LMFDB - Embedded newform 1050.2.b.f.251.7

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			251.7
Root			$0.137538 - 0.752908i$ of defining polynomial
Character	$\chi$	$=$	1050.251
Dual form			1050.2.b.f.251.16

$q$-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	$0.0372399\pi$
$13$			0.841723i			0.233452i	−0.993164	+	0.116726i	$0.962760\pi$
$14$	−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	$-0.546110\pi$
$17$	−1.19038			−0.288709			−0.144354	+	0.989526i	$0.546110\pi$
$18$	−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	$0.111498\pi$
$23$			3.29150i			0.686326i	−0.939276	+	0.343163i	$0.888502\pi$
$24$	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	$-0.848461\pi$
$37$	−10.8127			−1.77760			−0.888801	+	0.458294i	$0.848461\pi$
$38$	−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	$-0.615496\pi$
$43$	−4.65489			−0.709864			−0.354932	+	0.934892i	$0.615496\pi$
$44$			2.82843i			0.426401i
$45$		0			0
$46$	3.29150			0.485306
$47$	4.33981			0.633027			0.316513	−	0.948588i	$-0.397488\pi$
$47$	4.33981			0.633027			0.316513	+	0.948588i	$0.397488\pi$
$48$	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	$-0.667822\pi$
$53$		−	12.5830i		−	1.72841i	0.503141	−	0.864204i	$-0.332178\pi$
$54$	−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	$-0.591775\pi$
$67$	−4.65489			−0.568685			−0.284343	+	0.958723i	$0.591775\pi$
$68$	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	$-0.942525\pi$
$73$		−	3.06871i		−	0.359166i	0.983743	−	0.179583i	$-0.0574748\pi$
$74$			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	$-0.361118\pi$
$83$	7.70010			0.845196			0.422598	+	0.906317i	$0.361118\pi$
$84$	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	$0.135233\pi$
$97$			8.11905i			0.824365i	−0.911101	+	0.412182i	$0.864767\pi$
$98$	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	$0.212636\pi$
$103$			12.5730i			1.23886i	−0.785053	+	0.619429i	$0.787364\pi$
$104$	−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	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	−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	$-0.340732\pi$
$127$	10.8127			0.959474			0.479737	+	0.877412i	$0.340732\pi$
$128$			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	$-0.870081\pi$
$137$		−	9.29150i		−	0.793827i	0.917856	−	0.396913i	$-0.129919\pi$
$138$	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	$0.358397\pi$
$157$			22.6209i			1.80534i	−0.430330	+	0.902672i	$0.641603\pi$
$158$		−	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	$-0.353469\pi$
$167$	11.4821			0.888509			0.444255	+	0.895901i	$0.353469\pi$
$168$	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	$-0.609739\pi$
$173$	−8.89047			−0.675930			−0.337965	+	0.941159i	$0.609739\pi$
$174$	−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	$-0.401213\pi$
$193$	8.48528			0.610784			0.305392	+	0.952227i	$0.401213\pi$
$194$	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	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$	−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	$0.0508637\pi$
$223$			4.75216i			0.318228i	−0.987260	+	0.159114i	$0.949136\pi$
$224$	−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	$-0.485193\pi$
$227$	1.40122			0.0930023			0.0465011	+	0.998918i	$0.485193\pi$
$228$	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	$-0.971722\pi$
$233$		−	2.70850i		−	0.177440i	0.996057	−	0.0887198i	$-0.0282776\pi$
$234$	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	$-0.646154\pi$
$257$	−14.2098			−0.886384			−0.443192	+	0.896427i	$0.646154\pi$
$258$	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	$0.0650570\pi$
$263$			6.58301i			0.405925i	−0.979186	+	0.202963i	$0.934943\pi$
$264$	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	$-0.346170\pi$
$277$	15.4676			0.929359			0.464679	+	0.885479i	$0.346170\pi$
$278$	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	$-0.906418\pi$
$283$		−	9.74968i		−	0.579558i	0.957094	−	0.289779i	$-0.0935819\pi$
$284$		−	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	$-0.393209\pi$
$293$	11.2712			0.658472			0.329236	+	0.944248i	$0.393209\pi$
$294$	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	$0.138791\pi$
$307$			14.8000i			0.844682i	−0.906437	+	0.422341i	$0.861209\pi$
$308$	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	$-0.926305\pi$
$313$		−	8.11905i		−	0.458916i	0.973319	−	0.229458i	$-0.0736953\pi$
$314$	22.6209			1.27657
$315$		0			0
$316$	−7.29150			−0.410179
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$	−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	$-0.709419\pi$
$337$	−22.4499			−1.22293			−0.611463	+	0.791273i	$0.709419\pi$
$338$		−	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	$-0.777193\pi$
$347$		−	24.0000i		−	1.28839i	0.764862	−	0.644194i	$-0.222807\pi$
$348$	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	$-0.307629\pi$
$353$	21.3521			1.13646			0.568228	+	0.822871i	$0.307629\pi$
$354$	−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	$0.0679669\pi$
$367$			8.11905i			0.423811i	−0.977290	+	0.211905i	$0.932033\pi$
$368$			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	$-0.368857\pi$
$373$	15.4676			0.800883			0.400441	+	0.916322i	$0.368857\pi$
$374$	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	$-0.594771\pi$
$383$	−11.4821			−0.586706			−0.293353	+	0.956004i	$0.594771\pi$
$384$	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	$-0.818282\pi$
$397$		−	21.5338i		−	1.08075i	0.841424	−	0.540375i	$-0.181718\pi$
$398$	−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	$-0.779966\pi$
$433$		−	26.5313i		−	1.27501i	0.770445	−	0.637507i	$-0.220034\pi$
$434$	−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	$-0.898744\pi$
$443$		−	13.1660i		−	0.625536i	0.949830	−	0.312768i	$-0.101256\pi$
$444$	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	$-0.436405\pi$
$457$	8.48528			0.396925			0.198462	+	0.980109i	$0.436405\pi$
$458$	−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	$-0.687892\pi$
$463$	−23.9529			−1.11319			−0.556593	+	0.830786i	$0.687892\pi$
$464$		−	7.98430i		−	0.370662i
$465$		0			0
$466$	−2.70850			−0.125469
$467$	3.36028			0.155495			0.0777477	−	0.996973i	$-0.475227\pi$
$467$	3.36028			0.155495			0.0777477	+	0.996973i	$0.475227\pi$
$468$	−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	$-0.762798\pi$
$487$	−32.4382			−1.46991			−0.734957	+	0.678114i	$0.762798\pi$
$488$	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	$-0.438015\pi$
$503$	8.67963			0.387006			0.193503	+	0.981100i	$0.438015\pi$
$504$	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	$-0.970669\pi$
$523$		−	4.20861i		−	0.184030i	0.995758	−	0.0920149i	$-0.0293308\pi$
$524$	−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	$-0.618181\pi$
$547$	−16.9706			−0.725609			−0.362804	+	0.931865i	$0.618181\pi$
$548$			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	$0.0485124\pi$
$557$			7.16601i			0.303634i	−0.988409	+	0.151817i	$0.951488\pi$
$558$	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	$-0.370630\pi$
$563$	18.7605			0.790660			0.395330	+	0.918539i	$0.370630\pi$
$564$	−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	$-0.776871\pi$
$577$		−	30.9853i		−	1.28993i	0.764210	−	0.644967i	$-0.223129\pi$
$578$			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	$-0.864081\pi$
$587$	−44.1054			−1.82042			−0.910212	+	0.414143i	$0.864081\pi$
$588$	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	$-0.551934\pi$
$593$	−7.91094			−0.324863			−0.162432	+	0.986720i	$0.551934\pi$
$594$	−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	$0.160166\pi$
$607$			23.7608i			0.964421i	−0.876055	+	0.482210i	$0.839834\pi$
$608$	−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	$-0.800419\pi$
$613$	−40.0990			−1.61958			−0.809791	+	0.586719i	$0.800419\pi$
$614$	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	$0.0310221\pi$
$617$			4.83399i			0.194609i	−0.995255	+	0.0973045i	$0.968978\pi$
$618$	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	$0.390935\pi$
$643$			47.7669i			1.88374i	−0.335971	+	0.941872i	$0.609065\pi$
$644$	−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	$-0.402105\pi$
$647$	15.4002			0.605444			0.302722	+	0.953079i	$0.402105\pi$
$648$	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	$-0.877639\pi$
$653$		−	19.1660i		−	0.750024i	0.927020	−	0.375012i	$-0.122361\pi$
$654$	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	$-0.232982\pi$
$673$	38.5960			1.48777			0.743883	+	0.668309i	$0.232982\pi$
$674$			22.4499i			0.864740i
$675$		0			0
$676$	−12.2915			−0.472750
$677$	−42.4933			−1.63315			−0.816575	−	0.577239i	$-0.804130\pi$
$677$	−42.4933			−1.63315			−0.816575	+	0.577239i	$0.804130\pi$
$678$	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	$-0.966952\pi$
$683$		−	5.41699i		−	0.207276i	0.994615	−	0.103638i	$-0.0330483\pi$
$684$	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	$-0.958374\pi$
$727$		−	7.03196i		−	0.260801i	0.991461	−	0.130401i	$-0.0416263\pi$
$728$	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	$-0.847898\pi$
$733$		−	24.9007i		−	0.919728i	0.887989	−	0.459864i	$-0.152102\pi$
$734$	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	$0.213423\pi$
$743$			33.8745i			1.24274i	−0.783519	+	0.621368i	$0.786577\pi$
$744$	−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	$-0.481757\pi$
$757$	3.15194			0.114559			0.0572796	+	0.998358i	$0.481757\pi$
$758$			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	$-0.457784\pi$
$773$	7.35310			0.264473			0.132236	+	0.991218i	$0.457784\pi$
$774$	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	$0.146372\pi$
$787$			24.9007i			0.887614i	−0.896122	+	0.443807i	$0.853628\pi$
$788$		−	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	$-0.460825\pi$
$797$	6.93141			0.245523			0.122762	+	0.992436i	$0.460825\pi$
$798$	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	$-0.390810\pi$
$823$	19.2980			0.672686			0.336343	+	0.941740i	$0.390810\pi$
$824$	−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	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$	−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	$0.0321627\pi$
$853$			5.89206i			0.201740i	−0.994900	+	0.100870i	$0.967837\pi$
$854$	11.7313	+	23.9529i	0.401437	+	0.819651i
$855$		0			0
$856$		0			0
$857$	24.1545			0.825103			0.412551	−	0.910934i	$-0.364638\pi$
$857$	24.1545			0.825103			0.412551	+	0.910934i	$0.364638\pi$
$858$	−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	$-0.508078\pi$
$877$	−1.50295			−0.0507510			−0.0253755	+	0.999678i	$0.508078\pi$
$878$	−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	$-0.575501\pi$
$883$	−13.9647			−0.469948			−0.234974	+	0.972002i	$0.575501\pi$
$884$			1.00197i			0.0336998i
$885$		0			0
$886$	−13.1660			−0.442321
$887$	44.6632			1.49964			0.749822	−	0.661640i	$-0.230139\pi$
$887$	44.6632			1.49964			0.749822	+	0.661640i	$0.230139\pi$
$888$	−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	$-0.309455\pi$
$907$	33.9411			1.12700			0.563498	+	0.826117i	$0.309455\pi$
$908$	−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	$0.0159620\pi$
$937$			3.06871i			0.100250i	−0.998743	+	0.0501252i	$0.984038\pi$
$938$	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	$0.127507\pi$
$947$			24.0000i			0.779895i	−0.920837	+	0.389948i	$0.872493\pi$
$948$	−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	$0.149101\pi$
$953$			27.8745i			0.902944i	−0.892285	+	0.451472i	$0.850899\pi$
$954$	−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	$-0.207765\pi$
$967$	49.4087			1.58888			0.794439	+	0.607344i	$0.207765\pi$
$968$			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	$-0.688451\pi$
$977$		−	51.8745i		−	1.65961i	0.558052	−	0.829806i	$-0.311549\pi$
$978$		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	$-0.0470304\pi$
$983$	62.0225			1.97821			0.989105	+	0.147213i	$0.0470304\pi$
$984$	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	$-0.766871\pi$
$997$		−	42.2259i		−	1.33731i	0.743574	−	0.668653i	$-0.233129\pi$
$998$			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.251.7		16
3.2	odd	2	inner	1050.2.b.f.251.9		16
5.2	odd	4		210.2.d.b.209.3	yes	8
5.3	odd	4		210.2.d.a.209.6	yes	8
5.4	even	2	inner	1050.2.b.f.251.10		16
7.6	odd	2	inner	1050.2.b.f.251.2		16
15.2	even	4		210.2.d.a.209.4	yes	8
15.8	even	4		210.2.d.b.209.5	yes	8
15.14	odd	2	inner	1050.2.b.f.251.8		16
20.3	even	4		1680.2.k.e.209.3		8
20.7	even	4		1680.2.k.f.209.6		8
21.20	even	2	inner	1050.2.b.f.251.16		16
35.13	even	4		210.2.d.a.209.3	✓	8
35.27	even	4		210.2.d.b.209.6	yes	8
35.34	odd	2	inner	1050.2.b.f.251.15		16
60.23	odd	4		1680.2.k.f.209.4		8
60.47	odd	4		1680.2.k.e.209.5		8
105.62	odd	4		210.2.d.a.209.5	yes	8
105.83	odd	4		210.2.d.b.209.4	yes	8
105.104	even	2	inner	1050.2.b.f.251.1		16
140.27	odd	4		1680.2.k.f.209.3		8
140.83	odd	4		1680.2.k.e.209.6		8
420.83	even	4		1680.2.k.f.209.5		8
420.167	even	4		1680.2.k.e.209.4		8

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

Related objects

Downloads

Learn more