LMFDB - Embedded newform 384.3.i.d.161.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,3,Mod(161,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("384.161");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	384.i (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.4632421514$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 $ x^20 - 2x^18 + 6x^16 - 24x^14 - 24x^12 + 1216x^10 - 384x^8 - 6144x^6 + 24576x^4 - 131072*x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{23} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.4
Root			$-1.21144 + 1.59136i$ of defining polynomial
Character	$\chi$	$=$	384.161
Dual form			384.3.i.d.353.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14944 - 2.77106i) q^{3} +(-4.80434 - 4.80434i) q^{5} -7.36187i q^{7} +(-6.35757 + 6.37035i) q^{9} +O(q^{10})$	\(q+(-1.14944 - 2.77106i) q^{3} +(-4.80434 - 4.80434i) q^{5} -7.36187i q^{7} +(-6.35757 + 6.37035i) q^{9} +(0.514693 + 0.514693i) q^{11} +(-7.12969 - 7.12969i) q^{13} +(-7.79081 + 18.8354i) q^{15} -11.1126i q^{17} +(21.1403 + 21.1403i) q^{19} +(-20.4002 + 8.46203i) q^{21} -7.80231 q^{23} +21.1633i q^{25} +(24.9603 + 10.2949i) q^{27} +(-34.6058 + 34.6058i) q^{29} +24.8644 q^{31} +(0.834637 - 2.01786i) q^{33} +(-35.3689 + 35.3689i) q^{35} +(18.2760 - 18.2760i) q^{37} +(-11.5617 + 27.9520i) q^{39} -64.2448 q^{41} +(-7.24058 + 7.24058i) q^{43} +(61.1492 - 0.0613789i) q^{45} +23.0508i q^{47} -5.19710 q^{49} +(-30.7938 + 12.7733i) q^{51} +(-31.9199 - 31.9199i) q^{53} -4.94552i q^{55} +(34.2816 - 82.8807i) q^{57} +(-17.6272 - 17.6272i) q^{59} +(12.3933 + 12.3933i) q^{61} +(46.8976 + 46.8036i) q^{63} +68.5069i q^{65} +(-41.1425 - 41.1425i) q^{67} +(8.96830 + 21.6207i) q^{69} -25.6785 q^{71} +56.1845i q^{73} +(58.6449 - 24.3260i) q^{75} +(3.78910 - 3.78910i) q^{77} -35.7013 q^{79} +(-0.162608 - 80.9998i) q^{81} +(94.9424 - 94.9424i) q^{83} +(-53.3889 + 53.3889i) q^{85} +(135.672 + 56.1175i) q^{87} -44.8713 q^{89} +(-52.4878 + 52.4878i) q^{91} +(-28.5802 - 68.9008i) q^{93} -203.131i q^{95} -82.3636 q^{97} +(-6.55097 + 0.00657558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{3}+O(q^{10}) $ 20 * q + 6 * q^3	$ 20 q + 6 q^{3} - 92 q^{13} - 116 q^{15} + 52 q^{19} - 48 q^{21} - 18 q^{27} - 80 q^{31} + 60 q^{33} + 116 q^{37} - 172 q^{43} - 60 q^{45} - 364 q^{49} - 128 q^{51} + 244 q^{61} + 296 q^{63} - 356 q^{67} + 20 q^{69} + 146 q^{75} + 384 q^{79} - 188 q^{81} - 48 q^{85} - 136 q^{91} + 132 q^{93} + 472 q^{97} + 452 q^{99}+O(q^{100}) $ 20 * q + 6 * q^3 - 92 * q^13 - 116 * q^15 + 52 * q^19 - 48 * q^21 - 18 * q^27 - 80 * q^31 + 60 * q^33 + 116 * q^37 - 172 * q^43 - 60 * q^45 - 364 * q^49 - 128 * q^51 + 244 * q^61 + 296 * q^63 - 356 * q^67 + 20 * q^69 + 146 * q^75 + 384 * q^79 - 188 * q^81 - 48 * q^85 - 136 * q^91 + 132 * q^93 + 472 * q^97 + 452 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	−1.14944	−	2.77106i	−0.383147	−	0.923687i
$3$	−1.14944	−	2.77106i	−0.383147	−	0.923687i
$4$		0			0
$5$	−4.80434	−	4.80434i	−0.960868	−	0.960868i	0.0383950	−	0.999263i	$-0.487775\pi$
$5$	−4.80434	−	4.80434i	−0.960868	−	0.960868i	−0.999263	+	0.0383950i	$0.987775\pi$
$6$		0			0
$7$		−	7.36187i		−	1.05170i	−0.850579	−	0.525848i	$-0.823748\pi$
$7$		−	7.36187i		−	1.05170i	0.850579	−	0.525848i	$-0.176252\pi$
$8$		0			0
$9$	−6.35757	+	6.37035i	−0.706397	+	0.707816i
$10$		0			0
$11$	0.514693	+	0.514693i	0.0467903	+	0.0467903i	0.730115	−	0.683325i	$-0.239467\pi$
$11$	0.514693	+	0.514693i	0.0467903	+	0.0467903i	−0.683325	+	0.730115i	$0.739467\pi$
$12$		0			0
$13$	−7.12969	−	7.12969i	−0.548438	−	0.548438i	0.377551	−	0.925989i	$-0.376766\pi$
$13$	−7.12969	−	7.12969i	−0.548438	−	0.548438i	−0.925989	+	0.377551i	$0.876766\pi$
$14$		0			0
$15$	−7.79081	+	18.8354i	−0.519388	+	1.25569i
$16$		0			0
$17$		−	11.1126i		−	0.653684i	−0.945079	−	0.326842i	$-0.894015\pi$
$17$		−	11.1126i		−	0.653684i	0.945079	−	0.326842i	$-0.105985\pi$
$18$		0			0
$19$	21.1403	+	21.1403i	1.11265	+	1.11265i	0.992791	+	0.119858i	$0.0382440\pi$
$19$	21.1403	+	21.1403i	1.11265	+	1.11265i	0.119858	+	0.992791i	$0.461756\pi$
$20$		0			0
$21$	−20.4002	+	8.46203i	−0.971438	+	0.402954i
$22$		0			0
$23$	−7.80231			−0.339231			−0.169615	−	0.985510i	$-0.554253\pi$
$23$	−7.80231			−0.339231			−0.169615	+	0.985510i	$0.554253\pi$
$24$		0			0
$25$			21.1633i			0.846533i
$26$		0			0
$27$	24.9603	+	10.2949i	0.924455	+	0.381292i
$28$		0			0
$29$	−34.6058	+	34.6058i	−1.19330	+	1.19330i	−0.217169	+	0.976134i	$0.569682\pi$
$29$	−34.6058	+	34.6058i	−1.19330	+	1.19330i	−0.976134	+	0.217169i	$0.930318\pi$
$30$		0			0
$31$	24.8644			0.802078			0.401039	−	0.916061i	$-0.368649\pi$
$31$	24.8644			0.802078			0.401039	+	0.916061i	$0.368649\pi$
$32$		0			0
$33$	0.834637	−	2.01786i	0.0252920	−	0.0611472i
$34$		0			0
$35$	−35.3689	+	35.3689i	−1.01054	+	1.01054i
$36$		0			0
$37$	18.2760	−	18.2760i	0.493946	−	0.493946i	−0.415601	−	0.909547i	$-0.636429\pi$
$37$	18.2760	−	18.2760i	0.493946	−	0.493946i	0.909547	+	0.415601i	$0.136429\pi$
$38$		0			0
$39$	−11.5617	+	27.9520i	−0.296453	+	0.716717i
$40$		0			0
$41$	−64.2448			−1.56695			−0.783473	−	0.621426i	$-0.786554\pi$
$41$	−64.2448			−1.56695			−0.783473	+	0.621426i	$0.786554\pi$
$42$		0			0
$43$	−7.24058	+	7.24058i	−0.168386	+	0.168386i	−0.786269	−	0.617884i	$-0.787990\pi$
$43$	−7.24058	+	7.24058i	−0.168386	+	0.168386i	0.617884	+	0.786269i	$0.287990\pi$
$44$		0			0
$45$	61.1492	−	0.0613789i	1.35887	−	0.00136398i
$46$		0			0
$47$			23.0508i			0.490442i	0.969467	+	0.245221i	$0.0788606\pi$
$47$			23.0508i			0.490442i	−0.969467	+	0.245221i	$0.921139\pi$
$48$		0			0
$49$	−5.19710			−0.106063
$50$		0			0
$51$	−30.7938	+	12.7733i	−0.603800	+	0.250457i
$52$		0			0
$53$	−31.9199	−	31.9199i	−0.602263	−	0.602263i	0.338650	−	0.940913i	$-0.390030\pi$
$53$	−31.9199	−	31.9199i	−0.602263	−	0.602263i	−0.940913	+	0.338650i	$0.890030\pi$
$54$		0			0
$55$		−	4.94552i		−	0.0899185i
$56$		0			0
$57$	34.2816	−	82.8807i	0.601432	−	1.45405i
$58$		0			0
$59$	−17.6272	−	17.6272i	−0.298766	−	0.298766i	0.541764	−	0.840530i	$-0.317756\pi$
$59$	−17.6272	−	17.6272i	−0.298766	−	0.298766i	−0.840530	+	0.541764i	$0.817756\pi$
$60$		0			0
$61$	12.3933	+	12.3933i	0.203170	+	0.203170i	0.801357	−	0.598187i	$-0.204112\pi$
$61$	12.3933	+	12.3933i	0.203170	+	0.203170i	−0.598187	+	0.801357i	$0.704112\pi$
$62$		0			0
$63$	46.8976	+	46.8036i	0.744407	+	0.742914i
$64$		0			0
$65$			68.5069i			1.05395i
$66$		0			0
$67$	−41.1425	−	41.1425i	−0.614067	−	0.614067i	0.329936	−	0.944003i	$-0.392973\pi$
$67$	−41.1425	−	41.1425i	−0.614067	−	0.614067i	−0.944003	+	0.329936i	$0.892973\pi$
$68$		0			0
$69$	8.96830	+	21.6207i	0.129975	+	0.313343i
$70$		0			0
$71$	−25.6785			−0.361669			−0.180834	−	0.983514i	$-0.557880\pi$
$71$	−25.6785			−0.361669			−0.180834	+	0.983514i	$0.557880\pi$
$72$		0			0
$73$			56.1845i			0.769650i	0.922990	+	0.384825i	$0.125738\pi$
$73$			56.1845i			0.769650i	−0.922990	+	0.384825i	$0.874262\pi$
$74$		0			0
$75$	58.6449	−	24.3260i	0.781932	−	0.324347i
$76$		0			0
$77$	3.78910	−	3.78910i	0.0492091	−	0.0492091i
$78$		0			0
$79$	−35.7013			−0.451915			−0.225957	−	0.974137i	$-0.572551\pi$
$79$	−35.7013			−0.451915			−0.225957	+	0.974137i	$0.572551\pi$
$80$		0			0
$81$	−0.162608	−	80.9998i	−0.00200751	−	0.999998i
$82$		0			0
$83$	94.9424	−	94.9424i	1.14388	−	1.14388i	0.156151	−	0.987733i	$-0.450091\pi$
$83$	94.9424	−	94.9424i	1.14388	−	1.14388i	0.987733	−	0.156151i	$-0.0499086\pi$
$84$		0			0
$85$	−53.3889	+	53.3889i	−0.628104	+	0.628104i
$86$		0			0
$87$	135.672	+	56.1175i	1.55945	+	0.645028i
$88$		0			0
$89$	−44.8713			−0.504172			−0.252086	−	0.967705i	$-0.581117\pi$
$89$	−44.8713			−0.504172			−0.252086	+	0.967705i	$0.581117\pi$
$90$		0			0
$91$	−52.4878	+	52.4878i	−0.576789	+	0.576789i
$92$		0			0
$93$	−28.5802	−	68.9008i	−0.307314	−	0.740869i
$94$		0			0
$95$		−	203.131i		−	2.13822i
$96$		0			0
$97$	−82.3636			−0.849109			−0.424554	−	0.905402i	$-0.639569\pi$
$97$	−82.3636			−0.849109			−0.424554	+	0.905402i	$0.639569\pi$
$98$		0			0
$99$	−6.55097	+	0.00657558i	−0.0661714	+	6.64200e-5i
$100$		0			0
$101$	36.3420	+	36.3420i	0.359822	+	0.359822i	0.863747	−	0.503925i	$-0.168111\pi$
$101$	36.3420	+	36.3420i	0.359822	+	0.359822i	−0.503925	+	0.863747i	$0.668111\pi$
$102$		0			0
$103$		−	87.5176i		−	0.849685i	−0.905267	−	0.424843i	$-0.860329\pi$
$103$		−	87.5176i		−	0.849685i	0.905267	−	0.424843i	$-0.139671\pi$
$104$		0			0
$105$	138.664	+	57.3550i	1.32061	+	0.546238i
$106$		0			0
$107$	−104.866	−	104.866i	−0.980058	−	0.980058i	0.0197471	−	0.999805i	$-0.493714\pi$
$107$	−104.866	−	104.866i	−0.980058	−	0.980058i	−0.999805	+	0.0197471i	$0.993714\pi$
$108$		0			0
$109$	−7.64006	−	7.64006i	−0.0700923	−	0.0700923i	0.671192	−	0.741284i	$-0.265783\pi$
$109$	−7.64006	−	7.64006i	−0.0700923	−	0.0700923i	−0.741284	+	0.671192i	$0.765783\pi$
$110$		0			0
$111$	−71.6511	−	29.6367i	−0.645505	−	0.266998i
$112$		0			0
$113$			13.1273i			0.116171i	0.998312	+	0.0580853i	$0.0184995\pi$
$113$			13.1273i			0.116171i	−0.998312	+	0.0580853i	$0.981500\pi$
$114$		0			0
$115$	37.4849	+	37.4849i	0.325956	+	0.325956i
$116$		0			0
$117$	90.7461	−	0.0910869i	0.775607	−	0.000778521i
$118$		0			0
$119$	−81.8098			−0.687477
$120$		0			0
$121$		−	120.470i		−	0.995621i
$122$		0			0
$123$	73.8456	+	178.026i	0.600371	+	1.44737i
$124$		0			0
$125$	−18.4327	+	18.4327i	−0.147461	+	0.147461i
$126$		0			0
$127$	−88.2707			−0.695045			−0.347523	−	0.937672i	$-0.612977\pi$
$127$	−88.2707			−0.695045			−0.347523	+	0.937672i	$0.612977\pi$
$128$		0			0
$129$	28.3867	+	11.7415i	0.220052	+	0.0910192i
$130$		0			0
$131$	57.0518	−	57.0518i	0.435510	−	0.435510i	−0.454988	−	0.890498i	$-0.650356\pi$
$131$	57.0518	−	57.0518i	0.435510	−	0.435510i	0.890498	+	0.454988i	$0.150356\pi$
$132$		0			0
$133$	155.632	−	155.632i	1.17017	−	1.17017i
$134$		0			0
$135$	−70.4575	−	169.378i	−0.521907	−	1.25465i
$136$		0			0
$137$	165.112			1.20520			0.602599	−	0.798045i	$-0.294132\pi$
$137$	165.112			1.20520			0.602599	+	0.798045i	$0.294132\pi$
$138$		0			0
$139$	95.0802	−	95.0802i	0.684030	−	0.684030i	−0.276875	−	0.960906i	$-0.589299\pi$
$139$	95.0802	−	95.0802i	0.684030	−	0.684030i	0.960906	+	0.276875i	$0.0892990\pi$
$140$		0			0
$141$	63.8752	−	26.4955i	0.453015	−	0.187912i
$142$		0			0
$143$		−	7.33920i		−	0.0513231i
$144$		0			0
$145$	332.516			2.29321
$146$		0			0
$147$	5.97376	+	14.4015i	0.0406378	+	0.0979693i
$148$		0			0
$149$	131.077	+	131.077i	0.879709	+	0.879709i	0.993504	−	0.113795i	$-0.0363006\pi$
$149$	131.077	+	131.077i	0.879709	+	0.879709i	−0.113795	+	0.993504i	$0.536301\pi$
$150$		0			0
$151$			123.070i			0.815031i	0.913198	+	0.407515i	$0.133605\pi$
$151$			123.070i			0.815031i	−0.913198	+	0.407515i	$0.866395\pi$
$152$		0			0
$153$	70.7913	+	70.6494i	0.462688	+	0.461761i
$154$		0			0
$155$	−119.457	−	119.457i	−0.770690	−	0.770690i
$156$		0			0
$157$	−139.181	−	139.181i	−0.886503	−	0.886503i	0.107683	−	0.994185i	$-0.465657\pi$
$157$	−139.181	−	139.181i	−0.886503	−	0.886503i	−0.994185	+	0.107683i	$0.965657\pi$
$158$		0			0
$159$	−51.7620	+	125.142i	−0.325547	+	0.787058i
$160$		0			0
$161$			57.4396i			0.356768i
$162$		0			0
$163$	19.9311	+	19.9311i	0.122277	+	0.122277i	0.765597	−	0.643320i	$-0.222444\pi$
$163$	19.9311	+	19.9311i	0.122277	+	0.122277i	−0.643320	+	0.765597i	$0.722444\pi$
$164$		0			0
$165$	−13.7043	+	5.68458i	−0.0830566	+	0.0344520i
$166$		0			0
$167$	60.3220			0.361210			0.180605	−	0.983556i	$-0.442194\pi$
$167$	60.3220			0.361210			0.180605	+	0.983556i	$0.442194\pi$
$168$		0			0
$169$		−	67.3351i		−	0.398432i
$170$		0			0
$171$	−269.072	+	0.270083i	−1.57352	+	0.00157943i
$172$		0			0
$173$	−74.8292	+	74.8292i	−0.432539	+	0.432539i	−0.889491	−	0.456952i	$-0.848941\pi$
$173$	−74.8292	+	74.8292i	−0.432539	+	0.432539i	0.456952	+	0.889491i	$0.348941\pi$
$174$		0			0
$175$	155.802			0.890295
$176$		0			0
$177$	−28.5846	+	69.1074i	−0.161495	+	0.390438i
$178$		0			0
$179$	−3.96558	+	3.96558i	−0.0221541	+	0.0221541i	−0.718097	−	0.695943i	$-0.754987\pi$
$179$	−3.96558	+	3.96558i	−0.0221541	+	0.0221541i	0.695943	+	0.718097i	$0.254987\pi$
$180$		0			0
$181$	−158.820	+	158.820i	−0.877457	+	0.877457i	−0.993271	−	0.115814i	$-0.963052\pi$
$181$	−158.820	+	158.820i	−0.877457	+	0.877457i	0.115814	+	0.993271i	$0.463052\pi$
$182$		0			0
$183$	20.0973	−	48.5882i	0.109821	−	0.265509i
$184$		0			0
$185$	−175.608			−0.949233
$186$		0			0
$187$	5.71960	−	5.71960i	0.0305861	−	0.0305861i
$188$		0			0
$189$	75.7896	−	183.754i	0.401003	−	0.972245i
$190$		0			0
$191$		−	68.8639i		−	0.360544i	−0.983617	−	0.180272i	$-0.942302\pi$
$191$		−	68.8639i		−	0.360544i	0.983617	−	0.180272i	$-0.0576978\pi$
$192$		0			0
$193$	−366.645			−1.89971			−0.949856	−	0.312686i	$-0.898771\pi$
$193$	−366.645			−1.89971			−0.949856	+	0.312686i	$0.898771\pi$
$194$		0			0
$195$	189.837	−	78.7446i	0.973522	−	0.403819i
$196$		0			0
$197$	−246.744	−	246.744i	−1.25251	−	1.25251i	−0.954593	−	0.297912i	$-0.903710\pi$
$197$	−246.744	−	246.744i	−1.25251	−	1.25251i	−0.297912	−	0.954593i	$-0.596290\pi$
$198$		0			0
$199$			287.802i			1.44624i	0.690722	+	0.723120i	$0.257293\pi$
$199$			287.802i			1.44624i	−0.690722	+	0.723120i	$0.742707\pi$
$200$		0			0
$201$	−66.7176	+	161.299i	−0.331928	+	0.802484i
$202$		0			0
$203$	254.763	+	254.763i	1.25499	+	1.25499i
$204$		0			0
$205$	308.654	+	308.654i	1.50563	+	1.50563i
$206$		0			0
$207$	49.6037	−	49.7034i	0.239632	−	0.240113i
$208$		0			0
$209$			21.7616i			0.104122i
$210$		0			0
$211$	−156.146	−	156.146i	−0.740027	−	0.740027i	0.232556	−	0.972583i	$-0.425291\pi$
$211$	−156.146	−	156.146i	−0.740027	−	0.740027i	−0.972583	+	0.232556i	$0.925291\pi$
$212$		0			0
$213$	29.5159	+	71.1567i	0.138572	+	0.334069i
$214$		0			0
$215$	69.5724			0.323593
$216$		0			0
$217$		−	183.048i		−	0.843541i
$218$		0			0
$219$	155.691	−	64.5807i	0.710916	−	0.294889i
$220$		0			0
$221$	−79.2296	+	79.2296i	−0.358505	+	0.358505i
$222$		0			0
$223$	45.2998			0.203138			0.101569	−	0.994828i	$-0.467614\pi$
$223$	45.2998			0.203138			0.101569	+	0.994828i	$0.467614\pi$
$224$		0			0
$225$	−134.818	−	134.547i	−0.599190	−	0.597988i
$226$		0			0
$227$	−300.757	+	300.757i	−1.32492	+	1.32492i	−0.415186	+	0.909737i	$0.636283\pi$
$227$	−300.757	+	300.757i	−1.32492	+	1.32492i	−0.909737	+	0.415186i	$0.863717\pi$
$228$		0			0
$229$	−65.7088	+	65.7088i	−0.286938	+	0.286938i	−0.835868	−	0.548930i	$-0.815035\pi$
$229$	−65.7088	+	65.7088i	−0.286938	+	0.286938i	0.548930	+	0.835868i	$0.315035\pi$
$230$		0			0
$231$	−14.8552	−	6.14449i	−0.0643082	−	0.0265995i
$232$		0			0
$233$	−42.8218			−0.183785			−0.0918923	−	0.995769i	$-0.529292\pi$
$233$	−42.8218			−0.183785			−0.0918923	+	0.995769i	$0.529292\pi$
$234$		0			0
$235$	110.744	−	110.744i	0.471250	−	0.471250i
$236$		0			0
$237$	41.0365	+	98.9305i	0.173150	+	0.417428i
$238$		0			0
$239$			100.598i			0.420913i	0.977603	+	0.210456i	$0.0674950\pi$
$239$			100.598i			0.420913i	−0.977603	+	0.210456i	$0.932505\pi$
$240$		0			0
$241$	−5.23162			−0.0217080			−0.0108540	−	0.999941i	$-0.503455\pi$
$241$	−5.23162			−0.0217080			−0.0108540	+	0.999941i	$0.503455\pi$
$242$		0			0
$243$	−224.269	+	93.5551i	−0.922916	+	0.385001i
$244$		0			0
$245$	24.9686	+	24.9686i	0.101913	+	0.101913i
$246$		0			0
$247$		−	301.448i		−	1.22044i
$248$		0			0
$249$	−372.222	−	153.961i	−1.49487	−	0.618315i
$250$		0			0
$251$	−17.4381	−	17.4381i	−0.0694747	−	0.0694747i	0.671516	−	0.740990i	$-0.265644\pi$
$251$	−17.4381	−	17.4381i	−0.0694747	−	0.0694747i	−0.740990	+	0.671516i	$0.765644\pi$
$252$		0			0
$253$	−4.01579	−	4.01579i	−0.0158727	−	0.0158727i
$254$		0			0
$255$	209.311	+	86.5765i	0.820828	+	0.339516i
$256$		0			0
$257$		−	343.676i		−	1.33726i	−0.743595	−	0.668630i	$-0.766881\pi$
$257$		−	343.676i		−	1.33726i	0.743595	−	0.668630i	$-0.233119\pi$
$258$		0			0
$259$	−134.545	−	134.545i	−0.519480	−	0.519480i
$260$		0			0
$261$	−0.442114	−	440.460i	−0.00169392	−	1.68758i
$262$		0			0
$263$	98.0863			0.372952			0.186476	−	0.982460i	$-0.440293\pi$
$263$	98.0863			0.372952			0.186476	+	0.982460i	$0.440293\pi$
$264$		0			0
$265$			306.708i			1.15739i
$266$		0			0
$267$	51.5769	+	124.341i	0.193172	+	0.465697i
$268$		0			0
$269$	126.560	−	126.560i	0.470482	−	0.470482i	−0.431589	−	0.902070i	$-0.642047\pi$
$269$	126.560	−	126.560i	0.470482	−	0.470482i	0.902070	+	0.431589i	$0.142047\pi$
$270$		0			0
$271$	−206.487			−0.761945			−0.380972	−	0.924586i	$-0.624411\pi$
$271$	−206.487			−0.761945			−0.380972	+	0.924586i	$0.624411\pi$
$272$		0			0
$273$	205.779	+	85.1154i	0.753768	+	0.311778i
$274$		0			0
$275$	−10.8926	+	10.8926i	−0.0396095	+	0.0396095i
$276$		0			0
$277$	−183.416	+	183.416i	−0.662153	+	0.662153i	−0.955887	−	0.293734i	$-0.905102\pi$
$277$	−183.416	+	183.416i	−0.662153	+	0.662153i	0.293734	+	0.955887i	$0.405102\pi$
$278$		0			0
$279$	−158.077	+	158.395i	−0.566585	+	0.567723i
$280$		0			0
$281$	−109.143			−0.388409			−0.194204	−	0.980961i	$-0.562213\pi$
$281$	−109.143			−0.388409			−0.194204	+	0.980961i	$0.562213\pi$
$282$		0			0
$283$	−60.4623	+	60.4623i	−0.213648	+	0.213648i	−0.805815	−	0.592167i	$-0.798272\pi$
$283$	−60.4623	+	60.4623i	−0.213648	+	0.213648i	0.592167	+	0.805815i	$0.298272\pi$
$284$		0			0
$285$	−562.888	+	233.487i	−1.97504	+	0.819252i
$286$		0			0
$287$			472.962i			1.64795i
$288$		0			0
$289$	165.509			0.572697
$290$		0			0
$291$	94.6721	+	228.235i	0.325334	+	0.784311i
$292$		0			0
$293$	−19.4639	−	19.4639i	−0.0664296	−	0.0664296i	0.673111	−	0.739541i	$-0.264957\pi$
$293$	−19.4639	−	19.4639i	−0.0664296	−	0.0664296i	−0.739541	+	0.673111i	$0.764957\pi$
$294$		0			0
$295$			169.374i			0.574149i
$296$		0			0
$297$	7.54818	+	18.1456i	0.0254147	+	0.0610963i
$298$		0			0
$299$	55.6280	+	55.6280i	0.186047	+	0.186047i
$300$		0			0
$301$	53.3042	+	53.3042i	0.177090	+	0.177090i
$302$		0			0
$303$	58.9329	−	142.479i	0.194498	−	0.470227i
$304$		0			0
$305$		−	119.084i		−	0.390438i
$306$		0			0
$307$	408.201	+	408.201i	1.32964	+	1.32964i	0.905677	+	0.423967i	$0.139363\pi$
$307$	408.201	+	408.201i	1.32964	+	1.32964i	0.423967	+	0.905677i	$0.360637\pi$
$308$		0			0
$309$	−242.517	+	100.596i	−0.784844	+	0.325554i
$310$		0			0
$311$	−360.965			−1.16066			−0.580330	−	0.814381i	$-0.697076\pi$
$311$	−360.965			−1.16066			−0.580330	+	0.814381i	$0.697076\pi$
$312$		0			0
$313$			73.9217i			0.236172i	0.993003	+	0.118086i	$0.0376758\pi$
$313$			73.9217i			0.236172i	−0.993003	+	0.118086i	$0.962324\pi$
$314$		0			0
$315$	−0.451863	−	450.172i	−0.00143449	−	1.42912i
$316$		0			0
$317$	172.709	−	172.709i	0.544825	−	0.544825i	−0.380115	−	0.924939i	$-0.624116\pi$
$317$	172.709	−	172.709i	0.544825	−	0.544825i	0.924939	+	0.380115i	$0.124116\pi$
$318$		0			0
$319$	−35.6227			−0.111670
$320$		0			0
$321$	−170.053	+	411.128i	−0.529761	+	1.28077i
$322$		0			0
$323$	234.925	−	234.925i	0.727321	−	0.727321i
$324$		0			0
$325$	150.888	−	150.888i	0.464271	−	0.464271i
$326$		0			0
$327$	−12.3893	+	29.9529i	−0.0378877	+	0.0915990i
$328$		0			0
$329$	169.697			0.515796
$330$		0			0
$331$	−261.507	+	261.507i	−0.790051	+	0.790051i	−0.981502	−	0.191451i	$-0.938681\pi$
$331$	−261.507	+	261.507i	−0.790051	+	0.790051i	0.191451	+	0.981502i	$0.438681\pi$
$332$		0			0
$333$	0.233489	+	232.615i	0.000701168	+	0.698544i
$334$		0			0
$335$			395.325i			1.18007i
$336$		0			0
$337$	18.2211			0.0540684			0.0270342	−	0.999635i	$-0.491394\pi$
$337$	18.2211			0.0540684			0.0270342	+	0.999635i	$0.491394\pi$
$338$		0			0
$339$	36.3765	−	15.0890i	0.107305	−	0.0445104i
$340$		0			0
$341$	12.7975	+	12.7975i	0.0375294	+	0.0375294i
$342$		0			0
$343$		−	322.471i		−	0.940149i
$344$		0			0
$345$	60.7863	−	146.960i	0.176192	−	0.425970i
$346$		0			0
$347$	173.710	+	173.710i	0.500605	+	0.500605i	0.911626	−	0.411021i	$-0.134828\pi$
$347$	173.710	+	173.710i	0.500605	+	0.500605i	−0.411021	+	0.911626i	$0.634828\pi$
$348$		0			0
$349$	−387.899	−	387.899i	−1.11146	−	1.11146i	−0.992953	−	0.118506i	$-0.962189\pi$
$349$	−387.899	−	387.899i	−1.11146	−	1.11146i	−0.118506	−	0.992953i	$-0.537811\pi$
$350$		0			0
$351$	−104.560	−	251.358i	−0.297891	−	0.716121i
$352$		0			0
$353$			676.812i			1.91732i	0.284561	+	0.958658i	$0.408152\pi$
$353$			676.812i			1.91732i	−0.284561	+	0.958658i	$0.591848\pi$
$354$		0			0
$355$	123.368	+	123.368i	0.347516	+	0.347516i
$356$		0			0
$357$	94.0355	+	226.700i	0.263405	+	0.635014i
$358$		0			0
$359$	240.896			0.671020			0.335510	−	0.942037i	$-0.391091\pi$
$359$	240.896			0.671020			0.335510	+	0.942037i	$0.391091\pi$
$360$		0			0
$361$			532.827i			1.47598i
$362$		0			0
$363$	−333.830	+	138.473i	−0.919643	+	0.381469i
$364$		0			0
$365$	269.929	−	269.929i	0.739532	−	0.739532i
$366$		0			0
$367$	666.702			1.81663			0.908313	−	0.418291i	$-0.137371\pi$
$367$	666.702			1.81663			0.908313	+	0.418291i	$0.137371\pi$
$368$		0			0
$369$	408.441	−	409.261i	1.10689	−	1.10911i
$370$		0			0
$371$	−234.990	+	234.990i	−0.633397	+	0.633397i
$372$		0			0
$373$	358.513	−	358.513i	0.961160	−	0.961160i	−0.0381137	−	0.999273i	$-0.512135\pi$
$373$	358.513	−	358.513i	0.961160	−	0.961160i	0.999273	+	0.0381137i	$0.0121349\pi$
$374$		0			0
$375$	72.2653	+	29.8908i	0.192708	+	0.0797088i
$376$		0			0
$377$	493.457			1.30890
$378$		0			0
$379$	140.959	−	140.959i	0.371925	−	0.371925i	−0.496253	−	0.868178i	$-0.665291\pi$
$379$	140.959	−	140.959i	0.371925	−	0.371925i	0.868178	+	0.496253i	$0.165291\pi$
$380$		0			0
$381$	101.462	+	244.604i	0.266305	+	0.642004i
$382$		0			0
$383$		−	69.4683i		−	0.181379i	−0.995879	−	0.0906897i	$-0.971093\pi$
$383$		−	69.4683i		−	0.181379i	0.995879	−	0.0906897i	$-0.0289071\pi$
$384$		0			0
$385$	−36.4083			−0.0945669
$386$		0			0
$387$	−0.0925037	−	92.1575i	−0.000239028	−	0.238133i
$388$		0			0
$389$	265.362	+	265.362i	0.682165	+	0.682165i	0.960488	−	0.278322i	$-0.0897783\pi$
$389$	265.362	+	265.362i	0.682165	+	0.682165i	−0.278322	+	0.960488i	$0.589778\pi$
$390$		0			0
$391$			86.7042i			0.221750i
$392$		0			0
$393$	−223.672	−	92.5164i	−0.569139	−	0.235411i
$394$		0			0
$395$	171.521	+	171.521i	0.434230	+	0.434230i
$396$		0			0
$397$	−259.123	−	259.123i	−0.652703	−	0.652703i	0.300940	−	0.953643i	$-0.402700\pi$
$397$	−259.123	−	259.123i	−0.652703	−	0.652703i	−0.953643	+	0.300940i	$0.902700\pi$
$398$		0			0
$399$	−610.157	−	252.377i	−1.52922	−	0.632523i
$400$		0			0
$401$		−	664.163i		−	1.65627i	−0.560531	−	0.828133i	$-0.689403\pi$
$401$		−	664.163i		−	1.65627i	0.560531	−	0.828133i	$-0.310597\pi$
$402$		0			0
$403$	−177.275	−	177.275i	−0.439889	−	0.439889i
$404$		0			0
$405$	−388.369	+	389.932i	−0.958937	+	0.962795i
$406$		0			0
$407$	18.8131			0.0462237
$408$		0			0
$409$		−	530.421i		−	1.29687i	−0.761269	−	0.648437i	$-0.775423\pi$
$409$		−	530.421i		−	1.29687i	0.761269	−	0.648437i	$-0.224577\pi$
$410$		0			0
$411$	−189.787	−	457.536i	−0.461768	−	1.11323i
$412$		0			0
$413$	−129.769	+	129.769i	−0.314211	+	0.314211i
$414$		0			0
$415$	−912.271			−2.19824
$416$		0			0
$417$	−372.762	−	154.184i	−0.893914	−	0.369746i
$418$		0			0
$419$	404.149	−	404.149i	0.964556	−	0.964556i	−0.0348367	−	0.999393i	$-0.511091\pi$
$419$	404.149	−	404.149i	0.964556	−	0.964556i	0.999393	+	0.0348367i	$0.0110911\pi$
$420$		0			0
$421$	264.630	−	264.630i	0.628575	−	0.628575i	−0.319134	−	0.947710i	$-0.603392\pi$
$421$	264.630	−	264.630i	0.628575	−	0.628575i	0.947710	+	0.319134i	$0.103392\pi$
$422$		0			0
$423$	−146.842	−	146.547i	−0.347143	−	0.346447i
$424$		0			0
$425$	235.180			0.553366
$426$		0			0
$427$	91.2382	−	91.2382i	0.213673	−	0.213673i
$428$		0			0
$429$	−20.3374	+	8.43598i	−0.0474065	+	0.0196643i
$430$		0			0
$431$		−	766.652i		−	1.77877i	−0.457155	−	0.889387i	$-0.651132\pi$
$431$		−	766.652i		−	1.77877i	0.457155	−	0.889387i	$-0.348868\pi$
$432$		0			0
$433$	151.222			0.349243			0.174622	−	0.984636i	$-0.444130\pi$
$433$	151.222			0.349243			0.174622	+	0.984636i	$0.444130\pi$
$434$		0			0
$435$	−382.207	−	921.422i	−0.878638	−	2.11821i
$436$		0			0
$437$	−164.943	−	164.943i	−0.377445	−	0.377445i
$438$		0			0
$439$		−	565.007i		−	1.28703i	−0.765433	−	0.643516i	$-0.777475\pi$
$439$		−	565.007i		−	1.28703i	0.765433	−	0.643516i	$-0.222525\pi$
$440$		0			0
$441$	33.0409	−	33.1073i	0.0749228	−	0.0750733i
$442$		0			0
$443$	100.963	+	100.963i	0.227907	+	0.227907i	0.811818	−	0.583911i	$-0.198478\pi$
$443$	100.963	+	100.963i	0.227907	+	0.227907i	−0.583911	+	0.811818i	$0.698478\pi$
$444$		0			0
$445$	215.577	+	215.577i	0.484442	+	0.484442i
$446$		0			0
$447$	212.557	−	513.887i	0.475518	−	1.14963i
$448$		0			0
$449$		−	131.725i		−	0.293375i	−0.989183	−	0.146687i	$-0.953139\pi$
$449$		−	131.725i		−	0.293375i	0.989183	−	0.146687i	$-0.0468611\pi$
$450$		0			0
$451$	−33.0663	−	33.0663i	−0.0733178	−	0.0733178i
$452$		0			0
$453$	341.034	−	141.461i	0.752833	−	0.312277i
$454$		0			0
$455$	504.339			1.10844
$456$		0			0
$457$		−	137.963i		−	0.301888i	−0.988542	−	0.150944i	$-0.951769\pi$
$457$		−	137.963i		−	0.301888i	0.988542	−	0.150944i	$-0.0482313\pi$
$458$		0			0
$459$	114.403	−	277.374i	0.249245	−	0.604302i
$460$		0			0
$461$	303.536	−	303.536i	0.658430	−	0.658430i	−0.296579	−	0.955008i	$-0.595846\pi$
$461$	303.536	−	303.536i	0.658430	−	0.658430i	0.955008	+	0.296579i	$0.0958457\pi$
$462$		0			0
$463$	280.379			0.605570			0.302785	−	0.953059i	$-0.402084\pi$
$463$	280.379			0.605570			0.302785	+	0.953059i	$0.402084\pi$
$464$		0			0
$465$	−193.714	+	468.332i	−0.416589	+	1.00716i
$466$		0			0
$467$	65.6355	−	65.6355i	0.140547	−	0.140547i	−0.633333	−	0.773880i	$-0.718313\pi$
$467$	65.6355	−	65.6355i	0.140547	−	0.140547i	0.773880	+	0.633333i	$0.218313\pi$
$468$		0			0
$469$	−302.886	+	302.886i	−0.645812	+	0.645812i
$470$		0			0
$471$	−225.699	+	545.659i	−0.479190	+	1.15851i
$472$		0			0
$473$	−7.45335			−0.0157576
$474$		0			0
$475$	−447.400	+	447.400i	−0.941894	+	0.941894i
$476$		0			0
$477$	406.274	−	0.407800i	0.851728	−	0.000854927i
$478$		0			0
$479$			373.272i			0.779273i	0.920969	+	0.389636i	$0.127399\pi$
$479$			373.272i			0.779273i	−0.920969	+	0.389636i	$0.872601\pi$
$480$		0			0
$481$	−260.604			−0.541797
$482$		0			0
$483$	159.169	−	66.0234i	0.329542	−	0.136694i
$484$		0			0
$485$	395.702	+	395.702i	0.815881	+	0.815881i
$486$		0			0
$487$		−	0.0470526i		−	9.66171e-5i	−1.00000		4.83086e-5i	$-0.999985\pi$
$487$		−	0.0470526i		−	9.66171e-5i	1.00000		4.83086e-5i	$-1.53771e-5\pi$
$488$		0			0
$489$	32.3206	−	78.1398i	0.0660954	−	0.159795i
$490$		0			0
$491$	−273.442	−	273.442i	−0.556908	−	0.556908i	0.371518	−	0.928426i	$-0.378837\pi$
$491$	−273.442	−	273.442i	−0.556908	−	0.556908i	−0.928426	+	0.371518i	$0.878837\pi$
$492$		0			0
$493$	384.562	+	384.562i	0.780044	+	0.780044i
$494$		0			0
$495$	31.5047	+	31.4415i	0.0636458	+	0.0635182i
$496$		0			0
$497$			189.042i			0.380365i
$498$		0			0
$499$	46.2637	+	46.2637i	0.0927129	+	0.0927129i	0.751942	−	0.659229i	$-0.229117\pi$
$499$	46.2637	+	46.2637i	0.0927129	+	0.0927129i	−0.659229	+	0.751942i	$0.729117\pi$
$500$		0			0
$501$	−69.3366	−	167.156i	−0.138396	−	0.333645i
$502$		0			0
$503$	864.426			1.71854			0.859270	−	0.511522i	$-0.170918\pi$
$503$	864.426			1.71854			0.859270	+	0.511522i	$0.170918\pi$
$504$		0			0
$505$		−	349.198i		−	0.691482i
$506$		0			0
$507$	−186.590	+	77.3977i	−0.368027	+	0.152658i
$508$		0			0
$509$	171.041	−	171.041i	0.336033	−	0.336033i	−0.518839	−	0.854872i	$-0.673635\pi$
$509$	171.041	−	171.041i	0.336033	−	0.336033i	0.854872	+	0.518839i	$0.173635\pi$
$510$		0			0
$511$	413.623			0.809438
$512$		0			0
$513$	310.031	+	745.306i	0.604349	+	1.45284i
$514$		0			0
$515$	−420.464	+	420.464i	−0.816435	+	0.816435i
$516$		0			0
$517$	−11.8641	+	11.8641i	−0.0229479	+	0.0229479i
$518$		0			0
$519$	293.368	+	121.345i	0.565257	+	0.233805i
$520$		0			0
$521$	351.572			0.674802			0.337401	−	0.941361i	$-0.390452\pi$
$521$	351.572			0.674802			0.337401	+	0.941361i	$0.390452\pi$
$522$		0			0
$523$	287.638	−	287.638i	0.549977	−	0.549977i	−0.376457	−	0.926434i	$-0.622858\pi$
$523$	287.638	−	287.638i	0.549977	−	0.549977i	0.926434	+	0.376457i	$0.122858\pi$
$524$		0			0
$525$	−179.085	−	431.736i	−0.341114	−	0.822354i
$526$		0			0
$527$		−	276.309i		−	0.524306i
$528$		0			0
$529$	−468.124			−0.884922
$530$		0			0
$531$	224.357	−	0.225200i	0.422519	−	0.000424106i
$532$		0			0
$533$	458.045	+	458.045i	0.859372	+	0.859372i
$534$		0			0
$535$			1007.63i			1.88341i
$536$		0			0
$537$	15.5471	+	6.43067i	0.0289517	+	0.0119752i
$538$		0			0
$539$	−2.67491	−	2.67491i	−0.00496273	−	0.00496273i
$540$		0			0
$541$	−419.846	−	419.846i	−0.776056	−	0.776056i	0.203102	−	0.979158i	$-0.434898\pi$
$541$	−419.846	−	419.846i	−0.776056	−	0.776056i	−0.979158	+	0.203102i	$0.934898\pi$
$542$		0			0
$543$	622.654	+	257.545i	1.14669	+	0.474301i
$544$		0			0
$545$			73.4108i			0.134699i
$546$		0			0
$547$	−517.346	−	517.346i	−0.945789	−	0.945789i	0.0528155	−	0.998604i	$-0.483180\pi$
$547$	−517.346	−	517.346i	−0.945789	−	0.945789i	−0.998604	+	0.0528155i	$0.983180\pi$
$548$		0			0
$549$	−157.742	+	0.158334i	−0.287325	+	0.000288404i
$550$		0			0
$551$	−1463.16			−2.65546
$552$		0			0
$553$			262.828i			0.475277i
$554$		0			0
$555$	201.851	+	486.621i	0.363696	+	0.876794i
$556$		0			0
$557$	−31.8976	+	31.8976i	−0.0572667	+	0.0572667i	−0.735160	−	0.677893i	$-0.762893\pi$
$557$	−31.8976	+	31.8976i	−0.0572667	+	0.0572667i	0.677893	+	0.735160i	$0.262893\pi$
$558$		0			0
$559$	103.246			0.184698
$560$		0			0
$561$	−22.4237	−	9.27502i	−0.0399709	−	0.0165330i
$562$		0			0
$563$	32.9214	−	32.9214i	0.0584750	−	0.0584750i	−0.677265	−	0.735740i	$-0.736835\pi$
$563$	32.9214	−	32.9214i	0.0584750	−	0.0584750i	0.735740	+	0.677265i	$0.236835\pi$
$564$		0			0
$565$	63.0679	−	63.0679i	0.111625	−	0.111625i
$566$		0			0
$567$	−596.310	+	1.19710i	−1.05169	+	0.00211129i
$568$		0			0
$569$	647.095			1.13725			0.568624	−	0.822597i	$-0.307476\pi$
$569$	647.095			1.13725			0.568624	+	0.822597i	$0.307476\pi$
$570$		0			0
$571$	−451.861	+	451.861i	−0.791350	+	0.791350i	−0.981714	−	0.190363i	$-0.939033\pi$
$571$	−451.861	+	451.861i	−0.791350	+	0.791350i	0.190363	+	0.981714i	$0.439033\pi$
$572$		0			0
$573$	−190.826	+	79.1550i	−0.333030	+	0.138141i
$574$		0			0
$575$		−	165.123i		−	0.287170i
$576$		0			0
$577$	532.176			0.922315			0.461157	−	0.887318i	$-0.347434\pi$
$577$	532.176			0.922315			0.461157	+	0.887318i	$0.347434\pi$
$578$		0			0
$579$	421.436	+	1015.99i	0.727869	+	1.75474i
$580$		0			0
$581$	−698.953	−	698.953i	−1.20302	−	1.20302i
$582$		0			0
$583$		−	32.8579i		−	0.0563601i
$584$		0			0
$585$	−436.412	−	435.537i	−0.746004	−	0.744508i
$586$		0			0
$587$	−532.393	−	532.393i	−0.906973	−	0.906973i	0.0890534	−	0.996027i	$-0.471616\pi$
$587$	−532.393	−	532.393i	−0.906973	−	0.906973i	−0.996027	+	0.0890534i	$0.971616\pi$
$588$		0			0
$589$	525.642	+	525.642i	0.892431	+	0.892431i
$590$		0			0
$591$	−400.124	+	967.359i	−0.677029	+	1.63682i
$592$		0			0
$593$			254.750i			0.429595i	0.976659	+	0.214798i	$0.0689092\pi$
$593$			254.750i			0.429595i	−0.976659	+	0.214798i	$0.931091\pi$
$594$		0			0
$595$	393.042	+	393.042i	0.660574	+	0.660574i
$596$		0			0
$597$	797.517	−	330.811i	1.33587	−	0.554123i
$598$		0			0
$599$	624.772			1.04303			0.521513	−	0.853244i	$-0.325368\pi$
$599$	624.772			1.04303			0.521513	+	0.853244i	$0.325368\pi$
$600$		0			0
$601$			386.910i			0.643777i	0.946778	+	0.321889i	$0.104318\pi$
$601$			386.910i			0.643777i	−0.946778	+	0.321889i	$0.895682\pi$
$602$		0			0
$603$	523.658	−	0.525625i	0.868422	−	0.000871684i
$604$		0			0
$605$	−578.779	+	578.779i	−0.956660	+	0.956660i
$606$		0			0
$607$	−951.141			−1.56695			−0.783477	−	0.621421i	$-0.786556\pi$
$607$	−951.141			−1.56695			−0.783477	+	0.621421i	$0.786556\pi$
$608$		0			0
$609$	413.129	−	998.800i	0.678373	−	1.64007i
$610$		0			0
$611$	164.345	−	164.345i	0.268977	−	0.268977i
$612$		0			0
$613$	−387.896	+	387.896i	−0.632783	+	0.632783i	−0.948765	−	0.315982i	$-0.897666\pi$
$613$	−387.896	+	387.896i	−0.632783	+	0.632783i	0.315982	+	0.948765i	$0.397666\pi$
$614$		0			0
$615$	500.519	−	1210.08i	0.813852	−	1.96761i
$616$		0			0
$617$	−882.945			−1.43103			−0.715514	−	0.698598i	$-0.753808\pi$
$617$	−882.945			−1.43103			−0.715514	+	0.698598i	$0.753808\pi$
$618$		0			0
$619$	694.731	−	694.731i	1.12234	−	1.12234i	0.130955	−	0.991388i	$-0.458196\pi$
$619$	694.731	−	694.731i	1.12234	−	1.12234i	0.991388	−	0.130955i	$-0.0418043\pi$
$620$		0			0
$621$	−194.748	−	80.3239i	−0.313604	−	0.129346i
$622$		0			0
$623$			330.337i			0.530235i
$624$		0			0
$625$	706.197			1.12991
$626$		0			0
$627$	60.3027	−	25.0136i	0.0961765	−	0.0398942i
$628$		0			0
$629$	−203.094	−	203.094i	−0.322885	−	0.322885i
$630$		0			0
$631$		−	927.845i		−	1.47044i	−0.677831	−	0.735218i	$-0.737080\pi$
$631$		−	927.845i		−	1.47044i	0.677831	−	0.735218i	$-0.262920\pi$
$632$		0			0
$633$	−253.209	+	612.170i	−0.400014	+	0.967093i
$634$		0			0
$635$	424.082	+	424.082i	0.667846	+	0.667846i
$636$		0			0
$637$	37.0537	+	37.0537i	0.0581691	+	0.0581691i
$638$		0			0
$639$	163.253	−	163.581i	0.255482	−	0.255995i
$640$		0			0
$641$		−	759.287i		−	1.18453i	−0.805741	−	0.592267i	$-0.798233\pi$
$641$		−	759.287i		−	1.18453i	0.805741	−	0.592267i	$-0.201767\pi$
$642$		0			0
$643$	−274.424	−	274.424i	−0.426787	−	0.426787i	0.460746	−	0.887532i	$-0.347582\pi$
$643$	−274.424	−	274.424i	−0.426787	−	0.426787i	−0.887532	+	0.460746i	$0.847582\pi$
$644$		0			0
$645$	−79.9694	−	192.789i	−0.123984	−	0.298898i
$646$		0			0
$647$	−747.683			−1.15561			−0.577807	−	0.816173i	$-0.696092\pi$
$647$	−747.683			−1.15561			−0.577807	+	0.816173i	$0.696092\pi$
$648$		0			0
$649$		−	18.1452i		−	0.0279587i
$650$		0			0
$651$	−507.239	+	210.403i	−0.779168	+	0.323200i
$652$		0			0
$653$	−605.127	+	605.127i	−0.926688	+	0.926688i	−0.997490	−	0.0708022i	$-0.977444\pi$
$653$	−605.127	+	605.127i	−0.926688	+	0.926688i	0.0708022	+	0.997490i	$0.477444\pi$
$654$		0			0
$655$	−548.192			−0.836935
$656$		0			0
$657$	−357.914	−	357.197i	−0.544771	−	0.543678i
$658$		0			0
$659$	−588.767	+	588.767i	−0.893425	+	0.893425i	−0.994844	−	0.101418i	$-0.967662\pi$
$659$	−588.767	+	588.767i	−0.893425	+	0.893425i	0.101418	+	0.994844i	$0.467662\pi$
$660$		0			0
$661$	−3.60334	+	3.60334i	−0.00545135	+	0.00545135i	−0.709827	−	0.704376i	$-0.751227\pi$
$661$	−3.60334	+	3.60334i	−0.00545135	+	0.00545135i	0.704376	+	0.709827i	$0.251227\pi$
$662$		0			0
$663$	310.620	+	128.480i	0.468507	+	0.193786i
$664$		0			0
$665$	−1495.42			−2.24875
$666$		0			0
$667$	270.005	−	270.005i	0.404805	−	0.404805i
$668$		0			0
$669$	−52.0695	−	125.529i	−0.0778319	−	0.187636i
$670$		0			0
$671$			12.7575i			0.0190127i
$672$		0			0
$673$	−460.445			−0.684167			−0.342084	−	0.939670i	$-0.611133\pi$
$673$	−460.445			−0.684167			−0.342084	+	0.939670i	$0.611133\pi$
$674$		0			0
$675$	−217.874	+	528.242i	−0.322776	+	0.782581i
$676$		0			0
$677$	−150.713	−	150.713i	−0.222618	−	0.222618i	0.586982	−	0.809600i	$-0.300316\pi$
$677$	−150.713	−	150.713i	−0.222618	−	0.222618i	−0.809600	+	0.586982i	$0.800316\pi$
$678$		0			0
$679$			606.350i			0.893004i
$680$		0			0
$681$	1179.12	+	487.714i	1.73145	+	0.716174i
$682$		0			0
$683$	577.893	+	577.893i	0.846109	+	0.846109i	0.989645	−	0.143536i	$-0.0458473\pi$
$683$	577.893	+	577.893i	0.846109	+	0.846109i	−0.143536	+	0.989645i	$0.545847\pi$
$684$		0			0
$685$	−793.254	−	793.254i	−1.15803	−	1.15803i
$686$		0			0
$687$	257.612	+	106.555i	0.374981	+	0.155102i
$688$		0			0
$689$			455.158i			0.660607i
$690$		0			0
$691$	545.023	+	545.023i	0.788745	+	0.788745i	0.981288	−	0.192544i	$-0.0616737\pi$
$691$	545.023	+	545.023i	0.788745	+	0.788745i	−0.192544	+	0.981288i	$0.561674\pi$
$692$		0			0
$693$	0.0484085	+	48.2274i	6.98536e−5	+	0.0695922i
$694$		0			0
$695$	−913.595			−1.31453
$696$		0			0
$697$			713.929i			1.02429i
$698$		0			0
$699$	49.2212	+	118.662i	0.0704165	+	0.169760i
$700$		0			0
$701$	413.745	−	413.745i	0.590221	−	0.590221i	−0.347470	−	0.937691i	$-0.612959\pi$
$701$	413.745	−	413.745i	0.590221	−	0.590221i	0.937691	+	0.347470i	$0.112959\pi$
$702$		0			0
$703$	772.721			1.09918
$704$		0			0
$705$	−434.171	−	179.584i	−0.615846	−	0.254730i
$706$		0			0
$707$	267.545	−	267.545i	0.378423	−	0.378423i
$708$		0			0
$709$	−521.959	+	521.959i	−0.736191	+	0.736191i	−0.971839	−	0.235648i	$-0.924279\pi$
$709$	−521.959	+	521.959i	−0.736191	+	0.736191i	0.235648	+	0.971839i	$0.424279\pi$
$710$		0			0
$711$	226.973	−	227.429i	0.319231	−	0.319873i
$712$		0			0
$713$	−194.000			−0.272089
$714$		0			0
$715$	−35.2600	+	35.2600i	−0.0493147	+	0.0493147i
$716$		0			0
$717$	278.764	−	115.632i	0.388792	−	0.161272i
$718$		0			0
$719$			567.983i			0.789963i	0.918689	+	0.394981i	$0.129249\pi$
$719$			567.983i			0.789963i	−0.918689	+	0.394981i	$0.870751\pi$
$720$		0			0
$721$	−644.293			−0.893610
$722$		0			0
$723$	6.01344	+	14.4972i	0.00831735	+	0.0200514i
$724$		0			0
$725$	−732.374	−	732.374i	−1.01017	−	1.01017i
$726$		0			0
$727$			635.396i			0.873998i	0.899462	+	0.436999i	$0.143959\pi$
$727$			635.396i			0.873998i	−0.899462	+	0.436999i	$0.856041\pi$
$728$		0			0
$729$	517.031	+	513.926i	0.709233	+	0.704974i
$730$		0			0
$731$	80.4619	+	80.4619i	0.110071	+	0.110071i
$732$		0			0
$733$	637.378	+	637.378i	0.869547	+	0.869547i	0.992422	−	0.122875i	$-0.0392116\pi$
$733$	637.378	+	637.378i	0.869547	+	0.869547i	−0.122875	+	0.992422i	$0.539212\pi$
$734$		0			0
$735$	40.4897	−	97.8896i	0.0550880	−	0.133183i
$736$		0			0
$737$		−	42.3515i		−	0.0574648i
$738$		0			0
$739$	−397.296	−	397.296i	−0.537613	−	0.537613i	0.385214	−	0.922827i	$-0.374128\pi$
$739$	−397.296	−	397.296i	−0.537613	−	0.537613i	−0.922827	+	0.385214i	$0.874128\pi$
$740$		0			0
$741$	−835.331	+	346.497i	−1.12730	+	0.467607i
$742$		0			0
$743$	1160.78			1.56229			0.781145	−	0.624349i	$-0.214636\pi$
$743$	1160.78			1.56229			0.781145	+	0.624349i	$0.214636\pi$
$744$		0			0
$745$		−	1259.47i		−	1.69057i
$746$		0			0
$747$	1.21296	+	1208.42i	0.00162377	+	1.61770i
$748$		0			0
$749$	−772.011	+	772.011i	−1.03072	+	1.03072i
$750$		0			0
$751$	1220.14			1.62469			0.812343	−	0.583181i	$-0.198192\pi$
$751$	1220.14			1.62469			0.812343	+	0.583181i	$0.198192\pi$
$752$		0			0
$753$	−28.2781	+	68.3663i	−0.0375539	+	0.0907919i
$754$		0			0
$755$	591.268	−	591.268i	0.783136	−	0.783136i
$756$		0			0
$757$	−202.623	+	202.623i	−0.267666	+	0.267666i	−0.828159	−	0.560493i	$-0.810612\pi$
$757$	−202.623	+	202.623i	−0.267666	+	0.267666i	0.560493	+	0.828159i	$0.310612\pi$
$758$		0			0
$759$	−6.51210	+	15.7439i	−0.00857984	+	0.0207430i
$760$		0			0
$761$	−694.461			−0.912563			−0.456282	−	0.889835i	$-0.650819\pi$
$761$	−694.461			−0.912563			−0.456282	+	0.889835i	$0.650819\pi$
$762$		0			0
$763$	−56.2451	+	56.2451i	−0.0737157	+	0.0737157i
$764$		0			0
$765$	−0.682081	−	679.529i	−0.000891610	−	0.888273i
$766$		0			0
$767$			251.353i			0.327709i
$768$		0			0
$769$	405.268			0.527007			0.263503	−	0.964658i	$-0.415122\pi$
$769$	405.268			0.527007			0.263503	+	0.964658i	$0.415122\pi$
$770$		0			0
$771$	−952.347	+	395.035i	−1.23521	+	0.512367i
$772$		0			0
$773$	−142.479	−	142.479i	−0.184320	−	0.184320i	0.608916	−	0.793235i	$-0.291605\pi$
$773$	−142.479	−	142.479i	−0.184320	−	0.184320i	−0.793235	+	0.608916i	$0.791605\pi$
$774$		0			0
$775$			526.214i			0.678985i
$776$		0			0
$777$	−218.182	+	527.486i	−0.280800	+	0.678875i
$778$		0			0
$779$	−1358.16	−	1358.16i	−1.74346	−	1.74346i
$780$		0			0
$781$	−13.2165	−	13.2165i	−0.0169226	−	0.0169226i
$782$		0			0
$783$	−1220.03	+	507.507i	−1.55815	+	0.648158i
$784$		0			0
$785$			1337.34i			1.70362i
$786$		0			0
$787$	482.883	+	482.883i	0.613574	+	0.613574i	0.943876	−	0.330301i	$-0.107150\pi$
$787$	482.883	+	482.883i	0.613574	+	0.613574i	−0.330301	+	0.943876i	$0.607150\pi$
$788$		0			0
$789$	−112.744	−	271.803i	−0.142895	−	0.344491i
$790$		0			0
$791$	96.6413			0.122176
$792$		0			0
$793$		−	176.721i		−	0.222852i
$794$		0			0
$795$	849.908	−	352.543i	1.06907	−	0.443451i
$796$		0			0
$797$	552.965	−	552.965i	0.693808	−	0.693808i	−0.269260	−	0.963068i	$-0.586779\pi$
$797$	552.965	−	552.965i	0.693808	−	0.693808i	0.963068	+	0.269260i	$0.0867791\pi$
$798$		0			0
$799$	256.155			0.320595
$800$		0			0
$801$	285.272	−	285.846i	0.356145	−	0.356861i
$802$		0			0
$803$	−28.9178	+	28.9178i	−0.0360122	+	0.0360122i
$804$		0			0
$805$	275.959	−	275.959i	0.342806	−	0.342806i
$806$		0			0
$807$	−496.177	−	205.232i	−0.614842	−	0.254314i
$808$		0			0
$809$	−930.240			−1.14986			−0.574932	−	0.818201i	$-0.694972\pi$
$809$	−930.240			−1.14986			−0.574932	+	0.818201i	$0.694972\pi$
$810$		0			0
$811$	611.506	−	611.506i	0.754015	−	0.754015i	−0.221211	−	0.975226i	$-0.571001\pi$
$811$	611.506	−	611.506i	0.754015	−	0.754015i	0.975226	+	0.221211i	$0.0710010\pi$
$812$		0			0
$813$	237.345	+	572.188i	0.291937	+	0.703799i
$814$		0			0
$815$		−	191.511i		−	0.234983i
$816$		0			0
$817$	−306.137			−0.374708
$818$		0			0
$819$	−0.670570	−	668.061i	−0.000818767	−	0.815703i
$820$		0			0
$821$	963.577	+	963.577i	1.17366	+	1.17366i	0.981330	+	0.192334i	$0.0616056\pi$
$821$	963.577	+	963.577i	1.17366	+	1.17366i	0.192334	+	0.981330i	$0.438394\pi$
$822$		0			0
$823$		−	1112.81i		−	1.35214i	−0.736836	−	0.676071i	$-0.763681\pi$
$823$		−	1112.81i		−	1.35214i	0.736836	−	0.676071i	$-0.236319\pi$
$824$		0			0
$825$	42.7046	+	17.6637i	0.0517631	+	0.0214105i
$826$		0			0
$827$	−600.156	−	600.156i	−0.725703	−	0.725703i	0.244058	−	0.969761i	$-0.421521\pi$
$827$	−600.156	−	600.156i	−0.725703	−	0.725703i	−0.969761	+	0.244058i	$0.921521\pi$
$828$		0			0
$829$	921.578	+	921.578i	1.11167	+	1.11167i	0.992924	+	0.118750i	$0.0378887\pi$
$829$	921.578	+	921.578i	1.11167	+	1.11167i	0.118750	+	0.992924i	$0.462111\pi$
$830$		0			0
$831$	719.085	+	297.432i	0.865324	+	0.357920i
$832$		0			0
$833$			57.7535i			0.0693319i
$834$		0			0
$835$	−289.807	−	289.807i	−0.347075	−	0.347075i
$836$		0			0
$837$	620.622	+	255.976i	0.741484	+	0.305826i
$838$		0			0
$839$	−1230.19			−1.46625			−0.733127	−	0.680091i	$-0.761940\pi$
$839$	−1230.19			−1.46625			−0.733127	+	0.680091i	$0.761940\pi$
$840$		0			0
$841$		−	1554.12i		−	1.84794i
$842$		0			0
$843$	125.453	+	302.442i	0.148818	+	0.358768i
$844$		0			0
$845$	−323.501	+	323.501i	−0.382841	+	0.382841i
$846$		0			0
$847$	−886.886			−1.04709
$848$		0			0
$849$	237.043	+	98.0470i	0.279202	+	0.115485i
$850$		0			0
$851$	−142.595	+	142.595i	−0.167562	+	0.167562i
$852$		0			0
$853$	1032.73	−	1032.73i	1.21070	−	1.21070i	0.239902	−	0.970797i	$-0.422885\pi$
$853$	1032.73	−	1032.73i	1.21070	−	1.21070i	0.970797	−	0.239902i	$-0.0771152\pi$
$854$		0			0
$855$	1294.01	+	1291.42i	1.51346	+	1.51043i
$856$		0			0
$857$	609.799			0.711550			0.355775	−	0.934572i	$-0.384217\pi$
$857$	609.799			0.711550			0.355775	+	0.934572i	$0.384217\pi$
$858$		0			0
$859$	−889.225	+	889.225i	−1.03519	+	1.03519i	−0.0358288	+	0.999358i	$0.511407\pi$
$859$	−889.225	+	889.225i	−1.03519	+	1.03519i	−0.999358	+	0.0358288i	$0.988593\pi$
$860$		0			0
$861$	1310.61	−	543.642i	1.52219	−	0.631407i
$862$		0			0
$863$		−	1322.86i		−	1.53286i	−0.642329	−	0.766429i	$-0.722032\pi$
$863$		−	1322.86i		−	1.53286i	0.642329	−	0.766429i	$-0.277968\pi$
$864$		0			0
$865$	719.010			0.831225
$866$		0			0
$867$	−190.243	−	458.637i	−0.219427	−	0.528993i
$868$		0			0
$869$	−18.3752	−	18.3752i	−0.0211452	−	0.0211452i
$870$		0			0
$871$			586.667i			0.673555i
$872$		0			0
$873$	523.632	−	524.684i	0.599808	−	0.601013i
$874$		0			0
$875$	135.699	+	135.699i	0.155084	+	0.155084i
$876$		0			0
$877$	−853.500	−	853.500i	−0.973204	−	0.973204i	0.0264461	−	0.999650i	$-0.491581\pi$
$877$	−853.500	−	853.500i	−0.973204	−	0.973204i	−0.999650	+	0.0264461i	$0.991581\pi$
$878$		0			0
$879$	−31.5630	+	76.3081i	−0.0359078	+	0.0868124i
$880$		0			0
$881$		−	1075.39i		−	1.22064i	−0.792153	−	0.610322i	$-0.791040\pi$
$881$		−	1075.39i		−	1.22064i	0.792153	−	0.610322i	$-0.208960\pi$
$882$		0			0
$883$	−283.702	−	283.702i	−0.321294	−	0.321294i	0.527970	−	0.849263i	$-0.322954\pi$
$883$	−283.702	−	283.702i	−0.321294	−	0.321294i	−0.849263	+	0.527970i	$0.822954\pi$
$884$		0			0
$885$	469.346	−	194.685i	0.530334	−	0.219983i
$886$		0			0
$887$	−282.642			−0.318650			−0.159325	−	0.987226i	$-0.550932\pi$
$887$	−282.642			−0.318650			−0.159325	+	0.987226i	$0.550932\pi$
$888$		0			0
$889$			649.838i			0.730976i
$890$		0			0
$891$	41.6064	−	41.7738i	0.0466963	−	0.0468841i
$892$		0			0
$893$	−487.301	+	487.301i	−0.545690	+	0.545690i
$894$		0			0
$895$	38.1040			0.0425743
$896$		0			0
$897$	90.2076	−	218.090i	0.100566	−	0.243133i
$898$		0			0
$899$	−860.452	+	860.452i	−0.957122	+	0.957122i
$900$		0			0
$901$	−354.715	+	354.715i	−0.393690	+	0.393690i
$902$		0			0
$903$	86.4392	−	208.979i	0.0957245	−	0.231428i
$904$		0			0
$905$	1526.05			1.68624
$906$		0			0
$907$	216.816	−	216.816i	0.239047	−	0.239047i	−0.577408	−	0.816456i	$-0.695936\pi$
$907$	216.816	−	216.816i	0.239047	−	0.239047i	0.816456	+	0.577408i	$0.195936\pi$
$908$		0			0
$909$	−462.558	+	0.464295i	−0.508864	+	0.000510776i
$910$		0			0
$911$		−	1193.35i		−	1.30994i	−0.755657	−	0.654968i	$-0.772682\pi$
$911$		−	1193.35i		−	1.30994i	0.755657	−	0.654968i	$-0.227318\pi$
$912$		0			0
$913$	97.7324			0.107045
$914$		0			0
$915$	−329.988	+	136.880i	−0.360643	+	0.149595i
$916$		0			0
$917$	−420.008	−	420.008i	−0.458024	−	0.458024i
$918$		0			0
$919$			345.202i			0.375628i	0.982205	+	0.187814i	$0.0601402\pi$
$919$			345.202i			0.375628i	−0.982205	+	0.187814i	$0.939860\pi$
$920$		0			0
$921$	661.947	−	1600.35i	0.718727	−	1.73763i
$922$		0			0
$923$	183.080	+	183.080i	0.198353	+	0.198353i
$924$		0			0
$925$	386.781	+	386.781i	0.418141	+	0.418141i
$926$		0			0
$927$	557.517	+	556.399i	0.601421	+	0.600215i
$928$		0			0
$929$			1417.53i			1.52587i	0.646475	+	0.762935i	$0.276242\pi$
$929$			1417.53i			1.52587i	−0.646475	+	0.762935i	$0.723758\pi$
$930$		0			0
$931$	−109.868	−	109.868i	−0.118011	−	0.118011i
$932$		0			0
$933$	414.908	+	1000.26i	0.444704	+	1.07209i
$934$		0			0
$935$	−54.9578			−0.0587784
$936$		0			0
$937$			182.650i			0.194931i	0.995239	+	0.0974656i	$0.0310736\pi$
$937$			182.650i			0.194931i	−0.995239	+	0.0974656i	$0.968926\pi$
$938$		0			0
$939$	204.842	−	84.9687i	0.218149	−	0.0904885i
$940$		0			0
$941$	524.733	−	524.733i	0.557634	−	0.557634i	−0.371000	−	0.928633i	$-0.620985\pi$
$941$	524.733	−	524.733i	0.557634	−	0.557634i	0.928633	+	0.371000i	$0.120985\pi$
$942$		0			0
$943$	501.258			0.531556
$944$		0			0
$945$	−1246.94	+	518.699i	−1.31951	+	0.548888i
$946$		0			0
$947$	278.292	−	278.292i	0.293867	−	0.293867i	−0.544739	−	0.838606i	$-0.683371\pi$
$947$	278.292	−	278.292i	0.293867	−	0.293867i	0.838606	+	0.544739i	$0.183371\pi$
$948$		0			0
$949$	400.578	−	400.578i	0.422105	−	0.422105i
$950$		0			0
$951$	−677.108	−	280.069i	−0.711996	−	0.294500i
$952$		0			0
$953$	545.447			0.572348			0.286174	−	0.958178i	$-0.407617\pi$
$953$	545.447			0.572348			0.286174	+	0.958178i	$0.407617\pi$
$954$		0			0
$955$	−330.845	+	330.845i	−0.346435	+	0.346435i
$956$		0			0
$957$	40.9462	+	98.7128i	0.0427860	+	0.103148i
$958$		0			0
$959$		−	1215.53i		−	1.26750i
$960$		0			0
$961$	−342.761			−0.356672
$962$		0			0
$963$	1334.73	−	1.33974i	1.38601	−	0.00139122i
$964$		0			0
$965$	1761.48	+	1761.48i	1.82537	+	1.82537i
$966$		0			0
$967$			216.237i			0.223616i	0.993730	+	0.111808i	$0.0356642\pi$
$967$			216.237i			0.223616i	−0.993730	+	0.111808i	$0.964336\pi$
$968$		0			0
$969$	−921.024	−	380.959i	−0.950489	−	0.393147i
$970$		0			0
$971$	147.926	+	147.926i	0.152344	+	0.152344i	0.779164	−	0.626820i	$-0.215644\pi$
$971$	147.926	+	147.926i	0.152344	+	0.152344i	−0.626820	+	0.779164i	$0.715644\pi$
$972$		0			0
$973$	−699.968	−	699.968i	−0.719392	−	0.719392i
$974$		0			0
$975$	−591.557	−	244.683i	−0.606725	−	0.250957i
$976$		0			0
$977$		−	553.321i		−	0.566347i	−0.959069	−	0.283174i	$-0.908613\pi$
$977$		−	553.321i		−	0.566347i	0.959069	−	0.283174i	$-0.0913873\pi$
$978$		0			0
$979$	−23.0949	−	23.0949i	−0.0235903	−	0.0235903i
$980$		0			0
$981$	97.2420	−	0.0976072i	0.0991254	−	9.94977e-5i
$982$		0			0
$983$	1107.13			1.12628			0.563139	−	0.826362i	$-0.309594\pi$
$983$	1107.13			1.12628			0.563139	+	0.826362i	$0.309594\pi$
$984$		0			0
$985$			2370.88i			2.40698i
$986$		0			0
$987$	−195.057	−	470.241i	−0.197626	−	0.476434i
$988$		0			0
$989$	56.4932	−	56.4932i	0.0571216	−	0.0571216i
$990$		0			0
$991$	−1635.60			−1.65046			−0.825228	−	0.564800i	$-0.808953\pi$
$991$	−1635.60			−1.65046			−0.825228	+	0.564800i	$0.808953\pi$
$992$		0			0
$993$	1025.24	+	424.065i	1.03247	+	0.427054i
$994$		0			0
$995$	1382.70	−	1382.70i	1.38965	−	1.38965i
$996$		0			0
$997$	−152.140	+	152.140i	−0.152598	+	0.152598i	−0.779277	−	0.626679i	$-0.784414\pi$
$997$	−152.140	+	152.140i	−0.152598	+	0.152598i	0.626679	+	0.779277i	$0.284414\pi$
$998$		0			0
$999$	644.323	−	268.025i	0.644968	−	0.268293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.3.i.d.161.4		20
3.2	odd	2	inner	384.3.i.d.161.1		20
4.3	odd	2		384.3.i.c.161.7		20
8.3	odd	2		192.3.i.b.17.4		20
8.5	even	2		48.3.i.b.29.4	yes	20
12.11	even	2		384.3.i.c.161.10		20
16.3	odd	4		192.3.i.b.113.1		20
16.5	even	4	inner	384.3.i.d.353.1		20
16.11	odd	4		384.3.i.c.353.10		20
16.13	even	4		48.3.i.b.5.7	yes	20
24.5	odd	2		48.3.i.b.29.7	yes	20
24.11	even	2		192.3.i.b.17.1		20
48.5	odd	4	inner	384.3.i.d.353.4		20
48.11	even	4		384.3.i.c.353.7		20
48.29	odd	4		48.3.i.b.5.4	✓	20
48.35	even	4		192.3.i.b.113.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.b.5.4	✓	20	48.29	odd	4
48.3.i.b.5.7	yes	20	16.13	even	4
48.3.i.b.29.4	yes	20	8.5	even	2
48.3.i.b.29.7	yes	20	24.5	odd	2
192.3.i.b.17.1		20	24.11	even	2
192.3.i.b.17.4		20	8.3	odd	2
192.3.i.b.113.1		20	16.3	odd	4
192.3.i.b.113.4		20	48.35	even	4
384.3.i.c.161.7		20	4.3	odd	2
384.3.i.c.161.10		20	12.11	even	2
384.3.i.c.353.7		20	48.11	even	4
384.3.i.c.353.10		20	16.11	odd	4
384.3.i.d.161.1		20	3.2	odd	2	inner
384.3.i.d.161.4		20	1.1	even	1	trivial
384.3.i.d.353.1		20	16.5	even	4	inner
384.3.i.d.353.4		20	48.5	odd	4	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	384.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.14944 - 2.77106i) q^{3} +(-4.80434 - 4.80434i) q^{5} -7.36187i q^{7} +(-6.35757 + 6.37035i) q^{9} +O(q^{10})\)	\(q+(-1.14944 - 2.77106i) q^{3} +(-4.80434 - 4.80434i) q^{5} -7.36187i q^{7} +(-6.35757 + 6.37035i) q^{9} +(0.514693 + 0.514693i) q^{11} +(-7.12969 - 7.12969i) q^{13} +(-7.79081 + 18.8354i) q^{15} -11.1126i q^{17} +(21.1403 + 21.1403i) q^{19} +(-20.4002 + 8.46203i) q^{21} -7.80231 q^{23} +21.1633i q^{25} +(24.9603 + 10.2949i) q^{27} +(-34.6058 + 34.6058i) q^{29} +24.8644 q^{31} +(0.834637 - 2.01786i) q^{33} +(-35.3689 + 35.3689i) q^{35} +(18.2760 - 18.2760i) q^{37} +(-11.5617 + 27.9520i) q^{39} -64.2448 q^{41} +(-7.24058 + 7.24058i) q^{43} +(61.1492 - 0.0613789i) q^{45} +23.0508i q^{47} -5.19710 q^{49} +(-30.7938 + 12.7733i) q^{51} +(-31.9199 - 31.9199i) q^{53} -4.94552i q^{55} +(34.2816 - 82.8807i) q^{57} +(-17.6272 - 17.6272i) q^{59} +(12.3933 + 12.3933i) q^{61} +(46.8976 + 46.8036i) q^{63} +68.5069i q^{65} +(-41.1425 - 41.1425i) q^{67} +(8.96830 + 21.6207i) q^{69} -25.6785 q^{71} +56.1845i q^{73} +(58.6449 - 24.3260i) q^{75} +(3.78910 - 3.78910i) q^{77} -35.7013 q^{79} +(-0.162608 - 80.9998i) q^{81} +(94.9424 - 94.9424i) q^{83} +(-53.3889 + 53.3889i) q^{85} +(135.672 + 56.1175i) q^{87} -44.8713 q^{89} +(-52.4878 + 52.4878i) q^{91} +(-28.5802 - 68.9008i) q^{93} -203.131i q^{95} -82.3636 q^{97} +(-6.55097 + 0.00657558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{3}+O(q^{10}) \) 20 * q + 6 * q^3	\( 20 q + 6 q^{3} - 92 q^{13} - 116 q^{15} + 52 q^{19} - 48 q^{21} - 18 q^{27} - 80 q^{31} + 60 q^{33} + 116 q^{37} - 172 q^{43} - 60 q^{45} - 364 q^{49} - 128 q^{51} + 244 q^{61} + 296 q^{63} - 356 q^{67} + 20 q^{69} + 146 q^{75} + 384 q^{79} - 188 q^{81} - 48 q^{85} - 136 q^{91} + 132 q^{93} + 472 q^{97} + 452 q^{99}+O(q^{100}) \) 20 * q + 6 * q^3 - 92 * q^13 - 116 * q^15 + 52 * q^19 - 48 * q^21 - 18 * q^27 - 80 * q^31 + 60 * q^33 + 116 * q^37 - 172 * q^43 - 60 * q^45 - 364 * q^49 - 128 * q^51 + 244 * q^61 + 296 * q^63 - 356 * q^67 + 20 * q^69 + 146 * q^75 + 384 * q^79 - 188 * q^81 - 48 * q^85 - 136 * q^91 + 132 * q^93 + 472 * q^97 + 452 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more