LMFDB - Embedded newform 128.3.h.a.79.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(15,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("128.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.h (of order $8$, degree $4$, 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:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			79.5
Character	$\chi$	$=$	128.79
Dual form			128.3.h.a.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10785 + 2.67458i) q^{3} +(2.95565 - 7.13556i) q^{5} +(4.18452 - 4.18452i) q^{7} +(0.437918 - 0.437918i) q^{9} +O(q^{10})$	\(q+(1.10785 + 2.67458i) q^{3} +(2.95565 - 7.13556i) q^{5} +(4.18452 - 4.18452i) q^{7} +(0.437918 - 0.437918i) q^{9} +(-1.42655 + 3.44399i) q^{11} +(8.39996 + 20.2793i) q^{13} +22.3590 q^{15} -1.73115i q^{17} +(-14.2459 + 5.90085i) q^{19} +(15.8276 + 6.55601i) q^{21} +(-15.1565 - 15.1565i) q^{23} +(-24.5027 - 24.5027i) q^{25} +(25.7276 + 10.6567i) q^{27} +(-6.74107 + 2.79224i) q^{29} -31.1695i q^{31} -10.7916 q^{33} +(-17.4909 - 42.2268i) q^{35} +(5.30038 - 12.7962i) q^{37} +(-44.9327 + 44.9327i) q^{39} +(-18.5776 + 18.5776i) q^{41} +(-31.0691 + 75.0074i) q^{43} +(-1.83046 - 4.41911i) q^{45} +16.2824 q^{47} +13.9797i q^{49} +(4.63009 - 1.91784i) q^{51} +(-29.0670 - 12.0399i) q^{53} +(20.3584 + 20.3584i) q^{55} +(-31.5646 - 31.5646i) q^{57} +(-34.1002 - 14.1248i) q^{59} +(-68.7647 + 28.4833i) q^{61} -3.66495i q^{63} +169.531 q^{65} +(-10.5147 - 25.3846i) q^{67} +(23.7462 - 57.3284i) q^{69} +(32.2012 - 32.2012i) q^{71} +(-28.5494 + 28.5494i) q^{73} +(38.3891 - 92.6796i) q^{75} +(8.44203 + 20.3809i) q^{77} -22.4049 q^{79} +75.0427i q^{81} +(123.286 - 51.0669i) q^{83} +(-12.3527 - 5.11665i) q^{85} +(-14.9361 - 14.9361i) q^{87} +(61.0281 + 61.0281i) q^{89} +(120.009 + 49.7093i) q^{91} +(83.3652 - 34.5310i) q^{93} +119.093i q^{95} -69.9064 q^{97} +(0.883474 + 2.13290i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.10785	+	2.67458i	0.369282	+	0.891526i	0.993868	+	0.110570i	$0.0352677\pi$
$3$	1.10785	+	2.67458i	0.369282	+	0.891526i	−0.624586	+	0.780956i	$0.714732\pi$
$4$		0			0
$5$	2.95565	−	7.13556i	0.591129	−	1.42711i	−0.291284	−	0.956637i	$-0.594083\pi$
$5$	2.95565	−	7.13556i	0.591129	−	1.42711i	0.882413	−	0.470475i	$-0.155917\pi$
$6$		0			0
$7$	4.18452	−	4.18452i	0.597788	−	0.597788i	−0.341935	−	0.939723i	$-0.611082\pi$
$7$	4.18452	−	4.18452i	0.597788	−	0.597788i	0.939723	+	0.341935i	$0.111082\pi$
$8$		0			0
$9$	0.437918	−	0.437918i	0.0486575	−	0.0486575i
$10$		0			0
$11$	−1.42655	+	3.44399i	−0.129686	+	0.313090i	−0.975363	−	0.220605i	$-0.929197\pi$
$11$	−1.42655	+	3.44399i	−0.129686	+	0.313090i	0.845677	+	0.533695i	$0.179197\pi$
$12$		0			0
$13$	8.39996	+	20.2793i	0.646151	+	1.55995i	0.818247	+	0.574866i	$0.194946\pi$
$13$	8.39996	+	20.2793i	0.646151	+	1.55995i	−0.172096	+	0.985080i	$0.555054\pi$
$14$		0			0
$15$	22.3590			1.49060
$16$		0			0
$17$		−	1.73115i		−	0.101832i	−0.998703	−	0.0509161i	$-0.983786\pi$
$17$		−	1.73115i		−	0.101832i	0.998703	−	0.0509161i	$-0.0162141\pi$
$18$		0			0
$19$	−14.2459	+	5.90085i	−0.749785	+	0.310571i	−0.724654	−	0.689113i	$-0.758000\pi$
$19$	−14.2459	+	5.90085i	−0.749785	+	0.310571i	−0.0251314	+	0.999684i	$0.508000\pi$
$20$		0			0
$21$	15.8276	+	6.55601i	0.753696	+	0.312191i
$22$		0			0
$23$	−15.1565	−	15.1565i	−0.658979	−	0.658979i	0.296159	−	0.955139i	$-0.404294\pi$
$23$	−15.1565	−	15.1565i	−0.658979	−	0.658979i	−0.955139	+	0.296159i	$0.904294\pi$
$24$		0			0
$25$	−24.5027	−	24.5027i	−0.980107	−	0.980107i
$26$		0			0
$27$	25.7276	+	10.6567i	0.952874	+	0.394693i
$28$		0			0
$29$	−6.74107	+	2.79224i	−0.232451	+	0.0962842i	−0.495869	−	0.868398i	$-0.665150\pi$
$29$	−6.74107	+	2.79224i	−0.232451	+	0.0962842i	0.263418	+	0.964682i	$0.415150\pi$
$30$		0			0
$31$		−	31.1695i		−	1.00547i	−0.864442	−	0.502733i	$-0.832328\pi$
$31$		−	31.1695i		−	1.00547i	0.864442	−	0.502733i	$-0.167672\pi$
$32$		0			0
$33$	−10.7916			−0.327019
$34$		0			0
$35$	−17.4909	−	42.2268i	−0.499740	−	1.20648i
$36$		0			0
$37$	5.30038	−	12.7962i	0.143253	−	0.345844i	−0.835926	−	0.548843i	$-0.815069\pi$
$37$	5.30038	−	12.7962i	0.143253	−	0.345844i	0.979179	+	0.202998i	$0.0650686\pi$
$38$		0			0
$39$	−44.9327	+	44.9327i	−1.15212	+	1.15212i
$40$		0			0
$41$	−18.5776	+	18.5776i	−0.453111	+	0.453111i	−0.896386	−	0.443275i	$-0.853817\pi$
$41$	−18.5776	+	18.5776i	−0.453111	+	0.453111i	0.443275	+	0.896386i	$0.353817\pi$
$42$		0			0
$43$	−31.0691	+	75.0074i	−0.722537	+	1.74436i	−0.0565443	+	0.998400i	$0.518008\pi$
$43$	−31.0691	+	75.0074i	−0.722537	+	1.74436i	−0.665993	+	0.745958i	$0.731992\pi$
$44$		0			0
$45$	−1.83046	−	4.41911i	−0.0406768	−	0.0982026i
$46$		0			0
$47$	16.2824			0.346435			0.173217	−	0.984884i	$-0.444584\pi$
$47$	16.2824			0.346435			0.173217	+	0.984884i	$0.444584\pi$
$48$		0			0
$49$			13.9797i			0.285299i
$50$		0			0
$51$	4.63009	−	1.91784i	0.0907860	−	0.0376048i
$52$		0			0
$53$	−29.0670	−	12.0399i	−0.548434	−	0.227169i	0.0912216	−	0.995831i	$-0.470923\pi$
$53$	−29.0670	−	12.0399i	−0.548434	−	0.227169i	−0.639655	+	0.768662i	$0.720923\pi$
$54$		0			0
$55$	20.3584	+	20.3584i	0.370153	+	0.370153i
$56$		0			0
$57$	−31.5646	−	31.5646i	−0.553765	−	0.553765i
$58$		0			0
$59$	−34.1002	−	14.1248i	−0.577969	−	0.239403i	0.0744962	−	0.997221i	$-0.476265\pi$
$59$	−34.1002	−	14.1248i	−0.577969	−	0.239403i	−0.652465	+	0.757819i	$0.726265\pi$
$60$		0			0
$61$	−68.7647	+	28.4833i	−1.12729	+	0.466939i	−0.866859	−	0.498553i	$-0.833865\pi$
$61$	−68.7647	+	28.4833i	−1.12729	+	0.466939i	−0.260432	+	0.965492i	$0.583865\pi$
$62$		0			0
$63$		−	3.66495i		−	0.0581737i
$64$		0			0
$65$	169.531			2.60818
$66$		0			0
$67$	−10.5147	−	25.3846i	−0.156935	−	0.378875i	0.825782	−	0.563990i	$-0.190734\pi$
$67$	−10.5147	−	25.3846i	−0.156935	−	0.378875i	−0.982717	+	0.185115i	$0.940734\pi$
$68$		0			0
$69$	23.7462	−	57.3284i	0.344148	−	0.830847i
$70$		0			0
$71$	32.2012	−	32.2012i	0.453538	−	0.453538i	−0.442989	−	0.896527i	$-0.646082\pi$
$71$	32.2012	−	32.2012i	0.453538	−	0.453538i	0.896527	+	0.442989i	$0.146082\pi$
$72$		0			0
$73$	−28.5494	+	28.5494i	−0.391088	+	0.391088i	−0.875075	−	0.483987i	$-0.839188\pi$
$73$	−28.5494	+	28.5494i	−0.391088	+	0.391088i	0.483987	+	0.875075i	$0.339188\pi$
$74$		0			0
$75$	38.3891	−	92.6796i	0.511855	−	1.23573i
$76$		0			0
$77$	8.44203	+	20.3809i	0.109637	+	0.264686i
$78$		0			0
$79$	−22.4049			−0.283606			−0.141803	−	0.989895i	$-0.545290\pi$
$79$	−22.4049			−0.283606			−0.141803	+	0.989895i	$0.545290\pi$
$80$		0			0
$81$			75.0427i			0.926453i
$82$		0			0
$83$	123.286	−	51.0669i	1.48538	−	0.615264i	0.515073	−	0.857146i	$-0.327765\pi$
$83$	123.286	−	51.0669i	1.48538	−	0.615264i	0.970306	+	0.241882i	$0.0777648\pi$
$84$		0			0
$85$	−12.3527	−	5.11665i	−0.145326	−	0.0601959i
$86$		0			0
$87$	−14.9361	−	14.9361i	−0.171680	−	0.171680i
$88$		0			0
$89$	61.0281	+	61.0281i	0.685709	+	0.685709i	0.961280	−	0.275572i	$-0.0888672\pi$
$89$	61.0281	+	61.0281i	0.685709	+	0.685709i	−0.275572	+	0.961280i	$0.588867\pi$
$90$		0			0
$91$	120.009	+	49.7093i	1.31878	+	0.546256i
$92$		0			0
$93$	83.3652	−	34.5310i	0.896400	−	0.371301i
$94$		0			0
$95$			119.093i			1.25362i
$96$		0			0
$97$	−69.9064			−0.720684			−0.360342	−	0.932820i	$-0.617340\pi$
$97$	−69.9064			−0.720684			−0.360342	+	0.932820i	$0.617340\pi$
$98$		0			0
$99$	0.883474	+	2.13290i	0.00892398	+	0.0215444i
$100$		0			0
$101$	−10.4825	+	25.3069i	−0.103787	+	0.250564i	−0.967239	−	0.253867i	$-0.918298\pi$
$101$	−10.4825	+	25.3069i	−0.103787	+	0.250564i	0.863452	+	0.504431i	$0.168298\pi$
$102$		0			0
$103$	−116.721	+	116.721i	−1.13322	+	1.13322i	−0.143579	+	0.989639i	$0.545861\pi$
$103$	−116.721	+	116.721i	−1.13322	+	1.13322i	−0.989639	+	0.143579i	$0.954139\pi$
$104$		0			0
$105$	93.5616	−	93.5616i	0.891063	−	0.891063i
$106$		0			0
$107$	21.6236	−	52.2039i	0.202090	−	0.487887i	−0.790047	−	0.613046i	$-0.789944\pi$
$107$	21.6236	−	52.2039i	0.202090	−	0.487887i	0.992137	+	0.125159i	$0.0399440\pi$
$108$		0			0
$109$	−28.8284	−	69.5980i	−0.264481	−	0.638514i	0.734725	−	0.678366i	$-0.237311\pi$
$109$	−28.8284	−	69.5980i	−0.264481	−	0.638514i	−0.999206	+	0.0398518i	$0.987311\pi$
$110$		0			0
$111$	40.0965			0.361230
$112$		0			0
$113$		−	130.141i		−	1.15169i	−0.817559	−	0.575845i	$-0.804673\pi$
$113$		−	130.141i		−	1.15169i	0.817559	−	0.575845i	$-0.195327\pi$
$114$		0			0
$115$	−152.948	+	63.3530i	−1.32998	+	0.550895i
$116$		0			0
$117$	12.5592	+	5.20217i	0.107343	+	0.0444630i
$118$		0			0
$119$	−7.24401	−	7.24401i	−0.0608740	−	0.0608740i
$120$		0			0
$121$	75.7339	+	75.7339i	0.625900	+	0.625900i
$122$		0			0
$123$	−70.2682	−	29.1060i	−0.571286	−	0.236635i
$124$		0			0
$125$	−68.8726	+	28.5280i	−0.550981	+	0.228224i
$126$		0			0
$127$		−	56.3580i		−	0.443764i	−0.975074	−	0.221882i	$-0.928780\pi$
$127$		−	56.3580i		−	0.443764i	0.975074	−	0.221882i	$-0.0712200\pi$
$128$		0			0
$129$	−235.033			−1.82196
$130$		0			0
$131$	39.2631	+	94.7895i	0.299718	+	0.723584i	0.999953	+	0.00967128i	$0.00307851\pi$
$131$	39.2631	+	94.7895i	0.299718	+	0.723584i	−0.700235	+	0.713912i	$0.746921\pi$
$132$		0			0
$133$	−34.9201	+	84.3045i	−0.262557	+	0.633868i
$134$		0			0
$135$	152.083	−	152.083i	1.12654	−	1.12654i
$136$		0			0
$137$	62.6423	−	62.6423i	0.457243	−	0.457243i	−0.440506	−	0.897750i	$-0.645201\pi$
$137$	62.6423	−	62.6423i	0.457243	−	0.457243i	0.897750	+	0.440506i	$0.145201\pi$
$138$		0			0
$139$	−11.6343	+	28.0877i	−0.0837000	+	0.202070i	−0.960188	−	0.279353i	$-0.909880\pi$
$139$	−11.6343	+	28.0877i	−0.0837000	+	0.202070i	0.876488	+	0.481423i	$0.159880\pi$
$140$		0			0
$141$	18.0384	+	43.5487i	0.127932	+	0.308856i
$142$		0			0
$143$	−81.8247			−0.572201
$144$		0			0
$145$			56.3542i			0.388649i
$146$		0			0
$147$	−37.3897	+	15.4873i	−0.254352	+	0.105356i
$148$		0			0
$149$	−52.6977	−	21.8281i	−0.353676	−	0.146497i	0.198770	−	0.980046i	$-0.436305\pi$
$149$	−52.6977	−	21.8281i	−0.353676	−	0.146497i	−0.552446	+	0.833549i	$0.686305\pi$
$150$		0			0
$151$	48.5998	+	48.5998i	0.321853	+	0.321853i	0.849478	−	0.527625i	$-0.176917\pi$
$151$	48.5998	+	48.5998i	0.321853	+	0.321853i	−0.527625	+	0.849478i	$0.676917\pi$
$152$		0			0
$153$	−0.758099	−	0.758099i	−0.00495490	−	0.00495490i
$154$		0			0
$155$	−222.412	−	92.1259i	−1.43491	−	0.594361i
$156$		0			0
$157$	121.622	−	50.3774i	0.774661	−	0.320875i	0.0399023	−	0.999204i	$-0.487295\pi$
$157$	121.622	−	50.3774i	0.774661	−	0.320875i	0.734759	+	0.678328i	$0.237295\pi$
$158$		0			0
$159$		−	91.0803i		−	0.572832i
$160$		0			0
$161$	−126.845			−0.787860
$162$		0			0
$163$	13.0161	+	31.4236i	0.0798533	+	0.192783i	0.958764	−	0.284203i	$-0.0917291\pi$
$163$	13.0161	+	31.4236i	0.0798533	+	0.192783i	−0.878911	+	0.476986i	$0.841729\pi$
$164$		0			0
$165$	−31.8962	+	77.0043i	−0.193310	+	0.466692i
$166$		0			0
$167$	138.734	−	138.734i	0.830744	−	0.830744i	−0.156875	−	0.987619i	$-0.550142\pi$
$167$	138.734	−	138.734i	0.830744	−	0.830744i	0.987619	+	0.156875i	$0.0501419\pi$
$168$		0			0
$169$	−221.190	+	221.190i	−1.30881	+	1.30881i
$170$		0			0
$171$	−3.65445	+	8.82263i	−0.0213711	+	0.0515943i
$172$		0			0
$173$	−69.7574	−	168.409i	−0.403222	−	0.973464i	−0.986879	−	0.161464i	$-0.948379\pi$
$173$	−69.7574	−	168.409i	−0.403222	−	0.973464i	0.583656	−	0.812001i	$-0.301621\pi$
$174$		0			0
$175$	−205.064			−1.17179
$176$		0			0
$177$		−	106.852i		−	0.603682i
$178$		0			0
$179$	−45.0027	+	18.6407i	−0.251411	+	0.104138i	−0.504830	−	0.863219i	$-0.668445\pi$
$179$	−45.0027	+	18.6407i	−0.251411	+	0.104138i	0.253419	+	0.967357i	$0.418445\pi$
$180$		0			0
$181$	118.928	+	49.2615i	0.657060	+	0.272163i	0.686201	−	0.727412i	$-0.259277\pi$
$181$	118.928	+	49.2615i	0.657060	+	0.272163i	−0.0291408	+	0.999575i	$0.509277\pi$
$182$		0			0
$183$	−152.362	−	152.362i	−0.832577	−	0.832577i
$184$		0			0
$185$	−75.6423	−	75.6423i	−0.408877	−	0.408877i
$186$		0			0
$187$	5.96206	+	2.46956i	0.0318827	+	0.0132062i
$188$		0			0
$189$	152.251	−	63.0643i	0.805559	−	0.333674i
$190$		0			0
$191$			179.282i			0.938649i	0.883026	+	0.469325i	$0.155503\pi$
$191$			179.282i			0.938649i	−0.883026	+	0.469325i	$0.844497\pi$
$192$		0			0
$193$	179.924			0.932249			0.466125	−	0.884719i	$-0.345650\pi$
$193$	179.924			0.932249			0.466125	+	0.884719i	$0.345650\pi$
$194$		0			0
$195$	187.815	+	453.425i	0.963153	+	2.32526i
$196$		0			0
$197$	−93.2938	+	225.231i	−0.473573	+	1.14331i	0.489000	+	0.872284i	$0.337362\pi$
$197$	−93.2938	+	225.231i	−0.473573	+	1.14331i	−0.962573	+	0.271022i	$0.912638\pi$
$198$		0			0
$199$	131.782	−	131.782i	0.662220	−	0.662220i	−0.293683	−	0.955903i	$-0.594881\pi$
$199$	131.782	−	131.782i	0.662220	−	0.662220i	0.955903	+	0.293683i	$0.0948810\pi$
$200$		0			0
$201$	56.2446	−	56.2446i	0.279824	−	0.279824i
$202$		0			0
$203$	−16.5239	+	39.8923i	−0.0813987	+	0.196514i
$204$		0			0
$205$	77.6526	+	187.470i	0.378793	+	0.914487i
$206$		0			0
$207$	−13.2746			−0.0641286
$208$		0			0
$209$		−	57.4807i		−	0.275027i
$210$		0			0
$211$	182.694	−	75.6743i	0.865848	−	0.358646i	0.0948559	−	0.995491i	$-0.469761\pi$
$211$	182.694	−	75.6743i	0.865848	−	0.358646i	0.770992	+	0.636845i	$0.219761\pi$
$212$		0			0
$213$	121.799	+	50.4506i	0.571824	+	0.236857i
$214$		0			0
$215$	443.391	+	443.391i	2.06228	+	2.06228i
$216$		0			0
$217$	−130.429	−	130.429i	−0.601056	−	0.601056i
$218$		0			0
$219$	−107.986	−	44.7293i	−0.493087	−	0.204243i
$220$		0			0
$221$	35.1064	−	14.5416i	0.158853	−	0.0657989i
$222$		0			0
$223$		−	175.414i		−	0.786612i	−0.919408	−	0.393306i	$-0.871331\pi$
$223$		−	175.414i		−	0.786612i	0.919408	−	0.393306i	$-0.128669\pi$
$224$		0			0
$225$	−21.4603			−0.0953792
$226$		0			0
$227$	−157.825	−	381.024i	−0.695265	−	1.67852i	−0.733893	−	0.679265i	$-0.762299\pi$
$227$	−157.825	−	381.024i	−0.695265	−	1.67852i	0.0386277	−	0.999254i	$-0.487701\pi$
$228$		0			0
$229$	57.0597	−	137.754i	0.249169	−	0.601547i	−0.748965	−	0.662610i	$-0.769449\pi$
$229$	57.0597	−	137.754i	0.249169	−	0.601547i	0.998134	+	0.0610623i	$0.0194488\pi$
$230$		0			0
$231$	−45.1577	+	45.1577i	−0.195488	+	0.195488i
$232$		0			0
$233$	275.512	−	275.512i	1.18246	−	1.18246i	0.203349	−	0.979106i	$-0.434817\pi$
$233$	275.512	−	275.512i	1.18246	−	1.18246i	0.979106	−	0.203349i	$-0.0651826\pi$
$234$		0			0
$235$	48.1251	−	116.184i	0.204788	−	0.494401i
$236$		0			0
$237$	−24.8212	−	59.9236i	−0.104731	−	0.252842i
$238$		0			0
$239$	63.0374			0.263755			0.131877	−	0.991266i	$-0.457899\pi$
$239$	63.0374			0.263755			0.131877	+	0.991266i	$0.457899\pi$
$240$		0			0
$241$		−	194.368i		−	0.806507i	−0.915088	−	0.403253i	$-0.867879\pi$
$241$		−	194.368i		−	0.806507i	0.915088	−	0.403253i	$-0.132121\pi$
$242$		0			0
$243$	30.8408	−	12.7747i	0.126917	−	0.0525708i
$244$		0			0
$245$	99.7526	+	41.3189i	0.407154	+	0.168649i
$246$		0			0
$247$	−239.330	−	239.330i	−0.968949	−	0.968949i
$248$		0			0
$249$	273.165	+	273.165i	1.09705	+	1.09705i
$250$		0			0
$251$	317.091	+	131.343i	1.26331	+	0.523281i	0.910924	−	0.412574i	$-0.135370\pi$
$251$	317.091	+	131.343i	1.26331	+	0.523281i	0.352387	+	0.935854i	$0.385370\pi$
$252$		0			0
$253$	73.8205	−	30.5774i	0.291781	−	0.120859i
$254$		0			0
$255$		−	38.7067i		−	0.151791i
$256$		0			0
$257$	−180.756			−0.703330			−0.351665	−	0.936126i	$-0.614384\pi$
$257$	−180.756			−0.703330			−0.351665	+	0.936126i	$0.614384\pi$
$258$		0			0
$259$	−31.3666	−	75.7256i	−0.121106	−	0.292377i
$260$		0			0
$261$	−1.72926	+	4.17480i	−0.00662552	+	0.0159954i
$262$		0			0
$263$	−266.626	+	266.626i	−1.01379	+	1.01379i	−0.0138830	+	0.999904i	$0.504419\pi$
$263$	−266.626	+	266.626i	−1.01379	+	1.01379i	−0.999904	+	0.0138830i	$0.995581\pi$
$264$		0			0
$265$	−171.823	+	171.823i	−0.648390	+	0.648390i
$266$		0			0
$267$	−95.6146	+	230.834i	−0.358107	+	0.864547i
$268$		0			0
$269$	−156.911	−	378.816i	−0.583311	−	1.40824i	−0.889794	−	0.456362i	$-0.849152\pi$
$269$	−156.911	−	378.816i	−0.583311	−	1.40824i	0.306483	−	0.951876i	$-0.400848\pi$
$270$		0			0
$271$	323.931			1.19532			0.597659	−	0.801750i	$-0.296098\pi$
$271$	323.931			1.19532			0.597659	+	0.801750i	$0.296098\pi$
$272$		0			0
$273$			376.043i			1.37745i
$274$		0			0
$275$	119.341	−	49.4328i	0.433969	−	0.179756i
$276$		0			0
$277$	−289.883	−	120.073i	−1.04651	−	0.433478i	−0.207864	−	0.978158i	$-0.566651\pi$
$277$	−289.883	−	120.073i	−1.04651	−	0.433478i	−0.838644	+	0.544680i	$0.816651\pi$
$278$		0			0
$279$	−13.6497	−	13.6497i	−0.0489235	−	0.0489235i
$280$		0			0
$281$	297.826	+	297.826i	1.05988	+	1.05988i	0.998089	+	0.0617901i	$0.0196809\pi$
$281$	297.826	+	297.826i	1.05988	+	1.05988i	0.0617901	+	0.998089i	$0.480319\pi$
$282$		0			0
$283$	132.389	+	54.8372i	0.467804	+	0.193771i	0.604118	−	0.796895i	$-0.293526\pi$
$283$	132.389	+	54.8372i	0.467804	+	0.193771i	−0.136314	+	0.990666i	$0.543526\pi$
$284$		0			0
$285$	−318.525	+	131.937i	−1.11763	+	0.462938i
$286$		0			0
$287$			155.476i			0.541729i
$288$		0			0
$289$	286.003			0.989630
$290$		0			0
$291$	−77.4455	−	186.970i	−0.266136	−	0.642509i
$292$		0			0
$293$	18.1180	−	43.7407i	0.0618361	−	0.149286i	−0.889941	−	0.456075i	$-0.849255\pi$
$293$	18.1180	−	43.7407i	0.0618361	−	0.149286i	0.951777	+	0.306790i	$0.0992548\pi$
$294$		0			0
$295$	−201.576	+	201.576i	−0.683309	+	0.683309i
$296$		0			0
$297$	−73.4033	+	73.4033i	−0.247149	+	0.247149i
$298$		0			0
$299$	180.050	−	434.678i	0.602172	−	1.45377i
$300$		0			0
$301$	183.861	+	443.879i	0.610833	+	1.47468i
$302$		0			0
$303$	−79.2984			−0.261711
$304$		0			0
$305$			574.861i			1.88479i
$306$		0			0
$307$	−532.332	+	220.499i	−1.73398	+	0.718239i	−0.734779	+	0.678307i	$0.762714\pi$
$307$	−532.332	+	220.499i	−1.73398	+	0.718239i	−0.999202	+	0.0399320i	$0.987286\pi$
$308$		0			0
$309$	−441.490	−	182.871i	−1.42877	−	0.591816i
$310$		0			0
$311$	−383.582	−	383.582i	−1.23338	−	1.23338i	−0.962657	−	0.270725i	$-0.912737\pi$
$311$	−383.582	−	383.582i	−1.23338	−	1.23338i	−0.270725	−	0.962657i	$-0.587263\pi$
$312$		0			0
$313$	−362.165	−	362.165i	−1.15708	−	1.15708i	−0.985101	−	0.171974i	$-0.944985\pi$
$313$	−362.165	−	362.165i	−1.15708	−	1.15708i	−0.171974	−	0.985101i	$-0.555015\pi$
$314$		0			0
$315$	−26.1514	−	10.8323i	−0.0830204	−	0.0343882i
$316$		0			0
$317$	−487.277	+	201.837i	−1.53715	+	0.636709i	−0.980936	−	0.194329i	$-0.937747\pi$
$317$	−487.277	+	201.837i	−1.53715	+	0.636709i	−0.556215	+	0.831038i	$0.687747\pi$
$318$		0			0
$319$		−	27.1995i		−	0.0852648i
$320$		0			0
$321$	163.579			0.509592
$322$		0			0
$323$	10.2152	+	24.6618i	0.0316261	+	0.0763523i
$324$		0			0
$325$	291.076	−	702.719i	0.895618	−	2.16221i
$326$		0			0
$327$	154.208	−	154.208i	0.471584	−	0.471584i
$328$		0			0
$329$	68.1341	−	68.1341i	0.207095	−	0.207095i
$330$		0			0
$331$	−20.5475	+	49.6062i	−0.0620772	+	0.149868i	−0.951874	−	0.306489i	$-0.900846\pi$
$331$	−20.5475	+	49.6062i	−0.0620772	+	0.149868i	0.889797	+	0.456356i	$0.150846\pi$
$332$		0			0
$333$	−3.28257	−	7.92483i	−0.00985757	−	0.0237983i
$334$		0			0
$335$	−212.211			−0.633466
$336$		0			0
$337$		−	627.680i		−	1.86255i	−0.364315	−	0.931276i	$-0.618697\pi$
$337$		−	627.680i		−	1.86255i	0.364315	−	0.931276i	$-0.381303\pi$
$338$		0			0
$339$	348.072	−	144.176i	1.02676	−	0.425299i
$340$		0			0
$341$	107.347	+	44.4648i	0.314802	+	0.130395i
$342$		0			0
$343$	263.539	+	263.539i	0.768336	+	0.768336i
$344$		0			0
$345$	−338.885	−	338.885i	−0.982275	−	0.982275i
$346$		0			0
$347$	−320.625	−	132.807i	−0.923992	−	0.382730i	−0.130596	−	0.991436i	$-0.541689\pi$
$347$	−320.625	−	132.807i	−0.923992	−	0.382730i	−0.793396	+	0.608706i	$0.791689\pi$
$348$		0			0
$349$	14.5498	−	6.02674i	0.0416901	−	0.0172686i	−0.361741	−	0.932279i	$-0.617818\pi$
$349$	14.5498	−	6.02674i	0.0416901	−	0.0172686i	0.403431	+	0.915010i	$0.367818\pi$
$350$		0			0
$351$			611.254i			1.74146i
$352$		0			0
$353$	283.828			0.804045			0.402023	−	0.915630i	$-0.368307\pi$
$353$	283.828			0.804045			0.402023	+	0.915630i	$0.368307\pi$
$354$		0			0
$355$	−134.598	−	324.949i	−0.379150	−	0.915349i
$356$		0			0
$357$	11.3494	−	27.3999i	0.0317911	−	0.0767505i
$358$		0			0
$359$	−388.417	+	388.417i	−1.08194	+	1.08194i	−0.0856121	+	0.996329i	$0.527285\pi$
$359$	−388.417	+	388.417i	−1.08194	+	1.08194i	−0.996329	+	0.0856121i	$0.972715\pi$
$360$		0			0
$361$	−87.1393	+	87.1393i	−0.241383	+	0.241383i
$362$		0			0
$363$	−118.655	+	286.458i	−0.326872	+	0.789140i
$364$		0			0
$365$	119.334	+	288.098i	0.326943	+	0.789309i
$366$		0			0
$367$	529.617			1.44310			0.721548	−	0.692364i	$-0.243431\pi$
$367$	529.617			1.44310			0.721548	+	0.692364i	$0.243431\pi$
$368$		0			0
$369$			16.2709i			0.0440945i
$370$		0			0
$371$	−172.013	+	71.2499i	−0.463646	+	0.192048i
$372$		0			0
$373$	−36.8515	−	15.2644i	−0.0987975	−	0.0409233i	0.332737	−	0.943020i	$-0.392028\pi$
$373$	−36.8515	−	15.2644i	−0.0987975	−	0.0409233i	−0.431535	+	0.902096i	$0.642028\pi$
$374$		0			0
$375$	−152.601	−	152.601i	−0.406935	−	0.406935i
$376$		0			0
$377$	−113.249	−	113.249i	−0.300396	−	0.300396i
$378$		0			0
$379$	463.955	+	192.176i	1.22415	+	0.507061i	0.898728	−	0.438506i	$-0.144492\pi$
$379$	463.955	+	192.176i	1.22415	+	0.507061i	0.325426	+	0.945567i	$0.394492\pi$
$380$		0			0
$381$	150.734	−	62.4361i	0.395627	−	0.163874i
$382$		0			0
$383$		−	304.650i		−	0.795432i	−0.917509	−	0.397716i	$-0.869803\pi$
$383$		−	304.650i		−	0.795432i	0.917509	−	0.397716i	$-0.130197\pi$
$384$		0			0
$385$	170.380			0.442547
$386$		0			0
$387$	19.2414	+	46.4528i	0.0497193	+	0.120033i
$388$		0			0
$389$	−72.6039	+	175.281i	−0.186642	+	0.450594i	−0.989309	−	0.145833i	$-0.953414\pi$
$389$	−72.6039	+	175.281i	−0.186642	+	0.450594i	0.802667	+	0.596428i	$0.203414\pi$
$390$		0			0
$391$	−26.2382	+	26.2382i	−0.0671053	+	0.0671053i
$392$		0			0
$393$	−210.024	+	210.024i	−0.534413	+	0.534413i
$394$		0			0
$395$	−66.2209	+	159.871i	−0.167648	+	0.404737i
$396$		0			0
$397$	79.4405	+	191.786i	0.200102	+	0.483089i	0.991796	−	0.127829i	$-0.0408007\pi$
$397$	79.4405	+	191.786i	0.200102	+	0.483089i	−0.791694	+	0.610917i	$0.790801\pi$
$398$		0			0
$399$	−264.165			−0.662068
$400$		0			0
$401$			58.9969i			0.147124i	0.997291	+	0.0735622i	$0.0234368\pi$
$401$			58.9969i			0.147124i	−0.997291	+	0.0735622i	$0.976563\pi$
$402$		0			0
$403$	632.095	−	261.822i	1.56847	−	0.649683i
$404$		0			0
$405$	535.471	+	221.800i	1.32215	+	0.547653i
$406$		0			0
$407$	36.5089	+	36.5089i	0.0897025	+	0.0897025i
$408$		0			0
$409$	110.309	+	110.309i	0.269704	+	0.269704i	0.828981	−	0.559277i	$-0.188921\pi$
$409$	110.309	+	110.309i	0.269704	+	0.269704i	−0.559277	+	0.828981i	$0.688921\pi$
$410$		0			0
$411$	236.940	+	98.1437i	0.576496	+	0.238792i
$412$		0			0
$413$	−201.798	+	83.5875i	−0.488615	+	0.202391i
$414$		0			0
$415$		−	1030.65i		−	2.48350i
$416$		0			0
$417$	−88.0117			−0.211059
$418$		0			0
$419$	−4.61960	−	11.1527i	−0.0110253	−	0.0266174i	0.918271	−	0.395952i	$-0.129585\pi$
$419$	−4.61960	−	11.1527i	−0.0110253	−	0.0266174i	−0.929296	+	0.369335i	$0.879585\pi$
$420$		0			0
$421$	32.5432	−	78.5662i	0.0772998	−	0.186618i	−0.880506	−	0.474036i	$-0.842797\pi$
$421$	32.5432	−	78.5662i	0.0772998	−	0.186618i	0.957805	+	0.287418i	$0.0927967\pi$
$422$		0			0
$423$	7.13037	−	7.13037i	0.0168567	−	0.0168567i
$424$		0			0
$425$	−42.4177	+	42.4177i	−0.0998064	+	0.0998064i
$426$		0			0
$427$	−168.558	+	406.936i	−0.394750	+	0.953012i
$428$		0			0
$429$	−90.6492	−	218.847i	−0.211304	−	0.510132i
$430$		0			0
$431$	201.982			0.468636			0.234318	−	0.972160i	$-0.424714\pi$
$431$	201.982			0.468636			0.234318	+	0.972160i	$0.424714\pi$
$432$		0			0
$433$			643.404i			1.48592i	0.669334	+	0.742961i	$0.266579\pi$
$433$			643.404i			1.48592i	−0.669334	+	0.742961i	$0.733421\pi$
$434$		0			0
$435$	−150.724	+	62.4318i	−0.346491	+	0.143521i
$436$		0			0
$437$	305.355	+	126.482i	0.698753	+	0.289433i
$438$		0			0
$439$	218.953	+	218.953i	0.498753	+	0.498753i	0.911050	−	0.412296i	$-0.135273\pi$
$439$	218.953	+	218.953i	0.498753	+	0.498753i	−0.412296	+	0.911050i	$0.635273\pi$
$440$		0			0
$441$	6.12194	+	6.12194i	0.0138819	+	0.0138819i
$442$		0			0
$443$	−275.767	−	114.227i	−0.622499	−	0.257848i	0.0490630	−	0.998796i	$-0.484376\pi$
$443$	−275.767	−	114.227i	−0.622499	−	0.257848i	−0.671562	+	0.740948i	$0.734376\pi$
$444$		0			0
$445$	615.847	−	255.092i	1.38392	−	0.573240i
$446$		0			0
$447$		−	165.126i		−	0.369410i
$448$		0			0
$449$	−264.162			−0.588334			−0.294167	−	0.955754i	$-0.595042\pi$
$449$	−264.162			−0.588334			−0.294167	+	0.955754i	$0.595042\pi$
$450$		0			0
$451$	−37.4792	−	90.4828i	−0.0831024	−	0.200627i
$452$		0			0
$453$	−76.1428	+	183.825i	−0.168086	+	0.405795i
$454$		0			0
$455$	709.407	−	709.407i	1.55914	−	1.55914i
$456$		0			0
$457$	324.484	−	324.484i	0.710030	−	0.710030i	−0.256511	−	0.966541i	$-0.582573\pi$
$457$	324.484	−	324.484i	0.710030	−	0.710030i	0.966541	+	0.256511i	$0.0825731\pi$
$458$		0			0
$459$	18.4483	−	44.5382i	0.0401925	−	0.0970332i
$460$		0			0
$461$	−46.5472	−	112.375i	−0.100970	−	0.243763i	0.865320	−	0.501220i	$-0.167115\pi$
$461$	−46.5472	−	112.375i	−0.100970	−	0.243763i	−0.966290	+	0.257457i	$0.917115\pi$
$462$		0			0
$463$	602.217			1.30069			0.650343	−	0.759641i	$-0.274625\pi$
$463$	602.217			1.30069			0.650343	+	0.759641i	$0.274625\pi$
$464$		0			0
$465$		−	696.918i		−	1.49875i
$466$		0			0
$467$	−327.171	+	135.519i	−0.700580	+	0.290190i	−0.704400	−	0.709803i	$-0.748784\pi$
$467$	−327.171	+	135.519i	−0.700580	+	0.290190i	0.00382006	+	0.999993i	$0.498784\pi$
$468$		0			0
$469$	−150.221	−	62.2237i	−0.320301	−	0.132673i
$470$		0			0
$471$	269.477	+	269.477i	0.572137	+	0.572137i
$472$		0			0
$473$	−214.003	−	214.003i	−0.452439	−	0.452439i
$474$		0			0
$475$	493.650	+	204.477i	1.03926	+	0.430477i
$476$		0			0
$477$	−18.0014	+	7.45644i	−0.0377389	+	0.0156320i
$478$		0			0
$479$			151.023i			0.315289i	0.987496	+	0.157644i	$0.0503900\pi$
$479$			151.023i			0.315289i	−0.987496	+	0.157644i	$0.949610\pi$
$480$		0			0
$481$	304.022			0.632062
$482$		0			0
$483$	−140.525	−	339.258i	−0.290943	−	0.702398i
$484$		0			0
$485$	−206.618	+	498.821i	−0.426017	+	1.02850i
$486$		0			0
$487$	−382.894	+	382.894i	−0.786231	+	0.786231i	−0.980874	−	0.194643i	$-0.937645\pi$
$487$	−382.894	+	382.894i	−0.786231	+	0.786231i	0.194643	+	0.980874i	$0.437645\pi$
$488$		0			0
$489$	−69.6251	+	69.6251i	−0.142383	+	0.142383i
$490$		0			0
$491$	−205.776	+	496.786i	−0.419095	+	1.01178i	0.563516	+	0.826105i	$0.309448\pi$
$491$	−205.776	+	496.786i	−0.419095	+	1.01178i	−0.982610	+	0.185679i	$0.940552\pi$
$492$		0			0
$493$	4.83378	+	11.6698i	0.00980483	+	0.0236709i
$494$		0			0
$495$	17.8306			0.0360215
$496$		0			0
$497$		−	269.493i		−	0.542239i
$498$		0			0
$499$	−604.867	+	250.544i	−1.21216	+	0.502093i	−0.894909	−	0.446249i	$-0.852760\pi$
$499$	−604.867	+	250.544i	−1.21216	+	0.502093i	−0.317250	+	0.948342i	$0.602760\pi$
$500$		0			0
$501$	524.752	+	217.359i	1.04741	+	0.433851i
$502$		0			0
$503$	−324.203	−	324.203i	−0.644539	−	0.644539i	0.307129	−	0.951668i	$-0.400632\pi$
$503$	−324.203	−	324.203i	−0.644539	−	0.644539i	−0.951668	+	0.307129i	$0.900632\pi$
$504$		0			0
$505$	149.597	+	149.597i	0.296231	+	0.296231i
$506$		0			0
$507$	−836.633	−	346.545i	−1.65016	−	0.683521i
$508$		0			0
$509$	734.614	−	304.287i	1.44325	−	0.597813i	0.482666	−	0.875805i	$-0.339669\pi$
$509$	734.614	−	304.287i	1.44325	−	0.597813i	0.960584	+	0.277991i	$0.0896686\pi$
$510$		0			0
$511$			238.931i			0.467575i
$512$		0			0
$513$	−429.397			−0.837031
$514$		0			0
$515$	487.886	+	1177.86i	0.947351	+	2.28711i
$516$		0			0
$517$	−23.2277	+	56.0766i	−0.0449278	+	0.108465i
$518$		0			0
$519$	373.143	−	373.143i	0.718966	−	0.718966i
$520$		0			0
$521$	−16.7805	+	16.7805i	−0.0322082	+	0.0322082i	−0.723027	−	0.690819i	$-0.757250\pi$
$521$	−16.7805	+	16.7805i	−0.0322082	+	0.0322082i	0.690819	+	0.723027i	$0.257250\pi$
$522$		0			0
$523$	250.400	−	604.519i	0.478776	−	1.15587i	−0.481407	−	0.876497i	$-0.659874\pi$
$523$	250.400	−	604.519i	0.478776	−	1.15587i	0.960183	−	0.279371i	$-0.0901259\pi$
$524$		0			0
$525$	−227.179	−	548.459i	−0.432722	−	1.04468i
$526$		0			0
$527$	−53.9589			−0.102389
$528$		0			0
$529$		−	69.5595i		−	0.131492i
$530$		0			0
$531$	−21.1185	+	8.74759i	−0.0397713	+	0.0164738i
$532$		0			0
$533$	−532.791	−	220.689i	−0.999607	−	0.414051i
$534$		0			0
$535$	−308.593	−	308.593i	−0.576809	−	0.576809i
$536$		0			0
$537$	−99.7121	−	99.7121i	−0.185684	−	0.185684i
$538$		0			0
$539$	−48.1458	−	19.9427i	−0.0893244	−	0.0369994i
$540$		0			0
$541$	−870.996	+	360.778i	−1.60997	+	0.666873i	−0.992781	−	0.119939i	$-0.961730\pi$
$541$	−870.996	+	360.778i	−1.60997	+	0.666873i	−0.617192	+	0.786812i	$0.711730\pi$
$542$		0			0
$543$			372.656i			0.686291i
$544$		0			0
$545$	−581.827			−1.06757
$546$		0			0
$547$	−36.1835	−	87.3546i	−0.0661489	−	0.159698i	0.887348	−	0.461100i	$-0.152545\pi$
$547$	−36.1835	−	87.3546i	−0.0661489	−	0.159698i	−0.953497	+	0.301403i	$0.902545\pi$
$548$		0			0
$549$	−17.6400	+	42.5866i	−0.0321311	+	0.0775713i
$550$		0			0
$551$	79.5561	−	79.5561i	0.144385	−	0.144385i
$552$		0			0
$553$	−93.7536	+	93.7536i	−0.169536	+	0.169536i
$554$		0			0
$555$	118.511	−	286.111i	0.213534	−	0.515516i
$556$		0			0
$557$	288.342	+	696.118i	0.517669	+	1.24976i	0.939332	+	0.343010i	$0.111447\pi$
$557$	288.342	+	696.118i	0.517669	+	1.24976i	−0.421663	+	0.906753i	$0.638553\pi$
$558$		0			0
$559$	−1782.08			−3.18797
$560$		0			0
$561$			18.6819i			0.0333010i
$562$		0			0
$563$	609.320	−	252.389i	1.08227	−	0.448293i	0.230968	−	0.972961i	$-0.425811\pi$
$563$	609.320	−	252.389i	1.08227	−	0.448293i	0.851306	+	0.524669i	$0.175811\pi$
$564$		0			0
$565$	−928.629	−	384.651i	−1.64359	−	0.680797i
$566$		0			0
$567$	314.017	+	314.017i	0.553822	+	0.553822i
$568$		0			0
$569$	256.311	+	256.311i	0.450459	+	0.450459i	0.895507	−	0.445047i	$-0.146813\pi$
$569$	256.311	+	256.311i	0.450459	+	0.450459i	−0.445047	+	0.895507i	$0.646813\pi$
$570$		0			0
$571$	−346.136	−	143.374i	−0.606193	−	0.251094i	0.0584066	−	0.998293i	$-0.481398\pi$
$571$	−346.136	−	143.374i	−0.606193	−	0.251094i	−0.664600	+	0.747199i	$0.731398\pi$
$572$		0			0
$573$	−479.504	+	198.617i	−0.836830	+	0.346626i
$574$		0			0
$575$			742.751i			1.29174i
$576$		0			0
$577$	−354.659			−0.614661			−0.307330	−	0.951603i	$-0.599436\pi$
$577$	−354.659			−0.614661			−0.307330	+	0.951603i	$0.599436\pi$
$578$		0			0
$579$	199.328	+	481.221i	0.344263	+	0.831124i
$580$		0			0
$581$	302.204	−	729.584i	0.520144	−	1.25574i
$582$		0			0
$583$	82.9309	−	82.9309i	0.142249	−	0.142249i
$584$		0			0
$585$	74.2408	−	74.2408i	0.126907	−	0.126907i
$586$		0			0
$587$	230.018	−	555.312i	0.391853	−	0.946018i	−0.597683	−	0.801733i	$-0.703912\pi$
$587$	230.018	−	555.312i	0.391853	−	0.946018i	0.989536	−	0.144285i	$-0.0460882\pi$
$588$		0			0
$589$	183.926	+	444.038i	0.312269	+	0.753884i
$590$		0			0
$591$	−705.754			−1.19417
$592$		0			0
$593$			458.661i			0.773460i	0.922193	+	0.386730i	$0.126395\pi$
$593$			458.661i			0.773460i	−0.922193	+	0.386730i	$0.873605\pi$
$594$		0			0
$595$	−73.1008	+	30.2793i	−0.122858	+	0.0508896i
$596$		0			0
$597$	498.454	+	206.467i	0.834932	+	0.345840i
$598$		0			0
$599$	−265.583	−	265.583i	−0.443377	−	0.443377i	0.449768	−	0.893145i	$-0.351507\pi$
$599$	−265.583	−	265.583i	−0.443377	−	0.443377i	−0.893145	+	0.449768i	$0.851507\pi$
$600$		0			0
$601$	466.600	+	466.600i	0.776373	+	0.776373i	0.979212	−	0.202839i	$-0.0650168\pi$
$601$	466.600	+	466.600i	0.776373	+	0.776373i	−0.202839	+	0.979212i	$0.565017\pi$
$602$		0			0
$603$	−15.7209	−	6.51182i	−0.0260712	−	0.0107990i
$604$		0			0
$605$	764.246	−	316.561i	1.26322	−	0.523241i
$606$		0			0
$607$			90.4302i			0.148979i	0.997222	+	0.0744894i	$0.0237327\pi$
$607$			90.4302i			0.148979i	−0.997222	+	0.0744894i	$0.976267\pi$
$608$		0			0
$609$	−125.001			−0.205256
$610$		0			0
$611$	136.772	+	330.197i	0.223849	+	0.540420i
$612$		0			0
$613$	63.5389	−	153.397i	0.103652	−	0.250239i	−0.863542	−	0.504277i	$-0.831759\pi$
$613$	63.5389	−	153.397i	0.103652	−	0.250239i	0.967194	+	0.254038i	$0.0817589\pi$
$614$		0			0
$615$	−415.376	+	415.376i	−0.675408	+	0.675408i
$616$		0			0
$617$	181.842	−	181.842i	0.294720	−	0.294720i	−0.544221	−	0.838942i	$-0.683175\pi$
$617$	181.842	−	181.842i	0.294720	−	0.294720i	0.838942	+	0.544221i	$0.183175\pi$
$618$		0			0
$619$	388.636	−	938.250i	0.627844	−	1.51575i	−0.214451	−	0.976735i	$-0.568796\pi$
$619$	388.636	−	938.250i	0.627844	−	1.51575i	0.842296	−	0.539016i	$-0.181204\pi$
$620$		0			0
$621$	−228.422	−	551.460i	−0.367829	−	0.888019i
$622$		0			0
$623$	510.746			0.819817
$624$		0			0
$625$		−	290.538i		−	0.464860i
$626$		0			0
$627$	153.737	−	63.6798i	0.245194	−	0.101563i
$628$		0			0
$629$	−22.1522	−	9.17573i	−0.0352181	−	0.0145878i
$630$		0			0
$631$	241.593	+	241.593i	0.382873	+	0.382873i	0.872136	−	0.489263i	$-0.162734\pi$
$631$	241.593	+	241.593i	0.382873	+	0.382873i	−0.489263	+	0.872136i	$0.662734\pi$
$632$		0			0
$633$	404.793	+	404.793i	0.639484	+	0.639484i
$634$		0			0
$635$	−402.146	−	166.574i	−0.633301	−	0.262322i
$636$		0			0
$637$	−283.498	+	117.429i	−0.445051	+	0.184346i
$638$		0			0
$639$		−	28.2029i		−	0.0441361i
$640$		0			0
$641$	−385.038			−0.600684			−0.300342	−	0.953832i	$-0.597101\pi$
$641$	−385.038			−0.600684			−0.300342	+	0.953832i	$0.597101\pi$
$642$		0			0
$643$	−144.485	−	348.818i	−0.224705	−	0.542486i	0.770813	−	0.637062i	$-0.219850\pi$
$643$	−144.485	−	348.818i	−0.224705	−	0.542486i	−0.995518	+	0.0945760i	$0.969850\pi$
$644$		0			0
$645$	−694.674	+	1677.09i	−1.07701	+	2.60014i
$646$		0			0
$647$	580.537	−	580.537i	0.897276	−	0.897276i	−0.0979186	−	0.995194i	$-0.531218\pi$
$647$	580.537	−	580.537i	0.897276	−	0.897276i	0.995194	+	0.0979186i	$0.0312185\pi$
$648$		0			0
$649$	97.2911	−	97.2911i	0.149909	−	0.149909i
$650$		0			0
$651$	204.347	−	493.338i	0.313898	−	0.757816i
$652$		0			0
$653$	−467.055	−	1127.57i	−0.715246	−	1.72676i	−0.686457	−	0.727170i	$-0.740835\pi$
$653$	−467.055	−	1127.57i	−0.715246	−	1.72676i	−0.0287882	−	0.999586i	$-0.509165\pi$
$654$		0			0
$655$	792.423			1.20981
$656$		0			0
$657$			25.0046i			0.0380587i
$658$		0			0
$659$	287.435	−	119.060i	0.436169	−	0.180667i	−0.153784	−	0.988104i	$-0.549146\pi$
$659$	287.435	−	119.060i	0.436169	−	0.180667i	0.589953	+	0.807437i	$0.299146\pi$
$660$		0			0
$661$	−478.625	−	198.253i	−0.724093	−	0.299929i	−0.00997082	−	0.999950i	$-0.503174\pi$
$661$	−478.625	−	198.253i	−0.724093	−	0.299929i	−0.714122	+	0.700021i	$0.753174\pi$
$662$		0			0
$663$	77.7851	+	77.7851i	0.117323	+	0.117323i
$664$		0			0
$665$	498.348	+	498.348i	0.749396	+	0.749396i
$666$		0			0
$667$	144.492	+	59.8505i	0.216629	+	0.0897309i
$668$		0			0
$669$	469.160	−	194.332i	0.701285	−	0.290482i
$670$		0			0
$671$		−	277.458i		−	0.413499i
$672$		0			0
$673$	831.026			1.23481			0.617405	−	0.786646i	$-0.288184\pi$
$673$	831.026			1.23481			0.617405	+	0.786646i	$0.288184\pi$
$674$		0			0
$675$	−369.277	−	891.513i	−0.547077	−	1.32076i
$676$		0			0
$677$	−16.6301	+	40.1487i	−0.0245644	+	0.0593038i	−0.935686	−	0.352834i	$-0.885218\pi$
$677$	−16.6301	+	40.1487i	−0.0245644	+	0.0593038i	0.911121	+	0.412138i	$0.135218\pi$
$678$		0			0
$679$	−292.524	+	292.524i	−0.430816	+	0.430816i
$680$		0			0
$681$	844.232	−	844.232i	1.23969	−	1.23969i
$682$		0			0
$683$	−411.955	+	994.547i	−0.603155	+	1.45614i	0.267162	+	0.963652i	$0.413914\pi$
$683$	−411.955	+	994.547i	−0.603155	+	1.45614i	−0.870317	+	0.492493i	$0.836086\pi$
$684$		0			0
$685$	−261.839	−	632.136i	−0.382247	−	0.922827i
$686$		0			0
$687$	431.648			0.628309
$688$		0			0
$689$		−	690.593i		−	1.00231i
$690$		0			0
$691$	−657.136	+	272.195i	−0.950993	+	0.393914i	−0.803604	−	0.595164i	$-0.797087\pi$
$691$	−657.136	+	272.195i	−0.950993	+	0.393914i	−0.147389	+	0.989079i	$0.547087\pi$
$692$		0			0
$693$	12.6220	+	5.22822i	0.0182136	+	0.00754433i
$694$		0			0
$695$	166.034	+	166.034i	0.238898	+	0.238898i
$696$		0			0
$697$	32.1605	+	32.1605i	0.0461413	+	0.0461413i
$698$		0			0
$699$	1042.10	+	431.653i	1.49085	+	0.617530i
$700$		0			0
$701$	57.0623	−	23.6360i	0.0814012	−	0.0337175i	−0.341611	−	0.939841i	$-0.610973\pi$
$701$	57.0623	−	23.6360i	0.0814012	−	0.0337175i	0.423013	+	0.906124i	$0.360973\pi$
$702$		0			0
$703$			213.571i			0.303799i
$704$		0			0
$705$	364.059			0.516396
$706$		0			0
$707$	62.0332	+	149.761i	0.0877414	+	0.211827i
$708$		0			0
$709$	−167.767	+	405.025i	−0.236625	+	0.571262i	−0.996930	−	0.0783041i	$-0.975049\pi$
$709$	−167.767	+	405.025i	−0.236625	+	0.571262i	0.760305	+	0.649566i	$0.225049\pi$
$710$		0			0
$711$	−9.81149	+	9.81149i	−0.0137996	+	0.0137996i
$712$		0			0
$713$	−472.421	+	472.421i	−0.662582	+	0.662582i
$714$		0			0
$715$	−241.845	+	583.865i	−0.338245	+	0.816595i
$716$		0			0
$717$	69.8358	+	168.598i	0.0973999	+	0.235144i
$718$		0			0
$719$	−1154.30			−1.60542			−0.802712	−	0.596367i	$-0.796610\pi$
$719$	−1154.30			−1.60542			−0.802712	+	0.596367i	$0.796610\pi$
$720$		0			0
$721$			976.846i			1.35485i
$722$		0			0
$723$	519.853	−	215.330i	0.719022	−	0.297829i
$724$		0			0
$725$	233.592	+	96.7569i	0.322195	+	0.133458i
$726$		0			0
$727$	644.722	+	644.722i	0.886825	+	0.886825i	0.994217	−	0.107392i	$-0.0342500\pi$
$727$	644.722	+	644.722i	0.886825	+	0.886825i	−0.107392	+	0.994217i	$0.534250\pi$
$728$		0			0
$729$	545.902	+	545.902i	0.748837	+	0.748837i
$730$		0			0
$731$	129.849	+	53.7851i	0.177632	+	0.0735775i
$732$		0			0
$733$	508.297	−	210.544i	0.693448	−	0.287235i	−0.00798801	−	0.999968i	$-0.502543\pi$
$733$	508.297	−	210.544i	0.693448	−	0.287235i	0.701436	+	0.712733i	$0.252543\pi$
$734$		0			0
$735$			312.571i			0.425267i
$736$		0			0
$737$	102.424			0.138974
$738$		0			0
$739$	479.243	+	1157.00i	0.648503	+	1.56562i	0.814923	+	0.579569i	$0.196779\pi$
$739$	479.243	+	1157.00i	0.648503	+	1.56562i	−0.166421	+	0.986055i	$0.553221\pi$
$740$		0			0
$741$	374.967	−	905.249i	0.506028	−	1.22166i
$742$		0			0
$743$	106.350	−	106.350i	0.143136	−	0.143136i	−0.631908	−	0.775044i	$-0.717728\pi$
$743$	106.350	−	106.350i	0.143136	−	0.143136i	0.775044	+	0.631908i	$0.217728\pi$
$744$		0			0
$745$	−311.511	+	311.511i	−0.418136	+	0.418136i
$746$		0			0
$747$	31.6262	−	76.3524i	0.0423376	−	0.102212i
$748$		0			0
$749$	−127.964	−	308.932i	−0.170846	−	0.412460i
$750$		0			0
$751$	186.540			0.248389			0.124195	−	0.992258i	$-0.460365\pi$
$751$	186.540			0.248389			0.124195	+	0.992258i	$0.460365\pi$
$752$		0			0
$753$			993.594i			1.31951i
$754$		0			0
$755$	490.430	−	203.143i	0.649577	−	0.269064i
$756$		0			0
$757$	1190.57	+	493.151i	1.57275	+	0.651454i	0.987244	−	0.159214i	$-0.0508959\pi$
$757$	1190.57	+	493.151i	1.57275	+	0.651454i	0.585506	+	0.810668i	$0.300896\pi$
$758$		0			0
$759$	163.564	+	163.564i	0.215499	+	0.215499i
$760$		0			0
$761$	−1042.65	−	1042.65i	−1.37010	−	1.37010i	−0.860279	−	0.509823i	$-0.829711\pi$
$761$	−1042.65	−	1042.65i	−1.37010	−	1.37010i	−0.509823	−	0.860279i	$-0.670289\pi$
$762$		0			0
$763$	−411.867	−	170.601i	−0.539800	−	0.223592i
$764$		0			0
$765$	−7.65014	+	3.16879i	−0.0100002	+	0.00414221i
$766$		0			0
$767$		−	810.175i		−	1.05629i
$768$		0			0
$769$	362.542			0.471446			0.235723	−	0.971820i	$-0.424254\pi$
$769$	362.542			0.471446			0.235723	+	0.971820i	$0.424254\pi$
$770$		0			0
$771$	−200.250	−	483.445i	−0.259727	−	0.627037i
$772$		0			0
$773$	259.669	−	626.896i	0.335924	−	0.810991i	−0.662175	−	0.749350i	$-0.730366\pi$
$773$	259.669	−	626.896i	0.335924	−	0.810991i	0.998098	−	0.0616419i	$-0.0196337\pi$
$774$		0			0
$775$	−763.736	+	763.736i	−0.985465	+	0.985465i
$776$		0			0
$777$	167.785	−	167.785i	0.215939	−	0.215939i
$778$		0			0
$779$	155.031	−	374.278i	0.199013	−	0.480459i
$780$		0			0
$781$	64.9641	+	156.837i	0.0831807	+	0.200816i
$782$		0			0
$783$	−203.188			−0.259499
$784$		0			0
$785$		−	1016.74i		−	1.29521i
$786$		0			0
$787$	148.037	−	61.3188i	0.188103	−	0.0779147i	−0.286644	−	0.958037i	$-0.592540\pi$
$787$	148.037	−	61.3188i	0.188103	−	0.0779147i	0.474747	+	0.880122i	$0.342540\pi$
$788$		0			0
$789$	−1008.49	−	417.731i	−1.27819	−	0.529444i
$790$		0			0
$791$	−544.577	−	544.577i	−0.688466	−	0.688466i
$792$		0			0
$793$	−1155.24	−	1155.24i	−1.45680	−	1.45680i
$794$		0			0
$795$	−649.909	−	269.201i	−0.817495	−	0.338618i
$796$		0			0
$797$	−173.793	+	71.9875i	−0.218059	+	0.0903231i	−0.489039	−	0.872262i	$-0.662652\pi$
$797$	−173.793	+	71.9875i	−0.218059	+	0.0903231i	0.270980	+	0.962585i	$0.412652\pi$
$798$		0			0
$799$		−	28.1873i		−	0.0352782i
$800$		0			0
$801$	53.4505			0.0667297
$802$		0			0
$803$	−57.5968	−	139.051i	−0.0717271	−	0.173164i
$804$		0			0
$805$	−374.910	+	905.113i	−0.465727	+	1.12436i
$806$		0			0
$807$	839.340	−	839.340i	1.04007	−	1.04007i
$808$		0			0
$809$	−679.446	+	679.446i	−0.839859	+	0.839859i	−0.988840	−	0.148981i	$-0.952401\pi$
$809$	−679.446	+	679.446i	−0.839859	+	0.839859i	0.148981	+	0.988840i	$0.452401\pi$
$810$		0			0
$811$	−4.19630	+	10.1308i	−0.00517422	+	0.0124917i	−0.926446	−	0.376429i	$-0.877152\pi$
$811$	−4.19630	+	10.1308i	−0.00517422	+	0.0124917i	0.921271	+	0.388921i	$0.127152\pi$
$812$		0			0
$813$	358.866	+	866.379i	0.441410	+	1.06566i
$814$		0			0
$815$	262.696			0.322326
$816$		0			0
$817$		−	1251.88i		−	1.53229i
$818$		0			0
$819$	74.3225	−	30.7854i	0.0907479	−	0.0375890i
$820$		0			0
$821$	114.507	+	47.4303i	0.139472	+	0.0577714i	0.451328	−	0.892358i	$-0.350950\pi$
$821$	114.507	+	47.4303i	0.139472	+	0.0577714i	−0.311855	+	0.950130i	$0.600950\pi$
$822$		0			0
$823$	−701.981	−	701.981i	−0.852954	−	0.852954i	0.137542	−	0.990496i	$-0.456080\pi$
$823$	−701.981	−	701.981i	−0.852954	−	0.852954i	−0.990496	+	0.137542i	$0.956080\pi$
$824$		0			0
$825$	264.424	+	264.424i	0.320514	+	0.320514i
$826$		0			0
$827$	420.620	+	174.226i	0.508609	+	0.210673i	0.622205	−	0.782854i	$-0.286237\pi$
$827$	420.620	+	174.226i	0.508609	+	0.210673i	−0.113596	+	0.993527i	$0.536237\pi$
$828$		0			0
$829$	−917.677	+	380.114i	−1.10697	+	0.458521i	−0.859893	−	0.510475i	$-0.829470\pi$
$829$	−917.677	+	380.114i	−1.10697	+	0.458521i	−0.247076	+	0.968996i	$0.579470\pi$
$830$		0			0
$831$		−	908.337i		−	1.09306i
$832$		0			0
$833$	24.2008			0.0290526
$834$		0			0
$835$	−579.897	−	1400.00i	−0.694487	−	1.67664i
$836$		0			0
$837$	332.164	−	801.915i	0.396851	−	0.958083i
$838$		0			0
$839$	−125.592	+	125.592i	−0.149693	+	0.149693i	−0.777981	−	0.628288i	$-0.783756\pi$
$839$	−125.592	+	125.592i	−0.149693	+	0.149693i	0.628288	+	0.777981i	$0.283756\pi$
$840$		0			0
$841$	−557.031	+	557.031i	−0.662344	+	0.662344i
$842$		0			0
$843$	−466.613	+	1126.50i	−0.553515	+	1.33630i
$844$		0			0
$845$	924.554	+	2232.07i	1.09415	+	2.64150i
$846$		0			0
$847$	633.819			0.748311
$848$		0			0
$849$			414.835i			0.488616i
$850$		0			0
$851$	−274.282	+	113.611i	−0.322305	+	0.133503i
$852$		0			0
$853$	866.692	+	358.995i	1.01605	+	0.420862i	0.827659	−	0.561232i	$-0.189672\pi$
$853$	866.692	+	358.995i	1.01605	+	0.420862i	0.188392	+	0.982094i	$0.439672\pi$
$854$		0			0
$855$	52.1531	+	52.1531i	0.0609978	+	0.0609978i
$856$		0			0
$857$	−559.264	−	559.264i	−0.652584	−	0.652584i	0.301031	−	0.953614i	$-0.402669\pi$
$857$	−559.264	−	559.264i	−0.652584	−	0.652584i	−0.953614	+	0.301031i	$0.902669\pi$
$858$		0			0
$859$	−552.858	−	229.001i	−0.643607	−	0.266591i	0.0369150	−	0.999318i	$-0.488247\pi$
$859$	−552.858	−	229.001i	−0.643607	−	0.266591i	−0.680522	+	0.732728i	$0.738247\pi$
$860$		0			0
$861$	−415.833	+	172.244i	−0.482965	+	0.200051i
$862$		0			0
$863$			106.004i			0.122833i	0.998112	+	0.0614163i	$0.0195617\pi$
$863$			106.004i			0.122833i	−0.998112	+	0.0614163i	$0.980438\pi$
$864$		0			0
$865$	−1407.87			−1.62760
$866$		0			0
$867$	316.848	+	764.938i	0.365453	+	0.882281i
$868$		0			0
$869$	31.9616	−	77.1622i	0.0367798	−	0.0887943i
$870$		0			0
$871$	426.460	−	426.460i	0.489621	−	0.489621i
$872$		0			0
$873$	−30.6132	+	30.6132i	−0.0350667	+	0.0350667i
$874$		0			0
$875$	−168.823	+	407.574i	−0.192940	+	0.465799i
$876$		0			0
$877$	135.124	+	326.217i	0.154075	+	0.371969i	0.982003	−	0.188864i	$-0.0604807\pi$
$877$	135.124	+	326.217i	0.154075	+	0.371969i	−0.827928	+	0.560834i	$0.810481\pi$
$878$		0			0
$879$	137.060			0.155927
$880$		0			0
$881$			628.648i			0.713562i	0.934188	+	0.356781i	$0.116126\pi$
$881$			628.648i			0.713562i	−0.934188	+	0.356781i	$0.883874\pi$
$882$		0			0
$883$	−816.843	+	338.347i	−0.925077	+	0.383179i	−0.793809	−	0.608167i	$-0.791905\pi$
$883$	−816.843	+	338.347i	−0.925077	+	0.383179i	−0.131268	+	0.991347i	$0.541905\pi$
$884$		0			0
$885$	−762.446	−	315.815i	−0.861521	−	0.356854i
$886$		0			0
$887$	−22.4622	−	22.4622i	−0.0253238	−	0.0253238i	0.694332	−	0.719655i	$-0.255700\pi$
$887$	−22.4622	−	22.4622i	−0.0253238	−	0.0253238i	−0.719655	+	0.694332i	$0.755700\pi$
$888$		0			0
$889$	−235.831	−	235.831i	−0.265277	−	0.265277i
$890$		0			0
$891$	−258.446	−	107.052i	−0.290063	−	0.120148i
$892$		0			0
$893$	−231.958	+	96.0803i	−0.259752	+	0.107593i
$894$		0			0
$895$			376.214i			0.420351i
$896$		0			0
$897$	1362.05			1.51845
$898$		0			0
$899$	87.0327	+	210.116i	0.0968106	+	0.233721i
$900$		0			0
$901$	−20.8429	+	50.3192i	−0.0231331	+	0.0558482i
$902$		0			0
$903$	−983.499	+	983.499i	−1.08915	+	1.08915i
$904$		0			0
$905$	703.017	−	703.017i	0.776814	−	0.776814i
$906$		0			0
$907$	−554.178	+	1337.90i	−0.611001	+	1.47509i	0.250902	+	0.968012i	$0.419273\pi$
$907$	−554.178	+	1337.90i	−0.611001	+	1.47509i	−0.861903	+	0.507074i	$0.830727\pi$
$908$		0			0
$909$	6.49189	+	15.6728i	0.00714180	+	0.0172418i
$910$		0			0
$911$	267.709			0.293863			0.146931	−	0.989147i	$-0.453060\pi$
$911$	267.709			0.293863			0.146931	+	0.989147i	$0.453060\pi$
$912$		0			0
$913$			497.447i			0.544849i
$914$		0			0
$915$	−1537.51	+	636.858i	−1.68034	+	0.696020i
$916$		0			0
$917$	560.945	+	232.351i	0.611717	+	0.253382i
$918$		0			0
$919$	191.361	+	191.361i	0.208227	+	0.208227i	0.803514	−	0.595286i	$-0.202961\pi$
$919$	191.361	+	191.361i	0.208227	+	0.208227i	−0.595286	+	0.803514i	$0.702961\pi$
$920$		0			0
$921$	−1179.48	−	1179.48i	−1.28066	−	1.28066i
$922$		0			0
$923$	923.507	+	382.529i	1.00055	+	0.414441i
$924$		0			0
$925$	−443.416	+	183.669i	−0.479368	+	0.198561i
$926$		0			0
$927$			102.229i			0.110279i
$928$		0			0
$929$	−459.352			−0.494458			−0.247229	−	0.968957i	$-0.579520\pi$
$929$	−459.352			−0.494458			−0.247229	+	0.968957i	$0.579520\pi$
$930$		0			0
$931$	−82.4919	−	199.153i	−0.0886057	−	0.213913i
$932$		0			0
$933$	600.970	−	1450.87i	0.644126	−	1.55506i
$934$		0			0
$935$	35.2434	−	35.2434i	0.0376935	−	0.0376935i
$936$		0			0
$937$	−135.689	+	135.689i	−0.144812	+	0.144812i	−0.775796	−	0.630984i	$-0.782651\pi$
$937$	−135.689	+	135.689i	−0.144812	+	0.144812i	0.630984	+	0.775796i	$0.282651\pi$
$938$		0			0
$939$	567.415	−	1369.86i	0.604276	−	1.45885i
$940$		0			0
$941$	−471.321	−	1137.87i	−0.500873	−	1.20921i	−0.949009	−	0.315249i	$-0.897912\pi$
$941$	−471.321	−	1137.87i	−0.500873	−	1.20921i	0.448136	−	0.893965i	$-0.352088\pi$
$942$		0			0
$943$	563.142			0.597182
$944$		0			0
$945$		−	1272.79i		−	1.34687i
$946$		0			0
$947$	−300.223	+	124.357i	−0.317026	+	0.131316i	−0.535522	−	0.844521i	$-0.679885\pi$
$947$	−300.223	+	124.357i	−0.317026	+	0.131316i	0.218496	+	0.975838i	$0.429885\pi$
$948$		0			0
$949$	−818.776	−	339.148i	−0.862778	−	0.357374i
$950$		0			0
$951$	−1079.66	−	1079.66i	−1.13529	−	1.13529i
$952$		0			0
$953$	362.517	+	362.517i	0.380395	+	0.380395i	0.871245	−	0.490849i	$-0.163313\pi$
$953$	362.517	+	362.517i	0.380395	+	0.380395i	−0.490849	+	0.871245i	$0.663313\pi$
$954$		0			0
$955$	1279.28	+	529.894i	1.33956	+	0.554863i
$956$		0			0
$957$	72.7471	−	30.1328i	0.0760158	−	0.0314868i
$958$		0			0
$959$		−	524.256i		−	0.546669i
$960$		0			0
$961$	−10.5357			−0.0109633
$962$		0			0
$963$	−13.3917	−	32.3304i	−0.0139062	−	0.0335725i
$964$		0			0
$965$	531.792	−	1283.86i	0.551079	−	1.33042i
$966$		0			0
$967$	−642.315	+	642.315i	−0.664235	+	0.664235i	−0.956375	−	0.292141i	$-0.905632\pi$
$967$	−642.315	+	642.315i	−0.664235	+	0.664235i	0.292141	+	0.956375i	$0.405632\pi$
$968$		0			0
$969$	−54.6429	+	54.6429i	−0.0563910	+	0.0563910i
$970$		0			0
$971$	−114.682	+	276.867i	−0.118107	+	0.285136i	−0.971867	−	0.235532i	$-0.924317\pi$
$971$	−114.682	+	276.867i	−0.118107	+	0.285136i	0.853760	+	0.520667i	$0.174317\pi$
$972$		0			0
$973$	68.8494	+	166.217i	0.0707599	+	0.170830i
$974$		0			0
$975$	2201.94			2.25840
$976$		0			0
$977$			1952.32i			1.99828i	0.0414975	+	0.999139i	$0.486787\pi$
$977$			1952.32i			1.99828i	−0.0414975	+	0.999139i	$0.513213\pi$
$978$		0			0
$979$	−297.240	+	123.121i	−0.303616	+	0.125762i
$980$		0			0
$981$	−43.1027	−	17.8537i	−0.0439375	−	0.0181995i
$982$		0			0
$983$	−437.102	−	437.102i	−0.444661	−	0.444661i	0.448914	−	0.893575i	$-0.351811\pi$
$983$	−437.102	−	437.102i	−0.444661	−	0.444661i	−0.893575	+	0.448914i	$0.851811\pi$
$984$		0			0
$985$	1331.41	+	1331.41i	1.35168	+	1.35168i
$986$		0			0
$987$	257.712	+	106.748i	0.261107	+	0.108154i
$988$		0			0
$989$	1607.75	−	665.952i	1.62563	−	0.673359i
$990$		0			0
$991$		−	238.251i		−	0.240415i	−0.992749	−	0.120208i	$-0.961644\pi$
$991$		−	238.251i		−	0.240415i	0.992749	−	0.120208i	$-0.0383560\pi$
$992$		0			0
$993$	−155.439			−0.156535
$994$		0			0
$995$	−550.836	−	1329.84i	−0.553604	−	1.33652i
$996$		0			0
$997$	−262.900	+	634.696i	−0.263691	+	0.636606i	−0.999161	−	0.0409509i	$-0.986961\pi$
$997$	−262.900	+	634.696i	−0.263691	+	0.636606i	0.735470	+	0.677557i	$0.236961\pi$
$998$		0			0
$999$	272.732	−	272.732i	0.273005	−	0.273005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.h.a.79.5		28
4.3	odd	2		32.3.h.a.11.1	yes	28
8.3	odd	2		256.3.h.b.159.5		28
8.5	even	2		256.3.h.a.159.3		28
12.11	even	2		288.3.u.a.235.7		28
32.3	odd	8	inner	128.3.h.a.47.5		28
32.13	even	8		256.3.h.b.95.5		28
32.19	odd	8		256.3.h.a.95.3		28
32.29	even	8		32.3.h.a.3.1	✓	28
96.29	odd	8		288.3.u.a.163.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.1	✓	28	32.29	even	8
32.3.h.a.11.1	yes	28	4.3	odd	2
128.3.h.a.47.5		28	32.3	odd	8	inner
128.3.h.a.79.5		28	1.1	even	1	trivial
256.3.h.a.95.3		28	32.19	odd	8
256.3.h.a.159.3		28	8.5	even	2
256.3.h.b.95.5		28	32.13	even	8
256.3.h.b.159.5		28	8.3	odd	2
288.3.u.a.163.7		28	96.29	odd	8
288.3.u.a.235.7		28	12.11	even	2

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.10785 + 2.67458i) q^{3} +(2.95565 - 7.13556i) q^{5} +(4.18452 - 4.18452i) q^{7} +(0.437918 - 0.437918i) q^{9} +O(q^{10})\)	\(q+(1.10785 + 2.67458i) q^{3} +(2.95565 - 7.13556i) q^{5} +(4.18452 - 4.18452i) q^{7} +(0.437918 - 0.437918i) q^{9} +(-1.42655 + 3.44399i) q^{11} +(8.39996 + 20.2793i) q^{13} +22.3590 q^{15} -1.73115i q^{17} +(-14.2459 + 5.90085i) q^{19} +(15.8276 + 6.55601i) q^{21} +(-15.1565 - 15.1565i) q^{23} +(-24.5027 - 24.5027i) q^{25} +(25.7276 + 10.6567i) q^{27} +(-6.74107 + 2.79224i) q^{29} -31.1695i q^{31} -10.7916 q^{33} +(-17.4909 - 42.2268i) q^{35} +(5.30038 - 12.7962i) q^{37} +(-44.9327 + 44.9327i) q^{39} +(-18.5776 + 18.5776i) q^{41} +(-31.0691 + 75.0074i) q^{43} +(-1.83046 - 4.41911i) q^{45} +16.2824 q^{47} +13.9797i q^{49} +(4.63009 - 1.91784i) q^{51} +(-29.0670 - 12.0399i) q^{53} +(20.3584 + 20.3584i) q^{55} +(-31.5646 - 31.5646i) q^{57} +(-34.1002 - 14.1248i) q^{59} +(-68.7647 + 28.4833i) q^{61} -3.66495i q^{63} +169.531 q^{65} +(-10.5147 - 25.3846i) q^{67} +(23.7462 - 57.3284i) q^{69} +(32.2012 - 32.2012i) q^{71} +(-28.5494 + 28.5494i) q^{73} +(38.3891 - 92.6796i) q^{75} +(8.44203 + 20.3809i) q^{77} -22.4049 q^{79} +75.0427i q^{81} +(123.286 - 51.0669i) q^{83} +(-12.3527 - 5.11665i) q^{85} +(-14.9361 - 14.9361i) q^{87} +(61.0281 + 61.0281i) q^{89} +(120.009 + 49.7093i) q^{91} +(83.3652 - 34.5310i) q^{93} +119.093i q^{95} -69.9064 q^{97} +(0.883474 + 2.13290i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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