LMFDB - Embedded newform 684.3.g.d.343.18

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			343.18
Character	$\chi$	$=$	684.343
Dual form			684.3.g.d.343.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.363289 + 1.96673i) q^{2} +(-3.73604 - 1.42898i) q^{4} -0.0632854 q^{5} +2.71864i q^{7} +(4.16769 - 6.82864i) q^{8} +O(q^{10})$	\(q+(-0.363289 + 1.96673i) q^{2} +(-3.73604 - 1.42898i) q^{4} -0.0632854 q^{5} +2.71864i q^{7} +(4.16769 - 6.82864i) q^{8} +(0.0229909 - 0.124465i) q^{10} +1.99060i q^{11} +9.23116 q^{13} +(-5.34682 - 0.987652i) q^{14} +(11.9160 + 10.6775i) q^{16} -29.7896 q^{17} -4.35890i q^{19} +(0.236437 + 0.0904337i) q^{20} +(-3.91496 - 0.723162i) q^{22} +30.0752i q^{23} -24.9960 q^{25} +(-3.35358 + 18.1552i) q^{26} +(3.88489 - 10.1569i) q^{28} +1.04477 q^{29} -24.8831i q^{31} +(-25.3287 + 19.5565i) q^{32} +(10.8223 - 58.5881i) q^{34} -0.172050i q^{35} -22.4298 q^{37} +(8.57277 + 1.58354i) q^{38} +(-0.263754 + 0.432153i) q^{40} -32.4379 q^{41} -48.6063i q^{43} +(2.84453 - 7.43695i) q^{44} +(-59.1498 - 10.9260i) q^{46} +13.7195i q^{47} +41.6090 q^{49} +(9.08078 - 49.1603i) q^{50} +(-34.4880 - 13.1912i) q^{52} -87.2658 q^{53} -0.125976i q^{55} +(18.5646 + 11.3304i) q^{56} +(-0.379554 + 2.05478i) q^{58} -74.0260i q^{59} -31.9685 q^{61} +(48.9383 + 9.03977i) q^{62} +(-29.2608 - 56.9193i) q^{64} -0.584198 q^{65} -115.200i q^{67} +(111.295 + 42.5689i) q^{68} +(0.338376 + 0.0625039i) q^{70} +66.3216i q^{71} -74.8726 q^{73} +(8.14851 - 44.1133i) q^{74} +(-6.22879 + 16.2850i) q^{76} -5.41171 q^{77} -45.5922i q^{79} +(-0.754109 - 0.675728i) q^{80} +(11.7843 - 63.7965i) q^{82} -4.33233i q^{83} +1.88525 q^{85} +(95.5953 + 17.6581i) q^{86} +(13.5931 + 8.29618i) q^{88} -111.441 q^{89} +25.0962i q^{91} +(42.9770 - 112.362i) q^{92} +(-26.9826 - 4.98416i) q^{94} +0.275855i q^{95} -85.9678 q^{97} +(-15.1161 + 81.8336i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.363289	+	1.96673i	−0.181645	+	0.983364i
$2$	−0.363289	+	1.96673i	−0.181645	+	0.983364i
$3$		0			0
$3$		0			0
$4$	−3.73604	−	1.42898i	−0.934010	−	0.357246i
$5$	−0.0632854			−0.0126571			−0.00632854	−	0.999980i	$-0.502014\pi$
$5$	−0.0632854			−0.0126571			−0.00632854	+	0.999980i	$0.502014\pi$
$6$		0			0
$7$			2.71864i			0.388377i	0.980964	+	0.194188i	$0.0622073\pi$
$7$			2.71864i			0.388377i	−0.980964	+	0.194188i	$0.937793\pi$
$8$	4.16769	−	6.82864i	0.520961	−	0.853581i
$9$		0			0
$10$	0.0229909	−	0.124465i	0.00229909	−	0.0124465i
$11$			1.99060i			0.180963i	0.995898	+	0.0904816i	$0.0288406\pi$
$11$			1.99060i			0.180963i	−0.995898	+	0.0904816i	$0.971159\pi$
$12$		0			0
$13$	9.23116			0.710089			0.355045	−	0.934849i	$-0.384466\pi$
$13$	9.23116			0.710089			0.355045	+	0.934849i	$0.384466\pi$
$14$	−5.34682	−	0.987652i	−0.381916	−	0.0705466i
$15$		0			0
$16$	11.9160	+	10.6775i	0.744751	+	0.667343i
$17$	−29.7896			−1.75233			−0.876165	−	0.482011i	$-0.839906\pi$
$17$	−29.7896			−1.75233			−0.876165	+	0.482011i	$0.839906\pi$
$18$		0			0
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	0.236437	+	0.0904337i	0.0118218	+	0.00452169i
$21$		0			0
$22$	−3.91496	−	0.723162i	−0.177953	−	0.0328710i
$23$			30.0752i			1.30762i	0.756659	+	0.653809i	$0.226830\pi$
$23$			30.0752i			1.30762i	−0.756659	+	0.653809i	$0.773170\pi$
$24$		0			0
$25$	−24.9960			−0.999840
$26$	−3.35358	+	18.1552i	−0.128984	+	0.698277i
$27$		0			0
$28$	3.88489	−	10.1569i	0.138746	−	0.362748i
$29$	1.04477			0.0360266			0.0180133	−	0.999838i	$-0.494266\pi$
$29$	1.04477			0.0360266			0.0180133	+	0.999838i	$0.494266\pi$
$30$		0			0
$31$		−	24.8831i		−	0.802681i	−0.915929	−	0.401340i	$-0.868544\pi$
$31$		−	24.8831i		−	0.802681i	0.915929	−	0.401340i	$-0.131456\pi$
$32$	−25.3287	+	19.5565i	−0.791521	+	0.611142i
$33$		0			0
$34$	10.8223	−	58.5881i	0.318301	−	1.72318i
$35$		−	0.172050i		−	0.00491571i
$36$		0			0
$37$	−22.4298			−0.606211			−0.303105	−	0.952957i	$-0.598023\pi$
$37$	−22.4298			−0.606211			−0.303105	+	0.952957i	$0.598023\pi$
$38$	8.57277	+	1.58354i	0.225599	+	0.0416722i
$39$		0			0
$40$	−0.263754	+	0.432153i	−0.00659384	+	0.0108038i
$41$	−32.4379			−0.791167			−0.395584	−	0.918430i	$-0.629458\pi$
$41$	−32.4379			−0.791167			−0.395584	+	0.918430i	$0.629458\pi$
$42$		0			0
$43$		−	48.6063i		−	1.13038i	−0.824961	−	0.565189i	$-0.808803\pi$
$43$		−	48.6063i		−	1.13038i	0.824961	−	0.565189i	$-0.191197\pi$
$44$	2.84453	−	7.43695i	0.0646484	−	0.169022i
$45$		0			0
$46$	−59.1498	−	10.9260i	−1.28587	−	0.237522i
$47$			13.7195i			0.291905i	0.989292	+	0.145952i	$0.0466247\pi$
$47$			13.7195i			0.291905i	−0.989292	+	0.145952i	$0.953375\pi$
$48$		0			0
$49$	41.6090			0.849163
$50$	9.08078	−	49.1603i	0.181616	−	0.983207i
$51$		0			0
$52$	−34.4880	−	13.1912i	−0.663231	−	0.253676i
$53$	−87.2658			−1.64653			−0.823263	−	0.567661i	$-0.807849\pi$
$53$	−87.2658			−1.64653			−0.823263	+	0.567661i	$0.807849\pi$
$54$		0			0
$55$		−	0.125976i		−	0.00229047i
$56$	18.5646	+	11.3304i	0.331511	+	0.202329i
$57$		0			0
$58$	−0.379554	+	2.05478i	−0.00654404	+	0.0354273i
$59$		−	74.0260i		−	1.25468i	−0.778746	−	0.627339i	$-0.784144\pi$
$59$		−	74.0260i		−	1.25468i	0.778746	−	0.627339i	$-0.215856\pi$
$60$		0			0
$61$	−31.9685			−0.524073			−0.262037	−	0.965058i	$-0.584394\pi$
$61$	−31.9685			−0.524073			−0.262037	+	0.965058i	$0.584394\pi$
$62$	48.9383	+	9.03977i	0.789328	+	0.145803i
$63$		0			0
$64$	−29.2608	−	56.9193i	−0.457200	−	0.889364i
$65$	−0.584198			−0.00898765
$66$		0			0
$67$		−	115.200i		−	1.71940i	−0.510797	−	0.859701i	$-0.670650\pi$
$67$		−	115.200i		−	1.71940i	0.510797	−	0.859701i	$-0.329350\pi$
$68$	111.295	+	42.5689i	1.63669	+	0.626013i
$69$		0			0
$70$	0.338376	+	0.0625039i	0.00483394	+	0.000892913i
$71$			66.3216i			0.934107i	0.884229	+	0.467053i	$0.154684\pi$
$71$			66.3216i			0.934107i	−0.884229	+	0.467053i	$0.845316\pi$
$72$		0			0
$73$	−74.8726			−1.02565			−0.512826	−	0.858493i	$-0.671401\pi$
$73$	−74.8726			−1.02565			−0.512826	+	0.858493i	$0.671401\pi$
$74$	8.14851	−	44.1133i	0.110115	−	0.596126i
$75$		0			0
$76$	−6.22879	+	16.2850i	−0.0819578	+	0.214277i
$77$	−5.41171			−0.0702819
$78$		0			0
$79$		−	45.5922i		−	0.577116i	−0.957462	−	0.288558i	$-0.906824\pi$
$79$		−	45.5922i		−	0.577116i	0.957462	−	0.288558i	$-0.0931758\pi$
$80$	−0.754109	−	0.675728i	−0.00942637	−	0.00844660i
$81$		0			0
$82$	11.7843	−	63.7965i	0.143711	−	0.778006i
$83$		−	4.33233i		−	0.0521968i	−0.999659	−	0.0260984i	$-0.991692\pi$
$83$		−	4.33233i		−	0.0521968i	0.999659	−	0.0260984i	$-0.00830831\pi$
$84$		0			0
$85$	1.88525			0.0221794
$86$	95.5953	+	17.6581i	1.11157	+	0.205327i
$87$		0			0
$88$	13.5931	+	8.29618i	0.154467	+	0.0942748i
$89$	−111.441			−1.25215			−0.626076	−	0.779762i	$-0.715340\pi$
$89$	−111.441			−1.25215			−0.626076	+	0.779762i	$0.715340\pi$
$90$		0			0
$91$			25.0962i			0.275782i
$92$	42.9770	−	112.362i	0.467141	−	1.22133i
$93$		0			0
$94$	−26.9826	−	4.98416i	−0.287049	−	0.0530230i
$95$			0.275855i			0.00290373i
$96$		0			0
$97$	−85.9678			−0.886266			−0.443133	−	0.896456i	$-0.646133\pi$
$97$	−85.9678			−0.886266			−0.443133	+	0.896456i	$0.646133\pi$
$98$	−15.1161	+	81.8336i	−0.154246	+	0.835037i
$99$		0			0
$100$	93.3861	+	35.7189i	0.933861	+	0.357189i
$101$	−42.1501			−0.417327			−0.208664	−	0.977987i	$-0.566911\pi$
$101$	−42.1501			−0.417327			−0.208664	+	0.977987i	$0.566911\pi$
$102$		0			0
$103$			148.344i			1.44023i	0.693855	+	0.720115i	$0.255911\pi$
$103$			148.344i			1.44023i	−0.693855	+	0.720115i	$0.744089\pi$
$104$	38.4726	−	63.0363i	0.369929	−	0.606119i
$105$		0			0
$106$	31.7028	−	171.628i	0.299083	−	1.61913i
$107$		−	2.27701i		−	0.0212805i	−0.999943	−	0.0106403i	$-0.996613\pi$
$107$		−	2.27701i		−	0.0212805i	0.999943	−	0.0106403i	$-0.00338696\pi$
$108$		0			0
$109$	108.562			0.995982			0.497991	−	0.867182i	$-0.334071\pi$
$109$	108.562			0.995982			0.497991	+	0.867182i	$0.334071\pi$
$110$	0.247760	+	0.0457656i	0.00225236	+	0.000416051i
$111$		0			0
$112$	−29.0282	+	32.3953i	−0.259180	+	0.289244i
$113$	36.9953			0.327392			0.163696	−	0.986511i	$-0.447658\pi$
$113$	36.9953			0.327392			0.163696	+	0.986511i	$0.447658\pi$
$114$		0			0
$115$		−	1.90332i		−	0.0165506i
$116$	−3.90331	−	1.49296i	−0.0336492	−	0.0128704i
$117$		0			0
$118$	145.589	+	26.8929i	1.23381	+	0.227906i
$119$		−	80.9872i		−	0.680564i
$120$		0			0
$121$	117.038			0.967252
$122$	11.6138	−	62.8733i	0.0951951	−	0.515355i
$123$		0			0
$124$	−35.5575	+	92.9643i	−0.286754	+	0.749712i
$125$	3.16402			0.0253121
$126$		0			0
$127$		−	152.268i		−	1.19896i	−0.800389	−	0.599481i	$-0.795374\pi$
$127$		−	152.268i		−	1.19896i	0.800389	−	0.599481i	$-0.204626\pi$
$128$	122.575	−	36.8698i	0.957617	−	0.288046i
$129$		0			0
$130$	0.212233	−	1.14896i	0.00163256	−	0.00883814i
$131$			135.357i			1.03326i	0.856210	+	0.516628i	$0.172813\pi$
$131$			135.357i			1.03326i	−0.856210	+	0.516628i	$0.827187\pi$
$132$		0			0
$133$	11.8503			0.0890997
$134$	226.567	+	41.8509i	1.69080	+	0.312320i
$135$		0			0
$136$	−124.154	+	203.423i	−0.912895	+	1.49576i
$137$	4.70818			0.0343663			0.0171831	−	0.999852i	$-0.494530\pi$
$137$	4.70818			0.0343663			0.0171831	+	0.999852i	$0.494530\pi$
$138$		0			0
$139$			194.108i			1.39646i	0.715874	+	0.698230i	$0.246029\pi$
$139$			194.108i			1.39646i	−0.715874	+	0.698230i	$0.753971\pi$
$140$	−0.245857	+	0.642786i	−0.00175612	+	0.00459133i
$141$		0			0
$142$	−130.437	−	24.0939i	−0.918567	−	0.169676i
$143$			18.3755i			0.128500i
$144$		0			0
$145$	−0.0661188			−0.000455991
$146$	27.2004	−	147.254i	0.186304	−	1.00859i
$147$		0			0
$148$	83.7986	+	32.0518i	0.566207	+	0.216566i
$149$	−137.161			−0.920543			−0.460272	−	0.887778i	$-0.652248\pi$
$149$	−137.161			−0.920543			−0.460272	+	0.887778i	$0.652248\pi$
$150$		0			0
$151$		−	122.548i		−	0.811575i	−0.913968	−	0.405787i	$-0.866997\pi$
$151$		−	122.548i		−	0.811575i	0.913968	−	0.405787i	$-0.133003\pi$
$152$	−29.7654	−	18.1665i	−0.195825	−	0.119517i
$153$		0			0
$154$	1.96602	−	10.6434i	0.0127663	−	0.0691127i
$155$			1.57474i			0.0101596i
$156$		0			0
$157$	86.6984			0.552219			0.276110	−	0.961126i	$-0.410955\pi$
$157$	86.6984			0.552219			0.276110	+	0.961126i	$0.410955\pi$
$158$	89.6674	+	16.5632i	0.567515	+	0.104830i
$159$		0			0
$160$	1.60293	−	1.23764i	0.0100183	−	0.00773527i
$161$	−81.7637			−0.507849
$162$		0			0
$163$			175.883i			1.07904i	0.841974	+	0.539518i	$0.181394\pi$
$163$			175.883i			1.07904i	−0.841974	+	0.539518i	$0.818606\pi$
$164$	121.189	+	46.3532i	0.738959	+	0.282641i
$165$		0			0
$166$	8.52052	+	1.57389i	0.0513284	+	0.00948126i
$167$		−	249.396i		−	1.49339i	−0.665166	−	0.746695i	$-0.731639\pi$
$167$		−	249.396i		−	1.49339i	0.665166	−	0.746695i	$-0.268361\pi$
$168$		0			0
$169$	−83.7856			−0.495773
$170$	−0.684890	+	3.70777i	−0.00402877	+	0.0218104i
$171$		0			0
$172$	−69.4575	+	181.595i	−0.403823	+	1.05579i
$173$	−165.442			−0.956312			−0.478156	−	0.878275i	$-0.658695\pi$
$173$	−165.442			−0.956312			−0.478156	+	0.878275i	$0.658695\pi$
$174$		0			0
$175$		−	67.9551i		−	0.388315i
$176$	−21.2545	+	23.7200i	−0.120764	+	0.134773i
$177$		0			0
$178$	40.4855	−	219.175i	0.227447	−	1.23132i
$179$			129.412i			0.722972i	0.932378	+	0.361486i	$0.117730\pi$
$179$			129.412i			0.722972i	−0.932378	+	0.361486i	$0.882270\pi$
$180$		0			0
$181$	−14.1932			−0.0784155			−0.0392078	−	0.999231i	$-0.512483\pi$
$181$	−14.1932			−0.0784155			−0.0392078	+	0.999231i	$0.512483\pi$
$182$	−49.3574	−	9.11718i	−0.271194	−	0.0500944i
$183$		0			0
$184$	205.373	+	125.344i	1.11616	+	0.681218i
$185$	1.41948			0.00767285
$186$		0			0
$187$		−	59.2991i		−	0.317107i
$188$	19.6050	−	51.2567i	0.104282	−	0.272642i
$189$		0			0
$190$	−0.542531	−	0.100215i	−0.00285543	−	0.000527448i
$191$			212.476i			1.11244i	0.831035	+	0.556221i	$0.187749\pi$
$191$			212.476i			1.11244i	−0.831035	+	0.556221i	$0.812251\pi$
$192$		0			0
$193$	−143.244			−0.742196			−0.371098	−	0.928594i	$-0.621019\pi$
$193$	−143.244			−0.742196			−0.371098	+	0.928594i	$0.621019\pi$
$194$	31.2312	−	169.075i	0.160986	−	0.871523i
$195$		0			0
$196$	−155.453	−	59.4586i	−0.793128	−	0.303360i
$197$	−74.7401			−0.379391			−0.189696	−	0.981843i	$-0.560750\pi$
$197$	−74.7401			−0.379391			−0.189696	+	0.981843i	$0.560750\pi$
$198$		0			0
$199$			179.139i			0.900198i	0.892979	+	0.450099i	$0.148611\pi$
$199$			179.139i			0.900198i	−0.892979	+	0.450099i	$0.851389\pi$
$200$	−104.175	+	170.689i	−0.520877	+	0.853444i
$201$		0			0
$202$	15.3127	−	82.8978i	0.0758053	−	0.410385i
$203$			2.84036i			0.0139919i
$204$		0			0
$205$	2.05284			0.0100139
$206$	−291.752	−	53.8917i	−1.41627	−	0.261610i
$207$		0			0
$208$	109.999	+	98.5656i	0.528840	+	0.473873i
$209$	8.67681			0.0415158
$210$		0			0
$211$			331.712i			1.57210i	0.618165	+	0.786048i	$0.287876\pi$
$211$			331.712i			1.57210i	−0.618165	+	0.786048i	$0.712124\pi$
$212$	326.029	+	124.701i	1.53787	+	0.588214i
$213$		0			0
$214$	4.47827	+	0.827215i	0.0209265	+	0.00386549i
$215$			3.07607i			0.0143073i
$216$		0			0
$217$	67.6482			0.311743
$218$	−39.4394	+	213.512i	−0.180915	+	0.979413i
$219$		0			0
$220$	−0.180017	+	0.470650i	−0.000818259	+	0.00213932i
$221$	−274.993			−1.24431
$222$		0			0
$223$			55.0902i			0.247041i	0.992342	+	0.123521i	$0.0394185\pi$
$223$			55.0902i			0.247041i	−0.992342	+	0.123521i	$0.960582\pi$
$224$	−53.1672	−	68.8595i	−0.237353	−	0.307408i
$225$		0			0
$226$	−13.4400	+	72.7597i	−0.0594690	+	0.321945i
$227$			184.804i			0.814114i	0.913403	+	0.407057i	$0.133445\pi$
$227$			184.804i			0.814114i	−0.913403	+	0.407057i	$0.866555\pi$
$228$		0			0
$229$	−165.322			−0.721929			−0.360965	−	0.932580i	$-0.617552\pi$
$229$	−165.322			−0.721929			−0.360965	+	0.932580i	$0.617552\pi$
$230$	3.74332	+	0.691457i	0.0162753	+	0.00300633i
$231$		0			0
$232$	4.35428	−	7.13437i	0.0187685	−	0.0307516i
$233$	−369.798			−1.58711			−0.793557	−	0.608495i	$-0.791773\pi$
$233$	−369.798			−1.58711			−0.793557	+	0.608495i	$0.791773\pi$
$234$		0			0
$235$		−	0.868246i		−	0.00369466i
$236$	−105.782	+	276.564i	−0.448228	+	1.17188i
$237$		0			0
$238$	159.280	+	29.4218i	0.669243	+	0.123621i
$239$			143.070i			0.598618i	0.954156	+	0.299309i	$0.0967561\pi$
$239$			143.070i			0.598618i	−0.954156	+	0.299309i	$0.903244\pi$
$240$		0			0
$241$	291.493			1.20952			0.604758	−	0.796410i	$-0.293270\pi$
$241$	291.493			1.20952			0.604758	+	0.796410i	$0.293270\pi$
$242$	−42.5185	+	230.181i	−0.175696	+	0.951161i
$243$		0			0
$244$	119.435	+	45.6824i	0.489490	+	0.187223i
$245$	−2.63324			−0.0107479
$246$		0			0
$247$		−	40.2377i		−	0.162906i
$248$	−169.918	−	103.705i	−0.685153	−	0.418165i
$249$		0			0
$250$	−1.14945	+	6.22276i	−0.00459781	+	0.0248910i
$251$		−	226.901i		−	0.903988i	−0.892021	−	0.451994i	$-0.850713\pi$
$251$		−	226.901i		−	0.903988i	0.892021	−	0.451994i	$-0.149287\pi$
$252$		0			0
$253$	−59.8676			−0.236631
$254$	299.470	+	55.3175i	1.17902	+	0.217785i
$255$		0			0
$256$	27.9828	+	254.466i	0.109308	+	0.994008i
$257$	154.187			0.599951			0.299976	−	0.953947i	$-0.403021\pi$
$257$	154.187			0.599951			0.299976	+	0.953947i	$0.403021\pi$
$258$		0			0
$259$		−	60.9785i		−	0.235438i
$260$	2.18259	+	0.834808i	0.00839456	+	0.00321080i
$261$		0			0
$262$	−266.209	−	49.1736i	−1.01607	−	0.187685i
$263$		−	269.070i		−	1.02308i	−0.859259	−	0.511541i	$-0.829075\pi$
$263$		−	269.070i		−	1.02308i	0.859259	−	0.511541i	$-0.170925\pi$
$264$		0			0
$265$	5.52265			0.0208402
$266$	−4.30508	+	23.3063i	−0.0161845	+	0.0876175i
$267$		0			0
$268$	−164.619	+	430.392i	−0.614249	+	1.60594i
$269$	339.320			1.26141			0.630705	−	0.776022i	$-0.282766\pi$
$269$	339.320			1.26141			0.630705	+	0.776022i	$0.282766\pi$
$270$		0			0
$271$		−	68.9948i		−	0.254593i	−0.991865	−	0.127297i	$-0.959370\pi$
$271$		−	68.9948i		−	0.254593i	0.991865	−	0.127297i	$-0.0406300\pi$
$272$	−354.973	−	318.078i	−1.30505	−	1.16940i
$273$		0			0
$274$	−1.71043	+	9.25970i	−0.00624245	+	0.0337945i
$275$		−	49.7569i		−	0.180934i
$276$		0			0
$277$	266.506			0.962115			0.481057	−	0.876689i	$-0.340253\pi$
$277$	266.506			0.962115			0.481057	+	0.876689i	$0.340253\pi$
$278$	−381.757	−	70.5173i	−1.37323	−	0.253659i
$279$		0			0
$280$	−1.17487	−	0.717050i	−0.00419596	−	0.00256089i
$281$	50.2757			0.178917			0.0894586	−	0.995991i	$-0.471486\pi$
$281$	50.2757			0.178917			0.0894586	+	0.995991i	$0.471486\pi$
$282$		0			0
$283$			210.173i			0.742660i	0.928501	+	0.371330i	$0.121098\pi$
$283$			210.173i			0.742660i	−0.928501	+	0.371330i	$0.878902\pi$
$284$	94.7724	−	247.780i	0.333706	−	0.872465i
$285$		0			0
$286$	−36.1396	−	6.67563i	−0.126362	−	0.0233414i
$287$		−	88.1868i		−	0.307271i
$288$		0			0
$289$	598.421			2.07066
$290$	0.0240202	−	0.130038i	8.28284e−5	−	0.000448406i
$291$		0			0
$292$	279.727	+	106.992i	0.957969	+	0.366410i
$293$	234.497			0.800331			0.400165	−	0.916443i	$-0.368953\pi$
$293$	234.497			0.800331			0.400165	+	0.916443i	$0.368953\pi$
$294$		0			0
$295$			4.68476i			0.0158806i
$296$	−93.4803	+	153.165i	−0.315812	+	0.517450i
$297$		0			0
$298$	49.8291	−	269.758i	0.167212	−	0.905230i
$299$			277.629i			0.928526i
$300$		0			0
$301$	132.143			0.439013
$302$	241.018	+	44.5203i	0.798073	+	0.147418i
$303$		0			0
$304$	46.5421	−	51.9407i	0.153099	−	0.170858i
$305$	2.02314			0.00663323
$306$		0			0
$307$			392.515i			1.27855i	0.768978	+	0.639276i	$0.220766\pi$
$307$			392.515i			1.27855i	−0.768978	+	0.639276i	$0.779234\pi$
$308$	20.2184	+	7.73324i	0.0656441	+	0.0251079i
$309$		0			0
$310$	−3.09708	−	0.572085i	−0.00999058	−	0.00184544i
$311$			63.0913i			0.202866i	0.994842	+	0.101433i	$0.0323428\pi$
$311$			63.0913i			0.202866i	−0.994842	+	0.101433i	$0.967657\pi$
$312$		0			0
$313$	−371.447			−1.18673			−0.593366	−	0.804933i	$-0.702201\pi$
$313$	−371.447			−1.18673			−0.593366	+	0.804933i	$0.702201\pi$
$314$	−31.4966	+	170.512i	−0.100308	+	0.543033i
$315$		0			0
$316$	−65.1504	+	170.334i	−0.206172	+	0.539032i
$317$	377.070			1.18949			0.594747	−	0.803913i	$-0.297252\pi$
$317$	377.070			1.18949			0.594747	+	0.803913i	$0.297252\pi$
$318$		0			0
$319$			2.07972i			0.00651949i
$320$	1.85178	+	3.60216i	0.00578681	+	0.0112567i
$321$		0			0
$322$	29.7039	−	160.807i	0.0922480	−	0.499400i
$323$			129.850i			0.402012i
$324$		0			0
$325$	−230.742			−0.709976
$326$	−345.914	−	63.8964i	−1.06109	−	0.196001i
$327$		0			0
$328$	−135.191	+	221.507i	−0.412167	+	0.675325i
$329$	−37.2984			−0.113369
$330$		0			0
$331$		−	135.863i		−	0.410464i	−0.978713	−	0.205232i	$-0.934205\pi$
$331$		−	135.863i		−	0.410464i	0.978713	−	0.205232i	$-0.0657948\pi$
$332$	−6.19083	+	16.1858i	−0.0186471	+	0.0487523i
$333$		0			0
$334$	490.495	+	90.6030i	1.46855	+	0.271267i
$335$			7.29047i			0.0217626i
$336$		0			0
$337$	−550.252			−1.63280			−0.816398	−	0.577489i	$-0.804032\pi$
$337$	−550.252			−1.63280			−0.816398	+	0.577489i	$0.804032\pi$
$338$	30.4384	−	164.784i	0.0900545	−	0.487525i
$339$		0			0
$340$	−7.04336	−	2.69399i	−0.0207158	−	0.00792349i
$341$	49.5322			0.145256
$342$		0			0
$343$			246.333i			0.718172i
$344$	−331.915	−	202.576i	−0.964869	−	0.588883i
$345$		0			0
$346$	60.1033	−	325.379i	0.173709	−	0.940403i
$347$		−	80.2125i		−	0.231160i	−0.993298	−	0.115580i	$-0.963127\pi$
$347$		−	80.2125i		−	0.231160i	0.993298	−	0.115580i	$-0.0368726\pi$
$348$		0			0
$349$	−52.3572			−0.150021			−0.0750103	−	0.997183i	$-0.523899\pi$
$349$	−52.3572			−0.150021			−0.0750103	+	0.997183i	$0.523899\pi$
$350$	133.649	+	24.6873i	0.381855	+	0.0705353i
$351$		0			0
$352$	−38.9292	−	50.4191i	−0.110594	−	0.143236i
$353$	136.426			0.386475			0.193238	−	0.981152i	$-0.438101\pi$
$353$	136.426			0.386475			0.193238	+	0.981152i	$0.438101\pi$
$354$		0			0
$355$		−	4.19719i		−	0.0118231i
$356$	416.350	+	159.248i	1.16952	+	0.447326i
$357$		0			0
$358$	−254.518	−	47.0140i	−0.710944	−	0.131324i
$359$		−	255.590i		−	0.711950i	−0.934495	−	0.355975i	$-0.884149\pi$
$359$		−	255.590i		−	0.711950i	0.934495	−	0.355975i	$-0.115851\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	5.15624	−	27.9142i	0.0142438	−	0.0771110i
$363$		0			0
$364$	35.8620	−	93.7604i	0.0985221	−	0.257584i
$365$	4.73834			0.0129818
$366$		0			0
$367$		−	343.963i		−	0.937229i	−0.883403	−	0.468614i	$-0.844753\pi$
$367$		−	343.963i		−	0.937229i	0.883403	−	0.468614i	$-0.155247\pi$
$368$	−321.128	+	358.377i	−0.872630	+	0.973850i
$369$		0			0
$370$	−0.515681	+	2.79173i	−0.00139373	+	0.00754521i
$371$		−	237.244i		−	0.639472i
$372$		0			0
$373$	372.646			0.999052			0.499526	−	0.866299i	$-0.333508\pi$
$373$	372.646			0.999052			0.499526	+	0.866299i	$0.333508\pi$
$374$	116.625	+	21.5427i	0.311832	+	0.0576009i
$375$		0			0
$376$	93.6858	+	57.1787i	0.249164	+	0.152071i
$377$	9.64446			0.0255821
$378$		0			0
$379$			176.690i			0.466200i	0.972453	+	0.233100i	$0.0748869\pi$
$379$			176.690i			0.466200i	−0.972453	+	0.233100i	$0.925113\pi$
$380$	0.394191	−	1.03060i	0.00103735	−	0.00271212i
$381$		0			0
$382$	−417.883	−	77.1904i	−1.09393	−	0.202069i
$383$			100.064i			0.261263i	0.991431	+	0.130632i	$0.0417005\pi$
$383$			100.064i			0.261263i	−0.991431	+	0.130632i	$0.958300\pi$
$384$		0			0
$385$	0.342482			0.000889564
$386$	52.0390	−	281.722i	0.134816	−	0.729849i
$387$		0			0
$388$	321.179	+	122.847i	0.827782	+	0.316615i
$389$	603.829			1.55226			0.776130	−	0.630573i	$-0.217180\pi$
$389$	603.829			1.55226			0.776130	+	0.630573i	$0.217180\pi$
$390$		0			0
$391$		−	895.930i		−	2.29138i
$392$	173.413	−	284.133i	0.442381	−	0.724829i
$393$		0			0
$394$	27.1523	−	146.994i	0.0689145	−	0.373080i
$395$			2.88532i			0.00730460i
$396$		0			0
$397$	−341.215			−0.859483			−0.429741	−	0.902952i	$-0.641395\pi$
$397$	−341.215			−0.859483			−0.429741	+	0.902952i	$0.641395\pi$
$398$	−352.319	−	65.0794i	−0.885222	−	0.163516i
$399$		0			0
$400$	−297.853	−	266.894i	−0.744632	−	0.667236i
$401$	148.873			0.371254			0.185627	−	0.982620i	$-0.440568\pi$
$401$	148.873			0.371254			0.185627	+	0.982620i	$0.440568\pi$
$402$		0			0
$403$		−	229.700i		−	0.569975i
$404$	157.474	+	60.2317i	0.389788	+	0.149088i
$405$		0			0
$406$	−5.58621	−	1.03187i	−0.0137591	−	0.00254155i
$407$		−	44.6487i		−	0.109702i
$408$		0			0
$409$	165.435			0.404488			0.202244	−	0.979335i	$-0.435177\pi$
$409$	165.435			0.404488			0.202244	+	0.979335i	$0.435177\pi$
$410$	−0.745776	+	4.03738i	−0.00181897	+	0.00984728i
$411$		0			0
$412$	211.981	−	554.218i	0.514516	−	1.34519i
$413$	201.250			0.487288
$414$		0			0
$415$			0.274173i			0.000660658i
$416$	−233.813	+	180.530i	−0.562051	+	0.433966i
$417$		0			0
$418$	−3.15219	+	17.0649i	−0.00754113	+	0.0408252i
$419$		−	378.263i		−	0.902777i	−0.892328	−	0.451388i	$-0.850929\pi$
$419$		−	378.263i		−	0.902777i	0.892328	−	0.451388i	$-0.149071\pi$
$420$		0			0
$421$	−396.081			−0.940809			−0.470405	−	0.882451i	$-0.655892\pi$
$421$	−396.081			−0.940809			−0.470405	+	0.882451i	$0.655892\pi$
$422$	−652.388	−	120.508i	−1.54594	−	0.285563i
$423$		0			0
$424$	−363.697	+	595.907i	−0.857775	+	1.40544i
$425$	744.621			1.75205
$426$		0			0
$427$		−	86.9106i		−	0.203538i
$428$	−3.25381	+	8.50702i	−0.00760237	+	0.0198762i
$429$		0			0
$430$	−6.04979	−	1.11750i	−0.0140693	−	0.00259884i
$431$			698.348i			1.62030i	0.586225	+	0.810148i	$0.300614\pi$
$431$			698.348i			1.62030i	−0.586225	+	0.810148i	$0.699386\pi$
$432$		0			0
$433$	341.342			0.788318			0.394159	−	0.919042i	$-0.371036\pi$
$433$	341.342			0.788318			0.394159	+	0.919042i	$0.371036\pi$
$434$	−24.5759	+	133.046i	−0.0566264	+	0.306557i
$435$		0			0
$436$	−405.592	−	155.133i	−0.930258	−	0.355810i
$437$	131.095			0.299988
$438$		0			0
$439$		−	321.016i		−	0.731243i	−0.930764	−	0.365621i	$-0.880857\pi$
$439$		−	321.016i		−	0.731243i	0.930764	−	0.365621i	$-0.119143\pi$
$440$	−0.860243	−	0.525027i	−0.00195510	−	0.00119324i
$441$		0			0
$442$	99.9020	−	540.836i	0.226023	−	1.22361i
$443$		−	601.474i		−	1.35773i	−0.734263	−	0.678865i	$-0.762472\pi$
$443$		−	601.474i		−	1.35773i	0.734263	−	0.678865i	$-0.237528\pi$
$444$		0			0
$445$	7.05262			0.0158486
$446$	−108.347	−	20.0137i	−0.242931	−	0.0448737i
$447$		0			0
$448$	154.743	−	79.5495i	0.345408	−	0.177566i
$449$	657.045			1.46335			0.731676	−	0.681653i	$-0.238739\pi$
$449$	657.045			1.46335			0.731676	+	0.681653i	$0.238739\pi$
$450$		0			0
$451$		−	64.5707i		−	0.143172i
$452$	−138.216	−	52.8656i	−0.305787	−	0.116959i
$453$		0			0
$454$	−363.459	−	67.1373i	−0.800570	−	0.147879i
$455$		−	1.58822i		−	0.00349060i
$456$		0			0
$457$	−316.152			−0.691799			−0.345900	−	0.938272i	$-0.612426\pi$
$457$	−316.152			−0.691799			−0.345900	+	0.938272i	$0.612426\pi$
$458$	60.0596	−	325.143i	0.131135	−	0.709919i
$459$		0			0
$460$	−2.71982	+	7.11089i	−0.00591264	+	0.0154585i
$461$	589.434			1.27860			0.639300	−	0.768958i	$-0.279224\pi$
$461$	589.434			1.27860			0.639300	+	0.768958i	$0.279224\pi$
$462$		0			0
$463$		−	829.616i		−	1.79183i	−0.444229	−	0.895913i	$-0.646522\pi$
$463$		−	829.616i		−	1.79183i	0.444229	−	0.895913i	$-0.353478\pi$
$464$	12.4495	+	11.1555i	0.0268308	+	0.0240421i
$465$		0			0
$466$	134.344	−	727.292i	0.288291	−	1.56071i
$467$			158.171i			0.338696i	0.985556	+	0.169348i	$0.0541661\pi$
$467$			158.171i			0.338696i	−0.985556	+	0.169348i	$0.945834\pi$
$468$		0			0
$469$	313.187			0.667776
$470$	1.70760	+	0.315424i	0.00363320	+	0.000671116i
$471$		0			0
$472$	−505.497	−	308.517i	−1.07097	−	0.653638i
$473$	96.7554			0.204557
$474$		0			0
$475$			108.955i			0.229379i
$476$	−115.729	+	302.571i	−0.243129	+	0.635654i
$477$		0			0
$478$	−281.379	−	51.9757i	−0.588660	−	0.108736i
$479$		−	839.998i		−	1.75365i	−0.480810	−	0.876825i	$-0.659658\pi$
$479$		−	839.998i		−	1.75365i	0.480810	−	0.876825i	$-0.340342\pi$
$480$		0			0
$481$	−207.053			−0.430464
$482$	−105.896	+	573.288i	−0.219702	+	1.18939i
$483$		0			0
$484$	−437.257	−	167.245i	−0.903424	−	0.345547i
$485$	5.44051			0.0112175
$486$		0			0
$487$			104.862i			0.215323i	0.994188	+	0.107662i	$0.0343363\pi$
$487$			104.862i			0.215323i	−0.994188	+	0.107662i	$0.965664\pi$
$488$	−133.234	+	218.301i	−0.273021	+	0.447339i
$489$		0			0
$490$	0.956629	−	5.17887i	0.00195230	−	0.0105691i
$491$		−	952.418i		−	1.93975i	−0.243601	−	0.969875i	$-0.578329\pi$
$491$		−	952.418i		−	1.93975i	0.243601	−	0.969875i	$-0.421671\pi$
$492$		0			0
$493$	−31.1233			−0.0631305
$494$	79.1366	+	14.6179i	0.160196	+	0.0295910i
$495$		0			0
$496$	265.689	−	296.507i	0.535663	−	0.597797i
$497$	−180.304			−0.362785
$498$		0			0
$499$			250.159i			0.501321i	0.968075	+	0.250660i	$0.0806477\pi$
$499$			250.159i			0.501321i	−0.968075	+	0.250660i	$0.919352\pi$
$500$	−11.8209	−	4.52132i	−0.0236418	−	0.00904265i
$501$		0			0
$502$	446.253	+	82.4308i	0.888950	+	0.164205i
$503$			594.460i			1.18183i	0.806734	+	0.590915i	$0.201233\pi$
$503$			594.460i			1.18183i	−0.806734	+	0.590915i	$0.798767\pi$
$504$		0			0
$505$	2.66748			0.00528214
$506$	21.7493	−	117.743i	0.0429828	−	0.232694i
$507$		0			0
$508$	−217.589	+	568.881i	−0.428324	+	1.11984i
$509$	−478.859			−0.940783			−0.470392	−	0.882458i	$-0.655887\pi$
$509$	−478.859			−0.940783			−0.470392	+	0.882458i	$0.655887\pi$
$510$		0			0
$511$		−	203.551i		−	0.398339i
$512$	−510.631	−	37.4103i	−0.997327	−	0.0730669i
$513$		0			0
$514$	−56.0147	+	303.245i	−0.108978	+	0.589970i
$515$		−	9.38799i		−	0.0182291i
$516$		0			0
$517$	−27.3100			−0.0528241
$518$	119.928	+	22.1528i	0.231521	+	0.0427661i
$519$		0			0
$520$	−2.43475	+	3.98928i	−0.00468222	+	0.00767169i
$521$	525.429			1.00850			0.504250	−	0.863558i	$-0.331769\pi$
$521$	525.429			1.00850			0.504250	+	0.863558i	$0.331769\pi$
$522$		0			0
$523$			670.468i			1.28197i	0.767555	+	0.640983i	$0.221473\pi$
$523$			670.468i			1.28197i	−0.767555	+	0.640983i	$0.778527\pi$
$524$	193.422	−	505.698i	0.369126	−	0.965072i
$525$		0			0
$526$	529.188	+	97.7504i	1.00606	+	0.185837i
$527$			741.258i			1.40656i
$528$		0			0
$529$	−375.520			−0.709867
$530$	−2.00632	+	10.8616i	−0.00378551	+	0.0204935i
$531$		0			0
$532$	−44.2731	−	16.9338i	−0.0832201	−	0.0318305i
$533$	−299.439			−0.561800
$534$		0			0
$535$			0.144102i			0.000269349i
$536$	−786.660	−	480.117i	−1.46765	−	0.895741i
$537$		0			0
$538$	−123.271	+	667.349i	−0.229129	+	1.24043i
$539$			82.8267i			0.153667i
$540$		0			0
$541$	−492.916			−0.911120			−0.455560	−	0.890205i	$-0.650561\pi$
$541$	−492.916			−0.911120			−0.455560	+	0.890205i	$0.650561\pi$
$542$	135.694	+	25.0651i	0.250358	+	0.0462455i
$543$		0			0
$544$	754.531	−	582.582i	1.38701	−	1.07092i
$545$	−6.87039			−0.0126062
$546$		0			0
$547$		−	645.262i		−	1.17964i	−0.807535	−	0.589819i	$-0.799199\pi$
$547$		−	645.262i		−	1.17964i	0.807535	−	0.589819i	$-0.200801\pi$
$548$	−17.5899	−	6.72790i	−0.0320984	−	0.0122772i
$549$		0			0
$550$	97.8584	+	18.0762i	0.177924	+	0.0328658i
$551$		−	4.55405i		−	0.00826507i
$552$		0			0
$553$	123.949			0.224138
$554$	−96.8187	+	524.145i	−0.174763	+	0.946109i
$555$		0			0
$556$	277.377	−	725.195i	0.498879	−	1.30431i
$557$	−297.545			−0.534192			−0.267096	−	0.963670i	$-0.586064\pi$
$557$	−297.545			−0.534192			−0.267096	+	0.963670i	$0.586064\pi$
$558$		0			0
$559$		−	448.692i		−	0.802670i
$560$	1.83706	−	2.05015i	0.00328047	−	0.00366098i
$561$		0			0
$562$	−18.2646	+	98.8787i	−0.0324994	+	0.175941i
$563$			203.763i			0.361923i	0.983490	+	0.180962i	$0.0579210\pi$
$563$			203.763i			0.361923i	−0.983490	+	0.180962i	$0.942079\pi$
$564$		0			0
$565$	−2.34126			−0.00414382
$566$	−413.353	−	76.3536i	−0.730306	−	0.134900i
$567$		0			0
$568$	452.887	+	276.408i	0.797335	+	0.486633i
$569$	353.758			0.621719			0.310860	−	0.950456i	$-0.399383\pi$
$569$	353.758			0.621719			0.310860	+	0.950456i	$0.399383\pi$
$570$		0			0
$571$			264.495i			0.463214i	0.972809	+	0.231607i	$0.0743983\pi$
$571$			264.495i			0.463214i	−0.972809	+	0.231607i	$0.925602\pi$
$572$	26.2583	−	68.6517i	0.0459061	−	0.120020i
$573$		0			0
$574$	173.439	+	32.0373i	0.302159	+	0.0558142i
$575$		−	751.760i		−	1.30741i
$576$		0			0
$577$	−156.735			−0.271638			−0.135819	−	0.990734i	$-0.543367\pi$
$577$	−156.735			−0.271638			−0.135819	+	0.990734i	$0.543367\pi$
$578$	−217.400	+	1176.93i	−0.376125	+	2.03621i
$579$		0			0
$580$	0.247022	+	0.0944826i	0.000425901	+	0.000162901i
$581$	11.7780			0.0202720
$582$		0			0
$583$		−	173.711i		−	0.297961i
$584$	−312.045	+	511.278i	−0.534324	+	0.875476i
$585$		0			0
$586$	−85.1902	+	461.192i	−0.145376	+	0.787017i
$587$			965.700i			1.64514i	0.568661	+	0.822572i	$0.307462\pi$
$587$			965.700i			1.64514i	−0.568661	+	0.822572i	$0.692538\pi$
$588$		0			0
$589$	−108.463			−0.184148
$590$	−9.21366	−	1.70192i	−0.0156164	−	0.00288462i
$591$		0			0
$592$	−267.274	−	239.494i	−0.451476	−	0.404550i
$593$	−1168.73			−1.97088			−0.985439	−	0.170030i	$-0.945613\pi$
$593$	−1168.73			−1.97088			−0.985439	+	0.170030i	$0.945613\pi$
$594$		0			0
$595$			5.12530i			0.00861395i
$596$	512.439	+	196.001i	0.859797	+	0.328860i
$597$		0			0
$598$	−546.022	−	100.860i	−0.913080	−	0.168662i
$599$			752.786i			1.25674i	0.777916	+	0.628369i	$0.216277\pi$
$599$			752.786i			1.25674i	−0.777916	+	0.628369i	$0.783723\pi$
$600$		0			0
$601$	195.372			0.325079			0.162539	−	0.986702i	$-0.448032\pi$
$601$	195.372			0.325079			0.162539	+	0.986702i	$0.448032\pi$
$602$	−48.0061	+	259.889i	−0.0797443	+	0.431709i
$603$		0			0
$604$	−175.119	+	457.844i	−0.289932	+	0.758019i
$605$	−7.40676			−0.0122426
$606$		0			0
$607$			427.293i			0.703942i	0.936011	+	0.351971i	$0.114488\pi$
$607$			427.293i			0.703942i	−0.936011	+	0.351971i	$0.885512\pi$
$608$	85.2450	+	110.405i	0.140206	+	0.181587i
$609$		0			0
$610$	−0.734984	+	3.97896i	−0.00120489	+	0.00652288i
$611$			126.647i			0.207279i
$612$		0			0
$613$	796.278			1.29899			0.649493	−	0.760368i	$-0.274981\pi$
$613$	796.278			1.29899			0.649493	+	0.760368i	$0.274981\pi$
$614$	−771.971	−	142.597i	−1.25728	−	0.232242i
$615$		0			0
$616$	−22.5543	+	36.9546i	−0.0366141	+	0.0599913i
$617$	−207.993			−0.337104			−0.168552	−	0.985693i	$-0.553909\pi$
$617$	−207.993			−0.337104			−0.168552	+	0.985693i	$0.553909\pi$
$618$		0			0
$619$		−	151.796i		−	0.245228i	−0.992454	−	0.122614i	$-0.960872\pi$
$619$		−	151.796i		−	0.245228i	0.992454	−	0.122614i	$-0.0391277\pi$
$620$	2.25027	−	5.88328i	0.00362947	−	0.00948916i
$621$		0			0
$622$	−124.084	−	22.9204i	−0.199491	−	0.0368495i
$623$		−	302.969i		−	0.486307i
$624$		0			0
$625$	624.700			0.999519
$626$	134.943	−	730.536i	0.215564	−	1.16699i
$627$		0			0
$628$	−323.909	−	123.891i	−0.515778	−	0.197278i
$629$	668.175			1.06228
$630$		0			0
$631$		−	292.141i		−	0.462981i	−0.972837	−	0.231490i	$-0.925640\pi$
$631$		−	292.141i		−	0.462981i	0.972837	−	0.231490i	$-0.0743602\pi$
$632$	−311.333	−	190.014i	−0.492615	−	0.300655i
$633$		0			0
$634$	−136.985	+	741.593i	−0.216065	+	1.16971i
$635$			9.63635i			0.0151754i
$636$		0			0
$637$	384.100			0.602982
$638$	−4.09024	−	0.755540i	−0.00641104	−	0.00118423i
$639$		0			0
$640$	−7.75720	+	2.33332i	−0.0121206	+	0.00364581i
$641$	694.545			1.08353			0.541766	−	0.840529i	$-0.317756\pi$
$641$	694.545			1.08353			0.541766	+	0.840529i	$0.317756\pi$
$642$		0			0
$643$			1141.93i			1.77593i	0.459907	+	0.887967i	$0.347883\pi$
$643$			1141.93i			1.77593i	−0.459907	+	0.887967i	$0.652117\pi$
$644$	305.472	+	116.839i	0.474336	+	0.181427i
$645$		0			0
$646$	−255.380	−	47.1731i	−0.395324	−	0.0730234i
$647$		−	391.067i		−	0.604431i	−0.953240	−	0.302216i	$-0.902274\pi$
$647$		−	391.067i		−	0.604431i	0.953240	−	0.302216i	$-0.0977262\pi$
$648$		0			0
$649$	147.356			0.227051
$650$	83.8262	−	453.807i	0.128963	−	0.698165i
$651$		0			0
$652$	251.334	−	657.106i	0.385481	−	1.00783i
$653$	−607.536			−0.930376			−0.465188	−	0.885212i	$-0.654013\pi$
$653$	−607.536			−0.930376			−0.465188	+	0.885212i	$0.654013\pi$
$654$		0			0
$655$		−	8.56609i		−	0.0130780i
$656$	−386.530	−	346.355i	−0.589223	−	0.527980i
$657$		0			0
$658$	13.5501	−	73.3559i	0.0205929	−	0.111483i
$659$		−	100.926i		−	0.153150i	−0.997064	−	0.0765748i	$-0.975602\pi$
$659$		−	100.926i		−	0.153150i	0.997064	−	0.0765748i	$-0.0243984\pi$
$660$		0			0
$661$	−1219.43			−1.84483			−0.922413	−	0.386205i	$-0.873786\pi$
$661$	−1219.43			−1.84483			−0.922413	+	0.386205i	$0.873786\pi$
$662$	267.207	+	49.3578i	0.403635	+	0.0745586i
$663$		0			0
$664$	−29.5839	−	18.0558i	−0.0445541	−	0.0271925i
$665$	−0.749948			−0.00112774
$666$		0			0
$667$			31.4218i			0.0471091i
$668$	−356.383	+	931.755i	−0.533508	+	1.39484i
$669$		0			0
$670$	−14.3384	−	2.64855i	−0.0214006	−	0.00395306i
$671$		−	63.6363i		−	0.0948380i
$672$		0			0
$673$	841.408			1.25023			0.625117	−	0.780531i	$-0.285051\pi$
$673$	841.408			1.25023			0.625117	+	0.780531i	$0.285051\pi$
$674$	199.901	−	1082.20i	0.296589	−	1.60563i
$675$		0			0
$676$	313.027	+	119.728i	0.463057	+	0.177113i
$677$	−670.971			−0.991094			−0.495547	−	0.868581i	$-0.665032\pi$
$677$	−670.971			−0.991094			−0.495547	+	0.868581i	$0.665032\pi$
$678$		0			0
$679$		−	233.715i		−	0.344205i
$680$	7.85712	−	12.8737i	0.0115546	−	0.0189319i
$681$		0			0
$682$	−17.9945	+	97.4164i	−0.0263849	+	0.142839i
$683$			388.572i			0.568919i	0.958688	+	0.284459i	$0.0918141\pi$
$683$			388.572i			0.568919i	−0.958688	+	0.284459i	$0.908186\pi$
$684$		0			0
$685$	−0.297959			−0.000434976
$686$	−484.470	−	89.4902i	−0.706225	−	0.130452i
$687$		0			0
$688$	518.992	−	579.193i	0.754350	−	0.841850i
$689$	−805.565			−1.16918
$690$		0			0
$691$			972.178i			1.40691i	0.710737	+	0.703457i	$0.248361\pi$
$691$			972.178i			1.40691i	−0.710737	+	0.703457i	$0.751639\pi$
$692$	618.098	+	236.414i	0.893205	+	0.341638i
$693$		0			0
$694$	157.756	+	29.1403i	0.227314	+	0.0419890i
$695$		−	12.2842i		−	0.0176751i
$696$		0			0
$697$	966.311			1.38639
$698$	19.0208	−	102.972i	0.0272505	−	0.147525i
$699$		0			0
$700$	−97.1066	+	253.883i	−0.138724	+	0.362690i
$701$	−25.0862			−0.0357864			−0.0178932	−	0.999840i	$-0.505696\pi$
$701$	−25.0862			−0.0357864			−0.0178932	+	0.999840i	$0.505696\pi$
$702$		0			0
$703$			97.7692i			0.139074i
$704$	113.303	−	58.2464i	0.160942	−	0.0827364i
$705$		0			0
$706$	−49.5620	+	268.312i	−0.0702012	+	0.380046i
$707$		−	114.591i		−	0.162080i
$708$		0			0
$709$	−1114.25			−1.57157			−0.785787	−	0.618497i	$-0.787742\pi$
$709$	−1114.25			−1.57157			−0.785787	+	0.618497i	$0.787742\pi$
$710$	8.25472	+	1.52479i	0.0116264	+	0.00214760i
$711$		0			0
$712$	−464.453	+	760.994i	−0.652322	+	1.06881i
$713$	748.365			1.04960
$714$		0			0
$715$		−	1.16290i		−	0.00162644i
$716$	184.927	−	483.488i	0.258279	−	0.675263i
$717$		0			0
$718$	502.676	+	92.8532i	0.700106	+	0.129322i
$719$		−	1095.84i		−	1.52412i	−0.647508	−	0.762059i	$-0.724189\pi$
$719$		−	1095.84i		−	1.52412i	0.647508	−	0.762059i	$-0.275811\pi$
$720$		0			0
$721$	−403.293			−0.559352
$722$	6.90250	−	37.3678i	0.00956025	−	0.0517560i
$723$		0			0
$724$	53.0264	+	20.2819i	0.0732409	+	0.0280136i
$725$	−26.1151			−0.0360208
$726$		0			0
$727$		−	401.895i		−	0.552813i	−0.961041	−	0.276406i	$-0.910856\pi$
$727$		−	401.895i		−	0.552813i	0.961041	−	0.276406i	$-0.0891436\pi$
$728$	171.373	+	104.593i	0.235402	+	0.143672i
$729$		0			0
$730$	−1.72139	+	9.31903i	−0.00235807	+	0.0127658i
$731$			1447.96i			1.98080i
$732$		0			0
$733$	1307.63			1.78394			0.891970	−	0.452095i	$-0.149323\pi$
$733$	1307.63			1.78394			0.891970	+	0.452095i	$0.149323\pi$
$734$	676.482	+	124.958i	0.921637	+	0.170243i
$735$		0			0
$736$	−588.168	−	761.766i	−0.799141	−	1.03501i
$737$	229.317			0.311149
$738$		0			0
$739$			522.565i			0.707124i	0.935411	+	0.353562i	$0.115030\pi$
$739$			522.565i			0.707124i	−0.935411	+	0.353562i	$0.884970\pi$
$740$	−5.30323	−	2.02841i	−0.00716652	−	0.00274109i
$741$		0			0
$742$	466.595	+	86.1883i	0.628834	+	0.116157i
$743$			643.627i			0.866254i	0.901333	+	0.433127i	$0.142590\pi$
$743$			643.627i			0.866254i	−0.901333	+	0.433127i	$0.857410\pi$
$744$		0			0
$745$	8.68028			0.0116514
$746$	−135.378	+	732.894i	−0.181472	+	0.982432i
$747$		0			0
$748$	−84.7374	+	221.544i	−0.113285	+	0.296182i
$749$	6.19038			0.00826485
$750$		0			0
$751$		−	535.312i		−	0.712799i	−0.934334	−	0.356399i	$-0.884004\pi$
$751$		−	535.312i		−	0.712799i	0.934334	−	0.356399i	$-0.115996\pi$
$752$	−146.490	+	163.482i	−0.194801	+	0.217396i
$753$		0			0
$754$	−3.50373	+	18.9680i	−0.00464686	+	0.0251565i
$755$			7.75548i			0.0102722i
$756$		0			0
$757$	−1353.70			−1.78824			−0.894121	−	0.447825i	$-0.852199\pi$
$757$	−1353.70			−1.78824			−0.894121	+	0.447825i	$0.852199\pi$
$758$	−347.501	−	64.1895i	−0.458444	−	0.0846827i
$759$		0			0
$760$	1.88371	+	1.14968i	0.00247857	+	0.00151273i
$761$	−455.749			−0.598881			−0.299441	−	0.954115i	$-0.596800\pi$
$761$	−455.749			−0.598881			−0.299441	+	0.954115i	$0.596800\pi$
$762$		0			0
$763$			295.141i			0.386816i
$764$	303.625	−	793.820i	0.397415	−	1.03903i
$765$		0			0
$766$	−196.798	−	36.3521i	−0.256917	−	0.0474571i
$767$		−	683.346i		−	0.890934i
$768$		0			0
$769$	−906.083			−1.17826			−0.589131	−	0.808038i	$-0.700530\pi$
$769$	−906.083			−1.17826			−0.589131	+	0.808038i	$0.700530\pi$
$770$	−0.124420	+	0.673569i	−0.000161585	+	0.000874765i
$771$		0			0
$772$	535.165	+	204.693i	0.693219	+	0.265146i
$773$	215.658			0.278989			0.139494	−	0.990223i	$-0.455452\pi$
$773$	215.658			0.278989			0.139494	+	0.990223i	$0.455452\pi$
$774$		0			0
$775$			621.978i			0.802552i
$776$	−358.287	+	587.044i	−0.461710	+	0.756500i
$777$		0			0
$778$	−219.365	+	1187.57i	−0.281960	+	1.52644i
$779$			141.393i			0.181506i
$780$		0			0
$781$	−132.019			−0.169039
$782$	1762.05	+	325.482i	2.25326	+	0.416217i
$783$		0			0
$784$	495.814	+	444.279i	0.632415	+	0.566683i
$785$	−5.48674			−0.00698948
$786$		0			0
$787$		−	668.336i		−	0.849220i	−0.905376	−	0.424610i	$-0.860411\pi$
$787$		−	668.336i		−	0.849220i	0.905376	−	0.424610i	$-0.139589\pi$
$788$	279.232	+	106.802i	0.354356	+	0.135536i
$789$		0			0
$790$	−5.67464	−	1.04821i	−0.00718308	−	0.00132684i
$791$			100.577i			0.127151i
$792$		0			0
$793$	−295.106			−0.372139
$794$	123.960	−	671.076i	0.156120	−	0.845184i
$795$		0			0
$796$	255.987	−	669.272i	0.321592	−	0.840794i
$797$	−951.570			−1.19394			−0.596970	−	0.802264i	$-0.703629\pi$
$797$	−951.570			−1.19394			−0.596970	+	0.802264i	$0.703629\pi$
$798$		0			0
$799$		−	408.699i		−	0.511514i
$800$	633.115	−	488.835i	0.791394	−	0.611044i
$801$		0			0
$802$	−54.0839	+	292.792i	−0.0674363	+	0.365078i
$803$		−	149.041i		−	0.185605i
$804$		0			0
$805$	5.17444			0.00642788
$806$	451.758	+	83.4476i	0.560493	+	0.103533i
$807$		0			0
$808$	−175.668	+	287.828i	−0.217411	+	0.356223i
$809$	−383.297			−0.473792			−0.236896	−	0.971535i	$-0.576130\pi$
$809$	−383.297			−0.473792			−0.236896	+	0.971535i	$0.576130\pi$
$810$		0			0
$811$			123.996i			0.152893i	0.997074	+	0.0764466i	$0.0243575\pi$
$811$			123.996i			0.152893i	−0.997074	+	0.0764466i	$0.975643\pi$
$812$	4.05882	−	10.6117i	0.00499855	−	0.0130686i
$813$		0			0
$814$	87.8118	+	16.2204i	0.107877	+	0.0199268i
$815$		−	11.1308i		−	0.0136574i
$816$		0			0
$817$	−211.870			−0.259327
$818$	−60.1009	+	325.367i	−0.0734730	+	0.397759i
$819$		0			0
$820$	−7.66950	−	2.93348i	−0.00935305	−	0.00357741i
$821$	1013.33			1.23426			0.617129	−	0.786862i	$-0.288295\pi$
$821$	1013.33			1.23426			0.617129	+	0.786862i	$0.288295\pi$
$822$		0			0
$823$			968.877i			1.17725i	0.808406	+	0.588625i	$0.200331\pi$
$823$			968.877i			1.17725i	−0.808406	+	0.588625i	$0.799669\pi$
$824$	1012.99	+	618.250i	1.22935	+	0.750303i
$825$		0			0
$826$	−73.1119	+	395.804i	−0.0885132	+	0.479181i
$827$			19.2402i			0.0232650i	0.999932	+	0.0116325i	$0.00370283\pi$
$827$			19.2402i			0.0232650i	−0.999932	+	0.0116325i	$0.996297\pi$
$828$		0			0
$829$	1390.12			1.67686			0.838432	−	0.545007i	$-0.183473\pi$
$829$	1390.12			1.67686			0.838432	+	0.545007i	$0.183473\pi$
$830$	−0.539224	−	0.0996042i	−0.000649668	−	0.000120005i
$831$		0			0
$832$	−270.111	−	525.431i	−0.324653	−	0.631528i
$833$	−1239.52			−1.48801
$834$		0			0
$835$			15.7831i			0.0189020i
$836$	−32.4169	−	12.3990i	−0.0387762	−	0.0148314i
$837$		0			0
$838$	743.942	+	137.419i	0.887758	+	0.163985i
$839$		−	1248.78i		−	1.48841i	−0.667952	−	0.744205i	$-0.732829\pi$
$839$		−	1248.78i		−	1.48841i	0.667952	−	0.744205i	$-0.267171\pi$
$840$		0			0
$841$	−839.908			−0.998702
$842$	143.892	−	778.983i	0.170893	−	0.925158i
$843$		0			0
$844$	474.011	−	1239.29i	0.561625	−	1.46835i
$845$	5.30240			0.00627504
$846$		0			0
$847$			318.183i			0.375658i
$848$	−1039.86	−	931.779i	−1.22625	−	1.09880i
$849$		0			0
$850$	−270.513	+	1464.47i	−0.318250	+	1.72290i
$851$		−	674.581i		−	0.792692i
$852$		0			0
$853$	916.320			1.07423			0.537116	−	0.843508i	$-0.319514\pi$
$853$	916.320			1.07423			0.537116	+	0.843508i	$0.319514\pi$
$854$	170.930	+	31.5737i	0.200152	+	0.0369716i
$855$		0			0
$856$	−15.5489	−	9.48988i	−0.0181646	−	0.0110863i
$857$	−1671.81			−1.95077			−0.975384	−	0.220514i	$-0.929227\pi$
$857$	−1671.81			−1.95077			−0.975384	+	0.220514i	$0.929227\pi$
$858$		0			0
$859$			1173.42i			1.36603i	0.730404	+	0.683016i	$0.239332\pi$
$859$			1173.42i			1.36603i	−0.730404	+	0.683016i	$0.760668\pi$
$860$	4.39565	−	11.4923i	0.00511122	−	0.0133631i
$861$		0			0
$862$	−1373.46	−	253.702i	−1.59334	−	0.294318i
$863$		−	46.0227i		−	0.0533287i	−0.999644	−	0.0266643i	$-0.991511\pi$
$863$		−	46.0227i		−	0.0533287i	0.999644	−	0.0266643i	$-0.00848853\pi$
$864$		0			0
$865$	10.4701			0.0121041
$866$	−124.006	+	671.326i	−0.143194	+	0.775204i
$867$		0			0
$868$	−252.736	−	96.6681i	−0.291171	−	0.111369i
$869$	90.7556			0.104437
$870$		0			0
$871$		−	1063.43i		−	1.22093i
$872$	452.453	−	741.332i	0.518868	−	0.850151i
$873$		0			0
$874$	−47.6254	+	257.828i	−0.0544913	+	0.294998i
$875$			8.60181i			0.00983064i
$876$		0			0
$877$	109.119			0.124424			0.0622118	−	0.998063i	$-0.480185\pi$
$877$	109.119			0.124424			0.0622118	+	0.998063i	$0.480185\pi$
$878$	631.350	+	116.622i	0.719078	+	0.132826i
$879$		0			0
$880$	1.34510	−	1.50113i	0.00152853	−	0.00170583i
$881$	388.835			0.441357			0.220678	−	0.975347i	$-0.429173\pi$
$881$	388.835			0.441357			0.220678	+	0.975347i	$0.429173\pi$
$882$		0			0
$883$			1190.72i			1.34849i	0.738507	+	0.674245i	$0.235531\pi$
$883$			1190.72i			1.34849i	−0.738507	+	0.674245i	$0.764469\pi$
$884$	1027.38	+	392.960i	1.16220	+	0.444525i
$885$		0			0
$886$	1182.94	+	218.509i	1.33514	+	0.246624i
$887$			1084.95i			1.22317i	0.791178	+	0.611586i	$0.209468\pi$
$887$			1084.95i			1.22317i	−0.791178	+	0.611586i	$0.790532\pi$
$888$		0			0
$889$	413.962			0.465649
$890$	−2.56214	+	13.8706i	−0.00287881	+	0.0155849i
$891$		0			0
$892$	78.7229	−	205.819i	0.0882544	−	0.230739i
$893$	59.8020			0.0669676
$894$		0			0
$895$		−	8.18988i		−	0.00915071i
$896$	100.236	+	333.237i	0.111870	+	0.371916i
$897$		0			0
$898$	−238.697	+	1292.23i	−0.265810	+	1.43901i
$899$		−	25.9972i		−	0.0289179i
$900$		0			0
$901$	2599.62			2.88526
$902$	126.993	+	23.4578i	0.140790	+	0.0260065i
$903$		0			0
$904$	154.185	−	252.628i	0.170558	−	0.279455i
$905$	0.898223			0.000992511
$906$		0			0
$907$			1519.77i			1.67560i	0.545975	+	0.837802i	$0.316159\pi$
$907$			1519.77i			1.67560i	−0.545975	+	0.837802i	$0.683841\pi$
$908$	264.082	−	690.435i	0.290839	−	0.760391i
$909$		0			0
$910$	3.12360	+	0.576984i	0.00343253	+	0.000634048i
$911$			349.110i			0.383216i	0.981472	+	0.191608i	$0.0613702\pi$
$911$			349.110i			0.383216i	−0.981472	+	0.191608i	$0.938630\pi$
$912$		0			0
$913$	8.62392			0.00944569
$914$	114.855	−	621.786i	0.125662	−	0.680291i
$915$		0			0
$916$	617.649	+	236.242i	0.674289	+	0.257906i
$917$	−367.985			−0.401293
$918$		0			0
$919$			1015.93i			1.10547i	0.833357	+	0.552735i	$0.186416\pi$
$919$			1015.93i			1.10547i	−0.833357	+	0.552735i	$0.813584\pi$
$920$	−12.9971	−	7.93245i	−0.0141273	−	0.00862223i
$921$		0			0
$922$	−214.135	+	1159.26i	−0.232251	+	1.25733i
$923$			612.225i			0.663299i
$924$		0			0
$925$	560.655			0.606114
$926$	1631.63	+	301.391i	1.76202	+	0.325476i
$927$		0			0
$928$	−26.4627	+	20.4321i	−0.0285158	+	0.0220174i
$929$	780.222			0.839852			0.419926	−	0.907558i	$-0.362056\pi$
$929$	780.222			0.839852			0.419926	+	0.907558i	$0.362056\pi$
$930$		0			0
$931$		−	181.369i		−	0.194811i
$932$	1381.58	+	528.435i	1.48238	+	0.566990i
$933$		0			0
$934$	−311.079	−	57.4618i	−0.333061	−	0.0615223i
$935$			3.75276i			0.00401365i
$936$		0			0
$937$	−16.0773			−0.0171582			−0.00857911	−	0.999963i	$-0.502731\pi$
$937$	−16.0773			−0.0171582			−0.00857911	+	0.999963i	$0.502731\pi$
$938$	−113.777	+	615.954i	−0.121298	+	0.656667i
$939$		0			0
$940$	−1.24071	+	3.24380i	−0.00131990	+	0.00345085i
$941$	−1693.93			−1.80014			−0.900070	−	0.435745i	$-0.856485\pi$
$941$	−1693.93			−1.80014			−0.900070	+	0.435745i	$0.856485\pi$
$942$		0			0
$943$		−	975.576i		−	1.03455i
$944$	790.411	−	882.095i	0.837300	−	0.934423i
$945$		0			0
$946$	−35.1502	+	190.292i	−0.0371567	+	0.201154i
$947$		−	1749.39i		−	1.84729i	−0.383247	−	0.923646i	$-0.625194\pi$
$947$		−	1749.39i		−	1.84729i	0.383247	−	0.923646i	$-0.374806\pi$
$948$		0			0
$949$	−691.161			−0.728305
$950$	−214.285	−	39.5822i	−0.225563	−	0.0416655i
$951$		0			0
$952$	−553.033	−	337.529i	−0.580917	−	0.354547i
$953$	526.236			0.552189			0.276094	−	0.961130i	$-0.410960\pi$
$953$	526.236			0.552189			0.276094	+	0.961130i	$0.410960\pi$
$954$		0			0
$955$		−	13.4466i		−	0.0140802i
$956$	204.444	−	534.514i	0.213854	−	0.559115i
$957$		0			0
$958$	1652.05	+	305.162i	1.72448	+	0.318541i
$959$			12.7998i			0.0133471i
$960$		0			0
$961$	341.831			0.355703
$962$	75.2202	−	407.217i	0.0781915	−	0.423303i
$963$		0			0
$964$	−1089.03	−	416.539i	−1.12970	−	0.432094i
$965$	9.06524			0.00939403
$966$		0			0
$967$		−	1741.31i		−	1.80073i	−0.435136	−	0.900365i	$-0.643300\pi$
$967$		−	1741.31i		−	1.80073i	0.435136	−	0.900365i	$-0.356700\pi$
$968$	487.776	−	799.208i	0.503901	−	0.825628i
$969$		0			0
$970$	−1.97648	+	10.7000i	−0.00203761	+	0.0110309i
$971$		−	523.492i		−	0.539126i	−0.962983	−	0.269563i	$-0.913121\pi$
$971$		−	523.492i		−	0.539126i	0.962983	−	0.269563i	$-0.0868793\pi$
$972$		0			0
$973$	−527.709			−0.542352
$974$	−206.236	−	38.0954i	−0.211741	−	0.0391123i
$975$		0			0
$976$	−380.937	−	341.343i	−0.390304	−	0.349736i
$977$	−1675.59			−1.71503			−0.857517	−	0.514456i	$-0.827994\pi$
$977$	−1675.59			−1.71503			−0.857517	+	0.514456i	$0.827994\pi$
$978$		0			0
$979$		−	221.835i		−	0.226593i
$980$	9.83790	+	3.76286i	0.0100387	+	0.00383965i
$981$		0			0
$982$	1873.15	+	346.003i	1.90748	+	0.352345i
$983$			1575.80i			1.60305i	0.597959	+	0.801526i	$0.295978\pi$
$983$			1575.80i			1.60305i	−0.597959	+	0.801526i	$0.704022\pi$
$984$		0			0
$985$	4.72996			0.00480199
$986$	11.3068	−	61.2112i	0.0114673	−	0.0620803i
$987$		0			0
$988$	−57.4990	+	150.330i	−0.0581974	+	0.152156i
$989$	1461.84			1.47810
$990$		0			0
$991$		−	694.119i		−	0.700423i	−0.936671	−	0.350211i	$-0.886110\pi$
$991$		−	694.119i		−	0.700423i	0.936671	−	0.350211i	$-0.113890\pi$
$992$	486.628	+	630.256i	0.490552	+	0.635339i
$993$		0			0
$994$	65.5027	−	354.610i	0.0658980	−	0.356750i
$995$		−	11.3369i		−	0.0113939i
$996$		0			0
$997$	−800.753			−0.803162			−0.401581	−	0.915823i	$-0.631539\pi$
$997$	−800.753			−0.803162			−0.401581	+	0.915823i	$0.631539\pi$
$998$	−491.995	−	90.8801i	−0.492981	−	0.0910623i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.d.343.18	yes	36
3.2	odd	2	inner	684.3.g.d.343.19	yes	36
4.3	odd	2	inner	684.3.g.d.343.17	✓	36
12.11	even	2	inner	684.3.g.d.343.20	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.g.d.343.17	✓	36	4.3	odd	2	inner
684.3.g.d.343.18	yes	36	1.1	even	1	trivial
684.3.g.d.343.19	yes	36	3.2	odd	2	inner
684.3.g.d.343.20	yes	36	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(-0.363289 + 1.96673i) q^{2} +(-3.73604 - 1.42898i) q^{4} -0.0632854 q^{5} +2.71864i q^{7} +(4.16769 - 6.82864i) q^{8} +O(q^{10})\)	\(q+(-0.363289 + 1.96673i) q^{2} +(-3.73604 - 1.42898i) q^{4} -0.0632854 q^{5} +2.71864i q^{7} +(4.16769 - 6.82864i) q^{8} +(0.0229909 - 0.124465i) q^{10} +1.99060i q^{11} +9.23116 q^{13} +(-5.34682 - 0.987652i) q^{14} +(11.9160 + 10.6775i) q^{16} -29.7896 q^{17} -4.35890i q^{19} +(0.236437 + 0.0904337i) q^{20} +(-3.91496 - 0.723162i) q^{22} +30.0752i q^{23} -24.9960 q^{25} +(-3.35358 + 18.1552i) q^{26} +(3.88489 - 10.1569i) q^{28} +1.04477 q^{29} -24.8831i q^{31} +(-25.3287 + 19.5565i) q^{32} +(10.8223 - 58.5881i) q^{34} -0.172050i q^{35} -22.4298 q^{37} +(8.57277 + 1.58354i) q^{38} +(-0.263754 + 0.432153i) q^{40} -32.4379 q^{41} -48.6063i q^{43} +(2.84453 - 7.43695i) q^{44} +(-59.1498 - 10.9260i) q^{46} +13.7195i q^{47} +41.6090 q^{49} +(9.08078 - 49.1603i) q^{50} +(-34.4880 - 13.1912i) q^{52} -87.2658 q^{53} -0.125976i q^{55} +(18.5646 + 11.3304i) q^{56} +(-0.379554 + 2.05478i) q^{58} -74.0260i q^{59} -31.9685 q^{61} +(48.9383 + 9.03977i) q^{62} +(-29.2608 - 56.9193i) q^{64} -0.584198 q^{65} -115.200i q^{67} +(111.295 + 42.5689i) q^{68} +(0.338376 + 0.0625039i) q^{70} +66.3216i q^{71} -74.8726 q^{73} +(8.14851 - 44.1133i) q^{74} +(-6.22879 + 16.2850i) q^{76} -5.41171 q^{77} -45.5922i q^{79} +(-0.754109 - 0.675728i) q^{80} +(11.7843 - 63.7965i) q^{82} -4.33233i q^{83} +1.88525 q^{85} +(95.5953 + 17.6581i) q^{86} +(13.5931 + 8.29618i) q^{88} -111.441 q^{89} +25.0962i q^{91} +(42.9770 - 112.362i) q^{92} +(-26.9826 - 4.98416i) q^{94} +0.275855i q^{95} -85.9678 q^{97} +(-15.1161 + 81.8336i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4}+O(q^{10}) \) 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

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