LMFDB - Embedded newform 64.5.f.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,5,Mod(15,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, 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("64.15");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	64.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:	$6.61567763737$
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			47.2
Root			$2.24452 - 1.72109i$ of defining polynomial
Character	$\chi$	$=$	64.47
Dual form			64.5.f.a.15.2

$q$-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 $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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	−0.122921	−	0.992416i	$-0.539226\pi$
$5$	21.7374	−	21.7374i	0.869495	−	0.869495i	0.992416	+	0.122921i	$0.0392262\pi$
$6$		0			0
$7$	6.62054			0.135113			0.0675565	−	0.997715i	$-0.478480\pi$
$7$	6.62054			0.135113			0.0675565	+	0.997715i	$0.478480\pi$
$8$		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	$0.127078\pi$
$13$	221.402	+	221.402i	1.31007	+	1.31007i	0.388707	+	0.921362i	$0.372922\pi$
$14$		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	$-0.508276\pi$
$23$	−27.5037			−0.0519918			−0.0259959	+	0.999662i	$0.508276\pi$
$24$		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	$-0.203018\pi$
$29$	174.909	+	174.909i	0.207978	+	0.207978i	−0.595430	+	0.803407i	$0.703018\pi$
$30$		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	$-0.657715\pi$
$37$	553.474	−	553.474i	0.404291	−	0.404291i	0.879742	+	0.475451i	$0.157715\pi$
$38$		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	$-0.828380\pi$
$47$		−	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	$-0.816378\pi$
$53$	−822.415	+	822.415i	−0.292779	+	0.292779i	0.545398	+	0.838177i	$0.316378\pi$
$54$		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	0.374572	−	0.927198i	$-0.377790\pi$
$61$	−2056.32	−	2056.32i	−0.552626	−	0.552626i	−0.927198	+	0.374572i	$0.877790\pi$
$62$		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	$-0.400321\pi$
$71$	3105.84			0.616115			0.308058	+	0.951368i	$0.400321\pi$
$72$		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	$0.0883036\pi$
$79$			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	−0.695281	−	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	−0.415850	−	0.909433i	$-0.636516\pi$
$101$	5035.04	−	5035.04i	0.493583	−	0.493583i	0.909433	+	0.415850i	$0.136516\pi$
$102$		0			0
$103$	−1427.24			−0.134531			−0.0672653	−	0.997735i	$-0.521427\pi$
$103$	−1427.24			−0.134531			−0.0672653	+	0.997735i	$0.521427\pi$
$104$		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	0.707506	−	0.706708i	$-0.249820\pi$
$109$	9.47842	+	9.47842i	0.000797780	+	0.000797780i	−0.706708	+	0.707506i	$0.749820\pi$
$110$		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	−0.0706991	−	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	−0.390378	−	0.920654i	$-0.627656\pi$
$149$	11772.7	−	11772.7i	0.530276	−	0.530276i	0.920654	+	0.390378i	$0.127656\pi$
$150$		0			0
$151$	19454.9			0.853246			0.426623	−	0.904429i	$-0.359703\pi$
$151$	19454.9			0.853246			0.426623	+	0.904429i	$0.359703\pi$
$152$		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	$-0.0762436\pi$
$157$	18097.5	+	18097.5i	0.734208	+	0.734208i	−0.237242	+	0.971450i	$0.576244\pi$
$158$		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	$-0.434633\pi$
$167$	11374.1			0.407834			0.203917	+	0.978988i	$0.434633\pi$
$168$		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	$-0.335941\pi$
$173$	−11289.3	−	11289.3i	−0.377204	−	0.377204i	−0.870092	+	0.492888i	$0.835941\pi$
$174$		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	−0.272833	−	0.962061i	$-0.587961\pi$
$181$	22579.8	−	22579.8i	0.689228	−	0.689228i	0.962061	+	0.272833i	$0.0879608\pi$
$182$		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	$-0.787605\pi$
$197$	−6468.96	+	6468.96i	−0.166687	+	0.166687i	0.618834	+	0.785521i	$0.287605\pi$
$198$		0			0
$199$	−55793.6			−1.40889			−0.704446	−	0.709757i	$-0.748805\pi$
$199$	−55793.6			−1.40889			−0.704446	+	0.709757i	$0.748805\pi$
$200$		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	$0.0488201\pi$
$223$			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	−0.997170	−	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	−0.542213	−	0.840241i	$-0.682413\pi$
$229$	15628.9	−	15628.9i	0.298028	−	0.298028i	0.840241	+	0.542213i	$0.182413\pi$
$230$		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	$-0.905759\pi$
$239$		−	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	0.999919	−	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	$-0.867993\pi$
$263$	−126611.			−1.83047			−0.915233	+	0.402926i	$0.867993\pi$
$264$		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	$-0.0291975\pi$
$269$	65428.7	+	65428.7i	0.904198	+	0.904198i	−0.0915982	+	0.995796i	$0.529198\pi$
$270$		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	0.514477	−	0.857504i	$-0.327986\pi$
$277$	105271.	−	105271.i	1.37198	−	1.37198i	0.857504	−	0.514477i	$-0.172014\pi$
$278$		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	−0.920085	−	0.391719i	$-0.871881\pi$
$293$	−45359.7	+	45359.7i	−0.528367	+	0.528367i	0.391719	+	0.920085i	$0.371881\pi$
$294$		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	$-0.677570\pi$
$311$	−102401.			−1.05873			−0.529365	+	0.848394i	$0.677570\pi$
$312$		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	0.654439	−	0.756115i	$-0.272905\pi$
$317$	−10217.2	−	10217.2i	−0.101675	−	0.101675i	−0.756115	+	0.654439i	$0.772905\pi$
$318$		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	0.0571205	−	0.998367i	$-0.481808\pi$
$349$	−114645.	−	114645.i	−0.941247	−	0.941247i	−0.998367	+	0.0571205i	$0.981808\pi$
$350$		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	$-0.426488\pi$
$359$	59001.0			0.457794			0.228897	+	0.973451i	$0.426488\pi$
$360$		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	$-0.946411\pi$
$373$	−113849.	+	113849.i	−0.818300	+	0.818300i	0.167562	+	0.985862i	$0.446411\pi$
$374$		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	$0.0882304\pi$
$383$			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	$-0.612692\pi$
$389$	89476.2	−	89476.2i	0.591301	−	0.591301i	0.937983	+	0.346682i	$0.112692\pi$
$390$		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	$-0.0538479\pi$
$397$	128824.	+	128824.i	0.817363	+	0.817363i	−0.168362	+	0.985725i	$0.553848\pi$
$398$		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	−0.646490	−	0.762923i	$-0.723764\pi$
$421$	20636.7	−	20636.7i	0.116433	−	0.116433i	0.762923	+	0.646490i	$0.223764\pi$
$422$		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	$-0.222949\pi$
$439$	294699.			1.52915			0.764574	+	0.644536i	$0.222949\pi$
$440$		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	0.897323	−	0.441374i	$-0.145509\pi$
$461$	96898.8	+	96898.8i	0.455950	+	0.455950i	−0.441374	+	0.897323i	$0.645509\pi$
$462$		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	−0.311877	−	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	$0.156603\pi$
$479$			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	$-0.600287\pi$
$487$	−146986.			−0.619752			−0.309876	+	0.950777i	$0.600287\pi$
$488$		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	$-0.598663\pi$
$503$	−154345.			−0.610037			−0.305018	+	0.952346i	$0.598663\pi$
$504$		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	$-0.256948\pi$
$509$	−7996.84	−	7996.84i	−0.0308662	−	0.0308662i	−0.722371	+	0.691505i	$0.756948\pi$
$510$		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	0.994556	−	0.104204i	$-0.0332294\pi$
$541$	260589.	+	260589.i	0.890352	+	0.890352i	−0.104204	+	0.994556i	$0.533229\pi$
$542$		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	$-0.965114\pi$
$557$	−342322.	−	342322.i	−1.10338	−	1.10338i	−0.109377	−	0.994000i	$-0.534886\pi$
$558$		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	$-0.406046\pi$
$599$	208748.			0.581795			0.290897	+	0.956754i	$0.406046\pi$
$600$		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	$0.374877\pi$
$607$			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	−0.450800	+	0.892625i	$0.648861\pi$
$613$	−504818.	+	504818.i	−1.34343	+	1.34343i	−0.892625	+	0.450800i	$0.851139\pi$
$614$		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	$-0.746696\pi$
$631$	−557209.			−1.39946			−0.699728	+	0.714409i	$0.746696\pi$
$632$		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	$-0.205198\pi$
$647$	669197.			1.59862			0.799311	+	0.600918i	$0.205198\pi$
$648$		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	$-0.246761\pi$
$653$	6136.50	+	6136.50i	0.0143911	+	0.0143911i	−0.699875	+	0.714266i	$0.746761\pi$
$654$		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	−0.783861	−	0.620937i	$-0.786752\pi$
$661$	−71185.1	+	71185.1i	−0.162924	+	0.162924i	0.620937	+	0.783861i	$0.286752\pi$
$662$		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	$-0.415576\pi$
$677$	562443.	−	562443.i	1.22716	−	1.22716i	0.965033	−	0.262127i	$-0.0844240\pi$
$678$		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	0.606819	−	0.794840i	$-0.292445\pi$
$701$	−92393.5	−	92393.5i	−0.188021	−	0.188021i	−0.794840	+	0.606819i	$0.792445\pi$
$702$		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	$-0.736565\pi$
$709$	29997.3	−	29997.3i	0.0596746	−	0.0596746i	0.736314	+	0.676640i	$0.236565\pi$
$710$		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	$-0.511776\pi$
$727$	−39096.3			−0.0739719			−0.0369860	+	0.999316i	$0.511776\pi$
$728$		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	$-0.215191\pi$
$733$	82927.3	+	82927.3i	0.154344	+	0.154344i	−0.625711	+	0.780055i	$0.715191\pi$
$734$		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	$-0.333289\pi$
$743$	552181.			1.00024			0.500120	+	0.865956i	$0.333289\pi$
$744$		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	$-0.951143\pi$
$757$	−478701.	+	478701.i	−0.835357	+	0.835357i	0.152886	+	0.988244i	$0.451143\pi$
$758$		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	$-0.302955\pi$
$773$	833367.	−	833367.i	1.39469	−	1.39469i	0.814439	−	0.580250i	$-0.197045\pi$
$774$		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	0.746226	−	0.665693i	$-0.231864\pi$
$797$	51155.1	+	51155.1i	0.0805327	+	0.0805327i	−0.665693	+	0.746226i	$0.731864\pi$
$798$		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	$0.596089\pi$
$821$	−843960.	+	843960.i	−1.25209	+	1.25209i	−0.954781	+	0.297308i	$0.903911\pi$
$822$		0			0
$823$	562057.			0.829815			0.414907	−	0.909864i	$-0.363814\pi$
$823$	562057.			0.829815			0.414907	+	0.909864i	$0.363814\pi$
$824$		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	0.975645	−	0.219354i	$-0.0703949\pi$
$829$	519755.	+	519755.i	0.756291	+	0.756291i	−0.219354	+	0.975645i	$0.570395\pi$
$830$		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	$-0.428874\pi$
$839$	311968.			0.443186			0.221593	+	0.975139i	$0.428874\pi$
$840$		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	$-0.653738\pi$
$853$	306461.	−	306461.i	0.421190	−	0.421190i	0.885613	+	0.464424i	$0.153738\pi$
$854$		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	$0.207315\pi$
$863$			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	$-0.0892805\pi$
$877$	526163.	+	526163.i	0.684102	+	0.684102i	−0.276820	+	0.960922i	$0.589281\pi$
$878$		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	$-0.418479\pi$
$887$	398604.			0.506633			0.253317	+	0.967383i	$0.418479\pi$
$888$		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	$-0.822855\pi$
$911$		−	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	$-0.472370\pi$
$919$	146433.			0.173384			0.0866920	+	0.996235i	$0.472370\pi$
$920$		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	$-0.964929\pi$
$941$	−977475.	−	977475.i	−1.10389	−	1.10389i	−0.109954	−	0.993937i	$-0.535071\pi$
$942$		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	$-0.237587\pi$
$967$	1.37297e6			1.46828			0.734138	+	0.679001i	$0.237587\pi$
$968$		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	$-0.515305\pi$
$983$	−92886.2			−0.0961268			−0.0480634	+	0.998844i	$0.515305\pi$
$984$		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	$-0.839020\pi$
$997$	−388032.	+	388032.i	−0.390370	+	0.390370i	0.484449	+	0.874819i	$0.339020\pi$
$998$		0			0
$999$	−617028.			−0.618264

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.1	✓	14	4.3	odd	2
16.5.f.a.11.1	yes	14	16.5	even	4
64.5.f.a.15.2		14	16.11	odd	4	inner
64.5.f.a.47.2		14	1.1	even	1	trivial
128.5.f.a.31.6		14	16.3	odd	4
128.5.f.a.95.6		14	8.5	even	2
128.5.f.b.31.2		14	16.13	even	4
128.5.f.b.95.2		14	8.3	odd	2
144.5.m.a.19.7		14	12.11	even	2
144.5.m.a.91.7		14	48.5	odd	4
576.5.m.a.271.2		14	48.11	even	4
576.5.m.a.559.2		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	64.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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