LMFDB - Embedded newform 684.3.g.d.343.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.15
Character	$\chi$	$=$	684.343
Dual form			684.3.g.d.343.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.671560 - 1.88388i) q^{2} +(-3.09801 + 2.53028i) q^{4} -4.54598 q^{5} -5.76325i q^{7} +(6.84725 + 4.13706i) q^{8} +O(q^{10})$	\(q+(-0.671560 - 1.88388i) q^{2} +(-3.09801 + 2.53028i) q^{4} -4.54598 q^{5} -5.76325i q^{7} +(6.84725 + 4.13706i) q^{8} +(3.05290 + 8.56408i) q^{10} +10.1419i q^{11} -13.5653 q^{13} +(-10.8573 + 3.87037i) q^{14} +(3.19538 - 15.6777i) q^{16} +7.96492 q^{17} -4.35890i q^{19} +(14.0835 - 11.5026i) q^{20} +(19.1061 - 6.81087i) q^{22} +38.6743i q^{23} -4.33408 q^{25} +(9.10994 + 25.5555i) q^{26} +(14.5826 + 17.8546i) q^{28} +37.2619 q^{29} -14.8581i q^{31} +(-31.6808 + 4.50878i) q^{32} +(-5.34892 - 15.0050i) q^{34} +26.1996i q^{35} +6.53488 q^{37} +(-8.21165 + 2.92726i) q^{38} +(-31.1274 - 18.8070i) q^{40} +34.8954 q^{41} -40.2314i q^{43} +(-25.6617 - 31.4197i) q^{44} +(72.8578 - 25.9721i) q^{46} -50.1549i q^{47} +15.7849 q^{49} +(2.91059 + 8.16489i) q^{50} +(42.0256 - 34.3241i) q^{52} +31.9660 q^{53} -46.1047i q^{55} +(23.8429 - 39.4624i) q^{56} +(-25.0236 - 70.1970i) q^{58} -12.0203i q^{59} +108.607 q^{61} +(-27.9908 + 9.97807i) q^{62} +(29.7695 + 56.6549i) q^{64} +61.6677 q^{65} +67.6241i q^{67} +(-24.6754 + 20.1535i) q^{68} +(49.3570 - 17.5946i) q^{70} -17.9831i q^{71} +121.693 q^{73} +(-4.38857 - 12.3109i) q^{74} +(11.0292 + 13.5039i) q^{76} +58.4502 q^{77} -103.011i q^{79} +(-14.5261 + 71.2704i) q^{80} +(-23.4344 - 65.7388i) q^{82} +41.7786i q^{83} -36.2084 q^{85} +(-75.7911 + 27.0178i) q^{86} +(-41.9575 + 69.4439i) q^{88} -74.8835 q^{89} +78.1805i q^{91} +(-97.8568 - 119.814i) q^{92} +(-94.4859 + 33.6820i) q^{94} +19.8155i q^{95} +74.3694 q^{97} +(-10.6005 - 29.7369i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{4}+O(q^{10}) $ 36 * q - 12 * q^4	$ 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) $ 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−0.671560	−	1.88388i	−0.335780	−	0.941940i
$2$	−0.671560	−	1.88388i	−0.335780	−	0.941940i
$3$		0			0
$3$		0			0
$4$	−3.09801	+	2.53028i	−0.774504	+	0.632570i
$5$	−4.54598			−0.909196			−0.454598	−	0.890697i	$-0.650217\pi$
$5$	−4.54598			−0.909196			−0.454598	+	0.890697i	$0.650217\pi$
$6$		0			0
$7$		−	5.76325i		−	0.823322i	−0.911337	−	0.411661i	$-0.864949\pi$
$7$		−	5.76325i		−	0.823322i	0.911337	−	0.411661i	$-0.135051\pi$
$8$	6.84725	+	4.13706i	0.855906	+	0.517132i
$9$		0			0
$10$	3.05290	+	8.56408i	0.305290	+	0.856408i
$11$			10.1419i			0.921988i	0.887403	+	0.460994i	$0.152507\pi$
$11$			10.1419i			0.921988i	−0.887403	+	0.460994i	$0.847493\pi$
$12$		0			0
$13$	−13.5653			−1.04349			−0.521744	−	0.853102i	$-0.674718\pi$
$13$	−13.5653			−1.04349			−0.521744	+	0.853102i	$0.674718\pi$
$14$	−10.8573	+	3.87037i	−0.775520	+	0.276455i
$15$		0			0
$16$	3.19538	−	15.6777i	0.199712	−	0.979855i
$17$	7.96492			0.468525			0.234262	−	0.972173i	$-0.424733\pi$
$17$	7.96492			0.468525			0.234262	+	0.972173i	$0.424733\pi$
$18$		0			0
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	14.0835	−	11.5026i	0.704175	−	0.575130i
$21$		0			0
$22$	19.1061	−	6.81087i	0.868458	−	0.309585i
$23$			38.6743i			1.68149i	0.541430	+	0.840746i	$0.317883\pi$
$23$			38.6743i			1.68149i	−0.541430	+	0.840746i	$0.682117\pi$
$24$		0			0
$25$	−4.33408			−0.173363
$26$	9.10994	+	25.5555i	0.350382	+	0.982903i
$27$		0			0
$28$	14.5826	+	17.8546i	0.520808	+	0.637666i
$29$	37.2619			1.28489			0.642446	−	0.766331i	$-0.277920\pi$
$29$	37.2619			1.28489			0.642446	+	0.766331i	$0.277920\pi$
$30$		0			0
$31$		−	14.8581i		−	0.479292i	−0.970860	−	0.239646i	$-0.922969\pi$
$31$		−	14.8581i		−	0.479292i	0.970860	−	0.239646i	$-0.0770314\pi$
$32$	−31.6808	+	4.50878i	−0.990024	+	0.140899i
$33$		0			0
$34$	−5.34892	−	15.0050i	−0.157321	−	0.441323i
$35$			26.1996i			0.748561i
$36$		0			0
$37$	6.53488			0.176618			0.0883092	−	0.996093i	$-0.471854\pi$
$37$	6.53488			0.176618			0.0883092	+	0.996093i	$0.471854\pi$
$38$	−8.21165	+	2.92726i	−0.216096	+	0.0770332i
$39$		0			0
$40$	−31.1274	−	18.8070i	−0.778186	−	0.470174i
$41$	34.8954			0.851107			0.425554	−	0.904933i	$-0.360079\pi$
$41$	34.8954			0.851107			0.425554	+	0.904933i	$0.360079\pi$
$42$		0			0
$43$		−	40.2314i		−	0.935613i	−0.883831	−	0.467806i	$-0.845044\pi$
$43$		−	40.2314i		−	0.935613i	0.883831	−	0.467806i	$-0.154956\pi$
$44$	−25.6617	−	31.4197i	−0.583222	−	0.714083i
$45$		0			0
$46$	72.8578	−	25.9721i	1.58386	−	0.564611i
$47$		−	50.1549i		−	1.06713i	−0.845760	−	0.533563i	$-0.820853\pi$
$47$		−	50.1549i		−	1.06713i	0.845760	−	0.533563i	$-0.179147\pi$
$48$		0			0
$49$	15.7849			0.322141
$50$	2.91059	+	8.16489i	0.0582119	+	0.163298i
$51$		0			0
$52$	42.0256	−	34.3241i	0.808185	−	0.660079i
$53$	31.9660			0.603133			0.301567	−	0.953445i	$-0.402490\pi$
$53$	31.9660			0.603133			0.301567	+	0.953445i	$0.402490\pi$
$54$		0			0
$55$		−	46.1047i		−	0.838268i
$56$	23.8429	−	39.4624i	0.425766	−	0.704686i
$57$		0			0
$58$	−25.0236	−	70.1970i	−0.431441	−	1.21029i
$59$		−	12.0203i		−	0.203734i	−0.994798	−	0.101867i	$-0.967518\pi$
$59$		−	12.0203i		−	0.203734i	0.994798	−	0.101867i	$-0.0324816\pi$
$60$		0			0
$61$	108.607			1.78044			0.890220	−	0.455532i	$-0.150551\pi$
$61$	108.607			1.78044			0.890220	+	0.455532i	$0.150551\pi$
$62$	−27.9908	+	9.97807i	−0.451465	+	0.160937i
$63$		0			0
$64$	29.7695	+	56.6549i	0.465149	+	0.885232i
$65$	61.6677			0.948735
$66$		0			0
$67$			67.6241i			1.00931i	0.863320	+	0.504657i	$0.168381\pi$
$67$			67.6241i			1.00931i	−0.863320	+	0.504657i	$0.831619\pi$
$68$	−24.6754	+	20.1535i	−0.362874	+	0.296375i
$69$		0			0
$70$	49.3570	−	17.5946i	0.705100	−	0.251352i
$71$		−	17.9831i		−	0.253283i	−0.991949	−	0.126642i	$-0.959580\pi$
$71$		−	17.9831i		−	0.253283i	0.991949	−	0.126642i	$-0.0404198\pi$
$72$		0			0
$73$	121.693			1.66703			0.833515	−	0.552497i	$-0.186325\pi$
$73$	121.693			1.66703			0.833515	+	0.552497i	$0.186325\pi$
$74$	−4.38857	−	12.3109i	−0.0593050	−	0.166364i
$75$		0			0
$76$	11.0292	+	13.5039i	0.145121	+	0.177683i
$77$	58.4502			0.759093
$78$		0			0
$79$		−	103.011i		−	1.30393i	−0.758247	−	0.651967i	$-0.773944\pi$
$79$		−	103.011i		−	1.30393i	0.758247	−	0.651967i	$-0.226056\pi$
$80$	−14.5261	+	71.2704i	−0.181577	+	0.890880i
$81$		0			0
$82$	−23.4344	−	65.7388i	−0.285785	−	0.801693i
$83$			41.7786i			0.503356i	0.967811	+	0.251678i	$0.0809824\pi$
$83$			41.7786i			0.503356i	−0.967811	+	0.251678i	$0.919018\pi$
$84$		0			0
$85$	−36.2084			−0.425981
$86$	−75.7911	+	27.0178i	−0.881292	+	0.314160i
$87$		0			0
$88$	−41.9575	+	69.4439i	−0.476790	+	0.789135i
$89$	−74.8835			−0.841388			−0.420694	−	0.907203i	$-0.638213\pi$
$89$	−74.8835			−0.841388			−0.420694	+	0.907203i	$0.638213\pi$
$90$		0			0
$91$			78.1805i			0.859126i
$92$	−97.8568	−	119.814i	−1.06366	−	1.30232i
$93$		0			0
$94$	−94.4859	+	33.6820i	−1.00517	+	0.358319i
$95$			19.8155i			0.208584i
$96$		0			0
$97$	74.3694			0.766694			0.383347	−	0.923604i	$-0.374771\pi$
$97$	74.3694			0.766694			0.383347	+	0.923604i	$0.374771\pi$
$98$	−10.6005	−	29.7369i	−0.108169	−	0.303438i
$99$		0			0
$100$	13.4270	−	10.9664i	0.134270	−	0.109664i
$101$	−69.2309			−0.685454			−0.342727	−	0.939435i	$-0.611351\pi$
$101$	−69.2309			−0.685454			−0.342727	+	0.939435i	$0.611351\pi$
$102$		0			0
$103$		−	59.6601i		−	0.579224i	−0.957144	−	0.289612i	$-0.906474\pi$
$103$		−	59.6601i		−	0.579224i	0.957144	−	0.289612i	$-0.0935263\pi$
$104$	−92.8852	−	56.1206i	−0.893127	−	0.539621i
$105$		0			0
$106$	−21.4671	−	60.2202i	−0.202520	−	0.568115i
$107$			56.5802i			0.528787i	0.964415	+	0.264394i	$0.0851718\pi$
$107$			56.5802i			0.528787i	−0.964415	+	0.264394i	$0.914828\pi$
$108$		0			0
$109$	−177.055			−1.62436			−0.812180	−	0.583408i	$-0.801719\pi$
$109$	−177.055			−1.62436			−0.812180	+	0.583408i	$0.801719\pi$
$110$	−86.8558	+	30.9621i	−0.789598	+	0.281474i
$111$		0			0
$112$	−90.3544	−	18.4158i	−0.806736	−	0.164427i
$113$	188.229			1.66574			0.832872	−	0.553466i	$-0.186695\pi$
$113$	188.229			1.66574			0.832872	+	0.553466i	$0.186695\pi$
$114$		0			0
$115$		−	175.813i		−	1.52881i
$116$	−115.438	+	94.2829i	−0.995154	+	0.812784i
$117$		0			0
$118$	−22.6448	+	8.07234i	−0.191905	+	0.0684097i
$119$		−	45.9039i		−	0.385747i
$120$		0			0
$121$	18.1425			0.149938
$122$	−72.9360	−	204.602i	−0.597836	−	1.67707i
$123$		0			0
$124$	37.5950	+	46.0305i	0.303186	+	0.371213i
$125$	133.352			1.06682
$126$		0			0
$127$			64.1516i			0.505131i	0.967580	+	0.252565i	$0.0812743\pi$
$127$			64.1516i			0.505131i	−0.967580	+	0.252565i	$0.918726\pi$
$128$	86.7390	−	94.1294i	0.677648	−	0.735386i
$129$		0			0
$130$	−41.4136	−	116.175i	−0.318566	−	0.893651i
$131$			132.496i			1.01142i	0.862703	+	0.505711i	$0.168770\pi$
$131$			132.496i			1.01142i	−0.862703	+	0.505711i	$0.831230\pi$
$132$		0			0
$133$	−25.1214			−0.188883
$134$	127.396	−	45.4136i	0.950714	−	0.338908i
$135$		0			0
$136$	54.5378	+	32.9513i	0.401013	+	0.242289i
$137$	155.309			1.13364			0.566822	−	0.823841i	$-0.308173\pi$
$137$	155.309			1.13364			0.566822	+	0.823841i	$0.308173\pi$
$138$		0			0
$139$			101.242i			0.728363i	0.931328	+	0.364181i	$0.118651\pi$
$139$			101.242i			0.728363i	−0.931328	+	0.364181i	$0.881349\pi$
$140$	−66.2923	−	81.1668i	−0.473517	−	0.579763i
$141$		0			0
$142$	−33.8781	+	12.0767i	−0.238578	+	0.0850475i
$143$		−	137.578i		−	0.962083i
$144$		0			0
$145$	−169.392			−1.16822
$146$	−81.7243	−	229.255i	−0.559755	−	1.57024i
$147$		0			0
$148$	−20.2452	+	16.5351i	−0.136792	+	0.111723i
$149$	−163.681			−1.09853			−0.549266	−	0.835647i	$-0.685093\pi$
$149$	−163.681			−1.09853			−0.549266	+	0.835647i	$0.685093\pi$
$150$		0			0
$151$			157.725i			1.04454i	0.852781	+	0.522268i	$0.174914\pi$
$151$			157.725i			1.04454i	−0.852781	+	0.522268i	$0.825086\pi$
$152$	18.0330	−	29.8465i	0.118638	−	0.196358i
$153$		0			0
$154$	−39.2528	−	110.113i	−0.254888	−	0.715020i
$155$			67.5444i			0.435770i
$156$		0			0
$157$	92.1707			0.587074			0.293537	−	0.955948i	$-0.405168\pi$
$157$	92.1707			0.587074			0.293537	+	0.955948i	$0.405168\pi$
$158$	−194.060	+	69.1780i	−1.22823	+	0.437835i
$159$		0			0
$160$	144.020	−	20.4968i	0.900126	−	0.128105i
$161$	222.890			1.38441
$162$		0			0
$163$			242.544i			1.48800i	0.668180	+	0.744000i	$0.267074\pi$
$163$			242.544i			1.48800i	−0.668180	+	0.744000i	$0.732926\pi$
$164$	−108.106	+	88.2951i	−0.659186	+	0.538385i
$165$		0			0
$166$	78.7059	−	28.0568i	0.474132	−	0.169017i
$167$		−	89.1627i		−	0.533909i	−0.963709	−	0.266954i	$-0.913983\pi$
$167$		−	89.1627i		−	0.533909i	0.963709	−	0.266954i	$-0.0860173\pi$
$168$		0			0
$169$	15.0184			0.0888665
$170$	24.3161	+	68.2123i	0.143036	+	0.401249i
$171$		0			0
$172$	101.797	+	124.637i	0.591840	+	0.724636i
$173$	−38.0556			−0.219975			−0.109987	−	0.993933i	$-0.535081\pi$
$173$	−38.0556			−0.219975			−0.109987	+	0.993933i	$0.535081\pi$
$174$		0			0
$175$			24.9784i			0.142734i
$176$	159.001	+	32.4072i	0.903414	+	0.184132i
$177$		0			0
$178$	50.2888	+	141.072i	0.282521	+	0.792538i
$179$			126.591i			0.707213i	0.935394	+	0.353607i	$0.115045\pi$
$179$			126.591i			0.707213i	−0.935394	+	0.353607i	$0.884955\pi$
$180$		0			0
$181$	−75.2579			−0.415790			−0.207895	−	0.978151i	$-0.566661\pi$
$181$	−75.2579			−0.415790			−0.207895	+	0.978151i	$0.566661\pi$
$182$	147.283	−	52.5029i	0.809246	−	0.288477i
$183$		0			0
$184$	−159.998	+	264.812i	−0.869553	+	1.43920i
$185$	−29.7074			−0.160581
$186$		0			0
$187$			80.7792i			0.431974i
$188$	126.906	+	155.381i	0.675031	+	0.826493i
$189$		0			0
$190$	37.3300	−	13.3073i	0.196474	−	0.0700383i
$191$			96.0012i			0.502624i	0.967906	+	0.251312i	$0.0808621\pi$
$191$			96.0012i			0.502624i	−0.967906	+	0.251312i	$0.919138\pi$
$192$		0			0
$193$	−64.2184			−0.332738			−0.166369	−	0.986064i	$-0.553204\pi$
$193$	−64.2184			−0.332738			−0.166369	+	0.986064i	$0.553204\pi$
$194$	−49.9435	−	140.103i	−0.257441	−	0.722180i
$195$		0			0
$196$	−48.9019	+	39.9402i	−0.249499	+	0.203777i
$197$	278.216			1.41227			0.706133	−	0.708080i	$-0.250438\pi$
$197$	278.216			1.41227			0.706133	+	0.708080i	$0.250438\pi$
$198$		0			0
$199$		−	315.848i		−	1.58718i	−0.608456	−	0.793588i	$-0.708211\pi$
$199$		−	315.848i		−	1.58718i	0.608456	−	0.793588i	$-0.291789\pi$
$200$	−29.6765	−	17.9303i	−0.148382	−	0.0896516i
$201$		0			0
$202$	46.4927	+	130.423i	0.230162	+	0.645657i
$203$		−	214.750i		−	1.05788i
$204$		0			0
$205$	−158.634			−0.773823
$206$	−112.392	+	40.0653i	−0.545594	+	0.194492i
$207$		0			0
$208$	−43.3465	+	212.673i	−0.208397	+	1.02247i
$209$	44.2074			0.211519
$210$		0			0
$211$		−	279.723i		−	1.32570i	−0.748751	−	0.662852i	$-0.769346\pi$
$211$		−	279.723i		−	1.32570i	0.748751	−	0.662852i	$-0.230654\pi$
$212$	−99.0313	+	80.8830i	−0.467129	+	0.381524i
$213$		0			0
$214$	106.590	−	37.9970i	0.498086	−	0.177556i
$215$			182.891i			0.850655i
$216$		0			0
$217$	−85.6307			−0.394612
$218$	118.903	+	333.551i	0.545427	+	1.53005i
$219$		0			0
$220$	116.658	+	142.833i	0.530263	+	0.649241i
$221$	−108.047			−0.488900
$222$		0			0
$223$			84.7992i			0.380265i	0.981758	+	0.190133i	$0.0608918\pi$
$223$			84.7992i			0.380265i	−0.981758	+	0.190133i	$0.939108\pi$
$224$	25.9852	+	182.584i	0.116005	+	0.815108i
$225$		0			0
$226$	−126.407	−	354.601i	−0.559323	−	1.56903i
$227$			181.775i			0.800772i	0.916347	+	0.400386i	$0.131124\pi$
$227$			181.775i			0.800772i	−0.916347	+	0.400386i	$0.868876\pi$
$228$		0			0
$229$	−86.3488			−0.377069			−0.188534	−	0.982067i	$-0.560374\pi$
$229$	−86.3488			−0.377069			−0.188534	+	0.982067i	$0.560374\pi$
$230$	−331.210	+	118.069i	−1.44004	+	0.513342i
$231$		0			0
$232$	255.141	+	154.155i	1.09975	+	0.664459i
$233$	−64.5642			−0.277100			−0.138550	−	0.990355i	$-0.544244\pi$
$233$	−64.5642			−0.277100			−0.138550	+	0.990355i	$0.544244\pi$
$234$		0			0
$235$			228.003i			0.970226i
$236$	30.4147	+	37.2390i	0.128876	+	0.157792i
$237$		0			0
$238$	−86.4774	+	30.8272i	−0.363350	+	0.129526i
$239$		−	211.203i		−	0.883696i	−0.897090	−	0.441848i	$-0.854323\pi$
$239$		−	211.203i		−	0.883696i	0.897090	−	0.441848i	$-0.145677\pi$
$240$		0			0
$241$	357.833			1.48479			0.742393	−	0.669965i	$-0.233691\pi$
$241$	357.833			1.48479			0.742393	+	0.669965i	$0.233691\pi$
$242$	−12.1838	−	34.1783i	−0.0503462	−	0.141233i
$243$		0			0
$244$	−336.465	+	274.805i	−1.37896	+	1.12625i
$245$	−71.7579			−0.292889
$246$		0			0
$247$			59.1299i			0.239392i
$248$	61.4686	−	101.737i	0.247857	−	0.410229i
$249$		0			0
$250$	−89.5539	−	251.219i	−0.358216	−	1.00488i
$251$			291.037i			1.15951i	0.814791	+	0.579755i	$0.196852\pi$
$251$			291.037i			1.15951i	−0.814791	+	0.579755i	$0.803148\pi$
$252$		0			0
$253$	−392.230			−1.55032
$254$	120.854	−	43.0817i	0.475803	−	0.169613i
$255$		0			0
$256$	−235.579	−	100.192i	−0.920231	−	0.391377i
$257$	245.357			0.954698			0.477349	−	0.878714i	$-0.341598\pi$
$257$	245.357			0.954698			0.477349	+	0.878714i	$0.341598\pi$
$258$		0			0
$259$		−	37.6622i		−	0.145414i
$260$	−191.048	+	156.037i	−0.734798	+	0.600141i
$261$		0			0
$262$	249.607	−	88.9792i	0.952699	−	0.339615i
$263$			449.674i			1.70979i	0.518804	+	0.854893i	$0.326378\pi$
$263$			449.674i			1.70979i	−0.518804	+	0.854893i	$0.673622\pi$
$264$		0			0
$265$	−145.317			−0.548366
$266$	16.8706	+	47.3258i	0.0634231	+	0.177917i
$267$		0			0
$268$	−171.108	−	209.500i	−0.638462	−	0.781718i
$269$	349.797			1.30036			0.650179	−	0.759781i	$-0.274694\pi$
$269$	349.797			1.30036			0.650179	+	0.759781i	$0.274694\pi$
$270$		0			0
$271$			274.098i			1.01143i	0.862701	+	0.505715i	$0.168771\pi$
$271$			274.098i			1.01143i	−0.862701	+	0.505715i	$0.831229\pi$
$272$	25.4510	−	124.871i	0.0935698	−	0.459086i
$273$		0			0
$274$	−104.299	−	292.584i	−0.380655	−	1.06782i
$275$		−	43.9557i		−	0.159839i
$276$		0			0
$277$	371.834			1.34236			0.671180	−	0.741295i	$-0.265788\pi$
$277$	371.834			1.34236			0.671180	+	0.741295i	$0.265788\pi$
$278$	190.729	−	67.9904i	0.686075	−	0.244570i
$279$		0			0
$280$	−108.389	+	179.395i	−0.387105	+	0.640697i
$281$	−411.087			−1.46294			−0.731472	−	0.681872i	$-0.761166\pi$
$281$	−411.087			−1.46294			−0.731472	+	0.681872i	$0.761166\pi$
$282$		0			0
$283$			446.826i			1.57889i	0.613820	+	0.789446i	$0.289632\pi$
$283$			446.826i			1.57889i	−0.613820	+	0.789446i	$0.710368\pi$
$284$	45.5023	+	55.7120i	0.160219	+	0.196169i
$285$		0			0
$286$	−259.180	+	92.3918i	−0.906225	+	0.323048i
$287$		−	201.111i		−	0.700735i
$288$		0			0
$289$	−225.560			−0.780484
$290$	113.757	+	319.114i	0.392265	+	1.10039i
$291$		0			0
$292$	−377.007	+	307.918i	−1.29112	+	1.05451i
$293$	388.623			1.32636			0.663179	−	0.748461i	$-0.269207\pi$
$293$	388.623			1.32636			0.663179	+	0.748461i	$0.269207\pi$
$294$		0			0
$295$			54.6440i			0.185234i
$296$	44.7460	+	27.0352i	0.151169	+	0.0913351i
$297$		0			0
$298$	109.922	+	308.356i	0.368865	+	1.03475i
$299$		−	524.630i		−	1.75462i
$300$		0			0
$301$	−231.863			−0.770311
$302$	297.135	−	105.922i	0.983891	−	0.350734i
$303$		0			0
$304$	−68.3374	−	13.9284i	−0.224794	−	0.0458170i
$305$	−493.724			−1.61877
$306$		0			0
$307$		−	255.235i		−	0.831383i	−0.909506	−	0.415691i	$-0.863540\pi$
$307$		−	255.235i		−	0.831383i	0.909506	−	0.415691i	$-0.136460\pi$
$308$	−181.079	+	147.895i	−0.587920	+	0.480179i
$309$		0			0
$310$	127.246	−	45.3601i	0.410470	−	0.146323i
$311$			19.0897i			0.0613816i	0.999529	+	0.0306908i	$0.00977071\pi$
$311$			19.0897i			0.0613816i	−0.999529	+	0.0306908i	$0.990229\pi$
$312$		0			0
$313$	17.7208			0.0566161			0.0283081	−	0.999599i	$-0.490988\pi$
$313$	17.7208			0.0566161			0.0283081	+	0.999599i	$0.490988\pi$
$314$	−61.8981	−	173.639i	−0.197128	−	0.552989i
$315$		0			0
$316$	260.646	+	319.129i	0.824829	+	1.00990i
$317$	−197.890			−0.624258			−0.312129	−	0.950040i	$-0.601042\pi$
$317$	−197.890			−0.624258			−0.312129	+	0.950040i	$0.601042\pi$
$318$		0			0
$319$			377.905i			1.18466i
$320$	−135.332	−	257.552i	−0.422911	−	0.804850i
$321$		0			0
$322$	−149.684	−	419.898i	−0.464857	−	1.30403i
$323$		−	34.7183i		−	0.107487i
$324$		0			0
$325$	58.7932			0.180902
$326$	456.924	−	162.883i	1.40161	−	0.499640i
$327$		0			0
$328$	238.937	+	144.364i	0.728468	+	0.440135i
$329$	−289.055			−0.878588
$330$		0			0
$331$			60.7260i			0.183462i	0.995784	+	0.0917311i	$0.0292400\pi$
$331$			60.7260i			0.183462i	−0.995784	+	0.0917311i	$0.970760\pi$
$332$	−105.711	−	129.431i	−0.318408	−	0.389851i
$333$		0			0
$334$	−167.972	+	59.8781i	−0.502910	+	0.179276i
$335$		−	307.418i		−	0.917665i
$336$		0			0
$337$	337.385			1.00114			0.500571	−	0.865695i	$-0.333123\pi$
$337$	337.385			1.00114			0.500571	+	0.865695i	$0.333123\pi$
$338$	−10.0858	−	28.2929i	−0.0298396	−	0.0837069i
$339$		0			0
$340$	112.174	−	91.6172i	0.329924	−	0.269462i
$341$	150.688			0.441901
$342$		0			0
$343$		−	373.372i		−	1.08855i
$344$	166.439	−	275.474i	0.483835	−	0.800796i
$345$		0			0
$346$	25.5566	+	71.6922i	0.0738631	+	0.207203i
$347$			387.012i			1.11531i	0.830073	+	0.557654i	$0.188299\pi$
$347$			387.012i			1.11531i	−0.830073	+	0.557654i	$0.811701\pi$
$348$		0			0
$349$	200.808			0.575380			0.287690	−	0.957724i	$-0.407113\pi$
$349$	200.808			0.575380			0.287690	+	0.957724i	$0.407113\pi$
$350$	47.0563	−	16.7745i	0.134447	−	0.0479271i
$351$		0			0
$352$	−45.7274	−	321.302i	−0.129907	−	0.912790i
$353$	−287.293			−0.813861			−0.406930	−	0.913459i	$-0.633401\pi$
$353$	−287.293			−0.813861			−0.406930	+	0.913459i	$0.633401\pi$
$354$		0			0
$355$			81.7509i			0.230284i
$356$	231.990	−	189.476i	0.651658	−	0.532237i
$357$		0			0
$358$	238.483	−	85.0136i	0.666153	−	0.237468i
$359$		−	278.300i		−	0.775208i	−0.921826	−	0.387604i	$-0.873303\pi$
$359$		−	278.300i		−	0.775208i	0.921826	−	0.387604i	$-0.126697\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	50.5402	+	141.777i	0.139614	+	0.391649i
$363$		0			0
$364$	−197.818	−	242.204i	−0.543457	−	0.665396i
$365$	−553.215			−1.51566
$366$		0			0
$367$		−	668.281i		−	1.82093i	−0.413587	−	0.910464i	$-0.635724\pi$
$367$		−	668.281i		−	1.82093i	0.413587	−	0.910464i	$-0.364276\pi$
$368$	606.323	+	123.579i	1.64762	+	0.335813i
$369$		0			0
$370$	19.9503	+	55.9653i	0.0539198	+	0.151258i
$371$		−	184.228i		−	0.496573i
$372$		0			0
$373$	471.037			1.26284			0.631418	−	0.775443i	$-0.282473\pi$
$373$	471.037			1.26284			0.631418	+	0.775443i	$0.282473\pi$
$374$	152.178	−	54.2481i	0.406894	−	0.145048i
$375$		0			0
$376$	207.494	−	343.423i	0.551845	−	0.913359i
$377$	−505.470			−1.34077
$378$		0			0
$379$			2.46934i			0.00651542i	0.999995	+	0.00325771i	$0.00103696\pi$
$379$			2.46934i			0.00651542i	−0.999995	+	0.00325771i	$0.998963\pi$
$380$	−50.1386	−	61.3886i	−0.131944	−	0.161549i
$381$		0			0
$382$	180.855	−	64.4706i	0.473442	−	0.168771i
$383$		−	242.192i		−	0.632354i	−0.948700	−	0.316177i	$-0.897601\pi$
$383$		−	242.192i		−	0.632354i	0.948700	−	0.316177i	$-0.102399\pi$
$384$		0			0
$385$	−265.713			−0.690164
$386$	43.1265	+	120.980i	0.111727	+	0.313419i
$387$		0			0
$388$	−230.397	+	188.175i	−0.593808	+	0.484988i
$389$	−98.3542			−0.252839			−0.126419	−	0.991977i	$-0.540348\pi$
$389$	−98.3542			−0.252839			−0.126419	+	0.991977i	$0.540348\pi$
$390$		0			0
$391$			308.038i			0.787821i
$392$	108.083	+	65.3031i	0.275722	+	0.166590i
$393$		0			0
$394$	−186.839	−	524.126i	−0.474210	−	1.33027i
$395$			468.285i			1.18553i
$396$		0			0
$397$	248.534			0.626031			0.313016	−	0.949748i	$-0.398661\pi$
$397$	248.534			0.626031			0.313016	+	0.949748i	$0.398661\pi$
$398$	−595.020	+	212.111i	−1.49502	+	0.532942i
$399$		0			0
$400$	−13.8490	+	67.9483i	−0.0346226	+	0.169871i
$401$	−197.414			−0.492305			−0.246153	−	0.969231i	$-0.579166\pi$
$401$	−197.414			−0.492305			−0.246153	+	0.969231i	$0.579166\pi$
$402$		0			0
$403$			201.555i			0.500135i
$404$	214.478	−	175.173i	0.530887	−	0.433597i
$405$		0			0
$406$	−404.563	+	144.217i	−0.996460	+	0.355215i
$407$			66.2759i			0.162840i
$408$		0			0
$409$	253.296			0.619307			0.309653	−	0.950850i	$-0.399787\pi$
$409$	253.296			0.619307			0.309653	+	0.950850i	$0.399787\pi$
$410$	106.532	+	298.847i	0.259834	+	0.728895i
$411$		0			0
$412$	150.957	+	184.828i	0.366399	+	0.448611i
$413$	−69.2759			−0.167738
$414$		0			0
$415$		−	189.925i		−	0.457649i
$416$	429.760	−	61.1631i	1.03308	−	0.147027i
$417$		0			0
$418$	−29.6879	−	83.2814i	−0.0710237	−	0.199238i
$419$		−	496.744i		−	1.18555i	−0.805369	−	0.592773i	$-0.798033\pi$
$419$		−	496.744i		−	1.18555i	0.805369	−	0.592773i	$-0.201967\pi$
$420$		0			0
$421$	−227.768			−0.541016			−0.270508	−	0.962718i	$-0.587192\pi$
$421$	−227.768			−0.541016			−0.270508	+	0.962718i	$0.587192\pi$
$422$	−526.966	+	187.851i	−1.24873	+	0.445145i
$423$		0			0
$424$	218.879	+	132.245i	0.516225	+	0.311899i
$425$	−34.5206			−0.0812249
$426$		0			0
$427$		−	625.928i		−	1.46587i
$428$	−143.164	−	175.286i	−0.334495	−	0.409548i
$429$		0			0
$430$	344.545	−	122.822i	0.801267	−	0.285633i
$431$			70.6353i			0.163887i	0.996637	+	0.0819435i	$0.0261127\pi$
$431$			70.6353i			0.163887i	−0.996637	+	0.0819435i	$0.973887\pi$
$432$		0			0
$433$	−503.901			−1.16374			−0.581872	−	0.813280i	$-0.697680\pi$
$433$	−503.901			−1.16374			−0.581872	+	0.813280i	$0.697680\pi$
$434$	57.5062	+	161.318i	0.132503	+	0.371701i
$435$		0			0
$436$	548.519	−	447.999i	1.25807	−	1.02752i
$437$	168.577			0.385761
$438$		0			0
$439$		−	714.455i		−	1.62746i	−0.581243	−	0.813730i	$-0.697433\pi$
$439$		−	714.455i		−	1.62746i	0.581243	−	0.813730i	$-0.302567\pi$
$440$	190.738	−	315.690i	0.433495	−	0.717478i
$441$		0			0
$442$	72.5600	+	203.547i	0.164163	+	0.460515i
$443$		−	619.970i		−	1.39948i	−0.714397	−	0.699740i	$-0.753299\pi$
$443$		−	619.970i		−	1.39948i	0.714397	−	0.699740i	$-0.246701\pi$
$444$		0			0
$445$	340.419			0.764987
$446$	159.752	−	56.9477i	0.358187	−	0.127686i
$447$		0			0
$448$	326.516	−	171.569i	0.728831	−	0.382967i
$449$	−239.436			−0.533266			−0.266633	−	0.963798i	$-0.585911\pi$
$449$	−239.436			−0.533266			−0.266633	+	0.963798i	$0.585911\pi$
$450$		0			0
$451$			353.905i			0.784711i
$452$	−583.136	+	476.272i	−1.29012	+	1.05370i
$453$		0			0
$454$	342.443	−	122.073i	0.754280	−	0.268883i
$455$		−	355.407i		−	0.781114i
$456$		0			0
$457$	261.637			0.572509			0.286255	−	0.958154i	$-0.407590\pi$
$457$	261.637			0.572509			0.286255	+	0.958154i	$0.407590\pi$
$458$	57.9884	+	162.671i	0.126612	+	0.355177i
$459$		0			0
$460$	444.855	+	544.670i	0.967076	+	1.18406i
$461$	−820.778			−1.78043			−0.890215	−	0.455541i	$-0.849446\pi$
$461$	−820.778			−1.78043			−0.890215	+	0.455541i	$0.849446\pi$
$462$		0			0
$463$		−	664.942i		−	1.43616i	−0.695961	−	0.718080i	$-0.745021\pi$
$463$		−	664.942i		−	1.43616i	0.695961	−	0.718080i	$-0.254979\pi$
$464$	119.066	−	584.180i	0.256608	−	1.25901i
$465$		0			0
$466$	43.3587	+	121.631i	0.0930445	+	0.261011i
$467$			30.1761i			0.0646169i	0.999478	+	0.0323084i	$0.0102859\pi$
$467$			30.1761i			0.0646169i	−0.999478	+	0.0323084i	$0.989714\pi$
$468$		0			0
$469$	389.735			0.830991
$470$	429.531	−	153.118i	0.913895	−	0.325783i
$471$		0			0
$472$	49.7286	−	82.3058i	0.105357	−	0.174377i
$473$	408.021			0.862624
$474$		0			0
$475$			18.8918i			0.0397722i
$476$	116.150	+	142.211i	0.244012	+	0.298762i
$477$		0			0
$478$	−397.882	+	141.836i	−0.832389	+	0.296728i
$479$		−	50.6604i		−	0.105763i	−0.998601	−	0.0528814i	$-0.983159\pi$
$479$		−	50.6604i		−	0.105763i	0.998601	−	0.0528814i	$-0.0168405\pi$
$480$		0			0
$481$	−88.6479			−0.184299
$482$	−240.307	−	674.116i	−0.498561	−	1.39858i
$483$		0			0
$484$	−56.2057	+	45.9056i	−0.116128	+	0.0948462i
$485$	−338.081			−0.697075
$486$		0			0
$487$		−	601.236i		−	1.23457i	−0.786739	−	0.617285i	$-0.788232\pi$
$487$		−	601.236i		−	1.23457i	0.786739	−	0.617285i	$-0.211768\pi$
$488$	743.657	+	449.312i	1.52389	+	0.920722i
$489$		0			0
$490$	48.1897	+	135.183i	0.0983464	+	0.275884i
$491$		−	60.8938i		−	0.124020i	−0.998076	−	0.0620100i	$-0.980249\pi$
$491$		−	60.8938i		−	0.124020i	0.998076	−	0.0620100i	$-0.0197511\pi$
$492$		0			0
$493$	296.788			0.602004
$494$	111.394	−	39.7093i	0.225493	−	0.0803832i
$495$		0			0
$496$	−232.940	−	47.4772i	−0.469637	−	0.0957201i
$497$	−103.641			−0.208534
$498$		0			0
$499$			594.048i			1.19048i	0.803549	+	0.595238i	$0.202942\pi$
$499$			594.048i			1.19048i	−0.803549	+	0.595238i	$0.797058\pi$
$500$	−413.127	+	337.418i	−0.826253	+	0.674836i
$501$		0			0
$502$	548.279	−	195.449i	1.09219	−	0.389341i
$503$		−	247.278i		−	0.491607i	−0.969320	−	0.245804i	$-0.920948\pi$
$503$		−	247.278i		−	0.491607i	0.969320	−	0.245804i	$-0.0790518\pi$
$504$		0			0
$505$	314.722			0.623212
$506$	263.406	+	738.914i	0.520565	+	1.46030i
$507$		0			0
$508$	−162.321	−	198.743i	−0.319530	−	0.391226i
$509$	−171.323			−0.336587			−0.168293	−	0.985737i	$-0.553826\pi$
$509$	−171.323			−0.336587			−0.168293	+	0.985737i	$0.553826\pi$
$510$		0			0
$511$		−	701.349i		−	1.37250i
$512$	−30.5451	+	511.088i	−0.0596584	+	0.998219i
$513$		0			0
$514$	−164.772	−	462.224i	−0.320568	−	0.899268i
$515$			271.213i			0.526628i
$516$		0			0
$517$	508.664			0.983877
$518$	−70.9511	+	25.2924i	−0.136971	+	0.0488271i
$519$		0			0
$520$	422.254	+	255.123i	0.812027	+	0.490621i
$521$	258.497			0.496156			0.248078	−	0.968740i	$-0.420201\pi$
$521$	258.497			0.496156			0.248078	+	0.968740i	$0.420201\pi$
$522$		0			0
$523$			866.792i			1.65735i	0.559733	+	0.828673i	$0.310904\pi$
$523$			866.792i			1.65735i	−0.559733	+	0.828673i	$0.689096\pi$
$524$	−335.252	−	410.475i	−0.639795	−	0.783350i
$525$		0			0
$526$	847.132	−	301.983i	1.61052	−	0.574112i
$527$		−	118.343i		−	0.224560i
$528$		0			0
$529$	−966.702			−1.82741
$530$	97.5891	+	273.760i	0.184130	+	0.516528i
$531$		0			0
$532$	77.8266	−	63.5642i	0.146291	−	0.119482i
$533$	−473.368			−0.888120
$534$		0			0
$535$		−	257.213i		−	0.480771i
$536$	−279.765	+	463.039i	−0.521949	+	0.863878i
$537$		0			0
$538$	−234.909	−	658.975i	−0.436635	−	1.22486i
$539$			160.089i			0.297010i
$540$		0			0
$541$	−360.604			−0.666551			−0.333276	−	0.942829i	$-0.608154\pi$
$541$	−360.604			−0.666551			−0.333276	+	0.942829i	$0.608154\pi$
$542$	516.367	−	184.073i	0.952707	−	0.339618i
$543$		0			0
$544$	−252.335	+	35.9121i	−0.463851	+	0.0660148i
$545$	804.889			1.47686
$546$		0			0
$547$			130.335i			0.238272i	0.992878	+	0.119136i	$0.0380125\pi$
$547$			130.335i			0.238272i	−0.992878	+	0.119136i	$0.961987\pi$
$548$	−481.150	+	392.975i	−0.878011	+	0.717108i
$549$		0			0
$550$	−82.8072	+	29.5189i	−0.150559	+	0.0536707i
$551$		−	162.421i		−	0.294775i
$552$		0			0
$553$	−593.677			−1.07356
$554$	−249.709	−	700.490i	−0.450738	−	1.26442i
$555$		0			0
$556$	−256.172	−	313.651i	−0.460740	−	0.564120i
$557$	−354.943			−0.637241			−0.318621	−	0.947882i	$-0.603220\pi$
$557$	−354.943			−0.637241			−0.318621	+	0.947882i	$0.603220\pi$
$558$		0			0
$559$			545.752i			0.976301i
$560$	410.749	+	83.7179i	0.733481	+	0.149496i
$561$		0			0
$562$	276.070	+	774.439i	0.491227	+	1.37801i
$563$			286.972i			0.509720i	0.966978	+	0.254860i	$0.0820293\pi$
$563$			286.972i			0.509720i	−0.966978	+	0.254860i	$0.917971\pi$
$564$		0			0
$565$	−855.685			−1.51449
$566$	841.767	−	300.071i	1.48722	−	0.530160i
$567$		0			0
$568$	74.3972	−	123.135i	0.130981	−	0.216787i
$569$	−868.265			−1.52595			−0.762974	−	0.646429i	$-0.776262\pi$
$569$	−868.265			−1.52595			−0.762974	+	0.646429i	$0.776262\pi$
$570$		0			0
$571$		−	453.287i		−	0.793848i	−0.917851	−	0.396924i	$-0.870078\pi$
$571$		−	453.287i		−	0.793848i	0.917851	−	0.396924i	$-0.129922\pi$
$572$	348.110	+	426.218i	0.608585	+	0.745137i
$573$		0			0
$574$	−378.869	+	135.058i	−0.660051	+	0.235293i
$575$		−	167.617i		−	0.291509i
$576$		0			0
$577$	193.050			0.334576			0.167288	−	0.985908i	$-0.446499\pi$
$577$	193.050			0.334576			0.167288	+	0.985908i	$0.446499\pi$
$578$	151.477	+	424.928i	0.262071	+	0.735170i
$579$		0			0
$580$	524.778	−	428.608i	0.904790	−	0.738980i
$581$	240.780			0.414424
$582$		0			0
$583$			324.195i			0.556081i
$584$	833.263	+	503.452i	1.42682	+	0.862075i
$585$		0			0
$586$	−260.984	−	732.120i	−0.445365	−	1.24935i
$587$		−	418.147i		−	0.712346i	−0.934420	−	0.356173i	$-0.884081\pi$
$587$		−	418.147i		−	0.712346i	0.934420	−	0.356173i	$-0.115919\pi$
$588$		0			0
$589$	−64.7647			−0.109957
$590$	102.943	−	36.6967i	0.174479	−	0.0621978i
$591$		0			0
$592$	20.8815	−	102.452i	0.0352727	−	0.173060i
$593$	−375.775			−0.633684			−0.316842	−	0.948478i	$-0.602623\pi$
$593$	−375.775			−0.633684			−0.316842	+	0.948478i	$0.602623\pi$
$594$		0			0
$595$			208.678i			0.350719i
$596$	507.087	−	414.159i	0.850818	−	0.694898i
$597$		0			0
$598$	−988.341	+	352.321i	−1.65274	+	0.589165i
$599$			1002.88i			1.67425i	0.547010	+	0.837126i	$0.315766\pi$
$599$			1002.88i			1.67425i	−0.547010	+	0.837126i	$0.684234\pi$
$600$		0			0
$601$	922.775			1.53540			0.767700	−	0.640810i	$-0.221401\pi$
$601$	922.775			1.53540			0.767700	+	0.640810i	$0.221401\pi$
$602$	155.710	+	436.803i	0.258655	+	0.725587i
$603$		0			0
$604$	−399.088	−	488.634i	−0.660742	−	0.808997i
$605$	−82.4754			−0.136323
$606$		0			0
$607$		−	681.919i		−	1.12343i	−0.827332	−	0.561713i	$-0.810143\pi$
$607$		−	681.919i		−	1.12343i	0.827332	−	0.561713i	$-0.189857\pi$
$608$	19.6533	+	138.093i	0.0323245	+	0.227127i
$609$		0			0
$610$	331.565	+	930.117i	0.543550	+	1.52478i
$611$			680.368i			1.11353i
$612$		0			0
$613$	166.517			0.271643			0.135821	−	0.990733i	$-0.456633\pi$
$613$	166.517			0.271643			0.135821	+	0.990733i	$0.456633\pi$
$614$	−480.831	+	171.405i	−0.783113	+	0.279162i
$615$		0			0
$616$	400.223	+	241.812i	0.649712	+	0.392551i
$617$	599.924			0.972325			0.486162	−	0.873868i	$-0.338396\pi$
$617$	599.924			0.972325			0.486162	+	0.873868i	$0.338396\pi$
$618$		0			0
$619$			455.249i			0.735458i	0.929933	+	0.367729i	$0.119865\pi$
$619$			455.249i			0.735458i	−0.929933	+	0.367729i	$0.880135\pi$
$620$	−170.906	−	209.253i	−0.275655	−	0.337506i
$621$		0			0
$622$	35.9627	−	12.8199i	0.0578178	−	0.0206107i
$623$			431.573i			0.692733i
$624$		0			0
$625$	−497.864			−0.796582
$626$	−11.9006	−	33.3840i	−0.0190106	−	0.0533290i
$627$		0			0
$628$	−285.546	+	233.217i	−0.454691	+	0.371365i
$629$	52.0498			0.0827501
$630$		0			0
$631$			285.625i			0.452655i	0.974051	+	0.226327i	$0.0726719\pi$
$631$			285.625i			0.452655i	−0.974051	+	0.226327i	$0.927328\pi$
$632$	426.162	−	705.340i	0.674306	−	1.11605i
$633$		0			0
$634$	132.895	+	372.801i	0.209613	+	0.588014i
$635$		−	291.632i		−	0.459263i
$636$		0			0
$637$	−214.128			−0.336150
$638$	711.928	−	253.786i	1.11588	−	0.397784i
$639$		0			0
$640$	−394.314	+	427.910i	−0.616115	+	0.668610i
$641$	1163.68			1.81542			0.907709	−	0.419600i	$-0.137829\pi$
$641$	1163.68			1.81542			0.907709	+	0.419600i	$0.137829\pi$
$642$		0			0
$643$		−	132.794i		−	0.206523i	−0.994654	−	0.103261i	$-0.967072\pi$
$643$		−	132.794i		−	0.206523i	0.994654	−	0.103261i	$-0.0329278\pi$
$644$	−690.516	+	563.973i	−1.07223	+	0.875735i
$645$		0			0
$646$	−65.4051	+	23.3154i	−0.101246	+	0.0360920i
$647$			701.301i			1.08393i	0.840402	+	0.541964i	$0.182319\pi$
$647$			701.301i			1.08393i	−0.840402	+	0.541964i	$0.817681\pi$
$648$		0			0
$649$	121.908			0.187840
$650$	−39.4832	−	110.759i	−0.0607434	−	0.170399i
$651$		0			0
$652$	−613.703	−	751.404i	−0.941263	−	1.15246i
$653$	449.191			0.687888			0.343944	−	0.938990i	$-0.388237\pi$
$653$	449.191			0.687888			0.343944	+	0.938990i	$0.388237\pi$
$654$		0			0
$655$		−	602.325i		−	0.919580i
$656$	111.504	−	547.079i	0.169976	−	0.833962i
$657$		0			0
$658$	194.118	+	544.546i	0.295012	+	0.827577i
$659$		−	1200.98i		−	1.82243i	−0.411935	−	0.911213i	$-0.635147\pi$
$659$		−	1200.98i		−	1.82243i	0.411935	−	0.911213i	$-0.364853\pi$
$660$		0			0
$661$	591.521			0.894889			0.447444	−	0.894312i	$-0.352334\pi$
$661$	591.521			0.894889			0.447444	+	0.894312i	$0.352334\pi$
$662$	114.400	−	40.7811i	0.172810	−	0.0616029i
$663$		0			0
$664$	−172.840	+	286.068i	−0.260302	+	0.430826i
$665$	114.202			0.171732
$666$		0			0
$667$			1441.08i			2.16054i
$668$	225.607	+	276.227i	0.337734	+	0.413514i
$669$		0			0
$670$	−579.138	+	206.449i	−0.864386	+	0.308133i
$671$			1101.48i			1.64154i
$672$		0			0
$673$	1118.10			1.66137			0.830683	−	0.556746i	$-0.187950\pi$
$673$	1118.10			1.66137			0.830683	+	0.556746i	$0.187950\pi$
$674$	−226.574	−	635.593i	−0.336164	−	0.943016i
$675$		0			0
$676$	−46.5273	+	38.0008i	−0.0688274	+	0.0562142i
$677$	105.963			0.156519			0.0782596	−	0.996933i	$-0.475064\pi$
$677$	105.963			0.156519			0.0782596	+	0.996933i	$0.475064\pi$
$678$		0			0
$679$		−	428.609i		−	0.631236i
$680$	−247.928	−	149.796i	−0.364599	−	0.220288i
$681$		0			0
$682$	−101.196	−	283.879i	−0.148382	−	0.416245i
$683$		−	952.684i		−	1.39485i	−0.716657	−	0.697426i	$-0.754329\pi$
$683$		−	952.684i		−	1.39485i	0.716657	−	0.697426i	$-0.245671\pi$
$684$		0			0
$685$	−706.032			−1.03070
$686$	−703.388	+	250.742i	−1.02535	+	0.365513i
$687$		0			0
$688$	−630.734	−	128.555i	−0.916765	−	0.186853i
$689$	−433.630			−0.629362
$690$		0			0
$691$		−	1228.01i		−	1.77714i	−0.458738	−	0.888572i	$-0.651698\pi$
$691$		−	1228.01i		−	1.77714i	0.458738	−	0.888572i	$-0.348302\pi$
$692$	117.897	−	96.2913i	0.170371	−	0.139149i
$693$		0			0
$694$	729.085	−	259.902i	1.05055	−	0.374498i
$695$		−	460.246i		−	0.662225i
$696$		0			0
$697$	277.939			0.398765
$698$	−134.854	−	378.298i	−0.193201	−	0.541974i
$699$		0			0
$700$	−63.2023	−	77.3834i	−0.0902890	−	0.110548i
$701$	−965.982			−1.37801			−0.689003	−	0.724759i	$-0.741951\pi$
$701$	−965.982			−1.37801			−0.689003	+	0.724759i	$0.741951\pi$
$702$		0			0
$703$		−	28.4849i		−	0.0405191i
$704$	−574.586	+	301.919i	−0.816174	+	0.428862i
$705$		0			0
$706$	192.934	+	541.225i	0.273278	+	0.766608i
$707$			398.995i			0.564349i
$708$		0			0
$709$	900.429			1.27000			0.634999	−	0.772513i	$-0.281000\pi$
$709$	900.429			1.27000			0.634999	+	0.772513i	$0.281000\pi$
$710$	154.009	−	54.9006i	0.216914	−	0.0773248i
$711$		0			0
$712$	−512.746	−	309.797i	−0.720149	−	0.435109i
$713$	574.625			0.805925
$714$		0			0
$715$			625.426i			0.874722i
$716$	−320.311	−	392.181i	−0.447362	−	0.547739i
$717$		0			0
$718$	−524.283	+	186.895i	−0.730199	+	0.260299i
$719$			1271.11i			1.76788i	0.467599	+	0.883941i	$0.345119\pi$
$719$			1271.11i			1.76788i	−0.467599	+	0.883941i	$0.654881\pi$
$720$		0			0
$721$	−343.836			−0.476888
$722$	12.7596	+	35.7937i	0.0176726	+	0.0495758i
$723$		0			0
$724$	233.150	−	190.423i	0.322030	−	0.263016i
$725$	−161.496			−0.222753
$726$		0			0
$727$		−	188.308i		−	0.259020i	−0.991578	−	0.129510i	$-0.958660\pi$
$727$		−	188.308i		−	0.259020i	0.991578	−	0.129510i	$-0.0413404\pi$
$728$	−323.437	+	535.321i	−0.444282	+	0.735331i
$729$		0			0
$730$	371.517	+	1042.19i	0.508927	+	1.42766i
$731$		−	320.440i		−	0.438358i
$732$		0			0
$733$	−917.474			−1.25167			−0.625835	−	0.779955i	$-0.715242\pi$
$733$	−917.474			−1.25167			−0.625835	+	0.779955i	$0.715242\pi$
$734$	−1258.96	+	448.791i	−1.71521	+	0.611431i
$735$		0			0
$736$	−174.374	−	1225.23i	−0.236921	−	1.66472i
$737$	−685.835			−0.930576
$738$		0			0
$739$			581.020i			0.786225i	0.919490	+	0.393112i	$0.128602\pi$
$739$			581.020i			0.786225i	−0.919490	+	0.393112i	$0.871398\pi$
$740$	92.0341	−	75.1681i	0.124370	−	0.101579i
$741$		0			0
$742$	−347.064	+	123.720i	−0.467742	+	0.166739i
$743$			1330.67i			1.79094i	0.445122	+	0.895470i	$0.353160\pi$
$743$			1330.67i			1.79094i	−0.445122	+	0.895470i	$0.646840\pi$
$744$		0			0
$745$	744.092			0.998781
$746$	−316.330	−	887.379i	−0.424035	−	1.18952i
$747$		0			0
$748$	−204.394	−	250.255i	−0.273254	−	0.334566i
$749$	326.086			0.435362
$750$		0			0
$751$		−	269.737i		−	0.359171i	−0.983742	−	0.179585i	$-0.942524\pi$
$751$		−	269.737i		−	0.359171i	0.983742	−	0.179585i	$-0.0574756\pi$
$752$	−786.312	−	160.264i	−1.04563	−	0.213117i
$753$		0			0
$754$	339.454	+	952.246i	0.450204	+	1.26293i
$755$		−	717.015i		−	0.949688i
$756$		0			0
$757$	884.769			1.16878			0.584392	−	0.811472i	$-0.301333\pi$
$757$	884.769			1.16878			0.584392	+	0.811472i	$0.301333\pi$
$758$	4.65195	−	1.65831i	0.00613714	−	0.00218775i
$759$		0			0
$760$	−81.9777	+	135.681i	−0.107865	+	0.178528i
$761$	1030.00			1.35348			0.676742	−	0.736221i	$-0.263391\pi$
$761$	1030.00			1.35348			0.676742	+	0.736221i	$0.263391\pi$
$762$		0			0
$763$			1020.41i			1.33737i
$764$	−242.910	−	297.413i	−0.317945	−	0.389284i
$765$		0			0
$766$	−456.260	+	162.646i	−0.595640	+	0.212332i
$767$			163.059i			0.212594i
$768$		0			0
$769$	−1017.69			−1.32340			−0.661699	−	0.749769i	$-0.730164\pi$
$769$	−1017.69			−1.32340			−0.661699	+	0.749769i	$0.730164\pi$
$770$	178.442	+	500.572i	0.231743	+	0.650093i
$771$		0			0
$772$	198.950	−	162.490i	0.257707	−	0.210480i
$773$	1109.90			1.43583			0.717916	−	0.696130i	$-0.245096\pi$
$773$	1109.90			1.43583			0.717916	+	0.696130i	$0.245096\pi$
$774$		0			0
$775$			64.3960i			0.0830916i
$776$	509.225	+	307.670i	0.656218	+	0.396482i
$777$		0			0
$778$	66.0508	+	185.288i	0.0848981	+	0.238159i
$779$		−	152.106i		−	0.195257i
$780$		0			0
$781$	182.382			0.233524
$782$	580.307	−	206.866i	0.742080	−	0.264534i
$783$		0			0
$784$	50.4389	−	247.471i	0.0643353	−	0.315652i
$785$	−419.006			−0.533765
$786$		0			0
$787$			1481.33i			1.88225i	0.338065	+	0.941123i	$0.390228\pi$
$787$			1481.33i			1.88225i	−0.338065	+	0.941123i	$0.609772\pi$
$788$	−861.918	+	703.964i	−1.09380	+	0.893356i
$789$		0			0
$790$	882.193	−	314.482i	1.11670	−	0.398078i
$791$		−	1084.81i		−	1.37144i
$792$		0			0
$793$	−1473.29			−1.85787
$794$	−166.906	−	468.209i	−0.210209	−	0.589684i
$795$		0			0
$796$	799.183	+	978.502i	1.00400	+	1.22927i
$797$	1344.04			1.68637			0.843187	−	0.537621i	$-0.180677\pi$
$797$	1344.04			1.68637			0.843187	+	0.537621i	$0.180677\pi$
$798$		0			0
$799$		−	399.480i		−	0.499975i
$800$	137.307	−	19.5414i	0.171634	−	0.0244267i
$801$		0			0
$802$	132.576	+	371.905i	0.165306	+	0.463722i
$803$			1234.20i			1.53698i
$804$		0			0
$805$	−1013.25			−1.25870
$806$	379.705	−	135.356i	0.471098	−	0.167935i
$807$		0			0
$808$	−474.041	−	286.412i	−0.586684	−	0.354470i
$809$	182.408			0.225473			0.112737	−	0.993625i	$-0.464038\pi$
$809$	182.408			0.225473			0.112737	+	0.993625i	$0.464038\pi$
$810$		0			0
$811$			615.924i			0.759462i	0.925097	+	0.379731i	$0.123983\pi$
$811$			615.924i			0.759462i	−0.925097	+	0.379731i	$0.876017\pi$
$812$	543.376	+	665.298i	0.669183	+	0.819332i
$813$		0			0
$814$	124.856	−	44.5083i	0.153386	−	0.0546785i
$815$		−	1102.60i		−	1.35288i
$816$		0			0
$817$	−175.364			−0.214644
$818$	−170.104	−	477.180i	−0.207951	−	0.583350i
$819$		0			0
$820$	491.450	−	401.388i	0.599329	−	0.489497i
$821$	−1240.39			−1.51082			−0.755412	−	0.655250i	$-0.772563\pi$
$821$	−1240.39			−1.51082			−0.755412	+	0.655250i	$0.772563\pi$
$822$		0			0
$823$			684.605i			0.831841i	0.909401	+	0.415920i	$0.136540\pi$
$823$			684.605i			0.831841i	−0.909401	+	0.415920i	$0.863460\pi$
$824$	246.817	−	408.507i	0.299535	−	0.495761i
$825$		0			0
$826$	46.5229	+	130.508i	0.0563232	+	0.158000i
$827$		−	186.980i		−	0.226094i	−0.993590	−	0.113047i	$-0.963939\pi$
$827$		−	186.980i		−	0.226094i	0.993590	−	0.113047i	$-0.0360611\pi$
$828$		0			0
$829$	1014.04			1.22321			0.611604	−	0.791164i	$-0.290525\pi$
$829$	1014.04			1.22321			0.611604	+	0.791164i	$0.290525\pi$
$830$	−357.795	+	127.546i	−0.431079	+	0.153670i
$831$		0			0
$832$	−403.834	−	768.543i	−0.485377	−	0.923729i
$833$	125.726			0.150931
$834$		0			0
$835$			405.332i			0.485427i
$836$	−136.955	+	111.857i	−0.163822	+	0.133800i
$837$		0			0
$838$	−935.807	+	333.594i	−1.11671	+	0.398083i
$839$			266.413i			0.317536i	0.987316	+	0.158768i	$0.0507522\pi$
$839$			266.413i			0.317536i	−0.987316	+	0.158768i	$0.949248\pi$
$840$		0			0
$841$	547.448			0.650949
$842$	152.960	+	429.087i	0.181662	+	0.509605i
$843$		0			0
$844$	707.778	+	866.587i	0.838600	+	1.02676i
$845$	−68.2735			−0.0807970
$846$		0			0
$847$		−	104.560i		−	0.123447i
$848$	102.144	−	501.153i	0.120453	−	0.590983i
$849$		0			0
$850$	23.1827	+	65.0327i	0.0272737	+	0.0765091i
$851$			252.732i			0.296982i
$852$		0			0
$853$	−1336.98			−1.56738			−0.783692	−	0.621150i	$-0.786666\pi$
$853$	−1336.98			−1.56738			−0.783692	+	0.621150i	$0.786666\pi$
$854$	−1179.17	+	420.348i	−1.38077	+	0.492211i
$855$		0			0
$856$	−234.076	+	387.419i	−0.273453	+	0.452592i
$857$	−512.853			−0.598428			−0.299214	−	0.954186i	$-0.596724\pi$
$857$	−512.853			−0.598428			−0.299214	+	0.954186i	$0.596724\pi$
$858$		0			0
$859$			782.098i			0.910475i	0.890370	+	0.455237i	$0.150446\pi$
$859$			782.098i			0.910475i	−0.890370	+	0.455237i	$0.849554\pi$
$860$	−462.765	−	566.599i	−0.538099	−	0.658836i
$861$		0			0
$862$	133.068	−	47.4358i	0.154372	−	0.0550300i
$863$		−	494.483i		−	0.572982i	−0.958083	−	0.286491i	$-0.907511\pi$
$863$		−	494.483i		−	0.572982i	0.958083	−	0.286491i	$-0.0924888\pi$
$864$		0			0
$865$	173.000			0.200000
$866$	338.400	+	949.290i	0.390762	+	1.09618i
$867$		0			0
$868$	265.285	−	216.670i	0.305628	−	0.249619i
$869$	1044.72			1.20221
$870$		0			0
$871$		−	917.344i		−	1.05321i
$872$	−1212.34	−	732.487i	−1.39030	−	0.840008i
$873$		0			0
$874$	−113.210	−	317.580i	−0.129531	−	0.363364i
$875$		−	768.542i		−	0.878334i
$876$		0			0
$877$	−541.896			−0.617897			−0.308949	−	0.951079i	$-0.599977\pi$
$877$	−541.896			−0.617897			−0.308949	+	0.951079i	$0.599977\pi$
$878$	−1345.95	+	479.800i	−1.53297	+	0.546469i
$879$		0			0
$880$	−722.815	−	147.322i	−0.821380	−	0.167412i
$881$	−317.255			−0.360108			−0.180054	−	0.983657i	$-0.557627\pi$
$881$	−317.255			−0.360108			−0.180054	+	0.983657i	$0.557627\pi$
$882$		0			0
$883$		−	443.191i		−	0.501915i	−0.967998	−	0.250957i	$-0.919255\pi$
$883$		−	443.191i		−	0.501915i	0.967998	−	0.250957i	$-0.0807454\pi$
$884$	334.731	−	273.389i	0.378655	−	0.309263i
$885$		0			0
$886$	−1167.95	+	416.347i	−1.31823	+	0.469918i
$887$			574.737i			0.647956i	0.946065	+	0.323978i	$0.105020\pi$
$887$			574.737i			0.647956i	−0.946065	+	0.323978i	$0.894980\pi$
$888$		0			0
$889$	369.722			0.415885
$890$	−228.612	−	641.309i	−0.256867	−	0.720572i
$891$		0			0
$892$	−214.566	−	262.709i	−0.240544	−	0.294517i
$893$	−218.620			−0.244815
$894$		0			0
$895$		−	575.481i		−	0.642995i
$896$	−542.492	−	499.899i	−0.605459	−	0.557923i
$897$		0			0
$898$	160.796	+	451.069i	0.179060	+	0.502304i
$899$		−	553.639i		−	0.615839i
$900$		0			0
$901$	254.607			0.282583
$902$	666.714	−	237.668i	0.739151	−	0.263490i
$903$		0			0
$904$	1288.85	+	778.714i	1.42572	+	0.861409i
$905$	342.121			0.378034
$906$		0			0
$907$		−	634.305i		−	0.699344i	−0.936872	−	0.349672i	$-0.886293\pi$
$907$		−	634.305i		−	0.699344i	0.936872	−	0.349672i	$-0.113707\pi$
$908$	−459.942	−	563.142i	−0.506544	−	0.620201i
$909$		0			0
$910$	−669.544	+	238.677i	−0.735763	+	0.262282i
$911$		−	1816.19i		−	1.99363i	−0.0797693	−	0.996813i	$-0.525418\pi$
$911$		−	1816.19i		−	1.99363i	0.0797693	−	0.996813i	$-0.474582\pi$
$912$		0			0
$913$	−423.713			−0.464089
$914$	−175.705	−	492.892i	−0.192237	−	0.539270i
$915$		0			0
$916$	267.510	−	218.486i	0.292041	−	0.238522i
$917$	763.609			0.832726
$918$		0			0
$919$		−	185.518i		−	0.201869i	−0.994893	−	0.100935i	$-0.967817\pi$
$919$		−	185.518i		−	0.201869i	0.994893	−	0.100935i	$-0.0321833\pi$
$920$	727.346	−	1203.83i	0.790594	−	1.30851i
$921$		0			0
$922$	551.202	+	1546.25i	0.597833	+	1.67706i
$923$			243.947i			0.264298i
$924$		0			0
$925$	−28.3227			−0.0306191
$926$	−1252.67	+	446.548i	−1.35278	+	0.482234i
$927$		0			0
$928$	−1180.49	+	168.006i	−1.27207	+	0.181040i
$929$	1203.70			1.29570			0.647848	−	0.761770i	$-0.275669\pi$
$929$	1203.70			1.29570			0.647848	+	0.761770i	$0.275669\pi$
$930$		0			0
$931$		−	68.8049i		−	0.0739043i
$932$	200.021	−	163.365i	0.214615	−	0.175285i
$933$		0			0
$934$	56.8481	−	20.2651i	0.0608653	−	0.0216971i
$935$		−	367.221i		−	0.392749i
$936$		0			0
$937$	−1835.18			−1.95857			−0.979286	−	0.202481i	$-0.935100\pi$
$937$	−1835.18			−1.95857			−0.979286	+	0.202481i	$0.935100\pi$
$938$	−261.730	−	734.214i	−0.279030	−	0.782744i
$939$		0			0
$940$	−576.911	−	706.357i	−0.613736	−	0.751444i
$941$	514.256			0.546499			0.273250	−	0.961943i	$-0.411901\pi$
$941$	514.256			0.546499			0.273250	+	0.961943i	$0.411901\pi$
$942$		0			0
$943$			1349.56i			1.43113i
$944$	−188.450	−	38.4094i	−0.199629	−	0.0406880i
$945$		0			0
$946$	−274.011	−	768.663i	−0.289652	−	0.812540i
$947$			1283.94i			1.35580i	0.735155	+	0.677900i	$0.237110\pi$
$947$			1283.94i			1.35580i	−0.735155	+	0.677900i	$0.762890\pi$
$948$		0			0
$949$	−1650.81			−1.73953
$950$	35.5899	−	12.6870i	0.0374631	−	0.0133547i
$951$		0			0
$952$	189.907	−	314.315i	0.199482	−	0.330163i
$953$	334.065			0.350540			0.175270	−	0.984520i	$-0.443920\pi$
$953$	334.065			0.350540			0.175270	+	0.984520i	$0.443920\pi$
$954$		0			0
$955$		−	436.420i		−	0.456984i
$956$	534.403	+	654.311i	0.558999	+	0.684426i
$957$		0			0
$958$	−95.4381	+	34.0215i	−0.0996222	+	0.0355130i
$959$		−	895.086i		−	0.933353i
$960$		0			0
$961$	740.238			0.770279
$962$	59.5324	+	167.002i	0.0618840	+	0.173599i
$963$		0			0
$964$	−1108.57	+	905.418i	−1.14997	+	0.939230i
$965$	291.936			0.302524
$966$		0			0
$967$			1192.89i			1.23359i	0.787122	+	0.616797i	$0.211570\pi$
$967$			1192.89i			1.23359i	−0.787122	+	0.616797i	$0.788430\pi$
$968$	124.226	+	75.0565i	0.128333	+	0.0775377i
$969$		0			0
$970$	227.042	+	636.905i	0.234064	+	0.656603i
$971$		−	1610.40i		−	1.65849i	−0.558883	−	0.829246i	$-0.688770\pi$
$971$		−	1610.40i		−	1.65849i	0.558883	−	0.829246i	$-0.311230\pi$
$972$		0			0
$973$	583.486			0.599677
$974$	−1132.66	+	403.766i	−1.16289	+	0.414544i
$975$		0			0
$976$	347.040	−	1702.70i	0.355574	−	1.74457i
$977$	−177.241			−0.181413			−0.0907067	−	0.995878i	$-0.528913\pi$
$977$	−177.241			−0.181413			−0.0907067	+	0.995878i	$0.528913\pi$
$978$		0			0
$979$		−	759.459i		−	0.775750i
$980$	222.307	−	181.567i	0.226844	−	0.185273i
$981$		0			0
$982$	−114.717	+	40.8938i	−0.116819	+	0.0416434i
$983$			943.934i			0.960258i	0.877198	+	0.480129i	$0.159410\pi$
$983$			943.934i			0.960258i	−0.877198	+	0.480129i	$0.840590\pi$
$984$		0			0
$985$	−1264.77			−1.28403
$986$	−199.311	−	559.113i	−0.202141	−	0.567052i
$987$		0			0
$988$	−149.615	−	183.185i	−0.151432	−	0.185410i
$989$	1555.92			1.57323
$990$		0			0
$991$		−	1712.20i		−	1.72775i	−0.503707	−	0.863874i	$-0.668031\pi$
$991$		−	1712.20i		−	1.72775i	0.503707	−	0.863874i	$-0.331969\pi$
$992$	66.9916	+	470.714i	0.0675319	+	0.474511i
$993$		0			0
$994$	69.6013	+	195.248i	0.0700215	+	0.196426i
$995$			1435.84i			1.44305i
$996$		0			0
$997$	−1190.34			−1.19392			−0.596961	−	0.802270i	$-0.703625\pi$
$997$	−1190.34			−1.19392			−0.596961	+	0.802270i	$0.703625\pi$
$998$	1119.12	−	398.939i	1.12136	−	0.399738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.d.343.15	✓	36
3.2	odd	2	inner	684.3.g.d.343.22	yes	36
4.3	odd	2	inner	684.3.g.d.343.16	yes	36
12.11	even	2	inner	684.3.g.d.343.21	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.g.d.343.15	✓	36	1.1	even	1	trivial
684.3.g.d.343.16	yes	36	4.3	odd	2	inner
684.3.g.d.343.21	yes	36	12.11	even	2	inner
684.3.g.d.343.22	yes	36	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.671560 - 1.88388i) q^{2} +(-3.09801 + 2.53028i) q^{4} -4.54598 q^{5} -5.76325i q^{7} +(6.84725 + 4.13706i) q^{8} +O(q^{10})\)	\(q+(-0.671560 - 1.88388i) q^{2} +(-3.09801 + 2.53028i) q^{4} -4.54598 q^{5} -5.76325i q^{7} +(6.84725 + 4.13706i) q^{8} +(3.05290 + 8.56408i) q^{10} +10.1419i q^{11} -13.5653 q^{13} +(-10.8573 + 3.87037i) q^{14} +(3.19538 - 15.6777i) q^{16} +7.96492 q^{17} -4.35890i q^{19} +(14.0835 - 11.5026i) q^{20} +(19.1061 - 6.81087i) q^{22} +38.6743i q^{23} -4.33408 q^{25} +(9.10994 + 25.5555i) q^{26} +(14.5826 + 17.8546i) q^{28} +37.2619 q^{29} -14.8581i q^{31} +(-31.6808 + 4.50878i) q^{32} +(-5.34892 - 15.0050i) q^{34} +26.1996i q^{35} +6.53488 q^{37} +(-8.21165 + 2.92726i) q^{38} +(-31.1274 - 18.8070i) q^{40} +34.8954 q^{41} -40.2314i q^{43} +(-25.6617 - 31.4197i) q^{44} +(72.8578 - 25.9721i) q^{46} -50.1549i q^{47} +15.7849 q^{49} +(2.91059 + 8.16489i) q^{50} +(42.0256 - 34.3241i) q^{52} +31.9660 q^{53} -46.1047i q^{55} +(23.8429 - 39.4624i) q^{56} +(-25.0236 - 70.1970i) q^{58} -12.0203i q^{59} +108.607 q^{61} +(-27.9908 + 9.97807i) q^{62} +(29.7695 + 56.6549i) q^{64} +61.6677 q^{65} +67.6241i q^{67} +(-24.6754 + 20.1535i) q^{68} +(49.3570 - 17.5946i) q^{70} -17.9831i q^{71} +121.693 q^{73} +(-4.38857 - 12.3109i) q^{74} +(11.0292 + 13.5039i) q^{76} +58.4502 q^{77} -103.011i q^{79} +(-14.5261 + 71.2704i) q^{80} +(-23.4344 - 65.7388i) q^{82} +41.7786i q^{83} -36.2084 q^{85} +(-75.7911 + 27.0178i) q^{86} +(-41.9575 + 69.4439i) q^{88} -74.8835 q^{89} +78.1805i q^{91} +(-97.8568 - 119.814i) q^{92} +(-94.4859 + 33.6820i) q^{94} +19.8155i q^{95} +74.3694 q^{97} +(-10.6005 - 29.7369i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4}+O(q^{10}) \) 36 * q - 12 * q^4	\( 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) \) 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more