LMFDB - Embedded newform 684.3.be.a.581.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(425,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("684.425");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			581.9
Character	$\chi$	$=$	684.581
Dual form			684.3.be.a.425.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37911 - 1.82752i) q^{3} +(5.32501 - 3.07440i) q^{5} +(-6.67945 - 11.5692i) q^{7} +(2.32035 + 8.69574i) q^{9} +O(q^{10})$	\(q+(-2.37911 - 1.82752i) q^{3} +(5.32501 - 3.07440i) q^{5} +(-6.67945 - 11.5692i) q^{7} +(2.32035 + 8.69574i) q^{9} +(0.586623 - 0.338687i) q^{11} -21.9753 q^{13} +(-18.2873 - 2.41722i) q^{15} +(-10.9425 - 6.31763i) q^{17} +(7.16635 - 17.5967i) q^{19} +(-5.25168 + 39.7311i) q^{21} +34.7581i q^{23} +(6.40383 - 11.0918i) q^{25} +(10.3713 - 24.9286i) q^{27} +(33.0234 + 19.0661i) q^{29} +(19.7392 - 34.1893i) q^{31} +(-2.01460 - 0.266290i) q^{33} +(-71.1363 - 41.0706i) q^{35} -24.0074 q^{37} +(52.2818 + 40.1603i) q^{39} +(0.866161 - 0.500078i) q^{41} -11.8150 q^{43} +(39.0901 + 39.1713i) q^{45} +(31.5282 + 18.2028i) q^{47} +(-64.7302 + 112.116i) q^{49} +(14.4877 + 35.0279i) q^{51} +(-29.2948 + 16.9134i) q^{53} +(2.08251 - 3.60702i) q^{55} +(-49.2078 + 28.7678i) q^{57} +(53.6084 - 30.9508i) q^{59} +(-49.9685 + 86.5480i) q^{61} +(85.1037 - 84.9273i) q^{63} +(-117.019 + 67.5609i) q^{65} -31.6494 q^{67} +(63.5210 - 82.6933i) q^{69} +(-104.178 - 60.1470i) q^{71} +(9.08945 - 15.7434i) q^{73} +(-35.5058 + 14.6854i) q^{75} +(-7.83664 - 4.52448i) q^{77} +8.21376 q^{79} +(-70.2320 + 40.3543i) q^{81} +(-139.075 + 80.2951i) q^{83} -77.6916 q^{85} +(-43.7227 - 105.711i) q^{87} +(91.8708 - 53.0416i) q^{89} +(146.783 + 254.236i) q^{91} +(-109.443 + 45.2664i) q^{93} +(-15.9383 - 115.735i) q^{95} +51.4195 q^{97} +(4.30630 + 4.31525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	−2.37911	−	1.82752i	−0.793037	−	0.609173i
$3$	−2.37911	−	1.82752i	−0.793037	−	0.609173i
$4$		0			0
$5$	5.32501	−	3.07440i	1.06500	−	0.614879i	0.138191	−	0.990406i	$-0.455871\pi$
$5$	5.32501	−	3.07440i	1.06500	−	0.614879i	0.926812	+	0.375526i	$0.122538\pi$
$6$		0			0
$7$	−6.67945	−	11.5692i	−0.954208	−	1.65274i	−0.736171	−	0.676795i	$-0.763368\pi$
$7$	−6.67945	−	11.5692i	−0.954208	−	1.65274i	−0.218036	−	0.975941i	$-0.569965\pi$
$8$		0			0
$9$	2.32035	+	8.69574i	0.257817	+	0.966194i
$10$		0			0
$11$	0.586623	−	0.338687i	0.0533293	−	0.0307897i	−0.473098	−	0.881010i	$-0.656864\pi$
$11$	0.586623	−	0.338687i	0.0533293	−	0.0307897i	0.526428	+	0.850220i	$0.323531\pi$
$12$		0			0
$13$	−21.9753			−1.69041			−0.845205	−	0.534442i	$-0.820522\pi$
$13$	−21.9753			−1.69041			−0.845205	+	0.534442i	$0.820522\pi$
$14$		0			0
$15$	−18.2873	−	2.41722i	−1.21915	−	0.161148i
$16$		0			0
$17$	−10.9425	−	6.31763i	−0.643674	−	0.371625i	0.142354	−	0.989816i	$-0.454533\pi$
$17$	−10.9425	−	6.31763i	−0.643674	−	0.371625i	−0.786028	+	0.618190i	$0.787866\pi$
$18$		0			0
$19$	7.16635	−	17.5967i	0.377176	−	0.926141i
$19$	7.16635	−	17.5967i	0.377176	−	0.926141i
$20$		0			0
$21$	−5.25168	+	39.7311i	−0.250080	+	1.89196i
$22$		0			0
$23$			34.7581i			1.51122i	0.655022	+	0.755610i	$0.272659\pi$
$23$			34.7581i			1.51122i	−0.655022	+	0.755610i	$0.727341\pi$
$24$		0			0
$25$	6.40383	−	11.0918i	0.256153	−	0.443670i
$26$		0			0
$27$	10.3713	−	24.9286i	0.384121	−	0.923283i
$28$		0			0
$29$	33.0234	+	19.0661i	1.13874	+	0.657450i	0.946118	−	0.323823i	$-0.104968\pi$
$29$	33.0234	+	19.0661i	1.13874	+	0.657450i	0.192620	+	0.981273i	$0.438302\pi$
$30$		0			0
$31$	19.7392	−	34.1893i	0.636749	−	1.10288i	−0.349393	−	0.936976i	$-0.613612\pi$
$31$	19.7392	−	34.1893i	0.636749	−	1.10288i	0.986142	−	0.165905i	$-0.0530545\pi$
$32$		0			0
$33$	−2.01460	−	0.266290i	−0.0610484	−	0.00806940i
$34$		0			0
$35$	−71.1363	−	41.0706i	−2.03247	−	1.17345i
$36$		0			0
$37$	−24.0074			−0.648850			−0.324425	−	0.945911i	$-0.605171\pi$
$37$	−24.0074			−0.648850			−0.324425	+	0.945911i	$0.605171\pi$
$38$		0			0
$39$	52.2818	+	40.1603i	1.34056	+	1.02975i
$40$		0			0
$41$	0.866161	−	0.500078i	0.0211259	−	0.0121970i	−0.489400	−	0.872060i	$-0.662784\pi$
$41$	0.866161	−	0.500078i	0.0211259	−	0.0121970i	0.510526	+	0.859862i	$0.329451\pi$
$42$		0			0
$43$	−11.8150			−0.274768			−0.137384	−	0.990518i	$-0.543870\pi$
$43$	−11.8150			−0.274768			−0.137384	+	0.990518i	$0.543870\pi$
$44$		0			0
$45$	39.0901	+	39.1713i	0.868668	+	0.870473i
$46$		0			0
$47$	31.5282	+	18.2028i	0.670813	+	0.387294i	0.796384	−	0.604791i	$-0.206743\pi$
$47$	31.5282	+	18.2028i	0.670813	+	0.387294i	−0.125572	+	0.992085i	$0.540077\pi$
$48$		0			0
$49$	−64.7302	+	112.116i	−1.32102	+	2.28808i
$50$		0			0
$51$	14.4877	+	35.0279i	0.284073	+	0.686822i
$52$		0			0
$53$	−29.2948	+	16.9134i	−0.552732	+	0.319120i	−0.750223	−	0.661185i	$-0.770054\pi$
$53$	−29.2948	+	16.9134i	−0.552732	+	0.319120i	0.197491	+	0.980305i	$0.436721\pi$
$54$		0			0
$55$	2.08251	−	3.60702i	0.0378639	−	0.0655822i
$56$		0			0
$57$	−49.2078	+	28.7678i	−0.863295	+	0.504699i
$58$		0			0
$59$	53.6084	−	30.9508i	0.908617	−	0.524590i	0.0286309	−	0.999590i	$-0.490885\pi$
$59$	53.6084	−	30.9508i	0.908617	−	0.524590i	0.879986	+	0.475000i	$0.157552\pi$
$60$		0			0
$61$	−49.9685	+	86.5480i	−0.819156	+	1.41882i	0.0871484	+	0.996195i	$0.472225\pi$
$61$	−49.9685	+	86.5480i	−0.819156	+	1.41882i	−0.906305	+	0.422625i	$0.861109\pi$
$62$		0			0
$63$	85.1037	−	84.9273i	1.35085	−	1.34805i
$64$		0			0
$65$	−117.019	+	67.5609i	−1.80029	+	1.03940i
$66$		0			0
$67$	−31.6494			−0.472379			−0.236189	−	0.971707i	$-0.575899\pi$
$67$	−31.6494			−0.472379			−0.236189	+	0.971707i	$0.575899\pi$
$68$		0			0
$69$	63.5210	−	82.6933i	0.920595	−	1.19845i
$70$		0			0
$71$	−104.178	−	60.1470i	−1.46729	−	0.847141i	−0.467961	−	0.883749i	$-0.655011\pi$
$71$	−104.178	−	60.1470i	−1.46729	−	0.847141i	−0.999330	+	0.0366080i	$0.988345\pi$
$72$		0			0
$73$	9.08945	−	15.7434i	0.124513	−	0.215663i	−0.797030	−	0.603940i	$-0.793596\pi$
$73$	9.08945	−	15.7434i	0.124513	−	0.215663i	0.921542	+	0.388278i	$0.126930\pi$
$74$		0			0
$75$	−35.5058	+	14.6854i	−0.473411	+	0.195806i
$76$		0			0
$77$	−7.83664	−	4.52448i	−0.101774	−	0.0587595i
$78$		0			0
$79$	8.21376			0.103972			0.0519858	−	0.998648i	$-0.483445\pi$
$79$	8.21376			0.103972			0.0519858	+	0.998648i	$0.483445\pi$
$80$		0			0
$81$	−70.2320	+	40.3543i	−0.867061	+	0.498202i
$82$		0			0
$83$	−139.075	+	80.2951i	−1.67560	+	0.967410i	−0.711195	+	0.702995i	$0.751846\pi$
$83$	−139.075	+	80.2951i	−1.67560	+	0.967410i	−0.964409	+	0.264416i	$0.914821\pi$
$84$		0			0
$85$	−77.6916			−0.914019
$86$		0			0
$87$	−43.7227	−	105.711i	−0.502560	−	1.21507i
$88$		0			0
$89$	91.8708	−	53.0416i	1.03226	−	0.595973i	0.114626	−	0.993409i	$-0.463433\pi$
$89$	91.8708	−	53.0416i	1.03226	−	0.595973i	0.917630	+	0.397436i	$0.130100\pi$
$90$		0			0
$91$	146.783	+	254.236i	1.61300	+	2.79380i
$92$		0			0
$93$	−109.443	+	45.2664i	−1.17681	+	0.486736i
$94$		0			0
$95$	−15.9383	−	115.735i	−0.167771	−	1.21826i
$96$		0			0
$97$	51.4195			0.530098			0.265049	−	0.964235i	$-0.414612\pi$
$97$	51.4195			0.530098			0.265049	+	0.964235i	$0.414612\pi$
$98$		0			0
$99$	4.30630	+	4.31525i	0.0434980	+	0.0435884i
$100$		0			0
$101$	−2.56281	−	1.47964i	−0.0253744	−	0.0146499i	0.487259	−	0.873257i	$-0.337997\pi$
$101$	−2.56281	−	1.47964i	−0.0253744	−	0.0146499i	−0.512634	+	0.858608i	$0.671330\pi$
$102$		0			0
$103$	5.46277	−	9.46179i	0.0530366	−	0.0918620i	−0.838288	−	0.545227i	$-0.816443\pi$
$103$	5.46277	−	9.46179i	0.0530366	−	0.0918620i	0.891325	+	0.453365i	$0.149777\pi$
$104$		0			0
$105$	94.1840	+	227.714i	0.896991	+	2.16871i
$106$		0			0
$107$		−	14.7588i		−	0.137933i	−0.997619	−	0.0689664i	$-0.978030\pi$
$107$		−	14.7588i		−	0.137933i	0.997619	−	0.0689664i	$-0.0219701\pi$
$108$		0			0
$109$	16.1494	−	27.9716i	0.148160	−	0.256620i	−0.782388	−	0.622792i	$-0.785998\pi$
$109$	16.1494	−	27.9716i	0.148160	−	0.256620i	0.930547	+	0.366172i	$0.119332\pi$
$110$		0			0
$111$	57.1164	+	43.8740i	0.514562	+	0.395262i
$112$		0			0
$113$	−134.566	−	77.6917i	−1.19085	−	0.687537i	−0.232350	−	0.972632i	$-0.574641\pi$
$113$	−134.566	−	77.6917i	−1.19085	−	0.687537i	−0.958499	+	0.285095i	$0.907975\pi$
$114$		0			0
$115$	106.860	+	185.087i	0.929218	+	1.60945i
$116$		0			0
$117$	−50.9905	−	191.092i	−0.435816	−	1.63326i
$118$		0			0
$119$			168.793i			1.41843i
$120$		0			0
$121$	−60.2706	+	104.392i	−0.498104	+	0.862741i
$122$		0			0
$123$	−2.97460	−	0.393183i	−0.0241837	−	0.00319661i
$124$		0			0
$125$			74.9682i			0.599745i
$126$		0			0
$127$	6.01913	+	10.4254i	0.0473947	+	0.0820900i	0.888750	−	0.458393i	$-0.151575\pi$
$127$	6.01913	+	10.4254i	0.0473947	+	0.0820900i	−0.841355	+	0.540483i	$0.818241\pi$
$128$		0			0
$129$	28.1093	+	21.5922i	0.217902	+	0.167382i
$130$		0			0
$131$	−9.17388	+	5.29654i	−0.0700296	+	0.0404316i	−0.534606	−	0.845101i	$-0.679540\pi$
$131$	−9.17388	+	5.29654i	−0.0700296	+	0.0404316i	0.464576	+	0.885533i	$0.346207\pi$
$132$		0			0
$133$	−251.446	+	34.6276i	−1.89057	+	0.260358i
$134$		0			0
$135$	−21.4134	−	164.631i	−0.158618	−	1.21949i
$136$		0			0
$137$	−16.0097	−	9.24323i	−0.116859	−	0.0674688i	0.440431	−	0.897786i	$-0.354826\pi$
$137$	−16.0097	−	9.24323i	−0.116859	−	0.0674688i	−0.557290	+	0.830318i	$0.688159\pi$
$138$		0			0
$139$	−127.233			−0.915344			−0.457672	−	0.889121i	$-0.651317\pi$
$139$	−127.233			−0.915344			−0.457672	+	0.889121i	$0.651317\pi$
$140$		0			0
$141$	−41.7431	−	100.925i	−0.296051	−	0.715779i
$142$		0			0
$143$	−12.8912	+	7.44275i	−0.0901484	+	0.0520472i
$144$		0			0
$145$	234.467			1.61701
$146$		0			0
$147$	358.894	−	148.441i	2.44146	−	1.00980i
$148$		0			0
$149$	172.812	−	99.7729i	1.15981	−	0.669616i	0.208551	−	0.978011i	$-0.433125\pi$
$149$	172.812	−	99.7729i	1.15981	−	0.669616i	0.951258	+	0.308395i	$0.0997918\pi$
$150$		0			0
$151$	−86.0705	−	149.078i	−0.570003	−	0.987274i	−0.996565	−	0.0828158i	$-0.973609\pi$
$151$	−86.0705	−	149.078i	−0.570003	−	0.987274i	0.426562	−	0.904458i	$-0.359725\pi$
$152$		0			0
$153$	29.5462	−	109.812i	0.193112	−	0.717725i
$154$		0			0
$155$		−	242.745i		−	1.56609i
$156$		0			0
$157$	63.0568	+	109.218i	0.401636	+	0.695653i	0.993923	−	0.110073i	$-0.0351085\pi$
$157$	63.0568	+	109.218i	0.401636	+	0.695653i	−0.592288	+	0.805726i	$0.701775\pi$
$158$		0			0
$159$	100.605	+	13.2980i	0.632737	+	0.0836354i
$160$		0			0
$161$	402.121	−	232.165i	2.49765	−	1.44202i
$162$		0			0
$163$	−130.019			−0.797661			−0.398831	−	0.917025i	$-0.630584\pi$
$163$	−130.019			−0.797661			−0.398831	+	0.917025i	$0.630584\pi$
$164$		0			0
$165$	−11.5464	+	4.77567i	−0.0699784	+	0.0289435i
$166$		0			0
$167$		−	17.5080i		−	0.104838i	−0.998625	−	0.0524190i	$-0.983307\pi$
$167$		−	17.5080i		−	0.104838i	0.998625	−	0.0524190i	$-0.0166931\pi$
$168$		0			0
$169$	313.915			1.85749
$170$		0			0
$171$	169.645	+	21.4863i	0.992075	+	0.125651i
$172$		0			0
$173$		−	259.825i		−	1.50188i	−0.660370	−	0.750940i	$-0.729601\pi$
$173$		−	259.825i		−	1.50188i	0.660370	−	0.750940i	$-0.270399\pi$
$174$		0			0
$175$	−171.096			−0.977693
$176$		0			0
$177$	−184.104	−	24.3349i	−1.04013	−	0.137485i
$178$		0			0
$179$		−	120.898i		−	0.675407i	−0.941252	−	0.337704i	$-0.890350\pi$
$179$		−	120.898i		−	0.675407i	0.941252	−	0.337704i	$-0.109650\pi$
$180$		0			0
$181$	−110.148	−	190.783i	−0.608555	−	1.05405i	−0.991479	−	0.130268i	$-0.958416\pi$
$181$	−110.148	−	190.783i	−0.608555	−	1.05405i	0.382924	−	0.923780i	$-0.374917\pi$
$182$		0			0
$183$	277.049	−	114.589i	1.51393	−	0.626170i
$184$		0			0
$185$	−127.840	+	73.8084i	−0.691026	+	0.398964i
$186$		0			0
$187$	−8.55879			−0.0457689
$188$		0			0
$189$	−357.678	+	46.5229i	−1.89247	+	0.246153i
$190$		0			0
$191$	−87.7696	+	50.6738i	−0.459527	+	0.265308i	−0.711845	−	0.702336i	$-0.752140\pi$
$191$	−87.7696	+	50.6738i	−0.459527	+	0.265308i	0.252319	+	0.967644i	$0.418807\pi$
$192$		0			0
$193$	159.875	+	276.911i	0.828367	+	1.43477i	0.899318	+	0.437294i	$0.144063\pi$
$193$	159.875	+	276.911i	0.828367	+	1.43477i	−0.0709511	+	0.997480i	$0.522603\pi$
$194$		0			0
$195$	401.870	+	53.1193i	2.06087	+	0.272407i
$196$		0			0
$197$		−	362.670i		−	1.84096i	−0.390786	−	0.920482i	$-0.627797\pi$
$197$		−	362.670i		−	1.84096i	0.390786	−	0.920482i	$-0.372203\pi$
$198$		0			0
$199$	−63.0213	−	109.156i	−0.316690	−	0.548523i	0.663105	−	0.748526i	$-0.269238\pi$
$199$	−63.0213	−	109.156i	−0.316690	−	0.548523i	−0.979795	+	0.200003i	$0.935905\pi$
$200$		0			0
$201$	75.2974	+	57.8398i	0.374614	+	0.287760i
$202$		0			0
$203$		−	509.403i		−	2.50938i
$204$		0			0
$205$	3.07488	−	5.32585i	0.0149994	−	0.0259797i
$206$		0			0
$207$	−302.247	+	80.6508i	−1.46013	+	0.389618i
$208$		0			0
$209$	−1.75582	−	12.7498i	−0.00840105	−	0.0610036i
$210$		0			0
$211$	−26.3951	−	45.7177i	−0.125095	−	0.216672i	0.796675	−	0.604408i	$-0.206590\pi$
$211$	−26.3951	−	45.7177i	−0.125095	−	0.216672i	−0.921770	+	0.387737i	$0.873257\pi$
$212$		0			0
$213$	137.931	+	333.483i	0.647561	+	1.56565i
$214$		0			0
$215$	−62.9152	+	36.3241i	−0.292629	+	0.168949i
$216$		0			0
$217$	−527.389			−2.43036
$218$		0			0
$219$	−50.3961	+	20.8441i	−0.230119	+	0.0951787i
$220$		0			0
$221$	240.464	+	138.832i	1.08807	+	0.628200i
$222$		0			0
$223$	0.189234			0.000848582			0.000424291	−	1.00000i	$-0.499865\pi$
$223$	0.189234			0.000848582			0.000424291		1.00000i	$0.499865\pi$
$224$		0			0
$225$	111.310	+	29.9493i	0.494712	+	0.133108i
$226$		0			0
$227$	−17.0193	+	9.82612i	−0.0749751	+	0.0432869i	−0.537019	−	0.843570i	$-0.680450\pi$
$227$	−17.0193	+	9.82612i	−0.0749751	+	0.0432869i	0.462044	+	0.886857i	$0.347116\pi$
$228$		0			0
$229$	175.467	−	303.918i	0.766233	−	1.32715i	−0.173359	−	0.984859i	$-0.555462\pi$
$229$	175.467	−	303.918i	0.766233	−	1.32715i	0.939592	−	0.342296i	$-0.111204\pi$
$230$		0			0
$231$	10.3757	+	25.0859i	0.0449163	+	0.108597i
$232$		0			0
$233$	−212.611	−	122.751i	−0.912494	−	0.526829i	−0.0312613	−	0.999511i	$-0.509952\pi$
$233$	−212.611	−	122.751i	−0.912494	−	0.526829i	−0.881233	+	0.472683i	$0.843286\pi$
$234$		0			0
$235$	223.851			0.952556
$236$		0			0
$237$	−19.5414	−	15.0108i	−0.0824534	−	0.0633367i
$238$		0			0
$239$	−215.150	−	124.217i	−0.900210	−	0.519736i	−0.0229416	−	0.999737i	$-0.507303\pi$
$239$	−215.150	−	124.217i	−0.900210	−	0.519736i	−0.877268	+	0.480000i	$0.840637\pi$
$240$		0			0
$241$	7.22517	−	12.5144i	0.0299800	−	0.0519268i	−0.850646	−	0.525739i	$-0.823789\pi$
$241$	7.22517	−	12.5144i	0.0299800	−	0.0519268i	0.880626	+	0.473812i	$0.157122\pi$
$242$		0			0
$243$	240.838	+	32.3428i	0.991103	+	0.133098i
$244$		0			0
$245$			796.025i			3.24908i
$246$		0			0
$247$	−157.483	+	386.693i	−0.637583	+	1.56556i
$248$		0			0
$249$	477.616	+	63.1315i	1.91814	+	0.253540i
$250$		0			0
$251$	39.7299	−	22.9381i	0.158286	−	0.0913867i	−0.418765	−	0.908095i	$-0.637537\pi$
$251$	39.7299	−	22.9381i	0.158286	−	0.0913867i	0.577051	+	0.816708i	$0.304203\pi$
$252$		0			0
$253$	11.7721	+	20.3899i	0.0465300	+	0.0805923i
$254$		0			0
$255$	184.837	+	141.983i	0.724851	+	0.556796i
$256$		0			0
$257$			435.920i			1.69619i	0.529848	+	0.848093i	$0.322249\pi$
$257$			435.920i			1.69619i	−0.529848	+	0.848093i	$0.677751\pi$
$258$		0			0
$259$	160.357	+	277.746i	0.619137	+	1.07238i
$260$		0			0
$261$	−89.1678	+	331.403i	−0.341639	+	1.26974i
$262$		0			0
$263$			206.601i			0.785555i	0.919634	+	0.392778i	$0.128486\pi$
$263$			206.601i			0.785555i	−0.919634	+	0.392778i	$0.871514\pi$
$264$		0			0
$265$	−103.997	+	180.128i	−0.392441	+	0.679727i
$266$		0			0
$267$	−315.505	−	41.7036i	−1.18167	−	0.156193i
$268$		0			0
$269$	250.230	+	144.470i	0.930224	+	0.537065i	0.886882	−	0.461995i	$-0.152866\pi$
$269$	250.230	+	144.470i	0.930224	+	0.537065i	0.0433415	+	0.999060i	$0.486200\pi$
$270$		0			0
$271$	147.862	−	256.105i	0.545618	−	0.945037i	−0.452950	−	0.891536i	$-0.649628\pi$
$271$	147.862	−	256.105i	0.545618	−	0.945037i	0.998568	−	0.0535016i	$-0.0170382\pi$
$272$		0			0
$273$	115.407	−	873.105i	0.422738	−	3.19819i
$274$		0			0
$275$		−	8.67557i		−	0.0315475i
$276$		0			0
$277$	−46.2692	−	80.1406i	−0.167037	−	0.289316i	0.770340	−	0.637633i	$-0.220087\pi$
$277$	−46.2692	−	80.1406i	−0.167037	−	0.289316i	−0.937377	+	0.348317i	$0.886753\pi$
$278$		0			0
$279$	343.103	+	92.3160i	1.22976	+	0.330882i
$280$		0			0
$281$	45.6441	+	26.3526i	0.162434	+	0.0937815i	0.579014	−	0.815318i	$-0.303438\pi$
$281$	45.6441	+	26.3526i	0.162434	+	0.0937815i	−0.416579	+	0.909099i	$0.636771\pi$
$282$		0			0
$283$	−189.282	−	327.846i	−0.668842	−	1.15847i	−0.978228	−	0.207531i	$-0.933457\pi$
$283$	−189.282	−	327.846i	−0.668842	−	1.15847i	0.309387	−	0.950936i	$-0.399876\pi$
$284$		0			0
$285$	−173.589	+	304.474i	−0.609082	+	1.06833i
$286$		0			0
$287$	−11.5710	−	6.68050i	−0.0403170	−	0.0232770i
$288$		0			0
$289$	−64.6750	−	112.020i	−0.223789	−	0.387614i
$290$		0			0
$291$	−122.333	−	93.9701i	−0.420388	−	0.322921i
$292$		0			0
$293$	−413.513	−	238.742i	−1.41131	−	0.814818i	−0.415795	−	0.909458i	$-0.636497\pi$
$293$	−413.513	−	238.742i	−1.41131	−	0.814818i	−0.995512	+	0.0946404i	$0.969830\pi$
$294$		0			0
$295$	190.310	−	329.627i	0.645119	−	1.11738i
$296$		0			0
$297$	−2.35898	−	18.1363i	−0.00794268	−	0.0610650i
$298$		0			0
$299$		−	763.820i		−	2.55458i
$300$		0			0
$301$	78.9180	+	136.690i	0.262186	+	0.454120i
$302$		0			0
$303$	3.39314	+	8.20381i	0.0111985	+	0.0270753i
$304$		0			0
$305$			614.492i			2.01473i
$306$		0			0
$307$	24.3451	−	42.1669i	0.0792999	−	0.137351i	−0.823648	−	0.567101i	$-0.808065\pi$
$307$	24.3451	−	42.1669i	0.0792999	−	0.137351i	0.902948	+	0.429750i	$0.141398\pi$
$308$		0			0
$309$	−30.2881	+	12.5274i	−0.0980199	+	0.0405416i
$310$		0			0
$311$	58.5917	+	33.8279i	0.188398	+	0.108771i	0.591232	−	0.806501i	$-0.298642\pi$
$311$	58.5917	+	33.8279i	0.188398	+	0.108771i	−0.402835	+	0.915273i	$0.631975\pi$
$312$		0			0
$313$	1.36811	−	2.36963i	0.00437095	−	0.00757071i	−0.863832	−	0.503781i	$-0.831942\pi$
$313$	1.36811	−	2.36963i	0.00437095	−	0.00757071i	0.868203	+	0.496210i	$0.165275\pi$
$314$		0			0
$315$	192.078	−	713.881i	0.609772	−	2.26629i
$316$		0			0
$317$	−358.316	−	206.874i	−1.13034	−	0.652600i	−0.186316	−	0.982490i	$-0.559655\pi$
$317$	−358.316	−	206.874i	−1.13034	−	0.652600i	−0.944019	+	0.329890i	$0.892988\pi$
$318$		0			0
$319$	25.8297			0.0809708
$320$		0			0
$321$	−26.9720	+	35.1129i	−0.0840249	+	0.109386i
$322$		0			0
$323$	−189.587	+	147.277i	−0.586956	+	0.455965i
$324$		0			0
$325$	−140.726	+	243.745i	−0.433004	+	0.749985i
$326$		0			0
$327$	−89.5398	+	37.0342i	−0.273822	+	0.113254i
$328$		0			0
$329$		−	486.339i		−	1.47823i
$330$		0			0
$331$	198.804	+	344.339i	0.600617	+	1.04030i	0.992728	+	0.120382i	$0.0384118\pi$
$331$	198.804	+	344.339i	0.600617	+	1.04030i	−0.392110	+	0.919918i	$0.628255\pi$
$332$		0			0
$333$	−55.7056	−	208.763i	−0.167284	−	0.626915i
$334$		0			0
$335$	−168.533	+	97.3027i	−0.503084	+	0.290456i
$336$		0			0
$337$	17.0965	+	29.6119i	0.0507313	+	0.0878692i	0.890276	−	0.455422i	$-0.150511\pi$
$337$	17.0965	+	29.6119i	0.0507313	+	0.0878692i	−0.839545	+	0.543291i	$0.817178\pi$
$338$		0			0
$339$	178.164	+	430.759i	0.525559	+	1.27068i
$340$		0			0
$341$		−	26.7416i		−	0.0784212i
$342$		0			0
$343$	1074.86			3.13371
$344$		0			0
$345$	84.0180	−	635.632i	0.243531	−	1.84241i
$346$		0			0
$347$	103.128	−	59.5412i	0.297200	−	0.171588i	−0.343984	−	0.938975i	$-0.611777\pi$
$347$	103.128	−	59.5412i	0.297200	−	0.171588i	0.641184	+	0.767387i	$0.278443\pi$
$348$		0			0
$349$	196.268	+	339.946i	0.562373	+	0.974059i	0.997289	+	0.0735875i	$0.0234448\pi$
$349$	196.268	+	339.946i	0.562373	+	0.974059i	−0.434916	+	0.900471i	$0.643222\pi$
$350$		0			0
$351$	−227.912	+	547.815i	−0.649322	+	1.56073i
$352$		0			0
$353$	−285.889	+	165.058i	−0.809884	+	0.467587i	−0.846915	−	0.531728i	$-0.821543\pi$
$353$	−285.889	+	165.058i	−0.809884	+	0.467587i	0.0370318	+	0.999314i	$0.488210\pi$
$354$		0			0
$355$	−739.663			−2.08356
$356$		0			0
$357$	308.473	−	401.578i	0.864070	−	1.12487i
$358$		0			0
$359$	85.9500	+	49.6232i	0.239415	+	0.138226i	0.614908	−	0.788599i	$-0.289193\pi$
$359$	85.9500	+	49.6232i	0.239415	+	0.138226i	−0.375493	+	0.926825i	$0.622527\pi$
$360$		0			0
$361$	−258.287	−	252.208i	−0.715476	−	0.698638i
$362$		0			0
$363$	334.168	−	138.214i	0.920574	−	0.380755i
$364$		0			0
$365$		−	111.778i		−	0.306242i
$366$		0			0
$367$	−33.3195	+	57.7111i	−0.0907889	+	0.157251i	−0.907843	−	0.419310i	$-0.862272\pi$
$367$	−33.3195	+	57.7111i	−0.0907889	+	0.157251i	0.817054	+	0.576561i	$0.195606\pi$
$368$		0			0
$369$	6.35835	+	6.37156i	0.0172313	+	0.0172671i
$370$		0			0
$371$	391.347	+	225.944i	1.05484	+	0.609014i
$372$		0			0
$373$	163.975	−	284.013i	0.439611	−	0.761429i	−0.558048	−	0.829809i	$-0.688449\pi$
$373$	163.975	−	284.013i	0.439611	−	0.761429i	0.997659	+	0.0683793i	$0.0217828\pi$
$374$		0			0
$375$	137.006	−	178.358i	0.365349	−	0.475621i
$376$		0			0
$377$	−725.700	−	418.983i	−1.92493	−	1.11136i
$378$		0			0
$379$	−588.049			−1.55158			−0.775790	−	0.630991i	$-0.782649\pi$
$379$	−588.049			−1.55158			−0.775790	+	0.630991i	$0.782649\pi$
$380$		0			0
$381$	4.73250	−	35.8033i	0.0124213	−	0.0939720i
$382$		0			0
$383$	314.491	−	181.571i	0.821124	−	0.474076i	−0.0296797	−	0.999559i	$-0.509449\pi$
$383$	314.491	−	181.571i	0.821124	−	0.474076i	0.850804	+	0.525483i	$0.176115\pi$
$384$		0			0
$385$	−55.6402			−0.144520
$386$		0			0
$387$	−27.4150	−	102.741i	−0.0708399	−	0.265480i
$388$		0			0
$389$	363.165	+	209.673i	0.933585	+	0.539006i	0.887944	−	0.459952i	$-0.152133\pi$
$389$	363.165	+	209.673i	0.933585	+	0.539006i	0.0456415	+	0.998958i	$0.485467\pi$
$390$		0			0
$391$	219.589	−	380.339i	0.561608	−	0.972733i
$392$		0			0
$393$	31.5052	+	4.16437i	0.0801659	+	0.0105964i
$394$		0			0
$395$	43.7383	−	25.2523i	0.110730	−	0.0639300i
$396$		0			0
$397$	18.4059	−	31.8800i	0.0463625	−	0.0803022i	−0.841913	−	0.539613i	$-0.818570\pi$
$397$	18.4059	−	31.8800i	0.0463625	−	0.0803022i	0.888275	+	0.459311i	$0.151904\pi$
$398$		0			0
$399$	661.501	+	377.139i	1.65790	+	0.945212i
$400$		0			0
$401$	−479.111	+	276.615i	−1.19479	+	0.689813i	−0.959389	−	0.282085i	$-0.908974\pi$
$401$	−479.111	+	276.615i	−1.19479	+	0.689813i	−0.235402	+	0.971898i	$0.575641\pi$
$402$		0			0
$403$	−433.776	+	751.322i	−1.07637	+	1.86432i
$404$		0			0
$405$	−249.921	+	430.808i	−0.617088	+	1.06372i
$406$		0			0
$407$	−14.0833	+	8.13100i	−0.0346027	+	0.0199779i
$408$		0			0
$409$	−228.124			−0.557760			−0.278880	−	0.960326i	$-0.589963\pi$
$409$	−228.124			−0.557760			−0.278880	+	0.960326i	$0.589963\pi$
$410$		0			0
$411$	21.1968	+	51.2488i	0.0515737	+	0.124693i
$412$		0			0
$413$	−716.149	−	413.469i	−1.73402	−	1.00114i
$414$		0			0
$415$	−493.718	+	855.144i	−1.18968	+	2.06059i
$416$		0			0
$417$	302.701	+	232.520i	0.725902	+	0.557603i
$418$		0			0
$419$	−427.551	−	246.847i	−1.02041	−	0.589133i	−0.106187	−	0.994346i	$-0.533864\pi$
$419$	−427.551	−	246.847i	−1.02041	−	0.589133i	−0.914222	+	0.405213i	$0.867197\pi$
$420$		0			0
$421$	174.161			0.413684			0.206842	−	0.978374i	$-0.433681\pi$
$421$	174.161			0.413684			0.206842	+	0.978374i	$0.433681\pi$
$422$		0			0
$423$	−85.1306	+	316.398i	−0.201254	+	0.747986i
$424$		0			0
$425$	−140.147	+	80.9141i	−0.329758	+	0.190386i
$426$		0			0
$427$	1335.05			3.12658
$428$		0			0
$429$	44.2714	+	5.85182i	0.103197	+	0.0136406i
$430$		0			0
$431$	−183.318	+	105.838i	−0.425331	+	0.245565i	−0.697356	−	0.716725i	$-0.745640\pi$
$431$	−183.318	+	105.838i	−0.425331	+	0.245565i	0.272025	+	0.962290i	$0.412307\pi$
$432$		0			0
$433$	98.5927	+	170.768i	0.227697	+	0.394382i	0.957125	−	0.289675i	$-0.0935472\pi$
$433$	98.5927	+	170.768i	0.227697	+	0.394382i	−0.729428	+	0.684057i	$0.760214\pi$
$434$		0			0
$435$	−557.822	−	428.492i	−1.28235	−	0.985039i
$436$		0			0
$437$	611.627	+	249.089i	1.39960	+	0.569997i
$438$		0			0
$439$	−614.810			−1.40048			−0.700239	−	0.713908i	$-0.746923\pi$
$439$	−614.810			−1.40048			−0.700239	+	0.713908i	$0.746923\pi$
$440$		0			0
$441$	−1125.13	−	302.729i	−2.55131	−	0.686460i
$442$		0			0
$443$	481.861	+	278.203i	1.08772	+	0.627997i	0.932969	−	0.359956i	$-0.117208\pi$
$443$	481.861	+	278.203i	1.08772	+	0.627997i	0.154754	+	0.987953i	$0.450542\pi$
$444$		0			0
$445$	326.142	−	564.894i	0.732903	−	1.26943i
$446$		0			0
$447$	−593.475	−	78.4458i	−1.32768	−	0.175494i
$448$		0			0
$449$		−	257.610i		−	0.573742i	−0.957969	−	0.286871i	$-0.907385\pi$
$449$		−	257.610i		−	0.573742i	0.957969	−	0.286871i	$-0.0926150\pi$
$450$		0			0
$451$	0.338740	−	0.586715i	0.000751086	−	0.00130092i
$452$		0			0
$453$	−67.6723	+	511.970i	−0.149387	+	1.13018i
$454$		0			0
$455$	1563.24	+	902.540i	3.43570	+	1.98360i
$456$		0			0
$457$	215.637	+	373.494i	0.471853	+	0.817273i	0.999481	−	0.0322025i	$-0.0102521\pi$
$457$	215.637	+	373.494i	0.471853	+	0.817273i	−0.527629	+	0.849475i	$0.676919\pi$
$458$		0			0
$459$	−270.977	+	207.259i	−0.590364	+	0.451544i
$460$		0			0
$461$		−	151.493i		−	0.328617i	−0.986409	−	0.164309i	$-0.947461\pi$
$461$		−	151.493i		−	0.328617i	0.986409	−	0.164309i	$-0.0525393\pi$
$462$		0			0
$463$	−125.351	+	217.114i	−0.270736	+	0.468928i	−0.969050	−	0.246863i	$-0.920600\pi$
$463$	−125.351	+	217.114i	−0.270736	+	0.468928i	0.698315	+	0.715791i	$0.253934\pi$
$464$		0			0
$465$	−443.620	+	577.517i	−0.954022	+	1.24197i
$466$		0			0
$467$		−	263.024i		−	0.563220i	−0.959529	−	0.281610i	$-0.909132\pi$
$467$		−	263.024i		−	0.563220i	0.959529	−	0.281610i	$-0.0908685\pi$
$468$		0			0
$469$	211.400	+	366.156i	0.450747	+	0.780717i
$470$		0			0
$471$	49.5780	−	375.078i	0.105261	−	0.796344i
$472$		0			0
$473$	−6.93097	+	4.00160i	−0.0146532	+	0.00846004i
$474$		0			0
$475$	−149.286	−	192.174i	−0.314287	−	0.404576i
$476$		0			0
$477$	−215.048	−	215.495i	−0.450835	−	0.451772i
$478$		0			0
$479$	−552.766	−	319.140i	−1.15400	−	0.666262i	−0.204141	−	0.978941i	$-0.565440\pi$
$479$	−552.766	−	319.140i	−1.15400	−	0.666262i	−0.949859	+	0.312679i	$0.898773\pi$
$480$		0			0
$481$	527.572			1.09682
$482$		0			0
$483$	−1380.98	−	182.538i	−2.85917	−	0.377926i
$484$		0			0
$485$	273.809	−	158.084i	0.564556	−	0.325946i
$486$		0			0
$487$	−780.042			−1.60173			−0.800864	−	0.598846i	$-0.795626\pi$
$487$	−780.042			−1.60173			−0.800864	+	0.598846i	$0.795626\pi$
$488$		0			0
$489$	309.329	+	237.612i	0.632575	+	0.485914i
$490$		0			0
$491$	502.452	−	290.091i	1.02332	−	0.590816i	0.108258	−	0.994123i	$-0.465473\pi$
$491$	502.452	−	290.091i	1.02332	−	0.590816i	0.915065	+	0.403307i	$0.132139\pi$
$492$		0			0
$493$	−240.905	−	417.259i	−0.488651	−	0.846368i
$494$		0			0
$495$	36.1979	+	9.73947i	0.0731271	+	0.0196757i
$496$		0			0
$497$			1607.00i			3.23339i
$498$		0			0
$499$	−28.2604	−	48.9485i	−0.0566341	−	0.0980931i	0.836318	−	0.548244i	$-0.184704\pi$
$499$	−28.2604	−	48.9485i	−0.0566341	−	0.0980931i	−0.892952	+	0.450151i	$0.851370\pi$
$500$		0			0
$501$	−31.9961	+	41.6534i	−0.0638645	+	0.0831405i
$502$		0			0
$503$	−144.369	+	83.3516i	−0.287016	+	0.165709i	−0.636596	−	0.771198i	$-0.719658\pi$
$503$	−144.369	+	83.3516i	−0.287016	+	0.165709i	0.349579	+	0.936907i	$0.386325\pi$
$504$		0			0
$505$	−18.1960			−0.0360317
$506$		0			0
$507$	−746.840	−	573.686i	−1.47306	−	1.13153i
$508$		0			0
$509$			300.193i			0.589770i	0.955533	+	0.294885i	$0.0952813\pi$
$509$			300.193i			0.589770i	−0.955533	+	0.294885i	$0.904719\pi$
$510$		0			0
$511$	−242.850			−0.475245
$512$		0			0
$513$	−364.337	−	361.147i	−0.710209	−	0.703991i
$514$		0			0
$515$		−	67.1789i		−	0.130444i
$516$		0			0
$517$	24.6602			0.0476986
$518$		0			0
$519$	−474.836	+	618.154i	−0.914905	+	1.19105i
$520$		0			0
$521$		−	209.742i		−	0.402575i	−0.979532	−	0.201288i	$-0.935487\pi$
$521$		−	209.742i		−	0.402575i	0.979532	−	0.201288i	$-0.0645126\pi$
$522$		0			0
$523$	−492.016	−	852.197i	−0.940758	−	1.62944i	−0.764031	−	0.645180i	$-0.776782\pi$
$523$	−492.016	−	852.197i	−0.940758	−	1.62944i	−0.176727	−	0.984260i	$-0.556551\pi$
$524$		0			0
$525$	407.057	+	312.682i	0.775347	+	0.595584i
$526$		0			0
$527$	−431.991	+	249.410i	−0.819717	+	0.473264i
$528$		0			0
$529$	−679.123			−1.28379
$530$		0			0
$531$	393.531	+	394.348i	0.741112	+	0.742652i
$532$		0			0
$533$	−19.0342	+	10.9894i	−0.0357114	+	0.0206180i
$534$		0			0
$535$	−45.3744	−	78.5908i	−0.0848120	−	0.146899i
$536$		0			0
$537$	−220.943	+	287.630i	−0.411440	+	0.535623i
$538$		0			0
$539$			87.6930i			0.162696i
$540$		0			0
$541$	−486.250	−	842.210i	−0.898799	−	1.55677i	−0.829031	−	0.559202i	$-0.811107\pi$
$541$	−486.250	−	842.210i	−0.898799	−	1.55677i	−0.0697678	−	0.997563i	$-0.522226\pi$
$542$		0			0
$543$	−86.6035	+	655.192i	−0.159491	+	1.20661i
$544$		0			0
$545$		−	198.599i		−	0.364401i
$546$		0			0
$547$	531.315	−	920.265i	0.971326	−	1.68239i	0.279763	−	0.960069i	$-0.409744\pi$
$547$	531.315	−	920.265i	0.971326	−	1.68239i	0.691563	−	0.722316i	$-0.256923\pi$
$548$		0			0
$549$	−868.544	−	233.692i	−1.58205	−	0.425668i
$550$		0			0
$551$	572.157	−	444.468i	1.03840	−	0.806657i
$552$		0			0
$553$	−54.8634	−	95.0262i	−0.0992105	−	0.171838i
$554$		0			0
$555$	439.032	+	58.0314i	0.791048	+	0.104561i
$556$		0			0
$557$	719.310	−	415.294i	1.29140	−	0.745590i	0.312497	−	0.949919i	$-0.398834\pi$
$557$	719.310	−	415.294i	1.29140	−	0.745590i	0.978902	+	0.204329i	$0.0655011\pi$
$558$		0			0
$559$	259.640			0.464471
$560$		0			0
$561$	20.3623	+	15.6414i	0.0362965	+	0.0278812i
$562$		0			0
$563$	530.247	+	306.138i	0.941824	+	0.543762i	0.890532	−	0.454921i	$-0.150333\pi$
$563$	530.247	+	306.138i	0.941824	+	0.543762i	0.0512923	+	0.998684i	$0.483666\pi$
$564$		0			0
$565$	−955.420			−1.69101
$566$		0			0
$567$	935.976	+	542.979i	1.65075	+	0.957636i
$568$		0			0
$569$	177.066	−	102.229i	0.311188	−	0.179665i	−0.336270	−	0.941766i	$-0.609165\pi$
$569$	177.066	−	102.229i	0.311188	−	0.179665i	0.647458	+	0.762101i	$0.275832\pi$
$570$		0			0
$571$	−244.282	+	423.109i	−0.427814	+	0.740996i	−0.996679	−	0.0814355i	$-0.974050\pi$
$571$	−244.282	+	423.109i	−0.427814	+	0.740996i	0.568865	+	0.822431i	$0.307383\pi$
$572$		0			0
$573$	301.421	+	39.8419i	0.526040	+	0.0695322i
$574$		0			0
$575$	385.528	+	222.585i	0.670484	+	0.387104i
$576$		0			0
$577$	856.457			1.48433			0.742164	−	0.670219i	$-0.233800\pi$
$577$	856.457			1.48433			0.742164	+	0.670219i	$0.233800\pi$
$578$		0			0
$579$	125.701	−	950.978i	0.217099	−	1.64245i
$580$		0			0
$581$	1857.89	+	1072.65i	3.19775	+	1.84622i
$582$		0			0
$583$	−11.4567	+	19.8435i	−0.0196512	+	0.0340369i
$584$		0			0
$585$	−859.017	−	860.802i	−1.46841	−	1.47146i
$586$		0			0
$587$			586.816i			0.999686i	0.866116	+	0.499843i	$0.166609\pi$
$587$			586.816i			0.999686i	−0.866116	+	0.499843i	$0.833391\pi$
$588$		0			0
$589$	−460.161	−	592.357i	−0.781257	−	1.00570i
$590$		0			0
$591$	−662.786	+	862.832i	−1.12146	+	1.45995i
$592$		0			0
$593$	−316.266	+	182.596i	−0.533331	+	0.307919i	−0.742372	−	0.669988i	$-0.766299\pi$
$593$	−316.266	+	182.596i	−0.533331	+	0.307919i	0.209041	+	0.977907i	$0.432966\pi$
$594$		0			0
$595$	518.938	+	898.826i	0.872164	+	1.51063i
$596$		0			0
$597$	−49.5501	+	374.867i	−0.0829985	+	0.627919i
$598$		0			0
$599$		−	448.395i		−	0.748573i	−0.927313	−	0.374287i	$-0.877888\pi$
$599$		−	448.395i		−	0.748573i	0.927313	−	0.374287i	$-0.122112\pi$
$600$		0			0
$601$	323.504	+	560.326i	0.538277	+	0.932323i	0.998997	+	0.0447773i	$0.0142578\pi$
$601$	323.504	+	560.326i	0.538277	+	0.932323i	−0.460720	+	0.887545i	$0.652409\pi$
$602$		0			0
$603$	−73.4376	−	275.215i	−0.121787	−	0.456409i
$604$		0			0
$605$			741.183i			1.22510i
$606$		0			0
$607$	413.907	−	716.909i	0.681890	−	1.18107i	−0.292513	−	0.956262i	$-0.594491\pi$
$607$	413.907	−	716.909i	0.681890	−	1.18107i	0.974403	−	0.224807i	$-0.0721753\pi$
$608$		0			0
$609$	−930.944	+	1211.93i	−1.52864	+	1.99003i
$610$		0			0
$611$	−692.843	−	400.013i	−1.13395	−	0.654686i
$612$		0			0
$613$	420.668	−	728.618i	0.686244	−	1.18861i	−0.286800	−	0.957991i	$-0.592591\pi$
$613$	420.668	−	728.618i	0.686244	−	1.18861i	0.973044	−	0.230619i	$-0.0740752\pi$
$614$		0			0
$615$	−17.0486	+	7.05139i	−0.0277212	+	0.0114657i
$616$		0			0
$617$			1004.65i			1.62828i	0.580669	+	0.814139i	$0.302791\pi$
$617$			1004.65i			1.62828i	−0.580669	+	0.814139i	$0.697209\pi$
$618$		0			0
$619$	9.19386	+	15.9242i	0.0148528	+	0.0257257i	0.873356	−	0.487082i	$-0.161939\pi$
$619$	9.19386	+	15.9242i	0.0148528	+	0.0257257i	−0.858503	+	0.512808i	$0.828605\pi$
$620$		0			0
$621$	866.471	+	360.485i	1.39528	+	0.580491i
$622$		0			0
$623$	−1227.29	−	708.578i	−1.96997	−	1.13736i
$624$		0			0
$625$	390.578	+	676.500i	0.624924	+	1.08240i
$626$		0			0
$627$	−19.1231	+	33.5419i	−0.0304994	+	0.0534959i
$628$		0			0
$629$	262.700	+	151.670i	0.417648	+	0.241129i
$630$		0			0
$631$	511.523	+	885.984i	0.810655	+	1.40410i	0.912406	+	0.409285i	$0.134222\pi$
$631$	511.523	+	885.984i	0.810655	+	1.40410i	−0.101752	+	0.994810i	$0.532445\pi$
$632$		0			0
$633$	−20.7530	+	157.005i	−0.0327852	+	0.248034i
$634$		0			0
$635$	64.1038	+	37.0104i	0.100951	+	0.0582841i
$636$		0			0
$637$	1422.47	−	2463.79i	2.23307	−	3.86780i
$638$		0			0
$639$	281.294	−	1045.46i	0.440210	−	1.63609i
$640$		0			0
$641$			549.016i			0.856499i	0.903660	+	0.428250i	$0.140870\pi$
$641$			549.016i			0.856499i	−0.903660	+	0.428250i	$0.859130\pi$
$642$		0			0
$643$	275.137	+	476.551i	0.427896	+	0.741137i	0.996686	−	0.0813455i	$-0.0259217\pi$
$643$	275.137	+	476.551i	0.427896	+	0.741137i	−0.568790	+	0.822483i	$0.692588\pi$
$644$		0			0
$645$	216.065	+	28.5596i	0.334985	+	0.0442785i
$646$		0			0
$647$		−	246.104i		−	0.380376i	−0.981748	−	0.190188i	$-0.939090\pi$
$647$		−	246.104i		−	0.380376i	0.981748	−	0.190188i	$-0.0609098\pi$
$648$		0			0
$649$	20.9653	−	36.3129i	0.0323039	−	0.0559521i
$650$		0			0
$651$	1254.72	+	963.812i	1.92737	+	1.48051i
$652$		0			0
$653$	70.4998	+	40.7031i	0.107963	+	0.0623324i	0.553009	−	0.833175i	$-0.313479\pi$
$653$	70.4998	+	40.7031i	0.107963	+	0.0623324i	−0.445046	+	0.895508i	$0.646813\pi$
$654$		0			0
$655$	−32.5673	+	56.4083i	−0.0497211	+	0.0861195i
$656$		0			0
$657$	157.991	+	42.5094i	0.240474	+	0.0647022i
$658$		0			0
$659$	−492.796	−	284.516i	−0.747793	−	0.431738i	0.0771029	−	0.997023i	$-0.475433\pi$
$659$	−492.796	−	284.516i	−0.747793	−	0.431738i	−0.824896	+	0.565285i	$0.808766\pi$
$660$		0			0
$661$	183.113			0.277025			0.138512	−	0.990361i	$-0.455768\pi$
$661$	183.113			0.277025			0.138512	+	0.990361i	$0.455768\pi$
$662$		0			0
$663$	−318.373	−	769.750i	−0.480201	−	1.16101i
$664$		0			0
$665$	−1232.49	+	957.437i	−1.85337	+	1.43976i
$666$		0			0
$667$	−662.699	+	1147.83i	−0.993552	+	1.72088i
$668$		0			0
$669$	−0.450208	−	0.345828i	−0.000672957	−	0.000516933i
$670$		0			0
$671$			67.6947i			0.100886i
$672$		0			0
$673$	120.295	+	208.356i	0.178744	+	0.309593i	0.941451	−	0.337151i	$-0.109463\pi$
$673$	120.295	+	208.356i	0.178744	+	0.309593i	−0.762707	+	0.646744i	$0.776130\pi$
$674$		0			0
$675$	−210.087	−	274.674i	−0.311239	−	0.406925i
$676$		0			0
$677$	497.193	−	287.055i	0.734407	−	0.424010i	−0.0856253	−	0.996327i	$-0.527289\pi$
$677$	497.193	−	287.055i	0.734407	−	0.424010i	0.820032	+	0.572317i	$0.193955\pi$
$678$		0			0
$679$	−343.454	−	594.880i	−0.505824	−	0.876112i
$680$		0			0
$681$	58.4483	+	7.72572i	0.0858272	+	0.0113447i
$682$		0			0
$683$		−	1104.28i		−	1.61681i	−0.588628	−	0.808404i	$-0.700332\pi$
$683$		−	1104.28i		−	1.61681i	0.588628	−	0.808404i	$-0.299668\pi$
$684$		0			0
$685$	−113.669			−0.165941
$686$		0			0
$687$	−972.873	+	402.386i	−1.41612	+	0.585715i
$688$		0			0
$689$	643.763	−	371.677i	0.934344	−	0.539444i
$690$		0			0
$691$	−182.004	−	315.241i	−0.263393	−	0.456210i	0.703748	−	0.710449i	$-0.251508\pi$
$691$	−182.004	−	315.241i	−0.263393	−	0.456210i	−0.967141	+	0.254239i	$0.918175\pi$
$692$		0			0
$693$	21.1600	−	78.6438i	0.0305339	−	0.113483i
$694$		0			0
$695$	−677.516	+	391.164i	−0.974844	+	0.562826i
$696$		0			0
$697$	−12.6372			−0.0181309
$698$		0			0
$699$	281.496	+	680.589i	0.402712	+	0.973662i
$700$		0			0
$701$	−629.268	−	363.308i	−0.897672	−	0.518271i	−0.0212278	−	0.999775i	$-0.506758\pi$
$701$	−629.268	−	363.308i	−0.897672	−	0.518271i	−0.876444	+	0.481503i	$0.840091\pi$
$702$		0			0
$703$	−172.046	+	422.451i	−0.244731	+	0.600927i
$704$		0			0
$705$	−532.566	−	409.091i	−0.755412	−	0.580271i
$706$		0			0
$707$			39.5327i			0.0559162i
$708$		0			0
$709$	16.0021	−	27.7164i	0.0225699	−	0.0390922i	−0.854520	−	0.519419i	$-0.826148\pi$
$709$	16.0021	−	27.7164i	0.0225699	−	0.0390922i	0.877090	+	0.480327i	$0.159482\pi$
$710$		0			0
$711$	19.0588	+	71.4247i	0.0268056	+	0.100457i
$712$		0			0
$713$	1188.35	+	686.097i	1.66670	+	0.962268i
$714$		0			0
$715$	−45.7640	+	79.2655i	−0.0640055	+	0.110861i
$716$		0			0
$717$	284.857	+	688.717i	0.397291	+	0.960554i
$718$		0			0
$719$	−737.472	−	425.780i	−1.02569	−	0.592183i	−0.109944	−	0.993938i	$-0.535067\pi$
$719$	−737.472	−	425.780i	−1.02569	−	0.592183i	−0.915747	+	0.401755i	$0.868400\pi$
$720$		0			0
$721$	−145.953			−0.202432
$722$		0			0
$723$	−40.0597	+	16.5689i	−0.0554077	+	0.0229169i
$724$		0			0
$725$	422.952	−	244.192i	0.583382	−	0.336816i
$726$		0			0
$727$	572.256			0.787147			0.393574	−	0.919293i	$-0.371239\pi$
$727$	572.256			0.787147			0.393574	+	0.919293i	$0.371239\pi$
$728$		0			0
$729$	−513.874	−	517.083i	−0.704902	−	0.709305i
$730$		0			0
$731$	129.286	+	74.6431i	0.176861	+	0.102111i
$732$		0			0
$733$	−388.675	+	673.206i	−0.530253	+	0.918425i	0.469124	+	0.883132i	$0.344570\pi$
$733$	−388.675	+	673.206i	−0.530253	+	0.918425i	−0.999377	+	0.0352927i	$0.988764\pi$
$734$		0			0
$735$	1454.75	−	1893.83i	1.97925	−	2.57664i
$736$		0			0
$737$	−18.5662	+	10.7192i	−0.0251916	+	0.0145444i
$738$		0			0
$739$	186.632	−	323.256i	0.252546	−	0.437423i	−0.711680	−	0.702504i	$-0.752065\pi$
$739$	186.632	−	323.256i	0.252546	−	0.437423i	0.964226	+	0.265081i	$0.0853987\pi$
$740$		0			0
$741$	1081.36	−	632.183i	1.45932	−	0.853149i
$742$		0			0
$743$	561.225	−	324.023i	0.755349	−	0.436101i	−0.0722742	−	0.997385i	$-0.523026\pi$
$743$	561.225	−	324.023i	0.755349	−	0.436101i	0.827623	+	0.561284i	$0.189692\pi$
$744$		0			0
$745$	613.483	−	1062.58i	0.823467	−	1.42629i
$746$		0			0
$747$	−1020.93	−	1023.05i	−1.36670	−	1.36954i
$748$		0			0
$749$	−170.747	+	98.5808i	−0.227967	+	0.131617i
$750$		0			0
$751$	−405.165			−0.539501			−0.269750	−	0.962930i	$-0.586941\pi$
$751$	−405.165			−0.539501			−0.269750	+	0.962930i	$0.586941\pi$
$752$		0			0
$753$	−136.442	−	18.0349i	−0.181197	−	0.0239507i
$754$		0			0
$755$	−916.652	−	529.229i	−1.21411	−	0.700966i
$756$		0			0
$757$	473.100	−	819.433i	0.624966	−	1.08247i	−0.363581	−	0.931563i	$-0.618446\pi$
$757$	473.100	−	819.433i	0.624966	−	1.08247i	0.988547	−	0.150911i	$-0.0482207\pi$
$758$		0			0
$759$	9.25573	−	70.0235i	0.0121946	−	0.0922576i
$760$		0			0
$761$	−646.639	−	373.337i	−0.849722	−	0.490588i	0.0108347	−	0.999941i	$-0.496551\pi$
$761$	−646.639	−	373.337i	−0.849722	−	0.490588i	−0.860557	+	0.509354i	$0.829884\pi$
$762$		0			0
$763$	−431.476			−0.565500
$764$		0			0
$765$	−180.272	−	675.587i	−0.235649	−	0.883120i
$766$		0			0
$767$	−1178.06	+	680.155i	−1.53594	+	0.886773i
$768$		0			0
$769$	−680.159			−0.884472			−0.442236	−	0.896899i	$-0.645815\pi$
$769$	−680.159			−0.884472			−0.442236	+	0.896899i	$0.645815\pi$
$770$		0			0
$771$	796.651	−	1037.10i	1.03327	−	1.34514i
$772$		0			0
$773$	334.968	−	193.394i	0.433335	−	0.250186i	−0.267431	−	0.963577i	$-0.586175\pi$
$773$	334.968	−	193.394i	0.433335	−	0.250186i	0.700766	+	0.713391i	$0.252842\pi$
$774$		0			0
$775$	−252.813	−	437.885i	−0.326210	−	0.565013i
$776$		0			0
$777$	126.079	−	953.843i	0.162264	−	1.22760i
$778$		0			0
$779$	−2.59251	−	18.8253i	−0.00332799	−	0.0241660i
$780$		0			0
$781$	−81.4840			−0.104333
$782$		0			0
$783$	817.785	−	625.489i	1.04443	−	0.798836i
$784$		0			0
$785$	671.556	+	387.723i	0.855486	+	0.493915i
$786$		0			0
$787$	150.489	−	260.655i	0.191219	−	0.331201i	−0.754436	−	0.656374i	$-0.772089\pi$
$787$	150.489	−	260.655i	0.191219	−	0.331201i	0.945654	+	0.325173i	$0.105423\pi$
$788$		0			0
$789$	377.567	−	491.527i	0.478539	−	0.622975i
$790$		0			0
$791$			2075.75i			2.62421i
$792$		0			0
$793$	1098.08	−	1901.92i	1.38471	−	2.39839i
$794$		0			0
$795$	576.607	−	238.488i	0.725291	−	0.299985i
$796$		0			0
$797$	252.290	+	145.660i	0.316550	+	0.182760i	0.649854	−	0.760059i	$-0.274830\pi$
$797$	252.290	+	145.660i	0.316550	+	0.182760i	−0.333304	+	0.942820i	$0.608163\pi$
$798$		0			0
$799$	−229.997	−	398.367i	−0.287856	−	0.498582i
$800$		0			0
$801$	674.409	+	675.810i	0.841958	+	0.843707i
$802$		0			0
$803$		−	12.3139i		−	0.0153349i
$804$		0			0
$805$	1427.53	−	2472.56i	1.77333	−	3.07150i
$806$		0			0
$807$	−331.303	−	801.012i	−0.410537	−	0.992580i
$808$		0			0
$809$			1049.66i			1.29748i	0.761011	+	0.648739i	$0.224703\pi$
$809$			1049.66i			1.29748i	−0.761011	+	0.648739i	$0.775297\pi$
$810$		0			0
$811$	208.027	+	360.313i	0.256506	+	0.444282i	0.965304	−	0.261130i	$-0.0840952\pi$
$811$	208.027	+	360.313i	0.256506	+	0.444282i	−0.708797	+	0.705412i	$0.750762\pi$
$812$		0			0
$813$	−819.818	+	339.082i	−1.00839	+	0.417074i
$814$		0			0
$815$	−692.351	+	399.729i	−0.849511	+	0.490465i
$816$		0			0
$817$	−84.6708	+	207.906i	−0.103636	+	0.254474i
$818$		0			0
$819$	−1870.18	+	1866.31i	−2.28350	+	2.27876i
$820$		0			0
$821$	72.6869	+	41.9658i	0.0885345	+	0.0511154i	0.543614	−	0.839336i	$-0.317056\pi$
$821$	72.6869	+	41.9658i	0.0885345	+	0.0511154i	−0.455079	+	0.890451i	$0.650389\pi$
$822$		0			0
$823$	765.989			0.930728			0.465364	−	0.885119i	$-0.345923\pi$
$823$	765.989			0.930728			0.465364	+	0.885119i	$0.345923\pi$
$824$		0			0
$825$	−15.8548	+	20.6401i	−0.0192179	+	0.0250184i
$826$		0			0
$827$	−1372.99	+	792.695i	−1.66020	+	0.958518i	−0.687586	+	0.726103i	$0.741329\pi$
$827$	−1372.99	+	792.695i	−1.66020	+	0.958518i	−0.972617	+	0.232415i	$0.925337\pi$
$828$		0			0
$829$	−543.934			−0.656133			−0.328067	−	0.944655i	$-0.606397\pi$
$829$	−543.934			−0.656133			−0.328067	+	0.944655i	$0.606397\pi$
$830$		0			0
$831$	−36.3788	+	275.221i	−0.0437772	+	0.331193i
$832$		0			0
$833$	1416.62	−	817.883i	1.70062	−	0.981852i
$834$		0			0
$835$	−53.8264	−	93.2301i	−0.0644628	−	0.111653i
$836$		0			0
$837$	−647.572	−	846.658i	−0.773683	−	1.01154i
$838$		0			0
$839$			344.007i			0.410020i	0.978760	+	0.205010i	$0.0657227\pi$
$839$			344.007i			0.410020i	−0.978760	+	0.205010i	$0.934277\pi$
$840$		0			0
$841$	306.529	+	530.924i	0.364482	+	0.631301i
$842$		0			0
$843$	−60.4324	−	146.111i	−0.0716874	−	0.173323i
$844$		0			0
$845$	1671.60	−	965.101i	1.97823	−	1.14213i
$846$		0			0
$847$	1610.30			1.90118
$848$		0			0
$849$	−148.822	+	1125.90i	−0.175291	+	1.32615i
$850$		0			0
$851$		−	834.452i		−	0.980555i
$852$		0			0
$853$	−583.024			−0.683499			−0.341749	−	0.939791i	$-0.611019\pi$
$853$	−583.024			−0.683499			−0.341749	+	0.939791i	$0.611019\pi$
$854$		0			0
$855$	969.418	−	407.140i	1.13382	−	0.476188i
$856$		0			0
$857$		−	1404.53i		−	1.63889i	−0.573156	−	0.819446i	$-0.694281\pi$
$857$		−	1404.53i		−	1.63889i	0.573156	−	0.819446i	$-0.305719\pi$
$858$		0			0
$859$	−1087.44			−1.26593			−0.632967	−	0.774179i	$-0.718163\pi$
$859$	−1087.44			−1.26593			−0.632967	+	0.774179i	$0.718163\pi$
$860$		0			0
$861$	15.3199	+	37.0398i	0.0177931	+	0.0430195i
$862$		0			0
$863$		−	1009.86i		−	1.17018i	−0.810970	−	0.585088i	$-0.801060\pi$
$863$		−	1009.86i		−	1.17018i	0.810970	−	0.585088i	$-0.198940\pi$
$864$		0			0
$865$	−798.806	−	1383.57i	−0.923475	−	1.59951i
$866$		0			0
$867$	−50.8503	+	384.704i	−0.0586509	+	0.443719i
$868$		0			0
$869$	4.81837	−	2.78189i	0.00554473	−	0.00320125i
$870$		0			0
$871$	695.505			0.798514
$872$		0			0
$873$	119.311	+	447.131i	0.136668	+	0.512177i
$874$		0			0
$875$	867.318	−	500.746i	0.991221	−	0.572282i
$876$		0			0
$877$	303.466	+	525.619i	0.346028	+	0.599337i	0.985540	−	0.169443i	$-0.0541970\pi$
$877$	303.466	+	525.619i	0.346028	+	0.599337i	−0.639512	+	0.768781i	$0.720864\pi$
$878$		0			0
$879$	547.488	+	1323.70i	0.622853	+	1.50591i
$880$		0			0
$881$			1319.04i			1.49721i	0.663015	+	0.748606i	$0.269277\pi$
$881$			1319.04i			1.49721i	−0.663015	+	0.748606i	$0.730723\pi$
$882$		0			0
$883$	632.552	+	1095.61i	0.716367	+	1.24078i	0.962430	+	0.271530i	$0.0875295\pi$
$883$	632.552	+	1095.61i	0.716367	+	1.24078i	−0.246063	+	0.969254i	$0.579137\pi$
$884$		0			0
$885$	−1055.17	+	436.424i	−1.19228	+	0.493134i
$886$		0			0
$887$			485.196i			0.547008i	0.961871	+	0.273504i	$0.0881827\pi$
$887$			485.196i			0.547008i	−0.961871	+	0.273504i	$0.911817\pi$
$888$		0			0
$889$	80.4090	−	139.272i	0.0904488	−	0.156662i
$890$		0			0
$891$	−27.5322	+	47.4594i	−0.0309003	+	0.0532653i
$892$		0			0
$893$	546.251	−	424.344i	0.611704	−	0.475189i
$894$		0			0
$895$	−371.688	−	643.783i	−0.415294	−	0.719310i
$896$		0			0
$897$	−1395.90	+	1817.21i	−1.55618	+	2.02588i
$898$		0			0
$899$	1303.71	−	752.698i	1.45018	−	0.837261i
$900$		0			0
$901$	427.410			0.474372
$902$		0			0
$903$	62.0488	−	469.425i	0.0687140	−	0.519851i
$904$		0			0
$905$	−1173.08	−	677.280i	−1.29622	−	0.748375i
$906$		0			0
$907$	443.540			0.489018			0.244509	−	0.969647i	$-0.421373\pi$
$907$	443.540			0.489018			0.244509	+	0.969647i	$0.421373\pi$
$908$		0			0
$909$	6.91995	−	25.7188i	0.00761271	−	0.0282935i
$910$		0			0
$911$	−162.124	+	93.6021i	−0.177962	+	0.102747i	−0.586335	−	0.810069i	$-0.699430\pi$
$911$	−162.124	+	93.6021i	−0.177962	+	0.102747i	0.408373	+	0.912815i	$0.366096\pi$
$912$		0			0
$913$	−54.3897	+	94.2058i	−0.0595725	+	0.103183i
$914$		0			0
$915$	1123.00	−	1461.95i	1.22732	−	1.59776i
$916$		0			0
$917$	122.553	+	70.7560i	0.133646	+	0.0771603i
$918$		0			0
$919$	−829.412			−0.902516			−0.451258	−	0.892394i	$-0.649025\pi$
$919$	−829.412			−0.902516			−0.451258	+	0.892394i	$0.649025\pi$
$920$		0			0
$921$	−134.980	+	55.8287i	−0.146559	+	0.0606175i
$922$		0			0
$923$	2289.34	+	1321.75i	2.48032	+	1.43202i
$924$		0			0
$925$	−153.740	+	266.285i	−0.166205	+	0.287875i
$926$		0			0
$927$	94.9528	+	25.5482i	0.102430	+	0.0275601i
$928$		0			0
$929$		−	35.7942i		−	0.0385298i	−0.999814	−	0.0192649i	$-0.993867\pi$
$929$		−	35.7942i		−	0.0385298i	0.999814	−	0.0192649i	$-0.00613259\pi$
$930$		0			0
$931$	1508.99	+	1942.50i	1.62083	+	2.08647i
$932$		0			0
$933$	−77.5750	−	187.558i	−0.0831458	−	0.201027i
$934$		0			0
$935$	−45.5757	+	26.3131i	−0.0487440	+	0.0281424i
$936$		0			0
$937$	−678.876	−	1175.85i	−0.724521	−	1.25491i	−0.959171	−	0.282827i	$-0.908728\pi$
$937$	−678.876	−	1175.85i	−0.724521	−	1.25491i	0.234650	−	0.972080i	$-0.424606\pi$
$938$		0			0
$939$	−7.58543	+	3.13738i	−0.00807820	+	0.00334119i
$940$		0			0
$941$		−	1169.98i		−	1.24334i	−0.783279	−	0.621670i	$-0.786455\pi$
$941$		−	1169.98i		−	1.24334i	0.783279	−	0.621670i	$-0.213545\pi$
$942$		0			0
$943$	17.3818	+	30.1061i	0.0184324	+	0.0319259i
$944$		0			0
$945$	−1761.61	+	1347.38i	−1.86413	+	1.42580i
$946$		0			0
$947$			1036.15i			1.09414i	0.837086	+	0.547072i	$0.184258\pi$
$947$			1036.15i			1.09414i	−0.837086	+	0.547072i	$0.815742\pi$
$948$		0			0
$949$	−199.744	+	345.966i	−0.210478	+	0.364559i
$950$		0			0
$951$	474.409	+	1147.01i	0.498852	+	1.20611i
$952$		0			0
$953$	−21.9587	−	12.6779i	−0.0230416	−	0.0133031i	0.488435	−	0.872600i	$-0.337568\pi$
$953$	−21.9587	−	12.6779i	−0.0230416	−	0.0133031i	−0.511477	+	0.859297i	$0.670901\pi$
$954$		0			0
$955$	−311.583	+	539.677i	−0.326265	+	0.565107i
$956$		0			0
$957$	−61.4517	−	47.2042i	−0.0642129	−	0.0493252i
$958$		0			0
$959$			246.959i			0.257517i
$960$		0			0
$961$	−298.773	−	517.490i	−0.310898	−	0.538491i
$962$		0			0
$963$	128.339	−	34.2456i	0.133270	−	0.0355614i
$964$		0			0
$965$	1702.67	+	983.038i	1.76443	+	1.01869i
$966$		0			0
$967$	597.003	+	1034.04i	0.617376	+	1.06933i	0.989963	+	0.141329i	$0.0451376\pi$
$967$	597.003	+	1034.04i	0.617376	+	1.06933i	−0.372587	+	0.927997i	$0.621529\pi$
$968$		0			0
$969$	720.199	−	3.91398i	0.743240	−	0.00403920i
$970$		0			0
$971$	903.364	+	521.557i	0.930344	+	0.537134i	0.886920	−	0.461922i	$-0.152840\pi$
$971$	903.364	+	521.557i	0.930344	+	0.537134i	0.0434236	+	0.999057i	$0.486173\pi$
$972$		0			0
$973$	849.846	+	1471.98i	0.873429	+	1.51282i
$974$		0			0
$975$	780.253	−	322.717i	0.800259	−	0.330992i
$976$		0			0
$977$	−22.5462	−	13.0171i	−0.0230770	−	0.0133235i	0.488417	−	0.872610i	$-0.337574\pi$
$977$	−22.5462	−	13.0171i	−0.0230770	−	0.0133235i	−0.511494	+	0.859287i	$0.670908\pi$
$978$		0			0
$979$	35.9290	−	62.2308i	0.0366997	−	0.0635657i
$980$		0			0
$981$	280.706	+	75.5272i	0.286143	+	0.0769900i
$982$		0			0
$983$		−	327.709i		−	0.333376i	−0.986010	−	0.166688i	$-0.946693\pi$
$983$		−	327.709i		−	0.333376i	0.986010	−	0.166688i	$-0.0533073\pi$
$984$		0			0
$985$	−1114.99	−	1931.22i	−1.13197	−	1.96063i
$986$		0			0
$987$	−888.794	+	1157.06i	−0.900501	+	1.17230i
$988$		0			0
$989$		−	410.668i		−	0.415236i
$990$		0			0
$991$	−559.358	+	968.836i	−0.564438	+	0.977635i	0.432664	+	0.901555i	$0.357574\pi$
$991$	−559.358	+	968.836i	−0.564438	+	0.977635i	−0.997102	+	0.0760795i	$0.975760\pi$
$992$		0			0
$993$	156.309	−	1182.54i	0.157411	−	1.19088i
$994$		0			0
$995$	−671.179	−	387.505i	−0.674551	−	0.389452i
$996$		0			0
$997$	408.943	−	708.310i	0.410174	−	0.710441i	−0.584735	−	0.811224i	$-0.698801\pi$
$997$	408.943	−	708.310i	0.410174	−	0.710441i	0.994908	+	0.100783i	$0.0321348\pi$
$998$		0			0
$999$	−248.988	+	598.473i	−0.249237	+	0.599072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.be.a.581.9	yes	80
3.2	odd	2		2052.3.be.a.125.9		80
9.2	odd	6		684.3.m.a.353.35	✓	80
9.7	even	3		2052.3.m.a.1493.32		80
19.7	even	3		684.3.m.a.653.35	yes	80
57.26	odd	6		2052.3.m.a.881.9		80
171.7	even	3		2052.3.be.a.197.9		80
171.83	odd	6	inner	684.3.be.a.425.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.35	✓	80	9.2	odd	6
684.3.m.a.653.35	yes	80	19.7	even	3
684.3.be.a.425.9	yes	80	171.83	odd	6	inner
684.3.be.a.581.9	yes	80	1.1	even	1	trivial
2052.3.m.a.881.9		80	57.26	odd	6
2052.3.m.a.1493.32		80	9.7	even	3
2052.3.be.a.125.9		80	3.2	odd	2
2052.3.be.a.197.9		80	171.7	even	3

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.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.37911 - 1.82752i) q^{3} +(5.32501 - 3.07440i) q^{5} +(-6.67945 - 11.5692i) q^{7} +(2.32035 + 8.69574i) q^{9} +O(q^{10})\)	\(q+(-2.37911 - 1.82752i) q^{3} +(5.32501 - 3.07440i) q^{5} +(-6.67945 - 11.5692i) q^{7} +(2.32035 + 8.69574i) q^{9} +(0.586623 - 0.338687i) q^{11} -21.9753 q^{13} +(-18.2873 - 2.41722i) q^{15} +(-10.9425 - 6.31763i) q^{17} +(7.16635 - 17.5967i) q^{19} +(-5.25168 + 39.7311i) q^{21} +34.7581i q^{23} +(6.40383 - 11.0918i) q^{25} +(10.3713 - 24.9286i) q^{27} +(33.0234 + 19.0661i) q^{29} +(19.7392 - 34.1893i) q^{31} +(-2.01460 - 0.266290i) q^{33} +(-71.1363 - 41.0706i) q^{35} -24.0074 q^{37} +(52.2818 + 40.1603i) q^{39} +(0.866161 - 0.500078i) q^{41} -11.8150 q^{43} +(39.0901 + 39.1713i) q^{45} +(31.5282 + 18.2028i) q^{47} +(-64.7302 + 112.116i) q^{49} +(14.4877 + 35.0279i) q^{51} +(-29.2948 + 16.9134i) q^{53} +(2.08251 - 3.60702i) q^{55} +(-49.2078 + 28.7678i) q^{57} +(53.6084 - 30.9508i) q^{59} +(-49.9685 + 86.5480i) q^{61} +(85.1037 - 84.9273i) q^{63} +(-117.019 + 67.5609i) q^{65} -31.6494 q^{67} +(63.5210 - 82.6933i) q^{69} +(-104.178 - 60.1470i) q^{71} +(9.08945 - 15.7434i) q^{73} +(-35.5058 + 14.6854i) q^{75} +(-7.83664 - 4.52448i) q^{77} +8.21376 q^{79} +(-70.2320 + 40.3543i) q^{81} +(-139.075 + 80.2951i) q^{83} -77.6916 q^{85} +(-43.7227 - 105.711i) q^{87} +(91.8708 - 53.0416i) q^{89} +(146.783 + 254.236i) q^{91} +(-109.443 + 45.2664i) q^{93} +(-15.9383 - 115.735i) q^{95} +51.4195 q^{97} +(4.30630 + 4.31525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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