+	29.9611i	−0.369047	+	0.639208i	0.620370	+	0.784309i	$0.286983\pi$
$14$	32.2245	−	55.8144i	0.615168	−	1.06550i
$15$		0			0
$16$	−118.385	−	205.049i	−1.84976	−	3.20389i
$17$	39.2675			0.560221			0.280111	−	0.959968i	$-0.409629\pi$
$17$	39.2675			0.560221			0.280111	+	0.959968i	$0.409629\pi$
$18$		0			0
$19$	−146.561			−1.76965			−0.884825	−	0.465924i	$-0.845722\pi$
$19$	−146.561			−1.76965			−0.884825	+	0.465924i	$0.845722\pi$
$20$	−54.4951	−	94.3882i	−0.609273	−	1.05529i
$21$		0			0
$22$	153.494	−	265.859i	1.48750	−	2.57642i
$23$	11.7889	−	20.4189i	0.106876	−	0.185115i	−0.807627	−	0.589693i	$-0.799249\pi$
$23$	11.7889	−	20.4189i	0.106876	−	0.185115i	0.914503	+	0.404579i	$0.132582\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	188.851			1.42449
$27$		0			0
$28$	−257.359			−1.73701
$29$	−80.5013	−	139.432i	−0.515473	−	0.892826i	−0.999839	−	0.0179601i	$-0.994283\pi$
$29$	−80.5013	−	139.432i	−0.515473	−	0.892826i	0.484365	−	0.874866i	$-0.339051\pi$
$30$		0			0
$31$	14.7733	−	25.5880i	0.0855921	−	0.148250i	−0.820051	−	0.572290i	$-0.806055\pi$
$31$	14.7733	−	25.5880i	0.0855921	−	0.148250i	0.905643	+	0.424040i	$0.139388\pi$
$32$	−344.954	+	597.478i	−1.90562	+	3.30063i
$33$		0			0
$34$	−107.176	−	185.634i	−0.540603	−	0.936352i
$35$	−59.0326			−0.285095
$36$		0			0
$37$	−217.688			−0.967233			−0.483617	−	0.875280i	$-0.660677\pi$
$37$	−217.688			−0.967233			−0.483617	+	0.875280i	$0.660677\pi$
$38$	400.020	+	692.855i	1.70768	+	2.95779i
$39$		0			0
$40$	−188.300	+	326.146i	−0.744322	+	1.28920i
$41$	−71.1449	+	123.227i	−0.270999	+	0.469385i	−0.969118	−	0.246597i	$-0.920687\pi$
$41$	−71.1449	+	123.227i	−0.270999	+	0.469385i	0.698119	+	0.715982i	$0.254021\pi$
$42$		0			0
$43$	234.015	+	405.326i	0.829929	+	1.43748i	0.898093	+	0.439805i	$0.144952\pi$
$43$	234.015	+	405.326i	0.829929	+	1.43748i	−0.0681645	+	0.997674i	$0.521714\pi$
$44$	−1225.87			−4.20015
$45$		0			0
$46$	−128.705			−0.412533
$47$	−197.159	−	341.490i	−0.611886	−	1.05982i	−0.990922	−	0.134435i	$-0.957078\pi$
$47$	−197.159	−	341.490i	−0.611886	−	1.05982i	0.379037	−	0.925382i	$-0.376255\pi$
$48$		0			0
$49$	101.803	−	176.328i	0.296802	−	0.514076i
$50$	−68.2345	+	118.186i	−0.192996	+	0.334279i
$51$		0			0
$52$	−377.063	−	653.092i	−1.00556	−	1.74168i
$53$	−134.780			−0.349311			−0.174655	−	0.984630i	$-0.555881\pi$
$53$	−134.780			−0.349311			−0.174655	+	0.984630i	$0.555881\pi$
$54$		0			0
$55$	−281.188			−0.689371
$56$	444.634	+	770.129i	1.06101	+	1.83773i
$57$		0			0
$58$	−439.437	+	761.128i	−0.994844	+	1.72312i
$59$	65.5977	−	113.619i	0.144747	−	0.250710i	−0.784531	−	0.620089i	$-0.787096\pi$
$59$	65.5977	−	113.619i	0.144747	−	0.250710i	0.929279	+	0.369379i	$0.120430\pi$
$60$		0			0
$61$	−129.901	−	224.994i	−0.272657	−	0.472255i	0.696885	−	0.717183i	$-0.254569\pi$
$61$	−129.901	−	224.994i	−0.272657	−	0.472255i	−0.969541	+	0.244928i	$0.921236\pi$
$62$	−161.287			−0.330379
$63$		0			0
$64$	1871.88			3.65602
$65$	−86.4901	−	149.805i	−0.165043	−	0.285863i
$66$		0			0
$67$	−222.622	+	385.593i	−0.405935	+	0.703100i	−0.994430	−	0.105401i	$-0.966387\pi$
$67$	−222.622	+	385.593i	−0.405935	+	0.703100i	0.588495	+	0.808501i	$0.299721\pi$
$68$	−427.977	+	741.278i	−0.763233	+	1.32196i
$69$		0			0
$70$	161.122	+	279.072i	0.275111	+	0.476507i
$71$	560.841			0.937459			0.468729	−	0.883342i	$-0.344712\pi$
$71$	560.841			0.937459			0.468729	+	0.883342i	$0.344712\pi$
$72$		0			0
$73$	−88.6681			−0.142162			−0.0710809	−	0.997471i	$-0.522645\pi$
$73$	−88.6681			−0.142162			−0.0710809	+	0.997471i	$0.522645\pi$
$74$	594.152	+	1029.10i	0.933362	+	1.61663i
$75$		0			0
$76$	1597.37	−	2766.72i	2.41093	−	4.17585i
$77$	−331.985	+	575.015i	−0.491340	+	0.851027i
$78$		0			0
$79$	−225.171	−	390.008i	−0.320680	−	0.555434i	0.659948	−	0.751311i	$-0.270578\pi$
$79$	−225.171	−	390.008i	−0.320680	−	0.555434i	−0.980629	+	0.195877i	$0.937245\pi$
$80$	1183.85			1.65448
$81$		0			0
$82$	776.726			1.04604
$83$	−142.148	−	246.207i	−0.187985	−	0.325599i	0.756594	−	0.653886i	$-0.226862\pi$
$83$	−142.148	−	246.207i	−0.187985	−	0.325599i	−0.944578	+	0.328286i	$0.893529\pi$
$84$		0			0
$85$	−98.1687	+	170.033i	−0.125269	+	0.216973i
$86$	1277.43	−	2212.57i	1.60173	−	2.77428i
$87$		0			0
$88$	2117.91	+	3668.33i	2.56557	+	4.44369i
$89$	625.305			0.744744			0.372372	−	0.928083i	$-0.378545\pi$
$89$	625.305			0.744744			0.372372	+	0.928083i	$0.378545\pi$
$90$		0			0
$91$	−408.459			−0.470529
$92$	256.974	+	445.092i	0.291211	+	0.504392i
$93$		0			0
$94$	−1076.24	+	1864.11i	−1.18092	+	2.04541i
$95$	366.402	−	634.627i	0.395706	−	0.685382i
$96$		0			0
$97$	96.6307	+	167.369i	0.101148	+	0.175193i	0.912158	−	0.409839i	$-0.134415\pi$
$97$	96.6307	+	167.369i	0.101148	+	0.175193i	−0.811010	+	0.585032i	$0.801082\pi$
$98$	−1111.44			−1.14563
$99$		0			0
$100$	544.951			0.544951
$101$	−687.429	−	1190.66i	−0.677245	−	1.17302i	−0.975807	−	0.218633i	$-0.929840\pi$
$101$	−687.429	−	1190.66i	−0.677245	−	1.17302i	0.298562	−	0.954390i	$-0.403493\pi$
$102$		0			0
$103$	−1014.80	+	1757.69i	−0.970789	+	1.68146i	−0.277605	+	0.960695i	$0.589541\pi$
$103$	−1014.80	+	1757.69i	−0.970789	+	1.68146i	−0.693184	+	0.720761i	$0.743793\pi$
$104$	−1302.89	+	2256.67i	−1.22845	+	2.12774i
$105$		0			0
$106$	367.866	+	637.162i	0.337078	+	0.583836i
$107$	−823.062			−0.743630			−0.371815	−	0.928307i	$-0.621264\pi$
$107$	−823.062			−0.743630			−0.371815	+	0.928307i	$0.621264\pi$
$108$		0			0
$109$	−829.868			−0.729238			−0.364619	−	0.931157i	$-0.618801\pi$
$109$	−829.868			−0.729238			−0.364619	+	0.931157i	$0.618801\pi$
$110$	767.469	+	1329.29i	0.665230	+	1.15221i
$111$		0			0
$112$	1397.71	−	2420.91i	1.17921	−	2.04245i
$113$	751.683	−	1301.95i	0.625773	−	1.08387i	−0.362618	−	0.931938i	$-0.618117\pi$
$113$	751.683	−	1301.95i	0.625773	−	1.08387i	0.988391	−	0.151933i	$-0.0485498\pi$
$114$		0			0
$115$	58.9443	+	102.095i	0.0477964	+	0.0827858i
$116$	3509.54			2.80908
$117$		0			0
$118$	−716.164			−0.558714
$119$	231.806	+	401.500i	0.178568	+	0.309289i
$120$		0			0
$121$	−915.834	+	1586.27i	−0.688080	+	1.19179i
$122$	−709.095	+	1228.19i	−0.526217	+	0.911435i
$123$		0			0
$124$	322.028	+	557.768i	0.233217	+	0.403944i
$125$	125.000			0.0894427
$126$		0			0
$127$	−576.348			−0.402698			−0.201349	−	0.979520i	$-0.564532\pi$
$127$	−576.348			−0.402698			−0.201349	+	0.979520i	$0.564532\pi$
$128$	−2349.44	−	4069.36i	−1.62237	−	2.81003i
$129$		0			0
$130$	−472.129	+	817.751i	−0.318526	+	0.551704i
$131$	−1195.02	+	2069.83i	−0.797017	+	1.38047i	0.124534	+	0.992215i	$0.460257\pi$
$131$	−1195.02	+	2069.83i	−0.797017	+	1.38047i	−0.921551	+	0.388258i	$0.873077\pi$
$132$		0			0
$133$	−865.186	−	1498.55i	−0.564069	−	0.976996i
$134$	2430.48			1.56688
$135$		0			0
$136$	2957.63			1.86481
$137$	−501.230	−	868.155i	−0.312576	−	0.541398i	0.666343	−	0.745645i	$-0.267859\pi$
$137$	−501.230	−	868.155i	−0.312576	−	0.541398i	−0.978919	+	0.204248i	$0.934525\pi$
$138$		0			0
$139$	−65.9084	+	114.157i	−0.0402178	+	0.0696593i	−0.885434	−	0.464766i	$-0.846139\pi$
$139$	−65.9084	+	114.157i	−0.0402178	+	0.0696593i	0.845216	+	0.534425i	$0.179472\pi$
$140$	643.397	−	1114.40i	0.388407	−	0.672740i
$141$		0			0
$142$	−1530.75	−	2651.33i	−0.904630	−	1.56687i
$143$	−1945.60			−1.13776
$144$		0			0
$145$	805.013			0.461053
$146$	242.009	+	419.171i	0.137183	+	0.237609i
$147$		0			0
$148$	2372.58	−	4109.43i	1.31774	−	2.28239i
$149$	−509.743	+	882.900i	−0.280267	+	0.485436i	−0.971450	−	0.237243i	$-0.923756\pi$
$149$	−509.743	+	882.900i	−0.280267	+	0.485436i	0.691184	+	0.722679i	$0.257090\pi$
$150$		0			0
$151$	−1411.19	−	2444.25i	−0.760537	−	1.31729i	−0.942574	−	0.333997i	$-0.891603\pi$
$151$	−1411.19	−	2444.25i	−0.760537	−	1.31729i	0.182037	−	0.983292i	$-0.441731\pi$
$152$	−11039.0			−5.89065
$153$		0			0
$154$	3624.45			1.89654
$155$	73.8663	+	127.940i	0.0382779	+	0.0662993i
$156$		0			0
$157$	−238.250	+	412.661i	−0.121111	+	0.209770i	−0.920206	−	0.391434i	$-0.871979\pi$
$157$	−238.250	+	412.661i	−0.121111	+	0.209770i	0.799095	+	0.601205i	$0.205312\pi$
$158$	−1229.15	+	2128.96i	−0.618900	+	1.07197i
$159$		0			0
$160$	−1724.77	−	2987.39i	−0.852219	−	1.47609i
$161$	278.371			0.136265
$162$		0			0
$163$	−2242.26			−1.07747			−0.538734	−	0.842476i	$-0.681097\pi$
$163$	−2242.26			−1.07747			−0.538734	+	0.842476i	$0.681097\pi$
$164$	−1550.82	−	2686.10i	−0.738406	−	1.27896i
$165$		0			0
$166$	−775.949	+	1343.98i	−0.362803	+	0.628394i
$167$	−47.5195	+	82.3062i	−0.0220190	+	0.0381380i	−0.876825	−	0.480810i	$-0.840343\pi$
$167$	−47.5195	+	82.3062i	−0.0220190	+	0.0381380i	0.854806	+	0.518948i	$0.173676\pi$
$168$		0			0
$169$	500.056	+	866.123i	0.227609	+	0.394230i
$170$	1071.76			0.483530
$171$		0			0
$172$	−10202.1			−4.52270
$173$	1066.88	+	1847.89i	0.468864	+	0.812096i	0.999367	−	0.0355875i	$-0.0113302\pi$
$173$	1066.88	+	1847.89i	0.468864	+	0.812096i	−0.530503	+	0.847683i	$0.677997\pi$
$174$		0			0
$175$	147.581	−	255.619i	0.0637492	−	0.110417i
$176$	6657.68	−	11531.4i	2.85137	−	4.93872i
$177$		0			0
$178$	−1706.70	−	2956.08i	−0.718664	−	1.24476i
$179$	−1704.68			−0.711808			−0.355904	−	0.934523i	$-0.615827\pi$
$179$	−1704.68			−0.711808			−0.355904	+	0.934523i	$0.615827\pi$
$180$		0			0
$181$	−1360.98			−0.558902			−0.279451	−	0.960160i	$-0.590152\pi$
$181$	−1360.98			−0.558902			−0.279451	+	0.960160i	$0.590152\pi$
$182$	1114.84	+	1930.96i	0.454051	+	0.786440i
$183$		0			0
$184$	887.938	−	1537.95i	0.355759	−	0.616193i
$185$	544.219	−	942.615i	0.216280	−	0.374608i
$186$		0			0
$187$	1104.15	+	1912.45i	0.431785	+	0.747873i
$188$	8595.36			3.33447
$189$		0			0
$190$	−4000.20			−1.52739
$191$	548.421	+	949.892i	0.207761	+	0.359852i	0.951009	−	0.309164i	$-0.100049\pi$
$191$	548.421	+	949.892i	0.207761	+	0.359852i	−0.743248	+	0.669016i	$0.766716\pi$
$192$		0			0
$193$	1433.63	−	2483.13i	0.534691	−	0.926111i	−0.464488	−	0.885580i	$-0.653762\pi$
$193$	1433.63	−	2483.13i	0.534691	−	0.926111i	0.999178	−	0.0405316i	$-0.0129052\pi$
$194$	527.483	−	913.628i	0.195212	−	0.338117i
$195$		0			0
$196$	2219.11	+	3843.61i	0.808712	+	1.40073i
$197$	724.139			0.261892			0.130946	−	0.991389i	$-0.458199\pi$
$197$	724.139			0.261892			0.130946	+	0.991389i	$0.458199\pi$
$198$		0			0
$199$	−1693.65			−0.603315			−0.301658	−	0.953416i	$-0.597540\pi$
$199$	−1693.65			−0.603315			−0.301658	+	0.953416i	$0.597540\pi$
$200$	−941.501	−	1630.73i	−0.332871	−	0.576549i
$201$		0			0
$202$	−3752.51	+	6499.53i	−1.30706	+	2.26389i
$203$	950.440	−	1646.21i	0.328610	−	0.569169i
$204$		0			0
$205$	−355.725	−	616.133i	−0.121195	−	0.209915i
$206$	11079.1			3.74717
$207$		0			0
$208$	8191.30			2.73060
$209$	−4121.11	−	7137.98i	−1.36394	−	2.36241i
$210$		0			0
$211$	−473.726	+	820.517i	−0.154562	+	0.267710i	−0.932900	−	0.360137i	$-0.882730\pi$
$211$	−473.726	+	820.517i	−0.154562	+	0.267710i	0.778337	+	0.627846i	$0.216063\pi$
$212$	1468.97	−	2544.33i	0.475893	−	0.824270i
$213$		0			0
$214$	2246.45	+	3890.96i	0.717589	+	1.24290i
$215$	−2340.15			−0.742311
$216$		0			0
$217$	348.841			0.109129
$218$	2265.02	+	3923.14i	0.703701	+	1.21885i
$219$		0			0
$220$	3064.67	−	5308.17i	0.939183	−	1.62671i
$221$	−679.250	+	1176.50i	−0.206748	+	0.358098i
$222$		0			0
$223$	−55.9328	−	96.8784i	−0.0167961	−	0.0290918i	0.857505	−	0.514475i	$-0.172013\pi$
$223$	−55.9328	−	96.8784i	−0.0167961	−	0.0290918i	−0.874301	+	0.485384i	$0.838680\pi$
$224$	−8145.41			−2.42964
$225$		0			0
$226$	−8206.51			−2.41544
$227$	−600.350	−	1039.84i	−0.175536	−	0.304037i	0.764811	−	0.644255i	$-0.222832\pi$
$227$	−600.350	−	1039.84i	−0.175536	−	0.304037i	−0.940347	+	0.340218i	$0.889499\pi$
$228$		0			0
$229$	−411.190	+	712.202i	−0.118656	+	0.205518i	−0.919235	−	0.393709i	$-0.871192\pi$
$229$	−411.190	+	712.202i	−0.118656	+	0.205518i	0.800579	+	0.599227i	$0.204525\pi$
$230$	321.763	−	557.309i	0.0922452	−	0.159773i
$231$		0			0
$232$	−6063.37	−	10502.1i	−1.71586	−	2.97196i
$233$	−5329.21			−1.49840			−0.749202	−	0.662341i	$-0.769563\pi$
$233$	−5329.21			−1.49840			−0.749202	+	0.662341i	$0.769563\pi$
$234$		0			0
$235$	1971.59			0.547287
$236$	1429.90	+	2476.66i	0.394401	+	0.683123i
$237$		0			0
$238$	1265.37	−	2191.69i	0.344630	−	0.596917i
$239$	3542.81	−	6136.32i	0.958850	−	1.66078i	0.233548	−	0.972345i	$-0.424966\pi$
$239$	3542.81	−	6136.32i	0.958850	−	1.66078i	0.725302	−	0.688431i	$-0.241700\pi$
$240$		0			0
$241$	3280.05	+	5681.21i	0.876707	+	1.51850i	0.854933	+	0.518738i	$0.173598\pi$
$241$	3280.05	+	5681.21i	0.876707	+	1.51850i	0.0217738	+	0.999763i	$0.493069\pi$
$242$	9998.63			2.65593
$243$		0			0
$244$	5663.15			1.48584
$245$	509.015	+	881.641i	0.132734	+	0.229902i
$246$		0			0
$247$	2535.21	−	4391.12i	0.653084	−	1.13117i
$248$	1112.72	−	1927.29i	0.284911	−	0.493481i
$249$		0			0
$250$	−341.172	−	590.928i	−0.0863105	−	0.149494i
$251$	714.222			0.179607			0.0898033	−	0.995960i	$-0.471376\pi$
$251$	714.222			0.179607			0.0898033	+	0.995960i	$0.471376\pi$
$252$		0			0
$253$	1325.95			0.329494
$254$	1573.07	+	2724.64i	0.388595	+	0.673067i
$255$		0			0
$256$	−5337.51	+	9244.85i	−1.30310	+	2.25704i
$257$	−2198.29	+	3807.56i	−0.533563	+	0.924159i	0.465668	+	0.884959i	$0.345814\pi$
$257$	−2198.29	+	3807.56i	−0.533563	+	0.924159i	−0.999231	+	0.0391993i	$0.987519\pi$
$258$		0			0
$259$	−1285.07	−	2225.80i	−0.308302	−	0.533994i
$260$	3770.63			0.899402
$261$		0			0
$262$	13046.6			3.07643
$263$	3775.15	+	6538.76i	0.885118	+	1.53307i	0.845579	+	0.533851i	$0.179256\pi$
$263$	3775.15	+	6538.76i	0.885118	+	1.53307i	0.0395390	+	0.999218i	$0.487411\pi$
$264$		0			0
$265$	336.950	−	583.615i	0.0781082	−	0.135287i
$266$	−4722.84	+	8180.20i	−1.08863	+	1.88556i
$267$		0			0
$268$	−4852.72	−	8405.17i	−1.10607	−	1.91577i
$269$	−5536.86			−1.25497			−0.627487	−	0.778627i	$-0.715917\pi$
$269$	−5536.86			−1.25497			−0.627487	+	0.778627i	$0.715917\pi$
$270$		0			0
$271$	3058.25			0.685518			0.342759	−	0.939423i	$-0.388639\pi$
$271$	3058.25			0.685518			0.342759	+	0.939423i	$0.388639\pi$
$272$	−4648.68	−	8051.75i	−1.03628	−	1.79489i
$273$		0			0
$274$	−2736.09	+	4739.05i	−0.603260	+	1.04488i
$275$	702.970	−	1217.58i	0.154148	−	0.266992i
$276$		0			0
$277$	2035.09	+	3524.88i	0.441433	+	0.764584i	0.997796	−	0.0663552i	$-0.0211371\pi$
$277$	2035.09	+	3524.88i	0.441433	+	0.764584i	−0.556363	+	0.830939i	$0.687804\pi$
$278$	719.556			0.155238
$279$		0			0
$280$	−4446.34			−0.948998
$281$	−3723.09	−	6448.59i	−0.790396	−	1.36901i	−0.925722	−	0.378204i	$-0.876542\pi$
$281$	−3723.09	−	6448.59i	−0.790396	−	1.36901i	0.135326	−	0.990801i	$-0.456792\pi$
$282$		0			0
$283$	387.326	−	670.868i	0.0813573	−	0.140915i	−0.822476	−	0.568800i	$-0.807408\pi$
$283$	387.326	−	670.868i	0.0813573	−	0.140915i	0.903833	+	0.427885i	$0.140741\pi$
$284$	−6112.61	+	10587.4i	−1.27717	+	2.21213i
$285$		0			0
$286$	5310.28	+	9197.67i	1.09791	+	1.90164i
$287$	−1679.95			−0.345520
$288$		0			0
$289$	−3371.06			−0.686152
$290$	−2197.19	−	3805.64i	−0.444908	−	0.770603i
$291$		0			0
$292$	966.394	−	1673.84i	0.193678	−	0.335460i
$293$	−3374.62	+	5845.01i	−0.672857	+	1.16542i	0.304233	+	0.952598i	$0.401600\pi$
$293$	−3374.62	+	5845.01i	−0.672857	+	1.16542i	−0.977090	+	0.212825i	$0.931733\pi$
$294$		0			0
$295$	327.989	+	568.093i	0.0647330	+	0.112121i
$296$	−16396.3			−3.21964
$297$		0			0
$298$	5565.12			1.08181
$299$	407.848	+	706.413i	0.0788845	+	0.136632i
$300$		0			0
$301$	−2762.90	+	4785.48i	−0.529073	+	0.916381i
$302$	−7703.35	+	13342.6i	−1.46781	+	2.54232i
$303$		0			0
$304$	17350.6	+	30052.1i	3.27343	+	5.66975i
$305$	1299.01			0.243872
$306$		0			0
$307$	−2204.39			−0.409808			−0.204904	−	0.978782i	$-0.565688\pi$
$307$	−2204.39			−0.409808			−0.204904	+	0.978782i	$0.565688\pi$
$308$	−7236.62	−	12534.2i	−1.33878	−	2.31884i
$309$		0			0
$310$	403.218	−	698.394i	0.0738750	−	0.127955i
$311$	3016.49	−	5224.71i	0.549998	−	0.952625i	−0.448276	−	0.893895i	$-0.647962\pi$
$311$	3016.49	−	5224.71i	0.549998	−	0.952625i	0.998274	−	0.0587296i	$-0.0187050\pi$
$312$		0			0
$313$	2886.48	+	4999.53i	0.521257	+	0.902844i	0.999694	+	0.0247221i	$0.00787008\pi$
$313$	2886.48	+	4999.53i	0.521257	+	0.902844i	−0.478437	+	0.878122i	$0.658797\pi$
$314$	2601.09			0.467479
$315$		0			0
$316$	9816.57			1.74755
$317$	1651.04	+	2859.68i	0.292528	+	0.506674i	0.974407	−	0.224791i	$-0.0721701\pi$
$317$	1651.04	+	2859.68i	0.292528	+	0.506674i	−0.681879	+	0.731465i	$0.738837\pi$
$318$		0			0
$319$	4527.20	−	7841.35i	0.794592	−	1.37627i
$320$	−4679.71	+	8105.49i	−0.817511	+	1.41597i
$321$		0			0
$322$	−759.779	−	1315.98i	−0.131493	−	0.227753i
$323$	−5755.07			−0.991395
$324$		0			0
$325$	864.901			0.147619
$326$	6119.97	+	10600.1i	1.03974	+	1.80087i
$327$		0			0
$328$	−5358.64	+	9281.44i	−0.902078	+	1.56244i
$329$	2327.76	−	4031.80i	0.390072	−	0.675625i
$330$		0			0
$331$	−4026.58	−	6974.23i	−0.668642	−	1.15812i	−0.978284	−	0.207269i	$-0.933542\pi$
$331$	−4026.58	−	6974.23i	−0.668642	−	1.15812i	0.309642	−	0.950853i	$-0.399791\pi$
$332$	6197.08			1.02442
$333$		0			0
$334$	518.795			0.0849916
$335$	−1113.11	−	1927.96i	−0.181540	−	0.314436i
$336$		0			0
$337$	−1730.16	+	2996.73i	−0.279668	+	0.484398i	−0.971302	−	0.237849i	$-0.923558\pi$
$337$	−1730.16	+	2996.73i	−0.279668	+	0.484398i	0.691635	+	0.722248i	$0.256891\pi$
$338$	2729.69	−	4727.96i	0.439276	−	0.760849i
$339$		0			0
$340$	−2139.88	−	3706.39i	−0.341328	−	0.591197i
$341$	1661.62			0.263877
$342$		0			0
$343$	6453.51			1.01591
$344$	17626.0	+	30529.2i	2.76259	+	4.78495i
$345$		0			0
$346$	5823.84	−	10087.2i	0.904889	−	1.56731i
$347$	4664.14	−	8078.52i	0.721568	−	1.24979i	−0.238804	−	0.971068i	$-0.576755\pi$
$347$	4664.14	−	8078.52i	0.721568	−	1.24979i	0.960371	−	0.278724i	$-0.0899114\pi$
$348$		0			0
$349$	−4449.71	−	7707.13i	−0.682486	−	1.18210i	−0.974220	−	0.225601i	$-0.927566\pi$
$349$	−4449.71	−	7707.13i	−0.682486	−	1.18210i	0.291734	−	0.956499i	$-0.405768\pi$
$350$	−1611.22			−0.246067
$351$		0			0
$352$	−38798.8			−5.87495
$353$	−1861.23	−	3223.74i	−0.280632	−	0.486069i	0.690909	−	0.722942i	$-0.257211\pi$
$353$	−1861.23	−	3223.74i	−0.280632	−	0.486069i	−0.971541	+	0.236873i	$0.923877\pi$
$354$		0			0
$355$	−1402.10	+	2428.51i	−0.209622	+	0.363076i
$356$	−6815.21	+	11804.3i	−1.01462	+	1.75738i
$357$		0			0
$358$	4652.71	+	8058.73i	0.686881	+	1.18971i
$359$	11029.3			1.62145			0.810727	−	0.585425i	$-0.199072\pi$
$359$	11029.3			1.62145			0.810727	+	0.585425i	$0.199072\pi$
$360$		0			0
$361$	14621.1			2.13166
$362$	3714.64	+	6433.95i	0.539330	+	0.934146i
$363$		0			0
$364$	4451.80	−	7710.74i	0.641038	−	1.11031i
$365$	221.670	−	383.944i	0.0317883	−	0.0550590i
$366$		0			0
$367$	2426.56	+	4202.92i	0.345137	+	0.597794i	0.985379	−	0.170379i	$-0.0544992\pi$
$367$	2426.56	+	4202.92i	0.345137	+	0.597794i	−0.640242	+	0.768173i	$0.721166\pi$
$368$	−5582.49			−0.790781
$369$		0			0
$370$	−5941.52			−0.834824
$371$	−795.641	−	1378.09i	−0.111341	−	0.192849i
$372$		0			0
$373$	6186.89	−	10716.0i	0.858834	−	1.48754i	−0.0142081	−	0.999899i	$-0.504523\pi$
$373$	6186.89	−	10716.0i	0.858834	−	1.48754i	0.873042	−	0.487645i	$-0.162144\pi$
$374$	6027.31	−	10439.6i	0.833328	−	1.44337i
$375$		0			0
$376$	−14850.0	−	25721.0i	−2.03679	−	3.52782i
$377$	5570.06			0.760935
$378$		0			0
$379$	11150.6			1.51127			0.755634	−	0.654994i	$-0.227329\pi$
$379$	11150.6			1.51127			0.755634	+	0.654994i	$0.227329\pi$
$380$	7986.84	+	13833.6i	1.07820	+	1.86750i
$381$		0			0
$382$	2993.69	−	5185.23i	0.400970	−	0.694501i
$383$	−1099.80	+	1904.90i	−0.146728	+	0.254141i	−0.930016	−	0.367518i	$-0.880208\pi$
$383$	−1099.80	+	1904.90i	−0.146728	+	0.254141i	0.783288	+	0.621659i	$0.213541\pi$
$384$		0			0
$385$	−1659.93	−	2875.07i	−0.219734	−	0.380591i
$386$	−15651.7			−2.06386
$387$		0			0
$388$	−4212.72			−0.551207
$389$	−4609.46	−	7983.82i	−0.600794	−	1.04061i	−0.992701	−	0.120601i	$-0.961518\pi$
$389$	−4609.46	−	7983.82i	−0.600794	−	1.04061i	0.391907	−	0.920005i	$-0.371815\pi$
$390$		0			0
$391$	462.919	−	801.799i	0.0598742	−	0.103705i
$392$	7667.82	−	13281.1i	0.987968	−	1.71121i
$393$		0			0
$394$	−1976.45	−	3423.31i	−0.252721	−	0.437726i
$395$	2251.71			0.286825
$396$		0			0
$397$	1119.36			0.141509			0.0707544	−	0.997494i	$-0.477459\pi$
$397$	1119.36			0.141509			0.0707544	+	0.997494i	$0.477459\pi$
$398$	4622.61	+	8006.60i	0.582188	+	1.00838i
$399$		0			0
$400$	−2959.62	+	5126.22i	−0.369953	+	0.640777i
$401$	−6148.45	+	10649.4i	−0.765683	+	1.32620i	0.174202	+	0.984710i	$0.444265\pi$
$401$	−6148.45	+	10649.4i	−0.765683	+	1.32620i	−0.939885	+	0.341491i	$0.889068\pi$
$402$		0			0
$403$	511.096	+	885.245i	0.0631750	+	0.109422i
$404$	29969.2			3.69065
$405$		0			0
$406$	−10376.4			−1.26841
$407$	−6121.12	−	10602.1i	−0.745485	−	1.29122i
$408$		0			0
$409$	−1250.11	+	2165.25i	−0.151134	+	0.261772i	−0.931645	−	0.363370i	$-0.881626\pi$
$409$	−1250.11	+	2165.25i	−0.151134	+	0.261772i	0.780510	+	0.625143i	$0.214959\pi$
$410$	−1941.81	+	3363.32i	−0.233901	+	0.405128i
$411$		0			0
$412$	−22120.7	−	38314.1i	−2.64516	−	4.58155i
$413$	1548.96			0.184551
$414$		0			0
$415$	1421.48			0.168139
$416$	−11934.1	−	20670.4i	−1.40653	−	2.43618i
$417$		0			0
$418$	−22496.2	+	38964.5i	−2.63235	+	4.55937i
$419$	4166.49	−	7216.57i	0.485790	−	0.841414i	−0.514076	−	0.857744i	$-0.671865\pi$
$419$	4166.49	−	7216.57i	0.485790	−	0.841414i	0.999867	+	0.0163308i	$0.00519849\pi$
$420$		0			0
$421$	−5687.10	−	9850.35i	−0.658367	−	1.14032i	−0.981038	−	0.193814i	$-0.937914\pi$
$421$	−5687.10	−	9850.35i	−0.658367	−	1.14032i	0.322672	−	0.946511i	$-0.395419\pi$
$422$	5171.91			0.596598
$423$		0			0
$424$	−10151.6			−1.16275
$425$	−490.844	−	850.166i	−0.0560221	−	0.0970332i
$426$		0			0
$427$	1533.67	−	2656.40i	0.173816	−	0.301059i
$428$	8970.56	−	15537.5i	1.01310	−	1.75475i
$429$		0			0
$430$	6387.15	+	11062.9i	0.716316	+	1.24070i
$431$	−10030.2			−1.12097			−0.560484	−	0.828165i	$-0.689385\pi$
$431$	−10030.2			−1.12097			−0.560484	+	0.828165i	$0.689385\pi$
$432$		0			0
$433$	7609.38			0.844535			0.422267	−	0.906471i	$-0.361234\pi$
$433$	7609.38			0.844535			0.422267	+	0.906471i	$0.361234\pi$
$434$	−952.120	−	1649.12i	−0.105307	−	0.182397i
$435$		0			0
$436$	9044.74	−	15666.0i	0.993497	−	1.72079i
$437$	−1727.78	+	2992.61i	−0.189133	+	0.327588i
$438$		0			0
$439$	6185.24	+	10713.2i	0.672450	+	1.16472i	0.977207	+	0.212287i	$0.0680913\pi$
$439$	6185.24	+	10713.2i	0.672450	+	1.16472i	−0.304757	+	0.952430i	$0.598575\pi$
$440$	−21179.1			−2.29471
$441$		0			0
$442$	7415.72			0.798032
$443$	6042.21	+	10465.4i	0.648023	+	1.12241i	0.983594	+	0.180394i	$0.0577373\pi$
$443$	6042.21	+	10465.4i	0.648023	+	1.12241i	−0.335572	+	0.942015i	$0.608929\pi$
$444$		0			0
$445$	−1563.26	+	2707.65i	−0.166530	+	0.288438i
$446$	−305.324	+	528.836i	−0.0324159	+	0.0561460i
$447$		0			0
$448$	11050.2	+	19139.5i	1.16534	+	2.01843i
$449$	−625.550			−0.0657495			−0.0328747	−	0.999459i	$-0.510466\pi$
$449$	−625.550			−0.0657495			−0.0328747	+	0.999459i	$0.510466\pi$
$450$		0			0
$451$	−8002.04			−0.835480
$452$	16385.2	+	28380.0i	1.70508	+	2.95328i
$453$		0			0
$454$	−3277.16	+	5676.22i	−0.338777	+	0.586780i
$455$	1021.15	−	1768.68i	0.105213	−	0.182235i
$456$		0			0
$457$	−905.611	−	1568.56i	−0.0926974	−	0.160557i	0.815948	−	0.578125i	$-0.196216\pi$
$457$	−905.611	−	1568.56i	−0.0926974	−	0.160557i	−0.908645	+	0.417569i	$0.862882\pi$
$458$	4489.17			0.458003
$459$		0			0
$460$	−2569.74			−0.260467
$461$	5812.49	+	10067.5i	0.587233	+	1.01712i	0.994593	+	0.103850i	$0.0331163\pi$
$461$	5812.49	+	10067.5i	0.587233	+	1.01712i	−0.407359	+	0.913268i	$0.633550\pi$
$462$		0			0
$463$	−3645.94	+	6314.96i	−0.365964	+	0.633868i	−0.988930	−	0.148380i	$-0.952594\pi$
$463$	−3645.94	+	6314.96i	−0.365964	+	0.633868i	0.622966	+	0.782249i	$0.285927\pi$
$464$	−19060.3	+	33013.4i	−1.90701	+	3.30303i
$465$		0			0
$466$	14545.4	+	25193.4i	1.44593	+	2.50443i
$467$	−11637.6			−1.15316			−0.576579	−	0.817042i	$-0.695613\pi$
$467$	−11637.6			−1.15316			−0.576579	+	0.817042i	$0.695613\pi$
$468$		0			0
$469$	−5256.78			−0.517560
$470$	−5381.22	−	9320.55i	−0.528122	−	0.914734i
$471$		0			0
$472$	4940.83	−	8557.76i	0.481822	−	0.834540i
$473$	−13160.4	+	22794.5i	−1.27932	+	2.21584i
$474$		0			0
$475$	1832.01	+	3173.13i	0.176965	+	0.306512i
$476$	−10105.8			−0.973109
$477$		0			0
$478$	−38678.6			−3.70109
$479$	−6020.72	−	10428.2i	−0.574309	−	0.994732i	−0.996116	−	0.0880467i	$-0.971938\pi$
$479$	−6020.72	−	10428.2i	−0.574309	−	0.994732i	0.421807	−	0.906685i	$-0.361396\pi$
$480$		0			0
$481$	3765.57	−	6522.16i	0.356955	−	0.618263i
$482$	17905.0	−	31012.3i	1.69201	−	2.93065i
$483$		0			0
$484$	−19963.4	−	34577.6i	−1.87485	−	3.24733i
$485$	−966.307			−0.0904695
$486$		0			0
$487$	7037.81			0.654853			0.327427	−	0.944877i	$-0.393819\pi$
$487$	7037.81			0.654853			0.327427	+	0.944877i	$0.393819\pi$
$488$	−9784.12	−	16946.6i	−0.907595	−	1.57200i
$489$		0			0
$490$	2778.59	−	4812.66i	0.256171	−	0.443702i
$491$	−3301.53	+	5718.42i	−0.303454	+	0.525599i	−0.976916	−	0.213624i	$-0.931473\pi$
$491$	−3301.53	+	5718.42i	−0.303454	+	0.525599i	0.673462	+	0.739222i	$0.264807\pi$
$492$		0			0
$493$	−3161.09	−	5475.16i	−0.288779	−	0.500180i
$494$	−27678.2			−2.52085
$495$		0			0
$496$	−6995.72			−0.633301
$497$	3310.79	+	5734.46i	0.298811	+	0.517556i
$498$		0			0
$499$	18.3523	−	31.7872i	0.00164642	−	0.00285168i	−0.865201	−	0.501425i	$-0.832809\pi$
$499$	18.3523	−	31.7872i	0.00164642	−	0.00285168i	0.866847	+	0.498573i	$0.166143\pi$
$500$	−1362.38	+	2359.71i	−0.121855	+	0.211059i
$501$		0			0
$502$	−1949.38	−	3376.43i	−0.173317	−	0.300194i
$503$	21242.5			1.88302			0.941508	−	0.336990i	$-0.109409\pi$
$503$	21242.5			1.88302			0.941508	+	0.336990i	$0.109409\pi$
$504$		0			0
$505$	6874.29			0.605746
$506$	−3619.03	−	6268.35i	−0.317956	−	0.550715i
$507$		0			0
$508$	6281.62	−	10880.1i	0.548626	−	0.950248i
$509$	5640.20	−	9769.12i	0.491155	−	0.850705i	−0.508794	−	0.860889i	$-0.669908\pi$
$509$	5640.20	−	9769.12i	0.491155	−	0.850705i	0.999948	+	0.0101839i	$0.00324171\pi$
$510$		0			0
$511$	−523.430	−	906.608i	−0.0453135	−	0.0784853i
$512$	20681.3			1.78514
$513$		0			0
$514$	23999.9			2.05951
$515$	−5074.00	−	8788.43i	−0.434150	−	0.751970i
$516$		0			0
$517$	11087.8	−	19204.6i	0.943209	−	1.63369i
$518$	−7014.87	+	12150.1i	−0.595011	+	1.03059i
$519$		0			0
$520$	−6514.45	−	11283.4i	−0.549379	−	0.951553i
$521$	−10239.3			−0.861023			−0.430511	−	0.902585i	$-0.641667\pi$
$521$	−10239.3			−0.861023			−0.430511	+	0.902585i	$0.641667\pi$
$522$		0			0
$523$	−2822.00			−0.235942			−0.117971	−	0.993017i	$-0.537639\pi$
$523$	−2822.00			−0.235942			−0.117971	+	0.993017i	$0.537639\pi$
$524$	−26049.0	−	45118.3i	−2.17167	−	3.76145i
$525$		0			0
$526$	20607.6	−	35693.5i	1.70824	−	2.95876i
$527$	580.108	−	1004.78i	0.0479505	−	0.0830527i
$528$		0			0
$529$	5805.55	+	10055.5i	0.477155	+	0.826457i
$530$	−3678.66			−0.301492
$531$		0			0
$532$	37718.7			3.07390
$533$	−2461.33	−	4263.16i	−0.200023	−	0.346450i
$534$		0			0
$535$	2057.65	−	3563.96i	0.166281	−	0.288007i
$536$	−16767.9	+	29042.9i	−1.35124	+	2.34041i
$537$		0			0
$538$	15112.2	+	26175.1i	1.21103	+	2.09756i
$539$	11450.3			0.915028
$540$		0			0
$541$	−9409.63			−0.747785			−0.373892	−	0.927472i	$-0.621977\pi$
$541$	−9409.63			−0.747785			−0.373892	+	0.927472i	$0.621977\pi$
$542$	−8347.12	−	14457.6i	−0.661512	−	1.14577i
$543$		0			0
$544$	−13545.5	+	23461.5i	−1.06757	+	1.84908i
$545$	2074.67	−	3593.43i	0.163063	−	0.282433i
$546$		0			0
$547$	1918.21	+	3322.45i	0.149940	+	0.259703i	0.931205	−	0.364496i	$-0.118759\pi$
$547$	1918.21	+	3322.45i	0.149940	+	0.259703i	−0.781265	+	0.624199i	$0.785425\pi$
$548$	21851.6			1.70339
$549$		0			0
$550$	−7674.69			−0.594999
$551$	11798.3	+	20435.3i	0.912207	+	1.57999i
$552$		0			0
$553$	2658.49	−	4604.63i	0.204431	−	0.354085i
$554$	11109.1	−	19241.5i	0.851948	−	1.47562i
$555$		0			0
$556$	−1436.67	−	2488.39i	−0.109584	−	0.189804i
$557$	6145.92			0.467524			0.233762	−	0.972294i	$-0.424896\pi$
$557$	6145.92			0.467524			0.233762	+	0.972294i	$0.424896\pi$
$558$		0			0
$559$	−16192.0			−1.22513
$560$	6988.57	+	12104.6i	0.527359	+	0.913412i
$561$		0			0
$562$	−20323.5	+	35201.3i	−1.52543	+	2.64213i
$563$	−6623.93	+	11473.0i	−0.495854	+	0.858844i	−0.999989	−	0.00478126i	$-0.998478\pi$
$563$	−6623.93	+	11473.0i	−0.495854	+	0.858844i	0.504135	+	0.863625i	$0.331811\pi$
$564$		0			0
$565$	3758.41	+	6509.76i	0.279854	+	0.484722i
$566$	−4228.63			−0.314033
$567$		0			0
$568$	42242.6			3.12053
$569$	−3272.45	−	5668.04i	−0.241104	−	0.417604i	0.719925	−	0.694052i	$-0.244176\pi$
$569$	−3272.45	−	5668.04i	−0.241104	−	0.417604i	−0.961029	+	0.276448i	$0.910843\pi$
$570$		0			0
$571$	−10181.0	+	17634.1i	−0.746170	+	1.29241i	0.203475	+	0.979080i	$0.434776\pi$
$571$	−10181.0	+	17634.1i	−0.746170	+	1.29241i	−0.949646	+	0.313325i	$0.898557\pi$
$572$	21205.1	−	36728.3i	1.55005	−	2.68477i
$573$		0			0
$574$	4585.21	+	7941.82i	0.333420	+	0.577500i
$575$	−589.443			−0.0427504
$576$		0			0
$577$	−26247.4			−1.89375			−0.946876	−	0.321600i	$-0.895779\pi$
$577$	−26247.4			−1.89375			−0.946876	+	0.321600i	$0.895779\pi$
$578$	9200.91	+	15936.4i	0.662124	+	1.14683i
$579$		0			0
$580$	−8773.85	+	15196.8i	−0.628128	+	1.08795i
$581$	1678.27	−	2906.85i	0.119839	−	0.207567i
$582$		0			0
$583$	−3789.85	−	6564.22i	−0.269228	−	0.466316i
$584$	−6678.49			−0.473215
$585$		0			0
$586$	36842.4			2.59718
$587$	7049.08	+	12209.4i	0.495650	+	0.858492i	0.999987	−	0.00501514i	$-0.00159638\pi$
$587$	7049.08	+	12209.4i	0.495650	+	0.858492i	−0.504337	+	0.863507i	$0.668263\pi$
$588$		0			0
$589$	−2165.18	+	3750.20i	−0.151468	+	0.262350i
$590$	1790.41	−	3101.08i	0.124932	−	0.216389i
$591$		0			0
$592$	25770.9	+	44636.6i	1.78915	+	3.09891i
$593$	3476.71			0.240761			0.120380	−	0.992728i	$-0.461589\pi$
$593$	3476.71			0.240761			0.120380	+	0.992728i	$0.461589\pi$
$594$		0			0
$595$	−2318.06			−0.159716
$596$	−11111.4	−	19245.5i	−0.763658	−	1.32269i
$597$		0			0
$598$	2226.34	−	3856.14i	0.152244	−	0.263694i
$599$	8089.48	−	14011.4i	0.551798	−	0.955743i	−0.446347	−	0.894860i	$-0.647275\pi$
$599$	8089.48	−	14011.4i	0.551798	−	0.955743i	0.998145	−	0.0608826i	$-0.0193915\pi$
$600$		0			0
$601$	−4056.08	−	7025.34i	−0.275293	−	0.476821i	0.694916	−	0.719091i	$-0.255441\pi$
$601$	−4056.08	−	7025.34i	−0.275293	−	0.476821i	−0.970209	+	0.242270i	$0.922108\pi$
$602$	30164.0			2.04218
$603$		0			0
$604$	61522.3			4.14455
$605$	−4579.17	−	7931.35i	−0.307719	−	0.532984i
$606$		0			0
$607$	−10569.6	+	18307.1i	−0.706765	+	1.22415i	0.259286	+	0.965800i	$0.416513\pi$
$607$	−10569.6	+	18307.1i	−0.706765	+	1.22415i	−0.966051	+	0.258352i	$0.916821\pi$
$608$	50556.7	−	87566.8i	3.37228	−	5.84096i
$609$		0			0
$610$	−3545.48	−	6140.95i	−0.235331	−	0.407606i
$611$	13641.9			0.903258
$612$		0			0
$613$	−11440.3			−0.753785			−0.376892	−	0.926257i	$-0.623007\pi$
$613$	−11440.3			−0.753785			−0.376892	+	0.926257i	$0.623007\pi$
$614$	6016.62	+	10421.1i	0.395457	+	0.684952i
$615$		0			0
$616$	−25005.1	+	43310.2i	−1.63553	+	2.83282i
$617$	−10783.1	+	18676.9i	−0.703584	+	1.21864i	0.263616	+	0.964628i	$0.415085\pi$
$617$	−10783.1	+	18676.9i	−0.703584	+	1.21864i	−0.967200	+	0.254016i	$0.918249\pi$
$618$		0			0
$619$	7599.14	+	13162.1i	0.493433	+	0.854651i	0.999971	−	0.00756612i	$-0.00240839\pi$
$619$	7599.14	+	13162.1i	0.493433	+	0.854651i	−0.506538	+	0.862218i	$0.669075\pi$
$620$	−3220.28			−0.208596
$621$		0			0
$622$	−32932.6			−2.12295
$623$	3691.34	+	6393.59i	0.237384	+	0.411162i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	15756.6	−	27291.2i	1.00601	−	1.74245i
$627$		0			0
$628$	−5193.37	−	8995.19i	−0.329997	−	0.571572i
$629$	−8548.05			−0.541865
$630$		0			0
$631$	−4929.66			−0.311009			−0.155504	−	0.987835i	$-0.549700\pi$
$631$	−4929.66			−0.311009			−0.155504	+	0.987835i	$0.549700\pi$
$632$	−16959.9	−	29375.4i	−1.06745	−	1.84888i
$633$		0			0
$634$	9012.61	−	15610.3i	0.564569	−	0.977862i
$635$	1440.87	−	2495.66i	0.0900459	−	0.155964i
$636$		0			0
$637$	3521.99	+	6100.26i	0.219068	+	0.379436i
$638$	−49425.8			−3.06706
$639$		0			0
$640$	23494.4			1.45109
$641$	3767.86	+	6526.13i	0.232171	+	0.402132i	0.958447	−	0.285271i	$-0.0920838\pi$
$641$	3767.86	+	6526.13i	0.232171	+	0.402132i	−0.726276	+	0.687403i	$0.758750\pi$
$642$		0			0
$643$	7998.62	−	13854.0i	0.490568	−	0.849688i	−0.509373	−	0.860546i	$-0.670123\pi$
$643$	7998.62	−	13854.0i	0.490568	−	0.849688i	0.999941	+	0.0108576i	$0.00345614\pi$
$644$	−3033.97	+	5254.98i	−0.185644	+	0.321546i
$645$		0			0
$646$	15707.8	+	27206.7i	0.956678	+	1.65701i
$647$	6020.46			0.365825			0.182913	−	0.983129i	$-0.441447\pi$
$647$	6020.46			0.365825			0.182913	+	0.983129i	$0.441447\pi$
$648$		0			0
$649$	7378.12			0.446250
$650$	−2360.64	−	4088.75i	−0.142449	−	0.246729i
$651$		0			0
$652$	24438.4	−	42328.5i	1.46792	−	2.54251i
$653$	−5474.34	+	9481.84i	−0.328067	+	0.568228i	−0.982128	−	0.188213i	$-0.939730\pi$
$653$	−5474.34	+	9481.84i	−0.328067	+	0.568228i	0.654062	+	0.756441i	$0.273064\pi$
$654$		0			0
$655$	−5975.09	−	10349.2i	−0.356437	−	0.617367i
$656$	33690.0			2.00514
$657$		0			0
$658$	−25413.4			−1.50565
$659$	6169.14	+	10685.3i	0.364667	+	0.631622i	0.988723	−	0.149758i	$-0.0478495\pi$
$659$	6169.14	+	10685.3i	0.364667	+	0.631622i	−0.624056	+	0.781380i	$0.714516\pi$
$660$		0			0
$661$	−10008.4	+	17335.0i	−0.588928	+	1.02005i	0.405445	+	0.914119i	$0.367116\pi$
$661$	−10008.4	+	17335.0i	−0.588928	+	1.02005i	−0.994373	+	0.105934i	$0.966217\pi$
$662$	−21980.1	+	38070.6i	−1.29045	+	2.23513i
$663$		0			0
$664$	−10706.6	−	18544.3i	−0.625746	−	1.08382i
$665$	8651.86			0.504518
$666$		0			0
$667$	−3796.08			−0.220367
$668$	−1035.83	−	1794.11i	−0.0599963	−	0.103917i
$669$		0			0
$670$	−6076.20	+	10524.3i	−0.350364	+	0.606849i
$671$	7305.29	−	12653.1i	0.420295	−	0.727972i
$672$		0			0
$673$	4209.61	+	7291.26i	0.241112	+	0.417619i	0.961031	−	0.276439i	$-0.0891544\pi$
$673$	4209.61	+	7291.26i	0.241112	+	0.417619i	−0.719919	+	0.694058i	$0.755821\pi$
$674$	18889.1			1.07950
$675$		0			0
$676$	−21800.5			−1.24036
$677$	12853.5	+	22263.0i	0.729692	+	1.26386i	0.957013	+	0.290044i	$0.0936701\pi$
$677$	12853.5	+	22263.0i	0.729692	+	1.26386i	−0.227321	+	0.973820i	$0.572997\pi$
$678$		0			0
$679$	−1140.87	+	1976.05i	−0.0644810	+	0.111684i
$680$	−7394.08	+	12806.9i	−0.416985	+	0.722239i
$681$		0			0
$682$	−4535.20	−	7855.20i	−0.254636	−	0.441043i
$683$	19624.3			1.09942			0.549708	−	0.835357i	$-0.314739\pi$
$683$	19624.3			1.09942			0.549708	+	0.835357i	$0.314739\pi$
$684$		0			0
$685$	5012.30			0.279577
$686$	−17614.1	−	30508.5i	−0.980334	−	1.69799i
$687$		0			0
$688$	55407.7	−	95968.9i	3.07035	−	5.31799i
$689$	2331.43	−	4038.15i	0.128912	−	0.223282i
$690$		0			0
$691$	−3636.61	−	6298.80i	−0.200207	−	0.346769i	0.748388	−	0.663261i	$-0.230828\pi$
$691$	−3636.61	−	6298.80i	−0.200207	−	0.346769i	−0.948595	+	0.316492i	$0.897495\pi$
$692$	−46511.8			−2.55508
$693$		0			0
$694$	−50920.8			−2.78520
$695$	−329.542	−	570.783i	−0.0179860	−	0.0311526i
$696$		0			0
$697$	−2793.68	+	4838.80i	−0.151820	+	0.262959i
$698$	−24289.9	+	42071.3i	−1.31717	+	2.28141i
$699$		0			0
$700$	3216.98	+	5571.98i	0.173701	+	0.300859i
$701$	−17644.3			−0.950664			−0.475332	−	0.879807i	$-0.657672\pi$
$701$	−17644.3			−0.950664			−0.475332	+	0.879807i	$0.657672\pi$
$702$		0			0
$703$	31904.5			1.71166
$704$	52635.1	+	91166.7i	2.81784	+	4.88064i
$705$		0			0
$706$	−10160.0	+	17597.6i	−0.541609	+	0.938094i
$707$	8116.14	−	14057.6i	0.431738	−	0.747793i
$708$		0			0
$709$	−12152.2	−	21048.2i	−0.643703	−	1.11493i	−0.984600	−	0.174825i	$-0.944064\pi$
$709$	−12152.2	−	21048.2i	−0.643703	−	1.11493i	0.340897	−	0.940101i	$-0.389269\pi$
$710$	15307.5			0.809126
$711$		0			0
$712$	47098.1			2.47904
$713$	−348.320	−	603.307i	−0.0182955	−	0.0316887i
$714$		0			0
$715$	4864.00	−	8424.69i	0.254410	−	0.440651i
$716$	18579.3	−	32180.3i	0.969751	−	1.67966i
$717$		0			0
$718$	−30103.0	−	52139.9i	−1.56467	−	2.71009i
$719$	15170.2			0.786863			0.393431	−	0.919354i	$-0.371288\pi$
$719$	15170.2			0.786863			0.393431	+	0.919354i	$0.371288\pi$
$720$		0			0
$721$	−23962.5			−1.23774
$722$	−39906.4	−	69119.9i	−2.05701	−	3.56285i
$723$		0			0
$724$	14833.4	−	25692.2i	0.761435	−	1.31884i
$725$	−2012.53	+	3485.81i	−0.103095	+	0.178565i
$726$		0			0
$727$	8743.52	+	15144.2i	0.446051	+	0.772583i	0.998125	−	0.0612123i	$-0.0194967\pi$
$727$	8743.52	+	15144.2i	0.446051	+	0.772583i	−0.552074	+	0.833795i	$0.686163\pi$
$728$	−30765.2			−1.56625
$729$		0			0
$730$	−2420.09			−0.122701
$731$	9189.18	+	15916.1i	0.464944	+	0.805306i
$732$		0			0
$733$	−9349.02	+	16193.0i	−0.471097	+	0.815964i	−0.999453	−	0.0330590i	$-0.989475\pi$
$733$	−9349.02	+	16193.0i	−0.471097	+	0.815964i	0.528357	+	0.849023i	$0.322808\pi$
$734$	13246.0	−	22942.7i	0.666101	−	1.15372i
$735$		0			0
$736$	8133.23	+	14087.2i	0.407330	+	0.705516i
$737$	−25039.5			−1.25148
$738$		0			0
$739$	−35250.3			−1.75467			−0.877336	−	0.479876i	$-0.840682\pi$
$739$	−35250.3			−1.75467			−0.877336	+	0.479876i	$0.840682\pi$
$740$	11862.9	+	20547.2i	0.589310	+	1.02071i
$741$		0			0
$742$	−4343.21	+	7522.67i	−0.214885	+	0.372191i
$743$	−5566.78	+	9641.94i	−0.274866	+	0.476081i	−0.970101	−	0.242701i	$-0.921967\pi$
$743$	−5566.78	+	9641.94i	−0.274866	+	0.476081i	0.695236	+	0.718782i	$0.255300\pi$
$744$		0			0
$745$	−2548.71	−	4414.50i	−0.125339	−	0.217094i
$746$	−67545.5			−3.31503
$747$		0			0
$748$	−48136.8			−2.35301
$749$	−4858.75	−	8415.59i	−0.237029	−	0.410546i
$750$		0			0
$751$	−8598.81	+	14893.6i	−0.417809	+	0.723667i	−0.995719	−	0.0924337i	$-0.970535\pi$
$751$	−8598.81	+	14893.6i	−0.417809	+	0.723667i	0.577909	+	0.816101i	$0.303869\pi$
$752$	−46681.3	+	80854.5i	−2.26369	+	3.92082i
$753$		0			0
$754$	−15202.8	−	26332.0i	−0.734288	−	1.27182i
$755$	14111.9			0.680245
$756$		0			0
$757$	804.647			0.0386333			0.0193166	−	0.999813i	$-0.493851\pi$
$757$	804.647			0.0386333			0.0193166	+	0.999813i	$0.493851\pi$
$758$	−30434.3	−	52713.8i	−1.45834	−	2.52593i
$759$		0			0
$760$	27597.4	−	47800.1i	1.31719	−	2.28144i
$761$	−13104.4	+	22697.5i	−0.624225	+	1.08119i	0.364465	+	0.931217i	$0.381252\pi$
$761$	−13104.4	+	22697.5i	−0.624225	+	1.08119i	−0.988690	+	0.149973i	$0.952081\pi$
$762$		0			0
$763$	−4898.93	−	8485.19i	−0.232442	−	0.402601i
$764$	−23909.0			−1.13219
$765$		0			0
$766$	12007.0			0.566360
$767$	2269.42	+	3930.76i	0.106837	+	0.185047i
$768$		0			0
$769$	−18272.1	+	31648.2i	−0.856837	+	1.48409i	0.0180924	+	0.999836i	$0.494241\pi$
$769$	−18272.1	+	31648.2i	−0.856837	+	1.48409i	−0.874930	+	0.484250i	$0.839093\pi$
$770$	−9061.13	+	15694.3i	−0.424078	+	0.734525i
$771$		0			0
$772$	31250.4	+	54127.3i	1.45690	+	2.52342i
$773$	−42387.4			−1.97228			−0.986139	−	0.165923i	$-0.946940\pi$
$773$	−42387.4			−1.97228			−0.986139	+	0.165923i	$0.946940\pi$
$774$		0			0
$775$	−738.663			−0.0342368
$776$	7278.23	+	12606.3i	0.336692	+	0.583168i
$777$		0			0
$778$	−25161.9	+	43581.7i	−1.15951	+	2.00833i
$779$	10427.1	−	18060.2i	0.479574	−	0.830646i
$780$		0			0
$781$	15770.2	+	27314.7i	0.722537	+	1.25147i
$782$	−5053.92			−0.231110
$783$		0			0
$784$	−48207.8			−2.19606
$785$	−1191.25	−	2063.30i	−0.0541624	−	0.0938120i
$786$		0			0
$787$	−13424.7	+	23252.2i	−0.608054	+	1.05318i	0.383507	+	0.923538i	$0.374716\pi$
$787$	−13424.7	+	23252.2i	−0.608054	+	1.05318i	−0.991561	+	0.129642i	$0.958617\pi$
$788$	−7892.40	+	13670.0i	−0.356796	+	0.617988i
$789$		0			0
$790$	−6145.77	−	10644.8i	−0.276781	−	0.479398i
$791$	17749.5			0.797851
$792$		0			0
$793$	8988.09			0.402492
$794$	−3055.15	−	5291.68i	−0.136553	−	0.236517i
$795$		0			0
$796$	18459.1	−	31972.1i	0.821943	−	1.42365i
$797$	15653.5	−	27112.7i	0.695704	−	1.20500i	−0.274238	−	0.961662i	$-0.588426\pi$
$797$	15653.5	−	27112.7i	0.695704	−	1.20500i	0.969943	−	0.243333i	$-0.0782409\pi$
$798$		0			0
$799$	−7741.94	−	13409.4i	−0.342791	−	0.593732i
$800$	17247.7			0.762248
$801$		0			0
$802$	67125.7			2.95548
$803$	−2493.24	−	4318.42i	−0.109570	−	0.189780i
$804$		0			0
$805$	−695.927	+	1205.38i	−0.0304698	+	0.0527752i
$806$	2789.95	−	4832.34i	0.121925	−	0.211181i
$807$		0			0
$808$	−51777.2	−	89680.8i	−2.25435	−	3.90465i
$809$	−10011.9			−0.435106			−0.217553	−	0.976049i	$-0.569807\pi$
$809$	−10011.9			−0.435106			−0.217553	+	0.976049i	$0.569807\pi$
$810$		0			0
$811$	4603.68			0.199331			0.0996653	−	0.995021i	$-0.468223\pi$
$811$	4603.68			0.199331			0.0996653	+	0.995021i	$0.468223\pi$
$812$	20717.7	+	35884.2i	0.895381	+	1.55085i
$813$		0			0
$814$	−33413.7	+	57874.2i	−1.43876	+	2.49200i
$815$	5605.64	−	9709.26i	0.240929	−	0.417301i
$816$		0			0
$817$	−34297.4	−	59404.8i	−1.46868	−	2.54383i
$818$	13648.1			0.583367
$819$		0			0
$820$	15508.2			0.660451
$821$	17714.5	+	30682.4i	0.753033	+	1.30429i	0.946346	+	0.323154i	$0.104743\pi$
$821$	17714.5	+	30682.4i	0.753033	+	1.30429i	−0.193313	+	0.981137i	$0.561923\pi$
$822$		0			0
$823$	14148.8	−	24506.4i	0.599265	−	1.03796i	−0.393664	−	0.919254i	$-0.628793\pi$
$823$	14148.8	−	24506.4i	0.599265	−	1.03796i	0.992930	−	0.118704i	$-0.0378739\pi$
$824$	−76434.9	+	132389.i	−3.23147	+	5.59708i
$825$		0			0
$826$	−4227.70	−	7322.60i	−0.178088	−	0.308457i
$827$	41059.9			1.72647			0.863236	−	0.504800i	$-0.168434\pi$
$827$	41059.9			1.72647			0.863236	+	0.504800i	$0.168434\pi$
$828$		0			0
$829$	9030.68			0.378345			0.189173	−	0.981944i	$-0.439419\pi$
$829$	9030.68			0.378345			0.189173	+	0.981944i	$0.439419\pi$
$830$	−3879.75	−	6719.92i	−0.162251	−	0.281026i
$831$		0			0
$832$	−32379.9	+	56083.6i	−1.34924	+	2.33696i
$833$	3997.55	−	6923.96i	0.166275	−	0.287996i
$834$		0			0
$835$	−237.598	−	411.531i	−0.00984719	−	0.0170558i
$836$	179664.			7.43280
$837$		0			0
$838$	−45487.7			−1.87511
$839$	−2613.90	−	4527.41i	−0.107559	−	0.186298i	0.807222	−	0.590248i	$-0.200970\pi$
$839$	−2613.90	−	4527.41i	−0.107559	−	0.186298i	−0.914781	+	0.403951i	$0.867637\pi$
$840$		0			0
$841$	−766.434	+	1327.50i	−0.0314254	+	0.0544304i
$842$	−31044.5	+	53770.7i	−1.27062	+	2.20078i
$843$		0			0
$844$	−10326.3	−	17885.7i	−0.421144	−	0.729443i
$845$	−5000.56			−0.203579
$846$		0			0
$847$	−21625.6			−0.877290
$848$	15955.9	+	27636.5i	0.646142	+	1.11915i
$849$		0			0
$850$	−2679.40	+	4640.85i	−0.108121	+	0.187270i
$851$	−2566.29	+	4444.94i	−0.103374	+	0.179049i
$852$		0			0
$853$	15001.5	+	25983.3i	0.602158	+	1.04297i	0.992494	+	0.122295i	$0.0390254\pi$
$853$	15001.5	+	25983.3i	0.602158	+	1.04297i	−0.390336	+	0.920672i	$0.627641\pi$
$854$	−16743.9			−0.670918
$855$		0			0
$856$	−61993.1			−2.47533
$857$	−7835.86	−	13572.1i	−0.312331	−	0.540973i	0.666535	−	0.745473i	$-0.267776\pi$
$857$	−7835.86	−	13572.1i	−0.312331	−	0.540973i	−0.978867	+	0.204500i	$0.934443\pi$
$858$		0			0
$859$	15653.4	−	27112.5i	0.621755	−	1.07691i	−0.367404	−	0.930061i	$-0.619753\pi$
$859$	15653.4	−	27112.5i	0.621755	−	1.07691i	0.989159	−	0.146850i	$-0.0469133\pi$
$860$	25505.3	−	44176.5i	1.01131	−	1.75164i
$861$		0			0
$862$	27376.2	+	47416.9i	1.08171	+	1.87358i
$863$	13212.3			0.521150			0.260575	−	0.965454i	$-0.416088\pi$
$863$	13212.3			0.521150			0.260575	+	0.965454i	$0.416088\pi$
$864$		0			0
$865$	−10668.8			−0.419364
$866$	−20768.9	−	35972.8i	−0.814960	−	1.41155i
$867$		0			0
$868$	−3802.03	+	6585.30i	−0.148674	+	0.257511i
$869$	12663.1	−	21933.1i	0.494322	−	0.856190i
$870$		0			0
$871$	−7701.85	−	13340.0i	−0.299618	−	0.518953i
$872$	−62505.7			−2.42742
$873$		0			0
$874$	18863.1			0.730039
$875$	737.907	+	1278.09i	0.0285095	+	0.0493799i
$876$		0			0
$877$	−7720.32	+	13372.0i	−0.297260	+	0.514869i	−0.975508	−	0.219964i	$-0.929406\pi$
$877$	−7720.32	+	13372.0i	−0.297260	+	0.514869i	0.678248	+	0.734833i	$0.262739\pi$
$878$	33763.7	−	58480.5i	1.29780	−	2.24786i
$879$		0			0
$880$	33288.4	+	57657.2i	1.27517	+	2.20866i
$881$	−27563.1			−1.05406			−0.527029	−	0.849847i	$-0.676694\pi$
$881$	−27563.1			−1.05406			−0.527029	+	0.849847i	$0.676694\pi$
$882$		0			0
$883$	19897.7			0.758337			0.379169	−	0.925328i	$-0.376210\pi$
$883$	19897.7			0.758337			0.379169	+	0.925328i	$0.376210\pi$
$884$	−14806.3	−	25645.3i	−0.563337	−	0.975729i
$885$		0			0
$886$	32983.0	−	57128.2i	1.25066	−	2.16621i
$887$	−20030.8	+	34694.4i	−0.758251	+	1.31333i	0.185491	+	0.982646i	$0.440612\pi$
$887$	−20030.8	+	34694.4i	−0.758251	+	1.31333i	−0.943742	+	0.330683i	$0.892721\pi$
$888$		0			0
$889$	−3402.33	−	5893.01i	−0.128358	−	0.222323i
$890$	17067.0			0.642793
$891$		0			0
$892$	2438.45			0.0915306
$893$	28895.8	+	50049.0i	1.08282	+	1.87550i
$894$		0			0
$895$	4261.70	−	7381.47i	0.159165	−	0.275682i
$896$	27738.8	−	48044.9i	1.03425	−	1.79137i
$897$		0			0
$898$	1707.36	+	2957.24i	0.0634470	+	0.109893i
$899$	−4757.07			−0.176482
$900$		0			0
$901$	−5292.47			−0.195691
$902$	21840.6	+	37829.0i	0.806222	+	1.39642i
$903$		0			0
$904$	56616.8	−	98063.2i	2.08302	−	3.60789i
$905$	3402.46	−	5893.24i	0.124974	−	0.216462i
$906$		0			0
$907$	−13919.8	−	24109.8i	−0.509591	−	0.882638i	−0.999938	−	0.0111107i	$-0.996463\pi$
$907$	−13919.8	−	24109.8i	−0.509591	−	0.882638i	0.490347	−	0.871527i	$-0.336870\pi$
$908$	26172.9			0.956584
$909$		0			0
$910$	−11148.4			−0.406116
$911$	−11125.5	−	19270.0i	−0.404616	−	0.700815i	0.589661	−	0.807651i	$-0.299261\pi$
$911$	−11125.5	−	19270.0i	−0.404616	−	0.700815i	−0.994277	+	0.106836i	$0.965928\pi$
$912$		0			0
$913$	7994.04	−	13846.1i	0.289775	−	0.501904i
$914$	−4943.51	+	8562.41i	−0.178902	+	0.309868i
$915$		0			0
$916$	−8963.13	−	15524.6i	−0.323308	−	0.559986i
$917$	−28218.0			−1.01618
$918$		0			0
$919$	29480.5			1.05819			0.529093	−	0.848564i	$-0.322532\pi$
$919$	29480.5			1.05819			0.529093	+	0.848564i	$0.322532\pi$
$920$	4439.69	+	7689.77i	0.159100	+	0.275570i
$921$		0			0
$922$	31729.0	−	54956.2i	1.13334	−	1.96300i
$923$	−9701.44	+	16803.4i	−0.345966	+	0.599231i
$924$		0			0
$925$	2721.10	+	4713.08i	0.0967233	+	0.167530i
$926$	39804.6			1.41259
$927$		0			0
$928$	111077.			3.92919
$929$	−21175.9	−	36677.7i	−0.747857	−	1.29533i	−0.948848	−	0.315733i	$-0.897750\pi$
$929$	−21175.9	−	36677.7i	−0.747857	−	1.29533i	0.200992	−	0.979593i	$-0.435584\pi$
$930$		0			0
$931$	−14920.3	+	25842.8i	−0.525236	+	0.909735i
$932$	58083.1	−	100603.i	2.04139	−	3.53579i
$933$		0			0
$934$	31763.4	+	55015.9i	1.11277	+	1.92738i
$935$	−11041.5			−0.386200
$936$		0			0
$937$	−35930.6			−1.25272			−0.626362	−	0.779532i	$-0.715457\pi$
$937$	−35930.6			−1.25272			−0.626362	+	0.779532i	$0.715457\pi$
$938$	14347.8	+	24851.0i	0.499436	+	0.865048i
$939$		0			0
$940$	−21488.4	+	37219.0i	−0.745611	+	1.29144i
$941$	10782.0	−	18675.0i	0.373521	−	0.646957i	−0.616584	−	0.787289i	$-0.711484\pi$
$941$	10782.0	−	18675.0i	0.373521	−	0.646957i	0.990104	+	0.140333i	$0.0448172\pi$
$942$		0			0
$943$	1677.44	+	2905.40i	0.0579266	+	0.100332i
$944$	−31063.1			−1.07099
$945$		0			0
$946$	143679.			4.93807
$947$	8316.19	+	14404.1i	0.285364	+	0.494265i	0.972697	−	0.232077i	$-0.0745521\pi$
$947$	8316.19	+	14404.1i	0.285364	+	0.494265i	−0.687333	+	0.726342i	$0.741219\pi$
$948$		0			0
$949$	1533.78	−	2656.59i	0.0524644	−	0.0908710i
$950$	10000.5	−	17321.4i	0.341536	−	0.591557i
$951$		0			0
$952$	17459.7	+	30241.0i	0.594402	+	1.02953i
$953$	39557.8			1.34460			0.672299	−	0.740279i	$-0.265307\pi$
$953$	39557.8			1.34460			0.672299	+	0.740279i	$0.265307\pi$
$954$		0			0
$955$	−5484.21			−0.185827
$956$	77226.2	+	133760.i	2.61263	+	4.52521i
$957$		0			0
$958$	−32865.7	+	56925.0i	−1.10839	+	1.91980i
$959$	5917.77	−	10249.9i	0.199265	−	0.345137i
$960$		0			0
$961$	14459.0	+	25043.7i	0.485348	+	0.840647i
$962$	−41110.6			−1.37782
$963$		0			0
$964$	−142997.			−4.77762
$965$	7168.17	+	12415.6i	0.239121	+	0.414170i
$966$		0			0
$967$	5333.10	−	9237.20i	0.177354	−	0.307185i	−0.763620	−	0.645666i	$-0.776580\pi$
$967$	5333.10	−	9237.20i	0.177354	−	0.307185i	0.940973	+	0.338481i	$0.109913\pi$
$968$	−68980.7	+	119478.i	−2.29042	+	3.96712i
$969$		0			0
$970$	2637.42	+	4568.14i	0.0873014	+	0.151210i
$971$	31821.8			1.05171			0.525855	−	0.850574i	$-0.323746\pi$
$971$	31821.8			1.05171			0.525855	+	0.850574i	$0.323746\pi$
$972$		0			0
$973$	−1556.30			−0.0512771
$974$	−19208.8	−	33270.7i	−0.631921	−	1.09452i
$975$		0			0
$976$	−30756.5	+	53271.9i	−1.00870	+	1.74712i
$977$	−5563.23	+	9635.80i	−0.182173	+	0.315534i	−0.942620	−	0.333866i	$-0.891647\pi$
$977$	−5563.23	+	9635.80i	−0.182173	+	0.315534i	0.760447	+	0.649400i	$0.224980\pi$
$978$		0			0
$979$	17582.8	+	30454.4i	0.574004	+	0.994204i
$980$	−22191.1			−0.723334
$981$		0			0
$982$	36044.5			1.17131
$983$	495.612	+	858.426i	0.0160810	+	0.0278530i	0.873954	−	0.486009i	$-0.161548\pi$
$983$	495.612	+	858.426i	0.0160810	+	0.0278530i	−0.857873	+	0.513862i	$0.828214\pi$
$984$		0			0
$985$	−1810.35	+	3135.61i	−0.0585609	+	0.101430i
$986$	−17255.6	+	29887.6i	−0.557333	+	0.965329i
$987$		0			0
$988$	55262.6	+	95717.7i	1.77949	+	3.08217i
$989$	11035.1			0.354798
$990$		0			0
$991$	−48714.9			−1.56153			−0.780767	−	0.624822i	$-0.785171\pi$
$991$	−48714.9			−1.56153			−0.780767	+	0.624822i	$0.785171\pi$
$992$	10192.2	+	17653.4i	0.326212	+	0.565016i
$993$		0			0
$994$	18072.8	−	31303.0i	0.576694	−	0.998864i
$995$	4234.13	−	7333.72i	0.134905	−	0.233663i
$996$		0			0
$997$	21103.6	+	36552.5i	0.670369	+	1.16111i	0.977800	+	0.209542i	$0.0671974\pi$
$997$	21103.6	+	36552.5i	0.670369	+	1.16111i	−0.307431	+	0.951570i	$0.599469\pi$
$998$	−200.362			−0.00635505
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.q.271.1		6
3.2	odd	2		405.4.e.v.271.3		6
9.2	odd	6		405.4.e.v.136.3		6
9.4	even	3		135.4.a.h.1.3	yes	3
9.5	odd	6		135.4.a.e.1.1	✓	3
9.7	even	3	inner	405.4.e.q.136.1		6
36.23	even	6		2160.4.a.bi.1.2		3
36.31	odd	6		2160.4.a.bq.1.2		3
45.4	even	6		675.4.a.p.1.1		3
45.13	odd	12		675.4.b.n.649.1		6
45.14	odd	6		675.4.a.s.1.3		3
45.22	odd	12		675.4.b.n.649.6		6
45.23	even	12		675.4.b.m.649.6		6
45.32	even	12		675.4.b.m.649.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.4.a.e.1.1	✓	3	9.5	odd	6
135.4.a.h.1.3	yes	3	9.4	even	3
405.4.e.q.136.1		6	9.7	even	3	inner
405.4.e.q.271.1		6	1.1	even	1	trivial
405.4.e.v.136.3		6	9.2	odd	6
405.4.e.v.271.3		6	3.2	odd	2
675.4.a.p.1.1		3	45.4	even	6
675.4.a.s.1.3		3	45.14	odd	6
675.4.b.m.649.1		6	45.32	even	12
675.4.b.m.649.6		6	45.23	even	12
675.4.b.n.649.1		6	45.13	odd	12
675.4.b.n.649.6		6	45.22	odd	12
2160.4.a.bi.1.2		3	36.23	even	6
2160.4.a.bq.1.2		3	36.31	odd	6

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.72938 - 4.72742i) q^{2} +(-10.8990 + 18.8776i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(5.90326 + 10.2247i) q^{7} +75.3201 q^{8} +O(q^{10})\)	\(q+(-2.72938 - 4.72742i) q^{2} +(-10.8990 + 18.8776i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(5.90326 + 10.2247i) q^{7} +75.3201 q^{8} +27.2938 q^{10} +(28.1188 + 48.7032i) q^{11} +(-17.2980 + 29.9611i) q^{13} +(32.2245 - 55.8144i) q^{14} +(-118.385 - 205.049i) q^{16} +39.2675 q^{17} -146.561 q^{19} +(-54.4951 - 94.3882i) q^{20} +(153.494 - 265.859i) q^{22} +(11.7889 - 20.4189i) q^{23} +(-12.5000 - 21.6506i) q^{25} +188.851 q^{26} -257.359 q^{28} +(-80.5013 - 139.432i) q^{29} +(14.7733 - 25.5880i) q^{31} +(-344.954 + 597.478i) q^{32} +(-107.176 - 185.634i) q^{34} -59.0326 q^{35} -217.688 q^{37} +(400.020 + 692.855i) q^{38} +(-188.300 + 326.146i) q^{40} +(-71.1449 + 123.227i) q^{41} +(234.015 + 405.326i) q^{43} -1225.87 q^{44} -128.705 q^{46} +(-197.159 - 341.490i) q^{47} +(101.803 - 176.328i) q^{49} +(-68.2345 + 118.186i) q^{50} +(-377.063 - 653.092i) q^{52} -134.780 q^{53} -281.188 q^{55} +(444.634 + 770.129i) q^{56} +(-439.437 + 761.128i) q^{58} +(65.5977 - 113.619i) q^{59} +(-129.901 - 224.994i) q^{61} -161.287 q^{62} +1871.88 q^{64} +(-86.4901 - 149.805i) q^{65} +(-222.622 + 385.593i) q^{67} +(-427.977 + 741.278i) q^{68} +(161.122 + 279.072i) q^{70} +560.841 q^{71} -88.6681 q^{73} +(594.152 + 1029.10i) q^{74} +(1597.37 - 2766.72i) q^{76} +(-331.985 + 575.015i) q^{77} +(-225.171 - 390.008i) q^{79} +1183.85 q^{80} +776.726 q^{82} +(-142.148 - 246.207i) q^{83} +(-98.1687 + 170.033i) q^{85} +(1277.43 - 2212.57i) q^{86} +(2117.91 + 3668.33i) q^{88} +625.305 q^{89} -408.459 q^{91} +(256.974 + 445.092i) q^{92} +(-1076.24 + 1864.11i) q^{94} +(366.402 - 634.627i) q^{95} +(96.6307 + 167.369i) q^{97} -1111.44 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} - 17 q^{4} - 15 q^{5} + 4 q^{7} + 150 q^{8}+O(q^{10}) \) 6 * q - 5 * q^2 - 17 * q^4 - 15 * q^5 + 4 * q^7 + 150 * q^8	\( 6 q - 5 q^{2} - 17 q^{4} - 15 q^{5} + 4 q^{7} + 150 q^{8} + 50 q^{10} - 5 q^{11} - 7 q^{13} - 60 q^{14} - 161 q^{16} + 310 q^{17} - 100 q^{19} - 85 q^{20} + 229 q^{22} - 285 q^{23} - 75 q^{25} + 370 q^{26} - 668 q^{28} - 115 q^{29} + 115 q^{31} - 775 q^{32} - 413 q^{34} - 40 q^{35} - 768 q^{37} + 1150 q^{38} - 375 q^{40} - 580 q^{41} + 797 q^{43} - 2830 q^{44} - 570 q^{46} + 145 q^{47} - 577 q^{49} - 125 q^{50} - 825 q^{52} - 800 q^{53} + 50 q^{55} + 2190 q^{56} + 59 q^{58} - 380 q^{59} + 152 q^{61} - 2010 q^{62} + 5874 q^{64} - 35 q^{65} - 2 q^{67} - 475 q^{68} - 300 q^{70} + 80 q^{71} - 1960 q^{73} + 2720 q^{74} + 3276 q^{76} - 1950 q^{77} - 1013 q^{79} + 1610 q^{80} + 8 q^{82} - 270 q^{83} - 775 q^{85} + 1555 q^{86} + 5193 q^{88} + 2040 q^{89} - 1264 q^{91} + 1215 q^{92} - 3833 q^{94} + 250 q^{95} - 720 q^{97} - 610 q^{98}+O(q^{100}) \) 6 * q - 5 * q^2 - 17 * q^4 - 15 * q^5 + 4 * q^7 + 150 * q^8 + 50 * q^10 - 5 * q^11 - 7 * q^13 - 60 * q^14 - 161 * q^16 + 310 * q^17 - 100 * q^19 - 85 * q^20 + 229 * q^22 - 285 * q^23 - 75 * q^25 + 370 * q^26 - 668 * q^28 - 115 * q^29 + 115 * q^31 - 775 * q^32 - 413 * q^34 - 40 * q^35 - 768 * q^37 + 1150 * q^38 - 375 * q^40 - 580 * q^41 + 797 * q^43 - 2830 * q^44 - 570 * q^46 + 145 * q^47 - 577 * q^49 - 125 * q^50 - 825 * q^52 - 800 * q^53 + 50 * q^55 + 2190 * q^56 + 59 * q^58 - 380 * q^59 + 152 * q^61 - 2010 * q^62 + 5874 * q^64 - 35 * q^65 - 2 * q^67 - 475 * q^68 - 300 * q^70 + 80 * q^71 - 1960 * q^73 + 2720 * q^74 + 3276 * q^76 - 1950 * q^77 - 1013 * q^79 + 1610 * q^80 + 8 * q^82 - 270 * q^83 - 775 * q^85 + 1555 * q^86 + 5193 * q^88 + 2040 * q^89 - 1264 * q^91 + 1215 * q^92 - 3833 * q^94 + 250 * q^95 - 720 * q^97 - 610 * q^98

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