LMFDB - Embedded newform 39.3.l.b.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,3,Mod(7,39)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			28.1
Root			$2.24591 - 2.24591i$ of defining polynomial
Character	$\chi$	$=$	39.28
Dual form			39.3.l.b.7.1

$q$-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 $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

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

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	−0.609670	−	0.792655i	$-0.708698\pi$
$2$	−3.06798	−	0.822062i	−1.53399	−	0.411031i	−0.924317	+	0.381624i	$0.875365\pi$
$3$	−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	−0.124744	+	0.992189i	$0.539811\pi$
$5$	−5.58467	+	5.58467i	−1.11693	+	1.11693i	−0.992189	+	0.124744i	$0.960189\pi$
$6$	1.42385	+	5.31389i	0.237309	+	0.885648i
$7$	−7.30003	+	1.95604i	−1.04286	+	0.279434i	−0.739299	−	0.673378i	$-0.764843\pi$
$7$	−7.30003	+	1.95604i	−1.04286	+	0.279434i	−0.303562	+	0.952812i	$0.598176\pi$
$8$	−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	−0.682523	−	0.730865i	$-0.739117\pi$
$11$	3.01391	−	11.2481i	0.273992	−	1.02255i	0.956514	−	0.291686i	$-0.0942162\pi$
$12$		−	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	0.158961	−	0.987285i	$-0.449186\pi$
$17$	−10.4817	−	6.05163i	−0.616573	−	0.355978i	−0.775533	+	0.631307i	$0.782519\pi$
$18$	6.73774	−	6.73774i	0.374319	−	0.374319i
$19$	2.73246	+	10.1977i	0.143814	+	0.536720i	0.999805	+	0.0197301i	$0.00628070\pi$
$19$	2.73246	+	10.1977i	0.143814	+	0.536720i	−0.855992	+	0.516989i	$0.827053\pi$
$20$	−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	−0.579377	−	0.815060i	$-0.696704\pi$
$23$	−3.75368	+	2.16719i	−0.163204	+	0.0942256i	0.416174	+	0.909285i	$0.363371\pi$
$24$	−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	0.941233	+	0.337757i	$0.109668\pi$
$29$	22.1306	+	38.3313i	0.763123	+	1.32177i	−0.178111	+	0.984010i	$0.556998\pi$
$30$	−37.6280	−	21.7246i	−1.25427	−	0.724152i
$31$	−5.71913	+	5.71913i	−0.184488	+	0.184488i	−0.793308	−	0.608820i	$-0.791643\pi$
$31$	−5.71913	+	5.71913i	−0.184488	+	0.184488i	0.608820	+	0.793308i	$0.291643\pi$
$32$	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	−0.750324	−	0.661071i	$-0.770102\pi$
$37$	8.51041	−	31.7613i	0.230011	−	0.858413i	0.980335	−	0.197342i	$-0.0632309\pi$
$38$		−	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	−0.533202	−	0.845988i	$-0.679011\pi$
$41$	−58.1365	−	15.5776i	−1.41796	−	0.379942i	−0.884760	+	0.466046i	$0.845678\pi$
$42$	−20.7883	−	36.0064i	−0.494960	−	0.857296i
$43$	27.0185	+	15.5991i	0.628336	+	0.362770i	0.780107	−	0.625646i	$-0.215164\pi$
$43$	27.0185	+	15.5991i	0.628336	+	0.362770i	−0.151771	+	0.988416i	$0.548498\pi$
$44$	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	0.904100	−	0.427321i	$-0.140542\pi$
$47$	22.4086	+	22.4086i	0.476779	+	0.476779i	−0.427321	+	0.904100i	$0.640542\pi$
$48$	−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	−0.371186	−	0.928558i	$-0.621049\pi$
$59$	−13.4735	+	3.61020i	−0.228364	+	0.0611899i	0.142822	+	0.989748i	$0.454382\pi$
$60$	58.8913	+	58.8913i	0.981521	+	0.981521i
$61$	−42.0454	+	72.8249i	−0.689270	+	1.19385i	0.282805	+	0.959177i	$0.408735\pi$
$61$	−42.0454	+	72.8249i	−0.689270	+	1.19385i	−0.972074	+	0.234673i	$0.924598\pi$
$62$	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	0.691403	−	0.722470i	$-0.256993\pi$
$67$	62.2390	+	16.6769i	0.928940	+	0.248909i	0.237537	+	0.971378i	$0.423660\pi$
$68$	−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	−0.988362	−	0.152117i	$-0.951391\pi$
$71$	−14.8017	−	55.2406i	−0.208474	−	0.778036i	0.779888	−	0.625919i	$-0.215276\pi$
$72$	19.2202	−	5.15003i	0.266947	−	0.0715282i
$73$	−54.9623	−	54.9623i	−0.752909	−	0.752909i	0.222113	−	0.975021i	$-0.428705\pi$
$73$	−54.9623	−	54.9623i	−0.752909	−	0.752909i	−0.975021	+	0.222113i	$0.928705\pi$
$74$	−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	−0.868024	−	0.496523i	$-0.834610\pi$
$83$	−30.8346	+	30.8346i	−0.371501	+	0.371501i	0.496523	+	0.868024i	$0.334610\pi$
$84$	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	−0.925268	−	0.379313i	$-0.876160\pi$
$89$	5.84679	−	21.8205i	0.0656942	−	0.245174i	0.990963	+	0.134139i	$0.0428269\pi$
$90$			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	0.939884	+	0.341493i	$0.110933\pi$
$97$	28.7767	+	107.396i	0.296667	+	1.10718i	−0.643217	+	0.765684i	$0.722401\pi$
$98$	−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	−0.365637	−	0.930758i	$-0.619149\pi$
$101$	26.0181	−	15.0216i	0.257605	−	0.148728i	0.623242	+	0.782029i	$0.285815\pi$
$102$	17.2333	−	64.3154i	0.168954	−	0.630543i
$103$		−	122.717i		−	1.19143i	−0.803197	−	0.595713i	$-0.796869\pi$
$103$		−	122.717i		−	1.19143i	0.803197	−	0.595713i	$-0.203131\pi$
$104$	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	0.867207	−	0.497948i	$-0.165913\pi$
$107$	0.253390	+	0.438884i	0.00236813	+	0.00410172i	−0.864839	+	0.502049i	$0.832580\pi$
$108$	27.3972	+	15.8178i	0.253677	+	0.146461i
$109$	−29.9213	+	29.9213i	−0.274507	+	0.274507i	−0.830912	−	0.556404i	$-0.812181\pi$
$109$	−29.9213	+	29.9213i	−0.274507	+	0.274507i	0.556404	+	0.830912i	$0.312181\pi$
$110$	−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	−0.998866	−	0.0476155i	$-0.984838\pi$
$113$	−51.7762	+	89.6790i	−0.458197	+	0.793620i	0.540669	+	0.841235i	$0.318171\pi$
$114$	−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	−0.600989	+	0.799257i	$0.705226\pi$
$127$	−202.395	+	116.853i	−1.59366	+	0.920100i	−0.992672	+	0.120843i	$0.961440\pi$
$128$	−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	−0.246910	−	0.969038i	$-0.579415\pi$
$137$	3.25775	−	0.872910i	0.0237792	−	0.00637161i	0.270689	+	0.962667i	$0.412748\pi$
$138$	−16.8609	−	16.8609i	−0.122180	−	0.122180i
$139$	−18.1577	+	31.4501i	−0.130631	+	0.226260i	−0.923920	−	0.382586i	$-0.875034\pi$
$139$	−18.1577	+	31.4501i	−0.130631	+	0.226260i	0.793289	+	0.608845i	$0.208367\pi$
$140$	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	0.970934	+	0.239349i	$0.0769341\pi$
$149$	37.2135	+	138.883i	0.249755	+	0.932099i	−0.721178	+	0.692749i	$0.756399\pi$
$150$	198.617	−	53.2193i	1.32411	−	0.354795i
$151$	−120.042	−	120.042i	−0.794982	−	0.794982i	0.187318	−	0.982299i	$-0.440021\pi$
$151$	−120.042	−	120.042i	−0.794982	−	0.794982i	−0.982299	+	0.187318i	$0.940021\pi$
$152$	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	0.679242	−	0.733914i	$-0.262309\pi$
$163$	266.414	−	71.3853i	1.63444	−	0.437947i	0.955198	+	0.295967i	$0.0956420\pi$
$164$	−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	−0.418290	−	0.908313i	$-0.637370\pi$
$167$	66.4855	−	248.127i	0.398116	−	1.48579i	0.816407	−	0.577477i	$-0.195963\pi$
$168$		−	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	0.972293	−	0.233767i	$-0.0751052\pi$
$173$	217.286	+	125.450i	1.25599	+	0.725147i	0.283698	+	0.958914i	$0.408439\pi$
$174$	−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	−0.479189	−	0.877711i	$-0.659069\pi$
$179$	7.39919	−	4.27193i	0.0413363	−	0.0238655i	0.520526	+	0.853846i	$0.325736\pi$
$180$	37.3356	−	139.338i	0.207420	−	0.774101i
$181$			24.6075i			0.135953i	0.997687	+	0.0679764i	$0.0216543\pi$
$181$			24.6075i			0.135953i	−0.997687	+	0.0679764i	$0.978346\pi$
$182$	−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	−0.300775	−	0.953695i	$-0.597245\pi$
$191$	129.028	−	223.482i	0.675537	−	1.17006i	0.976312	−	0.216369i	$-0.0694214\pi$
$192$	−156.412	+	90.3043i	−0.814644	+	0.470335i
$193$	−9.79118	+	36.5412i	−0.0507315	+	0.189333i	−0.986641	−	0.162907i	$-0.947913\pi$
$193$	−9.79118	+	36.5412i	−0.0507315	+	0.189333i	0.935910	+	0.352239i	$0.114580\pi$
$194$		−	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	0.213815	−	0.976874i	$-0.431411\pi$
$197$	−17.6223	−	4.72189i	−0.0894534	−	0.0239690i	−0.303268	+	0.952905i	$0.598078\pi$
$198$	−55.4796	−	96.0934i	−0.280200	−	0.485320i
$199$	−113.637	−	65.6084i	−0.571040	−	0.329690i	0.186524	−	0.982450i	$-0.440278\pi$
$199$	−113.637	−	65.6084i	−0.571040	−	0.329690i	−0.757565	+	0.652760i	$0.773611\pi$
$200$	−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	−0.980899	−	0.194518i	$-0.937686\pi$
$211$	−139.029	−	240.806i	−0.658907	−	1.14126i	0.321992	−	0.946742i	$-0.395648\pi$
$212$	−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	0.695809	−	0.718227i	$-0.255046\pi$
$223$	209.460	+	56.1247i	0.939283	+	0.251680i	0.243474	+	0.969907i	$0.421713\pi$
$224$	−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	−0.993742	−	0.111699i	$-0.964371\pi$
$227$	−42.8998	−	160.104i	−0.188986	−	0.705305i	0.804756	−	0.593605i	$-0.202296\pi$
$228$	107.536	−	28.8142i	0.471650	−	0.126378i
$229$	161.998	+	161.998i	0.707415	+	0.707415i	0.965991	−	0.258576i	$-0.0832533\pi$
$229$	161.998	+	161.998i	0.707415	+	0.707415i	−0.258576	+	0.965991i	$0.583253\pi$
$230$	−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	$0.190822\pi$
$233$			262.925i			1.12843i	−0.825626	+	0.564217i	$0.809178\pi$
$234$	−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	−0.0198720	+	0.999803i	$0.506326\pi$
$239$	−243.702	+	243.702i	−1.01967	+	1.01967i	−0.999803	+	0.0198720i	$0.993674\pi$
$240$	−11.6347	−	43.4213i	−0.0484779	−	0.180922i
$241$	−292.541	+	78.3860i	−1.21386	+	0.325253i	−0.808276	−	0.588804i	$-0.799599\pi$
$241$	−292.541	+	78.3860i	−1.21386	+	0.325253i	−0.405586	+	0.914057i	$0.632932\pi$
$242$	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	0.812213	−	0.583360i	$-0.198262\pi$
$251$	178.992	+	103.341i	0.713115	+	0.411717i	−0.0990983	+	0.995078i	$0.531596\pi$
$252$	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	−0.762455	−	0.647041i	$-0.776006\pi$
$257$	−149.916	+	86.5538i	−0.583329	+	0.336785i	0.179126	+	0.983826i	$0.442673\pi$
$258$	−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	0.693967	−	0.720007i	$-0.255861\pi$
$263$	−72.7354	−	125.981i	−0.276561	−	0.479017i	−0.970528	+	0.240990i	$0.922528\pi$
$264$	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	−0.768392	−	0.639980i	$-0.778943\pi$
$269$	45.7415	−	79.2267i	0.170043	−	0.294523i	0.938435	+	0.345457i	$0.112276\pi$
$270$	112.884	−	65.1737i	0.418089	−	0.241384i
$271$	−98.2045	+	366.504i	−0.362378	+	1.35241i	0.508562	+	0.861025i	$0.330177\pi$
$271$	−98.2045	+	366.504i	−0.362378	+	1.35241i	−0.870940	+	0.491389i	$0.836489\pi$
$272$			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	0.831255	−	0.555891i	$-0.187623\pi$
$277$	212.035	+	122.418i	0.765468	+	0.441943i	−0.0657877	+	0.997834i	$0.520956\pi$
$278$	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	−0.995083	−	0.0990449i	$-0.968421\pi$
$281$	−307.450	−	307.450i	−1.09413	−	1.09413i	−0.0990449	−	0.995083i	$-0.531579\pi$
$282$	−87.1704	+	150.984i	−0.309115	+	0.535403i
$283$	−398.777	+	230.234i	−1.40911	+	0.813548i	−0.995302	−	0.0968187i	$-0.969133\pi$
$283$	−398.777	+	230.234i	−1.40911	+	0.813548i	−0.413804	+	0.910366i	$0.635800\pi$
$284$	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	−0.500084	−	0.865977i	$-0.666698\pi$
$293$	−146.553	+	39.2688i	−0.500181	+	0.134023i	−9.70470e−5		1.00000i	$0.500031\pi$
$294$	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	0.997890	+	0.0649236i	$0.0206804\pi$
$307$	326.284	+	326.284i	1.06281	+	1.06281i	0.0649236	+	0.997890i	$0.479320\pi$
$308$	−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	$0.000306590\pi$
$311$			0.599099i			0.00192636i	−1.00000		0.000963181i	$0.999693\pi$
$312$	−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	−0.931961	−	0.362559i	$-0.881903\pi$
$317$	−180.500	+	180.500i	−0.569402	+	0.569402i	0.362559	+	0.931961i	$0.381903\pi$
$318$	−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	0.998824	−	0.0484891i	$-0.0154406\pi$
$331$	36.2685	+	135.356i	0.109572	+	0.408930i	−0.889251	+	0.457419i	$0.848774\pi$
$332$	−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	$-0.856016\pi$
$337$		−	294.586i		−	0.874142i	0.899427	−	0.437071i	$-0.143984\pi$
$338$	−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	−0.477109	−	0.878844i	$-0.658315\pi$
$347$	181.324	−	314.062i	0.522547	−	0.905078i	0.999656	−	0.0262339i	$-0.00835146\pi$
$348$	404.210	−	233.371i	1.16152	−	0.670605i
$349$	−109.728	+	409.510i	−0.314407	+	1.17338i	0.610134	+	0.792298i	$0.291115\pi$
$349$	−109.728	+	409.510i	−0.314407	+	1.17338i	−0.924541	+	0.381083i	$0.875551\pi$
$350$		−	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	0.535738	−	0.844384i	$-0.320033\pi$
$353$	203.861	+	54.6243i	0.577509	+	0.154743i	0.0417709	+	0.999127i	$0.486700\pi$
$354$	−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	0.987501	−	0.157615i	$-0.0503806\pi$
$359$	297.929	+	297.929i	0.829885	+	0.829885i	−0.157615	+	0.987501i	$0.550381\pi$
$360$	−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	−0.940117	−	0.340853i	$-0.889284\pi$
$367$	−280.845	−	486.438i	−0.765246	−	1.32544i	0.174871	−	0.984591i	$-0.444049\pi$
$368$	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	−0.491147	−	0.871077i	$-0.663422\pi$
$373$	189.783	−	328.714i	0.508801	−	0.881270i	0.999948	−	0.0101929i	$-0.00324457\pi$
$374$	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	−0.428564	−	0.903511i	$-0.640980\pi$
$379$	−474.306	−	127.090i	−1.25147	−	0.335330i	−0.822903	+	0.568181i	$0.807647\pi$
$380$	−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	0.801709	+	0.597715i	$0.203924\pi$
$383$	155.600	+	580.707i	0.406266	+	1.51621i	−0.395443	+	0.918491i	$0.629409\pi$
$384$	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	$0.0322108\pi$
$389$			78.5941i			0.202041i	−0.994884	+	0.101021i	$0.967789\pi$
$390$	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	−0.966512	−	0.256621i	$-0.917391\pi$
$397$	−665.065	+	178.204i	−1.67523	+	0.448875i	−0.708713	+	0.705496i	$0.750724\pi$
$398$	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	0.551514	+	0.834165i	$0.314050\pi$
$401$	−137.621	+	513.607i	−0.343194	+	1.28082i	−0.894708	+	0.446651i	$0.852616\pi$
$402$			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	0.722361	+	0.691516i	$0.243057\pi$
$409$	180.997	+	675.491i	0.442536	+	1.65157i	−0.279825	+	0.960051i	$0.590277\pi$
$410$	−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	0.566680	−	0.823938i	$-0.308227\pi$
$419$	−180.258	−	312.217i	−0.430211	−	0.745147i	−0.996891	+	0.0787906i	$0.974894\pi$
$420$	−545.101	−	314.714i	−1.29786	−	0.749320i
$421$	−326.554	+	326.554i	−0.775663	+	0.775663i	−0.979090	−	0.203427i	$-0.934792\pi$
$421$	−326.554	+	326.554i	−0.775663	+	0.775663i	0.203427	+	0.979090i	$0.434792\pi$
$422$	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	0.271698	−	0.962383i	$-0.412415\pi$
$431$	11.1213	+	2.97995i	0.0258035	+	0.00691403i	−0.245894	+	0.969297i	$0.579082\pi$
$432$	−8.53764	−	14.7876i	−0.0197631	−	0.0342306i
$433$	−348.424	−	201.163i	−0.804675	−	0.464579i	0.0404284	−	0.999182i	$-0.487128\pi$
$433$	−348.424	−	201.163i	−0.804675	−	0.464579i	−0.845103	+	0.534603i	$0.820461\pi$
$434$	−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	0.398928	−	0.916982i	$-0.369382\pi$
$439$	611.317	−	352.944i	1.39252	−	0.803973i	0.993594	+	0.113009i	$0.0360490\pi$
$440$	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	0.279222	−	0.960227i	$-0.409924\pi$
$449$	449.516	−	120.447i	1.00115	−	0.268257i	0.721926	+	0.691970i	$0.243257\pi$
$450$	−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	0.473891	−	0.880584i	$-0.342849\pi$
$457$	202.908	+	54.3691i	0.444001	+	0.118970i	−0.0298902	+	0.999553i	$0.509516\pi$
$458$	−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	−0.611154	−	0.791511i	$-0.709295\pi$
$461$	−220.190	−	821.759i	−0.477635	−	1.78256i	0.133520	−	0.991046i	$-0.457372\pi$
$462$	−467.656	+	125.308i	−1.01224	+	0.271230i
$463$	167.655	+	167.655i	0.362107	+	0.362107i	0.864588	−	0.502481i	$-0.167579\pi$
$463$	167.655	+	167.655i	0.362107	+	0.362107i	−0.502481	+	0.864588i	$0.667579\pi$
$464$	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	$0.212311\pi$
$467$			577.797i			1.23725i	−0.785685	+	0.618627i	$0.787689\pi$
$468$	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	−0.895008	−	0.446050i	$-0.852830\pi$
$479$	49.3930	−	184.337i	0.103117	−	0.384838i	0.998125	+	0.0612129i	$0.0194969\pi$
$480$			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	−0.842442	−	0.538787i	$-0.818883\pi$
$487$	−186.160	−	694.760i	−0.382259	−	1.42661i	0.460183	−	0.887824i	$-0.347784\pi$
$488$	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	0.779781	−	0.626053i	$-0.215331\pi$
$491$	840.518	−	485.273i	1.71185	−	0.988336i	0.932068	−	0.362283i	$-0.118003\pi$
$492$	−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	−0.981612	−	0.190889i	$-0.938863\pi$
$499$	−394.571	+	394.571i	−0.790723	+	0.790723i	0.190889	+	0.981612i	$0.438863\pi$
$500$	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	−0.128833	+	0.991666i	$0.541123\pi$
$503$	−464.382	+	804.333i	−0.923225	+	1.59907i	−0.794392	+	0.607406i	$0.792210\pi$
$504$	−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	−0.182214	−	0.983259i	$-0.558326\pi$
$509$	−423.307	−	113.425i	−0.831645	−	0.222839i	−0.649431	+	0.760420i	$0.724993\pi$
$510$	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	0.892475	−	0.451096i	$-0.148967\pi$
$523$	29.0666	+	50.3449i	0.0555767	+	0.0962617i	−0.836899	+	0.547358i	$0.815634\pi$
$524$	−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	0.538231	−	0.842797i	$-0.319093\pi$
$541$	−164.770	−	164.770i	−0.304566	−	0.304566i	−0.842797	+	0.538231i	$0.819093\pi$
$542$	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	−0.990790	−	0.135405i	$-0.956766\pi$
$557$	−36.2263	+	135.199i	−0.0650383	+	0.242726i	0.925752	+	0.378131i	$0.123433\pi$
$558$			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	0.615393	−	0.788220i	$-0.288997\pi$
$563$	135.385	+	78.1645i	0.240471	+	0.138836i	−0.374922	+	0.927056i	$0.622331\pi$
$564$	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	−0.916145	−	0.400847i	$-0.868716\pi$
$569$	−584.405	+	337.406i	−1.02707	+	0.592981i	−0.110929	+	0.993828i	$0.535383\pi$
$570$	118.723	−	443.080i	0.208286	−	0.777333i
$571$			54.2917i			0.0950817i	0.998869	+	0.0475409i	$0.0151384\pi$
$571$			54.2917i			0.0950817i	−0.998869	+	0.0475409i	$0.984862\pi$
$572$	−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	−0.369395	−	0.929272i	$-0.620435\pi$
$577$	323.049	−	323.049i	0.559877	−	0.559877i	0.929272	+	0.369395i	$0.120435\pi$
$578$	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	0.465455	−	0.885071i	$-0.345891\pi$
$587$	250.071	+	67.0064i	0.426016	+	0.114151i	−0.0394395	+	0.999222i	$0.512557\pi$
$588$	−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	0.164740	−	0.986337i	$-0.447322\pi$
$593$	−487.207	−	487.207i	−0.821597	−	0.821597i	−0.986337	+	0.164740i	$0.947322\pi$
$594$	−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	0.954861	+	0.297052i	$0.0960034\pi$
$601$	441.546	+	764.780i	0.734685	+	1.27251i	−0.220176	+	0.975460i	$0.570663\pi$
$602$	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	−0.562662	−	0.826687i	$-0.690223\pi$
$607$	263.803	−	456.920i	0.434601	−	0.752750i	0.997263	+	0.0739364i	$0.0235562\pi$
$608$	−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	0.988085	−	0.153909i	$-0.0491862\pi$
$613$	1083.07	+	290.208i	1.76684	+	0.473423i	0.778752	+	0.627331i	$0.215853\pi$
$614$	−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	1.00000		0.000285474i	$9.08691e-5\pi$
$617$	82.7504	+	308.829i	0.134117	+	0.500533i	−0.865883	+	0.500247i	$0.833242\pi$
$618$	652.104	−	174.731i	1.05518	−	0.282736i
$619$	133.111	+	133.111i	0.215042	+	0.215042i	0.806405	−	0.591363i	$-0.201410\pi$
$619$	133.111	+	133.111i	0.215042	+	0.215042i	−0.591363	+	0.806405i	$0.701410\pi$
$620$	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	−0.0671801	−	0.997741i	$-0.521400\pi$
$631$	235.685	−	63.1517i	0.373511	−	0.100082i	0.440691	+	0.897659i	$0.354734\pi$
$632$	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	0.774886	−	0.632101i	$-0.217807\pi$
$641$	394.159	+	227.568i	0.614913	+	0.355020i	−0.159973	+	0.987121i	$0.551141\pi$
$642$	−1.97139	+	1.97139i	−0.00307071	+	0.00307071i
$643$	−54.7147	−	204.198i	−0.0850928	−	0.317571i	0.910239	−	0.414083i	$-0.135898\pi$
$643$	−54.7147	−	204.198i	−0.0850928	−	0.317571i	−0.995332	+	0.0965128i	$0.969231\pi$
$644$	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	−0.941727	−	0.336378i	$-0.890798\pi$
$647$	−725.468	+	418.849i	−1.12128	+	0.647371i	−0.179552	+	0.983748i	$0.557465\pi$
$648$	−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	0.607695	−	0.794170i	$-0.292094\pi$
$653$	−250.703	−	434.229i	−0.383924	−	0.664976i	−0.991619	+	0.129194i	$0.958761\pi$
$654$	−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	−0.999166	−	0.0408366i	$-0.986998\pi$
$659$	−305.919	+	529.868i	−0.464217	+	0.804048i	0.534948	+	0.844885i	$0.320331\pi$
$660$	839.905	−	484.919i	1.27258	−	0.734726i
$661$	161.747	−	603.648i	0.244700	−	0.913235i	−0.728833	−	0.684691i	$-0.759937\pi$
$661$	161.747	−	603.648i	0.244700	−	0.913235i	0.973534	−	0.228543i	$-0.0733963\pi$
$662$		−	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	−0.376317	−	0.926491i	$-0.622810\pi$
$673$	160.099	−	92.4331i	0.237888	−	0.137345i	0.614206	+	0.789146i	$0.289476\pi$
$674$	−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	−0.949746	−	0.313020i	$-0.898659\pi$
$683$	−1103.55	+	295.696i	−1.61574	+	0.432937i	−0.665995	+	0.745957i	$0.731993\pi$
$684$	−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	0.728934	−	0.684584i	$-0.240016\pi$
$691$	703.381	+	188.470i	1.01792	+	0.272750i	0.288984	+	0.957334i	$0.406683\pi$
$692$	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	$0.244337\pi$
$701$			973.569i			1.38883i	−0.719575	+	0.694415i	$0.755663\pi$
$702$	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	−0.371091	−	0.928596i	$-0.621016\pi$
$709$	−161.771	+	43.3463i	−0.228167	+	0.0611372i	0.142924	+	0.989734i	$0.454350\pi$
$710$	−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	0.824077	−	0.566478i	$-0.191694\pi$
$719$	536.036	+	309.481i	0.745530	+	0.430432i	−0.0785462	+	0.996910i	$0.525028\pi$
$720$	−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	$0.0128624\pi$
$727$			58.7377i			0.0807946i	−0.999184	+	0.0403973i	$0.987138\pi$
$728$	−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	−0.780993	−	0.624540i	$-0.785287\pi$
$733$	−114.680	+	114.680i	−0.156453	+	0.156453i	0.624540	+	0.780993i	$0.285287\pi$
$734$	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	−0.924315	−	0.381629i	$-0.875363\pi$
$739$	49.4982	−	184.730i	0.0669800	−	0.249973i	0.991295	+	0.131657i	$0.0420297\pi$
$740$			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	0.434732	−	0.900560i	$-0.356843\pi$
$743$	268.179	+	71.8585i	0.360941	+	0.0967139i	−0.0737908	+	0.997274i	$0.523510\pi$
$744$	−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	−0.997142	−	0.0755521i	$-0.975928\pi$
$751$	−1074.14	+	620.156i	−1.43028	+	0.825774i	−0.433141	+	0.901326i	$0.642595\pi$
$752$	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	0.980898	−	0.194525i	$-0.0623164\pi$
$757$	243.743	+	422.175i	0.321986	+	0.557695i	−0.658912	+	0.752220i	$0.728983\pi$
$758$	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	0.0203324	−	0.999793i	$-0.493528\pi$
$761$	409.294	−	109.670i	0.537837	−	0.144113i	0.517505	+	0.855680i	$0.326861\pi$
$762$	−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	0.894032	−	0.448003i	$-0.147865\pi$
$769$	1110.65	+	297.599i	1.44428	+	0.386995i	0.550253	+	0.834998i	$0.314531\pi$
$770$	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	−0.925486	−	0.378781i	$-0.876343\pi$
$773$	−242.244	−	904.069i	−0.313382	−	1.16956i	0.612104	−	0.790777i	$-0.290323\pi$
$774$	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	−0.844850	−	0.535003i	$-0.820311\pi$
$787$	−1030.19	+	276.039i	−1.30901	+	0.350748i	−0.464161	+	0.885751i	$0.653644\pi$
$788$	−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	−0.995020	−	0.0996795i	$-0.968218\pi$
$797$	−1258.35	−	726.507i	−1.57885	−	0.911552i	−0.583835	−	0.811872i	$-0.698448\pi$
$798$	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	0.887143	−	0.461495i	$-0.152687\pi$
$809$	35.5191	+	61.5210i	0.0439050	+	0.0760457i	−0.843238	+	0.537541i	$0.819353\pi$
$810$	−195.521	−	112.884i	−0.241384	−	0.139363i
$811$	688.757	−	688.757i	0.849269	−	0.849269i	−0.140773	−	0.990042i	$-0.544959\pi$
$811$	688.757	−	688.757i	0.849269	−	0.849269i	0.990042	+	0.140773i	$0.0449587\pi$
$812$	−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	−0.0640739	−	0.997945i	$-0.520409\pi$
$821$	−507.818	−	136.069i	−0.618536	−	0.165736i	−0.554462	+	0.832209i	$0.687076\pi$
$822$	9.27710	+	16.0684i	0.0112860	+	0.0195479i
$823$	−1054.57	−	608.856i	−1.28137	−	0.739801i	−0.304273	−	0.952585i	$-0.598414\pi$
$823$	−1054.57	−	608.856i	−1.28137	−	0.739801i	−0.977099	+	0.212784i	$0.931747\pi$
$824$	−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	0.200601	−	0.979673i	$-0.435711\pi$
$827$	−644.293	−	644.293i	−0.779072	−	0.779072i	−0.979673	+	0.200601i	$0.935711\pi$
$828$	39.5832	−	68.5602i	0.0478058	−	0.0828021i
$829$	681.917	−	393.705i	0.822578	−	0.474916i	−0.0287265	−	0.999587i	$-0.509145\pi$
$829$	681.917	−	393.705i	0.822578	−	0.474916i	0.851305	+	0.524672i	$0.175812\pi$
$830$	−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	−0.199883	−	0.979820i	$-0.564056\pi$
$839$	98.0991	−	26.2856i	0.116924	−	0.0313296i	0.316806	+	0.948490i	$0.397389\pi$
$840$	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	0.244668	−	0.969607i	$-0.421321\pi$
$853$	−618.373	−	618.373i	−0.724939	−	0.724939i	−0.969607	+	0.244668i	$0.921321\pi$
$854$	−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	$0.0361395\pi$
$857$			194.182i			0.226584i	−0.993562	+	0.113292i	$0.963861\pi$
$858$	−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	−0.706087	−	0.708125i	$-0.749541\pi$
$863$	1.75897	−	1.75897i	0.00203820	−	0.00203820i	0.708125	+	0.706087i	$0.249541\pi$
$864$	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	0.893916	−	0.448234i	$-0.147947\pi$
$877$	−91.5191	−	341.554i	−0.104355	−	0.389457i	−0.998271	+	0.0587764i	$0.981280\pi$
$878$	−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	0.238649	−	0.971106i	$-0.423295\pi$
$881$	1056.30	−	609.854i	1.19898	−	0.692229i	0.960327	+	0.278877i	$0.0899621\pi$
$882$	20.0167	−	74.7033i	0.0226947	−	0.0846976i
$883$		−	161.934i		−	0.183390i	−0.995787	−	0.0916952i	$-0.970771\pi$
$883$		−	161.934i		−	0.183390i	0.995787	−	0.0916952i	$-0.0292286\pi$
$884$	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	0.896782	−	0.442474i	$-0.145899\pi$
$887$	57.8301	+	100.165i	0.0651974	+	0.112925i	−0.831584	+	0.555399i	$0.812566\pi$
$888$	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	−0.546784	−	0.837273i	$-0.684148\pi$
$907$	−86.2343	+	49.7874i	−0.0950765	+	0.0548924i	0.451708	+	0.892166i	$0.350815\pi$
$908$	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	−0.475120	−	0.879921i	$-0.657595\pi$
$919$	481.991	−	834.834i	0.524474	−	0.908415i	0.999594	−	0.0284943i	$-0.00907124\pi$
$920$	−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	0.866646	−	0.498924i	$-0.166271\pi$
$929$	−123.886	−	462.347i	−0.133354	−	0.497683i	−0.999999	+	0.00124161i	$0.999605\pi$
$930$	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	−0.923465	−	0.383682i	$-0.874656\pi$
$941$	−507.937	+	507.937i	−0.539784	+	0.539784i	0.383682	+	0.923465i	$0.374656\pi$
$942$	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	0.830524	+	0.556983i	$0.188041\pi$
$947$	−158.360	+	591.006i	−0.167222	+	0.624083i	−0.997746	+	0.0670995i	$0.978626\pi$
$948$			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	0.886064	−	0.463562i	$-0.153429\pi$
$953$	884.041	+	510.401i	0.927640	+	0.535573i	0.0415756	+	0.999135i	$0.486762\pi$
$954$	−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	−0.757221	−	0.653158i	$-0.773444\pi$
$967$	−100.629	+	100.629i	−0.104063	+	0.104063i	0.653158	+	0.757221i	$0.273444\pi$
$968$	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	−0.169881	−	0.985465i	$-0.554338\pi$
$971$	746.211	−	1292.47i	0.768497	−	1.33108i	0.938378	−	0.345611i	$-0.112328\pi$
$972$	−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	0.00774697	−	0.999970i	$-0.497534\pi$
$977$	−474.362	−	127.105i	−0.485529	−	0.130097i	−0.493276	+	0.869873i	$0.664201\pi$
$978$	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	0.527909	−	0.849301i	$-0.322976\pi$
$983$	−315.927	−	315.927i	−0.321391	−	0.321391i	−0.849301	+	0.527909i	$0.822976\pi$
$984$	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	−0.883117	−	0.469154i	$-0.844559\pi$
$991$	−840.227	−	1455.32i	−0.847857	−	1.46853i	0.0352592	−	0.999378i	$-0.488774\pi$
$992$	−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	−0.944421	−	0.328737i	$-0.893377\pi$
$997$	−186.953	+	323.812i	−0.187516	+	0.324787i	0.756906	+	0.653524i	$0.226710\pi$
$998$	1534.90	−	886.172i	1.53797	−	0.887948i
$999$	44.2214	−	165.036i	0.0442656	−	0.165202i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.3.l.b.7.1	✓	12	13.7	odd	12	inner
39.3.l.b.28.1	yes	12	1.1	even	1	trivial
117.3.bd.d.28.3		12	3.2	odd	2
117.3.bd.d.46.3		12	39.20	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(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

Introduction

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