LMFDB - Embedded newform 220.3.p.b.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(41,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("220.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	220.p (of order $10$ , degree $4$ , 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 3 x^{15} + 33 x^{14} - 111 x^{13} + 735 x^{12} - 1436 x^{11} + 10633 x^{10} - 25103 x^{9} + \cdots + 75625$ x^16 - 3x^15 + 33x^14 - 111x^13 + 735x^12 - 1436x^11 + 10633x^10 - 25103x^9 + 232616x^8 - 600030x^7 + 1738315x^6 - 2296850x^5 + 2290475x^4 - 1918750x^3 + 1679000x^2 - 543125*x + 75625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$5$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			61.1
Root			$3.61325 - 2.62518i$ of defining polynomial
Character	$\chi$	$=$	220.61
Dual form			220.3.p.b.101.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30423 - 1.67412i) q^{3} +(0.690983 - 2.12663i) q^{5} +(1.86008 + 2.56018i) q^{7} +(-0.274352 - 0.844368i) q^{9} +(-8.20839 - 7.32272i) q^{11} +(1.09490 - 0.355754i) q^{13} +(-5.15242 + 3.74345i) q^{15} +(-16.6628 - 5.41408i) q^{17} +(-11.7724 + 16.2034i) q^{19} -9.01324i q^{21} -36.9406 q^{23} +(-4.04508 - 2.93893i) q^{25} +(-8.70265 + 26.7840i) q^{27} +(-2.94215 - 4.04952i) q^{29} +(-18.8909 - 58.1403i) q^{31} +(6.65491 + 30.6151i) q^{33} +(6.72982 - 2.18665i) q^{35} +(21.0660 - 15.3054i) q^{37} +(-3.11848 - 1.01326i) q^{39} +(35.4220 - 48.7542i) q^{41} +65.3933i q^{43} -1.98523 q^{45} +(21.5844 + 15.6820i) q^{47} +(12.0472 - 37.0775i) q^{49} +(29.3312 + 40.3709i) q^{51} +(0.957854 + 2.94797i) q^{53} +(-21.2446 + 12.3963i) q^{55} +(54.2529 - 17.6278i) q^{57} +(7.53304 - 5.47308i) q^{59} +(32.2647 + 10.4834i) q^{61} +(1.65142 - 2.27298i) q^{63} -2.57426i q^{65} -17.1176 q^{67} +(85.1197 + 61.8431i) q^{69} +(15.6778 - 48.2514i) q^{71} +(24.2807 + 33.4195i) q^{73} +(4.40069 + 13.5439i) q^{75} +(3.47921 - 34.6358i) q^{77} +(40.1596 - 13.0486i) q^{79} +(58.4283 - 42.4507i) q^{81} +(-76.7768 - 24.9463i) q^{83} +(-23.0275 + 31.6946i) q^{85} +14.2565i q^{87} -109.359 q^{89} +(2.94739 + 2.14140i) q^{91} +(-53.8049 + 165.595i) q^{93} +(26.3240 + 36.2319i) q^{95} +(-6.19215 - 19.0575i) q^{97} +(-3.93109 + 8.93991i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 9 q^{3} + 20 q^{5} + 10 q^{7} - 19 q^{9} + 23 q^{11} - 5 q^{13} + 15 q^{15} + 25 q^{17} + 30 q^{19} - 168 q^{23} - 20 q^{25} - 225 q^{27} - 105 q^{29} + 40 q^{31} + 106 q^{33} - 16 q^{37} + 115 q^{39}+ \cdots + 150 q^{99}+O(q^{100})$ 16 * q + 9 * q^3 + 20 * q^5 + 10 * q^7 - 19 * q^9 + 23 * q^11 - 5 * q^13 + 15 * q^15 + 25 * q^17 + 30 * q^19 - 168 * q^23 - 20 * q^25 - 225 * q^27 - 105 * q^29 + 40 * q^31 + 106 * q^33 - 16 * q^37 + 115 * q^39 + 255 * q^41 - 30 * q^45 + 102 * q^47 + 12 * q^49 + 380 * q^51 + 297 * q^53 + 55 * q^55 - 150 * q^57 - 22 * q^59 - 30 * q^61 - 320 * q^63 - 68 * q^67 - 137 * q^69 - 240 * q^71 + 85 * q^73 - 30 * q^75 + 226 * q^77 - 215 * q^79 - 463 * q^81 - 610 * q^83 + 25 * q^85 - 160 * q^89 + 161 * q^91 - 253 * q^93 + 90 * q^95 + 179 * q^97 + 150 * q^99

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$		0			0
$2$		0			0
$3$	−2.30423	−	1.67412i	−0.768078	−	0.558041i	0.133300	−	0.991076i	$-0.457443\pi$
$3$	−2.30423	−	1.67412i	−0.768078	−	0.558041i	−0.901377	+	0.433035i	$0.857443\pi$
$4$		0			0
$5$	0.690983	−	2.12663i	0.138197	−	0.425325i
$5$	0.690983	−	2.12663i	0.138197	−	0.425325i
$6$		0			0
$7$	1.86008	+	2.56018i	0.265725	+	0.365739i	0.920941	−	0.389703i	$-0.127422\pi$
$7$	1.86008	+	2.56018i	0.265725	+	0.365739i	−0.655216	+	0.755442i	$0.727422\pi$
$8$		0			0
$9$	−0.274352	−	0.844368i	−0.0304835	−	0.0938187i
$10$		0			0
$11$	−8.20839	−	7.32272i	−0.746218	−	0.665702i
$11$	−8.20839	−	7.32272i	−0.746218	−	0.665702i
$12$		0			0
$13$	1.09490	−	0.355754i	0.0842230	−	0.0273657i	−0.266602	−	0.963807i	$-0.585901\pi$
$13$	1.09490	−	0.355754i	0.0842230	−	0.0273657i	0.350825	+	0.936441i	$0.385901\pi$
$14$		0			0
$15$	−5.15242	+	3.74345i	−0.343495	+	0.249564i
$16$		0			0
$17$	−16.6628	−	5.41408i	−0.980167	−	0.318475i	−0.225253	−	0.974300i	$-0.572321\pi$
$17$	−16.6628	−	5.41408i	−0.980167	−	0.318475i	−0.754913	+	0.655825i	$0.772321\pi$
$18$		0			0
$19$	−11.7724	+	16.2034i	−0.619602	+	0.852809i	−0.997324	−	0.0731099i	$-0.976708\pi$
$19$	−11.7724	+	16.2034i	−0.619602	+	0.852809i	0.377722	+	0.925919i	$0.376708\pi$
$20$		0			0
$21$		−	9.01324i		−	0.429202i
$22$		0			0
$23$	−36.9406			−1.60611			−0.803056	−	0.595904i	$-0.796794\pi$
$23$	−36.9406			−1.60611			−0.803056	+	0.595904i	$0.796794\pi$
$24$		0			0
$25$	−4.04508	−	2.93893i	−0.161803	−	0.117557i
$26$		0			0
$27$	−8.70265	+	26.7840i	−0.322321	+	0.992001i
$28$		0			0
$29$	−2.94215	−	4.04952i	−0.101453	−	0.139639i	0.755272	−	0.655412i	$-0.227505\pi$
$29$	−2.94215	−	4.04952i	−0.101453	−	0.139639i	−0.856725	+	0.515773i	$0.827505\pi$
$30$		0			0
$31$	−18.8909	−	58.1403i	−0.609385	−	1.87549i	−0.463247	−	0.886229i	$-0.653316\pi$
$31$	−18.8909	−	58.1403i	−0.609385	−	1.87549i	−0.146138	−	0.989264i	$-0.546684\pi$
$32$		0			0
$33$	6.65491	+	30.6151i	0.201664	+	0.927731i
$34$		0			0
$35$	6.72982	−	2.18665i	0.192281	−	0.0624757i
$36$		0			0
$37$	21.0660	−	15.3054i	0.569352	−	0.413658i	−0.265518	−	0.964106i	$-0.585543\pi$
$37$	21.0660	−	15.3054i	0.569352	−	0.413658i	0.834870	+	0.550448i	$0.185543\pi$
$38$		0			0
$39$	−3.11848	−	1.01326i	−0.0799610	−	0.0259809i
$40$		0			0
$41$	35.4220	−	48.7542i	0.863951	−	1.18913i	−0.116662	−	0.993172i	$-0.537219\pi$
$41$	35.4220	−	48.7542i	0.863951	−	1.18913i	0.980613	−	0.195955i	$-0.0627807\pi$
$42$		0			0
$43$			65.3933i			1.52077i	0.649470	+	0.760387i	$0.274991\pi$
$43$			65.3933i			1.52077i	−0.649470	+	0.760387i	$0.725009\pi$
$44$		0			0
$45$	−1.98523			−0.0441162
$46$		0			0
$47$	21.5844	+	15.6820i	0.459242	+	0.333659i	0.793234	−	0.608917i	$-0.208396\pi$
$47$	21.5844	+	15.6820i	0.459242	+	0.333659i	−0.333992	+	0.942576i	$0.608396\pi$
$48$		0			0
$49$	12.0472	−	37.0775i	0.245862	−	0.756684i
$50$		0			0
$51$	29.3312	+	40.3709i	0.575122	+	0.791587i
$52$		0			0
$53$	0.957854	+	2.94797i	0.0180727	+	0.0556221i	0.959686	−	0.281074i	$-0.0906906\pi$
$53$	0.957854	+	2.94797i	0.0180727	+	0.0556221i	−0.941613	+	0.336696i	$0.890691\pi$
$54$		0			0
$55$	−21.2446	+	12.3963i	−0.386265	+	0.225388i
$56$		0			0
$57$	54.2529	−	17.6278i	0.951805	−	0.309260i
$58$		0			0
$59$	7.53304	−	5.47308i	0.127679	−	0.0927640i	−0.522113	−	0.852876i	$-0.674856\pi$
$59$	7.53304	−	5.47308i	0.127679	−	0.0927640i	0.649792	+	0.760112i	$0.274856\pi$
$60$		0			0
$61$	32.2647	+	10.4834i	0.528929	+	0.171860i	0.561294	−	0.827617i	$-0.310304\pi$
$61$	32.2647	+	10.4834i	0.528929	+	0.171860i	−0.0323646	+	0.999476i	$0.510304\pi$
$62$		0			0
$63$	1.65142	−	2.27298i	0.0262129	−	0.0360790i
$64$		0			0
$65$		−	2.57426i		−	0.0396040i
$66$		0			0
$67$	−17.1176			−0.255487			−0.127743	−	0.991807i	$-0.540773\pi$
$67$	−17.1176			−0.255487			−0.127743	+	0.991807i	$0.540773\pi$
$68$		0			0
$69$	85.1197	+	61.8431i	1.23362	+	0.896276i
$70$		0			0
$71$	15.6778	−	48.2514i	0.220814	−	0.679597i	−0.777875	−	0.628419i	$-0.783702\pi$
$71$	15.6778	−	48.2514i	0.220814	−	0.679597i	0.998690	−	0.0511781i	$-0.0162976\pi$
$72$		0			0
$73$	24.2807	+	33.4195i	0.332612	+	0.457801i	0.942265	−	0.334867i	$-0.108691\pi$
$73$	24.2807	+	33.4195i	0.332612	+	0.457801i	−0.609653	+	0.792668i	$0.708691\pi$
$74$		0			0
$75$	4.40069	+	13.5439i	0.0586759	+	0.180586i
$76$		0			0
$77$	3.47921	−	34.6358i	0.0451846	−	0.449815i
$78$		0			0
$79$	40.1596	−	13.0486i	0.508349	−	0.165173i	−0.0436020	−	0.999049i	$-0.513883\pi$
$79$	40.1596	−	13.0486i	0.508349	−	0.165173i	0.551951	+	0.833876i	$0.313883\pi$
$80$		0			0
$81$	58.4283	−	42.4507i	0.721337	−	0.524082i
$82$		0			0
$83$	−76.7768	−	24.9463i	−0.925022	−	0.300558i	−0.192497	−	0.981298i	$-0.561658\pi$
$83$	−76.7768	−	24.9463i	−0.925022	−	0.300558i	−0.732525	+	0.680740i	$0.761658\pi$
$84$		0			0
$85$	−23.0275	+	31.6946i	−0.270911	+	0.372878i
$86$		0			0
$87$			14.2565i			0.163868i
$88$		0			0
$89$	−109.359			−1.22875			−0.614377	−	0.789013i	$-0.710592\pi$
$89$	−109.359			−1.22875			−0.614377	+	0.789013i	$0.710592\pi$
$90$		0			0
$91$	2.94739	+	2.14140i	0.0323889	+	0.0235319i
$92$		0			0
$93$	−53.8049	+	165.595i	−0.578548	+	1.78059i
$94$		0			0
$95$	26.3240	+	36.2319i	0.277095	+	0.381388i
$96$		0			0
$97$	−6.19215	−	19.0575i	−0.0638366	−	0.196469i	0.914051	−	0.405599i	$-0.132937\pi$
$97$	−6.19215	−	19.0575i	−0.0638366	−	0.196469i	−0.977888	+	0.209130i	$0.932937\pi$
$98$		0			0
$99$	−3.93109	+	8.93991i	−0.0397079	+	0.0903021i
$100$		0			0
$101$	84.5534	−	27.4731i	0.837163	−	0.272011i	0.141103	−	0.989995i	$-0.454935\pi$
$101$	84.5534	−	27.4731i	0.837163	−	0.272011i	0.696059	+	0.717984i	$0.254935\pi$
$102$		0			0
$103$	−10.0547	+	7.30520i	−0.0976189	+	0.0709243i	−0.635524	−	0.772081i	$-0.719216\pi$
$103$	−10.0547	+	7.30520i	−0.0976189	+	0.0709243i	0.537905	+	0.843005i	$0.319216\pi$
$104$		0			0
$105$	−19.1678	−	6.22800i	−0.182550	−	0.0593142i
$106$		0			0
$107$	121.648	−	167.434i	1.13690	−	1.56481i	0.362648	−	0.931926i	$-0.381873\pi$
$107$	121.648	−	167.434i	1.13690	−	1.56481i	0.774250	−	0.632879i	$-0.218127\pi$
$108$		0			0
$109$		−	36.8795i		−	0.338344i	−0.985587	−	0.169172i	$-0.945891\pi$
$109$		−	36.8795i		−	0.338344i	0.985587	−	0.169172i	$-0.0541093\pi$
$110$		0			0
$111$	−74.1641			−0.668145
$112$		0			0
$113$	77.4778	+	56.2909i	0.685644	+	0.498150i	0.875225	−	0.483715i	$-0.160713\pi$
$113$	77.4778	+	56.2909i	0.685644	+	0.498150i	−0.189581	+	0.981865i	$0.560713\pi$
$114$		0			0
$115$	−25.5253	+	78.5588i	−0.221959	+	0.683120i
$116$		0			0
$117$	−0.600775	−	0.826896i	−0.00513483	−	0.00706749i
$118$		0			0
$119$	−17.1331	−	52.7304i	−0.143976	−	0.443112i
$120$		0			0
$121$	13.7555	+	120.216i	0.113682	+	0.993517i
$122$		0			0
$123$	−163.241	+	53.0402i	−1.32716	+	0.431221i
$124$		0			0
$125$	−9.04508	+	6.57164i	−0.0723607	+	0.0525731i
$126$		0			0
$127$	−135.861	−	44.1439i	−1.06977	−	0.347590i	−0.279373	−	0.960183i	$-0.590127\pi$
$127$	−135.861	−	44.1439i	−1.06977	−	0.347590i	−0.790399	+	0.612592i	$0.790127\pi$
$128$		0			0
$129$	109.476	−	150.681i	0.848654	−	1.16807i
$130$		0			0
$131$		−	53.7502i		−	0.410307i	−0.978730	−	0.205153i	$-0.934231\pi$
$131$		−	53.7502i		−	0.410307i	0.978730	−	0.205153i	$-0.0657693\pi$
$132$		0			0
$133$	−63.3811			−0.476550
$134$		0			0
$135$	50.9462	+	37.0146i	0.377379	+	0.274182i
$136$		0			0
$137$	65.5510	−	201.745i	0.478474	−	1.47259i	−0.362740	−	0.931890i	$-0.618159\pi$
$137$	65.5510	−	201.745i	0.478474	−	1.47259i	0.841214	−	0.540702i	$-0.181841\pi$
$138$		0			0
$139$	85.0507	+	117.062i	0.611876	+	0.842175i	0.996730	−	0.0808026i	$-0.0257483\pi$
$139$	85.0507	+	117.062i	0.611876	+	0.842175i	−0.384854	+	0.922977i	$0.625748\pi$
$140$		0			0
$141$	−23.4819	−	72.2699i	−0.166538	−	0.512552i
$142$		0			0
$143$	−11.5925	−	5.09747i	−0.0810661	−	0.0356467i
$144$		0			0
$145$	−10.6448	+	3.45870i	−0.0734123	+	0.0238531i
$146$		0			0
$147$	−89.8319	+	65.2667i	−0.611102	+	0.443991i
$148$		0			0
$149$	−195.225	−	63.4325i	−1.31024	−	0.425721i	−0.431105	−	0.902302i	$-0.641876\pi$
$149$	−195.225	−	63.4325i	−1.31024	−	0.425721i	−0.879131	+	0.476580i	$0.841876\pi$
$150$		0			0
$151$	66.5847	−	91.6459i	0.440958	−	0.606927i	−0.529467	−	0.848331i	$-0.677608\pi$
$151$	66.5847	−	91.6459i	0.440958	−	0.606927i	0.970425	+	0.241404i	$0.0776079\pi$
$152$		0			0
$153$			15.5549i			0.101666i
$154$		0			0
$155$	−136.696			−0.881910
$156$		0			0
$157$	22.8280	+	16.5855i	0.145401	+	0.105640i	0.658108	−	0.752924i	$-0.271357\pi$
$157$	22.8280	+	16.5855i	0.145401	+	0.105640i	−0.512707	+	0.858564i	$0.671357\pi$
$158$		0			0
$159$	2.72815	−	8.39638i	0.0171582	−	0.0528074i
$160$		0			0
$161$	−68.7123	−	94.5743i	−0.426784	−	0.587418i
$162$		0			0
$163$	−4.76360	−	14.6609i	−0.0292245	−	0.0899439i	0.935380	−	0.353643i	$-0.115057\pi$
$163$	−4.76360	−	14.6609i	−0.0292245	−	0.0899439i	−0.964605	+	0.263699i	$0.915057\pi$
$164$		0			0
$165$	69.7054	+	7.00201i	0.422457	+	0.0424364i
$166$		0			0
$167$	−144.953	+	47.0982i	−0.867984	+	0.282025i	−0.708959	−	0.705250i	$-0.750835\pi$
$167$	−144.953	+	47.0982i	−0.867984	+	0.282025i	−0.159025	+	0.987275i	$0.550835\pi$
$168$		0			0
$169$	−135.652	+	98.5567i	−0.802672	+	0.583176i
$170$		0			0
$171$	16.9114	+	5.49485i	0.0988971	+	0.0321336i
$172$		0			0
$173$	−22.1018	+	30.4205i	−0.127756	+	0.175841i	−0.868103	−	0.496384i	$-0.834661\pi$
$173$	−22.1018	+	30.4205i	−0.127756	+	0.175841i	0.740347	+	0.672224i	$0.234661\pi$
$174$		0			0
$175$		−	15.8228i		−	0.0904158i
$176$		0			0
$177$	−26.5205			−0.149833
$178$		0			0
$179$	−61.0790	−	44.3765i	−0.341223	−	0.247913i	0.403954	−	0.914779i	$-0.367635\pi$
$179$	−61.0790	−	44.3765i	−0.341223	−	0.247913i	−0.745178	+	0.666866i	$0.767635\pi$
$180$		0			0
$181$	−84.7110	+	260.714i	−0.468017	+	1.44041i	0.387132	+	0.922024i	$0.373466\pi$
$181$	−84.7110	+	260.714i	−0.468017	+	1.44041i	−0.855149	+	0.518383i	$0.826534\pi$
$182$		0			0
$183$	−56.7948	−	78.1713i	−0.310354	−	0.427166i
$184$		0			0
$185$	−17.9925	−	55.3753i	−0.0972569	−	0.299326i
$186$		0			0
$187$	97.1293	+	166.458i	0.519408	+	0.890151i
$188$		0			0
$189$	−84.7594	+	27.5400i	−0.448462	+	0.145714i
$190$		0			0
$191$	−15.7612	+	11.4512i	−0.0825195	+	0.0599539i	−0.628280	−	0.777987i	$-0.716241\pi$
$191$	−15.7612	+	11.4512i	−0.0825195	+	0.0599539i	0.545761	+	0.837941i	$0.316241\pi$
$192$		0			0
$193$	−114.271	−	37.1289i	−0.592077	−	0.192378i	−0.00237359	−	0.999997i	$-0.500756\pi$
$193$	−114.271	−	37.1289i	−0.592077	−	0.192378i	−0.589704	+	0.807620i	$0.700756\pi$
$194$		0			0
$195$	−4.30963	+	5.93170i	−0.0221007	+	0.0304190i
$196$		0			0
$197$		−	47.0754i		−	0.238962i	−0.992837	−	0.119481i	$-0.961877\pi$
$197$		−	47.0754i		−	0.238962i	0.992837	−	0.119481i	$-0.0381230\pi$
$198$		0			0
$199$	−17.6716			−0.0888022			−0.0444011	−	0.999014i	$-0.514138\pi$
$199$	−17.6716			−0.0888022			−0.0444011	+	0.999014i	$0.514138\pi$
$200$		0			0
$201$	39.4430	+	28.6570i	0.196234	+	0.142572i
$202$		0			0
$203$	4.89486	−	15.0648i	0.0241126	−	0.0742110i
$204$		0			0
$205$	−79.2060	−	109.018i	−0.386371	−	0.531794i
$206$		0			0
$207$	10.1347	+	31.1914i	0.0489600	+	0.150683i
$208$		0			0
$209$	215.286	−	46.7974i	1.03007	−	0.223911i
$210$		0			0
$211$	95.0482	−	30.8830i	0.450465	−	0.146365i	−0.0749935	−	0.997184i	$-0.523894\pi$
$211$	95.0482	−	30.8830i	0.450465	−	0.146365i	0.525459	+	0.850819i	$0.323894\pi$
$212$		0			0
$213$	−116.904	+	84.9358i	−0.548846	+	0.398760i
$214$		0			0
$215$	139.067	+	45.1856i	0.646824	+	0.210166i
$216$		0			0
$217$	113.711	−	156.510i	0.524013	−	0.721242i
$218$		0			0
$219$		−	117.655i		−	0.537238i
$220$		0			0
$221$	−20.1702			−0.0912679
$222$		0			0
$223$	192.574	+	139.913i	0.863562	+	0.627414i	0.928852	−	0.370452i	$-0.120797\pi$
$223$	192.574	+	139.913i	0.863562	+	0.627414i	−0.0652897	+	0.997866i	$0.520797\pi$
$224$		0			0
$225$	−1.37176	+	4.22184i	−0.00609671	+	0.0187637i
$226$		0			0
$227$	215.446	+	296.536i	0.949100	+	1.30632i	0.951926	+	0.306328i	$0.0991005\pi$
$227$	215.446	+	296.536i	0.949100	+	1.30632i	−0.00282596	+	0.999996i	$0.500900\pi$
$228$		0			0
$229$	81.1310	+	249.696i	0.354284	+	1.09037i	0.956424	+	0.291983i	$0.0943150\pi$
$229$	81.1310	+	249.696i	0.354284	+	1.09037i	−0.602140	+	0.798391i	$0.705685\pi$
$230$		0			0
$231$	−66.0014	+	73.9842i	−0.285721	+	0.320278i
$232$		0			0
$233$	357.456	−	116.145i	1.53415	−	0.498474i	0.584392	−	0.811471i	$-0.301333\pi$
$233$	357.456	−	116.145i	1.53415	−	0.498474i	0.949754	+	0.312997i	$0.101333\pi$
$234$		0			0
$235$	48.2642	−	35.0660i	0.205379	−	0.149217i
$236$		0			0
$237$	−114.382	−	37.1650i	−0.482625	−	0.156814i
$238$		0			0
$239$	176.904	−	243.488i	0.740185	−	1.01878i	−0.258423	−	0.966032i	$-0.583203\pi$
$239$	176.904	−	243.488i	0.740185	−	1.01878i	0.998608	−	0.0527452i	$-0.0167971\pi$
$240$		0			0
$241$		−	478.069i		−	1.98369i	−0.127452	−	0.991845i	$-0.540680\pi$
$241$		−	478.069i		−	1.98369i	0.127452	−	0.991845i	$-0.459320\pi$
$242$		0			0
$243$	47.7613			0.196549
$244$		0			0
$245$	−70.5256	−	51.2399i	−0.287860	−	0.209142i
$246$		0			0
$247$	−7.12522	+	21.9292i	−0.0288470	+	0.0887820i
$248$		0			0
$249$	135.149	+	186.016i	0.542765	+	0.747052i
$250$		0			0
$251$	−127.332	−	391.886i	−0.507297	−	1.56130i	−0.796875	−	0.604145i	$-0.793515\pi$
$251$	−127.332	−	391.886i	−0.507297	−	1.56130i	0.289578	−	0.957155i	$-0.406485\pi$
$252$		0			0
$253$	303.223	+	270.505i	1.19851	+	1.06919i
$254$		0			0
$255$	106.121	−	34.4809i	0.416162	−	0.135219i
$256$		0			0
$257$	−242.316	+	176.053i	−0.942864	+	0.685030i	−0.949108	−	0.314950i	$-0.898012\pi$
$257$	−242.316	+	176.053i	−0.942864	+	0.685030i	0.00624471	+	0.999981i	$0.498012\pi$
$258$		0			0
$259$	78.3688	+	25.4636i	0.302582	+	0.0983149i
$260$		0			0
$261$	−2.61210	+	3.59525i	−0.0100080	+	0.0137749i
$262$		0			0
$263$		−	283.233i		−	1.07693i	−0.842648	−	0.538465i	$-0.819004\pi$
$263$		−	283.233i		−	1.07693i	0.842648	−	0.538465i	$-0.180996\pi$
$264$		0			0
$265$	6.93109			0.0261551
$266$		0			0
$267$	251.989	+	183.081i	0.943778	+	0.685695i
$268$		0			0
$269$	−121.482	+	373.884i	−0.451607	+	1.38990i	0.423466	+	0.905912i	$0.360813\pi$
$269$	−121.482	+	373.884i	−0.451607	+	1.38990i	−0.875073	+	0.483991i	$0.839187\pi$
$270$		0			0
$271$	317.094	+	436.443i	1.17009	+	1.61049i	0.663075	+	0.748553i	$0.269251\pi$
$271$	317.094	+	436.443i	1.17009	+	1.61049i	0.507015	+	0.861937i	$0.330749\pi$
$272$		0			0
$273$	−3.20650	−	9.86859i	−0.0117454	−	0.0361487i
$274$		0			0
$275$	11.6827	+	53.7449i	0.0424826	+	0.195436i
$276$		0			0
$277$	−265.763	+	86.3517i	−0.959434	+	0.311739i	−0.746543	−	0.665337i	$-0.768288\pi$
$277$	−265.763	+	86.3517i	−0.959434	+	0.311739i	−0.212891	+	0.977076i	$0.568288\pi$
$278$		0			0
$279$	−43.9091	+	31.9018i	−0.157380	+	0.114343i
$280$		0			0
$281$	260.944	+	84.7859i	0.928627	+	0.301729i	0.734001	−	0.679148i	$-0.237651\pi$
$281$	260.944	+	84.7859i	0.928627	+	0.301729i	0.194626	+	0.980878i	$0.437651\pi$
$282$		0			0
$283$	307.491	−	423.225i	1.08654	−	1.49549i	0.234428	−	0.972133i	$-0.424678\pi$
$283$	307.491	−	423.225i	1.08654	−	1.49549i	0.852111	−	0.523360i	$-0.175322\pi$
$284$		0			0
$285$		−	127.556i		−	0.447566i
$286$		0			0
$287$	190.707			0.664484
$288$		0			0
$289$	14.5318	+	10.5579i	0.0502829	+	0.0365327i
$290$		0			0
$291$	−17.6364	+	54.2793i	−0.0606063	+	0.186527i
$292$		0			0
$293$	−237.293	−	326.605i	−0.809873	−	1.11469i	−0.991343	−	0.131298i	$-0.958086\pi$
$293$	−237.293	−	326.605i	−0.809873	−	1.11469i	0.181470	−	0.983396i	$-0.441914\pi$
$294$		0			0
$295$	−6.43399	−	19.8018i	−0.0218101	−	0.0671247i
$296$		0			0
$297$	267.567	−	156.127i	0.900898	−	0.525679i
$298$		0			0
$299$	−40.4462	+	13.1418i	−0.135272	+	0.0439524i
$300$		0			0
$301$	−167.418	+	121.637i	−0.556207	+	0.404108i
$302$		0			0
$303$	−240.824	−	78.2485i	−0.794799	−	0.258246i
$304$		0			0
$305$	44.5887	−	61.3711i	0.146192	−	0.201217i
$306$		0			0
$307$			290.845i			0.947378i	0.880692	+	0.473689i	$0.157078\pi$
$307$			290.845i			0.947378i	−0.880692	+	0.473689i	$0.842922\pi$
$308$		0			0
$309$	35.3983			0.114558
$310$		0			0
$311$	−43.2763	−	31.4421i	−0.139152	−	0.101100i	0.516031	−	0.856570i	$-0.327409\pi$
$311$	−43.2763	−	31.4421i	−0.139152	−	0.101100i	−0.655184	+	0.755470i	$0.727409\pi$
$312$		0			0
$313$	−63.2316	+	194.607i	−0.202018	+	0.621747i	0.797805	+	0.602916i	$0.205995\pi$
$313$	−63.2316	+	194.607i	−0.202018	+	0.621747i	−0.999823	+	0.0188313i	$0.994005\pi$
$314$		0			0
$315$	−3.69268	−	5.08253i	−0.0117228	−	0.0161350i
$316$		0			0
$317$	63.8642	+	196.554i	0.201464	+	0.620043i	0.999840	+	0.0178837i	$0.00569287\pi$
$317$	63.8642	+	196.554i	0.201464	+	0.620043i	−0.798376	+	0.602159i	$0.794307\pi$
$318$		0			0
$319$	−5.50319	+	54.7846i	−0.0172514	+	0.171738i
$320$		0			0
$321$	−560.611	+	182.154i	−1.74645	+	0.567457i
$322$		0			0
$323$	283.889	−	206.257i	0.878912	−	0.638567i
$324$		0			0
$325$	−5.47450	−	1.77877i	−0.0168446	−	0.00547314i
$326$		0			0
$327$	−61.7408	+	84.9789i	−0.188810	+	0.259874i
$328$		0			0
$329$			84.4295i			0.256625i
$330$		0			0
$331$	−311.605			−0.941405			−0.470702	−	0.882292i	$-0.655999\pi$
$331$	−311.605			−0.941405			−0.470702	+	0.882292i	$0.655999\pi$
$332$		0			0
$333$	−18.7029	−	13.5884i	−0.0561647	−	0.0408061i
$334$		0			0
$335$	−11.8280	+	36.4028i	−0.0353074	+	0.108665i
$336$		0			0
$337$	−288.729	−	397.401i	−0.856762	−	1.17923i	−0.982332	−	0.187147i	$-0.940076\pi$
$337$	−288.729	−	397.401i	−0.856762	−	1.17923i	0.125570	−	0.992085i	$-0.459924\pi$
$338$		0			0
$339$	−84.2889	−	259.415i	−0.248640	−	0.765235i
$340$		0			0
$341$	−270.681	+	615.572i	−0.793786	+	1.80520i
$342$		0			0
$343$	264.807	−	86.0411i	0.772033	−	0.250849i
$344$		0			0
$345$	190.333	−	138.285i	0.551691	−	0.400827i
$346$		0			0
$347$	−278.834	−	90.5985i	−0.803555	−	0.261091i	−0.121689	−	0.992568i	$-0.538831\pi$
$347$	−278.834	−	90.5985i	−0.803555	−	0.261091i	−0.681866	+	0.731477i	$0.738831\pi$
$348$		0			0
$349$	−207.438	+	285.514i	−0.594379	+	0.818093i	−0.995179	−	0.0980726i	$-0.968732\pi$
$349$	−207.438	+	285.514i	−0.594379	+	0.818093i	0.400800	+	0.916166i	$0.368732\pi$
$350$		0			0
$351$			32.4218i			0.0923698i
$352$		0			0
$353$	−203.115			−0.575397			−0.287698	−	0.957721i	$-0.592890\pi$
$353$	−203.115			−0.575397			−0.287698	+	0.957721i	$0.592890\pi$
$354$		0			0
$355$	−91.7796	−	66.6818i	−0.258534	−	0.187836i
$356$		0			0
$357$	−48.7984	+	150.186i	−0.136690	+	0.420689i
$358$		0			0
$359$	−242.797	−	334.182i	−0.676316	−	0.930869i	0.323567	−	0.946205i	$-0.395118\pi$
$359$	−242.797	−	334.182i	−0.676316	−	0.930869i	−0.999882	+	0.0153365i	$0.995118\pi$
$360$		0			0
$361$	−12.4039	−	38.1752i	−0.0343598	−	0.105749i
$362$		0			0
$363$	169.560	−	300.033i	0.467107	−	0.826537i
$364$		0			0
$365$	87.8483	−	28.5437i	0.240680	−	0.0782018i
$366$		0			0
$367$	−169.213	+	122.940i	−0.461070	+	0.334987i	−0.793951	−	0.607982i	$-0.791979\pi$
$367$	−169.213	+	122.940i	−0.461070	+	0.334987i	0.332881	+	0.942969i	$0.391979\pi$
$368$		0			0
$369$	−50.8846	−	16.5334i	−0.137899	−	0.0448060i
$370$		0			0
$371$	−5.76564	+	7.93572i	−0.0155408	+	0.0213901i
$372$		0			0
$373$		−	475.071i		−	1.27365i	−0.771009	−	0.636825i	$-0.780248\pi$
$373$		−	475.071i		−	1.27365i	0.771009	−	0.636825i	$-0.219752\pi$
$374$		0			0
$375$	31.8437			0.0849166
$376$		0			0
$377$	−4.66199	−	3.38713i	−0.0123660	−	0.00898444i
$378$		0			0
$379$	208.324	−	641.156i	0.549669	−	1.69171i	−0.159955	−	0.987124i	$-0.551135\pi$
$379$	208.324	−	641.156i	0.549669	−	1.69171i	0.709623	−	0.704581i	$-0.248865\pi$
$380$		0			0
$381$	239.153	+	329.166i	0.627699	+	0.863953i
$382$		0			0
$383$	−0.805937	−	2.48042i	−0.00210428	−	0.00647629i	0.949999	−	0.312253i	$-0.101084\pi$
$383$	−0.805937	−	2.48042i	−0.00210428	−	0.00647629i	−0.952103	+	0.305777i	$0.901084\pi$
$384$		0			0
$385$	−71.2533	−	31.3317i	−0.185073	−	0.0813811i
$386$		0			0
$387$	55.2160	−	17.9408i	0.142677	−	0.0463586i
$388$		0			0
$389$	−106.666	+	77.4972i	−0.274205	+	0.199221i	−0.716386	−	0.697704i	$-0.754205\pi$
$389$	−106.666	+	77.4972i	−0.274205	+	0.199221i	0.442181	+	0.896926i	$0.354205\pi$
$390$		0			0
$391$	615.534	+	199.999i	1.57426	+	0.511507i
$392$		0			0
$393$	−89.9845	+	123.853i	−0.228968	+	0.315148i
$394$		0			0
$395$		−	94.4209i		−	0.239040i
$396$		0			0
$397$	−313.373			−0.789352			−0.394676	−	0.918820i	$-0.629143\pi$
$397$	−313.373			−0.789352			−0.394676	+	0.918820i	$0.629143\pi$
$398$		0			0
$399$	146.045	+	106.108i	0.366027	+	0.265934i
$400$		0			0
$401$	−31.1430	+	95.8482i	−0.0776632	+	0.239023i	−0.982349	−	0.187056i	$-0.940105\pi$
$401$	−31.1430	+	95.8482i	−0.0776632	+	0.239023i	0.904686	+	0.426079i	$0.140105\pi$
$402$		0			0
$403$	−41.3673	−	56.9372i	−0.102648	−	0.141283i
$404$		0			0
$405$	−49.9037	−	153.588i	−0.123219	−	0.379229i
$406$		0			0
$407$	−284.995	−	28.6282i	−0.700234	−	0.0703395i
$408$		0			0
$409$	−111.586	+	36.2566i	−0.272827	+	0.0886469i	−0.442235	−	0.896899i	$-0.645814\pi$
$409$	−111.586	+	36.2566i	−0.272827	+	0.0886469i	0.169408	+	0.985546i	$0.445814\pi$
$410$		0			0
$411$	−488.791	+	355.127i	−1.18927	+	0.864057i
$412$		0			0
$413$	28.0241	+	9.10557i	0.0678549	+	0.0220474i
$414$		0			0
$415$	−106.103	+	146.038i	−0.255670	+	0.351899i
$416$		0			0
$417$		−	412.124i		−	0.988307i
$418$		0			0
$419$	−256.275			−0.611636			−0.305818	−	0.952090i	$-0.598930\pi$
$419$	−256.275			−0.611636			−0.305818	+	0.952090i	$0.598930\pi$
$420$		0			0
$421$	−435.803	−	316.630i	−1.03516	−	0.752089i	−0.0658267	−	0.997831i	$-0.520968\pi$
$421$	−435.803	−	316.630i	−1.03516	−	0.752089i	−0.969335	+	0.245742i	$0.920968\pi$
$422$		0			0
$423$	7.31965	−	22.5276i	0.0173041	−	0.0532566i
$424$		0			0
$425$	51.4910	+	70.8713i	0.121155	+	0.166756i
$426$		0			0
$427$	33.1754	+	102.103i	0.0776940	+	0.239118i
$428$		0			0
$429$	18.1779	+	31.1530i	0.0423728	+	0.0726176i
$430$		0			0
$431$	132.761	−	43.1365i	0.308029	−	0.100085i	−0.150923	−	0.988545i	$-0.548225\pi$
$431$	132.761	−	43.1365i	0.308029	−	0.100085i	0.458953	+	0.888461i	$0.348225\pi$
$432$		0			0
$433$	503.770	−	366.010i	1.16344	−	0.845289i	0.173232	−	0.984881i	$-0.444579\pi$
$433$	503.770	−	366.010i	1.16344	−	0.845289i	0.990209	+	0.139592i	$0.0445790\pi$
$434$		0			0
$435$	30.3184	+	9.85103i	0.0696974	+	0.0226461i
$436$		0			0
$437$	434.881	−	598.562i	0.995150	−	1.36971i
$438$		0			0
$439$			314.896i			0.717303i	0.933471	+	0.358652i	$0.116763\pi$
$439$			314.896i			0.717303i	−0.933471	+	0.358652i	$0.883237\pi$
$440$		0			0
$441$	−34.6123			−0.0784858
$442$		0			0
$443$	170.663	+	123.994i	0.385244	+	0.279896i	0.763504	−	0.645803i	$-0.223477\pi$
$443$	170.663	+	123.994i	0.385244	+	0.279896i	−0.378260	+	0.925700i	$0.623477\pi$
$444$		0			0
$445$	−75.5653	+	232.566i	−0.169810	+	0.522620i
$446$		0			0
$447$	343.650	+	472.994i	0.768793	+	1.05815i
$448$		0			0
$449$	60.2833	+	185.533i	0.134261	+	0.413214i	0.995474	−	0.0950304i	$-0.0302948\pi$
$449$	60.2833	+	185.533i	0.134261	+	0.413214i	−0.861213	+	0.508244i	$0.830295\pi$
$450$		0			0
$451$	−647.771	+	140.808i	−1.43630	+	0.312213i
$452$		0			0
$453$	−306.853	+	99.7027i	−0.677380	+	0.220094i
$454$		0			0
$455$	6.59056	−	4.78833i	0.0144848	−	0.0105238i
$456$		0			0
$457$	−526.185	−	170.968i	−1.15139	−	0.374109i	−0.329723	−	0.944078i	$-0.606955\pi$
$457$	−526.185	−	170.968i	−1.15139	−	0.374109i	−0.821667	+	0.569968i	$0.806955\pi$
$458$		0			0
$459$	290.022	−	399.181i	0.631856	−	0.869675i
$460$		0			0
$461$			632.590i			1.37221i	0.727501	+	0.686106i	$0.240681\pi$
$461$			632.590i			1.37221i	−0.727501	+	0.686106i	$0.759319\pi$
$462$		0			0
$463$	−322.161			−0.695812			−0.347906	−	0.937529i	$-0.613107\pi$
$463$	−322.161			−0.695812			−0.347906	+	0.937529i	$0.613107\pi$
$464$		0			0
$465$	314.980	+	228.846i	0.677375	+	0.492142i
$466$		0			0
$467$	61.5516	−	189.436i	0.131802	−	0.405645i	−0.863277	−	0.504731i	$-0.831592\pi$
$467$	61.5516	−	189.436i	0.131802	−	0.405645i	0.995079	+	0.0990856i	$0.0315918\pi$
$468$		0			0
$469$	−31.8401	−	43.8241i	−0.0678893	−	0.0934416i
$470$		0			0
$471$	−24.8348	−	76.4337i	−0.0527278	−	0.162280i
$472$		0			0
$473$	478.857	−	536.774i	1.01238	−	1.13483i
$474$		0			0
$475$	95.2411	−	30.9457i	0.200507	−	0.0651488i
$476$		0			0
$477$	2.22638	−	1.61756i	0.00466747	−	0.00339112i
$478$		0			0
$479$	−880.533	−	286.102i	−1.83827	−	0.597291i	−0.998524	−	0.0543170i	$-0.982702\pi$
$479$	−880.533	−	286.102i	−1.83827	−	0.597291i	−0.839749	−	0.542974i	$-0.817298\pi$
$480$		0			0
$481$	17.6202	−	24.2521i	0.0366325	−	0.0504203i
$482$		0			0
$483$			332.954i			0.689346i
$484$		0			0
$485$	−44.8068			−0.0923852
$486$		0			0
$487$	−382.122	−	277.628i	−0.784645	−	0.570078i	0.121725	−	0.992564i	$-0.461158\pi$
$487$	−382.122	−	277.628i	−0.784645	−	0.570078i	−0.906369	+	0.422486i	$0.861158\pi$
$488$		0			0
$489$	−13.5676	+	41.7569i	−0.0277457	+	0.0853924i
$490$		0			0
$491$	146.241	+	201.283i	0.297842	+	0.409945i	0.931542	−	0.363635i	$-0.118464\pi$
$491$	146.241	+	201.283i	0.297842	+	0.409945i	−0.633699	+	0.773580i	$0.718464\pi$
$492$		0			0
$493$	27.1001	+	83.4054i	0.0549697	+	0.169179i
$494$		0			0
$495$	16.2955	+	14.5373i	0.0329203	+	0.0293682i
$496$		0			0
$497$	152.694	−	49.6133i	0.307231	−	0.0998255i
$498$		0			0
$499$	139.811	−	101.579i	0.280183	−	0.203565i	−0.438814	−	0.898578i	$-0.644601\pi$
$499$	139.811	−	101.579i	0.280183	−	0.203565i	0.718997	+	0.695013i	$0.244601\pi$
$500$		0			0
$501$	412.854	+	134.145i	0.824061	+	0.267754i
$502$		0			0
$503$	−457.031	+	629.050i	−0.908611	+	1.25060i	0.0590276	+	0.998256i	$0.481200\pi$
$503$	−457.031	+	629.050i	−0.908611	+	1.25060i	−0.967639	+	0.252340i	$0.918800\pi$
$504$		0			0
$505$		−	198.797i		−	0.393658i
$506$		0			0
$507$	477.569			0.941951
$508$		0			0
$509$	412.058	+	299.378i	0.809544	+	0.588168i	0.913698	−	0.406393i	$-0.133214\pi$
$509$	412.058	+	299.378i	0.809544	+	0.588168i	−0.104154	+	0.994561i	$0.533214\pi$
$510$		0			0
$511$	−40.3958	+	124.326i	−0.0790525	+	0.243299i
$512$		0			0
$513$	−331.540	−	456.326i	−0.646277	−	0.889524i
$514$		0			0
$515$	8.58778	+	26.4305i	0.0166753	+	0.0513213i
$516$		0			0
$517$	−62.3384	−	286.780i	−0.120577	−	0.554701i
$518$		0			0
$519$	101.855	−	33.0948i	0.196253	−	0.0637664i
$520$		0			0
$521$	92.1924	−	66.9817i	0.176953	−	0.128564i	−0.495783	−	0.868446i	$-0.665119\pi$
$521$	92.1924	−	66.9817i	0.176953	−	0.128564i	0.672736	+	0.739883i	$0.265119\pi$
$522$		0			0
$523$	69.7725	+	22.6705i	0.133408	+	0.0433470i	0.374960	−	0.927041i	$-0.377656\pi$
$523$	69.7725	+	22.6705i	0.133408	+	0.0433470i	−0.241552	+	0.970388i	$0.577656\pi$
$524$		0			0
$525$	−26.4892	+	36.4593i	−0.0504557	+	0.0694463i
$526$		0			0
$527$			1071.06i			2.03237i
$528$		0			0
$529$	835.605			1.57959
$530$		0			0
$531$	−6.68800	−	4.85911i	−0.0125951	−	0.00915087i
$532$		0			0
$533$	21.4390	−	65.9825i	0.0402233	−	0.123794i
$534$		0			0
$535$	−272.013	−	374.394i	−0.508436	−	0.699802i
$536$		0			0
$537$	66.4485	+	204.507i	0.123740	+	0.380833i
$538$		0			0
$539$	−370.397	+	216.128i	−0.687192	+	0.400981i
$540$		0			0
$541$	769.990	−	250.185i	1.42327	−	0.462449i	0.506632	−	0.862163i	$-0.330890\pi$
$541$	769.990	−	250.185i	1.42327	−	0.462449i	0.916640	+	0.399714i	$0.130890\pi$
$542$		0			0
$543$	631.661	−	458.928i	1.16328	−	0.845172i
$544$		0			0
$545$	−78.4289	−	25.4831i	−0.143906	−	0.0467580i
$546$		0			0
$547$	−303.437	+	417.645i	−0.554729	+	0.763519i	−0.990644	−	0.136469i	$-0.956425\pi$
$547$	−303.437	+	417.645i	−0.554729	+	0.763519i	0.435916	+	0.899988i	$0.356425\pi$
$548$		0			0
$549$		−	30.1194i		−	0.0548623i
$550$		0			0
$551$	100.252			0.181946
$552$		0			0
$553$	108.107	+	78.5442i	0.195491	+	0.142033i
$554$		0			0
$555$	−51.2461	+	157.719i	−0.0923353	+	0.284179i
$556$		0			0
$557$	302.973	+	417.006i	0.543937	+	0.748665i	0.989174	−	0.146748i	$-0.0468807\pi$
$557$	302.973	+	417.006i	0.543937	+	0.748665i	−0.445237	+	0.895413i	$0.646881\pi$
$558$		0			0
$559$	23.2639	+	71.5990i	0.0416171	+	0.128084i
$560$		0			0
$561$	54.8631	−	546.165i	0.0977952	−	0.973556i
$562$		0			0
$563$	362.135	−	117.665i	0.643224	−	0.208996i	0.0308001	−	0.999526i	$-0.490194\pi$
$563$	362.135	−	117.665i	0.643224	−	0.208996i	0.612424	+	0.790529i	$0.290194\pi$
$564$		0			0
$565$	173.246	−	125.870i	0.306629	−	0.222779i
$566$		0			0
$567$	217.362	+	70.6253i	0.383355	+	0.124560i
$568$		0			0
$569$	−190.291	+	261.913i	−0.334430	+	0.460304i	−0.942804	−	0.333347i	$-0.891822\pi$
$569$	−190.291	+	261.913i	−0.334430	+	0.460304i	0.608374	+	0.793650i	$0.291822\pi$
$570$		0			0
$571$		−	99.2705i		−	0.173854i	−0.996215	−	0.0869268i	$-0.972295\pi$
$571$		−	99.2705i		−	0.173854i	0.996215	−	0.0869268i	$-0.0277046\pi$
$572$		0			0
$573$	55.4883			0.0968382
$574$		0			0
$575$	149.428	+	108.566i	0.259874	+	0.188810i
$576$		0			0
$577$	298.188	−	917.728i	0.516790	−	1.59052i	−0.263210	−	0.964738i	$-0.584781\pi$
$577$	298.188	−	917.728i	0.516790	−	1.59052i	0.780001	−	0.625779i	$-0.215219\pi$
$578$		0			0
$579$	201.149	+	276.857i	0.347407	+	0.478165i
$580$		0			0
$581$	−78.9439	−	242.964i	−0.135876	−	0.418183i
$582$		0			0
$583$	13.7247	−	31.2122i	0.0235416	−	0.0535372i
$584$		0			0
$585$	−2.17363	+	0.706254i	−0.00371560	+	0.00120727i
$586$		0			0
$587$	190.418	−	138.347i	0.324392	−	0.235684i	−0.413656	−	0.910433i	$-0.635748\pi$
$587$	190.418	−	138.347i	0.324392	−	0.235684i	0.738047	+	0.674749i	$0.235748\pi$
$588$		0			0
$589$	1164.46	+	378.356i	1.97701	+	0.642371i
$590$		0			0
$591$	−78.8101	+	108.473i	−0.133350	+	0.183541i
$592$		0			0
$593$			1004.87i			1.69456i	0.531149	+	0.847279i	$0.321761\pi$
$593$			1004.87i			1.69456i	−0.531149	+	0.847279i	$0.678239\pi$
$594$		0			0
$595$	−123.977			−0.208364
$596$		0			0
$597$	40.7196	+	29.5845i	0.0682070	+	0.0495553i
$598$		0			0
$599$	187.189	−	576.109i	0.312503	−	0.961784i	−0.664268	−	0.747495i	$-0.731257\pi$
$599$	187.189	−	576.109i	0.312503	−	0.961784i	0.976770	−	0.214289i	$-0.0687435\pi$
$600$		0			0
$601$	175.390	+	241.403i	0.291830	+	0.401670i	0.929607	−	0.368551i	$-0.120146\pi$
$601$	175.390	+	241.403i	0.291830	+	0.401670i	−0.637777	+	0.770221i	$0.720146\pi$
$602$		0			0
$603$	4.69625	+	14.4536i	0.00778814	+	0.0239694i
$604$		0			0
$605$	265.159	+	53.8142i	0.438279	+	0.0889490i
$606$		0			0
$607$	−341.758	+	111.044i	−0.563028	+	0.182939i	−0.576683	−	0.816968i	$-0.695653\pi$
$607$	−341.758	+	111.044i	−0.563028	+	0.182939i	0.0136553	+	0.999907i	$0.495653\pi$
$608$		0			0
$609$	−36.4993	+	26.5183i	−0.0599331	+	0.0435440i
$610$		0			0
$611$	29.2117	+	9.49144i	0.0478096	+	0.0155343i
$612$		0			0
$613$	−274.091	+	377.254i	−0.447131	+	0.615422i	−0.971778	−	0.235897i	$-0.924197\pi$
$613$	−274.091	+	377.254i	−0.447131	+	0.615422i	0.524647	+	0.851320i	$0.324197\pi$
$614$		0			0
$615$			383.803i			0.624070i
$616$		0			0
$617$	1068.85			1.73233			0.866166	−	0.499757i	$-0.166577\pi$
$617$	1068.85			1.73233			0.866166	+	0.499757i	$0.166577\pi$
$618$		0			0
$619$	−310.410	−	225.526i	−0.501470	−	0.364339i	0.308108	−	0.951351i	$-0.400304\pi$
$619$	−310.410	−	225.526i	−0.501470	−	0.364339i	−0.809578	+	0.587012i	$0.800304\pi$
$620$		0			0
$621$	321.481	−	989.417i	0.517683	−	1.59326i
$622$		0			0
$623$	−203.416	−	279.978i	−0.326511	−	0.449404i
$624$		0			0
$625$	7.72542	+	23.7764i	0.0123607	+	0.0380423i
$626$		0			0
$627$	−574.413	−	252.583i	−0.916129	−	0.402843i
$628$		0			0
$629$	−433.884	+	140.977i	−0.689800	+	0.224129i
$630$		0			0
$631$	797.244	−	579.232i	1.26346	−	0.917958i	0.264539	−	0.964375i	$-0.414780\pi$
$631$	797.244	−	579.232i	1.26346	−	0.917958i	0.998922	+	0.0464169i	$0.0147803\pi$
$632$		0			0
$633$	−270.715	−	87.9607i	−0.427670	−	0.138958i
$634$		0			0
$635$	−187.755	+	258.423i	−0.295678	+	0.406966i
$636$		0			0
$637$		−	44.8820i		−	0.0704584i
$638$		0			0
$639$	−45.0432			−0.0704901
$640$		0			0
$641$	−503.934	−	366.130i	−0.786169	−	0.571185i	0.120655	−	0.992694i	$-0.461500\pi$
$641$	−503.934	−	366.130i	−0.786169	−	0.571185i	−0.906824	+	0.421510i	$0.861500\pi$
$642$		0			0
$643$	−247.350	+	761.264i	−0.384681	+	1.18392i	0.552031	+	0.833823i	$0.313853\pi$
$643$	−247.350	+	761.264i	−0.384681	+	1.18392i	−0.936712	+	0.350102i	$0.886147\pi$
$644$		0			0
$645$	−244.797	−	336.934i	−0.379530	−	0.522378i
$646$		0			0
$647$	68.1874	+	209.859i	0.105390	+	0.324358i	0.989822	−	0.142312i	$-0.0454537\pi$
$647$	68.1874	+	209.859i	0.105390	+	0.324358i	−0.884432	+	0.466670i	$0.845454\pi$
$648$		0			0
$649$	−101.912	−	10.2372i	−0.157029	−	0.0157738i
$650$		0			0
$651$	−524.032	+	170.268i	−0.804965	+	0.261549i
$652$		0			0
$653$	−596.401	+	433.311i	−0.913325	+	0.663569i	−0.941854	−	0.336024i	$-0.890918\pi$
$653$	−596.401	+	433.311i	−0.913325	+	0.663569i	0.0285287	+	0.999593i	$0.490918\pi$
$654$		0			0
$655$	−114.307	−	37.1405i	−0.174514	−	0.0567030i
$656$		0			0
$657$	21.5569	−	29.6705i	0.0328111	−	0.0451606i
$658$		0			0
$659$			613.844i			0.931479i	0.884922	+	0.465739i	$0.154212\pi$
$659$			613.844i			0.931479i	−0.884922	+	0.465739i	$0.845788\pi$
$660$		0			0
$661$	410.333			0.620776			0.310388	−	0.950610i	$-0.399541\pi$
$661$	410.333			0.620776			0.310388	+	0.950610i	$0.399541\pi$
$662$		0			0
$663$	46.4769	+	33.7674i	0.0701008	+	0.0509312i
$664$		0			0
$665$	−43.7953	+	134.788i	−0.0658576	+	0.202689i
$666$		0			0
$667$	108.685	+	149.591i	0.162945	+	0.224275i
$668$		0			0
$669$	−209.504	−	644.786i	−0.313160	−	0.963806i
$670$		0			0
$671$	−188.074	−	322.317i	−0.280289	−	0.480354i
$672$		0			0
$673$	868.468	−	282.182i	1.29044	−	0.419290i	0.418197	−	0.908357i	$-0.362662\pi$
$673$	868.468	−	282.182i	1.29044	−	0.419290i	0.872247	+	0.489066i	$0.162662\pi$
$674$		0			0
$675$	113.919	−	82.7672i	0.168769	−	0.122618i
$676$		0			0
$677$	613.584	+	199.366i	0.906328	+	0.294484i	0.724846	−	0.688910i	$-0.241911\pi$
$677$	613.584	+	199.366i	0.906328	+	0.294484i	0.181482	+	0.983394i	$0.441911\pi$
$678$		0			0
$679$	37.2726	−	51.3014i	0.0548934	−	0.0755543i
$680$		0			0
$681$		−	1043.97i		−	1.53300i
$682$		0			0
$683$	−918.844			−1.34531			−0.672653	−	0.739958i	$-0.734845\pi$
$683$	−918.844			−1.34531			−0.672653	+	0.739958i	$0.734845\pi$
$684$		0			0
$685$	−383.742	−	278.805i	−0.560207	−	0.407015i
$686$		0			0
$687$	231.076	−	711.180i	0.336356	−	1.03520i
$688$		0			0
$689$	2.09751	+	2.88697i	0.00304428	+	0.00419009i
$690$		0			0
$691$	−223.430	−	687.647i	−0.323343	−	0.995148i	−0.972183	−	0.234223i	$-0.924745\pi$
$691$	−223.430	−	687.647i	−0.323343	−	0.995148i	0.648840	−	0.760925i	$-0.275255\pi$
$692$		0			0
$693$	−30.1999	+	6.56465i	−0.0435784	+	0.00947279i
$694$		0			0
$695$	307.716	−	99.9831i	0.442757	−	0.143861i
$696$		0			0
$697$	−854.190	+	620.605i	−1.22552	+	0.890395i
$698$		0			0
$699$	−1018.10	−	330.802i	−1.45651	−	0.473250i
$700$		0			0
$701$	−157.940	+	217.385i	−0.225306	+	0.310107i	−0.906672	−	0.421835i	$-0.861386\pi$
$701$	−157.940	+	217.385i	−0.225306	+	0.310107i	0.681366	+	0.731942i	$0.261386\pi$
$702$		0			0
$703$			521.522i			0.741852i
$704$		0			0
$705$	−169.917			−0.241017
$706$		0			0
$707$	227.612	+	165.370i	0.321940	+	0.233903i
$708$		0			0
$709$	−201.517	+	620.206i	−0.284227	+	0.874761i	0.702402	+	0.711780i	$0.252111\pi$
$709$	−201.517	+	620.206i	−0.284227	+	0.874761i	−0.986629	+	0.162981i	$0.947889\pi$
$710$		0			0
$711$	−22.0357	−	30.3296i	−0.0309926	−	0.0426576i
$712$		0			0
$713$	697.842	+	2147.74i	0.978740	+	3.01225i
$714$		0			0
$715$	−18.8506	+	21.1306i	−0.0263645	+	0.0295532i
$716$		0			0
$717$	−815.257	+	264.893i	−1.13704	+	0.369446i
$718$		0			0
$719$	−188.737	+	137.126i	−0.262500	+	0.190717i	−0.711248	−	0.702941i	$-0.751870\pi$
$719$	−188.737	+	137.126i	−0.262500	+	0.190717i	0.448749	+	0.893658i	$0.351870\pi$
$720$		0			0
$721$	−37.4052	−	12.1537i	−0.0518796	−	0.0168567i
$722$		0			0
$723$	−800.347	+	1101.58i	−1.10698	+	1.52363i
$724$		0			0
$725$			25.0274i			0.0345205i
$726$		0			0
$727$	−1255.99			−1.72764			−0.863818	−	0.503804i	$-0.831933\pi$
$727$	−1255.99			−1.72764			−0.863818	+	0.503804i	$0.831933\pi$
$728$		0			0
$729$	−635.908	−	462.014i	−0.872302	−	0.633764i
$730$		0			0
$731$	354.045	−	1089.64i	0.484329	−	1.49061i
$732$		0			0
$733$	−788.315	−	1085.02i	−1.07546	−	1.48025i	−0.864419	−	0.502773i	$-0.832313\pi$
$733$	−788.315	−	1085.02i	−1.07546	−	1.48025i	−0.211045	−	0.977476i	$-0.567687\pi$
$734$		0			0
$735$	76.7256	+	236.137i	0.104389	+	0.321275i
$736$		0			0
$737$	140.508	+	125.348i	0.190649	+	0.170078i
$738$		0			0
$739$	937.033	−	304.460i	1.26797	−	0.411990i	0.403644	−	0.914916i	$-0.367743\pi$
$739$	937.033	−	304.460i	1.26797	−	0.411990i	0.864329	+	0.502926i	$0.167743\pi$
$740$		0			0
$741$	53.1303	−	38.6014i	0.0717008	−	0.0520937i
$742$		0			0
$743$	−807.802	−	262.471i	−1.08722	−	0.353258i	−0.290046	−	0.957013i	$-0.593671\pi$
$743$	−807.802	−	262.471i	−1.08722	−	0.353258i	−0.797170	+	0.603755i	$0.793671\pi$
$744$		0			0
$745$	−269.795	+	371.340i	−0.362140	+	0.498443i
$746$		0			0
$747$			71.6720i			0.0959464i
$748$		0			0
$749$	654.936			0.874414
$750$		0			0
$751$	−119.879	−	87.0970i	−0.159625	−	0.115975i	0.505105	−	0.863058i	$-0.331454\pi$
$751$	−119.879	−	87.0970i	−0.159625	−	0.115975i	−0.664731	+	0.747083i	$0.731454\pi$
$752$		0			0
$753$	−362.664	+	1116.17i	−0.481626	+	1.48229i
$754$		0			0
$755$	−148.888	−	204.927i	−0.197202	−	0.271426i
$756$		0			0
$757$	−357.158	−	1099.22i	−0.471807	−	1.45207i	−0.850216	−	0.526434i	$-0.823529\pi$
$757$	−357.158	−	1099.22i	−0.471807	−	1.45207i	0.378409	−	0.925638i	$-0.376471\pi$
$758$		0			0
$759$	−245.836	−	1130.94i	−0.323895	−	1.49004i
$760$		0			0
$761$	−773.026	+	251.171i	−1.01580	+	0.330054i	−0.769163	−	0.639053i	$-0.779326\pi$
$761$	−773.026	+	251.171i	−1.01580	+	0.330054i	−0.246640	+	0.969107i	$0.579326\pi$
$762$		0			0
$763$	94.4179	−	68.5987i	0.123746	−	0.0899065i
$764$		0			0
$765$	33.0795	+	10.7482i	0.0432412	+	0.0140499i
$766$		0			0
$767$	6.30085	−	8.67238i	0.00821493	−	0.0113069i
$768$		0			0
$769$		−	298.253i		−	0.387845i	−0.981017	−	0.193923i	$-0.937879\pi$
$769$		−	298.253i		−	0.387845i	0.981017	−	0.193923i	$-0.0621211\pi$
$770$		0			0
$771$	853.087			1.10647
$772$		0			0
$773$	−371.743	−	270.087i	−0.480910	−	0.349401i	0.320768	−	0.947158i	$-0.396059\pi$
$773$	−371.743	−	270.087i	−0.480910	−	0.349401i	−0.801678	+	0.597756i	$0.796059\pi$
$774$		0			0
$775$	−94.4546	+	290.702i	−0.121877	+	0.375099i
$776$		0			0
$777$	−137.951	−	189.873i	−0.177543	−	0.244367i
$778$		0			0
$779$	372.979	+	1147.91i	0.478792	+	1.47357i
$780$		0			0
$781$	−482.021	+	281.262i	−0.617185	+	0.360131i
$782$		0			0
$783$	134.067	−	43.5610i	0.171222	−	0.0556334i
$784$		0			0
$785$	51.0449	−	37.0863i	0.0650254	−	0.0472437i
$786$		0			0
$787$	1085.65	+	352.749i	1.37948	+	0.448220i	0.902498	−	0.430694i	$-0.141731\pi$
$787$	1085.65	+	352.749i	1.37948	+	0.448220i	0.476980	+	0.878914i	$0.341731\pi$
$788$		0			0
$789$	−474.167	+	652.634i	−0.600972	+	0.827166i
$790$		0			0
$791$			303.062i			0.383138i
$792$		0			0
$793$	39.0561			0.0492511
$794$		0			0
$795$	−15.9709	−	11.6035i	−0.0200891	−	0.0145956i
$796$		0			0
$797$	12.7720	−	39.3082i	0.0160251	−	0.0493202i	−0.942724	−	0.333573i	$-0.891746\pi$
$797$	12.7720	−	39.3082i	0.0160251	−	0.0493202i	0.958749	+	0.284253i	$0.0917456\pi$
$798$		0			0
$799$	−274.754	−	378.166i	−0.343872	−	0.473299i
$800$		0			0
$801$	30.0029	+	92.3393i	0.0374568	+	0.115280i
$802$		0			0
$803$	45.4162	−	452.121i	0.0565582	−	0.563040i
$804$		0			0
$805$	−248.603	+	80.7761i	−0.308824	+	0.100343i
$806$		0			0
$807$	905.851	−	658.139i	1.12249	−	0.815538i
$808$		0			0
$809$	1068.33	+	347.122i	1.32056	+	0.429076i	0.882687	−	0.469961i	$-0.155732\pi$
$809$	1068.33	+	347.122i	1.32056	+	0.429076i	0.437872	+	0.899037i	$0.355732\pi$
$810$		0			0
$811$	508.261	−	699.561i	0.626709	−	0.862591i	−0.371111	−	0.928589i	$-0.621023\pi$
$811$	508.261	−	699.561i	0.626709	−	0.862591i	0.997820	+	0.0659976i	$0.0210230\pi$
$812$		0			0
$813$		−	1536.52i		−	1.88994i
$814$		0			0
$815$	−34.4697			−0.0422941
$816$		0			0
$817$	−1059.59	−	769.839i	−1.29693	−	0.942275i
$818$		0			0
$819$	0.999512	−	3.07618i	0.00122041	−	0.00375602i
$820$		0			0
$821$	548.650	+	755.152i	0.668271	+	0.919795i	0.999720	−	0.0236776i	$-0.00753753\pi$
$821$	548.650	+	755.152i	0.668271	+	0.919795i	−0.331449	+	0.943473i	$0.607538\pi$
$822$		0			0
$823$	−97.2207	−	299.215i	−0.118130	−	0.363566i	0.874457	−	0.485103i	$-0.161218\pi$
$823$	−97.2207	−	299.215i	−0.118130	−	0.363566i	−0.992587	+	0.121537i	$0.961218\pi$
$824$		0			0
$825$	63.0559	−	143.399i	0.0764314	−	0.173817i
$826$		0			0
$827$	502.779	−	163.363i	0.607955	−	0.197537i	0.0111699	−	0.999938i	$-0.496444\pi$
$827$	502.779	−	163.363i	0.607955	−	0.197537i	0.596785	+	0.802401i	$0.296444\pi$
$828$		0			0
$829$	799.815	−	581.100i	0.964795	−	0.700965i	0.0105359	−	0.999944i	$-0.496646\pi$
$829$	799.815	−	581.100i	0.964795	−	0.700965i	0.954260	+	0.298980i	$0.0966463\pi$
$830$		0			0
$831$	756.944	+	245.946i	0.910883	+	0.295964i
$832$		0			0
$833$	−401.482	+	552.592i	−0.481971	+	0.663376i
$834$		0			0
$835$			340.806i			0.408150i
$836$		0			0
$837$	1721.63			2.05691
$838$		0			0
$839$	−997.366	−	724.629i	−1.18876	−	0.863682i	−0.195624	−	0.980679i	$-0.562673\pi$
$839$	−997.366	−	724.629i	−1.18876	−	0.863682i	−0.993132	+	0.116997i	$0.962673\pi$
$840$		0			0
$841$	252.141	−	776.010i	0.299811	−	0.922723i
$842$		0			0
$843$	−459.334	−	632.219i	−0.544881	−	0.749964i
$844$		0			0
$845$	115.860	+	356.581i	0.137113	+	0.421990i
$846$		0			0
$847$	−282.187	+	258.827i	−0.333160	+	0.305580i
$848$		0			0
$849$	−1417.06	+	460.431i	−1.66909	+	0.542322i
$850$		0			0
$851$	−778.190	+	565.388i	−0.914442	+	0.664381i
$852$		0			0
$853$	577.351	+	187.593i	0.676847	+	0.219921i	0.627215	−	0.778846i	$-0.284195\pi$
$853$	577.351	+	187.593i	0.676847	+	0.219921i	0.0496328	+	0.998768i	$0.484195\pi$
$854$		0			0
$855$	23.3710	−	32.1674i	0.0273345	−	0.0376227i
$856$		0			0
$857$		−	237.750i		−	0.277422i	−0.990333	−	0.138711i	$-0.955704\pi$
$857$		−	237.750i		−	0.277422i	0.990333	−	0.138711i	$-0.0442959\pi$
$858$		0			0
$859$	792.390			0.922456			0.461228	−	0.887282i	$-0.347409\pi$
$859$	792.390			0.922456			0.461228	+	0.887282i	$0.347409\pi$
$860$		0			0
$861$	−439.433	−	319.267i	−0.510375	−	0.370809i
$862$		0			0
$863$	−240.235	+	739.366i	−0.278372	+	0.856740i	0.709936	+	0.704266i	$0.248724\pi$
$863$	−240.235	+	739.366i	−0.278372	+	0.856740i	−0.988308	+	0.152473i	$0.951276\pi$
$864$		0			0
$865$	49.4211	+	68.0223i	0.0571342	+	0.0786384i
$866$		0			0
$867$	−15.8093	−	48.6559i	−0.0182344	−	0.0561199i
$868$		0			0
$869$	−425.197	−	186.969i	−0.489295	−	0.215154i
$870$		0			0
$871$	−18.7421	+	6.08966i	−0.0215179	+	0.00699158i
$872$		0			0
$873$	−14.3927	+	10.4569i	−0.0164865	+	0.0119781i
$874$		0			0
$875$	−33.6491	−	10.9333i	−0.0384561	−	0.0124951i
$876$		0			0
$877$	−382.819	+	526.905i	−0.436509	+	0.600804i	−0.969432	−	0.245360i	$-0.921094\pi$
$877$	−382.819	+	526.905i	−0.436509	+	0.600804i	0.532922	+	0.846164i	$0.321094\pi$
$878$		0			0
$879$			1149.83i			1.30811i
$880$		0			0
$881$	1499.78			1.70236			0.851182	−	0.524870i	$-0.175886\pi$
$881$	1499.78			1.70236			0.851182	+	0.524870i	$0.175886\pi$
$882$		0			0
$883$	978.220	+	710.718i	1.10784	+	0.804890i	0.982322	−	0.187201i	$-0.0599417\pi$
$883$	978.220	+	710.718i	1.10784	+	0.804890i	0.125515	+	0.992092i	$0.459942\pi$
$884$		0			0
$885$	−18.3252	+	56.3992i	−0.0207065	+	0.0637279i
$886$		0			0
$887$	−561.641	−	773.033i	−0.633192	−	0.871514i	0.365038	−	0.930993i	$-0.381056\pi$
$887$	−561.641	−	773.033i	−0.633192	−	0.871514i	−0.998230	+	0.0594787i	$0.981056\pi$
$888$		0			0
$889$	−139.696	−	429.939i	−0.157138	−	0.483621i
$890$		0			0
$891$	−790.457	−	79.4026i	−0.887157	−	0.0891163i
$892$		0			0
$893$	−508.202	+	165.125i	−0.569095	+	0.184910i
$894$		0			0
$895$	−136.577	+	99.2288i	−0.152600	+	0.110870i
$896$		0			0
$897$	115.198	+	37.4302i	0.128426	+	0.0417282i
$898$		0			0
$899$	−179.860	+	247.556i	−0.200067	+	0.275369i
$900$		0			0
$901$		−	54.3074i		−	0.0602746i
$902$		0			0
$903$	589.405			0.652719
$904$		0			0
$905$	495.907	+	360.298i	0.547964	+	0.398119i
$906$		0			0
$907$	58.2947	−	179.413i	0.0642720	−	0.197809i	−0.913764	−	0.406246i	$-0.866838\pi$
$907$	58.2947	−	179.413i	0.0642720	−	0.197809i	0.978036	+	0.208437i	$0.0668377\pi$
$908$		0			0
$909$	−46.3948	−	63.8569i	−0.0510394	−	0.0702497i
$910$		0			0
$911$	71.0976	+	218.816i	0.0780434	+	0.240193i	0.982465	−	0.186447i	$-0.0596972\pi$
$911$	71.0976	+	218.816i	0.0780434	+	0.240193i	−0.904422	+	0.426640i	$0.859697\pi$
$912$		0			0
$913$	447.540	+	766.984i	0.490186	+	0.840071i
$914$		0			0
$915$	−205.486	+	66.7663i	−0.224574	+	0.0729686i
$916$		0			0
$917$	137.610	−	99.9795i	0.150065	−	0.109029i
$918$		0			0
$919$	1565.35	+	508.613i	1.70332	+	0.553441i	0.989198	−	0.146583i	$-0.0468276\pi$
$919$	1565.35	+	508.613i	1.70332	+	0.553441i	0.714119	+	0.700025i	$0.246828\pi$
$920$		0			0
$921$	486.910	−	670.175i	0.528676	−	0.727660i
$922$		0			0
$923$		−	58.4079i		−	0.0632805i
$924$		0			0
$925$	−130.195			−0.140751
$926$		0			0
$927$	8.92682	+	6.48571i	0.00962979	+	0.00699645i
$928$		0			0
$929$	192.268	−	591.741i	0.206963	−	0.636966i	−0.792664	−	0.609658i	$-0.791307\pi$
$929$	192.268	−	591.741i	0.206963	−	0.636966i	0.999627	−	0.0273076i	$-0.00869335\pi$
$930$		0			0
$931$	458.956	+	631.699i	0.492971	+	0.678516i
$932$		0			0
$933$	47.0808	+	144.900i	0.0504618	+	0.155305i
$934$		0			0
$935$	421.109	−	91.5379i	0.450384	−	0.0979015i
$936$		0			0
$937$	40.9237	−	13.2969i	0.0436753	−	0.0141910i	−0.287098	−	0.957901i	$-0.592691\pi$
$937$	40.9237	−	13.2969i	0.0436753	−	0.0141910i	0.330773	+	0.943710i	$0.392691\pi$
$938$		0			0
$939$	471.496	−	342.562i	0.502126	−	0.364816i
$940$		0			0
$941$	1126.76	+	366.107i	1.19741	+	0.389062i	0.838807	−	0.544428i	$-0.183253\pi$
$941$	1126.76	+	366.107i	1.19741	+	0.389062i	0.358603	+	0.933490i	$0.383253\pi$
$942$		0			0
$943$	−1308.51	+	1801.01i	−1.38760	+	1.90987i
$944$		0			0
$945$			199.281i			0.210880i
$946$		0			0
$947$	−486.719			−0.513959			−0.256979	−	0.966417i	$-0.582727\pi$
$947$	−486.719			−0.513959			−0.256979	+	0.966417i	$0.582727\pi$
$948$		0			0
$949$	38.4740	+	27.9530i	0.0405416	+	0.0294552i
$950$		0			0
$951$	181.897	−	559.822i	0.191269	−	0.588667i
$952$		0			0
$953$	−450.114	−	619.528i	−0.472312	−	0.650082i	0.504693	−	0.863299i	$-0.331606\pi$
$953$	−450.114	−	619.528i	−0.472312	−	0.650082i	−0.977005	+	0.213217i	$0.931606\pi$
$954$		0			0
$955$	13.4617	+	41.4308i	0.0140960	+	0.0433831i
$956$		0			0
$957$	104.397	−	117.023i	0.109088	−	0.122281i
$958$		0			0
$959$	638.433	−	207.439i	0.665728	−	0.216308i
$960$		0			0
$961$	−2245.96	+	1631.79i	−2.33711	+	1.69801i
$962$		0			0
$963$	−174.751	−	56.7799i	−0.181465	−	0.0589615i
$964$		0			0
$965$	−157.919	+	217.356i	−0.163646	+	0.225240i
$966$		0			0
$967$		−	1843.46i		−	1.90637i	−0.302386	−	0.953186i	$-0.597783\pi$
$967$		−	1843.46i		−	1.90637i	0.302386	−	0.953186i	$-0.402217\pi$
$968$		0			0
$969$	−999.445			−1.03142
$970$		0			0
$971$	−419.650	−	304.893i	−0.432183	−	0.313999i	0.350338	−	0.936623i	$-0.386067\pi$
$971$	−419.650	−	304.893i	−0.432183	−	0.313999i	−0.782521	+	0.622624i	$0.786067\pi$
$972$		0			0
$973$	−141.499	+	435.490i	−0.145426	+	0.447574i
$974$		0			0
$975$	9.63663	+	13.2637i	0.00988373	+	0.0136038i
$976$		0			0
$977$	490.456	+	1509.47i	0.502002	+	1.54500i	0.805753	+	0.592252i	$0.201761\pi$
$977$	490.456	+	1509.47i	0.502002	+	1.54500i	−0.303751	+	0.952751i	$0.598239\pi$
$978$		0			0
$979$	897.662	+	800.806i	0.916918	+	0.817984i
$980$		0			0
$981$	−31.1399	+	10.1180i	−0.0317430	+	0.0103139i
$982$		0			0
$983$	1555.78	−	1130.34i	1.58268	−	1.14989i	0.669149	−	0.743128i	$-0.266659\pi$
$983$	1555.78	−	1130.34i	1.58268	−	1.14989i	0.913535	−	0.406759i	$-0.133341\pi$
$984$		0			0
$985$	−100.112	−	32.5283i	−0.101636	−	0.0330237i
$986$		0			0
$987$	141.345	−	194.545i	0.143207	−	0.197108i
$988$		0			0
$989$		−	2415.66i		−	2.44253i
$990$		0			0
$991$	722.553			0.729115			0.364558	−	0.931181i	$-0.381220\pi$
$991$	722.553			0.729115			0.364558	+	0.931181i	$0.381220\pi$
$992$		0			0
$993$	718.010	+	521.665i	0.723072	+	0.525343i
$994$		0			0
$995$	−12.2108	+	37.5810i	−0.0122722	+	0.0377698i
$996$		0			0
$997$	43.6793	+	60.1194i	0.0438107	+	0.0603003i	0.830360	−	0.557227i	$-0.188135\pi$
$997$	43.6793	+	60.1194i	0.0438107	+	0.0603003i	−0.786550	+	0.617527i	$0.788135\pi$
$998$		0			0
$999$	226.609	+	697.430i	0.226835	+	0.698128i

Display

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.p.b.61.1	✓	16
11.2	odd	10	inner	220.3.p.b.101.1	yes	16
11.3	even	5		2420.3.f.a.241.13		16
11.8	odd	10		2420.3.f.a.241.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.p.b.61.1	✓	16	1.1	even	1	trivial
220.3.p.b.101.1	yes	16	11.2	odd	10	inner
2420.3.f.a.241.13		16	11.3	even	5
2420.3.f.a.241.14		16	11.8	odd	10

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Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.3.p.b.61.1

Level	$220$
Weight	$3$
Character	220.61
Analytic conductor	$5.995$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$