LMFDB - Embedded newform 147.4.c.a.146.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, 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:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 $ x^12 - x^11 - 29x^9 + 6x^8 - 49x^7 + 1564x^6 - 441x^5 + 486x^4 - 21141x^3 - 59049x + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.5
Root			$-2.23014 + 2.00661i$ of defining polynomial
Character	$\chi$	$=$	147.146
Dual form			147.4.c.a.146.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90883i q^{2} +(-5.08298 - 1.07856i) q^{3} +4.35636 q^{4} +1.24741 q^{5} +(-2.05878 + 9.70256i) q^{6} -23.5862i q^{8} +(24.6734 + 10.9646i) q^{9} +O(q^{10})$	\(q-1.90883i q^{2} +(-5.08298 - 1.07856i) q^{3} +4.35636 q^{4} +1.24741 q^{5} +(-2.05878 + 9.70256i) q^{6} -23.5862i q^{8} +(24.6734 + 10.9646i) q^{9} -2.38110i q^{10} -40.6907i q^{11} +(-22.1433 - 4.69858i) q^{12} -19.5973i q^{13} +(-6.34057 - 1.34540i) q^{15} -10.1712 q^{16} -104.718 q^{17} +(20.9295 - 47.0974i) q^{18} -40.4544i q^{19} +5.43418 q^{20} -77.6716 q^{22} +80.4045i q^{23} +(-25.4391 + 119.888i) q^{24} -123.444 q^{25} -37.4079 q^{26} +(-113.589 - 82.3444i) q^{27} -211.712i q^{29} +(-2.56815 + 12.1031i) q^{30} -100.025i q^{31} -169.275i q^{32} +(-43.8872 + 206.830i) q^{33} +199.890i q^{34} +(107.486 + 47.7656i) q^{36} -189.975 q^{37} -77.2206 q^{38} +(-21.1368 + 99.6127i) q^{39} -29.4217i q^{40} +186.753 q^{41} +158.618 q^{43} -177.263i q^{44} +(30.7779 + 13.6773i) q^{45} +153.479 q^{46} +358.069 q^{47} +(51.6999 + 10.9702i) q^{48} +235.634i q^{50} +(532.282 + 112.945i) q^{51} -85.3729i q^{52} +423.152i q^{53} +(-157.182 + 216.822i) q^{54} -50.7580i q^{55} +(-43.6323 + 205.629i) q^{57} -404.123 q^{58} +625.562 q^{59} +(-27.6218 - 5.86106i) q^{60} -807.799i q^{61} -190.931 q^{62} -404.486 q^{64} -24.4459i q^{65} +(394.804 + 83.7732i) q^{66} +298.544 q^{67} -456.192 q^{68} +(86.7208 - 408.695i) q^{69} +455.386i q^{71} +(258.613 - 581.953i) q^{72} -501.679i q^{73} +362.630i q^{74} +(627.464 + 133.141i) q^{75} -176.234i q^{76} +(190.144 + 40.3465i) q^{78} -61.9122 q^{79} -12.6876 q^{80} +(488.557 + 541.067i) q^{81} -356.479i q^{82} +73.1180 q^{83} -130.627 q^{85} -302.775i q^{86} +(-228.343 + 1076.13i) q^{87} -959.739 q^{88} +114.745 q^{89} +(26.1077 - 58.7498i) q^{90} +350.271i q^{92} +(-107.883 + 508.425i) q^{93} -683.493i q^{94} -50.4633i q^{95} +(-182.572 + 860.420i) q^{96} +1416.51i q^{97} +(446.156 - 1003.98i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 28 q^{4} + 6 q^{9}+O(q^{10}) $ 12 * q - 28 * q^4 + 6 * q^9	$ 12 q - 28 q^{4} + 6 q^{9} + 6 q^{15} - 268 q^{16} - 132 q^{18} - 268 q^{22} + 84 q^{25} + 1644 q^{30} + 852 q^{36} - 1528 q^{37} + 852 q^{39} - 1012 q^{43} - 1216 q^{46} + 2682 q^{51} + 270 q^{57} - 5740 q^{58} + 1836 q^{60} - 548 q^{64} - 1584 q^{67} + 5424 q^{72} + 4296 q^{78} - 3348 q^{79} - 1674 q^{81} + 348 q^{85} + 1108 q^{88} + 2958 q^{93} - 3354 q^{99}+O(q^{100}) $ 12 * q - 28 * q^4 + 6 * q^9 + 6 * q^15 - 268 * q^16 - 132 * q^18 - 268 * q^22 + 84 * q^25 + 1644 * q^30 + 852 * q^36 - 1528 * q^37 + 852 * q^39 - 1012 * q^43 - 1216 * q^46 + 2682 * q^51 + 270 * q^57 - 5740 * q^58 + 1836 * q^60 - 548 * q^64 - 1584 * q^67 + 5424 * q^72 + 4296 * q^78 - 3348 * q^79 - 1674 * q^81 + 348 * q^85 + 1108 * q^88 + 2958 * q^93 - 3354 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.90883i		−	0.674874i	−0.941348	−	0.337437i	$-0.890440\pi$
$2$		−	1.90883i		−	0.674874i	0.941348	−	0.337437i	$-0.109560\pi$
$3$	−5.08298	−	1.07856i	−0.978221	−	0.207568i
$3$	−5.08298	−	1.07856i	−0.978221	−	0.207568i
$4$	4.35636			0.544546
$5$	1.24741			0.111572			0.0557859	−	0.998443i	$-0.482234\pi$
$5$	1.24741			0.111572			0.0557859	+	0.998443i	$0.482234\pi$
$6$	−2.05878	+	9.70256i	−0.140082	+	0.660175i
$7$		0			0
$7$		0			0
$8$		−	23.5862i		−	1.04237i
$9$	24.6734	+	10.9646i	0.913831	+	0.406095i
$10$		−	2.38110i		−	0.0752969i
$11$		−	40.6907i		−	1.11534i	−0.830064	−	0.557668i	$-0.811696\pi$
$11$		−	40.6907i		−	1.11534i	0.830064	−	0.557668i	$-0.188304\pi$
$12$	−22.1433	−	4.69858i	−0.532686	−	0.113030i
$13$		−	19.5973i		−	0.418101i	−0.977905	−	0.209050i	$-0.932963\pi$
$13$		−	19.5973i		−	0.418101i	0.977905	−	0.209050i	$-0.0670373\pi$
$14$		0			0
$15$	−6.34057	−	1.34540i	−0.109142	−	0.0231588i
$16$	−10.1712			−0.158925
$17$	−104.718			−1.49400			−0.746999	−	0.664825i	$-0.768506\pi$
$17$	−104.718			−1.49400			−0.746999	+	0.664825i	$0.768506\pi$
$18$	20.9295	−	47.0974i	0.274063	−	0.616720i
$19$		−	40.4544i		−	0.488467i	−0.969716	−	0.244234i	$-0.921464\pi$
$19$		−	40.4544i		−	0.488467i	0.969716	−	0.244234i	$-0.0785364\pi$
$20$	5.43418			0.0607559
$21$		0			0
$22$	−77.6716			−0.752711
$23$			80.4045i			0.728935i	0.931216	+	0.364467i	$0.118749\pi$
$23$			80.4045i			0.728935i	−0.931216	+	0.364467i	$0.881251\pi$
$24$	−25.4391	+	119.888i	−0.216364	+	1.01967i
$25$	−123.444			−0.987552
$26$	−37.4079			−0.282165
$27$	−113.589	−	82.3444i	−0.809636	−	0.586933i
$28$		0			0
$29$		−	211.712i		−	1.35565i	−0.735222	−	0.677827i	$-0.762922\pi$
$29$		−	211.712i		−	1.35565i	0.735222	−	0.677827i	$-0.237078\pi$
$30$	−2.56815	+	12.1031i	−0.0156292	+	0.0736570i
$31$		−	100.025i		−	0.579517i	−0.957100	−	0.289758i	$-0.906425\pi$
$31$		−	100.025i		−	0.579517i	0.957100	−	0.289758i	$-0.0935749\pi$
$32$		−	169.275i		−	0.935119i
$33$	−43.8872	+	206.830i	−0.231508	+	1.09105i
$34$			199.890i			1.00826i
$35$		0			0
$36$	107.486	+	47.7656i	0.497622	+	0.221137i
$37$	−189.975			−0.844100			−0.422050	−	0.906572i	$-0.638689\pi$
$37$	−189.975			−0.844100			−0.422050	+	0.906572i	$0.638689\pi$
$38$	−77.2206			−0.329654
$39$	−21.1368	+	99.6127i	−0.0867844	+	0.408995i
$40$		−	29.4217i		−	0.116299i
$41$	186.753			0.711362			0.355681	−	0.934607i	$-0.384249\pi$
$41$	186.753			0.711362			0.355681	+	0.934607i	$0.384249\pi$
$42$		0			0
$43$	158.618			0.562536			0.281268	−	0.959629i	$-0.409245\pi$
$43$	158.618			0.562536			0.281268	+	0.959629i	$0.409245\pi$
$44$		−	177.263i		−	0.607352i
$45$	30.7779	+	13.6773i	0.101958	+	0.0453088i
$46$	153.479			0.491939
$47$	358.069			1.11127			0.555635	−	0.831426i	$-0.312475\pi$
$47$	358.069			1.11127			0.555635	+	0.831426i	$0.312475\pi$
$48$	51.6999	+	10.9702i	0.155463	+	0.0329877i
$49$		0			0
$50$			235.634i			0.666473i
$51$	532.282	+	112.945i	1.46146	+	0.310106i
$52$		−	85.3729i		−	0.227675i
$53$			423.152i			1.09669i	0.836254	+	0.548343i	$0.184741\pi$
$53$			423.152i			1.09669i	−0.836254	+	0.548343i	$0.815259\pi$
$54$	−157.182	+	216.822i	−0.396105	+	0.546402i
$55$		−	50.7580i		−	0.124440i
$56$		0			0
$57$	−43.6323	+	205.629i	−0.101390	+	0.477829i
$58$	−404.123			−0.914895
$59$	625.562			1.38036			0.690180	−	0.723638i	$-0.257531\pi$
$59$	625.562			1.38036			0.690180	+	0.723638i	$0.257531\pi$
$60$	−27.6218	−	5.86106i	−0.0594327	−	0.0126110i
$61$		−	807.799i		−	1.69554i	−0.530362	−	0.847772i	$-0.677944\pi$
$61$		−	807.799i		−	1.69554i	0.530362	−	0.847772i	$-0.322056\pi$
$62$	−190.931			−0.391101
$63$		0			0
$64$	−404.486			−0.790012
$65$		−	24.4459i		−	0.0466483i
$66$	394.804	+	83.7732i	0.736318	+	0.156239i
$67$	298.544			0.544373			0.272187	−	0.962245i	$-0.412253\pi$
$67$	298.544			0.544373			0.272187	+	0.962245i	$0.412253\pi$
$68$	−456.192			−0.813550
$69$	86.7208	−	408.695i	0.151304	−	0.713059i
$70$		0			0
$71$			455.386i			0.761189i	0.924742	+	0.380594i	$0.124281\pi$
$71$			455.386i			0.761189i	−0.924742	+	0.380594i	$0.875719\pi$
$72$	258.613	−	581.953i	0.423302	−	0.952553i
$73$		−	501.679i		−	0.804344i	−0.915564	−	0.402172i	$-0.868255\pi$
$73$		−	501.679i		−	0.804344i	0.915564	−	0.402172i	$-0.131745\pi$
$74$			362.630i			0.569661i
$75$	627.464	+	133.141i	0.966043	+	0.204984i
$76$		−	176.234i		−	0.265993i
$77$		0			0
$78$	190.144	+	40.3465i	0.276020	+	0.0585685i
$79$	−61.9122			−0.0881731			−0.0440865	−	0.999028i	$-0.514038\pi$
$79$	−61.9122			−0.0881731			−0.0440865	+	0.999028i	$0.514038\pi$
$80$	−12.6876			−0.0177315
$81$	488.557	+	541.067i	0.670174	+	0.742204i
$82$		−	356.479i		−	0.480080i
$83$	73.1180			0.0966957			0.0483478	−	0.998831i	$-0.484604\pi$
$83$	73.1180			0.0966957			0.0483478	+	0.998831i	$0.484604\pi$
$84$		0			0
$85$	−130.627			−0.166688
$86$		−	302.775i		−	0.379641i
$87$	−228.343	+	1076.13i	−0.281391	+	1.32613i
$88$	−959.739			−1.16260
$89$	114.745			0.136662			0.0683309	−	0.997663i	$-0.478233\pi$
$89$	114.745			0.136662			0.0683309	+	0.997663i	$0.478233\pi$
$90$	26.1077	−	58.7498i	0.0305777	−	0.0688086i
$91$		0			0
$92$			350.271i			0.396938i
$93$	−107.883	+	508.425i	−0.120289	+	0.566895i
$94$		−	683.493i		−	0.749967i
$95$		−	50.4633i		−	0.0544992i
$96$	−182.572	+	860.420i	−0.194101	+	0.914753i
$97$			1416.51i			1.48273i	0.671101	+	0.741366i	$0.265822\pi$
$97$			1416.51i			1.48273i	−0.671101	+	0.741366i	$0.734178\pi$
$98$		0			0
$99$	446.156	−	1003.98i	0.452933	−	1.01923i
$100$	−537.767			−0.537767
$101$	240.811			0.237244			0.118622	−	0.992940i	$-0.462152\pi$
$101$	240.811			0.237244			0.118622	+	0.992940i	$0.462152\pi$
$102$	215.592	−	1016.04i	0.209283	−	0.986300i
$103$			1109.04i			1.06094i	0.847705	+	0.530469i	$0.177984\pi$
$103$			1109.04i			1.06094i	−0.847705	+	0.530469i	$0.822016\pi$
$104$	−462.226			−0.435817
$105$		0			0
$106$	807.725			0.740124
$107$			1067.69i			0.964646i	0.875993	+	0.482323i	$0.160207\pi$
$107$			1067.69i			0.964646i	−0.875993	+	0.482323i	$0.839793\pi$
$108$	−494.834	−	358.722i	−0.440883	−	0.319612i
$109$	10.0875			0.00886430			0.00443215	−	0.999990i	$-0.498589\pi$
$109$	10.0875			0.00886430			0.00443215	+	0.999990i	$0.498589\pi$
$110$	−96.8885			−0.0839814
$111$	965.640	+	204.899i	0.825716	+	0.175208i
$112$		0			0
$113$		−	884.294i		−	0.736171i	−0.929792	−	0.368086i	$-0.880013\pi$
$113$		−	884.294i		−	0.736171i	0.929792	−	0.368086i	$-0.119987\pi$
$114$	392.511	+	83.2868i	0.322474	+	0.0684256i
$115$			100.297i			0.0813286i
$116$		−	922.295i		−	0.738215i
$117$	214.876	−	483.532i	0.169789	−	0.382073i
$118$		−	1194.09i		−	0.931569i
$119$		0			0
$120$	−31.7330	+	149.550i	−0.0241401	+	0.113767i
$121$	−324.732			−0.243976
$122$	−1541.95			−1.14428
$123$	−949.260	−	201.423i	−0.695869	−	0.147656i
$124$		−	435.745i		−	0.315573i
$125$	−309.912			−0.221755
$126$		0			0
$127$	−840.132			−0.587005			−0.293503	−	0.955958i	$-0.594821\pi$
$127$	−840.132			−0.587005			−0.293503	+	0.955958i	$0.594821\pi$
$128$		−	582.101i		−	0.401961i
$129$	−806.254	−	171.079i	−0.550284	−	0.116765i
$130$	−46.6631			−0.0314817
$131$	−517.902			−0.345415			−0.172707	−	0.984973i	$-0.555252\pi$
$131$	−517.902			−0.345415			−0.172707	+	0.984973i	$0.555252\pi$
$132$	−191.189	+	901.027i	−0.126067	+	0.594124i
$133$		0			0
$134$		−	569.871i		−	0.367383i
$135$	−141.692	−	102.717i	−0.0903325	−	0.0654852i
$136$			2469.91i			1.55730i
$137$		−	1098.07i		−	0.684777i	−0.939558	−	0.342389i	$-0.888764\pi$
$137$		−	1098.07i		−	0.684777i	0.939558	−	0.342389i	$-0.111236\pi$
$138$	−780.129	−	165.535i	−0.481225	−	0.102111i
$139$		−	828.268i		−	0.505416i	−0.967543	−	0.252708i	$-0.918679\pi$
$139$		−	828.268i		−	0.505416i	0.967543	−	0.252708i	$-0.0813212\pi$
$140$		0			0
$141$	−1820.06	−	386.197i	−1.08707	−	0.230664i
$142$	869.255			0.513706
$143$	−797.427			−0.466323
$144$	−250.958	−	111.523i	−0.145230	−	0.0645385i
$145$		−	264.092i		−	0.151253i
$146$	−957.621			−0.542830
$147$		0			0
$148$	−827.601			−0.459651
$149$			892.592i			0.490765i	0.969426	+	0.245382i	$0.0789135\pi$
$149$			892.592i			0.490765i	−0.969426	+	0.245382i	$0.921086\pi$
$150$	254.144	−	1197.72i	0.138339	−	0.651957i
$151$	1425.04			0.767999			0.383999	−	0.923333i	$-0.374546\pi$
$151$	1425.04			0.767999			0.383999	+	0.923333i	$0.374546\pi$
$152$	−954.166			−0.509165
$153$	−2583.76	−	1148.19i	−1.36526	−	0.606705i
$154$		0			0
$155$		−	124.772i		−	0.0646577i
$156$	−92.0795	+	433.949i	−0.0472581	+	0.222716i
$157$		−	282.754i		−	0.143734i	−0.997414	−	0.0718670i	$-0.977104\pi$
$157$		−	282.754i		−	0.143734i	0.997414	−	0.0718670i	$-0.0228957\pi$
$158$			118.180i			0.0595057i
$159$	456.393	−	2150.87i	0.227637	−	1.07280i
$160$		−	211.155i		−	0.104333i
$161$		0			0
$162$	1032.81	−	932.572i	0.500894	−	0.452283i
$163$	2316.13			1.11297			0.556484	−	0.830859i	$-0.312150\pi$
$163$	2316.13			1.11297			0.556484	+	0.830859i	$0.312150\pi$
$164$	813.562			0.387369
$165$	−54.7454	+	258.002i	−0.0258298	+	0.121730i
$166$		−	139.570i		−	0.0652574i
$167$	2344.70			1.08646			0.543229	−	0.839585i	$-0.317202\pi$
$167$	2344.70			1.08646			0.543229	+	0.839585i	$0.317202\pi$
$168$		0			0
$169$	1812.95			0.825192
$170$			249.345i			0.112493i
$171$	443.565	−	998.149i	0.198364	−	0.446376i
$172$	690.999			0.306327
$173$	1033.80			0.454326			0.227163	−	0.973857i	$-0.427055\pi$
$173$	1033.80			0.454326			0.227163	+	0.973857i	$0.427055\pi$
$174$	2054.15	+	435.869i	0.894969	+	0.189903i
$175$		0			0
$176$			413.872i			0.177255i
$177$	−3179.72	−	674.704i	−1.35030	−	0.286519i
$178$		−	219.028i		−	0.0922294i
$179$			144.882i			0.0604973i	0.999542	+	0.0302486i	$0.00962991\pi$
$179$			144.882i			0.0604973i	−0.999542	+	0.0302486i	$0.990370\pi$
$180$	134.080	+	59.5834i	0.0555207	+	0.0246727i
$181$			2057.17i			0.844797i	0.906410	+	0.422398i	$0.138812\pi$
$181$			2057.17i			0.844797i	−0.906410	+	0.422398i	$0.861188\pi$
$182$		0			0
$183$	−871.257	+	4106.03i	−0.351941	+	1.65862i
$184$	1896.44			0.759822
$185$	−236.977			−0.0941778
$186$	970.498	+	205.930i	0.382583	+	0.0811800i
$187$			4261.07i			1.66631i
$188$	1559.88			0.605137
$189$		0			0
$190$	−96.3259			−0.0367801
$191$		−	2948.72i		−	1.11708i	−0.829479	−	0.558538i	$-0.811362\pi$
$191$		−	2948.72i		−	1.11708i	0.829479	−	0.558538i	$-0.188638\pi$
$192$	2056.00	+	436.261i	0.772806	+	0.163981i
$193$	−2270.80			−0.846920			−0.423460	−	0.905915i	$-0.639185\pi$
$193$	−2270.80			−0.846920			−0.423460	+	0.905915i	$0.639185\pi$
$194$	2703.88			1.00066
$195$	−26.3662	+	124.258i	−0.00968270	+	0.0456323i
$196$		0			0
$197$		−	495.849i		−	0.179329i	−0.995972	−	0.0896645i	$-0.971421\pi$
$197$		−	495.849i		−	0.179329i	0.995972	−	0.0896645i	$-0.0285795\pi$
$198$	−1916.43	−	851.636i	−0.687851	−	0.305672i
$199$			839.706i			0.299121i	0.988753	+	0.149561i	$0.0477859\pi$
$199$			839.706i			0.299121i	−0.988753	+	0.149561i	$0.952214\pi$
$200$			2911.58i			1.02940i
$201$	−1517.50	−	321.997i	−0.532517	−	0.112995i
$202$		−	459.668i		−	0.160109i
$203$		0			0
$204$	2318.81	+	492.028i	0.795831	+	0.168867i
$205$	232.957			0.0793680
$206$	2116.96			0.715999
$207$	−881.601	+	1983.86i	−0.296017	+	0.666123i
$208$			199.328i			0.0664465i
$209$	−1646.12			−0.544805
$210$		0			0
$211$	4001.71			1.30564			0.652818	−	0.757514i	$-0.273586\pi$
$211$	4001.71			1.30564			0.652818	+	0.757514i	$0.273586\pi$
$212$			1843.40i			0.597195i
$213$	491.160	−	2314.72i	0.157999	−	0.744611i
$214$	2038.03			0.651014
$215$	197.862			0.0627632
$216$	−1942.19	+	2679.13i	−0.611803	+	0.843943i
$217$		0			0
$218$		−	19.2554i		−	0.00598228i
$219$	−541.089	+	2550.03i	−0.166956	+	0.786826i
$220$		−	221.120i		−	0.0677633i
$221$			2052.20i			0.624642i
$222$	391.117	−	1843.24i	0.118244	−	0.557254i
$223$		−	3040.54i		−	0.913047i	−0.889711	−	0.456523i	$-0.849095\pi$
$223$		−	3040.54i		−	0.913047i	0.889711	−	0.456523i	$-0.150905\pi$
$224$		0			0
$225$	−3045.79	−	1353.51i	−0.902455	−	0.401040i
$226$	−1687.97			−0.496823
$227$	4396.47			1.28548			0.642741	−	0.766084i	$-0.277797\pi$
$227$	4396.47			1.28548			0.642741	+	0.766084i	$0.277797\pi$
$228$	−190.078	+	895.795i	−0.0552116	+	0.260199i
$229$			1983.56i			0.572389i	0.958172	+	0.286194i	$0.0923903\pi$
$229$			1983.56i			0.572389i	−0.958172	+	0.286194i	$0.907610\pi$
$230$	191.451			0.0548865
$231$		0			0
$232$	−4993.49			−1.41310
$233$		−	4373.75i		−	1.22976i	−0.788621	−	0.614879i	$-0.789205\pi$
$233$		−	4373.75i		−	1.22976i	0.788621	−	0.614879i	$-0.210795\pi$
$234$	−922.982	−	410.162i	−0.257851	−	0.114586i
$235$	446.659			0.123986
$236$	2725.18			0.751669
$237$	314.699	+	66.7758i	0.0862527	+	0.0183019i
$238$		0			0
$239$			3826.41i			1.03561i	0.855500	+	0.517803i	$0.173250\pi$
$239$			3826.41i			1.03561i	−0.855500	+	0.517803i	$0.826750\pi$
$240$	64.4911	+	13.6843i	0.0173453	+	0.00368050i
$241$			3439.89i			0.919430i	0.888066	+	0.459715i	$0.152048\pi$
$241$			3439.89i			0.919430i	−0.888066	+	0.459715i	$0.847952\pi$
$242$			619.858i			0.164653i
$243$	−1899.75	−	3277.17i	−0.501520	−	0.865146i
$244$		−	3519.07i		−	0.923300i
$245$		0			0
$246$	−384.483	+	1811.98i	−0.0996493	+	0.469624i
$247$	−792.797			−0.204229
$248$	−2359.21			−0.604073
$249$	−371.657	−	78.8618i	−0.0945897	−	0.0200709i
$250$			591.569i			0.149656i
$251$	2046.61			0.514664			0.257332	−	0.966323i	$-0.417157\pi$
$251$	2046.61			0.514664			0.257332	+	0.966323i	$0.417157\pi$
$252$		0			0
$253$	3271.72			0.813008
$254$			1603.67i			0.396154i
$255$	663.975	+	140.889i	0.163058	+	0.0345991i
$256$	−4347.02			−1.06128
$257$	−6051.14			−1.46871			−0.734357	−	0.678763i	$-0.762516\pi$
$257$	−6051.14			−1.46871			−0.734357	+	0.678763i	$0.762516\pi$
$258$	−326.560	+	1539.00i	−0.0788014	+	0.371372i
$259$		0			0
$260$		−	106.495i		−	0.0254021i
$261$	2321.33	−	5223.66i	0.550524	−	1.23884i
$262$			988.588i			0.233111i
$263$		−	6274.28i		−	1.47106i	−0.677492	−	0.735530i	$-0.736933\pi$
$263$		−	6274.28i		−	1.47106i	0.677492	−	0.735530i	$-0.263067\pi$
$264$	4878.34	+	1035.13i	1.13728	+	0.241318i
$265$			527.844i			0.122359i
$266$		0			0
$267$	−583.245	−	123.758i	−0.133685	−	0.0283666i
$268$	1300.57			0.296436
$269$	−3336.35			−0.756212			−0.378106	−	0.925762i	$-0.623425\pi$
$269$	−3336.35			−0.756212			−0.378106	+	0.925762i	$0.623425\pi$
$270$	−196.070	+	270.466i	−0.0441942	+	0.0609631i
$271$		−	2843.17i		−	0.637308i	−0.947871	−	0.318654i	$-0.896769\pi$
$271$		−	2843.17i		−	0.637308i	0.947871	−	0.318654i	$-0.103231\pi$
$272$	1065.11			0.237433
$273$		0			0
$274$	−2096.03			−0.462138
$275$			5023.02i			1.10145i
$276$	377.787	−	1780.42i	0.0823918	−	0.388293i
$277$	6348.34			1.37702			0.688510	−	0.725226i	$-0.258265\pi$
$277$	6348.34			1.37702			0.688510	+	0.725226i	$0.258265\pi$
$278$	−1581.02			−0.341092
$279$	1096.73	−	2467.96i	0.235339	−	0.529580i
$280$		0			0
$281$		−	3735.88i		−	0.793110i	−0.918011	−	0.396555i	$-0.870206\pi$
$281$		−	3735.88i		−	0.793110i	0.918011	−	0.396555i	$-0.129794\pi$
$282$	−737.185	+	3474.18i	−0.155669	+	0.733633i
$283$		−	5517.12i		−	1.15886i	−0.815021	−	0.579432i	$-0.803274\pi$
$283$		−	5517.12i		−	1.15886i	0.815021	−	0.579432i	$-0.196726\pi$
$284$			1983.83i			0.414502i
$285$	−54.4275	+	256.504i	−0.0113123	+	0.0533122i
$286$			1522.15i			0.314709i
$287$		0			0
$288$	1856.02	−	4176.59i	0.379747	−	0.854541i
$289$	6052.96			1.23203
$290$	−504.107			−0.102077
$291$	1527.79	−	7200.11i	0.307768	−	1.45044i
$292$		−	2185.50i		−	0.438002i
$293$	−7574.50			−1.51026			−0.755131	−	0.655574i	$-0.772427\pi$
$293$	−7574.50			−1.51026			−0.755131	+	0.655574i	$0.772427\pi$
$294$		0			0
$295$	780.333			0.154009
$296$			4480.79i			0.879868i
$297$	−3350.65	+	4622.00i	−0.654628	+	0.903016i
$298$	1703.81			0.331204
$299$	1575.71			0.304768
$300$	2733.46	+	580.012i	0.526055	+	0.111623i
$301$		0			0
$302$		−	2720.15i		−	0.518302i
$303$	−1224.04	−	259.728i	−0.232077	−	0.0492442i
$304$			411.469i			0.0776295i
$305$		−	1007.66i		−	0.189175i
$306$	−2191.71	+	4931.97i	−0.409449	+	0.921379i
$307$			10635.6i			1.97723i	0.150480	+	0.988613i	$0.451918\pi$
$307$			10635.6i			1.97723i	−0.150480	+	0.988613i	$0.548082\pi$
$308$		0			0
$309$	1196.16	−	5637.21i	0.220217	−	1.03783i
$310$	−238.169			−0.0436358
$311$	−5771.19			−1.05226			−0.526132	−	0.850403i	$-0.676358\pi$
$311$	−5771.19			−1.05226			−0.526132	+	0.850403i	$0.676358\pi$
$312$	2349.49	+	498.536i	0.426325	+	0.0904618i
$313$			2344.52i			0.423387i	0.977336	+	0.211694i	$0.0678979\pi$
$313$			2344.52i			0.423387i	−0.977336	+	0.211694i	$0.932102\pi$
$314$	−539.730			−0.0970023
$315$		0			0
$316$	−269.712			−0.0480142
$317$		−	7912.13i		−	1.40186i	−0.713231	−	0.700929i	$-0.752769\pi$
$317$		−	7912.13i		−	1.40186i	0.713231	−	0.700929i	$-0.247231\pi$
$318$	−4105.65	−	871.177i	−0.724005	−	0.153626i
$319$	−8614.71			−1.51201
$320$	−504.560			−0.0881431
$321$	1151.56	−	5427.03i	0.200230	−	0.943637i
$322$		0			0
$323$			4236.32i			0.729769i
$324$	2128.33	+	2357.08i	0.364940	+	0.404164i
$325$			2419.17i			0.412896i
$326$		−	4421.11i		−	0.751112i
$327$	−51.2747	−	10.8800i	−0.00867124	−	0.00183995i
$328$		−	4404.78i		−	0.741505i
$329$		0			0
$330$	492.482	+	104.500i	0.0821523	+	0.0174319i
$331$	−4880.03			−0.810365			−0.405182	−	0.914236i	$-0.632792\pi$
$331$	−4880.03			−0.810365			−0.405182	+	0.914236i	$0.632792\pi$
$332$	318.528			0.0526552
$333$	−4687.34	−	2082.99i	−0.771365	−	0.342785i
$334$		−	4475.64i		−	0.733222i
$335$	372.407			0.0607367
$336$		0			0
$337$	−4136.39			−0.668616			−0.334308	−	0.942464i	$-0.608503\pi$
$337$	−4136.39			−0.668616			−0.334308	+	0.942464i	$0.608503\pi$
$338$		−	3460.61i		−	0.556900i
$339$	−953.760	+	4494.85i	−0.152806	+	0.720138i
$340$	−569.059			−0.0907692
$341$	−4070.09			−0.646356
$342$	−1905.30	−	846.691i	−0.301248	−	0.133871i
$343$		0			0
$344$		−	3741.20i		−	0.586373i
$345$	108.176	−	509.810i	0.0168812	−	0.0795573i
$346$		−	1973.35i		−	0.306613i
$347$		−	2320.76i		−	0.359034i	−0.983755	−	0.179517i	$-0.942547\pi$
$347$		−	2320.76i		−	0.359034i	0.983755	−	0.179517i	$-0.0574535\pi$
$348$	−994.747	+	4688.01i	−0.153230	+	0.722137i
$349$			226.795i			0.0347853i	0.999849	+	0.0173926i	$0.00553653\pi$
$349$			226.795i			0.0347853i	−0.999849	+	0.0173926i	$0.994463\pi$
$350$		0			0
$351$	−1613.73	+	2226.03i	−0.245397	+	0.338509i
$352$	−6887.90			−1.04297
$353$	1485.71			0.224012			0.112006	−	0.993708i	$-0.464272\pi$
$353$	1485.71			0.224012			0.112006	+	0.993708i	$0.464272\pi$
$354$	−1287.90	+	6069.55i	−0.193364	+	0.911280i
$355$			568.054i			0.0849272i
$356$	499.869			0.0744185
$357$		0			0
$358$	276.556			0.0408280
$359$			10877.2i			1.59910i	0.600599	+	0.799550i	$0.294929\pi$
$359$			10877.2i			1.59910i	−0.600599	+	0.799550i	$0.705071\pi$
$360$	322.596	−	725.934i	0.0472286	−	0.106278i
$361$	5222.44			0.761400
$362$	3926.79			0.570131
$363$	1650.61	+	350.241i	0.238662	+	0.0506416i
$364$		0			0
$365$		−	625.800i		−	0.0897421i
$366$	7837.72	+	1663.08i	1.11936	+	0.237516i
$367$		−	3810.15i		−	0.541930i	−0.962589	−	0.270965i	$-0.912657\pi$
$367$		−	3810.15i		−	0.541930i	0.962589	−	0.270965i	$-0.0873428\pi$
$368$		−	817.809i		−	0.115846i
$369$	4607.83	+	2047.66i	0.650065	+	0.288881i
$370$			452.349i			0.0635581i
$371$		0			0
$372$	−469.976	+	2214.89i	−0.0655030	+	0.308700i
$373$	−9739.09			−1.35193			−0.675967	−	0.736932i	$-0.736274\pi$
$373$	−9739.09			−1.35193			−0.675967	+	0.736932i	$0.736274\pi$
$374$	8133.66			1.12455
$375$	1575.28	+	334.257i	0.216925	+	0.0460292i
$376$		−	8445.48i		−	1.15836i
$377$	−4148.98			−0.566800
$378$		0			0
$379$	320.171			0.0433933			0.0216967	−	0.999765i	$-0.493093\pi$
$379$	320.171			0.0433933			0.0216967	+	0.999765i	$0.493093\pi$
$380$		−	219.836i		−	0.0296773i
$381$	4270.38	+	906.129i	0.574220	+	0.121844i
$382$	−5628.60			−0.753886
$383$	−4370.26			−0.583054			−0.291527	−	0.956563i	$-0.594163\pi$
$383$	−4370.26			−0.583054			−0.291527	+	0.956563i	$0.594163\pi$
$384$	−627.829	+	2958.81i	−0.0834343	+	0.393206i
$385$		0			0
$386$			4334.57i			0.571564i
$387$	3913.66	+	1739.18i	0.514063	+	0.228443i
$388$			6170.84i			0.807415i
$389$			13714.8i			1.78758i	0.448483	+	0.893791i	$0.351964\pi$
$389$			13714.8i			1.78758i	−0.448483	+	0.893791i	$0.648036\pi$
$390$	237.187	+	50.3287i	0.0307960	+	0.00653460i
$391$		−	8419.84i		−	1.08903i
$392$		0			0
$393$	2632.49	+	558.587i	0.337892	+	0.0716971i
$394$	−946.493			−0.121024
$395$	−77.2300			−0.00983763
$396$	1943.62	−	4373.70i	0.246642	−	0.555017i
$397$			2519.10i			0.318464i	0.987241	+	0.159232i	$0.0509018\pi$
$397$			2519.10i			0.318464i	−0.987241	+	0.159232i	$0.949098\pi$
$398$	1602.86			0.201869
$399$		0			0
$400$	1255.57			0.156946
$401$		−	2619.97i		−	0.326272i	−0.986604	−	0.163136i	$-0.947839\pi$
$401$		−	2619.97i		−	0.326272i	0.986604	−	0.163136i	$-0.0521609\pi$
$402$	−614.637	+	2896.64i	−0.0762570	+	0.359382i
$403$	−1960.22			−0.242296
$404$	1049.06			0.129190
$405$	609.431	+	674.933i	0.0747725	+	0.0828091i
$406$		0			0
$407$			7730.22i			0.941456i
$408$	2663.94	−	12554.5i	0.323247	−	1.52339i
$409$		−	13924.2i		−	1.68339i	−0.539954	−	0.841694i	$-0.681558\pi$
$409$		−	13924.2i		−	1.68339i	0.539954	−	0.841694i	$-0.318442\pi$
$410$		−	444.676i		−	0.0535634i
$411$	−1184.33	+	5581.47i	−0.142138	+	0.669863i
$412$			4831.36i			0.577729i
$413$		0			0
$414$	3786.85	+	1682.83i	0.449549	+	0.199774i
$415$	91.2082			0.0107885
$416$	−3317.32			−0.390974
$417$	−893.334	+	4210.07i	−0.104908	+	0.494408i
$418$			3142.16i			0.367675i
$419$	15171.1			1.76887			0.884433	−	0.466666i	$-0.154545\pi$
$419$	15171.1			1.76887			0.884433	+	0.466666i	$0.154545\pi$
$420$		0			0
$421$	−1052.53			−0.121846			−0.0609228	−	0.998142i	$-0.519404\pi$
$421$	−1052.53			−0.121846			−0.0609228	+	0.998142i	$0.519404\pi$
$422$		−	7638.60i		−	0.881140i
$423$	8834.78	+	3926.07i	1.01551	+	0.451281i
$424$	9980.54			1.14316
$425$	12926.9			1.47540
$426$	−4418.41	−	937.541i	−0.502518	−	0.106629i
$427$		0			0
$428$			4651.23i			0.525294i
$429$	4053.31	+	860.070i	0.456167	+	0.0967939i
$430$		−	377.685i		−	0.0423572i
$431$			7994.67i			0.893479i	0.894664	+	0.446740i	$0.147415\pi$
$431$			7994.67i			0.893479i	−0.894664	+	0.446740i	$0.852585\pi$
$432$	1155.33	+	837.540i	0.128671	+	0.0932781i
$433$			12889.4i			1.43055i	0.698845	+	0.715273i	$0.253697\pi$
$433$			12889.4i			1.43055i	−0.698845	+	0.715273i	$0.746303\pi$
$434$		0			0
$435$	−284.838	+	1342.38i	−0.0313953	+	0.147959i
$436$	43.9449			0.00482701
$437$	3252.72			0.356061
$438$	4867.57	+	1032.85i	0.531008	+	0.112674i
$439$		−	14383.8i		−	1.56378i	−0.623415	−	0.781891i	$-0.714255\pi$
$439$		−	14383.8i		−	1.56378i	0.623415	−	0.781891i	$-0.285745\pi$
$440$	−1197.19			−0.129713
$441$		0			0
$442$	3917.30			0.421554
$443$		−	3963.12i		−	0.425042i	−0.977157	−	0.212521i	$-0.931833\pi$
$443$		−	3963.12i		−	0.425042i	0.977157	−	0.212521i	$-0.0681674\pi$
$444$	4206.68	+	892.614i	0.449640	+	0.0954089i
$445$	143.134			0.0152476
$446$	−5803.87			−0.616191
$447$	962.710	−	4537.03i	0.101867	−	0.480076i
$448$		0			0
$449$		−	13479.1i		−	1.41675i	−0.705838	−	0.708373i	$-0.749430\pi$
$449$		−	13479.1i		−	1.41675i	0.705838	−	0.708373i	$-0.250570\pi$
$450$	−2583.62	+	5813.89i	−0.270651	+	0.609043i
$451$		−	7599.09i		−	0.793408i
$452$		−	3852.31i		−	0.400879i
$453$	−7243.44	−	1536.98i	−0.751272	−	0.159412i
$454$		−	8392.13i		−	0.867538i
$455$		0			0
$456$	4850.01	+	1029.12i	0.498076	+	0.105686i
$457$	3979.58			0.407346			0.203673	−	0.979039i	$-0.434712\pi$
$457$	3979.58			0.407346			0.203673	+	0.979039i	$0.434712\pi$
$458$	3786.27			0.386290
$459$	11894.8	+	8622.98i	1.20959	+	0.876876i
$460$			436.932i			0.0442871i
$461$	−9053.72			−0.914694			−0.457347	−	0.889288i	$-0.651200\pi$
$461$	−9053.72			−0.914694			−0.457347	+	0.889288i	$0.651200\pi$
$462$		0			0
$463$	−5736.10			−0.575764			−0.287882	−	0.957666i	$-0.592951\pi$
$463$	−5736.10			−0.575764			−0.287882	+	0.957666i	$0.592951\pi$
$464$			2153.36i			0.215447i
$465$	−134.574	+	634.215i	−0.0134209	+	0.0632495i
$466$	−8348.75			−0.829932
$467$	12392.6			1.22797			0.613984	−	0.789318i	$-0.289566\pi$
$467$	12392.6			1.22797			0.613984	+	0.789318i	$0.289566\pi$
$468$	936.077	−	2106.44i	0.0924576	−	0.208056i
$469$		0			0
$470$		−	852.596i		−	0.0836752i
$471$	−304.966	+	1437.23i	−0.0298346	+	0.140604i
$472$		−	14754.6i		−	1.43885i
$473$		−	6454.28i		−	0.627417i
$474$	127.464	−	600.707i	0.0123515	−	0.0582097i
$475$			4993.85i			0.482387i
$476$		0			0
$477$	−4639.67	+	10440.6i	−0.445359	+	1.00219i
$478$	7303.97			0.698903
$479$	8267.73			0.788648			0.394324	−	0.918972i	$-0.370979\pi$
$479$	8267.73			0.788648			0.394324	+	0.918972i	$0.370979\pi$
$480$	−227.743	+	1073.30i	−0.0216562	+	0.102061i
$481$			3723.00i			0.352919i
$482$	6566.17			0.620499
$483$		0			0
$484$	−1414.65			−0.132856
$485$			1766.97i			0.165431i
$486$	−6255.56	+	3626.31i	−0.583864	+	0.338462i
$487$	940.150			0.0874790			0.0437395	−	0.999043i	$-0.486073\pi$
$487$	940.150			0.0874790			0.0437395	+	0.999043i	$0.486073\pi$
$488$	−19052.9			−1.76739
$489$	−11772.9	−	2498.08i	−1.08873	−	0.231017i
$490$		0			0
$491$			1057.30i			0.0971801i	0.998819	+	0.0485900i	$0.0154728\pi$
$491$			1057.30i			0.0971801i	−0.998819	+	0.0485900i	$0.984527\pi$
$492$	−4135.32	−	877.472i	−0.378932	−	0.0804055i
$493$			22170.2i			2.02534i
$494$			1513.32i			0.137828i
$495$	556.539	−	1252.37i	0.0505345	−	0.113717i
$496$			1017.37i			0.0920995i
$497$		0			0
$498$	−150.534	+	709.431i	−0.0135454	+	0.0638361i
$499$	−6173.30			−0.553817			−0.276909	−	0.960896i	$-0.589310\pi$
$499$	−6173.30			−0.553817			−0.276909	+	0.960896i	$0.589310\pi$
$500$	−1350.09			−0.120756
$501$	−11918.1	−	2528.89i	−1.06280	−	0.225514i
$502$		−	3906.63i		−	0.347333i
$503$	4284.28			0.379775			0.189887	−	0.981806i	$-0.439188\pi$
$503$	4284.28			0.379775			0.189887	+	0.981806i	$0.439188\pi$
$504$		0			0
$505$	300.390			0.0264697
$506$		−	6245.15i		−	0.548678i
$507$	−9215.17	−	1955.36i	−0.807219	−	0.171284i
$508$	−3659.92			−0.319651
$509$	15101.0			1.31501			0.657507	−	0.753449i	$-0.271611\pi$
$509$	15101.0			1.31501			0.657507	+	0.753449i	$0.271611\pi$
$510$	268.932	−	1267.42i	0.0233500	−	0.110043i
$511$		0			0
$512$			3640.92i			0.314272i
$513$	−3331.19	+	4595.17i	−0.286697	+	0.395481i
$514$			11550.6i			0.991197i
$515$			1383.42i			0.118371i
$516$	−3512.34	−	745.281i	−0.299655	−	0.0635837i
$517$		−	14570.1i		−	1.23944i
$518$		0			0
$519$	−5254.79	−	1115.01i	−0.444431	−	0.0943037i
$520$	−576.586			−0.0486249
$521$	−13788.0			−1.15943			−0.579715	−	0.814819i	$-0.696836\pi$
$521$	−13788.0			−1.15943			−0.579715	+	0.814819i	$0.696836\pi$
$522$	−9971.09	−	4431.03i	−0.836059	−	0.371534i
$523$			961.304i			0.0803726i	0.999192	+	0.0401863i	$0.0127951\pi$
$523$			961.304i			0.0803726i	−0.999192	+	0.0401863i	$0.987205\pi$
$524$	−2256.17			−0.188094
$525$		0			0
$526$	−11976.5			−0.992780
$527$			10474.5i			0.865797i
$528$	446.384	−	2103.71i	0.0367924	−	0.173394i
$529$	5702.11			0.468654
$530$	1007.57			0.0825770
$531$	15434.8	+	6859.02i	1.26142	+	0.560557i
$532$		0			0
$533$		−	3659.84i		−	0.297421i
$534$	−236.234	+	1113.32i	−0.0191439	+	0.0902207i
$535$			1331.84i			0.107627i
$536$		−	7041.53i		−	0.567440i
$537$	156.264	−	736.434i	0.0125573	−	0.0591797i
$538$			6368.54i			0.510348i
$539$		0			0
$540$	−617.261	−	447.474i	−0.0491902	−	0.0356596i
$541$	−1195.69			−0.0950218			−0.0475109	−	0.998871i	$-0.515129\pi$
$541$	−1195.69			−0.0950218			−0.0475109	+	0.998871i	$0.515129\pi$
$542$	−5427.14			−0.430102
$543$	2218.77	−	10456.6i	0.175353	−	0.826397i
$544$			17726.2i			1.39707i
$545$	12.5833			0.000989006
$546$		0			0
$547$	18601.8			1.45403			0.727014	−	0.686622i	$-0.240907\pi$
$547$	18601.8			1.45403			0.727014	+	0.686622i	$0.240907\pi$
$548$		−	4783.59i		−	0.372892i
$549$	8857.17	−	19931.2i	0.688552	−	1.54944i
$550$	9588.10			0.743341
$551$	−8564.69			−0.662192
$552$	−9639.56	−	2045.41i	−0.743274	−	0.157715i
$553$		0			0
$554$		−	12117.9i		−	0.929315i
$555$	1204.55	+	255.593i	0.0921267	+	0.0195483i
$556$		−	3608.24i		−	0.275222i
$557$		−	6822.07i		−	0.518959i	−0.965749	−	0.259480i	$-0.916449\pi$
$557$		−	6822.07i		−	0.518959i	0.965749	−	0.259480i	$-0.0835511\pi$
$558$	−4710.92	−	2093.47i	−0.357400	−	0.158824i
$559$		−	3108.49i		−	0.235197i
$560$		0			0
$561$	4595.80	−	21658.9i	0.345873	−	1.63002i
$562$	−7131.16			−0.535249
$563$	−11359.6			−0.850356			−0.425178	−	0.905110i	$-0.639789\pi$
$563$	−11359.6			−0.850356			−0.425178	+	0.905110i	$0.639789\pi$
$564$	−7928.83	−	1682.42i	−0.591957	−	0.125607i
$565$		−	1103.08i		−	0.0821360i
$566$	−10531.2			−0.782087
$567$		0			0
$568$	10740.8			0.793443
$569$			21324.1i			1.57110i	0.618800	+	0.785549i	$0.287619\pi$
$569$			21324.1i			1.57110i	−0.618800	+	0.785549i	$0.712381\pi$
$570$	489.623	+	103.893i	0.0359790	+	0.00763437i
$571$	−14768.0			−1.08235			−0.541175	−	0.840910i	$-0.682020\pi$
$571$	−14768.0			−1.08235			−0.541175	+	0.840910i	$0.682020\pi$
$572$	−3473.88			−0.253934
$573$	−3180.36	+	14988.3i	−0.231870	+	1.09275i
$574$		0			0
$575$		−	9925.45i		−	0.719861i
$576$	−9980.06	−	4435.01i	−0.721937	−	0.320820i
$577$			19304.9i			1.39285i	0.717631	+	0.696424i	$0.245227\pi$
$577$			19304.9i			1.39285i	−0.717631	+	0.696424i	$0.754773\pi$
$578$		−	11554.1i		−	0.831464i
$579$	11542.4	+	2449.18i	0.828475	+	0.175794i
$580$		−	1150.48i		−	0.0823640i
$581$		0			0
$582$	−13743.8	−	2916.29i	−0.978863	−	0.207705i
$583$	17218.3			1.22317
$584$	−11832.7			−0.838426
$585$	268.038	−	603.164i	0.0189436	−	0.0426286i
$586$			14458.4i			1.01924i
$587$	−4397.46			−0.309204			−0.154602	−	0.987977i	$-0.549410\pi$
$587$	−4397.46			−0.309204			−0.154602	+	0.987977i	$0.549410\pi$
$588$		0			0
$589$	−4046.45			−0.283075
$590$		−	1489.52i		−	0.103937i
$591$	−534.801	+	2520.39i	−0.0372230	+	0.175423i
$592$	1932.27			0.134148
$593$	−21940.2			−1.51935			−0.759677	−	0.650301i	$-0.774643\pi$
$593$	−21940.2			−1.51935			−0.759677	+	0.650301i	$0.774643\pi$
$594$	8822.62	+	6395.82i	0.609422	+	0.441791i
$595$		0			0
$596$			3888.46i			0.267244i
$597$	905.670	−	4268.21i	0.0620881	−	0.292607i
$598$		−	3007.77i		−	0.205680i
$599$			5502.23i			0.375317i	0.982234	+	0.187659i	$0.0600899\pi$
$599$			5502.23i			0.375317i	−0.982234	+	0.187659i	$0.939910\pi$
$600$	3140.30	−	14799.5i	0.213670	−	1.00698i
$601$			5814.58i			0.394645i	0.980339	+	0.197322i	$0.0632246\pi$
$601$			5814.58i			0.394645i	−0.980339	+	0.197322i	$0.936775\pi$
$602$		0			0
$603$	7366.11	+	3273.41i	0.497465	+	0.221067i
$604$	6207.98			0.418210
$605$	−405.074			−0.0272208
$606$	−495.777	+	2336.48i	−0.0332336	+	0.156622i
$607$			13291.4i			0.888765i	0.895837	+	0.444382i	$0.146577\pi$
$607$			13291.4i			0.888765i	−0.895837	+	0.444382i	$0.853423\pi$
$608$	−6847.90			−0.456775
$609$		0			0
$610$	−1923.45			−0.127669
$611$		−	7017.18i		−	0.464623i
$612$	−11255.8	−	5001.94i	−0.743447	−	0.330378i
$613$	19594.3			1.29104			0.645520	−	0.763743i	$-0.276641\pi$
$613$	19594.3			1.29104			0.645520	+	0.763743i	$0.276641\pi$
$614$	20301.7			1.33438
$615$	−1184.12	−	251.257i	−0.0776394	−	0.0164743i
$616$		0			0
$617$			348.388i			0.0227319i	0.999935	+	0.0113660i	$0.00361797\pi$
$617$			348.388i			0.0227319i	−0.999935	+	0.0113660i	$0.996382\pi$
$618$	−10760.5	−	2283.26i	−0.700405	−	0.148619i
$619$			6775.41i			0.439946i	0.975506	+	0.219973i	$0.0705970\pi$
$619$			6775.41i			0.439946i	−0.975506	+	0.219973i	$0.929403\pi$
$620$		−	543.553i		−	0.0352091i
$621$	6620.86	−	9133.05i	0.427836	−	0.590172i
$622$			11016.2i			0.710145i
$623$		0			0
$624$	214.986	−	1013.18i	0.0137922	−	0.0649994i
$625$	15043.9			0.962810
$626$	4475.29			0.285733
$627$	8367.19	+	1775.43i	0.532940	+	0.113084i
$628$		−	1231.78i		−	0.0782697i
$629$	19893.9			1.26108
$630$		0			0
$631$	−7326.82			−0.462244			−0.231122	−	0.972925i	$-0.574240\pi$
$631$	−7326.82			−0.462244			−0.231122	+	0.972925i	$0.574240\pi$
$632$			1460.28i			0.0919092i
$633$	−20340.6	−	4316.07i	−1.27720	−	0.271009i
$634$	−15102.9			−0.946078
$635$	−1047.99			−0.0654932
$636$	1988.21	−	9369.98i	0.123959	−	0.584189i
$637$		0			0
$638$			16444.0i			1.02042i
$639$	−4993.11	+	11235.9i	−0.309115	+	0.695598i
$640$		−	726.120i		−	0.0448475i
$641$			2809.82i			0.173138i	0.996246	+	0.0865689i	$0.0275903\pi$
$641$			2809.82i			0.173138i	−0.996246	+	0.0865689i	$0.972410\pi$
$642$	−10359.3	−	2198.13i	−0.636836	−	0.135130i
$643$		−	27485.5i		−	1.68573i	−0.538128	−	0.842863i	$-0.680868\pi$
$643$		−	27485.5i		−	1.68573i	0.538128	−	0.842863i	$-0.319132\pi$
$644$		0			0
$645$	−1005.73	−	213.405i	−0.0613962	−	0.0130276i
$646$	8086.43			0.492502
$647$	29319.8			1.78158			0.890790	−	0.454416i	$-0.150152\pi$
$647$	29319.8			1.78158			0.890790	+	0.454416i	$0.150152\pi$
$648$	12761.7	−	11523.2i	0.773654	−	0.698571i
$649$		−	25454.5i		−	1.53957i
$650$	4617.78			0.278653
$651$		0			0
$652$	10089.9			0.606061
$653$		−	16743.8i		−	1.00343i	−0.865034	−	0.501713i	$-0.832704\pi$
$653$		−	16743.8i		−	1.00343i	0.865034	−	0.501713i	$-0.167296\pi$
$654$	−20.7680	+	97.8747i	−0.00124173	+	0.00585199i
$655$	−646.037			−0.0385386
$656$	−1899.49			−0.113053
$657$	5500.69	−	12378.1i	0.326640	−	0.735034i
$658$		0			0
$659$			9520.47i			0.562769i	0.959595	+	0.281385i	$0.0907937\pi$
$659$			9520.47i			0.562769i	−0.959595	+	0.281385i	$0.909206\pi$
$660$	−238.491	+	1123.95i	−0.0140655	+	0.0662875i
$661$		−	23345.1i		−	1.37371i	−0.726797	−	0.686853i	$-0.758992\pi$
$661$		−	23345.1i		−	1.37371i	0.726797	−	0.686853i	$-0.241008\pi$
$662$			9315.16i			0.546894i
$663$	2213.41	−	10431.3i	0.129656	−	0.611037i
$664$		−	1724.58i		−	0.100793i
$665$		0			0
$666$	−3976.08	+	8947.34i	−0.231337	+	0.520574i
$667$	17022.6			0.988183
$668$	10214.4			0.591626
$669$	−3279.39	+	15455.0i	−0.189519	+	0.893161i
$670$		−	710.863i		−	0.0409896i
$671$	−32869.9			−1.89110
$672$		0			0
$673$	−12283.5			−0.703559			−0.351780	−	0.936083i	$-0.614423\pi$
$673$	−12283.5			−0.703559			−0.351780	+	0.936083i	$0.614423\pi$
$674$			7895.67i			0.451231i
$675$	14021.8	+	10164.9i	0.799557	+	0.579626i
$676$	7897.85			0.449354
$677$	−12991.8			−0.737538			−0.368769	−	0.929521i	$-0.620221\pi$
$677$	−12991.8			−0.737538			−0.368769	+	0.929521i	$0.620221\pi$
$678$	8579.91	+	1820.57i	0.486002	+	0.103125i
$679$		0			0
$680$			3081.00i			0.173751i
$681$	−22347.2	−	4741.84i	−1.25748	−	0.266825i
$682$			7769.11i			0.436209i
$683$		−	8506.24i		−	0.476548i	−0.971198	−	0.238274i	$-0.923418\pi$
$683$		−	8506.24i		−	0.476548i	0.971198	−	0.238274i	$-0.0765816\pi$
$684$	1932.33	−	4348.30i	0.108018	−	0.243072i
$685$		−	1369.74i		−	0.0764018i
$686$		0			0
$687$	2139.38	−	10082.4i	0.118810	−	0.559923i
$688$	−1613.33			−0.0894009
$689$	8292.63			0.458525
$690$	−973.142	−	206.491i	−0.0536911	−	0.0113927i
$691$			25832.9i			1.42219i	0.703097	+	0.711093i	$0.251800\pi$
$691$			25832.9i			1.42219i	−0.703097	+	0.711093i	$0.748200\pi$
$692$	4503.61			0.247401
$693$		0			0
$694$	−4429.93			−0.242303
$695$		−	1033.19i		−	0.0563902i
$696$	25381.8	+	5385.76i	1.38232	+	0.293314i
$697$	−19556.4			−1.06277
$698$	432.913			0.0234757
$699$	−4717.33	+	22231.7i	−0.255259	+	1.20298i
$700$		0			0
$701$			22607.8i			1.21810i	0.793134	+	0.609048i	$0.208448\pi$
$701$			22607.8i			1.21810i	−0.793134	+	0.609048i	$0.791552\pi$
$702$	4249.12	+	3080.33i	0.228451	+	0.165612i
$703$			7685.33i			0.412315i
$704$			16458.8i			0.881129i
$705$	−2270.36	−	481.747i	−0.121286	−	0.0257356i
$706$		−	2835.96i		−	0.151180i
$707$		0			0
$708$	−13852.0	−	2939.26i	−0.735298	−	0.156023i
$709$	−10944.8			−0.579748			−0.289874	−	0.957065i	$-0.593613\pi$
$709$	−10944.8			−0.579748			−0.289874	+	0.957065i	$0.593613\pi$
$710$	1084.32			0.0573152
$711$	−1527.59	−	678.841i	−0.0805753	−	0.0358066i
$712$		−	2706.39i		−	0.142453i
$713$	8042.46			0.422430
$714$		0			0
$715$	−994.720			−0.0520285
$716$			631.160i			0.0329435i
$717$	4127.00	−	19449.6i	0.214959	−	1.01305i
$718$	20762.8			1.07919
$719$	25770.5			1.33669			0.668344	−	0.743852i	$-0.267003\pi$
$719$	25770.5			1.33669			0.668344	+	0.743852i	$0.267003\pi$
$720$	−313.048	−	139.114i	−0.0162036	−	0.00720068i
$721$		0			0
$722$		−	9968.76i		−	0.513849i
$723$	3710.11	−	17484.9i	0.190844	−	0.899405i
$724$			8961.78i			0.460030i
$725$			26134.6i			1.33878i
$726$	668.552	−	3150.73i	0.0341767	−	0.161067i
$727$		−	15593.1i		−	0.795485i	−0.917497	−	0.397742i	$-0.869794\pi$
$727$		−	15593.1i		−	0.795485i	0.917497	−	0.397742i	$-0.130206\pi$
$728$		0			0
$729$	6121.81	+	18706.8i	0.311020	+	0.950403i
$730$	−1194.55			−0.0605646
$731$	−16610.3			−0.840428
$732$	−3795.51	+	17887.4i	−0.191648	+	0.903191i
$733$		−	800.044i		−	0.0403142i	−0.999797	−	0.0201571i	$-0.993583\pi$
$733$		−	800.044i		−	0.0403142i	0.999797	−	0.0201571i	$-0.00641664\pi$
$734$	−7272.94			−0.365734
$735$		0			0
$736$	13610.4			0.681641
$737$		−	12148.0i		−	0.607159i
$738$	3908.64	−	8795.56i	0.194958	−	0.438712i
$739$	−908.890			−0.0452423			−0.0226211	−	0.999744i	$-0.507201\pi$
$739$	−908.890			−0.0452423			−0.0226211	+	0.999744i	$0.507201\pi$
$740$	−1032.36			−0.0512841
$741$	4029.77	+	855.076i	0.199781	+	0.0423914i
$742$		0			0
$743$			8109.00i			0.400391i	0.979756	+	0.200195i	$0.0641577\pi$
$743$			8109.00i			0.400391i	−0.979756	+	0.200195i	$0.935842\pi$
$744$	11991.8	+	2544.54i	0.590916	+	0.125386i
$745$			1113.43i			0.0547555i
$746$			18590.3i			0.912384i
$747$	1804.07	+	801.707i	0.0883635	+	0.0392676i
$748$			18562.8i			0.907382i
$749$		0			0
$750$	638.041	−	3006.94i	0.0310639	−	0.146397i
$751$	−20764.4			−1.00893			−0.504463	−	0.863433i	$-0.668310\pi$
$751$	−20764.4			−1.00893			−0.504463	+	0.863433i	$0.668310\pi$
$752$	−3641.98			−0.176608
$753$	−10402.9	−	2207.38i	−0.503455	−	0.106828i
$754$			7919.71i			0.382518i
$755$	1777.61			0.0856870
$756$		0			0
$757$	23295.6			1.11848			0.559242	−	0.829005i	$-0.311092\pi$
$757$	23295.6			1.11848			0.559242	+	0.829005i	$0.311092\pi$
$758$		−	611.152i		−	0.0292850i
$759$	−16630.1	−	3528.73i	−0.795301	−	0.168755i
$760$	−1190.24			−0.0568085
$761$	10028.8			0.477717			0.238858	−	0.971054i	$-0.423227\pi$
$761$	10028.8			0.477717			0.238858	+	0.971054i	$0.423227\pi$
$762$	1729.65	−	8151.43i	0.0822290	−	0.387526i
$763$		0			0
$764$		−	12845.7i		−	0.608299i
$765$	−3223.02	−	1432.27i	−0.152325	−	0.0676912i
$766$			8342.08i			0.393488i
$767$		−	12259.3i		−	0.577130i
$768$	22095.8	+	4688.51i	1.03817	+	0.220289i
$769$			13500.3i			0.633074i	0.948580	+	0.316537i	$0.102520\pi$
$769$			13500.3i			0.633074i	−0.948580	+	0.316537i	$0.897480\pi$
$770$		0			0
$771$	30757.8	+	6526.49i	1.43673	+	0.304858i
$772$	−9892.42			−0.461187
$773$	23289.7			1.08367			0.541833	−	0.840486i	$-0.317731\pi$
$773$	23289.7			1.08367			0.541833	+	0.840486i	$0.317731\pi$
$774$	3319.80	−	7470.51i	0.154170	−	0.346928i
$775$			12347.5i			0.572303i
$776$	33410.2			1.54556
$777$		0			0
$778$	26179.3			1.20639
$779$		−	7554.96i		−	0.347477i
$780$	−114.861	+	541.313i	−0.00527267	+	0.0248489i
$781$	18530.0			0.848982
$782$	−16072.0			−0.734956
$783$	−17433.3	+	24048.1i	−0.795677	+	1.09759i
$784$		0			0
$785$		−	352.711i		−	0.0160367i
$786$	1066.25	−	5024.98i	0.0483865	−	0.228034i
$787$		−	23827.7i		−	1.07924i	−0.841907	−	0.539622i	$-0.818567\pi$
$787$		−	23827.7i		−	1.07924i	0.841907	−	0.539622i	$-0.181433\pi$
$788$		−	2160.10i		−	0.0976528i
$789$	−6767.16	+	31892.1i	−0.305345	+	1.43902i
$790$			147.419i			0.00663916i
$791$		0			0
$792$	−23680.1	−	10523.1i	−1.06242	−	0.472125i
$793$	−15830.7			−0.708908
$794$	4808.54			0.214923
$795$	569.309	−	2683.02i	0.0253979	−	0.119694i
$796$			3658.06i			0.162885i
$797$	12609.3			0.560406			0.280203	−	0.959941i	$-0.409598\pi$
$797$	12609.3			0.560406			0.280203	+	0.959941i	$0.409598\pi$
$798$		0			0
$799$	−37496.4			−1.66023
$800$			20895.9i			0.923478i
$801$	2831.14	+	1258.12i	0.124886	+	0.0554977i
$802$	−5001.08			−0.220192
$803$	−20413.7			−0.897114
$804$	−6610.76	−	1402.74i	−0.289980	−	0.0615307i
$805$		0			0
$806$			3741.73i			0.163519i
$807$	16958.6	+	3598.44i	0.739742	+	0.156966i
$808$		−	5679.82i		−	0.247296i
$809$		−	34966.0i		−	1.51958i	−0.650169	−	0.759789i	$-0.725302\pi$
$809$		−	34966.0i		−	1.51958i	0.650169	−	0.759789i	$-0.274698\pi$
$810$	1288.33	−	1163.30i	0.0558857	−	0.0504620i
$811$		−	5691.42i		−	0.246428i	−0.992380	−	0.123214i	$-0.960680\pi$
$811$		−	5691.42i		−	0.246428i	0.992380	−	0.123214i	$-0.0393201\pi$
$812$		0			0
$813$	−3066.52	+	14451.8i	−0.132285	+	0.623428i
$814$	14755.7			0.635364
$815$	2889.17			0.124176
$816$	−5413.94	−	1148.78i	−0.232262	−	0.0492836i
$817$		−	6416.81i		−	0.274781i
$818$	−26578.9			−1.13607
$819$		0			0
$820$	1014.85			0.0432195
$821$			12109.4i			0.514764i	0.966310	+	0.257382i	$0.0828598\pi$
$821$			12109.4i			0.514764i	−0.966310	+	0.257382i	$0.917140\pi$
$822$	10654.1	+	2260.69i	0.452073	+	0.0959252i
$823$	−31721.9			−1.34357			−0.671784	−	0.740747i	$-0.734472\pi$
$823$	−31721.9			−1.34357			−0.671784	+	0.740747i	$0.734472\pi$
$824$	26158.0			1.10589
$825$	5417.61	−	25531.9i	0.228627	−	1.07746i
$826$		0			0
$827$		−	36401.9i		−	1.53061i	−0.643666	−	0.765307i	$-0.722587\pi$
$827$		−	36401.9i		−	1.53061i	0.643666	−	0.765307i	$-0.277413\pi$
$828$	−3840.57	+	8642.40i	−0.161195	+	0.362734i
$829$			31509.2i			1.32010i	0.751223	+	0.660049i	$0.229464\pi$
$829$			31509.2i			1.32010i	−0.751223	+	0.660049i	$0.770536\pi$
$830$		−	174.101i		−	0.00728088i
$831$	−32268.5	−	6847.04i	−1.34703	−	0.285826i
$832$			7926.83i			0.330305i
$833$		0			0
$834$	8036.32	+	1705.22i	0.333663	+	0.0707998i
$835$	2924.81			0.121218
$836$	−7171.09			−0.296671
$837$	−8236.50	+	11361.7i	−0.340137	+	0.469197i
$838$		−	28959.0i		−	1.19376i
$839$	13781.4			0.567090			0.283545	−	0.958959i	$-0.408490\pi$
$839$	13781.4			0.567090			0.283545	+	0.958959i	$0.408490\pi$
$840$		0			0
$841$	−20433.0			−0.837796
$842$			2009.10i			0.0822304i
$843$	−4029.35	+	18989.4i	−0.164624	+	0.775836i
$844$	17432.9			0.710979
$845$	2261.49			0.0920682
$846$	7494.20	−	16864.1i	0.304558	−	0.685343i
$847$		0			0
$848$		−	4303.95i		−	0.174290i
$849$	−5950.52	+	28043.4i	−0.240543	+	1.13362i
$850$		−	24675.2i		−	0.995709i
$851$		−	15274.9i		−	0.615294i
$852$	2139.67	−	10083.8i	0.0860374	−	0.405474i
$853$			11376.3i			0.456645i	0.973586	+	0.228322i	$0.0733240\pi$
$853$			11376.3i			0.456645i	−0.973586	+	0.228322i	$0.926676\pi$
$854$		0			0
$855$	553.308	−	1245.10i	0.0221318	−	0.0498030i
$856$	25182.7			1.00552
$857$	−43119.2			−1.71870			−0.859349	−	0.511390i	$-0.829131\pi$
$857$	−43119.2			−1.71870			−0.859349	+	0.511390i	$0.829131\pi$
$858$	1641.73	−	7737.08i	0.0653236	−	0.307855i
$859$		−	37326.7i		−	1.48262i	−0.671162	−	0.741311i	$-0.734204\pi$
$859$		−	37326.7i		−	1.48262i	0.671162	−	0.741311i	$-0.265796\pi$
$860$	861.960			0.0341774
$861$		0			0
$862$	15260.5			0.602986
$863$		−	34944.3i		−	1.37835i	−0.724594	−	0.689176i	$-0.757973\pi$
$863$		−	34944.3i		−	1.37835i	0.724594	−	0.689176i	$-0.242027\pi$
$864$	−13938.8	+	19227.7i	−0.548852	+	0.757106i
$865$	1289.58			0.0506900
$866$	24603.7			0.965437
$867$	−30767.1	−	6528.45i	−1.20520	−	0.255730i
$868$		0			0
$869$			2519.25i			0.0983426i
$870$	2562.37	+	543.708i	0.0998533	+	0.0211878i
$871$		−	5850.66i		−	0.227603i
$872$		−	237.926i		−	0.00923991i
$873$	−15531.4	+	34950.2i	−0.602130	+	1.35497i
$874$		−	6208.89i		−	0.240296i
$875$		0			0
$876$	−2357.18	+	11108.8i	−0.0909152	+	0.428462i
$877$	4109.19			0.158218			0.0791092	−	0.996866i	$-0.474792\pi$
$877$	4109.19			0.158218			0.0791092	+	0.996866i	$0.474792\pi$
$878$	−27456.2			−1.05536
$879$	38501.0	+	8169.52i	1.47737	+	0.313482i
$880$			516.269i			0.0197766i
$881$	−15697.6			−0.600301			−0.300151	−	0.953892i	$-0.597037\pi$
$881$	−15697.6			−0.600301			−0.300151	+	0.953892i	$0.597037\pi$
$882$		0			0
$883$	−44102.6			−1.68083			−0.840413	−	0.541946i	$-0.817688\pi$
$883$	−44102.6			−1.68083			−0.840413	+	0.541946i	$0.817688\pi$
$884$			8940.12i			0.340146i
$885$	−3966.42	−	841.633i	−0.150655	−	0.0319674i
$886$	−7564.93			−0.286850
$887$	−28328.9			−1.07237			−0.536185	−	0.844101i	$-0.680135\pi$
$887$	−28328.9			−1.07237			−0.536185	+	0.844101i	$0.680135\pi$
$888$	4832.79	−	22775.8i	0.182633	−	0.860704i
$889$		0			0
$890$		−	273.218i		−	0.0102902i
$891$	22016.4	−	19879.7i	0.827808	−	0.747469i
$892$		−	13245.7i		−	0.497195i
$893$		−	14485.5i		−	0.542819i
$894$	−8660.42	−	1837.65i	−0.323991	−	0.0687475i
$895$			180.728i			0.00674979i
$896$		0			0
$897$	−8009.31	−	1699.49i	−0.298131	−	0.0632602i
$898$	−25729.4			−0.956125
$899$	−21176.5			−0.785624
$900$	−13268.6	−	5896.38i	−0.491428	−	0.218384i
$901$		−	44311.8i		−	1.63845i
$902$	−14505.4			−0.535450
$903$		0			0
$904$	−20857.1			−0.767365
$905$			2566.14i			0.0942555i
$906$	−2933.84	+	13826.5i	−0.107583	+	0.507014i
$907$	14205.6			0.520054			0.260027	−	0.965601i	$-0.416269\pi$
$907$	14205.6			0.520054			0.260027	+	0.965601i	$0.416269\pi$
$908$	19152.6			0.700003
$909$	5941.64	+	2640.39i	0.216800	+	0.0963434i
$910$		0			0
$911$		−	17955.9i		−	0.653025i	−0.945193	−	0.326512i	$-0.894127\pi$
$911$		−	17955.9i		−	0.653025i	0.945193	−	0.326512i	$-0.105873\pi$
$912$	443.792	−	2091.49i	0.0161134	−	0.0759388i
$913$		−	2975.22i		−	0.107848i
$914$		−	7596.35i		−	0.274907i
$915$	−1086.82	+	5121.91i	−0.0392667	+	0.185055i
$916$			8641.09i			0.311692i
$917$		0			0
$918$	16459.8	−	22705.2i	0.591781	−	0.816323i
$919$	−42242.5			−1.51627			−0.758135	−	0.652097i	$-0.773889\pi$
$919$	−42242.5			−1.51627			−0.758135	+	0.652097i	$0.773889\pi$
$920$	2365.64			0.0847748
$921$	11471.1	−	54060.8i	0.410409	−	1.93416i
$922$			17282.0i			0.617303i
$923$	8924.34			0.318254
$924$		0			0
$925$	23451.3			0.833593
$926$			10949.2i			0.388568i
$927$	−12160.1	+	27363.7i	−0.430841	+	0.969517i
$928$	−35837.5			−1.26770
$929$	−44676.1			−1.57780			−0.788900	−	0.614522i	$-0.789349\pi$
$929$	−44676.1			−1.57780			−0.788900	+	0.614522i	$0.789349\pi$
$930$	1210.61	+	256.879i	0.0426854	+	0.00905741i
$931$		0			0
$932$		−	19053.6i		−	0.669660i
$933$	29334.8	+	6224.55i	1.02935	+	0.218416i
$934$		−	23655.4i		−	0.828724i
$935$			5315.30i			0.185913i
$936$	−11404.7	−	5068.11i	−0.398263	−	0.176983i
$937$			15309.3i			0.533761i	0.963730	+	0.266880i	$0.0859929\pi$
$937$			15309.3i			0.533761i	−0.963730	+	0.266880i	$0.914007\pi$
$938$		0			0
$939$	2528.70	−	11917.2i	0.0878817	−	0.414166i
$940$	1945.81			0.0675163
$941$	42384.4			1.46832			0.734162	−	0.678974i	$-0.237575\pi$
$941$	42384.4			1.46832			0.734162	+	0.678974i	$0.237575\pi$
$942$	2743.44	+	582.129i	0.0948897	+	0.0201346i
$943$			15015.7i			0.518537i
$944$	−6362.70			−0.219373
$945$		0			0
$946$	−12320.1			−0.423427
$947$			12295.4i			0.421908i	0.977496	+	0.210954i	$0.0676570\pi$
$947$			12295.4i			0.421908i	−0.977496	+	0.210954i	$0.932343\pi$
$948$	1370.94	+	290.900i	0.0469685	+	0.00996623i
$949$	−9831.55			−0.336297
$950$	9532.42			0.325550
$951$	−8533.67	+	40217.2i	−0.290981	+	1.37133i
$952$		0			0
$953$			1322.78i			0.0449621i	0.999747	+	0.0224811i	$0.00715655\pi$
$953$			1322.78i			0.0449621i	−0.999747	+	0.0224811i	$0.992843\pi$
$954$	19929.3	+	8856.35i	0.676349	+	0.300561i
$955$		−	3678.26i		−	0.124634i
$956$			16669.2i			0.563935i
$957$	43788.4	+	9291.45i	1.47908	+	0.313845i
$958$		−	15781.7i		−	0.532238i
$959$		0			0
$960$	2564.67	+	544.197i	0.0862234	+	0.0182957i
$961$	19786.0			0.664160
$962$	7106.57			0.238176
$963$	−11706.7	+	26343.5i	−0.391738	+	0.881524i
$964$			14985.4i			0.500672i
$965$	−2832.62			−0.0944925
$966$		0			0
$967$	36887.2			1.22669			0.613346	−	0.789814i	$-0.289823\pi$
$967$	36887.2			1.22669			0.613346	+	0.789814i	$0.289823\pi$
$968$			7659.19i			0.254314i
$969$	4569.11	−	21533.2i	0.151477	−	0.713875i
$970$	3372.85			0.111645
$971$	6819.58			0.225387			0.112693	−	0.993630i	$-0.464052\pi$
$971$	6819.58			0.225387			0.112693	+	0.993630i	$0.464052\pi$
$972$	−8276.02	−	14276.5i	−0.273100	−	0.471111i
$973$		0			0
$974$		−	1794.59i		−	0.0590373i
$975$	2609.21	−	12296.6i	0.0857041	−	0.403904i
$976$			8216.27i			0.269464i
$977$		−	49306.7i		−	1.61460i	−0.590144	−	0.807298i	$-0.700929\pi$
$977$		−	49306.7i		−	1.61460i	0.590144	−	0.807298i	$-0.299071\pi$
$978$	−4768.41	+	22472.4i	−0.155907	+	0.734754i
$979$		−	4669.03i		−	0.152424i
$980$		0			0
$981$	248.894	+	110.605i	0.00810047	+	0.00359975i
$982$	2018.21			0.0655843
$983$	−19531.1			−0.633718			−0.316859	−	0.948473i	$-0.602628\pi$
$983$	−19531.1			−0.633718			−0.316859	+	0.948473i	$0.602628\pi$
$984$	−4750.81	+	22389.4i	−0.153913	+	0.725355i
$985$		−	618.528i		−	0.0200081i
$986$	42319.1			1.36685
$987$		0			0
$988$	−3453.71			−0.111212
$989$			12753.6i			0.410052i
$990$	−2390.57	−	1062.34i	−0.0767448	−	0.0341044i
$991$	18570.8			0.595278			0.297639	−	0.954678i	$-0.403801\pi$
$991$	18570.8			0.595278			0.297639	+	0.954678i	$0.403801\pi$
$992$	−16931.7			−0.541917
$993$	24805.1	+	5263.39i	0.792716	+	0.168206i
$994$		0			0
$995$			1047.46i			0.0333735i
$996$	−1619.07	−	343.551i	−0.0515084	−	0.0109295i
$997$			22388.8i			0.711195i	0.934639	+	0.355598i	$0.115723\pi$
$997$			22388.8i			0.711195i	−0.934639	+	0.355598i	$0.884277\pi$
$998$			11783.8i			0.373757i
$999$	21579.0	+	15643.4i	0.683414	+	0.495430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.c.a.146.5		12
3.2	odd	2	inner	147.4.c.a.146.8		12
7.2	even	3		147.4.g.d.80.3		12
7.3	odd	6		147.4.g.d.68.4		12
7.4	even	3		21.4.g.a.5.4	yes	12
7.5	odd	6		21.4.g.a.17.3	yes	12
7.6	odd	2	inner	147.4.c.a.146.6		12
21.2	odd	6		147.4.g.d.80.4		12
21.5	even	6		21.4.g.a.17.4	yes	12
21.11	odd	6		21.4.g.a.5.3	✓	12
21.17	even	6		147.4.g.d.68.3		12
21.20	even	2	inner	147.4.c.a.146.7		12
28.11	odd	6		336.4.bc.d.257.3		12
28.19	even	6		336.4.bc.d.17.5		12
84.11	even	6		336.4.bc.d.257.5		12
84.47	odd	6		336.4.bc.d.17.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.3	✓	12	21.11	odd	6
21.4.g.a.5.4	yes	12	7.4	even	3
21.4.g.a.17.3	yes	12	7.5	odd	6
21.4.g.a.17.4	yes	12	21.5	even	6
147.4.c.a.146.5		12	1.1	even	1	trivial
147.4.c.a.146.6		12	7.6	odd	2	inner
147.4.c.a.146.7		12	21.20	even	2	inner
147.4.c.a.146.8		12	3.2	odd	2	inner
147.4.g.d.68.3		12	21.17	even	6
147.4.g.d.68.4		12	7.3	odd	6
147.4.g.d.80.3		12	7.2	even	3
147.4.g.d.80.4		12	21.2	odd	6
336.4.bc.d.17.3		12	84.47	odd	6
336.4.bc.d.17.5		12	28.19	even	6
336.4.bc.d.257.3		12	28.11	odd	6
336.4.bc.d.257.5		12	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.90883i q^{2} +(-5.08298 - 1.07856i) q^{3} +4.35636 q^{4} +1.24741 q^{5} +(-2.05878 + 9.70256i) q^{6} -23.5862i q^{8} +(24.6734 + 10.9646i) q^{9} +O(q^{10})\)	\(q-1.90883i q^{2} +(-5.08298 - 1.07856i) q^{3} +4.35636 q^{4} +1.24741 q^{5} +(-2.05878 + 9.70256i) q^{6} -23.5862i q^{8} +(24.6734 + 10.9646i) q^{9} -2.38110i q^{10} -40.6907i q^{11} +(-22.1433 - 4.69858i) q^{12} -19.5973i q^{13} +(-6.34057 - 1.34540i) q^{15} -10.1712 q^{16} -104.718 q^{17} +(20.9295 - 47.0974i) q^{18} -40.4544i q^{19} +5.43418 q^{20} -77.6716 q^{22} +80.4045i q^{23} +(-25.4391 + 119.888i) q^{24} -123.444 q^{25} -37.4079 q^{26} +(-113.589 - 82.3444i) q^{27} -211.712i q^{29} +(-2.56815 + 12.1031i) q^{30} -100.025i q^{31} -169.275i q^{32} +(-43.8872 + 206.830i) q^{33} +199.890i q^{34} +(107.486 + 47.7656i) q^{36} -189.975 q^{37} -77.2206 q^{38} +(-21.1368 + 99.6127i) q^{39} -29.4217i q^{40} +186.753 q^{41} +158.618 q^{43} -177.263i q^{44} +(30.7779 + 13.6773i) q^{45} +153.479 q^{46} +358.069 q^{47} +(51.6999 + 10.9702i) q^{48} +235.634i q^{50} +(532.282 + 112.945i) q^{51} -85.3729i q^{52} +423.152i q^{53} +(-157.182 + 216.822i) q^{54} -50.7580i q^{55} +(-43.6323 + 205.629i) q^{57} -404.123 q^{58} +625.562 q^{59} +(-27.6218 - 5.86106i) q^{60} -807.799i q^{61} -190.931 q^{62} -404.486 q^{64} -24.4459i q^{65} +(394.804 + 83.7732i) q^{66} +298.544 q^{67} -456.192 q^{68} +(86.7208 - 408.695i) q^{69} +455.386i q^{71} +(258.613 - 581.953i) q^{72} -501.679i q^{73} +362.630i q^{74} +(627.464 + 133.141i) q^{75} -176.234i q^{76} +(190.144 + 40.3465i) q^{78} -61.9122 q^{79} -12.6876 q^{80} +(488.557 + 541.067i) q^{81} -356.479i q^{82} +73.1180 q^{83} -130.627 q^{85} -302.775i q^{86} +(-228.343 + 1076.13i) q^{87} -959.739 q^{88} +114.745 q^{89} +(26.1077 - 58.7498i) q^{90} +350.271i q^{92} +(-107.883 + 508.425i) q^{93} -683.493i q^{94} -50.4633i q^{95} +(-182.572 + 860.420i) q^{96} +1416.51i q^{97} +(446.156 - 1003.98i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 28 q^{4} + 6 q^{9}+O(q^{10}) \) 12 * q - 28 * q^4 + 6 * q^9	\( 12 q - 28 q^{4} + 6 q^{9} + 6 q^{15} - 268 q^{16} - 132 q^{18} - 268 q^{22} + 84 q^{25} + 1644 q^{30} + 852 q^{36} - 1528 q^{37} + 852 q^{39} - 1012 q^{43} - 1216 q^{46} + 2682 q^{51} + 270 q^{57} - 5740 q^{58} + 1836 q^{60} - 548 q^{64} - 1584 q^{67} + 5424 q^{72} + 4296 q^{78} - 3348 q^{79} - 1674 q^{81} + 348 q^{85} + 1108 q^{88} + 2958 q^{93} - 3354 q^{99}+O(q^{100}) \) 12 * q - 28 * q^4 + 6 * q^9 + 6 * q^15 - 268 * q^16 - 132 * q^18 - 268 * q^22 + 84 * q^25 + 1644 * q^30 + 852 * q^36 - 1528 * q^37 + 852 * q^39 - 1012 * q^43 - 1216 * q^46 + 2682 * q^51 + 270 * q^57 - 5740 * q^58 + 1836 * q^60 - 548 * q^64 - 1584 * q^67 + 5424 * q^72 + 4296 * q^78 - 3348 * q^79 - 1674 * q^81 + 348 * q^85 + 1108 * q^88 + 2958 * q^93 - 3354 * q^99

Introduction

L-functions

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