LMFDB - Embedded newform 1050.2.b.f.251.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(251,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1050.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.101415451701035401216.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 18x^{12} + 145x^{8} - 72x^{4} + 16 $ x^16 - 18x^12 + 145x^8 - 72*x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.10
Root			$1.81768 - 0.332046i$ of defining polynomial
Character	$\chi$	$=$	1050.251
Dual form			1050.2.b.f.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.68014 + 0.420861i) q^{3} -1.00000 q^{4} +(-0.420861 - 1.68014i) q^{6} +(1.16372 + 2.37608i) q^{7} -1.00000i q^{8} +(2.64575 - 1.41421i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.68014 + 0.420861i) q^{3} -1.00000 q^{4} +(-0.420861 - 1.68014i) q^{6} +(1.16372 + 2.37608i) q^{7} -1.00000i q^{8} +(2.64575 - 1.41421i) q^{9} -2.82843i q^{11} +(1.68014 - 0.420861i) q^{12} -0.841723i q^{13} +(-2.37608 + 1.16372i) q^{14} +1.00000 q^{16} +1.19038 q^{17} +(1.41421 + 2.64575i) q^{18} -4.55066i q^{19} +(-2.95522 - 3.50238i) q^{21} +2.82843 q^{22} -3.29150i q^{23} +(0.420861 + 1.68014i) q^{24} +0.841723 q^{26} +(-3.85005 + 3.48957i) q^{27} +(-1.16372 - 2.37608i) q^{28} -7.98430i q^{29} +5.53019i q^{31} +1.00000i q^{32} +(1.19038 + 4.75216i) q^{33} +1.19038i q^{34} +(-2.64575 + 1.41421i) q^{36} +10.8127 q^{37} +4.55066 q^{38} +(0.354249 + 1.41421i) q^{39} +7.82087 q^{41} +(3.50238 - 2.95522i) q^{42} +4.65489 q^{43} +2.82843i q^{44} +3.29150 q^{46} -4.33981 q^{47} +(-1.68014 + 0.420861i) q^{48} +(-4.29150 + 5.53019i) q^{49} +(-2.00000 + 0.500983i) q^{51} +0.841723i q^{52} +12.5830i q^{53} +(-3.48957 - 3.85005i) q^{54} +(2.37608 - 1.16372i) q^{56} +(1.91520 + 7.64575i) q^{57} +7.98430 q^{58} +3.91044 q^{59} -10.0808i q^{61} -5.53019 q^{62} +(6.43920 + 4.64076i) q^{63} -1.00000 q^{64} +(-4.75216 + 1.19038i) q^{66} +4.65489 q^{67} -1.19038 q^{68} +(1.38527 + 5.53019i) q^{69} +12.6392i q^{71} +(-1.41421 - 2.64575i) q^{72} +3.06871i q^{73} +10.8127i q^{74} +4.55066i q^{76} +(6.72057 - 3.29150i) q^{77} +(-1.41421 + 0.354249i) q^{78} +7.29150 q^{79} +(5.00000 - 7.48331i) q^{81} +7.82087i q^{82} -7.70010 q^{83} +(2.95522 + 3.50238i) q^{84} +4.65489i q^{86} +(3.36028 + 13.4148i) q^{87} -2.82843 q^{88} +12.8712 q^{89} +(2.00000 - 0.979531i) q^{91} +3.29150i q^{92} +(-2.32744 - 9.29150i) q^{93} -4.33981i q^{94} +(-0.420861 - 1.68014i) q^{96} -8.11905i q^{97} +(-5.53019 - 4.29150i) q^{98} +(-4.00000 - 7.48331i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4}+O(q^{10}) $ 16 * q - 16 * q^4	$ 16 q - 16 q^{4} + 16 q^{16} - 16 q^{21} + 48 q^{39} - 32 q^{46} + 16 q^{49} - 32 q^{51} - 16 q^{64} + 32 q^{79} + 80 q^{81} + 16 q^{84} + 32 q^{91} - 64 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 16 * q^16 - 16 * q^21 + 48 * q^39 - 32 * q^46 + 16 * q^49 - 32 * q^51 - 16 * q^64 + 32 * q^79 + 80 * q^81 + 16 * q^84 + 32 * q^91 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.68014	+	0.420861i	−0.970030	+	0.242984i
$3$	−1.68014	+	0.420861i	−0.970030	+	0.242984i
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−0.420861	−	1.68014i	−0.171816	−	0.685915i
$7$	1.16372	+	2.37608i	0.439846	+	0.898073i
$7$	1.16372	+	2.37608i	0.439846	+	0.898073i
$8$		−	1.00000i		−	0.353553i
$9$	2.64575	−	1.41421i	0.881917	−	0.471405i
$10$		0			0
$11$		−	2.82843i		−	0.852803i	−0.904534	−	0.426401i	$-0.859781\pi$
$11$		−	2.82843i		−	0.852803i	0.904534	−	0.426401i	$-0.140219\pi$
$12$	1.68014	−	0.420861i	0.485015	−	0.121492i
$13$		−	0.841723i		−	0.233452i	−0.993164	−	0.116726i	$-0.962760\pi$
$13$		−	0.841723i		−	0.233452i	0.993164	−	0.116726i	$-0.0372399\pi$
$14$	−2.37608	+	1.16372i	−0.635034	+	0.311018i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.19038			0.288709			0.144354	−	0.989526i	$-0.453890\pi$
$17$	1.19038			0.288709			0.144354	+	0.989526i	$0.453890\pi$
$18$	1.41421	+	2.64575i	0.333333	+	0.623610i
$19$		−	4.55066i		−	1.04399i	−0.852948	−	0.521996i	$-0.825187\pi$
$19$		−	4.55066i		−	1.04399i	0.852948	−	0.521996i	$-0.174813\pi$
$20$		0			0
$21$	−2.95522	−	3.50238i	−0.644881	−	0.764283i
$22$	2.82843			0.603023
$23$		−	3.29150i		−	0.686326i	−0.939276	−	0.343163i	$-0.888502\pi$
$23$		−	3.29150i		−	0.686326i	0.939276	−	0.343163i	$-0.111498\pi$
$24$	0.420861	+	1.68014i	0.0859080	+	0.342957i
$25$		0			0
$26$	0.841723			0.165075
$27$	−3.85005	+	3.48957i	−0.740942	+	0.671569i
$28$	−1.16372	−	2.37608i	−0.219923	−	0.449037i
$29$		−	7.98430i		−	1.48265i	−0.671148	−	0.741323i	$-0.734198\pi$
$29$		−	7.98430i		−	1.48265i	0.671148	−	0.741323i	$-0.265802\pi$
$30$		0			0
$31$			5.53019i			0.993252i	0.867965	+	0.496626i	$0.165428\pi$
$31$			5.53019i			0.993252i	−0.867965	+	0.496626i	$0.834572\pi$
$32$			1.00000i			0.176777i
$33$	1.19038	+	4.75216i	0.207218	+	0.827245i
$34$			1.19038i			0.204148i
$35$		0			0
$36$	−2.64575	+	1.41421i	−0.440959	+	0.235702i
$37$	10.8127			1.77760			0.888801	−	0.458294i	$-0.151539\pi$
$37$	10.8127			1.77760			0.888801	+	0.458294i	$0.151539\pi$
$38$	4.55066			0.738214
$39$	0.354249	+	1.41421i	0.0567252	+	0.226455i
$40$		0			0
$41$	7.82087			1.22141			0.610707	−	0.791856i	$-0.290885\pi$
$41$	7.82087			1.22141			0.610707	+	0.791856i	$0.290885\pi$
$42$	3.50238	−	2.95522i	0.540429	−	0.456000i
$43$	4.65489			0.709864			0.354932	−	0.934892i	$-0.384504\pi$
$43$	4.65489			0.709864			0.354932	+	0.934892i	$0.384504\pi$
$44$			2.82843i			0.426401i
$45$		0			0
$46$	3.29150			0.485306
$47$	−4.33981			−0.633027			−0.316513	−	0.948588i	$-0.602512\pi$
$47$	−4.33981			−0.633027			−0.316513	+	0.948588i	$0.602512\pi$
$48$	−1.68014	+	0.420861i	−0.242508	+	0.0607461i
$49$	−4.29150	+	5.53019i	−0.613072	+	0.790027i
$50$		0			0
$51$	−2.00000	+	0.500983i	−0.280056	+	0.0701517i
$52$			0.841723i			0.116726i
$53$			12.5830i			1.72841i	0.503141	+	0.864204i	$0.332178\pi$
$53$			12.5830i			1.72841i	−0.503141	+	0.864204i	$0.667822\pi$
$54$	−3.48957	−	3.85005i	−0.474871	−	0.523925i
$55$		0			0
$56$	2.37608	−	1.16372i	0.317517	−	0.155509i
$57$	1.91520	+	7.64575i	0.253674	+	1.01270i
$58$	7.98430			1.04839
$59$	3.91044			0.509095			0.254548	−	0.967060i	$-0.418073\pi$
$59$	3.91044			0.509095			0.254548	+	0.967060i	$0.418073\pi$
$60$		0			0
$61$		−	10.0808i		−	1.29072i	−0.763878	−	0.645360i	$-0.776707\pi$
$61$		−	10.0808i		−	1.29072i	0.763878	−	0.645360i	$-0.223293\pi$
$62$	−5.53019			−0.702335
$63$	6.43920	+	4.64076i	0.811263	+	0.584681i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−4.75216	+	1.19038i	−0.584950	+	0.146525i
$67$	4.65489			0.568685			0.284343	−	0.958723i	$-0.408225\pi$
$67$	4.65489			0.568685			0.284343	+	0.958723i	$0.408225\pi$
$68$	−1.19038			−0.144354
$69$	1.38527	+	5.53019i	0.166766	+	0.665757i
$70$		0			0
$71$			12.6392i			1.50000i	0.661440	+	0.749998i	$0.269945\pi$
$71$			12.6392i			1.50000i	−0.661440	+	0.749998i	$0.730055\pi$
$72$	−1.41421	−	2.64575i	−0.166667	−	0.311805i
$73$			3.06871i			0.359166i	0.983743	+	0.179583i	$0.0574748\pi$
$73$			3.06871i			0.359166i	−0.983743	+	0.179583i	$0.942525\pi$
$74$			10.8127i			1.25695i
$75$		0			0
$76$			4.55066i			0.521996i
$77$	6.72057	−	3.29150i	0.765880	−	0.375102i
$78$	−1.41421	+	0.354249i	−0.160128	+	0.0401108i
$79$	7.29150			0.820358			0.410179	−	0.912005i	$-0.365466\pi$
$79$	7.29150			0.820358			0.410179	+	0.912005i	$0.365466\pi$
$80$		0			0
$81$	5.00000	−	7.48331i	0.555556	−	0.831479i
$82$			7.82087i			0.863671i
$83$	−7.70010			−0.845196			−0.422598	−	0.906317i	$-0.638882\pi$
$83$	−7.70010			−0.845196			−0.422598	+	0.906317i	$0.638882\pi$
$84$	2.95522	+	3.50238i	0.322441	+	0.382141i
$85$		0			0
$86$			4.65489i			0.501949i
$87$	3.36028	+	13.4148i	0.360260	+	1.43821i
$88$	−2.82843			−0.301511
$89$	12.8712			1.36435			0.682173	−	0.731191i	$-0.261035\pi$
$89$	12.8712			1.36435			0.682173	+	0.731191i	$0.261035\pi$
$90$		0			0
$91$	2.00000	−	0.979531i	0.209657	−	0.102683i
$92$			3.29150i			0.343163i
$93$	−2.32744	−	9.29150i	−0.241345	−	0.963484i
$94$		−	4.33981i		−	0.447618i
$95$		0			0
$96$	−0.420861	−	1.68014i	−0.0429540	−	0.171479i
$97$		−	8.11905i		−	0.824365i	−0.911101	−	0.412182i	$-0.864767\pi$
$97$		−	8.11905i		−	0.824365i	0.911101	−	0.412182i	$-0.135233\pi$
$98$	−5.53019	−	4.29150i	−0.558634	−	0.433507i
$99$	−4.00000	−	7.48331i	−0.402015	−	0.752101i
$100$		0			0
$101$	3.91044			0.389103			0.194551	−	0.980892i	$-0.437675\pi$
$101$	3.91044			0.389103			0.194551	+	0.980892i	$0.437675\pi$
$102$	−0.500983	−	2.00000i	−0.0496047	−	0.198030i
$103$		−	12.5730i		−	1.23886i	−0.785053	−	0.619429i	$-0.787364\pi$
$103$		−	12.5730i		−	1.23886i	0.785053	−	0.619429i	$-0.212636\pi$
$104$	−0.841723			−0.0825377
$105$		0			0
$106$	−12.5830			−1.22217
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	3.85005	−	3.48957i	0.370471	−	0.335784i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	−18.1669	+	4.55066i	−1.72433	+	0.431929i
$112$	1.16372	+	2.37608i	0.109961	+	0.224518i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−7.64575	+	1.91520i	−0.716090	+	0.179375i
$115$		0			0
$116$			7.98430i			0.741323i
$117$	−1.19038	−	2.22699i	−0.110050	−	0.205885i
$118$			3.91044i			0.359985i
$119$	1.38527	+	2.82843i	0.126987	+	0.259281i
$120$		0			0
$121$	3.00000			0.272727
$122$	10.0808			0.912677
$123$	−13.1402	+	3.29150i	−1.18481	+	0.296785i
$124$		−	5.53019i		−	0.496626i
$125$		0			0
$126$	−4.64076	+	6.43920i	−0.413432	+	0.573650i
$127$	−10.8127			−0.959474			−0.479737	−	0.877412i	$-0.659268\pi$
$127$	−10.8127			−0.959474			−0.479737	+	0.877412i	$0.659268\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−7.82087	+	1.95906i	−0.688589	+	0.172486i
$130$		0			0
$131$	8.96077			0.782906			0.391453	−	0.920198i	$-0.371973\pi$
$131$	8.96077			0.782906			0.391453	+	0.920198i	$0.371973\pi$
$132$	−1.19038	−	4.75216i	−0.103609	−	0.413622i
$133$	10.8127	−	5.29570i	0.937582	−	0.459196i
$134$			4.65489i			0.402121i
$135$		0			0
$136$		−	1.19038i		−	0.102074i
$137$			9.29150i			0.793827i	0.917856	+	0.396913i	$0.129919\pi$
$137$			9.29150i			0.793827i	−0.917856	+	0.396913i	$0.870081\pi$
$138$	−5.53019	+	1.38527i	−0.470761	+	0.117922i
$139$			15.6110i			1.32411i	0.749455	+	0.662056i	$0.230316\pi$
$139$			15.6110i			1.32411i	−0.749455	+	0.662056i	$0.769684\pi$
$140$		0			0
$141$	7.29150	−	1.82646i	0.614055	−	0.153816i
$142$	−12.6392			−1.06066
$143$	−2.38075			−0.199088
$144$	2.64575	−	1.41421i	0.220479	−	0.117851i
$145$		0			0
$146$	−3.06871			−0.253968
$147$	4.88289	−	11.0976i	0.402734	−	0.915317i
$148$	−10.8127			−0.888801
$149$		−	3.32941i		−	0.272756i	−0.990657	−	0.136378i	$-0.956454\pi$
$149$		−	3.32941i		−	0.272756i	0.990657	−	0.136378i	$-0.0435462\pi$
$150$		0			0
$151$	−22.5830			−1.83778			−0.918889	−	0.394515i	$-0.870913\pi$
$151$	−22.5830			−1.83778			−0.918889	+	0.394515i	$0.870913\pi$
$152$	−4.55066			−0.369107
$153$	3.14944	−	1.68345i	0.254617	−	0.136099i
$154$	3.29150	+	6.72057i	0.265237	+	0.541559i
$155$		0			0
$156$	−0.354249	−	1.41421i	−0.0283626	−	0.113228i
$157$		−	22.6209i		−	1.80534i	−0.430330	−	0.902672i	$-0.641603\pi$
$157$		−	22.6209i		−	1.80534i	0.430330	−	0.902672i	$-0.358397\pi$
$158$			7.29150i			0.580081i
$159$	−5.29570	−	21.1412i	−0.419976	−	1.67661i
$160$		0			0
$161$	7.82087	−	3.83039i	0.616371	−	0.301877i
$162$	7.48331	+	5.00000i	0.587945	+	0.392837i
$163$		0			0			−	1.00000i	$-0.5\pi$
$163$		0			0				1.00000i	$0.5\pi$
$164$	−7.82087			−0.610707
$165$		0			0
$166$		−	7.70010i		−	0.597643i
$167$	−11.4821			−0.888509			−0.444255	−	0.895901i	$-0.646531\pi$
$167$	−11.4821			−0.888509			−0.444255	+	0.895901i	$0.646531\pi$
$168$	−3.50238	+	2.95522i	−0.270215	+	0.228000i
$169$	12.2915			0.945500
$170$		0			0
$171$	−6.43560	−	12.0399i	−0.492143	−	0.920715i
$172$	−4.65489			−0.354932
$173$	8.89047			0.675930			0.337965	−	0.941159i	$-0.390261\pi$
$173$	8.89047			0.675930			0.337965	+	0.941159i	$0.390261\pi$
$174$	−13.4148	+	3.36028i	−1.01697	+	0.254742i
$175$		0			0
$176$		−	2.82843i		−	0.213201i
$177$	−6.57008	+	1.64575i	−0.493838	+	0.123702i
$178$			12.8712i			0.964738i
$179$		−	9.48725i		−	0.709110i	−0.935035	−	0.354555i	$-0.884632\pi$
$179$		−	9.48725i		−	0.709110i	0.935035	−	0.354555i	$-0.115368\pi$
$180$		0			0
$181$			12.0399i			0.894920i	0.894304	+	0.447460i	$0.147671\pi$
$181$			12.0399i			0.894920i	−0.894304	+	0.447460i	$0.852329\pi$
$182$	0.979531	+	2.00000i	0.0726077	+	0.148250i
$183$	4.24264	+	16.9373i	0.313625	+	1.25204i
$184$	−3.29150			−0.242653
$185$		0			0
$186$	9.29150	−	2.32744i	0.681286	−	0.170656i
$187$		−	3.36689i		−	0.246211i
$188$	4.33981			0.316513
$189$	−12.7719	−	5.08713i	−0.929018	−	0.370034i
$190$		0			0
$191$			7.98430i			0.577724i	0.957371	+	0.288862i	$0.0932768\pi$
$191$			7.98430i			0.577724i	−0.957371	+	0.288862i	$0.906723\pi$
$192$	1.68014	−	0.420861i	0.121254	−	0.0303731i
$193$	−8.48528			−0.610784			−0.305392	−	0.952227i	$-0.598787\pi$
$193$	−8.48528			−0.610784			−0.305392	+	0.952227i	$0.598787\pi$
$194$	8.11905			0.582914
$195$		0			0
$196$	4.29150	−	5.53019i	0.306536	−	0.395014i
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$	7.48331	−	4.00000i	0.531816	−	0.284268i
$199$		−	16.5906i		−	1.17607i	−0.808834	−	0.588037i	$-0.799901\pi$
$199$		−	16.5906i		−	1.17607i	0.808834	−	0.588037i	$-0.200099\pi$
$200$		0			0
$201$	−7.82087	+	1.95906i	−0.551642	+	0.138182i
$202$			3.91044i			0.275137i
$203$	18.9713	−	9.29150i	1.33153	−	0.652136i
$204$	2.00000	−	0.500983i	0.140028	−	0.0350758i
$205$		0			0
$206$	12.5730			0.876004
$207$	−4.65489	−	8.70850i	−0.323537	−	0.605282i
$208$		−	0.841723i		−	0.0583630i
$209$	−12.8712			−0.890320
$210$		0			0
$211$	21.1660			1.45713			0.728564	−	0.684978i	$-0.240188\pi$
$211$	21.1660			1.45713			0.728564	+	0.684978i	$0.240188\pi$
$212$		−	12.5830i		−	0.864204i
$213$	−5.31935	−	21.2356i	−0.364476	−	1.45504i
$214$		0			0
$215$		0			0
$216$	3.48957	+	3.85005i	0.237435	+	0.261963i
$217$	−13.1402	+	6.43560i	−0.892013	+	0.436877i
$218$		−	2.00000i		−	0.135457i
$219$	−1.29150	−	5.15587i	−0.0872717	−	0.348401i
$220$		0			0
$221$		−	1.00197i		−	0.0673996i
$222$	−4.55066	−	18.1669i	−0.305420	−	1.21928i
$223$		−	4.75216i		−	0.318228i	−0.987260	−	0.159114i	$-0.949136\pi$
$223$		−	4.75216i		−	0.318228i	0.987260	−	0.159114i	$-0.0508637\pi$
$224$	−2.37608	+	1.16372i	−0.158758	+	0.0777544i
$225$		0			0
$226$	6.00000			0.399114
$227$	−1.40122			−0.0930023			−0.0465011	−	0.998918i	$-0.514807\pi$
$227$	−1.40122			−0.0930023			−0.0465011	+	0.998918i	$0.514807\pi$
$228$	−1.91520	−	7.64575i	−0.126837	−	0.506352i
$229$		−	28.2835i		−	1.86903i	−0.355930	−	0.934513i	$-0.615836\pi$
$229$		−	28.2835i		−	1.86903i	0.355930	−	0.934513i	$-0.384164\pi$
$230$		0			0
$231$	−9.90624	+	8.35862i	−0.651782	+	0.549957i
$232$	−7.98430			−0.524195
$233$			2.70850i			0.177440i	0.996057	+	0.0887198i	$0.0282776\pi$
$233$			2.70850i			0.177440i	−0.996057	+	0.0887198i	$0.971722\pi$
$234$	2.22699	−	1.19038i	0.145583	−	0.0778173i
$235$		0			0
$236$	−3.91044			−0.254548
$237$	−12.2508	+	3.06871i	−0.795772	+	0.199334i
$238$	−2.82843	+	1.38527i	−0.183340	+	0.0897935i
$239$			22.1264i			1.43124i	0.698490	+	0.715620i	$0.253856\pi$
$239$			22.1264i			1.43124i	−0.698490	+	0.715620i	$0.746144\pi$
$240$		0			0
$241$			1.95906i			0.126194i	0.998007	+	0.0630972i	$0.0200978\pi$
$241$			1.95906i			0.126194i	−0.998007	+	0.0630972i	$0.979902\pi$
$242$			3.00000i			0.192847i
$243$	−5.25127	+	14.6773i	−0.336869	+	0.941551i
$244$			10.0808i			0.645360i
$245$		0			0
$246$	−3.29150	−	13.1402i	−0.209859	−	0.837787i
$247$	−3.83039			−0.243722
$248$	5.53019			0.351167
$249$	12.9373	−	3.24067i	0.819865	−	0.205369i
$250$		0			0
$251$	11.7313			0.740473			0.370237	−	0.928937i	$-0.379277\pi$
$251$	11.7313			0.740473			0.370237	+	0.928937i	$0.379277\pi$
$252$	−6.43920	−	4.64076i	−0.405632	−	0.292341i
$253$	−9.30978			−0.585301
$254$		−	10.8127i		−	0.678451i
$255$		0			0
$256$	1.00000			0.0625000
$257$	14.2098			0.886384			0.443192	−	0.896427i	$-0.353846\pi$
$257$	14.2098			0.886384			0.443192	+	0.896427i	$0.353846\pi$
$258$	−1.95906	−	7.82087i	−0.121966	−	0.486906i
$259$	12.5830	+	25.6919i	0.781870	+	1.59642i
$260$		0			0
$261$	−11.2915	−	21.1245i	−0.698926	−	1.30757i
$262$			8.96077i			0.553598i
$263$		−	6.58301i		−	0.405925i	−0.979186	−	0.202963i	$-0.934943\pi$
$263$		−	6.58301i		−	0.405925i	0.979186	−	0.202963i	$-0.0650570\pi$
$264$	4.75216	−	1.19038i	0.292475	−	0.0732626i
$265$		0			0
$266$	5.29570	+	10.8127i	0.324700	+	0.662971i
$267$	−21.6255	+	5.41699i	−1.32346	+	0.331515i
$268$	−4.65489			−0.284343
$269$	24.6025			1.50004			0.750021	−	0.661414i	$-0.230043\pi$
$269$	24.6025			1.50004			0.750021	+	0.661414i	$0.230043\pi$
$270$		0			0
$271$		−	7.48925i		−	0.454940i	−0.973785	−	0.227470i	$-0.926955\pi$
$271$		−	7.48925i		−	0.454940i	0.973785	−	0.227470i	$-0.0730453\pi$
$272$	1.19038			0.0721771
$273$	−2.94804	+	2.48747i	−0.178423	+	0.150549i
$274$	−9.29150			−0.561320
$275$		0			0
$276$	−1.38527	−	5.53019i	−0.0833832	−	0.332878i
$277$	−15.4676			−0.929359			−0.464679	−	0.885479i	$-0.653830\pi$
$277$	−15.4676			−0.929359			−0.464679	+	0.885479i	$0.653830\pi$
$278$	−15.6110			−0.936288
$279$	7.82087	+	14.6315i	0.468223	+	0.875965i
$280$		0			0
$281$		−	20.6235i		−	1.23029i	−0.788412	−	0.615147i	$-0.789097\pi$
$281$		−	20.6235i		−	1.23029i	0.788412	−	0.615147i	$-0.210903\pi$
$282$	1.82646	+	7.29150i	0.108764	+	0.434203i
$283$			9.74968i			0.579558i	0.957094	+	0.289779i	$0.0935819\pi$
$283$			9.74968i			0.579558i	−0.957094	+	0.289779i	$0.906418\pi$
$284$		−	12.6392i		−	0.749998i
$285$		0			0
$286$		−	2.38075i		−	0.140777i
$287$	9.10132	+	18.5830i	0.537234	+	1.09692i
$288$	1.41421	+	2.64575i	0.0833333	+	0.155902i
$289$	−15.5830			−0.916647
$290$		0			0
$291$	3.41699	+	13.6412i	0.200308	+	0.799659i
$292$		−	3.06871i		−	0.179583i
$293$	−11.2712			−0.658472			−0.329236	−	0.944248i	$-0.606791\pi$
$293$	−11.2712			−0.658472			−0.329236	+	0.944248i	$0.606791\pi$
$294$	11.0976	+	4.88289i	0.647227	+	0.284776i
$295$		0			0
$296$		−	10.8127i		−	0.628477i
$297$	9.87000	+	10.8896i	0.572716	+	0.631878i
$298$	3.32941			0.192868
$299$	−2.77053			−0.160224
$300$		0			0
$301$	5.41699	+	11.0604i	0.312230	+	0.637510i
$302$		−	22.5830i		−	1.29951i
$303$	−6.57008	+	1.64575i	−0.377441	+	0.0945459i
$304$		−	4.55066i		−	0.260998i
$305$		0			0
$306$	1.68345	+	3.14944i	0.0962362	+	0.180041i
$307$		−	14.8000i		−	0.844682i	−0.906437	−	0.422341i	$-0.861209\pi$
$307$		−	14.8000i		−	0.844682i	0.906437	−	0.422341i	$-0.138791\pi$
$308$	−6.72057	+	3.29150i	−0.382940	+	0.187551i
$309$	5.29150	+	21.1245i	0.301023	+	1.20173i
$310$		0			0
$311$	−2.77053			−0.157103			−0.0785513	−	0.996910i	$-0.525029\pi$
$311$	−2.77053			−0.157103			−0.0785513	+	0.996910i	$0.525029\pi$
$312$	1.41421	−	0.354249i	0.0800641	−	0.0200554i
$313$			8.11905i			0.458916i	0.973319	+	0.229458i	$0.0736953\pi$
$313$			8.11905i			0.458916i	−0.973319	+	0.229458i	$0.926305\pi$
$314$	22.6209			1.27657
$315$		0			0
$316$	−7.29150			−0.410179
$317$		−	6.00000i		−	0.336994i	−0.985702	−	0.168497i	$-0.946109\pi$
$317$		−	6.00000i		−	0.336994i	0.985702	−	0.168497i	$-0.0538913\pi$
$318$	21.1412	−	5.29570i	1.18554	−	0.296968i
$319$	−22.5830			−1.26441
$320$		0			0
$321$		0			0
$322$	3.83039	+	7.82087i	0.213459	+	0.435840i
$323$		−	5.41699i		−	0.301410i
$324$	−5.00000	+	7.48331i	−0.277778	+	0.415740i
$325$		0			0
$326$		0			0
$327$	3.36028	−	0.841723i	0.185824	−	0.0465474i
$328$		−	7.82087i		−	0.431835i
$329$	−5.05034	−	10.3117i	−0.278434	−	0.568505i
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	7.70010			0.422598
$333$	28.6078	−	15.2915i	1.56770	−	0.837969i
$334$		−	11.4821i		−	0.628271i
$335$		0			0
$336$	−2.95522	−	3.50238i	−0.161220	−	0.191071i
$337$	22.4499			1.22293			0.611463	−	0.791273i	$-0.290581\pi$
$337$	22.4499			1.22293			0.611463	+	0.791273i	$0.290581\pi$
$338$			12.2915i			0.668570i
$339$	2.52517	+	10.0808i	0.137148	+	0.547517i
$340$		0			0
$341$	15.6417			0.847048
$342$	12.0399	−	6.43560i	0.651044	−	0.347998i
$343$	−18.1343	−	3.76135i	−0.979159	−	0.203094i
$344$		−	4.65489i		−	0.250975i
$345$		0			0
$346$			8.89047i			0.477955i
$347$			24.0000i			1.28839i	0.764862	+	0.644194i	$0.222807\pi$
$347$			24.0000i			1.28839i	−0.764862	+	0.644194i	$0.777193\pi$
$348$	−3.36028	−	13.4148i	−0.180130	−	0.719106i
$349$			19.1822i			1.02680i	0.858150	+	0.513399i	$0.171614\pi$
$349$			19.1822i			1.02680i	−0.858150	+	0.513399i	$0.828386\pi$
$350$		0			0
$351$	2.93725	+	3.24067i	0.156779	+	0.172974i
$352$	2.82843			0.150756
$353$	−21.3521			−1.13646			−0.568228	−	0.822871i	$-0.692371\pi$
$353$	−21.3521			−1.13646			−0.568228	+	0.822871i	$0.692371\pi$
$354$	−1.64575	−	6.57008i	−0.0874707	−	0.349196i
$355$		0			0
$356$	−12.8712			−0.682173
$357$	−3.51782	−	4.16915i	−0.186183	−	0.220655i
$358$	9.48725			0.501417
$359$			26.7813i			1.41346i	0.707481	+	0.706732i	$0.249831\pi$
$359$			26.7813i			1.41346i	−0.707481	+	0.706732i	$0.750169\pi$
$360$		0			0
$361$	−1.70850			−0.0899209
$362$	−12.0399			−0.632804
$363$	−5.04042	+	1.26258i	−0.264554	+	0.0662685i
$364$	−2.00000	+	0.979531i	−0.104828	+	0.0513414i
$365$		0			0
$366$	−16.9373	+	4.24264i	−0.885324	+	0.221766i
$367$		−	8.11905i		−	0.423811i	−0.977290	−	0.211905i	$-0.932033\pi$
$367$		−	8.11905i		−	0.423811i	0.977290	−	0.211905i	$-0.0679669\pi$
$368$		−	3.29150i		−	0.171581i
$369$	20.6921	−	11.0604i	1.07719	−	0.575780i
$370$		0			0
$371$	−29.8982	+	14.6431i	−1.55224	+	0.760233i
$372$	2.32744	+	9.29150i	0.120672	+	0.481742i
$373$	−15.4676			−0.800883			−0.400441	−	0.916322i	$-0.631143\pi$
$373$	−15.4676			−0.800883			−0.400441	+	0.916322i	$0.631143\pi$
$374$	3.36689			0.174098
$375$		0			0
$376$			4.33981i			0.223809i
$377$	−6.72057			−0.346127
$378$	5.08713	−	12.7719i	0.261654	−	0.656915i
$379$	−14.5830			−0.749079			−0.374539	−	0.927211i	$-0.622199\pi$
$379$	−14.5830			−0.749079			−0.374539	+	0.927211i	$0.622199\pi$
$380$		0			0
$381$	18.1669	−	4.55066i	0.930719	−	0.233137i
$382$	−7.98430			−0.408512
$383$	11.4821			0.586706			0.293353	−	0.956004i	$-0.405229\pi$
$383$	11.4821			0.586706			0.293353	+	0.956004i	$0.405229\pi$
$384$	0.420861	+	1.68014i	0.0214770	+	0.0857394i
$385$		0			0
$386$		−	8.48528i		−	0.431889i
$387$	12.3157	−	6.58301i	0.626041	−	0.334633i
$388$			8.11905i			0.412182i
$389$		−	0.323511i		−	0.0164026i	−0.999966	−	0.00820132i	$-0.997389\pi$
$389$		−	0.323511i		−	0.0164026i	0.999966	−	0.00820132i	$-0.00261059\pi$
$390$		0			0
$391$		−	3.91813i		−	0.198148i
$392$	5.53019	+	4.29150i	0.279317	+	0.216754i
$393$	−15.0554	+	3.77124i	−0.759443	+	0.190234i
$394$	18.0000			0.906827
$395$		0			0
$396$	4.00000	+	7.48331i	0.201008	+	0.376051i
$397$			21.5338i			1.08075i	0.841424	+	0.540375i	$0.181718\pi$
$397$			21.5338i			1.08075i	−0.841424	+	0.540375i	$0.818282\pi$
$398$	16.5906			0.831610
$399$	−15.9382	+	13.4482i	−0.797906	+	0.673251i
$400$		0			0
$401$		−	7.48331i		−	0.373699i	−0.982389	−	0.186849i	$-0.940172\pi$
$401$		−	7.48331i		−	0.373699i	0.982389	−	0.186849i	$-0.0598277\pi$
$402$	−1.95906	−	7.82087i	−0.0977092	−	0.390070i
$403$	4.65489			0.231876
$404$	−3.91044			−0.194551
$405$		0			0
$406$	9.29150	+	18.9713i	0.461130	+	0.941531i
$407$		−	30.5830i		−	1.51594i
$408$	0.500983	+	2.00000i	0.0248024	+	0.0990148i
$409$		−	13.0194i		−	0.643770i	−0.946779	−	0.321885i	$-0.895684\pi$
$409$		−	13.0194i		−	0.643770i	0.946779	−	0.321885i	$-0.104316\pi$
$410$		0			0
$411$	−3.91044	−	15.6110i	−0.192888	−	0.770036i
$412$			12.5730i			0.619429i
$413$	4.55066	+	9.29150i	0.223923	+	0.457205i
$414$	8.70850	−	4.65489i	0.427999	−	0.228775i
$415$		0			0
$416$	0.841723			0.0412689
$417$	−6.57008	−	26.2288i	−0.321738	−	1.28443i
$418$		−	12.8712i		−	0.629551i
$419$	−21.8320			−1.06656			−0.533281	−	0.845938i	$-0.679041\pi$
$419$	−21.8320			−1.06656			−0.533281	+	0.845938i	$0.679041\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$			21.1660i			1.03035i
$423$	−11.4821	+	6.13742i	−0.558277	+	0.298412i
$424$	12.5830			0.611085
$425$		0			0
$426$	21.2356	−	5.31935i	1.02887	−	0.257723i
$427$	23.9529	−	11.7313i	1.15916	−	0.567718i
$428$		0			0
$429$	4.00000	−	1.00197i	0.193122	−	0.0483754i
$430$		0			0
$431$			16.4696i			0.793312i	0.917967	+	0.396656i	$0.129829\pi$
$431$			16.4696i			0.793312i	−0.917967	+	0.396656i	$0.870171\pi$
$432$	−3.85005	+	3.48957i	−0.185236	+	0.167892i
$433$			26.5313i			1.27501i	0.770445	+	0.637507i	$0.220034\pi$
$433$			26.5313i			1.27501i	−0.770445	+	0.637507i	$0.779966\pi$
$434$	−6.43560	−	13.1402i	−0.308919	−	0.630748i
$435$		0			0
$436$	2.00000			0.0957826
$437$	−14.9785			−0.716519
$438$	5.15587	−	1.29150i	0.246357	−	0.0617104i
$439$		−	18.5496i		−	0.885326i	−0.896688	−	0.442663i	$-0.854034\pi$
$439$		−	18.5496i		−	0.885326i	0.896688	−	0.442663i	$-0.145966\pi$
$440$		0			0
$441$	−3.53338	+	20.7006i	−0.168256	+	0.985743i
$442$	1.00197			0.0476587
$443$			13.1660i			0.625536i	0.949830	+	0.312768i	$0.101256\pi$
$443$			13.1660i			0.625536i	−0.949830	+	0.312768i	$0.898744\pi$
$444$	18.1669	−	4.55066i	0.862163	−	0.215965i
$445$		0			0
$446$	4.75216			0.225021
$447$	1.40122	+	5.59388i	0.0662755	+	0.264581i
$448$	−1.16372	−	2.37608i	−0.0549807	−	0.112259i
$449$			8.30781i			0.392070i	0.980597	+	0.196035i	$0.0628066\pi$
$449$			8.30781i			0.392070i	−0.980597	+	0.196035i	$0.937193\pi$
$450$		0			0
$451$		−	22.1208i		−	1.04163i
$452$			6.00000i			0.282216i
$453$	37.9426	−	9.50432i	1.78270	−	0.446552i
$454$		−	1.40122i		−	0.0657625i
$455$		0			0
$456$	7.64575	−	1.91520i	0.358045	−	0.0896873i
$457$	−8.48528			−0.396925			−0.198462	−	0.980109i	$-0.563595\pi$
$457$	−8.48528			−0.396925			−0.198462	+	0.980109i	$0.563595\pi$
$458$	28.2835			1.32160
$459$	−4.58301	+	4.15390i	−0.213916	+	0.193888i
$460$		0			0
$461$	−8.96077			−0.417345			−0.208672	−	0.977986i	$-0.566914\pi$
$461$	−8.96077			−0.417345			−0.208672	+	0.977986i	$0.566914\pi$
$462$	−8.35862	−	9.90624i	−0.388878	−	0.460880i
$463$	23.9529			1.11319			0.556593	−	0.830786i	$-0.312108\pi$
$463$	23.9529			1.11319			0.556593	+	0.830786i	$0.312108\pi$
$464$		−	7.98430i		−	0.370662i
$465$		0			0
$466$	−2.70850			−0.125469
$467$	−3.36028			−0.155495			−0.0777477	−	0.996973i	$-0.524773\pi$
$467$	−3.36028			−0.155495			−0.0777477	+	0.996973i	$0.524773\pi$
$468$	1.19038	+	2.22699i	0.0550251	+	0.102943i
$469$	5.41699	+	11.0604i	0.250134	+	0.510721i
$470$		0			0
$471$	9.52026	+	38.0063i	0.438670	+	1.75124i
$472$		−	3.91044i		−	0.179992i
$473$		−	13.1660i		−	0.605374i
$474$	−3.06871	−	12.2508i	−0.140951	−	0.562696i
$475$		0			0
$476$	−1.38527	−	2.82843i	−0.0634936	−	0.129641i
$477$	17.7951	+	33.2915i	0.814780	+	1.52431i
$478$	−22.1264			−1.01204
$479$	−39.1044			−1.78672			−0.893362	−	0.449338i	$-0.851660\pi$
$479$	−39.1044			−1.78672			−0.893362	+	0.449338i	$0.851660\pi$
$480$		0			0
$481$		−	9.10132i		−	0.414984i
$482$	−1.95906			−0.0892329
$483$	−11.5281	+	9.72711i	−0.524547	+	0.442599i
$484$	−3.00000			−0.136364
$485$		0			0
$486$	−14.6773	−	5.25127i	−0.665777	−	0.238202i
$487$	32.4382			1.46991			0.734957	−	0.678114i	$-0.237202\pi$
$487$	32.4382			1.46991			0.734957	+	0.678114i	$0.237202\pi$
$488$	−10.0808			−0.456339
$489$		0			0
$490$		0			0
$491$			14.1421i			0.638226i	0.947717	+	0.319113i	$0.103385\pi$
$491$			14.1421i			0.638226i	−0.947717	+	0.319113i	$0.896615\pi$
$492$	13.1402	−	3.29150i	0.592405	−	0.148392i
$493$		−	9.50432i		−	0.428053i
$494$		−	3.83039i		−	0.172338i
$495$		0			0
$496$			5.53019i			0.248313i
$497$	−30.0317	+	14.7085i	−1.34711	+	0.659766i
$498$	3.24067	+	12.9373i	0.145218	+	0.579732i
$499$	−1.41699			−0.0634334			−0.0317167	−	0.999497i	$-0.510097\pi$
$499$	−1.41699			−0.0634334			−0.0317167	+	0.999497i	$0.510097\pi$
$500$		0			0
$501$	19.2915	−	4.83236i	0.861881	−	0.215894i
$502$			11.7313i			0.523594i
$503$	−8.67963			−0.387006			−0.193503	−	0.981100i	$-0.561985\pi$
$503$	−8.67963			−0.387006			−0.193503	+	0.981100i	$0.561985\pi$
$504$	4.64076	−	6.43920i	0.206716	−	0.286825i
$505$		0			0
$506$		−	9.30978i		−	0.413870i
$507$	−20.6515	+	5.17302i	−0.917164	+	0.229742i
$508$	10.8127			0.479737
$509$	−30.1436			−1.33609			−0.668045	−	0.744121i	$-0.732869\pi$
$509$	−30.1436			−1.33609			−0.668045	+	0.744121i	$0.732869\pi$
$510$		0			0
$511$	−7.29150	+	3.57113i	−0.322557	+	0.157977i
$512$			1.00000i			0.0441942i
$513$	15.8799	+	17.5203i	0.701113	+	0.773538i
$514$			14.2098i			0.626768i
$515$		0			0
$516$	7.82087	−	1.95906i	0.344295	−	0.0862429i
$517$			12.2748i			0.539847i
$518$	−25.6919	+	12.5830i	−1.12884	+	0.552866i
$519$	−14.9373	+	3.74166i	−0.655673	+	0.164241i
$520$		0			0
$521$	−23.4626			−1.02792			−0.513958	−	0.857815i	$-0.671821\pi$
$521$	−23.4626			−1.02792			−0.513958	+	0.857815i	$0.671821\pi$
$522$	21.1245	−	11.2915i	0.924593	−	0.494216i
$523$			4.20861i			0.184030i	0.995758	+	0.0920149i	$0.0293308\pi$
$523$			4.20861i			0.184030i	−0.995758	+	0.0920149i	$0.970669\pi$
$524$	−8.96077			−0.391453
$525$		0			0
$526$	6.58301			0.287033
$527$			6.58301i			0.286760i
$528$	1.19038	+	4.75216i	0.0518045	+	0.206811i
$529$	12.1660			0.528957
$530$		0			0
$531$	10.3460	−	5.53019i	0.448980	−	0.239990i
$532$	−10.8127	+	5.29570i	−0.468791	+	0.229598i
$533$		−	6.58301i		−	0.285142i
$534$	−5.41699	−	21.6255i	−0.234416	−	0.935825i
$535$		0			0
$536$		−	4.65489i		−	0.201061i
$537$	3.99282	+	15.9399i	0.172303	+	0.687858i
$538$			24.6025i			1.06069i
$539$	15.6417	+	12.1382i	0.673737	+	0.522829i
$540$		0			0
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$	7.48925			0.321691
$543$	−5.06713	−	20.2288i	−0.217452	−	0.868099i
$544$			1.19038i			0.0510369i
$545$		0			0
$546$	−2.48747	−	2.94804i	−0.106454	−	0.126164i
$547$	16.9706			0.725609			0.362804	−	0.931865i	$-0.381819\pi$
$547$	16.9706			0.725609			0.362804	+	0.931865i	$0.381819\pi$
$548$		−	9.29150i		−	0.396913i
$549$	−14.2565	−	26.6714i	−0.608451	−	1.13831i
$550$		0			0
$551$	−36.3338			−1.54787
$552$	5.53019	−	1.38527i	0.235381	−	0.0589609i
$553$	8.48528	+	17.3252i	0.360831	+	0.736742i
$554$		−	15.4676i		−	0.657156i
$555$		0			0
$556$		−	15.6110i		−	0.662056i
$557$		−	7.16601i		−	0.303634i	−0.988409	−	0.151817i	$-0.951488\pi$
$557$		−	7.16601i		−	0.303634i	0.988409	−	0.151817i	$-0.0485124\pi$
$558$	−14.6315	+	7.82087i	−0.619401	+	0.331084i
$559$		−	3.91813i		−	0.165719i
$560$		0			0
$561$	1.41699	+	5.65685i	0.0598256	+	0.238833i
$562$	20.6235			0.869949
$563$	−18.7605			−0.790660			−0.395330	−	0.918539i	$-0.629370\pi$
$563$	−18.7605			−0.790660			−0.395330	+	0.918539i	$0.629370\pi$
$564$	−7.29150	+	1.82646i	−0.307028	+	0.0769079i
$565$		0			0
$566$	−9.74968			−0.409810
$567$	23.5996	+	3.17190i	0.991088	+	0.133207i
$568$	12.6392			0.530328
$569$		−	11.1362i		−	0.466855i	−0.972374	−	0.233428i	$-0.925006\pi$
$569$		−	11.1362i		−	0.466855i	0.972374	−	0.233428i	$-0.0749942\pi$
$570$		0			0
$571$	−34.5830			−1.44725			−0.723627	−	0.690191i	$-0.757526\pi$
$571$	−34.5830			−1.44725			−0.723627	+	0.690191i	$0.757526\pi$
$572$	2.38075			0.0995442
$573$	−3.36028	−	13.4148i	−0.140378	−	0.560409i
$574$	−18.5830	+	9.10132i	−0.775640	+	0.379882i
$575$		0			0
$576$	−2.64575	+	1.41421i	−0.110240	+	0.0589256i
$577$			30.9853i			1.28993i	0.764210	+	0.644967i	$0.223129\pi$
$577$			30.9853i			1.28993i	−0.764210	+	0.644967i	$0.776871\pi$
$578$		−	15.5830i		−	0.648168i
$579$	14.2565	−	3.57113i	0.592479	−	0.148411i
$580$		0			0
$581$	−8.96077	−	18.2960i	−0.371755	−	0.759048i
$582$	−13.6412	+	3.41699i	−0.565444	+	0.141639i
$583$	35.5901			1.47399
$584$	3.06871			0.126984
$585$		0			0
$586$		−	11.2712i		−	0.465610i
$587$	44.1054			1.82042			0.910212	−	0.414143i	$-0.135919\pi$
$587$	44.1054			1.82042			0.910212	+	0.414143i	$0.135919\pi$
$588$	−4.88289	+	11.0976i	−0.201367	+	0.457659i
$589$	25.1660			1.03695
$590$		0			0
$591$	7.57551	+	30.2425i	0.311615	+	1.24401i
$592$	10.8127			0.444400
$593$	7.91094			0.324863			0.162432	−	0.986720i	$-0.448066\pi$
$593$	7.91094			0.324863			0.162432	+	0.986720i	$0.448066\pi$
$594$	−10.8896	+	9.87000i	−0.446805	+	0.404971i
$595$		0			0
$596$			3.32941i			0.136378i
$597$	6.98233	+	27.8745i	0.285768	+	1.14083i
$598$		−	2.77053i		−	0.113296i
$599$			18.2960i			0.747556i	0.927518	+	0.373778i	$0.121938\pi$
$599$			18.2960i			0.747556i	−0.927518	+	0.373778i	$0.878062\pi$
$600$		0			0
$601$			11.0604i			0.451162i	0.974224	+	0.225581i	$0.0724281\pi$
$601$			11.0604i			0.451162i	−0.974224	+	0.225581i	$0.927572\pi$
$602$	−11.0604	+	5.41699i	−0.450787	+	0.220780i
$603$	12.3157	−	6.58301i	0.501533	−	0.268081i
$604$	22.5830			0.918889
$605$		0			0
$606$	−1.64575	−	6.57008i	−0.0668541	−	0.266891i
$607$		−	23.7608i		−	0.964421i	−0.876055	−	0.482210i	$-0.839834\pi$
$607$		−	23.7608i		−	0.964421i	0.876055	−	0.482210i	$-0.160166\pi$
$608$	4.55066			0.184554
$609$	−27.9641	+	23.5953i	−1.13316	+	0.956131i
$610$		0			0
$611$			3.65292i			0.147781i
$612$	−3.14944	+	1.68345i	−0.127309	+	0.0680493i
$613$	40.0990			1.61958			0.809791	−	0.586719i	$-0.199581\pi$
$613$	40.0990			1.61958			0.809791	+	0.586719i	$0.199581\pi$
$614$	14.8000			0.597280
$615$		0			0
$616$	−3.29150	−	6.72057i	−0.132618	−	0.270779i
$617$		−	4.83399i		−	0.194609i	−0.995255	−	0.0973045i	$-0.968978\pi$
$617$		−	4.83399i		−	0.194609i	0.995255	−	0.0973045i	$-0.0310221\pi$
$618$	−21.1245	+	5.29150i	−0.849751	+	0.212855i
$619$		−	0.632534i		−	0.0254237i	−0.999919	−	0.0127118i	$-0.995954\pi$
$619$		−	0.632534i		−	0.0254237i	0.999919	−	0.0127118i	$-0.00404641\pi$
$620$		0			0
$621$	11.4859	+	12.6724i	0.460915	+	0.508528i
$622$		−	2.77053i		−	0.111088i
$623$	14.9785	+	30.5830i	0.600101	+	1.22528i
$624$	0.354249	+	1.41421i	0.0141813	+	0.0566139i
$625$		0			0
$626$	−8.11905			−0.324502
$627$	21.6255	−	5.41699i	0.863637	−	0.216334i
$628$			22.6209i			0.902672i
$629$	12.8712			0.513209
$630$		0			0
$631$	−20.4575			−0.814401			−0.407200	−	0.913339i	$-0.633495\pi$
$631$	−20.4575			−0.814401			−0.407200	+	0.913339i	$0.633495\pi$
$632$		−	7.29150i		−	0.290040i
$633$	−35.5619	+	8.90796i	−1.41346	+	0.354060i
$634$	6.00000			0.238290
$635$		0			0
$636$	5.29570	+	21.1412i	0.209988	+	0.838304i
$637$	4.65489	+	3.61226i	0.184433	+	0.143123i
$638$		−	22.5830i		−	0.894070i
$639$	17.8745	+	33.4401i	0.707105	+	1.32287i
$640$		0			0
$641$		−	16.7931i		−	0.663287i	−0.943405	−	0.331644i	$-0.892397\pi$
$641$		−	16.7931i		−	0.663287i	0.943405	−	0.331644i	$-0.107603\pi$
$642$		0			0
$643$		−	47.7669i		−	1.88374i	−0.335971	−	0.941872i	$-0.609065\pi$
$643$		−	47.7669i		−	1.88374i	0.335971	−	0.941872i	$-0.390935\pi$
$644$	−7.82087	+	3.83039i	−0.308185	+	0.150939i
$645$		0			0
$646$	5.41699			0.213129
$647$	−15.4002			−0.605444			−0.302722	−	0.953079i	$-0.597895\pi$
$647$	−15.4002			−0.605444			−0.302722	+	0.953079i	$0.597895\pi$
$648$	−7.48331	−	5.00000i	−0.293972	−	0.196419i
$649$		−	11.0604i		−	0.434158i
$650$		0			0
$651$	19.3688	−	16.3429i	0.759125	−	0.640529i
$652$		0			0
$653$			19.1660i			0.750024i	0.927020	+	0.375012i	$0.122361\pi$
$653$			19.1660i			0.750024i	−0.927020	+	0.375012i	$0.877639\pi$
$654$	0.841723	+	3.36028i	0.0329140	+	0.131397i
$655$		0			0
$656$	7.82087			0.305354
$657$	4.33981	+	8.11905i	0.169312	+	0.316754i
$658$	10.3117	−	5.05034i	0.401994	−	0.196883i
$659$		−	32.7617i		−	1.27621i	−0.769948	−	0.638107i	$-0.779718\pi$
$659$		−	32.7617i		−	1.27621i	0.769948	−	0.638107i	$-0.220282\pi$
$660$		0			0
$661$			0.979531i			0.0380994i	0.999819	+	0.0190497i	$0.00606407\pi$
$661$			0.979531i			0.0380994i	−0.999819	+	0.0190497i	$0.993936\pi$
$662$			8.00000i			0.310929i
$663$	0.421689	+	1.68345i	0.0163770	+	0.0653796i
$664$			7.70010i			0.298822i
$665$		0			0
$666$	15.2915	+	28.6078i	0.592534	+	1.10853i
$667$	−26.2803			−1.01758
$668$	11.4821			0.444255
$669$	2.00000	+	7.98430i	0.0773245	+	0.308691i
$670$		0			0
$671$	−28.5129			−1.10073
$672$	3.50238	−	2.95522i	0.135107	−	0.114000i
$673$	−38.5960			−1.48777			−0.743883	−	0.668309i	$-0.767018\pi$
$673$	−38.5960			−1.48777			−0.743883	+	0.668309i	$0.767018\pi$
$674$			22.4499i			0.864740i
$675$		0			0
$676$	−12.2915			−0.472750
$677$	42.4933			1.63315			0.816575	−	0.577239i	$-0.195870\pi$
$677$	42.4933			1.63315			0.816575	+	0.577239i	$0.195870\pi$
$678$	−10.0808	+	2.52517i	−0.387153	+	0.0969785i
$679$	19.2915	−	9.44832i	0.740340	−	0.362593i
$680$		0			0
$681$	2.35425	−	0.589720i	0.0902150	−	0.0225981i
$682$			15.6417i			0.598953i
$683$			5.41699i			0.207276i	0.994615	+	0.103638i	$0.0330483\pi$
$683$			5.41699i			0.207276i	−0.994615	+	0.103638i	$0.966952\pi$
$684$	6.43560	+	12.0399i	0.246071	+	0.460358i
$685$		0			0
$686$	3.76135	−	18.1343i	0.143609	−	0.692370i
$687$	11.9034	+	47.5203i	0.454144	+	1.81301i
$688$	4.65489			0.177466
$689$	10.5914			0.403500
$690$		0			0
$691$			6.50972i			0.247641i	0.992305	+	0.123821i	$0.0395148\pi$
$691$			6.50972i			0.247641i	−0.992305	+	0.123821i	$0.960485\pi$
$692$	−8.89047			−0.337965
$693$	13.1261	−	18.2128i	0.498618	−	0.691848i
$694$	−24.0000			−0.911028
$695$		0			0
$696$	13.4148	−	3.36028i	0.508485	−	0.127371i
$697$	9.30978			0.352633
$698$	−19.1822			−0.726056
$699$	−1.13990	−	4.55066i	−0.0431151	−	0.172122i
$700$		0			0
$701$		−	1.32548i		−	0.0500626i	−0.999687	−	0.0250313i	$-0.992031\pi$
$701$		−	1.32548i		−	0.0500626i	0.999687	−	0.0250313i	$-0.00796854\pi$
$702$	−3.24067	+	2.93725i	−0.122311	+	0.110860i
$703$		−	49.2050i		−	1.85580i
$704$			2.82843i			0.106600i
$705$		0			0
$706$		−	21.3521i		−	0.803596i
$707$	4.55066	+	9.29150i	0.171145	+	0.349443i
$708$	6.57008	−	1.64575i	0.246919	−	0.0618511i
$709$	−20.5830			−0.773011			−0.386505	−	0.922287i	$-0.626318\pi$
$709$	−20.5830			−0.773011			−0.386505	+	0.922287i	$0.626318\pi$
$710$		0			0
$711$	19.2915	−	10.3117i	0.723488	−	0.386721i
$712$		−	12.8712i		−	0.482369i
$713$	18.2026			0.681694
$714$	4.16915	−	3.51782i	0.156027	−	0.131651i
$715$		0			0
$716$			9.48725i			0.354555i
$717$	−9.31216	−	37.1755i	−0.347769	−	1.38835i
$718$	−26.7813			−0.999470
$719$	36.3338			1.35502			0.677511	−	0.735512i	$-0.263058\pi$
$719$	36.3338			1.35502			0.677511	+	0.735512i	$0.263058\pi$
$720$		0			0
$721$	29.8745	−	14.6315i	1.11258	−	0.544906i
$722$		−	1.70850i		−	0.0635837i
$723$	−0.824494	−	3.29150i	−0.0306633	−	0.122412i
$724$		−	12.0399i		−	0.447460i
$725$		0			0
$726$	−1.26258	−	5.04042i	−0.0468589	−	0.187068i
$727$			7.03196i			0.260801i	0.991461	+	0.130401i	$0.0416263\pi$
$727$			7.03196i			0.260801i	−0.991461	+	0.130401i	$0.958374\pi$
$728$	−0.979531	−	2.00000i	−0.0363038	−	0.0741249i
$729$	2.64575	−	26.8701i	0.0979908	−	0.995187i
$730$		0			0
$731$	5.54107			0.204944
$732$	−4.24264	−	16.9373i	−0.156813	−	0.626019i
$733$			24.9007i			0.919728i	0.887989	+	0.459864i	$0.152102\pi$
$733$			24.9007i			0.919728i	−0.887989	+	0.459864i	$0.847898\pi$
$734$	8.11905			0.299680
$735$		0			0
$736$	3.29150			0.121326
$737$		−	13.1660i		−	0.484976i
$738$	11.0604	+	20.6921i	0.407138	+	0.761686i
$739$	−9.16601			−0.337177			−0.168589	−	0.985687i	$-0.553921\pi$
$739$	−9.16601			−0.337177			−0.168589	+	0.985687i	$0.553921\pi$
$740$		0			0
$741$	6.43560	−	1.61206i	0.236418	−	0.0592207i
$742$	−14.6431	−	29.8982i	−0.537566	−	1.09760i
$743$		−	33.8745i		−	1.24274i	−0.783519	−	0.621368i	$-0.786577\pi$
$743$		−	33.8745i		−	1.24274i	0.783519	−	0.621368i	$-0.213423\pi$
$744$	−9.29150	+	2.32744i	−0.340643	+	0.0853282i
$745$		0			0
$746$		−	15.4676i		−	0.566310i
$747$	−20.3725	+	10.8896i	−0.745392	+	0.398429i
$748$			3.36689i			0.123106i
$749$		0			0
$750$		0			0
$751$	21.1660			0.772359			0.386179	−	0.922424i	$-0.373795\pi$
$751$	21.1660			0.772359			0.386179	+	0.922424i	$0.373795\pi$
$752$	−4.33981			−0.158257
$753$	−19.7103	+	4.93725i	−0.718282	+	0.179924i
$754$		−	6.72057i		−	0.244749i
$755$		0			0
$756$	12.7719	+	5.08713i	0.464509	+	0.185017i
$757$	−3.15194			−0.114559			−0.0572796	−	0.998358i	$-0.518243\pi$
$757$	−3.15194			−0.114559			−0.0572796	+	0.998358i	$0.518243\pi$
$758$		−	14.5830i		−	0.529679i
$759$	15.6417	−	3.91813i	0.567759	−	0.142219i
$760$		0			0
$761$	20.6921			0.750087			0.375044	−	0.927007i	$-0.377628\pi$
$761$	20.6921			0.750087			0.375044	+	0.927007i	$0.377628\pi$
$762$	4.55066	+	18.1669i	0.164853	+	0.658118i
$763$	−2.32744	−	4.75216i	−0.0842591	−	0.172040i
$764$		−	7.98430i		−	0.288862i
$765$		0			0
$766$			11.4821i			0.414864i
$767$		−	3.29150i		−	0.118849i
$768$	−1.68014	+	0.420861i	−0.0606269	+	0.0151865i
$769$			35.1402i			1.26719i	0.773666	+	0.633594i	$0.218421\pi$
$769$			35.1402i			1.26719i	−0.773666	+	0.633594i	$0.781579\pi$
$770$		0			0
$771$	−23.8745	+	5.98036i	−0.859819	+	0.215378i
$772$	8.48528			0.305392
$773$	−7.35310			−0.264473			−0.132236	−	0.991218i	$-0.542216\pi$
$773$	−7.35310			−0.264473			−0.132236	+	0.991218i	$0.542216\pi$
$774$	6.58301	+	12.3157i	0.236621	+	0.442678i
$775$		0			0
$776$	−8.11905			−0.291457
$777$	−31.9540	−	37.8703i	−1.14634	−	1.35859i
$778$	0.323511			0.0115984
$779$		−	35.5901i		−	1.27515i
$780$		0			0
$781$	35.7490			1.27920
$782$	3.91813			0.140112
$783$	27.8618	+	30.7399i	0.995699	+	1.09856i
$784$	−4.29150	+	5.53019i	−0.153268	+	0.197507i
$785$		0			0
$786$	−3.77124	−	15.0554i	−0.134516	−	0.537007i
$787$		−	24.9007i		−	0.887614i	−0.896122	−	0.443807i	$-0.853628\pi$
$787$		−	24.9007i		−	0.887614i	0.896122	−	0.443807i	$-0.146372\pi$
$788$			18.0000i			0.641223i
$789$	2.77053	+	11.0604i	0.0986336	+	0.393760i
$790$		0			0
$791$	14.2565	−	6.98233i	0.506902	−	0.248263i
$792$	−7.48331	+	4.00000i	−0.265908	+	0.142134i
$793$	−8.48528			−0.301321
$794$	−21.5338			−0.764206
$795$		0			0
$796$			16.5906i			0.588037i
$797$	−6.93141			−0.245523			−0.122762	−	0.992436i	$-0.539175\pi$
$797$	−6.93141			−0.245523			−0.122762	+	0.992436i	$0.539175\pi$
$798$	−13.4482	−	15.9382i	−0.476061	−	0.564204i
$799$	−5.16601			−0.182760
$800$		0			0
$801$	34.0540	−	18.2026i	1.20324	−	0.643159i
$802$	7.48331			0.264245
$803$	8.67963			0.306297
$804$	7.82087	−	1.95906i	0.275821	−	0.0690908i
$805$		0			0
$806$			4.65489i			0.163961i
$807$	−41.3357	+	10.3542i	−1.45509	+	0.364487i
$808$		−	3.91044i		−	0.137569i
$809$			33.7637i			1.18707i	0.804809	+	0.593533i	$0.202268\pi$
$809$			33.7637i			1.18707i	−0.804809	+	0.593533i	$0.797732\pi$
$810$		0			0
$811$			28.6305i			1.00535i	0.864475	+	0.502676i	$0.167651\pi$
$811$			28.6305i			1.00535i	−0.864475	+	0.502676i	$0.832349\pi$
$812$	−18.9713	+	9.29150i	−0.665763	+	0.326068i
$813$	3.15194	+	12.5830i	0.110543	+	0.441305i
$814$	30.5830			1.07193
$815$		0			0
$816$	−2.00000	+	0.500983i	−0.0700140	+	0.0175379i
$817$		−	21.1828i		−	0.741093i
$818$	13.0194			0.455214
$819$	3.90624	−	5.42002i	0.136495	−	0.189391i
$820$		0			0
$821$		−	5.98036i		−	0.208716i	−0.994540	−	0.104358i	$-0.966721\pi$
$821$		−	5.98036i		−	0.208716i	0.994540	−	0.104358i	$-0.0332788\pi$
$822$	15.6110	−	3.91044i	0.544498	−	0.136392i
$823$	−19.2980			−0.672686			−0.336343	−	0.941740i	$-0.609190\pi$
$823$	−19.2980			−0.672686			−0.336343	+	0.941740i	$0.609190\pi$
$824$	−12.5730			−0.438002
$825$		0			0
$826$	−9.29150	+	4.55066i	−0.323293	+	0.158338i
$827$		−	36.0000i		−	1.25184i	−0.779886	−	0.625921i	$-0.784723\pi$
$827$		−	36.0000i		−	1.25184i	0.779886	−	0.625921i	$-0.215277\pi$
$828$	4.65489	+	8.70850i	0.161769	+	0.302641i
$829$			45.2211i			1.57059i	0.619120	+	0.785296i	$0.287489\pi$
$829$			45.2211i			1.57059i	−0.619120	+	0.785296i	$0.712511\pi$
$830$		0			0
$831$	25.9878	−	6.50972i	0.901506	−	0.225820i
$832$			0.841723i			0.0291815i
$833$	−5.10850	+	6.58301i	−0.176999	+	0.228088i
$834$	26.2288	−	6.57008i	0.908228	−	0.227503i
$835$		0			0
$836$	12.8712			0.445160
$837$	−19.2980	−	21.2915i	−0.667037	−	0.735942i
$838$		−	21.8320i		−	0.754173i
$839$	−26.2331			−0.905669			−0.452834	−	0.891595i	$-0.649587\pi$
$839$	−26.2331			−0.905669			−0.452834	+	0.891595i	$0.649587\pi$
$840$		0			0
$841$	−34.7490			−1.19824
$842$		−	10.0000i		−	0.344623i
$843$	8.67963	+	34.6504i	0.298942	+	1.19342i
$844$	−21.1660			−0.728564
$845$		0			0
$846$	−6.13742	−	11.4821i	−0.211009	−	0.394762i
$847$	3.49117	+	7.12824i	0.119958	+	0.244929i
$848$			12.5830i			0.432102i
$849$	−4.10326	−	16.3808i	−0.140824	−	0.562189i
$850$		0			0
$851$		−	35.5901i		−	1.22001i
$852$	5.31935	+	21.2356i	0.182238	+	0.727520i
$853$		−	5.89206i		−	0.201740i	−0.994900	−	0.100870i	$-0.967837\pi$
$853$		−	5.89206i		−	0.201740i	0.994900	−	0.100870i	$-0.0321627\pi$
$854$	11.7313	+	23.9529i	0.401437	+	0.819651i
$855$		0			0
$856$		0			0
$857$	−24.1545			−0.825103			−0.412551	−	0.910934i	$-0.635362\pi$
$857$	−24.1545			−0.825103			−0.412551	+	0.910934i	$0.635362\pi$
$858$	1.00197	+	4.00000i	0.0342066	+	0.136558i
$859$		−	2.59160i		−	0.0884241i	−0.999022	−	0.0442121i	$-0.985922\pi$
$859$		−	2.59160i		−	0.0884241i	0.999022	−	0.0442121i	$-0.0140777\pi$
$860$		0			0
$861$	−23.1124	−	27.3917i	−0.787668	−	0.933506i
$862$	−16.4696			−0.560956
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	−3.48957	−	3.85005i	−0.118718	−	0.130981i
$865$		0			0
$866$	−26.5313			−0.901571
$867$	26.1817	−	6.55829i	0.889176	−	0.222731i
$868$	13.1402	−	6.43560i	0.446006	−	0.218439i
$869$		−	20.6235i		−	0.699604i
$870$		0			0
$871$		−	3.91813i		−	0.132761i
$872$			2.00000i			0.0677285i
$873$	−11.4821	−	21.4810i	−0.388609	−	0.727021i
$874$		−	14.9785i		−	0.506656i
$875$		0			0
$876$	1.29150	+	5.15587i	0.0436358	+	0.174201i
$877$	1.50295			0.0507510			0.0253755	−	0.999678i	$-0.491922\pi$
$877$	1.50295			0.0507510			0.0253755	+	0.999678i	$0.491922\pi$
$878$	18.5496			0.626020
$879$	18.9373	−	4.74362i	0.638738	−	0.159998i
$880$		0			0
$881$	12.8712			0.433642			0.216821	−	0.976211i	$-0.430431\pi$
$881$	12.8712			0.433642			0.216821	+	0.976211i	$0.430431\pi$
$882$	−20.7006	−	3.53338i	−0.697026	−	0.118975i
$883$	13.9647			0.469948			0.234974	−	0.972002i	$-0.424499\pi$
$883$	13.9647			0.469948			0.234974	+	0.972002i	$0.424499\pi$
$884$			1.00197i			0.0336998i
$885$		0			0
$886$	−13.1660			−0.442321
$887$	−44.6632			−1.49964			−0.749822	−	0.661640i	$-0.769861\pi$
$887$	−44.6632			−1.49964			−0.749822	+	0.661640i	$0.769861\pi$
$888$	4.55066	+	18.1669i	0.152710	+	0.609642i
$889$	−12.5830	−	25.6919i	−0.422020	−	0.861678i
$890$		0			0
$891$	−21.1660	−	14.1421i	−0.709088	−	0.473779i
$892$			4.75216i			0.159114i
$893$			19.7490i			0.660876i
$894$	−5.59388	+	1.40122i	−0.187087	+	0.0468638i
$895$		0			0
$896$	2.37608	−	1.16372i	0.0793792	−	0.0388772i
$897$	4.65489	−	1.16601i	0.155422	−	0.0389320i
$898$	−8.30781			−0.277235
$899$	44.1547			1.47264
$900$		0			0
$901$			14.9785i			0.499006i
$902$	22.1208			0.736541
$903$	−13.7562	−	16.3032i	−0.457778	−	0.542537i
$904$	−6.00000			−0.199557
$905$		0			0
$906$	9.50432	+	37.9426i	0.315760	+	1.26056i
$907$	−33.9411			−1.12700			−0.563498	−	0.826117i	$-0.690545\pi$
$907$	−33.9411			−1.12700			−0.563498	+	0.826117i	$0.690545\pi$
$908$	1.40122			0.0465011
$909$	10.3460	−	5.53019i	0.343156	−	0.183425i
$910$		0			0
$911$			4.15390i			0.137625i	0.997630	+	0.0688125i	$0.0219210\pi$
$911$			4.15390i			0.137625i	−0.997630	+	0.0688125i	$0.978079\pi$
$912$	1.91520	+	7.64575i	0.0634185	+	0.253176i
$913$			21.7792i			0.720785i
$914$		−	8.48528i		−	0.280668i
$915$		0			0
$916$			28.2835i			0.934513i
$917$	10.4278	+	21.2915i	0.344358	+	0.703107i
$918$	−4.15390	−	4.58301i	−0.137099	−	0.151262i
$919$	−10.1255			−0.334009			−0.167005	−	0.985956i	$-0.553409\pi$
$919$	−10.1255			−0.334009			−0.167005	+	0.985956i	$0.553409\pi$
$920$		0			0
$921$	6.22876	+	24.8661i	0.205245	+	0.819367i
$922$		−	8.96077i		−	0.295107i
$923$	10.6387			0.350177
$924$	9.90624	−	8.35862i	0.325891	−	0.274978i
$925$		0			0
$926$			23.9529i			0.787141i
$927$	−17.7809	−	33.2651i	−0.584003	−	1.09257i
$928$	7.98430			0.262097
$929$	−30.7928			−1.01028			−0.505139	−	0.863038i	$-0.668559\pi$
$929$	−30.7928			−1.01028			−0.505139	+	0.863038i	$0.668559\pi$
$930$		0			0
$931$	25.1660	+	19.5292i	0.824783	+	0.640043i
$932$		−	2.70850i		−	0.0887198i
$933$	4.65489	−	1.16601i	0.152394	−	0.0381735i
$934$		−	3.36028i		−	0.109952i
$935$		0			0
$936$	−2.22699	+	1.19038i	−0.0727914	+	0.0389087i
$937$		−	3.06871i		−	0.100250i	−0.998743	−	0.0501252i	$-0.984038\pi$
$937$		−	3.06871i		−	0.100250i	0.998743	−	0.0501252i	$-0.0159620\pi$
$938$	−11.0604	+	5.41699i	−0.361134	+	0.176871i
$939$	−3.41699	−	13.6412i	−0.111509	−	0.445162i
$940$		0			0
$941$	−40.2443			−1.31193			−0.655963	−	0.754793i	$-0.727737\pi$
$941$	−40.2443			−1.31193			−0.655963	+	0.754793i	$0.727737\pi$
$942$	−38.0063	+	9.52026i	−1.23831	+	0.310187i
$943$		−	25.7424i		−	0.838288i
$944$	3.91044			0.127274
$945$		0			0
$946$	13.1660			0.428064
$947$		−	24.0000i		−	0.779895i	−0.920837	−	0.389948i	$-0.872493\pi$
$947$		−	24.0000i		−	0.779895i	0.920837	−	0.389948i	$-0.127507\pi$
$948$	12.2508	−	3.06871i	0.397886	−	0.0996671i
$949$	2.58301			0.0838479
$950$		0			0
$951$	2.52517	+	10.0808i	0.0818842	+	0.326894i
$952$	2.82843	−	1.38527i	0.0916698	−	0.0448967i
$953$		−	27.8745i		−	0.902944i	−0.892285	−	0.451472i	$-0.850899\pi$
$953$		−	27.8745i		−	0.902944i	0.892285	−	0.451472i	$-0.149101\pi$
$954$	−33.2915	+	17.7951i	−1.07785	+	0.576136i
$955$		0			0
$956$		−	22.1264i		−	0.715620i
$957$	37.9426	−	9.50432i	1.22651	−	0.307231i
$958$		−	39.1044i		−	1.26340i
$959$	−22.0773	+	10.8127i	−0.712915	+	0.349161i
$960$		0			0
$961$	0.416995			0.0134514
$962$	9.10132			0.293438
$963$		0			0
$964$		−	1.95906i		−	0.0630972i
$965$		0			0
$966$	−9.72711	−	11.5281i	−0.312965	−	0.370911i
$967$	−49.4087			−1.58888			−0.794439	−	0.607344i	$-0.792235\pi$
$967$	−49.4087			−1.58888			−0.794439	+	0.607344i	$0.792235\pi$
$968$		−	3.00000i		−	0.0964237i
$969$	2.27980	+	9.10132i	0.0732379	+	0.292376i
$970$		0			0
$971$	−24.6025			−0.789532			−0.394766	−	0.918782i	$-0.629174\pi$
$971$	−24.6025			−0.789532			−0.394766	+	0.918782i	$0.629174\pi$
$972$	5.25127	−	14.6773i	0.168435	−	0.470776i
$973$	−37.0931	+	18.1669i	−1.18915	+	0.582404i
$974$			32.4382i			1.03939i
$975$		0			0
$976$		−	10.0808i		−	0.322680i
$977$			51.8745i			1.65961i	0.558052	+	0.829806i	$0.311549\pi$
$977$			51.8745i			1.65961i	−0.558052	+	0.829806i	$0.688451\pi$
$978$		0			0
$979$		−	36.4053i		−	1.16352i
$980$		0			0
$981$	−5.29150	+	2.82843i	−0.168945	+	0.0903047i
$982$	−14.1421			−0.451294
$983$	−62.0225			−1.97821			−0.989105	−	0.147213i	$-0.952970\pi$
$983$	−62.0225			−1.97821			−0.989105	+	0.147213i	$0.952970\pi$
$984$	3.29150	+	13.1402i	0.104929	+	0.418893i
$985$		0			0
$986$	9.50432			0.302679
$987$	12.8251	+	15.1997i	0.408227	+	0.483812i
$988$	3.83039			0.121861
$989$		−	15.3216i		−	0.487198i
$990$		0			0
$991$	−0.708497			−0.0225062			−0.0112531	−	0.999937i	$-0.503582\pi$
$991$	−0.708497			−0.0225062			−0.0112531	+	0.999937i	$0.503582\pi$
$992$	−5.53019			−0.175584
$993$	−13.4411	+	3.36689i	−0.426541	+	0.106845i
$994$	−14.7085	−	30.0317i	−0.466525	−	0.952548i
$995$		0			0
$996$	−12.9373	+	3.24067i	−0.409933	+	0.102685i
$997$			42.2259i			1.33731i	0.743574	+	0.668653i	$0.233129\pi$
$997$			42.2259i			1.33731i	−0.743574	+	0.668653i	$0.766871\pi$
$998$		−	1.41699i		−	0.0448542i
$999$	−41.6295	+	37.7318i	−1.31710	+	1.19378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.b.f.251.10		16
3.2	odd	2	inner	1050.2.b.f.251.8		16
5.2	odd	4		210.2.d.a.209.6	yes	8
5.3	odd	4		210.2.d.b.209.3	yes	8
5.4	even	2	inner	1050.2.b.f.251.7		16
7.6	odd	2	inner	1050.2.b.f.251.15		16
15.2	even	4		210.2.d.b.209.5	yes	8
15.8	even	4		210.2.d.a.209.4	yes	8
15.14	odd	2	inner	1050.2.b.f.251.9		16
20.3	even	4		1680.2.k.f.209.6		8
20.7	even	4		1680.2.k.e.209.3		8
21.20	even	2	inner	1050.2.b.f.251.1		16
35.13	even	4		210.2.d.b.209.6	yes	8
35.27	even	4		210.2.d.a.209.3	✓	8
35.34	odd	2	inner	1050.2.b.f.251.2		16
60.23	odd	4		1680.2.k.e.209.5		8
60.47	odd	4		1680.2.k.f.209.4		8
105.62	odd	4		210.2.d.b.209.4	yes	8
105.83	odd	4		210.2.d.a.209.5	yes	8
105.104	even	2	inner	1050.2.b.f.251.16		16
140.27	odd	4		1680.2.k.e.209.6		8
140.83	odd	4		1680.2.k.f.209.3		8
420.83	even	4		1680.2.k.e.209.4		8
420.167	even	4		1680.2.k.f.209.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.d.a.209.3	✓	8	35.27	even	4
210.2.d.a.209.4	yes	8	15.8	even	4
210.2.d.a.209.5	yes	8	105.83	odd	4
210.2.d.a.209.6	yes	8	5.2	odd	4
210.2.d.b.209.3	yes	8	5.3	odd	4
210.2.d.b.209.4	yes	8	105.62	odd	4
210.2.d.b.209.5	yes	8	15.2	even	4
210.2.d.b.209.6	yes	8	35.13	even	4
1050.2.b.f.251.1		16	21.20	even	2	inner
1050.2.b.f.251.2		16	35.34	odd	2	inner
1050.2.b.f.251.7		16	5.4	even	2	inner
1050.2.b.f.251.8		16	3.2	odd	2	inner
1050.2.b.f.251.9		16	15.14	odd	2	inner
1050.2.b.f.251.10		16	1.1	even	1	trivial
1050.2.b.f.251.15		16	7.6	odd	2	inner
1050.2.b.f.251.16		16	105.104	even	2	inner
1680.2.k.e.209.3		8	20.7	even	4
1680.2.k.e.209.4		8	420.83	even	4
1680.2.k.e.209.5		8	60.23	odd	4
1680.2.k.e.209.6		8	140.27	odd	4
1680.2.k.f.209.3		8	140.83	odd	4
1680.2.k.f.209.4		8	60.47	odd	4
1680.2.k.f.209.5		8	420.167	even	4
1680.2.k.f.209.6		8	20.3	even	4

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.68014 + 0.420861i) q^{3} -1.00000 q^{4} +(-0.420861 - 1.68014i) q^{6} +(1.16372 + 2.37608i) q^{7} -1.00000i q^{8} +(2.64575 - 1.41421i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.68014 + 0.420861i) q^{3} -1.00000 q^{4} +(-0.420861 - 1.68014i) q^{6} +(1.16372 + 2.37608i) q^{7} -1.00000i q^{8} +(2.64575 - 1.41421i) q^{9} -2.82843i q^{11} +(1.68014 - 0.420861i) q^{12} -0.841723i q^{13} +(-2.37608 + 1.16372i) q^{14} +1.00000 q^{16} +1.19038 q^{17} +(1.41421 + 2.64575i) q^{18} -4.55066i q^{19} +(-2.95522 - 3.50238i) q^{21} +2.82843 q^{22} -3.29150i q^{23} +(0.420861 + 1.68014i) q^{24} +0.841723 q^{26} +(-3.85005 + 3.48957i) q^{27} +(-1.16372 - 2.37608i) q^{28} -7.98430i q^{29} +5.53019i q^{31} +1.00000i q^{32} +(1.19038 + 4.75216i) q^{33} +1.19038i q^{34} +(-2.64575 + 1.41421i) q^{36} +10.8127 q^{37} +4.55066 q^{38} +(0.354249 + 1.41421i) q^{39} +7.82087 q^{41} +(3.50238 - 2.95522i) q^{42} +4.65489 q^{43} +2.82843i q^{44} +3.29150 q^{46} -4.33981 q^{47} +(-1.68014 + 0.420861i) q^{48} +(-4.29150 + 5.53019i) q^{49} +(-2.00000 + 0.500983i) q^{51} +0.841723i q^{52} +12.5830i q^{53} +(-3.48957 - 3.85005i) q^{54} +(2.37608 - 1.16372i) q^{56} +(1.91520 + 7.64575i) q^{57} +7.98430 q^{58} +3.91044 q^{59} -10.0808i q^{61} -5.53019 q^{62} +(6.43920 + 4.64076i) q^{63} -1.00000 q^{64} +(-4.75216 + 1.19038i) q^{66} +4.65489 q^{67} -1.19038 q^{68} +(1.38527 + 5.53019i) q^{69} +12.6392i q^{71} +(-1.41421 - 2.64575i) q^{72} +3.06871i q^{73} +10.8127i q^{74} +4.55066i q^{76} +(6.72057 - 3.29150i) q^{77} +(-1.41421 + 0.354249i) q^{78} +7.29150 q^{79} +(5.00000 - 7.48331i) q^{81} +7.82087i q^{82} -7.70010 q^{83} +(2.95522 + 3.50238i) q^{84} +4.65489i q^{86} +(3.36028 + 13.4148i) q^{87} -2.82843 q^{88} +12.8712 q^{89} +(2.00000 - 0.979531i) q^{91} +3.29150i q^{92} +(-2.32744 - 9.29150i) q^{93} -4.33981i q^{94} +(-0.420861 - 1.68014i) q^{96} -8.11905i q^{97} +(-5.53019 - 4.29150i) q^{98} +(-4.00000 - 7.48331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4}+O(q^{10}) \) 16 * q - 16 * q^4	\( 16 q - 16 q^{4} + 16 q^{16} - 16 q^{21} + 48 q^{39} - 32 q^{46} + 16 q^{49} - 32 q^{51} - 16 q^{64} + 32 q^{79} + 80 q^{81} + 16 q^{84} + 32 q^{91} - 64 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 16 * q^16 - 16 * q^21 + 48 * q^39 - 32 * q^46 + 16 * q^49 - 32 * q^51 - 16 * q^64 + 32 * q^79 + 80 * q^81 + 16 * q^84 + 32 * q^91 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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