LMFDB - Embedded newform 124.5.o.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,5,Mod(13,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("124.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	124.o (of order $30$, degree $8$, 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:	$12.8178754224$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	124.17
Dual form			124.5.o.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.97256 - 8.07893i) q^{3} +(-1.91809 + 3.32223i) q^{5} +(7.45792 - 70.9574i) q^{7} +(6.77094 + 64.4212i) q^{9} +O(q^{10})$	\(q+(-8.97256 - 8.07893i) q^{3} +(-1.91809 + 3.32223i) q^{5} +(7.45792 - 70.9574i) q^{7} +(6.77094 + 64.4212i) q^{9} +(-44.3421 - 99.5939i) q^{11} +(-19.0251 + 89.5061i) q^{13} +(44.0503 - 14.3128i) q^{15} +(-72.8880 + 163.709i) q^{17} +(-338.912 + 72.0379i) q^{19} +(-640.176 + 576.417i) q^{21} +(182.351 + 250.985i) q^{23} +(305.142 + 528.521i) q^{25} +(-115.138 + 158.474i) q^{27} +(-319.530 - 103.822i) q^{29} +(142.017 + 950.448i) q^{31} +(-406.751 + 1251.85i) q^{33} +(221.432 + 160.880i) q^{35} +(-601.816 + 347.459i) q^{37} +(893.818 - 649.397i) q^{39} +(-1897.15 - 2107.00i) q^{41} +(-327.144 - 1539.09i) q^{43} +(-227.009 - 101.071i) q^{45} +(-311.296 - 958.070i) q^{47} +(-2630.79 - 559.192i) q^{49} +(1976.59 - 880.033i) q^{51} +(876.186 - 92.0908i) q^{53} +(415.926 + 43.7156i) q^{55} +(3622.90 + 2091.68i) q^{57} +(2431.01 - 2699.91i) q^{59} +4589.97i q^{61} +4621.65 q^{63} +(-260.868 - 234.887i) q^{65} +(-1849.73 + 3203.83i) q^{67} +(391.533 - 3725.19i) q^{69} +(261.987 + 2492.64i) q^{71} +(-1889.05 - 4242.88i) q^{73} +(1531.98 - 7207.41i) q^{75} +(-7397.62 + 2403.63i) q^{77} +(2444.81 - 5491.12i) q^{79} +(7445.58 - 1582.61i) q^{81} +(-3503.98 + 3155.00i) q^{83} +(-404.074 - 556.160i) q^{85} +(2028.24 + 3513.01i) q^{87} +(204.467 - 281.424i) q^{89} +(6209.23 + 2017.50i) q^{91} +(6404.35 - 9675.30i) q^{93} +(410.737 - 1264.12i) q^{95} +(3250.18 + 2361.39i) q^{97} +(6115.72 - 3530.91i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{7}{30}\right)$

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
$3$	−8.97256	−	8.07893i	−0.996952	−	0.897659i	−0.00220187	−	0.999998i	$-0.500701\pi$
$3$	−8.97256	−	8.07893i	−0.996952	−	0.897659i	−0.994750	+	0.102338i	$0.967368\pi$
$4$		0			0
$5$	−1.91809	+	3.32223i	−0.0767236	+	0.132889i	−0.901835	−	0.432082i	$-0.857779\pi$
$5$	−1.91809	+	3.32223i	−0.0767236	+	0.132889i	0.825111	+	0.564971i	$0.191113\pi$
$6$		0			0
$7$	7.45792	−	70.9574i	0.152202	−	1.44811i	−0.605675	−	0.795712i	$-0.707097\pi$
$7$	7.45792	−	70.9574i	0.152202	−	1.44811i	0.757877	−	0.652397i	$-0.226237\pi$
$8$		0			0
$9$	6.77094	+	64.4212i	0.0835919	+	0.795323i
$10$		0			0
$11$	−44.3421	−	99.5939i	−0.366463	−	0.823090i	−0.998827	−	0.0484188i	$-0.984582\pi$
$11$	−44.3421	−	99.5939i	−0.366463	−	0.823090i	0.632364	−	0.774672i	$-0.282085\pi$
$12$		0			0
$13$	−19.0251	+	89.5061i	−0.112575	+	0.529622i	0.885332	+	0.464958i	$0.153931\pi$
$13$	−19.0251	+	89.5061i	−0.112575	+	0.529622i	−0.997907	+	0.0646635i	$0.979403\pi$
$14$		0			0
$15$	44.0503	−	14.3128i	0.195779	−	0.0636125i
$16$		0			0
$17$	−72.8880	+	163.709i	−0.252208	+	0.566467i	−0.994634	−	0.103461i	$-0.967008\pi$
$17$	−72.8880	+	163.709i	−0.252208	+	0.566467i	0.742426	+	0.669928i	$0.233675\pi$
$18$		0			0
$19$	−338.912	+	72.0379i	−0.938814	+	0.199551i	−0.651813	−	0.758379i	$-0.725991\pi$
$19$	−338.912	+	72.0379i	−0.938814	+	0.199551i	−0.287000	+	0.957930i	$0.592658\pi$
$20$		0			0
$21$	−640.176	+	576.417i	−1.45165	+	1.30707i
$22$		0			0
$23$	182.351	+	250.985i	0.344710	+	0.474452i	0.945810	−	0.324722i	$-0.105271\pi$
$23$	182.351	+	250.985i	0.344710	+	0.474452i	−0.601100	+	0.799174i	$0.705271\pi$
$24$		0			0
$25$	305.142	+	528.521i	0.488227	+	0.845634i
$26$		0			0
$27$	−115.138	+	158.474i	−0.157940	+	0.217385i
$28$		0			0
$29$	−319.530	−	103.822i	−0.379941	−	0.123450i	0.112819	−	0.993616i	$-0.464012\pi$
$29$	−319.530	−	103.822i	−0.379941	−	0.123450i	−0.492760	+	0.870165i	$0.664012\pi$
$30$		0			0
$31$	142.017	+	950.448i	0.147780	+	0.989020i
$31$	142.017	+	950.448i	0.147780	+	0.989020i
$32$		0			0
$33$	−406.751	+	1251.85i	−0.373508	+	1.14954i
$34$		0			0
$35$	221.432	+	160.880i	0.180761	+	0.131330i
$36$		0			0
$37$	−601.816	+	347.459i	−0.439603	+	0.253805i	−0.703429	−	0.710765i	$-0.748349\pi$
$37$	−601.816	+	347.459i	−0.439603	+	0.253805i	0.263826	+	0.964570i	$0.415015\pi$
$38$		0			0
$39$	893.818	−	649.397i	0.587651	−	0.426954i
$40$		0			0
$41$	−1897.15	−	2107.00i	−1.12858	−	1.25342i	−0.963666	−	0.267110i	$-0.913931\pi$
$41$	−1897.15	−	2107.00i	−1.12858	−	1.25342i	−0.164916	−	0.986308i	$-0.552735\pi$
$42$		0			0
$43$	−327.144	−	1539.09i	−0.176930	−	0.832392i	−0.973651	−	0.228044i	$-0.926767\pi$
$43$	−327.144	−	1539.09i	−0.176930	−	0.832392i	0.796720	−	0.604348i	$-0.206566\pi$
$44$		0			0
$45$	−227.009	−	101.071i	−0.112103	−	0.0499116i
$46$		0			0
$47$	−311.296	−	958.070i	−0.140922	−	0.433712i	0.855542	−	0.517733i	$-0.173224\pi$
$47$	−311.296	−	958.070i	−0.140922	−	0.433712i	−0.996464	+	0.0840207i	$0.973224\pi$
$48$		0			0
$49$	−2630.79	−	559.192i	−1.09571	−	0.232900i
$50$		0			0
$51$	1976.59	−	880.033i	0.759933	−	0.338344i
$52$		0			0
$53$	876.186	−	92.0908i	0.311921	−	0.0327842i	0.0527253	−	0.998609i	$-0.483209\pi$
$53$	876.186	−	92.0908i	0.311921	−	0.0327842i	0.259196	+	0.965825i	$0.416543\pi$
$54$		0			0
$55$	415.926	+	43.7156i	0.137496	+	0.0144514i
$56$		0			0
$57$	3622.90	+	2091.68i	1.11508	+	0.643792i
$58$		0			0
$59$	2431.01	−	2699.91i	0.698366	−	0.775613i	−0.284750	−	0.958602i	$-0.591910\pi$
$59$	2431.01	−	2699.91i	0.698366	−	0.775613i	0.983115	+	0.182988i	$0.0585771\pi$
$60$		0			0
$61$			4589.97i			1.23353i	0.787146	+	0.616766i	$0.211558\pi$
$61$			4589.97i			1.23353i	−0.787146	+	0.616766i	$0.788442\pi$
$62$		0			0
$63$	4621.65			1.16444
$64$		0			0
$65$	−260.868	−	234.887i	−0.0617439	−	0.0555945i
$66$		0			0
$67$	−1849.73	+	3203.83i	−0.412059	+	0.713708i	−0.995115	−	0.0987246i	$-0.968524\pi$
$67$	−1849.73	+	3203.83i	−0.412059	+	0.713708i	0.583055	+	0.812432i	$0.301857\pi$
$68$		0			0
$69$	391.533	−	3725.19i	0.0822375	−	0.782438i
$70$		0			0
$71$	261.987	+	2492.64i	0.0519713	+	0.494474i	0.989286	+	0.145990i	$0.0466367\pi$
$71$	261.987	+	2492.64i	0.0519713	+	0.494474i	−0.937315	+	0.348484i	$0.886697\pi$
$72$		0			0
$73$	−1889.05	−	4242.88i	−0.354485	−	0.796187i	−0.999488	−	0.0320065i	$-0.989810\pi$
$73$	−1889.05	−	4242.88i	−0.354485	−	0.796187i	0.645002	−	0.764181i	$-0.276856\pi$
$74$		0			0
$75$	1531.98	−	7207.41i	0.272352	−	1.28132i
$76$		0			0
$77$	−7397.62	+	2403.63i	−1.24770	+	0.405403i
$78$		0			0
$79$	2444.81	−	5491.12i	0.391733	−	0.879847i	−0.604779	−	0.796394i	$-0.706738\pi$
$79$	2444.81	−	5491.12i	0.391733	−	0.879847i	0.996512	−	0.0834531i	$-0.0265949\pi$
$80$		0			0
$81$	7445.58	−	1582.61i	1.13482	−	0.241214i
$82$		0			0
$83$	−3503.98	+	3155.00i	−0.508634	+	0.457976i	−0.883046	−	0.469286i	$-0.844511\pi$
$83$	−3503.98	+	3155.00i	−0.508634	+	0.457976i	0.374412	+	0.927263i	$0.377845\pi$
$84$		0			0
$85$	−404.074	−	556.160i	−0.0559271	−	0.0769771i
$86$		0			0
$87$	2028.24	+	3513.01i	0.267966	+	0.464131i
$88$		0			0
$89$	204.467	−	281.424i	0.0258132	−	0.0355289i	−0.795915	−	0.605408i	$-0.793010\pi$
$89$	204.467	−	281.424i	0.0258132	−	0.0355289i	0.821729	+	0.569879i	$0.193010\pi$
$90$		0			0
$91$	6209.23	+	2017.50i	0.749816	+	0.243630i
$92$		0			0
$93$	6404.35	−	9675.30i	0.740473	−	1.11866i
$94$		0			0
$95$	410.737	−	1264.12i	0.0455110	−	0.140069i
$96$		0			0
$97$	3250.18	+	2361.39i	0.345433	+	0.250972i	0.746950	−	0.664880i	$-0.231517\pi$
$97$	3250.18	+	2361.39i	0.345433	+	0.250972i	−0.401518	+	0.915851i	$0.631517\pi$
$98$		0			0
$99$	6115.72	−	3530.91i	0.623990	−	0.360261i
$100$		0			0
$101$	−4274.01	+	3105.25i	−0.418980	+	0.304407i	−0.777227	−	0.629220i	$-0.783374\pi$
$101$	−4274.01	+	3105.25i	−0.418980	+	0.304407i	0.358247	+	0.933627i	$0.383374\pi$
$102$		0			0
$103$	1376.94	+	1529.25i	0.129790	+	0.144146i	0.804537	−	0.593903i	$-0.202414\pi$
$103$	1376.94	+	1529.25i	0.129790	+	0.144146i	−0.674747	+	0.738049i	$0.735747\pi$
$104$		0			0
$105$	−687.075	−	3232.43i	−0.0623197	−	0.293191i
$106$		0			0
$107$	−18807.8	−	8373.78i	−1.64275	−	0.731398i	−0.643332	−	0.765587i	$-0.722449\pi$
$107$	−18807.8	−	8373.78i	−1.64275	−	0.731398i	−0.999415	+	0.0341888i	$0.989115\pi$
$108$		0			0
$109$	−6241.97	−	19210.8i	−0.525374	−	1.61693i	−0.763575	−	0.645719i	$-0.776558\pi$
$109$	−6241.97	−	19210.8i	−0.525374	−	1.61693i	0.238202	−	0.971216i	$-0.423442\pi$
$110$		0			0
$111$	8206.93	+	1744.44i	0.666093	+	0.141582i
$112$		0			0
$113$	−22004.3	+	9796.97i	−1.72326	+	0.767246i	−0.726472	+	0.687196i	$0.758842\pi$
$113$	−22004.3	+	9796.97i	−1.72326	+	0.767246i	−0.996791	+	0.0800507i	$0.974492\pi$
$114$		0			0
$115$	−1183.60	+	124.401i	−0.0894970	+	0.00940651i
$116$		0			0
$117$	−5894.91	−	619.580i	−0.430631	−	0.0452612i
$118$		0			0
$119$	11072.8	+	6392.87i	0.781920	+	0.451442i
$120$		0			0
$121$	1844.01	−	2047.98i	0.125948	−	0.139880i
$122$		0			0
$123$			34232.1i			2.26268i
$124$		0			0
$125$	−4738.77			−0.303281
$126$		0			0
$127$	8332.86	+	7502.94i	0.516638	+	0.465183i	0.885724	−	0.464212i	$-0.153662\pi$
$127$	8332.86	+	7502.94i	0.516638	+	0.465183i	−0.369086	+	0.929395i	$0.620329\pi$
$128$		0			0
$129$	−9498.91	+	16452.6i	−0.570813	+	0.988678i
$130$		0			0
$131$	1483.77	−	14117.1i	0.0864617	−	0.822628i	−0.862250	−	0.506484i	$-0.830945\pi$
$131$	1483.77	−	14117.1i	0.0864617	−	0.822628i	0.948711	−	0.316144i	$-0.102388\pi$
$132$		0			0
$133$	2584.04	+	24585.5i	0.146082	+	1.38988i
$134$		0			0
$135$	−305.641	−	686.482i	−0.0167704	−	0.0376670i
$136$		0			0
$137$	−3176.84	+	14945.8i	−0.169260	+	0.796305i	0.808817	+	0.588060i	$0.200108\pi$
$137$	−3176.84	+	14945.8i	−0.169260	+	0.796305i	−0.978077	+	0.208244i	$0.933225\pi$
$138$		0			0
$139$	−29496.6	+	9584.02i	−1.52666	+	0.496041i	−0.947658	−	0.319286i	$-0.896557\pi$
$139$	−29496.6	+	9584.02i	−1.52666	+	0.496041i	−0.579000	+	0.815328i	$0.696557\pi$
$140$		0			0
$141$	−4947.06	+	11111.3i	−0.248834	+	0.558889i
$142$		0			0
$143$	9757.88	−	2074.10i	0.477181	−	0.101428i
$144$		0			0
$145$	957.808	−	862.414i	0.0455557	−	0.0410185i
$146$		0			0
$147$	19087.3	+	26271.4i	0.883302	+	1.21576i
$148$		0			0
$149$	−8074.00	−	13984.6i	−0.363678	−	0.629908i	0.624885	−	0.780716i	$-0.285146\pi$
$149$	−8074.00	−	13984.6i	−0.363678	−	0.629908i	−0.988563	+	0.150808i	$0.951812\pi$
$150$		0			0
$151$	10009.4	−	13776.8i	0.438991	−	0.604219i	−0.530996	−	0.847374i	$-0.678182\pi$
$151$	10009.4	−	13776.8i	0.438991	−	0.604219i	0.969988	+	0.243155i	$0.0781822\pi$
$152$		0			0
$153$	−11039.9	−	3587.07i	−0.471607	−	0.153234i
$154$		0			0
$155$	−3430.01	−	1351.23i	−0.142768	−	0.0562428i
$156$		0			0
$157$	−8215.79	+	25285.6i	−0.333311	+	1.02583i	0.634237	+	0.773139i	$0.281314\pi$
$157$	−8215.79	+	25285.6i	−0.333311	+	1.02583i	−0.967548	+	0.252688i	$0.918686\pi$
$158$		0			0
$159$	−8605.63	−	6252.35i	−0.340399	−	0.247314i
$160$		0			0
$161$	19169.2	−	11067.3i	0.739524	−	0.426965i
$162$		0			0
$163$	−14091.6	+	10238.1i	−0.530376	+	0.385341i	−0.820498	−	0.571649i	$-0.806304\pi$
$163$	−14091.6	+	10238.1i	−0.530376	+	0.385341i	0.290122	+	0.956990i	$0.406304\pi$
$164$		0			0
$165$	−3378.75	−	3752.48i	−0.124105	−	0.137832i
$166$		0			0
$167$	−9630.76	−	45309.2i	−0.345325	−	1.62463i	−0.717567	−	0.696490i	$-0.754744\pi$
$167$	−9630.76	−	45309.2i	−0.345325	−	1.62463i	0.372242	−	0.928136i	$-0.378589\pi$
$168$		0			0
$169$	18442.4	+	8211.08i	0.645719	+	0.287493i
$170$		0			0
$171$	−6935.52	−	21345.3i	−0.237185	−	0.729980i
$172$		0			0
$173$	−27600.0	−	5866.56i	−0.922183	−	0.196016i	−0.277729	−	0.960659i	$-0.589582\pi$
$173$	−27600.0	−	5866.56i	−0.922183	−	0.196016i	−0.644454	+	0.764643i	$0.722915\pi$
$174$		0			0
$175$	39778.2	−	17710.4i	1.29888	−	0.578298i
$176$		0			0
$177$	−43624.8	+	4585.15i	−1.39247	+	0.146355i
$178$		0			0
$179$	−3946.70	−	414.814i	−0.123176	−	0.0129464i	0.0427396	−	0.999086i	$-0.486391\pi$
$179$	−3946.70	−	414.814i	−0.123176	−	0.0129464i	−0.165916	+	0.986140i	$0.553058\pi$
$180$		0			0
$181$	11474.1	+	6624.57i	0.350236	+	0.202209i	0.664789	−	0.747031i	$-0.268521\pi$
$181$	11474.1	+	6624.57i	0.350236	+	0.202209i	−0.314553	+	0.949240i	$0.601855\pi$
$182$		0			0
$183$	37082.1	−	41183.8i	1.10729	−	1.22977i
$184$		0			0
$185$		−	2665.83i		−	0.0778913i
$186$		0			0
$187$	19536.4			0.558679
$188$		0			0
$189$	10386.2	+	9351.77i	0.290759	+	0.261800i
$190$		0			0
$191$	33014.5	−	57182.7i	0.904977	−	1.56747i	0.0840286	−	0.996463i	$-0.473221\pi$
$191$	33014.5	−	57182.7i	0.904977	−	1.56747i	0.820948	−	0.571003i	$-0.193445\pi$
$192$		0			0
$193$	−1056.86	+	10055.4i	−0.0283729	+	0.269950i	0.971134	+	0.238536i	$0.0766675\pi$
$193$	−1056.86	+	10055.4i	−0.0283729	+	0.269950i	−0.999506	+	0.0314135i	$0.989999\pi$
$194$		0			0
$195$	443.022	+	4215.07i	0.0116508	+	0.110850i
$196$		0			0
$197$	−16554.9	−	37183.0i	−0.426575	−	0.958102i	−0.991153	−	0.132723i	$-0.957628\pi$
$197$	−16554.9	−	37183.0i	−0.426575	−	0.958102i	0.564579	−	0.825379i	$-0.309039\pi$
$198$		0			0
$199$	−7148.41	+	33630.6i	−0.180511	+	0.849237i	0.790921	+	0.611918i	$0.209602\pi$
$199$	−7148.41	+	33630.6i	−0.180511	+	0.849237i	−0.971432	+	0.237318i	$0.923732\pi$
$200$		0			0
$201$	42480.4	−	13802.7i	1.05147	−	0.341643i
$202$		0			0
$203$	−9749.94	+	21898.7i	−0.236597	+	0.531406i
$204$		0			0
$205$	10638.8	−	2261.35i	0.253155	−	0.0538097i
$206$		0			0
$207$	−14934.1	+	13446.7i	−0.348528	+	0.313816i
$208$		0			0
$209$	22202.6	+	30559.3i	0.508290	+	0.699601i
$210$		0			0
$211$	−23401.3	−	40532.3i	−0.525624	−	0.910408i	−0.999555	−	0.0298455i	$-0.990498\pi$
$211$	−23401.3	−	40532.3i	−0.525624	−	0.910408i	0.473930	−	0.880562i	$-0.342835\pi$
$212$		0			0
$213$	17787.2	−	24482.0i	0.392056	−	0.539619i
$214$		0			0
$215$	5740.72	+	1865.27i	0.124191	+	0.0403520i
$216$		0			0
$217$	68500.5	−	2988.77i	1.45470	−	0.0634707i
$218$		0			0
$219$	−17328.3	+	53331.0i	−0.361300	+	1.11197i
$220$		0			0
$221$	−13266.3	−	9638.50i	−0.271621	−	0.197345i
$222$		0			0
$223$	2299.73	−	1327.75i	0.0462453	−	0.0266997i	−0.476699	−	0.879067i	$-0.658167\pi$
$223$	2299.73	−	1327.75i	0.0462453	−	0.0266997i	0.522944	+	0.852367i	$0.324834\pi$
$224$		0			0
$225$	−31981.9	+	23236.2i	−0.631741	+	0.458986i
$226$		0			0
$227$	−10586.3	−	11757.2i	−0.205443	−	0.228168i	0.631614	−	0.775283i	$-0.282393\pi$
$227$	−10586.3	−	11757.2i	−0.205443	−	0.228168i	−0.837057	+	0.547115i	$0.815726\pi$
$228$		0			0
$229$	−7191.72	−	33834.4i	−0.137139	−	0.645190i	−0.991990	−	0.126316i	$-0.959685\pi$
$229$	−7191.72	−	33834.4i	−0.137139	−	0.645190i	0.854851	−	0.518874i	$-0.173649\pi$
$230$		0			0
$231$	85794.4	+	38198.1i	1.60781	+	0.715844i
$232$		0			0
$233$	−14704.5	−	45255.7i	−0.270856	−	0.833608i	−0.990286	−	0.139044i	$-0.955597\pi$
$233$	−14704.5	−	45255.7i	−0.270856	−	0.833608i	0.719431	−	0.694564i	$-0.244403\pi$
$234$		0			0
$235$	3780.02	+	803.469i	0.0684477	+	0.0145490i
$236$		0			0
$237$	−66298.6	+	29518.0i	−1.18034	+	0.525522i
$238$		0			0
$239$	−72619.1	+	7632.58i	−1.27132	+	0.133621i	−0.716051	−	0.698048i	$-0.754052\pi$
$239$	−72619.1	+	7632.58i	−1.27132	+	0.133621i	−0.555271	+	0.831670i	$0.687385\pi$
$240$		0			0
$241$	110514.	+	11615.5i	1.90276	+	0.199988i	0.981831	−	0.189755i	$-0.0607694\pi$
$241$	110514.	+	11615.5i	1.90276	+	0.199988i	0.920924	+	0.389743i	$0.127436\pi$
$242$		0			0
$243$	−65850.9	−	38019.0i	−1.11519	−	0.643855i
$244$		0			0
$245$	6903.87	−	7667.52i	0.115017	−	0.127739i
$246$		0			0
$247$		−	31705.2i		−	0.519681i
$248$		0			0
$249$	56928.7			0.918191
$250$		0			0
$251$	60319.2	+	54311.6i	0.957432	+	0.862075i	0.990519	−	0.137377i	$-0.0438672\pi$
$251$	60319.2	+	54311.6i	0.957432	+	0.862075i	−0.0330870	+	0.999452i	$0.510534\pi$
$252$		0			0
$253$	16910.8	−	29290.3i	0.264194	−	0.457597i
$254$		0			0
$255$	−867.600	+	8254.66i	−0.0133426	+	0.126946i
$256$		0			0
$257$	−5126.19	−	48772.4i	−0.0776119	−	0.738428i	−0.962253	−	0.272156i	$-0.912263\pi$
$257$	−5126.19	−	48772.4i	−0.0776119	−	0.738428i	0.884641	−	0.466272i	$-0.154403\pi$
$258$		0			0
$259$	20166.5	+	45294.6i	0.300628	+	0.675222i
$260$		0			0
$261$	4524.80	−	21287.5i	0.0664229	−	0.312495i
$262$		0			0
$263$	−112152.	+	36440.5i	−1.62142	+	0.526832i	−0.972277	−	0.233832i	$-0.924873\pi$
$263$	−112152.	+	36440.5i	−1.62142	+	0.526832i	−0.649146	+	0.760664i	$0.724873\pi$
$264$		0			0
$265$	−1374.66	+	3087.53i	−0.0195750	+	0.0439662i
$266$		0			0
$267$	−4108.20	+	873.224i	−0.0576273	+	0.0122491i
$268$		0			0
$269$	−49076.0	+	44188.2i	−0.678210	+	0.610663i	−0.934511	−	0.355934i	$-0.884163\pi$
$269$	−49076.0	+	44188.2i	−0.678210	+	0.610663i	0.256301	+	0.966597i	$0.417496\pi$
$270$		0			0
$271$	32695.6	+	45001.7i	0.445196	+	0.612760i	0.971357	−	0.237625i	$-0.0763691\pi$
$271$	32695.6	+	45001.7i	0.445196	+	0.612760i	−0.526161	+	0.850385i	$0.676369\pi$
$272$		0			0
$273$	−39413.5	−	68266.1i	−0.528834	−	0.915967i
$274$		0			0
$275$	39106.9	−	53826.0i	0.517116	−	0.711749i
$276$		0			0
$277$	93007.8	+	30220.1i	1.21216	+	0.393854i	0.844221	−	0.535996i	$-0.180064\pi$
$277$	93007.8	+	30220.1i	1.21216	+	0.393854i	0.367939	+	0.929850i	$0.380064\pi$
$278$		0			0
$279$	−60267.4	+	15584.3i	−0.774238	+	0.200207i
$280$		0			0
$281$	35613.2	−	109606.i	0.451023	−	1.38811i	−0.424719	−	0.905325i	$-0.639627\pi$
$281$	35613.2	−	109606.i	0.451023	−	1.38811i	0.875742	−	0.482780i	$-0.160373\pi$
$282$		0			0
$283$	−118844.	−	86345.4i	−1.48390	−	1.07812i	−0.976273	−	0.216543i	$-0.930522\pi$
$283$	−118844.	−	86345.4i	−1.48390	−	1.07812i	−0.507630	−	0.861575i	$-0.669478\pi$
$284$		0			0
$285$	−13898.1	+	8024.07i	−0.171106	+	0.0987882i
$286$		0			0
$287$	−163656.	+	118903.i	−1.98686	+	1.44354i
$288$		0			0
$289$	34398.5	+	38203.4i	0.411854	+	0.457410i
$290$		0			0
$291$	−10084.9	−	47445.7i	−0.119093	−	0.560287i
$292$		0			0
$293$	74776.7	+	33292.7i	0.871026	+	0.387806i	0.793055	−	0.609150i	$-0.208489\pi$
$293$	74776.7	+	33292.7i	0.871026	+	0.387806i	0.0779709	+	0.996956i	$0.475156\pi$
$294$		0			0
$295$	4306.83	+	13255.1i	0.0494895	+	0.152313i
$296$		0			0
$297$	20888.5	+	4439.98i	0.236807	+	0.0503348i
$298$		0			0
$299$	−25934.0	+	11546.5i	−0.290086	+	0.129155i
$300$		0			0
$301$	−111650.	+	11734.9i	−1.23232	+	0.129522i
$302$		0			0
$303$	63436.0	+	6667.39i	0.690956	+	0.0726224i
$304$		0			0
$305$	−15249.0	−	8803.99i	−0.163923	−	0.0946411i
$306$		0			0
$307$	−72591.9	+	80621.4i	−0.770214	+	0.855409i	−0.992835	−	0.119496i	$-0.961872\pi$
$307$	−72591.9	+	80621.4i	−0.770214	+	0.855409i	0.222621	+	0.974905i	$0.428539\pi$
$308$		0			0
$309$		−	24845.5i		−	0.260214i
$310$		0			0
$311$	−131479.			−1.35937			−0.679684	−	0.733505i	$-0.737883\pi$
$311$	−131479.			−1.35937			−0.679684	+	0.733505i	$0.737883\pi$
$312$		0			0
$313$	95310.3	+	85817.8i	0.972862	+	0.875969i	0.992302	−	0.123842i	$-0.0395218\pi$
$313$	95310.3	+	85817.8i	0.972862	+	0.875969i	−0.0194403	+	0.999811i	$0.506188\pi$
$314$		0			0
$315$	−8864.75	+	15354.2i	−0.0893399	+	0.154741i
$316$		0			0
$317$	1544.91	−	14698.8i	0.0153739	−	0.146273i	−0.984142	−	0.177382i	$-0.943237\pi$
$317$	1544.91	−	14698.8i	0.0153739	−	0.146273i	0.999516	+	0.0311091i	$0.00990392\pi$
$318$		0			0
$319$	3828.63	+	36426.9i	0.0376237	+	0.357966i
$320$		0			0
$321$	101103.	+	227081.i	0.981193	+	2.20380i
$322$		0			0
$323$	12909.3	−	60733.6i	0.123737	−	0.582136i
$324$		0			0
$325$	−53111.2	+	17256.9i	−0.502828	+	0.163379i
$326$		0			0
$327$	−99196.3	+	222799.i	−0.927684	+	2.08361i
$328$		0			0
$329$	−70303.7	+	14943.5i	−0.649511	+	0.138058i
$330$		0			0
$331$	67073.2	−	60393.0i	0.612200	−	0.551227i	−0.303632	−	0.952789i	$-0.598199\pi$
$331$	67073.2	−	60393.0i	0.612200	−	0.551227i	0.915832	+	0.401562i	$0.131533\pi$
$332$		0			0
$333$	−26458.6	−	36417.1i	−0.238604	−	0.328410i
$334$		0			0
$335$	−7095.92	−	12290.5i	−0.0632294	−	0.109517i
$336$		0			0
$337$	32618.4	−	44895.4i	0.287212	−	0.395314i	−0.640894	−	0.767629i	$-0.721436\pi$
$337$	32618.4	−	44895.4i	0.287212	−	0.395314i	0.928106	+	0.372316i	$0.121436\pi$
$338$		0			0
$339$	276584.	+	89867.7i	2.40674	+	0.781996i
$340$		0			0
$341$	88361.6	−	56288.9i	0.759897	−	0.484076i
$342$		0			0
$343$	−6362.25	+	19581.0i	−0.0540783	+	0.166436i
$344$		0			0
$345$	11624.9	+	8446.01i	0.0976680	+	0.0709600i
$346$		0			0
$347$	121.498	−	70.1467i	0.00100904	−	0.000582571i	−0.499495	−	0.866317i	$-0.666481\pi$
$347$	121.498	−	70.1467i	0.00100904	−	0.000582571i	0.500504	+	0.865734i	$0.333148\pi$
$348$		0			0
$349$	−152912.	+	111097.i	−1.25542	+	0.912120i	−0.998524	−	0.0543182i	$-0.982701\pi$
$349$	−152912.	+	111097.i	−1.25542	+	0.912120i	−0.256901	+	0.966438i	$0.582701\pi$
$350$		0			0
$351$	−11993.9	−	13320.5i	−0.0973520	−	0.108120i
$352$		0			0
$353$	14514.3	+	68284.2i	0.116478	+	0.547988i	0.997228	+	0.0744056i	$0.0237059\pi$
$353$	14514.3	+	68284.2i	0.116478	+	0.547988i	−0.880750	+	0.473582i	$0.842961\pi$
$354$		0			0
$355$	−8783.65	−	3910.73i	−0.0696976	−	0.0310314i
$356$		0			0
$357$	−47703.6	−	146817.i	−0.374296	−	1.15196i
$358$		0			0
$359$	−178690.	−	37981.8i	−1.38647	−	0.294704i	−0.546558	−	0.837421i	$-0.684062\pi$
$359$	−178690.	−	37981.8i	−1.38647	−	0.294704i	−0.839916	+	0.542717i	$0.817396\pi$
$360$		0			0
$361$	−9382.42	+	4177.32i	−0.0719947	+	0.0320541i
$362$		0			0
$363$	−33090.9	+	3478.00i	−0.251128	+	0.0263947i
$364$		0			0
$365$	17719.2	+	1862.36i	0.133002	+	0.0139791i
$366$		0			0
$367$	38800.9	+	22401.7i	0.288078	+	0.166322i	0.637075	−	0.770802i	$-0.280144\pi$
$367$	38800.9	+	22401.7i	0.288078	+	0.166322i	−0.348997	+	0.937124i	$0.613478\pi$
$368$		0			0
$369$	122890.	−	136483.i	0.902532	−	1.00236i
$370$		0			0
$371$		−	62858.6i		−	0.456685i
$372$		0			0
$373$	51167.4			0.367770			0.183885	−	0.982948i	$-0.441133\pi$
$373$	51167.4			0.367770			0.183885	+	0.982948i	$0.441133\pi$
$374$		0			0
$375$	42518.9	+	38284.2i	0.302357	+	0.272243i
$376$		0			0
$377$	15371.8	−	26624.7i	0.108154	−	0.187328i
$378$		0			0
$379$	23871.1	−	227118.i	0.166186	−	1.58115i	−0.520284	−	0.853993i	$-0.674174\pi$
$379$	23871.1	−	227118.i	0.166186	−	1.58115i	0.686470	−	0.727158i	$-0.259159\pi$
$380$		0			0
$381$	−14151.4	−	134641.i	−0.0974874	−	0.927530i
$382$		0			0
$383$	−80059.5	−	179817.i	−0.545777	−	1.22584i	−0.950308	−	0.311311i	$-0.899232\pi$
$383$	−80059.5	−	179817.i	−0.545777	−	1.22584i	0.404531	−	0.914524i	$-0.367435\pi$
$384$		0			0
$385$	6203.89	−	29187.0i	0.0418545	−	0.196910i
$386$		0			0
$387$	96935.2	−	31496.1i	0.647231	−	0.210298i
$388$		0			0
$389$	31201.9	−	70080.5i	0.206197	−	0.463125i	−0.780612	−	0.625016i	$-0.785093\pi$
$389$	31201.9	−	70080.5i	0.206197	−	0.463125i	0.986809	+	0.161891i	$0.0517592\pi$
$390$		0			0
$391$	−54379.8	+	11558.8i	−0.355700	+	0.0756064i
$392$		0			0
$393$	−127364.	+	114679.i	−0.824638	+	0.742507i
$394$		0			0
$395$	13553.4	+	18654.7i	0.0868670	+	0.119562i
$396$		0			0
$397$	−82729.5	−	143292.i	−0.524903	−	0.909159i	−0.999579	−	0.0289988i	$-0.990768\pi$
$397$	−82729.5	−	143292.i	−0.524903	−	0.909159i	0.474676	−	0.880161i	$-0.342565\pi$
$398$		0			0
$399$	175439.	−	241472.i	1.10200	−	1.51677i
$400$		0			0
$401$	275651.	+	89564.3i	1.71423	+	0.556988i	0.991029	−	0.133645i	$-0.0426683\pi$
$401$	275651.	+	89564.3i	1.71423	+	0.556988i	0.723205	+	0.690634i	$0.242668\pi$
$402$		0			0
$403$	−87772.8	−	5371.01i	−0.540443	−	0.0330709i
$404$		0			0
$405$	−9023.52	+	27771.5i	−0.0550131	+	0.169313i
$406$		0			0
$407$	61290.6	+	44530.2i	0.370003	+	0.268823i
$408$		0			0
$409$	−108797.	+	62814.0i	−0.650385	+	0.375500i	−0.788604	−	0.614902i	$-0.789196\pi$
$409$	−108797.	+	62814.0i	−0.650385	+	0.375500i	0.138219	+	0.990402i	$0.455862\pi$
$410$		0			0
$411$	149251.	−	108437.i	0.883554	−	0.641940i
$412$		0			0
$413$	−173448.	−	192634.i	−1.01688	−	1.12936i
$414$		0			0
$415$	−3760.68	−	17692.6i	−0.0218359	−	0.102730i
$416$		0			0
$417$	342088.	+	152308.i	1.96728	+	0.875890i
$418$		0			0
$419$	5378.85	+	16554.4i	0.0306381	+	0.0942943i	0.965206	−	0.261490i	$-0.0842138\pi$
$419$	5378.85	+	16554.4i	0.0306381	+	0.0942943i	−0.934568	+	0.355784i	$0.884214\pi$
$420$		0			0
$421$	49297.9	+	10478.6i	0.278140	+	0.0591205i	0.344870	−	0.938651i	$-0.387923\pi$
$421$	49297.9	+	10478.6i	0.278140	+	0.0591205i	−0.0667294	+	0.997771i	$0.521256\pi$
$422$		0			0
$423$	59612.2	−	26541.1i	0.333161	−	0.148333i
$424$		0			0
$425$	−108765.	+	11431.7i	−0.602159	+	0.0632894i
$426$		0			0
$427$	325692.	+	34231.6i	1.78629	+	0.187747i
$428$		0			0
$429$	−104310.	−	60223.3i	−0.566774	−	0.327227i
$430$		0			0
$431$	141013.	−	156611.i	0.759111	−	0.843078i	−0.232465	−	0.972605i	$-0.574679\pi$
$431$	141013.	−	156611.i	0.759111	−	0.843078i	0.991576	+	0.129526i	$0.0413457\pi$
$432$		0			0
$433$			238669.i			1.27298i	0.771286	+	0.636489i	$0.219614\pi$
$433$			238669.i			1.27298i	−0.771286	+	0.636489i	$0.780386\pi$
$434$		0			0
$435$	−15561.4			−0.0822374
$436$		0			0
$437$	−79881.5	−	71925.6i	−0.418296	−	0.376635i
$438$		0			0
$439$	92212.0	−	159716.i	0.478474	−	0.828742i	−0.521221	−	0.853422i	$-0.674523\pi$
$439$	92212.0	−	159716.i	0.478474	−	0.828742i	0.999695	+	0.0246799i	$0.00785666\pi$
$440$		0			0
$441$	18210.9	−	173265.i	0.0936384	−	0.890910i
$442$		0			0
$443$	19481.7	+	185356.i	0.0992704	+	0.944495i	0.924882	+	0.380255i	$0.124164\pi$
$443$	19481.7	+	185356.i	0.0992704	+	0.944495i	−0.825611	+	0.564240i	$0.809169\pi$
$444$		0			0
$445$	542.770	+	1219.08i	0.00274092	+	0.00615620i
$446$		0			0
$447$	−40536.0	+	190707.i	−0.202874	+	0.954446i
$448$		0			0
$449$	−57150.0	+	18569.2i	−0.283481	+	0.0921085i	−0.447306	−	0.894381i	$-0.647617\pi$
$449$	−57150.0	+	18569.2i	−0.283481	+	0.0921085i	0.163825	+	0.986489i	$0.447617\pi$
$450$		0			0
$451$	−125721.	+	282373.i	−0.618092	+	1.38826i
$452$		0			0
$453$	−201112.	+	42747.7i	−0.980036	+	0.208313i
$454$		0			0
$455$	−18612.5	+	16758.7i	−0.0899045	+	0.0809503i
$456$		0			0
$457$	−23930.7	−	32937.8i	−0.114584	−	0.157711i	0.747873	−	0.663842i	$-0.231075\pi$
$457$	−23930.7	−	32937.8i	−0.114584	−	0.157711i	−0.862457	+	0.506131i	$0.831075\pi$
$458$		0			0
$459$	−17551.4	−	30400.0i	−0.0833080	−	0.144294i
$460$		0			0
$461$	−152512.	+	209915.i	−0.717632	+	0.987736i	0.281967	+	0.959424i	$0.409013\pi$
$461$	−152512.	+	209915.i	−0.717632	+	0.987736i	−0.999599	+	0.0283117i	$0.990987\pi$
$462$		0			0
$463$	−260860.	−	84758.5i	−1.21687	−	0.395386i	−0.370931	−	0.928661i	$-0.620961\pi$
$463$	−260860.	−	84758.5i	−1.21687	−	0.395386i	−0.845942	+	0.533275i	$0.820961\pi$
$464$		0			0
$465$	19859.5	+	39834.9i	0.0918463	+	0.184229i
$466$		0			0
$467$	12684.1	−	39037.7i	0.0581603	−	0.178999i	−0.917756	−	0.397145i	$-0.870001\pi$
$467$	12684.1	−	39037.7i	0.0581603	−	0.178999i	0.975916	+	0.218146i	$0.0700009\pi$
$468$		0			0
$469$	213540.	+	155146.i	0.970810	+	0.705335i
$470$		0			0
$471$	277997.	−	160502.i	1.25314	−	0.723499i
$472$		0			0
$473$	−138778.	+	100828.i	−0.620296	+	0.450671i
$474$		0			0
$475$	−141490.	−	157140.i	−0.627101	−	0.696467i
$476$		0			0
$477$	11865.2	+	55821.4i	0.0521481	+	0.245337i
$478$		0			0
$479$	−131535.	−	58563.3i	−0.573286	−	0.255244i	0.0995528	−	0.995032i	$-0.468259\pi$
$479$	−131535.	−	58563.3i	−0.573286	−	0.255244i	−0.672839	+	0.739789i	$0.734925\pi$
$480$		0			0
$481$	−19650.1	−	60476.7i	−0.0849325	−	0.261395i
$482$		0			0
$483$	−261409.	−	55564.3i	−1.12054	−	0.238178i
$484$		0			0
$485$	−14079.2	+	6268.47i	−0.0598543	+	0.0266488i
$486$		0			0
$487$	98460.3	−	10348.6i	0.415148	−	0.0436339i	0.105348	−	0.994435i	$-0.466404\pi$
$487$	98460.3	−	10348.6i	0.415148	−	0.0436339i	0.309801	+	0.950802i	$0.399738\pi$
$488$		0			0
$489$	209150.	+	21982.6i	0.874664	+	0.0919309i
$490$		0			0
$491$	417476.	+	241030.i	1.73168	+	0.999788i	0.876143	+	0.482052i	$0.160108\pi$
$491$	417476.	+	241030.i	1.73168	+	0.999788i	0.855541	+	0.517736i	$0.173225\pi$
$492$		0			0
$493$	40286.5	−	44742.6i	0.165754	−	0.184089i
$494$		0			0
$495$			27090.5i			0.110562i
$496$		0			0
$497$	178825.			0.723962
$498$		0			0
$499$	−50571.8	−	45535.1i	−0.203099	−	0.182871i	0.561304	−	0.827609i	$-0.310300\pi$
$499$	−50571.8	−	45535.1i	−0.203099	−	0.182871i	−0.764403	+	0.644738i	$0.776966\pi$
$500$		0			0
$501$	−279637.	+	484346.i	−1.11409	+	1.92966i
$502$		0			0
$503$	−31201.7	+	296864.i	−0.123322	+	1.17333i	0.741392	+	0.671072i	$0.234166\pi$
$503$	−31201.7	+	296864.i	−0.123322	+	1.17333i	−0.864715	+	0.502263i	$0.832501\pi$
$504$		0			0
$505$	−2118.42	−	20155.4i	−0.00830671	−	0.0790331i
$506$		0			0
$507$	−99138.7	−	222669.i	−0.385680	−	0.866252i
$508$		0			0
$509$	21965.9	−	103342.i	0.0847841	−	0.398878i	−0.915207	−	0.402983i	$-0.867973\pi$
$509$	21965.9	−	103342.i	0.0847841	−	0.398878i	0.999992	+	0.00410517i	$0.00130672\pi$
$510$		0			0
$511$	−315152.	+	102399.i	−1.20692	+	0.392152i
$512$		0			0
$513$	27605.5	−	62002.9i	0.104896	−	0.235601i
$514$		0			0
$515$	−7721.62	+	1641.28i	−0.0291135	+	0.00618826i
$516$		0			0
$517$	−81614.5	+	73486.0i	−0.305342	+	0.274931i
$518$		0			0
$519$	200247.	+	275617.i	0.743416	+	1.02322i
$520$		0			0
$521$	−59873.3	−	103704.i	−0.220576	−	0.382048i	0.734407	−	0.678709i	$-0.237460\pi$
$521$	−59873.3	−	103704.i	−0.220576	−	0.382048i	−0.954983	+	0.296661i	$0.904127\pi$
$522$		0			0
$523$	88511.4	−	121826.i	0.323591	−	0.445384i	−0.615969	−	0.787771i	$-0.711235\pi$
$523$	88511.4	−	121826.i	0.323591	−	0.445384i	0.939559	+	0.342386i	$0.111235\pi$
$524$		0			0
$525$	−499993.	−	162458.i	−1.81403	−	0.589416i
$526$		0			0
$527$	−165948.	−	46026.8i	−0.597519	−	0.165726i
$528$		0			0
$529$	56734.1	−	174610.i	0.202737	−	0.623960i
$530$		0			0
$531$	190392.	+	138328.i	0.675241	+	0.490591i
$532$		0			0
$533$	224682.	−	129720.i	0.790887	−	0.456619i
$534$		0			0
$535$	63894.7	−	46422.2i	0.223233	−	0.162188i
$536$		0			0
$537$	32060.7	+	35607.0i	0.111180	+	0.123477i
$538$		0			0
$539$	60962.7	+	286807.i	0.209839	+	0.987215i
$540$		0			0
$541$	−152245.	−	67784.0i	−0.520175	−	0.231597i	0.129817	−	0.991538i	$-0.458561\pi$
$541$	−152245.	−	67784.0i	−0.520175	−	0.231597i	−0.649992	+	0.759941i	$0.725228\pi$
$542$		0			0
$543$	−49432.6	−	152138.i	−0.167654	−	0.515986i
$544$		0			0
$545$	75795.4	+	16110.8i	0.255182	+	0.0542406i
$546$		0			0
$547$	−6648.51	+	2960.11i	−0.0222203	+	0.00989311i	−0.417817	−	0.908531i	$-0.637205\pi$
$547$	−6648.51	+	2960.11i	−0.0222203	+	0.00989311i	0.395596	+	0.918424i	$0.370538\pi$
$548$		0			0
$549$	−295692.	+	31078.4i	−0.981057	+	0.103113i
$550$		0			0
$551$	115772.	+	12168.1i	0.381328	+	0.0400792i
$552$		0			0
$553$	−371402.	−	214429.i	−1.21449	−	0.701187i
$554$		0			0
$555$	−21537.1	+	23919.3i	−0.0699198	+	0.0776538i
$556$		0			0
$557$			65738.0i			0.211888i	0.994372	+	0.105944i	$0.0337864\pi$
$557$			65738.0i			0.211888i	−0.994372	+	0.105944i	$0.966214\pi$
$558$		0			0
$559$	143982.			0.460771
$560$		0			0
$561$	−175292.	−	157834.i	−0.556976	−	0.501503i
$562$		0			0
$563$	−269707.	+	467146.i	−0.850894	+	1.47379i	0.0295088	+	0.999565i	$0.490606\pi$
$563$	−269707.	+	467146.i	−0.850894	+	1.47379i	−0.880403	+	0.474227i	$0.842728\pi$
$564$		0			0
$565$	9658.55	−	91895.0i	0.0302563	−	0.287869i
$566$		0			0
$567$	−56769.1	−	540122.i	−0.176582	−	1.68006i
$568$		0			0
$569$	−155176.	−	348530.i	−0.479291	−	1.07650i	−0.977785	−	0.209612i	$-0.932780\pi$
$569$	−155176.	−	348530.i	−0.479291	−	1.07650i	0.498494	−	0.866893i	$-0.333887\pi$
$570$		0			0
$571$	−61728.2	+	290408.i	−0.189326	+	0.890711i	0.776216	+	0.630467i	$0.217136\pi$
$571$	−61728.2	+	290408.i	−0.189326	+	0.890711i	−0.965543	+	0.260244i	$0.916197\pi$
$572$		0			0
$573$	−758200.	+	246354.i	−2.30927	+	0.750327i
$574$		0			0
$575$	−77008.0	+	172963.i	−0.232916	+	0.523139i
$576$		0			0
$577$	231614.	−	49231.2i	0.695687	−	0.147873i	0.153522	−	0.988145i	$-0.450938\pi$
$577$	231614.	−	49231.2i	0.695687	−	0.147873i	0.542165	+	0.840272i	$0.317605\pi$
$578$		0			0
$579$	90719.3	−	81684.0i	0.270609	−	0.243658i
$580$		0			0
$581$	197738.	+	272163.i	0.585785	+	0.806263i
$582$		0			0
$583$	−48023.6	−	83179.3i	−0.141292	−	0.244725i
$584$		0			0
$585$	13365.4	−	18395.8i	0.0390543	−	0.0537536i
$586$		0			0
$587$	362070.	+	117644.i	1.05079	+	0.341423i	0.782979	−	0.622048i	$-0.213699\pi$
$587$	362070.	+	117644.i	1.05079	+	0.341423i	0.267813	+	0.963471i	$0.413699\pi$
$588$		0			0
$589$	−116600.	−	311888.i	−0.336098	−	0.899016i
$590$		0			0
$591$	−151859.	+	467373.i	−0.434775	+	1.33810i
$592$		0			0
$593$	517684.	+	376120.i	1.47216	+	1.06959i	0.979980	+	0.199097i	$0.0638008\pi$
$593$	517684.	+	376120.i	1.47216	+	1.06959i	0.492183	+	0.870492i	$0.336199\pi$
$594$		0			0
$595$	−42477.2	+	24524.2i	−0.119984	+	0.0692725i
$596$		0			0
$597$	335839.	−	244001.i	0.942285	−	0.684610i
$598$		0			0
$599$	364528.	+	404849.i	1.01596	+	1.12834i	0.991692	+	0.128633i	$0.0410591\pi$
$599$	364528.	+	404849.i	1.01596	+	1.12834i	0.0242688	+	0.999705i	$0.492274\pi$
$600$		0			0
$601$	149282.	+	702317.i	0.413294	+	1.94439i	0.314377	+	0.949298i	$0.398205\pi$
$601$	149282.	+	702317.i	0.413294	+	1.94439i	0.0989171	+	0.995096i	$0.468462\pi$
$602$		0			0
$603$	−218919.	−	97469.1i	−0.602073	−	0.268060i
$604$		0			0
$605$	3266.88	+	10054.4i	0.00892529	+	0.0274692i
$606$		0			0
$607$	627036.	+	133281.i	1.70182	+	0.361734i	0.953452	−	0.301545i	$-0.0975022\pi$
$607$	627036.	+	133281.i	1.70182	+	0.361734i	0.748373	+	0.663279i	$0.230836\pi$
$608$		0			0
$609$	264400.	−	117719.i	0.712898	−	0.317403i
$610$		0			0
$611$	91675.6	−	9635.49i	0.245568	−	0.0258102i
$612$		0			0
$613$	47820.5	+	5026.14i	0.127260	+	0.0133756i	0.167945	−	0.985796i	$-0.446287\pi$
$613$	47820.5	+	5026.14i	0.127260	+	0.0133756i	−0.0406841	+	0.999172i	$0.512954\pi$
$614$		0			0
$615$	−113727.	−	65660.2i	−0.300686	−	0.173601i
$616$		0			0
$617$	−63109.0	+	70089.7i	−0.165776	+	0.184113i	−0.820309	−	0.571921i	$-0.806199\pi$
$617$	−63109.0	+	70089.7i	−0.165776	+	0.184113i	0.654533	+	0.756033i	$0.272865\pi$
$618$		0			0
$619$			141992.i			0.370582i	0.982684	+	0.185291i	$0.0593227\pi$
$619$			141992.i			0.370582i	−0.982684	+	0.185291i	$0.940677\pi$
$620$		0			0
$621$	−60770.1			−0.157582
$622$		0			0
$623$	−18444.2	−	16607.2i	−0.0475208	−	0.0427879i
$624$		0			0
$625$	−181624.	+	314582.i	−0.464958	+	0.805331i
$626$		0			0
$627$	47671.9	−	453568.i	0.121263	−	1.15374i
$628$		0			0
$629$	−13017.0	−	123848.i	−0.0329010	−	0.313032i
$630$		0			0
$631$	−126990.	−	285224.i	−0.318941	−	0.716354i	0.680931	−	0.732348i	$-0.261575\pi$
$631$	−126990.	−	285224.i	−0.318941	−	0.716354i	−0.999872	+	0.0159937i	$0.994909\pi$
$632$		0			0
$633$	−117488.	+	552736.i	−0.293214	+	1.37946i
$634$		0			0
$635$	−40909.7	+	13292.4i	−0.101456	+	0.0329651i
$636$		0			0
$637$	100102.	−	224833.i	0.246698	−	0.554092i
$638$		0			0
$639$	−158805.	+	33755.1i	−0.388922	+	0.0826679i
$640$		0			0
$641$	108326.	−	97537.0i	0.263643	−	0.237385i	−0.526698	−	0.850052i	$-0.676570\pi$
$641$	108326.	−	97537.0i	0.263643	−	0.237385i	0.790341	+	0.612667i	$0.209904\pi$
$642$		0			0
$643$	−256026.	−	352389.i	−0.619244	−	0.852316i	0.378054	−	0.925784i	$-0.376593\pi$
$643$	−256026.	−	352389.i	−0.619244	−	0.852316i	−0.997298	+	0.0734676i	$0.976593\pi$
$644$		0			0
$645$	−36439.5	−	63115.1i	−0.0875898	−	0.151710i
$646$		0			0
$647$	318528.	−	438417.i	0.760921	−	1.04732i	−0.236216	−	0.971701i	$-0.575907\pi$
$647$	318528.	−	438417.i	0.760921	−	1.04732i	0.997137	−	0.0756170i	$-0.0240926\pi$
$648$		0			0
$649$	−376691.	−	122394.i	−0.894326	−	0.290584i
$650$		0			0
$651$	−638771.	−	526594.i	−1.50724	−	1.24255i
$652$		0			0
$653$	238987.	−	735525.i	0.560463	−	1.72493i	−0.120598	−	0.992701i	$-0.538481\pi$
$653$	238987.	−	735525.i	0.560463	−	1.72493i	0.681061	−	0.732227i	$-0.261519\pi$
$654$		0			0
$655$	44054.3	+	32007.3i	0.102685	+	0.0746048i
$656$		0			0
$657$	260541.	−	150423.i	0.603594	−	0.348485i
$658$		0			0
$659$	632127.	−	459267.i	1.45557	−	1.05753i	0.471081	−	0.882090i	$-0.343864\pi$
$659$	632127.	−	459267.i	1.45557	−	1.05753i	0.984489	−	0.175444i	$-0.0561361\pi$
$660$		0			0
$661$	218530.	+	242702.i	0.500160	+	0.555484i	0.939372	−	0.342900i	$-0.111409\pi$
$661$	218530.	+	242702.i	0.500160	+	0.555484i	−0.439212	+	0.898383i	$0.644742\pi$
$662$		0			0
$663$	41163.6	+	193659.i	0.0936453	+	0.440566i
$664$		0			0
$665$	−86635.3	−	38572.5i	−0.195908	−	0.0872237i
$666$		0			0
$667$	−32209.1	−	99129.4i	−0.0723981	−	0.222818i
$668$		0			0
$669$	−31361.3	−	6666.05i	−0.0700716	−	0.0148942i
$670$		0			0
$671$	457134.	−	203529.i	1.01531	−	0.452045i
$672$		0			0
$673$	−22584.0	+	2373.67i	−0.0498621	+	0.00524072i	−0.129427	−	0.991589i	$-0.541314\pi$
$673$	−22584.0	+	2373.67i	−0.0498621	+	0.00524072i	0.0795646	+	0.996830i	$0.474647\pi$
$674$		0			0
$675$	−118890.	−	12495.9i	−0.260939	−	0.0274258i
$676$		0			0
$677$	−442263.	−	255341.i	−0.964947	−	0.557113i	−0.0672551	−	0.997736i	$-0.521424\pi$
$677$	−442263.	−	255341.i	−0.964947	−	0.557113i	−0.897692	+	0.440623i	$0.854757\pi$
$678$		0			0
$679$	191798.	−	213013.i	0.416010	−	0.462026i
$680$		0			0
$681$			191018.i			0.411890i
$682$		0			0
$683$	698442.			1.49723			0.748616	−	0.663004i	$-0.230719\pi$
$683$	698442.			1.49723			0.748616	+	0.663004i	$0.230719\pi$
$684$		0			0
$685$	−43560.1	−	39221.7i	−0.0928341	−	0.0835882i
$686$		0			0
$687$	−208818.	+	361683.i	−0.442439	+	0.766327i
$688$		0			0
$689$	−8426.84	+	80176.0i	−0.0177511	+	0.168891i
$690$		0			0
$691$	−94401.2	−	898168.i	−0.197707	−	1.88105i	−0.422091	−	0.906554i	$-0.638704\pi$
$691$	−94401.2	−	898168.i	−0.197707	−	1.88105i	0.224384	−	0.974501i	$-0.427963\pi$
$692$		0			0
$693$	−204934.	−	460289.i	−0.426724	−	0.958438i
$694$		0			0
$695$	24736.8	−	116377.i	0.0512122	−	0.240935i
$696$		0			0
$697$	483213.	−	157006.i	0.994657	−	0.323184i
$698$		0			0
$699$	−233681.	+	524856.i	−0.478266	+	1.07420i
$700$		0			0
$701$	190359.	−	40462.0i	0.387379	−	0.0823401i	−0.0101050	−	0.999949i	$-0.503217\pi$
$701$	190359.	−	40462.0i	0.387379	−	0.0823401i	0.397484	+	0.917609i	$0.369883\pi$
$702$		0			0
$703$	178932.	−	161111.i	0.362058	−	0.325999i
$704$		0			0
$705$	−27425.3	−	37747.7i	−0.0551790	−	0.0759473i
$706$		0			0
$707$	188465.	+	326431.i	0.377044	+	0.653060i
$708$		0			0
$709$	−163603.	+	225180.i	−0.325461	+	0.447959i	−0.940125	−	0.340830i	$-0.889292\pi$
$709$	−163603.	+	225180.i	−0.325461	+	0.447959i	0.614664	+	0.788789i	$0.289292\pi$
$710$		0			0
$711$	370298.	+	120317.i	0.732508	+	0.238006i
$712$		0			0
$713$	−212652.	+	208960.i	−0.418302	+	0.411040i
$714$		0			0
$715$	−11825.9	+	36396.2i	−0.0231324	+	0.0711942i
$716$		0			0
$717$	713243.	+	518201.i	1.38739	+	1.00800i
$718$		0			0
$719$	270787.	−	156339.i	0.523805	−	0.302419i	−0.214685	−	0.976683i	$-0.568872\pi$
$719$	270787.	−	156339.i	0.523805	−	0.302419i	0.738490	+	0.674264i	$0.235539\pi$
$720$		0			0
$721$	118781.	−	86299.1i	0.228494	−	0.166011i
$722$		0			0
$723$	−897753.	−	997055.i	−1.71743	−	1.90740i
$724$		0			0
$725$	−42630.1	−	200559.i	−0.0811036	−	0.381563i
$726$		0			0
$727$	−285354.	−	127048.i	−0.539903	−	0.240380i	0.118622	−	0.992940i	$-0.462152\pi$
$727$	−285354.	−	127048.i	−0.539903	−	0.240380i	−0.658524	+	0.752559i	$0.728819\pi$
$728$		0			0
$729$	93168.7	+	286744.i	0.175313	+	0.539559i
$730$		0			0
$731$	275808.	+	58624.9i	0.516146	+	0.109710i
$732$		0			0
$733$	683877.	−	304482.i	1.27283	−	0.566700i	0.344614	−	0.938745i	$-0.388010\pi$
$733$	683877.	−	304482.i	1.27283	−	0.566700i	0.928215	+	0.372045i	$0.121343\pi$
$734$		0			0
$735$	−123891.	+	13021.4i	−0.229332	+	0.0241037i
$736$		0			0
$737$	401104.	+	42157.7i	0.738451	+	0.0776143i
$738$		0			0
$739$	61022.2	+	35231.2i	0.111738	+	0.0645117i	0.554827	−	0.831966i	$-0.312784\pi$
$739$	61022.2	+	35231.2i	0.111738	+	0.0645117i	−0.443090	+	0.896477i	$0.646118\pi$
$740$		0			0
$741$	−256144.	+	284477.i	−0.466496	+	0.518097i
$742$		0			0
$743$		−	395574.i		−	0.716557i	−0.933615	−	0.358278i	$-0.883364\pi$
$743$		−	395574.i		−	0.716557i	0.933615	−	0.358278i	$-0.116636\pi$
$744$		0			0
$745$	61946.7			0.111611
$746$		0			0
$747$	−226974.	−	204368.i	−0.406757	−	0.366246i
$748$		0			0
$749$	−734448.	+	1.27210e6i	−1.30917	+	2.26756i
$750$		0			0
$751$	54770.7	−	521109.i	0.0971111	−	0.923950i	−0.832156	−	0.554542i	$-0.812894\pi$
$751$	54770.7	−	521109.i	0.0971111	−	0.923950i	0.929267	−	0.369408i	$-0.120440\pi$
$752$		0			0
$753$	−102438.	−	974629.i	−0.180663	−	1.71889i
$754$		0			0
$755$	26570.7	+	59678.8i	0.0466133	+	0.104695i
$756$		0			0
$757$	−229588.	+	1.08013e6i	−0.400643	+	1.88488i	0.0615635	+	0.998103i	$0.480391\pi$
$757$	−229588.	+	1.08013e6i	−0.400643	+	1.88488i	−0.462206	+	0.886773i	$0.652942\pi$
$758$		0			0
$759$	−388367.	+	126188.i	−0.674154	+	0.219046i
$760$		0			0
$761$	−200162.	+	449572.i	−0.345631	+	0.776300i	0.654170	+	0.756348i	$0.273018\pi$
$761$	−200162.	+	449572.i	−0.345631	+	0.776300i	−0.999801	+	0.0199523i	$0.993649\pi$
$762$		0			0
$763$	−1.40970e6	+	299641.i	−2.42146	+	0.514697i
$764$		0			0
$765$	33092.5	−	29796.6i	0.0565466	−	0.0509148i
$766$		0			0
$767$	195408.	+	268956.i	0.332164	+	0.457184i
$768$		0			0
$769$	−148110.	−	256534.i	−0.250456	−	0.433803i	0.713195	−	0.700965i	$-0.247247\pi$
$769$	−148110.	−	256534.i	−0.250456	−	0.433803i	−0.963651	+	0.267163i	$0.913914\pi$
$770$		0			0
$771$	−348034.	+	479028.i	−0.585481	+	0.805846i
$772$		0			0
$773$	−436759.	−	141911.i	−0.730941	−	0.237497i	−0.0801809	−	0.996780i	$-0.525550\pi$
$773$	−436759.	−	141911.i	−0.730941	−	0.237497i	−0.650760	+	0.759283i	$0.725550\pi$
$774$		0			0
$775$	−458997.	+	365080.i	−0.764199	+	0.607834i
$776$		0			0
$777$	184987.	−	569332.i	0.306408	−	0.943026i
$778$		0			0
$779$	794749.	+	577419.i	1.30965	+	0.951516i
$780$		0			0
$781$	236635.	−	136621.i	0.387951	−	0.223984i
$782$		0			0
$783$	53243.1	−	38683.3i	0.0868439	−	0.0630958i
$784$		0			0
$785$	−68246.0	−	75794.8i	−0.110748	−	0.122999i
$786$		0			0
$787$	121462.	+	571434.i	0.196106	+	0.922607i	0.960591	+	0.277966i	$0.0896601\pi$
$787$	121462.	+	571434.i	0.196106	+	0.922607i	−0.764485	+	0.644642i	$0.777007\pi$
$788$		0			0
$789$	1.30069e6	+	579106.i	2.08940	+	0.930259i
$790$		0			0
$791$	531060.	+	1.63444e6i	0.848772	+	2.61225i
$792$		0			0
$793$	−410831.	−	87324.8i	−0.653306	−	0.138864i
$794$		0			0
$795$	37278.1	−	16597.3i	0.0589821	−	0.0262605i
$796$		0			0
$797$	−444186.	+	46685.8i	−0.699275	+	0.0734968i	−0.447493	−	0.894287i	$-0.647683\pi$
$797$	−444186.	+	46685.8i	−0.699275	+	0.0734968i	−0.251782	+	0.967784i	$0.581017\pi$
$798$		0			0
$799$	179534.	+	18869.8i	0.281225	+	0.0295580i
$800$		0			0
$801$	19514.1	+	11266.5i	0.0304147	+	0.0175599i
$802$		0			0
$803$	−338801.	+	376276.i	−0.525428	+	0.583547i
$804$		0			0
$805$			84912.7i			0.131033i
$806$		0			0
$807$	797331.			1.22431
$808$		0			0
$809$	−566722.	−	510279.i	−0.865911	−	0.779670i	0.110887	−	0.993833i	$-0.464631\pi$
$809$	−566722.	−	510279.i	−0.865911	−	0.779670i	−0.976798	+	0.214163i	$0.931298\pi$
$810$		0			0
$811$	−377009.	+	652999.i	−0.573205	+	0.992820i	0.423029	+	0.906116i	$0.360967\pi$
$811$	−377009.	+	652999.i	−0.573205	+	0.992820i	−0.996234	+	0.0867042i	$0.972367\pi$
$812$		0			0
$813$	70201.9	−	667926.i	0.106211	−	1.01053i
$814$		0			0
$815$	−6984.50	−	66453.1i	−0.0105153	−	0.100046i
$816$		0			0
$817$	221746.	+	498050.i	0.332209	+	0.746155i
$818$		0			0
$819$	−87927.5	+	413666.i	−0.131086	+	0.616712i
$820$		0			0
$821$	1.03395e6	−	335952.i	1.53396	−	0.498415i	0.584260	−	0.811566i	$-0.301385\pi$
$821$	1.03395e6	−	335952.i	1.53396	−	0.498415i	0.949703	+	0.313151i	$0.101385\pi$
$822$		0			0
$823$	−195381.	+	438834.i	−0.288459	+	0.647889i	−0.998410	−	0.0563616i	$-0.982050\pi$
$823$	−195381.	+	438834.i	−0.288459	+	0.647889i	0.709952	+	0.704250i	$0.248717\pi$
$824$		0			0
$825$	−785746.	+	167015.i	−1.15445	+	0.245385i
$826$		0			0
$827$	−748957.	+	674364.i	−1.09508	+	0.986015i	−0.999955	−	0.00945040i	$-0.996992\pi$
$827$	−748957.	+	674364.i	−1.09508	+	0.986015i	−0.0951252	+	0.995465i	$0.530325\pi$
$828$		0			0
$829$	−644427.	−	886978.i	−0.937702	−	1.29064i	−0.956778	−	0.290818i	$-0.906073\pi$
$829$	−644427.	−	886978.i	−0.937702	−	1.29064i	0.0190764	−	0.999818i	$-0.493927\pi$
$830$		0			0
$831$	−590372.	−	1.02255e6i	−0.854917	−	1.48076i
$832$		0			0
$833$	283298.	−	389926.i	0.408276	−	0.561943i
$834$		0			0
$835$	169000.	+	54911.5i	0.242390	+	0.0787572i
$836$		0			0
$837$	−166973.	−	86926.7i	−0.238339	−	0.124080i
$838$		0			0
$839$	76268.0	−	234729.i	0.108347	−	0.333459i	−0.882154	−	0.470961i	$-0.843907\pi$
$839$	76268.0	−	234729.i	0.108347	−	0.333459i	0.990502	+	0.137502i	$0.0439073\pi$
$840$		0			0
$841$	−480882.	−	349381.i	−0.679902	−	0.493978i
$842$		0			0
$843$	−1.20504e6	+	695732.i	−1.69569	+	0.979009i
$844$		0			0
$845$	−62653.3	+	45520.3i	−0.0877466	+	0.0637516i
$846$		0			0
$847$	−131567.	−	146120.i	−0.183391	−	0.203677i
$848$		0			0
$849$	368759.	+	1.73487e6i	0.511596	+	2.40687i
$850$		0			0
$851$	−196949.	−	87687.4i	−0.271954	−	0.121082i
$852$		0			0
$853$	−141719.	−	436167.i	−0.194774	−	0.599453i	−0.999979	−	0.00645641i	$-0.997945\pi$
$853$	−141719.	−	436167.i	−0.194774	−	0.599453i	0.805205	−	0.592996i	$-0.202055\pi$
$854$		0			0
$855$	84217.1	+	17900.9i	0.115204	+	0.0244874i
$856$		0			0
$857$	506742.	−	225616.i	0.689962	−	0.307191i	−0.0316399	−	0.999499i	$-0.510073\pi$
$857$	506742.	−	225616.i	0.689962	−	0.307191i	0.721602	+	0.692309i	$0.243406\pi$
$858$		0			0
$859$	969164.	−	101863.i	1.31344	−	0.138048i	0.578223	−	0.815878i	$-0.303746\pi$
$859$	969164.	−	101863.i	1.31344	−	0.138048i	0.735218	+	0.677830i	$0.237080\pi$
$860$		0			0
$861$	2.42902e6	+	255300.i	3.27661	+	0.344385i
$862$		0			0
$863$	−1.00874e6	−	582398.i	−1.35444	−	0.781985i	−0.365571	−	0.930784i	$-0.619126\pi$
$863$	−1.00874e6	−	582398.i	−1.35444	−	0.781985i	−0.988868	+	0.148798i	$0.952460\pi$
$864$		0			0
$865$	72429.4	−	80441.0i	0.0968016	−	0.107509i
$866$		0			0
$867$		−	620685.i		−	0.825720i
$868$		0			0
$869$	−655290.			−0.867749
$870$		0			0
$871$	−251571.	−	226516.i	−0.331608	−	0.298581i
$872$		0			0
$873$	−130117.	+	225369.i	−0.170728	+	0.295710i
$874$		0			0
$875$	−35341.4	+	336251.i	−0.0461602	+	0.439185i
$876$		0			0
$877$	−30421.5	−	289441.i	−0.0395531	−	0.376323i	−0.996336	−	0.0855209i	$-0.972745\pi$
$877$	−30421.5	−	289441.i	−0.0395531	−	0.376323i	0.956783	−	0.290802i	$-0.0939221\pi$
$878$		0			0
$879$	−401969.	−	902837.i	−0.520253	−	1.16851i
$880$		0			0
$881$	133368.	−	627447.i	0.171830	−	0.808398i	−0.804813	−	0.593529i	$-0.797734\pi$
$881$	133368.	−	627447.i	0.171830	−	0.808398i	0.976643	−	0.214869i	$-0.0689324\pi$
$882$		0			0
$883$	−966328.	+	313979.i	−1.23938	+	0.402698i	−0.854103	−	0.520105i	$-0.825893\pi$
$883$	−966328.	+	313979.i	−1.23938	+	0.402698i	−0.385274	+	0.922802i	$0.625893\pi$
$884$		0			0
$885$	68443.4	−	153726.i	0.0873866	−	0.196274i
$886$		0			0
$887$	−1.23036e6	+	261521.i	−1.56381	+	0.332398i	−0.906826	−	0.421505i	$-0.861502\pi$
$887$	−1.23036e6	+	261521.i	−1.56381	+	0.332398i	−0.656985	+	0.753903i	$0.728169\pi$
$888$		0			0
$889$	594535.	−	535321.i	0.752270	−	0.677347i
$890$		0			0
$891$	−487771.	−	671359.i	−0.614413	−	0.845667i
$892$		0			0
$893$	174519.	+	302276.i	0.218847	+	0.379054i
$894$		0			0
$895$	8948.23	−	12316.2i	0.0111710	−	0.0153755i
$896$		0			0
$897$	325978.	+	105917.i	0.405138	+	0.131637i
$898$		0			0
$899$	53298.5	−	318441.i	0.0659471	−	0.394013i
$900$		0			0
$901$	−48787.3	+	150152.i	−0.0600976	+	0.184961i
$902$		0			0
$903$	1.09659e6	+	796719.i	1.34483	+	0.977079i
$904$		0			0
$905$	−44016.7	+	25413.1i	−0.0537428	+	0.0310284i
$906$		0			0
$907$	365519.	−	265565.i	0.444319	−	0.322817i	−0.343030	−	0.939325i	$-0.611453\pi$
$907$	365519.	−	265565.i	0.444319	−	0.322817i	0.787349	+	0.616508i	$0.211453\pi$
$908$		0			0
$909$	−228983.	−	254312.i	−0.277125	−	0.307778i
$910$		0			0
$911$	159021.	+	748137.i	0.191610	+	0.901456i	0.963916	+	0.266205i	$0.0857698\pi$
$911$	159021.	+	748137.i	0.191610	+	0.901456i	−0.772306	+	0.635251i	$0.780897\pi$
$912$		0			0
$913$	469593.	+	209076.i	0.563352	+	0.250820i
$914$		0			0
$915$	65695.4	+	202190.i	0.0784680	+	0.241500i
$916$		0			0
$917$	−990647.	−	210569.i	−1.17810	−	0.250412i
$918$		0			0
$919$	−1.09901e6	+	489313.i	−1.30128	+	0.579369i	−0.936155	−	0.351588i	$-0.885642\pi$
$919$	−1.09901e6	+	489313.i	−1.30128	+	0.579369i	−0.365130	+	0.930957i	$0.618975\pi$
$920$		0			0
$921$	1.30267e6	−	136916.i	1.53573	−	0.161412i
$922$		0			0
$923$	−228091.	−	23973.3i	−0.267735	−	0.0281401i
$924$		0			0
$925$	−367279.	−	212048.i	−0.429252	−	0.247829i
$926$		0			0
$927$	−89192.8	+	99058.7i	−0.103794	+	0.115274i
$928$		0			0
$929$		−	309878.i		−	0.359053i	−0.983753	−	0.179527i	$-0.942543\pi$
$929$		−	309878.i		−	0.359053i	0.983753	−	0.179527i	$-0.0574566\pi$
$930$		0			0
$931$	931890.			1.07514
$932$		0			0
$933$	1.17971e6	+	1.06221e6i	1.35522	+	1.22025i
$934$		0			0
$935$	−37472.7	+	64904.6i	−0.0428639	+	0.0742424i
$936$		0			0
$937$	28791.6	−	273934.i	0.0327934	−	0.312009i	−0.965813	−	0.259239i	$-0.916528\pi$
$937$	28791.6	−	273934.i	0.0327934	−	0.312009i	0.998607	−	0.0527698i	$-0.0168050\pi$
$938$		0			0
$939$	−161862.	−	1.54001e6i	−0.183575	−	1.74660i
$940$		0			0
$941$	−363405.	−	816221.i	−0.410404	−	0.921783i	−0.993963	−	0.109712i	$-0.965007\pi$
$941$	−363405.	−	816221.i	−0.410404	−	0.921783i	0.583559	−	0.812071i	$-0.301660\pi$
$942$		0			0
$943$	182877.	−	860369.i	0.205654	−	0.967524i
$944$		0			0
$945$	−50990.4	+	16567.8i	−0.0570985	+	0.0185524i
$946$		0			0
$947$	−444609.	+	998608.i	−0.495768	+	1.11351i	0.476400	+	0.879228i	$0.341941\pi$
$947$	−444609.	+	998608.i	−0.495768	+	1.11351i	−0.972168	+	0.234284i	$0.924725\pi$
$948$		0			0
$949$	415703.	−	88360.5i	0.461584	−	0.0981128i
$950$		0			0
$951$	−132612.	+	119405.i	−0.146630	+	0.132026i
$952$		0			0
$953$	531621.	+	731714.i	0.585351	+	0.805667i	0.994269	−	0.106904i	$-0.0340938\pi$
$953$	531621.	+	731714.i	0.585351	+	0.805667i	−0.408918	+	0.912571i	$0.634094\pi$
$954$		0			0
$955$	126649.	+	219363.i	0.138866	+	0.240523i
$956$		0			0
$957$	259938.	−	357774.i	0.283822	−	0.390648i
$958$		0			0
$959$	1.03682e6	+	336885.i	1.12737	+	0.366306i
$960$		0			0
$961$	−883183.	+	269959.i	−0.956322	+	0.292315i
$962$		0			0
$963$	412102.	−	1.26832e6i	0.444378	−	1.36765i
$964$		0			0
$965$	−31379.1	−	22798.2i	−0.0336965	−	0.0244820i
$966$		0			0
$967$	714945.	−	412774.i	0.764574	−	0.441427i	−0.0663614	−	0.997796i	$-0.521139\pi$
$967$	714945.	−	412774.i	0.764574	−	0.441427i	0.830936	+	0.556369i	$0.187806\pi$
$968$		0			0
$969$	−606493.	+	440643.i	−0.645919	+	0.469288i
$970$		0			0
$971$	1.04592e6	+	1.16161e6i	1.10932	+	1.23203i	0.970343	+	0.241733i	$0.0777159\pi$
$971$	1.04592e6	+	1.16161e6i	1.10932	+	1.23203i	0.138981	+	0.990295i	$0.455617\pi$
$972$		0			0
$973$	460073.	+	2.16447e6i	0.485961	+	2.28627i
$974$		0			0
$975$	615961.	+	274244.i	0.647954	+	0.288488i
$976$		0			0
$977$	−109399.	−	336694.i	−0.114610	−	0.352733i	0.877256	−	0.480024i	$-0.159372\pi$
$977$	−109399.	−	336694.i	−0.114610	−	0.352733i	−0.991865	+	0.127291i	$0.959372\pi$
$978$		0			0
$979$	−37094.6	−	7884.70i	−0.0387031	−	0.00822659i
$980$		0			0
$981$	1.19532e6	−	532190.i	1.24207	−	0.553005i
$982$		0			0
$983$	−1.53818e6	+	161669.i	−1.59184	+	0.167309i	−0.858594	−	0.512656i	$-0.828661\pi$
$983$	−1.53818e6	+	161669.i	−1.59184	+	0.167309i	−0.733244	+	0.679965i	$0.761995\pi$
$984$		0			0
$985$	155284.	+	16321.0i	0.160050	+	0.0168219i
$986$		0			0
$987$	751532.	+	433897.i	0.771460	+	0.445403i
$988$		0			0
$989$	326634.	−	362764.i	0.333941	−	0.370879i
$990$		0			0
$991$		−	1.40197e6i		−	1.42755i	−0.700377	−	0.713773i	$-0.746985\pi$
$991$		−	1.40197e6i		−	1.42755i	0.700377	−	0.713773i	$-0.253015\pi$
$992$		0			0
$993$	−1.08973e6			−1.10515
$994$		0			0
$995$	−98017.4	−	88255.2i	−0.0990050	−	0.0891445i
$996$		0			0
$997$	−376214.	+	651622.i	−0.378482	+	0.655549i	−0.990842	−	0.135030i	$-0.956887\pi$
$997$	−376214.	+	651622.i	−0.378482	+	0.655549i	0.612360	+	0.790579i	$0.290220\pi$
$998$		0			0
$999$	14228.8	−	135378.i	0.0142573	−	0.135649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.o.a.17.2	✓	88
31.11	odd	30	inner	124.5.o.a.73.2	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.o.a.17.2	✓	88	1.1	even	1	trivial
124.5.o.a.73.2	yes	88	31.11	odd	30	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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.o (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.97256 - 8.07893i) q^{3} +(-1.91809 + 3.32223i) q^{5} +(7.45792 - 70.9574i) q^{7} +(6.77094 + 64.4212i) q^{9} +O(q^{10})\)	\(q+(-8.97256 - 8.07893i) q^{3} +(-1.91809 + 3.32223i) q^{5} +(7.45792 - 70.9574i) q^{7} +(6.77094 + 64.4212i) q^{9} +(-44.3421 - 99.5939i) q^{11} +(-19.0251 + 89.5061i) q^{13} +(44.0503 - 14.3128i) q^{15} +(-72.8880 + 163.709i) q^{17} +(-338.912 + 72.0379i) q^{19} +(-640.176 + 576.417i) q^{21} +(182.351 + 250.985i) q^{23} +(305.142 + 528.521i) q^{25} +(-115.138 + 158.474i) q^{27} +(-319.530 - 103.822i) q^{29} +(142.017 + 950.448i) q^{31} +(-406.751 + 1251.85i) q^{33} +(221.432 + 160.880i) q^{35} +(-601.816 + 347.459i) q^{37} +(893.818 - 649.397i) q^{39} +(-1897.15 - 2107.00i) q^{41} +(-327.144 - 1539.09i) q^{43} +(-227.009 - 101.071i) q^{45} +(-311.296 - 958.070i) q^{47} +(-2630.79 - 559.192i) q^{49} +(1976.59 - 880.033i) q^{51} +(876.186 - 92.0908i) q^{53} +(415.926 + 43.7156i) q^{55} +(3622.90 + 2091.68i) q^{57} +(2431.01 - 2699.91i) q^{59} +4589.97i q^{61} +4621.65 q^{63} +(-260.868 - 234.887i) q^{65} +(-1849.73 + 3203.83i) q^{67} +(391.533 - 3725.19i) q^{69} +(261.987 + 2492.64i) q^{71} +(-1889.05 - 4242.88i) q^{73} +(1531.98 - 7207.41i) q^{75} +(-7397.62 + 2403.63i) q^{77} +(2444.81 - 5491.12i) q^{79} +(7445.58 - 1582.61i) q^{81} +(-3503.98 + 3155.00i) q^{83} +(-404.074 - 556.160i) q^{85} +(2028.24 + 3513.01i) q^{87} +(204.467 - 281.424i) q^{89} +(6209.23 + 2017.50i) q^{91} +(6404.35 - 9675.30i) q^{93} +(410.737 - 1264.12i) q^{95} +(3250.18 + 2361.39i) q^{97} +(6115.72 - 3530.91i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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