LMFDB - Embedded newform 256.3.h.a.95.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,3,Mod(31,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("256.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	256.h (of order $8$, degree $4$, 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:	$6.97549476762$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			95.7
Character	$\chi$	$=$	256.95
Dual form			256.3.h.a.159.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10187 - 5.07436i) q^{3} +(-1.74699 - 4.21761i) q^{5} +(0.392379 + 0.392379i) q^{7} +(-14.9674 - 14.9674i) q^{9} +O(q^{10})$	\(q+(2.10187 - 5.07436i) q^{3} +(-1.74699 - 4.21761i) q^{5} +(0.392379 + 0.392379i) q^{7} +(-14.9674 - 14.9674i) q^{9} +(2.90924 + 7.02353i) q^{11} +(4.50555 - 10.8774i) q^{13} -25.0737 q^{15} +10.5402i q^{17} +(-1.88707 - 0.781651i) q^{19} +(2.81580 - 1.16634i) q^{21} +(0.445453 - 0.445453i) q^{23} +(2.94139 - 2.94139i) q^{25} +(-61.7400 + 25.5735i) q^{27} +(-0.741814 - 0.307270i) q^{29} +47.6947i q^{31} +41.7548 q^{33} +(0.969419 - 2.34038i) q^{35} +(-14.5080 - 35.0255i) q^{37} +(-45.7256 - 45.7256i) q^{39} +(-11.3365 - 11.3365i) q^{41} +(-14.6421 - 35.3493i) q^{43} +(-36.9787 + 89.2744i) q^{45} +80.5164 q^{47} -48.6921i q^{49} +(53.4849 + 22.1542i) q^{51} +(66.6128 - 27.5919i) q^{53} +(24.5401 - 24.5401i) q^{55} +(-7.93277 + 7.93277i) q^{57} +(65.0706 - 26.9531i) q^{59} +(-87.4322 - 36.2156i) q^{61} -11.7457i q^{63} -53.7476 q^{65} +(-7.12379 + 17.1984i) q^{67} +(-1.32411 - 3.19668i) q^{69} +(14.8103 + 14.8103i) q^{71} +(18.6720 + 18.6720i) q^{73} +(-8.74326 - 21.1081i) q^{75} +(-1.61436 + 3.89741i) q^{77} +36.2398 q^{79} +176.540i q^{81} +(27.0868 + 11.2197i) q^{83} +(44.4545 - 18.4137i) q^{85} +(-3.11840 + 3.11840i) q^{87} +(-56.4944 + 56.4944i) q^{89} +(6.03592 - 2.50016i) q^{91} +(242.020 + 100.248i) q^{93} +9.32448i q^{95} +158.579 q^{97} +(61.5800 - 148.667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	$ 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} - 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{19} + 4 q^{21} + 68 q^{23} - 4 q^{25} - 100 q^{27} + 4 q^{29} - 8 q^{33} + 92 q^{35} + 4 q^{37} - 188 q^{39} - 4 q^{41} + 92 q^{43} + 40 q^{45} + 8 q^{47} + 224 q^{51} + 164 q^{53} - 252 q^{55} - 4 q^{57} + 124 q^{59} + 68 q^{61} - 8 q^{65} - 164 q^{67} - 188 q^{69} + 260 q^{71} - 4 q^{73} - 488 q^{75} - 220 q^{77} + 520 q^{79} - 484 q^{83} - 96 q^{85} + 452 q^{87} - 4 q^{89} - 196 q^{91} - 32 q^{93} - 8 q^{97} + 216 q^{99}+O(q^{100}) $ 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 - 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^19 + 4 * q^21 + 68 * q^23 - 4 * q^25 - 100 * q^27 + 4 * q^29 - 8 * q^33 + 92 * q^35 + 4 * q^37 - 188 * q^39 - 4 * q^41 + 92 * q^43 + 40 * q^45 + 8 * q^47 + 224 * q^51 + 164 * q^53 - 252 * q^55 - 4 * q^57 + 124 * q^59 + 68 * q^61 - 8 * q^65 - 164 * q^67 - 188 * q^69 + 260 * q^71 - 4 * q^73 - 488 * q^75 - 220 * q^77 + 520 * q^79 - 484 * q^83 - 96 * q^85 + 452 * q^87 - 4 * q^89 - 196 * q^91 - 32 * q^93 - 8 * q^97 + 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$

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
$3$	2.10187	−	5.07436i	0.700624	−	1.69145i	−0.0215732	−	0.999767i	$-0.506867\pi$
$3$	2.10187	−	5.07436i	0.700624	−	1.69145i	0.722197	−	0.691688i	$-0.243133\pi$
$4$		0			0
$5$	−1.74699	−	4.21761i	−0.349399	−	0.843523i	−0.996691	−	0.0812812i	$-0.974099\pi$
$5$	−1.74699	−	4.21761i	−0.349399	−	0.843523i	0.647293	−	0.762242i	$-0.275901\pi$
$6$		0			0
$7$	0.392379	+	0.392379i	0.0560541	+	0.0560541i	0.734578	−	0.678524i	$-0.237380\pi$
$7$	0.392379	+	0.392379i	0.0560541	+	0.0560541i	−0.678524	+	0.734578i	$0.737380\pi$
$8$		0			0
$9$	−14.9674	−	14.9674i	−1.66304	−	1.66304i
$10$		0			0
$11$	2.90924	+	7.02353i	0.264477	+	0.638503i	0.999205	−	0.0398581i	$-0.0126906\pi$
$11$	2.90924	+	7.02353i	0.264477	+	0.638503i	−0.734729	+	0.678361i	$0.762691\pi$
$12$		0			0
$13$	4.50555	−	10.8774i	0.346581	−	0.836720i	−0.650438	−	0.759559i	$-0.725415\pi$
$13$	4.50555	−	10.8774i	0.346581	−	0.836720i	0.997019	−	0.0771604i	$-0.0245853\pi$
$14$		0			0
$15$	−25.0737			−1.67158
$16$		0			0
$17$			10.5402i			0.620012i	0.950735	+	0.310006i	$0.100331\pi$
$17$			10.5402i			0.620012i	−0.950735	+	0.310006i	$0.899669\pi$
$18$		0			0
$19$	−1.88707	−	0.781651i	−0.0993196	−	0.0411395i	0.332470	−	0.943114i	$-0.392118\pi$
$19$	−1.88707	−	0.781651i	−0.0993196	−	0.0411395i	−0.431790	+	0.901974i	$0.642118\pi$
$20$		0			0
$21$	2.81580	−	1.16634i	0.134086	−	0.0555401i
$22$		0			0
$23$	0.445453	−	0.445453i	0.0193675	−	0.0193675i	−0.697357	−	0.716724i	$-0.745641\pi$
$23$	0.445453	−	0.445453i	0.0193675	−	0.0193675i	0.716724	+	0.697357i	$0.245641\pi$
$24$		0			0
$25$	2.94139	−	2.94139i	0.117656	−	0.117656i
$26$		0			0
$27$	−61.7400	+	25.5735i	−2.28667	+	0.947168i
$28$		0			0
$29$	−0.741814	−	0.307270i	−0.0255798	−	0.0105955i	0.369857	−	0.929089i	$-0.379407\pi$
$29$	−0.741814	−	0.307270i	−0.0255798	−	0.0105955i	−0.395437	+	0.918493i	$0.629407\pi$
$30$		0			0
$31$			47.6947i			1.53854i	0.638924	+	0.769270i	$0.279380\pi$
$31$			47.6947i			1.53854i	−0.638924	+	0.769270i	$0.720620\pi$
$32$		0			0
$33$	41.7548			1.26530
$34$		0			0
$35$	0.969419	−	2.34038i	0.0276977	−	0.0668681i
$36$		0			0
$37$	−14.5080	−	35.0255i	−0.392109	−	0.946635i	−0.989480	−	0.144670i	$-0.953788\pi$
$37$	−14.5080	−	35.0255i	−0.392109	−	0.946635i	0.597371	−	0.801965i	$-0.296212\pi$
$38$		0			0
$39$	−45.7256	−	45.7256i	−1.17245	−	1.17245i
$40$		0			0
$41$	−11.3365	−	11.3365i	−0.276501	−	0.276501i	0.555209	−	0.831711i	$-0.312638\pi$
$41$	−11.3365	−	11.3365i	−0.276501	−	0.276501i	−0.831711	+	0.555209i	$0.812638\pi$
$42$		0			0
$43$	−14.6421	−	35.3493i	−0.340515	−	0.822076i	−0.997664	−	0.0683149i	$-0.978238\pi$
$43$	−14.6421	−	35.3493i	−0.340515	−	0.822076i	0.657149	−	0.753761i	$-0.271762\pi$
$44$		0			0
$45$	−36.9787	+	89.2744i	−0.821748	+	1.98388i
$46$		0			0
$47$	80.5164			1.71312			0.856558	−	0.516051i	$-0.172598\pi$
$47$	80.5164			1.71312			0.856558	+	0.516051i	$0.172598\pi$
$48$		0			0
$49$		−	48.6921i		−	0.993716i
$50$		0			0
$51$	53.4849	+	22.1542i	1.04872	+	0.434395i
$52$		0			0
$53$	66.6128	−	27.5919i	1.25685	−	0.520602i	0.347905	−	0.937530i	$-0.386893\pi$
$53$	66.6128	−	27.5919i	1.25685	−	0.520602i	0.908940	+	0.416927i	$0.136893\pi$
$54$		0			0
$55$	24.5401	−	24.5401i	0.446184	−	0.446184i
$56$		0			0
$57$	−7.93277	+	7.93277i	−0.139171	+	0.139171i
$58$		0			0
$59$	65.0706	−	26.9531i	1.10289	−	0.456833i	0.244408	−	0.969673i	$-0.421406\pi$
$59$	65.0706	−	26.9531i	1.10289	−	0.456833i	0.858484	+	0.512840i	$0.171406\pi$
$60$		0			0
$61$	−87.4322	−	36.2156i	−1.43331	−	0.593698i	−0.475147	−	0.879906i	$-0.657605\pi$
$61$	−87.4322	−	36.2156i	−1.43331	−	0.593698i	−0.958168	+	0.286208i	$0.907605\pi$
$62$		0			0
$63$		−	11.7457i		−	0.186440i
$64$		0			0
$65$	−53.7476			−0.826887
$66$		0			0
$67$	−7.12379	+	17.1984i	−0.106325	+	0.256692i	−0.968084	−	0.250627i	$-0.919363\pi$
$67$	−7.12379	+	17.1984i	−0.106325	+	0.256692i	0.861759	+	0.507319i	$0.169363\pi$
$68$		0			0
$69$	−1.32411	−	3.19668i	−0.0191900	−	0.0463287i
$70$		0			0
$71$	14.8103	+	14.8103i	0.208596	+	0.208596i	0.803671	−	0.595074i	$-0.202877\pi$
$71$	14.8103	+	14.8103i	0.208596	+	0.208596i	−0.595074	+	0.803671i	$0.702877\pi$
$72$		0			0
$73$	18.6720	+	18.6720i	0.255781	+	0.255781i	0.823336	−	0.567555i	$-0.192110\pi$
$73$	18.6720	+	18.6720i	0.255781	+	0.255781i	−0.567555	+	0.823336i	$0.692110\pi$
$74$		0			0
$75$	−8.74326	−	21.1081i	−0.116577	−	0.281441i
$76$		0			0
$77$	−1.61436	+	3.89741i	−0.0209657	+	0.0506157i
$78$		0			0
$79$	36.2398			0.458732			0.229366	−	0.973340i	$-0.426335\pi$
$79$	36.2398			0.458732			0.229366	+	0.973340i	$0.426335\pi$
$80$		0			0
$81$			176.540i			2.17951i
$82$		0			0
$83$	27.0868	+	11.2197i	0.326347	+	0.135177i	0.539841	−	0.841767i	$-0.318484\pi$
$83$	27.0868	+	11.2197i	0.326347	+	0.135177i	−0.213494	+	0.976944i	$0.568484\pi$
$84$		0			0
$85$	44.4545	−	18.4137i	0.522994	−	0.216631i
$86$		0			0
$87$	−3.11840	+	3.11840i	−0.0358436	+	0.0358436i
$88$		0			0
$89$	−56.4944	+	56.4944i	−0.634769	+	0.634769i	−0.949260	−	0.314491i	$-0.898166\pi$
$89$	−56.4944	+	56.4944i	−0.634769	+	0.634769i	0.314491	+	0.949260i	$0.398166\pi$
$90$		0			0
$91$	6.03592	−	2.50016i	0.0663288	−	0.0274743i
$92$		0			0
$93$	242.020	+	100.248i	2.60237	+	1.07794i
$94$		0			0
$95$			9.32448i			0.0981525i
$96$		0			0
$97$	158.579			1.63484			0.817419	−	0.576043i	$-0.195404\pi$
$97$	158.579			1.63484			0.817419	+	0.576043i	$0.195404\pi$
$98$		0			0
$99$	61.5800	−	148.667i	0.622021	−	1.50169i
$100$		0			0
$101$	53.8420	+	129.986i	0.533089	+	1.28699i	0.929468	+	0.368903i	$0.120267\pi$
$101$	53.8420	+	129.986i	0.533089	+	1.28699i	−0.396379	+	0.918087i	$0.629733\pi$
$102$		0			0
$103$	−9.94607	−	9.94607i	−0.0965638	−	0.0965638i	0.657175	−	0.753738i	$-0.271751\pi$
$103$	−9.94607	−	9.94607i	−0.0965638	−	0.0965638i	−0.753738	+	0.657175i	$0.771751\pi$
$104$		0			0
$105$	−9.83837	−	9.83837i	−0.0936987	−	0.0936987i
$106$		0			0
$107$	68.8129	+	166.129i	0.643111	+	1.55261i	0.822461	+	0.568822i	$0.192601\pi$
$107$	68.8129	+	166.129i	0.643111	+	1.55261i	−0.179350	+	0.983785i	$0.557399\pi$
$108$		0			0
$109$	−3.61301	+	8.72257i	−0.0331469	+	0.0800236i	−0.939586	−	0.342313i	$-0.888790\pi$
$109$	−3.61301	+	8.72257i	−0.0331469	+	0.0800236i	0.906439	+	0.422336i	$0.138790\pi$
$110$		0			0
$111$	−208.226			−1.87591
$112$		0			0
$113$		−	85.8345i		−	0.759598i	−0.925069	−	0.379799i	$-0.875993\pi$
$113$		−	85.8345i		−	0.759598i	0.925069	−	0.379799i	$-0.124007\pi$
$114$		0			0
$115$	−2.65695	−	1.10055i	−0.0231039	−	0.00956997i
$116$		0			0
$117$	−230.241	+	95.3691i	−1.96788	+	0.815121i
$118$		0			0
$119$	−4.13575	+	4.13575i	−0.0347542	+	0.0347542i
$120$		0			0
$121$	44.6936	−	44.6936i	0.369369	−	0.369369i
$122$		0			0
$123$	−81.3537	+	33.6978i	−0.661412	+	0.273966i
$124$		0			0
$125$	−122.985	−	50.9419i	−0.983877	−	0.407535i
$126$		0			0
$127$			17.2873i			0.136120i	0.997681	+	0.0680601i	$0.0216810\pi$
$127$			17.2873i			0.136120i	−0.997681	+	0.0680601i	$0.978319\pi$
$128$		0			0
$129$	−210.151			−1.62908
$130$		0			0
$131$	−40.2223	+	97.1053i	−0.307041	+	0.741262i	0.692758	+	0.721171i	$0.256396\pi$
$131$	−40.2223	+	97.1053i	−0.307041	+	0.741262i	−0.999798	+	0.0200911i	$0.993604\pi$
$132$		0			0
$133$	−0.433744	−	1.04715i	−0.00326123	−	0.00787331i
$134$		0			0
$135$	215.719	+	215.719i	1.59792	+	1.59792i
$136$		0			0
$137$	25.5351	+	25.5351i	0.186387	+	0.186387i	0.794132	−	0.607745i	$-0.207926\pi$
$137$	25.5351	+	25.5351i	0.186387	+	0.186387i	−0.607745	+	0.794132i	$0.707926\pi$
$138$		0			0
$139$	−52.2202	−	126.071i	−0.375685	−	0.906984i	−0.992764	−	0.120083i	$-0.961684\pi$
$139$	−52.2202	−	126.071i	−0.375685	−	0.906984i	0.617079	−	0.786901i	$-0.288316\pi$
$140$		0			0
$141$	169.235	−	408.570i	1.20025	−	2.89766i
$142$		0			0
$143$	89.5052			0.625910
$144$		0			0
$145$			3.66548i			0.0252792i
$146$		0			0
$147$	−247.081	−	102.344i	−1.68083	−	0.696221i
$148$		0			0
$149$	−151.298	+	62.6697i	−1.01542	+	0.420602i	−0.827430	−	0.561569i	$-0.810198\pi$
$149$	−151.298	+	62.6697i	−1.01542	+	0.420602i	−0.187993	+	0.982170i	$0.560198\pi$
$150$		0			0
$151$	123.292	−	123.292i	0.816505	−	0.816505i	−0.169095	−	0.985600i	$-0.554084\pi$
$151$	123.292	−	123.292i	0.816505	−	0.816505i	0.985600	+	0.169095i	$0.0540845\pi$
$152$		0			0
$153$	157.759	−	157.759i	1.03111	−	1.03111i
$154$		0			0
$155$	201.158	−	83.3223i	1.29779	−	0.537563i
$156$		0			0
$157$	−107.069	−	44.3494i	−0.681968	−	0.282480i	0.0146813	−	0.999892i	$-0.495327\pi$
$157$	−107.069	−	44.3494i	−0.681968	−	0.282480i	−0.696649	+	0.717412i	$0.745327\pi$
$158$		0			0
$159$		−	396.012i		−	2.49064i
$160$		0			0
$161$	0.349573			0.00217126
$162$		0			0
$163$	−48.6441	+	117.437i	−0.298430	+	0.720474i	0.701539	+	0.712631i	$0.252497\pi$
$163$	−48.6441	+	117.437i	−0.298430	+	0.720474i	−0.999969	+	0.00784306i	$0.997503\pi$
$164$		0			0
$165$	−72.9453	−	176.106i	−0.442093	−	1.06731i
$166$		0			0
$167$	−88.6392	−	88.6392i	−0.530774	−	0.530774i	0.390029	−	0.920803i	$-0.372465\pi$
$167$	−88.6392	−	88.6392i	−0.530774	−	0.530774i	−0.920803	+	0.390029i	$0.872465\pi$
$168$		0			0
$169$	21.4841	+	21.4841i	0.127125	+	0.127125i
$170$		0			0
$171$	16.5452	+	39.9437i	0.0967558	+	0.233589i
$172$		0			0
$173$	−87.2836	+	210.721i	−0.504530	+	1.21804i	0.442463	+	0.896787i	$0.354105\pi$
$173$	−87.2836	+	210.721i	−0.504530	+	1.21804i	−0.946993	+	0.321255i	$0.895895\pi$
$174$		0			0
$175$	2.30827			0.0131901
$176$		0			0
$177$		−	386.844i		−	2.18556i
$178$		0			0
$179$	−5.53118	−	2.29109i	−0.0309005	−	0.0127994i	0.367180	−	0.930150i	$-0.380323\pi$
$179$	−5.53118	−	2.29109i	−0.0309005	−	0.0127994i	−0.398080	+	0.917351i	$0.630323\pi$
$180$		0			0
$181$	273.836	−	113.427i	1.51291	−	0.626666i	0.536751	−	0.843741i	$-0.319652\pi$
$181$	273.836	−	113.427i	1.51291	−	0.626666i	0.976155	+	0.217075i	$0.0696516\pi$
$182$		0			0
$183$	−367.542	+	367.542i	−2.00843	+	2.00843i
$184$		0			0
$185$	−122.379	+	122.379i	−0.661506	+	0.661506i
$186$		0			0
$187$	−74.0295	+	30.6640i	−0.395880	+	0.163979i
$188$		0			0
$189$	−34.2600	−	14.1909i	−0.181270	−	0.0750843i
$190$		0			0
$191$			140.503i			0.735620i	0.929901	+	0.367810i	$0.119892\pi$
$191$			140.503i			0.735620i	−0.929901	+	0.367810i	$0.880108\pi$
$192$		0			0
$193$	−159.719			−0.827560			−0.413780	−	0.910377i	$-0.635792\pi$
$193$	−159.719			−0.827560			−0.413780	+	0.910377i	$0.635792\pi$
$194$		0			0
$195$	−112.971	+	272.735i	−0.579336	+	1.39864i
$196$		0			0
$197$	23.3511	+	56.3745i	0.118533	+	0.286165i	0.971999	−	0.234984i	$-0.0755037\pi$
$197$	23.3511	+	56.3745i	0.118533	+	0.286165i	−0.853466	+	0.521149i	$0.825504\pi$
$198$		0			0
$199$	−138.741	−	138.741i	−0.697191	−	0.697191i	0.266613	−	0.963804i	$-0.414096\pi$
$199$	−138.741	−	138.741i	−0.697191	−	0.697191i	−0.963804	+	0.266613i	$0.914096\pi$
$200$		0			0
$201$	72.2974	+	72.2974i	0.359689	+	0.359689i
$202$		0			0
$203$	−0.170506	−	0.411638i	−0.000839931	−	0.00202777i
$204$		0			0
$205$	−28.0083	+	67.6180i	−0.136626	+	0.329844i
$206$		0			0
$207$	−13.3345			−0.0644180
$208$		0			0
$209$		−	15.5279i		−	0.0742963i
$210$		0			0
$211$	−194.276	−	80.4718i	−0.920740	−	0.381383i	−0.128582	−	0.991699i	$-0.541043\pi$
$211$	−194.276	−	80.4718i	−0.920740	−	0.381383i	−0.792158	+	0.610316i	$0.791043\pi$
$212$		0			0
$213$	106.283	−	44.0237i	0.498979	−	0.206684i
$214$		0			0
$215$	−123.510	+	123.510i	−0.574464	+	0.574464i
$216$		0			0
$217$	−18.7144	+	18.7144i	−0.0862414	+	0.0862414i
$218$		0			0
$219$	133.995	−	55.5025i	0.611849	−	0.253436i
$220$		0			0
$221$	114.650	+	47.4894i	0.518776	+	0.214884i
$222$		0			0
$223$			285.957i			1.28232i	0.767408	+	0.641160i	$0.221546\pi$
$223$			285.957i			1.28232i	−0.767408	+	0.641160i	$0.778454\pi$
$224$		0			0
$225$	−88.0496			−0.391332
$226$		0			0
$227$	8.02885	−	19.3834i	0.0353694	−	0.0853893i	−0.905208	−	0.424969i	$-0.860285\pi$
$227$	8.02885	−	19.3834i	0.0353694	−	0.0853893i	0.940577	+	0.339580i	$0.110285\pi$
$228$		0			0
$229$	66.9028	+	161.518i	0.292152	+	0.705317i	0.999999	−	0.00104819i	$-0.000333649\pi$
$229$	66.9028	+	161.518i	0.292152	+	0.705317i	−0.707848	+	0.706365i	$0.750334\pi$
$230$		0			0
$231$	16.3837	+	16.3837i	0.0709251	+	0.0709251i
$232$		0			0
$233$	282.286	+	282.286i	1.21153	+	1.21153i	0.970525	+	0.241001i	$0.0774758\pi$
$233$	282.286	+	282.286i	1.21153	+	1.21153i	0.241001	+	0.970525i	$0.422524\pi$
$234$		0			0
$235$	−140.662	−	339.587i	−0.598560	−	1.44505i
$236$		0			0
$237$	76.1714	−	183.894i	0.321398	−	0.775925i
$238$		0			0
$239$	−13.1618			−0.0550704			−0.0275352	−	0.999621i	$-0.508766\pi$
$239$	−13.1618			−0.0550704			−0.0275352	+	0.999621i	$0.508766\pi$
$240$		0			0
$241$			231.745i			0.961599i	0.876830	+	0.480800i	$0.159654\pi$
$241$			231.745i			0.961599i	−0.876830	+	0.480800i	$0.840346\pi$
$242$		0			0
$243$	340.169	+	140.903i	1.39987	+	0.579847i
$244$		0			0
$245$	−205.364	+	85.0647i	−0.838222	+	0.347203i
$246$		0			0
$247$	−17.0046	+	17.0046i	−0.0688445	+	0.0688445i
$248$		0			0
$249$	113.866	−	113.866i	0.457293	−	0.457293i
$250$		0			0
$251$	131.701	−	54.5521i	0.524703	−	0.217339i	−0.104578	−	0.994517i	$-0.533349\pi$
$251$	131.701	−	54.5521i	0.524703	−	0.217339i	0.629281	+	0.777177i	$0.283349\pi$
$252$		0			0
$253$	4.42459	+	1.83272i	0.0174885	+	0.00724397i
$254$		0			0
$255$		−	264.282i		−	1.03640i
$256$		0			0
$257$	−70.0955			−0.272745			−0.136373	−	0.990658i	$-0.543544\pi$
$257$	−70.0955			−0.272745			−0.136373	+	0.990658i	$0.543544\pi$
$258$		0			0
$259$	8.05061	−	19.4359i	0.0310834	−	0.0750420i
$260$		0			0
$261$	6.50399	+	15.7020i	0.0249195	+	0.0601610i
$262$		0			0
$263$	245.883	+	245.883i	0.934916	+	0.934916i	0.998008	−	0.0630921i	$-0.0200962\pi$
$263$	245.883	+	245.883i	0.934916	+	0.934916i	−0.0630921	+	0.998008i	$0.520096\pi$
$264$		0			0
$265$	−232.744	−	232.744i	−0.878280	−	0.878280i
$266$		0			0
$267$	167.929	+	405.417i	0.628949	+	1.51842i
$268$		0			0
$269$	−7.33716	+	17.7135i	−0.0272757	+	0.0658493i	−0.936931	−	0.349516i	$-0.886346\pi$
$269$	−7.33716	+	17.7135i	−0.0272757	+	0.0658493i	0.909655	+	0.415365i	$0.136346\pi$
$270$		0			0
$271$	−327.600			−1.20886			−0.604429	−	0.796659i	$-0.706599\pi$
$271$	−327.600			−1.20886			−0.604429	+	0.796659i	$0.706599\pi$
$272$		0			0
$273$		−	35.8835i		−	0.131441i
$274$		0			0
$275$	29.2161	+	12.1017i	0.106240	+	0.0440063i
$276$		0			0
$277$	31.9345	−	13.2277i	0.115287	−	0.0477535i	−0.324294	−	0.945956i	$-0.605127\pi$
$277$	31.9345	−	13.2277i	0.115287	−	0.0477535i	0.439581	+	0.898203i	$0.355127\pi$
$278$		0			0
$279$	713.864	−	713.864i	2.55865	−	2.55865i
$280$		0			0
$281$	−263.413	+	263.413i	−0.937413	+	0.937413i	−0.998154	−	0.0607409i	$-0.980654\pi$
$281$	−263.413	+	263.413i	−0.937413	+	0.937413i	0.0607409	+	0.998154i	$0.480654\pi$
$282$		0			0
$283$	−268.113	+	111.056i	−0.947397	+	0.392425i	−0.802252	−	0.596986i	$-0.796365\pi$
$283$	−268.113	+	111.056i	−0.947397	+	0.392425i	−0.145145	+	0.989410i	$0.546365\pi$
$284$		0			0
$285$	47.3158	+	19.5989i	0.166020	+	0.0687679i
$286$		0			0
$287$		−	8.89644i		−	0.0309980i
$288$		0			0
$289$	177.904			0.615585
$290$		0			0
$291$	333.313	−	804.689i	1.14541	−	2.76526i
$292$		0			0
$293$	−44.7772	−	108.102i	−0.152823	−	0.368948i	0.828863	−	0.559451i	$-0.188988\pi$
$293$	−44.7772	−	108.102i	−0.152823	−	0.368948i	−0.981687	+	0.190503i	$0.938988\pi$
$294$		0			0
$295$	−227.356	−	227.356i	−0.770698	−	0.770698i
$296$		0			0
$297$	−359.233	−	359.233i	−1.20954	−	1.20954i
$298$		0			0
$299$	−2.83834	−	6.85237i	−0.00949279	−	0.0229176i
$300$		0			0
$301$	8.12503	−	19.6155i	0.0269934	−	0.0651679i
$302$		0			0
$303$	772.765			2.55038
$304$		0			0
$305$			432.024i			1.41647i
$306$		0			0
$307$	430.497	+	178.318i	1.40227	+	0.580839i	0.950340	−	0.311215i	$-0.100736\pi$
$307$	430.497	+	178.318i	1.40227	+	0.580839i	0.451930	+	0.892054i	$0.350736\pi$
$308$		0			0
$309$	−71.3754	+	29.5646i	−0.230988	+	0.0956784i
$310$		0			0
$311$	61.3250	−	61.3250i	0.197187	−	0.197187i	−0.601606	−	0.798793i	$-0.705472\pi$
$311$	61.3250	−	61.3250i	0.197187	−	0.197187i	0.798793	+	0.601606i	$0.205472\pi$
$312$		0			0
$313$	129.308	−	129.308i	0.413124	−	0.413124i	−0.469701	−	0.882826i	$-0.655638\pi$
$313$	129.308	−	129.308i	0.413124	−	0.413124i	0.882826	+	0.469701i	$0.155638\pi$
$314$		0			0
$315$	−49.5390	+	20.5197i	−0.157267	+	0.0651420i
$316$		0			0
$317$	286.711	+	118.760i	0.904452	+	0.374636i	0.785930	−	0.618315i	$-0.212184\pi$
$317$	286.711	+	118.760i	0.904452	+	0.374636i	0.118522	+	0.992951i	$0.462184\pi$
$318$		0			0
$319$		−	6.10408i		−	0.0191350i
$320$		0			0
$321$	987.635			3.07674
$322$		0			0
$323$	8.23877	−	19.8901i	0.0255070	−	0.0615794i
$324$		0			0
$325$	−18.7420	−	45.2471i	−0.0576676	−	0.139222i
$326$		0			0
$327$	36.6674	+	36.6674i	0.112133	+	0.112133i
$328$		0			0
$329$	31.5929	+	31.5929i	0.0960271	+	0.0960271i
$330$		0			0
$331$	123.164	+	297.345i	0.372098	+	0.898324i	0.993395	+	0.114748i	$0.0366061\pi$
$331$	123.164	+	297.345i	0.372098	+	0.898324i	−0.621297	+	0.783575i	$0.713394\pi$
$332$		0			0
$333$	−307.092	+	741.386i	−0.922198	+	2.22638i
$334$		0			0
$335$	84.9812			0.253675
$336$		0			0
$337$			263.653i			0.782354i	0.920315	+	0.391177i	$0.127932\pi$
$337$			263.653i			0.782354i	−0.920315	+	0.391177i	$0.872068\pi$
$338$		0			0
$339$	−435.556	−	180.413i	−1.28483	−	0.532192i
$340$		0			0
$341$	−334.985	+	138.755i	−0.982362	+	0.406908i
$342$		0			0
$343$	38.3323	−	38.3323i	0.111756	−	0.111756i
$344$		0			0
$345$	−11.1691	+	11.1691i	−0.0323743	+	0.0323743i
$346$		0			0
$347$	−388.417	+	160.888i	−1.11936	+	0.463653i	−0.864151	−	0.503233i	$-0.832144\pi$
$347$	−388.417	+	160.888i	−1.11936	+	0.463653i	−0.255208	+	0.966886i	$0.582144\pi$
$348$		0			0
$349$	−448.277	−	185.683i	−1.28446	−	0.532042i	−0.367132	−	0.930169i	$-0.619660\pi$
$349$	−448.277	−	185.683i	−1.28446	−	0.532042i	−0.917330	+	0.398127i	$0.869660\pi$
$350$		0			0
$351$			786.791i			2.24157i
$352$		0			0
$353$	−106.951			−0.302976			−0.151488	−	0.988459i	$-0.548407\pi$
$353$	−106.951			−0.302976			−0.151488	+	0.988459i	$0.548407\pi$
$354$		0			0
$355$	36.5908	−	88.3379i	0.103073	−	0.248839i
$356$		0			0
$357$	12.2935	+	29.6791i	0.0344356	+	0.0831348i
$358$		0			0
$359$	208.761	+	208.761i	0.581508	+	0.581508i	0.935317	−	0.353810i	$-0.115114\pi$
$359$	208.761	+	208.761i	0.581508	+	0.581508i	−0.353810	+	0.935317i	$0.615114\pi$
$360$		0			0
$361$	−252.315	−	252.315i	−0.698935	−	0.698935i
$362$		0			0
$363$	−132.852	−	320.732i	−0.365982	−	0.883559i
$364$		0			0
$365$	46.1315	−	111.371i	0.126388	−	0.305127i
$366$		0			0
$367$	−711.002			−1.93734			−0.968668	−	0.248361i	$-0.920108\pi$
$367$	−711.002			−1.93734			−0.968668	+	0.248361i	$0.920108\pi$
$368$		0			0
$369$			339.356i			0.919665i
$370$		0			0
$371$	36.9639	+	15.3110i	0.0996332	+	0.0412694i
$372$		0			0
$373$	587.430	−	243.321i	1.57488	−	0.652336i	0.587287	−	0.809379i	$-0.300196\pi$
$373$	587.430	−	243.321i	1.57488	−	0.652336i	0.987592	+	0.157043i	$0.0501961\pi$
$374$		0			0
$375$	−516.995	+	516.995i	−1.37865	+	1.37865i
$376$		0			0
$377$	−6.68456	+	6.68456i	−0.0177309	+	0.0177309i
$378$		0			0
$379$	−34.5203	+	14.2988i	−0.0910825	+	0.0377276i	−0.427759	−	0.903893i	$-0.640697\pi$
$379$	−34.5203	+	14.2988i	−0.0910825	+	0.0377276i	0.336677	+	0.941620i	$0.390697\pi$
$380$		0			0
$381$	87.7220	+	36.3356i	0.230241	+	0.0953691i
$382$		0			0
$383$		−	347.623i		−	0.907631i	−0.891096	−	0.453815i	$-0.850063\pi$
$383$		−	347.623i		−	0.907631i	0.891096	−	0.453815i	$-0.149937\pi$
$384$		0			0
$385$	19.2580			0.0500209
$386$		0			0
$387$	−309.931	+	748.239i	−0.800855	+	1.93343i
$388$		0			0
$389$	60.7529	+	146.670i	0.156177	+	0.377045i	0.982529	−	0.186109i	$-0.0595878\pi$
$389$	60.7529	+	146.670i	0.156177	+	0.377045i	−0.826352	+	0.563154i	$0.809588\pi$
$390$		0			0
$391$	4.69517	+	4.69517i	0.0120081	+	0.0120081i
$392$		0			0
$393$	408.205	+	408.205i	1.03869	+	1.03869i
$394$		0			0
$395$	−63.3107	−	152.846i	−0.160280	−	0.386951i
$396$		0			0
$397$	−179.460	+	433.255i	−0.452041	+	1.09132i	0.519505	+	0.854468i	$0.326117\pi$
$397$	−179.460	+	433.255i	−0.452041	+	1.09132i	−0.971545	+	0.236855i	$0.923883\pi$
$398$		0			0
$399$	−6.22529			−0.0156022
$400$		0			0
$401$		−	680.550i		−	1.69713i	−0.529089	−	0.848566i	$-0.677466\pi$
$401$		−	680.550i		−	1.69713i	0.529089	−	0.848566i	$-0.322534\pi$
$402$		0			0
$403$	518.792	+	214.891i	1.28733	+	0.533228i
$404$		0			0
$405$	744.578	−	308.414i	1.83847	−	0.761517i
$406$		0			0
$407$	203.795	−	203.795i	0.500725	−	0.500725i
$408$		0			0
$409$	239.915	−	239.915i	0.586589	−	0.586589i	−0.350117	−	0.936706i	$-0.613858\pi$
$409$	239.915	−	239.915i	0.586589	−	0.586589i	0.936706	+	0.350117i	$0.113858\pi$
$410$		0			0
$411$	183.246	−	75.9028i	0.445853	−	0.184678i
$412$		0			0
$413$	36.1082	+	14.9565i	0.0874289	+	0.0362143i
$414$		0			0
$415$		−	133.843i		−	0.322512i
$416$		0			0
$417$	−749.489			−1.79734
$418$		0			0
$419$	33.5102	−	80.9009i	0.0799767	−	0.193081i	−0.878833	−	0.477129i	$-0.841678\pi$
$419$	33.5102	−	80.9009i	0.0799767	−	0.193081i	0.958810	+	0.284048i	$0.0916775\pi$
$420$		0			0
$421$	−37.2975	−	90.0441i	−0.0885926	−	0.213882i	0.873373	−	0.487052i	$-0.161928\pi$
$421$	−37.2975	−	90.0441i	−0.0885926	−	0.213882i	−0.961966	+	0.273170i	$0.911928\pi$
$422$		0			0
$423$	−1205.12	−	1205.12i	−2.84898	−	2.84898i
$424$		0			0
$425$	31.0028	+	31.0028i	0.0729479	+	0.0729479i
$426$		0			0
$427$	−20.0963	−	48.5167i	−0.0470639	−	0.113622i
$428$		0			0
$429$	188.128	−	454.182i	0.438527	−	1.05870i
$430$		0			0
$431$	509.094			1.18119			0.590596	−	0.806967i	$-0.298893\pi$
$431$	509.094			1.18119			0.590596	+	0.806967i	$0.298893\pi$
$432$		0			0
$433$			66.0083i			0.152444i	0.997091	+	0.0762220i	$0.0242858\pi$
$433$			66.0083i			0.152444i	−0.997091	+	0.0762220i	$0.975714\pi$
$434$		0			0
$435$	18.6000	+	7.70438i	0.0427586	+	0.0177112i
$436$		0			0
$437$	−1.18879	+	0.492414i	−0.00272035	+	0.00112681i
$438$		0			0
$439$	39.8501	−	39.8501i	0.0907747	−	0.0907747i	−0.660261	−	0.751036i	$-0.729554\pi$
$439$	39.8501	−	39.8501i	0.0907747	−	0.0907747i	0.751036	+	0.660261i	$0.229554\pi$
$440$		0			0
$441$	−728.792	+	728.792i	−1.65259	+	1.65259i
$442$		0			0
$443$	−193.778	+	80.2656i	−0.437423	+	0.181187i	−0.590517	−	0.807025i	$-0.701076\pi$
$443$	−193.778	+	80.2656i	−0.437423	+	0.181187i	0.153094	+	0.988212i	$0.451076\pi$
$444$		0			0
$445$	336.967	+	139.576i	0.757229	+	0.313655i
$446$		0			0
$447$			899.465i			2.01223i
$448$		0			0
$449$	124.217			0.276652			0.138326	−	0.990387i	$-0.455828\pi$
$449$	124.217			0.276652			0.138326	+	0.990387i	$0.455828\pi$
$450$		0			0
$451$	46.6418	−	112.603i	0.103419	−	0.249675i
$452$		0			0
$453$	−366.485	−	884.774i	−0.809019	−	1.95314i
$454$		0			0
$455$	−21.0894	−	21.0894i	−0.0463504	−	0.0463504i
$456$		0			0
$457$	−573.100	−	573.100i	−1.25405	−	1.25405i	−0.953889	−	0.300159i	$-0.902960\pi$
$457$	−573.100	−	573.100i	−1.25405	−	1.25405i	−0.300159	−	0.953889i	$-0.597040\pi$
$458$		0			0
$459$	−269.550	−	650.752i	−0.587256	−	1.41776i
$460$		0			0
$461$	86.0707	−	207.793i	0.186704	−	0.450744i	−0.802617	−	0.596495i	$-0.796560\pi$
$461$	86.0707	−	207.793i	0.186704	−	0.450744i	0.989321	+	0.145750i	$0.0465596\pi$
$462$		0			0
$463$	555.587			1.19997			0.599986	−	0.800010i	$-0.295173\pi$
$463$	555.587			1.19997			0.599986	+	0.800010i	$0.295173\pi$
$464$		0			0
$465$		−	1195.88i		−	2.57179i
$466$		0			0
$467$	−319.806	−	132.468i	−0.684809	−	0.283657i	0.0130269	−	0.999915i	$-0.495853\pi$
$467$	−319.806	−	132.468i	−0.684809	−	0.283657i	−0.697835	+	0.716258i	$0.745853\pi$
$468$		0			0
$469$	−9.54349	+	3.95304i	−0.0203486	+	0.00842866i
$470$		0			0
$471$	−450.090	+	450.090i	−0.955606	+	0.955606i
$472$		0			0
$473$	205.679	−	205.679i	0.434839	−	0.434839i
$474$		0			0
$475$	−7.84975	+	3.25147i	−0.0165258	+	0.00684521i
$476$		0			0
$477$	−1410.00	−	584.039i	−2.95597	−	1.22440i
$478$		0			0
$479$		−	239.576i		−	0.500159i	−0.968225	−	0.250079i	$-0.919543\pi$
$479$		−	239.576i		−	0.500159i	0.968225	−	0.250079i	$-0.0804567\pi$
$480$		0			0
$481$	−446.351			−0.927965
$482$		0			0
$483$	0.734757	−	1.77386i	0.00152124	−	0.00367259i
$484$		0			0
$485$	−277.037	−	668.826i	−0.571210	−	1.37902i
$486$		0			0
$487$	269.525	+	269.525i	0.553439	+	0.553439i	0.927432	−	0.373992i	$-0.122011\pi$
$487$	269.525	+	269.525i	0.553439	+	0.553439i	−0.373992	+	0.927432i	$0.622011\pi$
$488$		0			0
$489$	493.676	+	493.676i	1.00956	+	1.00956i
$490$		0			0
$491$	285.394	+	689.002i	0.581250	+	1.40326i	0.891680	+	0.452666i	$0.149527\pi$
$491$	285.394	+	689.002i	0.581250	+	1.40326i	−0.310430	+	0.950596i	$0.600473\pi$
$492$		0			0
$493$	3.23869	−	7.81888i	0.00656934	−	0.0158598i
$494$		0			0
$495$	−734.601			−1.48404
$496$		0			0
$497$			11.6225i			0.0233854i
$498$		0			0
$499$	581.267	+	240.769i	1.16486	+	0.482503i	0.879492	−	0.475914i	$-0.157883\pi$
$499$	581.267	+	240.769i	1.16486	+	0.482503i	0.285373	+	0.958417i	$0.407883\pi$
$500$		0			0
$501$	−636.096	+	263.479i	−1.26965	+	0.525907i
$502$		0			0
$503$	−204.189	+	204.189i	−0.405942	+	0.405942i	−0.880321	−	0.474379i	$-0.842673\pi$
$503$	−204.189	+	204.189i	−0.405942	+	0.405942i	0.474379	+	0.880321i	$0.342673\pi$
$504$		0			0
$505$	454.169	−	454.169i	0.899345	−	0.899345i
$506$		0			0
$507$	154.175	−	63.8615i	0.304093	−	0.125960i
$508$		0			0
$509$	397.562	+	164.676i	0.781066	+	0.323528i	0.737345	−	0.675516i	$-0.236079\pi$
$509$	397.562	+	164.676i	0.781066	+	0.323528i	0.0437202	+	0.999044i	$0.486079\pi$
$510$		0			0
$511$			14.6530i			0.0286751i
$512$		0			0
$513$	136.497			0.266077
$514$		0			0
$515$	−24.5730	+	59.3244i	−0.0477145	+	0.115193i
$516$		0			0
$517$	234.242	+	565.510i	0.453079	+	1.09383i
$518$		0			0
$519$	885.818	+	885.818i	1.70678	+	1.70678i
$520$		0			0
$521$	−333.835	−	333.835i	−0.640759	−	0.640759i	0.309983	−	0.950742i	$-0.399676\pi$
$521$	−333.835	−	333.835i	−0.640759	−	0.640759i	−0.950742	+	0.309983i	$0.899676\pi$
$522$		0			0
$523$	−211.672	−	511.022i	−0.404727	−	0.977097i	−0.986502	−	0.163748i	$-0.947642\pi$
$523$	−211.672	−	511.022i	−0.404727	−	0.977097i	0.581775	−	0.813350i	$-0.302358\pi$
$524$		0			0
$525$	4.85170	−	11.7130i	0.00924132	−	0.0223105i
$526$		0			0
$527$	−502.712			−0.953913
$528$		0			0
$529$			528.603i			0.999250i
$530$		0			0
$531$	−1377.35	−	570.518i	−2.59388	−	1.07442i
$532$		0			0
$533$	−174.389	+	72.2343i	−0.327184	+	0.135524i
$534$		0			0
$535$	580.452	−	580.452i	1.08496	−	1.08496i
$536$		0			0
$537$	−23.2517	+	23.2517i	−0.0432992	+	0.0432992i
$538$		0			0
$539$	341.990	−	141.657i	0.634490	−	0.262815i
$540$		0			0
$541$	529.582	+	219.360i	0.978896	+	0.405472i	0.814016	−	0.580842i	$-0.197277\pi$
$541$	529.582	+	219.360i	0.978896	+	0.405472i	0.164879	+	0.986314i	$0.447277\pi$
$542$		0			0
$543$		−	1627.95i		−	2.99807i
$544$		0			0
$545$	43.1003			0.0790832
$546$		0			0
$547$	−68.4960	+	165.364i	−0.125221	+	0.302311i	−0.974041	−	0.226371i	$-0.927314\pi$
$547$	−68.4960	+	165.364i	−0.125221	+	0.302311i	0.848820	+	0.528682i	$0.177314\pi$
$548$		0			0
$549$	766.577	+	1850.68i	1.39632	+	3.37100i
$550$		0			0
$551$	1.15968	+	1.15968i	0.00210468	+	0.00210468i
$552$		0			0
$553$	14.2197	+	14.2197i	0.0257138	+	0.0257138i
$554$		0			0
$555$	363.770	+	878.217i	0.655441	+	1.58237i
$556$		0			0
$557$	308.610	−	745.049i	0.554057	−	1.33761i	−0.360351	−	0.932817i	$-0.617343\pi$
$557$	308.610	−	745.049i	0.554057	−	1.33761i	0.914408	−	0.404794i	$-0.132657\pi$
$558$		0			0
$559$	−450.477			−0.805863
$560$		0			0
$561$			440.104i			0.784500i
$562$		0			0
$563$	−347.195	−	143.813i	−0.616687	−	0.255440i	0.0523978	−	0.998626i	$-0.483314\pi$
$563$	−347.195	−	143.813i	−0.616687	−	0.255440i	−0.669085	+	0.743186i	$0.733314\pi$
$564$		0			0
$565$	−362.017	+	149.952i	−0.640738	+	0.265402i
$566$		0			0
$567$	−69.2706	+	69.2706i	−0.122170	+	0.122170i
$568$		0			0
$569$	717.322	−	717.322i	1.26067	−	1.26067i	0.309903	−	0.950768i	$-0.399703\pi$
$569$	717.322	−	717.322i	1.26067	−	1.26067i	0.950768	−	0.309903i	$-0.100297\pi$
$570$		0			0
$571$	−327.041	+	135.465i	−0.572751	+	0.237241i	−0.650210	−	0.759754i	$-0.725319\pi$
$571$	−327.041	+	135.465i	−0.572751	+	0.237241i	0.0774591	+	0.996996i	$0.475319\pi$
$572$		0			0
$573$	712.966	+	295.320i	1.24427	+	0.515393i
$574$		0			0
$575$		−	2.62050i		−	0.00455740i
$576$		0			0
$577$	531.710			0.921507			0.460754	−	0.887528i	$-0.347579\pi$
$577$	531.710			0.921507			0.460754	+	0.887528i	$0.347579\pi$
$578$		0			0
$579$	−335.709	+	810.473i	−0.579808	+	1.39978i
$580$		0			0
$581$	6.22591	+	15.0307i	0.0107158	+	0.0258703i
$582$		0			0
$583$	387.585	+	387.585i	0.664812	+	0.664812i
$584$		0			0
$585$	804.460	+	804.460i	1.37515	+	1.37515i
$586$		0			0
$587$	105.581	+	254.894i	0.179865	+	0.434232i	0.987938	−	0.154850i	$-0.0494895\pi$
$587$	105.581	+	254.894i	0.179865	+	0.434232i	−0.808073	+	0.589082i	$0.799490\pi$
$588$		0			0
$589$	37.2806	−	90.0034i	0.0632948	−	0.152807i
$590$		0			0
$591$	335.145			0.567082
$592$		0			0
$593$			405.861i			0.684419i	0.939624	+	0.342210i	$0.111175\pi$
$593$			405.861i			0.684419i	−0.939624	+	0.342210i	$0.888825\pi$
$594$		0			0
$595$	24.6681	+	10.2179i	0.0414590	+	0.0171729i
$596$		0			0
$597$	−995.638	+	412.407i	−1.66774	+	0.690799i
$598$		0			0
$599$	−561.484	+	561.484i	−0.937370	+	0.937370i	−0.998151	−	0.0607815i	$-0.980641\pi$
$599$	−561.484	+	561.484i	−0.937370	+	0.937370i	0.0607815	+	0.998151i	$0.480641\pi$
$600$		0			0
$601$	−358.762	+	358.762i	−0.596941	+	0.596941i	−0.939497	−	0.342556i	$-0.888707\pi$
$601$	−358.762	+	358.762i	−0.596941	+	0.596941i	0.342556	+	0.939497i	$0.388707\pi$
$602$		0			0
$603$	364.038	−	150.790i	0.603712	−	0.250066i
$604$		0			0
$605$	−266.580	−	110.421i	−0.440628	−	0.182514i
$606$		0			0
$607$			571.923i			0.942213i	0.882076	+	0.471107i	$0.156145\pi$
$607$			571.923i			0.942213i	−0.882076	+	0.471107i	$0.843855\pi$
$608$		0			0
$609$	−2.44718			−0.00401836
$610$		0			0
$611$	362.771	−	875.806i	0.593733	−	1.43340i
$612$		0			0
$613$	−401.254	−	968.712i	−0.654574	−	1.58028i	−0.806068	−	0.591823i	$-0.798409\pi$
$613$	−401.254	−	968.712i	−0.654574	−	1.58028i	0.151494	−	0.988458i	$-0.451591\pi$
$614$		0			0
$615$	284.249	+	284.249i	0.462193	+	0.462193i
$616$		0			0
$617$	−151.870	−	151.870i	−0.246143	−	0.246143i	0.573242	−	0.819386i	$-0.305685\pi$
$617$	−151.870	−	151.870i	−0.246143	−	0.246143i	−0.819386	+	0.573242i	$0.805685\pi$
$618$		0			0
$619$	146.518	+	353.725i	0.236701	+	0.571446i	0.996938	−	0.0781999i	$-0.0249173\pi$
$619$	146.518	+	353.725i	0.236701	+	0.571446i	−0.760237	+	0.649646i	$0.774917\pi$
$620$		0			0
$621$	−16.1105	+	38.8941i	−0.0259428	+	0.0626314i
$622$		0			0
$623$	−44.3344			−0.0711628
$624$		0			0
$625$			503.703i			0.805924i
$626$		0			0
$627$	−78.7944	−	32.6377i	−0.125669	−	0.0520537i
$628$		0			0
$629$	369.176	−	152.918i	0.586925	−	0.243112i
$630$		0			0
$631$	682.535	−	682.535i	1.08167	−	1.08167i	0.0853189	−	0.996354i	$-0.472809\pi$
$631$	682.535	−	682.535i	1.08167	−	1.08167i	0.996354	−	0.0853189i	$-0.0271909\pi$
$632$		0			0
$633$	−816.687	+	816.687i	−1.29018	+	1.29018i
$634$		0			0
$635$	72.9111	−	30.2007i	0.114821	−	0.0475602i
$636$		0			0
$637$	−529.641	−	219.385i	−0.831462	−	0.344403i
$638$		0			0
$639$		−	443.344i		−	0.693808i
$640$		0			0
$641$	38.9310			0.0607348			0.0303674	−	0.999539i	$-0.490332\pi$
$641$	38.9310			0.0607348			0.0303674	+	0.999539i	$0.490332\pi$
$642$		0			0
$643$	318.631	−	769.243i	0.495538	−	1.19633i	−0.456326	−	0.889813i	$-0.650835\pi$
$643$	318.631	−	769.243i	0.495538	−	1.19633i	0.951864	−	0.306522i	$-0.0991652\pi$
$644$		0			0
$645$	367.132	+	886.335i	0.569197	+	1.37416i
$646$		0			0
$647$	157.445	+	157.445i	0.243346	+	0.243346i	0.818233	−	0.574887i	$-0.194954\pi$
$647$	157.445	+	157.445i	0.243346	+	0.243346i	−0.574887	+	0.818233i	$0.694954\pi$
$648$		0			0
$649$	378.612	+	378.612i	0.583378	+	0.583378i
$650$		0			0
$651$	55.6284	+	134.299i	0.0854507	+	0.206296i
$652$		0			0
$653$	15.6861	−	37.8696i	0.0240216	−	0.0579933i	−0.911414	−	0.411492i	$-0.865008\pi$
$653$	15.6861	−	37.8696i	0.0240216	−	0.0579933i	0.935435	+	0.353498i	$0.115008\pi$
$654$		0			0
$655$	479.821			0.732551
$656$		0			0
$657$		−	558.942i		−	0.850748i
$658$		0			0
$659$	187.169	+	77.5281i	0.284020	+	0.117645i	0.520146	−	0.854078i	$-0.325878\pi$
$659$	187.169	+	77.5281i	0.284020	+	0.117645i	−0.236125	+	0.971723i	$0.575878\pi$
$660$		0			0
$661$	−30.1818	+	12.5017i	−0.0456608	+	0.0189133i	−0.405397	−	0.914141i	$-0.632867\pi$
$661$	−30.1818	+	12.5017i	−0.0456608	+	0.0189133i	0.359736	+	0.933054i	$0.382867\pi$
$662$		0			0
$663$	481.957	−	481.957i	0.726934	−	0.726934i
$664$		0			0
$665$	−3.65873	+	3.65873i	−0.00550184	+	0.00550184i
$666$		0			0
$667$	−0.467318	+	0.193569i	−0.000700627	+	0.000290209i
$668$		0			0
$669$	1451.05	+	601.045i	2.16899	+	0.898423i
$670$		0			0
$671$		−	719.443i		−	1.07219i
$672$		0			0
$673$	−327.878			−0.487189			−0.243595	−	0.969877i	$-0.578327\pi$
$673$	−327.878			−0.487189			−0.243595	+	0.969877i	$0.578327\pi$
$674$		0			0
$675$	−106.380	+	256.823i	−0.157599	+	0.380479i
$676$		0			0
$677$	−117.661	−	284.058i	−0.173797	−	0.419583i	0.812846	−	0.582478i	$-0.197917\pi$
$677$	−117.661	−	284.058i	−0.173797	−	0.419583i	−0.986643	+	0.162895i	$0.947917\pi$
$678$		0			0
$679$	62.2231	+	62.2231i	0.0916393	+	0.0916393i
$680$		0			0
$681$	−81.4826	−	81.4826i	−0.119651	−	0.119651i
$682$		0			0
$683$	−324.811	−	784.162i	−0.475564	−	1.14811i	−0.961669	−	0.274213i	$-0.911583\pi$
$683$	−324.811	−	784.162i	−0.475564	−	1.14811i	0.486104	−	0.873901i	$-0.338417\pi$
$684$		0			0
$685$	63.0875	−	152.307i	0.0920985	−	0.222345i
$686$		0			0
$687$	960.220			1.39770
$688$		0			0
$689$		−	848.888i		−	1.23206i
$690$		0			0
$691$	826.286	+	342.259i	1.19578	+	0.495309i	0.889634	−	0.456674i	$-0.150959\pi$
$691$	826.286	+	342.259i	1.19578	+	0.495309i	0.306149	+	0.951984i	$0.400959\pi$
$692$		0			0
$693$	82.4966	−	34.1712i	0.119043	−	0.0493091i
$694$		0			0
$695$	−440.490	+	440.490i	−0.633798	+	0.633798i
$696$		0			0
$697$	119.490	−	119.490i	0.171434	−	0.171434i
$698$		0			0
$699$	2025.75	−	839.092i	2.89807	−	1.20042i
$700$		0			0
$701$	−430.597	−	178.359i	−0.614260	−	0.254435i	0.0537885	−	0.998552i	$-0.482870\pi$
$701$	−430.597	−	178.359i	−0.614260	−	0.254435i	−0.668049	+	0.744117i	$0.732870\pi$
$702$		0			0
$703$			77.4359i			0.110151i
$704$		0			0
$705$	−2018.84			−2.86361
$706$		0			0
$707$	−29.8773	+	72.1301i	−0.0422592	+	0.102023i
$708$		0			0
$709$	77.1066	+	186.152i	0.108754	+	0.262555i	0.968882	−	0.247523i	$-0.0796165\pi$
$709$	77.1066	+	186.152i	0.108754	+	0.262555i	−0.860128	+	0.510078i	$0.829616\pi$
$710$		0			0
$711$	−542.414	−	542.414i	−0.762889	−	0.762889i
$712$		0			0
$713$	21.2458	+	21.2458i	0.0297977	+	0.0297977i
$714$		0			0
$715$	−156.365	−	377.498i	−0.218692	−	0.527970i
$716$		0			0
$717$	−27.6645	+	66.7879i	−0.0385836	+	0.0931491i
$718$		0			0
$719$	−809.898			−1.12642			−0.563212	−	0.826313i	$-0.690434\pi$
$719$	−809.898			−1.12642			−0.563212	+	0.826313i	$0.690434\pi$
$720$		0			0
$721$		−	7.80525i		−	0.0108256i
$722$		0			0
$723$	1175.96	+	487.099i	1.62650	+	0.673719i
$724$		0			0
$725$	−3.08576	+	1.27817i	−0.00425623	+	0.00176299i
$726$		0			0
$727$	−542.456	+	542.456i	−0.746156	+	0.746156i	−0.973755	−	0.227599i	$-0.926913\pi$
$727$	−542.456	+	542.456i	−0.746156	+	0.746156i	0.227599	+	0.973755i	$0.426913\pi$
$728$		0			0
$729$	306.489	−	306.489i	0.420424	−	0.420424i
$730$		0			0
$731$	372.588	−	154.331i	0.509697	−	0.211123i
$732$		0			0
$733$	−562.276	−	232.903i	−0.767089	−	0.317739i	−0.0353965	−	0.999373i	$-0.511269\pi$
$733$	−562.276	−	232.903i	−0.767089	−	0.317739i	−0.731693	+	0.681635i	$0.761269\pi$
$734$		0			0
$735$			1220.89i			1.66107i
$736$		0			0
$737$	−141.518			−0.192019
$738$		0			0
$739$	−305.819	+	738.312i	−0.413828	+	0.999070i	0.570272	+	0.821456i	$0.306838\pi$
$739$	−305.819	+	738.312i	−0.413828	+	0.999070i	−0.984100	+	0.177614i	$0.943162\pi$
$740$		0			0
$741$	50.5461	+	122.029i	0.0682133	+	0.164681i
$742$		0			0
$743$	−581.334	−	581.334i	−0.782414	−	0.782414i	0.197823	−	0.980238i	$-0.436613\pi$
$743$	−581.334	−	581.334i	−0.782414	−	0.782414i	−0.980238	+	0.197823i	$0.936613\pi$
$744$		0			0
$745$	528.633	+	528.633i	0.709574	+	0.709574i
$746$		0			0
$747$	−237.488	−	573.348i	−0.317923	−	0.767534i
$748$		0			0
$749$	−38.1847	+	92.1861i	−0.0509810	+	0.123079i
$750$		0			0
$751$	187.901			0.250201			0.125100	−	0.992144i	$-0.460075\pi$
$751$	187.901			0.250201			0.125100	+	0.992144i	$0.460075\pi$
$752$		0			0
$753$		−	782.958i		−	1.03978i
$754$		0			0
$755$	−735.390	−	304.608i	−0.974026	−	0.403455i
$756$		0			0
$757$	168.645	−	69.8549i	0.222780	−	0.0922786i	−0.268502	−	0.963279i	$-0.586528\pi$
$757$	168.645	−	69.8549i	0.222780	−	0.0922786i	0.491282	+	0.871001i	$0.336528\pi$
$758$		0			0
$759$	18.5998	−	18.5998i	0.0245057	−	0.0245057i
$760$		0			0
$761$	391.406	−	391.406i	0.514331	−	0.514331i	−0.401520	−	0.915850i	$-0.631518\pi$
$761$	391.406	−	391.406i	0.514331	−	0.514331i	0.915850	+	0.401520i	$0.131518\pi$
$762$		0			0
$763$	−4.84022	+	2.00488i	−0.00634367	+	0.00262763i
$764$		0			0
$765$	−940.971	−	389.763i	−1.23003	−	0.509494i
$766$		0			0
$767$		−	829.235i		−	1.08114i
$768$		0			0
$769$	184.433			0.239835			0.119918	−	0.992784i	$-0.461737\pi$
$769$	184.433			0.239835			0.119918	+	0.992784i	$0.461737\pi$
$770$		0			0
$771$	−147.332	+	355.690i	−0.191092	+	0.461336i
$772$		0			0
$773$	140.532	+	339.275i	0.181801	+	0.438907i	0.988338	−	0.152277i	$-0.0486607\pi$
$773$	140.532	+	339.275i	0.181801	+	0.438907i	−0.806537	+	0.591184i	$0.798661\pi$
$774$		0			0
$775$	140.289	+	140.289i	0.181018	+	0.181018i
$776$		0			0
$777$	−81.7035	−	81.7035i	−0.105152	−	0.105152i
$778$		0			0
$779$	12.5317	+	30.2541i	0.0160869	+	0.0388371i
$780$		0			0
$781$	−60.9340	+	147.108i	−0.0780206	+	0.188358i
$782$		0			0
$783$	53.6576			0.0685282
$784$		0			0
$785$			529.054i			0.673954i
$786$		0			0
$787$	−926.743	−	383.870i	−1.17756	−	0.487763i	−0.293878	−	0.955843i	$-0.594946\pi$
$787$	−926.743	−	383.870i	−1.17756	−	0.487763i	−0.883686	+	0.468080i	$0.844946\pi$
$788$		0			0
$789$	1764.51	−	730.885i	2.23639	−	0.926344i
$790$		0			0
$791$	33.6796	−	33.6796i	0.0425785	−	0.0425785i
$792$		0			0
$793$	−787.860	+	787.860i	−0.993518	+	0.993518i
$794$		0			0
$795$	−1670.23	+	691.831i	−2.10091	+	0.870227i
$796$		0			0
$797$	871.860	+	361.136i	1.09393	+	0.453119i	0.855374	−	0.518010i	$-0.173327\pi$
$797$	871.860	+	361.136i	1.09393	+	0.453119i	0.238553	+	0.971130i	$0.423327\pi$
$798$		0			0
$799$			848.660i			1.06215i
$800$		0			0
$801$	1691.14			2.11129
$802$		0			0
$803$	−76.8221	+	185.465i	−0.0956689	+	0.230965i
$804$		0			0
$805$	−0.610701	−	1.47436i	−0.000758635	−	0.00183151i
$806$		0			0
$807$	74.4628	+	74.4628i	0.0922711	+	0.0922711i
$808$		0			0
$809$	744.003	+	744.003i	0.919658	+	0.919658i	0.997004	−	0.0773465i	$-0.0246448\pi$
$809$	744.003	+	744.003i	0.919658	+	0.919658i	−0.0773465	+	0.997004i	$0.524645\pi$
$810$		0			0
$811$	−307.315	−	741.925i	−0.378934	−	0.914827i	−0.992166	−	0.124924i	$-0.960131\pi$
$811$	−307.315	−	741.925i	−0.378934	−	0.914827i	0.613233	−	0.789902i	$-0.289869\pi$
$812$		0			0
$813$	−688.574	+	1662.36i	−0.846954	+	2.04473i
$814$		0			0
$815$	580.286			0.712007
$816$		0			0
$817$			78.1517i			0.0956569i
$818$		0			0
$819$	−127.763	−	52.9210i	−0.155998	−	0.0646166i
$820$		0			0
$821$	948.269	−	392.786i	1.15502	−	0.478424i	0.278804	−	0.960348i	$-0.410062\pi$
$821$	948.269	−	392.786i	1.15502	−	0.478424i	0.876213	+	0.481924i	$0.160062\pi$
$822$		0			0
$823$	−492.275	+	492.275i	−0.598147	+	0.598147i	−0.939819	−	0.341672i	$-0.889007\pi$
$823$	−492.275	+	492.275i	−0.598147	+	0.598147i	0.341672	+	0.939819i	$0.389007\pi$
$824$		0			0
$825$	122.817	−	122.817i	0.148869	−	0.148869i
$826$		0			0
$827$	−1350.77	+	559.506i	−1.63333	+	0.676549i	−0.995600	−	0.0937082i	$-0.970128\pi$
$827$	−1350.77	+	559.506i	−1.63333	+	0.676549i	−0.637734	+	0.770257i	$0.720128\pi$
$828$		0			0
$829$	−441.547	−	182.895i	−0.532627	−	0.220621i	0.100127	−	0.994975i	$-0.468075\pi$
$829$	−441.547	−	182.895i	−0.532627	−	0.220621i	−0.632753	+	0.774354i	$0.718075\pi$
$830$		0			0
$831$		−	189.850i		−	0.228460i
$832$		0			0
$833$	513.225			0.616116
$834$		0			0
$835$	−218.994	+	528.698i	−0.262268	+	0.633171i
$836$		0			0
$837$	−1219.72	−	2944.67i	−1.45726	−	3.51813i
$838$		0			0
$839$	−849.569	−	849.569i	−1.01260	−	1.01260i	−0.999920	−	0.0126775i	$-0.995965\pi$
$839$	−849.569	−	849.569i	−1.01260	−	1.01260i	−0.0126775	−	0.999920i	$-0.504035\pi$
$840$		0			0
$841$	−594.221	−	594.221i	−0.706565	−	0.706565i
$842$		0			0
$843$	782.994	+	1890.31i	0.928818	+	2.24236i
$844$		0			0
$845$	53.0792	−	128.144i	0.0628156	−	0.151650i
$846$		0			0
$847$	35.0736			0.0414093
$848$		0			0
$849$			1593.93i			1.87742i
$850$		0			0
$851$	−22.0649	−	9.13957i	−0.0259282	−	0.0107398i
$852$		0			0
$853$	−773.493	+	320.391i	−0.906791	+	0.375605i	−0.786827	−	0.617173i	$-0.788278\pi$
$853$	−773.493	+	320.391i	−0.906791	+	0.375605i	−0.119964	+	0.992778i	$0.538278\pi$
$854$		0			0
$855$	139.563	−	139.563i	0.163231	−	0.163231i
$856$		0			0
$857$	−259.040	+	259.040i	−0.302264	+	0.302264i	−0.841899	−	0.539635i	$-0.818562\pi$
$857$	−259.040	+	259.040i	−0.302264	+	0.302264i	0.539635	+	0.841899i	$0.318562\pi$
$858$		0			0
$859$	−762.123	+	315.682i	−0.887221	+	0.367499i	−0.779293	−	0.626660i	$-0.784422\pi$
$859$	−762.123	+	315.682i	−0.887221	+	0.367499i	−0.107928	+	0.994159i	$0.534422\pi$
$860$		0			0
$861$	−45.1438	−	18.6992i	−0.0524318	−	0.0217180i
$862$		0			0
$863$			1078.25i			1.24942i	0.780855	+	0.624712i	$0.214784\pi$
$863$			1078.25i			1.24942i	−0.780855	+	0.624712i	$0.785216\pi$
$864$		0			0
$865$	1041.22			1.20373
$866$		0			0
$867$	373.931	−	902.750i	0.431293	−	1.04123i
$868$		0			0
$869$	105.430	+	254.532i	0.121324	+	0.292902i
$870$		0			0
$871$	154.976	+	154.976i	0.177929	+	0.177929i
$872$		0			0
$873$	−2373.51	−	2373.51i	−2.71880	−	2.71880i
$874$		0			0
$875$	−28.2680	−	68.2450i	−0.0323063	−	0.0779943i
$876$		0			0
$877$	−387.984	+	936.676i	−0.442399	+	1.06805i	0.532706	+	0.846301i	$0.321175\pi$
$877$	−387.984	+	936.676i	−0.442399	+	1.06805i	−0.975105	+	0.221745i	$0.928825\pi$
$878$		0			0
$879$	−642.663			−0.731130
$880$		0			0
$881$		−	1281.50i		−	1.45460i	−0.686318	−	0.727301i	$-0.740774\pi$
$881$		−	1281.50i		−	1.45460i	0.686318	−	0.727301i	$-0.259226\pi$
$882$		0			0
$883$	−1014.19	−	420.092i	−1.14857	−	0.475755i	−0.274519	−	0.961582i	$-0.588519\pi$
$883$	−1014.19	−	420.092i	−1.14857	−	0.475755i	−0.874055	+	0.485826i	$0.838519\pi$
$884$		0			0
$885$	−1631.56	+	675.814i	−1.84357	+	0.763632i
$886$		0			0
$887$	57.0987	−	57.0987i	0.0643728	−	0.0643728i	−0.674187	−	0.738560i	$-0.735506\pi$
$887$	57.0987	−	57.0987i	0.0643728	−	0.0643728i	0.738560	+	0.674187i	$0.235506\pi$
$888$		0			0
$889$	−6.78316	+	6.78316i	−0.00763010	+	0.00763010i
$890$		0			0
$891$	−1239.94	+	513.598i	−1.39162	+	0.576429i
$892$		0			0
$893$	−151.940	−	62.9358i	−0.170146	−	0.0704768i
$894$		0			0
$895$			27.3309i			0.0305373i
$896$		0			0
$897$	−40.7372			−0.0454150
$898$		0			0
$899$	14.6551	−	35.3806i	0.0163016	−	0.0393555i
$900$		0			0
$901$	290.825	+	702.113i	0.322780	+	0.779260i
$902$		0			0
$903$	−82.4587	−	82.4587i	−0.0913164	−	0.0913164i
$904$		0			0
$905$	−956.779	−	956.779i	−1.05721	−	1.05721i
$906$		0			0
$907$	312.323	+	754.015i	0.344348	+	0.831329i	0.997266	+	0.0739002i	$0.0235446\pi$
$907$	312.323	+	754.015i	0.344348	+	0.831329i	−0.652918	+	0.757429i	$0.726455\pi$
$908$		0			0
$909$	1139.67	−	2751.42i	1.25377	−	3.02686i
$910$		0			0
$911$	−1374.15			−1.50840			−0.754201	−	0.656644i	$-0.771976\pi$
$911$	−1374.15			−1.50840			−0.754201	+	0.656644i	$0.771976\pi$
$912$		0			0
$913$			222.886i			0.244125i
$914$		0			0
$915$	2192.25	+	908.058i	2.39590	+	0.992413i
$916$		0			0
$917$	−53.8844	+	22.3196i	−0.0587616	+	0.0243399i
$918$		0			0
$919$	317.523	−	317.523i	0.345510	−	0.345510i	−0.512924	−	0.858434i	$-0.671438\pi$
$919$	317.523	−	317.523i	0.345510	−	0.345510i	0.858434	+	0.512924i	$0.171438\pi$
$920$		0			0
$921$	1809.70	−	1809.70i	1.96493	−	1.96493i
$922$		0			0
$923$	227.826	−	94.3687i	0.246832	−	0.102241i
$924$		0			0
$925$	−145.697	−	60.3498i	−0.157511	−	0.0652430i
$926$		0			0
$927$			297.733i			0.321179i
$928$		0			0
$929$	−46.9926			−0.0505841			−0.0252920	−	0.999680i	$-0.508052\pi$
$929$	−46.9926			−0.0505841			−0.0252920	+	0.999680i	$0.508052\pi$
$930$		0			0
$931$	−38.0602	+	91.8855i	−0.0408810	+	0.0986955i
$932$		0			0
$933$	−182.288	−	440.083i	−0.195379	−	0.471686i
$934$		0			0
$935$	258.658	+	258.658i	0.276640	+	0.276640i
$936$		0			0
$937$	381.311	+	381.311i	0.406949	+	0.406949i	0.880673	−	0.473724i	$-0.157091\pi$
$937$	381.311	+	381.311i	0.406949	+	0.406949i	−0.473724	+	0.880673i	$0.657091\pi$
$938$		0			0
$939$	−384.367	−	927.944i	−0.409337	−	0.988226i
$940$		0			0
$941$	−319.284	+	770.819i	−0.339303	+	0.819149i	0.658480	+	0.752598i	$0.271200\pi$
$941$	−319.284	+	770.819i	−0.339303	+	0.819149i	−0.997783	+	0.0665513i	$0.978800\pi$
$942$		0			0
$943$	−10.0998			−0.0107103
$944$		0			0
$945$			169.287i			0.179139i
$946$		0			0
$947$	−46.3711	−	19.2075i	−0.0489663	−	0.0202825i	0.358066	−	0.933696i	$-0.383436\pi$
$947$	−46.3711	−	19.2075i	−0.0489663	−	0.0202825i	−0.407032	+	0.913414i	$0.633436\pi$
$948$		0			0
$949$	287.230	−	118.975i	0.302666	−	0.125368i
$950$		0			0
$951$	1205.26	−	1205.26i	1.26736	−	1.26736i
$952$		0			0
$953$	−456.351	+	456.351i	−0.478858	+	0.478858i	−0.904766	−	0.425909i	$-0.859955\pi$
$953$	−456.351	+	456.351i	−0.478858	+	0.478858i	0.425909	+	0.904766i	$0.359955\pi$
$954$		0			0
$955$	592.589	−	245.459i	0.620512	−	0.257025i
$956$		0			0
$957$	−30.9743	−	12.8300i	−0.0323661	−	0.0134065i
$958$		0			0
$959$			20.0388i			0.0208955i
$960$		0			0
$961$	−1313.79			−1.36710
$962$		0			0
$963$	1456.56	−	3516.46i	1.51253	−	3.65157i
$964$		0			0
$965$	279.028	+	673.634i	0.289148	+	0.698066i
$966$		0			0
$967$	−476.069	−	476.069i	−0.492316	−	0.492316i	0.416719	−	0.909035i	$-0.363180\pi$
$967$	−476.069	−	476.069i	−0.492316	−	0.492316i	−0.909035	+	0.416719i	$0.863180\pi$
$968$		0			0
$969$	−83.6130	−	83.6130i	−0.0862879	−	0.0862879i
$970$		0			0
$971$	−502.303	−	1212.67i	−0.517305	−	1.24888i	−0.939553	−	0.342404i	$-0.888759\pi$
$971$	−502.303	−	1212.67i	−0.517305	−	1.24888i	0.422248	−	0.906480i	$-0.361241\pi$
$972$		0			0
$973$	28.9774	−	69.9576i	0.0297815	−	0.0718988i
$974$		0			0
$975$	−268.993			−0.275891
$976$		0			0
$977$			1.17535i			0.00120302i	1.00000		0.000601512i	$0.000191467\pi$
$977$			1.17535i			0.00120302i	−1.00000		0.000601512i	$0.999809\pi$
$978$		0			0
$979$	−561.146	−	232.434i	−0.573183	−	0.237420i
$980$		0			0
$981$	184.631	−	76.4767i	0.188207	−	0.0779579i
$982$		0			0
$983$	1006.98	−	1006.98i	1.02439	−	1.02439i	0.0246998	−	0.999695i	$-0.492137\pi$
$983$	1006.98	−	1006.98i	1.02439	−	1.02439i	0.999695	−	0.0246998i	$-0.00786298\pi$
$984$		0			0
$985$	196.972	−	196.972i	0.199971	−	0.199971i
$986$		0			0
$987$	226.718	−	93.9098i	0.229704	−	0.0951467i
$988$		0			0
$989$	−22.2688	−	9.22405i	−0.0225165	−	0.00932665i
$990$		0			0
$991$		−	1294.48i		−	1.30624i	−0.757256	−	0.653118i	$-0.773461\pi$
$991$		−	1294.48i		−	1.30624i	0.757256	−	0.653118i	$-0.226539\pi$
$992$		0			0
$993$	1767.71			1.78017
$994$		0			0
$995$	−342.777	+	827.536i	−0.344499	+	0.831694i
$996$		0			0
$997$	−82.2498	−	198.568i	−0.0824973	−	0.199166i	0.877248	−	0.480037i	$-0.159377\pi$
$997$	−82.2498	−	198.568i	−0.0824973	−	0.199166i	−0.959746	+	0.280871i	$0.909377\pi$
$998$		0			0
$999$	1791.45	+	1791.45i	1.79325	+	1.79325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.3.h.a.95.7		28
4.3	odd	2		256.3.h.b.95.1		28
8.3	odd	2		32.3.h.a.3.2	✓	28
8.5	even	2		128.3.h.a.47.1		28
24.11	even	2		288.3.u.a.163.6		28
32.5	even	8		32.3.h.a.11.2	yes	28
32.11	odd	8	inner	256.3.h.a.159.7		28
32.21	even	8		256.3.h.b.159.1		28
32.27	odd	8		128.3.h.a.79.1		28
96.5	odd	8		288.3.u.a.235.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.2	✓	28	8.3	odd	2
32.3.h.a.11.2	yes	28	32.5	even	8
128.3.h.a.47.1		28	8.5	even	2
128.3.h.a.79.1		28	32.27	odd	8
256.3.h.a.95.7		28	1.1	even	1	trivial
256.3.h.a.159.7		28	32.11	odd	8	inner
256.3.h.b.95.1		28	4.3	odd	2
256.3.h.b.159.1		28	32.21	even	8
288.3.u.a.163.6		28	24.11	even	2
288.3.u.a.235.6		28	96.5	odd	8

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	256.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.10187 - 5.07436i) q^{3} +(-1.74699 - 4.21761i) q^{5} +(0.392379 + 0.392379i) q^{7} +(-14.9674 - 14.9674i) q^{9} +O(q^{10})\)	\(q+(2.10187 - 5.07436i) q^{3} +(-1.74699 - 4.21761i) q^{5} +(0.392379 + 0.392379i) q^{7} +(-14.9674 - 14.9674i) q^{9} +(2.90924 + 7.02353i) q^{11} +(4.50555 - 10.8774i) q^{13} -25.0737 q^{15} +10.5402i q^{17} +(-1.88707 - 0.781651i) q^{19} +(2.81580 - 1.16634i) q^{21} +(0.445453 - 0.445453i) q^{23} +(2.94139 - 2.94139i) q^{25} +(-61.7400 + 25.5735i) q^{27} +(-0.741814 - 0.307270i) q^{29} +47.6947i q^{31} +41.7548 q^{33} +(0.969419 - 2.34038i) q^{35} +(-14.5080 - 35.0255i) q^{37} +(-45.7256 - 45.7256i) q^{39} +(-11.3365 - 11.3365i) q^{41} +(-14.6421 - 35.3493i) q^{43} +(-36.9787 + 89.2744i) q^{45} +80.5164 q^{47} -48.6921i q^{49} +(53.4849 + 22.1542i) q^{51} +(66.6128 - 27.5919i) q^{53} +(24.5401 - 24.5401i) q^{55} +(-7.93277 + 7.93277i) q^{57} +(65.0706 - 26.9531i) q^{59} +(-87.4322 - 36.2156i) q^{61} -11.7457i q^{63} -53.7476 q^{65} +(-7.12379 + 17.1984i) q^{67} +(-1.32411 - 3.19668i) q^{69} +(14.8103 + 14.8103i) q^{71} +(18.6720 + 18.6720i) q^{73} +(-8.74326 - 21.1081i) q^{75} +(-1.61436 + 3.89741i) q^{77} +36.2398 q^{79} +176.540i q^{81} +(27.0868 + 11.2197i) q^{83} +(44.4545 - 18.4137i) q^{85} +(-3.11840 + 3.11840i) q^{87} +(-56.4944 + 56.4944i) q^{89} +(6.03592 - 2.50016i) q^{91} +(242.020 + 100.248i) q^{93} +9.32448i q^{95} +158.579 q^{97} +(61.5800 - 148.667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	\( 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} - 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{19} + 4 q^{21} + 68 q^{23} - 4 q^{25} - 100 q^{27} + 4 q^{29} - 8 q^{33} + 92 q^{35} + 4 q^{37} - 188 q^{39} - 4 q^{41} + 92 q^{43} + 40 q^{45} + 8 q^{47} + 224 q^{51} + 164 q^{53} - 252 q^{55} - 4 q^{57} + 124 q^{59} + 68 q^{61} - 8 q^{65} - 164 q^{67} - 188 q^{69} + 260 q^{71} - 4 q^{73} - 488 q^{75} - 220 q^{77} + 520 q^{79} - 484 q^{83} - 96 q^{85} + 452 q^{87} - 4 q^{89} - 196 q^{91} - 32 q^{93} - 8 q^{97} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 - 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^19 + 4 * q^21 + 68 * q^23 - 4 * q^25 - 100 * q^27 + 4 * q^29 - 8 * q^33 + 92 * q^35 + 4 * q^37 - 188 * q^39 - 4 * q^41 + 92 * q^43 + 40 * q^45 + 8 * q^47 + 224 * q^51 + 164 * q^53 - 252 * q^55 - 4 * q^57 + 124 * q^59 + 68 * q^61 - 8 * q^65 - 164 * q^67 - 188 * q^69 + 260 * q^71 - 4 * q^73 - 488 * q^75 - 220 * q^77 + 520 * q^79 - 484 * q^83 - 96 * q^85 + 452 * q^87 - 4 * q^89 - 196 * q^91 - 32 * q^93 - 8 * q^97 + 216 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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