LMFDB - Embedded newform 1008.2.df.c.689.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(689,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))

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

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

chi := DirichletCharacter("1008.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			689.5
Root			$1.71298 - 0.256290i$ of defining polynomial
Character	$\chi$	$=$	1008.689
Dual form			1008.2.df.c.929.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.128499 + 1.72728i) q^{3} -3.61932 q^{5} +(-0.266972 + 2.63225i) q^{7} +(-2.96698 + 0.443907i) q^{9} -2.00379i q^{11} +(-2.95206 - 1.70437i) q^{13} +(-0.465079 - 6.25156i) q^{15} +(3.08709 - 5.34700i) q^{17} +(-0.877353 + 0.506540i) q^{19} +(-4.58093 - 0.122894i) q^{21} +3.02799i q^{23} +8.09945 q^{25} +(-1.14800 - 5.06775i) q^{27} +(5.04560 - 2.91308i) q^{29} +(-0.787812 + 0.454844i) q^{31} +(3.46111 - 0.257486i) q^{33} +(0.966257 - 9.52693i) q^{35} +(3.66825 + 6.35359i) q^{37} +(2.56459 - 5.31804i) q^{39} +(2.85045 - 4.93712i) q^{41} +(2.39949 + 4.15605i) q^{43} +(10.7384 - 1.60664i) q^{45} +(1.11511 - 1.93143i) q^{47} +(-6.85745 - 1.40547i) q^{49} +(9.63244 + 4.64518i) q^{51} +(-7.58088 - 4.37683i) q^{53} +7.25237i q^{55} +(-0.987674 - 1.45034i) q^{57} +(-4.49313 - 7.78233i) q^{59} +(-12.7410 - 7.35603i) q^{61} +(-0.376373 - 7.92833i) q^{63} +(10.6844 + 6.16866i) q^{65} +(-4.15821 - 7.20222i) q^{67} +(-5.23019 + 0.389094i) q^{69} -0.466287i q^{71} +(-3.65022 - 2.10746i) q^{73} +(1.04077 + 13.9900i) q^{75} +(5.27448 + 0.534957i) q^{77} +(1.91267 - 3.31284i) q^{79} +(8.60589 - 2.63412i) q^{81} +(-4.00481 - 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} +(5.68005 + 8.34083i) q^{87} +(2.39324 + 4.14521i) q^{89} +(5.27445 - 7.31553i) q^{91} +(-0.886874 - 1.30232i) q^{93} +(3.17542 - 1.83333i) q^{95} +(10.1835 - 5.87944i) q^{97} +(0.889499 + 5.94521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} - 6 q^{9} - 6 q^{13} + 18 q^{15} + 18 q^{17} - 18 q^{21} + 16 q^{25} + 36 q^{27} + 6 q^{29} - 6 q^{31} + 18 q^{33} + 30 q^{35} - 2 q^{37} + 30 q^{39} + 6 q^{41} + 2 q^{43} + 12 q^{45} + 18 q^{47}+ \cdots - 18 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 - 6 * q^9 - 6 * q^13 + 18 * q^15 + 18 * q^17 - 18 * q^21 + 16 * q^25 + 36 * q^27 + 6 * q^29 - 6 * q^31 + 18 * q^33 + 30 * q^35 - 2 * q^37 + 30 * q^39 + 6 * q^41 + 2 * q^43 + 12 * q^45 + 18 * q^47 + 10 * q^49 + 36 * q^53 + 6 * q^57 - 30 * q^59 - 60 * q^61 - 42 * q^63 + 42 * q^65 - 14 * q^67 + 42 * q^69 - 30 * q^75 - 18 * q^77 + 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 + 24 * q^89 + 12 * q^91 + 30 * q^93 + 66 * q^95 - 6 * q^97 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.128499	+	1.72728i	0.0741890	+	0.997244i
$3$	0.128499	+	1.72728i	0.0741890	+	0.997244i
$4$		0			0
$5$	−3.61932			−1.61861			−0.809304	−	0.587391i	$-0.800155\pi$
$5$	−3.61932			−1.61861			−0.809304	+	0.587391i	$0.800155\pi$
$6$		0			0
$7$	−0.266972	+	2.63225i	−0.100906	+	0.994896i
$7$	−0.266972	+	2.63225i	−0.100906	+	0.994896i
$8$		0			0
$9$	−2.96698	+	0.443907i	−0.988992	+	0.147969i
$10$		0			0
$11$		−	2.00379i		−	0.604167i	−0.953281	−	0.302083i	$-0.902318\pi$
$11$		−	2.00379i		−	0.604167i	0.953281	−	0.302083i	$-0.0976821\pi$
$12$		0			0
$13$	−2.95206	−	1.70437i	−0.818754	−	0.472708i	0.0312328	−	0.999512i	$-0.490057\pi$
$13$	−2.95206	−	1.70437i	−0.818754	−	0.472708i	−0.849987	+	0.526804i	$0.823390\pi$
$14$		0			0
$15$	−0.465079	−	6.25156i	−0.120083	−	1.61415i
$16$		0			0
$17$	3.08709	−	5.34700i	0.748730	−	1.29684i	−0.199702	−	0.979857i	$-0.563998\pi$
$17$	3.08709	−	5.34700i	0.748730	−	1.29684i	0.948432	−	0.316981i	$-0.102669\pi$
$18$		0			0
$19$	−0.877353	+	0.506540i	−0.201279	+	0.116208i	−0.597252	−	0.802054i	$-0.703741\pi$
$19$	−0.877353	+	0.506540i	−0.201279	+	0.116208i	0.395973	+	0.918262i	$0.370407\pi$
$20$		0			0
$21$	−4.58093	−	0.122894i	−0.999640	−	0.0268176i
$22$		0			0
$23$			3.02799i			0.631380i	0.948862	+	0.315690i	$0.102236\pi$
$23$			3.02799i			0.631380i	−0.948862	+	0.315690i	$0.897764\pi$
$24$		0			0
$25$	8.09945			1.61989
$26$		0			0
$27$	−1.14800	−	5.06775i	−0.220934	−	0.975289i
$28$		0			0
$29$	5.04560	−	2.91308i	0.936945	−	0.540945i	0.0479434	−	0.998850i	$-0.484733\pi$
$29$	5.04560	−	2.91308i	0.936945	−	0.540945i	0.889001	+	0.457905i	$0.151400\pi$
$30$		0			0
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	−0.569076	−	0.822285i	$-0.692699\pi$
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	0.427581	+	0.903977i	$0.359366\pi$
$32$		0			0
$33$	3.46111	−	0.257486i	0.602502	−	0.0448225i
$34$		0			0
$35$	0.966257	−	9.52693i	0.163327	−	1.61035i
$36$		0			0
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	0.992355	+	0.123413i	$0.0393839\pi$
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	−0.389299	+	0.921111i	$0.627283\pi$
$38$		0			0
$39$	2.56459	−	5.31804i	0.410663	−	0.851567i
$40$		0			0
$41$	2.85045	−	4.93712i	0.445165	−	0.771048i	−0.552899	−	0.833248i	$-0.686478\pi$
$41$	2.85045	−	4.93712i	0.445165	−	0.771048i	0.998064	+	0.0622002i	$0.0198117\pi$
$42$		0			0
$43$	2.39949	+	4.15605i	0.365919	+	0.633791i	0.988923	−	0.148428i	$-0.0474212\pi$
$43$	2.39949	+	4.15605i	0.365919	+	0.633791i	−0.623004	+	0.782219i	$0.714088\pi$
$44$		0			0
$45$	10.7384	−	1.60664i	1.60079	−	0.239504i
$46$		0			0
$47$	1.11511	−	1.93143i	0.162655	−	0.281727i	−0.773165	−	0.634205i	$-0.781327\pi$
$47$	1.11511	−	1.93143i	0.162655	−	0.281727i	0.935820	+	0.352478i	$0.114661\pi$
$48$		0			0
$49$	−6.85745	−	1.40547i	−0.979636	−	0.200782i
$50$		0			0
$51$	9.63244	+	4.64518i	1.34881	+	0.650455i
$52$		0			0
$53$	−7.58088	−	4.37683i	−1.04131	−	0.601203i	−0.121109	−	0.992639i	$-0.538645\pi$
$53$	−7.58088	−	4.37683i	−1.04131	−	0.601203i	−0.920205	+	0.391436i	$0.871978\pi$
$54$		0			0
$55$			7.25237i			0.977909i
$56$		0			0
$57$	−0.987674	−	1.45034i	−0.130821	−	0.192103i
$58$		0			0
$59$	−4.49313	−	7.78233i	−0.584956	−	1.01317i	−0.994881	−	0.101054i	$-0.967778\pi$
$59$	−4.49313	−	7.78233i	−0.584956	−	1.01317i	0.409925	−	0.912119i	$-0.365555\pi$
$60$		0			0
$61$	−12.7410	−	7.35603i	−1.63132	−	0.941843i	−0.983686	−	0.179892i	$-0.942425\pi$
$61$	−12.7410	−	7.35603i	−1.63132	−	0.941843i	−0.647634	−	0.761952i	$-0.724241\pi$
$62$		0			0
$63$	−0.376373	−	7.92833i	−0.0474185	−	0.998875i
$64$		0			0
$65$	10.6844	+	6.16866i	1.32524	+	0.765128i
$66$		0			0
$67$	−4.15821	−	7.20222i	−0.508006	−	0.879892i	−0.999957	−	0.00926908i	$-0.997050\pi$
$67$	−4.15821	−	7.20222i	−0.508006	−	0.879892i	0.491951	−	0.870623i	$-0.336284\pi$
$68$		0			0
$69$	−5.23019	+	0.389094i	−0.629640	+	0.0468415i
$70$		0			0
$71$		−	0.466287i		−	0.0553381i	−0.999617	−	0.0276691i	$-0.991192\pi$
$71$		−	0.466287i		−	0.0553381i	0.999617	−	0.0276691i	$-0.00880846\pi$
$72$		0			0
$73$	−3.65022	−	2.10746i	−0.427226	−	0.246659i	0.270938	−	0.962597i	$-0.412666\pi$
$73$	−3.65022	−	2.10746i	−0.427226	−	0.246659i	−0.698164	+	0.715938i	$0.746000\pi$
$74$		0			0
$75$	1.04077	+	13.9900i	0.120178	+	1.61543i
$76$		0			0
$77$	5.27448	+	0.534957i	0.601083	+	0.0609641i
$78$		0			0
$79$	1.91267	−	3.31284i	0.215192	−	0.372723i	−0.738140	−	0.674648i	$-0.764296\pi$
$79$	1.91267	−	3.31284i	0.215192	−	0.372723i	0.953332	+	0.301924i	$0.0976290\pi$
$80$		0			0
$81$	8.60589	−	2.63412i	0.956210	−	0.292680i
$82$		0			0
$83$	−4.00481	−	6.93654i	−0.439585	−	0.761384i	0.558072	−	0.829792i	$-0.311541\pi$
$83$	−4.00481	−	6.93654i	−0.439585	−	0.761384i	−0.997657	+	0.0684084i	$0.978208\pi$
$84$		0			0
$85$	−11.1732	+	19.3525i	−1.21190	+	2.09907i
$86$		0			0
$87$	5.68005	+	8.34083i	0.608965	+	0.894230i
$88$		0			0
$89$	2.39324	+	4.14521i	0.253683	+	0.439391i	0.964537	−	0.263948i	$-0.0850248\pi$
$89$	2.39324	+	4.14521i	0.253683	+	0.439391i	−0.710854	+	0.703339i	$0.751691\pi$
$90$		0			0
$91$	5.27445	−	7.31553i	0.552912	−	0.766876i
$92$		0			0
$93$	−0.886874	−	1.30232i	−0.0919646	−	0.135045i
$94$		0			0
$95$	3.17542	−	1.83333i	0.325791	−	0.188096i
$96$		0			0
$97$	10.1835	−	5.87944i	1.03398	−	0.596967i	0.115856	−	0.993266i	$-0.463039\pi$
$97$	10.1835	−	5.87944i	1.03398	−	0.596967i	0.918121	+	0.396299i	$0.129706\pi$
$98$		0			0
$99$	0.889499	+	5.94521i	0.0893980	+	0.597516i
$100$		0			0
$101$	−12.8922			−1.28282			−0.641411	−	0.767197i	$-0.721651\pi$
$101$	−12.8922			−1.28282			−0.641411	+	0.767197i	$0.721651\pi$
$102$		0			0
$103$			10.7588i			1.06010i	0.847968	+	0.530048i	$0.177826\pi$
$103$			10.7588i			1.06010i	−0.847968	+	0.530048i	$0.822174\pi$
$104$		0			0
$105$	16.5798	+	0.444792i	1.61803	+	0.0434072i
$106$		0			0
$107$	−2.28602	+	1.31983i	−0.220998	+	0.127593i	−0.606412	−	0.795151i	$-0.707392\pi$
$107$	−2.28602	+	1.31983i	−0.220998	+	0.127593i	0.385414	+	0.922744i	$0.374058\pi$
$108$		0			0
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	−0.564391	−	0.825507i	$-0.690889\pi$
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	0.997106	+	0.0760233i	$0.0242224\pi$
$110$		0			0
$111$	−10.5031	+	7.15251i	−0.996905	+	0.678886i
$112$		0			0
$113$	−1.46411	−	0.845306i	−0.137732	−	0.0795197i	0.429551	−	0.903043i	$-0.358672\pi$
$113$	−1.46411	−	0.845306i	−0.137732	−	0.0795197i	−0.567283	+	0.823523i	$0.692005\pi$
$114$		0			0
$115$		−	10.9593i		−	1.02196i
$116$		0			0
$117$	9.51527	+	3.74639i	0.879687	+	0.346354i
$118$		0			0
$119$	13.2505	+	9.55349i	1.21467	+	0.875767i
$120$		0			0
$121$	6.98481			0.634982
$122$		0			0
$123$	8.89405	+	4.28910i	0.801950	+	0.386735i
$124$		0			0
$125$	−11.2179			−1.00336
$126$		0			0
$127$	−17.9292			−1.59096			−0.795478	−	0.605983i	$-0.792780\pi$
$127$	−17.9292			−1.59096			−0.795478	+	0.605983i	$0.792780\pi$
$128$		0			0
$129$	−6.87031	+	4.67864i	−0.604897	+	0.411931i
$130$		0			0
$131$	−17.3313			−1.51425			−0.757123	−	0.653272i	$-0.773396\pi$
$131$	−17.3313			−1.51425			−0.757123	+	0.653272i	$0.773396\pi$
$132$		0			0
$133$	−1.09911	−	2.44464i	−0.0953049	−	0.211977i
$134$		0			0
$135$	4.15499	+	18.3418i	0.357605	+	1.57861i
$136$		0			0
$137$		0	0.000645123i		0	5.51166e-5i	−1.00000		2.75583e-5i	$-0.999991\pi$
$137$		0	0.000645123i		0	5.51166e-5i	1.00000		2.75583e-5i	$-8.77208e-6\pi$
$138$		0			0
$139$	−8.73273	−	5.04185i	−0.740701	−	0.427644i	0.0816233	−	0.996663i	$-0.473990\pi$
$139$	−8.73273	−	5.04185i	−0.740701	−	0.427644i	−0.822324	+	0.569019i	$0.807323\pi$
$140$		0			0
$141$	3.47940	+	1.67792i	0.293018	+	0.141306i
$142$		0			0
$143$	−3.41521	+	5.91532i	−0.285594	+	0.494664i
$144$		0			0
$145$	−18.2616	+	10.5434i	−1.51655	+	0.875578i
$146$		0			0
$147$	1.54647	−	12.0253i	0.127550	−	0.991832i
$148$		0			0
$149$		−	11.2475i		−	0.921433i	−0.887547	−	0.460716i	$-0.847593\pi$
$149$		−	11.2475i		−	0.921433i	0.887547	−	0.460716i	$-0.152407\pi$
$150$		0			0
$151$	4.72379			0.384417			0.192208	−	0.981354i	$-0.438435\pi$
$151$	4.72379			0.384417			0.192208	+	0.981354i	$0.438435\pi$
$152$		0			0
$153$	−6.78575	+	17.2348i	−0.548596	+	1.39335i
$154$		0			0
$155$	2.85134	−	1.64622i	0.229025	−	0.132228i
$156$		0			0
$157$	2.65845	−	1.53486i	0.212168	−	0.122495i	−0.390151	−	0.920751i	$-0.627577\pi$
$157$	2.65845	−	1.53486i	0.212168	−	0.122495i	0.602318	+	0.798256i	$0.294244\pi$
$158$		0			0
$159$	6.58586	−	13.6567i	0.522292	−	1.08305i
$160$		0			0
$161$	−7.97043	−	0.808390i	−0.628158	−	0.0637101i
$162$		0			0
$163$	1.43687	+	2.48873i	0.112544	+	0.194932i	0.916795	−	0.399357i	$-0.130767\pi$
$163$	1.43687	+	2.48873i	0.112544	+	0.194932i	−0.804251	+	0.594289i	$0.797433\pi$
$164$		0			0
$165$	−12.5268	+	0.931922i	−0.975214	+	0.0725500i
$166$		0			0
$167$	0.730517	−	1.26529i	0.0565291	−	0.0979113i	−0.836376	−	0.548156i	$-0.815330\pi$
$167$	0.730517	−	1.26529i	0.0565291	−	0.0979113i	0.892905	+	0.450245i	$0.148663\pi$
$168$		0			0
$169$	−0.690233	−	1.19552i	−0.0530948	−	0.0919630i
$170$		0			0
$171$	2.37823	−	1.89236i	0.181868	−	0.144712i
$172$		0			0
$173$	−1.53541	+	2.65940i	−0.116735	+	0.202191i	−0.918472	−	0.395486i	$-0.870576\pi$
$173$	−1.53541	+	2.65940i	−0.116735	+	0.202191i	0.801737	+	0.597677i	$0.203909\pi$
$174$		0			0
$175$	−2.16233	+	21.3197i	−0.163457	+	1.61162i
$176$		0			0
$177$	12.8649	−	8.76091i	0.966984	−	0.658510i
$178$		0			0
$179$	16.7310	+	9.65966i	1.25054	+	0.721997i	0.971216	−	0.238201i	$-0.0765578\pi$
$179$	16.7310	+	9.65966i	1.25054	+	0.721997i	0.279320	+	0.960198i	$0.409891\pi$
$180$		0			0
$181$			7.89318i			0.586695i	0.956006	+	0.293348i	$0.0947693\pi$
$181$			7.89318i			0.586695i	−0.956006	+	0.293348i	$0.905231\pi$
$182$		0			0
$183$	11.0687	−	22.9525i	0.818222	−	1.69670i
$184$		0			0
$185$	−13.2765	−	22.9957i	−0.976111	−	1.69067i
$186$		0			0
$187$	−10.7143	−	6.18590i	−0.783506	−	0.452358i
$188$		0			0
$189$	13.6461	−	1.66888i	0.992604	−	0.121393i
$190$		0			0
$191$	−11.5218	−	6.65211i	−0.833688	−	0.481330i	0.0214259	−	0.999770i	$-0.493179\pi$
$191$	−11.5218	−	6.65211i	−0.833688	−	0.481330i	−0.855114	+	0.518441i	$0.826513\pi$
$192$		0			0
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	0.724112	−	0.689682i	$-0.242250\pi$
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	−0.959338	+	0.282259i	$0.908916\pi$
$194$		0			0
$195$	−9.28205	+	19.2476i	−0.664701	+	1.37835i
$196$		0			0
$197$		−	4.44250i		−	0.316515i	−0.987398	−	0.158258i	$-0.949412\pi$
$197$		−	4.44250i		−	0.316515i	0.987398	−	0.158258i	$-0.0505876\pi$
$198$		0			0
$199$	−9.96868	−	5.75542i	−0.706661	−	0.407991i	0.103163	−	0.994665i	$-0.467104\pi$
$199$	−9.96868	−	5.75542i	−0.706661	−	0.407991i	−0.809823	+	0.586674i	$0.800437\pi$
$200$		0			0
$201$	11.9059	−	8.10786i	0.839779	−	0.571884i
$202$		0			0
$203$	6.32091	+	14.0590i	0.443641	+	0.986747i
$204$		0			0
$205$	−10.3167	+	17.8690i	−0.720547	+	1.24802i
$206$		0			0
$207$	−1.34415	−	8.98399i	−0.0934247	−	0.624430i
$208$		0			0
$209$	1.01500	+	1.75804i	0.0702092	+	0.121606i
$210$		0			0
$211$	−11.3005	+	19.5731i	−0.777961	+	1.34747i	0.155155	+	0.987890i	$0.450412\pi$
$211$	−11.3005	+	19.5731i	−0.777961	+	1.34747i	−0.933115	+	0.359577i	$0.882921\pi$
$212$		0			0
$213$	0.805408	−	0.0599175i	0.0551856	−	0.00410548i
$214$		0			0
$215$	−8.68453	−	15.0420i	−0.592280	−	1.02586i
$216$		0			0
$217$	−0.986937	−	2.19515i	−0.0669976	−	0.149016i
$218$		0			0
$219$	3.17111	−	6.57576i	0.214284	−	0.444348i
$220$		0			0
$221$	−18.2265	+	10.5231i	−1.22605	+	0.707860i
$222$		0			0
$223$	16.2994	−	9.41045i	1.09149	−	0.630170i	0.157515	−	0.987517i	$-0.449652\pi$
$223$	16.2994	−	9.41045i	1.09149	−	0.630170i	0.933972	+	0.357346i	$0.116318\pi$
$224$		0			0
$225$	−24.0309	+	3.59540i	−1.60206	+	0.239693i
$226$		0			0
$227$	14.6133			0.969919			0.484960	−	0.874537i	$-0.338834\pi$
$227$	14.6133			0.969919			0.484960	+	0.874537i	$0.338834\pi$
$228$		0			0
$229$		−	2.37919i		−	0.157221i	−0.996905	−	0.0786106i	$-0.974952\pi$
$229$		−	2.37919i		−	0.157221i	0.996905	−	0.0786106i	$-0.0250484\pi$
$230$		0			0
$231$	−0.246254	+	9.17924i	−0.0162023	+	0.603950i
$232$		0			0
$233$	−9.03470	+	5.21619i	−0.591883	+	0.341724i	−0.765842	−	0.643029i	$-0.777677\pi$
$233$	−9.03470	+	5.21619i	−0.591883	+	0.341724i	0.173959	+	0.984753i	$0.444344\pi$
$234$		0			0
$235$	−4.03593	+	6.99044i	−0.263275	+	0.456006i
$236$		0			0
$237$	5.96796	+	2.87801i	0.387661	+	0.186947i
$238$		0			0
$239$	−20.5971	−	11.8917i	−1.33232	−	0.769213i	−0.346662	−	0.937990i	$-0.612685\pi$
$239$	−20.5971	−	11.8917i	−1.33232	−	0.769213i	−0.985654	+	0.168777i	$0.946018\pi$
$240$		0			0
$241$			28.6487i			1.84542i	0.385489	+	0.922712i	$0.374033\pi$
$241$			28.6487i			1.84542i	−0.385489	+	0.922712i	$0.625967\pi$
$242$		0			0
$243$	5.65571	+	14.5263i	0.362814	+	0.931862i
$244$		0			0
$245$	24.8193	+	5.08685i	1.58565	+	0.324987i
$246$		0			0
$247$	3.45333			0.219730
$248$		0			0
$249$	11.4667	−	7.80876i	0.726673	−	0.494860i
$250$		0			0
$251$	−11.0301			−0.696216			−0.348108	−	0.937454i	$-0.613176\pi$
$251$	−11.0301			−0.696216			−0.348108	+	0.937454i	$0.613176\pi$
$252$		0			0
$253$	6.06748			0.381459
$254$		0			0
$255$	−34.8628	−	16.8124i	−2.18320	−	1.05283i
$256$		0			0
$257$	−15.0978			−0.941775			−0.470888	−	0.882193i	$-0.656066\pi$
$257$	−15.0978			−0.941775			−0.470888	+	0.882193i	$0.656066\pi$
$258$		0			0
$259$	−17.7035	+	7.95950i	−1.10004	+	0.494579i
$260$		0			0
$261$	−13.6770	+	10.8828i	−0.846588	+	0.673629i
$262$		0			0
$263$			19.6385i			1.21096i	0.795859	+	0.605482i	$0.207020\pi$
$263$			19.6385i			1.21096i	−0.795859	+	0.605482i	$0.792980\pi$
$264$		0			0
$265$	27.4376	+	15.8411i	1.68548	+	0.973112i
$266$		0			0
$267$	−6.85240	+	4.66644i	−0.419360	+	0.285581i
$268$		0			0
$269$	−0.245503	+	0.425223i	−0.0149686	+	0.0259263i	−0.873413	−	0.486981i	$-0.838098\pi$
$269$	−0.245503	+	0.425223i	−0.0149686	+	0.0259263i	0.858444	+	0.512907i	$0.171431\pi$
$270$		0			0
$271$	12.1927	−	7.03945i	0.740653	−	0.427616i	−0.0816537	−	0.996661i	$-0.526020\pi$
$271$	12.1927	−	7.03945i	0.740653	−	0.427616i	0.822307	+	0.569045i	$0.192687\pi$
$272$		0			0
$273$	13.3137	+	8.17039i	0.805782	+	0.494495i
$274$		0			0
$275$		−	16.2296i		−	0.978683i
$276$		0			0
$277$	30.7200			1.84579			0.922894	−	0.385054i	$-0.125817\pi$
$277$	30.7200			1.84579			0.922894	+	0.385054i	$0.125817\pi$
$278$		0			0
$279$	2.13551	−	1.69923i	0.127850	−	0.101730i
$280$		0			0
$281$	6.86286	−	3.96227i	0.409404	−	0.236369i	−0.281130	−	0.959670i	$-0.590709\pi$
$281$	6.86286	−	3.96227i	0.409404	−	0.236369i	0.690534	+	0.723300i	$0.257376\pi$
$282$		0			0
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	−0.173383	−	0.984855i	$-0.555470\pi$
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	0.766218	+	0.642581i	$0.222136\pi$
$284$		0			0
$285$	3.57471	+	5.24925i	0.211747	+	0.310939i
$286$		0			0
$287$	12.2347	+	8.82115i	0.722193	+	0.520696i
$288$		0			0
$289$	−10.5603	−	18.2909i	−0.621192	−	1.07594i
$290$		0			0
$291$	11.4640	+	16.8342i	0.672031	+	0.986839i
$292$		0			0
$293$	2.50937	−	4.34636i	0.146599	−	0.253917i	−0.783369	−	0.621557i	$-0.786501\pi$
$293$	2.50937	−	4.34636i	0.146599	−	0.253917i	0.929968	+	0.367639i	$0.119834\pi$
$294$		0			0
$295$	16.2621	+	28.1667i	0.946814	+	1.63993i
$296$		0			0
$297$	−10.1547	+	2.30037i	−0.589237	+	0.133481i
$298$		0			0
$299$	5.16083	−	8.93882i	0.298458	−	0.516945i
$300$		0			0
$301$	−11.5803	+	5.20651i	−0.667480	+	0.300098i
$302$		0			0
$303$	−1.65664	−	22.2684i	−0.0951712	−	1.27929i
$304$		0			0
$305$	46.1138	+	26.6238i	2.64047	+	1.52447i
$306$		0			0
$307$			17.5309i			1.00054i	0.865869	+	0.500271i	$0.166766\pi$
$307$			17.5309i			1.00054i	−0.865869	+	0.500271i	$0.833234\pi$
$308$		0			0
$309$	−18.5834	+	1.38250i	−1.05717	+	0.0786474i
$310$		0			0
$311$	−8.64759	−	14.9781i	−0.490360	−	0.849328i	0.509579	−	0.860424i	$-0.329801\pi$
$311$	−8.64759	−	14.9781i	−0.490360	−	0.849328i	−0.999938	+	0.0110959i	$0.996468\pi$
$312$		0			0
$313$	7.78988	+	4.49749i	0.440310	+	0.254213i	0.703729	−	0.710468i	$-0.251517\pi$
$313$	7.78988	+	4.49749i	0.440310	+	0.254213i	−0.263419	+	0.964681i	$0.584850\pi$
$314$		0			0
$315$	1.36221	+	28.6951i	0.0767520	+	1.61679i
$316$		0			0
$317$	−5.82002	−	3.36019i	−0.326885	−	0.188727i	0.327572	−	0.944826i	$-0.393770\pi$
$317$	−5.82002	−	3.36019i	−0.326885	−	0.188727i	−0.654457	+	0.756099i	$0.727103\pi$
$318$		0			0
$319$	−5.83721	−	10.1103i	−0.326821	−	0.566071i
$320$		0			0
$321$	−2.57347	−	3.77899i	−0.143637	−	0.210923i
$322$		0			0
$323$			6.25494i			0.348034i
$324$		0			0
$325$	−23.9100	−	13.8045i	−1.32629	−	0.765734i
$326$		0			0
$327$	14.0962	+	6.79780i	0.779521	+	0.375919i
$328$		0			0
$329$	4.78629	+	3.45088i	0.263876	+	0.190253i
$330$		0			0
$331$	−9.38725	+	16.2592i	−0.515970	+	0.893686i	0.483858	+	0.875146i	$0.339235\pi$
$331$	−9.38725	+	16.2592i	−0.515970	+	0.893686i	−0.999828	+	0.0185396i	$0.994098\pi$
$332$		0			0
$333$	−13.7040	−	17.2226i	−0.750975	−	0.943792i
$334$		0			0
$335$	15.0499	+	26.0671i	0.822262	+	1.42420i
$336$		0			0
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	−0.792458	−	0.609926i	$-0.791199\pi$
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	0.924441	+	0.381326i	$0.124532\pi$
$338$		0			0
$339$	1.27194	−	2.63755i	0.0690824	−	0.143252i
$340$		0			0
$341$	0.911413	+	1.57861i	0.0493558	+	0.0854868i
$342$		0			0
$343$	5.53030	−	17.6753i	0.298608	−	0.954376i
$344$		0			0
$345$	18.9297	−	1.40826i	1.01914	−	0.0758179i
$346$		0			0
$347$	15.1305	−	8.73559i	0.812247	−	0.468951i	−0.0354887	−	0.999370i	$-0.511299\pi$
$347$	15.1305	−	8.73559i	0.812247	−	0.468951i	0.847736	+	0.530419i	$0.177965\pi$
$348$		0			0
$349$	−20.6338	+	11.9129i	−1.10450	+	0.637683i	−0.937399	−	0.348257i	$-0.886774\pi$
$349$	−20.6338	+	11.9129i	−1.10450	+	0.637683i	−0.167101	+	0.985940i	$0.553440\pi$
$350$		0			0
$351$	−5.24835	+	16.9169i	−0.280136	+	0.902958i
$352$		0			0
$353$	10.0412			0.534441			0.267220	−	0.963635i	$-0.413895\pi$
$353$	10.0412			0.534441			0.267220	+	0.963635i	$0.413895\pi$
$354$		0			0
$355$			1.68764i			0.0895707i
$356$		0			0
$357$	−14.7989	+	24.1148i	−0.783238	+	1.27629i
$358$		0			0
$359$	−10.5353	+	6.08254i	−0.556030	+	0.321024i	−0.751550	−	0.659676i	$-0.770694\pi$
$359$	−10.5353	+	6.08254i	−0.556030	+	0.321024i	0.195521	+	0.980700i	$0.437360\pi$
$360$		0			0
$361$	−8.98683	+	15.5657i	−0.472991	+	0.819245i
$362$		0			0
$363$	0.897541	+	12.0647i	0.0471087	+	0.633233i
$364$		0			0
$365$	13.2113	+	7.62756i	0.691512	+	0.399245i
$366$		0			0
$367$		−	3.63061i		−	0.189516i	−0.995500	−	0.0947582i	$-0.969792\pi$
$367$		−	3.63061i		−	0.189516i	0.995500	−	0.0947582i	$-0.0302078\pi$
$368$		0			0
$369$	−6.26558	+	15.9136i	−0.326173	+	0.828431i
$370$		0			0
$371$	13.5448	−	18.7863i	0.703210	−	0.975335i
$372$		0			0
$373$	5.49231			0.284381			0.142191	−	0.989839i	$-0.454585\pi$
$373$	5.49231			0.284381			0.142191	+	0.989839i	$0.454585\pi$
$374$		0			0
$375$	−1.44149	−	19.3764i	−0.0744380	−	1.00059i
$376$		0			0
$377$	−19.8599			−1.02284
$378$		0			0
$379$	15.5960			0.801112			0.400556	−	0.916272i	$-0.368817\pi$
$379$	15.5960			0.801112			0.400556	+	0.916272i	$0.368817\pi$
$380$		0			0
$381$	−2.30388	−	30.9686i	−0.118031	−	1.58657i
$382$		0			0
$383$	−9.43067			−0.481885			−0.240942	−	0.970539i	$-0.577456\pi$
$383$	−9.43067			−0.481885			−0.240942	+	0.970539i	$0.577456\pi$
$384$		0			0
$385$	−19.0900	−	1.93618i	−0.972918	−	0.0986769i
$386$		0			0
$387$	−8.96414	−	11.2657i	−0.455673	−	0.572670i
$388$		0			0
$389$		−	6.42177i		−	0.325597i	−0.986659	−	0.162798i	$-0.947948\pi$
$389$		−	6.42177i		−	0.325597i	0.986659	−	0.162798i	$-0.0520520\pi$
$390$		0			0
$391$	16.1907	+	9.34769i	0.818798	+	0.472733i
$392$		0			0
$393$	−2.22706	−	29.9360i	−0.112340	−	1.51007i
$394$		0			0
$395$	−6.92255	+	11.9902i	−0.348311	+	0.603293i
$396$		0			0
$397$	5.99750	−	3.46266i	0.301006	−	0.173786i	−0.341889	−	0.939740i	$-0.611067\pi$
$397$	5.99750	−	3.46266i	0.301006	−	0.173786i	0.642895	+	0.765955i	$0.277733\pi$
$398$		0			0
$399$	4.08134	−	2.21260i	0.204323	−	0.110769i
$400$		0			0
$401$		−	10.5869i		−	0.528682i	−0.964429	−	0.264341i	$-0.914846\pi$
$401$		−	10.5869i		−	0.528682i	0.964429	−	0.264341i	$-0.0851545\pi$
$402$		0			0
$403$	3.10089			0.154466
$404$		0			0
$405$	−31.1474	+	9.53372i	−1.54773	+	0.473735i
$406$		0			0
$407$	12.7313	−	7.35042i	0.631067	−	0.364347i
$408$		0			0
$409$	7.72792	−	4.46172i	0.382121	−	0.220618i	−0.296620	−	0.954996i	$-0.595859\pi$
$409$	7.72792	−	4.46172i	0.382121	−	0.220618i	0.678741	+	0.734378i	$0.262526\pi$
$410$		0			0
$411$	0.00111431		8.28977e-5i	5.49647e−5		4.08904e-6i
$412$		0			0
$413$	21.6846	−	9.74937i	1.06703	−	0.479735i
$414$		0			0
$415$	14.4947	+	25.1055i	0.711516	+	1.23238i
$416$		0			0
$417$	7.58652	−	15.7317i	0.371513	−	0.770386i
$418$		0			0
$419$	17.1924	−	29.7781i	0.839903	−	1.45475i	−0.0500724	−	0.998746i	$-0.515945\pi$
$419$	17.1924	−	29.7781i	0.839903	−	1.45475i	0.889975	−	0.456009i	$-0.150721\pi$
$420$		0			0
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.865310	−	0.501237i	$-0.832879\pi$
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.00142877	−	0.999999i	$-0.500455\pi$
$422$		0			0
$423$	−2.45113	+	6.22550i	−0.119178	+	0.302694i
$424$		0			0
$425$	25.0037	−	43.3077i	1.21286	−	2.10073i
$426$		0			0
$427$	22.7644	−	31.5737i	1.10165	−	1.52796i
$428$		0			0
$429$	−10.6563	−	5.13891i	−0.514489	−	0.248109i
$430$		0			0
$431$	−26.7338	−	15.4348i	−1.28772	−	0.743466i	−0.309474	−	0.950908i	$-0.600153\pi$
$431$	−26.7338	−	15.4348i	−1.28772	−	0.743466i	−0.978247	+	0.207442i	$0.933486\pi$
$432$		0			0
$433$		−	23.2463i		−	1.11715i	−0.829455	−	0.558574i	$-0.811349\pi$
$433$		−	23.2463i		−	1.11715i	0.829455	−	0.558574i	$-0.188651\pi$
$434$		0			0
$435$	−20.5579	−	30.1881i	−0.985676	−	1.44741i
$436$		0			0
$437$	−1.53380	−	2.65662i	−0.0733716	−	0.127083i
$438$		0			0
$439$	−19.2887	−	11.1364i	−0.920601	−	0.531509i	−0.0367744	−	0.999324i	$-0.511708\pi$
$439$	−19.2887	−	11.1364i	−0.920601	−	0.531509i	−0.883827	+	0.467814i	$0.845042\pi$
$440$		0			0
$441$	20.9698	+	1.12594i	0.998562	+	0.0536160i
$442$		0			0
$443$	−15.5756	−	8.99259i	−0.740020	−	0.427251i	0.0820566	−	0.996628i	$-0.473851\pi$
$443$	−15.5756	−	8.99259i	−0.740020	−	0.427251i	−0.822077	+	0.569377i	$0.807185\pi$
$444$		0			0
$445$	−8.66188	−	15.0028i	−0.410612	−	0.711202i
$446$		0			0
$447$	19.4276	−	1.44530i	0.918894	−	0.0683601i
$448$		0			0
$449$			9.44363i			0.445673i	0.974856	+	0.222836i	$0.0715315\pi$
$449$			9.44363i			0.445673i	−0.974856	+	0.222836i	$0.928468\pi$
$450$		0			0
$451$	−9.89297	−	5.71171i	−0.465842	−	0.268954i
$452$		0			0
$453$	0.607002	+	8.15930i	0.0285195	+	0.383357i
$454$		0			0
$455$	−19.0899	+	26.4772i	−0.894948	+	1.24127i
$456$		0			0
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	−0.843649	−	0.536896i	$-0.819597\pi$
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	0.886790	+	0.462173i	$0.152930\pi$
$458$		0			0
$459$	−30.6412	−	9.50623i	−1.43021	−	0.443713i
$460$		0			0
$461$	18.1869	+	31.5007i	0.847050	+	1.46713i	0.883829	+	0.467810i	$0.154957\pi$
$461$	18.1869	+	31.5007i	0.847050	+	1.46713i	−0.0367790	+	0.999323i	$0.511710\pi$
$462$		0			0
$463$	15.9830	−	27.6834i	0.742794	−	1.28656i	−0.208425	−	0.978038i	$-0.566834\pi$
$463$	15.9830	−	27.6834i	0.742794	−	1.28656i	0.951219	−	0.308518i	$-0.0998330\pi$
$464$		0			0
$465$	3.20988	+	4.71352i	0.148855	+	0.218584i
$466$		0			0
$467$	12.2206	+	21.1666i	0.565500	+	0.979475i	0.997003	+	0.0773632i	$0.0246501\pi$
$467$	12.2206	+	21.1666i	0.565500	+	0.979475i	−0.431503	+	0.902112i	$0.642017\pi$
$468$		0			0
$469$	20.0682	−	9.02263i	0.926662	−	0.416627i
$470$		0			0
$471$	2.99273	+	4.39466i	0.137898	+	0.202495i
$472$		0			0
$473$	8.32786	−	4.80809i	0.382916	−	0.221076i
$474$		0			0
$475$	−7.10607	+	4.10269i	−0.326049	+	0.188245i
$476$		0			0
$477$	24.4352	+	9.62073i	1.11881	+	0.440503i
$478$		0			0
$479$	−10.9606			−0.500805			−0.250402	−	0.968142i	$-0.580563\pi$
$479$	−10.9606			−0.500805			−0.250402	+	0.968142i	$0.580563\pi$
$480$		0			0
$481$		−	25.0082i		−	1.14028i
$482$		0			0
$483$	0.372122	−	13.8710i	0.0169321	−	0.631153i
$484$		0			0
$485$	−36.8573	+	21.2796i	−1.67360	+	0.966255i
$486$		0			0
$487$	16.8087	−	29.1136i	0.761677	−	1.31926i	−0.180309	−	0.983610i	$-0.557710\pi$
$487$	16.8087	−	29.1136i	0.761677	−	1.31926i	0.941986	−	0.335653i	$-0.108957\pi$
$488$		0			0
$489$	−4.11408	+	2.80167i	−0.186045	+	0.126696i
$490$		0			0
$491$	19.6893	+	11.3676i	0.888568	+	0.513015i	0.873474	−	0.486871i	$-0.161862\pi$
$491$	19.6893	+	11.3676i	0.888568	+	0.513015i	0.0150939	+	0.999886i	$0.495195\pi$
$492$		0			0
$493$		−	35.9718i		−	1.62009i
$494$		0			0
$495$	−3.21938	−	21.5176i	−0.144700	−	0.967144i
$496$		0			0
$497$	1.22738	+	0.124486i	0.0550557	+	0.00558395i
$498$		0			0
$499$	−19.5235			−0.873992			−0.436996	−	0.899463i	$-0.643958\pi$
$499$	−19.5235			−0.873992			−0.436996	+	0.899463i	$0.643958\pi$
$500$		0			0
$501$	2.27938	+	1.09922i	0.101835	+	0.0491094i
$502$		0			0
$503$	−13.6867			−0.610262			−0.305131	−	0.952310i	$-0.598700\pi$
$503$	−13.6867			−0.610262			−0.305131	+	0.952310i	$0.598700\pi$
$504$		0			0
$505$	46.6609			2.07638
$506$		0			0
$507$	1.97630	−	1.34585i	0.0877705	−	0.0597712i
$508$		0			0
$509$	−2.29166			−0.101576			−0.0507881	−	0.998709i	$-0.516173\pi$
$509$	−2.29166			−0.101576			−0.0507881	+	0.998709i	$0.516173\pi$
$510$		0			0
$511$	6.52186	−	9.04566i	0.288510	−	0.400156i
$512$		0			0
$513$	3.57422	+	3.86470i	0.157806	+	0.170630i
$514$		0			0
$515$		−	38.9395i		−	1.71588i
$516$		0			0
$517$	−3.87018	−	2.23445i	−0.170210	−	0.0982710i
$518$		0			0
$519$	−4.79082	−	2.31034i	−0.210294	−	0.101413i
$520$		0			0
$521$	−8.54102	+	14.7935i	−0.374189	+	0.648114i	−0.990205	−	0.139619i	$-0.955412\pi$
$521$	−8.54102	+	14.7935i	−0.374189	+	0.648114i	0.616017	+	0.787733i	$0.288745\pi$
$522$		0			0
$523$	−35.7462	+	20.6381i	−1.56307	+	0.902440i	−0.566128	+	0.824317i	$0.691559\pi$
$523$	−35.7462	+	20.6381i	−1.56307	+	0.902440i	−0.996944	+	0.0781229i	$0.975107\pi$
$524$		0			0
$525$	−37.1030	−	0.995372i	−1.61931	−	0.0434416i
$526$		0			0
$527$			5.61657i			0.244662i
$528$		0			0
$529$	13.8313			0.601359
$530$		0			0
$531$	16.7857	+	21.0955i	0.728435	+	0.915465i
$532$		0			0
$533$	−16.8294	+	9.71644i	−0.728961	+	0.420866i
$534$		0			0
$535$	8.27382	−	4.77689i	0.357708	−	0.206523i
$536$		0			0
$537$	−14.5350	+	30.1404i	−0.627231	+	1.30065i
$538$		0			0
$539$	−2.81628	+	13.7409i	−0.121306	+	0.591864i
$540$		0			0
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.673880	+	0.738841i	$0.264627\pi$
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.302915	+	0.953018i	$0.402040\pi$
$542$		0			0
$543$	−13.6337	+	1.01427i	−0.585078	+	0.0435263i
$544$		0			0
$545$	−16.3509	+	28.3206i	−0.700395	+	1.21312i
$546$		0			0
$547$	−15.1095	−	26.1705i	−0.646037	−	1.11897i	−0.984061	−	0.177832i	$-0.943092\pi$
$547$	−15.1095	−	26.1705i	−0.646037	−	1.11897i	0.338024	−	0.941138i	$-0.390242\pi$
$548$		0			0
$549$	41.0677	+	16.1693i	1.75273	+	0.690091i
$550$		0			0
$551$	−2.95118	+	5.11160i	−0.125725	+	0.217761i
$552$		0			0
$553$	8.20958	+	5.91905i	0.349107	+	0.251704i
$554$		0			0
$555$	38.0139	−	25.8872i	1.61360	−	1.09885i
$556$		0			0
$557$	−22.0154	−	12.7106i	−0.932822	−	0.538565i	−0.0451189	−	0.998982i	$-0.514367\pi$
$557$	−22.0154	−	12.7106i	−0.932822	−	0.538565i	−0.887703	+	0.460417i	$0.847700\pi$
$558$		0			0
$559$		−	16.3585i		−	0.691892i
$560$		0			0
$561$	9.30799	−	19.3014i	0.392983	−	0.814907i
$562$		0			0
$563$	−1.44346	−	2.50015i	−0.0608346	−	0.105369i	0.834004	−	0.551758i	$-0.186043\pi$
$563$	−1.44346	−	2.50015i	−0.0608346	−	0.105369i	−0.894839	+	0.446390i	$0.852710\pi$
$564$		0			0
$565$	5.29909	+	3.05943i	0.222934	+	0.128711i
$566$		0			0
$567$	4.63613	+	23.3561i	0.194699	+	0.980863i
$568$		0			0
$569$	−38.5945	−	22.2826i	−1.61797	−	0.934134i	−0.987445	−	0.157963i	$-0.949507\pi$
$569$	−38.5945	−	22.2826i	−1.61797	−	0.934134i	−0.630523	−	0.776171i	$-0.717159\pi$
$570$		0			0
$571$	−3.26470	−	5.65462i	−0.136623	−	0.236638i	0.789593	−	0.613631i	$-0.210292\pi$
$571$	−3.26470	−	5.65462i	−0.136623	−	0.236638i	−0.926216	+	0.376992i	$0.876958\pi$
$572$		0			0
$573$	10.0095	−	20.7561i	0.418153	−	0.867100i
$574$		0			0
$575$			24.5251i			1.02277i
$576$		0			0
$577$	1.17720	+	0.679658i	0.0490076	+	0.0282945i	0.524304	−	0.851531i	$-0.324326\pi$
$577$	1.17720	+	0.679658i	0.0490076	+	0.0282945i	−0.475296	+	0.879826i	$0.657659\pi$
$578$		0			0
$579$	9.35666	−	6.37183i	0.388850	−	0.264804i
$580$		0			0
$581$	19.3279	−	8.68979i	0.801855	−	0.360513i
$582$		0			0
$583$	−8.77026	+	15.1905i	−0.363227	+	0.629128i
$584$		0			0
$585$	−34.4388	−	13.5594i	−1.42387	−	0.560611i
$586$		0			0
$587$	22.2025	+	38.4559i	0.916397	+	1.58725i	0.804843	+	0.593488i	$0.202250\pi$
$587$	22.2025	+	38.4559i	0.916397	+	1.58725i	0.111555	+	0.993758i	$0.464417\pi$
$588$		0			0
$589$	0.460793	−	0.798117i	0.0189866	−	0.0328858i
$590$		0			0
$591$	7.67343	−	0.570857i	0.315643	−	0.0234819i
$592$		0			0
$593$	−7.17564	−	12.4286i	−0.294668	−	0.510380i	0.680240	−	0.732990i	$-0.261876\pi$
$593$	−7.17564	−	12.4286i	−0.294668	−	0.510380i	−0.974908	+	0.222610i	$0.928542\pi$
$594$		0			0
$595$	−47.9576	−	34.5771i	−1.96607	−	1.41752i
$596$		0			0
$597$	8.66024	−	17.9582i	0.354440	−	0.734982i
$598$		0			0
$599$	3.03349	−	1.75139i	0.123945	−	0.0715597i	−0.436746	−	0.899585i	$-0.643869\pi$
$599$	3.03349	−	1.75139i	0.123945	−	0.0715597i	0.560691	+	0.828025i	$0.310536\pi$
$600$		0			0
$601$	−15.1846	+	8.76685i	−0.619394	+	0.357607i	−0.776633	−	0.629953i	$-0.783074\pi$
$601$	−15.1846	+	8.76685i	−0.619394	+	0.357607i	0.157239	+	0.987561i	$0.449741\pi$
$602$		0			0
$603$	15.5344	+	19.5230i	0.632610	+	0.795037i
$604$		0			0
$605$	−25.2802			−1.02779
$606$		0			0
$607$			0.0872864i			0.00354285i	0.999998	+	0.00177142i	$0.000563862\pi$
$607$			0.0872864i			0.00354285i	−0.999998	+	0.00177142i	$0.999436\pi$
$608$		0			0
$609$	−23.4715	+	12.7245i	−0.951114	+	0.515624i
$610$		0			0
$611$	−6.58373	+	3.80112i	−0.266349	+	0.153777i
$612$		0			0
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	−0.493681	−	0.869643i	$-0.664349\pi$
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	0.999973	−	0.00728071i	$-0.00231754\pi$
$614$		0			0
$615$	−32.1904	−	15.5236i	−1.29804	−	0.625972i
$616$		0			0
$617$	−10.6365	−	6.14101i	−0.428211	−	0.247228i	0.270373	−	0.962756i	$-0.412853\pi$
$617$	−10.6365	−	6.14101i	−0.428211	−	0.247228i	−0.698584	+	0.715528i	$0.746186\pi$
$618$		0			0
$619$			20.3076i			0.816229i	0.912931	+	0.408115i	$0.133814\pi$
$619$			20.3076i			0.816229i	−0.912931	+	0.408115i	$0.866186\pi$
$620$		0			0
$621$	15.3451	−	3.47615i	0.615778	−	0.139493i
$622$		0			0
$623$	−11.5501	+	5.19294i	−0.462747	+	0.208051i
$624$		0			0
$625$	0.103794			0.00415176
$626$		0			0
$627$	−2.90619	+	1.97910i	−0.116062	+	0.0790375i
$628$		0			0
$629$	45.2969			1.80610
$630$		0			0
$631$	45.9665			1.82990			0.914950	−	0.403568i	$-0.132230\pi$
$631$	45.9665			1.82990			0.914950	+	0.403568i	$0.132230\pi$
$632$		0			0
$633$	−35.2603	−	17.0040i	−1.40147	−	0.675850i
$634$		0			0
$635$	64.8913			2.57513
$636$		0			0
$637$	17.8482	+	15.8367i	0.707169	+	0.627472i
$638$		0			0
$639$	0.206988	+	1.38346i	0.00818833	+	0.0547290i
$640$		0			0
$641$			31.6509i			1.25013i	0.780571	+	0.625067i	$0.214928\pi$
$641$			31.6509i			1.25013i	−0.780571	+	0.625067i	$0.785072\pi$
$642$		0			0
$643$	−10.0106	−	5.77960i	−0.394778	−	0.227925i	0.289450	−	0.957193i	$-0.406528\pi$
$643$	−10.0106	−	5.77960i	−0.394778	−	0.227925i	−0.684228	+	0.729268i	$0.739861\pi$
$644$		0			0
$645$	24.8658	−	16.9335i	0.979091	−	0.666755i
$646$		0			0
$647$	−13.0365	+	22.5799i	−0.512519	+	0.887708i	0.487376	+	0.873192i	$0.337954\pi$
$647$	−13.0365	+	22.5799i	−0.512519	+	0.887708i	−0.999895	+	0.0145160i	$0.995379\pi$
$648$		0			0
$649$	−15.5942	+	9.00332i	−0.612126	+	0.353411i
$650$		0			0
$651$	3.66481	−	1.98679i	0.143635	−	0.0778684i
$652$		0			0
$653$			18.9315i			0.740847i	0.928863	+	0.370424i	$0.120788\pi$
$653$			18.9315i			0.740847i	−0.928863	+	0.370424i	$0.879212\pi$
$654$		0			0
$655$	62.7276			2.45097
$656$		0			0
$657$	11.7656	+	4.63242i	0.459021	+	0.180728i
$658$		0			0
$659$	−23.3508	+	13.4816i	−0.909618	+	0.525168i	−0.880308	−	0.474402i	$-0.842664\pi$
$659$	−23.3508	+	13.4816i	−0.909618	+	0.525168i	−0.0293098	+	0.999570i	$0.509331\pi$
$660$		0			0
$661$	22.3201	−	12.8865i	0.868151	−	0.501227i	0.00141768	−	0.999999i	$-0.499549\pi$
$661$	22.3201	−	12.8865i	0.868151	−	0.501227i	0.866733	+	0.498772i	$0.166215\pi$
$662$		0			0
$663$	−20.5184	−	30.1301i	−0.796869	−	1.17016i
$664$		0			0
$665$	3.97803	+	8.84793i	0.154261	+	0.343108i
$666$		0			0
$667$	8.82079	+	15.2780i	0.341542	+	0.591568i
$668$		0			0
$669$	18.3489	+	26.9443i	0.709410	+	1.04173i
$670$		0			0
$671$	−14.7400	+	25.5304i	−0.569030	+	0.985590i
$672$		0			0
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	0.500398	−	0.865795i	$-0.333187\pi$
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	−1.00000		0.000460130i	$0.999854\pi$
$674$		0			0
$675$	−9.29820	−	41.0460i	−0.357888	−	1.57986i
$676$		0			0
$677$	6.55382	−	11.3515i	0.251884	−	0.436275i	−0.712161	−	0.702016i	$-0.752283\pi$
$677$	6.55382	−	11.3515i	0.251884	−	0.436275i	0.964044	+	0.265741i	$0.0856166\pi$
$678$		0			0
$679$	12.7574	+	28.3751i	0.489585	+	1.08894i
$680$		0			0
$681$	1.87780	+	25.2412i	0.0719573	+	0.967246i
$682$		0			0
$683$	25.6910	+	14.8327i	0.983038	+	0.567557i	0.903186	−	0.429249i	$-0.141222\pi$
$683$	25.6910	+	14.8327i	0.983038	+	0.567557i	0.0798523	+	0.996807i	$0.474555\pi$
$684$		0			0
$685$			0.00233490i			8.92121e-5i
$686$		0			0
$687$	4.10952	−	0.305723i	0.156788	−	0.0116641i
$688$		0			0
$689$	14.9195	+	25.8413i	0.568387	+	0.984475i
$690$		0			0
$691$	−40.9767	−	23.6579i	−1.55883	−	0.899990i	−0.997369	−	0.0724857i	$-0.976907\pi$
$691$	−40.9767	−	23.6579i	−1.55883	−	0.899990i	−0.561459	−	0.827504i	$-0.689760\pi$
$692$		0			0
$693$	−15.8867	+	0.754174i	−0.603487	+	0.0286487i
$694$		0			0
$695$	31.6065	+	18.2480i	1.19890	+	0.692187i
$696$		0			0
$697$	−17.5992	−	30.4827i	−0.666616	−	1.15461i
$698$		0			0
$699$	−10.1708	−	14.9352i	−0.384693	−	0.564900i
$700$		0			0
$701$			13.7742i			0.520244i	0.965576	+	0.260122i	$0.0837627\pi$
$701$			13.7742i			0.520244i	−0.965576	+	0.260122i	$0.916237\pi$
$702$		0			0
$703$	−6.43670	−	3.71623i	−0.242765	−	0.140160i
$704$		0			0
$705$	−12.5930	−	6.07291i	−0.474281	−	0.228719i
$706$		0			0
$707$	3.44186	−	33.9355i	0.129444	−	1.27627i
$708$		0			0
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	−0.0767981	−	0.997047i	$-0.524470\pi$
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	0.901867	−	0.432014i	$-0.142197\pi$
$710$		0			0
$711$	−4.20425	+	10.6782i	−0.157672	+	0.400462i
$712$		0			0
$713$	−1.37726	−	2.38549i	−0.0515789	−	0.0893373i
$714$		0			0
$715$	12.3607	−	21.4094i	0.462265	−	0.800667i
$716$		0			0
$717$	17.8936	−	37.1050i	0.668250	−	1.38571i
$718$		0			0
$719$	−14.7930	−	25.6223i	−0.551687	−	0.955549i	−0.998153	−	0.0607489i	$-0.980651\pi$
$719$	−14.7930	−	25.6223i	−0.551687	−	0.955549i	0.446466	−	0.894800i	$-0.352682\pi$
$720$		0			0
$721$	−28.3198	−	2.87230i	−1.05469	−	0.106970i
$722$		0			0
$723$	−49.4843	+	3.68133i	−1.84034	+	0.136910i
$724$		0			0
$725$	40.8666	−	23.5943i	1.51775	−	0.876271i
$726$		0			0
$727$	10.1244	−	5.84534i	0.375494	−	0.216792i	−0.300362	−	0.953825i	$-0.597107\pi$
$727$	10.1244	−	5.84534i	0.375494	−	0.216792i	0.675856	+	0.737034i	$0.263774\pi$
$728$		0			0
$729$	−24.3642	+	11.6356i	−0.902377	+	0.430948i
$730$		0			0
$731$	29.6298			1.09590
$732$		0			0
$733$			33.0733i			1.22159i	0.791789	+	0.610795i	$0.209150\pi$
$733$			33.0733i			1.22159i	−0.791789	+	0.610795i	$0.790850\pi$
$734$		0			0
$735$	−5.59715	+	43.5234i	−0.206454	+	1.60539i
$736$		0			0
$737$	−14.4318	+	8.33219i	−0.531601	+	0.306920i
$738$		0			0
$739$	21.7528	−	37.6770i	0.800190	−	1.38597i	−0.119301	−	0.992858i	$-0.538065\pi$
$739$	21.7528	−	37.6770i	0.800190	−	1.38597i	0.919491	−	0.393111i	$-0.128601\pi$
$740$		0			0
$741$	0.443750	+	5.96486i	0.0163016	+	0.219125i
$742$		0			0
$743$	−18.0206	−	10.4042i	−0.661112	−	0.381693i	0.131589	−	0.991304i	$-0.457992\pi$
$743$	−18.0206	−	10.4042i	−0.661112	−	0.381693i	−0.792701	+	0.609611i	$0.791326\pi$
$744$		0			0
$745$			40.7083i			1.49144i
$746$		0			0
$747$	14.9614	+	18.8028i	0.547408	+	0.687958i
$748$		0			0
$749$	−2.86382	−	6.36972i	−0.104642	−	0.232745i
$750$		0			0
$751$	39.8984			1.45591			0.727957	−	0.685623i	$-0.240470\pi$
$751$	39.8984			1.45591			0.727957	+	0.685623i	$0.240470\pi$
$752$		0			0
$753$	−1.41736	−	19.0521i	−0.0516515	−	0.694297i
$754$		0			0
$755$	−17.0969			−0.622219
$756$		0			0
$757$	7.45545			0.270973			0.135486	−	0.990779i	$-0.456740\pi$
$757$	7.45545			0.270973			0.135486	+	0.990779i	$0.456740\pi$
$758$		0			0
$759$	0.779665	+	10.4802i	0.0283001	+	0.380408i
$760$		0			0
$761$	−8.64924			−0.313535			−0.156767	−	0.987636i	$-0.550107\pi$
$761$	−8.64924			−0.313535			−0.156767	+	0.987636i	$0.550107\pi$
$762$		0			0
$763$	19.3908	+	13.9807i	0.701995	+	0.506134i
$764$		0			0
$765$	24.5598	−	62.3782i	0.887961	−	2.25529i
$766$		0			0
$767$			30.6319i			1.10605i
$768$		0			0
$769$	−20.4818	−	11.8252i	−0.738592	−	0.426426i	0.0829652	−	0.996552i	$-0.473561\pi$
$769$	−20.4818	−	11.8252i	−0.738592	−	0.426426i	−0.821557	+	0.570126i	$0.806894\pi$
$770$		0			0
$771$	−1.94005	−	26.0781i	−0.0698693	−	0.939180i
$772$		0			0
$773$	−23.2849	+	40.3307i	−0.837501	+	1.45059i	0.0544774	+	0.998515i	$0.482651\pi$
$773$	−23.2849	+	40.3307i	−0.837501	+	1.45059i	−0.891978	+	0.452079i	$0.850683\pi$
$774$		0			0
$775$	−6.38084	+	3.68398i	−0.229207	+	0.132333i
$776$		0			0
$777$	−16.0232	−	29.5561i	−0.574828	−	1.06032i
$778$		0			0
$779$			5.77546i			0.206927i
$780$		0			0
$781$	−0.934344			−0.0334335
$782$		0			0
$783$	−20.5551	−	22.2256i	−0.734580	−	0.794279i
$784$		0			0
$785$	−9.62178	+	5.55513i	−0.343416	+	0.198271i
$786$		0			0
$787$	21.1657	−	12.2200i	0.754474	−	0.435596i	−0.0728341	−	0.997344i	$-0.523204\pi$
$787$	21.1657	−	12.2200i	0.754474	−	0.435596i	0.827308	+	0.561748i	$0.189871\pi$
$788$		0			0
$789$	−33.9212	+	2.52353i	−1.20763	+	0.0898401i
$790$		0			0
$791$	2.61593	−	3.62823i	0.0930118	−	0.129005i
$792$		0			0
$793$	25.0748	+	43.4309i	0.890433	+	1.54228i
$794$		0			0
$795$	−23.8363	+	49.4279i	−0.845386	+	1.75303i
$796$		0			0
$797$	24.9202	−	43.1631i	0.882719	−	1.52891i	0.0344128	−	0.999408i	$-0.489044\pi$
$797$	24.9202	−	43.1631i	0.882719	−	1.52891i	0.848306	−	0.529506i	$-0.177623\pi$
$798$		0			0
$799$	−6.88489	−	11.9250i	−0.243570	−	0.421875i
$800$		0			0
$801$	−8.94076	−	11.2364i	−0.315906	−	0.397017i
$802$		0			0
$803$	−4.22291	+	7.31430i	−0.149023	+	0.258116i
$804$		0			0
$805$	28.8475	+	2.92582i	1.01674	+	0.103122i
$806$		0			0
$807$	−0.766025	−	0.369410i	−0.0269654	−	0.0130039i
$808$		0			0
$809$	10.6735	+	6.16237i	0.375262	+	0.216657i	0.675755	−	0.737127i	$-0.263818\pi$
$809$	10.6735	+	6.16237i	0.375262	+	0.216657i	−0.300493	+	0.953784i	$0.597151\pi$
$810$		0			0
$811$			24.8017i			0.870906i	0.900212	+	0.435453i	$0.143412\pi$
$811$			24.8017i			0.870906i	−0.900212	+	0.435453i	$0.856588\pi$
$812$		0			0
$813$	13.7258	+	20.1556i	0.481386	+	0.706888i
$814$		0			0
$815$	−5.20047	−	9.00748i	−0.182165	−	0.315518i
$816$		0			0
$817$	−4.21041	−	2.43088i	−0.147304	−	0.0850457i
$818$		0			0
$819$	−12.4017	+	24.0464i	−0.433352	+	0.840248i
$820$		0			0
$821$	31.3573	+	18.1041i	1.09438	+	0.631839i	0.934738	−	0.355336i	$-0.115634\pi$
$821$	31.3573	+	18.1041i	1.09438	+	0.631839i	0.159639	+	0.987175i	$0.448967\pi$
$822$		0			0
$823$	−9.54093	−	16.5254i	−0.332576	−	0.576038i	0.650440	−	0.759557i	$-0.274584\pi$
$823$	−9.54093	−	16.5254i	−0.332576	−	0.576038i	−0.983016	+	0.183519i	$0.941251\pi$
$824$		0			0
$825$	28.0331	−	2.08549i	0.975986	−	0.0726075i
$826$		0			0
$827$		−	31.9013i		−	1.10932i	−0.832079	−	0.554658i	$-0.812849\pi$
$827$		−	31.9013i		−	1.10932i	0.832079	−	0.554658i	$-0.187151\pi$
$828$		0			0
$829$	13.0645	+	7.54278i	0.453748	+	0.261971i	0.709412	−	0.704794i	$-0.248961\pi$
$829$	13.0645	+	7.54278i	0.453748	+	0.261971i	−0.255664	+	0.966766i	$0.582294\pi$
$830$		0			0
$831$	3.94750	+	53.0620i	0.136937	+	1.84070i
$832$		0			0
$833$	−28.6846	+	32.3280i	−0.993864	+	1.12010i
$834$		0			0
$835$	−2.64397	+	4.57950i	−0.0914985	+	0.158480i
$836$		0			0
$837$	3.20945	+	3.47027i	0.110935	+	0.119950i
$838$		0			0
$839$	−8.19860	−	14.2004i	−0.283047	−	0.490252i	0.689087	−	0.724679i	$-0.258012\pi$
$839$	−8.19860	−	14.2004i	−0.283047	−	0.490252i	−0.972134	+	0.234427i	$0.924679\pi$
$840$		0			0
$841$	2.47206	−	4.28173i	0.0852434	−	0.147646i
$842$		0			0
$843$	7.72582	+	11.3449i	0.266091	+	0.390740i
$844$		0			0
$845$	2.49817	+	4.32696i	0.0859397	+	0.148852i
$846$		0			0
$847$	−1.86475	+	18.3857i	−0.0640735	+	0.631741i
$848$		0			0
$849$	11.2271	+	16.4863i	0.385312	+	0.565808i
$850$		0			0
$851$	−19.2386	+	11.1074i	−0.659492	+	0.380758i
$852$		0			0
$853$	−16.5936	+	9.58030i	−0.568153	+	0.328023i	−0.756411	−	0.654096i	$-0.773049\pi$
$853$	−16.5936	+	9.58030i	−0.568153	+	0.328023i	0.188258	+	0.982120i	$0.439716\pi$
$854$		0			0
$855$	−8.60756	+	6.84903i	−0.294372	+	0.234232i
$856$		0			0
$857$	16.1145			0.550460			0.275230	−	0.961378i	$-0.411246\pi$
$857$	16.1145			0.550460			0.275230	+	0.961378i	$0.411246\pi$
$858$		0			0
$859$			12.1048i			0.413009i	0.978446	+	0.206505i	$0.0662089\pi$
$859$			12.1048i			0.413009i	−0.978446	+	0.206505i	$0.933791\pi$
$860$		0			0
$861$	−13.6644	+	22.2663i	−0.465682	+	0.758833i
$862$		0			0
$863$	32.2728	−	18.6327i	1.09858	−	0.634265i	0.162732	−	0.986670i	$-0.447969\pi$
$863$	32.2728	−	18.6327i	1.09858	−	0.634265i	0.935848	+	0.352405i	$0.114636\pi$
$864$		0			0
$865$	5.55712	−	9.62522i	0.188948	−	0.327267i
$866$		0			0
$867$	30.2365	−	20.5909i	1.02689	−	0.699303i
$868$		0			0
$869$	−6.63824	−	3.83259i	−0.225187	−	0.130012i
$870$		0			0
$871$			28.3485i			0.960553i
$872$		0			0
$873$	−27.6043	+	21.9647i	−0.934262	+	0.743392i
$874$		0			0
$875$	2.99486	−	29.5282i	0.101245	−	0.998236i
$876$		0			0
$877$	−9.70948			−0.327866			−0.163933	−	0.986471i	$-0.552418\pi$
$877$	−9.70948			−0.327866			−0.163933	+	0.986471i	$0.552418\pi$
$878$		0			0
$879$	7.82983	+	3.77588i	0.264094	+	0.127357i
$880$		0			0
$881$	2.63241			0.0886881			0.0443440	−	0.999016i	$-0.485880\pi$
$881$	2.63241			0.0886881			0.0443440	+	0.999016i	$0.485880\pi$
$882$		0			0
$883$	36.3181			1.22220			0.611101	−	0.791553i	$-0.290727\pi$
$883$	36.3181			1.22220			0.611101	+	0.791553i	$0.290727\pi$
$884$		0			0
$885$	−46.5621	+	31.7085i	−1.56517	+	1.06587i
$886$		0			0
$887$	16.3642			0.549455			0.274728	−	0.961522i	$-0.411412\pi$
$887$	16.3642			0.549455			0.274728	+	0.961522i	$0.411412\pi$
$888$		0			0
$889$	4.78659	−	47.1940i	0.160537	−	1.58284i
$890$		0			0
$891$	−5.27824	−	17.2444i	−0.176828	−	0.577711i
$892$		0			0
$893$			2.25939i			0.0756076i
$894$		0			0
$895$	−60.5549	−	34.9614i	−2.02413	−	1.16863i
$896$		0			0
$897$	16.1030	+	7.76555i	0.537663	+	0.259284i
$898$		0			0
$899$	−2.64999	+	4.58992i	−0.0883822	+	0.153082i
$900$		0			0
$901$	−46.8058	+	27.0233i	−1.55933	+	0.900277i
$902$		0			0
$903$	−10.4812	−	19.3334i	−0.348791	−	0.643376i
$904$		0			0
$905$		−	28.5679i		−	0.949629i
$906$		0			0
$907$	−10.8333			−0.359714			−0.179857	−	0.983693i	$-0.557564\pi$
$907$	−10.8333			−0.359714			−0.179857	+	0.983693i	$0.557564\pi$
$908$		0			0
$909$	38.2509	−	5.72294i	1.26870	−	0.189818i
$910$		0			0
$911$	−36.8512	+	21.2760i	−1.22093	+	0.704907i	−0.965117	−	0.261818i	$-0.915678\pi$
$911$	−36.8512	+	21.2760i	−1.22093	+	0.704907i	−0.255817	+	0.966725i	$0.582345\pi$
$912$		0			0
$913$	−13.8994	+	8.02482i	−0.460003	+	0.265583i
$914$		0			0
$915$	−40.0611	+	83.0724i	−1.32438	+	2.74629i
$916$		0			0
$917$	4.62699	−	45.6204i	0.152797	−	1.50652i
$918$		0			0
$919$	12.9697	+	22.4641i	0.427829	+	0.741022i	0.996680	−	0.0814187i	$-0.0259451\pi$
$919$	12.9697	+	22.4641i	0.427829	+	0.741022i	−0.568851	+	0.822441i	$0.692612\pi$
$920$		0			0
$921$	−30.2807	+	2.25271i	−0.997785	+	0.0742292i
$922$		0			0
$923$	−0.794727	+	1.37651i	−0.0261588	+	0.0453083i
$924$		0			0
$925$	29.7108	+	51.4606i	0.976884	+	1.69201i
$926$		0			0
$927$	−4.77591	−	31.9211i	−0.156861	−	1.04843i
$928$		0			0
$929$	23.4456	−	40.6089i	0.769224	−	1.33234i	−0.168760	−	0.985657i	$-0.553976\pi$
$929$	23.4456	−	40.6089i	0.769224	−	1.33234i	0.937984	−	0.346678i	$-0.112690\pi$
$930$		0			0
$931$	6.72834	−	2.24048i	0.220512	−	0.0734287i
$932$		0			0
$933$	24.7601	−	16.8615i	0.810608	−	0.552019i
$934$		0			0
$935$	38.7784	+	22.3887i	1.26819	+	0.732189i
$936$		0			0
$937$		−	0.209357i		−	0.00683939i	−0.999994	−	0.00341969i	$-0.998911\pi$
$937$		−	0.209357i		−	0.00683939i	0.999994	−	0.00341969i	$-0.00108852\pi$
$938$		0			0
$939$	−6.76742	+	14.0332i	−0.220846	+	0.457956i
$940$		0			0
$941$	−0.388565	−	0.673014i	−0.0126669	−	0.0219396i	0.859622	−	0.510930i	$-0.170699\pi$
$941$	−0.388565	−	0.673014i	−0.0126669	−	0.0219396i	−0.872289	+	0.488990i	$0.837365\pi$
$942$		0			0
$943$	14.9496	+	8.63113i	0.486825	+	0.281068i
$944$		0			0
$945$	−49.3894	+	6.04021i	−1.60664	+	0.196488i
$946$		0			0
$947$	−43.1233	−	24.8972i	−1.40132	−	0.809052i	−0.406791	−	0.913521i	$-0.633352\pi$
$947$	−43.1233	−	24.8972i	−1.40132	−	0.809052i	−0.994528	+	0.104470i	$0.966686\pi$
$948$		0			0
$949$	7.18378	+	12.4427i	0.233196	+	0.403906i
$950$		0			0
$951$	5.05612	−	10.4846i	0.163956	−	0.339986i
$952$		0			0
$953$			41.4104i			1.34141i	0.741722	+	0.670707i	$0.234009\pi$
$953$			41.4104i			1.34141i	−0.741722	+	0.670707i	$0.765991\pi$
$954$		0			0
$955$	41.7010	+	24.0761i	1.34941	+	0.779084i
$956$		0			0
$957$	16.7133	−	11.3817i	0.540264	−	0.367917i
$958$		0			0
$959$	0.00169812		0.000172230i	5.48353e−5		5.56160e-6i
$960$		0			0
$961$	−15.0862	+	26.1301i	−0.486653	+	0.842907i
$962$		0			0
$963$	6.19668	−	4.93069i	0.199685	−	0.158889i
$964$		0			0
$965$	11.8274	+	20.4857i	0.380739	+	0.659459i
$966$		0			0
$967$	−22.8028	+	39.4956i	−0.733289	+	1.27009i	0.222181	+	0.975005i	$0.428682\pi$
$967$	−22.8028	+	39.4956i	−0.733289	+	1.27009i	−0.955470	+	0.295088i	$0.904651\pi$
$968$		0			0
$969$	−10.8040	+	0.803754i	−0.347075	+	0.0258203i
$970$		0			0
$971$	−4.36733	−	7.56444i	−0.140154	−	0.242754i	0.787400	−	0.616442i	$-0.211427\pi$
$971$	−4.36733	−	7.56444i	−0.140154	−	0.242754i	−0.927555	+	0.373688i	$0.878093\pi$
$972$		0			0
$973$	15.6028	−	21.6407i	0.500202	−	0.693768i
$974$		0			0
$975$	20.7717	−	43.0731i	0.665228	−	1.37944i
$976$		0			0
$977$	−12.9058	+	7.45114i	−0.412892	+	0.238383i	−0.692031	−	0.721867i	$-0.743284\pi$
$977$	−12.9058	+	7.45114i	−0.412892	+	0.238383i	0.279140	+	0.960250i	$0.409951\pi$
$978$		0			0
$979$	8.30615	−	4.79556i	0.265466	−	0.153267i
$980$		0			0
$981$	−9.93033	+	25.2216i	−0.317051	+	0.805262i
$982$		0			0
$983$	3.06917			0.0978912			0.0489456	−	0.998801i	$-0.484414\pi$
$983$	3.06917			0.0978912			0.0489456	+	0.998801i	$0.484414\pi$
$984$		0			0
$985$			16.0788i			0.512314i
$986$		0			0
$987$	−5.34559	+	8.71068i	−0.170152	+	0.277264i
$988$		0			0
$989$	−12.5845	+	7.26565i	−0.400163	+	0.231034i
$990$		0			0
$991$	−27.9075	+	48.3372i	−0.886510	+	1.53548i	−0.0425375	+	0.999095i	$0.513544\pi$
$991$	−27.9075	+	48.3372i	−0.886510	+	1.53548i	−0.843973	+	0.536386i	$0.819789\pi$
$992$		0			0
$993$	−29.2904	−	14.1251i	−0.929502	−	0.448246i
$994$		0			0
$995$	36.0798	+	20.8307i	1.14381	+	0.660377i
$996$		0			0
$997$			6.12692i			0.194042i	0.995282	+	0.0970208i	$0.0309313\pi$
$997$			6.12692i			0.194042i	−0.995282	+	0.0970208i	$0.969069\pi$
$998$		0			0
$999$	27.9872	−	25.8837i	0.885477	−	0.818924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.c.689.5		16
3.2	odd	2		3024.2.df.c.17.7		16
4.3	odd	2		126.2.t.a.59.2	yes	16
7.5	odd	6		1008.2.ca.c.257.8		16
9.2	odd	6		1008.2.ca.c.353.8		16
9.7	even	3		3024.2.ca.c.2033.7		16
12.11	even	2		378.2.t.a.17.8		16
21.5	even	6		3024.2.ca.c.2609.7		16
28.3	even	6		882.2.m.b.293.7		16
28.11	odd	6		882.2.m.a.293.6		16
28.19	even	6		126.2.l.a.5.5	✓	16
28.23	odd	6		882.2.l.b.509.8		16
28.27	even	2		882.2.t.a.815.3		16
36.7	odd	6		378.2.l.a.143.8		16
36.11	even	6		126.2.l.a.101.1	yes	16
36.23	even	6		1134.2.k.a.647.1		16
36.31	odd	6		1134.2.k.b.647.8		16
63.47	even	6	inner	1008.2.df.c.929.5		16
63.61	odd	6		3024.2.df.c.1601.7		16
84.11	even	6		2646.2.m.a.881.1		16
84.23	even	6		2646.2.l.a.1097.1		16
84.47	odd	6		378.2.l.a.341.4		16
84.59	odd	6		2646.2.m.b.881.4		16
84.83	odd	2		2646.2.t.b.2285.5		16
252.11	even	6		882.2.m.b.587.7		16
252.47	odd	6		126.2.t.a.47.2	yes	16
252.79	odd	6		2646.2.t.b.1979.5		16
252.83	odd	6		882.2.l.b.227.4		16
252.103	even	6		1134.2.k.a.971.1		16
252.115	even	6		2646.2.m.a.1763.1		16
252.131	odd	6		1134.2.k.b.971.8		16
252.151	odd	6		2646.2.m.b.1763.4		16
252.187	even	6		378.2.t.a.89.8		16
252.191	even	6		882.2.t.a.803.3		16
252.223	even	6		2646.2.l.a.521.5		16
252.227	odd	6		882.2.m.a.587.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	28.19	even	6
126.2.l.a.101.1	yes	16	36.11	even	6
126.2.t.a.47.2	yes	16	252.47	odd	6
126.2.t.a.59.2	yes	16	4.3	odd	2
378.2.l.a.143.8		16	36.7	odd	6
378.2.l.a.341.4		16	84.47	odd	6
378.2.t.a.17.8		16	12.11	even	2
378.2.t.a.89.8		16	252.187	even	6
882.2.l.b.227.4		16	252.83	odd	6
882.2.l.b.509.8		16	28.23	odd	6
882.2.m.a.293.6		16	28.11	odd	6
882.2.m.a.587.6		16	252.227	odd	6
882.2.m.b.293.7		16	28.3	even	6
882.2.m.b.587.7		16	252.11	even	6
882.2.t.a.803.3		16	252.191	even	6
882.2.t.a.815.3		16	28.27	even	2
1008.2.ca.c.257.8		16	7.5	odd	6
1008.2.ca.c.353.8		16	9.2	odd	6
1008.2.df.c.689.5		16	1.1	even	1	trivial
1008.2.df.c.929.5		16	63.47	even	6	inner
1134.2.k.a.647.1		16	36.23	even	6
1134.2.k.a.971.1		16	252.103	even	6
1134.2.k.b.647.8		16	36.31	odd	6
1134.2.k.b.971.8		16	252.131	odd	6
2646.2.l.a.521.5		16	252.223	even	6
2646.2.l.a.1097.1		16	84.23	even	6
2646.2.m.a.881.1		16	84.11	even	6
2646.2.m.a.1763.1		16	252.115	even	6
2646.2.m.b.881.4		16	84.59	odd	6
2646.2.m.b.1763.4		16	252.151	odd	6
2646.2.t.b.1979.5		16	252.79	odd	6
2646.2.t.b.2285.5		16	84.83	odd	2
3024.2.ca.c.2033.7		16	9.7	even	3
3024.2.ca.c.2609.7		16	21.5	even	6
3024.2.df.c.17.7		16	3.2	odd	2
3024.2.df.c.1601.7		16	63.61	odd	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.128499 + 1.72728i) q^{3} -3.61932 q^{5} +(-0.266972 + 2.63225i) q^{7} +(-2.96698 + 0.443907i) q^{9} -2.00379i q^{11} +(-2.95206 - 1.70437i) q^{13} +(-0.465079 - 6.25156i) q^{15} +(3.08709 - 5.34700i) q^{17} +(-0.877353 + 0.506540i) q^{19} +(-4.58093 - 0.122894i) q^{21} +3.02799i q^{23} +8.09945 q^{25} +(-1.14800 - 5.06775i) q^{27} +(5.04560 - 2.91308i) q^{29} +(-0.787812 + 0.454844i) q^{31} +(3.46111 - 0.257486i) q^{33} +(0.966257 - 9.52693i) q^{35} +(3.66825 + 6.35359i) q^{37} +(2.56459 - 5.31804i) q^{39} +(2.85045 - 4.93712i) q^{41} +(2.39949 + 4.15605i) q^{43} +(10.7384 - 1.60664i) q^{45} +(1.11511 - 1.93143i) q^{47} +(-6.85745 - 1.40547i) q^{49} +(9.63244 + 4.64518i) q^{51} +(-7.58088 - 4.37683i) q^{53} +7.25237i q^{55} +(-0.987674 - 1.45034i) q^{57} +(-4.49313 - 7.78233i) q^{59} +(-12.7410 - 7.35603i) q^{61} +(-0.376373 - 7.92833i) q^{63} +(10.6844 + 6.16866i) q^{65} +(-4.15821 - 7.20222i) q^{67} +(-5.23019 + 0.389094i) q^{69} -0.466287i q^{71} +(-3.65022 - 2.10746i) q^{73} +(1.04077 + 13.9900i) q^{75} +(5.27448 + 0.534957i) q^{77} +(1.91267 - 3.31284i) q^{79} +(8.60589 - 2.63412i) q^{81} +(-4.00481 - 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} +(5.68005 + 8.34083i) q^{87} +(2.39324 + 4.14521i) q^{89} +(5.27445 - 7.31553i) q^{91} +(-0.886874 - 1.30232i) q^{93} +(3.17542 - 1.83333i) q^{95} +(10.1835 - 5.87944i) q^{97} +(0.889499 + 5.94521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} - 6 q^{9} - 6 q^{13} + 18 q^{15} + 18 q^{17} - 18 q^{21} + 16 q^{25} + 36 q^{27} + 6 q^{29} - 6 q^{31} + 18 q^{33} + 30 q^{35} - 2 q^{37} + 30 q^{39} + 6 q^{41} + 2 q^{43} + 12 q^{45} + 18 q^{47}+ \cdots - 18 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 - 6 * q^9 - 6 * q^13 + 18 * q^15 + 18 * q^17 - 18 * q^21 + 16 * q^25 + 36 * q^27 + 6 * q^29 - 6 * q^31 + 18 * q^33 + 30 * q^35 - 2 * q^37 + 30 * q^39 + 6 * q^41 + 2 * q^43 + 12 * q^45 + 18 * q^47 + 10 * q^49 + 36 * q^53 + 6 * q^57 - 30 * q^59 - 60 * q^61 - 42 * q^63 + 42 * q^65 - 14 * q^67 + 42 * q^69 - 30 * q^75 - 18 * q^77 + 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 + 24 * q^89 + 12 * q^91 + 30 * q^93 + 66 * q^95 - 6 * q^97 - 18 * q^99

Introduction

L-functions

Modular forms

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Database

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