LMFDB - Embedded newform 128.5.f.b.31.2

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			31.2
Root			$2.24452 + 1.72109i$ of defining polynomial
Character	$\chi$	$=$	128.31
Dual form			128.5.f.b.95.2

$q$-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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

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

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	0.328820	−	0.944393i	$-0.393349\pi$
$3$	−5.54016	−	5.54016i	−0.615573	−	0.615573i	−0.944393	+	0.328820i	$0.893349\pi$
$4$		0			0
$5$	−21.7374	−	21.7374i	−0.869495	−	0.869495i	0.122921	−	0.992416i	$-0.460774\pi$
$5$	−21.7374	−	21.7374i	−0.869495	−	0.869495i	−0.992416	+	0.122921i	$0.960774\pi$
$6$		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	−0.222808	−	0.974862i	$-0.571522\pi$
$11$	90.9986	−	90.9986i	0.752054	−	0.752054i	0.974862	+	0.222808i	$0.0715223\pi$
$12$		0			0
$13$	−221.402	+	221.402i	−1.31007	+	1.31007i	−0.388707	+	0.921362i	$0.627078\pi$
$13$	−221.402	+	221.402i	−1.31007	+	1.31007i	−0.921362	+	0.388707i	$0.872922\pi$
$14$		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	0.992462	+	0.122552i	$0.0391079\pi$
$19$	402.520	+	402.520i	1.11501	+	1.11501i	0.122552	+	0.992462i	$0.460892\pi$
$20$		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	−0.803407	−	0.595430i	$-0.796982\pi$
$29$	−174.909	+	174.909i	−0.207978	+	0.207978i	0.595430	+	0.803407i	$0.296982\pi$
$30$		0			0
$31$			1083.96i			1.12795i	0.825791	+	0.563976i	$0.190729\pi$
$31$			1083.96i			1.12795i	−0.825791	+	0.563976i	$0.809271\pi$
$32$		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	0.475451	−	0.879742i	$-0.342285\pi$
$37$	−553.474	−	553.474i	−0.404291	−	0.404291i	−0.879742	+	0.475451i	$0.842285\pi$
$38$		0			0
$39$	2453.20			1.61289
$40$		0			0
$41$			1803.47i			1.07285i	0.843947	+	0.536427i	$0.180226\pi$
$41$			1803.47i			1.07285i	−0.843947	+	0.536427i	$0.819774\pi$
$42$		0			0
$43$	−17.8633	+	17.8633i	−0.00966108	+	0.00966108i	−0.711921	−	0.702260i	$-0.752175\pi$
$43$	−17.8633	+	17.8633i	−0.00966108	+	0.00966108i	0.702260	+	0.711921i	$0.252175\pi$
$44$		0			0
$45$	−426.342	+	426.342i	−0.210539	+	0.210539i
$46$		0			0
$47$		−	2268.26i		−	1.02683i	−0.858141	−	0.513414i	$-0.828380\pi$
$47$		−	2268.26i		−	1.02683i	0.858141	−	0.513414i	$-0.171620\pi$
$48$		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	0.838177	−	0.545398i	$-0.183622\pi$
$53$	822.415	+	822.415i	0.292779	+	0.292779i	−0.545398	+	0.838177i	$0.683622\pi$
$54$		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	−0.553488	−	0.832857i	$-0.686704\pi$
$59$	972.483	−	972.483i	0.279369	−	0.279369i	0.832857	+	0.553488i	$0.186704\pi$
$60$		0			0
$61$	2056.32	−	2056.32i	0.552626	−	0.552626i	−0.374572	−	0.927198i	$-0.622210\pi$
$61$	2056.32	−	2056.32i	0.552626	−	0.552626i	0.927198	+	0.374572i	$0.122210\pi$
$62$		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	−0.999619	−	0.0276077i	$-0.991211\pi$
$67$	−4611.22	−	4611.22i	−1.02723	−	1.02723i	−0.0276077	−	0.999619i	$-0.508789\pi$
$68$		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	$-0.978378\pi$
$73$		−	723.400i		−	0.135748i	0.997694	−	0.0678739i	$-0.0216216\pi$
$74$		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	$0.0883036\pi$
$79$			3418.44i			0.547739i	−0.961767	+	0.273869i	$0.911696\pi$
$80$		0			0
$81$	4587.64			0.699228
$82$		0			0
$83$	161.591	+	161.591i	0.0234563	+	0.0234563i	0.718738	−	0.695281i	$-0.244720\pi$
$83$	161.591	+	161.591i	0.0234563	+	0.0234563i	−0.695281	+	0.718738i	$0.744720\pi$
$84$		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	$0.0294586\pi$
$89$			1464.04i			0.184830i	−0.995721	+	0.0924150i	$0.970541\pi$
$90$		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	0.415850	−	0.909433i	$-0.363484\pi$
$101$	−5035.04	−	5035.04i	−0.493583	−	0.493583i	−0.909433	+	0.415850i	$0.863484\pi$
$102$		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	−0.992643	−	0.121079i	$-0.961365\pi$
$107$	−9978.53	+	9978.53i	−0.871564	+	0.871564i	0.121079	+	0.992643i	$0.461365\pi$
$108$		0			0
$109$	−9.47842	+	9.47842i	−0.000797780	+	0.000797780i	−0.707506	−	0.706708i	$-0.750180\pi$
$109$	−9.47842	+	9.47842i	−0.000797780	+	0.000797780i	0.706708	+	0.707506i	$0.250180\pi$
$110$		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	$0.0802537\pi$
$127$			8047.14i			0.498923i	−0.968385	+	0.249462i	$0.919746\pi$
$128$		0			0
$129$	197.931			0.0118942
$130$		0			0
$131$	15904.8	+	15904.8i	0.926799	+	0.926799i	0.997498	−	0.0706991i	$-0.0225230\pi$
$131$	15904.8	+	15904.8i	0.926799	+	0.926799i	−0.0706991	+	0.997498i	$0.522523\pi$
$132$		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	$0.311854\pi$
$137$			31169.3i			1.66068i	−0.557257	+	0.830340i	$0.688146\pi$
$138$		0			0
$139$	−21432.1	+	21432.1i	−1.10926	+	1.10926i	−0.116017	+	0.993247i	$0.537013\pi$
$139$	−21432.1	+	21432.1i	−1.10926	+	1.10926i	−0.993247	+	0.116017i	$0.962987\pi$
$140$		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	0.390378	−	0.920654i	$-0.372344\pi$
$149$	−11772.7	−	11772.7i	−0.530276	−	0.530276i	−0.920654	+	0.390378i	$0.872344\pi$
$150$		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	−0.971450	−	0.237242i	$-0.923756\pi$
$157$	−18097.5	+	18097.5i	−0.734208	+	0.734208i	0.237242	+	0.971450i	$0.423756\pi$
$158$		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	0.291418	−	0.956596i	$-0.405873\pi$
$163$	−17673.1	−	17673.1i	−0.665178	−	0.665178i	−0.956596	+	0.291418i	$0.905873\pi$
$164$		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	−0.492888	−	0.870092i	$-0.664059\pi$
$173$	11289.3	−	11289.3i	0.377204	−	0.377204i	0.870092	+	0.492888i	$0.164059\pi$
$174$		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	0.981628	−	0.190803i	$-0.0611091\pi$
$179$	25338.8	+	25338.8i	0.790825	+	0.790825i	−0.190803	+	0.981628i	$0.561109\pi$
$180$		0			0
$181$	−22579.8	−	22579.8i	−0.689228	−	0.689228i	0.272833	−	0.962061i	$-0.412039\pi$
$181$	−22579.8	−	22579.8i	−0.689228	−	0.689228i	−0.962061	+	0.272833i	$0.912039\pi$
$182$		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	$-0.668339\pi$
$191$		−	62994.4i		−	1.72677i	0.504543	−	0.863386i	$-0.331661\pi$
$192$		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	0.785521	−	0.618834i	$-0.212395\pi$
$197$	6468.96	+	6468.96i	0.166687	+	0.166687i	−0.618834	+	0.785521i	$0.712395\pi$
$198$		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	0.823482	−	0.567343i	$-0.192029\pi$
$211$	11403.6	+	11403.6i	0.256139	+	0.256139i	−0.567343	+	0.823482i	$0.692029\pi$
$212$		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	$0.0488201\pi$
$223$			15194.4i			0.305545i	−0.988261	+	0.152772i	$0.951180\pi$
$224$		0			0
$225$	6276.81			0.123986
$226$		0			0
$227$	−47509.0	−	47509.0i	−0.921986	−	0.921986i	0.0751841	−	0.997170i	$-0.476046\pi$
$227$	−47509.0	−	47509.0i	−0.921986	−	0.921986i	−0.997170	+	0.0751841i	$0.976046\pi$
$228$		0			0
$229$	−15628.9	−	15628.9i	−0.298028	−	0.298028i	0.542213	−	0.840241i	$-0.317587\pi$
$229$	−15628.9	−	15628.9i	−0.298028	−	0.298028i	−0.840241	+	0.542213i	$0.817587\pi$
$230$		0			0
$231$	6675.44			0.125100
$232$		0			0
$233$		−	63151.2i		−	1.16324i	−0.813460	−	0.581621i	$-0.802419\pi$
$233$		−	63151.2i		−	1.16324i	0.813460	−	0.581621i	$-0.197581\pi$
$234$		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	$-0.905759\pi$
$239$		−	33331.4i		−	0.583522i	0.956491	−	0.291761i	$-0.0942412\pi$
$240$		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	−0.0127130	−	0.999919i	$-0.504047\pi$
$251$	62195.0	−	62195.0i	0.987206	−	0.987206i	0.999919	+	0.0127130i	$0.00404679\pi$
$252$		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	−0.995796	−	0.0915982i	$-0.970802\pi$
$269$	−65428.7	+	65428.7i	−0.904198	+	0.904198i	0.0915982	+	0.995796i	$0.470802\pi$
$270$		0			0
$271$			93429.2i			1.27217i	0.771621	+	0.636083i	$0.219446\pi$
$271$			93429.2i			1.27217i	−0.771621	+	0.636083i	$0.780554\pi$
$272$		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	−0.857504	−	0.514477i	$-0.827986\pi$
$277$	−105271.	−	105271.i	−1.37198	−	1.37198i	−0.514477	−	0.857504i	$-0.672014\pi$
$278$		0			0
$279$	21260.1			0.273122
$280$		0			0
$281$			42955.1i			0.544004i	0.962297	+	0.272002i	$0.0876857\pi$
$281$			42955.1i			0.544004i	−0.962297	+	0.272002i	$0.912314\pi$
$282$		0			0
$283$	36538.7	−	36538.7i	0.456226	−	0.456226i	−0.441189	−	0.897414i	$-0.645443\pi$
$283$	36538.7	−	36538.7i	0.456226	−	0.456226i	0.897414	+	0.441189i	$0.145443\pi$
$284$		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	0.920085	−	0.391719i	$-0.128119\pi$
$293$	45359.7	+	45359.7i	0.528367	+	0.528367i	−0.391719	+	0.920085i	$0.628119\pi$
$294$		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	0.758339	−	0.651861i	$-0.226011\pi$
$307$	10035.4	+	10035.4i	0.106478	+	0.106478i	−0.651861	+	0.758339i	$0.726011\pi$
$308$		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	$-0.899342\pi$
$313$		−	60933.1i		−	0.621963i	0.950416	−	0.310981i	$-0.100658\pi$
$314$		0			0
$315$	2822.62	−	2822.62i	0.0284466	−	0.0284466i
$316$		0			0
$317$	10217.2	−	10217.2i	0.101675	−	0.101675i	−0.654439	−	0.756115i	$-0.727095\pi$
$317$	10217.2	−	10217.2i	0.101675	−	0.101675i	0.756115	+	0.654439i	$0.227095\pi$
$318$		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	−0.137692	+	0.990475i	$0.543968\pi$
$331$	−123603.	+	123603.i	−1.12817	+	1.12817i	−0.990475	+	0.137692i	$0.956032\pi$
$332$		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	−0.919395	−	0.393335i	$-0.871321\pi$
$347$	−63342.4	+	63342.4i	−0.526061	+	0.526061i	0.393335	+	0.919395i	$0.371321\pi$
$348$		0			0
$349$	114645.	−	114645.i	0.941247	−	0.941247i	−0.0571205	−	0.998367i	$-0.518192\pi$
$349$	114645.	−	114645.i	0.941247	−	0.941247i	0.998367	+	0.0571205i	$0.0181919\pi$
$350$		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	$-0.852888\pi$
$367$		−	120112.i		−	0.891775i	0.895089	−	0.445888i	$-0.147112\pi$
$368$		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	0.985862	−	0.167562i	$-0.0535894\pi$
$373$	113849.	+	113849.i	0.818300	+	0.818300i	−0.167562	+	0.985862i	$0.553589\pi$
$374$		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	−0.391981	−	0.919973i	$-0.628210\pi$
$379$	75841.4	−	75841.4i	0.527993	−	0.527993i	0.919973	+	0.391981i	$0.128210\pi$
$380$		0			0
$381$	44582.4	−	44582.4i	0.307124	−	0.307124i
$382$		0			0
$383$			80282.4i			0.547297i	0.961830	+	0.273648i	$0.0882304\pi$
$383$			80282.4i			0.547297i	−0.961830	+	0.273648i	$0.911770\pi$
$384$		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	0.346682	−	0.937983i	$-0.387308\pi$
$389$	−89476.2	−	89476.2i	−0.591301	−	0.591301i	−0.937983	+	0.346682i	$0.887308\pi$
$390$		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	−0.985725	−	0.168362i	$-0.946152\pi$
$397$	−128824.	+	128824.i	−0.817363	+	0.817363i	0.168362	+	0.985725i	$0.446152\pi$
$398$		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	$-0.915853\pi$
$409$		−	87416.4i		−	0.522572i	0.965261	−	0.261286i	$-0.0841466\pi$
$410$		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	0.102373	−	0.994746i	$-0.467356\pi$
$419$	−156666.	−	156666.i	−0.892373	−	0.892373i	−0.994746	+	0.102373i	$0.967356\pi$
$420$		0			0
$421$	−20636.7	−	20636.7i	−0.116433	−	0.116433i	0.646490	−	0.762923i	$-0.276236\pi$
$421$	−20636.7	−	20636.7i	−0.116433	−	0.116433i	−0.762923	+	0.646490i	$0.776236\pi$
$422$		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	$-0.708895\pi$
$431$		−	294349.i		−	1.58456i	0.610160	−	0.792279i	$-0.291105\pi$
$432$		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	−0.941948	−	0.335760i	$-0.891007\pi$
$443$	−118964.	+	118964.i	−0.606187	+	0.606187i	0.335760	+	0.941948i	$0.391007\pi$
$444$		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	$-0.864607\pi$
$457$		−	172358.i		−	0.825277i	0.910895	−	0.412638i	$-0.135393\pi$
$458$		0			0
$459$	73899.3	−	73899.3i	0.350764	−	0.350764i
$460$		0			0
$461$	−96898.8	+	96898.8i	−0.455950	+	0.455950i	−0.897323	−	0.441374i	$-0.854491\pi$
$461$	−96898.8	+	96898.8i	−0.455950	+	0.455950i	0.441374	+	0.897323i	$0.354491\pi$
$462$		0			0
$463$		−	142244.i		−	0.663549i	−0.943359	−	0.331775i	$-0.892353\pi$
$463$		−	142244.i		−	0.663549i	0.943359	−	0.331775i	$-0.107647\pi$
$464$		0			0
$465$	−261080.			−1.20745
$466$		0			0
$467$	139194.	+	139194.i	0.638246	+	0.638246i	0.950123	−	0.311877i	$-0.100958\pi$
$467$	139194.	+	139194.i	0.638246	+	0.638246i	−0.311877	+	0.950123i	$0.600958\pi$
$468$		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	$0.156603\pi$
$479$			216764.i			0.944749i	−0.881398	+	0.472374i	$0.843397\pi$
$480$		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	−0.131476	−	0.991319i	$-0.541972\pi$
$491$	207292.	−	207292.i	0.859843	−	0.859843i	0.991319	+	0.131476i	$0.0419716\pi$
$492$		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	0.695789	−	0.718246i	$-0.255055\pi$
$499$	−5591.76	−	5591.76i	−0.0224568	−	0.0224568i	−0.718246	+	0.695789i	$0.755055\pi$
$500$		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	−0.691505	−	0.722371i	$-0.743052\pi$
$509$	7996.84	−	7996.84i	0.0308662	−	0.0308662i	0.722371	+	0.691505i	$0.243052\pi$
$510$		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	$0.130145\pi$
$521$			215831.i			0.795130i	−0.917574	+	0.397565i	$0.869855\pi$
$522$		0			0
$523$	73690.2	−	73690.2i	0.269405	−	0.269405i	−0.559455	−	0.828861i	$-0.688990\pi$
$523$	73690.2	−	73690.2i	0.269405	−	0.269405i	0.828861	+	0.559455i	$0.188990\pi$
$524$		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	−0.994556	−	0.104204i	$-0.966771\pi$
$541$	−260589.	+	260589.i	−0.890352	+	0.890352i	0.104204	+	0.994556i	$0.466771\pi$
$542$		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	0.837766	−	0.546030i	$-0.183861\pi$
$547$	87290.1	+	87290.1i	0.291736	+	0.291736i	−0.546030	+	0.837766i	$0.683861\pi$
$548$		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	0.109377	−	0.994000i	$-0.465114\pi$
$557$	342322.	−	342322.i	1.10338	−	1.10338i	0.994000	−	0.109377i	$-0.0348855\pi$
$558$		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	0.818738	−	0.574167i	$-0.194674\pi$
$563$	77521.3	+	77521.3i	0.244571	+	0.244571i	−0.574167	+	0.818738i	$0.694674\pi$
$564$		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	$0.155787\pi$
$569$			304409.i			0.940229i	−0.882605	+	0.470115i	$0.844213\pi$
$570$		0			0
$571$	254051.	−	254051.i	0.779201	−	0.779201i	−0.200494	−	0.979695i	$-0.564255\pi$
$571$	254051.	−	254051.i	0.779201	−	0.779201i	0.979695	+	0.200494i	$0.0642547\pi$
$572$		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	−0.667435	−	0.744668i	$-0.732608\pi$
$587$	26612.4	−	26612.4i	0.0772339	−	0.0772339i	0.744668	+	0.667435i	$0.232608\pi$
$588$		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	$0.163999\pi$
$601$			355946.i			0.985451i	−0.870185	+	0.492725i	$0.836001\pi$
$602$		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	$0.374877\pi$
$607$			680696.i			1.84746i	−0.383040	+	0.923732i	$0.625123\pi$
$608$		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	0.892625	+	0.450800i	$0.148861\pi$
$613$	504818.	+	504818.i	1.34343	+	1.34343i	0.450800	+	0.892625i	$0.351139\pi$
$614$		0			0
$615$	−434378.			−1.14846
$616$		0			0
$617$		−	601668.i		−	1.58047i	−0.612803	−	0.790236i	$-0.709958\pi$
$617$		−	601668.i		−	1.58047i	0.612803	−	0.790236i	$-0.290042\pi$
$618$		0			0
$619$	34687.6	−	34687.6i	0.0905300	−	0.0905300i	−0.660391	−	0.750922i	$-0.729610\pi$
$619$	34687.6	−	34687.6i	0.0905300	−	0.0905300i	0.750922	+	0.660391i	$0.229610\pi$
$620$		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	0.806606	−	0.591089i	$-0.201302\pi$
$643$	89105.3	+	89105.3i	0.215517	+	0.215517i	−0.591089	+	0.806606i	$0.701302\pi$
$644$		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	−0.714266	−	0.699875i	$-0.753239\pi$
$653$	−6136.50	+	6136.50i	−0.0143911	+	0.0143911i	0.699875	+	0.714266i	$0.253239\pi$
$654$		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	−0.992247	−	0.124283i	$-0.960337\pi$
$659$	−484888.	−	484888.i	−1.11653	−	1.11653i	−0.124283	−	0.992247i	$-0.539663\pi$
$660$		0			0
$661$	71185.1	+	71185.1i	0.162924	+	0.162924i	0.783861	−	0.620937i	$-0.213248\pi$
$661$	71185.1	+	71185.1i	0.162924	+	0.162924i	−0.620937	+	0.783861i	$0.713248\pi$
$662$		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	−0.965033	−	0.262127i	$-0.915576\pi$
$677$	−562443.	−	562443.i	−1.22716	−	1.22716i	−0.262127	−	0.965033i	$-0.584424\pi$
$678$		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	−0.988981	−	0.148040i	$-0.952703\pi$
$683$	−392290.	+	392290.i	−0.840941	+	0.840941i	0.148040	+	0.988981i	$0.452703\pi$
$684$		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	0.104981	−	0.994474i	$-0.466522\pi$
$691$	−424716.	−	424716.i	−0.889493	−	0.889493i	−0.994474	+	0.104981i	$0.966522\pi$
$692$		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	−0.606819	−	0.794840i	$-0.707555\pi$
$701$	92393.5	−	92393.5i	0.188021	−	0.188021i	0.794840	+	0.606819i	$0.207555\pi$
$702$		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	0.676640	−	0.736314i	$-0.263435\pi$
$709$	−29997.3	−	29997.3i	−0.0596746	−	0.0596746i	−0.736314	+	0.676640i	$0.763435\pi$
$710$		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	$-0.911385\pi$
$719$		−	284133.i		−	0.549622i	0.961498	−	0.274811i	$-0.0886152\pi$
$720$		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	−0.780055	−	0.625711i	$-0.784809\pi$
$733$	−82927.3	+	82927.3i	−0.154344	+	0.154344i	0.625711	+	0.780055i	$0.284809\pi$
$734$		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	0.790830	−	0.612035i	$-0.209649\pi$
$739$	97643.8	+	97643.8i	0.178795	+	0.178795i	−0.612035	+	0.790830i	$0.709649\pi$
$740$		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	$0.0911008\pi$
$751$			318447.i			0.564621i	−0.959323	+	0.282310i	$0.908899\pi$
$752$		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	0.988244	−	0.152886i	$-0.0488569\pi$
$757$	478701.	+	478701.i	0.835357	+	0.835357i	−0.152886	+	0.988244i	$0.548857\pi$
$758$		0			0
$759$	−27731.8			−0.0481386
$760$		0			0
$761$		−	398315.i		−	0.687793i	−0.939008	−	0.343896i	$-0.888253\pi$
$761$		−	398315.i		−	0.687793i	0.939008	−	0.343896i	$-0.111747\pi$
$762$		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	−0.814439	−	0.580250i	$-0.802955\pi$
$773$	−833367.	−	833367.i	−1.39469	−	1.39469i	−0.580250	−	0.814439i	$-0.697045\pi$
$774$		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	0.888182	−	0.459491i	$-0.151968\pi$
$787$	265518.	+	265518.i	0.428691	+	0.428691i	−0.459491	+	0.888182i	$0.651968\pi$
$788$		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	−0.746226	−	0.665693i	$-0.768136\pi$
$797$	−51155.1	+	51155.1i	−0.0805327	+	0.0805327i	0.665693	+	0.746226i	$0.268136\pi$
$798$		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	$-0.846058\pi$
$809$		−	608654.i		−	0.929979i	0.885316	−	0.464990i	$-0.153942\pi$
$810$		0			0
$811$	693367.	−	693367.i	1.05420	−	1.05420i	0.0557512	−	0.998445i	$-0.482245\pi$
$811$	693367.	−	693367.i	1.05420	−	1.05420i	0.998445	−	0.0557512i	$-0.0177554\pi$
$812$		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	0.954781	+	0.297308i	$0.0960890\pi$
$821$	843960.	+	843960.i	1.25209	+	1.25209i	0.297308	+	0.954781i	$0.403911\pi$
$822$		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	−0.742214	−	0.670163i	$-0.766224\pi$
$827$	−49278.3	+	49278.3i	−0.0720518	+	0.0720518i	0.670163	+	0.742214i	$0.266224\pi$
$828$		0			0
$829$	−519755.	+	519755.i	−0.756291	+	0.756291i	−0.975645	−	0.219354i	$-0.929605\pi$
$829$	−519755.	+	519755.i	−0.756291	+	0.756291i	0.219354	+	0.975645i	$0.429605\pi$
$830$		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	0.464424	−	0.885613i	$-0.346262\pi$
$853$	−306461.	−	306461.i	−0.421190	−	0.421190i	−0.885613	+	0.464424i	$0.846262\pi$
$854$		0			0
$855$	−343223.			−0.469509
$856$		0			0
$857$		−	16157.2i		−	0.0219991i	−0.999940	−	0.0109995i	$-0.996499\pi$
$857$		−	16157.2i		−	0.0219991i	0.999940	−	0.0109995i	$-0.00350133\pi$
$858$		0			0
$859$	−74800.4	+	74800.4i	−0.101372	+	0.101372i	−0.755974	−	0.654602i	$-0.772836\pi$
$859$	−74800.4	+	74800.4i	−0.101372	+	0.101372i	0.654602	+	0.755974i	$0.272836\pi$
$860$		0			0
$861$	−66149.0	+	66149.0i	−0.0892313	+	0.0892313i
$862$		0			0
$863$			902987.i			1.21244i	0.795297	+	0.606220i	$0.207315\pi$
$863$			902987.i			1.21244i	−0.795297	+	0.606220i	$0.792685\pi$
$864$		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	−0.960922	−	0.276820i	$-0.910719\pi$
$877$	−526163.	+	526163.i	−0.684102	+	0.684102i	0.276820	+	0.960922i	$0.410719\pi$
$878$		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	0.997081	−	0.0763499i	$-0.0243266\pi$
$883$	717884.	+	717884.i	0.920731	+	0.920731i	−0.0763499	+	0.997081i	$0.524327\pi$
$884$		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	−0.175840	+	0.984419i	$0.556264\pi$
$907$	−954485.	+	954485.i	−1.16026	+	1.16026i	−0.984419	+	0.175840i	$0.943736\pi$
$908$		0			0
$909$	−98754.0	+	98754.0i	−0.119516	+	0.119516i
$910$		0			0
$911$		−	876782.i		−	1.05646i	−0.849100	−	0.528232i	$-0.822855\pi$
$911$		−	876782.i		−	1.05646i	0.849100	−	0.528232i	$-0.177145\pi$
$912$		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	$-0.677384\pi$
$937$		−	1.49027e6i		−	1.69740i	0.528871	−	0.848702i	$-0.322616\pi$
$938$		0			0
$939$	−337579.	+	337579.i	−0.382863	+	0.382863i
$940$		0			0
$941$	977475.	−	977475.i	1.10389	−	1.10389i	0.109954	−	0.993937i	$-0.464929\pi$
$941$	977475.	−	977475.i	1.10389	−	1.10389i	0.993937	−	0.109954i	$-0.0350705\pi$
$942$		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	0.310618	−	0.950535i	$-0.399464\pi$
$947$	−573883.	−	573883.i	−0.639917	−	0.639917i	−0.950535	+	0.310618i	$0.899464\pi$
$948$		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	$0.0628517\pi$
$953$			356334.i			0.392348i	−0.980569	+	0.196174i	$0.937148\pi$
$954$		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	−0.444890	−	0.895585i	$-0.646757\pi$
$971$	424934.	−	424934.i	0.450696	−	0.450696i	0.895585	+	0.444890i	$0.146757\pi$
$972$		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	$-0.772440\pi$
$991$		−	1.28759e6i		−	1.31109i	0.755157	−	0.655543i	$-0.227560\pi$
$992$		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	0.874819	−	0.484449i	$-0.160980\pi$
$997$	388032.	+	388032.i	0.390370	+	0.390370i	−0.484449	+	0.874819i	$0.660980\pi$
$998$		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.31.2		14
4.3	odd	2		128.5.f.a.31.6		14
8.3	odd	2		64.5.f.a.15.2		14
8.5	even	2		16.5.f.a.11.1	yes	14
16.3	odd	4	inner	128.5.f.b.95.2		14
16.5	even	4		64.5.f.a.47.2		14
16.11	odd	4		16.5.f.a.3.1	✓	14
16.13	even	4		128.5.f.a.95.6		14
24.5	odd	2		144.5.m.a.91.7		14
24.11	even	2		576.5.m.a.271.2		14
48.5	odd	4		576.5.m.a.559.2		14
48.11	even	4		144.5.m.a.19.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.1	✓	14	16.11	odd	4
16.5.f.a.11.1	yes	14	8.5	even	2
64.5.f.a.15.2		14	8.3	odd	2
64.5.f.a.47.2		14	16.5	even	4
128.5.f.a.31.6		14	4.3	odd	2
128.5.f.a.95.6		14	16.13	even	4
128.5.f.b.31.2		14	1.1	even	1	trivial
128.5.f.b.95.2		14	16.3	odd	4	inner
144.5.m.a.19.7		14	48.11	even	4
144.5.m.a.91.7		14	24.5	odd	2
576.5.m.a.271.2		14	24.11	even	2
576.5.m.a.559.2		14	48.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
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

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