LMFDB - Embedded newform 168.4.q.c.121.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(25,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [2,0,3,0,11] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	168.121
Dual form			168.4.q.c.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 + 2.59808i) q^{3} +(5.50000 - 9.52628i) q^{5} +(3.50000 - 18.1865i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-19.5000 - 33.7750i) q^{11} -32.0000 q^{13} +33.0000 q^{15} +(-6.00000 - 10.3923i) q^{17} +(44.0000 - 76.2102i) q^{19} +(52.5000 - 18.1865i) q^{21} +(46.0000 - 79.6743i) q^{23} +(2.00000 + 3.46410i) q^{25} -27.0000 q^{27} +255.000 q^{29} +(17.5000 + 30.3109i) q^{31} +(58.5000 - 101.325i) q^{33} +(-154.000 - 133.368i) q^{35} +(2.00000 - 3.46410i) q^{37} +(-48.0000 - 83.1384i) q^{39} +16.0000 q^{41} -330.000 q^{43} +(49.5000 + 85.7365i) q^{45} +(149.000 - 258.076i) q^{47} +(-318.500 - 127.306i) q^{49} +(18.0000 - 31.1769i) q^{51} +(358.500 + 620.940i) q^{53} -429.000 q^{55} +264.000 q^{57} +(108.500 + 187.928i) q^{59} +(-193.000 + 334.286i) q^{61} +(126.000 + 109.119i) q^{63} +(-176.000 + 304.841i) q^{65} +(-453.000 - 784.619i) q^{67} +276.000 q^{69} -34.0000 q^{71} +(419.000 + 725.729i) q^{73} +(-6.00000 + 10.3923i) q^{75} +(-682.500 + 236.425i) q^{77} +(-662.500 + 1147.48i) q^{79} +(-40.5000 - 70.1481i) q^{81} +1163.00 q^{83} -132.000 q^{85} +(382.500 + 662.509i) q^{87} +(27.0000 - 46.7654i) q^{89} +(-112.000 + 581.969i) q^{91} +(-52.5000 + 90.9327i) q^{93} +(-484.000 - 838.313i) q^{95} +7.00000 q^{97} +351.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 11 q^{5} + 7 q^{7} - 9 q^{9} - 39 q^{11} - 64 q^{13} + 66 q^{15} - 12 q^{17} + 88 q^{19} + 105 q^{21} + 92 q^{23} + 4 q^{25} - 54 q^{27} + 510 q^{29} + 35 q^{31} + 117 q^{33} - 308 q^{35}+ \cdots + 702 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 11 * q^5 + 7 * q^7 - 9 * q^9 - 39 * q^11 - 64 * q^13 + 66 * q^15 - 12 * q^17 + 88 * q^19 + 105 * q^21 + 92 * q^23 + 4 * q^25 - 54 * q^27 + 510 * q^29 + 35 * q^31 + 117 * q^33 - 308 * q^35 + 4 * q^37 - 96 * q^39 + 32 * q^41 - 660 * q^43 + 99 * q^45 + 298 * q^47 - 637 * q^49 + 36 * q^51 + 717 * q^53 - 858 * q^55 + 528 * q^57 + 217 * q^59 - 386 * q^61 + 252 * q^63 - 352 * q^65 - 906 * q^67 + 552 * q^69 - 68 * q^71 + 838 * q^73 - 12 * q^75 - 1365 * q^77 - 1325 * q^79 - 81 * q^81 + 2326 * q^83 - 264 * q^85 + 765 * q^87 + 54 * q^89 - 224 * q^91 - 105 * q^93 - 968 * q^95 + 14 * q^97 + 702 * q^99

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
$5$	5.50000	−	9.52628i	0.491935	−	0.852056i	−0.508022	−	0.861344i	$-0.669623\pi$
$5$	5.50000	−	9.52628i	0.491935	−	0.852056i	0.999957	+	0.00928781i	$0.00295644\pi$
$6$		0			0
$7$	3.50000	−	18.1865i	0.188982	−	0.981981i
$7$	3.50000	−	18.1865i	0.188982	−	0.981981i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−19.5000	−	33.7750i	−0.534497	−	0.925777i	−0.999187	−	0.0403032i	$-0.987168\pi$
$11$	−19.5000	−	33.7750i	−0.534497	−	0.925777i	0.464690	−	0.885473i	$-0.346166\pi$
$12$		0			0
$13$	−32.0000			−0.682708			−0.341354	−	0.939935i	$-0.610885\pi$
$13$	−32.0000			−0.682708			−0.341354	+	0.939935i	$0.610885\pi$
$14$		0			0
$15$	33.0000			0.568038
$16$		0			0
$17$	−6.00000	−	10.3923i	−0.0856008	−	0.148265i	0.820046	−	0.572297i	$-0.193948\pi$
$17$	−6.00000	−	10.3923i	−0.0856008	−	0.148265i	−0.905647	+	0.424032i	$0.860614\pi$
$18$		0			0
$19$	44.0000	−	76.2102i	0.531279	−	0.920201i	−0.468055	−	0.883699i	$-0.655045\pi$
$19$	44.0000	−	76.2102i	0.531279	−	0.920201i	0.999334	−	0.0365021i	$-0.0116216\pi$
$20$		0			0
$21$	52.5000	−	18.1865i	0.545545	−	0.188982i
$22$		0			0
$23$	46.0000	−	79.6743i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	46.0000	−	79.6743i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.0160000	+	0.0277128i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	255.000			1.63284			0.816419	−	0.577460i	$-0.195956\pi$
$29$	255.000			1.63284			0.816419	+	0.577460i	$0.195956\pi$
$30$		0			0
$31$	17.5000	+	30.3109i	0.101390	+	0.175613i	0.912258	−	0.409617i	$-0.134338\pi$
$31$	17.5000	+	30.3109i	0.101390	+	0.175613i	−0.810868	+	0.585230i	$0.801004\pi$
$32$		0			0
$33$	58.5000	−	101.325i	0.308592	−	0.534497i
$34$		0			0
$35$	−154.000	−	133.368i	−0.743736	−	0.644094i
$36$		0			0
$37$	2.00000	−	3.46410i	0.00888643	−	0.0153918i	−0.861548	−	0.507676i	$-0.830505\pi$
$37$	2.00000	−	3.46410i	0.00888643	−	0.0153918i	0.870434	+	0.492284i	$0.163838\pi$
$38$		0			0
$39$	−48.0000	−	83.1384i	−0.197081	−	0.341354i
$40$		0			0
$41$	16.0000			0.0609459			0.0304729	−	0.999536i	$-0.490299\pi$
$41$	16.0000			0.0609459			0.0304729	+	0.999536i	$0.490299\pi$
$42$		0			0
$43$	−330.000			−1.17034			−0.585169	−	0.810911i	$-0.698972\pi$
$43$	−330.000			−1.17034			−0.585169	+	0.810911i	$0.698972\pi$
$44$		0			0
$45$	49.5000	+	85.7365i	0.163978	+	0.284019i
$46$		0			0
$47$	149.000	−	258.076i	0.462423	−	0.800940i	−0.536658	−	0.843800i	$-0.680313\pi$
$47$	149.000	−	258.076i	0.462423	−	0.800940i	0.999081	+	0.0428596i	$0.0136468\pi$
$48$		0			0
$49$	−318.500	−	127.306i	−0.928571	−	0.371154i
$50$		0			0
$51$	18.0000	−	31.1769i	0.0494217	−	0.0856008i
$52$		0			0
$53$	358.500	+	620.940i	0.929128	+	1.60930i	0.784785	+	0.619768i	$0.212773\pi$
$53$	358.500	+	620.940i	0.929128	+	1.60930i	0.144343	+	0.989528i	$0.453893\pi$
$54$		0			0
$55$	−429.000			−1.05175
$56$		0			0
$57$	264.000			0.613468
$58$		0			0
$59$	108.500	+	187.928i	0.239415	+	0.414679i	0.960547	−	0.278119i	$-0.0897110\pi$
$59$	108.500	+	187.928i	0.239415	+	0.414679i	−0.721131	+	0.692798i	$0.756378\pi$
$60$		0			0
$61$	−193.000	+	334.286i	−0.405100	+	0.701654i	−0.994333	−	0.106309i	$-0.966097\pi$
$61$	−193.000	+	334.286i	−0.405100	+	0.701654i	0.589233	+	0.807963i	$0.299430\pi$
$62$		0			0
$63$	126.000	+	109.119i	0.251976	+	0.218218i
$64$		0			0
$65$	−176.000	+	304.841i	−0.335848	+	0.581706i
$66$		0			0
$67$	−453.000	−	784.619i	−0.826011	−	1.43069i	−0.901144	−	0.433520i	$-0.857271\pi$
$67$	−453.000	−	784.619i	−0.826011	−	1.43069i	0.0751326	−	0.997174i	$-0.476062\pi$
$68$		0			0
$69$	276.000			0.481543
$70$		0			0
$71$	−34.0000			−0.0568318			−0.0284159	−	0.999596i	$-0.509046\pi$
$71$	−34.0000			−0.0568318			−0.0284159	+	0.999596i	$0.509046\pi$
$72$		0			0
$73$	419.000	+	725.729i	0.671784	+	1.16356i	0.977398	+	0.211409i	$0.0678051\pi$
$73$	419.000	+	725.729i	0.671784	+	1.16356i	−0.305614	+	0.952156i	$0.598862\pi$
$74$		0			0
$75$	−6.00000	+	10.3923i	−0.00923760	+	0.0160000i
$76$		0			0
$77$	−682.500	+	236.425i	−1.01011	+	0.349911i
$78$		0			0
$79$	−662.500	+	1147.48i	−0.943507	+	1.63420i	−0.184795	+	0.982777i	$0.559162\pi$
$79$	−662.500	+	1147.48i	−0.943507	+	1.63420i	−0.758713	+	0.651425i	$0.774171\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	1163.00			1.53802			0.769011	−	0.639235i	$-0.220749\pi$
$83$	1163.00			1.53802			0.769011	+	0.639235i	$0.220749\pi$
$84$		0			0
$85$	−132.000			−0.168440
$86$		0			0
$87$	382.500	+	662.509i	0.471360	+	0.816419i
$88$		0			0
$89$	27.0000	−	46.7654i	0.0321572	−	0.0556980i	−0.849499	−	0.527590i	$-0.823096\pi$
$89$	27.0000	−	46.7654i	0.0321572	−	0.0556980i	0.881656	+	0.471892i	$0.156429\pi$
$90$		0			0
$91$	−112.000	+	581.969i	−0.129020	+	0.670406i
$92$		0			0
$93$	−52.5000	+	90.9327i	−0.0585376	+	0.101390i
$94$		0			0
$95$	−484.000	−	838.313i	−0.522709	−	0.905358i
$96$		0			0
$97$	7.00000			0.00732724			0.00366362	−	0.999993i	$-0.498834\pi$
$97$	7.00000			0.00732724			0.00366362	+	0.999993i	$0.498834\pi$
$98$		0			0
$99$	351.000			0.356332
$100$		0			0
$101$	23.0000	+	39.8372i	0.0226593	+	0.0392470i	0.877133	−	0.480248i	$-0.159453\pi$
$101$	23.0000	+	39.8372i	0.0226593	+	0.0392470i	−0.854473	+	0.519495i	$0.826120\pi$
$102$		0			0
$103$	−828.000	+	1434.14i	−0.792090	+	1.37194i	0.132581	+	0.991172i	$0.457674\pi$
$103$	−828.000	+	1434.14i	−0.792090	+	1.37194i	−0.924671	+	0.380768i	$0.875660\pi$
$104$		0			0
$105$	115.500	−	600.156i	0.107349	−	0.557802i
$106$		0			0
$107$	183.500	−	317.831i	0.165791	−	0.287158i	−0.771145	−	0.636660i	$-0.780316\pi$
$107$	183.500	−	317.831i	0.165791	−	0.287158i	0.936936	+	0.349501i	$0.113649\pi$
$108$		0			0
$109$	−811.000	−	1404.69i	−0.712658	−	1.23436i	−0.963856	−	0.266424i	$-0.914158\pi$
$109$	−811.000	−	1404.69i	−0.712658	−	1.23436i	0.251198	−	0.967936i	$-0.419175\pi$
$110$		0			0
$111$	12.0000			0.0102612
$112$		0			0
$113$	−736.000			−0.612717			−0.306359	−	0.951916i	$-0.599111\pi$
$113$	−736.000			−0.612717			−0.306359	+	0.951916i	$0.599111\pi$
$114$		0			0
$115$	−506.000	−	876.418i	−0.410302	−	0.710664i
$116$		0			0
$117$	144.000	−	249.415i	0.113785	−	0.197081i
$118$		0			0
$119$	−210.000	+	72.7461i	−0.161770	+	0.0560389i
$120$		0			0
$121$	−95.0000	+	164.545i	−0.0713749	+	0.123625i
$122$		0			0
$123$	24.0000	+	41.5692i	0.0175936	+	0.0304729i
$124$		0			0
$125$	1419.00			1.01535
$126$		0			0
$127$	1175.00			0.820979			0.410490	−	0.911865i	$-0.365358\pi$
$127$	1175.00			0.820979			0.410490	+	0.911865i	$0.365358\pi$
$128$		0			0
$129$	−495.000	−	857.365i	−0.337847	−	0.585169i
$130$		0			0
$131$	1270.50	−	2200.57i	0.847360	−	1.46767i	−0.0361967	−	0.999345i	$-0.511524\pi$
$131$	1270.50	−	2200.57i	0.847360	−	1.46767i	0.883556	−	0.468325i	$-0.155142\pi$
$132$		0			0
$133$	−1232.00	−	1066.94i	−0.803218	−	0.695607i
$134$		0			0
$135$	−148.500	+	257.210i	−0.0946729	+	0.163978i
$136$		0			0
$137$	401.000	+	694.552i	0.250071	+	0.433136i	0.963545	−	0.267546i	$-0.0862127\pi$
$137$	401.000	+	694.552i	0.250071	+	0.433136i	−0.713474	+	0.700682i	$0.752879\pi$
$138$		0			0
$139$	3110.00			1.89775			0.948873	−	0.315657i	$-0.102225\pi$
$139$	3110.00			1.89775			0.948873	+	0.315657i	$0.102225\pi$
$140$		0			0
$141$	894.000			0.533960
$142$		0			0
$143$	624.000	+	1080.80i	0.364906	+	0.632035i
$144$		0			0
$145$	1402.50	−	2429.20i	0.803250	−	1.39127i
$146$		0			0
$147$	−147.000	−	1018.45i	−0.0824786	−	0.571429i
$148$		0			0
$149$	−1299.00	+	2249.93i	−0.714216	+	1.23706i	0.249045	+	0.968492i	$0.419883\pi$
$149$	−1299.00	+	2249.93i	−0.714216	+	1.23706i	−0.963261	+	0.268567i	$0.913450\pi$
$150$		0			0
$151$	−666.500	−	1154.41i	−0.359199	−	0.622150i	0.628628	−	0.777706i	$-0.283617\pi$
$151$	−666.500	−	1154.41i	−0.359199	−	0.622150i	−0.987827	+	0.155555i	$0.950283\pi$
$152$		0			0
$153$	108.000			0.0570672
$154$		0			0
$155$	385.000			0.199509
$156$		0			0
$157$	−790.000	−	1368.32i	−0.401585	−	0.695566i	0.592332	−	0.805694i	$-0.298207\pi$
$157$	−790.000	−	1368.32i	−0.401585	−	0.695566i	−0.993917	+	0.110128i	$0.964874\pi$
$158$		0			0
$159$	−1075.50	+	1862.82i	−0.536432	+	0.929128i
$160$		0			0
$161$	−1288.00	−	1115.44i	−0.630488	−	0.546019i
$162$		0			0
$163$	−634.000	+	1098.12i	−0.304655	+	0.527677i	−0.977184	−	0.212393i	$-0.931874\pi$
$163$	−634.000	+	1098.12i	−0.304655	+	0.527677i	0.672530	+	0.740070i	$0.265208\pi$
$164$		0			0
$165$	−643.500	−	1114.57i	−0.303615	−	0.525876i
$166$		0			0
$167$	878.000			0.406836			0.203418	−	0.979092i	$-0.434795\pi$
$167$	878.000			0.406836			0.203418	+	0.979092i	$0.434795\pi$
$168$		0			0
$169$	−1173.00			−0.533910
$170$		0			0
$171$	396.000	+	685.892i	0.177093	+	0.306734i
$172$		0			0
$173$	1441.00	−	2495.89i	0.633279	−	1.09687i	−0.353598	−	0.935397i	$-0.615042\pi$
$173$	1441.00	−	2495.89i	0.633279	−	1.09687i	0.986877	−	0.161473i	$-0.0516246\pi$
$174$		0			0
$175$	70.0000	−	24.2487i	0.0302372	−	0.0104745i
$176$		0			0
$177$	−325.500	+	563.783i	−0.138226	+	0.239415i
$178$		0			0
$179$	−738.000	−	1278.25i	−0.308160	−	0.533749i	0.669800	−	0.742542i	$-0.266380\pi$
$179$	−738.000	−	1278.25i	−0.308160	−	0.533749i	−0.977960	+	0.208792i	$0.933047\pi$
$180$		0			0
$181$	4368.00			1.79376			0.896881	−	0.442272i	$-0.145827\pi$
$181$	4368.00			1.79376			0.896881	+	0.442272i	$0.145827\pi$
$182$		0			0
$183$	−1158.00			−0.467770
$184$		0			0
$185$	−22.0000	−	38.1051i	−0.00874309	−	0.0151435i
$186$		0			0
$187$	−234.000	+	405.300i	−0.0915068	+	0.158494i
$188$		0			0
$189$	−94.5000	+	491.036i	−0.0363696	+	0.188982i
$190$		0			0
$191$	−1508.00	+	2611.93i	−0.571283	+	0.989491i	0.425152	+	0.905122i	$0.360221\pi$
$191$	−1508.00	+	2611.93i	−0.571283	+	0.989491i	−0.996435	+	0.0843690i	$0.973113\pi$
$192$		0			0
$193$	781.500	+	1353.60i	0.291469	+	0.504840i	0.974157	−	0.225870i	$-0.0725225\pi$
$193$	781.500	+	1353.60i	0.291469	+	0.504840i	−0.682688	+	0.730710i	$0.739189\pi$
$194$		0			0
$195$	−1056.00			−0.387804
$196$		0			0
$197$	−1846.00			−0.667625			−0.333812	−	0.942640i	$-0.608335\pi$
$197$	−1846.00			−0.667625			−0.333812	+	0.942640i	$0.608335\pi$
$198$		0			0
$199$	1998.00	+	3460.64i	0.711731	+	1.23275i	0.964207	+	0.265151i	$0.0854218\pi$
$199$	1998.00	+	3460.64i	0.711731	+	1.23275i	−0.252476	+	0.967603i	$0.581245\pi$
$200$		0			0
$201$	1359.00	−	2353.86i	0.476898	−	0.826011i
$202$		0			0
$203$	892.500	−	4637.57i	0.308577	−	1.60342i
$204$		0			0
$205$	88.0000	−	152.420i	0.0299814	−	0.0519293i
$206$		0			0
$207$	414.000	+	717.069i	0.139010	+	0.240772i
$208$		0			0
$209$	−3432.00			−1.13587
$210$		0			0
$211$	4182.00			1.36446			0.682229	−	0.731138i	$-0.261011\pi$
$211$	4182.00			1.36446			0.682229	+	0.731138i	$0.261011\pi$
$212$		0			0
$213$	−51.0000	−	88.3346i	−0.0164059	−	0.0284159i
$214$		0			0
$215$	−1815.00	+	3143.67i	−0.575730	+	0.997194i
$216$		0			0
$217$	612.500	−	212.176i	0.191609	−	0.0663754i
$218$		0			0
$219$	−1257.00	+	2177.19i	−0.387855	+	0.671784i
$220$		0			0
$221$	192.000	+	332.554i	0.0584404	+	0.101222i
$222$		0			0
$223$	1159.00			0.348038			0.174019	−	0.984742i	$-0.444325\pi$
$223$	1159.00			0.348038			0.174019	+	0.984742i	$0.444325\pi$
$224$		0			0
$225$	−36.0000			−0.0106667
$226$		0			0
$227$	−892.500	−	1545.86i	−0.260957	−	0.451991i	0.705539	−	0.708671i	$-0.250705\pi$
$227$	−892.500	−	1545.86i	−0.260957	−	0.451991i	−0.966497	+	0.256680i	$0.917372\pi$
$228$		0			0
$229$	−294.000	+	509.223i	−0.0848387	+	0.146945i	−0.905322	−	0.424725i	$-0.860371\pi$
$229$	−294.000	+	509.223i	−0.0848387	+	0.146945i	0.820484	+	0.571670i	$0.193704\pi$
$230$		0			0
$231$	−1638.00	−	1418.55i	−0.466548	−	0.404042i
$232$		0			0
$233$	−3414.00	+	5913.22i	−0.959908	+	1.66261i	−0.237194	+	0.971462i	$0.576228\pi$
$233$	−3414.00	+	5913.22i	−0.959908	+	1.66261i	−0.722714	+	0.691147i	$0.757106\pi$
$234$		0			0
$235$	−1639.00	−	2838.83i	−0.454964	−	0.788021i
$236$		0			0
$237$	−3975.00			−1.08947
$238$		0			0
$239$	2508.00			0.678783			0.339391	−	0.940645i	$-0.389779\pi$
$239$	2508.00			0.678783			0.339391	+	0.940645i	$0.389779\pi$
$240$		0			0
$241$	2148.50	+	3721.31i	0.574262	+	0.994650i	0.996121	+	0.0879892i	$0.0280441\pi$
$241$	2148.50	+	3721.31i	0.574262	+	0.994650i	−0.421860	+	0.906661i	$0.638623\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−2964.50	+	2333.94i	−0.773041	+	0.608612i
$246$		0			0
$247$	−1408.00	+	2438.73i	−0.362708	+	0.628229i
$248$		0			0
$249$	1744.50	+	3021.56i	0.443989	+	0.769011i
$250$		0			0
$251$	−2489.00			−0.625913			−0.312957	−	0.949767i	$-0.601319\pi$
$251$	−2489.00			−0.625913			−0.312957	+	0.949767i	$0.601319\pi$
$252$		0			0
$253$	−3588.00			−0.891603
$254$		0			0
$255$	−198.000	−	342.946i	−0.0486245	−	0.0842201i
$256$		0			0
$257$	−893.000	+	1546.72i	−0.216746	+	0.375416i	−0.953811	−	0.300406i	$-0.902878\pi$
$257$	−893.000	+	1546.72i	−0.216746	+	0.375416i	0.737065	+	0.675822i	$0.236211\pi$
$258$		0			0
$259$	−56.0000	−	48.4974i	−0.0134350	−	0.0116351i
$260$		0			0
$261$	−1147.50	+	1987.53i	−0.272140	+	0.471360i
$262$		0			0
$263$	−1159.00	−	2007.45i	−0.271738	−	0.470663i	0.697569	−	0.716517i	$-0.254265\pi$
$263$	−1159.00	−	2007.45i	−0.271738	−	0.470663i	−0.969307	+	0.245854i	$0.920932\pi$
$264$		0			0
$265$	7887.00			1.82828
$266$		0			0
$267$	162.000			0.0371320
$268$		0			0
$269$	1374.50	+	2380.70i	0.311542	+	0.539606i	0.978696	−	0.205313i	$-0.0658213\pi$
$269$	1374.50	+	2380.70i	0.311542	+	0.539606i	−0.667155	+	0.744919i	$0.732488\pi$
$270$		0			0
$271$	−912.500	+	1580.50i	−0.204540	+	0.354274i	−0.949986	−	0.312292i	$-0.898903\pi$
$271$	−912.500	+	1580.50i	−0.204540	+	0.354274i	0.745446	+	0.666566i	$0.232237\pi$
$272$		0			0
$273$	−1680.00	+	581.969i	−0.372448	+	0.129020i
$274$		0			0
$275$	78.0000	−	135.100i	0.0171039	−	0.0296249i
$276$		0			0
$277$	152.000	+	263.272i	0.0329704	+	0.0571064i	0.882040	−	0.471175i	$-0.156170\pi$
$277$	152.000	+	263.272i	0.0329704	+	0.0571064i	−0.849069	+	0.528281i	$0.822837\pi$
$278$		0			0
$279$	−315.000			−0.0675934
$280$		0			0
$281$	4578.00			0.971888			0.485944	−	0.873990i	$-0.338476\pi$
$281$	4578.00			0.971888			0.485944	+	0.873990i	$0.338476\pi$
$282$		0			0
$283$	−2151.00	−	3725.64i	−0.451815	−	0.782567i	0.546684	−	0.837339i	$-0.315890\pi$
$283$	−2151.00	−	3725.64i	−0.451815	−	0.782567i	−0.998499	+	0.0547724i	$0.982557\pi$
$284$		0			0
$285$	1452.00	−	2514.94i	0.301786	−	0.522709i
$286$		0			0
$287$	56.0000	−	290.985i	0.0115177	−	0.0598476i
$288$		0			0
$289$	2384.50	−	4130.08i	0.485345	−	0.840642i
$290$		0			0
$291$	10.5000	+	18.1865i	0.00211519	+	0.00366362i
$292$		0			0
$293$	6727.00			1.34128			0.670641	−	0.741782i	$-0.266019\pi$
$293$	6727.00			1.34128			0.670641	+	0.741782i	$0.266019\pi$
$294$		0			0
$295$	2387.00			0.471107
$296$		0			0
$297$	526.500	+	911.925i	0.102864	+	0.178166i
$298$		0			0
$299$	−1472.00	+	2549.58i	−0.284709	+	0.493130i
$300$		0			0
$301$	−1155.00	+	6001.56i	−0.221173	+	1.14925i
$302$		0			0
$303$	−69.0000	+	119.512i	−0.0130823	+	0.0226593i
$304$		0			0
$305$	2123.00	+	3677.14i	0.398566	+	0.690337i
$306$		0			0
$307$	116.000			0.0215650			0.0107825	−	0.999942i	$-0.496568\pi$
$307$	116.000			0.0215650			0.0107825	+	0.999942i	$0.496568\pi$
$308$		0			0
$309$	−4968.00			−0.914627
$310$		0			0
$311$	1896.00	+	3283.97i	0.345699	+	0.598768i	0.985480	−	0.169789i	$-0.0543086\pi$
$311$	1896.00	+	3283.97i	0.345699	+	0.598768i	−0.639782	+	0.768557i	$0.720975\pi$
$312$		0			0
$313$	1843.50	−	3193.04i	0.332910	−	0.576617i	−0.650171	−	0.759788i	$-0.725303\pi$
$313$	1843.50	−	3193.04i	0.332910	−	0.576617i	0.983081	+	0.183171i	$0.0586362\pi$
$314$		0			0
$315$	1732.50	−	600.156i	0.309890	−	0.107349i
$316$		0			0
$317$	4140.50	−	7171.56i	0.733608	−	1.27065i	−0.221724	−	0.975110i	$-0.571168\pi$
$317$	4140.50	−	7171.56i	0.733608	−	1.27065i	0.955331	−	0.295536i	$-0.0954983\pi$
$318$		0			0
$319$	−4972.50	−	8612.62i	−0.872748	−	1.51164i
$320$		0			0
$321$	1101.00			0.191439
$322$		0			0
$323$	−1056.00			−0.181911
$324$		0			0
$325$	−64.0000	−	110.851i	−0.0109233	−	0.0189198i
$326$		0			0
$327$	2433.00	−	4214.08i	0.411453	−	0.712658i
$328$		0			0
$329$	−4172.00	−	3613.06i	−0.699118	−	0.605454i
$330$		0			0
$331$	3334.00	−	5774.66i	0.553635	−	0.958924i	−0.444373	−	0.895842i	$-0.646574\pi$
$331$	3334.00	−	5774.66i	0.553635	−	0.958924i	0.998008	−	0.0630824i	$-0.0200931\pi$
$332$		0			0
$333$	18.0000	+	31.1769i	0.00296214	+	0.00513058i
$334$		0			0
$335$	−9966.00			−1.62538
$336$		0			0
$337$	−8679.00			−1.40289			−0.701447	−	0.712722i	$-0.747462\pi$
$337$	−8679.00			−1.40289			−0.701447	+	0.712722i	$0.747462\pi$
$338$		0			0
$339$	−1104.00	−	1912.18i	−0.176876	−	0.306359i
$340$		0			0
$341$	682.500	−	1182.12i	0.108385	−	0.187729i
$342$		0			0
$343$	−3430.00	+	5346.84i	−0.539949	+	0.841698i
$344$		0			0
$345$	1518.00	−	2629.25i	0.236888	−	0.410302i
$346$		0			0
$347$	−4546.00	−	7873.90i	−0.703291	−	1.21814i	−0.967305	−	0.253617i	$-0.918380\pi$
$347$	−4546.00	−	7873.90i	−0.703291	−	1.21814i	0.264013	−	0.964519i	$-0.414954\pi$
$348$		0			0
$349$	11642.0			1.78562			0.892811	−	0.450432i	$-0.148730\pi$
$349$	11642.0			1.78562			0.892811	+	0.450432i	$0.148730\pi$
$350$		0			0
$351$	864.000			0.131387
$352$		0			0
$353$	−3404.00	−	5895.90i	−0.513248	−	0.888972i	−0.999882	−	0.0153659i	$-0.995109\pi$
$353$	−3404.00	−	5895.90i	−0.513248	−	0.888972i	0.486634	−	0.873606i	$-0.338225\pi$
$354$		0			0
$355$	−187.000	+	323.894i	−0.0279575	+	0.0484239i
$356$		0			0
$357$	−504.000	−	436.477i	−0.0747185	−	0.0647081i
$358$		0			0
$359$	−555.000	+	961.288i	−0.0815927	+	0.141323i	−0.903934	−	0.427672i	$-0.859334\pi$
$359$	−555.000	+	961.288i	−0.0815927	+	0.141323i	0.822342	+	0.568994i	$0.192667\pi$
$360$		0			0
$361$	−442.500	−	766.432i	−0.0645138	−	0.111741i
$362$		0			0
$363$	−570.000			−0.0824166
$364$		0			0
$365$	9218.00			1.32190
$366$		0			0
$367$	−479.500	−	830.518i	−0.0682008	−	0.118127i	0.829909	−	0.557899i	$-0.188393\pi$
$367$	−479.500	−	830.518i	−0.0682008	−	0.118127i	−0.898109	+	0.439772i	$0.855059\pi$
$368$		0			0
$369$	−72.0000	+	124.708i	−0.0101576	+	0.0175936i
$370$		0			0
$371$	12547.5	−	4346.58i	1.75589	−	0.608257i
$372$		0			0
$373$	−8.00000	+	13.8564i	−0.00111052	+	0.00192348i	−0.866580	−	0.499038i	$-0.833687\pi$
$373$	−8.00000	+	13.8564i	−0.00111052	+	0.00192348i	0.865470	+	0.500961i	$0.167020\pi$
$374$		0			0
$375$	2128.50	+	3686.67i	0.293107	+	0.507677i
$376$		0			0
$377$	−8160.00			−1.11475
$378$		0			0
$379$	−736.000			−0.0997514			−0.0498757	−	0.998755i	$-0.515883\pi$
$379$	−736.000			−0.0997514			−0.0498757	+	0.998755i	$0.515883\pi$
$380$		0			0
$381$	1762.50	+	3052.74i	0.236996	+	0.410490i
$382$		0			0
$383$	4207.00	−	7286.74i	0.561273	−	0.972154i	−0.436112	−	0.899892i	$-0.643645\pi$
$383$	4207.00	−	7286.74i	0.561273	−	0.972154i	0.997386	−	0.0722616i	$-0.0230217\pi$
$384$		0			0
$385$	−1501.50	+	7802.02i	−0.198762	+	1.03280i
$386$		0			0
$387$	1485.00	−	2572.10i	0.195056	−	0.337847i
$388$		0			0
$389$	−347.000	−	601.022i	−0.0452278	−	0.0783368i	0.842525	−	0.538657i	$-0.181068\pi$
$389$	−347.000	−	601.022i	−0.0452278	−	0.0783368i	−0.887753	+	0.460320i	$0.847735\pi$
$390$		0			0
$391$	−1104.00			−0.142792
$392$		0			0
$393$	7623.00			0.978447
$394$		0			0
$395$	7287.50	+	12622.3i	0.928288	+	1.60784i
$396$		0			0
$397$	−5738.00	+	9938.51i	−0.725395	+	1.25642i	0.233416	+	0.972377i	$0.425010\pi$
$397$	−5738.00	+	9938.51i	−0.725395	+	1.25642i	−0.958811	+	0.284045i	$0.908324\pi$
$398$		0			0
$399$	924.000	−	4801.24i	0.115934	−	0.602413i
$400$		0			0
$401$	6020.00	−	10426.9i	0.749687	−	1.29850i	−0.198286	−	0.980144i	$-0.563537\pi$
$401$	6020.00	−	10426.9i	0.749687	−	1.29850i	0.947973	−	0.318352i	$-0.103129\pi$
$402$		0			0
$403$	−560.000	−	969.948i	−0.0692198	−	0.119892i
$404$		0			0
$405$	−891.000			−0.109319
$406$		0			0
$407$	−156.000			−0.0189991
$408$		0			0
$409$	−6855.50	−	11874.1i	−0.828808	−	1.43554i	−0.898974	−	0.438003i	$-0.855686\pi$
$409$	−6855.50	−	11874.1i	−0.828808	−	1.43554i	0.0701651	−	0.997535i	$-0.477647\pi$
$410$		0			0
$411$	−1203.00	+	2083.66i	−0.144379	+	0.250071i
$412$		0			0
$413$	3797.50	−	1315.49i	0.452452	−	0.156734i
$414$		0			0
$415$	6396.50	−	11079.1i	0.756607	−	1.31048i
$416$		0			0
$417$	4665.00	+	8080.02i	0.547832	+	0.948873i
$418$		0			0
$419$	−4128.00			−0.481303			−0.240652	−	0.970612i	$-0.577361\pi$
$419$	−4128.00			−0.481303			−0.240652	+	0.970612i	$0.577361\pi$
$420$		0			0
$421$	−8442.00			−0.977287			−0.488644	−	0.872483i	$-0.662508\pi$
$421$	−8442.00			−0.977287			−0.488644	+	0.872483i	$0.662508\pi$
$422$		0			0
$423$	1341.00	+	2322.68i	0.154141	+	0.266980i
$424$		0			0
$425$	24.0000	−	41.5692i	0.00273923	−	0.00474448i
$426$		0			0
$427$	5404.00	+	4680.00i	0.612454	+	0.530401i
$428$		0			0
$429$	−1872.00	+	3242.40i	−0.210678	+	0.364906i
$430$		0			0
$431$	4782.00	+	8282.67i	0.534433	+	0.925666i	0.999191	+	0.0402277i	$0.0128083\pi$
$431$	4782.00	+	8282.67i	0.534433	+	0.925666i	−0.464757	+	0.885438i	$0.653858\pi$
$432$		0			0
$433$	−13394.0			−1.48655			−0.743273	−	0.668988i	$-0.766728\pi$
$433$	−13394.0			−1.48655			−0.743273	+	0.668988i	$0.766728\pi$
$434$		0			0
$435$	8415.00			0.927513
$436$		0			0
$437$	−4048.00	−	7011.34i	−0.443117	−	0.767501i
$438$		0			0
$439$	−7756.50	+	13434.7i	−0.843275	+	1.46059i	0.0438366	+	0.999039i	$0.486042\pi$
$439$	−7756.50	+	13434.7i	−0.843275	+	1.46059i	−0.887111	+	0.461556i	$0.847291\pi$
$440$		0			0
$441$	2425.50	−	1909.59i	0.261905	−	0.206197i
$442$		0			0
$443$	−6189.50	+	10720.5i	−0.663819	+	1.14977i	0.315784	+	0.948831i	$0.397732\pi$
$443$	−6189.50	+	10720.5i	−0.663819	+	1.14977i	−0.979604	+	0.200938i	$0.935601\pi$
$444$		0			0
$445$	−297.000	−	514.419i	−0.0316385	−	0.0547996i
$446$		0			0
$447$	−7794.00			−0.824706
$448$		0			0
$449$	−8368.00			−0.879533			−0.439767	−	0.898112i	$-0.644939\pi$
$449$	−8368.00			−0.879533			−0.439767	+	0.898112i	$0.644939\pi$
$450$		0			0
$451$	−312.000	−	540.400i	−0.0325754	−	0.0564223i
$452$		0			0
$453$	1999.50	−	3463.24i	0.207383	−	0.359199i
$454$		0			0
$455$	4928.00	+	4267.77i	0.507754	+	0.439728i
$456$		0			0
$457$	788.500	−	1365.72i	0.0807100	−	0.139794i	−0.822845	−	0.568266i	$-0.807615\pi$
$457$	788.500	−	1365.72i	0.0807100	−	0.139794i	0.903555	+	0.428472i	$0.140948\pi$
$458$		0			0
$459$	162.000	+	280.592i	0.0164739	+	0.0285336i
$460$		0			0
$461$	8202.00			0.828645			0.414322	−	0.910130i	$-0.364019\pi$
$461$	8202.00			0.828645			0.414322	+	0.910130i	$0.364019\pi$
$462$		0			0
$463$	−1936.00			−0.194327			−0.0971637	−	0.995268i	$-0.530977\pi$
$463$	−1936.00			−0.194327			−0.0971637	+	0.995268i	$0.530977\pi$
$464$		0			0
$465$	577.500	+	1000.26i	0.0575934	+	0.0997547i
$466$		0			0
$467$	−6578.00	+	11393.4i	−0.651806	+	1.12896i	0.330878	+	0.943674i	$0.392655\pi$
$467$	−6578.00	+	11393.4i	−0.651806	+	1.12896i	−0.982684	+	0.185288i	$0.940678\pi$
$468$		0			0
$469$	−15855.0	+	5492.33i	−1.56101	+	0.540751i
$470$		0			0
$471$	2370.00	−	4104.96i	0.231855	−	0.401585i
$472$		0			0
$473$	6435.00	+	11145.7i	0.625543	+	1.08347i
$474$		0			0
$475$	352.000			0.0340018
$476$		0			0
$477$	−6453.00			−0.619418
$478$		0			0
$479$	3315.00	+	5741.75i	0.316213	+	0.547698i	0.979695	−	0.200495i	$-0.0642551\pi$
$479$	3315.00	+	5741.75i	0.316213	+	0.547698i	−0.663481	+	0.748193i	$0.730922\pi$
$480$		0			0
$481$	−64.0000	+	110.851i	−0.00606684	+	0.0105081i
$482$		0			0
$483$	966.000	−	5019.48i	0.0910032	−	0.472866i
$484$		0			0
$485$	38.5000	−	66.6840i	0.00360453	−	0.00624322i
$486$		0			0
$487$	−2097.50	−	3632.98i	−0.195168	−	0.338041i	0.751788	−	0.659405i	$-0.229192\pi$
$487$	−2097.50	−	3632.98i	−0.195168	−	0.338041i	−0.946956	+	0.321365i	$0.895859\pi$
$488$		0			0
$489$	−3804.00			−0.351785
$490$		0			0
$491$	1107.00			0.101748			0.0508739	−	0.998705i	$-0.483799\pi$
$491$	1107.00			0.101748			0.0508739	+	0.998705i	$0.483799\pi$
$492$		0			0
$493$	−1530.00	−	2650.04i	−0.139772	−	0.242093i
$494$		0			0
$495$	1930.50	−	3343.72i	0.175292	−	0.303615i
$496$		0			0
$497$	−119.000	+	618.342i	−0.0107402	+	0.0558077i
$498$		0			0
$499$	−6815.00	+	11803.9i	−0.611385	+	1.05895i	0.379622	+	0.925142i	$0.376054\pi$
$499$	−6815.00	+	11803.9i	−0.611385	+	1.05895i	−0.991007	+	0.133809i	$0.957279\pi$
$500$		0			0
$501$	1317.00	+	2281.11i	0.117444	+	0.203418i
$502$		0			0
$503$	−11760.0			−1.04245			−0.521225	−	0.853419i	$-0.674525\pi$
$503$	−11760.0			−1.04245			−0.521225	+	0.853419i	$0.674525\pi$
$504$		0			0
$505$	506.000			0.0445875
$506$		0			0
$507$	−1759.50	−	3047.54i	−0.154127	−	0.266955i
$508$		0			0
$509$	9550.50	−	16542.0i	0.831667	−	1.44049i	−0.0650486	−	0.997882i	$-0.520720\pi$
$509$	9550.50	−	16542.0i	0.831667	−	1.44049i	0.896716	−	0.442607i	$-0.145946\pi$
$510$		0			0
$511$	14665.0	−	5080.11i	1.26955	−	0.439786i
$512$		0			0
$513$	−1188.00	+	2057.68i	−0.102245	+	0.177093i
$514$		0			0
$515$	9108.00	+	15775.5i	0.779313	+	1.34981i
$516$		0			0
$517$	−11622.0			−0.988656
$518$		0			0
$519$	8646.00			0.731247
$520$		0			0
$521$	−5295.00	−	9171.21i	−0.445256	−	0.771205i	0.552814	−	0.833304i	$-0.313554\pi$
$521$	−5295.00	−	9171.21i	−0.445256	−	0.771205i	−0.998070	+	0.0620991i	$0.980221\pi$
$522$		0			0
$523$	−8700.00	+	15068.8i	−0.727389	+	1.25987i	0.230594	+	0.973050i	$0.425933\pi$
$523$	−8700.00	+	15068.8i	−0.727389	+	1.25987i	−0.957983	+	0.286825i	$0.907400\pi$
$524$		0			0
$525$	168.000	+	145.492i	0.0139659	+	0.0120949i
$526$		0			0
$527$	210.000	−	363.731i	0.0173581	−	0.0300652i
$528$		0			0
$529$	1851.50	+	3206.89i	0.152174	+	0.263573i
$530$		0			0
$531$	−1953.00			−0.159610
$532$		0			0
$533$	−512.000			−0.0416082
$534$		0			0
$535$	−2018.50	−	3496.14i	−0.163117	−	0.282526i
$536$		0			0
$537$	2214.00	−	3834.76i	0.177916	−	0.308160i
$538$		0			0
$539$	1911.00	+	13239.8i	0.152714	+	1.05803i
$540$		0			0
$541$	3205.00	−	5551.22i	0.254702	−	0.441157i	−0.710113	−	0.704088i	$-0.751356\pi$
$541$	3205.00	−	5551.22i	0.254702	−	0.441157i	0.964814	+	0.262932i	$0.0846893\pi$
$542$		0			0
$543$	6552.00	+	11348.4i	0.517814	+	0.896881i
$544$		0			0
$545$	−17842.0			−1.40233
$546$		0			0
$547$	−24020.0			−1.87755			−0.938776	−	0.344528i	$-0.888039\pi$
$547$	−24020.0			−1.87755			−0.938776	+	0.344528i	$0.888039\pi$
$548$		0			0
$549$	−1737.00	−	3008.57i	−0.135033	−	0.233885i
$550$		0			0
$551$	11220.0	−	19433.6i	0.867492	−	1.50254i
$552$		0			0
$553$	18550.0	+	16064.8i	1.42645	+	1.23534i
$554$		0			0
$555$	66.0000	−	114.315i	0.00504783	−	0.00874309i
$556$		0			0
$557$	13069.5	+	22637.0i	0.994206	+	1.72201i	0.590197	+	0.807259i	$0.299050\pi$
$557$	13069.5	+	22637.0i	0.994206	+	1.72201i	0.404009	+	0.914755i	$0.367617\pi$
$558$		0			0
$559$	10560.0			0.798999
$560$		0			0
$561$	−1404.00			−0.105663
$562$		0			0
$563$	−4585.50	−	7942.32i	−0.343261	−	0.594545i	0.641775	−	0.766893i	$-0.278198\pi$
$563$	−4585.50	−	7942.32i	−0.343261	−	0.594545i	−0.985036	+	0.172348i	$0.944865\pi$
$564$		0			0
$565$	−4048.00	+	7011.34i	−0.301417	+	0.522070i
$566$		0			0
$567$	−1417.50	+	491.036i	−0.104990	+	0.0363696i
$568$		0			0
$569$	9804.00	−	16981.0i	0.722329	−	1.25111i	−0.237735	−	0.971330i	$-0.576405\pi$
$569$	9804.00	−	16981.0i	0.722329	−	1.25111i	0.960064	−	0.279780i	$-0.0902616\pi$
$570$		0			0
$571$	1837.00	+	3181.78i	0.134634	+	0.233193i	0.925458	−	0.378851i	$-0.123681\pi$
$571$	1837.00	+	3181.78i	0.134634	+	0.233193i	−0.790824	+	0.612044i	$0.790347\pi$
$572$		0			0
$573$	−9048.00			−0.659661
$574$		0			0
$575$	368.000			0.0266898
$576$		0			0
$577$	1936.50	+	3354.12i	0.139718	+	0.241999i	0.927390	−	0.374096i	$-0.122047\pi$
$577$	1936.50	+	3354.12i	0.139718	+	0.241999i	−0.787672	+	0.616095i	$0.788714\pi$
$578$		0			0
$579$	−2344.50	+	4060.79i	−0.168280	+	0.291469i
$580$		0			0
$581$	4070.50	−	21150.9i	0.290659	−	1.51031i
$582$		0			0
$583$	13981.5	−	24216.7i	0.993233	−	1.72033i
$584$		0			0
$585$	−1584.00	−	2743.57i	−0.111949	−	0.193902i
$586$		0			0
$587$	−13743.0			−0.966328			−0.483164	−	0.875530i	$-0.660512\pi$
$587$	−13743.0			−0.966328			−0.483164	+	0.875530i	$0.660512\pi$
$588$		0			0
$589$	3080.00			0.215466
$590$		0			0
$591$	−2769.00	−	4796.05i	−0.192727	−	0.333812i
$592$		0			0
$593$	−8178.00	+	14164.7i	−0.566324	+	0.980902i	0.430601	+	0.902542i	$0.358302\pi$
$593$	−8178.00	+	14164.7i	−0.566324	+	0.980902i	−0.996925	+	0.0783598i	$0.975032\pi$
$594$		0			0
$595$	−462.000	+	2400.62i	−0.0318322	+	0.165405i
$596$		0			0
$597$	−5994.00	+	10381.9i	−0.410918	+	0.711731i
$598$		0			0
$599$	−5391.00	−	9337.49i	−0.367730	−	0.636927i	0.621480	−	0.783430i	$-0.286532\pi$
$599$	−5391.00	−	9337.49i	−0.367730	−	0.636927i	−0.989210	+	0.146503i	$0.953198\pi$
$600$		0			0
$601$	25547.0			1.73392			0.866958	−	0.498381i	$-0.166072\pi$
$601$	25547.0			1.73392			0.866958	+	0.498381i	$0.166072\pi$
$602$		0			0
$603$	8154.00			0.550674
$604$		0			0
$605$	1045.00	+	1809.99i	0.0702236	+	0.121631i
$606$		0			0
$607$	−7149.50	+	12383.3i	−0.478071	+	0.828044i	−0.999684	−	0.0251387i	$-0.991997\pi$
$607$	−7149.50	+	12383.3i	−0.478071	+	0.828044i	0.521613	+	0.853182i	$0.325331\pi$
$608$		0			0
$609$	13387.5	−	4637.57i	0.890786	−	0.308577i
$610$		0			0
$611$	−4768.00	+	8258.42i	−0.315700	+	0.546808i
$612$		0			0
$613$	−11950.0	−	20698.0i	−0.787367	−	1.36376i	−0.927575	−	0.373638i	$-0.878110\pi$
$613$	−11950.0	−	20698.0i	−0.787367	−	1.36376i	0.140208	−	0.990122i	$-0.455223\pi$
$614$		0			0
$615$	528.000			0.0346195
$616$		0			0
$617$	−9246.00			−0.603290			−0.301645	−	0.953420i	$-0.597536\pi$
$617$	−9246.00			−0.603290			−0.301645	+	0.953420i	$0.597536\pi$
$618$		0			0
$619$	−6975.00	−	12081.1i	−0.452906	−	0.784456i	0.545659	−	0.838007i	$-0.316279\pi$
$619$	−6975.00	−	12081.1i	−0.452906	−	0.784456i	−0.998565	+	0.0535508i	$0.982946\pi$
$620$		0			0
$621$	−1242.00	+	2151.21i	−0.0802572	+	0.139010i
$622$		0			0
$623$	−756.000	−	654.715i	−0.0486172	−	0.0421037i
$624$		0			0
$625$	7554.50	−	13084.8i	0.483488	−	0.837426i
$626$		0			0
$627$	−5148.00	−	8916.60i	−0.327897	−	0.567934i
$628$		0			0
$629$	−48.0000			−0.00304274
$630$		0			0
$631$	15787.0			0.995991			0.497996	−	0.867180i	$-0.334070\pi$
$631$	15787.0			0.995991			0.497996	+	0.867180i	$0.334070\pi$
$632$		0			0
$633$	6273.00	+	10865.2i	0.393885	+	0.682229i
$634$		0			0
$635$	6462.50	−	11193.4i	0.403868	−	0.699521i
$636$		0			0
$637$	10192.0	+	4073.78i	0.633943	+	0.253390i
$638$		0			0
$639$	153.000	−	265.004i	0.00947197	−	0.0164059i
$640$		0			0
$641$	4219.00	+	7307.52i	0.259970	+	0.450280i	0.966233	−	0.257668i	$-0.0829541\pi$
$641$	4219.00	+	7307.52i	0.259970	+	0.450280i	−0.706264	+	0.707949i	$0.749621\pi$
$642$		0			0
$643$	22522.0			1.38131			0.690654	−	0.723185i	$-0.257323\pi$
$643$	22522.0			1.38131			0.690654	+	0.723185i	$0.257323\pi$
$644$		0			0
$645$	−10890.0			−0.664796
$646$		0			0
$647$	−8569.00	−	14841.9i	−0.520683	−	0.901850i	−0.999711	−	0.0240501i	$-0.992344\pi$
$647$	−8569.00	−	14841.9i	−0.520683	−	0.901850i	0.479027	−	0.877800i	$-0.340989\pi$
$648$		0			0
$649$	4231.50	−	7329.17i	0.255934	−	0.443290i
$650$		0			0
$651$	1470.00	+	1273.06i	0.0885005	+	0.0766437i
$652$		0			0
$653$	4981.50	−	8628.21i	0.298532	−	0.517072i	−0.677269	−	0.735736i	$-0.736836\pi$
$653$	4981.50	−	8628.21i	0.298532	−	0.517072i	0.975800	+	0.218664i	$0.0701698\pi$
$654$		0			0
$655$	−13975.5	−	24206.3i	−0.833692	−	1.44400i
$656$		0			0
$657$	−7542.00			−0.447856
$658$		0			0
$659$	−8664.00			−0.512142			−0.256071	−	0.966658i	$-0.582428\pi$
$659$	−8664.00			−0.512142			−0.256071	+	0.966658i	$0.582428\pi$
$660$		0			0
$661$	−1225.00	−	2121.76i	−0.0720832	−	0.124852i	0.827731	−	0.561125i	$-0.189631\pi$
$661$	−1225.00	−	2121.76i	−0.0720832	−	0.124852i	−0.899814	+	0.436273i	$0.856298\pi$
$662$		0			0
$663$	−576.000	+	997.661i	−0.0337406	+	0.0584404i
$664$		0			0
$665$	−16940.0	+	5868.19i	−0.987827	+	0.342193i
$666$		0			0
$667$	11730.0	−	20317.0i	0.680941	−	1.17942i
$668$		0			0
$669$	1738.50	+	3011.17i	0.100470	+	0.174019i
$670$		0			0
$671$	15054.0			0.866100
$672$		0			0
$673$	−6643.00			−0.380489			−0.190244	−	0.981737i	$-0.560928\pi$
$673$	−6643.00			−0.380489			−0.190244	+	0.981737i	$0.560928\pi$
$674$		0			0
$675$	−54.0000	−	93.5307i	−0.00307920	−	0.00533333i
$676$		0			0
$677$	−7796.50	+	13503.9i	−0.442605	+	0.766615i	−0.997882	−	0.0650508i	$-0.979279\pi$
$677$	−7796.50	+	13503.9i	−0.442605	+	0.766615i	0.555277	+	0.831666i	$0.312612\pi$
$678$		0			0
$679$	24.5000	−	127.306i	0.00138472	−	0.00719521i
$680$		0			0
$681$	2677.50	−	4637.57i	0.150664	−	0.260957i
$682$		0			0
$683$	185.500	+	321.295i	0.0103923	+	0.0180000i	0.871175	−	0.490973i	$-0.163359\pi$
$683$	185.500	+	321.295i	0.0103923	+	0.0180000i	−0.860782	+	0.508973i	$0.830025\pi$
$684$		0			0
$685$	8822.00			0.492075
$686$		0			0
$687$	−1764.00			−0.0979633
$688$		0			0
$689$	−11472.0	−	19870.1i	−0.634323	−	1.09868i
$690$		0			0
$691$	−4116.00	+	7129.12i	−0.226599	+	0.392481i	−0.956798	−	0.290753i	$-0.906094\pi$
$691$	−4116.00	+	7129.12i	−0.226599	+	0.392481i	0.730199	+	0.683235i	$0.239427\pi$
$692$		0			0
$693$	1228.50	−	6383.47i	0.0673403	−	0.349911i
$694$		0			0
$695$	17105.0	−	29626.7i	0.933568	−	1.61699i
$696$		0			0
$697$	−96.0000	−	166.277i	−0.00521701	−	0.00903613i
$698$		0			0
$699$	−20484.0			−1.10841
$700$		0			0
$701$	30751.0			1.65685			0.828423	−	0.560103i	$-0.189238\pi$
$701$	30751.0			1.65685			0.828423	+	0.560103i	$0.189238\pi$
$702$		0			0
$703$	−176.000	−	304.841i	−0.00944234	−	0.0163546i
$704$		0			0
$705$	4917.00	−	8516.49i	0.262674	−	0.454964i
$706$		0			0
$707$	805.000	−	278.860i	0.0428220	−	0.0148340i
$708$		0			0
$709$	−6159.00	+	10667.7i	−0.326243	+	0.565069i	−0.981763	−	0.190109i	$-0.939116\pi$
$709$	−6159.00	+	10667.7i	−0.326243	+	0.565069i	0.655520	+	0.755178i	$0.272449\pi$
$710$		0			0
$711$	−5962.50	−	10327.4i	−0.314502	−	0.544734i
$712$		0			0
$713$	3220.00			0.169130
$714$		0			0
$715$	13728.0			0.718039
$716$		0			0
$717$	3762.00	+	6515.98i	0.195948	+	0.339391i
$718$		0			0
$719$	−9011.00	+	15607.5i	−0.467390	+	0.809544i	−0.999306	−	0.0372537i	$-0.988139\pi$
$719$	−9011.00	+	15607.5i	−0.467390	+	0.809544i	0.531916	+	0.846797i	$0.321472\pi$
$720$		0			0
$721$	23184.0	+	20077.9i	1.19753	+	1.03709i
$722$		0			0
$723$	−6445.50	+	11163.9i	−0.331550	+	0.574262i
$724$		0			0
$725$	510.000	+	883.346i	0.0261254	+	0.0452505i
$726$		0			0
$727$	−1279.00			−0.0652483			−0.0326241	−	0.999468i	$-0.510386\pi$
$727$	−1279.00			−0.0652483			−0.0326241	+	0.999468i	$0.510386\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	1980.00	+	3429.46i	0.100182	+	0.173520i
$732$		0			0
$733$	18455.0	−	31965.0i	0.929947	−	1.61072i	0.146541	−	0.989205i	$-0.453186\pi$
$733$	18455.0	−	31965.0i	0.929947	−	1.61072i	0.783406	−	0.621510i	$-0.213481\pi$
$734$		0			0
$735$	−10510.5	−	4201.09i	−0.527463	−	0.210829i
$736$		0			0
$737$	−17667.0	+	30600.1i	−0.883002	+	1.52940i
$738$		0			0
$739$	15613.0	+	27042.5i	0.777177	+	1.34611i	0.933563	+	0.358413i	$0.116682\pi$
$739$	15613.0	+	27042.5i	0.777177	+	1.34611i	−0.156386	+	0.987696i	$0.549985\pi$
$740$		0			0
$741$	−8448.00			−0.418819
$742$		0			0
$743$	−17758.0			−0.876821			−0.438410	−	0.898775i	$-0.644458\pi$
$743$	−17758.0			−0.876821			−0.438410	+	0.898775i	$0.644458\pi$
$744$		0			0
$745$	14289.0	+	24749.3i	0.702696	+	1.21711i
$746$		0			0
$747$	−5233.50	+	9064.69i	−0.256337	+	0.443989i
$748$		0			0
$749$	−5138.00	−	4449.64i	−0.250652	−	0.217071i
$750$		0			0
$751$	−1009.50	+	1748.51i	−0.0490508	+	0.0849585i	−0.889508	−	0.456919i	$-0.848953\pi$
$751$	−1009.50	+	1748.51i	−0.0490508	+	0.0849585i	0.840458	+	0.541877i	$0.182286\pi$
$752$		0			0
$753$	−3733.50	−	6466.61i	−0.180686	−	0.312957i
$754$		0			0
$755$	−14663.0			−0.706810
$756$		0			0
$757$	−2398.00			−0.115134			−0.0575672	−	0.998342i	$-0.518334\pi$
$757$	−2398.00			−0.115134			−0.0575672	+	0.998342i	$0.518334\pi$
$758$		0			0
$759$	−5382.00	−	9321.90i	−0.257384	−	0.445802i
$760$		0			0
$761$	−5220.00	+	9041.31i	−0.248653	+	0.430679i	−0.963152	−	0.268957i	$-0.913321\pi$
$761$	−5220.00	+	9041.31i	−0.248653	+	0.430679i	0.714499	+	0.699636i	$0.246655\pi$
$762$		0			0
$763$	−28385.0	+	9832.85i	−1.34680	+	0.466544i
$764$		0			0
$765$	594.000	−	1028.84i	0.0280734	−	0.0486245i
$766$		0			0
$767$	−3472.00	−	6013.68i	−0.163451	−	0.283105i
$768$		0			0
$769$	−4739.00			−0.222227			−0.111114	−	0.993808i	$-0.535442\pi$
$769$	−4739.00			−0.222227			−0.111114	+	0.993808i	$0.535442\pi$
$770$		0			0
$771$	−5358.00			−0.250277
$772$		0			0
$773$	17015.0	+	29470.8i	0.791704	+	1.37127i	0.924911	+	0.380183i	$0.124139\pi$
$773$	17015.0	+	29470.8i	0.791704	+	1.37127i	−0.133208	+	0.991088i	$0.542528\pi$
$774$		0			0
$775$	−70.0000	+	121.244i	−0.00324448	+	0.00561961i
$776$		0			0
$777$	42.0000	−	218.238i	0.00193918	−	0.0100763i
$778$		0			0
$779$	704.000	−	1219.36i	0.0323792	−	0.0560825i
$780$		0			0
$781$	663.000	+	1148.35i	0.0303764	+	0.0526135i
$782$		0			0
$783$	−6885.00			−0.314240
$784$		0			0
$785$	−17380.0			−0.790215
$786$		0			0
$787$	−3613.00	−	6257.90i	−0.163646	−	0.283443i	0.772528	−	0.634981i	$-0.218992\pi$
$787$	−3613.00	−	6257.90i	−0.163646	−	0.283443i	−0.936174	+	0.351538i	$0.885659\pi$
$788$		0			0
$789$	3477.00	−	6022.34i	0.156888	−	0.271738i
$790$		0			0
$791$	−2576.00	+	13385.3i	−0.115793	+	0.601676i
$792$		0			0
$793$	6176.00	−	10697.1i	0.276565	−	0.479025i
$794$		0			0
$795$	11830.5	+	20491.0i	0.527779	+	0.914141i
$796$		0			0
$797$	4881.00			0.216931			0.108465	−	0.994100i	$-0.465406\pi$
$797$	4881.00			0.216931			0.108465	+	0.994100i	$0.465406\pi$
$798$		0			0
$799$	−3576.00			−0.158335
$800$		0			0
$801$	243.000	+	420.888i	0.0107191	+	0.0185660i
$802$		0			0
$803$	16341.0	−	28303.4i	0.718134	−	1.24384i
$804$		0			0
$805$	−17710.0	+	6134.92i	−0.775398	+	0.268606i
$806$		0			0
$807$	−4123.50	+	7142.11i	−0.179869	+	0.311542i
$808$		0			0
$809$	6556.00	+	11355.3i	0.284916	+	0.493488i	0.972589	−	0.232532i	$-0.0747011\pi$
$809$	6556.00	+	11355.3i	0.284916	+	0.493488i	−0.687673	+	0.726020i	$0.741368\pi$
$810$		0			0
$811$	40982.0			1.77444			0.887221	−	0.461344i	$-0.152633\pi$
$811$	40982.0			1.77444			0.887221	+	0.461344i	$0.152633\pi$
$812$		0			0
$813$	−5475.00			−0.236183
$814$		0			0
$815$	6974.00	+	12079.3i	0.299741	+	0.519166i
$816$		0			0
$817$	−14520.0	+	25149.4i	−0.621775	+	1.07695i
$818$		0			0
$819$	−4032.00	−	3491.81i	−0.172026	−	0.148979i
$820$		0			0
$821$	−19921.5	+	34505.1i	−0.846852	+	1.46679i	0.0371519	+	0.999310i	$0.488171\pi$
$821$	−19921.5	+	34505.1i	−0.846852	+	1.46679i	−0.884003	+	0.467480i	$0.845162\pi$
$822$		0			0
$823$	−3628.00	−	6283.88i	−0.153662	−	0.266151i	0.778909	−	0.627137i	$-0.215773\pi$
$823$	−3628.00	−	6283.88i	−0.153662	−	0.266151i	−0.932571	+	0.360986i	$0.882440\pi$
$824$		0			0
$825$	468.000			0.0197499
$826$		0			0
$827$	−23005.0			−0.967306			−0.483653	−	0.875260i	$-0.660690\pi$
$827$	−23005.0			−0.967306			−0.483653	+	0.875260i	$0.660690\pi$
$828$		0			0
$829$	−184.000	−	318.697i	−0.00770879	−	0.0133520i	0.862145	−	0.506661i	$-0.169120\pi$
$829$	−184.000	−	318.697i	−0.00770879	−	0.0133520i	−0.869854	+	0.493309i	$0.835787\pi$
$830$		0			0
$831$	−456.000	+	789.815i	−0.0190355	+	0.0329704i
$832$		0			0
$833$	588.000	+	4073.78i	0.0244574	+	0.169446i
$834$		0			0
$835$	4829.00	−	8364.07i	0.200137	−	0.346648i
$836$		0			0
$837$	−472.500	−	818.394i	−0.0195125	−	0.0337967i
$838$		0			0
$839$	−5556.00			−0.228623			−0.114311	−	0.993445i	$-0.536466\pi$
$839$	−5556.00			−0.228623			−0.114311	+	0.993445i	$0.536466\pi$
$840$		0			0
$841$	40636.0			1.66616
$842$		0			0
$843$	6867.00	+	11894.0i	0.280560	+	0.485944i
$844$		0			0
$845$	−6451.50	+	11174.3i	−0.262649	+	0.454921i
$846$		0			0
$847$	2660.00	+	2303.63i	0.107909	+	0.0934517i
$848$		0			0
$849$	6453.00	−	11176.9i	0.260856	−	0.451815i
$850$		0			0
$851$	−184.000	−	318.697i	−0.00741180	−	0.0128376i
$852$		0			0
$853$	−5674.00			−0.227754			−0.113877	−	0.993495i	$-0.536327\pi$
$853$	−5674.00			−0.227754			−0.113877	+	0.993495i	$0.536327\pi$
$854$		0			0
$855$	8712.00			0.348473
$856$		0			0
$857$	3913.00	+	6777.51i	0.155969	+	0.270146i	0.933411	−	0.358808i	$-0.116817\pi$
$857$	3913.00	+	6777.51i	0.155969	+	0.270146i	−0.777442	+	0.628954i	$0.783483\pi$
$858$		0			0
$859$	−1685.00	+	2918.51i	−0.0669284	+	0.115923i	−0.897548	−	0.440917i	$-0.854653\pi$
$859$	−1685.00	+	2918.51i	−0.0669284	+	0.115923i	0.830619	+	0.556841i	$0.187987\pi$
$860$		0			0
$861$	840.000	−	290.985i	0.0332487	−	0.0115177i
$862$		0			0
$863$	−13867.0	+	24018.3i	−0.546974	+	0.947386i	0.451506	+	0.892268i	$0.350887\pi$
$863$	−13867.0	+	24018.3i	−0.546974	+	0.947386i	−0.998480	+	0.0551180i	$0.982446\pi$
$864$		0			0
$865$	−15851.0	−	27454.7i	−0.623064	−	1.07918i
$866$		0			0
$867$	14307.0			0.560428
$868$		0			0
$869$	51675.0			2.01721
$870$		0			0
$871$	14496.0	+	25107.8i	0.563924	+	0.976746i
$872$		0			0
$873$	−31.5000	+	54.5596i	−0.00122121	+	0.00211519i
$874$		0			0
$875$	4966.50	−	25806.7i	0.191884	−	0.997058i
$876$		0			0
$877$	−22640.0	+	39213.6i	−0.871720	+	1.50986i	−0.0115039	+	0.999934i	$0.503662\pi$
$877$	−22640.0	+	39213.6i	−0.871720	+	1.50986i	−0.860216	+	0.509930i	$0.829671\pi$
$878$		0			0
$879$	10090.5	+	17477.3i	0.387195	+	0.670641i
$880$		0			0
$881$	−47610.0			−1.82068			−0.910341	−	0.413858i	$-0.864181\pi$
$881$	−47610.0			−1.82068			−0.910341	+	0.413858i	$0.864181\pi$
$882$		0			0
$883$	−28328.0			−1.07963			−0.539815	−	0.841784i	$-0.681506\pi$
$883$	−28328.0			−1.07963			−0.539815	+	0.841784i	$0.681506\pi$
$884$		0			0
$885$	3580.50	+	6201.61i	0.135997	+	0.235553i
$886$		0			0
$887$	24306.0	−	42099.2i	0.920085	−	1.59363i	0.120805	−	0.992676i	$-0.461453\pi$
$887$	24306.0	−	42099.2i	0.920085	−	1.59363i	0.799281	−	0.600958i	$-0.205214\pi$
$888$		0			0
$889$	4112.50	−	21369.2i	0.155151	−	0.806186i
$890$		0			0
$891$	−1579.50	+	2735.77i	−0.0593886	+	0.102864i
$892$		0			0
$893$	−13112.0	−	22710.7i	−0.491351	−	0.851045i
$894$		0			0
$895$	−16236.0			−0.606379
$896$		0			0
$897$	−8832.00			−0.328754
$898$		0			0
$899$	4462.50	+	7729.28i	0.165554	+	0.286747i
$900$		0			0
$901$	4302.00	−	7451.28i	0.159068	−	0.275514i
$902$		0			0
$903$	−17325.0	+	6001.56i	−0.638472	+	0.221173i
$904$		0			0
$905$	24024.0	−	41610.8i	0.882414	−	1.52839i
$906$		0			0
$907$	−2050.00	−	3550.70i	−0.0750487	−	0.129988i	0.826059	−	0.563584i	$-0.190578\pi$
$907$	−2050.00	−	3550.70i	−0.0750487	−	0.129988i	−0.901107	+	0.433596i	$0.857245\pi$
$908$		0			0
$909$	−414.000			−0.0151062
$910$		0			0
$911$	−13902.0			−0.505591			−0.252796	−	0.967520i	$-0.581350\pi$
$911$	−13902.0			−0.505591			−0.252796	+	0.967520i	$0.581350\pi$
$912$		0			0
$913$	−22678.5	−	39280.3i	−0.822069	−	1.42386i
$914$		0			0
$915$	−6369.00	+	11031.4i	−0.230112	+	0.398566i
$916$		0			0
$917$	−35574.0	−	30808.0i	−1.28109	−	1.10945i
$918$		0			0
$919$	−22912.0	+	39684.7i	−0.822413	+	1.42446i	0.0814682	+	0.996676i	$0.474039\pi$
$919$	−22912.0	+	39684.7i	−0.822413	+	1.42446i	−0.903881	+	0.427784i	$0.859294\pi$
$920$		0			0
$921$	174.000	+	301.377i	0.00622529	+	0.0107825i
$922$		0			0
$923$	1088.00			0.0387995
$924$		0			0
$925$	16.0000			0.000568732
$926$		0			0
$927$	−7452.00	−	12907.2i	−0.264030	−	0.457313i
$928$		0			0
$929$	−19437.0	+	33665.9i	−0.686445	+	1.18896i	0.286536	+	0.958070i	$0.407496\pi$
$929$	−19437.0	+	33665.9i	−0.686445	+	1.18896i	−0.972980	+	0.230888i	$0.925837\pi$
$930$		0			0
$931$	−23716.0	+	18671.5i	−0.834866	+	0.657287i
$932$		0			0
$933$	−5688.00	+	9851.90i	−0.199589	+	0.345699i
$934$		0			0
$935$	2574.00	+	4458.30i	0.0900308	+	0.155938i
$936$		0			0
$937$	−1829.00			−0.0637682			−0.0318841	−	0.999492i	$-0.510151\pi$
$937$	−1829.00			−0.0637682			−0.0318841	+	0.999492i	$0.510151\pi$
$938$		0			0
$939$	11061.0			0.384411
$940$		0			0
$941$	2927.50	+	5070.58i	0.101417	+	0.175660i	0.912269	−	0.409592i	$-0.134329\pi$
$941$	2927.50	+	5070.58i	0.101417	+	0.175660i	−0.810851	+	0.585252i	$0.800996\pi$
$942$		0			0
$943$	736.000	−	1274.79i	0.0254162	−	0.0440221i
$944$		0			0
$945$	4158.00	+	3600.93i	0.143132	+	0.123956i
$946$		0			0
$947$	−10560.0	+	18290.5i	−0.362359	+	0.627624i	−0.988349	−	0.152207i	$-0.951362\pi$
$947$	−10560.0	+	18290.5i	−0.362359	+	0.627624i	0.625990	+	0.779831i	$0.284695\pi$
$948$		0			0
$949$	−13408.0	−	23223.3i	−0.458632	−	0.794375i
$950$		0			0
$951$	24843.0			0.847097
$952$		0			0
$953$	21650.0			0.735900			0.367950	−	0.929846i	$-0.380060\pi$
$953$	21650.0			0.735900			0.367950	+	0.929846i	$0.380060\pi$
$954$		0			0
$955$	16588.0	+	28731.3i	0.562068	+	0.973531i
$956$		0			0
$957$	14917.5	−	25837.9i	0.503881	−	0.872748i
$958$		0			0
$959$	14035.0	−	4861.87i	0.472590	−	0.163710i
$960$		0			0
$961$	14283.0	−	24738.9i	0.479440	−	0.830415i
$962$		0			0
$963$	1651.50	+	2860.48i	0.0552636	+	0.0957194i
$964$		0			0
$965$	17193.0			0.573536
$966$		0			0
$967$	36597.0			1.21704			0.608521	−	0.793538i	$-0.291763\pi$
$967$	36597.0			1.21704			0.608521	+	0.793538i	$0.291763\pi$
$968$		0			0
$969$	−1584.00	−	2743.57i	−0.0525133	−	0.0909557i
$970$		0			0
$971$	27093.5	−	46927.3i	0.895440	−	1.55095i	0.0621799	−	0.998065i	$-0.480195\pi$
$971$	27093.5	−	46927.3i	0.895440	−	1.55095i	0.833260	−	0.552882i	$-0.186472\pi$
$972$		0			0
$973$	10885.0	−	56560.1i	0.358640	−	1.86355i
$974$		0			0
$975$	192.000	−	332.554i	0.00630659	−	0.0109233i
$976$		0			0
$977$	−18017.0	−	31206.4i	−0.589985	−	1.02188i	−0.994234	−	0.107234i	$-0.965800\pi$
$977$	−18017.0	−	31206.4i	−0.589985	−	1.02188i	0.404249	−	0.914649i	$-0.367533\pi$
$978$		0			0
$979$	−2106.00			−0.0687518
$980$		0			0
$981$	14598.0			0.475105
$982$		0			0
$983$	20314.0	+	35184.9i	0.659121	+	1.14163i	0.980844	+	0.194797i	$0.0624048\pi$
$983$	20314.0	+	35184.9i	0.659121	+	1.14163i	−0.321723	+	0.946834i	$0.604262\pi$
$984$		0			0
$985$	−10153.0	+	17585.5i	−0.328428	+	0.568854i
$986$		0			0
$987$	3129.00	−	16258.8i	0.100909	−	0.524338i
$988$		0			0
$989$	−15180.0	+	26292.5i	−0.488065	+	0.845353i
$990$		0			0
$991$	20215.5	+	35014.3i	0.647999	+	1.12237i	0.983600	+	0.180362i	$0.0577270\pi$
$991$	20215.5	+	35014.3i	0.647999	+	1.12237i	−0.335602	+	0.942004i	$0.608940\pi$
$992$		0			0
$993$	20004.0			0.639283
$994$		0			0
$995$	43956.0			1.40050
$996$		0			0
$997$	16633.0	+	28809.2i	0.528357	+	0.915142i	0.999453	+	0.0330600i	$0.0105252\pi$
$997$	16633.0	+	28809.2i	0.528357	+	0.915142i	−0.471096	+	0.882082i	$0.656141\pi$
$998$		0			0
$999$	−54.0000	+	93.5307i	−0.00171019	+	0.00296214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.q.c.121.1	yes	2
3.2	odd	2		504.4.s.a.289.1		2
4.3	odd	2		336.4.q.c.289.1		2
7.2	even	3		1176.4.a.c.1.1		1
7.4	even	3	inner	168.4.q.c.25.1	✓	2
7.5	odd	6		1176.4.a.n.1.1		1
21.11	odd	6		504.4.s.a.361.1		2
28.11	odd	6		336.4.q.c.193.1		2
28.19	even	6		2352.4.a.o.1.1		1
28.23	odd	6		2352.4.a.y.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.c.25.1	✓	2	7.4	even	3	inner
168.4.q.c.121.1	yes	2	1.1	even	1	trivial
336.4.q.c.193.1		2	28.11	odd	6
336.4.q.c.289.1		2	4.3	odd	2
504.4.s.a.289.1		2	3.2	odd	2
504.4.s.a.361.1		2	21.11	odd	6
1176.4.a.c.1.1		1	7.2	even	3
1176.4.a.n.1.1		1	7.5	odd	6
2352.4.a.o.1.1		1	28.19	even	6
2352.4.a.y.1.1		1	28.23	odd	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(5.50000 - 9.52628i) q^{5} +(3.50000 - 18.1865i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-19.5000 - 33.7750i) q^{11} -32.0000 q^{13} +33.0000 q^{15} +(-6.00000 - 10.3923i) q^{17} +(44.0000 - 76.2102i) q^{19} +(52.5000 - 18.1865i) q^{21} +(46.0000 - 79.6743i) q^{23} +(2.00000 + 3.46410i) q^{25} -27.0000 q^{27} +255.000 q^{29} +(17.5000 + 30.3109i) q^{31} +(58.5000 - 101.325i) q^{33} +(-154.000 - 133.368i) q^{35} +(2.00000 - 3.46410i) q^{37} +(-48.0000 - 83.1384i) q^{39} +16.0000 q^{41} -330.000 q^{43} +(49.5000 + 85.7365i) q^{45} +(149.000 - 258.076i) q^{47} +(-318.500 - 127.306i) q^{49} +(18.0000 - 31.1769i) q^{51} +(358.500 + 620.940i) q^{53} -429.000 q^{55} +264.000 q^{57} +(108.500 + 187.928i) q^{59} +(-193.000 + 334.286i) q^{61} +(126.000 + 109.119i) q^{63} +(-176.000 + 304.841i) q^{65} +(-453.000 - 784.619i) q^{67} +276.000 q^{69} -34.0000 q^{71} +(419.000 + 725.729i) q^{73} +(-6.00000 + 10.3923i) q^{75} +(-682.500 + 236.425i) q^{77} +(-662.500 + 1147.48i) q^{79} +(-40.5000 - 70.1481i) q^{81} +1163.00 q^{83} -132.000 q^{85} +(382.500 + 662.509i) q^{87} +(27.0000 - 46.7654i) q^{89} +(-112.000 + 581.969i) q^{91} +(-52.5000 + 90.9327i) q^{93} +(-484.000 - 838.313i) q^{95} +7.00000 q^{97} +351.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 11 q^{5} + 7 q^{7} - 9 q^{9} - 39 q^{11} - 64 q^{13} + 66 q^{15} - 12 q^{17} + 88 q^{19} + 105 q^{21} + 92 q^{23} + 4 q^{25} - 54 q^{27} + 510 q^{29} + 35 q^{31} + 117 q^{33} - 308 q^{35}+ \cdots + 702 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 11 * q^5 + 7 * q^7 - 9 * q^9 - 39 * q^11 - 64 * q^13 + 66 * q^15 - 12 * q^17 + 88 * q^19 + 105 * q^21 + 92 * q^23 + 4 * q^25 - 54 * q^27 + 510 * q^29 + 35 * q^31 + 117 * q^33 - 308 * q^35 + 4 * q^37 - 96 * q^39 + 32 * q^41 - 660 * q^43 + 99 * q^45 + 298 * q^47 - 637 * q^49 + 36 * q^51 + 717 * q^53 - 858 * q^55 + 528 * q^57 + 217 * q^59 - 386 * q^61 + 252 * q^63 - 352 * q^65 - 906 * q^67 + 552 * q^69 - 68 * q^71 + 838 * q^73 - 12 * q^75 - 1365 * q^77 - 1325 * q^79 - 81 * q^81 + 2326 * q^83 - 264 * q^85 + 765 * q^87 + 54 * q^89 - 224 * q^91 - 105 * q^93 - 968 * q^95 + 14 * q^97 + 702 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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