LMFDB - Embedded newform 684.3.s.a.601.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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, 2, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (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			601.6
Character	$\chi$	$=$	684.601
Dual form			684.3.s.a.445.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.67140 - 1.36514i) q^{3} +(-4.45215 + 7.71135i) q^{5} +(-2.28143 + 3.95155i) q^{7} +(5.27278 + 7.29368i) q^{9} +O(q^{10})$	\(q+(-2.67140 - 1.36514i) q^{3} +(-4.45215 + 7.71135i) q^{5} +(-2.28143 + 3.95155i) q^{7} +(5.27278 + 7.29368i) q^{9} +(-0.526632 + 0.912153i) q^{11} +16.8563i q^{13} +(22.4206 - 14.5223i) q^{15} +(3.48650 + 6.03879i) q^{17} +(17.6720 + 6.97862i) q^{19} +(11.4890 - 7.44171i) q^{21} -8.67438 q^{23} +(-27.1433 - 47.0136i) q^{25} +(-4.12881 - 26.6824i) q^{27} +(-32.0106 + 18.4813i) q^{29} +(-9.57498 + 5.52812i) q^{31} +(2.65206 - 1.71780i) q^{33} +(-20.3145 - 35.1858i) q^{35} +11.0819i q^{37} +(23.0113 - 45.0301i) q^{39} +(-18.4835 - 10.6715i) q^{41} +51.1871 q^{43} +(-79.7193 + 8.18769i) q^{45} +(-13.8872 - 24.0533i) q^{47} +(14.0902 + 24.4049i) q^{49} +(-1.07004 - 20.8916i) q^{51} +(-11.4429 - 6.60656i) q^{53} +(-4.68929 - 8.12209i) q^{55} +(-37.6822 - 42.7674i) q^{57} +(-23.2263 - 13.4097i) q^{59} +(-0.965926 - 1.67303i) q^{61} +(-40.8508 + 4.19564i) q^{63} +(-129.985 - 75.0470i) q^{65} +23.9413i q^{67} +(23.1728 + 11.8418i) q^{69} +(-102.629 + 59.2527i) q^{71} +(-46.1686 - 79.9664i) q^{73} +(8.33051 + 162.647i) q^{75} +(-2.40295 - 4.16203i) q^{77} -38.4785i q^{79} +(-25.3956 + 76.9160i) q^{81} +(36.8320 - 63.7949i) q^{83} -62.0896 q^{85} +(110.743 - 5.67208i) q^{87} +(86.6168 + 50.0082i) q^{89} +(-66.6087 - 38.4566i) q^{91} +(33.1253 - 1.69663i) q^{93} +(-132.493 + 105.205i) q^{95} -143.029i q^{97} +(-9.42977 + 0.968498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.67140	−	1.36514i	−0.890467	−	0.455047i
$3$	−2.67140	−	1.36514i	−0.890467	−	0.455047i
$4$		0			0
$5$	−4.45215	+	7.71135i	−0.890430	+	1.54227i	−0.0510696	+	0.998695i	$0.516263\pi$
$5$	−4.45215	+	7.71135i	−0.890430	+	1.54227i	−0.839361	+	0.543575i	$0.817070\pi$
$6$		0			0
$7$	−2.28143	+	3.95155i	−0.325918	+	0.564507i	−0.981698	−	0.190445i	$-0.939007\pi$
$7$	−2.28143	+	3.95155i	−0.325918	+	0.564507i	0.655779	+	0.754953i	$0.272340\pi$
$8$		0			0
$9$	5.27278	+	7.29368i	0.585864	+	0.810409i
$10$		0			0
$11$	−0.526632	+	0.912153i	−0.0478756	+	0.0829230i	−0.888970	−	0.457965i	$-0.848578\pi$
$11$	−0.526632	+	0.912153i	−0.0478756	+	0.0829230i	0.841095	+	0.540888i	$0.181912\pi$
$12$		0			0
$13$			16.8563i			1.29664i	0.761367	+	0.648321i	$0.224529\pi$
$13$			16.8563i			1.29664i	−0.761367	+	0.648321i	$0.775471\pi$
$14$		0			0
$15$	22.4206	−	14.5223i	1.49470	−	0.968154i
$16$		0			0
$17$	3.48650	+	6.03879i	0.205088	+	0.355223i	0.950161	−	0.311760i	$-0.100919\pi$
$17$	3.48650	+	6.03879i	0.205088	+	0.355223i	−0.745073	+	0.666983i	$0.767585\pi$
$18$		0			0
$19$	17.6720	+	6.97862i	0.930104	+	0.367296i
$19$	17.6720	+	6.97862i	0.930104	+	0.367296i
$20$		0			0
$21$	11.4890	−	7.44171i	0.547097	−	0.354367i
$22$		0			0
$23$	−8.67438			−0.377147			−0.188573	−	0.982059i	$-0.560386\pi$
$23$	−8.67438			−0.377147			−0.188573	+	0.982059i	$0.560386\pi$
$24$		0			0
$25$	−27.1433	−	47.0136i	−1.08573	−	1.88054i
$26$		0			0
$27$	−4.12881	−	26.6824i	−0.152919	−	0.988239i
$28$		0			0
$29$	−32.0106	+	18.4813i	−1.10381	+	0.637287i	−0.937220	−	0.348739i	$-0.886610\pi$
$29$	−32.0106	+	18.4813i	−1.10381	+	0.637287i	−0.166593	+	0.986026i	$0.553277\pi$
$30$		0			0
$31$	−9.57498	+	5.52812i	−0.308870	+	0.178326i	−0.646421	−	0.762981i	$-0.723735\pi$
$31$	−9.57498	+	5.52812i	−0.308870	+	0.178326i	0.337551	+	0.941307i	$0.390402\pi$
$32$		0			0
$33$	2.65206	−	1.71780i	0.0803656	−	0.0520546i
$34$		0			0
$35$	−20.3145	−	35.1858i	−0.580415	−	1.00531i
$36$		0			0
$37$			11.0819i			0.299510i	0.988723	+	0.149755i	$0.0478484\pi$
$37$			11.0819i			0.299510i	−0.988723	+	0.149755i	$0.952152\pi$
$38$		0			0
$39$	23.0113	−	45.0301i	0.590033	−	1.15462i
$40$		0			0
$41$	−18.4835	−	10.6715i	−0.450818	−	0.260280i	0.257357	−	0.966316i	$-0.417148\pi$
$41$	−18.4835	−	10.6715i	−0.450818	−	0.260280i	−0.708176	+	0.706036i	$0.750482\pi$
$42$		0			0
$43$	51.1871			1.19040			0.595199	−	0.803578i	$-0.297073\pi$
$43$	51.1871			1.19040			0.595199	+	0.803578i	$0.297073\pi$
$44$		0			0
$45$	−79.7193	+	8.18769i	−1.77154	+	0.181949i
$46$		0			0
$47$	−13.8872	−	24.0533i	−0.295472	−	0.511772i	0.679623	−	0.733562i	$-0.262143\pi$
$47$	−13.8872	−	24.0533i	−0.295472	−	0.511772i	−0.975094	+	0.221790i	$0.928810\pi$
$48$		0			0
$49$	14.0902	+	24.4049i	0.287554	+	0.498059i
$50$		0			0
$51$	−1.07004	−	20.8916i	−0.0209811	−	0.409639i
$52$		0			0
$53$	−11.4429	−	6.60656i	−0.215904	−	0.124652i	0.388148	−	0.921597i	$-0.373115\pi$
$53$	−11.4429	−	6.60656i	−0.215904	−	0.124652i	−0.604052	+	0.796945i	$0.706448\pi$
$54$		0			0
$55$	−4.68929	−	8.12209i	−0.0852598	−	0.147674i
$56$		0			0
$57$	−37.6822	−	42.7674i	−0.661091	−	0.750306i
$58$		0			0
$59$	−23.2263	−	13.4097i	−0.393667	−	0.227284i	0.290081	−	0.957002i	$-0.406318\pi$
$59$	−23.2263	−	13.4097i	−0.393667	−	0.227284i	−0.683748	+	0.729718i	$0.739651\pi$
$60$		0			0
$61$	−0.965926	−	1.67303i	−0.0158349	−	0.0274268i	0.857999	−	0.513651i	$-0.171707\pi$
$61$	−0.965926	−	1.67303i	−0.0158349	−	0.0274268i	−0.873834	+	0.486224i	$0.838374\pi$
$62$		0			0
$63$	−40.8508	+	4.19564i	−0.648426	+	0.0665975i
$64$		0			0
$65$	−129.985	−	75.0470i	−1.99977	−	1.15457i
$66$		0			0
$67$			23.9413i			0.357333i	0.983910	+	0.178666i	$0.0571782\pi$
$67$			23.9413i			0.357333i	−0.983910	+	0.178666i	$0.942822\pi$
$68$		0			0
$69$	23.1728	+	11.8418i	0.335837	+	0.171620i
$70$		0			0
$71$	−102.629	+	59.2527i	−1.44547	+	0.834545i	−0.998207	−	0.0598559i	$-0.980936\pi$
$71$	−102.629	+	59.2527i	−1.44547	+	0.834545i	−0.447267	+	0.894401i	$0.647603\pi$
$72$		0			0
$73$	−46.1686	−	79.9664i	−0.632447	−	1.09543i	−0.987050	−	0.160413i	$-0.948717\pi$
$73$	−46.1686	−	79.9664i	−0.632447	−	1.09543i	0.354603	−	0.935017i	$-0.384616\pi$
$74$		0			0
$75$	8.33051	+	162.647i	0.111073	+	2.16862i
$76$		0			0
$77$	−2.40295	−	4.16203i	−0.0312071	−	0.0540523i
$78$		0			0
$79$		−	38.4785i		−	0.487070i	−0.969892	−	0.243535i	$-0.921693\pi$
$79$		−	38.4785i		−	0.487070i	0.969892	−	0.243535i	$-0.0783071\pi$
$80$		0			0
$81$	−25.3956	+	76.9160i	−0.313526	+	0.949580i
$82$		0			0
$83$	36.8320	−	63.7949i	0.443759	−	0.768613i	−0.554206	−	0.832380i	$-0.686978\pi$
$83$	36.8320	−	63.7949i	0.443759	−	0.768613i	0.997965	+	0.0637666i	$0.0203113\pi$
$84$		0			0
$85$	−62.0896			−0.730466
$86$		0			0
$87$	110.743	−	5.67208i	1.27291	−	0.0651963i
$88$		0			0
$89$	86.6168	+	50.0082i	0.973222	+	0.561890i	0.900217	−	0.435442i	$-0.143408\pi$
$89$	86.6168	+	50.0082i	0.973222	+	0.561890i	0.0730051	+	0.997332i	$0.476741\pi$
$90$		0			0
$91$	−66.6087	−	38.4566i	−0.731964	−	0.422599i
$92$		0			0
$93$	33.1253	−	1.69663i	0.356186	−	0.0182433i
$94$		0			0
$95$	−132.493	+	105.205i	−1.39466	+	1.10742i
$96$		0			0
$97$		−	143.029i		−	1.47452i	−0.675607	−	0.737262i	$-0.736118\pi$
$97$		−	143.029i		−	1.47452i	0.675607	−	0.737262i	$-0.263882\pi$
$98$		0			0
$99$	−9.42977	+	0.968498i	−0.0952502	+	0.00978281i
$100$		0			0
$101$	−16.5909	−	28.7362i	−0.164266	−	0.284517i	0.772128	−	0.635467i	$-0.219192\pi$
$101$	−16.5909	−	28.7362i	−0.164266	−	0.284517i	−0.936394	+	0.350950i	$0.885859\pi$
$102$		0			0
$103$	140.802	−	81.2919i	1.36701	−	0.789241i	0.376462	−	0.926432i	$-0.377141\pi$
$103$	140.802	−	81.2919i	1.36701	−	0.789241i	0.990545	+	0.137191i	$0.0438073\pi$
$104$		0			0
$105$	6.23470	+	121.728i	0.0593781	+	1.15931i
$106$		0			0
$107$			126.606i			1.18323i	0.806220	+	0.591616i	$0.201510\pi$
$107$			126.606i			1.18323i	−0.806220	+	0.591616i	$0.798490\pi$
$108$		0			0
$109$	−91.6855	+	52.9346i	−0.841151	+	0.485639i	−0.857655	−	0.514225i	$-0.828080\pi$
$109$	−91.6855	+	52.9346i	−0.841151	+	0.485639i	0.0165041	+	0.999864i	$0.494746\pi$
$110$		0			0
$111$	15.1283	−	29.6041i	0.136291	−	0.266704i
$112$		0			0
$113$	−51.1065	+	29.5063i	−0.452270	+	0.261118i	−0.708788	−	0.705421i	$-0.750758\pi$
$113$	−51.1065	+	29.5063i	−0.452270	+	0.261118i	0.256519	+	0.966539i	$0.417425\pi$
$114$		0			0
$115$	38.6196	−	66.8912i	0.335823	−	0.581663i
$116$		0			0
$117$	−122.945	+	88.8798i	−1.05081	+	0.759657i
$118$		0			0
$119$	−31.8168			−0.267368
$120$		0			0
$121$	59.9453	+	103.828i	0.495416	+	0.858085i
$122$		0			0
$123$	34.8089	+	53.7405i	0.282999	+	0.436914i
$124$		0			0
$125$	260.777			2.08621
$126$		0			0
$127$	−205.351	−	118.560i	−1.61694	−	0.933541i	−0.987706	−	0.156325i	$-0.950035\pi$
$127$	−205.351	−	118.560i	−1.61694	−	0.933541i	−0.629234	−	0.777216i	$-0.716631\pi$
$128$		0			0
$129$	−136.741	−	69.8777i	−1.06001	−	0.541687i
$130$		0			0
$131$	61.9051	−	107.223i	0.472558	−	0.818494i	−0.526949	−	0.849897i	$-0.676664\pi$
$131$	61.9051	−	107.223i	0.472558	−	0.818494i	0.999507	+	0.0314029i	$0.00999751\pi$
$132$		0			0
$133$	−67.8937	+	53.9105i	−0.510479	+	0.405342i
$134$		0			0
$135$	224.140	+	86.9555i	1.66029	+	0.644115i
$136$		0			0
$137$	−74.0078	−	128.185i	−0.540203	−	0.935658i	−0.998892	−	0.0470616i	$-0.985014\pi$
$137$	−74.0078	−	128.185i	−0.540203	−	0.935658i	0.458689	−	0.888597i	$-0.348319\pi$
$138$		0			0
$139$	151.636			1.09091			0.545453	−	0.838142i	$-0.316358\pi$
$139$	151.636			1.09091			0.545453	+	0.838142i	$0.316358\pi$
$140$		0			0
$141$	4.26209	+	83.2139i	0.0302276	+	0.590170i
$142$		0			0
$143$	−15.3756	−	8.87709i	−0.107522	−	0.0620776i
$144$		0			0
$145$		−	329.126i		−	2.26984i
$146$		0			0
$147$	−4.32440	−	84.4303i	−0.0294177	−	0.574356i
$148$		0			0
$149$	41.0582	−	71.1149i	0.275559	−	0.477281i	−0.694717	−	0.719283i	$-0.744471\pi$
$149$	41.0582	−	71.1149i	0.275559	−	0.477281i	0.970276	+	0.242001i	$0.0778039\pi$
$150$		0			0
$151$	155.595	+	89.8330i	1.03043	+	0.594921i	0.917109	−	0.398637i	$-0.130517\pi$
$151$	155.595	+	89.8330i	1.03043	+	0.594921i	0.113324	+	0.993558i	$0.463850\pi$
$152$		0			0
$153$	−25.6615	+	57.2706i	−0.167722	+	0.374318i
$154$		0			0
$155$		−	98.4480i		−	0.635149i
$156$		0			0
$157$	118.748	−	205.678i	0.756358	−	1.31005i	−0.188338	−	0.982104i	$-0.560310\pi$
$157$	118.748	−	205.678i	0.756358	−	1.31005i	0.944696	−	0.327946i	$-0.106357\pi$
$158$		0			0
$159$	21.5497	+	33.2699i	0.135533	+	0.209245i
$160$		0			0
$161$	19.7900	−	34.2772i	0.122919	−	0.212902i
$162$		0			0
$163$	223.745			1.37267			0.686335	−	0.727286i	$-0.259219\pi$
$163$	223.745			1.37267			0.686335	+	0.727286i	$0.259219\pi$
$164$		0			0
$165$	1.43918	+	28.0989i	0.00872233	+	0.170296i
$166$		0			0
$167$			5.81572i			0.0348247i	0.999848	+	0.0174123i	$0.00554280\pi$
$167$			5.81572i			0.0348247i	−0.999848	+	0.0174123i	$0.994457\pi$
$168$		0			0
$169$	−115.136			−0.681281
$170$		0			0
$171$	42.2806	+	165.691i	0.247255	+	0.968950i
$172$		0			0
$173$			282.198i			1.63120i	0.578613	+	0.815602i	$0.303594\pi$
$173$			282.198i			1.63120i	−0.578613	+	0.815602i	$0.696406\pi$
$174$		0			0
$175$	247.702			1.41544
$176$		0			0
$177$	43.7407	+	67.5300i	0.247123	+	0.381526i
$178$		0			0
$179$		−	25.2455i		−	0.141036i	−0.997510	−	0.0705181i	$-0.977535\pi$
$179$		−	25.2455i		−	0.141036i	0.997510	−	0.0705181i	$-0.0224653\pi$
$180$		0			0
$181$	−136.039	−	78.5424i	−0.751599	−	0.433936i	0.0746723	−	0.997208i	$-0.476209\pi$
$181$	−136.039	−	78.5424i	−0.751599	−	0.433936i	−0.826271	+	0.563272i	$0.809542\pi$
$182$		0			0
$183$	0.296451	+	5.78797i	0.00161995	+	0.0316283i
$184$		0			0
$185$	−85.4561	−	49.3381i	−0.461925	−	0.266692i
$186$		0			0
$187$	−7.34440			−0.0392749
$188$		0			0
$189$	114.857	+	44.5589i	0.607707	+	0.235761i
$190$		0			0
$191$	−107.270	+	185.798i	−0.561625	+	0.972763i	0.435730	+	0.900078i	$0.356490\pi$
$191$	−107.270	+	185.798i	−0.561625	+	0.972763i	−0.997355	+	0.0726857i	$0.976843\pi$
$192$		0			0
$193$	−268.141	−	154.811i	−1.38933	−	0.802132i	−0.396093	−	0.918211i	$-0.629634\pi$
$193$	−268.141	−	154.811i	−1.38933	−	0.802132i	−0.993240	+	0.116079i	$0.962967\pi$
$194$		0			0
$195$	244.793	+	377.929i	1.25535	+	1.93810i
$196$		0			0
$197$	376.293			1.91012			0.955060	−	0.296414i	$-0.0957908\pi$
$197$	376.293			1.91012			0.955060	+	0.296414i	$0.0957908\pi$
$198$		0			0
$199$	−37.6504	+	65.2123i	−0.189198	+	0.327700i	−0.944983	−	0.327119i	$-0.893922\pi$
$199$	−37.6504	+	65.2123i	−0.189198	+	0.327700i	0.755785	+	0.654820i	$0.227255\pi$
$200$		0			0
$201$	32.6832	−	63.9568i	0.162603	−	0.318193i
$202$		0			0
$203$		−	168.655i		−	0.830814i
$204$		0			0
$205$	164.583	−	95.0221i	0.802844	−	0.463522i
$206$		0			0
$207$	−45.7381	−	63.2682i	−0.220957	−	0.305643i
$208$		0			0
$209$	−15.6722	+	12.4444i	−0.0749866	+	0.0595426i
$210$		0			0
$211$	279.402	+	161.313i	1.32418	+	0.764516i	0.984393	−	0.175986i	$-0.0563113\pi$
$211$	279.402	+	161.313i	1.32418	+	0.764516i	0.339788	+	0.940502i	$0.389645\pi$
$212$		0			0
$213$	355.051	−	18.1852i	1.66690	−	0.0853763i
$214$		0			0
$215$	−227.893	+	394.722i	−1.05997	+	1.83592i
$216$		0			0
$217$		−	50.4480i		−	0.232479i
$218$		0			0
$219$	14.1695	+	276.649i	0.0647011	+	1.26324i
$220$		0			0
$221$	−101.792	+	58.7696i	−0.460597	+	0.265926i
$222$		0			0
$223$			48.2068i			0.216174i	0.994141	+	0.108087i	$0.0344725\pi$
$223$			48.2068i			0.216174i	−0.994141	+	0.108087i	$0.965527\pi$
$224$		0			0
$225$	199.781	−	445.867i	0.887917	−	1.98163i
$226$		0			0
$227$	−137.892	−	79.6118i	−0.607453	−	0.350713i	0.164515	−	0.986375i	$-0.447394\pi$
$227$	−137.892	−	79.6118i	−0.607453	−	0.350713i	−0.771968	+	0.635662i	$0.780727\pi$
$228$		0			0
$229$	30.7008	+	53.1753i	0.134065	+	0.232207i	0.925240	−	0.379383i	$-0.123864\pi$
$229$	30.7008	+	53.1753i	0.134065	+	0.232207i	−0.791175	+	0.611590i	$0.790530\pi$
$230$		0			0
$231$	0.737485	+	14.3988i	0.00319258	+	0.0623325i
$232$		0			0
$233$	−123.485	−	213.882i	−0.529977	−	0.917947i	−0.999388	−	0.0349674i	$-0.988867\pi$
$233$	−123.485	−	213.882i	−0.529977	−	0.917947i	0.469412	−	0.882979i	$-0.344466\pi$
$234$		0			0
$235$	247.311			1.05239
$236$		0			0
$237$	−52.5286	+	102.792i	−0.221640	+	0.433720i
$238$		0			0
$239$	140.849	+	243.957i	0.589325	+	1.02074i	0.994321	+	0.106423i	$0.0339396\pi$
$239$	140.849	+	243.957i	0.589325	+	1.02074i	−0.404996	+	0.914319i	$0.632727\pi$
$240$		0			0
$241$	−72.7517	+	42.0032i	−0.301874	+	0.174287i	−0.643285	−	0.765627i	$-0.722429\pi$
$241$	−72.7517	+	42.0032i	−0.301874	+	0.174287i	0.341410	+	0.939914i	$0.389095\pi$
$242$		0			0
$243$	172.843	−	170.805i	0.711288	−	0.702901i
$244$		0			0
$245$	−250.926			−1.02419
$246$		0			0
$247$	−117.634	+	297.885i	−0.476251	+	1.20601i
$248$		0			0
$249$	−185.482	+	120.141i	−0.744908	+	0.482494i
$250$		0			0
$251$	−12.0665	+	20.8998i	−0.0480738	+	0.0832663i	−0.889061	−	0.457789i	$-0.848642\pi$
$251$	−12.0665	+	20.8998i	−0.0480738	+	0.0832663i	0.840987	+	0.541055i	$0.181975\pi$
$252$		0			0
$253$	4.56821	−	7.91236i	0.0180562	−	0.0312742i
$254$		0			0
$255$	165.866	+	84.7611i	0.650457	+	0.332397i
$256$		0			0
$257$			109.226i			0.425002i	0.977161	+	0.212501i	$0.0681609\pi$
$257$			109.226i			0.425002i	−0.977161	+	0.212501i	$0.931839\pi$
$258$		0			0
$259$	−43.7905	−	25.2825i	−0.169075	−	0.0976157i
$260$		0			0
$261$	−303.582	−	136.027i	−1.16315	−	0.521177i
$262$		0			0
$263$	−374.488			−1.42391			−0.711955	−	0.702225i	$-0.752190\pi$
$263$	−374.488			−1.42391			−0.711955	+	0.702225i	$0.752190\pi$
$264$		0			0
$265$	101.891	−	58.8268i	0.384494	−	0.221988i
$266$		0			0
$267$	−163.120	−	251.836i	−0.610936	−	0.943207i
$268$		0			0
$269$	−464.481	+	268.168i	−1.72670	+	0.996909i	−0.824065	+	0.566496i	$0.808299\pi$
$269$	−464.481	+	268.168i	−1.72670	+	0.996909i	−0.902632	+	0.430413i	$0.858368\pi$
$270$		0			0
$271$	123.546	+	213.989i	0.455891	+	0.789626i	0.998739	−	0.0502050i	$-0.0159875\pi$
$271$	123.546	+	213.989i	0.455891	+	0.789626i	−0.542848	+	0.839831i	$0.682654\pi$
$272$		0			0
$273$	125.440	+	193.663i	0.459487	+	0.709389i
$274$		0			0
$275$	57.1781			0.207920
$276$		0			0
$277$	−224.160	+	388.257i	−0.809243	+	1.40165i	0.104147	+	0.994562i	$0.466789\pi$
$277$	−224.160	+	388.257i	−0.809243	+	1.40165i	−0.913389	+	0.407087i	$0.866544\pi$
$278$		0			0
$279$	−90.8071	−	40.6883i	−0.325473	−	0.145836i
$280$		0			0
$281$	303.885	−	175.448i	1.08144	−	0.624371i	0.150158	−	0.988662i	$-0.452022\pi$
$281$	303.885	−	175.448i	1.08144	−	0.624371i	0.931285	+	0.364291i	$0.118689\pi$
$282$		0			0
$283$	82.4426	−	142.795i	0.291316	−	0.504575i	−0.682805	−	0.730601i	$-0.739240\pi$
$283$	82.4426	−	142.795i	0.291316	−	0.504575i	0.974121	+	0.226026i	$0.0725734\pi$
$284$		0			0
$285$	497.561	−	100.173i	1.74583	−	0.351485i
$286$		0			0
$287$	84.3378	−	48.6924i	0.293860	−	0.169660i
$288$		0			0
$289$	120.189	−	208.173i	0.415878	−	0.720321i
$290$		0			0
$291$	−195.255	+	382.088i	−0.670978	+	1.31302i
$292$		0			0
$293$	−56.9902	+	32.9033i	−0.194506	+	0.112298i	−0.594090	−	0.804398i	$-0.702488\pi$
$293$	−56.9902	+	32.9033i	−0.194506	+	0.112298i	0.399584	+	0.916696i	$0.369154\pi$
$294$		0			0
$295$	206.814	−	119.404i	0.701066	−	0.404760i
$296$		0			0
$297$	26.5128	+	10.2857i	0.0892688	+	0.0346321i
$298$		0			0
$299$		−	146.218i		−	0.489025i
$300$		0			0
$301$	−116.780	+	202.269i	−0.387973	+	0.671989i
$302$		0			0
$303$	5.09188	+	99.4148i	0.0168049	+	0.328102i
$304$		0			0
$305$	17.2018			0.0563993
$306$		0			0
$307$	−256.227	+	147.933i	−0.834615	+	0.481865i	−0.855430	−	0.517918i	$-0.826707\pi$
$307$	−256.227	+	147.933i	−0.834615	+	0.481865i	0.0208149	+	0.999783i	$0.493374\pi$
$308$		0			0
$309$	−487.113	+	24.9492i	−1.57642	+	0.0807417i
$310$		0			0
$311$	−102.633	−	177.766i	−0.330010	−	0.571594i	0.652504	−	0.757786i	$-0.273719\pi$
$311$	−102.633	−	177.766i	−0.330010	−	0.571594i	−0.982513	+	0.186192i	$0.940385\pi$
$312$		0			0
$313$	182.485	+	316.073i	0.583018	+	1.00982i	0.995119	+	0.0986790i	$0.0314617\pi$
$313$	182.485	+	316.073i	0.583018	+	1.00982i	−0.412101	+	0.911138i	$0.635205\pi$
$314$		0			0
$315$	149.520	−	333.695i	0.474666	−	1.05935i
$316$		0			0
$317$	−248.263	+	143.335i	−0.783164	+	0.452160i	−0.837551	−	0.546360i	$-0.816013\pi$
$317$	−248.263	+	143.335i	−0.783164	+	0.452160i	0.0543863	+	0.998520i	$0.482680\pi$
$318$		0			0
$319$		−	38.9314i		−	0.122042i
$320$		0			0
$321$	172.835	−	338.215i	0.538427	−	1.05363i
$322$		0			0
$323$	19.4709	+	131.048i	0.0602814	+	0.405722i
$324$		0			0
$325$	792.477	−	457.537i	2.43839	−	1.40781i
$326$		0			0
$327$	317.192	−	16.2461i	0.970006	−	0.0496823i
$328$		0			0
$329$	126.730			0.385198
$330$		0			0
$331$	−105.392	−	60.8478i	−0.318403	−	0.183830i	0.332277	−	0.943182i	$-0.392183\pi$
$331$	−105.392	−	60.8478i	−0.318403	−	0.183830i	−0.650681	+	0.759351i	$0.725516\pi$
$332$		0			0
$333$	−80.8275	+	58.4322i	−0.242725	+	0.175472i
$334$		0			0
$335$	−184.620	−	106.590i	−0.551103	−	0.318180i
$336$		0			0
$337$	2.64151	+	1.52507i	0.00783829	+	0.00452544i	0.503914	−	0.863754i	$-0.331893\pi$
$337$	2.64151	+	1.52507i	0.00783829	+	0.00452544i	−0.496076	+	0.868279i	$0.665226\pi$
$338$		0			0
$339$	176.806	−	9.05575i	0.521552	−	0.0267131i
$340$		0			0
$341$		−	11.6451i		−	0.0341500i
$342$		0			0
$343$	−352.163			−1.02671
$344$		0			0
$345$	−194.485	+	125.972i	−0.563723	+	0.365136i
$346$		0			0
$347$	−114.632	+	198.548i	−0.330352	+	0.572186i	−0.982581	−	0.185836i	$-0.940501\pi$
$347$	−114.632	+	198.548i	−0.330352	+	0.572186i	0.652229	+	0.758022i	$0.273834\pi$
$348$		0			0
$349$	−102.794	+	178.045i	−0.294540	+	0.510158i	−0.974878	−	0.222741i	$-0.928500\pi$
$349$	−102.794	+	178.045i	−0.294540	+	0.510158i	0.680338	+	0.732899i	$0.261833\pi$
$350$		0			0
$351$	449.769	−	69.5967i	1.28139	−	0.198281i
$352$		0			0
$353$	−171.317	+	296.730i	−0.485318	+	0.840595i	−0.999858	−	0.0168717i	$-0.994629\pi$
$353$	−171.317	+	296.730i	−0.485318	+	0.840595i	0.514540	+	0.857466i	$0.327963\pi$
$354$		0			0
$355$		−	1055.21i		−	2.97241i
$356$		0			0
$357$	84.9954	+	43.4344i	0.238082	+	0.121665i
$358$		0			0
$359$	−177.982	−	308.274i	−0.495772	−	0.858702i	0.504217	−	0.863577i	$-0.331781\pi$
$359$	−177.982	−	308.274i	−0.495772	−	0.858702i	−0.999988	+	0.00487566i	$0.998448\pi$
$360$		0			0
$361$	263.598	+	246.652i	0.730188	+	0.683247i
$362$		0			0
$363$	−18.3977	−	359.201i	−0.0506825	−	0.989535i
$364$		0			0
$365$	822.198			2.25260
$366$		0			0
$367$	−238.486	−	413.069i	−0.649825	−	1.12553i	−0.983165	−	0.182722i	$-0.941509\pi$
$367$	−238.486	−	413.069i	−0.649825	−	1.12553i	0.333340	−	0.942807i	$-0.391824\pi$
$368$		0			0
$369$	−19.6253	−	191.082i	−0.0531851	−	0.517836i
$370$		0			0
$371$	52.2123	−	30.1448i	0.140734	−	0.0812528i
$372$		0			0
$373$	113.432	−	65.4898i	0.304106	−	0.175576i	−0.340180	−	0.940360i	$-0.610488\pi$
$373$	113.432	−	65.4898i	0.304106	−	0.175576i	0.644286	+	0.764785i	$0.277155\pi$
$374$		0			0
$375$	−696.639	−	355.997i	−1.85770	−	0.949325i
$376$		0			0
$377$	−311.528	−	539.582i	−0.826333	−	1.43125i
$378$		0			0
$379$		−	121.104i		−	0.319534i	−0.987155	−	0.159767i	$-0.948926\pi$
$379$		−	121.104i		−	0.319534i	0.987155	−	0.159767i	$-0.0510743\pi$
$380$		0			0
$381$	386.725	+	597.054i	1.01503	+	1.56707i
$382$		0			0
$383$	−417.409	−	240.991i	−1.08984	−	0.629220i	−0.156307	−	0.987709i	$-0.549959\pi$
$383$	−417.409	−	240.991i	−1.08984	−	0.629220i	−0.933534	+	0.358489i	$0.883292\pi$
$384$		0			0
$385$	42.7931			0.111151
$386$		0			0
$387$	269.899	+	373.343i	0.697412	+	0.964710i
$388$		0			0
$389$	−273.111	−	473.042i	−0.702085	−	1.21605i	−0.967733	−	0.251977i	$-0.918919\pi$
$389$	−273.111	−	473.042i	−0.702085	−	1.21605i	0.265649	−	0.964070i	$-0.414414\pi$
$390$		0			0
$391$	−30.2432	−	52.3828i	−0.0773483	−	0.133971i
$392$		0			0
$393$	−311.747	+	201.926i	−0.793250	+	0.513806i
$394$		0			0
$395$	296.721	+	171.312i	0.751193	+	0.433702i
$396$		0			0
$397$	27.6892	+	47.9590i	0.0697460	+	0.120804i	0.898789	−	0.438381i	$-0.144448\pi$
$397$	27.6892	+	47.9590i	0.0697460	+	0.120804i	−0.829043	+	0.559184i	$0.811114\pi$
$398$		0			0
$399$	254.967	−	51.3321i	0.639015	−	0.128652i
$400$		0			0
$401$	−457.086	−	263.899i	−1.13987	−	0.658102i	−0.193469	−	0.981106i	$-0.561974\pi$
$401$	−457.086	−	263.899i	−1.13987	−	0.658102i	−0.946397	+	0.323004i	$0.895307\pi$
$402$		0			0
$403$	−93.1839	−	161.399i	−0.231226	−	0.400494i
$404$		0			0
$405$	−480.061	−	538.276i	−1.18534	−	1.32908i
$406$		0			0
$407$	−10.1084	−	5.83606i	−0.0248362	−	0.0143392i
$408$		0			0
$409$			241.831i			0.591275i	0.955300	+	0.295637i	$0.0955320\pi$
$409$			241.831i			0.591275i	−0.955300	+	0.295637i	$0.904468\pi$
$410$		0			0
$411$	22.7136	+	443.465i	0.0552643	+	1.07899i
$412$		0			0
$413$	105.978	−	61.1867i	0.256606	−	0.148152i
$414$		0			0
$415$	327.963	+	568.049i	0.790273	+	1.36879i
$416$		0			0
$417$	−405.080	−	207.004i	−0.971416	−	0.496413i
$418$		0			0
$419$	62.5857	+	108.402i	0.149369	+	0.258715i	0.930994	−	0.365033i	$-0.118942\pi$
$419$	62.5857	+	108.402i	0.149369	+	0.258715i	−0.781625	+	0.623748i	$0.785609\pi$
$420$		0			0
$421$			453.417i			1.07700i	0.842625	+	0.538500i	$0.181009\pi$
$421$			453.417i			1.07700i	−0.842625	+	0.538500i	$0.818991\pi$
$422$		0			0
$423$	102.213	−	228.116i	0.241638	−	0.539282i
$424$		0			0
$425$	189.270	−	327.825i	0.445341	−	0.771354i
$426$		0			0
$427$	8.81477			0.0206435
$428$		0			0
$429$	28.9559	+	44.7041i	0.0674962	+	0.104205i
$430$		0			0
$431$	696.599	+	402.182i	1.61624	+	0.933136i	0.987881	+	0.155211i	$0.0496058\pi$
$431$	696.599	+	402.182i	1.61624	+	0.933136i	0.628358	+	0.777925i	$0.283728\pi$
$432$		0			0
$433$	−53.8698	−	31.1017i	−0.124411	−	0.0718285i	0.436503	−	0.899703i	$-0.356217\pi$
$433$	−53.8698	−	31.1017i	−0.124411	−	0.0718285i	−0.560914	+	0.827874i	$0.689550\pi$
$434$		0			0
$435$	−449.304	+	879.229i	−1.03288	+	2.02122i
$436$		0			0
$437$	−153.293	−	60.5352i	−0.350786	−	0.138524i
$438$		0			0
$439$			465.349i			1.06002i	0.847991	+	0.530011i	$0.177812\pi$
$439$			465.349i			1.06002i	−0.847991	+	0.530011i	$0.822188\pi$
$440$		0			0
$441$	−103.707	+	231.451i	−0.235164	+	0.524832i
$442$		0			0
$443$	278.441	+	482.274i	0.628535	+	1.08865i	0.987846	+	0.155437i	$0.0496785\pi$
$443$	278.441	+	482.274i	0.628535	+	1.08865i	−0.359311	+	0.933218i	$0.616988\pi$
$444$		0			0
$445$	−771.262	+	445.288i	−1.73317	+	1.00065i
$446$		0			0
$447$	−206.765	+	133.926i	−0.462561	+	0.299611i
$448$		0			0
$449$			445.457i			0.992109i	0.868291	+	0.496054i	$0.165218\pi$
$449$			445.457i			0.992109i	−0.868291	+	0.496054i	$0.834782\pi$
$450$		0			0
$451$	19.4681	−	11.2399i	0.0431664	−	0.0249221i
$452$		0			0
$453$	−293.023	−	452.390i	−0.646850	−	0.998653i
$454$		0			0
$455$	593.104	−	342.429i	1.30353	−	0.752591i
$456$		0			0
$457$	−265.110	+	459.184i	−0.580110	+	1.00478i	0.415356	+	0.909659i	$0.363657\pi$
$457$	−265.110	+	459.184i	−0.580110	+	1.00478i	−0.995466	+	0.0951208i	$0.969676\pi$
$458$		0			0
$459$	146.735	−	117.961i	0.319683	−	0.256996i
$460$		0			0
$461$	738.736			1.60246			0.801232	−	0.598354i	$-0.204178\pi$
$461$	738.736			1.60246			0.801232	+	0.598354i	$0.204178\pi$
$462$		0			0
$463$	−450.313	−	779.964i	−0.972597	−	1.68459i	−0.687646	−	0.726046i	$-0.741356\pi$
$463$	−450.313	−	779.964i	−0.972597	−	1.68459i	−0.284951	−	0.958542i	$-0.591977\pi$
$464$		0			0
$465$	−134.395	+	262.994i	−0.289023	+	0.565579i
$466$		0			0
$467$	−20.7828			−0.0445027			−0.0222514	−	0.999752i	$-0.507083\pi$
$467$	−20.7828			−0.0445027			−0.0222514	+	0.999752i	$0.507083\pi$
$468$		0			0
$469$	−94.6052	−	54.6203i	−0.201717	−	0.116461i
$470$		0			0
$471$	−598.004	+	387.340i	−1.26965	+	0.822379i
$472$		0			0
$473$	−26.9568	+	46.6905i	−0.0569911	+	0.0987115i
$474$		0			0
$475$	−151.586	−	1020.25i	−0.319128	−	2.14788i
$476$		0			0
$477$	−12.1497	−	118.296i	−0.0254711	−	0.247999i
$478$		0			0
$479$	−379.098	−	656.617i	−0.791437	−	1.37081i	−0.925077	−	0.379779i	$-0.876000\pi$
$479$	−379.098	−	656.617i	−0.791437	−	1.37081i	0.133640	−	0.991030i	$-0.457333\pi$
$480$		0			0
$481$	−186.800			−0.388357
$482$		0			0
$483$	−99.6603	+	64.5522i	−0.206336	+	0.133648i
$484$		0			0
$485$	1102.95	+	636.786i	2.27411	+	1.31296i
$486$		0			0
$487$		−	241.518i		−	0.495930i	−0.968769	−	0.247965i	$-0.920238\pi$
$487$		−	241.518i		−	0.495930i	0.968769	−	0.247965i	$-0.0797617\pi$
$488$		0			0
$489$	−597.713	−	305.444i	−1.22232	−	0.624629i
$490$		0			0
$491$	−71.9479	+	124.617i	−0.146533	+	0.253803i	−0.929944	−	0.367701i	$-0.880145\pi$
$491$	−71.9479	+	124.617i	−0.146533	+	0.253803i	0.783411	+	0.621505i	$0.213478\pi$
$492$		0			0
$493$	−223.210	−	128.870i	−0.452758	−	0.261400i
$494$		0			0
$495$	34.5143	−	77.0282i	0.0697259	−	0.155612i
$496$		0			0
$497$		−	540.723i		−	1.08797i
$498$		0			0
$499$	−141.590	+	245.240i	−0.283747	+	0.491464i	−0.972304	−	0.233718i	$-0.924911\pi$
$499$	−141.590	+	245.240i	−0.283747	+	0.491464i	0.688558	+	0.725182i	$0.258244\pi$
$500$		0			0
$501$	7.93928	−	15.5361i	0.0158469	−	0.0310103i
$502$		0			0
$503$	269.400	−	466.614i	0.535586	−	0.927661i	−0.463549	−	0.886071i	$-0.653424\pi$
$503$	269.400	−	466.614i	0.535586	−	0.927661i	0.999135	−	0.0415903i	$-0.0132424\pi$
$504$		0			0
$505$	295.460			0.585069
$506$		0			0
$507$	307.576	+	157.178i	0.606659	+	0.310015i
$508$		0			0
$509$		−	804.739i		−	1.58102i	−0.612449	−	0.790510i	$-0.709816\pi$
$509$		−	804.739i		−	1.58102i	0.612449	−	0.790510i	$-0.290184\pi$
$510$		0			0
$511$	421.321			0.824504
$512$		0			0
$513$	113.242	−	500.345i	0.220745	−	0.975332i
$514$		0			0
$515$			1447.69i			2.81106i
$516$		0			0
$517$	29.2537			0.0565836
$518$		0			0
$519$	385.241	−	753.865i	0.742275	−	1.45253i
$520$		0			0
$521$			1019.07i			1.95599i	0.208620	+	0.977997i	$0.433103\pi$
$521$			1019.07i			1.95599i	−0.208620	+	0.977997i	$0.566897\pi$
$522$		0			0
$523$	−586.614	−	338.682i	−1.12163	−	0.647575i	−0.179815	−	0.983700i	$-0.557550\pi$
$523$	−586.614	−	338.682i	−1.12163	−	0.647575i	−0.941817	+	0.336126i	$0.890883\pi$
$524$		0			0
$525$	−661.711	−	338.148i	−1.26040	−	0.644091i
$526$		0			0
$527$	−66.7663	−	38.5475i	−0.126691	−	0.0731452i
$528$		0			0
$529$	−453.755			−0.857760
$530$		0			0
$531$	−24.6611	−	240.112i	−0.0464427	−	0.452189i
$532$		0			0
$533$	179.882	−	311.565i	0.337490	−	0.584550i
$534$		0			0
$535$	−976.303	−	563.669i	−1.82487	−	1.05359i
$536$		0			0
$537$	−34.4637	+	67.4409i	−0.0641781	+	0.125588i
$538$		0			0
$539$	−29.6813			−0.0550674
$540$		0			0
$541$	−333.796	+	578.151i	−0.616998	+	1.06867i	0.373033	+	0.927818i	$0.378318\pi$
$541$	−333.796	+	578.151i	−0.616998	+	1.06867i	−0.990030	+	0.140853i	$0.955015\pi$
$542$		0			0
$543$	256.195	+	395.531i	0.471813	+	0.728419i
$544$		0			0
$545$		−	942.692i		−	1.72971i
$546$		0			0
$547$	−387.363	+	223.644i	−0.708159	+	0.408856i	−0.810379	−	0.585906i	$-0.800739\pi$
$547$	−387.363	+	223.644i	−0.708159	+	0.408856i	0.102220	+	0.994762i	$0.467405\pi$
$548$		0			0
$549$	7.10946	−	15.8667i	0.0129498	−	0.0289011i
$550$		0			0
$551$	−694.665	+	103.212i	−1.26073	+	0.187317i
$552$		0			0
$553$	152.050	+	87.7860i	0.274954	+	0.158745i
$554$		0			0
$555$	160.934	+	248.461i	0.289971	+	0.447678i
$556$		0			0
$557$	−465.088	+	805.556i	−0.834988	+	1.44624i	0.0590530	+	0.998255i	$0.481192\pi$
$557$	−465.088	+	805.556i	−0.834988	+	1.44624i	−0.894041	+	0.447986i	$0.852141\pi$
$558$		0			0
$559$			862.828i			1.54352i
$560$		0			0
$561$	19.6199	+	10.0261i	0.0349730	+	0.0178719i
$562$		0			0
$563$	615.916	−	355.599i	1.09399	−	0.631615i	0.159354	−	0.987222i	$-0.449059\pi$
$563$	615.916	−	355.599i	1.09399	−	0.631615i	0.934636	+	0.355606i	$0.115726\pi$
$564$		0			0
$565$		−	525.467i		−	0.930029i
$566$		0			0
$567$	−245.999	−	275.830i	−0.433861	−	0.486473i
$568$		0			0
$569$	424.190	+	244.906i	0.745501	+	0.430415i	0.824066	−	0.566494i	$-0.191701\pi$
$569$	424.190	+	244.906i	0.745501	+	0.430415i	−0.0785653	+	0.996909i	$0.525034\pi$
$570$		0			0
$571$	−94.8843	−	164.344i	−0.166172	−	0.287819i	0.770899	−	0.636958i	$-0.219807\pi$
$571$	−94.8843	−	164.344i	−0.166172	−	0.287819i	−0.937071	+	0.349139i	$0.886474\pi$
$572$		0			0
$573$	540.203	−	349.901i	0.942762	−	0.610648i
$574$		0			0
$575$	235.451	+	407.813i	0.409480	+	0.709241i
$576$		0			0
$577$	−852.111			−1.47680			−0.738398	−	0.674366i	$-0.764417\pi$
$577$	−852.111			−1.47680			−0.738398	+	0.674366i	$0.764417\pi$
$578$		0			0
$579$	504.974	+	779.614i	0.872148	+	1.34648i
$580$		0			0
$581$	168.059	+	291.087i	0.289258	+	0.501010i
$582$		0			0
$583$	12.0524	−	6.95845i	0.0206730	−	0.0119356i
$584$		0			0
$585$	−138.015	−	1343.78i	−0.235922	−	2.29705i
$586$		0			0
$587$	−661.590			−1.12707			−0.563535	−	0.826092i	$-0.690559\pi$
$587$	−661.590			−1.12707			−0.563535	+	0.826092i	$0.690559\pi$
$588$		0			0
$589$	−207.787	+	30.8727i	−0.352780	+	0.0524154i
$590$		0			0
$591$	−1005.23	−	513.694i	−1.70090	−	0.869194i
$592$		0			0
$593$	−359.755	+	623.113i	−0.606669	+	1.05078i	0.385116	+	0.922868i	$0.374161\pi$
$593$	−359.755	+	623.113i	−0.606669	+	1.05078i	−0.991785	+	0.127914i	$0.959172\pi$
$594$		0			0
$595$	141.653	−	245.350i	0.238072	−	0.412353i
$596$		0			0
$597$	189.603	−	122.810i	0.317593	−	0.205712i
$598$		0			0
$599$		−	370.363i		−	0.618302i	−0.951013	−	0.309151i	$-0.899955\pi$
$599$		−	370.363i		−	0.618302i	0.951013	−	0.309151i	$-0.100045\pi$
$600$		0			0
$601$	335.465	+	193.681i	0.558178	+	0.322264i	0.752414	−	0.658691i	$-0.228889\pi$
$601$	335.465	+	193.681i	0.558178	+	0.322264i	−0.194236	+	0.980955i	$0.562223\pi$
$602$		0			0
$603$	−174.620	+	126.237i	−0.289586	+	0.209348i
$604$		0			0
$605$	−1067.54			−1.76453
$606$		0			0
$607$	834.955	−	482.061i	1.37554	−	0.794170i	0.383924	−	0.923365i	$-0.374572\pi$
$607$	834.955	−	482.061i	1.37554	−	0.794170i	0.991619	+	0.129194i	$0.0412391\pi$
$608$		0			0
$609$	−230.238	+	450.546i	−0.378059	+	0.739813i
$610$		0			0
$611$	405.450	−	234.087i	0.663585	−	0.383121i
$612$		0			0
$613$	−75.7056	−	131.126i	−0.123500	−	0.213909i	0.797645	−	0.603127i	$-0.206079\pi$
$613$	−75.7056	−	131.126i	−0.123500	−	0.213909i	−0.921146	+	0.389218i	$0.872745\pi$
$614$		0			0
$615$	−569.386	+	29.1631i	−0.925831	+	0.0474197i
$616$		0			0
$617$	392.782			0.636600			0.318300	−	0.947990i	$-0.396888\pi$
$617$	392.782			0.636600			0.318300	+	0.947990i	$0.396888\pi$
$618$		0			0
$619$	488.602	−	846.283i	0.789341	−	1.36718i	−0.137031	−	0.990567i	$-0.543756\pi$
$619$	488.602	−	846.283i	0.789341	−	1.36718i	0.926371	−	0.376611i	$-0.122911\pi$
$620$		0			0
$621$	35.8149	+	231.454i	0.0576729	+	0.372711i
$622$		0			0
$623$	−395.220	+	228.180i	−0.634382	+	0.366261i
$624$		0			0
$625$	−482.434	+	835.600i	−0.771895	+	1.33696i
$626$		0			0
$627$	58.8551	−	11.8492i	0.0938678	−	0.0188983i
$628$		0			0
$629$	−66.9210	+	38.6369i	−0.106393	+	0.0614258i
$630$		0			0
$631$	−365.773	+	633.537i	−0.579672	+	1.00402i	0.415845	+	0.909436i	$0.363486\pi$
$631$	−365.773	+	633.537i	−0.579672	+	1.00402i	−0.995517	+	0.0945855i	$0.969847\pi$
$632$		0			0
$633$	−526.181	−	812.355i	−0.831249	−	1.28334i
$634$		0			0
$635$	1828.51	−	1055.69i	2.87954	−	1.66251i
$636$		0			0
$637$	−411.377	+	237.509i	−0.645804	+	0.372855i
$638$		0			0
$639$	−973.308	−	436.114i	−1.52317	−	0.682495i
$640$		0			0
$641$		−	534.564i		−	0.833952i	−0.908917	−	0.416976i	$-0.863090\pi$
$641$		−	534.564i		−	0.833952i	0.908917	−	0.416976i	$-0.136910\pi$
$642$		0			0
$643$	−513.484	+	889.380i	−0.798575	+	1.38317i	0.121969	+	0.992534i	$0.461079\pi$
$643$	−513.484	+	889.380i	−0.798575	+	1.38317i	−0.920544	+	0.390638i	$0.872254\pi$
$644$		0			0
$645$	1147.64	−	743.355i	1.77929	−	1.15249i
$646$		0			0
$647$	83.2309			0.128641			0.0643206	−	0.997929i	$-0.479512\pi$
$647$	83.2309			0.128641			0.0643206	+	0.997929i	$0.479512\pi$
$648$		0			0
$649$	24.4635	−	14.1240i	0.0376941	−	0.0217627i
$650$		0			0
$651$	−68.8687	+	134.767i	−0.105789	+	0.207015i
$652$		0			0
$653$	−512.059	−	886.913i	−0.784165	−	1.35821i	−0.929497	−	0.368830i	$-0.879758\pi$
$653$	−512.059	−	886.913i	−0.784165	−	1.35821i	0.145332	−	0.989383i	$-0.453575\pi$
$654$		0			0
$655$	551.221	+	954.743i	0.841559	+	1.45762i
$656$		0			0
$657$	339.812	−	758.384i	0.517218	−	1.15431i
$658$		0			0
$659$	476.919	−	275.349i	0.723701	−	0.417829i	−0.0924121	−	0.995721i	$-0.529458\pi$
$659$	476.919	−	275.349i	0.723701	−	0.417829i	0.816113	+	0.577892i	$0.196124\pi$
$660$		0			0
$661$			439.526i			0.664942i	0.943114	+	0.332471i	$0.107882\pi$
$661$			439.526i			0.664942i	−0.943114	+	0.332471i	$0.892118\pi$
$662$		0			0
$663$	352.156	−	18.0369i	0.531155	−	0.0272050i
$664$		0			0
$665$	−113.450	−	763.570i	−0.170601	−	1.14823i
$666$		0			0
$667$	277.672	−	160.314i	0.416300	−	0.240351i
$668$		0			0
$669$	65.8091	−	128.780i	0.0983694	−	0.192496i
$670$		0			0
$671$	2.03475			0.00303242
$672$		0			0
$673$	388.654	+	224.389i	0.577495	+	0.333417i	0.760137	−	0.649763i	$-0.225132\pi$
$673$	388.654	+	224.389i	0.577495	+	0.333417i	−0.182642	+	0.983179i	$0.558465\pi$
$674$		0			0
$675$	−1142.37	+	918.360i	−1.69240	+	1.36053i
$676$		0			0
$677$	199.246	+	115.035i	0.294308	+	0.169919i	0.639883	−	0.768472i	$-0.278983\pi$
$677$	199.246	+	115.035i	0.294308	+	0.169919i	−0.345575	+	0.938391i	$0.612316\pi$
$678$		0			0
$679$	565.186	+	326.310i	0.832379	+	0.480574i
$680$		0			0
$681$	259.683	+	400.917i	0.381326	+	0.588718i
$682$		0			0
$683$		−	980.063i		−	1.43494i	−0.696590	−	0.717469i	$-0.745300\pi$
$683$		−	980.063i		−	1.43494i	0.696590	−	0.717469i	$-0.254700\pi$
$684$		0			0
$685$	1317.97			1.92405
$686$		0			0
$687$	−9.42234	−	183.964i	−0.0137152	−	0.267778i
$688$		0			0
$689$	111.362	−	192.885i	0.161629	−	0.279950i
$690$		0			0
$691$	102.099	−	176.841i	0.147756	−	0.255921i	−0.782642	−	0.622472i	$-0.786128\pi$
$691$	102.099	−	176.841i	0.147756	−	0.255921i	0.930398	+	0.366551i	$0.119462\pi$
$692$		0			0
$693$	17.6863	−	39.4718i	0.0255213	−	0.0569578i
$694$		0			0
$695$	−675.106	+	1169.32i	−0.971375	+	1.68247i
$696$		0			0
$697$		−	148.824i		−	0.213521i
$698$		0			0
$699$	37.8985	+	739.938i	0.0542182	+	1.05857i
$700$		0			0
$701$	170.159	+	294.724i	0.242738	+	0.420434i	0.961493	−	0.274829i	$-0.0886212\pi$
$701$	170.159	+	294.724i	0.242738	+	0.420434i	−0.718755	+	0.695263i	$0.755288\pi$
$702$		0			0
$703$	−77.3360	+	195.838i	−0.110009	+	0.278575i
$704$		0			0
$705$	−660.667	−	337.614i	−0.937117	−	0.478886i
$706$		0			0
$707$	151.403			0.214149
$708$		0			0
$709$	25.8318	+	44.7420i	0.0364341	+	0.0631058i	0.883667	−	0.468115i	$-0.155067\pi$
$709$	25.8318	+	44.7420i	0.0364341	+	0.0631058i	−0.847233	+	0.531221i	$0.821733\pi$
$710$		0			0
$711$	280.650	−	202.889i	0.394726	−	0.285357i
$712$		0			0
$713$	83.0570	−	47.9530i	0.116490	−	0.0672552i
$714$		0			0
$715$	136.909	−	79.0443i	0.191481	−	0.110551i
$716$		0			0
$717$	−43.2277	−	843.986i	−0.0602897	−	1.17711i
$718$		0			0
$719$	−320.673	−	555.422i	−0.445999	−	0.772492i	0.552122	−	0.833763i	$-0.313818\pi$
$719$	−320.673	−	555.422i	−0.445999	−	0.772492i	−0.998121	+	0.0612706i	$0.980485\pi$
$720$		0			0
$721$			741.846i			1.02891i
$722$		0			0
$723$	251.689	−	12.8912i	0.348118	−	0.0178301i
$724$		0			0
$725$	1737.75	+	1003.29i	2.39689	+	1.38385i
$726$		0			0
$727$	494.140			0.679698			0.339849	−	0.940480i	$-0.389624\pi$
$727$	494.140			0.679698			0.339849	+	0.940480i	$0.389624\pi$
$728$		0			0
$729$	−694.906	+	220.334i	−0.953232	+	0.302241i
$730$		0			0
$731$	178.464	+	309.108i	0.244137	+	0.422857i
$732$		0			0
$733$	427.809	+	740.986i	0.583641	+	1.01090i	0.995043	+	0.0994414i	$0.0317056\pi$
$733$	427.809	+	740.986i	0.583641	+	1.01090i	−0.411403	+	0.911454i	$0.634961\pi$
$734$		0			0
$735$	670.325	+	342.550i	0.912007	+	0.466054i
$736$		0			0
$737$	−21.8381	−	12.6082i	−0.0296311	−	0.0171075i
$738$		0			0
$739$	544.175	+	942.539i	0.736367	+	1.27543i	0.954121	+	0.299421i	$0.0967937\pi$
$739$	544.175	+	942.539i	0.736367	+	1.27543i	−0.217754	+	0.976004i	$0.569873\pi$
$740$		0			0
$741$	720.903	−	635.184i	0.972878	−	0.857198i
$742$		0			0
$743$	141.199	+	81.5216i	0.190040	+	0.109719i	0.592001	−	0.805937i	$-0.298338\pi$
$743$	141.199	+	81.5216i	0.190040	+	0.109719i	−0.401961	+	0.915657i	$0.631671\pi$
$744$		0			0
$745$	365.595	+	633.229i	0.490731	+	0.849972i
$746$		0			0
$747$	659.507	−	67.7356i	0.882874	−	0.0906768i
$748$		0			0
$749$	−500.290	−	288.842i	−0.667943	−	0.385637i
$750$		0			0
$751$			978.567i			1.30302i	0.758641	+	0.651509i	$0.225864\pi$
$751$			978.567i			1.30302i	−0.758641	+	0.651509i	$0.774136\pi$
$752$		0			0
$753$	60.7658	−	39.3594i	0.0806983	−	0.0522701i
$754$		0			0
$755$	−1385.47	+	799.901i	−1.83506	+	1.05947i
$756$		0			0
$757$	713.647	+	1236.07i	0.942731	+	1.63286i	0.760232	+	0.649652i	$0.225085\pi$
$757$	713.647	+	1236.07i	0.942731	+	1.63286i	0.182499	+	0.983206i	$0.441581\pi$
$758$		0			0
$759$	−23.0050	+	14.9009i	−0.0303096	+	0.0196322i
$760$		0			0
$761$	317.545	+	550.005i	0.417274	+	0.722740i	0.995664	−	0.0930206i	$-0.0296522\pi$
$761$	317.545	+	550.005i	0.417274	+	0.722740i	−0.578390	+	0.815760i	$0.696319\pi$
$762$		0			0
$763$		−	483.066i		−	0.633115i
$764$		0			0
$765$	−327.385	−	452.862i	−0.427954	−	0.591977i
$766$		0			0
$767$	226.039	−	391.511i	0.294706	−	0.510445i
$768$		0			0
$769$	−697.716			−0.907302			−0.453651	−	0.891179i	$-0.649879\pi$
$769$	−697.716			−0.907302			−0.453651	+	0.891179i	$0.649879\pi$
$770$		0			0
$771$	149.108	−	291.785i	0.193396	−	0.378450i
$772$		0			0
$773$	819.856	+	473.344i	1.06062	+	0.612347i	0.925603	−	0.378497i	$-0.123559\pi$
$773$	819.856	+	473.344i	1.06062	+	0.612347i	0.135014	+	0.990844i	$0.456892\pi$
$774$		0			0
$775$	519.793	+	300.103i	0.670701	+	0.387229i
$776$		0			0
$777$	82.4679	+	127.320i	0.106136	+	0.163861i
$778$		0			0
$779$	−252.169	−	317.576i	−0.323708	−	0.407671i
$780$		0			0
$781$		−	124.817i		−	0.159817i
$782$		0			0
$783$	625.293	+	777.815i	0.798586	+	0.993378i
$784$		0			0
$785$	1057.37	+	1831.42i	1.34697	+	2.33302i
$786$		0			0
$787$	−630.202	+	363.847i	−0.800765	+	0.462322i	−0.843739	−	0.536754i	$-0.819650\pi$
$787$	−630.202	+	363.847i	−0.800765	+	0.462322i	0.0429736	+	0.999076i	$0.486317\pi$
$788$		0			0
$789$	1000.41	+	511.230i	1.26795	+	0.647946i
$790$		0			0
$791$		−	269.266i		−	0.340413i
$792$		0			0
$793$	28.2012	−	16.2820i	0.0355627	−	0.0205321i
$794$		0			0
$795$	−352.499	+	18.0544i	−0.443394	+	0.0227100i
$796$		0			0
$797$	845.328	−	488.051i	1.06064	−	0.612360i	0.135029	−	0.990842i	$-0.456887\pi$
$797$	845.328	−	488.051i	1.06064	−	0.612360i	0.925609	+	0.378482i	$0.123554\pi$
$798$		0			0
$799$	96.8351	−	167.723i	0.121195	−	0.209917i
$800$		0			0
$801$	91.9672	+	895.437i	0.114815	+	1.11790i
$802$		0			0
$803$	97.2555			0.121115
$804$		0			0
$805$	176.216	+	305.215i	0.218902	+	0.379149i
$806$		0			0
$807$	1606.90	−	82.3032i	1.99121	−	0.101987i
$808$		0			0
$809$	−729.554			−0.901797			−0.450899	−	0.892575i	$-0.648896\pi$
$809$	−729.554			−0.901797			−0.450899	+	0.892575i	$0.648896\pi$
$810$		0			0
$811$	−839.889	−	484.910i	−1.03562	−	0.597916i	−0.117031	−	0.993128i	$-0.537338\pi$
$811$	−839.889	−	484.910i	−1.03562	−	0.597916i	−0.918590	+	0.395212i	$0.870671\pi$
$812$		0			0
$813$	−37.9175	−	740.308i	−0.0466389	−	0.910588i
$814$		0			0
$815$	−996.147	+	1725.38i	−1.22227	+	2.11703i
$816$		0			0
$817$	904.578	+	357.216i	1.10719	+	0.437228i
$818$		0			0
$819$	−70.7232	−	688.596i	−0.0863531	−	0.840776i
$820$		0			0
$821$	161.947	+	280.500i	0.197255	+	0.341656i	0.947637	−	0.319348i	$-0.103464\pi$
$821$	161.947	+	280.500i	0.197255	+	0.341656i	−0.750382	+	0.661004i	$0.770131\pi$
$822$		0			0
$823$	1235.10			1.50072			0.750362	−	0.661027i	$-0.229879\pi$
$823$	1235.10			1.50072			0.750362	+	0.661027i	$0.229879\pi$
$824$		0			0
$825$	−152.746	−	78.0562i	−0.185146	−	0.0946135i
$826$		0			0
$827$	200.684	+	115.865i	0.242665	+	0.140103i	0.616401	−	0.787432i	$-0.288590\pi$
$827$	200.684	+	115.865i	0.242665	+	0.140103i	−0.373736	+	0.927535i	$0.621923\pi$
$828$		0			0
$829$			127.878i			0.154256i	0.997021	+	0.0771281i	$0.0245751\pi$
$829$			127.878i			0.154256i	−0.997021	+	0.0771281i	$0.975425\pi$
$830$		0			0
$831$	1128.85	−	731.180i	1.35842	−	0.879880i
$832$		0			0
$833$	−98.2507	+	170.175i	−0.117948	+	0.204292i
$834$		0			0
$835$	−44.8471	−	25.8925i	−0.0537091	−	0.0310090i
$836$		0			0
$837$	187.037	+	232.659i	0.223461	+	0.277968i
$838$		0			0
$839$		−	185.566i		−	0.221175i	−0.993866	−	0.110587i	$-0.964727\pi$
$839$		−	185.566i		−	0.221175i	0.993866	−	0.110587i	$-0.0352732\pi$
$840$		0			0
$841$	262.618	−	454.868i	0.312269	−	0.540866i
$842$		0			0
$843$	−1051.31	+	53.8466i	−1.24711	+	0.0638750i
$844$		0			0
$845$	512.605	−	887.858i	0.606633	−	1.05072i
$846$		0			0
$847$	−547.044			−0.645860
$848$		0			0
$849$	−415.172	+	268.916i	−0.489013	+	0.316745i
$850$		0			0
$851$		−	96.1282i		−	0.112959i
$852$		0			0
$853$	−1350.44			−1.58316			−0.791581	−	0.611064i	$-0.790742\pi$
$853$	−1350.44			−1.58316			−0.791581	+	0.611064i	$0.790742\pi$
$854$		0			0
$855$	−1465.94	−	411.638i	−1.71455	−	0.481448i
$856$		0			0
$857$			178.226i			0.207965i	0.994579	+	0.103983i	$0.0331586\pi$
$857$			178.226i			0.207965i	−0.994579	+	0.103983i	$0.966841\pi$
$858$		0			0
$859$	319.958			0.372478			0.186239	−	0.982504i	$-0.440370\pi$
$859$	319.958			0.372478			0.186239	+	0.982504i	$0.440370\pi$
$860$		0			0
$861$	−291.772	+	14.9441i	−0.338876	+	0.0173567i
$862$		0			0
$863$		−	757.163i		−	0.877362i	−0.898643	−	0.438681i	$-0.855446\pi$
$863$		−	757.163i		−	0.877362i	0.898643	−	0.438681i	$-0.144554\pi$
$864$		0			0
$865$	−2176.13	−	1256.39i	−2.51576	−	1.45247i
$866$		0			0
$867$	−605.258	+	392.039i	−0.698106	+	0.452179i
$868$		0			0
$869$	35.0983	+	20.2640i	0.0403893	+	0.0233188i
$870$		0			0
$871$	−403.563			−0.463332
$872$		0			0
$873$	1043.21	−	754.160i	1.19497	−	0.863871i
$874$		0			0
$875$	−594.943	+	1030.47i	−0.679935	+	1.17768i
$876$		0			0
$877$	689.070	+	397.835i	0.785712	+	0.453631i	0.838451	−	0.544977i	$-0.183462\pi$
$877$	689.070	+	397.835i	0.785712	+	0.453631i	−0.0527385	+	0.998608i	$0.516795\pi$
$878$		0			0
$879$	197.161	−	10.0983i	0.224302	−	0.0114884i
$880$		0			0
$881$	812.402			0.922136			0.461068	−	0.887365i	$-0.347466\pi$
$881$	812.402			0.922136			0.461068	+	0.887365i	$0.347466\pi$
$882$		0			0
$883$	327.533	−	567.304i	0.370932	−	0.642474i	−0.618777	−	0.785567i	$-0.712372\pi$
$883$	327.533	−	567.304i	0.370932	−	0.642474i	0.989709	+	0.143093i	$0.0457048\pi$
$884$		0			0
$885$	−715.488	+	36.6462i	−0.808461	+	0.0414082i
$886$		0			0
$887$		−	464.445i		−	0.523613i	−0.965120	−	0.261807i	$-0.915682\pi$
$887$		−	464.445i		−	0.523613i	0.965120	−	0.261807i	$-0.0843183\pi$
$888$		0			0
$889$	936.989	−	540.971i	1.05398	−	0.608516i
$890$		0			0
$891$	−56.7850	−	63.6711i	−0.0637318	−	0.0714602i
$892$		0			0
$893$	−77.5551	−	521.982i	−0.0868478	−	0.584527i
$894$		0			0
$895$	194.677	+	112.397i	0.217516	+	0.125583i
$896$		0			0
$897$	−199.609	+	390.608i	−0.222529	+	0.435461i
$898$		0			0
$899$	204.334	−	353.917i	0.227290	−	0.393678i
$900$		0			0
$901$		−	92.1350i		−	0.102259i
$902$		0			0
$903$	588.091	−	380.920i	0.651263	−	0.421838i
$904$		0			0
$905$	1211.34	−	699.365i	1.33849	−	0.772779i
$906$		0			0
$907$		−	1549.89i		−	1.70881i	−0.519608	−	0.854405i	$-0.673922\pi$
$907$		−	1549.89i		−	1.70881i	0.519608	−	0.854405i	$-0.326078\pi$
$908$		0			0
$909$	122.113	−	272.528i	0.134338	−	0.299811i
$910$		0			0
$911$	−276.396	−	159.577i	−0.303398	−	0.175167i	0.340570	−	0.940219i	$-0.389380\pi$
$911$	−276.396	−	159.577i	−0.303398	−	0.175167i	−0.643968	+	0.765052i	$0.722713\pi$
$912$		0			0
$913$	38.7938	+	67.1928i	0.0424905	+	0.0735957i
$914$		0			0
$915$	−45.9529	−	23.4829i	−0.0502218	−	0.0256644i
$916$		0			0
$917$	282.464	+	489.242i	0.308030	+	0.533524i
$918$		0			0
$919$	−1193.65			−1.29886			−0.649431	−	0.760421i	$-0.724993\pi$
$919$	−1193.65			−1.29886			−0.649431	+	0.760421i	$0.724993\pi$
$920$		0			0
$921$	886.434	−	45.4018i	0.962469	−	0.0492962i
$922$		0			0
$923$	−998.784	−	1729.94i	−1.08211	−	1.87426i
$924$		0			0
$925$	520.997	−	300.798i	0.563240	−	0.325187i
$926$		0			0
$927$	1335.33	+	598.328i	1.44049	+	0.645446i
$928$		0			0
$929$	1612.12			1.73533			0.867664	−	0.497152i	$-0.165621\pi$
$929$	1612.12			1.73533			0.867664	+	0.497152i	$0.165621\pi$
$930$		0			0
$931$	78.6888	+	529.613i	0.0845207	+	0.568864i
$932$		0			0
$933$	31.4990	+	614.992i	0.0337610	+	0.659156i
$934$		0			0
$935$	32.6984	−	56.6353i	0.0349715	−	0.0605725i
$936$		0			0
$937$	−298.001	+	516.152i	−0.318037	+	0.550856i	−0.980078	−	0.198611i	$-0.936357\pi$
$937$	−298.001	+	516.152i	−0.318037	+	0.550856i	0.662041	+	0.749467i	$0.269690\pi$
$938$		0			0
$939$	−56.0061	−	1093.47i	−0.0596444	−	1.16451i
$940$		0			0
$941$			1310.21i			1.39236i	0.717867	+	0.696180i	$0.245119\pi$
$941$			1310.21i			1.39236i	−0.717867	+	0.696180i	$0.754881\pi$
$942$		0			0
$943$	160.333	+	92.5685i	0.170025	+	0.0981638i
$944$		0			0
$945$	−854.968	+	687.317i	−0.904728	+	0.727319i
$946$		0			0
$947$	45.4917			0.0480377			0.0240188	−	0.999712i	$-0.492354\pi$
$947$	45.4917			0.0480377			0.0240188	+	0.999712i	$0.492354\pi$
$948$		0			0
$949$	1347.94	−	778.234i	1.42038	−	0.820057i
$950$		0			0
$951$	858.883	−	43.9907i	0.903136	−	0.0462573i
$952$		0			0
$953$	381.297	−	220.142i	0.400102	−	0.230999i	−0.286426	−	0.958102i	$-0.592467\pi$
$953$	381.297	−	220.142i	0.400102	−	0.230999i	0.686528	+	0.727104i	$0.259134\pi$
$954$		0			0
$955$	−955.168	−	1654.40i	−1.00018	−	1.73236i
$956$		0			0
$957$	−53.1469	+	104.001i	−0.0555349	+	0.108674i
$958$		0			0
$959$	675.374			0.704248
$960$		0			0
$961$	−419.380	+	726.387i	−0.436399	+	0.755866i
$962$		0			0
$963$	−923.423	+	667.565i	−0.958903	+	0.693214i
$964$		0			0
$965$	2387.61	−	1378.49i	2.47421	−	1.42848i
$966$		0			0
$967$	378.829	−	656.151i	0.391757	−	0.678543i	−0.600924	−	0.799306i	$-0.705201\pi$
$967$	378.829	−	656.151i	0.391757	−	0.678543i	0.992681	+	0.120763i	$0.0385341\pi$
$968$		0			0
$969$	126.885	−	376.663i	0.130944	−	0.388713i
$970$		0			0
$971$	−1563.97	+	902.956i	−1.61068	+	0.929924i	−0.621463	+	0.783444i	$0.713461\pi$
$971$	−1563.97	+	902.956i	−1.61068	+	0.929924i	−0.989214	+	0.146480i	$0.953205\pi$
$972$		0			0
$973$	−345.946	+	599.197i	−0.355546	+	0.615824i
$974$		0			0
$975$	−2741.63	+	140.422i	−2.81192	+	0.144023i
$976$		0			0
$977$	−1432.56	+	827.090i	−1.46629	+	0.846561i	−0.999289	−	0.0376982i	$-0.987997\pi$
$977$	−1432.56	+	827.090i	−1.46629	+	0.846561i	−0.466997	+	0.884259i	$0.654664\pi$
$978$		0			0
$979$	−91.2303	+	52.6719i	−0.0931873	+	0.0538017i
$980$		0			0
$981$	−869.526	−	389.612i	−0.886367	−	0.397158i
$982$		0			0
$983$		−	673.714i		−	0.685365i	−0.939451	−	0.342683i	$-0.888664\pi$
$983$		−	673.714i		−	0.685365i	0.939451	−	0.342683i	$-0.111336\pi$
$984$		0			0
$985$	−1675.32	+	2901.73i	−1.70083	+	2.94592i
$986$		0			0
$987$	−338.548	−	173.005i	−0.343007	−	0.175283i
$988$		0			0
$989$	−444.017			−0.448955
$990$		0			0
$991$	−999.399	+	577.003i	−1.00848	+	0.582244i	−0.910745	−	0.412969i	$-0.864492\pi$
$991$	−999.399	+	577.003i	−1.00848	+	0.582244i	−0.0977305	+	0.995213i	$0.531158\pi$
$992$		0			0
$993$	198.477	+	306.423i	0.199876	+	0.308583i
$994$		0			0
$995$	−335.250	−	580.670i	−0.336935	−	0.583588i
$996$		0			0
$997$	−476.239	−	824.870i	−0.477672	−	0.827352i	0.522000	−	0.852945i	$-0.325186\pi$
$997$	−476.239	−	824.870i	−0.477672	−	0.827352i	−0.999672	+	0.0255931i	$0.991853\pi$
$998$		0			0
$999$	295.691	−	45.7549i	0.295987	−	0.0458007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.601.6	yes	80
3.2	odd	2		2052.3.s.a.829.40		80
9.4	even	3		684.3.bl.a.373.22	yes	80
9.5	odd	6		2052.3.bl.a.145.1		80
19.8	odd	6		684.3.bl.a.673.22	yes	80
57.8	even	6		2052.3.bl.a.1585.1		80
171.103	odd	6	inner	684.3.s.a.445.6	✓	80
171.122	even	6		2052.3.s.a.901.40		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.6	✓	80	171.103	odd	6	inner
684.3.s.a.601.6	yes	80	1.1	even	1	trivial
684.3.bl.a.373.22	yes	80	9.4	even	3
684.3.bl.a.673.22	yes	80	19.8	odd	6
2052.3.s.a.829.40		80	3.2	odd	2
2052.3.s.a.901.40		80	171.122	even	6
2052.3.bl.a.145.1		80	9.5	odd	6
2052.3.bl.a.1585.1		80	57.8	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.67140 - 1.36514i) q^{3} +(-4.45215 + 7.71135i) q^{5} +(-2.28143 + 3.95155i) q^{7} +(5.27278 + 7.29368i) q^{9} +O(q^{10})\)	\(q+(-2.67140 - 1.36514i) q^{3} +(-4.45215 + 7.71135i) q^{5} +(-2.28143 + 3.95155i) q^{7} +(5.27278 + 7.29368i) q^{9} +(-0.526632 + 0.912153i) q^{11} +16.8563i q^{13} +(22.4206 - 14.5223i) q^{15} +(3.48650 + 6.03879i) q^{17} +(17.6720 + 6.97862i) q^{19} +(11.4890 - 7.44171i) q^{21} -8.67438 q^{23} +(-27.1433 - 47.0136i) q^{25} +(-4.12881 - 26.6824i) q^{27} +(-32.0106 + 18.4813i) q^{29} +(-9.57498 + 5.52812i) q^{31} +(2.65206 - 1.71780i) q^{33} +(-20.3145 - 35.1858i) q^{35} +11.0819i q^{37} +(23.0113 - 45.0301i) q^{39} +(-18.4835 - 10.6715i) q^{41} +51.1871 q^{43} +(-79.7193 + 8.18769i) q^{45} +(-13.8872 - 24.0533i) q^{47} +(14.0902 + 24.4049i) q^{49} +(-1.07004 - 20.8916i) q^{51} +(-11.4429 - 6.60656i) q^{53} +(-4.68929 - 8.12209i) q^{55} +(-37.6822 - 42.7674i) q^{57} +(-23.2263 - 13.4097i) q^{59} +(-0.965926 - 1.67303i) q^{61} +(-40.8508 + 4.19564i) q^{63} +(-129.985 - 75.0470i) q^{65} +23.9413i q^{67} +(23.1728 + 11.8418i) q^{69} +(-102.629 + 59.2527i) q^{71} +(-46.1686 - 79.9664i) q^{73} +(8.33051 + 162.647i) q^{75} +(-2.40295 - 4.16203i) q^{77} -38.4785i q^{79} +(-25.3956 + 76.9160i) q^{81} +(36.8320 - 63.7949i) q^{83} -62.0896 q^{85} +(110.743 - 5.67208i) q^{87} +(86.6168 + 50.0082i) q^{89} +(-66.6087 - 38.4566i) q^{91} +(33.1253 - 1.69663i) q^{93} +(-132.493 + 105.205i) q^{95} -143.029i q^{97} +(-9.42977 + 0.968498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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