LMFDB - Embedded newform 100.6.g.a.21.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,6,Mod(21,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("100.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	100.g (of order $5$, degree $4$, 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:	$16.0383819813$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			21.9
Character	$\chi$	$=$	100.21
Dual form			100.6.g.a.81.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.7159 + 7.78556i) q^{3} +(-54.0256 + 14.3608i) q^{5} -52.1911 q^{7} +(-20.8755 - 64.2481i) q^{9} +O(q^{10})$	\(q+(10.7159 + 7.78556i) q^{3} +(-54.0256 + 14.3608i) q^{5} -52.1911 q^{7} +(-20.8755 - 64.2481i) q^{9} +(68.0239 - 209.356i) q^{11} +(-259.186 - 797.694i) q^{13} +(-690.740 - 266.731i) q^{15} +(734.415 - 533.583i) q^{17} +(439.493 - 319.311i) q^{19} +(-559.275 - 406.337i) q^{21} +(-668.427 + 2057.21i) q^{23} +(2712.54 - 1551.70i) q^{25} +(1271.13 - 3912.15i) q^{27} +(-3487.42 - 2533.76i) q^{29} +(-3435.34 + 2495.92i) q^{31} +(2358.89 - 1713.83i) q^{33} +(2819.66 - 749.505i) q^{35} +(-2364.24 - 7276.37i) q^{37} +(3433.07 - 10565.9i) q^{39} +(-4878.95 - 15015.9i) q^{41} -13604.1 q^{43} +(2050.46 + 3171.26i) q^{45} +(3649.00 + 2651.15i) q^{47} -14083.1 q^{49} +12024.2 q^{51} +(5167.88 + 3754.69i) q^{53} +(-668.519 + 12287.5i) q^{55} +7195.58 q^{57} +(1997.96 + 6149.08i) q^{59} +(-12079.1 + 37175.5i) q^{61} +(1089.52 + 3353.18i) q^{63} +(25458.2 + 39373.8i) q^{65} +(33291.0 - 24187.3i) q^{67} +(-23179.3 + 16840.8i) q^{69} +(-2970.57 - 2158.25i) q^{71} +(-15881.2 + 48877.4i) q^{73} +(41148.1 + 4490.75i) q^{75} +(-3550.24 + 10926.5i) q^{77} +(-3493.80 - 2538.40i) q^{79} +(30799.0 - 22376.8i) q^{81} +(10190.7 - 7403.97i) q^{83} +(-32014.5 + 39373.9i) q^{85} +(-17644.1 - 54303.0i) q^{87} +(-23397.7 + 72010.7i) q^{89} +(13527.2 + 41632.5i) q^{91} -56245.0 q^{93} +(-19158.4 + 23562.4i) q^{95} +(-24671.5 - 17924.9i) q^{97} -14870.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{3} + 116 q^{5} - 42 q^{7} - 1153 q^{9}+O(q^{10}) $ 52 * q + 2 * q^3 + 116 * q^5 - 42 * q^7 - 1153 * q^9	$ 52 q + 2 q^{3} + 116 q^{5} - 42 q^{7} - 1153 q^{9} - 5 q^{11} + 1458 q^{13} + 2418 q^{15} - 2329 q^{17} + 1912 q^{19} - 4818 q^{21} + 3594 q^{23} + 934 q^{25} + 3206 q^{27} - 1458 q^{29} + 5532 q^{31} + 2435 q^{33} - 5603 q^{35} + 22043 q^{37} - 9938 q^{39} + 4567 q^{41} - 35390 q^{43} - 59359 q^{45} - 5859 q^{47} + 165974 q^{49} + 68014 q^{51} + 20151 q^{53} - 97855 q^{55} - 241368 q^{57} - 116271 q^{59} + 39134 q^{61} + 262808 q^{63} + 190502 q^{65} + 40883 q^{67} - 51844 q^{69} - 109999 q^{71} - 187802 q^{73} - 164833 q^{75} + 102220 q^{77} + 122216 q^{79} - 264922 q^{81} + 125394 q^{83} + 83764 q^{85} + 205117 q^{87} - 107222 q^{89} + 58608 q^{91} - 490158 q^{93} - 82634 q^{95} + 129683 q^{97} + 302280 q^{99}+O(q^{100}) $ 52 * q + 2 * q^3 + 116 * q^5 - 42 * q^7 - 1153 * q^9 - 5 * q^11 + 1458 * q^13 + 2418 * q^15 - 2329 * q^17 + 1912 * q^19 - 4818 * q^21 + 3594 * q^23 + 934 * q^25 + 3206 * q^27 - 1458 * q^29 + 5532 * q^31 + 2435 * q^33 - 5603 * q^35 + 22043 * q^37 - 9938 * q^39 + 4567 * q^41 - 35390 * q^43 - 59359 * q^45 - 5859 * q^47 + 165974 * q^49 + 68014 * q^51 + 20151 * q^53 - 97855 * q^55 - 241368 * q^57 - 116271 * q^59 + 39134 * q^61 + 262808 * q^63 + 190502 * q^65 + 40883 * q^67 - 51844 * q^69 - 109999 * q^71 - 187802 * q^73 - 164833 * q^75 + 102220 * q^77 + 122216 * q^79 - 264922 * q^81 + 125394 * q^83 + 83764 * q^85 + 205117 * q^87 - 107222 * q^89 + 58608 * q^91 - 490158 * q^93 - 82634 * q^95 + 129683 * q^97 + 302280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	10.7159	+	7.78556i	0.687426	+	0.499444i	0.875813	−	0.482651i	$-0.160326\pi$
$3$	10.7159	+	7.78556i	0.687426	+	0.499444i	−0.188387	+	0.982095i	$0.560326\pi$
$4$		0			0
$5$	−54.0256	+	14.3608i	−0.966440	+	0.256893i
$5$	−54.0256	+	14.3608i	−0.966440	+	0.256893i
$6$		0			0
$7$	−52.1911			−0.402580			−0.201290	−	0.979532i	$-0.564513\pi$
$7$	−52.1911			−0.402580			−0.201290	+	0.979532i	$0.564513\pi$
$8$		0			0
$9$	−20.8755	−	64.2481i	−0.0859073	−	0.264396i
$10$		0			0
$11$	68.0239	−	209.356i	0.169504	−	0.521679i	−0.829836	−	0.558007i	$-0.811566\pi$
$11$	68.0239	−	209.356i	0.169504	−	0.521679i	0.999340	+	0.0363280i	$0.0115661\pi$
$12$		0			0
$13$	−259.186	−	797.694i	−0.425357	−	1.30911i	−0.902652	−	0.430371i	$-0.858383\pi$
$13$	−259.186	−	797.694i	−0.425357	−	1.30911i	0.477295	−	0.878743i	$-0.341617\pi$
$14$		0			0
$15$	−690.740	−	266.731i	−0.792659	−	0.306087i
$16$		0			0
$17$	734.415	−	533.583i	0.616338	−	0.447796i	−0.235302	−	0.971922i	$-0.575608\pi$
$17$	734.415	−	533.583i	0.616338	−	0.447796i	0.851640	+	0.524126i	$0.175608\pi$
$18$		0			0
$19$	439.493	−	319.311i	0.279298	−	0.202922i	−0.439313	−	0.898334i	$-0.644778\pi$
$19$	439.493	−	319.311i	0.279298	−	0.202922i	0.718611	+	0.695412i	$0.244778\pi$
$20$		0			0
$21$	−559.275	−	406.337i	−0.276743	−	0.201066i
$22$		0			0
$23$	−668.427	+	2057.21i	−0.263472	+	0.810884i	0.728569	+	0.684972i	$0.240186\pi$
$23$	−668.427	+	2057.21i	−0.263472	+	0.810884i	−0.992041	+	0.125912i	$0.959814\pi$
$24$		0			0
$25$	2712.54	−	1551.70i	0.868012	−	0.496544i
$26$		0			0
$27$	1271.13	−	3912.15i	0.335569	−	1.03278i
$28$		0			0
$29$	−3487.42	−	2533.76i	−0.770032	−	0.559461i	0.131939	−	0.991258i	$-0.457880\pi$
$29$	−3487.42	−	2533.76i	−0.770032	−	0.559461i	−0.901971	+	0.431797i	$0.857880\pi$
$30$		0			0
$31$	−3435.34	+	2495.92i	−0.642046	+	0.466473i	−0.860552	−	0.509362i	$-0.829881\pi$
$31$	−3435.34	+	2495.92i	−0.642046	+	0.466473i	0.218507	+	0.975835i	$0.429881\pi$
$32$		0			0
$33$	2358.89	−	1713.83i	0.377071	−	0.273958i
$34$		0			0
$35$	2819.66	−	749.505i	0.389069	−	0.103420i
$36$		0			0
$37$	−2364.24	−	7276.37i	−0.283914	−	0.873797i	−0.986722	−	0.162418i	$-0.948071\pi$
$37$	−2364.24	−	7276.37i	−0.283914	−	0.873797i	0.702808	−	0.711379i	$-0.251929\pi$
$38$		0			0
$39$	3433.07	−	10565.9i	0.361428	−	1.11236i
$40$		0			0
$41$	−4878.95	−	15015.9i	−0.453280	−	1.39505i	−0.873143	−	0.487465i	$-0.837922\pi$
$41$	−4878.95	−	15015.9i	−0.453280	−	1.39505i	0.419863	−	0.907588i	$-0.362078\pi$
$42$		0			0
$43$	−13604.1			−1.12201			−0.561006	−	0.827812i	$-0.689585\pi$
$43$	−13604.1			−1.12201			−0.561006	+	0.827812i	$0.689585\pi$
$44$		0			0
$45$	2050.46	+	3171.26i	0.150946	+	0.233453i
$46$		0			0
$47$	3649.00	+	2651.15i	0.240951	+	0.175061i	0.701707	−	0.712466i	$-0.252422\pi$
$47$	3649.00	+	2651.15i	0.240951	+	0.175061i	−0.460756	+	0.887527i	$0.652422\pi$
$48$		0			0
$49$	−14083.1			−0.837930
$50$		0			0
$51$	12024.2			0.647335
$52$		0			0
$53$	5167.88	+	3754.69i	0.252710	+	0.183605i	0.706927	−	0.707286i	$-0.250081\pi$
$53$	5167.88	+	3754.69i	0.252710	+	0.183605i	−0.454217	+	0.890891i	$0.650081\pi$
$54$		0			0
$55$	−668.519	+	12287.5i	−0.0297994	+	0.547716i
$56$		0			0
$57$	7195.58			0.293345
$58$		0			0
$59$	1997.96	+	6149.08i	0.0747234	+	0.229975i	0.981441	−	0.191763i	$-0.0614204\pi$
$59$	1997.96	+	6149.08i	0.0747234	+	0.229975i	−0.906718	+	0.421738i	$0.861420\pi$
$60$		0			0
$61$	−12079.1	+	37175.5i	−0.415632	+	1.27918i	0.496053	+	0.868292i	$0.334782\pi$
$61$	−12079.1	+	37175.5i	−0.415632	+	1.27918i	−0.911685	+	0.410891i	$0.865218\pi$
$62$		0			0
$63$	1089.52	+	3353.18i	0.0345845	+	0.106440i
$64$		0			0
$65$	25458.2	+	39373.8i	0.747385	+	1.15591i
$66$		0			0
$67$	33291.0	−	24187.3i	0.906024	−	0.658265i	−0.0339825	−	0.999422i	$-0.510819\pi$
$67$	33291.0	−	24187.3i	0.906024	−	0.658265i	0.940006	+	0.341158i	$0.110819\pi$
$68$		0			0
$69$	−23179.3	+	16840.8i	−0.586108	+	0.425833i
$70$		0			0
$71$	−2970.57	−	2158.25i	−0.0699349	−	0.0508107i	0.552268	−	0.833666i	$-0.313762\pi$
$71$	−2970.57	−	2158.25i	−0.0699349	−	0.0508107i	−0.622203	+	0.782856i	$0.713762\pi$
$72$		0			0
$73$	−15881.2	+	48877.4i	−0.348800	+	1.07350i	0.610717	+	0.791849i	$0.290881\pi$
$73$	−15881.2	+	48877.4i	−0.348800	+	1.07350i	−0.959518	+	0.281648i	$0.909119\pi$
$74$		0			0
$75$	41148.1	+	4490.75i	0.844689	+	0.0921862i
$76$		0			0
$77$	−3550.24	+	10926.5i	−0.0682388	+	0.210017i
$78$		0			0
$79$	−3493.80	−	2538.40i	−0.0629840	−	0.0457606i	0.555848	−	0.831284i	$-0.312394\pi$
$79$	−3493.80	−	2538.40i	−0.0629840	−	0.0457606i	−0.618832	+	0.785524i	$0.712394\pi$
$80$		0			0
$81$	30799.0	−	22376.8i	0.521584	−	0.378953i
$82$		0			0
$83$	10190.7	−	7403.97i	0.162371	−	0.117969i	−0.503633	−	0.863918i	$-0.668004\pi$
$83$	10190.7	−	7403.97i	0.162371	−	0.117969i	0.666004	+	0.745948i	$0.268004\pi$
$84$		0			0
$85$	−32014.5	+	39373.9i	−0.480618	+	0.591101i
$86$		0			0
$87$	−17644.1	−	54303.0i	−0.249920	−	0.769176i
$88$		0			0
$89$	−23397.7	+	72010.7i	−0.313111	+	0.963655i	0.663415	+	0.748252i	$0.269107\pi$
$89$	−23397.7	+	72010.7i	−0.313111	+	0.963655i	−0.976525	+	0.215403i	$0.930893\pi$
$90$		0			0
$91$	13527.2	+	41632.5i	0.171240	+	0.527023i
$92$		0			0
$93$	−56245.0			−0.674336
$94$		0			0
$95$	−19158.4	+	23562.4i	−0.217796	+	0.267862i
$96$		0			0
$97$	−24671.5	−	17924.9i	−0.266236	−	0.193432i	0.446656	−	0.894706i	$-0.352615\pi$
$97$	−24671.5	−	17924.9i	−0.266236	−	0.193432i	−0.712892	+	0.701274i	$0.752615\pi$
$98$		0			0
$99$	−14870.8			−0.152491
$100$		0			0
$101$	130966.			1.27748			0.638741	−	0.769422i	$-0.279456\pi$
$101$	130966.			1.27748			0.638741	+	0.769422i	$0.279456\pi$
$102$		0			0
$103$	−121826.	−	88511.7i	−1.13148	−	0.822068i	−0.145570	−	0.989348i	$-0.546502\pi$
$103$	−121826.	−	88511.7i	−1.13148	−	0.822068i	−0.985909	+	0.167280i	$0.946502\pi$
$104$		0			0
$105$	36050.5	+	13921.0i	0.319108	+	0.123225i
$106$		0			0
$107$	30647.7			0.258785			0.129392	−	0.991593i	$-0.458697\pi$
$107$	30647.7			0.258785			0.129392	+	0.991593i	$0.458697\pi$
$108$		0			0
$109$	46456.8	+	142979.i	0.374527	+	1.15267i	0.943797	+	0.330525i	$0.107226\pi$
$109$	46456.8	+	142979.i	0.374527	+	1.15267i	−0.569271	+	0.822150i	$0.692774\pi$
$110$		0			0
$111$	31315.7	−	96379.8i	0.241243	−	0.742470i
$112$		0			0
$113$	−54619.4	−	168101.i	−0.402393	−	1.23844i	−0.923052	−	0.384675i	$-0.874314\pi$
$113$	−54619.4	−	168101.i	−0.402393	−	1.23844i	0.520659	−	0.853765i	$-0.325686\pi$
$114$		0			0
$115$	6569.11	−	120741.i	0.0463193	−	0.851354i
$116$		0			0
$117$	−45839.7	+	33304.5i	−0.309583	+	0.224925i
$118$		0			0
$119$	−38329.9	+	27848.3i	−0.248125	+	0.180273i
$120$		0			0
$121$	91090.3	+	66181.0i	0.565599	+	0.410932i
$122$		0			0
$123$	64624.5	−	198894.i	0.385154	−	1.18538i
$124$		0			0
$125$	−124263.	+	122786.i	−0.711322	+	0.702866i
$126$		0			0
$127$	75774.1	−	233209.i	0.416881	−	1.28303i	−0.493677	−	0.869645i	$-0.664348\pi$
$127$	75774.1	−	233209.i	0.416881	−	1.28303i	0.910558	−	0.413381i	$-0.135652\pi$
$128$		0			0
$129$	−145780.	−	105915.i	−0.771299	−	0.560382i
$130$		0			0
$131$	313094.	−	227476.i	1.59403	−	1.15813i	0.696147	−	0.717899i	$-0.254896\pi$
$131$	313094.	−	227476.i	1.59403	−	1.15813i	0.897884	−	0.440232i	$-0.145104\pi$
$132$		0			0
$133$	−22937.7	+	16665.2i	−0.112440	+	0.0816923i
$134$		0			0
$135$	−12492.3	+	229611.i	−0.0589942	+	1.08432i
$136$		0			0
$137$	−60131.4	−	185065.i	−0.273716	−	0.842410i	−0.989556	−	0.144147i	$-0.953956\pi$
$137$	−60131.4	−	185065.i	−0.273716	−	0.842410i	0.715841	−	0.698264i	$-0.246044\pi$
$138$		0			0
$139$	−60025.3	+	184739.i	−0.263510	+	0.811001i	0.728522	+	0.685022i	$0.240207\pi$
$139$	−60025.3	+	184739.i	−0.263510	+	0.811001i	−0.992033	+	0.125980i	$0.959793\pi$
$140$		0			0
$141$	18461.6	+	56819.0i	0.0782027	+	0.240683i
$142$		0			0
$143$	−184633.			−0.755038
$144$		0			0
$145$	224797.	+	86805.8i	0.887912	+	0.342869i
$146$		0			0
$147$	−150913.	−	109645.i	−0.576014	−	0.418499i
$148$		0			0
$149$	−315574.			−1.16449			−0.582245	−	0.813013i	$-0.697826\pi$
$149$	−315574.			−1.16449			−0.582245	+	0.813013i	$0.697826\pi$
$150$		0			0
$151$	112610.			0.401916			0.200958	−	0.979600i	$-0.435595\pi$
$151$	112610.			0.401916			0.200958	+	0.979600i	$0.435595\pi$
$152$		0			0
$153$	−49613.0	−	36045.9i	−0.171343	−	0.124488i
$154$		0			0
$155$	149753.	−	184178.i	0.500665	−	0.615756i
$156$		0			0
$157$	−125126.			−0.405135			−0.202568	−	0.979268i	$-0.564929\pi$
$157$	−125126.			−0.405135			−0.202568	+	0.979268i	$0.564929\pi$
$158$		0			0
$159$	26146.2	+	80469.7i	0.0820192	+	0.252429i
$160$		0			0
$161$	34886.0	−	107368.i	0.106068	−	0.326445i
$162$		0			0
$163$	−135713.	−	417681.i	−0.400084	−	1.23133i	−0.924931	−	0.380136i	$-0.875877\pi$
$163$	−135713.	−	417681.i	−0.400084	−	1.23133i	0.524846	−	0.851197i	$-0.324123\pi$
$164$		0			0
$165$	−102829.	+	126466.i	−0.294038	+	0.361631i
$166$		0			0
$167$	444115.	−	322668.i	1.23227	−	0.895293i	0.235207	−	0.971945i	$-0.424423\pi$
$167$	444115.	−	322668.i	1.23227	−	0.895293i	0.997058	+	0.0766523i	$0.0244231\pi$
$168$		0			0
$169$	−268755.	+	195262.i	−0.723835	+	0.525897i
$170$		0			0
$171$	−29689.7	−	21570.9i	−0.0776455	−	0.0564127i
$172$		0			0
$173$	−36838.8	+	113378.i	−0.0935816	+	0.288015i	−0.986881	−	0.161447i	$-0.948384\pi$
$173$	−36838.8	+	113378.i	−0.0935816	+	0.288015i	0.893300	+	0.449461i	$0.148384\pi$
$174$		0			0
$175$	−141570.	+	80985.0i	−0.349444	+	0.199898i
$176$		0			0
$177$	−26464.1	+	81448.2i	−0.0634928	+	0.195411i
$178$		0			0
$179$	432829.	+	314469.i	1.00968	+	0.733576i	0.964142	−	0.265387i	$-0.0854997\pi$
$179$	432829.	+	314469.i	1.00968	+	0.733576i	0.0455384	+	0.998963i	$0.485500\pi$
$180$		0			0
$181$	345320.	−	250890.i	0.783475	−	0.569228i	−0.122545	−	0.992463i	$-0.539106\pi$
$181$	345320.	−	250890.i	0.783475	−	0.569228i	0.906020	+	0.423235i	$0.139106\pi$
$182$		0			0
$183$	−418871.	+	304327.i	−0.924596	+	0.671759i
$184$		0			0
$185$	232224.	+	359158.i	0.498858	+	0.771537i
$186$		0			0
$187$	−61751.1	−	190050.i	−0.129134	−	0.397434i
$188$		0			0
$189$	−66341.9	+	204179.i	−0.135093	+	0.415774i
$190$		0			0
$191$	170822.	+	525735.i	0.338813	+	1.04276i	0.964813	+	0.262935i	$0.0846906\pi$
$191$	170822.	+	525735.i	0.338813	+	1.04276i	−0.626001	+	0.779822i	$0.715309\pi$
$192$		0			0
$193$	−349402.			−0.675199			−0.337599	−	0.941290i	$-0.609615\pi$
$193$	−349402.			−0.675199			−0.337599	+	0.941290i	$0.609615\pi$
$194$		0			0
$195$	−33739.3	+	620132.i	−0.0635403	+	1.16788i
$196$		0			0
$197$	291222.	+	211585.i	0.534637	+	0.388436i	0.822089	−	0.569359i	$-0.192808\pi$
$197$	291222.	+	211585.i	0.534637	+	0.388436i	−0.287453	+	0.957795i	$0.592808\pi$
$198$		0			0
$199$	−136232.			−0.243863			−0.121931	−	0.992539i	$-0.538909\pi$
$199$	−136232.			−0.243863			−0.121931	+	0.992539i	$0.538909\pi$
$200$		0			0
$201$	545055.			0.951590
$202$		0			0
$203$	182012.	+	132240.i	0.309999	+	0.225228i
$204$		0			0
$205$	479228.	+	741176.i	0.796448	+	1.23179i
$206$		0			0
$207$	146125.			0.237028
$208$		0			0
$209$	−36953.5	−	113731.i	−0.0585181	−	0.180100i
$210$		0			0
$211$	−350608.	+	1.07906e6i	−0.542145	+	1.66855i	0.185539	+	0.982637i	$0.440597\pi$
$211$	−350608.	+	1.07906e6i	−0.542145	+	1.66855i	−0.727684	+	0.685913i	$0.759403\pi$
$212$		0			0
$213$	−15029.2	−	46255.1i	−0.0226980	−	0.0698572i
$214$		0			0
$215$	734967.	−	195365.i	1.08436	−	0.288237i
$216$		0			0
$217$	179294.	−	130265.i	0.258474	−	0.187793i
$218$		0			0
$219$	−550719.	+	400121.i	−0.775926	+	0.563743i
$220$		0			0
$221$	−615986.	−	447540.i	−0.848380	−	0.616384i
$222$		0			0
$223$	−303462.	+	933959.i	−0.408641	+	1.25767i	0.509176	+	0.860662i	$0.329950\pi$
$223$	−303462.	+	933959.i	−0.408641	+	1.25767i	−0.917817	+	0.397004i	$0.870050\pi$
$224$		0			0
$225$	−156319.	−	141883.i	−0.205853	−	0.186842i
$226$		0			0
$227$	382934.	−	1.17855e6i	0.493241	−	1.51804i	−0.326440	−	0.945218i	$-0.605849\pi$
$227$	382934.	−	1.17855e6i	0.493241	−	1.51804i	0.819680	−	0.572821i	$-0.194151\pi$
$228$		0			0
$229$	−946545.	−	687705.i	−1.19276	−	0.866590i	−0.199206	−	0.979958i	$-0.563836\pi$
$229$	−946545.	−	687705.i	−1.19276	−	0.866590i	−0.993553	+	0.113368i	$0.963836\pi$
$230$		0			0
$231$	−123113.	+	89447.0i	−0.151801	+	0.110290i
$232$		0			0
$233$	426378.	−	309782.i	0.514524	−	0.373823i	−0.300013	−	0.953935i	$-0.596991\pi$
$233$	426378.	−	309782.i	0.514524	−	0.373823i	0.814537	+	0.580112i	$0.196991\pi$
$234$		0			0
$235$	−235212.	−	90827.7i	−0.277837	−	0.107287i
$236$		0			0
$237$	−17676.4	−	54402.4i	−0.0204420	−	0.0629140i
$238$		0			0
$239$	219334.	−	675039.i	0.248376	−	0.764424i	−0.746686	−	0.665176i	$-0.768356\pi$
$239$	219334.	−	675039.i	0.248376	−	0.764424i	0.995063	−	0.0992478i	$-0.0316437\pi$
$240$		0			0
$241$	−250912.	−	772227.i	−0.278278	−	0.856451i	−0.988334	−	0.152305i	$-0.951330\pi$
$241$	−250912.	−	772227.i	−0.278278	−	0.856451i	0.710056	−	0.704145i	$-0.248670\pi$
$242$		0			0
$243$	−495320.			−0.538109
$244$		0			0
$245$	760847.	−	202244.i	0.809809	−	0.215259i
$246$		0			0
$247$	−368623.	−	267820.i	−0.384450	−	0.279319i
$248$		0			0
$249$	166846.			0.170537
$250$		0			0
$251$	699128.			0.700442			0.350221	−	0.936667i	$-0.386106\pi$
$251$	699128.			0.700442			0.350221	+	0.936667i	$0.386106\pi$
$252$		0			0
$253$	385220.	+	279878.i	0.378362	+	0.274896i
$254$		0			0
$255$	−649613.	+	172676.i	−0.625611	+	0.166296i
$256$		0			0
$257$	460545.			0.434950			0.217475	−	0.976066i	$-0.430218\pi$
$257$	460545.			0.434950			0.217475	+	0.976066i	$0.430218\pi$
$258$		0			0
$259$	123392.	+	379762.i	0.114298	+	0.351773i
$260$		0			0
$261$	−89987.6	+	276953.i	−0.0817676	+	0.251655i
$262$		0			0
$263$	−479893.	−	1.47696e6i	−0.427814	−	1.31668i	−0.900274	−	0.435324i	$-0.856634\pi$
$263$	−479893.	−	1.47696e6i	−0.427814	−	1.31668i	0.472460	−	0.881352i	$-0.343366\pi$
$264$		0			0
$265$	−333118.	−	128634.i	−0.291396	−	0.112523i
$266$		0			0
$267$	−811371.	+	589495.i	−0.696532	+	0.506060i
$268$		0			0
$269$	778085.	−	565312.i	0.655611	−	0.476330i	−0.209567	−	0.977794i	$-0.567205\pi$
$269$	778085.	−	565312.i	0.655611	−	0.476330i	0.865178	+	0.501465i	$0.167205\pi$
$270$		0			0
$271$	−1.52991e6	−	1.11155e6i	−1.26544	−	0.919400i	−0.266433	−	0.963853i	$-0.585845\pi$
$271$	−1.52991e6	−	1.11155e6i	−1.26544	−	0.919400i	−0.999011	+	0.0444538i	$0.985845\pi$
$272$		0			0
$273$	−179176.	+	551447.i	−0.145504	+	0.447814i
$274$		0			0
$275$	−140340.	−	673438.i	−0.111905	−	0.536990i
$276$		0			0
$277$	−216299.	+	665699.i	−0.169377	+	0.521289i	−0.999332	−	0.0365413i	$-0.988366\pi$
$277$	−216299.	+	665699.i	−0.169377	+	0.521289i	0.829955	+	0.557830i	$0.188366\pi$
$278$		0			0
$279$	232073.	+	168611.i	0.178490	+	0.129681i
$280$		0			0
$281$	883833.	−	642142.i	0.667736	−	0.485138i	−0.201531	−	0.979482i	$-0.564592\pi$
$281$	883833.	−	642142.i	0.667736	−	0.485138i	0.869266	+	0.494344i	$0.164592\pi$
$282$		0			0
$283$	1.06578e6	−	774332.i	0.791043	−	0.574726i	−0.117230	−	0.993105i	$-0.537402\pi$
$283$	1.06578e6	−	774332.i	0.791043	−	0.574726i	0.908273	+	0.418379i	$0.137402\pi$
$284$		0			0
$285$	−388746.	+	103334.i	−0.283500	+	0.0753584i
$286$		0			0
$287$	254638.	+	783695.i	0.182481	+	0.561620i
$288$		0			0
$289$	−184106.	+	566622.i	−0.129666	+	0.399069i
$290$		0			0
$291$	−124822.	−	384163.i	−0.0864090	−	0.265940i
$292$		0			0
$293$	360842.			0.245555			0.122777	−	0.992434i	$-0.460820\pi$
$293$	360842.			0.245555			0.122777	+	0.992434i	$0.460820\pi$
$294$		0			0
$295$	−196247.	−	303516.i	−0.131295	−	0.203061i
$296$		0			0
$297$	−732564.	−	532239.i	−0.481897	−	0.350119i
$298$		0			0
$299$	1.81427e6			1.17361
$300$		0			0
$301$	710011.			0.451699
$302$		0			0
$303$	1.40342e6	+	1.01964e6i	0.878174	+	0.638030i
$304$		0			0
$305$	118710.	−	2.18190e6i	0.0730695	−	1.34303i
$306$		0			0
$307$	−333815.			−0.202144			−0.101072	−	0.994879i	$-0.532227\pi$
$307$	−333815.			−0.202144			−0.101072	+	0.994879i	$0.532227\pi$
$308$		0			0
$309$	−616362.	−	1.89697e6i	−0.367231	−	1.13022i
$310$		0			0
$311$	−293389.	+	902957.i	−0.172005	+	0.529378i	−0.999484	−	0.0321189i	$-0.989774\pi$
$311$	−293389.	+	902957.i	−0.172005	+	0.529378i	0.827479	+	0.561497i	$0.189774\pi$
$312$		0			0
$313$	−290815.	−	895036.i	−0.167786	−	0.516392i	0.831445	−	0.555607i	$-0.187514\pi$
$313$	−290815.	−	895036.i	−0.167786	−	0.516392i	−0.999231	+	0.0392150i	$0.987514\pi$
$314$		0			0
$315$	−107016.	−	165512.i	−0.0607676	−	0.0939835i
$316$		0			0
$317$	−158539.	+	115185.i	−0.0886110	+	0.0643797i	−0.631209	−	0.775613i	$-0.717441\pi$
$317$	−158539.	+	115185.i	−0.0886110	+	0.0643797i	0.542598	+	0.839993i	$0.317441\pi$
$318$		0			0
$319$	−767685.	+	557756.i	−0.422383	+	0.306879i
$320$		0			0
$321$	328418.	+	238610.i	0.177895	+	0.129248i
$322$		0			0
$323$	152391.	−	469013.i	0.0812745	−	0.250137i
$324$		0			0
$325$	−1.94083e6	−	1.76159e6i	−1.01925	−	0.925118i
$326$		0			0
$327$	−615347.	+	1.89384e6i	−0.318237	+	0.979433i
$328$		0			0
$329$	−190445.	−	138367.i	−0.0970020	−	0.0704761i
$330$		0			0
$331$	−1.32376e6	+	961768.i	−0.664109	+	0.482503i	−0.868048	−	0.496480i	$-0.834626\pi$
$331$	−1.32376e6	+	961768.i	−0.664109	+	0.482503i	0.203939	+	0.978984i	$0.434626\pi$
$332$		0			0
$333$	−418139.	+	303796.i	−0.206638	+	0.150131i
$334$		0			0
$335$	−1.45122e6	+	1.78482e6i	−0.706513	+	0.868925i
$336$		0			0
$337$	403135.	+	1.24072e6i	0.193364	+	0.595113i	0.999992	+	0.00405350i	$0.00129027\pi$
$337$	403135.	+	1.24072e6i	0.193364	+	0.595113i	−0.806628	+	0.591060i	$0.798710\pi$
$338$		0			0
$339$	723466.	−	2.22660e6i	0.341916	−	1.05231i
$340$		0			0
$341$	288851.	+	888992.i	0.134520	+	0.414011i
$342$		0			0
$343$	1.61219e6			0.739913
$344$		0			0
$345$	1.01043e6	−	1.24271e6i	0.457045	−	0.562109i
$346$		0			0
$347$	1.09603e6	+	796311.i	0.488650	+	0.355025i	0.804665	−	0.593729i	$-0.202345\pi$
$347$	1.09603e6	+	796311.i	0.488650	+	0.355025i	−0.316015	+	0.948754i	$0.602345\pi$
$348$		0			0
$349$	3.31178e6			1.45545			0.727727	−	0.685867i	$-0.240577\pi$
$349$	3.31178e6			1.45545			0.727727	+	0.685867i	$0.240577\pi$
$350$		0			0
$351$	−3.45016e6			−1.49476
$352$		0			0
$353$	728231.	+	529091.i	0.311052	+	0.225992i	0.732348	−	0.680931i	$-0.238425\pi$
$353$	728231.	+	529091.i	0.311052	+	0.225992i	−0.421296	+	0.906923i	$0.638425\pi$
$354$		0			0
$355$	191481.	+	73940.9i	0.0806408	+	0.0311397i
$356$		0			0
$357$	−627555.			−0.260604
$358$		0			0
$359$	1.40608e6	+	4.32747e6i	0.575803	+	1.77214i	0.633427	+	0.773802i	$0.281648\pi$
$359$	1.40608e6	+	4.32747e6i	0.575803	+	1.77214i	−0.0576241	+	0.998338i	$0.518352\pi$
$360$		0			0
$361$	−673962.	+	2.07424e6i	−0.272187	+	0.837705i
$362$		0			0
$363$	460859.	+	1.41838e6i	0.183570	+	0.564970i
$364$		0			0
$365$	156076.	−	2.86870e6i	0.0613203	−	1.12707i
$366$		0			0
$367$	−1.93463e6	+	1.40559e6i	−0.749778	+	0.544745i	−0.895758	−	0.444542i	$-0.853366\pi$
$367$	−1.93463e6	+	1.40559e6i	−0.749778	+	0.544745i	0.145980	+	0.989288i	$0.453366\pi$
$368$		0			0
$369$	−862890.	+	626927.i	−0.329906	+	0.239690i
$370$		0			0
$371$	−269718.	−	195961.i	−0.101736	−	0.0739155i
$372$		0			0
$373$	−388951.	+	1.19707e6i	−0.144751	+	0.445499i	−0.996979	−	0.0776724i	$-0.975251\pi$
$373$	−388951.	+	1.19707e6i	−0.144751	+	0.445499i	0.852228	+	0.523171i	$0.175251\pi$
$374$		0			0
$375$	−2.28754e6	+	348303.i	−0.840023	+	0.127903i
$376$		0			0
$377$	−1.11727e6	+	3.43860e6i	−0.404860	+	1.24603i
$378$		0			0
$379$	1.23490e6	+	897209.i	0.441606	+	0.320845i	0.786273	−	0.617880i	$-0.212008\pi$
$379$	1.23490e6	+	897209.i	0.441606	+	0.320845i	−0.344667	+	0.938725i	$0.612008\pi$
$380$		0			0
$381$	2.62765e6	−	1.90910e6i	0.927374	−	0.673777i
$382$		0			0
$383$	−720372.	+	523381.i	−0.250934	+	0.182314i	−0.706141	−	0.708072i	$-0.749565\pi$
$383$	−720372.	+	523381.i	−0.250934	+	0.182314i	0.455207	+	0.890386i	$0.349565\pi$
$384$		0			0
$385$	34890.8	−	641297.i	0.0119966	−	0.220499i
$386$		0			0
$387$	283991.	+	874035.i	0.0963890	+	0.296655i
$388$		0			0
$389$	981494.	−	3.02073e6i	0.328862	−	1.01213i	−0.640805	−	0.767704i	$-0.721399\pi$
$389$	981494.	−	3.02073e6i	0.328862	−	1.01213i	0.969667	−	0.244429i	$-0.0786006\pi$
$390$		0			0
$391$	606789.	+	1.86750e6i	0.200722	+	0.617760i
$392$		0			0
$393$	5.12612e6			1.67420
$394$		0			0
$395$	225208.	+	86964.7i	0.0726259	+	0.0280447i
$396$		0			0
$397$	3.62514e6	+	2.63382e6i	1.15438	+	0.838706i	0.989057	−	0.147534i	$-0.0471335\pi$
$397$	3.62514e6	+	2.63382e6i	1.15438	+	0.838706i	0.165322	+	0.986240i	$0.447134\pi$
$398$		0			0
$399$	−375546.			−0.118095
$400$		0			0
$401$	−2.80402e6			−0.870803			−0.435402	−	0.900236i	$-0.643394\pi$
$401$	−2.80402e6			−0.870803			−0.435402	+	0.900236i	$0.643394\pi$
$402$		0			0
$403$	2.88138e6	+	2.09344e6i	0.883766	+	0.642094i
$404$		0			0
$405$	−1.34259e6	+	1.65122e6i	−0.406729	+	0.500226i
$406$		0			0
$407$	−1.68418e6			−0.503966
$408$		0			0
$409$	−61573.8	−	189505.i	−0.0182007	−	0.0560159i	0.941544	−	0.336891i	$-0.109375\pi$
$409$	−61573.8	−	189505.i	−0.0182007	−	0.0560159i	−0.959744	+	0.280875i	$0.909375\pi$
$410$		0			0
$411$	796475.	−	2.45130e6i	0.232577	−	0.715800i
$412$		0			0
$413$	−104276.	−	320928.i	−0.0300821	−	0.0925832i
$414$		0			0
$415$	−444231.	+	546350.i	−0.126616	+	0.155722i
$416$		0			0
$417$	−2.08152e6	+	1.51231e6i	−0.586193	+	0.425894i
$418$		0			0
$419$	5.12158e6	−	3.72104e6i	1.42518	−	1.03545i	0.434287	−	0.900775i	$-0.357001\pi$
$419$	5.12158e6	−	3.72104e6i	1.42518	−	1.03545i	0.990890	−	0.134676i	$-0.0429995\pi$
$420$		0			0
$421$	−3.63425e6	−	2.64044e6i	−0.999333	−	0.726058i	−0.0373875	−	0.999301i	$-0.511904\pi$
$421$	−3.63425e6	−	2.64044e6i	−0.999333	−	0.726058i	−0.961945	+	0.273243i	$0.911904\pi$
$422$		0			0
$423$	94156.9	−	289785.i	0.0255859	−	0.0787454i
$424$		0			0
$425$	1.16417e6	−	2.58695e6i	0.312638	−	0.694731i
$426$		0			0
$427$	630420.	−	1.94023e6i	0.167325	−	0.514973i
$428$		0			0
$429$	−1.97851e6	−	1.43747e6i	−0.519032	−	0.377099i
$430$		0			0
$431$	−3.00776e6	+	2.18526e6i	−0.779919	+	0.566644i	−0.904955	−	0.425508i	$-0.860095\pi$
$431$	−3.00776e6	+	2.18526e6i	−0.779919	+	0.566644i	0.125036	+	0.992152i	$0.460095\pi$
$432$		0			0
$433$	−5.91531e6	+	4.29773e6i	−1.51621	+	1.10159i	−0.552877	+	0.833263i	$0.686470\pi$
$433$	−5.91531e6	+	4.29773e6i	−1.51621	+	1.10159i	−0.963329	+	0.268324i	$0.913530\pi$
$434$		0			0
$435$	1.73307e6	+	2.68037e6i	0.439129	+	0.679159i
$436$		0			0
$437$	363119.	+	1.11756e6i	0.0909589	+	0.279943i
$438$		0			0
$439$	482094.	−	1.48373e6i	0.119391	−	0.367447i	−0.873447	−	0.486920i	$-0.838120\pi$
$439$	482094.	−	1.48373e6i	0.119391	−	0.367447i	0.992837	+	0.119473i	$0.0381205\pi$
$440$		0			0
$441$	293991.	+	904812.i	0.0719843	+	0.221545i
$442$		0			0
$443$	5.60613e6			1.35723			0.678616	−	0.734493i	$-0.262580\pi$
$443$	5.60613e6			1.35723			0.678616	+	0.734493i	$0.262580\pi$
$444$		0			0
$445$	229946.	−	4.22643e6i	0.0550459	−	1.01175i
$446$		0			0
$447$	−3.38166e6	−	2.45692e6i	−0.800501	−	0.581598i
$448$		0			0
$449$	−3.76556e6			−0.881483			−0.440741	−	0.897634i	$-0.645284\pi$
$449$	−3.76556e6			−0.881483			−0.440741	+	0.897634i	$0.645284\pi$
$450$		0			0
$451$	−3.47554e6			−0.804603
$452$		0			0
$453$	1.20672e6	+	876733.i	0.276287	+	0.200734i
$454$		0			0
$455$	−1.32869e6	−	2.05496e6i	−0.300882	−	0.465345i
$456$		0			0
$457$	4.19517e6			0.939634			0.469817	−	0.882764i	$-0.344320\pi$
$457$	4.19517e6			0.939634			0.469817	+	0.882764i	$0.344320\pi$
$458$		0			0
$459$	−1.15392e6	−	3.55139e6i	−0.255648	−	0.786805i
$460$		0			0
$461$	−629251.	+	1.93664e6i	−0.137902	+	0.424420i	−0.996030	−	0.0890162i	$-0.971628\pi$
$461$	−629251.	+	1.93664e6i	−0.137902	+	0.424420i	0.858128	+	0.513436i	$0.171628\pi$
$462$		0			0
$463$	−1.90524e6	−	5.86372e6i	−0.413045	−	1.27122i	−0.913988	−	0.405741i	$-0.867014\pi$
$463$	−1.90524e6	−	5.86372e6i	−0.413045	−	1.27122i	0.500943	−	0.865480i	$-0.332986\pi$
$464$		0			0
$465$	3.03867e6	−	807721.i	0.651705	−	0.173232i
$466$		0			0
$467$	5.89950e6	−	4.28624e6i	1.25177	−	0.909461i	0.253442	−	0.967350i	$-0.418437\pi$
$467$	5.89950e6	−	4.28624e6i	1.25177	−	0.909461i	0.998323	+	0.0578896i	$0.0184371\pi$
$468$		0			0
$469$	−1.73749e6	+	1.26236e6i	−0.364747	+	0.265004i
$470$		0			0
$471$	−1.34084e6	−	974179.i	−0.278500	−	0.202342i
$472$		0			0
$473$	−925400.	+	2.84809e6i	−0.190185	+	0.585330i
$474$		0			0
$475$	696668.	−	1.54810e6i	0.141674	−	0.314823i
$476$		0			0
$477$	133349.	−	410407.i	0.0268346	−	0.0825884i
$478$		0			0
$479$	−5.99035e6	−	4.35224e6i	−1.19293	−	0.866711i	−0.199355	−	0.979927i	$-0.563885\pi$
$479$	−5.99035e6	−	4.35224e6i	−1.19293	−	0.866711i	−0.993570	+	0.113216i	$0.963885\pi$
$480$		0			0
$481$	−5.19154e6	+	3.77187e6i	−1.02314	+	0.743352i
$482$		0			0
$483$	1.20975e6	−	878938.i	0.235955	−	0.171431i
$484$		0			0
$485$	1.59031e6	+	614102.i	0.306992	+	0.118546i
$486$		0			0
$487$	−1.87461e6	−	5.76945e6i	−0.358169	−	1.10233i	−0.954149	−	0.299332i	$-0.903236\pi$
$487$	−1.87461e6	−	5.76945e6i	−0.358169	−	1.10233i	0.595980	−	0.802999i	$-0.296764\pi$
$488$		0			0
$489$	1.79759e6	−	5.53243e6i	0.339954	−	1.04627i
$490$		0			0
$491$	−2.64327e6	−	8.13514e6i	−0.494809	−	1.52286i	−0.817255	−	0.576277i	$-0.804505\pi$
$491$	−2.64327e6	−	8.13514e6i	−0.494809	−	1.52286i	0.322446	−	0.946588i	$-0.395495\pi$
$492$		0			0
$493$	−3.91318e6			−0.725124
$494$		0			0
$495$	803402.	−	213556.i	0.147374	−	0.0391740i
$496$		0			0
$497$	155038.	+	112641.i	0.0281544	+	0.0204554i
$498$		0			0
$499$	8.04534e6			1.44641			0.723207	−	0.690631i	$-0.242667\pi$
$499$	8.04534e6			1.44641			0.723207	+	0.690631i	$0.242667\pi$
$500$		0			0
$501$	7.27125e6			1.29424
$502$		0			0
$503$	2.50605e6	+	1.82075e6i	0.441642	+	0.320872i	0.786287	−	0.617861i	$-0.212001\pi$
$503$	2.50605e6	+	1.82075e6i	0.441642	+	0.320872i	−0.344645	+	0.938733i	$0.612001\pi$
$504$		0			0
$505$	−7.07551e6	+	1.88077e6i	−1.23461	+	0.328176i
$506$		0			0
$507$	−4.40018e6			−0.760239
$508$		0			0
$509$	1.09450e6	+	3.36852e6i	0.187250	+	0.576295i	0.999980	−	0.00634508i	$-0.00201972\pi$
$509$	1.09450e6	+	3.36852e6i	0.187250	+	0.576295i	−0.812730	+	0.582640i	$0.802020\pi$
$510$		0			0
$511$	828859.	−	2.55097e6i	0.140420	−	0.432168i
$512$		0			0
$513$	−690535.	−	2.12525e6i	−0.115849	−	0.356547i
$514$		0			0
$515$	7.85282e6	+	3.03239e6i	1.30469	+	0.503810i
$516$		0			0
$517$	803253.	−	583598.i	0.132168	−	0.0960256i
$518$		0			0
$519$	−1.27747e6	+	928139.i	−0.208177	+	0.151250i
$520$		0			0
$521$	8.28374e6	+	6.01849e6i	1.33700	+	0.971389i	0.999548	+	0.0300467i	$0.00956560\pi$
$521$	8.28374e6	+	6.01849e6i	1.33700	+	0.971389i	0.337454	+	0.941342i	$0.390434\pi$
$522$		0			0
$523$	1.41378e6	−	4.35118e6i	0.226011	−	0.695589i	−0.772177	−	0.635408i	$-0.780832\pi$
$523$	1.41378e6	−	4.35118e6i	0.226011	−	0.695589i	0.998187	−	0.0601815i	$-0.0191679\pi$
$524$		0			0
$525$	−2.14757e6	−	234378.i	−0.340055	−	0.0371123i
$526$		0			0
$527$	−1.19118e6	+	3.66608e6i	−0.186832	+	0.575011i
$528$		0			0
$529$	1.42180e6	+	1.03300e6i	0.220902	+	0.160495i
$530$		0			0
$531$	353359.	−	256730.i	0.0543850	−	0.0395130i
$532$		0			0
$533$	−1.07135e7	+	7.78381e6i	−1.63348	+	1.18679i
$534$		0			0
$535$	−1.65576e6	+	440125.i	−0.250100	+	0.0664801i
$536$		0			0
$537$	2.18984e6	+	6.73963e6i	0.327700	+	1.00856i
$538$		0			0
$539$	−957986.	+	2.94838e6i	−0.142032	+	0.437131i
$540$		0			0
$541$	−670017.	−	2.06210e6i	−0.0984221	−	0.302912i	0.889708	−	0.456529i	$-0.150908\pi$
$541$	−670017.	−	2.06210e6i	−0.0984221	−	0.302912i	−0.988130	+	0.153617i	$0.950908\pi$
$542$		0			0
$543$	5.65373e6			0.822878
$544$		0			0
$545$	−4.56315e6	−	7.05739e6i	−0.658072	−	1.01778i
$546$		0			0
$547$	880485.	+	639710.i	0.125821	+	0.0914144i	0.648916	−	0.760860i	$-0.275223\pi$
$547$	880485.	+	639710.i	0.125821	+	0.0914144i	−0.523095	+	0.852274i	$0.675223\pi$
$548$		0			0
$549$	2.64062e6			0.373916
$550$		0			0
$551$	−2.34175e6			−0.328596
$552$		0			0
$553$	182345.	+	132482.i	0.0253561	+	0.0184223i
$554$		0			0
$555$	−307762.	+	5.65670e6i	−0.0424114	+	0.779526i
$556$		0			0
$557$	3.37172e6			0.460483			0.230242	−	0.973134i	$-0.426048\pi$
$557$	3.37172e6			0.460483			0.230242	+	0.973134i	$0.426048\pi$
$558$		0			0
$559$	3.52598e6	+	1.08519e7i	0.477255	+	1.46884i
$560$		0			0
$561$	817930.	−	2.51733e6i	0.109726	−	0.337701i
$562$		0			0
$563$	−3.92895e6	−	1.20921e7i	−0.522403	−	1.60779i	−0.769394	−	0.638774i	$-0.779442\pi$
$563$	−3.92895e6	−	1.20921e7i	−0.522403	−	1.60779i	0.246991	−	0.969018i	$-0.420558\pi$
$564$		0			0
$565$	5.36491e6	+	8.29740e6i	0.707036	+	1.09350i
$566$		0			0
$567$	−1.60744e6	+	1.16787e6i	−0.209979	+	0.152559i
$568$		0			0
$569$	−1.24317e7	+	9.03213e6i	−1.60971	+	1.16952i	−0.745322	+	0.666704i	$0.767704\pi$
$569$	−1.24317e7	+	9.03213e6i	−1.60971	+	1.16952i	−0.864391	+	0.502821i	$0.832296\pi$
$570$		0			0
$571$	4.14204e6	+	3.00937e6i	0.531648	+	0.386265i	0.820974	−	0.570966i	$-0.193431\pi$
$571$	4.14204e6	+	3.00937e6i	0.531648	+	0.386265i	−0.289326	+	0.957231i	$0.593431\pi$
$572$		0			0
$573$	−2.26263e6	+	6.96367e6i	−0.287891	+	0.886036i
$574$		0			0
$575$	1.37903e6	+	6.61745e6i	0.173942	+	0.834682i
$576$		0			0
$577$	3.59839e6	−	1.10747e7i	0.449954	−	1.38482i	−0.427003	−	0.904250i	$-0.640431\pi$
$577$	3.59839e6	−	1.10747e7i	0.449954	−	1.38482i	0.876958	−	0.480567i	$-0.159569\pi$
$578$		0			0
$579$	−3.74415e6	−	2.72029e6i	−0.464149	−	0.337224i
$580$		0			0
$581$	−531864.	+	386421.i	−0.0653672	+	0.0474921i
$582$		0			0
$583$	1.13761e6	−	826518.i	0.138618	−	0.100712i
$584$		0			0
$585$	1.99824e6	−	2.45759e6i	0.241411	−	0.296906i
$586$		0			0
$587$	−3.15296e6	−	9.70380e6i	−0.377679	−	1.16238i	−0.941653	−	0.336584i	$-0.890728\pi$
$587$	−3.15296e6	−	9.70380e6i	−0.377679	−	1.16238i	0.563975	−	0.825792i	$-0.309272\pi$
$588$		0			0
$589$	−712836.	+	2.19388e6i	−0.0846645	+	0.260570i
$590$		0			0
$591$	1.47340e6	+	4.53465e6i	0.173521	+	0.534042i
$592$		0			0
$593$	1.02108e6			0.119241			0.0596204	−	0.998221i	$-0.481011\pi$
$593$	1.02108e6			0.119241			0.0596204	+	0.998221i	$0.481011\pi$
$594$		0			0
$595$	1.67088e6	−	2.05497e6i	0.193487	−	0.237965i
$596$		0			0
$597$	−1.45985e6	−	1.06064e6i	−0.167638	−	0.121796i
$598$		0			0
$599$	449849.			0.0512271			0.0256135	−	0.999672i	$-0.491846\pi$
$599$	449849.			0.0512271			0.0256135	+	0.999672i	$0.491846\pi$
$600$		0			0
$601$	1.15648e7			1.30603			0.653016	−	0.757344i	$-0.273504\pi$
$601$	1.15648e7			1.30603			0.653016	+	0.757344i	$0.273504\pi$
$602$		0			0
$603$	−2.24895e6	−	1.63396e6i	−0.251876	−	0.182999i
$604$		0			0
$605$	−5.87162e6	−	2.26734e6i	−0.652183	−	0.251842i
$606$		0			0
$607$	−4.86370e6			−0.535791			−0.267895	−	0.963448i	$-0.586328\pi$
$607$	−4.86370e6			−0.535791			−0.267895	+	0.963448i	$0.586328\pi$
$608$		0			0
$609$	920866.	+	2.83413e6i	0.100613	+	0.309654i
$610$		0			0
$611$	1.16904e6	−	3.59792e6i	0.126685	−	0.389896i
$612$		0			0
$613$	−1.88789e6	−	5.81034e6i	−0.202921	−	0.624526i	−0.999792	−	0.0203772i	$-0.993513\pi$
$613$	−1.88789e6	−	5.81034e6i	−0.202921	−	0.624526i	0.796872	−	0.604149i	$-0.206487\pi$
$614$		0			0
$615$	−635111.	+	1.16734e7i	−0.0677114	+	1.24454i
$616$		0			0
$617$	−4.93504e6	+	3.58551e6i	−0.521888	+	0.379174i	−0.817315	−	0.576192i	$-0.804538\pi$
$617$	−4.93504e6	+	3.58551e6i	−0.521888	+	0.379174i	0.295427	+	0.955365i	$0.404538\pi$
$618$		0			0
$619$	−6.88480e6	+	5.00210e6i	−0.722213	+	0.524718i	−0.887090	−	0.461596i	$-0.847277\pi$
$619$	−6.88480e6	+	5.00210e6i	−0.722213	+	0.524718i	0.164878	+	0.986314i	$0.447277\pi$
$620$		0			0
$621$	7.19844e6	+	5.22997e6i	0.749047	+	0.544215i
$622$		0			0
$623$	1.22115e6	−	3.75832e6i	0.126052	−	0.387948i
$624$		0			0
$625$	4.95008e6	−	8.41808e6i	0.506888	−	0.862012i
$626$		0			0
$627$	489471.	−	1.50644e6i	0.0497231	−	0.153032i
$628$		0			0
$629$	−5.61888e6	−	4.08236e6i	−0.566270	−	0.411419i
$630$		0			0
$631$	2.82651e6	−	2.05358e6i	0.282603	−	0.205323i	−0.437449	−	0.899243i	$-0.644118\pi$
$631$	2.82651e6	−	2.05358e6i	0.282603	−	0.205323i	0.720052	+	0.693920i	$0.244118\pi$
$632$		0			0
$633$	−1.21582e7	+	8.83342e6i	−1.20603	+	0.876233i
$634$		0			0
$635$	−744687.	+	1.36874e7i	−0.0732891	+	1.34706i
$636$		0			0
$637$	3.65014e6	+	1.12340e7i	0.356419	+	1.09695i
$638$		0			0
$639$	−76651.2	+	235908.i	−0.00742620	+	0.0228555i
$640$		0			0
$641$	3.64810e6	+	1.12277e7i	0.350689	+	1.07931i	0.958467	+	0.285202i	$0.0920608\pi$
$641$	3.64810e6	+	1.12277e7i	0.350689	+	1.07931i	−0.607779	+	0.794107i	$0.707939\pi$
$642$		0			0
$643$	2.06216e7			1.96695			0.983477	−	0.181031i	$-0.0579435\pi$
$643$	2.06216e7			1.96695			0.983477	+	0.181031i	$0.0579435\pi$
$644$		0			0
$645$	9.39686e6	+	3.62862e6i	0.889372	+	0.343433i
$646$		0			0
$647$	1.35161e6	+	982000.i	0.126937	+	0.0922255i	0.649442	−	0.760411i	$-0.275002\pi$
$647$	1.35161e6	+	982000.i	0.126937	+	0.0922255i	−0.522505	+	0.852636i	$0.675002\pi$
$648$		0			0
$649$	1.42326e6			0.132639
$650$		0			0
$651$	2.93549e6			0.271474
$652$		0			0
$653$	−1.58236e7	−	1.14965e7i	−1.45218	−	1.05507i	−0.985315	−	0.170746i	$-0.945382\pi$
$653$	−1.58236e7	−	1.14965e7i	−1.45218	−	1.05507i	−0.466868	−	0.884327i	$-0.654618\pi$
$654$		0			0
$655$	−1.36484e7	+	1.67858e7i	−1.24302	+	1.52876i
$656$		0			0
$657$	3.47181e6			0.313792
$658$		0			0
$659$	6.54007e6	+	2.01283e7i	0.586636	+	1.80548i	0.592598	+	0.805498i	$0.298102\pi$
$659$	6.54007e6	+	2.01283e7i	0.586636	+	1.80548i	−0.00596214	+	0.999982i	$0.501898\pi$
$660$		0			0
$661$	5.90616e6	−	1.81773e7i	0.525777	−	1.61818i	−0.236997	−	0.971510i	$-0.576163\pi$
$661$	5.90616e6	−	1.81773e7i	0.525777	−	1.61818i	0.762774	−	0.646665i	$-0.223837\pi$
$662$		0			0
$663$	−3.11650e6	−	9.59159e6i	−0.275349	−	0.847436i
$664$		0			0
$665$	999896.	−	1.22975e6i	0.0876801	−	0.107836i
$666$		0			0
$667$	7.54355e6	−	5.48071e6i	0.656540	−	0.477004i
$668$		0			0
$669$	−1.05233e7	+	7.64560e6i	−0.909044	+	0.660459i
$670$		0			0
$671$	6.96126e6	+	5.05765e6i	0.596872	+	0.433653i
$672$		0			0
$673$	4.27549e6	−	1.31586e7i	0.363872	−	1.11988i	−0.586812	−	0.809723i	$-0.699617\pi$
$673$	4.27549e6	−	1.31586e7i	0.363872	−	1.11988i	0.950684	−	0.310160i	$-0.100383\pi$
$674$		0			0
$675$	−2.62248e6	−	1.25843e7i	−0.221540	−	1.06309i
$676$		0			0
$677$	−1.30059e6	+	4.00280e6i	−0.109061	+	0.335654i	−0.990662	−	0.136340i	$-0.956466\pi$
$677$	−1.30059e6	+	4.00280e6i	−0.109061	+	0.335654i	0.881601	+	0.471995i	$0.156466\pi$
$678$		0			0
$679$	1.28763e6	+	935521.i	0.107181	+	0.0778716i
$680$		0			0
$681$	1.32791e7	−	9.64786e6i	1.09724	−	0.797193i
$682$		0			0
$683$	−1.84439e7	+	1.34003e7i	−1.51287	+	1.09916i	−0.547985	+	0.836488i	$0.684605\pi$
$683$	−1.84439e7	+	1.34003e7i	−1.51287	+	1.09916i	−0.964884	+	0.262676i	$0.915395\pi$
$684$		0			0
$685$	5.90631e6	+	9.13474e6i	0.480939	+	0.743823i
$686$		0			0
$687$	−4.78892e6	−	1.47388e7i	−0.387120	−	1.19143i
$688$		0			0
$689$	1.65564e6	−	5.09555e6i	0.132868	−	0.408924i
$690$		0			0
$691$	−2.19337e6	−	6.75051e6i	−0.174750	−	0.537825i	0.824872	−	0.565320i	$-0.191247\pi$
$691$	−2.19337e6	−	6.75051e6i	−0.174750	−	0.537825i	−0.999622	+	0.0274942i	$0.991247\pi$
$692$		0			0
$693$	776122.			0.0613899
$694$		0			0
$695$	589912.	−	1.08427e7i	0.0463260	−	0.851478i
$696$		0			0
$697$	−1.15954e7	−	8.42454e6i	−0.904072	−	0.656847i
$698$		0			0
$699$	6.98086e6			0.540401
$700$		0			0
$701$	−3.52122e6			−0.270644			−0.135322	−	0.990802i	$-0.543207\pi$
$701$	−3.52122e6			−0.270644			−0.135322	+	0.990802i	$0.543207\pi$
$702$		0			0
$703$	−3.36249e6	−	2.44299e6i	−0.256609	−	0.186438i
$704$		0			0
$705$	−1.81336e6	−	2.80456e6i	−0.137408	−	0.212516i
$706$		0			0
$707$	−6.83526e6			−0.514288
$708$		0			0
$709$	−3.48026e6	−	1.07111e7i	−0.260014	−	0.800240i	−0.992800	−	0.119782i	$-0.961781\pi$
$709$	−3.48026e6	−	1.07111e7i	−0.260014	−	0.800240i	0.732786	−	0.680459i	$-0.238219\pi$
$710$		0			0
$711$	−90152.3	+	277460.i	−0.00668810	+	0.0205839i
$712$		0			0
$713$	−2.83835e6	−	8.73556e6i	−0.209095	−	0.643527i
$714$		0			0
$715$	9.97490e6	−	2.65147e6i	0.729698	−	0.193964i
$716$		0			0
$717$	7.60592e6	−	5.52602e6i	0.552527	−	0.401435i
$718$		0			0
$719$	−108383.	+	78744.5i	−0.00781875	+	0.00568065i	−0.591688	−	0.806167i	$-0.701538\pi$
$719$	−108383.	+	78744.5i	−0.00781875	+	0.00568065i	0.583869	+	0.811848i	$0.301538\pi$
$720$		0			0
$721$	6.35824e6	+	4.61953e6i	0.455511	+	0.330948i
$722$		0			0
$723$	3.32347e6	−	1.02286e7i	0.236454	−	0.727730i
$724$		0			0
$725$	−1.33914e7	−	1.46148e6i	−0.946194	−	0.103264i
$726$		0			0
$727$	7.43748e6	−	2.28902e7i	0.521903	−	1.60625i	−0.248457	−	0.968643i	$-0.579924\pi$
$727$	7.43748e6	−	2.28902e7i	0.521903	−	1.60625i	0.770360	−	0.637609i	$-0.220076\pi$
$728$		0			0
$729$	−1.27920e7	−	9.29390e6i	−0.891493	−	0.647708i
$730$		0			0
$731$	−9.99101e6	+	7.25890e6i	−0.691538	+	0.502432i
$732$		0			0
$733$	−9.40824e6	+	6.83549e6i	−0.646768	+	0.469905i	−0.862169	−	0.506621i	$-0.830894\pi$
$733$	−9.40824e6	+	6.83549e6i	−0.646768	+	0.469905i	0.215401	+	0.976526i	$0.430894\pi$
$734$		0			0
$735$	9.72775e6	+	3.75640e6i	0.664193	+	0.256480i
$736$		0			0
$737$	−2.79918e6	−	8.61498e6i	−0.189829	−	0.584232i
$738$		0			0
$739$	1.27173e6	−	3.91397e6i	0.0856609	−	0.263637i	−0.899047	−	0.437853i	$-0.855739\pi$
$739$	1.27173e6	−	3.91397e6i	0.0856609	−	0.263637i	0.984708	+	0.174216i	$0.0557390\pi$
$740$		0			0
$741$	−1.86500e6	−	5.73987e6i	−0.124776	−	0.384022i
$742$		0			0
$743$	−6.66582e6			−0.442977			−0.221489	−	0.975163i	$-0.571092\pi$
$743$	−6.66582e6			−0.442977			−0.221489	+	0.975163i	$0.571092\pi$
$744$		0			0
$745$	1.70491e7	−	4.53189e6i	1.12541	−	0.299150i
$746$		0			0
$747$	−688426.	−	500171.i	−0.0451394	−	0.0327957i
$748$		0			0
$749$	−1.59954e6			−0.104181
$750$		0			0
$751$	−2.86308e7			−1.85240			−0.926199	−	0.377035i	$-0.876944\pi$
$751$	−2.86308e7			−1.85240			−0.926199	+	0.377035i	$0.876944\pi$
$752$		0			0
$753$	7.49179e6	+	5.44310e6i	0.481502	+	0.349832i
$754$		0			0
$755$	−6.08383e6	+	1.61717e6i	−0.388427	+	0.103249i
$756$		0			0
$757$	2.03763e7			1.29236			0.646182	−	0.763183i	$-0.276365\pi$
$757$	2.03763e7			1.29236			0.646182	+	0.763183i	$0.276365\pi$
$758$		0			0
$759$	1.94897e6	+	5.99830e6i	0.122800	+	0.377941i
$760$		0			0
$761$	5.01770e6	−	1.54429e7i	0.314082	−	0.966645i	−0.662048	−	0.749461i	$-0.730313\pi$
$761$	5.01770e6	−	1.54429e7i	0.314082	−	0.966645i	0.976131	−	0.217184i	$-0.0696873\pi$
$762$		0			0
$763$	−2.42463e6	−	7.46225e6i	−0.150777	−	0.464043i
$764$		0			0
$765$	3.19802e6	+	1.23492e6i	0.197573	+	0.0762933i
$766$		0			0
$767$	4.38724e6	−	3.18752e6i	0.269279	−	0.195643i
$768$		0			0
$769$	−2.15245e7	+	1.56385e7i	−1.31256	+	0.953628i	−0.312563	+	0.949897i	$0.601188\pi$
$769$	−2.15245e7	+	1.56385e7i	−1.31256	+	0.953628i	−0.999993	+	0.00373100i	$0.998812\pi$
$770$		0			0
$771$	4.93515e6	+	3.58560e6i	0.298996	+	0.217233i
$772$		0			0
$773$	−6.75968e6	+	2.08042e7i	−0.406890	+	1.25228i	0.512416	+	0.858737i	$0.328751\pi$
$773$	−6.75968e6	+	2.08042e7i	−0.406890	+	1.25228i	−0.919306	+	0.393543i	$0.871249\pi$
$774$		0			0
$775$	−5.44557e6	+	1.21009e7i	−0.325679	+	0.723708i
$776$		0			0
$777$	−1.63440e6	+	5.03017e6i	−0.0971195	+	0.298903i
$778$		0			0
$779$	−6.93899e6	−	5.04147e6i	−0.409687	−	0.297655i
$780$		0			0
$781$	−653912.	+	475095.i	−0.0383611	+	0.0278710i
$782$		0			0
$783$	−1.43454e7	+	1.04225e7i	−0.836197	+	0.607532i
$784$		0			0
$785$	6.76003e6	−	1.79691e6i	0.391539	−	0.104076i
$786$		0			0
$787$	−4.27419e6	−	1.31546e7i	−0.245990	−	0.757079i	−0.995472	−	0.0950543i	$-0.969698\pi$
$787$	−4.27419e6	−	1.31546e7i	−0.245990	−	0.757079i	0.749482	−	0.662024i	$-0.230302\pi$
$788$		0			0
$789$	6.35647e6	−	1.95632e7i	0.363516	−	1.11879i
$790$		0			0
$791$	2.85065e6	+	8.77339e6i	0.161995	+	0.498570i
$792$		0			0
$793$	3.27854e7			1.85139
$794$		0			0
$795$	−2.56817e6	−	3.97195e6i	−0.144114	−	0.222887i
$796$		0			0
$797$	6.85274e6	+	4.97881e6i	0.382137	+	0.277639i	0.762226	−	0.647311i	$-0.224107\pi$
$797$	6.85274e6	+	4.97881e6i	0.382137	+	0.277639i	−0.380089	+	0.924950i	$0.624107\pi$
$798$		0			0
$799$	4.09449e6			0.226899
$800$		0			0
$801$	5.11499e6			0.281685
$802$		0			0
$803$	9.15247e6	+	6.64966e6i	0.500898	+	0.363924i
$804$		0			0
$805$	−342849.	+	6.30161e6i	−0.0186472	+	0.342738i
$806$		0			0
$807$	1.27392e7			0.688584
$808$		0			0
$809$	−4.12636e6	−	1.26996e7i	−0.221664	−	0.682212i	−0.998613	−	0.0526484i	$-0.983234\pi$
$809$	−4.12636e6	−	1.26996e7i	−0.221664	−	0.682212i	0.776949	−	0.629564i	$-0.216766\pi$
$810$		0			0
$811$	−3.96977e6	+	1.22177e7i	−0.211940	+	0.652285i	0.787417	+	0.616421i	$0.211418\pi$
$811$	−3.96977e6	+	1.22177e7i	−0.211940	+	0.652285i	−0.999357	+	0.0358634i	$0.988582\pi$
$812$		0			0
$813$	−7.74038e6	−	2.38224e7i	−0.410711	−	1.26404i
$814$		0			0
$815$	1.33302e7	+	2.06165e7i	0.702979	+	1.08723i
$816$		0			0
$817$	−5.97889e6	+	4.34392e6i	−0.313376	+	0.227681i
$818$		0			0
$819$	2.39242e6	−	1.73820e6i	0.124632	−	0.0905502i
$820$		0			0
$821$	336372.	+	244388.i	0.0174165	+	0.0126538i	0.596459	−	0.802643i	$-0.296574\pi$
$821$	336372.	+	244388.i	0.0174165	+	0.0126538i	−0.579043	+	0.815297i	$0.696574\pi$
$822$		0			0
$823$	−5.83711e6	+	1.79648e7i	−0.300399	+	0.924532i	0.680956	+	0.732325i	$0.261565\pi$
$823$	−5.83711e6	+	1.79648e7i	−0.300399	+	0.924532i	−0.981354	+	0.192207i	$0.938435\pi$
$824$		0			0
$825$	3.73922e6	−	8.30913e6i	0.191270	−	0.425031i
$826$		0			0
$827$	−5.34540e6	+	1.64515e7i	−0.271780	+	0.836451i	0.718274	+	0.695760i	$0.244932\pi$
$827$	−5.34540e6	+	1.64515e7i	−0.271780	+	0.836451i	−0.990054	+	0.140691i	$0.955068\pi$
$828$		0			0
$829$	−1.07761e6	−	782929.i	−0.0544597	−	0.0395673i	0.560222	−	0.828342i	$-0.310716\pi$
$829$	−1.07761e6	−	782929.i	−0.0544597	−	0.0395673i	−0.614682	+	0.788775i	$0.710716\pi$
$830$		0			0
$831$	−7.50068e6	+	5.44956e6i	−0.376789	+	0.273753i
$832$		0			0
$833$	−1.03428e7	+	7.51450e6i	−0.516448	+	0.375221i
$834$		0			0
$835$	−1.93598e7	+	2.38102e7i	−0.960915	+	1.18181i
$836$		0			0
$837$	5.39764e6	+	1.66122e7i	0.266312	+	0.819623i
$838$		0			0
$839$	3.27186e6	−	1.00697e7i	0.160468	−	0.493871i	−0.838205	−	0.545355i	$-0.816395\pi$
$839$	3.27186e6	−	1.00697e7i	0.160468	−	0.493871i	0.998674	+	0.0514837i	$0.0163950\pi$
$840$		0			0
$841$	−596140.	−	1.83473e6i	−0.0290642	−	0.0894504i
$842$		0			0
$843$	1.44705e7			0.701318
$844$		0			0
$845$	1.17155e7	−	1.44087e7i	0.564444	−	0.694197i
$846$		0			0
$847$	−4.75411e6	−	3.45406e6i	−0.227699	−	0.165433i
$848$		0			0
$849$	1.74494e7			0.830826
$850$		0			0
$851$	1.65493e7			0.783351
$852$		0			0
$853$	3.09804e7	+	2.25086e7i	1.45786	+	1.05920i	0.983915	+	0.178640i	$0.0571697\pi$
$853$	3.09804e7	+	2.25086e7i	1.45786	+	1.05920i	0.473943	+	0.880556i	$0.342830\pi$
$854$		0			0
$855$	1.91378e6	+	739011.i	0.0895317	+	0.0345729i
$856$		0			0
$857$	−1.76645e7			−0.821579			−0.410790	−	0.911730i	$-0.634747\pi$
$857$	−1.76645e7			−0.821579			−0.410790	+	0.911730i	$0.634747\pi$
$858$		0			0
$859$	1.05142e7	+	3.23595e7i	0.486177	+	1.49630i	0.830268	+	0.557364i	$0.188187\pi$
$859$	1.05142e7	+	3.23595e7i	0.486177	+	1.49630i	−0.344091	+	0.938936i	$0.611813\pi$
$860$		0			0
$861$	−3.37283e6	+	1.03805e7i	−0.155055	+	0.477211i
$862$		0			0
$863$	−7.29386e6	−	2.24482e7i	−0.333373	−	1.02602i	−0.967518	−	0.252802i	$-0.918648\pi$
$863$	−7.29386e6	−	2.24482e7i	−0.333373	−	1.02602i	0.634145	−	0.773214i	$-0.281352\pi$
$864$		0			0
$865$	362041.	−	6.65436e6i	0.0164520	−	0.302389i
$866$		0			0
$867$	−6.38433e6	+	4.63849e6i	−0.288448	+	0.209570i
$868$		0			0
$869$	−769090.	+	558777.i	−0.0345484	+	0.0251009i
$870$		0			0
$871$	−2.79226e7	−	2.02870e7i	−1.24713	−	0.906091i
$872$		0			0
$873$	−636611.	+	1.95929e6i	−0.0282708	+	0.0870087i
$874$		0			0
$875$	6.48542e6	−	6.40832e6i	0.286364	−	0.282960i
$876$		0			0
$877$	645047.	−	1.98525e6i	0.0283199	−	0.0871598i	−0.935898	−	0.352272i	$-0.885409\pi$
$877$	645047.	−	1.98525e6i	0.0283199	−	0.0871598i	0.964217	+	0.265113i	$0.0854091\pi$
$878$		0			0
$879$	3.86675e6	+	2.80936e6i	0.168801	+	0.122641i
$880$		0			0
$881$	−9.16056e6	+	6.65554e6i	−0.397633	+	0.288897i	−0.768576	−	0.639758i	$-0.779034\pi$
$881$	−9.16056e6	+	6.65554e6i	−0.397633	+	0.288897i	0.370943	+	0.928656i	$0.379034\pi$
$882$		0			0
$883$	−1.62414e7	+	1.18001e7i	−0.701006	+	0.509310i	−0.880260	−	0.474492i	$-0.842632\pi$
$883$	−1.62414e7	+	1.18001e7i	−0.701006	+	0.509310i	0.179254	+	0.983803i	$0.442632\pi$
$884$		0			0
$885$	260082.	−	4.78034e6i	0.0111623	−	0.205164i
$886$		0			0
$887$	1.22990e7	+	3.78526e7i	0.524883	+	1.61542i	0.764548	+	0.644567i	$0.222962\pi$
$887$	1.22990e7	+	3.78526e7i	0.524883	+	1.61542i	−0.239665	+	0.970856i	$0.577038\pi$
$888$		0			0
$889$	−3.95474e6	+	1.21714e7i	−0.167828	+	0.516520i
$890$		0			0
$891$	−2.58965e6	−	7.97011e6i	−0.109281	−	0.336333i
$892$		0			0
$893$	2.45025e6			0.102821
$894$		0			0
$895$	−2.78999e7	−	1.07736e7i	−1.16425	−	0.449577i
$896$		0			0
$897$	1.94415e7	+	1.41251e7i	0.806769	+	0.586152i
$898$		0			0
$899$	1.83045e7			0.755370
$900$		0			0
$901$	5.79880e6			0.237972
$902$		0			0
$903$	7.60841e6	+	5.52783e6i	0.310509	+	0.225598i
$904$		0			0
$905$	−1.50532e7	+	1.85135e7i	−0.610950	+	0.751394i
$906$		0			0
$907$	−8.36833e6			−0.337769			−0.168885	−	0.985636i	$-0.554017\pi$
$907$	−8.36833e6			−0.337769			−0.168885	+	0.985636i	$0.554017\pi$
$908$		0			0
$909$	−2.73397e6	−	8.41431e6i	−0.109745	−	0.337760i
$910$		0			0
$911$	−1.07790e7	+	3.31743e7i	−0.430310	+	1.32436i	0.467506	+	0.883990i	$0.345153\pi$
$911$	−1.07790e7	+	3.31743e7i	−0.430310	+	1.32436i	−0.897817	+	0.440369i	$0.854847\pi$
$912$		0			0
$913$	−856855.	−	2.63713e6i	−0.0340197	−	0.104702i
$914$		0			0
$915$	1.82594e7	−	2.24568e7i	0.720996	−	0.886737i
$916$		0			0
$917$	−1.63407e7	+	1.18722e7i	−0.641724	+	0.466240i
$918$		0			0
$919$	1.49441e7	−	1.08575e7i	0.583687	−	0.424074i	−0.256364	−	0.966580i	$-0.582525\pi$
$919$	1.49441e7	−	1.08575e7i	0.583687	−	0.424074i	0.840052	+	0.542507i	$0.182525\pi$
$920$		0			0
$921$	−3.57713e6	−	2.59894e6i	−0.138959	−	0.100960i
$922$		0			0
$923$	−951688.	+	2.92899e6i	−0.0367697	+	0.113166i
$924$		0			0
$925$	−1.77038e7	−	1.60688e7i	−0.680319	−	0.617491i
$926$		0			0
$927$	−3.14354e6	+	9.67481e6i	−0.120149	+	0.369780i
$928$		0			0
$929$	−3.89022e7	−	2.82641e7i	−1.47889	−	1.07447i	−0.977913	−	0.209012i	$-0.932975\pi$
$929$	−3.89022e7	−	2.82641e7i	−1.47889	−	1.07447i	−0.500974	−	0.865462i	$-0.667025\pi$
$930$		0			0
$931$	−6.18942e6	+	4.49688e6i	−0.234032	+	0.170034i
$932$		0			0
$933$	−1.01740e7	+	7.39181e6i	−0.382636	+	0.278001i
$934$		0			0
$935$	6.06541e6	+	9.38080e6i	0.226898	+	0.350922i
$936$		0			0
$937$	−3.54452e6	−	1.09089e7i	−0.131889	−	0.405913i	0.863204	−	0.504855i	$-0.168454\pi$
$937$	−3.54452e6	−	1.09089e7i	−0.131889	−	0.405913i	−0.995093	+	0.0989422i	$0.968454\pi$
$938$		0			0
$939$	3.85201e6	−	1.18553e7i	0.142569	−	0.438781i
$940$		0			0
$941$	−6.81604e6	−	2.09776e7i	−0.250933	−	0.772293i	−0.994604	−	0.103747i	$-0.966917\pi$
$941$	−6.81604e6	−	2.09776e7i	−0.250933	−	0.772293i	0.743671	−	0.668546i	$-0.233083\pi$
$942$		0			0
$943$	3.41520e7			1.25065
$944$		0			0
$945$	651989.	−	1.19836e7i	0.0237499	−	0.436525i
$946$		0			0
$947$	−8.95989e6	−	6.50974e6i	−0.324659	−	0.235879i	0.413502	−	0.910503i	$-0.364306\pi$
$947$	−8.95989e6	−	6.50974e6i	−0.324659	−	0.235879i	−0.738161	+	0.674625i	$0.764306\pi$
$948$		0			0
$949$	4.31054e7			1.55370
$950$		0			0
$951$	−2.59567e6			−0.0930675
$952$		0			0
$953$	3.98300e7	+	2.89382e7i	1.42062	+	1.03214i	0.991669	+	0.128815i	$0.0411173\pi$
$953$	3.98300e7	+	2.89382e7i	1.42062	+	1.03214i	0.428953	+	0.903327i	$0.358883\pi$
$954$		0			0
$955$	−1.67787e7	−	2.59500e7i	−0.595319	−	0.920724i
$956$		0			0
$957$	−1.25689e7			−0.443626
$958$		0			0
$959$	3.13832e6	+	9.65877e6i	0.110192	+	0.339137i
$960$		0			0
$961$	−3.27494e6	+	1.00792e7i	−0.114392	+	0.352062i
$962$		0			0
$963$	−639786.	−	1.96906e6i	−0.0222315	−	0.0684215i
$964$		0			0
$965$	1.88766e7	−	5.01768e6i	0.652539	−	0.173454i
$966$		0			0
$967$	−809479.	+	588121.i	−0.0278381	+	0.0202255i	−0.601617	−	0.798784i	$-0.705477\pi$
$967$	−809479.	+	588121.i	−0.0278381	+	0.0202255i	0.573779	+	0.819010i	$0.305477\pi$
$968$		0			0
$969$	5.28454e6	−	3.83944e6i	0.180800	−	0.131359i
$970$		0			0
$971$	−9.89345e6	−	7.18801e6i	−0.336744	−	0.244659i	0.406543	−	0.913632i	$-0.366734\pi$
$971$	−9.89345e6	−	7.18801e6i	−0.336744	−	0.244659i	−0.743287	+	0.668973i	$0.766734\pi$
$972$		0			0
$973$	3.13279e6	−	9.64174e6i	0.106084	−	0.326493i
$974$		0			0
$975$	−7.08279e6	−	3.39875e7i	−0.238612	−	1.14501i
$976$		0			0
$977$	−5.76892e6	+	1.77549e7i	−0.193356	+	0.595089i	0.806636	+	0.591049i	$0.201286\pi$
$977$	−5.76892e6	+	1.77549e7i	−0.193356	+	0.595089i	−0.999992	+	0.00403989i	$0.998714\pi$
$978$		0			0
$979$	1.34843e7	+	9.79689e6i	0.449646	+	0.326687i
$980$		0			0
$981$	8.21634e6	−	5.96952e6i	0.272587	−	0.198046i
$982$		0			0
$983$	3.85700e7	−	2.80228e7i	1.27311	−	0.924969i	0.273789	−	0.961790i	$-0.411723\pi$
$983$	3.85700e7	−	2.80228e7i	1.27311	−	0.924969i	0.999322	+	0.0368209i	$0.0117231\pi$
$984$		0			0
$985$	−1.87720e7	−	7.24885e6i	−0.616481	−	0.238056i
$986$		0			0
$987$	−963532.	−	2.96545e6i	−0.0314828	−	0.0968941i
$988$		0			0
$989$	9.09332e6	−	2.79864e7i	0.295619	−	0.909820i
$990$		0			0
$991$	4.06864e6	+	1.25220e7i	0.131603	+	0.405032i	0.995046	−	0.0994140i	$-0.0316968\pi$
$991$	4.06864e6	+	1.25220e7i	0.131603	+	0.405032i	−0.863443	+	0.504446i	$0.831697\pi$
$992$		0			0
$993$	−2.16732e7			−0.697509
$994$		0			0
$995$	7.36001e6	−	1.95639e6i	0.235679	−	0.0626467i
$996$		0			0
$997$	824877.	+	599308.i	0.0262816	+	0.0190947i	0.600848	−	0.799363i	$-0.294829\pi$
$997$	824877.	+	599308.i	0.0262816	+	0.0190947i	−0.574567	+	0.818458i	$0.694829\pi$
$998$		0			0
$999$	−3.14715e7			−0.997709

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.6.g.a.21.9	✓	52
25.6	even	5	inner	100.6.g.a.81.9	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.6.g.a.21.9	✓	52	1.1	even	1	trivial
100.6.g.a.81.9	yes	52	25.6	even	5	inner

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	100.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(10.7159 + 7.78556i) q^{3} +(-54.0256 + 14.3608i) q^{5} -52.1911 q^{7} +(-20.8755 - 64.2481i) q^{9} +O(q^{10})\)	\(q+(10.7159 + 7.78556i) q^{3} +(-54.0256 + 14.3608i) q^{5} -52.1911 q^{7} +(-20.8755 - 64.2481i) q^{9} +(68.0239 - 209.356i) q^{11} +(-259.186 - 797.694i) q^{13} +(-690.740 - 266.731i) q^{15} +(734.415 - 533.583i) q^{17} +(439.493 - 319.311i) q^{19} +(-559.275 - 406.337i) q^{21} +(-668.427 + 2057.21i) q^{23} +(2712.54 - 1551.70i) q^{25} +(1271.13 - 3912.15i) q^{27} +(-3487.42 - 2533.76i) q^{29} +(-3435.34 + 2495.92i) q^{31} +(2358.89 - 1713.83i) q^{33} +(2819.66 - 749.505i) q^{35} +(-2364.24 - 7276.37i) q^{37} +(3433.07 - 10565.9i) q^{39} +(-4878.95 - 15015.9i) q^{41} -13604.1 q^{43} +(2050.46 + 3171.26i) q^{45} +(3649.00 + 2651.15i) q^{47} -14083.1 q^{49} +12024.2 q^{51} +(5167.88 + 3754.69i) q^{53} +(-668.519 + 12287.5i) q^{55} +7195.58 q^{57} +(1997.96 + 6149.08i) q^{59} +(-12079.1 + 37175.5i) q^{61} +(1089.52 + 3353.18i) q^{63} +(25458.2 + 39373.8i) q^{65} +(33291.0 - 24187.3i) q^{67} +(-23179.3 + 16840.8i) q^{69} +(-2970.57 - 2158.25i) q^{71} +(-15881.2 + 48877.4i) q^{73} +(41148.1 + 4490.75i) q^{75} +(-3550.24 + 10926.5i) q^{77} +(-3493.80 - 2538.40i) q^{79} +(30799.0 - 22376.8i) q^{81} +(10190.7 - 7403.97i) q^{83} +(-32014.5 + 39373.9i) q^{85} +(-17644.1 - 54303.0i) q^{87} +(-23397.7 + 72010.7i) q^{89} +(13527.2 + 41632.5i) q^{91} -56245.0 q^{93} +(-19158.4 + 23562.4i) q^{95} +(-24671.5 - 17924.9i) q^{97} -14870.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{3} + 116 q^{5} - 42 q^{7} - 1153 q^{9}+O(q^{10}) \) 52 * q + 2 * q^3 + 116 * q^5 - 42 * q^7 - 1153 * q^9	\( 52 q + 2 q^{3} + 116 q^{5} - 42 q^{7} - 1153 q^{9} - 5 q^{11} + 1458 q^{13} + 2418 q^{15} - 2329 q^{17} + 1912 q^{19} - 4818 q^{21} + 3594 q^{23} + 934 q^{25} + 3206 q^{27} - 1458 q^{29} + 5532 q^{31} + 2435 q^{33} - 5603 q^{35} + 22043 q^{37} - 9938 q^{39} + 4567 q^{41} - 35390 q^{43} - 59359 q^{45} - 5859 q^{47} + 165974 q^{49} + 68014 q^{51} + 20151 q^{53} - 97855 q^{55} - 241368 q^{57} - 116271 q^{59} + 39134 q^{61} + 262808 q^{63} + 190502 q^{65} + 40883 q^{67} - 51844 q^{69} - 109999 q^{71} - 187802 q^{73} - 164833 q^{75} + 102220 q^{77} + 122216 q^{79} - 264922 q^{81} + 125394 q^{83} + 83764 q^{85} + 205117 q^{87} - 107222 q^{89} + 58608 q^{91} - 490158 q^{93} - 82634 q^{95} + 129683 q^{97} + 302280 q^{99}+O(q^{100}) \) 52 * q + 2 * q^3 + 116 * q^5 - 42 * q^7 - 1153 * q^9 - 5 * q^11 + 1458 * q^13 + 2418 * q^15 - 2329 * q^17 + 1912 * q^19 - 4818 * q^21 + 3594 * q^23 + 934 * q^25 + 3206 * q^27 - 1458 * q^29 + 5532 * q^31 + 2435 * q^33 - 5603 * q^35 + 22043 * q^37 - 9938 * q^39 + 4567 * q^41 - 35390 * q^43 - 59359 * q^45 - 5859 * q^47 + 165974 * q^49 + 68014 * q^51 + 20151 * q^53 - 97855 * q^55 - 241368 * q^57 - 116271 * q^59 + 39134 * q^61 + 262808 * q^63 + 190502 * q^65 + 40883 * q^67 - 51844 * q^69 - 109999 * q^71 - 187802 * q^73 - 164833 * q^75 + 102220 * q^77 + 122216 * q^79 - 264922 * q^81 + 125394 * q^83 + 83764 * q^85 + 205117 * q^87 - 107222 * q^89 + 58608 * q^91 - 490158 * q^93 - 82634 * q^95 + 129683 * q^97 + 302280 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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