LMFDB - Embedded newform 136.3.t.b.73.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(41,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 0, 11]))

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

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

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.t (of order $16$, degree $8$, 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:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			73.5
Character	$\chi$	$=$	136.73
Dual form			136.3.t.b.41.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.38532 + 3.56988i) q^{3} +(-0.996509 + 5.00979i) q^{5} +(-0.0460348 - 0.231433i) q^{7} +(-3.61016 + 8.71570i) q^{9} +O(q^{10})$	\(q+(2.38532 + 3.56988i) q^{3} +(-0.996509 + 5.00979i) q^{5} +(-0.0460348 - 0.231433i) q^{7} +(-3.61016 + 8.71570i) q^{9} +(-10.1061 - 6.75269i) q^{11} +(8.36248 + 8.36248i) q^{13} +(-20.2613 + 8.39252i) q^{15} +(7.52192 - 15.2453i) q^{17} +(5.53952 + 13.3736i) q^{19} +(0.716380 - 0.716380i) q^{21} +(-0.358092 + 0.535922i) q^{23} +(-1.00796 - 0.417511i) q^{25} +(-1.82674 + 0.363361i) q^{27} +(50.7212 + 10.0891i) q^{29} +(-25.6960 + 17.1695i) q^{31} -52.1850i q^{33} +1.20530 q^{35} +(14.6797 + 21.9698i) q^{37} +(-9.90588 + 49.8002i) q^{39} +(-11.2164 - 56.3888i) q^{41} +(26.0857 - 62.9765i) q^{43} +(-40.0663 - 26.7714i) q^{45} +(-47.1933 - 47.1933i) q^{47} +(45.2187 - 18.7302i) q^{49} +(72.3663 - 9.51264i) q^{51} +(5.09427 + 12.2987i) q^{53} +(43.9004 - 43.9004i) q^{55} +(-34.5286 + 51.6757i) q^{57} +(-75.1310 - 31.1203i) q^{59} +(-48.4479 + 9.63689i) q^{61} +(2.18329 + 0.434284i) q^{63} +(-50.2275 + 33.5610i) q^{65} -58.0686i q^{67} -2.76734 q^{69} +(15.4714 + 23.1546i) q^{71} +(-12.8014 + 64.3570i) q^{73} +(-0.913843 - 4.59420i) q^{75} +(-1.09756 + 2.64974i) q^{77} +(104.845 + 70.0553i) q^{79} +(54.3819 + 54.3819i) q^{81} +(25.2969 - 10.4783i) q^{83} +(68.8803 + 52.8754i) q^{85} +(84.9694 + 205.134i) q^{87} +(-60.4822 + 60.4822i) q^{89} +(1.55039 - 2.32032i) q^{91} +(-122.586 - 50.7769i) q^{93} +(-72.5190 + 14.4249i) q^{95} +(23.1484 + 4.60450i) q^{97} +(95.3391 - 63.7036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.38532	+	3.56988i	0.795106	+	1.18996i	0.978363	+	0.206896i	$0.0663361\pi$
$3$	2.38532	+	3.56988i	0.795106	+	1.18996i	−0.183257	+	0.983065i	$0.558664\pi$
$4$		0			0
$5$	−0.996509	+	5.00979i	−0.199302	+	1.00196i	0.743534	+	0.668699i	$0.233148\pi$
$5$	−0.996509	+	5.00979i	−0.199302	+	1.00196i	−0.942835	+	0.333259i	$0.891852\pi$
$6$		0			0
$7$	−0.0460348	−	0.231433i	−0.00657641	−	0.0330618i	0.977358	−	0.211594i	$-0.0678653\pi$
$7$	−0.0460348	−	0.231433i	−0.00657641	−	0.0330618i	−0.983934	+	0.178532i	$0.942865\pi$
$8$		0			0
$9$	−3.61016	+	8.71570i	−0.401129	+	0.968411i
$10$		0			0
$11$	−10.1061	−	6.75269i	−0.918738	−	0.613881i	0.00371410	−	0.999993i	$-0.498818\pi$
$11$	−10.1061	−	6.75269i	−0.918738	−	0.613881i	−0.922452	+	0.386112i	$0.873818\pi$
$12$		0			0
$13$	8.36248	+	8.36248i	0.643268	+	0.643268i	0.951357	−	0.308090i	$-0.0996897\pi$
$13$	8.36248	+	8.36248i	0.643268	+	0.643268i	−0.308090	+	0.951357i	$0.599690\pi$
$14$		0			0
$15$	−20.2613	+	8.39252i	−1.35076	+	0.559502i
$16$		0			0
$17$	7.52192	−	15.2453i	0.442466	−	0.896785i
$17$	7.52192	−	15.2453i	0.442466	−	0.896785i
$18$		0			0
$19$	5.53952	+	13.3736i	0.291554	+	0.703873i	0.999998	−	0.00189375i	$-0.000602799\pi$
$19$	5.53952	+	13.3736i	0.291554	+	0.703873i	−0.708445	+	0.705766i	$0.750603\pi$
$20$		0			0
$21$	0.716380	−	0.716380i	0.0341133	−	0.0341133i
$22$		0			0
$23$	−0.358092	+	0.535922i	−0.0155692	+	0.0233010i	−0.839173	−	0.543865i	$-0.816960\pi$
$23$	−0.358092	+	0.535922i	−0.0155692	+	0.0233010i	0.823603	+	0.567166i	$0.191960\pi$
$24$		0			0
$25$	−1.00796	−	0.417511i	−0.0403184	−	0.0167004i
$26$		0			0
$27$	−1.82674	+	0.363361i	−0.0676570	+	0.0134578i
$28$		0			0
$29$	50.7212	+	10.0891i	1.74901	+	0.347899i	0.962831	−	0.270105i	$-0.0870585\pi$
$29$	50.7212	+	10.0891i	1.74901	+	0.347899i	0.786175	+	0.618004i	$0.212058\pi$
$30$		0			0
$31$	−25.6960	+	17.1695i	−0.828903	+	0.553856i	−0.896084	−	0.443885i	$-0.853600\pi$
$31$	−25.6960	+	17.1695i	−0.828903	+	0.553856i	0.0671802	+	0.997741i	$0.478600\pi$
$32$		0			0
$33$		−	52.1850i		−	1.58136i
$34$		0			0
$35$	1.20530			0.0344372
$36$		0			0
$37$	14.6797	+	21.9698i	0.396749	+	0.593777i	0.975033	−	0.222058i	$-0.0712775\pi$
$37$	14.6797	+	21.9698i	0.396749	+	0.593777i	−0.578284	+	0.815835i	$0.696277\pi$
$38$		0			0
$39$	−9.90588	+	49.8002i	−0.253997	+	1.27693i
$40$		0			0
$41$	−11.2164	−	56.3888i	−0.273571	−	1.37534i	−0.836108	−	0.548564i	$-0.815175\pi$
$41$	−11.2164	−	56.3888i	−0.273571	−	1.37534i	0.562537	−	0.826772i	$-0.309825\pi$
$42$		0			0
$43$	26.0857	−	62.9765i	0.606644	−	1.46457i	−0.259983	−	0.965613i	$-0.583717\pi$
$43$	26.0857	−	62.9765i	0.606644	−	1.46457i	0.866627	−	0.498956i	$-0.166283\pi$
$44$		0			0
$45$	−40.0663	−	26.7714i	−0.890361	−	0.594920i
$46$		0			0
$47$	−47.1933	−	47.1933i	−1.00411	−	1.00411i	−0.999992	−	0.00412060i	$-0.998688\pi$
$47$	−47.1933	−	47.1933i	−1.00411	−	1.00411i	−0.00412060	−	0.999992i	$-0.501312\pi$
$48$		0			0
$49$	45.2187	−	18.7302i	0.922830	−	0.382249i
$50$		0			0
$51$	72.3663	−	9.51264i	1.41895	−	0.186522i
$52$		0			0
$53$	5.09427	+	12.2987i	0.0961183	+	0.232050i	0.964624	−	0.263629i	$-0.0849194\pi$
$53$	5.09427	+	12.2987i	0.0961183	+	0.232050i	−0.868506	+	0.495679i	$0.834919\pi$
$54$		0			0
$55$	43.9004	−	43.9004i	0.798189	−	0.798189i
$56$		0			0
$57$	−34.5286	+	51.6757i	−0.605765	+	0.906591i
$58$		0			0
$59$	−75.1310	−	31.1203i	−1.27341	−	0.527462i	−0.359408	−	0.933180i	$-0.617022\pi$
$59$	−75.1310	−	31.1203i	−1.27341	−	0.527462i	−0.913998	+	0.405718i	$0.867022\pi$
$60$		0			0
$61$	−48.4479	+	9.63689i	−0.794228	+	0.157982i	−0.575498	−	0.817804i	$-0.695192\pi$
$61$	−48.4479	+	9.63689i	−0.794228	+	0.157982i	−0.218731	+	0.975785i	$0.570192\pi$
$62$		0			0
$63$	2.18329	+	0.434284i	0.0346554	+	0.00689339i
$64$		0			0
$65$	−50.2275	+	33.5610i	−0.772731	+	0.516323i
$66$		0			0
$67$		−	58.0686i		−	0.866696i	−0.901227	−	0.433348i	$-0.857332\pi$
$67$		−	58.0686i		−	0.866696i	0.901227	−	0.433348i	$-0.142668\pi$
$68$		0			0
$69$	−2.76734			−0.0401064
$70$		0			0
$71$	15.4714	+	23.1546i	0.217907	+	0.326121i	0.924277	−	0.381721i	$-0.124669\pi$
$71$	15.4714	+	23.1546i	0.217907	+	0.326121i	−0.706370	+	0.707842i	$0.749669\pi$
$72$		0			0
$73$	−12.8014	+	64.3570i	−0.175362	+	0.881602i	0.788467	+	0.615078i	$0.210875\pi$
$73$	−12.8014	+	64.3570i	−0.175362	+	0.881602i	−0.963828	+	0.266525i	$0.914125\pi$
$74$		0			0
$75$	−0.913843	−	4.59420i	−0.0121846	−	0.0612560i
$76$		0			0
$77$	−1.09756	+	2.64974i	−0.0142540	+	0.0344123i
$78$		0			0
$79$	104.845	+	70.0553i	1.32715	+	0.886776i	0.998339	−	0.0576183i	$-0.0183506\pi$
$79$	104.845	+	70.0553i	1.32715	+	0.886776i	0.328815	+	0.944394i	$0.393351\pi$
$80$		0			0
$81$	54.3819	+	54.3819i	0.671381	+	0.671381i
$82$		0			0
$83$	25.2969	−	10.4783i	0.304782	−	0.126245i	−0.225051	−	0.974347i	$-0.572255\pi$
$83$	25.2969	−	10.4783i	0.304782	−	0.126245i	0.529833	+	0.848102i	$0.322255\pi$
$84$		0			0
$85$	68.8803	+	52.8754i	0.810357	+	0.622063i
$86$		0			0
$87$	84.9694	+	205.134i	0.976660	+	2.35786i
$88$		0			0
$89$	−60.4822	+	60.4822i	−0.679575	+	0.679575i	−0.959904	−	0.280329i	$-0.909557\pi$
$89$	−60.4822	+	60.4822i	−0.679575	+	0.679575i	0.280329	+	0.959904i	$0.409557\pi$
$90$		0			0
$91$	1.55039	−	2.32032i	0.0170372	−	0.0254980i
$92$		0			0
$93$	−122.586	−	50.7769i	−1.31813	−	0.545988i
$94$		0			0
$95$	−72.5190	+	14.4249i	−0.763358	+	0.151841i
$96$		0			0
$97$	23.1484	+	4.60450i	0.238643	+	0.0474690i	0.312963	−	0.949765i	$-0.398679\pi$
$97$	23.1484	+	4.60450i	0.238643	+	0.0474690i	−0.0743197	+	0.997234i	$0.523679\pi$
$98$		0			0
$99$	95.3391	−	63.7036i	0.963021	−	0.643470i
$100$		0			0
$101$		−	171.011i		−	1.69317i	−0.532250	−	0.846587i	$-0.678653\pi$
$101$		−	171.011i		−	1.69317i	0.532250	−	0.846587i	$-0.321347\pi$
$102$		0			0
$103$	−68.8345			−0.668297			−0.334148	−	0.942521i	$-0.608449\pi$
$103$	−68.8345			−0.668297			−0.334148	+	0.942521i	$0.608449\pi$
$104$		0			0
$105$	2.87503	+	4.30279i	0.0273813	+	0.0409790i
$106$		0			0
$107$	−26.5131	+	133.290i	−0.247786	+	1.24571i	0.633731	+	0.773553i	$0.281523\pi$
$107$	−26.5131	+	133.290i	−0.247786	+	1.24571i	−0.881517	+	0.472152i	$0.843477\pi$
$108$		0			0
$109$	6.16607	+	30.9989i	0.0565695	+	0.284394i	0.998707	−	0.0508321i	$-0.0161873\pi$
$109$	6.16607	+	30.9989i	0.0565695	+	0.284394i	−0.942138	+	0.335226i	$0.891187\pi$
$110$		0			0
$111$	−43.4136	+	104.810i	−0.391114	+	0.944232i
$112$		0			0
$113$	−170.059	−	113.630i	−1.50494	−	1.00557i	−0.988829	−	0.149052i	$-0.952378\pi$
$113$	−170.059	−	113.630i	−1.50494	−	1.00557i	−0.516115	−	0.856520i	$-0.672622\pi$
$114$		0			0
$115$	−2.32801	−	2.32801i	−0.0202436	−	0.0202436i
$116$		0			0
$117$	−103.075	+	42.6950i	−0.880981	+	0.364914i
$118$		0			0
$119$	−3.87454	−	1.03900i	−0.0325592	−	0.00873111i
$120$		0			0
$121$	10.2300	+	24.6975i	0.0845458	+	0.204112i
$122$		0			0
$123$	174.547	−	174.547i	1.41908	−	1.41908i
$124$		0			0
$125$	−67.8493	+	101.544i	−0.542795	+	0.812350i
$126$		0			0
$127$	−215.175	−	89.1284i	−1.69429	−	0.701799i	−0.694449	−	0.719542i	$-0.744352\pi$
$127$	−215.175	−	89.1284i	−1.69429	−	0.701799i	−0.999843	+	0.0177434i	$0.994352\pi$
$128$		0			0
$129$	287.041	−	57.0961i	2.22513	−	0.442605i
$130$		0			0
$131$	−63.6933	−	12.6694i	−0.486208	−	0.0967128i	−0.0541017	−	0.998535i	$-0.517230\pi$
$131$	−63.6933	−	12.6694i	−0.486208	−	0.0967128i	−0.432106	+	0.901823i	$0.642230\pi$
$132$		0			0
$133$	2.84007	−	1.89768i	0.0213539	−	0.0142682i
$134$		0			0
$135$		−	9.51368i		−	0.0704717i
$136$		0			0
$137$	104.055			0.759526			0.379763	−	0.925084i	$-0.376006\pi$
$137$	104.055			0.759526			0.379763	+	0.925084i	$0.376006\pi$
$138$		0			0
$139$	−21.3646	−	31.9743i	−0.153702	−	0.230031i	0.746625	−	0.665245i	$-0.231673\pi$
$139$	−21.3646	−	31.9743i	−0.153702	−	0.230031i	−0.900327	+	0.435214i	$0.856673\pi$
$140$		0			0
$141$	55.9034	−	281.045i	0.396478	−	1.99323i
$142$		0			0
$143$	−28.0429	−	140.981i	−0.196104	−	0.985884i
$144$		0			0
$145$	−101.088	+	244.048i	−0.697160	+	1.68309i
$146$		0			0
$147$	174.725	+	116.748i	1.18861	+	0.794203i
$148$		0			0
$149$	44.6137	+	44.6137i	0.299421	+	0.299421i	0.840787	−	0.541366i	$-0.182093\pi$
$149$	44.6137	+	44.6137i	0.299421	+	0.299421i	−0.541366	+	0.840787i	$0.682093\pi$
$150$		0			0
$151$	33.9109	−	14.0464i	0.224575	−	0.0930222i	−0.267559	−	0.963542i	$-0.586217\pi$
$151$	33.9109	−	14.0464i	0.224575	−	0.0930222i	0.492134	+	0.870519i	$0.336217\pi$
$152$		0			0
$153$	105.719	+	120.597i	0.690971	+	0.788216i
$154$		0			0
$155$	−60.4094	−	145.841i	−0.389738	−	0.940910i
$156$		0			0
$157$	−16.3997	+	16.3997i	−0.104457	+	0.104457i	−0.757404	−	0.652947i	$-0.773532\pi$
$157$	−16.3997	+	16.3997i	−0.104457	+	0.104457i	0.652947	+	0.757404i	$0.273532\pi$
$158$		0			0
$159$	−31.7533	+	47.5222i	−0.199706	+	0.298881i
$160$		0			0
$161$	0.140515	+	0.0582031i	0.000872762	+	0.000361510i
$162$		0			0
$163$	287.599	−	57.2070i	1.76441	−	0.350963i	0.796963	−	0.604028i	$-0.206439\pi$
$163$	287.599	−	57.2070i	1.76441	−	0.350963i	0.967449	+	0.253065i	$0.0814387\pi$
$164$		0			0
$165$	261.436	+	52.0028i	1.58446	+	0.315168i
$166$		0			0
$167$	33.1019	−	22.1180i	0.198215	−	0.132443i	−0.452502	−	0.891763i	$-0.649468\pi$
$167$	33.1019	−	22.1180i	0.198215	−	0.132443i	0.650717	+	0.759320i	$0.274468\pi$
$168$		0			0
$169$		−	29.1379i		−	0.172414i
$170$		0			0
$171$	−136.559			−0.798589
$172$		0			0
$173$	−179.192	−	268.180i	−1.03579	−	1.55017i	−0.818866	−	0.573985i	$-0.805397\pi$
$173$	−179.192	−	268.180i	−1.03579	−	1.55017i	−0.216926	−	0.976188i	$-0.569603\pi$
$174$		0			0
$175$	−0.0502244	+	0.252495i	−0.000286997	+	0.00144283i
$176$		0			0
$177$	−68.1157	−	342.441i	−0.384834	−	1.93469i
$178$		0			0
$179$	25.0566	−	60.4919i	0.139981	−	0.337944i	−0.838306	−	0.545200i	$-0.816454\pi$
$179$	25.0566	−	60.4919i	0.139981	−	0.337944i	0.978287	+	0.207257i	$0.0664535\pi$
$180$		0			0
$181$	87.3953	+	58.3957i	0.482847	+	0.322628i	0.773059	−	0.634334i	$-0.218726\pi$
$181$	87.3953	+	58.3957i	0.482847	+	0.322628i	−0.290212	+	0.956962i	$0.593726\pi$
$182$		0			0
$183$	−149.966	−	149.966i	−0.819488	−	0.819488i
$184$		0			0
$185$	−124.692	+	51.6492i	−0.674012	+	0.279185i
$186$		0			0
$187$	−178.965	+	103.278i	−0.957030	+	0.552289i
$188$		0			0
$189$	0.168187	+	0.406040i	0.000889880	+	0.00214836i
$190$		0			0
$191$	−172.869	+	172.869i	−0.905075	+	0.905075i	−0.995870	−	0.0907950i	$-0.971059\pi$
$191$	−172.869	+	172.869i	−0.905075	+	0.905075i	0.0907950	+	0.995870i	$0.471059\pi$
$192$		0			0
$193$	−106.686	+	159.666i	−0.552775	+	0.827287i	−0.997665	−	0.0682988i	$-0.978243\pi$
$193$	−106.686	+	159.666i	−0.552775	+	0.827287i	0.444890	+	0.895585i	$0.353243\pi$
$194$		0			0
$195$	−239.617	−	99.2528i	−1.22881	−	0.508989i
$196$		0			0
$197$	−79.3015	+	15.7740i	−0.402546	+	0.0800713i	−0.392211	−	0.919875i	$-0.628290\pi$
$197$	−79.3015	+	15.7740i	−0.402546	+	0.0800713i	−0.0103347	+	0.999947i	$0.503290\pi$
$198$		0			0
$199$	8.49440	+	1.68964i	0.0426854	+	0.00849066i	0.216387	−	0.976308i	$-0.430573\pi$
$199$	8.49440	+	1.68964i	0.0426854	+	0.00849066i	−0.173701	+	0.984798i	$0.555573\pi$
$200$		0			0
$201$	207.298	−	138.512i	1.03133	−	0.689115i
$202$		0			0
$203$		−	12.2030i		−	0.0601132i
$204$		0			0
$205$	293.673			1.43255
$206$		0			0
$207$	−3.37817	−	5.05578i	−0.0163196	−	0.0244241i
$208$		0			0
$209$	34.3246	−	172.562i	0.164233	−	0.825654i
$210$		0			0
$211$	6.00679	+	30.1982i	0.0284682	+	0.143119i	0.992405	−	0.123011i	$-0.0392549\pi$
$211$	6.00679	+	30.1982i	0.0284682	+	0.143119i	−0.963937	+	0.266130i	$0.914255\pi$
$212$		0			0
$213$	−45.7549	+	110.462i	−0.214812	+	0.518602i
$214$		0			0
$215$	289.504	+	193.441i	1.34653	+	0.899723i
$216$		0			0
$217$	5.15650	+	5.15650i	0.0237627	+	0.0237627i
$218$		0			0
$219$	−260.282	+	107.812i	−1.18850	+	0.492294i
$220$		0			0
$221$	190.391	−	64.5870i	0.861497	−	0.292249i
$222$		0			0
$223$	−23.2265	−	56.0738i	−0.104155	−	0.251452i	0.863207	−	0.504849i	$-0.168452\pi$
$223$	−23.2265	−	56.0738i	−0.104155	−	0.251452i	−0.967362	+	0.253397i	$0.918452\pi$
$224$		0			0
$225$	7.27780	−	7.27780i	0.0323458	−	0.0323458i
$226$		0			0
$227$	−203.683	+	304.833i	−0.897283	+	1.34288i	0.0417778	+	0.999127i	$0.486698\pi$
$227$	−203.683	+	304.833i	−0.897283	+	1.34288i	−0.939061	+	0.343752i	$0.888302\pi$
$228$		0			0
$229$	−126.630	−	52.4521i	−0.552972	−	0.229048i	0.0886591	−	0.996062i	$-0.471742\pi$
$229$	−126.630	−	52.4521i	−0.552972	−	0.229048i	−0.641631	+	0.767014i	$0.721742\pi$
$230$		0			0
$231$	−12.0773	+	2.40233i	−0.0522827	+	0.0103997i
$232$		0			0
$233$	121.145	+	24.0972i	0.519936	+	0.103422i	0.448080	−	0.893993i	$-0.352108\pi$
$233$	121.145	+	24.0972i	0.519936	+	0.103422i	0.0718556	+	0.997415i	$0.477108\pi$
$234$		0			0
$235$	283.457	−	189.400i	1.20620	−	0.805957i
$236$		0			0
$237$			541.389i			2.28434i
$238$		0			0
$239$	220.048			0.920705			0.460352	−	0.887736i	$-0.347723\pi$
$239$	220.048			0.920705			0.460352	+	0.887736i	$0.347723\pi$
$240$		0			0
$241$	−110.397	−	165.220i	−0.458077	−	0.685561i	0.528486	−	0.848942i	$-0.322760\pi$
$241$	−110.397	−	165.220i	−0.458077	−	0.685561i	−0.986563	+	0.163381i	$0.947760\pi$
$242$		0			0
$243$	−67.6890	+	340.296i	−0.278556	+	1.40039i
$244$		0			0
$245$	48.7734	+	245.201i	0.199075	+	1.00082i
$246$		0			0
$247$	−65.5122	+	158.160i	−0.265231	+	0.640325i
$248$		0			0
$249$	97.7475	+	65.3128i	0.392560	+	0.262300i
$250$		0			0
$251$	9.21771	+	9.21771i	0.0367239	+	0.0367239i	0.725230	−	0.688506i	$-0.241733\pi$
$251$	9.21771	+	9.21771i	0.0367239	+	0.0367239i	−0.688506	+	0.725230i	$0.741733\pi$
$252$		0			0
$253$	7.23783	−	2.99801i	0.0286080	−	0.0118498i
$254$		0			0
$255$	−24.4573	+	372.019i	−0.0959111	+	1.45890i
$256$		0			0
$257$	−121.978	−	294.480i	−0.474622	−	1.14584i	−0.962098	−	0.272702i	$-0.912083\pi$
$257$	−121.978	−	294.480i	−0.474622	−	1.14584i	0.487477	−	0.873136i	$-0.337917\pi$
$258$		0			0
$259$	4.40874	−	4.40874i	0.0170222	−	0.0170222i
$260$		0			0
$261$	−271.045	+	405.647i	−1.03849	+	1.55420i
$262$		0			0
$263$	250.797	+	103.883i	0.953599	+	0.394994i	0.804583	−	0.593841i	$-0.202389\pi$
$263$	250.797	+	103.883i	0.953599	+	0.394994i	0.149017	+	0.988835i	$0.452389\pi$
$264$		0			0
$265$	−66.6901	+	13.2655i	−0.251661	+	0.0500585i
$266$		0			0
$267$	−360.184	−	71.6450i	−1.34900	−	0.268333i
$268$		0			0
$269$	337.277	−	225.361i	1.25382	−	0.837774i	0.261953	−	0.965081i	$-0.415633\pi$
$269$	337.277	−	225.361i	1.25382	−	0.837774i	0.991863	+	0.127307i	$0.0406333\pi$
$270$		0			0
$271$		−	399.282i		−	1.47336i	−0.676239	−	0.736682i	$-0.736391\pi$
$271$		−	399.282i		−	1.47336i	0.676239	−	0.736682i	$-0.263609\pi$
$272$		0			0
$273$	11.9814			0.0438880
$274$		0			0
$275$	7.36725	+	11.0259i	0.0267900	+	0.0400940i
$276$		0			0
$277$	−57.4869	+	289.006i	−0.207534	+	1.04334i	0.726774	+	0.686877i	$0.241019\pi$
$277$	−57.4869	+	289.006i	−0.207534	+	1.04334i	−0.934308	+	0.356467i	$0.883981\pi$
$278$		0			0
$279$	−56.8777	−	285.943i	−0.203863	−	1.02489i
$280$		0			0
$281$	−158.536	+	382.739i	−0.564184	+	1.36206i	0.342208	+	0.939624i	$0.388825\pi$
$281$	−158.536	+	382.739i	−0.564184	+	1.36206i	−0.906392	+	0.422437i	$0.861175\pi$
$282$		0			0
$283$	244.512	+	163.378i	0.864000	+	0.577306i	0.906697	−	0.421782i	$-0.138595\pi$
$283$	244.512	+	163.378i	0.864000	+	0.577306i	−0.0426975	+	0.999088i	$0.513595\pi$
$284$		0			0
$285$	−224.476	−	224.476i	−0.787636	−	0.787636i
$286$		0			0
$287$	−12.5339	+	5.19170i	−0.0436720	+	0.0180895i
$288$		0			0
$289$	−175.841	−	229.349i	−0.608448	−	0.793594i
$290$		0			0
$291$	38.7787	+	93.6202i	0.133260	+	0.321719i
$292$		0			0
$293$	−4.42680	+	4.42680i	−0.0151085	+	0.0151085i	−0.714621	−	0.699512i	$-0.753401\pi$
$293$	−4.42680	+	4.42680i	−0.0151085	+	0.0151085i	0.699512	+	0.714621i	$0.253401\pi$
$294$		0			0
$295$	230.775	−	345.379i	0.782287	−	1.17078i
$296$		0			0
$297$	20.9149	+	8.66324i	0.0704206	+	0.0291692i
$298$		0			0
$299$	−7.47617	+	1.48710i	−0.0250039	+	0.00497359i
$300$		0			0
$301$	−15.7757	−	3.13798i	−0.0524109	−	0.0104252i
$302$		0			0
$303$	610.488	−	407.915i	2.01481	−	1.34625i
$304$		0			0
$305$		−	252.317i		−	0.827269i
$306$		0			0
$307$	−118.137			−0.384811			−0.192405	−	0.981316i	$-0.561629\pi$
$307$	−118.137			−0.384811			−0.192405	+	0.981316i	$0.561629\pi$
$308$		0			0
$309$	−164.192	−	245.731i	−0.531367	−	0.795247i
$310$		0			0
$311$	10.0677	−	50.6135i	0.0323719	−	0.162744i	−0.961218	−	0.275790i	$-0.911061\pi$
$311$	10.0677	−	50.6135i	0.0323719	−	0.162744i	0.993590	+	0.113046i	$0.0360606\pi$
$312$		0			0
$313$	4.15165	+	20.8718i	0.0132641	+	0.0666829i	0.986850	−	0.161636i	$-0.0516771\pi$
$313$	4.15165	+	20.8718i	0.0132641	+	0.0666829i	−0.973586	+	0.228319i	$0.926677\pi$
$314$		0			0
$315$	−4.35134	+	10.5051i	−0.0138138	+	0.0333494i
$316$		0			0
$317$	−45.3390	−	30.2945i	−0.143025	−	0.0955664i	0.481999	−	0.876172i	$-0.339911\pi$
$317$	−45.3390	−	30.2945i	−0.143025	−	0.0955664i	−0.625024	+	0.780605i	$0.714911\pi$
$318$		0			0
$319$	−444.466	−	444.466i	−1.39331	−	1.39331i
$320$		0			0
$321$	−539.073	+	223.292i	−1.67936	+	0.695612i
$322$		0			0
$323$	245.553	+	16.1432i	0.760225	+	0.0499788i
$324$		0			0
$325$	−4.93762	−	11.9205i	−0.0151927	−	0.0366784i
$326$		0			0
$327$	−95.9545	+	95.9545i	−0.293439	+	0.293439i
$328$		0			0
$329$	−8.74953	+	13.0946i	−0.0265943	+	0.0398012i
$330$		0			0
$331$	349.338	+	144.701i	1.05540	+	0.437162i	0.841818	−	0.539762i	$-0.181486\pi$
$331$	349.338	+	144.701i	1.05540	+	0.437162i	0.213586	+	0.976924i	$0.431486\pi$
$332$		0			0
$333$	−244.478	+	48.6297i	−0.734168	+	0.146035i
$334$		0			0
$335$	290.911	+	57.8659i	0.868392	+	0.172734i
$336$		0			0
$337$	−237.581	+	158.746i	−0.704988	+	0.471058i	−0.855668	−	0.517525i	$-0.826854\pi$
$337$	−237.581	+	158.746i	−0.704988	+	0.471058i	0.150680	+	0.988583i	$0.451854\pi$
$338$		0			0
$339$		−	878.132i		−	2.59036i
$340$		0			0
$341$	375.627			1.10155
$342$		0			0
$343$	−12.8401	−	19.2166i	−0.0374348	−	0.0560251i
$344$		0			0
$345$	2.75768	−	13.8638i	0.00799328	−	0.0401849i
$346$		0			0
$347$	79.0087	+	397.204i	0.227691	+	1.14468i	0.910317	+	0.413911i	$0.135838\pi$
$347$	79.0087	+	397.204i	0.227691	+	1.14468i	−0.682626	+	0.730768i	$0.739162\pi$
$348$		0			0
$349$	244.695	−	590.745i	0.701130	−	1.69268i	−0.0199252	−	0.999801i	$-0.506343\pi$
$349$	244.695	−	590.745i	0.701130	−	1.69268i	0.721056	−	0.692877i	$-0.243657\pi$
$350$		0			0
$351$	−18.3147	−	12.2375i	−0.0521786	−	0.0348646i
$352$		0			0
$353$	49.1876	+	49.1876i	0.139342	+	0.139342i	0.773337	−	0.633995i	$-0.218586\pi$
$353$	49.1876	+	49.1876i	0.139342	+	0.139342i	−0.633995	+	0.773337i	$0.718586\pi$
$354$		0			0
$355$	−131.417	+	54.4347i	−0.370189	+	0.153337i
$356$		0			0
$357$	−5.53291	−	16.3100i	−0.0154983	−	0.0456863i
$358$		0			0
$359$	−46.9818	−	113.424i	−0.130868	−	0.315944i	0.844839	−	0.535020i	$-0.179696\pi$
$359$	−46.9818	−	113.424i	−0.130868	−	0.315944i	−0.975708	+	0.219076i	$0.929696\pi$
$360$		0			0
$361$	107.099	−	107.099i	0.296674	−	0.296674i
$362$		0			0
$363$	−63.7653	+	95.4315i	−0.175662	+	0.262897i
$364$		0			0
$365$	−309.658	−	128.265i	−0.848378	−	0.351410i
$366$		0			0
$367$	546.020	−	108.610i	1.48779	−	0.295940i	0.616755	−	0.787155i	$-0.288447\pi$
$367$	546.020	−	108.610i	1.48779	−	0.295940i	0.871038	+	0.491215i	$0.163447\pi$
$368$		0			0
$369$	531.961	+	105.814i	1.44163	+	0.286758i
$370$		0			0
$371$	2.61180	−	1.74515i	0.00703989	−	0.00470390i
$372$		0			0
$373$			681.316i			1.82659i	0.407304	+	0.913293i	$0.366469\pi$
$373$			681.316i			1.82659i	−0.407304	+	0.913293i	$0.633531\pi$
$374$		0			0
$375$	−524.341			−1.39824
$376$		0			0
$377$	339.785	+	508.524i	0.901287	+	1.34887i
$378$		0			0
$379$	26.6533	−	133.995i	0.0703254	−	0.353550i	−0.929560	−	0.368670i	$-0.879813\pi$
$379$	26.6533	−	133.995i	0.0703254	−	0.353550i	0.999886	+	0.0151205i	$0.00481319\pi$
$380$		0			0
$381$	−195.083	−	980.749i	−0.512029	−	2.57414i
$382$		0			0
$383$	−42.2054	+	101.893i	−0.110197	+	0.266039i	−0.969352	−	0.245677i	$-0.920990\pi$
$383$	−42.2054	+	101.893i	−0.110197	+	0.266039i	0.859155	+	0.511716i	$0.170990\pi$
$384$		0			0
$385$	−12.1809	−	8.13904i	−0.0316388	−	0.0211404i
$386$		0			0
$387$	454.710	+	454.710i	1.17496	+	1.17496i
$388$		0			0
$389$	202.651	−	83.9409i	0.520955	−	0.215786i	−0.106682	−	0.994293i	$-0.534023\pi$
$389$	202.651	−	83.9409i	0.520955	−	0.215786i	0.627636	+	0.778507i	$0.284023\pi$
$390$		0			0
$391$	5.47678	+	9.49040i	0.0140071	+	0.0242721i
$392$		0			0
$393$	−106.701	−	257.598i	−0.271503	−	0.655466i
$394$		0			0
$395$	−455.441	+	455.441i	−1.15302	+	1.15302i
$396$		0			0
$397$	−210.360	+	314.826i	−0.529875	+	0.793014i	−0.995775	−	0.0918233i	$-0.970730\pi$
$397$	−210.360	+	314.826i	−0.529875	+	0.793014i	0.465900	+	0.884837i	$0.345730\pi$
$398$		0			0
$399$	13.5490	+	5.61216i	0.0339573	+	0.0140656i
$400$		0			0
$401$	750.341	−	149.252i	1.87117	−	0.372200i	0.877046	−	0.480406i	$-0.159511\pi$
$401$	750.341	−	149.252i	1.87117	−	0.372200i	0.994128	+	0.108206i	$0.0345107\pi$
$402$		0			0
$403$	−358.462	−	71.3025i	−0.889484	−	0.176929i
$404$		0			0
$405$	−326.634	+	218.250i	−0.806503	+	0.538888i
$406$		0			0
$407$		−	321.157i		−	0.789082i
$408$		0			0
$409$	−104.320			−0.255061			−0.127530	−	0.991835i	$-0.540705\pi$
$409$	−104.320			−0.255061			−0.127530	+	0.991835i	$0.540705\pi$
$410$		0			0
$411$	248.204	+	371.464i	0.603904	+	0.903806i
$412$		0			0
$413$	−3.74361	+	18.8204i	−0.00906443	+	0.0455700i
$414$		0			0
$415$	27.2856	+	137.174i	0.0657484	+	0.330539i
$416$		0			0
$417$	63.1833	−	152.538i	0.151519	−	0.365798i
$418$		0			0
$419$	−247.370	−	165.288i	−0.590383	−	0.394481i	0.224188	−	0.974546i	$-0.428027\pi$
$419$	−247.370	−	165.288i	−0.590383	−	0.394481i	−0.814570	+	0.580065i	$0.803027\pi$
$420$		0			0
$421$	−225.006	−	225.006i	−0.534455	−	0.534455i	0.387440	−	0.921895i	$-0.373359\pi$
$421$	−225.006	−	225.006i	−0.534455	−	0.534455i	−0.921895	+	0.387440i	$0.873359\pi$
$422$		0			0
$423$	581.698	−	240.947i	1.37517	−	0.569615i
$424$		0			0
$425$	−13.9469	+	12.2262i	−0.0328163	+	0.0287676i
$426$		0			0
$427$	4.46058	+	10.7688i	0.0104463	+	0.0252197i
$428$		0			0
$429$	436.396	−	436.396i	1.01724	−	1.01724i
$430$		0			0
$431$	110.346	−	165.144i	0.256022	−	0.383164i	−0.681086	−	0.732204i	$-0.738492\pi$
$431$	110.346	−	165.144i	0.256022	−	0.383164i	0.937108	+	0.349039i	$0.113492\pi$
$432$		0			0
$433$	−252.292	−	104.503i	−0.582660	−	0.241346i	0.0718294	−	0.997417i	$-0.477116\pi$
$433$	−252.292	−	104.503i	−0.582660	−	0.241346i	−0.654489	+	0.756071i	$0.727116\pi$
$434$		0			0
$435$	−1112.35	+	221.261i	−2.55713	+	0.508645i
$436$		0			0
$437$	−9.15085	−	1.82022i	−0.0209402	−	0.00416526i
$438$		0			0
$439$	−568.890	+	380.120i	−1.29588	+	0.865877i	−0.996109	−	0.0881345i	$-0.971909\pi$
$439$	−568.890	+	380.120i	−1.29588	+	0.865877i	−0.299769	+	0.954012i	$0.596909\pi$
$440$		0			0
$441$			461.731i			1.04701i
$442$		0			0
$443$	338.636			0.764415			0.382207	−	0.924077i	$-0.375164\pi$
$443$	338.636			0.764415			0.382207	+	0.924077i	$0.375164\pi$
$444$		0			0
$445$	−242.732	−	363.274i	−0.545465	−	0.816346i
$446$		0			0
$447$	−52.8477	+	265.684i	−0.118228	+	0.594370i
$448$		0			0
$449$	−10.9927	−	55.2641i	−0.0244827	−	0.123083i	0.966611	−	0.256247i	$-0.0824861\pi$
$449$	−10.9927	−	55.2641i	−0.0244827	−	0.123083i	−0.991094	+	0.133165i	$0.957486\pi$
$450$		0			0
$451$	−267.421	+	645.613i	−0.592952	+	1.43151i
$452$		0			0
$453$	131.032	+	87.5529i	0.289254	+	0.193273i
$454$		0			0
$455$	10.0793	+	10.0793i	0.0221524	+	0.0221524i
$456$		0			0
$457$	−569.625	+	235.947i	−1.24645	+	0.516294i	−0.905723	−	0.423870i	$-0.860671\pi$
$457$	−569.625	+	235.947i	−1.24645	+	0.516294i	−0.340722	+	0.940164i	$0.610671\pi$
$458$		0			0
$459$	−8.20103	+	30.5825i	−0.0178672	+	0.0666285i
$460$		0			0
$461$	307.654	+	742.742i	0.667362	+	1.61115i	0.786007	+	0.618218i	$0.212145\pi$
$461$	307.654	+	742.742i	0.667362	+	1.61115i	−0.118645	+	0.992937i	$0.537855\pi$
$462$		0			0
$463$	5.25852	−	5.25852i	0.0113575	−	0.0113575i	−0.701405	−	0.712763i	$-0.747444\pi$
$463$	5.25852	−	5.25852i	0.0113575	−	0.0113575i	0.712763	+	0.701405i	$0.247444\pi$
$464$		0			0
$465$	376.540	−	563.532i	0.809763	−	1.21190i
$466$		0			0
$467$	−156.855	−	64.9713i	−0.335877	−	0.139125i	0.208369	−	0.978050i	$-0.433184\pi$
$467$	−156.855	−	64.9713i	−0.335877	−	0.139125i	−0.544247	+	0.838925i	$0.683184\pi$
$468$		0			0
$469$	−13.4390	+	2.67318i	−0.0286545	+	0.00569974i
$470$		0			0
$471$	−97.6634	−	19.4265i	−0.207353	−	0.0412452i
$472$		0			0
$473$	−688.886	+	460.299i	−1.45642	+	0.973148i
$474$		0			0
$475$		−	15.7929i		−	0.0332481i
$476$		0			0
$477$	−125.583			−0.263276
$478$		0			0
$479$	71.4108	+	106.874i	0.149083	+	0.223119i	0.898493	−	0.438987i	$-0.144663\pi$
$479$	71.4108	+	106.874i	0.149083	+	0.223119i	−0.749410	+	0.662106i	$0.769663\pi$
$480$		0			0
$481$	−60.9628	+	306.480i	−0.126742	+	0.637174i
$482$		0			0
$483$	0.127394	+	0.640453i	0.000263756	+	0.00132599i
$484$		0			0
$485$	−46.1351	+	111.380i	−0.0951239	+	0.229650i
$486$		0			0
$487$	−616.313	−	411.807i	−1.26553	−	0.845600i	−0.272351	−	0.962198i	$-0.587801\pi$
$487$	−616.313	−	411.807i	−1.26553	−	0.845600i	−0.993179	+	0.116598i	$0.962801\pi$
$488$		0			0
$489$	890.238	+	890.238i	1.82053	+	1.82053i
$490$		0			0
$491$	860.296	−	356.346i	1.75213	−	0.725756i	0.754549	−	0.656244i	$-0.227856\pi$
$491$	860.296	−	356.346i	1.75213	−	0.725756i	0.997581	−	0.0695123i	$-0.0221443\pi$
$492$		0			0
$493$	535.332	−	697.373i	1.08587	−	1.41455i
$494$		0			0
$495$	224.135	+	541.110i	0.452798	+	1.09315i
$496$		0			0
$497$	4.64651	−	4.64651i	0.00934911	−	0.00934911i
$498$		0			0
$499$	−298.749	+	447.109i	−0.598695	+	0.896010i	−0.999800	−	0.0200220i	$-0.993626\pi$
$499$	−298.749	+	447.109i	−0.598695	+	0.896010i	0.401105	+	0.916032i	$0.368626\pi$
$500$		0			0
$501$	157.917	+	65.4114i	0.315204	+	0.130562i
$502$		0			0
$503$	−490.483	+	97.5631i	−0.975115	+	0.193963i	−0.656835	−	0.754034i	$-0.728105\pi$
$503$	−490.483	+	97.5631i	−0.975115	+	0.193963i	−0.318280	+	0.947997i	$0.603105\pi$
$504$		0			0
$505$	856.727	+	170.414i	1.69649	+	0.337453i
$506$		0			0
$507$	104.019	−	69.5032i	0.205165	−	0.137087i
$508$		0			0
$509$			448.993i			0.882108i	0.897481	+	0.441054i	$0.145395\pi$
$509$			448.993i			0.882108i	−0.897481	+	0.441054i	$0.854605\pi$
$510$		0			0
$511$	15.4836			0.0303006
$512$		0			0
$513$	−14.9787	−	22.4172i	−0.0291983	−	0.0436983i
$514$		0			0
$515$	68.5942	−	344.847i	0.133193	−	0.669605i
$516$		0			0
$517$	158.259	+	795.622i	0.306110	+	1.53892i
$518$		0			0
$519$	529.940	−	1279.39i	1.02108	−	2.46510i
$520$		0			0
$521$	−132.683	−	88.6559i	−0.254670	−	0.170165i	0.421682	−	0.906744i	$-0.361440\pi$
$521$	−132.683	−	88.6559i	−0.254670	−	0.170165i	−0.676351	+	0.736579i	$0.736440\pi$
$522$		0			0
$523$	237.936	+	237.936i	0.454944	+	0.454944i	0.896992	−	0.442047i	$-0.145748\pi$
$523$	237.936	+	237.936i	0.454944	+	0.454944i	−0.442047	+	0.896992i	$0.645748\pi$
$524$		0			0
$525$	−1.02118	+	0.422986i	−0.00194510	+	0.000805688i
$526$		0			0
$527$	68.4720	+	520.892i	0.129928	+	0.988411i
$528$		0			0
$529$	202.281	+	488.348i	0.382383	+	0.923154i
$530$		0			0
$531$	542.470	−	542.470i	1.02160	−	1.02160i
$532$		0			0
$533$	377.753	−	565.347i	0.708730	−	1.06069i
$534$		0			0
$535$	−641.336	−	265.650i	−1.19876	−	0.496542i
$536$		0			0
$537$	275.717	−	54.8435i	0.513440	−	0.102129i
$538$		0			0
$539$	−583.464	−	116.058i	−1.08249	−	0.215321i
$540$		0			0
$541$	−623.699	+	416.743i	−1.15286	+	0.770319i	−0.976820	−	0.214063i	$-0.931330\pi$
$541$	−623.699	+	416.743i	−1.15286	+	0.770319i	−0.176044	+	0.984382i	$0.556330\pi$
$542$		0			0
$543$			451.283i			0.831093i
$544$		0			0
$545$	−161.443			−0.296225
$546$		0			0
$547$	−289.723	−	433.601i	−0.529657	−	0.792688i	0.466097	−	0.884733i	$-0.345660\pi$
$547$	−289.723	−	433.601i	−0.529657	−	0.792688i	−0.995755	+	0.0920450i	$0.970660\pi$
$548$		0			0
$549$	90.9125	−	457.048i	0.165597	−	0.832510i
$550$		0			0
$551$	146.044	+	734.212i	0.265052	+	1.33251i
$552$		0			0
$553$	11.3866	−	27.4896i	0.0205905	−	0.0497099i
$554$		0			0
$555$	−481.813	−	321.937i	−0.868131	−	0.580067i
$556$		0			0
$557$	71.9623	+	71.9623i	0.129196	+	0.129196i	0.768748	−	0.639552i	$-0.220880\pi$
$557$	71.9623	+	71.9623i	0.129196	+	0.129196i	−0.639552	+	0.768748i	$0.720880\pi$
$558$		0			0
$559$	744.781	−	308.498i	1.33234	−	0.551875i
$560$		0			0
$561$	−795.578	−	392.531i	−1.41814	−	0.699699i
$562$		0			0
$563$	49.7499	+	120.107i	0.0883657	+	0.213334i	0.961884	−	0.273457i	$-0.0881673\pi$
$563$	49.7499	+	120.107i	0.0883657	+	0.213334i	−0.873518	+	0.486791i	$0.838167\pi$
$564$		0			0
$565$	738.725	−	738.725i	1.30748	−	1.30748i
$566$		0			0
$567$	10.0823	−	15.0892i	0.0177818	−	0.0266124i
$568$		0			0
$569$	−473.072	−	195.953i	−0.831409	−	0.344381i	−0.0739485	−	0.997262i	$-0.523560\pi$
$569$	−473.072	−	195.953i	−0.831409	−	0.344381i	−0.757460	+	0.652881i	$0.773560\pi$
$570$		0			0
$571$	−95.5778	+	19.0116i	−0.167387	+	0.0332953i	−0.278072	−	0.960560i	$-0.589695\pi$
$571$	−95.5778	+	19.0116i	−0.167387	+	0.0332953i	0.110685	+	0.993855i	$0.464695\pi$
$572$		0			0
$573$	−1029.47	−	204.775i	−1.79663	−	0.357373i
$574$		0			0
$575$	0.584696	−	0.390681i	0.00101686	−	0.000679446i
$576$		0			0
$577$		−	1039.52i		−	1.80159i	−0.434246	−	0.900794i	$-0.642985\pi$
$577$		−	1039.52i		−	1.80159i	0.434246	−	0.900794i	$-0.357015\pi$
$578$		0			0
$579$	−824.469			−1.42395
$580$		0			0
$581$	−3.58956	−	5.37216i	−0.00617825	−	0.00924641i
$582$		0			0
$583$	31.5657	−	158.692i	0.0541436	−	0.272198i
$584$		0			0
$585$	−111.178	−	558.929i	−0.190048	−	0.955433i
$586$		0			0
$587$	74.7915	−	180.563i	0.127413	−	0.307603i	−0.847281	−	0.531145i	$-0.821762\pi$
$587$	74.7915	−	180.563i	0.127413	−	0.307603i	0.974694	+	0.223542i	$0.0717620\pi$
$588$		0			0
$589$	−371.961	−	248.537i	−0.631514	−	0.421964i
$590$		0			0
$591$	−245.471	−	245.471i	−0.415348	−	0.415348i
$592$		0			0
$593$	180.167	−	74.6278i	0.303824	−	0.125848i	−0.225563	−	0.974229i	$-0.572422\pi$
$593$	180.167	−	74.6278i	0.303824	−	0.125848i	0.529387	+	0.848381i	$0.322422\pi$
$594$		0			0
$595$	9.06620	−	18.3753i	0.0152373	−	0.0308828i
$596$		0			0
$597$	14.2300	+	34.3543i	0.0238359	+	0.0575449i
$598$		0			0
$599$	−560.311	+	560.311i	−0.935411	+	0.935411i	−0.998037	−	0.0626264i	$-0.980052\pi$
$599$	−560.311	+	560.311i	−0.935411	+	0.935411i	0.0626264	+	0.998037i	$0.480052\pi$
$600$		0			0
$601$	612.466	−	916.620i	1.01908	−	1.52516i	0.178154	−	0.984003i	$-0.442987\pi$
$601$	612.466	−	916.620i	1.01908	−	1.52516i	0.840923	−	0.541155i	$-0.182013\pi$
$602$		0			0
$603$	506.109	+	209.637i	0.839318	+	0.347657i
$604$		0			0
$605$	−133.924	+	26.6391i	−0.221361	+	0.0440315i
$606$		0			0
$607$	−97.5048	−	19.3949i	−0.160634	−	0.0319521i	0.114118	−	0.993467i	$-0.463596\pi$
$607$	−97.5048	−	19.3949i	−0.160634	−	0.0319521i	−0.274752	+	0.961515i	$0.588596\pi$
$608$		0			0
$609$	43.5632	−	29.1080i	0.0715324	−	0.0477964i
$610$		0			0
$611$		−	789.305i		−	1.29183i
$612$		0			0
$613$	190.687			0.311072			0.155536	−	0.987830i	$-0.450290\pi$
$613$	190.687			0.311072			0.155536	+	0.987830i	$0.450290\pi$
$614$		0			0
$615$	700.504	+	1048.38i	1.13903	+	1.70468i
$616$		0			0
$617$	104.321	−	524.458i	0.169078	−	0.850013i	−0.799378	−	0.600828i	$-0.794838\pi$
$617$	104.321	−	524.458i	0.169078	−	0.850013i	0.968456	−	0.249184i	$-0.0801625\pi$
$618$		0			0
$619$	124.525	+	626.027i	0.201171	+	1.01135i	0.940961	+	0.338515i	$0.109925\pi$
$619$	124.525	+	626.027i	0.201171	+	1.01135i	−0.739790	+	0.672838i	$0.765075\pi$
$620$		0			0
$621$	0.459407	−	1.10911i	0.000739786	−	0.00178600i
$622$		0			0
$623$	16.7819	+	11.2133i	0.0269372	+	0.0179988i
$624$		0			0
$625$	−460.387	−	460.387i	−0.736619	−	0.736619i
$626$		0			0
$627$	697.900	−	289.080i	1.11308	−	0.461052i
$628$		0			0
$629$	445.356	−	58.5427i	0.708039	−	0.0930726i
$630$		0			0
$631$	−199.771	−	482.290i	−0.316595	−	0.764327i	−0.999430	−	0.0337549i	$-0.989253\pi$
$631$	−199.771	−	482.290i	−0.316595	−	0.764327i	0.682836	−	0.730572i	$-0.260747\pi$
$632$		0			0
$633$	−93.4759	+	93.4759i	−0.147671	+	0.147671i
$634$		0			0
$635$	660.938	−	989.164i	1.04085	−	1.55774i
$636$		0			0
$637$	534.771	+	221.509i	0.839515	+	0.347738i
$638$		0			0
$639$	−257.663	+	51.2523i	−0.403228	+	0.0802070i
$640$		0			0
$641$	−469.686	−	93.4263i	−0.732739	−	0.145751i	−0.185402	−	0.982663i	$-0.559359\pi$
$641$	−469.686	−	93.4263i	−0.732739	−	0.145751i	−0.547338	+	0.836912i	$0.684359\pi$
$642$		0			0
$643$	−179.162	+	119.712i	−0.278635	+	0.186178i	−0.687033	−	0.726626i	$-0.741087\pi$
$643$	−179.162	+	119.712i	−0.278635	+	0.186178i	0.408399	+	0.912804i	$0.366087\pi$
$644$		0			0
$645$			1494.91i			2.31769i
$646$		0			0
$647$	132.439			0.204697			0.102349	−	0.994749i	$-0.467364\pi$
$647$	132.439			0.204697			0.102349	+	0.994749i	$0.467364\pi$
$648$		0			0
$649$	549.137	+	821.841i	0.846128	+	1.26632i
$650$		0			0
$651$	−6.10820	+	30.7080i	−0.00938280	+	0.0471705i
$652$		0			0
$653$	66.9487	+	336.574i	0.102525	+	0.515427i	0.997583	+	0.0694787i	$0.0221336\pi$
$653$	66.9487	+	336.574i	0.102525	+	0.515427i	−0.895059	+	0.445949i	$0.852866\pi$
$654$		0			0
$655$	126.942	−	306.465i	0.193804	−	0.467885i
$656$		0			0
$657$	−514.701	−	343.912i	−0.783411	−	0.523458i
$658$		0			0
$659$	143.197	+	143.197i	0.217294	+	0.217294i	0.807357	−	0.590063i	$-0.200897\pi$
$659$	143.197	+	143.197i	0.217294	+	0.217294i	−0.590063	+	0.807357i	$0.700897\pi$
$660$		0			0
$661$	−110.702	+	45.8543i	−0.167477	+	0.0693711i	−0.464847	−	0.885391i	$-0.653891\pi$
$661$	−110.702	+	45.8543i	−0.167477	+	0.0693711i	0.297370	+	0.954762i	$0.403891\pi$
$662$		0			0
$663$	684.711	+	525.612i	1.03275	+	0.792779i
$664$		0			0
$665$	6.67680	+	16.1192i	0.0100403	+	0.0242394i
$666$		0			0
$667$	−23.5698	+	23.5698i	−0.0353370	+	0.0353370i
$668$		0			0
$669$	144.774	−	216.670i	0.216404	−	0.323871i
$670$		0			0
$671$	554.695	+	229.762i	0.826669	+	0.342418i
$672$		0			0
$673$	412.055	−	81.9629i	0.612267	−	0.121787i	0.120790	−	0.992678i	$-0.461457\pi$
$673$	412.055	−	81.9629i	0.612267	−	0.121787i	0.491477	+	0.870891i	$0.336457\pi$
$674$		0			0
$675$	1.99299	+	0.396430i	0.00295258	+	0.000587304i
$676$		0			0
$677$	−509.177	+	340.222i	−0.752109	+	0.502543i	−0.871555	−	0.490298i	$-0.836888\pi$
$677$	−509.177	+	340.222i	−0.752109	+	0.502543i	0.119446	+	0.992841i	$0.461888\pi$
$678$		0			0
$679$		−	5.56926i		−	0.00820215i
$680$		0			0
$681$	−1574.07			−2.31141
$682$		0			0
$683$	−364.126	−	544.954i	−0.533128	−	0.797882i	0.462948	−	0.886385i	$-0.346792\pi$
$683$	−364.126	−	544.954i	−0.533128	−	0.797882i	−0.996076	+	0.0885032i	$0.971792\pi$
$684$		0			0
$685$	−103.692	+	521.294i	−0.151375	+	0.761013i
$686$		0			0
$687$	−114.806	−	577.171i	−0.167113	−	0.840132i
$688$		0			0
$689$	−60.2465	+	145.448i	−0.0874405	+	0.211100i
$690$		0			0
$691$	984.285	+	657.678i	1.42444	+	0.951777i	0.998903	+	0.0468346i	$0.0149134\pi$
$691$	984.285	+	657.678i	1.42444	+	0.951777i	0.425533	+	0.904943i	$0.360087\pi$
$692$		0			0
$693$	−19.1320	−	19.1320i	−0.0276075	−	0.0276075i
$694$		0			0
$695$	181.475	−	75.1692i	0.261114	−	0.108157i
$696$		0			0
$697$	−944.036	−	253.154i	−1.35443	−	0.363205i
$698$		0			0
$699$	202.945	+	489.953i	0.290336	+	0.700934i
$700$		0			0
$701$	−426.663	+	426.663i	−0.608648	+	0.608648i	−0.942593	−	0.333944i	$-0.891620\pi$
$701$	−426.663	+	426.663i	−0.608648	+	0.608648i	0.333944	+	0.942593i	$0.391620\pi$
$702$		0			0
$703$	−212.496	+	318.022i	−0.302270	+	0.452379i
$704$		0			0
$705$	1352.27	+	560.128i	1.91811	+	0.794508i
$706$		0			0
$707$	−39.5775	+	7.87245i	−0.0559794	+	0.0111350i
$708$		0			0
$709$	660.721	+	131.426i	0.931906	+	0.185368i	0.637621	−	0.770350i	$-0.279919\pi$
$709$	660.721	+	131.426i	0.931906	+	0.185368i	0.294285	+	0.955718i	$0.404919\pi$
$710$		0			0
$711$	−989.089	+	660.888i	−1.39112	+	0.929519i
$712$		0			0
$713$		−	19.9193i		−	0.0279373i
$714$		0			0
$715$	734.232			1.02690
$716$		0			0
$717$	524.886	+	785.547i	0.732058	+	1.09560i
$718$		0			0
$719$	75.0077	−	377.089i	0.104322	−	0.524464i	−0.892918	−	0.450220i	$-0.851346\pi$
$719$	75.0077	−	377.089i	0.104322	−	0.524464i	0.997240	−	0.0742440i	$-0.0236544\pi$
$720$		0			0
$721$	3.16879	+	15.9306i	0.00439499	+	0.0220951i
$722$		0			0
$723$	326.485	−	788.205i	0.451570	−	1.09019i
$724$		0			0
$725$	−46.9127	−	31.3460i	−0.0647071	−	0.0432359i
$726$		0			0
$727$	172.867	+	172.867i	0.237782	+	0.237782i	0.815931	−	0.578149i	$-0.196225\pi$
$727$	172.867	+	172.867i	0.237782	+	0.237782i	−0.578149	+	0.815931i	$0.696225\pi$
$728$		0			0
$729$	−736.795	+	305.191i	−1.01069	+	0.418643i
$730$		0			0
$731$	−763.884	−	871.390i	−1.04498	−	1.19205i
$732$		0			0
$733$	−325.790	−	786.527i	−0.444462	−	1.07303i	−0.974366	−	0.224968i	$-0.927772\pi$
$733$	−325.790	−	786.527i	−0.444462	−	1.07303i	0.529905	−	0.848057i	$-0.322228\pi$
$734$		0			0
$735$	−758.997	+	758.997i	−1.03265	+	1.03265i
$736$		0			0
$737$	−392.119	+	586.848i	−0.532048	+	0.796266i
$738$		0			0
$739$	811.203	+	336.011i	1.09770	+	0.454684i	0.856687	−	0.515837i	$-0.172519\pi$
$739$	811.203	+	336.011i	1.09770	+	0.454684i	0.241017	+	0.970521i	$0.422519\pi$
$740$		0			0
$741$	−720.881	+	143.392i	−0.972849	+	0.193512i
$742$		0			0
$743$	−820.304	−	163.169i	−1.10404	−	0.219608i	−0.390766	−	0.920490i	$-0.627790\pi$
$743$	−820.304	−	163.169i	−1.10404	−	0.219608i	−0.713277	+	0.700882i	$0.752790\pi$
$744$		0			0
$745$	−267.963	+	179.047i	−0.359682	+	0.240332i
$746$		0			0
$747$			258.309i			0.345795i
$748$		0			0
$749$	32.0683			0.0428148
$750$		0			0
$751$	−133.600	−	199.946i	−0.177896	−	0.266240i	0.731796	−	0.681524i	$-0.238682\pi$
$751$	−133.600	−	199.946i	−0.177896	−	0.266240i	−0.909692	+	0.415284i	$0.863682\pi$
$752$		0			0
$753$	−10.9190	+	54.8933i	−0.0145006	+	0.0728995i
$754$		0			0
$755$	36.5767	+	183.884i	0.0484460	+	0.243555i
$756$		0			0
$757$	109.884	−	265.284i	0.145157	−	0.350441i	−0.834533	−	0.550958i	$-0.814262\pi$
$757$	109.884	−	265.284i	0.145157	−	0.350441i	0.979690	+	0.200517i	$0.0642623\pi$
$758$		0			0
$759$	27.9671	+	18.6870i	0.0368473	+	0.0246206i
$760$		0			0
$761$	996.415	+	996.415i	1.30935	+	1.30935i	0.921884	+	0.387466i	$0.126650\pi$
$761$	996.415	+	996.415i	1.30935	+	1.30935i	0.387466	+	0.921884i	$0.373350\pi$
$762$		0			0
$763$	6.89031	−	2.85406i	0.00903056	−	0.00374058i
$764$		0			0
$765$	−709.515	+	409.452i	−0.927470	+	0.535231i
$766$		0			0
$767$	−368.039	−	888.524i	−0.479842	−	1.15844i
$768$		0			0
$769$	−490.430	+	490.430i	−0.637750	+	0.637750i	−0.950000	−	0.312250i	$-0.898917\pi$
$769$	−490.430	+	490.430i	−0.637750	+	0.637750i	0.312250	+	0.950000i	$0.398917\pi$
$770$		0			0
$771$	760.304	−	1137.88i	0.986128	−	1.47584i
$772$		0			0
$773$	−1057.30	−	437.946i	−1.36778	−	0.566554i	−0.426596	−	0.904442i	$-0.640287\pi$
$773$	−1057.30	−	437.946i	−1.36778	−	0.566554i	−0.941186	+	0.337888i	$0.890287\pi$
$774$		0			0
$775$	33.0690	−	6.57784i	0.0426697	−	0.00848754i
$776$		0			0
$777$	26.2550	+	5.22243i	0.0337902	+	0.00672128i
$778$		0			0
$779$	691.986	−	462.371i	0.888301	−	0.593544i
$780$		0			0
$781$		−	338.477i		−	0.433389i
$782$		0			0
$783$	−96.3204			−0.123015
$784$		0			0
$785$	−65.8165	−	98.5014i	−0.0838427	−	0.125479i
$786$		0			0
$787$	−159.414	+	801.426i	−0.202559	+	1.01833i	0.736987	+	0.675907i	$0.236248\pi$
$787$	−159.414	+	801.426i	−0.202559	+	1.01833i	−0.939546	+	0.342424i	$0.888752\pi$
$788$		0			0
$789$	227.379	+	1143.11i	0.288186	+	1.44881i
$790$		0			0
$791$	−18.4690	+	44.5881i	−0.0233489	+	0.0563692i
$792$		0			0
$793$	−485.733	−	324.556i	−0.612526	−	0.409277i
$794$		0			0
$795$	−206.434	−	206.434i	−0.259665	−	0.259665i
$796$		0			0
$797$	177.963	−	73.7147i	0.223291	−	0.0924903i	−0.268233	−	0.963354i	$-0.586440\pi$
$797$	177.963	−	73.7147i	0.223291	−	0.0924903i	0.491525	+	0.870864i	$0.336440\pi$
$798$		0			0
$799$	−1074.46	+	364.494i	−1.34476	+	0.456187i
$800$		0			0
$801$	−308.794	−	745.495i	−0.385511	−	0.930706i
$802$		0			0
$803$	563.955	−	563.955i	0.702310	−	0.702310i
$804$		0			0
$805$	−0.431609	+	0.645949i	−0.000536160	+	0.000802421i
$806$		0			0
$807$	1609.03	+	666.480i	1.99384	+	0.825874i
$808$		0			0
$809$	445.793	−	88.6737i	0.551042	−	0.109609i	0.0882866	−	0.996095i	$-0.471861\pi$
$809$	445.793	−	88.6737i	0.551042	−	0.109609i	0.462755	+	0.886486i	$0.346861\pi$
$810$		0			0
$811$	516.811	+	102.800i	0.637252	+	0.126757i	0.503134	−	0.864208i	$-0.332180\pi$
$811$	516.811	+	102.800i	0.637252	+	0.126757i	0.134117	+	0.990965i	$0.457180\pi$
$812$		0			0
$813$	1425.39	−	952.414i	1.75325	−	1.17148i
$814$		0			0
$815$			1497.82i			1.83781i
$816$		0			0
$817$	986.723			1.20774
$818$		0			0
$819$	14.6260	+	21.8894i	0.0178584	+	0.0267270i
$820$		0			0
$821$	−8.39428	+	42.2009i	−0.0102245	+	0.0514018i	−0.985561	−	0.169322i	$-0.945842\pi$
$821$	−8.39428	+	42.2009i	−0.0102245	+	0.0514018i	0.975336	+	0.220724i	$0.0708421\pi$
$822$		0			0
$823$	262.654	+	1320.45i	0.319142	+	1.60444i	0.723828	+	0.689980i	$0.242381\pi$
$823$	262.654	+	1320.45i	0.319142	+	1.60444i	−0.404686	+	0.914456i	$0.632619\pi$
$824$		0			0
$825$	−21.7878	+	52.6004i	−0.0264095	+	0.0637581i
$826$		0			0
$827$	−369.072	−	246.606i	−0.446279	−	0.298194i	0.312051	−	0.950065i	$-0.398984\pi$
$827$	−369.072	−	246.606i	−0.446279	−	0.298194i	−0.758329	+	0.651872i	$0.773984\pi$
$828$		0			0
$829$	−441.687	−	441.687i	−0.532794	−	0.532794i	0.388609	−	0.921403i	$-0.372956\pi$
$829$	−441.687	−	441.687i	−0.532794	−	0.532794i	−0.921403	+	0.388609i	$0.872956\pi$
$830$		0			0
$831$	−1168.84	+	484.150i	−1.40655	+	0.582612i
$832$		0			0
$833$	54.5831	−	830.261i	0.0655260	−	0.996712i
$834$		0			0
$835$	77.8200	+	187.874i	0.0931976	+	0.224999i
$836$		0			0
$837$	40.7012	−	40.7012i	0.0486275	−	0.0486275i
$838$		0			0
$839$	−327.196	+	489.684i	−0.389983	+	0.583651i	−0.973567	−	0.228402i	$-0.926650\pi$
$839$	−327.196	+	489.684i	−0.389983	+	0.583651i	0.583584	+	0.812053i	$0.301650\pi$
$840$		0			0
$841$	1693.86	+	701.622i	2.01411	+	0.834271i
$842$		0			0
$843$	−1744.49	+	347.001i	−2.06939	+	0.411626i
$844$		0			0
$845$	145.975	+	29.0362i	0.172751	+	0.0343623i
$846$		0			0
$847$	5.24487	−	3.50451i	0.00619229	−	0.00413756i
$848$		0			0
$849$			1262.59i			1.48715i
$850$		0			0
$851$	−17.0308			−0.0200126
$852$		0			0
$853$	−694.125	−	1038.83i	−0.813746	−	1.21786i	−0.973043	−	0.230626i	$-0.925923\pi$
$853$	−694.125	−	1038.83i	−0.813746	−	1.21786i	0.159297	−	0.987231i	$-0.449077\pi$
$854$		0			0
$855$	136.082	−	684.130i	0.159160	−	0.800152i
$856$		0			0
$857$	−176.868	−	889.174i	−0.206380	−	1.03754i	−0.935546	−	0.353206i	$-0.885092\pi$
$857$	−176.868	−	889.174i	−0.206380	−	1.03754i	0.729166	−	0.684337i	$-0.239908\pi$
$858$		0			0
$859$	−507.553	+	1225.34i	−0.590864	+	1.42647i	0.291805	+	0.956478i	$0.405744\pi$
$859$	−507.553	+	1225.34i	−0.590864	+	1.42647i	−0.882669	+	0.469995i	$0.844256\pi$
$860$		0			0
$861$	−48.4310	−	32.3606i	−0.0562497	−	0.0375849i
$862$		0			0
$863$	−751.738	−	751.738i	−0.871075	−	0.871075i	0.121515	−	0.992590i	$-0.461225\pi$
$863$	−751.738	−	751.738i	−0.871075	−	0.871075i	−0.992590	+	0.121515i	$0.961225\pi$
$864$		0			0
$865$	1522.09	−	630.471i	1.75964	−	0.728868i
$866$		0			0
$867$	399.310	−	1174.80i	0.460565	−	1.35502i
$868$		0			0
$869$	−586.516	−	1415.97i	−0.674932	−	1.62943i
$870$		0			0
$871$	485.597	−	485.597i	0.557517	−	0.557517i
$872$		0			0
$873$	−123.701	+	185.131i	−0.141696	+	0.212063i
$874$		0			0
$875$	26.6240	+	11.0280i	0.0304274	+	0.0126034i
$876$		0			0
$877$	−708.689	+	140.967i	−0.808083	+	0.160738i	−0.581809	−	0.813326i	$-0.697655\pi$
$877$	−708.689	+	140.967i	−0.808083	+	0.160738i	−0.226275	+	0.974064i	$0.572655\pi$
$878$		0			0
$879$	−26.3625	−	5.24382i	−0.0299914	−	0.00596567i
$880$		0			0
$881$	−314.516	+	210.153i	−0.356998	+	0.238539i	−0.721116	−	0.692814i	$-0.756371\pi$
$881$	−314.516	+	210.153i	−0.356998	+	0.238539i	0.364118	+	0.931353i	$0.381371\pi$
$882$		0			0
$883$			1252.31i			1.41825i	0.705084	+	0.709124i	$0.250909\pi$
$883$			1252.31i			1.41825i	−0.705084	+	0.709124i	$0.749091\pi$
$884$		0			0
$885$	1783.43			2.01518
$886$		0			0
$887$	16.6033	+	24.8487i	0.0187185	+	0.0280143i	0.840711	−	0.541484i	$-0.182137\pi$
$887$	16.6033	+	24.8487i	0.0187185	+	0.0280143i	−0.821992	+	0.569499i	$0.807137\pi$
$888$		0			0
$889$	−10.7217	+	53.9016i	−0.0120604	+	0.0606317i
$890$		0			0
$891$	−182.365	−	916.813i	−0.204675	−	1.02897i
$892$		0			0
$893$	369.715	−	892.571i	0.414015	−	0.999520i
$894$		0			0
$895$	278.083	+	185.809i	0.310707	+	0.207608i
$896$		0			0
$897$	−23.1418	−	23.1418i	−0.0257991	−	0.0257991i
$898$		0			0
$899$	−1476.56	+	611.609i	−1.64244	+	0.680322i
$900$		0			0
$901$	225.816	+	14.8456i	0.250628	+	0.0164768i
$902$		0			0
$903$	−26.4278	−	63.8024i	−0.0292667	−	0.0706560i
$904$		0			0
$905$	−379.640	+	379.640i	−0.419492	+	0.419492i
$906$		0			0
$907$	778.713	−	1165.43i	0.858559	−	1.28492i	−0.0985313	−	0.995134i	$-0.531414\pi$
$907$	778.713	−	1165.43i	0.858559	−	1.28492i	0.957090	−	0.289790i	$-0.0935856\pi$
$908$		0			0
$909$	1490.48	+	617.376i	1.63969	+	0.679181i
$910$		0			0
$911$	711.652	−	141.556i	0.781177	−	0.155386i	0.211636	−	0.977349i	$-0.432121\pi$
$911$	711.652	−	141.556i	0.781177	−	0.155386i	0.569541	+	0.821963i	$0.307121\pi$
$912$		0			0
$913$	−326.410	−	64.9270i	−0.357514	−	0.0711139i
$914$		0			0
$915$	900.742	−	601.857i	0.984417	−	0.657767i
$916$		0			0
$917$			15.3239i			0.0167109i
$918$		0			0
$919$	−704.906			−0.767036			−0.383518	−	0.923534i	$-0.625288\pi$
$919$	−704.906			−0.767036			−0.383518	+	0.923534i	$0.625288\pi$
$920$		0			0
$921$	−281.794	−	421.735i	−0.305966	−	0.457910i
$922$		0			0
$923$	−64.2505	+	323.009i	−0.0696105	+	0.349956i
$924$		0			0
$925$	−5.62397	−	28.2736i	−0.00607997	−	0.0305661i
$926$		0			0
$927$	248.504	−	599.941i	0.268073	−	0.647186i
$928$		0			0
$929$	826.542	+	552.278i	0.889712	+	0.594486i	0.914222	−	0.405213i	$-0.132803\pi$
$929$	826.542	+	552.278i	0.889712	+	0.594486i	−0.0245106	+	0.999700i	$0.507803\pi$
$930$		0			0
$931$	500.979	+	500.979i	0.538109	+	0.538109i
$932$		0			0
$933$	204.699	−	84.7890i	0.219399	−	0.0908778i
$934$		0			0
$935$	−339.061	−	999.492i	−0.362632	−	1.06898i
$936$		0			0
$937$	−304.634	−	735.453i	−0.325117	−	0.784901i	−0.998941	−	0.0460096i	$-0.985350\pi$
$937$	−304.634	−	735.453i	−0.325117	−	0.784901i	0.673824	−	0.738892i	$-0.264650\pi$
$938$		0			0
$939$	−64.6067	+	64.6067i	−0.0688037	+	0.0688037i
$940$		0			0
$941$	−43.1737	+	64.6140i	−0.0458807	+	0.0686653i	−0.853701	−	0.520764i	$-0.825647\pi$
$941$	−43.1737	+	64.6140i	−0.0458807	+	0.0686653i	0.807820	+	0.589429i	$0.200647\pi$
$942$		0			0
$943$	34.2365	+	14.1812i	0.0363059	+	0.0150384i
$944$		0			0
$945$	−2.20178	+	0.437960i	−0.00232992	+	0.000463450i
$946$		0			0
$947$	−1070.10	−	212.857i	−1.12999	−	0.224769i	−0.405529	−	0.914082i	$-0.632913\pi$
$947$	−1070.10	−	212.857i	−1.12999	−	0.224769i	−0.724464	+	0.689313i	$0.757913\pi$
$948$		0			0
$949$	−645.235	+	431.132i	−0.679911	+	0.454302i
$950$		0			0
$951$		−	234.117i		−	0.246180i
$952$		0			0
$953$	507.810			0.532854			0.266427	−	0.963855i	$-0.414157\pi$
$953$	507.810			0.532854			0.266427	+	0.963855i	$0.414157\pi$
$954$		0			0
$955$	−693.773	−	1038.30i	−0.726463	−	1.08723i
$956$		0			0
$957$	526.498	−	2646.88i	0.550154	−	2.76581i
$958$		0			0
$959$	−4.79016	−	24.0817i	−0.00499495	−	0.0251113i
$960$		0			0
$961$	−2.26661	+	5.47209i	−0.00235860	+	0.00569416i
$962$		0			0
$963$	−1066.00	−	712.280i	−1.10696	−	0.739647i
$964$		0			0
$965$	−693.581	−	693.581i	−0.718737	−	0.718737i
$966$		0			0
$967$	−760.982	+	315.209i	−0.786951	+	0.325966i	−0.739717	−	0.672918i	$-0.765041\pi$
$967$	−760.982	+	315.209i	−0.786951	+	0.325966i	−0.0472342	+	0.998884i	$0.515041\pi$
$968$		0			0
$969$	528.092	+	915.101i	0.544987	+	0.944377i
$970$		0			0
$971$	−521.991	−	1260.20i	−0.537581	−	1.29784i	−0.926407	−	0.376525i	$-0.877119\pi$
$971$	−521.991	−	1260.20i	−0.537581	−	1.29784i	0.388825	−	0.921311i	$-0.372881\pi$
$972$		0			0
$973$	−6.41639	+	6.41639i	−0.00659444	+	0.00659444i
$974$		0			0
$975$	30.7769	−	46.0609i	0.0315660	−	0.0472419i
$976$		0			0
$977$	−389.262	−	161.238i	−0.398426	−	0.165034i	0.174468	−	0.984663i	$-0.444179\pi$
$977$	−389.262	−	161.238i	−0.398426	−	0.165034i	−0.572894	+	0.819629i	$0.694179\pi$
$978$		0			0
$979$	1019.66	−	202.823i	1.04153	−	0.207173i
$980$		0			0
$981$	−292.438	−	58.1695i	−0.298102	−	0.0592962i
$982$		0			0
$983$	−362.127	+	241.965i	−0.368390	+	0.246150i	−0.725961	−	0.687736i	$-0.758605\pi$
$983$	−362.127	+	241.965i	−0.368390	+	0.246150i	0.357572	+	0.933886i	$0.383605\pi$
$984$		0			0
$985$		−	413.003i		−	0.419292i
$986$		0			0
$987$	−67.6166			−0.0685072
$988$		0			0
$989$	24.4094	+	36.5313i	0.0246809	+	0.0369376i
$990$		0			0
$991$	126.058	−	633.736i	0.127203	−	0.639492i	−0.863600	−	0.504178i	$-0.831796\pi$
$991$	126.058	−	633.736i	0.127203	−	0.639492i	0.990803	−	0.135314i	$-0.0432043\pi$
$992$		0			0
$993$	316.719	+	1592.25i	0.318952	+	1.60348i
$994$		0			0
$995$	−16.9295	+	40.8714i	−0.0170146	+	0.0410768i
$996$		0			0
$997$	283.890	+	189.689i	0.284744	+	0.190260i	0.689737	−	0.724060i	$-0.257726\pi$
$997$	283.890	+	189.689i	0.284744	+	0.190260i	−0.404993	+	0.914320i	$0.632726\pi$
$998$		0			0
$999$	−34.7990	−	34.7990i	−0.0348338	−	0.0348338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.b.73.5	yes	40
4.3	odd	2		272.3.bh.g.209.1		40
17.7	odd	16	inner	136.3.t.b.41.5	✓	40
68.7	even	16		272.3.bh.g.177.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.b.41.5	✓	40	17.7	odd	16	inner
136.3.t.b.73.5	yes	40	1.1	even	1	trivial
272.3.bh.g.177.1		40	68.7	even	16
272.3.bh.g.209.1		40	4.3	odd	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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.38532 + 3.56988i) q^{3} +(-0.996509 + 5.00979i) q^{5} +(-0.0460348 - 0.231433i) q^{7} +(-3.61016 + 8.71570i) q^{9} +O(q^{10})\)	\(q+(2.38532 + 3.56988i) q^{3} +(-0.996509 + 5.00979i) q^{5} +(-0.0460348 - 0.231433i) q^{7} +(-3.61016 + 8.71570i) q^{9} +(-10.1061 - 6.75269i) q^{11} +(8.36248 + 8.36248i) q^{13} +(-20.2613 + 8.39252i) q^{15} +(7.52192 - 15.2453i) q^{17} +(5.53952 + 13.3736i) q^{19} +(0.716380 - 0.716380i) q^{21} +(-0.358092 + 0.535922i) q^{23} +(-1.00796 - 0.417511i) q^{25} +(-1.82674 + 0.363361i) q^{27} +(50.7212 + 10.0891i) q^{29} +(-25.6960 + 17.1695i) q^{31} -52.1850i q^{33} +1.20530 q^{35} +(14.6797 + 21.9698i) q^{37} +(-9.90588 + 49.8002i) q^{39} +(-11.2164 - 56.3888i) q^{41} +(26.0857 - 62.9765i) q^{43} +(-40.0663 - 26.7714i) q^{45} +(-47.1933 - 47.1933i) q^{47} +(45.2187 - 18.7302i) q^{49} +(72.3663 - 9.51264i) q^{51} +(5.09427 + 12.2987i) q^{53} +(43.9004 - 43.9004i) q^{55} +(-34.5286 + 51.6757i) q^{57} +(-75.1310 - 31.1203i) q^{59} +(-48.4479 + 9.63689i) q^{61} +(2.18329 + 0.434284i) q^{63} +(-50.2275 + 33.5610i) q^{65} -58.0686i q^{67} -2.76734 q^{69} +(15.4714 + 23.1546i) q^{71} +(-12.8014 + 64.3570i) q^{73} +(-0.913843 - 4.59420i) q^{75} +(-1.09756 + 2.64974i) q^{77} +(104.845 + 70.0553i) q^{79} +(54.3819 + 54.3819i) q^{81} +(25.2969 - 10.4783i) q^{83} +(68.8803 + 52.8754i) q^{85} +(84.9694 + 205.134i) q^{87} +(-60.4822 + 60.4822i) q^{89} +(1.55039 - 2.32032i) q^{91} +(-122.586 - 50.7769i) q^{93} +(-72.5190 + 14.4249i) q^{95} +(23.1484 + 4.60450i) q^{97} +(95.3391 - 63.7036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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