LMFDB - Embedded newform 1386.2.r.d.1277.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(89,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("1386.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.r (of order $6$, degree $2$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1277.7
Character	$\chi$	$=$	1386.1277
Dual form			1386.2.r.d.89.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.01268 + 3.48607i) q^{5} +(2.64157 + 0.148737i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.01268 + 3.48607i) q^{5} +(2.64157 + 0.148737i) q^{7} -1.00000i q^{8} +(3.48607 + 2.01268i) q^{10} +(-0.866025 - 0.500000i) q^{11} -5.78421i q^{13} +(2.36203 - 1.19197i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.655680 + 1.13567i) q^{17} +(5.95486 - 3.43804i) q^{19} +4.02536 q^{20} -1.00000 q^{22} +(2.08402 - 1.20321i) q^{23} +(-5.60177 + 9.70255i) q^{25} +(-2.89210 - 5.00927i) q^{26} +(1.44959 - 2.21330i) q^{28} -0.530917i q^{29} +(-2.04209 - 1.17900i) q^{31} +(-0.866025 - 0.500000i) q^{32} +1.31136i q^{34} +(4.79812 + 9.50804i) q^{35} +(4.33840 + 7.51433i) q^{37} +(3.43804 - 5.95486i) q^{38} +(3.48607 - 2.01268i) q^{40} -5.27341 q^{41} +0.642009 q^{43} +(-0.866025 + 0.500000i) q^{44} +(1.20321 - 2.08402i) q^{46} +(5.99941 + 10.3913i) q^{47} +(6.95575 + 0.785798i) q^{49} +11.2035i q^{50} +(-5.00927 - 2.89210i) q^{52} +(2.35898 + 1.36196i) q^{53} -4.02536i q^{55} +(0.148737 - 2.64157i) q^{56} +(-0.265458 - 0.459787i) q^{58} +(-0.834008 + 1.44455i) q^{59} +(-13.2851 + 7.67018i) q^{61} -2.35800 q^{62} -1.00000 q^{64} +(20.1641 - 11.6418i) q^{65} +(-3.09028 + 5.35251i) q^{67} +(0.655680 + 1.13567i) q^{68} +(8.90932 + 5.83514i) q^{70} +12.0531i q^{71} +(-10.5428 - 6.08687i) q^{73} +(7.51433 + 4.33840i) q^{74} -6.87608i q^{76} +(-2.21330 - 1.44959i) q^{77} +(-5.70820 - 9.88689i) q^{79} +(2.01268 - 3.48607i) q^{80} +(-4.56691 + 2.63671i) q^{82} -13.1957 q^{83} -5.27869 q^{85} +(0.555996 - 0.321005i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(1.06857 + 1.85081i) q^{89} +(0.860326 - 15.2794i) q^{91} -2.40642i q^{92} +(10.3913 + 5.99941i) q^{94} +(23.9705 + 13.8394i) q^{95} -15.3836i q^{97} +(6.41676 - 2.79736i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 + 8 * q^7	$ 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) $ 24 * q + 12 * q^4 + 8 * q^7 - 12 * q^16 + 12 * q^19 - 24 * q^22 + 4 * q^25 + 4 * q^28 + 20 * q^37 + 24 * q^43 + 12 * q^46 + 40 * q^49 - 28 * q^58 - 120 * q^61 - 24 * q^64 - 32 * q^67 + 48 * q^70 - 48 * q^73 - 64 * q^79 - 48 * q^82 + 32 * q^85 - 12 * q^88 + 56 * q^91 + 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.01268	+	3.48607i	0.900098	+	1.55902i	0.827365	+	0.561664i	$0.189839\pi$
$5$	2.01268	+	3.48607i	0.900098	+	1.55902i	0.0727330	+	0.997351i	$0.476828\pi$
$6$		0			0
$7$	2.64157	+	0.148737i	0.998419	+	0.0562173i
$7$	2.64157	+	0.148737i	0.998419	+	0.0562173i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	3.48607	+	2.01268i	1.10239	+	0.636466i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$12$		0			0
$13$		−	5.78421i		−	1.60425i	−0.597156	−	0.802125i	$-0.703703\pi$
$13$		−	5.78421i		−	1.60425i	0.597156	−	0.802125i	$-0.296297\pi$
$14$	2.36203	−	1.19197i	0.631280	−	0.318568i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.655680	+	1.13567i	−0.159026	+	0.275440i	−0.934518	−	0.355917i	$-0.884169\pi$
$17$	−0.655680	+	1.13567i	−0.159026	+	0.275440i	0.775492	+	0.631357i	$0.217502\pi$
$18$		0			0
$19$	5.95486	−	3.43804i	1.36614	−	0.788741i	0.375706	−	0.926739i	$-0.377400\pi$
$19$	5.95486	−	3.43804i	1.36614	−	0.788741i	0.990432	+	0.137998i	$0.0440668\pi$
$20$	4.02536			0.900098
$21$		0			0
$22$	−1.00000			−0.213201
$23$	2.08402	−	1.20321i	0.434548	−	0.250887i	−0.266734	−	0.963770i	$-0.585945\pi$
$23$	2.08402	−	1.20321i	0.434548	−	0.250887i	0.701282	+	0.712884i	$0.252611\pi$
$24$		0			0
$25$	−5.60177	+	9.70255i	−1.12035	+	1.94051i
$26$	−2.89210	−	5.00927i	−0.567188	−	0.982399i
$27$		0			0
$28$	1.44959	−	2.21330i	0.273947	−	0.418274i
$29$		−	0.530917i		−	0.0985888i	−0.998784	−	0.0492944i	$-0.984303\pi$
$29$		−	0.530917i		−	0.0985888i	0.998784	−	0.0492944i	$-0.0156972\pi$
$30$		0			0
$31$	−2.04209	−	1.17900i	−0.366770	−	0.211755i	0.305276	−	0.952264i	$-0.401251\pi$
$31$	−2.04209	−	1.17900i	−0.366770	−	0.211755i	−0.672046	+	0.740509i	$0.734585\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			1.31136i			0.224896i
$35$	4.79812	+	9.50804i	0.811031	+	1.60715i
$36$		0			0
$37$	4.33840	+	7.51433i	0.713229	+	1.23535i	0.963639	+	0.267209i	$0.0861013\pi$
$37$	4.33840	+	7.51433i	0.713229	+	1.23535i	−0.250410	+	0.968140i	$0.580565\pi$
$38$	3.43804	−	5.95486i	0.557724	−	0.966006i
$39$		0			0
$40$	3.48607	−	2.01268i	0.551195	−	0.318233i
$41$	−5.27341			−0.823569			−0.411784	−	0.911281i	$-0.635094\pi$
$41$	−5.27341			−0.823569			−0.411784	+	0.911281i	$0.635094\pi$
$42$		0			0
$43$	0.642009			0.0979055			0.0489527	−	0.998801i	$-0.484412\pi$
$43$	0.642009			0.0979055			0.0489527	+	0.998801i	$0.484412\pi$
$44$	−0.866025	+	0.500000i	−0.130558	+	0.0753778i
$45$		0			0
$46$	1.20321	−	2.08402i	0.177404	−	0.307272i
$47$	5.99941	+	10.3913i	0.875104	+	1.51572i	0.856652	+	0.515895i	$0.172541\pi$
$47$	5.99941	+	10.3913i	0.875104	+	1.51572i	0.0184524	+	0.999830i	$0.494126\pi$
$48$		0			0
$49$	6.95575	+	0.785798i	0.993679	+	0.112257i
$50$			11.2035i			1.58442i
$51$		0			0
$52$	−5.00927	−	2.89210i	−0.694661	−	0.401063i
$53$	2.35898	+	1.36196i	0.324031	+	0.187079i	0.653188	−	0.757196i	$-0.273431\pi$
$53$	2.35898	+	1.36196i	0.324031	+	0.187079i	−0.329157	+	0.944275i	$0.606765\pi$
$54$		0			0
$55$		−	4.02536i		−	0.542780i
$56$	0.148737	−	2.64157i	0.0198758	−	0.352994i
$57$		0			0
$58$	−0.265458	−	0.459787i	−0.0348564	−	0.0603730i
$59$	−0.834008	+	1.44455i	−0.108579	+	0.188064i	−0.915195	−	0.403012i	$-0.867963\pi$
$59$	−0.834008	+	1.44455i	−0.108579	+	0.188064i	0.806616	+	0.591076i	$0.201297\pi$
$60$		0			0
$61$	−13.2851	+	7.67018i	−1.70099	+	0.982066i	−0.756226	+	0.654310i	$0.772959\pi$
$61$	−13.2851	+	7.67018i	−1.70099	+	0.982066i	−0.944762	+	0.327756i	$0.893708\pi$
$62$	−2.35800			−0.299467
$63$		0			0
$64$	−1.00000			−0.125000
$65$	20.1641	−	11.6418i	2.50105	−	1.44398i
$66$		0			0
$67$	−3.09028	+	5.35251i	−0.377537	+	0.653914i	−0.990703	−	0.136040i	$-0.956562\pi$
$67$	−3.09028	+	5.35251i	−0.377537	+	0.653914i	0.613166	+	0.789954i	$0.289896\pi$
$68$	0.655680	+	1.13567i	0.0795128	+	0.137720i
$69$		0			0
$70$	8.90932	+	5.83514i	1.06487	+	0.697432i
$71$			12.0531i			1.43044i	0.698901	+	0.715219i	$0.253673\pi$
$71$			12.0531i			1.43044i	−0.698901	+	0.715219i	$0.746327\pi$
$72$		0			0
$73$	−10.5428	−	6.08687i	−1.23394	−	0.712414i	−0.266089	−	0.963948i	$-0.585732\pi$
$73$	−10.5428	−	6.08687i	−1.23394	−	0.712414i	−0.967848	+	0.251534i	$0.919065\pi$
$74$	7.51433	+	4.33840i	0.873523	+	0.504329i
$75$		0			0
$76$		−	6.87608i		−	0.788741i
$77$	−2.21330	−	1.44959i	−0.252228	−	0.165197i
$78$		0			0
$79$	−5.70820	−	9.88689i	−0.642222	−	1.11236i	−0.984936	−	0.172922i	$-0.944679\pi$
$79$	−5.70820	−	9.88689i	−0.642222	−	1.11236i	0.342713	−	0.939440i	$-0.388654\pi$
$80$	2.01268	−	3.48607i	0.225025	−	0.389754i
$81$		0			0
$82$	−4.56691	+	2.63671i	−0.504331	+	0.291176i
$83$	−13.1957			−1.44841			−0.724207	−	0.689582i	$-0.757794\pi$
$83$	−13.1957			−1.44841			−0.724207	+	0.689582i	$0.757794\pi$
$84$		0			0
$85$	−5.27869			−0.572555
$86$	0.555996	−	0.321005i	0.0599546	−	0.0346148i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	1.06857	+	1.85081i	0.113268	+	0.196185i	0.917086	−	0.398690i	$-0.130535\pi$
$89$	1.06857	+	1.85081i	0.113268	+	0.196185i	−0.803818	+	0.594875i	$0.797202\pi$
$90$		0			0
$91$	0.860326	−	15.2794i	0.0901867	−	1.60171i
$92$		−	2.40642i		−	0.250887i
$93$		0			0
$94$	10.3913	+	5.99941i	1.07178	+	0.618792i
$95$	23.9705	+	13.8394i	2.45932	+	1.41989i
$96$		0			0
$97$		−	15.3836i		−	1.56197i	−0.624552	−	0.780983i	$-0.714719\pi$
$97$		−	15.3836i		−	1.56197i	0.624552	−	0.780983i	$-0.285281\pi$
$98$	6.41676	−	2.79736i	0.648191	−	0.282576i
$99$		0			0
$100$	5.60177	+	9.70255i	0.560177	+	0.970255i
$101$	8.06738	−	13.9731i	0.802734	−	1.39038i	−0.115075	−	0.993357i	$-0.536711\pi$
$101$	8.06738	−	13.9731i	0.802734	−	1.39038i	0.917810	−	0.397020i	$-0.129956\pi$
$102$		0			0
$103$	−4.26648	+	2.46325i	−0.420388	+	0.242711i	−0.695243	−	0.718774i	$-0.744703\pi$
$103$	−4.26648	+	2.46325i	−0.420388	+	0.242711i	0.274855	+	0.961486i	$0.411370\pi$
$104$	−5.78421			−0.567188
$105$		0			0
$106$	2.72392			0.264570
$107$	5.46644	−	3.15605i	0.528461	−	0.305107i	−0.211929	−	0.977285i	$-0.567974\pi$
$107$	5.46644	−	3.15605i	0.528461	−	0.305107i	0.740389	+	0.672178i	$0.234641\pi$
$108$		0			0
$109$	9.23197	−	15.9902i	0.884262	−	1.53159i	0.0377057	−	0.999289i	$-0.487995\pi$
$109$	9.23197	−	15.9902i	0.884262	−	1.53159i	0.846557	−	0.532299i	$-0.178672\pi$
$110$	−2.01268	−	3.48607i	−0.191902	−	0.332383i
$111$		0			0
$112$	−1.19197	−	2.36203i	−0.112631	−	0.223191i
$113$			2.47936i			0.233239i	0.993177	+	0.116619i	$0.0372058\pi$
$113$			2.47936i			0.233239i	−0.993177	+	0.116619i	$0.962794\pi$
$114$		0			0
$115$	8.38894	+	4.84335i	0.782272	+	0.451645i
$116$	−0.459787	−	0.265458i	−0.0426902	−	0.0246472i
$117$		0			0
$118$			1.66802i			0.153553i
$119$	−1.90094	+	2.90243i	−0.174259	+	0.266065i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	−7.67018	+	13.2851i	−0.694426	+	1.20278i
$123$		0			0
$124$	−2.04209	+	1.17900i	−0.183385	+	0.105877i
$125$	−24.9715			−2.23352
$126$		0			0
$127$	−5.20830			−0.462161			−0.231081	−	0.972935i	$-0.574226\pi$
$127$	−5.20830			−0.462161			−0.231081	+	0.972935i	$0.574226\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	11.6418	−	20.1641i	1.02105	−	1.76851i
$131$	−5.39304	−	9.34102i	−0.471192	−	0.816128i	0.528265	−	0.849080i	$-0.322843\pi$
$131$	−5.39304	−	9.34102i	−0.471192	−	0.816128i	−0.999457	+	0.0329512i	$0.989509\pi$
$132$		0			0
$133$	16.2415	−	8.19611i	1.40832	−	0.710693i
$134$			6.18055i			0.533918i
$135$		0			0
$136$	1.13567	+	0.655680i	0.0973829	+	0.0562241i
$137$	−10.8079	−	6.23994i	−0.923380	−	0.533114i	−0.0386683	−	0.999252i	$-0.512312\pi$
$137$	−10.8079	−	6.23994i	−0.923380	−	0.533114i	−0.884712	+	0.466138i	$0.845645\pi$
$138$		0			0
$139$			2.51846i			0.213613i	0.994280	+	0.106806i	$0.0340625\pi$
$139$			2.51846i			0.213613i	−0.994280	+	0.106806i	$0.965937\pi$
$140$	10.6333	+	0.598720i	0.898675	+	0.0506011i
$141$		0			0
$142$	6.02654	+	10.4383i	0.505736	+	0.875961i
$143$	−2.89210	+	5.00927i	−0.241850	+	0.418896i
$144$		0			0
$145$	1.85081	−	1.06857i	0.153701	−	0.0887396i
$146$	−12.1737			−1.00751
$147$		0			0
$148$	8.67680			0.713229
$149$	−8.50142	+	4.90830i	−0.696464	+	0.402103i	−0.806029	−	0.591876i	$-0.798387\pi$
$149$	−8.50142	+	4.90830i	−0.696464	+	0.402103i	0.109565	+	0.993980i	$0.465054\pi$
$150$		0			0
$151$	−4.77440	+	8.26951i	−0.388535	+	0.672963i	−0.992253	−	0.124235i	$-0.960352\pi$
$151$	−4.77440	+	8.26951i	−0.388535	+	0.672963i	0.603717	+	0.797198i	$0.293686\pi$
$152$	−3.43804	−	5.95486i	−0.278862	−	0.483003i
$153$		0			0
$154$	−2.64157	−	0.148737i	−0.212864	−	0.0119856i
$155$		−	9.49181i		−	0.762401i
$156$		0			0
$157$	2.80476	+	1.61933i	0.223844	+	0.129236i	0.607729	−	0.794145i	$-0.292081\pi$
$157$	2.80476	+	1.61933i	0.223844	+	0.129236i	−0.383885	+	0.923381i	$0.625414\pi$
$158$	−9.88689	−	5.70820i	−0.786559	−	0.454120i
$159$		0			0
$160$		−	4.02536i		−	0.318233i
$161$	5.68404	−	2.86839i	0.447965	−	0.226061i
$162$		0			0
$163$	−7.34104	−	12.7151i	−0.574995	−	0.995920i	−0.996042	−	0.0888816i	$-0.971671\pi$
$163$	−7.34104	−	12.7151i	−0.574995	−	0.995920i	0.421047	−	0.907039i	$-0.361663\pi$
$164$	−2.63671	+	4.56691i	−0.205892	+	0.356616i
$165$		0			0
$166$	−11.4278	+	6.59784i	−0.886969	+	0.512092i
$167$	15.0124			1.16169			0.580847	−	0.814013i	$-0.302721\pi$
$167$	15.0124			1.16169			0.580847	+	0.814013i	$0.302721\pi$
$168$		0			0
$169$	−20.4571			−1.57362
$170$	−4.57148	+	2.63935i	−0.350617	+	0.202429i
$171$		0			0
$172$	0.321005	−	0.555996i	0.0244764	−	0.0423943i
$173$	−3.75098	−	6.49689i	−0.285182	−	0.493949i	0.687471	−	0.726211i	$-0.258721\pi$
$173$	−3.75098	−	6.49689i	−0.285182	−	0.493949i	−0.972653	+	0.232262i	$0.925387\pi$
$174$		0			0
$175$	−16.2406	+	24.7967i	−1.22767	+	1.87446i
$176$			1.00000i			0.0753778i
$177$		0			0
$178$	1.85081	+	1.06857i	0.138724	+	0.0800924i
$179$	−4.78596	−	2.76318i	−0.357719	−	0.206529i	0.310360	−	0.950619i	$-0.399550\pi$
$179$	−4.78596	−	2.76318i	−0.357719	−	0.206529i	−0.668080	+	0.744090i	$0.732884\pi$
$180$		0			0
$181$		−	1.64806i		−	0.122499i	−0.998122	−	0.0612496i	$-0.980491\pi$
$181$		−	1.64806i		−	0.122499i	0.998122	−	0.0612496i	$-0.0195086\pi$
$182$	−6.89462	−	13.6625i	−0.511063	−	1.01273i
$183$		0			0
$184$	−1.20321	−	2.08402i	−0.0887018	−	0.153636i
$185$	−17.4636	+	30.2479i	−1.28395	+	2.22387i
$186$		0			0
$187$	1.13567	−	0.655680i	0.0830484	−	0.0479480i
$188$	11.9988			0.875104
$189$		0			0
$190$	27.6787			2.00802
$191$	7.25034	−	4.18599i	0.524616	−	0.302887i	−0.214205	−	0.976789i	$-0.568716\pi$
$191$	7.25034	−	4.18599i	0.524616	−	0.302887i	0.738821	+	0.673901i	$0.235383\pi$
$192$		0			0
$193$	0.381727	−	0.661170i	0.0274773	−	0.0475921i	−0.851960	−	0.523607i	$-0.824586\pi$
$193$	0.381727	−	0.661170i	0.0274773	−	0.0475921i	0.879437	+	0.476015i	$0.157919\pi$
$194$	−7.69179	−	13.3226i	−0.552238	−	0.956505i
$195$		0			0
$196$	4.15840	−	5.63096i	0.297028	−	0.402212i
$197$		−	9.08208i		−	0.647072i	−0.946216	−	0.323536i	$-0.895128\pi$
$197$		−	9.08208i		−	0.647072i	0.946216	−	0.323536i	$-0.104872\pi$
$198$		0			0
$199$	12.2515	+	7.07339i	0.868484	+	0.501420i	0.866844	−	0.498579i	$-0.166145\pi$
$199$	12.2515	+	7.07339i	0.868484	+	0.501420i	0.00163989	+	0.999999i	$0.499478\pi$
$200$	9.70255	+	5.60177i	0.686074	+	0.396105i
$201$		0			0
$202$		−	16.1348i		−	1.13524i
$203$	0.0789670	−	1.40245i	0.00554239	−	0.0984328i
$204$		0			0
$205$	−10.6137	−	18.3835i	−0.741293	−	1.28396i
$206$	−2.46325	+	4.26648i	−0.171623	+	0.297259i
$207$		0			0
$208$	−5.00927	+	2.89210i	−0.347330	+	0.200531i
$209$	−6.87608			−0.475628
$210$		0			0
$211$	24.9602			1.71833			0.859166	−	0.511698i	$-0.170983\pi$
$211$	24.9602			1.71833			0.859166	+	0.511698i	$0.170983\pi$
$212$	2.35898	−	1.36196i	0.162015	−	0.0935397i
$213$		0			0
$214$	3.15605	−	5.46644i	0.215743	−	0.373678i
$215$	1.29216	+	2.23809i	0.0881245	+	0.152636i
$216$		0			0
$217$	−5.21896	−	3.41814i	−0.354286	−	0.232039i
$218$		−	18.4639i		−	1.25054i
$219$		0			0
$220$	−3.48607	−	2.01268i	−0.235030	−	0.135695i
$221$	6.56895	+	3.79259i	0.441876	+	0.255117i
$222$		0			0
$223$		−	1.46095i		−	0.0978323i	−0.998803	−	0.0489161i	$-0.984423\pi$
$223$		−	1.46095i		−	0.0978323i	0.998803	−	0.0489161i	$-0.0155767\pi$
$224$	−2.21330	−	1.44959i	−0.147882	−	0.0968550i
$225$		0			0
$226$	1.23968	+	2.14719i	0.0824624	+	0.142829i
$227$	−10.4814	+	18.1544i	−0.695678	+	1.20495i	0.274274	+	0.961652i	$0.411563\pi$
$227$	−10.4814	+	18.1544i	−0.695678	+	1.20495i	−0.969952	+	0.243298i	$0.921771\pi$
$228$		0			0
$229$	−23.5684	+	13.6072i	−1.55745	+	0.899191i	−0.559945	+	0.828530i	$0.689178\pi$
$229$	−23.5684	+	13.6072i	−1.55745	+	0.899191i	−0.997500	+	0.0706615i	$0.977489\pi$
$230$	9.68671			0.638723
$231$		0			0
$232$	−0.530917			−0.0348564
$233$	−5.80159	+	3.34955i	−0.380074	+	0.219436i	−0.677851	−	0.735200i	$-0.737088\pi$
$233$	−5.80159	+	3.34955i	−0.380074	+	0.219436i	0.297776	+	0.954636i	$0.403755\pi$
$234$		0			0
$235$	−24.1498	+	41.8287i	−1.57536	+	2.72860i
$236$	0.834008	+	1.44455i	0.0542893	+	0.0940319i
$237$		0			0
$238$	−0.195048	+	3.46404i	−0.0126431	+	0.224541i
$239$			13.7992i			0.892595i	0.894885	+	0.446298i	$0.147258\pi$
$239$			13.7992i			0.892595i	−0.894885	+	0.446298i	$0.852742\pi$
$240$		0			0
$241$	−15.1448	−	8.74387i	−0.975564	−	0.563242i	−0.0746361	−	0.997211i	$-0.523780\pi$
$241$	−15.1448	−	8.74387i	−0.975564	−	0.563242i	−0.900928	+	0.433969i	$0.857113\pi$
$242$	0.866025	+	0.500000i	0.0556702	+	0.0321412i
$243$		0			0
$244$			15.3404i			0.982066i
$245$	11.2604	+	25.8298i	0.719399	+	1.65020i
$246$		0			0
$247$	−19.8863	−	34.4442i	−1.26534	−	2.19163i
$248$	−1.17900	+	2.04209i	−0.0748666	+	0.129673i
$249$		0			0
$250$	−21.6259	+	12.4857i	−1.36774	+	0.789667i
$251$	−10.3791			−0.655123			−0.327562	−	0.944830i	$-0.606227\pi$
$251$	−10.3791			−0.655123			−0.327562	+	0.944830i	$0.606227\pi$
$252$		0			0
$253$	−2.40642			−0.151290
$254$	−4.51052	+	2.60415i	−0.283015	+	0.163399i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.82901	−	15.2923i	−0.550738	−	0.953907i	−0.998221	−	0.0596145i	$-0.981013\pi$
$257$	−8.82901	−	15.2923i	−0.550738	−	0.953907i	0.447483	−	0.894292i	$-0.352320\pi$
$258$		0			0
$259$	10.3425	+	20.4949i	0.642653	+	1.27349i
$260$		−	23.2835i		−	1.44398i
$261$		0			0
$262$	−9.34102	−	5.39304i	−0.577090	−	0.333183i
$263$	2.62678	+	1.51657i	0.161974	+	0.0935157i	0.578796	−	0.815472i	$-0.303523\pi$
$263$	2.62678	+	1.51657i	0.161974	+	0.0935157i	−0.416822	+	0.908988i	$0.636856\pi$
$264$		0			0
$265$			10.9647i			0.673559i
$266$	9.96752	−	15.2188i	0.611148	−	0.933125i
$267$		0			0
$268$	3.09028	+	5.35251i	0.188769	+	0.326957i
$269$	−2.42629	+	4.20246i	−0.147934	+	0.256228i	−0.930464	−	0.366384i	$-0.880596\pi$
$269$	−2.42629	+	4.20246i	−0.147934	+	0.256228i	0.782530	+	0.622613i	$0.213929\pi$
$270$		0			0
$271$	2.56205	−	1.47920i	0.155633	−	0.0898549i	−0.420161	−	0.907450i	$-0.638026\pi$
$271$	2.56205	−	1.47920i	0.155633	−	0.0898549i	0.575794	+	0.817595i	$0.304693\pi$
$272$	1.31136			0.0795128
$273$		0			0
$274$	−12.4799			−0.753937
$275$	9.70255	−	5.60177i	0.585086	−	0.337799i
$276$		0			0
$277$	−5.74172	+	9.94495i	−0.344987	+	0.597534i	−0.985351	−	0.170537i	$-0.945450\pi$
$277$	−5.74172	+	9.94495i	−0.344987	+	0.597534i	0.640365	+	0.768071i	$0.278783\pi$
$278$	1.25923	+	2.18105i	0.0755235	+	0.130811i
$279$		0			0
$280$	9.50804	−	4.79812i	0.568214	−	0.286743i
$281$		−	11.1113i		−	0.662847i	−0.943482	−	0.331424i	$-0.892471\pi$
$281$		−	11.1113i		−	0.662847i	0.943482	−	0.331424i	$-0.107529\pi$
$282$		0			0
$283$	2.32185	+	1.34052i	0.138019	+	0.0796856i	0.567420	−	0.823429i	$-0.307942\pi$
$283$	2.32185	+	1.34052i	0.138019	+	0.0796856i	−0.429400	+	0.903114i	$0.641275\pi$
$284$	10.4383	+	6.02654i	0.619398	+	0.357609i
$285$		0			0
$286$			5.78421i			0.342027i
$287$	−13.9301	−	0.784352i	−0.822266	−	0.0462988i
$288$		0			0
$289$	7.64017	+	13.2332i	0.449422	+	0.778421i
$290$	1.06857	−	1.85081i	0.0627483	−	0.108683i
$291$		0			0
$292$	−10.5428	+	6.08687i	−0.616969	+	0.356207i
$293$	6.53620			0.381849			0.190924	−	0.981605i	$-0.438851\pi$
$293$	6.53620			0.381849			0.190924	+	0.981605i	$0.438851\pi$
$294$		0			0
$295$	−6.71437			−0.390926
$296$	7.51433	−	4.33840i	0.436762	−	0.252164i
$297$		0			0
$298$	−4.90830	+	8.50142i	−0.284330	+	0.492474i
$299$	−6.95962	−	12.0544i	−0.402485	−	0.697124i
$300$		0			0
$301$	1.69591	+	0.0954905i	0.0977506	+	0.00550398i
$302$			9.54881i			0.549472i
$303$		0			0
$304$	−5.95486	−	3.43804i	−0.341535	−	0.197185i
$305$	−53.4775	−	30.8753i	−3.06211	−	1.76791i
$306$		0			0
$307$			33.9592i			1.93815i	0.246760	+	0.969077i	$0.420634\pi$
$307$			33.9592i			1.93815i	−0.246760	+	0.969077i	$0.579366\pi$
$308$	−2.36203	+	1.19197i	−0.134589	+	0.0679190i
$309$		0			0
$310$	−4.74591	−	8.22015i	−0.269549	−	0.466873i
$311$	12.7067	−	22.0087i	0.720533	−	1.24800i	−0.240253	−	0.970710i	$-0.577230\pi$
$311$	12.7067	−	22.0087i	0.720533	−	1.24800i	0.960786	−	0.277290i	$-0.0894363\pi$
$312$		0			0
$313$	7.44097	−	4.29605i	0.420589	−	0.242827i	−0.274740	−	0.961518i	$-0.588592\pi$
$313$	7.44097	−	4.29605i	0.420589	−	0.242827i	0.695329	+	0.718691i	$0.255259\pi$
$314$	3.23865			0.182768
$315$		0			0
$316$	−11.4164			−0.642222
$317$	5.95841	−	3.44009i	0.334658	−	0.193215i	−0.323249	−	0.946314i	$-0.604775\pi$
$317$	5.95841	−	3.44009i	0.334658	−	0.193215i	0.657907	+	0.753099i	$0.271442\pi$
$318$		0			0
$319$	−0.265458	+	0.459787i	−0.0148628	+	0.0257431i
$320$	−2.01268	−	3.48607i	−0.112512	−	0.194877i
$321$		0			0
$322$	3.48833	−	5.32612i	0.194397	−	0.296813i
$323$			9.01701i			0.501720i
$324$		0			0
$325$	56.1215	+	32.4018i	3.11306	+	1.79733i
$326$	−12.7151	−	7.34104i	−0.704222	−	0.406583i
$327$		0			0
$328$			5.27341i			0.291176i
$329$	14.3023	+	28.3416i	0.788510	+	1.56252i
$330$		0			0
$331$	4.58577	+	7.94279i	0.252057	+	0.436575i	0.964092	−	0.265569i	$-0.0855597\pi$
$331$	4.58577	+	7.94279i	0.252057	+	0.436575i	−0.712035	+	0.702144i	$0.752226\pi$
$332$	−6.59784	+	11.4278i	−0.362104	+	0.627182i
$333$		0			0
$334$	13.0011	−	7.50620i	0.711390	−	0.410721i
$335$	−24.8790			−1.35928
$336$		0			0
$337$	12.3285			0.671578			0.335789	−	0.941937i	$-0.390997\pi$
$337$	12.3285			0.671578			0.335789	+	0.941937i	$0.390997\pi$
$338$	−17.7163	+	10.2285i	−0.963642	+	0.556359i
$339$		0			0
$340$	−2.63935	+	4.57148i	−0.143139	+	0.247923i
$341$	1.17900	+	2.04209i	0.0638465	+	0.110585i
$342$		0			0
$343$	18.2572	+	3.11032i	0.985797	+	0.167941i
$344$		−	0.642009i		−	0.0346148i
$345$		0			0
$346$	−6.49689	−	3.75098i	−0.349275	−	0.201654i
$347$	19.5559	+	11.2906i	1.04982	+	0.606112i	0.922598	−	0.385762i	$-0.126062\pi$
$347$	19.5559	+	11.2906i	1.04982	+	0.606112i	0.127219	+	0.991875i	$0.459395\pi$
$348$		0			0
$349$		−	23.3095i		−	1.24773i	−0.781532	−	0.623866i	$-0.785561\pi$
$349$		−	23.3095i		−	1.24773i	0.781532	−	0.623866i	$-0.214439\pi$
$350$	−1.66638	+	29.5949i	−0.0890718	+	1.58191i
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−8.16582	+	14.1436i	−0.434623	+	0.752789i	−0.997265	−	0.0739120i	$-0.976452\pi$
$353$	−8.16582	+	14.1436i	−0.434623	+	0.752789i	0.562642	+	0.826701i	$0.309785\pi$
$354$		0			0
$355$	−42.0178	+	24.2590i	−2.23007	+	1.28753i
$356$	2.13713			0.113268
$357$		0			0
$358$	−5.52635			−0.292077
$359$	14.8416	−	8.56882i	0.783311	−	0.452245i	−0.0542911	−	0.998525i	$-0.517290\pi$
$359$	14.8416	−	8.56882i	0.783311	−	0.452245i	0.837603	+	0.546280i	$0.183957\pi$
$360$		0			0
$361$	14.1402	−	24.4916i	0.744224	−	1.28903i
$362$	−0.824029	−	1.42726i	−0.0433100	−	0.0750151i
$363$		0			0
$364$	−12.8022	−	8.38475i	−0.671016	−	0.439480i
$365$		−	49.0037i		−	2.56497i
$366$		0			0
$367$	−17.8720	−	10.3184i	−0.932911	−	0.538616i	−0.0451800	−	0.998979i	$-0.514386\pi$
$367$	−17.8720	−	10.3184i	−0.932911	−	0.538616i	−0.887731	+	0.460362i	$0.847719\pi$
$368$	−2.08402	−	1.20321i	−0.108637	−	0.0627216i
$369$		0			0
$370$			34.9273i			1.81578i
$371$	6.02883	+	3.94857i	0.313001	+	0.205000i
$372$		0			0
$373$	1.52356	+	2.63889i	0.0788871	+	0.136637i	0.902770	−	0.430124i	$-0.141530\pi$
$373$	1.52356	+	2.63889i	0.0788871	+	0.136637i	−0.823883	+	0.566760i	$0.808197\pi$
$374$	0.655680	−	1.13567i	0.0339044	−	0.0587241i
$375$		0			0
$376$	10.3913	−	5.99941i	0.535890	−	0.309396i
$377$	−3.07093			−0.158161
$378$		0			0
$379$	27.5315			1.41420			0.707100	−	0.707113i	$-0.250003\pi$
$379$	27.5315			1.41420			0.707100	+	0.707113i	$0.250003\pi$
$380$	23.9705	−	13.8394i	1.22966	−	0.709944i
$381$		0			0
$382$	4.18599	−	7.25034i	0.214174	−	0.370960i
$383$	−7.25284	−	12.5623i	−0.370603	−	0.641903i	0.619055	−	0.785347i	$-0.287516\pi$
$383$	−7.25284	−	12.5623i	−0.370603	−	0.641903i	−0.989658	+	0.143444i	$0.954182\pi$
$384$		0			0
$385$	0.598720	−	10.6333i	0.0305136	−	0.541921i
$386$		−	0.763454i		−	0.0388588i
$387$		0			0
$388$	−13.3226	−	7.69179i	−0.676351	−	0.390492i
$389$	−6.36070	−	3.67235i	−0.322501	−	0.186196i	0.330006	−	0.943979i	$-0.392949\pi$
$389$	−6.36070	−	3.67235i	−0.322501	−	0.186196i	−0.652507	+	0.757783i	$0.726283\pi$
$390$		0			0
$391$			3.15568i			0.159590i
$392$	0.785798	−	6.95575i	0.0396888	−	0.351319i
$393$		0			0
$394$	−4.54104	−	7.86532i	−0.228774	−	0.396249i
$395$	22.9776	−	39.7983i	1.15613	−	2.00247i
$396$		0			0
$397$	19.2219	−	11.0977i	0.964717	−	0.556980i	0.0670957	−	0.997747i	$-0.478627\pi$
$397$	19.2219	−	11.0977i	0.964717	−	0.556980i	0.897622	+	0.440767i	$0.145293\pi$
$398$	14.1468			0.709114
$399$		0			0
$400$	11.2035			0.560177
$401$	−6.13684	+	3.54311i	−0.306459	+	0.176934i	−0.645341	−	0.763895i	$-0.723285\pi$
$401$	−6.13684	+	3.54311i	−0.306459	+	0.176934i	0.338882	+	0.940829i	$0.389951\pi$
$402$		0			0
$403$	−6.81959	+	11.8119i	−0.339708	+	0.588391i
$404$	−8.06738	−	13.9731i	−0.401367	−	0.695188i
$405$		0			0
$406$	−0.632839	−	1.25404i	−0.0314073	−	0.0622371i
$407$		−	8.67680i		−	0.430093i
$408$		0			0
$409$	15.2627	+	8.81191i	0.754691	+	0.435721i	0.827386	−	0.561633i	$-0.189827\pi$
$409$	15.2627	+	8.81191i	0.754691	+	0.435721i	−0.0726956	+	0.997354i	$0.523160\pi$
$410$	−18.3835	−	10.6137i	−0.907895	−	0.524173i
$411$		0			0
$412$			4.92650i			0.242711i
$413$	−2.41795	+	3.69181i	−0.118979	+	0.181662i
$414$		0			0
$415$	−26.5587	−	46.0010i	−1.30372	−	2.25810i
$416$	−2.89210	+	5.00927i	−0.141797	+	0.245600i
$417$		0			0
$418$	−5.95486	+	3.43804i	−0.291262	+	0.168160i
$419$	−33.7027			−1.64649			−0.823243	−	0.567689i	$-0.807838\pi$
$419$	−33.7027			−1.64649			−0.823243	+	0.567689i	$0.807838\pi$
$420$		0			0
$421$	37.1841			1.81224			0.906120	−	0.423020i	$-0.139030\pi$
$421$	37.1841			1.81224			0.906120	+	0.423020i	$0.139030\pi$
$422$	21.6162	−	12.4801i	1.05226	−	0.607522i
$423$		0			0
$424$	1.36196	−	2.35898i	0.0661425	−	0.114562i
$425$	−7.34593	−	12.7235i	−0.356330	−	0.617181i
$426$		0			0
$427$	−36.2344	+	18.2853i	−1.75351	+	0.884888i
$428$		−	6.31210i		−	0.305107i
$429$		0			0
$430$	2.23809	+	1.29216i	0.107930	+	0.0623135i
$431$	−16.0885	−	9.28867i	−0.774953	−	0.447420i	0.0596854	−	0.998217i	$-0.480990\pi$
$431$	−16.0885	−	9.28867i	−0.774953	−	0.447420i	−0.834639	+	0.550798i	$0.814324\pi$
$432$		0			0
$433$		−	32.4162i		−	1.55782i	−0.627135	−	0.778910i	$-0.715773\pi$
$433$		−	32.4162i		−	1.55782i	0.627135	−	0.778910i	$-0.284227\pi$
$434$	−6.22882	−	0.350722i	−0.298993	−	0.0168352i
$435$		0			0
$436$	−9.23197	−	15.9902i	−0.442131	−	0.765794i
$437$	8.27337	−	14.3299i	0.395769	−	0.685492i
$438$		0			0
$439$	−13.9271	+	8.04080i	−0.664703	+	0.383766i	−0.794067	−	0.607831i	$-0.792040\pi$
$439$	−13.9271	+	8.04080i	−0.664703	+	0.383766i	0.129364	+	0.991597i	$0.458707\pi$
$440$	−4.02536			−0.191902
$441$		0			0
$442$	7.58517			0.360790
$443$	−23.9276	+	13.8146i	−1.13683	+	0.656352i	−0.945645	−	0.325202i	$-0.894568\pi$
$443$	−23.9276	+	13.8146i	−1.13683	+	0.656352i	−0.191190	+	0.981553i	$0.561235\pi$
$444$		0			0
$445$	−4.30136	+	7.45018i	−0.203904	+	0.353172i
$446$	−0.730474	−	1.26522i	−0.0345889	−	0.0599098i
$447$		0			0
$448$	−2.64157	−	0.148737i	−0.124802	−	0.00702716i
$449$		−	33.3354i		−	1.57319i	−0.617467	−	0.786597i	$-0.711841\pi$
$449$		−	33.3354i		−	1.57319i	0.617467	−	0.786597i	$-0.288159\pi$
$450$		0			0
$451$	4.56691	+	2.63671i	0.215047	+	0.124158i
$452$	2.14719	+	1.23968i	0.100995	+	0.0583097i
$453$		0			0
$454$			20.9629i			0.983837i
$455$	54.9965	−	27.7534i	2.57827	−	1.30110i
$456$		0			0
$457$	−2.22365	−	3.85147i	−0.104018	−	0.180164i	0.809319	−	0.587370i	$-0.199837\pi$
$457$	−2.22365	−	3.85147i	−0.104018	−	0.180164i	−0.913337	+	0.407206i	$0.866503\pi$
$458$	−13.6072	+	23.5684i	−0.635824	+	1.10128i
$459$		0			0
$460$	8.38894	−	4.84335i	0.391136	−	0.225823i
$461$	−13.4101			−0.624570			−0.312285	−	0.949988i	$-0.601094\pi$
$461$	−13.4101			−0.624570			−0.312285	+	0.949988i	$0.601094\pi$
$462$		0			0
$463$	5.13394			0.238594			0.119297	−	0.992859i	$-0.461936\pi$
$463$	5.13394			0.238594			0.119297	+	0.992859i	$0.461936\pi$
$464$	−0.459787	+	0.265458i	−0.0213451	+	0.0123236i
$465$		0			0
$466$	−3.34955	+	5.80159i	−0.155165	+	0.268753i
$467$	6.89106	+	11.9357i	0.318880	+	0.552317i	0.980255	−	0.197739i	$-0.0633599\pi$
$467$	6.89106	+	11.9357i	0.318880	+	0.552317i	−0.661374	+	0.750056i	$0.730027\pi$
$468$		0			0
$469$	−8.95929	+	13.6794i	−0.413702	+	0.631656i
$470$			48.2996i			2.22789i
$471$		0			0
$472$	1.44455	+	0.834008i	0.0664906	+	0.0383884i
$473$	−0.555996	−	0.321005i	−0.0255647	−	0.0147598i
$474$		0			0
$475$			77.0364i			3.53467i
$476$	1.56311	+	3.09747i	0.0716448	+	0.141972i
$477$		0			0
$478$	6.89959	+	11.9504i	0.315580	+	0.546601i
$479$	−14.7319	+	25.5163i	−0.673116	+	1.16587i	0.303900	+	0.952704i	$0.401711\pi$
$479$	−14.7319	+	25.5163i	−0.673116	+	1.16587i	−0.977016	+	0.213167i	$0.931622\pi$
$480$		0			0
$481$	43.4645	−	25.0942i	1.98181	−	1.14420i
$482$	−17.4877			−0.796545
$483$		0			0
$484$	1.00000			0.0454545
$485$	53.6282	−	30.9622i	2.43513	−	1.40592i
$486$		0			0
$487$	11.0352	−	19.1135i	0.500053	−	0.866117i	−0.499947	−	0.866056i	$-0.666647\pi$
$487$	11.0352	−	19.1135i	0.500053	−	0.866117i	1.00000		6.08379e-5i	$-1.93653e-5\pi$
$488$	7.67018	+	13.2851i	0.347213	+	0.601390i
$489$		0			0
$490$	22.6667	+	16.7391i	1.02398	+	0.756193i
$491$			18.0771i			0.815810i	0.913024	+	0.407905i	$0.133741\pi$
$491$			18.0771i			0.815810i	−0.913024	+	0.407905i	$0.866259\pi$
$492$		0			0
$493$	0.602946	+	0.348111i	0.0271553	+	0.0156781i
$494$	−34.4442	−	19.8863i	−1.54972	−	0.894729i
$495$		0			0
$496$			2.35800i			0.105877i
$497$	−1.79274	+	31.8390i	−0.0804154	+	1.42818i
$498$		0			0
$499$	−0.368619	−	0.638467i	−0.0165017	−	0.0285817i	0.857657	−	0.514223i	$-0.171920\pi$
$499$	−0.368619	−	0.638467i	−0.0165017	−	0.0285817i	−0.874158	+	0.485641i	$0.838586\pi$
$500$	−12.4857	+	21.6259i	−0.558379	+	0.967141i
$501$		0			0
$502$	−8.98857	+	5.18955i	−0.401180	+	0.231621i
$503$	10.1774			0.453787			0.226894	−	0.973920i	$-0.427143\pi$
$503$	10.1774			0.453787			0.226894	+	0.973920i	$0.427143\pi$
$504$		0			0
$505$	64.9483			2.89016
$506$	−2.08402	+	1.20321i	−0.0926460	+	0.0534892i
$507$		0			0
$508$	−2.60415	+	4.51052i	−0.115540	+	0.200122i
$509$	2.35282	+	4.07520i	0.104287	+	0.180630i	0.913447	−	0.406959i	$-0.133411\pi$
$509$	2.35282	+	4.07520i	0.104287	+	0.180630i	−0.809160	+	0.587589i	$0.800077\pi$
$510$		0			0
$511$	−26.9441	−	17.6470i	−1.19194	−	0.780656i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−15.2923	−	8.82901i	−0.674514	−	0.389431i
$515$	−17.1741	−	9.91548i	−0.756782	−	0.436928i
$516$		0			0
$517$		−	11.9988i		−	0.527708i
$518$	19.2043	+	12.5778i	0.843790	+	0.552639i
$519$		0			0
$520$	−11.6418	−	20.1641i	−0.510525	−	0.884256i
$521$	3.19015	−	5.52550i	0.139763	−	0.242077i	−0.787644	−	0.616131i	$-0.788699\pi$
$521$	3.19015	−	5.52550i	0.139763	−	0.242077i	0.927407	+	0.374054i	$0.122033\pi$
$522$		0			0
$523$	−3.62477	+	2.09276i	−0.158500	+	0.0915101i	−0.577152	−	0.816637i	$-0.695836\pi$
$523$	−3.62477	+	2.09276i	−0.158500	+	0.0915101i	0.418652	+	0.908147i	$0.362503\pi$
$524$	−10.7861			−0.471192
$525$		0			0
$526$	3.03314			0.132251
$527$	2.67791	−	1.54609i	0.116652	−	0.0673489i
$528$		0			0
$529$	−8.60457	+	14.9036i	−0.374112	+	0.647981i
$530$	5.48237	+	9.49575i	0.238139	+	0.412469i
$531$		0			0
$532$	1.02273	−	18.1636i	0.0443409	−	0.787493i
$533$			30.5025i			1.32121i
$534$		0			0
$535$	22.0044	+	12.7042i	0.951333	+	0.549252i
$536$	5.35251	+	3.09028i	0.231193	+	0.133480i
$537$		0			0
$538$			4.85258i			0.209210i
$539$	−5.63096	−	4.15840i	−0.242543	−	0.179115i
$540$		0			0
$541$	0.177282	+	0.307061i	0.00762194	+	0.0132016i	0.869811	−	0.493385i	$-0.164241\pi$
$541$	0.177282	+	0.307061i	0.00762194	+	0.0132016i	−0.862189	+	0.506586i	$0.830907\pi$
$542$	1.47920	−	2.56205i	0.0635370	−	0.110049i
$543$		0			0
$544$	1.13567	−	0.655680i	0.0486915	−	0.0281120i
$545$	74.3240			3.18369
$546$		0			0
$547$	0.859833			0.0367638			0.0183819	−	0.999831i	$-0.494149\pi$
$547$	0.859833			0.0367638			0.0183819	+	0.999831i	$0.494149\pi$
$548$	−10.8079	+	6.23994i	−0.461690	+	0.266557i
$549$		0			0
$550$	5.60177	−	9.70255i	0.238860	−	0.413718i
$551$	−1.82531	−	3.16154i	−0.0777610	−	0.134686i
$552$		0			0
$553$	−13.6080	−	26.9659i	−0.578673	−	1.14671i
$554$			11.4834i			0.487885i
$555$		0			0
$556$	2.18105	+	1.25923i	0.0924971	+	0.0534032i
$557$	24.4683	+	14.1268i	1.03675	+	0.598570i	0.918912	−	0.394463i	$-0.129069\pi$
$557$	24.4683	+	14.1268i	1.03675	+	0.598570i	0.117841	+	0.993032i	$0.462403\pi$
$558$		0			0
$559$		−	3.71351i		−	0.157065i
$560$	5.83514	−	8.90932i	0.246580	−	0.376487i
$561$		0			0
$562$	−5.55567	−	9.62270i	−0.234352	−	0.405909i
$563$	−15.4121	+	26.6945i	−0.649542	+	1.12504i	0.333691	+	0.942683i	$0.391706\pi$
$563$	−15.4121	+	26.6945i	−0.649542	+	1.12504i	−0.983233	+	0.182356i	$0.941628\pi$
$564$		0			0
$565$	−8.64322	+	4.99017i	−0.363623	+	0.209938i
$566$	2.68104			0.112692
$567$		0			0
$568$	12.0531			0.505736
$569$	−36.9884	+	21.3553i	−1.55063	+	0.895259i	−0.552544	+	0.833484i	$0.686343\pi$
$569$	−36.9884	+	21.3553i	−1.55063	+	0.895259i	−0.998090	+	0.0617750i	$0.980324\pi$
$570$		0			0
$571$	−14.6945	+	25.4516i	−0.614946	+	1.06512i	0.375448	+	0.926844i	$0.377489\pi$
$571$	−14.6945	+	25.4516i	−0.614946	+	1.06512i	−0.990394	+	0.138274i	$0.955844\pi$
$572$	2.89210	+	5.00927i	0.120925	+	0.209448i
$573$		0			0
$574$	−12.4560	+	6.28577i	−0.519902	+	0.262363i
$575$			26.9604i			1.12433i
$576$		0			0
$577$	−8.27344	−	4.77667i	−0.344428	−	0.198855i	0.317801	−	0.948158i	$-0.397056\pi$
$577$	−8.27344	−	4.77667i	−0.344428	−	0.198855i	−0.662228	+	0.749302i	$0.730389\pi$
$578$	13.2332	+	7.64017i	0.550427	+	0.317789i
$579$		0			0
$580$		−	2.13713i		−	0.0887396i
$581$	−34.8573	−	1.96269i	−1.44612	−	0.0814260i
$582$		0			0
$583$	−1.36196	−	2.35898i	−0.0564066	−	0.0976990i
$584$	−6.08687	+	10.5428i	−0.251876	+	0.436263i
$585$		0			0
$586$	5.66052	−	3.26810i	0.233834	−	0.135004i
$587$	23.4420			0.967554			0.483777	−	0.875191i	$-0.339265\pi$
$587$	23.4420			0.967554			0.483777	+	0.875191i	$0.339265\pi$
$588$		0			0
$589$	−16.2138			−0.668079
$590$	−5.81482	+	3.35719i	−0.239392	+	0.138213i
$591$		0			0
$592$	4.33840	−	7.51433i	0.178307	−	0.308837i
$593$	−16.4622	−	28.5133i	−0.676020	−	1.17090i	−0.976170	−	0.217008i	$-0.930370\pi$
$593$	−16.4622	−	28.5133i	−0.676020	−	1.17090i	0.300150	−	0.953892i	$-0.402963\pi$
$594$		0			0
$595$	−13.9440	−	0.785137i	−0.571649	−	0.0321875i
$596$			9.81660i			0.402103i
$597$		0			0
$598$	−12.0544	−	6.95962i	−0.492941	−	0.284600i
$599$	10.2217	+	5.90150i	0.417647	+	0.241129i	0.694070	−	0.719907i	$-0.255816\pi$
$599$	10.2217	+	5.90150i	0.417647	+	0.241129i	−0.276423	+	0.961036i	$0.589149\pi$
$600$		0			0
$601$		−	13.5763i		−	0.553787i	−0.960901	−	0.276894i	$-0.910695\pi$
$601$		−	13.5763i		−	0.553787i	0.960901	−	0.276894i	$-0.0893050\pi$
$602$	1.51645	−	0.765258i	0.0618057	−	0.0311896i
$603$		0			0
$604$	4.77440	+	8.26951i	0.194268	+	0.336482i
$605$	−2.01268	+	3.48607i	−0.0818271	+	0.141729i
$606$		0			0
$607$	−19.1502	+	11.0563i	−0.777281	+	0.448763i	−0.835466	−	0.549543i	$-0.814802\pi$
$607$	−19.1502	+	11.0563i	−0.777281	+	0.448763i	0.0581850	+	0.998306i	$0.481469\pi$
$608$	−6.87608			−0.278862
$609$		0			0
$610$	−61.7505			−2.50021
$611$	60.1054	−	34.7018i	2.43160	−	1.40389i
$612$		0			0
$613$	−7.34271	+	12.7179i	−0.296569	+	0.513673i	−0.975349	−	0.220669i	$-0.929176\pi$
$613$	−7.34271	+	12.7179i	−0.296569	+	0.513673i	0.678780	+	0.734342i	$0.262509\pi$
$614$	16.9796	+	29.4095i	0.685241	+	1.18687i
$615$		0			0
$616$	−1.44959	+	2.21330i	−0.0584058	+	0.0891762i
$617$			25.4764i			1.02564i	0.858496	+	0.512821i	$0.171399\pi$
$617$			25.4764i			1.02564i	−0.858496	+	0.512821i	$0.828601\pi$
$618$		0			0
$619$	−17.6624	−	10.1974i	−0.709911	−	0.409868i	0.101117	−	0.994875i	$-0.467758\pi$
$619$	−17.6624	−	10.1974i	−0.709911	−	0.409868i	−0.811028	+	0.585007i	$0.801092\pi$
$620$	−8.22015	−	4.74591i	−0.330129	−	0.190600i
$621$		0			0
$622$		−	25.4135i		−	1.01899i
$623$	2.54740	+	5.04797i	0.102060	+	0.202243i
$624$		0			0
$625$	−22.2508	−	38.5394i	−0.890030	−	1.54158i
$626$	4.29605	−	7.44097i	0.171705	−	0.297401i
$627$		0			0
$628$	2.80476	−	1.61933i	0.111922	−	0.0646182i
$629$	−11.3784			−0.453687
$630$		0			0
$631$	30.6750			1.22115			0.610576	−	0.791957i	$-0.290938\pi$
$631$	30.6750			1.22115			0.610576	+	0.791957i	$0.290938\pi$
$632$	−9.88689	+	5.70820i	−0.393279	+	0.227060i
$633$		0			0
$634$	3.44009	−	5.95841i	0.136623	−	0.236639i
$635$	−10.4826	−	18.1565i	−0.415991	−	0.720517i
$636$		0			0
$637$	4.54522	−	40.2335i	0.180088	−	1.59411i
$638$			0.530917i			0.0210192i
$639$		0			0
$640$	−3.48607	−	2.01268i	−0.137799	−	0.0795582i
$641$	−19.4844	−	11.2493i	−0.769588	−	0.444322i	0.0631395	−	0.998005i	$-0.479889\pi$
$641$	−19.4844	−	11.2493i	−0.769588	−	0.444322i	−0.832728	+	0.553683i	$0.813222\pi$
$642$		0			0
$643$		−	35.8596i		−	1.41417i	−0.707131	−	0.707083i	$-0.750011\pi$
$643$		−	35.8596i		−	1.41417i	0.707131	−	0.707083i	$-0.249989\pi$
$644$	0.357924	−	6.35672i	0.0141042	−	0.250490i
$645$		0			0
$646$	4.50851	+	7.80896i	0.177385	+	0.307239i
$647$	−14.2048	+	24.6034i	−0.558448	+	0.967261i	0.439178	+	0.898400i	$0.355270\pi$
$647$	−14.2048	+	24.6034i	−0.558448	+	0.967261i	−0.997626	+	0.0688607i	$0.978064\pi$
$648$		0			0
$649$	1.44455	−	0.834008i	0.0567034	−	0.0327377i
$650$	64.8036			2.54181
$651$		0			0
$652$	−14.6821			−0.574995
$653$	−21.5088	+	12.4181i	−0.841703	+	0.485958i	−0.857843	−	0.513912i	$-0.828196\pi$
$653$	−21.5088	+	12.4181i	−0.841703	+	0.485958i	0.0161395	+	0.999870i	$0.494862\pi$
$654$		0			0
$655$	21.7089	−	37.6010i	0.848238	−	1.46919i
$656$	2.63671	+	4.56691i	0.102946	+	0.178308i
$657$		0			0
$658$	26.5569	+	17.3934i	1.03530	+	0.678066i
$659$		−	16.6910i		−	0.650190i	−0.945681	−	0.325095i	$-0.894604\pi$
$659$		−	16.6910i		−	0.650190i	0.945681	−	0.325095i	$-0.105396\pi$
$660$		0			0
$661$	26.7814	+	15.4622i	1.04167	+	0.601411i	0.920307	−	0.391197i	$-0.127939\pi$
$661$	26.7814	+	15.4622i	1.04167	+	0.601411i	0.121367	+	0.992608i	$0.461272\pi$
$662$	7.94279	+	4.58577i	0.308705	+	0.178231i
$663$		0			0
$664$			13.1957i			0.512092i
$665$	61.2612	+	40.1229i	2.37561	+	1.55590i
$666$		0			0
$667$	−0.638804	−	1.10644i	−0.0247346	−	0.0428416i
$668$	7.50620	−	13.0011i	0.290424	−	0.503028i
$669$		0			0
$670$	−21.5458	+	12.4395i	−0.832387	+	0.480579i
$671$	15.3404			0.592208
$672$		0			0
$673$	−28.4673			−1.09733			−0.548667	−	0.836041i	$-0.684865\pi$
$673$	−28.4673			−1.09733			−0.548667	+	0.836041i	$0.684865\pi$
$674$	10.6768	−	6.16427i	0.411256	−	0.237439i
$675$		0			0
$676$	−10.2285	+	17.7163i	−0.393405	+	0.681398i
$677$	−10.4406	−	18.0836i	−0.401264	−	0.695010i	0.592615	−	0.805486i	$-0.298096\pi$
$677$	−10.4406	−	18.0836i	−0.401264	−	0.695010i	−0.993879	+	0.110476i	$0.964762\pi$
$678$		0			0
$679$	2.28811	−	40.6368i	0.0878095	−	1.55950i
$680$			5.27869i			0.202429i
$681$		0			0
$682$	2.04209	+	1.17900i	0.0781957	+	0.0451463i
$683$	25.2149	+	14.5578i	0.964822	+	0.557040i	0.897654	−	0.440701i	$-0.145270\pi$
$683$	25.2149	+	14.5578i	0.964822	+	0.557040i	0.0671682	+	0.997742i	$0.478604\pi$
$684$		0			0
$685$		−	50.2360i		−	1.91942i
$686$	17.3664	−	6.43500i	0.663051	−	0.245689i
$687$		0			0
$688$	−0.321005	−	0.555996i	−0.0122382	−	0.0211972i
$689$	7.87785	−	13.6448i	0.300122	−	0.519827i
$690$		0			0
$691$	0.472662	−	0.272891i	0.0179809	−	0.0103813i	−0.490983	−	0.871169i	$-0.663362\pi$
$691$	0.472662	−	0.272891i	0.0179809	−	0.0103813i	0.508964	+	0.860788i	$0.330029\pi$
$692$	−7.50196			−0.285182
$693$		0			0
$694$	22.5812			0.857172
$695$	−8.77951	+	5.06885i	−0.333026	+	0.192272i
$696$		0			0
$697$	3.45767	−	5.98886i	0.130969	−	0.226844i
$698$	−11.6548	−	20.1867i	−0.441140	−	0.764076i
$699$		0			0
$700$	13.3543	+	26.4631i	0.504746	+	1.00021i
$701$			18.0854i			0.683076i	0.939868	+	0.341538i	$0.110948\pi$
$701$			18.0854i			0.683076i	−0.939868	+	0.341538i	$0.889052\pi$
$702$		0			0
$703$	51.6692	+	29.8312i	1.94874	+	1.12511i
$704$	0.866025	+	0.500000i	0.0326396	+	0.0188445i
$705$		0			0
$706$			16.3316i			0.614649i
$707$	23.3889	−	35.7110i	0.879628	−	1.34305i
$708$		0			0
$709$	12.5429	+	21.7249i	0.471058	+	0.815897i	0.999452	−	0.0331026i	$-0.0105388\pi$
$709$	12.5429	+	21.7249i	0.471058	+	0.815897i	−0.528394	+	0.848999i	$0.677205\pi$
$710$	−24.2590	+	42.0178i	−0.910424	+	1.57690i
$711$		0			0
$712$	1.85081	−	1.06857i	0.0693620	−	0.0400462i
$713$	−5.67434			−0.212506
$714$		0			0
$715$	−23.2835			−0.870755
$716$	−4.78596	+	2.76318i	−0.178860	+	0.103265i
$717$		0			0
$718$	8.56882	−	14.8416i	0.319786	−	0.553885i
$719$	4.50368	+	7.80060i	0.167959	+	0.290913i	0.937702	−	0.347440i	$-0.112949\pi$
$719$	4.50368	+	7.80060i	0.167959	+	0.290913i	−0.769743	+	0.638354i	$0.779616\pi$
$720$		0			0
$721$	−11.6366	+	5.87226i	−0.433368	+	0.218694i
$722$		−	28.2805i		−	1.05249i
$723$		0			0
$724$	−1.42726	−	0.824029i	−0.0530437	−	0.0306248i
$725$	5.15124	+	2.97407i	0.191312	+	0.110454i
$726$		0			0
$727$		−	4.52605i		−	0.167862i	−0.996472	−	0.0839309i	$-0.973253\pi$
$727$		−	4.52605i		−	0.167862i	0.996472	−	0.0839309i	$-0.0267475\pi$
$728$	−15.2794	−	0.860326i	−0.566291	−	0.0318858i
$729$		0			0
$730$	−24.5018	−	42.4384i	−0.906854	−	1.57072i
$731$	−0.420952	+	0.729111i	−0.0155695	+	0.0269671i
$732$		0			0
$733$	21.2535	−	12.2707i	0.785016	−	0.453229i	−0.0531893	−	0.998584i	$-0.516939\pi$
$733$	21.2535	−	12.2707i	0.785016	−	0.453229i	0.838205	+	0.545355i	$0.183605\pi$
$734$	−20.6368			−0.761719
$735$		0			0
$736$	−2.40642			−0.0887018
$737$	5.35251	−	3.09028i	0.197162	−	0.113832i
$738$		0			0
$739$	0.893650	−	1.54785i	0.0328735	−	0.0569385i	−0.849121	−	0.528199i	$-0.822867\pi$
$739$	0.893650	−	1.54785i	0.0328735	−	0.0569385i	0.881994	+	0.471261i	$0.156201\pi$
$740$	17.4636	+	30.2479i	0.641976	+	1.11194i
$741$		0			0
$742$	7.19541	+	0.405147i	0.264152	+	0.0148734i
$743$		−	18.8397i		−	0.691162i	−0.938389	−	0.345581i	$-0.887682\pi$
$743$		−	18.8397i		−	0.691162i	0.938389	−	0.345581i	$-0.112318\pi$
$744$		0			0
$745$	−34.2213	−	19.7577i	−1.25377	−	0.723865i
$746$	2.63889	+	1.52356i	0.0966166	+	0.0557816i
$747$		0			0
$748$		−	1.31136i		−	0.0479480i
$749$	14.9094	−	7.52386i	0.544777	−	0.274916i
$750$		0			0
$751$	13.2768	+	22.9961i	0.484478	+	0.839141i	0.999841	−	0.0178314i	$-0.00567621\pi$
$751$	13.2768	+	22.9961i	0.484478	+	0.839141i	−0.515363	+	0.856972i	$0.672343\pi$
$752$	5.99941	−	10.3913i	0.218776	−	0.378931i
$753$		0			0
$754$	−2.65951	+	1.53547i	−0.0968535	+	0.0559184i
$755$	−38.4374			−1.39888
$756$		0			0
$757$	−8.49203			−0.308648			−0.154324	−	0.988020i	$-0.549320\pi$
$757$	−8.49203			−0.308648			−0.154324	+	0.988020i	$0.549320\pi$
$758$	23.8430	−	13.7658i	0.866017	−	0.499995i
$759$		0			0
$760$	13.8394	−	23.9705i	0.502006	−	0.869500i
$761$	−21.5357	−	37.3010i	−0.780670	−	1.35216i	−0.931552	−	0.363608i	$-0.881545\pi$
$761$	−21.5357	−	37.3010i	−0.780670	−	1.35216i	0.150882	−	0.988552i	$-0.451789\pi$
$762$		0			0
$763$	26.7652	−	40.8662i	0.968966	−	1.47945i
$764$		−	8.37197i		−	0.302887i
$765$		0			0
$766$	−12.5623	−	7.25284i	−0.453894	−	0.262056i
$767$	8.35555	+	4.82408i	0.301701	+	0.174187i
$768$		0			0
$769$			14.9802i			0.540198i	0.962833	+	0.270099i	$0.0870565\pi$
$769$			14.9802i			0.540198i	−0.962833	+	0.270099i	$0.912944\pi$
$770$	−4.79812	−	9.50804i	−0.172912	−	0.342646i
$771$		0			0
$772$	−0.381727	−	0.661170i	−0.0137387	−	0.0237960i
$773$	−21.0099	+	36.3902i	−0.755673	+	1.30886i	0.189366	+	0.981907i	$0.439357\pi$
$773$	−21.0099	+	36.3902i	−0.755673	+	1.30886i	−0.945039	+	0.326958i	$0.893977\pi$
$774$		0			0
$775$	22.8786	−	13.2090i	0.821824	−	0.474481i
$776$	−15.3836			−0.552238
$777$		0			0
$778$	−7.34471			−0.263321
$779$	−31.4024	+	18.1302i	−1.12511	+	0.649582i
$780$		0			0
$781$	6.02654	−	10.4383i	0.215647	−	0.373511i
$782$	1.57784	+	2.73290i	0.0564234	+	0.0977283i
$783$		0			0
$784$	−2.79736	−	6.41676i	−0.0999056	−	0.229170i
$785$			13.0368i			0.465302i
$786$		0			0
$787$	5.31665	+	3.06957i	0.189518	+	0.109418i	0.591757	−	0.806116i	$-0.298435\pi$
$787$	5.31665	+	3.06957i	0.189518	+	0.109418i	−0.402239	+	0.915535i	$0.631768\pi$
$788$	−7.86532	−	4.54104i	−0.280190	−	0.161768i
$789$		0			0
$790$		−	45.9551i		−	1.63501i
$791$	−0.368773	+	6.54940i	−0.0131121	+	0.232870i
$792$		0			0
$793$	44.3659	+	76.8441i	1.57548	+	2.72881i
$794$	11.0977	−	19.2219i	0.393844	−	0.682158i
$795$		0			0
$796$	12.2515	−	7.07339i	0.434242	−	0.250710i
$797$	25.7793			0.913149			0.456575	−	0.889685i	$-0.349076\pi$
$797$	25.7793			0.913149			0.456575	+	0.889685i	$0.349076\pi$
$798$		0			0
$799$	−15.7348			−0.556656
$800$	9.70255	−	5.60177i	0.343037	−	0.198052i
$801$		0			0
$802$	−3.54311	+	6.13684i	−0.125111	+	0.216699i
$803$	6.08687	+	10.5428i	0.214801	+	0.372046i
$804$		0			0
$805$	21.4396	+	14.0418i	0.755645	+	0.494908i
$806$			13.6392i			0.480419i
$807$		0			0
$808$	−13.9731	−	8.06738i	−0.491572	−	0.283810i
$809$	48.4673	+	27.9826i	1.70402	+	0.983816i	0.941601	+	0.336731i	$0.109321\pi$
$809$	48.4673	+	27.9826i	1.70402	+	0.983816i	0.762418	+	0.647085i	$0.224012\pi$
$810$		0			0
$811$			43.6485i			1.53271i	0.642420	+	0.766353i	$0.277930\pi$
$811$			43.6485i			1.53271i	−0.642420	+	0.766353i	$0.722070\pi$
$812$	−1.17508	−	0.769613i	−0.0412371	−	0.0270081i
$813$		0			0
$814$	−4.33840	−	7.51433i	−0.152061	−	0.263377i
$815$	29.5503	−	51.1827i	1.03510	−	1.79285i
$816$		0			0
$817$	3.82307	−	2.20725i	0.133752	−	0.0772220i
$818$	17.6238			0.616202
$819$		0			0
$820$	−21.2274			−0.741293
$821$	−33.4917	+	19.3364i	−1.16887	+	0.674845i	−0.953413	−	0.301669i	$-0.902456\pi$
$821$	−33.4917	+	19.3364i	−1.16887	+	0.674845i	−0.215454	+	0.976514i	$0.569123\pi$
$822$		0			0
$823$	−1.08198	+	1.87405i	−0.0377156	+	0.0653253i	−0.884267	−	0.466982i	$-0.845341\pi$
$823$	−1.08198	+	1.87405i	−0.0377156	+	0.0653253i	0.846551	+	0.532307i	$0.178675\pi$
$824$	2.46325	+	4.26648i	0.0858114	+	0.148630i
$825$		0			0
$826$	−0.248096	+	4.40618i	−0.00863236	+	0.153311i
$827$			19.9185i			0.692633i	0.938118	+	0.346317i	$0.112568\pi$
$827$			19.9185i			0.692633i	−0.938118	+	0.346317i	$0.887432\pi$
$828$		0			0
$829$	36.2441	+	20.9255i	1.25881	+	0.726773i	0.972843	−	0.231467i	$-0.0743524\pi$
$829$	36.2441	+	20.9255i	1.25881	+	0.726773i	0.285965	+	0.958240i	$0.407686\pi$
$830$	−46.0010	−	26.5587i	−1.59672	−	0.921866i
$831$		0			0
$832$			5.78421i			0.200531i
$833$	−5.45315	+	7.38421i	−0.188941	+	0.255848i
$834$		0			0
$835$	30.2152	+	52.3342i	1.04564	+	1.81110i
$836$	−3.43804	+	5.95486i	−0.118907	+	0.205953i
$837$		0			0
$838$	−29.1874	+	16.8514i	−1.00826	+	0.582121i
$839$	−39.5351			−1.36490			−0.682452	−	0.730931i	$-0.739086\pi$
$839$	−39.5351			−1.36490			−0.682452	+	0.730931i	$0.739086\pi$
$840$		0			0
$841$	28.7181			0.990280
$842$	32.2023	−	18.5920i	1.10977	−	0.640724i
$843$		0			0
$844$	12.4801	−	21.6162i	0.429583	−	0.744059i
$845$	−41.1735	−	71.3147i	−1.41641	−	2.45330i
$846$		0			0
$847$	1.19197	+	2.36203i	0.0409567	+	0.0811604i
$848$		−	2.72392i		−	0.0935397i
$849$		0			0
$850$	−12.7235	−	7.34593i	−0.436413	−	0.251963i
$851$	18.0826	+	10.4400i	0.619865	+	0.357879i
$852$		0			0
$853$		−	17.9975i		−	0.616221i	−0.951351	−	0.308111i	$-0.900303\pi$
$853$		−	17.9975i		−	0.616221i	0.951351	−	0.308111i	$-0.0996967\pi$
$854$	−22.2373	+	33.9528i	−0.760945	+	1.16184i
$855$		0			0
$856$	−3.15605	−	5.46644i	−0.107872	−	0.186839i
$857$	2.78701	−	4.82725i	0.0952026	−	0.164896i	−0.814491	−	0.580177i	$-0.802983\pi$
$857$	2.78701	−	4.82725i	0.0952026	−	0.164896i	0.909693	+	0.415281i	$0.136317\pi$
$858$		0			0
$859$	38.7836	−	22.3917i	1.32328	−	0.763996i	0.339030	−	0.940776i	$-0.389901\pi$
$859$	38.7836	−	22.3917i	1.32328	−	0.763996i	0.984251	+	0.176779i	$0.0565679\pi$
$860$	2.58432			0.0881245
$861$		0			0
$862$	−18.5773			−0.632747
$863$	28.4143	−	16.4050i	0.967233	−	0.558432i	0.0688414	−	0.997628i	$-0.478070\pi$
$863$	28.4143	−	16.4050i	0.967233	−	0.558432i	0.898392	+	0.439195i	$0.144736\pi$
$864$		0			0
$865$	15.0991	−	26.1523i	0.513383	−	0.889206i
$866$	−16.2081	−	28.0732i	−0.550773	−	0.953967i
$867$		0			0
$868$	−5.56968	+	2.81068i	−0.189047	+	0.0954006i
$869$			11.4164i			0.387275i
$870$		0			0
$871$	30.9601	+	17.8748i	1.04904	+	0.605664i
$872$	−15.9902	−	9.23197i	−0.541498	−	0.312634i
$873$		0			0
$874$		−	16.5467i		−	0.559702i
$875$	−65.9638	−	3.71418i	−2.22998	−	0.125562i
$876$		0			0
$877$	−11.4322	−	19.8012i	−0.386039	−	0.668640i	0.605873	−	0.795561i	$-0.292824\pi$
$877$	−11.4322	−	19.8012i	−0.386039	−	0.668640i	−0.991913	+	0.126921i	$0.959490\pi$
$878$	−8.04080	+	13.9271i	−0.271364	+	0.470016i
$879$		0			0
$880$	−3.48607	+	2.01268i	−0.117515	+	0.0678475i
$881$	−38.3927			−1.29348			−0.646741	−	0.762709i	$-0.723869\pi$
$881$	−38.3927			−1.29348			−0.646741	+	0.762709i	$0.723869\pi$
$882$		0			0
$883$	9.23037			0.310627			0.155313	−	0.987865i	$-0.450361\pi$
$883$	9.23037			0.310627			0.155313	+	0.987865i	$0.450361\pi$
$884$	6.56895	−	3.79259i	0.220938	−	0.127559i
$885$		0			0
$886$	−13.8146	+	23.9276i	−0.464111	+	0.803863i
$887$	−15.6602	−	27.1243i	−0.525819	−	0.910744i	−0.999548	−	0.0300738i	$-0.990426\pi$
$887$	−15.6602	−	27.1243i	−0.525819	−	0.910744i	0.473729	−	0.880671i	$-0.342908\pi$
$888$		0			0
$889$	−13.7581	−	0.774666i	−0.461431	−	0.0259815i
$890$			8.60273i			0.288364i
$891$		0			0
$892$	−1.26522	−	0.730474i	−0.0423626	−	0.0244581i
$893$	71.4513	+	41.2524i	2.39103	+	1.38046i
$894$		0			0
$895$		−	22.2456i		−	0.743587i
$896$	−2.36203	+	1.19197i	−0.0789100	+	0.0398210i
$897$		0			0
$898$	−16.6677	−	28.8693i	−0.556208	−	0.963381i
$899$	−0.625951	+	1.08418i	−0.0208766	+	0.0361594i
$900$		0			0
$901$	−3.09347	+	1.78602i	−0.103058	+	0.0595008i
$902$	5.27341			0.175585
$903$		0			0
$904$	2.47936			0.0824624
$905$	5.74524	−	3.31701i	0.190978	−	0.110261i
$906$		0			0
$907$	9.99860	−	17.3181i	0.331998	−	0.575037i	−0.650905	−	0.759159i	$-0.725611\pi$
$907$	9.99860	−	17.3181i	0.331998	−	0.575037i	0.982904	+	0.184121i	$0.0589439\pi$
$908$	10.4814	+	18.1544i	0.347839	+	0.602475i
$909$		0			0
$910$	33.7517	−	51.5333i	1.11886	−	1.70831i
$911$			19.9413i			0.660683i	0.943861	+	0.330342i	$0.107164\pi$
$911$			19.9413i			0.660683i	−0.943861	+	0.330342i	$0.892836\pi$
$912$		0			0
$913$	11.4278	+	6.59784i	0.378205	+	0.218357i
$914$	−3.85147	−	2.22365i	−0.127395	−	0.0735517i
$915$		0			0
$916$			27.2145i			0.899191i
$917$	−12.8567	−	25.4771i	−0.424566	−	0.841327i
$918$		0			0
$919$	−11.2142	−	19.4235i	−0.369922	−	0.640723i	0.619631	−	0.784893i	$-0.287282\pi$
$919$	−11.2142	−	19.4235i	−0.369922	−	0.640723i	−0.989553	+	0.144170i	$0.953949\pi$
$920$	4.84335	−	8.38894i	0.159681	−	0.276575i
$921$		0			0
$922$	−11.6135	+	6.70505i	−0.382470	+	0.220819i
$923$	69.7175			2.29478
$924$		0			0
$925$	−97.2109			−3.19627
$926$	4.44612	−	2.56697i	0.146109	−	0.0843559i
$927$		0			0
$928$	−0.265458	+	0.459787i	−0.00871410	+	0.0150933i
$929$	−11.5137	−	19.9423i	−0.377752	−	0.654285i	0.612983	−	0.790096i	$-0.289969\pi$
$929$	−11.5137	−	19.9423i	−0.377752	−	0.654285i	−0.990735	+	0.135811i	$0.956636\pi$
$930$		0			0
$931$	44.1222	−	19.2349i	1.44605	−	0.630397i
$932$			6.69909i			0.219436i
$933$		0			0
$934$	11.9357	+	6.89106i	0.390547	+	0.225482i
$935$	4.57148	+	2.63935i	0.149503	+	0.0863159i
$936$		0			0
$937$			7.34940i			0.240095i	0.992768	+	0.120047i	$0.0383046\pi$
$937$			7.34940i			0.240095i	−0.992768	+	0.120047i	$0.961695\pi$
$938$	−0.919277	+	16.3263i	−0.0300155	+	0.533074i
$939$		0			0
$940$	24.1498	+	41.8287i	0.787680	+	1.36430i
$941$	−25.8829	+	44.8305i	−0.843758	+	1.46143i	0.0429374	+	0.999078i	$0.486328\pi$
$941$	−25.8829	+	44.8305i	−0.843758	+	1.46143i	−0.886695	+	0.462354i	$0.847005\pi$
$942$		0			0
$943$	−10.9899	+	6.34502i	−0.357880	+	0.206622i
$944$	1.66802			0.0542893
$945$		0			0
$946$	−0.642009			−0.0208735
$947$	40.8148	−	23.5644i	1.32630	−	0.765741i	0.341577	−	0.939854i	$-0.389039\pi$
$947$	40.8148	−	23.5644i	1.32630	−	0.765741i	0.984726	+	0.174113i	$0.0557057\pi$
$948$		0			0
$949$	−35.2077	+	60.9816i	−1.14289	+	1.97955i
$950$	38.5182	+	66.7155i	1.24970	+	2.16454i
$951$		0			0
$952$	2.90243	+	1.90094i	0.0940681	+	0.0616097i
$953$		−	37.8914i		−	1.22742i	−0.789530	−	0.613712i	$-0.789676\pi$
$953$		−	37.8914i		−	1.22742i	0.789530	−	0.613712i	$-0.210324\pi$
$954$		0			0
$955$	29.1852	+	16.8501i	0.944412	+	0.545257i
$956$	11.9504	+	6.89959i	0.386505	+	0.223149i
$957$		0			0
$958$			29.4637i			0.951930i
$959$	−27.6217	−	18.0907i	−0.891950	−	0.584181i
$960$		0			0
$961$	−12.7199	−	22.0315i	−0.410320	−	0.710695i
$962$	25.0942	−	43.4645i	0.809070	−	1.40135i
$963$		0			0
$964$	−15.1448	+	8.74387i	−0.487782	+	0.281621i
$965$	3.07318			0.0989291
$966$		0			0
$967$	−20.4529			−0.657722			−0.328861	−	0.944378i	$-0.606665\pi$
$967$	−20.4529			−0.657722			−0.328861	+	0.944378i	$0.606665\pi$
$968$	0.866025	−	0.500000i	0.0278351	−	0.0160706i
$969$		0			0
$970$	30.9622	−	53.6282i	0.994138	−	1.72190i
$971$	10.3951	+	18.0049i	0.333596	+	0.577804i	0.983214	−	0.182456i	$-0.0584047\pi$
$971$	10.3951	+	18.0049i	0.333596	+	0.577804i	−0.649619	+	0.760260i	$0.725071\pi$
$972$		0			0
$973$	−0.374588	+	6.65268i	−0.0120087	+	0.213275i
$974$		−	22.0704i		−	0.707181i
$975$		0			0
$976$	13.2851	+	7.67018i	0.425247	+	0.245517i
$977$	44.7812	+	25.8544i	1.43268	+	0.827156i	0.997324	−	0.0731040i	$-0.0232905\pi$
$977$	44.7812	+	25.8544i	1.43268	+	0.827156i	0.435352	+	0.900260i	$0.356624\pi$
$978$		0			0
$979$		−	2.13713i		−	0.0683030i
$980$	27.9994	+	3.16312i	0.894409	+	0.101042i
$981$		0			0
$982$	9.03857	+	15.6553i	0.288432	+	0.499580i
$983$	10.5074	−	18.1994i	0.335135	−	0.580470i	−0.648376	−	0.761320i	$-0.724551\pi$
$983$	10.5074	−	18.1994i	0.335135	−	0.580470i	0.983511	+	0.180850i	$0.0578848\pi$
$984$		0			0
$985$	31.6607	−	18.2793i	1.00879	−	0.582428i
$986$	0.696222			0.0221722
$987$		0			0
$988$	−39.7727			−1.26534
$989$	1.33796	−	0.772472i	0.0425447	−	0.0245632i
$990$		0			0
$991$	−6.56437	+	11.3698i	−0.208524	+	0.361174i	−0.951250	−	0.308421i	$-0.900199\pi$
$991$	−6.56437	+	11.3698i	−0.208524	+	0.361174i	0.742726	+	0.669596i	$0.233533\pi$
$992$	1.17900	+	2.04209i	0.0374333	+	0.0648364i
$993$		0			0
$994$	14.3670	+	28.4698i	0.455692	+	0.903006i
$995$			56.9459i			1.80531i
$996$		0			0
$997$	4.72079	+	2.72555i	0.149509	+	0.0863190i	0.572888	−	0.819633i	$-0.305823\pi$
$997$	4.72079	+	2.72555i	0.149509	+	0.0863190i	−0.423379	+	0.905953i	$0.639156\pi$
$998$	−0.638467	−	0.368619i	−0.0202103	−	0.0116684i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.r.d.1277.7	yes	24
3.2	odd	2	inner	1386.2.r.d.1277.6	yes	24
7.5	odd	6	inner	1386.2.r.d.89.6	✓	24
21.5	even	6	inner	1386.2.r.d.89.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.r.d.89.6	✓	24	7.5	odd	6	inner
1386.2.r.d.89.7	yes	24	21.5	even	6	inner
1386.2.r.d.1277.6	yes	24	3.2	odd	2	inner
1386.2.r.d.1277.7	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.01268 + 3.48607i) q^{5} +(2.64157 + 0.148737i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.01268 + 3.48607i) q^{5} +(2.64157 + 0.148737i) q^{7} -1.00000i q^{8} +(3.48607 + 2.01268i) q^{10} +(-0.866025 - 0.500000i) q^{11} -5.78421i q^{13} +(2.36203 - 1.19197i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.655680 + 1.13567i) q^{17} +(5.95486 - 3.43804i) q^{19} +4.02536 q^{20} -1.00000 q^{22} +(2.08402 - 1.20321i) q^{23} +(-5.60177 + 9.70255i) q^{25} +(-2.89210 - 5.00927i) q^{26} +(1.44959 - 2.21330i) q^{28} -0.530917i q^{29} +(-2.04209 - 1.17900i) q^{31} +(-0.866025 - 0.500000i) q^{32} +1.31136i q^{34} +(4.79812 + 9.50804i) q^{35} +(4.33840 + 7.51433i) q^{37} +(3.43804 - 5.95486i) q^{38} +(3.48607 - 2.01268i) q^{40} -5.27341 q^{41} +0.642009 q^{43} +(-0.866025 + 0.500000i) q^{44} +(1.20321 - 2.08402i) q^{46} +(5.99941 + 10.3913i) q^{47} +(6.95575 + 0.785798i) q^{49} +11.2035i q^{50} +(-5.00927 - 2.89210i) q^{52} +(2.35898 + 1.36196i) q^{53} -4.02536i q^{55} +(0.148737 - 2.64157i) q^{56} +(-0.265458 - 0.459787i) q^{58} +(-0.834008 + 1.44455i) q^{59} +(-13.2851 + 7.67018i) q^{61} -2.35800 q^{62} -1.00000 q^{64} +(20.1641 - 11.6418i) q^{65} +(-3.09028 + 5.35251i) q^{67} +(0.655680 + 1.13567i) q^{68} +(8.90932 + 5.83514i) q^{70} +12.0531i q^{71} +(-10.5428 - 6.08687i) q^{73} +(7.51433 + 4.33840i) q^{74} -6.87608i q^{76} +(-2.21330 - 1.44959i) q^{77} +(-5.70820 - 9.88689i) q^{79} +(2.01268 - 3.48607i) q^{80} +(-4.56691 + 2.63671i) q^{82} -13.1957 q^{83} -5.27869 q^{85} +(0.555996 - 0.321005i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(1.06857 + 1.85081i) q^{89} +(0.860326 - 15.2794i) q^{91} -2.40642i q^{92} +(10.3913 + 5.99941i) q^{94} +(23.9705 + 13.8394i) q^{95} -15.3836i q^{97} +(6.41676 - 2.79736i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) \) 24 * q + 12 * q^4 + 8 * q^7	\( 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) \) 24 * q + 12 * q^4 + 8 * q^7 - 12 * q^16 + 12 * q^19 - 24 * q^22 + 4 * q^25 + 4 * q^28 + 20 * q^37 + 24 * q^43 + 12 * q^46 + 40 * q^49 - 28 * q^58 - 120 * q^61 - 24 * q^64 - 32 * q^67 + 48 * q^70 - 48 * q^73 - 64 * q^79 - 48 * q^82 + 32 * q^85 - 12 * q^88 + 56 * q^91 + 60 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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