LMFDB - Embedded newform 72.3.b.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(19,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("72.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.b (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:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.4752.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} - 6x + 6 $ x^4 + 3x^2 - 6x + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.1
Root			$-0.866025 - 1.99551i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.3.b.b.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 1.46081i) q^{2} +(-0.267949 + 3.99102i) q^{4} +7.98203i q^{5} +2.13878i q^{7} +(6.19615 - 5.06040i) q^{8} +O(q^{10})$	\(q+(-1.36603 - 1.46081i) q^{2} +(-0.267949 + 3.99102i) q^{4} +7.98203i q^{5} +2.13878i q^{7} +(6.19615 - 5.06040i) q^{8} +(11.6603 - 10.9037i) q^{10} +8.00000 q^{11} +11.6865i q^{13} +(3.12436 - 2.92163i) q^{14} +(-15.8564 - 2.13878i) q^{16} -11.8564 q^{17} +14.9282 q^{19} +(-31.8564 - 2.13878i) q^{20} +(-10.9282 - 11.6865i) q^{22} +4.27756i q^{23} -38.7128 q^{25} +(17.0718 - 15.9641i) q^{26} +(-8.53590 - 0.573084i) q^{28} -0.573084i q^{29} -57.4399i q^{31} +(18.5359 + 26.0849i) q^{32} +(16.1962 + 17.3200i) q^{34} -17.0718 q^{35} +27.6506i q^{37} +(-20.3923 - 21.8073i) q^{38} +(40.3923 + 49.4579i) q^{40} +31.5692 q^{41} +28.7846 q^{43} +(-2.14359 + 31.9281i) q^{44} +(6.24871 - 5.84325i) q^{46} -59.5787i q^{47} +44.4256 q^{49} +(52.8827 + 56.5522i) q^{50} +(-46.6410 - 3.13139i) q^{52} -31.3550i q^{53} +63.8562i q^{55} +(10.8231 + 13.2522i) q^{56} +(-0.837169 + 0.782847i) q^{58} +52.7846 q^{59} -59.5787i q^{61} +(-83.9090 + 78.4644i) q^{62} +(12.7846 - 62.7101i) q^{64} -93.2820 q^{65} -84.7846 q^{67} +(3.17691 - 47.3191i) q^{68} +(23.3205 + 24.9387i) q^{70} +42.4685i q^{71} -5.42563 q^{73} +(40.3923 - 37.7714i) q^{74} +(-4.00000 + 59.5787i) q^{76} +17.1102i q^{77} +44.6072i q^{79} +(17.0718 - 126.566i) q^{80} +(-43.1244 - 46.1167i) q^{82} -67.7128 q^{83} -94.6382i q^{85} +(-39.3205 - 42.0489i) q^{86} +(49.5692 - 40.4832i) q^{88} +133.138 q^{89} -24.9948 q^{91} +(-17.0718 - 1.14617i) q^{92} +(-87.0333 + 81.3860i) q^{94} +119.157i q^{95} +97.1384 q^{97} +(-60.6865 - 64.8975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 8 q^{4} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 8 * q^4 + 4 * q^8	$ 4 q - 2 q^{2} - 8 q^{4} + 4 q^{8} + 12 q^{10} + 32 q^{11} - 36 q^{14} - 8 q^{16} + 8 q^{17} + 32 q^{19} - 72 q^{20} - 16 q^{22} - 44 q^{25} + 96 q^{26} - 48 q^{28} + 88 q^{32} + 44 q^{34} - 96 q^{35} - 40 q^{38} + 120 q^{40} - 40 q^{41} + 32 q^{43} - 64 q^{44} - 72 q^{46} - 44 q^{49} + 118 q^{50} - 48 q^{52} + 168 q^{56} + 156 q^{58} + 128 q^{59} - 204 q^{62} - 32 q^{64} - 96 q^{65} - 256 q^{67} - 112 q^{68} + 24 q^{70} + 200 q^{73} + 120 q^{74} - 16 q^{76} + 96 q^{80} - 124 q^{82} - 160 q^{83} - 88 q^{86} + 32 q^{88} + 200 q^{89} + 288 q^{91} - 96 q^{92} - 168 q^{94} + 56 q^{97} - 170 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 8 * q^4 + 4 * q^8 + 12 * q^10 + 32 * q^11 - 36 * q^14 - 8 * q^16 + 8 * q^17 + 32 * q^19 - 72 * q^20 - 16 * q^22 - 44 * q^25 + 96 * q^26 - 48 * q^28 + 88 * q^32 + 44 * q^34 - 96 * q^35 - 40 * q^38 + 120 * q^40 - 40 * q^41 + 32 * q^43 - 64 * q^44 - 72 * q^46 - 44 * q^49 + 118 * q^50 - 48 * q^52 + 168 * q^56 + 156 * q^58 + 128 * q^59 - 204 * q^62 - 32 * q^64 - 96 * q^65 - 256 * q^67 - 112 * q^68 + 24 * q^70 + 200 * q^73 + 120 * q^74 - 16 * q^76 + 96 * q^80 - 124 * q^82 - 160 * q^83 - 88 * q^86 + 32 * q^88 + 200 * q^89 + 288 * q^91 - 96 * q^92 - 168 * q^94 + 56 * q^97 - 170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.36603	−	1.46081i	−0.683013	−	0.730406i
$2$	−1.36603	−	1.46081i	−0.683013	−	0.730406i
$3$		0			0
$3$		0			0
$4$	−0.267949	+	3.99102i	−0.0669873	+	0.997754i
$5$			7.98203i			1.59641i	0.602388	+	0.798203i	$0.294216\pi$
$5$			7.98203i			1.59641i	−0.602388	+	0.798203i	$0.705784\pi$
$6$		0			0
$7$			2.13878i			0.305540i	0.988262	+	0.152770i	$0.0488193\pi$
$7$			2.13878i			0.305540i	−0.988262	+	0.152770i	$0.951181\pi$
$8$	6.19615	−	5.06040i	0.774519	−	0.632551i
$9$		0			0
$10$	11.6603	−	10.9037i	1.16603	−	1.09037i
$11$	8.00000			0.727273			0.363636	−	0.931541i	$-0.381535\pi$
$11$	8.00000			0.727273			0.363636	+	0.931541i	$0.381535\pi$
$12$		0			0
$13$			11.6865i			0.898962i	0.893290	+	0.449481i	$0.148391\pi$
$13$			11.6865i			0.898962i	−0.893290	+	0.449481i	$0.851609\pi$
$14$	3.12436	−	2.92163i	0.223168	−	0.208688i
$15$		0			0
$16$	−15.8564	−	2.13878i	−0.991025	−	0.133674i
$17$	−11.8564			−0.697436			−0.348718	−	0.937228i	$-0.613383\pi$
$17$	−11.8564			−0.697436			−0.348718	+	0.937228i	$0.613383\pi$
$18$		0			0
$19$	14.9282			0.785695			0.392847	−	0.919604i	$-0.371490\pi$
$19$	14.9282			0.785695			0.392847	+	0.919604i	$0.371490\pi$
$20$	−31.8564	−	2.13878i	−1.59282	−	0.106939i
$21$		0			0
$22$	−10.9282	−	11.6865i	−0.496737	−	0.531205i
$23$			4.27756i			0.185981i	0.995667	+	0.0929904i	$0.0296426\pi$
$23$			4.27756i			0.185981i	−0.995667	+	0.0929904i	$0.970357\pi$
$24$		0			0
$25$	−38.7128			−1.54851
$26$	17.0718	−	15.9641i	0.656608	−	0.614002i
$27$		0			0
$28$	−8.53590	−	0.573084i	−0.304854	−	0.0204673i
$29$		−	0.573084i		−	0.0197615i	−0.999951	−	0.00988076i	$-0.996855\pi$
$29$		−	0.573084i		−	0.0197615i	0.999951	−	0.00988076i	$-0.00314519\pi$
$30$		0			0
$31$		−	57.4399i		−	1.85290i	−0.376417	−	0.926450i	$-0.622844\pi$
$31$		−	57.4399i		−	1.85290i	0.376417	−	0.926450i	$-0.377156\pi$
$32$	18.5359	+	26.0849i	0.579247	+	0.815152i
$33$		0			0
$34$	16.1962	+	17.3200i	0.476357	+	0.509412i
$35$	−17.0718			−0.487766
$36$		0			0
$37$			27.6506i			0.747313i	0.927567	+	0.373656i	$0.121896\pi$
$37$			27.6506i			0.747313i	−0.927567	+	0.373656i	$0.878104\pi$
$38$	−20.3923	−	21.8073i	−0.536640	−	0.573877i
$39$		0			0
$40$	40.3923	+	49.4579i	1.00981	+	1.23645i
$41$	31.5692			0.769981			0.384990	−	0.922921i	$-0.374205\pi$
$41$	31.5692			0.769981			0.384990	+	0.922921i	$0.374205\pi$
$42$		0			0
$43$	28.7846			0.669410			0.334705	−	0.942323i	$-0.391363\pi$
$43$	28.7846			0.669410			0.334705	+	0.942323i	$0.391363\pi$
$44$	−2.14359	+	31.9281i	−0.0487180	+	0.725639i
$45$		0			0
$46$	6.24871	−	5.84325i	0.135842	−	0.127027i
$47$		−	59.5787i		−	1.26763i	−0.773484	−	0.633816i	$-0.781488\pi$
$47$		−	59.5787i		−	1.26763i	0.773484	−	0.633816i	$-0.218512\pi$
$48$		0			0
$49$	44.4256			0.906645
$50$	52.8827	+	56.5522i	1.05765	+	1.13104i
$51$		0			0
$52$	−46.6410	−	3.13139i	−0.896943	−	0.0602190i
$53$		−	31.3550i		−	0.591604i	−0.955249	−	0.295802i	$-0.904413\pi$
$53$		−	31.3550i		−	0.591604i	0.955249	−	0.295802i	$-0.0955869\pi$
$54$		0			0
$55$			63.8562i			1.16102i
$56$	10.8231	+	13.2522i	0.193269	+	0.236646i
$57$		0			0
$58$	−0.837169	+	0.782847i	−0.0144339	+	0.0134974i
$59$	52.7846			0.894654			0.447327	−	0.894370i	$-0.352376\pi$
$59$	52.7846			0.894654			0.447327	+	0.894370i	$0.352376\pi$
$60$		0			0
$61$		−	59.5787i		−	0.976700i	−0.872648	−	0.488350i	$-0.837599\pi$
$61$		−	59.5787i		−	0.976700i	0.872648	−	0.488350i	$-0.162401\pi$
$62$	−83.9090	+	78.4644i	−1.35337	+	1.26555i
$63$		0			0
$64$	12.7846	−	62.7101i	0.199760	−	0.979845i
$65$	−93.2820			−1.43511
$66$		0			0
$67$	−84.7846			−1.26544			−0.632721	−	0.774380i	$-0.718062\pi$
$67$	−84.7846			−1.26544			−0.632721	+	0.774380i	$0.718062\pi$
$68$	3.17691	−	47.3191i	0.0467193	−	0.695869i
$69$		0			0
$70$	23.3205	+	24.9387i	0.333150	+	0.356267i
$71$			42.4685i			0.598147i	0.954230	+	0.299074i	$0.0966776\pi$
$71$			42.4685i			0.598147i	−0.954230	+	0.299074i	$0.903322\pi$
$72$		0			0
$73$	−5.42563			−0.0743236			−0.0371618	−	0.999309i	$-0.511832\pi$
$73$	−5.42563			−0.0743236			−0.0371618	+	0.999309i	$0.511832\pi$
$74$	40.3923	−	37.7714i	0.545842	−	0.510424i
$75$		0			0
$76$	−4.00000	+	59.5787i	−0.0526316	+	0.783930i
$77$			17.1102i			0.222211i
$78$		0			0
$79$			44.6072i			0.564649i	0.959319	+	0.282324i	$0.0911054\pi$
$79$			44.6072i			0.564649i	−0.959319	+	0.282324i	$0.908895\pi$
$80$	17.0718	−	126.566i	0.213397	−	1.58208i
$81$		0			0
$82$	−43.1244	−	46.1167i	−0.525907	−	0.562399i
$83$	−67.7128			−0.815817			−0.407909	−	0.913023i	$-0.633742\pi$
$83$	−67.7128			−0.815817			−0.407909	+	0.913023i	$0.633742\pi$
$84$		0			0
$85$		−	94.6382i		−	1.11339i
$86$	−39.3205	−	42.0489i	−0.457215	−	0.488941i
$87$		0			0
$88$	49.5692	−	40.4832i	0.563287	−	0.460037i
$89$	133.138			1.49594			0.747969	−	0.663734i	$-0.231029\pi$
$89$	133.138			1.49594			0.747969	+	0.663734i	$0.231029\pi$
$90$		0			0
$91$	−24.9948			−0.274669
$92$	−17.0718	−	1.14617i	−0.185563	−	0.0124583i
$93$		0			0
$94$	−87.0333	+	81.3860i	−0.925886	+	0.865809i
$95$			119.157i			1.25429i
$96$		0			0
$97$	97.1384			1.00143			0.500714	−	0.865613i	$-0.333071\pi$
$97$	97.1384			1.00143			0.500714	+	0.865613i	$0.333071\pi$
$98$	−60.6865	−	64.8975i	−0.619250	−	0.662220i
$99$		0			0
$100$	10.3731	−	154.503i	0.103731	−	1.54503i
$101$			62.1370i			0.615218i	0.951513	+	0.307609i	$0.0995288\pi$
$101$			62.1370i			0.615218i	−0.951513	+	0.307609i	$0.900471\pi$
$102$		0			0
$103$		−	27.8041i		−	0.269943i	−0.990849	−	0.134971i	$-0.956906\pi$
$103$		−	27.8041i		−	0.269943i	0.990849	−	0.134971i	$-0.0430943\pi$
$104$	59.1384	+	72.4114i	0.568639	+	0.696263i
$105$		0			0
$106$	−45.8038	+	42.8318i	−0.432112	+	0.404073i
$107$	−37.7795			−0.353079			−0.176540	−	0.984294i	$-0.556490\pi$
$107$	−37.7795			−0.353079			−0.176540	+	0.984294i	$0.556490\pi$
$108$		0			0
$109$			141.691i			1.29992i	0.759968	+	0.649960i	$0.225214\pi$
$109$			141.691i			1.29992i	−0.759968	+	0.649960i	$0.774786\pi$
$110$	93.2820	−	87.2293i	0.848018	−	0.792993i
$111$		0			0
$112$	4.57437	−	33.9133i	0.0408426	−	0.302798i
$113$	58.2872			0.515816			0.257908	−	0.966170i	$-0.416967\pi$
$113$	58.2872			0.515816			0.257908	+	0.966170i	$0.416967\pi$
$114$		0			0
$115$	−34.1436			−0.296901
$116$	2.28719	+	0.153557i	0.0197171	+	0.00132377i
$117$		0			0
$118$	−72.1051	−	77.1084i	−0.611060	−	0.653461i
$119$		−	25.3582i		−	0.213094i
$120$		0			0
$121$	−57.0000			−0.471074
$122$	−87.0333	+	81.3860i	−0.713388	+	0.667098i
$123$		0			0
$124$	229.244	+	15.3910i	1.84874	+	0.124121i
$125$		−	109.456i		−	0.875649i
$126$		0			0
$127$			185.152i			1.45789i	0.684571	+	0.728946i	$0.259990\pi$
$127$			185.152i			1.45789i	−0.684571	+	0.728946i	$0.740010\pi$
$128$	−109.072	+	66.9876i	−0.852123	+	0.523341i
$129$		0			0
$130$	127.426	+	136.268i	0.980197	+	1.04821i
$131$	−125.359			−0.956939			−0.478469	−	0.878104i	$-0.658808\pi$
$131$	−125.359			−0.956939			−0.478469	+	0.878104i	$0.658808\pi$
$132$		0			0
$133$			31.9281i			0.240061i
$134$	115.818	+	123.854i	0.864313	+	0.924287i
$135$		0			0
$136$	−73.4641	+	59.9982i	−0.540177	+	0.441163i
$137$	−99.5692			−0.726783			−0.363391	−	0.931637i	$-0.618381\pi$
$137$	−99.5692			−0.726783			−0.363391	+	0.931637i	$0.618381\pi$
$138$		0			0
$139$	177.492			1.27692			0.638461	−	0.769654i	$-0.279571\pi$
$139$	177.492			1.27692			0.638461	+	0.769654i	$0.279571\pi$
$140$	4.57437	−	68.1338i	0.0326741	−	0.486670i
$141$		0			0
$142$	62.0385	−	58.0130i	0.436891	−	0.408542i
$143$			93.4920i			0.653790i
$144$		0			0
$145$	4.57437			0.0315474
$146$	7.41154	+	7.92582i	0.0507640	+	0.0542865i
$147$		0			0
$148$	−110.354	−	7.40895i	−0.745634	−	0.0500605i
$149$		−	87.8023i		−	0.589277i	−0.955609	−	0.294639i	$-0.904801\pi$
$149$		−	87.8023i		−	0.589277i	0.955609	−	0.294639i	$-0.0951993\pi$
$150$		0			0
$151$		−	219.066i		−	1.45077i	−0.688345	−	0.725383i	$-0.741663\pi$
$151$		−	219.066i		−	1.45077i	0.688345	−	0.725383i	$-0.258337\pi$
$152$	92.4974	−	75.5427i	0.608536	−	0.496992i
$153$		0			0
$154$	24.9948	−	23.3730i	0.162304	−	0.151773i
$155$	458.487			2.95798
$156$		0			0
$157$		−	253.440i		−	1.61427i	−0.590370	−	0.807133i	$-0.701018\pi$
$157$		−	253.440i		−	1.61427i	0.590370	−	0.807133i	$-0.298982\pi$
$158$	65.1628	−	60.9346i	0.412423	−	0.385662i
$159$		0			0
$160$	−208.210	+	147.954i	−1.30131	+	0.924713i
$161$	−9.14875			−0.0568245
$162$		0			0
$163$	−102.354			−0.627938			−0.313969	−	0.949433i	$-0.601659\pi$
$163$	−102.354			−0.627938			−0.313969	+	0.949433i	$0.601659\pi$
$164$	−8.45895	+	125.993i	−0.0515789	+	0.768251i
$165$		0			0
$166$	92.4974	+	98.9158i	0.557213	+	0.595878i
$167$		−	281.090i		−	1.68318i	−0.540120	−	0.841588i	$-0.681621\pi$
$167$		−	281.090i		−	1.68318i	0.540120	−	0.841588i	$-0.318379\pi$
$168$		0			0
$169$	32.4256			0.191868
$170$	−138.249	+	129.278i	−0.813228	+	0.760460i
$171$		0			0
$172$	−7.71281	+	114.880i	−0.0448419	+	0.667906i
$173$			242.858i			1.40381i	0.712273	+	0.701903i	$0.247666\pi$
$173$			242.858i			1.40381i	−0.712273	+	0.701903i	$0.752334\pi$
$174$		0			0
$175$		−	82.7981i		−	0.473132i
$176$	−126.851	−	17.1102i	−0.720746	−	0.0972172i
$177$		0			0
$178$	−181.870	−	194.490i	−1.02174	−	1.09264i
$179$	−318.354			−1.77851			−0.889257	−	0.457409i	$-0.848778\pi$
$179$	−318.354			−1.77851			−0.889257	+	0.457409i	$0.848778\pi$
$180$		0			0
$181$			79.5132i			0.439299i	0.975579	+	0.219650i	$0.0704914\pi$
$181$			79.5132i			0.439299i	−0.975579	+	0.219650i	$0.929509\pi$
$182$	34.1436	+	36.5128i	0.187602	+	0.200620i
$183$		0			0
$184$	21.6462	+	26.5044i	0.117642	+	0.144046i
$185$	−220.708			−1.19301
$186$		0			0
$187$	−94.8513			−0.507226
$188$	237.779	+	15.9641i	1.26478	+	0.0849152i
$189$		0			0
$190$	174.067	−	162.772i	0.916140	−	0.856695i
$191$		−	352.887i		−	1.84758i	−0.382902	−	0.923789i	$-0.625075\pi$
$191$		−	352.887i		−	1.84758i	0.382902	−	0.923789i	$-0.374925\pi$
$192$		0			0
$193$	−284.277			−1.47294			−0.736469	−	0.676472i	$-0.763508\pi$
$193$	−284.277			−1.47294			−0.736469	+	0.676472i	$0.763508\pi$
$194$	−132.694	−	141.901i	−0.683988	−	0.731449i
$195$		0			0
$196$	−11.9038	+	177.303i	−0.0607337	+	0.904609i
$197$		−	75.8087i		−	0.384816i	−0.981315	−	0.192408i	$-0.938370\pi$
$197$		−	75.8087i		−	0.384816i	0.981315	−	0.192408i	$-0.0616297\pi$
$198$		0			0
$199$		−	104.186i		−	0.523547i	−0.965129	−	0.261774i	$-0.915693\pi$
$199$		−	104.186i		−	0.523547i	0.965129	−	0.261774i	$-0.0843074\pi$
$200$	−239.870	+	195.902i	−1.19935	+	0.979512i
$201$		0			0
$202$	90.7705	−	84.8807i	0.449359	−	0.420202i
$203$	1.22570			0.00603793
$204$		0			0
$205$			251.986i			1.22920i
$206$	−40.6166	+	37.9811i	−0.197168	+	0.184374i
$207$		0			0
$208$	24.9948	−	185.306i	0.120168	−	0.890894i
$209$	119.426			0.571414
$210$		0			0
$211$	136.918			0.648900			0.324450	−	0.945903i	$-0.394821\pi$
$211$	136.918			0.648900			0.324450	+	0.945903i	$0.394821\pi$
$212$	125.138	+	8.40156i	0.590276	+	0.0396300i
$213$		0			0
$214$	51.6077	+	55.1887i	0.241157	+	0.257891i
$215$			229.760i			1.06865i
$216$		0			0
$217$	122.851			0.566135
$218$	206.985	−	193.554i	0.949470	−	0.887862i
$219$		0			0
$220$	−254.851	−	17.1102i	−1.15841	−	0.0777738i
$221$		−	138.560i		−	0.626968i
$222$		0			0
$223$		−	53.1624i		−	0.238396i	−0.992870	−	0.119198i	$-0.961968\pi$
$223$		−	53.1624i		−	0.238396i	0.992870	−	0.119198i	$-0.0380324\pi$
$224$	−55.7898	+	39.6442i	−0.249061	+	0.176983i
$225$		0			0
$226$	−79.6218	−	85.1467i	−0.352309	−	0.376755i
$227$	119.846			0.527956			0.263978	−	0.964529i	$-0.414965\pi$
$227$	119.846			0.527956			0.263978	+	0.964529i	$0.414965\pi$
$228$		0			0
$229$			214.103i			0.934946i	0.884007	+	0.467473i	$0.154836\pi$
$229$			214.103i			0.934946i	−0.884007	+	0.467473i	$0.845164\pi$
$230$	46.6410	+	49.8774i	0.202787	+	0.216858i
$231$		0			0
$232$	−2.90004	−	3.55092i	−0.0125002	−	0.0153057i
$233$	127.436			0.546935			0.273468	−	0.961881i	$-0.411829\pi$
$233$	127.436			0.546935			0.273468	+	0.961881i	$0.411829\pi$
$234$		0			0
$235$	475.559			2.02365
$236$	−14.1436	+	210.664i	−0.0599305	+	0.892645i
$237$		0			0
$238$	−37.0436	+	34.6400i	−0.155646	+	0.145546i
$239$			319.281i			1.33590i	0.744204	+	0.667952i	$0.232829\pi$
$239$			319.281i			1.33590i	−0.744204	+	0.667952i	$0.767171\pi$
$240$		0			0
$241$	−247.415			−1.02662			−0.513310	−	0.858203i	$-0.671581\pi$
$241$	−247.415			−1.02662			−0.513310	+	0.858203i	$0.671581\pi$
$242$	77.8634	+	83.2663i	0.321750	+	0.344076i
$243$		0			0
$244$	237.779	+	15.9641i	0.974506	+	0.0654265i
$245$			354.607i			1.44737i
$246$		0			0
$247$			174.459i			0.706310i
$248$	−290.669	−	355.906i	−1.17205	−	1.43511i
$249$		0			0
$250$	−159.895	+	149.520i	−0.639580	+	0.598079i
$251$	214.851			0.855981			0.427991	−	0.903783i	$-0.359222\pi$
$251$	214.851			0.855981			0.427991	+	0.903783i	$0.359222\pi$
$252$		0			0
$253$			34.2205i			0.135259i
$254$	270.473	−	252.923i	1.06485	−	0.995759i
$255$		0			0
$256$	246.851	+	67.8267i	0.964263	+	0.264948i
$257$	84.2769			0.327926			0.163963	−	0.986467i	$-0.447572\pi$
$257$	84.2769			0.327926			0.163963	+	0.986467i	$0.447572\pi$
$258$		0			0
$259$	−59.1384			−0.228334
$260$	24.9948	−	372.290i	0.0961340	−	1.43188i
$261$		0			0
$262$	171.244	+	183.126i	0.653601	+	0.698954i
$263$			277.120i			1.05369i	0.849962	+	0.526844i	$0.176625\pi$
$263$			277.120i			1.05369i	−0.849962	+	0.526844i	$0.823375\pi$
$264$		0			0
$265$	250.277			0.944441
$266$	46.6410	−	43.6146i	0.175342	−	0.163965i
$267$		0			0
$268$	22.7180	−	338.377i	0.0847685	−	1.26260i
$269$		−	123.701i		−	0.459855i	−0.973208	−	0.229927i	$-0.926151\pi$
$269$		−	123.701i		−	0.459855i	0.973208	−	0.229927i	$-0.0738489\pi$
$270$		0			0
$271$		−	197.985i		−	0.730572i	−0.930895	−	0.365286i	$-0.880971\pi$
$271$		−	197.985i		−	0.730572i	0.930895	−	0.365286i	$-0.119029\pi$
$272$	188.000	+	25.3582i	0.691176	+	0.0932288i
$273$		0			0
$274$	136.014	+	145.452i	0.496402	+	0.530847i
$275$	−309.703			−1.12619
$276$		0			0
$277$		−	247.709i		−	0.894256i	−0.894470	−	0.447128i	$-0.852447\pi$
$277$		−	247.709i		−	0.894256i	0.894470	−	0.447128i	$-0.147553\pi$
$278$	−242.459	−	259.283i	−0.872154	−	0.932673i
$279$		0			0
$280$	−105.779	+	86.3902i	−0.377784	+	0.308536i
$281$	−443.128			−1.57697			−0.788484	−	0.615055i	$-0.789134\pi$
$281$	−443.128			−1.57697			−0.788484	+	0.615055i	$0.789134\pi$
$282$		0			0
$283$	−294.620			−1.04106			−0.520531	−	0.853843i	$-0.674266\pi$
$283$	−294.620			−1.04106			−0.520531	+	0.853843i	$0.674266\pi$
$284$	−169.492	−	11.3794i	−0.596804	−	0.0400683i
$285$		0			0
$286$	136.574	−	127.712i	0.477533	−	0.446547i
$287$			67.5196i			0.235260i
$288$		0			0
$289$	−148.426			−0.513583
$290$	−6.24871	−	6.68231i	−0.0215473	−	0.0230424i
$291$		0			0
$292$	1.45379	−	21.6538i	0.00497874	−	0.0741567i
$293$			66.7217i			0.227719i	0.993497	+	0.113859i	$0.0363214\pi$
$293$			66.7217i			0.227719i	−0.993497	+	0.113859i	$0.963679\pi$
$294$		0			0
$295$			421.328i			1.42823i
$296$	139.923	+	171.327i	0.472713	+	0.578808i
$297$		0			0
$298$	−128.263	+	119.940i	−0.430412	+	0.402484i
$299$	−49.9897			−0.167190
$300$		0			0
$301$			61.5639i			0.204531i
$302$	−320.014	+	299.249i	−1.05965	+	0.990892i
$303$		0			0
$304$	−236.708	−	31.9281i	−0.778644	−	0.105027i
$305$	475.559			1.55921
$306$		0			0
$307$	−524.210			−1.70753			−0.853763	−	0.520662i	$-0.825685\pi$
$307$	−524.210			−1.70753			−0.853763	+	0.520662i	$0.825685\pi$
$308$	−68.2872	−	4.58467i	−0.221712	−	0.0148853i
$309$		0			0
$310$	−626.305	−	669.764i	−2.02034	−	2.16053i
$311$		−	362.057i		−	1.16417i	−0.813128	−	0.582085i	$-0.802237\pi$
$311$		−	362.057i		−	1.16417i	0.813128	−	0.582085i	$-0.197763\pi$
$312$		0			0
$313$	252.277			0.805996			0.402998	−	0.915201i	$-0.367968\pi$
$313$	252.277			0.805996			0.402998	+	0.915201i	$0.367968\pi$
$314$	−370.228	+	346.205i	−1.17907	+	1.10256i
$315$		0			0
$316$	−178.028	−	11.9525i	−0.563380	−	0.0378243i
$317$			80.3934i			0.253607i	0.991928	+	0.126803i	$0.0404717\pi$
$317$			80.3934i			0.253607i	−0.991928	+	0.126803i	$0.959528\pi$
$318$		0			0
$319$		−	4.58467i		−	0.0143720i
$320$	500.554	+	102.047i	1.56423	+	0.318897i
$321$		0			0
$322$	12.4974	+	13.3646i	0.0388119	+	0.0415050i
$323$	−176.995			−0.547972
$324$		0			0
$325$		−	452.417i		−	1.39205i
$326$	139.818	+	149.520i	0.428889	+	0.458650i
$327$		0			0
$328$	195.608	−	159.753i	0.596365	−	0.487052i
$329$	127.426			0.387312
$330$		0			0
$331$	172.056			0.519808			0.259904	−	0.965635i	$-0.416309\pi$
$331$	172.056			0.519808			0.259904	+	0.965635i	$0.416309\pi$
$332$	18.1436	−	270.243i	0.0546494	−	0.813985i
$333$		0			0
$334$	−410.620	+	383.977i	−1.22940	+	1.14963i
$335$		−	676.753i		−	2.02016i
$336$		0			0
$337$	564.277			1.67441			0.837206	−	0.546888i	$-0.184187\pi$
$337$	564.277			1.67441			0.837206	+	0.546888i	$0.184187\pi$
$338$	−44.2942	−	47.3678i	−0.131048	−	0.140141i
$339$		0			0
$340$	377.703	+	25.3582i	1.11089	+	0.0745830i
$341$		−	459.519i		−	1.34756i
$342$		0			0
$343$			199.817i			0.582556i
$344$	178.354	−	145.662i	0.518470	−	0.423435i
$345$		0			0
$346$	354.771	−	331.751i	1.02535	−	0.958817i
$347$	286.123			0.824562			0.412281	−	0.911057i	$-0.364732\pi$
$347$	286.123			0.824562			0.412281	+	0.911057i	$0.364732\pi$
$348$		0			0
$349$		−	421.021i		−	1.20636i	−0.797603	−	0.603182i	$-0.793899\pi$
$349$		−	421.021i		−	1.20636i	0.797603	−	0.603182i	$-0.206101\pi$
$350$	−120.953	+	113.104i	−0.345579	+	0.323155i
$351$		0			0
$352$	148.287	+	208.679i	0.421270	+	0.592838i
$353$	−429.138			−1.21569			−0.607845	−	0.794056i	$-0.707966\pi$
$353$	−429.138			−1.21569			−0.607845	+	0.794056i	$0.707966\pi$
$354$		0			0
$355$	−338.985			−0.954886
$356$	−35.6743	+	531.358i	−0.100209	+	1.49258i
$357$		0			0
$358$	434.879	+	465.055i	1.21475	+	1.29904i
$359$			263.673i			0.734465i	0.930129	+	0.367233i	$0.119695\pi$
$359$			263.673i			0.734465i	−0.930129	+	0.367233i	$0.880305\pi$
$360$		0			0
$361$	−138.149			−0.382684
$362$	116.154	−	108.617i	0.320867	−	0.300047i
$363$		0			0
$364$	6.69735	−	99.7548i	0.0183993	−	0.274052i
$365$		−	43.3075i		−	0.118651i
$366$		0			0
$367$			129.544i			0.352981i	0.984302	+	0.176491i	$0.0564745\pi$
$367$			129.544i			0.352981i	−0.984302	+	0.176491i	$0.943525\pi$
$368$	9.14875	−	67.8267i	0.0248607	−	0.184312i
$369$		0			0
$370$	301.492	+	322.413i	0.814844	+	0.871385i
$371$	67.0615			0.180759
$372$		0			0
$373$			302.478i			0.810933i	0.914110	+	0.405467i	$0.132891\pi$
$373$			302.478i			0.810933i	−0.914110	+	0.405467i	$0.867109\pi$
$374$	129.569	+	138.560i	0.346442	+	0.370481i
$375$		0			0
$376$	−301.492	−	369.159i	−0.801841	−	0.981805i
$377$	6.69735			0.0177649
$378$		0			0
$379$	−116.210			−0.306623			−0.153312	−	0.988178i	$-0.548994\pi$
$379$	−116.210			−0.306623			−0.153312	+	0.988178i	$0.548994\pi$
$380$	−475.559	−	31.9281i	−1.25147	−	0.0840214i
$381$		0			0
$382$	−515.503	+	482.053i	−1.34948	+	1.26192i
$383$			566.151i			1.47820i	0.673595	+	0.739101i	$0.264749\pi$
$383$			566.151i			1.47820i	−0.673595	+	0.739101i	$0.735251\pi$
$384$		0			0
$385$	−136.574			−0.354739
$386$	388.329	+	415.275i	1.00603	+	1.07584i
$387$		0			0
$388$	−26.0282	+	387.681i	−0.0670829	+	0.999178i
$389$		−	350.104i		−	0.900011i	−0.893026	−	0.450006i	$-0.851422\pi$
$389$		−	350.104i		−	0.900011i	0.893026	−	0.450006i	$-0.148578\pi$
$390$		0			0
$391$		−	50.7165i		−	0.129710i
$392$	275.268	−	224.812i	0.702214	−	0.573499i
$393$		0			0
$394$	−110.742	+	103.557i	−0.281072	+	0.262834i
$395$	−356.056			−0.901408
$396$		0			0
$397$		−	544.149i		−	1.37065i	−0.728236	−	0.685326i	$-0.759660\pi$
$397$		−	544.149i		−	1.37065i	0.728236	−	0.685326i	$-0.240340\pi$
$398$	−152.196	+	142.321i	−0.382402	+	0.357589i
$399$		0			0
$400$	613.846	+	82.7981i	1.53462	+	0.206995i
$401$	296.431			0.739229			0.369614	−	0.929185i	$-0.379490\pi$
$401$	296.431			0.739229			0.369614	+	0.929185i	$0.379490\pi$
$402$		0			0
$403$	671.272			1.66569
$404$	−247.990	−	16.6496i	−0.613836	−	0.0412118i
$405$		0			0
$406$	−1.67434	−	1.79052i	−0.00412398	−	0.00441014i
$407$			221.205i			0.543500i
$408$		0			0
$409$	−247.415			−0.604927			−0.302464	−	0.953161i	$-0.597809\pi$
$409$	−247.415			−0.604927			−0.302464	+	0.953161i	$0.597809\pi$
$410$	368.105	−	344.220i	0.897817	−	0.839561i
$411$		0			0
$412$	110.967	+	7.45009i	0.269337	+	0.0180827i
$413$			112.895i			0.273353i
$414$		0			0
$415$		−	540.486i		−	1.30238i
$416$	−304.841	+	216.620i	−0.732791	+	0.520721i
$417$		0			0
$418$	−163.138	−	174.459i	−0.390283	−	0.417365i
$419$	92.1333			0.219889			0.109944	−	0.993938i	$-0.464933\pi$
$419$	92.1333			0.219889			0.109944	+	0.993938i	$0.464933\pi$
$420$		0			0
$421$			445.540i			1.05829i	0.848531	+	0.529145i	$0.177487\pi$
$421$			445.540i			1.05829i	−0.848531	+	0.529145i	$0.822513\pi$
$422$	−187.033	−	200.011i	−0.443207	−	0.473961i
$423$		0			0
$424$	−158.669	−	194.281i	−0.374220	−	0.458209i
$425$	458.995			1.07999
$426$		0			0
$427$	127.426			0.298421
$428$	10.1230	−	150.778i	0.0236518	−	0.352286i
$429$		0			0
$430$	335.636	−	313.857i	0.780549	−	0.729901i
$431$		−	186.677i		−	0.433125i	−0.976269	−	0.216563i	$-0.930515\pi$
$431$		−	186.677i		−	0.433125i	0.976269	−	0.216563i	$-0.0694845\pi$
$432$		0			0
$433$	291.128			0.672351			0.336176	−	0.941799i	$-0.390866\pi$
$433$	291.128			0.672351			0.336176	+	0.941799i	$0.390866\pi$
$434$	−167.818	−	179.463i	−0.386677	−	0.413509i
$435$		0			0
$436$	−565.492	−	37.9661i	−1.29700	−	0.0870782i
$437$			63.8562i			0.146124i
$438$		0			0
$439$		−	87.6899i		−	0.199749i	−0.995000	−	0.0998746i	$-0.968156\pi$
$439$		−	87.6899i		−	0.199749i	0.995000	−	0.0998746i	$-0.0318442\pi$
$440$	323.138	+	395.663i	0.734406	+	0.899234i
$441$		0			0
$442$	−202.410	+	189.276i	−0.457942	+	0.428227i
$443$	−20.7077			−0.0467441			−0.0233721	−	0.999727i	$-0.507440\pi$
$443$	−20.7077			−0.0467441			−0.0233721	+	0.999727i	$0.507440\pi$
$444$		0			0
$445$			1062.72i			2.38812i
$446$	−77.6603	+	72.6211i	−0.174126	+	0.162828i
$447$		0			0
$448$	134.123	+	27.3435i	0.299382	+	0.0610345i
$449$	−584.410			−1.30158			−0.650791	−	0.759257i	$-0.725563\pi$
$449$	−584.410			−1.30158			−0.650791	+	0.759257i	$0.725563\pi$
$450$		0			0
$451$	252.554			0.559986
$452$	−15.6180	+	232.625i	−0.0345531	+	0.514657i
$453$		0			0
$454$	−163.713	−	175.073i	−0.360601	−	0.385623i
$455$		−	199.510i		−	0.438483i
$456$		0			0
$457$	−269.692			−0.590136			−0.295068	−	0.955476i	$-0.595342\pi$
$457$	−269.692			−0.590136			−0.295068	+	0.955476i	$0.595342\pi$
$458$	312.764	−	292.470i	0.682891	−	0.638580i
$459$		0			0
$460$	9.14875	−	136.268i	0.0198886	−	0.296234i
$461$		−	44.4948i		−	0.0965181i	−0.998835	−	0.0482590i	$-0.984633\pi$
$461$		−	44.4948i		−	0.0965181i	0.998835	−	0.0482590i	$-0.0153673\pi$
$462$		0			0
$463$			611.065i			1.31980i	0.751355	+	0.659898i	$0.229400\pi$
$463$			611.065i			1.31980i	−0.751355	+	0.659898i	$0.770600\pi$
$464$	−1.22570	+	9.08705i	−0.00264159	+	0.0195842i
$465$		0			0
$466$	−174.081	−	186.160i	−0.373564	−	0.399485i
$467$	−146.410			−0.313512			−0.156756	−	0.987637i	$-0.550104\pi$
$467$	−146.410			−0.313512			−0.156756	+	0.987637i	$0.550104\pi$
$468$		0			0
$469$		−	181.336i		−	0.386643i
$470$	−649.626	−	694.703i	−1.38218	−	1.47809i
$471$		0			0
$472$	327.061	−	267.111i	0.692927	−	0.565914i
$473$	230.277			0.486843
$474$		0			0
$475$	−577.913			−1.21666
$476$	101.205	+	6.79472i	0.212616	+	0.0142746i
$477$		0			0
$478$	466.410	−	436.146i	0.975753	−	0.912440i
$479$		−	191.876i		−	0.400576i	−0.979737	−	0.200288i	$-0.935812\pi$
$479$		−	191.876i		−	0.400576i	0.979737	−	0.200288i	$-0.0641878\pi$
$480$		0			0
$481$	−323.138			−0.671805
$482$	337.976	+	361.428i	0.701194	+	0.749850i
$483$		0			0
$484$	15.2731	−	227.488i	0.0315560	−	0.470016i
$485$			775.362i			1.59868i
$486$		0			0
$487$		−	610.758i		−	1.25412i	−0.778969	−	0.627062i	$-0.784257\pi$
$487$		−	610.758i		−	1.25412i	0.778969	−	0.627062i	$-0.215743\pi$
$488$	−301.492	−	369.159i	−0.617812	−	0.756473i
$489$		0			0
$490$	518.014	−	484.402i	1.05717	−	0.988575i
$491$	142.354			0.289926			0.144963	−	0.989437i	$-0.453694\pi$
$491$	142.354			0.289926			0.144963	+	0.989437i	$0.453694\pi$
$492$		0			0
$493$			6.79472i			0.0137824i
$494$	254.851	−	238.315i	0.515893	−	0.482419i
$495$		0			0
$496$	−122.851	+	910.791i	−0.247684	+	1.83627i
$497$	−90.8306			−0.182758
$498$		0			0
$499$	91.3693			0.183105			0.0915524	−	0.995800i	$-0.470817\pi$
$499$	91.3693			0.183105			0.0915524	+	0.995800i	$0.470817\pi$
$500$	436.841	+	29.3287i	0.873682	+	0.0586573i
$501$		0			0
$502$	−293.492	−	313.857i	−0.584646	−	0.625214i
$503$		−	230.067i		−	0.457389i	−0.973498	−	0.228695i	$-0.926554\pi$
$503$		−	230.067i		−	0.457389i	0.973498	−	0.228695i	$-0.0734457\pi$
$504$		0			0
$505$	−495.979			−0.982137
$506$	49.9897	−	46.7460i	0.0987939	−	0.0923834i
$507$		0			0
$508$	−738.946	−	49.6114i	−1.45462	−	0.0976603i
$509$			527.387i			1.03612i	0.855343	+	0.518062i	$0.173346\pi$
$509$			527.387i			1.03612i	−0.855343	+	0.518062i	$0.826654\pi$
$510$		0			0
$511$		−	11.6042i		−	0.0227088i
$512$	−238.123	−	453.256i	−0.465084	−	0.885267i
$513$		0			0
$514$	−115.124	−	123.113i	−0.223977	−	0.239519i
$515$	221.933			0.430939
$516$		0			0
$517$		−	476.630i		−	0.921914i
$518$	80.7846	+	86.3902i	0.155955	+	0.166776i
$519$		0			0
$520$	−577.990	+	472.045i	−1.11152	+	0.907779i
$521$	−191.856			−0.368246			−0.184123	−	0.982903i	$-0.558945\pi$
$521$	−191.856			−0.368246			−0.184123	+	0.982903i	$0.558945\pi$
$522$		0			0
$523$	105.492			0.201706			0.100853	−	0.994901i	$-0.467843\pi$
$523$	105.492			0.201706			0.100853	+	0.994901i	$0.467843\pi$
$524$	33.5898	−	500.310i	0.0641027	−	0.954789i
$525$		0			0
$526$	404.820	−	378.553i	0.769620	−	0.719682i
$527$			681.031i			1.29228i
$528$		0			0
$529$	510.703			0.965411
$530$	−341.885	−	365.608i	−0.645065	−	0.689826i
$531$		0			0
$532$	−127.426	−	8.55511i	−0.239522	−	0.0160810i
$533$			368.934i			0.692184i
$534$		0			0
$535$		−	301.557i		−	0.563658i
$536$	−525.338	+	429.044i	−0.980109	+	0.800456i
$537$		0			0
$538$	−180.704	+	168.979i	−0.335881	+	0.314087i
$539$	355.405			0.659378
$540$		0			0
$541$			459.744i			0.849804i	0.905239	+	0.424902i	$0.139691\pi$
$541$			459.744i			0.849804i	−0.905239	+	0.424902i	$0.860309\pi$
$542$	−289.219	+	270.453i	−0.533615	+	0.498990i
$543$		0			0
$544$	−219.769	−	309.273i	−0.403987	−	0.568516i
$545$	−1130.98			−2.07520
$546$		0			0
$547$	67.3693			0.123161			0.0615807	−	0.998102i	$-0.480386\pi$
$547$	67.3693			0.123161			0.0615807	+	0.998102i	$0.480386\pi$
$548$	26.6795	−	397.382i	0.0486852	−	0.725150i
$549$		0			0
$550$	423.061	+	452.417i	0.769203	+	0.822577i
$551$		−	8.55511i		−	0.0155265i
$552$		0			0
$553$	−95.4050			−0.172523
$554$	−361.856	+	338.377i	−0.653170	+	0.610788i
$555$		0			0
$556$	−47.5589	+	708.374i	−0.0855376	+	1.27405i
$557$		−	476.671i		−	0.855782i	−0.903830	−	0.427891i	$-0.859257\pi$
$557$		−	476.671i		−	0.855782i	0.903830	−	0.427891i	$-0.140743\pi$
$558$		0			0
$559$			336.391i			0.601774i
$560$	270.697	+	36.5128i	0.483388	+	0.0652014i
$561$		0			0
$562$	605.324	+	647.327i	1.07709	+	1.15183i
$563$	910.123			1.61656			0.808280	−	0.588799i	$-0.200399\pi$
$563$	910.123			1.61656			0.808280	+	0.588799i	$0.200399\pi$
$564$		0			0
$565$			465.250i			0.823452i
$566$	402.459	+	430.385i	0.711058	+	0.760398i
$567$		0			0
$568$	214.908	+	263.141i	0.378358	+	0.463276i
$569$	124.123			0.218142			0.109071	−	0.994034i	$-0.465212\pi$
$569$	124.123			0.218142			0.109071	+	0.994034i	$0.465212\pi$
$570$		0			0
$571$	945.031			1.65504			0.827522	−	0.561433i	$-0.189750\pi$
$571$	945.031			1.65504			0.827522	+	0.561433i	$0.189750\pi$
$572$	−373.128	−	25.0511i	−0.652322	−	0.0437957i
$573$		0			0
$574$	98.6335	−	92.2335i	0.171835	−	0.160685i
$575$		−	165.596i		−	0.287994i
$576$		0			0
$577$	215.682			0.373799			0.186899	−	0.982379i	$-0.440156\pi$
$577$	215.682			0.373799			0.186899	+	0.982379i	$0.440156\pi$
$578$	202.753	+	216.822i	0.350784	+	0.375125i
$579$		0			0
$580$	−1.22570	+	18.2564i	−0.00211328	+	0.0314765i
$581$		−	144.823i		−	0.249265i
$582$		0			0
$583$		−	250.840i		−	0.430258i
$584$	−33.6180	+	27.4559i	−0.0575651	+	0.0470135i
$585$		0			0
$586$	97.4679	−	91.1435i	0.166327	−	0.155535i
$587$	−900.785			−1.53456			−0.767278	−	0.641314i	$-0.778389\pi$
$587$	−900.785			−1.53456			−0.767278	+	0.641314i	$0.778389\pi$
$588$		0			0
$589$		−	857.475i		−	1.45581i
$590$	615.482	−	575.545i	1.04319	−	0.975500i
$591$		0			0
$592$	59.1384	−	438.439i	0.0998960	−	0.740606i
$593$	508.585			0.857647			0.428824	−	0.903388i	$-0.358928\pi$
$593$	508.585			0.857647			0.428824	+	0.903388i	$0.358928\pi$
$594$		0			0
$595$	202.410			0.340185
$596$	350.420	+	23.5266i	0.587954	+	0.0394741i
$597$		0			0
$598$	68.2872	+	73.0256i	0.114193	+	0.122116i
$599$		−	846.934i		−	1.41391i	−0.707257	−	0.706957i	$-0.750067\pi$
$599$		−	846.934i		−	1.41391i	0.707257	−	0.706957i	$-0.249933\pi$
$600$		0			0
$601$	−406.000			−0.675541			−0.337770	−	0.941229i	$-0.609673\pi$
$601$	−406.000			−0.675541			−0.337770	+	0.941229i	$0.609673\pi$
$602$	89.9334	−	84.0979i	0.149391	−	0.139697i
$603$		0			0
$604$	874.295	+	58.6985i	1.44751	+	0.0971829i
$605$		−	454.976i		−	0.752026i
$606$		0			0
$607$			771.156i			1.27044i	0.772332	+	0.635219i	$0.219090\pi$
$607$			771.156i			1.27044i	−0.772332	+	0.635219i	$0.780910\pi$
$608$	276.708	+	389.400i	0.455111	+	0.640461i
$609$		0			0
$610$	−649.626	−	694.703i	−1.06496	−	1.13886i
$611$	696.267			1.13955
$612$		0			0
$613$			336.699i			0.549264i	0.961549	+	0.274632i	$0.0885560\pi$
$613$			336.699i			0.549264i	−0.961549	+	0.274632i	$0.911444\pi$
$614$	716.084	+	765.773i	1.16626	+	1.24719i
$615$		0			0
$616$	86.5847	+	106.018i	0.140560	+	0.172106i
$617$	908.831			1.47298			0.736492	−	0.676447i	$-0.236481\pi$
$617$	908.831			1.47298			0.736492	+	0.676447i	$0.236481\pi$
$618$		0			0
$619$	−1047.77			−1.69268			−0.846340	−	0.532643i	$-0.821199\pi$
$619$	−1047.77			−1.69268			−0.846340	+	0.532643i	$0.821199\pi$
$620$	−122.851	+	1829.83i	−0.198147	+	2.95134i
$621$		0			0
$622$	−528.897	+	494.579i	−0.850317	+	0.795143i
$623$			284.754i			0.457068i
$624$		0			0
$625$	−94.1384			−0.150622
$626$	−344.617	−	368.529i	−0.550506	−	0.588705i
$627$		0			0
$628$	1011.48	+	67.9090i	1.61064	+	0.108135i
$629$		−	327.836i		−	0.521202i
$630$		0			0
$631$		−	610.758i		−	0.967921i	−0.875090	−	0.483961i	$-0.839198\pi$
$631$		−	610.758i		−	0.967921i	0.875090	−	0.483961i	$-0.160802\pi$
$632$	225.731	+	276.393i	0.357169	+	0.437331i
$633$		0			0
$634$	117.440	−	109.819i	0.185236	−	0.173217i
$635$	−1477.89			−2.32739
$636$		0			0
$637$			519.180i			0.815040i
$638$	−6.69735	+	6.26278i	−0.0104974	+	0.00981627i
$639$		0			0
$640$	−534.697	−	870.614i	−0.835465	−	1.36034i
$641$	−9.60015			−0.0149768			−0.00748842	−	0.999972i	$-0.502384\pi$
$641$	−9.60015			−0.0149768			−0.00748842	+	0.999972i	$0.502384\pi$
$642$		0			0
$643$	86.1999			0.134059			0.0670295	−	0.997751i	$-0.478648\pi$
$643$	86.1999			0.134059			0.0670295	+	0.997751i	$0.478648\pi$
$644$	2.45140	−	36.5128i	0.00380652	−	0.0566969i
$645$		0			0
$646$	241.779	+	258.556i	0.374272	+	0.400242i
$647$		−	352.580i		−	0.544946i	−0.962163	−	0.272473i	$-0.912158\pi$
$647$		−	352.580i		−	0.544946i	0.962163	−	0.272473i	$-0.0878416\pi$
$648$		0			0
$649$	422.277			0.650658
$650$	−660.897	+	618.014i	−1.01677	+	0.950790i
$651$		0			0
$652$	27.4256	−	408.496i	0.0420638	−	0.626527i
$653$		−	319.322i		−	0.489008i	−0.969648	−	0.244504i	$-0.921375\pi$
$653$		−	319.322i		−	0.489008i	0.969648	−	0.244504i	$-0.0786252\pi$
$654$		0			0
$655$		−	1000.62i		−	1.52766i
$656$	−500.574	−	67.5196i	−0.763071	−	0.102926i
$657$		0			0
$658$	−174.067	−	186.145i	−0.264539	−	0.282895i
$659$	−275.328			−0.417797			−0.208898	−	0.977937i	$-0.566988\pi$
$659$	−275.328			−0.417797			−0.208898	+	0.977937i	$0.566988\pi$
$660$		0			0
$661$			133.668i			0.202221i	0.994875	+	0.101111i	$0.0322396\pi$
$661$			133.668i			0.202221i	−0.994875	+	0.101111i	$0.967760\pi$
$662$	−235.033	−	251.342i	−0.355035	−	0.379671i
$663$		0			0
$664$	−419.559	+	342.654i	−0.631866	+	0.516046i
$665$	−254.851			−0.383235
$666$		0			0
$667$	2.45140			0.00367526
$668$	1121.84	+	75.3179i	1.67939	+	0.112751i
$669$		0			0
$670$	−988.610	+	924.462i	−1.47554	+	1.37979i
$671$		−	476.630i		−	0.710327i
$672$		0			0
$673$	187.703			0.278904			0.139452	−	0.990229i	$-0.455466\pi$
$673$	187.703			0.278904			0.139452	+	0.990229i	$0.455466\pi$
$674$	−770.817	−	824.303i	−1.14364	−	1.22300i
$675$		0			0
$676$	−8.68842	+	129.411i	−0.0128527	+	0.191437i
$677$		−	1169.84i		−	1.72797i	−0.503515	−	0.863986i	$-0.667960\pi$
$677$		−	1169.84i		−	1.72797i	0.503515	−	0.863986i	$-0.332040\pi$
$678$		0			0
$679$			207.758i			0.305976i
$680$	−478.908	−	586.393i	−0.704276	−	0.862342i
$681$		0			0
$682$	−671.272	+	627.715i	−0.984269	+	0.920403i
$683$	−89.4566			−0.130976			−0.0654880	−	0.997853i	$-0.520860\pi$
$683$	−89.4566			−0.130976			−0.0654880	+	0.997853i	$0.520860\pi$
$684$		0			0
$685$		−	794.765i		−	1.16024i
$686$	291.895	−	272.955i	0.425503	−	0.397893i
$687$		0			0
$688$	−456.420	−	61.5639i	−0.663402	−	0.0894824i
$689$	366.431			0.531830
$690$		0			0
$691$	139.103			0.201306			0.100653	−	0.994922i	$-0.467907\pi$
$691$	139.103			0.201306			0.100653	+	0.994922i	$0.467907\pi$
$692$	−969.251	−	65.0737i	−1.40065	−	0.0940371i
$693$		0			0
$694$	−390.851	−	417.972i	−0.563186	−	0.602265i
$695$			1416.75i			2.03849i
$696$		0			0
$697$	−374.297			−0.537012
$698$	−615.033	+	575.126i	−0.881137	+	0.823962i
$699$		0			0
$700$	330.449	+	22.1857i	0.472069	+	0.0316938i
$701$			1218.34i			1.73801i	0.494804	+	0.869004i	$0.335240\pi$
$701$			1218.34i			1.73801i	−0.494804	+	0.869004i	$0.664760\pi$
$702$		0			0
$703$			412.773i			0.587160i
$704$	102.277	−	501.681i	0.145280	−	0.712615i
$705$		0			0
$706$	586.214	+	626.891i	0.830331	+	0.887948i
$707$	−132.897			−0.187974
$708$		0			0
$709$		−	1080.13i		−	1.52346i	−0.647895	−	0.761730i	$-0.724351\pi$
$709$		−	1080.13i		−	1.52346i	0.647895	−	0.761730i	$-0.275649\pi$
$710$	463.061	+	495.193i	0.652199	+	0.697455i
$711$		0			0
$712$	824.946	−	673.734i	1.15863	−	0.946256i
$713$	245.703			0.344604
$714$		0			0
$715$	−746.256			−1.04372
$716$	85.3027	−	1270.56i	0.119138	−	1.77452i
$717$		0			0
$718$	385.177	−	360.184i	0.536458	−	0.501649i
$719$			20.7736i			0.0288923i	0.999896	+	0.0144461i	$0.00459851\pi$
$719$			20.7736i			0.0288923i	−0.999896	+	0.0144461i	$0.995401\pi$
$720$		0			0
$721$	59.4669			0.0824783
$722$	188.715	+	201.809i	0.261378	+	0.279515i
$723$		0			0
$724$	−317.338	−	21.3055i	−0.438313	−	0.0294275i
$725$			22.1857i			0.0306010i
$726$		0			0
$727$			1031.17i			1.41838i	0.705015	+	0.709192i	$0.250940\pi$
$727$			1031.17i			1.41838i	−0.705015	+	0.709192i	$0.749060\pi$
$728$	−154.872	+	126.484i	−0.212736	+	0.173742i
$729$		0			0
$730$	−63.2642	+	59.1592i	−0.0866633	+	0.0810399i
$731$	−341.282			−0.466870
$732$		0			0
$733$		−	881.072i		−	1.20201i	−0.799246	−	0.601004i	$-0.794767\pi$
$733$		−	881.072i		−	1.20201i	0.799246	−	0.601004i	$-0.205233\pi$
$734$	189.240	−	176.961i	0.257820	−	0.241091i
$735$		0			0
$736$	−111.580	+	79.2884i	−0.151603	+	0.107729i
$737$	−678.277			−0.920321
$738$		0			0
$739$	−671.195			−0.908247			−0.454124	−	0.890939i	$-0.650048\pi$
$739$	−671.195			−0.908247			−0.454124	+	0.890939i	$0.650048\pi$
$740$	59.1384	−	880.848i	0.0799168	−	1.19033i
$741$		0			0
$742$	−91.6077	−	97.9643i	−0.123461	−	0.132027i
$743$			254.197i			0.342122i	0.985260	+	0.171061i	$0.0547195\pi$
$743$			254.197i			0.342122i	−0.985260	+	0.171061i	$0.945281\pi$
$744$		0			0
$745$	700.841			0.940726
$746$	441.864	−	413.193i	0.592311	−	0.553878i
$747$		0			0
$748$	25.4153	−	378.553i	0.0339777	−	0.506087i
$749$		−	80.8019i		−	0.107880i
$750$		0			0
$751$		−	728.994i		−	0.970698i	−0.874320	−	0.485349i	$-0.838693\pi$
$751$		−	728.994i		−	0.970698i	0.874320	−	0.485349i	$-0.161307\pi$
$752$	−127.426	+	944.704i	−0.169449	+	1.25626i
$753$		0			0
$754$	−9.14875	−	9.78357i	−0.0121336	−	0.0129756i
$755$	1748.59			2.31601
$756$		0			0
$757$			372.679i			0.492311i	0.969230	+	0.246155i	$0.0791674\pi$
$757$			372.679i			0.492311i	−0.969230	+	0.246155i	$0.920833\pi$
$758$	158.746	+	169.761i	0.209428	+	0.223960i
$759$		0			0
$760$	602.985	+	738.317i	0.793401	+	0.971470i
$761$	−1257.80			−1.65283			−0.826416	−	0.563060i	$-0.809624\pi$
$761$	−1257.80			−1.65283			−0.826416	+	0.563060i	$0.809624\pi$
$762$		0			0
$763$	−303.046			−0.397177
$764$	1408.38	+	94.5559i	1.84343	+	0.123764i
$765$		0			0
$766$	827.041	−	773.377i	1.07969	−	1.00963i
$767$			616.868i			0.804260i
$768$		0			0
$769$	247.703			0.322110			0.161055	−	0.986945i	$-0.448510\pi$
$769$	247.703			0.322110			0.161055	+	0.986945i	$0.448510\pi$
$770$	186.564	+	199.510i	0.242291	+	0.259103i
$771$		0			0
$772$	76.1718	−	1134.55i	0.0986681	−	1.46963i
$773$			587.805i			0.760420i	0.924900	+	0.380210i	$0.124148\pi$
$773$			587.805i			0.760420i	−0.924900	+	0.380210i	$0.875852\pi$
$774$		0			0
$775$			2223.66i			2.86924i
$776$	601.885	−	491.560i	0.775624	−	0.633453i
$777$		0			0
$778$	−511.437	+	478.251i	−0.657374	+	0.614719i
$779$	471.272			0.604970
$780$		0			0
$781$			339.748i			0.435016i
$782$	−74.0873	+	69.2800i	−0.0947407	+	0.0885933i
$783$		0			0
$784$	−704.431	−	95.0166i	−0.898509	−	0.121195i
$785$	2022.96			2.57702
$786$		0			0
$787$	−31.0821			−0.0394944			−0.0197472	−	0.999805i	$-0.506286\pi$
$787$	−31.0821			−0.0394944			−0.0197472	+	0.999805i	$0.506286\pi$
$788$	302.554	+	20.3129i	0.383951	+	0.0257778i
$789$		0			0
$790$	486.382	+	520.132i	0.615673	+	0.658395i
$791$			124.663i			0.157602i
$792$		0			0
$793$	696.267			0.878016
$794$	−794.900	+	743.321i	−1.00113	+	0.936173i
$795$		0			0
$796$	415.808	+	27.9165i	0.522371	+	0.0350710i
$797$		−	490.260i		−	0.615132i	−0.951527	−	0.307566i	$-0.900486\pi$
$797$		−	490.260i		−	0.615132i	0.951527	−	0.307566i	$-0.0995145\pi$
$798$		0			0
$799$			706.389i			0.884092i
$800$	−717.577	−	1009.82i	−0.896971	−	1.26227i
$801$		0			0
$802$	−404.932	−	433.030i	−0.504903	−	0.539938i
$803$	−43.4050			−0.0540536
$804$		0			0
$805$		−	73.0256i		−	0.0907150i
$806$	−916.974	−	980.602i	−1.13769	−	1.21663i
$807$		0			0
$808$	314.438	+	385.010i	0.389156	+	0.476498i
$809$	−676.102			−0.835726			−0.417863	−	0.908510i	$-0.637221\pi$
$809$	−676.102			−0.835726			−0.417863	+	0.908510i	$0.637221\pi$
$810$		0			0
$811$	−74.1793			−0.0914665			−0.0457332	−	0.998954i	$-0.514562\pi$
$811$	−74.1793			−0.0914665			−0.0457332	+	0.998954i	$0.514562\pi$
$812$	−0.328425	+	4.89179i	−0.000404465	+	0.00602437i
$813$		0			0
$814$	323.138	−	302.171i	0.396976	−	0.371217i
$815$		−	816.991i		−	1.00244i
$816$		0			0
$817$	429.703			0.525952
$818$	337.976	+	361.428i	0.413173	+	0.441843i
$819$		0			0
$820$	−1005.68	−	67.5196i	−1.22644	−	0.0823409i
$821$			1130.58i			1.37708i	0.725198	+	0.688540i	$0.241748\pi$
$821$			1130.58i			1.37708i	−0.725198	+	0.688540i	$0.758252\pi$
$822$		0			0
$823$		−	82.1839i		−	0.0998589i	−0.998753	−	0.0499295i	$-0.984100\pi$
$823$		−	82.1839i		−	0.0998589i	0.998753	−	0.0499295i	$-0.0158997\pi$
$824$	−140.700	−	172.279i	−0.170753	−	0.209076i
$825$		0			0
$826$	164.918	−	154.217i	0.199658	−	0.186703i
$827$	−1504.57			−1.81931			−0.909655	−	0.415365i	$-0.863654\pi$
$827$	−1504.57			−1.81931			−0.909655	+	0.415365i	$0.863654\pi$
$828$		0			0
$829$			1409.65i			1.70042i	0.526445	+	0.850209i	$0.323525\pi$
$829$			1409.65i			1.70042i	−0.526445	+	0.850209i	$0.676475\pi$
$830$	−789.549	+	738.317i	−0.951263	+	0.889539i
$831$		0			0
$832$	732.862	+	149.407i	0.880843	+	0.179576i
$833$	−526.728			−0.632327
$834$		0			0
$835$	2243.67			2.68703
$836$	−32.0000	+	476.630i	−0.0382775	+	0.570131i
$837$		0			0
$838$	−125.856	−	134.589i	−0.150187	−	0.160608i
$839$			288.110i			0.343397i	0.985150	+	0.171698i	$0.0549254\pi$
$839$			288.110i			0.343397i	−0.985150	+	0.171698i	$0.945075\pi$
$840$		0			0
$841$	840.672			0.999609
$842$	650.851	−	608.620i	0.772982	−	0.722826i
$843$		0			0
$844$	−36.6870	+	546.441i	−0.0434681	+	0.647442i
$845$			258.822i			0.306299i
$846$		0			0
$847$		−	121.910i		−	0.143932i
$848$	−67.0615	+	497.178i	−0.0790819	+	0.586295i
$849$		0			0
$850$	−626.999	−	670.506i	−0.737645	−	0.788830i
$851$	−118.277			−0.138986
$852$		0			0
$853$		−	645.132i		−	0.756310i	−0.925742	−	0.378155i	$-0.876559\pi$
$853$		−	645.132i		−	0.756310i	0.925742	−	0.378155i	$-0.123441\pi$
$854$	−174.067	−	186.145i	−0.203825	−	0.217968i
$855$		0			0
$856$	−234.087	+	191.179i	−0.273466	+	0.223340i
$857$	995.549			1.16167			0.580833	−	0.814022i	$-0.302727\pi$
$857$	995.549			1.16167			0.580833	+	0.814022i	$0.302727\pi$
$858$		0			0
$859$	−774.354			−0.901460			−0.450730	−	0.892660i	$-0.648836\pi$
$859$	−774.354			−0.901460			−0.450730	+	0.892660i	$0.648836\pi$
$860$	−916.974	−	61.5639i	−1.06625	−	0.0715859i
$861$		0			0
$862$	−272.700	+	255.005i	−0.316357	+	0.295830i
$863$		−	1007.33i		−	1.16724i	−0.812025	−	0.583622i	$-0.801635\pi$
$863$		−	1007.33i		−	1.16724i	0.812025	−	0.583622i	$-0.198365\pi$
$864$		0			0
$865$	−1938.50			−2.24104
$866$	−397.688	−	425.284i	−0.459225	−	0.491090i
$867$		0			0
$868$	−32.9179	+	490.301i	−0.0379238	+	0.564863i
$869$			356.858i			0.410654i
$870$		0			0
$871$		−	990.836i		−	1.13758i
$872$	717.015	+	877.941i	0.822265	+	1.00681i
$873$		0			0
$874$	93.2820	−	87.2293i	0.106730	−	0.0998046i
$875$	234.102			0.267546
$876$		0			0
$877$			681.645i			0.777246i	0.921397	+	0.388623i	$0.127049\pi$
$877$			681.645i			0.777246i	−0.921397	+	0.388623i	$0.872951\pi$
$878$	−128.099	+	119.787i	−0.145898	+	0.136431i
$879$		0			0
$880$	136.574	−	1012.53i	0.155198	−	1.15060i
$881$	679.108			0.770837			0.385419	−	0.922742i	$-0.374057\pi$
$881$	679.108			0.770837			0.385419	+	0.922742i	$0.374057\pi$
$882$		0			0
$883$	−1059.44			−1.19982			−0.599910	−	0.800068i	$-0.704797\pi$
$883$	−1059.44			−1.19982			−0.599910	+	0.800068i	$0.704797\pi$
$884$	552.995	+	37.1270i	0.625560	+	0.0419989i
$885$		0			0
$886$	28.2872	+	30.2500i	0.0319268	+	0.0341422i
$887$			856.411i			0.965514i	0.875754	+	0.482757i	$0.160365\pi$
$887$			856.411i			0.965514i	−0.875754	+	0.482757i	$0.839635\pi$
$888$		0			0
$889$	−396.000			−0.445444
$890$	1552.43	−	1451.70i	1.74430	−	1.63112i
$891$		0			0
$892$	212.172	+	14.2448i	0.237861	+	0.0159695i
$893$		−	889.403i		−	0.995972i
$894$		0			0
$895$		−	2541.11i		−	2.83923i
$896$	−143.272	−	233.280i	−0.159901	−	0.260358i
$897$		0			0
$898$	798.319	+	853.714i	0.888997	+	0.950684i
$899$	−32.9179			−0.0366161
$900$		0			0
$901$			371.758i			0.412606i
$902$	−344.995	−	368.934i	−0.382478	−	0.409018i
$903$		0			0
$904$	361.156	−	294.957i	0.399509	−	0.326280i
$905$	−634.677			−0.701300
$906$		0			0
$907$	−761.492			−0.839573			−0.419786	−	0.907623i	$-0.637895\pi$
$907$	−761.492			−0.839573			−0.419786	+	0.907623i	$0.637895\pi$
$908$	−32.1127	+	478.308i	−0.0353664	+	0.526770i
$909$		0			0
$910$	−291.446	+	272.535i	−0.320271	+	0.299489i
$911$			897.344i			0.985009i	0.870310	+	0.492505i	$0.163919\pi$
$911$			897.344i			0.985009i	−0.870310	+	0.492505i	$0.836081\pi$
$912$		0			0
$913$	−541.703			−0.593321
$914$	368.406	+	393.970i	0.403070	+	0.431039i
$915$		0			0
$916$	−854.487	−	57.3686i	−0.932846	−	0.0626295i
$917$		−	268.115i		−	0.292383i
$918$		0			0
$919$			62.6388i			0.0681598i	0.999419	+	0.0340799i	$0.0108501\pi$
$919$			62.6388i			0.0681598i	−0.999419	+	0.0340799i	$0.989150\pi$
$920$	−211.559	+	172.780i	−0.229955	+	0.187805i
$921$		0			0
$922$	−64.9986	+	60.7811i	−0.0704974	+	0.0659231i
$923$	−496.308			−0.537712
$924$		0			0
$925$		−	1070.43i		−	1.15722i
$926$	892.652	−	834.731i	0.963987	−	0.901437i
$927$		0			0
$928$	14.9488	−	10.6226i	0.0161086	−	0.0114468i
$929$	−253.313			−0.272673			−0.136336	−	0.990663i	$-0.543533\pi$
$929$	−253.313			−0.272673			−0.136336	+	0.990663i	$0.543533\pi$
$930$		0			0
$931$	663.195			0.712347
$932$	−34.1464	+	508.599i	−0.0366377	+	0.545707i
$933$		0			0
$934$	200.000	+	213.878i	0.214133	+	0.228991i
$935$		−	757.106i		−	0.809739i
$936$		0			0
$937$	−30.5538			−0.0326081			−0.0163040	−	0.999867i	$-0.505190\pi$
$937$	−30.5538			−0.0326081			−0.0163040	+	0.999867i	$0.505190\pi$
$938$	−264.897	+	247.709i	−0.282406	+	0.264082i
$939$		0			0
$940$	−127.426	+	1897.96i	−0.135559	+	2.01911i
$941$			388.745i			0.413119i	0.978434	+	0.206559i	$0.0662267\pi$
$941$			388.745i			0.413119i	−0.978434	+	0.206559i	$0.933773\pi$
$942$		0			0
$943$			135.039i			0.143202i
$944$	−836.974	−	112.895i	−0.886625	−	0.119592i
$945$		0			0
$946$	−314.564	−	336.391i	−0.332520	−	0.355594i
$947$	263.615			0.278369			0.139184	−	0.990266i	$-0.455552\pi$
$947$	263.615			0.278369			0.139184	+	0.990266i	$0.455552\pi$
$948$		0			0
$949$		−	63.4066i		−	0.0668141i
$950$	789.443	+	844.222i	0.830993	+	0.888655i
$951$		0			0
$952$	−128.323	−	157.123i	−0.134793	−	0.165046i
$953$	−1292.41			−1.35615			−0.678075	−	0.734993i	$-0.737185\pi$
$953$	−1292.41			−1.35615			−0.678075	+	0.734993i	$0.737185\pi$
$954$		0			0
$955$	2816.76			2.94949
$956$	−1274.26	−	85.5511i	−1.33290	−	0.0894886i
$957$		0			0
$958$	−280.295	+	262.107i	−0.292583	+	0.273598i
$959$		−	212.957i		−	0.222061i
$960$		0			0
$961$	−2338.34			−2.43324
$962$	441.415	+	472.045i	0.458852	+	0.490691i
$963$		0			0
$964$	66.2947	−	987.438i	0.0687705	−	1.02431i
$965$		−	2269.11i		−	2.35141i
$966$		0			0
$967$		−	1110.00i		−	1.14788i	−0.818896	−	0.573942i	$-0.805413\pi$
$967$		−	1110.00i		−	1.14788i	0.818896	−	0.573942i	$-0.194587\pi$
$968$	−353.181	+	288.443i	−0.364856	+	0.297978i
$969$		0			0
$970$	1132.66	−	1059.16i	1.16769	−	1.09192i
$971$	1341.66			1.38173			0.690866	−	0.722983i	$-0.257230\pi$
$971$	1341.66			1.38173			0.690866	+	0.722983i	$0.257230\pi$
$972$		0			0
$973$			379.617i			0.390151i
$974$	−892.204	+	834.311i	−0.916020	+	0.856583i
$975$		0			0
$976$	−127.426	+	944.704i	−0.130559	+	0.967934i
$977$	920.431			0.942099			0.471050	−	0.882107i	$-0.343875\pi$
$977$	920.431			0.942099			0.471050	+	0.882107i	$0.343875\pi$
$978$		0			0
$979$	1065.11			1.08795
$980$	−1415.24	−	95.0166i	−1.44412	−	0.0969557i
$981$		0			0
$982$	−194.459	−	207.952i	−0.198023	−	0.211764i
$983$		−	1697.84i		−	1.72720i	−0.504176	−	0.863601i	$-0.668204\pi$
$983$		−	1697.84i		−	1.72720i	0.504176	−	0.863601i	$-0.331796\pi$
$984$		0			0
$985$	605.108			0.614322
$986$	9.92581	−	9.28176i	0.0100667	−	0.00941355i
$987$		0			0
$988$	−696.267	−	46.7460i	−0.704723	−	0.0473138i
$989$			123.128i			0.124497i
$990$		0			0
$991$			284.765i			0.287351i	0.989625	+	0.143675i	$0.0458921\pi$
$991$			284.765i			0.287351i	−0.989625	+	0.143675i	$0.954108\pi$
$992$	1498.31	−	1064.70i	1.51040	−	1.07329i
$993$		0			0
$994$	124.077	+	132.687i	0.124826	+	0.133487i
$995$	831.615			0.835794
$996$		0			0
$997$			1093.80i			1.09710i	0.836119	+	0.548548i	$0.184819\pi$
$997$			1093.80i			1.09710i	−0.836119	+	0.548548i	$0.815181\pi$
$998$	−124.813	−	133.473i	−0.125063	−	0.133741i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.b.b.19.1		4
3.2	odd	2		24.3.b.a.19.4	yes	4
4.3	odd	2		288.3.b.b.271.4		4
8.3	odd	2	inner	72.3.b.b.19.2		4
8.5	even	2		288.3.b.b.271.1		4
12.11	even	2		96.3.b.a.79.3		4
15.2	even	4		600.3.p.a.499.4		8
15.8	even	4		600.3.p.a.499.5		8
15.14	odd	2		600.3.g.a.451.1		4
16.3	odd	4		2304.3.g.z.1279.8		8
16.5	even	4		2304.3.g.z.1279.1		8
16.11	odd	4		2304.3.g.z.1279.2		8
16.13	even	4		2304.3.g.z.1279.7		8
24.5	odd	2		96.3.b.a.79.4		4
24.11	even	2		24.3.b.a.19.3	✓	4
48.5	odd	4		768.3.g.h.511.8		8
48.11	even	4		768.3.g.h.511.4		8
48.29	odd	4		768.3.g.h.511.1		8
48.35	even	4		768.3.g.h.511.5		8
60.23	odd	4		2400.3.p.a.1999.6		8
60.47	odd	4		2400.3.p.a.1999.3		8
60.59	even	2		2400.3.g.a.751.2		4
120.29	odd	2		2400.3.g.a.751.1		4
120.53	even	4		2400.3.p.a.1999.7		8
120.59	even	2		600.3.g.a.451.2		4
120.77	even	4		2400.3.p.a.1999.2		8
120.83	odd	4		600.3.p.a.499.3		8
120.107	odd	4		600.3.p.a.499.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.3.b.a.19.3	✓	4	24.11	even	2
24.3.b.a.19.4	yes	4	3.2	odd	2
72.3.b.b.19.1		4	1.1	even	1	trivial
72.3.b.b.19.2		4	8.3	odd	2	inner
96.3.b.a.79.3		4	12.11	even	2
96.3.b.a.79.4		4	24.5	odd	2
288.3.b.b.271.1		4	8.5	even	2
288.3.b.b.271.4		4	4.3	odd	2
600.3.g.a.451.1		4	15.14	odd	2
600.3.g.a.451.2		4	120.59	even	2
600.3.p.a.499.3		8	120.83	odd	4
600.3.p.a.499.4		8	15.2	even	4
600.3.p.a.499.5		8	15.8	even	4
600.3.p.a.499.6		8	120.107	odd	4
768.3.g.h.511.1		8	48.29	odd	4
768.3.g.h.511.4		8	48.11	even	4
768.3.g.h.511.5		8	48.35	even	4
768.3.g.h.511.8		8	48.5	odd	4
2304.3.g.z.1279.1		8	16.5	even	4
2304.3.g.z.1279.2		8	16.11	odd	4
2304.3.g.z.1279.7		8	16.13	even	4
2304.3.g.z.1279.8		8	16.3	odd	4
2400.3.g.a.751.1		4	120.29	odd	2
2400.3.g.a.751.2		4	60.59	even	2
2400.3.p.a.1999.2		8	120.77	even	4
2400.3.p.a.1999.3		8	60.47	odd	4
2400.3.p.a.1999.6		8	60.23	odd	4
2400.3.p.a.1999.7		8	120.53	even	4

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 1.46081i) q^{2} +(-0.267949 + 3.99102i) q^{4} +7.98203i q^{5} +2.13878i q^{7} +(6.19615 - 5.06040i) q^{8} +O(q^{10})\)	\(q+(-1.36603 - 1.46081i) q^{2} +(-0.267949 + 3.99102i) q^{4} +7.98203i q^{5} +2.13878i q^{7} +(6.19615 - 5.06040i) q^{8} +(11.6603 - 10.9037i) q^{10} +8.00000 q^{11} +11.6865i q^{13} +(3.12436 - 2.92163i) q^{14} +(-15.8564 - 2.13878i) q^{16} -11.8564 q^{17} +14.9282 q^{19} +(-31.8564 - 2.13878i) q^{20} +(-10.9282 - 11.6865i) q^{22} +4.27756i q^{23} -38.7128 q^{25} +(17.0718 - 15.9641i) q^{26} +(-8.53590 - 0.573084i) q^{28} -0.573084i q^{29} -57.4399i q^{31} +(18.5359 + 26.0849i) q^{32} +(16.1962 + 17.3200i) q^{34} -17.0718 q^{35} +27.6506i q^{37} +(-20.3923 - 21.8073i) q^{38} +(40.3923 + 49.4579i) q^{40} +31.5692 q^{41} +28.7846 q^{43} +(-2.14359 + 31.9281i) q^{44} +(6.24871 - 5.84325i) q^{46} -59.5787i q^{47} +44.4256 q^{49} +(52.8827 + 56.5522i) q^{50} +(-46.6410 - 3.13139i) q^{52} -31.3550i q^{53} +63.8562i q^{55} +(10.8231 + 13.2522i) q^{56} +(-0.837169 + 0.782847i) q^{58} +52.7846 q^{59} -59.5787i q^{61} +(-83.9090 + 78.4644i) q^{62} +(12.7846 - 62.7101i) q^{64} -93.2820 q^{65} -84.7846 q^{67} +(3.17691 - 47.3191i) q^{68} +(23.3205 + 24.9387i) q^{70} +42.4685i q^{71} -5.42563 q^{73} +(40.3923 - 37.7714i) q^{74} +(-4.00000 + 59.5787i) q^{76} +17.1102i q^{77} +44.6072i q^{79} +(17.0718 - 126.566i) q^{80} +(-43.1244 - 46.1167i) q^{82} -67.7128 q^{83} -94.6382i q^{85} +(-39.3205 - 42.0489i) q^{86} +(49.5692 - 40.4832i) q^{88} +133.138 q^{89} -24.9948 q^{91} +(-17.0718 - 1.14617i) q^{92} +(-87.0333 + 81.3860i) q^{94} +119.157i q^{95} +97.1384 q^{97} +(-60.6865 - 64.8975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 8 q^{4} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 8 * q^4 + 4 * q^8	\( 4 q - 2 q^{2} - 8 q^{4} + 4 q^{8} + 12 q^{10} + 32 q^{11} - 36 q^{14} - 8 q^{16} + 8 q^{17} + 32 q^{19} - 72 q^{20} - 16 q^{22} - 44 q^{25} + 96 q^{26} - 48 q^{28} + 88 q^{32} + 44 q^{34} - 96 q^{35} - 40 q^{38} + 120 q^{40} - 40 q^{41} + 32 q^{43} - 64 q^{44} - 72 q^{46} - 44 q^{49} + 118 q^{50} - 48 q^{52} + 168 q^{56} + 156 q^{58} + 128 q^{59} - 204 q^{62} - 32 q^{64} - 96 q^{65} - 256 q^{67} - 112 q^{68} + 24 q^{70} + 200 q^{73} + 120 q^{74} - 16 q^{76} + 96 q^{80} - 124 q^{82} - 160 q^{83} - 88 q^{86} + 32 q^{88} + 200 q^{89} + 288 q^{91} - 96 q^{92} - 168 q^{94} + 56 q^{97} - 170 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 8 * q^4 + 4 * q^8 + 12 * q^10 + 32 * q^11 - 36 * q^14 - 8 * q^16 + 8 * q^17 + 32 * q^19 - 72 * q^20 - 16 * q^22 - 44 * q^25 + 96 * q^26 - 48 * q^28 + 88 * q^32 + 44 * q^34 - 96 * q^35 - 40 * q^38 + 120 * q^40 - 40 * q^41 + 32 * q^43 - 64 * q^44 - 72 * q^46 - 44 * q^49 + 118 * q^50 - 48 * q^52 + 168 * q^56 + 156 * q^58 + 128 * q^59 - 204 * q^62 - 32 * q^64 - 96 * q^65 - 256 * q^67 - 112 * q^68 + 24 * q^70 + 200 * q^73 + 120 * q^74 - 16 * q^76 + 96 * q^80 - 124 * q^82 - 160 * q^83 - 88 * q^86 + 32 * q^88 + 200 * q^89 + 288 * q^91 - 96 * q^92 - 168 * q^94 + 56 * q^97 - 170 * q^98

Introduction

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