LMFDB - Embedded newform 84.4.i.b.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,4,Mod(25,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("84.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	84.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.95616044048$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Root			$2.13746 - 0.656712i$ of defining polynomial
Character	$\chi$	$=$	84.37
Dual form			84.4.i.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +(6.41238 - 11.1066i) q^{5} +(6.32475 - 17.4068i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +(6.41238 - 11.1066i) q^{5} +(6.32475 - 17.4068i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(18.4124 + 31.8912i) q^{11} +87.1238 q^{13} +38.4743 q^{15} +(-51.2990 - 88.8525i) q^{17} +(-47.9124 + 82.9867i) q^{19} +(54.7114 - 9.67805i) q^{21} +(48.0000 - 83.1384i) q^{23} +(-19.7371 - 34.1857i) q^{25} -27.0000 q^{27} -212.021 q^{29} +(79.6238 + 137.912i) q^{31} +(-55.2371 + 95.6735i) q^{33} +(-152.773 - 181.865i) q^{35} +(-64.3351 + 111.432i) q^{37} +(130.686 + 226.354i) q^{39} -298.042 q^{41} -33.3297 q^{43} +(57.7114 + 99.9590i) q^{45} +(-135.598 + 234.863i) q^{47} +(-262.995 - 220.188i) q^{49} +(153.897 - 266.557i) q^{51} +(-224.134 - 388.212i) q^{53} +472.268 q^{55} -287.474 q^{57} +(334.237 + 578.916i) q^{59} +(121.846 - 211.043i) q^{61} +(107.211 + 127.627i) q^{63} +(558.670 - 967.645i) q^{65} +(167.789 + 290.618i) q^{67} +288.000 q^{69} -339.608 q^{71} +(459.160 + 795.288i) q^{73} +(59.2114 - 102.557i) q^{75} +(671.578 - 118.797i) q^{77} +(68.1495 - 118.038i) q^{79} +(-40.5000 - 70.1481i) q^{81} +287.464 q^{83} -1315.79 q^{85} +(-318.031 - 550.846i) q^{87} +(-80.9277 + 140.171i) q^{89} +(551.036 - 1516.55i) q^{91} +(-238.871 + 413.737i) q^{93} +(614.464 + 1064.28i) q^{95} +182.680 q^{97} -331.423 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 3 q^{5} - 20 q^{7} - 18 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 + 3 * q^5 - 20 * q^7 - 18 * q^9	$ 4 q + 6 q^{3} + 3 q^{5} - 20 q^{7} - 18 q^{9} + 51 q^{11} + 122 q^{13} + 18 q^{15} - 24 q^{17} - 169 q^{19} + 15 q^{21} + 192 q^{23} - 11 q^{25} - 108 q^{27} - 78 q^{29} + 92 q^{31} - 153 q^{33} - 294 q^{35} + 173 q^{37} + 183 q^{39} + 348 q^{41} - 994 q^{43} + 27 q^{45} - 180 q^{47} - 146 q^{49} + 72 q^{51} - 285 q^{53} + 666 q^{55} - 1014 q^{57} + 1269 q^{59} - 328 q^{61} + 225 q^{63} + 1374 q^{65} + 875 q^{67} + 1152 q^{69} - 2808 q^{71} + 1361 q^{73} + 33 q^{75} + 897 q^{77} + 182 q^{79} - 162 q^{81} - 798 q^{83} - 4176 q^{85} - 117 q^{87} - 822 q^{89} + 1955 q^{91} - 276 q^{93} + 510 q^{95} + 1682 q^{97} - 918 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 + 3 * q^5 - 20 * q^7 - 18 * q^9 + 51 * q^11 + 122 * q^13 + 18 * q^15 - 24 * q^17 - 169 * q^19 + 15 * q^21 + 192 * q^23 - 11 * q^25 - 108 * q^27 - 78 * q^29 + 92 * q^31 - 153 * q^33 - 294 * q^35 + 173 * q^37 + 183 * q^39 + 348 * q^41 - 994 * q^43 + 27 * q^45 - 180 * q^47 - 146 * q^49 + 72 * q^51 - 285 * q^53 + 666 * q^55 - 1014 * q^57 + 1269 * q^59 - 328 * q^61 + 225 * q^63 + 1374 * q^65 + 875 * q^67 + 1152 * q^69 - 2808 * q^71 + 1361 * q^73 + 33 * q^75 + 897 * q^77 + 182 * q^79 - 162 * q^81 - 798 * q^83 - 4176 * q^85 - 117 * q^87 - 822 * q^89 + 1955 * q^91 - 276 * q^93 + 510 * q^95 + 1682 * q^97 - 918 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	6.41238	−	11.1066i	0.573540	−	0.993401i	−0.422658	−	0.906289i	$-0.638903\pi$
$5$	6.41238	−	11.1066i	0.573540	−	0.993401i	0.996199	−	0.0871118i	$-0.0277637\pi$
$6$		0			0
$7$	6.32475	−	17.4068i	0.341504	−	0.939880i
$7$	6.32475	−	17.4068i	0.341504	−	0.939880i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	18.4124	+	31.8912i	0.504685	+	0.874141i	0.999985	+	0.00541879i	$0.00172486\pi$
$11$	18.4124	+	31.8912i	0.504685	+	0.874141i	−0.495300	+	0.868722i	$0.664942\pi$
$12$		0			0
$13$	87.1238			1.85875			0.929376	−	0.369134i	$-0.120346\pi$
$13$	87.1238			1.85875			0.929376	+	0.369134i	$0.120346\pi$
$14$		0			0
$15$	38.4743			0.662267
$16$		0			0
$17$	−51.2990	−	88.8525i	−0.731873	−	1.26764i	−0.956082	−	0.293100i	$-0.905313\pi$
$17$	−51.2990	−	88.8525i	−0.731873	−	1.26764i	0.224209	−	0.974541i	$-0.428020\pi$
$18$		0			0
$19$	−47.9124	+	82.9867i	−0.578519	+	1.00202i	0.417131	+	0.908846i	$0.363036\pi$
$19$	−47.9124	+	82.9867i	−0.578519	+	1.00202i	−0.995650	+	0.0931772i	$0.970298\pi$
$20$		0			0
$21$	54.7114	−	9.67805i	0.568524	−	0.100568i
$22$		0			0
$23$	48.0000	−	83.1384i	0.435161	−	0.753720i	−0.562148	−	0.827037i	$-0.690025\pi$
$23$	48.0000	−	83.1384i	0.435161	−	0.753720i	0.997309	+	0.0733164i	$0.0233583\pi$
$24$		0			0
$25$	−19.7371	−	34.1857i	−0.157897	−	0.273486i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−212.021			−1.35763			−0.678815	−	0.734309i	$-0.737506\pi$
$29$	−212.021			−1.35763			−0.678815	+	0.734309i	$0.737506\pi$
$30$		0			0
$31$	79.6238	+	137.912i	0.461318	+	0.799026i	0.999027	−	0.0441046i	$-0.0140435\pi$
$31$	79.6238	+	137.912i	0.461318	+	0.799026i	−0.537709	+	0.843130i	$0.680710\pi$
$32$		0			0
$33$	−55.2371	+	95.6735i	−0.291380	+	0.504685i
$34$		0			0
$35$	−152.773	−	181.865i	−0.737811	−	0.878310i
$36$		0			0
$37$	−64.3351	+	111.432i	−0.285855	+	0.495115i	−0.972816	−	0.231579i	$-0.925611\pi$
$37$	−64.3351	+	111.432i	−0.285855	+	0.495115i	0.686961	+	0.726694i	$0.258944\pi$
$38$		0			0
$39$	130.686	+	226.354i	0.536576	+	0.929376i
$40$		0			0
$41$	−298.042			−1.13527			−0.567637	−	0.823279i	$-0.692142\pi$
$41$	−298.042			−1.13527			−0.567637	+	0.823279i	$0.692142\pi$
$42$		0			0
$43$	−33.3297			−0.118203			−0.0591016	−	0.998252i	$-0.518824\pi$
$43$	−33.3297			−0.118203			−0.0591016	+	0.998252i	$0.518824\pi$
$44$		0			0
$45$	57.7114	+	99.9590i	0.191180	+	0.331134i
$46$		0			0
$47$	−135.598	+	234.863i	−0.420830	+	0.728899i	−0.996021	−	0.0891205i	$-0.971594\pi$
$47$	−135.598	+	234.863i	−0.420830	+	0.728899i	0.575191	+	0.818019i	$0.304928\pi$
$48$		0			0
$49$	−262.995	−	220.188i	−0.766749	−	0.641947i
$50$		0			0
$51$	153.897	−	266.557i	0.422547	−	0.731873i
$52$		0			0
$53$	−224.134	−	388.212i	−0.580890	−	1.00613i	−0.995374	−	0.0960750i	$-0.969371\pi$
$53$	−224.134	−	388.212i	−0.580890	−	1.00613i	0.414484	−	0.910057i	$-0.363962\pi$
$54$		0			0
$55$	472.268			1.15783
$56$		0			0
$57$	−287.474			−0.668016
$58$		0			0
$59$	334.237	+	578.916i	0.737525	+	1.27743i	0.953607	+	0.301055i	$0.0973389\pi$
$59$	334.237	+	578.916i	0.737525	+	1.27743i	−0.216082	+	0.976375i	$0.569328\pi$
$60$		0			0
$61$	121.846	−	211.043i	0.255750	−	0.442971i	−0.709349	−	0.704857i	$-0.751011\pi$
$61$	121.846	−	211.043i	0.255750	−	0.442971i	0.965099	+	0.261886i	$0.0843444\pi$
$62$		0			0
$63$	107.211	+	127.627i	0.214403	+	0.255231i
$64$		0			0
$65$	558.670	−	967.645i	1.06607	−	1.84649i
$66$		0			0
$67$	167.789	+	290.618i	0.305950	+	0.529921i	0.977472	−	0.211063i	$-0.0676927\pi$
$67$	167.789	+	290.618i	0.305950	+	0.529921i	−0.671522	+	0.740984i	$0.734359\pi$
$68$		0			0
$69$	288.000			0.502480
$70$		0			0
$71$	−339.608			−0.567663			−0.283831	−	0.958874i	$-0.591606\pi$
$71$	−339.608			−0.567663			−0.283831	+	0.958874i	$0.591606\pi$
$72$		0			0
$73$	459.160	+	795.288i	0.736173	+	1.27509i	0.954207	+	0.299147i	$0.0967022\pi$
$73$	459.160	+	795.288i	0.736173	+	1.27509i	−0.218034	+	0.975941i	$0.569964\pi$
$74$		0			0
$75$	59.2114	−	102.557i	0.0911619	−	0.157897i
$76$		0			0
$77$	671.578	−	118.797i	0.993940	−	0.175821i
$78$		0			0
$79$	68.1495	−	118.038i	0.0970559	−	0.168106i	−0.813409	−	0.581692i	$-0.802391\pi$
$79$	68.1495	−	118.038i	0.0970559	−	0.168106i	0.910465	+	0.413587i	$0.135724\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	287.464			0.380160			0.190080	−	0.981769i	$-0.439125\pi$
$83$	287.464			0.380160			0.190080	+	0.981769i	$0.439125\pi$
$84$		0			0
$85$	−1315.79			−1.67903
$86$		0			0
$87$	−318.031	−	550.846i	−0.391914	−	0.678815i
$88$		0			0
$89$	−80.9277	+	140.171i	−0.0963856	+	0.166945i	−0.910186	−	0.414200i	$-0.864062\pi$
$89$	−80.9277	+	140.171i	−0.0963856	+	0.166945i	0.813800	+	0.581144i	$0.197395\pi$
$90$		0			0
$91$	551.036	−	1516.55i	0.634772	−	1.74700i
$92$		0			0
$93$	−238.871	+	413.737i	−0.266342	+	0.461318i
$94$		0			0
$95$	614.464	+	1064.28i	0.663607	+	1.14940i
$96$		0			0
$97$	182.680			0.191220			0.0956101	−	0.995419i	$-0.469520\pi$
$97$	182.680			0.191220			0.0956101	+	0.995419i	$0.469520\pi$
$98$		0			0
$99$	−331.423			−0.336457
$100$		0			0
$101$	766.051	+	1326.84i	0.754703	+	1.30718i	0.945522	+	0.325558i	$0.105552\pi$
$101$	766.051	+	1326.84i	0.754703	+	1.30718i	−0.190819	+	0.981625i	$0.561114\pi$
$102$		0			0
$103$	−243.954	+	422.541i	−0.233374	+	0.404215i	−0.958799	−	0.284086i	$-0.908310\pi$
$103$	−243.954	+	422.541i	−0.233374	+	0.404215i	0.725425	+	0.688301i	$0.241643\pi$
$104$		0			0
$105$	243.340	−	669.715i	0.226167	−	0.622452i
$106$		0			0
$107$	−246.176	+	426.389i	−0.222418	+	0.385239i	−0.955542	−	0.294856i	$-0.904728\pi$
$107$	−246.176	+	426.389i	−0.222418	+	0.385239i	0.733124	+	0.680095i	$0.238062\pi$
$108$		0			0
$109$	−424.036	−	734.452i	−0.372617	−	0.645392i	0.617350	−	0.786689i	$-0.288206\pi$
$109$	−424.036	−	734.452i	−0.372617	−	0.645392i	−0.989967	+	0.141296i	$0.954873\pi$
$110$		0			0
$111$	−386.011			−0.330077
$112$		0			0
$113$	−736.350			−0.613009			−0.306505	−	0.951869i	$-0.599159\pi$
$113$	−736.350			−0.613009			−0.306505	+	0.951869i	$0.599159\pi$
$114$		0			0
$115$	−615.588	−	1066.23i	−0.499164	−	0.864578i
$116$		0			0
$117$	−392.057	+	679.062i	−0.309792	+	0.536576i
$118$		0			0
$119$	−1871.09	+	330.983i	−1.44137	+	0.254968i
$120$		0			0
$121$	−12.5312	+	21.7046i	−0.00941485	+	0.0163070i
$122$		0			0
$123$	−447.062	−	774.335i	−0.327726	−	0.567637i
$124$		0			0
$125$	1096.85			0.784839
$126$		0			0
$127$	−2511.37			−1.75471			−0.877355	−	0.479841i	$-0.840694\pi$
$127$	−2511.37			−1.75471			−0.877355	+	0.479841i	$0.840694\pi$
$128$		0			0
$129$	−49.9946	−	86.5931i	−0.0341223	−	0.0591016i
$130$		0			0
$131$	339.711	−	588.397i	0.226570	−	0.392431i	−0.730219	−	0.683213i	$-0.760582\pi$
$131$	339.711	−	588.397i	0.226570	−	0.392431i	0.956789	+	0.290782i	$0.0939153\pi$
$132$		0			0
$133$	1141.50	+	1358.87i	0.744215	+	0.885934i
$134$		0			0
$135$	−173.134	+	299.877i	−0.110378	+	0.191180i
$136$		0			0
$137$	82.2683	+	142.493i	0.0513040	+	0.0888612i	0.890537	−	0.454911i	$-0.150329\pi$
$137$	82.2683	+	142.493i	0.0513040	+	0.0888612i	−0.839233	+	0.543772i	$0.816996\pi$
$138$		0			0
$139$	−521.991			−0.318523			−0.159261	−	0.987236i	$-0.550911\pi$
$139$	−521.991			−0.318523			−0.159261	+	0.987236i	$0.550911\pi$
$140$		0			0
$141$	−813.588			−0.485932
$142$		0			0
$143$	1604.16	+	2778.48i	0.938085	+	1.62481i
$144$		0			0
$145$	−1359.56	+	2354.82i	−0.778656	+	1.34867i
$146$		0			0
$147$	177.572	−	1013.56i	0.0996318	−	0.568689i
$148$		0			0
$149$	1206.06	−	2088.96i	0.663117	−	1.14855i	−0.316675	−	0.948534i	$-0.602566\pi$
$149$	1206.06	−	2088.96i	0.663117	−	1.14855i	0.979792	−	0.200019i	$-0.0641003\pi$
$150$		0			0
$151$	787.289	+	1363.62i	0.424296	+	0.734902i	0.996354	−	0.0853111i	$-0.0271884\pi$
$151$	787.289	+	1363.62i	0.424296	+	0.734902i	−0.572059	+	0.820213i	$0.693855\pi$
$152$		0			0
$153$	923.382			0.487915
$154$		0			0
$155$	2042.31			1.05834
$156$		0			0
$157$	−1039.37	−	1800.24i	−0.528349	−	0.915128i	−0.999454	−	0.0330505i	$-0.989478\pi$
$157$	−1039.37	−	1800.24i	−0.528349	−	0.915128i	0.471104	−	0.882078i	$-0.343856\pi$
$158$		0			0
$159$	672.402	−	1164.64i	0.335377	−	0.580890i
$160$		0			0
$161$	−1143.59	−	1361.36i	−0.559797	−	0.666398i
$162$		0			0
$163$	1589.71	−	2753.46i	0.763901	−	1.32312i	−0.176924	−	0.984224i	$-0.556615\pi$
$163$	1589.71	−	2753.46i	0.763901	−	1.32312i	0.940826	−	0.338891i	$-0.110052\pi$
$164$		0			0
$165$	708.402	+	1226.99i	0.334237	+	0.578915i
$166$		0			0
$167$	−2979.28			−1.38050			−0.690250	−	0.723571i	$-0.742500\pi$
$167$	−2979.28			−1.38050			−0.690250	+	0.723571i	$0.742500\pi$
$168$		0			0
$169$	5393.55			2.45496
$170$		0			0
$171$	−431.211	−	746.880i	−0.192840	−	0.334008i
$172$		0			0
$173$	−8.18518	+	14.1772i	−0.00359716	+	0.00623046i	−0.867818	−	0.496882i	$-0.834478\pi$
$173$	−8.18518	+	14.1772i	−0.00359716	+	0.00623046i	0.864221	+	0.503112i	$0.167812\pi$
$174$		0			0
$175$	−719.897	+	127.345i	−0.310966	+	0.0550077i
$176$		0			0
$177$	−1002.71	+	1736.75i	−0.425810	+	0.737525i
$178$		0			0
$179$	−1349.15	−	2336.79i	−0.563351	−	0.975753i	−0.997201	−	0.0747677i	$-0.976178\pi$
$179$	−1349.15	−	2336.79i	−0.563351	−	0.975753i	0.433850	−	0.900985i	$-0.357155\pi$
$180$		0			0
$181$	31.3297			0.0128659			0.00643293	−	0.999979i	$-0.497952\pi$
$181$	31.3297			0.0128659			0.00643293	+	0.999979i	$0.497952\pi$
$182$		0			0
$183$	731.073			0.295314
$184$		0			0
$185$	825.082	+	1429.08i	0.327899	+	0.567937i
$186$		0			0
$187$	1889.07	−	3271.97i	0.738731	−	1.27952i
$188$		0			0
$189$	−170.768	+	469.984i	−0.0657226	+	0.180880i
$190$		0			0
$191$	772.587	−	1338.16i	0.292683	−	0.506942i	−0.681760	−	0.731576i	$-0.738785\pi$
$191$	772.587	−	1338.16i	0.292683	−	0.506942i	0.974443	+	0.224634i	$0.0721186\pi$
$192$		0			0
$193$	915.099	+	1585.00i	0.341297	+	0.591143i	0.984674	−	0.174406i	$-0.0558006\pi$
$193$	915.099	+	1585.00i	0.341297	+	0.591143i	−0.643377	+	0.765549i	$0.722467\pi$
$194$		0			0
$195$	3352.02			1.23099
$196$		0			0
$197$	4728.45			1.71009			0.855047	−	0.518551i	$-0.173528\pi$
$197$	4728.45			1.71009			0.855047	+	0.518551i	$0.173528\pi$
$198$		0			0
$199$	164.125	+	284.272i	0.0584648	+	0.101264i	0.893776	−	0.448513i	$-0.148046\pi$
$199$	164.125	+	284.272i	0.0584648	+	0.101264i	−0.835312	+	0.549777i	$0.814713\pi$
$200$		0			0
$201$	−503.366	+	871.855i	−0.176640	+	0.305950i
$202$		0			0
$203$	−1340.98	+	3690.61i	−0.463637	+	1.27601i
$204$		0			0
$205$	−1911.15	+	3310.22i	−0.651126	+	1.12778i
$206$		0			0
$207$	432.000	+	748.246i	0.145054	+	0.251240i
$208$		0			0
$209$	−3528.72			−1.16788
$210$		0			0
$211$	−4935.76			−1.61039			−0.805193	−	0.593013i	$-0.797938\pi$
$211$	−4935.76			−1.61039			−0.805193	+	0.593013i	$0.797938\pi$
$212$		0			0
$213$	−509.412	−	882.327i	−0.163870	−	0.283831i
$214$		0			0
$215$	−213.723	+	370.179i	−0.0677943	+	0.117423i
$216$		0			0
$217$	2904.22	−	513.735i	0.908530	−	0.160712i
$218$		0			0
$219$	−1377.48	+	2385.86i	−0.425029	+	0.736173i
$220$		0			0
$221$	−4469.36	−	7741.16i	−1.36037	−	2.35623i
$222$		0			0
$223$	3446.00			1.03480			0.517402	−	0.855742i	$-0.326899\pi$
$223$	3446.00			1.03480			0.517402	+	0.855742i	$0.326899\pi$
$224$		0			0
$225$	355.268			0.105265
$226$		0			0
$227$	−2862.37	−	4957.77i	−0.836927	−	1.44960i	−0.892452	−	0.451142i	$-0.851017\pi$
$227$	−2862.37	−	4957.77i	−0.836927	−	1.44960i	0.0555255	−	0.998457i	$-0.482317\pi$
$228$		0			0
$229$	−1508.57	+	2612.93i	−0.435325	+	0.754004i	−0.997322	−	0.0731345i	$-0.976700\pi$
$229$	−1508.57	+	2612.93i	−0.435325	+	0.754004i	0.561997	+	0.827139i	$0.310033\pi$
$230$		0			0
$231$	1316.01	+	1566.61i	0.374836	+	0.446215i
$232$		0			0
$233$	−190.856	+	330.573i	−0.0536627	+	0.0929466i	−0.891609	−	0.452806i	$-0.850423\pi$
$233$	−190.856	+	330.573i	−0.0536627	+	0.0929466i	0.837946	+	0.545753i	$0.183756\pi$
$234$		0			0
$235$	1739.01	+	3012.06i	0.482726	+	0.836106i
$236$		0			0
$237$	408.897			0.112071
$238$		0			0
$239$	−1377.38			−0.372785			−0.186392	−	0.982475i	$-0.559680\pi$
$239$	−1377.38			−0.372785			−0.186392	+	0.982475i	$0.559680\pi$
$240$		0			0
$241$	−2903.36	−	5028.77i	−0.776025	−	1.34411i	−0.934217	−	0.356706i	$-0.883900\pi$
$241$	−2903.36	−	5028.77i	−0.776025	−	1.34411i	0.158192	−	0.987408i	$-0.449434\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−4131.95	+	1509.04i	−1.07747	+	0.393507i
$246$		0			0
$247$	−4174.31	+	7230.11i	−1.07532	+	1.86251i
$248$		0			0
$249$	431.196	+	746.854i	0.109743	+	0.190080i
$250$		0			0
$251$	−4348.52			−1.09353			−0.546765	−	0.837286i	$-0.684141\pi$
$251$	−4348.52			−1.09353			−0.546765	+	0.837286i	$0.684141\pi$
$252$		0			0
$253$	3535.18			0.878477
$254$		0			0
$255$	−1973.69	−	3418.53i	−0.484695	−	0.839517i
$256$		0			0
$257$	2345.56	−	4062.62i	0.569307	−	0.986068i	−0.427328	−	0.904097i	$-0.640545\pi$
$257$	2345.56	−	4062.62i	0.569307	−	0.986068i	0.996635	−	0.0819713i	$-0.0261216\pi$
$258$		0			0
$259$	1532.77	+	1824.65i	0.367728	+	0.437753i
$260$		0			0
$261$	954.094	−	1652.54i	0.226272	−	0.391914i
$262$		0			0
$263$	3790.81	+	6565.87i	0.888788	+	1.53943i	0.841310	+	0.540553i	$0.181785\pi$
$263$	3790.81	+	6565.87i	0.888788	+	1.53943i	0.0474778	+	0.998872i	$0.484882\pi$
$264$		0			0
$265$	−5748.93			−1.33266
$266$		0			0
$267$	−485.566			−0.111297
$268$		0			0
$269$	1800.95	+	3119.33i	0.408200	+	0.707023i	0.994688	−	0.102935i	$-0.0328233\pi$
$269$	1800.95	+	3119.33i	0.408200	+	0.707023i	−0.586488	+	0.809958i	$0.699490\pi$
$270$		0			0
$271$	1918.13	−	3322.31i	0.429957	−	0.744707i	−0.566912	−	0.823778i	$-0.691862\pi$
$271$	1918.13	−	3322.31i	0.429957	−	0.744707i	0.996869	+	0.0790710i	$0.0251954\pi$
$272$		0			0
$273$	4766.66	−	843.188i	1.05675	−	0.186931i
$274$		0			0
$275$	726.815	−	1258.88i	0.159377	−	0.276048i
$276$		0			0
$277$	−2701.52	−	4679.17i	−0.585988	−	1.01496i	−0.994751	−	0.102321i	$-0.967373\pi$
$277$	−2701.52	−	4679.17i	−0.585988	−	1.01496i	0.408763	−	0.912640i	$-0.365960\pi$
$278$		0			0
$279$	−1433.23			−0.307545
$280$		0			0
$281$	150.842			0.0320230			0.0160115	−	0.999872i	$-0.494903\pi$
$281$	150.842			0.0320230			0.0160115	+	0.999872i	$0.494903\pi$
$282$		0			0
$283$	−908.571	−	1573.69i	−0.190844	−	0.330552i	0.754686	−	0.656086i	$-0.227789\pi$
$283$	−908.571	−	1573.69i	−0.190844	−	0.330552i	−0.945530	+	0.325534i	$0.894456\pi$
$284$		0			0
$285$	−1843.39	+	3192.85i	−0.383134	+	0.663607i
$286$		0			0
$287$	−1885.04	+	5187.96i	−0.387701	+	1.06702i
$288$		0			0
$289$	−2806.68	+	4861.31i	−0.571275	+	0.989478i
$290$		0			0
$291$	274.020	+	474.617i	0.0552005	+	0.0956101i
$292$		0			0
$293$	−2817.59			−0.561792			−0.280896	−	0.959738i	$-0.590632\pi$
$293$	−2817.59			−0.561792			−0.280896	+	0.959738i	$0.590632\pi$
$294$		0			0
$295$	8573.02			1.69200
$296$		0			0
$297$	−497.134	−	861.062i	−0.0971268	−	0.168228i
$298$		0			0
$299$	4181.94	−	7243.33i	0.808856	−	1.40098i
$300$		0			0
$301$	−210.802	+	580.165i	−0.0403669	+	0.111097i
$302$		0			0
$303$	−2298.15	+	3980.52i	−0.435728	+	0.754703i
$304$		0			0
$305$	−1562.64	−	2706.57i	−0.293365	−	0.508124i
$306$		0			0
$307$	8589.21			1.59678			0.798391	−	0.602139i	$-0.205685\pi$
$307$	8589.21			1.59678			0.798391	+	0.602139i	$0.205685\pi$
$308$		0			0
$309$	−1463.72			−0.269477
$310$		0			0
$311$	2999.15	+	5194.67i	0.546836	+	0.947147i	0.998489	+	0.0549538i	$0.0175011\pi$
$311$	2999.15	+	5194.67i	0.546836	+	0.947147i	−0.451653	+	0.892194i	$0.649166\pi$
$312$		0			0
$313$	2481.64	−	4298.32i	0.448148	−	0.776216i	−0.550117	−	0.835087i	$-0.685417\pi$
$313$	2481.64	−	4298.32i	0.448148	−	0.776216i	0.998266	+	0.0588717i	$0.0187503\pi$
$314$		0			0
$315$	2104.98	−	372.356i	0.376515	−	0.0666028i
$316$		0			0
$317$	1952.30	−	3381.49i	0.345906	−	0.599127i	−0.639612	−	0.768698i	$-0.720905\pi$
$317$	1952.30	−	3381.49i	0.345906	−	0.599127i	0.985518	+	0.169571i	$0.0542383\pi$
$318$		0			0
$319$	−3903.81	−	6761.59i	−0.685176	−	1.18676i
$320$		0			0
$321$	−1477.05			−0.256826
$322$		0			0
$323$	9831.43			1.69361
$324$		0			0
$325$	−1719.57	−	2978.39i	−0.293491	−	0.508342i
$326$		0			0
$327$	1272.11	−	2203.36i	0.215131	−	0.372617i
$328$		0			0
$329$	3230.59	+	3845.78i	0.541362	+	0.644452i
$330$		0			0
$331$	1224.86	−	2121.52i	0.203397	−	0.352295i	−0.746224	−	0.665695i	$-0.768135\pi$
$331$	1224.86	−	2121.52i	0.203397	−	0.352295i	0.949621	+	0.313401i	$0.101468\pi$
$332$		0			0
$333$	−579.016	−	1002.89i	−0.0952850	−	0.165038i
$334$		0			0
$335$	4303.69			0.701898
$336$		0			0
$337$	−1770.59			−0.286203			−0.143101	−	0.989708i	$-0.545707\pi$
$337$	−1770.59			−0.286203			−0.143101	+	0.989708i	$0.545707\pi$
$338$		0			0
$339$	−1104.53	−	1913.09i	−0.176960	−	0.306505i
$340$		0			0
$341$	−2932.13	+	5078.59i	−0.465641	+	0.806513i
$342$		0			0
$343$	−5496.15	+	3185.28i	−0.865201	+	0.501425i
$344$		0			0
$345$	1846.76	−	3198.69i	0.288193	−	0.499164i
$346$		0			0
$347$	2017.36	+	3494.17i	0.312097	+	0.540567i	0.978816	−	0.204741i	$-0.0656353\pi$
$347$	2017.36	+	3494.17i	0.312097	+	0.540567i	−0.666719	+	0.745309i	$0.732302\pi$
$348$		0			0
$349$	6791.53			1.04167			0.520834	−	0.853658i	$-0.325621\pi$
$349$	6791.53			1.04167			0.520834	+	0.853658i	$0.325621\pi$
$350$		0			0
$351$	−2352.34			−0.357717
$352$		0			0
$353$	5078.40	+	8796.05i	0.765712	+	1.32625i	0.939870	+	0.341534i	$0.110946\pi$
$353$	5078.40	+	8796.05i	0.765712	+	1.32625i	−0.174158	+	0.984718i	$0.555720\pi$
$354$		0			0
$355$	−2177.69	+	3771.88i	−0.325577	+	0.563917i
$356$		0			0
$357$	−3666.56	−	4364.77i	−0.543571	−	0.647081i
$358$		0			0
$359$	6421.36	−	11122.1i	0.944029	−	1.63511i	0.186347	−	0.982484i	$-0.440335\pi$
$359$	6421.36	−	11122.1i	0.944029	−	1.63511i	0.757683	−	0.652623i	$-0.226331\pi$
$360$		0			0
$361$	−1161.69	−	2012.11i	−0.169367	−	0.293353i
$362$		0			0
$363$	−75.1870			−0.0108713
$364$		0			0
$365$	11777.2			1.68890
$366$		0			0
$367$	957.408	+	1658.28i	0.136175	+	0.235862i	0.926046	−	0.377411i	$-0.123186\pi$
$367$	957.408	+	1658.28i	0.136175	+	0.235862i	−0.789871	+	0.613274i	$0.789852\pi$
$368$		0			0
$369$	1341.19	−	2323.00i	0.189212	−	0.327726i
$370$		0			0
$371$	−8175.13	+	1446.12i	−1.14402	+	0.202369i
$372$		0			0
$373$	−2857.43	+	4949.21i	−0.396654	+	0.687026i	−0.993311	−	0.115471i	$-0.963162\pi$
$373$	−2857.43	+	4949.21i	−0.396654	+	0.687026i	0.596656	+	0.802497i	$0.296496\pi$
$374$		0			0
$375$	1645.27	+	2849.69i	0.226564	+	0.392420i
$376$		0			0
$377$	−18472.0			−2.52350
$378$		0			0
$379$	−11570.3			−1.56815			−0.784075	−	0.620666i	$-0.786862\pi$
$379$	−11570.3			−1.56815			−0.784075	+	0.620666i	$0.786862\pi$
$380$		0			0
$381$	−3767.06	−	6524.74i	−0.506541	−	0.877355i
$382$		0			0
$383$	−3059.01	+	5298.36i	−0.408115	+	0.706876i	−0.994679	−	0.103027i	$-0.967147\pi$
$383$	−3059.01	+	5298.36i	−0.408115	+	0.706876i	0.586563	+	0.809903i	$0.300481\pi$
$384$		0			0
$385$	2986.98	−	8220.69i	0.395404	−	1.08822i
$386$		0			0
$387$	149.984	−	259.779i	0.0197005	−	0.0341223i
$388$		0			0
$389$	1629.23	+	2821.91i	0.212353	+	0.367806i	0.952450	−	0.304694i	$-0.0985541\pi$
$389$	1629.23	+	2821.91i	0.212353	+	0.367806i	−0.740098	+	0.672499i	$0.765221\pi$
$390$		0			0
$391$	−9849.41			−1.27393
$392$		0			0
$393$	2038.27			0.261621
$394$		0			0
$395$	−874.000	−	1513.81i	−0.111331	−	0.192831i
$396$		0			0
$397$	−361.963	+	626.938i	−0.0457592	+	0.0792572i	−0.887998	−	0.459848i	$-0.847904\pi$
$397$	−361.963	+	626.938i	−0.0457592	+	0.0792572i	0.842239	+	0.539105i	$0.181237\pi$
$398$		0			0
$399$	−1818.20	+	5004.01i	−0.228130	+	0.627855i
$400$		0			0
$401$	−5514.91	+	9552.11i	−0.686787	+	1.18955i	0.286085	+	0.958204i	$0.407646\pi$
$401$	−5514.91	+	9552.11i	−0.686787	+	1.18955i	−0.972872	+	0.231346i	$0.925687\pi$
$402$		0			0
$403$	6937.12	+	12015.4i	0.857475	+	1.48519i
$404$		0			0
$405$	−1038.80			−0.127453
$406$		0			0
$407$	−4738.25			−0.577067
$408$		0			0
$409$	−1341.78	−	2324.03i	−0.162217	−	0.280968i	0.773447	−	0.633861i	$-0.218531\pi$
$409$	−1341.78	−	2324.03i	−0.162217	−	0.280968i	−0.935663	+	0.352894i	$0.885198\pi$
$410$		0			0
$411$	−246.805	+	427.479i	−0.0296204	+	0.0513040i
$412$		0			0
$413$	12191.1	−	2156.51i	1.45250	−	0.256937i
$414$		0			0
$415$	1843.33	−	3192.74i	0.218037	−	0.377652i
$416$		0			0
$417$	−782.986	−	1356.17i	−0.0919497	−	0.159261i
$418$		0			0
$419$	10024.9			1.16885			0.584427	−	0.811446i	$-0.301319\pi$
$419$	10024.9			1.16885			0.584427	+	0.811446i	$0.301319\pi$
$420$		0			0
$421$	−5560.68			−0.643731			−0.321866	−	0.946785i	$-0.604310\pi$
$421$	−5560.68			−0.643731			−0.321866	+	0.946785i	$0.604310\pi$
$422$		0			0
$423$	−1220.38	−	2113.76i	−0.140277	−	0.242966i
$424$		0			0
$425$	−2024.99	+	3507.39i	−0.231121	+	0.400313i
$426$		0			0
$427$	−2902.94	−	3455.74i	−0.329000	−	0.391651i
$428$		0			0
$429$	−4812.47	+	8335.44i	−0.541604	+	0.938085i
$430$		0			0
$431$	−5763.11	−	9982.00i	−0.644081	−	1.11558i	−0.984513	−	0.175312i	$-0.943906\pi$
$431$	−5763.11	−	9982.00i	−0.644081	−	1.11558i	0.340431	−	0.940269i	$-0.389427\pi$
$432$		0			0
$433$	2228.79			0.247365			0.123683	−	0.992322i	$-0.460530\pi$
$433$	2228.79			0.247365			0.123683	+	0.992322i	$0.460530\pi$
$434$		0			0
$435$	−8157.34			−0.899114
$436$		0			0
$437$	4599.59	+	7966.72i	0.503497	+	0.872082i
$438$		0			0
$439$	−2304.63	+	3991.74i	−0.250556	+	0.433975i	−0.963679	−	0.267063i	$-0.913947\pi$
$439$	−2304.63	+	3991.74i	−0.250556	+	0.433975i	0.713123	+	0.701039i	$0.247280\pi$
$440$		0			0
$441$	2899.67	−	1059.00i	0.313106	−	0.114350i
$442$		0			0
$443$	−531.662	+	920.865i	−0.0570203	+	0.0987621i	−0.893127	−	0.449805i	$-0.851493\pi$
$443$	−531.662	+	920.865i	−0.0570203	+	0.0987621i	0.836106	+	0.548568i	$0.184827\pi$
$444$		0			0
$445$	1037.88	+	1797.66i	0.110562	+	0.191499i
$446$		0			0
$447$	7236.37			0.765702
$448$		0			0
$449$	−12265.9			−1.28923			−0.644613	−	0.764509i	$-0.722982\pi$
$449$	−12265.9			−1.28923			−0.644613	+	0.764509i	$0.722982\pi$
$450$		0			0
$451$	−5487.65	−	9504.89i	−0.572957	−	0.992390i
$452$		0			0
$453$	−2361.87	+	4090.87i	−0.244967	+	0.424296i
$454$		0			0
$455$	−13310.2	−	15844.8i	−1.37141	−	1.63256i
$456$		0			0
$457$	8895.59	−	15407.6i	0.910543	−	1.57711i	0.0972436	−	0.995261i	$-0.468997\pi$
$457$	8895.59	−	15407.6i	0.910543	−	1.57711i	0.813299	−	0.581846i	$-0.197669\pi$
$458$		0			0
$459$	1385.07	+	2399.02i	0.140849	+	0.243958i
$460$		0			0
$461$	15368.9			1.55272			0.776358	−	0.630293i	$-0.217065\pi$
$461$	15368.9			1.55272			0.776358	+	0.630293i	$0.217065\pi$
$462$		0			0
$463$	−4104.98			−0.412040			−0.206020	−	0.978548i	$-0.566051\pi$
$463$	−4104.98			−0.412040			−0.206020	+	0.978548i	$0.566051\pi$
$464$		0			0
$465$	3063.46	+	5306.08i	0.305516	+	0.529169i
$466$		0			0
$467$	−1903.68	+	3297.27i	−0.188634	+	0.326723i	−0.944795	−	0.327662i	$-0.893739\pi$
$467$	−1903.68	+	3297.27i	−0.188634	+	0.326723i	0.756161	+	0.654385i	$0.227073\pi$
$468$		0			0
$469$	6119.96	−	1082.58i	0.602545	−	0.106586i
$470$		0			0
$471$	3118.11	−	5400.73i	0.305043	−	0.528349i
$472$		0			0
$473$	−613.679	−	1062.92i	−0.0596554	−	0.103326i
$474$		0			0
$475$	3782.61			0.365385
$476$		0			0
$477$	4034.41			0.387260
$478$		0			0
$479$	−4937.33	−	8551.70i	−0.470965	−	0.815735i	0.528484	−	0.848943i	$-0.322761\pi$
$479$	−4937.33	−	8551.70i	−0.470965	−	0.815735i	−0.999448	+	0.0332085i	$0.989427\pi$
$480$		0			0
$481$	−5605.12	+	9708.35i	−0.531334	+	0.920297i
$482$		0			0
$483$	1821.53	−	5013.17i	0.171599	−	0.472271i
$484$		0			0
$485$	1171.41	−	2028.95i	0.109673	−	0.189958i
$486$		0			0
$487$	3381.86	+	5857.56i	0.314675	+	0.545033i	0.979368	−	0.202083i	$-0.0647711\pi$
$487$	3381.86	+	5857.56i	0.314675	+	0.545033i	−0.664693	+	0.747116i	$0.731438\pi$
$488$		0			0
$489$	9538.28			0.882077
$490$		0			0
$491$	−5574.29			−0.512351			−0.256175	−	0.966630i	$-0.582462\pi$
$491$	−5574.29			−0.512351			−0.256175	+	0.966630i	$0.582462\pi$
$492$		0			0
$493$	10876.5	+	18838.6i	0.993612	+	1.72099i
$494$		0			0
$495$	−2125.21	+	3680.97i	−0.192972	+	0.334237i
$496$		0			0
$497$	−2147.94	+	5911.50i	−0.193859	+	0.533535i
$498$		0			0
$499$	−2893.73	+	5012.09i	−0.259601	+	0.449643i	−0.966135	−	0.258037i	$-0.916925\pi$
$499$	−2893.73	+	5012.09i	−0.259601	+	0.449643i	0.706534	+	0.707679i	$0.250258\pi$
$500$		0			0
$501$	−4468.92	−	7740.39i	−0.398516	−	0.690250i
$502$		0			0
$503$	8296.10			0.735397			0.367699	−	0.929945i	$-0.380146\pi$
$503$	8296.10			0.735397			0.367699	+	0.929945i	$0.380146\pi$
$504$		0			0
$505$	19648.8			1.73141
$506$		0			0
$507$	8090.32	+	14012.9i	0.708686	+	1.22748i
$508$		0			0
$509$	4880.19	−	8452.74i	0.424972	−	0.736073i	−0.571446	−	0.820640i	$-0.693617\pi$
$509$	4880.19	−	8452.74i	0.424972	−	0.736073i	0.996418	+	0.0845670i	$0.0269507\pi$
$510$		0			0
$511$	16747.5	−	2962.51i	1.44984	−	0.256466i
$512$		0			0
$513$	1293.63	−	2240.64i	0.111336	−	0.192840i
$514$		0			0
$515$	3128.65	+	5418.98i	0.267699	+	0.463667i
$516$		0			0
$517$	−9986.73			−0.849547
$518$		0			0
$519$	−49.1111			−0.00415364
$520$		0			0
$521$	3268.99	+	5662.06i	0.274889	+	0.476121i	0.970107	−	0.242677i	$-0.0780256\pi$
$521$	3268.99	+	5662.06i	0.274889	+	0.476121i	−0.695218	+	0.718799i	$0.744692\pi$
$522$		0			0
$523$	5171.92	−	8958.02i	0.432413	−	0.748962i	−0.564667	−	0.825319i	$-0.690996\pi$
$523$	5171.92	−	8958.02i	0.432413	−	0.748962i	0.997081	+	0.0763570i	$0.0243289\pi$
$524$		0			0
$525$	−1410.70	−	1679.33i	−0.117272	−	0.139604i
$526$		0			0
$527$	8169.24	−	14149.5i	0.675252	−	1.16957i
$528$		0			0
$529$	1475.50	+	2555.64i	0.121271	+	0.210047i
$530$		0			0
$531$	−6016.27			−0.491683
$532$		0			0
$533$	−25966.5			−2.11020
$534$		0			0
$535$	3157.14	+	5468.33i	0.255131	+	0.441900i
$536$		0			0
$537$	4047.44	−	7010.37i	0.325251	−	0.563351i
$538$		0			0
$539$	2179.68	−	12441.4i	0.174184	−	0.994228i
$540$		0			0
$541$	3421.60	−	5926.38i	0.271915	−	0.470970i	−0.697437	−	0.716646i	$-0.745676\pi$
$541$	3421.60	−	5926.38i	0.271915	−	0.470970i	0.969352	+	0.245676i	$0.0790098\pi$
$542$		0			0
$543$	46.9946	+	81.3970i	0.00371405	+	0.00643293i
$544$		0			0
$545$	−10876.3			−0.854844
$546$		0			0
$547$	−18402.1			−1.43842			−0.719211	−	0.694791i	$-0.755497\pi$
$547$	−18402.1			−1.43842			−0.719211	+	0.694791i	$0.755497\pi$
$548$		0			0
$549$	1096.61	+	1899.38i	0.0852498	+	0.147657i
$550$		0			0
$551$	10158.4	−	17594.9i	0.785414	−	1.36038i
$552$		0			0
$553$	−1623.64	−	1932.83i	−0.124854	−	0.148630i
$554$		0			0
$555$	−2475.25	+	4287.25i	−0.189312	+	0.327899i
$556$		0			0
$557$	−323.239	−	559.866i	−0.0245890	−	0.0425894i	0.853469	−	0.521144i	$-0.174494\pi$
$557$	−323.239	−	559.866i	−0.0245890	−	0.0425894i	−0.878058	+	0.478554i	$0.841161\pi$
$558$		0			0
$559$	−2903.81			−0.219710
$560$		0			0
$561$	11334.4			0.853013
$562$		0			0
$563$	−3087.40	−	5347.53i	−0.231116	−	0.400305i	0.727021	−	0.686616i	$-0.240904\pi$
$563$	−3087.40	−	5347.53i	−0.231116	−	0.400305i	−0.958137	+	0.286311i	$0.907571\pi$
$564$		0			0
$565$	−4721.76	+	8178.32i	−0.351585	+	0.608964i
$566$		0			0
$567$	−1477.21	+	261.307i	−0.109412	+	0.0193543i
$568$		0			0
$569$	3418.59	−	5921.17i	0.251871	−	0.436253i	−0.712170	−	0.702007i	$-0.752287\pi$
$569$	3418.59	−	5921.17i	0.251871	−	0.436253i	0.964041	+	0.265754i	$0.0856208\pi$
$570$		0			0
$571$	2942.77	+	5097.03i	0.215676	+	0.373562i	0.953482	−	0.301451i	$-0.0974711\pi$
$571$	2942.77	+	5097.03i	0.215676	+	0.373562i	−0.737805	+	0.675014i	$0.764138\pi$
$572$		0			0
$573$	4635.52			0.337961
$574$		0			0
$575$	−3789.53			−0.274842
$576$		0			0
$577$	6001.62	+	10395.1i	0.433017	+	0.750007i	0.997131	−	0.0756896i	$-0.0241158\pi$
$577$	6001.62	+	10395.1i	0.433017	+	0.750007i	−0.564115	+	0.825696i	$0.690782\pi$
$578$		0			0
$579$	−2745.30	+	4754.99i	−0.197048	+	0.341297i
$580$		0			0
$581$	1818.14	−	5003.84i	0.129826	−	0.357305i
$582$		0			0
$583$	8253.68	−	14295.8i	0.586334	−	1.01556i
$584$		0			0
$585$	5028.03	+	8708.81i	0.355357	+	0.615496i
$586$		0			0
$587$	−12719.4			−0.894358			−0.447179	−	0.894445i	$-0.647571\pi$
$587$	−12719.4			−0.894358			−0.447179	+	0.894445i	$0.647571\pi$
$588$		0			0
$589$	−15259.9			−1.06752
$590$		0			0
$591$	7092.68	+	12284.9i	0.493661	+	0.855047i
$592$		0			0
$593$	−9580.20	+	16593.4i	−0.663426	+	1.14909i	0.316283	+	0.948665i	$0.397565\pi$
$593$	−9580.20	+	16593.4i	−0.663426	+	1.14909i	−0.979709	+	0.200423i	$0.935768\pi$
$594$		0			0
$595$	−8322.07	+	22903.8i	−0.573398	+	1.57809i
$596$		0			0
$597$	−492.374	+	852.817i	−0.0337547	+	0.0584648i
$598$		0			0
$599$	−533.983	−	924.885i	−0.0364240	−	0.0630881i	0.847239	−	0.531212i	$-0.178263\pi$
$599$	−533.983	−	924.885i	−0.0364240	−	0.0630881i	−0.883663	+	0.468124i	$0.844930\pi$
$600$		0			0
$601$	7554.96			0.512768			0.256384	−	0.966575i	$-0.417469\pi$
$601$	7554.96			0.512768			0.256384	+	0.966575i	$0.417469\pi$
$602$		0			0
$603$	−3020.20			−0.203967
$604$		0			0
$605$	160.709	+	278.356i	0.0107996	+	0.0187054i
$606$		0			0
$607$	5888.71	−	10199.5i	0.393765	−	0.682020i	−0.599178	−	0.800616i	$-0.704506\pi$
$607$	5888.71	−	10199.5i	0.393765	−	0.682020i	0.992943	+	0.118595i	$0.0378392\pi$
$608$		0			0
$609$	−11599.9	+	2051.95i	−0.771845	+	0.136534i
$610$		0			0
$611$	−11813.8	+	20462.1i	−0.782219	+	1.35484i
$612$		0			0
$613$	−13426.5	−	23255.3i	−0.884649	−	1.53226i	−0.846115	−	0.533000i	$-0.821065\pi$
$613$	−13426.5	−	23255.3i	−0.884649	−	1.53226i	−0.0385337	−	0.999257i	$-0.512269\pi$
$614$		0			0
$615$	−11466.9			−0.751855
$616$		0			0
$617$	−6816.72			−0.444782			−0.222391	−	0.974958i	$-0.571386\pi$
$617$	−6816.72			−0.444782			−0.222391	+	0.974958i	$0.571386\pi$
$618$		0			0
$619$	8356.74	+	14474.3i	0.542627	+	0.939857i	0.998752	+	0.0499414i	$0.0159034\pi$
$619$	8356.74	+	14474.3i	0.542627	+	0.939857i	−0.456126	+	0.889915i	$0.650763\pi$
$620$		0			0
$621$	−1296.00	+	2244.74i	−0.0837467	+	0.145054i
$622$		0			0
$623$	1928.08	+	2295.24i	0.123992	+	0.147603i
$624$		0			0
$625$	9500.53	−	16455.4i	0.608034	−	1.05315i
$626$		0			0
$627$	−5293.08	−	9167.89i	−0.337138	−	0.583940i
$628$		0			0
$629$	13201.3			0.836838
$630$		0			0
$631$	592.225			0.0373631			0.0186815	−	0.999825i	$-0.494053\pi$
$631$	592.225			0.0373631			0.0186815	+	0.999825i	$0.494053\pi$
$632$		0			0
$633$	−7403.63	−	12823.5i	−0.464878	−	0.805193i
$634$		0			0
$635$	−16103.9	+	27892.7i	−1.00640	+	1.74313i
$636$		0			0
$637$	−22913.1	−	19183.6i	−1.42520	−	1.19322i
$638$		0			0
$639$	1528.24	−	2646.98i	0.0946104	−	0.163870i
$640$		0			0
$641$	−3481.96	−	6030.92i	−0.214554	−	0.371618i	0.738581	−	0.674165i	$-0.235496\pi$
$641$	−3481.96	−	6030.92i	−0.214554	−	0.371618i	−0.953134	+	0.302547i	$0.902163\pi$
$642$		0			0
$643$	5466.06			0.335242			0.167621	−	0.985852i	$-0.446392\pi$
$643$	5466.06			0.335242			0.167621	+	0.985852i	$0.446392\pi$
$644$		0			0
$645$	−1282.34			−0.0782821
$646$		0			0
$647$	618.633	+	1071.50i	0.0375904	+	0.0651085i	0.884209	−	0.467092i	$-0.154698\pi$
$647$	618.633	+	1071.50i	0.0375904	+	0.0651085i	−0.846618	+	0.532201i	$0.821365\pi$
$648$		0			0
$649$	−12308.2	+	21318.4i	−0.744436	+	1.28940i
$650$		0			0
$651$	5691.05	+	6774.78i	0.342626	+	0.407872i
$652$		0			0
$653$	−13575.9	+	23514.2i	−0.813578	+	1.40916i	0.0967657	+	0.995307i	$0.469150\pi$
$653$	−13575.9	+	23514.2i	−0.813578	+	1.40916i	−0.910344	+	0.413852i	$0.864183\pi$
$654$		0			0
$655$	−4356.71	−	7546.05i	−0.259895	−	0.450151i
$656$		0			0
$657$	−8264.88			−0.490782
$658$		0			0
$659$	5900.66			0.348797			0.174398	−	0.984675i	$-0.444202\pi$
$659$	5900.66			0.348797			0.174398	+	0.984675i	$0.444202\pi$
$660$		0			0
$661$	−1809.49	−	3134.13i	−0.106477	−	0.184423i	0.807864	−	0.589369i	$-0.200624\pi$
$661$	−1809.49	−	3134.13i	−0.106477	−	0.184423i	−0.914341	+	0.404946i	$0.867290\pi$
$662$		0			0
$663$	13408.1	−	23223.5i	0.785410	−	1.36037i
$664$		0			0
$665$	22412.1	−	3964.54i	1.30692	−	0.231186i
$666$		0			0
$667$	−10177.0	+	17627.1i	−0.590787	+	1.02327i
$668$		0			0
$669$	5169.00	+	8952.98i	0.298722	+	0.517402i
$670$		0			0
$671$	8973.86			0.516292
$672$		0			0
$673$	−13952.5			−0.799151			−0.399576	−	0.916700i	$-0.630842\pi$
$673$	−13952.5			−0.799151			−0.399576	+	0.916700i	$0.630842\pi$
$674$		0			0
$675$	532.902	+	923.014i	0.0303873	+	0.0526323i
$676$		0			0
$677$	14459.4	−	25044.5i	0.820859	−	1.42177i	−0.0841848	−	0.996450i	$-0.526829\pi$
$677$	14459.4	−	25044.5i	0.820859	−	1.42177i	0.905044	−	0.425319i	$-0.139838\pi$
$678$		0			0
$679$	1155.41	−	3179.88i	0.0653026	−	0.179724i
$680$		0			0
$681$	8587.12	−	14873.3i	0.483200	−	0.836927i
$682$		0			0
$683$	5565.06	+	9638.97i	0.311773	+	0.540007i	0.978746	−	0.205075i	$-0.0657437\pi$
$683$	5565.06	+	9638.97i	0.311773	+	0.540007i	−0.666973	+	0.745082i	$0.732410\pi$
$684$		0			0
$685$	2110.14			0.117700
$686$		0			0
$687$	−9051.44			−0.502670
$688$		0			0
$689$	−19527.4	−	33822.5i	−1.07973	−	1.87015i
$690$		0			0
$691$	7012.64	−	12146.2i	0.386069	−	0.668690i	−0.605848	−	0.795580i	$-0.707166\pi$
$691$	7012.64	−	12146.2i	0.386069	−	0.668690i	0.991917	+	0.126890i	$0.0404995\pi$
$692$		0			0
$693$	−2096.17	+	5769.02i	−0.114902	+	0.316229i
$694$		0			0
$695$	−3347.20	+	5797.52i	−0.182686	+	0.316421i
$696$		0			0
$697$	15289.2	+	26481.7i	0.830877	+	1.43912i
$698$		0			0
$699$	−1145.14			−0.0619644
$700$		0			0
$701$	30366.7			1.63614			0.818070	−	0.575119i	$-0.195044\pi$
$701$	30366.7			1.63614			0.818070	+	0.575119i	$0.195044\pi$
$702$		0			0
$703$	−6164.90	−	10677.9i	−0.330745	−	0.572867i
$704$		0			0
$705$	−5217.03	+	9036.17i	−0.278702	+	0.482726i
$706$		0			0
$707$	27941.2	−	4942.59i	1.48633	−	0.262921i
$708$		0			0
$709$	−8445.48	+	14628.0i	−0.447358	+	0.774847i	−0.998213	−	0.0597542i	$-0.980968\pi$
$709$	−8445.48	+	14628.0i	−0.447358	+	0.774847i	0.550855	+	0.834601i	$0.314302\pi$
$710$		0			0
$711$	613.346	+	1062.35i	0.0323520	+	0.0560353i
$712$		0			0
$713$	15287.8			0.802989
$714$		0			0
$715$	41145.8			2.15212
$716$		0			0
$717$	−2066.08	−	3578.55i	−0.107614	−	0.186392i
$718$		0			0
$719$	−5503.61	+	9532.54i	−0.285466	+	0.494442i	−0.972722	−	0.231973i	$-0.925482\pi$
$719$	−5503.61	+	9532.54i	−0.285466	+	0.494442i	0.687256	+	0.726415i	$0.258815\pi$
$720$		0			0
$721$	5812.14	+	6918.93i	0.300216	+	0.357385i
$722$		0			0
$723$	8710.09	−	15086.3i	0.448038	−	0.776025i
$724$		0			0
$725$	4184.68	+	7248.08i	0.214366	+	0.371292i
$726$		0			0
$727$	−14618.0			−0.745737			−0.372869	−	0.927884i	$-0.621626\pi$
$727$	−14618.0			−0.745737			−0.372869	+	0.927884i	$0.621626\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	1709.78	+	2961.43i	0.0865096	+	0.149839i
$732$		0			0
$733$	14261.1	−	24701.0i	0.718617	−	1.24468i	−0.242930	−	0.970044i	$-0.578109\pi$
$733$	14261.1	−	24701.0i	0.718617	−	1.24468i	0.961548	−	0.274638i	$-0.0885581\pi$
$734$		0			0
$735$	−10118.5	−	8471.56i	−0.507793	−	0.425140i
$736$		0			0
$737$	−6178.77	+	10702.0i	−0.308817	+	0.534887i
$738$		0			0
$739$	−10119.7	−	17527.9i	−0.503735	−	0.872495i	−0.999991	−	0.00431822i	$-0.998625\pi$
$739$	−10119.7	−	17527.9i	−0.503735	−	0.872495i	0.496256	−	0.868176i	$-0.334708\pi$
$740$		0			0
$741$	−25045.8			−1.24168
$742$		0			0
$743$	13977.6			0.690159			0.345079	−	0.938573i	$-0.387852\pi$
$743$	13977.6			0.690159			0.345079	+	0.938573i	$0.387852\pi$
$744$		0			0
$745$	−15467.4	−	26790.4i	−0.760649	−	1.31748i
$746$		0			0
$747$	−1293.59	+	2240.56i	−0.0633601	+	0.109743i
$748$		0			0
$749$	5865.07	+	6981.94i	0.286122	+	0.340607i
$750$		0			0
$751$	−7513.90	+	13014.5i	−0.365095	+	0.632363i	−0.988791	−	0.149304i	$-0.952297\pi$
$751$	−7513.90	+	13014.5i	−0.365095	+	0.632363i	0.623697	+	0.781667i	$0.285630\pi$
$752$		0			0
$753$	−6522.78	−	11297.8i	−0.315675	−	0.546765i
$754$		0			0
$755$	20193.6			0.973403
$756$		0			0
$757$	20769.4			0.997196			0.498598	−	0.866833i	$-0.333848\pi$
$757$	20769.4			0.997196			0.498598	+	0.866833i	$0.333848\pi$
$758$		0			0
$759$	5302.76	+	9184.66i	0.253594	+	0.439238i
$760$		0			0
$761$	−5605.57	+	9709.13i	−0.267019	+	0.462491i	−0.968091	−	0.250600i	$-0.919372\pi$
$761$	−5605.57	+	9709.13i	−0.267019	+	0.462491i	0.701071	+	0.713091i	$0.252705\pi$
$762$		0			0
$763$	−15466.4	+	2735.89i	−0.733842	+	0.129811i
$764$		0			0
$765$	5921.07	−	10255.6i	0.279839	−	0.484695i
$766$		0			0
$767$	29120.0	+	50437.3i	1.37088	+	2.37443i
$768$		0			0
$769$	4305.86			0.201916			0.100958	−	0.994891i	$-0.467809\pi$
$769$	4305.86			0.201916			0.100958	+	0.994891i	$0.467809\pi$
$770$		0			0
$771$	14073.3			0.657379
$772$		0			0
$773$	−8320.24	−	14411.1i	−0.387139	−	0.670544i	0.604925	−	0.796283i	$-0.293203\pi$
$773$	−8320.24	−	14411.1i	−0.387139	−	0.670544i	−0.992063	+	0.125739i	$0.959870\pi$
$774$		0			0
$775$	3143.09	−	5443.99i	0.145681	−	0.252328i
$776$		0			0
$777$	−2441.42	+	6719.22i	−0.112723	+	0.310233i
$778$		0			0
$779$	14279.9	−	24733.5i	0.656778	−	1.13757i
$780$		0			0
$781$	−6252.99	−	10830.5i	−0.286491	−	0.496217i
$782$		0			0
$783$	5724.56			0.261276
$784$		0			0
$785$	−26659.4			−1.21212
$786$		0			0
$787$	4883.53	+	8458.51i	0.221193	+	0.383118i	0.955171	−	0.296056i	$-0.0956716\pi$
$787$	4883.53	+	8458.51i	0.221193	+	0.383118i	−0.733977	+	0.679174i	$0.762338\pi$
$788$		0			0
$789$	−11372.4	+	19697.6i	−0.513142	+	0.888788i
$790$		0			0
$791$	−4657.23	+	12817.5i	−0.209345	+	0.576155i
$792$		0			0
$793$	10615.6	−	18386.8i	0.475375	−	0.823374i
$794$		0			0
$795$	−8623.39	−	14936.2i	−0.384705	−	0.666328i
$796$		0			0
$797$	23118.5			1.02748			0.513738	−	0.857947i	$-0.328260\pi$
$797$	23118.5			1.02748			0.513738	+	0.857947i	$0.328260\pi$
$798$		0			0
$799$	27824.2			1.23198
$800$		0			0
$801$	−728.350	−	1261.54i	−0.0321285	−	0.0556483i
$802$		0			0
$803$	−16908.4	+	29286.3i	−0.743071	+	1.28704i
$804$		0			0
$805$	−22453.1	+	3971.79i	−0.983066	+	0.173897i
$806$		0			0
$807$	−5402.84	+	9358.00i	−0.235674	+	0.408200i
$808$		0			0
$809$	−5230.33	−	9059.20i	−0.227304	−	0.393701i	0.729705	−	0.683763i	$-0.239658\pi$
$809$	−5230.33	−	9059.20i	−0.227304	−	0.393701i	−0.957008	+	0.290061i	$0.906324\pi$
$810$		0			0
$811$	−9167.55			−0.396937			−0.198469	−	0.980107i	$-0.563597\pi$
$811$	−9167.55			−0.396937			−0.198469	+	0.980107i	$0.563597\pi$
$812$		0			0
$813$	11508.8			0.496472
$814$		0			0
$815$	−20387.7	−	35312.5i	−0.876256	−	1.51772i
$816$		0			0
$817$	1596.91	−	2765.92i	0.0683827	−	0.118442i
$818$		0			0
$819$	9340.66	+	11119.4i	0.398521	+	0.474410i
$820$		0			0
$821$	−14413.7	+	24965.2i	−0.612717	+	1.06126i	0.378064	+	0.925780i	$0.376590\pi$
$821$	−14413.7	+	24965.2i	−0.612717	+	1.06126i	−0.990780	+	0.135477i	$0.956743\pi$
$822$		0			0
$823$	−21397.2	−	37061.0i	−0.906268	−	1.56970i	−0.819206	−	0.573499i	$-0.805586\pi$
$823$	−21397.2	−	37061.0i	−0.906268	−	1.56970i	−0.0870618	−	0.996203i	$-0.527748\pi$
$824$		0			0
$825$	4360.89			0.184032
$826$		0			0
$827$	−6028.87			−0.253500			−0.126750	−	0.991935i	$-0.540455\pi$
$827$	−6028.87			−0.253500			−0.126750	+	0.991935i	$0.540455\pi$
$828$		0			0
$829$	9703.71	+	16807.3i	0.406542	+	0.704152i	0.994500	−	0.104740i	$-0.0334010\pi$
$829$	9703.71	+	16807.3i	0.406542	+	0.704152i	−0.587957	+	0.808892i	$0.700068\pi$
$830$		0			0
$831$	8104.57	−	14037.5i	0.338320	−	0.585988i
$832$		0			0
$833$	−6072.84	+	34663.2i	−0.252595	+	1.44179i
$834$		0			0
$835$	−19104.3	+	33089.5i	−0.791773	+	1.37139i
$836$		0			0
$837$	−2149.84	−	3723.63i	−0.0887806	−	0.153773i
$838$		0			0
$839$	−10599.5			−0.436156			−0.218078	−	0.975931i	$-0.569979\pi$
$839$	−10599.5			−0.436156			−0.218078	+	0.975931i	$0.569979\pi$
$840$		0			0
$841$	20563.8			0.843159
$842$		0			0
$843$	226.263	+	391.899i	0.00924425	+	0.0160115i
$844$		0			0
$845$	34585.5	−	59903.8i	1.40802	−	2.43876i
$846$		0			0
$847$	298.552	+	355.404i	0.0121114	+	0.0144177i
$848$		0			0
$849$	2725.71	−	4721.07i	0.110184	−	0.190844i
$850$		0			0
$851$	6176.17	+	10697.4i	0.248786	+	0.430909i
$852$		0			0
$853$	−34766.1			−1.39551			−0.697754	−	0.716338i	$-0.745817\pi$
$853$	−34766.1			−1.39551			−0.697754	+	0.716338i	$0.745817\pi$
$854$		0			0
$855$	−11060.4			−0.442405
$856$		0			0
$857$	−15002.0	−	25984.2i	−0.597968	−	1.03571i	−0.993121	−	0.117096i	$-0.962642\pi$
$857$	−15002.0	−	25984.2i	−0.597968	−	1.03571i	0.395153	−	0.918615i	$-0.370692\pi$
$858$		0			0
$859$	13065.3	−	22629.8i	0.518955	−	0.898857i	−0.480802	−	0.876829i	$-0.659655\pi$
$859$	13065.3	−	22629.8i	0.518955	−	0.898857i	0.999757	−	0.0220275i	$-0.00701214\pi$
$860$		0			0
$861$	−16306.3	+	2884.46i	−0.645431	+	0.114172i
$862$		0			0
$863$	−22334.2	+	38683.9i	−0.880955	+	1.52586i	−0.0306737	+	0.999529i	$0.509765\pi$
$863$	−22334.2	+	38683.9i	−0.880955	+	1.52586i	−0.850281	+	0.526329i	$0.823568\pi$
$864$		0			0
$865$	104.973	+	181.818i	0.00412623	+	0.00714684i
$866$		0			0
$867$	−16840.1			−0.659652
$868$		0			0
$869$	5019.18			0.195931
$870$		0			0
$871$	14618.4	+	25319.8i	0.568685	+	0.984992i
$872$		0			0
$873$	−822.061	+	1423.85i	−0.0318700	+	0.0552005i
$874$		0			0
$875$	6937.28	−	19092.6i	0.268026	−	0.737655i
$876$		0			0
$877$	−1839.28	+	3185.72i	−0.0708187	+	0.122662i	−0.899260	−	0.437414i	$-0.855895\pi$
$877$	−1839.28	+	3185.72i	−0.0708187	+	0.122662i	0.828442	+	0.560075i	$0.189228\pi$
$878$		0			0
$879$	−4226.38	−	7320.30i	−0.162175	−	0.280896i
$880$		0			0
$881$	−33443.6			−1.27894			−0.639468	−	0.768817i	$-0.720846\pi$
$881$	−33443.6			−1.27894			−0.639468	+	0.768817i	$0.720846\pi$
$882$		0			0
$883$	−21095.4			−0.803983			−0.401991	−	0.915644i	$-0.631682\pi$
$883$	−21095.4			−0.803983			−0.401991	+	0.915644i	$0.631682\pi$
$884$		0			0
$885$	12859.5	+	22273.3i	0.488439	+	0.846001i
$886$		0			0
$887$	−7226.65	+	12516.9i	−0.273560	+	0.473819i	−0.969771	−	0.244018i	$-0.921534\pi$
$887$	−7226.65	+	12516.9i	−0.273560	+	0.473819i	0.696211	+	0.717837i	$0.254868\pi$
$888$		0			0
$889$	−15883.8	+	43715.0i	−0.599242	+	1.64922i
$890$		0			0
$891$	1491.40	−	2583.18i	0.0560762	−	0.0971268i
$892$		0			0
$893$	−12993.6	−	22505.7i	−0.486916	−	0.843363i
$894$		0			0
$895$	−34604.9			−1.29242
$896$		0			0
$897$	25091.6			0.933986
$898$		0			0
$899$	−16881.9	−	29240.3i	−0.626299	−	1.08478i
$900$		0			0
$901$	−22995.7	+	39829.8i	−0.850276	+	1.47272i
$902$		0			0
$903$	−1823.51	+	322.567i	−0.0672013	+	0.0118874i
$904$		0			0
$905$	200.898	−	347.965i	0.00737909	−	0.0127810i
$906$		0			0
$907$	2602.04	+	4506.87i	0.0952584	+	0.164992i	0.909716	−	0.415230i	$-0.136299\pi$
$907$	2602.04	+	4506.87i	0.0952584	+	0.164992i	−0.814458	+	0.580223i	$0.802966\pi$
$908$		0			0
$909$	−13788.9			−0.503135
$910$		0			0
$911$	31584.8			1.14868			0.574342	−	0.818616i	$-0.305258\pi$
$911$	31584.8			1.14868			0.574342	+	0.818616i	$0.305258\pi$
$912$		0			0
$913$	5292.90	+	9167.57i	0.191861	+	0.332314i
$914$		0			0
$915$	4687.92	−	8119.71i	0.169375	−	0.293365i
$916$		0			0
$917$	−8093.54	−	9634.76i	−0.291464	−	0.346966i
$918$		0			0
$919$	23315.3	−	40383.3i	0.836889	−	1.44953i	−0.0555943	−	0.998453i	$-0.517705\pi$
$919$	23315.3	−	40383.3i	0.836889	−	1.44953i	0.892483	−	0.451081i	$-0.148961\pi$
$920$		0			0
$921$	12883.8	+	22315.4i	0.460951	+	0.798391i
$922$		0			0
$923$	−29587.9			−1.05514
$924$		0			0
$925$	5079.16			0.180543
$926$		0			0
$927$	−2195.59	−	3802.87i	−0.0777912	−	0.134738i
$928$		0			0
$929$	19246.3	−	33335.6i	0.679711	−	1.17729i	−0.295357	−	0.955387i	$-0.595439\pi$
$929$	19246.3	−	33335.6i	0.679711	−	1.17729i	0.975068	−	0.221907i	$-0.0712280\pi$
$930$		0			0
$931$	30873.4	−	11275.4i	1.08682	−	0.396923i
$932$		0			0
$933$	−8997.44	+	15584.0i	−0.315716	+	0.546836i
$934$		0			0
$935$	−24226.9	−	41962.2i	−0.847384	−	1.46771i
$936$		0			0
$937$	39893.8			1.39090			0.695450	−	0.718574i	$-0.255205\pi$
$937$	39893.8			1.39090			0.695450	+	0.718574i	$0.255205\pi$
$938$		0			0
$939$	14889.8			0.517477
$940$		0			0
$941$	16315.4	+	28259.0i	0.565213	+	0.978977i	0.997030	+	0.0770161i	$0.0245393\pi$
$941$	16315.4	+	28259.0i	0.565213	+	0.978977i	−0.431817	+	0.901961i	$0.642127\pi$
$942$		0			0
$943$	−14306.0	+	24778.7i	−0.494027	+	0.855680i
$944$		0			0
$945$	4124.88	+	4910.36i	0.141992	+	0.169031i
$946$		0			0
$947$	−15014.7	+	26006.1i	−0.515217	+	0.892382i	0.484627	+	0.874721i	$0.338955\pi$
$947$	−15014.7	+	26006.1i	−0.515217	+	0.892382i	−0.999844	+	0.0176614i	$0.994378\pi$
$948$		0			0
$949$	40003.7	+	69288.5i	1.36836	+	2.37007i
$950$		0			0
$951$	11713.8			0.399418
$952$		0			0
$953$	−34963.6			−1.18844			−0.594220	−	0.804303i	$-0.702539\pi$
$953$	−34963.6			−1.18844			−0.594220	+	0.804303i	$0.702539\pi$
$954$		0			0
$955$	−9908.24	−	17161.6i	−0.335731	−	0.581503i
$956$		0			0
$957$	11711.4	−	20284.8i	0.395587	−	0.685176i
$958$		0			0
$959$	3000.67	−	530.798i	0.101039	−	0.0178732i
$960$		0			0
$961$	2215.61	−	3837.56i	0.0743719	−	0.128816i
$962$		0			0
$963$	−2215.58	−	3837.50i	−0.0741393	−	0.128413i
$964$		0			0
$965$	23471.8			0.782990
$966$		0			0
$967$	20520.5			0.682414			0.341207	−	0.939988i	$-0.389164\pi$
$967$	20520.5			0.682414			0.341207	+	0.939988i	$0.389164\pi$
$968$		0			0
$969$	14747.1	+	25542.8i	0.488902	+	0.846804i
$970$		0			0
$971$	−19887.6	+	34446.4i	−0.657286	+	1.13845i	0.324029	+	0.946047i	$0.394962\pi$
$971$	−19887.6	+	34446.4i	−0.657286	+	1.13845i	−0.981315	+	0.192406i	$0.938371\pi$
$972$		0			0
$973$	−3301.46	+	9086.20i	−0.108777	+	0.299373i
$974$		0			0
$975$	5158.72	−	8935.16i	0.169447	−	0.293491i
$976$		0			0
$977$	3586.02	+	6211.17i	0.117428	+	0.203391i	0.918748	−	0.394845i	$-0.129202\pi$
$977$	3586.02	+	6211.17i	0.117428	+	0.203391i	−0.801320	+	0.598236i	$0.795868\pi$
$978$		0			0
$979$	−5960.29			−0.194578
$980$		0			0
$981$	7632.65			0.248412
$982$		0			0
$983$	−24174.1	−	41870.8i	−0.784369	−	1.35857i	−0.929375	−	0.369137i	$-0.879653\pi$
$983$	−24174.1	−	41870.8i	−0.784369	−	1.35857i	0.145006	−	0.989431i	$-0.453680\pi$
$984$		0			0
$985$	30320.6	−	52516.9i	0.980807	−	1.69881i
$986$		0			0
$987$	−5145.74	+	14162.0i	−0.165948	+	0.456718i
$988$		0			0
$989$	−1599.83	+	2770.98i	−0.0514373	+	0.0890921i
$990$		0			0
$991$	−18472.3	−	31994.9i	−0.592121	−	1.02558i	−0.993946	−	0.109867i	$-0.964958\pi$
$991$	−18472.3	−	31994.9i	−0.592121	−	1.02558i	0.401826	−	0.915716i	$-0.368376\pi$
$992$		0			0
$993$	7349.18			0.234863
$994$		0			0
$995$	4209.72			0.134128
$996$		0			0
$997$	−28294.8	−	49008.0i	−0.898802	−	1.55677i	−0.829028	−	0.559208i	$-0.811105\pi$
$997$	−28294.8	−	49008.0i	−0.898802	−	1.55677i	−0.0697741	−	0.997563i	$-0.522228\pi$
$998$		0			0
$999$	1737.05	−	3008.66i	0.0550128	−	0.0952850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.4.i.b.37.2	yes	4
3.2	odd	2		252.4.k.d.37.1		4
4.3	odd	2		336.4.q.h.289.2		4
7.2	even	3		588.4.a.g.1.1		2
7.3	odd	6		588.4.i.i.361.1		4
7.4	even	3	inner	84.4.i.b.25.2	✓	4
7.5	odd	6		588.4.a.h.1.2		2
7.6	odd	2		588.4.i.i.373.1		4
21.2	odd	6		1764.4.a.x.1.2		2
21.5	even	6		1764.4.a.p.1.1		2
21.11	odd	6		252.4.k.d.109.1		4
21.17	even	6		1764.4.k.z.361.2		4
21.20	even	2		1764.4.k.z.1549.2		4
28.11	odd	6		336.4.q.h.193.2		4
28.19	even	6		2352.4.a.bp.1.2		2
28.23	odd	6		2352.4.a.cb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.i.b.25.2	✓	4	7.4	even	3	inner
84.4.i.b.37.2	yes	4	1.1	even	1	trivial
252.4.k.d.37.1		4	3.2	odd	2
252.4.k.d.109.1		4	21.11	odd	6
336.4.q.h.193.2		4	28.11	odd	6
336.4.q.h.289.2		4	4.3	odd	2
588.4.a.g.1.1		2	7.2	even	3
588.4.a.h.1.2		2	7.5	odd	6
588.4.i.i.361.1		4	7.3	odd	6
588.4.i.i.373.1		4	7.6	odd	2
1764.4.a.p.1.1		2	21.5	even	6
1764.4.a.x.1.2		2	21.2	odd	6
1764.4.k.z.361.2		4	21.17	even	6
1764.4.k.z.1549.2		4	21.20	even	2
2352.4.a.bp.1.2		2	28.19	even	6
2352.4.a.cb.1.1		2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	84.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(6.41238 - 11.1066i) q^{5} +(6.32475 - 17.4068i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +(6.41238 - 11.1066i) q^{5} +(6.32475 - 17.4068i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(18.4124 + 31.8912i) q^{11} +87.1238 q^{13} +38.4743 q^{15} +(-51.2990 - 88.8525i) q^{17} +(-47.9124 + 82.9867i) q^{19} +(54.7114 - 9.67805i) q^{21} +(48.0000 - 83.1384i) q^{23} +(-19.7371 - 34.1857i) q^{25} -27.0000 q^{27} -212.021 q^{29} +(79.6238 + 137.912i) q^{31} +(-55.2371 + 95.6735i) q^{33} +(-152.773 - 181.865i) q^{35} +(-64.3351 + 111.432i) q^{37} +(130.686 + 226.354i) q^{39} -298.042 q^{41} -33.3297 q^{43} +(57.7114 + 99.9590i) q^{45} +(-135.598 + 234.863i) q^{47} +(-262.995 - 220.188i) q^{49} +(153.897 - 266.557i) q^{51} +(-224.134 - 388.212i) q^{53} +472.268 q^{55} -287.474 q^{57} +(334.237 + 578.916i) q^{59} +(121.846 - 211.043i) q^{61} +(107.211 + 127.627i) q^{63} +(558.670 - 967.645i) q^{65} +(167.789 + 290.618i) q^{67} +288.000 q^{69} -339.608 q^{71} +(459.160 + 795.288i) q^{73} +(59.2114 - 102.557i) q^{75} +(671.578 - 118.797i) q^{77} +(68.1495 - 118.038i) q^{79} +(-40.5000 - 70.1481i) q^{81} +287.464 q^{83} -1315.79 q^{85} +(-318.031 - 550.846i) q^{87} +(-80.9277 + 140.171i) q^{89} +(551.036 - 1516.55i) q^{91} +(-238.871 + 413.737i) q^{93} +(614.464 + 1064.28i) q^{95} +182.680 q^{97} -331.423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 3 q^{5} - 20 q^{7} - 18 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 + 3 * q^5 - 20 * q^7 - 18 * q^9	\( 4 q + 6 q^{3} + 3 q^{5} - 20 q^{7} - 18 q^{9} + 51 q^{11} + 122 q^{13} + 18 q^{15} - 24 q^{17} - 169 q^{19} + 15 q^{21} + 192 q^{23} - 11 q^{25} - 108 q^{27} - 78 q^{29} + 92 q^{31} - 153 q^{33} - 294 q^{35} + 173 q^{37} + 183 q^{39} + 348 q^{41} - 994 q^{43} + 27 q^{45} - 180 q^{47} - 146 q^{49} + 72 q^{51} - 285 q^{53} + 666 q^{55} - 1014 q^{57} + 1269 q^{59} - 328 q^{61} + 225 q^{63} + 1374 q^{65} + 875 q^{67} + 1152 q^{69} - 2808 q^{71} + 1361 q^{73} + 33 q^{75} + 897 q^{77} + 182 q^{79} - 162 q^{81} - 798 q^{83} - 4176 q^{85} - 117 q^{87} - 822 q^{89} + 1955 q^{91} - 276 q^{93} + 510 q^{95} + 1682 q^{97} - 918 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 + 3 * q^5 - 20 * q^7 - 18 * q^9 + 51 * q^11 + 122 * q^13 + 18 * q^15 - 24 * q^17 - 169 * q^19 + 15 * q^21 + 192 * q^23 - 11 * q^25 - 108 * q^27 - 78 * q^29 + 92 * q^31 - 153 * q^33 - 294 * q^35 + 173 * q^37 + 183 * q^39 + 348 * q^41 - 994 * q^43 + 27 * q^45 - 180 * q^47 - 146 * q^49 + 72 * q^51 - 285 * q^53 + 666 * q^55 - 1014 * q^57 + 1269 * q^59 - 328 * q^61 + 225 * q^63 + 1374 * q^65 + 875 * q^67 + 1152 * q^69 - 2808 * q^71 + 1361 * q^73 + 33 * q^75 + 897 * q^77 + 182 * q^79 - 162 * q^81 - 798 * q^83 - 4176 * q^85 - 117 * q^87 - 822 * q^89 + 1955 * q^91 - 276 * q^93 + 510 * q^95 + 1682 * q^97 - 918 * q^99

Introduction

L-functions

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