LMFDB - Embedded newform 154.3.g.a.65.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,3,Mod(65,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("154.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	154.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19619607115$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.7
Character	$\chi$	$=$	154.65
Dual form			154.3.g.a.109.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(1.83765 + 3.18290i) q^{3} +(1.00000 + 1.73205i) q^{4} +(4.33390 - 7.50654i) q^{5} -5.19765i q^{6} +(-3.85425 - 5.84335i) q^{7} -2.82843i q^{8} +(-2.25390 + 3.90387i) q^{9} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.83765 + 3.18290i) q^{3} +(1.00000 + 1.73205i) q^{4} +(4.33390 - 7.50654i) q^{5} -5.19765i q^{6} +(-3.85425 - 5.84335i) q^{7} -2.82843i q^{8} +(-2.25390 + 3.90387i) q^{9} +(-10.6159 + 6.12906i) q^{10} +(3.32669 - 10.4849i) q^{11} +(-3.67530 + 6.36580i) q^{12} +12.2989i q^{13} +(0.588602 + 9.88198i) q^{14} +31.8568 q^{15} +(-2.00000 + 3.46410i) q^{16} +(20.9123 - 12.0737i) q^{17} +(5.52091 - 3.18750i) q^{18} +(1.13867 + 0.657412i) q^{19} +17.3356 q^{20} +(11.5160 - 23.0057i) q^{21} +(-11.4883 + 10.4890i) q^{22} +(-19.4750 + 33.7316i) q^{23} +(9.00260 - 5.19765i) q^{24} +(-25.0654 - 43.4146i) q^{25} +(8.69664 - 15.0630i) q^{26} +16.5101 q^{27} +(6.26673 - 12.5191i) q^{28} +10.4699i q^{29} +(-39.0164 - 22.5261i) q^{30} +(2.46294 + 4.26595i) q^{31} +(4.89898 - 2.82843i) q^{32} +(39.4857 - 8.67903i) q^{33} -34.1497 q^{34} +(-60.5673 + 3.60758i) q^{35} -9.01561 q^{36} +(27.8153 - 48.1776i) q^{37} +(-0.929722 - 1.61033i) q^{38} +(-39.1462 + 22.6011i) q^{39} +(-21.2317 - 12.2581i) q^{40} +7.90895i q^{41} +(-30.3717 + 20.0331i) q^{42} +76.8973i q^{43} +(21.4871 - 4.72290i) q^{44} +(19.5364 + 33.8380i) q^{45} +(47.7037 - 27.5418i) q^{46} +(-14.2846 + 24.7416i) q^{47} -14.7012 q^{48} +(-19.2895 + 45.0435i) q^{49} +70.8958i q^{50} +(76.8590 + 44.3746i) q^{51} +(-21.3023 + 12.2989i) q^{52} +(2.22414 + 3.85232i) q^{53} +(-20.2207 - 11.6744i) q^{54} +(-64.2878 - 70.4125i) q^{55} +(-16.5275 + 10.9015i) q^{56} +4.83237i q^{57} +(7.40336 - 12.8230i) q^{58} +(18.7403 + 32.4591i) q^{59} +(31.8568 + 55.1775i) q^{60} +(-76.5806 - 44.2138i) q^{61} -6.96626i q^{62} +(31.4988 - 1.87617i) q^{63} -8.00000 q^{64} +(92.3222 + 53.3023i) q^{65} +(-54.4969 - 17.2910i) q^{66} +(-20.3909 - 35.3180i) q^{67} +(41.8247 + 24.1475i) q^{68} -143.153 q^{69} +(76.7304 + 38.4092i) q^{70} -19.0511 q^{71} +(11.0418 + 6.37500i) q^{72} +(-39.7316 + 22.9390i) q^{73} +(-68.1333 + 39.3368i) q^{74} +(92.1229 - 159.562i) q^{75} +2.62965i q^{76} +(-74.0889 + 20.9724i) q^{77} +63.9255 q^{78} +(-42.3874 - 24.4724i) q^{79} +(17.3356 + 30.0262i) q^{80} +(50.6250 + 87.6850i) q^{81} +(5.59247 - 9.68645i) q^{82} -63.2521i q^{83} +(51.3631 - 3.05935i) q^{84} -209.306i q^{85} +(54.3746 - 94.1796i) q^{86} +(-33.3247 + 19.2400i) q^{87} +(-29.6558 - 9.40931i) q^{88} +(-34.7727 + 60.2281i) q^{89} -55.2573i q^{90} +(71.8668 - 47.4031i) q^{91} -77.8999 q^{92} +(-9.05205 + 15.6786i) q^{93} +(34.9900 - 20.2015i) q^{94} +(9.86979 - 5.69832i) q^{95} +(18.0052 + 10.3953i) q^{96} +30.3381 q^{97} +(55.4753 - 41.5270i) q^{98} +(33.4337 + 36.6189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 4 q^{5} - 40 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 + 4 * q^5 - 40 * q^9	$ 32 q + 32 q^{4} + 4 q^{5} - 40 q^{9} - 6 q^{11} - 24 q^{14} + 128 q^{15} - 64 q^{16} + 16 q^{20} + 40 q^{22} + 20 q^{23} - 140 q^{25} - 16 q^{26} + 120 q^{27} + 40 q^{31} + 50 q^{33} - 16 q^{34} - 160 q^{36} - 116 q^{37} - 40 q^{38} + 48 q^{42} + 12 q^{44} - 284 q^{45} + 216 q^{47} + 248 q^{49} + 56 q^{53} - 372 q^{55} - 48 q^{56} + 104 q^{58} - 4 q^{59} + 128 q^{60} - 256 q^{64} - 160 q^{66} - 68 q^{67} - 208 q^{69} + 80 q^{70} - 184 q^{71} - 244 q^{75} - 362 q^{77} + 288 q^{78} + 16 q^{80} + 384 q^{81} + 224 q^{82} + 72 q^{86} + 40 q^{88} - 592 q^{89} + 804 q^{91} + 80 q^{92} - 68 q^{93} + 376 q^{97} + 432 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 + 4 * q^5 - 40 * q^9 - 6 * q^11 - 24 * q^14 + 128 * q^15 - 64 * q^16 + 16 * q^20 + 40 * q^22 + 20 * q^23 - 140 * q^25 - 16 * q^26 + 120 * q^27 + 40 * q^31 + 50 * q^33 - 16 * q^34 - 160 * q^36 - 116 * q^37 - 40 * q^38 + 48 * q^42 + 12 * q^44 - 284 * q^45 + 216 * q^47 + 248 * q^49 + 56 * q^53 - 372 * q^55 - 48 * q^56 + 104 * q^58 - 4 * q^59 + 128 * q^60 - 256 * q^64 - 160 * q^66 - 68 * q^67 - 208 * q^69 + 80 * q^70 - 184 * q^71 - 244 * q^75 - 362 * q^77 + 288 * q^78 + 16 * q^80 + 384 * q^81 + 224 * q^82 + 72 * q^86 + 40 * q^88 - 592 * q^89 + 804 * q^91 + 80 * q^92 - 68 * q^93 + 376 * q^97 + 432 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	1.83765	+	3.18290i	0.612549	+	1.06097i	0.990809	+	0.135267i	$0.0431893\pi$
$3$	1.83765	+	3.18290i	0.612549	+	1.06097i	−0.378260	+	0.925700i	$0.623477\pi$
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	4.33390	−	7.50654i	0.866781	−	1.50131i	0.00151253	−	0.999999i	$-0.499519\pi$
$5$	4.33390	−	7.50654i	0.866781	−	1.50131i	0.865268	−	0.501309i	$-0.167148\pi$
$6$		−	5.19765i		−	0.866276i
$7$	−3.85425	−	5.84335i	−0.550607	−	0.834764i
$7$	−3.85425	−	5.84335i	−0.550607	−	0.834764i
$8$		−	2.82843i		−	0.353553i
$9$	−2.25390	+	3.90387i	−0.250434	+	0.433764i
$10$	−10.6159	+	6.12906i	−1.06159	+	0.612906i
$11$	3.32669	−	10.4849i	0.302427	−	0.953173i
$11$	3.32669	−	10.4849i	0.302427	−	0.953173i
$12$	−3.67530	+	6.36580i	−0.306275	+	0.530483i
$13$			12.2989i			0.946070i	0.881044	+	0.473035i	$0.156842\pi$
$13$			12.2989i			0.946070i	−0.881044	+	0.473035i	$0.843158\pi$
$14$	0.588602	+	9.88198i	0.0420430	+	0.705856i
$15$	31.8568			2.12378
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	20.9123	−	12.0737i	1.23014	−	0.710220i	0.263079	−	0.964774i	$-0.415262\pi$
$17$	20.9123	−	12.0737i	1.23014	−	0.710220i	0.967058	+	0.254555i	$0.0819288\pi$
$18$	5.52091	−	3.18750i	0.306717	−	0.177083i
$19$	1.13867	+	0.657412i	0.0599301	+	0.0346007i	0.529666	−	0.848207i	$-0.322317\pi$
$19$	1.13867	+	0.657412i	0.0599301	+	0.0346007i	−0.469736	+	0.882807i	$0.655651\pi$
$20$	17.3356			0.866781
$21$	11.5160	−	23.0057i	0.548383	−	1.09551i
$22$	−11.4883	+	10.4890i	−0.522195	+	0.476773i
$23$	−19.4750	+	33.7316i	−0.846738	+	1.46659i	0.0373661	+	0.999302i	$0.488103\pi$
$23$	−19.4750	+	33.7316i	−0.846738	+	1.46659i	−0.884104	+	0.467291i	$0.845230\pi$
$24$	9.00260	−	5.19765i	0.375108	−	0.216569i
$25$	−25.0654	−	43.4146i	−1.00262	−	1.73658i
$26$	8.69664	−	15.0630i	0.334486	−	0.579347i
$27$	16.5101			0.611487
$28$	6.26673	−	12.5191i	0.223812	−	0.447111i
$29$			10.4699i			0.361032i	0.983572	+	0.180516i	$0.0577768\pi$
$29$			10.4699i			0.361032i	−0.983572	+	0.180516i	$0.942223\pi$
$30$	−39.0164	−	22.5261i	−1.30055	−	0.750871i
$31$	2.46294	+	4.26595i	0.0794498	+	0.137611i	0.903013	−	0.429614i	$-0.141350\pi$
$31$	2.46294	+	4.26595i	0.0794498	+	0.137611i	−0.823563	+	0.567225i	$0.808017\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	39.4857	−	8.67903i	1.19654	−	0.263001i
$34$	−34.1497			−1.00440
$35$	−60.5673	+	3.60758i	−1.73049	+	0.103074i
$36$	−9.01561			−0.250434
$37$	27.8153	−	48.1776i	0.751765	−	1.30210i	−0.195201	−	0.980763i	$-0.562536\pi$
$37$	27.8153	−	48.1776i	0.751765	−	1.30210i	0.946966	−	0.321333i	$-0.104131\pi$
$38$	−0.929722	−	1.61033i	−0.0244664	−	0.0423770i
$39$	−39.1462	+	22.6011i	−1.00375	+	0.579514i
$40$	−21.2317	−	12.2581i	−0.530793	−	0.306453i
$41$			7.90895i			0.192901i	0.995338	+	0.0964507i	$0.0307490\pi$
$41$			7.90895i			0.192901i	−0.995338	+	0.0964507i	$0.969251\pi$
$42$	−30.3717	+	20.0331i	−0.723136	+	0.476978i
$43$			76.8973i			1.78831i	0.447758	+	0.894155i	$0.352223\pi$
$43$			76.8973i			1.78831i	−0.447758	+	0.894155i	$0.647777\pi$
$44$	21.4871	−	4.72290i	0.488343	−	0.107339i
$45$	19.5364	+	33.8380i	0.434142	+	0.751956i
$46$	47.7037	−	27.5418i	1.03704	−	0.598734i
$47$	−14.2846	+	24.7416i	−0.303928	+	0.526418i	−0.977022	−	0.213139i	$-0.931631\pi$
$47$	−14.2846	+	24.7416i	−0.303928	+	0.526418i	0.673094	+	0.739557i	$0.264965\pi$
$48$	−14.7012			−0.306275
$49$	−19.2895	+	45.0435i	−0.393663	+	0.919255i
$50$			70.8958i			1.41792i
$51$	76.8590	+	44.3746i	1.50704	+	0.870090i
$52$	−21.3023	+	12.2989i	−0.409660	+	0.236517i
$53$	2.22414	+	3.85232i	0.0419649	+	0.0726853i	0.886245	−	0.463217i	$-0.153305\pi$
$53$	2.22414	+	3.85232i	0.0419649	+	0.0726853i	−0.844280	+	0.535902i	$0.819972\pi$
$54$	−20.2207	−	11.6744i	−0.374458	−	0.216193i
$55$	−64.2878	−	70.4125i	−1.16887	−	1.28023i
$56$	−16.5275	+	10.9015i	−0.295134	+	0.194669i
$57$			4.83237i			0.0847785i
$58$	7.40336	−	12.8230i	0.127644	−	0.221086i
$59$	18.7403	+	32.4591i	0.317632	+	0.550155i	0.979993	−	0.199030i	$-0.0637790\pi$
$59$	18.7403	+	32.4591i	0.317632	+	0.550155i	−0.662361	+	0.749184i	$0.730446\pi$
$60$	31.8568	+	55.1775i	0.530946	+	0.919625i
$61$	−76.5806	−	44.2138i	−1.25542	−	0.724817i	−0.283239	−	0.959049i	$-0.591409\pi$
$61$	−76.5806	−	44.2138i	−1.25542	−	0.724817i	−0.972181	+	0.234232i	$0.924742\pi$
$62$		−	6.96626i		−	0.112359i
$63$	31.4988	−	1.87617i	0.499981	−	0.0297805i
$64$	−8.00000			−0.125000
$65$	92.3222	+	53.3023i	1.42034	+	0.820035i
$66$	−54.4969	−	17.2910i	−0.825710	−	0.261985i
$67$	−20.3909	−	35.3180i	−0.304341	−	0.527135i	0.672773	−	0.739849i	$-0.265103\pi$
$67$	−20.3909	−	35.3180i	−0.304341	−	0.527135i	−0.977114	+	0.212714i	$0.931770\pi$
$68$	41.8247	+	24.1475i	0.615068	+	0.355110i
$69$	−143.153			−2.07467
$70$	76.7304	+	38.4092i	1.09615	+	0.548703i
$71$	−19.0511			−0.268326			−0.134163	−	0.990959i	$-0.542835\pi$
$71$	−19.0511			−0.268326			−0.134163	+	0.990959i	$0.542835\pi$
$72$	11.0418	+	6.37500i	0.153359	+	0.0885417i
$73$	−39.7316	+	22.9390i	−0.544268	+	0.314233i	−0.746807	−	0.665041i	$-0.768414\pi$
$73$	−39.7316	+	22.9390i	−0.544268	+	0.314233i	0.202539	+	0.979274i	$0.435081\pi$
$74$	−68.1333	+	39.3368i	−0.920721	+	0.531578i
$75$	92.1229	−	159.562i	1.22831	−	2.12749i
$76$			2.62965i			0.0346007i
$77$	−74.0889	+	20.9724i	−0.962193	+	0.272369i
$78$	63.9255			0.819557
$79$	−42.3874	−	24.4724i	−0.536550	−	0.309777i	0.207130	−	0.978314i	$-0.433588\pi$
$79$	−42.3874	−	24.4724i	−0.536550	−	0.309777i	−0.743680	+	0.668536i	$0.766921\pi$
$80$	17.3356	+	30.0262i	0.216695	+	0.375327i
$81$	50.6250	+	87.6850i	0.625000	+	1.08253i
$82$	5.59247	−	9.68645i	0.0682009	−	0.118127i
$83$		−	63.2521i		−	0.762074i	−0.924560	−	0.381037i	$-0.875567\pi$
$83$		−	63.2521i		−	0.762074i	0.924560	−	0.381037i	$-0.124433\pi$
$84$	51.3631	−	3.05935i	0.611466	−	0.0364208i
$85$		−	209.306i		−	2.46242i
$86$	54.3746	−	94.1796i	0.632263	−	1.09511i
$87$	−33.3247	+	19.2400i	−0.383043	+	0.221150i
$88$	−29.6558	−	9.40931i	−0.336997	−	0.106924i
$89$	−34.7727	+	60.2281i	−0.390704	+	0.676720i	−0.992543	−	0.121898i	$-0.961102\pi$
$89$	−34.7727	+	60.2281i	−0.390704	+	0.676720i	0.601838	+	0.798618i	$0.294435\pi$
$90$		−	55.2573i		−	0.613970i
$91$	71.8668	−	47.4031i	0.789745	−	0.520913i
$92$	−77.8999			−0.846738
$93$	−9.05205	+	15.6786i	−0.0973339	+	0.168587i
$94$	34.9900	−	20.2015i	0.372234	−	0.214909i
$95$	9.86979	−	5.69832i	0.103892	−	0.0599824i
$96$	18.0052	+	10.3953i	0.187554	+	0.108284i
$97$	30.3381			0.312764			0.156382	−	0.987697i	$-0.450017\pi$
$97$	30.3381			0.312764			0.156382	+	0.987697i	$0.450017\pi$
$98$	55.4753	−	41.5270i	0.566074	−	0.423745i
$99$	33.4337	+	36.6189i	0.337714	+	0.369888i
$100$	50.1309	−	86.8292i	0.501309	−	0.868292i
$101$	−11.5403	+	6.66282i	−0.114261	+	0.0659685i	−0.556041	−	0.831155i	$-0.687680\pi$
$101$	−11.5403	+	6.66282i	−0.114261	+	0.0659685i	0.441780	+	0.897123i	$0.354347\pi$
$102$	−62.7551	−	108.695i	−0.615246	−	1.06564i
$103$	−33.9028	+	58.7213i	−0.329153	+	0.570110i	−0.982344	−	0.187083i	$-0.940097\pi$
$103$	−33.9028	+	58.7213i	−0.329153	+	0.570110i	0.653191	+	0.757193i	$0.273430\pi$
$104$	34.7866			0.334486
$105$	−122.784	−	186.150i	−1.16937	−	1.77286i
$106$		−	6.29081i		−	0.0593473i
$107$	171.576	+	99.0593i	1.60351	+	0.925788i	0.990778	+	0.135499i	$0.0432637\pi$
$107$	171.576	+	99.0593i	1.60351	+	0.925788i	0.612734	+	0.790289i	$0.290070\pi$
$108$	16.5101	+	28.5964i	0.152872	+	0.264782i
$109$	145.837	−	84.1991i	1.33795	−	0.772468i	0.351451	−	0.936206i	$-0.385688\pi$
$109$	145.837	−	84.1991i	1.33795	−	0.772468i	0.986504	+	0.163738i	$0.0523552\pi$
$110$	28.9470	+	131.696i	0.263154	+	1.19723i
$111$	204.459			1.84197
$112$	27.9505	−	1.66482i	0.249558	−	0.0148644i
$113$	62.2652			0.551019			0.275510	−	0.961298i	$-0.411153\pi$
$113$	62.2652			0.551019			0.275510	+	0.961298i	$0.411153\pi$
$114$	3.41700	−	5.91842i	0.0299737	−	0.0519160i
$115$	168.805	+	292.379i	1.46787	+	2.54243i
$116$	−18.1344	+	10.4699i	−0.156331	+	0.0902580i
$117$	−48.0134	−	27.7205i	−0.410371	−	0.236928i
$118$		−	53.0055i		−	0.449200i
$119$	−151.152	−	75.6628i	−1.27019	−	0.635822i
$120$		−	90.1045i		−	0.750871i
$121$	−98.8662	−	69.7601i	−0.817076	−	0.576530i
$122$	62.5278	+	108.301i	0.512523	+	0.887716i
$123$	−25.1734	+	14.5339i	−0.204662	+	0.118162i
$124$	−4.92589	+	8.53189i	−0.0397249	+	0.0688056i
$125$	−217.830			−1.74264
$126$	−39.9047	−	19.9752i	−0.316704	−	0.158533i
$127$			139.849i			1.10118i	0.834777	+	0.550588i	$0.185597\pi$
$127$			139.849i			1.10118i	−0.834777	+	0.550588i	$0.814403\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	−244.756	+	141.310i	−1.89734	+	1.09543i
$130$	−75.3808	−	130.563i	−0.579852	−	1.00433i
$131$	−100.556	−	58.0561i	−0.767604	−	0.443177i	0.0644151	−	0.997923i	$-0.479482\pi$
$131$	−100.556	−	58.0561i	−0.767604	−	0.443177i	−0.832019	+	0.554747i	$0.812815\pi$
$132$	54.5182	+	59.7122i	0.413017	+	0.452365i
$133$	−0.547236	−	9.18749i	−0.00411456	−	0.0690789i
$134$			57.6741i			0.430404i
$135$	71.5534	−	123.934i	0.530025	−	0.918030i
$136$	−34.1497	−	59.1490i	−0.251101	−	0.434919i
$137$	80.8979	+	140.119i	0.590496	+	1.02277i	0.994166	+	0.107864i	$0.0344012\pi$
$137$	80.8979	+	140.119i	0.590496	+	1.02277i	−0.403670	+	0.914905i	$0.632265\pi$
$138$	175.325	+	101.224i	1.27047	+	0.733508i
$139$			3.01664i			0.0217025i	0.999941	+	0.0108512i	$0.00345412\pi$
$139$			3.01664i			0.0217025i	−0.999941	+	0.0108512i	$0.996546\pi$
$140$	−66.8158	−	101.298i	−0.477256	−	0.723558i
$141$	−105.000			−0.744683
$142$	23.3328	+	13.4712i	0.164315	+	0.0948675i
$143$	128.953	+	40.9147i	0.901768	+	0.286117i
$144$	−9.01561	−	15.6155i	−0.0626084	−	0.108441i
$145$	78.5929	+	45.3756i	0.542020	+	0.312936i
$146$	64.8814			0.444393
$147$	−178.816	+	21.3776i	−1.21644	+	0.145426i
$148$	111.261			0.751765
$149$	−48.3435	−	27.9112i	−0.324453	−	0.187323i	0.328923	−	0.944357i	$-0.393314\pi$
$149$	−48.3435	−	27.9112i	−0.324453	−	0.187323i	−0.653376	+	0.757034i	$0.726648\pi$
$150$	−225.654	+	130.281i	−1.50436	+	0.868543i
$151$	−14.5754	+	8.41511i	−0.0965259	+	0.0557292i	−0.547486	−	0.836815i	$-0.684415\pi$
$151$	−14.5754	+	8.41511i	−0.0965259	+	0.0557292i	0.450960	+	0.892544i	$0.351082\pi$
$152$	1.85944	−	3.22065i	0.0122332	−	0.0211885i
$153$			108.852i			0.711452i
$154$	105.570	+	26.7029i	0.685517	+	0.173395i
$155$	42.6967			0.275462
$156$	−78.2924	−	45.2021i	−0.501874	−	0.289757i
$157$	−33.7893	−	58.5248i	−0.215219	−	0.372770i	0.738122	−	0.674668i	$-0.235713\pi$
$157$	−33.7893	−	58.5248i	−0.215219	−	0.372770i	−0.953340	+	0.301898i	$0.902380\pi$
$158$	34.6092	+	59.9449i	0.219046	+	0.379398i
$159$	−8.17436	+	14.1584i	−0.0514111	+	0.0890466i
$160$		−	49.0325i		−	0.306453i
$161$	272.167	−	16.2111i	1.69048	−	0.100690i
$162$		−	143.189i		−	0.883883i
$163$	0.611628	−	1.05937i	0.00375232	−	0.00649921i	−0.864143	−	0.503246i	$-0.832139\pi$
$163$	0.611628	−	1.05937i	0.00375232	−	0.00649921i	0.867895	+	0.496747i	$0.165472\pi$
$164$	−13.6987	+	7.90895i	−0.0835287	+	0.0482253i
$165$	105.978	−	334.015i	0.642289	−	2.02433i
$166$	−44.7260	+	77.4677i	−0.269434	+	0.466673i
$167$			70.8963i			0.424529i	0.977212	+	0.212264i	$0.0680838\pi$
$167$			70.8963i			0.424529i	−0.977212	+	0.212264i	$0.931916\pi$
$168$	−65.0700	−	32.5723i	−0.387321	−	0.193883i
$169$	17.7369			0.104952
$170$	−148.001	+	256.346i	−0.870597	+	1.50792i
$171$	−5.13291	+	2.96349i	−0.0300170	+	0.0173303i
$172$	−133.190	+	76.8973i	−0.774361	+	0.447077i
$173$	1.80347	+	1.04124i	0.0104247	+	0.00601870i	0.505203	−	0.863000i	$-0.331418\pi$
$173$	1.80347	+	1.04124i	0.0104247	+	0.00601870i	−0.494779	+	0.869019i	$0.664751\pi$
$174$	54.4191			0.312753
$175$	−157.078	+	313.797i	−0.897590	+	1.79313i
$176$	29.6674	+	32.4938i	0.168565	+	0.184624i
$177$	−68.8761	+	119.297i	−0.389131	+	0.673994i
$178$	85.1753	−	49.1760i	0.478513	−	0.276270i
$179$	80.5335	+	139.488i	0.449908	+	0.779263i	0.998380	−	0.0569059i	$-0.0181235\pi$
$179$	80.5335	+	139.488i	0.449908	+	0.779263i	−0.548472	+	0.836169i	$0.684790\pi$
$180$	−39.0728	+	67.6760i	−0.217071	+	0.375978i
$181$	−79.7213			−0.440449			−0.220225	−	0.975449i	$-0.570679\pi$
$181$	−79.7213			−0.440449			−0.220225	+	0.975449i	$0.570679\pi$
$182$	−121.538	+	7.23916i	−0.667789	+	0.0397756i
$183$		−	324.998i		−	1.77594i
$184$	95.4074	+	55.0835i	0.518519	+	0.299367i
$185$	−241.098	−	417.594i	−1.30323	−	2.25726i
$186$	22.1729	−	12.8015i	0.119209	−	0.0688255i
$187$	−57.0230	−	259.429i	−0.304936	−	1.38732i
$188$	−57.1384			−0.303928
$189$	−63.6343	−	96.4746i	−0.336689	−	0.510448i
$190$	−16.1173			−0.0848279
$191$	103.873	−	179.914i	0.543839	−	0.941957i	−0.454840	−	0.890573i	$-0.650304\pi$
$191$	103.873	−	179.914i	0.543839	−	0.941957i	0.998679	−	0.0513835i	$-0.0163631\pi$
$192$	−14.7012	−	25.4632i	−0.0765687	−	0.132621i
$193$	137.267	−	79.2511i	0.711228	−	0.410627i	−0.100288	−	0.994958i	$-0.531976\pi$
$193$	137.267	−	79.2511i	0.711228	−	0.410627i	0.811515	+	0.584331i	$0.198643\pi$
$194$	−37.1564	−	21.4523i	−0.191528	−	0.110579i
$195$			391.803i			2.00925i
$196$	−97.3071	+	11.6331i	−0.496465	+	0.0593526i
$197$			109.885i			0.557791i	0.960321	+	0.278896i	$0.0899684\pi$
$197$			109.885i			0.557791i	−0.960321	+	0.278896i	$0.910032\pi$
$198$	−15.0542	−	68.4900i	−0.0760315	−	0.345909i
$199$	13.2017	+	22.8660i	0.0663401	+	0.114904i	0.897288	−	0.441446i	$-0.145534\pi$
$199$	13.2017	+	22.8660i	0.0663401	+	0.114904i	−0.830948	+	0.556351i	$0.812201\pi$
$200$	−122.795	+	70.8958i	−0.613975	+	0.354479i
$201$	74.9425	−	129.804i	0.372848	−	0.645792i
$202$	18.8453			0.0932935
$203$	61.1794	−	40.3537i	0.301377	−	0.198787i
$204$			177.498i			0.870090i
$205$	59.3689	+	34.2766i	0.289604	+	0.167203i
$206$	83.0445	−	47.9458i	0.403129	−	0.232746i
$207$	−87.7893	−	152.056i	−0.424103	−	0.734568i
$208$	−42.6047	−	24.5978i	−0.204830	−	0.118259i
$209$	10.6809	−	9.75185i	0.0511049	−	0.0466596i
$210$	18.7510	+	314.808i	0.0892902	+	1.49909i
$211$			265.383i			1.25774i	0.777511	+	0.628869i	$0.216482\pi$
$211$			265.383i			1.25774i	−0.777511	+	0.628869i	$0.783518\pi$
$212$	−4.44827	+	7.70464i	−0.0209824	+	0.0363426i
$213$	−35.0093	−	60.6378i	−0.164363	−	0.284685i
$214$	−140.091	−	242.645i	−0.654631	−	1.13385i
$215$	577.233	+	333.265i	2.68480	+	1.55007i
$216$		−	46.6978i		−	0.216193i
$217$	15.4346	−	30.8339i	0.0711272	−	0.142092i
$218$	−238.151			−1.09244
$219$	−146.025	−	84.3077i	−0.666782	−	0.384967i
$220$	57.6703	−	181.762i	0.262138	−	0.826192i
$221$	148.494	+	257.199i	0.671917	+	1.16380i
$222$	−250.410	−	144.574i	−1.12797	−	0.651236i
$223$	−92.5527			−0.415034			−0.207517	−	0.978231i	$-0.566538\pi$
$223$	−92.5527			−0.415034			−0.207517	+	0.978231i	$0.566538\pi$
$224$	−35.4094	−	17.7250i	−0.158078	−	0.0791294i
$225$	225.980			1.00436
$226$	−76.2590	−	44.0281i	−0.337429	−	0.194815i
$227$	−48.2885	+	27.8794i	−0.212725	+	0.122817i	−0.602577	−	0.798061i	$-0.705859\pi$
$227$	−48.2885	+	27.8794i	−0.212725	+	0.122817i	0.389852	+	0.920877i	$0.372526\pi$
$228$	−8.36991	+	4.83237i	−0.0367101	+	0.0211946i
$229$	−189.035	+	327.418i	−0.825481	+	1.42977i	0.0760706	+	0.997102i	$0.475763\pi$
$229$	−189.035	+	327.418i	−0.825481	+	1.42977i	−0.901551	+	0.432672i	$0.857571\pi$
$230$		−	477.453i		−	2.07588i
$231$	−202.902	−	197.278i	−0.878365	−	0.854015i
$232$	29.6134			0.127644
$233$	177.902	+	102.712i	0.763528	+	0.440823i	0.830561	−	0.556928i	$-0.188020\pi$
$233$	177.902	+	102.712i	0.763528	+	0.440823i	−0.0670329	+	0.997751i	$0.521353\pi$
$234$	39.2028	+	67.9012i	0.167533	+	0.290176i
$235$	123.816	+	214.456i	0.526877	+	0.912578i
$236$	−37.4806	+	64.9183i	−0.158816	+	0.275077i
$237$		−	179.887i		−	0.759015i
$238$	131.621	+	199.549i	0.553031	+	0.838440i
$239$		−	318.258i		−	1.33162i	−0.746119	−	0.665812i	$-0.768085\pi$
$239$		−	318.258i		−	1.33162i	0.746119	−	0.665812i	$-0.231915\pi$
$240$	−63.7135	+	110.355i	−0.265473	+	0.459813i
$241$	−396.980	+	229.196i	−1.64722	+	0.951022i	−0.669049	+	0.743219i	$0.733298\pi$
$241$	−396.980	+	229.196i	−1.64722	+	0.951022i	−0.978170	+	0.207804i	$0.933368\pi$
$242$	71.7581	+	155.347i	0.296521	+	0.641931i
$243$	−111.766	+	193.585i	−0.459943	+	0.796644i
$244$		−	176.855i		−	0.724817i
$245$	254.522	+	340.011i	1.03887	+	1.38780i
$246$	41.1080			0.167106
$247$	−8.08545	+	14.0044i	−0.0327346	+	0.0566980i
$248$	12.0659	−	6.96626i	0.0486529	−	0.0280898i
$249$	201.325	−	116.235i	0.808535	−	0.466808i
$250$	266.786	+	154.029i	1.06714	+	0.616115i
$251$	−215.083			−0.856903			−0.428452	−	0.903565i	$-0.640941\pi$
$251$	−215.083			−0.856903			−0.428452	+	0.903565i	$0.640941\pi$
$252$	34.7484	+	52.6814i	0.137891	+	0.209053i
$253$	288.885	+	316.408i	1.14184	+	1.25062i
$254$	98.8885	−	171.280i	0.389325	−	0.674330i
$255$	666.199	−	384.630i	2.61255	−	1.50835i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	251.078	−	434.879i	0.976955	−	1.69214i	0.303630	−	0.952790i	$-0.401801\pi$
$257$	251.078	−	434.879i	0.976955	−	1.69214i	0.673326	−	0.739346i	$-0.264865\pi$
$258$	399.686			1.54917
$259$	−388.726	+	23.1537i	−1.50087	+	0.0893966i
$260$			213.209i			0.820035i
$261$	−40.8733	−	23.5982i	−0.156603	−	0.0904145i
$262$	82.1038	+	142.208i	0.313373	+	0.542778i
$263$	228.459	−	131.901i	0.868666	−	0.501524i	0.00176104	−	0.999998i	$-0.499439\pi$
$263$	228.459	−	131.901i	0.868666	−	0.501524i	0.866905	+	0.498474i	$0.166106\pi$
$264$	−24.5480	−	111.682i	−0.0929848	−	0.423039i
$265$	38.5568			0.145497
$266$	−5.82631	+	11.6393i	−0.0219034	+	0.0437567i
$267$	−255.600			−0.957303
$268$	40.7817	−	70.6360i	0.152171	−	0.263567i
$269$	−23.5332	−	40.7607i	−0.0874841	−	0.151527i	0.818963	−	0.573846i	$-0.194549\pi$
$269$	−23.5332	−	40.7607i	−0.0874841	−	0.151527i	−0.906447	+	0.422319i	$0.861216\pi$
$270$	−175.269	+	101.192i	−0.649146	+	0.374784i
$271$	−433.549	−	250.310i	−1.59981	−	0.923652i	−0.991522	−	0.129938i	$-0.958522\pi$
$271$	−433.549	−	250.310i	−1.59981	−	0.923652i	−0.608291	−	0.793714i	$-0.708144\pi$
$272$			96.5899i			0.355110i
$273$	282.945	+	141.635i	1.03643	+	0.518808i
$274$		−	228.814i		−	0.835087i
$275$	−538.583	+	118.382i	−1.95848	+	0.430478i
$276$	−143.153	−	247.947i	−0.518669	−	0.898360i
$277$	−298.487	+	172.332i	−1.07757	+	0.622136i	−0.930240	−	0.366952i	$-0.880401\pi$
$277$	−298.487	+	172.332i	−1.07757	+	0.622136i	−0.147331	+	0.989087i	$0.547068\pi$
$278$	2.13309	−	3.69462i	0.00767299	−	0.0132900i
$279$	−22.2049			−0.0795876
$280$	10.2038	+	171.310i	0.0364421	+	0.611822i
$281$		−	264.040i		−	0.939642i	−0.882762	−	0.469821i	$-0.844318\pi$
$281$		−	264.040i		−	0.939642i	0.882762	−	0.469821i	$-0.155682\pi$
$282$	128.599	+	74.2464i	0.456023	+	0.263285i
$283$	361.766	−	208.866i	1.27833	−	0.738042i	0.301786	−	0.953376i	$-0.402417\pi$
$283$	361.766	−	208.866i	1.27833	−	0.738042i	0.976541	+	0.215334i	$0.0690839\pi$
$284$	−19.0511	−	32.9975i	−0.0670814	−	0.116188i
$285$	36.2744	+	20.9430i	0.127279	+	0.0734843i
$286$	−129.003	−	141.293i	−0.451060	−	0.494033i
$287$	46.2148	−	30.4831i	0.161027	−	0.106213i
$288$			25.5000i			0.0885417i
$289$	147.050	−	254.699i	0.508825	−	0.881310i
$290$	−64.1709	−	111.147i	−0.221279	−	0.383266i
$291$	55.7508	+	96.5632i	0.191583	+	0.331832i
$292$	−79.4631	−	45.8780i	−0.272134	−	0.157117i
$293$			8.68846i			0.0296535i	0.999890	+	0.0148267i	$0.00471967\pi$
$293$			8.68846i			0.0296535i	−0.999890	+	0.0148267i	$0.995280\pi$
$294$	234.120	+	100.260i	0.796328	+	0.341021i
$295$	324.874			1.10127
$296$	−136.267	−	78.6736i	−0.460360	−	0.265789i
$297$	54.9242	−	173.107i	0.184930	−	0.582853i
$298$	39.4723	+	68.3681i	0.132457	+	0.229423i
$299$	−414.862	−	239.521i	−1.38750	−	0.801073i
$300$	368.492			1.22831
$301$	449.338	−	296.382i	1.49282	−	0.984656i
$302$	23.8015			0.0788130
$303$	−42.4142	−	24.4878i	−0.139981	−	0.0808179i
$304$	−4.55469	+	2.62965i	−0.0149825	+	0.00865016i
$305$	−663.786	+	383.237i	−2.17635	+	1.25651i
$306$	76.9701	−	133.316i	0.251536	−	0.435673i
$307$		−	164.716i		−	0.536534i	−0.963345	−	0.268267i	$-0.913549\pi$
$307$		−	164.716i		−	0.536534i	0.963345	−	0.268267i	$-0.0864509\pi$
$308$	−110.414	−	107.353i	−0.358487	−	0.348550i
$309$	−249.205			−0.806490
$310$	−52.2925	−	30.1911i	−0.168686	−	0.0973906i
$311$	−302.586	−	524.094i	−0.972945	−	1.68519i	−0.686556	−	0.727077i	$-0.740879\pi$
$311$	−302.586	−	524.094i	−0.972945	−	1.68519i	−0.286389	−	0.958114i	$-0.592455\pi$
$312$	63.9255	+	110.722i	0.204889	+	0.354879i
$313$	−117.362	+	203.277i	−0.374959	+	0.649448i	−0.990321	−	0.138797i	$-0.955677\pi$
$313$	−117.362	+	203.277i	−0.374959	+	0.649448i	0.615362	+	0.788245i	$0.289010\pi$
$314$			95.5706i			0.304365i
$315$	122.429	−	244.578i	0.388664	−	0.776439i
$316$		−	97.8896i		−	0.309777i
$317$	16.6951	−	28.9167i	0.0526659	−	0.0912200i	−0.838491	−	0.544916i	$-0.816562\pi$
$317$	16.6951	−	28.9167i	0.0526659	−	0.0912200i	0.891156	+	0.453696i	$0.149895\pi$
$318$	20.0230	−	11.5603i	0.0629655	−	0.0363531i
$319$	109.776	+	34.8302i	0.344126	+	0.109186i
$320$	−34.6712	+	60.0523i	−0.108348	+	0.187664i
$321$			728.145i			2.26836i
$322$	−344.798	−	172.597i	−1.07080	−	0.536015i
$323$	31.7497			0.0982963
$324$	−101.250	+	175.370i	−0.312500	+	0.541266i
$325$	533.952	−	308.277i	1.64293	−	0.948546i
$326$	−1.49818	+	0.864973i	−0.00459564	+	0.00265329i
$327$	535.994	+	309.457i	1.63913	+	0.946350i
$328$	22.3699			0.0682009
$329$	199.631	−	11.8906i	0.606780	−	0.0361417i
$330$	−365.980	+	334.146i	−1.10903	+	1.01256i
$331$	−3.38917	+	5.87022i	−0.0102392	+	0.0177348i	−0.871100	−	0.491106i	$-0.836593\pi$
$331$	−3.38917	+	5.87022i	−0.0102392	+	0.0177348i	0.860860	+	0.508841i	$0.169926\pi$
$332$	109.556	−	63.2521i	0.329988	−	0.190518i
$333$	125.386	+	217.175i	0.376535	+	0.652177i
$334$	50.1313	−	86.8299i	0.150094	−	0.259970i
$335$	−353.488			−1.05519
$336$	56.6621	+	85.9042i	0.168637	+	0.255667i
$337$		−	406.741i		−	1.20695i	−0.797383	−	0.603474i	$-0.793783\pi$
$337$		−	406.741i		−	1.20695i	0.797383	−	0.603474i	$-0.206217\pi$
$338$	−21.7232	−	12.5419i	−0.0642699	−	0.0371062i
$339$	114.422	+	198.184i	0.337527	+	0.584613i
$340$	362.528	−	209.306i	1.06626	−	0.615605i
$341$	52.9215	−	11.6322i	0.155195	−	0.0341121i
$342$	8.38201			0.0245088
$343$	337.551	−	60.8937i	0.984115	−	0.177533i
$344$	217.498			0.632263
$345$	−620.409	+	1074.58i	−1.79829	+	3.11473i
$346$	−1.47253	−	2.55050i	−0.00425586	−	0.00737137i
$347$	−234.892	+	135.615i	−0.676922	+	0.390821i	−0.798694	−	0.601737i	$-0.794476\pi$
$347$	−234.892	+	135.615i	−0.676922	+	0.390821i	0.121772	+	0.992558i	$0.461142\pi$
$348$	−66.6495	−	38.4801i	−0.191521	−	0.110575i
$349$			155.924i			0.446774i	0.974730	+	0.223387i	$0.0717113\pi$
$349$			155.924i			0.446774i	−0.974730	+	0.223387i	$0.928289\pi$
$350$	414.269	−	273.250i	1.18363	−	0.780715i
$351$			203.057i			0.578509i
$352$	−13.3584	−	60.7746i	−0.0379499	−	0.172655i
$353$	92.0258	+	159.393i	0.260696	+	0.451539i	0.966427	−	0.256941i	$-0.0827145\pi$
$353$	92.0258	+	159.393i	0.260696	+	0.451539i	−0.705731	+	0.708480i	$0.749381\pi$
$354$	168.711	−	97.4055i	0.476586	−	0.275157i
$355$	−82.5658	+	143.008i	−0.232580	+	0.402840i
$356$	−139.091			−0.390704
$357$	−36.9378	−	620.145i	−0.103467	−	1.73710i
$358$		−	227.783i		−	0.636266i
$359$	48.4926	+	27.9972i	0.135077	+	0.0779867i	0.566016	−	0.824394i	$-0.308484\pi$
$359$	48.4926	+	27.9972i	0.135077	+	0.0779867i	−0.430939	+	0.902381i	$0.641817\pi$
$360$	95.7084	−	55.2573i	0.265857	−	0.153492i
$361$	−179.636	−	311.138i	−0.497606	−	0.861878i
$362$	97.6383	+	56.3715i	0.269719	+	0.155722i
$363$	40.3580	−	442.876i	0.111179	−	1.22004i
$364$	153.971	+	77.0739i	0.422998	+	0.211741i
$365$			397.662i			1.08948i
$366$	−229.808	+	398.040i	−0.627891	+	1.08754i
$367$	169.853	+	294.193i	0.462813	+	0.801616i	0.999100	−	0.0424197i	$-0.0135067\pi$
$367$	169.853	+	294.193i	0.462813	+	0.801616i	−0.536287	+	0.844036i	$0.680173\pi$
$368$	−77.8999	−	134.927i	−0.211684	−	0.366648i
$369$	−30.8756	−	17.8260i	−0.0836736	−	0.0483090i
$370$			681.928i			1.84305i
$371$	13.9381	−	27.8442i	0.0375689	−	0.0750518i
$372$	−36.2082			−0.0973339
$373$	32.8595	+	18.9714i	0.0880951	+	0.0508617i	0.543400	−	0.839474i	$-0.317137\pi$
$373$	32.8595	+	18.9714i	0.0880951	+	0.0508617i	−0.455305	+	0.890335i	$0.650470\pi$
$374$	−113.606	+	358.056i	−0.303758	+	0.957369i
$375$	−400.294	−	693.330i	−1.06745	−	1.84888i
$376$	69.9799	+	40.4029i	0.186117	+	0.107455i
$377$	−128.769			−0.341561
$378$	9.71791	+	163.153i	0.0257087	+	0.431622i
$379$	−576.759			−1.52179			−0.760896	−	0.648874i	$-0.775240\pi$
$379$	−576.759			−1.52179			−0.760896	+	0.648874i	$0.775240\pi$
$380$	19.7396	+	11.3966i	0.0519462	+	0.0299912i
$381$	−445.127	+	256.994i	−1.16831	+	0.674525i
$382$	−254.436	+	146.899i	−0.666064	+	0.384552i
$383$	24.3901	−	42.2449i	0.0636817	−	0.110300i	−0.832427	−	0.554135i	$-0.813049\pi$
$383$	24.3901	−	42.2449i	0.0636817	−	0.110300i	0.896108	+	0.443835i	$0.146382\pi$
$384$			41.5812i			0.108284i
$385$	−163.664	+	647.043i	−0.425100	+	1.68063i
$386$	−224.156			−0.580715
$387$	−300.197	−	173.319i	−0.775704	−	0.447853i
$388$	30.3381	+	52.5472i	0.0781910	+	0.135431i
$389$	−89.5398	−	155.087i	−0.230179	−	0.398682i	0.727681	−	0.685915i	$-0.240598\pi$
$389$	−89.5398	−	155.087i	−0.230179	−	0.398682i	−0.957861	+	0.287233i	$0.907265\pi$
$390$	277.047	−	479.859i	0.710376	−	1.23041i
$391$			940.542i			2.40548i
$392$	127.402	+	54.5589i	0.325006	+	0.139181i
$393$		−	426.747i		−	1.08587i
$394$	77.7003	−	134.581i	0.197209	−	0.341576i
$395$	−367.406	+	212.122i	−0.930142	+	0.537018i
$396$	−29.9922	+	94.5278i	−0.0757378	+	0.238706i
$397$	233.233	−	403.972i	0.587489	−	1.01756i	−0.407071	−	0.913397i	$-0.633450\pi$
$397$	233.233	−	403.972i	0.587489	−	1.01756i	0.994560	−	0.104165i	$-0.0332169\pi$
$398$		−	37.3400i		−	0.0938190i
$399$	28.2372	−	18.6252i	0.0707700	−	0.0466796i
$400$	200.523			0.501309
$401$	90.1640	−	156.169i	0.224848	−	0.389448i	−0.731426	−	0.681921i	$-0.761145\pi$
$401$	90.1640	−	156.169i	0.224848	−	0.389448i	0.956274	+	0.292473i	$0.0944782\pi$
$402$	−183.571	+	105.985i	−0.456644	+	0.263643i
$403$	−52.4665	+	30.2915i	−0.130190	+	0.0751651i
$404$	−23.0807	−	13.3256i	−0.0571304	−	0.0329842i
$405$	877.615			2.16695
$406$	−103.464	+	6.16262i	−0.254836	+	0.0151789i
$407$	−412.604	−	451.913i	−1.01377	−	1.11035i
$408$	125.510	−	217.390i	0.307623	−	0.532819i
$409$	−61.9818	+	35.7852i	−0.151545	+	0.0874944i	−0.573855	−	0.818957i	$-0.694553\pi$
$409$	−61.9818	+	35.7852i	−0.151545	+	0.0874944i	0.422310	+	0.906451i	$0.361219\pi$
$410$	−48.4745	−	83.9603i	−0.118230	−	0.204781i
$411$	−297.324	+	514.980i	−0.723416	+	1.25299i
$412$	−135.611			−0.329153
$413$	117.440	−	234.612i	0.284359	−	0.568067i
$414$			248.306i			0.599772i
$415$	−474.805	−	274.129i	−1.14411	−	0.660551i
$416$	34.7866	+	60.2521i	0.0836215	+	0.144837i
$417$	−9.60168	+	5.54353i	−0.0230256	+	0.0132938i
$418$	−19.9770	+	4.39098i	−0.0477919	+	0.0105047i
$419$	700.063			1.67080			0.835398	−	0.549646i	$-0.185237\pi$
$419$	700.063			1.67080			0.835398	+	0.549646i	$0.185237\pi$
$420$	199.638	−	398.818i	0.475328	−	0.949567i
$421$	−709.065			−1.68424			−0.842120	−	0.539290i	$-0.818693\pi$
$421$	−709.065			−1.68424			−0.842120	+	0.539290i	$0.818693\pi$
$422$	187.654	−	325.026i	0.444677	−	0.770204i
$423$	−64.3922	−	111.531i	−0.152227	−	0.263666i
$424$	10.8960	−	6.29081i	0.0256981	−	0.0148368i
$425$	−1048.35	−	605.267i	−2.46671	−	1.42416i
$426$			99.0212i			0.232444i
$427$	36.8040	+	617.899i	0.0861920	+	1.44707i
$428$			396.237i			0.925788i
$429$	106.743	+	485.631i	0.248817	+	1.13201i
$430$	−471.309	−	816.330i	−1.09607	−	1.89844i
$431$	−134.349	+	77.5664i	−0.311714	+	0.179968i	−0.647693	−	0.761901i	$-0.724266\pi$
$431$	−134.349	+	77.5664i	−0.311714	+	0.179968i	0.335979	+	0.941869i	$0.390933\pi$
$432$	−33.0203	+	57.1928i	−0.0764359	+	0.132391i
$433$	381.442			0.880929			0.440464	−	0.897770i	$-0.354814\pi$
$433$	381.442			0.880929			0.440464	+	0.897770i	$0.354814\pi$
$434$	−40.7063	+	26.8497i	−0.0937933	+	0.0618657i
$435$			333.538i			0.766754i
$436$	291.674	+	168.398i	0.668977	+	0.386234i
$437$	−44.3512	+	25.6062i	−0.101490	+	0.0585954i
$438$	119.229	+	206.511i	0.272213	+	0.471486i
$439$	−344.832	−	199.089i	−0.785495	−	0.453506i	0.0528793	−	0.998601i	$-0.483160\pi$
$439$	−344.832	−	199.089i	−0.785495	−	0.453506i	−0.838374	+	0.545095i	$0.816493\pi$
$440$	−199.157	+	181.833i	−0.452629	+	0.413257i
$441$	−132.367	−	176.827i	−0.300153	−	0.400969i
$442$		−	420.004i		−	0.950235i
$443$	−161.545	+	279.805i	−0.364662	+	0.631614i	−0.988722	−	0.149763i	$-0.952149\pi$
$443$	−161.545	+	279.805i	−0.364662	+	0.631614i	0.624060	+	0.781377i	$0.285482\pi$
$444$	204.459	+	354.134i	0.460494	+	0.797598i
$445$	301.403	+	522.045i	0.677310	+	1.17314i
$446$	113.353	+	65.4446i	0.254156	+	0.146737i
$447$		−	205.164i		−	0.458979i
$448$	30.8340	+	46.7468i	0.0688259	+	0.104346i
$449$	508.500			1.13252			0.566258	−	0.824228i	$-0.308390\pi$
$449$	508.500			1.13252			0.566258	+	0.824228i	$0.308390\pi$
$450$	−276.768	−	159.792i	−0.615040	−	0.355094i
$451$	82.9246	+	26.3107i	0.183868	+	0.0583385i
$452$	62.2652	+	107.846i	0.137755	+	0.238598i
$453$	−53.5689	−	30.9280i	−0.118254	−	0.0682738i
$454$	78.8548			0.173689
$455$	−44.3693	−	744.912i	−0.0975149	−	1.63717i
$456$	13.6680			0.0299737
$457$	416.099	+	240.235i	0.910502	+	0.525678i	0.880593	−	0.473874i	$-0.157145\pi$
$457$	416.099	+	240.235i	0.910502	+	0.525678i	0.0299092	+	0.999553i	$0.490478\pi$
$458$	463.039	−	267.336i	1.01100	−	0.583703i
$459$	345.266	−	199.339i	0.752213	−	0.434290i
$460$	−337.610	+	584.758i	−0.733936	+	1.27121i
$461$		−	153.537i		−	0.333052i	−0.986037	−	0.166526i	$-0.946745\pi$
$461$		−	153.537i		−	0.333052i	0.986037	−	0.166526i	$-0.0532550\pi$
$462$	109.007	+	385.088i	0.235947	+	0.833524i
$463$	−656.622			−1.41819			−0.709095	−	0.705113i	$-0.750896\pi$
$463$	−656.622			−1.41819			−0.709095	+	0.705113i	$0.750896\pi$
$464$	−36.2689	−	20.9399i	−0.0781657	−	0.0451290i
$465$	78.4614	+	135.899i	0.168734	+	0.292256i
$466$	−145.256	−	251.591i	−0.311709	−	0.539896i
$467$	214.837	−	372.108i	0.460036	−	0.796806i	−0.538926	−	0.842353i	$-0.681170\pi$
$467$	214.837	−	372.108i	0.460036	−	0.796806i	0.998962	+	0.0455470i	$0.0145031\pi$
$468$		−	110.882i		−	0.236928i
$469$	−127.784	+	255.275i	−0.272461	+	0.544297i
$470$		−	350.205i		−	0.745117i
$471$	124.186	−	215.096i	0.263664	−	0.456680i
$472$	91.8083	−	53.0055i	0.194509	−	0.112300i
$473$	806.261	+	255.814i	1.70457	+	0.540832i
$474$	−127.199	+	220.315i	−0.268352	+	0.464800i
$475$		−	65.9133i		−	0.138765i
$476$	−20.1006	−	337.467i	−0.0422281	−	0.708963i
$477$	−20.0520			−0.0420376
$478$	−225.043	+	389.785i	−0.470800	+	0.815450i
$479$	243.910	−	140.821i	0.509206	−	0.293990i	−0.223301	−	0.974749i	$-0.571683\pi$
$479$	243.910	−	140.821i	0.509206	−	0.293990i	0.732507	+	0.680759i	$0.238350\pi$
$480$	156.066	−	90.1045i	0.325137	−	0.187718i
$481$	592.531	+	342.098i	1.23187	+	0.711222i
$482$	648.265			1.34495
$483$	551.746	+	836.490i	1.14233	+	1.73186i
$484$	21.9618	−	241.001i	0.0453755	−	0.497937i
$485$	131.482	−	227.734i	0.271098	−	0.469555i
$486$	273.770	−	158.061i	0.563313	−	0.325229i
$487$	163.684	+	283.508i	0.336106	+	0.582152i	0.983697	−	0.179836i	$-0.0575567\pi$
$487$	163.684	+	283.508i	0.336106	+	0.582152i	−0.647591	+	0.761988i	$0.724223\pi$
$488$	−125.056	+	216.603i	−0.256261	+	0.443858i
$489$	4.49583			0.00919393
$490$	−71.3001	−	596.402i	−0.145510	−	1.21715i
$491$			530.235i			1.07991i	0.841694	+	0.539955i	$0.181559\pi$
$491$			530.235i			1.07991i	−0.841694	+	0.539955i	$0.818441\pi$
$492$	−50.3468	−	29.0677i	−0.102331	−	0.0590808i
$493$	126.411	+	218.951i	0.256412	+	0.444119i
$494$	19.8052	−	11.4346i	0.0400916	−	0.0231469i
$495$	419.780	−	92.2684i	0.848040	−	0.186401i
$496$	−19.7036			−0.0397249
$497$	73.4279	+	111.322i	0.147742	+	0.223989i
$498$	−328.763			−0.660166
$499$	166.808	−	288.920i	0.334285	−	0.578998i	−0.649063	−	0.760735i	$-0.724839\pi$
$499$	166.808	−	288.920i	0.334285	−	0.578998i	0.983347	+	0.181737i	$0.0581720\pi$
$500$	−217.830	−	377.292i	−0.435659	−	0.754584i
$501$	−225.656	+	130.283i	−0.450411	+	0.260045i
$502$	263.421	+	152.086i	0.524744	+	0.302961i
$503$		−	540.865i		−	1.07528i	−0.843175	−	0.537639i	$-0.819316\pi$
$503$		−	540.865i		−	1.07528i	0.843175	−	0.537639i	$-0.180684\pi$
$504$	−5.30661	−	89.0921i	−0.0105290	−	0.176770i
$505$			115.504i			0.228721i
$506$	−130.077	−	591.792i	−0.257069	−	1.16955i
$507$	32.5942	+	56.4549i	0.0642885	+	0.111351i
$508$	−242.226	+	139.849i	−0.476823	+	0.275294i
$509$	41.1847	−	71.3339i	0.0809129	−	0.140145i	−0.822729	−	0.568433i	$-0.807550\pi$
$509$	41.1847	−	71.3339i	0.0809129	−	0.140145i	0.903642	+	0.428288i	$0.140883\pi$
$510$	−1087.90			−2.13313
$511$	287.176	+	143.753i	0.561989	+	0.281316i
$512$			22.6274i			0.0441942i
$513$	18.7996	+	10.8540i	0.0366465	+	0.0211579i
$514$	−615.012	+	355.077i	−1.19652	+	0.690812i
$515$	293.863	+	508.985i	0.570607	+	0.988320i
$516$	−489.513	−	282.620i	−0.948668	−	0.547714i
$517$	211.893	+	232.080i	0.409851	+	0.448898i
$518$	492.462	+	246.513i	0.950698	+	0.475894i
$519$			7.65370i			0.0147470i
$520$	150.762	−	261.127i	0.289926	−	0.502167i
$521$	−275.190	−	476.643i	−0.528196	−	0.914862i	−0.999460	−	0.0328694i	$-0.989535\pi$
$521$	−275.190	−	476.643i	−0.528196	−	0.914862i	0.471264	−	0.881992i	$-0.343798\pi$
$522$	33.3729	+	57.8035i	0.0639327	+	0.110735i
$523$	−616.378	−	355.866i	−1.17854	−	0.680432i	−0.222866	−	0.974849i	$-0.571541\pi$
$523$	−616.378	−	355.866i	−1.17854	−	0.680432i	−0.955677	+	0.294417i	$0.904875\pi$
$524$		−	232.224i		−	0.443177i
$525$	−1287.44	+	76.6839i	−2.45226	+	0.146065i
$526$	−373.072			−0.709263
$527$	103.012	+	59.4739i	0.195468	+	0.112854i
$528$	−48.9063	+	154.140i	−0.0926256	+	0.291933i
$529$	−494.048	−	855.717i	−0.933929	−	1.61761i
$530$	−47.2222	−	27.2638i	−0.0890985	−	0.0514411i
$531$	−168.955			−0.318183
$532$	15.3660	−	10.1353i	0.0288834	−	0.0190514i
$533$	−97.2715			−0.182498
$534$	313.045	+	180.736i	0.586226	+	0.338458i
$535$	1487.19	−	858.627i	2.77979	−	1.60491i
$536$	−99.8944	+	57.6741i	−0.186370	+	0.107601i
$537$	−295.985	+	512.660i	−0.551182	+	0.954674i
$538$			66.5620i			0.123721i
$539$	408.106	+	352.094i	0.757154	+	0.653236i
$540$	286.214			0.530025
$541$	415.492	+	239.885i	0.768008	+	0.443409i	0.832163	−	0.554530i	$-0.187102\pi$
$541$	415.492	+	239.885i	0.768008	+	0.443409i	−0.0641557	+	0.997940i	$0.520435\pi$
$542$	353.991	+	613.131i	0.653121	+	1.13124i
$543$	−146.500	−	253.745i	−0.269797	−	0.467302i
$544$	68.2994	−	118.298i	0.125550	−	0.217460i
$545$		−	1459.64i		−	2.67824i
$546$	−246.385	−	373.539i	−0.451254	−	0.684137i
$547$		−	755.161i		−	1.38055i	−0.723547	−	0.690275i	$-0.757490\pi$
$547$		−	755.161i		−	1.38055i	0.723547	−	0.690275i	$-0.242510\pi$
$548$	−161.796	+	280.239i	−0.295248	+	0.511385i
$549$	345.210	−	199.307i	0.628799	−	0.363037i
$550$	743.335	+	235.848i	1.35152	+	0.428815i
$551$	−6.88306	+	11.9218i	−0.0124919	+	0.0216367i
$552$			404.897i			0.733508i
$553$	20.3710	+	342.007i	0.0368373	+	0.618458i
$554$	487.427			0.879833
$555$	886.106	−	1534.78i	1.59659	−	2.76537i
$556$	−5.22498	+	3.01664i	−0.00939745	+	0.00542562i
$557$	−83.7181	+	48.3347i	−0.150302	+	0.0867768i	−0.573265	−	0.819370i	$-0.694323\pi$
$557$	−83.7181	+	48.3347i	−0.150302	+	0.0867768i	0.422963	+	0.906147i	$0.360990\pi$
$558$	27.1954	+	15.7013i	0.0487373	+	0.0281385i
$559$	−945.753			−1.69187
$560$	108.638	−	217.026i	0.193996	−	0.387547i
$561$	720.949	−	658.238i	1.28511	−	1.17333i
$562$	−186.704	+	323.381i	−0.332214	+	0.575411i
$563$	−808.860	+	466.996i	−1.43670	+	0.829477i	−0.997619	−	0.0689719i	$-0.978028\pi$
$563$	−808.860	+	466.996i	−1.43670	+	0.829477i	−0.439078	+	0.898449i	$0.644695\pi$
$564$	−105.000	−	181.866i	−0.186171	−	0.322457i
$565$	269.851	−	467.396i	0.477613	−	0.827250i
$566$	−590.762			−1.04375
$567$	317.253	−	633.780i	0.559529	−	1.11778i
$568$			53.8847i			0.0948675i
$569$	550.093	+	317.597i	0.966772	+	0.558166i	0.898251	−	0.439483i	$-0.144838\pi$
$569$	550.093	+	317.597i	0.966772	+	0.558166i	0.0685216	+	0.997650i	$0.478172\pi$
$570$	−29.6179	−	51.2997i	−0.0519613	−	0.0899995i
$571$	73.0765	−	42.1908i	0.127980	−	0.0738893i	−0.434643	−	0.900603i	$-0.643126\pi$
$571$	73.0765	−	42.1908i	0.127980	−	0.0738893i	0.562623	+	0.826713i	$0.309792\pi$
$572$	58.0865	+	264.267i	0.101550	+	0.462006i
$573$	763.530			1.33251
$574$	−78.1561	+	4.65523i	−0.136160	+	0.00811015i
$575$	1952.59			3.39582
$576$	18.0312	−	31.2310i	0.0313042	−	0.0542205i
$577$	−537.726	−	931.368i	−0.931934	−	1.61416i	−0.780012	−	0.625764i	$-0.784787\pi$
$577$	−537.726	−	931.368i	−0.931934	−	1.61416i	−0.151921	−	0.988393i	$-0.548546\pi$
$578$	−360.198	+	207.961i	−0.623180	+	0.359793i
$579$	504.497	+	291.271i	0.871324	+	0.503059i
$580$			181.503i			0.312936i
$581$	−369.604	+	243.790i	−0.636152	+	0.419603i
$582$		−	157.687i		−	0.270940i
$583$	47.7902	−	10.5044i	0.0819729	−	0.0180178i
$584$	64.8814	+	112.378i	0.111098	+	0.192428i
$585$	−416.171	+	240.276i	−0.711403	+	0.410729i
$586$	6.14367	−	10.6412i	0.0104841	−	0.0181590i
$587$	−104.627			−0.178241			−0.0891204	−	0.996021i	$-0.528406\pi$
$587$	−104.627			−0.178241			−0.0891204	+	0.996021i	$0.528406\pi$
$588$	−215.843	−	288.341i	−0.367080	−	0.490376i
$589$			6.47668i			0.0109961i
$590$	−397.888	−	229.721i	−0.674387	−	0.389357i
$591$	−349.753	+	201.930i	−0.591798	+	0.341675i
$592$	111.261	+	192.710i	0.187941	+	0.325524i
$593$	737.874	+	426.012i	1.24431	+	0.718401i	0.969968	−	0.243232i	$-0.0782076\pi$
$593$	737.874	+	426.012i	1.24431	+	0.718401i	0.274339	+	0.961633i	$0.411541\pi$
$594$	−189.673	+	173.175i	−0.319316	+	0.291540i
$595$	−1223.05	+	806.717i	−2.05554	+	1.35583i
$596$		−	111.645i		−	0.187323i
$597$	−48.5201	+	84.0392i	−0.0812732	+	0.140769i
$598$	338.733	+	586.704i	0.566444	+	0.981110i
$599$	−277.593	−	480.805i	−0.463428	−	0.802680i	0.535701	−	0.844407i	$-0.320047\pi$
$599$	−277.593	−	480.805i	−0.463428	−	0.802680i	−0.999129	+	0.0417274i	$0.986714\pi$
$600$	−451.308	−	260.563i	−0.752180	−	0.434272i
$601$		−	349.078i		−	0.580829i	−0.956901	−	0.290414i	$-0.906207\pi$
$601$		−	349.078i		−	0.580829i	0.956901	−	0.290414i	$-0.0937931\pi$
$602$	−759.898	+	45.2619i	−1.26229	+	0.0751859i
$603$	183.836			0.304869
$604$	−29.1508	−	16.8302i	−0.0482629	−	0.0278646i
$605$	−952.134	+	439.810i	−1.57377	+	0.726959i
$606$	34.6310	+	59.9827i	0.0571469	+	0.0989813i
$607$	−130.948	−	75.6027i	−0.215729	−	0.124551i	0.388242	−	0.921558i	$-0.373083\pi$
$607$	−130.948	−	75.6027i	−0.215729	−	0.124551i	−0.603971	+	0.797006i	$0.706416\pi$
$608$	7.43777			0.0122332
$609$	240.868	+	120.572i	0.395514	+	0.197984i
$610$	1083.96			1.77698
$611$	−304.295	−	175.685i	−0.498028	−	0.287537i
$612$	−188.537	+	108.852i	−0.308068	+	0.177863i
$613$	115.633	−	66.7607i	0.188634	−	0.108908i	−0.402709	−	0.915328i	$-0.631931\pi$
$613$	115.633	−	66.7607i	0.188634	−	0.108908i	0.591343	+	0.806420i	$0.298598\pi$
$614$	−116.472	+	201.735i	−0.189693	+	0.328558i
$615$			251.954i			0.409681i
$616$	59.3189	+	209.555i	0.0962970	+	0.340187i
$617$	−416.677			−0.675327			−0.337664	−	0.941267i	$-0.609637\pi$
$617$	−416.677			−0.675327			−0.337664	+	0.941267i	$0.609637\pi$
$618$	305.213	+	176.215i	0.493872	+	0.285137i
$619$	79.9429	+	138.465i	0.129148	+	0.223692i	0.923347	−	0.383967i	$-0.125442\pi$
$619$	79.9429	+	138.465i	0.129148	+	0.223692i	−0.794198	+	0.607658i	$0.792109\pi$
$620$	42.6967	+	73.9528i	0.0688656	+	0.119279i
$621$	−321.535	+	556.914i	−0.517769	+	0.896802i
$622$			855.842i			1.37595i
$623$	485.956	−	28.9451i	0.780026	−	0.0464608i
$624$		−	180.808i		−	0.289757i
$625$	−317.416	+	549.781i	−0.507866	+	0.879650i
$626$	287.477	−	165.975i	0.459229	−	0.265136i
$627$	50.6669	+	16.0758i	0.0808085	+	0.0256393i
$628$	67.5786	−	117.050i	0.107609	−	0.186385i
$629$		−	1343.34i		−	2.13568i
$630$	−322.888	+	212.975i	−0.512520	+	0.338056i
$631$	104.171			0.165090			0.0825448	−	0.996587i	$-0.473695\pi$
$631$	104.171			0.165090			0.0825448	+	0.996587i	$0.473695\pi$
$632$	−69.2184	+	119.890i	−0.109523	+	0.189699i
$633$	−844.686	+	487.680i	−1.33442	+	0.770426i
$634$	−40.8944	+	23.6104i	−0.0645023	+	0.0372404i
$635$	1049.79	+	606.094i	1.65321	+	0.954478i
$636$	−32.6975			−0.0514111
$637$	−553.986	−	237.240i	−0.869679	−	0.372433i
$638$	−109.819	−	120.282i	−0.172130	−	0.188529i
$639$	42.9394	−	74.3732i	0.0671978	−	0.116390i
$640$	84.9268	−	49.0325i	0.132698	−	0.0766133i
$641$	−165.344	−	286.384i	−0.257946	−	0.446776i	0.707745	−	0.706468i	$-0.249712\pi$
$641$	−165.344	−	286.384i	−0.257946	−	0.446776i	−0.965692	+	0.259692i	$0.916379\pi$
$642$	514.876	−	891.791i	0.801988	−	1.38908i
$643$	−345.107			−0.536715			−0.268357	−	0.963319i	$-0.586481\pi$
$643$	−345.107			−0.536715			−0.268357	+	0.963319i	$0.586481\pi$
$644$	300.246	+	455.196i	0.466220	+	0.706826i
$645$			2449.70i			3.79798i
$646$	−38.8853	−	22.4504i	−0.0601939	−	0.0347530i
$647$	223.079	+	386.383i	0.344789	+	0.597192i	0.985315	−	0.170744i	$-0.0546171\pi$
$647$	223.079	+	386.383i	0.344789	+	0.597192i	−0.640526	+	0.767936i	$0.721284\pi$
$648$	248.011	−	143.189i	0.382733	−	0.220971i
$649$	402.674	−	88.5085i	0.620453	−	0.136377i
$650$	−871.940			−1.34145
$651$	126.505	−	7.53501i	0.194323	−	0.0115745i
$652$	2.44651			0.00375232
$653$	−586.033	+	1015.04i	−0.897447	+	1.55442i	−0.0667013	+	0.997773i	$0.521247\pi$
$653$	−586.033	+	1015.04i	−0.897447	+	1.55442i	−0.830746	+	0.556652i	$0.812086\pi$
$654$	−437.638	−	758.011i	−0.669171	−	1.15904i
$655$	−871.601	+	503.219i	−1.33069	+	0.768274i
$656$	−27.3974	−	15.8179i	−0.0417644	−	0.0241127i
$657$		−	206.809i		−	0.314778i
$658$	−252.904	−	126.597i	−0.384353	−	0.192397i
$659$			390.477i			0.592529i	0.955106	+	0.296264i	$0.0957410\pi$
$659$			390.477i			0.592529i	−0.955106	+	0.296264i	$0.904259\pi$
$660$	684.508	−	150.456i	1.03713	−	0.227964i
$661$	272.118	+	471.322i	0.411676	+	0.713045i	0.995073	−	0.0991427i	$-0.0316100\pi$
$661$	272.118	+	471.322i	0.411676	+	0.713045i	−0.583397	+	0.812187i	$0.698277\pi$
$662$	8.30174	−	4.79301i	0.0125404	−	0.00724020i
$663$	−545.759	+	945.282i	−0.823165	+	1.42576i
$664$	−178.904			−0.269434
$665$	−71.3380	−	35.7099i	−0.107275	−	0.0536990i
$666$		−	354.645i		−	0.532500i
$667$	−353.168	−	203.901i	−0.529487	−	0.305699i
$668$	−122.796	+	70.8963i	−0.183826	+	0.106132i
$669$	−170.079	−	294.586i	−0.254229	−	0.440338i
$670$	432.933	+	249.954i	0.646168	+	0.373065i
$671$	−718.338	+	655.854i	−1.07055	+	0.977428i
$672$	−8.65315	−	145.277i	−0.0128767	−	0.216186i
$673$			739.270i			1.09847i	0.835668	+	0.549234i	$0.185081\pi$
$673$			739.270i			1.09847i	−0.835668	+	0.549234i	$0.814919\pi$
$674$	−287.609	+	498.154i	−0.426720	+	0.739101i
$675$	−413.834	−	716.782i	−0.613088	−	1.06190i
$676$	17.7369	+	30.7213i	0.0262381	+	0.0454457i
$677$	273.044	+	157.642i	0.403315	+	0.232854i	0.687913	−	0.725793i	$-0.258527\pi$
$677$	273.044	+	157.642i	0.403315	+	0.232854i	−0.284598	+	0.958647i	$0.591860\pi$
$678$		−	323.633i		−	0.477335i
$679$	−116.931	−	177.276i	−0.172210	−	0.261084i
$680$	−592.006			−0.870597
$681$	−177.475	−	102.465i	−0.260609	−	0.150463i
$682$	−73.0405	−	23.1746i	−0.107098	−	0.0339804i
$683$	−307.477	−	532.566i	−0.450186	−	0.779745i	0.548211	−	0.836340i	$-0.315309\pi$
$683$	−307.477	−	532.566i	−0.450186	−	0.779745i	−0.998397	+	0.0565949i	$0.981976\pi$
$684$	−10.2658	−	5.92697i	−0.0150085	−	0.00866517i
$685$	1402.42			2.04732
$686$	−456.473	−	164.106i	−0.665412	−	0.239221i
$687$	−1389.52			−2.02259
$688$	−266.380	−	153.795i	−0.387180	−	0.223539i
$689$	−47.3793	+	27.3545i	−0.0687653	+	0.0397017i
$690$	1519.69	−	877.391i	2.20244	−	1.27158i
$691$	329.530	−	570.762i	0.476888	−	0.825995i	−0.522761	−	0.852479i	$-0.675098\pi$
$691$	329.530	−	570.762i	0.476888	−	0.825995i	0.999649	+	0.0264847i	$0.00843133\pi$
$692$			4.16494i			0.00601870i
$693$	85.1154	−	336.503i	0.122822	−	0.485575i
$694$	383.577			0.552704
$695$	22.6446	+	13.0738i	0.0325821	+	0.0188113i
$696$	54.4191	+	94.2566i	0.0781883	+	0.135426i
$697$	95.4906	+	165.395i	0.137002	+	0.237295i
$698$	110.255	−	190.967i	0.157958	−	0.273592i
$699$			754.993i			1.08010i
$700$	−700.591	+	41.7294i	−1.00084	+	0.0596134i
$701$			415.932i			0.593342i	0.954980	+	0.296671i	$0.0958764\pi$
$701$			415.932i			0.593342i	−0.954980	+	0.296671i	$0.904124\pi$
$702$	143.583	−	248.693i	0.204534	−	0.354263i
$703$	63.3450	−	36.5723i	0.0901068	−	0.0520232i
$704$	−26.6135	+	83.8792i	−0.0378033	+	0.119147i
$705$	−455.061	+	788.189i	−0.645477	+	1.11800i
$706$		−	260.288i		−	0.368680i
$707$	83.4126	+	41.7541i	0.117981	+	0.0590581i
$708$	−275.504			−0.389131
$709$	382.704	−	662.863i	0.539780	−	0.934927i	−0.459135	−	0.888366i	$-0.651841\pi$
$709$	382.704	−	662.863i	0.539780	−	0.934927i	0.998915	−	0.0465605i	$-0.0148260\pi$
$710$	202.244	−	116.766i	0.284851	−	0.164459i
$711$	191.074	−	110.317i	0.268740	−	0.155157i
$712$	170.351	+	98.3520i	0.239257	+	0.138135i
$713$	−191.863			−0.269093
$714$	−393.269	+	785.638i	−0.550797	+	1.10033i
$715$	865.997	−	790.669i	1.21118	−	1.10583i
$716$	−161.067	+	278.976i	−0.224954	+	0.389632i
$717$	1012.98	−	584.847i	1.41281	−	0.815686i
$718$	−39.5941	−	68.5789i	−0.0551449	−	0.0955138i
$719$	212.993	−	368.915i	0.296235	−	0.513095i	−0.679036	−	0.734105i	$-0.737602\pi$
$719$	212.993	−	368.915i	0.296235	−	0.513095i	0.975272	+	0.221010i	$0.0709354\pi$
$720$	−156.291			−0.217071
$721$	473.799	−	28.2210i	0.657142	−	0.0391414i
$722$			508.086i			0.703721i
$723$	−1459.02	−	842.365i	−2.01801	−	1.16510i
$724$	−79.7213	−	138.081i	−0.110112	−	0.190720i
$725$	454.548	−	262.433i	0.626962	−	0.361977i
$726$	−362.589	+	513.873i	−0.499434	+	0.707813i
$727$	111.550			0.153439			0.0767197	−	0.997053i	$-0.475555\pi$
$727$	111.550			0.153439			0.0767197	+	0.997053i	$0.475555\pi$
$728$	−134.076	−	203.270i	−0.184171	−	0.279217i
$729$	89.7023			0.123048
$730$	281.190	−	487.035i	0.385191	−	0.667171i
$731$	928.438	+	1608.10i	1.27009	+	2.19987i
$732$	562.913	−	324.998i	0.769007	−	0.443986i
$733$	226.345	+	130.680i	0.308793	+	0.178282i	0.646386	−	0.763010i	$-0.276280\pi$
$733$	226.345	+	130.680i	0.308793	+	0.178282i	−0.337593	+	0.941292i	$0.609613\pi$
$734$		−	480.415i		−	0.654517i
$735$	−614.501	+	1434.94i	−0.836055	+	1.95230i
$736$			220.334i			0.299367i
$737$	−438.140	+	96.3040i	−0.594491	+	0.130670i
$738$	25.2098	+	43.6646i	0.0341596	+	0.0591662i
$739$	149.401	−	86.2567i	0.202166	−	0.116721i	−0.395499	−	0.918466i	$-0.629428\pi$
$739$	149.401	−	86.2567i	0.202166	−	0.116721i	0.597666	+	0.801746i	$0.296095\pi$
$740$	482.196	−	835.187i	0.651616	−	1.12863i
$741$	−59.4329			−0.0802063
$742$	−36.7594	+	24.2464i	−0.0495410	+	0.0326770i
$743$		−	1015.29i		−	1.36647i	−0.730196	−	0.683237i	$-0.760571\pi$
$743$		−	1015.29i		−	1.36647i	0.730196	−	0.683237i	$-0.239429\pi$
$744$	44.3458	+	25.6031i	0.0596046	+	0.0344127i
$745$	−419.032	+	241.928i	−0.562460	+	0.324736i
$746$	−26.8296	−	46.4703i	−0.0359647	−	0.0622926i
$747$	246.928	+	142.564i	0.330560	+	0.190849i
$748$	392.322	−	358.196i	0.524494	−	0.478872i
$749$	−82.4578	−	1384.38i	−0.110091	−	1.84830i
$750$			1132.20i			1.50960i
$751$	258.388	−	447.541i	0.344058	−	0.595926i	−0.641124	−	0.767437i	$-0.721532\pi$
$751$	258.388	−	447.541i	0.344058	−	0.595926i	0.985182	+	0.171511i	$0.0548649\pi$
$752$	−57.1384	−	98.9666i	−0.0759819	−	0.131604i
$753$	−395.246	−	684.587i	−0.524895	−	0.909146i
$754$	157.709	+	91.0532i	0.209163	+	0.120760i
$755$			145.881i			0.193220i
$756$	103.465	−	206.692i	0.136858	−	0.273403i
$757$	−583.508			−0.770817			−0.385408	−	0.922746i	$-0.625939\pi$
$757$	−583.508			−0.770817			−0.385408	+	0.922746i	$0.625939\pi$
$758$	706.383	+	407.830i	0.931903	+	0.538035i
$759$	−476.224	+	1500.94i	−0.627437	+	1.97752i
$760$	−16.1173	−	27.9160i	−0.0212070	−	0.0367315i
$761$	−828.116	−	478.113i	−1.08819	−	0.628269i	−0.155099	−	0.987899i	$-0.549570\pi$
$761$	−828.116	−	478.113i	−1.08819	−	0.628269i	−0.933095	+	0.359629i	$0.882903\pi$
$762$	726.889			0.953922
$763$	−1054.10	−	527.653i	−1.38152	−	0.691550i
$764$	415.493			0.543839
$765$	817.103	+	471.755i	1.06811	+	0.616673i
$766$	−59.7433	+	34.4928i	−0.0779938	+	0.0450298i
$767$	−399.212	+	230.485i	−0.520485	+	0.300502i
$768$	29.4024	−	50.9264i	0.0382843	−	0.0663104i
$769$		−	730.236i		−	0.949592i	−0.880096	−	0.474796i	$-0.842522\pi$
$769$		−	730.236i		−	0.949592i	0.880096	−	0.474796i	$-0.157478\pi$
$770$	657.975	−	676.735i	0.854513	−	0.878877i
$771$	1845.57			2.39373
$772$	274.534	+	158.502i	0.355614	+	0.205314i
$773$	−322.274	−	558.194i	−0.416913	−	0.722114i	0.578714	−	0.815530i	$-0.303555\pi$
$773$	−322.274	−	558.194i	−0.416913	−	0.722114i	−0.995627	+	0.0934163i	$0.970221\pi$
$774$	245.110	+	424.543i	0.316680	+	0.548505i
$775$	123.470	−	213.856i	0.159316	−	0.275943i
$776$		−	85.8091i		−	0.110579i
$777$	−788.037	−	1194.73i	−1.01420	−	1.53761i
$778$			253.257i			0.325523i
$779$	−5.19944	+	9.00570i	−0.00667451	+	0.0115606i
$780$	−678.623	+	391.803i	−0.870030	+	0.502312i
$781$	−63.3773	+	199.749i	−0.0811489	+	0.255761i
$782$	665.064	−	1151.92i	0.850465	−	1.47305i
$783$			172.860i			0.220766i
$784$	−117.456	−	156.908i	−0.149817	−	0.200137i
$785$	−585.759			−0.746189
$786$	−301.756	+	522.656i	−0.383913	+	0.664957i
$787$	−1089.23	+	628.865i	−1.38402	+	0.799066i	−0.992633	−	0.121159i	$-0.961339\pi$
$787$	−1089.23	+	628.865i	−1.38402	+	0.799066i	−0.391389	+	0.920225i	$0.628005\pi$
$788$	−190.326	+	109.885i	−0.241531	+	0.139448i
$789$	839.655	+	484.775i	1.06420	+	0.614417i
$790$	599.972			0.759458
$791$	−239.986	−	363.837i	−0.303395	−	0.459971i
$792$	103.574	−	94.5647i	0.130775	−	0.119400i
$793$	543.782	−	941.858i	0.685727	−	1.18771i
$794$	−571.302	+	329.842i	−0.719524	+	0.415418i
$795$	70.8538	+	122.722i	0.0891243	+	0.154368i
$796$	−26.4034	+	45.7319i	−0.0331700	+	0.0574522i
$797$	−1445.34			−1.81348			−0.906739	−	0.421693i	$-0.861436\pi$
$797$	−1445.34			−1.81348			−0.906739	+	0.421693i	$0.861436\pi$
$798$	−47.7534	+	2.84434i	−0.0598414	+	0.00356434i
$799$			689.874i			0.863422i
$800$	−245.590	−	141.792i	−0.306988	−	0.177239i
$801$	−156.748	−	271.496i	−0.195691	−	0.338947i
$802$	−220.856	+	127.511i	−0.275381	+	0.158991i
$803$	108.339	+	492.892i	0.134917	+	0.613814i
$804$	299.770			0.372848
$805$	1057.86	−	2113.29i	1.31411	−	2.62521i
$806$	85.6774			0.106299
$807$	86.4916	−	149.808i	0.107177	−	0.185635i
$808$	18.8453	+	32.6410i	0.0233234	+	0.0403973i
$809$	883.112	−	509.865i	1.09161	−	0.630241i	0.157605	−	0.987502i	$-0.449623\pi$
$809$	883.112	−	509.865i	1.09161	−	0.630241i	0.934005	+	0.357261i	$0.116289\pi$
$810$	−1074.85	−	620.567i	−1.32698	−	0.766133i
$811$		−	41.8990i		−	0.0516634i	−0.999666	−	0.0258317i	$-0.991777\pi$
$811$		−	41.8990i		−	0.0516634i	0.999666	−	0.0258317i	$-0.00822341\pi$
$812$	131.074	+	65.6122i	0.161421	+	0.0808032i
$813$		−	1839.93i		−	2.26313i
$814$	185.784	+	845.233i	0.228236	+	1.03837i
$815$	−5.30148	−	9.18243i	−0.00650488	−	0.0112668i
$816$	−307.436	+	177.498i	−0.376760	+	0.217522i
$817$	−50.5532	+	87.5608i	−0.0618767	+	0.107174i
$818$	101.216			0.123736
$819$	23.0748	+	387.401i	0.0281744	+	0.473017i
$820$			137.107i			0.167203i
$821$	−770.760	−	444.999i	−0.938807	−	0.542020i	−0.0492206	−	0.998788i	$-0.515674\pi$
$821$	−770.760	−	444.999i	−0.938807	−	0.542020i	−0.889586	+	0.456768i	$0.849007\pi$
$822$	728.292	−	420.480i	0.886000	−	0.511532i
$823$	−501.981	−	869.457i	−0.609941	−	1.05645i	−0.991250	−	0.132001i	$-0.957860\pi$
$823$	−501.981	−	869.457i	−0.609941	−	1.05645i	0.381309	−	0.924448i	$-0.375474\pi$
$824$	166.089	+	95.8915i	0.201564	+	0.116373i
$825$	−1366.52	−	1496.71i	−1.65639	−	1.81420i
$826$	−309.730	+	204.297i	−0.374976	+	0.247333i
$827$			313.408i			0.378969i	0.981884	+	0.189485i	$0.0606817\pi$
$827$			313.408i			0.378969i	−0.981884	+	0.189485i	$0.939318\pi$
$828$	175.579	−	304.111i	0.212052	−	0.367284i
$829$	511.178	+	885.386i	0.616620	+	1.06802i	0.990098	+	0.140378i	$0.0448319\pi$
$829$	511.178	+	885.386i	0.616620	+	1.06802i	−0.373478	+	0.927639i	$0.621835\pi$
$830$	387.676	+	671.475i	0.467080	+	0.809006i
$831$	−1097.03	−	633.370i	−1.32013	−	0.762178i
$832$		−	98.3912i		−	0.118259i
$833$	140.455	+	1174.86i	0.168614	+	1.41040i
$834$	15.6795			0.0188003
$835$	532.186	+	307.258i	0.637349	+	0.367973i
$836$	27.5716	+	8.74804i	0.0329804	+	0.0104642i
$837$	40.6636	+	70.4314i	0.0485825	+	0.0841474i
$838$	−857.399	−	495.020i	−1.02315	−	0.590715i
$839$	−1218.82			−1.45271			−0.726355	−	0.687320i	$-0.758787\pi$
$839$	−1218.82			−1.45271			−0.726355	+	0.687320i	$0.758787\pi$
$840$	−526.512	+	347.286i	−0.626800	+	0.413435i
$841$	731.381			0.869656
$842$	868.424	+	501.385i	1.03138	+	0.595469i
$843$	840.411	−	485.212i	0.996929	−	0.575577i
$844$	−459.656	+	265.383i	−0.544616	+	0.314434i
$845$	76.8702	−	133.143i	0.0909706	−	0.157566i
$846$			182.129i			0.215282i
$847$	−26.5772	+	846.583i	−0.0313781	+	0.999508i
$848$	−17.7931			−0.0209824
$849$	1329.60	+	767.644i	1.56608	+	0.904175i
$850$	855.977	+	1482.60i	1.00703	+	1.74423i
$851$	1083.40	+	1876.51i	1.27310	+	2.20507i
$852$	70.0186	−	121.276i	0.0821814	−	0.142342i
$853$			706.524i			0.828281i	0.910213	+	0.414141i	$0.135918\pi$
$853$			706.524i			0.828281i	−0.910213	+	0.414141i	$0.864082\pi$
$854$	391.845	−	782.792i	0.458835	−	0.916619i
$855$			51.3739i			0.0600864i
$856$	280.182	−	485.289i	0.327315	−	0.566927i
$857$	−1311.40	+	757.139i	−1.53023	+	0.883476i	−0.530875	+	0.847450i	$0.678137\pi$
$857$	−1311.40	+	757.139i	−1.53023	+	0.883476i	−0.999351	+	0.0360262i	$0.988530\pi$
$858$	212.660	−	670.252i	0.247856	−	0.781179i
$859$	−254.639	+	441.047i	−0.296436	+	0.513442i	−0.975318	−	0.220805i	$-0.929132\pi$
$859$	−254.639	+	441.047i	−0.296436	+	0.513442i	0.678882	+	0.734248i	$0.262465\pi$
$860$			1333.06i			1.55007i
$861$	181.951	+	91.0798i	0.211325	+	0.105784i
$862$	219.391			0.254514
$863$	150.763	−	261.129i	0.174697	−	0.302583i	−0.765360	−	0.643603i	$-0.777439\pi$
$863$	150.763	−	261.129i	0.174697	−	0.302583i	0.940056	+	0.341020i	$0.110772\pi$
$864$	80.8829	−	46.6978i	0.0936144	−	0.0540483i
$865$	15.6322	−	9.02523i	0.0180719	−	0.0104338i
$866$	−467.169	−	269.720i	−0.539456	−	0.311455i
$867$	1080.91			1.24672
$868$	68.8404	−	4.10035i	0.0793093	−	0.00472391i
$869$	−397.601	+	363.016i	−0.457538	+	0.417740i
$870$	235.847	−	408.499i	0.271088	−	0.469539i
$871$	434.373	−	250.785i	0.498706	−	0.287928i
$872$	−238.151	−	412.489i	−0.273109	−	0.473038i
$873$	−68.3792	+	118.436i	−0.0783266	+	0.135666i
$874$	72.4252			0.0828663
$875$	839.570	+	1272.85i	0.959508	+	1.45469i
$876$		−	337.231i		−	0.384967i
$877$	−71.8819	−	41.5010i	−0.0819634	−	0.0473216i	0.458458	−	0.888716i	$-0.348402\pi$
$877$	−71.8819	−	41.5010i	−0.0819634	−	0.0473216i	−0.540422	+	0.841394i	$0.681735\pi$
$878$	281.554	+	487.666i	0.320677	+	0.555429i
$879$	−27.6545	+	15.9663i	−0.0314613	+	0.0181642i
$880$	372.492	−	81.8744i	0.423286	−	0.0930390i
$881$	1317.25			1.49517			0.747586	−	0.664166i	$-0.231213\pi$
$881$	1317.25			1.49517			0.747586	+	0.664166i	$0.231213\pi$
$882$	37.0805	+	310.166i	0.0420414	+	0.351662i
$883$	−591.064			−0.669382			−0.334691	−	0.942328i	$-0.608632\pi$
$883$	−591.064			−0.669382			−0.334691	+	0.942328i	$0.608632\pi$
$884$	−296.988	+	514.397i	−0.335959	+	0.581898i
$885$	597.005	+	1034.04i	0.674582	+	1.16841i
$886$	395.704	−	228.460i	0.446618	−	0.257855i
$887$	1127.96	+	651.230i	1.27166	+	0.734193i	0.975300	−	0.220883i	$-0.0708939\pi$
$887$	1127.96	+	651.230i	1.27166	+	0.734193i	0.296360	+	0.955076i	$0.404227\pi$
$888$		−	578.298i		−	0.651236i
$889$	817.189	−	539.015i	0.919223	−	0.606316i
$890$		−	852.496i		−	0.957861i
$891$	1087.78	−	239.097i	1.22086	−	0.268346i
$892$	−92.5527	−	160.306i	−0.103759	−	0.179715i
$893$	−32.5309	+	18.7817i	−0.0364288	+	0.0210322i
$894$	−145.073	+	251.273i	−0.162274	+	0.281066i
$895$	1396.10			1.55989
$896$	−4.70882	−	79.0558i	−0.00525537	−	0.0882320i
$897$		−	1760.62i		−	1.96279i
$898$	−622.783	−	359.564i	−0.693522	−	0.400405i
$899$	−44.6641	+	25.7868i	−0.0496820	+	0.0286839i
$900$	225.980	+	391.409i	0.251089	+	0.434899i
$901$	93.0238	+	53.7073i	0.103245	+	0.0596086i
$902$	−82.9570	−	90.8604i	−0.0919701	−	0.100732i
$903$	1769.08	+	885.553i	1.95911	+	0.980678i
$904$		−	176.113i		−	0.194815i
$905$	−345.505	+	598.432i	−0.381773	+	0.661250i
$906$	43.7389	+	75.7579i	0.0482769	+	0.0836180i
$907$	12.4924	+	21.6375i	0.0137733	+	0.0238561i	0.872830	−	0.488025i	$-0.162282\pi$
$907$	12.4924	+	21.6375i	0.0137733	+	0.0238561i	−0.859057	+	0.511881i	$0.828949\pi$
$908$	−96.5770	−	55.7588i	−0.106362	−	0.0614083i
$909$		−	60.0694i		−	0.0660829i
$910$	−472.391	+	943.700i	−0.519111	+	1.03703i
$911$	944.278			1.03653			0.518265	−	0.855220i	$-0.326578\pi$
$911$	944.278			1.03653			0.518265	+	0.855220i	$0.326578\pi$
$912$	−16.7398	−	9.66474i	−0.0183551	−	0.0105973i
$913$	−663.192	−	210.420i	−0.726388	−	0.230471i
$914$	−339.744	−	588.453i	−0.371711	−	0.643822i
$915$	−2439.61	−	1408.51i	−2.66624	−	1.53935i
$916$	−756.140			−0.825481
$917$	48.3264	+	811.348i	0.0527006	+	0.884785i
$918$	−563.816			−0.614179
$919$	−892.947	−	515.543i	−0.971650	−	0.560983i	−0.0719114	−	0.997411i	$-0.522910\pi$
$919$	−892.947	−	515.543i	−0.971650	−	0.560983i	−0.899739	+	0.436428i	$0.856243\pi$
$920$	826.973	−	477.453i	0.898884	−	0.518971i
$921$	524.274	−	302.690i	0.569244	−	0.328653i
$922$	−108.567	+	188.044i	−0.117752	+	0.203952i
$923$		−	234.308i		−	0.253855i
$924$	138.792	−	548.715i	0.150208	−	0.593847i
$925$	−2788.81			−3.01493
$926$	804.194	+	464.302i	0.868460	+	0.501406i
$927$	−152.827	−	264.704i	−0.164862	−	0.285549i
$928$	29.6134	+	51.2920i	0.0319110	+	0.0552715i
$929$	−388.437	+	672.793i	−0.418124	+	0.724212i	−0.995751	−	0.0920890i	$-0.970646\pi$
$929$	−388.437	+	672.793i	−0.418124	+	0.724212i	0.577627	+	0.816301i	$0.303979\pi$
$930$		−	221.922i		−	0.238626i
$931$	−51.5765	+	38.6086i	−0.0553991	+	0.0414700i
$932$			410.847i			0.440823i
$933$	1112.09	−	1926.20i	1.19195	−	2.06452i
$934$	−526.241	+	303.825i	−0.563427	+	0.325295i
$935$	−2194.55	−	696.296i	−2.34711	−	0.744701i
$936$	−78.4055	+	135.802i	−0.0837666	+	0.145088i
$937$			1401.44i			1.49567i	0.663883	+	0.747836i	$0.268907\pi$
$937$			1401.44i			1.49567i	−0.663883	+	0.747836i	$0.731093\pi$
$938$	337.010	−	222.290i	0.359286	−	0.236983i
$939$	−862.682			−0.918724
$940$	−247.632	+	428.912i	−0.263439	+	0.456289i
$941$	849.905	−	490.693i	0.903194	−	0.521459i	0.0249588	−	0.999688i	$-0.492055\pi$
$941$	849.905	−	490.693i	0.903194	−	0.521459i	0.878235	+	0.478229i	$0.158721\pi$
$942$	−304.192	+	175.625i	−0.322921	+	0.186439i
$943$	−266.782	−	154.027i	−0.282908	−	0.163337i
$944$	−149.922			−0.158816
$945$	−999.975	+	59.5617i	−1.05817	+	0.0630282i
$946$	−806.576	−	883.419i	−0.852617	−	0.933846i
$947$	49.4161	−	85.5912i	0.0521817	−	0.0903814i	−0.838755	−	0.544510i	$-0.816716\pi$
$947$	49.4161	−	85.5912i	0.0521817	−	0.0903814i	0.890936	+	0.454128i	$0.150049\pi$
$948$	311.573	−	179.887i	0.328663	−	0.189754i
$949$	−282.125	−	488.655i	−0.297286	−	0.514915i
$950$	−46.6078	+	80.7270i	−0.0490608	+	0.0849758i
$951$	122.719			0.129042
$952$	−214.007	+	427.524i	−0.224797	+	0.449080i
$953$			1294.82i			1.35868i	0.733823	+	0.679340i	$0.237734\pi$
$953$			1294.82i			1.35868i	−0.733823	+	0.679340i	$0.762266\pi$
$954$	24.5585	+	14.1789i	0.0257427	+	0.0148626i
$955$	−900.353	−	1559.46i	−0.942778	−	1.63294i
$956$	551.240	−	318.258i	0.576610	−	0.332906i
$957$	90.8688	+	413.412i	0.0949517	+	0.431988i
$958$	−398.303			−0.415765
$959$	506.965	−	1012.77i	0.528640	−	1.05607i
$960$	−254.854			−0.265473
$961$	468.368	−	811.237i	0.487375	−	0.844159i
$962$	−483.800	−	837.966i	−0.502910	−	0.871066i
$963$	−773.430	+	446.540i	−0.803146	+	0.463697i
$964$	−793.960	−	458.393i	−0.823610	−	0.475511i
$965$		−	1373.87i		−	1.42370i
$966$	−84.2599	−	1414.63i	−0.0872255	−	1.46442i
$967$		−	537.602i		−	0.555948i	−0.960589	−	0.277974i	$-0.910337\pi$
$967$		−	537.602i		−	0.555948i	0.960589	−	0.277974i	$-0.0896630\pi$
$968$	−197.311	+	279.636i	−0.203834	+	0.288880i
$969$	58.3448	+	101.056i	0.0602113	+	0.104289i
$970$	−322.065	+	185.944i	−0.332026	+	0.191695i
$971$	429.666	−	744.204i	0.442499	−	0.766430i	−0.555375	−	0.831600i	$-0.687425\pi$
$971$	429.666	−	744.204i	0.442499	−	0.766430i	0.997874	+	0.0651694i	$0.0207588\pi$
$972$	−447.064			−0.459943
$973$	17.6273	−	11.6269i	0.0181165	−	0.0119495i
$974$		−	462.967i		−	0.475326i
$975$	1962.43	+	1133.01i	2.01275	+	1.16206i
$976$	306.322	−	176.855i	0.313855	−	0.181204i
$977$	719.841	+	1246.80i	0.736787	+	1.27615i	0.953935	+	0.300013i	$0.0969911\pi$
$977$	719.841	+	1246.80i	0.736787	+	1.27615i	−0.217148	+	0.976139i	$0.569676\pi$
$978$	−5.50625	−	3.17903i	−0.00563011	−	0.00325055i
$979$	515.807	+	564.948i	0.526871	+	0.577067i
$980$	−334.395	+	780.856i	−0.341220	+	0.796792i
$981$			759.106i			0.773808i
$982$	374.933	−	649.403i	0.381806	−	0.661307i
$983$	362.256	+	627.445i	0.368520	+	0.638296i	0.989334	−	0.145662i	$-0.0465311\pi$
$983$	362.256	+	627.445i	0.368520	+	0.638296i	−0.620814	+	0.783958i	$0.713198\pi$
$984$	41.1080	+	71.2012i	0.0417764	+	0.0723589i
$985$	824.855	+	476.230i	0.837417	+	0.483483i
$986$		−	357.545i		−	0.362621i
$987$	404.697	+	613.553i	0.410028	+	0.621635i
$988$	−32.3418			−0.0327346
$989$	−2593.87	−	1497.57i	−2.62272	−	1.51423i
$990$	−579.367	−	183.824i	−0.585219	−	0.185681i
$991$	69.4869	+	120.355i	0.0701179	+	0.121448i	0.898953	−	0.438045i	$-0.144329\pi$
$991$	69.4869	+	120.355i	0.0701179	+	0.121448i	−0.828835	+	0.559493i	$0.810996\pi$
$992$	24.1318	+	13.9325i	0.0243264	+	0.0140449i
$993$	−24.9124			−0.0250880
$994$	−11.2135	−	188.263i	−0.0112812	−	0.189399i
$995$	228.859			0.230009
$996$	402.650	+	232.470i	0.404267	+	0.233404i
$997$	134.024	−	77.3790i	0.134428	−	0.0776118i	−0.431278	−	0.902219i	$-0.641937\pi$
$997$	134.024	−	77.3790i	0.134428	−	0.0776118i	0.565706	+	0.824607i	$0.308604\pi$
$998$	−408.594	+	235.902i	−0.409413	+	0.236375i
$999$	459.235	−	795.419i	0.459695	−	0.796215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.3.g.a.65.7	✓	32
7.2	even	3		1078.3.d.d.197.10		16
7.4	even	3	inner	154.3.g.a.109.15	yes	32
7.5	odd	6		1078.3.d.e.197.15		16
11.10	odd	2	inner	154.3.g.a.65.15	yes	32
77.32	odd	6	inner	154.3.g.a.109.7	yes	32
77.54	even	6		1078.3.d.e.197.7		16
77.65	odd	6		1078.3.d.d.197.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.3.g.a.65.7	✓	32	1.1	even	1	trivial
154.3.g.a.65.15	yes	32	11.10	odd	2	inner
154.3.g.a.109.7	yes	32	77.32	odd	6	inner
154.3.g.a.109.15	yes	32	7.4	even	3	inner
1078.3.d.d.197.2		16	77.65	odd	6
1078.3.d.d.197.10		16	7.2	even	3
1078.3.d.e.197.7		16	77.54	even	6
1078.3.d.e.197.15		16	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	154.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.83765 + 3.18290i) q^{3} +(1.00000 + 1.73205i) q^{4} +(4.33390 - 7.50654i) q^{5} -5.19765i q^{6} +(-3.85425 - 5.84335i) q^{7} -2.82843i q^{8} +(-2.25390 + 3.90387i) q^{9} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.83765 + 3.18290i) q^{3} +(1.00000 + 1.73205i) q^{4} +(4.33390 - 7.50654i) q^{5} -5.19765i q^{6} +(-3.85425 - 5.84335i) q^{7} -2.82843i q^{8} +(-2.25390 + 3.90387i) q^{9} +(-10.6159 + 6.12906i) q^{10} +(3.32669 - 10.4849i) q^{11} +(-3.67530 + 6.36580i) q^{12} +12.2989i q^{13} +(0.588602 + 9.88198i) q^{14} +31.8568 q^{15} +(-2.00000 + 3.46410i) q^{16} +(20.9123 - 12.0737i) q^{17} +(5.52091 - 3.18750i) q^{18} +(1.13867 + 0.657412i) q^{19} +17.3356 q^{20} +(11.5160 - 23.0057i) q^{21} +(-11.4883 + 10.4890i) q^{22} +(-19.4750 + 33.7316i) q^{23} +(9.00260 - 5.19765i) q^{24} +(-25.0654 - 43.4146i) q^{25} +(8.69664 - 15.0630i) q^{26} +16.5101 q^{27} +(6.26673 - 12.5191i) q^{28} +10.4699i q^{29} +(-39.0164 - 22.5261i) q^{30} +(2.46294 + 4.26595i) q^{31} +(4.89898 - 2.82843i) q^{32} +(39.4857 - 8.67903i) q^{33} -34.1497 q^{34} +(-60.5673 + 3.60758i) q^{35} -9.01561 q^{36} +(27.8153 - 48.1776i) q^{37} +(-0.929722 - 1.61033i) q^{38} +(-39.1462 + 22.6011i) q^{39} +(-21.2317 - 12.2581i) q^{40} +7.90895i q^{41} +(-30.3717 + 20.0331i) q^{42} +76.8973i q^{43} +(21.4871 - 4.72290i) q^{44} +(19.5364 + 33.8380i) q^{45} +(47.7037 - 27.5418i) q^{46} +(-14.2846 + 24.7416i) q^{47} -14.7012 q^{48} +(-19.2895 + 45.0435i) q^{49} +70.8958i q^{50} +(76.8590 + 44.3746i) q^{51} +(-21.3023 + 12.2989i) q^{52} +(2.22414 + 3.85232i) q^{53} +(-20.2207 - 11.6744i) q^{54} +(-64.2878 - 70.4125i) q^{55} +(-16.5275 + 10.9015i) q^{56} +4.83237i q^{57} +(7.40336 - 12.8230i) q^{58} +(18.7403 + 32.4591i) q^{59} +(31.8568 + 55.1775i) q^{60} +(-76.5806 - 44.2138i) q^{61} -6.96626i q^{62} +(31.4988 - 1.87617i) q^{63} -8.00000 q^{64} +(92.3222 + 53.3023i) q^{65} +(-54.4969 - 17.2910i) q^{66} +(-20.3909 - 35.3180i) q^{67} +(41.8247 + 24.1475i) q^{68} -143.153 q^{69} +(76.7304 + 38.4092i) q^{70} -19.0511 q^{71} +(11.0418 + 6.37500i) q^{72} +(-39.7316 + 22.9390i) q^{73} +(-68.1333 + 39.3368i) q^{74} +(92.1229 - 159.562i) q^{75} +2.62965i q^{76} +(-74.0889 + 20.9724i) q^{77} +63.9255 q^{78} +(-42.3874 - 24.4724i) q^{79} +(17.3356 + 30.0262i) q^{80} +(50.6250 + 87.6850i) q^{81} +(5.59247 - 9.68645i) q^{82} -63.2521i q^{83} +(51.3631 - 3.05935i) q^{84} -209.306i q^{85} +(54.3746 - 94.1796i) q^{86} +(-33.3247 + 19.2400i) q^{87} +(-29.6558 - 9.40931i) q^{88} +(-34.7727 + 60.2281i) q^{89} -55.2573i q^{90} +(71.8668 - 47.4031i) q^{91} -77.8999 q^{92} +(-9.05205 + 15.6786i) q^{93} +(34.9900 - 20.2015i) q^{94} +(9.86979 - 5.69832i) q^{95} +(18.0052 + 10.3953i) q^{96} +30.3381 q^{97} +(55.4753 - 41.5270i) q^{98} +(33.4337 + 36.6189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 4 q^{5} - 40 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 + 4 * q^5 - 40 * q^9	\( 32 q + 32 q^{4} + 4 q^{5} - 40 q^{9} - 6 q^{11} - 24 q^{14} + 128 q^{15} - 64 q^{16} + 16 q^{20} + 40 q^{22} + 20 q^{23} - 140 q^{25} - 16 q^{26} + 120 q^{27} + 40 q^{31} + 50 q^{33} - 16 q^{34} - 160 q^{36} - 116 q^{37} - 40 q^{38} + 48 q^{42} + 12 q^{44} - 284 q^{45} + 216 q^{47} + 248 q^{49} + 56 q^{53} - 372 q^{55} - 48 q^{56} + 104 q^{58} - 4 q^{59} + 128 q^{60} - 256 q^{64} - 160 q^{66} - 68 q^{67} - 208 q^{69} + 80 q^{70} - 184 q^{71} - 244 q^{75} - 362 q^{77} + 288 q^{78} + 16 q^{80} + 384 q^{81} + 224 q^{82} + 72 q^{86} + 40 q^{88} - 592 q^{89} + 804 q^{91} + 80 q^{92} - 68 q^{93} + 376 q^{97} + 432 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 + 4 * q^5 - 40 * q^9 - 6 * q^11 - 24 * q^14 + 128 * q^15 - 64 * q^16 + 16 * q^20 + 40 * q^22 + 20 * q^23 - 140 * q^25 - 16 * q^26 + 120 * q^27 + 40 * q^31 + 50 * q^33 - 16 * q^34 - 160 * q^36 - 116 * q^37 - 40 * q^38 + 48 * q^42 + 12 * q^44 - 284 * q^45 + 216 * q^47 + 248 * q^49 + 56 * q^53 - 372 * q^55 - 48 * q^56 + 104 * q^58 - 4 * q^59 + 128 * q^60 - 256 * q^64 - 160 * q^66 - 68 * q^67 - 208 * q^69 + 80 * q^70 - 184 * q^71 - 244 * q^75 - 362 * q^77 + 288 * q^78 + 16 * q^80 + 384 * q^81 + 224 * q^82 + 72 * q^86 + 40 * q^88 - 592 * q^89 + 804 * q^91 + 80 * q^92 - 68 * q^93 + 376 * q^97 + 432 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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