LMFDB - Embedded newform 256.3.h.a.95.2

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			95.2
Character	$\chi$	$=$	256.95
Dual form			256.3.h.a.159.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31872 + 3.18367i) q^{3} +(0.659338 + 1.59178i) q^{5} +(-9.54718 - 9.54718i) q^{7} +(-2.03276 - 2.03276i) q^{9} +O(q^{10})$	\(q+(-1.31872 + 3.18367i) q^{3} +(0.659338 + 1.59178i) q^{5} +(-9.54718 - 9.54718i) q^{7} +(-2.03276 - 2.03276i) q^{9} +(-3.96481 - 9.57189i) q^{11} +(-1.91784 + 4.63007i) q^{13} -5.93719 q^{15} -15.3143i q^{17} +(0.827335 + 0.342693i) q^{19} +(42.9851 - 17.8050i) q^{21} +(12.9230 - 12.9230i) q^{23} +(15.5786 - 15.5786i) q^{25} +(-19.5007 + 8.07746i) q^{27} +(-23.7905 - 9.85436i) q^{29} +25.1562i q^{31} +35.7022 q^{33} +(8.90221 - 21.4918i) q^{35} +(-13.6161 - 32.8721i) q^{37} +(-12.2115 - 12.2115i) q^{39} +(-32.9116 - 32.9116i) q^{41} +(-17.9473 - 43.3286i) q^{43} +(1.89544 - 4.57600i) q^{45} -20.1127 q^{47} +133.297i q^{49} +(48.7557 + 20.1953i) q^{51} +(-35.0503 + 14.5183i) q^{53} +(12.6222 - 12.6222i) q^{55} +(-2.18204 + 2.18204i) q^{57} +(-60.6706 + 25.1306i) q^{59} +(27.9825 + 11.5907i) q^{61} +38.8143i q^{63} -8.63457 q^{65} +(1.13412 - 2.73801i) q^{67} +(24.1008 + 58.1845i) q^{69} +(45.6144 + 45.6144i) q^{71} +(-29.1727 - 29.1727i) q^{73} +(29.0534 + 70.1410i) q^{75} +(-53.5318 + 129.237i) q^{77} -3.27983 q^{79} -98.6086i q^{81} +(56.7834 + 23.5205i) q^{83} +(24.3770 - 10.0973i) q^{85} +(62.7460 - 62.7460i) q^{87} +(-44.5059 + 44.5059i) q^{89} +(62.5140 - 25.8942i) q^{91} +(-80.0891 - 33.1740i) q^{93} +1.54289i q^{95} -106.417 q^{97} +(-11.3979 + 27.5169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.31872	+	3.18367i	−0.439573	+	1.06122i	0.536524	+	0.843885i	$0.319737\pi$
$3$	−1.31872	+	3.18367i	−0.439573	+	1.06122i	−0.976097	+	0.217337i	$0.930263\pi$
$4$		0			0
$5$	0.659338	+	1.59178i	0.131868	+	0.318356i	0.975997	−	0.217782i	$-0.0698823\pi$
$5$	0.659338	+	1.59178i	0.131868	+	0.318356i	−0.844130	+	0.536139i	$0.819882\pi$
$6$		0			0
$7$	−9.54718	−	9.54718i	−1.36388	−	1.36388i	−0.868907	−	0.494975i	$-0.835177\pi$
$7$	−9.54718	−	9.54718i	−1.36388	−	1.36388i	−0.494975	−	0.868907i	$-0.664823\pi$
$8$		0			0
$9$	−2.03276	−	2.03276i	−0.225863	−	0.225863i
$10$		0			0
$11$	−3.96481	−	9.57189i	−0.360437	−	0.870172i	−0.995236	−	0.0974947i	$-0.968917\pi$
$11$	−3.96481	−	9.57189i	−0.360437	−	0.870172i	0.634799	−	0.772677i	$-0.281083\pi$
$12$		0			0
$13$	−1.91784	+	4.63007i	−0.147526	+	0.356159i	−0.980317	−	0.197428i	$-0.936741\pi$
$13$	−1.91784	+	4.63007i	−0.147526	+	0.356159i	0.832792	+	0.553587i	$0.186741\pi$
$14$		0			0
$15$	−5.93719			−0.395813
$16$		0			0
$17$		−	15.3143i		−	0.900842i	−0.892816	−	0.450421i	$-0.851274\pi$
$17$		−	15.3143i		−	0.900842i	0.892816	−	0.450421i	$-0.148726\pi$
$18$		0			0
$19$	0.827335	+	0.342693i	0.0435439	+	0.0180365i	0.404349	−	0.914605i	$-0.367498\pi$
$19$	0.827335	+	0.342693i	0.0435439	+	0.0180365i	−0.360805	+	0.932641i	$0.617498\pi$
$20$		0			0
$21$	42.9851	−	17.8050i	2.04691	−	0.847857i
$22$		0			0
$23$	12.9230	−	12.9230i	0.561871	−	0.561871i	−0.367968	−	0.929839i	$-0.619946\pi$
$23$	12.9230	−	12.9230i	0.561871	−	0.561871i	0.929839	+	0.367968i	$0.119946\pi$
$24$		0			0
$25$	15.5786	−	15.5786i	0.623145	−	0.623145i
$26$		0			0
$27$	−19.5007	+	8.07746i	−0.722249	+	0.299165i
$28$		0			0
$29$	−23.7905	−	9.85436i	−0.820363	−	0.339805i	−0.0672825	−	0.997734i	$-0.521433\pi$
$29$	−23.7905	−	9.85436i	−0.820363	−	0.339805i	−0.753080	+	0.657929i	$0.771433\pi$
$30$		0			0
$31$			25.1562i			0.811491i	0.913986	+	0.405746i	$0.132988\pi$
$31$			25.1562i			0.811491i	−0.913986	+	0.405746i	$0.867012\pi$
$32$		0			0
$33$	35.7022			1.08188
$34$		0			0
$35$	8.90221	−	21.4918i	0.254349	−	0.614053i
$36$		0			0
$37$	−13.6161	−	32.8721i	−0.368001	−	0.888434i	−0.994078	−	0.108672i	$-0.965340\pi$
$37$	−13.6161	−	32.8721i	−0.368001	−	0.888434i	0.626076	−	0.779762i	$-0.284660\pi$
$38$		0			0
$39$	−12.2115	−	12.2115i	−0.313116	−	0.313116i
$40$		0			0
$41$	−32.9116	−	32.9116i	−0.802721	−	0.802721i	0.180799	−	0.983520i	$-0.442132\pi$
$41$	−32.9116	−	32.9116i	−0.802721	−	0.802721i	−0.983520	+	0.180799i	$0.942132\pi$
$42$		0			0
$43$	−17.9473	−	43.3286i	−0.417379	−	1.00764i	−0.983104	−	0.183048i	$-0.941404\pi$
$43$	−17.9473	−	43.3286i	−0.417379	−	1.00764i	0.565725	−	0.824594i	$-0.308596\pi$
$44$		0			0
$45$	1.89544	−	4.57600i	0.0421209	−	0.101689i
$46$		0			0
$47$	−20.1127			−0.427930			−0.213965	−	0.976841i	$-0.568638\pi$
$47$	−20.1127			−0.427930			−0.213965	+	0.976841i	$0.568638\pi$
$48$		0			0
$49$			133.297i			2.72035i
$50$		0			0
$51$	48.7557	+	20.1953i	0.955994	+	0.395986i
$52$		0			0
$53$	−35.0503	+	14.5183i	−0.661327	+	0.273931i	−0.687997	−	0.725714i	$-0.741510\pi$
$53$	−35.0503	+	14.5183i	−0.661327	+	0.273931i	0.0266698	+	0.999644i	$0.491510\pi$
$54$		0			0
$55$	12.6222	−	12.6222i	0.229495	−	0.229495i
$56$		0			0
$57$	−2.18204	+	2.18204i	−0.0382815	+	0.0382815i
$58$		0			0
$59$	−60.6706	+	25.1306i	−1.02832	+	0.425942i	−0.832104	−	0.554619i	$-0.812864\pi$
$59$	−60.6706	+	25.1306i	−1.02832	+	0.425942i	−0.196212	+	0.980562i	$0.562864\pi$
$60$		0			0
$61$	27.9825	+	11.5907i	0.458730	+	0.190012i	0.600067	−	0.799949i	$-0.295140\pi$
$61$	27.9825	+	11.5907i	0.458730	+	0.190012i	−0.141338	+	0.989961i	$0.545140\pi$
$62$		0			0
$63$			38.8143i			0.616100i
$64$		0			0
$65$	−8.63457			−0.132839
$66$		0			0
$67$	1.13412	−	2.73801i	0.0169272	−	0.0408659i	−0.915190	−	0.403023i	$-0.867960\pi$
$67$	1.13412	−	2.73801i	0.0169272	−	0.0408659i	0.932117	+	0.362157i	$0.117960\pi$
$68$		0			0
$69$	24.1008	+	58.1845i	0.349287	+	0.843253i
$70$		0			0
$71$	45.6144	+	45.6144i	0.642456	+	0.642456i	0.951159	−	0.308702i	$-0.0998947\pi$
$71$	45.6144	+	45.6144i	0.642456	+	0.642456i	−0.308702	+	0.951159i	$0.599895\pi$
$72$		0			0
$73$	−29.1727	−	29.1727i	−0.399626	−	0.399626i	0.478475	−	0.878101i	$-0.341190\pi$
$73$	−29.1727	−	29.1727i	−0.399626	−	0.399626i	−0.878101	+	0.478475i	$0.841190\pi$
$74$		0			0
$75$	29.0534	+	70.1410i	0.387378	+	0.935213i
$76$		0			0
$77$	−53.5318	+	129.237i	−0.695219	+	1.67841i
$78$		0			0
$79$	−3.27983			−0.0415169			−0.0207584	−	0.999785i	$-0.506608\pi$
$79$	−3.27983			−0.0415169			−0.0207584	+	0.999785i	$0.506608\pi$
$80$		0			0
$81$		−	98.6086i		−	1.21739i
$82$		0			0
$83$	56.7834	+	23.5205i	0.684138	+	0.283379i	0.697555	−	0.716531i	$-0.254271\pi$
$83$	56.7834	+	23.5205i	0.684138	+	0.283379i	−0.0134176	+	0.999910i	$0.504271\pi$
$84$		0			0
$85$	24.3770	−	10.0973i	0.286789	−	0.118792i
$86$		0			0
$87$	62.7460	−	62.7460i	0.721218	−	0.721218i
$88$		0			0
$89$	−44.5059	+	44.5059i	−0.500066	+	0.500066i	−0.911458	−	0.411392i	$-0.865043\pi$
$89$	−44.5059	+	44.5059i	−0.500066	+	0.500066i	0.411392	+	0.911458i	$0.365043\pi$
$90$		0			0
$91$	62.5140	−	25.8942i	0.686967	−	0.284551i
$92$		0			0
$93$	−80.0891	−	33.1740i	−0.861173	−	0.356709i
$94$		0			0
$95$			1.54289i			0.0162409i
$96$		0			0
$97$	−106.417			−1.09708			−0.548542	−	0.836123i	$-0.684817\pi$
$97$	−106.417			−1.09708			−0.548542	+	0.836123i	$0.684817\pi$
$98$		0			0
$99$	−11.3979	+	27.5169i	−0.115130	+	0.277949i
$100$		0			0
$101$	−3.62243	−	8.74531i	−0.0358656	−	0.0865872i	0.904932	−	0.425557i	$-0.139922\pi$
$101$	−3.62243	−	8.74531i	−0.0358656	−	0.0865872i	−0.940797	+	0.338969i	$0.889922\pi$
$102$		0			0
$103$	−26.0911	−	26.0911i	−0.253312	−	0.253312i	0.569015	−	0.822327i	$-0.307325\pi$
$103$	−26.0911	−	26.0911i	−0.253312	−	0.253312i	−0.822327	+	0.569015i	$0.807325\pi$
$104$		0			0
$105$	56.6834	+	56.6834i	0.539842	+	0.539842i
$106$		0			0
$107$	32.1753	+	77.6781i	0.300704	+	0.725963i	0.999939	+	0.0110713i	$0.00352416\pi$
$107$	32.1753	+	77.6781i	0.300704	+	0.725963i	−0.699235	+	0.714892i	$0.746476\pi$
$108$		0			0
$109$	36.0541	−	87.0422i	0.330771	−	0.798553i	−0.667760	−	0.744377i	$-0.732747\pi$
$109$	36.0541	−	87.0422i	0.330771	−	0.798553i	0.998531	−	0.0541760i	$-0.0172532\pi$
$110$		0			0
$111$	122.609			1.10459
$112$		0			0
$113$		−	6.32445i		−	0.0559686i	−0.999608	−	0.0279843i	$-0.991091\pi$
$113$		−	6.32445i		−	0.0559686i	0.999608	−	0.0279843i	$-0.00890884\pi$
$114$		0			0
$115$	29.0913	+	12.0500i	0.252968	+	0.104783i
$116$		0			0
$117$	13.3104	−	5.51333i	0.113764	−	0.0471225i
$118$		0			0
$119$	−146.208	+	146.208i	−1.22864	+	1.22864i
$120$		0			0
$121$	9.65850	−	9.65850i	0.0798223	−	0.0798223i
$122$		0			0
$123$	148.181	−	61.3784i	1.20472	−	0.499011i
$124$		0			0
$125$	74.8639	+	31.0096i	0.598911	+	0.248077i
$126$		0			0
$127$		−	34.6015i		−	0.272453i	−0.990678	−	0.136226i	$-0.956503\pi$
$127$		−	34.6015i		−	0.272453i	0.990678	−	0.136226i	$-0.0434975\pi$
$128$		0			0
$129$	161.611			1.25280
$130$		0			0
$131$	−68.0051	+	164.179i	−0.519123	+	1.25327i	0.419320	+	0.907838i	$0.362268\pi$
$131$	−68.0051	+	164.179i	−0.519123	+	1.25327i	−0.938443	+	0.345434i	$0.887732\pi$
$132$		0			0
$133$	−4.62696	−	11.1705i	−0.0347892	−	0.0839885i
$134$		0			0
$135$	−25.7151	−	25.7151i	−0.190482	−	0.190482i
$136$		0			0
$137$	71.5748	+	71.5748i	0.522444	+	0.522444i	0.918309	−	0.395865i	$-0.129555\pi$
$137$	71.5748	+	71.5748i	0.522444	+	0.522444i	−0.395865	+	0.918309i	$0.629555\pi$
$138$		0			0
$139$	−75.1916	−	181.529i	−0.540947	−	1.30596i	−0.924056	−	0.382258i	$-0.875147\pi$
$139$	−75.1916	−	181.529i	−0.540947	−	1.30596i	0.383109	−	0.923703i	$-0.374853\pi$
$140$		0			0
$141$	26.5230	−	64.0322i	0.188107	−	0.454129i
$142$		0			0
$143$	51.9224			0.363094
$144$		0			0
$145$		−	44.3667i		−	0.305977i
$146$		0			0
$147$	−424.374	−	175.781i	−2.88690	−	1.19579i
$148$		0			0
$149$	−211.685	+	87.6826i	−1.42070	+	0.588474i	−0.955037	−	0.296487i	$-0.904185\pi$
$149$	−211.685	+	87.6826i	−1.42070	+	0.588474i	−0.465665	+	0.884961i	$0.654185\pi$
$150$		0			0
$151$	−10.5820	+	10.5820i	−0.0700794	+	0.0700794i	−0.741278	−	0.671198i	$-0.765780\pi$
$151$	−10.5820	+	10.5820i	−0.0700794	+	0.0700794i	0.671198	+	0.741278i	$0.265780\pi$
$152$		0			0
$153$	−31.1304	+	31.1304i	−0.203467	+	0.203467i
$154$		0			0
$155$	−40.0432	+	16.5864i	−0.258343	+	0.107009i
$156$		0			0
$157$	−26.9641	−	11.1689i	−0.171746	−	0.0711394i	0.295154	−	0.955450i	$-0.404629\pi$
$157$	−26.9641	−	11.1689i	−0.171746	−	0.0711394i	−0.466900	+	0.884310i	$0.654629\pi$
$158$		0			0
$159$		−	130.734i		−	0.822228i
$160$		0			0
$161$	−246.757			−1.53265
$162$		0			0
$163$	111.743	−	269.771i	0.685540	−	1.65504i	−0.0680396	−	0.997683i	$-0.521674\pi$
$163$	111.743	−	269.771i	0.685540	−	1.65504i	0.753579	−	0.657357i	$-0.228326\pi$
$164$		0			0
$165$	23.5398	+	56.8301i	0.142665	+	0.344425i
$166$		0			0
$167$	10.3664	+	10.3664i	0.0620741	+	0.0620741i	0.737462	−	0.675388i	$-0.236024\pi$
$167$	10.3664	+	10.3664i	0.0620741	+	0.0620741i	−0.675388	+	0.737462i	$0.736024\pi$
$168$		0			0
$169$	101.742	+	101.742i	0.602021	+	0.602021i
$170$		0			0
$171$	−0.985162	−	2.37839i	−0.00576118	−	0.0139087i
$172$		0			0
$173$	88.6518	−	214.024i	0.512438	−	1.23714i	−0.430022	−	0.902818i	$-0.641494\pi$
$173$	88.6518	−	214.024i	0.512438	−	1.23714i	0.942461	−	0.334317i	$-0.108506\pi$
$174$		0			0
$175$	−297.464			−1.69979
$176$		0			0
$177$		−	226.295i		−	1.27850i
$178$		0			0
$179$	2.58312	+	1.06996i	0.0144308	+	0.00597744i	0.389887	−	0.920863i	$-0.372514\pi$
$179$	2.58312	+	1.06996i	0.0144308	+	0.00597744i	−0.375456	+	0.926840i	$0.622514\pi$
$180$		0			0
$181$	184.394	−	76.3786i	1.01875	−	0.421981i	0.190112	−	0.981762i	$-0.439115\pi$
$181$	184.394	−	76.3786i	1.01875	−	0.421981i	0.828640	+	0.559781i	$0.189115\pi$
$182$		0			0
$183$	−73.8021	+	73.8021i	−0.403290	+	0.403290i
$184$		0			0
$185$	43.3476	−	43.3476i	0.234311	−	0.234311i
$186$		0			0
$187$	−146.587	+	60.7183i	−0.783887	+	0.324697i
$188$		0			0
$189$	263.294	+	109.060i	1.39309	+	0.577036i
$190$		0			0
$191$		−	185.771i		−	0.972625i	−0.873785	−	0.486313i	$-0.838342\pi$
$191$		−	185.771i		−	0.972625i	0.873785	−	0.486313i	$-0.161658\pi$
$192$		0			0
$193$	208.055			1.07800			0.539002	−	0.842305i	$-0.318802\pi$
$193$	208.055			1.07800			0.539002	+	0.842305i	$0.318802\pi$
$194$		0			0
$195$	11.3866	−	27.4896i	0.0583926	−	0.140972i
$196$		0			0
$197$	−123.852	−	299.006i	−0.628691	−	1.51780i	−0.841250	−	0.540647i	$-0.818180\pi$
$197$	−123.852	−	299.006i	−0.628691	−	1.51780i	0.212558	−	0.977148i	$-0.431820\pi$
$198$		0			0
$199$	253.762	+	253.762i	1.27519	+	1.27519i	0.943329	+	0.331858i	$0.107676\pi$
$199$	253.762	+	253.762i	1.27519	+	1.27519i	0.331858	+	0.943329i	$0.392324\pi$
$200$		0			0
$201$	7.22134	+	7.22134i	0.0359270	+	0.0359270i
$202$		0			0
$203$	133.051	+	321.214i	0.655424	+	1.58233i
$204$		0			0
$205$	30.6882	−	74.0879i	0.149699	−	0.361404i
$206$		0			0
$207$	−52.5389			−0.253811
$208$		0			0
$209$		−	9.27787i		−	0.0443917i
$210$		0			0
$211$	102.533	+	42.4705i	0.485938	+	0.201282i	0.612182	−	0.790717i	$-0.290292\pi$
$211$	102.533	+	42.4705i	0.485938	+	0.201282i	−0.126244	+	0.991999i	$0.540292\pi$
$212$		0			0
$213$	−205.374	+	85.0685i	−0.964195	+	0.399383i
$214$		0			0
$215$	57.1364	−	57.1364i	0.265751	−	0.265751i
$216$		0			0
$217$	240.171	−	240.171i	1.10678	−	1.10678i
$218$		0			0
$219$	131.347	−	54.4056i	0.599757	−	0.248428i
$220$		0			0
$221$	70.9063	+	29.3704i	0.320843	+	0.132898i
$222$		0			0
$223$		−	187.153i		−	0.839252i	−0.907697	−	0.419626i	$-0.862161\pi$
$223$		−	187.153i		−	0.839252i	0.907697	−	0.419626i	$-0.137839\pi$
$224$		0			0
$225$	−63.3353			−0.281490
$226$		0			0
$227$	−2.72348	+	6.57507i	−0.0119977	+	0.0289650i	−0.929765	−	0.368154i	$-0.879990\pi$
$227$	−2.72348	+	6.57507i	−0.0119977	+	0.0289650i	0.917767	+	0.397119i	$0.129990\pi$
$228$		0			0
$229$	124.655	+	300.944i	0.544345	+	1.31416i	0.921631	+	0.388068i	$0.126857\pi$
$229$	124.655	+	300.944i	0.544345	+	1.31416i	−0.377286	+	0.926097i	$0.623143\pi$
$230$		0			0
$231$	−340.855	−	340.855i	−1.47556	−	1.47556i
$232$		0			0
$233$	−208.047	−	208.047i	−0.892904	−	0.892904i	0.101891	−	0.994796i	$-0.467511\pi$
$233$	−208.047	−	208.047i	−0.892904	−	0.892904i	−0.994796	+	0.101891i	$0.967511\pi$
$234$		0			0
$235$	−13.2611	−	32.0151i	−0.0564301	−	0.136234i
$236$		0			0
$237$	4.32518	−	10.4419i	0.0182497	−	0.0440587i
$238$		0			0
$239$	277.832			1.16248			0.581239	−	0.813733i	$-0.302568\pi$
$239$	277.832			1.16248			0.581239	+	0.813733i	$0.302568\pi$
$240$		0			0
$241$			63.2696i			0.262529i	0.991347	+	0.131265i	$0.0419038\pi$
$241$			63.2696i			0.262529i	−0.991347	+	0.131265i	$0.958096\pi$
$242$		0			0
$243$	138.431	+	57.3398i	0.569673	+	0.235966i
$244$		0			0
$245$	−212.180	+	87.8879i	−0.866041	+	0.358726i
$246$		0			0
$247$	−3.17339	+	3.17339i	−0.0128477	+	0.0128477i
$248$		0			0
$249$	−149.763	+	149.763i	−0.601457	+	0.601457i
$250$		0			0
$251$	161.948	−	67.0812i	0.645212	−	0.267256i	−0.0359886	−	0.999352i	$-0.511458\pi$
$251$	161.948	−	67.0812i	0.645212	−	0.267256i	0.681201	+	0.732097i	$0.261458\pi$
$252$		0			0
$253$	−174.935	−	72.4605i	−0.691443	−	0.286405i
$254$		0			0
$255$			90.9239i			0.356564i
$256$		0			0
$257$	−82.9690			−0.322836			−0.161418	−	0.986886i	$-0.551607\pi$
$257$	−82.9690			−0.322836			−0.161418	+	0.986886i	$0.551607\pi$
$258$		0			0
$259$	−183.840	+	443.830i	−0.709809	+	1.71363i
$260$		0			0
$261$	28.3289	+	68.3921i	0.108540	+	0.262039i
$262$		0			0
$263$	148.394	+	148.394i	0.564235	+	0.564235i	0.930508	−	0.366272i	$-0.119366\pi$
$263$	148.394	+	148.394i	0.564235	+	0.564235i	−0.366272	+	0.930508i	$0.619366\pi$
$264$		0			0
$265$	−46.2200	−	46.2200i	−0.174415	−	0.174415i
$266$		0			0
$267$	−83.0012	−	200.383i	−0.310866	−	0.750497i
$268$		0			0
$269$	−78.7117	+	190.027i	−0.292609	+	0.706420i	−1.00000		0.000402393i	$-0.999872\pi$
$269$	−78.7117	+	190.027i	−0.292609	+	0.706420i	0.707391	+	0.706822i	$0.249872\pi$
$270$		0			0
$271$	29.7996			0.109962			0.0549809	−	0.998487i	$-0.482490\pi$
$271$	29.7996			0.109962			0.0549809	+	0.998487i	$0.482490\pi$
$272$		0			0
$273$			233.171i			0.854106i
$274$		0			0
$275$	−210.883	−	87.3507i	−0.766848	−	0.317639i
$276$		0			0
$277$	368.831	−	152.775i	1.33152	−	0.551534i	0.400431	−	0.916327i	$-0.368860\pi$
$277$	368.831	−	152.775i	1.33152	−	0.551534i	0.931089	+	0.364793i	$0.118860\pi$
$278$		0			0
$279$	51.1367	−	51.1367i	0.183286	−	0.183286i
$280$		0			0
$281$	−280.258	+	280.258i	−0.997358	+	0.997358i	−0.999997	−	0.00263807i	$-0.999160\pi$
$281$	−280.258	+	280.258i	−0.997358	+	0.997358i	0.00263807	+	0.999997i	$0.499160\pi$
$282$		0			0
$283$	−176.650	+	73.1708i	−0.624204	+	0.258554i	−0.672288	−	0.740289i	$-0.734688\pi$
$283$	−176.650	+	73.1708i	−0.624204	+	0.258554i	0.0480840	+	0.998843i	$0.484688\pi$
$284$		0			0
$285$	−4.91204	−	2.03463i	−0.0172352	−	0.00713907i
$286$		0			0
$287$			628.425i			2.18963i
$288$		0			0
$289$	54.4719			0.188484
$290$		0			0
$291$	140.334	−	338.797i	0.482249	−	1.16425i
$292$		0			0
$293$	−11.3590	−	27.4231i	−0.0387679	−	0.0935940i	0.903310	−	0.428989i	$-0.141130\pi$
$293$	−11.3590	−	27.4231i	−0.0387679	−	0.0935940i	−0.942078	+	0.335395i	$0.891130\pi$
$294$		0			0
$295$	−80.0049	−	80.0049i	−0.271203	−	0.271203i
$296$		0			0
$297$	154.633	+	154.633i	0.520651	+	0.520651i
$298$		0			0
$299$	35.0503	+	84.6188i	0.117225	+	0.283006i
$300$		0			0
$301$	−242.320	+	585.012i	−0.805049	+	1.94356i
$302$		0			0
$303$	32.6191			0.107654
$304$		0			0
$305$			52.1843i			0.171096i
$306$		0			0
$307$	463.833	+	192.126i	1.51086	+	0.625817i	0.975734	−	0.218957i	$-0.0702655\pi$
$307$	463.833	+	192.126i	1.51086	+	0.625817i	0.535122	+	0.844775i	$0.320266\pi$
$308$		0			0
$309$	117.472	−	48.6586i	0.380169	−	0.157471i
$310$		0			0
$311$	−230.516	+	230.516i	−0.741210	+	0.741210i	−0.972811	−	0.231601i	$-0.925604\pi$
$311$	−230.516	+	230.516i	−0.741210	+	0.741210i	0.231601	+	0.972811i	$0.425604\pi$
$312$		0			0
$313$	2.89884	−	2.89884i	0.00926146	−	0.00926146i	−0.702461	−	0.711722i	$-0.747915\pi$
$313$	2.89884	−	2.89884i	0.00926146	−	0.00926146i	0.711722	+	0.702461i	$0.247915\pi$
$314$		0			0
$315$	−61.7839	+	25.5917i	−0.196139	+	0.0812436i
$316$		0			0
$317$	−510.087	−	211.285i	−1.60911	−	0.666514i	−0.616441	−	0.787401i	$-0.711426\pi$
$317$	−510.087	−	211.285i	−1.60911	−	0.666514i	−0.992666	+	0.120887i	$0.961426\pi$
$318$		0			0
$319$			266.791i			0.836335i
$320$		0			0
$321$	−289.731			−0.902590
$322$		0			0
$323$	5.24811	−	12.6701i	0.0162480	−	0.0392262i
$324$		0			0
$325$	42.2528	+	102.007i	0.130009	+	0.313869i
$326$		0			0
$327$	229.568	+	229.568i	0.702044	+	0.702044i
$328$		0			0
$329$	192.020	+	192.020i	0.583647	+	0.583647i
$330$		0			0
$331$	−95.3030	−	230.082i	−0.287924	−	0.695111i	0.712051	−	0.702128i	$-0.247766\pi$
$331$	−95.3030	−	230.082i	−0.287924	−	0.695111i	−0.999975	+	0.00701670i	$0.997766\pi$
$332$		0			0
$333$	−39.1429	+	94.4994i	−0.117546	+	0.283782i
$334$		0			0
$335$	5.10609			0.0152421
$336$		0			0
$337$			203.997i			0.605334i	0.953096	+	0.302667i	$0.0978769\pi$
$337$			203.997i			0.605334i	−0.953096	+	0.302667i	$0.902123\pi$
$338$		0			0
$339$	20.1349	+	8.34017i	0.0593951	+	0.0246023i
$340$		0			0
$341$	240.793	−	99.7396i	0.706137	−	0.292491i
$342$		0			0
$343$	804.800	−	804.800i	2.34636	−	2.34636i
$344$		0			0
$345$	−76.7264	+	76.7264i	−0.222395	+	0.222395i
$346$		0			0
$347$	−120.709	+	49.9993i	−0.347865	+	0.144090i	−0.549773	−	0.835314i	$-0.685286\pi$
$347$	−120.709	+	49.9993i	−0.347865	+	0.144090i	0.201908	+	0.979404i	$0.435286\pi$
$348$		0			0
$349$	−279.116	−	115.614i	−0.799759	−	0.331271i	−0.0548993	−	0.998492i	$-0.517484\pi$
$349$	−279.116	−	115.614i	−0.799759	−	0.331271i	−0.744860	+	0.667221i	$0.767484\pi$
$350$		0			0
$351$		−	105.781i		−	0.301370i
$352$		0			0
$353$	608.156			1.72282			0.861410	−	0.507910i	$-0.169582\pi$
$353$	608.156			1.72282			0.861410	+	0.507910i	$0.169582\pi$
$354$		0			0
$355$	−42.5329	+	102.683i	−0.119811	+	0.289249i
$356$		0			0
$357$	−272.671	−	658.287i	−0.763785	−	1.84394i
$358$		0			0
$359$	−196.029	−	196.029i	−0.546041	−	0.546041i	0.379252	−	0.925293i	$-0.376181\pi$
$359$	−196.029	−	196.029i	−0.546041	−	0.546041i	−0.925293	+	0.379252i	$0.876181\pi$
$360$		0			0
$361$	−254.699	−	254.699i	−0.705536	−	0.705536i
$362$		0			0
$363$	18.0126	+	43.4863i	0.0496215	+	0.119797i
$364$		0			0
$365$	27.2019	−	65.6713i	0.0745259	−	0.179921i
$366$		0			0
$367$	33.0375			0.0900203			0.0450102	−	0.998987i	$-0.485668\pi$
$367$	33.0375			0.0900203			0.0450102	+	0.998987i	$0.485668\pi$
$368$		0			0
$369$			133.803i			0.362609i
$370$		0			0
$371$	473.241	+	196.023i	1.27558	+	0.528363i
$372$		0			0
$373$	−115.583	+	47.8760i	−0.309874	+	0.128354i	−0.532201	−	0.846618i	$-0.678635\pi$
$373$	−115.583	+	47.8760i	−0.309874	+	0.128354i	0.222327	+	0.974972i	$0.428635\pi$
$374$		0			0
$375$	−197.449	+	197.449i	−0.526530	+	0.526530i
$376$		0			0
$377$	91.2527	−	91.2527i	0.242050	−	0.242050i
$378$		0			0
$379$	164.874	−	68.2930i	0.435024	−	0.180193i	−0.154415	−	0.988006i	$-0.549349\pi$
$379$	164.874	−	68.2930i	0.435024	−	0.180193i	0.589438	+	0.807813i	$0.299349\pi$
$380$		0			0
$381$	110.160	+	45.6297i	0.289133	+	0.119763i
$382$		0			0
$383$			307.309i			0.802373i	0.915996	+	0.401186i	$0.131402\pi$
$383$			307.309i			0.802373i	−0.915996	+	0.401186i	$0.868598\pi$
$384$		0			0
$385$	−241.013			−0.626008
$386$		0			0
$387$	−51.5942	+	124.559i	−0.133318	+	0.321859i
$388$		0			0
$389$	204.874	+	494.611i	0.526669	+	1.27149i	0.933693	+	0.358075i	$0.116567\pi$
$389$	204.874	+	494.611i	0.526669	+	1.27149i	−0.407024	+	0.913418i	$0.633433\pi$
$390$		0			0
$391$	−197.907	−	197.907i	−0.506157	−	0.506157i
$392$		0			0
$393$	−433.011	−	433.011i	−1.10181	−	1.10181i
$394$		0			0
$395$	−2.16252	−	5.22078i	−0.00547473	−	0.0132172i
$396$		0			0
$397$	224.796	−	542.706i	0.566237	−	1.36702i	−0.338467	−	0.940978i	$-0.609908\pi$
$397$	224.796	−	542.706i	0.566237	−	1.36702i	0.904705	−	0.426040i	$-0.140092\pi$
$398$		0			0
$399$	41.6647			0.104423
$400$		0			0
$401$		−	125.790i		−	0.313691i	−0.987623	−	0.156846i	$-0.949868\pi$
$401$		−	125.790i		−	0.313691i	0.987623	−	0.156846i	$-0.0501325\pi$
$402$		0			0
$403$	−116.475	−	48.2456i	−0.289020	−	0.119716i
$404$		0			0
$405$	156.963	−	65.0164i	0.387564	−	0.160534i
$406$		0			0
$407$	−260.663	+	260.663i	−0.640449	+	0.640449i
$408$		0			0
$409$	492.952	−	492.952i	1.20526	−	1.20526i	0.232717	−	0.972544i	$-0.425238\pi$
$409$	492.952	−	492.952i	1.20526	−	1.20526i	0.972544	−	0.232717i	$-0.0747617\pi$
$410$		0			0
$411$	−322.257	+	133.483i	−0.784081	+	0.324777i
$412$		0			0
$413$	819.159	+	339.307i	1.98344	+	0.821567i
$414$		0			0
$415$			105.895i			0.255168i
$416$		0			0
$417$	677.084			1.62370
$418$		0			0
$419$	203.456	−	491.187i	0.485576	−	1.17228i	−0.471349	−	0.881947i	$-0.656233\pi$
$419$	203.456	−	491.187i	0.485576	−	1.17228i	0.956925	−	0.290336i	$-0.0937672\pi$
$420$		0			0
$421$	0.995616	+	2.40363i	0.00236488	+	0.00570934i	0.925058	−	0.379827i	$-0.124016\pi$
$421$	0.995616	+	2.40363i	0.00236488	+	0.00570934i	−0.922693	+	0.385536i	$0.874016\pi$
$422$		0			0
$423$	40.8844	+	40.8844i	0.0966535	+	0.0966535i
$424$		0			0
$425$	−238.576	−	238.576i	−0.561355	−	0.561355i
$426$		0			0
$427$	−156.495	−	377.813i	−0.366499	−	0.884807i
$428$		0			0
$429$	−68.4710	+	165.304i	−0.159606	+	0.385323i
$430$		0			0
$431$	−404.244			−0.937920			−0.468960	−	0.883219i	$-0.655371\pi$
$431$	−404.244			−0.937920			−0.468960	+	0.883219i	$0.655371\pi$
$432$		0			0
$433$			446.431i			1.03102i	0.856884	+	0.515509i	$0.172397\pi$
$433$			446.431i			1.03102i	−0.856884	+	0.515509i	$0.827603\pi$
$434$		0			0
$435$	141.249	+	58.5072i	0.324710	+	0.134499i
$436$		0			0
$437$	15.1203	−	6.26304i	0.0346003	−	0.0143319i
$438$		0			0
$439$	203.077	−	203.077i	0.462590	−	0.462590i	−0.436914	−	0.899503i	$-0.643928\pi$
$439$	203.077	−	203.077i	0.462590	−	0.462590i	0.899503	+	0.436914i	$0.143928\pi$
$440$		0			0
$441$	270.962	−	270.962i	0.614426	−	0.614426i
$442$		0			0
$443$	−440.203	+	182.338i	−0.993685	+	0.411598i	−0.819478	−	0.573111i	$-0.805736\pi$
$443$	−440.203	+	182.338i	−0.993685	+	0.411598i	−0.174207	+	0.984709i	$0.555736\pi$
$444$		0			0
$445$	−100.188	−	41.4993i	−0.225142	−	0.0932568i
$446$		0			0
$447$		−	789.562i		−	1.76636i
$448$		0			0
$449$	−636.256			−1.41705			−0.708526	−	0.705685i	$-0.750639\pi$
$449$	−636.256			−1.41705			−0.708526	+	0.705685i	$0.750639\pi$
$450$		0			0
$451$	−184.538	+	445.514i	−0.409175	+	0.987836i
$452$		0			0
$453$	−19.7349	−	47.6442i	−0.0435648	−	0.105175i
$454$		0			0
$455$	82.4357	+	82.4357i	0.181177	+	0.181177i
$456$		0			0
$457$	−359.285	−	359.285i	−0.786181	−	0.786181i	0.194685	−	0.980866i	$-0.437632\pi$
$457$	−359.285	−	359.285i	−0.786181	−	0.786181i	−0.980866	+	0.194685i	$0.937632\pi$
$458$		0			0
$459$	123.701	+	298.640i	0.269501	+	0.650632i
$460$		0			0
$461$	−68.2156	+	164.687i	−0.147973	+	0.357239i	−0.980435	−	0.196844i	$-0.936931\pi$
$461$	−68.2156	+	164.687i	−0.147973	+	0.357239i	0.832462	+	0.554083i	$0.186931\pi$
$462$		0			0
$463$	−662.155			−1.43014			−0.715070	−	0.699053i	$-0.753605\pi$
$463$	−662.155			−1.43014			−0.715070	+	0.699053i	$0.753605\pi$
$464$		0			0
$465$		−	149.357i		−	0.321198i
$466$		0			0
$467$	−854.762	−	354.054i	−1.83033	−	0.758146i	−0.967607	−	0.252461i	$-0.918760\pi$
$467$	−854.762	−	354.054i	−1.83033	−	0.758146i	−0.862718	−	0.505685i	$-0.831240\pi$
$468$		0			0
$469$	−36.9680	+	15.3126i	−0.0788229	+	0.0326495i
$470$		0			0
$471$	71.1160	−	71.1160i	0.150989	−	0.150989i
$472$		0			0
$473$	−343.579	+	343.579i	−0.726383	+	0.726383i
$474$		0			0
$475$	18.2274	−	7.55005i	0.0383735	−	0.0158948i
$476$		0			0
$477$	100.761	+	41.7367i	0.211240	+	0.0874984i
$478$		0			0
$479$		−	926.802i		−	1.93487i	−0.253122	−	0.967434i	$-0.581458\pi$
$479$		−	926.802i		−	1.93487i	0.253122	−	0.967434i	$-0.418542\pi$
$480$		0			0
$481$	178.313			0.370714
$482$		0			0
$483$	325.403	−	785.592i	0.673712	−	1.62648i
$484$		0			0
$485$	−70.1649	−	169.393i	−0.144670	−	0.349264i
$486$		0			0
$487$	−586.001	−	586.001i	−1.20329	−	1.20329i	−0.973161	−	0.230127i	$-0.926086\pi$
$487$	−586.001	−	586.001i	−1.20329	−	1.20329i	−0.230127	−	0.973161i	$-0.573914\pi$
$488$		0			0
$489$	711.505	+	711.505i	1.45502	+	1.45502i
$490$		0			0
$491$	−17.1543	−	41.4142i	−0.0349375	−	0.0843466i	0.905448	−	0.424458i	$-0.139535\pi$
$491$	−17.1543	−	41.4142i	−0.0349375	−	0.0843466i	−0.940385	+	0.340111i	$0.889535\pi$
$492$		0			0
$493$	−150.913	+	364.335i	−0.306111	+	0.739017i
$494$		0			0
$495$	−51.3160			−0.103669
$496$		0			0
$497$		−	870.977i		−	1.75247i
$498$		0			0
$499$	−143.291	−	59.3531i	−0.287156	−	0.118944i	0.234456	−	0.972127i	$-0.424669\pi$
$499$	−143.291	−	59.3531i	−0.287156	−	0.118944i	−0.521612	+	0.853183i	$0.674669\pi$
$500$		0			0
$501$	−46.6734	+	19.3328i	−0.0931605	+	0.0385884i
$502$		0			0
$503$	−74.0929	+	74.0929i	−0.147302	+	0.147302i	−0.776912	−	0.629610i	$-0.783215\pi$
$503$	−74.0929	+	74.0929i	−0.147302	+	0.147302i	0.629610	+	0.776912i	$0.283215\pi$
$504$		0			0
$505$	11.5322	−	11.5322i	0.0228361	−	0.0228361i
$506$		0			0
$507$	−458.080	+	189.743i	−0.903511	+	0.374246i
$508$		0			0
$509$	−467.540	−	193.661i	−0.918546	−	0.380474i	−0.127224	−	0.991874i	$-0.540607\pi$
$509$	−467.540	−	193.661i	−0.918546	−	0.380474i	−0.791322	+	0.611400i	$0.790607\pi$
$510$		0			0
$511$			557.034i			1.09009i
$512$		0			0
$513$	−18.9017			−0.0368455
$514$		0			0
$515$	24.3285	−	58.7343i	0.0472399	−	0.114047i
$516$		0			0
$517$	79.7431	+	192.517i	0.154242	+	0.372373i
$518$		0			0
$519$	564.476	+	564.476i	1.08762	+	1.08762i
$520$		0			0
$521$	694.307	+	694.307i	1.33264	+	1.33264i	0.902998	+	0.429644i	$0.141361\pi$
$521$	694.307	+	694.307i	1.33264	+	1.33264i	0.429644	+	0.902998i	$0.358639\pi$
$522$		0			0
$523$	67.4311	+	162.793i	0.128931	+	0.311268i	0.975142	−	0.221581i	$-0.0711216\pi$
$523$	67.4311	+	162.793i	0.128931	+	0.311268i	−0.846211	+	0.532848i	$0.821122\pi$
$524$		0			0
$525$	392.271	−	947.026i	0.747183	−	1.80386i
$526$		0			0
$527$	385.250			0.731025
$528$		0			0
$529$			194.991i			0.368602i
$530$		0			0
$531$	174.414	+	72.2445i	0.328463	+	0.136054i
$532$		0			0
$533$	215.502	−	89.2638i	0.404319	−	0.167474i
$534$		0			0
$535$	−102.432	+	102.432i	−0.191462	+	0.191462i
$536$		0			0
$537$	−6.81281	+	6.81281i	−0.0126868	+	0.0126868i
$538$		0			0
$539$	1275.91	−	528.498i	2.36717	−	0.980515i
$540$		0			0
$541$	−125.547	−	52.0035i	−0.232066	−	0.0961247i	0.263620	−	0.964626i	$-0.415083\pi$
$541$	−125.547	−	52.0035i	−0.232066	−	0.0961247i	−0.495686	+	0.868502i	$0.665083\pi$
$542$		0			0
$543$			687.772i			1.26661i
$544$		0			0
$545$	162.324			0.297842
$546$		0			0
$547$	−278.945	+	673.432i	−0.509954	+	1.23114i	0.433956	+	0.900934i	$0.357117\pi$
$547$	−278.945	+	673.432i	−0.509954	+	1.23114i	−0.943910	+	0.330204i	$0.892883\pi$
$548$		0			0
$549$	−33.3206	−	80.4431i	−0.0606933	−	0.146527i
$550$		0			0
$551$	−16.3057	−	16.3057i	−0.0295929	−	0.0295929i
$552$		0			0
$553$	31.3132	+	31.3132i	0.0566241	+	0.0566241i
$554$		0			0
$555$	80.8410	+	195.168i	0.145660	+	0.351653i
$556$		0			0
$557$	228.207	−	550.942i	0.409708	−	0.989123i	−0.575506	−	0.817797i	$-0.695195\pi$
$557$	228.207	−	550.942i	0.409708	−	0.989123i	0.985214	−	0.171326i	$-0.0548051\pi$
$558$		0			0
$559$	235.035			0.420455
$560$		0			0
$561$		−	546.754i		−	0.974607i
$562$		0			0
$563$	−236.899	−	98.1268i	−0.420780	−	0.174293i	0.162239	−	0.986752i	$-0.448129\pi$
$563$	−236.899	−	98.1268i	−0.420780	−	0.174293i	−0.583019	+	0.812459i	$0.698129\pi$
$564$		0			0
$565$	10.0671	−	4.16995i	0.0178180	−	0.00738044i
$566$		0			0
$567$	−941.434	+	941.434i	−1.66038	+	1.66038i
$568$		0			0
$569$	−289.568	+	289.568i	−0.508907	+	0.508907i	−0.914191	−	0.405284i	$-0.867173\pi$
$569$	−289.568	+	289.568i	−0.508907	+	0.508907i	0.405284	+	0.914191i	$0.367173\pi$
$570$		0			0
$571$	801.877	−	332.148i	1.40434	−	0.581695i	0.453464	−	0.891275i	$-0.350188\pi$
$571$	801.877	−	332.148i	1.40434	−	0.581695i	0.950874	+	0.309579i	$0.100188\pi$
$572$		0			0
$573$	591.435	+	244.980i	1.03217	+	0.427540i
$574$		0			0
$575$		−	402.646i		−	0.700254i
$576$		0			0
$577$	−107.872			−0.186953			−0.0934767	−	0.995621i	$-0.529798\pi$
$577$	−107.872			−0.186953			−0.0934767	+	0.995621i	$0.529798\pi$
$578$		0			0
$579$	−274.365	+	662.377i	−0.473861	+	1.14400i
$580$		0			0
$581$	−317.567	−	766.676i	−0.546588	−	1.31958i
$582$		0			0
$583$	277.936	+	277.936i	0.476734	+	0.476734i
$584$		0			0
$585$	17.5520	+	17.5520i	0.0300035	+	0.0300035i
$586$		0			0
$587$	−292.393	−	705.899i	−0.498114	−	1.20255i	−0.950498	−	0.310730i	$-0.899426\pi$
$587$	−292.393	−	705.899i	−0.498114	−	1.20255i	0.452384	−	0.891823i	$-0.350574\pi$
$588$		0			0
$589$	−8.62087	+	20.8126i	−0.0146365	+	0.0353355i
$590$		0			0
$591$	1115.26			1.88707
$592$		0			0
$593$			247.178i			0.416826i	0.978041	+	0.208413i	$0.0668298\pi$
$593$			247.178i			0.416826i	−0.978041	+	0.208413i	$0.933170\pi$
$594$		0			0
$595$	−329.133	−	136.331i	−0.553164	−	0.229128i
$596$		0			0
$597$	−1142.54	+	473.254i	−1.91380	+	0.792720i
$598$		0			0
$599$	633.115	−	633.115i	1.05695	−	1.05695i	0.0586768	−	0.998277i	$-0.481312\pi$
$599$	633.115	−	633.115i	1.05695	−	1.05695i	0.998277	−	0.0586768i	$-0.0186881\pi$
$600$		0			0
$601$	−147.019	+	147.019i	−0.244624	+	0.244624i	−0.818760	−	0.574136i	$-0.805338\pi$
$601$	−147.019	+	147.019i	−0.244624	+	0.244624i	0.574136	+	0.818760i	$0.305338\pi$
$602$		0			0
$603$	−7.87114	+	3.26033i	−0.0130533	+	0.00540685i
$604$		0			0
$605$	21.7424	+	9.00601i	0.0359379	+	0.0148860i
$606$		0			0
$607$			52.6594i			0.0867536i	0.999059	+	0.0433768i	$0.0138116\pi$
$607$			52.6594i			0.0867536i	−0.999059	+	0.0433768i	$0.986188\pi$
$608$		0			0
$609$	−1198.09			−1.96731
$610$		0			0
$611$	38.5729	−	93.1233i	0.0631308	−	0.152411i
$612$		0			0
$613$	336.988	+	813.562i	0.549737	+	1.32718i	0.917675	+	0.397331i	$0.130064\pi$
$613$	336.988	+	813.562i	0.549737	+	1.32718i	−0.367939	+	0.929850i	$0.619936\pi$
$614$		0			0
$615$	195.402	+	195.402i	0.317727	+	0.317727i
$616$		0			0
$617$	−150.269	−	150.269i	−0.243547	−	0.243547i	0.574769	−	0.818316i	$-0.305092\pi$
$617$	−150.269	−	150.269i	−0.243547	−	0.243547i	−0.818316	+	0.574769i	$0.805092\pi$
$618$		0			0
$619$	4.34083	+	10.4797i	0.00701265	+	0.0169300i	0.927347	−	0.374202i	$-0.122083\pi$
$619$	4.34083	+	10.4797i	0.00701265	+	0.0169300i	−0.920334	+	0.391132i	$0.872083\pi$
$620$		0			0
$621$	−147.623	+	356.394i	−0.237718	+	0.573903i
$622$		0			0
$623$	849.811			1.36406
$624$		0			0
$625$		−	411.175i		−	0.657880i
$626$		0			0
$627$	29.5377	+	12.2349i	0.0471095	+	0.0195134i
$628$		0			0
$629$	−503.413	+	208.520i	−0.800338	+	0.331511i
$630$		0			0
$631$	−356.485	+	356.485i	−0.564952	+	0.564952i	−0.930710	−	0.365758i	$-0.880810\pi$
$631$	−356.485	+	356.485i	−0.564952	+	0.564952i	0.365758	+	0.930710i	$0.380810\pi$
$632$		0			0
$633$	−270.424	+	270.424i	−0.427210	+	0.427210i
$634$		0			0
$635$	55.0781	−	22.8141i	0.0867371	−	0.0359277i
$636$		0			0
$637$	−617.175	−	255.642i	−0.968878	−	0.401322i
$638$		0			0
$639$		−	185.447i		−	0.290214i
$640$		0			0
$641$	741.748			1.15717			0.578587	−	0.815621i	$-0.303604\pi$
$641$	741.748			1.15717			0.578587	+	0.815621i	$0.303604\pi$
$642$		0			0
$643$	181.837	−	438.994i	0.282795	−	0.682729i	−0.717103	−	0.696967i	$-0.754532\pi$
$643$	181.837	−	438.994i	0.282795	−	0.682729i	0.999899	+	0.0142385i	$0.00453240\pi$
$644$		0			0
$645$	106.556	+	257.250i	0.165204	+	0.398837i
$646$		0			0
$647$	−520.304	−	520.304i	−0.804180	−	0.804180i	0.179566	−	0.983746i	$-0.442531\pi$
$647$	−520.304	−	520.304i	−0.804180	−	0.804180i	−0.983746	+	0.179566i	$0.942531\pi$
$648$		0			0
$649$	481.095	+	481.095i	0.741286	+	0.741286i
$650$		0			0
$651$	447.907	+	1081.34i	0.688029	+	1.66105i
$652$		0			0
$653$	−161.753	+	390.507i	−0.247708	+	0.598019i	−0.998009	−	0.0630771i	$-0.979909\pi$
$653$	−161.753	+	390.507i	−0.247708	+	0.598019i	0.750301	+	0.661096i	$0.229909\pi$
$654$		0			0
$655$	−306.175			−0.467443
$656$		0			0
$657$			118.603i			0.180521i
$658$		0			0
$659$	70.1853	+	29.0717i	0.106503	+	0.0441149i	0.435299	−	0.900286i	$-0.356643\pi$
$659$	70.1853	+	29.0717i	0.106503	+	0.0441149i	−0.328796	+	0.944401i	$0.606643\pi$
$660$		0			0
$661$	81.1193	−	33.6007i	0.122722	−	0.0508331i	−0.320477	−	0.947256i	$-0.603843\pi$
$661$	81.1193	−	33.6007i	0.122722	−	0.0508331i	0.443199	+	0.896423i	$0.353843\pi$
$662$		0			0
$663$	−187.011	+	187.011i	−0.282068	+	0.282068i
$664$		0			0
$665$	14.7302	−	14.7302i	0.0221507	−	0.0221507i
$666$		0			0
$667$	−434.794	+	180.097i	−0.651865	+	0.270011i
$668$		0			0
$669$	595.833	+	246.802i	0.890633	+	0.368912i
$670$		0			0
$671$		−	313.801i		−	0.467661i
$672$		0			0
$673$	−851.239			−1.26484			−0.632421	−	0.774625i	$-0.717939\pi$
$673$	−851.239			−1.26484			−0.632421	+	0.774625i	$0.717939\pi$
$674$		0			0
$675$	−177.959	+	429.630i	−0.263642	+	0.636489i
$676$		0			0
$677$	380.410	+	918.390i	0.561905	+	1.35656i	0.908241	+	0.418448i	$0.137426\pi$
$677$	380.410	+	918.390i	0.561905	+	1.35656i	−0.346335	+	0.938111i	$0.612574\pi$
$678$		0			0
$679$	1015.98	+	1015.98i	1.49629	+	1.49629i
$680$		0			0
$681$	−17.3413	−	17.3413i	−0.0254645	−	0.0254645i
$682$		0			0
$683$	425.467	+	1027.17i	0.622939	+	1.50391i	0.848236	+	0.529618i	$0.177665\pi$
$683$	425.467	+	1027.17i	0.622939	+	1.50391i	−0.225297	+	0.974290i	$0.572335\pi$
$684$		0			0
$685$	−66.7395	+	161.123i	−0.0974299	+	0.235217i
$686$		0			0
$687$	−1122.49			−1.63390
$688$		0			0
$689$		−	190.129i		−	0.275950i
$690$		0			0
$691$	260.940	+	108.085i	0.377627	+	0.156418i	0.563420	−	0.826171i	$-0.309485\pi$
$691$	260.940	+	108.085i	0.377627	+	0.156418i	−0.185793	+	0.982589i	$0.559485\pi$
$692$		0			0
$693$	371.526	−	153.891i	0.536113	−	0.222065i
$694$		0			0
$695$	239.377	−	239.377i	0.344428	−	0.344428i
$696$		0			0
$697$	−504.018	+	504.018i	−0.723124	+	0.723124i
$698$		0			0
$699$	936.707	−	387.997i	1.34007	−	0.555074i
$700$		0			0
$701$	727.192	+	301.213i	1.03736	+	0.429690i	0.835365	−	0.549695i	$-0.185256\pi$
$701$	727.192	+	301.213i	1.03736	+	0.429690i	0.201999	+	0.979386i	$0.435256\pi$
$702$		0			0
$703$		−	31.8623i		−	0.0453234i
$704$		0			0
$705$	119.413			0.169380
$706$		0			0
$707$	−48.9091	+	118.077i	−0.0691783	+	0.167011i
$708$		0			0
$709$	−259.577	−	626.675i	−0.366118	−	0.883886i	−0.994379	−	0.105883i	$-0.966233\pi$
$709$	−259.577	−	626.675i	−0.366118	−	0.883886i	0.628261	−	0.778003i	$-0.283767\pi$
$710$		0			0
$711$	6.66713	+	6.66713i	0.00937711	+	0.00937711i
$712$		0			0
$713$	325.095	+	325.095i	0.455953	+	0.455953i
$714$		0			0
$715$	34.2344	+	82.6491i	0.0478803	+	0.115593i
$716$		0			0
$717$	−366.383	+	884.526i	−0.510994	+	1.23365i
$718$		0			0
$719$	−1034.71			−1.43910			−0.719549	−	0.694442i	$-0.755651\pi$
$719$	−1034.71			−1.43910			−0.719549	+	0.694442i	$0.755651\pi$
$720$		0			0
$721$			498.193i			0.690975i
$722$		0			0
$723$	−201.429	−	83.4348i	−0.278602	−	0.115401i
$724$		0			0
$725$	−524.141	+	217.106i	−0.722953	+	0.299457i
$726$		0			0
$727$	−227.066	+	227.066i	−0.312332	+	0.312332i	−0.845813	−	0.533480i	$-0.820884\pi$
$727$	−227.066	+	227.066i	−0.312332	+	0.312332i	0.533480	+	0.845813i	$0.320884\pi$
$728$		0			0
$729$	262.439	−	262.439i	0.359999	−	0.359999i
$730$		0			0
$731$	−663.548	+	274.850i	−0.907726	+	0.375992i
$732$		0			0
$733$	−973.386	−	403.190i	−1.32795	−	0.550054i	−0.397879	−	0.917438i	$-0.630254\pi$
$733$	−973.386	−	403.190i	−1.32795	−	0.550054i	−0.930070	+	0.367384i	$0.880254\pi$
$734$		0			0
$735$		−	791.410i		−	1.07675i
$736$		0			0
$737$	−30.7045			−0.0416615
$738$		0			0
$739$	387.131	−	934.616i	0.523857	−	1.26470i	−0.411632	−	0.911350i	$-0.635041\pi$
$739$	387.131	−	934.616i	0.523857	−	1.26470i	0.935490	−	0.353354i	$-0.114959\pi$
$740$		0			0
$741$	−5.91821	−	14.2878i	−0.00798679	−	0.0192818i
$742$		0			0
$743$	−528.819	−	528.819i	−0.711735	−	0.711735i	0.255163	−	0.966898i	$-0.417871\pi$
$743$	−528.819	−	528.819i	−0.711735	−	0.711735i	−0.966898	+	0.255163i	$0.917871\pi$
$744$		0			0
$745$	−279.143	−	279.143i	−0.374689	−	0.374689i
$746$		0			0
$747$	−67.6158	−	163.239i	−0.0905164	−	0.218526i
$748$		0			0
$749$	434.423	−	1048.79i	0.580004	−	1.40025i
$750$		0			0
$751$	176.760			0.235366			0.117683	−	0.993051i	$-0.462453\pi$
$751$	176.760			0.235366			0.117683	+	0.993051i	$0.462453\pi$
$752$		0			0
$753$			604.051i			0.802192i
$754$		0			0
$755$	−23.8213	−	9.86711i	−0.0315514	−	0.0130690i
$756$		0			0
$757$	59.8575	−	24.7938i	0.0790720	−	0.0327527i	−0.342797	−	0.939410i	$-0.611374\pi$
$757$	59.8575	−	24.7938i	0.0790720	−	0.0327527i	0.421869	+	0.906657i	$0.361374\pi$
$758$		0			0
$759$	461.381	−	461.381i	0.607879	−	0.607879i
$760$		0			0
$761$	713.497	−	713.497i	0.937579	−	0.937579i	−0.0605844	−	0.998163i	$-0.519296\pi$
$761$	713.497	−	713.497i	0.937579	−	0.937579i	0.998163	+	0.0605844i	$0.0192964\pi$
$762$		0			0
$763$	−1175.22	+	486.793i	−1.54026	+	0.637999i
$764$		0			0
$765$	−70.0782	−	29.0273i	−0.0916055	−	0.0379442i
$766$		0			0
$767$		−	329.106i		−	0.429082i
$768$		0			0
$769$	−147.511			−0.191821			−0.0959107	−	0.995390i	$-0.530576\pi$
$769$	−147.511			−0.191821			−0.0959107	+	0.995390i	$0.530576\pi$
$770$		0			0
$771$	109.413	−	264.146i	0.141910	−	0.342601i
$772$		0			0
$773$	−104.027	−	251.144i	−0.134576	−	0.324896i	0.842198	−	0.539169i	$-0.181262\pi$
$773$	−104.027	−	251.144i	−0.134576	−	0.324896i	−0.976774	+	0.214273i	$0.931262\pi$
$774$		0			0
$775$	391.899	+	391.899i	0.505677	+	0.505677i
$776$		0			0
$777$	−1170.57	−	1170.57i	−1.50653	−	1.50653i
$778$		0			0
$779$	−15.9503	−	38.5075i	−0.0204754	−	0.0494319i
$780$		0			0
$781$	255.764	−	617.468i	0.327482	−	0.790612i
$782$		0			0
$783$	543.531			0.694164
$784$		0			0
$785$		−	50.2850i		−	0.0640573i
$786$		0			0
$787$	999.730	+	414.102i	1.27031	+	0.526178i	0.913057	−	0.407832i	$-0.133715\pi$
$787$	999.730	+	414.102i	1.27031	+	0.526178i	0.357248	+	0.934010i	$0.383715\pi$
$788$		0			0
$789$	−668.127	+	276.747i	−0.846802	+	0.350757i
$790$		0			0
$791$	−60.3806	+	60.3806i	−0.0763345	+	0.0763345i
$792$		0			0
$793$	−107.332	+	107.332i	−0.135349	+	0.135349i
$794$		0			0
$795$	208.100	−	86.1980i	0.261762	−	0.108425i
$796$		0			0
$797$	1138.14	+	471.431i	1.42802	+	0.591507i	0.956863	−	0.290540i	$-0.0938348\pi$
$797$	1138.14	+	471.431i	1.42802	+	0.591507i	0.471162	+	0.882047i	$0.343835\pi$
$798$		0			0
$799$			308.012i			0.385497i
$800$		0			0
$801$	180.940			0.225893
$802$		0			0
$803$	−163.574	+	394.902i	−0.203703	+	0.491784i
$804$		0			0
$805$	−162.696	−	392.783i	−0.202107	−	0.487929i
$806$		0			0
$807$	−501.184	−	501.184i	−0.621046	−	0.621046i
$808$		0			0
$809$	−169.569	−	169.569i	−0.209603	−	0.209603i	0.594496	−	0.804099i	$-0.297352\pi$
$809$	−169.569	−	169.569i	−0.209603	−	0.209603i	−0.804099	+	0.594496i	$0.797352\pi$
$810$		0			0
$811$	−437.562	−	1056.37i	−0.539534	−	1.30255i	−0.925048	−	0.379849i	$-0.875976\pi$
$811$	−437.562	−	1056.37i	−0.539534	−	1.30255i	0.385514	−	0.922702i	$-0.374024\pi$
$812$		0			0
$813$	−39.2973	+	94.8722i	−0.0483362	+	0.116694i
$814$		0			0
$815$	503.094			0.617293
$816$		0			0
$817$		−	41.9977i		−	0.0514048i
$818$		0			0
$819$	−179.713	−	74.4396i	−0.219430	−	0.0908908i
$820$		0			0
$821$	930.724	−	385.518i	1.13365	−	0.469572i	0.264627	−	0.964351i	$-0.414751\pi$
$821$	930.724	−	385.518i	1.13365	−	0.469572i	0.869019	+	0.494779i	$0.164751\pi$
$822$		0			0
$823$	320.389	−	320.389i	0.389294	−	0.389294i	−0.485142	−	0.874435i	$-0.661232\pi$
$823$	320.389	−	320.389i	0.389294	−	0.389294i	0.874435	+	0.485142i	$0.161232\pi$
$824$		0			0
$825$	556.191	−	556.191i	0.674171	−	0.674171i
$826$		0			0
$827$	14.6406	−	6.06433i	0.0177032	−	0.00733293i	−0.373814	−	0.927504i	$-0.621950\pi$
$827$	14.6406	−	6.06433i	0.0177032	−	0.00733293i	0.391517	+	0.920171i	$0.371950\pi$
$828$		0			0
$829$	753.878	+	312.267i	0.909383	+	0.376679i	0.787820	−	0.615905i	$-0.211210\pi$
$829$	753.878	+	312.267i	0.909383	+	0.376679i	0.121562	+	0.992584i	$0.461210\pi$
$830$		0			0
$831$			1375.70i			1.65548i
$832$		0			0
$833$	2041.35			2.45061
$834$		0			0
$835$	−9.66607	+	23.3360i	−0.0115761	+	0.0279473i
$836$		0			0
$837$	−203.199	−	490.565i	−0.242770	−	0.586099i
$838$		0			0
$839$	233.705	+	233.705i	0.278552	+	0.278552i	0.832531	−	0.553979i	$-0.186891\pi$
$839$	233.705	+	233.705i	0.278552	+	0.278552i	−0.553979	+	0.832531i	$0.686891\pi$
$840$		0			0
$841$	−125.796	−	125.796i	−0.149579	−	0.149579i
$842$		0			0
$843$	−522.667	−	1261.83i	−0.620008	−	1.49683i
$844$		0			0
$845$	−94.8684	+	229.033i	−0.112270	+	0.271044i
$846$		0			0
$847$	−184.423			−0.217736
$848$		0			0
$849$		−	658.886i		−	0.776073i
$850$		0			0
$851$	−600.767	−	248.846i	−0.705954	−	0.292416i
$852$		0			0
$853$	979.574	−	405.753i	1.14839	−	0.475677i	0.274395	−	0.961617i	$-0.411523\pi$
$853$	979.574	−	405.753i	1.14839	−	0.475677i	0.873992	+	0.485940i	$0.161523\pi$
$854$		0			0
$855$	3.13633	−	3.13633i	0.00366822	−	0.00366822i
$856$		0			0
$857$	716.322	−	716.322i	0.835848	−	0.835848i	−0.152461	−	0.988309i	$-0.548720\pi$
$857$	716.322	−	716.322i	0.835848	−	0.835848i	0.988309	+	0.152461i	$0.0487198\pi$
$858$		0			0
$859$	398.325	−	164.992i	0.463708	−	0.192074i	−0.138583	−	0.990351i	$-0.544255\pi$
$859$	398.325	−	164.992i	0.463708	−	0.192074i	0.602291	+	0.798277i	$0.294255\pi$
$860$		0			0
$861$	−2000.70	−	828.716i	−2.32369	−	0.962504i
$862$		0			0
$863$			1279.79i			1.48295i	0.670980	+	0.741475i	$0.265874\pi$
$863$			1279.79i			1.48295i	−0.670980	+	0.741475i	$0.734126\pi$
$864$		0			0
$865$	399.132			0.461424
$866$		0			0
$867$	−71.8331	+	173.421i	−0.0828525	+	0.200024i
$868$		0			0
$869$	13.0039	+	31.3942i	0.0149642	+	0.0361268i
$870$		0			0
$871$	10.5021	+	10.5021i	0.0120576	+	0.0120576i
$872$		0			0
$873$	216.321	+	216.321i	0.247790	+	0.247790i
$874$		0			0
$875$	−418.684	−	1010.79i	−0.478496	−	1.15519i
$876$		0			0
$877$	351.648	−	848.954i	0.400967	−	0.968021i	−0.586464	−	0.809975i	$-0.699481\pi$
$877$	351.648	−	848.954i	0.400967	−	0.968021i	0.987432	−	0.158046i	$-0.0505194\pi$
$878$		0			0
$879$	102.285			0.116365
$880$		0			0
$881$			1327.06i			1.50632i	0.657839	+	0.753158i	$0.271471\pi$
$881$			1327.06i			1.50632i	−0.657839	+	0.753158i	$0.728529\pi$
$882$		0			0
$883$	412.717	+	170.953i	0.467403	+	0.193605i	0.603939	−	0.797030i	$-0.293597\pi$
$883$	412.717	+	170.953i	0.467403	+	0.193605i	−0.136536	+	0.990635i	$0.543597\pi$
$884$		0			0
$885$	360.213	−	149.205i	0.407020	−	0.168593i
$886$		0			0
$887$	411.723	−	411.723i	0.464174	−	0.464174i	−0.435847	−	0.900021i	$-0.643551\pi$
$887$	411.723	−	411.723i	0.464174	−	0.464174i	0.900021	+	0.435847i	$0.143551\pi$
$888$		0			0
$889$	−330.347	+	330.347i	−0.371594	+	0.371594i
$890$		0			0
$891$	−943.871	+	390.964i	−1.05934	+	0.438793i
$892$		0			0
$893$	−16.6400	−	6.89250i	−0.0186338	−	0.00771836i
$894$		0			0
$895$			4.81723i			0.00538238i
$896$		0			0
$897$	−315.620			−0.351861
$898$		0			0
$899$	247.898	−	598.480i	0.275749	−	0.665717i
$900$		0			0
$901$	222.338	+	536.772i	0.246768	+	0.595751i
$902$		0			0
$903$	−1542.93	−	1542.93i	−1.70867	−	1.70867i
$904$		0			0
$905$	243.156	+	243.156i	0.268681	+	0.268681i
$906$		0			0
$907$	307.189	+	741.619i	0.338687	+	0.817662i	0.997842	+	0.0656553i	$0.0209138\pi$
$907$	307.189	+	741.619i	0.338687	+	0.817662i	−0.659156	+	0.752006i	$0.729086\pi$
$908$		0			0
$909$	−10.4136	+	25.1407i	−0.0114561	+	0.0276575i
$910$		0			0
$911$	−708.126			−0.777307			−0.388653	−	0.921384i	$-0.627060\pi$
$911$	−708.126			−0.777307			−0.388653	+	0.921384i	$0.627060\pi$
$912$		0			0
$913$		−	636.779i		−	0.697458i
$914$		0			0
$915$	−166.137	−	68.8164i	−0.181571	−	0.0752091i
$916$		0			0
$917$	2216.70	−	918.187i	2.41734	−	1.00129i
$918$		0			0
$919$	−628.260	+	628.260i	−0.683635	+	0.683635i	−0.960817	−	0.277183i	$-0.910599\pi$
$919$	−628.260	+	628.260i	−0.683635	+	0.683635i	0.277183	+	0.960817i	$0.410599\pi$
$920$		0			0
$921$	−1223.33	+	1223.33i	−1.32826	+	1.32826i
$922$		0			0
$923$	−298.679	+	123.717i	−0.323596	+	0.134038i
$924$		0			0
$925$	−724.221	−	299.982i	−0.782941	−	0.324305i
$926$		0			0
$927$			106.074i			0.114427i
$928$		0			0
$929$	−972.033			−1.04632			−0.523161	−	0.852234i	$-0.675247\pi$
$929$	−972.033			−1.04632			−0.523161	+	0.852234i	$0.675247\pi$
$930$		0			0
$931$	−45.6801	+	110.281i	−0.0490656	+	0.118455i
$932$		0			0
$933$	−429.901	−	1037.87i	−0.460773	−	1.11241i
$934$		0			0
$935$	−193.301	−	193.301i	−0.206739	−	0.206739i
$936$		0			0
$937$	396.897	+	396.897i	0.423583	+	0.423583i	0.886435	−	0.462853i	$-0.153174\pi$
$937$	396.897	+	396.897i	0.423583	+	0.423583i	−0.462853	+	0.886435i	$0.653174\pi$
$938$		0			0
$939$	5.40618	+	13.0517i	0.00575738	+	0.0138996i
$940$		0			0
$941$	−486.386	+	1174.24i	−0.516882	+	1.24786i	0.422928	+	0.906163i	$0.361002\pi$
$941$	−486.386	+	1174.24i	−0.516882	+	1.24786i	−0.939809	+	0.341699i	$0.888998\pi$
$942$		0			0
$943$	−850.634			−0.902051
$944$		0			0
$945$			491.014i			0.519591i
$946$		0			0
$947$	−319.348	−	132.278i	−0.337221	−	0.139681i	0.207646	−	0.978204i	$-0.433420\pi$
$947$	−319.348	−	132.278i	−0.337221	−	0.139681i	−0.544867	+	0.838523i	$0.683420\pi$
$948$		0			0
$949$	191.020	−	79.1232i	0.201286	−	0.0833753i
$950$		0			0
$951$	1345.32	−	1345.32i	1.41464	−	1.41464i
$952$		0			0
$953$	234.445	−	234.445i	0.246007	−	0.246007i	−0.573322	−	0.819330i	$-0.694346\pi$
$953$	234.445	−	234.445i	0.246007	−	0.246007i	0.819330	+	0.573322i	$0.194346\pi$
$954$		0			0
$955$	295.708	−	122.486i	0.309642	−	0.128258i
$956$		0			0
$957$	−849.374	−	351.822i	−0.887538	−	0.367630i
$958$		0			0
$959$		−	1366.67i		−	1.42510i
$960$		0			0
$961$	328.164			0.341482
$962$		0			0
$963$	92.4964	−	223.306i	0.0960502	−	0.231886i
$964$		0			0
$965$	137.178	+	331.178i	0.142154	+	0.343189i
$966$		0			0
$967$	−431.918	−	431.918i	−0.446658	−	0.446658i	0.447584	−	0.894242i	$-0.352285\pi$
$967$	−431.918	−	431.918i	−0.446658	−	0.446658i	−0.894242	+	0.447584i	$0.852285\pi$
$968$		0			0
$969$	33.4165	+	33.4165i	0.0344855	+	0.0344855i
$970$		0			0
$971$	−391.385	−	944.887i	−0.403074	−	0.973107i	−0.986915	−	0.161239i	$-0.948451\pi$
$971$	−391.385	−	944.887i	−0.403074	−	0.973107i	0.583841	−	0.811868i	$-0.301549\pi$
$972$		0			0
$973$	−1015.22	+	2450.95i	−1.04339	+	2.51897i
$974$		0			0
$975$	−380.477			−0.390233
$976$		0			0
$977$		−	1157.98i		−	1.18524i	−0.805481	−	0.592621i	$-0.798093\pi$
$977$		−	1157.98i		−	1.18524i	0.805481	−	0.592621i	$-0.201907\pi$
$978$		0			0
$979$	602.463	+	249.548i	0.615386	+	0.254901i
$980$		0			0
$981$	−250.226	+	103.647i	−0.255072	+	0.105654i
$982$		0			0
$983$	−396.529	+	396.529i	−0.403386	+	0.403386i	−0.879425	−	0.476038i	$-0.842072\pi$
$983$	−396.529	+	396.529i	−0.403386	+	0.403386i	0.476038	+	0.879425i	$0.342072\pi$
$984$		0			0
$985$	394.291	−	394.291i	0.400296	−	0.400296i
$986$		0			0
$987$	−864.547	+	358.107i	−0.875934	+	0.362824i
$988$		0			0
$989$	−791.870	−	328.003i	−0.800678	−	0.331652i
$990$		0			0
$991$			134.269i			0.135489i	0.997703	+	0.0677444i	$0.0215802\pi$
$991$			134.269i			0.135489i	−0.997703	+	0.0677444i	$0.978420\pi$
$992$		0			0
$993$	858.182			0.864232
$994$		0			0
$995$	−236.619	+	571.249i	−0.237808	+	0.574120i
$996$		0			0
$997$	−470.645	−	1136.24i	−0.472061	−	1.13966i	−0.963251	−	0.268603i	$-0.913438\pi$
$997$	−470.645	−	1136.24i	−0.472061	−	1.13966i	0.491190	−	0.871052i	$-0.336562\pi$
$998$		0			0
$999$	531.046	+	531.046i	0.531577	+	0.531577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.3.h.a.95.2		28
4.3	odd	2		256.3.h.b.95.6		28
8.3	odd	2		32.3.h.a.3.4	✓	28
8.5	even	2		128.3.h.a.47.6		28
24.11	even	2		288.3.u.a.163.4		28
32.5	even	8		32.3.h.a.11.4	yes	28
32.11	odd	8	inner	256.3.h.a.159.2		28
32.21	even	8		256.3.h.b.159.6		28
32.27	odd	8		128.3.h.a.79.6		28
96.5	odd	8		288.3.u.a.235.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.4	✓	28	8.3	odd	2
32.3.h.a.11.4	yes	28	32.5	even	8
128.3.h.a.47.6		28	8.5	even	2
128.3.h.a.79.6		28	32.27	odd	8
256.3.h.a.95.2		28	1.1	even	1	trivial
256.3.h.a.159.2		28	32.11	odd	8	inner
256.3.h.b.95.6		28	4.3	odd	2
256.3.h.b.159.6		28	32.21	even	8
288.3.u.a.163.4		28	24.11	even	2
288.3.u.a.235.4		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)

\(f(q)\)	\(=\)	\(q+(-1.31872 + 3.18367i) q^{3} +(0.659338 + 1.59178i) q^{5} +(-9.54718 - 9.54718i) q^{7} +(-2.03276 - 2.03276i) q^{9} +O(q^{10})\)	\(q+(-1.31872 + 3.18367i) q^{3} +(0.659338 + 1.59178i) q^{5} +(-9.54718 - 9.54718i) q^{7} +(-2.03276 - 2.03276i) q^{9} +(-3.96481 - 9.57189i) q^{11} +(-1.91784 + 4.63007i) q^{13} -5.93719 q^{15} -15.3143i q^{17} +(0.827335 + 0.342693i) q^{19} +(42.9851 - 17.8050i) q^{21} +(12.9230 - 12.9230i) q^{23} +(15.5786 - 15.5786i) q^{25} +(-19.5007 + 8.07746i) q^{27} +(-23.7905 - 9.85436i) q^{29} +25.1562i q^{31} +35.7022 q^{33} +(8.90221 - 21.4918i) q^{35} +(-13.6161 - 32.8721i) q^{37} +(-12.2115 - 12.2115i) q^{39} +(-32.9116 - 32.9116i) q^{41} +(-17.9473 - 43.3286i) q^{43} +(1.89544 - 4.57600i) q^{45} -20.1127 q^{47} +133.297i q^{49} +(48.7557 + 20.1953i) q^{51} +(-35.0503 + 14.5183i) q^{53} +(12.6222 - 12.6222i) q^{55} +(-2.18204 + 2.18204i) q^{57} +(-60.6706 + 25.1306i) q^{59} +(27.9825 + 11.5907i) q^{61} +38.8143i q^{63} -8.63457 q^{65} +(1.13412 - 2.73801i) q^{67} +(24.1008 + 58.1845i) q^{69} +(45.6144 + 45.6144i) q^{71} +(-29.1727 - 29.1727i) q^{73} +(29.0534 + 70.1410i) q^{75} +(-53.5318 + 129.237i) q^{77} -3.27983 q^{79} -98.6086i q^{81} +(56.7834 + 23.5205i) q^{83} +(24.3770 - 10.0973i) q^{85} +(62.7460 - 62.7460i) q^{87} +(-44.5059 + 44.5059i) q^{89} +(62.5140 - 25.8942i) q^{91} +(-80.0891 - 33.1740i) q^{93} +1.54289i q^{95} -106.417 q^{97} +(-11.3979 + 27.5169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more