LMFDB - Embedded newform 400.3.bg.a.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(17,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("400.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, 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:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
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} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			33.1
Root			$1.84816i$ of defining polynomial
Character	$\chi$	$=$	400.33
Dual form			400.3.bg.a.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50268 - 0.396386i) q^{3} +(-3.83232 - 3.21144i) q^{5} +(1.84619 - 1.84619i) q^{7} +(-2.45322 - 0.797099i) q^{9} +O(q^{10})$	\(q+(-2.50268 - 0.396386i) q^{3} +(-3.83232 - 3.21144i) q^{5} +(1.84619 - 1.84619i) q^{7} +(-2.45322 - 0.797099i) q^{9} +(-0.224918 - 0.692225i) q^{11} +(10.9494 - 5.57900i) q^{13} +(8.31810 + 9.55628i) q^{15} +(-20.9271 + 3.31453i) q^{17} +(4.52135 - 6.22310i) q^{19} +(-5.35223 + 3.88862i) q^{21} +(-18.0093 + 35.3452i) q^{23} +(4.37333 + 24.6145i) q^{25} +(26.1430 + 13.3205i) q^{27} +(28.3088 + 38.9637i) q^{29} +(-31.6215 - 22.9744i) q^{31} +(0.288509 + 1.82157i) q^{33} +(-13.0041 + 1.14626i) q^{35} +(8.18285 + 16.0598i) q^{37} +(-29.6143 + 9.62228i) q^{39} +(-2.02980 + 6.24709i) q^{41} +(-15.0496 - 15.0496i) q^{43} +(6.84168 + 10.9331i) q^{45} +(-13.1485 + 83.0166i) q^{47} +42.1832i q^{49} +53.6878 q^{51} +(-64.5712 - 10.2271i) q^{53} +(-1.36108 + 3.37514i) q^{55} +(-13.7822 + 13.7822i) q^{57} +(74.4974 + 24.2057i) q^{59} +(-20.0819 - 61.8056i) q^{61} +(-6.00071 + 3.05752i) q^{63} +(-59.8783 - 13.7828i) q^{65} +(-61.2025 + 9.69353i) q^{67} +(59.0818 - 81.3191i) q^{69} +(43.2855 - 31.4488i) q^{71} +(-15.4463 + 30.3151i) q^{73} +(-1.18821 - 63.3358i) q^{75} +(-1.69322 - 0.862739i) q^{77} +(13.7883 + 18.9780i) q^{79} +(-41.3660 - 30.0541i) q^{81} +(8.10529 + 51.1748i) q^{83} +(90.8439 + 54.5039i) q^{85} +(-55.4032 - 108.735i) q^{87} +(142.975 - 46.4555i) q^{89} +(9.91480 - 30.5146i) q^{91} +(70.0319 + 70.0319i) q^{93} +(-37.3123 + 9.32888i) q^{95} +(9.98239 - 63.0263i) q^{97} +1.87746i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9	$ 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9} - 32 q^{11} - 8 q^{13} - 62 q^{17} - 30 q^{19} - 68 q^{21} + 18 q^{23} + 70 q^{25} + 40 q^{27} + 100 q^{29} - 132 q^{31} - 36 q^{33} - 150 q^{35} + 138 q^{37} + 320 q^{39} - 88 q^{41} + 78 q^{43} - 20 q^{45} + 22 q^{47} + 168 q^{51} + 182 q^{53} - 280 q^{55} + 280 q^{57} + 350 q^{59} + 372 q^{61} - 22 q^{63} - 910 q^{65} + 112 q^{67} - 30 q^{69} - 122 q^{71} - 248 q^{73} + 80 q^{75} + 16 q^{77} - 760 q^{79} - 144 q^{81} - 132 q^{83} - 30 q^{85} - 770 q^{87} + 550 q^{89} + 798 q^{91} + 54 q^{93} - 40 q^{95} - 292 q^{97}+O(q^{100}) $ 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9 - 32 * q^11 - 8 * q^13 - 62 * q^17 - 30 * q^19 - 68 * q^21 + 18 * q^23 + 70 * q^25 + 40 * q^27 + 100 * q^29 - 132 * q^31 - 36 * q^33 - 150 * q^35 + 138 * q^37 + 320 * q^39 - 88 * q^41 + 78 * q^43 - 20 * q^45 + 22 * q^47 + 168 * q^51 + 182 * q^53 - 280 * q^55 + 280 * q^57 + 350 * q^59 + 372 * q^61 - 22 * q^63 - 910 * q^65 + 112 * q^67 - 30 * q^69 - 122 * q^71 - 248 * q^73 + 80 * q^75 + 16 * q^77 - 760 * q^79 - 144 * q^81 - 132 * q^83 - 30 * q^85 - 770 * q^87 + 550 * q^89 + 798 * q^91 + 54 * q^93 - 40 * q^95 - 292 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{20}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.50268	−	0.396386i	−0.834227	−	0.132129i	−0.275313	−	0.961355i	$-0.588782\pi$
$3$	−2.50268	−	0.396386i	−0.834227	−	0.132129i	−0.558913	+	0.829226i	$0.688782\pi$
$4$		0			0
$5$	−3.83232	−	3.21144i	−0.766464	−	0.642288i
$5$	−3.83232	−	3.21144i	−0.766464	−	0.642288i
$6$		0			0
$7$	1.84619	−	1.84619i	0.263742	−	0.263742i	−0.562831	−	0.826572i	$-0.690288\pi$
$7$	1.84619	−	1.84619i	0.263742	−	0.263742i	0.826572	+	0.562831i	$0.190288\pi$
$8$		0			0
$9$	−2.45322	−	0.797099i	−0.272580	−	0.0885666i
$10$		0			0
$11$	−0.224918	−	0.692225i	−0.0204470	−	0.0629295i	0.940312	−	0.340313i	$-0.110533\pi$
$11$	−0.224918	−	0.692225i	−0.0204470	−	0.0629295i	−0.960759	+	0.277383i	$0.910533\pi$
$12$		0			0
$13$	10.9494	−	5.57900i	0.842262	−	0.429154i	0.0210512	−	0.999778i	$-0.493299\pi$
$13$	10.9494	−	5.57900i	0.842262	−	0.429154i	0.821211	+	0.570624i	$0.193299\pi$
$14$		0			0
$15$	8.31810	+	9.55628i	0.554540	+	0.637085i
$16$		0			0
$17$	−20.9271	+	3.31453i	−1.23101	+	0.194973i	−0.737849	−	0.674966i	$-0.764158\pi$
$17$	−20.9271	+	3.31453i	−1.23101	+	0.194973i	−0.493160	+	0.869939i	$0.664158\pi$
$18$		0			0
$19$	4.52135	−	6.22310i	0.237966	−	0.327532i	−0.673286	−	0.739382i	$-0.735118\pi$
$19$	4.52135	−	6.22310i	0.237966	−	0.327532i	0.911251	+	0.411851i	$0.135118\pi$
$20$		0			0
$21$	−5.35223	+	3.88862i	−0.254868	+	0.185173i
$22$		0			0
$23$	−18.0093	+	35.3452i	−0.783012	+	1.53675i	0.0595970	+	0.998223i	$0.481018\pi$
$23$	−18.0093	+	35.3452i	−0.783012	+	1.53675i	−0.842609	+	0.538525i	$0.818982\pi$
$24$		0			0
$25$	4.37333	+	24.6145i	0.174933	+	0.984580i
$26$		0			0
$27$	26.1430	+	13.3205i	0.968258	+	0.493352i
$28$		0			0
$29$	28.3088	+	38.9637i	0.976165	+	1.34358i	0.938870	+	0.344272i	$0.111874\pi$
$29$	28.3088	+	38.9637i	0.976165	+	1.34358i	0.0372955	+	0.999304i	$0.488126\pi$
$30$		0			0
$31$	−31.6215	−	22.9744i	−1.02005	−	0.741110i	−0.0537567	−	0.998554i	$-0.517120\pi$
$31$	−31.6215	−	22.9744i	−1.02005	−	0.741110i	−0.966293	+	0.257445i	$0.917120\pi$
$32$		0			0
$33$	0.288509	+	1.82157i	0.00874269	+	0.0551992i
$34$		0			0
$35$	−13.0041	+	1.14626i	−0.371546	+	0.0327504i
$36$		0			0
$37$	8.18285	+	16.0598i	0.221158	+	0.434047i	0.974751	−	0.223294i	$-0.0716810\pi$
$37$	8.18285	+	16.0598i	0.221158	+	0.434047i	−0.753593	+	0.657341i	$0.771681\pi$
$38$		0			0
$39$	−29.6143	+	9.62228i	−0.759342	+	0.246725i
$40$		0			0
$41$	−2.02980	+	6.24709i	−0.0495074	+	0.152368i	−0.972754	−	0.231840i	$-0.925525\pi$
$41$	−2.02980	+	6.24709i	−0.0495074	+	0.152368i	0.923247	+	0.384208i	$0.125525\pi$
$42$		0			0
$43$	−15.0496	−	15.0496i	−0.349990	−	0.349990i	0.510116	−	0.860106i	$-0.329603\pi$
$43$	−15.0496	−	15.0496i	−0.349990	−	0.349990i	−0.860106	+	0.510116i	$0.829603\pi$
$44$		0			0
$45$	6.84168	+	10.9331i	0.152037	+	0.242958i
$46$		0			0
$47$	−13.1485	+	83.0166i	−0.279756	+	1.76631i	0.302350	+	0.953197i	$0.402229\pi$
$47$	−13.1485	+	83.0166i	−0.279756	+	1.76631i	−0.582106	+	0.813113i	$0.697771\pi$
$48$		0			0
$49$			42.1832i			0.860881i
$50$		0			0
$51$	53.6878			1.05270
$52$		0			0
$53$	−64.5712	−	10.2271i	−1.21832	−	0.192964i	−0.486024	−	0.873945i	$-0.661553\pi$
$53$	−64.5712	−	10.2271i	−1.21832	−	0.192964i	−0.732300	+	0.680982i	$0.761553\pi$
$54$		0			0
$55$	−1.36108	+	3.37514i	−0.0247469	+	0.0613661i
$56$		0			0
$57$	−13.7822	+	13.7822i	−0.241794	+	0.241794i
$58$		0			0
$59$	74.4974	+	24.2057i	1.26267	+	0.410266i	0.862445	−	0.506151i	$-0.168932\pi$
$59$	74.4974	+	24.2057i	1.26267	+	0.410266i	0.400224	+	0.916417i	$0.368932\pi$
$60$		0			0
$61$	−20.0819	−	61.8056i	−0.329211	−	1.01321i	−0.969504	−	0.245076i	$-0.921187\pi$
$61$	−20.0819	−	61.8056i	−0.329211	−	1.01321i	0.640293	−	0.768131i	$-0.278813\pi$
$62$		0			0
$63$	−6.00071	+	3.05752i	−0.0952494	+	0.0485320i
$64$		0			0
$65$	−59.8783	−	13.7828i	−0.921204	−	0.212044i
$66$		0			0
$67$	−61.2025	+	9.69353i	−0.913470	+	0.144679i	−0.595439	−	0.803401i	$-0.703022\pi$
$67$	−61.2025	+	9.69353i	−0.913470	+	0.144679i	−0.318032	+	0.948080i	$0.603022\pi$
$68$		0			0
$69$	59.0818	−	81.3191i	0.856258	−	1.17854i
$70$		0			0
$71$	43.2855	−	31.4488i	0.609656	−	0.442941i	−0.239637	−	0.970862i	$-0.577029\pi$
$71$	43.2855	−	31.4488i	0.609656	−	0.442941i	0.849293	+	0.527922i	$0.177029\pi$
$72$		0			0
$73$	−15.4463	+	30.3151i	−0.211594	+	0.415276i	−0.972272	−	0.233853i	$-0.924866\pi$
$73$	−15.4463	+	30.3151i	−0.211594	+	0.415276i	0.760678	+	0.649129i	$0.224866\pi$
$74$		0			0
$75$	−1.18821	−	63.3358i	−0.0158429	−	0.844477i
$76$		0			0
$77$	−1.69322	−	0.862739i	−0.0219899	−	0.0112044i
$78$		0			0
$79$	13.7883	+	18.9780i	0.174536	+	0.240228i	0.887319	−	0.461157i	$-0.152565\pi$
$79$	13.7883	+	18.9780i	0.174536	+	0.240228i	−0.712783	+	0.701385i	$0.752565\pi$
$80$		0			0
$81$	−41.3660	−	30.0541i	−0.510691	−	0.371039i
$82$		0			0
$83$	8.10529	+	51.1748i	0.0976541	+	0.616564i	0.987172	+	0.159663i	$0.0510407\pi$
$83$	8.10529	+	51.1748i	0.0976541	+	0.616564i	−0.889517	+	0.456901i	$0.848959\pi$
$84$		0			0
$85$	90.8439	+	54.5039i	1.06875	+	0.641222i
$86$		0			0
$87$	−55.4032	−	108.735i	−0.636819	−	1.24983i
$88$		0			0
$89$	142.975	−	46.4555i	1.60646	−	0.521972i	0.637770	−	0.770227i	$-0.279857\pi$
$89$	142.975	−	46.4555i	1.60646	−	0.521972i	0.968695	+	0.248255i	$0.0798570\pi$
$90$		0			0
$91$	9.91480	−	30.5146i	0.108954	−	0.335326i
$92$		0			0
$93$	70.0319	+	70.0319i	0.753031	+	0.753031i
$94$		0			0
$95$	−37.3123	+	9.32888i	−0.392761	+	0.0981987i
$96$		0			0
$97$	9.98239	−	63.0263i	0.102911	−	0.649756i	−0.881273	−	0.472608i	$-0.843313\pi$
$97$	9.98239	−	63.0263i	0.102911	−	0.649756i	0.984184	−	0.177148i	$-0.0566873\pi$
$98$		0			0
$99$			1.87746i			0.0189643i
$100$		0			0
$101$	−60.0228			−0.594285			−0.297142	−	0.954833i	$-0.596034\pi$
$101$	−60.0228			−0.594285			−0.297142	+	0.954833i	$0.596034\pi$
$102$		0			0
$103$	−36.9917	−	5.85890i	−0.359142	−	0.0568825i	−0.0257438	−	0.999669i	$-0.508195\pi$
$103$	−36.9917	−	5.85890i	−0.359142	−	0.0568825i	−0.333398	+	0.942786i	$0.608195\pi$
$104$		0			0
$105$	32.9995	+	2.28591i	0.314281	+	0.0217706i
$106$		0			0
$107$	9.46731	−	9.46731i	0.0884795	−	0.0884795i	−0.661482	−	0.749961i	$-0.730072\pi$
$107$	9.46731	−	9.46731i	0.0884795	−	0.0884795i	0.749961	+	0.661482i	$0.230072\pi$
$108$		0			0
$109$	−159.887	−	51.9505i	−1.46685	−	0.476610i	−0.536698	−	0.843774i	$-0.680329\pi$
$109$	−159.887	−	51.9505i	−1.46685	−	0.476610i	−0.930156	+	0.367164i	$0.880329\pi$
$110$		0			0
$111$	−14.1132	−	43.4360i	−0.127146	−	0.391315i
$112$		0			0
$113$	−107.749	+	54.9006i	−0.953527	+	0.485846i	−0.860294	−	0.509798i	$-0.829720\pi$
$113$	−107.749	+	54.9006i	−0.953527	+	0.485846i	−0.0932331	+	0.995644i	$0.529720\pi$
$114$		0			0
$115$	182.526	−	77.6184i	1.58718	−	0.674943i
$116$		0			0
$117$	−31.3083	+	4.95875i	−0.267593	+	0.0423825i
$118$		0			0
$119$	−32.5163	+	44.7548i	−0.273246	+	0.376091i
$120$		0			0
$121$	97.4625	−	70.8106i	0.805475	−	0.585212i
$122$		0			0
$123$	7.55620	−	14.8299i	0.0614326	−	0.120568i
$124$		0			0
$125$	62.2880	−	108.375i	0.498304	−	0.867003i
$126$		0			0
$127$	20.8642	+	10.6308i	0.164285	+	0.0837074i	0.534200	−	0.845358i	$-0.320613\pi$
$127$	20.8642	+	10.6308i	0.164285	+	0.0837074i	−0.369915	+	0.929066i	$0.620613\pi$
$128$		0			0
$129$	31.6988	+	43.6297i	0.245727	+	0.338215i
$130$		0			0
$131$	−87.8890	−	63.8551i	−0.670908	−	0.487443i	0.199421	−	0.979914i	$-0.436094\pi$
$131$	−87.8890	−	63.8551i	−0.670908	−	0.487443i	−0.870329	+	0.492471i	$0.836094\pi$
$132$		0			0
$133$	−3.14176	−	19.8363i	−0.0236223	−	0.149145i
$134$		0			0
$135$	−57.4102	−	135.005i	−0.425261	−	1.00004i
$136$		0			0
$137$	−7.27525	−	14.2785i	−0.0531040	−	0.104223i	0.862929	−	0.505325i	$-0.168627\pi$
$137$	−7.27525	−	14.2785i	−0.0531040	−	0.104223i	−0.916033	+	0.401102i	$0.868627\pi$
$138$		0			0
$139$	190.092	−	61.7647i	1.36757	−	0.444350i	0.469007	−	0.883195i	$-0.344612\pi$
$139$	190.092	−	61.7647i	1.36757	−	0.444350i	0.898563	+	0.438844i	$0.144612\pi$
$140$		0			0
$141$	65.8132	−	202.552i	0.466760	−	1.43654i
$142$		0			0
$143$	−6.32464	−	6.32464i	−0.0442283	−	0.0442283i
$144$		0			0
$145$	16.6412	−	240.233i	0.114767	−	1.65678i
$146$		0			0
$147$	16.7208	−	105.571i	0.113747	−	0.718170i
$148$		0			0
$149$			278.483i			1.86902i	0.355942	+	0.934508i	$0.384160\pi$
$149$			278.483i			1.86902i	−0.355942	+	0.934508i	$0.615840\pi$
$150$		0			0
$151$	−216.796			−1.43574			−0.717869	−	0.696178i	$-0.754882\pi$
$151$	−216.796			−1.43574			−0.717869	+	0.696178i	$0.754882\pi$
$152$		0			0
$153$	53.9809	+	8.54973i	0.352816	+	0.0558806i
$154$		0			0
$155$	47.4030	+	189.596i	0.305826	+	1.22320i
$156$		0			0
$157$	−113.262	+	113.262i	−0.721414	+	0.721414i	−0.968893	−	0.247479i	$-0.920398\pi$
$157$	−113.262	+	113.262i	−0.721414	+	0.721414i	0.247479	+	0.968893i	$0.420398\pi$
$158$		0			0
$159$	157.547	+	51.1902i	0.990863	+	0.321951i
$160$		0			0
$161$	32.0054	+	98.5026i	0.198792	+	0.611817i
$162$		0			0
$163$	47.7817	−	24.3460i	0.293139	−	0.149362i	−0.301236	−	0.953550i	$-0.597399\pi$
$163$	47.7817	−	24.3460i	0.293139	−	0.149362i	0.594376	+	0.804188i	$0.297399\pi$
$164$		0			0
$165$	4.74421	−	7.90737i	0.0287528	−	0.0479235i
$166$		0			0
$167$	−261.151	+	41.3623i	−1.56378	+	0.247678i	−0.877470	−	0.479632i	$-0.840770\pi$
$167$	−261.151	+	41.3623i	−1.56378	+	0.247678i	−0.686309	+	0.727310i	$0.740770\pi$
$168$		0			0
$169$	−10.5714	+	14.5502i	−0.0625525	+	0.0860961i
$170$		0			0
$171$	−16.0523	+	11.6627i	−0.0938730	+	0.0682027i
$172$		0			0
$173$	18.7438	−	36.7868i	0.108346	−	0.212641i	−0.830467	−	0.557067i	$-0.811927\pi$
$173$	18.7438	−	36.7868i	0.108346	−	0.212641i	0.938813	+	0.344426i	$0.111927\pi$
$174$		0			0
$175$	53.5171	+	37.3691i	0.305812	+	0.213538i
$176$		0			0
$177$	−176.849	−	90.1088i	−0.999144	−	0.509089i
$178$		0			0
$179$	−84.9216	−	116.885i	−0.474422	−	0.652986i	0.502999	−	0.864287i	$-0.332230\pi$
$179$	−84.9216	−	116.885i	−0.474422	−	0.652986i	−0.977421	+	0.211301i	$0.932230\pi$
$180$		0			0
$181$	−35.1000	−	25.5016i	−0.193923	−	0.140893i	0.486587	−	0.873632i	$-0.338242\pi$
$181$	−35.1000	−	25.5016i	−0.193923	−	0.140893i	−0.680510	+	0.732739i	$0.738242\pi$
$182$		0			0
$183$	25.7596	+	162.640i	0.140763	+	0.888742i
$184$		0			0
$185$	20.2156	−	87.8248i	0.109274	−	0.474729i
$186$		0			0
$187$	7.00128	+	13.7408i	0.0374400	+	0.0734802i
$188$		0			0
$189$	72.8572	−	23.6727i	0.385488	−	0.125253i
$190$		0			0
$191$	48.7314	−	149.980i	0.255138	−	0.785235i	−0.738664	−	0.674074i	$-0.764543\pi$
$191$	48.7314	−	149.980i	0.255138	−	0.785235i	0.993802	−	0.111161i	$-0.0354569\pi$
$192$		0			0
$193$	76.0787	+	76.0787i	0.394190	+	0.394190i	0.876178	−	0.481988i	$-0.160085\pi$
$193$	76.0787	+	76.0787i	0.394190	+	0.394190i	−0.481988	+	0.876178i	$0.660085\pi$
$194$		0			0
$195$	144.393	+	58.2289i	0.740476	+	0.298610i
$196$		0			0
$197$	−5.96711	+	37.6748i	−0.0302899	+	0.191243i	−0.998194	−	0.0600782i	$-0.980865\pi$
$197$	−5.96711	+	37.6748i	−0.0302899	+	0.191243i	0.967904	+	0.251321i	$0.0808650\pi$
$198$		0			0
$199$			201.504i			1.01259i	0.862362	+	0.506293i	$0.168984\pi$
$199$			201.504i			1.01259i	−0.862362	+	0.506293i	$0.831016\pi$
$200$		0			0
$201$	157.013			0.781158
$202$		0			0
$203$	124.198	+	19.6710i	0.611813	+	0.0969016i
$204$		0			0
$205$	27.8410	−	17.4223i	0.135810	−	0.0849866i
$206$		0			0
$207$	72.3544	−	72.3544i	0.349538	−	0.349538i
$208$		0			0
$209$	−5.32471	−	1.73010i	−0.0254771	−	0.00827801i
$210$		0			0
$211$	−6.78952	−	20.8960i	−0.0321778	−	0.0990332i	0.933678	−	0.358114i	$-0.116580\pi$
$211$	−6.78952	−	20.8960i	−0.0321778	−	0.0990332i	−0.965856	+	0.259081i	$0.916580\pi$
$212$		0			0
$213$	−120.796	+	61.5485i	−0.567116	+	0.288960i
$214$		0			0
$215$	9.34398	+	106.005i	0.0434604	+	0.493049i
$216$		0			0
$217$	−100.795	+	15.9643i	−0.464491	+	0.0735682i
$218$		0			0
$219$	50.6737	−	69.7464i	0.231387	−	0.318477i
$220$		0			0
$221$	−210.648	+	153.045i	−0.953159	+	0.692510i
$222$		0			0
$223$	−190.231	+	373.349i	−0.853053	+	1.67421i	−0.121328	+	0.992613i	$0.538715\pi$
$223$	−190.231	+	373.349i	−0.853053	+	1.67421i	−0.731726	+	0.681599i	$0.761285\pi$
$224$		0			0
$225$	8.89147	−	63.8708i	0.0395176	−	0.283870i
$226$		0			0
$227$	−98.4029	−	50.1388i	−0.433493	−	0.220876i	0.223607	−	0.974679i	$-0.428217\pi$
$227$	−98.4029	−	50.1388i	−0.433493	−	0.220876i	−0.657100	+	0.753804i	$0.728217\pi$
$228$		0			0
$229$	−7.87652	−	10.8411i	−0.0343953	−	0.0473410i	0.791473	−	0.611204i	$-0.209315\pi$
$229$	−7.87652	−	10.8411i	−0.0343953	−	0.0473410i	−0.825868	+	0.563863i	$0.809315\pi$
$230$		0			0
$231$	3.89561	+	2.83033i	0.0168641	+	0.0122525i
$232$		0			0
$233$	47.5283	+	300.082i	0.203984	+	1.28790i	0.850894	+	0.525338i	$0.176061\pi$
$233$	47.5283	+	300.082i	0.203984	+	1.28790i	−0.646909	+	0.762567i	$0.723939\pi$
$234$		0			0
$235$	316.992	−	275.920i	1.34890	−	1.17413i
$236$		0			0
$237$	−26.9852	−	52.9614i	−0.113862	−	0.223466i
$238$		0			0
$239$	−272.615	+	88.5779i	−1.14065	+	0.370619i	−0.817613	−	0.575768i	$-0.804703\pi$
$239$	−272.615	+	88.5779i	−1.14065	+	0.370619i	−0.323035	+	0.946387i	$0.604703\pi$
$240$		0			0
$241$	−18.3766	+	56.5573i	−0.0762514	+	0.234678i	−0.981916	−	0.189317i	$-0.939373\pi$
$241$	−18.3766	+	56.5573i	−0.0762514	+	0.234678i	0.905665	+	0.423995i	$0.139373\pi$
$242$		0			0
$243$	−95.1119	−	95.1119i	−0.391407	−	0.391407i
$244$		0			0
$245$	135.469	−	161.659i	0.552933	−	0.659834i
$246$		0			0
$247$	14.7874	−	93.3639i	0.0598680	−	0.377991i
$248$		0			0
$249$		−	131.287i		−	0.527257i
$250$		0			0
$251$	130.804			0.521132			0.260566	−	0.965456i	$-0.416091\pi$
$251$	130.804			0.521132			0.260566	+	0.965456i	$0.416091\pi$
$252$		0			0
$253$	28.5174	+	4.51672i	0.112717	+	0.0178526i
$254$		0			0
$255$	−205.749	−	172.415i	−0.806858	−	0.676137i
$256$		0			0
$257$	64.9358	−	64.9358i	0.252668	−	0.252668i	−0.569395	−	0.822064i	$-0.692823\pi$
$257$	64.9358	−	64.9358i	0.252668	−	0.252668i	0.822064	+	0.569395i	$0.192823\pi$
$258$		0			0
$259$	44.7565	+	14.5423i	0.172805	+	0.0561477i
$260$		0			0
$261$	−38.3897	−	118.151i	−0.147087	−	0.452688i
$262$		0			0
$263$	139.472	−	71.0644i	0.530311	−	0.270207i	−0.168266	−	0.985742i	$-0.553817\pi$
$263$	139.472	−	71.0644i	0.530311	−	0.270207i	0.698577	+	0.715535i	$0.253817\pi$
$264$		0			0
$265$	214.614	+	246.560i	0.809864	+	0.930415i
$266$		0			0
$267$	−376.236	+	59.5899i	−1.40912	+	0.223183i
$268$		0			0
$269$	−194.659	+	267.925i	−0.723640	+	0.996005i	0.275755	+	0.961228i	$0.411072\pi$
$269$	−194.659	+	267.925i	−0.723640	+	0.996005i	−0.999395	+	0.0347774i	$0.988928\pi$
$270$		0			0
$271$	−151.790	+	110.282i	−0.560111	+	0.406945i	−0.831500	−	0.555525i	$-0.812517\pi$
$271$	−151.790	+	110.282i	−0.560111	+	0.406945i	0.271388	+	0.962470i	$0.412517\pi$
$272$		0			0
$273$	−36.9091	+	72.4383i	−0.135198	+	0.265342i
$274$		0			0
$275$	16.0551	−	8.56356i	0.0583823	−	0.0311402i
$276$		0			0
$277$	250.094	+	127.429i	0.902865	+	0.460033i	0.842840	−	0.538164i	$-0.180882\pi$
$277$	250.094	+	127.429i	0.902865	+	0.460033i	0.0600250	+	0.998197i	$0.480882\pi$
$278$		0			0
$279$	59.2617	+	81.5668i	0.212408	+	0.292354i
$280$		0			0
$281$	−253.823	−	184.413i	−0.903284	−	0.656274i	0.0360233	−	0.999351i	$-0.488531\pi$
$281$	−253.823	−	184.413i	−0.903284	−	0.656274i	−0.939307	+	0.343077i	$0.888531\pi$
$282$		0			0
$283$	−14.7828	−	93.3349i	−0.0522360	−	0.329805i	−0.999943	−	0.0106639i	$-0.996606\pi$
$283$	−14.7828	−	93.3349i	−0.0522360	−	0.329805i	0.947707	−	0.319141i	$-0.103394\pi$
$284$		0			0
$285$	97.0787	−	8.55712i	0.340627	−	0.0300250i
$286$		0			0
$287$	7.78592	+	15.2807i	0.0271286	+	0.0532430i
$288$		0			0
$289$	152.104	−	49.4215i	0.526311	−	0.171009i
$290$		0			0
$291$	−49.9655	+	153.778i	−0.171703	+	0.528447i
$292$		0			0
$293$	100.122	+	100.122i	0.341714	+	0.341714i	0.857012	−	0.515297i	$-0.172318\pi$
$293$	100.122	+	100.122i	0.341714	+	0.341714i	−0.515297	+	0.857012i	$0.672318\pi$
$294$		0			0
$295$	−207.763	−	332.008i	−0.704281	−	1.12545i
$296$		0			0
$297$	3.34078	−	21.0928i	0.0112484	−	0.0710196i
$298$		0			0
$299$			487.483i			1.63038i
$300$		0			0
$301$	−55.5688			−0.184614
$302$		0			0
$303$	150.218	+	23.7922i	0.495768	+	0.0785220i
$304$		0			0
$305$	−121.525	+	301.350i	−0.398442	+	0.988034i
$306$		0			0
$307$	−268.414	+	268.414i	−0.874313	+	0.874313i	−0.992939	−	0.118626i	$-0.962151\pi$
$307$	−268.414	+	268.414i	−0.874313	+	0.874313i	0.118626	+	0.992939i	$0.462151\pi$
$308$		0			0
$309$	90.2559	+	29.3259i	0.292090	+	0.0949059i
$310$		0			0
$311$	24.7131	+	76.0590i	0.0794632	+	0.244563i	0.982894	−	0.184171i	$-0.0589600\pi$
$311$	24.7131	+	76.0590i	0.0794632	+	0.244563i	−0.903431	+	0.428733i	$0.858960\pi$
$312$		0			0
$313$	−148.268	+	75.5464i	−0.473700	+	0.241362i	−0.674507	−	0.738269i	$-0.735644\pi$
$313$	−148.268	+	75.5464i	−0.473700	+	0.241362i	0.200807	+	0.979631i	$0.435644\pi$
$314$		0			0
$315$	32.8157	+	7.55354i	0.104177	+	0.0239795i
$316$		0			0
$317$	−476.155	+	75.4156i	−1.50207	+	0.237904i	−0.852632	−	0.522513i	$-0.824995\pi$
$317$	−476.155	+	75.4156i	−1.50207	+	0.237904i	−0.649436	+	0.760417i	$0.724995\pi$
$318$		0			0
$319$	20.6045	−	28.3597i	0.0645909	−	0.0889018i
$320$		0			0
$321$	−27.4463	+	19.9409i	−0.0855026	+	0.0621213i
$322$		0			0
$323$	−73.9922	+	145.218i	−0.229078	+	0.449591i
$324$		0			0
$325$	185.210	+	245.116i	0.569876	+	0.754202i
$326$		0			0
$327$	379.554	+	193.392i	1.16072	+	0.591414i
$328$		0			0
$329$	128.990	+	177.539i	0.392066	+	0.539633i
$330$		0			0
$331$	219.259	+	159.301i	0.662413	+	0.481271i	0.867477	−	0.497477i	$-0.165740\pi$
$331$	219.259	+	159.301i	0.662413	+	0.481271i	−0.205064	+	0.978749i	$0.565740\pi$
$332$		0			0
$333$	−7.27312	−	45.9206i	−0.0218412	−	0.137900i
$334$		0			0
$335$	265.678	+	159.399i	0.793068	+	0.475819i
$336$		0			0
$337$	−180.144	−	353.552i	−0.534551	−	1.04912i	−0.987506	−	0.157582i	$-0.949630\pi$
$337$	−180.144	−	353.552i	−0.534551	−	1.04912i	0.452955	−	0.891533i	$-0.350370\pi$
$338$		0			0
$339$	291.422	−	94.6888i	0.859652	−	0.279318i
$340$		0			0
$341$	−8.79121	+	27.0566i	−0.0257807	+	0.0793448i
$342$		0			0
$343$	168.342	+	168.342i	0.490792	+	0.490792i
$344$		0			0
$345$	−487.572	+	121.903i	−1.41325	+	0.353343i
$346$		0			0
$347$	−18.6937	+	118.028i	−0.0538724	+	0.340137i	0.946000	+	0.324167i	$0.105084\pi$
$347$	−18.6937	+	118.028i	−0.0538724	+	0.340137i	−0.999872	+	0.0159706i	$0.994916\pi$
$348$		0			0
$349$		−	282.531i		−	0.809544i	−0.914418	−	0.404772i	$-0.867351\pi$
$349$		−	282.531i		−	0.809544i	0.914418	−	0.404772i	$-0.132649\pi$
$350$		0			0
$351$	360.565			1.02725
$352$		0			0
$353$	−401.912	−	63.6566i	−1.13856	−	0.180330i	−0.441445	−	0.897288i	$-0.645534\pi$
$353$	−401.912	−	63.6566i	−1.13856	−	0.180330i	−0.697116	+	0.716958i	$0.745534\pi$
$354$		0			0
$355$	−266.880	−	18.4871i	−0.751774	−	0.0520762i
$356$		0			0
$357$	99.1180	−	99.1180i	0.277641	−	0.277641i
$358$		0			0
$359$	−539.418	−	175.268i	−1.50256	−	0.488210i	−0.561795	−	0.827277i	$-0.689889\pi$
$359$	−539.418	−	175.268i	−1.50256	−	0.488210i	−0.940763	+	0.339066i	$0.889889\pi$
$360$		0			0
$361$	93.2707	+	287.058i	0.258368	+	0.795174i
$362$		0			0
$363$	−271.986	+	138.584i	−0.749272	+	0.381773i
$364$		0			0
$365$	156.550	−	66.5723i	0.428905	−	0.182390i
$366$		0			0
$367$	396.398	−	62.7832i	1.08010	−	0.171071i	0.409073	−	0.912502i	$-0.365852\pi$
$367$	396.398	−	62.7832i	1.08010	−	0.171071i	0.671030	+	0.741430i	$0.265852\pi$
$368$		0			0
$369$	9.95910	−	13.7075i	0.0269894	−	0.0371478i
$370$		0			0
$371$	−138.092	+	100.330i	−0.372216	+	0.270430i
$372$		0			0
$373$	187.274	−	367.546i	0.502075	−	0.985379i	−0.491357	−	0.870958i	$-0.663499\pi$
$373$	187.274	−	367.546i	0.502075	−	0.985379i	0.993432	−	0.114420i	$-0.0365011\pi$
$374$		0			0
$375$	−198.845	+	246.539i	−0.530254	+	0.657437i
$376$		0			0
$377$	527.343	+	268.695i	1.39879	+	0.712719i
$378$		0			0
$379$	−68.8055	−	94.7026i	−0.181545	−	0.249875i	0.708539	−	0.705671i	$-0.249355\pi$
$379$	−68.8055	−	94.7026i	−0.181545	−	0.249875i	−0.890084	+	0.455796i	$0.849355\pi$
$380$		0			0
$381$	−48.0025	−	34.8759i	−0.125991	−	0.0915377i
$382$		0			0
$383$	14.3249	+	90.4436i	0.0374017	+	0.236145i	0.999306	−	0.0372401i	$-0.0118566\pi$
$383$	14.3249	+	90.4436i	0.0374017	+	0.236145i	−0.961905	+	0.273385i	$0.911857\pi$
$384$		0			0
$385$	3.71833	+	8.74397i	0.00965800	+	0.0227116i
$386$		0			0
$387$	24.9239	+	48.9159i	0.0644028	+	0.126398i
$388$		0			0
$389$	206.217	−	67.0040i	0.530121	−	0.172247i	−0.0317127	−	0.999497i	$-0.510096\pi$
$389$	206.217	−	67.0040i	0.530121	−	0.172247i	0.561833	+	0.827250i	$0.310096\pi$
$390$		0			0
$391$	259.730	−	799.367i	0.664271	−	2.04442i
$392$		0			0
$393$	194.647	+	194.647i	0.495285	+	0.495285i
$394$		0			0
$395$	8.10542	−	117.010i	0.0205201	−	0.296228i
$396$		0			0
$397$	21.2893	−	134.416i	0.0536255	−	0.338578i	−0.946259	−	0.323409i	$-0.895171\pi$
$397$	21.2893	−	134.416i	0.0536255	−	0.338578i	0.999885	−	0.0151696i	$-0.00482882\pi$
$398$		0			0
$399$			50.8893i			0.127542i
$400$		0			0
$401$	−23.8319			−0.0594311			−0.0297156	−	0.999558i	$-0.509460\pi$
$401$	−23.8319			−0.0594311			−0.0297156	+	0.999558i	$0.509460\pi$
$402$		0			0
$403$	−474.412	−	75.1394i	−1.17720	−	0.186450i
$404$		0			0
$405$	62.0106	+	248.021i	0.153112	+	0.612398i
$406$		0			0
$407$	9.27649	−	9.27649i	0.0227924	−	0.0227924i
$408$		0			0
$409$	287.240	+	93.3299i	0.702298	+	0.228190i	0.638332	−	0.769762i	$-0.279625\pi$
$409$	287.240	+	93.3299i	0.702298	+	0.228190i	0.0639666	+	0.997952i	$0.479625\pi$
$410$		0			0
$411$	12.5478	+	38.6183i	0.0305300	+	0.0939618i
$412$		0			0
$413$	182.225	−	92.8482i	0.441223	−	0.224814i
$414$		0			0
$415$	133.283	−	222.148i	0.321163	−	0.535296i
$416$		0			0
$417$	−500.223	+	79.2275i	−1.19957	+	0.189994i
$418$		0			0
$419$	400.071	−	550.650i	0.954823	−	1.31420i	0.00547150	−	0.999985i	$-0.498258\pi$
$419$	400.071	−	550.650i	0.954823	−	1.31420i	0.949351	−	0.314216i	$-0.101742\pi$
$420$		0			0
$421$	218.505	−	158.753i	0.519014	−	0.377086i	−0.297218	−	0.954810i	$-0.596059\pi$
$421$	218.505	−	158.753i	0.519014	−	0.377086i	0.816232	+	0.577724i	$0.196059\pi$
$422$		0			0
$423$	98.4287	−	193.177i	0.232692	−	0.456684i
$424$		0			0
$425$	−173.107	−	500.616i	−0.407310	−	1.17792i
$426$		0			0
$427$	−151.180	−	77.0300i	−0.354051	−	0.180398i
$428$		0			0
$429$	13.3216	+	18.3356i	0.0310526	+	0.0427402i
$430$		0			0
$431$	−668.833	−	485.936i	−1.55182	−	1.12746i	−0.942340	−	0.334656i	$-0.891380\pi$
$431$	−668.833	−	485.936i	−1.55182	−	1.12746i	−0.609476	−	0.792804i	$-0.708620\pi$
$432$		0			0
$433$	−113.968	−	719.567i	−0.263206	−	1.66182i	−0.665568	−	0.746337i	$-0.731811\pi$
$433$	−113.968	−	719.567i	−0.263206	−	1.66182i	0.402362	−	0.915481i	$-0.368189\pi$
$434$		0			0
$435$	−136.873	+	594.631i	−0.314650	+	1.36697i
$436$		0			0
$437$	138.531	+	271.881i	0.317003	+	0.622154i
$438$		0			0
$439$	472.354	−	153.477i	1.07598	−	0.349606i	0.283164	−	0.959071i	$-0.408616\pi$
$439$	472.354	−	153.477i	1.07598	−	0.349606i	0.792813	+	0.609465i	$0.208616\pi$
$440$		0			0
$441$	33.6242	−	103.485i	0.0762453	−	0.234659i
$442$		0			0
$443$	−367.664	−	367.664i	−0.829940	−	0.829940i	0.157568	−	0.987508i	$-0.449635\pi$
$443$	−367.664	−	367.664i	−0.829940	−	0.829940i	−0.987508	+	0.157568i	$0.949635\pi$
$444$		0			0
$445$	−697.116	−	281.124i	−1.56655	−	0.631740i
$446$		0			0
$447$	110.387	−	696.955i	0.246950	−	1.55918i
$448$		0			0
$449$			43.4706i			0.0968165i	0.998828	+	0.0484082i	$0.0154148\pi$
$449$			43.4706i			0.0968165i	−0.998828	+	0.0484082i	$0.984585\pi$
$450$		0			0
$451$	4.78093			0.0106007
$452$		0			0
$453$	542.572	+	85.9350i	1.19773	+	0.189702i
$454$		0			0
$455$	−135.993	+	85.1010i	−0.298885	+	0.187035i
$456$		0			0
$457$	181.132	−	181.132i	0.396349	−	0.396349i	−0.480594	−	0.876943i	$-0.659579\pi$
$457$	181.132	−	181.132i	0.396349	−	0.396349i	0.876943	+	0.480594i	$0.159579\pi$
$458$		0			0
$459$	−591.249	−	192.108i	−1.28812	−	0.418537i
$460$		0			0
$461$	−64.2056	−	197.605i	−0.139275	−	0.428643i	0.856956	−	0.515390i	$-0.172353\pi$
$461$	−64.2056	−	197.605i	−0.139275	−	0.428643i	−0.996230	+	0.0867467i	$0.972353\pi$
$462$		0			0
$463$	265.262	−	135.158i	0.572919	−	0.291917i	−0.143428	−	0.989661i	$-0.545813\pi$
$463$	265.262	−	135.158i	0.572919	−	0.291917i	0.716347	+	0.697744i	$0.245813\pi$
$464$		0			0
$465$	−43.4814	−	493.288i	−0.0935085	−	1.06083i
$466$		0			0
$467$	222.042	−	35.1679i	0.475464	−	0.0753060i	0.0858964	−	0.996304i	$-0.472625\pi$
$467$	222.042	−	35.1679i	0.475464	−	0.0753060i	0.389567	+	0.920998i	$0.372625\pi$
$468$		0			0
$469$	−95.0955	+	130.888i	−0.202762	+	0.279078i
$470$		0			0
$471$	328.354	−	238.563i	0.697142	−	0.506504i
$472$		0			0
$473$	−7.03277	+	13.8026i	−0.0148684	+	0.0291810i
$474$		0			0
$475$	172.952	+	84.0750i	0.364109	+	0.177000i
$476$		0			0
$477$	150.255	+	76.5589i	0.315001	+	0.160501i
$478$		0			0
$479$	135.106	+	185.957i	0.282058	+	0.388219i	0.926414	−	0.376506i	$-0.122875\pi$
$479$	135.106	+	185.957i	0.282058	+	0.388219i	−0.644356	+	0.764725i	$0.722875\pi$
$480$		0			0
$481$	179.195	+	130.193i	0.372546	+	0.270671i
$482$		0			0
$483$	−41.0544	−	259.207i	−0.0849987	−	0.536661i
$484$		0			0
$485$	−240.661	+	209.479i	−0.496208	+	0.431916i
$486$		0			0
$487$	200.863	+	394.215i	0.412449	+	0.809477i	1.00000		0.000289730i	$9.22238e-5\pi$
$487$	200.863	+	394.215i	0.412449	+	0.809477i	−0.587551	+	0.809187i	$0.699908\pi$
$488$		0			0
$489$	−129.233	+	41.9903i	−0.264280	+	0.0858696i
$490$		0			0
$491$	−220.205	+	677.722i	−0.448483	+	1.38029i	0.430135	+	0.902764i	$0.358466\pi$
$491$	−220.205	+	677.722i	−0.448483	+	1.38029i	−0.878618	+	0.477524i	$0.841534\pi$
$492$		0			0
$493$	−721.569	−	721.569i	−1.46363	−	1.46363i
$494$		0			0
$495$	6.02935	−	7.19503i	0.0121805	−	0.0145354i
$496$		0			0
$497$	21.8529	−	137.974i	0.0439697	−	0.277613i
$498$		0			0
$499$		−	413.251i		−	0.828158i	−0.910241	−	0.414079i	$-0.864104\pi$
$499$		−	413.251i		−	0.828158i	0.910241	−	0.414079i	$-0.135896\pi$
$500$		0			0
$501$	669.973			1.33727
$502$		0			0
$503$	246.237	+	39.0001i	0.489537	+	0.0775350i	0.396323	−	0.918111i	$-0.370286\pi$
$503$	246.237	+	39.0001i	0.489537	+	0.0775350i	0.0932137	+	0.995646i	$0.470286\pi$
$504$		0			0
$505$	230.026	+	192.759i	0.455498	+	0.381702i
$506$		0			0
$507$	32.2243	−	32.2243i	0.0635587	−	0.0635587i
$508$		0			0
$509$	−318.506	−	103.489i	−0.625749	−	0.203318i	−0.0210580	−	0.999778i	$-0.506703\pi$
$509$	−318.506	−	103.489i	−0.625749	−	0.203318i	−0.604691	+	0.796460i	$0.706703\pi$
$510$		0			0
$511$	27.4507	+	84.4844i	0.0537195	+	0.165332i
$512$		0			0
$513$	201.096	−	102.464i	0.392001	−	0.199734i
$514$		0			0
$515$	122.948	+	141.250i	0.238735	+	0.274271i
$516$		0			0
$517$	60.4235	−	9.57014i	0.116873	−	0.0185109i
$518$		0			0
$519$	−61.4916	+	84.6359i	−0.118481	+	0.163075i
$520$		0			0
$521$	−208.409	+	151.418i	−0.400018	+	0.290630i	−0.769548	−	0.638589i	$-0.779519\pi$
$521$	−208.409	+	151.418i	−0.400018	+	0.290630i	0.369530	+	0.929219i	$0.379519\pi$
$522$		0			0
$523$	351.099	−	689.071i	0.671317	−	1.31753i	−0.264273	−	0.964448i	$-0.585132\pi$
$523$	351.099	−	689.071i	0.671317	−	1.31753i	0.935591	−	0.353087i	$-0.114868\pi$
$524$		0			0
$525$	−119.124	−	114.736i	−0.226902	−	0.218545i
$526$		0			0
$527$	737.898	+	375.978i	1.40019	+	0.713430i
$528$		0			0
$529$	−614.011	−	845.113i	−1.16070	−	1.59757i
$530$		0			0
$531$	−163.464	−	118.764i	−0.307842	−	0.223661i
$532$		0			0
$533$	12.6274	+	79.7262i	0.0236912	+	0.149580i
$534$		0			0
$535$	−66.6854	+	5.87807i	−0.124646	+	0.0109870i
$536$		0			0
$537$	166.200	+	326.186i	0.309498	+	0.607424i
$538$		0			0
$539$	29.2002	−	9.48773i	0.0541748	−	0.0176025i
$540$		0			0
$541$	19.0936	−	58.7641i	0.0352932	−	0.108621i	−0.931858	−	0.362823i	$-0.881813\pi$
$541$	19.0936	−	58.7641i	0.0352932	−	0.108621i	0.967151	+	0.254202i	$0.0818128\pi$
$542$		0			0
$543$	77.7356	+	77.7356i	0.143159	+	0.143159i
$544$		0			0
$545$	445.903	+	712.558i	0.818170	+	1.30745i
$546$		0			0
$547$	−13.3557	+	84.3244i	−0.0244162	+	0.154158i	−0.996884	−	0.0788784i	$-0.974866\pi$
$547$	−13.3557	+	84.3244i	−0.0244162	+	0.154158i	0.972468	+	0.233036i	$0.0748661\pi$
$548$		0			0
$549$			167.630i			0.305337i
$550$		0			0
$551$	370.469			0.672357
$552$		0			0
$553$	60.4930	+	9.58114i	0.109391	+	0.0173258i
$554$		0			0
$555$	−85.4057	+	211.784i	−0.153884	+	0.381593i
$556$		0			0
$557$	59.2331	−	59.2331i	0.106343	−	0.106343i	−0.651933	−	0.758276i	$-0.726042\pi$
$557$	59.2331	−	59.2331i	0.106343	−	0.106343i	0.758276	+	0.651933i	$0.226042\pi$
$558$		0			0
$559$	−248.745	−	80.8223i	−0.444983	−	0.144584i
$560$		0			0
$561$	−12.0753	−	37.1640i	−0.0215246	−	0.0662460i
$562$		0			0
$563$	−254.074	+	129.457i	−0.451286	+	0.229942i	−0.664834	−	0.746991i	$-0.731498\pi$
$563$	−254.074	+	129.457i	−0.451286	+	0.229942i	0.213548	+	0.976933i	$0.431498\pi$
$564$		0			0
$565$	589.237	+	135.631i	1.04290	+	0.240055i
$566$		0			0
$567$	−131.855	+	20.8838i	−0.232549	+	0.0368321i
$568$		0			0
$569$	139.865	−	192.508i	0.245809	−	0.338327i	−0.668229	−	0.743955i	$-0.732947\pi$
$569$	139.865	−	192.508i	0.245809	−	0.338327i	0.914038	+	0.405629i	$0.132947\pi$
$570$		0			0
$571$	−774.265	+	562.537i	−1.35598	+	0.985178i	−0.357292	+	0.933993i	$0.616300\pi$
$571$	−774.265	+	562.537i	−1.35598	+	0.985178i	−0.998689	+	0.0511852i	$0.983700\pi$
$572$		0			0
$573$	−181.409	+	356.035i	−0.316595	+	0.621353i
$574$		0			0
$575$	−948.765	−	288.713i	−1.65003	−	0.502110i
$576$		0			0
$577$	898.960	+	458.043i	1.55799	+	0.793836i	0.999367	−	0.0355856i	$-0.0113296\pi$
$577$	898.960	+	458.043i	1.55799	+	0.793836i	0.558624	+	0.829421i	$0.311330\pi$
$578$		0			0
$579$	−160.244	−	220.557i	−0.276760	−	0.380928i
$580$		0			0
$581$	109.442	+	79.5146i	0.188369	+	0.136858i
$582$		0			0
$583$	7.44376	+	46.9981i	0.0127680	+	0.0806142i
$584$		0			0
$585$	135.908	+	81.5413i	0.232322	+	0.139387i
$586$		0			0
$587$	−3.26148	−	6.40101i	−0.00555618	−	0.0109046i	0.888212	−	0.459434i	$-0.151948\pi$
$587$	−3.26148	−	6.40101i	−0.00555618	−	0.0109046i	−0.893768	+	0.448530i	$0.851948\pi$
$588$		0			0
$589$	−285.944	+	92.9088i	−0.485473	+	0.157740i
$590$		0			0
$591$	29.8675	−	91.9228i	0.0505373	−	0.155538i
$592$		0			0
$593$	161.092	+	161.092i	0.271655	+	0.271655i	0.829766	−	0.558111i	$-0.188474\pi$
$593$	161.092	+	161.092i	0.271655	+	0.271655i	−0.558111	+	0.829766i	$0.688474\pi$
$594$		0			0
$595$	268.340	−	67.0907i	0.450991	−	0.112757i
$596$		0			0
$597$	79.8735	−	504.301i	0.133791	−	0.844726i
$598$		0			0
$599$			1018.75i			1.70076i	0.526173	+	0.850378i	$0.323627\pi$
$599$			1018.75i			1.70076i	−0.526173	+	0.850378i	$0.676373\pi$
$600$		0			0
$601$	56.8591			0.0946075			0.0473038	−	0.998881i	$-0.484937\pi$
$601$	56.8591			0.0946075			0.0473038	+	0.998881i	$0.484937\pi$
$602$		0			0
$603$	157.870	+	25.0041i	0.261807	+	0.0414662i
$604$		0			0
$605$	−600.911	−	41.6258i	−0.993242	−	0.0688030i
$606$		0			0
$607$	171.454	−	171.454i	0.282462	−	0.282462i	−0.551628	−	0.834090i	$-0.685993\pi$
$607$	171.454	−	171.454i	0.282462	−	0.282462i	0.834090	+	0.551628i	$0.185993\pi$
$608$		0			0
$609$	−303.031	−	98.4606i	−0.497587	−	0.161676i
$610$		0			0
$611$	319.181	+	982.338i	0.522391	+	1.60776i
$612$		0			0
$613$	−537.789	+	274.017i	−0.877307	+	0.447010i	−0.833815	−	0.552043i	$-0.813848\pi$
$613$	−537.789	+	274.017i	−0.877307	+	0.447010i	−0.0434918	+	0.999054i	$0.513848\pi$
$614$		0			0
$615$	−76.5830	+	32.5666i	−0.124525	+	0.0529538i
$616$		0			0
$617$	−138.102	+	21.8733i	−0.223829	+	0.0354510i	−0.267341	−	0.963602i	$-0.586145\pi$
$617$	−138.102	+	21.8733i	−0.223829	+	0.0354510i	0.0435126	+	0.999053i	$0.486145\pi$
$618$		0			0
$619$	97.5904	−	134.322i	0.157658	−	0.216998i	−0.722879	−	0.690974i	$-0.757182\pi$
$619$	97.5904	−	134.322i	0.157658	−	0.216998i	0.880538	+	0.473976i	$0.157182\pi$
$620$		0			0
$621$	−941.632	+	684.136i	−1.51632	+	1.10167i
$622$		0			0
$623$	178.194	−	349.726i	0.286026	−	0.561358i
$624$		0			0
$625$	−586.748	+	215.295i	−0.938797	+	0.344472i
$626$		0			0
$627$	12.6403	+	6.44054i	0.0201599	+	0.0102720i
$628$		0			0
$629$	−224.474	−	308.962i	−0.356875	−	0.491196i
$630$		0			0
$631$	583.662	+	424.055i	0.924979	+	0.672037i	0.944758	−	0.327768i	$-0.106296\pi$
$631$	583.662	+	424.055i	0.924979	+	0.672037i	−0.0197794	+	0.999804i	$0.506296\pi$
$632$		0			0
$633$	8.70913	+	54.9873i	0.0137585	+	0.0868677i
$634$		0			0
$635$	−45.8180	−	107.745i	−0.0721543	−	0.169677i
$636$		0			0
$637$	235.340	+	461.881i	0.369451	+	0.725087i
$638$		0			0
$639$	−131.257	+	42.6479i	−0.205410	+	0.0667416i
$640$		0			0
$641$	295.691	−	910.042i	0.461296	−	1.41972i	−0.402286	−	0.915514i	$-0.631784\pi$
$641$	295.691	−	910.042i	0.461296	−	1.41972i	0.863582	−	0.504209i	$-0.168216\pi$
$642$		0			0
$643$	−47.9432	−	47.9432i	−0.0745618	−	0.0745618i	0.668842	−	0.743404i	$-0.266790\pi$
$643$	−47.9432	−	47.9432i	−0.0745618	−	0.0745618i	−0.743404	+	0.668842i	$0.766790\pi$
$644$		0			0
$645$	18.6340	−	269.002i	0.0288900	−	0.417057i
$646$		0			0
$647$	155.194	−	979.858i	0.239867	−	1.51446i	−0.514203	−	0.857669i	$-0.671912\pi$
$647$	155.194	−	979.858i	0.239867	−	1.51446i	0.754070	−	0.656794i	$-0.228088\pi$
$648$		0			0
$649$		−	57.0133i		−	0.0878479i
$650$		0			0
$651$	258.585			0.397211
$652$		0			0
$653$	−302.339	−	47.8858i	−0.463000	−	0.0733320i	−0.0794232	−	0.996841i	$-0.525308\pi$
$653$	−302.339	−	47.8858i	−0.463000	−	0.0733320i	−0.383577	+	0.923509i	$0.625308\pi$
$654$		0			0
$655$	131.752	+	526.963i	0.201148	+	0.804524i
$656$		0			0
$657$	62.0574	−	62.0574i	0.0944557	−	0.0944557i
$658$		0			0
$659$	535.335	+	173.941i	0.812345	+	0.263947i	0.685591	−	0.727987i	$-0.259544\pi$
$659$	535.335	+	173.941i	0.812345	+	0.263947i	0.126754	+	0.991934i	$0.459544\pi$
$660$		0			0
$661$	357.954	+	1101.67i	0.541534	+	1.66667i	0.729092	+	0.684415i	$0.239943\pi$
$661$	357.954	+	1101.67i	0.541534	+	1.66667i	−0.187559	+	0.982253i	$0.560057\pi$
$662$		0			0
$663$	587.850	−	299.524i	0.886651	−	0.451771i
$664$		0			0
$665$	−51.6628	+	86.1086i	−0.0776885	+	0.129487i
$666$		0			0
$667$	−1887.00	+	298.872i	−2.82909	+	0.448083i
$668$		0			0
$669$	624.077	−	858.969i	0.932851	−	1.28396i
$670$		0			0
$671$	−38.2666	+	27.8023i	−0.0570292	+	0.0414342i
$672$		0			0
$673$	−18.8241	+	36.9443i	−0.0279704	+	0.0548950i	−0.904569	−	0.426328i	$-0.859807\pi$
$673$	−18.8241	+	36.9443i	−0.0279704	+	0.0548950i	0.876598	+	0.481223i	$0.159807\pi$
$674$		0			0
$675$	−213.546	+	701.751i	−0.316364	+	1.03963i
$676$		0			0
$677$	215.524	+	109.815i	0.318352	+	0.162209i	0.605863	−	0.795569i	$-0.292828\pi$
$677$	215.524	+	109.815i	0.318352	+	0.162209i	−0.287511	+	0.957777i	$0.592828\pi$
$678$		0			0
$679$	−97.9293	−	134.788i	−0.144226	−	0.198510i
$680$		0			0
$681$	226.397	+	164.487i	0.332447	+	0.241537i
$682$		0			0
$683$	−169.356	−	1069.27i	−0.247959	−	1.56555i	−0.726300	−	0.687377i	$-0.758762\pi$
$683$	−169.356	−	1069.27i	−0.247959	−	1.56555i	0.478341	−	0.878174i	$-0.341238\pi$
$684$		0			0
$685$	−17.9734	+	78.0837i	−0.0262385	+	0.113991i
$686$		0			0
$687$	15.4152	+	30.2539i	0.0224384	+	0.0440378i
$688$		0			0
$689$	−764.074	+	248.263i	−1.10896	+	0.360323i
$690$		0			0
$691$	60.8202	−	187.185i	0.0880177	−	0.270891i	−0.897353	−	0.441313i	$-0.854513\pi$
$691$	60.8202	−	187.185i	0.0880177	−	0.270891i	0.985371	+	0.170422i	$0.0545130\pi$
$692$		0			0
$693$	3.46615	+	3.46615i	0.00500167	+	0.00500167i
$694$		0			0
$695$	−926.847	−	373.767i	−1.33359	−	0.537795i
$696$		0			0
$697$	21.7718	−	137.462i	0.0312364	−	0.197219i
$698$		0			0
$699$		−	769.849i		−	1.10136i
$700$		0			0
$701$	179.635			0.256255			0.128127	−	0.991758i	$-0.459103\pi$
$701$	179.635			0.256255			0.128127	+	0.991758i	$0.459103\pi$
$702$		0			0
$703$	136.939	+	21.6890i	0.194792	+	0.0308521i
$704$		0			0
$705$	−902.701	+	564.889i	−1.28043	+	0.801261i
$706$		0			0
$707$	−110.814	+	110.814i	−0.156738	+	0.156738i
$708$		0			0
$709$	−65.4964	−	21.2811i	−0.0923785	−	0.0300156i	0.262463	−	0.964942i	$-0.415465\pi$
$709$	−65.4964	−	21.2811i	−0.0923785	−	0.0300156i	−0.354842	+	0.934926i	$0.615465\pi$
$710$		0			0
$711$	−18.6984	−	57.5479i	−0.0262988	−	0.0809394i
$712$		0			0
$713$	1381.52	−	703.918i	1.93761	−	0.987262i
$714$		0			0
$715$	3.92685	+	44.5492i	0.00549209	+	0.0623066i
$716$		0			0
$717$	717.379	−	113.622i	1.00053	−	0.158468i
$718$		0			0
$719$	−666.444	+	917.282i	−0.926904	+	1.27577i	0.0341503	+	0.999417i	$0.489128\pi$
$719$	−666.444	+	917.282i	−0.926904	+	1.27577i	−0.961055	+	0.276358i	$0.910872\pi$
$720$		0			0
$721$	−79.1103	+	57.4770i	−0.109723	+	0.0797185i
$722$		0			0
$723$	68.4092	−	134.261i	0.0946186	−	0.185699i
$724$		0			0
$725$	−835.269	+	867.208i	−1.15210	+	1.19615i
$726$		0			0
$727$	632.182	+	322.113i	0.869577	+	0.443071i	0.831058	−	0.556186i	$-0.187736\pi$
$727$	632.182	+	322.113i	0.869577	+	0.443071i	0.0385192	+	0.999258i	$0.487736\pi$
$728$		0			0
$729$	470.821	+	648.029i	0.645845	+	0.888929i
$730$		0			0
$731$	364.827	+	265.062i	0.499079	+	0.362602i
$732$		0			0
$733$	153.930	+	971.877i	0.210000	+	1.32589i	0.837142	+	0.546985i	$0.184225\pi$
$733$	153.930	+	971.877i	0.210000	+	1.32589i	−0.627142	+	0.778905i	$0.715775\pi$
$734$		0			0
$735$	−403.114	+	350.884i	−0.548454	+	0.477393i
$736$		0			0
$737$	20.4756	+	40.1857i	0.0277824	+	0.0545260i
$738$		0			0
$739$	−1239.16	+	402.628i	−1.67681	+	0.544828i	−0.984288	−	0.176571i	$-0.943500\pi$
$739$	−1239.16	+	402.628i	−1.67681	+	0.544828i	−0.692520	+	0.721399i	$0.743500\pi$
$740$		0			0
$741$	−74.0162	+	227.798i	−0.0998869	+	0.307420i
$742$		0			0
$743$	314.184	+	314.184i	0.422859	+	0.422859i	0.886187	−	0.463328i	$-0.153345\pi$
$743$	314.184	+	314.184i	0.422859	+	0.422859i	−0.463328	+	0.886187i	$0.653345\pi$
$744$		0			0
$745$	894.332	−	1067.24i	1.20045	−	1.43253i
$746$		0			0
$747$	20.9073	−	132.004i	0.0279884	−	0.176712i
$748$		0			0
$749$		−	34.9569i		−	0.0466715i
$750$		0			0
$751$	−87.3707			−0.116339			−0.0581696	−	0.998307i	$-0.518526\pi$
$751$	−87.3707			−0.116339			−0.0581696	+	0.998307i	$0.518526\pi$
$752$		0			0
$753$	−327.361	−	51.8489i	−0.434743	−	0.0688565i
$754$		0			0
$755$	830.833	+	696.228i	1.10044	+	0.922157i
$756$		0			0
$757$	−436.322	+	436.322i	−0.576382	+	0.576382i	−0.933905	−	0.357522i	$-0.883622\pi$
$757$	−436.322	+	436.322i	−0.576382	+	0.576382i	0.357522	+	0.933905i	$0.383622\pi$
$758$		0			0
$759$	−69.5797	−	22.6078i	−0.0916728	−	0.0297863i
$760$		0			0
$761$	328.146	+	1009.93i	0.431203	+	1.32711i	0.896928	+	0.442177i	$0.145794\pi$
$761$	328.146	+	1009.93i	0.431203	+	1.32711i	−0.465724	+	0.884930i	$0.654206\pi$
$762$		0			0
$763$	−391.093	+	199.272i	−0.512573	+	0.261169i
$764$		0			0
$765$	−179.415	−	206.122i	−0.234529	−	0.269440i
$766$		0			0
$767$	950.747	−	150.584i	1.23957	−	0.196328i
$768$		0			0
$769$	−495.875	+	682.513i	−0.644831	+	0.887534i	−0.998862	−	0.0477002i	$-0.984811\pi$
$769$	−495.875	+	682.513i	−0.644831	+	0.887534i	0.354031	+	0.935234i	$0.384811\pi$
$770$		0			0
$771$	−188.253	+	136.774i	−0.244168	+	0.177398i
$772$		0			0
$773$	253.631	−	497.779i	0.328113	−	0.643958i	−0.666740	−	0.745291i	$-0.732311\pi$
$773$	253.631	−	497.779i	0.328113	−	0.643958i	0.994853	+	0.101333i	$0.0323108\pi$
$774$		0			0
$775$	427.212	−	878.823i	0.551241	−	1.13397i
$776$		0			0
$777$	−106.247	−	54.1355i	−0.136740	−	0.0696724i
$778$		0			0
$779$	29.6988	+	40.8769i	0.0381243	+	0.0524736i
$780$		0			0
$781$	−31.5053	−	22.8899i	−0.0403397	−	0.0293085i
$782$		0			0
$783$	221.060	+	1395.72i	0.282324	+	1.78252i
$784$		0			0
$785$	797.790	−	70.3222i	1.01629	−	0.0895824i
$786$		0			0
$787$	244.196	+	479.262i	0.310287	+	0.608973i	0.992509	−	0.122172i	$-0.0389860\pi$
$787$	244.196	+	479.262i	0.310287	+	0.608973i	−0.682221	+	0.731146i	$0.738986\pi$
$788$		0			0
$789$	−377.222	+	122.567i	−0.478102	+	0.155345i
$790$		0			0
$791$	−97.5674	+	300.282i	−0.123347	+	0.379623i
$792$		0			0
$793$	−564.698	−	564.698i	−0.712104	−	0.712104i
$794$		0			0
$795$	−439.377	−	702.130i	−0.552676	−	0.883183i
$796$		0			0
$797$	159.378	−	1006.27i	0.199972	−	1.26258i	−0.659622	−	0.751598i	$-0.729283\pi$
$797$	159.378	−	1006.27i	0.199972	−	1.26258i	0.859594	−	0.510978i	$-0.170717\pi$
$798$		0			0
$799$		−	1780.88i		−	2.22889i
$800$		0			0
$801$	−387.780			−0.484119
$802$		0			0
$803$	24.4590	+	3.87393i	0.0304596	+	0.00482432i
$804$		0			0
$805$	193.680	−	480.277i	0.240596	−	0.596617i
$806$		0			0
$807$	593.372	−	593.372i	0.735281	−	0.735281i
$808$		0			0
$809$	−509.810	−	165.647i	−0.630173	−	0.204756i	−0.0235211	−	0.999723i	$-0.507488\pi$
$809$	−509.810	−	165.647i	−0.630173	−	0.204756i	−0.606652	+	0.794968i	$0.707488\pi$
$810$		0			0
$811$	337.483	+	1038.67i	0.416132	+	1.28072i	0.911234	+	0.411889i	$0.135131\pi$
$811$	337.483	+	1038.67i	0.416132	+	1.28072i	−0.495102	+	0.868835i	$0.664869\pi$
$812$		0			0
$813$	423.596	−	215.833i	0.521029	−	0.265477i
$814$		0			0
$815$	−261.300	−	60.1464i	−0.320614	−	0.0737992i
$816$		0			0
$817$	−161.699	+	25.6106i	−0.197918	+	0.0313472i
$818$		0			0
$819$	−48.6464	+	66.9560i	−0.0593973	+	0.0817534i
$820$		0			0
$821$	−353.280	+	256.673i	−0.430304	+	0.312634i	−0.781770	−	0.623566i	$-0.785683\pi$
$821$	−353.280	+	256.673i	−0.430304	+	0.312634i	0.351466	+	0.936200i	$0.385683\pi$
$822$		0			0
$823$	−154.326	+	302.881i	−0.187516	+	0.368021i	−0.965557	−	0.260193i	$-0.916214\pi$
$823$	−154.326	+	302.881i	−0.187516	+	0.368021i	0.778041	+	0.628214i	$0.216214\pi$
$824$		0			0
$825$	−43.5754	+	15.0678i	−0.0528186	+	0.0182640i
$826$		0			0
$827$	1176.24	+	599.324i	1.42230	+	0.724696i	0.984665	−	0.174458i	$-0.0558173\pi$
$827$	1176.24	+	599.324i	1.42230	+	0.724696i	0.437632	+	0.899154i	$0.355817\pi$
$828$		0			0
$829$	94.2063	+	129.664i	0.113638	+	0.156410i	0.862047	−	0.506828i	$-0.169182\pi$
$829$	94.2063	+	129.664i	0.113638	+	0.156410i	−0.748409	+	0.663238i	$0.769182\pi$
$830$		0			0
$831$	−575.393	−	418.048i	−0.692411	−	0.503066i
$832$		0			0
$833$	−139.817	−	882.773i	−0.167848	−	1.05975i
$834$		0			0
$835$	1133.65	+	680.157i	1.35766	+	0.814559i
$836$		0			0
$837$	−520.650	−	1021.83i	−0.622044	−	1.22083i
$838$		0			0
$839$	−556.528	+	180.827i	−0.663323	+	0.215527i	−0.621279	−	0.783589i	$-0.713387\pi$
$839$	−556.528	+	180.827i	−0.663323	+	0.215527i	−0.0420436	+	0.999116i	$0.513387\pi$
$840$		0			0
$841$	−456.900	+	1406.19i	−0.543282	+	1.67205i
$842$		0			0
$843$	562.139	+	562.139i	0.666831	+	0.666831i
$844$		0			0
$845$	87.2401	−	21.8119i	0.103243	−	0.0258129i
$846$		0			0
$847$	49.2044	−	310.664i	0.0580926	−	0.366782i
$848$		0			0
$849$			239.447i			0.282034i
$850$		0			0
$851$	−715.002			−0.840191
$852$		0			0
$853$	734.339	+	116.308i	0.860890	+	0.136352i	0.571242	−	0.820782i	$-0.306462\pi$
$853$	734.339	+	116.308i	0.860890	+	0.136352i	0.289648	+	0.957133i	$0.406462\pi$
$854$		0			0
$855$	98.9714	+	6.85586i	0.115756	+	0.00801855i
$856$		0			0
$857$	−818.405	+	818.405i	−0.954964	+	0.954964i	−0.999029	−	0.0440643i	$-0.985969\pi$
$857$	−818.405	+	818.405i	−0.954964	+	0.954964i	0.0440643	+	0.999029i	$0.485969\pi$
$858$		0			0
$859$	749.275	+	243.454i	0.872264	+	0.283416i	0.710742	−	0.703453i	$-0.248359\pi$
$859$	749.275	+	243.454i	0.872264	+	0.283416i	0.161523	+	0.986869i	$0.448359\pi$
$860$		0			0
$861$	−13.4286	−	41.3290i	−0.0155965	−	0.0480012i
$862$		0			0
$863$	−940.039	+	478.974i	−1.08927	+	0.555010i	−0.903937	−	0.427666i	$-0.859336\pi$
$863$	−940.039	+	478.974i	−1.08927	+	0.555010i	−0.185332	+	0.982676i	$0.559336\pi$
$864$		0			0
$865$	−189.971	+	80.7842i	−0.219620	+	0.0933921i
$866$		0			0
$867$	−400.257	+	63.3945i	−0.461658	+	0.0731194i
$868$		0			0
$869$	10.0358	−	13.8131i	0.0115487	−	0.0158954i
$870$		0			0
$871$	−616.051	+	447.587i	−0.707292	+	0.513878i
$872$		0			0
$873$	−74.7273	+	146.661i	−0.0855982	+	0.167996i
$874$		0			0
$875$	−85.0861	−	315.077i	−0.0972413	−	0.360088i
$876$		0			0
$877$	−607.027	−	309.296i	−0.692163	−	0.352674i	0.0722637	−	0.997386i	$-0.476978\pi$
$877$	−607.027	−	309.296i	−0.692163	−	0.352674i	−0.764426	+	0.644711i	$0.776978\pi$
$878$		0			0
$879$	−210.887	−	290.261i	−0.239917	−	0.330217i
$880$		0			0
$881$	−1031.43	−	749.378i	−1.17075	−	0.850599i	−0.179651	−	0.983730i	$-0.557497\pi$
$881$	−1031.43	−	749.378i	−1.17075	−	0.850599i	−0.991098	+	0.133131i	$0.957497\pi$
$882$		0			0
$883$	−159.690	−	1008.24i	−0.180849	−	1.14184i	−0.896390	−	0.443266i	$-0.853820\pi$
$883$	−159.690	−	1008.24i	−0.180849	−	1.14184i	0.715541	−	0.698571i	$-0.246180\pi$
$884$		0			0
$885$	388.361	+	913.264i	0.438826	+	1.03194i
$886$		0			0
$887$	−24.1860	−	47.4677i	−0.0272672	−	0.0535149i	0.876971	−	0.480543i	$-0.159560\pi$
$887$	−24.1860	−	47.4677i	−0.0272672	−	0.0535149i	−0.904238	+	0.427028i	$0.859560\pi$
$888$		0			0
$889$	58.1459	−	18.8927i	0.0654059	−	0.0212517i
$890$		0			0
$891$	−11.5003	+	35.3942i	−0.0129072	+	0.0397242i
$892$		0			0
$893$	457.171	+	457.171i	0.511950	+	0.511950i
$894$		0			0
$895$	−49.9209	+	720.659i	−0.0557775	+	0.805206i
$896$		0			0
$897$	193.231	−	1220.01i	0.215420	−	1.36011i
$898$		0			0
$899$		−	1882.47i		−	2.09396i
$900$		0			0
$901$	1385.19			1.53739
$902$		0			0
$903$	139.071	+	22.0267i	0.154010	+	0.0243928i
$904$		0			0
$905$	52.6174	+	210.452i	0.0581408	+	0.232543i
$906$		0			0
$907$	−545.754	+	545.754i	−0.601714	+	0.601714i	−0.940767	−	0.339053i	$-0.889893\pi$
$907$	−545.754	+	545.754i	−0.601714	+	0.601714i	0.339053	+	0.940767i	$0.389893\pi$
$908$		0			0
$909$	147.249	+	47.8441i	0.161990	+	0.0526338i
$910$		0			0
$911$	−286.195	−	880.816i	−0.314154	−	0.966868i	−0.976101	−	0.217317i	$-0.930270\pi$
$911$	−286.195	−	880.816i	−0.314154	−	0.966868i	0.661947	−	0.749551i	$-0.269730\pi$
$912$		0			0
$913$	33.6015	−	17.1208i	0.0368033	−	0.0187522i
$914$		0			0
$915$	423.589	−	706.013i	0.462939	−	0.771599i
$916$		0			0
$917$	−280.149	+	44.3712i	−0.305506	+	0.0483873i
$918$		0			0
$919$	−921.461	+	1268.28i	−1.00268	+	1.38007i	−0.0790096	+	0.996874i	$0.525176\pi$
$919$	−921.461	+	1268.28i	−1.00268	+	1.38007i	−0.923668	+	0.383194i	$0.874824\pi$
$920$		0			0
$921$	778.150	−	565.359i	0.844897	−	0.613854i
$922$		0			0
$923$	298.498	−	585.836i	0.323400	−	0.634708i
$924$		0			0
$925$	−359.517	+	271.651i	−0.388667	+	0.293677i
$926$		0			0
$927$	86.0785	+	43.8592i	0.0928571	+	0.0473131i
$928$		0			0
$929$	−166.174	−	228.719i	−0.178874	−	0.246199i	0.710160	−	0.704041i	$-0.248623\pi$
$929$	−166.174	−	228.719i	−0.178874	−	0.246199i	−0.889034	+	0.457842i	$0.848623\pi$
$930$		0			0
$931$	262.510	+	190.725i	0.281966	+	0.204860i
$932$		0			0
$933$	−31.7002	−	200.147i	−0.0339766	−	0.214520i
$934$		0			0
$935$	17.2966	−	75.1433i	0.0184990	−	0.0803672i
$936$		0			0
$937$	821.106	+	1611.51i	0.876314	+	1.71986i	0.671418	+	0.741079i	$0.265685\pi$
$937$	821.106	+	1611.51i	0.876314	+	1.71986i	0.204895	+	0.978784i	$0.434315\pi$
$938$		0			0
$939$	401.013	−	130.297i	0.427064	−	0.138762i
$940$		0			0
$941$	364.832	−	1122.84i	0.387707	−	1.19324i	−0.546790	−	0.837270i	$-0.684150\pi$
$941$	364.832	−	1122.84i	0.387707	−	1.19324i	0.934497	−	0.355970i	$-0.115850\pi$
$942$		0			0
$943$	−184.249	−	184.249i	−0.195386	−	0.195386i
$944$		0			0
$945$	−355.235	−	143.255i	−0.375910	−	0.151592i
$946$		0			0
$947$	204.601	−	1291.80i	0.216052	−	1.36410i	−0.606354	−	0.795195i	$-0.707368\pi$
$947$	204.601	−	1291.80i	0.216052	−	1.36410i	0.822405	−	0.568902i	$-0.192632\pi$
$948$		0			0
$949$			418.108i			0.440577i
$950$		0			0
$951$	1221.56			1.28450
$952$		0			0
$953$	1175.37	+	186.161i	1.23334	+	0.195342i	0.738868	−	0.673850i	$-0.235361\pi$
$953$	1175.37	+	186.161i	1.23334	+	0.195342i	0.494474	+	0.869192i	$0.335361\pi$
$954$		0			0
$955$	−668.405	+	418.273i	−0.699901	+	0.437982i
$956$		0			0
$957$	−62.8079	+	62.8079i	−0.0656300	+	0.0656300i
$958$		0			0
$959$	−39.7923	−	12.9293i	−0.0414936	−	0.0134821i
$960$		0			0
$961$	175.134	+	539.006i	0.182241	+	0.560881i
$962$		0			0
$963$	−30.7718	+	15.6790i	−0.0319541	+	0.0162814i
$964$		0			0
$965$	−47.2358	−	535.880i	−0.0489490	−	0.555316i
$966$		0			0
$967$	−414.000	+	65.5712i	−0.428129	+	0.0678089i	−0.366780	−	0.930308i	$-0.619540\pi$
$967$	−414.000	+	65.5712i	−0.428129	+	0.0678089i	−0.0613481	+	0.998116i	$0.519540\pi$
$968$		0			0
$969$	242.741	−	334.104i	0.250507	−	0.344793i
$970$		0			0
$971$	878.393	−	638.190i	0.904627	−	0.657250i	−0.0350230	−	0.999387i	$-0.511150\pi$
$971$	878.393	−	638.190i	0.904627	−	0.657250i	0.939650	+	0.342136i	$0.111150\pi$
$972$		0			0
$973$	236.917	−	464.976i	0.243491	−	0.477879i
$974$		0			0
$975$	−366.361	−	686.860i	−0.375755	−	0.704472i
$976$		0			0
$977$	−425.470	−	216.788i	−0.435486	−	0.221891i	0.222483	−	0.974937i	$-0.428584\pi$
$977$	−425.470	−	216.788i	−0.435486	−	0.221891i	−0.657968	+	0.753046i	$0.728584\pi$
$978$		0			0
$979$	−64.3153	−	88.5225i	−0.0656949	−	0.0904213i
$980$		0			0
$981$	350.829	+	254.892i	0.357623	+	0.259829i
$982$		0			0
$983$	55.8936	+	352.898i	0.0568602	+	0.359001i	0.999670	+	0.0256713i	$0.00817234\pi$
$983$	55.8936	+	352.898i	0.0568602	+	0.359001i	−0.942810	+	0.333330i	$0.891828\pi$
$984$		0			0
$985$	143.858	−	125.219i	0.146049	−	0.127126i
$986$		0			0
$987$	−252.446	−	495.454i	−0.255771	−	0.501979i
$988$		0			0
$989$	802.962	−	260.898i	0.811893	−	0.263800i
$990$		0			0
$991$	326.239	−	1004.06i	0.329202	−	1.01318i	−0.640307	−	0.768119i	$-0.721193\pi$
$991$	326.239	−	1004.06i	0.329202	−	1.01318i	0.969508	−	0.245059i	$-0.0788073\pi$
$992$		0			0
$993$	−485.590	−	485.590i	−0.489013	−	0.489013i
$994$		0			0
$995$	647.119	−	772.229i	0.650371	−	0.776110i
$996$		0			0
$997$	157.009	−	991.318i	0.157482	−	0.994301i	−0.774705	−	0.632323i	$-0.782102\pi$
$997$	157.009	−	991.318i	0.157482	−	0.994301i	0.932187	−	0.361978i	$-0.117898\pi$
$998$		0			0
$999$			528.849i			0.529379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.a.33.1		16
4.3	odd	2		50.3.f.a.33.2	✓	16
20.3	even	4		250.3.f.c.107.1		16
20.7	even	4		250.3.f.a.107.2		16
20.19	odd	2		250.3.f.b.143.1		16
25.22	odd	20	inner	400.3.bg.a.97.1		16
100.3	even	20		250.3.f.b.7.1		16
100.47	even	20		50.3.f.a.47.2	yes	16
100.71	odd	10		250.3.f.a.243.2		16
100.79	odd	10		250.3.f.c.243.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.33.2	✓	16	4.3	odd	2
50.3.f.a.47.2	yes	16	100.47	even	20
250.3.f.a.107.2		16	20.7	even	4
250.3.f.a.243.2		16	100.71	odd	10
250.3.f.b.7.1		16	100.3	even	20
250.3.f.b.143.1		16	20.19	odd	2
250.3.f.c.107.1		16	20.3	even	4
250.3.f.c.243.1		16	100.79	odd	10
400.3.bg.a.33.1		16	1.1	even	1	trivial
400.3.bg.a.97.1		16	25.22	odd	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.50268 - 0.396386i) q^{3} +(-3.83232 - 3.21144i) q^{5} +(1.84619 - 1.84619i) q^{7} +(-2.45322 - 0.797099i) q^{9} +O(q^{10})\)	\(q+(-2.50268 - 0.396386i) q^{3} +(-3.83232 - 3.21144i) q^{5} +(1.84619 - 1.84619i) q^{7} +(-2.45322 - 0.797099i) q^{9} +(-0.224918 - 0.692225i) q^{11} +(10.9494 - 5.57900i) q^{13} +(8.31810 + 9.55628i) q^{15} +(-20.9271 + 3.31453i) q^{17} +(4.52135 - 6.22310i) q^{19} +(-5.35223 + 3.88862i) q^{21} +(-18.0093 + 35.3452i) q^{23} +(4.37333 + 24.6145i) q^{25} +(26.1430 + 13.3205i) q^{27} +(28.3088 + 38.9637i) q^{29} +(-31.6215 - 22.9744i) q^{31} +(0.288509 + 1.82157i) q^{33} +(-13.0041 + 1.14626i) q^{35} +(8.18285 + 16.0598i) q^{37} +(-29.6143 + 9.62228i) q^{39} +(-2.02980 + 6.24709i) q^{41} +(-15.0496 - 15.0496i) q^{43} +(6.84168 + 10.9331i) q^{45} +(-13.1485 + 83.0166i) q^{47} +42.1832i q^{49} +53.6878 q^{51} +(-64.5712 - 10.2271i) q^{53} +(-1.36108 + 3.37514i) q^{55} +(-13.7822 + 13.7822i) q^{57} +(74.4974 + 24.2057i) q^{59} +(-20.0819 - 61.8056i) q^{61} +(-6.00071 + 3.05752i) q^{63} +(-59.8783 - 13.7828i) q^{65} +(-61.2025 + 9.69353i) q^{67} +(59.0818 - 81.3191i) q^{69} +(43.2855 - 31.4488i) q^{71} +(-15.4463 + 30.3151i) q^{73} +(-1.18821 - 63.3358i) q^{75} +(-1.69322 - 0.862739i) q^{77} +(13.7883 + 18.9780i) q^{79} +(-41.3660 - 30.0541i) q^{81} +(8.10529 + 51.1748i) q^{83} +(90.8439 + 54.5039i) q^{85} +(-55.4032 - 108.735i) q^{87} +(142.975 - 46.4555i) q^{89} +(9.91480 - 30.5146i) q^{91} +(70.0319 + 70.0319i) q^{93} +(-37.3123 + 9.32888i) q^{95} +(9.98239 - 63.0263i) q^{97} +1.87746i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9	\( 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9} - 32 q^{11} - 8 q^{13} - 62 q^{17} - 30 q^{19} - 68 q^{21} + 18 q^{23} + 70 q^{25} + 40 q^{27} + 100 q^{29} - 132 q^{31} - 36 q^{33} - 150 q^{35} + 138 q^{37} + 320 q^{39} - 88 q^{41} + 78 q^{43} - 20 q^{45} + 22 q^{47} + 168 q^{51} + 182 q^{53} - 280 q^{55} + 280 q^{57} + 350 q^{59} + 372 q^{61} - 22 q^{63} - 910 q^{65} + 112 q^{67} - 30 q^{69} - 122 q^{71} - 248 q^{73} + 80 q^{75} + 16 q^{77} - 760 q^{79} - 144 q^{81} - 132 q^{83} - 30 q^{85} - 770 q^{87} + 550 q^{89} + 798 q^{91} + 54 q^{93} - 40 q^{95} - 292 q^{97}+O(q^{100}) \) 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9 - 32 * q^11 - 8 * q^13 - 62 * q^17 - 30 * q^19 - 68 * q^21 + 18 * q^23 + 70 * q^25 + 40 * q^27 + 100 * q^29 - 132 * q^31 - 36 * q^33 - 150 * q^35 + 138 * q^37 + 320 * q^39 - 88 * q^41 + 78 * q^43 - 20 * q^45 + 22 * q^47 + 168 * q^51 + 182 * q^53 - 280 * q^55 + 280 * q^57 + 350 * q^59 + 372 * q^61 - 22 * q^63 - 910 * q^65 + 112 * q^67 - 30 * q^69 - 122 * q^71 - 248 * q^73 + 80 * q^75 + 16 * q^77 - 760 * q^79 - 144 * q^81 - 132 * q^83 - 30 * q^85 - 770 * q^87 + 550 * q^89 + 798 * q^91 + 54 * q^93 - 40 * q^95 - 292 * q^97

Introduction

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