LMFDB - Embedded newform 168.4.q.f.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,4,Mod(25,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("168.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.q (of order $3$, degree $2$, 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:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 173x^{6} + 9457x^{4} + 168048x^{2} + 746496 $ x^8 + 173x^6 + 9457x^4 + 168048*x^2 + 746496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$8.34231i$ of defining polynomial
Character	$\chi$	$=$	168.121
Dual form			168.4.q.f.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{3} +(-0.363171 + 0.629031i) q^{5} +(-18.1420 + 3.72380i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{3} +(-0.363171 + 0.629031i) q^{5} +(-18.1420 + 3.72380i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(32.2447 + 55.8495i) q^{11} +71.8475 q^{13} +2.17903 q^{15} +(-24.4517 - 42.3515i) q^{17} +(-17.1984 + 29.7885i) q^{19} +(36.8878 + 41.5487i) q^{21} +(0.451675 - 0.782324i) q^{23} +(62.2362 + 107.796i) q^{25} +27.0000 q^{27} +226.686 q^{29} +(137.898 + 238.846i) q^{31} +(96.7342 - 167.549i) q^{33} +(4.24627 - 12.7643i) q^{35} +(-147.605 + 255.658i) q^{37} +(-107.771 - 186.665i) q^{39} +186.604 q^{41} -455.317 q^{43} +(-3.26854 - 5.66128i) q^{45} +(-141.167 + 244.509i) q^{47} +(315.267 - 135.115i) q^{49} +(-73.3550 + 127.055i) q^{51} +(-178.107 - 308.491i) q^{53} -46.8414 q^{55} +103.191 q^{57} +(-364.685 - 631.653i) q^{59} +(-137.176 + 237.596i) q^{61} +(52.6150 - 158.160i) q^{63} +(-26.0929 + 45.1943i) q^{65} +(-96.6361 - 167.379i) q^{67} -2.71005 q^{69} +40.5277 q^{71} +(103.236 + 178.810i) q^{73} +(186.709 - 323.389i) q^{75} +(-792.958 - 893.151i) q^{77} +(-468.870 + 812.107i) q^{79} +(-40.5000 - 70.1481i) q^{81} +911.607 q^{83} +35.5206 q^{85} +(-340.029 - 588.948i) q^{87} +(474.988 - 822.703i) q^{89} +(-1303.46 + 267.546i) q^{91} +(413.693 - 716.537i) q^{93} +(-12.4919 - 21.6367i) q^{95} +39.4687 q^{97} -580.405 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} - 4 q^{5} + 18 q^{7} - 36 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 - 4 * q^5 + 18 * q^7 - 36 * q^9	$ 8 q - 12 q^{3} - 4 q^{5} + 18 q^{7} - 36 q^{9} - 14 q^{11} + 44 q^{13} + 24 q^{15} - 96 q^{17} + 26 q^{19} - 36 q^{21} - 96 q^{23} - 110 q^{25} + 216 q^{27} - 152 q^{29} - 238 q^{31} - 42 q^{33} + 152 q^{35} - 562 q^{37} - 66 q^{39} + 856 q^{41} - 516 q^{43} - 36 q^{45} + 80 q^{47} + 156 q^{49} - 288 q^{51} + 2952 q^{55} - 156 q^{57} - 262 q^{59} + 276 q^{61} - 54 q^{63} - 2196 q^{65} - 150 q^{67} + 576 q^{69} - 1696 q^{71} + 218 q^{73} - 330 q^{75} - 764 q^{77} - 1762 q^{79} - 324 q^{81} + 6900 q^{83} + 2904 q^{85} + 228 q^{87} + 344 q^{89} - 2806 q^{91} - 714 q^{93} - 2004 q^{95} - 1244 q^{97} + 252 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 - 4 * q^5 + 18 * q^7 - 36 * q^9 - 14 * q^11 + 44 * q^13 + 24 * q^15 - 96 * q^17 + 26 * q^19 - 36 * q^21 - 96 * q^23 - 110 * q^25 + 216 * q^27 - 152 * q^29 - 238 * q^31 - 42 * q^33 + 152 * q^35 - 562 * q^37 - 66 * q^39 + 856 * q^41 - 516 * q^43 - 36 * q^45 + 80 * q^47 + 156 * q^49 - 288 * q^51 + 2952 * q^55 - 156 * q^57 - 262 * q^59 + 276 * q^61 - 54 * q^63 - 2196 * q^65 - 150 * q^67 + 576 * q^69 - 1696 * q^71 + 218 * q^73 - 330 * q^75 - 764 * q^77 - 1762 * q^79 - 324 * q^81 + 6900 * q^83 + 2904 * q^85 + 228 * q^87 + 344 * q^89 - 2806 * q^91 - 714 * q^93 - 2004 * q^95 - 1244 * q^97 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$		0			0
$5$	−0.363171	+	0.629031i	−0.0324830	+	0.0562622i	−0.881810	−	0.471605i	$-0.843675\pi$
$5$	−0.363171	+	0.629031i	−0.0324830	+	0.0562622i	0.849327	+	0.527867i	$0.177008\pi$
$6$		0			0
$7$	−18.1420	+	3.72380i	−0.979578	+	0.201066i
$7$	−18.1420	+	3.72380i	−0.979578	+	0.201066i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	32.2447	+	55.8495i	0.883832	+	1.53084i	0.847046	+	0.531519i	$0.178379\pi$
$11$	32.2447	+	55.8495i	0.883832	+	1.53084i	0.0367856	+	0.999323i	$0.488288\pi$
$12$		0			0
$13$	71.8475			1.53284			0.766420	−	0.642340i	$-0.222036\pi$
$13$	71.8475			1.53284			0.766420	+	0.642340i	$0.222036\pi$
$14$		0			0
$15$	2.17903			0.0375081
$16$		0			0
$17$	−24.4517	−	42.3515i	−0.348847	−	0.604221i	0.637198	−	0.770700i	$-0.280093\pi$
$17$	−24.4517	−	42.3515i	−0.348847	−	0.604221i	−0.986045	+	0.166479i	$0.946760\pi$
$18$		0			0
$19$	−17.1984	+	29.7885i	−0.207663	+	0.359682i	−0.950978	−	0.309259i	$-0.899919\pi$
$19$	−17.1984	+	29.7885i	−0.207663	+	0.359682i	0.743315	+	0.668941i	$0.233252\pi$
$20$		0			0
$21$	36.8878	+	41.5487i	0.383313	+	0.431746i
$22$		0			0
$23$	0.451675	−	0.782324i	0.00409482	−	0.00709243i	−0.863971	−	0.503542i	$-0.832030\pi$
$23$	0.451675	−	0.782324i	0.00409482	−	0.00709243i	0.868066	+	0.496450i	$0.165363\pi$
$24$		0			0
$25$	62.2362	+	107.796i	0.497890	+	0.862370i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	226.686			1.45154			0.725769	−	0.687939i	$-0.241484\pi$
$29$	226.686			1.45154			0.725769	+	0.687939i	$0.241484\pi$
$30$		0			0
$31$	137.898	+	238.846i	0.798940	+	1.38380i	0.920307	+	0.391197i	$0.127939\pi$
$31$	137.898	+	238.846i	0.798940	+	1.38380i	−0.121367	+	0.992608i	$0.538728\pi$
$32$		0			0
$33$	96.7342	−	167.549i	0.510281	−	0.883832i
$34$		0			0
$35$	4.24627	−	12.7643i	0.0205072	−	0.0616444i
$36$		0			0
$37$	−147.605	+	255.658i	−0.655839	+	1.13595i	0.325844	+	0.945423i	$0.394352\pi$
$37$	−147.605	+	255.658i	−0.655839	+	1.13595i	−0.981683	+	0.190522i	$0.938982\pi$
$38$		0			0
$39$	−107.771	−	186.665i	−0.442493	−	0.766420i
$40$		0			0
$41$	186.604			0.710798			0.355399	−	0.934715i	$-0.384345\pi$
$41$	186.604			0.710798			0.355399	+	0.934715i	$0.384345\pi$
$42$		0			0
$43$	−455.317			−1.61477			−0.807386	−	0.590023i	$-0.799119\pi$
$43$	−455.317			−1.61477			−0.807386	+	0.590023i	$0.799119\pi$
$44$		0			0
$45$	−3.26854	−	5.66128i	−0.0108277	−	0.0187541i
$46$		0			0
$47$	−141.167	+	244.509i	−0.438114	+	0.758835i	−0.997544	−	0.0700420i	$-0.977687\pi$
$47$	−141.167	+	244.509i	−0.438114	+	0.758835i	0.559430	+	0.828877i	$0.311020\pi$
$48$		0			0
$49$	315.267	−	135.115i	0.919145	−	0.393920i
$50$		0			0
$51$	−73.3550	+	127.055i	−0.201407	+	0.348847i
$52$		0			0
$53$	−178.107	−	308.491i	−0.461602	−	0.799518i	0.537439	−	0.843303i	$-0.319392\pi$
$53$	−178.107	−	308.491i	−0.461602	−	0.799518i	−0.999041	+	0.0437844i	$0.986059\pi$
$54$		0			0
$55$	−46.8414			−0.114838
$56$		0			0
$57$	103.191			0.239788
$58$		0			0
$59$	−364.685	−	631.653i	−0.804711	−	1.39380i	−0.916486	−	0.400066i	$-0.868987\pi$
$59$	−364.685	−	631.653i	−0.804711	−	1.39380i	0.111776	−	0.993733i	$-0.464346\pi$
$60$		0			0
$61$	−137.176	+	237.596i	−0.287928	+	0.498706i	−0.973315	−	0.229473i	$-0.926300\pi$
$61$	−137.176	+	237.596i	−0.287928	+	0.498706i	0.685387	+	0.728179i	$0.259633\pi$
$62$		0			0
$63$	52.6150	−	158.160i	0.105220	−	0.316291i
$64$		0			0
$65$	−26.0929	+	45.1943i	−0.0497912	+	0.0862409i
$66$		0			0
$67$	−96.6361	−	167.379i	−0.176209	−	0.305202i	0.764370	−	0.644778i	$-0.223050\pi$
$67$	−96.6361	−	167.379i	−0.176209	−	0.305202i	−0.940579	+	0.339575i	$0.889717\pi$
$68$		0			0
$69$	−2.71005			−0.00472829
$70$		0			0
$71$	40.5277			0.0677429			0.0338715	−	0.999426i	$-0.489216\pi$
$71$	40.5277			0.0677429			0.0338715	+	0.999426i	$0.489216\pi$
$72$		0			0
$73$	103.236	+	178.810i	0.165519	+	0.286687i	0.936839	−	0.349760i	$-0.113737\pi$
$73$	103.236	+	178.810i	0.165519	+	0.286687i	−0.771320	+	0.636447i	$0.780403\pi$
$74$		0			0
$75$	186.709	−	323.389i	0.287457	−	0.497890i
$76$		0			0
$77$	−792.958	−	893.151i	−1.17358	−	1.32187i
$78$		0			0
$79$	−468.870	+	812.107i	−0.667747	+	1.15657i	0.310785	+	0.950480i	$0.399408\pi$
$79$	−468.870	+	812.107i	−0.667747	+	1.15657i	−0.978533	+	0.206092i	$0.933925\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	911.607			1.20556			0.602782	−	0.797906i	$-0.294059\pi$
$83$	911.607			1.20556			0.602782	+	0.797906i	$0.294059\pi$
$84$		0			0
$85$	35.5206			0.0453264
$86$		0			0
$87$	−340.029	−	588.948i	−0.419023	−	0.725769i
$88$		0			0
$89$	474.988	−	822.703i	0.565715	−	0.979846i	−0.431268	−	0.902224i	$-0.641934\pi$
$89$	474.988	−	822.703i	0.565715	−	0.979846i	0.996983	−	0.0776226i	$-0.0247329\pi$
$90$		0			0
$91$	−1303.46	+	267.546i	−1.50154	+	0.308203i
$92$		0			0
$93$	413.693	−	716.537i	0.461268	−	0.798940i
$94$		0			0
$95$	−12.4919	−	21.6367i	−0.0134910	−	0.0233671i
$96$		0			0
$97$	39.4687			0.0413138			0.0206569	−	0.999787i	$-0.493424\pi$
$97$	39.4687			0.0413138			0.0206569	+	0.999787i	$0.493424\pi$
$98$		0			0
$99$	−580.405			−0.589221
$100$		0			0
$101$	158.437	+	274.421i	0.156090	+	0.270356i	0.933455	−	0.358694i	$-0.116778\pi$
$101$	158.437	+	274.421i	0.156090	+	0.270356i	−0.777365	+	0.629049i	$0.783444\pi$
$102$		0			0
$103$	161.317	−	279.409i	0.154321	−	0.267291i	−0.778491	−	0.627656i	$-0.784014\pi$
$103$	161.317	−	279.409i	0.154321	−	0.267291i	0.932811	+	0.360365i	$0.117348\pi$
$104$		0			0
$105$	−39.5320	+	8.11426i	−0.0367421	+	0.00754163i
$106$		0			0
$107$	−340.726	+	590.154i	−0.307843	+	0.533200i	−0.977890	−	0.209119i	$-0.932940\pi$
$107$	−340.726	+	590.154i	−0.307843	+	0.533200i	0.670047	+	0.742318i	$0.266274\pi$
$108$		0			0
$109$	227.984	+	394.879i	0.200338	+	0.346996i	0.948637	−	0.316365i	$-0.102463\pi$
$109$	227.984	+	394.879i	0.200338	+	0.346996i	−0.748299	+	0.663361i	$0.769129\pi$
$110$		0			0
$111$	885.627			0.757297
$112$		0			0
$113$	−796.025			−0.662688			−0.331344	−	0.943510i	$-0.607502\pi$
$113$	−796.025			−0.662688			−0.331344	+	0.943510i	$0.607502\pi$
$114$		0			0
$115$	0.328071	+	0.568235i	0.000266024	+	0.000460767i
$116$		0			0
$117$	−323.314	+	559.996i	−0.255473	+	0.442493i
$118$		0			0
$119$	601.312	+	677.290i	0.463212	+	0.521740i
$120$		0			0
$121$	−1413.95	+	2449.03i	−1.06232	+	1.83999i
$122$		0			0
$123$	−279.907	−	484.813i	−0.205190	−	0.355399i
$124$		0			0
$125$	−181.202			−0.129658
$126$		0			0
$127$	2333.92			1.63072			0.815362	−	0.578952i	$-0.196538\pi$
$127$	2333.92			1.63072			0.815362	+	0.578952i	$0.196538\pi$
$128$		0			0
$129$	682.976	+	1182.95i	0.466145	+	0.807386i
$130$		0			0
$131$	943.489	−	1634.17i	0.629259	−	1.08991i	−0.358441	−	0.933552i	$-0.616692\pi$
$131$	943.489	−	1634.17i	0.629259	−	1.08991i	0.987701	−	0.156357i	$-0.0499750\pi$
$132$		0			0
$133$	201.088	−	604.468i	0.131102	−	0.394091i
$134$		0			0
$135$	−9.80562	+	16.9838i	−0.00625136	+	0.0108277i
$136$		0			0
$137$	−1473.63	−	2552.40i	−0.918983	−	1.59173i	−0.800963	−	0.598714i	$-0.795678\pi$
$137$	−1473.63	−	2552.40i	−0.918983	−	1.59173i	−0.118021	−	0.993011i	$-0.537655\pi$
$138$		0			0
$139$	955.433			0.583013			0.291506	−	0.956569i	$-0.405844\pi$
$139$	955.433			0.583013			0.291506	+	0.956569i	$0.405844\pi$
$140$		0			0
$141$	847.003			0.505890
$142$		0			0
$143$	2316.70	+	4012.65i	1.35477	+	2.34654i
$144$		0			0
$145$	−82.3259	+	142.593i	−0.0471503	+	0.0816667i
$146$		0			0
$147$	−823.938	−	616.415i	−0.462294	−	0.345857i
$148$		0			0
$149$	−1091.87	+	1891.17i	−0.600332	+	1.03981i	0.392439	+	0.919778i	$0.371631\pi$
$149$	−1091.87	+	1891.17i	−0.600332	+	1.03981i	−0.992771	+	0.120027i	$0.961702\pi$
$150$		0			0
$151$	−202.360	−	350.497i	−0.109058	−	0.188894i	0.806331	−	0.591465i	$-0.201450\pi$
$151$	−202.360	−	350.497i	−0.109058	−	0.188894i	−0.915389	+	0.402570i	$0.868117\pi$
$152$		0			0
$153$	440.130			0.232565
$154$		0			0
$155$	−200.322			−0.103808
$156$		0			0
$157$	464.791	+	805.042i	0.236270	+	0.409231i	0.959641	−	0.281228i	$-0.0907418\pi$
$157$	464.791	+	805.042i	0.236270	+	0.409231i	−0.723371	+	0.690459i	$0.757408\pi$
$158$		0			0
$159$	−534.322	+	925.472i	−0.266506	+	0.461602i
$160$		0			0
$161$	−5.28108	+	15.8749i	−0.00258514	+	0.00777092i
$162$		0			0
$163$	712.840	−	1234.68i	0.342540	−	0.593296i	−0.642364	−	0.766400i	$-0.722046\pi$
$163$	712.840	−	1234.68i	0.342540	−	0.593296i	0.984904	+	0.173104i	$0.0553796\pi$
$164$		0			0
$165$	70.2621	+	121.698i	0.0331509	+	0.0574190i
$166$		0			0
$167$	4185.15			1.93926			0.969631	−	0.244572i	$-0.0786474\pi$
$167$	4185.15			1.93926			0.969631	+	0.244572i	$0.0786474\pi$
$168$		0			0
$169$	2965.07			1.34960
$170$		0			0
$171$	−154.786	−	268.097i	−0.0692209	−	0.119894i
$172$		0			0
$173$	−1117.78	+	1936.05i	−0.491231	+	0.850837i	−0.999949	−	0.0100961i	$-0.996786\pi$
$173$	−1117.78	+	1936.05i	−0.491231	+	0.850837i	0.508718	+	0.860933i	$0.330120\pi$
$174$		0			0
$175$	−1530.50	−	1723.89i	−0.661115	−	0.744650i
$176$		0			0
$177$	−1094.05	+	1894.96i	−0.464600	+	0.804711i
$178$		0			0
$179$	470.740	+	815.345i	0.196563	+	0.340457i	0.947412	−	0.320017i	$-0.103689\pi$
$179$	470.740	+	815.345i	0.196563	+	0.340457i	−0.750849	+	0.660474i	$0.770355\pi$
$180$		0			0
$181$	−467.540			−0.192000			−0.0960000	−	0.995381i	$-0.530605\pi$
$181$	−467.540			−0.192000			−0.0960000	+	0.995381i	$0.530605\pi$
$182$		0			0
$183$	823.058			0.332471
$184$		0			0
$185$	−107.211	−	185.696i	−0.0426072	−	0.0737979i
$186$		0			0
$187$	1576.88	−	2731.23i	0.616645	−	1.06806i
$188$		0			0
$189$	−489.835	+	100.543i	−0.188520	+	0.0386953i
$190$		0			0
$191$	−137.701	+	238.506i	−0.0521660	+	0.0903542i	−0.890929	−	0.454142i	$-0.849946\pi$
$191$	−137.701	+	238.506i	−0.0521660	+	0.0903542i	0.838763	+	0.544496i	$0.183279\pi$
$192$		0			0
$193$	−820.148	−	1420.54i	−0.305884	−	0.529806i	0.671574	−	0.740937i	$-0.265619\pi$
$193$	−820.148	−	1420.54i	−0.305884	−	0.529806i	−0.977458	+	0.211131i	$0.932285\pi$
$194$		0			0
$195$	156.558			0.0574940
$196$		0			0
$197$	1303.88			0.471560			0.235780	−	0.971806i	$-0.424236\pi$
$197$	1303.88			0.471560			0.235780	+	0.971806i	$0.424236\pi$
$198$		0			0
$199$	663.678	+	1149.52i	0.236417	+	0.409485i	0.959683	−	0.281083i	$-0.0906937\pi$
$199$	663.678	+	1149.52i	0.236417	+	0.409485i	−0.723267	+	0.690569i	$0.757360\pi$
$200$		0			0
$201$	−289.908	+	502.136i	−0.101734	+	0.176209i
$202$		0			0
$203$	−4112.55	+	844.135i	−1.42189	+	0.291855i
$204$		0			0
$205$	−67.7693	+	117.380i	−0.0230889	+	0.0399911i
$206$		0			0
$207$	4.06508	+	7.04092i	0.00136494	+	0.00236414i
$208$		0			0
$209$	−2218.23			−0.734155
$210$		0			0
$211$	−4753.28			−1.55085			−0.775426	−	0.631439i	$-0.782465\pi$
$211$	−4753.28			−1.55085			−0.775426	+	0.631439i	$0.782465\pi$
$212$		0			0
$213$	−60.7915	−	105.294i	−0.0195557	−	0.0338715i
$214$		0			0
$215$	165.358	−	286.408i	0.0524527	−	0.0908507i
$216$		0			0
$217$	−3391.16	−	3819.64i	−1.06086	−	1.19490i
$218$		0			0
$219$	309.709	−	536.431i	0.0955624	−	0.165519i
$220$		0			0
$221$	−1756.79	−	3042.85i	−0.534727	−	0.926174i
$222$		0			0
$223$	513.149			0.154094			0.0770470	−	0.997027i	$-0.475451\pi$
$223$	513.149			0.154094			0.0770470	+	0.997027i	$0.475451\pi$
$224$		0			0
$225$	−1120.25			−0.331926
$226$		0			0
$227$	−1654.67	−	2865.97i	−0.483808	−	0.837980i	0.516019	−	0.856577i	$-0.327413\pi$
$227$	−1654.67	−	2865.97i	−0.483808	−	0.837980i	−0.999827	+	0.0185972i	$0.994080\pi$
$228$		0			0
$229$	2954.73	−	5117.75i	0.852639	−	1.47681i	−0.0261800	−	0.999657i	$-0.508334\pi$
$229$	2954.73	−	5117.75i	0.852639	−	1.47681i	0.878819	−	0.477156i	$-0.158332\pi$
$230$		0			0
$231$	−1131.04	+	3399.89i	−0.322151	+	0.968382i
$232$		0			0
$233$	176.786	−	306.202i	0.0497065	−	0.0860943i	−0.840102	−	0.542429i	$-0.817505\pi$
$233$	176.786	−	306.202i	0.0497065	−	0.0860943i	0.889808	+	0.456335i	$0.150838\pi$
$234$		0			0
$235$	−102.536	−	177.597i	−0.0284625	−	0.0492985i
$236$		0			0
$237$	2813.22			0.771048
$238$		0			0
$239$	−1652.55			−0.447259			−0.223629	−	0.974674i	$-0.571791\pi$
$239$	−1652.55			−0.447259			−0.223629	+	0.974674i	$0.571791\pi$
$240$		0			0
$241$	1553.47	+	2690.69i	0.415220	+	0.719182i	0.995452	−	0.0952696i	$-0.0303713\pi$
$241$	1553.47	+	2690.69i	0.415220	+	0.719182i	−0.580232	+	0.814451i	$0.697038\pi$
$242$		0			0
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−29.5044	+	247.382i	−0.00769374	+	0.0645088i
$246$		0			0
$247$	−1235.66	+	2140.23i	−0.318313	+	0.551335i
$248$		0			0
$249$	−1367.41	−	2368.42i	−0.348016	−	0.602782i
$250$		0			0
$251$	1771.77			0.445551			0.222776	−	0.974870i	$-0.428488\pi$
$251$	1771.77			0.445551			0.222776	+	0.974870i	$0.428488\pi$
$252$		0			0
$253$	58.2566			0.0144765
$254$		0			0
$255$	−53.2808	−	92.2851i	−0.0130846	−	0.0226632i
$256$		0			0
$257$	−739.063	+	1280.09i	−0.179383	+	0.310701i	−0.941669	−	0.336539i	$-0.890743\pi$
$257$	−739.063	+	1280.09i	−0.179383	+	0.310701i	0.762286	+	0.647240i	$0.224077\pi$
$258$		0			0
$259$	1725.82	−	5187.81i	0.414044	−	1.24461i
$260$		0			0
$261$	−1020.09	+	1766.84i	−0.241923	+	0.419023i
$262$		0			0
$263$	715.987	+	1240.13i	0.167869	+	0.290758i	0.937671	−	0.347525i	$-0.112978\pi$
$263$	715.987	+	1240.13i	0.167869	+	0.290758i	−0.769801	+	0.638284i	$0.779645\pi$
$264$		0			0
$265$	258.734			0.0599769
$266$		0			0
$267$	−2849.93			−0.653231
$268$		0			0
$269$	−142.699	−	247.162i	−0.0323439	−	0.0560213i	0.849400	−	0.527749i	$-0.176964\pi$
$269$	−142.699	−	247.162i	−0.0323439	−	0.0560213i	−0.881744	+	0.471728i	$0.843631\pi$
$270$		0			0
$271$	2624.66	−	4546.05i	0.588328	−	1.01901i	−0.406123	−	0.913818i	$-0.633120\pi$
$271$	2624.66	−	4546.05i	0.588328	−	1.01901i	0.994452	−	0.105196i	$-0.0335470\pi$
$272$		0			0
$273$	2650.29	+	2985.17i	0.587557	+	0.661797i
$274$		0			0
$275$	−4013.58	+	6951.72i	−0.880102	+	1.52438i
$276$		0			0
$277$	−3573.93	−	6190.24i	−0.775224	−	1.34273i	−0.934669	−	0.355520i	$-0.884304\pi$
$277$	−3573.93	−	6190.24i	−0.775224	−	1.34273i	0.159445	−	0.987207i	$-0.449029\pi$
$278$		0			0
$279$	−2482.16			−0.532627
$280$		0			0
$281$	4228.36			0.897661			0.448831	−	0.893617i	$-0.351841\pi$
$281$	4228.36			0.897661			0.448831	+	0.893617i	$0.351841\pi$
$282$		0			0
$283$	−4171.19	−	7224.71i	−0.876154	−	1.51754i	−0.855528	−	0.517756i	$-0.826768\pi$
$283$	−4171.19	−	7224.71i	−0.876154	−	1.51754i	−0.0206255	−	0.999787i	$-0.506566\pi$
$284$		0			0
$285$	−37.4758	+	64.9100i	−0.00778904	+	0.0134910i
$286$		0			0
$287$	−3385.38	+	694.878i	−0.696282	+	0.142918i
$288$		0			0
$289$	1260.73	−	2183.65i	0.256611	−	0.444464i
$290$		0			0
$291$	−59.2030	−	102.543i	−0.0119263	−	0.0206569i
$292$		0			0
$293$	5038.84			1.00468			0.502342	−	0.864669i	$-0.332472\pi$
$293$	5038.84			1.00468			0.502342	+	0.864669i	$0.332472\pi$
$294$		0			0
$295$	529.772			0.104558
$296$		0			0
$297$	870.608	+	1507.94i	0.170094	+	0.294611i
$298$		0			0
$299$	32.4517	−	56.2081i	0.00627670	−	0.0108716i
$300$		0			0
$301$	8260.38	−	1695.51i	1.58180	−	0.324677i
$302$		0			0
$303$	475.311	−	823.263i	0.0901186	−	0.156090i
$304$		0			0
$305$	−99.6369	−	172.576i	−0.0187055	−	0.0323990i
$306$		0			0
$307$	−4869.67			−0.905300			−0.452650	−	0.891688i	$-0.649521\pi$
$307$	−4869.67			−0.905300			−0.452650	+	0.891688i	$0.649521\pi$
$308$		0			0
$309$	−967.901			−0.178194
$310$		0			0
$311$	726.421	+	1258.20i	0.132449	+	0.229408i	0.924620	−	0.380891i	$-0.124383\pi$
$311$	726.421	+	1258.20i	0.132449	+	0.229408i	−0.792171	+	0.610299i	$0.791049\pi$
$312$		0			0
$313$	−2848.14	+	4933.12i	−0.514333	+	0.890850i	0.485529	+	0.874221i	$0.338627\pi$
$313$	−2848.14	+	4933.12i	−0.514333	+	0.890850i	−0.999862	+	0.0166299i	$0.994706\pi$
$314$		0			0
$315$	80.3794	+	90.5356i	0.0143774	+	0.0161940i
$316$		0			0
$317$	1735.73	−	3006.38i	0.307535	−	0.532666i	−0.670288	−	0.742101i	$-0.733829\pi$
$317$	1735.73	−	3006.38i	0.307535	−	0.532666i	0.977822	+	0.209435i	$0.0671626\pi$
$318$		0			0
$319$	7309.44	+	12660.3i	1.28291	+	2.22207i
$320$		0			0
$321$	2044.35			0.355466
$322$		0			0
$323$	1682.12			0.289770
$324$		0			0
$325$	4471.52	+	7744.90i	0.763185	+	1.32188i
$326$		0			0
$327$	683.951	−	1184.64i	0.115665	−	0.200338i
$328$		0			0
$329$	1650.56	−	4961.56i	0.276590	−	0.831428i
$330$		0			0
$331$	−3127.19	+	5416.45i	−0.519293	+	0.899441i	0.480456	+	0.877019i	$0.340471\pi$
$331$	−3127.19	+	5416.45i	−0.519293	+	0.899441i	−0.999749	+	0.0224223i	$0.992862\pi$
$332$		0			0
$333$	−1328.44	−	2300.93i	−0.218613	−	0.378649i
$334$		0			0
$335$	140.382			0.0228951
$336$		0			0
$337$	8006.96			1.29426			0.647132	−	0.762378i	$-0.275968\pi$
$337$	8006.96			1.29426			0.647132	+	0.762378i	$0.275968\pi$
$338$		0			0
$339$	1194.04	+	2068.13i	0.191302	+	0.331344i
$340$		0			0
$341$	−8892.94	+	15403.0i	−1.41226	+	2.44610i
$342$		0			0
$343$	−5216.44	+	3625.25i	−0.821169	+	0.570685i
$344$		0			0
$345$	0.984212	−	1.70471i	0.000153589	−	0.000266024i
$346$		0			0
$347$	−3817.80	−	6612.62i	−0.590634	−	1.02301i	−0.994147	−	0.108034i	$-0.965544\pi$
$347$	−3817.80	−	6612.62i	−0.590634	−	1.02301i	0.403513	−	0.914974i	$-0.367789\pi$
$348$		0			0
$349$	−10358.0			−1.58869			−0.794345	−	0.607468i	$-0.792185\pi$
$349$	−10358.0			−1.58869			−0.794345	+	0.607468i	$0.792185\pi$
$350$		0			0
$351$	1939.88			0.294995
$352$		0			0
$353$	−1692.12	−	2930.83i	−0.255134	−	0.441905i	0.709798	−	0.704405i	$-0.248786\pi$
$353$	−1692.12	−	2930.83i	−0.255134	−	0.441905i	−0.964932	+	0.262500i	$0.915453\pi$
$354$		0			0
$355$	−14.7185	+	25.4931i	−0.00220049	+	0.00381137i
$356$		0			0
$357$	857.683	−	2578.19i	0.127152	−	0.382219i
$358$		0			0
$359$	4097.31	−	7096.74i	0.602361	−	1.04332i	−0.390102	−	0.920772i	$-0.627560\pi$
$359$	4097.31	−	7096.74i	0.602361	−	1.04332i	0.992463	−	0.122548i	$-0.0391065\pi$
$360$		0			0
$361$	2837.93	+	4915.44i	0.413752	+	0.716640i
$362$		0			0
$363$	8483.67			1.22666
$364$		0			0
$365$	−149.970			−0.0215062
$366$		0			0
$367$	−402.755	−	697.592i	−0.0572851	−	0.0992208i	0.835961	−	0.548789i	$-0.184911\pi$
$367$	−402.755	−	697.592i	−0.0572851	−	0.0992208i	−0.893246	+	0.449569i	$0.851578\pi$
$368$		0			0
$369$	−839.720	+	1454.44i	−0.118466	+	0.205190i
$370$		0			0
$371$	4379.99	+	4933.41i	0.612931	+	0.690377i
$372$		0			0
$373$	−3952.86	+	6846.55i	−0.548716	+	0.950404i	0.449647	+	0.893206i	$0.351550\pi$
$373$	−3952.86	+	6846.55i	−0.548716	+	0.950404i	−0.998363	+	0.0571977i	$0.981783\pi$
$374$		0			0
$375$	271.803	+	470.777i	0.0374290	+	0.0648289i
$376$		0			0
$377$	16286.8			2.22497
$378$		0			0
$379$	3324.24			0.450540			0.225270	−	0.974296i	$-0.427674\pi$
$379$	3324.24			0.450540			0.225270	+	0.974296i	$0.427674\pi$
$380$		0			0
$381$	−3500.88	−	6063.70i	−0.470749	−	0.815362i
$382$		0			0
$383$	4235.38	−	7335.90i	0.565060	−	0.978712i	−0.431984	−	0.901881i	$-0.642186\pi$
$383$	4235.38	−	7335.90i	0.565060	−	0.978712i	0.997044	−	0.0768310i	$-0.0244802\pi$
$384$		0			0
$385$	849.798	−	174.428i	0.112493	−	0.0230901i
$386$		0			0
$387$	2048.93	−	3548.85i	0.269129	−	0.466145i
$388$		0			0
$389$	3954.20	+	6848.88i	0.515388	+	0.892678i	0.999840	+	0.0178606i	$0.00568551\pi$
$389$	3954.20	+	6848.88i	0.515388	+	0.892678i	−0.484452	+	0.874818i	$0.660981\pi$
$390$		0			0
$391$	−44.1769			−0.00571386
$392$		0			0
$393$	−5660.93			−0.726606
$394$		0			0
$395$	−340.560	−	589.868i	−0.0433809	−	0.0751379i
$396$		0			0
$397$	4890.79	−	8471.10i	0.618292	−	1.07091i	−0.371506	−	0.928431i	$-0.621158\pi$
$397$	4890.79	−	8471.10i	0.618292	−	1.07091i	0.989797	−	0.142482i	$-0.0455083\pi$
$398$		0			0
$399$	−1872.09	+	384.261i	−0.234891	+	0.0482134i
$400$		0			0
$401$	397.827	−	689.056i	0.0495424	−	0.0858100i	−0.840191	−	0.542291i	$-0.817557\pi$
$401$	397.827	−	689.056i	0.0495424	−	0.0858100i	0.889733	+	0.456481i	$0.150890\pi$
$402$		0			0
$403$	9907.60	+	17160.5i	1.22465	+	2.12115i
$404$		0			0
$405$	58.8337			0.00721844
$406$		0			0
$407$	−19037.9			−2.31860
$408$		0			0
$409$	−4292.36	−	7434.59i	−0.518933	−	0.898818i	−0.999758	−	0.0220017i	$-0.992996\pi$
$409$	−4292.36	−	7434.59i	−0.518933	−	0.898818i	0.480825	−	0.876817i	$-0.340337\pi$
$410$		0			0
$411$	−4420.89	+	7657.21i	−0.530575	+	0.918983i
$412$		0			0
$413$	8968.27	+	10101.4i	1.06852	+	1.20353i
$414$		0			0
$415$	−331.069	+	573.428i	−0.0391603	+	0.0678277i
$416$		0			0
$417$	−1433.15	−	2482.29i	−0.168301	−	0.291506i
$418$		0			0
$419$	−7447.09			−0.868292			−0.434146	−	0.900843i	$-0.642950\pi$
$419$	−7447.09			−0.868292			−0.434146	+	0.900843i	$0.642950\pi$
$420$		0			0
$421$	−4446.76			−0.514779			−0.257390	−	0.966308i	$-0.582862\pi$
$421$	−4446.76			−0.514779			−0.257390	+	0.966308i	$0.582862\pi$
$422$		0			0
$423$	−1270.50	−	2200.58i	−0.146038	−	0.252945i
$424$		0			0
$425$	3043.56	−	5271.60i	0.347375	−	0.601671i
$426$		0			0
$427$	1603.89	−	4821.30i	0.181775	−	0.546414i
$428$		0			0
$429$	6950.11	−	12037.9i	0.782178	−	1.35477i
$430$		0			0
$431$	4481.85	+	7762.79i	0.500889	+	0.867565i	0.999999	+	0.00102683i	$0.000326850\pi$
$431$	4481.85	+	7762.79i	0.500889	+	0.867565i	−0.499110	+	0.866538i	$0.666340\pi$
$432$		0			0
$433$	−16173.6			−1.79504			−0.897520	−	0.440973i	$-0.854633\pi$
$433$	−16173.6			−1.79504			−0.897520	+	0.440973i	$0.854633\pi$
$434$		0			0
$435$	493.955			0.0544445
$436$		0			0
$437$	15.5362	+	26.9095i	0.00170068	+	0.00294567i
$438$		0			0
$439$	3149.21	−	5454.60i	0.342378	−	0.593015i	−0.642496	−	0.766289i	$-0.722101\pi$
$439$	3149.21	−	5454.60i	0.342378	−	0.593015i	0.984874	+	0.173274i	$0.0554345\pi$
$440$		0			0
$441$	−365.585	+	3065.28i	−0.0394757	+	0.330988i
$442$		0			0
$443$	8392.35	−	14536.0i	0.900074	−	1.55897i	0.0726770	−	0.997356i	$-0.476846\pi$
$443$	8392.35	−	14536.0i	0.900074	−	1.55897i	0.827397	−	0.561618i	$-0.189821\pi$
$444$		0			0
$445$	345.004	+	597.564i	0.0367522	+	0.0636567i
$446$		0			0
$447$	6551.22			0.693203
$448$		0			0
$449$	2733.88			0.287349			0.143674	−	0.989625i	$-0.454108\pi$
$449$	2733.88			0.287349			0.143674	+	0.989625i	$0.454108\pi$
$450$		0			0
$451$	6017.01	+	10421.8i	0.628226	+	1.08812i
$452$		0			0
$453$	−607.079	+	1051.49i	−0.0629648	+	0.109058i
$454$		0			0
$455$	305.084	−	917.081i	0.0314342	−	0.0944910i
$456$		0			0
$457$	−4614.60	+	7992.72i	−0.472345	+	0.818126i	−0.999499	−	0.0316437i	$-0.989926\pi$
$457$	−4614.60	+	7992.72i	−0.472345	+	0.818126i	0.527154	+	0.849770i	$0.323259\pi$
$458$		0			0
$459$	−660.195	−	1143.49i	−0.0671357	−	0.116282i
$460$		0			0
$461$	−19726.7			−1.99298			−0.996491	−	0.0837048i	$-0.973325\pi$
$461$	−19726.7			−1.99298			−0.996491	+	0.0837048i	$0.973325\pi$
$462$		0			0
$463$	368.924			0.0370310			0.0185155	−	0.999829i	$-0.494106\pi$
$463$	368.924			0.0370310			0.0185155	+	0.999829i	$0.494106\pi$
$464$		0			0
$465$	300.482	+	520.451i	0.0299667	+	0.0519039i
$466$		0			0
$467$	6654.78	−	11526.4i	0.659414	−	1.14214i	−0.321353	−	0.946959i	$-0.604138\pi$
$467$	6654.78	−	11526.4i	0.659414	−	1.14214i	0.980768	−	0.195179i	$-0.0625289\pi$
$468$		0			0
$469$	2376.46	+	2676.73i	0.233976	+	0.263540i
$470$		0			0
$471$	1394.37	−	2415.12i	0.136410	−	0.236270i
$472$		0			0
$473$	−14681.6	−	25429.2i	−1.42719	−	2.47196i
$474$		0			0
$475$	−4281.46			−0.413572
$476$		0			0
$477$	3205.93			0.307735
$478$		0			0
$479$	−5781.39	−	10013.7i	−0.551479	−	0.955189i	−0.998168	−	0.0605002i	$-0.980730\pi$
$479$	−5781.39	−	10013.7i	−0.551479	−	0.955189i	0.446689	−	0.894689i	$-0.352603\pi$
$480$		0			0
$481$	−10605.0	+	18368.4i	−1.00530	+	1.74122i
$482$		0			0
$483$	49.1658	−	10.0917i	0.00463172	−	0.000950700i
$484$		0			0
$485$	−14.3339	+	24.8270i	−0.00134200	+	0.00232440i
$486$		0			0
$487$	−1314.06	−	2276.02i	−0.122271	−	0.211779i	0.798392	−	0.602138i	$-0.205684\pi$
$487$	−1314.06	−	2276.02i	−0.122271	−	0.211779i	−0.920663	+	0.390359i	$0.872351\pi$
$488$		0			0
$489$	−4277.04			−0.395531
$490$		0			0
$491$	−12319.9			−1.13236			−0.566181	−	0.824281i	$-0.691580\pi$
$491$	−12319.9			−1.13236			−0.566181	+	0.824281i	$0.691580\pi$
$492$		0			0
$493$	−5542.86	−	9600.51i	−0.506365	−	0.877049i
$494$		0			0
$495$	210.786	−	365.093i	0.0191397	−	0.0331509i
$496$		0			0
$497$	−735.254	+	150.917i	−0.0663595	+	0.0136208i
$498$		0			0
$499$	1652.90	−	2862.91i	0.148285	−	0.256837i	−0.782309	−	0.622891i	$-0.785958\pi$
$499$	1652.90	−	2862.91i	0.148285	−	0.256837i	0.930594	+	0.366054i	$0.119291\pi$
$500$		0			0
$501$	−6277.73	−	10873.3i	−0.559817	−	0.969631i
$502$		0			0
$503$	−3072.72			−0.272377			−0.136189	−	0.990683i	$-0.543485\pi$
$503$	−3072.72			−0.272377			−0.136189	+	0.990683i	$0.543485\pi$
$504$		0			0
$505$	−230.159			−0.0202811
$506$		0			0
$507$	−4447.60	−	7703.47i	−0.389595	−	0.674799i
$508$		0			0
$509$	−6784.91	+	11751.8i	−0.590836	+	1.02336i	0.403284	+	0.915075i	$0.367869\pi$
$509$	−6784.91	+	11751.8i	−0.590836	+	1.02336i	−0.994120	+	0.108284i	$0.965465\pi$
$510$		0			0
$511$	−2538.77	−	2859.55i	−0.219782	−	0.247552i
$512$		0			0
$513$	−464.357	+	804.291i	−0.0399647	+	0.0692209i
$514$		0			0
$515$	117.171	+	202.947i	0.0100256	+	0.0173648i
$516$		0			0
$517$	−18207.6			−1.54888
$518$		0			0
$519$	6706.66			0.567225
$520$		0			0
$521$	5366.68	+	9295.36i	0.451283	+	0.781645i	0.998466	−	0.0553681i	$-0.0176332\pi$
$521$	5366.68	+	9295.36i	0.451283	+	0.781645i	−0.547183	+	0.837013i	$0.684300\pi$
$522$		0			0
$523$	−4174.07	+	7229.71i	−0.348986	+	0.604461i	−0.986070	−	0.166334i	$-0.946807\pi$
$523$	−4174.07	+	7229.71i	−0.348986	+	0.604461i	0.637084	+	0.770794i	$0.280140\pi$
$524$		0			0
$525$	−2183.04	+	6562.20i	−0.181477	+	0.545520i
$526$		0			0
$527$	6743.65	−	11680.3i	0.557416	−	0.965473i
$528$		0			0
$529$	6083.09	+	10536.2i	0.499966	+	0.865967i
$530$		0			0
$531$	6564.33			0.536474
$532$		0			0
$533$	13407.1			1.08954
$534$		0			0
$535$	−247.483	−	428.654i	−0.0199993	−	0.0346399i
$536$		0			0
$537$	1412.22	−	2446.04i	0.113486	−	0.196563i
$538$		0			0
$539$	17711.8	+	13250.7i	1.41540	+	1.05891i
$540$		0			0
$541$	11553.6	−	20011.5i	0.918170	−	1.59032i	0.115978	−	0.993252i	$-0.463000\pi$
$541$	11553.6	−	20011.5i	0.918170	−	1.59032i	0.802192	−	0.597066i	$-0.203667\pi$
$542$		0			0
$543$	701.310	+	1214.71i	0.0554256	+	0.0960000i
$544$		0			0
$545$	−331.188			−0.0260304
$546$		0			0
$547$	13935.2			1.08926			0.544630	−	0.838676i	$-0.316670\pi$
$547$	13935.2			1.08926			0.544630	+	0.838676i	$0.316670\pi$
$548$		0			0
$549$	−1234.59	−	2138.37i	−0.0959761	−	0.166235i
$550$		0			0
$551$	−3898.65	+	6752.65i	−0.301430	+	0.522092i
$552$		0			0
$553$	5482.13	−	16479.3i	0.421562	−	1.26721i
$554$		0			0
$555$	−321.634	+	557.087i	−0.0245993	+	0.0426072i
$556$		0			0
$557$	7523.76	+	13031.5i	0.572337	+	0.991317i	0.996325	+	0.0856492i	$0.0272964\pi$
$557$	7523.76	+	13031.5i	0.572337	+	0.991317i	−0.423988	+	0.905668i	$0.639370\pi$
$558$		0			0
$559$	−32713.4			−2.47519
$560$		0			0
$561$	−9461.25			−0.712040
$562$		0			0
$563$	−7721.08	−	13373.3i	−0.577983	−	1.00110i	−0.995710	−	0.0925239i	$-0.970507\pi$
$563$	−7721.08	−	13373.3i	−0.577983	−	1.00110i	0.417727	−	0.908572i	$-0.362827\pi$
$564$		0			0
$565$	289.093	−	500.724i	0.0215261	−	0.0372843i
$566$		0			0
$567$	995.970	+	1121.81i	0.0737686	+	0.0830895i
$568$		0			0
$569$	6681.06	−	11571.9i	0.492240	−	0.852585i	−0.507720	−	0.861522i	$-0.669511\pi$
$569$	6681.06	−	11571.9i	0.492240	−	0.852585i	0.999960	+	0.00893696i	$0.00284476\pi$
$570$		0			0
$571$	11092.6	+	19213.0i	0.812981	+	1.40812i	0.910769	+	0.412917i	$0.135490\pi$
$571$	11092.6	+	19213.0i	0.812981	+	1.40812i	−0.0977876	+	0.995207i	$0.531177\pi$
$572$		0			0
$573$	826.208			0.0602362
$574$		0			0
$575$	112.442			0.00815507
$576$		0			0
$577$	9475.68	+	16412.4i	0.683671	+	1.18415i	0.973853	+	0.227181i	$0.0729508\pi$
$577$	9475.68	+	16412.4i	0.683671	+	1.18415i	−0.290182	+	0.956971i	$0.593716\pi$
$578$		0			0
$579$	−2460.44	+	4261.61i	−0.176602	+	0.305884i
$580$		0			0
$581$	−16538.4	+	3394.64i	−1.18094	+	0.242399i
$582$		0			0
$583$	11486.0	−	19894.4i	0.815957	−	1.41328i
$584$		0			0
$585$	−234.836	−	406.749i	−0.0165971	−	0.0287470i
$586$		0			0
$587$	19579.5			1.37672			0.688359	−	0.725371i	$-0.258332\pi$
$587$	19579.5			1.37672			0.688359	+	0.725371i	$0.258332\pi$
$588$		0			0
$589$	−9486.48			−0.663640
$590$		0			0
$591$	−1955.81	−	3387.57i	−0.136128	−	0.235780i
$592$		0			0
$593$	−2806.51	+	4861.01i	−0.194350	+	0.336624i	−0.946687	−	0.322154i	$-0.895593\pi$
$593$	−2806.51	+	4861.01i	−0.194350	+	0.336624i	0.752337	+	0.658778i	$0.228926\pi$
$594$		0			0
$595$	−644.415	+	132.272i	−0.0444007	+	0.00911362i
$596$		0			0
$597$	1991.03	−	3448.57i	0.136495	−	0.236417i
$598$		0			0
$599$	−10962.8	−	18988.0i	−0.747790	−	1.29521i	−0.948880	−	0.315637i	$-0.897782\pi$
$599$	−10962.8	−	18988.0i	−0.747790	−	1.29521i	0.201090	−	0.979573i	$-0.435552\pi$
$600$		0			0
$601$	−2067.51			−0.140326			−0.0701628	−	0.997536i	$-0.522352\pi$
$601$	−2067.51			−0.140326			−0.0701628	+	0.997536i	$0.522352\pi$
$602$		0			0
$603$	1739.45			0.117472
$604$		0			0
$605$	−1027.01	−	1778.83i	−0.0690146	−	0.119537i
$606$		0			0
$607$	5083.61	−	8805.07i	0.339930	−	0.588775i	−0.644490	−	0.764613i	$-0.722930\pi$
$607$	5083.61	−	8805.07i	0.339930	−	0.588775i	0.984419	+	0.175838i	$0.0562634\pi$
$608$		0			0
$609$	8361.95	+	9418.51i	0.556393	+	0.626695i
$610$		0			0
$611$	−10142.5	+	17567.3i	−0.671558	+	1.16317i
$612$		0			0
$613$	9093.05	+	15749.6i	0.599127	+	1.03772i	0.992950	+	0.118532i	$0.0378188\pi$
$613$	9093.05	+	15749.6i	0.599127	+	1.03772i	−0.393824	+	0.919186i	$0.628848\pi$
$614$		0			0
$615$	406.616			0.0266607
$616$		0			0
$617$	6584.41			0.429625			0.214812	−	0.976655i	$-0.431086\pi$
$617$	6584.41			0.429625			0.214812	+	0.976655i	$0.431086\pi$
$618$		0			0
$619$	3889.86	+	6737.43i	0.252579	+	0.437480i	0.964235	−	0.265048i	$-0.0853878\pi$
$619$	3889.86	+	6737.43i	0.252579	+	0.437480i	−0.711656	+	0.702528i	$0.752054\pi$
$620$		0			0
$621$	12.1952	−	21.1228i	0.000788048	−	0.00136494i
$622$		0			0
$623$	−5553.66	+	16694.3i	−0.357147	+	1.07358i
$624$		0			0
$625$	−7713.72	+	13360.6i	−0.493678	+	0.855075i
$626$		0			0
$627$	3327.35	+	5763.14i	0.211932	+	0.367078i
$628$		0			0
$629$	14436.7			0.915150
$630$		0			0
$631$	3787.78			0.238969			0.119484	−	0.992836i	$-0.461876\pi$
$631$	3787.78			0.238969			0.119484	+	0.992836i	$0.461876\pi$
$632$		0			0
$633$	7129.93	+	12349.4i	0.447692	+	0.775426i
$634$		0			0
$635$	−847.612	+	1468.11i	−0.0529708	+	0.0917481i
$636$		0			0
$637$	22651.1	−	9707.66i	1.40890	−	0.603817i
$638$		0			0
$639$	−182.374	+	315.882i	−0.0112905	+	0.0195557i
$640$		0			0
$641$	9965.44	+	17260.6i	0.614058	+	1.06358i	0.990549	+	0.137159i	$0.0437973\pi$
$641$	9965.44	+	17260.6i	0.614058	+	1.06358i	−0.376491	+	0.926420i	$0.622869\pi$
$642$		0			0
$643$	3185.18			0.195352			0.0976759	−	0.995218i	$-0.468859\pi$
$643$	3185.18			0.195352			0.0976759	+	0.995218i	$0.468859\pi$
$644$		0			0
$645$	−992.148			−0.0605671
$646$		0			0
$647$	8471.50	+	14673.1i	0.514759	+	0.891589i	0.999853	+	0.0171270i	$0.00545198\pi$
$647$	8471.50	+	14673.1i	0.514759	+	0.891589i	−0.485094	+	0.874462i	$0.661215\pi$
$648$		0			0
$649$	23518.3	−	40734.9i	1.42246	−	2.46377i
$650$		0			0
$651$	−4836.98	+	14539.9i	−0.291208	+	0.875369i
$652$		0			0
$653$	10039.4	−	17388.7i	0.601640	−	1.04207i	−0.390932	−	0.920419i	$-0.627847\pi$
$653$	10039.4	−	17388.7i	0.601640	−	1.04207i	0.992573	−	0.121652i	$-0.0388193\pi$
$654$		0			0
$655$	685.295	+	1186.97i	0.0408805	+	0.0708070i
$656$		0			0
$657$	−1858.25			−0.110346
$658$		0			0
$659$	−9442.46			−0.558158			−0.279079	−	0.960268i	$-0.590029\pi$
$659$	−9442.46			−0.558158			−0.279079	+	0.960268i	$0.590029\pi$
$660$		0			0
$661$	−380.995	−	659.902i	−0.0224190	−	0.0388309i	0.854598	−	0.519290i	$-0.173803\pi$
$661$	−380.995	−	659.902i	−0.0224190	−	0.0388309i	−0.877017	+	0.480459i	$0.840470\pi$
$662$		0			0
$663$	−5270.38	+	9128.56i	−0.308725	+	0.534727i
$664$		0			0
$665$	307.200	+	346.016i	0.0179138	+	0.0201773i
$666$		0			0
$667$	102.389	−	177.342i	0.00594378	−	0.0102949i
$668$		0			0
$669$	−769.723	−	1333.20i	−0.0444831	−	0.0770470i
$670$		0			0
$671$	−17692.8			−1.01792
$672$		0			0
$673$	−16111.6			−0.922818			−0.461409	−	0.887188i	$-0.652656\pi$
$673$	−16111.6			−0.922818			−0.461409	+	0.887188i	$0.652656\pi$
$674$		0			0
$675$	1680.38	+	2910.50i	0.0958189	+	0.165963i
$676$		0			0
$677$	−15620.7	+	27055.9i	−0.886786	+	1.53596i	−0.0431329	+	0.999069i	$0.513734\pi$
$677$	−15620.7	+	27055.9i	−0.886786	+	1.53596i	−0.843653	+	0.536889i	$0.819599\pi$
$678$		0			0
$679$	−716.042	+	146.974i	−0.0404700	+	0.00830682i
$680$		0			0
$681$	−4964.01	+	8597.92i	−0.279327	+	0.483808i
$682$		0			0
$683$	15056.8	+	26079.1i	0.843530	+	1.46104i	0.886892	+	0.461978i	$0.152860\pi$
$683$	15056.8	+	26079.1i	0.843530	+	1.46104i	−0.0433614	+	0.999059i	$0.513807\pi$
$684$		0			0
$685$	2140.72			0.119405
$686$		0			0
$687$	−17728.4			−0.984542
$688$		0			0
$689$	−12796.6	−	22164.3i	−0.707562	−	1.22553i
$690$		0			0
$691$	4875.43	−	8444.49i	0.268408	−	0.464896i	−0.700043	−	0.714101i	$-0.746836\pi$
$691$	4875.43	−	8444.49i	0.268408	−	0.464896i	0.968451	+	0.249204i	$0.0801691\pi$
$692$		0			0
$693$	10529.7	−	2161.31i	0.577188	−	0.118473i
$694$		0			0
$695$	−346.986	+	600.997i	−0.0189380	+	0.0328016i
$696$		0			0
$697$	−4562.79	−	7902.99i	−0.247960	−	0.429479i
$698$		0			0
$699$	−1060.71			−0.0573962
$700$		0			0
$701$	11851.6			0.638559			0.319280	−	0.947661i	$-0.396559\pi$
$701$	11851.6			0.638559			0.319280	+	0.947661i	$0.396559\pi$
$702$		0			0
$703$	−5077.13	−	8793.85i	−0.272386	−	0.471787i
$704$		0			0
$705$	−307.607	+	532.791i	−0.0164328	+	0.0284625i
$706$		0			0
$707$	−3896.26	−	4388.57i	−0.207262	−	0.233450i
$708$		0			0
$709$	−661.196	+	1145.22i	−0.0350236	+	0.0606627i	−0.883006	−	0.469362i	$-0.844484\pi$
$709$	−661.196	+	1145.22i	−0.0350236	+	0.0606627i	0.847982	+	0.530025i	$0.177817\pi$
$710$		0			0
$711$	−4219.83	−	7308.96i	−0.222582	−	0.385524i
$712$		0			0
$713$	249.140			0.0130861
$714$		0			0
$715$	−3365.44			−0.176028
$716$		0			0
$717$	2478.83	+	4293.46i	0.129112	+	0.223629i
$718$		0			0
$719$	−3650.78	+	6323.33i	−0.189362	+	0.327984i	−0.945038	−	0.326962i	$-0.893975\pi$
$719$	−3650.78	+	6323.33i	−0.189362	+	0.327984i	0.755676	+	0.654946i	$0.227309\pi$
$720$		0			0
$721$	−1886.15	+	5669.76i	−0.0974257	+	0.292861i
$722$		0			0
$723$	4660.42	−	8072.08i	0.239727	−	0.415220i
$724$		0			0
$725$	14108.1	+	24435.9i	0.722705	+	1.25176i
$726$		0			0
$727$	−6088.72			−0.310616			−0.155308	−	0.987866i	$-0.549637\pi$
$727$	−6088.72			−0.310616			−0.155308	+	0.987866i	$0.549637\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	11133.3	+	19283.4i	0.563309	+	0.975680i
$732$		0			0
$733$	13289.2	−	23017.6i	0.669644	−	1.15986i	−0.308360	−	0.951270i	$-0.599780\pi$
$733$	13289.2	−	23017.6i	0.669644	−	1.15986i	0.978004	−	0.208587i	$-0.0668865\pi$
$734$		0			0
$735$	686.974	−	294.418i	0.0344754	−	0.0147752i
$736$		0			0
$737$	6232.01	−	10794.2i	0.311478	−	0.539495i
$738$		0			0
$739$	−12609.9	−	21841.0i	−0.627689	−	1.08719i	−0.988014	−	0.154363i	$-0.950668\pi$
$739$	−12609.9	−	21841.0i	−0.627689	−	1.08719i	0.360325	−	0.932827i	$-0.382666\pi$
$740$		0			0
$741$	7413.98			0.367557
$742$		0			0
$743$	2634.28			0.130071			0.0650353	−	0.997883i	$-0.479284\pi$
$743$	2634.28			0.130071			0.0650353	+	0.997883i	$0.479284\pi$
$744$		0			0
$745$	−793.071	−	1373.64i	−0.0390012	−	0.0675520i
$746$		0			0
$747$	−4102.23	+	7105.27i	−0.200927	+	0.348016i
$748$		0			0
$749$	3983.84	−	11975.4i	0.194347	−	0.584207i
$750$		0			0
$751$	−2883.64	+	4994.62i	−0.140114	+	0.242685i	−0.927539	−	0.373725i	$-0.878080\pi$
$751$	−2883.64	+	4994.62i	−0.140114	+	0.242685i	0.787425	+	0.616410i	$0.211414\pi$
$752$		0			0
$753$	−2657.66	−	4603.20i	−0.128619	−	0.222776i
$754$		0			0
$755$	293.965			0.0141702
$756$		0			0
$757$	33378.7			1.60260			0.801302	−	0.598260i	$-0.204141\pi$
$757$	33378.7			1.60260			0.801302	+	0.598260i	$0.204141\pi$
$758$		0			0
$759$	−87.3849	−	151.355i	−0.00417901	−	0.00723826i
$760$		0			0
$761$	−1813.04	+	3140.28i	−0.0863637	+	0.149586i	−0.905971	−	0.423339i	$-0.860858\pi$
$761$	−1813.04	+	3140.28i	−0.0863637	+	0.149586i	0.819608	+	0.572925i	$0.194191\pi$
$762$		0			0
$763$	−5606.54	−	6314.95i	−0.266016	−	0.299628i
$764$		0			0
$765$	−159.843	+	276.855i	−0.00755440	+	0.0130846i
$766$		0			0
$767$	−26201.7	−	45382.7i	−1.23349	−	2.13647i
$768$		0			0
$769$	3426.15			0.160663			0.0803316	−	0.996768i	$-0.474402\pi$
$769$	3426.15			0.160663			0.0803316	+	0.996768i	$0.474402\pi$
$770$		0			0
$771$	4434.38			0.207134
$772$		0			0
$773$	−6554.09	−	11352.0i	−0.304960	−	0.528207i	0.672292	−	0.740286i	$-0.265310\pi$
$773$	−6554.09	−	11352.0i	−0.304960	−	0.528207i	−0.977252	+	0.212079i	$0.931976\pi$
$774$		0			0
$775$	−17164.4	+	29729.7i	−0.795568	+	1.37796i
$776$		0			0
$777$	−16067.1	+	3297.90i	−0.741831	+	0.152267i
$778$		0			0
$779$	−3209.30	+	5558.67i	−0.147606	+	0.255661i
$780$		0			0
$781$	1306.80	+	2263.45i	0.0598734	+	0.103704i
$782$		0			0
$783$	6120.53			0.279348
$784$		0			0
$785$	−675.194			−0.0306990
$786$		0			0
$787$	−19659.9	−	34051.9i	−0.890468	−	1.54234i	−0.839315	−	0.543646i	$-0.817043\pi$
$787$	−19659.9	−	34051.9i	−0.890468	−	1.54234i	−0.0511538	−	0.998691i	$-0.516290\pi$
$788$		0			0
$789$	2147.96	−	3720.38i	0.0969195	−	0.167869i
$790$		0			0
$791$	14441.5	−	2964.24i	0.649154	−	0.133244i
$792$		0			0
$793$	−9855.77	+	17070.7i	−0.441348	+	0.764437i
$794$		0			0
$795$	−388.100	−	672.209i	−0.0173138	−	0.0299884i
$796$		0			0
$797$	−14597.8			−0.648785			−0.324393	−	0.945923i	$-0.605160\pi$
$797$	−14597.8			−0.648785			−0.324393	+	0.945923i	$0.605160\pi$
$798$		0			0
$799$	13807.1			0.611339
$800$		0			0
$801$	4274.89	+	7404.33i	0.188572	+	0.326615i
$802$		0			0
$803$	−6657.65	+	11531.4i	−0.292582	+	0.506767i
$804$		0			0
$805$	−8.06786	−	9.08727i	−0.000353236	−	0.000397868i
$806$		0			0
$807$	−428.097	+	741.486i	−0.0186738	+	0.0323439i
$808$		0			0
$809$	−13413.7	−	23233.2i	−0.582943	−	1.00969i	−0.995128	−	0.0985870i	$-0.968568\pi$
$809$	−13413.7	−	23233.2i	−0.582943	−	1.00969i	0.412185	−	0.911100i	$-0.364766\pi$
$810$		0			0
$811$	−5177.09			−0.224158			−0.112079	−	0.993699i	$-0.535751\pi$
$811$	−5177.09			−0.224158			−0.112079	+	0.993699i	$0.535751\pi$
$812$		0			0
$813$	−15748.0			−0.679343
$814$		0			0
$815$	517.766	+	896.796i	0.0222534	+	0.0385441i
$816$		0			0
$817$	7830.74	−	13563.2i	0.335328	−	0.580805i
$818$		0			0
$819$	3780.25	−	11363.4i	0.161285	−	0.484823i
$820$		0			0
$821$	−10178.4	+	17629.5i	−0.432678	+	0.749420i	−0.997103	−	0.0760646i	$-0.975764\pi$
$821$	−10178.4	+	17629.5i	−0.432678	+	0.749420i	0.564425	+	0.825484i	$0.309098\pi$
$822$		0			0
$823$	−28.7869	−	49.8603i	−0.00121926	−	0.00211181i	0.865415	−	0.501056i	$-0.167055\pi$
$823$	−28.7869	−	49.8603i	−0.00121926	−	0.00211181i	−0.866634	+	0.498944i	$0.833721\pi$
$824$		0			0
$825$	24081.5			1.01625
$826$		0			0
$827$	−12296.6			−0.517044			−0.258522	−	0.966005i	$-0.583235\pi$
$827$	−12296.6			−0.517044			−0.258522	+	0.966005i	$0.583235\pi$
$828$		0			0
$829$	−11435.9	−	19807.5i	−0.479112	−	0.829846i	0.520601	−	0.853800i	$-0.325708\pi$
$829$	−11435.9	−	19807.5i	−0.479112	−	0.829846i	−0.999713	+	0.0239540i	$0.992374\pi$
$830$		0			0
$831$	−10721.8	+	18570.7i	−0.447576	+	0.775224i
$832$		0			0
$833$	−13431.1	−	10048.2i	−0.558656	−	0.417948i
$834$		0			0
$835$	−1519.93	+	2632.59i	−0.0629931	+	0.109107i
$836$		0			0
$837$	3723.23	+	6448.83i	0.153756	+	0.266313i
$838$		0			0
$839$	37571.3			1.54601			0.773007	−	0.634398i	$-0.218752\pi$
$839$	37571.3			1.54601			0.773007	+	0.634398i	$0.218752\pi$
$840$		0			0
$841$	26997.6			1.10696
$842$		0			0
$843$	−6342.54	−	10985.6i	−0.259132	−	0.448831i
$844$		0			0
$845$	−1076.83	+	1865.12i	−0.0438390	+	0.0759313i
$846$		0			0
$847$	16532.2	−	49695.6i	0.670663	−	2.01601i
$848$		0			0
$849$	−12513.6	+	21674.1i	−0.505848	+	0.876154i
$850$		0			0
$851$	133.339	+	230.949i	0.00537108	+	0.00930298i
$852$		0			0
$853$	−38354.5			−1.53955			−0.769774	−	0.638317i	$-0.779631\pi$
$853$	−38354.5			−1.53955			−0.769774	+	0.638317i	$0.779631\pi$
$854$		0			0
$855$	224.855			0.00899401
$856$		0			0
$857$	−18272.8	−	31649.5i	−0.728341	−	1.26152i	−0.957584	−	0.288154i	$-0.906958\pi$
$857$	−18272.8	−	31649.5i	−0.728341	−	1.26152i	0.229243	−	0.973369i	$-0.426375\pi$
$858$		0			0
$859$	9282.13	−	16077.1i	0.368687	−	0.638585i	−0.620673	−	0.784069i	$-0.713141\pi$
$859$	9282.13	−	16077.1i	0.368687	−	0.638585i	0.989361	+	0.145484i	$0.0464740\pi$
$860$		0			0
$861$	6883.42	+	7753.17i	0.272458	+	0.306884i
$862$		0			0
$863$	−18728.9	+	32439.3i	−0.738746	+	1.27955i	0.214314	+	0.976765i	$0.431248\pi$
$863$	−18728.9	+	32439.3i	−0.738746	+	1.27955i	−0.953060	+	0.302781i	$0.902085\pi$
$864$		0			0
$865$	−811.888	−	1406.23i	−0.0319133	−	0.0552755i
$866$		0			0
$867$	−7564.39			−0.296309
$868$		0			0
$869$	−60474.4			−2.36071
$870$		0			0
$871$	−6943.06	−	12025.7i	−0.270100	−	0.467826i
$872$		0			0
$873$	−177.609	+	307.628i	−0.00688563	+	0.0119263i
$874$		0			0
$875$	3287.38	−	674.762i	0.127010	−	0.0260698i
$876$		0			0
$877$	13564.4	−	23494.2i	0.522277	−	0.904611i	−0.477387	−	0.878693i	$-0.658416\pi$
$877$	13564.4	−	23494.2i	0.522277	−	0.904611i	0.999664	−	0.0259177i	$-0.00825080\pi$
$878$		0			0
$879$	−7558.27	−	13091.3i	−0.290027	−	0.502342i
$880$		0			0
$881$	23647.8			0.904329			0.452165	−	0.891935i	$-0.350652\pi$
$881$	23647.8			0.904329			0.452165	+	0.891935i	$0.350652\pi$
$882$		0			0
$883$	−4488.47			−0.171063			−0.0855316	−	0.996335i	$-0.527259\pi$
$883$	−4488.47			−0.171063			−0.0855316	+	0.996335i	$0.527259\pi$
$884$		0			0
$885$	−794.658	−	1376.39i	−0.0301832	−	0.0522788i
$886$		0			0
$887$	20513.4	−	35530.3i	0.776520	−	1.34497i	−0.157417	−	0.987532i	$-0.550317\pi$
$887$	20513.4	−	35530.3i	0.776520	−	1.34497i	0.933936	−	0.357439i	$-0.116350\pi$
$888$		0			0
$889$	−42342.0	+	8691.06i	−1.59742	+	0.327884i
$890$		0			0
$891$	2611.82	−	4523.81i	0.0982036	−	0.170094i
$892$		0			0
$893$	−4855.71	−	8410.33i	−0.181960	−	0.315163i
$894$		0			0
$895$	−683.836			−0.0255398
$896$		0			0
$897$	−194.710			−0.00724771
$898$		0			0
$899$	31259.5	+	54143.0i	1.15969	+	2.00864i
$900$		0			0
$901$	−8710.04	+	15086.2i	−0.322057	+	0.557819i
$902$		0			0
$903$	−16795.6	−	18917.8i	−0.618963	−	0.697171i
$904$		0			0
$905$	169.797	−	294.097i	0.00623673	−	0.0108023i
$906$		0			0
$907$	368.152	+	637.659i	0.0134777	+	0.0233441i	0.872686	−	0.488283i	$-0.162376\pi$
$907$	368.152	+	637.659i	0.0134777	+	0.0233441i	−0.859208	+	0.511627i	$0.829043\pi$
$908$		0			0
$909$	−2851.87			−0.104060
$910$		0			0
$911$	1287.54			0.0468256			0.0234128	−	0.999726i	$-0.492547\pi$
$911$	1287.54			0.0468256			0.0234128	+	0.999726i	$0.492547\pi$
$912$		0			0
$913$	29394.5	+	50912.8i	1.06552	+	1.84553i
$914$		0			0
$915$	−298.911	+	517.728i	−0.0107997	+	0.0187055i
$916$		0			0
$917$	−11031.5	+	33160.5i	−0.397264	+	1.19417i
$918$		0			0
$919$	−17140.0	+	29687.3i	−0.615230	+	1.06561i	0.375114	+	0.926979i	$0.377603\pi$
$919$	−17140.0	+	29687.3i	−0.615230	+	1.06561i	−0.990344	+	0.138631i	$0.955730\pi$
$920$		0			0
$921$	7304.51	+	12651.8i	0.261337	+	0.452650i
$922$		0			0
$923$	2911.81			0.103839
$924$		0			0
$925$	−36745.4			−1.30614
$926$		0			0
$927$	1451.85	+	2514.68i	0.0514402	+	0.0890971i
$928$		0			0
$929$	15737.9	−	27258.9i	0.555806	−	0.962685i	−0.442034	−	0.896998i	$-0.645743\pi$
$929$	15737.9	−	27258.9i	0.555806	−	0.962685i	0.997840	−	0.0656866i	$-0.0209238\pi$
$930$		0			0
$931$	−1397.22	+	11715.1i	−0.0491858	+	0.412402i
$932$		0			0
$933$	2179.26	−	3774.59i	0.0764693	−	0.132449i
$934$		0			0
$935$	1145.35	+	1983.81i	0.0400609	+	0.0693876i
$936$		0			0
$937$	52560.6			1.83253			0.916264	−	0.400575i	$-0.131190\pi$
$937$	52560.6			1.83253			0.916264	+	0.400575i	$0.131190\pi$
$938$		0			0
$939$	17088.8			0.593900
$940$		0			0
$941$	−7988.37	−	13836.3i	−0.276741	−	0.479330i	0.693832	−	0.720137i	$-0.255921\pi$
$941$	−7988.37	−	13836.3i	−0.276741	−	0.479330i	−0.970573	+	0.240807i	$0.922588\pi$
$942$		0			0
$943$	84.2846	−	145.985i	0.00291059	−	0.00504129i
$944$		0			0
$945$	114.649	−	344.635i	0.00394661	−	0.0118635i
$946$		0			0
$947$	4252.22	−	7365.06i	0.145912	−	0.252727i	−0.783801	−	0.621012i	$-0.786722\pi$
$947$	4252.22	−	7365.06i	0.145912	−	0.252727i	0.929713	+	0.368285i	$0.120055\pi$
$948$		0			0
$949$	7417.27	+	12847.1i	0.253714	+	0.439446i
$950$		0			0
$951$	−10414.4			−0.355111
$952$		0			0
$953$	29417.5			0.999923			0.499961	−	0.866048i	$-0.333348\pi$
$953$	29417.5			0.999923			0.499961	+	0.866048i	$0.333348\pi$
$954$		0			0
$955$	−100.018	−	173.237i	−0.00338902	−	0.00586995i
$956$		0			0
$957$	21928.3	−	37980.9i	0.740691	−	1.28291i
$958$		0			0
$959$	36239.3	+	40818.2i	1.22026	+	1.37444i
$960$		0			0
$961$	−23136.0	+	40072.7i	−0.776610	+	1.34513i
$962$		0			0
$963$	−3066.53	−	5311.39i	−0.102614	−	0.177733i
$964$		0			0
$965$	1191.42			0.0397441
$966$		0			0
$967$	3461.97			0.115129			0.0575643	−	0.998342i	$-0.481667\pi$
$967$	3461.97			0.115129			0.0575643	+	0.998342i	$0.481667\pi$
$968$		0			0
$969$	−2523.18	−	4370.28i	−0.0836494	−	0.144885i
$970$		0			0
$971$	21779.4	−	37723.0i	0.719809	−	1.24675i	−0.241266	−	0.970459i	$-0.577563\pi$
$971$	21779.4	−	37723.0i	0.719809	−	1.24675i	0.961075	−	0.276287i	$-0.0891039\pi$
$972$		0			0
$973$	−17333.5	+	3557.84i	−0.571106	+	0.117224i
$974$		0			0
$975$	13414.6	−	23234.7i	0.440625	−	0.763185i
$976$		0			0
$977$	2752.47	+	4767.42i	0.0901325	+	0.156114i	0.907567	−	0.419908i	$-0.137938\pi$
$977$	2752.47	+	4767.42i	0.0901325	+	0.156114i	−0.817434	+	0.576022i	$0.804604\pi$
$978$		0			0
$979$	61263.4			1.99999
$980$		0			0
$981$	−4103.71			−0.133559
$982$		0			0
$983$	15394.9	+	26664.7i	0.499511	+	0.865179i	1.00000		0.000564108i	$-0.000179561\pi$
$983$	15394.9	+	26664.7i	0.499511	+	0.865179i	−0.500488	+	0.865743i	$0.666846\pi$
$984$		0			0
$985$	−473.530	+	820.178i	−0.0153177	+	0.0265310i
$986$		0			0
$987$	−15366.4	+	3154.07i	−0.495559	+	0.101718i
$988$		0			0
$989$	−205.655	+	356.206i	−0.00661220	+	0.0114527i
$990$		0			0
$991$	10814.6	+	18731.4i	0.346656	+	0.600426i	0.985653	−	0.168783i	$-0.0539838\pi$
$991$	10814.6	+	18731.4i	0.346656	+	0.600426i	−0.638997	+	0.769209i	$0.720650\pi$
$992$		0			0
$993$	18763.1			0.599627
$994$		0			0
$995$	−964.114			−0.0307181
$996$		0			0
$997$	19097.9	+	33078.5i	0.606656	+	1.05076i	0.991787	+	0.127898i	$0.0408229\pi$
$997$	19097.9	+	33078.5i	0.606656	+	1.05076i	−0.385131	+	0.922862i	$0.625844\pi$
$998$		0			0
$999$	−3985.32	+	6902.78i	−0.126216	+	0.218613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.q.f.121.2	yes	8
3.2	odd	2		504.4.s.j.289.3		8
4.3	odd	2		336.4.q.m.289.2		8
7.2	even	3		1176.4.a.bd.1.3		4
7.4	even	3	inner	168.4.q.f.25.2	✓	8
7.5	odd	6		1176.4.a.ba.1.2		4
21.11	odd	6		504.4.s.j.361.3		8
28.11	odd	6		336.4.q.m.193.2		8
28.19	even	6		2352.4.a.cp.1.2		4
28.23	odd	6		2352.4.a.cm.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.f.25.2	✓	8	7.4	even	3	inner
168.4.q.f.121.2	yes	8	1.1	even	1	trivial
336.4.q.m.193.2		8	28.11	odd	6
336.4.q.m.289.2		8	4.3	odd	2
504.4.s.j.289.3		8	3.2	odd	2
504.4.s.j.361.3		8	21.11	odd	6
1176.4.a.ba.1.2		4	7.5	odd	6
1176.4.a.bd.1.3		4	7.2	even	3
2352.4.a.cm.1.3		4	28.23	odd	6
2352.4.a.cp.1.2		4	28.19	even	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{3} +(-0.363171 + 0.629031i) q^{5} +(-18.1420 + 3.72380i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{3} +(-0.363171 + 0.629031i) q^{5} +(-18.1420 + 3.72380i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(32.2447 + 55.8495i) q^{11} +71.8475 q^{13} +2.17903 q^{15} +(-24.4517 - 42.3515i) q^{17} +(-17.1984 + 29.7885i) q^{19} +(36.8878 + 41.5487i) q^{21} +(0.451675 - 0.782324i) q^{23} +(62.2362 + 107.796i) q^{25} +27.0000 q^{27} +226.686 q^{29} +(137.898 + 238.846i) q^{31} +(96.7342 - 167.549i) q^{33} +(4.24627 - 12.7643i) q^{35} +(-147.605 + 255.658i) q^{37} +(-107.771 - 186.665i) q^{39} +186.604 q^{41} -455.317 q^{43} +(-3.26854 - 5.66128i) q^{45} +(-141.167 + 244.509i) q^{47} +(315.267 - 135.115i) q^{49} +(-73.3550 + 127.055i) q^{51} +(-178.107 - 308.491i) q^{53} -46.8414 q^{55} +103.191 q^{57} +(-364.685 - 631.653i) q^{59} +(-137.176 + 237.596i) q^{61} +(52.6150 - 158.160i) q^{63} +(-26.0929 + 45.1943i) q^{65} +(-96.6361 - 167.379i) q^{67} -2.71005 q^{69} +40.5277 q^{71} +(103.236 + 178.810i) q^{73} +(186.709 - 323.389i) q^{75} +(-792.958 - 893.151i) q^{77} +(-468.870 + 812.107i) q^{79} +(-40.5000 - 70.1481i) q^{81} +911.607 q^{83} +35.5206 q^{85} +(-340.029 - 588.948i) q^{87} +(474.988 - 822.703i) q^{89} +(-1303.46 + 267.546i) q^{91} +(413.693 - 716.537i) q^{93} +(-12.4919 - 21.6367i) q^{95} +39.4687 q^{97} -580.405 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} - 4 q^{5} + 18 q^{7} - 36 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 - 4 * q^5 + 18 * q^7 - 36 * q^9	\( 8 q - 12 q^{3} - 4 q^{5} + 18 q^{7} - 36 q^{9} - 14 q^{11} + 44 q^{13} + 24 q^{15} - 96 q^{17} + 26 q^{19} - 36 q^{21} - 96 q^{23} - 110 q^{25} + 216 q^{27} - 152 q^{29} - 238 q^{31} - 42 q^{33} + 152 q^{35} - 562 q^{37} - 66 q^{39} + 856 q^{41} - 516 q^{43} - 36 q^{45} + 80 q^{47} + 156 q^{49} - 288 q^{51} + 2952 q^{55} - 156 q^{57} - 262 q^{59} + 276 q^{61} - 54 q^{63} - 2196 q^{65} - 150 q^{67} + 576 q^{69} - 1696 q^{71} + 218 q^{73} - 330 q^{75} - 764 q^{77} - 1762 q^{79} - 324 q^{81} + 6900 q^{83} + 2904 q^{85} + 228 q^{87} + 344 q^{89} - 2806 q^{91} - 714 q^{93} - 2004 q^{95} - 1244 q^{97} + 252 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 - 4 * q^5 + 18 * q^7 - 36 * q^9 - 14 * q^11 + 44 * q^13 + 24 * q^15 - 96 * q^17 + 26 * q^19 - 36 * q^21 - 96 * q^23 - 110 * q^25 + 216 * q^27 - 152 * q^29 - 238 * q^31 - 42 * q^33 + 152 * q^35 - 562 * q^37 - 66 * q^39 + 856 * q^41 - 516 * q^43 - 36 * q^45 + 80 * q^47 + 156 * q^49 - 288 * q^51 + 2952 * q^55 - 156 * q^57 - 262 * q^59 + 276 * q^61 - 54 * q^63 - 2196 * q^65 - 150 * q^67 + 576 * q^69 - 1696 * q^71 + 218 * q^73 - 330 * q^75 - 764 * q^77 - 1762 * q^79 - 324 * q^81 + 6900 * q^83 + 2904 * q^85 + 228 * q^87 + 344 * q^89 - 2806 * q^91 - 714 * q^93 - 2004 * q^95 - 1244 * q^97 + 252 * q^99

Introduction

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