LMFDB - Embedded newform 108.5.d.a.55.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(55,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("108.55");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.d (of order $2$, degree $1$, 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:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 6 x^{14} - 22 x^{13} + 19 x^{12} + 18 x^{11} + 1423 x^{10} + 660 x^{9} + \cdots + 2924100 $ x^16 - 2x^15 + 6x^14 - 22x^13 + 19x^12 + 18x^11 + 1423x^10 + 660x^9 - 7353x^8 - 22934x^7 - 36353x^6 - 16248x^5 + 360646x^4 + 1077384x^3 + 2005641x^2 + 2990790*x + 2924100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{26} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.6
Root			$2.91300 - 0.609585i$ of defining polynomial
Character	$\chi$	$=$	108.55
Dual form			108.5.d.a.55.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59266 + 3.66925i) q^{2} +(-10.9268 - 11.6878i) q^{4} -29.4580 q^{5} -32.9098i q^{7} +(60.2882 - 21.4787i) q^{8} +O(q^{10})$	\(q+(-1.59266 + 3.66925i) q^{2} +(-10.9268 - 11.6878i) q^{4} -29.4580 q^{5} -32.9098i q^{7} +(60.2882 - 21.4787i) q^{8} +(46.9167 - 108.089i) q^{10} +136.639i q^{11} +164.522 q^{13} +(120.754 + 52.4142i) q^{14} +(-17.2082 + 255.421i) q^{16} +380.756 q^{17} -439.574i q^{19} +(321.883 + 344.298i) q^{20} +(-501.364 - 217.620i) q^{22} +171.733i q^{23} +242.773 q^{25} +(-262.028 + 603.673i) q^{26} +(-384.642 + 359.600i) q^{28} +1041.21 q^{29} +1181.17i q^{31} +(-909.798 - 469.941i) q^{32} +(-606.417 + 1397.09i) q^{34} +969.456i q^{35} +2700.79 q^{37} +(1612.91 + 700.094i) q^{38} +(-1775.97 + 632.718i) q^{40} -1556.42 q^{41} -2218.02i q^{43} +(1597.01 - 1493.04i) q^{44} +(-630.130 - 273.512i) q^{46} -1292.12i q^{47} +1317.95 q^{49} +(-386.655 + 890.794i) q^{50} +(-1797.71 - 1922.90i) q^{52} -1015.00 q^{53} -4025.12i q^{55} +(-706.858 - 1984.07i) q^{56} +(-1658.29 + 3820.45i) q^{58} -2434.15i q^{59} +3839.98 q^{61} +(-4334.02 - 1881.21i) q^{62} +(3173.33 - 2589.82i) q^{64} -4846.48 q^{65} -2352.60i q^{67} +(-4160.46 - 4450.19i) q^{68} +(-3557.18 - 1544.02i) q^{70} +884.064i q^{71} +6921.45 q^{73} +(-4301.45 + 9909.89i) q^{74} +(-5137.65 + 4803.16i) q^{76} +4496.77 q^{77} +10308.0i q^{79} +(506.918 - 7524.19i) q^{80} +(2478.85 - 5710.89i) q^{82} -12322.0i q^{83} -11216.3 q^{85} +(8138.47 + 3532.56i) q^{86} +(2934.83 + 8237.73i) q^{88} +5751.10 q^{89} -5414.38i q^{91} +(2007.17 - 1876.49i) q^{92} +(4741.11 + 2057.91i) q^{94} +12949.0i q^{95} -8159.93 q^{97} +(-2099.04 + 4835.88i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{4}+O(q^{10}) $ 16 * q - 14 * q^4	$ 16 q - 14 q^{4} - 202 q^{10} - 352 q^{13} - 206 q^{16} + 738 q^{22} + 1632 q^{25} + 342 q^{28} - 2536 q^{34} + 3200 q^{37} - 2854 q^{40} + 36 q^{46} - 896 q^{49} + 2288 q^{52} + 2492 q^{58} - 2752 q^{61} + 682 q^{64} - 14166 q^{70} + 8240 q^{73} - 33084 q^{76} + 68 q^{82} + 8800 q^{85} + 48294 q^{88} + 52596 q^{94} - 6928 q^{97}+O(q^{100}) $ 16 * q - 14 * q^4 - 202 * q^10 - 352 * q^13 - 206 * q^16 + 738 * q^22 + 1632 * q^25 + 342 * q^28 - 2536 * q^34 + 3200 * q^37 - 2854 * q^40 + 36 * q^46 - 896 * q^49 + 2288 * q^52 + 2492 * q^58 - 2752 * q^61 + 682 * q^64 - 14166 * q^70 + 8240 * q^73 - 33084 * q^76 + 68 * q^82 + 8800 * q^85 + 48294 * q^88 + 52596 * q^94 - 6928 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.59266	+	3.66925i	−0.398166	+	0.917313i
$2$	−1.59266	+	3.66925i	−0.398166	+	0.917313i
$3$		0			0
$3$		0			0
$4$	−10.9268	−	11.6878i	−0.682928	−	0.730486i
$5$	−29.4580			−1.17832			−0.589160	−	0.808017i	$-0.700541\pi$
$5$	−29.4580			−1.17832			−0.589160	+	0.808017i	$0.700541\pi$
$6$		0			0
$7$		−	32.9098i		−	0.671628i	−0.941928	−	0.335814i	$-0.890989\pi$
$7$		−	32.9098i		−	0.671628i	0.941928	−	0.335814i	$-0.109011\pi$
$8$	60.2882	−	21.4787i	0.942003	−	0.335604i
$9$		0			0
$10$	46.9167	−	108.089i	0.469167	−	1.08089i
$11$			136.639i			1.12925i	0.825348	+	0.564625i	$0.190979\pi$
$11$			136.639i			1.12925i	−0.825348	+	0.564625i	$0.809021\pi$
$12$		0			0
$13$	164.522			0.973503			0.486751	−	0.873541i	$-0.338182\pi$
$13$	164.522			0.973503			0.486751	+	0.873541i	$0.338182\pi$
$14$	120.754	+	52.4142i	0.616094	+	0.267420i
$15$		0			0
$16$	−17.2082	+	255.421i	−0.0672195	+	0.997738i
$17$	380.756			1.31750			0.658748	−	0.752364i	$-0.271086\pi$
$17$	380.756			1.31750			0.658748	+	0.752364i	$0.271086\pi$
$18$		0			0
$19$		−	439.574i		−	1.21766i	−0.793302	−	0.608829i	$-0.791640\pi$
$19$		−	439.574i		−	1.21766i	0.793302	−	0.608829i	$-0.208360\pi$
$20$	321.883	+	344.298i	0.804707	+	0.860746i
$21$		0			0
$22$	−501.364	−	217.620i	−1.03588	−	0.449629i
$23$			171.733i			0.324636i	0.986738	+	0.162318i	$0.0518971\pi$
$23$			171.733i			0.324636i	−0.986738	+	0.162318i	$0.948103\pi$
$24$		0			0
$25$	242.773			0.388436
$26$	−262.028	+	603.673i	−0.387616	+	0.893007i
$27$		0			0
$28$	−384.642	+	359.600i	−0.490615	+	0.458674i
$29$	1041.21			1.23806			0.619029	−	0.785368i	$-0.287526\pi$
$29$	1041.21			1.23806			0.619029	+	0.785368i	$0.287526\pi$
$30$		0			0
$31$			1181.17i			1.22911i	0.788876	+	0.614553i	$0.210664\pi$
$31$			1181.17i			1.22911i	−0.788876	+	0.614553i	$0.789336\pi$
$32$	−909.798	−	469.941i	−0.888474	−	0.458927i
$33$		0			0
$34$	−606.417	+	1397.09i	−0.524582	+	1.20856i
$35$			969.456i			0.791393i
$36$		0			0
$37$	2700.79			1.97282			0.986410	−	0.164301i	$-0.0525370\pi$
$37$	2700.79			1.97282			0.986410	+	0.164301i	$0.0525370\pi$
$38$	1612.91	+	700.094i	1.11697	+	0.484830i
$39$		0			0
$40$	−1775.97	+	632.718i	−1.10998	+	0.395449i
$41$	−1556.42			−0.925887			−0.462944	−	0.886388i	$-0.653207\pi$
$41$	−1556.42			−0.925887			−0.462944	+	0.886388i	$0.653207\pi$
$42$		0			0
$43$		−	2218.02i		−	1.19958i	−0.800158	−	0.599789i	$-0.795251\pi$
$43$		−	2218.02i		−	1.19958i	0.800158	−	0.599789i	$-0.204749\pi$
$44$	1597.01	−	1493.04i	0.824901	−	0.771196i
$45$		0			0
$46$	−630.130	−	273.512i	−0.297793	−	0.129259i
$47$		−	1292.12i		−	0.584934i	−0.956276	−	0.292467i	$-0.905524\pi$
$47$		−	1292.12i		−	0.584934i	0.956276	−	0.292467i	$-0.0944761\pi$
$48$		0			0
$49$	1317.95			0.548915
$50$	−386.655	+	890.794i	−0.154662	+	0.356318i
$51$		0			0
$52$	−1797.71	−	1922.90i	−0.664832	−	0.711130i
$53$	−1015.00			−0.361337			−0.180669	−	0.983544i	$-0.557826\pi$
$53$	−1015.00			−0.361337			−0.180669	+	0.983544i	$0.557826\pi$
$54$		0			0
$55$		−	4025.12i		−	1.33062i
$56$	−706.858	−	1984.07i	−0.225401	−	0.632676i
$57$		0			0
$58$	−1658.29	+	3820.45i	−0.492952	+	1.13569i
$59$		−	2434.15i		−	0.699268i	−0.936886	−	0.349634i	$-0.886306\pi$
$59$		−	2434.15i		−	0.699268i	0.936886	−	0.349634i	$-0.113694\pi$
$60$		0			0
$61$	3839.98			1.03198			0.515988	−	0.856596i	$-0.327425\pi$
$61$	3839.98			1.03198			0.515988	+	0.856596i	$0.327425\pi$
$62$	−4334.02	−	1881.21i	−1.12748	−	0.489388i
$63$		0			0
$64$	3173.33	−	2589.82i	0.774740	−	0.632280i
$65$	−4846.48			−1.14710
$66$		0			0
$67$		−	2352.60i		−	0.524081i	−0.965057	−	0.262040i	$-0.915605\pi$
$67$		−	2352.60i		−	0.524081i	0.965057	−	0.262040i	$-0.0843954\pi$
$68$	−4160.46	−	4450.19i	−0.899754	−	0.962412i
$69$		0			0
$70$	−3557.18	−	1544.02i	−0.725955	−	0.315106i
$71$			884.064i			0.175375i	0.996148	+	0.0876874i	$0.0279476\pi$
$71$			884.064i			0.175375i	−0.996148	+	0.0876874i	$0.972052\pi$
$72$		0			0
$73$	6921.45			1.29883			0.649413	−	0.760436i	$-0.275014\pi$
$73$	6921.45			1.29883			0.649413	+	0.760436i	$0.275014\pi$
$74$	−4301.45	+	9909.89i	−0.785510	+	1.80969i
$75$		0			0
$76$	−5137.65	+	4803.16i	−0.889482	+	0.831572i
$77$	4496.77			0.758436
$78$		0			0
$79$			10308.0i			1.65165i	0.563924	+	0.825826i	$0.309291\pi$
$79$			10308.0i			1.65165i	−0.563924	+	0.825826i	$0.690709\pi$
$80$	506.918	−	7524.19i	0.0792060	−	1.17565i
$81$		0			0
$82$	2478.85	−	5710.89i	0.368657	−	0.849329i
$83$		−	12322.0i		−	1.78865i	−0.447417	−	0.894326i	$-0.647656\pi$
$83$		−	12322.0i		−	1.78865i	0.447417	−	0.894326i	$-0.352344\pi$
$84$		0			0
$85$	−11216.3			−1.55243
$86$	8138.47	+	3532.56i	1.10039	+	0.477631i
$87$		0			0
$88$	2934.83	+	8237.73i	0.378981	+	1.06376i
$89$	5751.10			0.726057			0.363028	−	0.931778i	$-0.381743\pi$
$89$	5751.10			0.726057			0.363028	+	0.931778i	$0.381743\pi$
$90$		0			0
$91$		−	5414.38i		−	0.653832i
$92$	2007.17	−	1876.49i	0.237142	−	0.221703i
$93$		0			0
$94$	4741.11	+	2057.91i	0.536568	+	0.232901i
$95$			12949.0i			1.43479i
$96$		0			0
$97$	−8159.93			−0.867247			−0.433624	−	0.901094i	$-0.642765\pi$
$97$	−8159.93			−0.867247			−0.433624	+	0.901094i	$0.642765\pi$
$98$	−2099.04	+	4835.88i	−0.218559	+	0.503527i
$99$		0			0
$100$	−2652.74	−	2837.47i	−0.265274	−	0.283747i
$101$	−11440.4			−1.12150			−0.560749	−	0.827986i	$-0.689487\pi$
$101$	−11440.4			−1.12150			−0.560749	+	0.827986i	$0.689487\pi$
$102$		0			0
$103$			11724.0i			1.10510i	0.833479	+	0.552552i	$0.186346\pi$
$103$			11724.0i			1.10510i	−0.833479	+	0.552552i	$0.813654\pi$
$104$	9918.73	−	3533.71i	0.917043	−	0.326711i
$105$		0			0
$106$	1616.55	−	3724.28i	0.143872	−	0.331460i
$107$			21224.4i			1.85382i	0.375286	+	0.926909i	$0.377544\pi$
$107$			21224.4i			1.85382i	−0.375286	+	0.926909i	$0.622456\pi$
$108$		0			0
$109$	−5752.64			−0.484188			−0.242094	−	0.970253i	$-0.577834\pi$
$109$	−5752.64			−0.484188			−0.242094	+	0.970253i	$0.577834\pi$
$110$	14769.2	+	6410.66i	1.22059	+	0.529806i
$111$		0			0
$112$	8405.85	+	566.318i	0.670109	+	0.0451465i
$113$	6018.68			0.471351			0.235675	−	0.971832i	$-0.424270\pi$
$113$	6018.68			0.471351			0.235675	+	0.971832i	$0.424270\pi$
$114$		0			0
$115$		−	5058.90i		−	0.382525i
$116$	−11377.1	−	12169.4i	−0.845504	−	0.904384i
$117$		0			0
$118$	8931.52	+	3876.79i	0.641448	+	0.278425i
$119$		−	12530.6i		−	0.884868i
$120$		0			0
$121$	−4029.28			−0.275205
$122$	−6115.80	+	14089.9i	−0.410898	+	0.946646i
$123$		0			0
$124$	13805.3	−	12906.5i	0.897845	−	0.839391i
$125$	11259.6			0.720617
$126$		0			0
$127$			7591.93i			0.470700i	0.971911	+	0.235350i	$0.0756237\pi$
$127$			7591.93i			0.470700i	−0.971911	+	0.235350i	$0.924376\pi$
$128$	4448.65	+	15768.5i	0.271524	+	0.962432i
$129$		0			0
$130$	7718.82	−	17783.0i	0.456735	−	1.05225i
$131$		−	3334.49i		−	0.194306i	−0.995269	−	0.0971532i	$-0.969026\pi$
$131$		−	3334.49i		−	0.194306i	0.995269	−	0.0971532i	$-0.0309737\pi$
$132$		0			0
$133$	−14466.3			−0.817813
$134$	8632.28	+	3746.90i	0.480746	+	0.208671i
$135$		0			0
$136$	22955.1	−	8178.14i	1.24109	−	0.442157i
$137$	11823.7			0.629960			0.314980	−	0.949098i	$-0.398002\pi$
$137$	11823.7			0.629960			0.314980	+	0.949098i	$0.398002\pi$
$138$		0			0
$139$			5544.34i			0.286959i	0.989653	+	0.143480i	$0.0458292\pi$
$139$			5544.34i			0.286959i	−0.989653	+	0.143480i	$0.954171\pi$
$140$	11330.8	−	10593.1i	0.578101	−	0.540464i
$141$		0			0
$142$	−3243.85	−	1408.02i	−0.160874	−	0.0698282i
$143$			22480.2i			1.09933i
$144$		0			0
$145$	−30671.8			−1.45883
$146$	−11023.5	+	25396.5i	−0.517149	+	1.19143i
$147$		0			0
$148$	−29511.1	−	31566.2i	−1.34729	−	1.44112i
$149$	11073.6			0.498790			0.249395	−	0.968402i	$-0.419768\pi$
$149$	11073.6			0.498790			0.249395	+	0.968402i	$0.419768\pi$
$150$		0			0
$151$		−	27450.4i		−	1.20391i	−0.798529	−	0.601956i	$-0.794388\pi$
$151$		−	27450.4i		−	1.20391i	0.798529	−	0.601956i	$-0.205612\pi$
$152$	−9441.47	−	26501.1i	−0.408651	−	1.14704i
$153$		0			0
$154$	−7161.84	+	16499.8i	−0.301984	+	0.695724i
$155$		−	34794.9i		−	1.44828i
$156$		0			0
$157$	14606.6			0.592583			0.296291	−	0.955098i	$-0.404250\pi$
$157$	14606.6			0.592583			0.296291	+	0.955098i	$0.404250\pi$
$158$	−37822.5	−	16417.1i	−1.51508	−	0.657632i
$159$		0			0
$160$	26800.8	+	13843.5i	1.04691	+	0.540762i
$161$	5651.68			0.218035
$162$		0			0
$163$			39065.5i			1.47034i	0.677883	+	0.735170i	$0.262898\pi$
$163$			39065.5i			1.47034i	−0.677883	+	0.735170i	$0.737102\pi$
$164$	17006.7	+	18191.1i	0.632314	+	0.676348i
$165$		0			0
$166$	45212.6	+	19624.8i	1.64075	+	0.712180i
$167$			3123.15i			0.111985i	0.998431	+	0.0559926i	$0.0178323\pi$
$167$			3123.15i			0.111985i	−0.998431	+	0.0559926i	$0.982168\pi$
$168$		0			0
$169$	−1493.53			−0.0522925
$170$	17863.8	−	41155.5i	0.618125	−	1.42407i
$171$		0			0
$172$	−25923.7	+	24235.9i	−0.876274	+	0.819225i
$173$	−50749.6			−1.69567			−0.847834	−	0.530262i	$-0.822093\pi$
$173$	−50749.6			−1.69567			−0.847834	+	0.530262i	$0.822093\pi$
$174$		0			0
$175$		−	7989.60i		−	0.260885i
$176$	−34900.5	−	2351.31i	−1.12670	−	0.0759076i
$177$		0			0
$178$	−9159.56	+	21102.2i	−0.289091	+	0.666022i
$179$		−	4456.66i		−	0.139092i	−0.997579	−	0.0695462i	$-0.977845\pi$
$179$		−	4456.66i		−	0.139092i	0.997579	−	0.0695462i	$-0.0221551\pi$
$180$		0			0
$181$	−8462.68			−0.258316			−0.129158	−	0.991624i	$-0.541227\pi$
$181$	−8462.68			−0.258316			−0.129158	+	0.991624i	$0.541227\pi$
$182$	19866.7	+	8623.29i	0.599769	+	0.260334i
$183$		0			0
$184$	3688.59	+	10353.4i	0.108949	+	0.305808i
$185$	−79559.9			−2.32461
$186$		0			0
$187$			52026.2i			1.48778i
$188$	−15102.0	+	14118.8i	−0.427286	+	0.399467i
$189$		0			0
$190$	−47513.1	−	20623.4i	−1.31615	−	0.571284i
$191$		−	17699.2i		−	0.485163i	−0.970131	−	0.242582i	$-0.922006\pi$
$191$		−	17699.2i		−	0.485163i	0.970131	−	0.242582i	$-0.0779942\pi$
$192$		0			0
$193$	10944.5			0.293820			0.146910	−	0.989150i	$-0.453067\pi$
$193$	10944.5			0.293820			0.146910	+	0.989150i	$0.453067\pi$
$194$	12996.0	−	29940.9i	0.345308	−	0.795538i
$195$		0			0
$196$	−14401.0	−	15403.9i	−0.374869	−	0.400975i
$197$	−10101.3			−0.260284			−0.130142	−	0.991495i	$-0.541543\pi$
$197$	−10101.3			−0.260284			−0.130142	+	0.991495i	$0.541543\pi$
$198$		0			0
$199$		−	31394.8i		−	0.792777i	−0.918083	−	0.396388i	$-0.870263\pi$
$199$		−	31394.8i		−	0.792777i	0.918083	−	0.396388i	$-0.129737\pi$
$200$	14636.3	−	5214.43i	0.365908	−	0.130361i
$201$		0			0
$202$	18220.7	−	41977.8i	0.446543	−	1.02877i
$203$		−	34265.9i		−	0.831515i
$204$		0			0
$205$	45848.9			1.09099
$206$	−43018.5	−	18672.5i	−1.01373	−	0.440015i
$207$		0			0
$208$	−2831.12	+	42022.4i	−0.0654383	+	0.971301i
$209$	60063.1			1.37504
$210$		0			0
$211$		−	83361.8i		−	1.87241i	−0.351448	−	0.936207i	$-0.614311\pi$
$211$		−	83361.8i		−	1.87241i	0.351448	−	0.936207i	$-0.385689\pi$
$212$	11090.7	+	11863.1i	0.246767	+	0.263952i
$213$		0			0
$214$	−77877.6	−	33803.3i	−1.70053	−	0.738127i
$215$			65338.3i			1.41349i
$216$		0			0
$217$	38872.1			0.825503
$218$	9162.02	−	21107.9i	0.192787	−	0.444152i
$219$		0			0
$220$	−47044.7	+	43981.8i	−0.971997	+	0.908715i
$221$	62642.8			1.28259
$222$		0			0
$223$		−	13301.4i		−	0.267478i	−0.991017	−	0.133739i	$-0.957302\pi$
$223$		−	13301.4i		−	0.267478i	0.991017	−	0.133739i	$-0.0426983\pi$
$224$	−15465.7	+	29941.2i	−0.308228	+	0.596724i
$225$		0			0
$226$	−9585.73	+	22084.1i	−0.187676	+	0.432377i
$227$		−	50075.5i		−	0.971792i	−0.874017	−	0.485896i	$-0.838493\pi$
$227$		−	50075.5i		−	0.971792i	0.874017	−	0.485896i	$-0.161507\pi$
$228$		0			0
$229$	60039.8			1.14490			0.572451	−	0.819939i	$-0.305993\pi$
$229$	60039.8			1.14490			0.572451	+	0.819939i	$0.305993\pi$
$230$	18562.4	+	8057.12i	0.350895	+	0.152308i
$231$		0			0
$232$	62772.5	−	22363.7i	1.16625	−	0.415497i
$233$	31252.0			0.575659			0.287830	−	0.957682i	$-0.407066\pi$
$233$	31252.0			0.575659			0.287830	+	0.957682i	$0.407066\pi$
$234$		0			0
$235$			38063.2i			0.689239i
$236$	−28449.8	+	26597.6i	−0.510805	+	0.477549i
$237$		0			0
$238$	45978.0	+	19957.0i	0.811701	+	0.352324i
$239$			62883.1i			1.10087i	0.834876	+	0.550437i	$0.185539\pi$
$239$			62883.1i			1.10087i	−0.834876	+	0.550437i	$0.814461\pi$
$240$		0			0
$241$	64613.0			1.11246			0.556232	−	0.831027i	$-0.312247\pi$
$241$	64613.0			1.11246			0.556232	+	0.831027i	$0.312247\pi$
$242$	6417.29	−	14784.5i	0.109577	−	0.252450i
$243$		0			0
$244$	−41958.9	−	44880.9i	−0.704765	−	0.753844i
$245$	−38824.0			−0.646797
$246$		0			0
$247$		−	72319.6i		−	1.18539i
$248$	25370.0	+	71210.7i	0.412493	+	1.15782i
$249$		0			0
$250$	−17932.8	+	41314.5i	−0.286925	+	0.661032i
$251$		−	78853.1i		−	1.25162i	−0.779977	−	0.625808i	$-0.784769\pi$
$251$		−	78853.1i		−	1.25162i	0.779977	−	0.625808i	$-0.215231\pi$
$252$		0			0
$253$	−23465.4			−0.366595
$254$	−27856.7	−	12091.4i	−0.431780	−	0.187417i
$255$		0			0
$256$	−64943.8	−	8790.66i	−0.990963	−	0.134135i
$257$	25571.1			0.387153			0.193576	−	0.981085i	$-0.437991\pi$
$257$	25571.1			0.387153			0.193576	+	0.981085i	$0.437991\pi$
$258$		0			0
$259$		−	88882.5i		−	1.32500i
$260$	52956.8	+	56644.6i	0.783384	+	0.837938i
$261$		0			0
$262$	12235.1	+	5310.73i	0.178240	+	0.0773662i
$263$			110011.i			1.59046i	0.606305	+	0.795232i	$0.292651\pi$
$263$			110011.i			1.59046i	−0.606305	+	0.795232i	$0.707349\pi$
$264$		0			0
$265$	29899.8			0.425771
$266$	23040.0	−	53080.5i	0.325625	−	0.750191i
$267$		0			0
$268$	−27496.6	+	25706.5i	−0.382834	+	0.357909i
$269$	39818.1			0.550270			0.275135	−	0.961406i	$-0.411277\pi$
$269$	39818.1			0.550270			0.275135	+	0.961406i	$0.411277\pi$
$270$		0			0
$271$			14054.7i			0.191375i	0.995411	+	0.0956873i	$0.0305049\pi$
$271$			14054.7i			0.191375i	−0.995411	+	0.0956873i	$0.969495\pi$
$272$	−6552.12	+	97253.1i	−0.0885614	+	1.31452i
$273$		0			0
$274$	−18831.2	+	43384.2i	−0.250829	+	0.577871i
$275$			33172.3i			0.438642i
$276$		0			0
$277$	−31583.7			−0.411627			−0.205813	−	0.978591i	$-0.565984\pi$
$277$	−31583.7			−0.411627			−0.205813	+	0.978591i	$0.565984\pi$
$278$	−20343.6	−	8830.27i	−0.263232	−	0.114257i
$279$		0			0
$280$	20822.6	+	58446.8i	0.265595	+	0.745494i
$281$	−66899.3			−0.847244			−0.423622	−	0.905839i	$-0.639242\pi$
$281$	−66899.3			−0.847244			−0.423622	+	0.905839i	$0.639242\pi$
$282$		0			0
$283$			160099.i			1.99901i	0.0314612	+	0.999505i	$0.489984\pi$
$283$			160099.i			1.99901i	−0.0314612	+	0.999505i	$0.510016\pi$
$284$	10332.7	−	9660.03i	0.128109	−	0.119768i
$285$		0			0
$286$	−82485.4	−	35803.3i	−1.00843	−	0.437715i
$287$			51221.4i			0.621852i
$288$		0			0
$289$	61454.3			0.735795
$290$	48849.9	−	112543.i	0.580855	−	1.33820i
$291$		0			0
$292$	−75629.6	−	80896.3i	−0.887005	−	0.948775i
$293$	92671.2			1.07947			0.539734	−	0.841836i	$-0.318525\pi$
$293$	92671.2			1.07947			0.539734	+	0.841836i	$0.318525\pi$
$294$		0			0
$295$			71705.2i			0.823961i
$296$	162826.	−	58009.4i	1.85840	−	0.662087i
$297$		0			0
$298$	−17636.6	+	40631.9i	−0.198601	+	0.457546i
$299$			28253.8i			0.316034i
$300$		0			0
$301$	−72994.5			−0.805670
$302$	100722.	+	43719.3i	1.10436	+	0.479357i
$303$		0			0
$304$	112277.	+	7564.28i	1.21490	+	0.0818503i
$305$	−113118.			−1.21600
$306$		0			0
$307$		−	86852.2i		−	0.921518i	−0.887525	−	0.460759i	$-0.847577\pi$
$307$		−	86852.2i		−	0.921518i	0.887525	−	0.460759i	$-0.152423\pi$
$308$	−49135.5	−	52557.2i	−0.517957	−	0.554027i
$309$		0			0
$310$	127671.	+	55416.6i	1.32853	+	0.576656i
$311$		−	43940.9i		−	0.454306i	−0.973859	−	0.227153i	$-0.927058\pi$
$311$		−	43940.9i		−	0.454306i	0.973859	−	0.227153i	$-0.0729417\pi$
$312$		0			0
$313$	−100801.			−1.02890			−0.514452	−	0.857519i	$-0.672005\pi$
$313$	−100801.			−1.02890			−0.514452	+	0.857519i	$0.672005\pi$
$314$	−23263.4	+	53595.2i	−0.235946	+	0.543584i
$315$		0			0
$316$	120477.	−	112634.i	1.20651	−	1.12796i
$317$	101986.			1.01490			0.507449	−	0.861682i	$-0.330589\pi$
$317$	101986.			1.01490			0.507449	+	0.861682i	$0.330589\pi$
$318$		0			0
$319$			142270.i			1.39808i
$320$	−93480.0	+	76290.9i	−0.912891	+	0.745028i
$321$		0			0
$322$	−9001.23	+	20737.5i	−0.0868141	+	0.200006i
$323$		−	167371.i		−	1.60426i
$324$		0			0
$325$	39941.4			0.378144
$326$	−143341.	−	62218.2i	−1.34876	−	0.585439i
$327$		0			0
$328$	−93833.6	+	33429.8i	−0.872189	+	0.310732i
$329$	−42523.4			−0.392858
$330$		0			0
$331$		−	39677.8i		−	0.362153i	−0.983469	−	0.181076i	$-0.942042\pi$
$331$		−	39677.8i		−	0.362153i	0.983469	−	0.181076i	$-0.0579581\pi$
$332$	−144017.	+	134641.i	−1.30658	+	1.22152i
$333$		0			0
$334$	−11459.6	−	4974.13i	−0.102725	−	0.0445887i
$335$			69302.8i			0.617534i
$336$		0			0
$337$	−129324.			−1.13873			−0.569364	−	0.822086i	$-0.692810\pi$
$337$	−129324.			−1.13873			−0.569364	+	0.822086i	$0.692810\pi$
$338$	2378.68	−	5480.12i	0.0208211	−	0.0479686i
$339$		0			0
$340$	122559.	+	131094.i	1.06020	+	1.13403i
$341$	−161394.			−1.38797
$342$		0			0
$343$		−	122390.i		−	1.04030i
$344$	−47640.1	−	133720.i	−0.402583	−	1.13001i
$345$		0			0
$346$	80827.1	−	186213.i	0.675157	−	1.55546i
$347$		−	174482.i		−	1.44908i	−0.689233	−	0.724540i	$-0.742052\pi$
$347$		−	174482.i		−	1.44908i	0.689233	−	0.724540i	$-0.257948\pi$
$348$		0			0
$349$	−39421.3			−0.323654			−0.161827	−	0.986819i	$-0.551739\pi$
$349$	−39421.3			−0.323654			−0.161827	+	0.986819i	$0.551739\pi$
$350$	29315.9	+	12724.7i	0.239313	+	0.103875i
$351$		0			0
$352$	64212.4	−	124314.i	0.518243	−	1.00331i
$353$	123080.			0.987733			0.493866	−	0.869538i	$-0.335583\pi$
$353$	123080.			0.987733			0.493866	+	0.869538i	$0.335583\pi$
$354$		0			0
$355$		−	26042.7i		−	0.206647i
$356$	−62841.3	−	67217.5i	−0.495844	−	0.530374i
$357$		0			0
$358$	16352.6	+	7097.96i	0.127591	+	0.0553818i
$359$		−	20967.0i		−	0.162685i	−0.996686	−	0.0813424i	$-0.974079\pi$
$359$		−	20967.0i		−	0.162685i	0.996686	−	0.0813424i	$-0.0259207\pi$
$360$		0			0
$361$	−62904.6			−0.482690
$362$	13478.2	−	31051.7i	0.102852	−	0.236956i
$363$		0			0
$364$	−63282.1	+	59162.1i	−0.477615	+	0.446520i
$365$	−203892.			−1.53043
$366$		0			0
$367$			58300.8i			0.432855i	0.976299	+	0.216427i	$0.0694405\pi$
$367$			58300.8i			0.432855i	−0.976299	+	0.216427i	$0.930560\pi$
$368$	−43864.1	−	2955.21i	−0.323902	−	0.0218219i
$369$		0			0
$370$	126712.	−	291925.i	0.925581	−	2.13240i
$371$			33403.3i			0.242684i
$372$		0			0
$373$	−79775.3			−0.573391			−0.286695	−	0.958022i	$-0.592557\pi$
$373$	−79775.3			−0.573391			−0.286695	+	0.958022i	$0.592557\pi$
$374$	−190897.	−	82860.3i	−1.36476	−	0.592384i
$375$		0			0
$376$	−27753.0	−	77899.5i	−0.196306	−	0.551009i
$377$	171301.			1.20525
$378$		0			0
$379$		−	80878.2i		−	0.563058i	−0.959553	−	0.281529i	$-0.909159\pi$
$379$		−	80878.2i		−	0.563058i	0.959553	−	0.281529i	$-0.0908415\pi$
$380$	151345.	−	141491.i	1.04809	−	0.979857i
$381$		0			0
$382$	64943.0	+	28188.9i	0.445047	+	0.193176i
$383$			99819.8i			0.680486i	0.940338	+	0.340243i	$0.110509\pi$
$383$			99819.8i			0.680486i	−0.940338	+	0.340243i	$0.889491\pi$
$384$		0			0
$385$	−132466.			−0.893680
$386$	−17430.9	+	40158.1i	−0.116989	+	0.269525i
$387$		0			0
$388$	89162.3	+	95371.4i	0.592267	+	0.633512i
$389$	−15583.1			−0.102981			−0.0514903	−	0.998673i	$-0.516397\pi$
$389$	−15583.1			−0.102981			−0.0514903	+	0.998673i	$0.516397\pi$
$390$		0			0
$391$			65388.3i			0.427707i
$392$	79456.6	−	28307.7i	0.517080	−	0.184218i
$393$		0			0
$394$	16088.0	−	37064.4i	0.103636	−	0.238762i
$395$		−	303652.i		−	1.94617i
$396$		0			0
$397$	−67256.6			−0.426730			−0.213365	−	0.976973i	$-0.568442\pi$
$397$	−67256.6			−0.426730			−0.213365	+	0.976973i	$0.568442\pi$
$398$	115195.	+	50001.3i	0.727225	+	0.315657i
$399$		0			0
$400$	−4177.68	+	62009.2i	−0.0261105	+	0.387558i
$401$	−151843.			−0.944288			−0.472144	−	0.881521i	$-0.656520\pi$
$401$	−151843.			−0.944288			−0.472144	+	0.881521i	$0.656520\pi$
$402$		0			0
$403$			194329.i			1.19654i
$404$	125008.	+	133713.i	0.765903	+	0.819239i
$405$		0			0
$406$	125730.	+	54574.0i	0.762760	+	0.331081i
$407$			369034.i			2.22781i
$408$		0			0
$409$	−64170.7			−0.383610			−0.191805	−	0.981433i	$-0.561434\pi$
$409$	−64170.7			−0.383610			−0.191805	+	0.981433i	$0.561434\pi$
$410$	−73021.9	+	168231.i	−0.434396	+	1.00078i
$411$		0			0
$412$	137028.	−	128107.i	0.807262	−	0.754706i
$413$	−80107.4			−0.469648
$414$		0			0
$415$			362982.i			2.10760i
$416$	−149682.	−	77315.6i	−0.864932	−	0.446766i
$417$		0			0
$418$	−95660.3	+	220387.i	−0.547494	+	1.26134i
$419$		−	85171.9i		−	0.485142i	−0.970134	−	0.242571i	$-0.922009\pi$
$419$		−	85171.9i		−	0.485142i	0.970134	−	0.242571i	$-0.0779907\pi$
$420$		0			0
$421$	214896.			1.21245			0.606224	−	0.795294i	$-0.292683\pi$
$421$	214896.			1.21245			0.606224	+	0.795294i	$0.292683\pi$
$422$	305875.	+	132767.i	1.71759	+	0.745532i
$423$		0			0
$424$	−61192.3	+	21800.8i	−0.340381	+	0.121266i
$425$	92437.2			0.511763
$426$		0			0
$427$		−	126373.i		−	0.693105i
$428$	248066.	−	231915.i	1.35419	−	1.26602i
$429$		0			0
$430$	−239743.	−	104062.i	−1.29661	−	0.562802i
$431$			19885.9i			0.107051i	0.998566	+	0.0535254i	$0.0170458\pi$
$431$			19885.9i			0.107051i	−0.998566	+	0.0535254i	$0.982954\pi$
$432$		0			0
$433$	103996.			0.554679			0.277339	−	0.960772i	$-0.410547\pi$
$433$	103996.			0.554679			0.277339	+	0.960772i	$0.410547\pi$
$434$	−61910.2	+	142632.i	−0.328687	+	0.757244i
$435$		0			0
$436$	62858.2	+	67235.6i	0.330666	+	0.353693i
$437$	75489.2			0.395296
$438$		0			0
$439$		−	55956.4i		−	0.290349i	−0.989406	−	0.145175i	$-0.953626\pi$
$439$		−	55956.4i		−	0.290349i	0.989406	−	0.145175i	$-0.0463744\pi$
$440$	−86454.1	−	242667.i	−0.446561	−	1.25345i
$441$		0			0
$442$	−99768.9	+	229852.i	−0.510682	+	1.17653i
$443$			22607.4i			0.115198i	0.998340	+	0.0575988i	$0.0183444\pi$
$443$			22607.4i			0.115198i	−0.998340	+	0.0575988i	$0.981656\pi$
$444$		0			0
$445$	−169416.			−0.855527
$446$	48806.2	+	21184.7i	0.245361	+	0.106501i
$447$		0			0
$448$	−85230.4	−	104434.i	−0.424657	−	0.520337i
$449$	−77577.5			−0.384807			−0.192404	−	0.981316i	$-0.561628\pi$
$449$	−77577.5			−0.384807			−0.192404	+	0.981316i	$0.561628\pi$
$450$		0			0
$451$		−	212668.i		−	1.04556i
$452$	−65765.2	−	70345.0i	−0.321899	−	0.344315i
$453$		0			0
$454$	183740.	+	79753.4i	0.891438	+	0.386934i
$455$			159497.i			0.770423i
$456$		0			0
$457$	−242860.			−1.16285			−0.581425	−	0.813600i	$-0.697505\pi$
$457$	−242860.			−1.16285			−0.581425	+	0.813600i	$0.697505\pi$
$458$	−95623.2	+	220301.i	−0.455861	+	1.05023i
$459$		0			0
$460$	−59127.2	+	55277.8i	−0.279429	+	0.261237i
$461$	199640.			0.939391			0.469696	−	0.882828i	$-0.344364\pi$
$461$	199640.			0.939391			0.469696	+	0.882828i	$0.344364\pi$
$462$		0			0
$463$		−	63490.8i		−	0.296175i	−0.988974	−	0.148088i	$-0.952688\pi$
$463$		−	63490.8i		−	0.296175i	0.988974	−	0.148088i	$-0.0473118\pi$
$464$	−17917.3	+	265946.i	−0.0832216	+	1.23526i
$465$		0			0
$466$	−49773.9	+	114671.i	−0.229208	+	0.528060i
$467$			112982.i			0.518053i	0.965870	+	0.259026i	$0.0834017\pi$
$467$			112982.i			0.518053i	−0.965870	+	0.259026i	$0.916598\pi$
$468$		0			0
$469$	−77423.5			−0.351987
$470$	−139664.	−	60621.9i	−0.632248	−	0.274431i
$471$		0			0
$472$	−52282.3	−	146751.i	−0.234677	−	0.658713i
$473$	303068.			1.35462
$474$		0			0
$475$		−	106717.i		−	0.472982i
$476$	−146455.	+	136920.i	−0.646383	+	0.604301i
$477$		0			0
$478$	−230734.	−	100152.i	−1.00985	−	0.438331i
$479$			313437.i			1.36609i	0.730376	+	0.683045i	$0.239345\pi$
$479$			313437.i			1.36609i	−0.730376	+	0.683045i	$0.760655\pi$
$480$		0			0
$481$	444339.			1.92055
$482$	−102907.	+	237081.i	−0.442945	+	1.02048i
$483$		0			0
$484$	44027.3	+	47093.4i	0.187945	+	0.201034i
$485$	240375.			1.02189
$486$		0			0
$487$			64950.6i			0.273858i	0.990581	+	0.136929i	$0.0437232\pi$
$487$			64950.6i			0.273858i	−0.990581	+	0.136929i	$0.956277\pi$
$488$	231506.	−	82477.7i	0.972125	−	0.346336i
$489$		0			0
$490$	61833.6	−	142455.i	0.257533	−	0.593316i
$491$		−	358585.i		−	1.48741i	−0.668510	−	0.743703i	$-0.733068\pi$
$491$		−	358585.i		−	1.48741i	0.668510	−	0.743703i	$-0.266932\pi$
$492$		0			0
$493$	396446.			1.63114
$494$	265359.	+	115181.i	1.08738	+	0.471983i
$495$		0			0
$496$	−301696.	−	20325.8i	−1.22633	−	0.0826198i
$497$	29094.4			0.117787
$498$		0			0
$499$			12696.3i			0.0509890i	0.999675	+	0.0254945i	$0.00811603\pi$
$499$			12696.3i			0.0509890i	−0.999675	+	0.0254945i	$0.991884\pi$
$500$	−123032.	−	131600.i	−0.492130	−	0.526401i
$501$		0			0
$502$	289332.	+	125586.i	1.14812	+	0.498351i
$503$		−	114739.i		−	0.453498i	−0.973953	−	0.226749i	$-0.927190\pi$
$503$		−	114739.i		−	0.453498i	0.973953	−	0.226749i	$-0.0728097\pi$
$504$		0			0
$505$	337011.			1.32148
$506$	37372.5	−	86100.5i	0.145966	−	0.336283i
$507$		0			0
$508$	88732.8	−	82955.8i	0.343840	−	0.321454i
$509$	44847.2			0.173101			0.0865505	−	0.996247i	$-0.472416\pi$
$509$	44847.2			0.173101			0.0865505	+	0.996247i	$0.472416\pi$
$510$		0			0
$511$		−	227783.i		−	0.872329i
$512$	135689.	−	224295.i	0.517611	−	0.855616i
$513$		0			0
$514$	−40726.1	+	93826.7i	−0.154151	+	0.355141i
$515$		−	345367.i		−	1.30216i
$516$		0			0
$517$	176554.			0.660536
$518$	326132.	+	141560.i	1.21544	+	0.527571i
$519$		0			0
$520$	−292186.	+	104096.i	−1.08057	+	0.384970i
$521$	−285591.			−1.05213			−0.526065	−	0.850444i	$-0.676333\pi$
$521$	−285591.			−1.05213			−0.526065	+	0.850444i	$0.676333\pi$
$522$		0			0
$523$			164178.i			0.600220i	0.953905	+	0.300110i	$0.0970234\pi$
$523$			164178.i			0.600220i	−0.953905	+	0.300110i	$0.902977\pi$
$524$	−38972.8	+	36435.5i	−0.141938	+	0.132697i
$525$		0			0
$526$	−403658.	−	175210.i	−1.45895	−	0.633269i
$527$			449738.i			1.61934i
$528$		0			0
$529$	250349.			0.894611
$530$	−47620.3	+	109710.i	−0.169527	+	0.390565i
$531$		0			0
$532$	158071.	+	169079.i	0.558507	+	0.597401i
$533$	−256065.			−0.901354
$534$		0			0
$535$		−	625227.i		−	2.18439i
$536$	−50530.7	−	141834.i	−0.175884	−	0.493686i
$537$		0			0
$538$	−63416.9	+	146103.i	−0.219099	+	0.504770i
$539$			180083.i			0.619863i
$540$		0			0
$541$	−300448.			−1.02654			−0.513269	−	0.858228i	$-0.671566\pi$
$541$	−300448.			−1.02654			−0.513269	+	0.858228i	$0.671566\pi$
$542$	−51570.4	−	22384.5i	−0.175551	−	0.0761989i
$543$		0			0
$544$	−346411.	−	178933.i	−1.17056	−	0.604634i
$545$	169461.			0.570528
$546$		0			0
$547$			74251.6i			0.248160i	0.992272	+	0.124080i	$0.0395979\pi$
$547$			74251.6i			0.248160i	−0.992272	+	0.124080i	$0.960402\pi$
$548$	−129196.	−	138193.i	−0.430217	−	0.460177i
$549$		0			0
$550$	−121717.	−	52832.3i	−0.402372	−	0.174652i
$551$		−	457688.i		−	1.50753i
$552$		0			0
$553$	339233.			1.10930
$554$	50302.2	−	115889.i	0.163896	−	0.377591i
$555$		0			0
$556$	64801.0	−	60582.1i	0.209620	−	0.195972i
$557$	−193413.			−0.623411			−0.311705	−	0.950179i	$-0.600900\pi$
$557$	−193413.			−0.623411			−0.311705	+	0.950179i	$0.600900\pi$
$558$		0			0
$559$		−	364913.i		−	1.16779i
$560$	−247619.	−	16682.6i	−0.789603	−	0.0531970i
$561$		0			0
$562$	106548.	−	245470.i	0.337344	−	0.777188i
$563$			177354.i			0.559530i	0.960068	+	0.279765i	$0.0902566\pi$
$563$			177354.i			0.559530i	−0.960068	+	0.279765i	$0.909743\pi$
$564$		0			0
$565$	−177298.			−0.555402
$566$	−587443.	−	254983.i	−1.83372	−	0.795938i
$567$		0			0
$568$	18988.5	+	53298.6i	0.0588565	+	0.165204i
$569$	−590091.			−1.82261			−0.911306	−	0.411730i	$-0.864925\pi$
$569$	−590091.			−1.82261			−0.911306	+	0.411730i	$0.864925\pi$
$570$		0			0
$571$			524012.i			1.60720i	0.595172	+	0.803598i	$0.297084\pi$
$571$			524012.i			1.60720i	−0.595172	+	0.803598i	$0.702916\pi$
$572$	262743.	−	245637.i	0.803044	−	0.750761i
$573$		0			0
$574$	−187944.	−	81578.4i	−0.570433	−	0.247600i
$575$			41692.0i			0.126100i
$576$		0			0
$577$	−337273.			−1.01305			−0.506523	−	0.862226i	$-0.669070\pi$
$577$	−337273.			−1.01305			−0.506523	+	0.862226i	$0.669070\pi$
$578$	−97876.1	+	225492.i	−0.292969	+	0.674955i
$579$		0			0
$580$	335146.	+	358486.i	0.996273	+	1.06565i
$581$	−405515.			−1.20131
$582$		0			0
$583$		−	138688.i		−	0.408040i
$584$	417282.	−	148663.i	1.22350	−	0.435892i
$585$		0			0
$586$	−147594.	+	340034.i	−0.429807	+	0.990210i
$587$		−	4289.71i		−	0.0124495i	−0.999981	−	0.00622475i	$-0.998019\pi$
$587$		−	4289.71i		−	0.0124495i	0.999981	−	0.00622475i	$-0.00198141\pi$
$588$		0			0
$589$	519212.			1.49663
$590$	−263105.	−	114202.i	−0.755830	−	0.328073i
$591$		0			0
$592$	−46475.7	+	689839.i	−0.132612	+	1.96836i
$593$	−150227.			−0.427207			−0.213604	−	0.976920i	$-0.568520\pi$
$593$	−150227.			−0.427207			−0.213604	+	0.976920i	$0.568520\pi$
$594$		0			0
$595$			369126.i			1.04266i
$596$	−121000.	−	129426.i	−0.340637	−	0.364359i
$597$		0			0
$598$	−103670.	−	44998.8i	−0.289902	−	0.125834i
$599$		−	473108.i		−	1.31858i	−0.751888	−	0.659290i	$-0.770857\pi$
$599$		−	473108.i		−	1.31858i	0.751888	−	0.659290i	$-0.229143\pi$
$600$		0			0
$601$	−83320.1			−0.230675			−0.115338	−	0.993326i	$-0.536795\pi$
$601$	−83320.1			−0.230675			−0.115338	+	0.993326i	$0.536795\pi$
$602$	116256.	−	267835.i	0.320790	−	0.739052i
$603$		0			0
$604$	−320834.	+	299946.i	−0.879441	+	0.822185i
$605$	118695.			0.324280
$606$		0			0
$607$			143905.i			0.390570i	0.980747	+	0.195285i	$0.0625632\pi$
$607$			143905.i			0.390570i	−0.980747	+	0.195285i	$0.937437\pi$
$608$	−206574.	+	399924.i	−0.558816	+	1.08186i
$609$		0			0
$610$	180159.	−	415059.i	0.484169	−	1.11545i
$611$		−	212582.i		−	0.569435i
$612$		0			0
$613$	−5563.04			−0.0148044			−0.00740221	−	0.999973i	$-0.502356\pi$
$613$	−5563.04			−0.0148044			−0.00740221	+	0.999973i	$0.502356\pi$
$614$	318683.	+	138326.i	0.845321	+	0.366917i
$615$		0			0
$616$	271102.	−	96584.6i	0.714449	−	0.254534i
$617$	300749.			0.790012			0.395006	−	0.918679i	$-0.370743\pi$
$617$	300749.			0.790012			0.395006	+	0.918679i	$0.370743\pi$
$618$		0			0
$619$		−	158539.i		−	0.413767i	−0.978366	−	0.206883i	$-0.933668\pi$
$619$		−	158539.i		−	0.413767i	0.978366	−	0.206883i	$-0.0663321\pi$
$620$	−406675.	+	380199.i	−1.05795	+	0.989070i
$621$		0			0
$622$	161230.	+	69983.1i	0.416741	+	0.180889i
$623$		−	189267.i		−	0.487640i
$624$		0			0
$625$	−483419.			−1.23755
$626$	160542.	−	369863.i	0.409675	−	0.943828i
$627$		0			0
$628$	−159604.	−	170718.i	−0.404691	−	0.432873i
$629$	1.02834e6			2.59918
$630$		0			0
$631$			557374.i			1.39987i	0.714206	+	0.699936i	$0.246788\pi$
$631$			557374.i			1.39987i	−0.714206	+	0.699936i	$0.753212\pi$
$632$	221401.	+	621449.i	0.554301	+	1.55586i
$633$		0			0
$634$	−162429.	+	374213.i	−0.404098	+	0.930979i
$635$		−	223643.i		−	0.554635i
$636$		0			0
$637$	216831.			0.534370
$638$	−522023.	−	226588.i	−1.28247	−	0.556667i
$639$		0			0
$640$	−131048.	−	464508.i	−0.319942	−	1.13405i
$641$	−101106.			−0.246071			−0.123036	−	0.992402i	$-0.539263\pi$
$641$	−101106.			−0.246071			−0.123036	+	0.992402i	$0.539263\pi$
$642$		0			0
$643$		−	406950.i		−	0.984281i	−0.870516	−	0.492141i	$-0.836215\pi$
$643$		−	406950.i		−	0.984281i	0.870516	−	0.492141i	$-0.163785\pi$
$644$	−61755.1	−	66055.6i	−0.148902	−	0.159271i
$645$		0			0
$646$	614126.	+	266565.i	1.47161	+	0.638761i
$647$			427706.i			1.02173i	0.859660	+	0.510866i	$0.170675\pi$
$647$			427706.i			1.02173i	−0.859660	+	0.510866i	$0.829325\pi$
$648$		0			0
$649$	332601.			0.789648
$650$	−63613.3	+	146555.i	−0.150564	+	0.346876i
$651$		0			0
$652$	456588.	−	426862.i	1.07406	−	1.00414i
$653$	−430055.			−1.00855			−0.504275	−	0.863543i	$-0.668240\pi$
$653$	−430055.			−1.00855			−0.504275	+	0.863543i	$0.668240\pi$
$654$		0			0
$655$			98227.4i			0.228955i
$656$	26783.1	−	397542.i	0.0622377	−	0.923793i
$657$		0			0
$658$	67725.4	−	156029.i	0.156423	−	0.360374i
$659$		−	179686.i		−	0.413755i	−0.978367	−	0.206878i	$-0.933670\pi$
$659$		−	179686.i		−	0.413755i	0.978367	−	0.206878i	$-0.0663302\pi$
$660$		0			0
$661$	−539348.			−1.23443			−0.617214	−	0.786795i	$-0.711739\pi$
$661$	−539348.			−1.23443			−0.617214	+	0.786795i	$0.711739\pi$
$662$	145588.	+	63193.4i	0.332208	+	0.144197i
$663$		0			0
$664$	−264660.	−	742872.i	−0.600279	−	1.68492i
$665$	426148.			0.963645
$666$		0			0
$667$			178809.i			0.401918i
$668$	36502.7	−	34126.2i	0.0818036	−	0.0764777i
$669$		0			0
$670$	−254290.	−	110376.i	−0.566473	−	0.245881i
$671$			524693.i			1.16536i
$672$		0			0
$673$	−758520.			−1.67470			−0.837350	−	0.546667i	$-0.815896\pi$
$673$	−758520.			−1.67470			−0.837350	+	0.546667i	$0.815896\pi$
$674$	205970.	−	474523.i	0.453403	−	1.04457i
$675$		0			0
$676$	16319.5	+	17456.0i	0.0357120	+	0.0381989i
$677$	394155.			0.859982			0.429991	−	0.902833i	$-0.358517\pi$
$677$	394155.			0.859982			0.429991	+	0.902833i	$0.358517\pi$
$678$		0			0
$679$			268542.i			0.582468i
$680$	−676211.	+	240911.i	−1.46239	+	0.521002i
$681$		0			0
$682$	257047.	−	592197.i	0.552642	−	1.27320i
$683$			483705.i			1.03691i	0.855106	+	0.518453i	$0.173492\pi$
$683$			483705.i			1.03691i	−0.855106	+	0.518453i	$0.826508\pi$
$684$		0			0
$685$	−348303.			−0.742294
$686$	449079.	+	194926.i	0.954277	+	0.414210i
$687$		0			0
$688$	566528.	+	38168.1i	1.19686	+	0.0806349i
$689$	−166989.			−0.351763
$690$		0			0
$691$			136607.i			0.286098i	0.989716	+	0.143049i	$0.0456907\pi$
$691$			136607.i			0.286098i	−0.989716	+	0.143049i	$0.954309\pi$
$692$	554533.	+	593150.i	1.15802	+	1.23866i
$693$		0			0
$694$	640219.	+	277891.i	1.32926	+	0.576974i
$695$		−	163325.i		−	0.338130i
$696$		0			0
$697$	−592615.			−1.21985
$698$	62784.9	−	144647.i	0.128868	−	0.296892i
$699$		0			0
$700$	−93380.6	+	87301.1i	−0.190573	+	0.178165i
$701$	−878847.			−1.78845			−0.894226	−	0.447617i	$-0.852273\pi$
$701$	−878847.			−1.78845			−0.894226	+	0.447617i	$0.852273\pi$
$702$		0			0
$703$		−	1.18720e6i		−	2.40222i
$704$	353871.	+	433602.i	0.714002	+	0.874875i
$705$		0			0
$706$	−196026.	+	451613.i	−0.393282	+	0.906061i
$707$			376502.i			0.753231i
$708$		0			0
$709$	445304.			0.885857			0.442929	−	0.896557i	$-0.353939\pi$
$709$	445304.			0.885857			0.442929	+	0.896557i	$0.353939\pi$
$710$	95557.4	+	41477.3i	0.189560	+	0.0822800i
$711$		0			0
$712$	346723.	−	123526.i	0.683948	−	0.243668i
$713$	−202846.			−0.399012
$714$		0			0
$715$		−	662220.i		−	1.29536i
$716$	−52088.4	+	48697.2i	−0.101605	+	0.0949900i
$717$		0			0
$718$	76933.2	+	33393.4i	0.149233	+	0.0647756i
$719$			731078.i			1.41418i	0.707121	+	0.707092i	$0.249993\pi$
$719$			731078.i			1.41418i	−0.707121	+	0.707092i	$0.750007\pi$
$720$		0			0
$721$	385836.			0.742219
$722$	100186.	−	230813.i	0.192191	−	0.442778i
$723$		0			0
$724$	92470.3	+	98909.8i	0.176411	+	0.188696i
$725$	252776.			0.480906
$726$		0			0
$727$			992100.i			1.87710i	0.345147	+	0.938549i	$0.387829\pi$
$727$			992100.i			1.87710i	−0.345147	+	0.938549i	$0.612171\pi$
$728$	−116294.	−	326423.i	−0.219429	−	0.615912i
$729$		0			0
$730$	324731.	−	748131.i	0.609366	−	1.40389i
$731$		−	844524.i		−	1.58044i
$732$		0			0
$733$	−121286.			−0.225737			−0.112868	−	0.993610i	$-0.536004\pi$
$733$	−121286.			−0.225737			−0.112868	+	0.993610i	$0.536004\pi$
$734$	−213920.	−	92853.6i	−0.397064	−	0.172348i
$735$		0			0
$736$	80704.2	−	156242.i	0.148984	−	0.288431i
$737$	321457.			0.591818
$738$		0			0
$739$			273800.i			0.501355i	0.968071	+	0.250677i	$0.0806534\pi$
$739$			273800.i			0.501355i	−0.968071	+	0.250677i	$0.919347\pi$
$740$	869338.	+	929878.i	1.58754	+	1.69810i
$741$		0			0
$742$	−122565.	−	53200.3i	−0.222618	−	0.0966287i
$743$		−	389402.i		−	0.705376i	−0.935741	−	0.352688i	$-0.885268\pi$
$743$		−	389402.i		−	0.705376i	0.935741	−	0.352688i	$-0.114732\pi$
$744$		0			0
$745$	−326207.			−0.587733
$746$	127055.	−	292716.i	0.228305	−	0.525979i
$747$		0			0
$748$	608071.	−	568483.i	1.08680	−	1.01605i
$749$	698489.			1.24508
$750$		0			0
$751$			430569.i			0.763419i	0.924282	+	0.381710i	$0.124665\pi$
$751$			430569.i			0.763419i	−0.924282	+	0.381710i	$0.875335\pi$
$752$	330034.	+	22235.0i	0.583611	+	0.0393189i
$753$		0			0
$754$	−272825.	+	628548.i	−0.479891	+	1.10559i
$755$			808633.i			1.41859i
$756$		0			0
$757$	−1.04226e6			−1.81880			−0.909401	−	0.415920i	$-0.863460\pi$
$757$	−1.04226e6			−1.81880			−0.909401	+	0.415920i	$0.863460\pi$
$758$	296762.	+	128812.i	0.516500	+	0.224190i
$759$		0			0
$760$	278127.	+	780670.i	0.481521	+	1.35158i
$761$	117139.			0.202271			0.101135	−	0.994873i	$-0.467752\pi$
$761$	117139.			0.202271			0.101135	+	0.994873i	$0.467752\pi$
$762$		0			0
$763$			189318.i			0.325195i
$764$	−206865.	+	193397.i	−0.354405	+	0.331331i
$765$		0			0
$766$	−366264.	−	158979.i	−0.624219	−	0.270946i
$767$		−	400471.i		−	0.680739i
$768$		0			0
$769$	−104458.			−0.176639			−0.0883197	−	0.996092i	$-0.528150\pi$
$769$	−104458.			−0.176639			−0.0883197	+	0.996092i	$0.528150\pi$
$770$	210973.	−	486050.i	0.355833	−	0.819785i
$771$		0			0
$772$	−119589.	−	127917.i	−0.200658	−	0.214631i
$773$	−34677.2			−0.0580343			−0.0290172	−	0.999579i	$-0.509238\pi$
$773$	−34677.2			−0.0580343			−0.0290172	+	0.999579i	$0.509238\pi$
$774$		0			0
$775$			286756.i			0.477429i
$776$	−491948.	+	175264.i	−0.816950	+	0.291052i
$777$		0			0
$778$	24818.7	−	57178.4i	0.0410034	−	0.0944654i
$779$			684161.i			1.12741i
$780$		0			0
$781$	−120798.			−0.198042
$782$	−239926.	−	104142.i	−0.392341	−	0.170298i
$783$		0			0
$784$	−22679.4	+	336631.i	−0.0368978	+	0.547674i
$785$	−430280.			−0.698252
$786$		0			0
$787$			1.08172e6i			1.74649i	0.487285	+	0.873243i	$0.337987\pi$
$787$			1.08172e6i			1.74649i	−0.487285	+	0.873243i	$0.662013\pi$
$788$	110376.	+	118062.i	0.177755	+	0.190133i
$789$		0			0
$790$	1.11418e6	+	483615.i	1.78525	+	0.774900i
$791$		−	198074.i		−	0.316573i
$792$		0			0
$793$	631762.			1.00463
$794$	107117.	−	246781.i	0.169910	−	0.391446i
$795$		0			0
$796$	−366935.	+	343046.i	−0.579112	+	0.541409i
$797$	370822.			0.583779			0.291889	−	0.956452i	$-0.405716\pi$
$797$	370822.			0.583779			0.291889	+	0.956452i	$0.405716\pi$
$798$		0			0
$799$		−	491982.i		−	0.770648i
$800$	−220874.	−	114089.i	−0.345116	−	0.178264i
$801$		0			0
$802$	241834.	−	557149.i	0.375983	−	0.866208i
$803$			945741.i			1.46670i
$804$		0			0
$805$	−166487.			−0.256915
$806$	−713041.	−	309500.i	−1.09760	−	0.476421i
$807$		0			0
$808$	−689722.	+	245725.i	−1.05646	+	0.376380i
$809$	763253.			1.16620			0.583098	−	0.812402i	$-0.301840\pi$
$809$	763253.			1.16620			0.583098	+	0.812402i	$0.301840\pi$
$810$		0			0
$811$		−	976424.i		−	1.48456i	−0.670091	−	0.742279i	$-0.733745\pi$
$811$		−	976424.i		−	1.48456i	0.670091	−	0.742279i	$-0.266255\pi$
$812$	−400492.	+	374418.i	−0.607410	+	0.567864i
$813$		0			0
$814$	−1.35408e6	−	587747.i	−2.04360	−	0.887037i
$815$		−	1.15079e6i		−	1.73253i
$816$		0			0
$817$	−974984.			−1.46067
$818$	102202.	−	235459.i	0.152741	−	0.351891i
$819$		0			0
$820$	−500984.	−	535872.i	−0.745068	−	0.796954i
$821$	−1.05933e6			−1.57162			−0.785808	−	0.618470i	$-0.787753\pi$
$821$	−1.05933e6			−1.57162			−0.785808	+	0.618470i	$0.787753\pi$
$822$		0			0
$823$			649256.i			0.958553i	0.877664	+	0.479277i	$0.159101\pi$
$823$			649256.i			0.958553i	−0.877664	+	0.479277i	$0.840899\pi$
$824$	251817.	+	706821.i	0.370877	+	1.04101i
$825$		0			0
$826$	127584.	−	293934.i	0.186998	−	0.430815i
$827$		−	1.23981e6i		−	1.81278i	−0.422439	−	0.906391i	$-0.638826\pi$
$827$		−	1.23981e6i		−	1.81278i	0.422439	−	0.906391i	$-0.361174\pi$
$828$		0			0
$829$	656712.			0.955577			0.477788	−	0.878475i	$-0.341439\pi$
$829$	656712.			0.955577			0.477788	+	0.878475i	$0.341439\pi$
$830$	−1.33187e6	−	578108.i	−1.93333	−	0.839175i
$831$		0			0
$832$	522083.	−	426082.i	0.754211	−	0.615526i
$833$	501816.			0.723194
$834$		0			0
$835$		−	92001.8i		−	0.131954i
$836$	−656300.	−	702004.i	−0.939053	−	1.00445i
$837$		0			0
$838$	312517.	+	135650.i	0.445027	+	0.193167i
$839$		−	895246.i		−	1.27180i	−0.771772	−	0.635899i	$-0.780629\pi$
$839$		−	895246.i		−	1.27180i	0.771772	−	0.635899i	$-0.219371\pi$
$840$		0			0
$841$	376830.			0.532787
$842$	−342257.	+	788507.i	−0.482756	+	1.11220i
$843$		0			0
$844$	−974314.	+	910881.i	−1.36777	+	1.27872i
$845$	43996.2			0.0616172
$846$		0			0
$847$			132603.i			0.184836i
$848$	17466.2	−	259251.i	0.0242889	−	0.360520i
$849$		0			0
$850$	−147221.	+	339176.i	−0.203767	+	0.469447i
$851$			463814.i			0.640449i
$852$		0			0
$853$	1.15283e6			1.58441			0.792206	−	0.610254i	$-0.208933\pi$
$853$	1.15283e6			1.58441			0.792206	+	0.610254i	$0.208933\pi$
$854$	463695.	+	201270.i	0.635794	+	0.275971i
$855$		0			0
$856$	455871.	+	1.27958e6i	0.622149	+	1.74630i
$857$	−576402.			−0.784809			−0.392404	−	0.919793i	$-0.628357\pi$
$857$	−576402.			−0.784809			−0.392404	+	0.919793i	$0.628357\pi$
$858$		0			0
$859$		−	365493.i		−	0.495327i	−0.968846	−	0.247664i	$-0.920337\pi$
$859$		−	365493.i		−	0.495327i	0.968846	−	0.247664i	$-0.0796628\pi$
$860$	763660.	−	713942.i	1.03253	−	0.965308i
$861$		0			0
$862$	−72966.3	−	31671.5i	−0.0981992	−	0.0426240i
$863$		−	233229.i		−	0.313156i	−0.987666	−	0.156578i	$-0.949954\pi$
$863$		−	233229.i		−	0.313156i	0.987666	−	0.156578i	$-0.0500463\pi$
$864$		0			0
$865$	1.49498e6			1.99804
$866$	−165631.	+	381588.i	−0.220854	+	0.508814i
$867$		0			0
$868$	−424749.	−	454328.i	−0.563759	−	0.603018i
$869$	−1.40847e6			−1.86513
$870$		0			0
$871$		−	387054.i		−	0.510194i
$872$	−346816.	+	123559.i	−0.456107	+	0.162496i
$873$		0			0
$874$	−120229.	+	276989.i	−0.157393	+	0.362610i
$875$		−	370553.i		−	0.483987i
$876$		0			0
$877$	−939899.			−1.22203			−0.611015	−	0.791619i	$-0.709238\pi$
$877$	−939899.			−1.22203			−0.611015	+	0.791619i	$0.709238\pi$
$878$	205318.	+	89119.8i	0.266341	+	0.115607i
$879$		0			0
$880$	1.02810e6	+	69264.9i	1.32761	+	0.0894434i
$881$	−918880.			−1.18388			−0.591939	−	0.805983i	$-0.701637\pi$
$881$	−918880.			−1.18388			−0.591939	+	0.805983i	$0.701637\pi$
$882$		0			0
$883$		−	842123.i		−	1.08008i	−0.841641	−	0.540038i	$-0.818410\pi$
$883$		−	842123.i		−	1.08008i	0.841641	−	0.540038i	$-0.181590\pi$
$884$	−684488.	−	732155.i	−0.875913	−	0.936911i
$885$		0			0
$886$	−82952.3	−	36006.0i	−0.105672	−	0.0458677i
$887$			255495.i			0.324740i	0.986730	+	0.162370i	$0.0519138\pi$
$887$			255495.i			0.324740i	−0.986730	+	0.162370i	$0.948086\pi$
$888$		0			0
$889$	249849.			0.316136
$890$	269822.	−	621629.i	0.340642	−	0.784786i
$891$		0			0
$892$	−155464.	+	145342.i	−0.195389	+	0.182668i
$893$	−567982.			−0.712249
$894$		0			0
$895$			131284.i			0.163895i
$896$	518937.	−	146404.i	0.646396	−	0.182363i
$897$		0			0
$898$	123555.	−	284651.i	0.153217	−	0.352989i
$899$			1.22984e6i			1.52170i
$900$		0			0
$901$	−386466.			−0.476060
$902$	780331.	+	338708.i	0.959105	+	0.416306i
$903$		0			0
$904$	362855.	−	129273.i	0.444014	−	0.158187i
$905$	249293.			0.304378
$906$		0			0
$907$		−	1.42137e6i		−	1.72780i	−0.503663	−	0.863900i	$-0.668014\pi$
$907$		−	1.42137e6i		−	1.72780i	0.503663	−	0.863900i	$-0.331986\pi$
$908$	−585271.	+	547167.i	−0.709880	+	0.663664i
$909$		0			0
$910$	−585234.	−	254025.i	−0.706719	−	0.306756i
$911$			42728.5i			0.0514851i	0.999669	+	0.0257425i	$0.00819501\pi$
$911$			42728.5i			0.0514851i	−0.999669	+	0.0257425i	$0.991805\pi$
$912$		0			0
$913$	1.68367e6			2.01983
$914$	386794.	−	891115.i	0.463007	−	1.06670i
$915$		0			0
$916$	−656045.	−	701731.i	−0.781885	−	0.836334i
$917$	−109737.			−0.130502
$918$		0			0
$919$		−	32211.9i		−	0.0381404i	−0.999818	−	0.0190702i	$-0.993929\pi$
$919$		−	32211.9i		−	0.0381404i	0.999818	−	0.0190702i	$-0.00607060\pi$
$920$	−108658.	−	304992.i	−0.128377	−	0.360340i
$921$		0			0
$922$	−317960.	+	732531.i	−0.374034	+	0.861716i
$923$			145448.i			0.170728i
$924$		0			0
$925$	655678.			0.766315
$926$	232964.	+	101120.i	0.271686	+	0.117927i
$927$		0			0
$928$	−947287.	−	489306.i	−1.09998	−	0.568178i
$929$	1.39589e6			1.61741			0.808706	−	0.588214i	$-0.200169\pi$
$929$	1.39589e6			1.61741			0.808706	+	0.588214i	$0.200169\pi$
$930$		0			0
$931$		−	579335.i		−	0.668391i
$932$	−341485.	−	365266.i	−0.393134	−	0.420511i
$933$		0			0
$934$	−414558.	−	179942.i	−0.475217	−	0.206271i
$935$		−	1.53259e6i		−	1.75308i
$936$		0			0
$937$	−525528.			−0.598572			−0.299286	−	0.954163i	$-0.596749\pi$
$937$	−525528.			−0.598572			−0.299286	+	0.954163i	$0.596749\pi$
$938$	123310.	−	284087.i	0.140149	−	0.322883i
$939$		0			0
$940$	444874.	−	415911.i	0.503479	−	0.470700i
$941$	1.40325e6			1.58473			0.792364	−	0.610048i	$-0.208850\pi$
$941$	1.40325e6			1.58473			0.792364	+	0.610048i	$0.208850\pi$
$942$		0			0
$943$		−	267287.i		−	0.300577i
$944$	621733.	+	41887.3i	0.697686	+	0.0470044i
$945$		0			0
$946$	−482686.	+	1.11203e6i	−0.539365	+	1.24261i
$947$			1.40028e6i			1.56140i	0.624905	+	0.780701i	$0.285138\pi$
$947$			1.40028e6i			1.56140i	−0.624905	+	0.780701i	$0.714862\pi$
$948$		0			0
$949$	1.13873e6			1.26441
$950$	391570.	+	169964.i	0.433873	+	0.188325i
$951$		0			0
$952$	−269141.	−	755448.i	−0.296965	−	0.833548i
$953$	−537716.			−0.592062			−0.296031	−	0.955178i	$-0.595663\pi$
$953$	−537716.			−0.592062			−0.296031	+	0.955178i	$0.595663\pi$
$954$		0			0
$955$			521384.i			0.571677i
$956$	734963.	−	687113.i	0.804174	−	0.751818i
$957$		0			0
$958$	−1.15008e6	−	499200.i	−1.25313	−	0.543931i
$959$		−	389116.i		−	0.423099i
$960$		0			0
$961$	−471644.			−0.510701
$962$	−707683.	+	1.63039e6i	−0.764696	+	1.76174i
$963$		0			0
$964$	−706016.	−	755182.i	−0.759732	−	0.812639i
$965$	−322403.			−0.346213
$966$		0			0
$967$		−	153678.i		−	0.164346i	−0.996618	−	0.0821732i	$-0.973814\pi$
$967$		−	153678.i		−	0.164346i	0.996618	−	0.0821732i	$-0.0261861\pi$
$968$	−242918.	+	86543.6i	−0.259244	+	0.0923601i
$969$		0			0
$970$	−382837.	+	881997.i	−0.406884	+	0.937397i
$971$			36471.1i			0.0386821i	0.999813	+	0.0193411i	$0.00615683\pi$
$971$			36471.1i			0.0386821i	−0.999813	+	0.0193411i	$0.993843\pi$
$972$		0			0
$973$	182463.			0.192730
$974$	−238320.	−	103444.i	−0.251214	−	0.109041i
$975$		0			0
$976$	−66079.2	+	980813.i	−0.0693689	+	1.02964i
$977$	−1.18898e6			−1.24562			−0.622811	−	0.782373i	$-0.714009\pi$
$977$	−1.18898e6			−1.24562			−0.622811	+	0.782373i	$0.714009\pi$
$978$		0			0
$979$			785825.i			0.819900i
$980$	424224.	+	453766.i	0.441716	+	0.472476i
$981$		0			0
$982$	1.31574e6	+	571106.i	1.36442	+	0.592235i
$983$		−	890220.i		−	0.921277i	−0.887588	−	0.460639i	$-0.847620\pi$
$983$		−	890220.i		−	0.921277i	0.887588	−	0.460639i	$-0.152380\pi$
$984$		0			0
$985$	297565.			0.306697
$986$	−631405.	+	1.45466e6i	−0.649463	+	1.49626i
$987$		0			0
$988$	−845256.	+	790225.i	−0.865913	+	0.809538i
$989$	380906.			0.389426
$990$		0			0
$991$			844659.i			0.860070i	0.902812	+	0.430035i	$0.141499\pi$
$991$			844659.i			0.860070i	−0.902812	+	0.430035i	$0.858501\pi$
$992$	555081.	−	1.07463e6i	0.564070	−	1.09203i
$993$		0			0
$994$	−46337.5	+	106755.i	−0.0468986	+	0.108047i
$995$			924826.i			0.934144i
$996$		0			0
$997$	1.30909e6			1.31698			0.658492	−	0.752587i	$-0.271194\pi$
$997$	1.30909e6			1.31698			0.658492	+	0.752587i	$0.271194\pi$
$998$	−46586.0	−	20221.0i	−0.0467729	−	0.0203021i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.d.a.55.6	yes	16
3.2	odd	2	inner	108.5.d.a.55.11	yes	16
4.3	odd	2	inner	108.5.d.a.55.5	✓	16
12.11	even	2	inner	108.5.d.a.55.12	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.5.d.a.55.5	✓	16	4.3	odd	2	inner
108.5.d.a.55.6	yes	16	1.1	even	1	trivial
108.5.d.a.55.11	yes	16	3.2	odd	2	inner
108.5.d.a.55.12	yes	16	12.11	even	2	inner

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59266 + 3.66925i) q^{2} +(-10.9268 - 11.6878i) q^{4} -29.4580 q^{5} -32.9098i q^{7} +(60.2882 - 21.4787i) q^{8} +O(q^{10})\)	\(q+(-1.59266 + 3.66925i) q^{2} +(-10.9268 - 11.6878i) q^{4} -29.4580 q^{5} -32.9098i q^{7} +(60.2882 - 21.4787i) q^{8} +(46.9167 - 108.089i) q^{10} +136.639i q^{11} +164.522 q^{13} +(120.754 + 52.4142i) q^{14} +(-17.2082 + 255.421i) q^{16} +380.756 q^{17} -439.574i q^{19} +(321.883 + 344.298i) q^{20} +(-501.364 - 217.620i) q^{22} +171.733i q^{23} +242.773 q^{25} +(-262.028 + 603.673i) q^{26} +(-384.642 + 359.600i) q^{28} +1041.21 q^{29} +1181.17i q^{31} +(-909.798 - 469.941i) q^{32} +(-606.417 + 1397.09i) q^{34} +969.456i q^{35} +2700.79 q^{37} +(1612.91 + 700.094i) q^{38} +(-1775.97 + 632.718i) q^{40} -1556.42 q^{41} -2218.02i q^{43} +(1597.01 - 1493.04i) q^{44} +(-630.130 - 273.512i) q^{46} -1292.12i q^{47} +1317.95 q^{49} +(-386.655 + 890.794i) q^{50} +(-1797.71 - 1922.90i) q^{52} -1015.00 q^{53} -4025.12i q^{55} +(-706.858 - 1984.07i) q^{56} +(-1658.29 + 3820.45i) q^{58} -2434.15i q^{59} +3839.98 q^{61} +(-4334.02 - 1881.21i) q^{62} +(3173.33 - 2589.82i) q^{64} -4846.48 q^{65} -2352.60i q^{67} +(-4160.46 - 4450.19i) q^{68} +(-3557.18 - 1544.02i) q^{70} +884.064i q^{71} +6921.45 q^{73} +(-4301.45 + 9909.89i) q^{74} +(-5137.65 + 4803.16i) q^{76} +4496.77 q^{77} +10308.0i q^{79} +(506.918 - 7524.19i) q^{80} +(2478.85 - 5710.89i) q^{82} -12322.0i q^{83} -11216.3 q^{85} +(8138.47 + 3532.56i) q^{86} +(2934.83 + 8237.73i) q^{88} +5751.10 q^{89} -5414.38i q^{91} +(2007.17 - 1876.49i) q^{92} +(4741.11 + 2057.91i) q^{94} +12949.0i q^{95} -8159.93 q^{97} +(-2099.04 + 4835.88i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{4}+O(q^{10}) \) 16 * q - 14 * q^4	\( 16 q - 14 q^{4} - 202 q^{10} - 352 q^{13} - 206 q^{16} + 738 q^{22} + 1632 q^{25} + 342 q^{28} - 2536 q^{34} + 3200 q^{37} - 2854 q^{40} + 36 q^{46} - 896 q^{49} + 2288 q^{52} + 2492 q^{58} - 2752 q^{61} + 682 q^{64} - 14166 q^{70} + 8240 q^{73} - 33084 q^{76} + 68 q^{82} + 8800 q^{85} + 48294 q^{88} + 52596 q^{94} - 6928 q^{97}+O(q^{100}) \) 16 * q - 14 * q^4 - 202 * q^10 - 352 * q^13 - 206 * q^16 + 738 * q^22 + 1632 * q^25 + 342 * q^28 - 2536 * q^34 + 3200 * q^37 - 2854 * q^40 + 36 * q^46 - 896 * q^49 + 2288 * q^52 + 2492 * q^58 - 2752 * q^61 + 682 * q^64 - 14166 * q^70 + 8240 * q^73 - 33084 * q^76 + 68 * q^82 + 8800 * q^85 + 48294 * q^88 + 52596 * q^94 - 6928 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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