LMFDB - Embedded newform 220.3.x.a.53.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(37,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("220.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.x (of order $20$, degree $8$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			53.7
Character	$\chi$	$=$	220.53
Dual form			220.3.x.a.137.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.350343 - 0.0554888i) q^{3} +(2.67198 + 4.22617i) q^{5} +(-12.2603 + 1.94184i) q^{7} +(-8.43985 - 2.74227i) q^{9} +(8.92266 - 6.43321i) q^{11} +(-18.8590 + 9.60916i) q^{13} +(-0.701602 - 1.62887i) q^{15} +(7.21907 + 3.67830i) q^{17} +(-18.4082 - 25.3367i) q^{19} +4.40304 q^{21} +(8.87555 + 8.87555i) q^{23} +(-10.7211 + 22.5845i) q^{25} +(5.64911 + 2.87837i) q^{27} +(-28.0576 + 38.6180i) q^{29} +(-4.52004 + 13.9112i) q^{31} +(-3.48296 + 1.75872i) q^{33} +(-40.9657 - 46.6255i) q^{35} +(-22.0242 + 3.48830i) q^{37} +(7.14033 - 2.32003i) q^{39} +(8.10462 - 5.88835i) q^{41} +(13.3511 + 13.3511i) q^{43} +(-10.9618 - 42.9955i) q^{45} +(-4.66029 + 29.4239i) q^{47} +(99.9416 - 32.4730i) q^{49} +(-2.32504 - 1.68924i) q^{51} +(50.6879 - 25.8268i) q^{53} +(51.0290 + 20.5193i) q^{55} +(5.04327 + 9.89797i) q^{57} +(36.4128 - 50.1180i) q^{59} +(6.77803 + 20.8606i) q^{61} +(108.800 + 17.2322i) q^{63} +(-91.0009 - 54.0261i) q^{65} +(-23.8508 + 23.8508i) q^{67} +(-2.61699 - 3.60198i) q^{69} +(-18.0597 - 55.5820i) q^{71} +(7.12433 + 44.9812i) q^{73} +(5.00924 - 7.31740i) q^{75} +(-96.9019 + 96.1992i) q^{77} +(-23.1431 - 7.51964i) q^{79} +(62.7949 + 45.6231i) q^{81} +(26.4738 - 51.9577i) q^{83} +(3.74405 + 40.3373i) q^{85} +(11.9726 - 11.9726i) q^{87} +72.5414i q^{89} +(212.557 - 154.432i) q^{91} +(2.35548 - 4.62289i) q^{93} +(57.8910 - 145.495i) q^{95} +(40.7619 + 79.9997i) q^{97} +(-92.9475 + 29.8269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.350343	−	0.0554888i	−0.116781	−	0.0184963i	0.0977704	−	0.995209i	$-0.468829\pi$
$3$	−0.350343	−	0.0554888i	−0.116781	−	0.0184963i	−0.214551	+	0.976713i	$0.568829\pi$
$4$		0			0
$5$	2.67198	+	4.22617i	0.534395	+	0.845235i
$5$	2.67198	+	4.22617i	0.534395	+	0.845235i
$6$		0			0
$7$	−12.2603	+	1.94184i	−1.75147	+	0.277405i	−0.948075	−	0.318047i	$-0.896973\pi$
$7$	−12.2603	+	1.94184i	−1.75147	+	0.277405i	−0.803391	+	0.595452i	$0.796973\pi$
$8$		0			0
$9$	−8.43985	−	2.74227i	−0.937761	−	0.304697i
$10$		0			0
$11$	8.92266	−	6.43321i	0.811151	−	0.584837i
$11$	8.92266	−	6.43321i	0.811151	−	0.584837i
$12$		0			0
$13$	−18.8590	+	9.60916i	−1.45070	+	0.739166i	−0.989006	−	0.147875i	$-0.952757\pi$
$13$	−18.8590	+	9.60916i	−1.45070	+	0.739166i	−0.461690	+	0.887041i	$0.652757\pi$
$14$		0			0
$15$	−0.701602	−	1.62887i	−0.0467735	−	0.108592i
$16$		0			0
$17$	7.21907	+	3.67830i	0.424651	+	0.216370i	0.653237	−	0.757153i	$-0.273410\pi$
$17$	7.21907	+	3.67830i	0.424651	+	0.216370i	−0.228586	+	0.973524i	$0.573410\pi$
$18$		0			0
$19$	−18.4082	−	25.3367i	−0.968852	−	1.33351i	−0.942625	−	0.333855i	$-0.891651\pi$
$19$	−18.4082	−	25.3367i	−0.968852	−	1.33351i	−0.0262275	−	0.999656i	$-0.508349\pi$
$20$		0			0
$21$	4.40304			0.209669
$22$		0			0
$23$	8.87555	+	8.87555i	0.385893	+	0.385893i	0.873220	−	0.487326i	$-0.162028\pi$
$23$	8.87555	+	8.87555i	0.385893	+	0.385893i	−0.487326	+	0.873220i	$0.662028\pi$
$24$		0			0
$25$	−10.7211	+	22.5845i	−0.428843	+	0.903379i
$26$		0			0
$27$	5.64911	+	2.87837i	0.209226	+	0.106606i
$28$		0			0
$29$	−28.0576	+	38.6180i	−0.967503	+	1.33165i	−0.0242052	+	0.999707i	$0.507706\pi$
$29$	−28.0576	+	38.6180i	−0.967503	+	1.33165i	−0.943298	+	0.331947i	$0.892294\pi$
$30$		0			0
$31$	−4.52004	+	13.9112i	−0.145808	+	0.448750i	−0.997114	−	0.0759191i	$-0.975811\pi$
$31$	−4.52004	+	13.9112i	−0.145808	+	0.448750i	0.851306	+	0.524669i	$0.175811\pi$
$32$		0			0
$33$	−3.48296	+	1.75872i	−0.105544	+	0.0532945i
$34$		0			0
$35$	−40.9657	−	46.6255i	−1.17045	−	1.33216i
$36$		0			0
$37$	−22.0242	+	3.48830i	−0.595250	+	0.0942783i	−0.446788	−	0.894640i	$-0.647432\pi$
$37$	−22.0242	+	3.48830i	−0.595250	+	0.0942783i	−0.148462	+	0.988918i	$0.547432\pi$
$38$		0			0
$39$	7.14033	−	2.32003i	0.183085	−	0.0594880i
$40$		0			0
$41$	8.10462	−	5.88835i	0.197674	−	0.143618i	−0.484545	−	0.874766i	$-0.661015\pi$
$41$	8.10462	−	5.88835i	0.197674	−	0.143618i	0.682219	+	0.731148i	$0.261015\pi$
$42$		0			0
$43$	13.3511	+	13.3511i	0.310491	+	0.310491i	0.845100	−	0.534609i	$-0.179541\pi$
$43$	13.3511	+	13.3511i	0.310491	+	0.310491i	−0.534609	+	0.845100i	$0.679541\pi$
$44$		0			0
$45$	−10.9618	−	42.9955i	−0.243595	−	0.955457i
$46$		0			0
$47$	−4.66029	+	29.4239i	−0.0991552	+	0.626041i	0.887197	+	0.461391i	$0.152650\pi$
$47$	−4.66029	+	29.4239i	−0.0991552	+	0.626041i	−0.986352	+	0.164650i	$0.947350\pi$
$48$		0			0
$49$	99.9416	−	32.4730i	2.03962	−	0.662714i
$50$		0			0
$51$	−2.32504	−	1.68924i	−0.0455891	−	0.0331224i
$52$		0			0
$53$	50.6879	−	25.8268i	0.956375	−	0.487297i	0.0951173	−	0.995466i	$-0.469677\pi$
$53$	50.6879	−	25.8268i	0.956375	−	0.487297i	0.861258	+	0.508169i	$0.169677\pi$
$54$		0			0
$55$	51.0290	+	20.5193i	0.927800	+	0.373078i
$56$		0			0
$57$	5.04327	+	9.89797i	0.0884784	+	0.173649i
$58$		0			0
$59$	36.4128	−	50.1180i	0.617167	−	0.849457i	−0.379976	−	0.924996i	$-0.624068\pi$
$59$	36.4128	−	50.1180i	0.617167	−	0.849457i	0.997143	+	0.0755390i	$0.0240677\pi$
$60$		0			0
$61$	6.77803	+	20.8606i	0.111115	+	0.341978i	0.991117	−	0.132993i	$-0.0424587\pi$
$61$	6.77803	+	20.8606i	0.111115	+	0.341978i	−0.880002	+	0.474971i	$0.842459\pi$
$62$		0			0
$63$	108.800	+	17.2322i	1.72698	+	0.273527i
$64$		0			0
$65$	−91.0009	−	54.0261i	−1.40001	−	0.831171i
$66$		0			0
$67$	−23.8508	+	23.8508i	−0.355983	+	0.355983i	−0.862330	−	0.506347i	$-0.830995\pi$
$67$	−23.8508	+	23.8508i	−0.355983	+	0.355983i	0.506347	+	0.862330i	$0.330995\pi$
$68$		0			0
$69$	−2.61699	−	3.60198i	−0.0379274	−	0.0522025i
$70$		0			0
$71$	−18.0597	−	55.5820i	−0.254362	−	0.782845i	−0.993955	−	0.109790i	$-0.964982\pi$
$71$	−18.0597	−	55.5820i	−0.254362	−	0.782845i	0.739593	−	0.673054i	$-0.235018\pi$
$72$		0			0
$73$	7.12433	+	44.9812i	0.0975935	+	0.616181i	0.987204	+	0.159461i	$0.0509758\pi$
$73$	7.12433	+	44.9812i	0.0975935	+	0.616181i	−0.889611	+	0.456720i	$0.849024\pi$
$74$		0			0
$75$	5.00924	−	7.31740i	0.0667898	−	0.0975654i
$76$		0			0
$77$	−96.9019	+	96.1992i	−1.25847	+	1.24934i
$78$		0			0
$79$	−23.1431	−	7.51964i	−0.292950	−	0.0951853i	0.158855	−	0.987302i	$-0.449220\pi$
$79$	−23.1431	−	7.51964i	−0.292950	−	0.0951853i	−0.451805	+	0.892117i	$0.649220\pi$
$80$		0			0
$81$	62.7949	+	45.6231i	0.775245	+	0.563249i
$82$		0			0
$83$	26.4738	−	51.9577i	0.318961	−	0.625997i	−0.674740	−	0.738055i	$-0.735744\pi$
$83$	26.4738	−	51.9577i	0.318961	−	0.625997i	0.993702	+	0.112058i	$0.0357443\pi$
$84$		0			0
$85$	3.74405	+	40.3373i	0.0440477	+	0.474557i
$86$		0			0
$87$	11.9726	−	11.9726i	0.137617	−	0.137617i
$88$		0			0
$89$			72.5414i			0.815072i	0.913189	+	0.407536i	$0.133612\pi$
$89$			72.5414i			0.815072i	−0.913189	+	0.407536i	$0.866388\pi$
$90$		0			0
$91$	212.557	−	154.432i	2.33580	−	1.69706i
$92$		0			0
$93$	2.35548	−	4.62289i	0.0253277	−	0.0497085i
$94$		0			0
$95$	57.8910	−	145.495i	0.609379	−	1.53153i
$96$		0			0
$97$	40.7619	+	79.9997i	0.420226	+	0.824740i	0.999951	+	0.00992731i	$0.00316001\pi$
$97$	40.7619	+	79.9997i	0.420226	+	0.824740i	−0.579725	+	0.814812i	$0.696840\pi$
$98$		0			0
$99$	−92.9475	+	29.8269i	−0.938863	+	0.301282i
$100$		0			0
$101$	−33.0013	+	101.568i	−0.326745	+	1.00562i	0.643901	+	0.765109i	$0.277315\pi$
$101$	−33.0013	+	101.568i	−0.326745	+	1.00562i	−0.970647	+	0.240510i	$0.922685\pi$
$102$		0			0
$103$	−15.8418	−	100.021i	−0.153804	−	0.971079i	−0.937006	−	0.349313i	$-0.886415\pi$
$103$	−15.8418	−	100.021i	−0.153804	−	0.971079i	0.783202	−	0.621767i	$-0.213585\pi$
$104$		0			0
$105$	11.7648	+	18.6080i	0.112046	+	0.177219i
$106$		0			0
$107$	−26.8561	+	169.563i	−0.250992	+	1.58470i	0.464172	+	0.885745i	$0.346352\pi$
$107$	−26.8561	+	169.563i	−0.250992	+	1.58470i	−0.715164	+	0.698956i	$0.753648\pi$
$108$		0			0
$109$		−	161.851i		−	1.48487i	−0.669919	−	0.742435i	$-0.733671\pi$
$109$		−	161.851i		−	1.48487i	0.669919	−	0.742435i	$-0.266329\pi$
$110$		0			0
$111$	7.90959			0.0712576
$112$		0			0
$113$	−170.989	−	27.0819i	−1.51317	−	0.239663i	−0.656028	−	0.754737i	$-0.727765\pi$
$113$	−170.989	−	27.0819i	−1.51317	−	0.239663i	−0.857146	+	0.515073i	$0.827765\pi$
$114$		0			0
$115$	−13.7943	+	61.2249i	−0.119951	+	0.532390i
$116$		0			0
$117$	185.518	−	29.3832i	1.58563	−	0.251139i
$118$		0			0
$119$	−95.6503	−	31.0787i	−0.803784	−	0.261165i
$120$		0			0
$121$	38.2276	−	114.803i	0.315931	−	0.948782i
$122$		0			0
$123$	−3.16613	+	1.61322i	−0.0257409	+	0.0131156i
$124$		0			0
$125$	−124.092	+	15.0361i	−0.992739	+	0.120288i
$126$		0			0
$127$	−184.032	−	93.7688i	−1.44907	−	0.738337i	−0.460295	−	0.887766i	$-0.652256\pi$
$127$	−184.032	−	93.7688i	−1.44907	−	0.738337i	−0.988772	+	0.149429i	$0.952256\pi$
$128$		0			0
$129$	−3.93662	−	5.41830i	−0.0305165	−	0.0420023i
$130$		0			0
$131$	13.3339			0.101785			0.0508927	−	0.998704i	$-0.483793\pi$
$131$	13.3339			0.101785			0.0508927	+	0.998704i	$0.483793\pi$
$132$		0			0
$133$	274.889	+	274.889i	2.06683	+	2.06683i
$134$		0			0
$135$	2.92982	+	31.5650i	0.0217024	+	0.233815i
$136$		0			0
$137$	−70.4787	−	35.9107i	−0.514443	−	0.262122i	0.177440	−	0.984132i	$-0.443218\pi$
$137$	−70.4787	−	35.9107i	−0.514443	−	0.262122i	−0.691883	+	0.722010i	$0.743218\pi$
$138$		0			0
$139$	11.2988	−	15.5514i	0.0812862	−	0.111881i	−0.766438	−	0.642319i	$-0.777973\pi$
$139$	11.2988	−	15.5514i	0.0812862	−	0.111881i	0.847724	+	0.530438i	$0.177973\pi$
$140$		0			0
$141$	3.26540	−	10.0499i	0.0231589	−	0.0712756i
$142$		0			0
$143$	−106.455	+	207.063i	−0.744441	+	1.44800i
$144$		0			0
$145$	−238.175	−	15.3899i	−1.64259	−	0.106138i
$146$		0			0
$147$	−36.8157	+	5.83103i	−0.250447	+	0.0396669i
$148$		0			0
$149$	−94.0120	+	30.5463i	−0.630953	+	0.205009i	−0.606997	−	0.794704i	$-0.707626\pi$
$149$	−94.0120	+	30.5463i	−0.630953	+	0.205009i	−0.0239556	+	0.999713i	$0.507626\pi$
$150$		0			0
$151$	−16.7508	+	12.1702i	−0.110932	+	0.0805972i	−0.641868	−	0.766815i	$-0.721840\pi$
$151$	−16.7508	+	12.1702i	−0.110932	+	0.0805972i	0.530936	+	0.847412i	$0.321840\pi$
$152$		0			0
$153$	−50.8409	−	50.8409i	−0.332294	−	0.332294i
$154$		0			0
$155$	−70.8688	+	18.0681i	−0.457218	+	0.116568i
$156$		0			0
$157$	−27.1588	+	171.474i	−0.172986	+	1.09219i	0.736495	+	0.676443i	$0.236479\pi$
$157$	−27.1588	+	171.474i	−0.172986	+	1.09219i	−0.909481	+	0.415746i	$0.863521\pi$
$158$		0			0
$159$	−19.1912	+	6.23560i	−0.120699	+	0.0392176i
$160$		0			0
$161$	−126.051	−	91.5817i	−0.782928	−	0.568830i
$162$		0			0
$163$	−205.471	+	104.693i	−1.26056	+	0.642287i	−0.951176	−	0.308650i	$-0.900123\pi$
$163$	−205.471	+	104.693i	−1.26056	+	0.642287i	−0.309384	+	0.950937i	$0.600123\pi$
$164$		0			0
$165$	−16.7390	−	10.0203i	−0.101449	−	0.0607292i
$166$		0			0
$167$	−62.0509	−	121.782i	−0.371562	−	0.729232i	0.627206	−	0.778853i	$-0.284198\pi$
$167$	−62.0509	−	121.782i	−0.371562	−	0.729232i	−0.998768	+	0.0496218i	$0.984198\pi$
$168$		0			0
$169$	163.992	−	225.715i	0.970366	−	1.33559i
$170$		0			0
$171$	85.8822	+	264.318i	0.502235	+	1.54572i
$172$		0			0
$173$	190.255	+	30.1335i	1.09974	+	0.174182i	0.679820	−	0.733379i	$-0.262058\pi$
$173$	190.255	+	30.1335i	1.09974	+	0.174182i	0.419921	+	0.907561i	$0.362058\pi$
$174$		0			0
$175$	87.5879	−	297.710i	0.500503	−	1.70120i
$176$		0			0
$177$	−15.5380	+	15.5380i	−0.0877851	+	0.0877851i
$178$		0			0
$179$	93.6028	+	128.833i	0.522921	+	0.719739i	0.986031	−	0.166562i	$-0.0532666\pi$
$179$	93.6028	+	128.833i	0.522921	+	0.719739i	−0.463110	+	0.886301i	$0.653267\pi$
$180$		0			0
$181$	7.83564	+	24.1156i	0.0432908	+	0.133235i	0.970366	−	0.241640i	$-0.0776854\pi$
$181$	7.83564	+	24.1156i	0.0432908	+	0.133235i	−0.927075	+	0.374876i	$0.877685\pi$
$182$		0			0
$183$	−1.21710	−	7.68448i	−0.00665083	−	0.0419917i
$184$		0			0
$185$	−73.5904	−	83.7576i	−0.397786	−	0.452744i
$186$		0			0
$187$	88.0765	−	13.6216i	0.470997	−	0.0728426i
$188$		0			0
$189$	−74.8489	−	24.3199i	−0.396026	−	0.128677i
$190$		0			0
$191$	62.3456	+	45.2967i	0.326417	+	0.237156i	0.738909	−	0.673806i	$-0.235341\pi$
$191$	62.3456	+	45.2967i	0.326417	+	0.237156i	−0.412492	+	0.910961i	$0.635341\pi$
$192$		0			0
$193$	8.54851	−	16.7774i	0.0442928	−	0.0869295i	−0.867799	−	0.496915i	$-0.834466\pi$
$193$	8.54851	−	16.7774i	0.0442928	−	0.0869295i	0.912092	+	0.409985i	$0.134466\pi$
$194$		0			0
$195$	28.8837	+	23.9772i	0.148121	+	0.122960i
$196$		0			0
$197$	−40.9468	+	40.9468i	−0.207852	+	0.207852i	−0.803354	−	0.595502i	$-0.796953\pi$
$197$	−40.9468	+	40.9468i	−0.207852	+	0.207852i	0.595502	+	0.803354i	$0.296953\pi$
$198$		0			0
$199$			318.283i			1.59941i	0.600393	+	0.799705i	$0.295011\pi$
$199$			318.283i			1.59941i	−0.600393	+	0.799705i	$0.704989\pi$
$200$		0			0
$201$	9.67942	−	7.03251i	0.0481563	−	0.0349876i
$202$		0			0
$203$	269.004	−	527.950i	1.32514	−	2.60074i
$204$		0			0
$205$	46.5406	+	18.5180i	0.227027	+	0.0903317i
$206$		0			0
$207$	−50.5691	−	99.2474i	−0.244295	−	0.479456i
$208$		0			0
$209$	−327.246	−	107.647i	−1.56577	−	0.515057i
$210$		0			0
$211$	−75.2908	+	231.721i	−0.356828	+	1.09820i	0.598113	+	0.801412i	$0.295917\pi$
$211$	−75.2908	+	231.721i	−0.356828	+	1.09820i	−0.954942	+	0.296793i	$0.904083\pi$
$212$		0			0
$213$	3.24290	+	20.4748i	0.0152249	+	0.0961260i
$214$		0			0
$215$	−20.7502	+	92.0979i	−0.0965127	+	0.428362i
$216$		0			0
$217$	28.4035	−	179.333i	0.130892	−	0.826418i
$218$		0			0
$219$		−	16.1542i		−	0.0737633i
$220$		0			0
$221$	−171.490			−0.775973
$222$		0			0
$223$	−0.586386	−	0.0928744i	−0.00262953	−	0.000416477i	0.155120	−	0.987896i	$-0.450424\pi$
$223$	−0.586386	−	0.0928744i	−0.00262953	−	0.000416477i	−0.157749	+	0.987479i	$0.550424\pi$
$224$		0			0
$225$	152.417	−	161.209i	0.677409	−	0.716486i
$226$		0			0
$227$	−202.161	+	32.0192i	−0.890577	+	0.141054i	−0.584923	−	0.811089i	$-0.698875\pi$
$227$	−202.161	+	32.0192i	−0.890577	+	0.141054i	−0.305654	+	0.952143i	$0.598875\pi$
$228$		0			0
$229$	180.637	+	58.6926i	0.788809	+	0.256300i	0.675597	−	0.737271i	$-0.263886\pi$
$229$	180.637	+	58.6926i	0.788809	+	0.256300i	0.113212	+	0.993571i	$0.463886\pi$
$230$		0			0
$231$	39.2868	−	28.3257i	0.170073	−	0.122622i
$232$		0			0
$233$	−61.7968	+	31.4870i	−0.265222	+	0.135137i	−0.581545	−	0.813514i	$-0.697552\pi$
$233$	−61.7968	+	31.4870i	−0.265222	+	0.135137i	0.316323	+	0.948652i	$0.397552\pi$
$234$		0			0
$235$	−136.803	+	58.9249i	−0.582140	+	0.250744i
$236$		0			0
$237$	7.69075	+	3.91863i	0.0324504	+	0.0165343i
$238$		0			0
$239$	141.009	+	194.083i	0.589998	+	0.812062i	0.994747	−	0.102365i	$-0.0326411\pi$
$239$	141.009	+	194.083i	0.589998	+	0.812062i	−0.404749	+	0.914428i	$0.632641\pi$
$240$		0			0
$241$	−149.627			−0.620857			−0.310429	−	0.950597i	$-0.600473\pi$
$241$	−149.627			−0.620857			−0.310429	+	0.950597i	$0.600473\pi$
$242$		0			0
$243$	−59.8166	−	59.8166i	−0.246159	−	0.246159i
$244$		0			0
$245$	404.278	+	335.603i	1.65011	+	1.36981i
$246$		0			0
$247$	590.625	+	300.939i	2.39120	+	1.21838i
$248$		0			0
$249$	−12.1580	+	16.7340i	−0.0488272	+	0.0672049i
$250$		0			0
$251$	69.3075	−	213.307i	0.276126	−	0.849827i	−0.712794	−	0.701374i	$-0.752570\pi$
$251$	69.3075	−	213.307i	0.276126	−	0.849827i	0.988919	−	0.148454i	$-0.0474296\pi$
$252$		0			0
$253$	136.292	+	22.0952i	0.538702	+	0.0873329i
$254$		0			0
$255$	0.926570	−	14.3396i	0.00363361	−	0.0562339i
$256$		0			0
$257$	309.762	−	49.0615i	1.20530	−	0.190901i	0.478710	−	0.877973i	$-0.341104\pi$
$257$	309.762	−	49.0615i	1.20530	−	0.190901i	0.726589	+	0.687072i	$0.241104\pi$
$258$		0			0
$259$	263.249	−	85.5349i	1.01641	−	0.330250i
$260$		0			0
$261$	342.703	−	248.988i	1.31304	−	0.953978i
$262$		0			0
$263$	−110.511	−	110.511i	−0.420194	−	0.420194i	0.465077	−	0.885270i	$-0.346027\pi$
$263$	−110.511	−	110.511i	−0.420194	−	0.420194i	−0.885270	+	0.465077i	$0.846027\pi$
$264$		0			0
$265$	244.585	+	145.207i	0.922963	+	0.547952i
$266$		0			0
$267$	4.02524	−	25.4143i	0.0150758	−	0.0951848i
$268$		0			0
$269$	328.445	−	106.718i	1.22098	−	0.396722i	0.373544	−	0.927613i	$-0.378143\pi$
$269$	328.445	−	106.718i	1.22098	−	0.396722i	0.847440	+	0.530891i	$0.178143\pi$
$270$		0			0
$271$	−298.886	−	217.153i	−1.10290	−	0.801303i	−0.121369	−	0.992608i	$-0.538728\pi$
$271$	−298.886	−	217.153i	−1.10290	−	0.801303i	−0.981531	+	0.191304i	$0.938728\pi$
$272$		0			0
$273$	−83.0372	+	42.3096i	−0.304166	+	0.154980i
$274$		0			0
$275$	49.6301	+	270.484i	0.180473	+	0.983580i
$276$		0			0
$277$	−194.904	−	382.521i	−0.703626	−	1.38094i	−0.914966	−	0.403531i	$-0.867783\pi$
$277$	−194.904	−	382.521i	−0.703626	−	1.38094i	0.211340	−	0.977413i	$-0.432217\pi$
$278$		0			0
$279$	76.2969	−	105.014i	0.273465	−	0.376393i
$280$		0			0
$281$	−31.5789	−	97.1898i	−0.112380	−	0.345871i	0.879011	−	0.476801i	$-0.158204\pi$
$281$	−31.5789	−	97.1898i	−0.112380	−	0.345871i	−0.991392	+	0.130930i	$0.958204\pi$
$282$		0			0
$283$	−344.690	−	54.5935i	−1.21799	−	0.192910i	−0.485834	−	0.874051i	$-0.661484\pi$
$283$	−344.690	−	54.5935i	−1.21799	−	0.192910i	−0.732152	+	0.681141i	$0.761484\pi$
$284$		0			0
$285$	−28.3551	+	47.7609i	−0.0994914	+	0.167582i
$286$		0			0
$287$	−87.9306	+	87.9306i	−0.306378	+	0.306378i
$288$		0			0
$289$	−131.285	−	180.698i	−0.454273	−	0.625253i
$290$		0			0
$291$	−9.84154	−	30.2891i	−0.0338197	−	0.104086i
$292$		0			0
$293$	4.18371	+	26.4149i	0.0142789	+	0.0901532i	0.993799	−	0.111195i	$-0.0354678\pi$
$293$	4.18371	+	26.4149i	0.0142789	+	0.0901532i	−0.979520	+	0.201348i	$0.935468\pi$
$294$		0			0
$295$	309.102	+	19.9729i	1.04780	+	0.0677048i
$296$		0			0
$297$	68.9222	−	10.6592i	0.232061	−	0.0358897i
$298$		0			0
$299$	−252.671	−	82.0978i	−0.845053	−	0.274574i
$300$		0			0
$301$	−189.614	−	137.762i	−0.629946	−	0.457682i
$302$		0			0
$303$	17.1976	−	33.7522i	0.0567578	−	0.111393i
$304$		0			0
$305$	−70.0499	+	84.3843i	−0.229672	+	0.276670i
$306$		0			0
$307$	−10.6495	+	10.6495i	−0.0346890	+	0.0346890i	−0.724239	−	0.689550i	$-0.757809\pi$
$307$	−10.6495	+	10.6495i	−0.0346890	+	0.0346890i	0.689550	+	0.724239i	$0.257809\pi$
$308$		0			0
$309$			35.9207i			0.116248i
$310$		0			0
$311$	−375.853	+	273.073i	−1.20853	+	0.878049i	−0.995097	−	0.0989088i	$-0.968465\pi$
$311$	−375.853	+	273.073i	−1.20853	+	0.878049i	−0.213434	+	0.976958i	$0.568465\pi$
$312$		0			0
$313$	−71.6274	+	140.577i	−0.228842	+	0.449127i	−0.976664	−	0.214772i	$-0.931099\pi$
$313$	−71.6274	+	140.577i	−0.228842	+	0.449127i	0.747823	+	0.663898i	$0.231099\pi$
$314$		0			0
$315$	217.884	+	505.851i	0.691696	+	1.60588i
$316$		0			0
$317$	−91.7142	−	179.999i	−0.289319	−	0.567821i	0.699904	−	0.714237i	$-0.253226\pi$
$317$	−91.7142	−	179.999i	−0.289319	−	0.567821i	−0.989223	+	0.146416i	$0.953226\pi$
$318$		0			0
$319$	−1.91084	+	525.075i	−0.00599009	+	1.64600i
$320$		0			0
$321$	18.8177	−	57.9149i	0.0586221	−	0.180420i
$322$		0			0
$323$	−39.6940	−	250.618i	−0.122892	−	0.775907i
$324$		0			0
$325$	−14.8286	−	528.942i	−0.0456264	−	1.62751i
$326$		0			0
$327$	−8.98091	+	56.7032i	−0.0274645	+	0.173404i
$328$		0			0
$329$		−	369.795i		−	1.12400i
$330$		0			0
$331$	532.628			1.60915			0.804573	−	0.593853i	$-0.202394\pi$
$331$	532.628			1.60915			0.804573	+	0.593853i	$0.202394\pi$
$332$		0			0
$333$	195.447	+	30.9558i	0.586928	+	0.0929603i
$334$		0			0
$335$	−164.527	−	37.0689i	−0.491124	−	0.110653i
$336$		0			0
$337$	280.502	−	44.4272i	0.832352	−	0.131832i	0.274307	−	0.961642i	$-0.411552\pi$
$337$	280.502	−	44.4272i	0.832352	−	0.131832i	0.558045	+	0.829811i	$0.311552\pi$
$338$		0			0
$339$	58.4019	+	18.9759i	0.172277	+	0.0559762i
$340$		0			0
$341$	49.1632	+	153.204i	0.144174	+	0.449278i
$342$		0			0
$343$	−620.306	+	316.062i	−1.80847	+	0.921463i
$344$		0			0
$345$	8.23004	−	20.6842i	0.0238552	−	0.0599543i
$346$		0			0
$347$	−114.283	−	58.2303i	−0.329347	−	0.167811i	0.281496	−	0.959562i	$-0.409169\pi$
$347$	−114.283	−	58.2303i	−0.329347	−	0.167811i	−0.610843	+	0.791752i	$0.709169\pi$
$348$		0			0
$349$	271.297	+	373.408i	0.777354	+	1.06994i	0.995569	+	0.0940353i	$0.0299766\pi$
$349$	271.297	+	373.408i	0.777354	+	1.06994i	−0.218215	+	0.975901i	$0.570023\pi$
$350$		0			0
$351$	−134.196			−0.382323
$352$		0			0
$353$	−79.2335	−	79.2335i	−0.224457	−	0.224457i	0.585915	−	0.810373i	$-0.300735\pi$
$353$	−79.2335	−	79.2335i	−0.224457	−	0.224457i	−0.810373	+	0.585915i	$0.800735\pi$
$354$		0			0
$355$	186.644	−	224.837i	0.525758	−	0.633344i
$356$		0			0
$357$	31.7859	+	16.1957i	0.0890360	+	0.0453661i
$358$		0			0
$359$	10.1402	−	13.9568i	0.0282458	−	0.0388770i	−0.794661	−	0.607054i	$-0.792351\pi$
$359$	10.1402	−	13.9568i	0.0282458	−	0.0388770i	0.822906	+	0.568177i	$0.192351\pi$
$360$		0			0
$361$	−191.532	+	589.474i	−0.530559	+	1.63289i
$362$		0			0
$363$	−19.7630	+	38.0991i	−0.0544436	+	0.104956i
$364$		0			0
$365$	−171.062	+	150.297i	−0.468664	+	0.411774i
$366$		0			0
$367$	108.237	−	17.1430i	0.294923	−	0.0467113i	−0.00721945	−	0.999974i	$-0.502298\pi$
$367$	108.237	−	17.1430i	0.294923	−	0.0467113i	0.302143	+	0.953263i	$0.402298\pi$
$368$		0			0
$369$	−84.5492	+	27.4717i	−0.229131	+	0.0744491i
$370$		0			0
$371$	−571.295	+	415.070i	−1.53988	+	1.11879i
$372$		0			0
$373$	60.7347	+	60.7347i	0.162828	+	0.162828i	0.783818	−	0.620990i	$-0.213269\pi$
$373$	60.7347	+	60.7347i	0.162828	+	0.162828i	−0.620990	+	0.783818i	$0.713269\pi$
$374$		0			0
$375$	44.3092	+	1.61797i	0.118158	+	0.00431459i
$376$		0			0
$377$	158.053	−	997.908i	0.419239	−	2.64697i
$378$		0			0
$379$	−648.436	+	210.690i	−1.71091	+	0.555909i	−0.990485	−	0.137620i	$-0.956055\pi$
$379$	−648.436	+	210.690i	−1.71091	+	0.555909i	−0.720428	+	0.693530i	$0.756055\pi$
$380$		0			0
$381$	59.2710	+	43.0629i	0.155567	+	0.113026i
$382$		0			0
$383$	360.399	−	183.633i	0.940990	−	0.479459i	0.0849601	−	0.996384i	$-0.472924\pi$
$383$	360.399	−	183.633i	0.940990	−	0.479459i	0.856030	+	0.516926i	$0.172924\pi$
$384$		0			0
$385$	−665.474	−	152.482i	−1.72850	−	0.396058i
$386$		0			0
$387$	−76.0689	−	149.294i	−0.196560	−	0.385772i
$388$		0			0
$389$	−411.817	+	566.817i	−1.05866	+	1.45711i	−0.177599	+	0.984103i	$0.556833\pi$
$389$	−411.817	+	566.817i	−1.05866	+	1.45711i	−0.881056	+	0.473011i	$0.843167\pi$
$390$		0			0
$391$	31.4263	+	96.7201i	0.0803740	+	0.247366i
$392$		0			0
$393$	−4.67143	−	0.739881i	−0.0118866	−	0.00188265i
$394$		0			0
$395$	−30.0584	−	117.899i	−0.0760973	−	0.298478i
$396$		0			0
$397$	264.463	−	264.463i	0.666155	−	0.666155i	−0.290669	−	0.956824i	$-0.593878\pi$
$397$	264.463	−	264.463i	0.666155	−	0.666155i	0.956824	+	0.290669i	$0.0938778\pi$
$398$		0			0
$399$	−81.0521	−	111.559i	−0.203138	−	0.279595i
$400$		0			0
$401$	−84.9644	−	261.494i	−0.211881	−	0.652104i	−0.999360	−	0.0357621i	$-0.988614\pi$
$401$	−84.9644	−	261.494i	−0.211881	−	0.652104i	0.787479	−	0.616341i	$-0.211386\pi$
$402$		0			0
$403$	−48.4318	−	305.787i	−0.120178	−	0.758776i
$404$		0			0
$405$	−25.0249	+	387.286i	−0.0617898	+	0.956262i
$406$		0			0
$407$	−174.074	+	172.811i	−0.427700	+	0.424598i
$408$		0			0
$409$	197.874	+	64.2931i	0.483799	+	0.157196i	0.540754	−	0.841181i	$-0.318139\pi$
$409$	197.874	+	64.2931i	0.483799	+	0.157196i	−0.0569547	+	0.998377i	$0.518139\pi$
$410$		0			0
$411$	22.6990	+	16.4918i	0.0552288	+	0.0401261i
$412$		0			0
$413$	−349.110	+	685.168i	−0.845303	+	1.65900i
$414$		0			0
$415$	290.320	−	26.9471i	0.699566	−	0.0649327i
$416$		0			0
$417$	−4.82137	+	4.82137i	−0.0115620	+	0.0115620i
$418$		0			0
$419$			8.44454i			0.0201540i	0.999949	+	0.0100770i	$0.00320767\pi$
$419$			8.44454i			0.0201540i	−0.999949	+	0.0100770i	$0.996792\pi$
$420$		0			0
$421$	−391.978	+	284.789i	−0.931064	+	0.676458i	−0.946253	−	0.323427i	$-0.895165\pi$
$421$	−391.978	+	284.789i	−0.931064	+	0.676458i	0.0151892	+	0.999885i	$0.495165\pi$
$422$		0			0
$423$	120.021	−	235.554i	0.283737	−	0.556865i
$424$		0			0
$425$	−160.469	+	123.603i	−0.377573	+	0.290832i
$426$		0			0
$427$	−123.608	−	242.595i	−0.289481	−	0.568139i
$428$		0			0
$429$	48.7854	−	66.6361i	0.113719	−	0.155329i
$430$		0			0
$431$	−20.6383	+	63.5181i	−0.0478847	+	0.147374i	−0.972140	−	0.234401i	$-0.924687\pi$
$431$	−20.6383	+	63.5181i	−0.0478847	+	0.147374i	0.924255	+	0.381775i	$0.124687\pi$
$432$		0			0
$433$	−74.2965	−	469.089i	−0.171585	−	1.08335i	−0.911697	−	0.410863i	$-0.865227\pi$
$433$	−74.2965	−	469.089i	−0.171585	−	1.08335i	0.740112	−	0.672484i	$-0.234773\pi$
$434$		0			0
$435$	82.5890	+	18.6078i	0.189860	+	0.0427766i
$436$		0			0
$437$	61.4943	−	388.260i	0.140719	−	0.888466i
$438$		0			0
$439$		−	113.504i		−	0.258550i	−0.991609	−	0.129275i	$-0.958735\pi$
$439$		−	113.504i		−	0.258550i	0.991609	−	0.129275i	$-0.0412650\pi$
$440$		0			0
$441$	−932.542			−2.11461
$442$		0			0
$443$	−284.291	−	45.0273i	−0.641741	−	0.101642i	−0.172921	−	0.984936i	$-0.555321\pi$
$443$	−284.291	−	45.0273i	−0.641741	−	0.101642i	−0.468820	+	0.883294i	$0.655321\pi$
$444$		0			0
$445$	−306.573	+	193.829i	−0.688927	+	0.435571i
$446$		0			0
$447$	34.6314	−	5.48507i	0.0774751	−	0.0122709i
$448$		0			0
$449$	57.4458	+	18.6653i	0.127942	+	0.0415707i	0.372288	−	0.928117i	$-0.378573\pi$
$449$	57.4458	+	18.6653i	0.127942	+	0.0415707i	−0.244346	+	0.969688i	$0.578573\pi$
$450$		0			0
$451$	34.4338	−	104.678i	0.0763498	−	0.232103i
$452$		0			0
$453$	6.54383	−	3.33425i	0.0144455	−	0.00736037i
$454$		0			0
$455$	1220.61	+	485.666i	2.68265	+	1.06740i
$456$		0			0
$457$	370.313	+	188.684i	0.810313	+	0.412875i	0.809497	−	0.587124i	$-0.199740\pi$
$457$	370.313	+	188.684i	0.810313	+	0.412875i	0.000816565		1.00000i	$0.499740\pi$
$458$		0			0
$459$	30.1938	+	41.5582i	0.0657817	+	0.0905408i
$460$		0			0
$461$	816.237			1.77058			0.885290	−	0.465039i	$-0.153960\pi$
$461$	816.237			1.77058			0.885290	+	0.465039i	$0.153960\pi$
$462$		0			0
$463$	−211.921	−	211.921i	−0.457712	−	0.457712i	0.440192	−	0.897904i	$-0.354910\pi$
$463$	−211.921	−	211.921i	−0.457712	−	0.457712i	−0.897904	+	0.440192i	$0.854910\pi$
$464$		0			0
$465$	25.8309	−	2.39759i	0.0555504	−	0.00515610i
$466$		0			0
$467$	−167.892	−	85.5450i	−0.359511	−	0.183180i	0.264900	−	0.964276i	$-0.414661\pi$
$467$	−167.892	−	85.5450i	−0.359511	−	0.183180i	−0.624411	+	0.781096i	$0.714661\pi$
$468$		0			0
$469$	246.103	−	338.732i	0.524740	−	0.722243i
$470$		0			0
$471$	19.0297	−	58.5675i	0.0404028	−	0.124347i
$472$		0			0
$473$	205.018	+	33.2369i	0.433441	+	0.0702682i
$474$		0			0
$475$	769.572	−	144.103i	1.62015	−	0.303374i
$476$		0			0
$477$	−498.622	+	78.9739i	−1.04533	+	0.165564i
$478$		0			0
$479$	38.5182	−	12.5153i	0.0804137	−	0.0261280i	−0.268534	−	0.963270i	$-0.586539\pi$
$479$	38.5182	−	12.5153i	0.0804137	−	0.0261280i	0.348948	+	0.937142i	$0.386539\pi$
$480$		0			0
$481$	381.836	−	277.420i	0.793839	−	0.576758i
$482$		0			0
$483$	39.0794	+	39.0794i	0.0809098	+	0.0809098i
$484$		0			0
$485$	−229.178	+	386.024i	−0.472532	+	0.795926i
$486$		0			0
$487$	29.4028	−	185.642i	0.0603754	−	0.381195i	−0.938936	−	0.344092i	$-0.888187\pi$
$487$	29.4028	−	185.642i	0.0603754	−	0.381195i	0.999311	−	0.0371035i	$-0.0118131\pi$
$488$		0			0
$489$	77.7946	−	25.2770i	0.159089	−	0.0516912i
$490$		0			0
$491$	158.315	+	115.023i	0.322434	+	0.234262i	0.737213	−	0.675660i	$-0.236141\pi$
$491$	158.315	+	115.023i	0.322434	+	0.234262i	−0.414779	+	0.909922i	$0.636141\pi$
$492$		0			0
$493$	−344.598	+	175.581i	−0.698982	+	0.356149i
$494$		0			0
$495$	−374.407	−	313.115i	−0.756379	−	0.632556i
$496$		0			0
$497$	329.348	+	646.381i	0.662671	+	1.30057i
$498$		0			0
$499$	−311.179	+	428.301i	−0.623605	+	0.858319i	−0.997609	−	0.0691080i	$-0.977985\pi$
$499$	−311.179	+	428.301i	−0.623605	+	0.858319i	0.374004	+	0.927427i	$0.377985\pi$
$500$		0			0
$501$	14.9815	+	46.1084i	0.0299033	+	0.0920328i
$502$		0			0
$503$	228.733	+	36.2277i	0.454738	+	0.0720234i	0.379602	−	0.925150i	$-0.376061\pi$
$503$	228.733	+	36.2277i	0.454738	+	0.0720234i	0.0751357	+	0.997173i	$0.476061\pi$
$504$		0			0
$505$	−517.421	+	131.917i	−1.02460	+	0.261222i
$506$		0			0
$507$	−69.9780	+	69.9780i	−0.138024	+	0.138024i
$508$		0			0
$509$	545.647	+	751.019i	1.07200	+	1.47548i	0.868037	+	0.496500i	$0.165382\pi$
$509$	545.647	+	751.019i	1.07200	+	1.47548i	0.203962	+	0.978979i	$0.434618\pi$
$510$		0			0
$511$	−174.692	−	537.647i	−0.341863	−	1.05215i
$512$		0			0
$513$	−31.0616	−	196.115i	−0.0605490	−	0.382291i
$514$		0			0
$515$	380.378	−	334.204i	0.738598	−	0.648941i
$516$		0			0
$517$	147.708	+	292.520i	0.285702	+	0.565804i
$518$		0			0
$519$	−64.9825	−	21.1141i	−0.125207	−	0.0406822i
$520$		0			0
$521$	−527.372	−	383.158i	−1.01223	−	0.735428i	−0.0475546	−	0.998869i	$-0.515143\pi$
$521$	−527.372	−	383.158i	−1.01223	−	0.735428i	−0.964676	+	0.263440i	$0.915143\pi$
$522$		0			0
$523$	−251.596	+	493.784i	−0.481062	+	0.944138i	0.515143	+	0.857104i	$0.327739\pi$
$523$	−251.596	+	493.784i	−0.481062	+	0.944138i	−0.996205	+	0.0870338i	$0.972261\pi$
$524$		0			0
$525$	−47.2054	+	99.4404i	−0.0899150	+	0.189410i
$526$		0			0
$527$	−83.8002	+	83.8002i	−0.159014	+	0.159014i
$528$		0			0
$529$		−	371.449i		−	0.702173i
$530$		0			0
$531$	−444.756	+	323.134i	−0.837582	+	0.608539i
$532$		0			0
$533$	−96.2633	+	188.927i	−0.180607	+	0.354460i
$534$		0			0
$535$	−788.362	+	339.570i	−1.47357	+	0.634710i
$536$		0			0
$537$	−25.6442	−	50.3297i	−0.0477547	−	0.0937238i
$538$		0			0
$539$	682.839	−	932.691i	1.26686	−	1.73041i
$540$		0			0
$541$	285.480	−	878.616i	0.527689	−	1.62406i	−0.231249	−	0.972895i	$-0.574281\pi$
$541$	285.480	−	878.616i	0.527689	−	1.62406i	0.758937	−	0.651164i	$-0.225719\pi$
$542$		0			0
$543$	−1.40701	−	8.88352i	−0.00259118	−	0.0163601i
$544$		0			0
$545$	684.009	−	432.461i	1.25506	−	0.793507i
$546$		0			0
$547$	−118.583	+	748.704i	−0.216788	+	1.36875i	0.603759	+	0.797167i	$0.293669\pi$
$547$	−118.583	+	748.704i	−0.216788	+	1.36875i	−0.820547	+	0.571579i	$0.806331\pi$
$548$		0			0
$549$		−	194.648i		−	0.354550i
$550$		0			0
$551$	1494.94			2.71314
$552$		0			0
$553$	298.342	+	47.2527i	0.539497	+	0.0854480i
$554$		0			0
$555$	21.1342	+	33.4273i	0.0380797	+	0.0602294i
$556$		0			0
$557$	711.018	−	112.614i	1.27651	−	0.202180i	0.518873	−	0.854851i	$-0.326352\pi$
$557$	711.018	−	112.614i	1.27651	−	0.202180i	0.757641	+	0.652672i	$0.226352\pi$
$558$		0			0
$559$	−380.082	−	123.496i	−0.679932	−	0.220923i
$560$		0			0
$561$	−31.6128	−	0.115044i	−0.0563508	−	0.000205070i
$562$		0			0
$563$	679.556	−	346.251i	1.20703	−	0.615010i	0.269525	−	0.962993i	$-0.413133\pi$
$563$	679.556	−	346.251i	1.20703	−	0.615010i	0.937501	+	0.347983i	$0.113133\pi$
$564$		0			0
$565$	−342.425	−	794.990i	−0.606062	−	1.40706i
$566$		0			0
$567$	−858.474	−	437.414i	−1.51406	−	0.771454i
$568$		0			0
$569$	−406.990	−	560.173i	−0.715272	−	0.984487i	−0.999668	−	0.0257802i	$-0.991793\pi$
$569$	−406.990	−	560.173i	−0.715272	−	0.984487i	0.284396	−	0.958707i	$-0.408207\pi$
$570$		0			0
$571$	468.711			0.820860			0.410430	−	0.911892i	$-0.365379\pi$
$571$	468.711			0.820860			0.410430	+	0.911892i	$0.365379\pi$
$572$		0			0
$573$	−19.3289	−	19.3289i	−0.0337327	−	0.0337327i
$574$		0			0
$575$	−295.605	+	105.294i	−0.514096	+	0.183120i
$576$		0			0
$577$	873.348	+	444.993i	1.51360	+	0.771218i	0.996411	−	0.0846520i	$-0.0269779\pi$
$577$	873.348	+	444.993i	1.51360	+	0.771218i	0.517191	+	0.855870i	$0.326978\pi$
$578$		0			0
$579$	−3.92586	+	5.40349i	−0.00678042	+	0.00933245i
$580$		0			0
$581$	−223.682	+	688.423i	−0.384995	+	1.18489i
$582$		0			0
$583$	286.122	−	556.529i	0.490774	−	0.954595i
$584$		0			0
$585$	619.880	+	705.522i	1.05962	+	1.20602i
$586$		0			0
$587$	831.311	−	131.667i	1.41620	−	0.224304i	0.599043	−	0.800717i	$-0.295548\pi$
$587$	831.311	−	131.667i	1.41620	−	0.224304i	0.817159	+	0.576412i	$0.195548\pi$
$588$		0			0
$589$	435.671	−	141.558i	0.739679	−	0.240336i
$590$		0			0
$591$	16.6175	−	12.0733i	0.0281176	−	0.0204286i
$592$		0			0
$593$	607.974	+	607.974i	1.02525	+	1.02525i	0.999673	+	0.0255782i	$0.00814267\pi$
$593$	607.974	+	607.974i	1.02525	+	1.02525i	0.0255782	+	0.999673i	$0.491857\pi$
$594$		0			0
$595$	−124.232	−	487.276i	−0.208793	−	0.818952i
$596$		0			0
$597$	17.6611	−	111.508i	0.0295831	−	0.186781i
$598$		0			0
$599$	61.8895	−	20.1091i	0.103321	−	0.0335711i	−0.256900	−	0.966438i	$-0.582701\pi$
$599$	61.8895	−	20.1091i	0.103321	−	0.0335711i	0.360221	+	0.932867i	$0.382701\pi$
$600$		0			0
$601$	246.929	+	179.404i	0.410864	+	0.298510i	0.773951	−	0.633245i	$-0.218277\pi$
$601$	246.929	+	179.404i	0.410864	+	0.298510i	−0.363088	+	0.931755i	$0.618277\pi$
$602$		0			0
$603$	266.703	−	135.892i	0.442293	−	0.225360i
$604$		0			0
$605$	587.319	−	145.193i	0.970776	−	0.239989i
$606$		0			0
$607$	30.4016	+	59.6664i	0.0500849	+	0.0982972i	0.914692	−	0.404151i	$-0.132433\pi$
$607$	30.4016	+	59.6664i	0.0500849	+	0.0982972i	−0.864607	+	0.502448i	$0.832433\pi$
$608$		0			0
$609$	−123.539	+	170.037i	−0.202855	+	0.279206i
$610$		0			0
$611$	−194.851	−	599.689i	−0.318905	−	0.981488i
$612$		0			0
$613$	−506.882	−	80.2823i	−0.826888	−	0.130966i	−0.271375	−	0.962474i	$-0.587478\pi$
$613$	−506.882	−	80.2823i	−0.826888	−	0.130966i	−0.555513	+	0.831508i	$0.687478\pi$
$614$		0			0
$615$	−15.2776	−	9.07012i	−0.0248416	−	0.0147482i
$616$		0			0
$617$	−593.471	+	593.471i	−0.961866	+	0.961866i	−0.999299	−	0.0374332i	$-0.988082\pi$
$617$	−593.471	+	593.471i	−0.961866	+	0.961866i	0.0374332	+	0.999299i	$0.488082\pi$
$618$		0			0
$619$	677.380	+	932.333i	1.09431	+	1.50619i	0.842715	+	0.538360i	$0.180956\pi$
$619$	677.380	+	932.333i	1.09431	+	1.50619i	0.251598	+	0.967832i	$0.419044\pi$
$620$		0			0
$621$	24.5919	+	75.6860i	0.0396004	+	0.121878i
$622$		0			0
$623$	−140.863	−	889.377i	−0.226105	−	1.42757i
$624$		0			0
$625$	−395.117	−	484.260i	−0.632187	−	0.774816i
$626$		0			0
$627$	108.675	+	55.8718i	0.173326	+	0.0891098i
$628$		0			0
$629$	−171.825	−	55.8295i	−0.273172	−	0.0887591i
$630$		0			0
$631$	−110.345	−	80.1705i	−0.174874	−	0.127053i	0.496905	−	0.867805i	$-0.334470\pi$
$631$	−110.345	−	80.1705i	−0.174874	−	0.127053i	−0.671779	+	0.740752i	$0.734470\pi$
$632$		0			0
$633$	39.2355	−	77.0040i	0.0619834	−	0.121649i
$634$		0			0
$635$	−95.4451	−	1028.30i	−0.150307	−	1.61937i
$636$		0			0
$637$	−1572.76	+	1572.76i	−2.46902	+	2.46902i
$638$		0			0
$639$			518.628i			0.811624i
$640$		0			0
$641$	−225.218	+	163.631i	−0.351355	+	0.255274i	−0.749437	−	0.662076i	$-0.769676\pi$
$641$	−225.218	+	163.631i	−0.351355	+	0.255274i	0.398082	+	0.917350i	$0.369676\pi$
$642$		0			0
$643$	−230.607	+	452.591i	−0.358642	+	0.703874i	−0.997876	−	0.0651376i	$-0.979251\pi$
$643$	−230.607	+	452.591i	−0.358642	+	0.703874i	0.639234	+	0.769012i	$0.279251\pi$
$644$		0			0
$645$	12.3801	−	31.1144i	0.0191939	−	0.0482394i
$646$		0			0
$647$	−295.583	−	580.115i	−0.456852	−	0.896622i	−0.998432	−	0.0559732i	$-0.982174\pi$
$647$	−295.583	−	580.115i	−0.456852	−	0.896622i	0.541580	−	0.840649i	$-0.317826\pi$
$648$		0			0
$649$	2.47987	−	681.437i	0.00382106	−	1.04998i
$650$		0			0
$651$	−19.9019	+	61.2518i	−0.0305713	+	0.0940888i
$652$		0			0
$653$	159.378	+	1006.27i	0.244070	+	1.54100i	0.739983	+	0.672626i	$0.234834\pi$
$653$	159.378	+	1006.27i	0.244070	+	1.54100i	−0.495912	+	0.868373i	$0.665166\pi$
$654$		0			0
$655$	35.6278	+	56.3513i	0.0543936	+	0.0860325i
$656$		0			0
$657$	63.2226	−	399.171i	0.0962291	−	0.607567i
$658$		0			0
$659$			519.838i			0.788828i	0.918933	+	0.394414i	$0.129052\pi$
$659$			519.838i			0.788828i	−0.918933	+	0.394414i	$0.870948\pi$
$660$		0			0
$661$	−299.078			−0.452463			−0.226231	−	0.974074i	$-0.572641\pi$
$661$	−299.078			−0.452463			−0.226231	+	0.974074i	$0.572641\pi$
$662$		0			0
$663$	60.0803	+	9.51578i	0.0906188	+	0.0143526i
$664$		0			0
$665$	−427.231	+	1896.23i	−0.642453	+	2.85147i
$666$		0			0
$667$	−591.782	+	93.7291i	−0.887229	+	0.140523i
$668$		0			0
$669$	0.200282	+	0.0650757i	0.000299376	+	9.72731e-5i
$670$		0			0
$671$	194.679	+	142.528i	0.290133	+	0.212411i
$672$		0			0
$673$	206.433	−	105.183i	0.306736	−	0.156290i	−0.293846	−	0.955853i	$-0.594935\pi$
$673$	206.433	−	105.183i	0.306736	−	0.156290i	0.600582	+	0.799563i	$0.294935\pi$
$674$		0			0
$675$	−125.571	+	96.7230i	−0.186031	+	0.143293i
$676$		0			0
$677$	−328.869	−	167.567i	−0.485774	−	0.247514i	0.193910	−	0.981019i	$-0.437883\pi$
$677$	−328.869	−	167.567i	−0.485774	−	0.247514i	−0.679684	+	0.733505i	$0.737883\pi$
$678$		0			0
$679$	−655.098	−	901.665i	−0.964798	−	1.32793i
$680$		0			0
$681$	72.6023			0.106611
$682$		0			0
$683$	−398.725	−	398.725i	−0.583785	−	0.583785i	0.352156	−	0.935941i	$-0.385449\pi$
$683$	−398.725	−	398.725i	−0.583785	−	0.583785i	−0.935941	+	0.352156i	$0.885449\pi$
$684$		0			0
$685$	−36.5526	−	393.808i	−0.0533615	−	0.574902i
$686$		0			0
$687$	−60.0282	−	30.5859i	−0.0873772	−	0.0445209i
$688$		0			0
$689$	−707.751	+	974.136i	−1.02722	+	1.41384i
$690$		0			0
$691$	96.4604	−	296.874i	0.139595	−	0.429630i	−0.856681	−	0.515846i	$-0.827478\pi$
$691$	96.4604	−	296.874i	0.139595	−	0.429630i	0.996276	+	0.0862161i	$0.0274776\pi$
$692$		0			0
$693$	1081.64	−	546.175i	1.56081	−	0.788131i
$694$		0			0
$695$	95.9131	+	6.19752i	0.138005	+	0.00891730i
$696$		0			0
$697$	80.1669	−	12.6972i	0.115017	−	0.0182169i
$698$		0			0
$699$	23.3972	−	7.60222i	0.0334724	−	0.0108758i
$700$		0			0
$701$	−320.859	+	233.118i	−0.457716	+	0.332550i	−0.792635	−	0.609697i	$-0.791291\pi$
$701$	−320.859	+	233.118i	−0.457716	+	0.332550i	0.334919	+	0.942247i	$0.391291\pi$
$702$		0			0
$703$	493.808	+	493.808i	0.702430	+	0.702430i
$704$		0			0
$705$	51.1975	−	13.0529i	0.0726206	−	0.0185147i
$706$		0			0
$707$	207.377	−	1309.33i	0.293320	−	1.85195i
$708$		0			0
$709$	−118.249	+	38.4214i	−0.166783	+	0.0541910i	−0.391218	−	0.920298i	$-0.627946\pi$
$709$	−118.249	+	38.4214i	−0.166783	+	0.0541910i	0.224435	+	0.974489i	$0.427946\pi$
$710$		0			0
$711$	174.703	+	126.929i	0.245715	+	0.178522i
$712$		0			0
$713$	−163.588	+	83.3521i	−0.229436	+	0.116903i
$714$		0			0
$715$	−1159.53	+	103.371i	−1.62172	+	0.144575i
$716$		0			0
$717$	−38.6322	−	75.8200i	−0.0538803	−	0.105746i
$718$		0			0
$719$	318.617	−	438.538i	0.443139	−	0.609928i	−0.527767	−	0.849389i	$-0.676971\pi$
$719$	318.617	−	438.538i	0.443139	−	0.609928i	0.970906	+	0.239461i	$0.0769707\pi$
$720$		0			0
$721$	388.449	+	1195.52i	0.538765	+	1.65815i
$722$		0			0
$723$	52.4206	+	8.30260i	0.0725042	+	0.0114835i
$724$		0			0
$725$	−571.359	−	1047.69i	−0.788081	−	1.44509i
$726$		0			0
$727$	299.978	−	299.978i	0.412624	−	0.412624i	−0.470028	−	0.882652i	$-0.655756\pi$
$727$	299.978	−	299.978i	0.412624	−	0.412624i	0.882652	+	0.470028i	$0.155756\pi$
$728$		0			0
$729$	−392.971	−	540.878i	−0.539055	−	0.741946i
$730$		0			0
$731$	47.2731	+	145.492i	0.0646691	+	0.199031i
$732$		0			0
$733$	47.6287	+	300.716i	0.0649778	+	0.410254i	0.998642	+	0.0521033i	$0.0165925\pi$
$733$	47.6287	+	300.716i	0.0649778	+	0.410254i	−0.933664	+	0.358150i	$0.883407\pi$
$734$		0			0
$735$	−123.014	−	140.009i	−0.167365	−	0.190489i
$736$		0			0
$737$	−59.3754	+	366.250i	−0.0805636	+	0.496947i
$738$		0			0
$739$	858.134	+	278.825i	1.16121	+	0.377300i	0.825355	−	0.564614i	$-0.190975\pi$
$739$	858.134	+	278.825i	1.16121	+	0.377300i	0.335855	+	0.941914i	$0.390975\pi$
$740$		0			0
$741$	−190.223	−	138.205i	−0.256711	−	0.186511i
$742$		0			0
$743$	7.04706	−	13.8306i	0.00948460	−	0.0186146i	−0.886216	−	0.463273i	$-0.846675\pi$
$743$	7.04706	−	13.8306i	0.00948460	−	0.0186146i	0.895700	+	0.444658i	$0.146675\pi$
$744$		0			0
$745$	−380.292	−	315.692i	−0.510459	−	0.423747i
$746$		0			0
$747$	−365.917	+	365.917i	−0.489849	+	0.489849i
$748$		0			0
$749$		−	2131.04i		−	2.84518i
$750$		0			0
$751$	−239.838	+	174.253i	−0.319359	+	0.232028i	−0.735902	−	0.677088i	$-0.763241\pi$
$751$	−239.838	+	174.253i	−0.319359	+	0.232028i	0.416543	+	0.909116i	$0.363241\pi$
$752$		0			0
$753$	−36.1175	+	70.8846i	−0.0479648	+	0.0941363i
$754$		0			0
$755$	−96.1910	−	38.2734i	−0.127405	−	0.0506932i
$756$		0			0
$757$	568.338	+	1115.43i	0.750777	+	1.47348i	0.876492	+	0.481417i	$0.159878\pi$
$757$	568.338	+	1115.43i	0.750777	+	1.47348i	−0.125715	+	0.992066i	$0.540122\pi$
$758$		0			0
$759$	−46.5228	−	15.3036i	−0.0612948	−	0.0201628i
$760$		0			0
$761$	79.7890	−	245.565i	0.104848	−	0.322688i	−0.884847	−	0.465882i	$-0.845737\pi$
$761$	79.7890	−	245.565i	0.104848	−	0.322688i	0.989695	+	0.143194i	$0.0457373\pi$
$762$		0			0
$763$	314.287	+	1984.33i	0.411910	+	2.60070i
$764$		0			0
$765$	79.0168	−	350.708i	0.103290	−	0.458442i
$766$		0			0
$767$	−205.120	+	1295.07i	−0.267431	+	1.68849i
$768$		0			0
$769$			419.115i			0.545013i	0.962154	+	0.272506i	$0.0878526\pi$
$769$			419.115i			0.545013i	−0.962154	+	0.272506i	$0.912147\pi$
$770$		0			0
$771$	−111.245			−0.144287
$772$		0			0
$773$	−654.254	−	103.624i	−0.846383	−	0.134054i	−0.281844	−	0.959460i	$-0.590946\pi$
$773$	−654.254	−	103.624i	−0.846383	−	0.134054i	−0.564539	+	0.825407i	$0.690946\pi$
$774$		0			0
$775$	−265.718	−	251.226i	−0.342863	−	0.324163i
$776$		0			0
$777$	−96.9736	+	15.3591i	−0.124805	+	0.0197672i
$778$		0			0
$779$	−298.383	−	96.9505i	−0.383033	−	0.124455i
$780$		0			0
$781$	−518.711	−	379.757i	−0.664162	−	0.486245i
$782$		0			0
$783$	−269.657	+	137.397i	−0.344390	+	0.175475i
$784$		0			0
$785$	−797.245	+	343.396i	−1.01560	+	0.437447i
$786$		0			0
$787$	−542.288	−	276.310i	−0.689057	−	0.351092i	0.0741490	−	0.997247i	$-0.476376\pi$
$787$	−542.288	−	276.310i	−0.689057	−	0.351092i	−0.763206	+	0.646155i	$0.776376\pi$
$788$		0			0
$789$	32.5846	+	44.8488i	0.0412986	+	0.0568426i
$790$		0			0
$791$	2148.96			2.71676
$792$		0			0
$793$	−328.281	−	328.281i	−0.413973	−	0.413973i
$794$		0			0
$795$	−77.6312	−	64.4440i	−0.0976493	−	0.0810616i
$796$		0			0
$797$	−793.235	−	404.173i	−0.995276	−	0.507118i	−0.121055	−	0.992646i	$-0.538628\pi$
$797$	−793.235	−	404.173i	−0.995276	−	0.507118i	−0.874221	+	0.485527i	$0.838628\pi$
$798$		0			0
$799$	−141.873	+	195.271i	−0.177563	+	0.244395i
$800$		0			0
$801$	198.928	−	612.238i	0.248350	−	0.764343i
$802$		0			0
$803$	352.942	+	355.520i	0.439529	+	0.442739i
$804$		0			0
$805$	50.2337	−	777.419i	0.0624021	−	0.965738i
$806$		0			0
$807$	−120.990	+	19.1629i	−0.149925	+	0.0237458i
$808$		0			0
$809$	−646.431	+	210.038i	−0.799050	+	0.259627i	−0.679953	−	0.733256i	$-0.738000\pi$
$809$	−646.431	+	210.038i	−0.799050	+	0.259627i	−0.119097	+	0.992883i	$0.538000\pi$
$810$		0			0
$811$	372.607	−	270.715i	0.459441	−	0.333803i	−0.333871	−	0.942619i	$-0.608355\pi$
$811$	372.607	−	270.715i	0.459441	−	0.333803i	0.793312	+	0.608815i	$0.208355\pi$
$812$		0			0
$813$	92.6628	+	92.6628i	0.113976	+	0.113976i
$814$		0			0
$815$	−991.464	−	588.620i	−1.21652	−	0.722233i
$816$		0			0
$817$	92.5032	−	584.042i	0.113223	−	0.714862i
$818$		0			0
$819$	−2217.45	+	720.492i	−2.70751	+	0.879722i
$820$		0			0
$821$	1088.17	+	790.600i	1.32542	+	0.962972i	0.999848	+	0.0174539i	$0.00555603\pi$
$821$	1088.17	+	790.600i	1.32542	+	0.962972i	0.325570	+	0.945518i	$0.394444\pi$
$822$		0			0
$823$	−812.415	+	413.946i	−0.987138	+	0.502972i	−0.871540	−	0.490324i	$-0.836878\pi$
$823$	−812.415	+	413.946i	−0.987138	+	0.502972i	−0.115598	+	0.993296i	$0.536878\pi$
$824$		0			0
$825$	−2.37869	−	97.5161i	−0.00288326	−	0.118201i
$826$		0			0
$827$	635.908	+	1248.04i	0.768933	+	1.50912i	0.858318	+	0.513119i	$0.171510\pi$
$827$	635.908	+	1248.04i	0.768933	+	1.50912i	−0.0893846	+	0.995997i	$0.528490\pi$
$828$		0			0
$829$	−48.1019	+	66.2066i	−0.0580240	+	0.0798632i	−0.837043	−	0.547137i	$-0.815718\pi$
$829$	−48.1019	+	66.2066i	−0.0580240	+	0.0798632i	0.779019	+	0.627000i	$0.215718\pi$
$830$		0			0
$831$	47.0577	+	144.829i	0.0566277	+	0.174282i
$832$		0			0
$833$	840.930	+	133.190i	1.00952	+	0.159892i
$834$		0			0
$835$	348.872	−	587.636i	0.417811	−	0.703755i
$836$		0			0
$837$	−65.5758	+	65.5758i	−0.0783463	+	0.0783463i
$838$		0			0
$839$	−96.5954	−	132.952i	−0.115132	−	0.158465i	0.747562	−	0.664192i	$-0.231224\pi$
$839$	−96.5954	−	132.952i	−0.115132	−	0.158465i	−0.862694	+	0.505727i	$0.831224\pi$
$840$		0			0
$841$	−444.235	−	1367.22i	−0.528223	−	1.62570i
$842$		0			0
$843$	5.67048	+	35.8020i	0.00672655	+	0.0424698i
$844$		0			0
$845$	1392.10	+	89.9516i	1.64745	+	0.106452i
$846$		0			0
$847$	−245.753	+	1481.74i	−0.290145	+	1.74940i
$848$		0			0
$849$	117.730	+	38.2529i	0.138669	+	0.0450564i
$850$		0			0
$851$	−226.438	−	164.517i	−0.266084	−	0.193321i
$852$		0			0
$853$	−326.827	+	641.434i	−0.383150	+	0.751974i	−0.999366	−	0.0356029i	$-0.988665\pi$
$853$	−326.827	+	641.434i	−0.383150	+	0.751974i	0.616216	+	0.787577i	$0.288665\pi$
$854$		0			0
$855$	−887.579	+	1069.21i	−1.03810	+	1.25053i
$856$		0			0
$857$	−822.727	+	822.727i	−0.960008	+	0.960008i	−0.999231	−	0.0392223i	$-0.987512\pi$
$857$	−822.727	+	822.727i	−0.960008	+	0.960008i	0.0392223	+	0.999231i	$0.487512\pi$
$858$		0			0
$859$		−	998.912i		−	1.16288i	−0.813590	−	0.581439i	$-0.802490\pi$
$859$		−	998.912i		−	1.16288i	0.813590	−	0.581439i	$-0.197510\pi$
$860$		0			0
$861$	35.6850	−	25.9267i	0.0414460	−	0.0301123i
$862$		0			0
$863$	395.613	−	776.434i	0.458416	−	0.899692i	−0.539903	−	0.841727i	$-0.681539\pi$
$863$	395.613	−	776.434i	0.458416	−	0.899692i	0.998319	−	0.0579645i	$-0.0184610\pi$
$864$		0			0
$865$	381.008	+	884.568i	0.440472	+	1.02262i
$866$		0			0
$867$	35.9680	+	70.5911i	0.0414855	+	0.0814200i
$868$		0			0
$869$	−254.873	+	81.7890i	−0.293295	+	0.0941186i
$870$		0			0
$871$	220.617	−	678.991i	0.253292	−	0.779553i
$872$		0			0
$873$	−124.643	−	786.966i	−0.142776	−	0.901450i
$874$		0			0
$875$	1492.21	−	425.313i	1.70538	−	0.486072i
$876$		0			0
$877$	149.590	−	944.476i	0.170571	−	1.07694i	−0.742711	−	0.669612i	$-0.766461\pi$
$877$	149.590	−	944.476i	0.170571	−	1.07694i	0.913282	−	0.407328i	$-0.133539\pi$
$878$		0			0
$879$		−	9.48641i		−	0.0107923i
$880$		0			0
$881$	688.978			0.782041			0.391021	−	0.920382i	$-0.372122\pi$
$881$	688.978			0.782041			0.391021	+	0.920382i	$0.372122\pi$
$882$		0			0
$883$	−1375.23	−	217.815i	−1.55745	−	0.246676i	−0.682498	−	0.730888i	$-0.739106\pi$
$883$	−1375.23	−	217.815i	−1.55745	−	0.246676i	−0.874951	+	0.484212i	$0.839106\pi$
$884$		0			0
$885$	−107.183	−	24.1490i	−0.121111	−	0.0272871i
$886$		0			0
$887$	1248.93	−	197.812i	1.40804	−	0.223012i	0.594302	−	0.804242i	$-0.297428\pi$
$887$	1248.93	−	197.812i	1.40804	−	0.223012i	0.813739	+	0.581230i	$0.197428\pi$
$888$		0			0
$889$	2438.36	+	792.271i	2.74281	+	0.891194i
$890$		0			0
$891$	853.800	+	3.10713i	0.958249	+	0.00348724i
$892$		0			0
$893$	831.293	−	423.565i	0.930899	−	0.474317i
$894$		0			0
$895$	−294.367	+	739.821i	−0.328902	+	0.826616i
$896$		0			0
$897$	83.9659	+	42.7828i	0.0936075	+	0.0476954i
$898$		0			0
$899$	−410.403	−	564.871i	−0.456510	−	0.628332i
$900$		0			0
$901$	460.918			0.511562
$902$		0			0
$903$	58.7855	+	58.7855i	0.0651002	+	0.0651002i
$904$		0			0
$905$	−80.9801	+	97.5511i	−0.0894808	+	0.107791i
$906$		0			0
$907$	370.591	+	188.825i	0.408589	+	0.208187i	0.646191	−	0.763176i	$-0.276361\pi$
$907$	370.591	+	188.825i	0.408589	+	0.208187i	−0.237601	+	0.971363i	$0.576361\pi$
$908$		0			0
$909$	557.052	−	766.716i	0.612818	−	0.843472i
$910$		0			0
$911$	−123.474	+	380.014i	−0.135537	+	0.417140i	−0.995673	−	0.0929246i	$-0.970378\pi$
$911$	−123.474	+	380.014i	−0.135537	+	0.417140i	0.860136	+	0.510064i	$0.170378\pi$
$912$		0			0
$913$	−98.0385	−	633.913i	−0.107381	−	0.694318i
$914$		0			0
$915$	29.2239	−	25.6764i	0.0319386	−	0.0280617i
$916$		0			0
$917$	−163.477	+	25.8922i	−0.178274	+	0.0282358i
$918$		0			0
$919$	1476.20	−	479.647i	1.60631	−	0.521923i	0.637655	−	0.770322i	$-0.279904\pi$
$919$	1476.20	−	479.647i	1.60631	−	0.521923i	0.968658	+	0.248399i	$0.0799045\pi$
$920$		0			0
$921$	4.32192	−	3.14006i	0.00469263	−	0.00340940i
$922$		0			0
$923$	874.685	+	874.685i	0.947654	+	0.947654i
$924$		0			0
$925$	157.342	−	534.804i	0.170100	−	0.578167i
$926$		0			0
$927$	−140.583	+	887.606i	−0.151654	+	0.957504i
$928$		0			0
$929$	−520.229	+	169.033i	−0.559988	+	0.181951i	−0.575316	−	0.817931i	$-0.695121\pi$
$929$	−520.229	+	169.033i	−0.559988	+	0.181951i	0.0153279	+	0.999883i	$0.495121\pi$
$930$		0			0
$931$	−2662.50	−	1934.42i	−2.85983	−	2.07779i
$932$		0			0
$933$	146.830	−	74.8135i	0.157374	−	0.0801860i
$934$		0			0
$935$	292.906	+	335.830i	0.313268	+	0.359177i
$936$		0			0
$937$	−327.072	−	641.915i	−0.349063	−	0.685074i	0.648002	−	0.761639i	$-0.275605\pi$
$937$	−327.072	−	641.915i	−0.349063	−	0.685074i	−0.997065	+	0.0765643i	$0.975605\pi$
$938$		0			0
$939$	32.8946	−	45.2755i	0.0350315	−	0.0482167i
$940$		0			0
$941$	334.973	+	1030.94i	0.355975	+	1.09558i	0.955442	+	0.295179i	$0.0953794\pi$
$941$	334.973	+	1030.94i	0.355975	+	1.09558i	−0.599467	+	0.800400i	$0.704621\pi$
$942$		0			0
$943$	124.195	+	19.6706i	0.131702	+	0.0208596i
$944$		0			0
$945$	−97.2145	−	381.307i	−0.102872	−	0.403499i
$946$		0			0
$947$	515.763	−	515.763i	0.544629	−	0.544629i	−0.380254	−	0.924882i	$-0.624163\pi$
$947$	515.763	−	515.763i	0.544629	−	0.544629i	0.924882	+	0.380254i	$0.124163\pi$
$948$		0			0
$949$	−566.590	−	779.844i	−0.597039	−	0.821754i
$950$		0			0
$951$	22.1435	+	68.1506i	0.0232844	+	0.0716620i
$952$		0			0
$953$	7.91666	+	49.9838i	0.00830709	+	0.0524489i	0.991494	−	0.130155i	$-0.0415474\pi$
$953$	7.91666	+	49.9838i	0.00830709	+	0.0524489i	−0.983187	+	0.182604i	$0.941547\pi$
$954$		0			0
$955$	−24.8458	+	384.515i	−0.0260166	+	0.402634i
$956$		0			0
$957$	29.8053	−	183.850i	0.0311445	−	0.192111i
$958$		0			0
$959$	933.820	+	303.416i	0.973743	+	0.316388i
$960$		0			0
$961$	604.373	+	439.103i	0.628900	+	0.456923i
$962$		0			0
$963$	691.650	−	1357.44i	0.718224	−	1.40959i
$964$		0			0
$965$	93.7456	−	8.70133i	0.0971457	−	0.00901692i
$966$		0			0
$967$	19.7869	−	19.7869i	0.0204622	−	0.0204622i	−0.696802	−	0.717264i	$-0.745394\pi$
$967$	19.7869	−	19.7869i	0.0204622	−	0.0204622i	0.717264	+	0.696802i	$0.245394\pi$
$968$		0			0
$969$			90.0048i			0.0928842i
$970$		0			0
$971$	84.7721	−	61.5905i	0.0873039	−	0.0634300i	−0.543277	−	0.839553i	$-0.682817\pi$
$971$	84.7721	−	61.5905i	0.0873039	−	0.0634300i	0.630581	+	0.776123i	$0.282817\pi$
$972$		0			0
$973$	−108.328	+	212.605i	−0.111334	+	0.218505i
$974$		0			0
$975$	−24.1553	+	186.134i	−0.0247747	+	0.190906i
$976$		0			0
$977$	−119.502	−	234.535i	−0.122315	−	0.240057i	0.821728	−	0.569881i	$-0.193011\pi$
$977$	−119.502	−	234.535i	−0.122315	−	0.240057i	−0.944042	+	0.329824i	$0.893011\pi$
$978$		0			0
$979$	466.674	+	647.262i	0.476684	+	0.661146i
$980$		0			0
$981$	−443.839	+	1366.00i	−0.452435	+	1.39245i
$982$		0			0
$983$	−170.672	−	1077.58i	−0.173624	−	1.09622i	−0.908460	−	0.417972i	$-0.862741\pi$
$983$	−170.672	−	1077.58i	−0.173624	−	1.09622i	0.734836	−	0.678245i	$-0.237259\pi$
$984$		0			0
$985$	−282.457	−	63.6394i	−0.286759	−	0.0646085i
$986$		0			0
$987$	−20.5195	+	129.555i	−0.0207897	+	0.131261i
$988$		0			0
$989$			236.997i			0.239633i
$990$		0			0
$991$	−1245.65			−1.25696			−0.628482	−	0.777824i	$-0.716323\pi$
$991$	−1245.65			−1.25696			−0.628482	+	0.777824i	$0.716323\pi$
$992$		0			0
$993$	−186.602	−	29.5549i	−0.187918	−	0.0297632i
$994$		0			0
$995$	−1345.12	+	850.444i	−1.35188	+	0.854718i
$996$		0			0
$997$	−338.256	+	53.5746i	−0.339274	+	0.0537358i	−0.323747	−	0.946144i	$-0.604943\pi$
$997$	−338.256	+	53.5746i	−0.339274	+	0.0537358i	−0.0155273	+	0.999879i	$0.504943\pi$
$998$		0			0
$999$	−134.458	−	43.6880i	−0.134593	−	0.0437318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.x.a.53.7	✓	96
5.2	odd	4	inner	220.3.x.a.97.7	yes	96
11.5	even	5	inner	220.3.x.a.93.7	yes	96
55.27	odd	20	inner	220.3.x.a.137.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.x.a.53.7	✓	96	1.1	even	1	trivial
220.3.x.a.93.7	yes	96	11.5	even	5	inner
220.3.x.a.97.7	yes	96	5.2	odd	4	inner
220.3.x.a.137.7	yes	96	55.27	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.350343 - 0.0554888i) q^{3} +(2.67198 + 4.22617i) q^{5} +(-12.2603 + 1.94184i) q^{7} +(-8.43985 - 2.74227i) q^{9} +(8.92266 - 6.43321i) q^{11} +(-18.8590 + 9.60916i) q^{13} +(-0.701602 - 1.62887i) q^{15} +(7.21907 + 3.67830i) q^{17} +(-18.4082 - 25.3367i) q^{19} +4.40304 q^{21} +(8.87555 + 8.87555i) q^{23} +(-10.7211 + 22.5845i) q^{25} +(5.64911 + 2.87837i) q^{27} +(-28.0576 + 38.6180i) q^{29} +(-4.52004 + 13.9112i) q^{31} +(-3.48296 + 1.75872i) q^{33} +(-40.9657 - 46.6255i) q^{35} +(-22.0242 + 3.48830i) q^{37} +(7.14033 - 2.32003i) q^{39} +(8.10462 - 5.88835i) q^{41} +(13.3511 + 13.3511i) q^{43} +(-10.9618 - 42.9955i) q^{45} +(-4.66029 + 29.4239i) q^{47} +(99.9416 - 32.4730i) q^{49} +(-2.32504 - 1.68924i) q^{51} +(50.6879 - 25.8268i) q^{53} +(51.0290 + 20.5193i) q^{55} +(5.04327 + 9.89797i) q^{57} +(36.4128 - 50.1180i) q^{59} +(6.77803 + 20.8606i) q^{61} +(108.800 + 17.2322i) q^{63} +(-91.0009 - 54.0261i) q^{65} +(-23.8508 + 23.8508i) q^{67} +(-2.61699 - 3.60198i) q^{69} +(-18.0597 - 55.5820i) q^{71} +(7.12433 + 44.9812i) q^{73} +(5.00924 - 7.31740i) q^{75} +(-96.9019 + 96.1992i) q^{77} +(-23.1431 - 7.51964i) q^{79} +(62.7949 + 45.6231i) q^{81} +(26.4738 - 51.9577i) q^{83} +(3.74405 + 40.3373i) q^{85} +(11.9726 - 11.9726i) q^{87} +72.5414i q^{89} +(212.557 - 154.432i) q^{91} +(2.35548 - 4.62289i) q^{93} +(57.8910 - 145.495i) q^{95} +(40.7619 + 79.9997i) q^{97} +(-92.9475 + 29.8269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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