LMFDB - Embedded newform 128.4.g.a.81.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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([0, 7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.g (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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			81.7
Character	$\chi$	$=$	128.81
Dual form			128.4.g.a.49.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65706 + 0.686375i) q^{3} +(-4.13953 - 9.99370i) q^{5} +(-24.2273 + 24.2273i) q^{7} +(-16.8172 - 16.8172i) q^{9} +O(q^{10})$	\(q+(1.65706 + 0.686375i) q^{3} +(-4.13953 - 9.99370i) q^{5} +(-24.2273 + 24.2273i) q^{7} +(-16.8172 - 16.8172i) q^{9} +(-3.73492 + 1.54705i) q^{11} +(-23.2063 + 56.0248i) q^{13} -19.4014i q^{15} -26.9981i q^{17} +(-22.7209 + 54.8531i) q^{19} +(-56.7750 + 23.5170i) q^{21} +(-76.0566 - 76.0566i) q^{23} +(5.64994 - 5.64994i) q^{25} +(-34.8562 - 84.1503i) q^{27} +(-108.152 - 44.7980i) q^{29} -176.000 q^{31} -7.25082 q^{33} +(342.410 + 141.831i) q^{35} +(129.191 + 311.894i) q^{37} +(-76.9081 + 76.9081i) q^{39} +(70.4988 + 70.4988i) q^{41} +(103.155 - 42.7281i) q^{43} +(-98.4506 + 237.681i) q^{45} -249.437i q^{47} -830.925i q^{49} +(18.5308 - 44.7374i) q^{51} +(597.516 - 247.499i) q^{53} +(30.9216 + 30.9216i) q^{55} +(-75.2996 + 75.2996i) q^{57} +(75.6443 + 182.622i) q^{59} +(-309.654 - 128.263i) q^{61} +814.869 q^{63} +655.959 q^{65} +(297.717 + 123.318i) q^{67} +(-73.8267 - 178.233i) q^{69} +(-675.279 + 675.279i) q^{71} +(350.175 + 350.175i) q^{73} +(13.2403 - 5.48429i) q^{75} +(53.0061 - 127.968i) q^{77} -564.246i q^{79} +478.776i q^{81} +(-105.327 + 254.281i) q^{83} +(-269.811 + 111.760i) q^{85} +(-148.465 - 148.465i) q^{87} +(-448.959 + 448.959i) q^{89} +(-795.106 - 1919.56i) q^{91} +(-291.641 - 120.802i) q^{93} +642.239 q^{95} -1765.41 q^{97} +(88.8278 + 36.7937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

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
$3$	1.65706	+	0.686375i	0.318900	+	0.132093i	0.536391	−	0.843969i	$-0.319787\pi$
$3$	1.65706	+	0.686375i	0.318900	+	0.132093i	−0.217491	+	0.976062i	$0.569787\pi$
$4$		0			0
$5$	−4.13953	−	9.99370i	−0.370251	−	0.893864i	−0.993708	−	0.112006i	$-0.964272\pi$
$5$	−4.13953	−	9.99370i	−0.370251	−	0.893864i	0.623457	−	0.781858i	$-0.285728\pi$
$6$		0			0
$7$	−24.2273	+	24.2273i	−1.30815	+	1.30815i	−0.385403	+	0.922748i	$0.625938\pi$
$7$	−24.2273	+	24.2273i	−1.30815	+	1.30815i	−0.922748	+	0.385403i	$0.874062\pi$
$8$		0			0
$9$	−16.8172	−	16.8172i	−0.622858	−	0.622858i
$10$		0			0
$11$	−3.73492	+	1.54705i	−0.102375	+	0.0424049i	−0.433283	−	0.901258i	$-0.642645\pi$
$11$	−3.73492	+	1.54705i	−0.102375	+	0.0424049i	0.330908	+	0.943663i	$0.392645\pi$
$12$		0			0
$13$	−23.2063	+	56.0248i	−0.495097	+	1.19527i	0.456999	+	0.889467i	$0.348924\pi$
$13$	−23.2063	+	56.0248i	−0.495097	+	1.19527i	−0.952095	+	0.305802i	$0.901076\pi$
$14$		0			0
$15$		−	19.4014i		−	0.333961i
$16$		0			0
$17$		−	26.9981i		−	0.385177i	−0.981280	−	0.192589i	$-0.938312\pi$
$17$		−	26.9981i		−	0.385177i	0.981280	−	0.192589i	$-0.0616883\pi$
$18$		0			0
$19$	−22.7209	+	54.8531i	−0.274344	+	0.662324i	−0.999660	−	0.0260920i	$-0.991694\pi$
$19$	−22.7209	+	54.8531i	−0.274344	+	0.662324i	0.725316	+	0.688416i	$0.241694\pi$
$20$		0			0
$21$	−56.7750	+	23.5170i	−0.589968	+	0.244373i
$22$		0			0
$23$	−76.0566	−	76.0566i	−0.689517	−	0.689517i	0.272608	−	0.962125i	$-0.412114\pi$
$23$	−76.0566	−	76.0566i	−0.689517	−	0.689517i	−0.962125	+	0.272608i	$0.912114\pi$
$24$		0			0
$25$	5.64994	−	5.64994i	0.0451996	−	0.0451996i
$26$		0			0
$27$	−34.8562	−	84.1503i	−0.248447	−	0.599805i
$28$		0			0
$29$	−108.152	−	44.7980i	−0.692527	−	0.286854i	0.00852531	−	0.999964i	$-0.497286\pi$
$29$	−108.152	−	44.7980i	−0.692527	−	0.286854i	−0.701053	+	0.713109i	$0.747286\pi$
$30$		0			0
$31$	−176.000			−1.01969			−0.509846	−	0.860266i	$-0.670298\pi$
$31$	−176.000			−1.01969			−0.509846	+	0.860266i	$0.670298\pi$
$32$		0			0
$33$	−7.25082			−0.0382487
$34$		0			0
$35$	342.410	+	141.831i	1.65365	+	0.684966i
$36$		0			0
$37$	129.191	+	311.894i	0.574021	+	1.38581i	0.898105	+	0.439782i	$0.144944\pi$
$37$	129.191	+	311.894i	0.574021	+	1.38581i	−0.324083	+	0.946029i	$0.605056\pi$
$38$		0			0
$39$	−76.9081	+	76.9081i	−0.315773	+	0.315773i
$40$		0			0
$41$	70.4988	+	70.4988i	0.268538	+	0.268538i	0.828511	−	0.559973i	$-0.189188\pi$
$41$	70.4988	+	70.4988i	0.268538	+	0.268538i	−0.559973	+	0.828511i	$0.689188\pi$
$42$		0			0
$43$	103.155	−	42.7281i	0.365836	−	0.151534i	−0.192190	−	0.981358i	$-0.561559\pi$
$43$	103.155	−	42.7281i	0.365836	−	0.151534i	0.558026	+	0.829824i	$0.311559\pi$
$44$		0			0
$45$	−98.4506	+	237.681i	−0.326137	+	0.787364i
$46$		0			0
$47$		−	249.437i		−	0.774131i	−0.922052	−	0.387066i	$-0.873489\pi$
$47$		−	249.437i		−	0.774131i	0.922052	−	0.387066i	$-0.126511\pi$
$48$		0			0
$49$		−	830.925i		−	2.42252i
$50$		0			0
$51$	18.5308	−	44.7374i	0.0508792	−	0.122833i
$52$		0			0
$53$	597.516	−	247.499i	1.54859	−	0.641446i	0.565528	−	0.824729i	$-0.308672\pi$
$53$	597.516	−	247.499i	1.54859	−	0.641446i	0.983060	+	0.183282i	$0.0586723\pi$
$54$		0			0
$55$	30.9216	+	30.9216i	0.0758085	+	0.0758085i
$56$		0			0
$57$	−75.2996	+	75.2996i	−0.174977	+	0.174977i
$58$		0			0
$59$	75.6443	+	182.622i	0.166916	+	0.402971i	0.985099	−	0.171986i	$-0.0550185\pi$
$59$	75.6443	+	182.622i	0.166916	+	0.402971i	−0.818183	+	0.574958i	$0.805019\pi$
$60$		0			0
$61$	−309.654	−	128.263i	−0.649953	−	0.269219i	0.0332511	−	0.999447i	$-0.489414\pi$
$61$	−309.654	−	128.263i	−0.649953	−	0.269219i	−0.683204	+	0.730228i	$0.739414\pi$
$62$		0			0
$63$	814.869			1.62958
$64$		0			0
$65$	655.959			1.25172
$66$		0			0
$67$	297.717	+	123.318i	0.542864	+	0.224862i	0.637227	−	0.770676i	$-0.280081\pi$
$67$	297.717	+	123.318i	0.542864	+	0.224862i	−0.0943627	+	0.995538i	$0.530081\pi$
$68$		0			0
$69$	−73.8267	−	178.233i	−0.128807	−	0.310968i
$70$		0			0
$71$	−675.279	+	675.279i	−1.12874	+	1.12874i	−0.138363	+	0.990382i	$0.544184\pi$
$71$	−675.279	+	675.279i	−1.12874	+	1.12874i	−0.990382	+	0.138363i	$0.955816\pi$
$72$		0			0
$73$	350.175	+	350.175i	0.561437	+	0.561437i	0.929715	−	0.368279i	$-0.120053\pi$
$73$	350.175	+	350.175i	0.561437	+	0.561437i	−0.368279	+	0.929715i	$0.620053\pi$
$74$		0			0
$75$	13.2403	−	5.48429i	0.0203847	−	0.00844362i
$76$		0			0
$77$	53.0061	−	127.968i	0.0784494	−	0.189393i
$78$		0			0
$79$		−	564.246i		−	0.803578i	−0.915732	−	0.401789i	$-0.868389\pi$
$79$		−	564.246i		−	0.803578i	0.915732	−	0.401789i	$-0.131611\pi$
$80$		0			0
$81$			478.776i			0.656758i
$82$		0			0
$83$	−105.327	+	254.281i	−0.139290	+	0.336276i	−0.978096	−	0.208155i	$-0.933254\pi$
$83$	−105.327	+	254.281i	−0.139290	+	0.336276i	0.838806	+	0.544431i	$0.183254\pi$
$84$		0			0
$85$	−269.811	+	111.760i	−0.344296	+	0.142612i
$86$		0			0
$87$	−148.465	−	148.465i	−0.182956	−	0.182956i
$88$		0			0
$89$	−448.959	+	448.959i	−0.534715	+	0.534715i	−0.921972	−	0.387257i	$-0.873423\pi$
$89$	−448.959	+	448.959i	−0.534715	+	0.534715i	0.387257	+	0.921972i	$0.373423\pi$
$90$		0			0
$91$	−795.106	−	1919.56i	−0.915932	−	2.21125i
$92$		0			0
$93$	−291.641	−	120.802i	−0.325180	−	0.134694i
$94$		0			0
$95$	642.239			0.693604
$96$		0			0
$97$	−1765.41			−1.84794			−0.923972	−	0.382459i	$-0.875077\pi$
$97$	−1765.41			−1.84794			−0.923972	+	0.382459i	$0.875077\pi$
$98$		0			0
$99$	88.8278	+	36.7937i	0.0901770	+	0.0373526i
$100$		0			0
$101$	298.207	+	719.936i	0.293790	+	0.709271i	0.999999	+	0.00126791i	$0.000403589\pi$
$101$	298.207	+	719.936i	0.293790	+	0.709271i	−0.706210	+	0.708003i	$0.749596\pi$
$102$		0			0
$103$	228.925	−	228.925i	0.218997	−	0.218997i	−0.589079	−	0.808076i	$-0.700509\pi$
$103$	228.925	−	228.925i	0.218997	−	0.218997i	0.808076	+	0.589079i	$0.200509\pi$
$104$		0			0
$105$	470.043	+	470.043i	0.436872	+	0.436872i
$106$		0			0
$107$	−1637.14	+	678.126i	−1.47914	+	0.612681i	−0.968923	−	0.247362i	$-0.920436\pi$
$107$	−1637.14	+	678.126i	−1.47914	+	0.612681i	−0.510221	+	0.860044i	$0.670436\pi$
$108$		0			0
$109$	154.640	−	373.333i	0.135888	−	0.328063i	−0.841257	−	0.540635i	$-0.818184\pi$
$109$	154.640	−	373.333i	0.135888	−	0.328063i	0.977145	+	0.212572i	$0.0681841\pi$
$110$		0			0
$111$			605.498i			0.517760i
$112$		0			0
$113$		−	681.111i		−	0.567023i	−0.958969	−	0.283511i	$-0.908501\pi$
$113$		−	681.111i		−	0.567023i	0.958969	−	0.283511i	$-0.0914993\pi$
$114$		0			0
$115$	−445.249	+	1074.93i	−0.361041	+	0.871629i
$116$		0			0
$117$	1332.44	−	551.916i	1.05286	−	0.436108i
$118$		0			0
$119$	654.092	+	654.092i	0.503870	+	0.503870i
$120$		0			0
$121$	−929.603	+	929.603i	−0.698424	+	0.698424i
$122$		0			0
$123$	68.4318	+	165.209i	0.0501649	+	0.121109i
$124$		0			0
$125$	−1329.06	−	550.517i	−0.951001	−	0.393918i
$126$		0			0
$127$	−574.582			−0.401464			−0.200732	−	0.979646i	$-0.564332\pi$
$127$	−574.582			−0.401464			−0.200732	+	0.979646i	$0.564332\pi$
$128$		0			0
$129$	200.261			0.136682
$130$		0			0
$131$	−749.541	−	310.470i	−0.499906	−	0.207068i	0.118459	−	0.992959i	$-0.462205\pi$
$131$	−749.541	−	310.470i	−0.499906	−	0.207068i	−0.618365	+	0.785891i	$0.712205\pi$
$132$		0			0
$133$	−778.476	−	1879.41i	−0.507537	−	1.22530i
$134$		0			0
$135$	−696.685	+	696.685i	−0.444156	+	0.444156i
$136$		0			0
$137$	−274.564	−	274.564i	−0.171223	−	0.171223i	0.616293	−	0.787517i	$-0.288634\pi$
$137$	−274.564	−	274.564i	−0.171223	−	0.171223i	−0.787517	+	0.616293i	$0.788634\pi$
$138$		0			0
$139$	239.497	−	99.2027i	0.146143	−	0.0605343i	−0.308413	−	0.951252i	$-0.599798\pi$
$139$	239.497	−	99.2027i	0.146143	−	0.0605343i	0.454556	+	0.890718i	$0.349798\pi$
$140$		0			0
$141$	171.208	−	413.331i	0.102257	−	0.246871i
$142$		0			0
$143$		−	245.150i		−	0.143360i
$144$		0			0
$145$			1266.28i			0.725233i
$146$		0			0
$147$	570.326	−	1376.89i	0.319998	−	0.772543i
$148$		0			0
$149$	176.116	−	72.9498i	0.0968323	−	0.0401092i	−0.333741	−	0.942665i	$-0.608311\pi$
$149$	176.116	−	72.9498i	0.0968323	−	0.0401092i	0.430574	+	0.902555i	$0.358311\pi$
$150$		0			0
$151$	339.506	+	339.506i	0.182971	+	0.182971i	0.792649	−	0.609678i	$-0.208701\pi$
$151$	339.506	+	339.506i	0.182971	+	0.182971i	−0.609678	+	0.792649i	$0.708701\pi$
$152$		0			0
$153$	−454.032	+	454.032i	−0.239911	+	0.239911i
$154$		0			0
$155$	728.555	+	1758.89i	0.377542	+	0.911466i
$156$		0			0
$157$	1222.00	+	506.170i	0.621188	+	0.257304i	0.671004	−	0.741454i	$-0.265863\pi$
$157$	1222.00	+	506.170i	0.621188	+	0.257304i	−0.0498158	+	0.998758i	$0.515863\pi$
$158$		0			0
$159$	1160.00			0.578576
$160$		0			0
$161$	3685.29			1.80399
$162$		0			0
$163$	−1346.92	−	557.911i	−0.647231	−	0.268092i	0.0348231	−	0.999393i	$-0.488913\pi$
$163$	−1346.92	−	557.911i	−0.647231	−	0.268092i	−0.682054	+	0.731302i	$0.738913\pi$
$164$		0			0
$165$	30.0150	+	72.4626i	0.0141616	+	0.0341891i
$166$		0			0
$167$	2521.77	−	2521.77i	1.16851	−	1.16851i	0.185946	−	0.982560i	$-0.440465\pi$
$167$	2521.77	−	2521.77i	1.16851	−	1.16851i	0.982560	−	0.185946i	$-0.0595351\pi$
$168$		0			0
$169$	−1046.74	−	1046.74i	−0.476440	−	0.476440i
$170$		0			0
$171$	1304.57	−	540.372i	0.583411	−	0.241657i
$172$		0			0
$173$	−541.973	+	1308.44i	−0.238182	+	0.575022i	−0.997095	−	0.0761701i	$-0.975731\pi$
$173$	−541.973	+	1308.44i	−0.238182	+	0.575022i	0.758913	+	0.651192i	$0.225731\pi$
$174$		0			0
$175$			273.766i			0.118256i
$176$		0			0
$177$			354.534i			0.150556i
$178$		0			0
$179$	54.1456	−	130.719i	0.0226091	−	0.0545833i	−0.912172	−	0.409808i	$-0.865596\pi$
$179$	54.1456	−	130.719i	0.0226091	−	0.0545833i	0.934781	+	0.355225i	$0.115596\pi$
$180$		0			0
$181$	−1585.39	+	656.689i	−0.651055	+	0.269676i	−0.683669	−	0.729792i	$-0.739617\pi$
$181$	−1585.39	+	656.689i	−0.651055	+	0.269676i	0.0326139	+	0.999468i	$0.489617\pi$
$182$		0			0
$183$	−425.077	−	425.077i	−0.171708	−	0.171708i
$184$		0			0
$185$	2582.18	−	2582.18i	1.02619	−	1.02619i
$186$		0			0
$187$	41.7676	+	100.836i	0.0163334	+	0.0394323i
$188$		0			0
$189$	2883.21	+	1194.26i	1.10964	+	0.459629i
$190$		0			0
$191$	−2679.22			−1.01498			−0.507490	−	0.861658i	$-0.669427\pi$
$191$	−2679.22			−1.01498			−0.507490	+	0.861658i	$0.669427\pi$
$192$		0			0
$193$	−3139.34			−1.17085			−0.585426	−	0.810726i	$-0.699073\pi$
$193$	−3139.34			−1.17085			−0.585426	+	0.810726i	$0.699073\pi$
$194$		0			0
$195$	1086.96	+	450.233i	0.399173	+	0.165343i
$196$		0			0
$197$	1321.44	+	3190.23i	0.477911	+	1.15378i	0.960587	+	0.277981i	$0.0896652\pi$
$197$	1321.44	+	3190.23i	0.477911	+	1.15378i	−0.482675	+	0.875799i	$0.660335\pi$
$198$		0			0
$199$	106.853	−	106.853i	0.0380632	−	0.0380632i	−0.687819	−	0.725882i	$-0.741432\pi$
$199$	106.853	−	106.853i	0.0380632	−	0.0380632i	0.725882	+	0.687819i	$0.241432\pi$
$200$		0			0
$201$	408.691	+	408.691i	0.143417	+	0.143417i
$202$		0			0
$203$	3705.56	−	1534.89i	1.28118	−	0.530682i
$204$		0			0
$205$	412.712	−	996.375i	0.140610	−	0.339463i
$206$		0			0
$207$			2558.11i			0.858943i
$208$		0			0
$209$		−	240.022i		−	0.0794387i
$210$		0			0
$211$	1037.64	−	2505.10i	0.338552	−	0.817336i	−0.659304	−	0.751877i	$-0.729149\pi$
$211$	1037.64	−	2505.10i	0.338552	−	0.817336i	0.997855	−	0.0654593i	$-0.0208512\pi$
$212$		0			0
$213$	−1582.47	+	655.480i	−0.509056	+	0.210858i
$214$		0			0
$215$	−854.024	−	854.024i	−0.270902	−	0.270902i
$216$		0			0
$217$	4264.00	−	4264.00i	1.33391	−	1.33391i
$218$		0			0
$219$	339.908	+	820.611i	0.104881	+	0.253204i
$220$		0			0
$221$	1512.57	+	626.526i	0.460390	+	0.190700i
$222$		0			0
$223$	−3307.18			−0.993119			−0.496559	−	0.868003i	$-0.665404\pi$
$223$	−3307.18			−0.993119			−0.496559	+	0.868003i	$0.665404\pi$
$224$		0			0
$225$	−190.032			−0.0563058
$226$		0			0
$227$	5187.26	+	2148.63i	1.51670	+	0.628237i	0.976927	−	0.213575i	$-0.0685108\pi$
$227$	5187.26	+	2148.63i	1.51670	+	0.628237i	0.539771	+	0.841812i	$0.318511\pi$
$228$		0			0
$229$	−1736.52	−	4192.34i	−0.501103	−	1.20977i	−0.948883	−	0.315627i	$-0.897785\pi$
$229$	−1736.52	−	4192.34i	−0.501103	−	1.20977i	0.447780	−	0.894144i	$-0.352215\pi$
$230$		0			0
$231$	175.668	−	175.668i	0.0500351	−	0.0500351i
$232$		0			0
$233$	−817.096	−	817.096i	−0.229741	−	0.229741i	0.582843	−	0.812585i	$-0.301940\pi$
$233$	−817.096	−	817.096i	−0.229741	−	0.229741i	−0.812585	+	0.582843i	$0.801940\pi$
$234$		0			0
$235$	−2492.80	+	1032.55i	−0.691968	+	0.286623i
$236$		0			0
$237$	387.284	−	934.987i	0.106147	−	0.256261i
$238$		0			0
$239$		−	2423.25i		−	0.655844i	−0.944705	−	0.327922i	$-0.893652\pi$
$239$		−	2423.25i		−	0.655844i	0.944705	−	0.327922i	$-0.106348\pi$
$240$		0			0
$241$			3879.72i			1.03699i	0.855080	+	0.518496i	$0.173508\pi$
$241$			3879.72i			1.03699i	−0.855080	+	0.518496i	$0.826492\pi$
$242$		0			0
$243$	−1269.74	+	3065.42i	−0.335200	+	0.809246i
$244$		0			0
$245$	−8304.01	+	3439.63i	−2.16540	+	0.896940i
$246$		0			0
$247$	−2545.87	−	2545.87i	−0.655829	−	0.655829i
$248$		0			0
$249$	−349.064	+	349.064i	−0.0888394	+	0.0888394i
$250$		0			0
$251$	2070.97	+	4999.76i	0.520791	+	1.25730i	0.937413	+	0.348220i	$0.113214\pi$
$251$	2070.97	+	4999.76i	0.520791	+	1.25730i	−0.416622	+	0.909080i	$0.636786\pi$
$252$		0			0
$253$	401.729	+	166.402i	0.0998280	+	0.0413501i
$254$		0			0
$255$	−523.801			−0.128634
$256$		0			0
$257$	−1525.85			−0.370349			−0.185175	−	0.982706i	$-0.559285\pi$
$257$	−1525.85			−0.370349			−0.185175	+	0.982706i	$0.559285\pi$
$258$		0			0
$259$	−10686.3	−	4426.40i	−2.56376	−	1.06194i
$260$		0			0
$261$	1065.43	+	2572.18i	0.252677	+	0.610016i
$262$		0			0
$263$	−532.444	+	532.444i	−0.124836	+	0.124836i	−0.766765	−	0.641928i	$-0.778135\pi$
$263$	−532.444	+	532.444i	−0.124836	+	0.124836i	0.641928	+	0.766765i	$0.278135\pi$
$264$		0			0
$265$	−4946.87	−	4946.87i	−1.14673	−	1.14673i
$266$		0			0
$267$	−1052.11	+	435.796i	−0.241153	+	0.0998888i
$268$		0			0
$269$	−930.585	+	2246.63i	−0.210925	+	0.509217i	−0.993566	−	0.113256i	$-0.963872\pi$
$269$	−930.585	+	2246.63i	−0.210925	+	0.509217i	0.782641	+	0.622473i	$0.213872\pi$
$270$		0			0
$271$			3425.60i			0.767862i	0.923362	+	0.383931i	$0.125430\pi$
$271$			3425.60i			0.767862i	−0.923362	+	0.383931i	$0.874570\pi$
$272$		0			0
$273$		−	3726.55i		−	0.826158i
$274$		0			0
$275$	−12.3613	+	29.8428i	−0.00271060	+	0.00654397i
$276$		0			0
$277$	4215.07	−	1745.94i	0.914293	−	0.378712i	0.124594	−	0.992208i	$-0.460237\pi$
$277$	4215.07	−	1745.94i	0.914293	−	0.378712i	0.789698	+	0.613495i	$0.210237\pi$
$278$		0			0
$279$	2959.81	+	2959.81i	0.635123	+	0.635123i
$280$		0			0
$281$	−2404.35	+	2404.35i	−0.510433	+	0.510433i	−0.914659	−	0.404226i	$-0.867541\pi$
$281$	−2404.35	+	2404.35i	−0.510433	+	0.510433i	0.404226	+	0.914659i	$0.367541\pi$
$282$		0			0
$283$	3013.10	+	7274.27i	0.632899	+	1.52795i	0.835962	+	0.548787i	$0.184910\pi$
$283$	3013.10	+	7274.27i	0.632899	+	1.52795i	−0.203063	+	0.979166i	$0.565090\pi$
$284$		0			0
$285$	1064.23	+	440.817i	0.221191	+	0.0916201i
$286$		0			0
$287$	−3415.99			−0.702577
$288$		0			0
$289$	4184.10			0.851638
$290$		0			0
$291$	−2925.39	−	1211.74i	−0.589310	−	0.244100i
$292$		0			0
$293$	−1059.63	−	2558.17i	−0.211277	−	0.510068i	0.782343	−	0.622848i	$-0.214025\pi$
$293$	−1059.63	−	2558.17i	−0.211277	−	0.510068i	−0.993620	+	0.112780i	$0.964025\pi$
$294$		0			0
$295$	1511.93	−	1511.93i	0.298401	−	0.298401i
$296$		0			0
$297$	260.370	+	260.370i	0.0508694	+	0.0508694i
$298$		0			0
$299$	6026.05	−	2496.07i	1.16554	−	0.482781i
$300$		0			0
$301$	−1463.97	+	3534.35i	−0.280339	+	0.676799i
$302$		0			0
$303$			1397.66i			0.264994i
$304$		0			0
$305$			3625.54i			0.680648i
$306$		0			0
$307$	3277.84	−	7913.41i	0.609369	−	1.47115i	−0.254319	−	0.967120i	$-0.581851\pi$
$307$	3277.84	−	7913.41i	0.609369	−	1.47115i	0.863688	−	0.504027i	$-0.168149\pi$
$308$		0			0
$309$	536.470	−	222.213i	0.0987660	−	0.0409102i
$310$		0			0
$311$	−5107.89	−	5107.89i	−0.931324	−	0.931324i	0.0664648	−	0.997789i	$-0.478828\pi$
$311$	−5107.89	−	5107.89i	−0.931324	−	0.931324i	−0.997789	+	0.0664648i	$0.978828\pi$
$312$		0			0
$313$	−1761.64	+	1761.64i	−0.318128	+	0.318128i	−0.848048	−	0.529920i	$-0.822222\pi$
$313$	−1761.64	+	1761.64i	−0.318128	+	0.318128i	0.529920	+	0.848048i	$0.322222\pi$
$314$		0			0
$315$	−3373.17	−	8143.56i	−0.603355	−	1.45663i
$316$		0			0
$317$	−4091.81	−	1694.88i	−0.724981	−	0.300297i	−0.0104934	−	0.999945i	$-0.503340\pi$
$317$	−4091.81	−	1694.88i	−0.724981	−	0.300297i	−0.714488	+	0.699648i	$0.753340\pi$
$318$		0			0
$319$	473.243			0.0830612
$320$		0			0
$321$	−3178.28			−0.552630
$322$		0			0
$323$	1480.93	+	613.422i	0.255112	+	0.105671i
$324$		0			0
$325$	185.423	+	447.651i	0.0316475	+	0.0764038i
$326$		0			0
$327$	512.493	−	512.493i	0.0866695	−	0.0866695i
$328$		0			0
$329$	6043.19	+	6043.19i	1.01268	+	1.01268i
$330$		0			0
$331$	−6396.05	+	2649.33i	−1.06211	+	0.439941i	−0.844200	−	0.536028i	$-0.819924\pi$
$331$	−6396.05	+	2649.33i	−1.06211	+	0.439941i	−0.217911	+	0.975969i	$0.569924\pi$
$332$		0			0
$333$	3072.55	−	7417.78i	0.505629	−	1.22070i
$334$		0			0
$335$		−	3485.77i		−	0.568502i
$336$		0			0
$337$			3692.32i			0.596835i	0.954435	+	0.298418i	$0.0964588\pi$
$337$			3692.32i			0.596835i	−0.954435	+	0.298418i	$0.903541\pi$
$338$		0			0
$339$	467.498	−	1128.64i	0.0748997	−	0.180824i
$340$		0			0
$341$	657.344	−	272.281i	0.104391	−	0.0432400i
$342$		0			0
$343$	11821.1	+	11821.1i	1.86087	+	1.86087i
$344$		0			0
$345$	−1475.60	+	1475.60i	−0.230272	+	0.230272i
$346$		0			0
$347$	−3771.01	−	9104.01i	−0.583395	−	1.40844i	−0.889717	−	0.456513i	$-0.849098\pi$
$347$	−3771.01	−	9104.01i	−0.583395	−	1.40844i	0.306322	−	0.951928i	$-0.400902\pi$
$348$		0			0
$349$	2347.30	+	972.282i	0.360023	+	0.149126i	0.555360	−	0.831610i	$-0.312580\pi$
$349$	2347.30	+	972.282i	0.360023	+	0.149126i	−0.195338	+	0.980736i	$0.562580\pi$
$350$		0			0
$351$	5523.39			0.839934
$352$		0			0
$353$	822.940			0.124081			0.0620406	−	0.998074i	$-0.480239\pi$
$353$	822.940			0.124081			0.0620406	+	0.998074i	$0.480239\pi$
$354$		0			0
$355$	9543.87	+	3953.20i	1.42686	+	0.591026i
$356$		0			0
$357$	634.915	+	1532.82i	0.0941268	+	0.227242i
$358$		0			0
$359$	3701.59	−	3701.59i	0.544185	−	0.544185i	−0.380568	−	0.924753i	$-0.624272\pi$
$359$	3701.59	−	3701.59i	0.544185	−	0.544185i	0.924753	+	0.380568i	$0.124272\pi$
$360$		0			0
$361$	2357.42	+	2357.42i	0.343698	+	0.343698i
$362$		0			0
$363$	−2178.46	+	902.347i	−0.314985	+	0.130471i
$364$		0			0
$365$	2049.99	−	4949.10i	0.293976	−	0.709720i
$366$		0			0
$367$			3736.68i			0.531479i	0.964045	+	0.265740i	$0.0856162\pi$
$367$			3736.68i			0.531479i	−0.964045	+	0.265740i	$0.914384\pi$
$368$		0			0
$369$		−	2371.18i		−	0.334522i
$370$		0			0
$371$	−8479.97	+	20472.5i	−1.18668	+	2.86490i
$372$		0			0
$373$	8948.08	−	3706.42i	1.24213	−	0.514507i	0.337750	−	0.941236i	$-0.390334\pi$
$373$	8948.08	−	3706.42i	1.24213	−	0.514507i	0.904379	+	0.426729i	$0.140334\pi$
$374$		0			0
$375$	−1824.47	−	1824.47i	−0.251241	−	0.251241i
$376$		0			0
$377$	5019.60	−	5019.60i	0.685736	−	0.685736i
$378$		0			0
$379$	−761.220	−	1837.75i	−0.103170	−	0.249073i	0.863863	−	0.503727i	$-0.168038\pi$
$379$	−761.220	−	1837.75i	−0.103170	−	0.249073i	−0.967032	+	0.254654i	$0.918038\pi$
$380$		0			0
$381$	−952.114	−	394.379i	−0.128027	−	0.0530305i
$382$		0			0
$383$	12159.8			1.62229			0.811143	−	0.584848i	$-0.198846\pi$
$383$	12159.8			1.62229			0.811143	+	0.584848i	$0.198846\pi$
$384$		0			0
$385$	−1498.29			−0.198338
$386$		0			0
$387$	−2453.33	−	1016.20i	−0.322248	−	0.133480i
$388$		0			0
$389$	−2365.98	−	5711.99i	−0.308381	−	0.744497i	−0.999758	−	0.0220031i	$-0.992996\pi$
$389$	−2365.98	−	5711.99i	−0.308381	−	0.744497i	0.691377	−	0.722494i	$-0.257004\pi$
$390$		0			0
$391$	−2053.39	+	2053.39i	−0.265586	+	0.265586i
$392$		0			0
$393$	−1028.93	−	1028.93i	−0.132068	−	0.132068i
$394$		0			0
$395$	−5638.91	+	2335.71i	−0.718289	+	0.297525i
$396$		0			0
$397$	−533.914	+	1288.98i	−0.0674972	+	0.162953i	−0.954028	−	0.299716i	$-0.903108\pi$
$397$	−533.914	+	1288.98i	−0.0674972	+	0.162953i	0.886531	+	0.462669i	$0.153108\pi$
$398$		0			0
$399$		−	3648.61i		−	0.457792i
$400$		0			0
$401$		−	4956.51i		−	0.617248i	−0.951184	−	0.308624i	$-0.900131\pi$
$401$		−	4956.51i		−	0.617248i	0.951184	−	0.308624i	$-0.0998685\pi$
$402$		0			0
$403$	4084.29	−	9860.35i	0.504846	−	1.21881i
$404$		0			0
$405$	4784.75	−	1981.91i	0.587052	−	0.243165i
$406$		0			0
$407$	−965.032	−	965.032i	−0.117530	−	0.117530i
$408$		0			0
$409$	−3226.79	+	3226.79i	−0.390108	+	0.390108i	−0.874726	−	0.484618i	$-0.838959\pi$
$409$	−3226.79	+	3226.79i	−0.390108	+	0.390108i	0.484618	+	0.874726i	$0.338959\pi$
$410$		0			0
$411$	−266.514	−	643.422i	−0.0319858	−	0.0772205i
$412$		0			0
$413$	−6257.08	−	2591.77i	−0.745499	−	0.308796i
$414$		0			0
$415$	2977.21			0.352158
$416$		0			0
$417$	464.949			0.0546011
$418$		0			0
$419$	1822.54	+	754.920i	0.212498	+	0.0880197i	0.486394	−	0.873740i	$-0.338312\pi$
$419$	1822.54	+	754.920i	0.212498	+	0.0880197i	−0.273895	+	0.961760i	$0.588312\pi$
$420$		0			0
$421$	−215.665	−	520.662i	−0.0249664	−	0.0602743i	0.910905	−	0.412617i	$-0.135385\pi$
$421$	−215.665	−	520.662i	−0.0249664	−	0.0602743i	−0.935871	+	0.352343i	$0.885385\pi$
$422$		0			0
$423$	−4194.83	+	4194.83i	−0.482174	+	0.482174i
$424$		0			0
$425$	−152.538	−	152.538i	−0.0174098	−	0.0174098i
$426$		0			0
$427$	10609.5	−	4394.61i	1.20242	−	0.498057i
$428$		0			0
$429$	168.264	−	406.226i	0.0189368	−	0.0457175i
$430$		0			0
$431$		−	2199.14i		−	0.245775i	−0.992421	−	0.122888i	$-0.960785\pi$
$431$		−	2199.14i		−	0.245775i	0.992421	−	0.122888i	$-0.0392155\pi$
$432$		0			0
$433$			273.133i			0.0303139i	0.999885	+	0.0151569i	$0.00482479\pi$
$433$			273.133i			0.0303139i	−0.999885	+	0.0151569i	$0.995175\pi$
$434$		0			0
$435$	−869.143	+	2098.30i	−0.0957982	+	0.231277i
$436$		0			0
$437$	5900.01	−	2443.87i	0.645849	−	0.267519i
$438$		0			0
$439$	−2910.64	−	2910.64i	−0.316440	−	0.316440i	0.530958	−	0.847398i	$-0.321832\pi$
$439$	−2910.64	−	2910.64i	−0.316440	−	0.316440i	−0.847398	+	0.530958i	$0.821832\pi$
$440$		0			0
$441$	−13973.8	+	13973.8i	−1.50889	+	1.50889i
$442$		0			0
$443$	−1439.20	−	3474.54i	−0.154353	−	0.372642i	0.827720	−	0.561142i	$-0.189638\pi$
$443$	−1439.20	−	3474.54i	−0.154353	−	0.372642i	−0.982073	+	0.188499i	$0.939638\pi$
$444$		0			0
$445$	6345.25	+	2628.29i	0.675941	+	0.279984i
$446$		0			0
$447$	341.905			0.0361780
$448$		0			0
$449$	13543.2			1.42348			0.711738	−	0.702445i	$-0.247908\pi$
$449$	13543.2			1.42348			0.711738	+	0.702445i	$0.247908\pi$
$450$		0			0
$451$	−372.373	−	154.242i	−0.0388788	−	0.0161041i
$452$		0			0
$453$	329.552	+	795.609i	0.0341804	+	0.0825187i
$454$		0			0
$455$	−15892.1	+	15892.1i	−1.63744	+	1.63744i
$456$		0			0
$457$	3832.14	+	3832.14i	0.392253	+	0.392253i	0.875490	−	0.483237i	$-0.160539\pi$
$457$	3832.14	+	3832.14i	0.392253	+	0.392253i	−0.483237	+	0.875490i	$0.660539\pi$
$458$		0			0
$459$	−2271.90	+	941.053i	−0.231031	+	0.0956963i
$460$		0			0
$461$	−6014.95	+	14521.4i	−0.607688	+	1.46709i	0.257821	+	0.966193i	$0.416996\pi$
$461$	−6014.95	+	14521.4i	−0.607688	+	1.46709i	−0.865508	+	0.500895i	$0.833004\pi$
$462$		0			0
$463$		−	13168.4i		−	1.32178i	−0.750481	−	0.660892i	$-0.770178\pi$
$463$		−	13168.4i		−	1.32178i	0.750481	−	0.660892i	$-0.229822\pi$
$464$		0			0
$465$			3414.64i			0.340537i
$466$		0			0
$467$	2737.75	−	6609.51i	0.271280	−	0.654929i	−0.728258	−	0.685303i	$-0.759670\pi$
$467$	2737.75	−	6609.51i	0.271280	−	0.654929i	0.999539	+	0.0303741i	$0.00966986\pi$
$468$		0			0
$469$	−10200.6	+	4225.21i	−1.00430	+	0.415996i
$470$		0			0
$471$	1677.50	+	1677.50i	0.164109	+	0.164109i
$472$		0			0
$473$	−319.172	+	319.172i	−0.0310265	+	0.0310265i
$474$		0			0
$475$	181.545	+	438.289i	0.0175365	+	0.0423370i
$476$		0			0
$477$	−14210.8	−	5886.29i	−1.36408	−	0.565021i
$478$		0			0
$479$	2141.84			0.204307			0.102153	−	0.994769i	$-0.467427\pi$
$479$	2141.84			0.204307			0.102153	+	0.994769i	$0.467427\pi$
$480$		0			0
$481$	−20471.8			−1.94061
$482$		0			0
$483$	6106.74	+	2529.49i	0.575292	+	0.238294i
$484$		0			0
$485$	7307.98	+	17643.0i	0.684203	+	1.65181i
$486$		0			0
$487$	3210.83	−	3210.83i	0.298761	−	0.298761i	−0.541767	−	0.840528i	$-0.682245\pi$
$487$	3210.83	−	3210.83i	0.298761	−	0.298761i	0.840528	+	0.541767i	$0.182245\pi$
$488$		0			0
$489$	−1848.98	−	1848.98i	−0.170989	−	0.170989i
$490$		0			0
$491$	−10597.1	+	4389.47i	−0.974015	+	0.403450i	−0.812205	−	0.583372i	$-0.801733\pi$
$491$	−10597.1	+	4389.47i	−0.974015	+	0.403450i	−0.161810	+	0.986822i	$0.551733\pi$
$492$		0			0
$493$	−1209.46	+	2919.90i	−0.110490	+	0.266746i
$494$		0			0
$495$		−	1040.03i		−	0.0944358i
$496$		0			0
$497$		−	32720.4i		−	2.95314i
$498$		0			0
$499$	−3963.81	+	9569.49i	−0.355600	+	0.858495i	0.640307	+	0.768119i	$0.278807\pi$
$499$	−3963.81	+	9569.49i	−0.355600	+	0.858495i	−0.995908	+	0.0903763i	$0.971193\pi$
$500$		0			0
$501$	5909.60	−	2447.83i	0.526989	−	0.218286i
$502$		0			0
$503$	−13198.2	−	13198.2i	−1.16994	−	1.16994i	−0.982223	−	0.187716i	$-0.939892\pi$
$503$	−13198.2	−	13198.2i	−1.16994	−	1.16994i	−0.187716	−	0.982223i	$-0.560108\pi$
$504$		0			0
$505$	5960.39	−	5960.39i	0.525216	−	0.525216i
$506$		0			0
$507$	−1016.05	−	2452.96i	−0.0890027	−	0.214871i
$508$		0			0
$509$	−14481.7	−	5998.52i	−1.26108	−	0.522357i	−0.350840	−	0.936435i	$-0.614104\pi$
$509$	−14481.7	−	5998.52i	−1.26108	−	0.522357i	−0.910241	+	0.414078i	$0.864104\pi$
$510$		0			0
$511$	−16967.6			−1.46889
$512$		0			0
$513$	5407.87			0.465426
$514$		0			0
$515$	−3235.45	−	1340.17i	−0.276837	−	0.114670i
$516$		0			0
$517$	385.893	+	931.628i	0.0328270	+	0.0792514i
$518$		0			0
$519$	−1796.16	+	1796.16i	−0.151913	+	0.151913i
$520$		0			0
$521$	1814.60	+	1814.60i	0.152590	+	0.152590i	0.779274	−	0.626684i	$-0.215588\pi$
$521$	1814.60	+	1814.60i	0.152590	+	0.152590i	−0.626684	+	0.779274i	$0.715588\pi$
$522$		0			0
$523$	−4063.96	+	1683.35i	−0.339779	+	0.140741i	−0.546047	−	0.837754i	$-0.683868\pi$
$523$	−4063.96	+	1683.35i	−0.339779	+	0.140741i	0.206268	+	0.978496i	$0.433868\pi$
$524$		0			0
$525$	−187.906	+	453.645i	−0.0156207	+	0.0377118i
$526$		0			0
$527$			4751.66i			0.392762i
$528$		0			0
$529$		−	597.782i		−	0.0491314i
$530$		0			0
$531$	1799.05	−	4343.30i	0.147029	−	0.354959i
$532$		0			0
$533$	−5585.70	+	2313.67i	−0.453927	+	0.188023i
$534$		0			0
$535$	13554.0	+	13554.0i	1.09531	+	1.09531i
$536$		0			0
$537$	179.445	−	179.445i	0.0144201	−	0.0144201i
$538$		0			0
$539$	1285.48	+	3103.44i	0.102727	+	0.248004i
$540$		0			0
$541$	5389.43	+	2232.38i	0.428299	+	0.177407i	0.586411	−	0.810014i	$-0.300541\pi$
$541$	5389.43	+	2232.38i	0.428299	+	0.177407i	−0.158111	+	0.987421i	$0.550541\pi$
$542$		0			0
$543$	−3077.81			−0.243244
$544$		0			0
$545$	−4371.11			−0.343556
$546$		0			0
$547$	20016.3	+	8291.01i	1.56460	+	0.648077i	0.985880	−	0.167452i	$-0.0535539\pi$
$547$	20016.3	+	8291.01i	1.56460	+	0.648077i	0.578716	+	0.815529i	$0.303554\pi$
$548$		0			0
$549$	3050.48	+	7364.51i	0.237143	+	0.572513i
$550$		0			0
$551$	4914.61	−	4914.61i	0.379981	−	0.379981i
$552$		0			0
$553$	13670.2	+	13670.2i	1.05120	+	1.05120i
$554$		0			0
$555$	6051.17	−	2506.48i	0.462807	−	0.191701i
$556$		0			0
$557$	819.599	−	1978.69i	0.0623474	−	0.150520i	−0.889635	−	0.456672i	$-0.849041\pi$
$557$	819.599	−	1978.69i	0.0623474	−	0.150520i	0.951983	+	0.306152i	$0.0990414\pi$
$558$		0			0
$559$			6770.79i			0.512297i
$560$		0			0
$561$			195.759i			0.0147325i
$562$		0			0
$563$	−4297.82	+	10375.9i	−0.321726	+	0.776715i	0.677428	+	0.735589i	$0.263095\pi$
$563$	−4297.82	+	10375.9i	−0.321726	+	0.776715i	−0.999154	+	0.0411260i	$0.986905\pi$
$564$		0			0
$565$	−6806.82	+	2819.48i	−0.506841	+	0.209940i
$566$		0			0
$567$	−11599.5	−	11599.5i	−0.859139	−	0.859139i
$568$		0			0
$569$	3794.16	−	3794.16i	0.279542	−	0.279542i	−0.553384	−	0.832926i	$-0.686664\pi$
$569$	3794.16	−	3794.16i	0.279542	−	0.279542i	0.832926	+	0.553384i	$0.186664\pi$
$570$		0			0
$571$	3323.60	+	8023.87i	0.243587	+	0.588071i	0.997634	−	0.0687495i	$-0.0219009\pi$
$571$	3323.60	+	8023.87i	0.243587	+	0.588071i	−0.754047	+	0.656820i	$0.771901\pi$
$572$		0			0
$573$	−4439.61	−	1838.95i	−0.323678	−	0.134072i
$574$		0			0
$575$	−859.431			−0.0623318
$576$		0			0
$577$	7285.88			0.525676			0.262838	−	0.964840i	$-0.415342\pi$
$577$	7285.88			0.525676			0.262838	+	0.964840i	$0.415342\pi$
$578$		0			0
$579$	−5202.06	−	2154.76i	−0.373385	−	0.154661i
$580$		0			0
$581$	−3608.76	−	8712.31i	−0.257688	−	0.622113i
$582$		0			0
$583$	−1848.78	+	1848.78i	−0.131336	+	0.131336i
$584$		0			0
$585$	−11031.4	−	11031.4i	−0.779642	−	0.779642i
$586$		0			0
$587$	24501.2	−	10148.7i	1.72278	−	0.713600i	0.723042	−	0.690804i	$-0.242743\pi$
$587$	24501.2	−	10148.7i	1.72278	−	0.713600i	0.999740	−	0.0227951i	$-0.00725653\pi$
$588$		0			0
$589$	3998.87	−	9654.12i	0.279746	−	0.675367i
$590$		0			0
$591$			6193.40i			0.431070i
$592$		0			0
$593$			9134.01i			0.632528i	0.948671	+	0.316264i	$0.102428\pi$
$593$			9134.01i			0.632528i	−0.948671	+	0.316264i	$0.897572\pi$
$594$		0			0
$595$	3829.17	−	9244.44i	0.263833	−	0.636950i
$596$		0			0
$597$	250.401	−	103.720i	0.0171662	−	0.00711049i
$598$		0			0
$599$	−5461.25	−	5461.25i	−0.372522	−	0.372522i	0.495873	−	0.868395i	$-0.334848\pi$
$599$	−5461.25	−	5461.25i	−0.372522	−	0.372522i	−0.868395	+	0.495873i	$0.834848\pi$
$600$		0			0
$601$	14729.8	−	14729.8i	0.999738	−	0.999738i	−0.000262159	−	1.00000i	$-0.500083\pi$
$601$	14729.8	−	14729.8i	0.999738	−	0.999738i	1.00000		0.000262159i	$8.34479e-5\pi$
$602$		0			0
$603$	−2932.89	−	7080.62i	−0.198070	−	0.478184i
$604$		0			0
$605$	13138.3	+	5442.06i	0.882888	+	0.365704i
$606$		0			0
$607$	−881.096			−0.0589169			−0.0294585	−	0.999566i	$-0.509378\pi$
$607$	−881.096			−0.0589169			−0.0294585	+	0.999566i	$0.509378\pi$
$608$		0			0
$609$	7193.83			0.478668
$610$		0			0
$611$	13974.7	+	5788.51i	0.925295	+	0.383270i
$612$		0			0
$613$	−1693.73	−	4089.02i	−0.111597	−	0.269419i	0.858207	−	0.513303i	$-0.171578\pi$
$613$	−1693.73	−	4089.02i	−0.111597	−	0.269419i	−0.969804	+	0.243884i	$0.921578\pi$
$614$		0			0
$615$	1367.77	−	1367.77i	0.0896813	−	0.0896813i
$616$		0			0
$617$	−21041.5	−	21041.5i	−1.37293	−	1.37293i	−0.856068	−	0.516863i	$-0.827100\pi$
$617$	−21041.5	−	21041.5i	−1.37293	−	1.37293i	−0.516863	−	0.856068i	$-0.672900\pi$
$618$		0			0
$619$	−6142.30	+	2544.22i	−0.398837	+	0.165204i	−0.573081	−	0.819499i	$-0.694252\pi$
$619$	−6142.30	+	2544.22i	−0.398837	+	0.165204i	0.174244	+	0.984703i	$0.444252\pi$
$620$		0			0
$621$	−3749.14	+	9051.24i	−0.242267	+	0.584885i
$622$		0			0
$623$		−	21754.2i		−	1.39898i
$624$		0			0
$625$			14562.4i			0.931992i
$626$		0			0
$627$	164.745	−	397.730i	0.0104933	−	0.0253330i
$628$		0			0
$629$	8420.55	−	3487.90i	0.533783	−	0.221100i
$630$		0			0
$631$	12002.6	+	12002.6i	0.757234	+	0.757234i	0.975818	−	0.218584i	$-0.0701438\pi$
$631$	12002.6	+	12002.6i	0.757234	+	0.757234i	−0.218584	+	0.975818i	$0.570144\pi$
$632$		0			0
$633$	3438.87	−	3438.87i	0.215929	−	0.215929i
$634$		0			0
$635$	2378.50	+	5742.20i	0.148642	+	0.358854i
$636$		0			0
$637$	46552.4	+	19282.6i	2.89556	+	1.19938i
$638$		0			0
$639$	22712.6			1.40610
$640$		0			0
$641$	8356.78			0.514934			0.257467	−	0.966287i	$-0.417112\pi$
$641$	8356.78			0.514934			0.257467	+	0.966287i	$0.417112\pi$
$642$		0			0
$643$	−24447.4	−	10126.4i	−1.49939	−	0.621070i	−0.526058	−	0.850449i	$-0.676330\pi$
$643$	−24447.4	−	10126.4i	−1.49939	−	0.621070i	−0.973337	+	0.229379i	$0.926330\pi$
$644$		0			0
$645$	−828.984	−	2001.34i	−0.0506065	−	0.122175i
$646$		0			0
$647$	−12516.3	+	12516.3i	−0.760533	+	0.760533i	−0.976419	−	0.215885i	$-0.930736\pi$
$647$	−12516.3	+	12516.3i	−0.760533	+	0.760533i	0.215885	+	0.976419i	$0.430736\pi$
$648$		0			0
$649$	−565.051	−	565.051i	−0.0341759	−	0.0341759i
$650$		0			0
$651$	9992.38	−	4138.98i	0.601585	−	0.249185i
$652$		0			0
$653$	−1943.05	+	4690.95i	−0.116443	+	0.281119i	−0.971346	−	0.237669i	$-0.923617\pi$
$653$	−1943.05	+	4690.95i	−0.116443	+	0.281119i	0.854903	+	0.518788i	$0.173617\pi$
$654$		0			0
$655$			8775.89i			0.523515i
$656$		0			0
$657$		−	11777.9i		−	0.699391i
$658$		0			0
$659$	3982.05	−	9613.52i	0.235385	−	0.568269i	−0.761410	−	0.648271i	$-0.775492\pi$
$659$	3982.05	−	9613.52i	0.235385	−	0.568269i	0.996795	+	0.0800014i	$0.0254925\pi$
$660$		0			0
$661$	−2718.83	+	1126.18i	−0.159985	+	0.0662680i	−0.461239	−	0.887276i	$-0.652595\pi$
$661$	−2718.83	+	1126.18i	−0.159985	+	0.0662680i	0.301254	+	0.953544i	$0.402595\pi$
$662$		0			0
$663$	2076.38	+	2076.38i	0.121629	+	0.121629i
$664$		0			0
$665$	−15559.7	+	15559.7i	−0.907339	+	0.907339i
$666$		0			0
$667$	4818.48	+	11632.8i	0.279719	+	0.675301i
$668$		0			0
$669$	−5480.19	−	2269.97i	−0.316706	−	0.131184i
$670$		0			0
$671$	1354.96			0.0779548
$672$		0			0
$673$	−4348.42			−0.249063			−0.124531	−	0.992216i	$-0.539743\pi$
$673$	−4348.42			−0.249063			−0.124531	+	0.992216i	$0.539743\pi$
$674$		0			0
$675$	−672.380	−	278.509i	−0.0383406	−	0.0158812i
$676$		0			0
$677$	−4462.91	−	10774.4i	−0.253358	−	0.611661i	0.745113	−	0.666939i	$-0.232396\pi$
$677$	−4462.91	−	10774.4i	−0.253358	−	0.611661i	−0.998471	+	0.0552774i	$0.982396\pi$
$678$		0			0
$679$	42771.2	−	42771.2i	2.41739	−	2.41739i
$680$		0			0
$681$	7120.81	+	7120.81i	0.400690	+	0.400690i
$682$		0			0
$683$	−19860.3	+	8226.41i	−1.11264	+	0.460871i	−0.861846	−	0.507170i	$-0.830692\pi$
$683$	−19860.3	+	8226.41i	−1.11264	+	0.460871i	−0.250794	+	0.968040i	$0.580692\pi$
$684$		0			0
$685$	−1607.35	+	3880.48i	−0.0896548	+	0.216446i
$686$		0			0
$687$		−	8138.84i		−	0.451989i
$688$		0			0
$689$			39219.3i			2.16856i
$690$		0			0
$691$	764.618	−	1845.95i	0.0420947	−	0.101626i	−0.901434	−	0.432917i	$-0.857484\pi$
$691$	764.618	−	1845.95i	0.0420947	−	0.101626i	0.943528	+	0.331291i	$0.107484\pi$
$692$		0			0
$693$	−3043.47	+	1260.65i	−0.166828	+	0.0691024i
$694$		0			0
$695$	−1982.81	−	1982.81i	−0.108219	−	0.108219i
$696$		0			0
$697$	1903.34	−	1903.34i	0.103435	−	0.103435i
$698$		0			0
$699$	−793.139	−	1914.81i	−0.0429174	−	0.103612i
$700$		0			0
$701$	−22956.1	−	9508.72i	−1.23686	−	0.512324i	−0.334128	−	0.942528i	$-0.608442\pi$
$701$	−22956.1	−	9508.72i	−1.23686	−	0.512324i	−0.902732	+	0.430203i	$0.858442\pi$
$702$		0			0
$703$	−20043.6			−1.07533
$704$		0			0
$705$	−4839.43			−0.258530
$706$		0			0
$707$	−24666.9	−	10217.4i	−1.31215	−	0.543512i
$708$		0			0
$709$	−6852.40	−	16543.2i	−0.362972	−	0.876292i	−0.994863	−	0.101234i	$-0.967721\pi$
$709$	−6852.40	−	16543.2i	−0.362972	−	0.876292i	0.631891	−	0.775058i	$-0.282279\pi$
$710$		0			0
$711$	−9489.02	+	9489.02i	−0.500515	+	0.500515i
$712$		0			0
$713$	13385.9	+	13385.9i	0.703096	+	0.703096i
$714$		0			0
$715$	−2449.95	+	1014.80i	−0.128144	+	0.0530790i
$716$		0			0
$717$	1663.25	−	4015.45i	0.0866324	−	0.209149i
$718$		0			0
$719$			29422.6i			1.52612i	0.646329	+	0.763059i	$0.276303\pi$
$719$			29422.6i			1.52612i	−0.646329	+	0.763059i	$0.723697\pi$
$720$		0			0
$721$			11092.5i			0.572962i
$722$		0			0
$723$	−2662.94	+	6428.92i	−0.136979	+	0.330697i
$724$		0			0
$725$	−864.158	+	357.946i	−0.0442676	+	0.0183362i
$726$		0			0
$727$	11609.7	+	11609.7i	0.592267	+	0.592267i	0.938243	−	0.345976i	$-0.112452\pi$
$727$	11609.7	+	11609.7i	0.592267	+	0.592267i	−0.345976	+	0.938243i	$0.612452\pi$
$728$		0			0
$729$	4932.69	−	4932.69i	0.250607	−	0.250607i
$730$		0			0
$731$	−1153.58	−	2784.99i	−0.0583675	−	0.140912i
$732$		0			0
$733$	−11834.5	−	4902.00i	−0.596338	−	0.247011i	0.0640365	−	0.997948i	$-0.479603\pi$
$733$	−11834.5	−	4902.00i	−0.596338	−	0.247011i	−0.660375	+	0.750936i	$0.729603\pi$
$734$		0			0
$735$	−16121.1			−0.809028
$736$		0			0
$737$	−1302.73			−0.0651108
$738$		0			0
$739$	−16285.3	−	6745.57i	−0.810640	−	0.335778i	−0.0614306	−	0.998111i	$-0.519566\pi$
$739$	−16285.3	−	6745.57i	−0.810640	−	0.335778i	−0.749209	+	0.662333i	$0.769566\pi$
$740$		0			0
$741$	−2471.23	−	5966.07i	−0.122514	−	0.295775i
$742$		0			0
$743$	20708.3	−	20708.3i	1.02249	−	1.02249i	0.0227537	−	0.999741i	$-0.492757\pi$
$743$	20708.3	−	20708.3i	1.02249	−	1.02249i	0.999741	−	0.0227537i	$-0.00724334\pi$
$744$		0			0
$745$	−1458.08	−	1458.08i	−0.0717044	−	0.0717044i
$746$		0			0
$747$	6047.57	−	2504.99i	0.296210	−	0.122694i
$748$		0			0
$749$	23234.3	−	56092.7i	1.13346	−	2.73642i
$750$		0			0
$751$			26417.1i			1.28359i	0.766878	+	0.641793i	$0.221809\pi$
$751$			26417.1i			1.28359i	−0.766878	+	0.641793i	$0.778191\pi$
$752$		0			0
$753$			9706.35i			0.469746i
$754$		0			0
$755$	1987.53	−	4798.32i	0.0958061	−	0.231296i
$756$		0			0
$757$	−20911.7	+	8661.89i	−1.00402	+	0.415881i	−0.823272	−	0.567648i	$-0.807854\pi$
$757$	−20911.7	+	8661.89i	−1.00402	+	0.415881i	−0.180753	+	0.983528i	$0.557854\pi$
$758$		0			0
$759$	551.473	+	551.473i	0.0263731	+	0.0263731i
$760$		0			0
$761$	−8497.64	+	8497.64i	−0.404782	+	0.404782i	−0.879914	−	0.475132i	$-0.842400\pi$
$761$	−8497.64	+	8497.64i	−0.404782	+	0.404782i	0.475132	+	0.879914i	$0.342400\pi$
$762$		0			0
$763$	5298.35	+	12791.4i	0.251393	+	0.606918i
$764$		0			0
$765$	6416.94	+	2657.98i	0.303275	+	0.125620i
$766$		0			0
$767$	−11986.8			−0.564298
$768$		0			0
$769$	−31834.2			−1.49281			−0.746405	−	0.665492i	$-0.768222\pi$
$769$	−31834.2			−1.49281			−0.746405	+	0.665492i	$0.768222\pi$
$770$		0			0
$771$	−2528.41	−	1047.30i	−0.118105	−	0.0489205i
$772$		0			0
$773$	14033.5	+	33879.9i	0.652976	+	1.57642i	0.808438	+	0.588581i	$0.200313\pi$
$773$	14033.5	+	33879.9i	0.652976	+	1.57642i	−0.155463	+	0.987842i	$0.549687\pi$
$774$		0			0
$775$	−994.388	+	994.388i	−0.0460896	+	0.0460896i
$776$		0			0
$777$	−14669.6	−	14669.6i	−0.677308	−	0.677308i
$778$		0			0
$779$	−5468.87	+	2265.28i	−0.251531	+	0.104188i
$780$		0			0
$781$	1477.42	−	3566.80i	0.0676904	−	0.163419i
$782$		0			0
$783$			10662.5i			0.486650i
$784$		0			0
$785$		−	14307.6i		−	0.650525i
$786$		0			0
$787$	7882.13	−	19029.1i	0.357011	−	0.861900i	−0.638706	−	0.769450i	$-0.720530\pi$
$787$	7882.13	−	19029.1i	0.357011	−	0.861900i	0.995717	−	0.0924500i	$-0.0294698\pi$
$788$		0			0
$789$	−1247.74	+	516.833i	−0.0563002	+	0.0233203i
$790$		0			0
$791$	16501.5	+	16501.5i	0.741751	+	0.741751i
$792$		0			0
$793$	14371.8	−	14371.8i	0.643579	−	0.643579i
$794$		0			0
$795$	−4801.83	−	11592.6i	−0.214218	−	0.517168i
$796$		0			0
$797$	28060.5	+	11623.0i	1.24712	+	0.516574i	0.905933	−	0.423422i	$-0.139171\pi$
$797$	28060.5	+	11623.0i	1.24712	+	0.516574i	0.341186	+	0.939996i	$0.389171\pi$
$798$		0			0
$799$	−6734.35			−0.298178
$800$		0			0
$801$	15100.4			0.666102
$802$		0			0
$803$	−1849.61	−	766.135i	−0.0812845	−	0.0336692i
$804$		0			0
$805$	−15255.4	−	36829.7i	−0.667927	−	1.61252i
$806$		0			0
$807$	−3084.06	+	3084.06i	−0.134528	+	0.134528i
$808$		0			0
$809$	−14787.2	−	14787.2i	−0.642633	−	0.642633i	0.308569	−	0.951202i	$-0.400150\pi$
$809$	−14787.2	−	14787.2i	−0.642633	−	0.642633i	−0.951202	+	0.308569i	$0.900150\pi$
$810$		0			0
$811$	−26961.4	+	11167.8i	−1.16738	+	0.483544i	−0.880325	−	0.474371i	$-0.842675\pi$
$811$	−26961.4	+	11167.8i	−1.16738	+	0.483544i	−0.287053	+	0.957915i	$0.592675\pi$
$812$		0			0
$813$	−2351.25	+	5676.41i	−0.101429	+	0.244871i
$814$		0			0
$815$			15770.2i			0.677798i
$816$		0			0
$817$			6629.18i			0.283875i
$818$		0			0
$819$	−18910.1	+	45652.9i	−0.806802	+	1.94779i
$820$		0			0
$821$	−26459.7	+	10960.0i	−1.12479	+	0.465902i	−0.866006	−	0.500033i	$-0.833321\pi$
$821$	−26459.7	+	10960.0i	−1.12479	+	0.465902i	−0.258782	+	0.965936i	$0.583321\pi$
$822$		0			0
$823$	−16724.6	−	16724.6i	−0.708363	−	0.708363i	0.257828	−	0.966191i	$-0.416993\pi$
$823$	−16724.6	−	16724.6i	−0.708363	−	0.708363i	−0.966191	+	0.257828i	$0.916993\pi$
$824$		0			0
$825$	−40.9668	+	40.9668i	−0.00172882	+	0.00172882i
$826$		0			0
$827$	3883.90	+	9376.57i	0.163309	+	0.394263i	0.984258	−	0.176739i	$-0.0565549\pi$
$827$	3883.90	+	9376.57i	0.163309	+	0.394263i	−0.820949	+	0.571002i	$0.806555\pi$
$828$		0			0
$829$	−4058.22	−	1680.97i	−0.170021	−	0.0704251i	0.296049	−	0.955173i	$-0.404331\pi$
$829$	−4058.22	−	1680.97i	−0.170021	−	0.0704251i	−0.466071	+	0.884748i	$0.654331\pi$
$830$		0			0
$831$	8182.98			0.341594
$832$		0			0
$833$	−22433.4			−0.933100
$834$		0			0
$835$	−35640.8	−	14762.9i	−1.47713	−	0.611845i
$836$		0			0
$837$	6134.68	+	14810.4i	0.253340	+	0.611617i
$838$		0			0
$839$	−724.855	+	724.855i	−0.0298269	+	0.0298269i	−0.721863	−	0.692036i	$-0.756714\pi$
$839$	−724.855	+	724.855i	−0.0298269	+	0.0298269i	0.692036	+	0.721863i	$0.256714\pi$
$840$		0			0
$841$	−7555.66	−	7555.66i	−0.309798	−	0.309798i
$842$		0			0
$843$	−5634.44	+	2333.86i	−0.230202	+	0.0953528i
$844$		0			0
$845$	−6127.80	+	14793.8i	−0.249471	+	0.602275i
$846$		0			0
$847$		−	45043.5i		−	1.82729i
$848$		0			0
$849$			14122.0i			0.570866i
$850$		0			0
$851$	13895.8	−	33547.4i	0.559743	−	1.35134i
$852$		0			0
$853$	23925.7	−	9910.36i	0.960376	−	0.397801i	0.153255	−	0.988187i	$-0.451024\pi$
$853$	23925.7	−	9910.36i	0.960376	−	0.397801i	0.807121	+	0.590386i	$0.201024\pi$
$854$		0			0
$855$	−10800.6	−	10800.6i	−0.432016	−	0.432016i
$856$		0			0
$857$	−25248.3	+	25248.3i	−1.00638	+	1.00638i	−0.00639889	+	0.999980i	$0.502037\pi$
$857$	−25248.3	+	25248.3i	−1.00638	+	1.00638i	−0.999980	+	0.00639889i	$0.997963\pi$
$858$		0			0
$859$	13363.0	+	32261.1i	0.530780	+	1.28142i	0.931008	+	0.365000i	$0.118931\pi$
$859$	13363.0	+	32261.1i	0.530780	+	1.28142i	−0.400228	+	0.916416i	$0.631069\pi$
$860$		0			0
$861$	−5660.49	−	2344.65i	−0.224052	−	0.0928054i
$862$		0			0
$863$	37879.2			1.49412			0.747058	−	0.664758i	$-0.231466\pi$
$863$	37879.2			1.49412			0.747058	+	0.664758i	$0.231466\pi$
$864$		0			0
$865$	15319.7			0.602178
$866$		0			0
$867$	6933.29	+	2871.86i	0.271588	+	0.112495i
$868$		0			0
$869$	872.919	+	2107.41i	0.0340757	+	0.0822659i
$870$		0			0
$871$	−13817.8	+	13817.8i	−0.537541	+	0.537541i
$872$		0			0
$873$	29689.3	+	29689.3i	1.15101	+	1.15101i
$874$		0			0
$875$	45537.2	−	18862.1i	1.75936	−	0.728750i
$876$		0			0
$877$	−17752.3	+	42857.9i	−0.683527	+	1.65018i	0.0739053	+	0.997265i	$0.476454\pi$
$877$	−17752.3	+	42857.9i	−0.683527	+	1.65018i	−0.757432	+	0.652914i	$0.773546\pi$
$878$		0			0
$879$		−	4966.34i		−	0.190569i
$880$		0			0
$881$			7584.20i			0.290032i	0.989429	+	0.145016i	$0.0463234\pi$
$881$			7584.20i			0.290032i	−0.989429	+	0.145016i	$0.953677\pi$
$882$		0			0
$883$	9800.89	−	23661.4i	0.373529	−	0.901779i	−0.619617	−	0.784904i	$-0.712712\pi$
$883$	9800.89	−	23661.4i	0.373529	−	0.901779i	0.993147	−	0.116875i	$-0.0372878\pi$
$884$		0			0
$885$	3543.11	−	1467.60i	0.134577	−	0.0557435i
$886$		0			0
$887$	8905.97	+	8905.97i	0.337129	+	0.337129i	0.855286	−	0.518157i	$-0.173382\pi$
$887$	8905.97	+	8905.97i	0.337129	+	0.337129i	−0.518157	+	0.855286i	$0.673382\pi$
$888$		0			0
$889$	13920.6	−	13920.6i	0.525176	−	0.525176i
$890$		0			0
$891$	−740.693	−	1788.19i	−0.0278498	−	0.0672353i
$892$		0			0
$893$	13682.4	+	5667.44i	0.512726	+	0.212378i
$894$		0			0
$895$	−1530.51			−0.0571611
$896$		0			0
$897$	11698.7			0.435462
$898$		0			0
$899$	19034.7	+	7884.42i	0.706165	+	0.292503i
$900$		0			0
$901$	−6682.03	−	16131.8i	−0.247071	−	0.596481i
$902$		0			0
$903$	−4851.77	+	4851.77i	−0.178801	+	0.178801i
$904$		0			0
$905$	13125.5	+	13125.5i	0.482107	+	0.482107i
$906$		0			0
$907$	23324.8	−	9661.45i	0.853900	−	0.353697i	0.0875813	−	0.996157i	$-0.472086\pi$
$907$	23324.8	−	9661.45i	0.853900	−	0.353697i	0.766319	+	0.642460i	$0.222086\pi$
$908$		0			0
$909$	7092.28	−	17122.3i	0.258786	−	0.624764i
$910$		0			0
$911$		−	28451.4i		−	1.03473i	−0.855765	−	0.517364i	$-0.826913\pi$
$911$		−	28451.4i		−	1.03473i	0.855765	−	0.517364i	$-0.173087\pi$
$912$		0			0
$913$		−	1112.66i		−	0.0403327i
$914$		0			0
$915$	−2488.48	+	6007.71i	−0.0899087	+	0.217059i
$916$		0			0
$917$	25681.2	−	10637.5i	0.924830	−	0.383077i
$918$		0			0
$919$	−23087.8	−	23087.8i	−0.828721	−	0.828721i	0.158618	−	0.987340i	$-0.449296\pi$
$919$	−23087.8	−	23087.8i	−0.828721	−	0.828721i	−0.987340	+	0.158618i	$0.949296\pi$
$920$		0			0
$921$	10863.1	−	10863.1i	0.388656	−	0.388656i
$922$		0			0
$923$	−22161.7	−	53503.1i	−0.790316	−	1.90799i
$924$		0			0
$925$	2492.10	+	1032.26i	0.0885835	+	0.0366925i
$926$		0			0
$927$	−7699.74			−0.272808
$928$		0			0
$929$	29125.2			1.02860			0.514298	−	0.857612i	$-0.328053\pi$
$929$	29125.2			1.02860			0.514298	+	0.857612i	$0.328053\pi$
$930$		0			0
$931$	45578.8	+	18879.3i	1.60449	+	0.664603i
$932$		0			0
$933$	−4958.13	−	11970.0i	−0.173978	−	0.420021i
$934$		0			0
$935$	834.826	−	834.826i	0.0291997	−	0.0291997i
$936$		0			0
$937$	−23895.1	−	23895.1i	−0.833105	−	0.833105i	0.154835	−	0.987940i	$-0.450515\pi$
$937$	−23895.1	−	23895.1i	−0.833105	−	0.833105i	−0.987940	+	0.154835i	$0.950515\pi$
$938$		0			0
$939$	−4128.29	+	1709.99i	−0.143473	+	0.0594286i
$940$		0			0
$941$	1918.84	−	4632.49i	0.0664743	−	0.160483i	−0.887151	−	0.461479i	$-0.847319\pi$
$941$	1918.84	−	4632.49i	0.0664743	−	0.160483i	0.953625	+	0.300996i	$0.0973190\pi$
$942$		0			0
$943$		−	10723.8i		−	0.370323i
$944$		0			0
$945$		−	33757.6i		−	1.16205i
$946$		0			0
$947$	−14686.5	+	35456.3i	−0.503957	+	1.21666i	0.443355	+	0.896346i	$0.353788\pi$
$947$	−14686.5	+	35456.3i	−0.503957	+	1.21666i	−0.947312	+	0.320313i	$0.896212\pi$
$948$		0			0
$949$	−27744.8	+	11492.3i	−0.949034	+	0.393103i
$950$		0			0
$951$	−5617.03	−	5617.03i	−0.191530	−	0.191530i
$952$		0			0
$953$	11229.5	−	11229.5i	0.381698	−	0.381698i	−0.490016	−	0.871714i	$-0.663009\pi$
$953$	11229.5	−	11229.5i	0.381698	−	0.381698i	0.871714	+	0.490016i	$0.163009\pi$
$954$		0			0
$955$	11090.7	+	26775.3i	0.375797	+	0.907254i
$956$		0			0
$957$	784.190	+	324.822i	0.0264883	+	0.0109718i
$958$		0			0
$959$	13303.9			0.447972
$960$		0			0
$961$	1184.85			0.0397721
$962$		0			0
$963$	38936.2	+	16127.9i	1.30291	+	0.539683i
$964$		0			0
$965$	12995.4	+	31373.6i	0.433509	+	1.04658i
$966$		0			0
$967$	−23938.4	+	23938.4i	−0.796076	+	0.796076i	−0.982474	−	0.186398i	$-0.940319\pi$
$967$	−23938.4	+	23938.4i	−0.796076	+	0.796076i	0.186398	+	0.982474i	$0.440319\pi$
$968$		0			0
$969$	2032.95	+	2032.95i	0.0673970	+	0.0673970i
$970$		0			0
$971$	−28947.0	+	11990.2i	−0.956698	+	0.396277i	−0.805744	−	0.592264i	$-0.798234\pi$
$971$	−28947.0	+	11990.2i	−0.956698	+	0.396277i	−0.150954	+	0.988541i	$0.548234\pi$
$972$		0			0
$973$	−3398.94	+	8205.77i	−0.111989	+	0.270365i
$974$		0			0
$975$			869.053i			0.0285456i
$976$		0			0
$977$		−	60103.7i		−	1.96815i	−0.177743	−	0.984077i	$-0.556880\pi$
$977$		−	60103.7i		−	1.96815i	0.177743	−	0.984077i	$-0.443120\pi$
$978$		0			0
$979$	982.262	−	2371.39i	0.0320666	−	0.0774157i
$980$		0			0
$981$	−8879.00	+	3677.80i	−0.288975	+	0.119697i
$982$		0			0
$983$	40035.9	+	40035.9i	1.29903	+	1.29903i	0.929034	+	0.369995i	$0.120641\pi$
$983$	40035.9	+	40035.9i	1.29903	+	1.29903i	0.369995	+	0.929034i	$0.379359\pi$
$984$		0			0
$985$	26412.1	−	26412.1i	0.854376	−	0.854376i
$986$		0			0
$987$	5866.01	+	14161.8i	0.189176	+	0.456712i
$988$		0			0
$989$	−11095.4	−	4595.85i	−0.356736	−	0.147765i
$990$		0			0
$991$	−15618.9			−0.500658			−0.250329	−	0.968161i	$-0.580539\pi$
$991$	−15618.9			−0.500658			−0.250329	+	0.968161i	$0.580539\pi$
$992$		0			0
$993$	−12417.0			−0.396821
$994$		0			0
$995$	−1510.17	−	625.533i	−0.0481162	−	0.0199304i
$996$		0			0
$997$	18691.7	+	45125.8i	0.593754	+	1.43345i	0.879851	+	0.475249i	$0.157642\pi$
$997$	18691.7	+	45125.8i	0.593754	+	1.43345i	−0.286097	+	0.958201i	$0.592358\pi$
$998$		0			0
$999$	21742.9	−	21742.9i	0.688602	−	0.688602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.81.7		44
4.3	odd	2		32.4.g.a.29.1	yes	44
8.3	odd	2		256.4.g.b.161.7		44
8.5	even	2		256.4.g.a.161.5		44
32.5	even	8		256.4.g.a.97.5		44
32.11	odd	8		32.4.g.a.21.1	✓	44
32.21	even	8	inner	128.4.g.a.49.7		44
32.27	odd	8		256.4.g.b.97.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.1	✓	44	32.11	odd	8
32.4.g.a.29.1	yes	44	4.3	odd	2
128.4.g.a.49.7		44	32.21	even	8	inner
128.4.g.a.81.7		44	1.1	even	1	trivial
256.4.g.a.97.5		44	32.5	even	8
256.4.g.a.161.5		44	8.5	even	2
256.4.g.b.97.7		44	32.27	odd	8
256.4.g.b.161.7		44	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.65706 + 0.686375i) q^{3} +(-4.13953 - 9.99370i) q^{5} +(-24.2273 + 24.2273i) q^{7} +(-16.8172 - 16.8172i) q^{9} +O(q^{10})\)	\(q+(1.65706 + 0.686375i) q^{3} +(-4.13953 - 9.99370i) q^{5} +(-24.2273 + 24.2273i) q^{7} +(-16.8172 - 16.8172i) q^{9} +(-3.73492 + 1.54705i) q^{11} +(-23.2063 + 56.0248i) q^{13} -19.4014i q^{15} -26.9981i q^{17} +(-22.7209 + 54.8531i) q^{19} +(-56.7750 + 23.5170i) q^{21} +(-76.0566 - 76.0566i) q^{23} +(5.64994 - 5.64994i) q^{25} +(-34.8562 - 84.1503i) q^{27} +(-108.152 - 44.7980i) q^{29} -176.000 q^{31} -7.25082 q^{33} +(342.410 + 141.831i) q^{35} +(129.191 + 311.894i) q^{37} +(-76.9081 + 76.9081i) q^{39} +(70.4988 + 70.4988i) q^{41} +(103.155 - 42.7281i) q^{43} +(-98.4506 + 237.681i) q^{45} -249.437i q^{47} -830.925i q^{49} +(18.5308 - 44.7374i) q^{51} +(597.516 - 247.499i) q^{53} +(30.9216 + 30.9216i) q^{55} +(-75.2996 + 75.2996i) q^{57} +(75.6443 + 182.622i) q^{59} +(-309.654 - 128.263i) q^{61} +814.869 q^{63} +655.959 q^{65} +(297.717 + 123.318i) q^{67} +(-73.8267 - 178.233i) q^{69} +(-675.279 + 675.279i) q^{71} +(350.175 + 350.175i) q^{73} +(13.2403 - 5.48429i) q^{75} +(53.0061 - 127.968i) q^{77} -564.246i q^{79} +478.776i q^{81} +(-105.327 + 254.281i) q^{83} +(-269.811 + 111.760i) q^{85} +(-148.465 - 148.465i) q^{87} +(-448.959 + 448.959i) q^{89} +(-795.106 - 1919.56i) q^{91} +(-291.641 - 120.802i) q^{93} +642.239 q^{95} -1765.41 q^{97} +(88.8278 + 36.7937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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