LMFDB - Embedded newform 336.4.q.c.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(193,336)] 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("336.193"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, degree $2$, not 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:	$19.8246417619$
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:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.4.q.c.193.1

$q$-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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−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	$0.0128324\pi$
$11$	19.5000	+	33.7750i	0.534497	+	0.925777i	−0.464690	+	0.885473i	$0.653834\pi$
$12$		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	$0.344955\pi$
$19$	−44.0000	+	76.2102i	−0.531279	+	0.920201i	−0.999334	+	0.0365021i	$0.988378\pi$
$20$		0			0
$21$	52.5000	−	18.1865i	0.545545	−	0.188982i
$22$		0			0
$23$	−46.0000	+	79.6743i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−46.0000	+	79.6743i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		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	0.810868	−	0.585230i	$-0.198996\pi$
$31$	−17.5000	−	30.3109i	−0.101390	−	0.175613i	−0.912258	+	0.409617i	$0.865662\pi$
$32$		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	$-0.301028\pi$
$43$	330.000			1.17034			0.585169	+	0.810911i	$0.301028\pi$
$44$		0			0
$45$	49.5000	+	85.7365i	0.163978	+	0.284019i
$46$		0			0
$47$	−149.000	+	258.076i	−0.462423	+	0.800940i	−0.999081	−	0.0428596i	$-0.986353\pi$
$47$	−149.000	+	258.076i	−0.462423	+	0.800940i	0.536658	+	0.843800i	$0.319687\pi$
$48$		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	0.721131	−	0.692798i	$-0.243622\pi$
$59$	−108.500	−	187.928i	−0.239415	−	0.414679i	−0.960547	+	0.278119i	$0.910289\pi$
$60$		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	$0.142729\pi$
$67$	453.000	+	784.619i	0.826011	+	1.43069i	−0.0751326	+	0.997174i	$0.523938\pi$
$68$		0			0
$69$	276.000			0.481543
$70$		0			0
$71$	34.0000			0.0568318			0.0284159	−	0.999596i	$-0.490954\pi$
$71$	34.0000			0.0568318			0.0284159	+	0.999596i	$0.490954\pi$
$72$		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	$-0.440838\pi$
$79$	662.500	−	1147.48i	0.943507	−	1.63420i	0.758713	−	0.651425i	$-0.225829\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−1163.00			−1.53802			−0.769011	−	0.639235i	$-0.779251\pi$
$83$	−1163.00			−1.53802			−0.769011	+	0.639235i	$0.779251\pi$
$84$		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	$-0.542326\pi$
$103$	828.000	−	1434.14i	0.792090	−	1.37194i	0.924671	−	0.380768i	$-0.124340\pi$
$104$		0			0
$105$	115.500	−	600.156i	0.107349	−	0.557802i
$106$		0			0
$107$	−183.500	+	317.831i	−0.165791	+	0.287158i	−0.936936	−	0.349501i	$-0.886351\pi$
$107$	−183.500	+	317.831i	−0.165791	+	0.287158i	0.771145	+	0.636660i	$0.219684\pi$
$108$		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	$-0.634642\pi$
$127$	−1175.00			−0.820979			−0.410490	+	0.911865i	$0.634642\pi$
$128$		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	$0.488476\pi$
$131$	−1270.50	+	2200.57i	−0.847360	+	1.46767i	−0.883556	+	0.468325i	$0.844858\pi$
$132$		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	$-0.897775\pi$
$139$	−3110.00			−1.89775			−0.948873	+	0.315657i	$0.897775\pi$
$140$		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	0.987827	−	0.155555i	$-0.0497167\pi$
$151$	666.500	+	1154.41i	0.359199	+	0.622150i	−0.628628	+	0.777706i	$0.716383\pi$
$152$		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	−0.672530	−	0.740070i	$-0.734792\pi$
$163$	634.000	−	1098.12i	0.304655	−	0.527677i	0.977184	+	0.212393i	$0.0681256\pi$
$164$		0			0
$165$	−643.500	−	1114.57i	−0.303615	−	0.525876i
$166$		0			0
$167$	−878.000			−0.406836			−0.203418	−	0.979092i	$-0.565205\pi$
$167$	−878.000			−0.406836			−0.203418	+	0.979092i	$0.565205\pi$
$168$		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	0.977960	−	0.208792i	$-0.0669533\pi$
$179$	738.000	+	1278.25i	0.308160	+	0.533749i	−0.669800	+	0.742542i	$0.733620\pi$
$180$		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	$-0.639779\pi$
$191$	1508.00	−	2611.93i	0.571283	−	0.989491i	0.996435	−	0.0843690i	$-0.0268874\pi$
$192$		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	$-0.914578\pi$
$199$	−1998.00	−	3460.64i	−0.711731	−	1.23275i	0.252476	−	0.967603i	$-0.418755\pi$
$200$		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	$-0.738989\pi$
$211$	−4182.00			−1.36446			−0.682229	+	0.731138i	$0.738989\pi$
$212$		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	$-0.555675\pi$
$223$	−1159.00			−0.348038			−0.174019	+	0.984742i	$0.555675\pi$
$224$		0			0
$225$	−36.0000			−0.0106667
$226$		0			0
$227$	892.500	+	1545.86i	0.260957	+	0.451991i	0.966497	−	0.256680i	$-0.0826285\pi$
$227$	892.500	+	1545.86i	0.260957	+	0.451991i	−0.705539	+	0.708671i	$0.749295\pi$
$228$		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	$-0.610221\pi$
$239$	−2508.00			−0.678783			−0.339391	+	0.940645i	$0.610221\pi$
$240$		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	$-0.398681\pi$
$251$	2489.00			0.625913			0.312957	+	0.949767i	$0.398681\pi$
$252$		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	0.969307	−	0.245854i	$-0.0790684\pi$
$263$	1159.00	+	2007.45i	0.271738	+	0.470663i	−0.697569	+	0.716517i	$0.745735\pi$
$264$		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	−0.745446	−	0.666566i	$-0.767763\pi$
$271$	912.500	−	1580.50i	0.204540	−	0.354274i	0.949986	+	0.312292i	$0.101097\pi$
$272$		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	0.998499	−	0.0547724i	$-0.0174433\pi$
$283$	2151.00	+	3725.64i	0.451815	+	0.782567i	−0.546684	+	0.837339i	$0.684110\pi$
$284$		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	$-0.503432\pi$
$307$	−116.000			−0.0215650			−0.0107825	+	0.999942i	$0.503432\pi$
$308$		0			0
$309$	−4968.00			−0.914627
$310$		0			0
$311$	−1896.00	−	3283.97i	−0.345699	−	0.598768i	0.639782	−	0.768557i	$-0.279025\pi$
$311$	−1896.00	−	3283.97i	−0.345699	−	0.598768i	−0.985480	+	0.169789i	$0.945691\pi$
$312$		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	$0.353426\pi$
$331$	−3334.00	+	5774.66i	−0.553635	+	0.958924i	−0.998008	+	0.0630824i	$0.979907\pi$
$332$		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	$0.0816203\pi$
$347$	4546.00	+	7873.90i	0.703291	+	1.21814i	−0.264013	+	0.964519i	$0.585046\pi$
$348$		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	−0.822342	−	0.568994i	$-0.807333\pi$
$359$	555.000	−	961.288i	0.0815927	−	0.141323i	0.903934	+	0.427672i	$0.140666\pi$
$360$		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	0.898109	−	0.439772i	$-0.144941\pi$
$367$	479.500	+	830.518i	0.0682008	+	0.118127i	−0.829909	+	0.557899i	$0.811607\pi$
$368$		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	$-0.484117\pi$
$379$	736.000			0.0997514			0.0498757	+	0.998755i	$0.484117\pi$
$380$		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	$0.356355\pi$
$383$	−4207.00	+	7286.74i	−0.561273	+	0.972154i	−0.997386	+	0.0722616i	$0.976978\pi$
$384$		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	$-0.422639\pi$
$419$	4128.00			0.481303			0.240652	+	0.970612i	$0.422639\pi$
$420$		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	$-0.987192\pi$
$431$	−4782.00	−	8282.67i	−0.534433	−	0.925666i	0.464757	−	0.885438i	$-0.346142\pi$
$432$		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	$-0.513958\pi$
$439$	7756.50	−	13434.7i	0.843275	−	1.46059i	0.887111	−	0.461556i	$-0.152709\pi$
$440$		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	$-0.602268\pi$
$443$	6189.50	−	10720.5i	0.663819	−	1.14977i	0.979604	−	0.200938i	$-0.0643990\pi$
$444$		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	$-0.469023\pi$
$463$	1936.00			0.194327			0.0971637	+	0.995268i	$0.469023\pi$
$464$		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	$-0.607345\pi$
$467$	6578.00	−	11393.4i	0.651806	−	1.12896i	0.982684	−	0.185288i	$-0.0593218\pi$
$468$		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	0.663481	−	0.748193i	$-0.269078\pi$
$479$	−3315.00	−	5741.75i	−0.316213	−	0.547698i	−0.979695	+	0.200495i	$0.935745\pi$
$480$		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	0.946956	−	0.321365i	$-0.104141\pi$
$487$	2097.50	+	3632.98i	0.195168	+	0.338041i	−0.751788	+	0.659405i	$0.770808\pi$
$488$		0			0
$489$	−3804.00			−0.351785
$490$		0			0
$491$	−1107.00			−0.101748			−0.0508739	−	0.998705i	$-0.516201\pi$
$491$	−1107.00			−0.101748			−0.0508739	+	0.998705i	$0.516201\pi$
$492$		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	$-0.623946\pi$
$499$	6815.00	−	11803.9i	0.611385	−	1.05895i	0.991007	−	0.133809i	$-0.0427208\pi$
$500$		0			0
$501$	1317.00	+	2281.11i	0.117444	+	0.203418i
$502$		0			0
$503$	11760.0			1.04245			0.521225	−	0.853419i	$-0.325475\pi$
$503$	11760.0			1.04245			0.521225	+	0.853419i	$0.325475\pi$
$504$		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	$-0.574067\pi$
$523$	8700.00	−	15068.8i	0.727389	−	1.25987i	0.957983	−	0.286825i	$-0.0925997\pi$
$524$		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	$-0.111961\pi$
$547$	24020.0			1.87755			0.938776	+	0.344528i	$0.111961\pi$
$548$		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	0.985036	−	0.172348i	$-0.0551352\pi$
$563$	4585.50	+	7942.32i	0.343261	+	0.594545i	−0.641775	+	0.766893i	$0.721802\pi$
$564$		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	0.790824	−	0.612044i	$-0.209653\pi$
$571$	−1837.00	−	3181.78i	−0.134634	−	0.233193i	−0.925458	+	0.378851i	$0.876319\pi$
$572$		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	$-0.339488\pi$
$587$	13743.0			0.966328			0.483164	+	0.875530i	$0.339488\pi$
$588$		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	0.989210	−	0.146503i	$-0.0468017\pi$
$599$	5391.00	+	9337.49i	0.367730	+	0.636927i	−0.621480	+	0.783430i	$0.713468\pi$
$600$		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	−0.521613	−	0.853182i	$-0.674669\pi$
$607$	7149.50	−	12383.3i	0.478071	−	0.828044i	0.999684	+	0.0251387i	$0.00800273\pi$
$608$		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	0.998565	−	0.0535508i	$-0.0170539\pi$
$619$	6975.00	+	12081.1i	0.452906	+	0.784456i	−0.545659	+	0.838007i	$0.683721\pi$
$620$		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	$-0.665930\pi$
$631$	−15787.0			−0.995991			−0.497996	+	0.867180i	$0.665930\pi$
$632$		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	$-0.742677\pi$
$643$	−22522.0			−1.38131			−0.690654	+	0.723185i	$0.742677\pi$
$644$		0			0
$645$	−10890.0			−0.664796
$646$		0			0
$647$	8569.00	+	14841.9i	0.520683	+	0.901850i	0.999711	+	0.0240501i	$0.00765613\pi$
$647$	8569.00	+	14841.9i	0.520683	+	0.901850i	−0.479027	+	0.877800i	$0.659011\pi$
$648$		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	$-0.417572\pi$
$659$	8664.00			0.512142			0.256071	+	0.966658i	$0.417572\pi$
$660$		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	0.860782	−	0.508973i	$-0.169975\pi$
$683$	−185.500	−	321.295i	−0.0103923	−	0.0180000i	−0.871175	+	0.490973i	$0.836641\pi$
$684$		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	−0.730199	−	0.683235i	$-0.760573\pi$
$691$	4116.00	−	7129.12i	0.226599	−	0.392481i	0.956798	+	0.290753i	$0.0939059\pi$
$692$		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	−0.531916	−	0.846797i	$-0.678528\pi$
$719$	9011.00	−	15607.5i	0.467390	−	0.809544i	0.999306	+	0.0372537i	$0.0118610\pi$
$720$		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	$-0.489614\pi$
$727$	1279.00			0.0652483			0.0326241	+	0.999468i	$0.489614\pi$
$728$		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	$-0.883318\pi$
$739$	−15613.0	−	27042.5i	−0.777177	−	1.34611i	0.156386	−	0.987696i	$-0.450015\pi$
$740$		0			0
$741$	−8448.00			−0.418819
$742$		0			0
$743$	17758.0			0.876821			0.438410	−	0.898775i	$-0.355542\pi$
$743$	17758.0			0.876821			0.438410	+	0.898775i	$0.355542\pi$
$744$		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	−0.840458	−	0.541877i	$-0.817714\pi$
$751$	1009.50	−	1748.51i	0.0490508	−	0.0849585i	0.889508	+	0.456919i	$0.151047\pi$
$752$		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	0.936174	−	0.351538i	$-0.114341\pi$
$787$	3613.00	+	6257.90i	0.163646	+	0.283443i	−0.772528	+	0.634981i	$0.781008\pi$
$788$		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	$-0.847367\pi$
$811$	−40982.0			−1.77444			−0.887221	+	0.461344i	$0.847367\pi$
$812$		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	0.932571	−	0.360986i	$-0.117560\pi$
$823$	3628.00	+	6283.88i	0.153662	+	0.266151i	−0.778909	+	0.627137i	$0.784227\pi$
$824$		0			0
$825$	468.000			0.0197499
$826$		0			0
$827$	23005.0			0.967306			0.483653	−	0.875260i	$-0.339310\pi$
$827$	23005.0			0.967306			0.483653	+	0.875260i	$0.339310\pi$
$828$		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	$-0.463534\pi$
$839$	5556.00			0.228623			0.114311	+	0.993445i	$0.463534\pi$
$840$		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	−0.830619	−	0.556841i	$-0.812013\pi$
$859$	1685.00	−	2918.51i	0.0669284	−	0.115923i	0.897548	+	0.440917i	$0.145347\pi$
$860$		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	$-0.649113\pi$
$863$	13867.0	−	24018.3i	0.546974	−	0.947386i	0.998480	−	0.0551180i	$-0.0175535\pi$
$864$		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	$-0.318494\pi$
$883$	28328.0			1.07963			0.539815	+	0.841784i	$0.318494\pi$
$884$		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	$0.538547\pi$
$887$	−24306.0	+	42099.2i	−0.920085	+	1.59363i	−0.799281	+	0.600958i	$0.794786\pi$
$888$		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	0.901107	−	0.433596i	$-0.142755\pi$
$907$	2050.00	+	3550.70i	0.0750487	+	0.129988i	−0.826059	+	0.563584i	$0.809422\pi$
$908$		0			0
$909$	−414.000			−0.0151062
$910$		0			0
$911$	13902.0			0.505591			0.252796	−	0.967520i	$-0.418650\pi$
$911$	13902.0			0.505591			0.252796	+	0.967520i	$0.418650\pi$
$912$		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	$-0.525961\pi$
$919$	22912.0	−	39684.7i	0.822413	−	1.42446i	0.903881	−	0.427784i	$-0.140706\pi$
$920$		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	−0.625990	−	0.779831i	$-0.715305\pi$
$947$	10560.0	−	18290.5i	0.362359	−	0.627624i	0.988349	+	0.152207i	$0.0486381\pi$
$948$		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	$-0.708237\pi$
$967$	−36597.0			−1.21704			−0.608521	+	0.793538i	$0.708237\pi$
$968$		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	$0.519805\pi$
$971$	−27093.5	+	46927.3i	−0.895440	+	1.55095i	−0.833260	+	0.552882i	$0.813528\pi$
$972$		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	$-0.937595\pi$
$983$	−20314.0	−	35184.9i	−0.659121	−	1.14163i	0.321723	−	0.946834i	$-0.395738\pi$
$984$		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	$-0.942273\pi$
$991$	−20215.5	−	35014.3i	−0.647999	−	1.12237i	0.335602	−	0.942004i	$-0.391060\pi$
$992$		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	336.4.q.c.289.1		2
4.3	odd	2		168.4.q.c.121.1	yes	2
7.2	even	3		2352.4.a.y.1.1		1
7.4	even	3	inner	336.4.q.c.193.1		2
7.5	odd	6		2352.4.a.o.1.1		1
12.11	even	2		504.4.s.a.289.1		2
28.11	odd	6		168.4.q.c.25.1	✓	2
28.19	even	6		1176.4.a.n.1.1		1
28.23	odd	6		1176.4.a.c.1.1		1
84.11	even	6		504.4.s.a.361.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.c.25.1	✓	2	28.11	odd	6
168.4.q.c.121.1	yes	2	4.3	odd	2
336.4.q.c.193.1		2	7.4	even	3	inner
336.4.q.c.289.1		2	1.1	even	1	trivial
504.4.s.a.289.1		2	12.11	even	2
504.4.s.a.361.1		2	84.11	even	6
1176.4.a.c.1.1		1	28.23	odd	6
1176.4.a.n.1.1		1	28.19	even	6
2352.4.a.o.1.1		1	7.5	odd	6
2352.4.a.y.1.1		1	7.2	even	3

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not 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

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Representations

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Database

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