LMFDB - Embedded newform 288.4.i.c.193.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,4,Mod(97,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, 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("288.97");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	288.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:	$16.9925500817$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11x^{14} + 37x^{12} - 702x^{10} - 15606x^{8} - 56862x^{6} + 242757x^{4} + 5845851x^{2} + 43046721 $ x^16 + 11x^14 + 37x^12 - 702x^10 - 15606x^8 - 56862x^6 + 242757x^4 + 5845851*x^2 + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.8
Root			$-1.86932 + 2.34641i$ of defining polynomial
Character	$\chi$	$=$	288.193
Dual form			288.4.i.c.97.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.83603 + 1.90073i) q^{3} +(7.51347 - 13.0137i) q^{5} +(-4.38125 - 7.58855i) q^{7} +(19.7745 + 18.3840i) q^{9} +O(q^{10})$	\(q+(4.83603 + 1.90073i) q^{3} +(7.51347 - 13.0137i) q^{5} +(-4.38125 - 7.58855i) q^{7} +(19.7745 + 18.3840i) q^{9} +(-18.5475 - 32.1252i) q^{11} +(18.7948 - 32.5535i) q^{13} +(61.0710 - 48.6537i) q^{15} +16.9864 q^{17} -79.0046 q^{19} +(-6.76411 - 45.0260i) q^{21} +(57.7079 - 99.9531i) q^{23} +(-50.4045 - 87.3032i) q^{25} +(60.6870 + 126.491i) q^{27} +(-90.0106 - 155.903i) q^{29} +(-108.522 + 187.966i) q^{31} +(-28.6350 - 190.612i) q^{33} -131.674 q^{35} +265.910 q^{37} +(152.767 - 121.706i) q^{39} +(23.2800 - 40.3222i) q^{41} +(0.305555 + 0.529236i) q^{43} +(387.819 - 119.212i) q^{45} +(244.124 + 422.835i) q^{47} +(133.109 - 230.552i) q^{49} +(82.1467 + 32.2865i) q^{51} +754.726 q^{53} -557.425 q^{55} +(-382.069 - 150.166i) q^{57} +(-302.960 + 524.743i) q^{59} +(-49.5794 - 85.8741i) q^{61} +(52.8708 - 230.604i) q^{63} +(-282.428 - 489.179i) q^{65} +(506.923 - 878.016i) q^{67} +(469.061 - 373.689i) q^{69} +317.454 q^{71} -905.663 q^{73} +(-77.8184 - 518.007i) q^{75} +(-162.522 + 281.497i) q^{77} +(-345.376 - 598.209i) q^{79} +(53.0587 + 727.067i) q^{81} +(564.408 + 977.584i) q^{83} +(127.627 - 221.056i) q^{85} +(-138.965 - 925.038i) q^{87} -329.193 q^{89} -329.378 q^{91} +(-882.089 + 702.738i) q^{93} +(-593.599 + 1028.14i) q^{95} +(606.171 + 1049.92i) q^{97} +(223.822 - 976.236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{5} - 6 q^{9}+O(q^{10}) $ 16 * q - 10 * q^5 - 6 * q^9	$ 16 q - 10 q^{5} - 6 q^{9} + 78 q^{13} - 188 q^{17} + 66 q^{21} - 238 q^{25} - 314 q^{29} - 336 q^{33} - 320 q^{37} + 368 q^{41} + 402 q^{45} + 14 q^{49} + 112 q^{53} - 1146 q^{57} + 482 q^{61} + 846 q^{65} - 642 q^{69} - 3204 q^{73} + 822 q^{77} + 954 q^{81} + 3248 q^{85} - 3832 q^{89} - 1602 q^{93} + 3864 q^{97}+O(q^{100}) $ 16 * q - 10 * q^5 - 6 * q^9 + 78 * q^13 - 188 * q^17 + 66 * q^21 - 238 * q^25 - 314 * q^29 - 336 * q^33 - 320 * q^37 + 368 * q^41 + 402 * q^45 + 14 * q^49 + 112 * q^53 - 1146 * q^57 + 482 * q^61 + 846 * q^65 - 642 * q^69 - 3204 * q^73 + 822 * q^77 + 954 * q^81 + 3248 * q^85 - 3832 * q^89 - 1602 * q^93 + 3864 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.83603	+	1.90073i	0.930695	+	0.365795i
$3$	4.83603	+	1.90073i	0.930695	+	0.365795i
$4$		0			0
$5$	7.51347	−	13.0137i	0.672025	−	1.16398i	−0.305303	−	0.952255i	$-0.598758\pi$
$5$	7.51347	−	13.0137i	0.672025	−	1.16398i	0.977329	−	0.211727i	$-0.0679088\pi$
$6$		0			0
$7$	−4.38125	−	7.58855i	−0.236565	−	0.409743i	0.723161	−	0.690679i	$-0.242688\pi$
$7$	−4.38125	−	7.58855i	−0.236565	−	0.409743i	−0.959726	+	0.280936i	$0.909355\pi$
$8$		0			0
$9$	19.7745	+	18.3840i	0.732387	+	0.680888i
$10$		0			0
$11$	−18.5475	−	32.1252i	−0.508389	−	0.880556i	−0.999953	−	0.00971434i	$-0.996908\pi$
$11$	−18.5475	−	32.1252i	−0.508389	−	0.880556i	0.491564	−	0.870842i	$-0.336426\pi$
$12$		0			0
$13$	18.7948	−	32.5535i	0.400979	−	0.694516i	−0.592865	−	0.805302i	$-0.702003\pi$
$13$	18.7948	−	32.5535i	0.400979	−	0.694516i	0.993844	+	0.110786i	$0.0353367\pi$
$14$		0			0
$15$	61.0710	−	48.6537i	1.05123	−	0.837489i
$16$		0			0
$17$	16.9864			0.242341			0.121171	−	0.992632i	$-0.461335\pi$
$17$	16.9864			0.242341			0.121171	+	0.992632i	$0.461335\pi$
$18$		0			0
$19$	−79.0046			−0.953942			−0.476971	−	0.878919i	$-0.658265\pi$
$19$	−79.0046			−0.953942			−0.476971	+	0.878919i	$0.658265\pi$
$20$		0			0
$21$	−6.76411	−	45.0260i	−0.0702880	−	0.467880i
$22$		0			0
$23$	57.7079	−	99.9531i	0.523171	−	0.906159i	−0.476465	−	0.879193i	$-0.658082\pi$
$23$	57.7079	−	99.9531i	0.523171	−	0.906159i	0.999636	−	0.0269657i	$-0.00858449\pi$
$24$		0			0
$25$	−50.4045	−	87.3032i	−0.403236	−	0.698426i
$26$		0			0
$27$	60.6870	+	126.491i	0.432564	+	0.901603i
$28$		0			0
$29$	−90.0106	−	155.903i	−0.576364	−	0.998292i	−0.995892	−	0.0905493i	$-0.971138\pi$
$29$	−90.0106	−	155.903i	−0.576364	−	0.998292i	0.419528	−	0.907742i	$-0.362196\pi$
$30$		0			0
$31$	−108.522	+	187.966i	−0.628747	+	1.08902i	0.359057	+	0.933316i	$0.383098\pi$
$31$	−108.522	+	187.966i	−0.628747	+	1.08902i	−0.987804	+	0.155705i	$0.950235\pi$
$32$		0			0
$33$	−28.6350	−	190.612i	−0.151052	−	1.00550i
$34$		0			0
$35$	−131.674			−0.635911
$36$		0			0
$37$	265.910			1.18150			0.590748	−	0.806856i	$-0.298833\pi$
$37$	265.910			1.18150			0.590748	+	0.806856i	$0.298833\pi$
$38$		0			0
$39$	152.767	−	121.706i	0.627240	−	0.499706i
$40$		0			0
$41$	23.2800	−	40.3222i	0.0886763	−	0.153592i	−0.818276	−	0.574826i	$-0.805070\pi$
$41$	23.2800	−	40.3222i	0.0886763	−	0.153592i	0.906952	+	0.421234i	$0.138403\pi$
$42$		0			0
$43$	0.305555	+	0.529236i	0.00108364	+	0.00187693i	0.866567	−	0.499061i	$-0.166322\pi$
$43$	0.305555	+	0.529236i	0.00108364	+	0.00187693i	−0.865483	+	0.500938i	$0.832988\pi$
$44$		0			0
$45$	387.819	−	119.212i	1.28472	−	0.394912i
$46$		0			0
$47$	244.124	+	422.835i	0.757640	+	1.31227i	0.944051	+	0.329800i	$0.106981\pi$
$47$	244.124	+	422.835i	0.757640	+	1.31227i	−0.186410	+	0.982472i	$0.559685\pi$
$48$		0			0
$49$	133.109	−	230.552i	0.388074	−	0.672164i
$50$		0			0
$51$	82.1467	+	32.2865i	0.225546	+	0.0886473i
$52$		0			0
$53$	754.726			1.95603			0.978015	−	0.208536i	$-0.0668699\pi$
$53$	754.726			1.95603			0.978015	+	0.208536i	$0.0668699\pi$
$54$		0			0
$55$	−557.425			−1.36660
$56$		0			0
$57$	−382.069	−	150.166i	−0.887829	−	0.348947i
$58$		0			0
$59$	−302.960	+	524.743i	−0.668510	+	1.15789i	0.309811	+	0.950798i	$0.399734\pi$
$59$	−302.960	+	524.743i	−0.668510	+	1.15789i	−0.978321	+	0.207095i	$0.933599\pi$
$60$		0			0
$61$	−49.5794	−	85.8741i	−0.104065	−	0.180247i	0.809291	−	0.587409i	$-0.199852\pi$
$61$	−49.5794	−	85.8741i	−0.104065	−	0.180247i	−0.913356	+	0.407162i	$0.866518\pi$
$62$		0			0
$63$	52.8708	−	230.604i	0.105732	−	0.461165i
$64$		0			0
$65$	−282.428	−	489.179i	−0.538936	−	0.933465i
$66$		0			0
$67$	506.923	−	878.016i	0.924335	−	1.60100i	0.131708	−	0.991289i	$-0.457954\pi$
$67$	506.923	−	878.016i	0.924335	−	1.60100i	0.792627	−	0.609707i	$-0.208713\pi$
$68$		0			0
$69$	469.061	−	373.689i	0.818382	−	0.651984i
$70$		0			0
$71$	317.454			0.530633			0.265316	−	0.964161i	$-0.414524\pi$
$71$	317.454			0.530633			0.265316	+	0.964161i	$0.414524\pi$
$72$		0			0
$73$	−905.663			−1.45205			−0.726026	−	0.687667i	$-0.758635\pi$
$73$	−905.663			−1.45205			−0.726026	+	0.687667i	$0.758635\pi$
$74$		0			0
$75$	−77.8184	−	518.007i	−0.119809	−	0.797524i
$76$		0			0
$77$	−162.522	+	281.497i	−0.240534	+	0.416618i
$78$		0			0
$79$	−345.376	−	598.209i	−0.491872	−	0.851947i	0.508084	−	0.861307i	$-0.330354\pi$
$79$	−345.376	−	598.209i	−0.491872	−	0.851947i	−0.999956	+	0.00936040i	$0.997020\pi$
$80$		0			0
$81$	53.0587	+	727.067i	0.0727828	+	0.997348i
$82$		0			0
$83$	564.408	+	977.584i	0.746408	+	1.29282i	0.949534	+	0.313664i	$0.101557\pi$
$83$	564.408	+	977.584i	0.746408	+	1.29282i	−0.203126	+	0.979153i	$0.565110\pi$
$84$		0			0
$85$	127.627	−	221.056i	0.162859	−	0.282081i
$86$		0			0
$87$	−138.965	−	925.038i	−0.171249	−	1.13994i
$88$		0			0
$89$	−329.193			−0.392072			−0.196036	−	0.980597i	$-0.562807\pi$
$89$	−329.193			−0.392072			−0.196036	+	0.980597i	$0.562807\pi$
$90$		0			0
$91$	−329.378			−0.379431
$92$		0			0
$93$	−882.089	+	702.738i	−0.983530	+	0.783554i
$94$		0			0
$95$	−593.599	+	1028.14i	−0.641073	+	1.11037i
$96$		0			0
$97$	606.171	+	1049.92i	0.634509	+	1.09900i	0.986619	+	0.163043i	$0.0521309\pi$
$97$	606.171	+	1049.92i	0.634509	+	1.09900i	−0.352110	+	0.935959i	$0.614536\pi$
$98$		0			0
$99$	223.822	−	976.236i	0.227222	−	0.991064i
$100$		0			0
$101$	−34.9804	−	60.5878i	−0.0344622	−	0.0596902i	0.848280	−	0.529548i	$-0.177638\pi$
$101$	−34.9804	−	60.5878i	−0.0344622	−	0.0596902i	−0.882742	+	0.469858i	$0.844305\pi$
$102$		0			0
$103$	−471.043	+	815.870i	−0.450614	+	0.780486i	−0.998424	−	0.0561167i	$-0.982128\pi$
$103$	−471.043	+	815.870i	−0.450614	+	0.780486i	0.547811	+	0.836602i	$0.315461\pi$
$104$		0			0
$105$	−636.778	−	250.276i	−0.591840	−	0.232613i
$106$		0			0
$107$	1346.36			1.21643			0.608214	−	0.793773i	$-0.291886\pi$
$107$	1346.36			1.21643			0.608214	+	0.793773i	$0.291886\pi$
$108$		0			0
$109$	630.012			0.553617			0.276808	−	0.960925i	$-0.410723\pi$
$109$	630.012			0.553617			0.276808	+	0.960925i	$0.410723\pi$
$110$		0			0
$111$	1285.95	+	505.423i	1.09961	+	0.432186i
$112$		0			0
$113$	−1020.80	+	1768.07i	−0.849809	+	1.47191i	0.0315696	+	0.999502i	$0.489949\pi$
$113$	−1020.80	+	1768.07i	−0.849809	+	1.47191i	−0.881379	+	0.472411i	$0.843384\pi$
$114$		0			0
$115$	−867.174	−	1501.99i	−0.703169	−	1.21792i
$116$		0			0
$117$	970.118	−	298.205i	0.766560	−	0.235633i
$118$		0			0
$119$	−74.4215	−	128.902i	−0.0573295	−	0.0992976i
$120$		0			0
$121$	−22.5196	+	39.0051i	−0.0169193	+	0.0293051i
$122$		0			0
$123$	189.224	−	150.750i	0.138714	−	0.110510i
$124$		0			0
$125$	363.516			0.260111
$126$		0			0
$127$	−1987.33			−1.38856			−0.694281	−	0.719704i	$-0.744278\pi$
$127$	−1987.33			−1.38856			−0.694281	+	0.719704i	$0.744278\pi$
$128$		0			0
$129$	0.471739	+	3.14018i	0.000321971	+	0.00214324i
$130$		0			0
$131$	−1137.56	+	1970.31i	−0.758694	+	1.31410i	0.184822	+	0.982772i	$0.440829\pi$
$131$	−1137.56	+	1970.31i	−0.758694	+	1.31410i	−0.943517	+	0.331325i	$0.892504\pi$
$132$		0			0
$133$	346.139	+	599.530i	0.225669	+	0.390871i
$134$		0			0
$135$	2102.09	+	160.626i	1.34014	+	0.102404i
$136$		0			0
$137$	189.701	+	328.572i	0.118301	+	0.204904i	0.919095	−	0.394037i	$-0.128922\pi$
$137$	189.701	+	328.572i	0.118301	+	0.204904i	−0.800793	+	0.598941i	$0.795589\pi$
$138$		0			0
$139$	−1204.64	+	2086.49i	−0.735079	+	1.27319i	0.219610	+	0.975588i	$0.429522\pi$
$139$	−1204.64	+	2086.49i	−0.735079	+	1.27319i	−0.954689	+	0.297606i	$0.903812\pi$
$140$		0			0
$141$	376.897	+	2508.86i	0.225109	+	1.49847i
$142$		0			0
$143$	−1394.38			−0.815414
$144$		0			0
$145$	−2705.17			−1.54932
$146$		0			0
$147$	1081.94	−	861.953i	0.607053	−	0.483624i
$148$		0			0
$149$	−162.785	+	281.952i	−0.0895025	+	0.155023i	−0.907301	−	0.420482i	$-0.861861\pi$
$149$	−162.785	+	281.952i	−0.0895025	+	0.155023i	0.817798	+	0.575505i	$0.195194\pi$
$150$		0			0
$151$	−366.492	−	634.783i	−0.197515	−	0.342105i	0.750207	−	0.661203i	$-0.229954\pi$
$151$	−366.492	−	634.783i	−0.197515	−	0.342105i	−0.947722	+	0.319097i	$0.896620\pi$
$152$		0			0
$153$	335.896	+	312.277i	0.177488	+	0.165007i
$154$		0			0
$155$	1630.76	+	2824.55i	0.845067	+	1.46370i
$156$		0			0
$157$	−909.978	+	1576.13i	−0.462574	+	0.801202i	−0.999088	−	0.0426892i	$-0.986407\pi$
$157$	−909.978	+	1576.13i	−0.462574	+	0.801202i	0.536514	+	0.843891i	$0.319741\pi$
$158$		0			0
$159$	3649.88	+	1434.53i	1.82047	+	0.715506i
$160$		0			0
$161$	−1011.33			−0.495056
$162$		0			0
$163$	−2400.24			−1.15338			−0.576691	−	0.816963i	$-0.695656\pi$
$163$	−2400.24			−1.15338			−0.576691	+	0.816963i	$0.695656\pi$
$164$		0			0
$165$	−2695.72	−	1059.51i	−1.27189	−	0.499897i
$166$		0			0
$167$	1493.82	−	2587.37i	0.692188	−	1.19890i	−0.278932	−	0.960311i	$-0.589980\pi$
$167$	1493.82	−	2587.37i	0.692188	−	1.19890i	0.971119	−	0.238594i	$-0.0766864\pi$
$168$		0			0
$169$	392.015	+	678.989i	0.178432	+	0.309053i
$170$		0			0
$171$	−1562.27	−	1452.42i	−0.698655	−	0.649528i
$172$		0			0
$173$	665.167	+	1152.10i	0.292322	+	0.506316i	0.974358	−	0.225002i	$-0.0722388\pi$
$173$	665.167	+	1152.10i	0.292322	+	0.506316i	−0.682036	+	0.731318i	$0.738905\pi$
$174$		0			0
$175$	−441.670	+	764.994i	−0.190783	+	0.330447i
$176$		0			0
$177$	−2462.52	+	1961.83i	−1.04573	+	0.833108i
$178$		0			0
$179$	293.898			0.122720			0.0613602	−	0.998116i	$-0.480456\pi$
$179$	293.898			0.122720			0.0613602	+	0.998116i	$0.480456\pi$
$180$		0			0
$181$	−901.322			−0.370137			−0.185068	−	0.982726i	$-0.559251\pi$
$181$	−901.322			−0.370137			−0.185068	+	0.982726i	$0.559251\pi$
$182$		0			0
$183$	−76.5445	−	509.527i	−0.0309198	−	0.205821i
$184$		0			0
$185$	1997.91	−	3460.48i	0.793995	−	1.37524i
$186$		0			0
$187$	−315.055	−	545.691i	−0.123204	−	0.213395i
$188$		0			0
$189$	694.001	−	1014.72i	0.267096	−	0.390528i
$190$		0			0
$191$	−953.794	−	1652.02i	−0.361331	−	0.625843i	0.626850	−	0.779140i	$-0.284344\pi$
$191$	−953.794	−	1652.02i	−0.361331	−	0.625843i	−0.988180	+	0.153297i	$0.951011\pi$
$192$		0			0
$193$	1484.41	−	2571.07i	0.553626	−	0.958908i	−0.444383	−	0.895837i	$-0.646577\pi$
$193$	1484.41	−	2571.07i	0.553626	−	0.958908i	0.998009	−	0.0630715i	$-0.0200896\pi$
$194$		0			0
$195$	−436.033	−	2902.51i	−0.160128	−	1.06591i
$196$		0			0
$197$	−1898.69			−0.686679			−0.343339	−	0.939211i	$-0.611558\pi$
$197$	−1898.69			−0.686679			−0.343339	+	0.939211i	$0.611558\pi$
$198$		0			0
$199$	−2023.98			−0.720986			−0.360493	−	0.932762i	$-0.617391\pi$
$199$	−2023.98			−0.720986			−0.360493	+	0.932762i	$0.617391\pi$
$200$		0			0
$201$	4120.36	−	3282.59i	1.44591	−	1.15192i
$202$		0			0
$203$	−788.718	+	1366.10i	−0.272695	+	0.472322i
$204$		0			0
$205$	−349.827	−	605.919i	−0.119185	−	0.206435i
$206$		0			0
$207$	2978.68	−	915.617i	1.00016	−	0.307439i
$208$		0			0
$209$	1465.34	+	2538.04i	0.484974	+	0.839999i
$210$		0			0
$211$	2560.94	−	4435.68i	0.835557	−	1.44723i	−0.0580185	−	0.998316i	$-0.518478\pi$
$211$	2560.94	−	4435.68i	0.835557	−	1.44723i	0.893576	−	0.448912i	$-0.148188\pi$
$212$		0			0
$213$	1535.22	+	603.395i	0.493857	+	0.194103i
$214$		0			0
$215$	9.18311			0.00291294
$216$		0			0
$217$	1901.85			0.594958
$218$		0			0
$219$	−4379.82	−	1721.42i	−1.35142	−	0.531154i
$220$		0			0
$221$	319.255	−	552.965i	0.0971737	−	0.168310i
$222$		0			0
$223$	−437.916	−	758.493i	−0.131502	−	0.227769i	0.792754	−	0.609542i	$-0.208647\pi$
$223$	−437.916	−	758.493i	−0.131502	−	0.227769i	−0.924256	+	0.381773i	$0.875313\pi$
$224$		0			0
$225$	608.258	−	2653.01i	0.180225	−	0.786077i
$226$		0			0
$227$	2463.32	+	4266.60i	0.720249	+	1.24751i	0.960900	+	0.276897i	$0.0893060\pi$
$227$	2463.32	+	4266.60i	0.720249	+	1.24751i	−0.240650	+	0.970612i	$0.577361\pi$
$228$		0			0
$229$	2007.45	−	3477.01i	0.579285	−	1.00335i	−0.416277	−	0.909238i	$-0.636665\pi$
$229$	2007.45	−	3477.01i	0.579285	−	1.00335i	0.995562	−	0.0941129i	$-0.0300015\pi$
$230$		0			0
$231$	−1321.01	+	1052.42i	−0.376261	+	0.299758i
$232$		0			0
$233$	1732.93			0.487246			0.243623	−	0.969870i	$-0.421664\pi$
$233$	1732.93			0.487246			0.243623	+	0.969870i	$0.421664\pi$
$234$		0			0
$235$	7336.87			2.03661
$236$		0			0
$237$	−533.218	−	3549.43i	−0.146144	−	0.972827i
$238$		0			0
$239$	−683.836	+	1184.44i	−0.185078	+	0.320565i	−0.943603	−	0.331080i	$-0.892587\pi$
$239$	−683.836	+	1184.44i	−0.185078	+	0.320565i	0.758525	+	0.651644i	$0.225920\pi$
$240$		0			0
$241$	3175.24	+	5499.68i	0.848695	+	1.46998i	0.882373	+	0.470550i	$0.155944\pi$
$241$	3175.24	+	5499.68i	0.848695	+	1.46998i	−0.0336786	+	0.999433i	$0.510722\pi$
$242$		0			0
$243$	−1125.36	+	3616.97i	−0.297087	+	0.954851i
$244$		0			0
$245$	−2000.23	−	3464.49i	−0.521591	−	0.903422i
$246$		0			0
$247$	−1484.87	+	2571.87i	−0.382511	+	0.662528i
$248$		0			0
$249$	871.377	+	5800.42i	0.221772	+	1.47625i
$250$		0			0
$251$	311.077			0.0782272			0.0391136	−	0.999235i	$-0.487547\pi$
$251$	311.077			0.0782272			0.0391136	+	0.999235i	$0.487547\pi$
$252$		0			0
$253$	−4281.35			−1.06390
$254$		0			0
$255$	1037.37	−	826.450i	0.254756	−	0.202958i
$256$		0			0
$257$	2073.62	−	3591.62i	0.503304	−	0.871748i	−0.496689	−	0.867929i	$-0.665451\pi$
$257$	2073.62	−	3591.62i	0.503304	−	0.871748i	0.999993	−	0.00381914i	$-0.00121567\pi$
$258$		0			0
$259$	−1165.02	−	2017.87i	−0.279501	−	0.484109i
$260$		0			0
$261$	1086.21	−	4737.65i	0.257603	−	1.12358i
$262$		0			0
$263$	383.920	+	664.968i	0.0900133	+	0.155908i	0.907516	−	0.420016i	$-0.137976\pi$
$263$	383.920	+	664.968i	0.0900133	+	0.155908i	−0.817503	+	0.575924i	$0.804642\pi$
$264$		0			0
$265$	5670.61	−	9821.79i	1.31450	−	2.27678i
$266$		0			0
$267$	−1591.99	−	625.706i	−0.364899	−	0.143418i
$268$		0			0
$269$	−3676.90			−0.833401			−0.416700	−	0.909044i	$-0.636814\pi$
$269$	−3676.90			−0.833401			−0.416700	+	0.909044i	$0.636814\pi$
$270$		0			0
$271$	−2287.83			−0.512825			−0.256413	−	0.966567i	$-0.582541\pi$
$271$	−2287.83			−0.512825			−0.256413	+	0.966567i	$0.582541\pi$
$272$		0			0
$273$	−1592.88	−	626.058i	−0.353134	−	0.138794i
$274$		0			0
$275$	−1869.76	+	3238.51i	−0.410002	+	0.710144i
$276$		0			0
$277$	−389.935	−	675.387i	−0.0845810	−	0.146499i	0.820632	−	0.571458i	$-0.193622\pi$
$277$	−389.935	−	675.387i	−0.0845810	−	0.146499i	−0.905213	+	0.424959i	$0.860288\pi$
$278$		0			0
$279$	−5601.53	+	1721.85i	−1.20199	+	0.369479i
$280$		0			0
$281$	319.108	+	552.712i	0.0677452	+	0.117338i	0.897908	−	0.440182i	$-0.145086\pi$
$281$	319.108	+	552.712i	0.0677452	+	0.117338i	−0.830163	+	0.557520i	$0.811753\pi$
$282$		0			0
$283$	2626.85	−	4549.83i	0.551766	−	0.955688i	−0.446381	−	0.894843i	$-0.647287\pi$
$283$	2626.85	−	4549.83i	0.551766	−	0.955688i	0.998147	−	0.0608445i	$-0.0193794\pi$
$284$		0			0
$285$	−4824.89	+	3843.87i	−1.00281	+	0.798916i
$286$		0			0
$287$	−407.982			−0.0839109
$288$		0			0
$289$	−4624.46			−0.941271
$290$		0			0
$291$	935.853	+	6229.61i	0.188525	+	1.25494i
$292$		0			0
$293$	1435.65	−	2486.62i	0.286251	−	0.495801i	−0.686661	−	0.726978i	$-0.740924\pi$
$293$	1435.65	−	2486.62i	0.286251	−	0.495801i	0.972912	+	0.231177i	$0.0742575\pi$
$294$		0			0
$295$	4552.57	+	7885.28i	0.898511	+	1.55627i
$296$		0			0
$297$	2937.97	−	4295.68i	0.574001	−	0.839262i
$298$		0			0
$299$	−2169.21	−	3757.19i	−0.419561	−	0.726701i
$300$		0			0
$301$	2.67742	−	4.63743i	0.000512705	−	0.000888031i
$302$		0			0
$303$	−54.0054	−	359.493i	−0.0102394	−	0.0681595i
$304$		0			0
$305$	−1490.05			−0.279739
$306$		0			0
$307$	8374.05			1.55678			0.778392	−	0.627779i	$-0.216036\pi$
$307$	8374.05			1.55678			0.778392	+	0.627779i	$0.216036\pi$
$308$		0			0
$309$	−3828.72	+	3050.25i	−0.704882	+	0.561562i
$310$		0			0
$311$	3570.52	−	6184.32i	0.651015	−	1.12759i	−0.331862	−	0.943328i	$-0.607677\pi$
$311$	3570.52	−	6184.32i	0.651015	−	1.12759i	0.982877	−	0.184263i	$-0.0589899\pi$
$312$		0			0
$313$	−403.631	−	699.109i	−0.0728900	−	0.126249i	0.827277	−	0.561795i	$-0.189889\pi$
$313$	−403.631	−	699.109i	−0.0728900	−	0.126249i	−0.900167	+	0.435545i	$0.856556\pi$
$314$		0			0
$315$	−2603.77	−	2420.68i	−0.465734	−	0.432984i
$316$		0			0
$317$	852.157	+	1475.98i	0.150984	+	0.261512i	0.931589	−	0.363512i	$-0.118422\pi$
$317$	852.157	+	1475.98i	0.150984	+	0.261512i	−0.780605	+	0.625024i	$0.785089\pi$
$318$		0			0
$319$	−3338.94	+	5783.22i	−0.586034	+	1.01504i
$320$		0			0
$321$	6511.06	+	2559.07i	1.13212	+	0.444964i
$322$		0			0
$323$	−1342.00			−0.231179
$324$		0			0
$325$	−3789.36			−0.646757
$326$		0			0
$327$	3046.76	+	1197.48i	0.515248	+	0.202510i
$328$		0			0
$329$	2139.13	−	3705.09i	0.358463	−	0.620876i
$330$		0			0
$331$	2457.96	+	4257.31i	0.408162	+	0.706957i	0.994684	−	0.102976i	$-0.0328365\pi$
$331$	2457.96	+	4257.31i	0.408162	+	0.706957i	−0.586522	+	0.809933i	$0.699503\pi$
$332$		0			0
$333$	5258.23	+	4888.48i	0.865312	+	0.804466i
$334$		0			0
$335$	−7617.50	−	13193.9i	−1.24235	−	2.15182i
$336$		0			0
$337$	−2926.98	+	5069.68i	−0.473124	+	0.819475i	−0.999527	−	0.0307606i	$-0.990207\pi$
$337$	−2926.98	+	5069.68i	−0.473124	+	0.819475i	0.526403	+	0.850235i	$0.323540\pi$
$338$		0			0
$339$	−8297.23	+	6610.19i	−1.32933	+	1.05905i
$340$		0			0
$341$	8051.26			1.27859
$342$		0			0
$343$	−5338.28			−0.840349
$344$		0			0
$345$	−1338.81	−	8911.94i	−0.208925	−	1.39073i
$346$		0			0
$347$	4089.73	−	7083.62i	0.632703	−	1.09587i	−0.354293	−	0.935134i	$-0.615279\pi$
$347$	4089.73	−	7083.62i	0.632703	−	1.09587i	0.986997	−	0.160740i	$-0.0513881\pi$
$348$		0			0
$349$	6235.26	+	10799.8i	0.956349	+	1.65645i	0.731250	+	0.682109i	$0.238937\pi$
$349$	6235.26	+	10799.8i	0.956349	+	1.65645i	0.225099	+	0.974336i	$0.427730\pi$
$350$		0			0
$351$	5258.33	+	401.802i	0.799627	+	0.0611015i
$352$		0			0
$353$	3299.28	+	5714.52i	0.497459	+	0.861624i	0.999996	−	0.00293169i	$-0.000933188\pi$
$353$	3299.28	+	5714.52i	0.497459	+	0.861624i	−0.502537	+	0.864556i	$0.667600\pi$
$354$		0			0
$355$	2385.19	−	4131.26i	0.356599	−	0.617647i
$356$		0			0
$357$	−114.898	−	764.829i	−0.0170337	−	0.113387i
$358$		0			0
$359$	5493.11			0.807564			0.403782	−	0.914855i	$-0.367695\pi$
$359$	5493.11			0.807564			0.403782	+	0.914855i	$0.367695\pi$
$360$		0			0
$361$	−617.277			−0.0899951
$362$		0			0
$363$	−183.044	+	145.826i	−0.0264664	+	0.0210851i
$364$		0			0
$365$	−6804.67	+	11786.0i	−0.975816	+	1.69016i
$366$		0			0
$367$	696.804	+	1206.90i	0.0991086	+	0.171661i	0.911316	−	0.411708i	$-0.135068\pi$
$367$	696.804	+	1206.90i	0.0991086	+	0.171661i	−0.812207	+	0.583369i	$0.801734\pi$
$368$		0			0
$369$	1201.63	−	369.370i	0.169524	−	0.0521101i
$370$		0			0
$371$	−3306.64	−	5727.27i	−0.462729	−	0.801469i
$372$		0			0
$373$	6626.12	−	11476.8i	0.919805	−	1.59315i	0.120096	−	0.992762i	$-0.461680\pi$
$373$	6626.12	−	11476.8i	0.919805	−	1.59315i	0.799709	−	0.600387i	$-0.204987\pi$
$374$		0			0
$375$	1757.97	+	690.945i	0.242084	+	0.0951473i
$376$		0			0
$377$	−6766.91			−0.924439
$378$		0			0
$379$	−276.612			−0.0374897			−0.0187449	−	0.999824i	$-0.505967\pi$
$379$	−276.612			−0.0374897			−0.0187449	+	0.999824i	$0.505967\pi$
$380$		0			0
$381$	−9610.82	−	3777.38i	−1.29233	−	0.507930i
$382$		0			0
$383$	5005.97	−	8670.59i	0.667867	−	1.15678i	−0.310633	−	0.950530i	$-0.600541\pi$
$383$	5005.97	−	8670.59i	0.667867	−	1.15678i	0.978500	−	0.206249i	$-0.0661257\pi$
$384$		0			0
$385$	2442.22	+	4230.04i	0.323291	+	0.559956i
$386$		0			0
$387$	−3.68729	+	16.0827i	−0.000484329	+	0.00211248i
$388$		0			0
$389$	−4011.27	−	6947.73i	−0.522827	−	0.905562i	−0.999647	−	0.0265618i	$-0.991544\pi$
$389$	−4011.27	−	6947.73i	−0.522827	−	0.905562i	0.476820	−	0.879001i	$-0.341789\pi$
$390$		0			0
$391$	980.248	−	1697.84i	0.126786	−	0.219600i
$392$		0			0
$393$	−9246.30	+	7366.30i	−1.18680	+	0.945497i
$394$		0			0
$395$	−10379.9			−1.32220
$396$		0			0
$397$	−10767.5			−1.36122			−0.680612	−	0.732644i	$-0.738286\pi$
$397$	−10767.5			−1.36122			−0.680612	+	0.732644i	$0.738286\pi$
$398$		0			0
$399$	534.395	+	3557.26i	0.0670507	+	0.446331i
$400$		0			0
$401$	−4601.84	+	7970.63i	−0.573080	+	0.992604i	0.423167	+	0.906052i	$0.360918\pi$
$401$	−4601.84	+	7970.63i	−0.573080	+	0.992604i	−0.996247	+	0.0865522i	$0.972415\pi$
$402$		0			0
$403$	4079.29	+	7065.54i	0.504228	+	0.873349i
$404$		0			0
$405$	9860.49	+	4772.30i	1.20981	+	0.585525i
$406$		0			0
$407$	−4931.97	−	8542.42i	−0.600660	−	1.04037i
$408$		0			0
$409$	−3907.03	+	6767.17i	−0.472348	+	0.818130i	−0.999499	−	0.0316412i	$-0.989927\pi$
$409$	−3907.03	+	6767.17i	−0.472348	+	0.818130i	0.527152	+	0.849771i	$0.323260\pi$
$410$		0			0
$411$	292.875	+	1949.55i	0.0351495	+	0.233977i
$412$		0			0
$413$	5309.38			0.632585
$414$		0			0
$415$	16962.7			2.00642
$416$		0			0
$417$	−9791.52	+	7800.66i	−1.14986	+	0.916067i
$418$		0			0
$419$	−694.410	+	1202.75i	−0.0809646	+	0.140235i	−0.903665	−	0.428241i	$-0.859133\pi$
$419$	−694.410	+	1202.75i	−0.0809646	+	0.140235i	0.822700	+	0.568476i	$0.192467\pi$
$420$		0			0
$421$	4629.73	+	8018.93i	0.535960	+	0.928310i	0.999116	+	0.0420336i	$0.0133836\pi$
$421$	4629.73	+	8018.93i	0.535960	+	0.928310i	−0.463156	+	0.886277i	$0.653283\pi$
$422$		0			0
$423$	−2945.97	+	12849.3i	−0.338624	+	1.47696i
$424$		0			0
$425$	−856.190	−	1482.96i	−0.0977207	−	0.169257i
$426$		0			0
$427$	−434.440	+	752.471i	−0.0492365	+	0.0852802i
$428$		0			0
$429$	−6743.28	−	2650.34i	−0.758902	−	0.298274i
$430$		0			0
$431$	−4531.60			−0.506449			−0.253225	−	0.967408i	$-0.581491\pi$
$431$	−4531.60			−0.506449			−0.253225	+	0.967408i	$0.581491\pi$
$432$		0			0
$433$	−4029.42			−0.447209			−0.223604	−	0.974680i	$-0.571782\pi$
$433$	−4029.42			−0.447209			−0.223604	+	0.974680i	$0.571782\pi$
$434$		0			0
$435$	−13082.3	−	5141.79i	−1.44195	−	0.566736i
$436$		0			0
$437$	−4559.19	+	7896.75i	−0.499075	+	0.864423i
$438$		0			0
$439$	−1560.26	−	2702.44i	−0.169629	−	0.293805i	0.768661	−	0.639657i	$-0.220923\pi$
$439$	−1560.26	−	2702.44i	−0.169629	−	0.293805i	−0.938289	+	0.345851i	$0.887590\pi$
$440$		0			0
$441$	6870.63	−	2111.96i	0.741889	−	0.228049i
$442$		0			0
$443$	1587.57	+	2749.75i	0.170266	+	0.294909i	0.938513	−	0.345245i	$-0.112204\pi$
$443$	1587.57	+	2749.75i	0.170266	+	0.294909i	−0.768247	+	0.640154i	$0.778871\pi$
$444$		0			0
$445$	−2473.38	+	4284.02i	−0.263482	+	0.456365i
$446$		0			0
$447$	−1323.15	+	1054.12i	−0.140006	+	0.111540i
$448$		0			0
$449$	−4189.57			−0.440352			−0.220176	−	0.975460i	$-0.570663\pi$
$449$	−4189.57			−0.440352			−0.220176	+	0.975460i	$0.570663\pi$
$450$		0			0
$451$	−1727.14			−0.180328
$452$		0			0
$453$	−565.819	−	3766.43i	−0.0586854	−	0.390646i
$454$		0			0
$455$	−2474.77	+	4286.43i	−0.254987	+	0.441651i
$456$		0			0
$457$	−369.905	−	640.694i	−0.0378631	−	0.0655807i	0.846473	−	0.532432i	$-0.178722\pi$
$457$	−369.905	−	640.694i	−0.0378631	−	0.0655807i	−0.884336	+	0.466851i	$0.845388\pi$
$458$		0			0
$459$	1030.85	+	2148.63i	0.104828	+	0.218496i
$460$		0			0
$461$	−3209.48	−	5558.98i	−0.324252	−	0.561622i	0.657108	−	0.753796i	$-0.271779\pi$
$461$	−3209.48	−	5558.98i	−0.324252	−	0.561622i	−0.981361	+	0.192175i	$0.938446\pi$
$462$		0			0
$463$	−932.839	+	1615.73i	−0.0936344	+	0.162180i	−0.909038	−	0.416714i	$-0.863182\pi$
$463$	−932.839	+	1615.73i	−0.0936344	+	0.162180i	0.815403	+	0.578893i	$0.196515\pi$
$464$		0			0
$465$	2517.68	+	16759.3i	0.251086	+	1.67138i
$466$		0			0
$467$	17148.6			1.69923			0.849617	−	0.527400i	$-0.176833\pi$
$467$	17148.6			1.69923			0.849617	+	0.527400i	$0.176833\pi$
$468$		0			0
$469$	−8883.82			−0.874662
$470$		0			0
$471$	−7396.48	+	5892.59i	−0.723592	+	0.576468i
$472$		0			0
$473$	11.3346	−	19.6320i	0.00110183	−	0.00190842i
$474$		0			0
$475$	3982.19	+	6897.35i	0.384664	+	0.666258i
$476$		0			0
$477$	14924.3	+	13874.9i	1.43257	+	1.33184i
$478$		0			0
$479$	1441.48	+	2496.72i	0.137501	+	0.238159i	0.926550	−	0.376171i	$-0.122760\pi$
$479$	1441.48	+	2496.72i	0.137501	+	0.238159i	−0.789049	+	0.614330i	$0.789426\pi$
$480$		0			0
$481$	4997.71	−	8656.29i	0.473755	−	0.820567i
$482$		0			0
$483$	−4890.83	−	1922.27i	−0.460747	−	0.181089i
$484$		0			0
$485$	18217.8			1.70562
$486$		0			0
$487$	14628.2			1.36112			0.680561	−	0.732692i	$-0.261736\pi$
$487$	14628.2			1.36112			0.680561	+	0.732692i	$0.261736\pi$
$488$		0			0
$489$	−11607.6	−	4562.20i	−1.07345	−	0.421902i
$490$		0			0
$491$	1295.00	−	2243.00i	0.119027	−	0.206162i	−0.800355	−	0.599526i	$-0.795356\pi$
$491$	1295.00	−	2243.00i	0.119027	−	0.206162i	0.919383	+	0.393365i	$0.128689\pi$
$492$		0			0
$493$	−1528.95	−	2648.23i	−0.139677	−	0.241927i
$494$		0			0
$495$	−11022.8	−	10247.7i	−1.00088	−	0.930503i
$496$		0			0
$497$	−1390.85	−	2409.02i	−0.125529	−	0.217423i
$498$		0			0
$499$	87.2493	−	151.120i	0.00782728	−	0.0135573i	−0.862085	−	0.506763i	$-0.830842\pi$
$499$	87.2493	−	151.120i	0.00782728	−	0.0135573i	0.869913	+	0.493206i	$0.164175\pi$
$500$		0			0
$501$	12142.1	−	9673.29i	1.08277	−	0.862616i
$502$		0			0
$503$	−9744.10			−0.863753			−0.431877	−	0.901933i	$-0.642148\pi$
$503$	−9744.10			−0.863753			−0.431877	+	0.901933i	$0.642148\pi$
$504$		0			0
$505$	−1051.30			−0.0926378
$506$		0			0
$507$	605.222	+	4028.73i	0.0530155	+	0.352904i
$508$		0			0
$509$	−730.150	+	1264.66i	−0.0635822	+	0.110128i	−0.896064	−	0.443925i	$-0.853586\pi$
$509$	−730.150	+	1264.66i	−0.0635822	+	0.110128i	0.832482	+	0.554052i	$0.186919\pi$
$510$		0			0
$511$	3967.94	+	6872.67i	0.343505	+	0.594968i
$512$		0			0
$513$	−4794.55	−	9993.40i	−0.412641	−	0.860077i
$514$		0			0
$515$	7078.33	+	12260.0i	0.605648	+	1.04901i
$516$		0			0
$517$	9055.77	−	15685.1i	0.770353	−	1.33429i
$518$		0			0
$519$	1026.93	+	6835.91i	0.0868544	+	0.578156i
$520$		0			0
$521$	−610.148			−0.0513072			−0.0256536	−	0.999671i	$-0.508167\pi$
$521$	−610.148			−0.0513072			−0.0256536	+	0.999671i	$0.508167\pi$
$522$		0			0
$523$	4438.21			0.371069			0.185535	−	0.982638i	$-0.440598\pi$
$523$	4438.21			0.371069			0.185535	+	0.982638i	$0.440598\pi$
$524$		0			0
$525$	−3589.98	+	2860.05i	−0.298437	+	0.237757i
$526$		0			0
$527$	−1843.40	+	3192.86i	−0.152371	+	0.263915i
$528$		0			0
$529$	−576.912	−	999.241i	−0.0474161	−	0.0821272i
$530$		0			0
$531$	−15637.7	+	4806.89i	−1.27800	+	0.392846i
$532$		0			0
$533$	−875.084	−	1515.69i	−0.0711146	−	0.123174i
$534$		0			0
$535$	10115.9	−	17521.2i	0.817471	−	1.41590i
$536$		0			0
$537$	1421.30	+	558.620i	0.114215	+	0.0448905i
$538$		0			0
$539$	−9875.38			−0.789170
$540$		0			0
$541$	22847.5			1.81570			0.907848	−	0.419299i	$-0.137724\pi$
$541$	22847.5			1.81570			0.907848	+	0.419299i	$0.137724\pi$
$542$		0			0
$543$	−4358.82	−	1713.17i	−0.344484	−	0.135394i
$544$		0			0
$545$	4733.58	−	8198.80i	0.372044	−	0.644400i
$546$		0			0
$547$	−7549.55	−	13076.2i	−0.590120	−	1.02212i	−0.994216	−	0.107401i	$-0.965747\pi$
$547$	−7549.55	−	13076.2i	−0.590120	−	1.02212i	0.404096	−	0.914717i	$-0.367586\pi$
$548$		0			0
$549$	598.301	−	2609.58i	0.0465116	−	0.202867i
$550$		0			0
$551$	7111.25	+	12317.0i	0.549818	+	0.952312i
$552$		0			0
$553$	−3026.36	+	5241.81i	−0.232719	+	0.403082i
$554$		0			0
$555$	16239.4	−	12937.5i	1.24202	−	0.989489i
$556$		0			0
$557$	−1398.82			−0.106410			−0.0532048	−	0.998584i	$-0.516944\pi$
$557$	−1398.82			−0.106410			−0.0532048	+	0.998584i	$0.516944\pi$
$558$		0			0
$559$	22.9713			0.00173807
$560$		0			0
$561$	−486.405	−	3237.81i	−0.0366062	−	0.243673i
$562$		0			0
$563$	9836.23	−	17036.8i	0.736319	−	1.27534i	−0.217823	−	0.975988i	$-0.569896\pi$
$563$	9836.23	−	17036.8i	0.736319	−	1.27534i	0.954142	−	0.299354i	$-0.0967711\pi$
$564$		0			0
$565$	15339.4	+	26568.7i	1.14219	+	1.97832i
$566$		0			0
$567$	5284.91	−	3588.10i	0.391438	−	0.265760i
$568$		0			0
$569$	−379.827	−	657.880i	−0.0279845	−	0.0484706i	0.851694	−	0.524039i	$-0.175576\pi$
$569$	−379.827	−	657.880i	−0.0279845	−	0.0484706i	−0.879678	+	0.475569i	$0.842242\pi$
$570$		0			0
$571$	−6263.95	+	10849.5i	−0.459086	+	0.795161i	−0.998913	−	0.0466155i	$-0.985156\pi$
$571$	−6263.95	+	10849.5i	−0.459086	+	0.795161i	0.539827	+	0.841776i	$0.318490\pi$
$572$		0			0
$573$	−1472.54	−	9802.13i	−0.107358	−	0.714642i
$574$		0			0
$575$	−11635.0			−0.843846
$576$		0			0
$577$	−23985.7			−1.73057			−0.865284	−	0.501282i	$-0.832862\pi$
$577$	−23985.7			−1.73057			−0.865284	+	0.501282i	$0.832862\pi$
$578$		0			0
$579$	12065.5	−	9612.31i	0.866021	−	0.689938i
$580$		0			0
$581$	4945.63	−	8566.08i	0.353148	−	0.611671i
$582$		0			0
$583$	−13998.3	−	24245.7i	−0.994424	−	1.72239i
$584$		0			0
$585$	3408.20	−	14865.4i	0.240875	−	1.05061i
$586$		0			0
$587$	−8671.73	−	15019.9i	−0.609745	−	1.05611i	−0.991282	−	0.131756i	$-0.957938\pi$
$587$	−8671.73	−	15019.9i	−0.609745	−	1.05611i	0.381537	−	0.924354i	$-0.375395\pi$
$588$		0			0
$589$	8573.74	−	14850.2i	0.599788	−	1.03886i
$590$		0			0
$591$	−9182.11	−	3608.89i	−0.639089	−	0.251184i
$592$		0			0
$593$	−12719.9			−0.880851			−0.440425	−	0.897789i	$-0.645172\pi$
$593$	−12719.9			−0.880851			−0.440425	+	0.897789i	$0.645172\pi$
$594$		0			0
$595$	−2236.66			−0.154107
$596$		0			0
$597$	−9788.04	−	3847.04i	−0.671018	−	0.263733i
$598$		0			0
$599$	−1773.84	+	3072.38i	−0.120997	+	0.209573i	−0.920161	−	0.391540i	$-0.871942\pi$
$599$	−1773.84	+	3072.38i	−0.120997	+	0.209573i	0.799164	+	0.601113i	$0.205276\pi$
$600$		0			0
$601$	−8366.32	−	14490.9i	−0.567836	−	0.983521i	−0.996780	−	0.0801895i	$-0.974447\pi$
$601$	−8366.32	−	14490.9i	−0.567836	−	0.983521i	0.428944	−	0.903331i	$-0.358886\pi$
$602$		0			0
$603$	26165.5	−	8043.03i	1.76707	−	0.543180i
$604$		0			0
$605$	338.401	+	586.127i	0.0227404	+	0.0393875i
$606$		0			0
$607$	−4986.53	+	8636.93i	−0.333438	+	0.577532i	−0.983184	−	0.182620i	$-0.941542\pi$
$607$	−4986.53	+	8636.93i	−0.333438	+	0.577532i	0.649745	+	0.760152i	$0.274876\pi$
$608$		0			0
$609$	−6410.85	+	5107.37i	−0.426570	+	0.339837i
$610$		0			0
$611$	18353.0			1.21519
$612$		0			0
$613$	−25595.4			−1.68644			−0.843221	−	0.537567i	$-0.819344\pi$
$613$	−25595.4			−1.68644			−0.843221	+	0.537567i	$0.819344\pi$
$614$		0			0
$615$	−540.090	−	3595.17i	−0.0354123	−	0.235726i
$616$		0			0
$617$	517.197	−	895.812i	0.0337465	−	0.0584506i	−0.848659	−	0.528941i	$-0.822589\pi$
$617$	517.197	−	895.812i	0.0337465	−	0.0584506i	0.882405	+	0.470490i	$0.155923\pi$
$618$		0			0
$619$	−2678.19	−	4638.76i	−0.173902	−	0.301208i	0.765878	−	0.642985i	$-0.222304\pi$
$619$	−2678.19	−	4638.76i	−0.173902	−	0.301208i	−0.939781	+	0.341778i	$0.888971\pi$
$620$		0			0
$621$	16145.3	+	1233.70i	1.04330	+	0.0797212i
$622$		0			0
$623$	1442.28	+	2498.10i	0.0927505	+	0.160649i
$624$		0			0
$625$	9031.83	−	15643.6i	0.578037	−	1.00119i
$626$		0			0
$627$	2262.30	+	15059.3i	0.144095	+	0.959184i
$628$		0			0
$629$	4516.84			0.286325
$630$		0			0
$631$	−25916.3			−1.63504			−0.817520	−	0.575901i	$-0.804652\pi$
$631$	−25916.3			−1.63504			−0.817520	+	0.575901i	$0.804652\pi$
$632$		0			0
$633$	20815.8	−	16583.5i	1.30704	−	1.04129i
$634$		0			0
$635$	−14931.8	+	25862.6i	−0.933149	+	1.61626i
$636$		0			0
$637$	−5003.51	−	8666.34i	−0.311219	−	0.539047i
$638$		0			0
$639$	6277.49	+	5836.08i	0.388629	+	0.361301i
$640$		0			0
$641$	5231.39	+	9061.03i	0.322352	+	0.558329i	0.980973	−	0.194145i	$-0.0621933\pi$
$641$	5231.39	+	9061.03i	0.322352	+	0.558329i	−0.658621	+	0.752475i	$0.728860\pi$
$642$		0			0
$643$	−7241.44	+	12542.5i	−0.444128	+	0.769253i	−0.997991	−	0.0633553i	$-0.979820\pi$
$643$	−7241.44	+	12542.5i	−0.444128	+	0.769253i	0.553863	+	0.832608i	$0.313153\pi$
$644$		0			0
$645$	44.4098	+	17.4546i	0.00271106	+	0.00106554i
$646$		0			0
$647$	22464.0			1.36499			0.682496	−	0.730889i	$-0.260894\pi$
$647$	22464.0			1.36499			0.682496	+	0.730889i	$0.260894\pi$
$648$		0			0
$649$	22476.6			1.35945
$650$		0			0
$651$	9197.41	+	3614.90i	0.553725	+	0.217633i
$652$		0			0
$653$	4203.85	−	7281.29i	0.251929	−	0.436353i	−0.712128	−	0.702050i	$-0.752268\pi$
$653$	4203.85	−	7281.29i	0.251929	−	0.436353i	0.964057	+	0.265696i	$0.0856018\pi$
$654$		0			0
$655$	17094.0	+	29607.7i	1.01972	+	1.76621i
$656$		0			0
$657$	−17909.0	−	16649.7i	−1.06347	−	0.988685i
$658$		0			0
$659$	−13914.2	−	24100.1i	−0.822490	−	1.42459i	−0.903822	−	0.427908i	$-0.859251\pi$
$659$	−13914.2	−	24100.1i	−0.822490	−	1.42459i	0.0813321	−	0.996687i	$-0.474083\pi$
$660$		0			0
$661$	−555.029	+	961.339i	−0.0326598	+	0.0565685i	−0.881893	−	0.471449i	$-0.843731\pi$
$661$	−555.029	+	961.339i	−0.0326598	+	0.0565685i	0.849233	+	0.528017i	$0.177064\pi$
$662$		0			0
$663$	2594.96	−	2067.34i	0.152006	−	0.121099i
$664$		0			0
$665$	10402.8			0.606622
$666$		0			0
$667$	−20777.3			−1.20615
$668$		0			0
$669$	−676.088	−	4500.46i	−0.0390719	−	0.260086i
$670$		0			0
$671$	−1839.15	+	3185.50i	−0.105812	+	0.183271i
$672$		0			0
$673$	11428.6	+	19794.9i	0.654591	+	1.13378i	0.981996	+	0.188901i	$0.0604925\pi$
$673$	11428.6	+	19794.9i	0.654591	+	1.13378i	−0.327405	+	0.944884i	$0.606174\pi$
$674$		0			0
$675$	7984.21	−	11673.9i	0.455278	−	0.665673i
$676$		0			0
$677$	−8184.21	−	14175.5i	−0.464616	−	0.804738i	0.534569	−	0.845125i	$-0.320474\pi$
$677$	−8184.21	−	14175.5i	−0.464616	−	0.804738i	−0.999184	+	0.0403874i	$0.987141\pi$
$678$		0			0
$679$	5311.57	−	9199.91i	0.300205	−	0.519971i
$680$		0			0
$681$	3803.07	+	25315.6i	0.214000	+	1.42451i
$682$		0			0
$683$	−12719.9			−0.712610			−0.356305	−	0.934370i	$-0.615964\pi$
$683$	−12719.9			−0.712610			−0.356305	+	0.934370i	$0.615964\pi$
$684$		0			0
$685$	5701.25			0.318005
$686$		0			0
$687$	16317.0	−	12999.3i	0.906159	−	0.721914i
$688$		0			0
$689$	14184.9	−	24568.9i	0.784327	−	1.35849i
$690$		0			0
$691$	875.387	+	1516.21i	0.0481929	+	0.0834725i	0.889116	−	0.457683i	$-0.151320\pi$
$691$	875.387	+	1516.21i	0.0481929	+	0.0834725i	−0.840923	+	0.541155i	$0.817987\pi$
$692$		0			0
$693$	−8388.83	+	2578.65i	−0.459835	+	0.141349i
$694$		0			0
$695$	18102.0	+	31353.6i	0.987983	+	1.71124i
$696$		0			0
$697$	395.443	−	684.927i	0.0214899	−	0.0372216i
$698$		0			0
$699$	8380.53	+	3293.84i	0.453478	+	0.178232i
$700$		0			0
$701$	18087.4			0.974538			0.487269	−	0.873252i	$-0.337993\pi$
$701$	18087.4			0.974538			0.487269	+	0.873252i	$0.337993\pi$
$702$		0			0
$703$	−21008.1			−1.12708
$704$		0			0
$705$	35481.3	+	13945.4i	1.89547	+	0.744984i
$706$		0			0
$707$	−306.516	+	530.901i	−0.0163051	+	0.0282413i
$708$		0			0
$709$	−15032.0	−	26036.2i	−0.796245	−	1.37914i	−0.922045	−	0.387082i	$-0.873483\pi$
$709$	−15032.0	−	26036.2i	−0.796245	−	1.37914i	0.125800	−	0.992056i	$-0.459850\pi$
$710$		0			0
$711$	4167.84	−	18178.7i	0.219840	−	0.958865i
$712$		0			0
$713$	12525.2	+	21694.2i	0.657884	+	1.13949i
$714$		0			0
$715$	−10476.7	+	18146.1i	−0.547979	+	0.949127i
$716$		0			0
$717$	−5558.35	+	4428.20i	−0.289512	+	0.230647i
$718$		0			0
$719$	16707.1			0.866581			0.433290	−	0.901254i	$-0.357352\pi$
$719$	16707.1			0.866581			0.433290	+	0.901254i	$0.357352\pi$
$720$		0			0
$721$	8255.02			0.426398
$722$		0			0
$723$	4902.18	+	32631.9i	0.252163	+	1.67855i
$724$		0			0
$725$	−9073.89	+	15716.4i	−0.464822	+	0.805095i
$726$		0			0
$727$	−17011.8	−	29465.2i	−0.867856	−	1.50317i	−0.864183	−	0.503178i	$-0.832164\pi$
$727$	−17011.8	−	29465.2i	−0.867856	−	1.50317i	−0.00367354	−	0.999993i	$-0.501169\pi$
$728$		0			0
$729$	−12317.2	+	15352.8i	−0.625777	+	0.780002i
$730$		0			0
$731$	5.19027	+	8.98980i	0.000262611	+	0.000454856i
$732$		0			0
$733$	−11848.0	+	20521.3i	−0.597019	+	1.03407i	0.396240	+	0.918147i	$0.370315\pi$
$733$	−11848.0	+	20521.3i	−0.597019	+	1.03407i	−0.993259	+	0.115920i	$0.963018\pi$
$734$		0			0
$735$	−3088.10	−	20556.3i	−0.154975	−	1.03161i
$736$		0			0
$737$	−37608.6			−1.87969
$738$		0			0
$739$	−31542.7			−1.57012			−0.785058	−	0.619422i	$-0.787367\pi$
$739$	−31542.7			−1.57012			−0.785058	+	0.619422i	$0.787367\pi$
$740$		0			0
$741$	−12069.3	+	9615.33i	−0.598350	+	0.476691i
$742$		0			0
$743$	−12503.0	+	21655.9i	−0.617350	+	1.06928i	0.372617	+	0.927985i	$0.378460\pi$
$743$	−12503.0	+	21655.9i	−0.617350	+	1.06928i	−0.989967	+	0.141296i	$0.954873\pi$
$744$		0			0
$745$	2446.16	+	4236.88i	0.120296	+	0.208359i
$746$		0			0
$747$	−6811.01	+	29707.3i	−0.333604	+	1.45506i
$748$		0			0
$749$	−5898.75	−	10216.9i	−0.287765	−	0.498423i
$750$		0			0
$751$	−1369.85	+	2372.65i	−0.0665600	+	0.115285i	−0.897385	−	0.441249i	$-0.854536\pi$
$751$	−1369.85	+	2372.65i	−0.0665600	+	0.115285i	0.830825	+	0.556534i	$0.187869\pi$
$752$		0			0
$753$	1504.38	+	591.274i	0.0728057	+	0.0286152i
$754$		0			0
$755$	−11014.5			−0.530939
$756$		0			0
$757$	10152.3			0.487441			0.243721	−	0.969845i	$-0.421632\pi$
$757$	10152.3			0.487441			0.243721	+	0.969845i	$0.421632\pi$
$758$		0			0
$759$	−20704.8	−	8137.69i	−0.990165	−	0.389169i
$760$		0			0
$761$	12770.2	−	22118.7i	0.608305	−	1.05361i	−0.383215	−	0.923659i	$-0.625183\pi$
$761$	12770.2	−	22118.7i	0.608305	−	1.05361i	0.991520	−	0.129956i	$-0.0414835\pi$
$762$		0			0
$763$	−2760.24	−	4780.87i	−0.130966	−	0.226840i
$764$		0			0
$765$	6587.63	−	2024.97i	0.311342	−	0.0957034i
$766$		0			0
$767$	11388.1	+	19724.8i	0.536117	+	0.928581i
$768$		0			0
$769$	−8291.76	+	14361.7i	−0.388828	+	0.673469i	−0.992292	−	0.123921i	$-0.960453\pi$
$769$	−8291.76	+	14361.7i	−0.388828	+	0.673469i	0.603464	+	0.797390i	$0.293787\pi$
$770$		0			0
$771$	16854.8	−	13427.8i	0.787304	−	0.627225i
$772$		0			0
$773$	−37404.8			−1.74044			−0.870219	−	0.492665i	$-0.836023\pi$
$773$	−37404.8			−1.74044			−0.870219	+	0.492665i	$0.836023\pi$
$774$		0			0
$775$	21880.0			1.01413
$776$		0			0
$777$	−1798.64	−	11972.9i	−0.0830450	−	0.552798i
$778$		0			0
$779$	−1839.23	+	3185.64i	−0.0845920	+	0.146518i
$780$		0			0
$781$	−5887.99	−	10198.3i	−0.269768	−	0.467252i
$782$		0			0
$783$	14257.9	−	20846.9i	0.650749	−	0.951477i
$784$		0			0
$785$	13674.2	+	23684.4i	0.621723	+	1.07686i
$786$		0			0
$787$	8000.81	−	13857.8i	0.362387	−	0.627672i	−0.625967	−	0.779850i	$-0.715295\pi$
$787$	8000.81	−	13857.8i	0.362387	−	0.627672i	0.988353	+	0.152178i	$0.0486287\pi$
$788$		0			0
$789$	592.725	+	3945.54i	0.0267447	+	0.178029i
$790$		0			0
$791$	17889.4			0.804141
$792$		0			0
$793$	−3727.33			−0.166912
$794$		0			0
$795$	46091.8	−	36720.2i	2.05624	−	1.63815i
$796$		0			0
$797$	−19254.6	+	33350.0i	−0.855752	+	1.48221i	0.0201934	+	0.999796i	$0.493572\pi$
$797$	−19254.6	+	33350.0i	−0.855752	+	1.48221i	−0.875946	+	0.482410i	$0.839762\pi$
$798$		0			0
$799$	4146.77	+	7182.42i	0.183607	+	0.318017i
$800$		0			0
$801$	−6509.61	−	6051.88i	−0.287148	−	0.266957i
$802$		0			0
$803$	16797.8	+	29094.6i	0.738208	+	1.27861i
$804$		0			0
$805$	−7598.61	+	13161.2i	−0.332690	+	0.576237i
$806$		0			0
$807$	−17781.6	−	6988.80i	−0.775642	−	0.304854i
$808$		0			0
$809$	−28844.9			−1.25356			−0.626781	−	0.779195i	$-0.715628\pi$
$809$	−28844.9			−1.25356			−0.626781	+	0.779195i	$0.715628\pi$
$810$		0			0
$811$	−6640.88			−0.287537			−0.143769	−	0.989611i	$-0.545922\pi$
$811$	−6640.88			−0.287537			−0.143769	+	0.989611i	$0.545922\pi$
$812$		0			0
$813$	−11064.0	−	4348.54i	−0.477284	−	0.187589i
$814$		0			0
$815$	−18034.1	+	31236.0i	−0.775101	+	1.34252i
$816$		0			0
$817$	−24.1402	−	41.8121i	−0.00103373	−	0.00179048i
$818$		0			0
$819$	−6513.27	−	6055.28i	−0.277890	−	0.258350i
$820$		0			0
$821$	17334.7	+	30024.5i	0.736886	+	1.27632i	0.953891	+	0.300154i	$0.0970380\pi$
$821$	17334.7	+	30024.5i	0.736886	+	1.27632i	−0.217005	+	0.976171i	$0.569629\pi$
$822$		0			0
$823$	18262.3	−	31631.2i	0.773492	−	1.33973i	−0.162147	−	0.986767i	$-0.551842\pi$
$823$	18262.3	−	31631.2i	0.773492	−	1.33973i	0.935638	−	0.352960i	$-0.114825\pi$
$824$		0			0
$825$	−15197.7	+	12107.7i	−0.641354	+	0.510951i
$826$		0			0
$827$	−28174.1			−1.18465			−0.592326	−	0.805698i	$-0.701790\pi$
$827$	−28174.1			−1.18465			−0.592326	+	0.805698i	$0.701790\pi$
$828$		0			0
$829$	−12023.2			−0.503721			−0.251860	−	0.967764i	$-0.581042\pi$
$829$	−12023.2			−0.503721			−0.251860	+	0.967764i	$0.581042\pi$
$830$		0			0
$831$	−602.011	−	4007.36i	−0.0251306	−	0.167285i
$832$		0			0
$833$	2261.04	−	3916.24i	0.0940462	−	0.162893i
$834$		0			0
$835$	−22447.6	−	38880.3i	−0.930336	−	1.61139i
$836$		0			0
$837$	−30361.9	−	2320.03i	−1.25384	−	0.0958089i
$838$		0			0
$839$	16836.6	+	29161.9i	0.692807	+	1.19998i	0.970914	+	0.239427i	$0.0769595\pi$
$839$	16836.6	+	29161.9i	0.692807	+	1.19998i	−0.278108	+	0.960550i	$0.589707\pi$
$840$		0			0
$841$	−4009.33	+	6944.36i	−0.164391	+	0.284733i
$842$		0			0
$843$	492.664	+	3279.47i	0.0201284	+	0.133987i
$844$		0			0
$845$	11781.6			0.479643
$846$		0			0
$847$	394.656			0.0160101
$848$		0			0
$849$	21351.5	−	17010.2i	0.863113	−	0.687620i
$850$		0			0
$851$	15345.1	−	26578.5i	0.618124	−	1.07062i
$852$		0			0
$853$	7556.85	+	13088.9i	0.303331	+	0.525386i	0.976888	−	0.213750i	$-0.0685677\pi$
$853$	7556.85	+	13088.9i	0.303331	+	0.525386i	−0.673557	+	0.739135i	$0.735234\pi$
$854$		0			0
$855$	−30639.5	+	9418.27i	−1.22555	+	0.376723i
$856$		0			0
$857$	−528.642	−	915.634i	−0.0210712	−	0.0364965i	0.855298	−	0.518137i	$-0.173374\pi$
$857$	−528.642	−	915.634i	−0.0210712	−	0.0364965i	−0.876369	+	0.481641i	$0.840041\pi$
$858$		0			0
$859$	−2162.63	+	3745.79i	−0.0859000	+	0.148783i	−0.905774	−	0.423760i	$-0.860710\pi$
$859$	−2162.63	+	3745.79i	−0.0859000	+	0.148783i	0.819874	+	0.572543i	$0.194043\pi$
$860$		0			0
$861$	−1973.02	−	775.463i	−0.0780955	−	0.0306942i
$862$		0			0
$863$	−10198.7			−0.402279			−0.201139	−	0.979563i	$-0.564464\pi$
$863$	−10198.7			−0.402279			−0.201139	+	0.979563i	$0.564464\pi$
$864$		0			0
$865$	19990.8			0.785791
$866$		0			0
$867$	−22364.1	−	8789.85i	−0.876036	−	0.344313i
$868$		0			0
$869$	−12811.7	+	22190.6i	−0.500125	+	0.866241i
$870$		0			0
$871$	−19055.0	−	33004.2i	−0.741278	−	1.28393i
$872$		0			0
$873$	−7314.98	+	31905.4i	−0.283591	+	1.23692i
$874$		0			0
$875$	−1592.65	−	2758.56i	−0.0615331	−	0.106578i
$876$		0			0
$877$	−22552.6	+	39062.3i	−0.868356	+	1.50404i	−0.00468034	+	0.999989i	$0.501490\pi$
$877$	−22552.6	+	39062.3i	−0.868356	+	1.50404i	−0.863676	+	0.504048i	$0.831844\pi$
$878$		0			0
$879$	11669.2	−	9296.59i	0.447774	−	0.356731i
$880$		0			0
$881$	35020.2			1.33923			0.669614	−	0.742709i	$-0.266460\pi$
$881$	35020.2			1.33923			0.669614	+	0.742709i	$0.266460\pi$
$882$		0			0
$883$	2478.66			0.0944659			0.0472329	−	0.998884i	$-0.484960\pi$
$883$	2478.66			0.0944659			0.0472329	+	0.998884i	$0.484960\pi$
$884$		0			0
$885$	7028.60	+	46786.7i	0.266965	+	1.77708i
$886$		0			0
$887$	−6036.32	+	10455.2i	−0.228500	+	0.395774i	−0.957364	−	0.288885i	$-0.906716\pi$
$887$	−6036.32	+	10455.2i	−0.228500	+	0.395774i	0.728863	+	0.684659i	$0.240049\pi$
$888$		0			0
$889$	8707.01	+	15081.0i	0.328486	+	0.568954i
$890$		0			0
$891$	22373.1	−	15189.8i	0.841219	−	0.571130i
$892$		0			0
$893$	−19286.9	−	33405.9i	−0.722745	−	1.25183i
$894$		0			0
$895$	2208.19	−	3824.70i	0.0824712	−	0.142844i
$896$		0			0
$897$	−3349.00	−	22293.0i	−0.124660	−	0.829811i
$898$		0			0
$899$	39072.6			1.44955
$900$		0			0
$901$	12820.0			0.474026
$902$		0			0
$903$	21.7626	−	17.3377i	0.000802009	−	0.000638941i
$904$		0			0
$905$	−6772.06	+	11729.5i	−0.248741	+	0.430832i
$906$		0			0
$907$	23844.1	+	41299.1i	0.872909	+	1.51192i	0.858973	+	0.512020i	$0.171103\pi$
$907$	23844.1	+	41299.1i	0.872909	+	1.51192i	0.0139361	+	0.999903i	$0.495564\pi$
$908$		0			0
$909$	422.127	−	1841.17i	0.0154027	−	0.0671813i
$910$		0			0
$911$	−2878.94	−	4986.47i	−0.104702	−	0.181349i	0.808914	−	0.587926i	$-0.200056\pi$
$911$	−2878.94	−	4986.47i	−0.104702	−	0.181349i	−0.913616	+	0.406577i	$0.866722\pi$
$912$		0			0
$913$	20936.7	−	36263.5i	0.758932	−	1.31451i
$914$		0			0
$915$	−7205.96	−	2832.19i	−0.260351	−	0.102327i
$916$		0			0
$917$	19935.7			0.717923
$918$		0			0
$919$	17169.9			0.616303			0.308151	−	0.951337i	$-0.400290\pi$
$919$	17169.9			0.616303			0.308151	+	0.951337i	$0.400290\pi$
$920$		0			0
$921$	40497.2	+	15916.8i	1.44889	+	0.569464i
$922$		0			0
$923$	5966.48	−	10334.2i	0.212772	−	0.368533i
$924$		0			0
$925$	−13403.1	−	23214.8i	−0.476422	−	0.825187i
$926$		0			0
$927$	−24313.5	+	7473.75i	−0.861447	+	0.264800i
$928$		0			0
$929$	16772.7	+	29051.2i	0.592353	+	1.02599i	0.993915	+	0.110153i	$0.0351342\pi$
$929$	16772.7	+	29051.2i	0.592353	+	1.02599i	−0.401562	+	0.915832i	$0.631533\pi$
$930$		0			0
$931$	−10516.2	+	18214.7i	−0.370200	+	0.641205i
$932$		0			0
$933$	29021.9	−	23121.0i	1.01836	−	0.811306i
$934$		0			0
$935$	−9468.62			−0.331184
$936$		0			0
$937$	−32857.8			−1.14559			−0.572795	−	0.819698i	$-0.694141\pi$
$937$	−32857.8			−1.14559			−0.572795	+	0.819698i	$0.694141\pi$
$938$		0			0
$939$	−623.156	−	4148.11i	−0.0216570	−	0.144162i
$940$		0			0
$941$	16761.3	−	29031.4i	0.580662	−	1.00574i	−0.414740	−	0.909940i	$-0.636127\pi$
$941$	16761.3	−	29031.4i	0.580662	−	1.00574i	0.995401	−	0.0957952i	$-0.0305394\pi$
$942$		0			0
$943$	−2686.88	−	4653.82i	−0.0927857	−	0.160710i
$944$		0			0
$945$	−7990.88	−	16655.6i	−0.275072	−	0.573340i
$946$		0			0
$947$	5471.83	+	9477.49i	0.187762	+	0.325213i	0.944504	−	0.328501i	$-0.106543\pi$
$947$	5471.83	+	9477.49i	0.187762	+	0.325213i	−0.756742	+	0.653714i	$0.773210\pi$
$948$		0			0
$949$	−17021.7	+	29482.5i	−0.582243	+	1.00847i
$950$		0			0
$951$	1315.63	+	8757.61i	0.0448602	+	0.298617i
$952$		0			0
$953$	−1723.29			−0.0585758			−0.0292879	−	0.999571i	$-0.509324\pi$
$953$	−1723.29			−0.0585758			−0.0292879	+	0.999571i	$0.509324\pi$
$954$		0			0
$955$	−28665.2			−0.971293
$956$		0			0
$957$	−27139.6	+	21621.4i	−0.916717	+	0.730326i
$958$		0			0
$959$	1662.25	−	2879.11i	0.0559718	−	0.0969461i
$960$		0			0
$961$	−8658.59	−	14997.1i	−0.290645	−	0.503411i
$962$		0			0
$963$	26623.6	+	24751.5i	0.890897	+	0.828252i
$964$		0			0
$965$	−22306.1	−	38635.3i	−0.744102	−	1.28882i
$966$		0			0
$967$	−11942.6	+	20685.2i	−0.397154	+	0.687891i	−0.993374	−	0.114930i	$-0.963336\pi$
$967$	−11942.6	+	20685.2i	−0.397154	+	0.687891i	0.596219	+	0.802822i	$0.296669\pi$
$968$		0			0
$969$	−6489.96	−	2550.78i	−0.215158	−	0.0845643i
$970$		0			0
$971$	10239.1			0.338402			0.169201	−	0.985582i	$-0.445881\pi$
$971$	10239.1			0.338402			0.169201	+	0.985582i	$0.445881\pi$
$972$		0			0
$973$	21111.3			0.695576
$974$		0			0
$975$	−18325.5	−	7202.55i	−0.601934	−	0.236581i
$976$		0			0
$977$	19674.8	−	34077.7i	0.644269	−	1.11591i	−0.340200	−	0.940353i	$-0.610495\pi$
$977$	19674.8	−	34077.7i	0.644269	−	1.11591i	0.984470	−	0.175554i	$-0.0561718\pi$
$978$		0			0
$979$	6105.71	+	10575.4i	0.199325	+	0.345241i
$980$		0			0
$981$	12458.1	+	11582.1i	0.405462	+	0.376951i
$982$		0			0
$983$	7589.28	+	13145.0i	0.246247	+	0.426511i	0.962481	−	0.271348i	$-0.0874694\pi$
$983$	7589.28	+	13145.0i	0.246247	+	0.426511i	−0.716235	+	0.697859i	$0.754136\pi$
$984$		0			0
$985$	−14265.7	+	24709.0i	−0.461466	+	0.799282i
$986$		0			0
$987$	17387.3	−	13852.0i	0.560733	−	0.446722i
$988$		0			0
$989$	70.5317			0.00226772
$990$		0			0
$991$	9427.97			0.302209			0.151105	−	0.988518i	$-0.451717\pi$
$991$	9427.97			0.302209			0.151105	+	0.988518i	$0.451717\pi$
$992$		0			0
$993$	3794.78	+	25260.4i	0.121273	+	0.807266i
$994$		0			0
$995$	−15207.1	+	26339.5i	−0.484521	+	0.839214i
$996$		0			0
$997$	−9806.10	−	16984.7i	−0.311497	−	0.539528i	0.667190	−	0.744888i	$-0.267497\pi$
$997$	−9806.10	−	16984.7i	−0.311497	−	0.539528i	−0.978687	+	0.205360i	$0.934164\pi$
$998$		0			0
$999$	16137.3	+	33635.3i	0.511072	+	1.06524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.4.i.c.193.8	yes	16
3.2	odd	2		864.4.i.c.577.1		16
4.3	odd	2	inner	288.4.i.c.193.1	yes	16
9.2	odd	6		864.4.i.c.289.1		16
9.7	even	3	inner	288.4.i.c.97.8	yes	16
12.11	even	2		864.4.i.c.577.2		16
36.7	odd	6	inner	288.4.i.c.97.1	✓	16
36.11	even	6		864.4.i.c.289.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.4.i.c.97.1	✓	16	36.7	odd	6	inner
288.4.i.c.97.8	yes	16	9.7	even	3	inner
288.4.i.c.193.1	yes	16	4.3	odd	2	inner
288.4.i.c.193.8	yes	16	1.1	even	1	trivial
864.4.i.c.289.1		16	9.2	odd	6
864.4.i.c.289.2		16	36.11	even	6
864.4.i.c.577.1		16	3.2	odd	2
864.4.i.c.577.2		16	12.11	even	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	288.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.83603 + 1.90073i) q^{3} +(7.51347 - 13.0137i) q^{5} +(-4.38125 - 7.58855i) q^{7} +(19.7745 + 18.3840i) q^{9} +O(q^{10})\)	\(q+(4.83603 + 1.90073i) q^{3} +(7.51347 - 13.0137i) q^{5} +(-4.38125 - 7.58855i) q^{7} +(19.7745 + 18.3840i) q^{9} +(-18.5475 - 32.1252i) q^{11} +(18.7948 - 32.5535i) q^{13} +(61.0710 - 48.6537i) q^{15} +16.9864 q^{17} -79.0046 q^{19} +(-6.76411 - 45.0260i) q^{21} +(57.7079 - 99.9531i) q^{23} +(-50.4045 - 87.3032i) q^{25} +(60.6870 + 126.491i) q^{27} +(-90.0106 - 155.903i) q^{29} +(-108.522 + 187.966i) q^{31} +(-28.6350 - 190.612i) q^{33} -131.674 q^{35} +265.910 q^{37} +(152.767 - 121.706i) q^{39} +(23.2800 - 40.3222i) q^{41} +(0.305555 + 0.529236i) q^{43} +(387.819 - 119.212i) q^{45} +(244.124 + 422.835i) q^{47} +(133.109 - 230.552i) q^{49} +(82.1467 + 32.2865i) q^{51} +754.726 q^{53} -557.425 q^{55} +(-382.069 - 150.166i) q^{57} +(-302.960 + 524.743i) q^{59} +(-49.5794 - 85.8741i) q^{61} +(52.8708 - 230.604i) q^{63} +(-282.428 - 489.179i) q^{65} +(506.923 - 878.016i) q^{67} +(469.061 - 373.689i) q^{69} +317.454 q^{71} -905.663 q^{73} +(-77.8184 - 518.007i) q^{75} +(-162.522 + 281.497i) q^{77} +(-345.376 - 598.209i) q^{79} +(53.0587 + 727.067i) q^{81} +(564.408 + 977.584i) q^{83} +(127.627 - 221.056i) q^{85} +(-138.965 - 925.038i) q^{87} -329.193 q^{89} -329.378 q^{91} +(-882.089 + 702.738i) q^{93} +(-593.599 + 1028.14i) q^{95} +(606.171 + 1049.92i) q^{97} +(223.822 - 976.236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{5} - 6 q^{9}+O(q^{10}) \) 16 * q - 10 * q^5 - 6 * q^9	\( 16 q - 10 q^{5} - 6 q^{9} + 78 q^{13} - 188 q^{17} + 66 q^{21} - 238 q^{25} - 314 q^{29} - 336 q^{33} - 320 q^{37} + 368 q^{41} + 402 q^{45} + 14 q^{49} + 112 q^{53} - 1146 q^{57} + 482 q^{61} + 846 q^{65} - 642 q^{69} - 3204 q^{73} + 822 q^{77} + 954 q^{81} + 3248 q^{85} - 3832 q^{89} - 1602 q^{93} + 3864 q^{97}+O(q^{100}) \) 16 * q - 10 * q^5 - 6 * q^9 + 78 * q^13 - 188 * q^17 + 66 * q^21 - 238 * q^25 - 314 * q^29 - 336 * q^33 - 320 * q^37 + 368 * q^41 + 402 * q^45 + 14 * q^49 + 112 * q^53 - 1146 * q^57 + 482 * q^61 + 846 * q^65 - 642 * q^69 - 3204 * q^73 + 822 * q^77 + 954 * q^81 + 3248 * q^85 - 3832 * q^89 - 1602 * q^93 + 3864 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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