LMFDB - Embedded newform 128.5.f.b.95.2

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			95.2
Root			$2.24452 - 1.72109i$ of defining polynomial
Character	$\chi$	$=$	128.95
Dual form			128.5.f.b.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.54016 + 5.54016i) q^{3} +(-21.7374 + 21.7374i) q^{5} -6.62054 q^{7} +19.6133i q^{9} +O(q^{10})$	\(q+(-5.54016 + 5.54016i) q^{3} +(-21.7374 + 21.7374i) q^{5} -6.62054 q^{7} +19.6133i q^{9} +(90.9986 + 90.9986i) q^{11} +(-221.402 - 221.402i) q^{13} -240.857i q^{15} -132.575 q^{17} +(402.520 - 402.520i) q^{19} +(36.6788 - 36.6788i) q^{21} +27.5037 q^{23} -320.028i q^{25} +(-557.414 - 557.414i) q^{27} +(-174.909 - 174.909i) q^{29} -1083.96i q^{31} -1008.29 q^{33} +(143.913 - 143.913i) q^{35} +(-553.474 + 553.474i) q^{37} +2453.20 q^{39} -1803.47i q^{41} +(-17.8633 - 17.8633i) q^{43} +(-426.342 - 426.342i) q^{45} +2268.26i q^{47} -2357.17 q^{49} +(734.489 - 734.489i) q^{51} +(822.415 - 822.415i) q^{53} -3956.14 q^{55} +4460.05i q^{57} +(972.483 + 972.483i) q^{59} +(2056.32 + 2056.32i) q^{61} -129.851i q^{63} +9625.38 q^{65} +(-4611.22 + 4611.22i) q^{67} +(-152.375 + 152.375i) q^{69} -3105.84 q^{71} +723.400i q^{73} +(1773.00 + 1773.00i) q^{75} +(-602.460 - 602.460i) q^{77} -3418.44i q^{79} +4587.64 q^{81} +(161.591 - 161.591i) q^{83} +(2881.84 - 2881.84i) q^{85} +1938.05 q^{87} -1464.04i q^{89} +(1465.80 + 1465.80i) q^{91} +(6005.32 + 6005.32i) q^{93} +17499.5i q^{95} -8264.99 q^{97} +(-1784.78 + 1784.78i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−5.54016	+	5.54016i	−0.615573	+	0.615573i	−0.944393	−	0.328820i	$-0.893349\pi$
$3$	−5.54016	+	5.54016i	−0.615573	+	0.615573i	0.328820	+	0.944393i	$0.393349\pi$
$4$		0			0
$5$	−21.7374	+	21.7374i	−0.869495	+	0.869495i	−0.992416	−	0.122921i	$-0.960774\pi$
$5$	−21.7374	+	21.7374i	−0.869495	+	0.869495i	0.122921	+	0.992416i	$0.460774\pi$
$6$		0			0
$7$	−6.62054			−0.135113			−0.0675565	−	0.997715i	$-0.521520\pi$
$7$	−6.62054			−0.135113			−0.0675565	+	0.997715i	$0.521520\pi$
$8$		0			0
$9$			19.6133i			0.242140i
$10$		0			0
$11$	90.9986	+	90.9986i	0.752054	+	0.752054i	0.974862	−	0.222808i	$-0.0715223\pi$
$11$	90.9986	+	90.9986i	0.752054	+	0.752054i	−0.222808	+	0.974862i	$0.571522\pi$
$12$		0			0
$13$	−221.402	−	221.402i	−1.31007	−	1.31007i	−0.921362	−	0.388707i	$-0.872922\pi$
$13$	−221.402	−	221.402i	−1.31007	−	1.31007i	−0.388707	−	0.921362i	$-0.627078\pi$
$14$		0			0
$15$		−	240.857i		−	1.07048i
$16$		0			0
$17$	−132.575			−0.458738			−0.229369	−	0.973339i	$-0.573666\pi$
$17$	−132.575			−0.458738			−0.229369	+	0.973339i	$0.573666\pi$
$18$		0			0
$19$	402.520	−	402.520i	1.11501	−	1.11501i	0.122552	−	0.992462i	$-0.460892\pi$
$19$	402.520	−	402.520i	1.11501	−	1.11501i	0.992462	−	0.122552i	$-0.0391079\pi$
$20$		0			0
$21$	36.6788	−	36.6788i	0.0831720	−	0.0831720i
$22$		0			0
$23$	27.5037			0.0519918			0.0259959	−	0.999662i	$-0.491724\pi$
$23$	27.5037			0.0519918			0.0259959	+	0.999662i	$0.491724\pi$
$24$		0			0
$25$		−	320.028i		−	0.512044i
$26$		0			0
$27$	−557.414	−	557.414i	−0.764628	−	0.764628i
$28$		0			0
$29$	−174.909	−	174.909i	−0.207978	−	0.207978i	0.595430	−	0.803407i	$-0.296982\pi$
$29$	−174.909	−	174.909i	−0.207978	−	0.207978i	−0.803407	+	0.595430i	$0.796982\pi$
$30$		0			0
$31$		−	1083.96i		−	1.12795i	−0.825791	−	0.563976i	$-0.809271\pi$
$31$		−	1083.96i		−	1.12795i	0.825791	−	0.563976i	$-0.190729\pi$
$32$		0			0
$33$	−1008.29			−0.925888
$34$		0			0
$35$	143.913	−	143.913i	0.117480	−	0.117480i
$36$		0			0
$37$	−553.474	+	553.474i	−0.404291	+	0.404291i	−0.879742	−	0.475451i	$-0.842285\pi$
$37$	−553.474	+	553.474i	−0.404291	+	0.404291i	0.475451	+	0.879742i	$0.342285\pi$
$38$		0			0
$39$	2453.20			1.61289
$40$		0			0
$41$		−	1803.47i		−	1.07285i	−0.843947	−	0.536427i	$-0.819774\pi$
$41$		−	1803.47i		−	1.07285i	0.843947	−	0.536427i	$-0.180226\pi$
$42$		0			0
$43$	−17.8633	−	17.8633i	−0.00966108	−	0.00966108i	0.702260	−	0.711921i	$-0.252175\pi$
$43$	−17.8633	−	17.8633i	−0.00966108	−	0.00966108i	−0.711921	+	0.702260i	$0.752175\pi$
$44$		0			0
$45$	−426.342	−	426.342i	−0.210539	−	0.210539i
$46$		0			0
$47$			2268.26i			1.02683i	0.858141	+	0.513414i	$0.171620\pi$
$47$			2268.26i			1.02683i	−0.858141	+	0.513414i	$0.828380\pi$
$48$		0			0
$49$	−2357.17			−0.981744
$50$		0			0
$51$	734.489	−	734.489i	0.282387	−	0.282387i
$52$		0			0
$53$	822.415	−	822.415i	0.292779	−	0.292779i	−0.545398	−	0.838177i	$-0.683622\pi$
$53$	822.415	−	822.415i	0.292779	−	0.292779i	0.838177	+	0.545398i	$0.183622\pi$
$54$		0			0
$55$	−3956.14			−1.30782
$56$		0			0
$57$			4460.05i			1.37275i
$58$		0			0
$59$	972.483	+	972.483i	0.279369	+	0.279369i	0.832857	−	0.553488i	$-0.186704\pi$
$59$	972.483	+	972.483i	0.279369	+	0.279369i	−0.553488	+	0.832857i	$0.686704\pi$
$60$		0			0
$61$	2056.32	+	2056.32i	0.552626	+	0.552626i	0.927198	−	0.374572i	$-0.122210\pi$
$61$	2056.32	+	2056.32i	0.552626	+	0.552626i	−0.374572	+	0.927198i	$0.622210\pi$
$62$		0			0
$63$		−	129.851i		−	0.0327163i
$64$		0			0
$65$	9625.38			2.27820
$66$		0			0
$67$	−4611.22	+	4611.22i	−1.02723	+	1.02723i	−0.0276077	+	0.999619i	$0.508789\pi$
$67$	−4611.22	+	4611.22i	−1.02723	+	1.02723i	−0.999619	+	0.0276077i	$0.991211\pi$
$68$		0			0
$69$	−152.375	+	152.375i	−0.0320048	+	0.0320048i
$70$		0			0
$71$	−3105.84			−0.616115			−0.308058	−	0.951368i	$-0.599679\pi$
$71$	−3105.84			−0.616115			−0.308058	+	0.951368i	$0.599679\pi$
$72$		0			0
$73$			723.400i			0.135748i	0.997694	+	0.0678739i	$0.0216216\pi$
$73$			723.400i			0.135748i	−0.997694	+	0.0678739i	$0.978378\pi$
$74$		0			0
$75$	1773.00	+	1773.00i	0.315200	+	0.315200i
$76$		0			0
$77$	−602.460	−	602.460i	−0.101612	−	0.101612i
$78$		0			0
$79$		−	3418.44i		−	0.547739i	−0.961767	−	0.273869i	$-0.911696\pi$
$79$		−	3418.44i		−	0.547739i	0.961767	−	0.273869i	$-0.0883036\pi$
$80$		0			0
$81$	4587.64			0.699228
$82$		0			0
$83$	161.591	−	161.591i	0.0234563	−	0.0234563i	−0.695281	−	0.718738i	$-0.744720\pi$
$83$	161.591	−	161.591i	0.0234563	−	0.0234563i	0.718738	+	0.695281i	$0.244720\pi$
$84$		0			0
$85$	2881.84	−	2881.84i	0.398871	−	0.398871i
$86$		0			0
$87$	1938.05			0.256051
$88$		0			0
$89$		−	1464.04i		−	0.184830i	−0.995721	−	0.0924150i	$-0.970541\pi$
$89$		−	1464.04i		−	0.184830i	0.995721	−	0.0924150i	$-0.0294586\pi$
$90$		0			0
$91$	1465.80	+	1465.80i	0.177007	+	0.177007i
$92$		0			0
$93$	6005.32	+	6005.32i	0.694337	+	0.694337i
$94$		0			0
$95$			17499.5i			1.93900i
$96$		0			0
$97$	−8264.99			−0.878413			−0.439207	−	0.898386i	$-0.644740\pi$
$97$	−8264.99			−0.878413			−0.439207	+	0.898386i	$0.644740\pi$
$98$		0			0
$99$	−1784.78	+	1784.78i	−0.182102	+	0.182102i
$100$		0			0
$101$	−5035.04	+	5035.04i	−0.493583	+	0.493583i	−0.909433	−	0.415850i	$-0.863484\pi$
$101$	−5035.04	+	5035.04i	−0.493583	+	0.493583i	0.415850	+	0.909433i	$0.363484\pi$
$102$		0			0
$103$	1427.24			0.134531			0.0672653	−	0.997735i	$-0.478573\pi$
$103$	1427.24			0.134531			0.0672653	+	0.997735i	$0.478573\pi$
$104$		0			0
$105$			1594.60i			0.144635i
$106$		0			0
$107$	−9978.53	−	9978.53i	−0.871564	−	0.871564i	0.121079	−	0.992643i	$-0.461365\pi$
$107$	−9978.53	−	9978.53i	−0.871564	−	0.871564i	−0.992643	+	0.121079i	$0.961365\pi$
$108$		0			0
$109$	−9.47842	−	9.47842i	−0.000797780	−	0.000797780i	0.706708	−	0.707506i	$-0.250180\pi$
$109$	−9.47842	−	9.47842i	−0.000797780	−	0.000797780i	−0.707506	+	0.706708i	$0.750180\pi$
$110$		0			0
$111$		−	6132.67i		−	0.497741i
$112$		0			0
$113$	−13634.7			−1.06780			−0.533900	−	0.845548i	$-0.679274\pi$
$113$	−13634.7			−1.06780			−0.533900	+	0.845548i	$0.679274\pi$
$114$		0			0
$115$	−597.858	+	597.858i	−0.0452067	+	0.0452067i
$116$		0			0
$117$	4342.42	−	4342.42i	0.317220	−	0.317220i
$118$		0			0
$119$	877.721			0.0619816
$120$		0			0
$121$			1920.47i			0.131171i
$122$		0			0
$123$	9991.49	+	9991.49i	0.660419	+	0.660419i
$124$		0			0
$125$	−6629.30	−	6629.30i	−0.424275	−	0.424275i
$126$		0			0
$127$		−	8047.14i		−	0.498923i	−0.968385	−	0.249462i	$-0.919746\pi$
$127$		−	8047.14i		−	0.498923i	0.968385	−	0.249462i	$-0.0802537\pi$
$128$		0			0
$129$	197.931			0.0118942
$130$		0			0
$131$	15904.8	−	15904.8i	0.926799	−	0.926799i	−0.0706991	−	0.997498i	$-0.522523\pi$
$131$	15904.8	−	15904.8i	0.926799	−	0.926799i	0.997498	+	0.0706991i	$0.0225230\pi$
$132$		0			0
$133$	−2664.90	+	2664.90i	−0.150653	+	0.150653i
$134$		0			0
$135$	24233.4			1.32968
$136$		0			0
$137$		−	31169.3i		−	1.66068i	−0.557257	−	0.830340i	$-0.688146\pi$
$137$		−	31169.3i		−	1.66068i	0.557257	−	0.830340i	$-0.311854\pi$
$138$		0			0
$139$	−21432.1	−	21432.1i	−1.10926	−	1.10926i	−0.993247	−	0.116017i	$-0.962987\pi$
$139$	−21432.1	−	21432.1i	−1.10926	−	1.10926i	−0.116017	−	0.993247i	$-0.537013\pi$
$140$		0			0
$141$	−12566.5	−	12566.5i	−0.632088	−	0.632088i
$142$		0			0
$143$		−	40294.4i		−	1.97048i
$144$		0			0
$145$	7604.14			0.361671
$146$		0			0
$147$	13059.1	−	13059.1i	0.604335	−	0.604335i
$148$		0			0
$149$	−11772.7	+	11772.7i	−0.530276	+	0.530276i	−0.920654	−	0.390378i	$-0.872344\pi$
$149$	−11772.7	+	11772.7i	−0.530276	+	0.530276i	0.390378	+	0.920654i	$0.372344\pi$
$150$		0			0
$151$	−19454.9			−0.853246			−0.426623	−	0.904429i	$-0.640297\pi$
$151$	−19454.9			−0.853246			−0.426623	+	0.904429i	$0.640297\pi$
$152$		0			0
$153$		−	2600.25i		−	0.111079i
$154$		0			0
$155$	23562.5	+	23562.5i	0.980749	+	0.980749i
$156$		0			0
$157$	−18097.5	−	18097.5i	−0.734208	−	0.734208i	0.237242	−	0.971450i	$-0.423756\pi$
$157$	−18097.5	−	18097.5i	−0.734208	−	0.734208i	−0.971450	+	0.237242i	$0.923756\pi$
$158$		0			0
$159$			9112.62i			0.360453i
$160$		0			0
$161$	−182.089			−0.00702478
$162$		0			0
$163$	−17673.1	+	17673.1i	−0.665178	+	0.665178i	−0.956596	−	0.291418i	$-0.905873\pi$
$163$	−17673.1	+	17673.1i	−0.665178	+	0.665178i	0.291418	+	0.956596i	$0.405873\pi$
$164$		0			0
$165$	21917.6	−	21917.6i	0.805056	−	0.805056i
$166$		0			0
$167$	−11374.1			−0.407834			−0.203917	−	0.978988i	$-0.565367\pi$
$167$	−11374.1			−0.407834			−0.203917	+	0.978988i	$0.565367\pi$
$168$		0			0
$169$			69476.3i			2.43256i
$170$		0			0
$171$	7894.76	+	7894.76i	0.269989	+	0.269989i
$172$		0			0
$173$	11289.3	+	11289.3i	0.377204	+	0.377204i	0.870092	−	0.492888i	$-0.164059\pi$
$173$	11289.3	+	11289.3i	0.377204	+	0.377204i	−0.492888	+	0.870092i	$0.664059\pi$
$174$		0			0
$175$			2118.76i			0.0691838i
$176$		0			0
$177$	−10775.4			−0.343944
$178$		0			0
$179$	25338.8	−	25338.8i	0.790825	−	0.790825i	−0.190803	−	0.981628i	$-0.561109\pi$
$179$	25338.8	−	25338.8i	0.790825	−	0.790825i	0.981628	+	0.190803i	$0.0611091\pi$
$180$		0			0
$181$	−22579.8	+	22579.8i	−0.689228	+	0.689228i	−0.962061	−	0.272833i	$-0.912039\pi$
$181$	−22579.8	+	22579.8i	−0.689228	+	0.689228i	0.272833	+	0.962061i	$0.412039\pi$
$182$		0			0
$183$	−22784.7			−0.680363
$184$		0			0
$185$		−	24062.2i		−	0.703058i
$186$		0			0
$187$	−12064.2	−	12064.2i	−0.344996	−	0.344996i
$188$		0			0
$189$	3690.38	+	3690.38i	0.103311	+	0.103311i
$190$		0			0
$191$			62994.4i			1.72677i	0.504543	+	0.863386i	$0.331661\pi$
$191$			62994.4i			1.72677i	−0.504543	+	0.863386i	$0.668339\pi$
$192$		0			0
$193$	−25039.7			−0.672225			−0.336112	−	0.941822i	$-0.609112\pi$
$193$	−25039.7			−0.672225			−0.336112	+	0.941822i	$0.609112\pi$
$194$		0			0
$195$	−53326.1	+	53326.1i	−1.40240	+	1.40240i
$196$		0			0
$197$	6468.96	−	6468.96i	0.166687	−	0.166687i	−0.618834	−	0.785521i	$-0.712395\pi$
$197$	6468.96	−	6468.96i	0.166687	−	0.166687i	0.785521	+	0.618834i	$0.212395\pi$
$198$		0			0
$199$	55793.6			1.40889			0.704446	−	0.709757i	$-0.251195\pi$
$199$	55793.6			1.40889			0.704446	+	0.709757i	$0.251195\pi$
$200$		0			0
$201$		−	51093.8i		−	1.26467i
$202$		0			0
$203$	1157.99	+	1157.99i	0.0281005	+	0.0281005i
$204$		0			0
$205$	39202.6	+	39202.6i	0.932841	+	0.932841i
$206$		0			0
$207$			539.439i			0.0125893i
$208$		0			0
$209$	73257.5			1.67710
$210$		0			0
$211$	11403.6	−	11403.6i	0.256139	−	0.256139i	−0.567343	−	0.823482i	$-0.692029\pi$
$211$	11403.6	−	11403.6i	0.256139	−	0.256139i	0.823482	+	0.567343i	$0.192029\pi$
$212$		0			0
$213$	17206.8	−	17206.8i	0.379264	−	0.379264i
$214$		0			0
$215$	776.604			0.0168005
$216$		0			0
$217$			7176.41i			0.152401i
$218$		0			0
$219$	−4007.75	−	4007.75i	−0.0835627	−	0.0835627i
$220$		0			0
$221$	29352.4	+	29352.4i	0.600979	+	0.600979i
$222$		0			0
$223$		−	15194.4i		−	0.305545i	−0.988261	−	0.152772i	$-0.951180\pi$
$223$		−	15194.4i		−	0.305545i	0.988261	−	0.152772i	$-0.0488201\pi$
$224$		0			0
$225$	6276.81			0.123986
$226$		0			0
$227$	−47509.0	+	47509.0i	−0.921986	+	0.921986i	−0.997170	−	0.0751841i	$-0.976046\pi$
$227$	−47509.0	+	47509.0i	−0.921986	+	0.921986i	0.0751841	+	0.997170i	$0.476046\pi$
$228$		0			0
$229$	−15628.9	+	15628.9i	−0.298028	+	0.298028i	−0.840241	−	0.542213i	$-0.817587\pi$
$229$	−15628.9	+	15628.9i	−0.298028	+	0.298028i	0.542213	+	0.840241i	$0.317587\pi$
$230$		0			0
$231$	6675.44			0.125100
$232$		0			0
$233$			63151.2i			1.16324i	0.813460	+	0.581621i	$0.197581\pi$
$233$			63151.2i			1.16324i	−0.813460	+	0.581621i	$0.802419\pi$
$234$		0			0
$235$	−49306.1	−	49306.1i	−0.892823	−	0.892823i
$236$		0			0
$237$	18938.7	+	18938.7i	0.337173	+	0.337173i
$238$		0			0
$239$			33331.4i			0.583522i	0.956491	+	0.291761i	$0.0942412\pi$
$239$			33331.4i			0.583522i	−0.956491	+	0.291761i	$0.905759\pi$
$240$		0			0
$241$	5625.72			0.0968599			0.0484299	−	0.998827i	$-0.484578\pi$
$241$	5625.72			0.0968599			0.0484299	+	0.998827i	$0.484578\pi$
$242$		0			0
$243$	19734.3	−	19734.3i	0.334202	−	0.334202i
$244$		0			0
$245$	51238.7	−	51238.7i	0.853622	−	0.853622i
$246$		0			0
$247$	−178237.			−2.92149
$248$		0			0
$249$			1790.47i			0.0288782i
$250$		0			0
$251$	62195.0	+	62195.0i	0.987206	+	0.987206i	0.999919	−	0.0127130i	$-0.00404679\pi$
$251$	62195.0	+	62195.0i	0.987206	+	0.987206i	−0.0127130	+	0.999919i	$0.504047\pi$
$252$		0			0
$253$	2502.80	+	2502.80i	0.0391007	+	0.0391007i
$254$		0			0
$255$			31931.7i			0.491068i
$256$		0			0
$257$	22791.9			0.345075			0.172538	−	0.985003i	$-0.444803\pi$
$257$	22791.9			0.345075			0.172538	+	0.985003i	$0.444803\pi$
$258$		0			0
$259$	3664.30	−	3664.30i	0.0546250	−	0.0546250i
$260$		0			0
$261$	3430.55	−	3430.55i	0.0503597	−	0.0503597i
$262$		0			0
$263$	126611.			1.83047			0.915233	−	0.402926i	$-0.132007\pi$
$263$	126611.			1.83047			0.915233	+	0.402926i	$0.132007\pi$
$264$		0			0
$265$			35754.3i			0.509139i
$266$		0			0
$267$	8111.00	+	8111.00i	0.113776	+	0.113776i
$268$		0			0
$269$	−65428.7	−	65428.7i	−0.904198	−	0.904198i	0.0915982	−	0.995796i	$-0.470802\pi$
$269$	−65428.7	−	65428.7i	−0.904198	−	0.904198i	−0.995796	+	0.0915982i	$0.970802\pi$
$270$		0			0
$271$		−	93429.2i		−	1.27217i	−0.771621	−	0.636083i	$-0.780554\pi$
$271$		−	93429.2i		−	1.27217i	0.771621	−	0.636083i	$-0.219446\pi$
$272$		0			0
$273$	−16241.5			−0.217922
$274$		0			0
$275$	29122.0	−	29122.0i	0.385085	−	0.385085i
$276$		0			0
$277$	−105271.	+	105271.i	−1.37198	+	1.37198i	−0.514477	+	0.857504i	$0.672014\pi$
$277$	−105271.	+	105271.i	−1.37198	+	1.37198i	−0.857504	+	0.514477i	$0.827986\pi$
$278$		0			0
$279$	21260.1			0.273122
$280$		0			0
$281$		−	42955.1i		−	0.544004i	−0.962297	−	0.272002i	$-0.912314\pi$
$281$		−	42955.1i		−	0.544004i	0.962297	−	0.272002i	$-0.0876857\pi$
$282$		0			0
$283$	36538.7	+	36538.7i	0.456226	+	0.456226i	0.897414	−	0.441189i	$-0.145443\pi$
$283$	36538.7	+	36538.7i	0.456226	+	0.456226i	−0.441189	+	0.897414i	$0.645443\pi$
$284$		0			0
$285$	−96949.8	−	96949.8i	−1.19360	−	1.19360i
$286$		0			0
$287$			11939.9i			0.144957i
$288$		0			0
$289$	−65944.8			−0.789559
$290$		0			0
$291$	45789.3	−	45789.3i	0.540727	−	0.540727i
$292$		0			0
$293$	45359.7	−	45359.7i	0.528367	−	0.528367i	−0.391719	−	0.920085i	$-0.628119\pi$
$293$	45359.7	−	45359.7i	0.528367	−	0.528367i	0.920085	+	0.391719i	$0.128119\pi$
$294$		0			0
$295$	−42278.5			−0.485820
$296$		0			0
$297$		−	101448.i		−	1.15008i
$298$		0			0
$299$	−6089.36	−	6089.36i	−0.0681129	−	0.0681129i
$300$		0			0
$301$	118.265	+	118.265i	0.00130534	+	0.00130534i
$302$		0			0
$303$		−	55789.9i		−	0.607673i
$304$		0			0
$305$	−89398.0			−0.961011
$306$		0			0
$307$	10035.4	−	10035.4i	0.106478	−	0.106478i	−0.651861	−	0.758339i	$-0.726011\pi$
$307$	10035.4	−	10035.4i	0.106478	−	0.106478i	0.758339	+	0.651861i	$0.226011\pi$
$308$		0			0
$309$	−7907.11	+	7907.11i	−0.0828134	+	0.0828134i
$310$		0			0
$311$	102401.			1.05873			0.529365	−	0.848394i	$-0.322430\pi$
$311$	102401.			1.05873			0.529365	+	0.848394i	$0.322430\pi$
$312$		0			0
$313$			60933.1i			0.621963i	0.950416	+	0.310981i	$0.100658\pi$
$313$			60933.1i			0.621963i	−0.950416	+	0.310981i	$0.899342\pi$
$314$		0			0
$315$	2822.62	+	2822.62i	0.0284466	+	0.0284466i
$316$		0			0
$317$	10217.2	+	10217.2i	0.101675	+	0.101675i	0.756115	−	0.654439i	$-0.227095\pi$
$317$	10217.2	+	10217.2i	0.101675	+	0.101675i	−0.654439	+	0.756115i	$0.727095\pi$
$318$		0			0
$319$		−	31833.0i		−	0.312821i
$320$		0			0
$321$	110565.			1.07302
$322$		0			0
$323$	−53364.3	+	53364.3i	−0.511500	+	0.511500i
$324$		0			0
$325$	−70854.6	+	70854.6i	−0.670813	+	0.670813i
$326$		0			0
$327$	105.024			0.000982183
$328$		0			0
$329$		−	15017.1i		−	0.138738i
$330$		0			0
$331$	−123603.	−	123603.i	−1.12817	−	1.12817i	−0.990475	−	0.137692i	$-0.956032\pi$
$331$	−123603.	−	123603.i	−1.12817	−	1.12817i	−0.137692	−	0.990475i	$-0.543968\pi$
$332$		0			0
$333$	−10855.5	−	10855.5i	−0.0978949	−	0.0978949i
$334$		0			0
$335$		−	200472.i		−	1.78634i
$336$		0			0
$337$	−102441.			−0.902018			−0.451009	−	0.892519i	$-0.648936\pi$
$337$	−102441.			−0.902018			−0.451009	+	0.892519i	$0.648936\pi$
$338$		0			0
$339$	75538.6	−	75538.6i	0.657309	−	0.657309i
$340$		0			0
$341$	98639.0	−	98639.0i	0.848281	−	0.848281i
$342$		0			0
$343$	31501.6			0.267760
$344$		0			0
$345$		−	6624.45i		−	0.0556560i
$346$		0			0
$347$	−63342.4	−	63342.4i	−0.526061	−	0.526061i	0.393335	−	0.919395i	$-0.371321\pi$
$347$	−63342.4	−	63342.4i	−0.526061	−	0.526061i	−0.919395	+	0.393335i	$0.871321\pi$
$348$		0			0
$349$	114645.	+	114645.i	0.941247	+	0.941247i	0.998367	−	0.0571205i	$-0.0181919\pi$
$349$	114645.	+	114645.i	0.941247	+	0.941247i	−0.0571205	+	0.998367i	$0.518192\pi$
$350$		0			0
$351$			246824.i			2.00343i
$352$		0			0
$353$	−94430.7			−0.757816			−0.378908	−	0.925434i	$-0.623700\pi$
$353$	−94430.7			−0.757816			−0.378908	+	0.925434i	$0.623700\pi$
$354$		0			0
$355$	67512.8	−	67512.8i	0.535709	−	0.535709i
$356$		0			0
$357$	−4862.71	+	4862.71i	−0.0381542	+	0.0381542i
$358$		0			0
$359$	−59001.0			−0.457794			−0.228897	−	0.973451i	$-0.573512\pi$
$359$	−59001.0			−0.457794			−0.228897	+	0.973451i	$0.573512\pi$
$360$		0			0
$361$		−	193724.i		−	1.48651i
$362$		0			0
$363$	−10639.7	−	10639.7i	−0.0807453	−	0.0807453i
$364$		0			0
$365$	−15724.8	−	15724.8i	−0.118032	−	0.118032i
$366$		0			0
$367$			120112.i			0.891775i	0.895089	+	0.445888i	$0.147112\pi$
$367$			120112.i			0.891775i	−0.895089	+	0.445888i	$0.852888\pi$
$368$		0			0
$369$	35372.0			0.259781
$370$		0			0
$371$	−5444.83	+	5444.83i	−0.0395582	+	0.0395582i
$372$		0			0
$373$	113849.	−	113849.i	0.818300	−	0.818300i	−0.167562	−	0.985862i	$-0.553589\pi$
$373$	113849.	−	113849.i	0.818300	−	0.818300i	0.985862	+	0.167562i	$0.0535894\pi$
$374$		0			0
$375$	73454.7			0.522345
$376$		0			0
$377$			77450.4i			0.544930i
$378$		0			0
$379$	75841.4	+	75841.4i	0.527993	+	0.527993i	0.919973	−	0.391981i	$-0.128210\pi$
$379$	75841.4	+	75841.4i	0.527993	+	0.527993i	−0.391981	+	0.919973i	$0.628210\pi$
$380$		0			0
$381$	44582.4	+	44582.4i	0.307124	+	0.307124i
$382$		0			0
$383$		−	80282.4i		−	0.547297i	−0.961830	−	0.273648i	$-0.911770\pi$
$383$		−	80282.4i		−	0.547297i	0.961830	−	0.273648i	$-0.0882304\pi$
$384$		0			0
$385$	26191.8			0.176703
$386$		0			0
$387$	350.360	−	350.360i	0.00233933	−	0.00233933i
$388$		0			0
$389$	−89476.2	+	89476.2i	−0.591301	+	0.591301i	−0.937983	−	0.346682i	$-0.887308\pi$
$389$	−89476.2	+	89476.2i	−0.591301	+	0.591301i	0.346682	+	0.937983i	$0.387308\pi$
$390$		0			0
$391$	−3646.31			−0.0238507
$392$		0			0
$393$			176230.i			1.14102i
$394$		0			0
$395$	74307.8	+	74307.8i	0.476256	+	0.476256i
$396$		0			0
$397$	−128824.	−	128824.i	−0.817363	−	0.817363i	0.168362	−	0.985725i	$-0.446152\pi$
$397$	−128824.	−	128824.i	−0.817363	−	0.817363i	−0.985725	+	0.168362i	$0.946152\pi$
$398$		0			0
$399$		−	29527.9i		−	0.185476i
$400$		0			0
$401$	71110.1			0.442224			0.221112	−	0.975248i	$-0.429031\pi$
$401$	71110.1			0.442224			0.221112	+	0.975248i	$0.429031\pi$
$402$		0			0
$403$	−239991.	+	239991.i	−1.47769	+	1.47769i
$404$		0			0
$405$	−99723.2	+	99723.2i	−0.607976	+	0.607976i
$406$		0			0
$407$	−100731.			−0.608097
$408$		0			0
$409$			87416.4i			0.522572i	0.965261	+	0.261286i	$0.0841466\pi$
$409$			87416.4i			0.522572i	−0.965261	+	0.261286i	$0.915853\pi$
$410$		0			0
$411$	172683.	+	172683.i	1.02227	+	1.02227i
$412$		0			0
$413$	−6438.36	−	6438.36i	−0.0377464	−	0.0377464i
$414$		0			0
$415$			7025.11i			0.0407903i
$416$		0			0
$417$	237474.			1.36567
$418$		0			0
$419$	−156666.	+	156666.i	−0.892373	+	0.892373i	−0.994746	−	0.102373i	$-0.967356\pi$
$419$	−156666.	+	156666.i	−0.892373	+	0.892373i	0.102373	+	0.994746i	$0.467356\pi$
$420$		0			0
$421$	−20636.7	+	20636.7i	−0.116433	+	0.116433i	−0.762923	−	0.646490i	$-0.776236\pi$
$421$	−20636.7	+	20636.7i	−0.116433	+	0.116433i	0.646490	+	0.762923i	$0.276236\pi$
$422$		0			0
$423$	−44488.2			−0.248636
$424$		0			0
$425$			42427.8i			0.234894i
$426$		0			0
$427$	−13614.0	−	13614.0i	−0.0746670	−	0.0746670i
$428$		0			0
$429$	223238.	+	223238.i	1.21298	+	1.21298i
$430$		0			0
$431$			294349.i			1.58456i	0.610160	+	0.792279i	$0.291105\pi$
$431$			294349.i			1.58456i	−0.610160	+	0.792279i	$0.708895\pi$
$432$		0			0
$433$	240460.			1.28253			0.641264	−	0.767321i	$-0.278411\pi$
$433$	240460.			1.28253			0.641264	+	0.767321i	$0.278411\pi$
$434$		0			0
$435$	−42128.1	+	42128.1i	−0.222635	+	0.222635i
$436$		0			0
$437$	11070.8	−	11070.8i	0.0579716	−	0.0579716i
$438$		0			0
$439$	−294699.			−1.52915			−0.764574	−	0.644536i	$-0.777051\pi$
$439$	−294699.			−1.52915			−0.764574	+	0.644536i	$0.777051\pi$
$440$		0			0
$441$		−	46231.9i		−	0.237719i
$442$		0			0
$443$	−118964.	−	118964.i	−0.606187	−	0.606187i	0.335760	−	0.941948i	$-0.391007\pi$
$443$	−118964.	−	118964.i	−0.606187	−	0.606187i	−0.941948	+	0.335760i	$0.891007\pi$
$444$		0			0
$445$	31824.4	+	31824.4i	0.160709	+	0.160709i
$446$		0			0
$447$		−	130445.i		−	0.652847i
$448$		0			0
$449$	−82129.5			−0.407386			−0.203693	−	0.979035i	$-0.565294\pi$
$449$	−82129.5			−0.407386			−0.203693	+	0.979035i	$0.565294\pi$
$450$		0			0
$451$	164113.	−	164113.i	0.806844	−	0.806844i
$452$		0			0
$453$	107783.	−	107783.i	0.525235	−	0.525235i
$454$		0			0
$455$	−63725.2			−0.307814
$456$		0			0
$457$			172358.i			0.825277i	0.910895	+	0.412638i	$0.135393\pi$
$457$			172358.i			0.825277i	−0.910895	+	0.412638i	$0.864607\pi$
$458$		0			0
$459$	73899.3	+	73899.3i	0.350764	+	0.350764i
$460$		0			0
$461$	−96898.8	−	96898.8i	−0.455950	−	0.455950i	0.441374	−	0.897323i	$-0.354491\pi$
$461$	−96898.8	−	96898.8i	−0.455950	−	0.455950i	−0.897323	+	0.441374i	$0.854491\pi$
$462$		0			0
$463$			142244.i			0.663549i	0.943359	+	0.331775i	$0.107647\pi$
$463$			142244.i			0.663549i	−0.943359	+	0.331775i	$0.892353\pi$
$464$		0			0
$465$	−261080.			−1.20745
$466$		0			0
$467$	139194.	−	139194.i	0.638246	−	0.638246i	−0.311877	−	0.950123i	$-0.600958\pi$
$467$	139194.	−	139194.i	0.638246	−	0.638246i	0.950123	+	0.311877i	$0.100958\pi$
$468$		0			0
$469$	30528.8	−	30528.8i	0.138792	−	0.138792i
$470$		0			0
$471$	200526.			0.903917
$472$		0			0
$473$		−	3251.08i		−	0.0145313i
$474$		0			0
$475$	−128818.	−	128818.i	−0.570936	−	0.570936i
$476$		0			0
$477$	16130.3	+	16130.3i	0.0708934	+	0.0708934i
$478$		0			0
$479$		−	216764.i		−	0.944749i	−0.881398	−	0.472374i	$-0.843397\pi$
$479$		−	216764.i		−	0.944749i	0.881398	−	0.472374i	$-0.156603\pi$
$480$		0			0
$481$	245080.			1.05930
$482$		0			0
$483$	1008.80	−	1008.80i	0.00432426	−	0.00432426i
$484$		0			0
$485$	179659.	−	179659.i	0.763776	−	0.763776i
$486$		0			0
$487$	146986.			0.619752			0.309876	−	0.950777i	$-0.399713\pi$
$487$	146986.			0.619752			0.309876	+	0.950777i	$0.399713\pi$
$488$		0			0
$489$		−	195824.i		−	0.818931i
$490$		0			0
$491$	207292.	+	207292.i	0.859843	+	0.859843i	0.991319	−	0.131476i	$-0.0419716\pi$
$491$	207292.	+	207292.i	0.859843	+	0.859843i	−0.131476	+	0.991319i	$0.541972\pi$
$492$		0			0
$493$	23188.7	+	23188.7i	0.0954074	+	0.0954074i
$494$		0			0
$495$		−	77593.1i		−	0.316674i
$496$		0			0
$497$	20562.3			0.0832452
$498$		0			0
$499$	−5591.76	+	5591.76i	−0.0224568	+	0.0224568i	−0.718246	−	0.695789i	$-0.755055\pi$
$499$	−5591.76	+	5591.76i	−0.0224568	+	0.0224568i	0.695789	+	0.718246i	$0.255055\pi$
$500$		0			0
$501$	63014.2	−	63014.2i	0.251051	−	0.251051i
$502$		0			0
$503$	154345.			0.610037			0.305018	−	0.952346i	$-0.401337\pi$
$503$	154345.			0.610037			0.305018	+	0.952346i	$0.401337\pi$
$504$		0			0
$505$		−	218897.i		−	0.858337i
$506$		0			0
$507$	−384909.	−	384909.i	−1.49742	−	1.49742i
$508$		0			0
$509$	7996.84	+	7996.84i	0.0308662	+	0.0308662i	0.722371	−	0.691505i	$-0.243052\pi$
$509$	7996.84	+	7996.84i	0.0308662	+	0.0308662i	−0.691505	+	0.722371i	$0.743052\pi$
$510$		0			0
$511$		−	4789.30i		−	0.0183413i
$512$		0			0
$513$	−448740.			−1.70514
$514$		0			0
$515$	−31024.4	+	31024.4i	−0.116974	+	0.116974i
$516$		0			0
$517$	−206409.	+	206409.i	−0.772231	+	0.772231i
$518$		0			0
$519$	−125089.			−0.464393
$520$		0			0
$521$		−	215831.i		−	0.795130i	−0.917574	−	0.397565i	$-0.869855\pi$
$521$		−	215831.i		−	0.795130i	0.917574	−	0.397565i	$-0.130145\pi$
$522$		0			0
$523$	73690.2	+	73690.2i	0.269405	+	0.269405i	0.828861	−	0.559455i	$-0.188990\pi$
$523$	73690.2	+	73690.2i	0.269405	+	0.269405i	−0.559455	+	0.828861i	$0.688990\pi$
$524$		0			0
$525$	−11738.2	−	11738.2i	−0.0425877	−	0.0425877i
$526$		0			0
$527$			143707.i			0.517435i
$528$		0			0
$529$	−279085.			−0.997297
$530$		0			0
$531$	−19073.6	+	19073.6i	−0.0676464	+	0.0676464i
$532$		0			0
$533$	−399290.	+	399290.i	−1.40551	+	1.40551i
$534$		0			0
$535$	433814.			1.51564
$536$		0			0
$537$			280762.i			0.973622i
$538$		0			0
$539$	−214499.	−	214499.i	−0.738325	−	0.738325i
$540$		0			0
$541$	−260589.	−	260589.i	−0.890352	−	0.890352i	0.104204	−	0.994556i	$-0.466771\pi$
$541$	−260589.	−	260589.i	−0.890352	−	0.890352i	−0.994556	+	0.104204i	$0.966771\pi$
$542$		0			0
$543$		−	250191.i		−	0.848540i
$544$		0			0
$545$	412.072			0.00138733
$546$		0			0
$547$	87290.1	−	87290.1i	0.291736	−	0.291736i	−0.546030	−	0.837766i	$-0.683861\pi$
$547$	87290.1	−	87290.1i	0.291736	−	0.291736i	0.837766	+	0.546030i	$0.183861\pi$
$548$		0			0
$549$	−40331.3	+	40331.3i	−0.133813	+	0.133813i
$550$		0			0
$551$	−140809.			−0.463796
$552$		0			0
$553$			22631.9i			0.0740066i
$554$		0			0
$555$	133308.	+	133308.i	0.432783	+	0.432783i
$556$		0			0
$557$	342322.	+	342322.i	1.10338	+	1.10338i	0.994000	+	0.109377i	$0.0348855\pi$
$557$	342322.	+	342322.i	1.10338	+	1.10338i	0.109377	+	0.994000i	$0.465114\pi$
$558$		0			0
$559$			7909.94i			0.0253134i
$560$		0			0
$561$	133675.			0.424741
$562$		0			0
$563$	77521.3	−	77521.3i	0.244571	−	0.244571i	−0.574167	−	0.818738i	$-0.694674\pi$
$563$	77521.3	−	77521.3i	0.244571	−	0.244571i	0.818738	+	0.574167i	$0.194674\pi$
$564$		0			0
$565$	296383.	−	296383.i	0.928447	−	0.928447i
$566$		0			0
$567$	−30372.6			−0.0944749
$568$		0			0
$569$		−	304409.i		−	0.940229i	−0.882605	−	0.470115i	$-0.844213\pi$
$569$		−	304409.i		−	0.940229i	0.882605	−	0.470115i	$-0.155787\pi$
$570$		0			0
$571$	254051.	+	254051.i	0.779201	+	0.779201i	0.979695	−	0.200494i	$-0.0642547\pi$
$571$	254051.	+	254051.i	0.779201	+	0.779201i	−0.200494	+	0.979695i	$0.564255\pi$
$572$		0			0
$573$	−348999.	−	348999.i	−1.06295	−	1.06295i
$574$		0			0
$575$		−	8801.94i		−	0.0266221i
$576$		0			0
$577$	−486229.			−1.46046			−0.730229	−	0.683202i	$-0.760587\pi$
$577$	−486229.			−1.46046			−0.730229	+	0.683202i	$0.760587\pi$
$578$		0			0
$579$	138724.	−	138724.i	0.413803	−	0.413803i
$580$		0			0
$581$	−1069.82	+	1069.82i	−0.00316926	+	0.00316926i
$582$		0			0
$583$	149677.			0.440371
$584$		0			0
$585$			188786.i			0.551642i
$586$		0			0
$587$	26612.4	+	26612.4i	0.0772339	+	0.0772339i	0.744668	−	0.667435i	$-0.232608\pi$
$587$	26612.4	+	26612.4i	0.0772339	+	0.0772339i	−0.667435	+	0.744668i	$0.732608\pi$
$588$		0			0
$589$	−436317.	−	436317.i	−1.25768	−	1.25768i
$590$		0			0
$591$			71678.1i			0.205216i
$592$		0			0
$593$	301795.			0.858228			0.429114	−	0.903250i	$-0.358826\pi$
$593$	301795.			0.858228			0.429114	+	0.903250i	$0.358826\pi$
$594$		0			0
$595$	−19079.4	+	19079.4i	−0.0538927	+	0.0538927i
$596$		0			0
$597$	−309105.	+	309105.i	−0.867276	+	0.867276i
$598$		0			0
$599$	−208748.			−0.581795			−0.290897	−	0.956754i	$-0.593954\pi$
$599$	−208748.			−0.581795			−0.290897	+	0.956754i	$0.593954\pi$
$600$		0			0
$601$		−	355946.i		−	0.985451i	−0.870185	−	0.492725i	$-0.836001\pi$
$601$		−	355946.i		−	0.985451i	0.870185	−	0.492725i	$-0.163999\pi$
$602$		0			0
$603$	−90441.4	−	90441.4i	−0.248733	−	0.248733i
$604$		0			0
$605$	−41746.1	−	41746.1i	−0.114053	−	0.114053i
$606$		0			0
$607$		−	680696.i		−	1.84746i	−0.383040	−	0.923732i	$-0.625123\pi$
$607$		−	680696.i		−	1.84746i	0.383040	−	0.923732i	$-0.374877\pi$
$608$		0			0
$609$	−12830.9			−0.0345958
$610$		0			0
$611$	502197.	−	502197.i	1.34522	−	1.34522i
$612$		0			0
$613$	504818.	−	504818.i	1.34343	−	1.34343i	0.450800	−	0.892625i	$-0.351139\pi$
$613$	504818.	−	504818.i	1.34343	−	1.34343i	0.892625	−	0.450800i	$-0.148861\pi$
$614$		0			0
$615$	−434378.			−1.14846
$616$		0			0
$617$			601668.i			1.58047i	0.612803	+	0.790236i	$0.290042\pi$
$617$			601668.i			1.58047i	−0.612803	+	0.790236i	$0.709958\pi$
$618$		0			0
$619$	34687.6	+	34687.6i	0.0905300	+	0.0905300i	0.750922	−	0.660391i	$-0.229610\pi$
$619$	34687.6	+	34687.6i	0.0905300	+	0.0905300i	−0.660391	+	0.750922i	$0.729610\pi$
$620$		0			0
$621$	−15330.9	−	15330.9i	−0.0397544	−	0.0397544i
$622$		0			0
$623$			9692.72i			0.0249729i
$624$		0			0
$625$	488225.			1.24985
$626$		0			0
$627$	−405858.	+	405858.i	−1.03238	+	1.03238i
$628$		0			0
$629$	73377.0	−	73377.0i	0.185464	−	0.185464i
$630$		0			0
$631$	557209.			1.39946			0.699728	−	0.714409i	$-0.253304\pi$
$631$	557209.			1.39946			0.699728	+	0.714409i	$0.253304\pi$
$632$		0			0
$633$			126355.i			0.315345i
$634$		0			0
$635$	174924.	+	174924.i	0.433812	+	0.433812i
$636$		0			0
$637$	521881.	+	521881.i	1.28615	+	1.28615i
$638$		0			0
$639$		−	60915.8i		−	0.149186i
$640$		0			0
$641$	354670.			0.863193			0.431597	−	0.902067i	$-0.357950\pi$
$641$	354670.			0.863193			0.431597	+	0.902067i	$0.357950\pi$
$642$		0			0
$643$	89105.3	−	89105.3i	0.215517	−	0.215517i	−0.591089	−	0.806606i	$-0.701302\pi$
$643$	89105.3	−	89105.3i	0.215517	−	0.215517i	0.806606	+	0.591089i	$0.201302\pi$
$644$		0			0
$645$	−4302.51	+	4302.51i	−0.0103420	+	0.0103420i
$646$		0			0
$647$	−669197.			−1.59862			−0.799311	−	0.600918i	$-0.794802\pi$
$647$	−669197.			−1.59862			−0.799311	+	0.600918i	$0.794802\pi$
$648$		0			0
$649$			176989.i			0.420201i
$650$		0			0
$651$	−39758.5	−	39758.5i	−0.0938140	−	0.0938140i
$652$		0			0
$653$	−6136.50	−	6136.50i	−0.0143911	−	0.0143911i	0.699875	−	0.714266i	$-0.253239\pi$
$653$	−6136.50	−	6136.50i	−0.0143911	−	0.0143911i	−0.714266	+	0.699875i	$0.753239\pi$
$654$		0			0
$655$			691457.i			1.61169i
$656$		0			0
$657$	−14188.3			−0.0328700
$658$		0			0
$659$	−484888.	+	484888.i	−1.11653	+	1.11653i	−0.124283	+	0.992247i	$0.539663\pi$
$659$	−484888.	+	484888.i	−1.11653	+	1.11653i	−0.992247	+	0.124283i	$0.960337\pi$
$660$		0			0
$661$	71185.1	−	71185.1i	0.162924	−	0.162924i	−0.620937	−	0.783861i	$-0.713248\pi$
$661$	71185.1	−	71185.1i	0.162924	−	0.162924i	0.783861	+	0.620937i	$0.213248\pi$
$662$		0			0
$663$	−325234.			−0.739892
$664$		0			0
$665$		−	115856.i		−	0.261984i
$666$		0			0
$667$	−4810.65	−	4810.65i	−0.0108131	−	0.0108131i
$668$		0			0
$669$	84179.5	+	84179.5i	0.188085	+	0.188085i
$670$		0			0
$671$			374244.i			0.831209i
$672$		0			0
$673$	116807.			0.257893			0.128947	−	0.991652i	$-0.458840\pi$
$673$	116807.			0.257893			0.128947	+	0.991652i	$0.458840\pi$
$674$		0			0
$675$	−178388.	+	178388.i	−0.391523	+	0.391523i
$676$		0			0
$677$	−562443.	+	562443.i	−1.22716	+	1.22716i	−0.262127	+	0.965033i	$0.584424\pi$
$677$	−562443.	+	562443.i	−1.22716	+	1.22716i	−0.965033	+	0.262127i	$0.915576\pi$
$678$		0			0
$679$	54718.7			0.118685
$680$		0			0
$681$		−	526415.i		−	1.13510i
$682$		0			0
$683$	−392290.	−	392290.i	−0.840941	−	0.840941i	0.148040	−	0.988981i	$-0.452703\pi$
$683$	−392290.	−	392290.i	−0.840941	−	0.840941i	−0.988981	+	0.148040i	$0.952703\pi$
$684$		0			0
$685$	677539.	+	677539.i	1.44395	+	1.44395i
$686$		0			0
$687$		−	173173.i		−	0.366916i
$688$		0			0
$689$	−364168.			−0.767120
$690$		0			0
$691$	−424716.	+	424716.i	−0.889493	+	0.889493i	−0.994474	−	0.104981i	$-0.966522\pi$
$691$	−424716.	+	424716.i	−0.889493	+	0.889493i	0.104981	+	0.994474i	$0.466522\pi$
$692$		0			0
$693$	11816.2	−	11816.2i	0.0246044	−	0.0246044i
$694$		0			0
$695$	931755.			1.92900
$696$		0			0
$697$			239095.i			0.492159i
$698$		0			0
$699$	−349868.	−	349868.i	−0.716060	−	0.716060i
$700$		0			0
$701$	92393.5	+	92393.5i	0.188021	+	0.188021i	0.794840	−	0.606819i	$-0.207555\pi$
$701$	92393.5	+	92393.5i	0.188021	+	0.188021i	−0.606819	+	0.794840i	$0.707555\pi$
$702$		0			0
$703$			445569.i			0.901580i
$704$		0			0
$705$	546327.			1.09920
$706$		0			0
$707$	33334.7	−	33334.7i	0.0666896	−	0.0666896i
$708$		0			0
$709$	−29997.3	+	29997.3i	−0.0596746	+	0.0596746i	−0.736314	−	0.676640i	$-0.763435\pi$
$709$	−29997.3	+	29997.3i	−0.0596746	+	0.0596746i	0.676640	+	0.736314i	$0.263435\pi$
$710$		0			0
$711$	67046.9			0.132629
$712$		0			0
$713$		−	29812.9i		−	0.0586443i
$714$		0			0
$715$	875896.	+	875896.i	1.71333	+	1.71333i
$716$		0			0
$717$	−184661.	−	184661.i	−0.359200	−	0.359200i
$718$		0			0
$719$			284133.i			0.549622i	0.961498	+	0.274811i	$0.0886152\pi$
$719$			284133.i			0.549622i	−0.961498	+	0.274811i	$0.911385\pi$
$720$		0			0
$721$	−9449.07			−0.0181769
$722$		0			0
$723$	−31167.4	+	31167.4i	−0.0596243	+	0.0596243i
$724$		0			0
$725$	−55975.8	+	55975.8i	−0.106494	+	0.106494i
$726$		0			0
$727$	39096.3			0.0739719			0.0369860	−	0.999316i	$-0.488224\pi$
$727$	39096.3			0.0739719			0.0369860	+	0.999316i	$0.488224\pi$
$728$		0			0
$729$			590261.i			1.11068i
$730$		0			0
$731$	2368.24	+	2368.24i	0.00443191	+	0.00443191i
$732$		0			0
$733$	−82927.3	−	82927.3i	−0.154344	−	0.154344i	0.625711	−	0.780055i	$-0.284809\pi$
$733$	−82927.3	−	82927.3i	−0.154344	−	0.154344i	−0.780055	+	0.625711i	$0.784809\pi$
$734$		0			0
$735$			567741.i			1.05093i
$736$		0			0
$737$	−839229.			−1.54506
$738$		0			0
$739$	97643.8	−	97643.8i	0.178795	−	0.178795i	−0.612035	−	0.790830i	$-0.709649\pi$
$739$	97643.8	−	97643.8i	0.178795	−	0.178795i	0.790830	+	0.612035i	$0.209649\pi$
$740$		0			0
$741$	987462.	−	987462.i	1.79839	−	1.79839i
$742$		0			0
$743$	−552181.			−1.00024			−0.500120	−	0.865956i	$-0.666711\pi$
$743$	−552181.			−1.00024			−0.500120	+	0.865956i	$0.666711\pi$
$744$		0			0
$745$		−	511813.i		−	0.922145i
$746$		0			0
$747$	3169.33	+	3169.33i	0.00567971	+	0.00567971i
$748$		0			0
$749$	66063.3	+	66063.3i	0.117760	+	0.117760i
$750$		0			0
$751$		−	318447.i		−	0.564621i	−0.959323	−	0.282310i	$-0.908899\pi$
$751$		−	318447.i		−	0.564621i	0.959323	−	0.282310i	$-0.0911008\pi$
$752$		0			0
$753$	−689140.			−1.21539
$754$		0			0
$755$	422898.	−	422898.i	0.741894	−	0.741894i
$756$		0			0
$757$	478701.	−	478701.i	0.835357	−	0.835357i	−0.152886	−	0.988244i	$-0.548857\pi$
$757$	478701.	−	478701.i	0.835357	−	0.835357i	0.988244	+	0.152886i	$0.0488569\pi$
$758$		0			0
$759$	−27731.8			−0.0481386
$760$		0			0
$761$			398315.i			0.687793i	0.939008	+	0.343896i	$0.111747\pi$
$761$			398315.i			0.687793i	−0.939008	+	0.343896i	$0.888253\pi$
$762$		0			0
$763$	62.7523	+	62.7523i	0.000107790	+	0.000107790i
$764$		0			0
$765$	56522.5	+	56522.5i	0.0965826	+	0.0965826i
$766$		0			0
$767$		−	430619.i		−	0.731985i
$768$		0			0
$769$	658868.			1.11416			0.557078	−	0.830460i	$-0.311922\pi$
$769$	658868.			1.11416			0.557078	+	0.830460i	$0.311922\pi$
$770$		0			0
$771$	−126271.	+	126271.i	−0.212419	+	0.212419i
$772$		0			0
$773$	−833367.	+	833367.i	−1.39469	+	1.39469i	−0.580250	+	0.814439i	$0.697045\pi$
$773$	−833367.	+	833367.i	−1.39469	+	1.39469i	−0.814439	+	0.580250i	$0.802955\pi$
$774$		0			0
$775$	−346898.			−0.577561
$776$		0			0
$777$			40601.6i			0.0672513i
$778$		0			0
$779$	−725932.	−	725932.i	−1.19625	−	1.19625i
$780$		0			0
$781$	−282627.	−	282627.i	−0.463352	−	0.463352i
$782$		0			0
$783$			194994.i			0.318051i
$784$		0			0
$785$	786784.			1.27678
$786$		0			0
$787$	265518.	−	265518.i	0.428691	−	0.428691i	−0.459491	−	0.888182i	$-0.651968\pi$
$787$	265518.	−	265518.i	0.428691	−	0.428691i	0.888182	+	0.459491i	$0.151968\pi$
$788$		0			0
$789$	−701447.	+	701447.i	−1.12679	+	1.12679i
$790$		0			0
$791$	90269.3			0.144274
$792$		0			0
$793$		−	910545.i		−	1.44795i
$794$		0			0
$795$	−198084.	−	198084.i	−0.313412	−	0.313412i
$796$		0			0
$797$	−51155.1	−	51155.1i	−0.0805327	−	0.0805327i	0.665693	−	0.746226i	$-0.268136\pi$
$797$	−51155.1	−	51155.1i	−0.0805327	−	0.0805327i	−0.746226	+	0.665693i	$0.768136\pi$
$798$		0			0
$799$		−	300716.i		−	0.471046i
$800$		0			0
$801$	28714.7			0.0447547
$802$		0			0
$803$	−65828.4	+	65828.4i	−0.102090	+	0.102090i
$804$		0			0
$805$	3958.14	−	3958.14i	0.00610801	−	0.00610801i
$806$		0			0
$807$	724970.			1.11320
$808$		0			0
$809$			608654.i			0.929979i	0.885316	+	0.464990i	$0.153942\pi$
$809$			608654.i			0.929979i	−0.885316	+	0.464990i	$0.846058\pi$
$810$		0			0
$811$	693367.	+	693367.i	1.05420	+	1.05420i	0.998445	+	0.0557512i	$0.0177554\pi$
$811$	693367.	+	693367.i	1.05420	+	1.05420i	0.0557512	+	0.998445i	$0.482245\pi$
$812$		0			0
$813$	517612.	+	517612.i	0.783111	+	0.783111i
$814$		0			0
$815$		−	768335.i		−	1.15674i
$816$		0			0
$817$	−14380.7			−0.0215445
$818$		0			0
$819$	−28749.2	+	28749.2i	−0.0428605	+	0.0428605i
$820$		0			0
$821$	843960.	−	843960.i	1.25209	−	1.25209i	0.297308	−	0.954781i	$-0.403911\pi$
$821$	843960.	−	843960.i	1.25209	−	1.25209i	0.954781	−	0.297308i	$-0.0960890\pi$
$822$		0			0
$823$	−562057.			−0.829815			−0.414907	−	0.909864i	$-0.636186\pi$
$823$	−562057.			−0.829815			−0.414907	+	0.909864i	$0.636186\pi$
$824$		0			0
$825$			322681.i			0.474096i
$826$		0			0
$827$	−49278.3	−	49278.3i	−0.0720518	−	0.0720518i	0.670163	−	0.742214i	$-0.266224\pi$
$827$	−49278.3	−	49278.3i	−0.0720518	−	0.0720518i	−0.742214	+	0.670163i	$0.766224\pi$
$828$		0			0
$829$	−519755.	−	519755.i	−0.756291	−	0.756291i	0.219354	−	0.975645i	$-0.429605\pi$
$829$	−519755.	−	519755.i	−0.756291	−	0.756291i	−0.975645	+	0.219354i	$0.929605\pi$
$830$		0			0
$831$		−	1.16643e6i		−	1.68911i
$832$		0			0
$833$	312503.			0.450364
$834$		0			0
$835$	247243.	−	247243.i	0.354610	−	0.354610i
$836$		0			0
$837$	−604215.	+	604215.i	−0.862464	+	0.862464i
$838$		0			0
$839$	−311968.			−0.443186			−0.221593	−	0.975139i	$-0.571126\pi$
$839$	−311968.			−0.443186			−0.221593	+	0.975139i	$0.571126\pi$
$840$		0			0
$841$		−	646094.i		−	0.913491i
$842$		0			0
$843$	237978.	+	237978.i	0.334874	+	0.334874i
$844$		0			0
$845$	−1.51023e6	−	1.51023e6i	−2.11510	−	2.11510i
$846$		0			0
$847$		−	12714.6i		−	0.0177229i
$848$		0			0
$849$	−404860.			−0.561681
$850$		0			0
$851$	−15222.6	+	15222.6i	−0.0210198	+	0.0210198i
$852$		0			0
$853$	−306461.	+	306461.i	−0.421190	+	0.421190i	−0.885613	−	0.464424i	$-0.846262\pi$
$853$	−306461.	+	306461.i	−0.421190	+	0.421190i	0.464424	+	0.885613i	$0.346262\pi$
$854$		0			0
$855$	−343223.			−0.469509
$856$		0			0
$857$			16157.2i			0.0219991i	0.999940	+	0.0109995i	$0.00350133\pi$
$857$			16157.2i			0.0219991i	−0.999940	+	0.0109995i	$0.996499\pi$
$858$		0			0
$859$	−74800.4	−	74800.4i	−0.101372	−	0.101372i	0.654602	−	0.755974i	$-0.272836\pi$
$859$	−74800.4	−	74800.4i	−0.101372	−	0.101372i	−0.755974	+	0.654602i	$0.772836\pi$
$860$		0			0
$861$	−66149.0	−	66149.0i	−0.0892313	−	0.0892313i
$862$		0			0
$863$		−	902987.i		−	1.21244i	−0.795297	−	0.606220i	$-0.792685\pi$
$863$		−	902987.i		−	1.21244i	0.795297	−	0.606220i	$-0.207315\pi$
$864$		0			0
$865$	−490801.			−0.655954
$866$		0			0
$867$	365344.	−	365344.i	0.486031	−	0.486031i
$868$		0			0
$869$	311073.	−	311073.i	0.411929	−	0.411929i
$870$		0			0
$871$	2.04186e6			2.69147
$872$		0			0
$873$		−	162104.i		−	0.212699i
$874$		0			0
$875$	43889.6	+	43889.6i	0.0573251	+	0.0573251i
$876$		0			0
$877$	−526163.	−	526163.i	−0.684102	−	0.684102i	0.276820	−	0.960922i	$-0.410719\pi$
$877$	−526163.	−	526163.i	−0.684102	−	0.684102i	−0.960922	+	0.276820i	$0.910719\pi$
$878$		0			0
$879$			502600.i			0.650496i
$880$		0			0
$881$	−1.39036e6			−1.79133			−0.895664	−	0.444732i	$-0.853299\pi$
$881$	−1.39036e6			−1.79133			−0.895664	+	0.444732i	$0.853299\pi$
$882$		0			0
$883$	717884.	−	717884.i	0.920731	−	0.920731i	−0.0763499	−	0.997081i	$-0.524327\pi$
$883$	717884.	−	717884.i	0.920731	−	0.920731i	0.997081	+	0.0763499i	$0.0243266\pi$
$884$		0			0
$885$	234229.	−	234229.i	0.299058	−	0.299058i
$886$		0			0
$887$	−398604.			−0.506633			−0.253317	−	0.967383i	$-0.581521\pi$
$887$	−398604.			−0.506633			−0.253317	+	0.967383i	$0.581521\pi$
$888$		0			0
$889$			53276.4i			0.0674111i
$890$		0			0
$891$	417468.	+	417468.i	0.525858	+	0.525858i
$892$		0			0
$893$	913022.	+	913022.i	1.14493	+	1.14493i
$894$		0			0
$895$			1.10160e6i			1.37524i
$896$		0			0
$897$	67472.0			0.0838569
$898$		0			0
$899$	−189595.	+	189595.i	−0.234589	+	0.234589i
$900$		0			0
$901$	−109032.	+	109032.i	−0.134309	+	0.134309i
$902$		0			0
$903$	−1310.41			−0.00160706
$904$		0			0
$905$		−	981651.i		−	1.19856i
$906$		0			0
$907$	−954485.	−	954485.i	−1.16026	−	1.16026i	−0.984419	−	0.175840i	$-0.943736\pi$
$907$	−954485.	−	954485.i	−1.16026	−	1.16026i	−0.175840	−	0.984419i	$-0.556264\pi$
$908$		0			0
$909$	−98754.0	−	98754.0i	−0.119516	−	0.119516i
$910$		0			0
$911$			876782.i			1.05646i	0.849100	+	0.528232i	$0.177145\pi$
$911$			876782.i			1.05646i	−0.849100	+	0.528232i	$0.822855\pi$
$912$		0			0
$913$	29409.0			0.0352808
$914$		0			0
$915$	495279.	−	495279.i	0.591572	−	0.591572i
$916$		0			0
$917$	−105298.	+	105298.i	−0.125223	+	0.125223i
$918$		0			0
$919$	−146433.			−0.173384			−0.0866920	−	0.996235i	$-0.527630\pi$
$919$	−146433.			−0.173384			−0.0866920	+	0.996235i	$0.527630\pi$
$920$		0			0
$921$			111196.i			0.131090i
$922$		0			0
$923$	687637.	+	687637.i	0.807153	+	0.807153i
$924$		0			0
$925$	177127.	+	177127.i	0.207015	+	0.207015i
$926$		0			0
$927$			27992.8i			0.0325752i
$928$		0			0
$929$	−357969.			−0.414776			−0.207388	−	0.978259i	$-0.566496\pi$
$929$	−357969.			−0.414776			−0.207388	+	0.978259i	$0.566496\pi$
$930$		0			0
$931$	−948808.	+	948808.i	−1.09466	+	1.09466i
$932$		0			0
$933$	−567320.	+	567320.i	−0.651726	+	0.651726i
$934$		0			0
$935$	524487.			0.599945
$936$		0			0
$937$			1.49027e6i			1.69740i	0.528871	+	0.848702i	$0.322616\pi$
$937$			1.49027e6i			1.69740i	−0.528871	+	0.848702i	$0.677384\pi$
$938$		0			0
$939$	−337579.	−	337579.i	−0.382863	−	0.382863i
$940$		0			0
$941$	977475.	+	977475.i	1.10389	+	1.10389i	0.993937	+	0.109954i	$0.0350705\pi$
$941$	977475.	+	977475.i	1.10389	+	1.10389i	0.109954	+	0.993937i	$0.464929\pi$
$942$		0			0
$943$		−	49602.0i		−	0.0557796i
$944$		0			0
$945$	−160438.			−0.179657
$946$		0			0
$947$	−573883.	+	573883.i	−0.639917	+	0.639917i	−0.950535	−	0.310618i	$-0.899464\pi$
$947$	−573883.	+	573883.i	−0.639917	+	0.639917i	0.310618	+	0.950535i	$0.399464\pi$
$948$		0			0
$949$	160162.	−	160162.i	0.177839	−	0.177839i
$950$		0			0
$951$	−113210.			−0.125177
$952$		0			0
$953$		−	356334.i		−	0.392348i	−0.980569	−	0.196174i	$-0.937148\pi$
$953$		−	356334.i		−	0.392348i	0.980569	−	0.196174i	$-0.0628517\pi$
$954$		0			0
$955$	−1.36933e6	−	1.36933e6i	−1.50142	−	1.50142i
$956$		0			0
$957$	176360.	+	176360.i	0.192564	+	0.192564i
$958$		0			0
$959$			206358.i			0.224380i
$960$		0			0
$961$	−251453.			−0.272276
$962$		0			0
$963$	195712.	−	195712.i	0.211040	−	0.211040i
$964$		0			0
$965$	544298.	−	544298.i	0.584496	−	0.584496i
$966$		0			0
$967$	−1.37297e6			−1.46828			−0.734138	−	0.679001i	$-0.762413\pi$
$967$	−1.37297e6			−1.46828			−0.734138	+	0.679001i	$0.762413\pi$
$968$		0			0
$969$		−	591293.i		−	0.629731i
$970$		0			0
$971$	424934.	+	424934.i	0.450696	+	0.450696i	0.895585	−	0.444890i	$-0.146757\pi$
$971$	424934.	+	424934.i	0.450696	+	0.450696i	−0.444890	+	0.895585i	$0.646757\pi$
$972$		0			0
$973$	141892.	+	141892.i	0.149876	+	0.149876i
$974$		0			0
$975$		−	785091.i		−	0.825868i
$976$		0			0
$977$	985948.			1.03292			0.516458	−	0.856313i	$-0.327250\pi$
$977$	985948.			1.03292			0.516458	+	0.856313i	$0.327250\pi$
$978$		0			0
$979$	133225.	−	133225.i	0.139002	−	0.139002i
$980$		0			0
$981$	185.903	−	185.903i	0.000193174	−	0.000193174i
$982$		0			0
$983$	92886.2			0.0961268			0.0480634	−	0.998844i	$-0.484695\pi$
$983$	92886.2			0.0961268			0.0480634	+	0.998844i	$0.484695\pi$
$984$		0			0
$985$			281236.i			0.289867i
$986$		0			0
$987$	83197.3	+	83197.3i	0.0854034	+	0.0854034i
$988$		0			0
$989$	−491.308	−	491.308i	−0.000502297	−	0.000502297i
$990$		0			0
$991$			1.28759e6i			1.31109i	0.755157	+	0.655543i	$0.227560\pi$
$991$			1.28759e6i			1.31109i	−0.755157	+	0.655543i	$0.772440\pi$
$992$		0			0
$993$	1.36956e6			1.38894
$994$		0			0
$995$	−1.21281e6	+	1.21281e6i	−1.22503	+	1.22503i
$996$		0			0
$997$	388032.	−	388032.i	0.390370	−	0.390370i	−0.484449	−	0.874819i	$-0.660980\pi$
$997$	388032.	−	388032.i	0.390370	−	0.390370i	0.874819	+	0.484449i	$0.160980\pi$
$998$		0			0
$999$	617028.			0.618264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.f.b.95.2		14
4.3	odd	2		128.5.f.a.95.6		14
8.3	odd	2		64.5.f.a.47.2		14
8.5	even	2		16.5.f.a.3.1	✓	14
16.3	odd	4		16.5.f.a.11.1	yes	14
16.5	even	4		128.5.f.a.31.6		14
16.11	odd	4	inner	128.5.f.b.31.2		14
16.13	even	4		64.5.f.a.15.2		14
24.5	odd	2		144.5.m.a.19.7		14
24.11	even	2		576.5.m.a.559.2		14
48.29	odd	4		576.5.m.a.271.2		14
48.35	even	4		144.5.m.a.91.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.1	✓	14	8.5	even	2
16.5.f.a.11.1	yes	14	16.3	odd	4
64.5.f.a.15.2		14	16.13	even	4
64.5.f.a.47.2		14	8.3	odd	2
128.5.f.a.31.6		14	16.5	even	4
128.5.f.a.95.6		14	4.3	odd	2
128.5.f.b.31.2		14	16.11	odd	4	inner
128.5.f.b.95.2		14	1.1	even	1	trivial
144.5.m.a.19.7		14	24.5	odd	2
144.5.m.a.91.7		14	48.35	even	4
576.5.m.a.271.2		14	48.29	odd	4
576.5.m.a.559.2		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)

\(f(q)\)	\(=\)	\(q+(-5.54016 + 5.54016i) q^{3} +(-21.7374 + 21.7374i) q^{5} -6.62054 q^{7} +19.6133i q^{9} +O(q^{10})\)	\(q+(-5.54016 + 5.54016i) q^{3} +(-21.7374 + 21.7374i) q^{5} -6.62054 q^{7} +19.6133i q^{9} +(90.9986 + 90.9986i) q^{11} +(-221.402 - 221.402i) q^{13} -240.857i q^{15} -132.575 q^{17} +(402.520 - 402.520i) q^{19} +(36.6788 - 36.6788i) q^{21} +27.5037 q^{23} -320.028i q^{25} +(-557.414 - 557.414i) q^{27} +(-174.909 - 174.909i) q^{29} -1083.96i q^{31} -1008.29 q^{33} +(143.913 - 143.913i) q^{35} +(-553.474 + 553.474i) q^{37} +2453.20 q^{39} -1803.47i q^{41} +(-17.8633 - 17.8633i) q^{43} +(-426.342 - 426.342i) q^{45} +2268.26i q^{47} -2357.17 q^{49} +(734.489 - 734.489i) q^{51} +(822.415 - 822.415i) q^{53} -3956.14 q^{55} +4460.05i q^{57} +(972.483 + 972.483i) q^{59} +(2056.32 + 2056.32i) q^{61} -129.851i q^{63} +9625.38 q^{65} +(-4611.22 + 4611.22i) q^{67} +(-152.375 + 152.375i) q^{69} -3105.84 q^{71} +723.400i q^{73} +(1773.00 + 1773.00i) q^{75} +(-602.460 - 602.460i) q^{77} -3418.44i q^{79} +4587.64 q^{81} +(161.591 - 161.591i) q^{83} +(2881.84 - 2881.84i) q^{85} +1938.05 q^{87} -1464.04i q^{89} +(1465.80 + 1465.80i) q^{91} +(6005.32 + 6005.32i) q^{93} +17499.5i q^{95} -8264.99 q^{97} +(-1784.78 + 1784.78i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{3} + 2 q^{5} - 4 q^{7}+O(q^{10}) \) 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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