LMFDB - Embedded newform 867.2.h.m.688.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(688,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.688"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-120] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			688.10
Character	$\chi$	$=$	867.688
Dual form			867.2.h.m.712.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01764 - 1.01764i) q^{2} +(0.382683 - 0.923880i) q^{3} -0.0711653i q^{4} +(-2.13781 - 0.885508i) q^{5} +(-0.550741 - 1.32961i) q^{6} +(-4.10362 + 1.69978i) q^{7} +(1.96285 + 1.96285i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-3.07663 + 1.27438i) q^{10} +(1.73146 + 4.18012i) q^{11} +(-0.0657482 - 0.0272338i) q^{12} +1.17466i q^{13} +(-2.44624 + 5.90574i) q^{14} +(-1.63621 + 1.63621i) q^{15} +4.13727 q^{16} -1.43915 q^{18} +(-3.44089 + 3.44089i) q^{19} +(-0.0630175 + 0.152138i) q^{20} +4.44173i q^{21} +(6.01584 + 2.49184i) q^{22} +(-0.239329 - 0.577792i) q^{23} +(2.56459 - 1.06229i) q^{24} +(0.250554 + 0.250554i) q^{25} +(1.19538 + 1.19538i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(0.120965 + 0.292036i) q^{28} +(1.39535 + 0.577974i) q^{29} +3.33012i q^{30} +(-3.34309 + 8.07094i) q^{31} +(0.284528 - 0.284528i) q^{32} +4.52453 q^{33} +10.2779 q^{35} +(-0.0503215 + 0.0503215i) q^{36} +(3.36476 - 8.12325i) q^{37} +7.00315i q^{38} +(1.08524 + 0.449523i) q^{39} +(-2.45807 - 5.93431i) q^{40} +(-0.429571 + 0.177934i) q^{41} +(4.52006 + 4.52006i) q^{42} +(1.07004 + 1.07004i) q^{43} +(0.297480 - 0.123220i) q^{44} +(0.885508 + 2.13781i) q^{45} +(-0.831531 - 0.344432i) q^{46} +6.01904i q^{47} +(1.58326 - 3.82234i) q^{48} +(9.00072 - 9.00072i) q^{49} +0.509946 q^{50} +0.0835951 q^{52} +(-5.03689 + 5.03689i) q^{53} +(-0.550741 + 1.32961i) q^{54} -10.4695i q^{55} +(-11.3912 - 4.71839i) q^{56} +(1.86220 + 4.49574i) q^{57} +(2.00813 - 0.831794i) q^{58} +(-7.35565 - 7.35565i) q^{59} +(0.116441 + 0.116441i) q^{60} +(-2.36404 + 0.979219i) q^{61} +(4.81123 + 11.6153i) q^{62} +(4.10362 + 1.69978i) q^{63} +7.69544i q^{64} +(1.04017 - 2.51119i) q^{65} +(4.60432 - 4.60432i) q^{66} +3.71801 q^{67} -0.625397 q^{69} +(10.4592 - 10.4592i) q^{70} +(-5.83321 + 14.0826i) q^{71} -2.77589i q^{72} +(2.49619 + 1.03396i) q^{73} +(-4.84241 - 11.6906i) q^{74} +(0.327365 - 0.135599i) q^{75} +(0.244872 + 0.244872i) q^{76} +(-14.2105 - 14.2105i) q^{77} +(1.56183 - 0.646933i) q^{78} +(-6.38975 - 15.4262i) q^{79} +(-8.84467 - 3.66358i) q^{80} +1.00000i q^{81} +(-0.256075 + 0.618220i) q^{82} +(-3.14987 + 3.14987i) q^{83} +0.316097 q^{84} +2.17782 q^{86} +(1.06796 - 1.06796i) q^{87} +(-4.80635 + 11.6036i) q^{88} -1.54030i q^{89} +(3.07663 + 1.27438i) q^{90} +(-1.99666 - 4.82036i) q^{91} +(-0.0411187 + 0.0170319i) q^{92} +(6.17723 + 6.17723i) q^{93} +(6.12519 + 6.12519i) q^{94} +(10.4029 - 4.30902i) q^{95} +(-0.153985 - 0.371753i) q^{96} +(3.54665 + 1.46907i) q^{97} -18.3189i q^{98} +(1.73146 - 4.18012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 120 q^{16} + 24 q^{18} + 72 q^{33} - 96 q^{50} - 144 q^{52} + 48 q^{67} - 72 q^{69} + 120 q^{84} + 48 q^{86}+O(q^{100}) $ 48 * q - 120 * q^16 + 24 * q^18 + 72 * q^33 - 96 * q^50 - 144 * q^52 + 48 * q^67 - 72 * q^69 + 120 * q^84 + 48 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$	1.01764	−	1.01764i	0.719577	−	0.719577i	−0.248941	−	0.968519i	$-0.580083\pi$
$2$	1.01764	−	1.01764i	0.719577	−	0.719577i	0.968519	+	0.248941i	$0.0800826\pi$
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$4$		−	0.0711653i		−	0.0355827i
$5$	−2.13781	−	0.885508i	−0.956056	−	0.396011i	−0.150552	−	0.988602i	$-0.548105\pi$
$5$	−2.13781	−	0.885508i	−0.956056	−	0.396011i	−0.805504	+	0.592591i	$0.798105\pi$
$6$	−0.550741	−	1.32961i	−0.224839	−	0.542809i
$7$	−4.10362	+	1.69978i	−1.55102	+	0.642455i	−0.983501	−	0.180904i	$-0.942098\pi$
$7$	−4.10362	+	1.69978i	−1.55102	+	0.642455i	−0.567522	+	0.823358i	$0.692098\pi$
$8$	1.96285	+	1.96285i	0.693973	+	0.693973i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	−3.07663	+	1.27438i	−0.972917	+	0.402995i
$11$	1.73146	+	4.18012i	0.522055	+	1.26035i	0.936624	+	0.350335i	$0.113932\pi$
$11$	1.73146	+	4.18012i	0.522055	+	1.26035i	−0.414569	+	0.910018i	$0.636068\pi$
$12$	−0.0657482	−	0.0272338i	−0.0189799	−	0.00786172i
$13$			1.17466i			0.325792i	0.986643	+	0.162896i	$0.0520835\pi$
$13$			1.17466i			0.325792i	−0.986643	+	0.162896i	$0.947916\pi$
$14$	−2.44624	+	5.90574i	−0.653785	+	1.57838i
$15$	−1.63621	+	1.63621i	−0.422466	+	0.422466i
$16$	4.13727			1.03432
$17$		0			0
$17$		0			0
$18$	−1.43915			−0.339212
$19$	−3.44089	+	3.44089i	−0.789394	+	0.789394i	−0.981395	−	0.192001i	$-0.938502\pi$
$19$	−3.44089	+	3.44089i	−0.789394	+	0.789394i	0.192001	+	0.981395i	$0.438502\pi$
$20$	−0.0630175	+	0.152138i	−0.0140911	+	0.0340190i
$21$			4.44173i			0.969264i
$22$	6.01584	+	2.49184i	1.28258	+	0.531262i
$23$	−0.239329	−	0.577792i	−0.0499036	−	0.120478i	0.896962	−	0.442108i	$-0.145769\pi$
$23$	−0.239329	−	0.577792i	−0.0499036	−	0.120478i	−0.946865	+	0.321630i	$0.895769\pi$
$24$	2.56459	−	1.06229i	0.523494	−	0.216839i
$25$	0.250554	+	0.250554i	0.0501108	+	0.0501108i
$26$	1.19538	+	1.19538i	0.234432	+	0.234432i
$27$	−0.923880	+	0.382683i	−0.177801	+	0.0736475i
$28$	0.120965	+	0.292036i	0.0228603	+	0.0551895i
$29$	1.39535	+	0.577974i	0.259111	+	0.107327i	0.508457	−	0.861087i	$-0.330216\pi$
$29$	1.39535	+	0.577974i	0.259111	+	0.107327i	−0.249347	+	0.968414i	$0.580216\pi$
$30$			3.33012i			0.607994i
$31$	−3.34309	+	8.07094i	−0.600437	+	1.44958i	0.272695	+	0.962101i	$0.412085\pi$
$31$	−3.34309	+	8.07094i	−0.600437	+	1.44958i	−0.873132	+	0.487483i	$0.837915\pi$
$32$	0.284528	−	0.284528i	0.0502979	−	0.0502979i
$33$	4.52453			0.787619
$34$		0			0
$35$	10.2779			1.73728
$36$	−0.0503215	+	0.0503215i	−0.00838692	+	0.00838692i
$37$	3.36476	−	8.12325i	0.553163	−	1.33545i	−0.361928	−	0.932206i	$-0.617881\pi$
$37$	3.36476	−	8.12325i	0.553163	−	1.33545i	0.915091	−	0.403248i	$-0.132119\pi$
$38$			7.00315i			1.13606i
$39$	1.08524	+	0.449523i	0.173778	+	0.0719813i
$40$	−2.45807	−	5.93431i	−0.388656	−	0.938298i
$41$	−0.429571	+	0.177934i	−0.0670878	+	0.0277887i	−0.415975	−	0.909376i	$-0.636560\pi$
$41$	−0.429571	+	0.177934i	−0.0670878	+	0.0277887i	0.348887	+	0.937165i	$0.386560\pi$
$42$	4.52006	+	4.52006i	0.697460	+	0.697460i
$43$	1.07004	+	1.07004i	0.163180	+	0.163180i	0.783974	−	0.620794i	$-0.213190\pi$
$43$	1.07004	+	1.07004i	0.163180	+	0.163180i	−0.620794	+	0.783974i	$0.713190\pi$
$44$	0.297480	−	0.123220i	0.0448467	−	0.0185761i
$45$	0.885508	+	2.13781i	0.132004	+	0.318685i
$46$	−0.831531	−	0.344432i	−0.122603	−	0.0507837i
$47$			6.01904i			0.877968i	0.898495	+	0.438984i	$0.144661\pi$
$47$			6.01904i			0.877968i	−0.898495	+	0.438984i	$0.855339\pi$
$48$	1.58326	−	3.82234i	0.228524	−	0.551707i
$49$	9.00072	−	9.00072i	1.28582	−	1.28582i
$50$	0.509946			0.0721172
$51$		0			0
$52$	0.0835951			0.0115925
$53$	−5.03689	+	5.03689i	−0.691870	+	0.691870i	−0.962643	−	0.270773i	$-0.912721\pi$
$53$	−5.03689	+	5.03689i	−0.691870	+	0.691870i	0.270773	+	0.962643i	$0.412721\pi$
$54$	−0.550741	+	1.32961i	−0.0749463	+	0.180936i
$55$		−	10.4695i		−	1.41171i
$56$	−11.3912	−	4.71839i	−1.52221	−	0.630521i
$57$	1.86220	+	4.49574i	0.246654	+	0.595475i
$58$	2.00813	−	0.831794i	0.263680	−	0.109220i
$59$	−7.35565	−	7.35565i	−0.957624	−	0.957624i	0.0415136	−	0.999138i	$-0.486782\pi$
$59$	−7.35565	−	7.35565i	−0.957624	−	0.957624i	−0.999138	+	0.0415136i	$0.986782\pi$
$60$	0.116441	+	0.116441i	0.0150325	+	0.0150325i
$61$	−2.36404	+	0.979219i	−0.302685	+	0.125376i	−0.528856	−	0.848711i	$-0.677379\pi$
$61$	−2.36404	+	0.979219i	−0.302685	+	0.125376i	0.226172	+	0.974087i	$0.427379\pi$
$62$	4.81123	+	11.6153i	0.611027	+	1.47515i
$63$	4.10362	+	1.69978i	0.517008	+	0.214152i
$64$			7.69544i			0.961930i
$65$	1.04017	−	2.51119i	0.129017	−	0.311475i
$66$	4.60432	−	4.60432i	0.566753	−	0.566753i
$67$	3.71801			0.454227			0.227114	−	0.973868i	$-0.427071\pi$
$67$	3.71801			0.454227			0.227114	+	0.973868i	$0.427071\pi$
$68$		0			0
$69$	−0.625397			−0.0752890
$70$	10.4592	−	10.4592i	1.25011	−	1.25011i
$71$	−5.83321	+	14.0826i	−0.692274	+	1.67130i	0.0478729	+	0.998853i	$0.484756\pi$
$71$	−5.83321	+	14.0826i	−0.692274	+	1.67130i	−0.740147	+	0.672445i	$0.765244\pi$
$72$		−	2.77589i		−	0.327142i
$73$	2.49619	+	1.03396i	0.292157	+	0.121016i	0.523948	−	0.851750i	$-0.324459\pi$
$73$	2.49619	+	1.03396i	0.292157	+	0.121016i	−0.231791	+	0.972766i	$0.574459\pi$
$74$	−4.84241	−	11.6906i	−0.562919	−	1.35901i
$75$	0.327365	−	0.135599i	0.0378008	−	0.0156576i
$76$	0.244872	+	0.244872i	0.0280888	+	0.0280888i
$77$	−14.2105	−	14.2105i	−1.61944	−	1.61944i
$78$	1.56183	−	0.646933i	0.176843	−	0.0732507i
$79$	−6.38975	−	15.4262i	−0.718903	−	1.73558i	−0.676453	−	0.736486i	$-0.736484\pi$
$79$	−6.38975	−	15.4262i	−0.718903	−	1.73558i	−0.0424495	−	0.999099i	$-0.513516\pi$
$80$	−8.84467	−	3.66358i	−0.988864	−	0.409601i
$81$			1.00000i			0.111111i
$82$	−0.256075	+	0.618220i	−0.0282787	+	0.0682709i
$83$	−3.14987	+	3.14987i	−0.345743	+	0.345743i	−0.858521	−	0.512778i	$-0.828616\pi$
$83$	−3.14987	+	3.14987i	−0.345743	+	0.345743i	0.512778	+	0.858521i	$0.328616\pi$
$84$	0.316097			0.0344890
$85$		0			0
$86$	2.17782			0.234841
$87$	1.06796	−	1.06796i	0.114497	−	0.114497i
$88$	−4.80635	+	11.6036i	−0.512359	+	1.23694i
$89$		−	1.54030i		−	0.163272i	−0.996662	−	0.0816359i	$-0.973986\pi$
$89$		−	1.54030i		−	0.163272i	0.996662	−	0.0816359i	$-0.0260145\pi$
$90$	3.07663	+	1.27438i	0.324306	+	0.134332i
$91$	−1.99666	−	4.82036i	−0.209307	−	0.505311i
$92$	−0.0411187	+	0.0170319i	−0.00428693	+	0.00177570i
$93$	6.17723	+	6.17723i	0.640549	+	0.640549i
$94$	6.12519	+	6.12519i	0.631766	+	0.631766i
$95$	10.4029	−	4.30902i	1.06731	−	0.442096i
$96$	−0.153985	−	0.371753i	−0.0157161	−	0.0379419i
$97$	3.54665	+	1.46907i	0.360108	+	0.149161i	0.555399	−	0.831584i	$-0.312565\pi$
$97$	3.54665	+	1.46907i	0.360108	+	0.149161i	−0.195292	+	0.980745i	$0.562565\pi$
$98$		−	18.3189i		−	1.85049i
$99$	1.73146	−	4.18012i	0.174018	−	0.420118i
$100$	0.0178308	−	0.0178308i	0.00178308	−	0.00178308i
$101$	−11.9158			−1.18567			−0.592833	−	0.805325i	$-0.701991\pi$
$101$	−11.9158			−1.18567			−0.592833	+	0.805325i	$0.701991\pi$
$102$		0			0
$103$	−1.41240			−0.139168			−0.0695838	−	0.997576i	$-0.522167\pi$
$103$	−1.41240			−0.139168			−0.0695838	+	0.997576i	$0.522167\pi$
$104$	−2.30568	+	2.30568i	−0.226091	+	0.226091i
$105$	3.93318	−	9.49555i	0.383840	−	0.926671i
$106$			10.2514i			0.995708i
$107$	14.4624	+	5.99053i	1.39813	+	0.579126i	0.949267	−	0.314472i	$-0.101828\pi$
$107$	14.4624	+	5.99053i	1.39813	+	0.579126i	0.448867	+	0.893598i	$0.351828\pi$
$108$	0.0272338	+	0.0657482i	0.00262057	+	0.00632662i
$109$	9.37158	−	3.88184i	0.897635	−	0.371812i	0.114324	−	0.993443i	$-0.463530\pi$
$109$	9.37158	−	3.88184i	0.897635	−	0.371812i	0.783310	+	0.621631i	$0.213530\pi$
$110$	−10.6541	−	10.6541i	−1.01583	−	1.01583i
$111$	−6.21727	−	6.21727i	−0.590117	−	0.590117i
$112$	−16.9778	+	7.03242i	−1.60425	+	0.664501i
$113$	0.305672	+	0.737958i	0.0287552	+	0.0694212i	0.937605	−	0.347703i	$-0.113038\pi$
$113$	0.305672	+	0.737958i	0.0287552	+	0.0694212i	−0.908850	+	0.417124i	$0.863038\pi$
$114$	6.47006	+	2.67999i	0.605977	+	0.251004i
$115$			1.44713i			0.134946i
$116$	0.0411317	−	0.0993008i	0.00381899	−	0.00921985i
$117$	0.830610	−	0.830610i	0.0767899	−	0.0767899i
$118$	−14.9708			−1.37817
$119$		0			0
$120$	−6.42326			−0.586360
$121$	−6.69726	+	6.69726i	−0.608842	+	0.608842i
$122$	−1.40925	+	3.40222i	−0.127587	+	0.308023i
$123$			0.464965i			0.0419245i
$124$	0.574371	+	0.237912i	0.0515801	+	0.0213652i
$125$	4.11377	+	9.93152i	0.367947	+	0.888303i
$126$	5.90574	−	2.44624i	0.526125	−	0.217928i
$127$	2.38080	+	2.38080i	0.211262	+	0.211262i	0.804803	−	0.593542i	$-0.202271\pi$
$127$	2.38080	+	2.38080i	0.211262	+	0.211262i	−0.593542	+	0.804803i	$0.702271\pi$
$128$	8.40021	+	8.40021i	0.742481	+	0.742481i
$129$	1.39808	−	0.579102i	0.123094	−	0.0509871i
$130$	−1.49697	−	3.61400i	−0.131293	−	0.316968i
$131$	1.33007	+	0.550932i	0.116209	+	0.0481352i	0.440030	−	0.897983i	$-0.354968\pi$
$131$	1.33007	+	0.550932i	0.116209	+	0.0481352i	−0.323822	+	0.946118i	$0.604968\pi$
$132$		−	0.321990i		−	0.0280256i
$133$	8.27137	−	19.9688i	0.717218	−	1.73152i
$134$	3.78358	−	3.78358i	0.326852	−	0.326852i
$135$	2.31394			0.199153
$136$		0			0
$137$	7.86924			0.672315			0.336157	−	0.941806i	$-0.390873\pi$
$137$	7.86924			0.672315			0.336157	+	0.941806i	$0.390873\pi$
$138$	−0.636427	+	0.636427i	−0.0541762	+	0.0541762i
$139$	3.76095	−	9.07974i	0.319000	−	0.770133i	−0.680308	−	0.732926i	$-0.738154\pi$
$139$	3.76095	−	9.07974i	0.319000	−	0.770133i	0.999308	−	0.0372068i	$-0.0118460\pi$
$140$		−	0.731431i		−	0.0618172i
$141$	5.56087	+	2.30339i	0.468310	+	0.193980i
$142$	8.39489	+	20.2670i	0.704483	+	1.70077i
$143$	−4.91022	+	2.03388i	−0.410613	+	0.170081i
$144$	−2.92549	−	2.92549i	−0.243791	−	0.243791i
$145$	−2.47119	−	2.47119i	−0.205221	−	0.205221i
$146$	3.59241	−	1.48802i	0.297310	−	0.123150i
$147$	−4.87115	−	11.7600i	−0.401766	−	0.969949i
$148$	−0.578094	−	0.239454i	−0.0475190	−	0.0196830i
$149$		−	6.30050i		−	0.516157i	−0.966124	−	0.258078i	$-0.916911\pi$
$149$		−	6.30050i		−	0.516157i	0.966124	−	0.258078i	$-0.0830893\pi$
$150$	0.195148	−	0.471129i	0.0159338	−	0.0384675i
$151$	−7.65646	+	7.65646i	−0.623074	+	0.623074i	−0.946316	−	0.323243i	$-0.895227\pi$
$151$	−7.65646	+	7.65646i	−0.623074	+	0.623074i	0.323243	+	0.946316i	$0.395227\pi$
$152$	−13.5079			−1.09564
$153$		0			0
$154$	−28.9223			−2.33062
$155$	14.2938	−	14.2938i	1.14810	−	1.14810i
$156$	0.0319904	−	0.0772318i	0.00256129	−	0.00618349i
$157$		−	10.8250i		−	0.863933i	−0.901890	−	0.431966i	$-0.857820\pi$
$157$		−	10.8250i		−	0.863933i	0.901890	−	0.431966i	$-0.142180\pi$
$158$	−22.2007	−	9.19583i	−1.76619	−	0.731581i
$159$	2.72595	+	6.58102i	0.216182	+	0.521909i
$160$	−0.860217	+	0.356313i	−0.0680061	+	0.0281691i
$161$	1.96423	+	1.96423i	0.154803	+	0.154803i
$162$	1.01764	+	1.01764i	0.0799530	+	0.0799530i
$163$	10.4196	−	4.31595i	0.816129	−	0.338052i	0.0647322	−	0.997903i	$-0.479381\pi$
$163$	10.4196	−	4.31595i	0.816129	−	0.338052i	0.751396	+	0.659851i	$0.229381\pi$
$164$	0.0126628	+	0.0305706i	0.000988795	+	0.00238716i
$165$	−9.67256	−	4.00651i	−0.753008	−	0.311906i
$166$			6.41084i			0.497577i
$167$	−4.73261	+	11.4255i	−0.366220	+	0.884134i	0.628142	+	0.778099i	$0.283816\pi$
$167$	−4.73261	+	11.4255i	−0.366220	+	0.884134i	−0.994362	+	0.106035i	$0.966184\pi$
$168$	−8.71845	+	8.71845i	−0.672643	+	0.672643i
$169$	11.6202			0.893860
$170$		0			0
$171$	4.86615			0.372124
$172$	0.0761498	−	0.0761498i	0.00580637	−	0.00580637i
$173$	1.22359	−	2.95401i	0.0930279	−	0.224589i	−0.870516	−	0.492141i	$-0.836215\pi$
$173$	1.22359	−	2.95401i	0.0930279	−	0.224589i	0.963544	+	0.267551i	$0.0862145\pi$
$174$		−	2.17358i		−	0.164779i
$175$	−1.45407	−	0.602294i	−0.109917	−	0.0455291i
$176$	7.16352	+	17.2943i	0.539971	+	1.30360i
$177$	−9.61062	+	3.98085i	−0.722379	+	0.299219i
$178$	−1.56747	−	1.56747i	−0.117487	−	0.117487i
$179$	13.4446	+	13.4446i	1.00489	+	1.00489i	0.999988	+	0.00490576i	$0.00156156\pi$
$179$	13.4446	+	13.4446i	1.00489	+	1.00489i	0.00490576	+	0.999988i	$0.498438\pi$
$180$	0.152138	−	0.0630175i	0.0113397	−	0.00469705i
$181$	4.59970	+	11.1047i	0.341893	+	0.825402i	0.997524	+	0.0703214i	$0.0224025\pi$
$181$	4.59970	+	11.1047i	0.341893	+	0.825402i	−0.655632	+	0.755081i	$0.727598\pi$
$182$	−6.93724	−	2.87350i	−0.514222	−	0.212998i
$183$			2.55882i			0.189154i
$184$	0.664352	−	1.60389i	0.0489767	−	0.118240i
$185$	−14.3864	+	14.3864i	−1.05771	+	1.05771i
$186$	12.5723			0.921849
$187$		0			0
$188$	0.428347			0.0312404
$189$	3.14078	−	3.14078i	0.228458	−	0.228458i
$190$	6.20134	−	14.9714i	0.449893	−	1.08614i
$191$		−	22.3102i		−	1.61431i	−0.590341	−	0.807154i	$-0.701007\pi$
$191$		−	22.3102i		−	1.61431i	0.590341	−	0.807154i	$-0.298993\pi$
$192$	7.10966	+	2.94492i	0.513096	+	0.212531i
$193$	−1.33783	−	3.22980i	−0.0962989	−	0.232486i	0.868388	−	0.495885i	$-0.165156\pi$
$193$	−1.33783	−	3.22980i	−0.0962989	−	0.232486i	−0.964687	+	0.263399i	$0.915156\pi$
$194$	5.10418	−	2.11422i	0.366458	−	0.151792i
$195$	−1.92198	−	1.92198i	−0.137636	−	0.137636i
$196$	−0.640539	−	0.640539i	−0.0457528	−	0.0457528i
$197$	11.0840	−	4.59115i	0.789704	−	0.327106i	0.0488795	−	0.998805i	$-0.484435\pi$
$197$	11.0840	−	4.59115i	0.789704	−	0.327106i	0.740825	+	0.671699i	$0.234435\pi$
$198$	−2.49184	−	6.01584i	−0.177087	−	0.427527i
$199$	−3.71632	−	1.53935i	−0.263443	−	0.109122i	0.247053	−	0.969002i	$-0.420538\pi$
$199$	−3.71632	−	1.53935i	−0.263443	−	0.109122i	−0.510495	+	0.859881i	$0.670538\pi$
$200$			0.983601i			0.0695511i
$201$	1.42282	−	3.43499i	0.100358	−	0.242286i
$202$	−12.1259	+	12.1259i	−0.853179	+	0.853179i
$203$	−6.70843			−0.470839
$204$		0			0
$205$	1.07590			0.0751443
$206$	−1.43731	+	1.43731i	−0.100142	+	0.100142i
$207$	−0.239329	+	0.577792i	−0.0166345	+	0.0401593i
$208$			4.85988i			0.336972i
$209$	−20.3411	−	8.42556i	−1.40702	−	0.582808i
$210$	−5.66046	−	13.6656i	−0.390609	−	0.943013i
$211$	−14.7453	+	6.10770i	−1.01511	+	0.420471i	−0.827315	−	0.561738i	$-0.810133\pi$
$211$	−14.7453	+	6.10770i	−1.01511	+	0.420471i	−0.187792	+	0.982209i	$0.560133\pi$
$212$	0.358452	+	0.358452i	0.0246186	+	0.0246186i
$213$	10.7784	+	10.7784i	0.738521	+	0.738521i
$214$	20.8136	−	8.62129i	1.42279	−	0.589339i
$215$	−1.34001	−	3.23507i	−0.0913879	−	0.220630i
$216$	−2.56459	−	1.06229i	−0.174498	−	0.0722795i
$217$		−	38.8026i		−	2.63409i
$218$	5.58656	−	13.4872i	0.378370	−	0.913465i
$219$	1.91050	−	1.91050i	0.129100	−	0.129100i
$220$	−0.745066			−0.0502323
$221$		0			0
$222$	−12.6538			−0.849269
$223$	−3.78708	+	3.78708i	−0.253601	+	0.253601i	−0.822445	−	0.568844i	$-0.807391\pi$
$223$	−3.78708	+	3.78708i	−0.253601	+	0.253601i	0.568844	+	0.822445i	$0.307391\pi$
$224$	−0.683961	+	1.65123i	−0.0456991	+	0.110327i
$225$		−	0.354337i		−	0.0236225i
$226$	1.06204	+	0.439909i	0.0706455	+	0.0292623i
$227$	0.655438	+	1.58237i	0.0435029	+	0.105025i	0.944137	−	0.329552i	$-0.106898\pi$
$227$	0.655438	+	1.58237i	0.0435029	+	0.105025i	−0.900634	+	0.434577i	$0.856898\pi$
$228$	0.319941	−	0.132524i	0.0211886	−	0.00877660i
$229$	−0.269138	−	0.269138i	−0.0177852	−	0.0177852i	0.698158	−	0.715943i	$-0.254003\pi$
$229$	−0.269138	−	0.269138i	−0.0177852	−	0.0177852i	−0.715943	+	0.698158i	$0.754003\pi$
$230$	1.47266	+	1.47266i	0.0971040	+	0.0971040i
$231$	−18.5669	+	7.69068i	−1.22162	+	0.506010i
$232$	1.60439	+	3.87335i	0.105334	+	0.254298i
$233$	8.28055	+	3.42992i	0.542477	+	0.224701i	0.637058	−	0.770816i	$-0.280151\pi$
$233$	8.28055	+	3.42992i	0.542477	+	0.224701i	−0.0945809	+	0.995517i	$0.530151\pi$
$234$		−	1.69052i		−	0.110513i
$235$	5.32991	−	12.8675i	0.347685	−	0.839386i
$236$	−0.523468	+	0.523468i	−0.0340748	+	0.0340748i
$237$	−16.6972			−1.08460
$238$		0			0
$239$	−6.70928			−0.433987			−0.216994	−	0.976173i	$-0.569625\pi$
$239$	−6.70928			−0.433987			−0.216994	+	0.976173i	$0.569625\pi$
$240$	−6.76942	+	6.76942i	−0.436964	+	0.436964i
$241$	−3.38289	+	8.16701i	−0.217911	+	0.526083i	−0.994598	−	0.103803i	$-0.966899\pi$
$241$	−3.38289	+	8.16701i	−0.217911	+	0.526083i	0.776687	+	0.629887i	$0.216899\pi$
$242$			13.6307i			0.876218i
$243$	0.923880	+	0.382683i	0.0592669	+	0.0245492i
$244$	0.0696865	+	0.168238i	0.00446122	+	0.0107703i
$245$	−27.2120	+	11.2716i	−1.73851	+	0.720115i
$246$	0.473165	+	0.473165i	0.0301679	+	0.0301679i
$247$	−4.04187	−	4.04187i	−0.257178	−	0.257178i
$248$	−22.4041	+	9.28006i	−1.42266	+	0.589285i
$249$	1.70470	+	4.11550i	0.108031	+	0.260809i
$250$	14.2930	+	5.92035i	0.903968	+	0.374436i
$251$		−	24.4193i		−	1.54133i	−0.637238	−	0.770667i	$-0.719923\pi$
$251$		−	24.4193i		−	1.54133i	0.637238	−	0.770667i	$-0.280077\pi$
$252$	0.120965	−	0.292036i	0.00762008	−	0.0183965i
$253$	2.00085	−	2.00085i	0.125792	−	0.125792i
$254$	4.84557			0.304038
$255$		0			0
$256$	1.70583			0.106614
$257$	−18.3372	+	18.3372i	−1.14384	+	1.14384i	−0.156103	+	0.987741i	$0.549893\pi$
$257$	−18.3372	+	18.3372i	−1.14384	+	1.14384i	−0.987741	+	0.156103i	$0.950107\pi$
$258$	0.833417	−	2.01205i	0.0518863	−	0.125265i
$259$			39.0541i			2.42670i
$260$	−0.178710	−	0.0740241i	−0.0110831	−	0.00459078i
$261$	−0.577974	−	1.39535i	−0.0357757	−	0.0863702i
$262$	1.91417	−	0.792877i	0.118258	−	0.0489841i
$263$	1.23144	+	1.23144i	0.0759336	+	0.0759336i	0.744054	−	0.668120i	$-0.232901\pi$
$263$	1.23144	+	1.23144i	0.0759336	+	0.0759336i	−0.668120	+	0.744054i	$0.732901\pi$
$264$	8.88098	+	8.88098i	0.546586	+	0.546586i
$265$	15.2281	−	6.30769i	0.935455	−	0.387478i
$266$	−11.9038	−	28.7383i	−0.729867	−	1.76206i
$267$	−1.42305	−	0.589449i	−0.0870895	−	0.0360737i
$268$		−	0.264594i		−	0.0161626i
$269$	−12.0462	+	29.0821i	−0.734469	+	1.77317i	−0.107381	+	0.994218i	$0.534246\pi$
$269$	−12.0462	+	29.0821i	−0.734469	+	1.77317i	−0.627089	+	0.778948i	$0.715754\pi$
$270$	2.35475	−	2.35475i	0.143306	−	0.143306i
$271$	19.8066			1.20316			0.601582	−	0.798811i	$-0.294537\pi$
$271$	19.8066			1.20316			0.601582	+	0.798811i	$0.294537\pi$
$272$		0			0
$273$	−5.21752			−0.315779
$274$	8.00803	−	8.00803i	0.483783	−	0.483783i
$275$	−0.613521	+	1.48117i	−0.0369967	+	0.0893180i
$276$			0.0445066i			0.00267898i
$277$	−2.15332	−	0.891933i	−0.129380	−	0.0535911i	0.317054	−	0.948407i	$-0.397306\pi$
$277$	−2.15332	−	0.891933i	−0.129380	−	0.0535911i	−0.446434	+	0.894816i	$0.647306\pi$
$278$	−5.41259	−	13.0671i	−0.324625	−	0.783715i
$279$	8.07094	−	3.34309i	0.483195	−	0.200146i
$280$	20.1740	+	20.1740i	1.20563	+	1.20563i
$281$	−0.216479	−	0.216479i	−0.0129140	−	0.0129140i	0.700620	−	0.713534i	$-0.252907\pi$
$281$	−0.216479	−	0.216479i	−0.0129140	−	0.0129140i	−0.713534	+	0.700620i	$0.752907\pi$
$282$	8.00295	−	3.31493i	0.476569	−	0.197401i
$283$	−7.00854	−	16.9201i	−0.416615	−	1.00580i	−0.983321	−	0.181877i	$-0.941783\pi$
$283$	−7.00854	−	16.9201i	−0.416615	−	1.00580i	0.566707	−	0.823920i	$-0.308217\pi$
$284$	1.00219	+	0.415122i	0.0594693	+	0.0246330i
$285$		−	11.2600i		−	0.666985i
$286$	−2.92707	+	7.06656i	−0.173081	+	0.417855i
$287$	1.46035	−	1.46035i	0.0862017	−	0.0862017i
$288$	−0.402383			−0.0237106
$289$		0			0
$290$	−5.02955			−0.295345
$291$	2.71449	−	2.71449i	0.159126	−	0.159126i
$292$	0.0735819	−	0.177642i	0.00430606	−	0.0103957i
$293$		−	15.2652i		−	0.891801i	−0.895083	−	0.445900i	$-0.852884\pi$
$293$		−	15.2652i		−	0.891801i	0.895083	−	0.445900i	$-0.147116\pi$
$294$	−16.9245	−	7.01034i	−0.987055	−	0.408851i
$295$	9.21147	+	22.2384i	0.536312	+	1.29477i
$296$	22.5493	−	9.34021i	1.31065	−	0.542889i
$297$	−3.19932	−	3.19932i	−0.185644	−	0.185644i
$298$	−6.41161	−	6.41161i	−0.371415	−	0.371415i
$299$	0.678709	−	0.281130i	0.0392507	−	0.0162582i
$300$	−0.00964995	−	0.0232970i	−0.000557140	−	0.00134505i
$301$	−6.20987	−	2.57221i	−0.357931	−	0.148260i
$302$			15.5830i			0.896699i
$303$	−4.55998	+	11.0088i	−0.261964	+	0.632437i
$304$	−14.2359	+	14.2359i	−0.816484	+	0.816484i
$305$	5.92097			0.339034
$306$		0			0
$307$	29.9884			1.71153			0.855765	−	0.517365i	$-0.173087\pi$
$307$	29.9884			1.71153			0.855765	+	0.517365i	$0.173087\pi$
$308$	−1.01130	+	1.01130i	−0.0576240	+	0.0576240i
$309$	−0.540501	+	1.30488i	−0.0307480	+	0.0742323i
$310$		−	29.0917i		−	1.65230i
$311$	21.5491	+	8.92592i	1.22194	+	0.506143i	0.898025	−	0.439945i	$-0.145002\pi$
$311$	21.5491	+	8.92592i	1.22194	+	0.506143i	0.323911	+	0.946087i	$0.395002\pi$
$312$	1.24783	+	3.01252i	0.0706443	+	0.170550i
$313$	22.1332	−	9.16787i	1.25104	−	0.518198i	0.343893	−	0.939009i	$-0.388254\pi$
$313$	22.1332	−	9.16787i	1.25104	−	0.518198i	0.907149	+	0.420810i	$0.138254\pi$
$314$	−11.0160	−	11.0160i	−0.621666	−	0.621666i
$315$	−7.26758	−	7.26758i	−0.409482	−	0.409482i
$316$	−1.09781	+	0.454728i	−0.0617567	+	0.0255805i
$317$	7.18848	+	17.3545i	0.403746	+	0.974728i	0.986748	+	0.162258i	$0.0518776\pi$
$317$	7.18848	+	17.3545i	0.403746	+	0.974728i	−0.583003	+	0.812470i	$0.698122\pi$
$318$	9.47110	+	3.92306i	0.531113	+	0.219994i
$319$			6.83348i			0.382602i
$320$	6.81438	−	16.4514i	0.380935	−	0.919659i
$321$	11.0690	−	11.0690i	0.617814	−	0.617814i
$322$	3.99775			0.222786
$323$		0			0
$324$	0.0711653			0.00395363
$325$	−0.294316	+	0.294316i	−0.0163257	+	0.0163257i
$326$	6.21132	−	14.9955i	0.344013	−	0.830522i
$327$		−	10.1437i		−	0.560949i
$328$	−1.19244	−	0.493926i	−0.0658417	−	0.0272725i
$329$	−10.2310	−	24.6999i	−0.564054	−	1.36175i
$330$	−13.9203	+	5.76598i	−0.766288	+	0.317407i
$331$	16.7492	+	16.7492i	0.920618	+	0.920618i	0.997073	−	0.0764554i	$-0.0243603\pi$
$331$	16.7492	+	16.7492i	0.920618	+	0.920618i	−0.0764554	+	0.997073i	$0.524360\pi$
$332$	0.224161	+	0.224161i	0.0123025	+	0.0123025i
$333$	−8.12325	+	3.36476i	−0.445151	+	0.184388i
$334$	6.81096	+	16.4431i	0.372679	+	0.899727i
$335$	−7.94838	−	3.29233i	−0.434267	−	0.179879i
$336$			18.3766i			1.00253i
$337$	2.32316	−	5.60861i	0.126551	−	0.305521i	−0.847887	−	0.530176i	$-0.822126\pi$
$337$	2.32316	−	5.60861i	0.126551	−	0.305521i	0.974438	+	0.224656i	$0.0721257\pi$
$338$	11.8251	−	11.8251i	0.643201	−	0.643201i
$339$	0.798760			0.0433827
$340$		0			0
$341$	−39.5259			−2.14045
$342$	4.95197	−	4.95197i	0.267772	−	0.267772i
$343$	−9.73791	+	23.5094i	−0.525797	+	1.26939i
$344$			4.20066i			0.226484i
$345$	1.33698	+	0.553794i	0.0719805	+	0.0298153i
$346$	−1.76094	−	4.25128i	−0.0946685	−	0.228550i
$347$	−6.59194	+	2.73047i	−0.353874	+	0.146579i	−0.552537	−	0.833489i	$-0.686340\pi$
$347$	−6.59194	+	2.73047i	−0.353874	+	0.146579i	0.198663	+	0.980068i	$0.436340\pi$
$348$	−0.0760015	−	0.0760015i	−0.00407411	−	0.00407411i
$349$	−11.1599	−	11.1599i	−0.597377	−	0.597377i	0.342236	−	0.939614i	$-0.388816\pi$
$349$	−11.1599	−	11.1599i	−0.597377	−	0.597377i	−0.939614	+	0.342236i	$0.888816\pi$
$350$	−2.09262	+	0.866793i	−0.111855	+	0.0463321i
$351$	−0.449523	−	1.08524i	−0.0239938	−	0.0579260i
$352$	1.68201	+	0.696711i	0.0896514	+	0.0371348i
$353$			35.2308i			1.87515i	0.347788	+	0.937573i	$0.386933\pi$
$353$			35.2308i			1.87515i	−0.347788	+	0.937573i	$0.613067\pi$
$354$	−5.72906	+	13.8312i	−0.304496	+	0.735118i
$355$	24.9405	−	24.9405i	1.32371	−	1.32371i
$356$	−0.109616			−0.00580965
$357$		0			0
$358$	27.3633			1.44620
$359$	18.1950	−	18.1950i	0.960294	−	0.960294i	−0.0389472	−	0.999241i	$-0.512400\pi$
$359$	18.1950	−	18.1950i	0.960294	−	0.960294i	0.999241	+	0.0389472i	$0.0124004\pi$
$360$	−2.45807	+	5.93431i	−0.129552	+	0.312766i
$361$		−	4.67944i		−	0.246287i
$362$	15.9813	+	6.61968i	0.839959	+	0.347922i
$363$	3.62453	+	8.75039i	0.190239	+	0.459277i
$364$	−0.343042	+	0.142093i	−0.0179803	+	0.00744769i
$365$	−4.42080	−	4.42080i	−0.231395	−	0.231395i
$366$	2.60395	+	2.60395i	0.136111	+	0.136111i
$367$	7.63212	−	3.16133i	0.398394	−	0.165020i	−0.174486	−	0.984660i	$-0.555826\pi$
$367$	7.63212	−	3.16133i	0.398394	−	0.165020i	0.572879	+	0.819640i	$0.305826\pi$
$368$	−0.990168	−	2.39048i	−0.0516161	−	0.124612i
$369$	0.429571	+	0.177934i	0.0223626	+	0.00926289i
$370$			29.2802i			1.52221i
$371$	12.1079	−	29.2311i	0.628611	−	1.51760i
$372$	0.439605	−	0.439605i	0.0227924	−	0.0227924i
$373$	−23.4360			−1.21347			−0.606734	−	0.794905i	$-0.707521\pi$
$373$	−23.4360			−1.21347			−0.606734	+	0.794905i	$0.707521\pi$
$374$		0			0
$375$	10.7498			0.555117
$376$	−11.8145	+	11.8145i	−0.609286	+	0.609286i
$377$	−0.678923	+	1.63907i	−0.0349663	+	0.0844162i
$378$		−	6.39233i		−	0.328786i
$379$	−13.9155	−	5.76401i	−0.714794	−	0.296077i	−0.00450702	−	0.999990i	$-0.501435\pi$
$379$	−13.9155	−	5.76401i	−0.714794	−	0.296077i	−0.710287	+	0.703913i	$0.751435\pi$
$380$	−0.306653	−	0.740325i	−0.0157310	−	0.0379779i
$381$	3.11066	−	1.28848i	0.159364	−	0.0660108i
$382$	−22.7036	−	22.7036i	−1.16162	−	1.16162i
$383$	11.3123	+	11.3123i	0.578031	+	0.578031i	0.934360	−	0.356330i	$-0.115972\pi$
$383$	11.3123	+	11.3123i	0.578031	+	0.578031i	−0.356330	+	0.934360i	$0.615972\pi$
$384$	10.9754	−	4.54616i	0.560086	−	0.231995i
$385$	17.7958	+	42.9629i	0.906958	+	2.18959i
$386$	−4.64818	−	1.92534i	−0.236586	−	0.0979972i
$387$		−	1.51327i		−	0.0769236i
$388$	0.104547	−	0.252398i	0.00530756	−	0.0128136i
$389$	2.11419	−	2.11419i	0.107194	−	0.107194i	−0.651476	−	0.758669i	$-0.725850\pi$
$389$	2.11419	−	2.11419i	0.107194	−	0.107194i	0.758669	+	0.651476i	$0.225850\pi$
$390$	−3.91176			−0.198080
$391$		0			0
$392$	35.3341			1.78464
$393$	1.01799	−	1.01799i	0.0513508	−	0.0513508i
$394$	6.60738	−	15.9516i	0.332875	−	0.803631i
$395$			38.6364i			1.94401i
$396$	−0.297480	−	0.123220i	−0.0149489	−	0.00619204i
$397$	−4.84196	−	11.6895i	−0.243011	−	0.586681i	0.754568	−	0.656222i	$-0.227847\pi$
$397$	−4.84196	−	11.6895i	−0.243011	−	0.586681i	−0.997579	+	0.0695410i	$0.977847\pi$
$398$	−5.34835	+	2.21536i	−0.268089	+	0.111046i
$399$	−15.2835	−	15.2835i	−0.765132	−	0.765132i
$400$	1.03661	+	1.03661i	0.0518305	+	0.0518305i
$401$	−13.5523	+	5.61353i	−0.676767	+	0.280326i	−0.694475	−	0.719517i	$-0.744363\pi$
$401$	−13.5523	+	5.61353i	−0.676767	+	0.280326i	0.0177074	+	0.999843i	$0.494363\pi$
$402$	−2.04766	−	4.94349i	−0.102128	−	0.246559i
$403$	−9.48061	−	3.92700i	−0.472263	−	0.195618i
$404$			0.847992i			0.0421892i
$405$	0.885508	−	2.13781i	0.0440012	−	0.106228i
$406$	−6.82674	+	6.82674i	−0.338805	+	0.338805i
$407$	39.7821			1.97193
$408$		0			0
$409$	−16.3219			−0.807067			−0.403534	−	0.914965i	$-0.632218\pi$
$409$	−16.3219			−0.807067			−0.403534	+	0.914965i	$0.632218\pi$
$410$	1.09488	−	1.09488i	0.0540721	−	0.0540721i
$411$	3.01143	−	7.27023i	0.148543	−	0.358614i
$412$			0.100514i			0.00495196i
$413$	42.6878	+	17.6819i	2.10053	+	0.870067i
$414$	0.344432	+	0.831531i	0.0169279	+	0.0408675i
$415$	9.52304	−	3.94457i	0.467468	−	0.193631i
$416$	0.334223	+	0.334223i	0.0163866	+	0.0163866i
$417$	−6.94933	−	6.94933i	−0.340310	−	0.340310i
$418$	−29.2740	+	12.1257i	−1.43184	+	0.593086i
$419$	6.01187	+	14.5139i	0.293699	+	0.709053i	0.999999	+	0.00114011i	$0.000362907\pi$
$419$	6.01187	+	14.5139i	0.293699	+	0.709053i	−0.706300	+	0.707912i	$0.749637\pi$
$420$	−0.675754	−	0.279906i	−0.0329734	−	0.0136580i
$421$			22.1035i			1.07726i	0.842542	+	0.538630i	$0.181058\pi$
$421$			22.1035i			1.07726i	−0.842542	+	0.538630i	$0.818942\pi$
$422$	−8.78992	+	21.2207i	−0.427886	+	1.03301i
$423$	4.25611	−	4.25611i	0.206939	−	0.206939i
$424$	−19.7733			−0.960278
$425$		0			0
$426$	21.9369			1.06285
$427$	8.03669	−	8.03669i	0.388923	−	0.388923i
$428$	0.426318	−	1.02922i	0.0206069	−	0.0497493i
$429$			5.31478i			0.256600i
$430$	−4.65576	−	1.92848i	−0.224521	−	0.0929996i
$431$	1.59016	+	3.83898i	0.0765952	+	0.184917i	0.957539	−	0.288304i	$-0.0930913\pi$
$431$	1.59016	+	3.83898i	0.0765952	+	0.184917i	−0.880944	+	0.473221i	$0.843091\pi$
$432$	−3.82234	+	1.58326i	−0.183902	+	0.0761748i
$433$	−9.24653	−	9.24653i	−0.444360	−	0.444360i	0.449114	−	0.893474i	$-0.351740\pi$
$433$	−9.24653	−	9.24653i	−0.444360	−	0.444360i	−0.893474	+	0.449114i	$0.851740\pi$
$434$	−39.4869	−	39.4869i	−1.89543	−	1.89543i
$435$	−3.22877	+	1.33740i	−0.154808	+	0.0641234i
$436$	−0.276252	−	0.666932i	−0.0132301	−	0.0319402i
$437$	2.81162	+	1.16461i	0.134498	+	0.0557110i
$438$		−	3.88839i		−	0.185795i
$439$	−4.43676	+	10.7113i	−0.211755	+	0.511222i	−0.993693	−	0.112134i	$-0.964231\pi$
$439$	−4.43676	+	10.7113i	−0.211755	+	0.511222i	0.781938	+	0.623356i	$0.214231\pi$
$440$	20.5501	−	20.5501i	0.979687	−	0.979687i
$441$	−12.7289			−0.606140
$442$		0			0
$443$	17.6619			0.839144			0.419572	−	0.907722i	$-0.362180\pi$
$443$	17.6619			0.839144			0.419572	+	0.907722i	$0.362180\pi$
$444$	−0.442454	+	0.442454i	−0.0209979	+	0.0209979i
$445$	−1.36395	+	3.29287i	−0.0646575	+	0.156097i
$446$			7.70773i			0.364971i
$447$	−5.82090	−	2.41110i	−0.275319	−	0.114041i
$448$	−13.0805	−	31.5792i	−0.617996	−	1.49198i
$449$	32.4665	−	13.4480i	1.53219	−	0.634652i	0.552199	−	0.833712i	$-0.313789\pi$
$449$	32.4665	−	13.4480i	1.53219	−	0.634652i	0.979987	+	0.199060i	$0.0637888\pi$
$450$	−0.360586	−	0.360586i	−0.0169982	−	0.0169982i
$451$	−1.48757	−	1.48757i	−0.0700471	−	0.0700471i
$452$	0.0525170	−	0.0217533i	0.00247019	−	0.00102319i
$453$	4.14364	+	10.0036i	0.194685	+	0.470012i
$454$	2.27727	+	0.943276i	0.106878	+	0.0442701i
$455$			12.0730i			0.565993i
$456$	−5.16925	+	12.4797i	−0.242072	+	0.584415i
$457$	17.4165	−	17.4165i	0.814708	−	0.814708i	−0.170628	−	0.985336i	$-0.554580\pi$
$457$	17.4165	−	17.4165i	0.814708	−	0.814708i	0.985336	+	0.170628i	$0.0545795\pi$
$458$	−0.547769			−0.0255956
$459$		0			0
$460$	0.102986			0.00480174
$461$	0.710025	−	0.710025i	0.0330691	−	0.0330691i	−0.690379	−	0.723448i	$-0.742556\pi$
$461$	0.710025	−	0.710025i	0.0330691	−	0.0330691i	0.723448	+	0.690379i	$0.242556\pi$
$462$	−11.0681	+	26.7207i	−0.514934	+	1.24316i
$463$			20.4600i			0.950856i	0.879755	+	0.475428i	$0.157707\pi$
$463$			20.4600i			0.950856i	−0.879755	+	0.475428i	$0.842293\pi$
$464$	5.77295	+	2.39123i	0.268002	+	0.111010i
$465$	−7.73573	−	18.6757i	−0.358736	−	0.866065i
$466$	11.9170	−	4.93618i	0.552044	−	0.228664i
$467$	24.8661	+	24.8661i	1.15066	+	1.15066i	0.986420	+	0.164244i	$0.0525186\pi$
$467$	24.8661	+	24.8661i	1.15066	+	1.15066i	0.164244	+	0.986420i	$0.447481\pi$
$468$	−0.0591106	−	0.0591106i	−0.00273239	−	0.00273239i
$469$	−15.2573	+	6.31978i	−0.704517	+	0.291820i
$470$	−7.67057	−	18.5184i	−0.353817	−	0.854189i
$471$	−10.0010	−	4.14257i	−0.460824	−	0.190879i
$472$		−	28.8761i		−	1.32913i
$473$	−2.62016	+	6.32563i	−0.120475	+	0.290853i
$474$	−16.9917	+	16.9917i	−0.780454	+	0.780454i
$475$	−1.72426			−0.0791144
$476$		0			0
$477$	7.12324			0.326151
$478$	−6.82761	+	6.82761i	−0.312287	+	0.312287i
$479$	−1.47609	+	3.56359i	−0.0674442	+	0.162825i	−0.954008	−	0.299782i	$-0.903086\pi$
$479$	−1.47609	+	3.56359i	−0.0674442	+	0.162825i	0.886563	+	0.462607i	$0.153086\pi$
$480$			0.931092i			0.0424983i
$481$	9.54205	+	3.95245i	0.435080	+	0.180216i
$482$	4.86849	+	11.7536i	0.221754	+	0.535361i
$483$	2.56639	−	1.06303i	0.116775	−	0.0483698i
$484$	0.476613	+	0.476613i	0.0216642	+	0.0216642i
$485$	−6.28117	−	6.28117i	−0.285213	−	0.285213i
$486$	1.32961	−	0.550741i	0.0603121	−	0.0249821i
$487$	−7.79484	−	18.8184i	−0.353218	−	0.852744i	−0.996219	−	0.0868783i	$-0.972311\pi$
$487$	−7.79484	−	18.8184i	−0.353218	−	0.852744i	0.643001	−	0.765865i	$-0.277689\pi$
$488$	−6.56233	−	2.71821i	−0.297063	−	0.123047i
$489$		−	11.2781i		−	0.510015i
$490$	−16.2215	+	39.1623i	−0.732814	+	1.76917i
$491$	−4.51612	+	4.51612i	−0.203810	+	0.203810i	−0.801630	−	0.597820i	$-0.796034\pi$
$491$	−4.51612	+	4.51612i	−0.203810	+	0.203810i	0.597820	+	0.801630i	$0.296034\pi$
$492$	0.0330894			0.00149178
$493$		0			0
$494$	−8.22631			−0.370119
$495$	−7.40306	+	7.40306i	−0.332743	+	0.332743i
$496$	−13.8313	+	33.3916i	−0.621042	+	1.49933i
$497$		−	67.7048i		−	3.03698i
$498$	5.92284	+	2.45332i	0.265409	+	0.109936i
$499$	0.629073	+	1.51872i	0.0281612	+	0.0679871i	0.937335	−	0.348431i	$-0.113285\pi$
$499$	0.629073	+	1.51872i	0.0281612	+	0.0679871i	−0.909173	+	0.416418i	$0.863285\pi$
$500$	0.706780	−	0.292758i	0.0316082	−	0.0130925i
$501$	8.74472	+	8.74472i	0.390685	+	0.390685i
$502$	−24.8500	−	24.8500i	−1.10911	−	1.10911i
$503$	−24.5863	+	10.1840i	−1.09625	+	0.454080i	−0.856181	−	0.516676i	$-0.827169\pi$
$503$	−24.5863	+	10.1840i	−1.09625	+	0.454080i	−0.240066	+	0.970757i	$0.577169\pi$
$504$	4.71839	+	11.3912i	0.210174	+	0.507404i
$505$	25.4737	+	10.5515i	1.13356	+	0.469537i
$506$		−	4.07227i		−	0.181035i
$507$	4.44685	−	10.7356i	0.197491	−	0.476787i
$508$	0.169430	−	0.169430i	0.00751726	−	0.00751726i
$509$	−14.0065			−0.620827			−0.310413	−	0.950602i	$-0.600467\pi$
$509$	−14.0065			−0.620827			−0.310413	+	0.950602i	$0.600467\pi$
$510$		0			0
$511$	−12.0009			−0.530890
$512$	−15.0645	+	15.0645i	−0.665764	+	0.665764i
$513$	1.86220	−	4.49574i	0.0822180	−	0.198492i
$514$			37.3212i			1.64617i
$515$	3.01943	+	1.25069i	0.133052	+	0.0551120i
$516$	−0.0412120	−	0.0994945i	−0.00181426	−	0.00438000i
$517$	−25.1603	+	10.4217i	−1.10655	+	0.458348i
$518$	39.7428	+	39.7428i	1.74620	+	1.74620i
$519$	−2.26090	−	2.26090i	−0.0992426	−	0.0992426i
$520$	6.97080	−	2.88740i	0.305690	−	0.126621i
$521$	−7.25624	−	17.5181i	−0.317901	−	0.767482i	−0.999365	−	0.0356300i	$-0.988656\pi$
$521$	−7.25624	−	17.5181i	−0.317901	−	0.767482i	0.681464	−	0.731852i	$-0.261344\pi$
$522$	−2.00813	−	0.831794i	−0.0878934	−	0.0364066i
$523$			20.3838i			0.891320i	0.895202	+	0.445660i	$0.147031\pi$
$523$			20.3838i			0.891320i	−0.895202	+	0.445660i	$0.852969\pi$
$524$	0.0392073	−	0.0946548i	0.00171278	−	0.00413501i
$525$	−1.11289	+	1.11289i	−0.0485706	+	0.0485706i
$526$	2.50631			0.109280
$527$		0			0
$528$	18.7192			0.814648
$529$	15.9869	−	15.9869i	0.695082	−	0.695082i
$530$	9.07774	−	21.9156i	0.394312	−	0.951952i
$531$			10.4025i			0.451428i
$532$	−1.42109	−	0.588635i	−0.0616121	−	0.0255205i
$533$	−0.209012	−	0.504600i	−0.00905333	−	0.0218567i
$534$	−2.04800	+	0.848308i	−0.0886254	+	0.0367099i
$535$	−25.6132	−	25.6132i	−1.10735	−	1.10735i
$536$	7.29790	+	7.29790i	0.315221	+	0.315221i
$537$	17.5662	−	7.27614i	0.758036	−	0.313989i
$538$	17.3363	+	41.8536i	0.747422	+	1.80444i
$539$	53.2085	+	22.0397i	2.29185	+	0.949316i
$540$		−	0.164673i		−	0.00708638i
$541$	−8.62619	+	20.8255i	−0.370869	+	0.895356i	0.622735	+	0.782433i	$0.286021\pi$
$541$	−8.62619	+	20.8255i	−0.370869	+	0.895356i	−0.993604	+	0.112923i	$0.963979\pi$
$542$	20.1559	−	20.1559i	0.865769	−	0.865769i
$543$	12.0196			0.515810
$544$		0			0
$545$	−23.4720			−1.00543
$546$	−5.30953	+	5.30953i	−0.227227	+	0.227227i
$547$	−1.26565	+	3.05554i	−0.0541152	+	0.130646i	−0.948625	−	0.316403i	$-0.897525\pi$
$547$	−1.26565	+	3.05554i	−0.0541152	+	0.130646i	0.894510	+	0.447049i	$0.147525\pi$
$548$		−	0.560018i		−	0.0239228i
$549$	2.36404	+	0.979219i	0.100895	+	0.0417920i
$550$	0.882952	+	2.13163i	0.0376492	+	0.0908932i
$551$	−6.79000	+	2.81251i	−0.289264	+	0.119817i
$552$	−1.22756	−	1.22756i	−0.0522485	−	0.0522485i
$553$	52.4422	+	52.4422i	2.23007	+	2.23007i
$554$	−3.09895	+	1.28363i	−0.131662	+	0.0545362i
$555$	7.78587	+	18.7967i	0.330492	+	0.797877i
$556$	−0.646163	−	0.267649i	−0.0274034	−	0.0113509i
$557$			34.4355i			1.45908i	0.683938	+	0.729540i	$0.260266\pi$
$557$			34.4355i			1.45908i	−0.683938	+	0.729540i	$0.739734\pi$
$558$	4.81123	−	11.6153i	0.203676	−	0.491716i
$559$	−1.25693	+	1.25693i	−0.0531626	+	0.0531626i
$560$	42.5224			1.79690
$561$		0			0
$562$	−0.440593			−0.0185853
$563$	3.32673	−	3.32673i	0.140205	−	0.140205i	−0.633521	−	0.773726i	$-0.718391\pi$
$563$	3.32673	−	3.32673i	0.140205	−	0.140205i	0.773726	+	0.633521i	$0.218391\pi$
$564$	0.163921	−	0.395741i	0.00690234	−	0.0166637i
$565$		−	1.84829i		−	0.0777580i
$566$	−24.3507	−	10.0864i	−1.02353	−	0.423962i
$567$	−1.69978	−	4.10362i	−0.0713839	−	0.172336i
$568$	−39.0918	+	16.1923i	−1.64025	+	0.679416i
$569$	26.3569	+	26.3569i	1.10494	+	1.10494i	0.993806	+	0.111131i	$0.0354473\pi$
$569$	26.3569	+	26.3569i	1.10494	+	1.10494i	0.111131	+	0.993806i	$0.464553\pi$
$570$	−11.4586	−	11.4586i	−0.479947	−	0.479947i
$571$	−18.7661	+	7.77318i	−0.785337	+	0.325297i	−0.739067	−	0.673632i	$-0.764733\pi$
$571$	−18.7661	+	7.77318i	−0.785337	+	0.325297i	−0.0462700	+	0.998929i	$0.514733\pi$
$572$	0.144742	+	0.349437i	0.00605195	+	0.0146107i
$573$	−20.6119	−	8.53774i	−0.861075	−	0.356669i
$574$		−	2.97221i		−	0.124058i
$575$	0.0848032	−	0.204733i	0.00353654	−	0.00853796i
$576$	5.44150	−	5.44150i	0.226729	−	0.226729i
$577$	33.5408			1.39632			0.698161	−	0.715941i	$-0.254002\pi$
$577$	33.5408			1.39632			0.698161	+	0.715941i	$0.254002\pi$
$578$		0			0
$579$	−3.49591			−0.145285
$580$	−0.175863	+	0.175863i	−0.00730233	+	0.00730233i
$581$	7.57179	−	18.2799i	0.314131	−	0.758379i
$582$		−	5.52472i		−	0.229007i
$583$	−29.7760	−	12.3336i	−1.23320	−	0.510806i
$584$	2.87015	+	6.92916i	0.118768	+	0.286731i
$585$	−2.51119	+	1.04017i	−0.103825	+	0.0430058i
$586$	−15.5344	−	15.5344i	−0.641719	−	0.641719i
$587$	15.4407	+	15.4407i	0.637304	+	0.637304i	0.949890	−	0.312585i	$-0.101195\pi$
$587$	15.4407	+	15.4407i	0.637304	+	0.637304i	−0.312585	+	0.949890i	$0.601195\pi$
$588$	−0.836905	+	0.346657i	−0.0345134	+	0.0142959i
$589$	−16.2680	−	39.2744i	−0.670311	−	1.61828i
$590$	32.0046	+	13.2567i	1.31761	+	0.545771i
$591$		−	11.9973i		−	0.493501i
$592$	13.9209	−	33.6080i	0.572146	−	1.38128i
$593$	−17.3995	+	17.3995i	−0.714511	+	0.714511i	−0.967476	−	0.252965i	$-0.918594\pi$
$593$	−17.3995	+	17.3995i	−0.714511	+	0.714511i	0.252965	+	0.967476i	$0.418594\pi$
$594$	−6.51150			−0.267170
$595$		0			0
$596$	−0.448377			−0.0183662
$597$	−2.84435	+	2.84435i	−0.116411	+	0.116411i
$598$	0.404590	−	0.976767i	0.0165449	−	0.0399430i
$599$			40.9057i			1.67136i	0.549215	+	0.835681i	$0.314927\pi$
$599$			40.9057i			1.67136i	−0.549215	+	0.835681i	$0.685073\pi$
$600$	0.908729	+	0.376408i	0.0370987	+	0.0153668i
$601$	−14.1040	−	34.0500i	−0.575313	−	1.38893i	−0.896978	−	0.442074i	$-0.854243\pi$
$601$	−14.1040	−	34.0500i	−0.575313	−	1.38893i	0.321666	−	0.946853i	$-0.395757\pi$
$602$	−8.93696	+	3.70181i	−0.364243	+	0.150875i
$603$	−2.62903	−	2.62903i	−0.107062	−	0.107062i
$604$	0.544874	+	0.544874i	0.0221706	+	0.0221706i
$605$	20.2479	−	8.38696i	0.823195	−	0.340979i
$606$	6.56251	+	15.8433i	0.266584	+	0.643591i
$607$	−44.5665	−	18.4600i	−1.80890	−	0.749270i	−0.982521	−	0.186150i	$-0.940399\pi$
$607$	−44.5665	−	18.4600i	−1.80890	−	0.749270i	−0.826375	−	0.563120i	$-0.809601\pi$
$608$			1.95806i			0.0794097i
$609$	−2.56720	+	6.19778i	−0.104028	+	0.251147i
$610$	6.02539	−	6.02539i	0.243961	−	0.243961i
$611$	−7.07033			−0.286035
$612$		0			0
$613$	26.2900			1.06184			0.530922	−	0.847421i	$-0.321846\pi$
$613$	26.2900			1.06184			0.530922	+	0.847421i	$0.321846\pi$
$614$	30.5173	−	30.5173i	1.23158	−	1.23158i
$615$	0.411730	−	0.994004i	0.0166026	−	0.0400821i
$616$		−	55.7863i		−	2.24769i
$617$	−3.61492	−	1.49735i	−0.145531	−	0.0602810i	0.308729	−	0.951150i	$-0.400096\pi$
$617$	−3.61492	−	1.49735i	−0.145531	−	0.0602810i	−0.454260	+	0.890869i	$0.650096\pi$
$618$	0.777864	+	1.87793i	0.0312903	+	0.0755415i
$619$	7.85884	−	3.25524i	0.315873	−	0.130839i	−0.219114	−	0.975699i	$-0.570317\pi$
$619$	7.85884	−	3.25524i	0.315873	−	0.130839i	0.534987	+	0.844860i	$0.320317\pi$
$620$	−1.01722	−	1.01722i	−0.0408526	−	0.0408526i
$621$	0.442223	+	0.442223i	0.0177458	+	0.0177458i
$622$	31.0125	−	12.8458i	1.24349	−	0.515069i
$623$	2.61817	+	6.32082i	0.104895	+	0.253238i
$624$	4.48994	+	1.85980i	0.179742	+	0.0744514i
$625$		−	26.6461i		−	1.06585i
$626$	13.1940	−	31.8531i	0.527337	−	1.27310i
$627$	−15.5684	+	15.5684i	−0.621742	+	0.621742i
$628$	−0.770368			−0.0307410
$629$		0			0
$630$	−14.7915			−0.589307
$631$	5.13631	−	5.13631i	0.204473	−	0.204473i	−0.597440	−	0.801913i	$-0.703815\pi$
$631$	5.13631	−	5.13631i	0.204473	−	0.204473i	0.801913	+	0.597440i	$0.203815\pi$
$632$	17.7372	−	42.8215i	0.705549	−	1.70335i
$633$			15.9602i			0.634360i
$634$	24.9759	+	10.3453i	0.991918	+	0.410866i
$635$	−2.98147	−	7.19790i	−0.118316	−	0.285640i
$636$	0.468340	−	0.193993i	0.0185709	−	0.00769232i
$637$	10.5728	+	10.5728i	0.418909	+	0.418909i
$638$	6.95400	+	6.95400i	0.275311	+	0.275311i
$639$	14.0826	−	5.83321i	0.557099	−	0.230758i
$640$	−10.5196	−	25.3965i	−0.415822	−	1.00388i
$641$	−35.6808	−	14.7795i	−1.40931	−	0.583755i	−0.457158	−	0.889385i	$-0.651133\pi$
$641$	−35.6808	−	14.7795i	−1.40931	−	0.583755i	−0.952150	+	0.305631i	$0.901133\pi$
$642$		−	22.5285i		−	0.889130i
$643$	−12.1073	+	29.2295i	−0.477464	+	1.15270i	0.483331	+	0.875438i	$0.339427\pi$
$643$	−12.1073	+	29.2295i	−0.477464	+	1.15270i	−0.960795	+	0.277261i	$0.910573\pi$
$644$	0.139785	−	0.139785i	0.00550831	−	0.00550831i
$645$	−3.50161			−0.137876
$646$		0			0
$647$	2.64576			0.104016			0.0520078	−	0.998647i	$-0.483438\pi$
$647$	2.64576			0.104016			0.0520078	+	0.998647i	$0.483438\pi$
$648$	−1.96285	+	1.96285i	−0.0771081	+	0.0771081i
$649$	18.0115	−	43.4835i	0.707012	−	1.70688i
$650$			0.599013i			0.0234952i
$651$	−35.8489	−	14.8491i	−1.40503	−	0.581982i
$652$	−0.307146	−	0.741517i	−0.0120288	−	0.0290400i
$653$	32.4620	−	13.4462i	1.27034	−	0.526191i	0.357271	−	0.934001i	$-0.383707\pi$
$653$	32.4620	−	13.4462i	1.27034	−	0.526191i	0.913067	+	0.407810i	$0.133707\pi$
$654$	−10.3226	−	10.3226i	−0.403646	−	0.403646i
$655$	−2.35557	−	2.35557i	−0.0920398	−	0.0920398i
$656$	−1.77725	+	0.736162i	−0.0693900	+	0.0287423i
$657$	−1.03396	−	2.49619i	−0.0403385	−	0.0973858i
$658$	−35.5469	−	14.7240i	−1.38576	−	0.574002i
$659$			23.7941i			0.926888i	0.886126	+	0.463444i	$0.153387\pi$
$659$			23.7941i			0.926888i	−0.886126	+	0.463444i	$0.846613\pi$
$660$	−0.285124	+	0.688351i	−0.0110985	+	0.0267940i
$661$	−24.9657	+	24.9657i	−0.971054	+	0.971054i	−0.999593	−	0.0285391i	$-0.990914\pi$
$661$	−24.9657	+	24.9657i	−0.971054	+	0.971054i	0.0285391	+	0.999593i	$0.490914\pi$
$662$	34.0891			1.32491
$663$		0			0
$664$	−12.3654			−0.479872
$665$	−35.3651	+	35.3651i	−1.37140	+	1.37140i
$666$	−4.84241	+	11.6906i	−0.187640	+	0.453002i
$667$		−	0.944550i		−	0.0365731i
$668$	0.813102	+	0.336798i	0.0314599	+	0.0130311i
$669$	2.04955	+	4.94805i	0.0792402	+	0.191303i
$670$	−11.4390	+	4.73817i	−0.441925	+	0.183051i
$671$	−8.18650	−	8.18650i	−0.316036	−	0.316036i
$672$	1.26379	+	1.26379i	0.0487519	+	0.0487519i
$673$	−21.5310	+	8.91843i	−0.829959	+	0.343780i	−0.756887	−	0.653546i	$-0.773280\pi$
$673$	−21.5310	+	8.91843i	−0.829959	+	0.343780i	−0.0730727	+	0.997327i	$0.523280\pi$
$674$	−3.34339	−	8.07166i	−0.128783	−	0.310909i
$675$	−0.327365	−	0.135599i	−0.0126003	−	0.00521921i
$676$		−	0.826954i		−	0.0318059i
$677$	3.94269	−	9.51850i	0.151530	−	0.365826i	−0.829827	−	0.558021i	$-0.811561\pi$
$677$	3.94269	−	9.51850i	0.151530	−	0.365826i	0.981357	+	0.192195i	$0.0615608\pi$
$678$	0.812847	−	0.812847i	0.0312172	−	0.0312172i
$679$	−17.0512			−0.654365
$680$		0			0
$681$	1.71274			0.0656324
$682$	−40.2230	+	40.2230i	−1.54022	+	1.54022i
$683$	−10.5585	+	25.4905i	−0.404010	+	0.975368i	0.582672	+	0.812708i	$0.302007\pi$
$683$	−10.5585	+	25.4905i	−0.404010	+	0.975368i	−0.986682	+	0.162660i	$0.947993\pi$
$684$		−	0.346301i		−	0.0132412i
$685$	−16.8229	−	6.96828i	−0.642771	−	0.266244i
$686$	14.0144	+	33.8336i	0.535070	+	1.29177i
$687$	−0.351646	+	0.145657i	−0.0134161	+	0.00555714i
$688$	4.42704	+	4.42704i	0.168779	+	0.168779i
$689$	−5.91663	−	5.91663i	−0.225406	−	0.225406i
$690$	1.92412	−	0.796995i	0.0732499	−	0.0303411i
$691$	9.76768	+	23.5813i	0.371580	+	0.897073i	0.993483	+	0.113979i	$0.0363597\pi$
$691$	9.76768	+	23.5813i	0.371580	+	0.897073i	−0.621903	+	0.783094i	$0.713640\pi$
$692$	−0.210223	−	0.0870773i	−0.00799149	−	0.00331018i
$693$			20.0967i			0.763411i
$694$	−3.92957	+	9.48682i	−0.149164	+	0.360115i
$695$	−16.0804	+	16.0804i	−0.609963	+	0.609963i
$696$	4.19248			0.158916
$697$		0			0
$698$	−22.7135			−0.859718
$699$	6.33766	−	6.33766i	0.239712	−	0.239712i
$700$	−0.0428624	+	0.103479i	−0.00162005	+	0.00391114i
$701$			14.8327i			0.560225i	0.959967	+	0.280113i	$0.0903718\pi$
$701$			14.8327i			0.560225i	−0.959967	+	0.280113i	$0.909628\pi$
$702$	−1.56183	−	0.646933i	−0.0589476	−	0.0244169i
$703$	16.3734	+	39.5290i	0.617536	+	1.49086i
$704$	−32.1679	+	13.3244i	−1.21237	+	0.502181i
$705$	−9.84839	−	9.84839i	−0.370912	−	0.370912i
$706$	35.8521	+	35.8521i	1.34931	+	1.34931i
$707$	48.8979	−	20.2542i	1.83900	−	0.761737i
$708$	0.283299	+	0.683943i	0.0106470	+	0.0257042i
$709$	−4.33759	−	1.79669i	−0.162902	−	0.0674761i	0.299742	−	0.954020i	$-0.403099\pi$
$709$	−4.33759	−	1.79669i	−0.162902	−	0.0674761i	−0.462644	+	0.886544i	$0.653099\pi$
$710$		−	50.7607i		−	1.90502i
$711$	−6.38975	+	15.4262i	−0.239634	+	0.578528i
$712$	3.02339	−	3.02339i	0.113306	−	0.113306i
$713$	5.46342			0.204607
$714$		0			0
$715$	12.2981			0.459923
$716$	0.956787	−	0.956787i	0.0357568	−	0.0357568i
$717$	−2.56753	+	6.19857i	−0.0958862	+	0.231490i
$718$		−	37.0317i		−	1.38201i
$719$	0.381407	+	0.157984i	0.0142241	+	0.00589181i	0.389784	−	0.920906i	$-0.372550\pi$
$719$	0.381407	+	0.157984i	0.0142241	+	0.00589181i	−0.375560	+	0.926798i	$0.622550\pi$
$720$	3.66358	+	8.84467i	0.136534	+	0.329621i
$721$	5.79594	−	2.40076i	0.215852	−	0.0894089i
$722$	−4.76197	−	4.76197i	−0.177222	−	0.177222i
$723$	6.25076	+	6.25076i	0.232468	+	0.232468i
$724$	0.790266	−	0.327339i	0.0293700	−	0.0121655i
$725$	0.204798	+	0.494426i	0.00760600	+	0.0183625i
$726$	12.5932	+	5.21626i	0.467376	+	0.193594i
$727$		−	32.9236i		−	1.22107i	−0.791990	−	0.610534i	$-0.790955\pi$
$727$		−	32.9236i		−	1.22107i	0.791990	−	0.610534i	$-0.209045\pi$
$728$	5.54250	−	13.3808i	0.205419	−	0.495925i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	−8.99753			−0.333013
$731$		0			0
$732$	0.182099			0.00673059
$733$	−25.8776	+	25.8776i	−0.955812	+	0.955812i	−0.999064	−	0.0432525i	$-0.986228\pi$
$733$	−25.8776	+	25.8776i	−0.955812	+	0.955812i	0.0432525	+	0.999064i	$0.486228\pi$
$734$	4.54964	−	10.9838i	0.167930	−	0.405420i
$735$			29.4540i			1.08643i
$736$	−0.232494	−	0.0963020i	−0.00856983	−	0.00354974i
$737$	6.43760	+	15.5417i	0.237132	+	0.572487i
$738$	0.618220	−	0.256075i	0.0227570	−	0.00942625i
$739$	−31.8384	−	31.8384i	−1.17119	−	1.17119i	−0.981926	−	0.189267i	$-0.939389\pi$
$739$	−31.8384	−	31.8384i	−1.17119	−	1.17119i	−0.189267	−	0.981926i	$-0.560611\pi$
$740$	1.02381	+	1.02381i	0.0376361	+	0.0376361i
$741$	−5.28096	+	2.18745i	−0.194001	+	0.0803579i
$742$	−17.4251	−	42.0680i	−0.639697	−	1.54437i
$743$	18.2394	+	7.55501i	0.669139	+	0.277167i	0.691279	−	0.722588i	$-0.257048\pi$
$743$	18.2394	+	7.55501i	0.669139	+	0.277167i	−0.0221393	+	0.999755i	$0.507048\pi$
$744$			24.2500i			0.889047i
$745$	−5.57914	+	13.4692i	−0.204404	+	0.493475i
$746$	−23.8493	+	23.8493i	−0.873184	+	0.873184i
$747$	4.45459			0.162985
$748$		0			0
$749$	−69.5308			−2.54060
$750$	10.9394	−	10.9394i	0.399450	−	0.399450i
$751$	−8.90272	+	21.4931i	−0.324865	+	0.784294i	0.674093	+	0.738647i	$0.264535\pi$
$751$	−8.90272	+	21.4931i	−0.324865	+	0.784294i	−0.998958	+	0.0456467i	$0.985465\pi$
$752$			24.9024i			0.908097i
$753$	−22.5605	−	9.34487i	−0.822151	−	0.340546i
$754$	0.977075	+	2.35887i	0.0355830	+	0.0859049i
$755$	23.1479	−	9.58816i	0.842437	−	0.348949i
$756$	−0.223514	−	0.223514i	−0.00812914	−	0.00812914i
$757$	6.94688	+	6.94688i	0.252489	+	0.252489i	0.821990	−	0.569502i	$-0.192864\pi$
$757$	6.94688	+	6.94688i	0.252489	+	0.252489i	−0.569502	+	0.821990i	$0.692864\pi$
$758$	−20.0266	+	8.29530i	−0.727400	+	0.301299i
$759$	−1.08285	−	2.61424i	−0.0393050	−	0.0948907i
$760$	28.8773	+	11.9614i	1.04749	+	0.433884i
$761$		−	38.2412i		−	1.38624i	−0.720822	−	0.693121i	$-0.756235\pi$
$761$		−	38.2412i		−	1.38624i	0.720822	−	0.693121i	$-0.243765\pi$
$762$	1.85432	−	4.47673i	0.0671750	−	0.162175i
$763$	−31.8592	+	31.8592i	−1.15338	+	1.15338i
$764$	−1.58771			−0.0574414
$765$		0			0
$766$	23.0236			0.831876
$767$	8.64039	−	8.64039i	0.311986	−	0.311986i
$768$	0.652793	−	1.57598i	0.0235557	−	0.0568684i
$769$		−	44.2020i		−	1.59396i	−0.604002	−	0.796982i	$-0.706428\pi$
$769$		−	44.2020i		−	1.59396i	0.604002	−	0.796982i	$-0.293572\pi$
$770$	61.8302	+	25.6109i	2.22821	+	0.922953i
$771$	9.92402	+	23.9587i	0.357405	+	0.862852i
$772$	−0.229850	+	0.0952070i	−0.00827248	+	0.00342657i
$773$	3.60023	+	3.60023i	0.129491	+	0.129491i	0.768882	−	0.639391i	$-0.220813\pi$
$773$	3.60023	+	3.60023i	0.129491	+	0.129491i	−0.639391	+	0.768882i	$0.720813\pi$
$774$	−1.53995	−	1.53995i	−0.0553525	−	0.0553525i
$775$	−2.85983	+	1.18458i	−0.102728	+	0.0425515i
$776$	4.07798	+	9.84511i	0.146391	+	0.353419i
$777$	36.0813	+	14.9453i	1.29441	+	0.536161i
$778$		−	4.30295i		−	0.154268i
$779$	0.865856	−	2.09036i	0.0310225	−	0.0748949i
$780$	−0.136779	+	0.136779i	−0.00489746	+	0.00489746i
$781$	−68.9670			−2.46783
$782$		0			0
$783$	−1.51032			−0.0539744
$784$	37.2384	−	37.2384i	1.32994	−	1.32994i
$785$	−9.58567	+	23.1418i	−0.342127	+	0.825968i
$786$		−	2.07189i		−	0.0739017i
$787$	8.56912	+	3.54944i	0.305456	+	0.126524i	0.530146	−	0.847906i	$-0.322137\pi$
$787$	8.56912	+	3.54944i	0.305456	+	0.126524i	−0.224690	+	0.974430i	$0.572137\pi$
$788$	−0.326731	−	0.788798i	−0.0116393	−	0.0280998i
$789$	1.60895	−	0.666448i	0.0572801	−	0.0237262i
$790$	39.3178	+	39.3178i	1.39886	+	1.39886i
$791$	−2.50873	−	2.50873i	−0.0892000	−	0.0892000i
$792$	11.6036	−	4.80635i	0.412314	−	0.170786i
$793$	−1.15025	−	2.77695i	−0.0408465	−	0.0986123i
$794$	−16.8230	−	6.96833i	−0.597028	−	0.247297i
$795$		−	16.4828i		−	0.584584i
$796$	−0.109548	+	0.264473i	−0.00388284	+	0.00937399i
$797$	17.4851	−	17.4851i	0.619353	−	0.619353i	−0.326013	−	0.945365i	$-0.605705\pi$
$797$	17.4851	−	17.4851i	0.619353	−	0.619353i	0.945365	+	0.326013i	$0.105705\pi$
$798$	−31.1061			−1.10114
$799$		0			0
$800$	0.142579			0.00504094
$801$	−1.08916	+	1.08916i	−0.0384835	+	0.0384835i
$802$	−8.07874	+	19.5038i	−0.285270	+	0.688703i
$803$			12.2246i			0.431398i
$804$	−0.244453	−	0.101256i	−0.00862118	−	0.00357101i
$805$	−2.45980	−	5.93849i	−0.0866967	−	0.209304i
$806$	−13.6441	+	5.65156i	−0.480592	+	0.199068i
$807$	22.2585	+	22.2585i	0.783535	+	0.783535i
$808$	−23.3889	−	23.3889i	−0.822820	−	0.822820i
$809$	−27.4403	+	11.3661i	−0.964750	+	0.399613i	−0.808755	−	0.588145i	$-0.799858\pi$
$809$	−27.4403	+	11.3661i	−0.964750	+	0.399613i	−0.155995	+	0.987758i	$0.549858\pi$
$810$	−1.27438	−	3.07663i	−0.0447772	−	0.108102i
$811$	26.1245	+	10.8211i	0.917357	+	0.379982i	0.790868	−	0.611986i	$-0.209629\pi$
$811$	26.1245	+	10.8211i	0.917357	+	0.379982i	0.126489	+	0.991968i	$0.459629\pi$
$812$			0.477408i			0.0167537i
$813$	7.57965	−	18.2989i	0.265830	−	0.641770i
$814$	40.4837	−	40.4837i	1.41895	−	1.41895i
$815$	−26.0970			−0.914137
$816$		0			0
$817$	−7.36378			−0.257626
$818$	−16.6098	+	16.6098i	−0.580747	+	0.580747i
$819$	−1.99666	+	4.82036i	−0.0697689	+	0.168437i
$820$		−	0.0765670i		−	0.00267383i
$821$	−39.6154	−	16.4093i	−1.38259	−	0.572687i	−0.437416	−	0.899259i	$-0.644106\pi$
$821$	−39.6154	−	16.4093i	−1.38259	−	0.572687i	−0.945172	+	0.326572i	$0.894106\pi$
$822$	−4.33391	−	10.4630i	−0.151163	−	0.364939i
$823$	−26.9738	+	11.1729i	−0.940249	+	0.389464i	−0.799557	−	0.600590i	$-0.794932\pi$
$823$	−26.9738	+	11.1729i	−0.940249	+	0.389464i	−0.140691	+	0.990054i	$0.544932\pi$
$824$	−2.77233	−	2.77233i	−0.0965785	−	0.0965785i
$825$	1.13364	+	1.13364i	0.0394683	+	0.0394683i
$826$	61.4343	−	25.4469i	2.13757	−	0.885411i
$827$	−19.5285	−	47.1459i	−0.679071	−	1.63942i	−0.765712	−	0.643183i	$-0.777613\pi$
$827$	−19.5285	−	47.1459i	−0.679071	−	1.63942i	0.0866414	−	0.996240i	$-0.472387\pi$
$828$	0.0411187	+	0.0170319i	0.00142898	+	0.000591901i
$829$		−	16.2122i		−	0.563072i	−0.959551	−	0.281536i	$-0.909156\pi$
$829$		−	16.2122i		−	0.563072i	0.959551	−	0.281536i	$-0.0908438\pi$
$830$	5.67685	−	13.7051i	0.197046	−	0.475712i
$831$	−1.64808	+	1.64808i	−0.0571712	+	0.0571712i
$832$	−9.03952			−0.313389
$833$		0			0
$834$	−14.1438			−0.489759
$835$	20.2348	−	20.2348i	0.700254	−	0.700254i
$836$	−0.599608	+	1.44758i	−0.0207379	+	0.0500656i
$837$		−	8.73592i		−	0.301958i
$838$	20.8878	+	8.65201i	0.721557	+	0.298879i
$839$	−13.6913	−	33.0538i	−0.472678	−	1.14114i	−0.962975	−	0.269590i	$-0.913112\pi$
$839$	−13.6913	−	33.0538i	−0.472678	−	1.14114i	0.490298	−	0.871555i	$-0.336888\pi$
$840$	26.3586	−	10.9181i	0.909458	−	0.376710i
$841$	−18.8931	−	18.8931i	−0.651488	−	0.651488i
$842$	22.4933	+	22.4933i	0.775172	+	0.775172i
$843$	−0.282843	+	0.117157i	−0.00974164	+	0.00403512i
$844$	0.434656	+	1.04935i	0.0149615	+	0.0361202i
$845$	−24.8417	−	10.2898i	−0.854580	−	0.353978i
$846$		−	8.66233i		−	0.297817i
$847$	16.0992	−	38.8669i	0.553174	−	1.33548i
$848$	−20.8390	+	20.8390i	−0.715613	+	0.715613i
$849$	−18.3142			−0.628542
$850$		0			0
$851$	−5.49883			−0.188498
$852$	0.767046	−	0.767046i	0.0262786	−	0.0262786i
$853$	19.8733	−	47.9783i	0.680447	−	1.64275i	−0.0827423	−	0.996571i	$-0.526368\pi$
$853$	19.8733	−	47.9783i	0.680447	−	1.64275i	0.763190	−	0.646174i	$-0.223632\pi$
$854$		−	16.3568i		−	0.559720i
$855$	−10.4029	−	4.30902i	−0.355771	−	0.147365i
$856$	16.6290	+	40.1461i	0.568369	+	1.37216i
$857$	33.7150	−	13.9652i	1.15168	−	0.477043i	0.276586	−	0.960989i	$-0.410797\pi$
$857$	33.7150	−	13.9652i	1.15168	−	0.477043i	0.875098	+	0.483946i	$0.160797\pi$
$858$	5.40851	+	5.40851i	0.184644	+	0.184644i
$859$	−18.4107	−	18.4107i	−0.628166	−	0.628166i	0.319440	−	0.947606i	$-0.396505\pi$
$859$	−18.4107	−	18.4107i	−0.628166	−	0.628166i	−0.947606	+	0.319440i	$0.896505\pi$
$860$	−0.230225	+	0.0953622i	−0.00785060	+	0.00325182i
$861$	−0.790336	−	1.90804i	−0.0269346	−	0.0650258i
$862$	5.52488	+	2.28848i	0.188178	+	0.0779460i
$863$			37.5428i			1.27797i	0.769218	+	0.638986i	$0.220646\pi$
$863$			37.5428i			1.27797i	−0.769218	+	0.638986i	$0.779354\pi$
$864$	−0.153985	+	0.371753i	−0.00523869	+	0.0126473i
$865$	−5.23160	+	5.23160i	−0.177880	+	0.177880i
$866$	−18.8192			−0.639502
$867$		0			0
$868$	−2.76140			−0.0937280
$869$	53.4198	−	53.4198i	1.81214	−	1.81214i
$870$	−1.92473	+	4.64670i	−0.0652543	+	0.157538i
$871$			4.36740i			0.147984i
$872$	26.0145	+	10.7756i	0.880962	+	0.364906i
$873$	−1.46907	−	3.54665i	−0.0497205	−	0.120036i
$874$	4.04636	−	1.67606i	0.136870	−	0.0566935i
$875$	−33.7627	−	33.7627i	−1.14139	−	1.14139i
$876$	−0.135962	−	0.135962i	−0.00459372	−	0.00459372i
$877$	−36.0995	+	14.9529i	−1.21899	+	0.504923i	−0.897089	−	0.441849i	$-0.854323\pi$
$877$	−36.0995	+	14.9529i	−1.21899	+	0.504923i	−0.321903	+	0.946773i	$0.604323\pi$
$878$	6.38518	+	15.4152i	0.215489	+	0.520238i
$879$	−14.1032	−	5.84173i	−0.475688	−	0.197037i
$880$		−	43.3151i		−	1.46015i
$881$	16.9276	−	40.8669i	0.570306	−	1.37684i	−0.330989	−	0.943635i	$-0.607382\pi$
$881$	16.9276	−	40.8669i	0.570306	−	1.37684i	0.901295	−	0.433206i	$-0.142618\pi$
$882$	−12.9534	+	12.9534i	−0.436164	+	0.436164i
$883$	21.8625			0.735733			0.367866	−	0.929879i	$-0.380088\pi$
$883$	21.8625			0.735733			0.367866	+	0.929879i	$0.380088\pi$
$884$		0			0
$885$	24.0707			0.809128
$886$	17.9734	−	17.9734i	0.603829	−	0.603829i
$887$	0.167234	−	0.403739i	0.00561517	−	0.0135562i	−0.921047	−	0.389451i	$-0.872665\pi$
$887$	0.167234	−	0.403739i	0.00561517	−	0.0135562i	0.926662	+	0.375895i	$0.122665\pi$
$888$		−	24.4071i		−	0.819050i
$889$	−13.8167	−	5.72307i	−0.463398	−	0.191946i
$890$	1.96294	+	4.73895i	0.0657978	+	0.158850i
$891$	−4.18012	+	1.73146i	−0.140039	+	0.0580062i
$892$	0.269509	+	0.269509i	0.00902381	+	0.00902381i
$893$	−20.7109	−	20.7109i	−0.693063	−	0.693063i
$894$	−8.37717	+	3.46994i	−0.280175	+	0.116052i
$895$	−16.8366	−	40.6471i	−0.562785	−	1.35868i
$896$	−48.7498	−	20.1928i	−1.62862	−	0.674594i
$897$		−	0.734629i		−	0.0245285i
$898$	19.3538	−	46.7242i	0.645845	−	1.55921i
$899$	−9.32959	+	9.32959i	−0.311159	+	0.311159i
$900$	−0.0252165			−0.000840551
$901$		0			0
$902$	−3.02762			−0.100809
$903$	−4.75283	+	4.75283i	−0.158164	+	0.158164i
$904$	−0.848513	+	2.04849i	−0.0282211	+	0.0681318i
$905$		−	27.8127i		−	0.924524i
$906$	14.3968	+	5.96334i	0.478301	+	0.198119i
$907$	6.50831	+	15.7125i	0.216105	+	0.521724i	0.994339	−	0.106250i	$-0.0338845\pi$
$907$	6.50831	+	15.7125i	0.216105	+	0.521724i	−0.778234	+	0.627974i	$0.783884\pi$
$908$	0.112610	−	0.0466444i	0.00373708	−	0.00154795i
$909$	8.42574	+	8.42574i	0.279464	+	0.279464i
$910$	12.2860	+	12.2860i	0.407276	+	0.407276i
$911$	−17.6827	+	7.32440i	−0.585853	+	0.242668i	−0.655865	−	0.754878i	$-0.727696\pi$
$911$	−17.6827	+	7.32440i	−0.585853	+	0.242668i	0.0700126	+	0.997546i	$0.477696\pi$
$912$	7.70440	+	18.6001i	0.255118	+	0.615910i
$913$	−18.6207	−	7.71295i	−0.616255	−	0.255261i
$914$		−	35.4472i		−	1.17249i
$915$	2.26586	−	5.47027i	0.0749070	−	0.180841i
$916$	−0.0191533	+	0.0191533i	−0.000632843	+	0.000632843i
$917$	−6.39456			−0.211167
$918$		0			0
$919$	−48.0934			−1.58645			−0.793227	−	0.608926i	$-0.791601\pi$
$919$	−48.0934			−1.58645			−0.793227	+	0.608926i	$0.791601\pi$
$920$	−2.84051	+	2.84051i	−0.0936488	+	0.0936488i
$921$	11.4761	−	27.7057i	0.378149	−	0.912934i
$922$		−	1.44509i		−	0.0475916i
$923$	−16.5423	−	6.85203i	−0.544496	−	0.225537i
$924$	0.547310	+	1.32132i	0.0180052	+	0.0434683i
$925$	2.87837	−	1.19226i	0.0946402	−	0.0392013i
$926$	20.8208	+	20.8208i	0.684214	+	0.684214i
$927$	0.998716	+	0.998716i	0.0328021	+	0.0328021i
$928$	0.561467	−	0.232567i	0.0184310	−	0.00763439i
$929$	−1.99849	−	4.82478i	−0.0655683	−	0.158296i	0.887699	−	0.460424i	$-0.152303\pi$
$929$	−1.99849	−	4.82478i	−0.0655683	−	0.158296i	−0.953267	+	0.302129i	$0.902303\pi$
$930$	−26.8772	−	11.1329i	−0.881339	−	0.365063i
$931$			61.9410i			2.03003i
$932$	0.244091	−	0.589289i	0.00799548	−	0.0193028i
$933$	16.4930	−	16.4930i	0.539955	−	0.539955i
$934$	50.6092			1.65598
$935$		0			0
$936$	3.26073			0.106580
$937$	4.62160	−	4.62160i	0.150981	−	0.150981i	−0.627575	−	0.778556i	$-0.715952\pi$
$937$	4.62160	−	4.62160i	0.150981	−	0.150981i	0.778556	+	0.627575i	$0.215952\pi$
$938$	−9.09514	+	21.9576i	−0.296967	+	0.716942i
$939$		−	23.9568i		−	0.781800i
$940$	−0.915723	−	0.379305i	−0.0298676	−	0.0123716i
$941$	−3.23443	−	7.80860i	−0.105439	−	0.254553i	0.862351	−	0.506311i	$-0.168991\pi$
$941$	−3.23443	−	7.80860i	−0.105439	−	0.254553i	−0.967790	+	0.251758i	$0.918991\pi$
$942$	−14.3930	+	5.96179i	−0.468951	+	0.194246i
$943$	0.205618	+	0.205618i	0.00669584	+	0.00669584i
$944$	−30.4323	−	30.4323i	−0.990487	−	0.990487i
$945$	−9.49555	+	3.93318i	−0.308890	+	0.127947i
$946$	3.77082	+	9.10356i	0.122600	+	0.295982i
$947$	42.8011	+	17.7288i	1.39085	+	0.576109i	0.947360	−	0.320171i	$-0.103740\pi$
$947$	42.8011	+	17.7288i	1.39085	+	0.576109i	0.443489	+	0.896280i	$0.353740\pi$
$948$			1.18826i			0.0385930i
$949$	−1.21455	+	2.93218i	−0.0394259	+	0.0951825i
$950$	−1.75467	+	1.75467i	−0.0569289	+	0.0569289i
$951$	18.7844			0.609126
$952$		0			0
$953$	34.8809			1.12990			0.564951	−	0.825124i	$-0.308895\pi$
$953$	34.8809			1.12990			0.564951	+	0.825124i	$0.308895\pi$
$954$	7.24886	−	7.24886i	0.234691	−	0.234691i
$955$	−19.7558	+	47.6948i	−0.639284	+	1.54337i
$956$			0.477468i			0.0154424i
$957$	6.31332	+	2.61506i	0.204081	+	0.0845329i
$958$	2.12432	+	5.12856i	0.0686337	+	0.165696i
$959$	−32.2924	+	13.3759i	−1.04278	+	0.431932i
$960$	−12.5913	−	12.5913i	−0.406383	−	0.406383i
$961$	−32.0435	−	32.0435i	−1.03366	−	1.03366i
$962$	13.7325	−	5.68818i	0.442753	−	0.183394i
$963$	−5.99053	−	14.4624i	−0.193042	−	0.466045i
$964$	0.581208	+	0.240744i	0.0187194	+	0.00775385i
$965$			8.08934i			0.260405i
$966$	1.52987	−	3.69344i	0.0492228	−	0.118834i
$967$	31.9196	−	31.9196i	1.02647	−	1.02647i	0.0268254	−	0.999640i	$-0.491460\pi$
$967$	31.9196	−	31.9196i	1.02647	−	1.02647i	0.999640	−	0.0268254i	$-0.00853983\pi$
$968$	−26.2915			−0.845039
$969$		0			0
$970$	−12.7839			−0.410466
$971$	−29.8403	+	29.8403i	−0.957619	+	0.957619i	−0.999138	−	0.0415185i	$-0.986780\pi$
$971$	−29.8403	+	29.8403i	−0.957619	+	0.957619i	0.0415185	+	0.999138i	$0.486780\pi$
$972$	0.0272338	−	0.0657482i	0.000873524	−	0.00210887i
$973$			43.6526i			1.39944i
$974$	−27.0826	−	11.2180i	−0.867782	−	0.359447i
$975$	0.159283	+	0.384542i	0.00510113	+	0.0123152i
$976$	−9.78068	+	4.05129i	−0.313072	+	0.129679i
$977$	−26.8753	−	26.8753i	−0.859818	−	0.859818i	0.131498	−	0.991316i	$-0.458021\pi$
$977$	−26.8753	−	26.8753i	−0.859818	−	0.859818i	−0.991316	+	0.131498i	$0.958021\pi$
$978$	−11.4770	−	11.4770i	−0.366995	−	0.366995i
$979$	6.43865	−	2.66698i	0.205780	−	0.0852370i
$980$	0.802146	+	1.93655i	0.0256236	+	0.0618608i
$981$	−9.37158	−	3.88184i	−0.299212	−	0.123937i
$982$			9.19154i			0.293314i
$983$	16.6000	−	40.0759i	0.529458	−	1.27822i	−0.402421	−	0.915455i	$-0.631831\pi$
$983$	16.6000	−	40.0759i	0.529458	−	1.27822i	0.931879	−	0.362769i	$-0.118169\pi$
$984$	−0.912657	+	0.912657i	−0.0290944	+	0.0290944i
$985$	−27.7610			−0.884539
$986$		0			0
$987$	−26.7349			−0.850983
$988$	−0.287641	+	0.287641i	−0.00915109	+	0.00915109i
$989$	0.362169	−	0.874353i	0.0115163	−	0.0278028i
$990$			15.0672i			0.478868i
$991$	37.1943	+	15.4064i	1.18151	+	0.489399i	0.884983	−	0.465624i	$-0.154170\pi$
$991$	37.1943	+	15.4064i	1.18151	+	0.489399i	0.296532	+	0.955023i	$0.404170\pi$
$992$	1.34520	+	3.24761i	0.0427103	+	0.103112i
$993$	21.8838	−	9.06459i	0.694463	−	0.287656i
$994$	−68.8989	−	68.8989i	−2.18534	−	2.18534i
$995$	6.58166	+	6.58166i	0.208653	+	0.208653i
$996$	0.292881	−	0.121315i	0.00928029	−	0.00384402i
$997$	12.1801	+	29.4054i	0.385749	+	0.931279i	0.990830	+	0.135116i	$0.0431406\pi$
$997$	12.1801	+	29.4054i	0.385749	+	0.931279i	−0.605081	+	0.796164i	$0.706859\pi$
$998$	2.18567	+	0.905333i	0.0691861	+	0.0286578i
$999$			8.79254i			0.278184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.m.688.10		48
17.2	even	8	inner	867.2.h.m.712.9		48
17.3	odd	16		867.2.e.k.616.4		24
17.4	even	4	inner	867.2.h.m.757.3		48
17.5	odd	16		867.2.e.k.829.10		24
17.6	odd	16		867.2.d.g.577.9		12
17.7	odd	16		867.2.a.o.1.2	✓	6
17.8	even	8	inner	867.2.h.m.733.3		48
17.9	even	8	inner	867.2.h.m.733.4		48
17.10	odd	16		867.2.a.p.1.2	yes	6
17.11	odd	16		867.2.d.g.577.10		12
17.12	odd	16		867.2.e.k.829.9		24
17.13	even	4	inner	867.2.h.m.757.4		48
17.14	odd	16		867.2.e.k.616.3		24
17.15	even	8	inner	867.2.h.m.712.10		48
17.16	even	2	inner	867.2.h.m.688.9		48
51.41	even	16		2601.2.a.bh.1.5		6
51.44	even	16		2601.2.a.bi.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.o.1.2	✓	6	17.7	odd	16
867.2.a.p.1.2	yes	6	17.10	odd	16
867.2.d.g.577.9		12	17.6	odd	16
867.2.d.g.577.10		12	17.11	odd	16
867.2.e.k.616.3		24	17.14	odd	16
867.2.e.k.616.4		24	17.3	odd	16
867.2.e.k.829.9		24	17.12	odd	16
867.2.e.k.829.10		24	17.5	odd	16
867.2.h.m.688.9		48	17.16	even	2	inner
867.2.h.m.688.10		48	1.1	even	1	trivial
867.2.h.m.712.9		48	17.2	even	8	inner
867.2.h.m.712.10		48	17.15	even	8	inner
867.2.h.m.733.3		48	17.8	even	8	inner
867.2.h.m.733.4		48	17.9	even	8	inner
867.2.h.m.757.3		48	17.4	even	4	inner
867.2.h.m.757.4		48	17.13	even	4	inner
2601.2.a.bh.1.5		6	51.41	even	16
2601.2.a.bi.1.5		6	51.44	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.01764 - 1.01764i) q^{2} +(0.382683 - 0.923880i) q^{3} -0.0711653i q^{4} +(-2.13781 - 0.885508i) q^{5} +(-0.550741 - 1.32961i) q^{6} +(-4.10362 + 1.69978i) q^{7} +(1.96285 + 1.96285i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-3.07663 + 1.27438i) q^{10} +(1.73146 + 4.18012i) q^{11} +(-0.0657482 - 0.0272338i) q^{12} +1.17466i q^{13} +(-2.44624 + 5.90574i) q^{14} +(-1.63621 + 1.63621i) q^{15} +4.13727 q^{16} -1.43915 q^{18} +(-3.44089 + 3.44089i) q^{19} +(-0.0630175 + 0.152138i) q^{20} +4.44173i q^{21} +(6.01584 + 2.49184i) q^{22} +(-0.239329 - 0.577792i) q^{23} +(2.56459 - 1.06229i) q^{24} +(0.250554 + 0.250554i) q^{25} +(1.19538 + 1.19538i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(0.120965 + 0.292036i) q^{28} +(1.39535 + 0.577974i) q^{29} +3.33012i q^{30} +(-3.34309 + 8.07094i) q^{31} +(0.284528 - 0.284528i) q^{32} +4.52453 q^{33} +10.2779 q^{35} +(-0.0503215 + 0.0503215i) q^{36} +(3.36476 - 8.12325i) q^{37} +7.00315i q^{38} +(1.08524 + 0.449523i) q^{39} +(-2.45807 - 5.93431i) q^{40} +(-0.429571 + 0.177934i) q^{41} +(4.52006 + 4.52006i) q^{42} +(1.07004 + 1.07004i) q^{43} +(0.297480 - 0.123220i) q^{44} +(0.885508 + 2.13781i) q^{45} +(-0.831531 - 0.344432i) q^{46} +6.01904i q^{47} +(1.58326 - 3.82234i) q^{48} +(9.00072 - 9.00072i) q^{49} +0.509946 q^{50} +0.0835951 q^{52} +(-5.03689 + 5.03689i) q^{53} +(-0.550741 + 1.32961i) q^{54} -10.4695i q^{55} +(-11.3912 - 4.71839i) q^{56} +(1.86220 + 4.49574i) q^{57} +(2.00813 - 0.831794i) q^{58} +(-7.35565 - 7.35565i) q^{59} +(0.116441 + 0.116441i) q^{60} +(-2.36404 + 0.979219i) q^{61} +(4.81123 + 11.6153i) q^{62} +(4.10362 + 1.69978i) q^{63} +7.69544i q^{64} +(1.04017 - 2.51119i) q^{65} +(4.60432 - 4.60432i) q^{66} +3.71801 q^{67} -0.625397 q^{69} +(10.4592 - 10.4592i) q^{70} +(-5.83321 + 14.0826i) q^{71} -2.77589i q^{72} +(2.49619 + 1.03396i) q^{73} +(-4.84241 - 11.6906i) q^{74} +(0.327365 - 0.135599i) q^{75} +(0.244872 + 0.244872i) q^{76} +(-14.2105 - 14.2105i) q^{77} +(1.56183 - 0.646933i) q^{78} +(-6.38975 - 15.4262i) q^{79} +(-8.84467 - 3.66358i) q^{80} +1.00000i q^{81} +(-0.256075 + 0.618220i) q^{82} +(-3.14987 + 3.14987i) q^{83} +0.316097 q^{84} +2.17782 q^{86} +(1.06796 - 1.06796i) q^{87} +(-4.80635 + 11.6036i) q^{88} -1.54030i q^{89} +(3.07663 + 1.27438i) q^{90} +(-1.99666 - 4.82036i) q^{91} +(-0.0411187 + 0.0170319i) q^{92} +(6.17723 + 6.17723i) q^{93} +(6.12519 + 6.12519i) q^{94} +(10.4029 - 4.30902i) q^{95} +(-0.153985 - 0.371753i) q^{96} +(3.54665 + 1.46907i) q^{97} -18.3189i q^{98} +(1.73146 - 4.18012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 120 q^{16} + 24 q^{18} + 72 q^{33} - 96 q^{50} - 144 q^{52} + 48 q^{67} - 72 q^{69} + 120 q^{84} + 48 q^{86}+O(q^{100}) \) 48 * q - 120 * q^16 + 24 * q^18 + 72 * q^33 - 96 * q^50 - 144 * q^52 + 48 * q^67 - 72 * q^69 + 120 * q^84 + 48 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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