LMFDB - Embedded newform 42.4.f.a.17.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,4,Mod(5,42)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("42.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.47808022024$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 $ x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 - 24x^11 + 714x^10 - 1940x^9 - 2834x^8 - 17460x^7 + 57834x^6 - 17496x^5 + 59049x^4 - 118098x^3 - 531441x^2 - 9565938x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$2.30541 - 1.91966i$ of defining polynomial
Character	$\chi$	$=$	42.17
Dual form			42.4.f.a.5.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 + 1.00000i) q^{2} +(-3.99309 - 3.32495i) q^{3} +(2.00000 - 3.46410i) q^{4} +(9.90442 + 17.1550i) q^{5} +(10.2412 + 1.76589i) q^{6} +(18.4277 + 1.84901i) q^{7} +8.00000i q^{8} +(4.88947 + 26.5536i) q^{9} +(-34.3099 - 19.8088i) q^{10} +(4.28742 + 2.47535i) q^{11} +(-19.5041 + 7.18256i) q^{12} +17.7414i q^{13} +(-33.7668 + 15.2251i) q^{14} +(17.4901 - 101.433i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(0.947671 - 1.64141i) q^{17} +(-35.0224 - 41.1027i) q^{18} +(83.9968 - 48.4956i) q^{19} +79.2354 q^{20} +(-67.4356 - 68.6545i) q^{21} -9.90138 q^{22} +(-135.935 + 78.4822i) q^{23} +(26.5996 - 31.9447i) q^{24} +(-133.695 + 231.567i) q^{25} +(-17.7414 - 30.7289i) q^{26} +(68.7652 - 122.288i) q^{27} +(43.2606 - 60.1375i) q^{28} -92.0138i q^{29} +(71.1391 + 193.177i) q^{30} +(67.3521 + 38.8857i) q^{31} +(27.7128 + 16.0000i) q^{32} +(-8.88966 - 24.1397i) q^{33} +3.79068i q^{34} +(150.796 + 334.440i) q^{35} +(101.763 + 36.1696i) q^{36} +(-124.469 - 215.587i) q^{37} +(-96.9912 + 167.994i) q^{38} +(58.9891 - 70.8428i) q^{39} +(-137.240 + 79.2354i) q^{40} +343.701 q^{41} +(185.456 + 51.4774i) q^{42} -24.5859 q^{43} +(17.1497 - 9.90138i) q^{44} +(-407.099 + 346.877i) q^{45} +(156.964 - 271.870i) q^{46} +(-235.248 - 407.461i) q^{47} +(-14.1271 + 81.9294i) q^{48} +(336.162 + 68.1462i) q^{49} -534.781i q^{50} +(-9.24175 + 3.40335i) q^{51} +(61.4579 + 35.4827i) q^{52} +(-344.910 - 199.134i) q^{53} +(3.18314 + 280.574i) q^{54} +98.0675i q^{55} +(-14.7921 + 147.422i) q^{56} +(-496.652 - 85.6379i) q^{57} +(92.0138 + 159.373i) q^{58} +(335.568 - 581.220i) q^{59} +(-316.394 - 263.453i) q^{60} +(-273.703 + 158.023i) q^{61} -155.543 q^{62} +(41.0038 + 498.363i) q^{63} -64.0000 q^{64} +(-304.352 + 175.718i) q^{65} +(39.5371 + 32.9216i) q^{66} +(116.895 - 202.469i) q^{67} +(-3.79068 - 6.56566i) q^{68} +(803.750 + 138.591i) q^{69} +(-595.627 - 428.472i) q^{70} -152.225i q^{71} +(-212.429 + 39.1157i) q^{72} +(539.897 + 311.709i) q^{73} +(431.174 + 248.939i) q^{74} +(1303.80 - 480.137i) q^{75} -387.965i q^{76} +(74.4305 + 53.5425i) q^{77} +(-31.3293 + 181.692i) q^{78} +(-151.191 - 261.870i) q^{79} +(158.471 - 274.479i) q^{80} +(-681.186 + 259.666i) q^{81} +(-595.307 + 343.701i) q^{82} -856.438 q^{83} +(-372.697 + 96.2949i) q^{84} +37.5446 q^{85} +(42.5840 - 24.5859i) q^{86} +(-305.941 + 367.419i) q^{87} +(-19.8028 + 34.2994i) q^{88} +(453.577 + 785.618i) q^{89} +(358.239 - 1007.91i) q^{90} +(-32.8040 + 326.933i) q^{91} +627.858i q^{92} +(-139.650 - 379.216i) q^{93} +(814.922 + 470.495i) q^{94} +(1663.88 + 960.642i) q^{95} +(-57.4605 - 156.033i) q^{96} -70.3731i q^{97} +(-650.396 + 218.130i) q^{98} +(-44.7661 + 125.950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9} - 36 q^{10} - 128 q^{16} - 48 q^{18} - 342 q^{19} - 450 q^{21} + 24 q^{22} - 48 q^{24} - 194 q^{25} + 88 q^{28} + 360 q^{30} + 804 q^{31} + 1332 q^{33} + 144 q^{36}+ \cdots - 4284 q^{99}+O(q^{100}) $ 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9 - 36 * q^10 - 128 * q^16 - 48 * q^18 - 342 * q^19 - 450 * q^21 + 24 * q^22 - 48 * q^24 - 194 * q^25 + 88 * q^28 + 360 * q^30 + 804 * q^31 + 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 - 144 * q^40 - 180 * q^42 + 1732 * q^43 - 2394 * q^45 + 168 * q^46 + 820 * q^49 + 1638 * q^51 + 744 * q^52 + 180 * q^54 - 2664 * q^57 - 780 * q^58 - 4620 * q^61 - 2016 * q^63 - 1024 * q^64 - 2016 * q^66 - 706 * q^67 - 60 * q^70 + 192 * q^72 + 3294 * q^73 + 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 + 432 * q^82 - 432 * q^84 + 5232 * q^85 + 1026 * q^87 + 48 * q^88 + 4098 * q^91 + 2016 * q^93 + 3888 * q^94 - 192 * q^96 - 4284 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$3$	−3.99309	−	3.32495i	−0.768470	−	0.639886i
$3$	−3.99309	−	3.32495i	−0.768470	−	0.639886i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	9.90442	+	17.1550i	0.885879	+	1.53439i	0.844703	+	0.535235i	$0.179777\pi$
$5$	9.90442	+	17.1550i	0.885879	+	1.53439i	0.0411754	+	0.999152i	$0.486890\pi$
$6$	10.2412	+	1.76589i	0.696824	+	0.120154i
$7$	18.4277	+	1.84901i	0.995004	+	0.0998373i
$7$	18.4277	+	1.84901i	0.995004	+	0.0998373i
$8$			8.00000i			0.353553i
$9$	4.88947	+	26.5536i	0.181091	+	0.983466i
$10$	−34.3099	−	19.8088i	−1.08498	−	0.626411i
$11$	4.28742	+	2.47535i	0.117519	+	0.0678495i	0.557607	−	0.830105i	$-0.311720\pi$
$11$	4.28742	+	2.47535i	0.117519	+	0.0678495i	−0.440088	+	0.897954i	$0.645053\pi$
$12$	−19.5041	+	7.18256i	−0.469196	+	0.172786i
$13$			17.7414i			0.378505i	0.981928	+	0.189253i	$0.0606065\pi$
$13$			17.7414i			0.378505i	−0.981928	+	0.189253i	$0.939394\pi$
$14$	−33.7668	+	15.2251i	−0.644611	+	0.290649i
$15$	17.4901	−	101.433i	0.301062	−	1.74599i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	0.947671	−	1.64141i	0.0135202	−	0.0234177i	−0.859186	−	0.511663i	$-0.829030\pi$
$17$	0.947671	−	1.64141i	0.0135202	−	0.0234177i	0.872706	+	0.488245i	$0.162363\pi$
$18$	−35.0224	−	41.1027i	−0.458603	−	0.538222i
$19$	83.9968	−	48.4956i	1.01422	−	0.585561i	0.101796	−	0.994805i	$-0.467541\pi$
$19$	83.9968	−	48.4956i	1.01422	−	0.585561i	0.912425	+	0.409245i	$0.134208\pi$
$20$	79.2354			0.885879
$21$	−67.4356	−	68.6545i	−0.700746	−	0.713411i
$22$	−9.90138			−0.0959537
$23$	−135.935	+	78.4822i	−1.23237	+	0.711508i	−0.967523	−	0.252783i	$-0.918654\pi$
$23$	−135.935	+	78.4822i	−1.23237	+	0.711508i	−0.264845	+	0.964291i	$0.585321\pi$
$24$	26.5996	−	31.9447i	0.226234	−	0.271695i
$25$	−133.695	+	231.567i	−1.06956	+	1.85254i
$26$	−17.7414	−	30.7289i	−0.133822	−	0.231786i
$27$	68.7652	−	122.288i	0.490143	−	0.871642i
$28$	43.2606	−	60.1375i	0.291982	−	0.405890i
$29$		−	92.0138i		−	0.589191i	−0.955622	−	0.294595i	$-0.904815\pi$
$29$		−	92.0138i		−	0.589191i	0.955622	−	0.294595i	$-0.0951849\pi$
$30$	71.1391	+	193.177i	0.432939	+	1.17564i
$31$	67.3521	+	38.8857i	0.390219	+	0.225293i	0.682255	−	0.731114i	$-0.260999\pi$
$31$	67.3521	+	38.8857i	0.390219	+	0.225293i	−0.292036	+	0.956407i	$0.594333\pi$
$32$	27.7128	+	16.0000i	0.153093	+	0.0883883i
$33$	−8.88966	−	24.1397i	−0.0468937	−	0.127339i
$34$			3.79068i			0.0191205i
$35$	150.796	+	334.440i	0.728264	+	1.61516i
$36$	101.763	+	36.1696i	0.471126	+	0.167452i
$37$	−124.469	−	215.587i	−0.553044	−	0.957901i	−0.998053	−	0.0623743i	$-0.980133\pi$
$37$	−124.469	−	215.587i	−0.553044	−	0.957901i	0.445009	−	0.895526i	$-0.353201\pi$
$38$	−96.9912	+	167.994i	−0.414054	+	0.717163i
$39$	58.9891	−	70.8428i	0.242200	−	0.290870i
$40$	−137.240	+	79.2354i	−0.542488	+	0.313205i
$41$	343.701			1.30920			0.654598	−	0.755977i	$-0.272838\pi$
$41$	343.701			1.30920			0.654598	+	0.755977i	$0.272838\pi$
$42$	185.456	+	51.4774i	0.681346	+	0.189122i
$43$	−24.5859			−0.0871934			−0.0435967	−	0.999049i	$-0.513882\pi$
$43$	−24.5859			−0.0871934			−0.0435967	+	0.999049i	$0.513882\pi$
$44$	17.1497	−	9.90138i	0.0587594	−	0.0339248i
$45$	−407.099	+	346.877i	−1.34859	+	1.14910i
$46$	156.964	−	271.870i	0.503112	−	0.871415i
$47$	−235.248	−	407.461i	−0.730093	−	1.26456i	−0.956843	−	0.290606i	$-0.906143\pi$
$47$	−235.248	−	407.461i	−0.730093	−	1.26456i	0.226750	−	0.973953i	$-0.427190\pi$
$48$	−14.1271	+	81.9294i	−0.0424807	+	0.246364i
$49$	336.162	+	68.1462i	0.980065	+	0.198677i
$50$		−	534.781i		−	1.51259i
$51$	−9.24175	+	3.40335i	−0.0253746	+	0.00934441i
$52$	61.4579	+	35.4827i	0.163898	+	0.0946263i
$53$	−344.910	−	199.134i	−0.893907	−	0.516097i	−0.0186885	−	0.999825i	$-0.505949\pi$
$53$	−344.910	−	199.134i	−0.893907	−	0.516097i	−0.875218	+	0.483728i	$0.839282\pi$
$54$	3.18314	+	280.574i	0.00802167	+	0.707061i
$55$			98.0675i			0.240426i
$56$	−14.7921	+	147.422i	−0.0352978	+	0.351787i
$57$	−496.652	−	85.6379i	−1.15409	−	0.199000i
$58$	92.0138	+	159.373i	0.208310	+	0.360804i
$59$	335.568	−	581.220i	0.740461	−	1.28252i	−0.211825	−	0.977308i	$-0.567941\pi$
$59$	335.568	−	581.220i	0.740461	−	1.28252i	0.952286	−	0.305208i	$-0.0987261\pi$
$60$	−316.394	−	263.453i	−0.680771	−	0.566862i
$61$	−273.703	+	158.023i	−0.574494	+	0.331684i	−0.758942	−	0.651158i	$-0.774284\pi$
$61$	−273.703	+	158.023i	−0.574494	+	0.331684i	0.184448	+	0.982842i	$0.440950\pi$
$62$	−155.543			−0.318612
$63$	41.0038	+	498.363i	0.0819999	+	0.996632i
$64$	−64.0000			−0.125000
$65$	−304.352	+	175.718i	−0.580773	+	0.335310i
$66$	39.5371	+	32.9216i	0.0737375	+	0.0613994i
$67$	116.895	−	202.469i	0.213150	−	0.369186i	−0.739549	−	0.673103i	$-0.764961\pi$
$67$	116.895	−	202.469i	0.213150	−	0.369186i	0.952699	+	0.303917i	$0.0982944\pi$
$68$	−3.79068	−	6.56566i	−0.00676012	−	0.0117089i
$69$	803.750	+	138.591i	1.40232	+	0.241803i
$70$	−595.627	−	428.472i	−1.01702	−	0.731602i
$71$		−	152.225i		−	0.254447i	−0.991874	−	0.127224i	$-0.959393\pi$
$71$		−	152.225i		−	0.254447i	0.991874	−	0.127224i	$-0.0406066\pi$
$72$	−212.429	+	39.1157i	−0.347708	+	0.0640254i
$73$	539.897	+	311.709i	0.865618	+	0.499765i	0.865890	−	0.500235i	$-0.166753\pi$
$73$	539.897	+	311.709i	0.865618	+	0.499765i	−0.000271580		1.00000i	$0.500086\pi$
$74$	431.174	+	248.939i	0.677338	+	0.391061i
$75$	1303.80	−	480.137i	2.00734	−	0.739220i
$76$		−	387.965i		−	0.585561i
$77$	74.4305	+	53.5425i	0.110158	+	0.0792433i
$78$	−31.3293	+	181.692i	−0.0454788	+	0.263751i
$79$	−151.191	−	261.870i	−0.215320	−	0.372945i	0.738052	−	0.674744i	$-0.235746\pi$
$79$	−151.191	−	261.870i	−0.215320	−	0.372945i	−0.953371	+	0.301799i	$0.902413\pi$
$80$	158.471	−	274.479i	0.221470	−	0.383597i
$81$	−681.186	+	259.666i	−0.934412	+	0.356194i
$82$	−595.307	+	343.701i	−0.801716	+	0.462871i
$83$	−856.438			−1.13261			−0.566303	−	0.824197i	$-0.691627\pi$
$83$	−856.438			−1.13261			−0.566303	+	0.824197i	$0.691627\pi$
$84$	−372.697	+	96.2949i	−0.484103	+	0.125079i
$85$	37.5446			0.0479092
$86$	42.5840	−	24.5859i	0.0533948	−	0.0308275i
$87$	−305.941	+	367.419i	−0.377015	+	0.452775i
$88$	−19.8028	+	34.2994i	−0.0239884	+	0.0415492i
$89$	453.577	+	785.618i	0.540214	+	0.935678i	0.998891	+	0.0470750i	$0.0149900\pi$
$89$	453.577	+	785.618i	0.540214	+	0.935678i	−0.458678	+	0.888603i	$0.651677\pi$
$90$	358.239	−	1007.91i	0.419574	−	1.18047i
$91$	−32.8040	+	326.933i	−0.0377889	+	0.376614i
$92$			627.858i			0.711508i
$93$	−139.650	−	379.216i	−0.155710	−	0.422827i
$94$	814.922	+	470.495i	0.894178	+	0.516254i
$95$	1663.88	+	960.642i	1.79695	+	1.03747i
$96$	−57.4605	−	156.033i	−0.0610889	−	0.165886i
$97$		−	70.3731i		−	0.0736629i	−0.999321	−	0.0368315i	$-0.988274\pi$
$97$		−	70.3731i		−	0.0736629i	0.999321	−	0.0368315i	$-0.0117265\pi$
$98$	−650.396	+	218.130i	−0.670408	+	0.224841i
$99$	−44.7661	+	125.950i	−0.0454461	+	0.127863i
$100$	534.781	+	926.268i	0.534781	+	0.926268i
$101$	119.274	−	206.588i	0.117507	−	0.203527i	−0.801272	−	0.598300i	$-0.795843\pi$
$101$	119.274	−	206.588i	0.117507	−	0.203527i	0.918779	+	0.394772i	$0.129177\pi$
$102$	12.6038	−	15.1365i	0.0122349	−	0.0146935i
$103$	−16.9592	+	9.79138i	−0.0162237	+	0.00936674i	−0.508090	−	0.861304i	$-0.669648\pi$
$103$	−16.9592	+	9.79138i	−0.0162237	+	0.00936674i	0.491866	+	0.870671i	$0.336315\pi$
$104$	−141.931			−0.133822
$105$	509.854	−	1836.84i	0.473873	−	1.70721i
$106$	796.536			0.729872
$107$	−419.010	+	241.915i	−0.378572	+	0.218569i	−0.677197	−	0.735802i	$-0.736805\pi$
$107$	−419.010	+	241.915i	−0.378572	+	0.218569i	0.298625	+	0.954371i	$0.403472\pi$
$108$	−286.088	−	482.786i	−0.254896	−	0.430149i
$109$	−21.4023	+	37.0698i	−0.0188070	+	0.0325747i	−0.875276	−	0.483624i	$-0.839320\pi$
$109$	−21.4023	+	37.0698i	−0.0188070	+	0.0325747i	0.856469	+	0.516199i	$0.172653\pi$
$110$	−98.0675	−	169.858i	−0.0850033	−	0.147230i
$111$	−219.799	+	1274.71i	−0.187950	+	1.09000i
$112$	−121.801	−	270.134i	−0.102760	−	0.227904i
$113$			378.359i			0.314983i	0.987520	+	0.157491i	$0.0503406\pi$
$113$			378.359i			0.314983i	−0.987520	+	0.157491i	$0.949659\pi$
$114$	945.864	−	348.323i	0.777090	−	0.286170i
$115$	−2692.72	−	1554.64i	−2.18346	−	1.26062i
$116$	−318.745	−	184.028i	−0.255127	−	0.147298i
$117$	−471.097	+	86.7457i	−0.372247	+	0.0685440i
$118$			1342.27i			1.04717i
$119$	20.4984	−	28.4953i	0.0157906	−	0.0219509i
$120$	811.463	+	139.921i	0.617301	+	0.106442i
$121$	−653.245	−	1131.45i	−0.490793	−	0.850078i
$122$	316.045	−	547.407i	0.234536	−	0.406229i
$123$	−1372.43	−	1142.79i	−1.00608	−	0.837737i
$124$	269.408	−	155.543i	0.195109	−	0.112647i
$125$	−2820.59			−2.01825
$126$	−569.384	−	822.186i	−0.402577	−	0.581319i
$127$	112.805			0.0788177			0.0394088	−	0.999223i	$-0.487453\pi$
$127$	112.805			0.0788177			0.0394088	+	0.999223i	$0.487453\pi$
$128$	110.851	−	64.0000i	0.0765466	−	0.0441942i
$129$	98.1736	+	81.7468i	0.0670054	+	0.0557938i
$130$	351.436	−	608.705i	0.237100	−	0.410669i
$131$	−790.927	−	1369.93i	−0.527508	−	0.913671i	−0.999486	−	0.0320608i	$-0.989793\pi$
$131$	−790.927	−	1369.93i	−0.527508	−	0.913671i	0.471977	−	0.881611i	$-0.343540\pi$
$132$	−101.402	−	17.4848i	−0.0668628	−	0.0115292i
$133$	1637.54	−	738.353i	1.06761	−	0.481378i
$134$			467.581i			0.301439i
$135$	2778.93	−	31.5271i	1.77164	−	0.0200994i
$136$	13.1313	+	7.58137i	0.00827942	+	0.00478013i
$137$	1597.31	+	922.210i	0.996115	+	0.575107i	0.907097	−	0.420923i	$-0.138294\pi$
$137$	1597.31	+	922.210i	0.996115	+	0.575107i	0.0890187	+	0.996030i	$0.471627\pi$
$138$	−1530.73	+	563.704i	−0.944233	+	0.347722i
$139$		−	55.8671i		−	0.0340905i	−0.999855	−	0.0170453i	$-0.994574\pi$
$139$		−	55.8671i		−	0.0340905i	0.999855	−	0.0170453i	$-0.00542594\pi$
$140$	1460.13	+	146.507i	0.881453	+	0.0884437i
$141$	−415.421	+	2409.21i	−0.248119	+	1.43895i
$142$	152.225	+	263.661i	0.0899608	+	0.155817i
$143$	−43.9160	+	76.0647i	−0.0256814	+	0.0444815i
$144$	328.822	−	280.179i	0.190290	−	0.162141i
$145$	1578.49	−	911.344i	0.904046	−	0.521951i
$146$	−1246.84			−0.706774
$147$	−1115.74	−	1389.84i	−0.626020	−	0.779807i
$148$	−995.755			−0.553044
$149$	2951.20	−	1703.87i	1.62263	−	0.936824i	0.636414	−	0.771348i	$-0.280417\pi$
$149$	2951.20	−	1703.87i	1.62263	−	0.936824i	0.986214	−	0.165477i	$-0.0529163\pi$
$150$	−1778.12	+	2135.43i	−0.967885	+	1.16238i
$151$	−1627.89	+	2819.59i	−0.877324	+	1.51957i	−0.0230569	+	0.999734i	$0.507340\pi$
$151$	−1627.89	+	2819.59i	−0.877324	+	1.51957i	−0.854267	+	0.519835i	$0.825993\pi$
$152$	387.965	+	671.975i	0.207027	+	0.358581i
$153$	48.2191	+	17.1384i	0.0254790	+	0.00905595i
$154$	−182.460	−	18.3078i	−0.0954743	−	0.00957976i
$155$			1540.56i			0.798329i
$156$	−127.428	−	346.030i	−0.0654002	−	0.177593i
$157$	2199.76	+	1270.03i	1.11822	+	0.645602i	0.940945	−	0.338560i	$-0.109940\pi$
$157$	2199.76	+	1270.03i	1.11822	+	0.645602i	0.177271	+	0.984162i	$0.443273\pi$
$158$	523.739	+	302.381i	0.263712	+	0.152254i
$159$	715.146	+	1941.97i	0.356697	+	0.968604i
$160$			633.883i			0.313205i
$161$	−2650.09	+	1194.90i	−1.29725	+	0.584917i
$162$	920.184	−	1130.94i	0.446274	−	0.548488i
$163$	−862.851	−	1494.50i	−0.414624	−	0.718150i	0.580765	−	0.814071i	$-0.302754\pi$
$163$	−862.851	−	1494.50i	−0.414624	−	0.718150i	−0.995389	+	0.0959216i	$0.969420\pi$
$164$	687.402	−	1190.61i	0.327299	−	0.566899i
$165$	326.069	−	391.592i	0.153845	−	0.184760i
$166$	1483.39	−	856.438i	0.693576	−	0.400436i
$167$	485.621			0.225021			0.112510	−	0.993651i	$-0.464111\pi$
$167$	485.621			0.225021			0.112510	+	0.993651i	$0.464111\pi$
$168$	549.236	−	539.485i	0.252229	−	0.247751i
$169$	1882.24			0.856734
$170$	−65.0291	+	37.5446i	−0.0293382	+	0.0169384i
$171$	1698.43	+	1993.30i	0.759546	+	0.891412i
$172$	−49.1718	+	85.1680i	−0.0217983	+	0.0377558i
$173$	−726.552	−	1258.43i	−0.319299	−	0.553042i	0.661043	−	0.750348i	$-0.270114\pi$
$173$	−726.552	−	1258.43i	−0.319299	−	0.553042i	−0.980342	+	0.197306i	$0.936781\pi$
$174$	162.486	−	942.329i	0.0707934	−	0.410562i
$175$	−2891.87	+	4020.05i	−1.24917	+	1.73650i
$176$		−	79.2110i		−	0.0339248i
$177$	−3272.48	+	1205.12i	−1.38969	+	0.511764i
$178$	−1571.24	−	907.153i	−0.661624	−	0.381989i
$179$	1099.44	+	634.760i	0.459082	+	0.265051i	0.711658	−	0.702526i	$-0.247944\pi$
$179$	1099.44	+	634.760i	0.459082	+	0.265051i	−0.252576	+	0.967577i	$0.581278\pi$
$180$	387.419	+	2103.98i	0.160425	+	0.871232i
$181$		−	3289.26i		−	1.35076i	−0.737468	−	0.675382i	$-0.763979\pi$
$181$		−	3289.26i		−	1.35076i	0.737468	−	0.675382i	$-0.236021\pi$
$182$	−270.115	−	599.068i	−0.110012	−	0.243988i
$183$	1618.34	+	279.051i	0.653721	+	0.112721i
$184$	−627.858	−	1087.48i	−0.251556	−	0.435708i
$185$	2465.59	−	4270.53i	0.979860	−	1.69717i
$186$	621.096	+	517.172i	0.244844	+	0.203876i
$187$	8.12614	−	4.69163i	0.00317776	−	0.00183468i
$188$	−1881.98			−0.730093
$189$	1493.30	−	2126.34i	0.574717	−	0.818352i
$190$	−3842.57			−1.46721
$191$	−1713.46	+	989.265i	−0.649117	+	0.374768i	−0.788118	−	0.615524i	$-0.788944\pi$
$191$	−1713.46	+	989.265i	−0.649117	+	0.374768i	0.139001	+	0.990292i	$0.455611\pi$
$192$	255.557	+	212.797i	0.0960587	+	0.0799858i
$193$	459.923	−	796.611i	0.171534	−	0.297105i	−0.767423	−	0.641142i	$-0.778461\pi$
$193$	459.923	−	796.611i	0.171534	−	0.297105i	0.938956	+	0.344037i	$0.111794\pi$
$194$	70.3731	+	121.890i	0.0260438	+	0.0451091i
$195$	1799.56	+	310.299i	0.660867	+	0.113954i
$196$	908.390	−	1028.21i	0.331046	−	0.374711i
$197$		−	3061.98i		−	1.10740i	−0.832717	−	0.553699i	$-0.813216\pi$
$197$		−	3061.98i		−	1.10740i	0.832717	−	0.553699i	$-0.186784\pi$
$198$	−48.4125	−	262.917i	−0.0173764	−	0.0943672i
$199$	−451.592	−	260.727i	−0.160867	−	0.0928766i	0.417405	−	0.908720i	$-0.362940\pi$
$199$	−451.592	−	260.727i	−0.160867	−	0.0928766i	−0.578272	+	0.815844i	$0.696273\pi$
$200$	−1852.54	−	1069.56i	−0.654970	−	0.378147i
$201$	−1139.97	+	419.804i	−0.400036	+	0.147317i
$202$			477.094i			0.166179i
$203$	170.135	−	1695.60i	0.0588232	−	0.586247i
$204$	−6.69393	+	38.8211i	−0.00229740	+	0.0133236i
$205$	3404.16	+	5896.18i	1.15979	+	2.00881i
$206$	19.5828	−	33.9183i	0.00662328	−	0.0114719i
$207$	−2748.64	−	3225.83i	−0.922915	−	1.08314i
$208$	245.831	−	141.931i	0.0819488	−	0.0473131i
$209$	480.173			0.158920
$210$	953.746	+	3691.35i	0.313403	+	1.21299i
$211$	99.6288			0.0325058			0.0162529	−	0.999868i	$-0.494826\pi$
$211$	99.6288			0.0325058			0.0162529	+	0.999868i	$0.494826\pi$
$212$	−1379.64	+	796.536i	−0.446953	+	0.258049i
$213$	−506.140	+	607.847i	−0.162817	+	0.195535i
$214$	483.831	−	838.020i	0.154551	−	0.267691i
$215$	−243.509	−	421.770i	−0.0772427	−	0.133788i
$216$	978.304	+	550.122i	0.308172	+	0.173292i
$217$	1169.25	+	841.111i	0.365777	+	0.263126i
$218$		−	85.6091i		−	0.0265972i
$219$	−1119.44	−	3039.81i	−0.345409	−	0.937951i
$220$	339.716	+	196.135i	0.104107	+	0.0601064i
$221$	29.1209	+	16.8130i	0.00886373	+	0.00511748i
$222$	−894.009	−	2427.67i	−0.270279	−	0.733938i
$223$			1782.29i			0.535206i	0.963529	+	0.267603i	$0.0862316\pi$
$223$			1782.29i			0.535206i	−0.963529	+	0.267603i	$0.913768\pi$
$224$	481.100	+	346.085i	0.143504	+	0.103231i
$225$	−6802.63	−	2417.85i	−2.01559	−	0.716400i
$226$	−378.359	−	655.337i	−0.111363	−	0.192887i
$227$	−1721.58	+	2981.86i	−0.503370	+	0.871863i	0.496622	+	0.867967i	$0.334573\pi$
$227$	−1721.58	+	2981.86i	−0.503370	+	0.871863i	−0.999992	+	0.00389579i	$0.998760\pi$
$228$	−1289.96	+	1549.18i	−0.374692	+	0.449986i
$229$	−4706.78	+	2717.46i	−1.35822	+	0.784169i	−0.989384	−	0.145325i	$-0.953577\pi$
$229$	−4706.78	+	2717.46i	−1.35822	+	0.784169i	−0.368837	+	0.929494i	$0.620244\pi$
$230$	6218.57			1.78278
$231$	−119.182	−	461.277i	−0.0339462	−	0.131384i
$232$	736.110			0.208310
$233$	−3815.33	+	2202.78i	−1.07275	+	0.619351i	−0.928931	−	0.370253i	$-0.879271\pi$
$233$	−3815.33	+	2202.78i	−1.07275	+	0.619351i	−0.143817	+	0.989604i	$0.545938\pi$
$234$	729.218	−	621.345i	0.203720	−	0.173584i
$235$	4659.98	−	8071.33i	1.29355	−	2.24049i
$236$	−1342.27	−	2324.88i	−0.370230	−	0.641258i
$237$	−266.986	+	1548.37i	−0.0731755	+	0.424377i
$238$	−7.00902	+	69.8537i	−0.00190894	+	0.0190250i
$239$		−	2020.29i		−	0.546786i	−0.961902	−	0.273393i	$-0.911854\pi$
$239$		−	2020.29i		−	0.546786i	0.961902	−	0.273393i	$-0.0881459\pi$
$240$	−1545.42	+	569.113i	−0.415651	+	0.153067i
$241$	−1966.82	−	1135.54i	−0.525700	−	0.303513i	0.213563	−	0.976929i	$-0.431493\pi$
$241$	−1966.82	−	1135.54i	−0.525700	−	0.303513i	−0.739264	+	0.673416i	$0.764826\pi$
$242$	2262.91	+	1306.49i	0.601096	+	0.347043i
$243$	3583.41	+	1228.04i	0.945991	+	0.324193i
$244$			1264.18i			0.331684i
$245$	2160.45	+	6441.80i	0.563371	+	1.67980i
$246$	3519.90	+	606.938i	0.912279	+	0.157305i
$247$	860.378	+	1490.22i	0.221638	+	0.383888i
$248$	−311.086	+	538.817i	−0.0796531	+	0.137963i
$249$	3419.83	+	2847.61i	0.870373	+	0.724738i
$250$	4885.41	−	2820.59i	1.23592	−	0.713559i
$251$	4513.50			1.13502			0.567510	−	0.823367i	$-0.307907\pi$
$251$	4513.50			1.13502			0.567510	+	0.823367i	$0.307907\pi$
$252$	1808.39	+	854.685i	0.452054	+	0.213651i
$253$	−777.082			−0.193102
$254$	−195.384	+	112.805i	−0.0482658	+	0.0278663i
$255$	−149.919	−	124.834i	−0.0368167	−	0.0306564i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2969.31	+	5142.99i	0.720701	+	1.24829i	0.960719	+	0.277523i	$0.0895134\pi$
$257$	2969.31	+	5142.99i	0.720701	+	1.24829i	−0.240018	+	0.970769i	$0.577153\pi$
$258$	−251.788	−	43.4160i	−0.0607584	−	0.0104766i
$259$	−1895.06	−	4202.93i	−0.454647	−	1.00833i
$260$			1405.74i			0.335310i
$261$	2443.30	−	449.898i	0.579449	−	0.106697i
$262$	2739.85	+	1581.85i	0.646063	+	0.373005i
$263$	−4727.20	−	2729.25i	−1.10833	−	0.639897i	−0.169936	−	0.985455i	$-0.554356\pi$
$263$	−4727.20	−	2729.25i	−1.10833	−	0.639897i	−0.938397	+	0.345558i	$0.887690\pi$
$264$	193.118	−	71.1173i	0.0450211	−	0.0165794i
$265$		−	7889.23i		−	1.82880i
$266$	−2097.95	+	2916.40i	−0.483585	+	0.672241i
$267$	800.967	−	4645.16i	0.183589	−	1.06472i
$268$	−467.581	−	809.875i	−0.106575	−	0.184593i
$269$	−2642.46	+	4576.87i	−0.598935	+	1.03739i	0.394043	+	0.919092i	$0.371076\pi$
$269$	−2642.46	+	4576.87i	−0.598935	+	1.03739i	−0.992979	+	0.118294i	$0.962257\pi$
$270$	−4781.71	+	2833.53i	−1.07780	+	0.638679i
$271$	−5436.74	+	3138.90i	−1.21866	+	0.703596i	−0.964632	−	0.263599i	$-0.915090\pi$
$271$	−5436.74	+	3138.90i	−1.21866	+	0.703596i	−0.254033	+	0.967196i	$0.581757\pi$
$272$	−30.3255			−0.00676012
$273$	1218.02	−	1196.40i	0.270030	−	0.265236i
$274$	−3688.84			−0.813325
$275$	−1146.42	+	661.884i	−0.251387	+	0.145139i
$276$	2087.59	−	2507.09i	0.455284	−	0.546772i
$277$	−3748.17	+	6492.02i	−0.813017	+	1.40819i	0.0977256	+	0.995213i	$0.468843\pi$
$277$	−3748.17	+	6492.02i	−0.813017	+	1.40819i	−0.910743	+	0.412974i	$0.864490\pi$
$278$	55.8671	+	96.7646i	0.0120528	+	0.0208761i
$279$	−703.240	+	1978.57i	−0.150903	+	0.424566i
$280$	−2675.52	+	1206.37i	−0.571047	+	0.257480i
$281$		−	745.889i		−	0.158349i	−0.996861	−	0.0791744i	$-0.974772\pi$
$281$		−	745.889i		−	0.158349i	0.996861	−	0.0791744i	$-0.0252284\pi$
$282$	−1689.68	−	4588.30i	−0.356805	−	0.968898i
$283$	2280.55	+	1316.68i	0.479027	+	0.276566i	0.720011	−	0.693963i	$-0.244137\pi$
$283$	2280.55	+	1316.68i	0.479027	+	0.276566i	−0.240984	+	0.970529i	$0.577470\pi$
$284$	−527.323	−	304.450i	−0.110179	−	0.0636119i
$285$	−3449.94	−	9368.24i	−0.717040	−	1.94711i
$286$		−	175.664i		−	0.0363190i
$287$	6333.63	+	635.507i	1.30266	+	0.130707i
$288$	−289.357	+	814.106i	−0.0592031	+	0.166568i
$289$	2454.70	+	4251.67i	0.499634	+	0.865392i
$290$	−1822.69	+	3156.99i	−0.369075	+	0.639257i
$291$	−233.987	+	281.006i	−0.0471359	+	0.0566077i
$292$	2159.59	−	1246.84i	0.432809	−	0.249882i
$293$	−889.363			−0.177328			−0.0886640	−	0.996062i	$-0.528260\pi$
$293$	−889.363			−0.177328			−0.0886640	+	0.996062i	$0.528260\pi$
$294$	3322.36	+	1291.52i	0.659061	+	0.256201i
$295$	13294.4			2.62383
$296$	1724.70	−	995.755i	0.338669	−	0.195531i
$297$	597.530	−	354.083i	0.116742	−	0.0691783i
$298$	−3407.75	+	5902.39i	−0.662435	+	1.14737i
$299$	−1392.38	−	2411.68i	−0.269309	−	0.466457i
$300$	944.364	−	5476.78i	0.181743	−	1.05401i
$301$	−453.062	−	45.4596i	−0.0867577	−	0.00870515i
$302$		−	6511.56i		−	1.24072i
$303$	−1163.16	+	428.345i	−0.220534	+	0.0812137i
$304$	−1343.95	−	775.930i	−0.253555	−	0.146390i
$305$	−5421.75	−	3130.25i	−1.01786	−	0.587664i
$306$	−100.656	+	18.5344i	−0.0188044	+	0.00346256i
$307$			3995.12i			0.742715i	0.928490	+	0.371357i	$0.121107\pi$
$307$			3995.12i			0.742715i	−0.928490	+	0.371357i	$0.878893\pi$
$308$	334.338	−	150.750i	0.0618528	−	0.0278889i
$309$	100.275	+	17.2905i	0.0184610	+	0.00318325i
$310$	−1540.56	−	2668.33i	−0.282252	−	0.488875i
$311$	256.008	−	443.420i	0.0466782	−	0.0808489i	−0.841742	−	0.539879i	$-0.818470\pi$
$311$	256.008	−	443.420i	0.0466782	−	0.0808489i	0.888420	+	0.459031i	$0.151803\pi$
$312$	566.742	+	471.912i	0.102838	+	0.0856307i
$313$	−1271.68	+	734.205i	−0.229647	+	0.132587i	−0.610409	−	0.792086i	$-0.708995\pi$
$313$	−1271.68	+	734.205i	−0.229647	+	0.132587i	0.380762	+	0.924673i	$0.375662\pi$
$314$	−5080.13			−0.913019
$315$	−8143.28	+	5639.42i	−1.45658	+	1.00871i
$316$	−1209.52			−0.215320
$317$	6545.26	−	3778.91i	1.15968	−	0.669542i	0.208453	−	0.978032i	$-0.433157\pi$
$317$	6545.26	−	3778.91i	1.15968	−	0.669542i	0.951227	+	0.308491i	$0.0998239\pi$
$318$	−3180.64	−	2648.44i	−0.560884	−	0.467035i
$319$	227.766	−	394.502i	0.0399763	−	0.0692410i
$320$	−633.883	−	1097.92i	−0.110735	−	0.191798i
$321$	2477.50	+	427.196i	0.430780	+	0.0742796i
$322$	3395.19	−	4719.73i	0.587598	−	0.816832i
$323$		−	183.832i		−	0.0316677i
$324$	−462.864	+	2879.03i	−0.0793663	+	0.493661i
$325$	−4108.31	−	2371.93i	−0.701194	−	0.404835i
$326$	2989.00	+	1725.70i	0.507809	+	0.293183i
$327$	208.716	−	76.8616i	0.0352968	−	0.0129983i
$328$			2749.61i			0.462871i
$329$	−3581.68	−	7943.55i	−0.600196	−	1.33113i
$330$	−173.176	+	1004.33i	−0.0288880	+	0.167534i
$331$	−2932.76	−	5079.69i	−0.487007	−	0.843520i	0.512882	−	0.858459i	$-0.328578\pi$
$331$	−2932.76	−	5079.69i	−0.487007	−	0.843520i	−0.999888	+	0.0149389i	$0.995245\pi$
$332$	−1712.88	+	2966.79i	−0.283151	+	0.490432i
$333$	5116.03	−	4359.21i	0.841911	−	0.717368i
$334$	−841.121	+	485.621i	−0.137797	+	0.0795569i
$335$	4631.12			0.755300
$336$	−411.819	+	1483.65i	−0.0668648	+	0.240892i
$337$	−8489.10			−1.37220			−0.686099	−	0.727508i	$-0.740678\pi$
$337$	−8489.10			−1.37220			−0.686099	+	0.727508i	$0.740678\pi$
$338$	−3260.14	+	1882.24i	−0.524640	+	0.302901i
$339$	1258.02	−	1510.82i	0.201553	−	0.242055i
$340$	75.0891	−	130.058i	0.0119773	−	0.0207453i
$341$	192.511	+	333.439i	0.0305720	+	0.0529523i
$342$	−4935.07	−	1754.07i	−0.780287	−	0.277336i
$343$	6068.70	+	1877.35i	0.955333	+	0.295531i
$344$		−	196.687i		−	0.0308275i
$345$	5583.16	+	15161.0i	0.871267	+	2.36591i
$346$	2516.85	+	1453.10i	0.391060	+	0.225779i
$347$	968.873	+	559.379i	0.149890	+	0.0865390i	0.573069	−	0.819507i	$-0.305753\pi$
$347$	968.873	+	559.379i	0.149890	+	0.0865390i	−0.423179	+	0.906046i	$0.639086\pi$
$348$	660.895	+	1794.65i	0.101804	+	0.276446i
$349$		−	2364.44i		−	0.362652i	−0.983423	−	0.181326i	$-0.941961\pi$
$349$		−	2364.44i		−	0.362652i	0.983423	−	0.181326i	$-0.0580389\pi$
$350$	988.817	−	9854.80i	0.151013	−	1.50503i
$351$	2169.55	+	1219.99i	0.329921	+	0.185522i
$352$	79.2110	+	137.198i	0.0119942	+	0.0207746i
$353$	1411.12	−	2444.13i	0.212766	−	0.368522i	−0.739813	−	0.672812i	$-0.765086\pi$
$353$	1411.12	−	2444.13i	0.212766	−	0.368522i	0.952579	+	0.304291i	$0.0984194\pi$
$354$	4462.98	−	5359.80i	0.670070	−	0.804718i
$355$	2611.41	−	1507.70i	0.390421	−	0.225410i
$356$	3628.61			0.540214
$357$	−176.597	+	45.6280i	−0.0261807	+	0.00676439i
$358$	−2539.04			−0.374839
$359$	−4504.97	+	2600.95i	−0.662293	+	0.382375i	−0.793150	−	0.609026i	$-0.791560\pi$
$359$	−4504.97	+	2600.95i	−0.662293	+	0.382375i	0.130857	+	0.991401i	$0.458227\pi$
$360$	−2775.01	−	3256.79i	−0.406267	−	0.476800i
$361$	1274.15	−	2206.89i	0.185763	−	0.321751i
$362$	3289.26	+	5697.16i	0.477568	+	0.827171i
$363$	−1153.56	+	6690.00i	−0.166794	+	0.967311i
$364$	1066.92	+	767.502i	0.153631	+	0.110517i
$365$			12349.2i			1.77092i
$366$	−3082.09	+	1135.01i	−0.440174	+	0.162098i
$367$	−4876.42	−	2815.40i	−0.693589	−	0.400444i	0.111366	−	0.993779i	$-0.464477\pi$
$367$	−4876.42	−	2815.40i	−0.693589	−	0.400444i	−0.804955	+	0.593336i	$0.797811\pi$
$368$	2174.96	+	1255.72i	0.308092	+	0.177877i
$369$	1680.51	+	9126.49i	0.237084	+	1.28755i
$370$			9862.38i			1.38573i
$371$	−5987.71	−	4307.33i	−0.837915	−	0.602764i
$372$	−1592.94	−	274.672i	−0.222017	−	0.0382824i
$373$	−3422.23	−	5927.47i	−0.475057	−	0.822822i	0.524535	−	0.851389i	$-0.324239\pi$
$373$	−3422.23	−	5927.47i	−0.475057	−	0.822822i	−0.999592	+	0.0285664i	$0.990906\pi$
$374$	−9.38325	+	16.2523i	−0.00129732	+	0.00224702i
$375$	11262.9	+	9378.32i	1.55096	+	1.29145i
$376$	3259.69	−	1881.98i	0.447089	−	0.258127i
$377$	1632.45			0.223012
$378$	−460.127	+	5176.23i	−0.0626095	+	0.704330i
$379$	5690.62			0.771260			0.385630	−	0.922654i	$-0.373984\pi$
$379$	5690.62			0.771260			0.385630	+	0.922654i	$0.373984\pi$
$380$	6655.52	−	3842.57i	0.898477	−	0.518736i
$381$	−450.441	−	375.071i	−0.0605690	−	0.0504343i
$382$	1978.53	−	3426.91i	0.265001	−	0.458995i
$383$	2151.66	+	3726.78i	0.287062	+	0.497206i	0.973107	−	0.230353i	$-0.0739881\pi$
$383$	2151.66	+	3726.78i	0.287062	+	0.497206i	−0.686045	+	0.727559i	$0.740655\pi$
$384$	−655.435	−	113.017i	−0.0871029	−	0.0150192i
$385$	−181.328	+	1807.16i	−0.0240035	+	0.239225i
$386$			1839.69i			0.242585i
$387$	−120.212	−	652.844i	−0.0157900	−	0.0857517i
$388$	−243.779	−	140.746i	−0.0318970	−	0.0184157i
$389$	−6143.61	−	3547.01i	−0.800754	−	0.462315i	0.0429809	−	0.999076i	$-0.486315\pi$
$389$	−6143.61	−	3547.01i	−0.800754	−	0.462315i	−0.843735	+	0.536760i	$0.819648\pi$
$390$	−3427.22	+	1262.10i	−0.444985	+	0.163870i
$391$			297.501i			0.0384790i
$392$	−545.170	+	2689.30i	−0.0702429	+	0.346505i
$393$	−1396.69	+	8100.02i	−0.179271	+	1.03967i
$394$	3061.98	+	5303.51i	0.391524	+	0.678139i
$395$	2994.91	−	5187.34i	0.381494	−	0.660768i
$396$	346.770	+	406.973i	0.0440047	+	0.0516444i
$397$	3898.27	−	2250.67i	0.492817	−	0.284528i	−0.232925	−	0.972495i	$-0.574830\pi$
$397$	3898.27	−	2250.67i	0.492817	−	0.284528i	0.725742	+	0.687967i	$0.241496\pi$
$398$	1042.91			0.131347
$399$	−8993.82	−	2496.43i	−1.12846	−	0.313227i
$400$	4278.25			0.534781
$401$	6038.64	−	3486.41i	0.752008	−	0.434172i	−0.0744107	−	0.997228i	$-0.523708\pi$
$401$	6038.64	−	3486.41i	0.752008	−	0.434172i	0.826419	+	0.563055i	$0.190374\pi$
$402$	1554.68	−	1867.09i	0.192887	−	0.231647i
$403$	−689.886	+	1194.92i	−0.0852746	+	0.147700i
$404$	−477.094	−	826.351i	−0.0587533	−	0.101764i
$405$	−11201.3	−	9113.89i	−1.37432	−	1.11820i
$406$	1400.92	+	3107.01i	0.171248	+	0.379799i
$407$		−	1232.42i		−	0.150095i
$408$	−27.2268	−	73.9340i	−0.00330375	−	0.00897127i
$409$	12431.9	+	7177.56i	1.50298	+	0.867745i	0.999994	+	0.00344923i	$0.00109793\pi$
$409$	12431.9	+	7177.56i	1.50298	+	0.867745i	0.502984	+	0.864296i	$0.332235\pi$
$410$	−11792.4	−	6808.32i	−1.42045	−	0.820095i
$411$	−3311.92	−	8993.45i	−0.397481	−	1.07935i
$412$			78.3311i			0.00936674i
$413$	7258.43	−	10090.1i	0.864804	−	1.20218i
$414$	7986.61	+	2838.67i	0.948117	+	0.336988i
$415$	−8482.52	−	14692.2i	−1.00335	−	1.73785i
$416$	−283.862	+	491.663i	−0.0334554	+	0.0579465i
$417$	−185.755	+	223.082i	−0.0218141	+	0.0261975i
$418$	−831.685	+	480.173i	−0.0973183	+	0.0561867i
$419$	−14839.8			−1.73024			−0.865122	−	0.501562i	$-0.832759\pi$
$419$	−14839.8			−1.73024			−0.865122	+	0.501562i	$0.832759\pi$
$420$	−5343.29	−	5439.86i	−0.620776	−	0.631996i
$421$	−11073.0			−1.28187			−0.640935	−	0.767595i	$-0.721453\pi$
$421$	−11073.0			−1.28187			−0.640935	+	0.767595i	$0.721453\pi$
$422$	−172.562	+	99.6288i	−0.0199057	+	0.0114925i
$423$	9669.31	−	8238.93i	1.11144	−	0.947023i
$424$	1593.07	−	2759.28i	0.182468	−	0.316044i
$425$	253.398	+	438.899i	0.0289215	+	0.0500934i
$426$	268.812	−	1558.96i	0.0305728	−	0.177305i
$427$	−5335.92	+	2405.92i	−0.604738	+	0.272671i
$428$			1935.32i			0.218569i
$429$	428.271	−	157.715i	0.0481984	−	0.0177495i
$430$	843.540	+	487.018i	0.0946026	+	0.0546189i
$431$	5552.06	+	3205.49i	0.620495	+	0.358243i	0.777062	−	0.629424i	$-0.216709\pi$
$431$	5552.06	+	3205.49i	0.620495	+	0.358243i	−0.156566	+	0.987667i	$0.550043\pi$
$432$	−2244.59	+	25.4651i	−0.249984	+	0.00283609i
$433$		−	12881.0i		−	1.42961i	−0.699322	−	0.714807i	$-0.746514\pi$
$433$		−	12881.0i		−	1.42961i	0.699322	−	0.714807i	$-0.253486\pi$
$434$	−2866.30	−	287.601i	−0.317021	−	0.0318094i
$435$	−9333.23	−	1609.33i	−1.02872	−	0.177383i
$436$	85.6091	+	148.279i	0.00940352	+	0.0162874i
$437$	−7612.09	+	13184.5i	−0.833262	+	1.44325i
$438$	4978.73	+	4145.67i	0.543134	+	0.452255i
$439$	−8024.85	+	4633.15i	−0.872449	+	0.503709i	−0.868161	−	0.496282i	$-0.834698\pi$
$439$	−8024.85	+	4633.15i	−0.872449	+	0.503709i	−0.00428790	+	0.999991i	$0.501365\pi$
$440$	−784.540			−0.0850033
$441$	−165.872	+	9259.51i	−0.0179108	+	0.999840i
$442$	−67.2519			−0.00723721
$443$	7691.54	−	4440.71i	0.824912	−	0.476263i	−0.0271952	−	0.999630i	$-0.508658\pi$
$443$	7691.54	−	4440.71i	0.824912	−	0.476263i	0.852108	+	0.523367i	$0.175324\pi$
$444$	3976.13	+	3310.83i	0.424998	+	0.353885i
$445$	−8984.83	+	15562.2i	−0.957128	+	1.65779i
$446$	−1782.29	−	3087.02i	−0.189224	−	0.327746i
$447$	−17449.7	−	3008.86i	−1.84640	−	0.318376i
$448$	−1179.37	−	118.337i	−0.124375	−	0.0124797i
$449$		−	6080.93i		−	0.639147i	−0.947562	−	0.319573i	$-0.896460\pi$
$449$		−	6080.93i		−	0.639147i	0.947562	−	0.319573i	$-0.103540\pi$
$450$	14200.4	−	2614.79i	1.48758	−	0.273917i
$451$	1473.59	+	850.778i	0.153855	+	0.0888283i
$452$	1310.67	+	756.718i	0.136391	+	0.0787457i
$453$	15875.3	−	5846.21i	1.64655	−	0.606356i
$454$		−	6886.30i		−	0.711873i
$455$	−5933.43	+	2675.33i	−0.611348	+	0.275652i
$456$	685.103	−	3973.21i	0.0703572	−	0.408033i
$457$	−278.827	−	482.943i	−0.0285404	−	0.0494335i	0.851402	−	0.524513i	$-0.175753\pi$
$457$	−278.827	−	482.943i	−0.0285404	−	0.0494335i	−0.879943	+	0.475080i	$0.842419\pi$
$458$	5434.92	−	9413.55i	0.554491	−	0.960407i
$459$	−135.558	−	228.761i	−0.0137850	−	0.0232629i
$460$	−10770.9	+	6218.57i	−1.09173	+	0.630309i
$461$	7422.24			0.749866			0.374933	−	0.927052i	$-0.377666\pi$
$461$	7422.24			0.749866			0.374933	+	0.927052i	$0.377666\pi$
$462$	667.706	+	679.774i	0.0672391	+	0.0684544i
$463$	10478.8			1.05182			0.525908	−	0.850541i	$-0.323726\pi$
$463$	10478.8			1.05182			0.525908	+	0.850541i	$0.323726\pi$
$464$	−1274.98	+	736.110i	−0.127564	+	0.0736488i
$465$	5122.29	−	6151.60i	0.510840	−	0.613492i
$466$	4405.56	−	7630.65i	0.437948	−	0.758548i
$467$	4708.74	+	8155.78i	0.466584	+	0.808147i	0.999271	−	0.0381650i	$-0.0121512\pi$
$467$	4708.74	+	8155.78i	0.466584	+	0.808147i	−0.532688	+	0.846312i	$0.678818\pi$
$468$	−641.697	+	1805.42i	−0.0633813	+	0.178324i
$469$	2528.48	−	3514.90i	0.248943	−	0.346062i
$470$			18639.9i			1.82935i
$471$	−4561.04	−	12385.4i	−0.446203	−	1.21166i
$472$	4649.76	+	2684.54i	0.453438	+	0.261792i
$473$	−105.410	−	60.8586i	−0.0102469	−	0.00591603i
$474$	−1085.94	−	2948.84i	−0.105229	−	0.285748i
$475$			25934.5i			2.50517i
$476$	−57.7137	−	127.999i	−0.00555736	−	0.0123253i
$477$	3601.30	−	10132.3i	0.345686	−	0.972588i
$478$	2020.29	+	3499.25i	0.193318	+	0.334837i
$479$	−5303.15	+	9185.32i	−0.505860	+	0.876176i	0.494117	+	0.869396i	$0.335492\pi$
$479$	−5303.15	+	9185.32i	−0.505860	+	0.876176i	−0.999977	+	0.00678003i	$0.997842\pi$
$480$	2107.63	−	2531.15i	0.200416	−	0.240689i
$481$	3824.81	−	2208.25i	0.362570	−	0.209330i
$482$	4542.17			0.429232
$483$	14555.0	+	4040.06i	1.37117	+	0.380599i
$484$	−5225.96			−0.490793
$485$	1207.25	−	697.005i	0.113027	−	0.0652564i
$486$	−7434.69	+	1456.38i	−0.693918	+	0.135932i
$487$	6387.19	−	11062.9i	0.594314	−	1.02938i	−0.399329	−	0.916808i	$-0.630757\pi$
$487$	6387.19	−	11062.9i	0.594314	−	1.02938i	0.993643	−	0.112575i	$-0.0359098\pi$
$488$	−1264.18	−	2189.63i	−0.117268	−	0.203114i
$489$	−1523.70	+	8836.61i	−0.140908	+	0.817188i
$490$	−10183.8	−	8997.08i	−0.938893	−	0.829483i
$491$			18689.8i			1.71784i	0.512110	+	0.858920i	$0.328864\pi$
$491$			18689.8i			1.71784i	−0.512110	+	0.858920i	$0.671136\pi$
$492$	−6703.58	+	2468.65i	−0.614270	+	0.226210i
$493$	−151.033	−	87.1988i	−0.0137975	−	0.00796600i
$494$	−2980.44	−	1720.76i	−0.271450	−	0.156722i
$495$	−2604.04	+	479.497i	−0.236451	+	0.0435390i
$496$		−	1244.34i		−	0.112647i
$497$	281.466	−	2805.16i	0.0254033	−	0.253176i
$498$	−8770.93	−	1512.37i	−0.789226	−	0.136087i
$499$	6862.74	+	11886.6i	0.615668	+	1.06637i	0.990267	+	0.139182i	$0.0444471\pi$
$499$	6862.74	+	11886.6i	0.615668	+	1.06637i	−0.374599	+	0.927187i	$0.622220\pi$
$500$	−5641.18	+	9770.82i	−0.504563	+	0.873928i
$501$	−1939.13	−	1614.66i	−0.172922	−	0.143988i
$502$	−7817.62	+	4513.50i	−0.695055	+	0.401290i
$503$	5480.28			0.485793			0.242896	−	0.970052i	$-0.421902\pi$
$503$	5480.28			0.485793			0.242896	+	0.970052i	$0.421902\pi$
$504$	−3986.90	+	328.031i	−0.352363	+	0.0289914i
$505$	4725.34			0.416386
$506$	1345.95	−	777.082i	0.118250	−	0.0682718i
$507$	−7515.96	−	6258.36i	−0.658374	−	0.548212i
$508$	225.610	−	390.769i	0.0197044	−	0.0341290i
$509$	−5331.28	−	9234.05i	−0.464253	−	0.804111i	0.534914	−	0.844906i	$-0.320344\pi$
$509$	−5331.28	−	9234.05i	−0.464253	−	0.804111i	−0.999168	+	0.0407959i	$0.987011\pi$
$510$	384.500	+	66.2996i	0.0333842	+	0.00575646i
$511$	9372.71	+	6742.37i	0.811398	+	0.583689i
$512$		−	512.000i		−	0.0441942i
$513$	−154.368	−	13606.6i	−0.0132856	−	1.17105i
$514$	−10286.0	−	5938.61i	−0.882675	−	0.509613i
$515$	−335.942	−	193.956i	−0.0287444	−	0.0165956i
$516$	479.526	−	176.590i	0.0409108	−	0.0150658i
$517$		−	2329.28i		−	0.198146i
$518$	7485.27	+	5384.62i	0.634911	+	0.456731i
$519$	−1283.01	+	7440.75i	−0.108512	+	0.629311i
$520$	−1405.74	−	2434.82i	−0.118550	−	0.205334i
$521$	−5750.00	+	9959.29i	−0.483517	+	0.837475i	−0.999821	−	0.0189300i	$-0.993974\pi$
$521$	−5750.00	+	9959.29i	−0.483517	+	0.837475i	0.516304	+	0.856405i	$0.327307\pi$
$522$	−3782.02	+	3222.54i	−0.317116	+	0.270205i
$523$	8319.57	−	4803.31i	0.695582	−	0.401594i	−0.110118	−	0.993919i	$-0.535123\pi$
$523$	8319.57	−	4803.31i	0.695582	−	0.401594i	0.805700	+	0.592324i	$0.201789\pi$
$524$	−6327.42			−0.527508
$525$	24913.9	−	6437.09i	2.07111	−	0.535119i
$526$	10917.0			0.904951
$527$	127.655	−	73.7018i	0.0105517	−	0.00609203i
$528$	−263.372	+	316.296i	−0.0217080	+	0.0260701i
$529$	6235.42	−	10800.1i	0.512486	−	0.887653i
$530$	7889.23	+	13664.5i	0.646578	+	1.11991i
$531$	17074.2	+	6068.67i	1.39540	+	0.495966i
$532$	717.352	−	7149.31i	0.0584608	−	0.582635i
$533$			6097.72i			0.495538i
$534$	3257.84	+	8846.61i	0.264009	+	0.716911i
$535$	−8300.10	−	4792.07i	−0.670738	−	0.387251i
$536$	1619.75	+	935.163i	0.130527	+	0.0753599i
$537$	−2279.60	−	6190.22i	−0.183188	−	0.497444i
$538$		−	10569.8i		−	0.847022i
$539$	1272.58	+	1124.29i	0.101696	+	0.0898452i
$540$	5448.64	−	9689.54i	0.434208	−	0.772169i
$541$	8782.28	+	15211.3i	0.697929	+	1.20885i	0.969183	+	0.246341i	$0.0792282\pi$
$541$	8782.28	+	15211.3i	0.697929	+	1.20885i	−0.271254	+	0.962508i	$0.587438\pi$
$542$	6277.80	−	10873.5i	0.497518	−	0.861726i
$543$	−10936.6	+	13134.3i	−0.864336	+	1.03802i
$544$	52.5253	−	30.3255i	0.00413971	−	0.00239006i
$545$	−847.909			−0.0666430
$546$	−913.279	+	3290.25i	−0.0715838	+	0.257893i
$547$	−14541.1			−1.13662			−0.568311	−	0.822814i	$-0.692403\pi$
$547$	−14541.1			−1.13662			−0.568311	+	0.822814i	$0.692403\pi$
$548$	6389.26	−	3688.84i	0.498058	−	0.287554i
$549$	−5534.33	−	6495.16i	−0.430236	−	0.504930i
$550$	1323.77	−	2292.83i	0.102628	−	0.177758i
$551$	−4462.26	−	7728.87i	−0.345007	−	0.597570i
$552$	−1108.73	+	6430.00i	−0.0854902	+	0.495795i
$553$	−2301.90	−	5105.22i	−0.177010	−	0.392578i
$554$		−	14992.7i		−	1.14978i
$555$	−24044.6	+	8854.64i	−1.83899	+	0.677223i
$556$	−193.529	−	111.734i	−0.0147616	−	0.00852263i
$557$	11945.8	+	6896.92i	0.908726	+	0.524653i	0.880021	−	0.474935i	$-0.157528\pi$
$557$	11945.8	+	6896.92i	0.908726	+	0.524653i	0.0287052	+	0.999588i	$0.490862\pi$
$558$	−760.522	−	4130.22i	−0.0576979	−	0.313345i
$559$		−	436.187i		−	0.0330031i
$560$	3427.77	−	4765.02i	0.258660	−	0.359569i
$561$	−48.0478	−	8.28490i	−0.00361600	−	0.000623509i
$562$	745.889	+	1291.92i	0.0559847	+	0.0969684i
$563$	4598.06	−	7964.08i	0.344201	−	0.596174i	−0.641007	−	0.767535i	$-0.721483\pi$
$563$	4598.06	−	7964.08i	0.344201	−	0.596174i	0.985208	+	0.171361i	$0.0548165\pi$
$564$	7514.91	+	6257.48i	0.561055	+	0.467177i
$565$	−6490.74	+	3747.43i	−0.483305	+	0.279036i
$566$	−5266.71			−0.391124
$567$	−13032.8	+	3525.53i	−0.965305	+	0.261126i
$568$	1217.80			0.0899608
$569$	−15644.0	+	9032.06i	−1.15260	+	0.665455i	−0.949520	−	0.313707i	$-0.898429\pi$
$569$	−15644.0	+	9032.06i	−1.15260	+	0.665455i	−0.203082	+	0.979162i	$0.565096\pi$
$570$	15343.7	+	12776.3i	1.12750	+	0.938845i
$571$	−7626.26	+	13209.1i	−0.558930	+	0.968095i	0.438656	+	0.898655i	$0.355455\pi$
$571$	−7626.26	+	13209.1i	−0.558930	+	0.968095i	−0.997586	+	0.0694402i	$0.977879\pi$
$572$	175.664	+	304.259i	0.0128407	+	0.0222407i
$573$	10131.2	+	1746.93i	0.738636	+	0.127363i
$574$	−11605.7	+	5232.90i	−0.843922	+	0.380517i
$575$		−	41970.8i		−	3.04401i
$576$	−312.926	−	1699.43i	−0.0226364	−	0.122933i
$577$	−4709.42	−	2718.99i	−0.339785	−	0.196175i	0.320392	−	0.947285i	$-0.396185\pi$
$577$	−4709.42	−	2718.99i	−0.339785	−	0.196175i	−0.660177	+	0.751110i	$0.729519\pi$
$578$	−8503.34	−	4909.41i	−0.611925	−	0.353295i
$579$	−4485.20	+	1651.71i	−0.321932	+	0.118554i
$580$		−	7290.75i		−	0.521951i
$581$	−15782.2	−	1583.56i	−1.12695	−	0.113076i
$582$	124.271	−	720.703i	0.00885087	−	0.0513301i
$583$	−985.851	−	1707.54i	−0.0700339	−	0.121302i
$584$	−2493.68	+	4319.17i	−0.176694	+	0.306042i
$585$	−6154.06	−	7222.48i	−0.434939	−	0.510449i
$586$	1540.42	−	889.363i	0.108591	−	0.0626949i
$587$	23972.1			1.68558			0.842791	−	0.538241i	$-0.180911\pi$
$587$	23972.1			1.68558			0.842791	+	0.538241i	$0.180911\pi$
$588$	−7046.02	+	1085.37i	−0.494171	+	0.0761226i
$589$	7543.15			0.527691
$590$	−23026.6	+	13294.4i	−1.60676	+	0.927666i
$591$	−10180.9	+	12226.8i	−0.708608	+	0.851001i
$592$	−1991.51	+	3449.40i	−0.138261	+	0.239475i
$593$	697.071	+	1207.36i	0.0482720	+	0.0836095i	0.889152	−	0.457612i	$-0.151295\pi$
$593$	697.071	+	1207.36i	0.0482720	+	0.0836095i	−0.840880	+	0.541222i	$0.817962\pi$
$594$	−680.870	+	1210.82i	−0.0470311	+	0.0836373i
$595$	691.861	+	69.4203i	0.0476698	+	0.00478312i
$596$		−	13631.0i		−	0.936824i
$597$	936.343	+	2542.62i	0.0641909	+	0.174309i
$598$	4823.35	+	2784.76i	0.329835	+	0.190430i
$599$	−20811.2	−	12015.4i	−1.41957	−	0.819591i	−0.423312	−	0.905984i	$-0.639133\pi$
$599$	−20811.2	−	12015.4i	−1.41957	−	0.819591i	−0.996261	+	0.0863929i	$0.972466\pi$
$600$	3841.10	+	10430.4i	0.261354	+	0.709701i
$601$		−	10741.9i		−	0.729073i	−0.931189	−	0.364536i	$-0.881227\pi$
$601$		−	10741.9i		−	0.729073i	0.931189	−	0.364536i	$-0.118773\pi$
$602$	830.186	−	374.324i	0.0562058	−	0.0253427i
$603$	5947.83	+	2114.03i	0.401682	+	0.142769i
$604$	6511.56	+	11278.4i	0.438662	+	0.759785i
$605$	12940.0	−	22412.8i	0.869566	−	1.50613i
$606$	1586.31	−	1905.08i	0.106336	−	0.127704i
$607$	23506.4	−	13571.4i	1.57182	−	0.907492i	0.575876	−	0.817537i	$-0.304661\pi$
$607$	23506.4	−	13571.4i	1.57182	−	0.907492i	0.995946	−	0.0899549i	$-0.0286723\pi$
$608$	3103.72			0.207027
$609$	−6317.16	+	6205.01i	−0.420335	+	0.412873i
$610$	12521.0			0.831082
$611$	7228.91	−	4173.61i	0.478642	−	0.276344i
$612$	155.807	−	132.759i	0.0102911	−	0.00876872i
$613$	−14388.2	+	24921.1i	−0.948015	+	1.64201i	−0.198415	+	0.980118i	$0.563579\pi$
$613$	−14388.2	+	24921.1i	−0.948015	+	1.64201i	−0.749600	+	0.661891i	$0.769754\pi$
$614$	−3995.12	−	6919.75i	−0.262589	−	0.454818i
$615$	6011.37	−	34862.6i	0.394149	−	2.28585i
$616$	−428.340	+	595.444i	−0.0280167	+	0.0389466i
$617$		−	2160.03i		−	0.140939i	−0.997514	−	0.0704697i	$-0.977550\pi$
$617$		−	2160.03i		−	0.140939i	0.997514	−	0.0704697i	$-0.0224498\pi$
$618$	−190.972	+	70.3272i	−0.0124305	+	0.00457763i
$619$	2505.32	+	1446.45i	0.162677	+	0.0939218i	0.579128	−	0.815236i	$-0.303393\pi$
$619$	2505.32	+	1446.45i	0.162677	+	0.0939218i	−0.416451	+	0.909158i	$0.636726\pi$
$620$	5336.67	+	3081.13i	0.345687	+	0.199582i
$621$	249.820	+	22020.1i	0.0161432	+	1.42292i
$622$			1024.03i			0.0660129i
$623$	6905.77	+	15315.8i	0.444099	+	0.984936i
$624$	−1453.54	−	250.634i	−0.0932502	−	0.0160792i
$625$	−11224.4	−	19441.3i	−0.718364	−	1.24424i
$626$	1468.41	−	2543.36i	0.0937532	−	0.162385i
$627$	−1917.37	−	1596.55i	−0.122125	−	0.101691i
$628$	8799.03	−	5080.13i	0.559108	−	0.322801i
$629$	−471.824			−0.0299092
$630$	8465.16	−	17911.0i	0.535333	−	1.13269i
$631$	−13779.4			−0.869335			−0.434667	−	0.900591i	$-0.643134\pi$
$631$	−13779.4			−0.869335			−0.434667	+	0.900591i	$0.643134\pi$
$632$	2094.96	−	1209.52i	0.131856	−	0.0761270i
$633$	−397.826	−	331.260i	−0.0249797	−	0.0208000i
$634$	−7557.82	+	13090.5i	−0.473437	+	0.820018i
$635$	1117.27	+	1935.17i	0.0698229	+	0.120937i
$636$	8157.46	+	1406.60i	0.508592	+	0.0876967i
$637$	−1209.01	+	5963.98i	−0.0752002	+	0.370960i
$638$			911.063i			0.0565350i
$639$	4042.12	−	744.298i	0.250241	−	0.0460782i
$640$	2195.84	+	1267.77i	0.135622	+	0.0783013i
$641$	12252.1	+	7073.73i	0.754957	+	0.435875i	0.827482	−	0.561492i	$-0.189772\pi$
$641$	12252.1	+	7073.73i	0.754957	+	0.435875i	−0.0725251	+	0.997367i	$0.523106\pi$
$642$	−4718.35	+	1737.57i	−0.290060	+	0.106817i
$643$			4248.35i			0.260557i	0.991477	+	0.130279i	$0.0415872\pi$
$643$			4248.35i			0.260557i	−0.991477	+	0.130279i	$0.958413\pi$
$644$	−1160.92	+	11570.0i	−0.0710350	+	0.707953i
$645$	−430.010	+	2493.82i	−0.0262506	+	0.152239i
$646$	183.832	+	318.406i	0.0111962	+	0.0193924i
$647$	−8314.83	+	14401.7i	−0.505239	+	0.875100i	0.494742	+	0.869040i	$0.335262\pi$
$647$	−8314.83	+	14401.7i	−0.505239	+	0.875100i	−0.999982	+	0.00606041i	$0.998071\pi$
$648$	−2077.33	−	5449.49i	−0.125934	−	0.330364i
$649$	2877.44	−	1661.29i	0.174036	−	0.100480i
$650$	9487.74			0.572523
$651$	−1872.25	−	7246.30i	−0.112718	−	0.436260i
$652$	−6902.81			−0.414624
$653$	−26164.5	+	15106.1i	−1.56798	+	0.905276i	−0.571581	+	0.820546i	$0.693670\pi$
$653$	−26164.5	+	15106.1i	−1.56798	+	0.905276i	−0.996404	+	0.0847307i	$0.972997\pi$
$654$	−284.646	+	341.845i	−0.0170192	+	0.0204391i
$655$	15667.4	−	27136.7i	0.934617	−	1.61880i
$656$	−2749.61	−	4762.46i	−0.163650	−	0.283449i
$657$	−5637.20	+	15860.3i	−0.334746	+	0.941809i
$658$	14147.2	+	10177.0i	0.838169	+	0.602947i
$659$			533.821i			0.0315549i	0.999876	+	0.0157775i	$0.00502233\pi$
$659$			533.821i			0.0315549i	−0.999876	+	0.0157775i	$0.994978\pi$
$660$	−704.376	−	1912.72i	−0.0415421	−	0.112807i
$661$	−6638.24	−	3832.59i	−0.390617	−	0.225523i	0.291811	−	0.956476i	$-0.405742\pi$
$661$	−6638.24	−	3832.59i	−0.390617	−	0.225523i	−0.682427	+	0.730954i	$0.739076\pi$
$662$	10159.4	+	5865.53i	0.596459	+	0.344366i
$663$	−60.3801	−	163.961i	−0.00353691	−	0.00960441i
$664$		−	6851.50i		−	0.400436i
$665$	28885.3	+	20779.0i	1.68440	+	1.21169i
$666$	−4502.00	+	12666.4i	−0.261936	+	0.736957i
$667$	7221.45	+	12507.9i	0.419214	+	0.726099i
$668$	971.243	−	1682.24i	0.0562552	−	0.0974369i
$669$	5926.02	−	7116.84i	0.342471	−	0.411290i
$670$	−8021.34	+	4631.12i	−0.462525	+	0.267039i
$671$	−1564.64			−0.0900184
$672$	−770.359	−	2981.58i	−0.0442221	−	0.171156i
$673$	−28054.4			−1.60686			−0.803430	−	0.595400i	$-0.796994\pi$
$673$	−28054.4			−1.60686			−0.803430	+	0.595400i	$0.796994\pi$
$674$	14703.5	−	8489.10i	0.840296	−	0.485145i
$675$	19124.3	+	32273.1i	1.09051	+	1.84028i
$676$	3764.49	−	6520.29i	0.214183	−	0.370977i
$677$	−5256.30	−	9104.19i	−0.298399	−	0.516842i	0.677371	−	0.735642i	$-0.263119\pi$
$677$	−5256.30	−	9104.19i	−0.298399	−	0.516842i	−0.975770	+	0.218799i	$0.929786\pi$
$678$	−668.141	+	3874.84i	−0.0378463	+	0.219487i
$679$	130.121	−	1296.82i	0.00735431	−	0.0732949i
$680$			300.356i			0.0169384i
$681$	16788.9	−	6182.66i	0.944717	−	0.347900i
$682$	−666.878	−	385.022i	−0.0374430	−	0.0216177i
$683$	−15679.7	−	9052.66i	−0.878427	−	0.507160i	−0.00828788	−	0.999966i	$-0.502638\pi$
$683$	−15679.7	−	9052.66i	−0.878427	−	0.507160i	−0.870140	+	0.492805i	$0.835971\pi$
$684$	10301.9	−	1896.94i	0.575879	−	0.106040i
$685$			36535.8i			2.03790i
$686$	−12388.7	+	2817.04i	−0.689506	+	0.156786i
$687$	27830.0	+	4798.73i	1.54553	+	0.266496i
$688$	196.687	+	340.672i	0.0108992	+	0.0188779i
$689$	3532.91	−	6119.18i	0.195346	−	0.338348i
$690$	−24831.3	−	20676.4i	−1.37002	−	1.14078i
$691$	7660.53	−	4422.81i	0.421737	−	0.243490i	−0.274083	−	0.961706i	$-0.588374\pi$
$691$	7660.53	−	4422.81i	0.421737	−	0.243490i	0.695820	+	0.718216i	$0.255041\pi$
$692$	−5812.42			−0.319299
$693$	−1057.82	+	2238.19i	−0.0579845	+	0.122687i
$694$	−2237.52			−0.122385
$695$	958.398	−	553.331i	0.0523080	−	0.0302001i
$696$	−2939.35	−	2447.53i	−0.160080	−	0.133295i
$697$	325.715	−	564.156i	0.0177006	−	0.0306584i
$698$	2364.44	+	4095.33i	0.128217	+	0.222078i
$699$	22559.0	+	3889.87i	1.22069	+	0.210484i
$700$	8142.12	+	18057.8i	0.439633	+	0.975031i
$701$		−	32985.2i		−	1.77723i	−0.458658	−	0.888613i	$-0.651670\pi$
$701$		−	32985.2i		−	1.77723i	0.458658	−	0.888613i	$-0.348330\pi$
$702$	−4977.77	+	56.4732i	−0.267626	+	0.00303624i
$703$	−20910.1	−	12072.4i	−1.12182	−	0.647682i
$704$	−274.395	−	158.422i	−0.0146898	−	0.00848119i
$705$	−45444.4	+	16735.3i	−2.42771	+	0.894026i
$706$			5644.49i			0.300897i
$707$	2579.92	−	3586.41i	0.137239	−	0.190779i
$708$	−2370.30	+	13746.4i	−0.125821	+	0.729693i
$709$	−7996.91	−	13851.1i	−0.423597	−	0.733692i	0.572691	−	0.819771i	$-0.305899\pi$
$709$	−7996.91	−	13851.1i	−0.423597	−	0.733692i	−0.996288	+	0.0860795i	$0.972566\pi$
$710$	−3015.40	+	5222.83i	−0.159389	+	0.276069i
$711$	6214.34	−	5295.05i	0.327786	−	0.279297i
$712$	−6284.94	+	3628.61i	−0.330812	+	0.190994i
$713$	−12207.4			−0.641191
$714$	260.247	−	255.627i	0.0136408	−	0.0133986i
$715$	−1739.85			−0.0910024
$716$	4397.74	−	2539.04i	0.229541	−	0.132526i
$717$	−6717.36	+	8067.20i	−0.349881	+	0.420188i
$718$	5201.89	−	9009.94i	0.270380	−	0.468312i
$719$	10462.3	+	18121.2i	0.542668	+	0.939928i	0.998750	+	0.0499905i	$0.0159191\pi$
$719$	10462.3	+	18121.2i	0.542668	+	0.939928i	−0.456082	+	0.889938i	$0.650748\pi$
$720$	8063.25	+	2865.91i	0.417361	+	0.148342i
$721$	−330.623	+	149.075i	−0.0170778	+	0.00770021i
$722$			5096.59i			0.262708i
$723$	4078.05	+	11073.9i	0.209771	+	0.569629i
$724$	−11394.3	−	6578.51i	−0.584898	−	0.337691i
$725$	21307.4	+	12301.8i	1.09150	+	0.630176i
$726$	−4691.97	−	12741.0i	−0.239856	−	0.651325i
$727$		−	21598.1i		−	1.10183i	−0.834562	−	0.550915i	$-0.814279\pi$
$727$		−	21598.1i		−	1.10183i	0.834562	−	0.550915i	$-0.185721\pi$
$728$	−2615.46	−	262.432i	−0.133153	−	0.0133604i
$729$	−10225.7	−	16818.3i	−0.519519	−	0.854459i
$730$	−12349.2	−	21389.5i	−0.626116	−	1.08446i
$731$	−23.2993	+	40.3557i	−0.00117887	+	0.00204187i
$732$	4203.34	−	5047.99i	0.212240	−	0.254889i
$733$	8894.03	−	5134.97i	0.448170	−	0.258751i	−0.258887	−	0.965908i	$-0.583356\pi$
$733$	8894.03	−	5134.97i	0.448170	−	0.258751i	0.707057	+	0.707157i	$0.250022\pi$
$734$	11261.6			0.566313
$735$	12791.8	−	32906.0i	0.641949	−	1.65137i
$736$	−5022.86			−0.251556
$737$	1002.36	−	578.713i	0.0500982	−	0.0289242i
$738$	−12037.2	−	14127.0i	−0.600402	−	0.704639i
$739$	9022.60	−	15627.6i	0.449123	−	0.777903i	−0.549206	−	0.835687i	$-0.685070\pi$
$739$	9022.60	−	15627.6i	0.449123	−	0.777903i	0.998329	+	0.0577833i	$0.0184032\pi$
$740$	−9862.38	−	17082.1i	−0.489930	−	0.848584i
$741$	1519.33	−	8811.28i	0.0753226	−	0.436829i
$742$	14678.4	+	1472.81i	0.726225	+	0.0728684i
$743$			29700.6i			1.46650i	0.679960	+	0.733249i	$0.261997\pi$
$743$			29700.6i			1.46650i	−0.679960	+	0.733249i	$0.738003\pi$
$744$	3033.73	−	1117.20i	0.149492	−	0.0550516i
$745$	58459.8	+	33751.8i	2.87490	+	1.65983i
$746$	11854.9	+	6844.45i	0.581823	+	0.335916i
$747$	−4187.52	−	22741.5i	−0.205105	−	1.11388i
$748$		−	37.5330i		−	0.00183468i
$749$	−8168.70	+	3683.20i	−0.398502	+	0.179681i
$750$	−28886.2	−	4980.85i	−1.40636	−	0.242500i
$751$	9431.09	+	16335.1i	0.458249	+	0.793711i	0.998869	−	0.0475563i	$-0.0151434\pi$
$751$	9431.09	+	16335.1i	0.458249	+	0.793711i	−0.540619	+	0.841267i	$0.681810\pi$
$752$	−3763.96	+	6519.37i	−0.182523	+	0.316140i
$753$	−18022.8	−	15007.2i	−0.872228	−	0.726283i
$754$	−2827.49	+	1632.45i	−0.136566	+	0.0788465i
$755$	−64493.3			−3.10881
$756$	−4379.27	−	9425.62i	−0.210678	−	0.453448i
$757$	12141.1			0.582929			0.291464	−	0.956582i	$-0.405858\pi$
$757$	12141.1			0.582929			0.291464	+	0.956582i	$0.405858\pi$
$758$	−9856.44	+	5690.62i	−0.472298	+	0.272681i
$759$	3102.96	+	2583.76i	0.148393	+	0.123563i
$760$	−7685.14	+	13311.0i	−0.366802	+	0.635319i
$761$	−12563.5	−	21760.6i	−0.598457	−	1.03656i	−0.993049	−	0.117702i	$-0.962447\pi$
$761$	−12563.5	−	21760.6i	−0.598457	−	1.03656i	0.394592	−	0.918856i	$-0.370886\pi$
$762$	1155.26	+	199.202i	0.0549220	+	0.00947023i
$763$	−462.938	+	643.540i	−0.0219652	+	0.0305343i
$764$			7914.12i			0.374768i
$765$	183.573	+	996.943i	0.00867593	+	0.0471170i
$766$	−7453.57	−	4303.32i	−0.351578	−	0.202983i
$767$	10311.6	+	5953.43i	0.485439	+	0.280268i
$768$	1248.26	−	459.684i	0.0586495	−	0.0215982i
$769$		−	23475.2i		−	1.10083i	−0.834892	−	0.550413i	$-0.814470\pi$
$769$		−	23475.2i		−	1.10083i	0.834892	−	0.550413i	$-0.185530\pi$
$770$	−1493.09	−	3311.42i	−0.0698796	−	0.154981i
$771$	5243.47	−	30409.2i	0.244927	−	1.42044i
$772$	−1839.69	−	3186.44i	−0.0857669	−	0.148553i
$773$	15695.6	−	27185.6i	0.730313	−	1.26494i	−0.226436	−	0.974026i	$-0.572708\pi$
$773$	15695.6	−	27185.6i	0.730313	−	1.26494i	0.956749	−	0.290913i	$-0.0939592\pi$
$774$	861.057	+	1010.55i	0.0399871	+	0.0469294i
$775$	−18009.3	+	10397.7i	−0.834727	+	0.481930i
$776$	562.985			0.0260438
$777$	−6407.36	+	23083.6i	−0.295834	+	1.06579i
$778$	14188.1			0.653813
$779$	28869.8	−	16668.0i	1.32781	−	0.766614i
$780$	4674.02	−	5613.25i	0.214560	−	0.257675i
$781$	376.809	−	652.653i	0.0172641	−	0.0299024i
$782$	−297.501	−	515.288i	−0.0136044	−	0.0235635i
$783$	−11252.2	−	6327.35i	−0.513563	−	0.288788i
$784$	−1745.04	−	5203.17i	−0.0794933	−	0.237025i
$785$			50315.7i			2.28770i
$786$	−5680.88	−	15426.3i	−0.257799	−	0.700050i
$787$	−4012.16	−	2316.42i	−0.181726	−	0.104919i	0.406378	−	0.913705i	$-0.366792\pi$
$787$	−4012.16	−	2316.42i	−0.181726	−	0.104919i	−0.588103	+	0.808786i	$0.700125\pi$
$788$	−10607.0	−	6123.97i	−0.479517	−	0.276849i
$789$	9801.51	+	26615.8i	0.442260	+	1.20095i
$790$			11979.6i			0.539515i
$791$	−699.591	+	6972.30i	−0.0314470	+	0.313409i
$792$	−1007.60	−	358.129i	−0.0452063	−	0.0160676i
$793$	−2803.54	−	4855.87i	−0.125544	−	0.217449i
$794$	−4501.33	+	7796.53i	−0.201192	+	0.348474i
$795$	−26231.3	+	31502.4i	−1.17022	+	1.40538i
$796$	−1806.37	+	1042.91i	−0.0804335	+	0.0464383i
$797$	−121.248			−0.00538874			−0.00269437	−	0.999996i	$-0.500858\pi$
$797$	−121.248			−0.00538874			−0.00269437	+	0.999996i	$0.500858\pi$
$798$	18074.2	−	4669.88i	0.801778	−	0.207158i
$799$	−891.749			−0.0394841
$800$	−7410.14	+	4278.25i	−0.327485	+	0.189074i
$801$	−18643.2	+	15885.3i	−0.822379	+	0.700725i
$802$	−6972.82	+	12077.3i	−0.307006	+	0.531750i
$803$	1543.18	+	2672.86i	0.0678176	+	0.117464i
$804$	−825.697	+	4788.58i	−0.0362190	+	0.210050i
$805$	−46746.2	−	33627.4i	−2.04669	−	1.47231i
$806$		−	2759.54i		−	0.120596i
$807$	25769.4	−	9489.81i	1.12407	−	0.413949i
$808$	1652.70	+	954.188i	0.0719577	+	0.0415448i
$809$	11357.9	+	6557.47i	0.493599	+	0.284979i	0.726066	−	0.687625i	$-0.241347\pi$
$809$	11357.9	+	6557.47i	0.493599	+	0.284979i	−0.232467	+	0.972604i	$0.574680\pi$
$810$	28515.1	+	4584.40i	1.23694	+	0.198864i
$811$		−	2601.55i		−	0.112642i	−0.998413	−	0.0563211i	$-0.982063\pi$
$811$		−	2601.55i		−	0.112642i	0.998413	−	0.0563211i	$-0.0179371\pi$
$812$	−5533.48	−	3980.57i	−0.239147	−	0.172033i
$813$	32146.0	+	5542.95i	1.38673	+	0.239114i
$814$	1232.42	+	2134.61i	0.0530666	+	0.0919141i
$815$	17092.1	−	29604.4i	0.734613	−	1.27239i
$816$	121.092	+	100.831i	0.00519495	+	0.00432571i
$817$	−2065.14	+	1192.31i	−0.0884333	+	0.0510570i
$818$	−28710.3			−1.22718
$819$	−8841.64	+	727.463i	−0.377230	+	0.0310374i
$820$	27233.3			1.15979
$821$	−13977.1	+	8069.68i	−0.594158	+	0.343038i	−0.766740	−	0.641958i	$-0.778122\pi$
$821$	−13977.1	+	8069.68i	−0.594158	+	0.343038i	0.172582	+	0.984995i	$0.444789\pi$
$822$	14729.9	+	12265.2i	0.625015	+	0.520435i
$823$	−9786.73	+	16951.1i	−0.414513	+	0.717957i	−0.995377	−	0.0960431i	$-0.969381\pi$
$823$	−9786.73	+	16951.1i	−0.414513	+	0.717957i	0.580864	+	0.814000i	$0.302715\pi$
$824$	−78.3311	−	135.673i	−0.00331164	−	0.00573593i
$825$	6778.47	+	1168.81i	0.286056	+	0.0493247i
$826$	−2481.88	+	24735.0i	−0.104547	+	1.04194i
$827$			19041.3i			0.800641i	0.916375	+	0.400320i	$0.131101\pi$
$827$			19041.3i			0.800641i	−0.916375	+	0.400320i	$0.868899\pi$
$828$	−16671.9	+	3069.89i	−0.699744	+	0.128848i
$829$	−4754.65	−	2745.10i	−0.199199	−	0.115007i	0.397083	−	0.917783i	$-0.370023\pi$
$829$	−4754.65	−	2745.10i	−0.199199	−	0.115007i	−0.596282	+	0.802775i	$0.703356\pi$
$830$	29384.3	+	16965.0i	1.22885	+	0.709476i
$831$	36552.4	−	13460.7i	1.52586	−	0.561911i
$832$		−	1135.45i		−	0.0473131i
$833$	430.427	−	487.202i	0.0179033	−	0.0202647i
$834$	98.6551	−	572.144i	0.00409610	−	0.0237551i
$835$	4809.80	+	8330.82i	0.199341	+	0.345269i
$836$	960.347	−	1663.37i	0.0397300	−	0.0688144i
$837$	9386.74	−	5562.36i	0.387638	−	0.229705i
$838$	25703.3	−	14839.8i	1.05955	−	0.611733i
$839$	25774.7			1.06060			0.530299	−	0.847811i	$-0.322080\pi$
$839$	25774.7			1.06060			0.530299	+	0.847811i	$0.322080\pi$
$840$	14694.7	+	4078.83i	0.603590	+	0.167539i
$841$	15922.5			0.652854
$842$	19179.1	−	11073.0i	0.784982	−	0.453210i
$843$	−2480.04	+	2978.40i	−0.101325	+	0.121686i
$844$	199.258	−	345.124i	0.00812646	−	0.0140754i
$845$	18642.5	+	32289.8i	0.758962	+	1.31456i
$846$	−8508.81	+	23939.6i	−0.345790	+	0.972883i
$847$	−9945.75	−	22058.0i	−0.403471	−	0.894830i
$848$			6372.29i			0.258049i
$849$	−4728.56	−	12840.3i	−0.191147	−	0.519056i
$850$	−877.797	−	506.797i	−0.0354214	−	0.0204506i
$851$	33839.5	+	19537.3i	1.36311	+	0.786990i
$852$	1093.36	+	2969.01i	0.0439649	+	0.119386i
$853$			15407.3i			0.618447i	0.950989	+	0.309224i	$0.100069\pi$
$853$			15407.3i			0.618447i	−0.950989	+	0.309224i	$0.899931\pi$
$854$	6836.16	−	9503.09i	0.273921	−	0.380783i
$855$	−17373.0	+	48879.0i	−0.694906	+	1.95512i
$856$	−1935.32	−	3352.08i	−0.0772757	−	0.133845i
$857$	5708.14	−	9886.78i	0.227522	−	0.394079i	−0.729551	−	0.683926i	$-0.760271\pi$
$857$	5708.14	−	9886.78i	0.227522	−	0.394079i	0.957073	+	0.289847i	$0.0936043\pi$
$858$	−584.073	+	701.441i	−0.0232400	+	0.0279100i
$859$	−32407.3	+	18710.4i	−1.28722	+	0.743178i	−0.978158	−	0.207863i	$-0.933349\pi$
$859$	−32407.3	+	18710.4i	−1.28722	+	0.743178i	−0.309064	+	0.951041i	$0.600016\pi$
$860$	−1948.07			−0.0772427
$861$	−23177.7	−	23596.6i	−0.917414	−	0.933995i
$862$	−12821.9			−0.506632
$863$	−30175.4	+	17421.8i	−1.19025	+	0.687189i	−0.958362	−	0.285554i	$-0.907822\pi$
$863$	−30175.4	+	17421.8i	−1.19025	+	0.687189i	−0.231884	+	0.972743i	$0.574489\pi$
$864$	3862.28	−	2288.70i	0.152081	−	0.0901194i
$865$	14392.2	−	24928.0i	0.565720	−	0.979856i
$866$	12881.0	+	22310.6i	0.505445	+	0.875457i
$867$	4334.74	−	25139.0i	0.169799	−	0.984737i
$868$	5252.18	−	2368.16i	0.205381	−	0.0926045i
$869$		−	1496.99i		−	0.0584374i
$870$	17775.0	−	6545.78i	0.692675	−	0.255084i
$871$	3592.07	+	2073.88i	0.139739	+	0.0806783i
$872$	−296.559	−	171.218i	−0.0115169	−	0.00664929i
$873$	1868.66	−	344.087i	0.0724450	−	0.0133397i
$874$		−	30448.3i		−	1.17841i
$875$	−51977.1	−	5215.31i	−2.00817	−	0.201497i
$876$	−12769.1	−	2201.78i	−0.492497	−	0.0849215i
$877$	14281.1	+	24735.6i	0.549874	+	0.952409i	0.998283	+	0.0585807i	$0.0186575\pi$
$877$	14281.1	+	24735.6i	0.549874	+	0.952409i	−0.448409	+	0.893828i	$0.648009\pi$
$878$	9266.30	−	16049.7i	0.356176	−	0.616915i
$879$	3551.30	+	2957.08i	0.136271	+	0.113470i
$880$	1358.86	−	784.540i	0.0520537	−	0.0300532i
$881$	−25098.4			−0.959804			−0.479902	−	0.877322i	$-0.659328\pi$
$881$	−25098.4			−0.959804			−0.479902	+	0.877322i	$0.659328\pi$
$882$	−8972.22	−	16203.8i	−0.342529	−	0.618607i
$883$	−32704.3			−1.24642			−0.623208	−	0.782056i	$-0.714171\pi$
$883$	−32704.3			−1.24642			−0.623208	+	0.782056i	$0.714171\pi$
$884$	116.484	−	67.2519i	0.00443187	−	0.00255874i
$885$	−53085.8	−	44203.2i	−2.01634	−	1.67896i
$886$	−8881.43	+	15383.1i	−0.336769	+	0.583301i
$887$	−11659.7	−	20195.2i	−0.441368	−	0.764472i	0.556423	−	0.830899i	$-0.312173\pi$
$887$	−11659.7	−	20195.2i	−0.441368	−	0.764472i	−0.997791	+	0.0664269i	$0.978840\pi$
$888$	−10197.7	−	1758.39i	−0.385374	−	0.0664503i
$889$	2078.74	+	208.578i	0.0784239	+	0.00786894i
$890$		−	35939.3i		−	1.35358i
$891$	−3563.30	−	572.874i	−0.133979	−	0.0215399i
$892$	6174.03	+	3564.58i	0.231751	+	0.133802i
$893$	−39520.1	−	22816.9i	−1.48095	−	0.855028i
$894$	33232.6	−	12238.2i	1.24325	−	0.457837i
$895$			25147.7i			0.939213i
$896$	2161.07	−	974.409i	0.0805763	−	0.0363312i
$897$	−2458.79	+	14259.6i	−0.0915236	+	0.530786i
$898$	6080.93	+	10532.5i	0.225972	+	0.391396i
$899$	3578.02	−	6197.32i	0.132741	−	0.229913i
$900$	−21980.9	+	18729.3i	−0.814109	+	0.693678i
$901$	−653.723	+	377.427i	−0.0241717	+	0.0139555i
$902$	−3403.11			−0.125622
$903$	1657.97	+	1687.93i	0.0611004	+	0.0622047i
$904$	−3026.87			−0.111363
$905$	56427.1	−	32578.2i	2.07260	−	1.19661i
$906$	−21650.6	+	26001.2i	−0.793922	+	0.953458i
$907$	18663.6	−	32326.3i	0.683258	−	1.18344i	−0.290723	−	0.956807i	$-0.593896\pi$
$907$	18663.6	−	32326.3i	0.683258	−	1.18344i	0.973981	−	0.226631i	$-0.0727710\pi$
$908$	6886.30	+	11927.4i	0.251685	+	0.435931i
$909$	6068.83	+	2157.04i	0.221442	+	0.0787067i
$910$	7601.67	−	10567.2i	0.276915	−	0.384946i
$911$		−	33130.2i		−	1.20489i	−0.798161	−	0.602444i	$-0.794194\pi$
$911$		−	33130.2i		−	1.20489i	0.798161	−	0.602444i	$-0.205806\pi$
$912$	2786.58	+	7566.91i	0.101176	+	0.274743i
$913$	−3671.91	−	2119.98i	−0.133102	−	0.0768467i
$914$	965.885	+	557.654i	0.0349548	+	0.0201811i
$915$	11241.6	+	30526.4i	0.406159	+	1.10292i
$916$			21739.7i			0.784169i
$917$	−12042.0	−	26707.1i	−0.433654	−	0.961772i
$918$	463.555	+	260.667i	0.0166662	+	0.00937179i
$919$	11879.4	+	20575.7i	0.426404	+	0.738553i	0.996550	−	0.0829898i	$-0.0264469\pi$
$919$	11879.4	+	20575.7i	0.426404	+	0.738553i	−0.570146	+	0.821543i	$0.693114\pi$
$920$	12437.1	−	21541.8i	0.445696	−	0.771968i
$921$	13283.5	−	15952.8i	0.475253	−	0.570754i
$922$	−12855.7	+	7422.24i	−0.459197	+	0.265118i
$923$	2700.68			0.0963097
$924$	−1836.27	−	509.697i	−0.0653777	−	0.0181470i
$925$	66563.8			2.36606
$926$	−18149.8	+	10478.8i	−0.644103	+	0.371873i
$927$	−342.918	−	402.452i	−0.0121498	−	0.0142592i
$928$	1472.22	−	2549.96i	0.0520776	−	0.0902010i
$929$	−17720.4	−	30692.6i	−0.625819	−	1.08395i	−0.988382	−	0.151991i	$-0.951431\pi$
$929$	−17720.4	−	30692.6i	−0.625819	−	1.08395i	0.362563	−	0.931959i	$-0.381902\pi$
$930$	−2720.47	+	15777.2i	−0.0959221	+	0.556295i
$931$	31541.4	−	10578.3i	1.11034	−	0.372385i
$932$			17622.2i			0.619351i
$933$	−2496.61	+	919.398i	−0.0876049	+	0.0322612i
$934$	−16311.6	−	9417.49i	−0.571446	−	0.329925i
$935$	160.969	+	92.9357i	0.00563023	+	0.00325061i
$936$	−693.966	−	3768.77i	−0.0242340	−	0.131609i
$937$			42936.0i			1.49697i	0.663154	+	0.748483i	$0.269218\pi$
$937$			42936.0i			1.49697i	−0.663154	+	0.748483i	$0.730782\pi$
$938$	−864.564	+	8616.46i	−0.0300949	+	0.299933i
$939$	7519.12	+	1296.53i	0.261318	+	0.0450591i
$940$	−18639.9	−	32285.3i	−0.646774	−	1.12025i
$941$	−16115.3	+	27912.5i	−0.558282	+	0.966972i	0.439359	+	0.898312i	$0.355206\pi$
$941$	−16115.3	+	27912.5i	−0.558282	+	0.966972i	−0.997640	+	0.0686602i	$0.978128\pi$
$942$	20285.4	+	16891.1i	0.701628	+	0.584228i
$943$	−46721.1	+	26974.4i	−1.61341	+	0.931503i
$944$	−10738.2			−0.370230
$945$	51267.6	+	4557.29i	1.76480	+	0.156877i
$946$	243.434			0.00836652
$947$	9522.57	−	5497.86i	0.326760	−	0.188655i	−0.327642	−	0.944802i	$-0.606254\pi$
$947$	9522.57	−	5497.86i	0.326760	−	0.188655i	0.654402	+	0.756147i	$0.272921\pi$
$948$	4829.73	+	4021.60i	0.165467	+	0.137780i
$949$	−5530.15	+	9578.50i	−0.189164	+	0.327641i
$950$	−25934.5	−	44919.9i	−0.885713	−	1.53410i
$951$	−38700.5	−	6673.14i	−1.31961	−	0.227541i
$952$	227.962	+	163.987i	0.00776082	+	0.00558284i
$953$		−	10083.0i		−	0.342728i	−0.985208	−	0.171364i	$-0.945183\pi$
$953$		−	10083.0i		−	0.342728i	0.985208	−	0.171364i	$-0.0548174\pi$
$954$	3894.64	+	21150.9i	0.132173	+	0.717804i
$955$	−33941.6	−	19596.2i	−1.15008	−	0.663998i
$956$	−6998.50	−	4040.58i	−0.236765	−	0.136696i
$957$	−2221.19	+	817.971i	−0.0750269	+	0.0276293i
$958$		−	21212.6i		−	0.715394i
$959$	27729.7	+	19947.7i	0.933721	+	0.671684i
$960$	−1119.37	+	6491.71i	−0.0376328	+	0.218249i
$961$	−11871.3	−	20561.7i	−0.398486	−	0.690198i
$962$	−4416.51	+	7649.62i	−0.148019	+	0.256376i
$963$	−8472.46	−	9943.38i	−0.283511	−	0.332732i
$964$	−7867.26	+	4542.17i	−0.262850	+	0.151757i
$965$	18221.1			0.607832
$966$	−29250.1	+	7557.44i	−0.974231	+	0.251715i
$967$	−24809.9			−0.825061			−0.412530	−	0.910944i	$-0.635355\pi$
$967$	−24809.9			−0.825061			−0.412530	+	0.910944i	$0.635355\pi$
$968$	9051.63	−	5225.96i	0.300548	−	0.173521i
$969$	−611.230	+	734.055i	−0.0202637	+	0.0243357i
$970$	−1394.01	+	2414.50i	−0.0461432	+	0.0799225i
$971$	−3033.74	−	5254.60i	−0.100265	−	0.173664i	0.811529	−	0.584313i	$-0.198636\pi$
$971$	−3033.74	−	5254.60i	−0.100265	−	0.173664i	−0.911794	+	0.410648i	$0.865302\pi$
$972$	11420.9	−	9957.21i	0.376877	−	0.328578i
$973$	103.299	−	1029.50i	0.00340351	−	0.0339202i
$974$			25548.7i			0.840487i
$975$	8518.28	+	23131.3i	0.279798	+	0.759788i
$976$	4379.25	+	2528.36i	0.143623	+	0.0829211i
$977$	−11370.3	−	6564.62i	−0.372331	−	0.214965i	0.302146	−	0.953262i	$-0.402297\pi$
$977$	−11370.3	−	6564.62i	−0.372331	−	0.214965i	−0.674476	+	0.738297i	$0.735630\pi$
$978$	−6197.48	−	16829.2i	−0.202631	−	0.550242i
$979$			4491.03i			0.146613i
$980$	26636.0	+	5399.59i	0.868219	+	0.176004i
$981$	−1088.98	−	387.056i	−0.0354420	−	0.0125971i
$982$	−18689.8	−	32371.7i	−0.607348	−	1.05196i
$983$	13427.3	−	23256.8i	0.435671	−	0.754605i	−0.561679	−	0.827355i	$-0.689844\pi$
$983$	13427.3	−	23256.8i	0.435671	−	0.754605i	0.997350	+	0.0727505i	$0.0231777\pi$
$984$	9142.30	−	10979.4i	0.296185	−	0.355702i
$985$	52528.2	−	30327.2i	1.69918	−	0.981019i
$986$	348.795			0.0112656
$987$	−12109.9	+	43628.2i	−0.390540	+	1.40699i
$988$	6883.02			0.221638
$989$	3342.09	−	1929.56i	0.107454	−	0.0620387i
$990$	4030.84	−	3434.56i	0.129402	−	0.110260i
$991$	−13495.1	+	23374.1i	−0.432578	+	0.749247i	−0.997094	−	0.0761745i	$-0.975729\pi$
$991$	−13495.1	+	23374.1i	−0.432578	+	0.749247i	0.564516	+	0.825422i	$0.309063\pi$
$992$	1244.34	+	2155.27i	0.0398266	+	0.0689816i
$993$	−5178.94	+	30034.9i	−0.165507	+	0.959849i
$994$	2317.65	+	5140.14i	0.0739550	+	0.164020i
$995$		−	10329.4i		−	0.329109i
$996$	16704.1	−	6151.42i	0.531414	−	0.195698i
$997$	12247.7	+	7071.22i	0.389056	+	0.224622i	0.681751	−	0.731584i	$-0.261219\pi$
$997$	12247.7	+	7071.22i	0.389056	+	0.224622i	−0.292695	+	0.956206i	$0.594552\pi$
$998$	−23773.2	−	13725.5i	−0.754036	−	0.435343i
$999$	−34922.9	+	396.203i	−1.10602	+	0.0125479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.4.f.a.17.2	yes	16
3.2	odd	2	inner	42.4.f.a.17.5	yes	16
4.3	odd	2		336.4.bc.e.17.6		16
7.2	even	3		294.4.f.a.215.8		16
7.3	odd	6		294.4.d.a.293.5		16
7.4	even	3		294.4.d.a.293.4		16
7.5	odd	6	inner	42.4.f.a.5.5	yes	16
7.6	odd	2		294.4.f.a.227.3		16
12.11	even	2		336.4.bc.e.17.8		16
21.2	odd	6		294.4.f.a.215.3		16
21.5	even	6	inner	42.4.f.a.5.2	✓	16
21.11	odd	6		294.4.d.a.293.13		16
21.17	even	6		294.4.d.a.293.12		16
21.20	even	2		294.4.f.a.227.8		16
28.19	even	6		336.4.bc.e.257.8		16
84.47	odd	6		336.4.bc.e.257.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.2	✓	16	21.5	even	6	inner
42.4.f.a.5.5	yes	16	7.5	odd	6	inner
42.4.f.a.17.2	yes	16	1.1	even	1	trivial
42.4.f.a.17.5	yes	16	3.2	odd	2	inner
294.4.d.a.293.4		16	7.4	even	3
294.4.d.a.293.5		16	7.3	odd	6
294.4.d.a.293.12		16	21.17	even	6
294.4.d.a.293.13		16	21.11	odd	6
294.4.f.a.215.3		16	21.2	odd	6
294.4.f.a.215.8		16	7.2	even	3
294.4.f.a.227.3		16	7.6	odd	2
294.4.f.a.227.8		16	21.20	even	2
336.4.bc.e.17.6		16	4.3	odd	2
336.4.bc.e.17.8		16	12.11	even	2
336.4.bc.e.257.6		16	84.47	odd	6
336.4.bc.e.257.8		16	28.19	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	42.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} +(-3.99309 - 3.32495i) q^{3} +(2.00000 - 3.46410i) q^{4} +(9.90442 + 17.1550i) q^{5} +(10.2412 + 1.76589i) q^{6} +(18.4277 + 1.84901i) q^{7} +8.00000i q^{8} +(4.88947 + 26.5536i) q^{9} +(-34.3099 - 19.8088i) q^{10} +(4.28742 + 2.47535i) q^{11} +(-19.5041 + 7.18256i) q^{12} +17.7414i q^{13} +(-33.7668 + 15.2251i) q^{14} +(17.4901 - 101.433i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(0.947671 - 1.64141i) q^{17} +(-35.0224 - 41.1027i) q^{18} +(83.9968 - 48.4956i) q^{19} +79.2354 q^{20} +(-67.4356 - 68.6545i) q^{21} -9.90138 q^{22} +(-135.935 + 78.4822i) q^{23} +(26.5996 - 31.9447i) q^{24} +(-133.695 + 231.567i) q^{25} +(-17.7414 - 30.7289i) q^{26} +(68.7652 - 122.288i) q^{27} +(43.2606 - 60.1375i) q^{28} -92.0138i q^{29} +(71.1391 + 193.177i) q^{30} +(67.3521 + 38.8857i) q^{31} +(27.7128 + 16.0000i) q^{32} +(-8.88966 - 24.1397i) q^{33} +3.79068i q^{34} +(150.796 + 334.440i) q^{35} +(101.763 + 36.1696i) q^{36} +(-124.469 - 215.587i) q^{37} +(-96.9912 + 167.994i) q^{38} +(58.9891 - 70.8428i) q^{39} +(-137.240 + 79.2354i) q^{40} +343.701 q^{41} +(185.456 + 51.4774i) q^{42} -24.5859 q^{43} +(17.1497 - 9.90138i) q^{44} +(-407.099 + 346.877i) q^{45} +(156.964 - 271.870i) q^{46} +(-235.248 - 407.461i) q^{47} +(-14.1271 + 81.9294i) q^{48} +(336.162 + 68.1462i) q^{49} -534.781i q^{50} +(-9.24175 + 3.40335i) q^{51} +(61.4579 + 35.4827i) q^{52} +(-344.910 - 199.134i) q^{53} +(3.18314 + 280.574i) q^{54} +98.0675i q^{55} +(-14.7921 + 147.422i) q^{56} +(-496.652 - 85.6379i) q^{57} +(92.0138 + 159.373i) q^{58} +(335.568 - 581.220i) q^{59} +(-316.394 - 263.453i) q^{60} +(-273.703 + 158.023i) q^{61} -155.543 q^{62} +(41.0038 + 498.363i) q^{63} -64.0000 q^{64} +(-304.352 + 175.718i) q^{65} +(39.5371 + 32.9216i) q^{66} +(116.895 - 202.469i) q^{67} +(-3.79068 - 6.56566i) q^{68} +(803.750 + 138.591i) q^{69} +(-595.627 - 428.472i) q^{70} -152.225i q^{71} +(-212.429 + 39.1157i) q^{72} +(539.897 + 311.709i) q^{73} +(431.174 + 248.939i) q^{74} +(1303.80 - 480.137i) q^{75} -387.965i q^{76} +(74.4305 + 53.5425i) q^{77} +(-31.3293 + 181.692i) q^{78} +(-151.191 - 261.870i) q^{79} +(158.471 - 274.479i) q^{80} +(-681.186 + 259.666i) q^{81} +(-595.307 + 343.701i) q^{82} -856.438 q^{83} +(-372.697 + 96.2949i) q^{84} +37.5446 q^{85} +(42.5840 - 24.5859i) q^{86} +(-305.941 + 367.419i) q^{87} +(-19.8028 + 34.2994i) q^{88} +(453.577 + 785.618i) q^{89} +(358.239 - 1007.91i) q^{90} +(-32.8040 + 326.933i) q^{91} +627.858i q^{92} +(-139.650 - 379.216i) q^{93} +(814.922 + 470.495i) q^{94} +(1663.88 + 960.642i) q^{95} +(-57.4605 - 156.033i) q^{96} -70.3731i q^{97} +(-650.396 + 218.130i) q^{98} +(-44.7661 + 125.950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9} - 36 q^{10} - 128 q^{16} - 48 q^{18} - 342 q^{19} - 450 q^{21} + 24 q^{22} - 48 q^{24} - 194 q^{25} + 88 q^{28} + 360 q^{30} + 804 q^{31} + 1332 q^{33} + 144 q^{36}+ \cdots - 4284 q^{99}+O(q^{100}) \) 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9 - 36 * q^10 - 128 * q^16 - 48 * q^18 - 342 * q^19 - 450 * q^21 + 24 * q^22 - 48 * q^24 - 194 * q^25 + 88 * q^28 + 360 * q^30 + 804 * q^31 + 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 - 144 * q^40 - 180 * q^42 + 1732 * q^43 - 2394 * q^45 + 168 * q^46 + 820 * q^49 + 1638 * q^51 + 744 * q^52 + 180 * q^54 - 2664 * q^57 - 780 * q^58 - 4620 * q^61 - 2016 * q^63 - 1024 * q^64 - 2016 * q^66 - 706 * q^67 - 60 * q^70 + 192 * q^72 + 3294 * q^73 + 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 + 432 * q^82 - 432 * q^84 + 5232 * q^85 + 1026 * q^87 + 48 * q^88 + 4098 * q^91 + 2016 * q^93 + 3888 * q^94 - 192 * q^96 - 4284 * q^99

Introduction

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