LMFDB - Embedded newform 684.3.m.a.653.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(353,684)]

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, 4]))

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

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.m (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			653.30
Character	$\chi$	$=$	684.653
Dual form			684.3.m.a.353.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99633 + 2.23935i) q^{3} +3.96092i q^{5} +(-6.03683 - 10.4561i) q^{7} +(-1.02935 + 8.94094i) q^{9} +O(q^{10})$	\(q+(1.99633 + 2.23935i) q^{3} +3.96092i q^{5} +(-6.03683 - 10.4561i) q^{7} +(-1.02935 + 8.94094i) q^{9} +(13.9578 - 8.05857i) q^{11} +(-11.3972 - 19.7406i) q^{13} +(-8.86988 + 7.90730i) q^{15} +(7.80805 - 4.50798i) q^{17} +(7.69436 - 17.3723i) q^{19} +(11.3633 - 34.3923i) q^{21} +(3.57360 - 2.06322i) q^{23} +9.31110 q^{25} +(-22.0768 + 15.5440i) q^{27} +32.5606i q^{29} +(17.6133 - 30.5071i) q^{31} +(45.9104 + 15.1689i) q^{33} +(41.4158 - 23.9114i) q^{35} -12.1006 q^{37} +(21.4534 - 64.9310i) q^{39} -17.7572i q^{41} +(-0.131207 + 0.227258i) q^{43} +(-35.4144 - 4.07717i) q^{45} -62.9065i q^{47} +(-48.3866 + 83.8080i) q^{49} +(25.6824 + 8.48553i) q^{51} +(70.5478 + 40.7308i) q^{53} +(31.9193 + 55.2859i) q^{55} +(54.2631 - 17.4505i) q^{57} +17.2013i q^{59} -68.4804 q^{61} +(99.7013 - 43.2120i) q^{63} +(78.1909 - 45.1435i) q^{65} +(37.2470 + 64.5137i) q^{67} +(11.7544 + 3.88367i) q^{69} +(-104.803 + 60.5078i) q^{71} +(22.6715 + 39.2682i) q^{73} +(18.5880 + 20.8508i) q^{75} +(-168.522 - 97.2963i) q^{77} +(37.4287 - 64.8283i) q^{79} +(-78.8809 - 18.4067i) q^{81} +(44.5212 - 25.7043i) q^{83} +(17.8558 + 30.9271i) q^{85} +(-72.9145 + 65.0017i) q^{87} +(-20.7932 - 12.0050i) q^{89} +(-137.606 + 238.341i) q^{91} +(103.478 - 21.4600i) q^{93} +(68.8103 + 30.4767i) q^{95} +(67.9519 - 117.696i) q^{97} +(57.6837 + 133.091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.99633	+	2.23935i	0.665443	+	0.746449i
$3$	1.99633	+	2.23935i	0.665443	+	0.746449i
$4$		0			0
$5$			3.96092i			0.792184i	0.918211	+	0.396092i	$0.129634\pi$
$5$			3.96092i			0.792184i	−0.918211	+	0.396092i	$0.870366\pi$
$6$		0			0
$7$	−6.03683	−	10.4561i	−0.862404	−	1.49373i	−0.869602	−	0.493753i	$-0.835625\pi$
$7$	−6.03683	−	10.4561i	−0.862404	−	1.49373i	0.00719814	−	0.999974i	$-0.497709\pi$
$8$		0			0
$9$	−1.02935	+	8.94094i	−0.114372	+	0.993438i
$10$		0			0
$11$	13.9578	−	8.05857i	1.26890	−	0.732597i	0.294116	−	0.955770i	$-0.404975\pi$
$11$	13.9578	−	8.05857i	1.26890	−	0.732597i	0.974779	+	0.223173i	$0.0716414\pi$
$12$		0			0
$13$	−11.3972	−	19.7406i	−0.876710	−	1.51851i	−0.854930	−	0.518743i	$-0.826400\pi$
$13$	−11.3972	−	19.7406i	−0.876710	−	1.51851i	−0.0217797	−	0.999763i	$-0.506933\pi$
$14$		0			0
$15$	−8.86988	+	7.90730i	−0.591325	+	0.527153i
$16$		0			0
$17$	7.80805	−	4.50798i	0.459297	−	0.265175i	−0.252452	−	0.967610i	$-0.581237\pi$
$17$	7.80805	−	4.50798i	0.459297	−	0.265175i	0.711749	+	0.702434i	$0.247904\pi$
$18$		0			0
$19$	7.69436	−	17.3723i	0.404966	−	0.914332i
$19$	7.69436	−	17.3723i	0.404966	−	0.914332i
$20$		0			0
$21$	11.3633	−	34.3923i	0.541111	−	1.63773i
$22$		0			0
$23$	3.57360	−	2.06322i	0.155374	−	0.0897053i	−0.420297	−	0.907387i	$-0.638074\pi$
$23$	3.57360	−	2.06322i	0.155374	−	0.0897053i	0.575671	+	0.817681i	$0.304741\pi$
$24$		0			0
$25$	9.31110			0.372444
$26$		0			0
$27$	−22.0768	+	15.5440i	−0.817659	+	0.575703i
$28$		0			0
$29$			32.5606i			1.12278i	0.827551	+	0.561390i	$0.189733\pi$
$29$			32.5606i			1.12278i	−0.827551	+	0.561390i	$0.810267\pi$
$30$		0			0
$31$	17.6133	−	30.5071i	0.568171	−	0.984101i	−0.428576	−	0.903506i	$-0.640985\pi$
$31$	17.6133	−	30.5071i	0.568171	−	0.984101i	0.996747	−	0.0805952i	$-0.0256821\pi$
$32$		0			0
$33$	45.9104	+	15.1689i	1.39122	+	0.459664i
$34$		0			0
$35$	41.4158	−	23.9114i	1.18331	−	0.683183i
$36$		0			0
$37$	−12.1006			−0.327042			−0.163521	−	0.986540i	$-0.552285\pi$
$37$	−12.1006			−0.327042			−0.163521	+	0.986540i	$0.552285\pi$
$38$		0			0
$39$	21.4534	−	64.9310i	0.550087	−	1.66490i
$40$		0			0
$41$		−	17.7572i		−	0.433101i	−0.976271	−	0.216551i	$-0.930519\pi$
$41$		−	17.7572i		−	0.433101i	0.976271	−	0.216551i	$-0.0694807\pi$
$42$		0			0
$43$	−0.131207	+	0.227258i	−0.00305133	+	0.00528506i	−0.867547	−	0.497355i	$-0.834305\pi$
$43$	−0.131207	+	0.227258i	−0.00305133	+	0.00528506i	0.864496	+	0.502640i	$0.167638\pi$
$44$		0			0
$45$	−35.4144	−	4.07717i	−0.786986	−	0.0906037i
$46$		0			0
$47$		−	62.9065i		−	1.33844i	−0.743066	−	0.669218i	$-0.766629\pi$
$47$		−	62.9065i		−	1.33844i	0.743066	−	0.669218i	$-0.233371\pi$
$48$		0			0
$49$	−48.3866	+	83.8080i	−0.987481	+	1.71037i
$50$		0			0
$51$	25.6824	+	8.48553i	0.503576	+	0.166383i
$52$		0			0
$53$	70.5478	+	40.7308i	1.33109	+	0.768506i	0.985467	−	0.169867i	$-0.0543339\pi$
$53$	70.5478	+	40.7308i	1.33109	+	0.768506i	0.345624	+	0.938373i	$0.387667\pi$
$54$		0			0
$55$	31.9193	+	55.2859i	0.580352	+	1.00520i
$56$		0			0
$57$	54.2631	−	17.4505i	0.951984	−	0.306149i
$58$		0			0
$59$			17.2013i			0.291547i	0.989318	+	0.145774i	$0.0465671\pi$
$59$			17.2013i			0.291547i	−0.989318	+	0.145774i	$0.953433\pi$
$60$		0			0
$61$	−68.4804			−1.12263			−0.561315	−	0.827602i	$-0.689704\pi$
$61$	−68.4804			−1.12263			−0.561315	+	0.827602i	$0.689704\pi$
$62$		0			0
$63$	99.7013	−	43.2120i	1.58256	−	0.685904i
$64$		0			0
$65$	78.1909	−	45.1435i	1.20294	−	0.694516i
$66$		0			0
$67$	37.2470	+	64.5137i	0.555925	+	0.962891i	0.997831	+	0.0658294i	$0.0209693\pi$
$67$	37.2470	+	64.5137i	0.555925	+	0.962891i	−0.441906	+	0.897062i	$0.645697\pi$
$68$		0			0
$69$	11.7544	+	3.88367i	0.170353	+	0.0562851i
$70$		0			0
$71$	−104.803	+	60.5078i	−1.47609	+	0.852222i	−0.999636	−	0.0269762i	$-0.991412\pi$
$71$	−104.803	+	60.5078i	−1.47609	+	0.852222i	−0.476456	+	0.879198i	$0.658079\pi$
$72$		0			0
$73$	22.6715	+	39.2682i	0.310568	+	0.537920i	0.978486	−	0.206315i	$-0.0661473\pi$
$73$	22.6715	+	39.2682i	0.310568	+	0.537920i	−0.667917	+	0.744236i	$0.732814\pi$
$74$		0			0
$75$	18.5880	+	20.8508i	0.247840	+	0.278011i
$76$		0			0
$77$	−168.522	−	97.2963i	−2.18860	−	1.26359i
$78$		0			0
$79$	37.4287	−	64.8283i	0.473780	−	0.820612i	−0.525769	−	0.850627i	$-0.676222\pi$
$79$	37.4287	−	64.8283i	0.473780	−	0.820612i	0.999549	+	0.0300155i	$0.00955568\pi$
$80$		0			0
$81$	−78.8809	−	18.4067i	−0.973838	−	0.227243i
$82$		0			0
$83$	44.5212	−	25.7043i	0.536400	−	0.309690i	−0.207219	−	0.978295i	$-0.566441\pi$
$83$	44.5212	−	25.7043i	0.536400	−	0.309690i	0.743618	+	0.668604i	$0.233108\pi$
$84$		0			0
$85$	17.8558	+	30.9271i	0.210068	+	0.363848i
$86$		0			0
$87$	−72.9145	+	65.0017i	−0.838098	+	0.747146i
$88$		0			0
$89$	−20.7932	−	12.0050i	−0.233632	−	0.134887i	0.378614	−	0.925554i	$-0.376401\pi$
$89$	−20.7932	−	12.0050i	−0.233632	−	0.134887i	−0.612246	+	0.790667i	$0.709734\pi$
$90$		0			0
$91$	−137.606	+	238.341i	−1.51216	+	2.61913i
$92$		0			0
$93$	103.478	−	21.4600i	1.11267	−	0.230752i
$94$		0			0
$95$	68.8103	+	30.4767i	0.724319	+	0.320808i
$96$		0			0
$97$	67.9519	−	117.696i	0.700535	−	1.21336i	−0.267744	−	0.963490i	$-0.586278\pi$
$97$	67.9519	−	117.696i	0.700535	−	1.21336i	0.968279	−	0.249872i	$-0.0803887\pi$
$98$		0			0
$99$	57.6837	+	133.091i	0.582664	+	1.34436i
$100$		0			0
$101$		−	155.767i		−	1.54225i	−0.636683	−	0.771125i	$-0.719694\pi$
$101$		−	155.767i		−	1.54225i	0.636683	−	0.771125i	$-0.280306\pi$
$102$		0			0
$103$	65.0924	−	112.743i	0.631965	−	1.09459i	−0.355185	−	0.934796i	$-0.615582\pi$
$103$	65.0924	−	112.743i	0.631965	−	1.09459i	0.987150	−	0.159799i	$-0.0510845\pi$
$104$		0			0
$105$	136.225	+	45.0092i	1.29738	+	0.428659i
$106$		0			0
$107$		−	68.7768i		−	0.642774i	−0.946948	−	0.321387i	$-0.895851\pi$
$107$		−	68.7768i		−	0.642774i	0.946948	−	0.321387i	$-0.104149\pi$
$108$		0			0
$109$	−27.4720	−	47.5829i	−0.252037	−	0.436540i	0.712050	−	0.702129i	$-0.247767\pi$
$109$	−27.4720	−	47.5829i	−0.252037	−	0.436540i	−0.964086	+	0.265589i	$0.914434\pi$
$110$		0			0
$111$	−24.1567	−	27.0974i	−0.217628	−	0.244120i
$112$		0			0
$113$	−5.96136	−	3.44179i	−0.0527554	−	0.0304584i	0.473390	−	0.880853i	$-0.343030\pi$
$113$	−5.96136	−	3.44179i	−0.0527554	−	0.0304584i	−0.526146	+	0.850394i	$0.676363\pi$
$114$		0			0
$115$	8.17226	+	14.1548i	0.0710631	+	0.123085i
$116$		0			0
$117$	188.231	−	81.5820i	1.60881	−	0.697282i
$118$		0			0
$119$	−94.2717	−	54.4278i	−0.792199	−	0.457376i
$120$		0			0
$121$	69.3810	−	120.171i	0.573397	−	0.993152i
$122$		0			0
$123$	39.7644	−	35.4491i	0.323288	−	0.288204i
$124$		0			0
$125$			135.904i			1.08723i
$126$		0			0
$127$	10.9101	−	18.8968i	0.0859059	−	0.148793i	−0.819871	−	0.572548i	$-0.805955\pi$
$127$	10.9101	−	18.8968i	0.0859059	−	0.148793i	0.905777	+	0.423755i	$0.139288\pi$
$128$		0			0
$129$	−0.770841	+	0.159862i	−0.00597551	+	0.00123924i
$130$		0			0
$131$			33.8889i			0.258694i	0.991599	+	0.129347i	$0.0412881\pi$
$131$			33.8889i			0.258694i	−0.991599	+	0.129347i	$0.958712\pi$
$132$		0			0
$133$	−228.096	+	24.4207i	−1.71501	+	0.183614i
$134$		0			0
$135$	−61.5685	−	87.4444i	−0.456063	−	0.647736i
$136$		0			0
$137$		−	181.387i		−	1.32399i	−0.749508	−	0.661996i	$-0.769710\pi$
$137$		−	181.387i		−	1.32399i	0.749508	−	0.661996i	$-0.230290\pi$
$138$		0			0
$139$	23.2236	+	40.2244i	0.167076	+	0.289384i	0.937391	−	0.348280i	$-0.113234\pi$
$139$	23.2236	+	40.2244i	0.167076	+	0.289384i	−0.770314	+	0.637664i	$0.779901\pi$
$140$		0			0
$141$	140.869	−	125.582i	0.999074	−	0.890652i
$142$		0			0
$143$	−318.162	−	183.691i	−2.22491	−	1.28455i
$144$		0			0
$145$	−128.970			−0.889449
$146$		0			0
$147$	−284.271	+	58.9540i	−1.93381	+	0.401047i
$148$		0			0
$149$		−	270.026i		−	1.81226i	−0.423001	−	0.906129i	$-0.639023\pi$
$149$		−	270.026i		−	1.81226i	0.423001	−	0.906129i	$-0.360977\pi$
$150$		0			0
$151$	88.8801	+	153.945i	0.588610	+	1.01950i	0.994415	+	0.105543i	$0.0336580\pi$
$151$	88.8801	+	153.945i	0.588610	+	1.01950i	−0.405805	+	0.913960i	$0.633009\pi$
$152$		0			0
$153$	32.2684	+	74.4516i	0.210905	+	0.486612i
$154$		0			0
$155$	120.836	+	69.7649i	0.779589	+	0.450096i
$156$		0			0
$157$	−16.5176			−0.105208			−0.0526038	−	0.998615i	$-0.516752\pi$
$157$	−16.5176			−0.105208			−0.0526038	+	0.998615i	$0.516752\pi$
$158$		0			0
$159$	49.6262	+	239.293i	0.312115	+	1.50499i
$160$		0			0
$161$	−43.1465	−	24.9106i	−0.267990	−	0.154724i
$162$		0			0
$163$	197.434			1.21125			0.605626	−	0.795749i	$-0.292923\pi$
$163$	197.434			1.21125			0.605626	+	0.795749i	$0.292923\pi$
$164$		0			0
$165$	−60.0829	+	181.847i	−0.364139	+	1.10211i
$166$		0			0
$167$	−118.671	+	68.5146i	−0.710603	+	0.410267i	−0.811284	−	0.584652i	$-0.801231\pi$
$167$	−118.671	+	68.5146i	−0.710603	+	0.410267i	0.100681	+	0.994919i	$0.467898\pi$
$168$		0			0
$169$	−175.294	+	303.617i	−1.03724	+	1.79655i
$170$		0			0
$171$	147.405	+	86.6769i	0.862015	+	0.506883i
$172$		0			0
$173$	65.4756	+	37.8024i	0.378472	+	0.218511i	0.677153	−	0.735842i	$-0.263213\pi$
$173$	65.4756	+	37.8024i	0.378472	+	0.218511i	−0.298681	+	0.954353i	$0.596547\pi$
$174$		0			0
$175$	−56.2095	−	97.3578i	−0.321197	−	0.556330i
$176$		0			0
$177$	−38.5197	+	34.3394i	−0.217625	+	0.194008i
$178$		0			0
$179$			230.214i			1.28611i	0.765820	+	0.643055i	$0.222334\pi$
$179$			230.214i			1.28611i	−0.765820	+	0.643055i	$0.777666\pi$
$180$		0			0
$181$	−77.5967	+	134.401i	−0.428711	+	0.742549i	−0.996759	−	0.0804464i	$-0.974365\pi$
$181$	−77.5967	+	134.401i	−0.428711	+	0.742549i	0.568048	+	0.822995i	$0.307699\pi$
$182$		0			0
$183$	−136.709	−	153.351i	−0.747046	−	0.837986i
$184$		0			0
$185$		−	47.9294i		−	0.259078i
$186$		0			0
$187$	72.6557	−	125.843i	0.388533	−	0.672959i
$188$		0			0
$189$	295.803	+	137.001i	1.56510	+	0.724871i
$190$		0			0
$191$	−56.6731	+	32.7202i	−0.296718	+	0.171310i	−0.640967	−	0.767568i	$-0.721467\pi$
$191$	−56.6731	+	32.7202i	−0.296718	+	0.171310i	0.344250	+	0.938878i	$0.388133\pi$
$192$		0			0
$193$	−67.3588			−0.349009			−0.174505	−	0.984656i	$-0.555832\pi$
$193$	−67.3588			−0.349009			−0.174505	+	0.984656i	$0.555832\pi$
$194$		0			0
$195$	257.187	+	84.9752i	1.31891	+	0.435770i
$196$		0			0
$197$			247.679i			1.25726i	0.777706	+	0.628628i	$0.216383\pi$
$197$			247.679i			1.25726i	−0.777706	+	0.628628i	$0.783617\pi$
$198$		0			0
$199$	−134.396	+	232.781i	−0.675357	+	1.16975i	0.301007	+	0.953622i	$0.402677\pi$
$199$	−134.396	+	232.781i	−0.675357	+	1.16975i	−0.976364	+	0.216131i	$0.930656\pi$
$200$		0			0
$201$	−70.1113	+	212.199i	−0.348812	+	1.05572i
$202$		0			0
$203$	340.457	−	196.563i	1.67713	−	0.968290i
$204$		0			0
$205$	70.3347			0.343096
$206$		0			0
$207$	14.7687	+	34.0752i	0.0713462	+	0.164614i
$208$		0			0
$209$	−32.5992	−	304.485i	−0.155977	−	1.45687i
$210$		0			0
$211$	−151.874			−0.719782			−0.359891	−	0.932994i	$-0.617186\pi$
$211$	−151.874			−0.719782			−0.359891	+	0.932994i	$0.617186\pi$
$212$		0			0
$213$	−344.718	−	113.896i	−1.61840	−	0.534722i
$214$		0			0
$215$	−0.900149	−	0.519701i	−0.00418674	−	0.00241722i
$216$		0			0
$217$	−425.314			−1.95997
$218$		0			0
$219$	−42.6753	+	129.162i	−0.194865	+	0.589779i
$220$		0			0
$221$	−177.980	−	102.757i	−0.805341	−	0.464964i
$222$		0			0
$223$	−45.4208	+	78.6712i	−0.203681	+	0.352786i	−0.949712	−	0.313126i	$-0.898624\pi$
$223$	−45.4208	+	78.6712i	−0.203681	+	0.352786i	0.746031	+	0.665912i	$0.231957\pi$
$224$		0			0
$225$	−9.58437	+	83.2500i	−0.0425972	+	0.370000i
$226$		0			0
$227$	167.766	−	96.8596i	0.739056	−	0.426694i	−0.0826697	−	0.996577i	$-0.526345\pi$
$227$	167.766	−	96.8596i	0.739056	−	0.426694i	0.821726	+	0.569883i	$0.193011\pi$
$228$		0			0
$229$	114.878	−	198.974i	0.501648	−	0.868881i	−0.498350	−	0.866976i	$-0.666060\pi$
$229$	114.878	−	198.974i	0.501648	−	0.868881i	0.999998	−	0.00190456i	$-0.000606241\pi$
$230$		0			0
$231$	−118.545	−	571.615i	−0.513183	−	2.47452i
$232$		0			0
$233$	165.357	−	95.4689i	0.709686	−	0.409738i	−0.101259	−	0.994860i	$-0.532287\pi$
$233$	165.357	−	95.4689i	0.709686	−	0.409738i	0.810945	+	0.585123i	$0.198954\pi$
$234$		0			0
$235$	249.168			1.06029
$236$		0			0
$237$	219.893	−	45.6029i	0.927819	−	0.192417i
$238$		0			0
$239$	236.368	+	136.467i	0.988986	+	0.570991i	0.904971	−	0.425473i	$-0.139892\pi$
$239$	236.368	+	136.467i	0.988986	+	0.570991i	0.0840147	+	0.996465i	$0.473226\pi$
$240$		0			0
$241$	−448.904			−1.86267			−0.931337	−	0.364158i	$-0.881357\pi$
$241$	−448.904			−1.86267			−0.931337	+	0.364158i	$0.881357\pi$
$242$		0			0
$243$	−116.253	−	213.387i	−0.478408	−	0.878138i
$244$		0			0
$245$	−331.957	−	191.655i	−1.35493	−	0.782267i
$246$		0			0
$247$	−430.634	+	46.1050i	−1.74346	+	0.186660i
$248$		0			0
$249$	146.440	+	48.3841i	0.588111	+	0.194314i
$250$		0			0
$251$	59.5359	+	34.3731i	0.237195	+	0.136945i	0.613887	−	0.789394i	$-0.289605\pi$
$251$	59.5359	+	34.3731i	0.237195	+	0.136945i	−0.376692	+	0.926339i	$0.622938\pi$
$252$		0			0
$253$	33.2532	−	57.5962i	0.131436	−	0.227653i
$254$		0			0
$255$	−33.6105	+	101.726i	−0.131806	+	0.398925i
$256$		0			0
$257$	−256.450	+	148.061i	−0.997860	+	0.576115i	−0.907614	−	0.419805i	$-0.862098\pi$
$257$	−256.450	+	148.061i	−0.997860	+	0.576115i	−0.0902453	+	0.995920i	$0.528765\pi$
$258$		0			0
$259$	73.0490	+	126.525i	0.282042	+	0.488512i
$260$		0			0
$261$	−291.123	−	33.5162i	−1.11541	−	0.128415i
$262$		0			0
$263$	134.418	+	77.6060i	0.511093	+	0.295080i	0.733283	−	0.679924i	$-0.237987\pi$
$263$	134.418	+	77.6060i	0.511093	+	0.295080i	−0.222190	+	0.975003i	$0.571320\pi$
$264$		0			0
$265$	−161.332	+	279.434i	−0.608798	+	1.05447i
$266$		0			0
$267$	−14.6268	−	70.5292i	−0.0547821	−	0.264154i
$268$		0			0
$269$	−375.343	+	216.704i	−1.39533	+	0.805592i	−0.993899	−	0.110298i	$-0.964819\pi$
$269$	−375.343	+	216.704i	−1.39533	+	0.805592i	−0.401428	+	0.915891i	$0.631486\pi$
$270$		0			0
$271$	−11.2795	−	19.5367i	−0.0416217	−	0.0720910i	0.844464	−	0.535612i	$-0.179919\pi$
$271$	−11.2795	−	19.5367i	−0.0416217	−	0.0720910i	−0.886086	+	0.463521i	$0.846586\pi$
$272$		0			0
$273$	−808.435	+	167.659i	−2.96130	+	0.614134i
$274$		0			0
$275$	129.963	−	75.0341i	0.472593	−	0.272851i
$276$		0			0
$277$	−72.4225	−	125.439i	−0.261453	−	0.452850i	0.705175	−	0.709033i	$-0.250868\pi$
$277$	−72.4225	−	125.439i	−0.261453	−	0.452850i	−0.966628	+	0.256183i	$0.917535\pi$
$278$		0			0
$279$	254.632	+	188.882i	0.912660	+	0.676996i
$280$		0			0
$281$		−	33.4205i		−	0.118934i	−0.998230	−	0.0594671i	$-0.981060\pi$
$281$		−	33.4205i		−	0.118934i	0.998230	−	0.0594671i	$-0.0189401\pi$
$282$		0			0
$283$	39.2274			0.138613			0.0693063	−	0.997595i	$-0.477921\pi$
$283$	39.2274			0.138613			0.0693063	+	0.997595i	$0.477921\pi$
$284$		0			0
$285$	69.1200	+	214.932i	0.242526	+	0.754146i
$286$		0			0
$287$	−185.670	+	107.197i	−0.646935	+	0.373508i
$288$		0			0
$289$	−103.856	+	179.884i	−0.359364	+	0.622437i
$290$		0			0
$291$	399.217	−	82.7923i	1.37188	−	0.284510i
$292$		0			0
$293$	287.114	+	165.766i	0.979912	+	0.565753i	0.902244	−	0.431227i	$-0.141919\pi$
$293$	287.114	+	165.766i	0.979912	+	0.565753i	0.0776687	+	0.996979i	$0.475252\pi$
$294$		0			0
$295$	−68.1330			−0.230959
$296$		0			0
$297$	−182.882	+	394.868i	−0.615765	+	1.32952i
$298$		0			0
$299$	−81.4583	−	47.0300i	−0.272436	−	0.157291i
$300$		0			0
$301$	3.16830			0.0105259
$302$		0			0
$303$	348.817	−	310.963i	1.15121	−	1.02628i
$304$		0			0
$305$		−	271.245i		−	0.889329i
$306$		0			0
$307$	89.4260	+	154.890i	0.291290	+	0.504529i	0.974115	−	0.226053i	$-0.0725823\pi$
$307$	89.4260	+	154.890i	0.291290	+	0.504529i	−0.682825	+	0.730582i	$0.739249\pi$
$308$		0			0
$309$	382.417	−	79.3082i	1.23760	−	0.256661i
$310$		0			0
$311$	278.477	+	160.779i	0.895424	+	0.516973i	0.875713	−	0.482833i	$-0.160392\pi$
$311$	278.477	+	160.779i	0.895424	+	0.516973i	0.0197111	+	0.999806i	$0.493725\pi$
$312$		0			0
$313$	−216.484			−0.691641			−0.345820	−	0.938301i	$-0.612399\pi$
$313$	−216.484			−0.691641			−0.345820	+	0.938301i	$0.612399\pi$
$314$		0			0
$315$	171.159	+	394.909i	0.543363	+	1.25368i
$316$		0			0
$317$			322.150i			1.01625i	0.861284	+	0.508123i	$0.169661\pi$
$317$			322.150i			1.01625i	−0.861284	+	0.508123i	$0.830339\pi$
$318$		0			0
$319$	262.392	+	454.476i	0.822545	+	1.42469i
$320$		0			0
$321$	154.015	−	137.301i	0.479798	−	0.427729i
$322$		0			0
$323$	−18.2361	−	170.330i	−0.0564584	−	0.527337i
$324$		0			0
$325$	−106.121	−	183.807i	−0.326525	−	0.565559i
$326$		0			0
$327$	51.7115	−	156.510i	0.158139	−	0.478625i
$328$		0			0
$329$	−657.756	+	379.755i	−1.99926	+	1.15427i
$330$		0			0
$331$	155.064	+	268.579i	0.468471	+	0.811416i	0.999351	−	0.0360315i	$-0.0114717\pi$
$331$	155.064	+	268.579i	0.468471	+	0.811416i	−0.530879	+	0.847447i	$0.678138\pi$
$332$		0			0
$333$	12.4557	−	108.190i	0.0374045	−	0.324896i
$334$		0			0
$335$	−255.534	+	147.532i	−0.762787	+	0.440395i
$336$		0			0
$337$	463.800			1.37626			0.688131	−	0.725586i	$-0.258431\pi$
$337$	463.800			1.37626			0.688131	+	0.725586i	$0.258431\pi$
$338$		0			0
$339$	−4.19346	−	20.2205i	−0.0123701	−	0.0596475i
$340$		0			0
$341$		−	567.752i		−	1.66496i
$342$		0			0
$343$	576.796			1.68162
$344$		0			0
$345$	−15.3829	+	46.5581i	−0.0445882	+	0.134951i
$346$		0			0
$347$			567.679i			1.63596i	0.575245	+	0.817981i	$0.304907\pi$
$347$			567.679i			1.63596i	−0.575245	+	0.817981i	$0.695093\pi$
$348$		0			0
$349$	110.715	+	191.763i	0.317234	+	0.549465i	0.979910	−	0.199441i	$-0.0639127\pi$
$349$	110.715	+	191.763i	0.317234	+	0.549465i	−0.662676	+	0.748906i	$0.730579\pi$
$350$		0			0
$351$	558.461	+	258.650i	1.59106	+	0.736895i
$352$		0			0
$353$	330.736	−	190.950i	0.936928	−	0.540936i	0.0479322	−	0.998851i	$-0.484737\pi$
$353$	330.736	−	190.950i	0.936928	−	0.540936i	0.888996	+	0.457915i	$0.151404\pi$
$354$		0			0
$355$	−239.667	−	415.115i	−0.675117	−	1.16934i
$356$		0			0
$357$	−66.3146	−	319.763i	−0.185755	−	0.895694i
$358$		0			0
$359$	−553.318	+	319.458i	−1.54128	+	0.889856i	−0.542518	+	0.840044i	$0.682529\pi$
$359$	−553.318	+	319.458i	−1.54128	+	0.889856i	−0.998759	+	0.0498123i	$0.984138\pi$
$360$		0			0
$361$	−242.594	−	267.337i	−0.672005	−	0.740547i
$362$		0			0
$363$	407.613	−	84.5334i	1.12290	−	0.232874i
$364$		0			0
$365$	−155.538	+	89.8000i	−0.426132	+	0.246027i
$366$		0			0
$367$	−34.4305			−0.0938161			−0.0469080	−	0.998899i	$-0.514937\pi$
$367$	−34.4305			−0.0938161			−0.0469080	+	0.998899i	$0.514937\pi$
$368$		0			0
$369$	158.766	+	18.2783i	0.430259	+	0.0495347i
$370$		0			0
$371$		−	983.539i		−	2.65105i
$372$		0			0
$373$	−179.525	+	310.946i	−0.481299	+	0.833634i	−0.999770	−	0.0214610i	$-0.993168\pi$
$373$	−179.525	+	310.946i	−0.481299	+	0.833634i	0.518471	+	0.855095i	$0.326502\pi$
$374$		0			0
$375$	−304.335	+	271.308i	−0.811561	+	0.723488i
$376$		0			0
$377$	642.766	−	371.101i	1.70495	−	0.984352i
$378$		0			0
$379$	−285.289			−0.752740			−0.376370	−	0.926469i	$-0.622828\pi$
$379$	−285.289			−0.752740			−0.376370	+	0.926469i	$0.622828\pi$
$380$		0			0
$381$	64.0965	−	13.2928i	0.168232	−	0.0348891i
$382$		0			0
$383$		−	432.538i		−	1.12934i	−0.825316	−	0.564671i	$-0.809003\pi$
$383$		−	432.538i		−	1.12934i	0.825316	−	0.564671i	$-0.190997\pi$
$384$		0			0
$385$	385.383	−	667.503i	1.00100	−	1.73377i
$386$		0			0
$387$	−1.89684	−	1.40704i	−0.00490139	−	0.00363577i
$388$		0			0
$389$			106.924i			0.274869i	0.990511	+	0.137434i	$0.0438856\pi$
$389$			106.924i			0.274869i	−0.990511	+	0.137434i	$0.956114\pi$
$390$		0			0
$391$	18.6019	−	32.2195i	0.0475752	−	0.0824027i
$392$		0			0
$393$	−75.8890	+	67.6533i	−0.193102	+	0.172146i
$394$		0			0
$395$	256.780	+	148.252i	0.650076	+	0.375321i
$396$		0			0
$397$	213.672	+	370.091i	0.538217	+	0.932220i	0.999000	+	0.0447068i	$0.0142354\pi$
$397$	213.672	+	370.091i	0.538217	+	0.932220i	−0.460783	+	0.887513i	$0.652431\pi$
$398$		0			0
$399$	−510.041	−	462.034i	−1.27830	−	1.15798i
$400$		0			0
$401$		−	258.464i		−	0.644548i	−0.946646	−	0.322274i	$-0.895553\pi$
$401$		−	258.464i		−	0.644548i	0.946646	−	0.322274i	$-0.104447\pi$
$402$		0			0
$403$	−802.971			−1.99248
$404$		0			0
$405$	72.9074	−	312.441i	0.180018	−	0.771459i
$406$		0			0
$407$	−168.898	+	97.5132i	−0.414982	+	0.239590i
$408$		0			0
$409$	219.754	+	380.625i	0.537295	+	0.930622i	0.999048	+	0.0436140i	$0.0138872\pi$
$409$	219.754	+	380.625i	0.537295	+	0.930622i	−0.461753	+	0.887008i	$0.652779\pi$
$410$		0			0
$411$	406.188	−	362.108i	0.988292	−	0.881040i
$412$		0			0
$413$	179.858	−	103.841i	0.435492	−	0.251432i
$414$		0			0
$415$	101.813	+	176.345i	0.245332	+	0.424927i
$416$		0			0
$417$	−43.7145	+	132.307i	−0.104831	+	0.317283i
$418$		0			0
$419$	−602.592	−	347.907i	−1.43817	−	0.830326i	−0.440445	−	0.897780i	$-0.645179\pi$
$419$	−602.592	−	347.907i	−1.43817	−	0.830326i	−0.997722	+	0.0674535i	$0.978513\pi$
$420$		0			0
$421$	143.187	−	248.008i	0.340112	−	0.589092i	−0.644341	−	0.764738i	$-0.722868\pi$
$421$	143.187	−	248.008i	0.340112	−	0.589092i	0.984453	+	0.175646i	$0.0562015\pi$
$422$		0			0
$423$	562.443	+	64.7526i	1.32965	+	0.153080i
$424$		0			0
$425$	72.7016	−	41.9743i	0.171063	−	0.0987630i
$426$		0			0
$427$	413.404	+	716.037i	0.968160	+	1.67690i
$428$		0			0
$429$	−223.808	−	1079.18i	−0.521696	−	2.51557i
$430$		0			0
$431$	316.602	+	182.790i	0.734575	+	0.424107i	0.820093	−	0.572230i	$-0.193921\pi$
$431$	316.602	+	182.790i	0.734575	+	0.424107i	−0.0855187	+	0.996337i	$0.527255\pi$
$432$		0			0
$433$	356.861	−	618.102i	0.824160	−	1.42749i	−0.0784001	−	0.996922i	$-0.524981\pi$
$433$	356.861	−	618.102i	0.824160	−	1.42749i	0.902560	−	0.430564i	$-0.141685\pi$
$434$		0			0
$435$	−257.467	−	288.809i	−0.591877	−	0.663928i
$436$		0			0
$437$	−8.34631	−	77.9569i	−0.0190991	−	0.178391i
$438$		0			0
$439$	169.668	−	293.874i	0.386488	−	0.669417i	−0.605486	−	0.795856i	$-0.707021\pi$
$439$	169.668	−	293.874i	0.386488	−	0.669417i	0.991974	+	0.126439i	$0.0403547\pi$
$440$		0			0
$441$	−699.516	−	518.889i	−1.58620	−	1.17662i
$442$		0			0
$443$			362.351i			0.817948i	0.912546	+	0.408974i	$0.134113\pi$
$443$			362.351i			0.817948i	−0.912546	+	0.408974i	$0.865887\pi$
$444$		0			0
$445$	47.5508	−	82.3604i	0.106856	−	0.185080i
$446$		0			0
$447$	604.683	−	539.061i	1.35276	−	1.20595i
$448$		0			0
$449$			528.543i			1.17716i	0.808440	+	0.588578i	$0.200312\pi$
$449$			528.543i			1.17716i	−0.808440	+	0.588578i	$0.799688\pi$
$450$		0			0
$451$	−143.097	−	247.852i	−0.317289	−	0.549560i
$452$		0			0
$453$	−167.302	+	506.358i	−0.369320	+	1.11779i
$454$		0			0
$455$	−944.050	−	545.047i	−2.07483	−	1.19791i
$456$		0			0
$457$	−192.523	−	333.460i	−0.421276	−	0.729671i	0.574789	−	0.818302i	$-0.305084\pi$
$457$	−192.523	−	333.460i	−0.421276	−	0.729671i	−0.996065	+	0.0886308i	$0.971751\pi$
$458$		0			0
$459$	−102.305	+	220.890i	−0.222886	+	0.481242i
$460$		0			0
$461$	300.661	+	173.587i	0.652193	+	0.376544i	0.789296	−	0.614013i	$-0.210446\pi$
$461$	300.661	+	173.587i	0.652193	+	0.376544i	−0.137103	+	0.990557i	$0.543779\pi$
$462$		0			0
$463$	351.439	−	608.710i	0.759047	−	1.31471i	−0.184289	−	0.982872i	$-0.558998\pi$
$463$	351.439	−	608.710i	0.759047	−	1.31471i	0.943337	−	0.331837i	$-0.107668\pi$
$464$		0			0
$465$	85.0012	+	409.868i	0.182798	+	0.881437i
$466$		0			0
$467$		−	79.7158i		−	0.170698i	−0.996351	−	0.0853488i	$-0.972800\pi$
$467$		−	79.7158i		−	0.170698i	0.996351	−	0.0853488i	$-0.0272005\pi$
$468$		0			0
$469$	449.707	−	778.916i	0.958864	−	1.66080i
$470$		0			0
$471$	−32.9745	−	36.9886i	−0.0700096	−	0.0785320i
$472$		0			0
$473$			4.22937i			0.00894158i
$474$		0			0
$475$	71.6430	−	161.755i	0.150827	−	0.340537i
$476$		0			0
$477$	−436.790	+	588.838i	−0.915702	+	1.23446i
$478$		0			0
$479$		−	836.060i		−	1.74543i	−0.488232	−	0.872714i	$-0.662358\pi$
$479$		−	836.060i		−	1.74543i	0.488232	−	0.872714i	$-0.337642\pi$
$480$		0			0
$481$	137.913	+	238.872i	0.286721	+	0.496616i
$482$		0			0
$483$	−30.3510	−	146.350i	−0.0628384	−	0.303001i
$484$		0			0
$485$	466.185	+	269.152i	0.961207	+	0.554953i
$486$		0			0
$487$	103.687			0.212909			0.106455	−	0.994318i	$-0.466050\pi$
$487$	103.687			0.212909			0.106455	+	0.994318i	$0.466050\pi$
$488$		0			0
$489$	394.143	+	442.124i	0.806019	+	0.904138i
$490$		0			0
$491$		−	587.375i		−	1.19628i	−0.801390	−	0.598142i	$-0.795906\pi$
$491$		−	587.375i		−	1.19628i	0.801390	−	0.598142i	$-0.204094\pi$
$492$		0			0
$493$	146.783	+	254.235i	0.297734	+	0.515690i
$494$		0			0
$495$	−527.164	+	228.481i	−1.06498	+	0.461577i
$496$		0			0
$497$	1265.35	+	730.550i	2.54598	+	1.46992i
$498$		0			0
$499$	848.727			1.70086			0.850428	−	0.526091i	$-0.176343\pi$
$499$	848.727			1.70086			0.850428	+	0.526091i	$0.176343\pi$
$500$		0			0
$501$	−390.334	−	128.967i	−0.779109	−	0.257420i
$502$		0			0
$503$	557.422	+	321.828i	1.10820	+	0.639817i	0.938361	−	0.345656i	$-0.112344\pi$
$503$	557.422	+	321.828i	1.10820	+	0.639817i	0.169834	+	0.985473i	$0.445677\pi$
$504$		0			0
$505$	616.982			1.22175
$506$		0			0
$507$	−1029.85	+	213.577i	−2.03126	+	0.421256i
$508$		0			0
$509$	644.052	−	371.844i	1.26533	−	0.730538i	0.291228	−	0.956654i	$-0.405936\pi$
$509$	644.052	−	371.844i	1.26533	−	0.730538i	0.974100	+	0.226116i	$0.0726028\pi$
$510$		0			0
$511$	273.728	−	474.111i	0.535671	−	0.927809i
$512$		0			0
$513$	100.168	+	503.126i	0.195260	+	0.980752i
$514$		0			0
$515$	446.567	+	257.826i	0.867121	+	0.500632i
$516$		0			0
$517$	−506.936	−	878.039i	−0.980534	−	1.69833i
$518$		0			0
$519$	46.0582	+	222.089i	0.0887441	+	0.427916i
$520$		0			0
$521$			289.315i			0.555307i	0.960681	+	0.277654i	$0.0895568\pi$
$521$			289.315i			0.555307i	−0.960681	+	0.277654i	$0.910443\pi$
$522$		0			0
$523$	−332.610	+	576.097i	−0.635965	+	1.10152i	0.350345	+	0.936621i	$0.386064\pi$
$523$	−332.610	+	576.097i	−0.635965	+	1.10152i	−0.986310	+	0.164903i	$0.947269\pi$
$524$		0			0
$525$	105.805	−	320.231i	0.201534	−	0.609963i
$526$		0			0
$527$		−	317.602i		−	0.602660i
$528$		0			0
$529$	−255.986	+	443.381i	−0.483906	+	0.838150i
$530$		0			0
$531$	−153.796	−	17.7061i	−0.289634	−	0.0333449i
$532$		0			0
$533$	−350.537	+	202.382i	−0.657667	+	0.379704i
$534$		0			0
$535$	272.420			0.509195
$536$		0			0
$537$	−515.529	+	459.582i	−0.960016	+	0.855833i
$538$		0			0
$539$			1559.71i			2.89370i
$540$		0			0
$541$	108.091	−	187.219i	0.199799	−	0.346062i	−0.748664	−	0.662949i	$-0.769304\pi$
$541$	108.091	−	187.219i	0.199799	−	0.346062i	0.948463	+	0.316888i	$0.102638\pi$
$542$		0			0
$543$	−455.880	+	94.5434i	−0.839557	+	0.174113i
$544$		0			0
$545$	188.472	−	108.814i	0.345820	−	0.199660i
$546$		0			0
$547$	−404.904			−0.740226			−0.370113	−	0.928987i	$-0.620681\pi$
$547$	−404.904			−0.740226			−0.370113	+	0.928987i	$0.620681\pi$
$548$		0			0
$549$	70.4902	−	612.279i	0.128397	−	1.11526i
$550$		0			0
$551$	565.653	+	250.533i	1.02659	+	0.454688i
$552$		0			0
$553$	−903.801			−1.63436
$554$		0			0
$555$	107.330	−	95.6828i	0.193388	−	0.172401i
$556$		0			0
$557$	301.106	+	173.843i	0.540585	+	0.312107i	0.745316	−	0.666712i	$-0.232299\pi$
$557$	301.106	+	173.843i	0.540585	+	0.312107i	−0.204731	+	0.978818i	$0.565632\pi$
$558$		0			0
$559$	5.98159			0.0107005
$560$		0			0
$561$	426.852	−	88.5234i	0.760876	−	0.157796i
$562$		0			0
$563$	272.302	+	157.214i	0.483663	+	0.279243i	0.721942	−	0.691954i	$-0.243250\pi$
$563$	272.302	+	157.214i	0.483663	+	0.279243i	−0.238279	+	0.971197i	$0.576583\pi$
$564$		0			0
$565$	13.6327	−	23.6125i	0.0241286	−	0.0417920i
$566$		0			0
$567$	283.728	+	935.904i	0.500403	+	1.65062i
$568$		0			0
$569$	377.181	−	217.766i	0.662884	−	0.382716i	−0.130491	−	0.991450i	$-0.541655\pi$
$569$	377.181	−	217.766i	0.662884	−	0.382716i	0.793375	+	0.608733i	$0.208322\pi$
$570$		0			0
$571$	238.902	−	413.791i	0.418393	−	0.724678i	−0.577385	−	0.816472i	$-0.695927\pi$
$571$	238.902	−	413.791i	0.418393	−	0.724678i	0.995778	+	0.0917941i	$0.0292602\pi$
$572$		0			0
$573$	−186.410	−	61.5904i	−0.325323	−	0.107488i
$574$		0			0
$575$	33.2742	−	19.2109i	0.0578682	−	0.0334102i
$576$		0			0
$577$	−1012.34			−1.75448			−0.877242	−	0.480049i	$-0.840619\pi$
$577$	−1012.34			−1.75448			−0.877242	+	0.480049i	$0.840619\pi$
$578$		0			0
$579$	−134.470	−	150.840i	−0.232246	−	0.260518i
$580$		0			0
$581$	−537.533	−	310.345i	−0.925186	−	0.534156i
$582$		0			0
$583$	1312.93			2.25202
$584$		0			0
$585$	323.140	+	745.568i	0.552376	+	1.27448i
$586$		0			0
$587$	293.061	+	169.199i	0.499252	+	0.288243i	0.728405	−	0.685147i	$-0.240262\pi$
$587$	293.061	+	169.199i	0.499252	+	0.288243i	−0.229153	+	0.973390i	$0.573596\pi$
$588$		0			0
$589$	−394.456	−	540.716i	−0.669705	−	0.918024i
$590$		0			0
$591$	−554.640	+	494.449i	−0.938477	+	0.836632i
$592$		0			0
$593$	619.042	+	357.404i	1.04392	+	0.602705i	0.920940	−	0.389705i	$-0.127423\pi$
$593$	619.042	+	357.404i	1.04392	+	0.602705i	0.122975	+	0.992410i	$0.460756\pi$
$594$		0			0
$595$	215.584	−	373.403i	0.362326	−	0.627568i
$596$		0			0
$597$	−789.575	+	163.747i	−1.32257	+	0.274284i
$598$		0			0
$599$	−788.749	+	455.384i	−1.31678	+	0.760241i	−0.983209	−	0.182485i	$-0.941586\pi$
$599$	−788.749	+	455.384i	−1.31678	+	0.760241i	−0.333567	+	0.942726i	$0.608252\pi$
$600$		0			0
$601$	518.851	+	898.676i	0.863312	+	1.49530i	0.868713	+	0.495316i	$0.164948\pi$
$601$	518.851	+	898.676i	0.863312	+	1.49530i	−0.00540074	+	0.999985i	$0.501719\pi$
$602$		0			0
$603$	−615.153	+	266.616i	−1.02015	+	0.442150i
$604$		0			0
$605$	475.989	+	274.813i	0.786759	+	0.454236i
$606$		0			0
$607$	−245.610	+	425.410i	−0.404630	+	0.700840i	−0.994278	−	0.106820i	$-0.965933\pi$
$607$	−245.610	+	425.410i	−0.404630	+	0.700840i	0.589648	+	0.807660i	$0.299266\pi$
$608$		0			0
$609$	1119.84	+	369.997i	1.83881	+	0.607548i
$610$		0			0
$611$	−1241.81	+	716.959i	−2.03242	+	1.17342i
$612$		0			0
$613$	−426.072	−	737.979i	−0.695061	−	1.20388i	−0.970160	−	0.242465i	$-0.922044\pi$
$613$	−426.072	−	737.979i	−0.695061	−	1.20388i	0.275100	−	0.961416i	$-0.411289\pi$
$614$		0			0
$615$	140.411	+	157.504i	0.228311	+	0.256104i
$616$		0			0
$617$	−474.863	+	274.163i	−0.769633	+	0.444348i	−0.832744	−	0.553659i	$-0.813231\pi$
$617$	−474.863	+	274.163i	−0.769633	+	0.444348i	0.0631109	+	0.998007i	$0.479898\pi$
$618$		0			0
$619$	−354.141	−	613.391i	−0.572118	−	0.990938i	−0.996348	−	0.0853837i	$-0.972788\pi$
$619$	−354.141	−	613.391i	−0.572118	−	0.990938i	0.424230	−	0.905555i	$-0.360545\pi$
$620$		0			0
$621$	−46.8230	+	101.097i	−0.0753994	+	0.162798i
$622$		0			0
$623$			289.888i			0.465310i
$624$		0			0
$625$	−305.526			−0.488841
$626$		0			0
$627$	616.770	−	680.854i	0.983684	−	1.08589i
$628$		0			0
$629$	−94.4818	+	54.5491i	−0.150210	+	0.0867235i
$630$		0			0
$631$	471.188	−	816.121i	0.746732	−	1.29338i	−0.202650	−	0.979251i	$-0.564955\pi$
$631$	471.188	−	816.121i	0.746732	−	1.29338i	0.949381	−	0.314126i	$-0.101711\pi$
$632$		0			0
$633$	−303.190	−	340.098i	−0.478974	−	0.537280i
$634$		0			0
$635$	74.8486	+	43.2139i	0.117872	+	0.0680533i
$636$		0			0
$637$	2205.89			3.46294
$638$		0			0
$639$	−433.118	−	999.317i	−0.677806	−	1.56388i
$640$		0			0
$641$	−369.500	−	213.331i	−0.576442	−	0.332809i	0.183276	−	0.983062i	$-0.441330\pi$
$641$	−369.500	−	213.331i	−0.576442	−	0.332809i	−0.759718	+	0.650252i	$0.774663\pi$
$642$		0			0
$643$	590.704			0.918668			0.459334	−	0.888264i	$-0.348088\pi$
$643$	590.704			0.918668			0.459334	+	0.888264i	$0.348088\pi$
$644$		0			0
$645$	−0.633202	−	3.05324i	−0.000981708	−	0.00473371i
$646$		0			0
$647$			595.345i			0.920162i	0.887877	+	0.460081i	$0.152180\pi$
$647$			595.345i			0.920162i	−0.887877	+	0.460081i	$0.847820\pi$
$648$		0			0
$649$	138.618	+	240.093i	0.213587	+	0.369943i
$650$		0			0
$651$	−849.066	−	952.425i	−1.30425	−	1.46302i
$652$		0			0
$653$	−906.009	−	523.084i	−1.38746	−	0.801048i	−0.394428	−	0.918927i	$-0.629057\pi$
$653$	−906.009	−	523.084i	−1.38746	−	0.801048i	−0.993028	+	0.117879i	$0.962391\pi$
$654$		0			0
$655$	−134.231			−0.204933
$656$		0			0
$657$	−374.431	+	162.284i	−0.569911	+	0.247007i
$658$		0			0
$659$			323.660i			0.491138i	0.969379	+	0.245569i	$0.0789748\pi$
$659$			323.660i			0.491138i	−0.969379	+	0.245569i	$0.921025\pi$
$660$		0			0
$661$	114.328	+	198.021i	0.172961	+	0.299578i	0.939454	−	0.342675i	$-0.111333\pi$
$661$	114.328	+	198.021i	0.172961	+	0.299578i	−0.766492	+	0.642253i	$0.778000\pi$
$662$		0			0
$663$	−125.199	−	603.696i	−0.188836	−	0.910552i
$664$		0			0
$665$	−96.7284	−	903.470i	−0.145456	−	1.35860i
$666$		0			0
$667$	67.1798	+	116.359i	0.100719	+	0.174451i
$668$		0			0
$669$	−266.847	+	55.3405i	−0.398875	+	0.0827213i
$670$		0			0
$671$	−955.839	+	551.854i	−1.42450	+	0.822435i
$672$		0			0
$673$	−52.3224	−	90.6251i	−0.0777451	−	0.134658i	0.824532	−	0.565816i	$-0.191439\pi$
$673$	−52.3224	−	90.6251i	−0.0777451	−	0.134658i	−0.902277	+	0.431157i	$0.858105\pi$
$674$		0			0
$675$	−205.559	+	144.732i	−0.304532	+	0.214417i
$676$		0			0
$677$	893.825	−	516.050i	1.32027	−	0.762260i	0.336501	−	0.941683i	$-0.390756\pi$
$677$	893.825	−	516.050i	1.32027	−	0.762260i	0.983772	+	0.179423i	$0.0574231\pi$
$678$		0			0
$679$	−1640.86			−2.41658
$680$		0			0
$681$	551.818	+	182.322i	0.810305	+	0.267727i
$682$		0			0
$683$		−	40.8914i		−	0.0598703i	−0.999552	−	0.0299351i	$-0.990470\pi$
$683$		−	40.8914i		−	0.0598703i	0.999552	−	0.0299351i	$-0.00953007\pi$
$684$		0			0
$685$	718.459			1.04884
$686$		0			0
$687$	674.904	−	139.966i	0.982393	−	0.203735i
$688$		0			0
$689$		−	1856.87i		−	2.69503i
$690$		0			0
$691$	359.412	+	622.520i	0.520133	+	0.900897i	0.999726	+	0.0234062i	$0.00745110\pi$
$691$	359.412	+	622.520i	0.520133	+	0.900897i	−0.479593	+	0.877491i	$0.659216\pi$
$692$		0			0
$693$	1043.39	−	1406.60i	1.50561	−	2.02972i
$694$		0			0
$695$	−159.326	+	91.9868i	−0.229246	+	0.132355i
$696$		0			0
$697$	−80.0489	−	138.649i	−0.114848	−	0.198922i
$698$		0			0
$699$	543.895	+	179.704i	0.778104	+	0.257088i
$700$		0			0
$701$	−614.261	+	354.644i	−0.876263	+	0.505911i	−0.869425	−	0.494066i	$-0.835510\pi$
$701$	−614.261	+	354.644i	−0.876263	+	0.505911i	−0.00683877	+	0.999977i	$0.502177\pi$
$702$		0			0
$703$	−93.1061	+	210.215i	−0.132441	+	0.299025i
$704$		0			0
$705$	497.420	+	557.973i	0.705560	+	0.791450i
$706$		0			0
$707$	−1628.72	+	940.341i	−2.30370	+	1.33004i
$708$		0			0
$709$	−582.136			−0.821067			−0.410533	−	0.911846i	$-0.634657\pi$
$709$	−582.136			−0.821067			−0.410533	+	0.911846i	$0.634657\pi$
$710$		0			0
$711$	541.099	+	401.378i	0.761040	+	0.564527i
$712$		0			0
$713$		−	145.361i		−	0.203872i
$714$		0			0
$715$	727.584	−	1260.21i	1.01760	−	1.76254i
$716$		0			0
$717$	166.271	+	801.742i	0.231898	+	1.11819i
$718$		0			0
$719$	445.208	−	257.041i	0.619204	−	0.357498i	−0.157355	−	0.987542i	$-0.550297\pi$
$719$	445.208	−	257.041i	0.619204	−	0.357498i	0.776559	+	0.630044i	$0.216963\pi$
$720$		0			0
$721$	−1571.81			−2.18004
$722$		0			0
$723$	−896.161	−	1005.25i	−1.23950	−	1.39039i
$724$		0			0
$725$			303.175i			0.418173i
$726$		0			0
$727$	−141.230	+	244.618i	−0.194265	+	0.336476i	−0.946659	−	0.322237i	$-0.895565\pi$
$727$	−141.230	+	244.618i	−0.194265	+	0.336476i	0.752395	+	0.658713i	$0.228899\pi$
$728$		0			0
$729$	245.769	−	686.323i	0.337132	−	0.941458i
$730$		0			0
$731$			2.36592i			0.00323655i
$732$		0			0
$733$	−363.972	+	630.418i	−0.496551	+	0.860052i	−0.999992	−	0.00397748i	$-0.998734\pi$
$733$	−363.972	+	630.418i	−0.496551	+	0.860052i	0.503441	+	0.864030i	$0.332067\pi$
$734$		0			0
$735$	−233.512	−	1125.97i	−0.317703	−	1.53194i
$736$		0			0
$737$	1039.78	+	600.315i	1.41082	+	0.814538i
$738$		0			0
$739$	452.621	+	783.962i	0.612477	+	1.06084i	0.990822	+	0.135176i	$0.0431601\pi$
$739$	452.621	+	783.962i	0.612477	+	1.06084i	−0.378345	+	0.925665i	$0.623507\pi$
$740$		0			0
$741$	−962.931	−	872.297i	−1.29950	−	1.17719i
$742$		0			0
$743$			1108.03i			1.49129i	0.666341	+	0.745647i	$0.267860\pi$
$743$			1108.03i			1.49129i	−0.666341	+	0.745647i	$0.732140\pi$
$744$		0			0
$745$	1069.55			1.43564
$746$		0			0
$747$	183.993	+	424.520i	0.246309	+	0.568300i
$748$		0			0
$749$	−719.137	+	415.194i	−0.960129	+	0.554331i
$750$		0			0
$751$	617.846	+	1070.14i	0.822697	+	1.42495i	0.903666	+	0.428237i	$0.140865\pi$
$751$	617.846	+	1070.14i	0.822697	+	1.42495i	−0.0809692	+	0.996717i	$0.525802\pi$
$752$		0			0
$753$	41.8800	+	201.941i	0.0556175	+	0.268183i
$754$		0			0
$755$	−609.764	+	352.047i	−0.807634	+	0.466288i
$756$		0			0
$757$	−562.964	−	975.082i	−0.743678	−	1.28809i	−0.950810	−	0.309775i	$-0.899746\pi$
$757$	−562.964	−	975.082i	−0.743678	−	1.28809i	0.207132	−	0.978313i	$-0.433587\pi$
$758$		0			0
$759$	195.362	−	40.5155i	0.257394	−	0.0533802i
$760$		0			0
$761$	751.713	+	434.002i	0.987796	+	0.570304i	0.904615	−	0.426230i	$-0.140159\pi$
$761$	751.713	+	434.002i	0.987796	+	0.570304i	0.0831813	+	0.996534i	$0.473492\pi$
$762$		0			0
$763$	−331.688	+	574.500i	−0.434715	+	0.752948i
$764$		0			0
$765$	−294.897	+	127.813i	−0.385486	+	0.167075i
$766$		0			0
$767$	339.563	−	196.047i	0.442716	−	0.255602i
$768$		0			0
$769$	252.639	+	437.583i	0.328529	+	0.569029i	0.982220	−	0.187733i	$-0.0601138\pi$
$769$	252.639	+	437.583i	0.328529	+	0.569029i	−0.653691	+	0.756761i	$0.726780\pi$
$770$		0			0
$771$	−843.519	−	278.701i	−1.09406	−	0.361480i
$772$		0			0
$773$	−106.301	−	61.3729i	−0.137518	−	0.0793958i	0.429663	−	0.902989i	$-0.358632\pi$
$773$	−106.301	−	61.3729i	−0.137518	−	0.0793958i	−0.567180	+	0.823594i	$0.691966\pi$
$774$		0			0
$775$	163.999	−	284.055i	0.211612	−	0.366523i
$776$		0			0
$777$	−137.503	+	416.167i	−0.176966	+	0.535607i
$778$		0			0
$779$	−308.483	−	136.630i	−0.395998	−	0.175391i
$780$		0			0
$781$	−975.212	+	1689.12i	−1.24867	+	2.16276i
$782$		0			0
$783$	−506.122	−	718.834i	−0.646388	−	0.918051i
$784$		0			0
$785$		−	65.4248i		−	0.0833437i
$786$		0			0
$787$	99.1669	−	171.762i	0.126006	−	0.218249i	−0.796120	−	0.605139i	$-0.793117\pi$
$787$	99.1669	−	171.762i	0.126006	−	0.218249i	0.922126	+	0.386890i	$0.126451\pi$
$788$		0			0
$789$	94.5547	+	455.934i	0.119841	+	0.577864i
$790$		0			0
$791$			83.1101i			0.105070i
$792$		0			0
$793$	780.487	+	1351.84i	0.984220	+	1.70472i
$794$		0			0
$795$	−947.821	+	196.566i	−1.19223	+	0.247252i
$796$		0			0
$797$	1105.31	+	638.151i	1.38684	+	0.800691i	0.992958	−	0.118470i	$-0.0377990\pi$
$797$	1105.31	+	638.151i	1.38684	+	0.800691i	0.393881	+	0.919162i	$0.371132\pi$
$798$		0			0
$799$	−283.581	−	491.177i	−0.354920	−	0.614739i
$800$		0			0
$801$	128.739	−	173.554i	0.160723	−	0.216671i
$802$		0			0
$803$	632.891	+	365.400i	0.788158	+	0.455043i
$804$		0			0
$805$	98.6690	−	170.900i	0.122570	−	0.212298i
$806$		0			0
$807$	−1234.58	−	407.910i	−1.52984	−	0.505465i
$808$		0			0
$809$		−	1049.44i		−	1.29720i	−0.761128	−	0.648602i	$-0.775354\pi$
$809$		−	1049.44i		−	1.29720i	0.761128	−	0.648602i	$-0.224646\pi$
$810$		0			0
$811$	247.735	−	429.090i	0.305469	−	0.529088i	−0.671897	−	0.740645i	$-0.734520\pi$
$811$	247.735	−	429.090i	0.305469	−	0.529088i	0.977366	+	0.211557i	$0.0678534\pi$
$812$		0			0
$813$	21.2318	−	64.2603i	0.0261153	−	0.0790409i
$814$		0			0
$815$			782.021i			0.959535i
$816$		0			0
$817$	2.93843	+	4.02797i	0.00359661	+	0.00493020i
$818$		0			0
$819$	−1989.35	−	1475.66i	−2.42900	−	1.80179i
$820$		0			0
$821$			283.927i			0.345831i	0.984937	+	0.172915i	$0.0553187\pi$
$821$			283.927i			0.345831i	−0.984937	+	0.172915i	$0.944681\pi$
$822$		0			0
$823$	−398.100	−	689.530i	−0.483718	−	0.837824i	0.516107	−	0.856524i	$-0.327381\pi$
$823$	−398.100	−	689.530i	−0.483718	−	0.837824i	−0.999825	+	0.0186997i	$0.994047\pi$
$824$		0			0
$825$	427.476	+	141.239i	0.518153	+	0.171199i
$826$		0			0
$827$	921.590	+	532.080i	1.11438	+	0.643386i	0.939959	−	0.341286i	$-0.110862\pi$
$827$	921.590	+	532.080i	1.11438	+	0.643386i	0.174417	+	0.984672i	$0.444196\pi$
$828$		0			0
$829$	30.3330			0.0365899			0.0182949	−	0.999833i	$-0.494176\pi$
$829$	30.3330			0.0365899			0.0182949	+	0.999833i	$0.494176\pi$
$830$		0			0
$831$	136.323	−	412.597i	0.164047	−	0.496507i
$832$		0			0
$833$			872.503i			1.04742i
$834$		0			0
$835$	−271.381	−	470.045i	−0.325007	−	0.562929i
$836$		0			0
$837$	85.3574	+	947.280i	0.101980	+	1.13176i
$838$		0			0
$839$	−1054.44	−	608.778i	−1.25678	−	0.725600i	−0.284330	−	0.958727i	$-0.591771\pi$
$839$	−1054.44	−	608.778i	−1.25678	−	0.725600i	−0.972446	+	0.233126i	$0.925104\pi$
$840$		0			0
$841$	−219.194			−0.260635
$842$		0			0
$843$	74.8401	−	66.7183i	0.0887782	−	0.0791438i
$844$		0			0
$845$	−1202.60	−	694.324i	−1.42320	−	0.821685i
$846$		0			0
$847$	−1675.36			−1.97800
$848$		0			0
$849$	78.3107	+	87.8437i	0.0922387	+	0.103467i
$850$		0			0
$851$	−43.2426	+	24.9661i	−0.0508139	+	0.0293374i
$852$		0			0
$853$	−282.564	+	489.416i	−0.331260	+	0.573758i	−0.982759	−	0.184891i	$-0.940807\pi$
$853$	−282.564	+	489.416i	−0.331260	+	0.573758i	0.651499	+	0.758649i	$0.274140\pi$
$854$		0			0
$855$	−343.321	+	583.858i	−0.401545	+	0.682875i
$856$		0			0
$857$	112.874	+	65.1679i	0.131708	+	0.0760419i	0.564407	−	0.825497i	$-0.309105\pi$
$857$	112.874	+	65.1679i	0.131708	+	0.0760419i	−0.432698	+	0.901539i	$0.642438\pi$
$858$		0			0
$859$	−158.988	−	275.376i	−0.185085	−	0.320577i	0.758520	−	0.651650i	$-0.225923\pi$
$859$	−158.988	−	275.376i	−0.185085	−	0.320577i	−0.943605	+	0.331073i	$0.892589\pi$
$860$		0			0
$861$	−610.710	−	201.780i	−0.709303	−	0.234356i
$862$		0			0
$863$		−	449.132i		−	0.520431i	−0.965551	−	0.260216i	$-0.916206\pi$
$863$		−	449.132i		−	0.520431i	0.965551	−	0.260216i	$-0.0837936\pi$
$864$		0			0
$865$	−149.732	+	259.344i	−0.173101	+	0.299819i
$866$		0			0
$867$	−610.154	+	126.538i	−0.703754	+	0.145949i
$868$		0			0
$869$		−	1206.49i		−	1.38836i
$870$		0			0
$871$	849.025	−	1470.55i	0.974770	−	1.68835i
$872$		0			0
$873$	982.368	+	728.704i	1.12528	+	0.834713i
$874$		0			0
$875$	1421.02	−	820.426i	1.62402	−	0.937630i
$876$		0			0
$877$	−1420.74			−1.62000			−0.810000	−	0.586430i	$-0.800533\pi$
$877$	−1420.74			−1.62000			−0.810000	+	0.586430i	$0.800533\pi$
$878$		0			0
$879$	201.968	+	973.871i	0.229770	+	1.10793i
$880$		0			0
$881$			1534.41i			1.74166i	0.491580	+	0.870832i	$0.336419\pi$
$881$			1534.41i			1.74166i	−0.491580	+	0.870832i	$0.663581\pi$
$882$		0			0
$883$	255.107	−	441.859i	0.288910	−	0.500406i	−0.684640	−	0.728881i	$-0.740041\pi$
$883$	255.107	−	441.859i	0.288910	−	0.500406i	0.973550	+	0.228475i	$0.0733739\pi$
$884$		0			0
$885$	−136.016	−	152.573i	−0.153690	−	0.172399i
$886$		0			0
$887$	128.442	−	74.1563i	0.144805	−	0.0836034i	−0.425847	−	0.904795i	$-0.640024\pi$
$887$	128.442	−	74.1563i	0.144805	−	0.0836034i	0.570652	+	0.821192i	$0.306690\pi$
$888$		0			0
$889$	−263.448			−0.296342
$890$		0			0
$891$	−1249.34	+	378.749i	−1.40218	+	0.425083i
$892$		0			0
$893$	−1092.83	−	484.025i	−1.22377	−	0.542021i
$894$		0			0
$895$	−911.859			−1.01884
$896$		0			0
$897$	−57.3011	−	276.301i	−0.0638808	−	0.308028i
$898$		0			0
$899$	993.331	+	573.500i	1.10493	+	0.637931i
$900$		0			0
$901$	734.455			0.815155
$902$		0			0
$903$	6.32497	+	7.09493i	0.00700440	+	0.00785706i
$904$		0			0
$905$	−532.353	−	307.354i	−0.588236	−	0.339618i
$906$		0			0
$907$	668.842	−	1158.47i	0.737422	−	1.27725i	−0.216230	−	0.976342i	$-0.569376\pi$
$907$	668.842	−	1158.47i	0.737422	−	1.27725i	0.953652	−	0.300911i	$-0.0972906\pi$
$908$		0			0
$909$	1392.71	+	160.339i	1.53213	+	0.176390i
$910$		0			0
$911$	−728.807	+	420.777i	−0.800008	+	0.461885i	−0.843474	−	0.537170i	$-0.819493\pi$
$911$	−728.807	+	420.777i	−0.800008	+	0.461885i	0.0434662	+	0.999055i	$0.486160\pi$
$912$		0			0
$913$	414.280	−	717.553i	0.453757	−	0.785929i
$914$		0			0
$915$	607.413	−	541.495i	0.663839	−	0.591798i
$916$		0			0
$917$	354.345	−	204.581i	0.386418	−	0.223099i
$918$		0			0
$919$	1282.29			1.39531			0.697657	−	0.716431i	$-0.254226\pi$
$919$	1282.29			1.39531			0.697657	+	0.716431i	$0.254226\pi$
$920$		0			0
$921$	−168.330	+	509.468i	−0.182768	+	0.553168i
$922$		0			0
$923$	2388.92	+	1379.24i	2.58821	+	1.49430i
$924$		0			0
$925$	−112.670			−0.121805
$926$		0			0
$927$	941.028	+	698.039i	1.01513	+	0.753009i
$928$		0			0
$929$	−563.774	−	325.495i	−0.606861	−	0.350371i	0.164875	−	0.986315i	$-0.447278\pi$
$929$	−563.774	−	325.495i	−0.606861	−	0.350371i	−0.771736	+	0.635943i	$0.780611\pi$
$930$		0			0
$931$	1083.63	+	1485.43i	1.16395	+	1.59553i
$932$		0			0
$933$	195.892	+	944.573i	0.209959	+	1.01240i
$934$		0			0
$935$	498.456	+	287.784i	0.533108	+	0.307790i
$936$		0			0
$937$	252.334	−	437.056i	0.269300	−	0.466441i	−0.699381	−	0.714749i	$-0.746541\pi$
$937$	252.334	−	437.056i	0.269300	−	0.466441i	0.968681	+	0.248308i	$0.0798743\pi$
$938$		0			0
$939$	−432.172	−	484.782i	−0.460247	−	0.516275i
$940$		0			0
$941$	1241.70	−	716.898i	1.31956	−	0.761847i	0.335900	−	0.941897i	$-0.390959\pi$
$941$	1241.70	−	716.898i	1.31956	−	0.761847i	0.983657	+	0.180050i	$0.0576261\pi$
$942$		0			0
$943$	−36.6369	−	63.4570i	−0.0388515	−	0.0672927i
$944$		0			0
$945$	−542.648	+	1171.65i	−0.574231	+	1.23984i
$946$		0			0
$947$	−695.809	−	401.725i	−0.734751	−	0.424208i	0.0854070	−	0.996346i	$-0.472781\pi$
$947$	−695.809	−	401.725i	−0.734751	−	0.424208i	−0.820158	+	0.572138i	$0.806114\pi$
$948$		0			0
$949$	516.784	−	895.097i	0.544557	−	0.943200i
$950$		0			0
$951$	−721.406	+	643.117i	−0.758576	+	0.676254i
$952$		0			0
$953$	796.306	−	459.747i	0.835578	−	0.482421i	−0.0201809	−	0.999796i	$-0.506424\pi$
$953$	796.306	−	459.747i	0.835578	−	0.482421i	0.855759	+	0.517375i	$0.173091\pi$
$954$		0			0
$955$	−129.602	−	224.477i	−0.135709	−	0.235055i
$956$		0			0
$957$	−493.909	+	1494.87i	−0.516102	+	1.56204i
$958$		0			0
$959$	−1896.60	+	1095.00i	−1.97768	+	1.14182i
$960$		0			0
$961$	−139.957	−	242.412i	−0.145636	−	0.252250i
$962$		0			0
$963$	614.930	+	70.7953i	0.638556	+	0.0735154i
$964$		0			0
$965$		−	266.803i		−	0.276480i
$966$		0			0
$967$	−603.095			−0.623676			−0.311838	−	0.950135i	$-0.600945\pi$
$967$	−603.095			−0.623676			−0.311838	+	0.950135i	$0.600945\pi$
$968$		0			0
$969$	345.022	−	380.871i	0.356060	−	0.393056i
$970$		0			0
$971$	562.056	−	324.503i	0.578842	−	0.334195i	−0.181831	−	0.983330i	$-0.558202\pi$
$971$	562.056	−	324.503i	0.578842	−	0.334195i	0.760673	+	0.649135i	$0.224869\pi$
$972$		0			0
$973$	280.394	−	485.656i	0.288174	−	0.499132i
$974$		0			0
$975$	199.755	−	604.579i	0.204877	−	0.620081i
$976$		0			0
$977$	−45.8246	−	26.4568i	−0.0469033	−	0.0270796i	0.476365	−	0.879248i	$-0.341954\pi$
$977$	−45.8246	−	26.4568i	−0.0469033	−	0.0270796i	−0.523268	+	0.852168i	$0.675287\pi$
$978$		0			0
$979$	−386.972			−0.395273
$980$		0			0
$981$	453.714	−	196.646i	0.462502	−	0.200455i
$982$		0			0
$983$	−779.865	−	450.255i	−0.793352	−	0.458042i	0.0477892	−	0.998857i	$-0.484782\pi$
$983$	−779.865	−	450.255i	−0.793352	−	0.458042i	−0.841141	+	0.540815i	$0.818116\pi$
$984$		0			0
$985$	−981.039			−0.995978
$986$		0			0
$987$	−2163.50	−	714.827i	−2.19200	−	0.724242i
$988$		0			0
$989$			1.08284i			0.00109488i
$990$		0			0
$991$	456.255	+	790.257i	0.460399	+	0.797434i	0.998981	−	0.0451394i	$-0.0143732\pi$
$991$	456.255	+	790.257i	0.460399	+	0.797434i	−0.538582	+	0.842573i	$0.681040\pi$
$992$		0			0
$993$	−291.882	+	883.413i	−0.293940	+	0.889641i
$994$		0			0
$995$	−922.026	−	532.332i	−0.926660	−	0.535007i
$996$		0			0
$997$	1284.31			1.28818			0.644088	−	0.764951i	$-0.277237\pi$
$997$	1284.31			1.28818			0.644088	+	0.764951i	$0.277237\pi$
$998$		0			0
$999$	267.142	−	188.091i	0.267409	−	0.188279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.653.30	yes	80
3.2	odd	2		2052.3.m.a.881.13		80
9.2	odd	6		684.3.be.a.425.24	yes	80
9.7	even	3		2052.3.be.a.197.13		80
19.11	even	3		684.3.be.a.581.24	yes	80
57.11	odd	6		2052.3.be.a.125.13		80
171.11	odd	6	inner	684.3.m.a.353.30	✓	80
171.106	even	3		2052.3.m.a.1493.28		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.30	✓	80	171.11	odd	6	inner
684.3.m.a.653.30	yes	80	1.1	even	1	trivial
684.3.be.a.425.24	yes	80	9.2	odd	6
684.3.be.a.581.24	yes	80	19.11	even	3
2052.3.m.a.881.13		80	3.2	odd	2
2052.3.m.a.1493.28		80	171.106	even	3
2052.3.be.a.125.13		80	57.11	odd	6
2052.3.be.a.197.13		80	9.7	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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99633 + 2.23935i) q^{3} +3.96092i q^{5} +(-6.03683 - 10.4561i) q^{7} +(-1.02935 + 8.94094i) q^{9} +O(q^{10})\)	\(q+(1.99633 + 2.23935i) q^{3} +3.96092i q^{5} +(-6.03683 - 10.4561i) q^{7} +(-1.02935 + 8.94094i) q^{9} +(13.9578 - 8.05857i) q^{11} +(-11.3972 - 19.7406i) q^{13} +(-8.86988 + 7.90730i) q^{15} +(7.80805 - 4.50798i) q^{17} +(7.69436 - 17.3723i) q^{19} +(11.3633 - 34.3923i) q^{21} +(3.57360 - 2.06322i) q^{23} +9.31110 q^{25} +(-22.0768 + 15.5440i) q^{27} +32.5606i q^{29} +(17.6133 - 30.5071i) q^{31} +(45.9104 + 15.1689i) q^{33} +(41.4158 - 23.9114i) q^{35} -12.1006 q^{37} +(21.4534 - 64.9310i) q^{39} -17.7572i q^{41} +(-0.131207 + 0.227258i) q^{43} +(-35.4144 - 4.07717i) q^{45} -62.9065i q^{47} +(-48.3866 + 83.8080i) q^{49} +(25.6824 + 8.48553i) q^{51} +(70.5478 + 40.7308i) q^{53} +(31.9193 + 55.2859i) q^{55} +(54.2631 - 17.4505i) q^{57} +17.2013i q^{59} -68.4804 q^{61} +(99.7013 - 43.2120i) q^{63} +(78.1909 - 45.1435i) q^{65} +(37.2470 + 64.5137i) q^{67} +(11.7544 + 3.88367i) q^{69} +(-104.803 + 60.5078i) q^{71} +(22.6715 + 39.2682i) q^{73} +(18.5880 + 20.8508i) q^{75} +(-168.522 - 97.2963i) q^{77} +(37.4287 - 64.8283i) q^{79} +(-78.8809 - 18.4067i) q^{81} +(44.5212 - 25.7043i) q^{83} +(17.8558 + 30.9271i) q^{85} +(-72.9145 + 65.0017i) q^{87} +(-20.7932 - 12.0050i) q^{89} +(-137.606 + 238.341i) q^{91} +(103.478 - 21.4600i) q^{93} +(68.8103 + 30.4767i) q^{95} +(67.9519 - 117.696i) q^{97} +(57.6837 + 133.091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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