LMFDB - Embedded newform 39.3.l.b.7.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [39,3,Mod(7,39)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("39.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(39, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

Level:	$N$	$=$	$39 = 3 \cdot 13$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	39.l (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.06267303101$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - 4 x^{11} + 8 x^{10} + 8 x^{9} + 178 x^{8} - 620 x^{7} + 1088 x^{6} + 640 x^{5} + 7921 x^{4} + \cdots + 5184$ x^12 - 4x^11 + 8x^10 + 8x^9 + 178x^8 - 620x^7 + 1088x^6 + 640x^5 + 7921x^4 - 22128x^3 + 28800x^2 - 17280*x + 5184
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.1
Root			$2.24591 + 2.24591i$ of defining polynomial
Character	$\chi$	$=$	39.7
Dual form			39.3.l.b.28.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.06798 + 0.822062i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(5.27259 - 3.04413i) q^{4} +(-5.58467 - 5.58467i) q^{5} +(1.42385 - 5.31389i) q^{6} +(-7.30003 - 1.95604i) q^{7} +(-4.69005 + 4.69005i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(21.7246 + 12.5427i) q^{10} +(3.01391 + 11.2481i) q^{11} +10.5452i q^{12} +(-12.4428 - 3.76518i) q^{13} +24.0043 q^{14} +(13.2135 - 3.54054i) q^{15} +(-1.64307 + 2.84588i) q^{16} +(-10.4817 + 6.05163i) q^{17} +(6.73774 + 6.73774i) q^{18} +(2.73246 - 10.1977i) q^{19} +(-46.4461 - 12.4452i) q^{20} +(9.25606 - 9.25606i) q^{21} +(-18.4932 - 32.0311i) q^{22} +(-3.75368 - 2.16719i) q^{23} +(-2.97337 - 11.0968i) q^{24} +37.3770i q^{25} +(41.2694 + 1.32273i) q^{26} +5.19615 q^{27} +(-44.4444 + 11.9089i) q^{28} +(22.1306 - 38.3313i) q^{29} +(-37.6280 + 21.7246i) q^{30} +(-5.71913 - 5.71913i) q^{31} +(9.56812 - 35.7087i) q^{32} +(-19.4822 - 5.22024i) q^{33} +(27.1829 - 27.1829i) q^{34} +(29.8444 + 51.6920i) q^{35} +(-15.8178 - 9.13239i) q^{36} +(8.51041 + 31.7613i) q^{37} +33.5325i q^{38} +(16.4236 - 15.4035i) q^{39} +52.3847 q^{40} +(-58.1365 + 15.5776i) q^{41} +(-20.7883 + 36.0064i) q^{42} +(27.0185 - 15.5991i) q^{43} +(50.1316 + 50.1316i) q^{44} +(-6.13239 + 22.8864i) q^{45} +(13.2978 + 3.56313i) q^{46} +(22.4086 - 22.4086i) q^{47} +(-2.84588 - 4.92921i) q^{48} +(7.02906 + 4.05823i) q^{49} +(-30.7262 - 114.672i) q^{50} -20.9635i q^{51} +(-77.0675 + 18.0253i) q^{52} -54.7345 q^{53} +(-15.9417 + 4.27156i) q^{54} +(45.9850 - 79.6483i) q^{55} +(43.4114 - 25.0636i) q^{56} +(12.9301 + 12.9301i) q^{57} +(-36.3854 + 135.792i) q^{58} +(-13.4735 - 3.61020i) q^{59} +(58.8913 - 58.8913i) q^{60} +(-42.0454 - 72.8249i) q^{61} +(22.2476 + 12.8447i) q^{62} +(5.86811 + 21.9001i) q^{63} +104.274i q^{64} +(48.4616 + 90.5162i) q^{65} +64.0623 q^{66} +(62.2390 - 16.6769i) q^{67} +(-36.8439 + 63.8155i) q^{68} +(6.50157 - 3.75368i) q^{69} +(-134.056 - 134.056i) q^{70} +(-14.8017 + 55.2406i) q^{71} +(19.2202 + 5.15003i) q^{72} +(-54.9623 + 54.9623i) q^{73} +(-52.2194 - 90.4467i) q^{74} +(-56.0655 - 32.3694i) q^{75} +(-16.6359 - 62.0861i) q^{76} -88.0064i q^{77} +(-37.7245 + 60.7586i) q^{78} -45.0309 q^{79} +(25.0693 - 6.71729i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(165.555 - 95.5835i) q^{82} +(-30.8346 - 30.8346i) q^{83} +(20.6267 - 76.9800i) q^{84} +(92.3333 + 24.7406i) q^{85} +(-70.0685 + 70.0685i) q^{86} +(38.3313 + 66.3917i) q^{87} +(-66.8893 - 38.6186i) q^{88} +(5.84679 + 21.8205i) q^{89} -75.2561i q^{90} +(83.4680 + 51.8245i) q^{91} -26.3888 q^{92} +(13.5316 - 3.62578i) q^{93} +(-50.3279 + 87.1704i) q^{94} +(-72.2104 + 41.6907i) q^{95} +(45.2768 + 45.2768i) q^{96} +(28.7767 - 107.396i) q^{97} +(-24.9011 - 6.67223i) q^{98} +(24.7024 - 24.7024i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 2 q^{2} - 12 q^{4} + 4 q^{5} + 6 q^{6} - 32 q^{7} - 24 q^{8} - 18 q^{9} + 30 q^{10} + 22 q^{11} + 2 q^{13} + 92 q^{14} + 52 q^{16} - 6 q^{17} + 12 q^{18} + 4 q^{19} - 208 q^{20} + 54 q^{21} - 98 q^{22}+ \cdots - 24 q^{99}+O(q^{100})$ 12 * q - 2 * q^2 - 12 * q^4 + 4 * q^5 + 6 * q^6 - 32 * q^7 - 24 * q^8 - 18 * q^9 + 30 * q^10 + 22 * q^11 + 2 * q^13 + 92 * q^14 + 52 * q^16 - 6 * q^17 + 12 * q^18 + 4 * q^19 - 208 * q^20 + 54 * q^21 - 98 * q^22 - 18 * q^23 - 54 * q^24 - 44 * q^26 - 78 * q^28 + 128 * q^29 + 6 * q^30 - 66 * q^31 + 358 * q^32 - 6 * q^33 + 336 * q^34 + 14 * q^35 + 36 * q^36 - 36 * q^37 - 18 * q^39 - 12 * q^40 - 326 * q^41 - 6 * q^42 + 60 * q^43 - 236 * q^44 - 24 * q^45 - 138 * q^46 + 40 * q^47 - 144 * q^48 + 78 * q^49 - 40 * q^50 - 392 * q^52 + 80 * q^53 - 18 * q^54 + 166 * q^55 - 102 * q^56 + 250 * q^58 - 164 * q^59 + 396 * q^60 - 98 * q^61 + 228 * q^62 + 66 * q^63 + 514 * q^65 + 60 * q^66 - 230 * q^67 + 78 * q^68 - 54 * q^69 - 92 * q^70 + 70 * q^71 - 18 * q^72 + 106 * q^73 - 16 * q^74 - 150 * q^75 + 534 * q^76 - 456 * q^78 + 16 * q^79 + 124 * q^80 - 54 * q^81 - 156 * q^82 - 176 * q^83 - 30 * q^84 + 90 * q^85 - 612 * q^86 + 48 * q^87 - 318 * q^88 - 476 * q^89 + 106 * q^91 + 228 * q^92 + 66 * q^93 - 374 * q^94 - 234 * q^95 + 384 * q^96 - 306 * q^97 - 350 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$ .

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$

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

)

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

$2$	−3.06798	+	0.822062i	−1.53399	+	0.411031i	−0.924317	−	0.381624i	$-0.875365\pi$
$2$	−3.06798	+	0.822062i	−1.53399	+	0.411031i	−0.609670	+	0.792655i	$0.708698\pi$
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	5.27259	−	3.04413i	1.31815	−	0.761032i
$5$	−5.58467	−	5.58467i	−1.11693	−	1.11693i	−0.992189	−	0.124744i	$-0.960189\pi$
$5$	−5.58467	−	5.58467i	−1.11693	−	1.11693i	−0.124744	−	0.992189i	$-0.539811\pi$
$6$	1.42385	−	5.31389i	0.237309	−	0.885648i
$7$	−7.30003	−	1.95604i	−1.04286	−	0.279434i	−0.303562	−	0.952812i	$-0.598176\pi$
$7$	−7.30003	−	1.95604i	−1.04286	−	0.279434i	−0.739299	+	0.673378i	$0.764843\pi$
$8$	−4.69005	+	4.69005i	−0.586256	+	0.586256i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$	21.7246	+	12.5427i	2.17246	+	1.25427i
$11$	3.01391	+	11.2481i	0.273992	+	1.02255i	0.956514	+	0.291686i	$0.0942162\pi$
$11$	3.01391	+	11.2481i	0.273992	+	1.02255i	−0.682523	+	0.730865i	$0.739117\pi$
$12$			10.5452i			0.878764i
$13$	−12.4428	−	3.76518i	−0.957139	−	0.289629i
$13$	−12.4428	−	3.76518i	−0.957139	−	0.289629i
$14$	24.0043			1.71459
$15$	13.2135	−	3.54054i	0.880897	−	0.236036i
$16$	−1.64307	+	2.84588i	−0.102692	+	0.177868i
$17$	−10.4817	+	6.05163i	−0.616573	+	0.355978i	−0.775533	−	0.631307i	$-0.782519\pi$
$17$	−10.4817	+	6.05163i	−0.616573	+	0.355978i	0.158961	+	0.987285i	$0.449186\pi$
$18$	6.73774	+	6.73774i	0.374319	+	0.374319i
$19$	2.73246	−	10.1977i	0.143814	−	0.536720i	−0.855992	−	0.516989i	$-0.827053\pi$
$19$	2.73246	−	10.1977i	0.143814	−	0.536720i	0.999805	−	0.0197301i	$-0.00628070\pi$
$20$	−46.4461	−	12.4452i	−2.32230	−	0.622259i
$21$	9.25606	−	9.25606i	0.440765	−	0.440765i
$22$	−18.4932	−	32.0311i	−0.840599	−	1.45596i
$23$	−3.75368	−	2.16719i	−0.163204	−	0.0942256i	0.416174	−	0.909285i	$-0.363371\pi$
$23$	−3.75368	−	2.16719i	−0.163204	−	0.0942256i	−0.579377	+	0.815060i	$0.696704\pi$
$24$	−2.97337	−	11.0968i	−0.123891	−	0.462366i
$25$			37.3770i			1.49508i
$26$	41.2694	+	1.32273i	1.58729	+	0.0508743i
$27$	5.19615			0.192450
$28$	−44.4444	+	11.9089i	−1.58730	+	0.425316i
$29$	22.1306	−	38.3313i	0.763123	−	1.32177i	−0.178111	−	0.984010i	$-0.556998\pi$
$29$	22.1306	−	38.3313i	0.763123	−	1.32177i	0.941233	−	0.337757i	$-0.109668\pi$
$30$	−37.6280	+	21.7246i	−1.25427	+	0.724152i
$31$	−5.71913	−	5.71913i	−0.184488	−	0.184488i	0.608820	−	0.793308i	$-0.291643\pi$
$31$	−5.71913	−	5.71913i	−0.184488	−	0.184488i	−0.793308	+	0.608820i	$0.791643\pi$
$32$	9.56812	−	35.7087i	0.299004	−	1.11590i
$33$	−19.4822	−	5.22024i	−0.590370	−	0.158189i
$34$	27.1829	−	27.1829i	0.799497	−	0.799497i
$35$	29.8444	+	51.6920i	0.852697	+	1.47691i
$36$	−15.8178	−	9.13239i	−0.439382	−	0.253677i
$37$	8.51041	+	31.7613i	0.230011	+	0.858413i	0.980335	+	0.197342i	$0.0632309\pi$
$37$	8.51041	+	31.7613i	0.230011	+	0.858413i	−0.750324	+	0.661071i	$0.770102\pi$
$38$			33.5325i			0.882433i
$39$	16.4236	−	15.4035i	0.421117	−	0.394961i
$40$	52.3847			1.30962
$41$	−58.1365	+	15.5776i	−1.41796	+	0.379942i	−0.884760	−	0.466046i	$-0.845678\pi$
$41$	−58.1365	+	15.5776i	−1.41796	+	0.379942i	−0.533202	+	0.845988i	$0.679011\pi$
$42$	−20.7883	+	36.0064i	−0.494960	+	0.857296i
$43$	27.0185	−	15.5991i	0.628336	−	0.362770i	−0.151771	−	0.988416i	$-0.548498\pi$
$43$	27.0185	−	15.5991i	0.628336	−	0.362770i	0.780107	+	0.625646i	$0.215164\pi$
$44$	50.1316	+	50.1316i	1.13936	+	1.13936i
$45$	−6.13239	+	22.8864i	−0.136275	+	0.508586i
$46$	13.2978	+	3.56313i	0.289082	+	0.0774592i
$47$	22.4086	−	22.4086i	0.476779	−	0.476779i	−0.427321	−	0.904100i	$-0.640542\pi$
$47$	22.4086	−	22.4086i	0.476779	−	0.476779i	0.904100	+	0.427321i	$0.140542\pi$
$48$	−2.84588	−	4.92921i	−0.0592892	−	0.102692i
$49$	7.02906	+	4.05823i	0.143450	+	0.0828210i
$50$	−30.7262	−	114.672i	−0.614524	−	2.29343i
$51$		−	20.9635i		−	0.411048i
$52$	−77.0675	+	18.0253i	−1.48207	+	0.346640i
$53$	−54.7345			−1.03273			−0.516363	−	0.856370i	$-0.672714\pi$
$53$	−54.7345			−1.03273			−0.516363	+	0.856370i	$0.672714\pi$
$54$	−15.9417	+	4.27156i	−0.295216	+	0.0791029i
$55$	45.9850	−	79.6483i	0.836090	−	1.44815i
$56$	43.4114	−	25.0636i	0.775203	−	0.447564i
$57$	12.9301	+	12.9301i	0.226844	+	0.226844i
$58$	−36.3854	+	135.792i	−0.627334	+	2.34124i
$59$	−13.4735	−	3.61020i	−0.228364	−	0.0611899i	0.142822	−	0.989748i	$-0.454382\pi$
$59$	−13.4735	−	3.61020i	−0.228364	−	0.0611899i	−0.371186	+	0.928558i	$0.621049\pi$
$60$	58.8913	−	58.8913i	0.981521	−	0.981521i
$61$	−42.0454	−	72.8249i	−0.689270	−	1.19385i	−0.972074	−	0.234673i	$-0.924598\pi$
$61$	−42.0454	−	72.8249i	−0.689270	−	1.19385i	0.282805	−	0.959177i	$-0.408735\pi$
$62$	22.2476	+	12.8447i	0.358832	+	0.207172i
$63$	5.86811	+	21.9001i	0.0931446	+	0.347620i
$64$			104.274i			1.62929i
$65$	48.4616	+	90.5162i	0.745564	+	1.39256i
$66$	64.0623			0.970641
$67$	62.2390	−	16.6769i	0.928940	−	0.248909i	0.237537	−	0.971378i	$-0.423660\pi$
$67$	62.2390	−	16.6769i	0.928940	−	0.248909i	0.691403	+	0.722470i	$0.256993\pi$
$68$	−36.8439	+	63.8155i	−0.541822	+	0.938463i
$69$	6.50157	−	3.75368i	0.0942256	−	0.0544012i
$70$	−134.056	−	134.056i	−1.91508	−	1.91508i
$71$	−14.8017	+	55.2406i	−0.208474	+	0.778036i	0.779888	+	0.625919i	$0.215276\pi$
$71$	−14.8017	+	55.2406i	−0.208474	+	0.778036i	−0.988362	+	0.152117i	$0.951391\pi$
$72$	19.2202	+	5.15003i	0.266947	+	0.0715282i
$73$	−54.9623	+	54.9623i	−0.752909	+	0.752909i	−0.975021	−	0.222113i	$-0.928705\pi$
$73$	−54.9623	+	54.9623i	−0.752909	+	0.752909i	0.222113	+	0.975021i	$0.428705\pi$
$74$	−52.2194	−	90.4467i	−0.705668	−	1.22225i
$75$	−56.0655	−	32.3694i	−0.747540	−	0.431592i
$76$	−16.6359	−	62.0861i	−0.218894	−	0.816922i
$77$		−	88.0064i		−	1.14294i
$78$	−37.7245	+	60.7586i	−0.483647	+	0.778957i
$79$	−45.0309			−0.570012			−0.285006	−	0.958526i	$-0.591996\pi$
$79$	−45.0309			−0.570012			−0.285006	+	0.958526i	$0.591996\pi$
$80$	25.0693	−	6.71729i	0.313366	−	0.0839662i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	165.555	−	95.5835i	2.01897	−	1.16565i
$83$	−30.8346	−	30.8346i	−0.371501	−	0.371501i	0.496523	−	0.868024i	$-0.334610\pi$
$83$	−30.8346	−	30.8346i	−0.371501	−	0.371501i	−0.868024	+	0.496523i	$0.834610\pi$
$84$	20.6267	−	76.9800i	0.245556	−	0.916429i
$85$	92.3333	+	24.7406i	1.08627	+	0.291066i
$86$	−70.0685	+	70.0685i	−0.814750	+	0.814750i
$87$	38.3313	+	66.3917i	0.440589	+	0.763123i
$88$	−66.8893	−	38.6186i	−0.760106	−	0.438847i
$89$	5.84679	+	21.8205i	0.0656942	+	0.245174i	0.990963	−	0.134139i	$-0.0428269\pi$
$89$	5.84679	+	21.8205i	0.0656942	+	0.245174i	−0.925268	+	0.379313i	$0.876160\pi$
$90$		−	75.2561i		−	0.836179i
$91$	83.4680	+	51.8245i	0.917231	+	0.569500i
$92$	−26.3888			−0.286835
$93$	13.5316	−	3.62578i	0.145501	−	0.0389869i
$94$	−50.3279	+	87.1704i	−0.535403	+	0.927345i
$95$	−72.2104	+	41.6907i	−0.760110	+	0.438850i
$96$	45.2768	+	45.2768i	0.471634	+	0.471634i
$97$	28.7767	−	107.396i	0.296667	−	1.10718i	−0.643217	−	0.765684i	$-0.722401\pi$
$97$	28.7767	−	107.396i	0.296667	−	1.10718i	0.939884	−	0.341493i	$-0.110933\pi$
$98$	−24.9011	−	6.67223i	−0.254093	−	0.0680840i
$99$	24.7024	−	24.7024i	0.249520	−	0.249520i
$100$	113.780	+	197.073i	1.13780	+	1.97073i
$101$	26.0181	+	15.0216i	0.257605	+	0.148728i	0.623242	−	0.782029i	$-0.285815\pi$
$101$	26.0181	+	15.0216i	0.257605	+	0.148728i	−0.365637	+	0.930758i	$0.619149\pi$
$102$	17.2333	+	64.3154i	0.168954	+	0.630543i
$103$			122.717i			1.19143i	0.803197	+	0.595713i	$0.203131\pi$
$103$			122.717i			1.19143i	−0.803197	+	0.595713i	$0.796869\pi$
$104$	76.0163	−	40.6985i	0.730926	−	0.391332i
$105$	−103.384			−0.984610
$106$	167.924	−	44.9951i	1.58419	−	0.424482i
$107$	0.253390	−	0.438884i	0.00236813	−	0.00410172i	−0.864839	−	0.502049i	$-0.832580\pi$
$107$	0.253390	−	0.438884i	0.00236813	−	0.00410172i	0.867207	+	0.497948i	$0.165913\pi$
$108$	27.3972	−	15.8178i	0.253677	−	0.146461i
$109$	−29.9213	−	29.9213i	−0.274507	−	0.274507i	0.556404	−	0.830912i	$-0.312181\pi$
$109$	−29.9213	−	29.9213i	−0.274507	−	0.274507i	−0.830912	+	0.556404i	$0.812181\pi$
$110$	−75.6049	+	282.161i	−0.687318	+	2.56510i
$111$	−55.0121	−	14.7405i	−0.495605	−	0.132797i
$112$	17.5611	−	17.5611i	0.156796	−	0.156796i
$113$	−51.7762	−	89.6790i	−0.458197	−	0.793620i	0.540669	−	0.841235i	$-0.318171\pi$
$113$	−51.7762	−	89.6790i	−0.458197	−	0.793620i	−0.998866	+	0.0476155i	$0.984838\pi$
$114$	−50.2987	−	29.0400i	−0.441217	−	0.254736i
$115$	8.86003	+	33.0661i	0.0770437	+	0.287531i
$116$		−	269.473i		−	2.32304i
$117$	8.88198	+	37.9751i	0.0759144	+	0.324574i
$118$	44.3041			0.375458
$119$	88.3541	−	23.6744i	0.742472	−	0.198945i
$120$	−45.3665	+	78.5771i	−0.378054	+	0.654809i
$121$	−12.6460	+	7.30120i	−0.104513	+	0.0603405i
$122$	188.861	+	188.861i	1.54804	+	1.54804i
$123$	26.9812	−	100.695i	0.219360	−	0.818661i
$124$	−47.5644	−	12.7448i	−0.383583	−	0.102781i
$125$	69.1213	−	69.1213i	0.552970	−	0.552970i
$126$	−36.0064	−	62.3650i	−0.285765	−	0.494960i
$127$	−202.395	−	116.853i	−1.59366	−	0.920100i	−0.992672	−	0.120843i	$-0.961440\pi$
$127$	−202.395	−	116.853i	−1.59366	−	0.920100i	−0.600989	−	0.799257i	$-0.705226\pi$
$128$	−47.4475	−	177.077i	−0.370684	−	1.38341i
$129$			54.0369i			0.418891i
$130$	−223.089	−	237.863i	−1.71607	−	1.82972i
$131$	−15.9680			−0.121893			−0.0609467	−	0.998141i	$-0.519412\pi$
$131$	−15.9680			−0.121893			−0.0609467	+	0.998141i	$0.519412\pi$
$132$	−118.613	+	31.7822i	−0.898581	+	0.240774i
$133$	−39.8940	+	69.0985i	−0.299955	+	0.519537i
$134$	−177.238	+	102.329i	−1.32267	+	0.763646i
$135$	−29.0188	−	29.0188i	−0.214954	−	0.214954i
$136$	20.7774	−	77.5423i	0.152775	−	0.570164i
$137$	3.25775	+	0.872910i	0.0237792	+	0.00637161i	0.270689	−	0.962667i	$-0.412748\pi$
$137$	3.25775	+	0.872910i	0.0237792	+	0.00637161i	−0.246910	+	0.969038i	$0.579415\pi$
$138$	−16.8609	+	16.8609i	−0.122180	+	0.122180i
$139$	−18.1577	−	31.4501i	−0.130631	−	0.226260i	0.793289	−	0.608845i	$-0.208367\pi$
$139$	−18.1577	−	31.4501i	−0.130631	−	0.226260i	−0.923920	+	0.382586i	$0.875034\pi$
$140$	314.714	+	181.700i	2.24796	+	1.29786i
$141$	14.2065	+	53.0194i	0.100755	+	0.376024i
$142$		−	181.645i		−	1.27919i
$143$	4.84950	−	151.305i	0.0339126	−	1.05808i
$144$	9.85842			0.0684612
$145$	−337.659	+	90.4755i	−2.32868	+	0.623969i
$146$	123.441	−	213.805i	0.845484	−	1.46442i
$147$	−12.1747	+	7.02906i	−0.0828210	+	0.0478167i
$148$	141.557	+	141.557i	0.956468	+	0.956468i
$149$	37.2135	−	138.883i	0.249755	−	0.932099i	−0.721178	−	0.692749i	$-0.756399\pi$
$149$	37.2135	−	138.883i	0.249755	−	0.932099i	0.970934	−	0.239349i	$-0.0769341\pi$
$150$	198.617	+	53.2193i	1.32411	+	0.354795i
$151$	−120.042	+	120.042i	−0.794982	+	0.794982i	−0.982299	−	0.187318i	$-0.940021\pi$
$151$	−120.042	+	120.042i	−0.794982	+	0.794982i	0.187318	+	0.982299i	$0.440021\pi$
$152$	35.0122	+	60.6430i	0.230344	+	0.398967i
$153$	31.4452	+	18.1549i	0.205524	+	0.118659i
$154$	72.3467	+	270.002i	0.469784	+	1.75326i
$155$			63.8788i			0.412121i
$156$	39.7045	−	131.212i	0.254516	−	0.841100i
$157$	15.4414			0.0983529			0.0491764	−	0.998790i	$-0.484340\pi$
$157$	15.4414			0.0983529			0.0491764	+	0.998790i	$0.484340\pi$
$158$	138.154	−	37.0182i	0.874391	−	0.234292i
$159$	47.4014	−	82.1017i	0.298122	−	0.516363i
$160$	−252.856	+	145.986i	−1.58035	+	0.912415i
$161$	23.1629	+	23.1629i	0.143869	+	0.143869i
$162$	7.39855	−	27.6118i	0.0456701	−	0.170443i
$163$	266.414	+	71.3853i	1.63444	+	0.437947i	0.955198	−	0.295967i	$-0.0956420\pi$
$163$	266.414	+	71.3853i	1.63444	+	0.437947i	0.679242	+	0.733914i	$0.262309\pi$
$164$	−259.109	+	259.109i	−1.57993	+	1.57993i
$165$	79.6483	+	137.955i	0.482717	+	0.836090i
$166$	119.948	+	69.2518i	0.722576	+	0.417180i
$167$	66.4855	+	248.127i	0.398116	+	1.48579i	0.816407	+	0.577477i	$0.195963\pi$
$167$	66.4855	+	248.127i	0.398116	+	1.48579i	−0.418290	+	0.908313i	$0.637370\pi$
$168$			86.8228i			0.516802i
$169$	140.647	+	93.6988i	0.832230	+	0.554431i
$170$	−303.615			−1.78597
$171$	−30.5930	+	8.19737i	−0.178907	+	0.0479379i
$172$	94.9714	−	164.495i	0.552160	−	0.956368i
$173$	217.286	−	125.450i	1.25599	−	0.725147i	0.283698	−	0.958914i	$-0.408439\pi$
$173$	217.286	−	125.450i	1.25599	−	0.725147i	0.972293	+	0.233767i	$0.0751052\pi$
$174$	−172.177	−	172.177i	−0.989525	−	0.989525i
$175$	73.1107	−	272.853i	0.417776	−	1.55916i
$176$	−36.9627	−	9.90412i	−0.210015	−	0.0562734i
$177$	17.0837	−	17.0837i	0.0965179	−	0.0965179i
$178$	−35.8756	−	62.1383i	−0.201548	−	0.349092i
$179$	7.39919	+	4.27193i	0.0413363	+	0.0238655i	0.520526	−	0.853846i	$-0.325736\pi$
$179$	7.39919	+	4.27193i	0.0413363	+	0.0238655i	−0.479189	+	0.877711i	$0.659069\pi$
$180$	37.3356	+	139.338i	0.207420	+	0.774101i
$181$		−	24.6075i		−	0.135953i	−0.997687	−	0.0679764i	$-0.978346\pi$
$181$		−	24.6075i		−	0.135953i	0.997687	−	0.0679764i	$-0.0216543\pi$
$182$	−298.681	−	90.3805i	−1.64110	−	0.496596i
$183$	145.650			0.795900
$184$	27.7692	−	7.44073i	0.150919	−	0.0404387i
$185$	129.848	−	224.904i	0.701883	−	1.21570i
$186$	−38.5340	+	22.2476i	−0.207172	+	0.119611i
$187$	−99.6601	−	99.6601i	−0.532941	−	0.532941i
$188$	49.9367	−	186.366i	0.265621	−	0.991310i
$189$	−37.9320	−	10.1639i	−0.200699	−	0.0537770i
$190$	187.268	−	187.268i	0.985619	−	0.985619i
$191$	129.028	+	223.482i	0.675537	+	1.17006i	0.976312	+	0.216369i	$0.0694214\pi$
$191$	129.028	+	223.482i	0.675537	+	1.17006i	−0.300775	+	0.953695i	$0.597245\pi$
$192$	−156.412	−	90.3043i	−0.814644	−	0.470335i
$193$	−9.79118	−	36.5412i	−0.0507315	−	0.189333i	0.935910	−	0.352239i	$-0.114580\pi$
$193$	−9.79118	−	36.5412i	−0.0507315	−	0.189333i	−0.986641	+	0.162907i	$0.947913\pi$
$194$			353.145i			1.82034i
$195$	−177.743	−	5.69687i	−0.911504	−	0.0292147i
$196$	49.4151			0.252118
$197$	−17.6223	+	4.72189i	−0.0894534	+	0.0239690i	−0.303268	−	0.952905i	$-0.598078\pi$
$197$	−17.6223	+	4.72189i	−0.0894534	+	0.0239690i	0.213815	+	0.976874i	$0.431411\pi$
$198$	−55.4796	+	96.0934i	−0.280200	+	0.485320i
$199$	−113.637	+	65.6084i	−0.571040	+	0.329690i	−0.757565	−	0.652760i	$-0.773611\pi$
$199$	−113.637	+	65.6084i	−0.571040	+	0.329690i	0.186524	+	0.982450i	$0.440278\pi$
$200$	−175.300	−	175.300i	−0.876499	−	0.876499i
$201$	−28.8852	+	107.801i	−0.143707	+	0.536324i
$202$	−92.1716	−	24.6973i	−0.456295	−	0.122264i
$203$	−236.531	+	236.531i	−1.16518	+	1.16518i
$204$	−63.8155	−	110.532i	−0.312821	−	0.541822i
$205$	411.668	+	237.677i	2.00814	+	1.15940i
$206$	−100.881	−	376.493i	−0.489713	−	1.82763i
$207$			13.0031i			0.0628171i
$208$	31.1597	−	29.2243i	0.149806	−	0.140501i
$209$	122.939			0.588227
$210$	317.180	−	84.9880i	1.51038	−	0.404705i
$211$	−139.029	+	240.806i	−0.658907	+	1.14126i	0.321992	+	0.946742i	$0.395648\pi$
$211$	−139.029	+	240.806i	−0.658907	+	1.14126i	−0.980899	+	0.194518i	$0.937686\pi$
$212$	−288.592	+	166.619i	−1.36128	+	0.785938i
$213$	−70.0422	−	70.0422i	−0.328837	−	0.328837i
$214$	−0.416604	+	1.55479i	−0.00194675	+	0.00726537i
$215$	−238.005	−	63.7732i	−1.10700	−	0.296620i
$216$	−24.3702	+	24.3702i	−0.112825	+	0.112825i
$217$	30.5630	+	52.9366i	0.140843	+	0.243947i
$218$	116.395	+	67.2006i	0.533921	+	0.308260i
$219$	−34.8447	−	130.042i	−0.159108	−	0.593800i
$220$		−	559.937i		−	2.54517i
$221$	153.208	−	35.8336i	0.693247	−	0.162143i
$222$	180.893			0.814835
$223$	209.460	−	56.1247i	0.939283	−	0.251680i	0.243474	−	0.969907i	$-0.421713\pi$
$223$	209.460	−	56.1247i	0.939283	−	0.251680i	0.695809	+	0.718227i	$0.255046\pi$
$224$	−139.695	+	241.959i	−0.623639	+	1.08017i
$225$	97.1082	−	56.0655i	0.431592	−	0.249180i
$226$	232.570	+	232.570i	1.02907	+	1.02907i
$227$	−42.8998	+	160.104i	−0.188986	+	0.705305i	0.804756	+	0.593605i	$0.202296\pi$
$227$	−42.8998	+	160.104i	−0.188986	+	0.705305i	−0.993742	+	0.111699i	$0.964371\pi$
$228$	107.536	+	28.8142i	0.471650	+	0.126378i
$229$	161.998	−	161.998i	0.707415	−	0.707415i	−0.258576	−	0.965991i	$-0.583253\pi$
$229$	161.998	−	161.998i	0.707415	−	0.707415i	0.965991	+	0.258576i	$0.0832533\pi$
$230$	−54.3647	−	94.1624i	−0.236368	−	0.409402i
$231$	132.010	+	76.2158i	0.571470	+	0.329938i
$232$	75.9821	+	283.569i	0.327509	+	1.22228i
$233$		−	262.925i		−	1.12843i	−0.825626	−	0.564217i	$-0.809178\pi$
$233$		−	262.925i		−	1.12843i	0.825626	−	0.564217i	$-0.190822\pi$
$234$	−58.4676	−	109.205i	−0.249862	−	0.466689i
$235$	−250.289			−1.06506
$236$	−82.0300	+	21.9799i	−0.347585	+	0.0931350i
$237$	38.9979	−	67.5464i	0.164548	−	0.285006i
$238$	−251.606	+	145.265i	−1.05717	+	0.610357i
$239$	−243.702	−	243.702i	−1.01967	−	1.01967i	−0.999803	−	0.0198720i	$-0.993674\pi$
$239$	−243.702	−	243.702i	−1.01967	−	1.01967i	−0.0198720	−	0.999803i	$-0.506326\pi$
$240$	−11.6347	+	43.4213i	−0.0484779	+	0.180922i
$241$	−292.541	−	78.3860i	−1.21386	−	0.325253i	−0.405586	−	0.914057i	$-0.632932\pi$
$241$	−292.541	−	78.3860i	−1.21386	−	0.325253i	−0.808276	+	0.588804i	$0.799599\pi$
$242$	32.7957	−	32.7957i	0.135520	−	0.135520i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$	−443.377	−	255.984i	−1.81712	−	1.04911i
$245$	−16.5911	−	61.9188i	−0.0677188	−	0.252730i
$246$			331.111i			1.34598i
$247$	−72.3955	+	116.599i	−0.293099	+	0.472063i
$248$	53.6460			0.216314
$249$	72.9554	−	19.5483i	0.292994	−	0.0785074i
$250$	−155.240	+	268.884i	−0.620962	+	1.07554i
$251$	178.992	−	103.341i	0.713115	−	0.411717i	−0.0990983	−	0.995078i	$-0.531596\pi$
$251$	178.992	−	103.341i	0.713115	−	0.411717i	0.812213	+	0.583360i	$0.198262\pi$
$252$	97.6068	+	97.6068i	0.387329	+	0.387329i
$253$	13.0634	−	48.7533i	0.0516340	−	0.192701i
$254$	717.003	+	192.120i	2.82285	+	0.756379i
$255$	−117.074	+	117.074i	−0.459113	+	0.459113i
$256$	82.5869	+	143.045i	0.322605	+	0.558768i
$257$	−149.916	−	86.5538i	−0.583329	−	0.336785i	0.179126	−	0.983826i	$-0.442673\pi$
$257$	−149.916	−	86.5538i	−0.583329	−	0.336785i	−0.762455	+	0.647041i	$0.776006\pi$
$258$	−44.4217	−	165.784i	−0.172177	−	0.642573i
$259$		−	248.505i		−	0.959478i
$260$	531.061	+	329.731i	2.04254	+	1.26820i
$261$	−132.783			−0.508749
$262$	48.9896	−	13.1267i	0.186983	−	0.0501020i
$263$	−72.7354	+	125.981i	−0.276561	+	0.479017i	−0.970528	−	0.240990i	$-0.922528\pi$
$263$	−72.7354	+	125.981i	−0.276561	+	0.479017i	0.693967	+	0.720007i	$0.255861\pi$
$264$	115.856	−	66.8893i	0.438847	−	0.253369i
$265$	305.674	+	305.674i	1.15349	+	1.15349i
$266$	65.5907	−	244.788i	0.246582	−	0.920255i
$267$	−37.7942	−	10.1269i	−0.141551	−	0.0379286i
$268$	277.394	−	277.394i	1.03505	−	1.03505i
$269$	45.7415	+	79.2267i	0.170043	+	0.294523i	0.938435	−	0.345457i	$-0.112276\pi$
$269$	45.7415	+	79.2267i	0.170043	+	0.294523i	−0.768392	+	0.639980i	$0.778943\pi$
$270$	112.884	+	65.1737i	0.418089	+	0.241384i
$271$	−98.2045	−	366.504i	−0.362378	−	1.35241i	−0.870940	−	0.491389i	$-0.836489\pi$
$271$	−98.2045	−	366.504i	−0.362378	−	1.35241i	0.508562	−	0.861025i	$-0.330177\pi$
$272$		−	39.7730i		−	0.146224i
$273$	−150.022	+	80.3206i	−0.549532	+	0.294215i
$274$	−10.7123			−0.0390959
$275$	−420.418	+	112.651i	−1.52879	+	0.409639i
$276$	22.8534	−	39.5832i	0.0828021	−	0.143417i
$277$	212.035	−	122.418i	0.765468	−	0.441943i	−0.0657877	−	0.997834i	$-0.520956\pi$
$277$	212.035	−	122.418i	0.765468	−	0.441943i	0.831255	+	0.555891i	$0.187623\pi$
$278$	81.5614	+	81.5614i	0.293386	+	0.293386i
$279$	−6.28004	+	23.4374i	−0.0225091	+	0.0840051i
$280$	−382.410	−	102.466i	−1.36575	−	0.365951i
$281$	−307.450	+	307.450i	−1.09413	+	1.09413i	−0.0990449	+	0.995083i	$0.531579\pi$
$281$	−307.450	+	307.450i	−1.09413	+	1.09413i	−0.995083	+	0.0990449i	$0.968421\pi$
$282$	−87.1704	−	150.984i	−0.309115	−	0.535403i
$283$	−398.777	−	230.234i	−1.40911	−	0.813548i	−0.413804	−	0.910366i	$-0.635800\pi$
$283$	−398.777	−	230.234i	−1.40911	−	0.813548i	−0.995302	+	0.0968187i	$0.969133\pi$
$284$	90.1164	+	336.319i	0.317311	+	1.18422i
$285$		−	144.421i		−	0.506740i
$286$	109.504	+	468.187i	0.382881	+	1.63702i
$287$	454.868			1.58491
$288$	−107.126	+	28.7044i	−0.371966	+	0.0996679i
$289$	−71.2555	+	123.418i	−0.246559	+	0.427053i
$290$	961.553	−	555.153i	3.31570	−	1.91432i
$291$	136.173	+	136.173i	0.467948	+	0.467948i
$292$	−122.481	+	457.106i	−0.419456	+	1.56543i
$293$	−146.553	−	39.2688i	−0.500181	−	0.134023i	−9.70470e−5	−	1.00000i	$-0.500031\pi$
$293$	−146.553	−	39.2688i	−0.500181	−	0.134023i	−0.500084	+	0.865977i	$0.666698\pi$
$294$	31.5733	−	31.5733i	0.107392	−	0.107392i
$295$	55.0830	+	95.4066i	0.186722	+	0.323412i
$296$	−188.876	−	109.048i	−0.638095	−	0.368404i
$297$	15.6607	+	58.4466i	0.0527297	+	0.196790i
$298$			456.680i			1.53248i
$299$	38.5465	+	41.0992i	0.128918	+	0.137456i
$300$	−394.147			−1.31382
$301$	−227.748	+	61.0249i	−0.756637	+	0.202740i
$302$	269.605	−	466.969i	0.892730	−	1.54625i
$303$	−45.0647	+	26.0181i	−0.148728	+	0.0858683i
$304$	24.5317	+	24.5317i	0.0806965	+	0.0806965i
$305$	−171.893	+	641.512i	−0.563583	+	2.10332i
$306$	−111.398	−	29.8489i	−0.364044	−	0.0975454i
$307$	326.284	−	326.284i	1.06281	−	1.06281i	0.0649236	−	0.997890i	$-0.479320\pi$
$307$	326.284	−	326.284i	1.06281	−	1.06281i	0.997890	−	0.0649236i	$-0.0206804\pi$
$308$	−267.903	−	464.021i	−0.869815	−	1.50656i
$309$	−184.075	−	106.276i	−0.595713	−	0.343935i
$310$	−52.5123	−	195.979i	−0.169395	−	0.632189i
$311$		−	0.599099i		−	0.00192636i	−1.00000		0.000963181i	$-0.999693\pi$
$311$		−	0.599099i		−	0.00192636i	1.00000		0.000963181i	$-0.000306590\pi$
$312$	−4.78428	+	149.270i	−0.0153342	+	0.478431i
$313$	−20.6721			−0.0660452			−0.0330226	−	0.999455i	$-0.510513\pi$
$313$	−20.6721			−0.0660452			−0.0330226	+	0.999455i	$0.510513\pi$
$314$	−47.3738	+	12.6938i	−0.150872	+	0.0404261i
$315$	89.5332	−	155.076i	0.284232	−	0.492305i
$316$	−237.429	+	137.080i	−0.751359	+	0.433797i
$317$	−180.500	−	180.500i	−0.569402	−	0.569402i	0.362559	−	0.931961i	$-0.381903\pi$
$317$	−180.500	−	180.500i	−0.569402	−	0.569402i	−0.931961	+	0.362559i	$0.881903\pi$
$318$	−77.9338	+	290.853i	−0.245075	+	0.914632i
$319$	497.852	+	133.399i	1.56066	+	0.418178i
$320$	582.338	−	582.338i	1.81981	−	1.81981i
$321$	0.438884	+	0.760170i	0.00136724	+	0.00236813i
$322$	−90.1044	−	52.0218i	−0.279827	−	0.161558i
$323$	33.0717	+	123.425i	0.102389	+	0.382121i
$324$			54.7943i			0.169118i
$325$	140.731	−	465.074i	0.433019	−	1.43100i
$326$	−876.034			−2.68722
$327$	70.7945	−	18.9693i	0.216497	−	0.0580102i
$328$	199.603	−	345.723i	0.608546	−	1.05403i
$329$	−207.416	+	119.752i	−0.630443	+	0.363986i
$330$	−357.766	−	357.766i	−1.08414	−	1.08414i
$331$	36.2685	−	135.356i	0.109572	−	0.408930i	−0.889251	−	0.457419i	$-0.848774\pi$
$331$	36.2685	−	135.356i	0.109572	−	0.408930i	0.998824	+	0.0484891i	$0.0154406\pi$
$332$	−256.442	−	68.7135i	−0.772417	−	0.206968i
$333$	69.7526	−	69.7526i	0.209467	−	0.209467i
$334$	−407.951	−	706.593i	−1.22141	−	2.11555i
$335$	−440.719	−	254.449i	−1.31558	−	0.759549i
$336$	11.1333	+	41.5500i	0.0331348	+	0.123661i
$337$			294.586i			0.874142i	0.899427	+	0.437071i	$0.143984\pi$
$337$			294.586i			0.874142i	−0.899427	+	0.437071i	$0.856016\pi$
$338$	−508.527	−	171.845i	−1.50452	−	0.508418i
$339$	179.358			0.529080
$340$	562.149	−	150.627i	1.65338	−	0.443022i
$341$	47.0921	−	81.5660i	0.138100	−	0.239196i
$342$	87.1199	−	50.2987i	0.254736	−	0.147072i
$343$	218.481	+	218.481i	0.636972	+	0.636972i
$344$	−53.5573	+	199.879i	−0.155690	+	0.581042i
$345$	−57.2721	−	15.3460i	−0.166006	−	0.0444812i
$346$	−563.502	+	563.502i	−1.62862	+	1.62862i
$347$	181.324	+	314.062i	0.522547	+	0.905078i	0.999656	+	0.0262339i	$0.00835146\pi$
$347$	181.324	+	314.062i	0.522547	+	0.905078i	−0.477109	+	0.878844i	$0.658315\pi$
$348$	404.210	+	233.371i	1.16152	+	0.670605i
$349$	−109.728	−	409.510i	−0.314407	−	1.17338i	−0.924541	−	0.381083i	$-0.875551\pi$
$349$	−109.728	−	409.510i	−0.314407	−	1.17338i	0.610134	−	0.792298i	$-0.291115\pi$
$350$			897.208i			2.56345i
$351$	−64.6547	−	19.5645i	−0.184201	−	0.0557392i
$352$	430.491			1.22299
$353$	203.861	−	54.6243i	0.577509	−	0.154743i	0.0417709	−	0.999127i	$-0.486700\pi$
$353$	203.861	−	54.6243i	0.577509	−	0.154743i	0.535738	+	0.844384i	$0.320033\pi$
$354$	−38.3685	+	66.4561i	−0.108385	+	0.187729i
$355$	391.162	−	225.838i	1.10187	−	0.636163i
$356$	97.2521	+	97.2521i	0.273180	+	0.273180i
$357$	−41.0053	+	153.034i	−0.114861	+	0.428666i
$358$	−26.2123	−	7.02357i	−0.0732188	−	0.0196189i
$359$	297.929	−	297.929i	0.829885	−	0.829885i	−0.157615	−	0.987501i	$-0.550381\pi$
$359$	297.929	−	297.929i	0.829885	−	0.829885i	0.987501	+	0.157615i	$0.0503806\pi$
$360$	−78.5771	−	136.099i	−0.218270	−	0.378054i
$361$	216.109	+	124.771i	0.598640	+	0.345625i
$362$	20.2288	+	75.4951i	0.0558808	+	0.208550i
$363$		−	25.2921i		−	0.0696752i
$364$	597.853	+	19.1619i	1.64245	+	0.0526424i
$365$	613.892			1.68190
$366$	−446.850	+	119.733i	−1.22090	+	0.327139i
$367$	−280.845	+	486.438i	−0.765246	+	1.32544i	0.174871	+	0.984591i	$0.444049\pi$
$367$	−280.845	+	486.438i	−0.765246	+	1.32544i	−0.940117	+	0.340853i	$0.889284\pi$
$368$	12.3351	−	7.12169i	0.0335193	−	0.0193524i
$369$	127.677	+	127.677i	0.346007	+	0.346007i
$370$	−213.487	+	796.743i	−0.576991	+	2.15336i
$371$	399.563	+	107.063i	1.07699	+	0.288578i
$372$	60.3092	−	60.3092i	0.162121	−	0.162121i
$373$	189.783	+	328.714i	0.508801	+	0.881270i	0.999948	+	0.0101929i	$0.00324457\pi$
$373$	189.783	+	328.714i	0.508801	+	0.881270i	−0.491147	+	0.871077i	$0.663422\pi$
$374$	387.681	+	223.828i	1.03658	+	0.598470i
$375$	43.8211	+	163.543i	0.116856	+	0.436114i
$376$			210.195i			0.559030i
$377$	−419.690	+	393.623i	−1.11324	+	1.04409i
$378$	124.730			0.329973
$379$	−474.306	+	127.090i	−1.25147	+	0.335330i	−0.822903	−	0.568181i	$-0.807647\pi$
$379$	−474.306	+	127.090i	−1.25147	+	0.335330i	−0.428564	+	0.903511i	$0.640980\pi$
$380$	−253.824	+	439.636i	−0.667958	+	1.15694i
$381$	350.558	−	202.395i	0.920100	−	0.531220i
$382$	−579.570	−	579.570i	−1.51720	−	1.51720i
$383$	155.600	−	580.707i	0.406266	−	1.51621i	−0.395443	−	0.918491i	$-0.629409\pi$
$383$	155.600	−	580.707i	0.406266	−	1.51621i	0.801709	−	0.597715i	$-0.203924\pi$
$384$	306.706	+	82.1816i	0.798713	+	0.214014i
$385$	−491.486	+	491.486i	−1.27659	+	1.27659i
$386$	60.0782	+	104.058i	0.155643	+	0.269582i
$387$	−81.0554	−	46.7973i	−0.209445	−	0.120923i
$388$	−175.200	−	653.856i	−0.451547	−	1.68519i
$389$		−	78.5941i		−	0.202041i	−0.994884	−	0.101021i	$-0.967789\pi$
$389$		−	78.5941i		−	0.202041i	0.994884	−	0.101021i	$-0.0322108\pi$
$390$	549.995	−	128.638i	1.41024	−	0.329841i
$391$	52.4601			0.134169
$392$	−52.0000	+	13.9333i	−0.132653	+	0.0355442i
$393$	13.8287	−	23.9521i	0.0351876	−	0.0609467i
$394$	50.1832	−	28.9733i	0.127368	−	0.0735362i
$395$	251.483	+	251.483i	0.636665	+	0.636665i
$396$	55.0483	−	205.443i	0.139011	−	0.518796i
$397$	−665.065	−	178.204i	−1.67523	−	0.448875i	−0.708713	−	0.705496i	$-0.750724\pi$
$397$	−665.065	−	178.204i	−1.67523	−	0.448875i	−0.966512	+	0.256621i	$0.917391\pi$
$398$	294.701	−	294.701i	0.740456	−	0.740456i
$399$	−69.0985	−	119.682i	−0.173179	−	0.299955i
$400$	−106.370	−	61.4130i	−0.265926	−	0.153532i
$401$	−137.621	−	513.607i	−0.343194	−	1.28082i	−0.894708	−	0.446651i	$-0.852616\pi$
$401$	−137.621	−	513.607i	−0.343194	−	1.28082i	0.551514	−	0.834165i	$-0.314050\pi$
$402$		−	354.476i		−	0.881782i
$403$	49.6284	+	92.6955i	0.123147	+	0.230014i
$404$	182.910			0.452748
$405$	68.6592	−	18.3972i	0.169529	−	0.0454251i
$406$	531.228	−	920.114i	1.30844	−	2.26629i
$407$	−331.603	+	191.451i	−0.814749	+	0.470396i
$408$	98.3197	+	98.3197i	0.240980	+	0.240980i
$409$	180.997	−	675.491i	0.442536	−	1.65157i	−0.279825	−	0.960051i	$-0.590277\pi$
$409$	180.997	−	675.491i	0.442536	−	1.65157i	0.722361	−	0.691516i	$-0.243057\pi$
$410$	−1458.37	−	390.770i	−3.55701	−	0.953098i
$411$	−4.13066	+	4.13066i	−0.0100503	+	0.0100503i
$412$	373.566	+	647.036i	0.906714	+	1.57048i
$413$	91.2950	+	52.7092i	0.221053	+	0.127625i
$414$	−10.6894	−	39.8933i	−0.0258197	−	0.0963606i
$415$			344.402i			0.829883i
$416$	−253.504	+	408.291i	−0.609385	+	0.981468i
$417$	62.9002			0.150840
$418$	−377.175	+	101.064i	−0.902332	+	0.241779i
$419$	−180.258	+	312.217i	−0.430211	+	0.745147i	−0.996891	−	0.0787906i	$-0.974894\pi$
$419$	−180.258	+	312.217i	−0.430211	+	0.745147i	0.566680	+	0.823938i	$0.308227\pi$
$420$	−545.101	+	314.714i	−1.29786	+	0.749320i
$421$	−326.554	−	326.554i	−0.775663	−	0.775663i	0.203427	−	0.979090i	$-0.434792\pi$
$421$	−326.554	−	326.554i	−0.775663	−	0.775663i	−0.979090	+	0.203427i	$0.934792\pi$
$422$	228.581	−	853.077i	0.541662	−	2.02151i
$423$	−91.8323	−	24.6064i	−0.217098	−	0.0581711i
$424$	256.707	−	256.707i	0.605442	−	0.605442i
$425$	−226.192	−	391.775i	−0.532216	−	0.921825i
$426$	272.467	+	157.309i	0.639594	+	0.369270i
$427$	164.485	+	613.866i	0.385210	+	1.43762i
$428$		−	3.08541i		−	0.00720890i
$429$	222.758	+	138.308i	0.519250	+	0.322397i
$430$	782.619			1.82004
$431$	11.1213	−	2.97995i	0.0258035	−	0.00691403i	−0.245894	−	0.969297i	$-0.579082\pi$
$431$	11.1213	−	2.97995i	0.0258035	−	0.00691403i	0.271698	+	0.962383i	$0.412415\pi$
$432$	−8.53764	+	14.7876i	−0.0197631	+	0.0342306i
$433$	−348.424	+	201.163i	−0.804675	+	0.464579i	−0.845103	−	0.534603i	$-0.820461\pi$
$433$	−348.424	+	201.163i	−0.804675	+	0.464579i	0.0404284	+	0.999182i	$0.487128\pi$
$434$	−137.284	−	137.284i	−0.316322	−	0.316322i
$435$	156.708	−	584.843i	0.360249	−	1.34447i
$436$	−248.847	−	66.6783i	−0.570750	−	0.152932i
$437$	−32.3571	+	32.3571i	−0.0740436	+	0.0740436i
$438$	213.805	+	370.322i	0.488140	+	0.845484i
$439$	611.317	+	352.944i	1.39252	+	0.803973i	0.993594	−	0.113009i	$-0.0360490\pi$
$439$	611.317	+	352.944i	1.39252	+	0.803973i	0.398928	+	0.916982i	$0.369382\pi$
$440$	157.883	+	589.226i	0.358824	+	1.33915i
$441$		−	24.3494i		−	0.0552140i
$442$	−440.580	+	235.883i	−0.996787	+	0.533672i
$443$	47.8296			0.107968			0.0539838	−	0.998542i	$-0.482808\pi$
$443$	47.8296			0.107968			0.0539838	+	0.998542i	$0.482808\pi$
$444$	−334.928	+	89.7437i	−0.754342	+	0.202125i
$445$	89.2078	−	154.513i	0.200467	−	0.347219i
$446$	−596.480	+	344.378i	−1.33740	+	0.772148i
$447$	176.096	+	176.096i	0.393951	+	0.393951i
$448$	203.965	−	761.206i	0.455278	−	1.69912i
$449$	449.516	+	120.447i	1.00115	+	0.268257i	0.721926	−	0.691970i	$-0.243257\pi$
$449$	449.516	+	120.447i	1.00115	+	0.268257i	0.279222	+	0.960227i	$0.409924\pi$
$450$	−251.836	+	251.836i	−0.559636	+	0.559636i
$451$	−350.436	−	606.973i	−0.777020	−	1.34584i
$452$	−545.989	−	315.227i	−1.20794	−	0.697405i
$453$	−76.1037	−	284.023i	−0.167999	−	0.626982i
$454$		−	526.462i		−	1.15961i
$455$	−176.718	−	755.563i	−0.388392	−	1.66058i
$456$	−121.286			−0.265978
$457$	202.908	−	54.3691i	0.444001	−	0.118970i	−0.0298902	−	0.999553i	$-0.509516\pi$
$457$	202.908	−	54.3691i	0.444001	−	0.118970i	0.473891	+	0.880584i	$0.342849\pi$
$458$	−363.833	+	630.178i	−0.794396	+	1.37593i
$459$	−54.4647	+	31.4452i	−0.118659	+	0.0685081i
$460$	147.373	+	147.373i	0.320375	+	0.320375i
$461$	−220.190	+	821.759i	−0.477635	+	1.78256i	0.133520	+	0.991046i	$0.457372\pi$
$461$	−220.190	+	821.759i	−0.477635	+	1.78256i	−0.611154	+	0.791511i	$0.709295\pi$
$462$	−467.656	−	125.308i	−1.01224	−	0.271230i
$463$	167.655	−	167.655i	0.362107	−	0.362107i	−0.502481	−	0.864588i	$-0.667579\pi$
$463$	167.655	−	167.655i	0.362107	−	0.362107i	0.864588	+	0.502481i	$0.167579\pi$
$464$	72.7241	+	125.962i	0.156733	+	0.271470i
$465$	−95.8182	−	55.3207i	−0.206061	−	0.118969i
$466$	216.141	+	806.648i	0.463821	+	1.73100i
$467$		−	577.797i		−	1.23725i	−0.785685	−	0.618627i	$-0.787689\pi$
$467$		−	577.797i		−	1.23725i	0.785685	−	0.618627i	$-0.212311\pi$
$468$	162.432	+	173.189i	0.347077	+	0.370063i
$469$	−486.967			−1.03831
$470$	767.882	−	205.753i	1.63379	−	0.437773i
$471$	−13.3726	+	23.1621i	−0.0283920	+	0.0491764i
$472$	80.1233	−	46.2592i	0.169753	−	0.0980068i
$473$	256.891	+	256.891i	0.543110	+	0.543110i
$474$	−64.1174	+	239.289i	−0.135269	+	0.504830i
$475$	381.158	+	102.131i	0.802438	+	0.215013i
$476$	393.787	−	393.787i	0.827283	−	0.827283i
$477$	82.1017	+	142.204i	0.172121	+	0.298122i
$478$	948.011	+	547.334i	1.98329	+	1.14505i
$479$	49.3930	+	184.337i	0.103117	+	0.384838i	0.998125	−	0.0612129i	$-0.0194969\pi$
$479$	49.3930	+	184.337i	0.103117	+	0.384838i	−0.895008	+	0.446050i	$0.852830\pi$
$480$		−	505.712i		−	1.05357i
$481$	13.6936	−	427.242i	0.0284690	−	0.888238i
$482$	961.946			1.99574
$483$	−54.8039	+	14.6847i	−0.113466	+	0.0304030i
$484$	−44.4516	+	76.9924i	−0.0918421	+	0.159075i
$485$	−760.480	+	439.063i	−1.56800	+	0.905285i
$486$	35.0103	+	35.0103i	0.0720377	+	0.0720377i
$487$	−186.160	+	694.760i	−0.382259	+	1.42661i	0.460183	+	0.887824i	$0.347784\pi$
$487$	−186.160	+	694.760i	−0.382259	+	1.42661i	−0.842442	+	0.538787i	$0.818883\pi$
$488$	538.747	+	144.357i	1.10399	+	0.295813i
$489$	−337.799	+	337.799i	−0.690796	+	0.690796i
$490$	101.802	+	176.327i	0.207760	+	0.359850i
$491$	840.518	+	485.273i	1.71185	+	0.988336i	0.932068	+	0.362283i	$0.118003\pi$
$491$	840.518	+	485.273i	1.71185	+	0.988336i	0.779781	+	0.626053i	$0.215331\pi$
$492$	−164.269	−	613.059i	−0.333879	−	1.24605i
$493$			535.704i			1.08662i
$494$	126.256	−	417.238i	0.255578	−	0.844611i
$495$	−275.910			−0.557394
$496$	25.6729	−	6.87903i	0.0517598	−	0.0138690i
$497$	216.105	−	374.305i	0.434819	−	0.753129i
$498$	−207.755	+	119.948i	−0.417180	+	0.240859i
$499$	−394.571	−	394.571i	−0.790723	−	0.790723i	0.190889	−	0.981612i	$-0.438863\pi$
$499$	−394.571	−	394.571i	−0.790723	−	0.790723i	−0.981612	+	0.190889i	$0.938863\pi$
$500$	154.034	−	574.862i	0.308068	−	1.14972i
$501$	−429.769	−	115.156i	−0.857822	−	0.229853i
$502$	−464.190	+	464.190i	−0.924681	+	0.924681i
$503$	−464.382	−	804.333i	−0.923225	−	1.59907i	−0.794392	−	0.607406i	$-0.792210\pi$
$503$	−464.382	−	804.333i	−0.923225	−	1.59907i	−0.128833	−	0.991666i	$-0.541123\pi$
$504$	−130.234	−	75.1907i	−0.258401	−	0.149188i
$505$	−61.4120	−	229.193i	−0.121608	−	0.453847i
$506$			160.313i			0.316824i
$507$	−262.352	+	129.825i	−0.517460	+	0.256064i
$508$	−1422.86			−2.80090
$509$	−423.307	+	113.425i	−0.831645	+	0.222839i	−0.649431	−	0.760420i	$-0.724993\pi$
$509$	−423.307	+	113.425i	−0.831645	+	0.222839i	−0.182214	+	0.983259i	$0.558326\pi$
$510$	262.938	−	455.422i	0.515565	−	0.892984i
$511$	508.735	−	293.718i	0.995567	−	0.574791i
$512$	147.550	+	147.550i	0.288184	+	0.288184i
$513$	14.1983	−	52.9887i	0.0276769	−	0.103292i
$514$	531.090	+	142.305i	1.03325	+	0.276858i
$515$	685.333	−	685.333i	1.33074	−	1.33074i
$516$	164.495	+	284.914i	0.318789	+	0.552160i
$517$	319.591	+	184.516i	0.618165	+	0.356898i
$518$	204.286	+	762.406i	0.394375	+	1.47183i
$519$			434.573i			0.837327i
$520$	−651.813	−	197.238i	−1.25349	−	0.379304i
$521$	100.115			0.192160			0.0960801	−	0.995374i	$-0.469370\pi$
$521$	100.115			0.192160			0.0960801	+	0.995374i	$0.469370\pi$
$522$	407.376	−	109.156i	0.780414	−	0.209111i
$523$	29.0666	−	50.3449i	0.0555767	−	0.0962617i	−0.836899	−	0.547358i	$-0.815634\pi$
$523$	29.0666	−	50.3449i	0.0555767	−	0.0962617i	0.892475	+	0.451096i	$0.148967\pi$
$524$	−84.1929	+	48.6088i	−0.160673	+	0.0927649i
$525$	345.964	+	345.964i	0.658978	+	0.658978i
$526$	119.586	−	446.301i	0.227350	−	0.848481i
$527$	94.5564	+	25.3363i	0.179424	+	0.0480765i
$528$	46.8668	−	46.8668i	0.0887629	−	0.0887629i
$529$	−255.107	−	441.858i	−0.482243	−	0.835269i
$530$	−1189.08	−	686.517i	−2.24355	−	1.29531i
$531$	10.8306	+	40.4204i	0.0203966	+	0.0761213i
$532$			485.770i			0.913102i
$533$	782.033	+	25.0650i	1.46723	+	0.0470264i
$534$	124.277			0.232728
$535$	−3.86612	+	1.03592i	−0.00722640	+	0.00193631i
$536$	−213.688	+	370.119i	−0.398672	+	0.690521i
$537$	−12.8158	+	7.39919i	−0.0238655	+	0.0137788i
$538$	−205.463	−	205.463i	−0.381902	−	0.381902i
$539$	−24.4623	+	91.2944i	−0.0453845	+	0.169377i
$540$	−241.341	−	64.6671i	−0.446928	−	0.119754i
$541$	−164.770	+	164.770i	−0.304566	+	0.304566i	−0.842797	−	0.538231i	$-0.819093\pi$
$541$	−164.770	+	164.770i	−0.304566	+	0.304566i	0.538231	+	0.842797i	$0.319093\pi$
$542$	602.578	+	1043.70i	1.11177	+	1.92564i
$543$	36.9112	+	21.3107i	0.0679764	+	0.0392462i
$544$	115.805	+	432.192i	0.212878	+	0.794470i
$545$			334.201i			0.613212i
$546$	394.236	−	369.749i	0.722043	−	0.677196i
$547$	−503.473			−0.920426			−0.460213	−	0.887809i	$-0.652227\pi$
$547$	−503.473			−0.920426			−0.460213	+	0.887809i	$0.652227\pi$
$548$	19.8340	−	5.31451i	0.0361934	−	0.00969800i
$549$	−126.136	+	218.475i	−0.229757	+	0.397950i
$550$	1197.23	−	691.219i	2.17678	−	1.25676i
$551$	−330.419	−	330.419i	−0.599671	−	0.599671i
$552$	−12.8877	+	48.0976i	−0.0233473	+	0.0871334i
$553$	328.727	+	88.0821i	0.594443	+	0.159280i
$554$	−549.881	+	549.881i	−0.992566	+	0.992566i
$555$	224.904	+	389.545i	0.405232	+	0.701883i
$556$	−191.476	−	110.549i	−0.344382	−	0.198829i
$557$	−36.2263	−	135.199i	−0.0650383	−	0.242726i	0.925752	−	0.378131i	$-0.123433\pi$
$557$	−36.2263	−	135.199i	−0.0650383	−	0.242726i	−0.990790	+	0.135405i	$0.956766\pi$
$558$		−	77.0680i		−	0.138115i
$559$	−394.919	+	92.3673i	−0.706474	+	0.165237i
$560$	−196.146			−0.350260
$561$	235.798	−	63.1819i	0.420318	−	0.112624i
$562$	690.506	−	1195.99i	1.22866	−	2.12810i
$563$	135.385	−	78.1645i	0.240471	−	0.138836i	−0.374922	−	0.927056i	$-0.622331\pi$
$563$	135.385	−	78.1645i	0.240471	−	0.138836i	0.615393	+	0.788220i	$0.288997\pi$
$564$	236.303	+	236.303i	0.418977	+	0.418977i
$565$	−211.675	+	789.980i	−0.374645	+	1.39820i
$566$	1412.70	+	378.533i	2.49594	+	0.668786i
$567$	48.0959	−	48.0959i	0.0848252	−	0.0848252i
$568$	−189.660	−	328.502i	−0.333909	−	0.578348i
$569$	−584.405	−	337.406i	−1.02707	−	0.592981i	−0.110929	−	0.993828i	$-0.535383\pi$
$569$	−584.405	−	337.406i	−1.02707	−	0.592981i	−0.916145	+	0.400847i	$0.868716\pi$
$570$	118.723	+	443.080i	0.208286	+	0.777333i
$571$		−	54.2917i		−	0.0950817i	−0.998869	−	0.0475409i	$-0.984862\pi$
$571$		−	54.2917i		−	0.0950817i	0.998869	−	0.0475409i	$-0.0151384\pi$
$572$	−435.023	−	812.533i	−0.760530	−	1.42051i
$573$	−446.965			−0.780043
$574$	−1395.52	+	373.930i	−2.43123	+	0.651445i
$575$	81.0030	−	140.301i	0.140875	−	0.244002i
$576$	270.913	−	156.412i	0.470335	−	0.271548i
$577$	323.049	+	323.049i	0.559877	+	0.559877i	0.929272	−	0.369395i	$-0.120435\pi$
$577$	323.049	+	323.049i	0.559877	+	0.559877i	−0.369395	+	0.929272i	$0.620435\pi$
$578$	117.153	−	437.220i	0.202687	−	0.756437i
$579$	63.2912	+	16.9588i	0.109311	+	0.0292898i
$580$	−1504.92	+	1504.92i	−2.59469	+	2.59469i
$581$	164.780	+	285.407i	0.283614	+	0.491234i
$582$	−529.718	−	305.833i	−0.910168	−	0.525486i
$583$	−164.965	−	615.656i	−0.282958	−	1.05601i
$584$		−	515.552i		−	0.882795i
$585$	162.476	−	261.681i	0.277736	−	0.447318i
$586$	481.903			0.822359
$587$	250.071	−	67.0064i	0.426016	−	0.114151i	−0.0394395	−	0.999222i	$-0.512557\pi$
$587$	250.071	−	67.0064i	0.426016	−	0.114151i	0.465455	+	0.885071i	$0.345891\pi$
$588$	−42.7947	+	74.1227i	−0.0727802	+	0.126059i
$589$	−73.9490	+	42.6945i	−0.125550	+	0.0724864i
$590$	−247.423	−	247.423i	−0.419362	−	0.419362i
$591$	8.17855	−	30.5228i	0.0138385	−	0.0516459i
$592$	−104.372	−	27.9664i	−0.176304	−	0.0472405i
$593$	−487.207	+	487.207i	−0.821597	+	0.821597i	−0.986337	−	0.164740i	$-0.947322\pi$
$593$	−487.207	+	487.207i	−0.821597	+	0.821597i	0.164740	+	0.986337i	$0.447322\pi$
$594$	−96.0934	−	166.439i	−0.161773	−	0.280200i
$595$	−625.642	−	361.215i	−1.05150	−	0.607083i
$596$	−226.565	−	845.554i	−0.380143	−	1.41871i
$597$		−	227.274i		−	0.380694i
$598$	−152.046	−	94.4038i	−0.254257	−	0.157866i
$599$	−133.236			−0.222431			−0.111215	−	0.993796i	$-0.535474\pi$
$599$	−133.236			−0.222431			−0.111215	+	0.993796i	$0.535474\pi$
$600$	414.764	−	111.136i	0.691273	−	0.185226i
$601$	441.546	−	764.780i	0.734685	−	1.27251i	−0.220176	−	0.975460i	$-0.570663\pi$
$601$	441.546	−	764.780i	0.734685	−	1.27251i	0.954861	−	0.297052i	$-0.0960034\pi$
$602$	648.559	−	374.446i	1.07734	−	0.622003i
$603$	−136.686	−	136.686i	−0.226677	−	0.226677i
$604$	−267.509	+	998.357i	−0.442896	+	1.65291i
$605$	111.399	+	29.8492i	0.184130	+	0.0493375i
$606$	116.869	−	116.869i	0.192853	−	0.192853i
$607$	263.803	+	456.920i	0.434601	+	0.752750i	0.997263	−	0.0739364i	$-0.0235562\pi$
$607$	263.803	+	456.920i	0.434601	+	0.752750i	−0.562662	+	0.826687i	$0.690223\pi$
$608$	−338.001	−	195.145i	−0.555923	−	0.320962i
$609$	−149.955	−	559.638i	−0.246231	−	0.918946i
$610$		−	2109.45i		−	3.45811i
$611$	−363.199	+	194.454i	−0.594433	+	0.318255i
$612$	221.063			0.361215
$613$	1083.07	−	290.208i	1.76684	−	0.473423i	0.778752	−	0.627331i	$-0.215853\pi$
$613$	1083.07	−	290.208i	1.76684	−	0.473423i	0.988085	+	0.153909i	$0.0491862\pi$
$614$	−732.805	+	1269.26i	−1.19349	+	2.06719i
$615$	−713.031	+	411.668i	−1.15940	+	0.669380i
$616$	412.754	+	412.754i	0.670056	+	0.670056i
$617$	82.7504	−	308.829i	0.134117	−	0.500533i	−0.865883	−	0.500247i	$-0.833242\pi$
$617$	82.7504	−	308.829i	0.134117	−	0.500533i	1.00000		0.000285474i	$-9.08691e-5\pi$
$618$	652.104	+	174.731i	1.05518	+	0.282736i
$619$	133.111	−	133.111i	0.215042	−	0.215042i	−0.591363	−	0.806405i	$-0.701410\pi$
$619$	133.111	−	133.111i	0.215042	−	0.215042i	0.806405	+	0.591363i	$0.201410\pi$
$620$	194.455	+	336.807i	0.313638	+	0.543236i
$621$	−19.5047	−	11.2610i	−0.0314085	−	0.0181337i
$622$	0.492496	+	1.83802i	0.000791794	+	0.00295502i
$623$		−	170.727i		−	0.274040i
$624$	16.8514	+	72.0484i	0.0270054	+	0.115462i
$625$	162.386			0.259818
$626$	63.4216	−	16.9938i	0.101313	−	0.0271466i
$627$	−106.469	+	184.409i	−0.169806	+	0.294113i
$628$	81.4161	−	47.0056i	0.129643	−	0.0748497i
$629$	−281.411	−	281.411i	−0.447395	−	0.447395i
$630$	−147.204	+	549.371i	−0.233656	+	0.872018i
$631$	235.685	+	63.1517i	0.373511	+	0.100082i	0.440691	−	0.897659i	$-0.354734\pi$
$631$	235.685	+	63.1517i	0.373511	+	0.100082i	−0.0671801	+	0.997741i	$0.521400\pi$
$632$	211.197	−	211.197i	0.334173	−	0.334173i
$633$	−240.806	−	417.088i	−0.380420	−	0.658907i
$634$	702.153	+	405.388i	1.10750	+	0.639414i
$635$	477.724	+	1782.89i	0.752322	+	2.80770i
$636$		−	577.184i		−	0.907523i
$637$	−72.1813	−	76.9615i	−0.113314	−	0.120819i
$638$	−1637.06			−2.56592
$639$	165.722	−	44.4050i	0.259345	−	0.0694914i
$640$	−723.935	+	1253.89i	−1.13115	+	1.95921i
$641$	394.159	−	227.568i	0.614913	−	0.355020i	−0.159973	−	0.987121i	$-0.551141\pi$
$641$	394.159	−	227.568i	0.614913	−	0.355020i	0.774886	+	0.632101i	$0.217807\pi$
$642$	−1.97139	−	1.97139i	−0.00307071	−	0.00307071i
$643$	−54.7147	+	204.198i	−0.0850928	+	0.317571i	−0.995332	−	0.0965128i	$-0.969231\pi$
$643$	−54.7147	+	204.198i	−0.0850928	+	0.317571i	0.910239	+	0.414083i	$0.135898\pi$
$644$	192.639	+	51.6175i	0.299129	+	0.0801514i
$645$	301.778	−	301.778i	0.467873	−	0.467873i
$646$	−202.926	−	351.478i	−0.314127	−	0.544084i
$647$	−725.468	−	418.849i	−1.12128	−	0.647371i	−0.179552	−	0.983748i	$-0.557465\pi$
$647$	−725.468	−	418.849i	−1.12128	−	0.647371i	−0.941727	+	0.336378i	$0.890798\pi$
$648$	−15.4501	−	57.6605i	−0.0238427	−	0.0889823i
$649$		−	162.431i		−	0.250279i
$650$	−49.4397	+	1542.53i	−0.0760611	+	2.37312i
$651$	−105.873			−0.162632
$652$	1622.00	−	434.612i	2.48772	−	0.666584i
$653$	−250.703	+	434.229i	−0.383924	+	0.664976i	−0.991619	−	0.129194i	$-0.958761\pi$
$653$	−250.703	+	434.229i	−0.383924	+	0.664976i	0.607695	+	0.794170i	$0.292094\pi$
$654$	−201.602	+	116.395i	−0.308260	+	0.177974i
$655$	89.1762	+	89.1762i	0.136147	+	0.136147i
$656$	51.1902	−	191.045i	0.0780339	−	0.291226i
$657$	225.240	+	60.3528i	0.342831	+	0.0918612i
$658$	537.903	−	537.903i	0.817482	−	0.817482i
$659$	−305.919	−	529.868i	−0.464217	−	0.804048i	0.534948	−	0.844885i	$-0.320331\pi$
$659$	−305.919	−	529.868i	−0.464217	−	0.804048i	−0.999166	+	0.0408366i	$0.986998\pi$
$660$	839.905	+	484.919i	1.27258	+	0.734726i
$661$	161.747	+	603.648i	0.244700	+	0.913235i	0.973534	+	0.228543i	$0.0733963\pi$
$661$	161.747	+	603.648i	0.244700	+	0.913235i	−0.728833	+	0.684691i	$0.759937\pi$
$662$			445.083i			0.672331i
$663$	−78.9312	+	260.844i	−0.119052	+	0.393430i
$664$	289.231			0.435589
$665$	608.687	−	163.097i	0.915318	−	0.245259i
$666$	−156.658	+	271.340i	−0.235223	+	0.407418i
$667$	−166.142	+	95.9222i	−0.249089	+	0.143811i
$668$	1105.88	+	1105.88i	1.65551	+	1.65551i
$669$	−97.2108	+	362.796i	−0.145308	+	0.542295i
$670$	1561.29	+	418.346i	2.33028	+	0.624396i
$671$	692.417	−	692.417i	1.03192	−	1.03192i
$672$	−241.959	−	419.085i	−0.360058	−	0.623639i
$673$	160.099	+	92.4331i	0.237888	+	0.137345i	0.614206	−	0.789146i	$-0.289476\pi$
$673$	160.099	+	92.4331i	0.237888	+	0.137345i	−0.376317	+	0.926491i	$0.622810\pi$
$674$	−242.168	−	903.782i	−0.359299	−	1.34092i
$675$			194.216i			0.287728i
$676$	1026.80	+	65.8881i	1.51894	+	0.0974677i
$677$	−984.771			−1.45461			−0.727305	−	0.686315i	$-0.759227\pi$
$677$	−984.771			−1.45461			−0.727305	+	0.686315i	$0.759227\pi$
$678$	−550.266	+	147.443i	−0.811602	+	0.217468i
$679$	−420.142	+	727.707i	−0.618765	+	1.07173i
$680$	−549.083	+	317.013i	−0.807474	+	0.466196i
$681$	−203.004	−	203.004i	−0.298097	−	0.298097i
$682$	−77.4253	+	288.955i	−0.113527	+	0.423688i
$683$	−1103.55	−	295.696i	−1.61574	−	0.432937i	−0.665995	−	0.745957i	$-0.731993\pi$
$683$	−1103.55	−	295.696i	−1.61574	−	0.432937i	−0.949746	+	0.313020i	$0.898659\pi$
$684$	−136.350	+	136.350i	−0.199343	+	0.199343i
$685$	−13.3185	−	23.0683i	−0.0194431	−	0.0336764i
$686$	−849.900	−	490.690i	−1.23892	−	0.715292i
$687$	102.703	+	383.291i	0.149494	+	0.557920i
$688$			102.522i			0.149014i
$689$	681.050	+	206.085i	0.988462	+	0.299108i
$690$	188.325			0.272935
$691$	703.381	−	188.470i	1.01792	−	0.272750i	0.288984	−	0.957334i	$-0.406683\pi$
$691$	703.381	−	188.470i	1.01792	−	0.272750i	0.728934	+	0.684584i	$0.240016\pi$
$692$	763.774	−	1322.90i	1.10372	−	1.91170i
$693$	−228.647	+	132.010i	−0.329938	+	0.190490i
$694$	−814.476	−	814.476i	−1.17360	−	1.17360i
$695$	−74.2335	+	277.043i	−0.106811	+	0.398623i
$696$	−491.156	−	131.605i	−0.705684	−	0.189087i
$697$	515.101	−	515.101i	0.739026	−	0.739026i
$698$	673.285	+	1166.16i	0.964592	+	1.67072i
$699$	394.388	+	227.700i	0.564217	+	0.325751i
$700$	−445.117	−	1661.20i	−0.635881	−	2.37314i
$701$		−	973.569i		−	1.38883i	−0.719575	−	0.694415i	$-0.755663\pi$
$701$		−	973.569i		−	1.38883i	0.719575	−	0.694415i	$-0.244337\pi$
$702$	214.442	+	6.87312i	0.305473	+	0.00979076i
$703$	347.145			0.493806
$704$	−1172.88	+	314.274i	−1.66603	+	0.446411i
$705$	216.757	−	375.434i	0.307457	−	0.532531i
$706$	−580.535	+	335.172i	−0.822288	+	0.474748i
$707$	−160.550	−	160.550i	−0.227087	−	0.227087i
$708$	38.0702	−	142.080i	0.0537715	−	0.200678i
$709$	−161.771	−	43.3463i	−0.228167	−	0.0611372i	0.142924	−	0.989734i	$-0.454350\pi$
$709$	−161.771	−	43.3463i	−0.228167	−	0.0611372i	−0.371091	+	0.928596i	$0.621016\pi$
$710$	−1014.42	+	1014.42i	−1.42877	+	1.42877i
$711$	67.5464	+	116.994i	0.0950019	+	0.164548i
$712$	−129.761	−	74.9175i	−0.182249	−	0.105221i
$713$	9.07335	+	33.8622i	0.0127256	+	0.0474926i
$714$		−	503.213i		−	0.704780i
$715$	−872.072	+	817.907i	−1.21968	+	1.14393i
$716$	52.0172			0.0726497
$717$	576.606	−	154.501i	0.804192	−	0.215483i
$718$	−669.122	+	1158.95i	−0.931925	+	1.61414i
$719$	536.036	−	309.481i	0.745530	−	0.430432i	−0.0785462	−	0.996910i	$-0.525028\pi$
$719$	536.036	−	309.481i	0.745530	−	0.430432i	0.824077	+	0.566478i	$0.191694\pi$
$720$	−55.0560	−	55.0560i	−0.0764666	−	0.0764666i
$721$	240.039	−	895.837i	0.332925	−	1.24249i
$722$	−765.586	−	205.138i	−1.06037	−	0.284125i
$723$	370.927	−	370.927i	0.513038	−	0.513038i
$724$	−74.9083	−	129.745i	−0.103465	−	0.179206i
$725$	1432.71	+	827.173i	1.97615	+	1.14093i
$726$	20.7917	+	77.5955i	0.0286387	+	0.106881i
$727$		−	58.7377i		−	0.0807946i	−0.999184	−	0.0403973i	$-0.987138\pi$
$727$		−	58.7377i		−	0.0807946i	0.999184	−	0.0403973i	$-0.0128624\pi$
$728$	−634.528	+	148.409i	−0.871605	+	0.203859i
$729$	27.0000			0.0370370
$730$	−1883.41	+	504.657i	−2.58001	+	0.691311i
$731$	−188.800	+	327.011i	−0.258277	+	0.447348i
$732$	767.951	−	443.377i	1.04911	−	0.605706i
$733$	−114.680	−	114.680i	−0.156453	−	0.156453i	0.624540	−	0.780993i	$-0.285287\pi$
$733$	−114.680	−	114.680i	−0.156453	−	0.156453i	−0.780993	+	0.624540i	$0.785287\pi$
$734$	461.744	−	1723.25i	0.629079	−	2.34775i
$735$	107.247	+	28.7366i	0.145914	+	0.0390974i
$736$	−113.303	+	113.303i	−0.153945	+	0.153945i
$737$	375.165	+	649.805i	0.509043	+	0.881689i
$738$	−496.666	−	286.750i	−0.672990	−	0.388551i
$739$	49.4982	+	184.730i	0.0669800	+	0.249973i	0.991295	−	0.131657i	$-0.0420297\pi$
$739$	49.4982	+	184.730i	0.0669800	+	0.249973i	−0.924315	+	0.381629i	$0.875363\pi$
$740$		−	1581.10i		−	2.13662i
$741$	−112.203	−	209.571i	−0.151421	−	0.282822i
$742$	−1313.86			−1.77070
$743$	268.179	−	71.8585i	0.360941	−	0.0967139i	−0.0737908	−	0.997274i	$-0.523510\pi$
$743$	268.179	−	71.8585i	0.360941	−	0.0967139i	0.434732	+	0.900560i	$0.356843\pi$
$744$	−46.4588	+	80.4690i	−0.0624446	+	0.108157i
$745$	−983.438	+	567.788i	−1.32005	+	0.762132i
$746$	−852.472	−	852.472i	−1.14272	−	1.14272i
$747$	−33.8587	+	126.362i	−0.0453263	+	0.169160i
$748$	−828.844	−	222.088i	−1.10808	−	0.296909i
$749$	−2.70823	+	2.70823i	−0.00361579	+	0.00361579i
$750$	−268.884	−	465.721i	−0.358512	−	0.620962i
$751$	−1074.14	−	620.156i	−1.43028	−	0.825774i	−0.433141	−	0.901326i	$-0.642595\pi$
$751$	−1074.14	−	620.156i	−1.43028	−	0.825774i	−0.997142	+	0.0755521i	$0.975928\pi$
$752$	26.9533	+	100.591i	0.0358422	+	0.133765i
$753$			357.984i			0.475410i
$754$	964.018	−	1552.64i	1.27854	−	2.05920i
$755$	1340.79			1.77588
$756$	−230.940	+	61.8802i	−0.305476	+	0.0818521i
$757$	243.743	−	422.175i	0.321986	−	0.557695i	−0.658912	−	0.752220i	$-0.728983\pi$
$757$	243.743	−	422.175i	0.321986	−	0.557695i	0.980898	+	0.194525i	$0.0623164\pi$
$758$	1350.68	−	779.818i	1.78191	−	1.02878i
$759$	61.8167	+	61.8167i	0.0814450	+	0.0814450i
$760$	143.139	−	534.202i	0.188341	−	0.702898i
$761$	409.294	+	109.670i	0.537837	+	0.144113i	0.517505	−	0.855680i	$-0.326861\pi$
$761$	409.294	+	109.670i	0.537837	+	0.144113i	0.0203324	+	0.999793i	$0.493528\pi$
$762$	−909.123	+	909.123i	−1.19307	+	1.19307i
$763$	159.899	+	276.953i	0.209566	+	0.362979i
$764$	1360.62	+	785.553i	1.78091	+	1.02821i
$765$	−74.2219	−	277.000i	−0.0970221	−	0.362091i
$766$			1909.51i			2.49283i
$767$	154.055	+	95.6511i	0.200854	+	0.124708i
$768$	−286.089			−0.372512
$769$	1110.65	−	297.599i	1.44428	−	0.386995i	0.550253	−	0.834998i	$-0.314531\pi$
$769$	1110.65	−	297.599i	1.44428	−	0.386995i	0.894032	+	0.448003i	$0.147865\pi$
$770$	1103.84	−	1911.90i	1.43355	−	2.48299i
$771$	259.662	−	149.916i	0.336785	−	0.194443i
$772$	−162.861	−	162.861i	−0.210960	−	0.210960i
$773$	−242.244	+	904.069i	−0.313382	+	1.16956i	0.612104	+	0.790777i	$0.290323\pi$
$773$	−242.244	+	904.069i	−0.313382	+	1.16956i	−0.925486	+	0.378781i	$0.876343\pi$
$774$	287.146	+	76.9406i	0.370990	+	0.0994064i
$775$	213.764	−	213.764i	0.275824	−	0.275824i
$776$	368.729	+	638.658i	0.475166	+	0.823012i
$777$	372.757	+	215.211i	0.479739	+	0.276977i
$778$	64.6092	+	241.125i	0.0830452	+	0.309929i
$779$			635.422i			0.815689i
$780$	−954.509	+	511.036i	−1.22373	+	0.655175i
$781$	−665.960			−0.852701
$782$	−160.946	+	43.1254i	−0.205814	+	0.0551476i
$783$	114.994	−	199.175i	0.146863	−	0.254374i
$784$	−23.0985	+	13.3359i	−0.0294623	+	0.0170101i
$785$	−86.2350	−	86.2350i	−0.109854	−	0.109854i
$786$	−22.7361	+	84.8524i	−0.0289264	+	0.107955i
$787$	−1030.19	−	276.039i	−1.30901	−	0.350748i	−0.464161	−	0.885751i	$-0.653644\pi$
$787$	−1030.19	−	276.039i	−1.30901	−	0.350748i	−0.844850	+	0.535003i	$0.820311\pi$
$788$	−78.5412	+	78.5412i	−0.0996715	+	0.0996715i
$789$	−125.981	−	218.206i	−0.159672	−	0.276561i
$790$	−978.277	−	564.808i	−1.23833	−	0.714947i
$791$	202.552	+	755.936i	0.256071	+	0.955671i
$792$			231.711i			0.292565i
$793$	248.965	+	1064.45i	0.313953	+	1.34231i
$794$	2186.90			2.75428
$795$	−723.232	+	193.789i	−0.909725	+	0.243760i
$796$	−399.441	+	691.852i	−0.501810	+	0.869160i
$797$	−1258.35	+	726.507i	−1.57885	+	0.911552i	−0.583835	+	0.811872i	$0.698448\pi$
$797$	−1258.35	+	726.507i	−1.57885	+	0.911552i	−0.995020	+	0.0996795i	$0.968218\pi$
$798$	310.379	+	310.379i	0.388945	+	0.388945i
$799$	−99.2725	+	370.490i	−0.124246	+	0.463692i
$800$	1334.68	+	357.627i	1.66835	+	0.447034i
$801$	47.9211	−	47.9211i	0.0598266	−	0.0598266i
$802$	844.434	+	1462.60i	1.05291	+	1.82369i
$803$	−783.871	−	452.568i	−0.976178	−	0.563596i
$804$	175.861	+	656.321i	0.218732	+	0.816319i
$805$		−	258.714i		−	0.321384i
$806$	−228.460	−	243.590i	−0.283449	−	0.302221i
$807$	−158.453			−0.196349
$808$	−192.478	+	51.5744i	−0.238215	+	0.0638296i
$809$	35.5191	−	61.5210i	0.0439050	−	0.0760457i	−0.843238	−	0.537541i	$-0.819353\pi$
$809$	35.5191	−	61.5210i	0.0439050	−	0.0760457i	0.887143	+	0.461495i	$0.152687\pi$
$810$	−195.521	+	112.884i	−0.241384	+	0.139363i
$811$	688.757	+	688.757i	0.849269	+	0.849269i	0.990042	−	0.140773i	$-0.0449587\pi$
$811$	688.757	+	688.757i	0.849269	+	0.849269i	−0.140773	+	0.990042i	$0.544959\pi$
$812$	−527.099	+	1967.16i	−0.649137	+	2.42261i
$813$	634.804	+	170.095i	0.780817	+	0.209219i
$814$	859.965	−	859.965i	1.05647	−	1.05647i
$815$	−1089.17	−	1886.49i	−1.33640	−	2.31472i
$816$	59.6595	+	34.4444i	0.0731121	+	0.0422113i
$817$	−85.2478	−	318.149i	−0.104343	−	0.389412i
$818$			2221.18i			2.71538i
$819$	9.44203	−	294.593i	0.0115287	−	0.359698i
$820$	2894.08			3.52936
$821$	−507.818	+	136.069i	−0.618536	+	0.165736i	−0.554462	−	0.832209i	$-0.687076\pi$
$821$	−507.818	+	136.069i	−0.618536	+	0.165736i	−0.0640739	+	0.997945i	$0.520409\pi$
$822$	9.27710	−	16.0684i	0.0112860	−	0.0195479i
$823$	−1054.57	+	608.856i	−1.28137	+	0.739801i	−0.977099	−	0.212784i	$-0.931747\pi$
$823$	−1054.57	+	608.856i	−1.28137	+	0.739801i	−0.304273	+	0.952585i	$0.598414\pi$
$824$	−575.549	−	575.549i	−0.698481	−	0.698481i
$825$	195.117	−	728.186i	0.236505	−	0.882650i
$826$	−323.421	−	86.6604i	−0.391551	−	0.104916i
$827$	−644.293	+	644.293i	−0.779072	+	0.779072i	−0.979673	−	0.200601i	$-0.935711\pi$
$827$	−644.293	+	644.293i	−0.779072	+	0.779072i	0.200601	+	0.979673i	$0.435711\pi$
$828$	39.5832	+	68.5602i	0.0478058	+	0.0828021i
$829$	681.917	+	393.705i	0.822578	+	0.474916i	0.851305	−	0.524672i	$-0.175812\pi$
$829$	681.917	+	393.705i	0.822578	+	0.474916i	−0.0287265	+	0.999587i	$0.509145\pi$
$830$	−283.119	−	1056.62i	−0.341108	−	1.27303i
$831$			424.069i			0.510312i
$832$	392.612	−	1297.47i	0.471890	−	1.55946i
$833$	−98.2357			−0.117930
$834$	−192.976	+	51.7078i	−0.231386	+	0.0619998i
$835$	1014.41	−	1757.01i	1.21486	−	2.10420i
$836$	648.208	−	374.243i	0.775369	−	0.447659i
$837$	−29.7175	−	29.7175i	−0.0355047	−	0.0355047i
$838$	296.367	−	1106.06i	0.353660	−	1.31988i
$839$	98.0991	+	26.2856i	0.116924	+	0.0313296i	0.316806	−	0.948490i	$-0.397389\pi$
$839$	98.0991	+	26.2856i	0.116924	+	0.0313296i	−0.199883	+	0.979820i	$0.564056\pi$
$840$	484.876	−	484.876i	0.577234	−	0.577234i
$841$	−559.023	−	968.257i	−0.664713	−	1.15132i
$842$	1270.31	+	733.412i	1.50868	+	0.871036i
$843$	−194.915	−	727.434i	−0.231216	−	0.862911i
$844$			1692.89i			2.00580i
$845$	−262.189	−	1308.74i	−0.310283	−	1.54881i
$846$	301.967			0.356935
$847$	106.598	−	28.5628i	0.125853	−	0.0337223i
$848$	89.9325	−	155.768i	0.106053	−	0.183688i
$849$	690.702	−	398.777i	0.813548	−	0.469702i
$850$	1016.01	+	1016.01i	1.19531	+	1.19531i
$851$	36.8873	−	137.665i	0.0433458	−	0.161769i
$852$	−582.521	−	156.086i	−0.683711	−	0.183200i
$853$	−618.373	+	618.373i	−0.724939	+	0.724939i	−0.969607	−	0.244668i	$-0.921321\pi$
$853$	−618.373	+	618.373i	−0.724939	+	0.724939i	0.244668	+	0.969607i	$0.421321\pi$
$854$	−1009.27	−	1748.11i	−1.18182	−	2.04697i
$855$	216.631	+	125.072i	0.253370	+	0.146283i
$856$	0.869978	+	3.24680i	0.00101633	+	0.00379299i
$857$		−	194.182i		−	0.226584i	−0.993562	−	0.113292i	$-0.963861\pi$
$857$		−	194.182i		−	0.226584i	0.993562	−	0.113292i	$-0.0361395\pi$
$858$	−797.115	−	241.206i	−0.929038	−	0.281126i
$859$	330.896			0.385211			0.192605	−	0.981276i	$-0.438306\pi$
$859$	330.896			0.385211			0.192605	+	0.981276i	$0.438306\pi$
$860$	−1449.04	+	388.268i	−1.68492	+	0.451474i
$861$	−393.927	+	682.302i	−0.457523	+	0.792453i
$862$	−31.6702	+	18.2848i	−0.0367404	+	0.0212121i
$863$	1.75897	+	1.75897i	0.00203820	+	0.00203820i	0.708125	−	0.706087i	$-0.249541\pi$
$863$	1.75897	+	1.75897i	0.00203820	+	0.00203820i	−0.706087	+	0.708125i	$0.749541\pi$
$864$	49.7174	−	185.548i	0.0575433	−	0.214754i
$865$	−1914.07	−	512.874i	−2.21280	−	0.592918i
$866$	903.589	−	903.589i	1.04340	−	1.04340i
$867$	−123.418	−	213.767i	−0.142351	−	0.246559i
$868$	322.292	+	186.075i	0.371304	+	0.214372i
$869$	−135.719	−	506.510i	−0.156178	−	0.582866i
$870$			1923.11i			2.21047i
$871$	−837.219	−	26.8338i	−0.961216	−	0.0308080i
$872$	280.665			0.321863
$873$	−322.188	+	86.3301i	−0.369059	+	0.0988891i
$874$	72.6712	−	125.870i	0.0831478	−	0.144016i
$875$	−639.791	+	369.383i	−0.731190	+	0.422152i
$876$	−579.587	−	579.587i	−0.661629	−	0.661629i
$877$	−91.5191	+	341.554i	−0.104355	+	0.389457i	−0.998271	−	0.0587764i	$-0.981280\pi$
$877$	−91.5191	+	341.554i	−0.104355	+	0.389457i	0.893916	+	0.448234i	$0.147947\pi$
$878$	−2165.65	−	580.284i	−2.46657	−	0.660915i
$879$	185.822	−	185.822i	0.211401	−	0.211401i
$880$	151.113	+	261.735i	0.171719	+	0.297427i
$881$	1056.30	+	609.854i	1.19898	+	0.692229i	0.960327	−	0.278877i	$-0.0899621\pi$
$881$	1056.30	+	609.854i	1.19898	+	0.692229i	0.238649	+	0.971106i	$0.423295\pi$
$882$	20.0167	+	74.7033i	0.0226947	+	0.0846976i
$883$			161.934i			0.183390i	0.995787	+	0.0916952i	$0.0292286\pi$
$883$			161.934i			0.183390i	−0.995787	+	0.0916952i	$0.970771\pi$
$884$	698.718	−	655.320i	0.790405	−	0.741312i
$885$	−190.813			−0.215608
$886$	−146.740	+	39.3189i	−0.165621	+	0.0443780i
$887$	57.8301	−	100.165i	0.0651974	−	0.112925i	−0.831584	−	0.555399i	$-0.812566\pi$
$887$	57.8301	−	100.165i	0.0651974	−	0.112925i	0.896782	+	0.442474i	$0.145899\pi$
$888$	327.143	−	188.876i	0.368404	−	0.212698i
$889$	1248.92	+	1248.92i	1.40486	+	1.40486i
$890$	−146.669	+	547.375i	−0.164796	+	0.615028i
$891$	−101.233	−	27.1252i	−0.113617	−	0.0304435i
$892$	933.546	−	933.546i	1.04658	−	1.04658i
$893$	−167.285	−	289.747i	−0.187330	−	0.324464i
$894$	−685.021	−	395.497i	−0.766242	−	0.442390i
$895$	−17.4647	−	65.1793i	−0.0195137	−	0.0728260i
$896$			1385.47i			1.54629i
$897$	−95.0310	+	22.2267i	−0.105943	+	0.0247790i
$898$	−1478.12			−1.64601
$899$	−345.789	+	92.6538i	−0.384637	+	0.103063i
$900$	341.341	−	591.220i	0.379268	−	0.656911i
$901$	573.712	−	331.233i	0.636750	−	0.367628i
$902$	1574.10	+	1574.10i	1.74512	+	1.74512i
$903$	105.698	−	394.471i	0.117052	−	0.436845i
$904$	663.432	+	177.766i	0.733885	+	0.196644i
$905$	−137.424	+	137.424i	−0.151850	+	0.151850i
$906$	466.969	+	808.814i	0.515418	+	0.892730i
$907$	−86.2343	−	49.7874i	−0.0950765	−	0.0548924i	0.451708	−	0.892166i	$-0.350815\pi$
$907$	−86.2343	−	49.7874i	−0.0950765	−	0.0548924i	−0.546784	+	0.837273i	$0.684148\pi$
$908$	261.185	+	974.756i	0.287649	+	1.07352i
$909$		−	90.1294i		−	0.0991522i
$910$	1163.29	+	2172.78i	1.27834	+	2.38767i
$911$	−902.996			−0.991214			−0.495607	−	0.868547i	$-0.665054\pi$
$911$	−902.996			−0.991214			−0.495607	+	0.868547i	$0.665054\pi$
$912$	−58.0427	+	15.5525i	−0.0636433	+	0.0170532i
$913$	253.896	−	439.762i	0.278090	−	0.481667i
$914$	−577.823	+	333.606i	−0.632191	+	0.364996i
$915$	−813.405	−	813.405i	−0.888967	−	0.888967i
$916$	361.005	−	1347.29i	0.394111	−	1.47084i
$917$	116.567	+	31.2341i	0.127118	+	0.0340611i
$918$	141.246	−	141.246i	0.153863	−	0.153863i
$919$	481.991	+	834.834i	0.524474	+	0.908415i	0.999594	+	0.0284943i	$0.00907124\pi$
$919$	481.991	+	834.834i	0.524474	+	0.908415i	−0.475120	+	0.879921i	$0.657595\pi$
$920$	−196.636	−	113.528i	−0.213734	−	0.123400i
$921$	206.856	+	771.996i	0.224599	+	0.838215i
$922$		−	2702.15i		−	2.93074i
$923$	392.165	−	631.617i	0.424881	−	0.684308i
$924$	928.043			1.00438
$925$	−1187.14	+	318.093i	−1.28339	+	0.343885i
$926$	−376.540	+	652.186i	−0.406630	+	0.704304i
$927$	318.828	−	184.075i	0.343935	−	0.198571i
$928$	−1157.01	−	1157.01i	−1.24678	−	1.24678i
$929$	−123.886	+	462.347i	−0.133354	+	0.497683i	−0.999999	−	0.00124161i	$-0.999605\pi$
$929$	−123.886	+	462.347i	−0.133354	+	0.497683i	0.866646	+	0.498924i	$0.166271\pi$
$930$	339.445	+	90.9540i	0.364995	+	0.0978000i
$931$	60.5911	−	60.5911i	0.0650818	−	0.0650818i
$932$	−800.378	−	1386.30i	−0.858775	−	1.48744i
$933$	0.898648	+	0.518835i	0.000963181	+	0.000556093i
$934$	474.985	+	1772.67i	0.508549	+	1.89793i
$935$			1113.14i			1.19052i
$936$	−219.762	−	136.448i	−0.234789	−	0.145778i
$937$	405.888			0.433178			0.216589	−	0.976263i	$-0.430507\pi$
$937$	405.888			0.433178			0.216589	+	0.976263i	$0.430507\pi$
$938$	1494.00	−	400.317i	1.59275	−	0.426777i
$939$	17.9026	−	31.0082i	0.0190656	−	0.0330226i
$940$	−1319.67	+	761.913i	−1.40391	+	0.810546i
$941$	−507.937	−	507.937i	−0.539784	−	0.539784i	0.383682	−	0.923465i	$-0.374656\pi$
$941$	−507.937	−	507.937i	−0.539784	−	0.539784i	−0.923465	+	0.383682i	$0.874656\pi$
$942$	21.9863	−	82.0539i	0.0233400	−	0.0871060i
$943$	251.985	+	67.5193i	0.267217	+	0.0716005i
$944$	32.4121	−	32.4121i	0.0343348	−	0.0343348i
$945$	155.076	+	268.600i	0.164102	+	0.284232i
$946$	−999.315	−	576.955i	−1.05636	−	0.609889i
$947$	−158.360	−	591.006i	−0.167222	−	0.624083i	−0.997746	−	0.0670995i	$-0.978626\pi$
$947$	−158.360	−	591.006i	−0.167222	−	0.624083i	0.830524	−	0.556983i	$-0.188041\pi$
$948$		−	474.859i		−	0.500906i
$949$	890.829	−	476.942i	0.938702	−	0.502574i
$950$	−1253.34			−1.31931
$951$	427.068	−	114.433i	0.449073	−	0.120329i
$952$	−303.351	+	525.419i	−0.318646	+	0.551911i
$953$	884.041	−	510.401i	0.927640	−	0.535573i	0.0415756	−	0.999135i	$-0.486762\pi$
$953$	884.041	−	510.401i	0.927640	−	0.535573i	0.886064	+	0.463562i	$0.153429\pi$
$954$	−368.787	−	368.787i	−0.386569	−	0.386569i
$955$	527.498	−	1968.65i	0.552354	−	2.06141i
$956$	−2026.80	−	543.080i	−2.12009	−	0.568075i
$957$	−631.251	+	631.251i	−0.659614	+	0.659614i
$958$	−303.073	−	524.938i	−0.316360	−	0.547952i
$959$	−22.0742	−	12.7445i	−0.0230179	−	0.0132894i
$960$	369.187	+	1377.83i	0.384570	+	1.43524i
$961$		−	895.583i		−	0.931928i
$962$	309.208	+	1322.03i	0.321422	+	1.37425i
$963$	−1.52034			−0.00157875
$964$	−1781.06	+	477.234i	−1.84758	+	0.495057i
$965$	−149.390	+	258.751i	−0.154808	+	0.268135i
$966$	156.065	−	90.1044i	0.161558	−	0.0932758i
$967$	−100.629	−	100.629i	−0.104063	−	0.104063i	0.653158	−	0.757221i	$-0.273444\pi$
$967$	−100.629	−	100.629i	−0.104063	−	0.104063i	−0.757221	+	0.653158i	$0.773444\pi$
$968$	25.0676	−	93.5536i	0.0258963	−	0.0966463i
$969$	−213.779	−	57.2818i	−0.220618	−	0.0591143i
$970$	1972.20	−	1972.20i	2.03319	−	2.03319i
$971$	746.211	+	1292.47i	0.768497	+	1.33108i	0.938378	+	0.345611i	$0.112328\pi$
$971$	746.211	+	1292.47i	0.768497	+	1.33108i	−0.169881	+	0.985465i	$0.554338\pi$
$972$	−82.1915	−	47.4533i	−0.0845592	−	0.0488202i
$973$	71.0343	+	265.104i	0.0730055	+	0.272460i
$974$		−	2284.54i		−	2.34552i
$975$	575.735	+	613.863i	0.590497	+	0.629603i
$976$	276.334			0.283130
$977$	−474.362	+	127.105i	−0.485529	+	0.130097i	−0.493276	−	0.869873i	$-0.664201\pi$
$977$	−474.362	+	127.105i	−0.485529	+	0.130097i	0.00774697	+	0.999970i	$0.497534\pi$
$978$	758.668	−	1314.05i	0.775734	−	1.34361i
$979$	−227.817	+	131.530i	−0.232703	+	0.134351i
$980$	−275.967	−	275.967i	−0.281599	−	0.281599i
$981$	−32.8558	+	122.620i	−0.0334922	+	0.124995i
$982$	−2977.61	−	797.849i	−3.03219	−	0.812473i
$983$	−315.927	+	315.927i	−0.321391	+	0.321391i	−0.849301	−	0.527909i	$-0.822976\pi$
$983$	−315.927	+	315.927i	−0.321391	+	0.321391i	0.527909	+	0.849301i	$0.322976\pi$
$984$	345.723	+	598.809i	0.351344	+	0.608546i
$985$	124.785	+	72.0446i	0.126685	+	0.0731417i
$986$	−440.382	−	1643.53i	−0.446635	−	1.66686i
$987$		−	414.831i		−	0.420295i
$988$	−26.7679	+	835.162i	−0.0270930	+	0.845306i
$989$	−135.225			−0.136729
$990$	846.484	−	226.815i	0.855035	−	0.229106i
$991$	−840.227	+	1455.32i	−0.847857	+	1.46853i	0.0352592	+	0.999378i	$0.488774\pi$
$991$	−840.227	+	1455.32i	−0.847857	+	1.46853i	−0.883117	+	0.469154i	$0.844559\pi$
$992$	−258.944	+	149.501i	−0.261032	+	0.150707i
$993$	171.624	+	171.624i	0.172834	+	0.172834i
$994$	−355.303	+	1326.01i	−0.357448	+	1.33401i
$995$	1001.03	+	268.224i	1.00606	+	0.269572i
$996$	325.156	−	325.156i	0.326462	−	0.326462i
$997$	−186.953	−	323.812i	−0.187516	−	0.324787i	0.756906	−	0.653524i	$-0.226710\pi$
$997$	−186.953	−	323.812i	−0.187516	−	0.324787i	−0.944421	+	0.328737i	$0.893377\pi$
$998$	1534.90	+	886.172i	1.53797	+	0.887948i
$999$	44.2214	+	165.036i	0.0442656	+	0.165202i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.3.l.b.7.1	✓	12
3.2	odd	2		117.3.bd.d.46.3		12
13.2	odd	12	inner	39.3.l.b.28.1	yes	12
39.2	even	12		117.3.bd.d.28.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.3.l.b.7.1	✓	12	1.1	even	1	trivial
39.3.l.b.28.1	yes	12	13.2	odd	12	inner
117.3.bd.d.28.3		12	39.2	even	12
117.3.bd.d.46.3		12	3.2	odd	2

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Classical	Maass
Hilbert	Bianchi

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

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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	39.3.l.b.7.1

Level	$39$
Weight	$3$
Character	39.7
Analytic conductor	$1.063$
Analytic rank	$0$
Dimension	$12$
Inner twists	$2$