LMFDB - Embedded newform 216.3.h.e.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(53,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("216.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.h (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.629407744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 2x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.3
Root			$0.767178 - 1.18804i$ of defining polynomial
Character	$\chi$	$=$	216.53
Dual form			216.3.h.e.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.420861 - 1.95522i) q^{2} +(-3.64575 + 1.64575i) q^{4} -2.22699 q^{5} -8.64575 q^{7} +(4.75216 + 6.43560i) q^{8} +O(q^{10})$	\(q+(-0.420861 - 1.95522i) q^{2} +(-3.64575 + 1.64575i) q^{4} -2.22699 q^{5} -8.64575 q^{7} +(4.75216 + 6.43560i) q^{8} +(0.937254 + 4.35425i) q^{10} +19.8504 q^{11} +14.5203i q^{13} +(3.63866 + 16.9043i) q^{14} +(10.5830 - 12.0000i) q^{16} +5.29570i q^{17} +24.2915i q^{19} +(8.11905 - 3.66507i) q^{20} +(-8.35425 - 38.8118i) q^{22} +29.6528i q^{23} -20.0405 q^{25} +(28.3903 - 6.11102i) q^{26} +(31.5203 - 14.2288i) q^{28} -6.13742 q^{29} +10.1255 q^{31} +(-27.9166 - 15.6417i) q^{32} +(10.3542 - 2.22876i) q^{34} +19.2540 q^{35} +16.6458i q^{37} +(47.4952 - 10.2234i) q^{38} +(-10.5830 - 14.3320i) q^{40} -7.82087i q^{41} -1.54249i q^{43} +(-72.3695 + 32.6687i) q^{44} +(57.9778 - 12.4797i) q^{46} -63.7069i q^{47} +25.7490 q^{49} +(8.43428 + 39.1836i) q^{50} +(-23.8967 - 52.9373i) q^{52} -76.5253 q^{53} -44.2065 q^{55} +(-41.0860 - 55.6406i) q^{56} +(2.58301 + 12.0000i) q^{58} +41.0332 q^{59} +52.0627i q^{61} +(-4.26143 - 19.7975i) q^{62} +(-18.8340 + 61.1660i) q^{64} -32.3365i q^{65} +110.247i q^{67} +(-8.71541 - 19.3068i) q^{68} +(-8.10326 - 37.6458i) q^{70} +100.690i q^{71} -93.9150 q^{73} +(32.5461 - 7.00555i) q^{74} +(-39.9778 - 88.5608i) q^{76} -171.621 q^{77} -10.7712 q^{79} +(-23.5682 + 26.7239i) q^{80} +(-15.2915 + 3.29150i) q^{82} +118.996 q^{83} -11.7935i q^{85} +(-3.01590 + 0.649173i) q^{86} +(94.3320 + 127.749i) q^{88} -146.071i q^{89} -125.539i q^{91} +(-48.8012 - 108.107i) q^{92} +(-124.561 + 26.8118i) q^{94} -54.0969i q^{95} -3.70850 q^{97} +(-10.8368 - 50.3449i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 48 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 - 48 * q^7	$ 8 q - 8 q^{4} - 48 q^{7} - 56 q^{10} - 88 q^{22} + 136 q^{25} + 104 q^{28} + 208 q^{31} + 104 q^{34} + 104 q^{46} - 48 q^{49} - 424 q^{52} + 112 q^{55} - 64 q^{58} - 320 q^{64} + 168 q^{70} - 328 q^{73} + 40 q^{76} - 192 q^{79} - 80 q^{82} + 416 q^{88} - 552 q^{94} - 72 q^{97}+O(q^{100}) $ 8 * q - 8 * q^4 - 48 * q^7 - 56 * q^10 - 88 * q^22 + 136 * q^25 + 104 * q^28 + 208 * q^31 + 104 * q^34 + 104 * q^46 - 48 * q^49 - 424 * q^52 + 112 * q^55 - 64 * q^58 - 320 * q^64 + 168 * q^70 - 328 * q^73 + 40 * q^76 - 192 * q^79 - 80 * q^82 + 416 * q^88 - 552 * q^94 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.420861	−	1.95522i	−0.210431	−	0.977609i
$2$	−0.420861	−	1.95522i	−0.210431	−	0.977609i
$3$		0			0
$3$		0			0
$4$	−3.64575	+	1.64575i	−0.911438	+	0.411438i
$5$	−2.22699			−0.445398			−0.222699	−	0.974887i	$-0.571487\pi$
$5$	−2.22699			−0.445398			−0.222699	+	0.974887i	$0.571487\pi$
$6$		0			0
$7$	−8.64575			−1.23511			−0.617554	−	0.786529i	$-0.711876\pi$
$7$	−8.64575			−1.23511			−0.617554	+	0.786529i	$0.711876\pi$
$8$	4.75216	+	6.43560i	0.594020	+	0.804450i
$9$		0			0
$10$	0.937254	+	4.35425i	0.0937254	+	0.435425i
$11$	19.8504			1.80458			0.902289	−	0.431132i	$-0.141886\pi$
$11$	19.8504			1.80458			0.902289	+	0.431132i	$0.141886\pi$
$12$		0			0
$13$			14.5203i			1.11694i	0.829524	+	0.558472i	$0.188612\pi$
$13$			14.5203i			1.11694i	−0.829524	+	0.558472i	$0.811388\pi$
$14$	3.63866	+	16.9043i	0.259905	+	1.20745i
$15$		0			0
$16$	10.5830	−	12.0000i	0.661438	−	0.750000i
$17$			5.29570i			0.311512i	0.987796	+	0.155756i	$0.0497813\pi$
$17$			5.29570i			0.311512i	−0.987796	+	0.155756i	$0.950219\pi$
$18$		0			0
$19$			24.2915i			1.27850i	0.768999	+	0.639250i	$0.220755\pi$
$19$			24.2915i			1.27850i	−0.768999	+	0.639250i	$0.779245\pi$
$20$	8.11905	−	3.66507i	0.405952	−	0.183254i
$21$		0			0
$22$	−8.35425	−	38.8118i	−0.379739	−	1.76417i
$23$			29.6528i			1.28925i	0.764497	+	0.644627i	$0.222987\pi$
$23$			29.6528i			1.28925i	−0.764497	+	0.644627i	$0.777013\pi$
$24$		0			0
$25$	−20.0405			−0.801621
$26$	28.3903	−	6.11102i	1.09193	−	0.235039i
$27$		0			0
$28$	31.5203	−	14.2288i	1.12572	−	0.508170i
$29$	−6.13742			−0.211635			−0.105818	−	0.994386i	$-0.533746\pi$
$29$	−6.13742			−0.211635			−0.105818	+	0.994386i	$0.533746\pi$
$30$		0			0
$31$	10.1255			0.326629			0.163314	−	0.986574i	$-0.447782\pi$
$31$	10.1255			0.326629			0.163314	+	0.986574i	$0.447782\pi$
$32$	−27.9166	−	15.6417i	−0.872393	−	0.488804i
$33$		0			0
$34$	10.3542	−	2.22876i	0.304537	−	0.0655517i
$35$	19.2540			0.550114
$36$		0			0
$37$			16.6458i			0.449885i	0.974372	+	0.224943i	$0.0722195\pi$
$37$			16.6458i			0.449885i	−0.974372	+	0.224943i	$0.927781\pi$
$38$	47.4952	−	10.2234i	1.24987	−	0.269036i
$39$		0			0
$40$	−10.5830	−	14.3320i	−0.264575	−	0.358301i
$41$		−	7.82087i		−	0.190753i	−0.995441	−	0.0953765i	$-0.969595\pi$
$41$		−	7.82087i		−	0.190753i	0.995441	−	0.0953765i	$-0.0304055\pi$
$42$		0			0
$43$		−	1.54249i		−	0.0358718i	−0.999839	−	0.0179359i	$-0.994291\pi$
$43$		−	1.54249i		−	0.0358718i	0.999839	−	0.0179359i	$-0.00570948\pi$
$44$	−72.3695	+	32.6687i	−1.64476	+	0.742472i
$45$		0			0
$46$	57.9778	−	12.4797i	1.26039	−	0.271299i
$47$		−	63.7069i		−	1.35547i	−0.735308	−	0.677733i	$-0.762963\pi$
$47$		−	63.7069i		−	1.35547i	0.735308	−	0.677733i	$-0.237037\pi$
$48$		0			0
$49$	25.7490			0.525490
$50$	8.43428	+	39.1836i	0.168686	+	0.783671i
$51$		0			0
$52$	−23.8967	−	52.9373i	−0.459553	−	1.01802i
$53$	−76.5253			−1.44387			−0.721936	−	0.691959i	$-0.756748\pi$
$53$	−76.5253			−1.44387			−0.721936	+	0.691959i	$0.756748\pi$
$54$		0			0
$55$	−44.2065			−0.803755
$56$	−41.0860	−	55.6406i	−0.733678	−	0.993583i
$57$		0			0
$58$	2.58301	+	12.0000i	0.0445346	+	0.206897i
$59$	41.0332			0.695477			0.347739	−	0.937592i	$-0.386950\pi$
$59$	41.0332			0.695477			0.347739	+	0.937592i	$0.386950\pi$
$60$		0			0
$61$			52.0627i			0.853488i	0.904373	+	0.426744i	$0.140339\pi$
$61$			52.0627i			0.853488i	−0.904373	+	0.426744i	$0.859661\pi$
$62$	−4.26143	−	19.7975i	−0.0687327	−	0.319315i
$63$		0			0
$64$	−18.8340	+	61.1660i	−0.294281	+	0.955719i
$65$		−	32.3365i		−	0.497484i
$66$		0			0
$67$			110.247i			1.64548i	0.568419	+	0.822739i	$0.307555\pi$
$67$			110.247i			1.64548i	−0.568419	+	0.822739i	$0.692445\pi$
$68$	−8.71541	−	19.3068i	−0.128168	−	0.283924i
$69$		0			0
$70$	−8.10326	−	37.6458i	−0.115761	−	0.537796i
$71$			100.690i			1.41817i	0.705125	+	0.709083i	$0.250891\pi$
$71$			100.690i			1.41817i	−0.705125	+	0.709083i	$0.749109\pi$
$72$		0			0
$73$	−93.9150			−1.28651			−0.643254	−	0.765653i	$-0.722416\pi$
$73$	−93.9150			−1.28651			−0.643254	+	0.765653i	$0.722416\pi$
$74$	32.5461	−	7.00555i	0.439812	−	0.0946697i
$75$		0			0
$76$	−39.9778	−	88.5608i	−0.526023	−	1.16527i
$77$	−171.621			−2.22885
$78$		0			0
$79$	−10.7712			−0.136345			−0.0681724	−	0.997674i	$-0.521717\pi$
$79$	−10.7712			−0.136345			−0.0681724	+	0.997674i	$0.521717\pi$
$80$	−23.5682	+	26.7239i	−0.294603	+	0.334048i
$81$		0			0
$82$	−15.2915	+	3.29150i	−0.186482	+	0.0401403i
$83$	118.996			1.43369			0.716846	−	0.697231i	$-0.245585\pi$
$83$	118.996			1.43369			0.716846	+	0.697231i	$0.245585\pi$
$84$		0			0
$85$		−	11.7935i		−	0.138747i
$86$	−3.01590	+	0.649173i	−0.0350686	+	0.00754853i
$87$		0			0
$88$	94.3320	+	127.749i	1.07195	+	1.45169i
$89$		−	146.071i		−	1.64125i	−0.571466	−	0.820626i	$-0.693625\pi$
$89$		−	146.071i		−	1.64125i	0.571466	−	0.820626i	$-0.306375\pi$
$90$		0			0
$91$		−	125.539i		−	1.37954i
$92$	−48.8012	−	108.107i	−0.530448	−	1.17508i
$93$		0			0
$94$	−124.561	+	26.8118i	−1.32511	+	0.285232i
$95$		−	54.0969i		−	0.569441i
$96$		0			0
$97$	−3.70850			−0.0382319			−0.0191160	−	0.999817i	$-0.506085\pi$
$97$	−3.70850			−0.0382319			−0.0191160	+	0.999817i	$0.506085\pi$
$98$	−10.8368	−	50.3449i	−0.110579	−	0.513724i
$99$		0			0
$100$	73.0627	−	32.9817i	0.730627	−	0.329817i
$101$	−109.598			−1.08513			−0.542563	−	0.840015i	$-0.682546\pi$
$101$	−109.598			−1.08513			−0.542563	+	0.840015i	$0.682546\pi$
$102$		0			0
$103$	159.391			1.54748			0.773742	−	0.633501i	$-0.218383\pi$
$103$	159.391			1.54748			0.773742	+	0.633501i	$0.218383\pi$
$104$	−93.4466	+	69.0026i	−0.898525	+	0.663486i
$105$		0			0
$106$	32.2065	+	149.624i	0.303835	+	1.41154i
$107$	49.8355			0.465752			0.232876	−	0.972506i	$-0.425186\pi$
$107$	49.8355			0.465752			0.232876	+	0.972506i	$0.425186\pi$
$108$		0			0
$109$		−	115.956i		−	1.06381i	−0.846803	−	0.531906i	$-0.821476\pi$
$109$		−	115.956i		−	1.06381i	0.846803	−	0.531906i	$-0.178524\pi$
$110$	18.6048	+	86.4334i	0.169135	+	0.785758i
$111$		0			0
$112$	−91.4980	+	103.749i	−0.816947	+	0.926330i
$113$			170.025i			1.50464i	0.658796	+	0.752322i	$0.271066\pi$
$113$			170.025i			1.50464i	−0.658796	+	0.752322i	$0.728934\pi$
$114$		0			0
$115$		−	66.0366i		−	0.574231i
$116$	22.3755	−	10.1007i	0.192892	−	0.0870748i
$117$		0			0
$118$	−17.2693	−	80.2288i	−0.146350	−	0.679905i
$119$		−	45.7853i		−	0.384751i
$120$		0			0
$121$	273.037			2.25650
$122$	101.794	−	21.9112i	0.834377	−	0.179600i
$123$		0			0
$124$	−36.9150	+	16.6640i	−0.297702	+	0.134387i
$125$	100.305			0.802438
$126$		0			0
$127$	−106.583			−0.839236			−0.419618	−	0.907701i	$-0.637836\pi$
$127$	−106.583			−0.839236			−0.419618	+	0.907701i	$0.637836\pi$
$128$	127.519	+	11.0821i	0.996245	+	0.0865792i
$129$		0			0
$130$	−63.2248	+	13.6092i	−0.486345	+	0.104686i
$131$	65.5488			0.500372			0.250186	−	0.968198i	$-0.419508\pi$
$131$	65.5488			0.500372			0.250186	+	0.968198i	$0.419508\pi$
$132$		0			0
$133$		−	210.018i		−	1.57908i
$134$	215.557	−	46.3987i	1.60863	−	0.346259i
$135$		0			0
$136$	−34.0810	+	25.1660i	−0.250596	+	0.185044i
$137$			141.829i			1.03525i	0.855609	+	0.517623i	$0.173183\pi$
$137$			141.829i			1.03525i	−0.855609	+	0.517623i	$0.826817\pi$
$138$		0			0
$139$		−	171.207i		−	1.23170i	−0.787863	−	0.615851i	$-0.788812\pi$
$139$		−	171.207i		−	1.23170i	0.787863	−	0.615851i	$-0.211188\pi$
$140$	−70.1953	+	31.6873i	−0.501395	+	0.226338i
$141$		0			0
$142$	196.871	−	42.3765i	1.38641	−	0.298426i
$143$			288.232i			2.01561i
$144$		0			0
$145$	13.6680			0.0942619
$146$	39.5252	+	183.624i	0.270721	+	1.25770i
$147$		0			0
$148$	−27.3948	−	60.6863i	−0.185100	−	0.410042i
$149$	216.916			1.45581			0.727905	−	0.685678i	$-0.240494\pi$
$149$	216.916			1.45581			0.727905	+	0.685678i	$0.240494\pi$
$150$		0			0
$151$	−60.7268			−0.402164			−0.201082	−	0.979574i	$-0.564446\pi$
$151$	−60.7268			−0.402164			−0.201082	+	0.979574i	$0.564446\pi$
$152$	−156.330	+	115.437i	−1.02849	+	0.759454i
$153$		0			0
$154$	72.2288	+	335.557i	0.469018	+	2.17894i
$155$	−22.5494			−0.145480
$156$		0			0
$157$			192.207i			1.22425i	0.790763	+	0.612123i	$0.209684\pi$
$157$			192.207i			1.22425i	−0.790763	+	0.612123i	$0.790316\pi$
$158$	4.53320	+	21.0601i	0.0286911	+	0.133292i
$159$		0			0
$160$	62.1699	+	34.8340i	0.388562	+	0.217712i
$161$		−	256.371i		−	1.59237i
$162$		0			0
$163$		−	6.29150i		−	0.0385982i	−0.999814	−	0.0192991i	$-0.993857\pi$
$163$		−	6.29150i		−	0.0385982i	0.999814	−	0.0192991i	$-0.00614347\pi$
$164$	12.8712	+	28.5129i	0.0784830	+	0.173859i
$165$		0			0
$166$	−50.0810	−	232.664i	−0.301693	−	1.40159i
$167$		−	214.092i		−	1.28199i	−0.767545	−	0.640995i	$-0.778522\pi$
$167$		−	214.092i		−	1.28199i	0.767545	−	0.640995i	$-0.221478\pi$
$168$		0			0
$169$	−41.8379			−0.247562
$170$	−23.0588	+	4.96342i	−0.135640	+	0.0291966i
$171$		0			0
$172$	2.53855	+	5.62352i	0.0147590	+	0.0326949i
$173$	44.0491			0.254619			0.127309	−	0.991863i	$-0.459366\pi$
$173$	44.0491			0.254619			0.127309	+	0.991863i	$0.459366\pi$
$174$		0			0
$175$	173.265			0.990088
$176$	210.076	−	238.204i	1.19362	−	1.35343i
$177$		0			0
$178$	−285.601	+	61.4758i	−1.60450	+	0.345370i
$179$	−132.570			−0.740613			−0.370306	−	0.928910i	$-0.620747\pi$
$179$	−132.570			−0.740613			−0.370306	+	0.928910i	$0.620747\pi$
$180$		0			0
$181$		−	141.516i		−	0.781858i	−0.920421	−	0.390929i	$-0.872154\pi$
$181$		−	141.516i		−	0.781858i	0.920421	−	0.390929i	$-0.127846\pi$
$182$	−245.455	+	52.8343i	−1.34865	+	0.290299i
$183$		0			0
$184$	−190.834	+	140.915i	−1.03714	+	0.765843i
$185$		−	37.0699i		−	0.200378i
$186$		0			0
$187$			105.122i			0.562147i
$188$	104.846	+	232.259i	0.557690	+	1.23542i
$189$		0			0
$190$	−105.771	+	22.7673i	−0.556691	+	0.119828i
$191$			1.45679i			0.00762718i	0.999993	+	0.00381359i	$0.00121391\pi$
$191$			1.45679i			0.00762718i	−0.999993	+	0.00381359i	$0.998786\pi$
$192$		0			0
$193$	−243.539			−1.26186			−0.630929	−	0.775841i	$-0.717326\pi$
$193$	−243.539			−1.26186			−0.630929	+	0.775841i	$0.717326\pi$
$194$	1.56076	+	7.25092i	0.00804517	+	0.0373759i
$195$		0			0
$196$	−93.8745	+	42.3765i	−0.478952	+	0.216207i
$197$	−4.99752			−0.0253681			−0.0126841	−	0.999920i	$-0.504038\pi$
$197$	−4.99752			−0.0253681			−0.0126841	+	0.999920i	$0.504038\pi$
$198$		0			0
$199$	102.476			0.514954			0.257477	−	0.966284i	$-0.417109\pi$
$199$	102.476			0.514954			0.257477	+	0.966284i	$0.417109\pi$
$200$	−95.2357	−	128.973i	−0.476179	−	0.644864i
$201$		0			0
$202$	46.1255	+	214.288i	0.228344	+	1.06083i
$203$	53.0626			0.261392
$204$		0			0
$205$			17.4170i			0.0849610i
$206$	−67.0815	−	311.644i	−0.325638	−	1.51283i
$207$		0			0
$208$	174.243	+	153.668i	0.837707	+	0.738788i
$209$			482.195i			2.30715i
$210$		0			0
$211$		−	9.54642i		−	0.0452437i	−0.999744	−	0.0226219i	$-0.992799\pi$
$211$		−	9.54642i		−	0.0452437i	0.999744	−	0.0226219i	$-0.00720138\pi$
$212$	278.992	−	125.942i	1.31600	−	0.594064i
$213$		0			0
$214$	−20.9738	−	97.4392i	−0.0980086	−	0.455323i
$215$			3.43510i			0.0159772i
$216$		0			0
$217$	−87.5425			−0.403422
$218$	−226.718	+	48.8012i	−1.03999	+	0.223859i
$219$		0			0
$220$	161.166	−	72.7530i	0.732573	−	0.330695i
$221$	−76.8950			−0.347941
$222$		0			0
$223$	51.1294			0.229280			0.114640	−	0.993407i	$-0.463429\pi$
$223$	51.1294			0.229280			0.114640	+	0.993407i	$0.463429\pi$
$224$	241.360	+	135.235i	1.07750	+	0.603726i
$225$		0			0
$226$	332.435	−	71.5568i	1.47095	−	0.316623i
$227$	−235.539			−1.03762			−0.518809	−	0.854890i	$-0.673624\pi$
$227$	−235.539			−1.03762			−0.518809	+	0.854890i	$0.673624\pi$
$228$		0			0
$229$		−	206.332i		−	0.901013i	−0.892773	−	0.450507i	$-0.851243\pi$
$229$		−	206.332i		−	0.901013i	0.892773	−	0.450507i	$-0.148757\pi$
$230$	−129.116	+	27.7923i	−0.561373	+	0.120836i
$231$		0			0
$232$	−29.1660	−	39.4980i	−0.125716	−	0.170250i
$233$		−	210.356i		−	0.902815i	−0.892318	−	0.451407i	$-0.850922\pi$
$233$		−	210.356i		−	0.902815i	0.892318	−	0.451407i	$-0.149078\pi$
$234$		0			0
$235$			141.875i			0.603721i
$236$	−149.597	+	67.5304i	−0.633884	+	0.286146i
$237$		0			0
$238$	−89.5203	+	19.2693i	−0.376136	+	0.0809633i
$239$			23.1457i			0.0968440i	0.998827	+	0.0484220i	$0.0154192\pi$
$239$			23.1457i			0.0968440i	−0.998827	+	0.0484220i	$0.984581\pi$
$240$		0			0
$241$	81.6275			0.338703			0.169352	−	0.985556i	$-0.445833\pi$
$241$	81.6275			0.338703			0.169352	+	0.985556i	$0.445833\pi$
$242$	−114.911	−	533.846i	−0.474837	−	2.20597i
$243$		0			0
$244$	−85.6823	−	189.808i	−0.351157	−	0.777901i
$245$	−57.3428			−0.234052
$246$		0			0
$247$	−352.719			−1.42801
$248$	48.1179	+	65.1637i	0.194024	+	0.262757i
$249$		0			0
$250$	−42.2144	−	196.118i	−0.168858	−	0.784470i
$251$	−232.769			−0.927366			−0.463683	−	0.886001i	$-0.653472\pi$
$251$	−232.769			−0.927366			−0.463683	+	0.886001i	$0.653472\pi$
$252$		0			0
$253$			588.620i			2.32656i
$254$	44.8567	+	208.393i	0.176601	+	0.820445i
$255$		0			0
$256$	−32.0000	−	253.992i	−0.125000	−	0.992157i
$257$		−	298.491i		−	1.16145i	−0.814102	−	0.580723i	$-0.802770\pi$
$257$		−	298.491i		−	1.16145i	0.814102	−	0.580723i	$-0.197230\pi$
$258$		0			0
$259$		−	143.915i		−	0.555656i
$260$	53.2178	+	117.891i	0.204684	+	0.453426i
$261$		0			0
$262$	−27.5869	−	128.162i	−0.105294	−	0.489168i
$263$		−	400.163i		−	1.52153i	−0.649027	−	0.760766i	$-0.724824\pi$
$263$		−	400.163i		−	1.52153i	0.649027	−	0.760766i	$-0.275176\pi$
$264$		0			0
$265$	170.421			0.643098
$266$	−410.631	+	88.3886i	−1.54373	+	0.332288i
$267$		0			0
$268$	−181.439	−	401.933i	−0.677012	−	1.49975i
$269$	446.650			1.66041			0.830205	−	0.557459i	$-0.188224\pi$
$269$	446.650			1.66041			0.830205	+	0.557459i	$0.188224\pi$
$270$		0			0
$271$	−30.3503			−0.111994			−0.0559969	−	0.998431i	$-0.517834\pi$
$271$	−30.3503			−0.111994			−0.0559969	+	0.998431i	$0.517834\pi$
$272$	63.5484	+	56.0444i	0.233634	+	0.206046i
$273$		0			0
$274$	277.306	−	59.6902i	1.01207	−	0.217847i
$275$	−397.811			−1.44659
$276$		0			0
$277$			149.284i			0.538930i	0.963010	+	0.269465i	$0.0868469\pi$
$277$			149.284i			0.538930i	−0.963010	+	0.269465i	$0.913153\pi$
$278$	−334.746	+	72.0542i	−1.20412	+	0.259188i
$279$		0			0
$280$	91.4980	+	123.911i	0.326779	+	0.442540i
$281$			81.9607i			0.291675i	0.989309	+	0.145838i	$0.0465877\pi$
$281$			81.9607i			0.291675i	−0.989309	+	0.145838i	$0.953412\pi$
$282$		0			0
$283$			462.207i			1.63324i	0.577177	+	0.816619i	$0.304154\pi$
$283$			462.207i			1.63324i	−0.577177	+	0.816619i	$0.695846\pi$
$284$	−165.710	−	367.090i	−0.583488	−	1.29257i
$285$		0			0
$286$	563.557	−	121.306i	1.97048	−	0.424146i
$287$			67.6173i			0.235600i
$288$		0			0
$289$	260.956			0.902960
$290$	−5.75233	−	26.7239i	−0.0198356	−	0.0921513i
$291$		0			0
$292$	342.391	−	154.561i	1.17257	−	0.529318i
$293$	335.860			1.14628			0.573139	−	0.819458i	$-0.305725\pi$
$293$	335.860			1.14628			0.573139	+	0.819458i	$0.305725\pi$
$294$		0			0
$295$	−91.3804			−0.309764
$296$	−107.125	+	79.1032i	−0.361910	+	0.267241i
$297$		0			0
$298$	−91.2915	−	424.118i	−0.306347	−	1.42321i
$299$	−430.567			−1.44002
$300$		0			0
$301$			13.3360i			0.0443055i
$302$	25.5576	+	118.734i	0.0846277	+	0.393159i
$303$		0			0
$304$	291.498	+	257.077i	0.958875	+	0.845648i
$305$		−	115.943i		−	0.380142i
$306$		0			0
$307$		−	40.6275i		−	0.132337i	−0.997808	−	0.0661685i	$-0.978923\pi$
$307$		−	40.6275i		−	0.132337i	0.997808	−	0.0661685i	$-0.0210775\pi$
$308$	625.688	−	282.446i	2.03146	−	0.917032i
$309$		0			0
$310$	9.49016	+	44.0889i	0.0306134	+	0.142222i
$311$		−	30.9512i		−	0.0995215i	−0.998761	−	0.0497608i	$-0.984154\pi$
$311$		−	30.9512i		−	0.0995215i	0.998761	−	0.0497608i	$-0.0158459\pi$
$312$		0			0
$313$	−285.612			−0.912497			−0.456249	−	0.889852i	$-0.650807\pi$
$313$	−285.612			−0.912497			−0.456249	+	0.889852i	$0.650807\pi$
$314$	375.806	−	80.8923i	1.19683	−	0.257619i
$315$		0			0
$316$	39.2693	−	17.7268i	0.124270	−	0.0560974i
$317$	173.426			0.547084			0.273542	−	0.961860i	$-0.411805\pi$
$317$	173.426			0.547084			0.273542	+	0.961860i	$0.411805\pi$
$318$		0			0
$319$	−121.830			−0.381912
$320$	41.9431	−	136.216i	0.131072	−	0.425675i
$321$		0			0
$322$	−501.261	+	107.897i	−1.55671	+	0.335083i
$323$	−128.641			−0.398268
$324$		0			0
$325$		−	290.994i		−	0.895365i
$326$	−12.3013	+	2.64785i	−0.0377339	+	0.00812224i
$327$		0			0
$328$	50.3320	−	37.1660i	0.153451	−	0.113311i
$329$			550.794i			1.67414i
$330$		0			0
$331$			228.705i			0.690950i	0.938428	+	0.345475i	$0.112282\pi$
$331$			228.705i			0.690950i	−0.938428	+	0.345475i	$0.887718\pi$
$332$	−433.832	+	195.839i	−1.30672	+	0.589875i
$333$		0			0
$334$	−418.597	+	90.1033i	−1.25329	+	0.269770i
$335$		−	245.519i		−	0.732893i
$336$		0			0
$337$	−403.207			−1.19646			−0.598229	−	0.801325i	$-0.704129\pi$
$337$	−403.207			−1.19646			−0.598229	+	0.801325i	$0.704129\pi$
$338$	17.6080	+	81.8022i	0.0520946	+	0.242018i
$339$		0			0
$340$	19.4091	+	42.9961i	0.0570856	+	0.126459i
$341$	200.995			0.589427
$342$		0			0
$343$	201.022			0.586071
$344$	9.92683	−	7.33014i	0.0288571	−	0.0213086i
$345$		0			0
$346$	−18.5385	−	86.1255i	−0.0535796	−	0.248918i
$347$	−166.941			−0.481097			−0.240548	−	0.970637i	$-0.577327\pi$
$347$	−166.941			−0.481097			−0.240548	+	0.970637i	$0.577327\pi$
$348$		0			0
$349$			552.395i			1.58279i	0.611303	+	0.791397i	$0.290646\pi$
$349$			552.395i			1.58279i	−0.611303	+	0.791397i	$0.709354\pi$
$350$	−72.9207	−	338.771i	−0.208345	−	0.967918i
$351$		0			0
$352$	−554.154	−	310.494i	−1.57430	−	0.882085i
$353$			54.0815i			0.153205i	0.997062	+	0.0766027i	$0.0244073\pi$
$353$			54.0815i			0.153205i	−0.997062	+	0.0766027i	$0.975593\pi$
$354$		0			0
$355$		−	224.235i		−	0.631649i
$356$	240.397	+	532.540i	0.675273	+	1.49590i
$357$		0			0
$358$	55.7935	+	259.203i	0.155848	+	0.724030i
$359$			623.374i			1.73642i	0.496198	+	0.868209i	$0.334729\pi$
$359$			623.374i			1.73642i	−0.496198	+	0.868209i	$0.665271\pi$
$360$		0			0
$361$	−229.077			−0.634563
$362$	−276.695	+	59.5588i	−0.764351	+	0.164527i
$363$		0			0
$364$	206.605	+	457.682i	0.567597	+	1.25737i
$365$	209.148			0.573008
$366$		0			0
$367$	61.2653			0.166936			0.0834678	−	0.996510i	$-0.473400\pi$
$367$	61.2653			0.166936			0.0834678	+	0.996510i	$0.473400\pi$
$368$	355.834	+	313.816i	0.966941	+	0.852762i
$369$		0			0
$370$	−72.4797	+	15.6013i	−0.195891	+	0.0421657i
$371$	661.618			1.78334
$372$		0			0
$373$		−	72.7712i		−	0.195097i	−0.995231	−	0.0975486i	$-0.968900\pi$
$373$		−	72.7712i		−	0.195097i	0.995231	−	0.0975486i	$-0.0311001\pi$
$374$	205.536	−	44.2416i	0.549560	−	0.118293i
$375$		0			0
$376$	409.992	−	302.745i	1.09040	−	0.805173i
$377$		−	89.1170i		−	0.236385i
$378$		0			0
$379$			341.405i			0.900805i	0.892826	+	0.450403i	$0.148720\pi$
$379$			341.405i			0.900805i	−0.892826	+	0.450403i	$0.851280\pi$
$380$	89.0301	+	197.224i	0.234290	+	0.519010i
$381$		0			0
$382$	2.84834	−	0.613107i	0.00745640	−	0.00160499i
$383$		−	318.059i		−	0.830441i	−0.909721	−	0.415221i	$-0.863704\pi$
$383$		−	318.059i		−	0.830441i	0.909721	−	0.415221i	$-0.136296\pi$
$384$		0			0
$385$	382.199			0.992724
$386$	102.496	+	476.171i	0.265534	+	1.23360i
$387$		0			0
$388$	13.5203	−	6.10326i	0.0348460	−	0.0157301i
$389$	308.645			0.793432			0.396716	−	0.917941i	$-0.370150\pi$
$389$	308.645			0.793432			0.396716	+	0.917941i	$0.370150\pi$
$390$		0			0
$391$	−157.033			−0.401618
$392$	122.363	+	165.710i	0.312152	+	0.422731i
$393$		0			0
$394$	2.10326	+	9.77124i	0.00533823	+	0.0248001i
$395$	23.9874			0.0607277
$396$		0			0
$397$			172.044i			0.433361i	0.976243	+	0.216681i	$0.0695230\pi$
$397$			172.044i			0.433361i	−0.976243	+	0.216681i	$0.930477\pi$
$398$	−43.1281	−	200.362i	−0.108362	−	0.503423i
$399$		0			0
$400$	−212.089	+	240.486i	−0.530222	+	0.601216i
$401$			329.110i			0.820724i	0.911923	+	0.410362i	$0.134598\pi$
$401$			329.110i			0.820724i	−0.911923	+	0.410362i	$0.865402\pi$
$402$		0			0
$403$			147.025i			0.364826i
$404$	399.566	−	180.371i	0.989026	−	0.446462i
$405$		0			0
$406$	−22.3320	−	103.749i	−0.0550050	−	0.255539i
$407$			330.424i			0.811853i
$408$		0			0
$409$	−353.458			−0.864199			−0.432100	−	0.901826i	$-0.642227\pi$
$409$	−353.458			−0.864199			−0.432100	+	0.901826i	$0.642227\pi$
$410$	34.0540	−	7.33014i	0.0830586	−	0.0178784i
$411$		0			0
$412$	−581.099	+	262.318i	−1.41044	+	0.636693i
$413$	−354.763			−0.858989
$414$		0			0
$415$	−265.004			−0.638564
$416$	227.122	−	405.356i	0.545967	−	0.974414i
$417$		0			0
$418$	942.796	−	202.937i	2.25549	−	0.485496i
$419$	327.287			0.781115			0.390557	−	0.920579i	$-0.372282\pi$
$419$	327.287			0.781115			0.390557	+	0.920579i	$0.372282\pi$
$420$		0			0
$421$		−	501.759i		−	1.19183i	−0.803048	−	0.595914i	$-0.796790\pi$
$421$		−	501.759i		−	1.19183i	0.803048	−	0.595914i	$-0.203210\pi$
$422$	−18.6653	+	4.01772i	−0.0442307	+	0.00952067i
$423$		0			0
$424$	−363.660	−	492.486i	−0.857689	−	1.16152i
$425$		−	106.129i		−	0.249714i
$426$		0			0
$427$		−	450.122i		−	1.05415i
$428$	−181.688	+	82.0168i	−0.424504	+	0.191628i
$429$		0			0
$430$	6.71637	−	1.44570i	0.0156195	−	0.00336210i
$431$			29.8267i			0.0692035i	0.999401	+	0.0346017i	$0.0110163\pi$
$431$			29.8267i			0.0692035i	−0.999401	+	0.0346017i	$0.988984\pi$
$432$		0			0
$433$	519.859			1.20060			0.600299	−	0.799776i	$-0.295048\pi$
$433$	519.859			1.20060			0.600299	+	0.799776i	$0.295048\pi$
$434$	36.8433	+	171.165i	0.0848923	+	0.394388i
$435$		0			0
$436$	190.834	+	422.745i	0.437693	+	0.969599i
$437$	−720.312			−1.64831
$438$		0			0
$439$	386.450			0.880295			0.440148	−	0.897925i	$-0.354926\pi$
$439$	386.450			0.880295			0.440148	+	0.897925i	$0.354926\pi$
$440$	−210.076	−	284.496i	−0.477446	−	0.646581i
$441$		0			0
$442$	32.3621	+	150.346i	0.0732175	+	0.340150i
$443$	378.527			0.854462			0.427231	−	0.904143i	$-0.359489\pi$
$443$	378.527			0.854462			0.427231	+	0.904143i	$0.359489\pi$
$444$		0			0
$445$			325.299i			0.731010i
$446$	−21.5184	−	99.9692i	−0.0482475	−	0.224146i
$447$		0			0
$448$	162.834	−	528.826i	0.363469	−	1.18042i
$449$		−	289.127i		−	0.643935i	−0.946751	−	0.321968i	$-0.895656\pi$
$449$		−	289.127i		−	0.643935i	0.946751	−	0.321968i	$-0.104344\pi$
$450$		0			0
$451$		−	155.247i		−	0.344228i
$452$	−279.818	−	619.868i	−0.619067	−	1.37139i
$453$		0			0
$454$	99.1294	+	460.531i	0.218347	+	1.01438i
$455$			279.573i			0.614446i
$456$		0			0
$457$	485.365			1.06207			0.531034	−	0.847351i	$-0.321804\pi$
$457$	485.365			1.06207			0.531034	+	0.847351i	$0.321804\pi$
$458$	−403.424	+	86.8372i	−0.880838	+	0.189601i
$459$		0			0
$460$	108.680	+	240.753i	0.236260	+	0.523376i
$461$	−215.037			−0.466457			−0.233228	−	0.972422i	$-0.574929\pi$
$461$	−215.037			−0.466457			−0.233228	+	0.972422i	$0.574929\pi$
$462$		0			0
$463$	−374.755			−0.809407			−0.404704	−	0.914448i	$-0.632625\pi$
$463$	−374.755			−0.809407			−0.404704	+	0.914448i	$0.632625\pi$
$464$	−64.9524	+	73.6491i	−0.139984	+	0.158726i
$465$		0			0
$466$	−411.292	+	88.5307i	−0.882600	+	0.189980i
$467$	−268.050			−0.573982			−0.286991	−	0.957933i	$-0.592655\pi$
$467$	−268.050			−0.573982			−0.286991	+	0.957933i	$0.592655\pi$
$468$		0			0
$469$		−	953.169i		−	2.03234i
$470$	277.396	−	59.7095i	0.590203	−	0.127042i
$471$		0			0
$472$	194.996	+	264.073i	0.413127	+	0.559477i
$473$		−	30.6189i		−	0.0647334i
$474$		0			0
$475$		−	486.814i		−	1.02487i
$476$	75.3512	+	166.922i	0.158301	+	0.350676i
$477$		0			0
$478$	45.2549	−	9.74114i	0.0946756	−	0.0203790i
$479$		−	512.109i		−	1.06912i	−0.845130	−	0.534560i	$-0.820477\pi$
$479$		−	512.109i		−	1.06912i	0.845130	−	0.534560i	$-0.179523\pi$
$480$		0			0
$481$	−241.701			−0.502496
$482$	−34.3538	−	159.599i	−0.0712735	−	0.331119i
$483$		0			0
$484$	−995.423	+	449.350i	−2.05666	+	0.928410i
$485$	8.25878			0.0170284
$486$		0			0
$487$	885.804			1.81890			0.909450	−	0.415814i	$-0.136503\pi$
$487$	885.804			1.81890			0.909450	+	0.415814i	$0.136503\pi$
$488$	−335.055	+	247.410i	−0.686589	+	0.506989i
$489$		0			0
$490$	24.1334	+	112.118i	0.0492518	+	0.228811i
$491$	434.847			0.885636			0.442818	−	0.896612i	$-0.353979\pi$
$491$	434.847			0.885636			0.442818	+	0.896612i	$0.353979\pi$
$492$		0			0
$493$		−	32.5020i		−	0.0659269i
$494$	148.446	+	689.642i	0.300498	+	1.39604i
$495$		0			0
$496$	107.158	−	121.506i	0.216045	−	0.244972i
$497$		−	870.539i		−	1.75159i
$498$		0			0
$499$		−	712.980i		−	1.42882i	−0.699728	−	0.714409i	$-0.746696\pi$
$499$		−	712.980i		−	1.42882i	0.699728	−	0.714409i	$-0.253304\pi$
$500$	−365.686	+	165.077i	−0.731372	+	0.330153i
$501$		0			0
$502$	97.9634	+	455.114i	0.195146	+	0.906601i
$503$			68.4403i			0.136064i	0.997683	+	0.0680321i	$0.0216720\pi$
$503$			68.4403i			0.136064i	−0.997683	+	0.0680321i	$0.978328\pi$
$504$		0			0
$505$	244.073			0.483313
$506$	1150.88	−	247.727i	2.27447	−	0.489580i
$507$		0			0
$508$	388.575	−	175.409i	0.764912	−	0.345294i
$509$	−7.45117			−0.0146388			−0.00731942	−	0.999973i	$-0.502330\pi$
$509$	−7.45117			−0.0146388			−0.00731942	+	0.999973i	$0.502330\pi$
$510$		0			0
$511$	811.966			1.58897
$512$	−483.142	+	169.462i	−0.943637	+	0.330981i
$513$		0			0
$514$	−583.616	+	125.624i	−1.13544	+	0.244404i
$515$	−354.962			−0.689246
$516$		0			0
$517$		−	1264.60i		−	2.44604i
$518$	−281.385	+	60.5683i	−0.543215	+	0.116927i
$519$		0			0
$520$	208.105	−	153.668i	0.400201	−	0.295515i
$521$			426.007i			0.817673i	0.912608	+	0.408836i	$0.134065\pi$
$521$			426.007i			0.817673i	−0.912608	+	0.408836i	$0.865935\pi$
$522$		0			0
$523$		−	270.875i		−	0.517924i	−0.965887	−	0.258962i	$-0.916619\pi$
$523$		−	270.875i		−	0.517924i	0.965887	−	0.258962i	$-0.0833805\pi$
$524$	−238.974	+	107.877i	−0.456058	+	0.205872i
$525$		0			0
$526$	−782.405	+	168.413i	−1.48746	+	0.320177i
$527$			53.6216i			0.101749i
$528$		0			0
$529$	−350.292			−0.662177
$530$	−71.7236	−	333.210i	−0.135328	−	0.628698i
$531$		0			0
$532$	345.638	+	765.674i	0.649695	+	1.43924i
$533$	113.561			0.213060
$534$		0			0
$535$	−110.983			−0.207445
$536$	−709.506	+	523.911i	−1.32371	+	0.977447i
$537$		0			0
$538$	−187.978	−	873.298i	−0.349401	−	1.62323i
$539$	511.127			0.948288
$540$		0			0
$541$			964.379i			1.78259i	0.453428	+	0.891293i	$0.350201\pi$
$541$			964.379i			1.78259i	−0.453428	+	0.891293i	$0.649799\pi$
$542$	12.7733	+	59.3415i	0.0235669	+	0.109486i
$543$		0			0
$544$	82.8340	−	147.838i	0.152268	−	0.271761i
$545$			258.232i			0.473820i
$546$		0			0
$547$			485.162i			0.886951i	0.896287	+	0.443475i	$0.146255\pi$
$547$			485.162i			0.886951i	−0.896287	+	0.443475i	$0.853745\pi$
$548$	−233.415	−	517.072i	−0.425939	−	0.943562i
$549$		0			0
$550$	167.423	+	777.808i	0.304406	+	1.41420i
$551$		−	149.087i		−	0.270576i
$552$		0			0
$553$	93.1255			0.168401
$554$	291.882	−	62.8277i	0.526863	−	0.113407i
$555$		0			0
$556$	281.763	+	624.176i	0.506769	+	1.12262i
$557$	−930.917			−1.67130			−0.835652	−	0.549259i	$-0.814910\pi$
$557$	−930.917			−1.67130			−0.835652	+	0.549259i	$0.814910\pi$
$558$		0			0
$559$	22.3973			0.0400667
$560$	203.765	−	231.048i	0.363866	−	0.412586i
$561$		0			0
$562$	160.251	−	34.4941i	0.285144	−	0.0613774i
$563$	−511.376			−0.908305			−0.454153	−	0.890924i	$-0.650058\pi$
$563$	−511.376			−0.908305			−0.454153	+	0.890924i	$0.650058\pi$
$564$		0			0
$565$		−	378.643i		−	0.670165i
$566$	903.714	−	194.525i	1.59667	−	0.343684i
$567$		0			0
$568$	−648.000	+	478.494i	−1.14085	+	0.842419i
$569$			88.0640i			0.154770i	0.997001	+	0.0773849i	$0.0246570\pi$
$569$			88.0640i			0.154770i	−0.997001	+	0.0773849i	$0.975343\pi$
$570$		0			0
$571$			451.288i			0.790346i	0.918607	+	0.395173i	$0.129315\pi$
$571$			451.288i			0.790346i	−0.918607	+	0.395173i	$0.870685\pi$
$572$	−474.359	−	1050.82i	−0.829298	−	1.83710i
$573$		0			0
$574$	132.207	−	28.4575i	0.230325	−	0.0495775i
$575$		−	594.258i		−	1.03349i
$576$		0			0
$577$	−177.405			−0.307461			−0.153731	−	0.988113i	$-0.549129\pi$
$577$	−177.405			−0.307461			−0.153731	+	0.988113i	$0.549129\pi$
$578$	−109.826	−	510.225i	−0.190011	−	0.882742i
$579$		0			0
$580$	−49.8301	+	22.4941i	−0.0859139	+	0.0387829i
$581$	−1028.81			−1.77076
$582$		0			0
$583$	−1519.05			−2.60558
$584$	−446.299	−	604.400i	−0.764211	−	1.03493i
$585$		0			0
$586$	−141.350	−	656.678i	−0.241212	−	1.12061i
$587$	−74.8077			−0.127441			−0.0637204	−	0.997968i	$-0.520297\pi$
$587$	−74.8077			−0.127441			−0.0637204	+	0.997968i	$0.520297\pi$
$588$		0			0
$589$			245.963i			0.417595i
$590$	38.4585	+	178.669i	0.0651839	+	0.302828i
$591$		0			0
$592$	199.749	+	176.162i	0.337414	+	0.297571i
$593$			149.087i			0.251412i	0.992068	+	0.125706i	$0.0401196\pi$
$593$			149.087i			0.251412i	−0.992068	+	0.125706i	$0.959880\pi$
$594$		0			0
$595$			101.963i			0.171367i
$596$	−790.821	+	356.989i	−1.32688	+	0.598976i
$597$		0			0
$598$	181.209	+	841.852i	0.303025	+	1.40778i
$599$			234.452i			0.391406i	0.980663	+	0.195703i	$0.0626989\pi$
$599$			234.452i			0.391406i	−0.980663	+	0.195703i	$0.937301\pi$
$600$		0			0
$601$	20.8627			0.0347133			0.0173567	−	0.999849i	$-0.494475\pi$
$601$	20.8627			0.0347133			0.0173567	+	0.999849i	$0.494475\pi$
$602$	26.0747	−	5.61259i	0.0433135	−	0.00932324i
$603$		0			0
$604$	221.395	−	99.9412i	0.366548	−	0.165466i
$605$	−608.050			−1.00504
$606$		0			0
$607$	119.103			0.196216			0.0981081	−	0.995176i	$-0.468721\pi$
$607$	119.103			0.196216			0.0981081	+	0.995176i	$0.468721\pi$
$608$	379.961	−	678.136i	0.624936	−	1.11536i
$609$		0			0
$610$	−226.694	+	48.7960i	−0.371630	+	0.0799935i
$611$	925.040			1.51398
$612$		0			0
$613$			610.586i			0.996061i	0.867159	+	0.498031i	$0.165943\pi$
$613$			610.586i			0.996061i	−0.867159	+	0.498031i	$0.834057\pi$
$614$	−79.4355	+	17.0985i	−0.129374	+	0.0278478i
$615$		0			0
$616$	−815.571	−	1104.49i	−1.32398	−	1.79300i
$617$		−	1199.40i		−	1.94393i	−0.235127	−	0.971965i	$-0.575551\pi$
$617$		−	1199.40i		−	1.94393i	0.235127	−	0.971965i	$-0.424449\pi$
$618$		0			0
$619$		−	982.482i		−	1.58721i	−0.608434	−	0.793604i	$-0.708202\pi$
$619$		−	982.482i		−	1.58721i	0.608434	−	0.793604i	$-0.291798\pi$
$620$	82.2094	−	37.1106i	0.132596	−	0.0598559i
$621$		0			0
$622$	−60.5163	+	13.0262i	−0.0972931	+	0.0209424i
$623$			1262.90i			2.02712i
$624$		0			0
$625$	277.635			0.444217
$626$	120.203	+	558.433i	0.192017	+	0.892066i
$627$		0			0
$628$	−316.324	−	700.737i	−0.503701	−	1.11582i
$629$	−88.1509			−0.140145
$630$		0			0
$631$	−25.8928			−0.0410345			−0.0205173	−	0.999789i	$-0.506531\pi$
$631$	−25.8928			−0.0410345			−0.0205173	+	0.999789i	$0.506531\pi$
$632$	−51.1867	−	69.3195i	−0.0809915	−	0.109683i
$633$		0			0
$634$	−72.9882	−	339.085i	−0.115123	−	0.534834i
$635$	237.359			0.373794
$636$		0			0
$637$			373.882i			0.586943i
$638$	51.2736	+	238.204i	0.0803661	+	0.373361i
$639$		0			0
$640$	−283.984	−	24.6798i	−0.443725	−	0.0385622i
$641$		−	74.7736i		−	0.116651i	−0.998298	−	0.0583257i	$-0.981424\pi$
$641$		−	74.7736i		−	0.116651i	0.998298	−	0.0583257i	$-0.0185762\pi$
$642$		0			0
$643$			804.936i			1.25184i	0.779886	+	0.625922i	$0.215277\pi$
$643$			804.936i			1.25184i	−0.779886	+	0.625922i	$0.784723\pi$
$644$	421.923	+	934.666i	0.655160	+	1.45134i
$645$		0			0
$646$	54.1398	+	251.520i	0.0838078	+	0.389350i
$647$		−	1114.00i		−	1.72179i	−0.508782	−	0.860895i	$-0.669904\pi$
$647$		−	1114.00i		−	1.72179i	0.508782	−	0.860895i	$-0.330096\pi$
$648$		0			0
$649$	814.523			1.25504
$650$	−568.956	+	122.468i	−0.875316	+	0.188412i
$651$		0			0
$652$	10.3542	+	22.9373i	0.0158807	+	0.0351798i
$653$	789.281			1.20870			0.604350	−	0.796719i	$-0.293433\pi$
$653$	789.281			1.20870			0.604350	+	0.796719i	$0.293433\pi$
$654$		0			0
$655$	−145.976			−0.222865
$656$	−93.8504	−	82.7683i	−0.143065	−	0.126171i
$657$		0			0
$658$	1076.92	−	231.808i	1.63666	−	0.352292i
$659$	1233.28			1.87144			0.935722	−	0.352739i	$-0.114750\pi$
$659$	1233.28			1.87144			0.935722	+	0.352739i	$0.114750\pi$
$660$		0			0
$661$		−	4.49943i		−	0.00680700i	−0.999994	−	0.00340350i	$-0.998917\pi$
$661$		−	4.49943i		−	0.00680700i	0.999994	−	0.00340350i	$-0.00108337\pi$
$662$	447.167	−	96.2529i	0.675479	−	0.145397i
$663$		0			0
$664$	565.490	+	765.814i	0.851642	+	1.15333i
$665$			467.709i			0.703321i
$666$		0			0
$667$		−	181.992i		−	0.272852i
$668$	352.343	+	780.528i	0.527460	+	1.16845i
$669$		0			0
$670$	−480.043	+	103.329i	−0.716482	+	0.154223i
$671$			1033.46i			1.54018i
$672$		0			0
$673$	−163.620			−0.243120			−0.121560	−	0.992584i	$-0.538790\pi$
$673$	−163.620			−0.243120			−0.121560	+	0.992584i	$0.538790\pi$
$674$	169.694	+	788.356i	0.251772	+	1.16967i
$675$		0			0
$676$	152.531	−	68.8548i	0.225637	−	0.101856i
$677$	−686.078			−1.01341			−0.506704	−	0.862120i	$-0.669136\pi$
$677$	−686.078			−1.01341			−0.506704	+	0.862120i	$0.669136\pi$
$678$		0			0
$679$	32.0627			0.0472205
$680$	75.8981	−	56.0444i	0.111615	−	0.0824183i
$681$		0			0
$682$	−84.5909	−	392.988i	−0.124034	−	0.576229i
$683$	267.879			0.392210			0.196105	−	0.980583i	$-0.437171\pi$
$683$	267.879			0.392210			0.196105	+	0.980583i	$0.437171\pi$
$684$		0			0
$685$		−	315.851i		−	0.461096i
$686$	−84.6025	−	393.042i	−0.123327	−	0.572948i
$687$		0			0
$688$	−18.5098	−	16.3241i	−0.0269038	−	0.0237270i
$689$		−	1111.17i		−	1.61272i
$690$		0			0
$691$			576.037i			0.833627i	0.908992	+	0.416814i	$0.136853\pi$
$691$			576.037i			0.833627i	−0.908992	+	0.416814i	$0.863147\pi$
$692$	−160.592	+	72.4938i	−0.232069	+	0.104760i
$693$		0			0
$694$	70.2589	+	326.405i	0.101238	+	0.470324i
$695$			381.275i			0.548597i
$696$		0			0
$697$	41.4170			0.0594218
$698$	1080.05	−	232.482i	1.54735	−	0.333068i
$699$		0			0
$700$	−631.682	+	285.152i	−0.902403	+	0.407360i
$701$	−356.794			−0.508978			−0.254489	−	0.967076i	$-0.581907\pi$
$701$	−356.794			−0.508978			−0.254489	+	0.967076i	$0.581907\pi$
$702$		0			0
$703$	−404.350			−0.575178
$704$	−373.861	+	1214.17i	−0.531053	+	1.72467i
$705$		0			0
$706$	105.741	−	22.7608i	0.149775	−	0.0322391i
$707$	947.555			1.34025
$708$		0			0
$709$		−	1146.88i		−	1.61760i	−0.588081	−	0.808802i	$-0.700116\pi$
$709$		−	1146.88i		−	1.61760i	0.588081	−	0.808802i	$-0.299884\pi$
$710$	−438.429	+	94.3720i	−0.617505	+	0.132918i
$711$		0			0
$712$	940.057	−	694.154i	1.32031	−	0.974936i
$713$			300.250i			0.421108i
$714$		0			0
$715$		−	641.890i		−	0.897749i
$716$	483.316	−	218.177i	0.675023	−	0.304716i
$717$		0			0
$718$	1218.83	−	262.354i	1.69754	−	0.365396i
$719$			79.3640i			0.110381i	0.998476	+	0.0551905i	$0.0175766\pi$
$719$			79.3640i			0.110381i	−0.998476	+	0.0551905i	$0.982423\pi$
$720$		0			0
$721$	−1378.05			−1.91131
$722$	96.4097	+	447.896i	0.133531	+	0.620354i
$723$		0			0
$724$	232.901	+	515.933i	0.321686	+	0.712615i
$725$	122.997			0.169651
$726$		0			0
$727$	871.940			1.19937			0.599683	−	0.800237i	$-0.295293\pi$
$727$	871.940			1.19937			0.599683	+	0.800237i	$0.295293\pi$
$728$	807.916	−	596.579i	1.10978	−	0.819477i
$729$		0			0
$730$	−88.0222	−	408.929i	−0.120578	−	0.560177i
$731$	8.16855			0.0111745
$732$		0			0
$733$			1266.45i			1.72776i	0.503696	+	0.863881i	$0.331973\pi$
$733$			1266.45i			1.72776i	−0.503696	+	0.863881i	$0.668027\pi$
$734$	−25.7842	−	119.787i	−0.0351284	−	0.163198i
$735$		0			0
$736$	463.822	−	827.806i	0.630193	−	1.12474i
$737$			2188.44i			2.96939i
$738$		0			0
$739$			560.199i			0.758050i	0.925387	+	0.379025i	$0.123740\pi$
$739$			560.199i			0.758050i	−0.925387	+	0.379025i	$0.876260\pi$
$740$	61.0079	+	135.148i	0.0824430	+	0.182632i
$741$		0			0
$742$	−278.450	−	1293.61i	−0.375269	−	1.74341i
$743$		−	470.187i		−	0.632823i	−0.948622	−	0.316411i	$-0.897522\pi$
$743$		−	470.187i		−	0.632823i	0.948622	−	0.316411i	$-0.102478\pi$
$744$		0			0
$745$	−483.069			−0.648415
$746$	−142.284	+	30.6266i	−0.190729	+	0.0410544i
$747$		0			0
$748$	−173.004	−	383.247i	−0.231289	−	0.512362i
$749$	−430.865			−0.575254
$750$		0			0
$751$	1127.93			1.50190			0.750952	−	0.660357i	$-0.229595\pi$
$751$	1127.93			1.50190			0.750952	+	0.660357i	$0.229595\pi$
$752$	−764.482	−	674.210i	−1.01660	−	0.896556i
$753$		0			0
$754$	−174.243	+	37.5059i	−0.231092	+	0.0497426i
$755$	135.238			0.179123
$756$		0			0
$757$		−	450.055i		−	0.594524i	−0.954796	−	0.297262i	$-0.903926\pi$
$757$		−	450.055i		−	0.594524i	0.954796	−	0.297262i	$-0.0960735\pi$
$758$	667.521	−	143.684i	0.880635	−	0.189557i
$759$		0			0
$760$	348.146	−	257.077i	0.458087	−	0.338259i
$761$			223.932i			0.294261i	0.989117	+	0.147130i	$0.0470037\pi$
$761$			223.932i			0.294261i	−0.989117	+	0.147130i	$0.952996\pi$
$762$		0			0
$763$			1002.52i			1.31392i
$764$	−2.39752	−	5.31110i	−0.00313811	−	0.00695170i
$765$		0			0
$766$	−621.875	+	133.859i	−0.811847	+	0.174750i
$767$			595.812i			0.776809i
$768$		0			0
$769$	562.393			0.731331			0.365665	−	0.930746i	$-0.380841\pi$
$769$	562.393			0.731331			0.365665	+	0.930746i	$0.380841\pi$
$770$	−160.853	−	747.282i	−0.208900	−	0.970495i
$771$		0			0
$772$	887.881	−	400.804i	1.15010	−	0.519176i
$773$	857.103			1.10880			0.554400	−	0.832250i	$-0.312948\pi$
$773$	857.103			1.10880			0.554400	+	0.832250i	$0.312948\pi$
$774$		0			0
$775$	−202.920			−0.261832
$776$	−17.6234	−	23.8664i	−0.0227105	−	0.0307557i
$777$		0			0
$778$	−129.897	−	603.468i	−0.166962	−	0.775666i
$779$	189.981			0.243878
$780$		0			0
$781$			1998.73i			2.55919i
$782$	66.0890	+	307.033i	0.0845128	+	0.392625i
$783$		0			0
$784$	272.502	−	308.988i	0.347579	−	0.394118i
$785$		−	428.042i		−	0.545276i
$786$		0			0
$787$			386.624i			0.491262i	0.969363	+	0.245631i	$0.0789952\pi$
$787$			386.624i			0.491262i	−0.969363	+	0.245631i	$0.921005\pi$
$788$	18.2197	−	8.22468i	0.0231215	−	0.0104374i
$789$		0			0
$790$	−10.0954	−	46.9007i	−0.0127790	−	0.0593679i
$791$		−	1469.99i		−	1.85840i
$792$		0			0
$793$	−755.965			−0.953297
$794$	336.384	−	72.4069i	0.423658	−	0.0911925i
$795$		0			0
$796$	−373.601	+	168.650i	−0.469348	+	0.211871i
$797$	1049.51			1.31682			0.658410	−	0.752659i	$-0.271229\pi$
$797$	1049.51			1.31682			0.658410	+	0.752659i	$0.271229\pi$
$798$		0			0
$799$	337.373			0.422243
$800$	559.463	+	313.469i	0.699329	+	0.391836i
$801$		0			0
$802$	643.482	−	138.510i	0.802347	−	0.172706i
$803$	−1864.25			−2.32160
$804$		0			0
$805$			570.936i			0.709237i
$806$	287.465	−	61.8771i	0.356657	−	0.0767705i
$807$		0			0
$808$	−520.826	−	705.328i	−0.644587	−	0.872931i
$809$		−	467.780i		−	0.578220i	−0.957296	−	0.289110i	$-0.906641\pi$
$809$		−	467.780i		−	0.578220i	0.957296	−	0.289110i	$-0.0933593\pi$
$810$		0			0
$811$		−	1.80922i		−	0.00223085i	−0.999999	−	0.00111543i	$-0.999645\pi$
$811$		−	1.80922i		−	0.00223085i	0.999999	−	0.00111543i	$-0.000355051\pi$
$812$	−193.453	+	87.3279i	−0.238243	+	0.107547i
$813$		0			0
$814$	646.051	−	139.063i	0.793674	−	0.170839i
$815$			14.0111i			0.0171915i
$816$		0			0
$817$	37.4693			0.0458621
$818$	148.757	+	691.086i	0.181854	+	0.844849i
$819$		0			0
$820$	−28.6640	−	63.4980i	−0.0349561	−	0.0774366i
$821$	737.637			0.898462			0.449231	−	0.893416i	$-0.351698\pi$
$821$	737.637			0.898462			0.449231	+	0.893416i	$0.351698\pi$
$822$		0			0
$823$	−290.172			−0.352579			−0.176289	−	0.984338i	$-0.556409\pi$
$823$	−290.172			−0.352579			−0.176289	+	0.984338i	$0.556409\pi$
$824$	757.450	+	1025.78i	0.919236	+	1.24487i
$825$		0			0
$826$	149.306	+	693.638i	0.180758	+	0.839755i
$827$	−429.517			−0.519368			−0.259684	−	0.965694i	$-0.583618\pi$
$827$	−429.517			−0.519368			−0.259684	+	0.965694i	$0.583618\pi$
$828$		0			0
$829$		−	718.136i		−	0.866268i	−0.901330	−	0.433134i	$-0.857408\pi$
$829$		−	718.136i		−	0.866268i	0.901330	−	0.433134i	$-0.142592\pi$
$830$	111.530	+	518.140i	0.134373	+	0.624265i
$831$		0			0
$832$	−888.146	−	273.474i	−1.06748	−	0.328695i
$833$			136.359i			0.163696i
$834$		0			0
$835$			476.782i			0.570996i
$836$	−793.573	−	1757.96i	−0.949250	−	2.10283i
$837$		0			0
$838$	−137.743	−	639.918i	−0.164371	−	0.763625i
$839$			1171.31i			1.39608i	0.716059	+	0.698040i	$0.245944\pi$
$839$			1171.31i			1.39608i	−0.716059	+	0.698040i	$0.754056\pi$
$840$		0			0
$841$	−803.332			−0.955210
$842$	−981.049	+	211.171i	−1.16514	+	0.250797i
$843$		0			0
$844$	15.7110	+	34.8039i	0.0186150	+	0.0412368i
$845$	93.1726			0.110263
$846$		0			0
$847$	−2360.61			−2.78702
$848$	−809.867	+	918.303i	−0.955032	+	1.08290i
$849$		0			0
$850$	−207.505	+	44.6654i	−0.244123	+	0.0525476i
$851$	−493.594			−0.580016
$852$		0			0
$853$		−	94.3059i		−	0.110558i	−0.998471	−	0.0552789i	$-0.982395\pi$
$853$		−	94.3059i		−	0.110558i	0.998471	−	0.0552789i	$-0.0176048\pi$
$854$	−880.086	+	189.439i	−1.03055	+	0.221825i
$855$		0			0
$856$	236.826	+	320.721i	0.276666	+	0.374675i
$857$		−	651.269i		−	0.759940i	−0.924999	−	0.379970i	$-0.875934\pi$
$857$		−	651.269i		−	0.759940i	0.924999	−	0.379970i	$-0.124066\pi$
$858$		0			0
$859$			470.587i			0.547831i	0.961754	+	0.273916i	$0.0883189\pi$
$859$			470.587i			0.547831i	−0.961754	+	0.273916i	$0.911681\pi$
$860$	−5.65332	−	12.5235i	−0.00657363	−	0.0145622i
$861$		0			0
$862$	58.3177	−	12.5529i	0.0676539	−	0.0145625i
$863$		−	269.299i		−	0.312049i	−0.987753	−	0.156025i	$-0.950132\pi$
$863$		−	269.299i		−	0.312049i	0.987753	−	0.156025i	$-0.0498679\pi$
$864$		0			0
$865$	−98.0968			−0.113407
$866$	−218.789	−	1016.44i	−0.252643	−	1.17371i
$867$		0			0
$868$	319.158	−	144.073i	0.367694	−	0.165983i
$869$	−213.813			−0.246045
$870$		0			0
$871$	−1600.82			−1.83791
$872$	746.244	−	551.039i	0.855784	−	0.631926i
$873$		0			0
$874$	303.152	+	1408.37i	0.346855	+	1.61140i
$875$	−867.210			−0.991097
$876$		0			0
$877$			1011.57i			1.15344i	0.816942	+	0.576719i	$0.195667\pi$
$877$			1011.57i			1.15344i	−0.816942	+	0.576719i	$0.804333\pi$
$878$	−162.642	−	755.593i	−0.185241	−	0.860584i
$879$		0			0
$880$	−467.838	+	530.478i	−0.531634	+	0.602816i
$881$		−	803.454i		−	0.911979i	−0.889985	−	0.455990i	$-0.849285\pi$
$881$		−	803.454i		−	0.911979i	0.889985	−	0.455990i	$-0.150715\pi$
$882$		0			0
$883$		−	458.660i		−	0.519434i	−0.965685	−	0.259717i	$-0.916371\pi$
$883$		−	458.660i		−	0.519434i	0.965685	−	0.259717i	$-0.0836293\pi$
$884$	280.340	−	126.550i	0.317127	−	0.143156i
$885$		0			0
$886$	−159.307	−	740.102i	−0.179805	−	0.835329i
$887$		−	56.5044i		−	0.0637028i	−0.999493	−	0.0318514i	$-0.989860\pi$
$887$		−	56.5044i		−	0.0637028i	0.999493	−	0.0318514i	$-0.0101403\pi$
$888$		0			0
$889$	921.490			1.03655
$890$	636.031	−	136.906i	0.714642	−	0.153827i
$891$		0			0
$892$	−186.405	+	84.1463i	−0.208974	+	0.0943344i
$893$	1547.54			1.73296
$894$		0			0
$895$	295.231			0.329867
$896$	−1102.50	−	95.8134i	−1.23047	−	0.106935i
$897$		0			0
$898$	−565.306	+	121.682i	−0.629517	+	0.135504i
$899$	−62.1444			−0.0691262
$900$		0			0
$901$		−	405.255i		−	0.449783i
$902$	−303.542	+	65.3375i	−0.336521	+	0.0724362i
$903$		0			0
$904$	−1094.21	+	807.984i	−1.21041	+	0.893788i
$905$			315.155i			0.348238i
$906$		0			0
$907$		−	462.461i		−	0.509880i	−0.966957	−	0.254940i	$-0.917944\pi$
$907$		−	462.461i		−	0.509880i	0.966957	−	0.254940i	$-0.0820558\pi$
$908$	858.718	−	387.639i	0.945725	−	0.426915i
$909$		0			0
$910$	546.626	−	117.661i	0.600688	−	0.129298i
$911$			199.274i			0.218742i	0.994001	+	0.109371i	$0.0348836\pi$
$911$			199.274i			0.218742i	−0.994001	+	0.109371i	$0.965116\pi$
$912$		0			0
$913$	2362.12			2.58721
$914$	−204.271	−	948.994i	−0.223492	−	1.03829i
$915$		0			0
$916$	339.571	+	752.235i	0.370711	+	0.821218i
$917$	−566.718			−0.618013
$918$		0			0
$919$	1663.67			1.81031			0.905154	−	0.425084i	$-0.139755\pi$
$919$	1663.67			1.81031			0.905154	+	0.425084i	$0.139755\pi$
$920$	424.985	−	313.816i	0.461941	−	0.341105i
$921$		0			0
$922$	90.5006	+	420.443i	0.0981568	+	0.456012i
$923$	−1462.04			−1.58401
$924$		0			0
$925$		−	333.589i		−	0.360637i
$926$	157.720	+	732.729i	0.170324	+	0.791283i
$927$		0			0
$928$	171.336	+	96.0000i	0.184629	+	0.103448i
$929$			826.068i			0.889201i	0.895729	+	0.444601i	$0.146654\pi$
$929$			826.068i			0.889201i	−0.895729	+	0.444601i	$0.853346\pi$
$930$		0			0
$931$			625.482i			0.671839i
$932$	346.193	+	766.905i	0.371452	+	0.822860i
$933$		0			0
$934$	112.812	+	524.095i	0.120783	+	0.561130i
$935$		−	234.105i		−	0.250379i
$936$		0			0
$937$	−536.859			−0.572955			−0.286477	−	0.958087i	$-0.592484\pi$
$937$	−536.859			−0.572955			−0.286477	+	0.958087i	$0.592484\pi$
$938$	−1863.65	+	401.152i	−1.98684	+	0.427667i
$939$		0			0
$940$	−233.490	−	517.239i	−0.248394	−	0.550254i
$941$	−1261.70			−1.34081			−0.670406	−	0.741995i	$-0.733880\pi$
$941$	−1261.70			−1.34081			−0.670406	+	0.741995i	$0.733880\pi$
$942$		0			0
$943$	231.911			0.245929
$944$	434.254	−	492.398i	0.460015	−	0.521608i
$945$		0			0
$946$	−59.8666	+	12.8863i	−0.0632840	+	0.0136219i
$947$	−173.218			−0.182912			−0.0914560	−	0.995809i	$-0.529152\pi$
$947$	−173.218			−0.182912			−0.0914560	+	0.995809i	$0.529152\pi$
$948$		0			0
$949$		−	1363.67i		−	1.43696i
$950$	−951.828	+	204.881i	−1.00192	+	0.215665i
$951$		0			0
$952$	294.656	−	217.579i	0.309513	−	0.228549i
$953$			1457.32i			1.52919i	0.644510	+	0.764596i	$0.277061\pi$
$953$			1457.32i			1.52919i	−0.644510	+	0.764596i	$0.722939\pi$
$954$		0			0
$955$		−	3.24426i		−	0.00339713i
$956$	−38.0921	−	84.3835i	−0.0398453	−	0.0882673i
$957$		0			0
$958$	−1001.28	+	215.527i	−1.04518	+	0.224976i
$959$		−	1226.22i		−	1.27864i
$960$		0			0
$961$	−858.474			−0.893314
$962$	101.722	+	472.577i	0.105741	+	0.491245i
$963$		0			0
$964$	−297.593	+	134.339i	−0.308707	+	0.139355i
$965$	542.358			0.562029
$966$		0			0
$967$	1148.30			1.18748			0.593742	−	0.804655i	$-0.297650\pi$
$967$	1148.30			1.18748			0.593742	+	0.804655i	$0.297650\pi$
$968$	1297.51	+	1757.16i	1.34041	+	1.81524i
$969$		0			0
$970$	−3.47580	−	16.1477i	−0.00358330	−	0.0166471i
$971$	−15.1851			−0.0156386			−0.00781932	−	0.999969i	$-0.502489\pi$
$971$	−15.1851			−0.0156386			−0.00781932	+	0.999969i	$0.502489\pi$
$972$		0			0
$973$			1480.21i			1.52128i
$974$	−372.801	−	1731.94i	−0.382752	−	1.77817i
$975$		0			0
$976$	624.753	+	550.980i	0.640116	+	0.564529i
$977$			149.435i			0.152953i	0.997071	+	0.0764764i	$0.0243670\pi$
$977$			149.435i			0.152953i	−0.997071	+	0.0764764i	$0.975633\pi$
$978$		0			0
$979$		−	2899.57i		−	2.96177i
$980$	209.058	−	94.3720i	0.213324	−	0.0962979i
$981$		0			0
$982$	−183.010	−	850.221i	−0.186365	−	0.865805i
$983$		−	683.140i		−	0.694954i	−0.937688	−	0.347477i	$-0.887038\pi$
$983$		−	683.140i		−	0.694954i	0.937688	−	0.347477i	$-0.112962\pi$
$984$		0			0
$985$	11.1294			0.0112989
$986$	−63.5484	+	13.6788i	−0.0644507	+	0.0138730i
$987$		0			0
$988$	1285.93	−	580.488i	1.30154	−	0.587538i
$989$	45.7391			0.0462479
$990$		0			0
$991$	−1531.80			−1.54571			−0.772854	−	0.634584i	$-0.781171\pi$
$991$	−1531.80			−1.54571			−0.772854	+	0.634584i	$0.781171\pi$
$992$	−282.669	−	158.380i	−0.284949	−	0.159658i
$993$		0			0
$994$	−1702.09	+	366.376i	−1.71237	+	0.368588i
$995$	−228.213			−0.229359
$996$		0			0
$997$		−	194.125i		−	0.194710i	−0.995250	−	0.0973548i	$-0.968962\pi$
$997$		−	194.125i		−	0.194710i	0.995250	−	0.0973548i	$-0.0310382\pi$
$998$	−1394.03	+	300.066i	−1.39683	+	0.300667i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.h.e.53.3	✓	8
3.2	odd	2	inner	216.3.h.e.53.6	yes	8
4.3	odd	2		864.3.h.f.593.4		8
8.3	odd	2		864.3.h.f.593.5		8
8.5	even	2	inner	216.3.h.e.53.5	yes	8
12.11	even	2		864.3.h.f.593.6		8
24.5	odd	2	inner	216.3.h.e.53.4	yes	8
24.11	even	2		864.3.h.f.593.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.h.e.53.3	✓	8	1.1	even	1	trivial
216.3.h.e.53.4	yes	8	24.5	odd	2	inner
216.3.h.e.53.5	yes	8	8.5	even	2	inner
216.3.h.e.53.6	yes	8	3.2	odd	2	inner
864.3.h.f.593.3		8	24.11	even	2
864.3.h.f.593.4		8	4.3	odd	2
864.3.h.f.593.5		8	8.3	odd	2
864.3.h.f.593.6		8	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.420861 - 1.95522i) q^{2} +(-3.64575 + 1.64575i) q^{4} -2.22699 q^{5} -8.64575 q^{7} +(4.75216 + 6.43560i) q^{8} +O(q^{10})\)	\(q+(-0.420861 - 1.95522i) q^{2} +(-3.64575 + 1.64575i) q^{4} -2.22699 q^{5} -8.64575 q^{7} +(4.75216 + 6.43560i) q^{8} +(0.937254 + 4.35425i) q^{10} +19.8504 q^{11} +14.5203i q^{13} +(3.63866 + 16.9043i) q^{14} +(10.5830 - 12.0000i) q^{16} +5.29570i q^{17} +24.2915i q^{19} +(8.11905 - 3.66507i) q^{20} +(-8.35425 - 38.8118i) q^{22} +29.6528i q^{23} -20.0405 q^{25} +(28.3903 - 6.11102i) q^{26} +(31.5203 - 14.2288i) q^{28} -6.13742 q^{29} +10.1255 q^{31} +(-27.9166 - 15.6417i) q^{32} +(10.3542 - 2.22876i) q^{34} +19.2540 q^{35} +16.6458i q^{37} +(47.4952 - 10.2234i) q^{38} +(-10.5830 - 14.3320i) q^{40} -7.82087i q^{41} -1.54249i q^{43} +(-72.3695 + 32.6687i) q^{44} +(57.9778 - 12.4797i) q^{46} -63.7069i q^{47} +25.7490 q^{49} +(8.43428 + 39.1836i) q^{50} +(-23.8967 - 52.9373i) q^{52} -76.5253 q^{53} -44.2065 q^{55} +(-41.0860 - 55.6406i) q^{56} +(2.58301 + 12.0000i) q^{58} +41.0332 q^{59} +52.0627i q^{61} +(-4.26143 - 19.7975i) q^{62} +(-18.8340 + 61.1660i) q^{64} -32.3365i q^{65} +110.247i q^{67} +(-8.71541 - 19.3068i) q^{68} +(-8.10326 - 37.6458i) q^{70} +100.690i q^{71} -93.9150 q^{73} +(32.5461 - 7.00555i) q^{74} +(-39.9778 - 88.5608i) q^{76} -171.621 q^{77} -10.7712 q^{79} +(-23.5682 + 26.7239i) q^{80} +(-15.2915 + 3.29150i) q^{82} +118.996 q^{83} -11.7935i q^{85} +(-3.01590 + 0.649173i) q^{86} +(94.3320 + 127.749i) q^{88} -146.071i q^{89} -125.539i q^{91} +(-48.8012 - 108.107i) q^{92} +(-124.561 + 26.8118i) q^{94} -54.0969i q^{95} -3.70850 q^{97} +(-10.8368 - 50.3449i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 48 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 - 48 * q^7	\( 8 q - 8 q^{4} - 48 q^{7} - 56 q^{10} - 88 q^{22} + 136 q^{25} + 104 q^{28} + 208 q^{31} + 104 q^{34} + 104 q^{46} - 48 q^{49} - 424 q^{52} + 112 q^{55} - 64 q^{58} - 320 q^{64} + 168 q^{70} - 328 q^{73} + 40 q^{76} - 192 q^{79} - 80 q^{82} + 416 q^{88} - 552 q^{94} - 72 q^{97}+O(q^{100}) \) 8 * q - 8 * q^4 - 48 * q^7 - 56 * q^10 - 88 * q^22 + 136 * q^25 + 104 * q^28 + 208 * q^31 + 104 * q^34 + 104 * q^46 - 48 * q^49 - 424 * q^52 + 112 * q^55 - 64 * q^58 - 320 * q^64 + 168 * q^70 - 328 * q^73 + 40 * q^76 - 192 * q^79 - 80 * q^82 + 416 * q^88 - 552 * q^94 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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