LMFDB - Embedded newform 128.3.h.a.79.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(15,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, 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("128.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.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:	$3.48774738381$
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			79.6
Character	$\chi$	$=$	128.79
Dual form			128.3.h.a.47.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31872 + 3.18367i) q^{3} +(-0.659338 + 1.59178i) q^{5} +(-9.54718 + 9.54718i) q^{7} +(-2.03276 + 2.03276i) q^{9} +O(q^{10})$	\(q+(1.31872 + 3.18367i) q^{3} +(-0.659338 + 1.59178i) q^{5} +(-9.54718 + 9.54718i) q^{7} +(-2.03276 + 2.03276i) q^{9} +(3.96481 - 9.57189i) q^{11} +(1.91784 + 4.63007i) q^{13} -5.93719 q^{15} +15.3143i q^{17} +(-0.827335 + 0.342693i) q^{19} +(-42.9851 - 17.8050i) q^{21} +(12.9230 + 12.9230i) q^{23} +(15.5786 + 15.5786i) q^{25} +(19.5007 + 8.07746i) q^{27} +(23.7905 - 9.85436i) q^{29} -25.1562i q^{31} +35.7022 q^{33} +(-8.90221 - 21.4918i) q^{35} +(13.6161 - 32.8721i) q^{37} +(-12.2115 + 12.2115i) q^{39} +(-32.9116 + 32.9116i) q^{41} +(17.9473 - 43.3286i) q^{43} +(-1.89544 - 4.57600i) q^{45} -20.1127 q^{47} -133.297i q^{49} +(-48.7557 + 20.1953i) q^{51} +(35.0503 + 14.5183i) q^{53} +(12.6222 + 12.6222i) q^{55} +(-2.18204 - 2.18204i) q^{57} +(60.6706 + 25.1306i) q^{59} +(-27.9825 + 11.5907i) q^{61} -38.8143i q^{63} -8.63457 q^{65} +(-1.13412 - 2.73801i) q^{67} +(-24.1008 + 58.1845i) q^{69} +(45.6144 - 45.6144i) q^{71} +(-29.1727 + 29.1727i) q^{73} +(-29.0534 + 70.1410i) q^{75} +(53.5318 + 129.237i) q^{77} -3.27983 q^{79} +98.6086i q^{81} +(-56.7834 + 23.5205i) q^{83} +(-24.3770 - 10.0973i) q^{85} +(62.7460 + 62.7460i) q^{87} +(-44.5059 - 44.5059i) q^{89} +(-62.5140 - 25.8942i) q^{91} +(80.0891 - 33.1740i) q^{93} -1.54289i q^{95} -106.417 q^{97} +(11.3979 + 27.5169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$

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	0.976097	+	0.217337i	$0.0697372\pi$
$3$	1.31872	+	3.18367i	0.439573	+	1.06122i	−0.536524	+	0.843885i	$0.680263\pi$
$4$		0			0
$5$	−0.659338	+	1.59178i	−0.131868	+	0.318356i	−0.975997	−	0.217782i	$-0.930118\pi$
$5$	−0.659338	+	1.59178i	−0.131868	+	0.318356i	0.844130	+	0.536139i	$0.180118\pi$
$6$		0			0
$7$	−9.54718	+	9.54718i	−1.36388	+	1.36388i	−0.494975	+	0.868907i	$0.664823\pi$
$7$	−9.54718	+	9.54718i	−1.36388	+	1.36388i	−0.868907	+	0.494975i	$0.835177\pi$
$8$		0			0
$9$	−2.03276	+	2.03276i	−0.225863	+	0.225863i
$10$		0			0
$11$	3.96481	−	9.57189i	0.360437	−	0.870172i	−0.634799	−	0.772677i	$-0.718917\pi$
$11$	3.96481	−	9.57189i	0.360437	−	0.870172i	0.995236	−	0.0974947i	$-0.0310829\pi$
$12$		0			0
$13$	1.91784	+	4.63007i	0.147526	+	0.356159i	0.980317	−	0.197428i	$-0.0632587\pi$
$13$	1.91784	+	4.63007i	0.147526	+	0.356159i	−0.832792	+	0.553587i	$0.813259\pi$
$14$		0			0
$15$	−5.93719			−0.395813
$16$		0			0
$17$			15.3143i			0.900842i	0.892816	+	0.450421i	$0.148726\pi$
$17$			15.3143i			0.900842i	−0.892816	+	0.450421i	$0.851274\pi$
$18$		0			0
$19$	−0.827335	+	0.342693i	−0.0435439	+	0.0180365i	−0.404349	−	0.914605i	$-0.632502\pi$
$19$	−0.827335	+	0.342693i	−0.0435439	+	0.0180365i	0.360805	+	0.932641i	$0.382502\pi$
$20$		0			0
$21$	−42.9851	−	17.8050i	−2.04691	−	0.847857i
$22$		0			0
$23$	12.9230	+	12.9230i	0.561871	+	0.561871i	0.929839	−	0.367968i	$-0.119946\pi$
$23$	12.9230	+	12.9230i	0.561871	+	0.561871i	−0.367968	+	0.929839i	$0.619946\pi$
$24$		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	$-0.478567\pi$
$29$	23.7905	−	9.85436i	0.820363	−	0.339805i	0.753080	+	0.657929i	$0.228567\pi$
$30$		0			0
$31$		−	25.1562i		−	0.811491i	−0.913986	−	0.405746i	$-0.867012\pi$
$31$		−	25.1562i		−	0.811491i	0.913986	−	0.405746i	$-0.132988\pi$
$32$		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	−0.626076	−	0.779762i	$-0.715340\pi$
$37$	13.6161	−	32.8721i	0.368001	−	0.888434i	0.994078	−	0.108672i	$-0.0346599\pi$
$38$		0			0
$39$	−12.2115	+	12.2115i	−0.313116	+	0.313116i
$40$		0			0
$41$	−32.9116	+	32.9116i	−0.802721	+	0.802721i	−0.983520	−	0.180799i	$-0.942132\pi$
$41$	−32.9116	+	32.9116i	−0.802721	+	0.802721i	0.180799	+	0.983520i	$0.442132\pi$
$42$		0			0
$43$	17.9473	−	43.3286i	0.417379	−	1.00764i	−0.565725	−	0.824594i	$-0.691404\pi$
$43$	17.9473	−	43.3286i	0.417379	−	1.00764i	0.983104	−	0.183048i	$-0.0585964\pi$
$44$		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	$-0.258490\pi$
$53$	35.0503	+	14.5183i	0.661327	+	0.273931i	−0.0266698	+	0.999644i	$0.508490\pi$
$54$		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	$-0.187136\pi$
$59$	60.6706	+	25.1306i	1.02832	+	0.425942i	0.196212	+	0.980562i	$0.437136\pi$
$60$		0			0
$61$	−27.9825	+	11.5907i	−0.458730	+	0.190012i	−0.600067	−	0.799949i	$-0.704860\pi$
$61$	−27.9825	+	11.5907i	−0.458730	+	0.190012i	0.141338	+	0.989961i	$0.454860\pi$
$62$		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	$-0.132040\pi$
$67$	−1.13412	−	2.73801i	−0.0169272	−	0.0408659i	−0.932117	+	0.362157i	$0.882040\pi$
$68$		0			0
$69$	−24.1008	+	58.1845i	−0.349287	+	0.843253i
$70$		0			0
$71$	45.6144	−	45.6144i	0.642456	−	0.642456i	−0.308702	−	0.951159i	$-0.599895\pi$
$71$	45.6144	−	45.6144i	0.642456	−	0.642456i	0.951159	+	0.308702i	$0.0998947\pi$
$72$		0			0
$73$	−29.1727	+	29.1727i	−0.399626	+	0.399626i	−0.878101	−	0.478475i	$-0.841190\pi$
$73$	−29.1727	+	29.1727i	−0.399626	+	0.399626i	0.478475	+	0.878101i	$0.341190\pi$
$74$		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	$-0.745729\pi$
$83$	−56.7834	+	23.5205i	−0.684138	+	0.283379i	0.0134176	+	0.999910i	$0.495729\pi$
$84$		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	0.411392	−	0.911458i	$-0.365043\pi$
$89$	−44.5059	−	44.5059i	−0.500066	−	0.500066i	−0.911458	+	0.411392i	$0.865043\pi$
$90$		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	$-0.860078\pi$
$101$	3.62243	−	8.74531i	0.0358656	−	0.0865872i	0.940797	+	0.338969i	$0.110078\pi$
$102$		0			0
$103$	−26.0911	+	26.0911i	−0.253312	+	0.253312i	−0.822327	−	0.569015i	$-0.807325\pi$
$103$	−26.0911	+	26.0911i	−0.253312	+	0.253312i	0.569015	+	0.822327i	$0.307325\pi$
$104$		0			0
$105$	56.6834	−	56.6834i	0.539842	−	0.539842i
$106$		0			0
$107$	−32.1753	+	77.6781i	−0.300704	+	0.725963i	0.699235	+	0.714892i	$0.253524\pi$
$107$	−32.1753	+	77.6781i	−0.300704	+	0.725963i	−0.999939	+	0.0110713i	$0.996476\pi$
$108$		0			0
$109$	−36.0541	−	87.0422i	−0.330771	−	0.798553i	−0.998531	−	0.0541760i	$-0.982747\pi$
$109$	−36.0541	−	87.0422i	−0.330771	−	0.798553i	0.667760	−	0.744377i	$-0.267253\pi$
$110$		0			0
$111$	122.609			1.10459
$112$		0			0
$113$			6.32445i			0.0559686i	0.999608	+	0.0279843i	$0.00890884\pi$
$113$			6.32445i			0.0559686i	−0.999608	+	0.0279843i	$0.991091\pi$
$114$		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	$0.0434975\pi$
$127$			34.6015i			0.272453i	−0.990678	+	0.136226i	$0.956503\pi$
$128$		0			0
$129$	161.611			1.25280
$130$		0			0
$131$	68.0051	+	164.179i	0.519123	+	1.25327i	0.938443	+	0.345434i	$0.112268\pi$
$131$	68.0051	+	164.179i	0.519123	+	1.25327i	−0.419320	+	0.907838i	$0.637732\pi$
$132$		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	−0.395865	−	0.918309i	$-0.629555\pi$
$137$	71.5748	−	71.5748i	0.522444	−	0.522444i	0.918309	+	0.395865i	$0.129555\pi$
$138$		0			0
$139$	75.1916	−	181.529i	0.540947	−	1.30596i	−0.383109	−	0.923703i	$-0.625147\pi$
$139$	75.1916	−	181.529i	0.540947	−	1.30596i	0.924056	−	0.382258i	$-0.124853\pi$
$140$		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	$-0.0958152\pi$
$149$	211.685	+	87.6826i	1.42070	+	0.588474i	0.465665	+	0.884961i	$0.345815\pi$
$150$		0			0
$151$	−10.5820	−	10.5820i	−0.0700794	−	0.0700794i	0.671198	−	0.741278i	$-0.265780\pi$
$151$	−10.5820	−	10.5820i	−0.0700794	−	0.0700794i	−0.741278	+	0.671198i	$0.765780\pi$
$152$		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	$-0.595371\pi$
$157$	26.9641	−	11.1689i	0.171746	−	0.0711394i	0.466900	+	0.884310i	$0.345371\pi$
$158$		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	−0.753579	−	0.657357i	$-0.771674\pi$
$163$	−111.743	−	269.771i	−0.685540	−	1.65504i	0.0680396	−	0.997683i	$-0.478326\pi$
$164$		0			0
$165$	−23.5398	+	56.8301i	−0.142665	+	0.344425i
$166$		0			0
$167$	10.3664	−	10.3664i	0.0620741	−	0.0620741i	−0.675388	−	0.737462i	$-0.736024\pi$
$167$	10.3664	−	10.3664i	0.0620741	−	0.0620741i	0.737462	+	0.675388i	$0.236024\pi$
$168$		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	−0.942461	−	0.334317i	$-0.891494\pi$
$173$	−88.6518	−	214.024i	−0.512438	−	1.23714i	0.430022	−	0.902818i	$-0.358506\pi$
$174$		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	$-0.627486\pi$
$179$	−2.58312	+	1.06996i	−0.0144308	+	0.00597744i	0.375456	+	0.926840i	$0.377486\pi$
$180$		0			0
$181$	−184.394	−	76.3786i	−1.01875	−	0.421981i	−0.190112	−	0.981762i	$-0.560885\pi$
$181$	−184.394	−	76.3786i	−1.01875	−	0.421981i	−0.828640	+	0.559781i	$0.810885\pi$
$182$		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	$0.161658\pi$
$191$			185.771i			0.972625i	−0.873785	+	0.486313i	$0.838342\pi$
$192$		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	−0.212558	−	0.977148i	$-0.568180\pi$
$197$	123.852	−	299.006i	0.628691	−	1.51780i	0.841250	−	0.540647i	$-0.181820\pi$
$198$		0			0
$199$	253.762	−	253.762i	1.27519	−	1.27519i	0.331858	−	0.943329i	$-0.392324\pi$
$199$	253.762	−	253.762i	1.27519	−	1.27519i	0.943329	−	0.331858i	$-0.107676\pi$
$200$		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	$-0.709708\pi$
$211$	−102.533	+	42.4705i	−0.485938	+	0.201282i	0.126244	+	0.991999i	$0.459708\pi$
$212$		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	$0.137839\pi$
$223$			187.153i			0.839252i	−0.907697	+	0.419626i	$0.862161\pi$
$224$		0			0
$225$	−63.3353			−0.281490
$226$		0			0
$227$	2.72348	+	6.57507i	0.0119977	+	0.0289650i	0.929765	−	0.368154i	$-0.120010\pi$
$227$	2.72348	+	6.57507i	0.0119977	+	0.0289650i	−0.917767	+	0.397119i	$0.870010\pi$
$228$		0			0
$229$	−124.655	+	300.944i	−0.544345	+	1.31416i	0.377286	+	0.926097i	$0.376857\pi$
$229$	−124.655	+	300.944i	−0.544345	+	1.31416i	−0.921631	+	0.388068i	$0.873143\pi$
$230$		0			0
$231$	−340.855	+	340.855i	−1.47556	+	1.47556i
$232$		0			0
$233$	−208.047	+	208.047i	−0.892904	+	0.892904i	−0.994796	−	0.101891i	$-0.967511\pi$
$233$	−208.047	+	208.047i	−0.892904	+	0.892904i	0.101891	+	0.994796i	$0.467511\pi$
$234$		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	$-0.958096\pi$
$241$		−	63.2696i		−	0.262529i	0.991347	−	0.131265i	$-0.0419038\pi$
$242$		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	$-0.488542\pi$
$251$	−161.948	−	67.0812i	−0.645212	−	0.267256i	−0.681201	+	0.732097i	$0.738542\pi$
$252$		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	−0.366272	−	0.930508i	$-0.619366\pi$
$263$	148.394	−	148.394i	0.564235	−	0.564235i	0.930508	+	0.366272i	$0.119366\pi$
$264$		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	$-0.000128086\pi$
$269$	78.7117	+	190.027i	0.292609	+	0.706420i	−0.707391	+	0.706822i	$0.750128\pi$
$270$		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	$-0.631140\pi$
$277$	−368.831	−	152.775i	−1.33152	−	0.551534i	−0.931089	+	0.364793i	$0.881140\pi$
$278$		0			0
$279$	51.1367	+	51.1367i	0.183286	+	0.183286i
$280$		0			0
$281$	−280.258	−	280.258i	−0.997358	−	0.997358i	0.00263807	−	0.999997i	$-0.499160\pi$
$281$	−280.258	−	280.258i	−0.997358	−	0.997358i	−0.999997	+	0.00263807i	$0.999160\pi$
$282$		0			0
$283$	176.650	+	73.1708i	0.624204	+	0.258554i	0.672288	−	0.740289i	$-0.265312\pi$
$283$	176.650	+	73.1708i	0.624204	+	0.258554i	−0.0480840	+	0.998843i	$0.515312\pi$
$284$		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	$-0.858870\pi$
$293$	11.3590	−	27.4231i	0.0387679	−	0.0935940i	0.942078	+	0.335395i	$0.108870\pi$
$294$		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	$-0.929734\pi$
$307$	−463.833	+	192.126i	−1.51086	+	0.625817i	−0.535122	+	0.844775i	$0.679734\pi$
$308$		0			0
$309$	−117.472	−	48.6586i	−0.380169	−	0.157471i
$310$		0			0
$311$	−230.516	−	230.516i	−0.741210	−	0.741210i	0.231601	−	0.972811i	$-0.425604\pi$
$311$	−230.516	−	230.516i	−0.741210	−	0.741210i	−0.972811	+	0.231601i	$0.925604\pi$
$312$		0			0
$313$	2.89884	+	2.89884i	0.00926146	+	0.00926146i	0.711722	−	0.702461i	$-0.247915\pi$
$313$	2.89884	+	2.89884i	0.00926146	+	0.00926146i	−0.702461	+	0.711722i	$0.747915\pi$
$314$		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	$-0.288574\pi$
$317$	510.087	−	211.285i	1.60911	−	0.666514i	0.992666	+	0.120887i	$0.0385738\pi$
$318$		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	$-0.752234\pi$
$331$	95.3030	−	230.082i	0.287924	−	0.695111i	0.999975	+	0.00701670i	$0.00223350\pi$
$332$		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	$-0.902123\pi$
$337$		−	203.997i		−	0.605334i	0.953096	−	0.302667i	$-0.0978769\pi$
$338$		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	$-0.314714\pi$
$347$	120.709	+	49.9993i	0.347865	+	0.144090i	−0.201908	+	0.979404i	$0.564714\pi$
$348$		0			0
$349$	279.116	−	115.614i	0.799759	−	0.331271i	0.0548993	−	0.998492i	$-0.482516\pi$
$349$	279.116	−	115.614i	0.799759	−	0.331271i	0.744860	+	0.667221i	$0.232516\pi$
$350$		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	−0.925293	−	0.379252i	$-0.876181\pi$
$359$	−196.029	+	196.029i	−0.546041	+	0.546041i	0.379252	+	0.925293i	$0.376181\pi$
$360$		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	$-0.321365\pi$
$373$	115.583	+	47.8760i	0.309874	+	0.128354i	−0.222327	+	0.974972i	$0.571365\pi$
$374$		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	$-0.450651\pi$
$379$	−164.874	−	68.2930i	−0.435024	−	0.180193i	−0.589438	+	0.807813i	$0.700651\pi$
$380$		0			0
$381$	−110.160	+	45.6297i	−0.289133	+	0.119763i
$382$		0			0
$383$		−	307.309i		−	0.802373i	−0.915996	−	0.401186i	$-0.868598\pi$
$383$		−	307.309i		−	0.802373i	0.915996	−	0.401186i	$-0.131402\pi$
$384$		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	0.407024	+	0.913418i	$0.366567\pi$
$389$	−204.874	+	494.611i	−0.526669	+	1.27149i	−0.933693	+	0.358075i	$0.883433\pi$
$390$		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	−0.904705	−	0.426040i	$-0.859908\pi$
$397$	−224.796	−	542.706i	−0.566237	−	1.36702i	0.338467	−	0.940978i	$-0.390092\pi$
$398$		0			0
$399$	41.6647			0.104423
$400$		0			0
$401$			125.790i			0.313691i	0.987623	+	0.156846i	$0.0501325\pi$
$401$			125.790i			0.313691i	−0.987623	+	0.156846i	$0.949868\pi$
$402$		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	0.972544	+	0.232717i	$0.0747617\pi$
$409$	492.952	+	492.952i	1.20526	+	1.20526i	0.232717	+	0.972544i	$0.425238\pi$
$410$		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	−0.956925	−	0.290336i	$-0.906233\pi$
$419$	−203.456	−	491.187i	−0.485576	−	1.17228i	0.471349	−	0.881947i	$-0.343767\pi$
$420$		0			0
$421$	−0.995616	+	2.40363i	−0.00236488	+	0.00570934i	−0.925058	−	0.379827i	$-0.875984\pi$
$421$	−0.995616	+	2.40363i	−0.00236488	+	0.00570934i	0.922693	+	0.385536i	$0.125984\pi$
$422$		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	$-0.827603\pi$
$433$		−	446.431i		−	1.03102i	0.856884	−	0.515509i	$-0.172397\pi$
$434$		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	0.899503	−	0.436914i	$-0.143928\pi$
$439$	203.077	+	203.077i	0.462590	+	0.462590i	−0.436914	+	0.899503i	$0.643928\pi$
$440$		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	$-0.194264\pi$
$443$	440.203	+	182.338i	0.993685	+	0.411598i	0.174207	+	0.984709i	$0.444264\pi$
$444$		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	−0.980866	−	0.194685i	$-0.937632\pi$
$457$	−359.285	+	359.285i	−0.786181	+	0.786181i	0.194685	+	0.980866i	$0.437632\pi$
$458$		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	$-0.0630692\pi$
$461$	68.2156	+	164.687i	0.147973	+	0.357239i	−0.832462	+	0.554083i	$0.813069\pi$
$462$		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	0.862718	−	0.505685i	$-0.168760\pi$
$467$	854.762	−	354.054i	1.83033	−	0.758146i	0.967607	−	0.252461i	$-0.0812399\pi$
$468$		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	$0.418542\pi$
$479$			926.802i			1.93487i	−0.253122	+	0.967434i	$0.581458\pi$
$480$		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	−0.230127	+	0.973161i	$0.573914\pi$
$487$	−586.001	+	586.001i	−1.20329	+	1.20329i	−0.973161	+	0.230127i	$0.926086\pi$
$488$		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	$-0.860465\pi$
$491$	17.1543	−	41.4142i	0.0349375	−	0.0843466i	0.940385	+	0.340111i	$0.110465\pi$
$492$		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	$-0.575331\pi$
$499$	143.291	−	59.3531i	0.287156	−	0.118944i	0.521612	+	0.853183i	$0.325331\pi$
$500$		0			0
$501$	46.6734	+	19.3328i	0.0931605	+	0.0385884i
$502$		0			0
$503$	−74.0929	−	74.0929i	−0.147302	−	0.147302i	0.629610	−	0.776912i	$-0.283215\pi$
$503$	−74.0929	−	74.0929i	−0.147302	−	0.147302i	−0.776912	+	0.629610i	$0.783215\pi$
$504$		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	$-0.459393\pi$
$509$	467.540	−	193.661i	0.918546	−	0.380474i	0.791322	+	0.611400i	$0.209393\pi$
$510$		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	0.429644	−	0.902998i	$-0.358639\pi$
$521$	694.307	−	694.307i	1.33264	−	1.33264i	0.902998	−	0.429644i	$-0.141361\pi$
$522$		0			0
$523$	−67.4311	+	162.793i	−0.128931	+	0.311268i	−0.975142	−	0.221581i	$-0.928878\pi$
$523$	−67.4311	+	162.793i	−0.128931	+	0.311268i	0.846211	+	0.532848i	$0.178878\pi$
$524$		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	$-0.584917\pi$
$541$	125.547	−	52.0035i	0.232066	−	0.0961247i	0.495686	+	0.868502i	$0.334917\pi$
$542$		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	0.943910	+	0.330204i	$0.107117\pi$
$547$	278.945	+	673.432i	0.509954	+	1.23114i	−0.433956	+	0.900934i	$0.642883\pi$
$548$		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	−0.985214	−	0.171326i	$-0.945195\pi$
$557$	−228.207	−	550.942i	−0.409708	−	0.989123i	0.575506	−	0.817797i	$-0.304805\pi$
$558$		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	$-0.551871\pi$
$563$	236.899	−	98.1268i	0.420780	−	0.174293i	0.583019	+	0.812459i	$0.301871\pi$
$564$		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	0.405284	−	0.914191i	$-0.367173\pi$
$569$	−289.568	−	289.568i	−0.508907	−	0.508907i	−0.914191	+	0.405284i	$0.867173\pi$
$570$		0			0
$571$	−801.877	−	332.148i	−1.40434	−	0.581695i	−0.453464	−	0.891275i	$-0.649812\pi$
$571$	−801.877	−	332.148i	−1.40434	−	0.581695i	−0.950874	+	0.309579i	$0.899812\pi$
$572$		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	−0.452384	−	0.891823i	$-0.649426\pi$
$587$	292.393	−	705.899i	0.498114	−	1.20255i	0.950498	−	0.310730i	$-0.100574\pi$
$588$		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	$-0.933170\pi$
$593$		−	247.178i		−	0.416826i	0.978041	−	0.208413i	$-0.0668298\pi$
$594$		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	0.998277	+	0.0586768i	$0.0186881\pi$
$599$	633.115	+	633.115i	1.05695	+	1.05695i	0.0586768	+	0.998277i	$0.481312\pi$
$600$		0			0
$601$	−147.019	−	147.019i	−0.244624	−	0.244624i	0.574136	−	0.818760i	$-0.305338\pi$
$601$	−147.019	−	147.019i	−0.244624	−	0.244624i	−0.818760	+	0.574136i	$0.805338\pi$
$602$		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	$-0.986188\pi$
$607$		−	52.6594i		−	0.0867536i	0.999059	−	0.0433768i	$-0.0138116\pi$
$608$		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	0.367939	+	0.929850i	$0.380064\pi$
$613$	−336.988	+	813.562i	−0.549737	+	1.32718i	−0.917675	+	0.397331i	$0.869936\pi$
$614$		0			0
$615$	195.402	−	195.402i	0.317727	−	0.317727i
$616$		0			0
$617$	−150.269	+	150.269i	−0.243547	+	0.243547i	−0.818316	−	0.574769i	$-0.805092\pi$
$617$	−150.269	+	150.269i	−0.243547	+	0.243547i	0.574769	+	0.818316i	$0.305092\pi$
$618$		0			0
$619$	−4.34083	+	10.4797i	−0.00701265	+	0.0169300i	−0.927347	−	0.374202i	$-0.877917\pi$
$619$	−4.34083	+	10.4797i	−0.00701265	+	0.0169300i	0.920334	+	0.391132i	$0.127917\pi$
$620$		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	0.365758	−	0.930710i	$-0.380810\pi$
$631$	−356.485	−	356.485i	−0.564952	−	0.564952i	−0.930710	+	0.365758i	$0.880810\pi$
$632$		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	$-0.245468\pi$
$643$	−181.837	−	438.994i	−0.282795	−	0.682729i	−0.999899	+	0.0142385i	$0.995468\pi$
$644$		0			0
$645$	−106.556	+	257.250i	−0.165204	+	0.398837i
$646$		0			0
$647$	−520.304	+	520.304i	−0.804180	+	0.804180i	−0.983746	−	0.179566i	$-0.942531\pi$
$647$	−520.304	+	520.304i	−0.804180	+	0.804180i	0.179566	+	0.983746i	$0.442531\pi$
$648$		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	$-0.0200914\pi$
$653$	161.753	+	390.507i	0.247708	+	0.598019i	−0.750301	+	0.661096i	$0.770091\pi$
$654$		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	$-0.643357\pi$
$659$	−70.1853	+	29.0717i	−0.106503	+	0.0441149i	0.328796	+	0.944401i	$0.393357\pi$
$660$		0			0
$661$	−81.1193	−	33.6007i	−0.122722	−	0.0508331i	0.320477	−	0.947256i	$-0.396157\pi$
$661$	−81.1193	−	33.6007i	−0.122722	−	0.0508331i	−0.443199	+	0.896423i	$0.646157\pi$
$662$		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	0.346335	+	0.938111i	$0.387426\pi$
$677$	−380.410	+	918.390i	−0.561905	+	1.35656i	−0.908241	+	0.418448i	$0.862574\pi$
$678$		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	0.225297	+	0.974290i	$0.427665\pi$
$683$	−425.467	+	1027.17i	−0.622939	+	1.50391i	−0.848236	+	0.529618i	$0.822335\pi$
$684$		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	$-0.690515\pi$
$691$	−260.940	+	108.085i	−0.377627	+	0.156418i	0.185793	+	0.982589i	$0.440515\pi$
$692$		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	$-0.814744\pi$
$701$	−727.192	+	301.213i	−1.03736	+	0.429690i	−0.201999	+	0.979386i	$0.564744\pi$
$702$		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	−0.628261	−	0.778003i	$-0.716233\pi$
$709$	259.577	−	626.675i	0.366118	−	0.883886i	0.994379	−	0.105883i	$-0.0337670\pi$
$710$		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	0.533480	−	0.845813i	$-0.320884\pi$
$727$	−227.066	−	227.066i	−0.312332	−	0.312332i	−0.845813	+	0.533480i	$0.820884\pi$
$728$		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	$-0.369746\pi$
$733$	973.386	−	403.190i	1.32795	−	0.550054i	0.930070	+	0.367384i	$0.119746\pi$
$734$		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	−0.935490	−	0.353354i	$-0.885041\pi$
$739$	−387.131	−	934.616i	−0.523857	−	1.26470i	0.411632	−	0.911350i	$-0.364959\pi$
$740$		0			0
$741$	5.91821	−	14.2878i	0.00798679	−	0.0192818i
$742$		0			0
$743$	−528.819	+	528.819i	−0.711735	+	0.711735i	−0.966898	−	0.255163i	$-0.917871\pi$
$743$	−528.819	+	528.819i	−0.711735	+	0.711735i	0.255163	+	0.966898i	$0.417871\pi$
$744$		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	$-0.388626\pi$
$757$	−59.8575	−	24.7938i	−0.0790720	−	0.0327527i	−0.421869	+	0.906657i	$0.638626\pi$
$758$		0			0
$759$	461.381	+	461.381i	0.607879	+	0.607879i
$760$		0			0
$761$	713.497	+	713.497i	0.937579	+	0.937579i	0.998163	−	0.0605844i	$-0.0192964\pi$
$761$	713.497	+	713.497i	0.937579	+	0.937579i	−0.0605844	+	0.998163i	$0.519296\pi$
$762$		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	$-0.818738\pi$
$773$	104.027	−	251.144i	0.134576	−	0.324896i	0.976774	+	0.214273i	$0.0687384\pi$
$774$		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	$-0.866285\pi$
$787$	−999.730	+	414.102i	−1.27031	+	0.526178i	−0.357248	+	0.934010i	$0.616285\pi$
$788$		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	$-0.906165\pi$
$797$	−1138.14	+	471.431i	−1.42802	+	0.591507i	−0.471162	+	0.882047i	$0.656165\pi$
$798$		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	−0.804099	−	0.594496i	$-0.797352\pi$
$809$	−169.569	+	169.569i	−0.209603	+	0.209603i	0.594496	+	0.804099i	$0.297352\pi$
$810$		0			0
$811$	437.562	−	1056.37i	0.539534	−	1.30255i	−0.385514	−	0.922702i	$-0.625976\pi$
$811$	437.562	−	1056.37i	0.539534	−	1.30255i	0.925048	−	0.379849i	$-0.124024\pi$
$812$		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	$-0.585249\pi$
$821$	−930.724	−	385.518i	−1.13365	−	0.469572i	−0.869019	+	0.494779i	$0.835249\pi$
$822$		0			0
$823$	320.389	+	320.389i	0.389294	+	0.389294i	0.874435	−	0.485142i	$-0.161232\pi$
$823$	320.389	+	320.389i	0.389294	+	0.389294i	−0.485142	+	0.874435i	$0.661232\pi$
$824$		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	$-0.378050\pi$
$827$	−14.6406	−	6.06433i	−0.0177032	−	0.00733293i	−0.391517	+	0.920171i	$0.628050\pi$
$828$		0			0
$829$	−753.878	+	312.267i	−0.909383	+	0.376679i	−0.787820	−	0.615905i	$-0.788790\pi$
$829$	−753.878	+	312.267i	−0.909383	+	0.376679i	−0.121562	+	0.992584i	$0.538790\pi$
$830$		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	−0.553979	−	0.832531i	$-0.686891\pi$
$839$	233.705	−	233.705i	0.278552	−	0.278552i	0.832531	+	0.553979i	$0.186891\pi$
$840$		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	$-0.588477\pi$
$853$	−979.574	−	405.753i	−1.14839	−	0.475677i	−0.873992	+	0.485940i	$0.838477\pi$
$854$		0			0
$855$	3.13633	+	3.13633i	0.00366822	+	0.00366822i
$856$		0			0
$857$	716.322	+	716.322i	0.835848	+	0.835848i	0.988309	−	0.152461i	$-0.0487198\pi$
$857$	716.322	+	716.322i	0.835848	+	0.835848i	−0.152461	+	0.988309i	$0.548720\pi$
$858$		0			0
$859$	−398.325	−	164.992i	−0.463708	−	0.192074i	0.138583	−	0.990351i	$-0.455745\pi$
$859$	−398.325	−	164.992i	−0.463708	−	0.192074i	−0.602291	+	0.798277i	$0.705745\pi$
$860$		0			0
$861$	2000.70	−	828.716i	2.32369	−	0.962504i
$862$		0			0
$863$		−	1279.79i		−	1.48295i	−0.670980	−	0.741475i	$-0.734126\pi$
$863$		−	1279.79i		−	1.48295i	0.670980	−	0.741475i	$-0.265874\pi$
$864$		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	−0.987432	−	0.158046i	$-0.949481\pi$
$877$	−351.648	−	848.954i	−0.400967	−	0.968021i	0.586464	−	0.809975i	$-0.300519\pi$
$878$		0			0
$879$	102.285			0.116365
$880$		0			0
$881$		−	1327.06i		−	1.50632i	−0.657839	−	0.753158i	$-0.728529\pi$
$881$		−	1327.06i		−	1.50632i	0.657839	−	0.753158i	$-0.271471\pi$
$882$		0			0
$883$	−412.717	+	170.953i	−0.467403	+	0.193605i	−0.603939	−	0.797030i	$-0.706403\pi$
$883$	−412.717	+	170.953i	−0.467403	+	0.193605i	0.136536	+	0.990635i	$0.456403\pi$
$884$		0			0
$885$	−360.213	−	149.205i	−0.407020	−	0.168593i
$886$		0			0
$887$	411.723	+	411.723i	0.464174	+	0.464174i	0.900021	−	0.435847i	$-0.143551\pi$
$887$	411.723	+	411.723i	0.464174	+	0.464174i	−0.435847	+	0.900021i	$0.643551\pi$
$888$		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	0.659156	+	0.752006i	$0.270914\pi$
$907$	−307.189	+	741.619i	−0.338687	+	0.817662i	−0.997842	+	0.0656553i	$0.979086\pi$
$908$		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	0.277183	−	0.960817i	$-0.410599\pi$
$919$	−628.260	−	628.260i	−0.683635	−	0.683635i	−0.960817	+	0.277183i	$0.910599\pi$
$920$		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	−0.462853	−	0.886435i	$-0.653174\pi$
$937$	396.897	−	396.897i	0.423583	−	0.423583i	0.886435	+	0.462853i	$0.153174\pi$
$938$		0			0
$939$	−5.40618	+	13.0517i	−0.00575738	+	0.0138996i
$940$		0			0
$941$	486.386	+	1174.24i	0.516882	+	1.24786i	0.939809	+	0.341699i	$0.111002\pi$
$941$	486.386	+	1174.24i	0.516882	+	1.24786i	−0.422928	+	0.906163i	$0.638998\pi$
$942$		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	$-0.566580\pi$
$947$	319.348	−	132.278i	0.337221	−	0.139681i	0.544867	+	0.838523i	$0.316580\pi$
$948$		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	0.819330	−	0.573322i	$-0.194346\pi$
$953$	234.445	+	234.445i	0.246007	+	0.246007i	−0.573322	+	0.819330i	$0.694346\pi$
$954$		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	−0.894242	−	0.447584i	$-0.852285\pi$
$967$	−431.918	+	431.918i	−0.446658	+	0.446658i	0.447584	+	0.894242i	$0.352285\pi$
$968$		0			0
$969$	33.4165	−	33.4165i	0.0344855	−	0.0344855i
$970$		0			0
$971$	391.385	−	944.887i	0.403074	−	0.973107i	−0.583841	−	0.811868i	$-0.698451\pi$
$971$	391.385	−	944.887i	0.403074	−	0.973107i	0.986915	−	0.161239i	$-0.0515490\pi$
$972$		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	$0.201907\pi$
$977$			1157.98i			1.18524i	−0.805481	+	0.592621i	$0.798093\pi$
$978$		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	0.476038	−	0.879425i	$-0.342072\pi$
$983$	−396.529	−	396.529i	−0.403386	−	0.403386i	−0.879425	+	0.476038i	$0.842072\pi$
$984$		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	$-0.978420\pi$
$991$		−	134.269i		−	0.135489i	0.997703	−	0.0677444i	$-0.0215802\pi$
$992$		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	−0.491190	−	0.871052i	$-0.663438\pi$
$997$	470.645	−	1136.24i	0.472061	−	1.13966i	0.963251	−	0.268603i	$-0.0865620\pi$
$998$		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	128.3.h.a.79.6		28
4.3	odd	2		32.3.h.a.11.4	yes	28
8.3	odd	2		256.3.h.b.159.6		28
8.5	even	2		256.3.h.a.159.2		28
12.11	even	2		288.3.u.a.235.4		28
32.3	odd	8	inner	128.3.h.a.47.6		28
32.13	even	8		256.3.h.b.95.6		28
32.19	odd	8		256.3.h.a.95.2		28
32.29	even	8		32.3.h.a.3.4	✓	28
96.29	odd	8		288.3.u.a.163.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.4	✓	28	32.29	even	8
32.3.h.a.11.4	yes	28	4.3	odd	2
128.3.h.a.47.6		28	32.3	odd	8	inner
128.3.h.a.79.6		28	1.1	even	1	trivial
256.3.h.a.95.2		28	32.19	odd	8
256.3.h.a.159.2		28	8.5	even	2
256.3.h.b.95.6		28	32.13	even	8
256.3.h.b.159.6		28	8.3	odd	2
288.3.u.a.163.4		28	96.29	odd	8
288.3.u.a.235.4		28	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.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

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Representations

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Database

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