LMFDB - Embedded newform 128.4.g.a.49.7

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			49.7
Character	$\chi$	$=$	128.49
Dual form			128.4.g.a.81.7

$q$-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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

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

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
$3$	1.65706	−	0.686375i	0.318900	−	0.132093i	−0.217491	−	0.976062i	$-0.569787\pi$
$3$	1.65706	−	0.686375i	0.318900	−	0.132093i	0.536391	+	0.843969i	$0.319787\pi$
$4$		0			0
$5$	−4.13953	+	9.99370i	−0.370251	+	0.893864i	0.623457	+	0.781858i	$0.285728\pi$
$5$	−4.13953	+	9.99370i	−0.370251	+	0.893864i	−0.993708	+	0.112006i	$0.964272\pi$
$6$		0			0
$7$	−24.2273	−	24.2273i	−1.30815	−	1.30815i	−0.922748	−	0.385403i	$-0.874062\pi$
$7$	−24.2273	−	24.2273i	−1.30815	−	1.30815i	−0.385403	−	0.922748i	$-0.625938\pi$
$8$		0			0
$9$	−16.8172	+	16.8172i	−0.622858	+	0.622858i
$10$		0			0
$11$	−3.73492	−	1.54705i	−0.102375	−	0.0424049i	0.330908	−	0.943663i	$-0.392645\pi$
$11$	−3.73492	−	1.54705i	−0.102375	−	0.0424049i	−0.433283	+	0.901258i	$0.642645\pi$
$12$		0			0
$13$	−23.2063	−	56.0248i	−0.495097	−	1.19527i	−0.952095	−	0.305802i	$-0.901076\pi$
$13$	−23.2063	−	56.0248i	−0.495097	−	1.19527i	0.456999	−	0.889467i	$-0.348924\pi$
$14$		0			0
$15$			19.4014i			0.333961i
$16$		0			0
$17$			26.9981i			0.385177i	0.981280	+	0.192589i	$0.0616883\pi$
$17$			26.9981i			0.385177i	−0.981280	+	0.192589i	$0.938312\pi$
$18$		0			0
$19$	−22.7209	−	54.8531i	−0.274344	−	0.662324i	0.725316	−	0.688416i	$-0.241694\pi$
$19$	−22.7209	−	54.8531i	−0.274344	−	0.662324i	−0.999660	+	0.0260920i	$0.991694\pi$
$20$		0			0
$21$	−56.7750	−	23.5170i	−0.589968	−	0.244373i
$22$		0			0
$23$	−76.0566	+	76.0566i	−0.689517	+	0.689517i	−0.962125	−	0.272608i	$-0.912114\pi$
$23$	−76.0566	+	76.0566i	−0.689517	+	0.689517i	0.272608	+	0.962125i	$0.412114\pi$
$24$		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	−0.701053	−	0.713109i	$-0.747286\pi$
$29$	−108.152	+	44.7980i	−0.692527	+	0.286854i	0.00852531	+	0.999964i	$0.497286\pi$
$30$		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	−0.324083	−	0.946029i	$-0.605056\pi$
$37$	129.191	−	311.894i	0.574021	−	1.38581i	0.898105	−	0.439782i	$-0.144944\pi$
$38$		0			0
$39$	−76.9081	−	76.9081i	−0.315773	−	0.315773i
$40$		0			0
$41$	70.4988	−	70.4988i	0.268538	−	0.268538i	−0.559973	−	0.828511i	$-0.689188\pi$
$41$	70.4988	−	70.4988i	0.268538	−	0.268538i	0.828511	+	0.559973i	$0.189188\pi$
$42$		0			0
$43$	103.155	+	42.7281i	0.365836	+	0.151534i	0.558026	−	0.829824i	$-0.311559\pi$
$43$	103.155	+	42.7281i	0.365836	+	0.151534i	−0.192190	+	0.981358i	$0.561559\pi$
$44$		0			0
$45$	−98.4506	−	237.681i	−0.326137	−	0.787364i
$46$		0			0
$47$			249.437i			0.774131i	0.922052	+	0.387066i	$0.126511\pi$
$47$			249.437i			0.774131i	−0.922052	+	0.387066i	$0.873489\pi$
$48$		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	0.983060	−	0.183282i	$-0.0586723\pi$
$53$	597.516	+	247.499i	1.54859	+	0.641446i	0.565528	+	0.824729i	$0.308672\pi$
$54$		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	−0.818183	−	0.574958i	$-0.805019\pi$
$59$	75.6443	−	182.622i	0.166916	−	0.402971i	0.985099	+	0.171986i	$0.0550185\pi$
$60$		0			0
$61$	−309.654	+	128.263i	−0.649953	+	0.269219i	−0.683204	−	0.730228i	$-0.739414\pi$
$61$	−309.654	+	128.263i	−0.649953	+	0.269219i	0.0332511	+	0.999447i	$0.489414\pi$
$62$		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	−0.0943627	−	0.995538i	$-0.530081\pi$
$67$	297.717	−	123.318i	0.542864	−	0.224862i	0.637227	+	0.770676i	$0.280081\pi$
$68$		0			0
$69$	−73.8267	+	178.233i	−0.128807	+	0.310968i
$70$		0			0
$71$	−675.279	−	675.279i	−1.12874	−	1.12874i	−0.990382	−	0.138363i	$-0.955816\pi$
$71$	−675.279	−	675.279i	−1.12874	−	1.12874i	−0.138363	−	0.990382i	$-0.544184\pi$
$72$		0			0
$73$	350.175	−	350.175i	0.561437	−	0.561437i	−0.368279	−	0.929715i	$-0.620053\pi$
$73$	350.175	−	350.175i	0.561437	−	0.561437i	0.929715	+	0.368279i	$0.120053\pi$
$74$		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	$0.131611\pi$
$79$			564.246i			0.803578i	−0.915732	+	0.401789i	$0.868389\pi$
$80$		0			0
$81$		−	478.776i		−	0.656758i
$82$		0			0
$83$	−105.327	−	254.281i	−0.139290	−	0.336276i	0.838806	−	0.544431i	$-0.183254\pi$
$83$	−105.327	−	254.281i	−0.139290	−	0.336276i	−0.978096	+	0.208155i	$0.933254\pi$
$84$		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	0.387257	−	0.921972i	$-0.373423\pi$
$89$	−448.959	−	448.959i	−0.534715	−	0.534715i	−0.921972	+	0.387257i	$0.873423\pi$
$90$		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	−0.706210	−	0.708003i	$-0.749596\pi$
$101$	298.207	−	719.936i	0.293790	−	0.709271i	0.999999	−	0.00126791i	$-0.000403589\pi$
$102$		0			0
$103$	228.925	+	228.925i	0.218997	+	0.218997i	0.808076	−	0.589079i	$-0.200509\pi$
$103$	228.925	+	228.925i	0.218997	+	0.218997i	−0.589079	+	0.808076i	$0.700509\pi$
$104$		0			0
$105$	470.043	−	470.043i	0.436872	−	0.436872i
$106$		0			0
$107$	−1637.14	−	678.126i	−1.47914	−	0.612681i	−0.510221	−	0.860044i	$-0.670436\pi$
$107$	−1637.14	−	678.126i	−1.47914	−	0.612681i	−0.968923	+	0.247362i	$0.920436\pi$
$108$		0			0
$109$	154.640	+	373.333i	0.135888	+	0.328063i	0.977145	−	0.212572i	$-0.0681841\pi$
$109$	154.640	+	373.333i	0.135888	+	0.328063i	−0.841257	+	0.540635i	$0.818184\pi$
$110$		0			0
$111$		−	605.498i		−	0.517760i
$112$		0			0
$113$			681.111i			0.567023i	0.958969	+	0.283511i	$0.0914993\pi$
$113$			681.111i			0.567023i	−0.958969	+	0.283511i	$0.908501\pi$
$114$		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	−0.618365	−	0.785891i	$-0.712205\pi$
$131$	−749.541	+	310.470i	−0.499906	+	0.207068i	0.118459	+	0.992959i	$0.462205\pi$
$132$		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	−0.787517	−	0.616293i	$-0.788634\pi$
$137$	−274.564	+	274.564i	−0.171223	+	0.171223i	0.616293	+	0.787517i	$0.288634\pi$
$138$		0			0
$139$	239.497	+	99.2027i	0.146143	+	0.0605343i	0.454556	−	0.890718i	$-0.349798\pi$
$139$	239.497	+	99.2027i	0.146143	+	0.0605343i	−0.308413	+	0.951252i	$0.599798\pi$
$140$		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	0.430574	−	0.902555i	$-0.358311\pi$
$149$	176.116	+	72.9498i	0.0968323	+	0.0401092i	−0.333741	+	0.942665i	$0.608311\pi$
$150$		0			0
$151$	339.506	−	339.506i	0.182971	−	0.182971i	−0.609678	−	0.792649i	$-0.708701\pi$
$151$	339.506	−	339.506i	0.182971	−	0.182971i	0.792649	+	0.609678i	$0.208701\pi$
$152$		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	−0.0498158	−	0.998758i	$-0.515863\pi$
$157$	1222.00	−	506.170i	0.621188	−	0.257304i	0.671004	+	0.741454i	$0.265863\pi$
$158$		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	−0.682054	−	0.731302i	$-0.738913\pi$
$163$	−1346.92	+	557.911i	−0.647231	+	0.268092i	0.0348231	+	0.999393i	$0.488913\pi$
$164$		0			0
$165$	30.0150	−	72.4626i	0.0141616	−	0.0341891i
$166$		0			0
$167$	2521.77	+	2521.77i	1.16851	+	1.16851i	0.982560	+	0.185946i	$0.0595351\pi$
$167$	2521.77	+	2521.77i	1.16851	+	1.16851i	0.185946	+	0.982560i	$0.440465\pi$
$168$		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	0.758913	−	0.651192i	$-0.225731\pi$
$173$	−541.973	−	1308.44i	−0.238182	−	0.575022i	−0.997095	+	0.0761701i	$0.975731\pi$
$174$		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	0.934781	−	0.355225i	$-0.115596\pi$
$179$	54.1456	+	130.719i	0.0226091	+	0.0545833i	−0.912172	+	0.409808i	$0.865596\pi$
$180$		0			0
$181$	−1585.39	−	656.689i	−0.651055	−	0.269676i	0.0326139	−	0.999468i	$-0.489617\pi$
$181$	−1585.39	−	656.689i	−0.651055	−	0.269676i	−0.683669	+	0.729792i	$0.739617\pi$
$182$		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	−0.482675	−	0.875799i	$-0.660335\pi$
$197$	1321.44	−	3190.23i	0.477911	−	1.15378i	0.960587	−	0.277981i	$-0.0896652\pi$
$198$		0			0
$199$	106.853	+	106.853i	0.0380632	+	0.0380632i	0.725882	−	0.687819i	$-0.241432\pi$
$199$	106.853	+	106.853i	0.0380632	+	0.0380632i	−0.687819	+	0.725882i	$0.741432\pi$
$200$		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	0.997855	+	0.0654593i	$0.0208512\pi$
$211$	1037.64	+	2505.10i	0.338552	+	0.817336i	−0.659304	+	0.751877i	$0.729149\pi$
$212$		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	0.539771	−	0.841812i	$-0.318511\pi$
$227$	5187.26	−	2148.63i	1.51670	−	0.628237i	0.976927	+	0.213575i	$0.0685108\pi$
$228$		0			0
$229$	−1736.52	+	4192.34i	−0.501103	+	1.20977i	0.447780	+	0.894144i	$0.352215\pi$
$229$	−1736.52	+	4192.34i	−0.501103	+	1.20977i	−0.948883	+	0.315627i	$0.897785\pi$
$230$		0			0
$231$	175.668	+	175.668i	0.0500351	+	0.0500351i
$232$		0			0
$233$	−817.096	+	817.096i	−0.229741	+	0.229741i	−0.812585	−	0.582843i	$-0.801940\pi$
$233$	−817.096	+	817.096i	−0.229741	+	0.229741i	0.582843	+	0.812585i	$0.301940\pi$
$234$		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	$0.106348\pi$
$239$			2423.25i			0.655844i	−0.944705	+	0.327922i	$0.893652\pi$
$240$		0			0
$241$		−	3879.72i		−	1.03699i	−0.855080	−	0.518496i	$-0.826492\pi$
$241$		−	3879.72i		−	1.03699i	0.855080	−	0.518496i	$-0.173508\pi$
$242$		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	−0.416622	−	0.909080i	$-0.636786\pi$
$251$	2070.97	−	4999.76i	0.520791	−	1.25730i	0.937413	−	0.348220i	$-0.113214\pi$
$252$		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	0.641928	−	0.766765i	$-0.278135\pi$
$263$	−532.444	−	532.444i	−0.124836	−	0.124836i	−0.766765	+	0.641928i	$0.778135\pi$
$264$		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	0.782641	−	0.622473i	$-0.213872\pi$
$269$	−930.585	−	2246.63i	−0.210925	−	0.509217i	−0.993566	+	0.113256i	$0.963872\pi$
$270$		0			0
$271$		−	3425.60i		−	0.767862i	−0.923362	−	0.383931i	$-0.874570\pi$
$271$		−	3425.60i		−	0.767862i	0.923362	−	0.383931i	$-0.125430\pi$
$272$		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	0.789698	−	0.613495i	$-0.210237\pi$
$277$	4215.07	+	1745.94i	0.914293	+	0.378712i	0.124594	+	0.992208i	$0.460237\pi$
$278$		0			0
$279$	2959.81	−	2959.81i	0.635123	−	0.635123i
$280$		0			0
$281$	−2404.35	−	2404.35i	−0.510433	−	0.510433i	0.404226	−	0.914659i	$-0.367541\pi$
$281$	−2404.35	−	2404.35i	−0.510433	−	0.510433i	−0.914659	+	0.404226i	$0.867541\pi$
$282$		0			0
$283$	3013.10	−	7274.27i	0.632899	−	1.52795i	−0.203063	−	0.979166i	$-0.565090\pi$
$283$	3013.10	−	7274.27i	0.632899	−	1.52795i	0.835962	−	0.548787i	$-0.184910\pi$
$284$		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	−0.993620	−	0.112780i	$-0.964025\pi$
$293$	−1059.63	+	2558.17i	−0.211277	+	0.510068i	0.782343	+	0.622848i	$0.214025\pi$
$294$		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	0.863688	+	0.504027i	$0.168149\pi$
$307$	3277.84	+	7913.41i	0.609369	+	1.47115i	−0.254319	+	0.967120i	$0.581851\pi$
$308$		0			0
$309$	536.470	+	222.213i	0.0987660	+	0.0409102i
$310$		0			0
$311$	−5107.89	+	5107.89i	−0.931324	+	0.931324i	−0.997789	−	0.0664648i	$-0.978828\pi$
$311$	−5107.89	+	5107.89i	−0.931324	+	0.931324i	0.0664648	+	0.997789i	$0.478828\pi$
$312$		0			0
$313$	−1761.64	−	1761.64i	−0.318128	−	0.318128i	0.529920	−	0.848048i	$-0.322222\pi$
$313$	−1761.64	−	1761.64i	−0.318128	−	0.318128i	−0.848048	+	0.529920i	$0.822222\pi$
$314$		0			0
$315$	−3373.17	+	8143.56i	−0.603355	+	1.45663i
$316$		0			0
$317$	−4091.81	+	1694.88i	−0.724981	+	0.300297i	−0.714488	−	0.699648i	$-0.753340\pi$
$317$	−4091.81	+	1694.88i	−0.724981	+	0.300297i	−0.0104934	+	0.999945i	$0.503340\pi$
$318$		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	−0.217911	−	0.975969i	$-0.569924\pi$
$331$	−6396.05	−	2649.33i	−1.06211	−	0.439941i	−0.844200	+	0.536028i	$0.819924\pi$
$332$		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	$-0.903541\pi$
$337$		−	3692.32i		−	0.596835i	0.954435	−	0.298418i	$-0.0964588\pi$
$338$		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	0.306322	+	0.951928i	$0.400902\pi$
$347$	−3771.01	+	9104.01i	−0.583395	+	1.40844i	−0.889717	+	0.456513i	$0.849098\pi$
$348$		0			0
$349$	2347.30	−	972.282i	0.360023	−	0.149126i	−0.195338	−	0.980736i	$-0.562580\pi$
$349$	2347.30	−	972.282i	0.360023	−	0.149126i	0.555360	+	0.831610i	$0.312580\pi$
$350$		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	0.924753	−	0.380568i	$-0.124272\pi$
$359$	3701.59	+	3701.59i	0.544185	+	0.544185i	−0.380568	+	0.924753i	$0.624272\pi$
$360$		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	$-0.914384\pi$
$367$		−	3736.68i		−	0.531479i	0.964045	−	0.265740i	$-0.0856162\pi$
$368$		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	0.904379	−	0.426729i	$-0.140334\pi$
$373$	8948.08	+	3706.42i	1.24213	+	0.514507i	0.337750	+	0.941236i	$0.390334\pi$
$374$		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	−0.967032	−	0.254654i	$-0.918038\pi$
$379$	−761.220	+	1837.75i	−0.103170	+	0.249073i	0.863863	+	0.503727i	$0.168038\pi$
$380$		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	0.691377	+	0.722494i	$0.257004\pi$
$389$	−2365.98	+	5711.99i	−0.308381	+	0.744497i	−0.999758	+	0.0220031i	$0.992996\pi$
$390$		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	0.886531	−	0.462669i	$-0.153108\pi$
$397$	−533.914	−	1288.98i	−0.0674972	−	0.162953i	−0.954028	+	0.299716i	$0.903108\pi$
$398$		0			0
$399$			3648.61i			0.457792i
$400$		0			0
$401$			4956.51i			0.617248i	0.951184	+	0.308624i	$0.0998685\pi$
$401$			4956.51i			0.617248i	−0.951184	+	0.308624i	$0.900131\pi$
$402$		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	0.484618	−	0.874726i	$-0.338959\pi$
$409$	−3226.79	−	3226.79i	−0.390108	−	0.390108i	−0.874726	+	0.484618i	$0.838959\pi$
$410$		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	−0.273895	−	0.961760i	$-0.588312\pi$
$419$	1822.54	−	754.920i	0.212498	−	0.0880197i	0.486394	+	0.873740i	$0.338312\pi$
$420$		0			0
$421$	−215.665	+	520.662i	−0.0249664	+	0.0602743i	−0.935871	−	0.352343i	$-0.885385\pi$
$421$	−215.665	+	520.662i	−0.0249664	+	0.0602743i	0.910905	+	0.412617i	$0.135385\pi$
$422$		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	$0.0392155\pi$
$431$			2199.14i			0.245775i	−0.992421	+	0.122888i	$0.960785\pi$
$432$		0			0
$433$		−	273.133i		−	0.0303139i	−0.999885	−	0.0151569i	$-0.995175\pi$
$433$		−	273.133i		−	0.0303139i	0.999885	−	0.0151569i	$-0.00482479\pi$
$434$		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	−0.847398	−	0.530958i	$-0.821832\pi$
$439$	−2910.64	+	2910.64i	−0.316440	+	0.316440i	0.530958	+	0.847398i	$0.321832\pi$
$440$		0			0
$441$	−13973.8	−	13973.8i	−1.50889	−	1.50889i
$442$		0			0
$443$	−1439.20	+	3474.54i	−0.154353	+	0.372642i	−0.982073	−	0.188499i	$-0.939638\pi$
$443$	−1439.20	+	3474.54i	−0.154353	+	0.372642i	0.827720	+	0.561142i	$0.189638\pi$
$444$		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	−0.483237	−	0.875490i	$-0.660539\pi$
$457$	3832.14	−	3832.14i	0.392253	−	0.392253i	0.875490	+	0.483237i	$0.160539\pi$
$458$		0			0
$459$	−2271.90	−	941.053i	−0.231031	−	0.0956963i
$460$		0			0
$461$	−6014.95	−	14521.4i	−0.607688	−	1.46709i	−0.865508	−	0.500895i	$-0.833004\pi$
$461$	−6014.95	−	14521.4i	−0.607688	−	1.46709i	0.257821	−	0.966193i	$-0.416996\pi$
$462$		0			0
$463$			13168.4i			1.32178i	0.750481	+	0.660892i	$0.229822\pi$
$463$			13168.4i			1.32178i	−0.750481	+	0.660892i	$0.770178\pi$
$464$		0			0
$465$		−	3414.64i		−	0.340537i
$466$		0			0
$467$	2737.75	+	6609.51i	0.271280	+	0.654929i	0.999539	−	0.0303741i	$-0.00966986\pi$
$467$	2737.75	+	6609.51i	0.271280	+	0.654929i	−0.728258	+	0.685303i	$0.759670\pi$
$468$		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	0.840528	−	0.541767i	$-0.182245\pi$
$487$	3210.83	+	3210.83i	0.298761	+	0.298761i	−0.541767	+	0.840528i	$0.682245\pi$
$488$		0			0
$489$	−1848.98	+	1848.98i	−0.170989	+	0.170989i
$490$		0			0
$491$	−10597.1	−	4389.47i	−0.974015	−	0.403450i	−0.161810	−	0.986822i	$-0.551733\pi$
$491$	−10597.1	−	4389.47i	−0.974015	−	0.403450i	−0.812205	+	0.583372i	$0.801733\pi$
$492$		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	−0.995908	−	0.0903763i	$-0.971193\pi$
$499$	−3963.81	−	9569.49i	−0.355600	−	0.858495i	0.640307	−	0.768119i	$-0.278807\pi$
$500$		0			0
$501$	5909.60	+	2447.83i	0.526989	+	0.218286i
$502$		0			0
$503$	−13198.2	+	13198.2i	−1.16994	+	1.16994i	−0.187716	+	0.982223i	$0.560108\pi$
$503$	−13198.2	+	13198.2i	−1.16994	+	1.16994i	−0.982223	+	0.187716i	$0.939892\pi$
$504$		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	−0.910241	−	0.414078i	$-0.864104\pi$
$509$	−14481.7	+	5998.52i	−1.26108	+	0.522357i	−0.350840	+	0.936435i	$0.614104\pi$
$510$		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	−0.626684	−	0.779274i	$-0.715588\pi$
$521$	1814.60	−	1814.60i	0.152590	−	0.152590i	0.779274	+	0.626684i	$0.215588\pi$
$522$		0			0
$523$	−4063.96	−	1683.35i	−0.339779	−	0.140741i	0.206268	−	0.978496i	$-0.433868\pi$
$523$	−4063.96	−	1683.35i	−0.339779	−	0.140741i	−0.546047	+	0.837754i	$0.683868\pi$
$524$		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	−0.158111	−	0.987421i	$-0.550541\pi$
$541$	5389.43	−	2232.38i	0.428299	−	0.177407i	0.586411	+	0.810014i	$0.300541\pi$
$542$		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	0.578716	−	0.815529i	$-0.303554\pi$
$547$	20016.3	−	8291.01i	1.56460	−	0.648077i	0.985880	+	0.167452i	$0.0535539\pi$
$548$		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	0.951983	−	0.306152i	$-0.0990414\pi$
$557$	819.599	+	1978.69i	0.0623474	+	0.150520i	−0.889635	+	0.456672i	$0.849041\pi$
$558$		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	−0.999154	−	0.0411260i	$-0.986905\pi$
$563$	−4297.82	−	10375.9i	−0.321726	−	0.776715i	0.677428	−	0.735589i	$-0.263095\pi$
$564$		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	0.832926	−	0.553384i	$-0.186664\pi$
$569$	3794.16	+	3794.16i	0.279542	+	0.279542i	−0.553384	+	0.832926i	$0.686664\pi$
$570$		0			0
$571$	3323.60	−	8023.87i	0.243587	−	0.588071i	−0.754047	−	0.656820i	$-0.771901\pi$
$571$	3323.60	−	8023.87i	0.243587	−	0.588071i	0.997634	+	0.0687495i	$0.0219009\pi$
$572$		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	0.999740	+	0.0227951i	$0.00725653\pi$
$587$	24501.2	+	10148.7i	1.72278	+	0.713600i	0.723042	+	0.690804i	$0.242743\pi$
$588$		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	$-0.897572\pi$
$593$		−	9134.01i		−	0.632528i	0.948671	−	0.316264i	$-0.102428\pi$
$594$		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	−0.868395	−	0.495873i	$-0.834848\pi$
$599$	−5461.25	+	5461.25i	−0.372522	+	0.372522i	0.495873	+	0.868395i	$0.334848\pi$
$600$		0			0
$601$	14729.8	+	14729.8i	0.999738	+	0.999738i	1.00000		0.000262159i	$-8.34479e-5\pi$
$601$	14729.8	+	14729.8i	0.999738	+	0.999738i	−0.000262159		1.00000i	$0.500083\pi$
$602$		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	−0.969804	−	0.243884i	$-0.921578\pi$
$613$	−1693.73	+	4089.02i	−0.111597	+	0.269419i	0.858207	+	0.513303i	$0.171578\pi$
$614$		0			0
$615$	1367.77	+	1367.77i	0.0896813	+	0.0896813i
$616$		0			0
$617$	−21041.5	+	21041.5i	−1.37293	+	1.37293i	−0.516863	+	0.856068i	$0.672900\pi$
$617$	−21041.5	+	21041.5i	−1.37293	+	1.37293i	−0.856068	+	0.516863i	$0.827100\pi$
$618$		0			0
$619$	−6142.30	−	2544.22i	−0.398837	−	0.165204i	0.174244	−	0.984703i	$-0.444252\pi$
$619$	−6142.30	−	2544.22i	−0.398837	−	0.165204i	−0.573081	+	0.819499i	$0.694252\pi$
$620$		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	−0.218584	−	0.975818i	$-0.570144\pi$
$631$	12002.6	−	12002.6i	0.757234	−	0.757234i	0.975818	+	0.218584i	$0.0701438\pi$
$632$		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	−0.973337	−	0.229379i	$-0.926330\pi$
$643$	−24447.4	+	10126.4i	−1.49939	+	0.621070i	−0.526058	+	0.850449i	$0.676330\pi$
$644$		0			0
$645$	−828.984	+	2001.34i	−0.0506065	+	0.122175i
$646$		0			0
$647$	−12516.3	−	12516.3i	−0.760533	−	0.760533i	0.215885	−	0.976419i	$-0.430736\pi$
$647$	−12516.3	−	12516.3i	−0.760533	−	0.760533i	−0.976419	+	0.215885i	$0.930736\pi$
$648$		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	0.854903	−	0.518788i	$-0.173617\pi$
$653$	−1943.05	−	4690.95i	−0.116443	−	0.281119i	−0.971346	+	0.237669i	$0.923617\pi$
$654$		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	0.996795	−	0.0800014i	$-0.0254925\pi$
$659$	3982.05	+	9613.52i	0.235385	+	0.568269i	−0.761410	+	0.648271i	$0.775492\pi$
$660$		0			0
$661$	−2718.83	−	1126.18i	−0.159985	−	0.0662680i	0.301254	−	0.953544i	$-0.402595\pi$
$661$	−2718.83	−	1126.18i	−0.159985	−	0.0662680i	−0.461239	+	0.887276i	$0.652595\pi$
$662$		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	−0.998471	−	0.0552774i	$-0.982396\pi$
$677$	−4462.91	+	10774.4i	−0.253358	+	0.611661i	0.745113	+	0.666939i	$0.232396\pi$
$678$		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	−0.250794	−	0.968040i	$-0.580692\pi$
$683$	−19860.3	−	8226.41i	−1.11264	−	0.460871i	−0.861846	+	0.507170i	$0.830692\pi$
$684$		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	0.943528	−	0.331291i	$-0.107484\pi$
$691$	764.618	+	1845.95i	0.0420947	+	0.101626i	−0.901434	+	0.432917i	$0.857484\pi$
$692$		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	−0.902732	−	0.430203i	$-0.858442\pi$
$701$	−22956.1	+	9508.72i	−1.23686	+	0.512324i	−0.334128	+	0.942528i	$0.608442\pi$
$702$		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	0.631891	+	0.775058i	$0.282279\pi$
$709$	−6852.40	+	16543.2i	−0.362972	+	0.876292i	−0.994863	+	0.101234i	$0.967721\pi$
$710$		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	$-0.723697\pi$
$719$		−	29422.6i		−	1.52612i	0.646329	−	0.763059i	$-0.276303\pi$
$720$		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	−0.345976	−	0.938243i	$-0.612452\pi$
$727$	11609.7	−	11609.7i	0.592267	−	0.592267i	0.938243	+	0.345976i	$0.112452\pi$
$728$		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	−0.660375	−	0.750936i	$-0.729603\pi$
$733$	−11834.5	+	4902.00i	−0.596338	+	0.247011i	0.0640365	+	0.997948i	$0.479603\pi$
$734$		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	−0.749209	−	0.662333i	$-0.769566\pi$
$739$	−16285.3	+	6745.57i	−0.810640	+	0.335778i	−0.0614306	+	0.998111i	$0.519566\pi$
$740$		0			0
$741$	−2471.23	+	5966.07i	−0.122514	+	0.295775i
$742$		0			0
$743$	20708.3	+	20708.3i	1.02249	+	1.02249i	0.999741	+	0.0227537i	$0.00724334\pi$
$743$	20708.3	+	20708.3i	1.02249	+	1.02249i	0.0227537	+	0.999741i	$0.492757\pi$
$744$		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	$-0.778191\pi$
$751$		−	26417.1i		−	1.28359i	0.766878	−	0.641793i	$-0.221809\pi$
$752$		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	−0.180753	−	0.983528i	$-0.557854\pi$
$757$	−20911.7	−	8661.89i	−1.00402	−	0.415881i	−0.823272	+	0.567648i	$0.807854\pi$
$758$		0			0
$759$	551.473	−	551.473i	0.0263731	−	0.0263731i
$760$		0			0
$761$	−8497.64	−	8497.64i	−0.404782	−	0.404782i	0.475132	−	0.879914i	$-0.342400\pi$
$761$	−8497.64	−	8497.64i	−0.404782	−	0.404782i	−0.879914	+	0.475132i	$0.842400\pi$
$762$		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	−0.155463	−	0.987842i	$-0.549687\pi$
$773$	14033.5	−	33879.9i	0.652976	−	1.57642i	0.808438	−	0.588581i	$-0.200313\pi$
$774$		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	0.995717	+	0.0924500i	$0.0294698\pi$
$787$	7882.13	+	19029.1i	0.357011	+	0.861900i	−0.638706	+	0.769450i	$0.720530\pi$
$788$		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	0.341186	−	0.939996i	$-0.389171\pi$
$797$	28060.5	−	11623.0i	1.24712	−	0.516574i	0.905933	+	0.423422i	$0.139171\pi$
$798$		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	−0.951202	−	0.308569i	$-0.900150\pi$
$809$	−14787.2	+	14787.2i	−0.642633	+	0.642633i	0.308569	+	0.951202i	$0.400150\pi$
$810$		0			0
$811$	−26961.4	−	11167.8i	−1.16738	−	0.483544i	−0.287053	−	0.957915i	$-0.592675\pi$
$811$	−26961.4	−	11167.8i	−1.16738	−	0.483544i	−0.880325	+	0.474371i	$0.842675\pi$
$812$		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	−0.258782	−	0.965936i	$-0.583321\pi$
$821$	−26459.7	−	10960.0i	−1.12479	−	0.465902i	−0.866006	+	0.500033i	$0.833321\pi$
$822$		0			0
$823$	−16724.6	+	16724.6i	−0.708363	+	0.708363i	−0.966191	−	0.257828i	$-0.916993\pi$
$823$	−16724.6	+	16724.6i	−0.708363	+	0.708363i	0.257828	+	0.966191i	$0.416993\pi$
$824$		0			0
$825$	−40.9668	−	40.9668i	−0.00172882	−	0.00172882i
$826$		0			0
$827$	3883.90	−	9376.57i	0.163309	−	0.394263i	−0.820949	−	0.571002i	$-0.806555\pi$
$827$	3883.90	−	9376.57i	0.163309	−	0.394263i	0.984258	+	0.176739i	$0.0565549\pi$
$828$		0			0
$829$	−4058.22	+	1680.97i	−0.170021	+	0.0704251i	−0.466071	−	0.884748i	$-0.654331\pi$
$829$	−4058.22	+	1680.97i	−0.170021	+	0.0704251i	0.296049	+	0.955173i	$0.404331\pi$
$830$		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	0.692036	−	0.721863i	$-0.256714\pi$
$839$	−724.855	−	724.855i	−0.0298269	−	0.0298269i	−0.721863	+	0.692036i	$0.756714\pi$
$840$		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	0.807121	−	0.590386i	$-0.201024\pi$
$853$	23925.7	+	9910.36i	0.960376	+	0.397801i	0.153255	+	0.988187i	$0.451024\pi$
$854$		0			0
$855$	−10800.6	+	10800.6i	−0.432016	+	0.432016i
$856$		0			0
$857$	−25248.3	−	25248.3i	−1.00638	−	1.00638i	−0.999980	−	0.00639889i	$-0.997963\pi$
$857$	−25248.3	−	25248.3i	−1.00638	−	1.00638i	−0.00639889	−	0.999980i	$-0.502037\pi$
$858$		0			0
$859$	13363.0	−	32261.1i	0.530780	−	1.28142i	−0.400228	−	0.916416i	$-0.631069\pi$
$859$	13363.0	−	32261.1i	0.530780	−	1.28142i	0.931008	−	0.365000i	$-0.118931\pi$
$860$		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	−0.757432	−	0.652914i	$-0.773546\pi$
$877$	−17752.3	−	42857.9i	−0.683527	−	1.65018i	0.0739053	−	0.997265i	$-0.476454\pi$
$878$		0			0
$879$			4966.34i			0.190569i
$880$		0			0
$881$		−	7584.20i		−	0.290032i	−0.989429	−	0.145016i	$-0.953677\pi$
$881$		−	7584.20i		−	0.290032i	0.989429	−	0.145016i	$-0.0463234\pi$
$882$		0			0
$883$	9800.89	+	23661.4i	0.373529	+	0.901779i	0.993147	+	0.116875i	$0.0372878\pi$
$883$	9800.89	+	23661.4i	0.373529	+	0.901779i	−0.619617	+	0.784904i	$0.712712\pi$
$884$		0			0
$885$	3543.11	+	1467.60i	0.134577	+	0.0557435i
$886$		0			0
$887$	8905.97	−	8905.97i	0.337129	−	0.337129i	−0.518157	−	0.855286i	$-0.673382\pi$
$887$	8905.97	−	8905.97i	0.337129	−	0.337129i	0.855286	+	0.518157i	$0.173382\pi$
$888$		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	0.766319	−	0.642460i	$-0.222086\pi$
$907$	23324.8	+	9661.45i	0.853900	+	0.353697i	0.0875813	+	0.996157i	$0.472086\pi$
$908$		0			0
$909$	7092.28	+	17122.3i	0.258786	+	0.624764i
$910$		0			0
$911$			28451.4i			1.03473i	0.855765	+	0.517364i	$0.173087\pi$
$911$			28451.4i			1.03473i	−0.855765	+	0.517364i	$0.826913\pi$
$912$		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	−0.987340	−	0.158618i	$-0.949296\pi$
$919$	−23087.8	+	23087.8i	−0.828721	+	0.828721i	0.158618	+	0.987340i	$0.449296\pi$
$920$		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	−0.987940	−	0.154835i	$-0.950515\pi$
$937$	−23895.1	+	23895.1i	−0.833105	+	0.833105i	0.154835	+	0.987940i	$0.450515\pi$
$938$		0			0
$939$	−4128.29	−	1709.99i	−0.143473	−	0.0594286i
$940$		0			0
$941$	1918.84	+	4632.49i	0.0664743	+	0.160483i	0.953625	−	0.300996i	$-0.0973190\pi$
$941$	1918.84	+	4632.49i	0.0664743	+	0.160483i	−0.887151	+	0.461479i	$0.847319\pi$
$942$		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	−0.947312	−	0.320313i	$-0.896212\pi$
$947$	−14686.5	−	35456.3i	−0.503957	−	1.21666i	0.443355	−	0.896346i	$-0.353788\pi$
$948$		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	0.871714	−	0.490016i	$-0.163009\pi$
$953$	11229.5	+	11229.5i	0.381698	+	0.381698i	−0.490016	+	0.871714i	$0.663009\pi$
$954$		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	0.186398	−	0.982474i	$-0.440319\pi$
$967$	−23938.4	−	23938.4i	−0.796076	−	0.796076i	−0.982474	+	0.186398i	$0.940319\pi$
$968$		0			0
$969$	2032.95	−	2032.95i	0.0673970	−	0.0673970i
$970$		0			0
$971$	−28947.0	−	11990.2i	−0.956698	−	0.396277i	−0.150954	−	0.988541i	$-0.548234\pi$
$971$	−28947.0	−	11990.2i	−0.956698	−	0.396277i	−0.805744	+	0.592264i	$0.798234\pi$
$972$		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	$0.443120\pi$
$977$			60103.7i			1.96815i	−0.177743	+	0.984077i	$0.556880\pi$
$978$		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	0.369995	−	0.929034i	$-0.379359\pi$
$983$	40035.9	−	40035.9i	1.29903	−	1.29903i	0.929034	−	0.369995i	$-0.120641\pi$
$984$		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	−0.286097	−	0.958201i	$-0.592358\pi$
$997$	18691.7	−	45125.8i	0.593754	−	1.43345i	0.879851	−	0.475249i	$-0.157642\pi$
$998$		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.49.7		44
4.3	odd	2		32.4.g.a.21.1	✓	44
8.3	odd	2		256.4.g.b.97.7		44
8.5	even	2		256.4.g.a.97.5		44
32.3	odd	8		32.4.g.a.29.1	yes	44
32.13	even	8		256.4.g.a.161.5		44
32.19	odd	8		256.4.g.b.161.7		44
32.29	even	8	inner	128.4.g.a.81.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.1	✓	44	4.3	odd	2
32.4.g.a.29.1	yes	44	32.3	odd	8
128.4.g.a.49.7		44	1.1	even	1	trivial
128.4.g.a.81.7		44	32.29	even	8	inner
256.4.g.a.97.5		44	8.5	even	2
256.4.g.a.161.5		44	32.13	even	8
256.4.g.b.97.7		44	8.3	odd	2
256.4.g.b.161.7		44	32.19	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
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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