LMFDB - Embedded newform 431.3.f.a.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [431,3,Mod(47,431)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(431, base_ring=CyclotomicField(86))

chi = DirichletCharacter(H, H._module([63]))

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

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

chi := DirichletCharacter("431.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 431 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	431.f (of order $86$, degree $42$, 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:	$11.7438993939$
Analytic rank:	$0$
Dimension:	$2982$
Relative dimension:	$71$ over $\Q(\zeta_{86})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{86}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	431.101
Dual form			431.3.f.a.367.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67388 + 3.25571i) q^{2} +(0.204533 + 1.85887i) q^{3} +(-5.47036 - 7.64616i) q^{4} +(4.80381 + 2.25193i) q^{5} +(-6.39430 - 2.44561i) q^{6} +(0.397750 + 1.78556i) q^{7} +(19.5632 - 2.87911i) q^{8} +(5.37113 - 1.19647i) q^{9} +(-15.3726 + 11.8704i) q^{10} +(-10.5510 + 5.92152i) q^{11} +(13.0943 - 11.7326i) q^{12} +(11.5747 - 5.95095i) q^{13} +(-6.47904 - 1.69384i) q^{14} +(-3.20350 + 9.39024i) q^{15} +(-11.2306 + 32.9196i) q^{16} +(13.1145 + 23.3675i) q^{17} +(-5.09525 + 19.4896i) q^{18} +(-26.0993 + 12.2349i) q^{19} +(-9.05992 - 49.0496i) q^{20} +(-3.23776 + 1.10457i) q^{21} +(-1.61765 - 44.2630i) q^{22} +(7.27573 + 7.54649i) q^{23} +(9.35322 + 35.7766i) q^{24} +(2.01356 + 2.41955i) q^{25} +47.6450i q^{26} +(8.75698 + 25.6688i) q^{27} +(11.4768 - 12.8089i) q^{28} +(-32.1584 + 44.9493i) q^{29} +(-25.2096 - 26.1478i) q^{30} +(-16.6892 - 43.6355i) q^{31} +(-33.4797 - 34.7256i) q^{32} +(-13.1654 - 18.4018i) q^{33} +(-98.0300 + 3.58264i) q^{34} +(-2.11024 + 9.47318i) q^{35} +(-38.5304 - 34.5234i) q^{36} +(-2.04106 - 0.533603i) q^{37} +(3.85387 - 105.452i) q^{38} +(13.4294 + 20.2986i) q^{39} +(100.462 + 30.2244i) q^{40} +(3.19822 - 9.37474i) q^{41} +(1.82345 - 12.3901i) q^{42} +(-46.5736 + 60.3148i) q^{43} +(102.995 + 48.2820i) q^{44} +(28.4963 + 6.34782i) q^{45} +(-36.7479 + 11.0558i) q^{46} +(2.93194 - 40.0589i) q^{47} +(-63.4902 - 14.1430i) q^{48} +(41.3370 - 19.3780i) q^{49} +(-11.2478 + 2.50556i) q^{50} +(-40.7547 + 29.1575i) q^{51} +(-108.820 - 55.9480i) q^{52} +(87.3782 - 6.39526i) q^{53} +(-98.2283 - 14.4562i) q^{54} +(-64.0200 + 4.68566i) q^{55} +(12.9221 + 33.7861i) q^{56} +(-28.0812 - 46.0127i) q^{57} +(-92.5126 - 179.938i) q^{58} +(-23.2160 + 45.1555i) q^{59} +(89.3236 - 26.8735i) q^{60} +(-6.68564 - 15.7326i) q^{61} +(170.000 + 18.7053i) q^{62} +(4.27273 + 9.11456i) q^{63} +(35.8664 - 10.7906i) q^{64} +(69.0037 - 2.52184i) q^{65} +(81.9481 - 12.0603i) q^{66} +(100.137 + 26.1791i) q^{67} +(106.931 - 228.104i) q^{68} +(-12.5398 + 15.0681i) q^{69} +(-27.3097 - 22.7273i) q^{70} +(5.11764 - 69.9222i) q^{71} +(101.632 - 38.8709i) q^{72} +(6.77721 + 10.2438i) q^{73} +(5.15374 - 5.75192i) q^{74} +(-4.08578 + 4.23782i) q^{75} +(236.322 + 132.631i) q^{76} +(-14.7699 - 16.4842i) q^{77} +(-88.5656 + 9.74499i) q^{78} +(8.80568 - 29.2688i) q^{79} +(-128.082 + 132.849i) q^{80} +(-1.08143 + 0.506955i) q^{81} +(25.1680 + 26.1046i) q^{82} +(-111.141 + 12.2290i) q^{83} +(26.1574 + 18.7140i) q^{84} +(10.3774 + 141.786i) q^{85} +(-118.409 - 252.590i) q^{86} +(-90.1322 - 50.5846i) q^{87} +(-189.363 + 146.222i) q^{88} +(6.74264 - 1.24543i) q^{89} +(-68.3659 + 82.1502i) q^{90} +(15.2296 + 18.3002i) q^{91} +(17.9008 - 96.9134i) q^{92} +(77.6990 - 39.9478i) q^{93} +(125.513 + 76.5993i) q^{94} -152.928 q^{95} +(57.7026 - 69.3369i) q^{96} +(33.2592 - 10.0062i) q^{97} +(-6.10389 + 167.018i) q^{98} +(-49.5860 + 44.4293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2982 q - 43 q^{2} - 41 q^{3} - 187 q^{4} - 41 q^{5} - 33 q^{6} - 43 q^{7} - 37 q^{8} - 252 q^{9} - 23 q^{10} + 187 q^{11} + 19 q^{12} - 43 q^{13} - 43 q^{14} - 71 q^{15} - 359 q^{16} - 43 q^{17} - 93 q^{18}+ \cdots - 609 q^{99}+O(q^{100}) $ 2982 * q - 43 * q^2 - 41 * q^3 - 187 * q^4 - 41 * q^5 - 33 * q^6 - 43 * q^7 - 37 * q^8 - 252 * q^9 - 23 * q^10 + 187 * q^11 + 19 * q^12 - 43 * q^13 - 43 * q^14 - 71 * q^15 - 359 * q^16 - 43 * q^17 - 93 * q^18 - 55 * q^19 + 9 * q^20 - 172 * q^21 - 47 * q^22 + 45 * q^23 + 17 * q^24 - 436 * q^25 + 37 * q^27 - 43 * q^28 - 93 * q^29 - 911 * q^30 - 43 * q^31 + 181 * q^32 + 733 * q^33 - 43 * q^34 - 43 * q^35 - 521 * q^36 - 43 * q^37 + 691 * q^38 - 43 * q^39 + 199 * q^40 + 456 * q^41 - 43 * q^42 - 43 * q^43 - 161 * q^44 - 3 * q^45 - 279 * q^46 - 43 * q^47 + 271 * q^48 + 362 * q^49 - 21 * q^50 - 43 * q^51 - 2107 * q^52 + 53 * q^53 - 2864 * q^54 + 111 * q^55 - 1978 * q^56 + 11 * q^57 - 349 * q^58 + 59 * q^59 + 29 * q^60 - 1433 * q^61 - 43 * q^62 - 2451 * q^63 - 801 * q^64 - 43 * q^65 - 253 * q^66 + 3053 * q^67 - 43 * q^68 + 25 * q^69 - 1978 * q^70 + 2021 * q^71 - 63 * q^72 - 43 * q^73 - 43 * q^74 - 401 * q^75 - 225 * q^76 + 645 * q^77 + 344 * q^78 + 3397 * q^79 + 227 * q^80 - 1054 * q^81 - 845 * q^82 - 43 * q^83 + 6106 * q^84 - 43 * q^85 - 43 * q^86 - 1021 * q^87 + 6277 * q^88 - 43 * q^89 - 815 * q^90 - 147 * q^91 - 239 * q^92 + 2193 * q^93 - 43 * q^94 - 70 * q^95 + 129 * q^96 + 125 * q^97 + 643 * q^98 - 609 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/431\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{37}{86}\right)$

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 $

$2$	−1.67388	+	3.25571i	−0.836938	+	1.62786i	−0.0600691	+	0.998194i	$0.519132\pi$
$2$	−1.67388	+	3.25571i	−0.836938	+	1.62786i	−0.776869	+	0.629662i	$0.783193\pi$
$3$	0.204533	+	1.85887i	0.0681778	+	0.619622i	0.978576	+	0.205888i	$0.0660083\pi$
$3$	0.204533	+	1.85887i	0.0681778	+	0.619622i	−0.910398	+	0.413734i	$0.864224\pi$
$4$	−5.47036	−	7.64616i	−1.36759	−	1.91154i
$5$	4.80381	+	2.25193i	0.960762	+	0.450387i	0.840175	−	0.542316i	$-0.182452\pi$
$5$	4.80381	+	2.25193i	0.960762	+	0.450387i	0.120587	+	0.992703i	$0.461522\pi$
$6$	−6.39430	−	2.44561i	−1.06572	−	0.407602i
$7$	0.397750	+	1.78556i	0.0568214	+	0.255079i	0.996118	−	0.0880263i	$-0.0280560\pi$
$7$	0.397750	+	1.78556i	0.0568214	+	0.255079i	−0.939297	+	0.343106i	$0.888521\pi$
$8$	19.5632	−	2.87911i	2.44540	−	0.359889i
$9$	5.37113	−	1.19647i	0.596792	−	0.132941i
$10$	−15.3726	+	11.8704i	−1.53726	+	1.18704i
$11$	−10.5510	+	5.92152i	−0.959184	+	0.538320i	−0.888349	−	0.459168i	$-0.848148\pi$
$11$	−10.5510	+	5.92152i	−0.959184	+	0.538320i	−0.0708344	+	0.997488i	$0.522566\pi$
$12$	13.0943	−	11.7326i	1.09119	−	0.977714i
$13$	11.5747	−	5.95095i	0.890360	−	0.457765i	0.0493475	−	0.998782i	$-0.484286\pi$
$13$	11.5747	−	5.95095i	0.890360	−	0.457765i	0.841012	+	0.541016i	$0.181960\pi$
$14$	−6.47904	−	1.69384i	−0.462789	−	0.120989i
$15$	−3.20350	+	9.39024i	−0.213567	+	0.626016i
$16$	−11.2306	+	32.9196i	−0.701913	+	2.05748i
$17$	13.1145	+	23.3675i	0.771440	+	1.37456i	0.922485	+	0.386033i	$0.126155\pi$
$17$	13.1145	+	23.3675i	0.771440	+	1.37456i	−0.151044	+	0.988527i	$0.548264\pi$
$18$	−5.09525	+	19.4896i	−0.283069	+	1.08276i
$19$	−26.0993	+	12.2349i	−1.37365	+	0.643940i	−0.963408	−	0.268037i	$-0.913625\pi$
$19$	−26.0993	+	12.2349i	−1.37365	+	0.643940i	−0.410240	+	0.911978i	$0.634555\pi$
$20$	−9.05992	−	49.0496i	−0.452996	−	2.45248i
$21$	−3.23776	+	1.10457i	−0.154179	+	0.0525985i
$22$	−1.61765	−	44.2630i	−0.0735297	−	2.01195i
$23$	7.27573	+	7.54649i	0.316336	+	0.328108i	0.859130	−	0.511758i	$-0.171006\pi$
$23$	7.27573	+	7.54649i	0.316336	+	0.328108i	−0.542794	+	0.839866i	$0.682633\pi$
$24$	9.35322	+	35.7766i	0.389717	+	1.49069i
$25$	2.01356	+	2.41955i	0.0805425	+	0.0967819i
$26$			47.6450i			1.83250i
$27$	8.75698	+	25.6688i	0.324333	+	0.950697i
$28$	11.4768	−	12.8089i	0.409886	−	0.457460i
$29$	−32.1584	+	44.9493i	−1.10891	+	1.54997i	−0.307809	+	0.951448i	$0.599596\pi$
$29$	−32.1584	+	44.9493i	−1.10891	+	1.54997i	−0.801103	+	0.598527i	$0.795753\pi$
$30$	−25.2096	−	26.1478i	−0.840321	−	0.871593i
$31$	−16.6892	−	43.6355i	−0.538360	−	1.40760i	−0.883227	−	0.468945i	$-0.844634\pi$
$31$	−16.6892	−	43.6355i	−0.538360	−	1.40760i	0.344868	−	0.938651i	$-0.387924\pi$
$32$	−33.4797	−	34.7256i	−1.04624	−	1.08518i
$33$	−13.1654	−	18.4018i	−0.398950	−	0.557630i
$34$	−98.0300	+	3.58264i	−2.88323	+	0.105372i
$35$	−2.11024	+	9.47318i	−0.0602926	+	0.270662i
$36$	−38.5304	−	34.5234i	−1.07029	−	0.958984i
$37$	−2.04106	−	0.533603i	−0.0551638	−	0.0144217i	0.225249	−	0.974301i	$-0.427681\pi$
$37$	−2.04106	−	0.533603i	−0.0551638	−	0.0144217i	−0.280412	+	0.959880i	$0.590471\pi$
$38$	3.85387	−	105.452i	0.101418	−	2.77504i
$39$	13.4294	+	20.2986i	0.344344	+	0.520477i
$40$	100.462	+	30.2244i	2.51154	+	0.755610i
$41$	3.19822	−	9.37474i	0.0780053	−	0.228652i	−0.900507	−	0.434842i	$-0.856804\pi$
$41$	3.19822	−	9.37474i	0.0780053	−	0.228652i	0.978512	+	0.206190i	$0.0661065\pi$
$42$	1.82345	−	12.3901i	0.0434154	−	0.295003i
$43$	−46.5736	+	60.3148i	−1.08311	+	1.40267i	−0.174681	+	0.984625i	$0.555889\pi$
$43$	−46.5736	+	60.3148i	−1.08311	+	1.40267i	−0.908426	+	0.418045i	$0.862715\pi$
$44$	102.995	+	48.2820i	2.34079	+	1.09732i
$45$	28.4963	+	6.34782i	0.633251	+	0.141063i
$46$	−36.7479	+	11.0558i	−0.798867	+	0.240343i
$47$	2.93194	−	40.0589i	0.0623816	−	0.852318i	−0.870508	−	0.492155i	$-0.836209\pi$
$47$	2.93194	−	40.0589i	0.0623816	−	0.852318i	0.932889	−	0.360163i	$-0.117279\pi$
$48$	−63.4902	−	14.1430i	−1.32271	−	0.294647i
$49$	41.3370	−	19.3780i	0.843611	−	0.395469i
$50$	−11.2478	+	2.50556i	−0.224956	+	0.0501111i
$51$	−40.7547	+	29.1575i	−0.799113	+	0.571716i
$52$	−108.820	−	55.9480i	−2.09268	−	1.07592i
$53$	87.3782	−	6.39526i	1.64865	−	0.120665i	0.783234	−	0.621727i	$-0.213569\pi$
$53$	87.3782	−	6.39526i	1.64865	−	0.120665i	0.865411	+	0.501062i	$0.167057\pi$
$54$	−98.2283	−	14.4562i	−1.81904	−	0.267708i
$55$	−64.0200	+	4.68566i	−1.16400	+	0.0851938i
$56$	12.9221	+	33.7861i	0.230751	+	0.603323i
$57$	−28.0812	−	46.0127i	−0.492652	−	0.807241i
$58$	−92.5126	−	179.938i	−1.59504	−	3.10238i
$59$	−23.2160	+	45.1555i	−0.393492	+	0.765347i	−0.999548	−	0.0300751i	$-0.990425\pi$
$59$	−23.2160	+	45.1555i	−0.393492	+	0.765347i	0.606055	+	0.795422i	$0.292751\pi$
$60$	89.3236	−	26.8735i	1.48873	−	0.447891i
$61$	−6.68564	−	15.7326i	−0.109601	−	0.257912i	0.856467	−	0.516202i	$-0.172655\pi$
$61$	−6.68564	−	15.7326i	−0.109601	−	0.257912i	−0.966067	+	0.258291i	$0.916841\pi$
$62$	170.000	+	18.7053i	2.74194	+	0.301699i
$63$	4.27273	+	9.11456i	0.0678211	+	0.144676i
$64$	35.8664	−	10.7906i	0.560413	−	0.168603i
$65$	69.0037	−	2.52184i	1.06160	−	0.0387975i
$66$	81.9481	−	12.0603i	1.24164	−	0.182731i
$67$	100.137	+	26.1791i	1.49458	+	0.390733i	0.907934	−	0.419113i	$-0.137659\pi$
$67$	100.137	+	26.1791i	1.49458	+	0.390733i	0.586642	+	0.809846i	$0.300450\pi$
$68$	106.931	−	228.104i	1.57251	−	3.35447i
$69$	−12.5398	+	15.0681i	−0.181736	+	0.218378i
$70$	−27.3097	−	22.7273i	−0.390138	−	0.324675i
$71$	5.11764	−	69.9222i	0.0720795	−	0.984819i	−0.831257	−	0.555888i	$-0.812378\pi$
$71$	5.11764	−	69.9222i	0.0720795	−	0.984819i	0.903337	−	0.428932i	$-0.141110\pi$
$72$	101.632	−	38.8709i	1.41155	−	0.539874i
$73$	6.77721	+	10.2438i	0.0928385	+	0.140326i	0.877460	−	0.479649i	$-0.159236\pi$
$73$	6.77721	+	10.2438i	0.0928385	+	0.140326i	−0.784622	+	0.619974i	$0.787143\pi$
$74$	5.15374	−	5.75192i	0.0696451	−	0.0777286i
$75$	−4.08578	+	4.23782i	−0.0544770	+	0.0565043i
$76$	236.322	+	132.631i	3.10951	+	1.74514i
$77$	−14.7699	−	16.4842i	−0.191817	−	0.214080i
$78$	−88.5656	+	9.74499i	−1.13546	+	0.124936i
$79$	8.80568	−	29.2688i	0.111464	−	0.370491i	−0.883780	−	0.467903i	$-0.845010\pi$
$79$	8.80568	−	29.2688i	0.111464	−	0.370491i	0.995244	+	0.0974114i	$0.0310563\pi$
$80$	−128.082	+	132.849i	−1.60103	+	1.66061i
$81$	−1.08143	+	0.506955i	−0.0133510	+	0.00625870i
$82$	25.1680	+	26.1046i	0.306927	+	0.318349i
$83$	−111.141	+	12.2290i	−1.33905	+	0.147338i	−0.750365	−	0.661023i	$-0.770122\pi$
$83$	−111.141	+	12.2290i	−1.33905	+	0.147338i	−0.588687	+	0.808361i	$0.700355\pi$
$84$	26.1574	+	18.7140i	0.311398	+	0.222786i
$85$	10.3774	+	141.786i	0.122087	+	1.66807i
$86$	−118.409	−	252.590i	−1.37685	−	2.93709i
$87$	−90.1322	−	50.5846i	−1.03600	−	0.581432i
$88$	−189.363	+	146.222i	−2.15186	+	1.66161i
$89$	6.74264	−	1.24543i	0.0757600	−	0.0139936i	−0.143622	−	0.989633i	$-0.545875\pi$
$89$	6.74264	−	1.24543i	0.0757600	−	0.0139936i	0.219382	+	0.975639i	$0.429596\pi$
$90$	−68.3659	+	82.1502i	−0.759621	+	0.912780i
$91$	15.2296	+	18.3002i	0.167358	+	0.201102i
$92$	17.9008	−	96.9134i	0.194574	−	1.05341i
$93$	77.6990	−	39.9478i	0.835474	−	0.429547i
$94$	125.513	+	76.5993i	1.33524	+	0.814886i
$95$	−152.928			−1.60977
$96$	57.7026	−	69.3369i	0.601069	−	0.722259i
$97$	33.2592	−	10.0062i	0.342879	−	0.103157i	−0.112005	−	0.993708i	$-0.535727\pi$
$97$	33.2592	−	10.0062i	0.342879	−	0.103157i	0.454884	+	0.890551i	$0.349681\pi$
$98$	−6.10389	+	167.018i	−0.0622846	+	1.70426i
$99$	−49.5860	+	44.4293i	−0.500869	+	0.448780i
$100$	7.48534	−	28.6318i	0.0748534	−	0.286318i
$101$	1.51047	−	5.02060i	0.0149552	−	0.0497089i	−0.949800	−	0.312856i	$-0.898714\pi$
$101$	1.51047	−	5.02060i	0.0149552	−	0.0497089i	0.964756	+	0.263148i	$0.0847606\pi$
$102$	−26.7101	−	181.492i	−0.261863	−	1.77933i
$103$	−175.436	−	32.4046i	−1.70326	−	0.314608i	−0.760814	−	0.648970i	$-0.775200\pi$
$103$	−175.436	−	32.4046i	−1.70326	−	0.314608i	−0.942445	+	0.334362i	$0.891479\pi$
$104$	209.305	−	149.745i	2.01254	−	1.43985i
$105$	−18.0410	−	1.98507i	−0.171819	−	0.0189055i
$106$	−125.439	+	295.183i	−1.18339	+	2.78475i
$107$	23.5903	−	42.0335i	0.220471	−	0.392837i	−0.739406	−	0.673260i	$-0.764893\pi$
$107$	23.5903	−	42.0335i	0.220471	−	0.392837i	0.959876	+	0.280423i	$0.0904749\pi$
$108$	148.364	−	207.375i	1.37374	−	1.92014i
$109$	−109.256	+	61.3172i	−1.00235	+	0.562543i	−0.901692	−	0.432378i	$-0.857675\pi$
$109$	−109.256	+	61.3172i	−1.00235	+	0.562543i	−0.100653	+	0.994922i	$0.532093\pi$
$110$	91.9064	−	216.274i	0.835513	−	1.96613i
$111$	0.574432	−	3.90320i	0.00517506	−	0.0351639i
$112$	−63.2468	−	6.95912i	−0.564703	−	0.0621350i
$113$	−31.9860	+	106.317i	−0.283062	+	0.940857i	0.692553	+	0.721367i	$0.256486\pi$
$113$	−31.9860	+	106.317i	−0.283062	+	0.940857i	−0.975615	+	0.219490i	$0.929561\pi$
$114$	196.809	−	14.4045i	1.72639	−	0.126356i
$115$	17.9570	+	52.6364i	0.156148	+	0.457707i
$116$	519.608			4.47938
$117$	55.0490	−	45.8121i	0.470504	−	0.391556i
$118$	−108.152	−	151.169i	−0.916546	−	1.28110i
$119$	−36.5077	+	32.7111i	−0.306788	+	0.274883i
$120$	−35.6354	+	192.927i	−0.296961	+	1.60772i
$121$	13.2259	−	21.6714i	0.109305	−	0.179103i
$122$	62.4118	+	4.56796i	0.511572	+	0.0374423i
$123$	18.0805	+	4.02761i	0.146996	+	0.0327448i
$124$	−242.348	+	366.310i	−1.95442	+	2.95411i
$125$	−29.3240	−	112.166i	−0.234592	−	0.897328i
$126$	−36.8264	−	1.34587i	−0.292273	−	0.0106815i
$127$	−74.5619	+	8.20415i	−0.587102	+	0.0645996i	−0.398044	−	0.917366i	$-0.630311\pi$
$127$	−74.5619	+	8.20415i	−0.587102	+	0.0645996i	−0.189058	+	0.981966i	$0.560543\pi$
$128$	10.1412	−	54.9037i	0.0792283	−	0.428935i
$129$	−121.643	−	74.2377i	−0.942970	−	0.575486i
$130$	−107.293	+	228.877i	−0.825333	+	1.76060i
$131$	1.55888	−	10.5924i	0.0118998	−	0.0808580i	−0.982567	−	0.185909i	$-0.940477\pi$
$131$	1.55888	−	10.5924i	0.0118998	−	0.0808580i	0.994467	+	0.105051i	$0.0335004\pi$
$132$	−68.6839	+	201.329i	−0.520332	+	1.52522i
$133$	−32.2270	−	41.7354i	−0.242308	−	0.313800i
$134$	−252.848	+	282.195i	−1.88693	+	2.10593i
$135$	−15.7376	+	143.028i	−0.116575	+	1.05947i
$136$	323.839	+	419.386i	2.38117	+	3.08372i
$137$	10.9956	+	150.233i	0.0802600	+	1.09659i	0.873223	+	0.487320i	$0.162025\pi$
$137$	10.9956	+	150.233i	0.0802600	+	1.09659i	−0.792963	+	0.609269i	$0.791463\pi$
$138$	−28.0674	−	66.0481i	−0.203387	−	0.478609i
$139$	124.195	+	47.5005i	0.893487	+	0.341730i	0.760462	−	0.649383i	$-0.224973\pi$
$139$	124.195	+	47.5005i	0.893487	+	0.341730i	0.133026	+	0.991113i	$0.457531\pi$
$140$	83.9772	−	35.6865i	0.599837	−	0.254903i
$141$	75.0639	−	2.74332i	0.532368	−	0.0194561i
$142$	219.080	+	133.703i	1.54282	+	0.941568i
$143$	−86.8860	+	131.328i	−0.607594	+	0.918380i
$144$	−20.9337	+	190.253i	−0.145373	+	1.32120i
$145$	−255.706	+	143.509i	−1.76349	+	0.989718i
$146$	−44.6950	+	4.91784i	−0.306130	+	0.0336839i
$147$	44.4759	+	72.8764i	0.302557	+	0.495758i
$148$	7.08532	+	18.5253i	0.0478738	+	0.125171i
$149$	−134.571	−	63.0842i	−0.903160	−	0.423384i	−0.0836808	−	0.996493i	$-0.526668\pi$
$149$	−134.571	−	63.0842i	−0.903160	−	0.423384i	−0.819480	+	0.573108i	$0.805737\pi$
$150$	−6.95805	−	20.3957i	−0.0463870	−	0.135971i
$151$	264.824	+	19.3826i	1.75380	+	0.128362i	0.911673	−	0.410916i	$-0.134791\pi$
$151$	264.824	+	19.3826i	1.75380	+	0.128362i	0.842128	+	0.539278i	$0.181303\pi$
$152$	−475.362	+	314.496i	−3.12738	+	2.06905i
$153$	98.3982	+	109.819i	0.643126	+	0.717771i
$154$	78.3906	−	20.4940i	0.509030	−	0.133078i
$155$	18.0927	−	247.199i	0.116727	−	1.59484i
$156$	81.7426	−	213.724i	0.523991	−	1.37003i
$157$	−4.07246	+	9.58329i	−0.0259392	+	0.0610401i	−0.932810	−	0.360370i	$-0.882651\pi$
$157$	−4.07246	+	9.58329i	−0.0259392	+	0.0610401i	0.906870	+	0.421410i	$0.138465\pi$
$158$	80.5512	+	77.6611i	0.509818	+	0.491526i
$159$	29.7597	+	161.116i	0.187168	+	1.01331i
$160$	−82.6304	−	242.210i	−0.516440	−	1.51381i
$161$	−10.5808	+	15.9928i	−0.0657190	+	0.0993344i
$162$	0.159686	−	4.36942i	0.000985719	−	0.0269717i
$163$	149.630	−	57.2288i	0.917978	−	0.351097i	0.147867	−	0.989007i	$-0.452759\pi$
$163$	149.630	−	57.2288i	0.917978	−	0.351097i	0.770110	+	0.637911i	$0.220201\pi$
$164$	−89.1762	+	26.8291i	−0.543757	+	0.163592i
$165$	−21.8042	−	118.046i	−0.132147	−	0.715432i
$166$	146.223	−	382.314i	0.880860	−	2.30310i
$167$	183.969	−	177.368i	1.10161	−	1.06209i	0.103891	−	0.994589i	$-0.466871\pi$
$167$	183.969	−	177.368i	1.10161	−	1.06209i	0.997719	−	0.0674976i	$-0.0215015\pi$
$168$	−60.1608	+	30.9308i	−0.358100	+	0.184112i
$169$	0.225148	−	0.314699i	0.00133224	−	0.00186212i
$170$	−478.985	−	203.547i	−2.81756	−	1.19733i
$171$	−125.544	+	96.9421i	−0.734177	+	0.566913i
$172$	715.951	+	26.1654i	4.16251	+	0.152125i
$173$	105.475	+	172.827i	0.609681	+	0.999001i	0.997026	+	0.0770657i	$0.0245551\pi$
$173$	105.475	+	172.827i	0.609681	+	0.999001i	−0.387345	+	0.921935i	$0.626608\pi$
$174$	315.559	−	208.772i	1.81356	−	1.19984i
$175$	−3.51934	+	4.55770i	−0.0201105	+	0.0260440i
$176$	−76.4397	−	413.838i	−0.434317	−	2.35135i
$177$	−88.6865	−	33.9197i	−0.501054	−	0.191637i
$178$	−7.23160	+	24.0368i	−0.0406269	+	0.135038i
$179$	209.015	+	117.305i	1.16768	+	0.655333i	0.947384	−	0.320100i	$-0.103717\pi$
$179$	209.015	+	117.305i	1.16768	+	0.655333i	0.220295	+	0.975433i	$0.429298\pi$
$180$	−107.348	−	252.612i	−0.596380	−	1.40340i
$181$	−7.28215	+	32.6907i	−0.0402329	+	0.180611i	−0.992006	−	0.126192i	$-0.959724\pi$
$181$	−7.28215	+	32.6907i	−0.0402329	+	0.180611i	0.951773	+	0.306803i	$0.0992594\pi$
$182$	−85.0728	+	18.9508i	−0.467433	+	0.104125i
$183$	27.8774	−	15.6456i	0.152336	−	0.0854949i
$184$	164.064	+	126.686i	0.891652	+	0.688511i
$185$	−8.60323	−	7.15966i	−0.0465039	−	0.0387009i
$186$			319.833i			1.71953i
$187$	−276.743	−	168.894i	−1.47991	−	0.903174i
$188$	−322.336	+	196.719i	−1.71455	+	1.04638i
$189$	−42.3500	+	25.8458i	−0.224074	+	0.136750i
$190$	255.983	−	497.891i	1.34728	−	2.62048i
$191$	112.579	−	145.795i	0.589419	−	0.763324i	−0.398688	−	0.917086i	$-0.630535\pi$
$191$	112.579	−	145.795i	0.589419	−	0.763324i	0.988108	+	0.153763i	$0.0491392\pi$
$192$	27.3942	+	64.4639i	0.142678	+	0.335749i
$193$	−258.040	+	67.4604i	−1.33699	+	0.349536i	−0.851339	−	0.524615i	$-0.824209\pi$
$193$	−258.040	+	67.4604i	−1.33699	+	0.349536i	−0.485654	+	0.874151i	$0.661418\pi$
$194$	−23.0945	+	125.032i	−0.119044	+	0.644493i
$195$	18.8013	+	127.753i	0.0964170	+	0.655143i
$196$	−374.295	−	210.065i	−1.90967	−	1.07176i
$197$	−213.082	+	47.4660i	−1.08163	+	0.240944i	−0.721820	−	0.692080i	$-0.756694\pi$
$197$	−213.082	+	47.4660i	−1.08163	+	0.240944i	−0.359813	+	0.933024i	$0.617159\pi$
$198$	−61.6480	−	235.807i	−0.311354	−	1.19094i
$199$	82.1925	+	42.2581i	0.413028	+	0.212352i	0.651258	−	0.758856i	$-0.274242\pi$
$199$	82.1925	+	42.2581i	0.413028	+	0.212352i	−0.238230	+	0.971209i	$0.576567\pi$
$200$	46.3579	+	41.5369i	0.231790	+	0.207684i
$201$	−28.1822	+	191.495i	−0.140210	+	0.952712i
$202$	13.8173	+	13.3215i	0.0684023	+	0.0659481i
$203$	−93.0504	−	39.5421i	−0.458377	−	0.194789i
$204$	445.886	+	152.115i	2.18572	+	0.745663i
$205$	36.4749	−	37.8323i	0.177926	−	0.184548i
$206$	399.158	−	516.927i	1.93766	−	2.50935i
$207$	48.1080	+	31.8280i	0.232406	+	0.153758i
$208$	65.9123	+	447.867i	0.316886	+	2.15320i
$209$	202.926	−	283.638i	0.970936	−	1.35712i
$210$	36.6612	−	55.4135i	0.174577	−	0.263874i
$211$	151.475	−	126.058i	0.717891	−	0.597433i	−0.206696	−	0.978405i	$-0.566271\pi$
$211$	151.475	−	126.058i	0.717891	−	0.597433i	0.924587	+	0.380972i	$0.124411\pi$
$212$	−526.889	−	633.124i	−2.48533	−	2.98643i
$213$	131.023	−	4.78841i	0.615130	−	0.0224808i
$214$	97.3617	+	147.162i	0.454961	+	0.687674i
$215$	−359.556	+	184.860i	−1.67235	+	0.859816i
$216$	245.218	+	476.952i	1.13527	+	2.20811i
$217$	71.2755	−	47.1554i	0.328458	−	0.217306i
$218$	−16.7508	−	458.342i	−0.0768384	−	2.10249i
$219$	−17.6556	+	14.6931i	−0.0806193	+	0.0670919i
$220$	386.040	+	463.875i	1.75473	+	2.10852i
$221$	290.855	+	192.428i	1.31609	+	0.870714i
$222$	11.7462	+	8.40366i	0.0529106	+	0.0378543i
$223$	298.446	−	43.9221i	1.33832	−	0.196960i	0.561917	−	0.827194i	$-0.310064\pi$
$223$	298.446	−	43.9221i	1.33832	−	0.196960i	0.776406	+	0.630233i	$0.217041\pi$
$224$	48.6880	−	73.5920i	0.217357	−	0.328536i
$225$	13.7100	+	10.5865i	0.0609335	+	0.0470513i
$226$	−292.596	−	282.098i	−1.29467	−	1.24822i
$227$	−89.1477	+	261.313i	−0.392721	+	1.15116i	0.554942	+	0.831889i	$0.312740\pi$
$227$	−89.1477	+	261.313i	−0.392721	+	1.15116i	−0.947663	+	0.319271i	$0.896562\pi$
$228$	−198.207	+	466.419i	−0.869328	+	2.04570i
$229$	275.638	−	285.896i	1.20366	−	1.24845i	0.243219	−	0.969972i	$-0.421797\pi$
$229$	275.638	−	285.896i	1.20366	−	1.24845i	0.960442	−	0.278482i	$-0.0898311\pi$
$230$	−201.427	−	29.6439i	−0.875768	−	0.128886i
$231$	27.6209	−	30.8268i	0.119571	−	0.133449i
$232$	−499.709	+	971.940i	−2.15392	+	4.18940i
$233$	258.679	−	67.6275i	1.11021	−	0.290247i	0.347947	−	0.937514i	$-0.386879\pi$
$233$	258.679	−	67.6275i	1.11021	−	0.290247i	0.762263	+	0.647268i	$0.224088\pi$
$234$	57.0058	+	255.907i	0.243615	+	1.09362i
$235$	104.295	−	185.833i	0.443807	−	0.790779i
$236$	472.266	−	69.5032i	2.00113	−	0.294505i
$237$	56.2079	+	10.3821i	0.237164	+	0.0438064i
$238$	−45.3884	−	173.613i	−0.190707	−	0.729466i
$239$	27.5438	−	11.7049i	0.115246	−	0.0489743i	−0.332714	−	0.943028i	$-0.607964\pi$
$239$	27.5438	−	11.7049i	0.115246	−	0.0489743i	0.447960	+	0.894053i	$0.352151\pi$
$240$	−273.146	−	210.916i	−1.13811	−	0.878817i
$241$	237.254	+	121.980i	0.984454	+	0.506143i	0.873049	−	0.487632i	$-0.162139\pi$
$241$	237.254	+	121.980i	0.984454	+	0.506143i	0.111405	+	0.993775i	$0.464465\pi$
$242$	48.4175	+	79.3350i	0.200072	+	0.327831i
$243$	125.994	+	206.449i	0.518495	+	0.849586i
$244$	−83.7214	+	137.183i	−0.343120	+	0.562224i
$245$	242.213			0.988624
$246$	−43.3773	+	52.1233i	−0.176331	+	0.211883i
$247$	−229.282	+	296.930i	−0.928268	+	1.20215i
$248$	−452.125	−	805.601i	−1.82309	−	3.24839i
$249$	−45.4643	−	204.096i	−0.182587	−	0.819662i
$250$	414.265	+	92.2814i	1.65706	+	0.369126i
$251$	−205.010	+	87.1197i	−0.816772	+	0.347090i	−0.758878	−	0.651232i	$-0.774252\pi$
$251$	−205.010	+	87.1197i	−0.816772	+	0.347090i	−0.0578934	+	0.998323i	$0.518438\pi$
$252$	46.3180	−	82.5299i	0.183802	−	0.327500i
$253$	−121.453	−	36.5398i	−0.480052	−	0.144426i
$254$	98.0972	−	256.485i	0.386209	−	1.00978i
$255$	−261.439	+	48.2902i	−1.02525	+	0.189373i
$256$	280.356	+	216.484i	1.09514	+	0.845639i
$257$	2.13367	+	3.22504i	0.00830220	+	0.0125488i	0.838125	−	0.545478i	$-0.183652\pi$
$257$	2.13367	+	3.22504i	0.00830220	+	0.0125488i	−0.829823	+	0.558027i	$0.811559\pi$
$258$	445.312	−	271.770i	1.72602	−	1.05337i
$259$	0.140947	−	3.85667i	0.000544198	−	0.0148906i
$260$	−396.758	−	513.818i	−1.52599	−	1.97622i
$261$	−118.947	+	279.905i	−0.455735	+	1.07243i
$262$	31.8764	+	22.8056i	0.121666	+	0.0870443i
$263$	−139.425	−	271.183i	−0.530133	−	1.03112i	−0.989725	−	0.142985i	$-0.954330\pi$
$263$	−139.425	−	271.183i	−0.530133	−	1.03112i	0.459592	−	0.888130i	$-0.347996\pi$
$264$	−310.538	−	322.094i	−1.17628	−	1.22005i
$265$	434.150	+	166.048i	1.63830	+	0.626597i
$266$	189.822	−	35.0620i	0.713618	−	0.131812i
$267$	3.69418	+	12.2789i	0.0138359	+	0.0459886i
$268$	−347.613	−	908.870i	−1.29706	−	3.39131i
$269$	−74.3347	−	2.71667i	−0.276337	−	0.0100991i	−0.101997	−	0.994785i	$-0.532523\pi$
$269$	−74.3347	−	2.71667i	−0.276337	−	0.0100991i	−0.174340	+	0.984686i	$0.555779\pi$
$270$	−439.316	−	290.649i	−1.62710	−	1.07648i
$271$	−236.103	+	80.5470i	−0.871227	+	0.297222i	−0.722261	−	0.691621i	$-0.756897\pi$
$271$	−236.103	+	80.5470i	−0.871227	+	0.297222i	−0.148967	+	0.988842i	$0.547595\pi$
$272$	−916.533	+	169.292i	−3.36961	+	0.622398i
$273$	−30.9027	+	32.0528i	−0.113197	+	0.117409i
$274$	−507.520	−	215.673i	−1.85226	−	0.787126i
$275$	−35.5726	−	13.6053i	−0.129355	−	0.0494740i
$276$	183.810	+	13.4532i	0.665980	+	0.0487434i
$277$	−48.0877	−	183.938i	−0.173602	−	0.664036i	−0.995530	−	0.0944449i	$-0.969892\pi$
$277$	−48.0877	−	183.938i	−0.173602	−	0.664036i	0.821928	−	0.569591i	$-0.192898\pi$
$278$	−362.535	+	324.832i	−1.30408	+	1.16846i
$279$	−141.848	−	214.404i	−0.508417	−	0.768473i
$280$	−14.0088	+	191.402i	−0.0500314	+	0.683577i
$281$	427.355	−	145.793i	1.52084	−	0.518838i	0.568186	−	0.822900i	$-0.307646\pi$
$281$	427.355	−	145.793i	1.52084	−	0.518838i	0.952652	+	0.304063i	$0.0983432\pi$
$282$	−116.716	+	248.978i	−0.413887	+	0.882902i
$283$	123.617	−	47.2796i	0.436810	−	0.167066i	−0.128922	−	0.991655i	$-0.541152\pi$
$283$	123.617	−	47.2796i	0.436810	−	0.167066i	0.565732	+	0.824589i	$0.308594\pi$
$284$	−562.632	+	343.369i	−1.98110	+	1.20905i
$285$	−31.2790	−	284.273i	−0.109751	−	0.997450i
$286$	−282.131	−	502.703i	−0.986471	−	1.75770i
$287$	18.0112	+	1.98180i	0.0627568	+	0.00690521i
$288$	−221.372	−	146.459i	−0.768654	−	0.508537i
$289$	−223.499	+	366.218i	−0.773355	+	1.26719i
$290$	−39.2041	−	1072.72i	−0.135187	−	3.69904i
$291$	25.4028	+	59.7779i	0.0872950	+	0.205422i
$292$	41.2517	−	107.857i	0.141273	−	0.369372i
$293$	79.4212	−	33.7504i	0.271062	−	0.115189i	−0.251310	−	0.967907i	$-0.580861\pi$
$293$	79.4212	−	33.7504i	0.271062	−	0.115189i	0.522372	+	0.852718i	$0.325047\pi$
$294$	−311.712	+	22.8144i	−1.06024	+	0.0775999i
$295$	−213.213	+	164.637i	−0.722755	+	0.558093i
$296$	−41.4660	−	4.56256i	−0.140088	−	0.0154141i
$297$	−244.393	−	218.978i	−0.822874	−	0.737298i
$298$	430.639	−	332.529i	1.44510	−	1.11587i
$299$	129.123	+	44.0506i	0.431849	+	0.147327i
$300$	54.7538	+	8.05808i	0.182513	+	0.0268603i
$301$	−126.220	−	59.1696i	−0.419336	−	0.196577i
$302$	−506.387	+	829.747i	−1.67678	+	2.74751i
$303$	9.64156	+	1.78089i	0.0318203	+	0.00587751i
$304$	−109.655	−	996.584i	−0.360709	−	3.27824i
$305$	3.31228	−	90.6322i	0.0108599	−	0.297155i
$306$	−522.245	+	136.533i	−1.70668	+	0.446186i
$307$	223.482	+	147.854i	0.727955	+	0.481610i	0.860425	−	0.509577i	$-0.170198\pi$
$307$	223.482	+	147.854i	0.727955	+	0.481610i	−0.132471	+	0.991187i	$0.542291\pi$
$308$	−45.2440	+	203.107i	−0.146896	+	0.659439i
$309$	24.3534	−	332.739i	0.0788135	−	1.07683i
$310$	774.525	+	472.686i	2.49847	+	1.52479i
$311$	−0.468000	−	0.0864439i	−0.00150482	−	0.000277955i	0.180884	−	0.983504i	$-0.442104\pi$
$311$	−0.468000	−	0.0864439i	−0.00150482	−	0.000277955i	−0.182389	+	0.983226i	$0.558383\pi$
$312$	321.165	+	358.441i	1.02937	+	1.14885i
$313$	60.9500	−	43.6060i	0.194729	−	0.139316i	−0.480310	−	0.877099i	$-0.659476\pi$
$313$	60.9500	−	43.6060i	0.194729	−	0.139316i	0.675039	+	0.737782i	$0.264127\pi$
$314$	−24.3836	−	29.3000i	−0.0776549	−	0.0933121i
$315$			53.4065i			0.169545i
$316$	−271.964	+	92.7814i	−0.860647	+	0.293612i
$317$	−2.88975	−	39.4825i	−0.00911592	−	0.124551i	0.990828	−	0.135128i	$-0.0431446\pi$
$317$	−2.88975	−	39.4825i	−0.00911592	−	0.124551i	−0.999944	+	0.0105776i	$0.996633\pi$
$318$	−574.363	−	172.800i	−1.80617	−	0.543396i
$319$	73.1364	−	664.688i	0.229268	−	2.08366i
$320$	196.595	+	28.9328i	0.614360	+	0.0904151i
$321$	82.9597	+	35.2540i	0.258441	+	0.109826i
$322$	−34.3572	−	61.2179i	−0.106699	−	0.190118i
$323$	−628.178	−	449.423i	−1.94482	−	1.39140i
$324$	9.79209	+	5.49559i	0.0302225	+	0.0169617i
$325$	37.7050	+	16.0229i	0.116015	+	0.0493011i
$326$	−64.1424	+	582.947i	−0.196756	+	1.78818i
$327$	−136.327	−	190.550i	−0.416902	−	0.582722i
$328$	35.5765	−	192.608i	0.108465	−	0.587220i
$329$	72.6936	−	10.6983i	0.220953	−	0.0325176i
$330$	420.822	+	126.607i	1.27522	+	0.383656i
$331$	311.152	+	81.3458i	0.940036	+	0.245758i	0.691097	−	0.722762i	$-0.257128\pi$
$331$	311.152	+	81.3458i	0.940036	+	0.245758i	0.248939	+	0.968519i	$0.419918\pi$
$332$	701.489	+	782.908i	2.11292	+	2.35816i
$333$	−11.6012	−	0.423984i	−0.0348386	−	0.00127322i
$334$	269.519	+	895.843i	0.806943	+	2.68216i
$335$	422.084	+	351.261i	1.25995	+	1.04854i
$336$		−	118.991i		−	0.354139i
$337$	−53.9160	+	88.3448i	−0.159988	+	0.262151i	−0.923463	−	0.383687i	$-0.874654\pi$
$337$	−53.9160	+	88.3448i	−0.159988	+	0.262151i	0.763475	+	0.645837i	$0.223492\pi$
$338$	0.647700	+	1.25978i	0.00191627	+	0.00372717i
$339$	−204.171	−	37.7123i	−0.602274	−	0.111246i
$340$	1027.35	−	854.968i	3.02162	−	2.51461i
$341$	434.476	+	361.574i	1.27412	+	1.06033i
$342$	−105.470	−	571.005i	−0.308392	−	1.66961i
$343$	105.826	+	137.049i	0.308530	+	0.399560i
$344$	−737.477	+	1314.04i	−2.14383	+	3.81989i
$345$	−94.1711	+	44.1456i	−0.272960	+	0.127958i
$346$	−739.227	+	54.1045i	−2.13649	+	0.156371i
$347$	216.238	−	302.245i	0.623163	−	0.871022i	−0.375274	−	0.926914i	$-0.622451\pi$
$347$	216.238	−	302.245i	0.623163	−	0.871022i	0.998437	+	0.0558916i	$0.0178001\pi$
$348$	106.277	+	965.881i	0.305394	+	2.77552i
$349$	77.5693	−	74.7862i	0.222262	−	0.214287i	−0.574624	−	0.818418i	$-0.694852\pi$
$349$	77.5693	−	74.7862i	0.222262	−	0.214287i	0.796885	+	0.604131i	$0.206480\pi$
$350$	−8.94762	−	19.0870i	−0.0255646	−	0.0545343i
$351$	254.113	+	244.996i	0.723969	+	0.697994i
$352$	558.874	+	168.140i	1.58771	+	0.477671i
$353$	35.5802	+	323.364i	0.100794	+	0.916046i	0.932583	+	0.360955i	$0.117549\pi$
$353$	35.5802	+	323.364i	0.100794	+	0.916046i	−0.831790	+	0.555091i	$0.812683\pi$
$354$	258.883	−	231.960i	0.731308	−	0.655255i
$355$	182.044	−	324.368i	0.512801	−	0.913713i
$356$	−46.4075	−	44.7424i	−0.130358	−	0.125681i
$357$	−68.2726	−	61.1725i	−0.191240	−	0.171352i
$358$	−731.775	+	484.138i	−2.04406	+	1.35234i
$359$	9.51984	+	24.8906i	0.0265177	+	0.0693331i	0.946631	−	0.322318i	$-0.104462\pi$
$359$	9.51984	+	24.8906i	0.0265177	+	0.0693331i	−0.920114	+	0.391651i	$0.871904\pi$
$360$	575.755	+	42.1398i	1.59932	+	0.117055i
$361$	300.561	−	361.162i	0.832579	−	1.00045i
$362$	−94.2419	−	78.4287i	−0.260337	−	0.216654i
$363$	42.9895	+	20.1526i	0.118428	+	0.0555169i
$364$	56.6154	−	216.557i	0.155537	−	0.594936i
$365$	9.48815	+	64.4709i	0.0259949	+	0.176633i
$366$	4.27409	+	116.950i	0.0116778	+	0.319534i
$367$	67.3698	+	223.928i	0.183569	+	0.610158i	0.999488	+	0.0319914i	$0.0101849\pi$
$367$	67.3698	+	223.928i	0.183569	+	0.610158i	−0.815919	+	0.578166i	$0.803769\pi$
$368$	−330.138	+	154.762i	−0.897115	+	0.420550i
$369$	5.96144	−	54.1795i	0.0161557	−	0.146828i
$370$	37.7105	−	16.0252i	0.101920	−	0.0433115i
$371$	46.1737	+	153.475i	0.124457	+	0.413679i
$372$	−730.489	−	375.571i	−1.96368	−	1.00960i
$373$	−264.672	+	136.077i	−0.709576	+	0.364818i	−0.774070	−	0.633100i	$-0.781782\pi$
$373$	−264.672	+	136.077i	−0.709576	+	0.364818i	0.0644938	+	0.997918i	$0.479457\pi$
$374$	1013.10	−	618.287i	2.70883	−	1.65317i
$375$	202.504	−	77.4511i	0.540010	−	0.206536i
$376$	−57.9760	−	792.123i	−0.154191	−	2.10671i
$377$	−104.733	+	711.647i	−0.277805	+	1.88766i
$378$	−13.2579	−	181.142i	−0.0350738	−	0.479212i
$379$	−115.066	+	223.804i	−0.303603	+	0.590512i	−0.990702	−	0.136052i	$-0.956559\pi$
$379$	−115.066	+	223.804i	−0.303603	+	0.590512i	0.687098	+	0.726564i	$0.258884\pi$
$380$	836.573	+	1169.31i	2.20151	+	3.07714i
$381$	−30.5008	−	136.923i	−0.0800547	−	0.359377i
$382$	286.222	+	610.568i	0.749273	+	1.59834i
$383$	24.8192	−	111.417i	0.0648022	−	0.290907i	−0.932776	−	0.360456i	$-0.882621\pi$
$383$	24.8192	−	111.417i	0.0648022	−	0.290907i	0.997579	+	0.0695492i	$0.0221561\pi$
$384$	104.133	+	7.62154i	0.271179	+	0.0198478i
$385$	−33.8304	−	112.448i	−0.0878712	−	0.292072i
$386$	212.295	−	953.024i	0.549987	−	2.46897i
$387$	−177.988	+	379.683i	−0.459917	+	0.981093i
$388$	−258.449	−	199.568i	−0.666106	−	0.514350i
$389$	3.45752	+	0.508841i	0.00888821	+	0.00130807i	0.150044	−	0.988679i	$-0.452059\pi$
$389$	3.45752	+	0.508841i	0.00888821	+	0.00130807i	−0.141156	+	0.989987i	$0.545082\pi$
$390$	−447.398	−	152.631i	−1.14717	−	0.391361i
$391$	−80.9252	+	268.984i	−0.206970	+	0.687939i
$392$	752.893	−	498.109i	1.92065	−	1.27069i
$393$	20.0087	+	0.731246i	0.0509127	+	0.00186068i
$394$	202.137	−	773.185i	0.513038	−	1.96240i
$395$	108.212	−	120.772i	0.273955	−	0.305752i
$396$	610.967	+	136.099i	1.54285	+	0.343683i
$397$	−15.4097	−	421.649i	−0.0388155	−	1.06209i	−0.865965	−	0.500105i	$-0.833295\pi$
$397$	−15.4097	−	421.649i	−0.0388155	−	1.06209i	0.827149	−	0.561982i	$-0.189961\pi$
$398$	−275.160	+	196.860i	−0.691358	+	0.494624i
$399$	70.9890	−	68.4420i	0.177917	−	0.171534i
$400$	−102.264	+	39.1127i	−0.255660	+	0.0977818i
$401$	500.839	−	482.869i	1.24897	−	1.20416i	0.279180	−	0.960239i	$-0.409937\pi$
$401$	500.839	−	482.869i	1.24897	−	1.20416i	0.969794	−	0.243924i	$-0.0784348\pi$
$402$	−576.279	−	412.292i	−1.43353	−	1.02560i
$403$	−452.844	−	405.750i	−1.12368	−	1.00682i
$404$	−46.6511	+	15.9152i	−0.115473	+	0.0393939i
$405$	−6.33663			−0.0156460
$406$	284.493	−	236.757i	0.700721	−	0.583145i
$407$	24.6950	−	6.45612i	0.0606757	−	0.0158627i
$408$	−713.347	+	687.753i	−1.74840	+	1.68567i
$409$	478.673	−	17.4938i	1.17035	−	0.0427721i	0.555569	−	0.831471i	$-0.312501\pi$
$409$	478.673	−	17.4938i	1.17035	−	0.0427721i	0.614780	+	0.788698i	$0.289245\pi$
$410$	62.1165	+	182.078i	0.151504	+	0.444094i
$411$	−277.014	+	51.1670i	−0.673999	+	0.124494i
$412$	711.925	+	1518.67i	1.72797	+	3.68610i
$413$	−89.8618	−	23.4930i	−0.217583	−	0.0568837i
$414$	−184.150	+	103.350i	−0.444806	+	0.249637i
$415$	−561.441	−	191.537i	−1.35287	−	0.461535i
$416$	−594.168	−	202.702i	−1.42829	−	0.487264i
$417$	−62.8950	+	240.577i	−0.150827	+	0.576923i
$418$	583.771	+	1135.44i	1.39658	+	2.71637i
$419$	335.159	+	374.060i	0.799903	+	0.892745i	0.996137	−	0.0878121i	$-0.0279875\pi$
$419$	335.159	+	374.060i	0.799903	+	0.892745i	−0.196234	+	0.980557i	$0.562871\pi$
$420$	83.5125	+	148.803i	0.198839	+	0.354294i
$421$	170.785	+	221.174i	0.405665	+	0.525354i	0.949470	−	0.313858i	$-0.101621\pi$
$421$	170.785	+	221.174i	0.405665	+	0.525354i	−0.543805	+	0.839212i	$0.683017\pi$
$422$	156.860	+	704.165i	0.371705	+	1.66864i
$423$	−32.1815	−	218.670i	−0.0760793	−	0.516950i
$424$	1690.99	−	376.683i	3.98818	−	0.888404i
$425$	−30.1320	+	78.7831i	−0.0708988	+	0.185372i
$426$	−203.726	+	434.587i	−0.478231	+	1.02016i
$427$	25.4323	−	18.1952i	0.0595604	−	0.0426118i
$428$	−450.443	+	49.5628i	−1.05244	+	0.115801i
$429$	−261.893	−	134.648i	−0.610473	−	0.313866i
$430$		−	1480.04i		−	3.44196i
$431$	−313.236	−	296.048i	−0.726765	−	0.686887i
$431$	−313.236	−	296.048i	−0.726765	−	0.686887i
$432$	−943.353			−2.18369
$433$	−76.8475	+	149.469i	−0.177477	+	0.345195i	−0.961172	−	0.275951i	$-0.911007\pi$
$433$	−76.8475	+	149.469i	−0.177477	+	0.345195i	0.783695	+	0.621146i	$0.213333\pi$
$434$	34.2181	+	310.985i	0.0788435	+	0.716555i
$435$	−319.065	−	445.971i	−0.733482	−	1.02522i
$436$	1066.51	+	499.959i	2.44612	+	1.14669i
$437$	−282.222	−	107.941i	−0.645816	−	0.247004i
$438$	−18.2832	−	82.0761i	−0.0417425	−	0.187388i
$439$	−419.840	+	61.7876i	−0.956355	+	0.140746i	−0.605643	−	0.795737i	$-0.707084\pi$
$439$	−419.840	+	61.7876i	−0.956355	+	0.140746i	−0.350713	+	0.936483i	$0.614061\pi$
$440$	−1238.95	+	275.987i	−2.81579	+	0.627244i
$441$	198.841	−	153.540i	0.450887	−	0.348163i
$442$	−1113.34	+	624.839i	−2.51888	+	1.41366i
$443$	304.880	−	273.174i	0.688217	−	0.616645i	−0.247712	−	0.968834i	$-0.579679\pi$
$443$	304.880	−	273.174i	0.688217	−	0.616645i	0.935929	+	0.352188i	$0.114562\pi$
$444$	−32.9868	+	16.9597i	−0.0742947	+	0.0381975i
$445$	35.1950	+	9.20118i	0.0790899	+	0.0206768i
$446$	−356.564	+	1045.17i	−0.799471	+	2.34344i
$447$	89.7409	−	263.052i	0.200763	−	0.588484i
$448$	33.5331	+	59.7496i	0.0748506	+	0.133370i
$449$	196.621	−	752.084i	0.437908	−	1.67502i	−0.265403	−	0.964138i	$-0.585505\pi$
$449$	196.621	−	752.084i	0.437908	−	1.67502i	0.703311	−	0.710883i	$-0.251704\pi$
$450$	−57.4156	+	26.9153i	−0.127590	+	0.0598119i
$451$	21.7682	+	117.851i	0.0482666	+	0.261311i
$452$	987.890	−	337.021i	2.18560	−	0.745622i
$453$	18.1357	+	496.237i	0.0400346	+	1.09545i
$454$	−701.539	−	727.646i	−1.54524	−	1.60274i
$455$	31.9491	+	122.207i	0.0702177	+	0.268587i
$456$	−681.834	−	819.309i	−1.49525	−	1.79673i
$457$		−	148.173i		−	0.324229i	−0.986772	−	0.162115i	$-0.948169\pi$
$457$		−	148.173i		−	0.324229i	0.986772	−	0.162115i	$-0.0518314\pi$
$458$	469.410	+	1375.95i	1.02491	+	3.00426i
$459$	−484.973	+	541.262i	−1.05659	+	1.17922i
$460$	304.235	−	425.242i	0.661380	−	0.924440i
$461$	−94.2767	−	97.7851i	−0.204505	−	0.212115i	0.609796	−	0.792558i	$-0.291251\pi$
$461$	−94.2767	−	97.7851i	−0.204505	−	0.212115i	−0.814301	+	0.580443i	$0.802879\pi$
$462$	54.1291	+	141.526i	0.117163	+	0.306333i
$463$	−14.8823	−	15.4361i	−0.0321432	−	0.0333394i	0.703639	−	0.710558i	$-0.251557\pi$
$463$	−14.8823	−	15.4361i	−0.0321432	−	0.0333394i	−0.735782	+	0.677218i	$0.763185\pi$
$464$	−1118.55	−	1563.45i	−2.41067	−	3.36951i
$465$	463.211	−	16.9287i	0.996153	−	0.0364058i
$466$	−212.821	+	955.384i	−0.456697	+	2.05018i
$467$	223.913	+	200.627i	0.479470	+	0.429607i	0.871537	−	0.490329i	$-0.163124\pi$
$467$	223.913	+	200.627i	0.479470	+	0.429607i	−0.392067	+	0.919937i	$0.628240\pi$
$468$	−651.425	−	170.305i	−1.39193	−	0.363899i
$469$	−6.91503	+	189.212i	−0.0147442	+	0.403438i
$470$	430.443	+	650.615i	0.915835	+	1.38429i
$471$	−18.6470	−	5.61005i	−0.0395903	−	0.0119109i
$472$	−324.173	+	950.229i	−0.686807	+	2.01320i
$473$	134.244	−	912.170i	0.283813	−	1.92848i
$474$	−127.886	+	165.618i	−0.269802	+	0.349406i
$475$	−82.1555	−	38.5129i	−0.172959	−	0.0810798i
$476$	449.825	+	100.203i	0.945010	+	0.210510i
$477$	461.668	−	138.895i	0.967858	−	0.291185i
$478$	−7.99733	+	109.267i	−0.0167308	+	0.228593i
$479$	616.640	+	137.362i	1.28735	+	0.286769i	0.807127	−	0.590378i	$-0.201021\pi$
$479$	616.640	+	137.362i	1.28735	+	0.286769i	0.480221	+	0.877147i	$0.340556\pi$
$480$	433.335	−	203.139i	0.902780	−	0.423206i
$481$	−26.8001	+	5.96997i	−0.0557174	+	0.0124116i
$482$	−794.266	+	568.249i	−1.64786	+	1.17894i
$483$	−31.8927	−	16.3971i	−0.0660303	−	0.0339485i
$484$	−238.054	+	17.4233i	−0.491847	+	0.0359985i
$485$	182.304	+	26.8296i	0.375885	+	0.0553189i
$486$	−883.039	+	64.6301i	−1.81695	+	0.132984i
$487$	2.96129	+	7.74259i	0.00608067	+	0.0158985i	0.937023	−	0.349269i	$-0.113570\pi$
$487$	2.96129	+	7.74259i	0.00608067	+	0.0158985i	−0.930942	+	0.365167i	$0.881012\pi$
$488$	−176.089	−	288.532i	−0.360837	−	0.591255i
$489$	136.985	+	266.438i	0.280133	+	0.544862i
$490$	−405.434	+	788.575i	−0.827417	+	1.60934i
$491$	184.482	−	55.5023i	0.375727	−	0.113039i	−0.0946373	−	0.995512i	$-0.530169\pi$
$491$	184.482	−	55.5023i	0.375727	−	0.113039i	0.470364	+	0.882472i	$0.344123\pi$
$492$	−68.1112	−	160.279i	−0.138437	−	0.325771i
$493$	−1472.09	−	161.976i	−2.98599	−	0.328553i
$494$	−582.930	−	1243.50i	−1.18002	−	2.51721i
$495$	−338.254	+	101.765i	−0.683341	+	0.205587i
$496$	1623.89	−	59.3474i	3.27398	−	0.119652i
$497$	126.885	−	18.6737i	0.255303	−	0.0375728i
$498$	740.579	+	193.613i	1.48711	+	0.388780i
$499$	−37.9094	+	80.8681i	−0.0759707	+	0.162060i	−0.939801	−	0.341723i	$-0.888989\pi$
$499$	−37.9094	+	80.8681i	−0.0759707	+	0.162060i	0.863830	+	0.503784i	$0.168059\pi$
$500$	−697.226	+	837.804i	−1.39445	+	1.67561i
$501$	367.332	+	305.696i	0.733198	+	0.610172i
$502$	59.5244	−	813.280i	0.118575	−	1.62008i
$503$	421.155	−	161.078i	0.837287	−	0.320235i	0.0993064	−	0.995057i	$-0.468338\pi$
$503$	421.155	−	161.078i	0.837287	−	0.320235i	0.737981	+	0.674822i	$0.235779\pi$
$504$	109.830	+	166.009i	0.217917	+	0.329382i
$505$	18.5621	−	20.7165i	0.0367566	−	0.0410228i
$506$	322.260	−	334.253i	0.636878	−	0.660579i
$507$	0.631034	+	0.354153i	0.00124464	+	0.000698527i
$508$	470.611	+	525.233i	0.926400	+	1.03392i
$509$	−267.289	+	29.4101i	−0.525125	+	0.0577802i	−0.368049	−	0.929806i	$-0.619974\pi$
$509$	−267.289	+	29.4101i	−0.525125	+	0.0577802i	−0.157076	+	0.987587i	$0.550207\pi$
$510$	280.398	−	932.002i	0.549799	−	1.82745i
$511$	−15.5952	+	16.1755i	−0.0305189	+	0.0316547i
$512$	−971.876	+	455.597i	−1.89820	+	0.889837i
$513$	−542.606	−	562.798i	−1.05771	−	1.09707i
$514$	−14.0713	+	1.54828i	−0.0273761	+	0.00301222i
$515$	−769.787	−	550.735i	−1.49473	−	1.06939i
$516$	97.7979	+	1336.21i	0.189531	+	2.58955i
$517$	206.275	+	440.024i	0.398984	+	0.851111i
$518$	12.3203	+	6.91447i	0.0237843	+	0.0133484i
$519$	−299.689	+	231.413i	−0.577436	+	0.445882i
$520$	1342.67	−	248.005i	2.58207	−	0.476932i
$521$	−190.083	+	228.408i	−0.364842	+	0.438404i	−0.919150	−	0.393908i	$-0.871123\pi$
$521$	−190.083	+	228.408i	−0.364842	+	0.438404i	0.554307	+	0.832312i	$0.312983\pi$
$522$	−712.188	−	855.783i	−1.36435	−	1.63943i
$523$	−86.2381	+	466.885i	−0.164891	+	0.892706i	0.793783	+	0.608201i	$0.208108\pi$
$523$	−86.2381	+	466.885i	−0.164891	+	0.892706i	−0.958674	+	0.284505i	$0.908171\pi$
$524$	−89.5188	+	46.0248i	−0.170837	+	0.0878335i
$525$	−9.19199	−	5.60979i	−0.0175085	−	0.0106853i
$526$	1116.28			2.12220
$527$	800.783	−	962.241i	1.51951	−	1.82588i
$528$	753.635	−	226.735i	1.42734	−	0.429422i
$529$	15.3069	−	418.835i	0.0289355	−	0.791748i
$530$	−1267.32	+	1135.52i	−2.39117	+	2.14250i
$531$	−70.6692	+	270.313i	−0.133087	+	0.509065i
$532$	−142.822	+	474.721i	−0.268463	+	0.892332i
$533$	−18.7703	−	127.542i	−0.0352163	−	0.239291i
$534$	−46.1603	−	8.52624i	−0.0864425	−	0.0159667i
$535$	207.980	−	148.797i	0.388748	−	0.278125i
$536$	2034.37	+	223.844i	3.79546	+	0.417620i
$537$	−175.303	+	412.523i	−0.326449	+	0.768199i
$538$	133.272	−	237.465i	0.247717	−	0.441385i
$539$	−321.400	+	449.235i	−0.596290	+	0.833460i
$540$	1179.71	−	662.084i	2.18464	−	1.22608i
$541$	−159.428	+	375.167i	−0.294692	+	0.693469i	−0.999879	−	0.0155529i	$-0.995049\pi$
$541$	−159.428	+	375.167i	−0.294692	+	0.693469i	0.705187	+	0.709022i	$0.250863\pi$
$542$	132.969	−	903.508i	0.245330	−	1.66699i
$543$	−62.2570	−	6.85022i	−0.114654	−	0.0126155i
$544$	372.383	−	1237.75i	0.684527	−	2.27527i
$545$	−662.926	+	48.5199i	−1.21638	+	0.0890273i
$546$	−52.6272	−	154.263i	−0.0963868	−	0.282533i
$547$	−230.840			−0.422011			−0.211005	−	0.977485i	$-0.567674\pi$
$547$	−230.840			−0.422011			−0.211005	+	0.977485i	$0.567674\pi$
$548$	1088.55	−	905.901i	1.98641	−	1.65310i
$549$	−54.7331	−	76.5028i	−0.0996960	−	0.139349i
$550$	103.839	−	93.0403i	0.188798	−	0.169164i
$551$	289.366	−	1566.60i	0.525164	−	2.84319i
$552$	−201.936	+	330.884i	−0.365826	+	0.599428i
$553$	55.7636	+	4.08137i	0.100838	+	0.00738041i
$554$	679.342	+	151.330i	1.22625	+	0.273158i
$555$	11.5492	−	17.4566i	0.0208094	−	0.0314534i
$556$	−316.194	−	1209.46i	−0.568694	−	2.17528i
$557$	218.715	+	7.99324i	0.392666	+	0.0143505i	0.232143	−	0.972682i	$-0.425426\pi$
$557$	218.715	+	7.99324i	0.392666	+	0.0143505i	0.160523	+	0.987032i	$0.448682\pi$
$558$	935.474	−	102.931i	1.67648	−	0.184465i
$559$	−180.144	+	975.282i	−0.322261	+	1.74469i
$560$	−288.154	−	175.858i	−0.514561	−	0.314032i
$561$	257.347	−	548.972i	0.458730	−	0.978559i
$562$	−240.679	+	1635.39i	−0.428254	+	2.90994i
$563$	108.057	−	316.740i	0.191930	−	0.562593i	−0.807705	−	0.589586i	$-0.799291\pi$
$563$	108.057	−	316.740i	0.191930	−	0.562593i	0.999636	+	0.0269930i	$0.00859318\pi$
$564$	−431.602	−	558.944i	−0.765252	−	0.991035i
$565$	−393.073	+	438.695i	−0.695704	+	0.776452i
$566$	−52.9914	+	481.603i	−0.0936243	+	0.850888i
$567$	−1.33534	−	1.72932i	−0.00235509	−	0.00304994i
$568$	−101.196	−	1382.64i	−0.178162	−	2.43422i
$569$	241.617	+	568.573i	0.424635	+	0.999249i	0.985242	+	0.171167i	$0.0547538\pi$
$569$	241.617	+	568.573i	0.424635	+	0.999249i	−0.560607	+	0.828082i	$0.689432\pi$
$570$	977.869	+	374.003i	1.71556	+	0.656146i
$571$	−361.798	+	153.747i	−0.633622	+	0.269260i	−0.684013	−	0.729469i	$-0.739767\pi$
$571$	−361.798	+	153.747i	−0.633622	+	0.269260i	0.0503916	+	0.998730i	$0.483953\pi$
$572$	1479.46	−	54.0688i	2.58646	−	0.0945258i
$573$	294.039	+	179.450i	0.513158	+	0.313176i
$574$	−36.6007	+	55.3220i	−0.0637643	+	0.0963798i
$575$	−3.60895	+	32.7993i	−0.00627643	+	0.0570423i
$576$	179.733	−	100.871i	0.312036	−	0.175123i
$577$	234.562	−	25.8091i	0.406519	−	0.0447299i	0.0961996	−	0.995362i	$-0.469331\pi$
$577$	234.562	−	25.8091i	0.406519	−	0.0447299i	0.310320	+	0.950632i	$0.399564\pi$
$578$	−818.189	−	1340.65i	−1.41555	−	2.31947i
$579$	−178.178	−	465.863i	−0.307733	−	0.804600i
$580$	2496.10	+	1170.12i	4.30362	+	2.01745i
$581$	−66.0420	−	193.585i	−0.113670	−	0.333193i
$582$	−237.141	−	17.3565i	−0.407458	−	0.0298221i
$583$	−884.060	+	584.888i	−1.51640	+	1.00324i
$584$	162.077	+	180.889i	0.277529	+	0.309741i
$585$	367.611	−	96.1060i	0.628394	−	0.164284i
$586$	−23.0599	+	315.067i	−0.0393514	+	0.537656i
$587$	−208.810	+	545.955i	−0.355724	+	0.930077i	0.632153	+	0.774843i	$0.282171\pi$
$587$	−208.810	+	545.955i	−0.355724	+	0.930077i	−0.987878	+	0.155234i	$0.950387\pi$
$588$	313.926	−	738.730i	0.533888	−	1.25634i
$589$	969.450	+	934.667i	1.64592	+	1.58687i
$590$	−179.120	−	969.742i	−0.303594	−	1.64363i
$591$	−131.815	−	386.382i	−0.223038	−	0.653777i
$592$	40.4883	−	61.1982i	0.0683925	−	0.103375i
$593$	33.1914	−	908.200i	0.0559721	−	1.53153i	−0.614094	−	0.789233i	$-0.710479\pi$
$593$	33.1914	−	908.200i	0.0559721	−	1.53153i	0.670066	−	0.742301i	$-0.266266\pi$
$594$	1122.01	−	429.133i	1.88891	−	0.722447i
$595$	−249.039	+	74.9248i	−0.418554	+	0.125924i
$596$	253.799	+	1374.04i	0.425837	+	2.30544i
$597$	−61.7410	+	161.428i	−0.103419	+	0.270399i
$598$	−359.552	+	346.652i	−0.601258	+	0.579685i
$599$	−787.514	+	404.889i	−1.31471	+	0.675941i	−0.965329	−	0.261037i	$-0.915935\pi$
$599$	−787.514	+	404.889i	−1.31471	+	0.675941i	−0.349386	+	0.936979i	$0.613610\pi$
$600$	−67.7298	+	94.6689i	−0.112883	+	0.157782i
$601$	−562.026	−	238.835i	−0.935152	−	0.397396i	−0.130705	−	0.991421i	$-0.541724\pi$
$601$	−562.026	−	238.835i	−0.935152	−	0.397396i	−0.804447	+	0.594025i	$0.797538\pi$
$602$	403.916	−	311.894i	0.670957	−	0.518096i
$603$	569.169	+	20.8011i	0.943896	+	0.0344960i
$604$	−1300.48	−	2130.92i	−2.15311	−	3.52801i
$605$	112.337	−	74.3217i	0.185682	−	0.122846i
$606$	−21.9368	+	28.4092i	−0.0361994	+	0.0468798i
$607$	−29.3178	−	158.724i	−0.0482996	−	0.261489i	0.950485	−	0.310769i	$-0.100587\pi$
$607$	−29.3178	−	158.724i	−0.0482996	−	0.261489i	−0.998785	+	0.0492795i	$0.984307\pi$
$608$	1298.66	+	496.696i	2.13596	+	0.816934i
$609$	54.4716	−	181.056i	0.0894444	−	0.297301i
$610$	289.528	+	162.491i	0.474636	+	0.266379i
$611$	−204.453	−	481.117i	−0.334620	−	0.787426i
$612$	301.420	−	1353.12i	0.492516	−	2.21098i
$613$	91.1792	−	20.3110i	0.148743	−	0.0331338i	−0.142427	−	0.989805i	$-0.545491\pi$
$613$	91.1792	−	20.3110i	0.148743	−	0.0331338i	0.291169	+	0.956672i	$0.405956\pi$
$614$	−855.453	+	480.103i	−1.39325	+	0.781927i
$615$	77.7855	+	60.0640i	0.126480	+	0.0976651i
$616$	−336.406	−	279.959i	−0.546114	−	0.454479i
$617$			832.377i			1.34907i	0.738242	+	0.674536i	$0.235656\pi$
$617$			832.377i			1.34907i	−0.738242	+	0.674536i	$0.764344\pi$
$618$	1042.54	+	636.252i	1.68696	+	1.02953i
$619$	−505.773	+	308.669i	−0.817082	+	0.498658i	−0.865940	−	0.500148i	$-0.833279\pi$
$619$	−505.773	+	308.669i	−0.817082	+	0.498658i	0.0488584	+	0.998806i	$0.484442\pi$
$620$	−1989.10	+	1213.93i	−3.20823	+	1.95795i
$621$	−129.996	+	252.844i	−0.209333	+	0.407156i
$622$	1.06481	−	1.37898i	0.00171191	−	0.00221700i
$623$	4.90567	+	11.5440i	0.00787427	+	0.0185297i
$624$	−819.043	+	214.126i	−1.31257	+	0.343150i
$625$	126.017	−	682.246i	0.201627	−	1.09159i
$626$	39.9457	+	271.427i	0.0638111	+	0.433589i
$627$	568.750	+	319.198i	0.907098	+	0.509088i
$628$	95.5532	−	21.2854i	0.152155	−	0.0338939i
$629$	−14.2985	−	54.6924i	−0.0227321	−	0.0869514i
$630$	−173.876	−	89.3960i	−0.275994	−	0.141898i
$631$	244.905	+	219.436i	0.388122	+	0.347758i	0.838328	−	0.545166i	$-0.183533\pi$
$631$	244.905	+	219.436i	0.388122	+	0.347758i	−0.450207	+	0.892924i	$0.648650\pi$
$632$	87.9993	−	597.945i	0.139239	−	0.946116i
$633$	265.308	+	255.789i	0.419127	+	0.404089i
$634$	133.381	+	56.6807i	0.210380	+	0.0894017i
$635$	−376.657	−	128.497i	−0.593160	−	0.202358i
$636$	1069.13	−	1108.91i	1.68102	−	1.74357i
$637$	363.145	−	470.288i	0.570086	−	0.738286i
$638$	2041.61	+	1350.72i	3.20002	+	2.11711i
$639$	−56.1723	−	381.684i	−0.0879066	−	0.597315i
$640$	172.356	−	240.909i	0.269306	−	0.376421i
$641$	−444.421	+	671.743i	−0.693325	+	1.04796i	0.302180	+	0.953251i	$0.402286\pi$
$641$	−444.421	+	671.743i	−0.693325	+	1.04796i	−0.995505	+	0.0947105i	$0.969807\pi$
$642$	−253.641	+	211.082i	−0.395080	+	0.328788i
$643$	−295.888	−	355.546i	−0.460168	−	0.552949i	0.487119	−	0.873335i	$-0.338048\pi$
$643$	−295.888	−	355.546i	−0.460168	−	0.552949i	−0.947287	+	0.320386i	$0.896187\pi$
$644$	180.164	−	6.58436i	0.279758	−	0.0102242i
$645$	−417.172	−	630.556i	−0.646778	−	0.977606i
$646$	2514.68	−	1292.89i	3.89270	−	2.00137i
$647$	219.454	+	426.841i	0.339187	+	0.659724i	0.995500	−	0.0947655i	$-0.0302101\pi$
$647$	219.454	+	426.841i	0.339187	+	0.659724i	−0.656312	+	0.754489i	$0.727885\pi$
$648$	−19.6967	+	13.0312i	−0.0303962	+	0.0201099i
$649$	−22.4362	−	613.911i	−0.0345705	−	0.945934i
$650$	−115.279	+	95.9362i	−0.177353	+	0.147594i
$651$	102.234	+	122.847i	0.157041	+	0.188705i
$652$	−1256.11	−	831.036i	−1.92655	−	1.27460i
$653$	544.022	+	389.215i	0.833112	+	0.596041i	0.916300	−	0.400493i	$-0.131161\pi$
$653$	544.022	+	389.215i	0.833112	+	0.596041i	−0.0831874	+	0.996534i	$0.526510\pi$
$654$	848.571	−	124.884i	1.29751	−	0.190954i
$655$	31.3419	−	47.3734i	0.0478503	−	0.0723257i
$656$	272.695	+	210.568i	0.415693	+	0.320988i
$657$	48.6577	+	46.9119i	0.0740604	+	0.0714032i
$658$	−86.8497	+	254.577i	−0.131990	+	0.386895i
$659$	65.5792	−	154.321i	0.0995133	−	0.234174i	−0.863111	−	0.505014i	$-0.831487\pi$
$659$	65.5792	−	154.321i	0.0995133	−	0.234174i	0.962624	+	0.270840i	$0.0873013\pi$
$660$	−783.324	+	812.474i	−1.18685	+	1.23102i
$661$	−671.829	−	98.8728i	−1.01638	−	0.149581i	−0.383267	−	0.923638i	$-0.625201\pi$
$661$	−671.829	−	98.8728i	−1.01638	−	0.149581i	−0.633116	+	0.774057i	$0.718224\pi$
$662$	−785.668	+	876.858i	−1.18681	+	1.32456i
$663$	−298.208	+	580.018i	−0.449786	+	0.874839i
$664$	−2139.08	+	559.228i	−3.22150	+	0.842210i
$665$	−60.8272	−	273.062i	−0.0914694	−	0.410620i
$666$	20.7994	−	37.0606i	0.0312304	−	0.0556466i
$667$	−573.185	+	84.3554i	−0.859348	+	0.126470i
$668$	−2362.56	−	436.388i	−3.53677	−	0.653275i
$669$	142.688	+	545.788i	0.213285	+	0.815826i
$670$	−1850.12	+	786.215i	−2.76137	+	1.17346i
$671$	163.701	+	126.406i	0.243966	+	0.188385i
$672$	146.756	+	75.4525i	0.218387	+	0.112281i
$673$	−326.606	−	535.165i	−0.485299	−	0.795192i	0.512690	−	0.858574i	$-0.328649\pi$
$673$	−326.606	−	535.165i	−0.485299	−	0.795192i	−0.997989	+	0.0633810i	$0.979812\pi$
$674$	−197.376	−	323.413i	−0.292843	−	0.479842i
$675$	−44.4742	+	72.8737i	−0.0658877	+	0.107961i
$676$	−3.63788			−0.00538148
$677$	−66.3208	+	79.6928i	−0.0979628	+	0.117715i	−0.815372	−	0.578938i	$-0.803467\pi$
$677$	−66.3208	+	79.6928i	−0.0979628	+	0.117715i	0.717409	+	0.696652i	$0.245328\pi$
$678$	464.537	−	601.596i	0.685158	−	0.887310i
$679$	31.0955	+	55.4063i	0.0457960	+	0.0815998i
$680$	611.233	+	2743.92i	0.898873	+	4.03517i
$681$	−503.980	−	112.266i	−0.740059	−	0.164855i
$682$	−1904.44	+	809.299i	−2.79243	+	1.18666i
$683$	467.084	−	832.254i	0.683871	−	1.21853i	−0.281978	−	0.959421i	$-0.590990\pi$
$683$	467.084	−	832.254i	0.683871	−	1.21853i	0.965849	−	0.259107i	$-0.0834281\pi$
$684$	1428.01	+	429.624i	2.08773	+	0.628105i
$685$	−285.493	+	746.451i	−0.416778	+	1.08971i
$686$	−623.332	+	115.135i	−0.908647	+	0.167836i
$687$	587.819	+	453.899i	0.855632	+	0.660698i
$688$	−1462.49	−	2210.56i	−2.12571	−	3.21302i
$689$	973.316	−	594.006i	1.41265	−	0.862128i
$690$	13.9055	−	380.488i	0.0201529	−	0.551432i
$691$	532.491	+	689.599i	0.770609	+	0.997973i	0.999698	+	0.0245671i	$0.00782075\pi$
$691$	532.491	+	689.599i	0.770609	+	0.997973i	−0.229089	+	0.973406i	$0.573575\pi$
$692$	744.479	−	1751.90i	1.07584	−	2.53165i
$693$	−99.0537	−	70.8669i	−0.142935	−	0.102261i
$694$	622.067	+	1209.93i	0.896350	+	1.74341i
$695$	489.640	+	507.862i	0.704518	+	0.730736i
$696$	−1908.91	−	730.098i	−2.74269	−	1.04899i
$697$	261.007	−	48.2105i	0.374472	−	0.0691686i
$698$	113.641	+	377.726i	0.162809	+	0.541155i
$699$	178.619	+	467.017i	0.255535	+	0.668122i
$700$	54.1010	+	1.97720i	0.0772872	+	0.00282457i
$701$	−972.046	−	643.099i	−1.38666	−	0.917403i	−0.386668	−	0.922219i	$-0.626374\pi$
$701$	−972.046	−	643.099i	−1.38666	−	0.917403i	−0.999988	+	0.00481623i	$0.998467\pi$
$702$	−1222.99	+	417.226i	−1.74215	+	0.594339i
$703$	59.7988	−	11.0454i	0.0850624	−	0.0157118i
$704$	−314.531	+	326.236i	−0.446777	+	0.463403i
$705$	366.770	+	155.861i	0.520242	+	0.221079i
$706$	−1112.34	−	425.433i	−1.57555	−	0.602596i
$707$	9.56534	+	0.700093i	0.0135295	+	0.000990230i
$708$	225.791	+	863.664i	0.318914	+	1.21986i
$709$	639.046	−	572.588i	0.901335	−	0.807600i	−0.0806142	−	0.996745i	$-0.525688\pi$
$709$	639.046	−	572.588i	0.901335	−	0.807600i	0.981949	+	0.189146i	$0.0605719\pi$
$710$	751.330	+	1135.64i	1.05821	+	1.59949i
$711$	12.2772	−	167.742i	0.0172675	−	0.235925i
$712$	128.322	−	43.7774i	0.180228	−	0.0614852i
$713$	207.869	−	443.424i	0.291541	−	0.621914i
$714$	313.440	−	119.881i	0.438991	−	0.167900i
$715$	−713.126	+	435.215i	−0.997380	+	0.608692i
$716$	−246.454	−	2239.86i	−0.344210	−	3.12829i
$717$	27.3914	+	48.8063i	0.0382028	+	0.0680701i
$718$	−96.9716	−	10.6699i	−0.135058	−	0.0148606i
$719$	−612.328	−	405.112i	−0.851638	−	0.563439i	0.0486089	−	0.998818i	$-0.484521\pi$
$719$	−612.328	−	405.112i	−0.851638	−	0.563439i	−0.900247	+	0.435379i	$0.856614\pi$
$720$	−528.998	+	866.796i	−0.734720	+	1.20388i
$721$	−11.9192	−	326.139i	−0.0165315	−	0.452343i
$722$	672.736	+	1583.08i	0.931767	+	2.19263i
$723$	−178.219	+	465.972i	−0.246499	+	0.644497i
$724$	289.794	−	123.149i	0.400268	−	0.170096i
$725$	−173.510	+	12.6993i	−0.239324	+	0.0175163i
$726$	−137.570	+	106.228i	−0.189491	+	0.146320i
$727$	161.332	+	17.7516i	0.221915	+	0.0244176i	0.219645	−	0.975580i	$-0.429510\pi$
$727$	161.332	+	17.7516i	0.221915	+	0.0244176i	0.00226998	+	0.999997i	$0.499277\pi$
$728$	350.628	+	314.164i	0.481632	+	0.431544i
$729$	−366.500	+	283.002i	−0.502743	+	0.388206i
$730$	−225.781	−	77.0257i	−0.309289	−	0.105515i
$731$	−2020.20	−	297.311i	−2.76361	−	0.406719i
$732$	−272.128	−	127.568i	−0.371760	−	0.174274i
$733$	673.581	−	1103.70i	0.918937	−	1.50574i	0.0572115	−	0.998362i	$-0.481779\pi$
$733$	673.581	−	1103.70i	0.918937	−	1.50574i	0.861726	−	0.507374i	$-0.169384\pi$
$734$	−841.813	−	155.491i	−1.14688	−	0.211840i
$735$	49.5406	+	450.241i	0.0674022	+	0.612573i
$736$	18.4672	−	505.309i	0.0250913	−	0.686561i
$737$	−1211.56	+	316.744i	−1.64391	+	0.429775i
$738$	166.414	+	110.099i	0.225493	+	0.149185i
$739$	−135.592	+	608.693i	−0.183481	+	0.823671i	0.793198	+	0.608964i	$0.208415\pi$
$739$	−135.592	+	608.693i	−0.183481	+	0.823671i	−0.976678	+	0.214707i	$0.931120\pi$
$740$	−7.68117	+	104.948i	−0.0103800	+	0.141821i
$741$	−598.850	−	365.473i	−0.808164	−	0.493216i
$742$	−576.959	−	106.570i	−0.777573	−	0.143625i
$743$	621.226	+	693.330i	0.836105	+	0.933149i	0.998564	−	0.0535665i	$-0.0170589\pi$
$743$	621.226	+	693.330i	0.836105	+	0.933149i	−0.162459	+	0.986715i	$0.551943\pi$
$744$	1405.03	−	1005.21i	1.88848	−	1.35109i
$745$	−504.391	−	606.089i	−0.677036	−	0.813543i
$746$		−	1089.47i		−	1.46042i
$747$	−582.323	+	198.661i	−0.779549	+	0.265945i
$748$	222.494	+	3039.93i	0.297452	+	4.06407i
$749$	84.4362	+	25.4031i	0.112732	+	0.0339160i
$750$	−86.8078	+	788.938i	−0.115744	+	1.05192i
$751$	−644.533	−	94.8556i	−0.858233	−	0.126306i	−0.297924	−	0.954590i	$-0.596294\pi$
$751$	−644.533	−	94.8556i	−0.858233	−	0.126306i	−0.560309	+	0.828284i	$0.689317\pi$
$752$	1285.80	+	546.404i	1.70984	+	0.726602i
$753$	−203.875	−	363.267i	−0.270751	−	0.482426i
$754$	−2141.61	−	1532.19i	−2.84033	−	2.03208i
$755$	1228.52	+	689.477i	1.62717	+	0.913214i
$756$	429.291	+	182.429i	0.567846	+	0.241308i
$757$	80.5701	−	732.248i	0.106433	−	0.967302i	−0.815184	−	0.579202i	$-0.803364\pi$
$757$	80.5701	−	732.248i	0.106433	−	0.967302i	0.921617	−	0.388100i	$-0.126868\pi$
$758$	−536.036	−	749.241i	−0.707171	−	0.988445i
$759$	43.0814	−	233.239i	0.0567607	−	0.307297i
$760$	−2991.77	+	440.297i	−3.93654	+	0.579339i
$761$	−810.548	−	243.857i	−1.06511	−	0.320443i	−0.293117	−	0.956077i	$-0.594693\pi$
$761$	−810.548	−	243.857i	−1.06511	−	0.320443i	−0.771991	+	0.635633i	$0.780739\pi$
$762$	496.835	+	129.890i	0.652015	+	0.170459i
$763$	−152.942	−	170.693i	−0.200448	−	0.223713i
$764$	−1730.62	−	63.2479i	−2.26521	−	0.0827852i
$765$	225.381	+	749.136i	0.294616	+	0.979262i
$766$	321.198	+	267.303i	0.419319	+	0.348960i
$767$			660.818i			0.861562i
$768$	−345.072	+	565.422i	−0.449313	+	0.736227i
$769$	−63.6234	−	123.748i	−0.0827352	−	0.160921i	0.844327	−	0.535828i	$-0.180000\pi$
$769$	−63.6234	−	123.748i	−0.0827352	−	0.160921i	−0.927063	+	0.374907i	$0.877675\pi$
$770$	422.725	+	78.0812i	0.548993	+	0.101404i
$771$	−5.55851	+	4.62583i	−0.00720949	+	0.00599978i
$772$	1927.38	+	1603.98i	2.49661	+	2.07770i
$773$	49.0625	+	265.620i	0.0634703	+	0.343623i	0.999975	−	0.00703175i	$-0.00223829\pi$
$773$	49.0625	+	265.620i	0.0634703	+	0.343623i	−0.936505	+	0.350654i	$0.885959\pi$
$774$	−938.208	−	1215.02i	−1.21216	−	1.56979i
$775$	71.9735	−	128.243i	0.0928690	−	0.165475i
$776$	621.849	−	291.511i	0.801352	−	0.375658i
$777$	7.19786	−	0.526815i	0.00926365	−	0.000678012i
$778$	−7.44409	+	10.4049i	−0.00956825	+	0.0133740i
$779$	31.2273	+	283.804i	0.0400864	+	0.364318i
$780$	873.969	−	842.612i	1.12047	−	1.08027i
$781$	360.049	+	768.055i	0.461011	+	0.983425i
$782$	−740.276	−	713.715i	−0.946644	−	0.912680i
$783$	−1435.40	−	431.849i	−1.83321	−	0.551531i
$784$	173.676	+	1578.42i	0.221525	+	2.01329i
$785$	−41.1442	+	36.8654i	−0.0524130	+	0.0469623i
$786$	−35.8728	+	63.9185i	−0.0456397	+	0.0813212i
$787$	−495.502	−	477.724i	−0.629609	−	0.607019i	0.309392	−	0.950935i	$-0.399875\pi$
$787$	−495.502	−	477.724i	−0.629609	−	0.607019i	−0.939001	+	0.343915i	$0.888247\pi$
$788$	1528.57	+	1369.60i	1.93981	+	1.73807i
$789$	475.577	−	314.639i	0.602759	−	0.398781i
$790$	212.065	+	554.465i	0.268437	+	0.701855i
$791$	−202.557	−	14.8253i	−0.256077	−	0.0187424i
$792$	−842.146	+	1011.94i	−1.06332	+	1.27771i
$793$	−171.008	−	142.314i	−0.215647	−	0.179463i
$794$	1398.56	+	655.618i	1.76141	+	0.825715i
$795$	−219.863	+	840.989i	−0.276558	+	1.05785i
$796$	−126.511	−	859.625i	−0.158933	−	1.07993i
$797$	−37.2524	−	1019.32i	−0.0467407	−	1.27894i	−0.791318	−	0.611405i	$-0.790605\pi$
$797$	−37.2524	−	1019.32i	−0.0467407	−	1.27894i	0.744577	−	0.667537i	$-0.232651\pi$
$798$	104.001	+	345.683i	0.130327	+	0.433187i
$799$	974.529	−	456.840i	1.21969	−	0.571765i
$800$	16.6068	−	150.928i	0.0207585	−	0.188660i
$801$	34.7255	−	14.7567i	0.0433527	−	0.0184229i
$802$	733.741	+	2438.85i	0.914889	+	3.04096i
$803$	−132.165	−	67.9508i	−0.164589	−	0.0846212i
$804$	1618.37	−	832.061i	2.01290	−	1.03490i
$805$	−86.8427	+	52.9994i	−0.107879	+	0.0658377i
$806$	2079.01	−	795.154i	2.57942	−	0.986544i
$807$	−10.1540	−	138.734i	−0.0125824	−	0.171913i
$808$	15.0949	−	102.568i	0.0186818	−	0.126940i
$809$	101.895	+	1392.18i	0.125951	+	1.72087i	0.567282	+	0.823523i	$0.307995\pi$
$809$	101.895	+	1392.18i	0.125951	+	1.72087i	−0.441331	+	0.897344i	$0.645494\pi$
$810$	10.6067	−	20.6302i	0.0130947	−	0.0254694i
$811$	−721.042	−	1007.83i	−0.889078	−	1.24270i	−0.969289	−	0.245925i	$-0.920908\pi$
$811$	−721.042	−	1007.83i	−0.889078	−	1.24270i	0.0802110	−	0.996778i	$-0.474441\pi$
$812$	206.674	+	927.789i	0.254524	+	1.14260i
$813$	−198.017	−	422.409i	−0.243563	−	0.519568i
$814$	−20.3171	+	91.2066i	−0.0249596	+	0.112047i
$815$	847.671	+	62.0415i	1.04009	+	0.0761246i
$816$	−502.153	−	1669.09i	−0.615384	−	2.04545i
$817$	477.596	−	2144.00i	0.584573	−	2.62423i
$818$	−744.285	+	1587.70i	−0.909883	+	1.94096i
$819$	103.696	+	80.0713i	0.126613	+	0.0977671i
$820$	−488.803	−	71.9369i	−0.596101	−	0.0877279i
$821$	1046.08	+	356.873i	1.27415	+	0.434681i	0.875855	−	0.482574i	$-0.160298\pi$
$821$	1046.08	+	356.873i	1.27415	+	0.434681i	0.398299	+	0.917255i	$0.369601\pi$
$822$	297.102	−	987.524i	0.361437	−	1.20137i
$823$	1049.47	−	694.325i	1.27518	−	0.843651i	0.281906	−	0.959442i	$-0.409033\pi$
$823$	1049.47	−	694.325i	1.27518	−	0.843651i	0.993274	+	0.115791i	$0.0369404\pi$
$824$	−3525.38	−	128.840i	−4.27838	−	0.156359i
$825$	18.0147	−	68.9074i	0.0218361	−	0.0835241i
$826$	226.904	−	253.240i	0.274702	−	0.306586i
$827$	312.320	+	69.5722i	0.377654	+	0.0841261i	0.402150	−	0.915574i	$-0.368263\pi$
$827$	312.320	+	69.5722i	0.377654	+	0.0841261i	−0.0244956	+	0.999700i	$0.507798\pi$
$828$	−19.8064	−	541.953i	−0.0239208	−	0.654532i
$829$	−496.347	+	355.106i	−0.598730	+	0.428355i	−0.840371	−	0.542011i	$-0.817663\pi$
$829$	−496.347	+	355.106i	−0.598730	+	0.428355i	0.241641	+	0.970366i	$0.422314\pi$
$830$	1563.37	−	1507.28i	1.88358	−	1.81600i
$831$	332.080	−	127.010i	0.399615	−	0.152840i
$832$	350.928	−	338.337i	0.421789	−	0.406655i
$833$	994.928	+	711.810i	1.19439	+	0.854514i
$834$	−677.970	−	607.464i	−0.812914	−	0.728374i
$835$	1283.17	−	437.758i	1.53674	−	0.524261i
$836$	−3278.82			−3.92203
$837$	973.924	−	810.506i	1.16359	−	0.968346i
$838$	−1778.85	+	465.052i	−2.12273	+	0.554954i
$839$	−420.076	+	405.004i	−0.500686	+	0.482722i	−0.901099	−	0.433613i	$-0.857239\pi$
$839$	−420.076	+	405.004i	−0.500686	+	0.482722i	0.400413	+	0.916335i	$0.368867\pi$
$840$	−358.655	+	13.1076i	−0.426970	+	0.0156042i
$841$	−714.729	−	2095.04i	−0.849856	−	2.49113i
$842$	−1005.95	+	185.809i	−1.19472	+	0.220676i
$843$	358.419	+	764.577i	0.425171	+	0.906971i
$844$	−1792.49	−	468.617i	−2.12380	−	0.555234i
$845$	1.79025	−	1.00474i	0.00211864	−	0.00118904i
$846$	765.794	+	261.253i	0.905194	+	0.308809i
$847$	43.9562	+	14.9958i	0.0518963	+	0.0177046i
$848$	−770.781	+	2948.28i	−0.908940	+	3.47674i
$849$	113.170	+	220.118i	0.133298	+	0.259267i
$850$	−206.058	−	229.974i	−0.242421	−	0.270558i
$851$	−10.8234	−	19.2852i	−0.0127184	−	0.0226618i
$852$	−753.354	−	975.627i	−0.884219	−	1.14510i
$853$	−176.576	−	792.676i	−0.207006	−	0.929280i	−0.961893	−	0.273425i	$-0.911843\pi$
$853$	−176.576	−	792.676i	−0.207006	−	0.929280i	0.754887	−	0.655855i	$-0.227692\pi$
$854$	16.6679	+	113.257i	0.0195175	+	0.132619i
$855$	−821.398	+	182.974i	−0.960700	+	0.214005i
$856$	340.484	−	890.230i	0.397762	−	1.03999i
$857$	175.087	−	373.494i	0.204302	−	0.435815i	−0.776685	−	0.629889i	$-0.783100\pi$
$857$	175.087	−	373.494i	0.204302	−	0.435815i	0.980987	+	0.194074i	$0.0621701\pi$
$858$	876.753	−	627.263i	1.02186	−	0.731076i
$859$	542.582	−	59.7010i	0.631644	−	0.0695006i	0.212118	−	0.977244i	$-0.431964\pi$
$859$	542.582	−	59.7010i	0.631644	−	0.0695006i	0.419526	+	0.907743i	$0.362196\pi$
$860$	3380.37	+	1737.97i	3.93067	+	2.02089i
$861$			33.8858i			0.0393563i
$862$	1488.17	−	524.257i	1.72641	−	0.608187i
$863$	1002.01			1.16108			0.580540	−	0.814232i	$-0.302841\pi$
$863$	1002.01			1.16108			0.580540	+	0.814232i	$0.302841\pi$
$864$	598.185	−	1163.48i	0.692343	−	1.34662i
$865$	117.486	+	1067.75i	0.135822	+	1.23439i
$866$	−357.996	−	500.387i	−0.413391	−	0.577814i
$867$	−726.463	−	340.552i	−0.837904	−	0.392793i
$868$	−750.461	−	287.027i	−0.864586	−	0.330676i
$869$	80.4070	+	360.959i	0.0925282	+	0.415373i
$870$	1986.03	−	292.283i	2.28279	−	0.335957i
$871$	1314.84	−	292.893i	1.50957	−	0.336272i
$872$	−1960.85	+	1514.12i	−2.24869	+	1.73638i
$873$	166.668	−	93.5384i	0.190914	−	0.107146i
$874$	823.828	−	738.153i	0.942595	−	0.844569i
$875$	188.615	−	96.9736i	0.215560	−	0.110827i
$876$	208.929	+	54.6211i	0.238503	+	0.0623529i
$877$	260.527	−	763.666i	0.297066	−	0.870771i	−0.691817	−	0.722073i	$-0.743189\pi$
$877$	260.527	−	763.666i	0.297066	−	0.870771i	0.988883	−	0.148698i	$-0.0475082\pi$
$878$	501.598	−	1470.30i	0.571296	−	1.67460i
$879$	78.9817	+	140.730i	0.0898541	+	0.160103i
$880$	564.733	−	2160.14i	0.641742	−	2.45470i
$881$	9.05940	−	4.24687i	0.0102831	−	0.00482051i	−0.419308	−	0.907844i	$-0.637727\pi$
$881$	9.05940	−	4.24687i	0.0102831	−	0.00482051i	0.429591	+	0.903023i	$0.358658\pi$
$882$	167.047	+	904.377i	0.189395	+	1.02537i
$883$	−120.949	+	41.2620i	−0.136975	+	0.0467293i	−0.390521	−	0.920594i	$-0.627705\pi$
$883$	−120.949	+	41.2620i	−0.136975	+	0.0467293i	0.253547	+	0.967323i	$0.418403\pi$
$884$	−119.747	−	3276.57i	−0.135460	−	3.70653i
$885$	−349.648	−	362.660i	−0.395083	−	0.409785i
$886$	379.043	+	1449.86i	0.427814	+	1.63641i
$887$	489.656	+	588.382i	0.552036	+	0.663340i	0.969425	−	0.245388i	$-0.0789153\pi$
$887$	489.656	+	588.382i	0.552036	+	0.663340i	−0.417389	+	0.908728i	$0.637055\pi$
$888$		−	78.0130i		−	0.0878525i
$889$	−44.3059	−	129.871i	−0.0498380	−	0.146087i
$890$	−88.8685	+	99.1832i	−0.0998523	+	0.111442i
$891$	8.40828	−	11.7526i	0.00943690	−	0.0131904i
$892$	−1968.44	−	2041.70i	−2.20677	−	2.28890i
$893$	413.594	+	1081.38i	0.463151	+	1.21096i
$894$	706.207	+	732.488i	0.789940	+	0.819337i
$895$	739.904	+	1034.20i	0.826708	+	1.15553i
$896$	102.067	−	3.73019i	0.113914	−	0.00416316i
$897$	−55.4743	+	249.032i	−0.0618442	+	0.277628i
$898$	2119.45	+	1899.04i	2.36019	+	2.11474i
$899$	2498.08	+	653.084i	2.77873	+	0.726456i
$900$	5.94761	−	162.741i	0.00660846	−	0.180824i
$901$	1295.36	+	1957.94i	1.43769	+	2.17308i
$902$	−420.127	−	126.398i	−0.465773	−	0.140130i
$903$	84.1721	−	246.729i	0.0932138	−	0.273232i
$904$	−319.651	+	2171.99i	−0.353596	+	2.40264i
$905$	−108.599	+	140.641i	−0.119999	+	0.155404i
$906$	−1645.96	−	771.595i	−1.81673	−	0.851650i
$907$	−1108.95	−	247.029i	−1.22265	−	0.272358i	−0.441825	−	0.897101i	$-0.645669\pi$
$907$	−1108.95	−	247.029i	−1.22265	−	0.272358i	−0.780830	+	0.624743i	$0.785204\pi$
$908$	2485.71	−	747.840i	2.73757	−	0.823612i
$909$	2.10595	−	28.7735i	0.00231678	−	0.0316540i
$910$	−451.349	−	100.542i	−0.495988	−	0.110486i
$911$	−582.919	+	273.261i	−0.639867	+	0.299957i	−0.717010	−	0.697063i	$-0.754490\pi$
$911$	−582.919	+	273.261i	−0.639867	+	0.299957i	0.0771433	+	0.997020i	$0.475420\pi$
$912$	1830.09	−	407.670i	2.00668	−	0.447006i
$913$	1100.24	−	787.155i	1.20508	−	0.862163i
$914$	482.408	+	248.023i	0.527799	+	0.271360i
$915$	169.151	−	12.3802i	0.184864	−	0.0135303i
$916$	−3693.85	−	543.621i	−4.03258	−	0.593473i
$917$	19.5334	−	1.42966i	0.0213014	−	0.00155906i
$918$	−950.409	−	2484.94i	−1.03530	−	2.70690i
$919$	−277.743	−	455.100i	−0.302223	−	0.495212i	0.665780	−	0.746148i	$-0.268099\pi$
$919$	−277.743	−	455.100i	−0.302223	−	0.495212i	−0.968004	+	0.250936i	$0.919262\pi$
$920$	502.843	+	978.037i	0.546569	+	1.06308i
$921$	−229.132	+	445.664i	−0.248786	+	0.483892i
$922$	476.168	−	143.258i	0.516451	−	0.155377i
$923$	−356.868	−	839.781i	−0.386640	−	0.909839i
$924$	−386.803	−	42.5604i	−0.418618	−	0.0460611i
$925$	−2.81872	−	6.01288i	−0.00304727	−	0.00650042i
$926$	75.1668	−	22.6143i	0.0811737	−	0.0244215i
$927$	−981.059	+	35.8542i	−1.05832	+	0.0386777i
$928$	2637.55	−	388.167i	2.84219	−	0.418283i
$929$	1179.26	+	308.299i	1.26938	+	0.331861i	0.825591	−	0.564268i	$-0.190842\pi$
$929$	1179.26	+	308.299i	1.26938	+	0.331861i	0.443793	+	0.896129i	$0.353632\pi$
$930$	−720.244	+	1536.42i	−0.774456	+	1.65206i
$931$	−841.780	+	1011.50i	−0.904167	+	1.08647i
$932$	−1932.16	−	1607.95i	−2.07313	−	1.72527i
$933$	0.0649661	−	0.887629i	6.96314e−5	−	0.000951371i
$934$	−1027.98	+	393.171i	−1.10063	+	0.420954i
$935$	−949.082	−	1434.54i	−1.01506	−	1.53427i
$936$	945.038	−	1054.72i	1.00966	−	1.12684i
$937$	−205.696	+	213.351i	−0.219526	+	0.227696i	−0.820607	−	0.571492i	$-0.806365\pi$
$937$	−205.696	+	213.351i	−0.219526	+	0.227696i	0.601081	+	0.799188i	$0.294737\pi$
$938$	−604.446	−	339.231i	−0.644398	−	0.361654i
$939$	93.5241	+	104.379i	0.0995996	+	0.111160i
$940$	−1991.44	+	219.121i	−2.11855	+	0.233107i
$941$	312.445	−	1038.52i	0.332035	−	1.10364i	−0.616603	−	0.787274i	$-0.711492\pi$
$941$	312.445	−	1038.52i	0.332035	−	1.10364i	0.948638	−	0.316363i	$-0.102462\pi$
$942$	49.4775	−	51.3188i	0.0525239	−	0.0544785i
$943$	94.0157	−	44.0727i	0.0996985	−	0.0467367i
$944$	−1225.77	−	1271.39i	−1.29849	−	1.34681i
$945$	−261.644	+	28.7891i	−0.276872	+	0.0304646i
$946$	2745.05	+	1963.92i	2.90175	+	2.07602i
$947$	−45.0341	−	615.299i	−0.0475545	−	0.649735i	−0.966716	−	0.255853i	$-0.917644\pi$
$947$	−45.0341	−	615.299i	−0.0475545	−	0.649735i	0.919161	−	0.393882i	$-0.128868\pi$
$948$	−228.094	−	486.569i	−0.240605	−	0.513258i
$949$	139.404	+	78.2374i	0.146896	+	0.0824419i
$950$	262.905	−	203.009i	0.276742	−	0.213693i
$951$	72.8017	−	13.4472i	0.0765528	−	0.0141400i
$952$	−620.030	+	745.044i	−0.651292	+	0.782609i
$953$	290.111	+	348.605i	0.304419	+	0.365797i	0.898779	−	0.438402i	$-0.144455\pi$
$953$	290.111	+	348.605i	0.304419	+	0.365797i	−0.594360	+	0.804199i	$0.702595\pi$
$954$	−320.573	+	1735.55i	−0.336030	+	1.81924i
$955$	869.129	−	446.850i	0.910083	−	0.467906i
$956$	−240.172	−	146.575i	−0.251226	−	0.153321i
$957$	1250.52			1.30671
$958$	−1479.39	+	1777.67i	−1.54425	+	1.85561i
$959$	−263.875	+	79.3883i	−0.275157	+	0.0827824i
$960$	−13.5720	+	371.362i	−0.0141374	+	0.386836i
$961$	−909.801	+	815.185i	−0.946723	+	0.848268i
$962$	25.4235	−	97.2462i	0.0264278	−	0.101088i
$963$	76.4150	−	253.993i	0.0793510	−	0.263752i
$964$	−365.180	−	2481.36i	−0.378817	−	2.57402i
$965$	−1391.49	−	257.021i	−1.44196	−	0.266343i
$966$	106.769	−	76.3865i	0.110527	−	0.0790751i
$967$	151.480	+	16.6676i	0.156650	+	0.0172364i	0.187356	−	0.982292i	$-0.440008\pi$
$967$	151.480	+	16.6676i	0.156650	+	0.0172364i	−0.0307062	+	0.999528i	$0.509776\pi$
$968$	196.347	−	462.042i	0.202837	−	0.477316i
$969$	706.933	−	1259.62i	0.729549	−	1.29992i
$970$	−392.505	+	548.621i	−0.404644	+	0.565589i
$971$	−590.201	+	331.237i	−0.607828	+	0.341130i	−0.762649	−	0.646813i	$-0.776101\pi$
$971$	−590.201	+	331.237i	−0.607828	+	0.341130i	0.154821	+	0.987943i	$0.450520\pi$
$972$	889.312	−	2092.73i	0.914930	−	2.15301i
$973$	−35.4163	+	240.650i	−0.0363991	+	0.247328i
$974$	−30.1645	−	3.31903i	−0.0309697	−	0.00340763i
$975$	−22.0724	+	73.3657i	−0.0226384	+	0.0752469i
$976$	592.996	−	43.4017i	0.607577	−	0.0444689i
$977$	516.327	+	1513.48i	0.528482	+	1.54911i	0.808130	+	0.589004i	$0.200480\pi$
$977$	516.327	+	1513.48i	0.528482	+	1.54911i	−0.279648	+	0.960102i	$0.590218\pi$
$978$	−1096.74			−1.12141
$979$	−63.7670	+	53.0673i	−0.0651348	+	0.0542056i
$980$	−1324.99	−	1852.00i	−1.35203	−	1.88979i
$981$	−513.462	+	460.064i	−0.523407	+	0.468975i
$982$	−128.100	+	693.524i	−0.130448	+	0.706236i
$983$	903.805	−	1480.94i	0.919435	−	1.50655i	0.0582244	−	0.998304i	$-0.481456\pi$
$983$	903.805	−	1480.94i	0.919435	−	1.50655i	0.861211	−	0.508248i	$-0.169707\pi$
$984$	365.309	+	26.7372i	0.371249	+	0.0271719i
$985$	−1130.49	−	251.828i	−1.14771	−	0.255663i
$986$	2991.45	−	4521.59i	3.03393	−	4.58579i
$987$	34.7550	+	132.940i	0.0352127	+	0.134691i
$988$	3524.63	+	128.813i	3.56744	+	0.130377i
$989$	−794.022	+	87.3672i	−0.802853	+	0.0883390i
$990$	234.876	−	1271.60i	0.237249	−	1.28444i
$991$	−158.915	−	96.9847i	−0.160359	−	0.0978655i	0.438458	−	0.898752i	$-0.355525\pi$
$991$	−158.915	−	96.9847i	−0.160359	−	0.0978655i	−0.598816	+	0.800886i	$0.704362\pi$
$992$	−956.522	+	2040.45i	−0.964236	+	2.05690i
$993$	−87.5699	+	595.028i	−0.0881873	+	0.599222i
$994$	−151.595	+	444.360i	−0.152510	+	0.447042i
$995$	299.675	+	388.092i	0.301181	+	0.390042i
$996$	−1311.84	+	1464.10i	−1.31711	+	1.46998i
$997$	143.983	−	1308.57i	0.144417	−	1.31250i	−0.674364	−	0.738399i	$-0.735582\pi$
$997$	143.983	−	1308.57i	0.144417	−	1.31250i	0.818781	−	0.574106i	$-0.194650\pi$
$998$	−199.828	−	258.785i	−0.200228	−	0.259304i
$999$	−4.17657	−	57.0643i	−0.00418075	−	0.0571214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	431.3.f.a.101.4	✓	2982
431.367	odd	86	inner	431.3.f.a.367.4	yes	2982

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
431.3.f.a.101.4	✓	2982	1.1	even	1	trivial
431.3.f.a.367.4	yes	2982	431.367	odd	86	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 431 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	431.f (of order \(86\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67388 + 3.25571i) q^{2} +(0.204533 + 1.85887i) q^{3} +(-5.47036 - 7.64616i) q^{4} +(4.80381 + 2.25193i) q^{5} +(-6.39430 - 2.44561i) q^{6} +(0.397750 + 1.78556i) q^{7} +(19.5632 - 2.87911i) q^{8} +(5.37113 - 1.19647i) q^{9} +(-15.3726 + 11.8704i) q^{10} +(-10.5510 + 5.92152i) q^{11} +(13.0943 - 11.7326i) q^{12} +(11.5747 - 5.95095i) q^{13} +(-6.47904 - 1.69384i) q^{14} +(-3.20350 + 9.39024i) q^{15} +(-11.2306 + 32.9196i) q^{16} +(13.1145 + 23.3675i) q^{17} +(-5.09525 + 19.4896i) q^{18} +(-26.0993 + 12.2349i) q^{19} +(-9.05992 - 49.0496i) q^{20} +(-3.23776 + 1.10457i) q^{21} +(-1.61765 - 44.2630i) q^{22} +(7.27573 + 7.54649i) q^{23} +(9.35322 + 35.7766i) q^{24} +(2.01356 + 2.41955i) q^{25} +47.6450i q^{26} +(8.75698 + 25.6688i) q^{27} +(11.4768 - 12.8089i) q^{28} +(-32.1584 + 44.9493i) q^{29} +(-25.2096 - 26.1478i) q^{30} +(-16.6892 - 43.6355i) q^{31} +(-33.4797 - 34.7256i) q^{32} +(-13.1654 - 18.4018i) q^{33} +(-98.0300 + 3.58264i) q^{34} +(-2.11024 + 9.47318i) q^{35} +(-38.5304 - 34.5234i) q^{36} +(-2.04106 - 0.533603i) q^{37} +(3.85387 - 105.452i) q^{38} +(13.4294 + 20.2986i) q^{39} +(100.462 + 30.2244i) q^{40} +(3.19822 - 9.37474i) q^{41} +(1.82345 - 12.3901i) q^{42} +(-46.5736 + 60.3148i) q^{43} +(102.995 + 48.2820i) q^{44} +(28.4963 + 6.34782i) q^{45} +(-36.7479 + 11.0558i) q^{46} +(2.93194 - 40.0589i) q^{47} +(-63.4902 - 14.1430i) q^{48} +(41.3370 - 19.3780i) q^{49} +(-11.2478 + 2.50556i) q^{50} +(-40.7547 + 29.1575i) q^{51} +(-108.820 - 55.9480i) q^{52} +(87.3782 - 6.39526i) q^{53} +(-98.2283 - 14.4562i) q^{54} +(-64.0200 + 4.68566i) q^{55} +(12.9221 + 33.7861i) q^{56} +(-28.0812 - 46.0127i) q^{57} +(-92.5126 - 179.938i) q^{58} +(-23.2160 + 45.1555i) q^{59} +(89.3236 - 26.8735i) q^{60} +(-6.68564 - 15.7326i) q^{61} +(170.000 + 18.7053i) q^{62} +(4.27273 + 9.11456i) q^{63} +(35.8664 - 10.7906i) q^{64} +(69.0037 - 2.52184i) q^{65} +(81.9481 - 12.0603i) q^{66} +(100.137 + 26.1791i) q^{67} +(106.931 - 228.104i) q^{68} +(-12.5398 + 15.0681i) q^{69} +(-27.3097 - 22.7273i) q^{70} +(5.11764 - 69.9222i) q^{71} +(101.632 - 38.8709i) q^{72} +(6.77721 + 10.2438i) q^{73} +(5.15374 - 5.75192i) q^{74} +(-4.08578 + 4.23782i) q^{75} +(236.322 + 132.631i) q^{76} +(-14.7699 - 16.4842i) q^{77} +(-88.5656 + 9.74499i) q^{78} +(8.80568 - 29.2688i) q^{79} +(-128.082 + 132.849i) q^{80} +(-1.08143 + 0.506955i) q^{81} +(25.1680 + 26.1046i) q^{82} +(-111.141 + 12.2290i) q^{83} +(26.1574 + 18.7140i) q^{84} +(10.3774 + 141.786i) q^{85} +(-118.409 - 252.590i) q^{86} +(-90.1322 - 50.5846i) q^{87} +(-189.363 + 146.222i) q^{88} +(6.74264 - 1.24543i) q^{89} +(-68.3659 + 82.1502i) q^{90} +(15.2296 + 18.3002i) q^{91} +(17.9008 - 96.9134i) q^{92} +(77.6990 - 39.9478i) q^{93} +(125.513 + 76.5993i) q^{94} -152.928 q^{95} +(57.7026 - 69.3369i) q^{96} +(33.2592 - 10.0062i) q^{97} +(-6.10389 + 167.018i) q^{98} +(-49.5860 + 44.4293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2982 q - 43 q^{2} - 41 q^{3} - 187 q^{4} - 41 q^{5} - 33 q^{6} - 43 q^{7} - 37 q^{8} - 252 q^{9} - 23 q^{10} + 187 q^{11} + 19 q^{12} - 43 q^{13} - 43 q^{14} - 71 q^{15} - 359 q^{16} - 43 q^{17} - 93 q^{18}+ \cdots - 609 q^{99}+O(q^{100}) \) 2982 * q - 43 * q^2 - 41 * q^3 - 187 * q^4 - 41 * q^5 - 33 * q^6 - 43 * q^7 - 37 * q^8 - 252 * q^9 - 23 * q^10 + 187 * q^11 + 19 * q^12 - 43 * q^13 - 43 * q^14 - 71 * q^15 - 359 * q^16 - 43 * q^17 - 93 * q^18 - 55 * q^19 + 9 * q^20 - 172 * q^21 - 47 * q^22 + 45 * q^23 + 17 * q^24 - 436 * q^25 + 37 * q^27 - 43 * q^28 - 93 * q^29 - 911 * q^30 - 43 * q^31 + 181 * q^32 + 733 * q^33 - 43 * q^34 - 43 * q^35 - 521 * q^36 - 43 * q^37 + 691 * q^38 - 43 * q^39 + 199 * q^40 + 456 * q^41 - 43 * q^42 - 43 * q^43 - 161 * q^44 - 3 * q^45 - 279 * q^46 - 43 * q^47 + 271 * q^48 + 362 * q^49 - 21 * q^50 - 43 * q^51 - 2107 * q^52 + 53 * q^53 - 2864 * q^54 + 111 * q^55 - 1978 * q^56 + 11 * q^57 - 349 * q^58 + 59 * q^59 + 29 * q^60 - 1433 * q^61 - 43 * q^62 - 2451 * q^63 - 801 * q^64 - 43 * q^65 - 253 * q^66 + 3053 * q^67 - 43 * q^68 + 25 * q^69 - 1978 * q^70 + 2021 * q^71 - 63 * q^72 - 43 * q^73 - 43 * q^74 - 401 * q^75 - 225 * q^76 + 645 * q^77 + 344 * q^78 + 3397 * q^79 + 227 * q^80 - 1054 * q^81 - 845 * q^82 - 43 * q^83 + 6106 * q^84 - 43 * q^85 - 43 * q^86 - 1021 * q^87 + 6277 * q^88 - 43 * q^89 - 815 * q^90 - 147 * q^91 - 239 * q^92 + 2193 * q^93 - 43 * q^94 - 70 * q^95 + 129 * q^96 + 125 * q^97 + 643 * q^98 - 609 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more