LMFDB - Embedded newform 1050.3.c.c.449.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(449,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1050.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.c (of order $2$, degree $1$, 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.28
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.c.449.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(2.35293 + 1.86110i) q^{3} +2.00000 q^{4} +(3.32755 + 2.63200i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(2.07259 + 8.75810i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(2.35293 + 1.86110i) q^{3} +2.00000 q^{4} +(3.32755 + 2.63200i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(2.07259 + 8.75810i) q^{9} +19.0319i q^{11} +(4.70587 + 3.72221i) q^{12} +1.55479i q^{13} +3.74166i q^{14} +4.00000 q^{16} -28.9019 q^{17} +(2.93108 + 12.3858i) q^{18} -23.3574 q^{19} +(-4.92402 + 6.22527i) q^{21} +26.9152i q^{22} +23.7695 q^{23} +(6.65510 + 5.26400i) q^{24} +2.19880i q^{26} +(-11.4231 + 24.4645i) q^{27} +5.29150i q^{28} -18.0074i q^{29} +7.88473 q^{31} +5.65685 q^{32} +(-35.4204 + 44.7809i) q^{33} -40.8735 q^{34} +(4.14517 + 17.5162i) q^{36} -20.5218i q^{37} -33.0324 q^{38} +(-2.89362 + 3.65831i) q^{39} -50.8988i q^{41} +(-6.96361 + 8.80387i) q^{42} +31.2503i q^{43} +38.0639i q^{44} +33.6151 q^{46} +15.7642 q^{47} +(9.41173 + 7.44442i) q^{48} -7.00000 q^{49} +(-68.0043 - 53.7895i) q^{51} +3.10957i q^{52} +78.7951 q^{53} +(-16.1547 + 34.5981i) q^{54} +7.48331i q^{56} +(-54.9585 - 43.4706i) q^{57} -25.4663i q^{58} +89.1948i q^{59} +56.4152 q^{61} +11.1507 q^{62} +(-23.1718 + 5.48355i) q^{63} +8.00000 q^{64} +(-50.0920 + 63.3297i) q^{66} +56.2048i q^{67} -57.8038 q^{68} +(55.9280 + 44.2375i) q^{69} +28.4101i q^{71} +(5.86216 + 24.7717i) q^{72} +120.253i q^{73} -29.0222i q^{74} -46.7149 q^{76} -50.3538 q^{77} +(-4.09220 + 5.17363i) q^{78} +72.1123 q^{79} +(-72.4088 + 36.3038i) q^{81} -71.9818i q^{82} +104.179 q^{83} +(-9.84804 + 12.4505i) q^{84} +44.1946i q^{86} +(33.5136 - 42.3702i) q^{87} +53.8304i q^{88} +36.3947i q^{89} -4.11358 q^{91} +47.5389 q^{92} +(18.5522 + 14.6743i) q^{93} +22.2940 q^{94} +(13.3102 + 10.5280i) q^{96} -57.1642i q^{97} -9.89949 q^{98} +(-166.684 + 39.4453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	2.35293	+	1.86110i	0.784311	+	0.620368i
$3$	2.35293	+	1.86110i	0.784311	+	0.620368i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	3.32755	+	2.63200i	0.554592	+	0.438666i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	2.82843			0.353553
$9$	2.07259	+	8.75810i	0.230287	+	0.973123i
$10$		0			0
$11$			19.0319i			1.73018i	0.501620	+	0.865088i	$0.332737\pi$
$11$			19.0319i			1.73018i	−0.501620	+	0.865088i	$0.667263\pi$
$12$	4.70587	+	3.72221i	0.392155	+	0.310184i
$13$			1.55479i			0.119599i	0.998210	+	0.0597995i	$0.0190461\pi$
$13$			1.55479i			0.119599i	−0.998210	+	0.0597995i	$0.980954\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	−28.9019			−1.70011			−0.850056	−	0.526692i	$-0.823432\pi$
$17$	−28.9019			−1.70011			−0.850056	+	0.526692i	$0.823432\pi$
$18$	2.93108	+	12.3858i	0.162838	+	0.688102i
$19$	−23.3574			−1.22934			−0.614669	−	0.788785i	$-0.710711\pi$
$19$	−23.3574			−1.22934			−0.614669	+	0.788785i	$0.710711\pi$
$20$		0			0
$21$	−4.92402	+	6.22527i	−0.234477	+	0.296442i
$22$			26.9152i			1.22342i
$23$	23.7695			1.03346			0.516728	−	0.856150i	$-0.327150\pi$
$23$	23.7695			1.03346			0.516728	+	0.856150i	$0.327150\pi$
$24$	6.65510	+	5.26400i	0.277296	+	0.219333i
$25$		0			0
$26$			2.19880i			0.0845693i
$27$	−11.4231	+	24.4645i	−0.423077	+	0.906094i
$28$			5.29150i			0.188982i
$29$		−	18.0074i		−	0.620945i	−0.950582	−	0.310472i	$-0.899513\pi$
$29$		−	18.0074i		−	0.620945i	0.950582	−	0.310472i	$-0.100487\pi$
$30$		0			0
$31$	7.88473			0.254346			0.127173	−	0.991881i	$-0.459410\pi$
$31$	7.88473			0.254346			0.127173	+	0.991881i	$0.459410\pi$
$32$	5.65685			0.176777
$33$	−35.4204	+	44.7809i	−1.07335	+	1.35700i
$34$	−40.8735			−1.20216
$35$		0			0
$36$	4.14517	+	17.5162i	0.115144	+	0.486561i
$37$		−	20.5218i		−	0.554642i	−0.960777	−	0.277321i	$-0.910553\pi$
$37$		−	20.5218i		−	0.554642i	0.960777	−	0.277321i	$-0.0894466\pi$
$38$	−33.0324			−0.869274
$39$	−2.89362	+	3.65831i	−0.0741954	+	0.0938028i
$40$		0			0
$41$		−	50.8988i		−	1.24143i	−0.784034	−	0.620717i	$-0.786841\pi$
$41$		−	50.8988i		−	1.24143i	0.784034	−	0.620717i	$-0.213159\pi$
$42$	−6.96361	+	8.80387i	−0.165800	+	0.209616i
$43$			31.2503i			0.726752i	0.931643	+	0.363376i	$0.118376\pi$
$43$			31.2503i			0.726752i	−0.931643	+	0.363376i	$0.881624\pi$
$44$			38.0639i			0.865088i
$45$		0			0
$46$	33.6151			0.730763
$47$	15.7642			0.335409			0.167704	−	0.985837i	$-0.446365\pi$
$47$	15.7642			0.335409			0.167704	+	0.985837i	$0.446365\pi$
$48$	9.41173	+	7.44442i	0.196078	+	0.155092i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	−68.0043	−	53.7895i	−1.33342	−	1.05470i
$52$			3.10957i			0.0597995i
$53$	78.7951			1.48670			0.743350	−	0.668903i	$-0.233236\pi$
$53$	78.7951			1.48670			0.743350	+	0.668903i	$0.233236\pi$
$54$	−16.1547	+	34.5981i	−0.299161	+	0.640705i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	−54.9585	−	43.4706i	−0.964184	−	0.762642i
$58$		−	25.4663i		−	0.439074i
$59$			89.1948i			1.51178i	0.654700	+	0.755889i	$0.272795\pi$
$59$			89.1948i			1.51178i	−0.654700	+	0.755889i	$0.727205\pi$
$60$		0			0
$61$	56.4152			0.924840			0.462420	−	0.886661i	$-0.346981\pi$
$61$	56.4152			0.924840			0.462420	+	0.886661i	$0.346981\pi$
$62$	11.1507			0.179850
$63$	−23.1718	+	5.48355i	−0.367806	+	0.0870404i
$64$	8.00000			0.125000
$65$		0			0
$66$	−50.0920	+	63.3297i	−0.758970	+	0.959541i
$67$			56.2048i			0.838878i	0.907784	+	0.419439i	$0.137773\pi$
$67$			56.2048i			0.838878i	−0.907784	+	0.419439i	$0.862227\pi$
$68$	−57.8038			−0.850056
$69$	55.9280	+	44.2375i	0.810550	+	0.641123i
$70$		0			0
$71$			28.4101i			0.400143i	0.979781	+	0.200071i	$0.0641174\pi$
$71$			28.4101i			0.400143i	−0.979781	+	0.200071i	$0.935883\pi$
$72$	5.86216	+	24.7717i	0.0814188	+	0.344051i
$73$			120.253i			1.64730i	0.567102	+	0.823648i	$0.308065\pi$
$73$			120.253i			1.64730i	−0.567102	+	0.823648i	$0.691935\pi$
$74$		−	29.0222i		−	0.392191i
$75$		0			0
$76$	−46.7149			−0.614669
$77$	−50.3538			−0.653945
$78$	−4.09220	+	5.17363i	−0.0524641	+	0.0663286i
$79$	72.1123			0.912814			0.456407	−	0.889771i	$-0.349136\pi$
$79$	72.1123			0.912814			0.456407	+	0.889771i	$0.349136\pi$
$80$		0			0
$81$	−72.4088	+	36.3038i	−0.893936	+	0.448196i
$82$		−	71.9818i		−	0.877827i
$83$	104.179			1.25517			0.627587	−	0.778547i	$-0.284043\pi$
$83$	104.179			1.25517			0.627587	+	0.778547i	$0.284043\pi$
$84$	−9.84804	+	12.4505i	−0.117239	+	0.148221i
$85$		0			0
$86$			44.1946i			0.513891i
$87$	33.5136	−	42.3702i	0.385214	−	0.487014i
$88$			53.8304i			0.611709i
$89$			36.3947i			0.408929i	0.978874	+	0.204465i	$0.0655453\pi$
$89$			36.3947i			0.408929i	−0.978874	+	0.204465i	$0.934455\pi$
$90$		0			0
$91$	−4.11358			−0.0452042
$92$	47.5389			0.516728
$93$	18.5522	+	14.6743i	0.199486	+	0.157788i
$94$	22.2940			0.237170
$95$		0			0
$96$	13.3102	+	10.5280i	0.138648	+	0.109667i
$97$		−	57.1642i		−	0.589321i	−0.955602	−	0.294661i	$-0.904793\pi$
$97$		−	57.1642i		−	0.589321i	0.955602	−	0.294661i	$-0.0952066\pi$
$98$	−9.89949			−0.101015
$99$	−166.684	+	39.4453i	−1.68367	+	0.398437i
$100$		0			0
$101$		−	144.925i		−	1.43490i	−0.696610	−	0.717450i	$-0.745309\pi$
$101$		−	144.925i		−	1.43490i	0.696610	−	0.717450i	$-0.254691\pi$
$102$	−96.1726	−	76.0698i	−0.942868	−	0.745782i
$103$		−	173.742i		−	1.68681i	−0.537276	−	0.843407i	$-0.680547\pi$
$103$		−	173.742i		−	1.68681i	0.537276	−	0.843407i	$-0.319453\pi$
$104$			4.39760i			0.0422846i
$105$		0			0
$106$	111.433			1.05126
$107$	93.7622			0.876282			0.438141	−	0.898906i	$-0.355637\pi$
$107$	93.7622			0.876282			0.438141	+	0.898906i	$0.355637\pi$
$108$	−22.8462	+	48.9291i	−0.211539	+	0.453047i
$109$	−196.881			−1.80625			−0.903125	−	0.429378i	$-0.858733\pi$
$109$	−196.881			−1.80625			−0.903125	+	0.429378i	$0.858733\pi$
$110$		0			0
$111$	38.1931	−	48.2863i	0.344082	−	0.435012i
$112$			10.5830i			0.0944911i
$113$	114.317			1.01166			0.505829	−	0.862634i	$-0.331187\pi$
$113$	114.317			1.01166			0.505829	+	0.862634i	$0.331187\pi$
$114$	−77.7230	−	61.4767i	−0.681781	−	0.539270i
$115$		0			0
$116$		−	36.0148i		−	0.310472i
$117$	−13.6170	+	3.22243i	−0.116384	+	0.0275421i
$118$			126.141i			1.06899i
$119$		−	76.4673i		−	0.642582i
$120$		0			0
$121$	−241.214			−1.99351
$122$	79.7832			0.653960
$123$	94.7280	−	119.762i	0.770146	−	0.973671i
$124$	15.7695			0.127173
$125$		0			0
$126$	−32.7698	+	7.75490i	−0.260078	+	0.0615469i
$127$			14.2601i			0.112284i	0.998423	+	0.0561422i	$0.0178800\pi$
$127$			14.2601i			0.112284i	−0.998423	+	0.0561422i	$0.982120\pi$
$128$	11.3137			0.0883883
$129$	−58.1601	+	73.5299i	−0.450853	+	0.569999i
$130$		0			0
$131$			86.1081i			0.657313i	0.944449	+	0.328657i	$0.106596\pi$
$131$			86.1081i			0.657313i	−0.944449	+	0.328657i	$0.893404\pi$
$132$	−70.8408	+	89.5617i	−0.536673	+	0.678498i
$133$		−	61.7980i		−	0.464646i
$134$			79.4856i			0.593176i
$135$		0			0
$136$	−81.7470			−0.601081
$137$	87.4123			0.638046			0.319023	−	0.947747i	$-0.396645\pi$
$137$	87.4123			0.638046			0.319023	+	0.947747i	$0.396645\pi$
$138$	79.0941	+	62.5612i	0.573146	+	0.453342i
$139$	−188.559			−1.35654			−0.678269	−	0.734814i	$-0.737270\pi$
$139$	−188.559			−1.35654			−0.678269	+	0.734814i	$0.737270\pi$
$140$		0			0
$141$	37.0921	+	29.3388i	0.263065	+	0.208077i
$142$			40.1780i			0.282944i
$143$	−29.5906			−0.206927
$144$	8.29034	+	35.0324i	0.0575718	+	0.243281i
$145$		0			0
$146$			170.063i			1.16481i
$147$	−16.4705	−	13.0277i	−0.112044	−	0.0886240i
$148$		−	41.0435i		−	0.277321i
$149$		−	120.358i		−	0.807775i	−0.914809	−	0.403888i	$-0.867659\pi$
$149$		−	120.358i		−	0.807775i	0.914809	−	0.403888i	$-0.132341\pi$
$150$		0			0
$151$	−41.6199			−0.275628			−0.137814	−	0.990458i	$-0.544008\pi$
$151$	−41.6199			−0.275628			−0.137814	+	0.990458i	$0.544008\pi$
$152$	−66.0648			−0.434637
$153$	−59.9017	−	253.126i	−0.391514	−	1.65442i
$154$	−71.2110			−0.462409
$155$		0			0
$156$	−5.78724	+	7.31662i	−0.0370977	+	0.0469014i
$157$		−	58.4437i		−	0.372253i	−0.982526	−	0.186126i	$-0.940407\pi$
$157$		−	58.4437i		−	0.372253i	0.982526	−	0.186126i	$-0.0595934\pi$
$158$	101.982			0.645457
$159$	185.400	+	146.646i	1.16604	+	0.922301i
$160$		0			0
$161$			62.8881i			0.390609i
$162$	−102.401	+	51.3414i	−0.632108	+	0.316922i
$163$			79.4862i			0.487646i	0.969820	+	0.243823i	$0.0784015\pi$
$163$			79.4862i			0.487646i	−0.969820	+	0.243823i	$0.921598\pi$
$164$		−	101.798i		−	0.620717i
$165$		0			0
$166$	147.332			0.887542
$167$	72.1686			0.432147			0.216074	−	0.976377i	$-0.430675\pi$
$167$	72.1686			0.432147			0.216074	+	0.976377i	$0.430675\pi$
$168$	−13.9272	+	17.6077i	−0.0829002	+	0.104808i
$169$	166.583			0.985696
$170$		0			0
$171$	−48.4103	−	204.567i	−0.283101	−	1.19630i
$172$			62.5006i			0.363376i
$173$	235.654			1.36216			0.681080	−	0.732209i	$-0.261511\pi$
$173$	235.654			1.36216			0.681080	+	0.732209i	$0.261511\pi$
$174$	47.3955	−	59.9205i	0.272388	−	0.344371i
$175$		0			0
$176$			76.1277i			0.432544i
$177$	−166.001	+	209.869i	−0.937858	+	1.18570i
$178$			51.4699i			0.289157i
$179$			132.607i			0.740823i	0.928868	+	0.370411i	$0.120783\pi$
$179$			132.607i			0.740823i	−0.928868	+	0.370411i	$0.879217\pi$
$180$		0			0
$181$	47.9269			0.264790			0.132395	−	0.991197i	$-0.457733\pi$
$181$	47.9269			0.264790			0.132395	+	0.991197i	$0.457733\pi$
$182$	−5.81748			−0.0319642
$183$	132.741	+	104.995i	0.725362	+	0.573741i
$184$	67.2302			0.365382
$185$		0			0
$186$	26.2368	+	20.7526i	0.141058	+	0.111573i
$187$		−	550.059i		−	2.94149i
$188$	31.5284			0.167704
$189$	−64.7271	−	30.2226i	−0.342471	−	0.159908i
$190$		0			0
$191$			183.885i			0.962750i	0.876515	+	0.481375i	$0.159863\pi$
$191$			183.885i			0.962750i	−0.876515	+	0.481375i	$0.840137\pi$
$192$	18.8235	+	14.8888i	0.0980389	+	0.0775460i
$193$		−	107.757i		−	0.558325i	−0.960244	−	0.279162i	$-0.909943\pi$
$193$		−	107.757i		−	0.558325i	0.960244	−	0.279162i	$-0.0900568\pi$
$194$		−	80.8423i		−	0.416713i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	297.246			1.50886			0.754432	−	0.656378i	$-0.227912\pi$
$197$	297.246			1.50886			0.754432	+	0.656378i	$0.227912\pi$
$198$	−235.726	+	55.7841i	−1.19054	+	0.281738i
$199$	−246.886			−1.24064			−0.620318	−	0.784351i	$-0.712996\pi$
$199$	−246.886			−1.24064			−0.620318	+	0.784351i	$0.712996\pi$
$200$		0			0
$201$	−104.603	+	132.246i	−0.520413	+	0.657941i
$202$		−	204.955i		−	1.01463i
$203$	47.6431			0.234695
$204$	−136.009	−	107.579i	−0.666709	−	0.527348i
$205$		0			0
$206$		−	245.708i		−	1.19276i
$207$	49.2643	+	208.176i	0.237992	+	1.00568i
$208$			6.21915i			0.0298997i
$209$		−	444.537i		−	2.12697i
$210$		0			0
$211$	292.191			1.38479			0.692396	−	0.721517i	$-0.256555\pi$
$211$	292.191			1.38479			0.692396	+	0.721517i	$0.256555\pi$
$212$	157.590			0.743350
$213$	−52.8742	+	66.8471i	−0.248236	+	0.313836i
$214$	132.600			0.619625
$215$		0			0
$216$	−32.3094	+	69.1961i	−0.149580	+	0.320352i
$217$			20.8610i			0.0961338i
$218$	−278.432			−1.27721
$219$	−223.802	+	282.946i	−1.02193	+	1.29199i
$220$		0			0
$221$		−	44.9363i		−	0.203332i
$222$	54.0133	−	68.2872i	0.243303	−	0.307600i
$223$			226.770i			1.01691i	0.861090	+	0.508453i	$0.169782\pi$
$223$			226.770i			1.01691i	−0.861090	+	0.508453i	$0.830218\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	161.669			0.715350
$227$	293.354			1.29231			0.646155	−	0.763206i	$-0.276376\pi$
$227$	293.354			1.29231			0.646155	+	0.763206i	$0.276376\pi$
$228$	−109.917	−	86.9412i	−0.482092	−	0.381321i
$229$	183.861			0.802889			0.401444	−	0.915883i	$-0.368508\pi$
$229$	183.861			0.802889			0.401444	+	0.915883i	$0.368508\pi$
$230$		0			0
$231$	−118.479	−	93.7136i	−0.512896	−	0.405686i
$232$		−	50.9326i		−	0.219537i
$233$	−338.163			−1.45134			−0.725671	−	0.688042i	$-0.758470\pi$
$233$	−338.163			−1.45134			−0.725671	+	0.688042i	$0.758470\pi$
$234$	−19.2573	+	4.55720i	−0.0822963	+	0.0194752i
$235$		0			0
$236$			178.390i			0.755889i
$237$	169.675	+	134.208i	0.715930	+	0.566280i
$238$		−	108.141i		−	0.454374i
$239$		−	295.300i		−	1.23557i	−0.786349	−	0.617783i	$-0.788031\pi$
$239$		−	295.300i		−	1.23557i	0.786349	−	0.617783i	$-0.211969\pi$
$240$		0			0
$241$	−224.922			−0.933286			−0.466643	−	0.884446i	$-0.654537\pi$
$241$	−224.922			−0.933286			−0.466643	+	0.884446i	$0.654537\pi$
$242$	−341.129			−1.40962
$243$	−237.938	−	49.3398i	−0.979170	−	0.203044i
$244$	112.830			0.462420
$245$		0			0
$246$	133.966	−	169.368i	0.544576	−	0.688489i
$247$		−	36.3158i		−	0.147028i
$248$	22.3014			0.0899250
$249$	245.127	+	193.889i	0.984446	+	0.778670i
$250$		0			0
$251$		−	26.3337i		−	0.104915i	−0.998623	−	0.0524575i	$-0.983295\pi$
$251$		−	26.3337i		−	0.104915i	0.998623	−	0.0524575i	$-0.0167054\pi$
$252$	−46.3435	+	10.9671i	−0.183903	+	0.0435202i
$253$			452.379i			1.78806i
$254$			20.1668i			0.0793970i
$255$		0			0
$256$	16.0000			0.0625000
$257$	129.147			0.502518			0.251259	−	0.967920i	$-0.419155\pi$
$257$	129.147			0.502518			0.251259	+	0.967920i	$0.419155\pi$
$258$	−82.2508	+	103.987i	−0.318801	+	0.403050i
$259$	54.2955			0.209635
$260$		0			0
$261$	157.711	−	37.3219i	0.604256	−	0.142996i
$262$			121.775i			0.464791i
$263$	234.149			0.890301			0.445150	−	0.895456i	$-0.353150\pi$
$263$	234.149			0.890301			0.445150	+	0.895456i	$0.353150\pi$
$264$	−100.184	+	126.659i	−0.379485	+	0.479770i
$265$		0			0
$266$		−	87.3955i		−	0.328555i
$267$	−67.7343	+	85.6343i	−0.253686	+	0.320728i
$268$			112.410i			0.419439i
$269$		−	109.020i		−	0.405280i	−0.979253	−	0.202640i	$-0.935048\pi$
$269$		−	109.020i		−	0.405280i	0.979253	−	0.202640i	$-0.0649522\pi$
$270$		0			0
$271$	204.213			0.753554			0.376777	−	0.926304i	$-0.377032\pi$
$271$	204.213			0.753554			0.376777	+	0.926304i	$0.377032\pi$
$272$	−115.608			−0.425028
$273$	−9.67898	−	7.65580i	−0.0354541	−	0.0280432i
$274$	123.620			0.451167
$275$		0			0
$276$	111.856	+	88.4749i	0.405275	+	0.320561i
$277$			343.561i			1.24029i	0.784486	+	0.620146i	$0.212927\pi$
$277$			343.561i			1.24029i	−0.784486	+	0.620146i	$0.787073\pi$
$278$	−266.662			−0.959217
$279$	16.3418	+	69.0553i	0.0585727	+	0.247510i
$280$		0			0
$281$		−	402.006i		−	1.43063i	−0.698804	−	0.715313i	$-0.746284\pi$
$281$		−	402.006i		−	1.43063i	0.698804	−	0.715313i	$-0.253716\pi$
$282$	52.4562	+	41.4914i	0.186015	+	0.147133i
$283$		−	290.257i		−	1.02564i	−0.858496	−	0.512821i	$-0.828601\pi$
$283$		−	290.257i		−	1.02564i	0.858496	−	0.512821i	$-0.171399\pi$
$284$			56.8203i			0.200071i
$285$		0			0
$286$	−41.8474			−0.146320
$287$	134.666			0.469218
$288$	11.7243	+	49.5433i	0.0407094	+	0.172025i
$289$	546.321			1.89038
$290$		0			0
$291$	106.388	−	134.503i	0.365596	−	0.462211i
$292$			240.505i			0.823648i
$293$	−443.480			−1.51358			−0.756792	−	0.653655i	$-0.773235\pi$
$293$	−443.480			−1.51358			−0.756792	+	0.653655i	$0.773235\pi$
$294$	−23.2928	−	18.4240i	−0.0792274	−	0.0626666i
$295$		0			0
$296$		−	58.0443i		−	0.196096i
$297$	−465.607	−	217.403i	−1.56770	−	0.731998i
$298$		−	170.213i		−	0.571183i
$299$			36.9565i			0.123600i
$300$		0			0
$301$	−82.6806			−0.274686
$302$	−58.8594			−0.194899
$303$	269.720	−	340.999i	0.890166	−	1.12541i
$304$	−93.4297			−0.307335
$305$		0			0
$306$	−84.7138	−	357.974i	−0.276842	−	1.16985i
$307$			37.5506i			0.122315i	0.998128	+	0.0611574i	$0.0194791\pi$
$307$			37.5506i			0.122315i	−0.998128	+	0.0611574i	$0.980521\pi$
$308$	−100.708			−0.326972
$309$	323.351	−	408.803i	1.04644	−	1.32299i
$310$		0			0
$311$			133.398i			0.428933i	0.976731	+	0.214467i	$0.0688013\pi$
$311$			133.398i			0.428933i	−0.976731	+	0.214467i	$0.931199\pi$
$312$	−8.18439	+	10.3473i	−0.0262320	+	0.0331643i
$313$		−	220.130i		−	0.703290i	−0.936133	−	0.351645i	$-0.885622\pi$
$313$		−	220.130i		−	0.703290i	0.936133	−	0.351645i	$-0.114378\pi$
$314$		−	82.6518i		−	0.263222i
$315$		0			0
$316$	144.225			0.456407
$317$	−328.688			−1.03687			−0.518435	−	0.855117i	$-0.673485\pi$
$317$	−328.688			−1.03687			−0.518435	+	0.855117i	$0.673485\pi$
$318$	262.195	+	207.389i	0.824511	+	0.652165i
$319$	342.716			1.07434
$320$		0			0
$321$	220.616	+	174.501i	0.687278	+	0.543617i
$322$			88.9372i			0.276203i
$323$	675.075			2.09001
$324$	−144.818	+	72.6077i	−0.446968	+	0.224098i
$325$		0			0
$326$			112.411i			0.344817i
$327$	−463.248	−	366.416i	−1.41666	−	1.12054i
$328$		−	143.964i		−	0.438914i
$329$			41.7082i			0.126773i
$330$		0			0
$331$	−440.198			−1.32990			−0.664952	−	0.746886i	$-0.731548\pi$
$331$	−440.198			−1.32990			−0.664952	+	0.746886i	$0.731548\pi$
$332$	208.359			0.627587
$333$	179.732	−	42.5331i	0.539735	−	0.127727i
$334$	102.062			0.305574
$335$		0			0
$336$	−19.6961	+	24.9011i	−0.0586193	+	0.0741104i
$337$		−	136.800i		−	0.405934i	−0.979186	−	0.202967i	$-0.934942\pi$
$337$		−	136.800i		−	0.405934i	0.979186	−	0.202967i	$-0.0650584\pi$
$338$	235.583			0.696992
$339$	268.981	+	212.756i	0.793454	+	0.627600i
$340$		0			0
$341$			150.062i			0.440064i
$342$	−68.4625	−	289.301i	−0.200183	−	0.845910i
$343$		−	18.5203i		−	0.0539949i
$344$			88.3892i			0.256945i
$345$		0			0
$346$	333.265			0.963192
$347$	101.080			0.291296			0.145648	−	0.989336i	$-0.453473\pi$
$347$	101.080			0.291296			0.145648	+	0.989336i	$0.453473\pi$
$348$	67.0273	−	84.7404i	0.192607	−	0.243507i
$349$	−66.6889			−0.191086			−0.0955428	−	0.995425i	$-0.530459\pi$
$349$	−66.6889			−0.191086			−0.0955428	+	0.995425i	$0.530459\pi$
$350$		0			0
$351$	−38.0371	−	17.7605i	−0.108368	−	0.0505996i
$352$			107.661i			0.305855i
$353$	−163.078			−0.461976			−0.230988	−	0.972957i	$-0.574196\pi$
$353$	−163.078			−0.461976			−0.230988	+	0.972957i	$0.574196\pi$
$354$	−234.761	+	296.800i	−0.663166	+	0.838419i
$355$		0			0
$356$			72.7894i			0.204465i
$357$	142.314	−	179.922i	0.398637	−	0.503984i
$358$			187.535i			0.523841i
$359$		−	316.890i		−	0.882702i	−0.897334	−	0.441351i	$-0.854499\pi$
$359$		−	316.890i		−	0.882702i	0.897334	−	0.441351i	$-0.145501\pi$
$360$		0			0
$361$	184.570			0.511273
$362$	67.7789			0.187235
$363$	−567.561	−	448.925i	−1.56353	−	1.23671i
$364$	−8.22716			−0.0226021
$365$		0			0
$366$	187.724	+	148.485i	0.512908	+	0.405696i
$367$			492.889i			1.34302i	0.740994	+	0.671511i	$0.234354\pi$
$367$			492.889i			1.34302i	−0.740994	+	0.671511i	$0.765646\pi$
$368$	95.0779			0.258364
$369$	445.777	−	105.492i	1.20807	−	0.285887i
$370$		0			0
$371$			208.472i			0.561920i
$372$	37.1045	+	29.3486i	0.0997432	+	0.0788941i
$373$		−	614.112i		−	1.64641i	−0.567742	−	0.823207i	$-0.692183\pi$
$373$		−	614.112i		−	1.64641i	0.567742	−	0.823207i	$-0.307817\pi$
$374$		−	777.901i		−	2.07995i
$375$		0			0
$376$	44.5879			0.118585
$377$	27.9977			0.0742644
$378$	−91.5379	−	42.7413i	−0.242164	−	0.113072i
$379$	−492.230			−1.29876			−0.649380	−	0.760464i	$-0.724972\pi$
$379$	−492.230			−1.29876			−0.649380	+	0.760464i	$0.724972\pi$
$380$		0			0
$381$	−26.5395	+	33.5531i	−0.0696576	+	0.0880658i
$382$			260.053i			0.680767i
$383$	−292.505			−0.763722			−0.381861	−	0.924220i	$-0.624717\pi$
$383$	−292.505			−0.763722			−0.381861	+	0.924220i	$0.624717\pi$
$384$	26.6204	+	21.0560i	0.0693239	+	0.0548333i
$385$		0			0
$386$		−	152.391i		−	0.394795i
$387$	−273.694	+	64.7689i	−0.707218	+	0.167362i
$388$		−	114.328i		−	0.294661i
$389$			447.326i			1.14994i	0.818175	+	0.574969i	$0.194986\pi$
$389$			447.326i			1.14994i	−0.818175	+	0.574969i	$0.805014\pi$
$390$		0			0
$391$	−686.983			−1.75699
$392$	−19.7990			−0.0505076
$393$	−160.256	+	202.606i	−0.407776	+	0.515538i
$394$	420.370			1.06693
$395$		0			0
$396$	−333.367	+	78.8906i	−0.841837	+	0.199219i
$397$			293.499i			0.739293i	0.929172	+	0.369646i	$0.120521\pi$
$397$			293.499i			0.739293i	−0.929172	+	0.369646i	$0.879479\pi$
$398$	−349.150			−0.877262
$399$	115.012	−	145.406i	0.288252	−	0.364427i
$400$		0			0
$401$		−	450.848i		−	1.12431i	−0.827032	−	0.562155i	$-0.809972\pi$
$401$		−	450.848i		−	1.12431i	0.827032	−	0.562155i	$-0.190028\pi$
$402$	−147.931	+	187.024i	−0.367988	+	0.465235i
$403$			12.2591i			0.0304195i
$404$		−	289.850i		−	0.717450i
$405$		0			0
$406$	67.3775			0.165955
$407$	390.569			0.959629
$408$	−192.345	−	152.140i	−0.471434	−	0.372891i
$409$	−304.167			−0.743686			−0.371843	−	0.928296i	$-0.621274\pi$
$409$	−304.167			−0.743686			−0.371843	+	0.928296i	$0.621274\pi$
$410$		0			0
$411$	205.675	+	162.683i	0.500427	+	0.395823i
$412$		−	347.484i		−	0.843407i
$413$	−235.987			−0.571398
$414$	69.6702	+	294.405i	0.168285	+	0.711122i
$415$		0			0
$416$			8.79520i			0.0211423i
$417$	−443.666	−	350.928i	−1.06395	−	0.841553i
$418$		−	628.670i		−	1.50400i
$419$		−	151.970i		−	0.362698i	−0.983419	−	0.181349i	$-0.941954\pi$
$419$		−	151.970i		−	0.362698i	0.983419	−	0.181349i	$-0.0580463\pi$
$420$		0			0
$421$	165.499			0.393109			0.196554	−	0.980493i	$-0.437025\pi$
$421$	165.499			0.393109			0.196554	+	0.980493i	$0.437025\pi$
$422$	413.221			0.979196
$423$	32.6727	+	138.065i	0.0772404	+	0.326394i
$424$	222.866			0.525628
$425$		0			0
$426$	−74.7754	+	94.5361i	−0.175529	+	0.221916i
$427$			149.261i			0.349556i
$428$	187.524			0.438141
$429$	−69.6247	−	55.0712i	−0.162295	−	0.128371i
$430$		0			0
$431$		−	240.737i		−	0.558555i	−0.960210	−	0.279277i	$-0.909905\pi$
$431$		−	240.737i		−	0.558555i	0.960210	−	0.279277i	$-0.0900949\pi$
$432$	−45.6923	+	97.8581i	−0.105769	+	0.226523i
$433$		−	551.714i		−	1.27417i	−0.770795	−	0.637083i	$-0.780141\pi$
$433$		−	551.714i		−	1.27417i	0.770795	−	0.637083i	$-0.219859\pi$
$434$			29.5020i			0.0679769i
$435$		0			0
$436$	−393.762			−0.903125
$437$	−555.194			−1.27047
$438$	−316.504	+	400.146i	−0.722613	+	0.913576i
$439$	−85.9944			−0.195887			−0.0979435	−	0.995192i	$-0.531226\pi$
$439$	−85.9944			−0.195887			−0.0979435	+	0.995192i	$0.531226\pi$
$440$		0			0
$441$	−14.5081	−	61.3067i	−0.0328982	−	0.139018i
$442$		−	63.5496i		−	0.143777i
$443$	407.274			0.919354			0.459677	−	0.888086i	$-0.347965\pi$
$443$	407.274			0.919354			0.459677	+	0.888086i	$0.347965\pi$
$444$	76.3863	−	96.5727i	0.172041	−	0.217506i
$445$		0			0
$446$			320.701i			0.719061i
$447$	224.000	−	283.195i	0.501118	−	0.633547i
$448$			21.1660i			0.0472456i
$449$			373.874i			0.832682i	0.909209	+	0.416341i	$0.136688\pi$
$449$			373.874i			0.832682i	−0.909209	+	0.416341i	$0.863312\pi$
$450$		0			0
$451$	968.703			2.14790
$452$	228.635			0.505829
$453$	−97.9287	−	77.4589i	−0.216178	−	0.170991i
$454$	414.866			0.913801
$455$		0			0
$456$	−155.446	−	122.953i	−0.340890	−	0.269635i
$457$			29.2307i			0.0639623i	0.999488	+	0.0319811i	$0.0101816\pi$
$457$			29.2307i			0.0639623i	−0.999488	+	0.0319811i	$0.989818\pi$
$458$	260.019			0.567728
$459$	330.149	−	707.072i	0.719279	−	1.54046i
$460$		0			0
$461$		−	354.370i		−	0.768699i	−0.923188	−	0.384350i	$-0.874426\pi$
$461$		−	354.370i		−	0.768699i	0.923188	−	0.384350i	$-0.125574\pi$
$462$	−167.555	−	132.531i	−0.362672	−	0.286864i
$463$			488.004i			1.05400i	0.849864	+	0.527002i	$0.176684\pi$
$463$			488.004i			1.05400i	−0.849864	+	0.527002i	$0.823316\pi$
$464$		−	72.0296i		−	0.155236i
$465$		0			0
$466$	−478.234			−1.02625
$467$	400.445			0.857484			0.428742	−	0.903427i	$-0.358957\pi$
$467$	400.445			0.857484			0.428742	+	0.903427i	$0.358957\pi$
$468$	−27.2340	+	6.44486i	−0.0581922	+	0.0137711i
$469$	−148.704			−0.317066
$470$		0			0
$471$	108.770	−	137.514i	0.230934	−	0.291962i
$472$			252.281i			0.534494i
$473$	−594.754			−1.25741
$474$	239.957	+	189.799i	0.506239	+	0.400421i
$475$		0			0
$476$		−	152.935i		−	0.321291i
$477$	163.310	+	690.096i	0.342368	+	1.44674i
$478$		−	417.617i		−	0.873677i
$479$		−	724.371i		−	1.51226i	−0.654424	−	0.756128i	$-0.727089\pi$
$479$		−	724.371i		−	1.51226i	0.654424	−	0.756128i	$-0.272911\pi$
$480$		0			0
$481$	31.9070			0.0663347
$482$	−318.088			−0.659933
$483$	−117.041	+	147.972i	−0.242322	+	0.306359i
$484$	−482.429			−0.996754
$485$		0			0
$486$	−336.495	−	69.7770i	−0.692377	−	0.143574i
$487$		−	497.194i		−	1.02093i	−0.859898	−	0.510466i	$-0.829473\pi$
$487$		−	497.194i		−	1.02093i	0.859898	−	0.510466i	$-0.170527\pi$
$488$	159.566			0.326980
$489$	−147.932	+	187.026i	−0.302520	+	0.382466i
$490$		0			0
$491$		−	520.399i		−	1.05988i	−0.848036	−	0.529938i	$-0.822215\pi$
$491$		−	520.399i		−	1.05988i	0.848036	−	0.529938i	$-0.177785\pi$
$492$	189.456	−	239.523i	0.385073	−	0.486835i
$493$			520.449i			1.05568i
$494$		−	51.3583i		−	0.103964i
$495$		0			0
$496$	31.5389			0.0635865
$497$	−75.1662			−0.151240
$498$	346.662	+	274.200i	0.696109	+	0.550603i
$499$	−645.961			−1.29451			−0.647256	−	0.762273i	$-0.724084\pi$
$499$	−645.961			−1.29451			−0.647256	+	0.762273i	$0.724084\pi$
$500$		0			0
$501$	169.808	+	134.313i	0.338938	+	0.268090i
$502$		−	37.2414i		−	0.0741861i
$503$	21.7943			0.0433287			0.0216644	−	0.999765i	$-0.493103\pi$
$503$	21.7943			0.0433287			0.0216644	+	0.999765i	$0.493103\pi$
$504$	−65.5397	+	15.5098i	−0.130039	+	0.0307734i
$505$		0			0
$506$			639.761i			1.26435i
$507$	391.958	+	310.028i	0.773092	+	0.611494i
$508$			28.5202i			0.0561422i
$509$			466.441i			0.916386i	0.888853	+	0.458193i	$0.151503\pi$
$509$			466.441i			0.916386i	−0.888853	+	0.458193i	$0.848497\pi$
$510$		0			0
$511$	−318.158			−0.622619
$512$	22.6274			0.0441942
$513$	266.814	−	571.429i	0.520105	−	1.11390i
$514$	182.642			0.355334
$515$		0			0
$516$	−116.320	+	147.060i	−0.225427	+	0.285000i
$517$			300.023i			0.580316i
$518$	76.7854			0.148234
$519$	554.477	+	438.576i	1.06836	+	0.845040i
$520$		0			0
$521$			234.319i			0.449749i	0.974388	+	0.224875i	$0.0721973\pi$
$521$			234.319i			0.449749i	−0.974388	+	0.224875i	$0.927803\pi$
$522$	223.037	−	52.7811i	0.427273	−	0.101113i
$523$		−	569.920i		−	1.08971i	−0.838529	−	0.544856i	$-0.816584\pi$
$523$		−	569.920i		−	1.08971i	0.838529	−	0.544856i	$-0.183416\pi$
$524$			172.216i			0.328657i
$525$		0			0
$526$	331.137			0.629538
$527$	−227.884			−0.432417
$528$	−141.682	+	179.123i	−0.268336	+	0.339249i
$529$	35.9879			0.0680300
$530$		0			0
$531$	−781.178	+	184.864i	−1.47114	+	0.348143i
$532$		−	123.596i		−	0.232323i
$533$	79.1368			0.148474
$534$	−95.7908	+	121.105i	−0.179383	+	0.226789i
$535$		0			0
$536$			158.971i			0.296588i
$537$	−246.796	+	312.016i	−0.459583	+	0.581035i
$538$		−	154.178i		−	0.286576i
$539$		−	133.224i		−	0.247168i
$540$		0			0
$541$	−891.572			−1.64801			−0.824003	−	0.566585i	$-0.808264\pi$
$541$	−891.572			−1.64801			−0.824003	+	0.566585i	$0.808264\pi$
$542$	288.801			0.532843
$543$	112.769	+	89.1970i	0.207677	+	0.164267i
$544$	−163.494			−0.300540
$545$		0			0
$546$	−13.6881	−	10.8269i	−0.0250699	−	0.0198295i
$547$		−	196.251i		−	0.358777i	−0.983778	−	0.179389i	$-0.942588\pi$
$547$		−	196.251i		−	0.358777i	0.983778	−	0.179389i	$-0.0574119\pi$
$548$	174.825			0.319023
$549$	116.925	+	494.090i	0.212979	+	0.899982i
$550$		0			0
$551$			420.607i			0.763352i
$552$	158.188	+	125.122i	0.286573	+	0.226671i
$553$			190.791i			0.345011i
$554$			485.869i			0.877019i
$555$		0			0
$556$	−377.118			−0.678269
$557$	1016.07			1.82418			0.912089	−	0.409992i	$-0.134468\pi$
$557$	1016.07			1.82418			0.912089	+	0.409992i	$0.134468\pi$
$558$	23.1108	+	97.6589i	0.0414171	+	0.175016i
$559$	−48.5876			−0.0869187
$560$		0			0
$561$	1023.72	−	1294.25i	1.82481	−	2.30705i
$562$		−	568.522i		−	1.01161i
$563$	−104.346			−0.185340			−0.0926698	−	0.995697i	$-0.529540\pi$
$563$	−104.346			−0.185340			−0.0926698	+	0.995697i	$0.529540\pi$
$564$	74.1843	+	58.6777i	0.131532	+	0.104038i
$565$		0			0
$566$		−	410.485i		−	0.725238i
$567$	−96.0509	−	191.576i	−0.169402	−	0.337876i
$568$			80.3560i			0.141472i
$569$		−	12.9324i		−	0.0227284i	−0.999935	−	0.0113642i	$-0.996383\pi$
$569$		−	12.9324i		−	0.0227284i	0.999935	−	0.0113642i	$-0.00361741\pi$
$570$		0			0
$571$	986.261			1.72725			0.863626	−	0.504133i	$-0.168188\pi$
$571$	986.261			1.72725			0.863626	+	0.504133i	$0.168188\pi$
$572$	−59.1812			−0.103464
$573$	−342.230	+	432.670i	−0.597259	+	0.755096i
$574$	190.446			0.331787
$575$		0			0
$576$	16.5807	+	70.0648i	0.0287859	+	0.121640i
$577$			305.085i			0.528744i	0.964421	+	0.264372i	$0.0851646\pi$
$577$			305.085i			0.528744i	−0.964421	+	0.264372i	$0.914835\pi$
$578$	772.615			1.33670
$579$	200.546	−	253.544i	0.346367	−	0.437900i
$580$		0			0
$581$			275.633i			0.474411i
$582$	150.456	−	190.217i	0.258515	−	0.326833i
$583$			1499.62i			2.57225i
$584$			340.126i			0.582407i
$585$		0			0
$586$	−627.176			−1.07027
$587$	−469.411			−0.799679			−0.399839	−	0.916585i	$-0.630934\pi$
$587$	−469.411			−0.799679			−0.399839	+	0.916585i	$0.630934\pi$
$588$	−32.9411	−	26.0555i	−0.0560222	−	0.0443120i
$589$	−184.167			−0.312678
$590$		0			0
$591$	699.401	+	553.206i	1.18342	+	0.936051i
$592$		−	82.0871i		−	0.138661i
$593$	280.787			0.473502			0.236751	−	0.971570i	$-0.423917\pi$
$593$	280.787			0.473502			0.236751	+	0.971570i	$0.423917\pi$
$594$	−658.468	−	307.455i	−1.10853	−	0.517601i
$595$		0			0
$596$		−	240.717i		−	0.403888i
$597$	−580.907	−	459.481i	−0.973044	−	0.769650i
$598$			52.2643i			0.0873985i
$599$		−	257.993i		−	0.430706i	−0.976536	−	0.215353i	$-0.930910\pi$
$599$		−	257.993i		−	0.430706i	0.976536	−	0.215353i	$-0.0690902\pi$
$600$		0			0
$601$	−373.606			−0.621641			−0.310820	−	0.950469i	$-0.600604\pi$
$601$	−373.606			−0.621641			−0.310820	+	0.950469i	$0.600604\pi$
$602$	−116.928			−0.194233
$603$	−492.248	+	116.489i	−0.816331	+	0.193183i
$604$	−83.2397			−0.137814
$605$		0			0
$606$	381.442	−	482.245i	0.629443	−	0.795784i
$607$		−	227.281i		−	0.374434i	−0.982319	−	0.187217i	$-0.940053\pi$
$607$		−	227.281i		−	0.374434i	0.982319	−	0.187217i	$-0.0599467\pi$
$608$	−132.130			−0.217318
$609$	112.101	+	88.6688i	0.184074	+	0.145597i
$610$		0			0
$611$			24.5100i			0.0401146i
$612$	−119.803	−	506.252i	−0.195757	−	0.827209i
$613$			731.598i			1.19347i	0.802438	+	0.596736i	$0.203536\pi$
$613$			731.598i			1.19347i	−0.802438	+	0.596736i	$0.796464\pi$
$614$			53.1046i			0.0864896i
$615$		0			0
$616$	−142.422			−0.231204
$617$	488.323			0.791447			0.395724	−	0.918370i	$-0.370494\pi$
$617$	488.323			0.791447			0.395724	+	0.918370i	$0.370494\pi$
$618$	457.288	−	578.134i	0.739948	−	0.935492i
$619$	−304.696			−0.492240			−0.246120	−	0.969239i	$-0.579156\pi$
$619$	−304.696			−0.492240			−0.246120	+	0.969239i	$0.579156\pi$
$620$		0			0
$621$	−271.521	+	581.509i	−0.437232	+	0.936407i
$622$			188.654i			0.303302i
$623$	−96.2913			−0.154561
$624$	−11.5745	+	14.6332i	−0.0185488	+	0.0234507i
$625$		0			0
$626$		−	311.311i		−	0.497301i
$627$	827.330	−	1045.97i	1.31951	−	1.66821i
$628$		−	116.887i		−	0.186126i
$629$			593.118i			0.942955i
$630$		0			0
$631$	−568.874			−0.901544			−0.450772	−	0.892639i	$-0.648851\pi$
$631$	−568.874			−0.901544			−0.450772	+	0.892639i	$0.648851\pi$
$632$	203.964			0.322728
$633$	687.506	+	543.798i	1.08611	+	0.859081i
$634$	−464.835			−0.733177
$635$		0			0
$636$	370.799	+	293.292i	0.583018	+	0.461151i
$637$		−	10.8835i		−	0.0170856i
$638$	484.673			0.759676
$639$	−248.819	+	58.8824i	−0.389388	+	0.0921478i
$640$		0			0
$641$			565.547i			0.882289i	0.897436	+	0.441144i	$0.145427\pi$
$641$			565.547i			0.882289i	−0.897436	+	0.441144i	$0.854573\pi$
$642$	311.998	+	246.782i	0.485979	+	0.384396i
$643$			47.4562i			0.0738043i	0.999319	+	0.0369022i	$0.0117490\pi$
$643$			47.4562i			0.0738043i	−0.999319	+	0.0369022i	$0.988251\pi$
$644$			125.776i			0.195305i
$645$		0			0
$646$	954.700			1.47786
$647$	−427.152			−0.660204			−0.330102	−	0.943945i	$-0.607083\pi$
$647$	−427.152			−0.660204			−0.330102	+	0.943945i	$0.607083\pi$
$648$	−204.803	+	102.683i	−0.316054	+	0.158461i
$649$	−1697.55			−2.61564
$650$		0			0
$651$	−38.8246	+	49.0846i	−0.0596383	+	0.0753988i
$652$			158.972i			0.243823i
$653$	−1157.00			−1.77182			−0.885910	−	0.463856i	$-0.846465\pi$
$653$	−1157.00			−1.77182			−0.885910	+	0.463856i	$0.846465\pi$
$654$	−655.132	−	518.191i	−1.00173	−	0.792341i
$655$		0			0
$656$		−	203.595i		−	0.310359i
$657$	−1053.18	+	249.234i	−1.60302	+	0.379351i
$658$			58.9843i			0.0896418i
$659$		−	522.811i		−	0.793340i	−0.917961	−	0.396670i	$-0.870166\pi$
$659$		−	522.811i		−	0.793340i	0.917961	−	0.396670i	$-0.129834\pi$
$660$		0			0
$661$	885.681			1.33991			0.669956	−	0.742401i	$-0.266313\pi$
$661$	885.681			1.33991			0.669956	+	0.742401i	$0.266313\pi$
$662$	−622.534			−0.940384
$663$	83.6312	−	105.732i	0.126141	−	0.159475i
$664$	294.664			0.443771
$665$		0			0
$666$	254.179	−	60.1509i	0.381650	−	0.0903167i
$667$		−	428.026i		−	0.641719i
$668$	144.337			0.216074
$669$	−422.042	+	533.575i	−0.630856	+	0.797570i
$670$		0			0
$671$			1073.69i			1.60013i
$672$	−27.8545	+	35.2155i	−0.0414501	+	0.0524040i
$673$			969.877i			1.44112i	0.693390	+	0.720562i	$0.256116\pi$
$673$			969.877i			1.44112i	−0.693390	+	0.720562i	$0.743884\pi$
$674$		−	193.464i		−	0.287039i
$675$		0			0
$676$	333.165			0.492848
$677$	−497.683			−0.735130			−0.367565	−	0.929998i	$-0.619809\pi$
$677$	−497.683			−0.735130			−0.367565	+	0.929998i	$0.619809\pi$
$678$	380.397	+	300.883i	0.561057	+	0.443780i
$679$	151.242			0.222743
$680$		0			0
$681$	690.243	+	545.963i	1.01357	+	0.801708i
$682$			212.219i			0.311172i
$683$	1188.03			1.73943			0.869716	−	0.493553i	$-0.164302\pi$
$683$	1188.03			1.73943			0.869716	+	0.493553i	$0.164302\pi$
$684$	−96.8205	−	409.134i	−0.141551	−	0.598149i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	432.614	+	342.185i	0.629714	+	0.498086i
$688$			125.001i			0.181688i
$689$			122.510i			0.177808i
$690$		0			0
$691$	−1194.03			−1.72797			−0.863985	−	0.503517i	$-0.832039\pi$
$691$	−1194.03			−1.72797			−0.863985	+	0.503517i	$0.832039\pi$
$692$	471.307			0.681080
$693$	−104.362	−	441.003i	−0.150595	−	0.636369i
$694$	142.948			0.205977
$695$		0			0
$696$	94.7909	−	119.841i	0.136194	−	0.172185i
$697$			1471.07i			2.11058i
$698$	−94.3123			−0.135118
$699$	−795.674	−	629.356i	−1.13830	−	0.900366i
$700$		0			0
$701$			724.767i			1.03390i	0.856014	+	0.516952i	$0.172933\pi$
$701$			724.767i			1.03390i	−0.856014	+	0.516952i	$0.827067\pi$
$702$	−53.7926	−	25.1171i	−0.0766277	−	0.0357793i
$703$			479.336i			0.681843i
$704$			152.255i			0.216272i
$705$		0			0
$706$	−230.627			−0.326666
$707$	383.435			0.542341
$708$	−332.002	+	419.739i	−0.468929	+	0.592852i
$709$	−336.704			−0.474900			−0.237450	−	0.971400i	$-0.576312\pi$
$709$	−336.704			−0.474900			−0.237450	+	0.971400i	$0.576312\pi$
$710$		0			0
$711$	149.459	+	631.567i	0.210209	+	0.888280i
$712$			102.940i			0.144578i
$713$	187.416			0.262855
$714$	201.262	−	254.449i	0.281879	−	0.356371i
$715$		0			0
$716$			265.215i			0.370411i
$717$	549.584	−	694.821i	0.766505	−	0.969068i
$718$		−	448.150i		−	0.624165i
$719$		−	819.998i		−	1.14047i	−0.821482	−	0.570235i	$-0.806852\pi$
$719$		−	819.998i		−	1.14047i	0.821482	−	0.570235i	$-0.193148\pi$
$720$		0			0
$721$	459.678			0.637555
$722$	261.021			0.361525
$723$	−529.226	−	418.603i	−0.731987	−	0.578981i
$724$	95.8538			0.132395
$725$		0			0
$726$	−802.653	−	634.876i	−1.10558	−	0.874485i
$727$		−	1265.71i		−	1.74100i	−0.492168	−	0.870500i	$-0.663796\pi$
$727$		−	1265.71i		−	1.74100i	0.492168	−	0.870500i	$-0.336204\pi$
$728$	−11.6350			−0.0159821
$729$	−468.026	−	558.921i	−0.642011	−	0.766695i
$730$		0			0
$731$		−	903.194i		−	1.23556i
$732$	265.482	+	209.989i	0.362681	+	0.286870i
$733$			244.877i			0.334075i	0.985951	+	0.167038i	$0.0534201\pi$
$733$			244.877i			0.334075i	−0.985951	+	0.167038i	$0.946580\pi$
$734$			697.051i			0.949660i
$735$		0			0
$736$	134.460			0.182691
$737$	−1069.69			−1.45141
$738$	630.424	−	149.188i	0.854233	−	0.202152i
$739$	887.684			1.20120			0.600598	−	0.799551i	$-0.294929\pi$
$739$	887.684			1.20120			0.600598	+	0.799551i	$0.294929\pi$
$740$		0			0
$741$	67.5875	−	85.4487i	0.0912112	−	0.115315i
$742$			294.824i			0.397337i
$743$	1200.69			1.61600			0.807999	−	0.589183i	$-0.200550\pi$
$743$	1200.69			1.61600			0.807999	+	0.589183i	$0.200550\pi$
$744$	52.4737	+	41.5052i	0.0705291	+	0.0557866i
$745$		0			0
$746$		−	868.486i		−	1.16419i
$747$	215.921	+	912.414i	0.289051	+	1.22144i
$748$		−	1100.12i		−	1.47075i
$749$			248.071i			0.331204i
$750$		0			0
$751$	423.204			0.563521			0.281760	−	0.959485i	$-0.409082\pi$
$751$	423.204			0.563521			0.281760	+	0.959485i	$0.409082\pi$
$752$	63.0569			0.0838522
$753$	49.0097	−	61.9614i	0.0650859	−	0.0822860i
$754$	39.5947			0.0525128
$755$		0			0
$756$	−129.454	−	60.4453i	−0.171236	−	0.0799541i
$757$			1039.54i			1.37323i	0.727020	+	0.686617i	$0.240905\pi$
$757$			1039.54i			1.37323i	−0.727020	+	0.686617i	$0.759095\pi$
$758$	−696.119			−0.918362
$759$	−841.924	+	1064.42i	−1.10925	+	1.40239i
$760$		0			0
$761$		−	653.459i		−	0.858684i	−0.903142	−	0.429342i	$-0.858746\pi$
$761$		−	653.459i		−	0.858684i	0.903142	−	0.429342i	$-0.141254\pi$
$762$	−37.5326	+	47.4512i	−0.0492554	+	0.0622719i
$763$		−	520.899i		−	0.682698i
$764$			367.771i			0.481375i
$765$		0			0
$766$	−413.665			−0.540033
$767$	−138.679			−0.180807
$768$	37.6469	+	29.7777i	0.0490194	+	0.0387730i
$769$	631.211			0.820820			0.410410	−	0.911901i	$-0.365386\pi$
$769$	631.211			0.820820			0.410410	+	0.911901i	$0.365386\pi$
$770$		0			0
$771$	303.875	+	240.356i	0.394131	+	0.311746i
$772$		−	215.513i		−	0.279162i
$773$	525.003			0.679176			0.339588	−	0.940574i	$-0.389712\pi$
$773$	525.003			0.679176			0.339588	+	0.940574i	$0.389712\pi$
$774$	−387.061	+	91.5971i	−0.500079	+	0.118343i
$775$		0			0
$776$		−	161.685i		−	0.208357i
$777$	127.754	+	101.050i	0.164419	+	0.130051i
$778$			632.615i			0.813130i
$779$			1188.87i			1.52614i
$780$		0			0
$781$	−540.700			−0.692317
$782$	−971.541			−1.24238
$783$	440.543	+	205.700i	0.562634	+	0.262708i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	−226.636	+	286.529i	−0.288341	+	0.364541i
$787$		−	406.916i		−	0.517047i	−0.966005	−	0.258524i	$-0.916764\pi$
$787$		−	406.916i		−	0.517047i	0.966005	−	0.258524i	$-0.0832360\pi$
$788$	594.493			0.754432
$789$	550.937	+	435.776i	0.698273	+	0.552314i
$790$		0			0
$791$			302.455i			0.382371i
$792$	−471.453	+	111.568i	−0.595268	+	0.140869i
$793$			87.7136i			0.110610i
$794$			415.071i			0.522759i
$795$		0			0
$796$	−493.773			−0.620318
$797$	−599.391			−0.752059			−0.376030	−	0.926608i	$-0.622711\pi$
$797$	−599.391			−0.752059			−0.376030	+	0.926608i	$0.622711\pi$
$798$	162.652	−	205.636i	0.203825	−	0.257689i
$799$	−455.616			−0.570233
$800$		0			0
$801$	−318.748	+	75.4311i	−0.397938	+	0.0941712i
$802$		−	637.596i		−	0.795007i
$803$	−2288.64			−2.85011
$804$	−209.206	+	264.492i	−0.260206	+	0.328971i
$805$		0			0
$806$			17.3370i			0.0215099i
$807$	202.898	−	256.518i	0.251423	−	0.317866i
$808$		−	409.910i		−	0.507314i
$809$			528.965i			0.653851i	0.945050	+	0.326925i	$0.106013\pi$
$809$			528.965i			0.653851i	−0.945050	+	0.326925i	$0.893987\pi$
$810$		0			0
$811$	−462.281			−0.570013			−0.285007	−	0.958526i	$-0.591996\pi$
$811$	−462.281			−0.570013			−0.285007	+	0.958526i	$0.591996\pi$
$812$	95.2862			0.117348
$813$	480.500	+	380.062i	0.591021	+	0.467481i
$814$	552.348			0.678560
$815$		0			0
$816$	−272.017	−	215.158i	−0.333354	−	0.263674i
$817$		−	729.927i		−	0.893424i
$818$	−430.158			−0.525865
$819$	−8.52574	−	36.0272i	−0.0104099	−	0.0439892i
$820$		0			0
$821$			955.594i			1.16394i	0.813210	+	0.581970i	$0.197718\pi$
$821$			955.594i			1.16394i	−0.813210	+	0.581970i	$0.802282\pi$
$822$	290.869	+	230.069i	0.353855	+	0.279889i
$823$			339.294i			0.412265i	0.978524	+	0.206132i	$0.0660877\pi$
$823$			339.294i			0.412265i	−0.978524	+	0.206132i	$0.933912\pi$
$824$		−	491.416i		−	0.596379i
$825$		0			0
$826$	−333.737			−0.404039
$827$	−1124.72			−1.36000			−0.680001	−	0.733211i	$-0.738021\pi$
$827$	−1124.72			−1.36000			−0.680001	+	0.733211i	$0.738021\pi$
$828$	98.5285	+	416.351i	0.118996	+	0.502839i
$829$	918.780			1.10830			0.554149	−	0.832417i	$-0.313044\pi$
$829$	918.780			1.10830			0.554149	+	0.832417i	$0.313044\pi$
$830$		0			0
$831$	−639.403	+	808.376i	−0.769438	+	0.972775i
$832$			12.4383i			0.0149499i
$833$	202.313			0.242873
$834$	−627.439	−	496.286i	−0.752325	−	0.595068i
$835$		0			0
$836$		−	889.074i		−	1.06349i
$837$	−90.0680	+	192.896i	−0.107608	+	0.230461i
$838$		−	214.919i		−	0.256466i
$839$		−	477.085i		−	0.568635i	−0.958730	−	0.284317i	$-0.908233\pi$
$839$		−	477.085i		−	0.568635i	0.958730	−	0.284317i	$-0.0917670\pi$
$840$		0			0
$841$	516.733			0.614427
$842$	234.051			0.277970
$843$	748.175	−	945.893i	0.887515	−	1.12206i
$844$	584.383			0.692396
$845$		0			0
$846$	46.2061	+	195.253i	0.0546172	+	0.230795i
$847$		−	638.193i		−	0.753475i
$848$	315.180			0.371675
$849$	540.198	−	682.954i	0.636275	−	0.804422i
$850$		0			0
$851$		−	487.792i		−	0.573198i
$852$	−105.748	+	133.694i	−0.124118	+	0.156918i
$853$			203.019i			0.238006i	0.992894	+	0.119003i	$0.0379698\pi$
$853$			203.019i			0.238006i	−0.992894	+	0.119003i	$0.962030\pi$
$854$			211.086i			0.247174i
$855$		0			0
$856$	265.200			0.309813
$857$	209.889			0.244912			0.122456	−	0.992474i	$-0.460923\pi$
$857$	209.889			0.244912			0.122456	+	0.992474i	$0.460923\pi$
$858$	−98.4642	−	77.8824i	−0.114760	−	0.0907720i
$859$	−708.676			−0.825001			−0.412501	−	0.910957i	$-0.635345\pi$
$859$	−708.676			−0.825001			−0.412501	+	0.910957i	$0.635345\pi$
$860$		0			0
$861$	316.859	+	250.627i	0.368013	+	0.291088i
$862$		−	340.454i		−	0.394958i
$863$	−996.198			−1.15434			−0.577171	−	0.816623i	$-0.695844\pi$
$863$	−996.198			−1.15434			−0.577171	+	0.816623i	$0.695844\pi$
$864$	−64.6187	+	138.392i	−0.0747902	+	0.160176i
$865$		0			0
$866$		−	780.242i		−	0.900972i
$867$	1285.46	+	1016.76i	1.48265	+	1.17273i
$868$			41.7221i			0.0480669i
$869$			1372.44i			1.57933i
$870$		0			0
$871$	−87.3865			−0.100329
$872$	−556.864			−0.638606
$873$	500.650	−	118.478i	0.573482	−	0.135713i
$874$	−785.163			−0.898356
$875$		0			0
$876$	−447.605	+	565.892i	−0.510965	+	0.645996i
$877$			510.287i			0.581855i	0.956745	+	0.290927i	$0.0939638\pi$
$877$			510.287i			0.581855i	−0.956745	+	0.290927i	$0.906036\pi$
$878$	−121.614			−0.138513
$879$	−1043.48	−	825.363i	−1.18712	−	0.938979i
$880$		0			0
$881$		−	469.010i		−	0.532361i	−0.963923	−	0.266181i	$-0.914238\pi$
$881$		−	469.010i		−	0.532361i	0.963923	−	0.266181i	$-0.0857617\pi$
$882$	−20.5175	−	86.7008i	−0.0232625	−	0.0983002i
$883$			978.480i			1.10813i	0.832473	+	0.554065i	$0.186924\pi$
$883$			978.480i			1.10813i	−0.832473	+	0.554065i	$0.813076\pi$
$884$		−	89.8726i		−	0.101666i
$885$		0			0
$886$	575.972			0.650082
$887$	162.637			0.183356			0.0916778	−	0.995789i	$-0.470777\pi$
$887$	162.637			0.183356			0.0916778	+	0.995789i	$0.470777\pi$
$888$	108.027	−	136.574i	0.121651	−	0.153800i
$889$	−37.7287			−0.0424395
$890$		0			0
$891$	−690.932	−	1378.08i	−0.775457	−	1.54667i
$892$			453.540i			0.508453i
$893$	−368.212			−0.412331
$894$	316.783	−	400.499i	0.354344	−	0.447985i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	−68.7798	+	86.9561i	−0.0766776	+	0.0969410i
$898$			528.738i			0.588795i
$899$		−	141.984i		−	0.157935i
$900$		0			0
$901$	−2277.33			−2.52756
$902$	1369.95			1.51879
$903$	−194.542	−	153.877i	−0.215439	−	0.170407i
$904$	323.338			0.357675
$905$		0			0
$906$	−138.492	−	109.543i	−0.152861	−	0.120909i
$907$		−	446.893i		−	0.492716i	−0.969179	−	0.246358i	$-0.920766\pi$
$907$		−	446.893i		−	0.492716i	0.969179	−	0.246358i	$-0.0792339\pi$
$908$	586.709			0.646155
$909$	1269.27	−	300.369i	1.39633	−	0.330439i
$910$		0			0
$911$			1085.65i			1.19171i	0.803092	+	0.595855i	$0.203187\pi$
$911$			1085.65i			1.19171i	−0.803092	+	0.595855i	$0.796813\pi$
$912$	−219.834	−	173.882i	−0.241046	−	0.190661i
$913$			1982.74i			2.17167i
$914$			41.3385i			0.0452281i
$915$		0			0
$916$	367.723			0.401444
$917$	−227.821			−0.248441
$918$	466.901	−	999.951i	0.508607	−	1.08927i
$919$	−601.801			−0.654843			−0.327422	−	0.944878i	$-0.606180\pi$
$919$	−601.801			−0.654843			−0.327422	+	0.944878i	$0.606180\pi$
$920$		0			0
$921$	−69.8856	+	88.3541i	−0.0758801	+	0.0959328i
$922$		−	501.155i		−	0.543553i
$923$	−44.1717			−0.0478567
$924$	−236.958	−	187.427i	−0.256448	−	0.202843i
$925$		0			0
$926$			690.142i			0.745293i
$927$	1521.65	−	360.095i	1.64148	−	0.388452i
$928$		−	101.865i		−	0.109769i
$929$			1434.34i			1.54397i	0.635643	+	0.771983i	$0.280735\pi$
$929$			1434.34i			1.54397i	−0.635643	+	0.771983i	$0.719265\pi$
$930$		0			0
$931$	163.502			0.175620
$932$	−676.325			−0.725671
$933$	−248.268	+	313.877i	−0.266096	+	0.336417i
$934$	566.315			0.606333
$935$		0			0
$936$	−38.5146	+	9.11440i	−0.0411481	+	0.00973761i
$937$			49.4833i			0.0528104i	0.999651	+	0.0264052i	$0.00840601\pi$
$937$			49.4833i			0.0528104i	−0.999651	+	0.0264052i	$0.991594\pi$
$938$	−210.299			−0.224200
$939$	409.685	−	517.951i	0.436299	−	0.551598i
$940$		0			0
$941$			1178.58i			1.25248i	0.779631	+	0.626239i	$0.215406\pi$
$941$			1178.58i			1.25248i	−0.779631	+	0.626239i	$0.784594\pi$
$942$	153.824	−	194.474i	0.163295	−	0.206448i
$943$		−	1209.84i		−	1.28297i
$944$			356.779i			0.377944i
$945$		0			0
$946$	−841.109			−0.889122
$947$	640.256			0.676089			0.338044	−	0.941130i	$-0.390235\pi$
$947$	640.256			0.676089			0.338044	+	0.941130i	$0.390235\pi$
$948$	339.351	+	268.417i	0.357965	+	0.283140i
$949$	−186.967			−0.197015
$950$		0			0
$951$	−773.380	−	611.722i	−0.813228	−	0.643241i
$952$		−	216.282i		−	0.227187i
$953$	1270.84			1.33352			0.666759	−	0.745273i	$-0.267681\pi$
$953$	1270.84			1.33352			0.666759	+	0.745273i	$0.267681\pi$
$954$	230.955	+	975.943i	0.242091	+	1.02300i
$955$		0			0
$956$		−	590.600i		−	0.617783i
$957$	806.387	+	637.829i	0.842620	+	0.666488i
$958$		−	1024.41i		−	1.06933i
$959$			231.271i			0.241159i
$960$		0			0
$961$	−898.831			−0.935308
$962$	45.1233			0.0469057
$963$	194.330	+	821.179i	0.201797	+	0.852730i
$964$	−449.844			−0.466643
$965$		0			0
$966$	−165.521	+	209.263i	−0.171347	+	0.216629i
$967$			201.964i			0.208856i	0.994532	+	0.104428i	$0.0333012\pi$
$967$			201.964i			0.208856i	−0.994532	+	0.104428i	$0.966699\pi$
$968$	−682.258			−0.704811
$969$	1588.41	+	1256.38i	1.63922	+	1.29658i
$970$		0			0
$971$			900.525i			0.927420i	0.885987	+	0.463710i	$0.153482\pi$
$971$			900.525i			0.927420i	−0.885987	+	0.463710i	$0.846518\pi$
$972$	−475.876	−	98.6795i	−0.489585	−	0.101522i
$973$		−	498.880i		−	0.512723i
$974$		−	703.138i		−	0.721908i
$975$		0			0
$976$	225.661			0.231210
$977$	−820.874			−0.840199			−0.420099	−	0.907478i	$-0.638005\pi$
$977$	−820.874			−0.840199			−0.420099	+	0.907478i	$0.638005\pi$
$978$	−209.208	+	264.494i	−0.213914	+	0.270444i
$979$	−692.661			−0.707519
$980$		0			0
$981$	−408.053	−	1724.31i	−0.415956	−	1.75770i
$982$		−	735.956i		−	0.749446i
$983$	−1354.26			−1.37768			−0.688840	−	0.724914i	$-0.741880\pi$
$983$	−1354.26			−1.37768			−0.688840	+	0.724914i	$0.741880\pi$
$984$	267.931	−	338.737i	0.272288	−	0.344245i
$985$		0			0
$986$			736.025i			0.746476i
$987$	−77.6233	+	98.1366i	−0.0786457	+	0.0994291i
$988$		−	72.6317i		−	0.0735138i
$989$			742.804i			0.751065i
$990$		0			0
$991$	1289.97			1.30168			0.650841	−	0.759214i	$-0.274416\pi$
$991$	1289.97			1.30168			0.650841	+	0.759214i	$0.274416\pi$
$992$	44.6028			0.0449625
$993$	−1035.76	−	819.254i	−1.04306	−	0.825030i
$994$	−106.301			−0.106943
$995$		0			0
$996$	490.254	+	387.777i	0.492223	+	0.389335i
$997$		−	757.496i		−	0.759775i	−0.925033	−	0.379888i	$-0.875963\pi$
$997$		−	757.496i		−	0.759775i	0.925033	−	0.379888i	$-0.124037\pi$
$998$	−913.528			−0.915358
$999$	502.055	+	234.422i	0.502558	+	0.234657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.c.449.28		32
3.2	odd	2	inner	1050.3.c.c.449.6		32
5.2	odd	4		1050.3.e.d.701.14		16
5.3	odd	4		210.3.e.a.71.3	✓	16
5.4	even	2	inner	1050.3.c.c.449.5		32
15.2	even	4		1050.3.e.d.701.6		16
15.8	even	4		210.3.e.a.71.11	yes	16
15.14	odd	2	inner	1050.3.c.c.449.27		32
20.3	even	4		1680.3.l.c.1121.11		16
60.23	odd	4		1680.3.l.c.1121.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.3	✓	16	5.3	odd	4
210.3.e.a.71.11	yes	16	15.8	even	4
1050.3.c.c.449.5		32	5.4	even	2	inner
1050.3.c.c.449.6		32	3.2	odd	2	inner
1050.3.c.c.449.27		32	15.14	odd	2	inner
1050.3.c.c.449.28		32	1.1	even	1	trivial
1050.3.e.d.701.6		16	15.2	even	4
1050.3.e.d.701.14		16	5.2	odd	4
1680.3.l.c.1121.11		16	20.3	even	4
1680.3.l.c.1121.12		16	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(2.35293 + 1.86110i) q^{3} +2.00000 q^{4} +(3.32755 + 2.63200i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(2.07259 + 8.75810i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(2.35293 + 1.86110i) q^{3} +2.00000 q^{4} +(3.32755 + 2.63200i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(2.07259 + 8.75810i) q^{9} +19.0319i q^{11} +(4.70587 + 3.72221i) q^{12} +1.55479i q^{13} +3.74166i q^{14} +4.00000 q^{16} -28.9019 q^{17} +(2.93108 + 12.3858i) q^{18} -23.3574 q^{19} +(-4.92402 + 6.22527i) q^{21} +26.9152i q^{22} +23.7695 q^{23} +(6.65510 + 5.26400i) q^{24} +2.19880i q^{26} +(-11.4231 + 24.4645i) q^{27} +5.29150i q^{28} -18.0074i q^{29} +7.88473 q^{31} +5.65685 q^{32} +(-35.4204 + 44.7809i) q^{33} -40.8735 q^{34} +(4.14517 + 17.5162i) q^{36} -20.5218i q^{37} -33.0324 q^{38} +(-2.89362 + 3.65831i) q^{39} -50.8988i q^{41} +(-6.96361 + 8.80387i) q^{42} +31.2503i q^{43} +38.0639i q^{44} +33.6151 q^{46} +15.7642 q^{47} +(9.41173 + 7.44442i) q^{48} -7.00000 q^{49} +(-68.0043 - 53.7895i) q^{51} +3.10957i q^{52} +78.7951 q^{53} +(-16.1547 + 34.5981i) q^{54} +7.48331i q^{56} +(-54.9585 - 43.4706i) q^{57} -25.4663i q^{58} +89.1948i q^{59} +56.4152 q^{61} +11.1507 q^{62} +(-23.1718 + 5.48355i) q^{63} +8.00000 q^{64} +(-50.0920 + 63.3297i) q^{66} +56.2048i q^{67} -57.8038 q^{68} +(55.9280 + 44.2375i) q^{69} +28.4101i q^{71} +(5.86216 + 24.7717i) q^{72} +120.253i q^{73} -29.0222i q^{74} -46.7149 q^{76} -50.3538 q^{77} +(-4.09220 + 5.17363i) q^{78} +72.1123 q^{79} +(-72.4088 + 36.3038i) q^{81} -71.9818i q^{82} +104.179 q^{83} +(-9.84804 + 12.4505i) q^{84} +44.1946i q^{86} +(33.5136 - 42.3702i) q^{87} +53.8304i q^{88} +36.3947i q^{89} -4.11358 q^{91} +47.5389 q^{92} +(18.5522 + 14.6743i) q^{93} +22.2940 q^{94} +(13.3102 + 10.5280i) q^{96} -57.1642i q^{97} -9.89949 q^{98} +(-166.684 + 39.4453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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