LMFDB - Embedded newform 169.3.f.g.19.1

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			19.1
Character	$\chi$	$=$	169.19
Dual form			169.3.f.g.89.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.834643 - 3.11493i) q^{2} +(1.02304 - 1.77195i) q^{3} +(-5.54206 + 3.19971i) q^{4} +(-5.50472 + 5.50472i) q^{5} +(-6.37336 - 1.70774i) q^{6} +(-0.846854 + 3.16050i) q^{7} +(5.47136 + 5.47136i) q^{8} +(2.40680 + 4.16870i) q^{9} +(21.7413 + 12.5523i) q^{10} +(-4.90135 + 1.31331i) q^{11} +13.0937i q^{12} +10.5516 q^{14} +(4.12256 + 15.3856i) q^{15} +(-0.322570 + 0.558708i) q^{16} +(-8.72503 + 5.03740i) q^{17} +(10.9764 - 10.9764i) q^{18} +(-11.4845 - 3.07725i) q^{19} +(12.8940 - 48.1209i) q^{20} +(4.73388 + 4.73388i) q^{21} +(8.18176 + 14.1712i) q^{22} +(-27.5785 - 15.9225i) q^{23} +(15.2924 - 4.09757i) q^{24} -35.6038i q^{25} +28.2636 q^{27} +(-5.41937 - 20.2254i) q^{28} +(-16.3339 + 28.2912i) q^{29} +(44.4842 - 25.6830i) q^{30} +(-8.05564 + 8.05564i) q^{31} +(31.9056 + 8.54908i) q^{32} +(-2.68713 + 10.0285i) q^{33} +(22.9734 + 22.9734i) q^{34} +(-12.7360 - 22.0593i) q^{35} +(-26.6772 - 15.4021i) q^{36} +(42.7934 - 11.4664i) q^{37} +38.3417i q^{38} -60.2365 q^{40} +(12.2352 + 45.6623i) q^{41} +(10.7946 - 18.6968i) q^{42} +(-20.1558 + 11.6370i) q^{43} +(22.9614 - 22.9614i) q^{44} +(-36.1962 - 9.69875i) q^{45} +(-26.5792 + 99.1947i) q^{46} +(-64.6057 - 64.6057i) q^{47} +(0.660002 + 1.14316i) q^{48} +(33.1636 + 19.1470i) q^{49} +(-110.903 + 29.7165i) q^{50} +20.6138i q^{51} -48.7831 q^{53} +(-23.5900 - 88.0391i) q^{54} +(19.7511 - 34.2100i) q^{55} +(-21.9257 + 12.6588i) q^{56} +(-17.2018 + 17.2018i) q^{57} +(101.758 + 27.2660i) q^{58} +(-6.31406 + 23.5644i) q^{59} +(-72.0768 - 72.0768i) q^{60} +(-6.30335 - 10.9177i) q^{61} +(31.8163 + 18.3692i) q^{62} +(-15.2134 + 4.07641i) q^{63} -103.939i q^{64} +33.4809 q^{66} +(4.48316 + 16.7314i) q^{67} +(32.2364 - 55.8351i) q^{68} +(-56.4276 + 32.5785i) q^{69} +(-58.0833 + 58.0833i) q^{70} +(-38.8404 - 10.4073i) q^{71} +(-9.63998 + 35.9769i) q^{72} +(76.5080 + 76.5080i) q^{73} +(-71.4344 - 123.728i) q^{74} +(-63.0881 - 36.4239i) q^{75} +(73.4939 - 19.6926i) q^{76} -16.6029i q^{77} -94.0887 q^{79} +(-1.29987 - 4.85119i) q^{80} +(7.25346 - 12.5634i) q^{81} +(132.023 - 76.2235i) q^{82} +(33.6177 - 33.6177i) q^{83} +(-41.3825 - 11.0884i) q^{84} +(20.2994 - 75.7583i) q^{85} +(53.0713 + 53.0713i) q^{86} +(33.4204 + 57.8858i) q^{87} +(-34.0027 - 19.6314i) q^{88} +(-35.0471 + 9.39084i) q^{89} +120.844i q^{90} +203.789 q^{92} +(6.03298 + 22.5154i) q^{93} +(-147.319 + 255.165i) q^{94} +(80.1582 - 46.2793i) q^{95} +(47.7891 - 47.7891i) q^{96} +(40.1144 + 10.7486i) q^{97} +(31.9619 - 119.283i) 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.834643	−	3.11493i	−0.417321	−	1.55746i	−0.780140	−	0.625605i	$-0.784852\pi$
$2$	−0.834643	−	3.11493i	−0.417321	−	1.55746i	0.362819	−	0.931860i	$-0.381814\pi$
$3$	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	−0.106646	+	0.994297i	$0.534011\pi$
$5$	−5.50472	+	5.50472i	−1.10094	+	1.10094i	−0.994297	+	0.106646i	$0.965989\pi$
$6$	−6.37336	−	1.70774i	−1.06223	−	0.284623i
$7$	−0.846854	+	3.16050i	−0.120979	+	0.451500i	−0.999665	−	0.0259011i	$-0.991754\pi$
$7$	−0.846854	+	3.16050i	−0.120979	+	0.451500i	0.878685	+	0.477401i	$0.158421\pi$
$8$	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
$11$	−4.90135	+	1.31331i	−0.445578	+	0.119392i	−0.474629	−	0.880186i	$-0.657418\pi$
$11$	−4.90135	+	1.31331i	−0.445578	+	0.119392i	0.0290518	+	0.999578i	$0.490751\pi$
$12$			13.0937i			1.09114i
$13$		0			0
$13$		0			0
$14$	10.5516			0.753683
$15$	4.12256	+	15.3856i	0.274837	+	1.02571i
$16$	−0.322570	+	0.558708i	−0.0201607	+	0.0349193i
$17$	−8.72503	+	5.03740i	−0.513237	+	0.296318i	−0.734163	−	0.678973i	$-0.762425\pi$
$17$	−8.72503	+	5.03740i	−0.513237	+	0.296318i	0.220926	+	0.975291i	$0.429092\pi$
$18$	10.9764	−	10.9764i	0.609799	−	0.609799i
$19$	−11.4845	−	3.07725i	−0.604446	−	0.161961i	−0.0563988	−	0.998408i	$-0.517962\pi$
$19$	−11.4845	−	3.07725i	−0.604446	−	0.161961i	−0.548047	+	0.836448i	$0.684629\pi$
$20$	12.8940	−	48.1209i	0.644698	−	2.40605i
$21$	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	−0.238719	−	0.971089i	$-0.576728\pi$
$23$	−27.5785	−	15.9225i	−1.19907	−	0.692281i	−0.960347	+	0.278807i	$0.910061\pi$
$24$	15.2924	−	4.09757i	0.637181	−	0.170732i
$25$		−	35.6038i		−	1.42415i
$26$		0			0
$27$	28.2636			1.04680
$28$	−5.41937	−	20.2254i	−0.193549	−	0.722334i
$29$	−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	−0.824997	−	0.565137i	$-0.808823\pi$
$31$	−8.05564	+	8.05564i	−0.259859	+	0.259859i	0.565137	+	0.824997i	$0.308823\pi$
$32$	31.9056	+	8.54908i	0.997050	+	0.267159i
$33$	−2.68713	+	10.0285i	−0.0814283	+	0.303894i
$34$	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
$37$	42.7934	−	11.4664i	1.15658	−	0.309904i	0.370979	−	0.928641i	$-0.379022\pi$
$37$	42.7934	−	11.4664i	1.15658	−	0.309904i	0.785598	+	0.618737i	$0.212355\pi$
$38$			38.3417i			1.00899i
$39$		0			0
$40$	−60.2365			−1.50591
$41$	12.2352	+	45.6623i	0.298419	+	1.11372i	0.938464	+	0.345378i	$0.112249\pi$
$41$	12.2352	+	45.6623i	0.298419	+	1.11372i	−0.640045	+	0.768338i	$0.721084\pi$
$42$	10.7946	−	18.6968i	0.257015	−	0.445162i
$43$	−20.1558	+	11.6370i	−0.468740	+	0.270627i	−0.715712	−	0.698395i	$-0.753898\pi$
$43$	−20.1558	+	11.6370i	−0.468740	+	0.270627i	0.246972	+	0.969023i	$0.420564\pi$
$44$	22.9614	−	22.9614i	0.521849	−	0.521849i
$45$	−36.1962	−	9.69875i	−0.804361	−	0.215528i
$46$	−26.5792	+	99.1947i	−0.577808	+	2.15641i
$47$	−64.6057	−	64.6057i	−1.37459	−	1.37459i	−0.853506	−	0.521082i	$-0.825528\pi$
$47$	−64.6057	−	64.6057i	−1.37459	−	1.37459i	−0.521082	−	0.853506i	$-0.674472\pi$
$48$	0.660002	+	1.14316i	0.0137500	+	0.0238158i
$49$	33.1636	+	19.1470i	0.676809	+	0.390756i
$50$	−110.903	+	29.7165i	−2.21807	+	0.594329i
$51$			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	$0.652229\pi$
$54$	−23.5900	−	88.0391i	−0.436852	−	1.63035i
$55$	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
$58$	101.758	+	27.2660i	1.75445	+	0.470104i
$59$	−6.31406	+	23.5644i	−0.107018	+	0.399397i	−0.998566	−	0.0535290i	$-0.982953\pi$
$59$	−6.31406	+	23.5644i	−0.107018	+	0.399397i	0.891548	+	0.452926i	$0.149620\pi$
$60$	−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
$63$	−15.2134	+	4.07641i	−0.241482	+	0.0647049i
$64$		−	103.939i		−	1.62404i
$65$		0			0
$66$	33.4809			0.507287
$67$	4.48316	+	16.7314i	0.0669128	+	0.249722i	0.991278	−	0.131787i	$-0.0420714\pi$
$67$	4.48316	+	16.7314i	0.0669128	+	0.249722i	−0.924365	+	0.381508i	$0.875405\pi$
$68$	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
$71$	−38.8404	−	10.4073i	−0.547048	−	0.146581i	−0.0252987	−	0.999680i	$-0.508054\pi$
$71$	−38.8404	−	10.4073i	−0.547048	−	0.146581i	−0.521749	+	0.853099i	$0.674720\pi$
$72$	−9.63998	+	35.9769i	−0.133889	+	0.499679i
$73$	76.5080	+	76.5080i	1.04806	+	1.04806i	0.998786	+	0.0492695i	$0.0156893\pi$
$73$	76.5080	+	76.5080i	1.04806	+	1.04806i	0.0492695	+	0.998786i	$0.484311\pi$
$74$	−71.4344	−	123.728i	−0.965329	−	1.67200i
$75$	−63.0881	−	36.4239i	−0.841175	−	0.485653i
$76$	73.4939	−	19.6926i	0.967025	−	0.259114i
$77$		−	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	$0.703045\pi$
$80$	−1.29987	−	4.85119i	−0.0162484	−	0.0606399i
$81$	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	−0.474970	−	0.880002i	$-0.657541\pi$
$83$	33.6177	−	33.6177i	0.405032	−	0.405032i	0.880002	+	0.474970i	$0.157541\pi$
$84$	−41.3825	−	11.0884i	−0.492649	−	0.132005i
$85$	20.2994	−	75.7583i	0.238816	−	0.891274i
$86$	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
$89$	−35.0471	+	9.39084i	−0.393788	+	0.105515i	−0.450279	−	0.892888i	$-0.648675\pi$
$89$	−35.0471	+	9.39084i	−0.393788	+	0.105515i	0.0564911	+	0.998403i	$0.482009\pi$
$90$			120.844i			1.34271i
$91$		0			0
$92$	203.789			2.21510
$93$	6.03298	+	22.5154i	0.0648708	+	0.242101i
$94$	−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
$97$	40.1144	+	10.7486i	0.413550	+	0.110810i	0.459594	−	0.888129i	$-0.347995\pi$
$97$	40.1144	+	10.7486i	0.413550	+	0.110810i	−0.0460441	+	0.998939i	$0.514661\pi$
$98$	31.9619	−	119.283i	0.326142	−	1.21718i
$99$	−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	0.394484	−	0.918903i	$-0.370923\pi$
$101$	−20.6108	−	11.8997i	−0.204067	−	0.117818i	−0.598551	+	0.801085i	$0.704257\pi$
$102$	64.2104	−	17.2051i	0.629514	−	0.168678i
$103$			99.0034i			0.961198i	0.876940	+	0.480599i	$0.159581\pi$
$103$			99.0034i			0.961198i	−0.876940	+	0.480599i	$0.840419\pi$
$104$		0			0
$105$	−52.1174			−0.496356
$106$	40.7165	+	151.956i	0.384118	+	1.43355i
$107$	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	−0.0369580	−	0.999317i	$-0.511767\pi$
$109$	104.897	−	104.897i	0.962359	−	0.962359i	0.999317	+	0.0369580i	$0.0117668\pi$
$110$	−123.047	−	32.9703i	−1.11861	−	0.299730i
$111$	23.4612	−	87.5582i	0.211362	−	0.788813i
$112$	−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
$115$	239.461	−	64.1633i	2.08227	−	0.557942i
$116$		−	209.055i		−	1.80220i
$117$		0			0
$118$	78.6714			0.666707
$119$	−8.53188	−	31.8414i	−0.0716965	−	0.267575i
$120$	−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
$123$	93.4283	+	25.0340i	0.759580	+	0.203529i
$124$	18.8691	−	70.4205i	0.152170	−	0.567907i
$125$	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	0.839457	−	0.543425i	$-0.182873\pi$
$127$	100.148	+	57.8204i	0.788566	+	0.455279i	−0.0508914	+	0.998704i	$0.516206\pi$
$128$	−196.139	+	52.5553i	−1.53234	+	0.410588i
$129$			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	$0.431870\pi$
$132$	−17.1961	−	64.1766i	−0.130273	−	0.486187i
$133$	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
$136$	−75.2992	−	20.1764i	−0.553670	−	0.148356i
$137$	8.17673	−	30.5160i	0.0596841	−	0.222744i	−0.929642	−	0.368465i	$-0.879883\pi$
$137$	8.17673	−	30.5160i	0.0596841	−	0.222744i	0.989326	+	0.145721i	$0.0465501\pi$
$138$	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
$141$	−180.572	+	48.3841i	−1.28065	+	0.343149i
$142$			129.671i			0.913180i
$143$		0			0
$144$	−3.10545			−0.0215656
$145$	−65.8214	−	245.649i	−0.453941	−	1.69413i
$146$	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
$149$	−171.694	−	46.0054i	−1.15231	−	0.308761i	−0.368420	−	0.929659i	$-0.620101\pi$
$149$	−171.694	−	46.0054i	−1.15231	−	0.308761i	−0.783891	+	0.620899i	$0.786768\pi$
$150$	−60.8020	+	226.916i	−0.405346	+	1.51277i
$151$	−32.9910	−	32.9910i	−0.218484	−	0.218484i	0.589376	−	0.807859i	$-0.299374\pi$
$151$	−32.9910	−	32.9910i	−0.218484	−	0.218484i	−0.807859	+	0.589376i	$0.799374\pi$
$152$	−45.9989	−	79.6724i	−0.302624	−	0.524160i
$153$	−41.9988	−	24.2480i	−0.274502	−	0.158484i
$154$	−51.7169	+	13.8575i	−0.335824	+	0.0899838i
$155$		−	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	$0.437421\pi$
$158$	78.5305	+	293.080i	0.497028	+	1.85494i
$159$	−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
$162$	−45.1880	−	12.1081i	−0.278938	−	0.0747413i
$163$	−41.6113	+	155.296i	−0.255284	+	0.952734i	0.712648	+	0.701522i	$0.247496\pi$
$163$	−41.6113	+	155.296i	−0.255284	+	0.952734i	−0.967932	+	0.251212i	$0.919171\pi$
$164$	−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
$167$	−16.2249	+	4.34745i	−0.0971551	+	0.0260326i	−0.307069	−	0.951687i	$-0.599348\pi$
$167$	−16.2249	+	4.34745i	−0.0971551	+	0.0260326i	0.209914	+	0.977720i	$0.432682\pi$
$168$			51.8015i			0.308342i
$169$		0			0
$170$	−252.925			−1.48779
$171$	−14.8127	−	55.2816i	−0.0866238	−	0.323284i
$172$	74.4699	−	128.986i	0.432964	−	0.749916i
$173$	−33.5017	+	19.3422i	−0.193651	+	0.111805i	−0.593691	−	0.804693i	$-0.702330\pi$
$173$	−33.5017	+	19.3422i	−0.193651	+	0.111805i	0.400039	+	0.916498i	$0.368996\pi$
$174$	152.416	−	152.416i	0.875955	−	0.875955i
$175$	112.526	+	30.1512i	0.643005	+	0.172293i
$176$	0.847272	−	3.16206i	0.00481405	−	0.0179663i
$177$	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	0.987437	−	0.158016i	$-0.0505096\pi$
$179$	240.631	+	138.929i	1.34431	+	0.776137i	0.356873	+	0.934153i	$0.383843\pi$
$180$	231.635	−	62.0663i	1.28686	−	0.344813i
$181$			13.3679i			0.0738556i	0.999318	+	0.0369278i	$0.0117572\pi$
$181$			13.3679i			0.0738556i	−0.999318	+	0.0369278i	$0.988243\pi$
$182$		0			0
$183$	−25.7942			−0.140952
$184$	−63.7744	−	238.009i	−0.346600	−	1.29353i
$185$	−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
$188$	564.768	+	151.329i	3.00408	+	0.804942i
$189$	−23.9351	+	89.3271i	−0.126641	+	0.472630i
$190$	−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
$193$	−226.302	+	60.6375i	−1.17255	+	0.314184i	−0.791968	−	0.610563i	$-0.790943\pi$
$193$	−226.302	+	60.6375i	−1.17255	+	0.314184i	−0.380583	+	0.924747i	$0.624277\pi$
$194$		−	133.925i		−	0.690333i
$195$		0			0
$196$	−245.060			−1.25030
$197$	25.1743	+	93.9516i	0.127788	+	0.476912i	0.999924	−	0.0123525i	$-0.00393201\pi$
$197$	25.1743	+	93.9516i	0.127788	+	0.476912i	−0.872136	+	0.489264i	$0.837265\pi$
$198$	−39.3837	+	68.2146i	−0.198908	+	0.344518i
$199$	231.474	−	133.641i	1.16318	−	0.671564i	0.211119	−	0.977460i	$-0.432289\pi$
$199$	231.474	−	133.641i	1.16318	−	0.671564i	0.952065	+	0.305896i	$0.0989560\pi$
$200$	194.801	−	194.801i	0.974005	−	0.974005i
$201$	34.2335	+	9.17285i	0.170316	+	0.0456361i
$202$	−19.8639	+	74.1332i	−0.0983362	+	0.366996i
$203$	−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
$206$	308.389	−	82.6325i	1.49703	−	0.401129i
$207$		−	153.289i		−	0.740525i
$208$		0			0
$209$	60.3309			0.288664
$210$	43.4994	+	162.342i	0.207140	+	0.773057i
$211$	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
$214$	−453.289	−	121.458i	−2.11817	−	0.567562i
$215$	46.8939	−	175.010i	0.218111	−	0.814002i
$216$	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
$219$	213.839	−	57.2979i	0.976432	−	0.261634i
$220$			252.792i			1.14905i
$221$		0			0
$222$	−292.319			−1.31675
$223$	47.7476	+	178.197i	0.214115	+	0.799088i	0.986476	+	0.163904i	$0.0524088\pi$
$223$	47.7476	+	178.197i	0.214115	+	0.799088i	−0.772361	+	0.635183i	$0.780925\pi$
$224$	−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
$227$	215.806	+	57.8250i	0.950687	+	0.254736i	0.700654	−	0.713502i	$-0.252892\pi$
$227$	215.806	+	57.8250i	0.950687	+	0.254736i	0.250033	+	0.968237i	$0.419559\pi$
$228$	40.2925	−	150.374i	0.176722	−	0.659534i
$229$	−7.86632	−	7.86632i	−0.0343508	−	0.0343508i	0.689723	−	0.724074i	$-0.257732\pi$
$229$	−7.86632	−	7.86632i	−0.0343508	−	0.0343508i	−0.724074	+	0.689723i	$0.757732\pi$
$230$	−399.728	−	692.350i	−1.73795	−	3.01022i
$231$	−29.4195	−	16.9854i	−0.127357	−	0.0735297i
$232$	−244.160	+	65.4225i	−1.05241	+	0.281994i
$233$		−	39.1708i		−	0.168115i	−0.996461	−	0.0840575i	$-0.973212\pi$
$233$		−	39.1708i		−	0.168115i	0.996461	−	0.0840575i	$-0.0267879\pi$
$234$		0			0
$235$	711.272			3.02669
$236$	−40.4063	−	150.798i	−0.171213	−	0.638976i
$237$	−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	−0.162466	+	0.986714i	$0.551945\pi$
$239$	−274.654	+	274.654i	−1.14918	+	1.14918i	−0.986714	+	0.162466i	$0.948055\pi$
$240$	−9.92588	−	2.65963i	−0.0413578	−	0.0110818i
$241$	−88.8999	+	331.779i	−0.368879	+	1.37668i	0.493205	+	0.869913i	$0.335825\pi$
$241$	−88.8999	+	331.779i	−0.368879	+	1.37668i	−0.862085	+	0.506764i	$0.830842\pi$
$242$	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
$245$	−287.955	+	77.1574i	−1.17533	+	0.314928i
$246$		−	311.917i		−	1.26796i
$247$		0			0
$248$	−88.1506			−0.355446
$249$	−25.1767	−	93.9609i	−0.101111	−	0.377353i
$250$	133.102	−	230.540i	0.532410	−	0.922161i
$251$	15.1070	−	8.72206i	0.0601874	−	0.0347492i	−0.469604	−	0.882877i	$-0.655603\pi$
$251$	15.1070	−	8.72206i	0.0601874	−	0.0347492i	0.529792	+	0.848128i	$0.322270\pi$
$252$	71.2701	−	71.2701i	0.282818	−	0.282818i
$253$	156.083	+	41.8224i	0.616930	+	0.165306i
$254$	96.5188	−	360.213i	0.379995	−	1.41816i
$255$	−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	0.878530	−	0.477686i	$-0.158524\pi$
$257$	232.356	+	134.151i	0.904107	+	0.521986i	0.0255766	+	0.999673i	$0.491858\pi$
$258$	148.333	−	39.7458i	0.574936	−	0.154054i
$259$			144.959i			0.559687i
$260$		0			0
$261$	−157.250			−0.602491
$262$	−46.4480	−	173.346i	−0.177282	−	0.661626i
$263$	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
$266$	−121.179	−	32.4698i	−0.455560	−	0.122067i
$267$	−19.2143	+	71.7088i	−0.0719638	+	0.268572i
$268$	−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
$271$	−135.707	+	36.3626i	−0.500764	+	0.134179i	−0.500354	−	0.865821i	$-0.666797\pi$
$271$	−135.707	+	36.3626i	−0.500764	+	0.134179i	−0.000409306		1.00000i	$0.500130\pi$
$272$		−	6.49967i		−	0.0238958i
$273$		0			0
$274$	−101.880			−0.371824
$275$	46.7590	+	174.507i	0.170033	+	0.634570i
$276$	208.483	−	361.104i	0.755374	−	1.30835i
$277$	−469.067	+	270.816i	−1.69338	+	0.977676i	−0.741632	+	0.670807i	$0.765948\pi$
$277$	−469.067	+	270.816i	−1.69338	+	0.977676i	−0.951752	+	0.306869i	$0.900719\pi$
$278$	−533.344	+	533.344i	−1.91850	+	1.91850i
$279$	−52.9698	−	14.1932i	−0.189856	−	0.0508718i
$280$	51.0115	−	190.378i	0.182184	−	0.679920i
$281$	57.5732	+	57.5732i	0.204887	+	0.204887i	0.802090	−	0.597203i	$-0.203721\pi$
$281$	57.5732	+	57.5732i	0.204887	+	0.204887i	−0.597203	+	0.802090i	$0.703721\pi$
$282$	301.426	+	522.085i	1.06889	+	1.85137i
$283$	132.682	+	76.6042i	0.468842	+	0.270686i	0.715755	−	0.698352i	$-0.246083\pi$
$283$	132.682	+	76.6042i	0.468842	+	0.270686i	−0.246913	+	0.969038i	$0.579416\pi$
$284$	248.556	−	66.6004i	0.875197	−	0.234508i
$285$		−	189.382i		−	0.664497i
$286$		0			0
$287$	−154.677			−0.538945
$288$	41.1518	+	153.581i	0.142888	+	0.533267i
$289$	−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
$292$	−668.815	−	179.208i	−2.29046	−	0.613728i
$293$	−60.5070	+	225.815i	−0.206509	+	0.770700i	0.782476	+	0.622681i	$0.213957\pi$
$293$	−60.5070	+	225.815i	−0.206509	+	0.770700i	−0.988984	+	0.148020i	$0.952710\pi$
$294$	−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
$297$	−138.530	+	37.1190i	−0.466430	+	0.124980i
$298$			573.214i			1.92354i
$299$		0			0
$300$	466.184			1.55395
$301$	−19.7096	−	73.5573i	−0.0654805	−	0.244377i
$302$	−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
$305$	94.7972	+	25.4008i	0.310810	+	0.0832814i
$306$	−40.4769	+	151.062i	−0.132277	+	0.493666i
$307$	115.257	+	115.257i	0.375429	+	0.375429i	0.869450	−	0.494021i	$-0.164473\pi$
$307$	115.257	+	115.257i	0.375429	+	0.375429i	−0.494021	+	0.869450i	$0.664473\pi$
$308$	53.1245	+	92.0143i	0.172482	+	0.298748i
$309$	175.429	+	101.284i	0.567731	+	0.327780i
$310$	−276.257	+	74.0228i	−0.891152	+	0.238783i
$311$			511.349i			1.64421i	0.569336	+	0.822105i	$0.307201\pi$
$311$			511.349i			1.64421i	−0.569336	+	0.822105i	$0.692799\pi$
$312$		0			0
$313$	59.4173			0.189832			0.0949158	−	0.995485i	$-0.469742\pi$
$313$	59.4173			0.189832			0.0949158	+	0.995485i	$0.469742\pi$
$314$	−51.1923	−	191.052i	−0.163033	−	0.608447i
$315$	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	−0.500138	−	0.865946i	$-0.666717\pi$
$317$	115.961	−	115.961i	0.365808	−	0.365808i	0.865946	+	0.500138i	$0.166717\pi$
$318$	310.912	+	83.3087i	0.977712	+	0.261977i
$319$	42.9032	−	160.117i	0.134493	−	0.501934i
$320$	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
$323$	115.704	−	31.0027i	0.358216	−	0.0959837i
$324$			92.8358i			0.286530i
$325$		0			0
$326$	518.466			1.59039
$327$	−78.5589	−	293.186i	−0.240241	−	0.896592i
$328$	−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
$331$	−528.576	−	141.631i	−1.59691	−	0.427890i	−0.652800	−	0.757531i	$-0.726406\pi$
$331$	−528.576	−	141.631i	−1.59691	−	0.427890i	−0.944106	+	0.329641i	$0.893072\pi$
$332$	−78.7443	+	293.878i	−0.237182	+	0.885174i
$333$	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
$336$	−4.17187	+	1.11785i	−0.0124163	+	0.00332693i
$337$		−	514.522i		−	1.52677i	−0.645942	−	0.763386i	$-0.723535\pi$
$337$		−	514.522i		−	1.52677i	0.645942	−	0.763386i	$-0.276465\pi$
$338$		0			0
$339$	83.7991			0.247195
$340$	129.904	+	484.809i	0.382071	+	1.42591i
$341$	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
$344$	−173.950	−	46.6097i	−0.505668	−	0.135493i
$345$	131.283	−	489.953i	0.380529	−	1.42015i
$346$	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
$349$	634.579	−	170.035i	1.81828	−	0.487206i	0.821703	−	0.569916i	$-0.193024\pi$
$349$	634.579	−	170.035i	1.81828	−	0.487206i	0.996574	+	0.0827101i	$0.0263576\pi$
$350$		−	375.676i		−	1.07336i
$351$		0			0
$352$	−167.608			−0.476160
$353$	−18.7227	−	69.8740i	−0.0530388	−	0.197943i	0.934323	−	0.356429i	$-0.116006\pi$
$353$	−18.7227	−	69.8740i	−0.0530388	−	0.197943i	−0.987361	+	0.158485i	$0.949339\pi$
$354$	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
$357$	−65.1498	−	17.4568i	−0.182492	−	0.0488987i
$358$	231.912	−	865.506i	0.647798	−	2.41761i
$359$	−336.848	−	336.848i	−0.938295	−	0.938295i	0.0599089	−	0.998204i	$-0.480919\pi$
$359$	−336.848	−	336.848i	−0.938295	−	0.938295i	−0.998204	+	0.0599089i	$0.980919\pi$
$360$	−144.977	−	251.108i	−0.402714	−	0.697522i
$361$	−190.212	−	109.819i	−0.526902	−	0.304207i
$362$	41.6399	−	11.1574i	0.115027	−	0.0308215i
$363$			194.892i			0.536893i
$364$		0			0
$365$	−842.310			−2.30770
$366$	21.5289	+	80.3471i	0.0588223	+	0.219528i
$367$	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
$370$	1074.31	+	287.861i	2.90355	+	0.778004i
$371$	41.3121	−	154.179i	0.111353	−	0.415577i
$372$	−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
$375$	163.146	−	43.7148i	0.435055	−	0.116573i
$376$		−	706.961i		−	1.88022i
$377$		0			0
$378$	298.225			0.788955
$379$	2.45213	+	9.15147i	0.00647000	+	0.0241464i	0.969085	−	0.246726i	$-0.0793546\pi$
$379$	2.45213	+	9.15147i	0.00647000	+	0.0241464i	−0.962615	+	0.270872i	$0.912688\pi$
$380$	−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
$383$	83.0919	+	22.2644i	0.216950	+	0.0581316i	0.365657	−	0.930750i	$-0.380844\pi$
$383$	83.0919	+	22.2644i	0.216950	+	0.0581316i	−0.148707	+	0.988881i	$0.547511\pi$
$384$	−107.532	+	401.314i	−0.280031	+	1.04509i
$385$	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
$388$	−256.709	+	68.7848i	−0.661620	+	0.177281i
$389$			34.7670i			0.0893754i	0.999001	+	0.0446877i	$0.0142293\pi$
$389$			34.7670i			0.0893754i	−0.999001	+	0.0446877i	$0.985771\pi$
$390$		0			0
$391$	320.831			0.820541
$392$	76.6898	+	286.210i	0.195637	+	0.730128i
$393$	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
$396$	150.982	+	40.4556i	0.381268	+	0.102161i
$397$	49.0156	−	182.929i	0.123465	−	0.460778i	−0.876315	−	0.481738i	$-0.840006\pi$
$397$	49.0156	−	182.929i	0.123465	−	0.460778i	0.999780	+	0.0209602i	$0.00667233\pi$
$398$	−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
$401$	−233.635	+	62.6022i	−0.582630	+	0.156115i	−0.538083	−	0.842892i	$-0.680851\pi$
$401$	−233.635	+	62.6022i	−0.582630	+	0.156115i	−0.0445472	+	0.999007i	$0.514185\pi$
$402$		−	114.291i		−	0.284306i
$403$		0			0
$404$	152.302			0.376984
$405$	29.2295	+	109.086i	0.0721716	+	0.269348i
$406$	−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
$409$	450.091	+	120.602i	1.10047	+	0.294869i	0.762955	−	0.646452i	$-0.223748\pi$
$409$	450.091	+	120.602i	1.10047	+	0.294869i	0.337513	+	0.941321i	$0.390414\pi$
$410$	−307.160	+	1146.34i	−0.749171	+	2.79594i
$411$	−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
$414$	−477.483	+	127.941i	−1.15334	+	0.309037i
$415$			370.112i			0.891835i
$416$		0			0
$417$	−478.562			−1.14763
$418$	−50.3547	−	187.926i	−0.120466	−	0.449585i
$419$	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	−0.851826	−	0.523825i	$-0.824504\pi$
$421$	−138.088	+	138.088i	−0.328000	+	0.328000i	0.523825	+	0.851826i	$0.324504\pi$
$422$	−496.710	−	133.093i	−1.17704	−	0.315386i
$423$	113.829	−	424.814i	0.269098	−	1.00429i
$424$	−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
$427$	39.8435	−	10.6760i	0.0933103	−	0.0250024i
$428$			931.251i			2.17582i
$429$		0			0
$430$	−584.285			−1.35880
$431$	−43.8570	−	163.677i	−0.101756	−	0.379760i	0.896201	−	0.443649i	$-0.146316\pi$
$431$	−43.8570	−	163.677i	−0.101756	−	0.379760i	−0.997957	+	0.0638890i	$0.979650\pi$
$432$	−9.11700	+	15.7911i	−0.0211042	+	0.0365535i
$433$	−561.144	+	323.977i	−1.29594	+	0.748214i	−0.979701	−	0.200464i	$-0.935755\pi$
$433$	−561.144	+	323.977i	−1.29594	+	0.748214i	−0.316244	+	0.948678i	$0.602422\pi$
$434$	−84.9996	+	84.9996i	−0.195852	+	0.195852i
$435$	−502.615	−	134.675i	−1.15544	−	0.309598i
$436$	−245.706	+	916.986i	−0.563545	+	2.10318i
$437$	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	0.250088	−	0.968223i	$-0.419541\pi$
$439$	−203.421	−	117.445i	−0.463374	−	0.267529i	−0.713462	+	0.700694i	$0.752874\pi$
$440$	295.241	−	79.1095i	0.671001	−	0.179794i
$441$			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	$0.737324\pi$
$444$	150.138	+	560.322i	0.338148	+	1.26199i
$445$	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
$448$	328.498	+	88.0208i	0.733255	+	0.196475i
$449$	−133.980	+	500.022i	−0.298397	+	1.11363i	0.640084	+	0.768305i	$0.278899\pi$
$449$	−133.980	+	500.022i	−0.298397	+	1.11363i	−0.938482	+	0.345329i	$0.887767\pi$
$450$	−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
$453$	−92.2094	+	24.7074i	−0.203553	+	0.0545418i
$454$		−	720.483i		−	1.58697i
$455$		0			0
$456$	−188.234			−0.412794
$457$	33.4099	+	124.688i	0.0731071	+	0.272839i	0.992797	−	0.119805i	$-0.0382270\pi$
$457$	33.4099	+	124.688i	0.0731071	+	0.272839i	−0.919690	+	0.392644i	$0.871560\pi$
$458$	−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
$461$	−436.918	−	117.072i	−0.947762	−	0.253952i	−0.248349	−	0.968671i	$-0.579888\pi$
$461$	−436.918	−	117.072i	−0.947762	−	0.253952i	−0.699412	+	0.714719i	$0.746555\pi$
$462$	−28.3534	+	105.816i	−0.0613711	+	0.229040i
$463$	315.336	+	315.336i	0.681072	+	0.681072i	0.960242	−	0.279170i	$-0.0900592\pi$
$463$	315.336	+	315.336i	0.681072	+	0.681072i	−0.279170	+	0.960242i	$0.590059\pi$
$464$	−10.5377	−	18.2518i	−0.0227106	−	0.0393358i
$465$	−157.151	−	90.7310i	−0.337958	−	0.195120i
$466$	−122.014	+	32.6936i	−0.261833	+	0.0701580i
$467$		−	578.767i		−	1.23933i	−0.784866	−	0.619665i	$-0.787268\pi$
$467$		−	578.767i		−	1.23933i	0.784866	−	0.619665i	$-0.212732\pi$
$468$		0			0
$469$	−56.6761			−0.120844
$470$	−593.658	−	2215.56i	−1.26310	−	4.71396i
$471$	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
$474$	599.662	+	160.679i	1.26511	+	0.338985i
$475$	−109.562	+	408.891i	−0.230657	+	0.860823i
$476$	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
$479$	188.883	−	50.6111i	0.394328	−	0.105660i	−0.0562058	−	0.998419i	$-0.517900\pi$
$479$	188.883	−	50.6111i	0.394328	−	0.105660i	0.450534	+	0.892759i	$0.351234\pi$
$480$			526.131i			1.09611i
$481$		0			0
$482$	1107.67			2.29807
$483$	−55.1784	−	205.929i	−0.114241	−	0.426353i
$484$	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
$487$	643.217	+	172.350i	1.32077	+	0.353901i	0.849268	−	0.527962i	$-0.177044\pi$
$487$	643.217	+	172.350i	1.32077	+	0.353901i	0.471507	+	0.881862i	$0.343710\pi$
$488$	25.2469	−	94.2227i	0.0517354	−	0.193079i
$489$	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	0.318036	−	0.948079i	$-0.396977\pi$
$491$	−168.907	−	97.5186i	−0.344006	−	0.198612i	−0.662042	+	0.749466i	$0.730310\pi$
$492$	−597.887	+	160.203i	−1.21522	+	0.325616i
$493$		−	329.123i		−	0.667591i
$494$		0			0
$495$	190.148			0.384138
$496$	−1.90224	−	7.09927i	−0.00383517	−	0.0143130i
$497$	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	−0.849587	−	0.527448i	$-0.823149\pi$
$499$	−160.747	+	160.747i	−0.322139	+	0.322139i	0.527448	+	0.849587i	$0.323149\pi$
$500$	−510.265	−	136.725i	−1.02053	−	0.273450i
$501$	−8.89519	+	33.1973i	−0.0177549	+	0.0662621i
$502$	−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
$505$	178.961	−	47.9524i	0.354378	−	0.0949553i
$506$		−	521.095i		−	1.02983i
$507$		0			0
$508$	−740.034			−1.45676
$509$	166.732	+	622.252i	0.327568	+	1.22250i	0.911705	+	0.410845i	$0.134766\pi$
$509$	166.732	+	622.252i	0.327568	+	1.22250i	−0.584138	+	0.811655i	$0.698567\pi$
$510$	−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
$513$	−324.592	−	86.9743i	−0.632734	−	0.169540i
$514$	223.936	−	835.739i	0.435672	−	1.62595i
$515$	−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
$518$	451.537	−	120.989i	0.871692	−	0.233569i
$519$			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	$0.217836\pi$
$522$	131.248	+	489.823i	0.251432	+	0.938358i
$523$	−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
$526$	−37.7687	−	10.1201i	−0.0718036	−	0.0192397i
$527$	29.7063	−	110.865i	0.0563686	−	0.210370i
$528$	−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
$531$	−113.430	+	30.3933i	−0.213615	+	0.0572379i
$532$			248.954i			0.467959i
$533$		0			0
$534$	239.405			0.448324
$535$	293.206	+	1094.26i	0.548048	+	2.04534i
$536$	−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
$539$	−187.693	−	50.2921i	−0.348224	−	0.0933064i
$540$	364.430	−	1360.07i	0.674870	−	2.51865i
$541$	−532.661	−	532.661i	−0.984586	−	0.984586i	0.0152973	−	0.999883i	$-0.495131\pi$
$541$	−532.661	−	532.661i	−0.984586	−	0.984586i	−0.999883	+	0.0152973i	$0.995131\pi$
$542$	226.534	+	392.368i	0.417959	+	0.723926i
$543$	23.6872	+	13.6758i	0.0436228	+	0.0251856i
$544$	−321.443	+	86.1303i	−0.590887	+	0.158328i
$545$			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	$0.653875\pi$
$548$	52.3263	+	195.284i	0.0954859	+	0.356358i
$549$	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
$552$	−486.984	−	130.487i	−0.882217	−	0.236389i
$553$	79.6794	−	297.367i	0.144086	−	0.537735i
$554$	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
$557$	521.046	−	139.614i	0.935450	−	0.250653i	0.241273	−	0.970457i	$-0.422435\pi$
$557$	521.046	−	139.614i	0.935450	−	0.250653i	0.694177	+	0.719804i	$0.255768\pi$
$558$			176.844i			0.316924i
$559$		0			0
$560$	16.4330			0.0293446
$561$	−27.0723	−	101.035i	−0.0482573	−	0.180099i
$562$	131.283	−	227.389i	0.233600	−	0.404608i
$563$	612.760	−	353.777i	1.08838	−	0.628379i	0.155238	−	0.987877i	$-0.450386\pi$
$563$	612.760	−	353.777i	1.08838	−	0.628379i	0.933146	+	0.359498i	$0.117052\pi$
$564$	845.924	−	845.924i	1.49987	−	1.49987i
$565$	−307.973	−	82.5211i	−0.545085	−	0.146055i
$566$	127.874	−	477.233i	0.225926	−	0.843168i
$567$	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	0.432538	−	0.901616i	$-0.357618\pi$
$569$	−75.1164	−	43.3685i	−0.132015	−	0.0762188i	−0.564553	+	0.825397i	$0.690951\pi$
$570$	−589.910	+	158.066i	−1.03493	+	0.277309i
$571$		−	819.215i		−	1.43470i	−0.696712	−	0.717351i	$-0.745354\pi$
$571$		−	819.215i		−	1.43470i	0.696712	−	0.717351i	$-0.254646\pi$
$572$		0			0
$573$	670.217			1.16966
$574$	129.100	+	481.809i	0.224913	+	0.839388i
$575$	−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	−0.907256	−	0.420578i	$-0.861827\pi$
$577$	−280.814	+	280.814i	−0.486679	+	0.486679i	0.420578	+	0.907256i	$0.361827\pi$
$578$	584.044	+	156.494i	1.01046	+	0.270751i
$579$	−124.069	+	463.030i	−0.214281	+	0.799707i
$580$	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
$583$	239.103	−	64.0675i	0.410126	−	0.109893i
$584$			837.205i			1.43357i
$585$		0			0
$586$	753.900			1.28652
$587$	112.215	+	418.790i	0.191166	+	0.713442i	0.993226	+	0.116198i	$0.0370708\pi$
$587$	112.215	+	418.790i	0.191166	+	0.713442i	−0.802060	+	0.597244i	$0.796263\pi$
$588$	−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
$591$	192.232	+	51.5083i	0.325265	+	0.0871545i
$592$	−7.39748	+	27.6078i	−0.0124957	+	0.0466347i
$593$	−390.547	−	390.547i	−0.658596	−	0.658596i	0.296452	−	0.955048i	$-0.404197\pi$
$593$	−390.547	−	390.547i	−0.658596	−	0.658596i	−0.955048	+	0.296452i	$0.904197\pi$
$594$	231.246	+	400.530i	0.389303	+	0.674292i
$595$	222.244	+	128.312i	0.373519	+	0.215651i
$596$	1098.74	−	294.407i	1.84353	−	0.493972i
$597$		−	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	$0.584758\pi$
$600$	−145.889	−	544.466i	−0.243149	−	0.907443i
$601$	−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
$604$	288.400	+	77.2765i	0.477483	+	0.127941i
$605$	191.920	−	716.255i	0.317223	−	1.18389i
$606$	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
$609$	−211.250	+	56.6044i	−0.346881	+	0.0929464i
$610$		−	316.487i		−	0.518831i
$611$		0			0
$612$	310.346			0.507102
$613$	−164.918	−	615.481i	−0.269033	−	1.00405i	−0.959735	−	0.280907i	$-0.909365\pi$
$613$	−164.918	−	615.481i	−0.269033	−	1.00405i	0.690702	−	0.723140i	$-0.257302\pi$
$614$	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
$617$	−386.513	−	103.566i	−0.626439	−	0.167854i	−0.0683856	−	0.997659i	$-0.521785\pi$
$617$	−386.513	−	103.566i	−0.626439	−	0.167854i	−0.558053	+	0.829805i	$0.688451\pi$
$618$	169.072	−	630.985i	0.273579	−	1.02101i
$619$	524.800	+	524.800i	0.847819	+	0.847819i	0.989861	−	0.142041i	$-0.0453666\pi$
$619$	524.800	+	524.800i	0.847819	+	0.847819i	−0.142041	+	0.989861i	$0.545367\pi$
$620$	283.776	+	491.514i	0.457703	+	0.792765i
$621$	−779.468	−	450.026i	−1.25518	−	0.724680i
$622$	1592.82	−	426.794i	2.56080	−	0.686164i
$623$		−	118.719i		−	0.190560i
$624$		0			0
$625$	247.464			0.395943
$626$	−49.5922	−	185.081i	−0.0792208	−	0.295656i
$627$	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
$630$	−381.927	−	102.337i	−0.606233	−	0.162440i
$631$	−78.4079	+	292.622i	−0.124260	+	0.463744i	−0.999812	−	0.0193793i	$-0.993831\pi$
$631$	−78.4079	+	292.622i	−0.124260	+	0.463744i	0.875552	+	0.483123i	$0.160498\pi$
$632$	−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
$635$	−869.571	+	233.001i	−1.36940	+	0.366930i
$636$		−	638.749i		−	1.00432i
$637$		0			0
$638$	−534.562			−0.837871
$639$	−50.0963	−	186.962i	−0.0783980	−	0.292585i
$640$	790.388	−	1368.99i	1.23498	−	2.13905i
$641$	−802.665	+	463.419i	−1.25221	+	0.722962i	−0.971547	−	0.236845i	$-0.923887\pi$
$641$	−802.665	+	463.419i	−1.25221	+	0.722962i	−0.280660	+	0.959807i	$0.590553\pi$
$642$	−678.948	+	678.948i	−1.05755	+	1.05755i
$643$	−765.787	−	205.192i	−1.19096	−	0.319117i	−0.391695	−	0.920095i	$-0.628111\pi$
$643$	−765.787	−	205.192i	−1.19096	−	0.319117i	−0.799265	+	0.600978i	$0.794778\pi$
$644$	−172.579	+	644.075i	−0.267980	+	1.00012i
$645$	−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	0.868754	−	0.495243i	$-0.164921\pi$
$647$	565.632	+	326.568i	0.874238	+	0.504742i	0.00548379	+	0.999985i	$0.498254\pi$
$648$	108.425	−	29.0524i	0.167322	−	0.0448339i
$649$		−	123.790i		−	0.190739i
$650$		0			0
$651$	−76.2689			−0.117157
$652$	−266.288	−	993.801i	−0.408418	−	1.52423i
$653$	−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
$656$	−29.4586	−	7.89342i	−0.0449065	−	0.0120326i
$657$	−134.799	+	503.078i	−0.205174	+	0.765720i
$658$	−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
$661$	−697.517	+	186.899i	−1.05525	+	0.282752i	−0.744418	−	0.667714i	$-0.767273\pi$
$661$	−697.517	+	186.899i	−1.05525	+	0.282752i	−0.310828	+	0.950466i	$0.600606\pi$
$662$			1764.69i			2.66569i
$663$		0			0
$664$	367.869			0.554019
$665$	78.3836	+	292.532i	0.117870	+	0.439897i
$666$	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
$669$	364.603	+	97.6950i	0.544996	+	0.146031i
$670$	−112.548	+	420.035i	−0.167982	+	0.626918i
$671$	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	0.642334	−	0.766425i	$-0.277966\pi$
$673$	201.737	+	116.473i	0.299757	+	0.173065i	−0.342577	+	0.939490i	$0.611300\pi$
$674$	−1602.70	+	429.442i	−2.37789	+	0.637155i
$675$		−	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	$0.310552\pi$
$678$	−69.9423	−	261.028i	−0.103160	−	0.384998i
$679$	−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
$682$	−180.068	−	48.2490i	−0.264029	−	0.0707463i
$683$	−205.332	+	766.309i	−0.300632	+	1.12197i	0.636008	+	0.771682i	$0.280584\pi$
$683$	−205.332	+	766.309i	−0.300632	+	1.12197i	−0.936640	+	0.350293i	$0.886082\pi$
$684$	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
$687$	−21.9862	+	5.89120i	−0.0320033	+	0.00857525i
$688$		−	15.0150i		−	0.0218241i
$689$		0			0
$690$	−1635.74			−2.37064
$691$	−238.407	−	889.748i	−0.345018	−	1.28762i	−0.892592	−	0.450866i	$-0.851115\pi$
$691$	−238.407	−	889.748i	−0.345018	−	1.28762i	0.547574	−	0.836757i	$-0.315552\pi$
$692$	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
$695$	1758.78	+	471.264i	2.53062	+	0.678078i
$696$	−133.859	+	499.569i	−0.192326	+	0.717771i
$697$	−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
$700$	−720.100	+	192.950i	−1.02871	+	0.275643i
$701$			1256.17i			1.79197i	0.444079	+	0.895987i	$0.353531\pi$
$701$			1256.17i			1.79197i	−0.444079	+	0.895987i	$0.646469\pi$
$702$		0			0
$703$	−526.744			−0.749281
$704$	136.504	+	509.440i	0.193898	+	0.723636i
$705$	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
$708$	−308.544	−	82.6741i	−0.435797	−	0.116771i
$709$	−50.4214	+	188.175i	−0.0711162	+	0.265409i	−0.992325	−	0.123660i	$-0.960537\pi$
$709$	−50.4214	+	188.175i	−0.0711162	+	0.265409i	0.921208	+	0.389070i	$0.127203\pi$
$710$	−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
$713$	350.428	−	93.8970i	0.491484	−	0.131693i
$714$			217.507i			0.304632i
$715$		0			0
$716$	−1778.12			−2.48341
$717$	205.692	+	767.654i	0.286879	+	1.07065i
$718$	−768.110	+	1330.41i	−1.06979	+	1.85293i
$719$	−847.432	+	489.265i	−1.17863	+	0.680480i	−0.955696	−	0.294355i	$-0.904895\pi$
$719$	−847.432	+	489.265i	−1.17863	+	0.680480i	−0.222929	+	0.974835i	$0.571562\pi$
$720$	17.0946	−	17.0946i	0.0237425	−	0.0237425i
$721$	−312.900	−	83.8414i	−0.433981	−	0.116285i
$722$	−183.319	+	684.155i	−0.253904	+	0.947583i
$723$	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
$726$	607.075	−	162.665i	0.836192	−	0.224057i
$727$			470.571i			0.647278i	0.946181	+	0.323639i	$0.104906\pi$
$727$			470.571i			0.647278i	−0.946181	+	0.323639i	$0.895094\pi$
$728$		0			0
$729$	590.294			0.809731
$730$	703.028	+	2623.74i	0.963052	+	3.59416i
$731$	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	−0.779982	−	0.625802i	$-0.784772\pi$
$733$	−113.014	+	113.014i	−0.154181	+	0.154181i	0.625802	+	0.779982i	$0.284772\pi$
$734$	−155.708	−	41.7218i	−0.212136	−	0.0568417i
$735$	−157.870	+	589.177i	−0.214788	+	0.801601i
$736$	−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
$739$	−233.349	+	62.5256i	−0.315763	+	0.0846084i	−0.413220	−	0.910631i	$-0.635596\pi$
$739$	−233.349	+	62.5256i	−0.315763	+	0.0846084i	0.0974569	+	0.995240i	$0.468929\pi$
$740$		−	2207.10i		−	2.98257i
$741$		0			0
$742$	−514.738			−0.693716
$743$	−40.0554	−	149.489i	−0.0539103	−	0.201196i	0.933718	−	0.358010i	$-0.116545\pi$
$743$	−40.0554	−	149.489i	−0.0539103	−	0.201196i	−0.987628	+	0.156814i	$0.949878\pi$
$744$	−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
$747$	221.053	+	59.2309i	0.295921	+	0.0792918i
$748$	−84.6731	+	316.004i	−0.113199	+	0.422466i
$749$	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	−0.357289	−	0.933994i	$-0.616299\pi$
$751$	−1009.94	−	583.090i	−1.34480	−	0.776419i	−0.987507	+	0.157575i	$0.949632\pi$
$752$	56.9356	−	15.2559i	0.0757123	−	0.0202870i
$753$		−	35.6919i		−	0.0473996i
$754$		0			0
$755$	363.212			0.481076
$756$	−153.171	−	571.641i	−0.202607	−	0.756139i
$757$	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
$760$	691.785	+	185.363i	0.910243	+	0.243899i
$761$	248.434	−	927.170i	0.326458	−	1.21836i	−0.586381	−	0.810036i	$-0.699448\pi$
$761$	248.434	−	927.170i	0.326458	−	1.21836i	0.912838	−	0.408321i	$-0.133886\pi$
$762$	−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
$765$	364.670	−	97.7130i	0.476693	−	0.127729i
$766$		−	277.408i		−	0.362152i
$767$		0			0
$768$	489.153			0.636918
$769$	−292.755	−	1092.58i	−0.380695	−	1.42077i	−0.844842	−	0.535016i	$-0.820306\pi$
$769$	−292.755	−	1092.58i	−0.380695	−	1.42077i	0.464147	−	0.885758i	$-0.346361\pi$
$770$	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
$773$	399.515	+	107.050i	0.516837	+	0.138486i	0.507803	−	0.861473i	$-0.330458\pi$
$773$	399.515	+	107.050i	0.516837	+	0.138486i	0.00903396	+	0.999959i	$0.497124\pi$
$774$	−93.5062	+	348.970i	−0.120809	+	0.450866i
$775$	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
$778$	108.297	−	29.0181i	0.139199	−	0.0372983i
$779$		−	562.058i		−	0.721513i
$780$		0			0
$781$	204.039			0.261253
$782$	−267.780	−	999.367i	−0.342429	−	1.27796i
$783$	−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
$786$	−354.678	−	95.0358i	−0.451245	−	0.120911i
$787$	347.048	−	1295.20i	0.440975	−	1.64574i	−0.285373	−	0.958416i	$-0.592118\pi$
$787$	347.048	−	1295.20i	0.440975	−	1.64574i	0.726349	−	0.687326i	$-0.241216\pi$
$788$	−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
$791$	−129.442	+	34.6838i	−0.163643	+	0.0438481i
$792$		−	188.996i		−	0.238631i
$793$		0			0
$794$	−610.721			−0.769170
$795$	−201.111	−	750.557i	−0.252970	−	0.944097i
$796$	−855.226	+	1481.30i	−1.07440	+	1.86092i
$797$	1133.61	−	654.489i	1.42234	−	0.821191i	0.425845	−	0.904796i	$-0.359977\pi$
$797$	1133.61	−	654.489i	1.42234	−	0.821191i	0.996499	+	0.0836053i	$0.0266435\pi$
$798$	−181.505	+	181.505i	−0.227450	+	0.227450i
$799$	889.131	+	238.242i	1.11281	+	0.298175i
$800$	304.380	−	1135.96i	0.380475	−	1.41995i
$801$	−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
$804$	−219.075	+	58.7009i	−0.272481	+	0.0730110i
$805$			811.152i			1.00764i
$806$		0			0
$807$	242.337			0.300294
$808$	−47.6618	−	177.876i	−0.0589874	−	0.220144i
$809$	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	−0.144007	−	0.989577i	$-0.545999\pi$
$811$	685.757	−	685.757i	0.845570	−	0.845570i	0.989577	+	0.144007i	$0.0459987\pi$
$812$	660.720	+	177.039i	0.813694	+	0.218029i
$813$	−74.4004	+	277.666i	−0.0915134	+	0.341533i
$814$	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
$817$	267.289	−	71.6199i	0.327159	−	0.0876620i
$818$		−	1502.66i		−	1.83700i
$819$		0			0
$820$	2355.07			2.87204
$821$	−91.7762	−	342.513i	−0.111786	−	0.417191i	0.887241	−	0.461307i	$-0.152619\pi$
$821$	−91.7762	−	342.513i	−0.111786	−	0.417191i	−0.999026	+	0.0441166i	$0.985953\pi$
$822$	−104.227	+	180.526i	−0.126796	+	0.219618i
$823$	−761.836	+	439.846i	−0.925681	+	0.534442i	−0.885443	−	0.464748i	$-0.846145\pi$
$823$	−761.836	+	439.846i	−0.925681	+	0.534442i	−0.0402381	+	0.999190i	$0.512812\pi$
$824$	−541.683	+	541.683i	−0.657382	+	0.657382i
$825$	357.053	+	95.6721i	0.432792	+	0.115966i
$826$	−66.6232	+	248.641i	−0.0806576	+	0.301018i
$827$	496.734	+	496.734i	0.600645	+	0.600645i	0.940484	−	0.339838i	$-0.110372\pi$
$827$	496.734	+	496.734i	0.600645	+	0.600645i	−0.339838	+	0.940484i	$0.610372\pi$
$828$	490.479	+	849.535i	0.592366	+	1.02601i
$829$	−841.504	−	485.843i	−1.01508	−	0.586059i	−0.102408	−	0.994743i	$-0.532655\pi$
$829$	−841.504	−	485.843i	−1.01508	−	0.586059i	−0.912676	+	0.408684i	$0.865988\pi$
$830$	1152.87	−	308.911i	1.38900	−	0.372182i
$831$			1108.22i			1.33360i
$832$		0			0
$833$	−385.805			−0.463152
$834$	399.429	+	1490.69i	0.478931	+	1.78740i
$835$	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
$838$	−2162.68	−	579.488i	−2.58076	−	0.691514i
$839$	16.6003	−	61.9530i	0.0197858	−	0.0738415i	−0.955327	−	0.295551i	$-0.904497\pi$
$839$	16.6003	−	61.9530i	0.0197858	−	0.0738415i	0.975113	+	0.221709i	$0.0711636\pi$
$840$	−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
$843$	160.916	−	43.1173i	0.190885	−	0.0511475i
$844$			1020.46i			1.20907i
$845$		0			0
$846$	−1418.27			−1.67645
$847$	−80.6644	−	301.044i	−0.0952355	−	0.355424i
$848$	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
$851$	−1362.75	−	365.148i	−1.60135	−	0.429081i
$852$	136.269	−	508.563i	0.159940	−	0.596905i
$853$	−118.160	−	118.160i	−0.138523	−	0.138523i	0.634445	−	0.772968i	$-0.281229\pi$
$853$	−118.160	−	118.160i	−0.138523	−	0.138523i	−0.772968	+	0.634445i	$0.781229\pi$
$854$	−66.5102	−	115.199i	−0.0778808	−	0.134893i
$855$	385.849	+	222.770i	0.451285	+	0.260550i
$856$	1087.63	−	291.429i	1.27059	−	0.340454i
$857$		−	1001.36i		−	1.16845i	−0.811592	−	0.584225i	$-0.801399\pi$
$857$		−	1001.36i		−	1.16845i	0.811592	−	0.584225i	$-0.198601\pi$
$858$		0			0
$859$	−1088.25			−1.26688			−0.633438	−	0.773793i	$-0.718357\pi$
$859$	−1088.25			−1.26688			−0.633438	+	0.773793i	$0.718357\pi$
$860$	300.094	+	1119.96i	0.348946	+	1.30228i
$861$	−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	0.278082	−	0.960557i	$-0.410301\pi$
$863$	1068.95	−	1068.95i	1.23864	−	1.23864i	0.960557	−	0.278082i	$-0.0896989\pi$
$864$	901.767	+	241.628i	1.04371	+	0.279662i
$865$	77.9440	−	290.891i	0.0901086	−	0.336290i
$866$	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
$869$	461.162	−	123.568i	0.530681	−	0.142196i
$870$			1678.02i			1.92875i
$871$		0			0
$872$	1147.86			1.31635
$873$	51.7395	+	193.094i	0.0592663	+	0.221185i
$874$	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
$877$	827.023	+	221.600i	0.943014	+	0.252680i	0.697395	−	0.716687i	$-0.254342\pi$
$877$	827.023	+	221.600i	0.943014	+	0.252680i	0.245618	+	0.969367i	$0.421009\pi$
$878$	−196.050	+	731.668i	−0.223291	+	0.833335i
$879$	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	0.993176	−	0.116626i	$-0.0372080\pi$
$881$	1223.50	+	706.388i	1.38876	+	0.801802i	0.395587	+	0.918429i	$0.370541\pi$
$882$	574.182	−	153.852i	0.651000	−	0.174435i
$883$			249.675i			0.282757i	0.989956	+	0.141379i	$0.0451535\pi$
$883$			249.675i			0.282757i	−0.989956	+	0.141379i	$0.954847\pi$
$884$		0			0
$885$	−388.582			−0.439076
$886$	501.668	+	1872.25i	0.566217	+	2.11315i
$887$	−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
$890$	−879.846	−	235.754i	−0.988591	−	0.264892i
$891$	−19.0521	+	71.1035i	−0.0213829	+	0.0798019i
$892$	−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
$895$	−2089.37	+	559.845i	−2.33449	+	0.625525i
$896$		−	664.404i		−	0.741522i
$897$		0			0
$898$	1669.36			1.85897
$899$	−96.3235	−	359.484i	−0.107145	−	0.399871i
$900$	−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
$903$	−150.503	−	40.3273i	−0.166671	−	0.0446592i
$904$	−82.0210	+	306.107i	−0.0907312	+	0.338613i
$905$	−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	0.967843	−	0.251556i	$-0.0809424\pi$
$907$	1119.16	+	646.145i	1.23391	+	0.712398i	0.266067	+	0.963955i	$0.414276\pi$
$908$	−1381.03	+	370.046i	−1.52096	+	0.407540i
$909$		−	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	$0.519046\pi$
$912$	−4.06199	−	15.1595i	−0.00445393	−	0.0166223i
$913$	−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
$916$	68.7655	+	18.4257i	0.0750715	+	0.0201154i
$917$	−47.1275	+	175.882i	−0.0513931	+	0.191802i
$918$	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
$921$	322.141	−	86.3174i	0.349773	−	0.0937214i
$922$			1458.68i			1.58209i
$923$		0			0
$924$	217.393			0.235274
$925$	−408.249	−	1523.61i	−0.441350	−	1.64714i
$926$	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
$929$	531.264	+	142.352i	0.571866	+	0.153231i	0.533152	−	0.846019i	$-0.321007\pi$
$929$	531.264	+	142.352i	0.571866	+	0.153231i	0.0387140	+	0.999250i	$0.487674\pi$
$930$	−151.456	+	565.241i	−0.162856	+	0.607786i
$931$	−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
$934$	−1802.82	+	483.064i	−1.93021	+	0.517199i
$935$			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	$0.747043\pi$
$938$	47.3043	+	176.542i	0.0504310	+	0.188211i
$939$	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	−0.522655	−	0.852544i	$-0.675058\pi$
$941$	310.426	−	310.426i	0.329889	−	0.329889i	0.852544	+	0.522655i	$0.175058\pi$
$942$	−390.906	−	104.743i	−0.414975	−	0.111192i
$943$	389.629	−	1454.11i	0.413180	−	1.54201i
$944$	−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
$947$	−750.497	+	201.095i	−0.792499	+	0.212350i	−0.632288	−	0.774733i	$-0.717884\pi$
$947$	−750.497	+	201.095i	−0.792499	+	0.212350i	−0.160211	+	0.987083i	$0.551217\pi$
$948$		−	1231.97i		−	1.29954i
$949$		0			0
$950$	1365.11			1.43696
$951$	−86.8448	−	324.109i	−0.0913195	−	0.340809i
$952$	127.535	−	220.897i	0.133965	−	0.232034i
$953$	−147.254	+	85.0174i	−0.154517	+	0.0892102i	−0.575265	−	0.817967i	$-0.695101\pi$
$953$	−147.254	+	85.0174i	−0.154517	+	0.0892102i	0.420748	+	0.907178i	$0.361768\pi$
$954$	−535.462	+	535.462i	−0.561281	+	0.561281i
$955$	−2463.14	−	659.995i	−2.57920	−	0.691094i
$956$	643.336	−	2400.96i	0.672945	−	2.51147i
$957$	−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
$960$	1599.16	−	428.493i	1.66579	−	0.446347i
$961$			831.213i			0.864946i
$962$		0			0
$963$	700.481			0.727394
$964$	−568.908	−	2123.19i	−0.590153	−	2.20248i
$965$	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	−0.969913	−	0.243453i	$-0.921720\pi$
$967$	−702.486	+	702.486i	−0.726460	+	0.726460i	0.243453	+	0.969913i	$0.421720\pi$
$968$	−711.914	−	190.757i	−0.735448	−	0.197063i
$969$	63.4338	−	236.738i	0.0654631	−	0.244312i
$970$	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
$973$	739.220	−	198.073i	0.759733	−	0.203570i
$974$		−	2147.43i		−	2.20475i
$975$		0			0
$976$	8.13310			0.00833309
$977$	314.547	+	1173.90i	0.321951	+	1.20154i	0.917341	+	0.398102i	$0.130331\pi$
$977$	314.547	+	1173.90i	0.321951	+	1.20154i	−0.595390	+	0.803437i	$0.703002\pi$
$978$	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
$981$	689.750	+	184.818i	0.703110	+	0.188398i
$982$	−162.786	+	607.527i	−0.165770	+	0.618663i
$983$	−511.256	−	511.256i	−0.520098	−	0.520098i	0.397503	−	0.917601i	$-0.369877\pi$
$983$	−511.256	−	511.256i	−0.520098	−	0.520098i	−0.917601	+	0.397503i	$0.869877\pi$
$984$	374.209	+	648.150i	0.380294	+	0.658689i
$985$	−655.754	−	378.600i	−0.665740	−	0.384365i
$986$	−1025.19	+	274.700i	−1.03975	+	0.278600i
$987$		−	611.672i		−	0.619728i
$988$		0			0
$989$	741.158			0.749401
$990$	−158.706	−	592.298i	−0.160309	−	0.598281i
$991$	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
$994$	−409.827	−	109.813i	−0.412301	−	0.110476i
$995$	−538.539	+	2009.85i	−0.541245	+	2.01995i
$996$	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
$999$	1209.49	−	324.083i	1.21070	−	0.324407i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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