LMFDB - Embedded newform 128.5.f.b.95.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,5,Mod(31,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("128.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	128.f (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.2313552747$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 15x^12 - 34x^11 + 62x^10 - 312x^9 + 1432x^8 - 4960x^7 + 11456x^6 - 19968x^5 + 31744x^4 - 139264x^3 + 491520x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{42} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			95.5
Root			$2.79265 + 0.448449i$ of defining polynomial
Character	$\chi$	$=$	128.95
Dual form			128.5.f.b.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.63552 - 4.63552i) q^{3} +(29.2002 - 29.2002i) q^{5} +59.6196 q^{7} +38.0239i q^{9} +O(q^{10})$	\(q+(4.63552 - 4.63552i) q^{3} +(29.2002 - 29.2002i) q^{5} +59.6196 q^{7} +38.0239i q^{9} +(18.0837 + 18.0837i) q^{11} +(-50.7721 - 50.7721i) q^{13} -270.716i q^{15} -223.769 q^{17} +(-14.7360 + 14.7360i) q^{19} +(276.368 - 276.368i) q^{21} +739.082 q^{23} -1080.30i q^{25} +(551.738 + 551.738i) q^{27} +(-938.904 - 938.904i) q^{29} +938.741i q^{31} +167.655 q^{33} +(1740.90 - 1740.90i) q^{35} +(-263.837 + 263.837i) q^{37} -470.710 q^{39} -248.841i q^{41} +(-1035.00 - 1035.00i) q^{43} +(1110.31 + 1110.31i) q^{45} -2018.46i q^{47} +1153.50 q^{49} +(-1037.29 + 1037.29i) q^{51} +(-833.240 + 833.240i) q^{53} +1056.09 q^{55} +136.618i q^{57} +(2223.17 + 2223.17i) q^{59} +(341.374 + 341.374i) q^{61} +2266.97i q^{63} -2965.11 q^{65} +(-4845.43 + 4845.43i) q^{67} +(3426.03 - 3426.03i) q^{69} -4180.93 q^{71} +9071.36i q^{73} +(-5007.74 - 5007.74i) q^{75} +(1078.14 + 1078.14i) q^{77} -735.536i q^{79} +2035.24 q^{81} +(-1441.90 + 1441.90i) q^{83} +(-6534.10 + 6534.10i) q^{85} -8704.61 q^{87} +5071.77i q^{89} +(-3027.01 - 3027.01i) q^{91} +(4351.55 + 4351.55i) q^{93} +860.586i q^{95} -2523.85 q^{97} +(-687.613 + 687.613i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{3} + 2 q^{5} - 4 q^{7}+O(q^{10}) $ 14 * q + 2 * q^3 + 2 * q^5 - 4 * q^7	$ 14 q + 2 q^{3} + 2 q^{5} - 4 q^{7} - 94 q^{11} + 2 q^{13} - 4 q^{17} + 706 q^{19} + 164 q^{21} + 1148 q^{23} + 1664 q^{27} - 862 q^{29} - 4 q^{33} - 1340 q^{35} + 1826 q^{37} + 2684 q^{39} - 1694 q^{43} - 1410 q^{45} + 682 q^{49} + 3012 q^{51} + 482 q^{53} - 11780 q^{55} + 2786 q^{59} + 3778 q^{61} - 2020 q^{65} - 7998 q^{67} - 9628 q^{69} + 19964 q^{71} - 17570 q^{75} + 9508 q^{77} + 1454 q^{81} + 17282 q^{83} - 9948 q^{85} - 49284 q^{87} + 28036 q^{91} - 8896 q^{93} - 4 q^{97} - 49214 q^{99}+O(q^{100}) $ 14 * q + 2 * q^3 + 2 * q^5 - 4 * q^7 - 94 * q^11 + 2 * q^13 - 4 * q^17 + 706 * q^19 + 164 * q^21 + 1148 * q^23 + 1664 * q^27 - 862 * q^29 - 4 * q^33 - 1340 * q^35 + 1826 * q^37 + 2684 * q^39 - 1694 * q^43 - 1410 * q^45 + 682 * q^49 + 3012 * q^51 + 482 * q^53 - 11780 * q^55 + 2786 * q^59 + 3778 * q^61 - 2020 * q^65 - 7998 * q^67 - 9628 * q^69 + 19964 * q^71 - 17570 * q^75 + 9508 * q^77 + 1454 * q^81 + 17282 * q^83 - 9948 * q^85 - 49284 * q^87 + 28036 * q^91 - 8896 * q^93 - 4 * q^97 - 49214 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.63552	−	4.63552i	0.515058	−	0.515058i	−0.401014	−	0.916072i	$-0.631342\pi$
$3$	4.63552	−	4.63552i	0.515058	−	0.515058i	0.916072	+	0.401014i	$0.131342\pi$
$4$		0			0
$5$	29.2002	−	29.2002i	1.16801	−	1.16801i	0.185330	−	0.982676i	$-0.440665\pi$
$5$	29.2002	−	29.2002i	1.16801	−	1.16801i	0.982676	−	0.185330i	$-0.0593353\pi$
$6$		0			0
$7$	59.6196			1.21673			0.608363	−	0.793659i	$-0.291826\pi$
$7$	59.6196			1.21673			0.608363	+	0.793659i	$0.291826\pi$
$8$		0			0
$9$			38.0239i			0.469431i
$10$		0			0
$11$	18.0837	+	18.0837i	0.149452	+	0.149452i	0.777873	−	0.628421i	$-0.216299\pi$
$11$	18.0837	+	18.0837i	0.149452	+	0.149452i	−0.628421	+	0.777873i	$0.716299\pi$
$12$		0			0
$13$	−50.7721	−	50.7721i	−0.300427	−	0.300427i	0.540754	−	0.841181i	$-0.318139\pi$
$13$	−50.7721	−	50.7721i	−0.300427	−	0.300427i	−0.841181	+	0.540754i	$0.818139\pi$
$14$		0			0
$15$		−	270.716i		−	1.20318i
$16$		0			0
$17$	−223.769			−0.774289			−0.387144	−	0.922019i	$-0.626538\pi$
$17$	−223.769			−0.774289			−0.387144	+	0.922019i	$0.626538\pi$
$18$		0			0
$19$	−14.7360	+	14.7360i	−0.0408199	+	0.0408199i	−0.727222	−	0.686402i	$-0.759189\pi$
$19$	−14.7360	+	14.7360i	−0.0408199	+	0.0408199i	0.686402	+	0.727222i	$0.259189\pi$
$20$		0			0
$21$	276.368	−	276.368i	0.626684	−	0.626684i
$22$		0			0
$23$	739.082			1.39713			0.698565	−	0.715547i	$-0.253822\pi$
$23$	739.082			1.39713			0.698565	+	0.715547i	$0.253822\pi$
$24$		0			0
$25$		−	1080.30i		−	1.72848i
$26$		0			0
$27$	551.738	+	551.738i	0.756842	+	0.756842i
$28$		0			0
$29$	−938.904	−	938.904i	−1.11641	−	1.11641i	−0.992263	−	0.124150i	$-0.960380\pi$
$29$	−938.904	−	938.904i	−1.11641	−	1.11641i	−0.124150	−	0.992263i	$-0.539620\pi$
$30$		0			0
$31$			938.741i			0.976838i	0.872609	+	0.488419i	$0.162426\pi$
$31$			938.741i			0.976838i	−0.872609	+	0.488419i	$0.837574\pi$
$32$		0			0
$33$	167.655			0.153953
$34$		0			0
$35$	1740.90	−	1740.90i	1.42114	−	1.42114i
$36$		0			0
$37$	−263.837	+	263.837i	−0.192722	+	0.192722i	−0.796871	−	0.604149i	$-0.793513\pi$
$37$	−263.837	+	263.837i	−0.192722	+	0.192722i	0.604149	+	0.796871i	$0.293513\pi$
$38$		0			0
$39$	−470.710			−0.309474
$40$		0			0
$41$		−	248.841i		−	0.148031i	−0.997257	−	0.0740157i	$-0.976418\pi$
$41$		−	248.841i		−	0.148031i	0.997257	−	0.0740157i	$-0.0235815\pi$
$42$		0			0
$43$	−1035.00	−	1035.00i	−0.559765	−	0.559765i	0.369476	−	0.929240i	$-0.379537\pi$
$43$	−1035.00	−	1035.00i	−0.559765	−	0.559765i	−0.929240	+	0.369476i	$0.879537\pi$
$44$		0			0
$45$	1110.31	+	1110.31i	0.548299	+	0.548299i
$46$		0			0
$47$		−	2018.46i		−	0.913746i	−0.889532	−	0.456873i	$-0.848969\pi$
$47$		−	2018.46i		−	0.913746i	0.889532	−	0.456873i	$-0.151031\pi$
$48$		0			0
$49$	1153.50			0.480424
$50$		0			0
$51$	−1037.29	+	1037.29i	−0.398803	+	0.398803i
$52$		0			0
$53$	−833.240	+	833.240i	−0.296632	+	0.296632i	−0.839693	−	0.543061i	$-0.817265\pi$
$53$	−833.240	+	833.240i	−0.296632	+	0.296632i	0.543061	+	0.839693i	$0.317265\pi$
$54$		0			0
$55$	1056.09			0.349122
$56$		0			0
$57$			136.618i			0.0420492i
$58$		0			0
$59$	2223.17	+	2223.17i	0.638660	+	0.638660i	0.950225	−	0.311565i	$-0.100853\pi$
$59$	2223.17	+	2223.17i	0.638660	+	0.638660i	−0.311565	+	0.950225i	$0.600853\pi$
$60$		0			0
$61$	341.374	+	341.374i	0.0917425	+	0.0917425i	0.751489	−	0.659746i	$-0.229336\pi$
$61$	341.374	+	341.374i	0.0917425	+	0.0917425i	−0.659746	+	0.751489i	$0.729336\pi$
$62$		0			0
$63$			2266.97i			0.571170i
$64$		0			0
$65$	−2965.11			−0.701800
$66$		0			0
$67$	−4845.43	+	4845.43i	−1.07940	+	1.07940i	−0.0828379	+	0.996563i	$0.526398\pi$
$67$	−4845.43	+	4845.43i	−1.07940	+	1.07940i	−0.996563	+	0.0828379i	$0.973602\pi$
$68$		0			0
$69$	3426.03	−	3426.03i	0.719602	−	0.719602i
$70$		0			0
$71$	−4180.93			−0.829386			−0.414693	−	0.909961i	$-0.636111\pi$
$71$	−4180.93			−0.829386			−0.414693	+	0.909961i	$0.636111\pi$
$72$		0			0
$73$			9071.36i			1.70226i	0.524953	+	0.851131i	$0.324083\pi$
$73$			9071.36i			1.70226i	−0.524953	+	0.851131i	$0.675917\pi$
$74$		0			0
$75$	−5007.74	−	5007.74i	−0.890265	−	0.890265i
$76$		0			0
$77$	1078.14	+	1078.14i	0.181842	+	0.181842i
$78$		0			0
$79$		−	735.536i		−	0.117855i	−0.998262	−	0.0589277i	$-0.981232\pi$
$79$		−	735.536i		−	0.117855i	0.998262	−	0.0589277i	$-0.0187682\pi$
$80$		0			0
$81$	2035.24			0.310203
$82$		0			0
$83$	−1441.90	+	1441.90i	−0.209305	+	0.209305i	−0.803972	−	0.594667i	$-0.797284\pi$
$83$	−1441.90	+	1441.90i	−0.209305	+	0.209305i	0.594667	+	0.803972i	$0.297284\pi$
$84$		0			0
$85$	−6534.10	+	6534.10i	−0.904374	+	0.904374i
$86$		0			0
$87$	−8704.61			−1.15003
$88$		0			0
$89$			5071.77i			0.640294i	0.947368	+	0.320147i	$0.103732\pi$
$89$			5071.77i			0.640294i	−0.947368	+	0.320147i	$0.896268\pi$
$90$		0			0
$91$	−3027.01	−	3027.01i	−0.365537	−	0.365537i
$92$		0			0
$93$	4351.55	+	4351.55i	0.503128	+	0.503128i
$94$		0			0
$95$			860.586i			0.0953558i
$96$		0			0
$97$	−2523.85			−0.268238			−0.134119	−	0.990965i	$-0.542820\pi$
$97$	−2523.85			−0.268238			−0.134119	+	0.990965i	$0.542820\pi$
$98$		0			0
$99$	−687.613	+	687.613i	−0.0701575	+	0.0701575i
$100$		0			0
$101$	−425.990	+	425.990i	−0.0417596	+	0.0417596i	−0.727678	−	0.685919i	$-0.759401\pi$
$101$	−425.990	+	425.990i	−0.0417596	+	0.0417596i	0.685919	+	0.727678i	$0.259401\pi$
$102$		0			0
$103$	13178.6			1.24221			0.621103	−	0.783729i	$-0.286685\pi$
$103$	13178.6			1.24221			0.621103	+	0.783729i	$0.286685\pi$
$104$		0			0
$105$		−	16140.0i		−	1.46394i
$106$		0			0
$107$	10821.5	+	10821.5i	0.945190	+	0.945190i	0.998574	−	0.0533845i	$-0.0170009\pi$
$107$	10821.5	+	10821.5i	0.945190	+	0.945190i	−0.0533845	+	0.998574i	$0.517001\pi$
$108$		0			0
$109$	1428.57	+	1428.57i	0.120240	+	0.120240i	0.764666	−	0.644426i	$-0.222904\pi$
$109$	1428.57	+	1428.57i	0.120240	+	0.120240i	−0.644426	+	0.764666i	$0.722904\pi$
$110$		0			0
$111$			2446.04i			0.198526i
$112$		0			0
$113$	20121.5			1.57581			0.787904	−	0.615798i	$-0.211166\pi$
$113$	20121.5			1.57581			0.787904	+	0.615798i	$0.211166\pi$
$114$		0			0
$115$	21581.3	−	21581.3i	1.63186	−	1.63186i
$116$		0			0
$117$	1930.56	−	1930.56i	0.141030	−	0.141030i
$118$		0			0
$119$	−13341.0			−0.942098
$120$		0			0
$121$		−	13987.0i		−	0.955328i
$122$		0			0
$123$	−1153.51	−	1153.51i	−0.0762447	−	0.0762447i
$124$		0			0
$125$	−13294.8	−	13294.8i	−0.850865	−	0.850865i
$126$		0			0
$127$		−	2630.54i		−	0.163094i	−0.996669	−	0.0815470i	$-0.974014\pi$
$127$		−	2630.54i		−	0.163094i	0.996669	−	0.0815470i	$-0.0259861\pi$
$128$		0			0
$129$	−9595.57			−0.576622
$130$		0			0
$131$	−12437.0	+	12437.0i	−0.724722	+	0.724722i	−0.969563	−	0.244841i	$-0.921264\pi$
$131$	−12437.0	+	12437.0i	−0.724722	+	0.724722i	0.244841	+	0.969563i	$0.421264\pi$
$132$		0			0
$133$	−878.554	+	878.554i	−0.0496667	+	0.0496667i
$134$		0			0
$135$	32221.6			1.76799
$136$		0			0
$137$			15392.0i			0.820078i	0.912068	+	0.410039i	$0.134485\pi$
$137$			15392.0i			0.820078i	−0.912068	+	0.410039i	$0.865515\pi$
$138$		0			0
$139$	−12151.3	−	12151.3i	−0.628915	−	0.628915i	0.318880	−	0.947795i	$-0.396693\pi$
$139$	−12151.3	−	12151.3i	−0.628915	−	0.628915i	−0.947795	+	0.318880i	$0.896693\pi$
$140$		0			0
$141$	−9356.63	−	9356.63i	−0.470632	−	0.470632i
$142$		0			0
$143$		−	1836.29i		−	0.0897987i
$144$		0			0
$145$	−54832.3			−2.60796
$146$		0			0
$147$	5347.06	−	5347.06i	0.247446	−	0.247446i
$148$		0			0
$149$	20803.7	−	20803.7i	0.937062	−	0.937062i	−0.0610710	−	0.998133i	$-0.519452\pi$
$149$	20803.7	−	20803.7i	0.937062	−	0.937062i	0.998133	+	0.0610710i	$0.0194516\pi$
$150$		0			0
$151$	−7756.67			−0.340190			−0.170095	−	0.985428i	$-0.554407\pi$
$151$	−7756.67			−0.340190			−0.170095	+	0.985428i	$0.554407\pi$
$152$		0			0
$153$		−	8508.60i		−	0.363475i
$154$		0			0
$155$	27411.4	+	27411.4i	1.14095	+	1.14095i
$156$		0			0
$157$	−7040.20	−	7040.20i	−0.285618	−	0.285618i	0.549727	−	0.835345i	$-0.314732\pi$
$157$	−7040.20	−	7040.20i	−0.285618	−	0.285618i	−0.835345	+	0.549727i	$0.814732\pi$
$158$		0			0
$159$			7725.00i			0.305565i
$160$		0			0
$161$	44063.8			1.69993
$162$		0			0
$163$	−7273.43	+	7273.43i	−0.273756	+	0.273756i	−0.830610	−	0.556854i	$-0.812008\pi$
$163$	−7273.43	+	7273.43i	−0.273756	+	0.273756i	0.556854	+	0.830610i	$0.312008\pi$
$164$		0			0
$165$	4895.54	−	4895.54i	0.179818	−	0.179818i
$166$		0			0
$167$	30069.6			1.07819			0.539095	−	0.842245i	$-0.318766\pi$
$167$	30069.6			1.07819			0.539095	+	0.842245i	$0.318766\pi$
$168$		0			0
$169$		−	23405.4i		−	0.819488i
$170$		0			0
$171$	−560.320	−	560.320i	−0.0191621	−	0.0191621i
$172$		0			0
$173$	8329.72	+	8329.72i	0.278316	+	0.278316i	0.832436	−	0.554121i	$-0.186945\pi$
$173$	8329.72	+	8329.72i	0.278316	+	0.278316i	−0.554121	+	0.832436i	$0.686945\pi$
$174$		0			0
$175$		−	64406.9i		−	2.10308i
$176$		0			0
$177$	20611.1			0.657893
$178$		0			0
$179$	7537.56	−	7537.56i	0.235247	−	0.235247i	−0.579632	−	0.814879i	$-0.696803\pi$
$179$	7537.56	−	7537.56i	0.235247	−	0.235247i	0.814879	+	0.579632i	$0.196803\pi$
$180$		0			0
$181$	−3802.64	+	3802.64i	−0.116072	+	0.116072i	−0.762757	−	0.646685i	$-0.776155\pi$
$181$	−3802.64	+	3802.64i	−0.116072	+	0.116072i	0.646685	+	0.762757i	$0.276155\pi$
$182$		0			0
$183$	3164.89			0.0945054
$184$		0			0
$185$			15408.2i			0.450202i
$186$		0			0
$187$	−4046.58	−	4046.58i	−0.115719	−	0.115719i
$188$		0			0
$189$	32894.4	+	32894.4i	0.920869	+	0.920869i
$190$		0			0
$191$			52248.1i			1.43220i	0.697997	+	0.716100i	$0.254075\pi$
$191$			52248.1i			1.43220i	−0.697997	+	0.716100i	$0.745925\pi$
$192$		0			0
$193$	−24380.0			−0.654514			−0.327257	−	0.944935i	$-0.606124\pi$
$193$	−24380.0			−0.654514			−0.327257	+	0.944935i	$0.606124\pi$
$194$		0			0
$195$	−13744.8	+	13744.8i	−0.361468	+	0.361468i
$196$		0			0
$197$	−31537.9	+	31537.9i	−0.812644	+	0.812644i	−0.985030	−	0.172386i	$-0.944852\pi$
$197$	−31537.9	+	31537.9i	−0.812644	+	0.812644i	0.172386	+	0.985030i	$0.444852\pi$
$198$		0			0
$199$	−71129.4			−1.79615			−0.898076	−	0.439841i	$-0.855035\pi$
$199$	−71129.4			−1.79615			−0.898076	+	0.439841i	$0.855035\pi$
$200$		0			0
$201$			44922.2i			1.11191i
$202$		0			0
$203$	−55977.1	−	55977.1i	−1.35837	−	1.35837i
$204$		0			0
$205$	−7266.19	−	7266.19i	−0.172902	−	0.172902i
$206$		0			0
$207$			28102.8i			0.655857i
$208$		0			0
$209$	−532.962			−0.0122012
$210$		0			0
$211$	13393.4	−	13393.4i	0.300833	−	0.300833i	−0.540507	−	0.841340i	$-0.681767\pi$
$211$	13393.4	−	13393.4i	0.300833	−	0.300833i	0.841340	+	0.540507i	$0.181767\pi$
$212$		0			0
$213$	−19380.8	+	19380.8i	−0.427181	+	0.427181i
$214$		0			0
$215$	−60444.6			−1.30762
$216$		0			0
$217$			55967.4i			1.18854i
$218$		0			0
$219$	42050.4	+	42050.4i	0.876763	+	0.876763i
$220$		0			0
$221$	11361.2	+	11361.2i	0.232617	+	0.232617i
$222$		0			0
$223$			54266.9i			1.09125i	0.838029	+	0.545626i	$0.183708\pi$
$223$			54266.9i			1.09125i	−0.838029	+	0.545626i	$0.816292\pi$
$224$		0			0
$225$	41077.2			0.811401
$226$		0			0
$227$	−14529.0	+	14529.0i	−0.281957	+	0.281957i	−0.833889	−	0.551932i	$-0.813891\pi$
$227$	−14529.0	+	14529.0i	−0.281957	+	0.281957i	0.551932	+	0.833889i	$0.313891\pi$
$228$		0			0
$229$	−21618.1	+	21618.1i	−0.412237	+	0.412237i	−0.882517	−	0.470280i	$-0.844153\pi$
$229$	−21618.1	+	21618.1i	−0.412237	+	0.412237i	0.470280	+	0.882517i	$0.344153\pi$
$230$		0			0
$231$	9995.50			0.187318
$232$		0			0
$233$		−	92103.6i		−	1.69654i	−0.529562	−	0.848271i	$-0.677644\pi$
$233$		−	92103.6i		−	1.69654i	0.529562	−	0.848271i	$-0.322356\pi$
$234$		0			0
$235$	−58939.5	−	58939.5i	−1.06726	−	1.06726i
$236$		0			0
$237$	−3409.59	−	3409.59i	−0.0607024	−	0.0607024i
$238$		0			0
$239$		−	70411.0i		−	1.23266i	−0.787487	−	0.616332i	$-0.788618\pi$
$239$		−	70411.0i		−	1.23266i	0.787487	−	0.616332i	$-0.211382\pi$
$240$		0			0
$241$	22402.6			0.385714			0.192857	−	0.981227i	$-0.438225\pi$
$241$	22402.6			0.385714			0.192857	+	0.981227i	$0.438225\pi$
$242$		0			0
$243$	−35256.4	+	35256.4i	−0.597070	+	0.597070i
$244$		0			0
$245$	33682.3	−	33682.3i	0.561138	−	0.561138i
$246$		0			0
$247$	1496.35			0.0245268
$248$		0			0
$249$			13367.9i			0.215608i
$250$		0			0
$251$	72407.6	+	72407.6i	1.14931	+	1.14931i	0.986689	+	0.162621i	$0.0519947\pi$
$251$	72407.6	+	72407.6i	1.14931	+	1.14931i	0.162621	+	0.986689i	$0.448005\pi$
$252$		0			0
$253$	13365.3	+	13365.3i	0.208804	+	0.208804i
$254$		0			0
$255$			60577.9i			0.931609i
$256$		0			0
$257$	−56466.3			−0.854916			−0.427458	−	0.904035i	$-0.640591\pi$
$257$	−56466.3			−0.854916			−0.427458	+	0.904035i	$0.640591\pi$
$258$		0			0
$259$	−15729.9	+	15729.9i	−0.234490	+	0.234490i
$260$		0			0
$261$	35700.8	−	35700.8i	0.524080	−	0.524080i
$262$		0			0
$263$	76515.5			1.10621			0.553105	−	0.833111i	$-0.313443\pi$
$263$	76515.5			1.10621			0.553105	+	0.833111i	$0.313443\pi$
$264$		0			0
$265$			48661.5i			0.692937i
$266$		0			0
$267$	23510.3	+	23510.3i	0.329788	+	0.329788i
$268$		0			0
$269$	−1928.97	−	1928.97i	−0.0266576	−	0.0266576i	0.693652	−	0.720310i	$-0.256000\pi$
$269$	−1928.97	−	1928.97i	−0.0266576	−	0.0266576i	−0.720310	+	0.693652i	$0.756000\pi$
$270$		0			0
$271$		−	128685.i		−	1.75222i	−0.482109	−	0.876111i	$-0.660129\pi$
$271$		−	128685.i		−	1.75222i	0.482109	−	0.876111i	$-0.339871\pi$
$272$		0			0
$273$	−28063.5			−0.376545
$274$		0			0
$275$	19535.8	−	19535.8i	0.258324	−	0.258324i
$276$		0			0
$277$	−56674.5	+	56674.5i	−0.738632	+	0.738632i	−0.972313	−	0.233681i	$-0.924923\pi$
$277$	−56674.5	+	56674.5i	−0.738632	+	0.738632i	0.233681	+	0.972313i	$0.424923\pi$
$278$		0			0
$279$	−35694.6			−0.458558
$280$		0			0
$281$			10599.7i			0.134240i	0.997745	+	0.0671200i	$0.0213810\pi$
$281$			10599.7i			0.134240i	−0.997745	+	0.0671200i	$0.978619\pi$
$282$		0			0
$283$	−63293.6	−	63293.6i	−0.790291	−	0.790291i	0.191251	−	0.981541i	$-0.438746\pi$
$283$	−63293.6	−	63293.6i	−0.790291	−	0.790291i	−0.981541	+	0.191251i	$0.938746\pi$
$284$		0			0
$285$	3989.26	+	3989.26i	0.0491137	+	0.0491137i
$286$		0			0
$287$		−	14835.8i		−	0.180114i
$288$		0			0
$289$	−33448.2			−0.400477
$290$		0			0
$291$	−11699.3	+	11699.3i	−0.138158	+	0.138158i
$292$		0			0
$293$	89072.9	−	89072.9i	1.03755	−	1.03755i	0.0382867	−	0.999267i	$-0.487810\pi$
$293$	89072.9	−	89072.9i	1.03755	−	1.03755i	0.999267	−	0.0382867i	$-0.0121900\pi$
$294$		0			0
$295$	129834.			1.49192
$296$		0			0
$297$			19954.9i			0.226223i
$298$		0			0
$299$	−37524.7	−	37524.7i	−0.419735	−	0.419735i
$300$		0			0
$301$	−61706.6	−	61706.6i	−0.681080	−	0.681080i
$302$		0			0
$303$			3949.36i			0.0430172i
$304$		0			0
$305$	19936.3			0.214312
$306$		0			0
$307$	124227.	−	124227.i	1.31807	−	1.31807i	0.402769	−	0.915302i	$-0.368048\pi$
$307$	124227.	−	124227.i	1.31807	−	1.31807i	0.915302	−	0.402769i	$-0.131952\pi$
$308$		0			0
$309$	61089.5	−	61089.5i	0.639808	−	0.639808i
$310$		0			0
$311$	15733.9			0.162673			0.0813364	−	0.996687i	$-0.474081\pi$
$311$	15733.9			0.162673			0.0813364	+	0.996687i	$0.474081\pi$
$312$		0			0
$313$		−	104554.i		−	1.06721i	−0.845733	−	0.533606i	$-0.820837\pi$
$313$		−	104554.i		−	1.06721i	0.845733	−	0.533606i	$-0.179163\pi$
$314$		0			0
$315$	66196.0	+	66196.0i	0.667130	+	0.667130i
$316$		0			0
$317$	−45847.9	−	45847.9i	−0.456248	−	0.456248i	0.441174	−	0.897422i	$-0.354562\pi$
$317$	−45847.9	−	45847.9i	−0.456248	−	0.456248i	−0.897422	+	0.441174i	$0.854562\pi$
$318$		0			0
$319$		−	33957.7i		−	0.333700i
$320$		0			0
$321$	100326.			0.973654
$322$		0			0
$323$	3297.46	−	3297.46i	0.0316064	−	0.0316064i
$324$		0			0
$325$	−54849.0	+	54849.0i	−0.519281	+	0.519281i
$326$		0			0
$327$	13244.3			0.123861
$328$		0			0
$329$		−	120340.i		−	1.11178i
$330$		0			0
$331$	137545.	+	137545.i	1.25542	+	1.25542i	0.953258	+	0.302159i	$0.0977073\pi$
$331$	137545.	+	137545.i	1.25542	+	1.25542i	0.302159	+	0.953258i	$0.402293\pi$
$332$		0			0
$333$	−10032.1	−	10032.1i	−0.0904700	−	0.0904700i
$334$		0			0
$335$			282975.i			2.52149i
$336$		0			0
$337$	−40849.6			−0.359690			−0.179845	−	0.983695i	$-0.557560\pi$
$337$	−40849.6			−0.359690			−0.179845	+	0.983695i	$0.557560\pi$
$338$		0			0
$339$	93273.5	−	93273.5i	0.811632	−	0.811632i
$340$		0			0
$341$	−16975.9	+	16975.9i	−0.145990	+	0.145990i
$342$		0			0
$343$	−74375.6			−0.632182
$344$		0			0
$345$		−	200081.i		−	1.68100i
$346$		0			0
$347$	−21361.1	−	21361.1i	−0.177404	−	0.177404i	0.612819	−	0.790223i	$-0.290035\pi$
$347$	−21361.1	−	21361.1i	−0.177404	−	0.177404i	−0.790223	+	0.612819i	$0.790035\pi$
$348$		0			0
$349$	−139275.	−	139275.i	−1.14347	−	1.14347i	−0.987812	−	0.155654i	$-0.950252\pi$
$349$	−139275.	−	139275.i	−1.14347	−	1.14347i	−0.155654	−	0.987812i	$-0.549748\pi$
$350$		0			0
$351$		−	56025.8i		−	0.454751i
$352$		0			0
$353$	−100461.			−0.806209			−0.403105	−	0.915154i	$-0.632069\pi$
$353$	−100461.			−0.806209			−0.403105	+	0.915154i	$0.632069\pi$
$354$		0			0
$355$	−122084.	+	122084.i	−0.968728	+	0.968728i
$356$		0			0
$357$	−61842.6	+	61842.6i	−0.485234	+	0.485234i
$358$		0			0
$359$	96352.7			0.747609			0.373805	−	0.927507i	$-0.378053\pi$
$359$	96352.7			0.747609			0.373805	+	0.927507i	$0.378053\pi$
$360$		0			0
$361$			129887.i			0.996667i
$362$		0			0
$363$	−64836.8	−	64836.8i	−0.492049	−	0.492049i
$364$		0			0
$365$	264885.	+	264885.i	1.98825	+	1.98825i
$366$		0			0
$367$		−	190661.i		−	1.41557i	−0.706429	−	0.707784i	$-0.749695\pi$
$367$		−	190661.i		−	1.41557i	0.706429	−	0.707784i	$-0.250305\pi$
$368$		0			0
$369$	9461.91			0.0694906
$370$		0			0
$371$	−49677.5	+	49677.5i	−0.360920	+	0.360920i
$372$		0			0
$373$	−51771.9	+	51771.9i	−0.372114	+	0.372114i	−0.868247	−	0.496133i	$-0.834753\pi$
$373$	−51771.9	+	51771.9i	−0.372114	+	0.372114i	0.496133	+	0.868247i	$0.334753\pi$
$374$		0			0
$375$	−123256.			−0.876489
$376$		0			0
$377$			95340.2i			0.670801i
$378$		0			0
$379$	−121232.	−	121232.i	−0.843990	−	0.843990i	0.145385	−	0.989375i	$-0.453558\pi$
$379$	−121232.	−	121232.i	−0.843990	−	0.843990i	−0.989375	+	0.145385i	$0.953558\pi$
$380$		0			0
$381$	−12193.9	−	12193.9i	−0.0840028	−	0.0840028i
$382$		0			0
$383$			8262.20i			0.0563246i	0.999603	+	0.0281623i	$0.00896552\pi$
$383$			8262.20i			0.0563246i	−0.999603	+	0.0281623i	$0.991034\pi$
$384$		0			0
$385$	62963.9			0.424786
$386$		0			0
$387$	39355.0	−	39355.0i	0.262771	−	0.262771i
$388$		0			0
$389$	−43964.9	+	43964.9i	−0.290541	+	0.290541i	−0.837294	−	0.546753i	$-0.815864\pi$
$389$	−43964.9	+	43964.9i	−0.290541	+	0.290541i	0.546753	+	0.837294i	$0.315864\pi$
$390$		0			0
$391$	−165384.			−1.08178
$392$		0			0
$393$			115303.i			0.746547i
$394$		0			0
$395$	−21477.8	−	21477.8i	−0.137656	−	0.137656i
$396$		0			0
$397$	−72864.3	−	72864.3i	−0.462311	−	0.462311i	0.437101	−	0.899412i	$-0.356005\pi$
$397$	−72864.3	−	72864.3i	−0.462311	−	0.462311i	−0.899412	+	0.437101i	$0.856005\pi$
$398$		0			0
$399$			8145.10i			0.0511624i
$400$		0			0
$401$	237249.			1.47542			0.737711	−	0.675116i	$-0.235907\pi$
$401$	237249.			1.47542			0.737711	+	0.675116i	$0.235907\pi$
$402$		0			0
$403$	47661.9	−	47661.9i	0.293468	−	0.293468i
$404$		0			0
$405$	59429.3	−	59429.3i	0.362319	−	0.362319i
$406$		0			0
$407$	−9542.29			−0.0576055
$408$		0			0
$409$			150042.i			0.896945i	0.893797	+	0.448473i	$0.148032\pi$
$409$			150042.i			0.896945i	−0.893797	+	0.448473i	$0.851968\pi$
$410$		0			0
$411$	71350.1	+	71350.1i	0.422387	+	0.422387i
$412$		0			0
$413$	132545.	+	132545.i	0.777074	+	0.777074i
$414$		0			0
$415$			84207.5i			0.488939i
$416$		0			0
$417$	−112655.			−0.647855
$418$		0			0
$419$	−71760.1	+	71760.1i	−0.408747	+	0.408747i	−0.881302	−	0.472554i	$-0.843332\pi$
$419$	−71760.1	+	71760.1i	−0.408747	+	0.408747i	0.472554	+	0.881302i	$0.343332\pi$
$420$		0			0
$421$	209821.	−	209821.i	1.18382	−	1.18382i	0.205070	−	0.978747i	$-0.434258\pi$
$421$	209821.	−	209821.i	1.18382	−	1.18382i	0.978747	−	0.205070i	$-0.0657424\pi$
$422$		0			0
$423$	76750.0			0.428941
$424$		0			0
$425$			241738.i			1.33834i
$426$		0			0
$427$	20352.6	+	20352.6i	0.111626	+	0.111626i
$428$		0			0
$429$	−8512.18	−	8512.18i	−0.0462515	−	0.0462515i
$430$		0			0
$431$			123853.i			0.666731i	0.942798	+	0.333366i	$0.108184\pi$
$431$			123853.i			0.666731i	−0.942798	+	0.333366i	$0.891816\pi$
$432$		0			0
$433$	−265114.			−1.41402			−0.707012	−	0.707202i	$-0.749957\pi$
$433$	−265114.			−1.41402			−0.707012	+	0.707202i	$0.749957\pi$
$434$		0			0
$435$	−254176.	+	254176.i	−1.34325	+	1.34325i
$436$		0			0
$437$	−10891.1	+	10891.1i	−0.0570307	+	0.0570307i
$438$		0			0
$439$	186089.			0.965590			0.482795	−	0.875734i	$-0.339622\pi$
$439$	186089.			0.965590			0.482795	+	0.875734i	$0.339622\pi$
$440$		0			0
$441$			43860.5i			0.225526i
$442$		0			0
$443$	−25618.8	−	25618.8i	−0.130542	−	0.130542i	0.638817	−	0.769359i	$-0.279424\pi$
$443$	−25618.8	−	25618.8i	−0.130542	−	0.130542i	−0.769359	+	0.638817i	$0.779424\pi$
$444$		0			0
$445$	148096.	+	148096.i	0.747867	+	0.747867i
$446$		0			0
$447$		−	192872.i		−	0.965282i
$448$		0			0
$449$	−2307.59			−0.0114463			−0.00572316	−	0.999984i	$-0.501822\pi$
$449$	−2307.59			−0.0114463			−0.00572316	+	0.999984i	$0.501822\pi$
$450$		0			0
$451$	4499.96	−	4499.96i	0.0221236	−	0.0221236i
$452$		0			0
$453$	−35956.2	+	35956.2i	−0.175217	+	0.175217i
$454$		0			0
$455$	−176778.			−0.853899
$456$		0			0
$457$		−	262378.i		−	1.25631i	−0.778090	−	0.628153i	$-0.783811\pi$
$457$		−	262378.i		−	1.25631i	0.778090	−	0.628153i	$-0.216189\pi$
$458$		0			0
$459$	−123462.	−	123462.i	−0.586014	−	0.586014i
$460$		0			0
$461$	−136771.	−	136771.i	−0.643564	−	0.643564i	0.307866	−	0.951430i	$-0.400385\pi$
$461$	−136771.	−	136771.i	−0.643564	−	0.643564i	−0.951430	+	0.307866i	$0.900385\pi$
$462$		0			0
$463$		−	22250.8i		−	0.103797i	−0.998652	−	0.0518983i	$-0.983473\pi$
$463$		−	22250.8i		−	0.103797i	0.998652	−	0.0518983i	$-0.0165272\pi$
$464$		0			0
$465$	254132.			1.17531
$466$		0			0
$467$	−175541.	+	175541.i	−0.804906	+	0.804906i	−0.983858	−	0.178952i	$-0.942729\pi$
$467$	−175541.	+	175541.i	−0.804906	+	0.804906i	0.178952	+	0.983858i	$0.442729\pi$
$468$		0			0
$469$	−288883.	+	288883.i	−1.31334	+	1.31334i
$470$		0			0
$471$	−65269.9			−0.294219
$472$		0			0
$473$		−	37433.4i		−	0.167316i
$474$		0			0
$475$	15919.3	+	15919.3i	0.0705563	+	0.0705563i
$476$		0			0
$477$	−31683.1	−	31683.1i	−0.139249	−	0.139249i
$478$		0			0
$479$		−	117920.i		−	0.513945i	−0.966419	−	0.256973i	$-0.917275\pi$
$479$		−	117920.i		−	0.513945i	0.966419	−	0.256973i	$-0.0827250\pi$
$480$		0			0
$481$	26791.1			0.115798
$482$		0			0
$483$	204258.	−	204258.i	0.875559	−	0.875559i
$484$		0			0
$485$	−73696.7	+	73696.7i	−0.313303	+	0.313303i
$486$		0			0
$487$	−449942.			−1.89714			−0.948568	−	0.316574i	$-0.897467\pi$
$487$	−449942.			−1.89714			−0.948568	+	0.316574i	$0.897467\pi$
$488$		0			0
$489$			67432.3i			0.282001i
$490$		0			0
$491$	122509.	+	122509.i	0.508166	+	0.508166i	0.913963	−	0.405797i	$-0.133006\pi$
$491$	122509.	+	122509.i	0.508166	+	0.508166i	−0.405797	+	0.913963i	$0.633006\pi$
$492$		0			0
$493$	210098.	+	210098.i	0.864426	+	0.864426i
$494$		0			0
$495$			40156.8i			0.163889i
$496$		0			0
$497$	−249266.			−1.00914
$498$		0			0
$499$	44886.9	−	44886.9i	0.180268	−	0.180268i	−0.611205	−	0.791473i	$-0.709315\pi$
$499$	44886.9	−	44886.9i	0.180268	−	0.180268i	0.791473	+	0.611205i	$0.209315\pi$
$500$		0			0
$501$	139388.	−	139388.i	0.555330	−	0.555330i
$502$		0			0
$503$	235778.			0.931896			0.465948	−	0.884812i	$-0.345713\pi$
$503$	235778.			0.931896			0.465948	+	0.884812i	$0.345713\pi$
$504$		0			0
$505$			24877.9i			0.0975509i
$506$		0			0
$507$	−108496.	−	108496.i	−0.422083	−	0.422083i
$508$		0			0
$509$	−227812.	−	227812.i	−0.879308	−	0.879308i	0.114155	−	0.993463i	$-0.463584\pi$
$509$	−227812.	−	227812.i	−0.879308	−	0.879308i	−0.993463	+	0.114155i	$0.963584\pi$
$510$		0			0
$511$			540831.i			2.07119i
$512$		0			0
$513$	−16260.8			−0.0617884
$514$		0			0
$515$	384816.	−	384816.i	1.45090	−	1.45090i
$516$		0			0
$517$	36501.3	−	36501.3i	0.136561	−	0.136561i
$518$		0			0
$519$	77225.1			0.286697
$520$		0			0
$521$		−	539683.i		−	1.98822i	−0.108395	−	0.994108i	$-0.534571\pi$
$521$		−	539683.i		−	1.98822i	0.108395	−	0.994108i	$-0.465429\pi$
$522$		0			0
$523$	175071.	+	175071.i	0.640044	+	0.640044i	0.950566	−	0.310522i	$-0.100504\pi$
$523$	175071.	+	175071.i	0.640044	+	0.640044i	−0.310522	+	0.950566i	$0.600504\pi$
$524$		0			0
$525$	−298560.	−	298560.i	−1.08321	−	1.08321i
$526$		0			0
$527$		−	210062.i		−	0.756354i
$528$		0			0
$529$	266401.			0.951972
$530$		0			0
$531$	−84533.9	+	84533.9i	−0.299807	+	0.299807i
$532$		0			0
$533$	−12634.2	+	12634.2i	−0.0444726	+	0.0444726i
$534$		0			0
$535$	631977.			2.20797
$536$		0			0
$537$		−	69880.9i		−	0.242332i
$538$		0			0
$539$	20859.5	+	20859.5i	0.0718003	+	0.0718003i
$540$		0			0
$541$	142203.	+	142203.i	0.485863	+	0.485863i	0.906998	−	0.421135i	$-0.138368\pi$
$541$	142203.	+	142203.i	0.485863	+	0.485863i	−0.421135	+	0.906998i	$0.638368\pi$
$542$		0			0
$543$			35254.4i			0.119568i
$544$		0			0
$545$	83428.9			0.280882
$546$		0			0
$547$	265412.	−	265412.i	0.887045	−	0.887045i	−0.107193	−	0.994238i	$-0.534186\pi$
$547$	265412.	−	265412.i	0.887045	−	0.887045i	0.994238	+	0.107193i	$0.0341862\pi$
$548$		0			0
$549$	−12980.4	+	12980.4i	−0.0430668	+	0.0430668i
$550$		0			0
$551$	27671.3			0.0911438
$552$		0			0
$553$		−	43852.4i		−	0.143398i
$554$		0			0
$555$	71424.8	+	71424.8i	0.231880	+	0.231880i
$556$		0			0
$557$	−168105.	−	168105.i	−0.541837	−	0.541837i	0.382230	−	0.924067i	$-0.375156\pi$
$557$	−168105.	−	168105.i	−0.541837	−	0.541837i	−0.924067	+	0.382230i	$0.875156\pi$
$558$		0			0
$559$			105099.i			0.336336i
$560$		0			0
$561$	−37516.0			−0.119204
$562$		0			0
$563$	181113.	−	181113.i	0.571389	−	0.571389i	−0.361127	−	0.932517i	$-0.617608\pi$
$563$	181113.	−	181113.i	0.571389	−	0.571389i	0.932517	+	0.361127i	$0.117608\pi$
$564$		0			0
$565$	587551.	−	587551.i	1.84055	−	1.84055i
$566$		0			0
$567$	121340.			0.377432
$568$		0			0
$569$			124083.i			0.383254i	0.981468	+	0.191627i	$0.0613765\pi$
$569$			124083.i			0.383254i	−0.981468	+	0.191627i	$0.938624\pi$
$570$		0			0
$571$	92801.0	+	92801.0i	0.284630	+	0.284630i	0.834952	−	0.550322i	$-0.185495\pi$
$571$	92801.0	+	92801.0i	0.284630	+	0.284630i	−0.550322	+	0.834952i	$0.685495\pi$
$572$		0			0
$573$	242197.	+	242197.i	0.737666	+	0.737666i
$574$		0			0
$575$		−	798429.i		−	2.41491i
$576$		0			0
$577$	182478.			0.548098			0.274049	−	0.961716i	$-0.411637\pi$
$577$	182478.			0.548098			0.274049	+	0.961716i	$0.411637\pi$
$578$		0			0
$579$	−113014.	+	113014.i	−0.337112	+	0.337112i
$580$		0			0
$581$	−85965.6	+	85965.6i	−0.254667	+	0.254667i
$582$		0			0
$583$	−30136.1			−0.0886646
$584$		0			0
$585$		−	112745.i		−	0.329447i
$586$		0			0
$587$	−197015.	−	197015.i	−0.571772	−	0.571772i	0.360851	−	0.932623i	$-0.382486\pi$
$587$	−197015.	−	197015.i	−0.571772	−	0.571772i	−0.932623	+	0.360851i	$0.882486\pi$
$588$		0			0
$589$	−13833.3	−	13833.3i	−0.0398744	−	0.0398744i
$590$		0			0
$591$			292389.i			0.837116i
$592$		0			0
$593$	−478257.			−1.36004			−0.680020	−	0.733194i	$-0.738029\pi$
$593$	−478257.			−1.36004			−0.680020	+	0.733194i	$0.738029\pi$
$594$		0			0
$595$	−389561.	+	389561.i	−1.10038	+	1.10038i
$596$		0			0
$597$	−329722.	+	329722.i	−0.925121	+	0.925121i
$598$		0			0
$599$	−141800.			−0.395206			−0.197603	−	0.980282i	$-0.563316\pi$
$599$	−141800.			−0.395206			−0.197603	+	0.980282i	$0.563316\pi$
$600$		0			0
$601$		−	50813.1i		−	0.140678i	−0.997523	−	0.0703391i	$-0.977592\pi$
$601$		−	50813.1i		−	0.140678i	0.997523	−	0.0703391i	$-0.0224081\pi$
$602$		0			0
$603$	−184242.	−	184242.i	−0.506705	−	0.506705i
$604$		0			0
$605$	−408421.	−	408421.i	−1.11583	−	1.11583i
$606$		0			0
$607$		−	448023.i		−	1.21597i	−0.793948	−	0.607985i	$-0.791978\pi$
$607$		−	448023.i		−	1.21597i	0.793948	−	0.607985i	$-0.208022\pi$
$608$		0			0
$609$	−518965.			−1.39928
$610$		0			0
$611$	−102482.	+	102482.i	−0.274514	+	0.274514i
$612$		0			0
$613$	−8742.04	+	8742.04i	−0.0232644	+	0.0232644i	−0.718643	−	0.695379i	$-0.755237\pi$
$613$	−8742.04	+	8742.04i	−0.0232644	+	0.0232644i	0.695379	+	0.718643i	$0.255237\pi$
$614$		0			0
$615$	−67365.1			−0.178109
$616$		0			0
$617$			488336.i			1.28277i	0.767220	+	0.641384i	$0.221639\pi$
$617$			488336.i			1.28277i	−0.767220	+	0.641384i	$0.778361\pi$
$618$		0			0
$619$	416206.	+	416206.i	1.08624	+	1.08624i	0.995912	+	0.0903309i	$0.0287925\pi$
$619$	416206.	+	416206.i	1.08624	+	1.08624i	0.0903309	+	0.995912i	$0.471208\pi$
$620$		0			0
$621$	407779.	+	407779.i	1.05741	+	1.05741i
$622$		0			0
$623$			302377.i			0.779062i
$624$		0			0
$625$	−101233.			−0.259155
$626$		0			0
$627$	−2470.56	+	2470.56i	−0.00628434	+	0.00628434i
$628$		0			0
$629$	59038.6	−	59038.6i	0.149223	−	0.149223i
$630$		0			0
$631$	77166.0			0.193806			0.0969030	−	0.995294i	$-0.469106\pi$
$631$	77166.0			0.193806			0.0969030	+	0.995294i	$0.469106\pi$
$632$		0			0
$633$		−	124171.i		−	0.309893i
$634$		0			0
$635$	−76812.3	−	76812.3i	−0.190495	−	0.190495i
$636$		0			0
$637$	−58565.5	−	58565.5i	−0.144332	−	0.144332i
$638$		0			0
$639$		−	158976.i		−	0.389340i
$640$		0			0
$641$	692532.			1.68548			0.842740	−	0.538321i	$-0.180941\pi$
$641$	692532.			1.68548			0.842740	+	0.538321i	$0.180941\pi$
$642$		0			0
$643$	−515879.	+	515879.i	−1.24774	+	1.24774i	−0.291031	+	0.956714i	$0.593998\pi$
$643$	−515879.	+	515879.i	−1.24774	+	1.24774i	−0.956714	+	0.291031i	$0.906002\pi$
$644$		0			0
$645$	−280192.	+	280192.i	−0.673498	+	0.673498i
$646$		0			0
$647$	−187947.			−0.448980			−0.224490	−	0.974476i	$-0.572072\pi$
$647$	−187947.			−0.448980			−0.224490	+	0.974476i	$0.572072\pi$
$648$		0			0
$649$			80406.4i			0.190898i
$650$		0			0
$651$	259438.	+	259438.i	0.612169	+	0.612169i
$652$		0			0
$653$	−363478.	−	363478.i	−0.852415	−	0.852415i	0.138015	−	0.990430i	$-0.455928\pi$
$653$	−363478.	−	363478.i	−0.852415	−	0.852415i	−0.990430	+	0.138015i	$0.955928\pi$
$654$		0			0
$655$			726322.i			1.69296i
$656$		0			0
$657$	−344929.			−0.799096
$658$		0			0
$659$	59401.3	−	59401.3i	0.136781	−	0.136781i	−0.635401	−	0.772182i	$-0.719165\pi$
$659$	59401.3	−	59401.3i	0.136781	−	0.136781i	0.772182	+	0.635401i	$0.219165\pi$
$660$		0			0
$661$	352242.	−	352242.i	0.806191	−	0.806191i	−0.177864	−	0.984055i	$-0.556919\pi$
$661$	352242.	−	352242.i	0.806191	−	0.806191i	0.984055	+	0.177864i	$0.0569187\pi$
$662$		0			0
$663$	105331.			0.239622
$664$		0			0
$665$			51307.8i			0.116022i
$666$		0			0
$667$	−693927.	−	693927.i	−1.55977	−	1.55977i
$668$		0			0
$669$	251555.	+	251555.i	0.562058	+	0.562058i
$670$		0			0
$671$			12346.6i			0.0274222i
$672$		0			0
$673$	678354.			1.49771			0.748853	−	0.662736i	$-0.230605\pi$
$673$	678354.			1.49771			0.748853	+	0.662736i	$0.230605\pi$
$674$		0			0
$675$	596041.	−	596041.i	1.30818	−	1.30818i
$676$		0			0
$677$	348304.	−	348304.i	0.759943	−	0.759943i	−0.216369	−	0.976312i	$-0.569421\pi$
$677$	348304.	−	348304.i	0.759943	−	0.759943i	0.976312	+	0.216369i	$0.0694214\pi$
$678$		0			0
$679$	−150471.			−0.326372
$680$		0			0
$681$			134699.i			0.290448i
$682$		0			0
$683$	218970.	+	218970.i	0.469401	+	0.469401i	0.901721	−	0.432319i	$-0.142305\pi$
$683$	218970.	+	218970.i	0.469401	+	0.469401i	−0.432319	+	0.901721i	$0.642305\pi$
$684$		0			0
$685$	449450.	+	449450.i	0.957856	+	0.957856i
$686$		0			0
$687$			200422.i			0.424652i
$688$		0			0
$689$	84610.7			0.178233
$690$		0			0
$691$	−166441.	+	166441.i	−0.348581	+	0.348581i	−0.859581	−	0.511000i	$-0.829275\pi$
$691$	−166441.	+	166441.i	−0.348581	+	0.348581i	0.511000	+	0.859581i	$0.329275\pi$
$692$		0			0
$693$	−40995.2	+	40995.2i	−0.0853625	+	0.0853625i
$694$		0			0
$695$	−709638.			−1.46915
$696$		0			0
$697$			55683.0i			0.114619i
$698$		0			0
$699$	−426948.	−	426948.i	−0.873817	−	0.873817i
$700$		0			0
$701$	606601.	+	606601.i	1.23443	+	1.23443i	0.962244	+	0.272188i	$0.0877473\pi$
$701$	606601.	+	606601.i	1.23443	+	1.23443i	0.272188	+	0.962244i	$0.412253\pi$
$702$		0			0
$703$		−	7775.80i		−	0.0157338i
$704$		0			0
$705$	−546430.			−1.09940
$706$		0			0
$707$	−25397.3	+	25397.3i	−0.0508100	+	0.0508100i
$708$		0			0
$709$	−590171.	+	590171.i	−1.17405	+	1.17405i	−0.192811	+	0.981236i	$0.561760\pi$
$709$	−590171.	+	590171.i	−1.17405	+	1.17405i	−0.981236	+	0.192811i	$0.938240\pi$
$710$		0			0
$711$	27968.0			0.0553251
$712$		0			0
$713$			693806.i			1.36477i
$714$		0			0
$715$	−53620.1	−	53620.1i	−0.104885	−	0.104885i
$716$		0			0
$717$	−326391.	−	326391.i	−0.634893	−	0.634893i
$718$		0			0
$719$		−	319294.i		−	0.617637i	−0.951121	−	0.308819i	$-0.900066\pi$
$719$		−	319294.i		−	0.617637i	0.951121	−	0.308819i	$-0.0999336\pi$
$720$		0			0
$721$	785701.			1.51143
$722$		0			0
$723$	103848.	−	103848.i	0.198665	−	0.198665i
$724$		0			0
$725$	−1.01430e6	+	1.01430e6i	−1.92969	+	1.92969i
$726$		0			0
$727$	−295780.			−0.559628			−0.279814	−	0.960054i	$-0.590273\pi$
$727$	−295780.			−0.559628			−0.279814	+	0.960054i	$0.590273\pi$
$728$		0			0
$729$			491717.i			0.925253i
$730$		0			0
$731$	231602.	+	231602.i	0.433419	+	0.433419i
$732$		0			0
$733$	−353645.	−	353645.i	−0.658203	−	0.658203i	0.296752	−	0.954955i	$-0.404097\pi$
$733$	−353645.	−	353645.i	−0.658203	−	0.658203i	−0.954955	+	0.296752i	$0.904097\pi$
$734$		0			0
$735$		−	312270.i		−	0.578036i
$736$		0			0
$737$	−175247.			−0.322637
$738$		0			0
$739$	23782.9	−	23782.9i	0.0435488	−	0.0435488i	−0.684997	−	0.728546i	$-0.740197\pi$
$739$	23782.9	−	23782.9i	0.0435488	−	0.0435488i	0.728546	+	0.684997i	$0.240197\pi$
$740$		0			0
$741$	6936.38	−	6936.38i	0.0126327	−	0.0126327i
$742$		0			0
$743$	−912931.			−1.65371			−0.826857	−	0.562412i	$-0.809873\pi$
$743$	−912931.			−1.65371			−0.826857	+	0.562412i	$0.809873\pi$
$744$		0			0
$745$		−	1.21494e6i		−	2.18899i
$746$		0			0
$747$	−54826.8	−	54826.8i	−0.0982543	−	0.0982543i
$748$		0			0
$749$	645172.	+	645172.i	1.15004	+	1.15004i
$750$		0			0
$751$			799005.i			1.41667i	0.705875	+	0.708336i	$0.250554\pi$
$751$			799005.i			1.41667i	−0.705875	+	0.708336i	$0.749446\pi$
$752$		0			0
$753$	671294.			1.18392
$754$		0			0
$755$	−226496.	+	226496.i	−0.397344	+	0.397344i
$756$		0			0
$757$	24122.0	−	24122.0i	0.0420940	−	0.0420940i	−0.685746	−	0.727841i	$-0.740524\pi$
$757$	24122.0	−	24122.0i	0.0420940	−	0.0420940i	0.727841	+	0.685746i	$0.240524\pi$
$758$		0			0
$759$	123910.			0.215092
$760$		0			0
$761$		−	97444.6i		−	0.168263i	−0.996455	−	0.0841315i	$-0.973188\pi$
$761$		−	97444.6i		−	0.168263i	0.996455	−	0.0841315i	$-0.0268116\pi$
$762$		0			0
$763$	85170.8	+	85170.8i	0.146299	+	0.146299i
$764$		0			0
$765$	−248452.	−	248452.i	−0.424542	−	0.424542i
$766$		0			0
$767$		−	225750.i		−	0.383741i
$768$		0			0
$769$	−747937.			−1.26477			−0.632386	−	0.774653i	$-0.717924\pi$
$769$	−747937.			−1.26477			−0.632386	+	0.774653i	$0.717924\pi$
$770$		0			0
$771$	−261751.	+	261751.i	−0.440331	+	0.440331i
$772$		0			0
$773$	328529.	−	328529.i	0.549813	−	0.549813i	−0.376574	−	0.926387i	$-0.622898\pi$
$773$	328529.	−	328529.i	0.549813	−	0.549813i	0.926387	+	0.376574i	$0.122898\pi$
$774$		0			0
$775$	1.01412e6			1.68844
$776$		0			0
$777$			145832.i			0.241552i
$778$		0			0
$779$	3666.92	+	3666.92i	0.00604263	+	0.00604263i
$780$		0			0
$781$	−75606.7	−	75606.7i	−0.123953	−	0.123953i
$782$		0			0
$783$		−	1.03606e6i		−	1.68990i
$784$		0			0
$785$	−411150.			−0.667207
$786$		0			0
$787$	76254.3	−	76254.3i	0.123116	−	0.123116i	−0.642864	−	0.765980i	$-0.722254\pi$
$787$	76254.3	−	76254.3i	0.123116	−	0.123116i	0.765980	+	0.642864i	$0.222254\pi$
$788$		0			0
$789$	354689.	−	354689.i	0.569762	−	0.569762i
$790$		0			0
$791$	1.19964e6			1.91733
$792$		0			0
$793$		−	34664.5i		−	0.0551238i
$794$		0			0
$795$	225571.	+	225571.i	0.356902	+	0.356902i
$796$		0			0
$797$	−10472.2	−	10472.2i	−0.0164862	−	0.0164862i	0.698816	−	0.715302i	$-0.253711\pi$
$797$	−10472.2	−	10472.2i	−0.0164862	−	0.0164862i	−0.715302	+	0.698816i	$0.753711\pi$
$798$		0			0
$799$			451671.i			0.707503i
$800$		0			0
$801$	−192849.			−0.300574
$802$		0			0
$803$	−164044.	+	164044.i	−0.254407	+	0.254407i
$804$		0			0
$805$	1.28667e6	−	1.28667e6i	1.98552	−	1.98552i
$806$		0			0
$807$	−17883.5			−0.0274604
$808$		0			0
$809$		−	569939.i		−	0.870826i	−0.900231	−	0.435413i	$-0.856602\pi$
$809$		−	569939.i		−	0.870826i	0.900231	−	0.435413i	$-0.143398\pi$
$810$		0			0
$811$	207525.	+	207525.i	0.315521	+	0.315521i	0.847044	−	0.531523i	$-0.178380\pi$
$811$	207525.	+	207525.i	0.315521	+	0.315521i	−0.531523	+	0.847044i	$0.678380\pi$
$812$		0			0
$813$	−596522.	−	596522.i	−0.902496	−	0.902496i
$814$		0			0
$815$			424771.i			0.639498i
$816$		0			0
$817$	30503.6			0.0456991
$818$		0			0
$819$	115099.	−	115099.i	0.171595	−	0.171595i
$820$		0			0
$821$	597985.	−	597985.i	0.887163	−	0.887163i	−0.107086	−	0.994250i	$-0.534152\pi$
$821$	597985.	−	597985.i	0.887163	−	0.887163i	0.994250	+	0.107086i	$0.0341521\pi$
$822$		0			0
$823$	−17487.0			−0.0258176			−0.0129088	−	0.999917i	$-0.504109\pi$
$823$	−17487.0			−0.0258176			−0.0129088	+	0.999917i	$0.504109\pi$
$824$		0			0
$825$		−	181117.i		−	0.266104i
$826$		0			0
$827$	−108277.	−	108277.i	−0.158316	−	0.158316i	0.623504	−	0.781820i	$-0.285709\pi$
$827$	−108277.	−	108277.i	−0.158316	−	0.158316i	−0.781820	+	0.623504i	$0.785709\pi$
$828$		0			0
$829$	−368289.	−	368289.i	−0.535895	−	0.535895i	0.386426	−	0.922321i	$-0.373710\pi$
$829$	−368289.	−	368289.i	−0.535895	−	0.535895i	−0.922321	+	0.386426i	$0.873710\pi$
$830$		0			0
$831$			525431.i			0.760876i
$832$		0			0
$833$	−258117.			−0.371987
$834$		0			0
$835$	878038.	−	878038.i	1.25933	−	1.25933i
$836$		0			0
$837$	−517939.	+	517939.i	−0.739311	+	0.739311i
$838$		0			0
$839$	−105615.			−0.150038			−0.0750188	−	0.997182i	$-0.523902\pi$
$839$	−105615.			−0.150038			−0.0750188	+	0.997182i	$0.523902\pi$
$840$		0			0
$841$			1.05580e6i			1.49276i
$842$		0			0
$843$	49135.2	+	49135.2i	0.0691414	+	0.0691414i
$844$		0			0
$845$	−683441.	−	683441.i	−0.957167	−	0.957167i
$846$		0			0
$847$		−	833897.i		−	1.16237i
$848$		0			0
$849$	−586797.			−0.814090
$850$		0			0
$851$	−194997.	+	194997.i	−0.269258	+	0.269258i
$852$		0			0
$853$	−1.00366e6	+	1.00366e6i	−1.37939	+	1.37939i	−0.533742	+	0.845647i	$0.679215\pi$
$853$	−1.00366e6	+	1.00366e6i	−1.37939	+	1.37939i	−0.845647	+	0.533742i	$0.820785\pi$
$854$		0			0
$855$	−32722.9			−0.0447630
$856$		0			0
$857$		−	677179.i		−	0.922024i	−0.887394	−	0.461012i	$-0.847487\pi$
$857$		−	677179.i		−	0.922024i	0.887394	−	0.461012i	$-0.152513\pi$
$858$		0			0
$859$	750520.	+	750520.i	1.01713	+	1.01713i	0.999851	+	0.0172783i	$0.00550014\pi$
$859$	750520.	+	750520.i	1.01713	+	1.01713i	0.0172783	+	0.999851i	$0.494500\pi$
$860$		0			0
$861$	−68771.6	−	68771.6i	−0.0927690	−	0.0927690i
$862$		0			0
$863$			61525.8i			0.0826106i	0.999147	+	0.0413053i	$0.0131516\pi$
$863$			61525.8i			0.0826106i	−0.999147	+	0.0413053i	$0.986848\pi$
$864$		0			0
$865$	486458.			0.650149
$866$		0			0
$867$	−155050.	+	155050.i	−0.206269	+	0.206269i
$868$		0			0
$869$	13301.2	−	13301.2i	0.0176137	−	0.0176137i
$870$		0			0
$871$	492025.			0.648562
$872$		0			0
$873$		−	95966.7i		−	0.125919i
$874$		0			0
$875$	−792629.	−	792629.i	−1.03527	−	1.03527i
$876$		0			0
$877$	818941.	+	818941.i	1.06476	+	1.06476i	0.997752	+	0.0670114i	$0.0213464\pi$
$877$	818941.	+	818941.i	1.06476	+	1.06476i	0.0670114	+	0.997752i	$0.478654\pi$
$878$		0			0
$879$		−	825798.i		−	1.06880i
$880$		0			0
$881$	349159.			0.449853			0.224927	−	0.974376i	$-0.427786\pi$
$881$	349159.			0.449853			0.224927	+	0.974376i	$0.427786\pi$
$882$		0			0
$883$	−353886.	+	353886.i	−0.453881	+	0.453881i	−0.896640	−	0.442760i	$-0.853999\pi$
$883$	−353886.	+	353886.i	−0.453881	+	0.453881i	0.442760	+	0.896640i	$0.353999\pi$
$884$		0			0
$885$	601848.	−	601848.i	0.768423	−	0.768423i
$886$		0			0
$887$	1.16958e6			1.48656			0.743282	−	0.668978i	$-0.233268\pi$
$887$	1.16958e6			1.48656			0.743282	+	0.668978i	$0.233268\pi$
$888$		0			0
$889$		−	156832.i		−	0.198441i
$890$		0			0
$891$	36804.6	+	36804.6i	0.0463604	+	0.0463604i
$892$		0			0
$893$	29744.1	+	29744.1i	0.0372990	+	0.0372990i
$894$		0			0
$895$		−	440196.i		−	0.549540i
$896$		0			0
$897$	−347893.			−0.432375
$898$		0			0
$899$	881387.	−	881387.i	1.09055	−	1.09055i
$900$		0			0
$901$	186454.	−	186454.i	0.229679	−	0.229679i
$902$		0			0
$903$	−572084.			−0.701591
$904$		0			0
$905$			222075.i			0.271146i
$906$		0			0
$907$	−110870.	−	110870.i	−0.134772	−	0.134772i	0.636503	−	0.771274i	$-0.280380\pi$
$907$	−110870.	−	110870.i	−0.134772	−	0.134772i	−0.771274	+	0.636503i	$0.780380\pi$
$908$		0			0
$909$	−16197.8	−	16197.8i	−0.0196033	−	0.0196033i
$910$		0			0
$911$			162563.i			0.195877i	0.995192	+	0.0979387i	$0.0312249\pi$
$911$			162563.i			0.195877i	−0.995192	+	0.0979387i	$0.968775\pi$
$912$		0			0
$913$	−52149.8			−0.0625621
$914$		0			0
$915$	92415.3	−	92415.3i	0.110383	−	0.110383i
$916$		0			0
$917$	−741487.	+	741487.i	−0.881789	+	0.881789i
$918$		0			0
$919$	−615695.			−0.729012			−0.364506	−	0.931201i	$-0.618762\pi$
$919$	−615695.			−0.729012			−0.364506	+	0.931201i	$0.618762\pi$
$920$		0			0
$921$		−	1.15171e6i		−	1.35776i
$922$		0			0
$923$	212275.	+	212275.i	0.249170	+	0.249170i
$924$		0			0
$925$	285023.	+	285023.i	0.333116	+	0.333116i
$926$		0			0
$927$			501101.i			0.583131i
$928$		0			0
$929$	228015.			0.264199			0.132099	−	0.991236i	$-0.457828\pi$
$929$	228015.			0.264199			0.132099	+	0.991236i	$0.457828\pi$
$930$		0			0
$931$	−16997.9	+	16997.9i	−0.0196108	+	0.0196108i
$932$		0			0
$933$	72934.7	−	72934.7i	0.0837859	−	0.0837859i
$934$		0			0
$935$	−236321.			−0.270321
$936$		0			0
$937$		−	431768.i		−	0.491781i	−0.969298	−	0.245890i	$-0.920920\pi$
$937$		−	431768.i		−	0.491781i	0.969298	−	0.245890i	$-0.0790803\pi$
$938$		0			0
$939$	−484660.	−	484660.i	−0.549675	−	0.549675i
$940$		0			0
$941$	532946.	+	532946.i	0.601871	+	0.601871i	0.940809	−	0.338938i	$-0.110068\pi$
$941$	532946.	+	532946.i	0.601871	+	0.601871i	−0.338938	+	0.940809i	$0.610068\pi$
$942$		0			0
$943$		−	183914.i		−	0.206819i
$944$		0			0
$945$	1.92104e6			2.15116
$946$		0			0
$947$	1.02432e6	−	1.02432e6i	1.14218	−	1.14218i	0.154128	−	0.988051i	$-0.450743\pi$
$947$	1.02432e6	−	1.02432e6i	1.14218	−	1.14218i	0.988051	−	0.154128i	$-0.0492569\pi$
$948$		0			0
$949$	460572.	−	460572.i	0.511405	−	0.511405i
$950$		0			0
$951$	−425057.			−0.469988
$952$		0			0
$953$		−	264733.i		−	0.291490i	−0.989322	−	0.145745i	$-0.953442\pi$
$953$		−	264733.i		−	0.291490i	0.989322	−	0.145745i	$-0.0465578\pi$
$954$		0			0
$955$	1.52565e6	+	1.52565e6i	1.67282	+	1.67282i
$956$		0			0
$957$	−157411.	−	157411.i	−0.171875	−	0.171875i
$958$		0			0
$959$			917667.i			0.997810i
$960$		0			0
$961$	42286.5			0.0457883
$962$		0			0
$963$	−411475.	+	411475.i	−0.443702	+	0.443702i
$964$		0			0
$965$	−711899.	+	711899.i	−0.764476	+	0.764476i
$966$		0			0
$967$	61058.3			0.0652967			0.0326484	−	0.999467i	$-0.489606\pi$
$967$	61058.3			0.0652967			0.0326484	+	0.999467i	$0.489606\pi$
$968$		0			0
$969$		−	30570.9i		−	0.0325582i
$970$		0			0
$971$	−404297.	−	404297.i	−0.428807	−	0.428807i	0.459415	−	0.888222i	$-0.348059\pi$
$971$	−404297.	−	404297.i	−0.428807	−	0.428807i	−0.888222	+	0.459415i	$0.848059\pi$
$972$		0			0
$973$	−724454.	−	724454.i	−0.765218	−	0.765218i
$974$		0			0
$975$			508507.i			0.534919i
$976$		0			0
$977$	−1.83431e6			−1.92169			−0.960845	−	0.277086i	$-0.910631\pi$
$977$	−1.83431e6			−1.92169			−0.960845	+	0.277086i	$0.910631\pi$
$978$		0			0
$979$	−91716.3	+	91716.3i	−0.0956932	+	0.0956932i
$980$		0			0
$981$	−54319.9	+	54319.9i	−0.0564444	+	0.0564444i
$982$		0			0
$983$	586823.			0.607296			0.303648	−	0.952784i	$-0.401795\pi$
$983$	586823.			0.607296			0.303648	+	0.952784i	$0.401795\pi$
$984$		0			0
$985$			1.84182e6i			1.89835i
$986$		0			0
$987$	−557839.	−	557839.i	−0.572630	−	0.572630i
$988$		0			0
$989$	−764953.	−	764953.i	−0.782064	−	0.782064i
$990$		0			0
$991$			1.20757e6i			1.22961i	0.788680	+	0.614804i	$0.210765\pi$
$991$			1.20757e6i			1.22961i	−0.788680	+	0.614804i	$0.789235\pi$
$992$		0			0
$993$	1.27518e6			1.29322
$994$		0			0
$995$	−2.07699e6	+	2.07699e6i	−2.09792	+	2.09792i
$996$		0			0
$997$	−833662.	+	833662.i	−0.838686	+	0.838686i	−0.988686	−	0.150000i	$-0.952073\pi$
$997$	−833662.	+	833662.i	−0.838686	+	0.838686i	0.150000	+	0.988686i	$0.452073\pi$
$998$		0			0
$999$	−291138.			−0.291721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.f.b.95.5		14
4.3	odd	2		128.5.f.a.95.3		14
8.3	odd	2		64.5.f.a.47.5		14
8.5	even	2		16.5.f.a.3.3	✓	14
16.3	odd	4		16.5.f.a.11.3	yes	14
16.5	even	4		128.5.f.a.31.3		14
16.11	odd	4	inner	128.5.f.b.31.5		14
16.13	even	4		64.5.f.a.15.5		14
24.5	odd	2		144.5.m.a.19.5		14
24.11	even	2		576.5.m.a.559.7		14
48.29	odd	4		576.5.m.a.271.7		14
48.35	even	4		144.5.m.a.91.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.3	✓	14	8.5	even	2
16.5.f.a.11.3	yes	14	16.3	odd	4
64.5.f.a.15.5		14	16.13	even	4
64.5.f.a.47.5		14	8.3	odd	2
128.5.f.a.31.3		14	16.5	even	4
128.5.f.a.95.3		14	4.3	odd	2
128.5.f.b.31.5		14	16.11	odd	4	inner
128.5.f.b.95.5		14	1.1	even	1	trivial
144.5.m.a.19.5		14	24.5	odd	2
144.5.m.a.91.5		14	48.35	even	4
576.5.m.a.271.7		14	48.29	odd	4
576.5.m.a.559.7		14	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	128.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.63552 - 4.63552i) q^{3} +(29.2002 - 29.2002i) q^{5} +59.6196 q^{7} +38.0239i q^{9} +O(q^{10})\)	\(q+(4.63552 - 4.63552i) q^{3} +(29.2002 - 29.2002i) q^{5} +59.6196 q^{7} +38.0239i q^{9} +(18.0837 + 18.0837i) q^{11} +(-50.7721 - 50.7721i) q^{13} -270.716i q^{15} -223.769 q^{17} +(-14.7360 + 14.7360i) q^{19} +(276.368 - 276.368i) q^{21} +739.082 q^{23} -1080.30i q^{25} +(551.738 + 551.738i) q^{27} +(-938.904 - 938.904i) q^{29} +938.741i q^{31} +167.655 q^{33} +(1740.90 - 1740.90i) q^{35} +(-263.837 + 263.837i) q^{37} -470.710 q^{39} -248.841i q^{41} +(-1035.00 - 1035.00i) q^{43} +(1110.31 + 1110.31i) q^{45} -2018.46i q^{47} +1153.50 q^{49} +(-1037.29 + 1037.29i) q^{51} +(-833.240 + 833.240i) q^{53} +1056.09 q^{55} +136.618i q^{57} +(2223.17 + 2223.17i) q^{59} +(341.374 + 341.374i) q^{61} +2266.97i q^{63} -2965.11 q^{65} +(-4845.43 + 4845.43i) q^{67} +(3426.03 - 3426.03i) q^{69} -4180.93 q^{71} +9071.36i q^{73} +(-5007.74 - 5007.74i) q^{75} +(1078.14 + 1078.14i) q^{77} -735.536i q^{79} +2035.24 q^{81} +(-1441.90 + 1441.90i) q^{83} +(-6534.10 + 6534.10i) q^{85} -8704.61 q^{87} +5071.77i q^{89} +(-3027.01 - 3027.01i) q^{91} +(4351.55 + 4351.55i) q^{93} +860.586i q^{95} -2523.85 q^{97} +(-687.613 + 687.613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{3} + 2 q^{5} - 4 q^{7}+O(q^{10}) \) 14 * q + 2 * q^3 + 2 * q^5 - 4 * q^7	\( 14 q + 2 q^{3} + 2 q^{5} - 4 q^{7} - 94 q^{11} + 2 q^{13} - 4 q^{17} + 706 q^{19} + 164 q^{21} + 1148 q^{23} + 1664 q^{27} - 862 q^{29} - 4 q^{33} - 1340 q^{35} + 1826 q^{37} + 2684 q^{39} - 1694 q^{43} - 1410 q^{45} + 682 q^{49} + 3012 q^{51} + 482 q^{53} - 11780 q^{55} + 2786 q^{59} + 3778 q^{61} - 2020 q^{65} - 7998 q^{67} - 9628 q^{69} + 19964 q^{71} - 17570 q^{75} + 9508 q^{77} + 1454 q^{81} + 17282 q^{83} - 9948 q^{85} - 49284 q^{87} + 28036 q^{91} - 8896 q^{93} - 4 q^{97} - 49214 q^{99}+O(q^{100}) \) 14 * q + 2 * q^3 + 2 * q^5 - 4 * q^7 - 94 * q^11 + 2 * q^13 - 4 * q^17 + 706 * q^19 + 164 * q^21 + 1148 * q^23 + 1664 * q^27 - 862 * q^29 - 4 * q^33 - 1340 * q^35 + 1826 * q^37 + 2684 * q^39 - 1694 * q^43 - 1410 * q^45 + 682 * q^49 + 3012 * q^51 + 482 * q^53 - 11780 * q^55 + 2786 * q^59 + 3778 * q^61 - 2020 * q^65 - 7998 * q^67 - 9628 * q^69 + 19964 * q^71 - 17570 * q^75 + 9508 * q^77 + 1454 * q^81 + 17282 * q^83 - 9948 * q^85 - 49284 * q^87 + 28036 * q^91 - 8896 * q^93 - 4 * q^97 - 49214 * q^99

Introduction

L-functions

Modular forms

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