LMFDB - Embedded newform 128.5.f.a.95.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("128.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			95.6
Root			$2.24452 + 1.72109i$ of defining polynomial
Character	$\chi$	$=$	128.95
Dual form			128.5.f.a.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.54016 - 5.54016i) q^{3} +(-21.7374 + 21.7374i) q^{5} +6.62054 q^{7} +19.6133i q^{9} +O(q^{10})$	\(q+(5.54016 - 5.54016i) q^{3} +(-21.7374 + 21.7374i) q^{5} +6.62054 q^{7} +19.6133i q^{9} +(-90.9986 - 90.9986i) q^{11} +(-221.402 - 221.402i) q^{13} +240.857i q^{15} -132.575 q^{17} +(-402.520 + 402.520i) q^{19} +(36.6788 - 36.6788i) q^{21} -27.5037 q^{23} -320.028i q^{25} +(557.414 + 557.414i) q^{27} +(-174.909 - 174.909i) q^{29} +1083.96i q^{31} -1008.29 q^{33} +(-143.913 + 143.913i) q^{35} +(-553.474 + 553.474i) q^{37} -2453.20 q^{39} -1803.47i q^{41} +(17.8633 + 17.8633i) q^{43} +(-426.342 - 426.342i) q^{45} -2268.26i q^{47} -2357.17 q^{49} +(-734.489 + 734.489i) q^{51} +(822.415 - 822.415i) q^{53} +3956.14 q^{55} +4460.05i q^{57} +(-972.483 - 972.483i) q^{59} +(2056.32 + 2056.32i) q^{61} +129.851i q^{63} +9625.38 q^{65} +(4611.22 - 4611.22i) q^{67} +(-152.375 + 152.375i) q^{69} +3105.84 q^{71} +723.400i q^{73} +(-1773.00 - 1773.00i) q^{75} +(-602.460 - 602.460i) q^{77} +3418.44i q^{79} +4587.64 q^{81} +(-161.591 + 161.591i) q^{83} +(2881.84 - 2881.84i) q^{85} -1938.05 q^{87} -1464.04i q^{89} +(-1465.80 - 1465.80i) q^{91} +(6005.32 + 6005.32i) q^{93} -17499.5i q^{95} -8264.99 q^{97} +(1784.78 - 1784.78i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) $ 14 * q - 2 * q^3 + 2 * q^5 + 4 * q^7	$ 14 q - 2 q^{3} + 2 q^{5} + 4 q^{7} + 94 q^{11} + 2 q^{13} - 4 q^{17} - 706 q^{19} + 164 q^{21} - 1148 q^{23} - 1664 q^{27} - 862 q^{29} - 4 q^{33} + 1340 q^{35} + 1826 q^{37} - 2684 q^{39} + 1694 q^{43} - 1410 q^{45} + 682 q^{49} - 3012 q^{51} + 482 q^{53} + 11780 q^{55} - 2786 q^{59} + 3778 q^{61} - 2020 q^{65} + 7998 q^{67} - 9628 q^{69} - 19964 q^{71} + 17570 q^{75} + 9508 q^{77} + 1454 q^{81} - 17282 q^{83} - 9948 q^{85} + 49284 q^{87} - 28036 q^{91} - 8896 q^{93} - 4 q^{97} + 49214 q^{99}+O(q^{100}) $ 14 * q - 2 * q^3 + 2 * q^5 + 4 * q^7 + 94 * q^11 + 2 * q^13 - 4 * q^17 - 706 * q^19 + 164 * q^21 - 1148 * q^23 - 1664 * q^27 - 862 * q^29 - 4 * q^33 + 1340 * q^35 + 1826 * q^37 - 2684 * q^39 + 1694 * q^43 - 1410 * q^45 + 682 * q^49 - 3012 * q^51 + 482 * q^53 + 11780 * q^55 - 2786 * q^59 + 3778 * q^61 - 2020 * q^65 + 7998 * q^67 - 9628 * q^69 - 19964 * q^71 + 17570 * q^75 + 9508 * q^77 + 1454 * q^81 - 17282 * q^83 - 9948 * q^85 + 49284 * q^87 - 28036 * q^91 - 8896 * q^93 - 4 * q^97 + 49214 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	5.54016	−	5.54016i	0.615573	−	0.615573i	−0.328820	−	0.944393i	$-0.606651\pi$
$3$	5.54016	−	5.54016i	0.615573	−	0.615573i	0.944393	+	0.328820i	$0.106651\pi$
$4$		0			0
$5$	−21.7374	+	21.7374i	−0.869495	+	0.869495i	−0.992416	−	0.122921i	$-0.960774\pi$
$5$	−21.7374	+	21.7374i	−0.869495	+	0.869495i	0.122921	+	0.992416i	$0.460774\pi$
$6$		0			0
$7$	6.62054			0.135113			0.0675565	−	0.997715i	$-0.478480\pi$
$7$	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	0.222808	−	0.974862i	$-0.428478\pi$
$11$	−90.9986	−	90.9986i	−0.752054	−	0.752054i	−0.974862	+	0.222808i	$0.928478\pi$
$12$		0			0
$13$	−221.402	−	221.402i	−1.31007	−	1.31007i	−0.921362	−	0.388707i	$-0.872922\pi$
$13$	−221.402	−	221.402i	−1.31007	−	1.31007i	−0.388707	−	0.921362i	$-0.627078\pi$
$14$		0			0
$15$			240.857i			1.07048i
$16$		0			0
$17$	−132.575			−0.458738			−0.229369	−	0.973339i	$-0.573666\pi$
$17$	−132.575			−0.458738			−0.229369	+	0.973339i	$0.573666\pi$
$18$		0			0
$19$	−402.520	+	402.520i	−1.11501	+	1.11501i	−0.122552	+	0.992462i	$0.539108\pi$
$19$	−402.520	+	402.520i	−1.11501	+	1.11501i	−0.992462	+	0.122552i	$0.960892\pi$
$20$		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	0.595430	−	0.803407i	$-0.296982\pi$
$29$	−174.909	−	174.909i	−0.207978	−	0.207978i	−0.803407	+	0.595430i	$0.796982\pi$
$30$		0			0
$31$			1083.96i			1.12795i	0.825791	+	0.563976i	$0.190729\pi$
$31$			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	−0.879742	−	0.475451i	$-0.842285\pi$
$37$	−553.474	+	553.474i	−0.404291	+	0.404291i	0.475451	+	0.879742i	$0.342285\pi$
$38$		0			0
$39$	−2453.20			−1.61289
$40$		0			0
$41$		−	1803.47i		−	1.07285i	−0.843947	−	0.536427i	$-0.819774\pi$
$41$		−	1803.47i		−	1.07285i	0.843947	−	0.536427i	$-0.180226\pi$
$42$		0			0
$43$	17.8633	+	17.8633i	0.00966108	+	0.00966108i	0.711921	−	0.702260i	$-0.247825\pi$
$43$	17.8633	+	17.8633i	0.00966108	+	0.00966108i	−0.702260	+	0.711921i	$0.747825\pi$
$44$		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	−0.545398	−	0.838177i	$-0.683622\pi$
$53$	822.415	−	822.415i	0.292779	−	0.292779i	0.838177	+	0.545398i	$0.183622\pi$
$54$		0			0
$55$	3956.14			1.30782
$56$		0			0
$57$			4460.05i			1.37275i
$58$		0			0
$59$	−972.483	−	972.483i	−0.279369	−	0.279369i	0.553488	−	0.832857i	$-0.313296\pi$
$59$	−972.483	−	972.483i	−0.279369	−	0.279369i	−0.832857	+	0.553488i	$0.813296\pi$
$60$		0			0
$61$	2056.32	+	2056.32i	0.552626	+	0.552626i	0.927198	−	0.374572i	$-0.122210\pi$
$61$	2056.32	+	2056.32i	0.552626	+	0.552626i	−0.374572	+	0.927198i	$0.622210\pi$
$62$		0			0
$63$			129.851i			0.0327163i
$64$		0			0
$65$	9625.38			2.27820
$66$		0			0
$67$	4611.22	−	4611.22i	1.02723	−	1.02723i	0.0276077	−	0.999619i	$-0.491211\pi$
$67$	4611.22	−	4611.22i	1.02723	−	1.02723i	0.999619	−	0.0276077i	$-0.00878893\pi$
$68$		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	−0.718738	−	0.695281i	$-0.755280\pi$
$83$	−161.591	+	161.591i	−0.0234563	+	0.0234563i	0.695281	+	0.718738i	$0.255280\pi$
$84$		0			0
$85$	2881.84	−	2881.84i	0.398871	−	0.398871i
$86$		0			0
$87$	−1938.05			−0.256051
$88$		0			0
$89$		−	1464.04i		−	0.184830i	−0.995721	−	0.0924150i	$-0.970541\pi$
$89$		−	1464.04i		−	0.184830i	0.995721	−	0.0924150i	$-0.0294586\pi$
$90$		0			0
$91$	−1465.80	−	1465.80i	−0.177007	−	0.177007i
$92$		0			0
$93$	6005.32	+	6005.32i	0.694337	+	0.694337i
$94$		0			0
$95$		−	17499.5i		−	1.93900i
$96$		0			0
$97$	−8264.99			−0.878413			−0.439207	−	0.898386i	$-0.644740\pi$
$97$	−8264.99			−0.878413			−0.439207	+	0.898386i	$0.644740\pi$
$98$		0			0
$99$	1784.78	−	1784.78i	0.182102	−	0.182102i
$100$		0			0
$101$	−5035.04	+	5035.04i	−0.493583	+	0.493583i	−0.909433	−	0.415850i	$-0.863484\pi$
$101$	−5035.04	+	5035.04i	−0.493583	+	0.493583i	0.415850	+	0.909433i	$0.363484\pi$
$102$		0			0
$103$	−1427.24			−0.134531			−0.0672653	−	0.997735i	$-0.521427\pi$
$103$	−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	0.992643	−	0.121079i	$-0.0386355\pi$
$107$	9978.53	+	9978.53i	0.871564	+	0.871564i	−0.121079	+	0.992643i	$0.538635\pi$
$108$		0			0
$109$	−9.47842	−	9.47842i	−0.000797780	−	0.000797780i	0.706708	−	0.707506i	$-0.250180\pi$
$109$	−9.47842	−	9.47842i	−0.000797780	−	0.000797780i	−0.707506	+	0.706708i	$0.750180\pi$
$110$		0			0
$111$			6132.67i			0.497741i
$112$		0			0
$113$	−13634.7			−1.06780			−0.533900	−	0.845548i	$-0.679274\pi$
$113$	−13634.7			−1.06780			−0.533900	+	0.845548i	$0.679274\pi$
$114$		0			0
$115$	597.858	−	597.858i	0.0452067	−	0.0452067i
$116$		0			0
$117$	4342.42	−	4342.42i	0.317220	−	0.317220i
$118$		0			0
$119$	−877.721			−0.0619816
$120$		0			0
$121$			1920.47i			0.131171i
$122$		0			0
$123$	−9991.49	−	9991.49i	−0.660419	−	0.660419i
$124$		0			0
$125$	−6629.30	−	6629.30i	−0.424275	−	0.424275i
$126$		0			0
$127$			8047.14i			0.498923i	0.968385	+	0.249462i	$0.0802537\pi$
$127$			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	$-0.977477\pi$
$131$	−15904.8	+	15904.8i	−0.926799	+	0.926799i	0.0706991	+	0.997498i	$0.477477\pi$
$132$		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	$0.0370126\pi$
$139$	21432.1	+	21432.1i	1.10926	+	1.10926i	0.116017	+	0.993247i	$0.462987\pi$
$140$		0			0
$141$	−12566.5	−	12566.5i	−0.632088	−	0.632088i
$142$		0			0
$143$			40294.4i			1.97048i
$144$		0			0
$145$	7604.14			0.361671
$146$		0			0
$147$	−13059.1	+	13059.1i	−0.604335	+	0.604335i
$148$		0			0
$149$	−11772.7	+	11772.7i	−0.530276	+	0.530276i	−0.920654	−	0.390378i	$-0.872344\pi$
$149$	−11772.7	+	11772.7i	−0.530276	+	0.530276i	0.390378	+	0.920654i	$0.372344\pi$
$150$		0			0
$151$	19454.9			0.853246			0.426623	−	0.904429i	$-0.359703\pi$
$151$	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	0.237242	−	0.971450i	$-0.423756\pi$
$157$	−18097.5	−	18097.5i	−0.734208	−	0.734208i	−0.971450	+	0.237242i	$0.923756\pi$
$158$		0			0
$159$		−	9112.62i		−	0.360453i
$160$		0			0
$161$	−182.089			−0.00702478
$162$		0			0
$163$	17673.1	−	17673.1i	0.665178	−	0.665178i	−0.291418	−	0.956596i	$-0.594127\pi$
$163$	17673.1	−	17673.1i	0.665178	−	0.665178i	0.956596	+	0.291418i	$0.0941270\pi$
$164$		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	0.870092	−	0.492888i	$-0.164059\pi$
$173$	11289.3	+	11289.3i	0.377204	+	0.377204i	−0.492888	+	0.870092i	$0.664059\pi$
$174$		0			0
$175$		−	2118.76i		−	0.0691838i
$176$		0			0
$177$	−10775.4			−0.343944
$178$		0			0
$179$	−25338.8	+	25338.8i	−0.790825	+	0.790825i	−0.981628	−	0.190803i	$-0.938891\pi$
$179$	−25338.8	+	25338.8i	−0.790825	+	0.790825i	0.190803	+	0.981628i	$0.438891\pi$
$180$		0			0
$181$	−22579.8	+	22579.8i	−0.689228	+	0.689228i	−0.962061	−	0.272833i	$-0.912039\pi$
$181$	−22579.8	+	22579.8i	−0.689228	+	0.689228i	0.272833	+	0.962061i	$0.412039\pi$
$182$		0			0
$183$	22784.7			0.680363
$184$		0			0
$185$		−	24062.2i		−	0.703058i
$186$		0			0
$187$	12064.2	+	12064.2i	0.344996	+	0.344996i
$188$		0			0
$189$	3690.38	+	3690.38i	0.103311	+	0.103311i
$190$		0			0
$191$		−	62994.4i		−	1.72677i	−0.504543	−	0.863386i	$-0.668339\pi$
$191$		−	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	−0.618834	−	0.785521i	$-0.712395\pi$
$197$	6468.96	−	6468.96i	0.166687	−	0.166687i	0.785521	+	0.618834i	$0.212395\pi$
$198$		0			0
$199$	−55793.6			−1.40889			−0.704446	−	0.709757i	$-0.748805\pi$
$199$	−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	−0.823482	−	0.567343i	$-0.807971\pi$
$211$	−11403.6	+	11403.6i	−0.256139	+	0.256139i	0.567343	+	0.823482i	$0.307971\pi$
$212$		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	$-0.523954\pi$
$227$	47509.0	−	47509.0i	0.921986	−	0.921986i	0.997170	+	0.0751841i	$0.0239544\pi$
$228$		0			0
$229$	−15628.9	+	15628.9i	−0.298028	+	0.298028i	−0.840241	−	0.542213i	$-0.817587\pi$
$229$	−15628.9	+	15628.9i	−0.298028	+	0.298028i	0.542213	+	0.840241i	$0.317587\pi$
$230$		0			0
$231$	−6675.44			−0.125100
$232$		0			0
$233$			63151.2i			1.16324i	0.813460	+	0.581621i	$0.197581\pi$
$233$			63151.2i			1.16324i	−0.813460	+	0.581621i	$0.802419\pi$
$234$		0			0
$235$	49306.1	+	49306.1i	0.892823	+	0.892823i
$236$		0			0
$237$	18938.7	+	18938.7i	0.337173	+	0.337173i
$238$		0			0
$239$		−	33331.4i		−	0.583522i	−0.956491	−	0.291761i	$-0.905759\pi$
$239$		−	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	$-0.495953\pi$
$251$	−62195.0	−	62195.0i	−0.987206	−	0.987206i	−0.999919	+	0.0127130i	$0.995953\pi$
$252$		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	0.0915982	−	0.995796i	$-0.470802\pi$
$269$	−65428.7	−	65428.7i	−0.904198	−	0.904198i	−0.995796	+	0.0915982i	$0.970802\pi$
$270$		0			0
$271$			93429.2i			1.27217i	0.771621	+	0.636083i	$0.219446\pi$
$271$			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	$0.672014\pi$
$277$	−105271.	+	105271.i	−1.37198	+	1.37198i	−0.857504	+	0.514477i	$0.827986\pi$
$278$		0			0
$279$	−21260.1			−0.273122
$280$		0			0
$281$		−	42955.1i		−	0.544004i	−0.962297	−	0.272002i	$-0.912314\pi$
$281$		−	42955.1i		−	0.544004i	0.962297	−	0.272002i	$-0.0876857\pi$
$282$		0			0
$283$	−36538.7	−	36538.7i	−0.456226	−	0.456226i	0.441189	−	0.897414i	$-0.354557\pi$
$283$	−36538.7	−	36538.7i	−0.456226	−	0.456226i	−0.897414	+	0.441189i	$0.854557\pi$
$284$		0			0
$285$	−96949.8	−	96949.8i	−1.19360	−	1.19360i
$286$		0			0
$287$		−	11939.9i		−	0.144957i
$288$		0			0
$289$	−65944.8			−0.789559
$290$		0			0
$291$	−45789.3	+	45789.3i	−0.540727	+	0.540727i
$292$		0			0
$293$	45359.7	−	45359.7i	0.528367	−	0.528367i	−0.391719	−	0.920085i	$-0.628119\pi$
$293$	45359.7	−	45359.7i	0.528367	−	0.528367i	0.920085	+	0.391719i	$0.128119\pi$
$294$		0			0
$295$	42278.5			0.485820
$296$		0			0
$297$		−	101448.i		−	1.15008i
$298$		0			0
$299$	6089.36	+	6089.36i	0.0681129	+	0.0681129i
$300$		0			0
$301$	118.265	+	118.265i	0.00130534	+	0.00130534i
$302$		0			0
$303$			55789.9i			0.607673i
$304$		0			0
$305$	−89398.0			−0.961011
$306$		0			0
$307$	−10035.4	+	10035.4i	−0.106478	+	0.106478i	−0.758339	−	0.651861i	$-0.773989\pi$
$307$	−10035.4	+	10035.4i	−0.106478	+	0.106478i	0.651861	+	0.758339i	$0.273989\pi$
$308$		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	0.756115	−	0.654439i	$-0.227095\pi$
$317$	10217.2	+	10217.2i	0.101675	+	0.101675i	−0.654439	+	0.756115i	$0.727095\pi$
$318$		0			0
$319$			31833.0i			0.312821i
$320$		0			0
$321$	110565.			1.07302
$322$		0			0
$323$	53364.3	−	53364.3i	0.511500	−	0.511500i
$324$		0			0
$325$	−70854.6	+	70854.6i	−0.670813	+	0.670813i
$326$		0			0
$327$	−105.024			−0.000982183
$328$		0			0
$329$		−	15017.1i		−	0.138738i
$330$		0			0
$331$	123603.	+	123603.i	1.12817	+	1.12817i	0.990475	+	0.137692i	$0.0439684\pi$
$331$	123603.	+	123603.i	1.12817	+	1.12817i	0.137692	+	0.990475i	$0.456032\pi$
$332$		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	$-0.128679\pi$
$347$	63342.4	+	63342.4i	0.526061	+	0.526061i	−0.393335	+	0.919395i	$0.628679\pi$
$348$		0			0
$349$	114645.	+	114645.i	0.941247	+	0.941247i	0.998367	−	0.0571205i	$-0.0181919\pi$
$349$	114645.	+	114645.i	0.941247	+	0.941247i	−0.0571205	+	0.998367i	$0.518192\pi$
$350$		0			0
$351$		−	246824.i		−	2.00343i
$352$		0			0
$353$	−94430.7			−0.757816			−0.378908	−	0.925434i	$-0.623700\pi$
$353$	−94430.7			−0.757816			−0.378908	+	0.925434i	$0.623700\pi$
$354$		0			0
$355$	−67512.8	+	67512.8i	−0.535709	+	0.535709i
$356$		0			0
$357$	−4862.71	+	4862.71i	−0.0381542	+	0.0381542i
$358$		0			0
$359$	59001.0			0.457794			0.228897	−	0.973451i	$-0.426488\pi$
$359$	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	−0.167562	−	0.985862i	$-0.553589\pi$
$373$	113849.	−	113849.i	0.818300	−	0.818300i	0.985862	+	0.167562i	$0.0535894\pi$
$374$		0			0
$375$	−73454.7			−0.522345
$376$		0			0
$377$			77450.4i			0.544930i
$378$		0			0
$379$	−75841.4	−	75841.4i	−0.527993	−	0.527993i	0.391981	−	0.919973i	$-0.371790\pi$
$379$	−75841.4	−	75841.4i	−0.527993	−	0.527993i	−0.919973	+	0.391981i	$0.871790\pi$
$380$		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	−0.937983	−	0.346682i	$-0.887308\pi$
$389$	−89476.2	+	89476.2i	−0.591301	+	0.591301i	0.346682	+	0.937983i	$0.387308\pi$
$390$		0			0
$391$	3646.31			0.0238507
$392$		0			0
$393$			176230.i			1.14102i
$394$		0			0
$395$	−74307.8	−	74307.8i	−0.476256	−	0.476256i
$396$		0			0
$397$	−128824.	−	128824.i	−0.817363	−	0.817363i	0.168362	−	0.985725i	$-0.446152\pi$
$397$	−128824.	−	128824.i	−0.817363	−	0.817363i	−0.985725	+	0.168362i	$0.946152\pi$
$398$		0			0
$399$			29527.9i			0.185476i
$400$		0			0
$401$	71110.1			0.442224			0.221112	−	0.975248i	$-0.429031\pi$
$401$	71110.1			0.442224			0.221112	+	0.975248i	$0.429031\pi$
$402$		0			0
$403$	239991.	−	239991.i	1.47769	−	1.47769i
$404$		0			0
$405$	−99723.2	+	99723.2i	−0.607976	+	0.607976i
$406$		0			0
$407$	100731.			0.608097
$408$		0			0
$409$			87416.4i			0.522572i	0.965261	+	0.261286i	$0.0841466\pi$
$409$			87416.4i			0.522572i	−0.965261	+	0.261286i	$0.915853\pi$
$410$		0			0
$411$	−172683.	−	172683.i	−1.02227	−	1.02227i
$412$		0			0
$413$	−6438.36	−	6438.36i	−0.0377464	−	0.0377464i
$414$		0			0
$415$		−	7025.11i		−	0.0407903i
$416$		0			0
$417$	237474.			1.36567
$418$		0			0
$419$	156666.	−	156666.i	0.892373	−	0.892373i	−0.102373	−	0.994746i	$-0.532644\pi$
$419$	156666.	−	156666.i	0.892373	−	0.892373i	0.994746	+	0.102373i	$0.0326436\pi$
$420$		0			0
$421$	−20636.7	+	20636.7i	−0.116433	+	0.116433i	−0.762923	−	0.646490i	$-0.776236\pi$
$421$	−20636.7	+	20636.7i	−0.116433	+	0.116433i	0.646490	+	0.762923i	$0.276236\pi$
$422$		0			0
$423$	44488.2			0.248636
$424$		0			0
$425$			42427.8i			0.234894i
$426$		0			0
$427$	13614.0	+	13614.0i	0.0746670	+	0.0746670i
$428$		0			0
$429$	223238.	+	223238.i	1.21298	+	1.21298i
$430$		0			0
$431$		−	294349.i		−	1.58456i	−0.610160	−	0.792279i	$-0.708895\pi$
$431$		−	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	0.941948	−	0.335760i	$-0.108993\pi$
$443$	118964.	+	118964.i	0.606187	+	0.606187i	−0.335760	+	0.941948i	$0.608993\pi$
$444$		0			0
$445$	31824.4	+	31824.4i	0.160709	+	0.160709i
$446$		0			0
$447$			130445.i			0.652847i
$448$		0			0
$449$	−82129.5			−0.407386			−0.203693	−	0.979035i	$-0.565294\pi$
$449$	−82129.5			−0.407386			−0.203693	+	0.979035i	$0.565294\pi$
$450$		0			0
$451$	−164113.	+	164113.i	−0.806844	+	0.806844i
$452$		0			0
$453$	107783.	−	107783.i	0.525235	−	0.525235i
$454$		0			0
$455$	63725.2			0.307814
$456$		0			0
$457$			172358.i			0.825277i	0.910895	+	0.412638i	$0.135393\pi$
$457$			172358.i			0.825277i	−0.910895	+	0.412638i	$0.864607\pi$
$458$		0			0
$459$	−73899.3	−	73899.3i	−0.350764	−	0.350764i
$460$		0			0
$461$	−96898.8	−	96898.8i	−0.455950	−	0.455950i	0.441374	−	0.897323i	$-0.354491\pi$
$461$	−96898.8	−	96898.8i	−0.455950	−	0.455950i	−0.897323	+	0.441374i	$0.854491\pi$
$462$		0			0
$463$		−	142244.i		−	0.663549i	−0.943359	−	0.331775i	$-0.892353\pi$
$463$		−	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	$-0.899042\pi$
$467$	−139194.	+	139194.i	−0.638246	+	0.638246i	0.311877	+	0.950123i	$0.399042\pi$
$468$		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	0.131476	−	0.991319i	$-0.458028\pi$
$491$	−207292.	−	207292.i	−0.859843	−	0.859843i	−0.991319	+	0.131476i	$0.958028\pi$
$492$		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	$-0.744945\pi$
$499$	5591.76	−	5591.76i	0.0224568	−	0.0224568i	0.718246	+	0.695789i	$0.244945\pi$
$500$		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	0.722371	−	0.691505i	$-0.243052\pi$
$509$	7996.84	+	7996.84i	0.0308662	+	0.0308662i	−0.691505	+	0.722371i	$0.743052\pi$
$510$		0			0
$511$			4789.30i			0.0183413i
$512$		0			0
$513$	−448740.			−1.70514
$514$		0			0
$515$	31024.4	−	31024.4i	0.116974	−	0.116974i
$516$		0			0
$517$	−206409.	+	206409.i	−0.772231	+	0.772231i
$518$		0			0
$519$	125089.			0.464393
$520$		0			0
$521$		−	215831.i		−	0.795130i	−0.917574	−	0.397565i	$-0.869855\pi$
$521$		−	215831.i		−	0.795130i	0.917574	−	0.397565i	$-0.130145\pi$
$522$		0			0
$523$	−73690.2	−	73690.2i	−0.269405	−	0.269405i	0.559455	−	0.828861i	$-0.311010\pi$
$523$	−73690.2	−	73690.2i	−0.269405	−	0.269405i	−0.828861	+	0.559455i	$0.811010\pi$
$524$		0			0
$525$	−11738.2	−	11738.2i	−0.0425877	−	0.0425877i
$526$		0			0
$527$		−	143707.i		−	0.517435i
$528$		0			0
$529$	−279085.			−0.997297
$530$		0			0
$531$	19073.6	−	19073.6i	0.0676464	−	0.0676464i
$532$		0			0
$533$	−399290.	+	399290.i	−1.40551	+	1.40551i
$534$		0			0
$535$	−433814.			−1.51564
$536$		0			0
$537$			280762.i			0.973622i
$538$		0			0
$539$	214499.	+	214499.i	0.738325	+	0.738325i
$540$		0			0
$541$	−260589.	−	260589.i	−0.890352	−	0.890352i	0.104204	−	0.994556i	$-0.466771\pi$
$541$	−260589.	−	260589.i	−0.890352	−	0.890352i	−0.994556	+	0.104204i	$0.966771\pi$
$542$		0			0
$543$			250191.i			0.848540i
$544$		0			0
$545$	412.072			0.00138733
$546$		0			0
$547$	−87290.1	+	87290.1i	−0.291736	+	0.291736i	−0.837766	−	0.546030i	$-0.816139\pi$
$547$	−87290.1	+	87290.1i	−0.291736	+	0.291736i	0.546030	+	0.837766i	$0.316139\pi$
$548$		0			0
$549$	−40331.3	+	40331.3i	−0.133813	+	0.133813i
$550$		0			0
$551$	140809.			0.463796
$552$		0			0
$553$			22631.9i			0.0740066i
$554$		0			0
$555$	−133308.	−	133308.i	−0.432783	−	0.432783i
$556$		0			0
$557$	342322.	+	342322.i	1.10338	+	1.10338i	0.994000	+	0.109377i	$0.0348855\pi$
$557$	342322.	+	342322.i	1.10338	+	1.10338i	0.109377	+	0.994000i	$0.465114\pi$
$558$		0			0
$559$		−	7909.94i		−	0.0253134i
$560$		0			0
$561$	133675.			0.424741
$562$		0			0
$563$	−77521.3	+	77521.3i	−0.244571	+	0.244571i	−0.818738	−	0.574167i	$-0.805326\pi$
$563$	−77521.3	+	77521.3i	−0.244571	+	0.244571i	0.574167	+	0.818738i	$0.305326\pi$
$564$		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	0.200494	−	0.979695i	$-0.435745\pi$
$571$	−254051.	−	254051.i	−0.779201	−	0.779201i	−0.979695	+	0.200494i	$0.935745\pi$
$572$		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	$-0.267392\pi$
$587$	−26612.4	−	26612.4i	−0.0772339	−	0.0772339i	−0.744668	+	0.667435i	$0.767392\pi$
$588$		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	$-0.351139\pi$
$613$	504818.	−	504818.i	1.34343	−	1.34343i	0.892625	−	0.450800i	$-0.148861\pi$
$614$		0			0
$615$	434378.			1.14846
$616$		0			0
$617$			601668.i			1.58047i	0.612803	+	0.790236i	$0.290042\pi$
$617$			601668.i			1.58047i	−0.612803	+	0.790236i	$0.709958\pi$
$618$		0			0
$619$	−34687.6	−	34687.6i	−0.0905300	−	0.0905300i	0.660391	−	0.750922i	$-0.270390\pi$
$619$	−34687.6	−	34687.6i	−0.0905300	−	0.0905300i	−0.750922	+	0.660391i	$0.770390\pi$
$620$		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	−0.806606	−	0.591089i	$-0.798698\pi$
$643$	−89105.3	+	89105.3i	−0.215517	+	0.215517i	0.591089	+	0.806606i	$0.298698\pi$
$644$		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	0.699875	−	0.714266i	$-0.253239\pi$
$653$	−6136.50	−	6136.50i	−0.0143911	−	0.0143911i	−0.714266	+	0.699875i	$0.753239\pi$
$654$		0			0
$655$		−	691457.i		−	1.61169i
$656$		0			0
$657$	−14188.3			−0.0328700
$658$		0			0
$659$	484888.	−	484888.i	1.11653	−	1.11653i	0.124283	−	0.992247i	$-0.460337\pi$
$659$	484888.	−	484888.i	1.11653	−	1.11653i	0.992247	−	0.124283i	$-0.0396632\pi$
$660$		0			0
$661$	71185.1	−	71185.1i	0.162924	−	0.162924i	−0.620937	−	0.783861i	$-0.713248\pi$
$661$	71185.1	−	71185.1i	0.162924	−	0.162924i	0.783861	+	0.620937i	$0.213248\pi$
$662$		0			0
$663$	325234.			0.739892
$664$		0			0
$665$		−	115856.i		−	0.261984i
$666$		0			0
$667$	4810.65	+	4810.65i	0.0108131	+	0.0108131i
$668$		0			0
$669$	84179.5	+	84179.5i	0.188085	+	0.188085i
$670$		0			0
$671$		−	374244.i		−	0.831209i
$672$		0			0
$673$	116807.			0.257893			0.128947	−	0.991652i	$-0.458840\pi$
$673$	116807.			0.257893			0.128947	+	0.991652i	$0.458840\pi$
$674$		0			0
$675$	178388.	−	178388.i	0.391523	−	0.391523i
$676$		0			0
$677$	−562443.	+	562443.i	−1.22716	+	1.22716i	−0.262127	+	0.965033i	$0.584424\pi$
$677$	−562443.	+	562443.i	−1.22716	+	1.22716i	−0.965033	+	0.262127i	$0.915576\pi$
$678$		0			0
$679$	−54718.7			−0.118685
$680$		0			0
$681$		−	526415.i		−	1.13510i
$682$		0			0
$683$	392290.	+	392290.i	0.840941	+	0.840941i	0.988981	−	0.148040i	$-0.0472965\pi$
$683$	392290.	+	392290.i	0.840941	+	0.840941i	−0.148040	+	0.988981i	$0.547297\pi$
$684$		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	$-0.533478\pi$
$691$	424716.	−	424716.i	0.889493	−	0.889493i	0.994474	+	0.104981i	$0.0334781\pi$
$692$		0			0
$693$	11816.2	−	11816.2i	0.0246044	−	0.0246044i
$694$		0			0
$695$	−931755.			−1.92900
$696$		0			0
$697$			239095.i			0.492159i
$698$		0			0
$699$	349868.	+	349868.i	0.716060	+	0.716060i
$700$		0			0
$701$	92393.5	+	92393.5i	0.188021	+	0.188021i	0.794840	−	0.606819i	$-0.207555\pi$
$701$	92393.5	+	92393.5i	0.188021	+	0.188021i	−0.606819	+	0.794840i	$0.707555\pi$
$702$		0			0
$703$		−	445569.i		−	0.901580i
$704$		0			0
$705$	546327.			1.09920
$706$		0			0
$707$	−33334.7	+	33334.7i	−0.0666896	+	0.0666896i
$708$		0			0
$709$	−29997.3	+	29997.3i	−0.0596746	+	0.0596746i	−0.736314	−	0.676640i	$-0.763435\pi$
$709$	−29997.3	+	29997.3i	−0.0596746	+	0.0596746i	0.676640	+	0.736314i	$0.263435\pi$
$710$		0			0
$711$	−67046.9			−0.132629
$712$		0			0
$713$		−	29812.9i		−	0.0586443i
$714$		0			0
$715$	−875896.	−	875896.i	−1.71333	−	1.71333i
$716$		0			0
$717$	−184661.	−	184661.i	−0.359200	−	0.359200i
$718$		0			0
$719$		−	284133.i		−	0.549622i	−0.961498	−	0.274811i	$-0.911385\pi$
$719$		−	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	0.625711	−	0.780055i	$-0.284809\pi$
$733$	−82927.3	−	82927.3i	−0.154344	−	0.154344i	−0.780055	+	0.625711i	$0.784809\pi$
$734$		0			0
$735$		−	567741.i		−	1.05093i
$736$		0			0
$737$	−839229.			−1.54506
$738$		0			0
$739$	−97643.8	+	97643.8i	−0.178795	+	0.178795i	−0.790830	−	0.612035i	$-0.790351\pi$
$739$	−97643.8	+	97643.8i	−0.178795	+	0.178795i	0.612035	+	0.790830i	$0.290351\pi$
$740$		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	−0.152886	−	0.988244i	$-0.548857\pi$
$757$	478701.	−	478701.i	0.835357	−	0.835357i	0.988244	+	0.152886i	$0.0488569\pi$
$758$		0			0
$759$	27731.8			0.0481386
$760$		0			0
$761$			398315.i			0.687793i	0.939008	+	0.343896i	$0.111747\pi$
$761$			398315.i			0.687793i	−0.939008	+	0.343896i	$0.888253\pi$
$762$		0			0
$763$	−62.7523	−	62.7523i	−0.000107790	−	0.000107790i
$764$		0			0
$765$	56522.5	+	56522.5i	0.0965826	+	0.0965826i
$766$		0			0
$767$			430619.i			0.731985i
$768$		0			0
$769$	658868.			1.11416			0.557078	−	0.830460i	$-0.311922\pi$
$769$	658868.			1.11416			0.557078	+	0.830460i	$0.311922\pi$
$770$		0			0
$771$	126271.	−	126271.i	0.212419	−	0.212419i
$772$		0			0
$773$	−833367.	+	833367.i	−1.39469	+	1.39469i	−0.580250	+	0.814439i	$0.697045\pi$
$773$	−833367.	+	833367.i	−1.39469	+	1.39469i	−0.814439	+	0.580250i	$0.802955\pi$
$774$		0			0
$775$	346898.			0.577561
$776$		0			0
$777$			40601.6i			0.0672513i
$778$		0			0
$779$	725932.	+	725932.i	1.19625	+	1.19625i
$780$		0			0
$781$	−282627.	−	282627.i	−0.463352	−	0.463352i
$782$		0			0
$783$		−	194994.i		−	0.318051i
$784$		0			0
$785$	786784.			1.27678
$786$		0			0
$787$	−265518.	+	265518.i	−0.428691	+	0.428691i	−0.888182	−	0.459491i	$-0.848032\pi$
$787$	−265518.	+	265518.i	−0.428691	+	0.428691i	0.459491	+	0.888182i	$0.348032\pi$
$788$		0			0
$789$	−701447.	+	701447.i	−1.12679	+	1.12679i
$790$		0			0
$791$	−90269.3			−0.144274
$792$		0			0
$793$		−	910545.i		−	1.44795i
$794$		0			0
$795$	198084.	+	198084.i	0.313412	+	0.313412i
$796$		0			0
$797$	−51155.1	−	51155.1i	−0.0805327	−	0.0805327i	0.665693	−	0.746226i	$-0.268136\pi$
$797$	−51155.1	−	51155.1i	−0.0805327	−	0.0805327i	−0.746226	+	0.665693i	$0.768136\pi$
$798$		0			0
$799$			300716.i			0.471046i
$800$		0			0
$801$	28714.7			0.0447547
$802$		0			0
$803$	65828.4	−	65828.4i	0.102090	−	0.102090i
$804$		0			0
$805$	3958.14	−	3958.14i	0.00610801	−	0.00610801i
$806$		0			0
$807$	−724970.			−1.11320
$808$		0			0
$809$			608654.i			0.929979i	0.885316	+	0.464990i	$0.153942\pi$
$809$			608654.i			0.929979i	−0.885316	+	0.464990i	$0.846058\pi$
$810$		0			0
$811$	−693367.	−	693367.i	−1.05420	−	1.05420i	−0.998445	−	0.0557512i	$-0.982245\pi$
$811$	−693367.	−	693367.i	−1.05420	−	1.05420i	−0.0557512	−	0.998445i	$-0.517755\pi$
$812$		0			0
$813$	517612.	+	517612.i	0.783111	+	0.783111i
$814$		0			0
$815$			768335.i			1.15674i
$816$		0			0
$817$	−14380.7			−0.0215445
$818$		0			0
$819$	28749.2	−	28749.2i	0.0428605	−	0.0428605i
$820$		0			0
$821$	843960.	−	843960.i	1.25209	−	1.25209i	0.297308	−	0.954781i	$-0.403911\pi$
$821$	843960.	−	843960.i	1.25209	−	1.25209i	0.954781	−	0.297308i	$-0.0960890\pi$
$822$		0			0
$823$	562057.			0.829815			0.414907	−	0.909864i	$-0.363814\pi$
$823$	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	0.742214	−	0.670163i	$-0.233776\pi$
$827$	49278.3	+	49278.3i	0.0720518	+	0.0720518i	−0.670163	+	0.742214i	$0.733776\pi$
$828$		0			0
$829$	−519755.	−	519755.i	−0.756291	−	0.756291i	0.219354	−	0.975645i	$-0.429605\pi$
$829$	−519755.	−	519755.i	−0.756291	−	0.756291i	−0.975645	+	0.219354i	$0.929605\pi$
$830$		0			0
$831$			1.16643e6i			1.68911i
$832$		0			0
$833$	312503.			0.450364
$834$		0			0
$835$	−247243.	+	247243.i	−0.354610	+	0.354610i
$836$		0			0
$837$	−604215.	+	604215.i	−0.862464	+	0.862464i
$838$		0			0
$839$	311968.			0.443186			0.221593	−	0.975139i	$-0.428874\pi$
$839$	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	−0.885613	−	0.464424i	$-0.846262\pi$
$853$	−306461.	+	306461.i	−0.421190	+	0.421190i	0.464424	+	0.885613i	$0.346262\pi$
$854$		0			0
$855$	343223.			0.469509
$856$		0			0
$857$			16157.2i			0.0219991i	0.999940	+	0.0109995i	$0.00350133\pi$
$857$			16157.2i			0.0219991i	−0.999940	+	0.0109995i	$0.996499\pi$
$858$		0			0
$859$	74800.4	+	74800.4i	0.101372	+	0.101372i	0.755974	−	0.654602i	$-0.227164\pi$
$859$	74800.4	+	74800.4i	0.101372	+	0.101372i	−0.654602	+	0.755974i	$0.727164\pi$
$860$		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	0.276820	−	0.960922i	$-0.410719\pi$
$877$	−526163.	−	526163.i	−0.684102	−	0.684102i	−0.960922	+	0.276820i	$0.910719\pi$
$878$		0			0
$879$		−	502600.i		−	0.650496i
$880$		0			0
$881$	−1.39036e6			−1.79133			−0.895664	−	0.444732i	$-0.853299\pi$
$881$	−1.39036e6			−1.79133			−0.895664	+	0.444732i	$0.853299\pi$
$882$		0			0
$883$	−717884.	+	717884.i	−0.920731	+	0.920731i	−0.997081	−	0.0763499i	$-0.975673\pi$
$883$	−717884.	+	717884.i	−0.920731	+	0.920731i	0.0763499	+	0.997081i	$0.475673\pi$
$884$		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	$0.0562640\pi$
$907$	954485.	+	954485.i	1.16026	+	1.16026i	0.175840	+	0.984419i	$0.443736\pi$
$908$		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	$0.0350705\pi$
$941$	977475.	+	977475.i	1.10389	+	1.10389i	0.109954	+	0.993937i	$0.464929\pi$
$942$		0			0
$943$			49602.0i			0.0557796i
$944$		0			0
$945$	−160438.			−0.179657
$946$		0			0
$947$	573883.	−	573883.i	0.639917	−	0.639917i	−0.310618	−	0.950535i	$-0.600536\pi$
$947$	573883.	−	573883.i	0.639917	−	0.639917i	0.950535	+	0.310618i	$0.100536\pi$
$948$		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	0.444890	−	0.895585i	$-0.353243\pi$
$971$	−424934.	−	424934.i	−0.450696	−	0.450696i	−0.895585	+	0.444890i	$0.853243\pi$
$972$		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	−0.484449	−	0.874819i	$-0.660980\pi$
$997$	388032.	−	388032.i	0.390370	−	0.390370i	0.874819	+	0.484449i	$0.160980\pi$
$998$		0			0
$999$	−617028.			−0.618264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.f.a.95.6		14
4.3	odd	2		128.5.f.b.95.2		14
8.3	odd	2		16.5.f.a.3.1	✓	14
8.5	even	2		64.5.f.a.47.2		14
16.3	odd	4		64.5.f.a.15.2		14
16.5	even	4		128.5.f.b.31.2		14
16.11	odd	4	inner	128.5.f.a.31.6		14
16.13	even	4		16.5.f.a.11.1	yes	14
24.5	odd	2		576.5.m.a.559.2		14
24.11	even	2		144.5.m.a.19.7		14
48.29	odd	4		144.5.m.a.91.7		14
48.35	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	8.3	odd	2
16.5.f.a.11.1	yes	14	16.13	even	4
64.5.f.a.15.2		14	16.3	odd	4
64.5.f.a.47.2		14	8.5	even	2
128.5.f.a.31.6		14	16.11	odd	4	inner
128.5.f.a.95.6		14	1.1	even	1	trivial
128.5.f.b.31.2		14	16.5	even	4
128.5.f.b.95.2		14	4.3	odd	2
144.5.m.a.19.7		14	24.11	even	2
144.5.m.a.91.7		14	48.29	odd	4
576.5.m.a.271.2		14	48.35	even	4
576.5.m.a.559.2		14	24.5	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
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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