LMFDB - Embedded newform 169.3.f.g.150.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,3,Mod(19,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("169.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	169.f (of order $12$, degree $4$, not 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:	$4.60491646769$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			150.12
Character	$\chi$	$=$	169.150
Dual form			169.3.f.g.80.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.11493 - 0.834643i) q^{2} +(1.02304 - 1.77195i) q^{3} +(5.54206 - 3.19971i) q^{4} +(-5.50472 - 5.50472i) q^{5} +(1.70774 - 6.37336i) q^{6} +(3.16050 + 0.846854i) q^{7} +(5.47136 - 5.47136i) q^{8} +(2.40680 + 4.16870i) q^{9} +(-21.7413 - 12.5523i) q^{10} +(1.31331 + 4.90135i) q^{11} -13.0937i q^{12} +10.5516 q^{14} +(-15.3856 + 4.12256i) q^{15} +(-0.322570 + 0.558708i) q^{16} +(8.72503 - 5.03740i) q^{17} +(10.9764 + 10.9764i) q^{18} +(3.07725 - 11.4845i) q^{19} +(-48.1209 - 12.8940i) q^{20} +(4.73388 - 4.73388i) q^{21} +(8.18176 + 14.1712i) q^{22} +(27.5785 + 15.9225i) q^{23} +(-4.09757 - 15.2924i) q^{24} +35.6038i q^{25} +28.2636 q^{27} +(20.2254 - 5.41937i) q^{28} +(-16.3339 + 28.2912i) q^{29} +(-44.4842 + 25.6830i) q^{30} +(-8.05564 - 8.05564i) q^{31} +(-8.54908 + 31.9056i) q^{32} +(10.0285 + 2.68713i) q^{33} +(22.9734 - 22.9734i) q^{34} +(-12.7360 - 22.0593i) q^{35} +(26.6772 + 15.4021i) q^{36} +(-11.4664 - 42.7934i) q^{37} -38.3417i q^{38} -60.2365 q^{40} +(-45.6623 + 12.2352i) q^{41} +(10.7946 - 18.6968i) q^{42} +(20.1558 - 11.6370i) q^{43} +(22.9614 + 22.9614i) q^{44} +(9.69875 - 36.1962i) q^{45} +(99.1947 + 26.5792i) q^{46} +(-64.6057 + 64.6057i) q^{47} +(0.660002 + 1.14316i) q^{48} +(-33.1636 - 19.1470i) q^{49} +(29.7165 + 110.903i) q^{50} -20.6138i q^{51} -48.7831 q^{53} +(88.0391 - 23.5900i) q^{54} +(19.7511 - 34.2100i) q^{55} +(21.9257 - 12.6588i) q^{56} +(-17.2018 - 17.2018i) q^{57} +(-27.2660 + 101.758i) q^{58} +(23.5644 + 6.31406i) q^{59} +(-72.0768 + 72.0768i) q^{60} +(-6.30335 - 10.9177i) q^{61} +(-31.8163 - 18.3692i) q^{62} +(4.07641 + 15.2134i) q^{63} +103.939i q^{64} +33.4809 q^{66} +(-16.7314 + 4.48316i) q^{67} +(32.2364 - 55.8351i) q^{68} +(56.4276 - 32.5785i) q^{69} +(-58.0833 - 58.0833i) q^{70} +(10.4073 - 38.8404i) q^{71} +(35.9769 + 9.63998i) q^{72} +(76.5080 - 76.5080i) q^{73} +(-71.4344 - 123.728i) q^{74} +(63.0881 + 36.4239i) q^{75} +(-19.6926 - 73.4939i) q^{76} +16.6029i q^{77} -94.0887 q^{79} +(4.85119 - 1.29987i) q^{80} +(7.25346 - 12.5634i) q^{81} +(-132.023 + 76.2235i) q^{82} +(33.6177 + 33.6177i) q^{83} +(11.0884 - 41.3825i) q^{84} +(-75.7583 - 20.2994i) q^{85} +(53.0713 - 53.0713i) q^{86} +(33.4204 + 57.8858i) q^{87} +(34.0027 + 19.6314i) q^{88} +(9.39084 + 35.0471i) q^{89} -120.844i q^{90} +203.789 q^{92} +(-22.5154 + 6.03298i) q^{93} +(-147.319 + 255.165i) q^{94} +(-80.1582 + 46.2793i) q^{95} +(47.7891 + 47.7891i) q^{96} +(-10.7486 + 40.1144i) q^{97} +(-119.283 - 31.9619i) q^{98} +(-17.2714 + 17.2714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{3} - 84 q^{9} + 376 q^{14} - 188 q^{16} + 136 q^{22} + 120 q^{27} - 84 q^{29} - 176 q^{35} - 1048 q^{40} + 368 q^{42} + 368 q^{48} - 88 q^{53} + 704 q^{55} + 8 q^{61} - 1480 q^{66} + 168 q^{68}+ \cdots - 1132 q^{94}+O(q^{100}) $ 48 * q - 12 * q^3 - 84 * q^9 + 376 * q^14 - 188 * q^16 + 136 * q^22 + 120 * q^27 - 84 * q^29 - 176 * q^35 - 1048 * q^40 + 368 * q^42 + 368 * q^48 - 88 * q^53 + 704 * q^55 + 8 * q^61 - 1480 * q^66 + 168 * q^68 - 744 * q^74 - 600 * q^79 - 240 * q^81 + 952 * q^87 + 3472 * q^92 - 1132 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	3.11493	−	0.834643i	1.55746	−	0.417321i	0.625605	−	0.780140i	$-0.284852\pi$
$2$	3.11493	−	0.834643i	1.55746	−	0.417321i	0.931860	+	0.362819i	$0.118186\pi$
$3$	1.02304	−	1.77195i	0.341012	−	0.590650i	−0.643609	−	0.765354i	$-0.722564\pi$
$3$	1.02304	−	1.77195i	0.341012	−	0.590650i	0.984621	+	0.174705i	$0.0558971\pi$
$4$	5.54206	−	3.19971i	1.38551	−	0.799927i
$5$	−5.50472	−	5.50472i	−1.10094	−	1.10094i	−0.994297	−	0.106646i	$-0.965989\pi$
$5$	−5.50472	−	5.50472i	−1.10094	−	1.10094i	−0.106646	−	0.994297i	$-0.534011\pi$
$6$	1.70774	−	6.37336i	0.284623	−	1.06223i
$7$	3.16050	+	0.846854i	0.451500	+	0.120979i	0.477401	−	0.878685i	$-0.341579\pi$
$7$	3.16050	+	0.846854i	0.451500	+	0.120979i	−0.0259011	+	0.999665i	$0.508246\pi$
$8$	5.47136	−	5.47136i	0.683920	−	0.683920i
$9$	2.40680	+	4.16870i	0.267422	+	0.463189i
$10$	−21.7413	−	12.5523i	−2.17413	−	1.25523i
$11$	1.31331	+	4.90135i	0.119392	+	0.445578i	0.999578	−	0.0290518i	$-0.00924876\pi$
$11$	1.31331	+	4.90135i	0.119392	+	0.445578i	−0.880186	+	0.474629i	$0.842582\pi$
$12$		−	13.0937i		−	1.09114i
$13$		0			0
$13$		0			0
$14$	10.5516			0.753683
$15$	−15.3856	+	4.12256i	−1.02571	+	0.274837i
$16$	−0.322570	+	0.558708i	−0.0201607	+	0.0349193i
$17$	8.72503	−	5.03740i	0.513237	−	0.296318i	−0.220926	−	0.975291i	$-0.570908\pi$
$17$	8.72503	−	5.03740i	0.513237	−	0.296318i	0.734163	+	0.678973i	$0.237575\pi$
$18$	10.9764	+	10.9764i	0.609799	+	0.609799i
$19$	3.07725	−	11.4845i	0.161961	−	0.604446i	−0.836448	−	0.548047i	$-0.815371\pi$
$19$	3.07725	−	11.4845i	0.161961	−	0.604446i	0.998408	−	0.0563988i	$-0.0179618\pi$
$20$	−48.1209	−	12.8940i	−2.40605	−	0.644698i
$21$	4.73388	−	4.73388i	0.225423	−	0.225423i
$22$	8.18176	+	14.1712i	0.371898	+	0.644147i
$23$	27.5785	+	15.9225i	1.19907	+	0.692281i	0.960347	−	0.278807i	$-0.0899391\pi$
$23$	27.5785	+	15.9225i	1.19907	+	0.692281i	0.238719	+	0.971089i	$0.423272\pi$
$24$	−4.09757	−	15.2924i	−0.170732	−	0.637181i
$25$			35.6038i			1.42415i
$26$		0			0
$27$	28.2636			1.04680
$28$	20.2254	−	5.41937i	0.722334	−	0.193549i
$29$	−16.3339	+	28.2912i	−0.563239	+	0.975559i	0.433972	+	0.900927i	$0.357112\pi$
$29$	−16.3339	+	28.2912i	−0.563239	+	0.975559i	−0.997211	+	0.0746329i	$0.976222\pi$
$30$	−44.4842	+	25.6830i	−1.48281	+	0.856098i
$31$	−8.05564	−	8.05564i	−0.259859	−	0.259859i	0.565137	−	0.824997i	$-0.308823\pi$
$31$	−8.05564	−	8.05564i	−0.259859	−	0.259859i	−0.824997	+	0.565137i	$0.808823\pi$
$32$	−8.54908	+	31.9056i	−0.267159	+	0.997050i
$33$	10.0285	+	2.68713i	0.303894	+	0.0814283i
$34$	22.9734	−	22.9734i	0.675689	−	0.675689i
$35$	−12.7360	−	22.0593i	−0.363885	−	0.630267i
$36$	26.6772	+	15.4021i	0.741034	+	0.427836i
$37$	−11.4664	−	42.7934i	−0.309904	−	1.15658i	−0.928641	−	0.370979i	$-0.879022\pi$
$37$	−11.4664	−	42.7934i	−0.309904	−	1.15658i	0.618737	−	0.785598i	$-0.287645\pi$
$38$		−	38.3417i		−	1.00899i
$39$		0			0
$40$	−60.2365			−1.50591
$41$	−45.6623	+	12.2352i	−1.11372	+	0.298419i	−0.768338	−	0.640045i	$-0.778916\pi$
$41$	−45.6623	+	12.2352i	−1.11372	+	0.298419i	−0.345378	+	0.938464i	$0.612249\pi$
$42$	10.7946	−	18.6968i	0.257015	−	0.445162i
$43$	20.1558	−	11.6370i	0.468740	−	0.270627i	−0.246972	−	0.969023i	$-0.579436\pi$
$43$	20.1558	−	11.6370i	0.468740	−	0.270627i	0.715712	+	0.698395i	$0.246102\pi$
$44$	22.9614	+	22.9614i	0.521849	+	0.521849i
$45$	9.69875	−	36.1962i	0.215528	−	0.804361i
$46$	99.1947	+	26.5792i	2.15641	+	0.577808i
$47$	−64.6057	+	64.6057i	−1.37459	+	1.37459i	−0.521082	+	0.853506i	$0.674472\pi$
$47$	−64.6057	+	64.6057i	−1.37459	+	1.37459i	−0.853506	+	0.521082i	$0.825528\pi$
$48$	0.660002	+	1.14316i	0.0137500	+	0.0238158i
$49$	−33.1636	−	19.1470i	−0.676809	−	0.390756i
$50$	29.7165	+	110.903i	0.594329	+	2.21807i
$51$		−	20.6138i		−	0.404191i
$52$		0			0
$53$	−48.7831			−0.920436			−0.460218	−	0.887806i	$-0.652229\pi$
$53$	−48.7831			−0.920436			−0.460218	+	0.887806i	$0.652229\pi$
$54$	88.0391	−	23.5900i	1.63035	−	0.436852i
$55$	19.7511	−	34.2100i	0.359112	−	0.622000i
$56$	21.9257	−	12.6588i	0.391530	−	0.226050i
$57$	−17.2018	−	17.2018i	−0.301785	−	0.301785i
$58$	−27.2660	+	101.758i	−0.470104	+	1.75445i
$59$	23.5644	+	6.31406i	0.399397	+	0.107018i	0.452926	−	0.891548i	$-0.350380\pi$
$59$	23.5644	+	6.31406i	0.399397	+	0.107018i	−0.0535290	+	0.998566i	$0.517047\pi$
$60$	−72.0768	+	72.0768i	−1.20128	+	1.20128i
$61$	−6.30335	−	10.9177i	−0.103334	−	0.178979i	0.809723	−	0.586813i	$-0.199618\pi$
$61$	−6.30335	−	10.9177i	−0.103334	−	0.178979i	−0.913056	+	0.407834i	$0.866284\pi$
$62$	−31.8163	−	18.3692i	−0.513167	−	0.296277i
$63$	4.07641	+	15.2134i	0.0647049	+	0.241482i
$64$			103.939i			1.62404i
$65$		0			0
$66$	33.4809			0.507287
$67$	−16.7314	+	4.48316i	−0.249722	+	0.0669128i	−0.381508	−	0.924365i	$-0.624595\pi$
$67$	−16.7314	+	4.48316i	−0.249722	+	0.0669128i	0.131787	+	0.991278i	$0.457929\pi$
$68$	32.2364	−	55.8351i	0.474065	−	0.821105i
$69$	56.4276	−	32.5785i	0.817791	−	0.472152i
$70$	−58.0833	−	58.0833i	−0.829762	−	0.829762i
$71$	10.4073	−	38.8404i	0.146581	−	0.547048i	−0.853099	−	0.521749i	$-0.825280\pi$
$71$	10.4073	−	38.8404i	0.146581	−	0.547048i	0.999680	−	0.0252987i	$-0.00805370\pi$
$72$	35.9769	+	9.63998i	0.499679	+	0.133889i
$73$	76.5080	−	76.5080i	1.04806	−	1.04806i	0.0492695	−	0.998786i	$-0.484311\pi$
$73$	76.5080	−	76.5080i	1.04806	−	1.04806i	0.998786	−	0.0492695i	$-0.0156893\pi$
$74$	−71.4344	−	123.728i	−0.965329	−	1.67200i
$75$	63.0881	+	36.4239i	0.841175	+	0.485653i
$76$	−19.6926	−	73.4939i	−0.259114	−	0.967025i
$77$			16.6029i			0.215622i
$78$		0			0
$79$	−94.0887			−1.19100			−0.595498	−	0.803357i	$-0.703045\pi$
$79$	−94.0887			−1.19100			−0.595498	+	0.803357i	$0.703045\pi$
$80$	4.85119	−	1.29987i	0.0606399	−	0.0162484i
$81$	7.25346	−	12.5634i	0.0895489	−	0.155103i
$82$	−132.023	+	76.2235i	−1.61004	+	0.929555i
$83$	33.6177	+	33.6177i	0.405032	+	0.405032i	0.880002	−	0.474970i	$-0.157541\pi$
$83$	33.6177	+	33.6177i	0.405032	+	0.405032i	−0.474970	+	0.880002i	$0.657541\pi$
$84$	11.0884	−	41.3825i	0.132005	−	0.492649i
$85$	−75.7583	−	20.2994i	−0.891274	−	0.238816i
$86$	53.0713	−	53.0713i	0.617108	−	0.617108i
$87$	33.4204	+	57.8858i	0.384143	+	0.665354i
$88$	34.0027	+	19.6314i	0.386394	+	0.223085i
$89$	9.39084	+	35.0471i	0.105515	+	0.393788i	0.998403	−	0.0564911i	$-0.0179913\pi$
$89$	9.39084	+	35.0471i	0.105515	+	0.393788i	−0.892888	+	0.450279i	$0.851325\pi$
$90$		−	120.844i		−	1.34271i
$91$		0			0
$92$	203.789			2.21510
$93$	−22.5154	+	6.03298i	−0.242101	+	0.0648708i
$94$	−147.319	+	255.165i	−1.56723	+	2.71452i
$95$	−80.1582	+	46.2793i	−0.843770	+	0.487151i
$96$	47.7891	+	47.7891i	0.497803	+	0.497803i
$97$	−10.7486	+	40.1144i	−0.110810	+	0.413550i	−0.998939	−	0.0460441i	$-0.985339\pi$
$97$	−10.7486	+	40.1144i	−0.110810	+	0.413550i	0.888129	+	0.459594i	$0.152005\pi$
$98$	−119.283	−	31.9619i	−1.21718	−	0.326142i
$99$	−17.2714	+	17.2714i	−0.174458	+	0.174458i
$100$	113.922	+	197.318i	1.13922	+	1.97318i
$101$	20.6108	+	11.8997i	0.204067	+	0.117818i	0.598551	−	0.801085i	$-0.295743\pi$
$101$	20.6108	+	11.8997i	0.204067	+	0.117818i	−0.394484	+	0.918903i	$0.629077\pi$
$102$	−17.2051	−	64.2104i	−0.168678	−	0.629514i
$103$		−	99.0034i		−	0.961198i	−0.876940	−	0.480599i	$-0.840419\pi$
$103$		−	99.0034i		−	0.961198i	0.876940	−	0.480599i	$-0.159581\pi$
$104$		0			0
$105$	−52.1174			−0.496356
$106$	−151.956	+	40.7165i	−1.43355	+	0.384118i
$107$	72.7606	−	126.025i	0.680006	−	1.17780i	−0.294972	−	0.955506i	$-0.595310\pi$
$107$	72.7606	−	126.025i	0.680006	−	1.17780i	0.974978	−	0.222299i	$-0.0713562\pi$
$108$	156.638	−	90.4352i	1.45036	−	0.837363i
$109$	104.897	+	104.897i	0.962359	+	0.962359i	0.999317	−	0.0369580i	$-0.0117668\pi$
$109$	104.897	+	104.897i	0.962359	+	0.962359i	−0.0369580	+	0.999317i	$0.511767\pi$
$110$	32.9703	−	123.047i	0.299730	−	1.11861i
$111$	−87.5582	−	23.4612i	−0.788813	−	0.211362i
$112$	−1.49263	+	1.49263i	−0.0133270	+	0.0133270i
$113$	20.4781	+	35.4690i	0.181222	+	0.313885i	0.942297	−	0.334778i	$-0.108661\pi$
$113$	20.4781	+	35.4690i	0.181222	+	0.313885i	−0.761075	+	0.648664i	$0.775328\pi$
$114$	−67.9396	−	39.2249i	−0.595961	−	0.344078i
$115$	−64.1633	−	239.461i	−0.557942	−	2.08227i
$116$			209.055i			1.80220i
$117$		0			0
$118$	78.6714			0.666707
$119$	31.8414	−	8.53188i	0.267575	−	0.0716965i
$120$	−61.6241	+	106.736i	−0.513534	+	0.889467i
$121$	82.4906	−	47.6260i	0.681740	−	0.393603i
$122$	−28.7469	−	28.7469i	−0.235630	−	0.235630i
$123$	−25.0340	+	93.4283i	−0.203529	+	0.759580i
$124$	−70.4205	−	18.8691i	−0.567907	−	0.152170i
$125$	58.3709	−	58.3709i	0.466967	−	0.466967i
$126$	25.3955	+	43.9862i	0.201551	+	0.349097i
$127$	−100.148	−	57.8204i	−0.788566	−	0.455279i	0.0508914	−	0.998704i	$-0.483794\pi$
$127$	−100.148	−	57.8204i	−0.788566	−	0.455279i	−0.839457	+	0.543425i	$0.817127\pi$
$128$	52.5553	+	196.139i	0.410588	+	1.53234i
$129$		−	47.6201i		−	0.369148i
$130$		0			0
$131$	55.6501			0.424810			0.212405	−	0.977182i	$-0.431870\pi$
$131$	55.6501			0.424810			0.212405	+	0.977182i	$0.431870\pi$
$132$	64.1766	−	17.1961i	0.486187	−	0.130273i
$133$	19.4513	−	33.6907i	0.146251	−	0.253313i
$134$	−48.3752	+	27.9294i	−0.361009	+	0.208429i
$135$	−155.583	−	155.583i	−1.15247	−	1.15247i
$136$	20.1764	−	75.2992i	0.148356	−	0.553670i
$137$	−30.5160	−	8.17673i	−0.222744	−	0.0596841i	0.145721	−	0.989326i	$-0.453450\pi$
$137$	−30.5160	−	8.17673i	−0.222744	−	0.0596841i	−0.368465	+	0.929642i	$0.620117\pi$
$138$	148.577	−	148.577i	1.07664	−	1.07664i
$139$	−116.947	−	202.558i	−0.841343	−	1.45725i	−0.888759	−	0.458374i	$-0.848432\pi$
$139$	−116.947	−	202.558i	−0.841343	−	1.45725i	0.0474162	−	0.998875i	$-0.484901\pi$
$140$	−141.167	−	81.5028i	−1.00834	−	0.582163i
$141$	48.3841	+	180.572i	0.343149	+	1.28065i
$142$		−	129.671i		−	0.913180i
$143$		0			0
$144$	−3.10545			−0.0215656
$145$	245.649	−	65.8214i	1.69413	−	0.453941i
$146$	174.460	−	302.174i	1.19493	−	2.06968i
$147$	−67.8551	+	39.1762i	−0.461600	+	0.266505i
$148$	−200.474	−	200.474i	−1.35455	−	1.35455i
$149$	46.0054	−	171.694i	0.308761	−	1.15231i	−0.620899	−	0.783891i	$-0.713232\pi$
$149$	46.0054	−	171.694i	0.308761	−	1.15231i	0.929659	−	0.368420i	$-0.120101\pi$
$150$	226.916	+	60.8020i	1.51277	+	0.405346i
$151$	−32.9910	+	32.9910i	−0.218484	+	0.218484i	−0.807859	−	0.589376i	$-0.799374\pi$
$151$	−32.9910	+	32.9910i	−0.218484	+	0.218484i	0.589376	+	0.807859i	$0.299374\pi$
$152$	−45.9989	−	79.6724i	−0.302624	−	0.524160i
$153$	41.9988	+	24.2480i	0.274502	+	0.158484i
$154$	13.8575	+	51.7169i	0.0899838	+	0.335824i
$155$			88.6880i			0.572181i
$156$		0			0
$157$	61.3344			0.390665			0.195332	−	0.980737i	$-0.437421\pi$
$157$	61.3344			0.390665			0.195332	+	0.980737i	$0.437421\pi$
$158$	−293.080	+	78.5305i	−1.85494	+	0.497028i
$159$	−49.9068	+	86.4411i	−0.313879	+	0.543655i
$160$	222.692	−	128.571i	1.39182	−	0.803569i
$161$	73.6779	+	73.6779i	0.457627	+	0.457627i
$162$	12.1081	−	45.1880i	0.0747413	−	0.278938i
$163$	155.296	+	41.6113i	0.952734	+	0.255284i	0.701522	−	0.712648i	$-0.252504\pi$
$163$	155.296	+	41.6113i	0.952734	+	0.255284i	0.251212	+	0.967932i	$0.419171\pi$
$164$	−213.914	+	213.914i	−1.30435	+	1.30435i
$165$	−40.4122	−	69.9960i	−0.244923	−	0.424218i
$166$	132.775	+	76.6580i	0.799852	+	0.461795i
$167$	4.34745	+	16.2249i	0.0260326	+	0.0971551i	0.977720	−	0.209914i	$-0.0673184\pi$
$167$	4.34745	+	16.2249i	0.0260326	+	0.0971551i	−0.951687	+	0.307069i	$0.900652\pi$
$168$		−	51.8015i		−	0.308342i
$169$		0			0
$170$	−252.925			−1.48779
$171$	55.2816	−	14.8127i	0.323284	−	0.0866238i
$172$	74.4699	−	128.986i	0.432964	−	0.749916i
$173$	33.5017	−	19.3422i	0.193651	−	0.111805i	−0.400039	−	0.916498i	$-0.631004\pi$
$173$	33.5017	−	19.3422i	0.193651	−	0.111805i	0.593691	+	0.804693i	$0.297670\pi$
$174$	152.416	+	152.416i	0.875955	+	0.875955i
$175$	−30.1512	+	112.526i	−0.172293	+	0.643005i
$176$	−3.16206	−	0.847272i	−0.0179663	−	0.00481405i
$177$	35.2954	−	35.2954i	0.199409	−	0.199409i
$178$	58.5036	+	101.331i	0.328672	+	0.569277i
$179$	−240.631	−	138.929i	−1.34431	−	0.776137i	−0.356873	−	0.934153i	$-0.616157\pi$
$179$	−240.631	−	138.929i	−1.34431	−	0.776137i	−0.987437	+	0.158016i	$0.949490\pi$
$180$	−62.0663	−	231.635i	−0.344813	−	1.28686i
$181$		−	13.3679i		−	0.0738556i	−0.999318	−	0.0369278i	$-0.988243\pi$
$181$		−	13.3679i		−	0.0738556i	0.999318	−	0.0369278i	$-0.0117572\pi$
$182$		0			0
$183$	−25.7942			−0.140952
$184$	238.009	−	63.7744i	1.29353	−	0.346600i
$185$	−172.446	+	298.685i	−0.932140	+	1.61451i
$186$	−65.0985	+	37.5846i	−0.349992	+	0.202068i
$187$	36.1488	+	36.1488i	0.193309	+	0.193309i
$188$	−151.329	+	564.768i	−0.804942	+	3.00408i
$189$	89.3271	+	23.9351i	0.472630	+	0.126641i
$190$	−211.060	+	211.060i	−1.11084	+	1.11084i
$191$	163.781	+	283.678i	0.857494	+	1.48522i	0.874312	+	0.485365i	$0.161313\pi$
$191$	163.781	+	283.678i	0.857494	+	1.48522i	−0.0168172	+	0.999859i	$0.505353\pi$
$192$	184.174	+	106.333i	0.959239	+	0.553817i
$193$	60.6375	+	226.302i	0.314184	+	1.17255i	0.924747	+	0.380583i	$0.124277\pi$
$193$	60.6375	+	226.302i	0.314184	+	1.17255i	−0.610563	+	0.791968i	$0.709057\pi$
$194$			133.925i			0.690333i
$195$		0			0
$196$	−245.060			−1.25030
$197$	−93.9516	+	25.1743i	−0.476912	+	0.127788i	−0.489264	−	0.872136i	$-0.662735\pi$
$197$	−93.9516	+	25.1743i	−0.476912	+	0.127788i	0.0123525	+	0.999924i	$0.496068\pi$
$198$	−39.3837	+	68.2146i	−0.198908	+	0.344518i
$199$	−231.474	+	133.641i	−1.16318	+	0.671564i	−0.952065	−	0.305896i	$-0.901044\pi$
$199$	−231.474	+	133.641i	−1.16318	+	0.671564i	−0.211119	+	0.977460i	$0.567711\pi$
$200$	194.801	+	194.801i	0.974005	+	0.974005i
$201$	−9.17285	+	34.2335i	−0.0456361	+	0.170316i
$202$	74.1332	+	19.8639i	0.366996	+	0.0983362i
$203$	−75.5820	+	75.5820i	−0.372325	+	0.372325i
$204$	−65.9580	−	114.243i	−0.323323	−	0.560013i
$205$	318.709	+	184.007i	1.55468	+	0.897595i
$206$	−82.6325	−	308.389i	−0.401129	−	1.49703i
$207$			153.289i			0.740525i
$208$		0			0
$209$	60.3309			0.288664
$210$	−162.342	+	43.4994i	−0.773057	+	0.207140i
$211$	79.7306	−	138.097i	0.377870	−	0.654490i	−0.612882	−	0.790174i	$-0.709990\pi$
$211$	79.7306	−	138.097i	0.377870	−	0.654490i	0.990752	+	0.135684i	$0.0433233\pi$
$212$	−270.359	+	156.092i	−1.27528	+	0.736281i
$213$	−58.1762	−	58.1762i	−0.273128	−	0.273128i
$214$	121.458	−	453.289i	0.567562	−	2.11817i
$215$	−175.010	−	46.8939i	−0.814002	−	0.218111i
$216$	154.640	−	154.640i	0.715927	−	0.715927i
$217$	−18.6379	−	32.2818i	−0.0858890	−	0.148764i
$218$	414.299	+	239.195i	1.90045	+	1.09723i
$219$	−57.2979	−	213.839i	−0.261634	−	0.976432i
$220$		−	252.792i		−	1.14905i
$221$		0			0
$222$	−292.319			−1.31675
$223$	−178.197	+	47.7476i	−0.799088	+	0.214115i	−0.635183	−	0.772361i	$-0.719075\pi$
$223$	−178.197	+	47.7476i	−0.799088	+	0.214115i	−0.163904	+	0.986476i	$0.552409\pi$
$224$	−54.0388	+	93.5979i	−0.241244	+	0.417848i
$225$	−148.421	+	85.6912i	−0.659651	+	0.380850i
$226$	93.3917	+	93.3917i	0.413238	+	0.413238i
$227$	−57.8250	+	215.806i	−0.254736	+	0.950687i	0.713502	+	0.700654i	$0.247108\pi$
$227$	−57.8250	+	215.806i	−0.254736	+	0.950687i	−0.968237	+	0.250033i	$0.919559\pi$
$228$	−150.374	−	40.2925i	−0.659534	−	0.176722i
$229$	−7.86632	+	7.86632i	−0.0343508	+	0.0343508i	−0.724074	−	0.689723i	$-0.757732\pi$
$229$	−7.86632	+	7.86632i	−0.0343508	+	0.0343508i	0.689723	+	0.724074i	$0.257732\pi$
$230$	−399.728	−	692.350i	−1.73795	−	3.01022i
$231$	29.4195	+	16.9854i	0.127357	+	0.0735297i
$232$	65.4225	+	244.160i	0.281994	+	1.05241i
$233$			39.1708i			0.168115i	0.996461	+	0.0840575i	$0.0267879\pi$
$233$			39.1708i			0.168115i	−0.996461	+	0.0840575i	$0.973212\pi$
$234$		0			0
$235$	711.272			3.02669
$236$	150.798	−	40.4063i	0.638976	−	0.171213i
$237$	−96.2561	+	166.720i	−0.406144	+	0.703462i
$238$	92.0627	−	53.1524i	0.386818	−	0.223330i
$239$	−274.654	−	274.654i	−1.14918	−	1.14918i	−0.986714	−	0.162466i	$-0.948055\pi$
$239$	−274.654	−	274.654i	−1.14918	−	1.14918i	−0.162466	−	0.986714i	$-0.551945\pi$
$240$	2.65963	−	9.92588i	0.0110818	−	0.0413578i
$241$	331.779	+	88.8999i	1.37668	+	0.368879i	0.869913	−	0.493205i	$-0.164175\pi$
$241$	331.779	+	88.8999i	1.37668	+	0.368879i	0.506764	+	0.862085i	$0.330842\pi$
$242$	217.202	−	217.202i	0.897528	−	0.897528i
$243$	112.345	+	194.587i	0.462325	+	0.800771i
$244$	−69.8671	−	40.3378i	−0.286340	−	0.165319i
$245$	77.1574	+	287.955i	0.314928	+	1.17533i
$246$			311.917i			1.26796i
$247$		0			0
$248$	−88.1506			−0.355446
$249$	93.9609	−	25.1767i	0.377353	−	0.101111i
$250$	133.102	−	230.540i	0.532410	−	0.922161i
$251$	−15.1070	+	8.72206i	−0.0601874	+	0.0347492i	−0.529792	−	0.848128i	$-0.677730\pi$
$251$	−15.1070	+	8.72206i	−0.0601874	+	0.0347492i	0.469604	+	0.882877i	$0.344397\pi$
$252$	71.2701	+	71.2701i	0.282818	+	0.282818i
$253$	−41.8224	+	156.083i	−0.165306	+	0.616930i
$254$	−360.213	−	96.5188i	−1.41816	−	0.379995i
$255$	−113.473	+	113.473i	−0.444992	+	0.444992i
$256$	119.535	+	207.040i	0.466933	+	0.808752i
$257$	−232.356	−	134.151i	−0.904107	−	0.521986i	−0.0255766	−	0.999673i	$-0.508142\pi$
$257$	−232.356	−	134.151i	−0.904107	−	0.521986i	−0.878530	+	0.477686i	$0.841476\pi$
$258$	−39.7458	−	148.333i	−0.154054	−	0.574936i
$259$		−	144.959i		−	0.559687i
$260$		0			0
$261$	−157.250			−0.602491
$262$	173.346	−	46.4480i	0.661626	−	0.177282i
$263$	6.06253	−	10.5006i	0.0230515	−	0.0399263i	−0.854270	−	0.519830i	$-0.825995\pi$
$263$	6.06253	−	10.5006i	0.0230515	−	0.0399263i	0.877321	+	0.479904i	$0.159329\pi$
$264$	69.5718	−	40.1673i	0.263530	−	0.152149i
$265$	268.537	+	268.537i	1.01335	+	1.01335i
$266$	32.4698	−	121.179i	0.122067	−	0.455560i
$267$	71.7088	+	19.2143i	0.268572	+	0.0719638i
$268$	−78.3814	+	78.3814i	−0.292468	+	0.292468i
$269$	59.2202	+	102.572i	0.220150	+	0.381310i	0.954853	−	0.297078i	$-0.0960121\pi$
$269$	59.2202	+	102.572i	0.220150	+	0.381310i	−0.734704	+	0.678388i	$0.762679\pi$
$270$	−614.486	−	354.774i	−2.27588	−	1.31398i
$271$	36.3626	+	135.707i	0.134179	+	0.500764i	1.00000		0.000409306i	$0.000130286\pi$
$271$	36.3626	+	135.707i	0.134179	+	0.500764i	−0.865821	+	0.500354i	$0.833203\pi$
$272$			6.49967i			0.0238958i
$273$		0			0
$274$	−101.880			−0.371824
$275$	−174.507	+	46.7590i	−0.634570	+	0.170033i
$276$	208.483	−	361.104i	0.755374	−	1.30835i
$277$	469.067	−	270.816i	1.69338	−	0.977676i	0.741632	−	0.670807i	$-0.234052\pi$
$277$	469.067	−	270.816i	1.69338	−	0.977676i	0.951752	−	0.306869i	$-0.0992812\pi$
$278$	−533.344	−	533.344i	−1.91850	−	1.91850i
$279$	14.1932	−	52.9698i	0.0508718	−	0.189856i
$280$	−190.378	−	51.0115i	−0.679920	−	0.182184i
$281$	57.5732	−	57.5732i	0.204887	−	0.204887i	−0.597203	−	0.802090i	$-0.703721\pi$
$281$	57.5732	−	57.5732i	0.204887	−	0.204887i	0.802090	+	0.597203i	$0.203721\pi$
$282$	301.426	+	522.085i	1.06889	+	1.85137i
$283$	−132.682	−	76.6042i	−0.468842	−	0.270686i	0.246913	−	0.969038i	$-0.420584\pi$
$283$	−132.682	−	76.6042i	−0.468842	−	0.270686i	−0.715755	+	0.698352i	$0.753917\pi$
$284$	−66.6004	−	248.556i	−0.234508	−	0.875197i
$285$			189.382i			0.664497i
$286$		0			0
$287$	−154.677			−0.538945
$288$	−153.581	+	41.1518i	−0.533267	+	0.142888i
$289$	−93.7492	+	162.378i	−0.324392	+	0.561863i
$290$	710.242	−	410.058i	2.44911	−	1.41399i
$291$	60.0844	+	60.0844i	0.206476	+	0.206476i
$292$	179.208	−	668.815i	0.613728	−	2.29046i
$293$	225.815	+	60.5070i	0.770700	+	0.206509i	0.622681	−	0.782476i	$-0.286043\pi$
$293$	225.815	+	60.5070i	0.770700	+	0.206509i	0.148020	+	0.988984i	$0.452710\pi$
$294$	−178.666	+	178.666i	−0.607707	+	0.607707i
$295$	−94.9582	−	164.472i	−0.321892	−	0.557534i
$296$	−296.875	−	171.401i	−1.00296	−	0.579057i
$297$	37.1190	+	138.530i	0.124980	+	0.466430i
$298$		−	573.214i		−	1.92354i
$299$		0			0
$300$	466.184			1.55395
$301$	73.5573	−	19.7096i	0.244377	−	0.0654805i
$302$	−75.2290	+	130.300i	−0.249103	+	0.431458i
$303$	42.1711	−	24.3475i	0.139179	−	0.0803549i
$304$	5.42384	+	5.42384i	0.0178416	+	0.0178416i
$305$	−25.4008	+	94.7972i	−0.0832814	+	0.310810i
$306$	151.062	+	40.4769i	0.493666	+	0.132277i
$307$	115.257	−	115.257i	0.375429	−	0.375429i	−0.494021	−	0.869450i	$-0.664473\pi$
$307$	115.257	−	115.257i	0.375429	−	0.375429i	0.869450	+	0.494021i	$0.164473\pi$
$308$	53.1245	+	92.0143i	0.172482	+	0.298748i
$309$	−175.429	−	101.284i	−0.567731	−	0.327780i
$310$	74.0228	+	276.257i	0.238783	+	0.891152i
$311$		−	511.349i		−	1.64421i	−0.569336	−	0.822105i	$-0.692799\pi$
$311$		−	511.349i		−	1.64421i	0.569336	−	0.822105i	$-0.307201\pi$
$312$		0			0
$313$	59.4173			0.189832			0.0949158	−	0.995485i	$-0.469742\pi$
$313$	59.4173			0.189832			0.0949158	+	0.995485i	$0.469742\pi$
$314$	191.052	−	51.1923i	0.608447	−	0.163033i
$315$	61.3058	−	106.185i	0.194622	−	0.337095i
$316$	−521.445	+	301.056i	−1.65014	+	0.952710i
$317$	115.961	+	115.961i	0.365808	+	0.365808i	0.865946	−	0.500138i	$-0.166717\pi$
$317$	115.961	+	115.961i	0.365808	+	0.365808i	−0.500138	+	0.865946i	$0.666717\pi$
$318$	−83.3087	+	310.912i	−0.261977	+	0.977712i
$319$	−160.117	−	42.9032i	−0.501934	−	0.134493i
$320$	572.153	−	572.153i	1.78798	−	1.78798i
$321$	−148.873	−	257.856i	−0.463780	−	0.803291i
$322$	290.996	+	168.007i	0.903715	+	0.521760i
$323$	−31.0027	−	115.704i	−0.0959837	−	0.358216i
$324$		−	92.8358i		−	0.286530i
$325$		0			0
$326$	518.466			1.59039
$327$	293.186	−	78.5589i	0.896592	−	0.240241i
$328$	−182.892	+	316.778i	−0.557597	+	0.965786i
$329$	−258.898	+	149.475i	−0.786923	+	0.454330i
$330$	−184.303	−	184.303i	−0.558494	−	0.558494i
$331$	141.631	−	528.576i	0.427890	−	1.59691i	−0.329641	−	0.944106i	$-0.606928\pi$
$331$	141.631	−	528.576i	0.427890	−	1.59691i	0.757531	−	0.652800i	$-0.226406\pi$
$332$	293.878	+	78.7443i	0.885174	+	0.237182i
$333$	150.795	−	150.795i	0.452838	−	0.452838i
$334$	27.0840	+	46.9109i	0.0810898	+	0.140452i
$335$	116.780	+	67.4229i	0.348597	+	0.201262i
$336$	1.11785	+	4.17187i	0.00332693	+	0.0124163i
$337$			514.522i			1.52677i	0.645942	+	0.763386i	$0.276465\pi$
$337$			514.522i			1.52677i	−0.645942	+	0.763386i	$0.723535\pi$
$338$		0			0
$339$	83.7991			0.247195
$340$	−484.809	+	129.904i	−1.42591	+	0.382071i
$341$	28.9040	−	50.0631i	0.0847624	−	0.146813i
$342$	159.835	−	92.2808i	0.467354	−	0.269827i
$343$	−201.968	−	201.968i	−0.588827	−	0.588827i
$344$	46.6097	−	173.950i	0.135493	−	0.505668i
$345$	−489.953	−	131.283i	−1.42015	−	0.380529i
$346$	88.2116	−	88.2116i	0.254947	−	0.254947i
$347$	86.2782	+	149.438i	0.248640	+	0.430658i	0.963149	−	0.268969i	$-0.0866829\pi$
$347$	86.2782	+	149.438i	0.248640	+	0.430658i	−0.714508	+	0.699627i	$0.753350\pi$
$348$	370.435	+	213.871i	1.06447	+	0.614572i
$349$	−170.035	−	634.579i	−0.487206	−	1.81828i	−0.569916	−	0.821703i	$-0.693024\pi$
$349$	−170.035	−	634.579i	−0.487206	−	1.81828i	0.0827101	−	0.996574i	$-0.473642\pi$
$350$			375.676i			1.07336i
$351$		0			0
$352$	−167.608			−0.476160
$353$	69.8740	−	18.7227i	0.197943	−	0.0530388i	−0.158485	−	0.987361i	$-0.550661\pi$
$353$	69.8740	−	18.7227i	0.197943	−	0.0530388i	0.356429	+	0.934323i	$0.383994\pi$
$354$	80.4836	−	139.402i	0.227355	−	0.393790i
$355$	−271.094	+	156.516i	−0.763646	+	0.440891i
$356$	164.185	+	164.185i	0.461194	+	0.461194i
$357$	17.4568	−	65.1498i	0.0488987	−	0.182492i
$358$	−865.506	−	231.912i	−2.41761	−	0.647798i
$359$	−336.848	+	336.848i	−0.938295	+	0.938295i	−0.998204	−	0.0599089i	$-0.980919\pi$
$359$	−336.848	+	336.848i	−0.938295	+	0.938295i	0.0599089	+	0.998204i	$0.480919\pi$
$360$	−144.977	−	251.108i	−0.402714	−	0.697522i
$361$	190.212	+	109.819i	0.526902	+	0.304207i
$362$	−11.1574	−	41.6399i	−0.0308215	−	0.115027i
$363$		−	194.892i		−	0.536893i
$364$		0			0
$365$	−842.310			−2.30770
$366$	−80.3471	+	21.5289i	−0.219528	+	0.0588223i
$367$	24.9938	−	43.2905i	0.0681030	−	0.117958i	−0.829963	−	0.557818i	$-0.811639\pi$
$367$	24.9938	−	43.2905i	0.0681030	−	0.117958i	0.898066	+	0.439860i	$0.144972\pi$
$368$	−17.7920	+	10.2722i	−0.0483479	+	0.0279137i
$369$	−160.905	−	160.905i	−0.436056	−	0.436056i
$370$	−287.861	+	1074.31i	−0.778004	+	2.90355i
$371$	−154.179	−	41.3121i	−0.415577	−	0.111353i
$372$	−105.478	+	105.478i	−0.283542	+	0.283542i
$373$	−113.491	−	196.572i	−0.304265	−	0.527003i	0.672832	−	0.739795i	$-0.265078\pi$
$373$	−113.491	−	196.572i	−0.304265	−	0.527003i	−0.977097	+	0.212792i	$0.931744\pi$
$374$	142.772	+	82.4296i	0.381744	+	0.220400i
$375$	−43.7148	−	163.146i	−0.116573	−	0.435055i
$376$			706.961i			1.88022i
$377$		0			0
$378$	298.225			0.788955
$379$	−9.15147	+	2.45213i	−0.0241464	+	0.00647000i	−0.270872	−	0.962615i	$-0.587312\pi$
$379$	−9.15147	+	2.45213i	−0.0241464	+	0.00647000i	0.246726	+	0.969085i	$0.420645\pi$
$380$	−296.161	+	512.965i	−0.779370	+	1.34991i
$381$	−204.910	+	118.305i	−0.537820	+	0.310511i
$382$	746.937	+	746.937i	1.95533	+	1.95533i
$383$	−22.2644	+	83.0919i	−0.0581316	+	0.216950i	−0.988881	−	0.148707i	$-0.952489\pi$
$383$	−22.2644	+	83.0919i	−0.0581316	+	0.216950i	0.930750	+	0.365657i	$0.119156\pi$
$384$	401.314	+	107.532i	1.04509	+	0.280031i
$385$	91.3943	−	91.3943i	0.237388	−	0.237388i
$386$	377.763	+	654.305i	0.978661	+	1.69509i
$387$	97.0221	+	56.0157i	0.250703	+	0.144743i
$388$	68.7848	+	256.709i	0.177281	+	0.661620i
$389$		−	34.7670i		−	0.0893754i	−0.999001	−	0.0446877i	$-0.985771\pi$
$389$		−	34.7670i		−	0.0893754i	0.999001	−	0.0446877i	$-0.0142293\pi$
$390$		0			0
$391$	320.831			0.820541
$392$	−286.210	+	76.6898i	−0.730128	+	0.195637i
$393$	56.9320	−	98.6091i	0.144865	−	0.250914i
$394$	−271.641	+	156.832i	−0.689445	+	0.398051i
$395$	517.932	+	517.932i	1.31122	+	1.31122i
$396$	−40.4556	+	150.982i	−0.102161	+	0.381268i
$397$	−182.929	−	49.0156i	−0.460778	−	0.123465i	0.0209602	−	0.999780i	$-0.493328\pi$
$397$	−182.929	−	49.0156i	−0.460778	−	0.123465i	−0.481738	+	0.876315i	$0.659994\pi$
$398$	−609.481	+	609.481i	−1.53136	+	1.53136i
$399$	−39.7988	−	68.9335i	−0.0997463	−	0.172766i
$400$	−19.8921	−	11.4847i	−0.0497304	−	0.0287118i
$401$	62.6022	+	233.635i	0.156115	+	0.582630i	0.999007	+	0.0445472i	$0.0141845\pi$
$401$	62.6022	+	233.635i	0.156115	+	0.582630i	−0.842892	+	0.538083i	$0.819149\pi$
$402$			114.291i			0.284306i
$403$		0			0
$404$	152.302			0.376984
$405$	−109.086	+	29.2295i	−0.269348	+	0.0721716i
$406$	−172.349	+	298.516i	−0.424504	+	0.735262i
$407$	194.686	−	112.402i	0.478345	−	0.276173i
$408$	−112.785	−	112.785i	−0.276434	−	0.276434i
$409$	−120.602	+	450.091i	−0.294869	+	1.10047i	0.646452	+	0.762955i	$0.276252\pi$
$409$	−120.602	+	450.091i	−0.294869	+	1.10047i	−0.941321	+	0.337513i	$0.890414\pi$
$410$	1146.34	+	307.160i	2.79594	+	0.749171i
$411$	−45.7076	+	45.7076i	−0.111211	+	0.111211i
$412$	−316.782	−	548.683i	−0.768888	−	1.33175i
$413$	69.1282	+	39.9112i	0.167381	+	0.0966373i
$414$	127.941	+	477.483i	0.309037	+	1.15334i
$415$		−	370.112i		−	0.891835i
$416$		0			0
$417$	−478.562			−1.14763
$418$	187.926	−	50.3547i	0.449585	−	0.120466i
$419$	347.147	−	601.277i	0.828514	−	1.43503i	−0.0706893	−	0.997498i	$-0.522520\pi$
$419$	347.147	−	601.277i	0.828514	−	1.43503i	0.899204	−	0.437531i	$-0.144147\pi$
$420$	−288.837	+	166.760i	−0.687708	+	0.397049i
$421$	−138.088	−	138.088i	−0.328000	−	0.328000i	0.523825	−	0.851826i	$-0.324504\pi$
$421$	−138.088	−	138.088i	−0.328000	−	0.328000i	−0.851826	+	0.523825i	$0.824504\pi$
$422$	133.093	−	496.710i	0.315386	−	1.17704i
$423$	−424.814	−	113.829i	−1.00429	−	0.269098i
$424$	−266.910	+	266.910i	−0.629504	+	0.629504i
$425$	179.351	+	310.644i	0.422001	+	0.730928i
$426$	−229.771	−	132.658i	−0.539369	−	0.311405i
$427$	−10.6760	−	39.8435i	−0.0250024	−	0.0933103i
$428$		−	931.251i		−	2.17582i
$429$		0			0
$430$	−584.285			−1.35880
$431$	163.677	−	43.8570i	0.379760	−	0.101756i	−0.0638890	−	0.997957i	$-0.520350\pi$
$431$	163.677	−	43.8570i	0.379760	−	0.101756i	0.443649	+	0.896201i	$0.353684\pi$
$432$	−9.11700	+	15.7911i	−0.0211042	+	0.0365535i
$433$	561.144	−	323.977i	1.29594	−	0.748214i	0.316244	−	0.948678i	$-0.397578\pi$
$433$	561.144	−	323.977i	1.29594	−	0.748214i	0.979701	+	0.200464i	$0.0642450\pi$
$434$	−84.9996	−	84.9996i	−0.195852	−	0.195852i
$435$	134.675	−	502.615i	0.309598	−	1.15544i
$436$	916.986	+	245.706i	2.10318	+	0.563545i
$437$	267.727	−	267.727i	0.612648	−	0.612648i
$438$	−356.958	−	618.269i	−0.814972	−	1.41157i
$439$	203.421	+	117.445i	0.463374	+	0.267529i	0.713462	−	0.700694i	$-0.247126\pi$
$439$	203.421	+	117.445i	0.463374	+	0.267529i	−0.250088	+	0.968223i	$0.580459\pi$
$440$	−79.1095	−	295.241i	−0.179794	−	0.671001i
$441$		−	184.332i		−	0.417987i
$442$		0			0
$443$	−601.057			−1.35679			−0.678394	−	0.734698i	$-0.737324\pi$
$443$	−601.057			−1.35679			−0.678394	+	0.734698i	$0.737324\pi$
$444$	−560.322	+	150.138i	−1.26199	+	0.338148i
$445$	141.230	−	244.618i	0.317372	−	0.549704i
$446$	−515.217	+	297.461i	−1.15520	+	0.666953i
$447$	−257.168	−	257.168i	−0.575321	−	0.575321i
$448$	−88.0208	+	328.498i	−0.196475	+	0.733255i
$449$	500.022	+	133.980i	1.11363	+	0.298397i	0.768305	−	0.640084i	$-0.221101\pi$
$449$	500.022	+	133.980i	1.11363	+	0.298397i	0.345329	+	0.938482i	$0.387767\pi$
$450$	−390.801	+	390.801i	−0.868446	+	0.868446i
$451$	−119.938	−	207.739i	−0.265938	−	0.460618i
$452$	226.981	+	131.048i	0.502171	+	0.289928i
$453$	24.7074	+	92.2094i	0.0545418	+	0.203553i
$454$			720.483i			1.58697i
$455$		0			0
$456$	−188.234			−0.412794
$457$	−124.688	+	33.4099i	−0.272839	+	0.0731071i	−0.392644	−	0.919690i	$-0.628440\pi$
$457$	−124.688	+	33.4099i	−0.272839	+	0.0731071i	0.119805	+	0.992797i	$0.461773\pi$
$458$	−17.9375	+	31.0686i	−0.0391648	+	0.0678354i
$459$	246.601	−	142.375i	0.537257	−	0.310185i
$460$	−1121.80	−	1121.80i	−2.43870	−	2.43870i
$461$	117.072	−	436.918i	0.253952	−	0.947762i	−0.714719	−	0.699412i	$-0.753445\pi$
$461$	117.072	−	436.918i	0.253952	−	0.947762i	0.968671	−	0.248349i	$-0.0798881\pi$
$462$	105.816	+	28.3534i	0.229040	+	0.0613711i
$463$	315.336	−	315.336i	0.681072	−	0.681072i	−0.279170	−	0.960242i	$-0.590059\pi$
$463$	315.336	−	315.336i	0.681072	−	0.681072i	0.960242	+	0.279170i	$0.0900592\pi$
$464$	−10.5377	−	18.2518i	−0.0227106	−	0.0393358i
$465$	157.151	+	90.7310i	0.337958	+	0.195120i
$466$	32.6936	+	122.014i	0.0701580	+	0.261833i
$467$			578.767i			1.23933i	0.784866	+	0.619665i	$0.212732\pi$
$467$			578.767i			1.23933i	−0.784866	+	0.619665i	$0.787268\pi$
$468$		0			0
$469$	−56.6761			−0.120844
$470$	2215.56	−	593.658i	4.71396	−	1.26310i
$471$	62.7472	−	108.681i	0.133221	−	0.230746i
$472$	163.476	−	94.3827i	0.346347	−	0.199963i
$473$	83.5079	+	83.5079i	0.176549	+	0.176549i
$474$	−160.679	+	599.662i	−0.338985	+	1.26511i
$475$	408.891	+	109.562i	0.860823	+	0.230657i
$476$	149.167	−	149.167i	0.313377	−	0.313377i
$477$	−117.411	−	203.362i	−0.246145	−	0.426335i
$478$	−1084.77	−	626.290i	−2.26939	−	1.31023i
$479$	−50.6111	−	188.883i	−0.105660	−	0.394328i	0.892759	−	0.450534i	$-0.148766\pi$
$479$	−50.6111	−	188.883i	−0.105660	−	0.394328i	−0.998419	+	0.0562058i	$0.982100\pi$
$480$		−	526.131i		−	1.09611i
$481$		0			0
$482$	1107.67			2.29807
$483$	205.929	−	55.1784i	0.426353	−	0.114241i
$484$	304.778	−	527.892i	0.629707	−	1.09069i
$485$	279.986	−	161.650i	0.577291	−	0.333299i
$486$	512.358	+	512.358i	1.05423	+	1.05423i
$487$	−172.350	+	643.217i	−0.353901	+	1.32077i	0.527962	+	0.849268i	$0.322956\pi$
$487$	−172.350	+	643.217i	−0.353901	+	1.32077i	−0.881862	+	0.471507i	$0.843710\pi$
$488$	−94.2227	−	25.2469i	−0.193079	−	0.0517354i
$489$	232.606	−	232.606i	0.475677	−	0.475677i
$490$	480.680	+	832.562i	0.980979	+	1.69911i
$491$	168.907	+	97.5186i	0.344006	+	0.198612i	0.662042	−	0.749466i	$-0.269690\pi$
$491$	168.907	+	97.5186i	0.344006	+	0.198612i	−0.318036	+	0.948079i	$0.603023\pi$
$492$	160.203	+	597.887i	0.325616	+	1.21522i
$493$			329.123i			0.667591i
$494$		0			0
$495$	190.148			0.384138
$496$	7.09927	−	1.90224i	0.0143130	−	0.00383517i
$497$	65.7843	−	113.942i	0.132363	−	0.229259i
$498$	271.668	−	156.848i	0.545518	−	0.314955i
$499$	−160.747	−	160.747i	−0.322139	−	0.322139i	0.527448	−	0.849587i	$-0.323149\pi$
$499$	−160.747	−	160.747i	−0.322139	−	0.322139i	−0.849587	+	0.527448i	$0.823149\pi$
$500$	136.725	−	510.265i	0.273450	−	1.02053i
$501$	33.1973	+	8.89519i	0.0662621	+	0.0177549i
$502$	−39.7776	+	39.7776i	−0.0792382	+	0.0792382i
$503$	−247.660	−	428.960i	−0.492366	−	0.852803i	0.507595	−	0.861596i	$-0.330534\pi$
$503$	−247.660	−	428.960i	−0.492366	−	0.852803i	−0.999961	+	0.00879272i	$0.997201\pi$
$504$	105.541	+	60.9343i	0.209407	+	0.120901i
$505$	−47.9524	−	178.961i	−0.0949553	−	0.354378i
$506$			521.095i			1.02983i
$507$		0			0
$508$	−740.034			−1.45676
$509$	−622.252	+	166.732i	−1.22250	+	0.327568i	−0.811655	−	0.584138i	$-0.801433\pi$
$509$	−622.252	+	166.732i	−1.22250	+	0.327568i	−0.410845	+	0.911705i	$0.634766\pi$
$510$	−258.751	+	448.169i	−0.507354	+	0.878763i
$511$	306.595	−	177.013i	0.599990	−	0.346404i
$512$	−29.1874	−	29.1874i	−0.0570067	−	0.0570067i
$513$	86.9743	−	324.592i	0.169540	−	0.632734i
$514$	−835.739	−	223.936i	−1.62595	−	0.435672i
$515$	−544.986	+	544.986i	−1.05822	+	1.05822i
$516$	−152.371	−	263.914i	−0.295292	−	0.511460i
$517$	−401.503	−	231.808i	−0.776601	−	0.448371i
$518$	−120.989	−	451.537i	−0.233569	−	0.871692i
$519$		−	79.1511i		−	0.152507i
$520$		0			0
$521$	807.372			1.54966			0.774830	−	0.632170i	$-0.217836\pi$
$521$	807.372			1.54966			0.774830	+	0.632170i	$0.217836\pi$
$522$	−489.823	+	131.248i	−0.938358	+	0.251432i
$523$	−168.756	+	292.295i	−0.322670	+	0.558881i	−0.981038	−	0.193815i	$-0.937914\pi$
$523$	−168.756	+	292.295i	−0.322670	+	0.558881i	0.658368	+	0.752696i	$0.271247\pi$
$524$	308.416	−	178.064i	0.588580	−	0.339817i
$525$	168.544	+	168.544i	0.321037	+	0.321037i
$526$	10.1201	−	37.7687i	0.0192397	−	0.0718036i
$527$	−110.865	−	29.7063i	−0.210370	−	0.0563686i
$528$	−4.73623	+	4.73623i	−0.00897012	+	0.00897012i
$529$	242.550	+	420.109i	0.458507	+	0.794157i
$530$	1060.61	+	612.342i	2.00114	+	1.15536i
$531$	30.3933	+	113.430i	0.0572379	+	0.213615i
$532$		−	248.954i		−	0.467959i
$533$		0			0
$534$	239.405			0.448324
$535$	−1094.26	+	293.206i	−2.04534	+	0.548048i
$536$	−67.0143	+	116.072i	−0.125027	+	0.216553i
$537$	−492.349	+	284.258i	−0.916850	+	0.529344i
$538$	270.078	+	270.078i	0.502004	+	0.502004i
$539$	50.2921	−	187.693i	0.0933064	−	0.348224i
$540$	−1360.07	−	364.430i	−2.51865	−	0.674870i
$541$	−532.661	+	532.661i	−0.984586	+	0.984586i	−0.999883	−	0.0152973i	$-0.995131\pi$
$541$	−532.661	+	532.661i	−0.984586	+	0.984586i	0.0152973	+	0.999883i	$0.495131\pi$
$542$	226.534	+	392.368i	0.417959	+	0.723926i
$543$	−23.6872	−	13.6758i	−0.0436228	−	0.0251856i
$544$	86.1303	+	321.443i	0.158328	+	0.590887i
$545$		−	1154.86i		−	2.11900i
$546$		0			0
$547$	−508.494			−0.929606			−0.464803	−	0.885414i	$-0.653875\pi$
$547$	−508.494			−0.929606			−0.464803	+	0.885414i	$0.653875\pi$
$548$	−195.284	+	52.3263i	−0.356358	+	0.0954859i
$549$	30.3418	−	52.5535i	0.0552674	−	0.0957259i
$550$	−504.549	+	291.302i	−0.917363	+	0.529640i
$551$	274.646	+	274.646i	0.498450	+	0.498450i
$552$	130.487	−	486.984i	0.236389	−	0.882217i
$553$	−297.367	−	79.6794i	−0.537735	−	0.144086i
$554$	1235.08	−	1235.08i	2.22938	−	2.22938i
$555$	352.836	+	611.130i	0.635741	+	1.10114i
$556$	−1296.25	−	748.391i	−2.33139	−	1.34603i
$557$	−139.614	−	521.046i	−0.250653	−	0.935450i	−0.970457	−	0.241273i	$-0.922435\pi$
$557$	−139.614	−	521.046i	−0.250653	−	0.935450i	0.719804	−	0.694177i	$-0.244232\pi$
$558$		−	176.844i		−	0.316924i
$559$		0			0
$560$	16.4330			0.0293446
$561$	101.035	−	27.0723i	0.180099	−	0.0482573i
$562$	131.283	−	227.389i	0.233600	−	0.404608i
$563$	−612.760	+	353.777i	−1.08838	+	0.628379i	−0.933146	−	0.359498i	$-0.882948\pi$
$563$	−612.760	+	353.777i	−1.08838	+	0.628379i	−0.155238	+	0.987877i	$0.549614\pi$
$564$	845.924	+	845.924i	1.49987	+	1.49987i
$565$	82.5211	−	307.973i	0.146055	−	0.545085i
$566$	−477.233	−	127.874i	−0.843168	−	0.225926i
$567$	33.5639	−	33.5639i	0.0591956	−	0.0591956i
$568$	−155.568	−	269.452i	−0.273887	−	0.474386i
$569$	75.1164	+	43.3685i	0.132015	+	0.0762188i	0.564553	−	0.825397i	$-0.309049\pi$
$569$	75.1164	+	43.3685i	0.132015	+	0.0762188i	−0.432538	+	0.901616i	$0.642382\pi$
$570$	158.066	+	589.910i	0.277309	+	1.03493i
$571$			819.215i			1.43470i	0.696712	+	0.717351i	$0.254646\pi$
$571$			819.215i			1.43470i	−0.696712	+	0.717351i	$0.745354\pi$
$572$		0			0
$573$	670.217			1.16966
$574$	−481.809	+	129.100i	−0.839388	+	0.224913i
$575$	−566.900	+	981.900i	−0.985914	+	1.70765i
$576$	−433.289	+	250.159i	−0.752237	+	0.434304i
$577$	−280.814	−	280.814i	−0.486679	−	0.486679i	0.420578	−	0.907256i	$-0.361827\pi$
$577$	−280.814	−	280.814i	−0.486679	−	0.486679i	−0.907256	+	0.420578i	$0.861827\pi$
$578$	−156.494	+	584.044i	−0.270751	+	1.01046i
$579$	463.030	+	124.069i	0.799707	+	0.214281i
$580$	1150.79	−	1150.79i	1.98412	−	1.98412i
$581$	77.7794	+	134.718i	0.133872	+	0.231873i
$582$	237.308	+	137.010i	0.407745	+	0.235412i
$583$	−64.0675	−	239.103i	−0.109893	−	0.410126i
$584$		−	837.205i		−	1.43357i
$585$		0			0
$586$	753.900			1.28652
$587$	−418.790	+	112.215i	−0.713442	+	0.191166i	−0.597244	−	0.802060i	$-0.703737\pi$
$587$	−418.790	+	112.215i	−0.713442	+	0.191166i	−0.116198	+	0.993226i	$0.537071\pi$
$588$	−250.705	+	434.233i	−0.426369	+	0.738492i
$589$	−117.304	+	67.7255i	−0.199158	+	0.114984i
$590$	−433.064	−	433.064i	−0.734007	−	0.734007i
$591$	−51.5083	+	192.232i	−0.0871545	+	0.325265i
$592$	27.6078	+	7.39748i	0.0466347	+	0.0124957i
$593$	−390.547	+	390.547i	−0.658596	+	0.658596i	−0.955048	−	0.296452i	$-0.904197\pi$
$593$	−390.547	+	390.547i	−0.658596	+	0.658596i	0.296452	+	0.955048i	$0.404197\pi$
$594$	231.246	+	400.530i	0.389303	+	0.674292i
$595$	−222.244	−	128.312i	−0.373519	−	0.215651i
$596$	−294.407	−	1098.74i	−0.493972	−	1.84353i
$597$			546.879i			0.916045i
$598$		0			0
$599$	−315.242			−0.526281			−0.263140	−	0.964758i	$-0.584758\pi$
$599$	−315.242			−0.526281			−0.263140	+	0.964758i	$0.584758\pi$
$600$	544.466	−	145.889i	0.907443	−	0.243149i
$601$	−229.868	+	398.143i	−0.382476	+	0.662468i	−0.991416	−	0.130749i	$-0.958262\pi$
$601$	−229.868	+	398.143i	−0.382476	+	0.662468i	0.608940	+	0.793217i	$0.291595\pi$
$602$	212.675	−	122.788i	0.353281	−	0.203967i
$603$	−58.9579	−	58.9579i	−0.0977743	−	0.0977743i
$604$	−77.2765	+	288.400i	−0.127941	+	0.477483i
$605$	−716.255	−	191.920i	−1.18389	−	0.317223i
$606$	111.039	−	111.039i	0.183232	−	0.183232i
$607$	−448.920	−	777.551i	−0.739571	−	1.28097i	−0.952689	−	0.303948i	$-0.901695\pi$
$607$	−448.920	−	777.551i	−0.739571	−	1.28097i	0.213118	−	0.977027i	$-0.431638\pi$
$608$	340.111	+	196.363i	0.559394	+	0.322966i
$609$	56.6044	+	211.250i	0.0929464	+	0.346881i
$610$			316.487i			0.518831i
$611$		0			0
$612$	310.346			0.507102
$613$	615.481	−	164.918i	1.00405	−	0.269033i	0.280907	−	0.959735i	$-0.409365\pi$
$613$	615.481	−	164.918i	1.00405	−	0.269033i	0.723140	+	0.690702i	$0.242698\pi$
$614$	262.819	−	455.215i	0.428043	−	0.741393i
$615$	652.102	−	376.491i	1.06033	−	0.612181i
$616$	90.8405	+	90.8405i	0.147468	+	0.147468i
$617$	103.566	−	386.513i	0.167854	−	0.626439i	−0.829805	−	0.558053i	$-0.811549\pi$
$617$	103.566	−	386.513i	0.167854	−	0.626439i	0.997659	−	0.0683856i	$-0.0217848\pi$
$618$	−630.985	−	169.072i	−1.02101	−	0.273579i
$619$	524.800	−	524.800i	0.847819	−	0.847819i	−0.142041	−	0.989861i	$-0.545367\pi$
$619$	524.800	−	524.800i	0.847819	−	0.847819i	0.989861	+	0.142041i	$0.0453666\pi$
$620$	283.776	+	491.514i	0.457703	+	0.792765i
$621$	779.468	+	450.026i	1.25518	+	0.724680i
$622$	−426.794	−	1592.82i	−0.686164	−	2.56080i
$623$			118.719i			0.190560i
$624$		0			0
$625$	247.464			0.395943
$626$	185.081	−	49.5922i	0.295656	−	0.0792208i
$627$	61.7206	−	106.903i	0.0984379	−	0.170500i
$628$	339.919	−	196.252i	0.541272	−	0.312503i
$629$	−315.613	−	315.613i	−0.501769	−	0.501769i
$630$	102.337	−	381.927i	0.162440	−	0.606233i
$631$	292.622	+	78.4079i	0.463744	+	0.124260i	0.483123	−	0.875552i	$-0.339502\pi$
$631$	292.622	+	78.4079i	0.463744	+	0.124260i	−0.0193793	+	0.999812i	$0.506169\pi$
$632$	−514.793	+	514.793i	−0.814546	+	0.814546i
$633$	−163.134	−	282.557i	−0.257716	−	0.446377i
$634$	457.997	+	264.424i	0.722392	+	0.417073i
$635$	233.001	+	869.571i	0.366930	+	1.36940i
$636$			638.749i			1.00432i
$637$		0			0
$638$	−534.562			−0.837871
$639$	186.962	−	50.0963i	0.292585	−	0.0783980i
$640$	790.388	−	1368.99i	1.23498	−	2.13905i
$641$	802.665	−	463.419i	1.25221	−	0.722962i	0.280660	−	0.959807i	$-0.409447\pi$
$641$	802.665	−	463.419i	1.25221	−	0.722962i	0.971547	+	0.236845i	$0.0761134\pi$
$642$	−678.948	−	678.948i	−1.05755	−	1.05755i
$643$	205.192	−	765.787i	0.319117	−	1.19096i	−0.600978	−	0.799265i	$-0.705222\pi$
$643$	205.192	−	765.787i	0.319117	−	1.19096i	0.920095	−	0.391695i	$-0.128111\pi$
$644$	644.075	+	172.579i	1.00012	+	0.267980i
$645$	−262.135	+	262.135i	−0.406411	+	0.406411i
$646$	−193.143	−	334.533i	−0.298982	−	0.517853i
$647$	−565.632	−	326.568i	−0.874238	−	0.504742i	−0.00548379	−	0.999985i	$-0.501746\pi$
$647$	−565.632	−	326.568i	−0.874238	−	0.504742i	−0.868754	+	0.495243i	$0.835079\pi$
$648$	−29.0524	−	108.425i	−0.0448339	−	0.167322i
$649$			123.790i			0.190739i
$650$		0			0
$651$	−76.2689			−0.117157
$652$	993.801	−	266.288i	1.52423	−	0.408418i
$653$	−497.150	+	861.089i	−0.761333	+	1.31867i	0.180831	+	0.983514i	$0.442121\pi$
$653$	−497.150	+	861.089i	−0.761333	+	1.31867i	−0.942164	+	0.335152i	$0.891212\pi$
$654$	847.684	−	489.411i	1.29615	−	0.748335i
$655$	−306.338	−	306.338i	−0.467692	−	0.467692i
$656$	7.89342	−	29.4586i	0.0120326	−	0.0449065i
$657$	503.078	+	134.799i	0.765720	+	0.205174i
$658$	−681.690	+	681.690i	−1.03600	+	1.03600i
$659$	554.342	+	960.149i	0.841187	+	1.45698i	0.888892	+	0.458118i	$0.151476\pi$
$659$	554.342	+	960.149i	0.841187	+	1.45698i	−0.0477042	+	0.998862i	$0.515190\pi$
$660$	−447.934	−	258.615i	−0.678687	−	0.391840i
$661$	186.899	+	697.517i	0.282752	+	1.05525i	0.950466	+	0.310828i	$0.100606\pi$
$661$	186.899	+	697.517i	0.282752	+	1.05525i	−0.667714	+	0.744418i	$0.732727\pi$
$662$		−	1764.69i		−	2.66569i
$663$		0			0
$664$	367.869			0.554019
$665$	−292.532	+	78.3836i	−0.439897	+	0.117870i
$666$	343.856	−	595.576i	0.516301	−	0.894259i
$667$	−900.932	+	520.153i	−1.35072	+	0.779840i
$668$	76.0088	+	76.0088i	0.113786	+	0.113786i
$669$	−97.6950	+	364.603i	−0.146031	+	0.544996i
$670$	420.035	+	112.548i	0.626918	+	0.167982i
$671$	45.2334	−	45.2334i	0.0674119	−	0.0674119i
$672$	110.567	+	191.508i	0.164534	+	0.284982i
$673$	−201.737	−	116.473i	−0.299757	−	0.173065i	0.342577	−	0.939490i	$-0.388700\pi$
$673$	−201.737	−	116.473i	−0.299757	−	0.173065i	−0.642334	+	0.766425i	$0.722034\pi$
$674$	429.442	+	1602.70i	0.637155	+	2.37789i
$675$			1006.29i			1.49080i
$676$		0			0
$677$	759.119			1.12130			0.560649	−	0.828053i	$-0.310552\pi$
$677$	759.119			1.12130			0.560649	+	0.828053i	$0.310552\pi$
$678$	261.028	−	69.9423i	0.384998	−	0.103160i
$679$	−67.9420	+	117.679i	−0.100062	+	0.173312i
$680$	−525.566	+	303.436i	−0.772891	+	0.446229i
$681$	323.240	+	323.240i	0.474655	+	0.474655i
$682$	48.2490	−	180.068i	0.0707463	−	0.264029i
$683$	766.309	+	205.332i	1.12197	+	0.300632i	0.771682	−	0.636008i	$-0.219416\pi$
$683$	766.309	+	205.332i	1.12197	+	0.300632i	0.350293	+	0.936640i	$0.386082\pi$
$684$	258.978	−	258.978i	0.378622	−	0.378622i
$685$	122.971	+	212.992i	0.179520	+	0.310938i
$686$	−797.686	−	460.544i	−1.16281	−	0.671347i
$687$	5.89120	+	21.9862i	0.00857525	+	0.0320033i
$688$			15.0150i			0.0218241i
$689$		0			0
$690$	−1635.74			−2.37064
$691$	889.748	−	238.407i	1.28762	−	0.345018i	0.450866	−	0.892592i	$-0.351115\pi$
$691$	889.748	−	238.407i	1.28762	−	0.345018i	0.836757	+	0.547574i	$0.184448\pi$
$692$	123.779	−	214.391i	0.178871	−	0.309814i
$693$	−69.2125	+	39.9599i	−0.0998738	+	0.0576622i
$694$	393.478	+	393.478i	0.566971	+	0.566971i
$695$	−471.264	+	1758.78i	−0.678078	+	2.53062i
$696$	499.569	+	133.859i	0.717771	+	0.192326i
$697$	−336.772	+	336.772i	−0.483173	+	0.483173i
$698$	−1059.29	−	1834.75i	−1.51761	−	2.62858i
$699$	69.4087	+	40.0731i	0.0992971	+	0.0573292i
$700$	192.950	+	720.100i	0.275643	+	1.02871i
$701$		−	1256.17i		−	1.79197i	−0.444079	−	0.895987i	$-0.646469\pi$
$701$		−	1256.17i		−	1.79197i	0.444079	−	0.895987i	$-0.353531\pi$
$702$		0			0
$703$	−526.744			−0.749281
$704$	−509.440	+	136.504i	−0.723636	+	0.193898i
$705$	727.656	−	1260.34i	1.03214	−	1.78771i
$706$	202.026	−	116.640i	0.286156	−	0.165212i
$707$	55.0632	+	55.0632i	0.0778829	+	0.0778829i
$708$	82.6741	−	308.544i	0.116771	−	0.435797i
$709$	188.175	+	50.4214i	0.265409	+	0.0711162i	0.389070	−	0.921208i	$-0.372797\pi$
$709$	188.175	+	50.4214i	0.265409	+	0.0711162i	−0.123660	+	0.992325i	$0.539463\pi$
$710$	−713.805	+	713.805i	−1.00536	+	1.00536i
$711$	−226.453	−	392.227i	−0.318499	−	0.551656i
$712$	243.136	+	140.375i	0.341483	+	0.197155i
$713$	−93.8970	−	350.428i	−0.131693	−	0.491484i
$714$		−	217.507i		−	0.304632i
$715$		0			0
$716$	−1778.12			−2.48341
$717$	−767.654	+	205.692i	−1.07065	+	0.286879i
$718$	−768.110	+	1330.41i	−1.06979	+	1.85293i
$719$	847.432	−	489.265i	1.17863	−	0.680480i	0.222929	−	0.974835i	$-0.428438\pi$
$719$	847.432	−	489.265i	1.17863	−	0.680480i	0.955696	+	0.294355i	$0.0951048\pi$
$720$	17.0946	+	17.0946i	0.0237425	+	0.0237425i
$721$	83.8414	−	312.900i	0.116285	−	0.433981i
$722$	684.155	+	183.319i	0.947583	+	0.253904i
$723$	496.948	−	496.948i	0.687341	−	0.687341i
$724$	−42.7732	−	74.0854i	−0.0590791	−	0.102328i
$725$	−1007.28	−	581.551i	−1.38934	−	0.802139i
$726$	−162.665	−	607.075i	−0.224057	−	0.836192i
$727$		−	470.571i		−	0.647278i	−0.946181	−	0.323639i	$-0.895094\pi$
$727$		−	470.571i		−	0.647278i	0.946181	−	0.323639i	$-0.104906\pi$
$728$		0			0
$729$	590.294			0.809731
$730$	−2623.74	+	703.028i	−3.59416	+	0.963052i
$731$	117.240	−	203.066i	0.160383	−	0.277792i
$732$	−142.953	+	82.5339i	−0.195291	+	0.112751i
$733$	−113.014	−	113.014i	−0.154181	−	0.154181i	0.625802	−	0.779982i	$-0.284772\pi$
$733$	−113.014	−	113.014i	−0.154181	−	0.154181i	−0.779982	+	0.625802i	$0.784772\pi$
$734$	41.7218	−	155.708i	0.0568417	−	0.212136i
$735$	589.177	+	157.870i	0.801601	+	0.214788i
$736$	−743.787	+	743.787i	−1.01058	+	1.01058i
$737$	−43.9471	−	76.1185i	−0.0596297	−	0.103282i
$738$	−635.505	−	366.909i	−0.861118	−	0.497167i
$739$	62.5256	+	233.349i	0.0846084	+	0.315763i	0.995240	−	0.0974569i	$-0.0310708\pi$
$739$	62.5256	+	233.349i	0.0846084	+	0.315763i	−0.910631	+	0.413220i	$0.864404\pi$
$740$			2207.10i			2.98257i
$741$		0			0
$742$	−514.738			−0.693716
$743$	149.489	−	40.0554i	0.201196	−	0.0539103i	−0.156814	−	0.987628i	$-0.550122\pi$
$743$	149.489	−	40.0554i	0.201196	−	0.0539103i	0.358010	+	0.933718i	$0.383455\pi$
$744$	−90.1811	+	156.198i	−0.121211	+	0.209944i
$745$	−1198.38	+	691.882i	−1.60856	+	0.928701i
$746$	−517.583	−	517.583i	−0.693812	−	0.693812i
$747$	−59.2309	+	221.053i	−0.0792918	+	0.295921i
$748$	316.004	+	84.6731i	0.422466	+	0.113199i
$749$	336.685	−	336.685i	0.449513	−	0.449513i
$750$	−272.337	−	471.701i	−0.363116	−	0.628935i
$751$	1009.94	+	583.090i	1.34480	+	0.776419i	0.987507	−	0.157575i	$-0.0503677\pi$
$751$	1009.94	+	583.090i	1.34480	+	0.776419i	0.357289	+	0.933994i	$0.383701\pi$
$752$	−15.2559	−	56.9356i	−0.0202870	−	0.0757123i
$753$			35.6919i			0.0473996i
$754$		0			0
$755$	363.212			0.481076
$756$	571.641	−	153.171i	0.756139	−	0.202607i
$757$	597.091	−	1034.19i	0.788759	−	1.36617i	−0.137968	−	0.990437i	$-0.544057\pi$
$757$	597.091	−	1034.19i	0.788759	−	1.36617i	0.926727	−	0.375734i	$-0.122609\pi$
$758$	−26.4595	+	15.2764i	−0.0349071	+	0.0201536i
$759$	233.786	+	233.786i	0.308018	+	0.308018i
$760$	−185.363	+	691.785i	−0.243899	+	0.910243i
$761$	−927.170	−	248.434i	−1.21836	−	0.326458i	−0.408321	−	0.912838i	$-0.633886\pi$
$761$	−927.170	−	248.434i	−1.21836	−	0.326458i	−0.810036	+	0.586381i	$0.800552\pi$
$762$	−539.537	+	539.537i	−0.708054	+	0.708054i
$763$	242.695	+	420.360i	0.318080	+	0.550930i
$764$	1815.37	+	1048.11i	2.37614	+	1.37187i
$765$	−97.7130	−	364.670i	−0.127729	−	0.476693i
$766$			277.408i			0.362152i
$767$		0			0
$768$	489.153			0.636918
$769$	1092.58	−	292.755i	1.42077	−	0.380695i	0.535016	−	0.844842i	$-0.320306\pi$
$769$	1092.58	−	292.755i	1.42077	−	0.380695i	0.885758	+	0.464147i	$0.153639\pi$
$770$	208.405	−	360.969i	0.270656	−	0.468790i
$771$	−475.416	+	274.481i	−0.616622	+	0.356007i
$772$	1060.16	+	1060.16i	1.37326	+	1.37326i
$773$	−107.050	+	399.515i	−0.138486	+	0.516837i	0.861473	+	0.507803i	$0.169542\pi$
$773$	−107.050	+	399.515i	−0.138486	+	0.516837i	−0.999959	+	0.00903396i	$0.997124\pi$
$774$	348.970	+	93.5062i	0.450866	+	0.120809i
$775$	286.811	−	286.811i	0.370079	−	0.370079i
$776$	160.670	+	278.289i	0.207050	+	0.358620i
$777$	−256.860	−	148.298i	−0.330579	−	0.190860i
$778$	−29.0181	−	108.297i	−0.0372983	−	0.139199i
$779$			562.058i			0.721513i
$780$		0			0
$781$	204.039			0.261253
$782$	999.367	−	267.780i	1.27796	−	0.342429i
$783$	−461.656	+	799.611i	−0.589599	+	1.02122i
$784$	21.3952	−	12.3525i	0.0272898	−	0.0157558i
$785$	−337.628	−	337.628i	−0.430100	−	0.430100i
$786$	95.0358	−	354.678i	0.120911	−	0.451245i
$787$	−1295.20	−	347.048i	−1.64574	−	0.440975i	−0.687326	−	0.726349i	$-0.741216\pi$
$787$	−1295.20	−	347.048i	−1.64574	−	0.440975i	−0.958416	+	0.285373i	$0.907882\pi$
$788$	−440.135	+	440.135i	−0.558547	+	0.558547i
$789$	−12.4044	−	21.4850i	−0.0157216	−	0.0272307i
$790$	2045.61	+	1181.03i	2.58938	+	1.49498i
$791$	34.6838	+	129.442i	0.0438481	+	0.163643i
$792$			188.996i			0.238631i
$793$		0			0
$794$	−610.721			−0.769170
$795$	750.557	−	201.111i	0.944097	−	0.252970i
$796$	−855.226	+	1481.30i	−1.07440	+	1.86092i
$797$	−1133.61	+	654.489i	−1.42234	+	0.821191i	−0.996499	−	0.0836053i	$-0.973357\pi$
$797$	−1133.61	+	654.489i	−1.42234	+	0.821191i	−0.425845	+	0.904796i	$0.640023\pi$
$798$	−181.505	−	181.505i	−0.227450	−	0.227450i
$799$	−238.242	+	889.131i	−0.298175	+	1.11281i
$800$	−1135.96	−	304.380i	−1.41995	−	0.380475i
$801$	−123.499	+	123.499i	−0.154181	+	0.154181i
$802$	390.003	+	675.505i	0.486288	+	0.842275i
$803$	475.472	+	274.514i	0.592119	+	0.341860i
$804$	58.7009	+	219.075i	0.0730110	+	0.272481i
$805$		−	811.152i		−	1.00764i
$806$		0			0
$807$	242.337			0.300294
$808$	177.876	−	47.6618i	0.220144	−	0.0589874i
$809$	12.0403	−	20.8545i	0.0148830	−	0.0257781i	−0.858488	−	0.512834i	$-0.828596\pi$
$809$	12.0403	−	20.8545i	0.0148830	−	0.0257781i	0.873371	+	0.487056i	$0.161929\pi$
$810$	−315.399	+	182.096i	−0.389381	+	0.224809i
$811$	685.757	+	685.757i	0.845570	+	0.845570i	0.989577	−	0.144007i	$-0.0459987\pi$
$811$	685.757	+	685.757i	0.845570	+	0.845570i	−0.144007	+	0.989577i	$0.545999\pi$
$812$	−177.039	+	660.720i	−0.218029	+	0.813694i
$813$	277.666	+	74.4004i	0.341533	+	0.0915134i
$814$	512.619	−	512.619i	0.629753	−	0.629753i
$815$	−625.800	−	1083.92i	−0.767852	−	1.32996i
$816$	11.5171	+	6.64939i	0.0141141	+	0.00814876i
$817$	−71.6199	−	267.289i	−0.0876620	−	0.327159i
$818$			1502.66i			1.83700i
$819$		0			0
$820$	2355.07			2.87204
$821$	342.513	−	91.7762i	0.417191	−	0.111786i	−0.0441166	−	0.999026i	$-0.514047\pi$
$821$	342.513	−	91.7762i	0.417191	−	0.111786i	0.461307	+	0.887241i	$0.347381\pi$
$822$	−104.227	+	180.526i	−0.126796	+	0.219618i
$823$	761.836	−	439.846i	0.925681	−	0.534442i	0.0402381	−	0.999190i	$-0.487188\pi$
$823$	761.836	−	439.846i	0.925681	−	0.534442i	0.885443	+	0.464748i	$0.153855\pi$
$824$	−541.683	−	541.683i	−0.657382	−	0.657382i
$825$	−95.6721	+	357.053i	−0.115966	+	0.432792i
$826$	248.641	+	66.6232i	0.301018	+	0.0806576i
$827$	496.734	−	496.734i	0.600645	−	0.600645i	−0.339838	−	0.940484i	$-0.610372\pi$
$827$	496.734	−	496.734i	0.600645	−	0.600645i	0.940484	+	0.339838i	$0.110372\pi$
$828$	490.479	+	849.535i	0.592366	+	1.02601i
$829$	841.504	+	485.843i	1.01508	+	0.586059i	0.912676	−	0.408684i	$-0.134012\pi$
$829$	841.504	+	485.843i	1.01508	+	0.586059i	0.102408	+	0.994743i	$0.467345\pi$
$830$	−308.911	−	1152.87i	−0.372182	−	1.38900i
$831$		−	1108.22i		−	1.33360i
$832$		0			0
$833$	−385.805			−0.463152
$834$	−1490.69	+	399.429i	−1.78740	+	0.478931i
$835$	65.3820	−	113.245i	0.0783018	−	0.135623i
$836$	334.357	−	193.041i	0.399949	−	0.230910i
$837$	−227.681	−	227.681i	−0.272021	−	0.272021i
$838$	579.488	−	2162.68i	0.691514	−	2.58076i
$839$	−61.9530	−	16.6003i	−0.0738415	−	0.0197858i	0.221709	−	0.975113i	$-0.428836\pi$
$839$	−61.9530	−	16.6003i	−0.0738415	−	0.0197858i	−0.295551	+	0.955327i	$0.595503\pi$
$840$	−285.153	+	285.153i	−0.339468	+	0.339468i
$841$	−113.096	−	195.887i	−0.134477	−	0.232922i
$842$	−545.389	−	314.880i	−0.647730	−	0.373967i
$843$	−43.1173	−	160.916i	−0.0511475	−	0.190885i
$844$		−	1020.46i		−	1.20907i
$845$		0			0
$846$	−1418.27			−1.67645
$847$	301.044	−	80.6644i	0.355424	−	0.0952355i
$848$	15.7360	−	27.2555i	0.0185566	−	0.0321409i
$849$	−271.477	+	156.738i	−0.319761	+	0.184614i
$850$	817.942	+	817.942i	0.962284	+	0.962284i
$851$	365.148	−	1362.75i	0.429081	−	1.60135i
$852$	−508.563	−	136.269i	−0.596905	−	0.159940i
$853$	−118.160	+	118.160i	−0.138523	+	0.138523i	−0.772968	−	0.634445i	$-0.781229\pi$
$853$	−118.160	+	118.160i	−0.138523	+	0.138523i	0.634445	+	0.772968i	$0.281229\pi$
$854$	−66.5102	−	115.199i	−0.0778808	−	0.134893i
$855$	−385.849	−	222.770i	−0.451285	−	0.260550i
$856$	−291.429	−	1087.63i	−0.340454	−	1.27059i
$857$			1001.36i			1.16845i	0.811592	+	0.584225i	$0.198601\pi$
$857$			1001.36i			1.16845i	−0.811592	+	0.584225i	$0.801399\pi$
$858$		0			0
$859$	−1088.25			−1.26688			−0.633438	−	0.773793i	$-0.718357\pi$
$859$	−1088.25			−1.26688			−0.633438	+	0.773793i	$0.718357\pi$
$860$	−1119.96	+	300.094i	−1.30228	+	0.348946i
$861$	−158.240	+	274.080i	−0.183787	+	0.318328i
$862$	473.236	−	273.223i	0.548998	−	0.316964i
$863$	1068.95	+	1068.95i	1.23864	+	1.23864i	0.960557	+	0.278082i	$0.0896989\pi$
$863$	1068.95	+	1068.95i	1.23864	+	1.23864i	0.278082	+	0.960557i	$0.410301\pi$
$864$	−241.628	+	901.767i	−0.279662	+	1.04371i
$865$	−290.891	−	77.9440i	−0.336290	−	0.0901086i
$866$	1477.52	−	1477.52i	1.70614	−	1.70614i
$867$	191.817	+	332.238i	0.221243	+	0.383204i
$868$	−206.585	−	119.272i	−0.238001	−	0.137410i
$869$	−123.568	−	461.162i	−0.142196	−	0.530681i
$870$		−	1678.02i		−	1.92875i
$871$		0			0
$872$	1147.86			1.31635
$873$	−193.094	+	51.7395i	−0.221185	+	0.0592663i
$874$	610.495	−	1057.41i	0.698507	−	1.20985i
$875$	233.913	−	135.050i	0.267329	−	0.154343i
$876$	−1001.77	−	1001.77i	−1.14357	−	1.14357i
$877$	−221.600	+	827.023i	−0.252680	+	0.943014i	0.716687	+	0.697395i	$0.245658\pi$
$877$	−221.600	+	827.023i	−0.252680	+	0.943014i	−0.969367	+	0.245618i	$0.921009\pi$
$878$	731.668	+	196.050i	0.833335	+	0.223291i
$879$	338.232	−	338.232i	0.384792	−	0.384792i
$880$	12.7423	+	22.0703i	0.0144799	+	0.0250798i
$881$	−1223.50	−	706.388i	−1.38876	−	0.801802i	−0.395587	−	0.918429i	$-0.629459\pi$
$881$	−1223.50	−	706.388i	−1.38876	−	0.801802i	−0.993176	+	0.116626i	$0.962792\pi$
$882$	−153.852	−	574.182i	−0.174435	−	0.651000i
$883$		−	249.675i		−	0.282757i	−0.989956	−	0.141379i	$-0.954847\pi$
$883$		−	249.675i		−	0.282757i	0.989956	−	0.141379i	$-0.0451535\pi$
$884$		0			0
$885$	−388.582			−0.439076
$886$	−1872.25	+	501.668i	−2.11315	+	0.566217i
$887$	−407.874	+	706.459i	−0.459836	+	0.796459i	−0.998952	−	0.0457724i	$-0.985425\pi$
$887$	−407.874	+	706.459i	−0.459836	+	0.796459i	0.539116	+	0.842232i	$0.318758\pi$
$888$	−607.427	+	350.698i	−0.684039	+	0.394930i
$889$	−267.552	−	267.552i	−0.300958	−	0.300958i
$890$	235.754	−	879.846i	0.264892	−	0.988591i
$891$	71.1035	+	19.0521i	0.0798019	+	0.0213829i
$892$	−834.797	+	834.797i	−0.935871	+	0.935871i
$893$	543.154	+	940.770i	0.608235	+	1.05349i
$894$	−1015.71	−	586.418i	−1.13614	−	0.655948i
$895$	559.845	+	2089.37i	0.625525	+	2.33449i
$896$			664.404i			0.741522i
$897$		0			0
$898$	1669.36			1.85897
$899$	359.484	−	96.3235i	0.399871	−	0.107145i
$900$	−548.373	+	949.811i	−0.609304	+	1.05535i
$901$	−425.634	+	245.740i	−0.472402	+	0.272741i
$902$	−546.986	−	546.986i	−0.606414	−	0.606414i
$903$	40.3273	−	150.503i	0.0446592	−	0.166671i
$904$	306.107	+	82.0210i	0.338613	+	0.0907312i
$905$	−73.5863	+	73.5863i	−0.0813108	+	0.0813108i
$906$	153.924	+	266.604i	0.169894	+	0.294265i
$907$	−1119.16	−	646.145i	−1.23391	−	0.712398i	−0.266067	−	0.963955i	$-0.585724\pi$
$907$	−1119.16	−	646.145i	−1.23391	−	0.712398i	−0.967843	+	0.251556i	$0.919058\pi$
$908$	370.046	+	1381.03i	0.407540	+	1.52096i
$909$			114.560i			0.126029i
$910$		0			0
$911$	−108.954			−0.119598			−0.0597992	−	0.998210i	$-0.519046\pi$
$911$	−108.954			−0.119598			−0.0597992	+	0.998210i	$0.519046\pi$
$912$	15.1595	−	4.06199i	0.0166223	−	0.00445393i
$913$	−120.622	+	208.923i	−0.132116	+	0.228831i
$914$	−360.508	+	208.139i	−0.394429	+	0.227723i
$915$	141.990	+	141.990i	0.155180	+	0.155180i
$916$	−18.4257	+	68.7655i	−0.0201154	+	0.0750715i
$917$	175.882	+	47.1275i	0.191802	+	0.0513931i
$918$	649.312	−	649.312i	0.707311	−	0.707311i
$919$	334.516	+	579.399i	0.364000	+	0.630467i	0.988615	−	0.150466i	$-0.0480774\pi$
$919$	334.516	+	579.399i	0.364000	+	0.630467i	−0.624615	+	0.780933i	$0.714744\pi$
$920$	−1661.23	−	959.114i	−1.80569	−	1.04252i
$921$	−86.3174	−	322.141i	−0.0937214	−	0.349773i
$922$		−	1458.68i		−	1.58209i
$923$		0			0
$924$	217.393			0.235274
$925$	1523.61	−	408.249i	1.64714	−	0.441350i
$926$	719.057	−	1245.44i	0.776520	−	1.34497i
$927$	412.715	−	238.281i	0.445216	−	0.257046i
$928$	−763.009	−	763.009i	−0.822208	−	0.822208i
$929$	−142.352	+	531.264i	−0.153231	+	0.571866i	0.846019	+	0.533152i	$0.178993\pi$
$929$	−142.352	+	531.264i	−0.153231	+	0.571866i	−0.999250	+	0.0387140i	$0.987674\pi$
$930$	565.241	+	151.456i	0.607786	+	0.162856i
$931$	−321.947	+	321.947i	−0.345807	+	0.345807i
$932$	125.335	+	217.087i	0.134480	+	0.232926i
$933$	−906.085	−	523.128i	−0.971152	−	0.560695i
$934$	483.064	+	1802.82i	0.517199	+	1.93021i
$935$		−	397.978i		−	0.425645i
$936$		0			0
$937$	−1312.75			−1.40101			−0.700507	−	0.713646i	$-0.747043\pi$
$937$	−1312.75			−1.40101			−0.700507	+	0.713646i	$0.747043\pi$
$938$	−176.542	+	47.3043i	−0.188211	+	0.0504310i
$939$	60.7860	−	105.284i	0.0647348	−	0.112124i
$940$	3941.91	−	2275.86i	4.19352	−	2.42113i
$941$	310.426	+	310.426i	0.329889	+	0.329889i	0.852544	−	0.522655i	$-0.175058\pi$
$941$	310.426	+	310.426i	0.329889	+	0.329889i	−0.522655	+	0.852544i	$0.675058\pi$
$942$	104.743	−	390.906i	0.111192	−	0.414975i
$943$	−1454.11	−	389.629i	−1.54201	−	0.413180i
$944$	−11.1289	+	11.1289i	−0.0117891	+	0.0117891i
$945$	−359.964	−	623.476i	−0.380915	−	0.659763i
$946$	329.820	+	190.422i	0.348647	+	0.201292i
$947$	201.095	+	750.497i	0.212350	+	0.792499i	0.987083	+	0.160211i	$0.0512175\pi$
$947$	201.095	+	750.497i	0.212350	+	0.792499i	−0.774733	+	0.632288i	$0.782116\pi$
$948$			1231.97i			1.29954i
$949$		0			0
$950$	1365.11			1.43696
$951$	324.109	−	86.8448i	0.340809	−	0.0913195i
$952$	127.535	−	220.897i	0.133965	−	0.232034i
$953$	147.254	−	85.0174i	0.154517	−	0.0892102i	−0.420748	−	0.907178i	$-0.638232\pi$
$953$	147.254	−	85.0174i	0.154517	−	0.0892102i	0.575265	+	0.817967i	$0.304899\pi$
$954$	−535.462	−	535.462i	−0.561281	−	0.561281i
$955$	659.995	−	2463.14i	0.691094	−	2.57920i
$956$	−2400.96	−	643.336i	−2.51147	−	0.672945i
$957$	−239.827	+	239.827i	−0.250603	+	0.250603i
$958$	−315.300	−	546.116i	−0.329123	−	0.570058i
$959$	−89.5212	−	51.6851i	−0.0933485	−	0.0538948i
$960$	−428.493	−	1599.16i	−0.446347	−	1.66579i
$961$		−	831.213i		−	0.864946i
$962$		0			0
$963$	700.481			0.727394
$964$	2123.19	−	568.908i	2.20248	−	0.590153i
$965$	911.938	−	1579.52i	0.945013	−	1.63681i
$966$	595.399	−	343.754i	0.616355	−	0.355853i
$967$	−702.486	−	702.486i	−0.726460	−	0.726460i	0.243453	−	0.969913i	$-0.421720\pi$
$967$	−702.486	−	702.486i	−0.726460	−	0.726460i	−0.969913	+	0.243453i	$0.921720\pi$
$968$	190.757	−	711.914i	0.197063	−	0.735448i
$969$	−236.738	−	63.4338i	−0.244312	−	0.0654631i
$970$	737.217	−	737.217i	0.760018	−	0.760018i
$971$	−521.890	−	903.939i	−0.537476	−	0.930936i	−0.999039	−	0.0438288i	$-0.986044\pi$
$971$	−521.890	−	903.939i	−0.537476	−	0.930936i	0.461563	−	0.887108i	$-0.347289\pi$
$972$	1245.25	+	718.943i	1.28112	+	0.739653i
$973$	−198.073	−	739.220i	−0.203570	−	0.759733i
$974$			2147.43i			2.20475i
$975$		0			0
$976$	8.13310			0.00833309
$977$	−1173.90	+	314.547i	−1.20154	+	0.321951i	−0.803437	−	0.595390i	$-0.796998\pi$
$977$	−1173.90	+	314.547i	−1.20154	+	0.321951i	−0.398102	+	0.917341i	$0.630331\pi$
$978$	530.408	−	918.694i	0.542340	−	0.939360i
$979$	−159.445	+	92.0557i	−0.162865	+	0.0940303i
$980$	1348.98	+	1348.98i	1.37651	+	1.37651i
$981$	−184.818	+	689.750i	−0.188398	+	0.703110i
$982$	607.527	+	162.786i	0.618663	+	0.165770i
$983$	−511.256	+	511.256i	−0.520098	+	0.520098i	−0.917601	−	0.397503i	$-0.869877\pi$
$983$	−511.256	+	511.256i	−0.520098	+	0.520098i	0.397503	+	0.917601i	$0.369877\pi$
$984$	374.209	+	648.150i	0.380294	+	0.658689i
$985$	655.754	+	378.600i	0.665740	+	0.384365i
$986$	274.700	+	1025.19i	0.278600	+	1.03975i
$987$			611.672i			0.619728i
$988$		0			0
$989$	741.158			0.749401
$990$	592.298	−	158.706i	0.598281	−	0.160309i
$991$	2.60955	−	4.51988i	0.00263325	−	0.00456093i	−0.864706	−	0.502279i	$-0.832495\pi$
$991$	2.60955	−	4.51988i	0.00263325	−	0.00456093i	0.867339	+	0.497718i	$0.165828\pi$
$992$	325.889	−	188.152i	0.328517	−	0.189669i
$993$	−791.715	−	791.715i	−0.797296	−	0.797296i
$994$	109.813	−	409.827i	0.110476	−	0.412301i
$995$	2009.85	+	538.539i	2.01995	+	0.541245i
$996$	440.178	−	440.178i	0.441946	−	0.441946i
$997$	136.426	+	236.297i	0.136836	+	0.237008i	0.926298	−	0.376793i	$-0.122973\pi$
$997$	136.426	+	236.297i	0.136836	+	0.237008i	−0.789461	+	0.613801i	$0.789640\pi$
$998$	−634.883	−	366.550i	−0.636156	−	0.367285i
$999$	−324.083	−	1209.49i	−0.324407	−	1.21070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.3.f.g.150.12		48
13.2	odd	12	inner	169.3.f.g.80.12		48
13.3	even	3	inner	169.3.f.g.89.1		48
13.4	even	6		169.3.d.e.99.12	yes	24
13.5	odd	4	inner	169.3.f.g.19.1		48
13.6	odd	12		169.3.d.e.70.1	✓	24
13.7	odd	12		169.3.d.e.70.12	yes	24
13.8	odd	4	inner	169.3.f.g.19.12		48
13.9	even	3		169.3.d.e.99.1	yes	24
13.10	even	6	inner	169.3.f.g.89.12		48
13.11	odd	12	inner	169.3.f.g.80.1		48
13.12	even	2	inner	169.3.f.g.150.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.3.d.e.70.1	✓	24	13.6	odd	12
169.3.d.e.70.12	yes	24	13.7	odd	12
169.3.d.e.99.1	yes	24	13.9	even	3
169.3.d.e.99.12	yes	24	13.4	even	6
169.3.f.g.19.1		48	13.5	odd	4	inner
169.3.f.g.19.12		48	13.8	odd	4	inner
169.3.f.g.80.1		48	13.11	odd	12	inner
169.3.f.g.80.12		48	13.2	odd	12	inner
169.3.f.g.89.1		48	13.3	even	3	inner
169.3.f.g.89.12		48	13.10	even	6	inner
169.3.f.g.150.1		48	13.12	even	2	inner
169.3.f.g.150.12		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	169.f (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.11493 - 0.834643i) q^{2} +(1.02304 - 1.77195i) q^{3} +(5.54206 - 3.19971i) q^{4} +(-5.50472 - 5.50472i) q^{5} +(1.70774 - 6.37336i) q^{6} +(3.16050 + 0.846854i) q^{7} +(5.47136 - 5.47136i) q^{8} +(2.40680 + 4.16870i) q^{9} +(-21.7413 - 12.5523i) q^{10} +(1.31331 + 4.90135i) q^{11} -13.0937i q^{12} +10.5516 q^{14} +(-15.3856 + 4.12256i) q^{15} +(-0.322570 + 0.558708i) q^{16} +(8.72503 - 5.03740i) q^{17} +(10.9764 + 10.9764i) q^{18} +(3.07725 - 11.4845i) q^{19} +(-48.1209 - 12.8940i) q^{20} +(4.73388 - 4.73388i) q^{21} +(8.18176 + 14.1712i) q^{22} +(27.5785 + 15.9225i) q^{23} +(-4.09757 - 15.2924i) q^{24} +35.6038i q^{25} +28.2636 q^{27} +(20.2254 - 5.41937i) q^{28} +(-16.3339 + 28.2912i) q^{29} +(-44.4842 + 25.6830i) q^{30} +(-8.05564 - 8.05564i) q^{31} +(-8.54908 + 31.9056i) q^{32} +(10.0285 + 2.68713i) q^{33} +(22.9734 - 22.9734i) q^{34} +(-12.7360 - 22.0593i) q^{35} +(26.6772 + 15.4021i) q^{36} +(-11.4664 - 42.7934i) q^{37} -38.3417i q^{38} -60.2365 q^{40} +(-45.6623 + 12.2352i) q^{41} +(10.7946 - 18.6968i) q^{42} +(20.1558 - 11.6370i) q^{43} +(22.9614 + 22.9614i) q^{44} +(9.69875 - 36.1962i) q^{45} +(99.1947 + 26.5792i) q^{46} +(-64.6057 + 64.6057i) q^{47} +(0.660002 + 1.14316i) q^{48} +(-33.1636 - 19.1470i) q^{49} +(29.7165 + 110.903i) q^{50} -20.6138i q^{51} -48.7831 q^{53} +(88.0391 - 23.5900i) q^{54} +(19.7511 - 34.2100i) q^{55} +(21.9257 - 12.6588i) q^{56} +(-17.2018 - 17.2018i) q^{57} +(-27.2660 + 101.758i) q^{58} +(23.5644 + 6.31406i) q^{59} +(-72.0768 + 72.0768i) q^{60} +(-6.30335 - 10.9177i) q^{61} +(-31.8163 - 18.3692i) q^{62} +(4.07641 + 15.2134i) q^{63} +103.939i q^{64} +33.4809 q^{66} +(-16.7314 + 4.48316i) q^{67} +(32.2364 - 55.8351i) q^{68} +(56.4276 - 32.5785i) q^{69} +(-58.0833 - 58.0833i) q^{70} +(10.4073 - 38.8404i) q^{71} +(35.9769 + 9.63998i) q^{72} +(76.5080 - 76.5080i) q^{73} +(-71.4344 - 123.728i) q^{74} +(63.0881 + 36.4239i) q^{75} +(-19.6926 - 73.4939i) q^{76} +16.6029i q^{77} -94.0887 q^{79} +(4.85119 - 1.29987i) q^{80} +(7.25346 - 12.5634i) q^{81} +(-132.023 + 76.2235i) q^{82} +(33.6177 + 33.6177i) q^{83} +(11.0884 - 41.3825i) q^{84} +(-75.7583 - 20.2994i) q^{85} +(53.0713 - 53.0713i) q^{86} +(33.4204 + 57.8858i) q^{87} +(34.0027 + 19.6314i) q^{88} +(9.39084 + 35.0471i) q^{89} -120.844i q^{90} +203.789 q^{92} +(-22.5154 + 6.03298i) q^{93} +(-147.319 + 255.165i) q^{94} +(-80.1582 + 46.2793i) q^{95} +(47.7891 + 47.7891i) q^{96} +(-10.7486 + 40.1144i) q^{97} +(-119.283 - 31.9619i) q^{98} +(-17.2714 + 17.2714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{3} - 84 q^{9} + 376 q^{14} - 188 q^{16} + 136 q^{22} + 120 q^{27} - 84 q^{29} - 176 q^{35} - 1048 q^{40} + 368 q^{42} + 368 q^{48} - 88 q^{53} + 704 q^{55} + 8 q^{61} - 1480 q^{66} + 168 q^{68}+ \cdots - 1132 q^{94}+O(q^{100}) \) 48 * q - 12 * q^3 - 84 * q^9 + 376 * q^14 - 188 * q^16 + 136 * q^22 + 120 * q^27 - 84 * q^29 - 176 * q^35 - 1048 * q^40 + 368 * q^42 + 368 * q^48 - 88 * q^53 + 704 * q^55 + 8 * q^61 - 1480 * q^66 + 168 * q^68 - 744 * q^74 - 600 * q^79 - 240 * q^81 + 952 * q^87 + 3472 * q^92 - 1132 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more