LMFDB - Embedded newform 431.3.f.a.101.61

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			101.61
Character	$\chi$	$=$	431.101
Dual form			431.3.f.a.367.61

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36915 - 2.66302i) q^{2} +(0.389464 + 3.53958i) q^{3} +(-2.88966 - 4.03900i) q^{4} +(2.44851 + 1.14782i) q^{5} +(9.95921 + 3.80907i) q^{6} +(1.14577 + 5.14355i) q^{7} +(-2.86250 + 0.421272i) q^{8} +(-3.59225 + 0.800208i) q^{9} +(6.40905 - 4.94890i) q^{10} +(-9.71760 + 5.45378i) q^{11} +(13.1710 - 11.8012i) q^{12} +(-4.81208 + 2.47406i) q^{13} +(15.2661 + 3.99109i) q^{14} +(-3.10918 + 9.11374i) q^{15} +(3.61669 - 10.6014i) q^{16} +(9.75194 + 17.3761i) q^{17} +(-2.78737 + 10.6618i) q^{18} +(4.09796 - 1.92105i) q^{19} +(-2.43934 - 13.2064i) q^{20} +(-17.7598 + 6.05879i) q^{21} +(1.21865 + 33.3452i) q^{22} +(24.2209 + 25.1222i) q^{23} +(-2.60597 - 9.96796i) q^{24} +(-11.3141 - 13.5953i) q^{25} +16.2020i q^{26} +(6.11637 + 17.9285i) q^{27} +(17.4639 - 19.4909i) q^{28} +(2.13559 - 2.98501i) q^{29} +(20.0131 + 20.7579i) q^{30} +(16.9451 + 44.3048i) q^{31} +(-31.3126 - 32.4779i) q^{32} +(-23.0887 - 32.2721i) q^{33} +(59.6248 - 2.17907i) q^{34} +(-3.09840 + 13.9092i) q^{35} +(13.6124 + 12.1968i) q^{36} +(-37.3028 - 9.75224i) q^{37} +(0.494954 - 13.5432i) q^{38} +(-10.6313 - 16.0692i) q^{39} +(-7.49240 - 2.25413i) q^{40} +(-0.350998 + 1.02886i) q^{41} +(-8.18115 + 55.5900i) q^{42} +(37.6488 - 48.7568i) q^{43} +(50.1084 + 23.4898i) q^{44} +(-9.71417 - 2.16392i) q^{45} +(100.063 - 30.1045i) q^{46} +(4.08666 - 55.8359i) q^{47} +(38.9330 + 8.67269i) q^{48} +(19.2237 - 9.01168i) q^{49} +(-51.6953 + 11.5156i) q^{50} +(-57.7061 + 41.2851i) q^{51} +(23.8980 + 12.2868i) q^{52} +(72.2397 - 5.28726i) q^{53} +(56.1183 + 8.25890i) q^{54} +(-30.0536 + 2.19964i) q^{55} +(-5.44661 - 14.2407i) q^{56} +(8.39570 + 13.7569i) q^{57} +(-5.02519 - 9.77406i) q^{58} +(-10.8906 + 21.1823i) q^{59} +(45.7949 - 13.7776i) q^{60} +(-25.4347 - 59.8528i) q^{61} +(141.185 + 15.5348i) q^{62} +(-8.23182 - 17.5601i) q^{63} +(-86.4555 + 26.0106i) q^{64} +(-14.6222 + 0.534389i) q^{65} +(-117.553 + 17.3003i) q^{66} +(-95.6726 - 25.0121i) q^{67} +(42.0024 - 89.5992i) q^{68} +(-79.4890 + 95.5159i) q^{69} +(32.7983 + 27.2949i) q^{70} +(4.90399 - 67.0031i) q^{71} +(9.94570 - 3.80391i) q^{72} +(47.3644 + 71.5914i) q^{73} +(-77.0437 + 85.9859i) q^{74} +(43.7152 - 45.3420i) q^{75} +(-19.6008 - 11.0005i) q^{76} +(-39.1860 - 43.7341i) q^{77} +(-57.3484 + 6.31012i) q^{78} +(20.3643 - 67.6880i) q^{79} +(21.0239 - 21.8063i) q^{80} +(-91.0683 + 42.6910i) q^{81} +(2.25930 + 2.34338i) q^{82} +(-17.9354 + 1.97345i) q^{83} +(75.7912 + 54.2239i) q^{84} +(3.93319 + 53.7391i) q^{85} +(-78.2934 - 167.015i) q^{86} +(11.3974 + 6.39654i) q^{87} +(25.5190 - 19.7052i) q^{88} +(-106.838 + 19.7341i) q^{89} +(-19.0628 + 22.9063i) q^{90} +(-18.2390 - 21.9165i) q^{91} +(31.4787 - 170.423i) q^{92} +(-150.221 + 77.2338i) q^{93} +(-143.097 - 87.3307i) q^{94} +12.2389 q^{95} +(102.763 - 123.482i) q^{96} +(-35.7289 + 10.7492i) q^{97} +(2.32184 - 63.5313i) q^{98} +(30.5439 - 27.3675i) 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 $

$2$	1.36915	−	2.66302i	0.684577	−	1.33151i	−0.247372	−	0.968920i	$-0.579567\pi$
$2$	1.36915	−	2.66302i	0.684577	−	1.33151i	0.931949	−	0.362590i	$-0.118107\pi$
$3$	0.389464	+	3.53958i	0.129821	+	1.17986i	0.864924	+	0.501903i	$0.167367\pi$
$3$	0.389464	+	3.53958i	0.129821	+	1.17986i	−0.735102	+	0.677956i	$0.762866\pi$
$4$	−2.88966	−	4.03900i	−0.722415	−	1.00975i
$5$	2.44851	+	1.14782i	0.489703	+	0.229563i	0.653494	−	0.756932i	$-0.273303\pi$
$5$	2.44851	+	1.14782i	0.489703	+	0.229563i	−0.163791	+	0.986495i	$0.552372\pi$
$6$	9.95921	+	3.80907i	1.65987	+	0.634846i
$7$	1.14577	+	5.14355i	0.163682	+	0.734793i	0.986133	+	0.165957i	$0.0530712\pi$
$7$	1.14577	+	5.14355i	0.163682	+	0.734793i	−0.822451	+	0.568836i	$0.807394\pi$
$8$	−2.86250	+	0.421272i	−0.357812	+	0.0526590i
$9$	−3.59225	+	0.800208i	−0.399139	+	0.0889120i
$10$	6.40905	−	4.94890i	0.640905	−	0.494890i
$11$	−9.71760	+	5.45378i	−0.883418	+	0.495798i	−0.863699	−	0.504007i	$-0.831858\pi$
$11$	−9.71760	+	5.45378i	−0.883418	+	0.495798i	−0.0197185	+	0.999806i	$0.506277\pi$
$12$	13.1710	−	11.8012i	1.09758	−	0.983436i
$13$	−4.81208	+	2.47406i	−0.370160	+	0.190312i	−0.632311	−	0.774714i	$-0.717894\pi$
$13$	−4.81208	+	2.47406i	−0.370160	+	0.190312i	0.262151	+	0.965027i	$0.415568\pi$
$14$	15.2661	+	3.99109i	1.09044	+	0.285078i
$15$	−3.10918	+	9.11374i	−0.207278	+	0.607583i
$16$	3.61669	−	10.6014i	0.226043	−	0.662586i
$17$	9.75194	+	17.3761i	0.573644	+	1.02212i	0.993424	+	0.114498i	$0.0365259\pi$
$17$	9.75194	+	17.3761i	0.573644	+	1.02212i	−0.419780	+	0.907626i	$0.637893\pi$
$18$	−2.78737	+	10.6618i	−0.154854	+	0.592325i
$19$	4.09796	−	1.92105i	0.215682	−	0.101108i	−0.313594	−	0.949557i	$-0.601533\pi$
$19$	4.09796	−	1.92105i	0.215682	−	0.101108i	0.529276	+	0.848449i	$0.322463\pi$
$20$	−2.43934	−	13.2064i	−0.121967	−	0.660318i
$21$	−17.7598	+	6.05879i	−0.845703	+	0.288514i
$22$	1.21865	+	33.3452i	0.0553931	+	1.51569i
$23$	24.2209	+	25.1222i	1.05308	+	1.09227i	0.995579	+	0.0939259i	$0.0299417\pi$
$23$	24.2209	+	25.1222i	1.05308	+	1.09227i	0.0575027	+	0.998345i	$0.481686\pi$
$24$	−2.60597	−	9.96796i	−0.108582	−	0.415332i
$25$	−11.3141	−	13.5953i	−0.452564	−	0.543812i
$26$			16.2020i			0.623155i
$27$	6.11637	+	17.9285i	0.226532	+	0.664020i
$28$	17.4639	−	19.4909i	0.623712	−	0.696104i
$29$	2.13559	−	2.98501i	0.0736411	−	0.102931i	−0.774839	−	0.632158i	$-0.782169\pi$
$29$	2.13559	−	2.98501i	0.0736411	−	0.102931i	0.848480	+	0.529227i	$0.177518\pi$
$30$	20.0131	+	20.7579i	0.667104	+	0.691930i
$31$	16.9451	+	44.3048i	0.546617	+	1.42919i	0.874759	+	0.484558i	$0.161019\pi$
$31$	16.9451	+	44.3048i	0.546617	+	1.42919i	−0.328142	+	0.944628i	$0.606422\pi$
$32$	−31.3126	−	32.4779i	−0.978520	−	1.01493i
$33$	−23.0887	−	32.2721i	−0.699659	−	0.977944i
$34$	59.6248	−	2.17907i	1.75367	−	0.0640904i
$35$	−3.09840	+	13.9092i	−0.0885258	+	0.397405i
$36$	13.6124	+	12.1968i	0.378123	+	0.338800i
$37$	−37.3028	−	9.75224i	−1.00818	−	0.263574i	−0.288205	−	0.957569i	$-0.593058\pi$
$37$	−37.3028	−	9.75224i	−1.00818	−	0.263574i	−0.719980	+	0.693995i	$0.755849\pi$
$38$	0.494954	−	13.5432i	0.0130251	−	0.356399i
$39$	−10.6313	−	16.0692i	−0.272597	−	0.412030i
$40$	−7.49240	−	2.25413i	−0.187310	−	0.0563532i
$41$	−0.350998	+	1.02886i	−0.00856093	+	0.0250941i	−0.950637	−	0.310305i	$-0.899569\pi$
$41$	−0.350998	+	1.02886i	−0.00856093	+	0.0250941i	0.942076	+	0.335399i	$0.108871\pi$
$42$	−8.18115	+	55.5900i	−0.194789	+	1.32357i
$43$	37.6488	−	48.7568i	0.875553	−	1.13388i	−0.114533	−	0.993419i	$-0.536537\pi$
$43$	37.6488	−	48.7568i	0.875553	−	1.13388i	0.990086	−	0.140460i	$-0.0448582\pi$
$44$	50.1084	+	23.4898i	1.13883	+	0.533860i
$45$	−9.71417	−	2.16392i	−0.215870	−	0.0480872i
$46$	100.063	−	30.1045i	2.17529	−	0.654446i
$47$	4.08666	−	55.8359i	0.0869502	−	1.18800i	−0.757673	−	0.652635i	$-0.773664\pi$
$47$	4.08666	−	55.8359i	0.0869502	−	1.18800i	0.844623	−	0.535362i	$-0.179825\pi$
$48$	38.9330	+	8.67269i	0.811104	+	0.180681i
$49$	19.2237	−	9.01168i	0.392319	−	0.183912i
$50$	−51.6953	+	11.5156i	−1.03391	+	0.230312i
$51$	−57.7061	+	41.2851i	−1.13149	+	0.809513i
$52$	23.8980	+	12.2868i	0.459578	+	0.236285i
$53$	72.2397	−	5.28726i	1.36301	−	0.0997597i	0.628212	−	0.778042i	$-0.283787\pi$
$53$	72.2397	−	5.28726i	1.36301	−	0.0997597i	0.734801	+	0.678283i	$0.237275\pi$
$54$	56.1183	+	8.25890i	1.03923	+	0.152943i
$55$	−30.0536	+	2.19964i	−0.546429	+	0.0399935i
$56$	−5.44661	−	14.2407i	−0.0972609	−	0.254298i
$57$	8.39570	+	13.7569i	0.147293	+	0.241349i
$58$	−5.02519	−	9.77406i	−0.0866413	−	0.168518i
$59$	−10.8906	+	21.1823i	−0.184586	+	0.359022i	−0.963330	−	0.268320i	$-0.913532\pi$
$59$	−10.8906	+	21.1823i	−0.184586	+	0.359022i	0.778744	+	0.627342i	$0.215857\pi$
$60$	45.7949	−	13.7776i	0.763248	−	0.229627i
$61$	−25.4347	−	59.8528i	−0.416962	−	0.981193i	−0.987167	−	0.159691i	$-0.948950\pi$
$61$	−25.4347	−	59.8528i	−0.416962	−	0.981193i	0.570205	−	0.821502i	$-0.306864\pi$
$62$	141.185	+	15.5348i	2.27718	+	0.250561i
$63$	−8.23182	−	17.5601i	−0.130664	−	0.278731i
$64$	−86.4555	+	26.0106i	−1.35087	+	0.406415i
$65$	−14.6222	+	0.534389i	−0.224957	+	0.00822138i
$66$	−117.553	+	17.3003i	−1.78111	+	0.262125i
$67$	−95.6726	−	25.0121i	−1.42795	−	0.373315i	−0.543287	−	0.839547i	$-0.682820\pi$
$67$	−95.6726	−	25.0121i	−1.42795	−	0.373315i	−0.884662	+	0.466233i	$0.845611\pi$
$68$	42.0024	−	89.5992i	0.617682	−	1.31763i
$69$	−79.4890	+	95.5159i	−1.15201	+	1.38429i
$70$	32.7983	+	27.2949i	0.468547	+	0.389927i
$71$	4.90399	−	67.0031i	0.0690703	−	0.943705i	−0.844115	−	0.536162i	$-0.819874\pi$
$71$	4.90399	−	67.0031i	0.0690703	−	0.943705i	0.913186	−	0.407544i	$-0.133615\pi$
$72$	9.94570	−	3.80391i	0.138135	−	0.0528320i
$73$	47.3644	+	71.5914i	0.648828	+	0.980704i	0.999030	+	0.0440301i	$0.0140198\pi$
$73$	47.3644	+	71.5914i	0.648828	+	0.980704i	−0.350202	+	0.936674i	$0.613887\pi$
$74$	−77.0437	+	85.9859i	−1.04113	+	1.16197i
$75$	43.7152	−	45.3420i	0.582869	−	0.604560i
$76$	−19.6008	−	11.0005i	−0.257906	−	0.144744i
$77$	−39.1860	−	43.7341i	−0.508909	−	0.567976i
$78$	−57.3484	+	6.31012i	−0.735236	+	0.0808990i
$79$	20.3643	−	67.6880i	0.257776	−	0.856810i	−0.727540	−	0.686066i	$-0.759336\pi$
$79$	20.3643	−	67.6880i	0.257776	−	0.856810i	0.985315	−	0.170744i	$-0.0546172\pi$
$80$	21.0239	−	21.8063i	0.262799	−	0.272579i
$81$	−91.0683	+	42.6910i	−1.12430	+	0.527050i
$82$	2.25930	+	2.34338i	0.0275525	+	0.0285778i
$83$	−17.9354	+	1.97345i	−0.216089	+	0.0237766i	−0.216768	−	0.976223i	$-0.569551\pi$
$83$	−17.9354	+	1.97345i	−0.216089	+	0.0237766i	0.000678672		1.00000i	$0.499784\pi$
$84$	75.7912	+	54.2239i	0.902276	+	0.645523i
$85$	3.93319	+	53.7391i	0.0462728	+	0.632224i
$86$	−78.2934	−	167.015i	−0.910389	−	1.94204i
$87$	11.3974	+	6.39654i	0.131005	+	0.0735235i
$88$	25.5190	−	19.7052i	0.289989	−	0.223922i
$89$	−106.838	+	19.7341i	−1.20043	+	0.221731i	−0.744093	−	0.668076i	$-0.767118\pi$
$89$	−106.838	+	19.7341i	−1.20043	+	0.221731i	−0.456338	+	0.889806i	$0.650839\pi$
$90$	−19.0628	+	22.9063i	−0.211808	+	0.254514i
$91$	−18.2390	−	21.9165i	−0.200429	−	0.240840i
$92$	31.4787	−	170.423i	0.342160	−	1.85242i
$93$	−150.221	+	77.2338i	−1.61528	+	0.830471i
$94$	−143.097	−	87.3307i	−1.52231	−	0.929050i
$95$	12.2389			0.128831
$96$	102.763	−	123.482i	1.07045	−	1.28628i
$97$	−35.7289	+	10.7492i	−0.368339	+	0.110817i	−0.466890	−	0.884315i	$-0.654626\pi$
$97$	−35.7289	+	10.7492i	−0.368339	+	0.110817i	0.0985513	+	0.995132i	$0.468579\pi$
$98$	2.32184	−	63.5313i	0.0236923	−	0.648279i
$99$	30.5439	−	27.3675i	0.308524	−	0.276439i
$100$	−22.2176	+	84.9834i	−0.222176	+	0.849834i
$101$	7.22674	−	24.0207i	0.0715519	−	0.237828i	−0.914413	−	0.404783i	$-0.867347\pi$
$101$	7.22674	−	24.0207i	0.0715519	−	0.237828i	0.985965	+	0.166955i	$0.0533935\pi$
$102$	30.9347	+	210.198i	0.303282	+	2.06077i
$103$	92.1450	+	17.0201i	0.894612	+	0.165243i	0.609064	−	0.793121i	$-0.291545\pi$
$103$	92.1450	+	17.0201i	0.894612	+	0.165243i	0.285548	+	0.958364i	$0.407824\pi$
$104$	12.7323	−	9.10919i	0.122426	−	0.0875883i
$105$	−50.4394	−	5.54991i	−0.480375	−	0.0528563i
$106$	84.8271	−	199.615i	0.800256	−	1.88316i
$107$	−27.8440	+	49.6127i	−0.260224	+	0.463670i	−0.970780	−	0.239971i	$-0.922862\pi$
$107$	−27.8440	+	49.6127i	−0.260224	+	0.463670i	0.710556	+	0.703641i	$0.248444\pi$
$108$	54.7392	−	76.5114i	0.506845	−	0.708439i
$109$	−14.2229	+	7.98227i	−0.130485	+	0.0732318i	−0.553289	−	0.832990i	$-0.686627\pi$
$109$	−14.2229	+	7.98227i	−0.130485	+	0.0732318i	0.422804	+	0.906221i	$0.361046\pi$
$110$	−35.2903	+	83.0450i	−0.320821	+	0.754954i
$111$	19.9907	−	135.834i	0.180096	−	1.22373i
$112$	58.6726	+	6.45583i	0.523863	+	0.0576413i
$113$	34.9179	−	116.062i	0.309008	−	1.02710i	−0.653744	−	0.756716i	$-0.726803\pi$
$113$	34.9179	−	116.062i	0.309008	−	1.02710i	0.962753	−	0.270384i	$-0.0871507\pi$
$114$	48.1298	−	3.52265i	0.422192	−	0.0309004i
$115$	30.4695	+	89.3133i	0.264952	+	0.776637i
$116$	−18.2276			−0.157135
$117$	15.3064	−	12.7381i	0.130824	−	0.108873i
$118$	41.4980	+	58.0036i	0.351678	+	0.491556i
$119$	−78.2013	+	70.0687i	−0.657154	+	0.588813i
$120$	5.06064	−	27.3978i	0.0421720	−	0.228315i
$121$	1.65419	−	2.71049i	0.0136710	−	0.0224007i
$122$	−194.213	−	14.2146i	−1.59191	−	0.116513i
$123$	−3.77843	−	0.841681i	−0.0307189	−	0.00684294i
$124$	129.982	−	196.467i	1.04824	−	1.58441i
$125$	−29.1974	−	111.681i	−0.233579	−	0.893452i
$126$	−58.0335	−	2.12091i	−0.460583	−	0.0168327i
$127$	74.5359	−	8.20128i	0.586897	−	0.0645770i	0.188952	−	0.981986i	$-0.439491\pi$
$127$	74.5359	−	8.20128i	0.586897	−	0.0645770i	0.397945	+	0.917409i	$0.369724\pi$
$128$	−16.3265	+	88.3900i	−0.127550	+	0.690547i
$129$	187.241	+	114.272i	1.45148	+	0.885828i
$130$	−18.5970	+	39.6709i	−0.143054	+	0.305161i
$131$	2.96681	−	20.1591i	0.0226474	−	0.153886i	−0.975023	−	0.222103i	$-0.928708\pi$
$131$	2.96681	−	20.1591i	0.0226474	−	0.153886i	0.997671	+	0.0682170i	$0.0217310\pi$
$132$	−63.6287	+	186.511i	−0.482036	+	1.41296i
$133$	14.5763	+	18.8770i	0.109596	+	0.141932i
$134$	−197.598	+	220.533i	−1.47461	+	1.64577i
$135$	−5.60265	+	50.9187i	−0.0415011	+	0.377176i
$136$	−35.2349	−	45.6308i	−0.259081	−	0.335521i
$137$	−16.8116	−	229.697i	−0.122713	−	1.67662i	−0.601643	−	0.798765i	$-0.705487\pi$
$137$	−16.8116	−	229.697i	−0.122713	−	1.67662i	0.478931	−	0.877853i	$-0.341025\pi$
$138$	145.528	+	342.457i	1.05455	+	2.48157i
$139$	225.591	+	86.2812i	1.62296	+	0.620728i	0.988362	−	0.152117i	$-0.0486090\pi$
$139$	225.591	+	86.2812i	1.62296	+	0.620728i	0.634594	+	0.772845i	$0.281167\pi$
$140$	65.1326	−	27.6784i	0.465233	−	0.197703i
$141$	199.227	−	7.28103i	1.41296	−	0.0516385i
$142$	−171.716	−	104.797i	−1.20927	−	0.738006i
$143$	33.2689	−	50.2860i	0.232650	−	0.351650i
$144$	−4.50875	+	40.9769i	−0.0313107	+	0.284562i
$145$	8.65527	−	4.85757i	0.0596915	−	0.0335005i
$146$	255.498	−	28.1128i	1.74999	−	0.192554i
$147$	39.3845	+	64.5339i	0.267922	+	0.439006i
$148$	68.4032	+	178.847i	0.462184	+	1.20843i
$149$	−169.647	−	79.5270i	−1.13857	−	0.533738i	−0.239216	−	0.970966i	$-0.576891\pi$
$149$	−169.647	−	79.5270i	−1.13857	−	0.533738i	−0.899351	+	0.437228i	$0.855960\pi$
$150$	−60.8939	−	178.495i	−0.405959	−	1.18996i
$151$	−263.662	−	19.2976i	−1.74611	−	0.127799i	−0.837767	−	0.546027i	$-0.816139\pi$
$151$	−263.662	−	19.2976i	−1.74611	−	0.127799i	−0.908342	+	0.418229i	$0.862651\pi$
$152$	−10.9211	+	7.22534i	−0.0718494	+	0.0475351i
$153$	−48.9359	−	54.6158i	−0.319843	−	0.356966i
$154$	−170.116	+	44.4743i	−1.10465	+	0.288794i
$155$	−9.36332	+	127.931i	−0.0604085	+	0.825360i
$156$	−34.1828	+	89.3743i	−0.219120	+	0.572912i
$157$	67.0946	−	157.887i	0.427354	−	1.00565i	−0.557170	−	0.830398i	$-0.688113\pi$
$157$	67.0946	−	157.887i	0.427354	−	1.00565i	0.984524	−	0.175249i	$-0.0560731\pi$
$158$	−152.373	−	146.906i	−0.964384	−	0.929783i
$159$	46.8495	+	253.639i	0.294651	+	1.59521i
$160$	−39.3907	−	115.464i	−0.246192	−	0.721648i
$161$	−101.466	+	153.366i	−0.630223	+	0.952582i
$162$	−10.9993	+	300.967i	−0.0678967	+	1.85782i
$163$	8.47469	−	3.24129i	0.0519920	−	0.0198852i	−0.331097	−	0.943597i	$-0.607419\pi$
$163$	8.47469	−	3.24129i	0.0519920	−	0.0198852i	0.383088	+	0.923712i	$0.374860\pi$
$164$	5.16983	−	1.55537i	0.0315234	−	0.00948397i
$165$	−19.4906	−	105.520i	−0.118125	−	0.639518i
$166$	−19.3009	+	50.4643i	−0.116271	+	0.304002i
$167$	7.87241	−	7.58996i	0.0471402	−	0.0454489i	−0.670132	−	0.742242i	$-0.733763\pi$
$167$	7.87241	−	7.58996i	0.0471402	−	0.0454489i	0.717272	+	0.696793i	$0.245390\pi$
$168$	48.2848	−	24.8249i	0.287410	−	0.147768i
$169$	−81.2990	+	113.635i	−0.481059	+	0.672398i
$170$	148.493	+	63.1028i	0.873490	+	0.371193i
$171$	−13.1837	+	10.1801i	−0.0770975	+	0.0595328i
$172$	−305.721	−	11.1730i	−1.77745	−	0.0649594i
$173$	−78.2820	−	128.270i	−0.452497	−	0.741445i	0.542638	−	0.839967i	$-0.317426\pi$
$173$	−78.2820	−	128.270i	−0.452497	−	0.741445i	−0.995135	+	0.0985223i	$0.968588\pi$
$174$	32.6389	−	21.5937i	0.187580	−	0.124102i
$175$	56.9647	−	73.7717i	0.325512	−	0.421553i
$176$	22.6721	+	122.745i	0.128819	+	0.697412i
$177$	−79.2179	−	30.2983i	−0.447559	−	0.171177i
$178$	−93.7259	+	311.532i	−0.526550	+	1.75018i
$179$	83.2028	+	46.6957i	0.464820	+	0.260870i	0.704127	−	0.710074i	$-0.251339\pi$
$179$	83.2028	+	46.6957i	0.464820	+	0.260870i	−0.239307	+	0.970944i	$0.576920\pi$
$180$	19.3306	+	45.4886i	0.107392	+	0.252714i
$181$	−78.2280	+	351.177i	−0.432199	+	1.94020i	−0.108278	+	0.994121i	$0.534534\pi$
$181$	−78.2280	+	351.177i	−0.432199	+	1.94020i	−0.323921	+	0.946084i	$0.605001\pi$
$182$	−83.3360	+	18.5639i	−0.457890	+	0.101999i
$183$	201.948	−	113.339i	1.10354	−	0.619336i
$184$	−79.9155	−	61.7087i	−0.434323	−	0.335373i
$185$	−80.1427	−	66.6953i	−0.433204	−	0.360515i
$186$			505.786i			2.71928i
$187$	−189.531	−	115.669i	−1.01353	−	0.618551i
$188$	−237.330	+	144.841i	−1.26240	+	0.770429i
$189$	−85.2084	+	52.0019i	−0.450838	+	0.275142i
$190$	16.7570	−	32.5925i	0.0881945	−	0.171539i
$191$	26.7189	−	34.6021i	0.139889	−	0.181163i	−0.716351	−	0.697740i	$-0.754189\pi$
$191$	26.7189	−	34.6021i	0.139889	−	0.181163i	0.856241	+	0.516577i	$0.172794\pi$
$192$	−125.738	−	295.886i	−0.654884	−	1.54107i
$193$	147.755	−	38.6281i	0.765569	−	0.200146i	0.150490	−	0.988612i	$-0.451915\pi$
$193$	147.755	−	38.6281i	0.765569	−	0.200146i	0.615079	+	0.788466i	$0.289124\pi$
$194$	−20.2929	+	109.864i	−0.104603	+	0.566309i
$195$	−7.58635	−	51.5484i	−0.0389043	−	0.264351i
$196$	−91.9480	−	51.6037i	−0.469123	−	0.263284i
$197$	−329.251	+	73.3437i	−1.67132	+	0.372303i	−0.948016	−	0.318223i	$-0.896914\pi$
$197$	−329.251	+	73.3437i	−1.67132	+	0.372303i	−0.723308	+	0.690526i	$0.757379\pi$
$198$	−31.0608	−	118.809i	−0.156873	−	0.600047i
$199$	109.828	+	56.4664i	0.551899	+	0.283751i	0.710624	−	0.703572i	$-0.248413\pi$
$199$	109.828	+	56.4664i	0.551899	+	0.283751i	−0.158725	+	0.987323i	$0.550738\pi$
$200$	38.1138	+	34.1501i	0.190569	+	0.170751i
$201$	51.2712	−	348.382i	0.255081	−	1.73324i
$202$	−54.0730	−	52.1329i	−0.267688	−	0.258084i
$203$	17.8005	+	7.56438i	0.0876870	+	0.0372629i
$204$	333.502	+	113.775i	1.63481	+	0.557721i
$205$	−2.04036	+	2.11629i	−0.00995300	+	0.0103234i
$206$	171.485	−	222.081i	0.832453	−	1.07806i
$207$	−107.111	−	70.8637i	−0.517442	−	0.342337i
$208$	8.82467	+	59.9626i	0.0424263	+	0.288282i
$209$	−29.3454	+	41.0173i	−0.140408	+	0.196255i
$210$	−83.8388	+	126.722i	−0.399232	+	0.603440i
$211$	18.1718	−	15.1227i	0.0861222	−	0.0716714i	−0.595607	−	0.803276i	$-0.703089\pi$
$211$	18.1718	−	15.1227i	0.0861222	−	0.0716714i	0.681730	+	0.731604i	$0.261228\pi$
$212$	−230.103	−	276.498i	−1.08539	−	1.30424i
$213$	239.073	−	8.73725i	1.12241	−	0.0410199i
$214$	93.9969	+	142.077i	0.439238	+	0.663909i
$215$	148.147	−	76.1678i	0.689058	−	0.354269i
$216$	−25.0609	−	48.7437i	−0.116023	−	0.225665i
$217$	−208.469	+	137.921i	−0.960684	+	0.635583i
$218$	1.78364	+	48.8048i	0.00818183	+	0.223875i
$219$	−234.957	+	195.532i	−1.07286	+	0.892842i
$220$	95.7291	+	115.030i	0.435132	+	0.522866i
$221$	−89.9167	−	59.4883i	−0.406863	−	0.269178i
$222$	−334.360	−	239.214i	−1.50612	−	1.07754i
$223$	384.740	−	56.6220i	1.72529	−	0.253910i	0.791356	−	0.611355i	$-0.209375\pi$
$223$	384.740	−	56.6220i	1.72529	−	0.253910i	0.933934	+	0.357445i	$0.116352\pi$
$224$	131.174	−	198.270i	0.585600	−	0.885136i
$225$	51.5221	+	39.7841i	0.228987	+	0.176818i
$226$	−261.268	−	251.894i	−1.15605	−	1.11458i
$227$	36.0540	−	105.683i	0.158828	−	0.465563i	−0.837952	−	0.545744i	$-0.816247\pi$
$227$	36.0540	−	105.683i	0.158828	−	0.465563i	0.996780	+	0.0801802i	$0.0255496\pi$
$228$	31.3034	−	73.6630i	0.137295	−	0.323083i
$229$	266.789	−	276.717i	1.16502	−	1.20837i	0.191073	−	0.981576i	$-0.438803\pi$
$229$	266.789	−	276.717i	1.16502	−	1.20837i	0.973943	−	0.226795i	$-0.0728246\pi$
$230$	279.560	+	41.1428i	1.21548	+	0.178882i
$231$	139.539	−	155.735i	0.604065	−	0.674176i
$232$	−4.85562	+	9.44425i	−0.0209294	+	0.0407080i
$233$	222.540	−	58.1795i	0.955106	−	0.249697i	0.257580	−	0.966257i	$-0.417075\pi$
$233$	222.540	−	58.1795i	0.955106	−	0.249697i	0.697526	+	0.716560i	$0.254284\pi$
$234$	−12.9650	−	58.2018i	−0.0554060	−	0.248726i
$235$	74.0955	−	132.024i	0.315300	−	0.561805i
$236$	117.026	−	17.2226i	0.495871	−	0.0729771i
$237$	247.518	+	45.7189i	1.04438	+	0.192907i
$238$	79.5248	+	304.186i	0.334138	+	1.27809i
$239$	173.124	−	73.5699i	0.724370	−	0.307824i	0.00263810	−	0.999997i	$-0.499160\pi$
$239$	173.124	−	73.5699i	0.724370	−	0.307824i	0.721732	+	0.692173i	$0.243346\pi$
$240$	85.3733	+	65.9231i	0.355722	+	0.274680i
$241$	−135.944	−	69.8934i	−0.564081	−	0.290014i	0.151599	−	0.988442i	$-0.451558\pi$
$241$	−135.944	−	69.8934i	−0.564081	−	0.290014i	−0.715680	+	0.698428i	$0.753883\pi$
$242$	−4.95325	−	8.11621i	−0.0204680	−	0.0335381i
$243$	−97.7620	−	160.189i	−0.402313	−	0.659214i
$244$	−168.248	+	275.685i	−0.689541	+	1.12986i
$245$	57.4131			0.234339
$246$	−7.41466	+	8.90964i	−0.0301409	+	0.0362181i
$247$	−14.9669	+	19.3828i	−0.0605949	+	0.0784730i
$248$	−67.1697	−	119.684i	−0.270846	−	0.482595i
$249$	−13.9704	−	62.7151i	−0.0561060	−	0.251868i
$250$	−337.386	−	75.1559i	−1.34954	−	0.300624i
$251$	307.732	−	130.772i	1.22602	−	0.521003i	0.321289	−	0.946981i	$-0.395884\pi$
$251$	307.732	−	130.772i	1.22602	−	0.521003i	0.904734	+	0.425978i	$0.140070\pi$
$252$	−47.1380	+	83.9910i	−0.187056	+	0.333298i
$253$	−372.380	−	112.032i	−1.47186	−	0.442816i
$254$	80.2108	−	209.719i	0.315791	−	0.825666i
$255$	−188.682	+	34.8513i	−0.739929	+	0.136672i
$256$	−72.8053	−	56.2184i	−0.284396	−	0.219603i
$257$	93.2962	+	141.017i	0.363020	+	0.548706i	0.969091	−	0.246705i	$-0.0793480\pi$
$257$	93.2962	+	141.017i	0.363020	+	0.548706i	−0.606070	+	0.795411i	$0.707255\pi$
$258$	560.670	−	342.172i	2.17314	−	1.32625i
$259$	7.42049	−	203.043i	0.0286505	−	0.783949i
$260$	44.4116	+	57.5150i	0.170814	+	0.221212i
$261$	−5.28296	+	12.4318i	−0.0202412	+	0.0476315i
$262$	−49.6221	−	35.5016i	−0.189397	−	0.135502i
$263$	14.8189	+	28.8229i	0.0563455	+	0.109593i	0.915825	−	0.401577i	$-0.131538\pi$
$263$	14.8189	+	28.8229i	0.0563455	+	0.109593i	−0.859480	+	0.511170i	$0.829212\pi$
$264$	79.6868	+	82.6522i	0.301844	+	0.313077i
$265$	182.949	+	69.9719i	0.690372	+	0.264045i
$266$	70.2270	−	12.9716i	0.264011	−	0.0487654i
$267$	−111.460	−	370.477i	−0.417453	−	1.38756i
$268$	175.437	+	458.698i	0.654617	+	1.71156i
$269$	10.8019	+	0.394771i	0.0401558	+	0.00146755i	0.0565926	−	0.998397i	$-0.481976\pi$
$269$	10.8019	+	0.394771i	0.0401558	+	0.00146755i	−0.0164367	+	0.999865i	$0.505232\pi$
$270$	127.927	+	84.6355i	0.473803	+	0.313465i
$271$	106.170	−	36.2201i	0.391771	−	0.133654i	−0.120004	−	0.992773i	$-0.538291\pi$
$271$	106.170	−	36.2201i	0.391771	−	0.133654i	0.511774	+	0.859120i	$0.328988\pi$
$272$	219.480	−	40.5401i	0.806913	−	0.149044i
$273$	70.4716	−	73.0942i	0.258138	−	0.267744i
$274$	−634.704	−	269.720i	−2.31644	−	0.984380i
$275$	184.091	+	70.4090i	0.669424	+	0.256033i
$276$	615.485	+	45.0477i	2.23002	+	0.163216i
$277$	60.1633	+	230.128i	0.217196	+	0.830787i	0.982367	+	0.186960i	$0.0598636\pi$
$277$	60.1633	+	230.128i	0.217196	+	0.830787i	−0.765171	+	0.643827i	$0.777346\pi$
$278$	538.637	−	482.621i	1.93754	−	1.73605i
$279$	−96.3243	−	145.594i	−0.345248	−	0.521843i
$280$	3.00962	−	41.1203i	0.0107486	−	0.146858i
$281$	349.575	−	119.259i	1.24404	−	0.424407i	0.378666	−	0.925534i	$-0.376383\pi$
$281$	349.575	−	119.259i	1.24404	−	0.424407i	0.865374	+	0.501126i	$0.167081\pi$
$282$	253.383	−	540.514i	0.898520	−	1.91672i
$283$	−138.813	+	53.0917i	−0.490507	+	0.187603i	−0.589949	−	0.807440i	$-0.700852\pi$
$283$	−138.813	+	53.0917i	−0.490507	+	0.187603i	0.0994423	+	0.995043i	$0.468294\pi$
$284$	−284.797	+	173.809i	−1.00281	+	0.612003i
$285$	4.76662	+	43.3206i	0.0167250	+	0.152002i
$286$	−88.3624	−	157.445i	−0.308959	−	0.550507i
$287$	−5.69415	−	0.626535i	−0.0198403	−	0.00218305i
$288$	138.472	+	91.6122i	0.480805	+	0.318098i
$289$	−56.2768	+	92.2131i	−0.194730	+	0.319076i
$290$	−1.08543	−	29.6999i	−0.00374285	−	0.102414i
$291$	−51.9628	−	122.279i	−0.178566	−	0.420202i
$292$	152.291	−	398.180i	0.521544	−	1.36363i
$293$	256.394	−	108.956i	0.875065	−	0.371862i	0.0934505	−	0.995624i	$-0.470210\pi$
$293$	256.394	−	108.956i	0.875065	−	0.371862i	0.781615	+	0.623762i	$0.214396\pi$
$294$	225.778	−	16.5249i	0.767954	−	0.0562070i
$295$	−50.9791	+	39.3648i	−0.172811	+	0.133440i
$296$	110.888	+	12.2011i	0.374620	+	0.0412199i
$297$	−157.215	−	140.865i	−0.529342	−	0.474293i
$298$	−444.054	+	342.887i	−1.49011	+	1.15063i
$299$	−178.707	−	60.9663i	−0.597682	−	0.203901i
$300$	−309.459	−	45.5429i	−1.03153	−	0.151810i
$301$	293.920	+	137.784i	0.976479	+	0.457755i
$302$	−412.384	+	675.717i	−1.36551	+	2.23747i
$303$	87.8376	+	16.2244i	0.289893	+	0.0535459i
$304$	−5.54468	−	50.3919i	−0.0182391	−	0.165763i
$305$	6.42283	−	175.745i	0.0210585	−	0.576212i
$306$	−212.444	+	55.5400i	−0.694260	+	0.181503i
$307$	−408.227	−	270.080i	−1.32973	−	0.879740i	−0.331755	−	0.943366i	$-0.607641\pi$
$307$	−408.227	−	270.080i	−1.32973	−	0.879740i	−0.997974	+	0.0636258i	$0.979734\pi$
$308$	−63.4083	+	284.649i	−0.205871	+	0.924185i
$309$	−24.3566	+	332.783i	−0.0788240	+	1.07697i
$310$	327.862	+	200.091i	1.05762	+	0.645456i
$311$	−468.862	−	86.6033i	−1.50760	−	0.278467i	−0.637153	−	0.770737i	$-0.719888\pi$
$311$	−468.862	−	86.6033i	−1.50760	−	0.278467i	−0.870443	+	0.492270i	$0.836167\pi$
$312$	37.2015	+	41.5193i	0.119235	+	0.133075i
$313$	−113.497	+	81.2000i	−0.362610	+	0.259425i	−0.748521	−	0.663111i	$-0.769236\pi$
$313$	−113.497	+	81.2000i	−0.362610	+	0.259425i	0.385912	+	0.922536i	$0.373887\pi$
$314$	−328.593	−	394.845i	−1.04647	−	1.25747i
$315$		−	52.4447i		−	0.166491i
$316$	−332.238	+	113.344i	−1.05139	+	0.358683i
$317$	13.7944	+	188.472i	0.0435154	+	0.594550i	0.973755	+	0.227598i	$0.0730871\pi$
$317$	13.7944	+	188.472i	0.0435154	+	0.594550i	−0.930240	+	0.366952i	$0.880401\pi$
$318$	739.590	+	222.509i	2.32575	+	0.699715i
$319$	−4.47323	+	40.6542i	−0.0140227	+	0.127443i
$320$	−241.543	−	35.5477i	−0.754821	−	0.111087i
$321$	−186.452	−	79.2336i	−0.580848	−	0.246834i
$322$	269.494	+	480.187i	0.836937	+	1.49126i
$323$	73.3433	+	52.4727i	0.227069	+	0.162454i
$324$	435.586	+	244.463i	1.34440	+	0.754514i
$325$	88.0799	+	37.4299i	0.271015	+	0.115169i
$326$	2.97151	−	27.0061i	0.00911508	−	0.0828408i
$327$	−33.7932	−	47.2342i	−0.103343	−	0.144447i
$328$	0.571301	−	3.09297i	0.00174177	−	0.00942979i
$329$	291.877	−	42.9554i	0.887164	−	0.130563i
$330$	−307.689	−	92.5697i	−0.932390	−	0.280514i
$331$	−17.0905	−	4.46803i	−0.0516328	−	0.0134986i	0.227027	−	0.973888i	$-0.427099\pi$
$331$	−17.0905	−	4.46803i	−0.0516328	−	0.0134986i	−0.278660	+	0.960390i	$0.589890\pi$
$332$	59.7980	+	66.7385i	0.180114	+	0.201020i
$333$	141.805	+	5.18246i	0.425841	+	0.0155630i
$334$	−9.43368	−	31.3562i	−0.0282445	−	0.0938809i
$335$	−205.546	−	171.057i	−0.613571	−	0.510618i
$336$			210.191i			0.625568i
$337$	−186.004	+	304.779i	−0.551940	+	0.904389i	0.448006	+	0.894031i	$0.352134\pi$
$337$	−186.004	+	304.779i	−0.551940	+	0.904389i	−0.999946	+	0.0103580i	$0.996703\pi$
$338$	191.302	+	372.085i	0.565982	+	1.10084i
$339$	424.411	+	78.3927i	1.25195	+	0.231247i
$340$	205.687	−	171.174i	0.604961	−	0.503452i
$341$	−406.295	−	338.121i	−1.19148	−	0.991557i
$342$	9.05935	+	49.0465i	0.0264893	+	0.143411i
$343$	226.190	+	292.926i	0.659446	+	0.854011i
$344$	−87.2296	+	155.427i	−0.253574	+	0.451821i
$345$	−304.265	+	142.633i	−0.881926	+	0.413430i
$346$	−448.765	+	32.8454i	−1.29701	+	0.0949289i
$347$	294.694	−	411.907i	0.849262	−	1.18705i	−0.131397	−	0.991330i	$-0.541946\pi$
$347$	294.694	−	411.907i	0.849262	−	1.18705i	0.980660	−	0.195721i	$-0.0627048\pi$
$348$	−7.09901	−	64.5181i	−0.0203994	−	0.185397i
$349$	−218.959	+	211.103i	−0.627389	+	0.604879i	−0.938410	−	0.345524i	$-0.887701\pi$
$349$	−218.959	+	211.103i	−0.627389	+	0.604879i	0.311021	+	0.950403i	$0.399329\pi$
$350$	−118.462	−	252.703i	−0.338464	−	0.722008i
$351$	−73.7888	−	71.1413i	−0.210224	−	0.202682i
$352$	481.411	+	144.835i	1.36764	+	0.411463i
$353$	−29.6737	−	269.684i	−0.0840615	−	0.763978i	−0.959703	−	0.281016i	$-0.909328\pi$
$353$	−29.6737	−	269.684i	−0.0840615	−	0.763978i	0.875641	−	0.482962i	$-0.160439\pi$
$354$	−189.146	+	169.476i	−0.534312	+	0.478746i
$355$	88.9147	−	158.429i	0.250464	−	0.446279i
$356$	388.433	+	374.496i	1.09110	+	1.05196i
$357$	−278.470	−	249.511i	−0.780029	−	0.698909i
$358$	238.269	−	157.637i	0.665556	−	0.440327i
$359$	31.8907	+	83.3815i	0.0888321	+	0.232260i	0.971185	−	0.238329i	$-0.0765996\pi$
$359$	31.8907	+	83.3815i	0.0888321	+	0.232260i	−0.882352	+	0.470589i	$0.844041\pi$
$360$	28.7184	+	2.10191i	0.0797732	+	0.00583865i
$361$	−217.819	+	261.737i	−0.603377	+	0.725033i
$362$	828.085	+	689.138i	2.28753	+	1.90370i
$363$	10.2382	+	4.79949i	0.0282045	+	0.0132217i
$364$	−35.8161	+	136.999i	−0.0983960	+	0.376370i
$365$	33.7987	+	229.658i	0.0925991	+	0.629200i
$366$	−25.3255	−	692.969i	−0.0691954	−	1.89336i
$367$	26.0831	+	86.6965i	0.0710711	+	0.236230i	0.985824	−	0.167784i	$-0.0536611\pi$
$367$	26.0831	+	86.6965i	0.0710711	+	0.236230i	−0.914753	+	0.404014i	$0.867615\pi$
$368$	353.930	−	165.915i	0.961766	−	0.450857i
$369$	0.437572	−	3.97679i	0.00118583	−	0.0107772i
$370$	−287.339	+	122.106i	−0.776591	+	0.330015i
$371$	109.966	+	365.511i	0.296404	+	0.985204i
$372$	746.034	+	383.563i	2.00547	+	1.03108i
$373$	−156.386	+	80.4037i	−0.419266	+	0.215560i	−0.653991	−	0.756502i	$-0.726907\pi$
$373$	−156.386	+	80.4037i	−0.419266	+	0.215560i	0.234725	+	0.972062i	$0.424581\pi$
$374$	−567.526	+	346.356i	−1.51745	+	0.926085i
$375$	383.934	−	146.842i	1.02382	−	0.391580i
$376$	11.8240	+	161.551i	0.0314469	+	0.429658i
$377$	−2.89154	+	19.6477i	−0.00766988	+	0.0521159i
$378$	21.8189	+	298.110i	0.0577218	+	0.788651i
$379$	−21.6679	+	42.1444i	−0.0571713	+	0.111199i	−0.916188	−	0.400748i	$-0.868750\pi$
$379$	−21.6679	+	42.1444i	−0.0571713	+	0.111199i	0.859017	+	0.511947i	$0.171076\pi$
$380$	−35.3663	−	49.4330i	−0.0930692	−	0.130087i
$381$	58.0581	+	260.631i	0.152384	+	0.684072i
$382$	−55.5639	−	118.528i	−0.145455	−	0.310284i
$383$	−133.670	+	600.066i	−0.349009	+	1.56675i	0.407772	+	0.913084i	$0.366306\pi$
$383$	−133.670	+	600.066i	−0.349009	+	1.56675i	−0.756781	+	0.653668i	$0.773229\pi$
$384$	−319.222	−	23.3640i	−0.831307	−	0.0608438i
$385$	−45.7486	−	152.062i	−0.118828	−	0.394966i
$386$	99.4313	−	446.362i	0.257594	−	1.15638i
$387$	−96.2284	+	205.274i	−0.248652	+	0.530423i
$388$	146.660	+	113.248i	0.377991	+	0.291875i
$389$	0.239303	+	0.0352182i	0.000615176	+	9.05351e-5i	0.145909	−	0.989298i	$-0.453389\pi$
$389$	0.239303	+	0.0352182i	0.000615176	+	9.05351e-5i	−0.145294	+	0.989389i	$0.546413\pi$
$390$	−147.661	−	50.3750i	−0.378618	−	0.129167i
$391$	−200.326	+	665.855i	−0.512343	+	1.70295i
$392$	−51.2312	+	33.8943i	−0.130692	+	0.0864650i
$393$	72.5102	+	2.64999i	0.184504	+	0.00674297i
$394$	−255.479	+	977.220i	−0.648423	+	2.48025i
$395$	127.556	−	142.360i	0.322925	−	0.360406i
$396$	−198.799	−	44.2843i	−0.502017	−	0.111829i
$397$	8.93517	+	244.488i	0.0225067	+	0.615839i	0.961964	+	0.273175i	$0.0880737\pi$
$397$	8.93517	+	244.488i	0.0225067	+	0.615839i	−0.939458	+	0.342665i	$0.888670\pi$
$398$	300.742	−	215.163i	0.755634	−	0.540610i
$399$	−61.1396	+	58.9460i	−0.153232	+	0.147734i
$400$	−185.048	+	70.7750i	−0.462621	+	0.176938i
$401$	10.6169	−	10.2360i	0.0264761	−	0.0255261i	−0.680719	−	0.732545i	$-0.738332\pi$
$401$	10.6169	−	10.2360i	0.0264761	−	0.0255261i	0.707195	+	0.707019i	$0.249960\pi$
$402$	−857.550	−	613.524i	−2.13321	−	1.52618i
$403$	−191.154	−	171.275i	−0.474328	−	0.425000i
$404$	−117.902	+	40.2227i	−0.291838	+	0.0995611i
$405$	−271.983			−0.671564
$406$	44.5157	−	37.0462i	0.109644	−	0.0912468i
$407$	415.681	−	108.673i	1.02133	−	0.267010i
$408$	147.791	−	142.488i	0.362233	−	0.349236i
$409$	−612.084	+	22.3695i	−1.49654	+	0.0546931i	−0.772477	−	0.635043i	$-0.780982\pi$
$409$	−612.084	+	22.3695i	−1.49654	+	0.0546931i	−0.724061	+	0.689736i	$0.757726\pi$
$410$	2.84216	+	8.33106i	0.00693211	+	0.0203197i
$411$	806.482	−	148.965i	1.96224	−	0.362445i
$412$	−197.524	−	421.356i	−0.479427	−	1.02271i
$413$	−121.430	−	31.7461i	−0.294020	−	0.0768670i
$414$	−335.362	+	188.214i	−0.810053	+	0.454624i
$415$	−46.1802	−	15.7545i	−0.111278	−	0.0379626i
$416$	231.031	+	78.8169i	0.555364	+	0.189464i
$417$	−217.540	+	832.101i	−0.521678	+	1.99545i
$418$	69.0516	+	134.306i	0.165195	+	0.321307i
$419$	−15.8192	−	17.6553i	−0.0377546	−	0.0421367i	0.725597	−	0.688120i	$-0.241564\pi$
$419$	−15.8192	−	17.6553i	−0.0377546	−	0.0421367i	−0.763351	+	0.645983i	$0.776448\pi$
$420$	123.337	+	219.762i	0.293659	+	0.523244i
$421$	230.163	+	298.071i	0.546706	+	0.708008i	0.981271	−	0.192632i	$-0.0617025\pi$
$421$	230.163	+	298.071i	0.546706	+	0.708008i	−0.434565	+	0.900640i	$0.643098\pi$
$422$	−15.3920	−	69.0970i	−0.0364740	−	0.163737i
$423$	30.0000	+	203.847i	0.0709220	+	0.481907i
$424$	−204.558	+	45.5673i	−0.482449	+	0.107470i
$425$	125.899	−	329.175i	0.296233	−	0.774530i
$426$	304.060	−	648.618i	0.713755	−	1.52258i
$427$	278.713	−	199.402i	0.652724	−	0.466984i
$428$	280.846	−	30.9018i	0.656181	−	0.0722005i
$429$	190.948	+	98.1732i	0.445101	+	0.228842i
$430$		−	498.805i		−	1.16001i
$431$	130.444	+	410.786i	0.302655	+	0.953100i
$431$	130.444	+	410.786i	0.302655	+	0.953100i
$432$	212.188			0.491177
$433$	−39.9435	+	77.6907i	−0.0922483	+	0.179424i	−0.930930	−	0.365198i	$-0.881001\pi$
$433$	−39.9435	+	77.6907i	−0.0922483	+	0.179424i	0.838682	+	0.544622i	$0.183327\pi$
$434$	81.8623	+	743.991i	0.188623	+	1.71427i
$435$	20.5647	+	28.7442i	0.0472751	+	0.0660785i
$436$	73.3397	+	34.3802i	0.168210	+	0.0788538i
$437$	147.517	+	56.4205i	0.337568	+	0.129109i
$438$	199.015	+	893.408i	0.454372	+	2.03974i
$439$	282.432	−	41.5653i	0.643352	−	0.0946818i	0.183986	−	0.982929i	$-0.441100\pi$
$439$	282.432	−	41.5653i	0.643352	−	0.0946818i	0.459366	+	0.888247i	$0.348077\pi$
$440$	85.1016	−	18.9572i	0.193413	−	0.0430845i
$441$	−61.8450	+	47.7551i	−0.140238	+	0.108288i
$442$	−281.528	+	158.001i	−0.636942	+	0.357469i
$443$	−17.3914	+	15.5827i	−0.0392582	+	0.0351755i	−0.686716	−	0.726926i	$-0.740948\pi$
$443$	−17.3914	+	15.5827i	−0.0392582	+	0.0351755i	0.647458	+	0.762101i	$0.275832\pi$
$444$	−606.402	+	311.773i	−1.36577	+	0.702191i
$445$	−284.246	−	74.3117i	−0.638756	−	0.166993i
$446$	375.982	−	1102.09i	0.843010	−	2.47106i
$447$	215.421	−	631.450i	0.481926	−	1.41264i
$448$	−232.845	−	414.886i	−0.519744	−	0.926084i
$449$	−23.4292	+	89.6180i	−0.0521809	+	0.199595i	−0.988413	−	0.151787i	$-0.951497\pi$
$449$	−23.4292	+	89.6180i	−0.0521809	+	0.199595i	0.936232	+	0.351381i	$0.114288\pi$
$450$	176.488	−	82.7339i	0.392194	−	0.183853i
$451$	−2.20031	−	11.9123i	−0.00487875	−	0.0264131i
$452$	−569.677	+	194.347i	−1.26035	+	0.429971i
$453$	−34.3818	−	940.770i	−0.0758979	−	2.07675i
$454$	−232.072	−	240.709i	−0.511172	−	0.530195i
$455$	−19.5024	−	74.5978i	−0.0428625	−	0.163951i
$456$	−29.8280	−	35.8421i	−0.0654124	−	0.0786011i
$457$			208.988i			0.457305i	0.973508	+	0.228652i	$0.0734319\pi$
$457$			208.988i			0.457305i	−0.973508	+	0.228652i	$0.926568\pi$
$458$	−371.628	−	1089.33i	−0.811415	−	2.37845i
$459$	−251.882	+	281.117i	−0.548762	+	0.612455i
$460$	272.690	−	381.151i	0.592805	−	0.828590i
$461$	49.4871	+	51.3287i	0.107347	+	0.111342i	0.771421	−	0.636325i	$-0.219546\pi$
$461$	49.4871	+	51.3287i	0.107347	+	0.111342i	−0.664074	+	0.747667i	$0.731174\pi$
$462$	−223.675	−	584.820i	−0.484144	−	1.26584i
$463$	−448.261	−	464.942i	−0.968166	−	1.00420i	−0.999989	−	0.00470182i	$-0.998503\pi$
$463$	−448.261	−	464.942i	−0.968166	−	1.00420i	0.0318229	−	0.999494i	$-0.489869\pi$
$464$	−23.9215	−	33.4361i	−0.0515549	−	0.0720605i
$465$	−456.468	+	16.6823i	−0.981651	+	0.0358758i
$466$	149.758	−	672.284i	0.321368	−	1.44267i
$467$	−133.030	−	119.195i	−0.284861	−	0.255236i	0.512572	−	0.858644i	$-0.328693\pi$
$467$	−133.030	−	119.195i	−0.284861	−	0.255236i	−0.797433	+	0.603408i	$0.793809\pi$
$468$	−95.6798	−	25.0140i	−0.204444	−	0.0534487i
$469$	19.0317	−	520.755i	0.0405794	−	1.11035i
$470$	−250.135	−	378.079i	−0.532202	−	0.804424i
$471$	584.983	+	175.995i	1.24200	+	0.373663i
$472$	22.2507	−	65.2221i	0.0471413	−	0.138183i
$473$	−99.9468	+	679.127i	−0.211304	+	1.43579i
$474$	460.640	−	596.549i	0.971815	−	1.25854i
$475$	−72.4819	−	33.9781i	−0.152593	−	0.0715328i
$476$	508.983	+	113.381i	1.06929	+	0.238195i
$477$	−255.272	+	76.8000i	−0.535162	+	0.161006i
$478$	41.1157	−	561.762i	0.0860161	−	1.17524i
$479$	−324.502	−	72.2860i	−0.677458	−	0.150910i	−0.134811	−	0.990871i	$-0.543043\pi$
$479$	−324.502	−	72.2860i	−0.677458	−	0.150910i	−0.542647	+	0.839961i	$0.682578\pi$
$480$	393.352	−	184.396i	0.819482	−	0.384158i
$481$	203.632	−	45.3610i	0.423351	−	0.0943055i
$482$	−372.255	+	266.326i	−0.772314	+	0.552543i
$483$	−582.368	−	299.416i	−1.20573	−	0.619908i
$484$	−15.7277	+	1.15112i	−0.0324953	+	0.00237835i
$485$	−99.8207	−	14.6906i	−0.205816	−	0.0302898i
$486$	−560.438	+	41.0188i	−1.15316	+	0.0844007i
$487$	329.811	+	862.325i	0.677230	+	1.77069i	0.636194	+	0.771529i	$0.280508\pi$
$487$	329.811	+	862.325i	0.677230	+	1.77069i	0.0410366	+	0.999158i	$0.486934\pi$
$488$	98.0209	+	160.613i	0.200863	+	0.329126i
$489$	14.7734	+	28.7345i	0.0302115	+	0.0587617i
$490$	78.6073	−	152.892i	0.160423	−	0.312025i
$491$	168.808	−	50.7868i	0.343805	−	0.103435i	−0.111517	−	0.993763i	$-0.535571\pi$
$491$	168.808	−	50.7868i	0.343805	−	0.103435i	0.455321	+	0.890327i	$0.349524\pi$
$492$	7.51882	+	17.6933i	0.0152822	+	0.0359619i
$493$	72.6940	+	7.99862i	0.147452	+	0.0162244i
$494$	31.1249	+	66.3953i	0.0630058	+	0.134404i
$495$	106.200	−	31.9508i	0.214545	−	0.0645471i
$496$	530.977	−	19.4053i	1.07052	−	0.0391236i
$497$	350.253	−	51.5465i	0.704734	−	0.103715i
$498$	−186.139	−	48.6632i	−0.373774	−	0.0977172i
$499$	159.460	−	340.159i	0.319559	−	0.681681i	−0.679067	−	0.734076i	$-0.737616\pi$
$499$	159.460	−	340.159i	0.319559	−	0.681681i	0.998626	+	0.0523946i	$0.0166854\pi$
$500$	−366.712	+	440.650i	−0.733423	+	0.881300i
$501$	29.9313	+	24.9090i	0.0597431	+	0.0497186i
$502$	73.0839	−	998.542i	0.145585	−	1.98913i
$503$	695.355	−	265.951i	1.38241	−	0.528729i	0.450946	−	0.892551i	$-0.351087\pi$
$503$	695.355	−	265.951i	1.38241	−	0.528729i	0.931468	+	0.363822i	$0.118528\pi$
$504$	30.9611	+	46.7978i	0.0614308	+	0.0928527i
$505$	45.2661	−	50.5199i	0.0896358	−	0.100039i
$506$	−808.190	+	838.266i	−1.59721	+	1.65665i
$507$	−433.884	−	243.507i	−0.855786	−	0.480291i
$508$	−248.508	−	277.352i	−0.489190	−	0.545968i
$509$	−386.234	+	42.4978i	−0.758809	+	0.0834928i	−0.480495	−	0.876997i	$-0.659543\pi$
$509$	−386.234	+	42.4978i	−0.758809	+	0.0834928i	−0.278314	+	0.960490i	$0.589776\pi$
$510$	−165.525	+	550.180i	−0.324558	+	1.07878i
$511$	−313.965	+	325.649i	−0.614413	+	0.637278i
$512$	−574.938	+	269.520i	−1.12293	+	0.526406i
$513$	59.5062	+	61.7206i	0.115996	+	0.120313i
$514$	503.269	−	55.3753i	0.979123	−	0.107734i
$515$	206.082	+	147.439i	0.400160	+	0.286290i
$516$	−79.5198	−	1086.48i	−0.154108	−	2.10557i
$517$	264.804	+	564.878i	0.512193	+	1.09261i
$518$	−530.548	−	297.758i	−1.02422	−	0.574822i
$519$	423.533	−	327.042i	0.816057	−	0.630138i
$520$	41.6309	−	7.68962i	0.0800594	−	0.0147877i
$521$	−150.749	+	181.144i	−0.289346	+	0.347685i	−0.893403	−	0.449255i	$-0.851689\pi$
$521$	−150.749	+	181.144i	−0.289346	+	0.347685i	0.604057	+	0.796941i	$0.293550\pi$
$522$	25.8730	+	31.0897i	0.0495652	+	0.0595588i
$523$	−25.9627	+	140.560i	−0.0496419	+	0.268757i	−0.998962	−	0.0455546i	$-0.985495\pi$
$523$	−25.9627	+	140.560i	−0.0496419	+	0.268757i	0.949320	+	0.314311i	$0.101774\pi$
$524$	−89.9958	+	46.2700i	−0.171748	+	0.0883016i
$525$	283.307	+	172.899i	0.539632	+	0.329332i
$526$	97.0453			0.184497
$527$	−604.596	+	726.498i	−1.14724	+	1.37855i
$528$	−425.634	+	128.054i	−0.806125	+	0.242527i
$529$	−25.1556	+	688.319i	−0.0475531	+	1.30117i
$530$	436.821	−	391.394i	0.824191	−	0.738479i
$531$	22.1714	−	84.8069i	0.0417541	−	0.159712i
$532$	34.1236	−	113.422i	0.0641421	−	0.213199i
$533$	−0.856430	−	5.81935i	−0.00160681	−	0.0109181i
$534$	−1139.19	−	210.420i	−2.13332	−	0.394045i
$535$	−125.123	+	89.5176i	−0.233874	+	0.167323i
$536$	284.399	+	31.2928i	0.530595	+	0.0583821i
$537$	−132.879	+	312.689i	−0.247446	+	0.582289i
$538$	15.8408	−	28.2252i	0.0294438	−	0.0524633i
$539$	−137.660	+	192.413i	−0.255399	+	0.356982i
$540$	221.851	−	124.509i	0.410835	−	0.230572i
$541$	334.028	−	786.033i	0.617427	−	1.45293i	−0.256343	−	0.966586i	$-0.582518\pi$
$541$	334.028	−	786.033i	0.617427	−	1.45293i	0.873769	−	0.486340i	$-0.161669\pi$
$542$	48.9079	−	332.323i	0.0902359	−	0.613143i
$543$	−1273.49	−	140.123i	−2.34528	−	0.258054i
$544$	258.980	−	860.814i	0.476067	−	1.58238i
$545$	−43.9871	+	3.21944i	−0.0807102	+	0.00590723i
$546$	−98.1648	−	287.744i	−0.179789	−	0.527004i
$547$	17.9309			0.0327805			0.0163902	−	0.999866i	$-0.494783\pi$
$547$	17.9309			0.0327805			0.0163902	+	0.999866i	$0.494783\pi$
$548$	−879.166	+	731.647i	−1.60432	+	1.33512i
$549$	139.262	+	194.653i	0.253666	+	0.354560i
$550$	439.550	−	393.839i	0.799182	−	0.716070i
$551$	3.01723	−	16.3350i	0.00547592	−	0.0296462i
$552$	187.299	−	306.900i	0.339309	−	0.555979i
$553$	371.489	+	27.1895i	0.671771	+	0.0491673i
$554$	695.208	+	154.864i	1.25489	+	0.279538i
$555$	204.860	−	309.647i	0.369118	−	0.557922i
$556$	−303.391	−	1160.49i	−0.545667	−	2.08721i
$557$	791.050	+	28.9100i	1.42020	+	0.0519031i	0.735796	−	0.677203i	$-0.236808\pi$
$557$	791.050	+	28.9100i	1.42020	+	0.0519031i	0.684401	+	0.729106i	$0.260064\pi$
$558$	−519.603	+	57.1726i	−0.931188	+	0.102460i
$559$	−60.5417	+	327.767i	−0.108304	+	0.586346i
$560$	136.251	+	83.1526i	0.243305	+	0.148487i
$561$	335.604	−	715.908i	0.598225	−	1.27613i
$562$	161.034	−	1094.21i	0.286538	−	1.94699i
$563$	−74.6445	+	218.801i	−0.132583	+	0.388634i	−0.992569	−	0.121685i	$-0.961170\pi$
$563$	−74.6445	+	218.801i	−0.132583	+	0.388634i	0.859985	+	0.510319i	$0.170473\pi$
$564$	−605.106	−	783.639i	−1.07288	−	1.38943i
$565$	218.715	−	244.101i	0.387106	−	0.432037i
$566$	−48.6728	+	442.354i	−0.0859943	+	0.781544i
$567$	−323.927	−	419.500i	−0.571300	−	0.739859i
$568$	14.1889	+	193.862i	0.0249804	+	0.341306i
$569$	186.884	+	439.774i	0.328443	+	0.772890i	0.999504	+	0.0314882i	$0.0100247\pi$
$569$	186.884	+	439.774i	0.328443	+	0.772890i	−0.671062	+	0.741402i	$0.734161\pi$
$570$	121.890	+	46.6189i	0.213842	+	0.0817876i
$571$	−316.504	+	134.500i	−0.554297	+	0.235551i	−0.650099	−	0.759850i	$-0.725273\pi$
$571$	−316.504	+	134.500i	−0.554297	+	0.235551i	0.0958016	+	0.995400i	$0.469459\pi$
$572$	−299.241	+	10.9362i	−0.523149	+	0.0191192i
$573$	132.883	+	81.0973i	0.231907	+	0.141531i
$574$	−9.46464	+	14.3058i	−0.0164889	+	0.0249230i
$575$	67.5070	−	613.525i	0.117403	−	1.06700i
$576$	289.756	−	162.619i	0.503049	−	0.282325i
$577$	−872.386	+	95.9897i	−1.51193	+	0.166360i	−0.826982	−	0.562228i	$-0.809944\pi$
$577$	−872.386	+	95.9897i	−1.51193	+	0.166360i	−0.684952	+	0.728588i	$0.740177\pi$
$578$	168.514	+	276.120i	0.291546	+	0.477716i
$579$	194.273	+	507.945i	0.335531	+	0.877280i
$580$	−44.6306	−	20.9219i	−0.0769492	−	0.0360723i
$581$	−30.7005	−	89.9904i	−0.0528407	−	0.154889i
$582$	−396.776	−	29.0402i	−0.681745	−	0.0498973i
$583$	−673.161	+	445.359i	−1.15465	+	0.763909i
$584$	−165.740	−	184.977i	−0.283801	−	0.316741i
$585$	52.0991	−	13.6205i	0.0890582	−	0.0232829i
$586$	60.8916	−	831.960i	0.103911	−	1.41973i
$587$	−146.218	+	382.302i	−0.249094	+	0.651281i	−0.999958	−	0.00917602i	$-0.997079\pi$
$587$	−146.218	+	382.302i	−0.249094	+	0.651281i	0.750864	+	0.660457i	$0.229637\pi$
$588$	146.845	−	345.555i	0.249736	−	0.587679i
$589$	154.552	+	149.007i	0.262397	+	0.252983i
$590$	35.0310	+	189.655i	0.0593746	+	0.321449i
$591$	−387.837	−	1136.84i	−0.656239	−	1.92359i
$592$	−238.300	+	360.191i	−0.402534	+	0.608430i
$593$	16.2979	−	445.951i	0.0274838	−	0.752025i	−0.912153	−	0.409850i	$-0.865581\pi$
$593$	16.2979	−	445.951i	0.0274838	−	0.752025i	0.939637	−	0.342174i	$-0.111163\pi$
$594$	−590.377	+	225.800i	−0.993901	+	0.380135i
$595$	−271.903	+	81.8034i	−0.456980	+	0.137485i
$596$	169.011	+	915.009i	0.283575	+	1.53525i
$597$	−157.093	+	410.736i	−0.263138	+	0.688000i
$598$	−407.032	+	392.428i	−0.680655	+	0.656234i
$599$	−161.026	+	82.7894i	−0.268825	+	0.138213i	−0.586403	−	0.810020i	$-0.699456\pi$
$599$	−161.026	+	82.7894i	−0.268825	+	0.138213i	0.317577	+	0.948232i	$0.397131\pi$
$600$	−106.033	+	148.207i	−0.176722	+	0.247012i
$601$	450.423	+	191.409i	0.749456	+	0.318484i	0.731946	−	0.681362i	$-0.238612\pi$
$601$	450.423	+	191.409i	0.749456	+	0.318484i	0.0175099	+	0.999847i	$0.494426\pi$
$602$	769.344	−	594.068i	1.27798	−	0.986824i
$603$	363.695	+	13.2917i	0.603142	+	0.0220427i
$604$	683.952	+	1120.70i	1.13237	+	1.85546i
$605$	7.16144	−	4.73797i	0.0118371	−	0.00783135i
$606$	163.469	−	211.699i	0.269751	−	0.349339i
$607$	114.929	+	622.217i	0.189340	+	1.02507i	0.933906	+	0.357520i	$0.116378\pi$
$607$	114.929	+	622.217i	0.189340	+	1.02507i	−0.744566	+	0.667549i	$0.767343\pi$
$608$	−190.709	−	72.9402i	−0.313667	−	0.119967i
$609$	−19.8421	+	65.9522i	−0.0325814	+	0.108296i
$610$	−459.218	−	257.725i	−0.752816	−	0.422501i
$611$	118.476	+	278.797i	0.193905	+	0.456297i
$612$	−79.1851	+	355.473i	−0.129387	+	0.580839i
$613$	−716.265	+	159.555i	−1.16846	+	0.260285i	−0.758409	−	0.651779i	$-0.774023\pi$
$613$	−716.265	+	159.555i	−1.16846	+	0.260285i	−0.410049	+	0.912064i	$0.634488\pi$
$614$	−1278.15	+	717.335i	−2.08168	+	1.16830i
$615$	−8.28544	−	6.39781i	−0.0134723	−	0.0104029i
$616$	130.594	+	108.681i	0.212003	+	0.176430i
$617$			885.578i			1.43530i	0.696405	+	0.717649i	$0.254782\pi$
$617$			885.578i			1.43530i	−0.696405	+	0.717649i	$0.745218\pi$
$618$	852.861	+	520.493i	1.38003	+	0.842222i
$619$	−15.5668	+	9.50027i	−0.0251483	+	0.0153478i	−0.533458	−	0.845827i	$-0.679108\pi$
$619$	−15.5668	+	9.50027i	−0.0251483	+	0.0153478i	0.508310	+	0.861174i	$0.330271\pi$
$620$	543.770	−	331.858i	0.877048	−	0.535255i
$621$	−302.261	+	587.902i	−0.486733	+	0.946702i
$622$	−872.570	+	1130.02i	−1.40285	+	1.81675i
$623$	−223.916	−	526.918i	−0.359415	−	0.845775i
$624$	−208.806	+	54.5889i	−0.334624	+	0.0874823i
$625$	−23.6170	+	127.860i	−0.0377872	+	0.204576i
$626$	60.8427	+	413.420i	0.0971929	+	0.660415i
$627$	−156.613	−	87.8955i	−0.249781	−	0.140184i
$628$	−831.586	+	185.244i	−1.32418	+	0.294974i
$629$	−194.319	−	743.281i	−0.308934	−	1.18169i
$630$	−139.661	−	71.8048i	−0.221685	−	0.113976i
$631$	918.373	+	822.865i	1.45542	+	1.30407i	0.869724	+	0.493538i	$0.164296\pi$
$631$	918.373	+	822.865i	1.45542	+	1.30407i	0.585700	+	0.810528i	$0.300820\pi$
$632$	−29.7776	+	202.335i	−0.0471164	+	0.320151i
$633$	60.6051	+	58.4307i	0.0957427	+	0.0923076i
$634$	520.792	+	221.313i	0.821438	+	0.349074i
$635$	191.916	+	65.4725i	0.302229	+	0.103106i
$636$	889.070	−	922.156i	1.39791	−	1.44993i
$637$	−70.2104	+	90.9255i	−0.110220	+	0.142740i
$638$	102.138	+	67.5741i	0.160092	+	0.105916i
$639$	36.0000	+	244.616i	0.0563381	+	0.382811i
$640$	−141.431	+	197.684i	−0.220986	+	0.308882i
$641$	134.628	−	203.490i	0.210028	−	0.317457i	−0.713740	−	0.700411i	$-0.753000\pi$
$641$	134.628	−	203.490i	0.210028	−	0.317457i	0.923768	+	0.382954i	$0.125093\pi$
$642$	−466.283	+	388.043i	−0.726297	+	0.604429i
$643$	383.684	+	461.044i	0.596708	+	0.717020i	0.978273	−	0.207323i	$-0.0664750\pi$
$643$	383.684	+	461.044i	0.596708	+	0.717020i	−0.381564	+	0.924342i	$0.624614\pi$
$644$	912.647	−	33.3540i	1.41715	−	0.0517919i
$645$	327.300	+	494.715i	0.507442	+	0.767000i
$646$	240.154	−	123.472i	0.371755	−	0.191133i
$647$	−156.845	−	305.066i	−0.242419	−	0.471509i	0.736315	−	0.676638i	$-0.236564\pi$
$647$	−156.845	−	305.066i	−0.242419	−	0.471509i	−0.978735	+	0.205130i	$0.934238\pi$
$648$	242.698	−	160.567i	0.374534	−	0.247789i
$649$	−9.69342	−	265.236i	−0.0149359	−	0.408684i
$650$	220.272	−	183.311i	0.338879	−	0.282017i
$651$	−569.375	−	684.175i	−0.874616	−	1.05096i
$652$	−37.5806	−	24.8631i	−0.0576389	−	0.0381335i
$653$	−28.5477	−	20.4241i	−0.0437177	−	0.0312773i	0.559790	−	0.828635i	$-0.310882\pi$
$653$	−28.5477	−	20.4241i	−0.0437177	−	0.0312773i	−0.603508	+	0.797357i	$0.706231\pi$
$654$	−172.054	+	25.3210i	−0.263079	+	0.0387172i
$655$	30.4032	−	45.9545i	0.0464171	−	0.0701596i
$656$	9.63788	+	7.44213i	0.0146919	+	0.0113447i
$657$	−227.433	−	219.273i	−0.346169	−	0.333749i
$658$	285.233	−	836.087i	0.433485	−	1.27065i
$659$	134.864	−	317.362i	0.204650	−	0.481581i	−0.785964	−	0.618272i	$-0.787833\pi$
$659$	134.864	−	317.362i	0.204650	−	0.481581i	0.990614	+	0.136692i	$0.0436469\pi$
$660$	−369.876	+	383.641i	−0.560418	+	0.581274i
$661$	−301.838	−	44.4214i	−0.456639	−	0.0672033i	−0.0866485	−	0.996239i	$-0.527616\pi$
$661$	−301.838	−	44.4214i	−0.456639	−	0.0672033i	−0.369990	+	0.929036i	$0.620639\pi$
$662$	−35.2979	+	39.3948i	−0.0533201	+	0.0595088i
$663$	175.544	−	341.436i	0.264773	−	0.514986i
$664$	50.5086	−	13.2047i	0.0760672	−	0.0198866i
$665$	14.0230	+	62.9515i	0.0210873	+	0.0946639i
$666$	207.954	−	370.534i	0.312243	−	0.556357i
$667$	126.716	−	18.6487i	0.189979	−	0.0279591i
$668$	−53.4045	−	9.86431i	−0.0799468	−	0.0147669i
$669$	350.260	+	1339.76i	0.523558	+	2.00264i
$670$	−736.952	+	313.171i	−1.09993	+	0.467419i
$671$	573.588	+	442.910i	0.854825	+	0.660075i
$672$	752.882	+	387.083i	1.12036	+	0.576017i
$673$	−456.442	−	747.908i	−0.678219	−	1.11130i	−0.987085	−	0.160199i	$-0.948787\pi$
$673$	−456.442	−	747.908i	−0.678219	−	1.11130i	0.308866	−	0.951106i	$-0.400051\pi$
$674$	556.965	+	912.621i	0.826357	+	1.35404i
$675$	174.543	−	285.999i	0.258582	−	0.423702i
$676$	693.900			1.02648
$677$	−239.067	+	287.269i	−0.353127	+	0.424326i	−0.915350	−	0.402660i	$-0.868086\pi$
$677$	−239.067	+	287.269i	−0.353127	+	0.424326i	0.562223	+	0.826986i	$0.309946\pi$
$678$	789.845	−	1022.88i	1.16496	−	1.50868i
$679$	−96.2264	−	171.457i	−0.141718	−	0.252514i
$680$	−33.8975	−	152.171i	−0.0498493	−	0.223781i
$681$	388.115	+	86.4562i	0.569919	+	0.126955i
$682$	−1456.70	+	619.031i	−2.13593	+	0.907670i
$683$	337.576	−	601.496i	0.494255	−	0.880668i	−0.505585	−	0.862777i	$-0.668723\pi$
$683$	337.576	−	601.496i	0.494255	−	0.880668i	0.999840	−	0.0178913i	$-0.00569528\pi$
$684$	79.2138	+	23.8319i	0.115810	+	0.0348419i
$685$	222.486	−	581.712i	0.324797	−	0.849215i
$686$	1089.76	−	201.288i	1.58857	−	0.293423i
$687$	1083.37	+	836.548i	1.57695	+	1.21768i
$688$	−380.726	−	575.467i	−0.553380	−	0.836435i
$689$	−334.542	+	204.168i	−0.485548	+	0.296325i
$690$	−36.7492	+	1005.55i	−0.0532597	+	1.45732i
$691$	−523.277	−	677.666i	−0.757275	−	0.980704i	−0.999944	−	0.0105945i	$-0.996628\pi$
$691$	−523.277	−	677.666i	−0.757275	−	0.980704i	0.242669	−	0.970109i	$-0.421977\pi$
$692$	−291.874	+	686.838i	−0.421784	+	0.992540i
$693$	175.762	+	125.747i	0.253625	+	0.181453i
$694$	−693.435	−	1348.74i	−0.999186	−	1.94343i
$695$	453.328	+	470.198i	0.652270	+	0.676544i
$696$	−35.3197	−	13.5087i	−0.0507468	−	0.0194090i
$697$	−21.3005	+	3.93440i	−0.0305602	+	0.00564476i
$698$	262.383	+	872.124i	0.375907	+	1.24946i
$699$	292.602	+	765.038i	0.418601	+	1.09447i
$700$	−462.573	−	16.9054i	−0.660818	−	0.0241505i
$701$	218.405	+	144.496i	0.311563	+	0.206128i	0.697838	−	0.716256i	$-0.254146\pi$
$701$	218.405	+	144.496i	0.311563	+	0.206128i	−0.386275	+	0.922383i	$0.626239\pi$
$702$	−290.479	+	99.0976i	−0.413788	+	0.141165i
$703$	−171.600	+	31.6961i	−0.244097	+	0.0450870i
$704$	698.283	−	724.269i	0.991880	−	1.02879i
$705$	496.167	+	210.848i	0.703783	+	0.299076i
$706$	−758.803	−	290.217i	−1.07479	−	0.411073i
$707$	131.832	+	9.64883i	0.186466	+	0.0136476i
$708$	106.538	+	407.513i	0.150477	+	0.575584i
$709$	22.8944	−	20.5135i	0.0322911	−	0.0289330i	−0.651016	−	0.759064i	$-0.725657\pi$
$709$	22.8944	−	20.5135i	0.0322911	−	0.0289330i	0.683308	+	0.730131i	$0.260541\pi$
$710$	−300.162	−	453.695i	−0.422763	−	0.639007i
$711$	−18.9891	+	259.448i	−0.0267077	+	0.364906i
$712$	297.511	−	101.497i	0.417853	−	0.142551i
$713$	−702.609	+	1498.80i	−0.985426	+	2.10210i
$714$	−1045.72	+	399.954i	−1.46459	+	0.560160i
$715$	139.178	−	84.9393i	0.194655	−	0.118796i
$716$	−51.8238	−	470.991i	−0.0723796	−	0.657809i
$717$	327.832	+	584.135i	0.457228	+	0.814693i
$718$	265.710	+	29.2364i	0.370069	+	0.0407192i
$719$	−557.512	−	368.846i	−0.775398	−	0.512999i	0.100825	−	0.994904i	$-0.467852\pi$
$719$	−557.512	−	368.846i	−0.775398	−	0.512999i	−0.876223	+	0.481905i	$0.839945\pi$
$720$	−58.0737	+	95.1574i	−0.0806579	+	0.132163i
$721$	18.0340	+	493.454i	0.0250124	+	0.684402i
$722$	398.783	+	938.414i	0.552331	+	1.29974i
$723$	194.448	−	508.404i	0.268946	−	0.703187i
$724$	1644.46	−	698.819i	2.27135	−	0.965220i
$725$	−64.7444	+	4.73868i	−0.0893026	+	0.00653611i
$726$	26.7988	−	20.6934i	0.0369130	−	0.0285033i
$727$	−950.988	−	104.638i	−1.30810	−	0.143932i	−0.571691	−	0.820469i	$-0.693712\pi$
$727$	−950.988	−	104.638i	−1.30810	−	0.143932i	−0.736409	+	0.676537i	$0.763480\pi$
$728$	61.4419	+	55.0522i	0.0843982	+	0.0756212i
$729$	−187.538	+	144.812i	−0.257254	+	0.198645i
$730$	657.860	+	224.431i	0.901178	+	0.307439i
$731$	1214.35	+	178.716i	1.66122	+	0.244481i
$732$	−1041.34	−	488.158i	−1.42259	−	0.666882i
$733$	3.69389	−	6.05266i	0.00503941	−	0.00825739i	−0.851063	−	0.525063i	$-0.824042\pi$
$733$	3.69389	−	6.05266i	0.00503941	−	0.00825739i	0.856103	+	0.516806i	$0.172879\pi$
$734$	266.586	+	49.2410i	0.363196	+	0.0670858i
$735$	22.3604	+	203.218i	0.0304223	+	0.276487i
$736$	57.4980	−	1573.29i	0.0781222	−	2.13762i
$737$	1066.12	−	278.720i	1.44656	−	0.378181i
$738$	−9.99118	−	6.61010i	−0.0135382	−	0.00895678i
$739$	256.110	−	1149.72i	0.346563	−	1.55577i	−0.416308	−	0.909224i	$-0.636676\pi$
$739$	256.110	−	1149.72i	0.346563	−	1.55577i	0.762872	−	0.646550i	$-0.223789\pi$
$740$	−37.7973	+	516.424i	−0.0510775	+	0.697870i
$741$	−74.4362	−	45.4277i	−0.100454	−	0.0613060i
$742$	1123.92	+	207.599i	1.51472	+	0.279783i
$743$	−340.933	−	380.504i	−0.458860	−	0.512118i	0.469941	−	0.882698i	$-0.344275\pi$
$743$	−340.933	−	380.504i	−0.458860	−	0.512118i	−0.928801	+	0.370580i	$0.879159\pi$
$744$	397.470	−	284.365i	0.534233	−	0.382211i
$745$	−324.099	−	389.446i	−0.435033	−	0.522746i
$746$			526.545i			0.705824i
$747$	62.8493	−	21.4412i	0.0841356	−	0.0287031i
$748$	80.4921	+	1099.76i	0.107610	+	1.47027i
$749$	−287.088	−	86.3720i	−0.383296	−	0.115316i
$750$	134.620	−	1223.47i	0.179494	−	1.63130i
$751$	486.676	+	71.6239i	0.648038	+	0.0953714i	0.461590	−	0.887093i	$-0.347279\pi$
$751$	486.676	+	71.6239i	0.648038	+	0.0953714i	0.186448	+	0.982465i	$0.440302\pi$
$752$	−577.157	−	245.265i	−0.767496	−	0.326150i
$753$	582.728	+	1038.31i	0.773875	+	1.37890i
$754$	48.3633	+	34.6010i	0.0641423	+	0.0458899i
$755$	−623.431	−	349.886i	−0.825736	−	0.463426i
$756$	456.259	+	193.889i	0.603517	+	0.256467i
$757$	120.243	−	1092.81i	0.158842	−	1.44361i	−0.603980	−	0.797000i	$-0.706419\pi$
$757$	120.243	−	1092.81i	0.158842	−	1.44361i	0.762822	−	0.646609i	$-0.223813\pi$
$758$	82.5647	+	115.404i	0.108924	+	0.152248i
$759$	251.519	−	1361.70i	0.331382	−	1.79407i
$760$	−35.0338	+	5.15591i	−0.0460972	+	0.00678410i
$761$	−433.438	−	130.402i	−0.569563	−	0.171356i	−0.00971727	−	0.999953i	$-0.503093\pi$
$761$	−433.438	−	130.402i	−0.569563	−	0.171356i	−0.559846	+	0.828597i	$0.689140\pi$
$762$	773.557	+	202.234i	1.01517	+	0.265399i
$763$	−57.3534	−	64.0102i	−0.0751683	−	0.0838928i
$764$	−216.967	−	7.92935i	−0.283988	−	0.0103787i
$765$	−57.1315	−	189.897i	−0.0746816	−	0.248231i
$766$	1414.97	+	1177.55i	1.84722	+	1.53727i
$767$		−	128.875i		−	0.168025i
$768$	170.634	−	279.595i	0.222180	−	0.364056i
$769$	586.535	+	1140.82i	0.762724	+	1.48351i	0.872005	+	0.489497i	$0.162820\pi$
$769$	586.535	+	1140.82i	0.762724	+	1.48351i	−0.109281	+	0.994011i	$0.534855\pi$
$770$	−467.581	−	86.3666i	−0.607248	−	0.112164i
$771$	−462.807	+	385.151i	−0.600268	+	0.499547i
$772$	−582.980	−	485.160i	−0.755156	−	0.628445i
$773$	−252.458	−	1366.78i	−0.326595	−	1.76816i	−0.593896	−	0.804542i	$-0.702411\pi$
$773$	−252.458	−	1366.78i	−0.326595	−	1.76816i	0.267301	−	0.963613i	$-0.413868\pi$
$774$	414.897	+	537.309i	0.536042	+	0.694198i
$775$	410.618	−	731.642i	0.529829	−	0.944055i
$776$	97.7454	−	45.8212i	0.125961	−	0.0590479i
$777$	721.576	−	52.8126i	0.928670	−	0.0679699i
$778$	0.421430	−	0.589051i	0.000541683	−	0.000757135i
$779$	0.538109	+	4.89051i	0.000690769	+	0.00627793i
$780$	−186.282	+	179.599i	−0.238823	+	0.230255i
$781$	317.765	+	677.854i	0.406869	+	0.867931i
$782$	1498.91	+	1445.13i	1.91676	+	1.84799i
$783$	66.5790	+	20.0306i	0.0850306	+	0.0255819i
$784$	−26.0103	−	236.390i	−0.0331764	−	0.301517i
$785$	345.507	−	309.575i	0.440136	−	0.394364i
$786$	106.335	−	189.468i	0.135286	−	0.241053i
$787$	−625.805	−	603.352i	−0.795178	−	0.766648i	0.181031	−	0.983477i	$-0.442056\pi$
$787$	−625.805	−	603.352i	−0.795178	−	0.766648i	−0.976210	+	0.216829i	$0.930429\pi$
$788$	1247.66	+	1117.91i	1.58332	+	1.41866i
$789$	−96.2495	+	63.6781i	−0.121989	+	0.0807073i
$790$	−204.466	−	534.596i	−0.258817	−	0.676704i
$791$	636.980	+	46.6209i	0.805285	+	0.0589392i
$792$	−75.9026	+	91.2065i	−0.0958366	+	0.115160i
$793$	270.473	+	225.090i	0.341076	+	0.283846i
$794$	663.311	+	310.947i	0.835404	+	0.391621i
$795$	−176.419	+	674.813i	−0.221911	+	0.848821i
$796$	−89.2971	−	606.764i	−0.112182	−	0.762266i
$797$	−10.9254	−	298.945i	−0.0137081	−	0.375087i	−0.988431	−	0.151671i	$-0.951535\pi$
$797$	−10.9254	−	298.945i	−0.0137081	−	0.375087i	0.974723	−	0.223417i	$-0.0717211\pi$
$798$	73.2649	+	243.522i	0.0918106	+	0.305165i
$799$	1010.06	−	473.498i	1.26416	−	0.592613i
$800$	−87.2727	+	793.162i	−0.109091	+	0.991453i
$801$	367.999	−	156.383i	0.459425	−	0.195234i
$802$	−12.7225	−	42.2877i	−0.0158634	−	0.0527278i
$803$	−850.712	−	437.381i	−1.05942	−	0.544684i
$804$	−1555.27	+	799.621i	−1.93442	+	0.994553i
$805$	−424.476	+	259.054i	−0.527300	+	0.321806i
$806$	−717.828	+	274.546i	−0.890605	+	0.340628i
$807$	2.80964	+	38.3880i	0.00348159	+	0.0475688i
$808$	−10.5673	+	71.8034i	−0.0130783	+	0.0888656i
$809$	−13.2154	−	180.561i	−0.0163354	−	0.223191i	−0.999237	−	0.0390583i	$-0.987564\pi$
$809$	−13.2154	−	180.561i	−0.0163354	−	0.223191i	0.982901	−	0.184132i	$-0.0589474\pi$
$810$	−372.387	+	724.297i	−0.459737	+	0.894194i
$811$	−754.514	−	1054.62i	−0.930350	−	1.30039i	−0.953730	−	0.300664i	$-0.902792\pi$
$811$	−754.514	−	1054.62i	−0.930350	−	1.30039i	0.0233802	−	0.999727i	$-0.492557\pi$
$812$	−20.8847	−	93.7547i	−0.0257201	−	0.115461i
$813$	169.553	+	361.690i	0.208553	+	0.444883i
$814$	279.732	−	1255.76i	0.343651	−	1.54270i
$815$	24.4708	+	1.79103i	0.0300255	+	0.00219758i
$816$	228.975	+	761.079i	0.280606	+	0.932695i
$817$	60.6192	−	272.129i	0.0741973	−	0.333083i
$818$	−778.466	+	1660.62i	−0.951670	+	2.03010i
$819$	83.0569	+	64.1345i	0.101413	+	0.0783083i
$820$	14.4437	+	2.12567i	0.0176142	+	0.00259228i
$821$	−1468.34	−	500.929i	−1.78848	−	0.610145i	−0.788492	−	0.615044i	$-0.789138\pi$
$821$	−1468.34	−	500.929i	−1.78848	−	0.610145i	−0.999988	+	0.00489972i	$0.998440\pi$
$822$	707.501	−	2351.63i	0.860707	−	2.86087i
$823$	97.2915	−	64.3674i	0.118216	−	0.0782108i	−0.491272	−	0.871006i	$-0.663468\pi$
$823$	97.2915	−	64.3674i	0.118216	−	0.0782108i	0.609488	+	0.792795i	$0.291375\pi$
$824$	−270.935	−	9.90169i	−0.328804	−	0.0120166i
$825$	−177.521	+	679.028i	−0.215177	+	0.823064i
$826$	−250.797	+	279.906i	−0.303629	+	0.338870i
$827$	180.892	+	40.2955i	0.218733	+	0.0487249i	0.325428	−	0.945567i	$-0.394492\pi$
$827$	180.892	+	40.2955i	0.218733	+	0.0487249i	−0.106694	+	0.994292i	$0.534027\pi$
$828$	23.2944	+	637.392i	0.0281333	+	0.769797i
$829$	−468.301	+	335.041i	−0.564899	+	0.404150i	−0.828091	−	0.560593i	$-0.810573\pi$
$829$	−468.301	+	335.041i	−0.564899	+	0.404150i	0.263193	+	0.964743i	$0.415224\pi$
$830$	−105.182	+	101.408i	−0.126726	+	0.122179i
$831$	−791.125	+	302.580i	−0.952015	+	0.364115i
$832$	351.679	−	339.061i	0.422691	−	0.407526i
$833$	344.056	+	246.151i	0.413032	+	0.295499i
$834$	1918.06	+	1718.59i	2.29983	+	2.06065i
$835$	27.9876	−	9.54804i	0.0335181	−	0.0114348i
$836$	250.467			0.299602
$837$	−690.677	+	574.786i	−0.825182	+	0.686721i
$838$	−68.6752	+	17.9541i	−0.0819513	+	0.0214249i
$839$	−186.368	+	179.682i	−0.222132	+	0.214162i	−0.796830	−	0.604203i	$-0.793491\pi$
$839$	−186.368	+	179.682i	−0.222132	+	0.214162i	0.574699	+	0.818365i	$0.305119\pi$
$840$	146.721	−	5.36211i	0.174667	−	0.00638346i
$841$	267.193	+	783.206i	0.317709	+	0.931280i
$842$	1108.90	−	204.824i	1.31698	−	0.243259i
$843$	558.272	+	1190.90i	0.662244	+	1.41270i
$844$	−113.591	−	29.6965i	−0.134586	−	0.0351855i
$845$	−329.494	+	184.921i	−0.389934	+	0.218841i
$846$	583.922	+	199.207i	0.690215	+	0.235469i
$847$	15.8369	+	5.40279i	0.0186976	+	0.00637873i
$848$	205.216	−	784.963i	0.242000	−	0.925664i
$849$	−241.985	−	470.664i	−0.285024	−	0.554375i
$850$	−704.226	−	785.963i	−0.828501	−	0.924662i
$851$	−658.510	−	1173.34i	−0.773807	−	1.37878i
$852$	−726.128	−	940.368i	−0.852263	−	1.10372i
$853$	221.608	+	994.829i	0.259798	+	1.16627i	0.912636	+	0.408774i	$0.134043\pi$
$853$	221.608	+	994.829i	0.259798	+	1.16627i	−0.652838	+	0.757498i	$0.726422\pi$
$854$	−149.411	−	1015.23i	−0.174954	−	1.18880i
$855$	−43.9653	+	9.79368i	−0.0514214	+	0.0114546i
$856$	58.8029	−	153.746i	0.0686949	−	0.179610i
$857$	101.450	−	216.411i	0.118377	−	0.252522i	−0.837413	−	0.546571i	$-0.815933\pi$
$857$	101.450	−	216.411i	0.118377	−	0.252522i	0.955790	+	0.294049i	$0.0950028\pi$
$858$	522.875	−	374.085i	0.609411	−	0.435996i
$859$	537.534	−	59.1455i	0.625767	−	0.0688540i	0.209072	−	0.977900i	$-0.432956\pi$
$859$	537.534	−	59.1455i	0.625767	−	0.0688540i	0.416695	+	0.909046i	$0.363188\pi$
$860$	−735.738	−	378.269i	−0.855509	−	0.439848i
$861$		−	20.3989i		−	0.0236921i
$862$	1272.53	+	215.053i	1.47625	+	0.249482i
$863$	−895.530			−1.03769			−0.518847	−	0.854867i	$-0.673639\pi$
$863$	−895.530			−1.03769			−0.518847	+	0.854867i	$0.673639\pi$
$864$	390.762	−	760.036i	0.452270	−	0.879672i
$865$	−44.4443	−	403.924i	−0.0513807	−	0.466964i
$866$	152.203	+	212.741i	0.175754	+	0.245659i
$867$	−348.313	−	163.283i	−0.401745	−	0.188331i
$868$	1159.47	+	443.459i	1.33579	+	0.510898i
$869$	171.263	+	768.827i	0.197081	+	0.884726i
$870$	104.702	−	15.4090i	0.120348	−	0.0177115i
$871$	522.266	−	116.340i	0.599616	−	0.133570i
$872$	37.3502	−	28.8409i	0.0428328	−	0.0330744i
$873$	119.746	−	67.2044i	0.137166	−	0.0769810i
$874$	352.223	−	315.593i	0.403001	−	0.361090i
$875$	540.986	−	278.140i	0.618269	−	0.317874i
$876$	1468.70	+	383.969i	1.67660	+	0.438321i
$877$	−39.4855	+	115.741i	−0.0450234	+	0.131974i	−0.966648	−	0.256108i	$-0.917560\pi$
$877$	−39.4855	+	115.741i	−0.0450234	+	0.131974i	0.921625	+	0.388082i	$0.126862\pi$
$878$	276.003	−	809.030i	0.314354	−	0.921447i
$879$	485.514	+	865.093i	0.552348	+	0.984178i
$880$	−85.3753	+	326.565i	−0.0970174	+	0.371097i
$881$	778.274	−	364.840i	0.883399	−	0.414120i	0.0711732	−	0.997464i	$-0.477326\pi$
$881$	778.274	−	364.840i	0.883399	−	0.414120i	0.812225	+	0.583344i	$0.198256\pi$
$882$	42.4977	+	230.079i	0.0481833	+	0.260860i
$883$	−189.857	+	64.7702i	−0.215014	+	0.0733524i	−0.428297	−	0.903638i	$-0.640886\pi$
$883$	−189.857	+	64.7702i	−0.215014	+	0.0733524i	0.213284	+	0.976990i	$0.431584\pi$
$884$	19.5551	+	535.075i	0.0221211	+	0.605289i
$885$	−159.189	−	165.113i	−0.179875	−	0.186569i
$886$	17.6857	+	67.6487i	0.0199613	+	0.0763529i
$887$	−488.471	−	586.959i	−0.550700	−	0.661736i	0.418440	−	0.908244i	$-0.362577\pi$
$887$	−488.471	−	586.959i	−0.550700	−	0.661736i	−0.969141	+	0.246509i	$0.920717\pi$
$888$			397.247i			0.447350i
$889$	127.585	+	373.982i	0.143515	+	0.420677i
$890$	−587.070	+	655.210i	−0.659630	+	0.736191i
$891$	652.137	−	911.521i	0.731916	−	1.02303i
$892$	−1340.46	−	1390.35i	−1.50276	−	1.55869i
$893$	−90.5162	−	236.664i	−0.101362	−	0.265021i
$894$	−1386.62	−	1438.22i	−1.55103	−	1.60875i
$895$	150.125	+	209.837i	0.167738	+	0.234454i
$896$	−473.345	+	17.2990i	−0.528286	+	0.0193070i
$897$	146.195	−	656.291i	0.162982	−	0.731651i
$898$	206.576	+	185.093i	0.230040	+	0.206117i
$899$	168.438	+	44.0355i	0.187362	+	0.0489828i
$900$	11.8067	−	323.061i	0.0131186	−	0.358956i
$901$	796.349	+	1203.68i	0.883851	+	1.33594i
$902$	−34.7353	−	10.4503i	−0.0385092	−	0.0115857i
$903$	−373.226	+	1094.02i	−0.413318	+	1.21153i
$904$	−51.0586	+	346.938i	−0.0564808	+	0.383781i
$905$	−594.629	+	770.070i	−0.657049	+	0.850907i
$906$	−2552.36	−	1196.50i	−2.81718	−	1.32064i
$907$	−1523.17	−	339.300i	−1.67935	−	0.374091i	−0.728814	−	0.684712i	$-0.759928\pi$
$907$	−1523.17	−	339.300i	−1.67935	−	0.374091i	−0.950534	+	0.310622i	$0.899463\pi$
$908$	−531.037	+	159.765i	−0.584843	+	0.175953i
$909$	−6.73874	+	92.0712i	−0.00741336	+	0.101288i
$910$	−225.357	−	50.2005i	−0.247645	−	0.0551654i
$911$	−808.855	+	379.176i	−0.887876	+	0.416219i	−0.813876	−	0.581039i	$-0.802646\pi$
$911$	−808.855	+	379.176i	−0.887876	+	0.416219i	−0.0740004	+	0.997258i	$0.523577\pi$
$912$	176.207	−	39.2517i	0.193209	−	0.0430391i
$913$	163.526	−	116.993i	0.179109	−	0.128141i
$914$	556.540	+	286.137i	0.608906	+	0.313060i
$915$	624.563	−	45.7122i	0.682583	−	0.0499586i
$916$	−1888.59	−	277.943i	−2.06178	−	0.303431i
$917$	107.089	−	7.83788i	0.116782	−	0.00854731i
$918$	403.755	+	1055.66i	0.439820	+	1.14995i
$919$	−291.501	−	477.643i	−0.317194	−	0.519742i	0.654476	−	0.756082i	$-0.272889\pi$
$919$	−291.501	−	477.643i	−0.317194	−	0.519742i	−0.971670	+	0.236341i	$0.924052\pi$
$920$	−124.844	−	242.823i	−0.135700	−	0.263938i
$921$	796.980	−	1550.14i	0.865342	−	1.68310i
$922$	204.445	−	61.5083i	0.221741	−	0.0667118i
$923$	142.171	+	334.557i	0.154032	+	0.362467i
$924$	−1032.23	−	113.578i	−1.11714	−	0.122920i
$925$	289.463	+	617.481i	0.312933	+	0.667547i
$926$	−1851.89	+	557.150i	−1.99988	+	0.601674i
$927$	−344.628	+	12.5949i	−0.371767	+	0.0135867i
$928$	−163.818	+	24.1090i	−0.176528	+	0.0259795i
$929$	−1307.52	−	341.830i	−1.40744	−	0.367954i	−0.530149	−	0.847904i	$-0.677864\pi$
$929$	−1307.52	−	341.830i	−1.40744	−	0.367954i	−0.877296	+	0.479950i	$0.840655\pi$
$930$	−580.549	+	1238.42i	−0.624246	+	1.33164i
$931$	61.4659	−	73.8590i	0.0660214	−	0.0793330i
$932$	−878.051	−	730.720i	−0.942115	−	0.784034i
$933$	123.934	−	1693.30i	0.132834	−	1.81490i
$934$	−499.558	+	191.065i	−0.534859	+	0.204566i
$935$	−331.302	−	500.764i	−0.354334	−	0.535576i
$936$	−38.4484	+	42.9110i	−0.0410774	+	0.0458451i
$937$	288.259	−	298.986i	0.307640	−	0.319089i	−0.548182	−	0.836359i	$-0.684680\pi$
$937$	288.259	−	298.986i	0.307640	−	0.319089i	0.855822	+	0.517271i	$0.173052\pi$
$938$	−1360.72	−	763.675i	−1.45066	−	0.814152i
$939$	−331.617	−	370.106i	−0.353160	−	0.394150i
$940$	−747.357	+	82.2326i	−0.795061	+	0.0874815i
$941$	−57.4244	+	190.870i	−0.0610248	+	0.202838i	−0.982727	−	0.185060i	$-0.940752\pi$
$941$	−57.4244	+	190.870i	−0.0610248	+	0.202838i	0.921702	+	0.387898i	$0.126799\pi$
$942$	1269.61	−	1316.86i	1.34778	−	1.39794i
$943$	−34.3487	+	16.1020i	−0.0364250	+	0.0170753i
$944$	185.174	+	192.065i	0.196159	+	0.203459i
$945$	−268.322	+	29.5239i	−0.283939	+	0.0312422i
$946$	1671.69	+	1195.99i	1.76711	+	1.26426i
$947$	32.6714	+	446.388i	0.0344999	+	0.471371i	0.986334	+	0.164758i	$0.0526842\pi$
$947$	32.6714	+	446.388i	0.0344999	+	0.471371i	−0.951834	+	0.306613i	$0.900804\pi$
$948$	−530.584	−	1131.84i	−0.559688	−	1.19392i
$949$	−405.043	−	227.321i	−0.426810	−	0.239538i
$950$	−189.723	+	146.499i	−0.199709	+	0.154210i
$951$	−661.740	+	122.230i	−0.695836	+	0.128527i
$952$	194.333	−	233.515i	0.204131	−	0.245289i
$953$	−1075.23	−	1292.02i	−1.12825	−	1.35574i	−0.926496	−	0.376304i	$-0.877195\pi$
$953$	−1075.23	−	1292.02i	−1.12825	−	1.35574i	−0.201758	−	0.979435i	$-0.564666\pi$
$954$	−144.987	+	784.946i	−0.151978	+	0.822795i
$955$	105.138	−	54.0554i	0.110093	−	0.0566025i
$956$	−797.420	−	486.658i	−0.834121	−	0.509057i
$957$	−145.641			−0.152185
$958$	−636.793	+	765.186i	−0.664710	+	0.798733i
$959$	1162.19	−	349.652i	1.21188	−	0.364601i
$960$	31.7517	−	868.804i	0.0330747	−	0.905004i
$961$	−960.049	+	860.208i	−0.999011	+	0.895117i
$962$	158.006	−	604.382i	0.164248	−	0.628256i
$963$	60.3222	−	200.502i	0.0626398	−	0.208206i
$964$	110.531	+	751.045i	0.114659	+	0.779092i
$965$	406.117	+	75.0137i	0.420847	+	0.0777344i
$966$	−1594.70	+	1140.91i	−1.65083	+	1.18107i
$967$	776.510	+	85.4404i	0.803009	+	0.0883562i	0.501556	−	0.865125i	$-0.332761\pi$
$967$	776.510	+	85.4404i	0.803009	+	0.0883562i	0.301453	+	0.953481i	$0.402528\pi$
$968$	−3.59325	+	8.45563i	−0.00371204	+	0.00873515i
$969$	−157.167	+	280.041i	−0.162195	+	0.289000i
$970$	−175.791	+	245.711i	−0.181228	+	0.253310i
$971$	1235.83	−	693.581i	1.27274	−	0.714296i	0.301742	−	0.953389i	$-0.402432\pi$
$971$	1235.83	−	693.581i	1.27274	−	0.714296i	0.970996	+	0.239094i	$0.0768504\pi$
$972$	−364.505	+	857.753i	−0.375006	+	0.882462i
$973$	−185.315	+	1259.20i	−0.190458	+	1.29414i
$974$	2747.95	+	302.360i	2.82130	+	0.310432i
$975$	−98.1821	+	326.343i	−0.100700	+	0.334711i
$976$	−726.511	+	53.1738i	−0.744376	+	0.0544813i
$977$	−243.656	−	714.214i	−0.249392	−	0.731028i	−0.997707	−	0.0676840i	$-0.978439\pi$
$977$	−243.656	−	714.214i	−0.249392	−	0.731028i	0.748315	−	0.663344i	$-0.230863\pi$
$978$	96.7475			0.0989238
$979$	930.587	−	774.441i	0.950549	−	0.791053i
$980$	−165.904	−	231.892i	−0.169290	−	0.236624i
$981$	44.7047	−	40.0556i	0.0455705	−	0.0408314i
$982$	95.8779	−	519.074i	0.0976353	−	0.528589i
$983$	−434.415	+	711.815i	−0.441927	+	0.724126i	−0.993965	−	0.109693i	$-0.965013\pi$
$983$	−434.415	+	711.815i	−0.441927	+	0.724126i	0.552038	+	0.833819i	$0.313850\pi$
$984$	11.1703	+	0.817562i	0.0113519	+	0.000830855i
$985$	−890.360	−	198.336i	−0.903919	−	0.201357i
$986$	120.830	−	182.634i	0.122545	−	0.185228i
$987$	265.720	+	1016.39i	0.269219	+	1.02978i
$988$	121.537	+	4.44173i	0.123013	+	0.00449568i
$989$	2136.77	−	235.111i	2.16053	−	0.237726i
$990$	60.3183	−	326.558i	0.0609276	−	0.329857i
$991$	857.488	+	523.318i	0.865276	+	0.528070i	0.881708	−	0.471795i	$-0.156394\pi$
$991$	857.488	+	523.318i	0.865276	+	0.528070i	−0.0164325	+	0.999865i	$0.505231\pi$
$992$	908.329	−	1937.64i	0.915654	−	1.95327i
$993$	9.15882	−	62.2332i	0.00922339	−	0.0626719i
$994$	342.280	−	1003.30i	0.344346	−	1.00936i
$995$	204.102	+	264.321i	0.205128	+	0.265649i
$996$	−212.937	+	237.652i	−0.213792	+	0.238606i
$997$	18.1518	−	164.970i	0.0182064	−	0.165466i	−0.981449	−	0.191725i	$-0.938592\pi$
$997$	18.1518	−	164.970i	0.0182064	−	0.165466i	0.999655	+	0.0262588i	$0.00835938\pi$
$998$	−687.525	−	890.375i	−0.688903	−	0.892159i
$999$	−53.3145	−	728.434i	−0.0533678	−	0.729163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	431.3.f.a.101.61	✓	2982
431.367	odd	86	inner	431.3.f.a.367.61	yes	2982

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
431.3.f.a.101.61	✓	2982	1.1	even	1	trivial
431.3.f.a.367.61	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+(1.36915 - 2.66302i) q^{2} +(0.389464 + 3.53958i) q^{3} +(-2.88966 - 4.03900i) q^{4} +(2.44851 + 1.14782i) q^{5} +(9.95921 + 3.80907i) q^{6} +(1.14577 + 5.14355i) q^{7} +(-2.86250 + 0.421272i) q^{8} +(-3.59225 + 0.800208i) q^{9} +(6.40905 - 4.94890i) q^{10} +(-9.71760 + 5.45378i) q^{11} +(13.1710 - 11.8012i) q^{12} +(-4.81208 + 2.47406i) q^{13} +(15.2661 + 3.99109i) q^{14} +(-3.10918 + 9.11374i) q^{15} +(3.61669 - 10.6014i) q^{16} +(9.75194 + 17.3761i) q^{17} +(-2.78737 + 10.6618i) q^{18} +(4.09796 - 1.92105i) q^{19} +(-2.43934 - 13.2064i) q^{20} +(-17.7598 + 6.05879i) q^{21} +(1.21865 + 33.3452i) q^{22} +(24.2209 + 25.1222i) q^{23} +(-2.60597 - 9.96796i) q^{24} +(-11.3141 - 13.5953i) q^{25} +16.2020i q^{26} +(6.11637 + 17.9285i) q^{27} +(17.4639 - 19.4909i) q^{28} +(2.13559 - 2.98501i) q^{29} +(20.0131 + 20.7579i) q^{30} +(16.9451 + 44.3048i) q^{31} +(-31.3126 - 32.4779i) q^{32} +(-23.0887 - 32.2721i) q^{33} +(59.6248 - 2.17907i) q^{34} +(-3.09840 + 13.9092i) q^{35} +(13.6124 + 12.1968i) q^{36} +(-37.3028 - 9.75224i) q^{37} +(0.494954 - 13.5432i) q^{38} +(-10.6313 - 16.0692i) q^{39} +(-7.49240 - 2.25413i) q^{40} +(-0.350998 + 1.02886i) q^{41} +(-8.18115 + 55.5900i) q^{42} +(37.6488 - 48.7568i) q^{43} +(50.1084 + 23.4898i) q^{44} +(-9.71417 - 2.16392i) q^{45} +(100.063 - 30.1045i) q^{46} +(4.08666 - 55.8359i) q^{47} +(38.9330 + 8.67269i) q^{48} +(19.2237 - 9.01168i) q^{49} +(-51.6953 + 11.5156i) q^{50} +(-57.7061 + 41.2851i) q^{51} +(23.8980 + 12.2868i) q^{52} +(72.2397 - 5.28726i) q^{53} +(56.1183 + 8.25890i) q^{54} +(-30.0536 + 2.19964i) q^{55} +(-5.44661 - 14.2407i) q^{56} +(8.39570 + 13.7569i) q^{57} +(-5.02519 - 9.77406i) q^{58} +(-10.8906 + 21.1823i) q^{59} +(45.7949 - 13.7776i) q^{60} +(-25.4347 - 59.8528i) q^{61} +(141.185 + 15.5348i) q^{62} +(-8.23182 - 17.5601i) q^{63} +(-86.4555 + 26.0106i) q^{64} +(-14.6222 + 0.534389i) q^{65} +(-117.553 + 17.3003i) q^{66} +(-95.6726 - 25.0121i) q^{67} +(42.0024 - 89.5992i) q^{68} +(-79.4890 + 95.5159i) q^{69} +(32.7983 + 27.2949i) q^{70} +(4.90399 - 67.0031i) q^{71} +(9.94570 - 3.80391i) q^{72} +(47.3644 + 71.5914i) q^{73} +(-77.0437 + 85.9859i) q^{74} +(43.7152 - 45.3420i) q^{75} +(-19.6008 - 11.0005i) q^{76} +(-39.1860 - 43.7341i) q^{77} +(-57.3484 + 6.31012i) q^{78} +(20.3643 - 67.6880i) q^{79} +(21.0239 - 21.8063i) q^{80} +(-91.0683 + 42.6910i) q^{81} +(2.25930 + 2.34338i) q^{82} +(-17.9354 + 1.97345i) q^{83} +(75.7912 + 54.2239i) q^{84} +(3.93319 + 53.7391i) q^{85} +(-78.2934 - 167.015i) q^{86} +(11.3974 + 6.39654i) q^{87} +(25.5190 - 19.7052i) q^{88} +(-106.838 + 19.7341i) q^{89} +(-19.0628 + 22.9063i) q^{90} +(-18.2390 - 21.9165i) q^{91} +(31.4787 - 170.423i) q^{92} +(-150.221 + 77.2338i) q^{93} +(-143.097 - 87.3307i) q^{94} +12.2389 q^{95} +(102.763 - 123.482i) q^{96} +(-35.7289 + 10.7492i) q^{97} +(2.32184 - 63.5313i) q^{98} +(30.5439 - 27.3675i) 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