LMFDB - Embedded newform 272.2.l.c.205.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(69,272)] 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("272.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.3
Character	$\chi$	$=$	272.205
Dual form			272.2.l.c.69.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37038 - 0.349388i) q^{2} +(0.724061 + 0.724061i) q^{3} +(1.75586 + 0.957585i) q^{4} +(0.100057 - 0.100057i) q^{5} +(-0.739257 - 1.24521i) q^{6} -2.62804i q^{7} +(-2.07161 - 1.92573i) q^{8} -1.95147i q^{9} +(-0.172075 + 0.102157i) q^{10} +(1.93625 - 1.93625i) q^{11} +(0.577997 + 1.96470i) q^{12} +(1.48714 + 1.48714i) q^{13} +(-0.918206 + 3.60140i) q^{14} +0.144896 q^{15} +(2.16606 + 3.36276i) q^{16} +1.00000 q^{17} +(-0.681820 + 2.67425i) q^{18} +(2.90615 + 2.90615i) q^{19} +(0.271500 - 0.0798729i) q^{20} +(1.90286 - 1.90286i) q^{21} +(-3.32989 + 1.97688i) q^{22} -5.35151i q^{23} +(-0.105630 - 2.89432i) q^{24} +4.97998i q^{25} +(-1.51835 - 2.55753i) q^{26} +(3.58517 - 3.58517i) q^{27} +(2.51657 - 4.61446i) q^{28} +(-0.891113 - 0.891113i) q^{29} +(-0.198561 - 0.0506248i) q^{30} +1.44426 q^{31} +(-1.79341 - 5.36504i) q^{32} +2.80393 q^{33} +(-1.37038 - 0.349388i) q^{34} +(-0.262955 - 0.262955i) q^{35} +(1.86870 - 3.42650i) q^{36} +(-1.18829 + 1.18829i) q^{37} +(-2.96714 - 4.99789i) q^{38} +2.15356i q^{39} +(-0.399964 + 0.0145970i) q^{40} +4.71764i q^{41} +(-3.27247 + 1.94280i) q^{42} +(7.44242 - 7.44242i) q^{43} +(5.25390 - 1.54565i) q^{44} +(-0.195259 - 0.195259i) q^{45} +(-1.86975 + 7.33357i) q^{46} -12.1594 q^{47} +(-0.866487 + 4.00321i) q^{48} +0.0934039 q^{49} +(1.73994 - 6.82444i) q^{50} +(0.724061 + 0.724061i) q^{51} +(1.18714 + 4.03527i) q^{52} +(-4.79265 + 4.79265i) q^{53} +(-6.16564 + 3.66041i) q^{54} -0.387472i q^{55} +(-5.06089 + 5.44428i) q^{56} +4.20846i q^{57} +(0.909815 + 1.53250i) q^{58} +(-6.48840 + 6.48840i) q^{59} +(0.254416 + 0.138750i) q^{60} +(1.30973 + 1.30973i) q^{61} +(-1.97918 - 0.504608i) q^{62} -5.12854 q^{63} +(0.583156 + 7.97872i) q^{64} +0.297599 q^{65} +(-3.84243 - 0.979658i) q^{66} +(-2.81837 - 2.81837i) q^{67} +(1.75586 + 0.957585i) q^{68} +(3.87482 - 3.87482i) q^{69} +(0.268474 + 0.452221i) q^{70} -6.09170i q^{71} +(-3.75800 + 4.04269i) q^{72} +13.5126i q^{73} +(2.04358 - 1.21323i) q^{74} +(-3.60581 + 3.60581i) q^{75} +(2.31989 + 7.88567i) q^{76} +(-5.08854 - 5.08854i) q^{77} +(0.752429 - 2.95119i) q^{78} -2.30465 q^{79} +(0.553200 + 0.119739i) q^{80} -0.662648 q^{81} +(1.64829 - 6.46494i) q^{82} +(0.632423 + 0.632423i) q^{83} +(5.16331 - 1.51900i) q^{84} +(0.100057 - 0.100057i) q^{85} +(-12.7992 + 7.59861i) q^{86} -1.29044i q^{87} +(-7.73984 + 0.282472i) q^{88} +11.0377i q^{89} +(0.199357 + 0.335800i) q^{90} +(3.90827 - 3.90827i) q^{91} +(5.12453 - 9.39648i) q^{92} +(1.04573 + 1.04573i) q^{93} +(16.6629 + 4.24834i) q^{94} +0.581564 q^{95} +(2.58609 - 5.18316i) q^{96} -17.9190 q^{97} +(-0.127998 - 0.0326342i) q^{98} +(-3.77853 - 3.77853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{4} - 16 q^{6} - 18 q^{8} - 6 q^{10} - 4 q^{11} + 2 q^{12} + 14 q^{14} + 24 q^{15} + 26 q^{16} + 32 q^{17} + 10 q^{18} - 14 q^{20} - 8 q^{22} - 50 q^{24} - 6 q^{26} + 12 q^{27} - 8 q^{29} + 36 q^{30}+ \cdots - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^4 - 16 * q^6 - 18 * q^8 - 6 * q^10 - 4 * q^11 + 2 * q^12 + 14 * q^14 + 24 * q^15 + 26 * q^16 + 32 * q^17 + 10 * q^18 - 14 * q^20 - 8 * q^22 - 50 * q^24 - 6 * q^26 + 12 * q^27 - 8 * q^29 + 36 * q^30 - 24 * q^31 + 10 * q^32 + 12 * q^35 + 16 * q^36 - 8 * q^37 - 34 * q^38 - 38 * q^40 - 12 * q^42 - 12 * q^43 + 38 * q^44 - 40 * q^45 + 26 * q^46 + 32 * q^47 + 30 * q^48 - 32 * q^49 - 2 * q^50 - 54 * q^52 + 8 * q^53 - 52 * q^54 - 36 * q^56 - 26 * q^58 - 12 * q^59 + 28 * q^60 + 6 * q^62 - 40 * q^63 + 10 * q^64 + 28 * q^66 + 8 * q^67 - 2 * q^68 - 32 * q^70 - 32 * q^72 - 14 * q^74 + 8 * q^75 + 30 * q^76 + 56 * q^77 + 108 * q^78 + 48 * q^79 + 90 * q^80 - 64 * q^81 + 32 * q^82 + 4 * q^83 - 8 * q^84 - 54 * q^86 - 66 * q^88 - 66 * q^90 - 28 * q^91 + 24 * q^92 - 24 * q^93 + 12 * q^94 - 40 * q^95 + 70 * q^96 + 12 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−1.37038	−	0.349388i	−0.969002	−	0.247055i
$2$	−1.37038	−	0.349388i	−0.969002	−	0.247055i
$3$	0.724061	+	0.724061i	0.418037	+	0.418037i	0.884527	−	0.466490i	$-0.154482\pi$
$3$	0.724061	+	0.724061i	0.418037	+	0.418037i	−0.466490	+	0.884527i	$0.654482\pi$
$4$	1.75586	+	0.957585i	0.877928	+	0.478793i
$5$	0.100057	−	0.100057i	0.0447471	−	0.0447471i	−0.684379	−	0.729126i	$-0.739927\pi$
$5$	0.100057	−	0.100057i	0.0447471	−	0.0447471i	0.729126	+	0.684379i	$0.239927\pi$
$6$	−0.739257	−	1.24521i	−0.301801	−	0.508356i
$7$		−	2.62804i		−	0.993306i	−0.867949	−	0.496653i	$-0.834562\pi$
$7$		−	2.62804i		−	0.993306i	0.867949	−	0.496653i	$-0.165438\pi$
$8$	−2.07161	−	1.92573i	−0.732426	−	0.680847i
$9$		−	1.95147i		−	0.650490i
$10$	−0.172075	+	0.102157i	−0.0544150	+	0.0323050i
$11$	1.93625	−	1.93625i	0.583801	−	0.583801i	−0.352145	−	0.935946i	$-0.614548\pi$
$11$	1.93625	−	1.93625i	0.583801	−	0.583801i	0.935946	+	0.352145i	$0.114548\pi$
$12$	0.577997	+	1.96470i	0.166853	+	0.567159i
$13$	1.48714	+	1.48714i	0.412459	+	0.412459i	0.882594	−	0.470136i	$-0.155795\pi$
$13$	1.48714	+	1.48714i	0.412459	+	0.412459i	−0.470136	+	0.882594i	$0.655795\pi$
$14$	−0.918206	+	3.60140i	−0.245401	+	0.962515i
$15$	0.144896			0.0374119
$16$	2.16606	+	3.36276i	0.541515	+	0.840691i
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	−0.681820	+	2.67425i	−0.160707	+	0.630326i
$19$	2.90615	+	2.90615i	0.666716	+	0.666716i	0.956954	−	0.290238i	$-0.0937345\pi$
$19$	2.90615	+	2.90615i	0.666716	+	0.666716i	−0.290238	+	0.956954i	$0.593734\pi$
$20$	0.271500	−	0.0798729i	0.0607093	−	0.0178601i
$21$	1.90286	−	1.90286i	0.415239	−	0.415239i
$22$	−3.32989	+	1.97688i	−0.709935	+	0.421473i
$23$		−	5.35151i		−	1.11587i	−0.829886	−	0.557933i	$-0.811594\pi$
$23$		−	5.35151i		−	1.11587i	0.829886	−	0.557933i	$-0.188406\pi$
$24$	−0.105630	−	2.89432i	−0.0215617	−	0.590800i
$25$			4.97998i			0.995995i
$26$	−1.51835	−	2.55753i	−0.297773	−	0.501573i
$27$	3.58517	−	3.58517i	0.689966	−	0.689966i
$28$	2.51657	−	4.61446i	0.475588	−	0.872051i
$29$	−0.891113	−	0.891113i	−0.165476	−	0.165476i	0.619512	−	0.784987i	$-0.287331\pi$
$29$	−0.891113	−	0.891113i	−0.165476	−	0.165476i	−0.784987	+	0.619512i	$0.787331\pi$
$30$	−0.198561	−	0.0506248i	−0.0362522	−	0.00924277i
$31$	1.44426			0.259397			0.129699	−	0.991553i	$-0.458599\pi$
$31$	1.44426			0.259397			0.129699	+	0.991553i	$0.458599\pi$
$32$	−1.79341	−	5.36504i	−0.317032	−	0.948415i
$33$	2.80393			0.488101
$34$	−1.37038	−	0.349388i	−0.235017	−	0.0599196i
$35$	−0.262955	−	0.262955i	−0.0444475	−	0.0444475i
$36$	1.86870	−	3.42650i	0.311450	−	0.571083i
$37$	−1.18829	+	1.18829i	−0.195354	+	0.195354i	−0.798005	−	0.602651i	$-0.794111\pi$
$37$	−1.18829	+	1.18829i	−0.195354	+	0.195354i	0.602651	+	0.798005i	$0.294111\pi$
$38$	−2.96714	−	4.99789i	−0.481334	−	0.810765i
$39$			2.15356i			0.344846i
$40$	−0.399964	+	0.0145970i	−0.0632398	+	0.00230799i
$41$			4.71764i			0.736772i	0.929673	+	0.368386i	$0.120090\pi$
$41$			4.71764i			0.736772i	−0.929673	+	0.368386i	$0.879910\pi$
$42$	−3.27247	+	1.94280i	−0.504953	+	0.299780i
$43$	7.44242	−	7.44242i	1.13496	−	1.13496i	0.145617	−	0.989341i	$-0.453483\pi$
$43$	7.44242	−	7.44242i	1.13496	−	1.13496i	0.989341	−	0.145617i	$-0.0465167\pi$
$44$	5.25390	−	1.54565i	0.792055	−	0.233016i
$45$	−0.195259	−	0.195259i	−0.0291075	−	0.0291075i
$46$	−1.86975	+	7.33357i	−0.275680	+	1.08128i
$47$	−12.1594			−1.77363			−0.886813	−	0.462128i	$-0.847086\pi$
$47$	−12.1594			−1.77363			−0.886813	+	0.462128i	$0.847086\pi$
$48$	−0.866487	+	4.00321i	−0.125067	+	0.577813i
$49$	0.0934039			0.0133434
$50$	1.73994	−	6.82444i	0.246065	−	0.965121i
$51$	0.724061	+	0.724061i	0.101389	+	0.101389i
$52$	1.18714	+	4.03527i	0.164627	+	0.559591i
$53$	−4.79265	+	4.79265i	−0.658321	+	0.658321i	−0.954983	−	0.296662i	$-0.904127\pi$
$53$	−4.79265	+	4.79265i	−0.658321	+	0.658321i	0.296662	+	0.954983i	$0.404127\pi$
$54$	−6.16564	+	3.66041i	−0.839037	+	0.498119i
$55$		−	0.387472i		−	0.0522468i
$56$	−5.06089	+	5.44428i	−0.676289	+	0.727523i
$57$			4.20846i			0.557424i
$58$	0.909815	+	1.53250i	0.119465	+	0.201228i
$59$	−6.48840	+	6.48840i	−0.844717	+	0.844717i	−0.989468	−	0.144751i	$-0.953762\pi$
$59$	−6.48840	+	6.48840i	−0.844717	+	0.844717i	0.144751	+	0.989468i	$0.453762\pi$
$60$	0.254416	+	0.138750i	0.0328449	+	0.0179125i
$61$	1.30973	+	1.30973i	0.167693	+	0.167693i	0.785965	−	0.618271i	$-0.212167\pi$
$61$	1.30973	+	1.30973i	0.167693	+	0.167693i	−0.618271	+	0.785965i	$0.712167\pi$
$62$	−1.97918	−	0.504608i	−0.251356	−	0.0640853i
$63$	−5.12854			−0.646136
$64$	0.583156	+	7.97872i	0.0728945	+	0.997340i
$65$	0.297599			0.0369126
$66$	−3.84243	−	0.979658i	−0.472970	−	0.120588i
$67$	−2.81837	−	2.81837i	−0.344318	−	0.344318i	0.513670	−	0.857988i	$-0.328286\pi$
$67$	−2.81837	−	2.81837i	−0.344318	−	0.344318i	−0.857988	+	0.513670i	$0.828286\pi$
$68$	1.75586	+	0.957585i	0.212929	+	0.116124i
$69$	3.87482	−	3.87482i	0.466474	−	0.466474i
$70$	0.268474	+	0.452221i	0.0320888	+	0.0540507i
$71$		−	6.09170i		−	0.722952i	−0.932381	−	0.361476i	$-0.882273\pi$
$71$		−	6.09170i		−	0.722952i	0.932381	−	0.361476i	$-0.117727\pi$
$72$	−3.75800	+	4.04269i	−0.442884	+	0.476436i
$73$			13.5126i			1.58153i	0.612121	+	0.790764i	$0.290317\pi$
$73$			13.5126i			1.58153i	−0.612121	+	0.790764i	$0.709683\pi$
$74$	2.04358	−	1.21323i	0.237561	−	0.141035i
$75$	−3.60581	+	3.60581i	−0.416363	+	0.416363i
$76$	2.31989	+	7.88567i	0.266110	+	0.904548i
$77$	−5.08854	−	5.08854i	−0.579893	−	0.579893i
$78$	0.752429	−	2.95119i	0.0851958	−	0.334156i
$79$	−2.30465			−0.259293			−0.129647	−	0.991560i	$-0.541384\pi$
$79$	−2.30465			−0.259293			−0.129647	+	0.991560i	$0.541384\pi$
$80$	0.553200	+	0.119739i	0.0618497	+	0.0133872i
$81$	−0.662648			−0.0736275
$82$	1.64829	−	6.46494i	0.182023	−	0.713933i
$83$	0.632423	+	0.632423i	0.0694175	+	0.0694175i	0.740963	−	0.671546i	$-0.234369\pi$
$83$	0.632423	+	0.632423i	0.0694175	+	0.0694175i	−0.671546	+	0.740963i	$0.734369\pi$
$84$	5.16331	−	1.51900i	0.563363	−	0.165736i
$85$	0.100057	−	0.100057i	0.0108528	−	0.0108528i
$86$	−12.7992	+	7.59861i	−1.38017	+	0.819379i
$87$		−	1.29044i		−	0.138350i
$88$	−7.73984	+	0.282472i	−0.825070	+	0.0301116i
$89$			11.0377i			1.16999i	0.811036	+	0.584996i	$0.198904\pi$
$89$			11.0377i			1.16999i	−0.811036	+	0.584996i	$0.801096\pi$
$90$	0.199357	+	0.335800i	0.0210141	+	0.0353964i
$91$	3.90827	−	3.90827i	0.409698	−	0.409698i
$92$	5.12453	−	9.39648i	0.534269	−	0.979651i
$93$	1.04573	+	1.04573i	0.108438	+	0.108438i
$94$	16.6629	+	4.24834i	1.71865	+	0.438183i
$95$	0.581564			0.0596672
$96$	2.58609	−	5.18316i	0.263941	−	0.529004i
$97$	−17.9190			−1.81939			−0.909697	−	0.415272i	$-0.863686\pi$
$97$	−17.9190			−1.81939			−0.909697	+	0.415272i	$0.863686\pi$
$98$	−0.127998	−	0.0326342i	−0.0129298	−	0.00329655i
$99$	−3.77853	−	3.77853i	−0.379757	−	0.379757i
$100$	−4.76875	+	8.74412i	−0.476875	+	0.874412i
$101$	8.80831	−	8.80831i	0.876460	−	0.876460i	−0.116707	−	0.993166i	$-0.537234\pi$
$101$	8.80831	−	8.80831i	0.876460	−	0.876460i	0.993166	+	0.116707i	$0.0372337\pi$
$102$	−0.739257	−	1.24521i	−0.0731974	−	0.123295i
$103$		−	0.748496i		−	0.0737515i	−0.999320	−	0.0368758i	$-0.988259\pi$
$103$		−	0.748496i		−	0.0737515i	0.999320	−	0.0368758i	$-0.0117406\pi$
$104$	−0.216953	−	5.94461i	−0.0212740	−	0.582917i
$105$		−	0.380791i		−	0.0371614i
$106$	8.24222	−	4.89323i	0.800555	−	0.475273i
$107$	0.777335	−	0.777335i	0.0751478	−	0.0751478i	−0.668534	−	0.743682i	$-0.733078\pi$
$107$	0.777335	−	0.777335i	0.0751478	−	0.0751478i	0.743682	+	0.668534i	$0.233078\pi$
$108$	9.72814	−	2.86193i	0.936091	−	0.275390i
$109$	0.462768	+	0.462768i	0.0443251	+	0.0443251i	0.728922	−	0.684597i	$-0.240022\pi$
$109$	0.462768	+	0.462768i	0.0443251	+	0.0443251i	−0.684597	+	0.728922i	$0.740022\pi$
$110$	−0.135378	+	0.530982i	−0.0129078	+	0.0506272i
$111$	−1.72079			−0.163330
$112$	8.83748	−	5.69249i	0.835063	−	0.537890i
$113$	4.80084			0.451625			0.225812	−	0.974171i	$-0.427496\pi$
$113$	4.80084			0.451625			0.225812	+	0.974171i	$0.427496\pi$
$114$	1.47039	−	5.76717i	0.137714	−	0.540145i
$115$	−0.535458	−	0.535458i	−0.0499318	−	0.0499318i
$116$	−0.711350	−	2.41798i	−0.0660471	−	0.224504i
$117$	2.90211	−	2.90211i	0.268300	−	0.268300i
$118$	11.1585	−	6.62457i	1.02722	−	0.609841i
$119$		−	2.62804i		−	0.240912i
$120$	−0.300167	−	0.279029i	−0.0274014	−	0.0254718i
$121$			3.50188i			0.318353i
$122$	−1.33721	−	2.25242i	−0.121066	−	0.203925i
$123$	−3.41586	+	3.41586i	−0.307998	+	0.307998i
$124$	2.53592	+	1.38300i	0.227732	+	0.124197i
$125$	0.998571	+	0.998571i	0.0893149	+	0.0893149i
$126$	7.02803	+	1.79185i	0.626106	+	0.159631i
$127$	−12.7782			−1.13388			−0.566940	−	0.823759i	$-0.691873\pi$
$127$	−12.7782			−1.13388			−0.566940	+	0.823759i	$0.691873\pi$
$128$	1.98853	−	11.1376i	0.175763	−	0.984433i
$129$	10.7775			0.948909
$130$	−0.407822	−	0.103978i	−0.0357684	−	0.00911944i
$131$	9.29049	+	9.29049i	0.811714	+	0.811714i	0.984891	−	0.173177i	$-0.0554033\pi$
$131$	9.29049	+	9.29049i	0.811714	+	0.811714i	−0.173177	+	0.984891i	$0.555403\pi$
$132$	4.92329	+	2.68500i	0.428517	+	0.233699i
$133$	7.63748	−	7.63748i	0.662253	−	0.662253i
$134$	2.87752	+	4.84692i	0.248579	+	0.418710i
$135$		−	0.717446i		−	0.0617479i
$136$	−2.07161	−	1.92573i	−0.177639	−	0.165130i
$137$		−	8.56962i		−	0.732152i	−0.930585	−	0.366076i	$-0.880701\pi$
$137$		−	8.56962i		−	0.732152i	0.930585	−	0.366076i	$-0.119299\pi$
$138$	−6.66377	+	3.95614i	−0.567258	+	0.336769i
$139$	7.33080	−	7.33080i	0.621790	−	0.621790i	−0.324199	−	0.945989i	$-0.605095\pi$
$139$	7.33080	−	7.33080i	0.621790	−	0.621790i	0.945989	+	0.324199i	$0.105095\pi$
$140$	−0.209909	−	0.713513i	−0.0177406	−	0.0603029i
$141$	−8.80413	−	8.80413i	−0.741441	−	0.741441i
$142$	−2.12837	+	8.34791i	−0.178609	+	0.700541i
$143$	5.75895			0.481587
$144$	6.56233	−	4.22700i	0.546861	−	0.352250i
$145$	−0.178325			−0.0148091
$146$	4.72114	−	18.5173i	0.390724	−	1.53250i
$147$	0.0676302	+	0.0676302i	0.00557804	+	0.00557804i
$148$	−3.22436	+	0.948577i	−0.265040	+	0.0779725i
$149$	−10.3084	+	10.3084i	−0.844501	+	0.844501i	−0.989440	−	0.144940i	$-0.953701\pi$
$149$	−10.3084	+	10.3084i	−0.844501	+	0.844501i	0.144940	+	0.989440i	$0.453701\pi$
$150$	6.20114	−	3.68148i	0.506321	−	0.300592i
$151$			6.30991i			0.513493i	0.966479	+	0.256747i	$0.0826506\pi$
$151$			6.30991i			0.513493i	−0.966479	+	0.256747i	$0.917349\pi$
$152$	−0.423967	−	11.6169i	−0.0343882	−	0.942252i
$153$		−	1.95147i		−	0.157767i
$154$	5.19533	+	8.75108i	0.418652	+	0.705182i
$155$	0.144509	−	0.144509i	0.0116073	−	0.0116073i
$156$	−2.06222	+	3.78134i	−0.165110	+	0.302750i
$157$	−9.08875	−	9.08875i	−0.725361	−	0.725361i	0.244331	−	0.969692i	$-0.421432\pi$
$157$	−9.08875	−	9.08875i	−0.725361	−	0.725361i	−0.969692	+	0.244331i	$0.921432\pi$
$158$	3.15823	+	0.805217i	0.251256	+	0.0640596i
$159$	−6.94034			−0.550405
$160$	−0.716256	−	0.357369i	−0.0566250	−	0.0282525i
$161$	−14.0640			−1.10840
$162$	0.908076	+	0.231521i	0.0713452	+	0.0181900i
$163$	2.71120	+	2.71120i	0.212357	+	0.212357i	0.805268	−	0.592911i	$-0.202021\pi$
$163$	2.71120	+	2.71120i	0.212357	+	0.212357i	−0.592911	+	0.805268i	$0.702021\pi$
$164$	−4.51755	+	8.28350i	−0.352761	+	0.646833i
$165$	0.280554	−	0.280554i	0.0218411	−	0.0218411i
$166$	−0.645696	−	1.08762i	−0.0501157	−	0.0844155i
$167$			13.1921i			1.02084i	0.859927	+	0.510418i	$0.170509\pi$
$167$			13.1921i			1.02084i	−0.859927	+	0.510418i	$0.829491\pi$
$168$	−7.60639	+	0.277601i	−0.586845	+	0.0214174i
$169$		−	8.57682i		−	0.659756i
$170$	−0.172075	+	0.102157i	−0.0131976	+	0.00783511i
$171$	5.67127	−	5.67127i	0.433692	−	0.433692i
$172$	20.1946	−	5.94106i	1.53982	−	0.453002i
$173$	12.2454	+	12.2454i	0.931000	+	0.931000i	0.997768	−	0.0667688i	$-0.0212690\pi$
$173$	12.2454	+	12.2454i	0.931000	+	0.931000i	−0.0667688	+	0.997768i	$0.521269\pi$
$174$	−0.450865	+	1.76839i	−0.0341800	+	0.134061i
$175$	13.0876			0.989328
$176$	10.7052	+	2.31712i	0.806933	+	0.174659i
$177$	−9.39599			−0.706246
$178$	3.85643	−	15.1258i	0.289052	−	1.13372i
$179$	16.5720	+	16.5720i	1.23865	+	1.23865i	0.960554	+	0.278094i	$0.0897028\pi$
$179$	16.5720	+	16.5720i	1.23865	+	1.23865i	0.278094	+	0.960554i	$0.410297\pi$
$180$	−0.155870	−	0.529824i	−0.0116178	−	0.0394908i
$181$	−7.36115	+	7.36115i	−0.547150	+	0.547150i	−0.925615	−	0.378465i	$-0.876452\pi$
$181$	−7.36115	+	7.36115i	−0.547150	+	0.547150i	0.378465	+	0.925615i	$0.376452\pi$
$182$	−6.72129	+	3.99029i	−0.498215	+	0.295780i
$183$			1.89665i			0.140204i
$184$	−10.3055	+	11.0863i	−0.759735	+	0.817289i
$185$			0.237795i			0.0174830i
$186$	−1.06768	−	1.79842i	−0.0782862	−	0.131866i
$187$	1.93625	−	1.93625i	0.141593	−	0.141593i
$188$	−21.3501	−	11.6436i	−1.55712	−	0.849199i
$189$	−9.42197	−	9.42197i	−0.685347	−	0.685347i
$190$	−0.796961	−	0.203192i	−0.0578176	−	0.0147411i
$191$	−15.7409			−1.13897			−0.569485	−	0.822002i	$-0.692857\pi$
$191$	−15.7409			−1.13897			−0.569485	+	0.822002i	$0.692857\pi$
$192$	−5.35484	+	6.19932i	−0.386452	+	0.447397i
$193$	−17.4282			−1.25451			−0.627256	−	0.778813i	$-0.715822\pi$
$193$	−17.4282			−1.25451			−0.627256	+	0.778813i	$0.715822\pi$
$194$	24.5557	+	6.26067i	1.76300	+	0.449490i
$195$	0.215480	+	0.215480i	0.0154308	+	0.0154308i
$196$	0.164004	+	0.0894422i	0.0117146	+	0.00638873i
$197$	19.1709	−	19.1709i	1.36587	−	1.36587i	0.499625	−	0.866242i	$-0.333471\pi$
$197$	19.1709	−	19.1709i	1.36587	−	1.36587i	0.866242	−	0.499625i	$-0.166529\pi$
$198$	3.85783	+	6.49818i	0.274164	+	0.461806i
$199$			20.4340i			1.44853i	0.689523	+	0.724264i	$0.257820\pi$
$199$			20.4340i			1.44853i	−0.689523	+	0.724264i	$0.742180\pi$
$200$	9.59007	−	10.3166i	0.678121	−	0.729493i
$201$		−	4.08134i		−	0.287876i
$202$	−15.1482	+	8.99317i	−1.06582	+	0.632757i
$203$	−2.34188	+	2.34188i	−0.164368	+	0.164368i
$204$	0.577997	+	1.96470i	0.0404679	+	0.137556i
$205$	0.472036	+	0.472036i	0.0329684	+	0.0329684i
$206$	−0.261516	+	1.02572i	−0.0182207	+	0.0714653i
$207$	−10.4433			−0.725860
$208$	−1.77967	+	8.22214i	−0.123398	+	0.570103i
$209$	11.2541			0.778459
$210$	−0.133044	+	0.521827i	−0.00918090	+	0.0360095i
$211$	2.87667	+	2.87667i	0.198038	+	0.198038i	0.799158	−	0.601121i	$-0.205279\pi$
$211$	2.87667	+	2.87667i	0.198038	+	0.198038i	−0.601121	+	0.799158i	$0.705279\pi$
$212$	−13.0046	+	3.82583i	−0.893157	+	0.262759i
$213$	4.41076	−	4.41076i	0.302221	−	0.302221i
$214$	−1.33683	+	0.793649i	−0.0913840	+	0.0542527i
$215$		−	1.48934i		−	0.101572i
$216$	−14.3311	+	0.523026i	−0.975110	+	0.0355874i
$217$		−	3.79558i		−	0.257661i
$218$	−0.472480	−	0.795851i	−0.0320004	−	0.0539019i
$219$	−9.78394	+	9.78394i	−0.661137	+	0.661137i
$220$	0.371038	−	0.680346i	0.0250154	−	0.0458689i
$221$	1.48714	+	1.48714i	0.100036	+	0.100036i
$222$	2.35813	+	0.601223i	0.158267	+	0.0403515i
$223$	7.95897			0.532972			0.266486	−	0.963839i	$-0.414137\pi$
$223$	7.95897			0.532972			0.266486	+	0.963839i	$0.414137\pi$
$224$	−14.0996	+	4.71314i	−0.942066	+	0.314910i
$225$	9.71828			0.647885
$226$	−6.57895	−	1.67735i	−0.437625	−	0.111576i
$227$	−9.46740	−	9.46740i	−0.628373	−	0.628373i	0.319285	−	0.947659i	$-0.396557\pi$
$227$	−9.46740	−	9.46740i	−0.628373	−	0.628373i	−0.947659	+	0.319285i	$0.896557\pi$
$228$	−4.02996	+	7.38945i	−0.266891	+	0.489378i
$229$	−6.64475	+	6.64475i	−0.439097	+	0.439097i	−0.891708	−	0.452611i	$-0.850493\pi$
$229$	−6.64475	+	6.64475i	−0.439097	+	0.439097i	0.452611	+	0.891708i	$0.350493\pi$
$230$	0.546696	+	0.920862i	0.0360481	+	0.0607198i
$231$		−	7.36883i		−	0.484833i
$232$	0.130001	+	3.56208i	0.00853498	+	0.233862i
$233$			9.69196i			0.634941i	0.948268	+	0.317471i	$0.102834\pi$
$233$			9.69196i			0.634941i	−0.948268	+	0.317471i	$0.897166\pi$
$234$	−4.99094	+	2.96302i	−0.326268	+	0.193699i
$235$	−1.21664	+	1.21664i	−0.0793646	+	0.0793646i
$236$	−17.6059	+	5.17950i	−1.14605	+	0.337156i
$237$	−1.66871	−	1.66871i	−0.108394	−	0.108394i
$238$	−0.918206	+	3.60140i	−0.0595185	+	0.233444i
$239$	24.0720			1.55709			0.778544	−	0.627590i	$-0.215958\pi$
$239$	24.0720			1.55709			0.778544	+	0.627590i	$0.215958\pi$
$240$	0.313852	+	0.487249i	0.0202591	+	0.0314518i
$241$	16.5827			1.06819			0.534094	−	0.845425i	$-0.320653\pi$
$241$	16.5827			1.06819			0.534094	+	0.845425i	$0.320653\pi$
$242$	1.22352	−	4.79889i	0.0786506	−	0.308485i
$243$	−11.2353	−	11.2353i	−0.720745	−	0.720745i
$244$	1.04552	+	3.55387i	0.0669324	+	0.227513i
$245$	0.00934576	−	0.00934576i	0.000597079	−	0.000597079i
$246$	5.87448	−	3.48755i	0.374543	−	0.222358i
$247$			8.64371i			0.549986i
$248$	−2.99195	−	2.78125i	−0.189989	−	0.176610i
$249$			0.915826i			0.0580381i
$250$	−1.01953	−	1.71731i	−0.0644806	−	0.108612i
$251$	−8.65825	+	8.65825i	−0.546504	+	0.546504i	−0.925428	−	0.378924i	$-0.876294\pi$
$251$	−8.65825	+	8.65825i	−0.546504	+	0.546504i	0.378924	+	0.925428i	$0.376294\pi$
$252$	−9.00498	−	4.91102i	−0.567261	−	0.309365i
$253$	−10.3618	−	10.3618i	−0.651444	−	0.651444i
$254$	17.5109	+	4.46454i	1.09873	+	0.280130i
$255$	0.144896			0.00907371
$256$	−6.61637	+	14.5679i	−0.413523	+	0.910494i
$257$	−1.98761			−0.123984			−0.0619919	−	0.998077i	$-0.519745\pi$
$257$	−1.98761			−0.123984			−0.0619919	+	0.998077i	$0.519745\pi$
$258$	−14.7693	−	3.76554i	−0.919494	−	0.234432i
$259$	3.12287	+	3.12287i	0.194046	+	0.194046i
$260$	0.522541	+	0.284977i	0.0324066	+	0.0176735i
$261$	−1.73898	+	1.73898i	−0.107640	+	0.107640i
$262$	−9.48547	−	15.9774i	−0.586014	−	0.987090i
$263$			12.2436i			0.754970i	0.926016	+	0.377485i	$0.123211\pi$
$263$			12.2436i			0.754970i	−0.926016	+	0.377485i	$0.876789\pi$
$264$	−5.80865	−	5.39959i	−0.357497	−	0.332322i
$265$			0.959081i			0.0589158i
$266$	−13.1347	+	7.79777i	−0.805337	+	0.478112i
$267$	−7.99195	+	7.99195i	−0.489100	+	0.489100i
$268$	−2.24982	−	7.64747i	−0.137430	−	0.467144i
$269$	7.98261	+	7.98261i	0.486708	+	0.486708i	0.907266	−	0.420558i	$-0.138166\pi$
$269$	7.98261	+	7.98261i	0.486708	+	0.486708i	−0.420558	+	0.907266i	$0.638166\pi$
$270$	−0.250667	+	0.983170i	−0.0152551	+	0.0598338i
$271$	0.445628			0.0270700			0.0135350	−	0.999908i	$-0.495692\pi$
$271$	0.445628			0.0270700			0.0135350	+	0.999908i	$0.495692\pi$
$272$	2.16606	+	3.36276i	0.131337	+	0.203898i
$273$	5.65965			0.342537
$274$	−2.99412	+	11.7436i	−0.180882	+	0.709457i
$275$	9.64247	+	9.64247i	0.581463	+	0.581463i
$276$	10.5141	−	3.09315i	0.632874	−	0.186186i
$277$	22.1926	−	22.1926i	1.33342	−	1.33342i	0.431133	−	0.902289i	$-0.358114\pi$
$277$	22.1926	−	22.1926i	1.33342	−	1.33342i	0.902289	−	0.431133i	$-0.141886\pi$
$278$	−12.6072	+	7.48465i	−0.756132	+	0.448899i
$279$		−	2.81844i		−	0.168735i
$280$	0.0383615	+	1.05112i	0.00229254	+	0.0628165i
$281$		−	29.1670i		−	1.73996i	−0.493087	−	0.869980i	$-0.664132\pi$
$281$		−	29.1670i		−	1.73996i	0.493087	−	0.869980i	$-0.335868\pi$
$282$	8.98890	+	15.1410i	0.535281	+	0.901635i
$283$	7.50613	−	7.50613i	0.446193	−	0.446193i	−0.447894	−	0.894087i	$-0.647826\pi$
$283$	7.50613	−	7.50613i	0.446193	−	0.446193i	0.894087	+	0.447894i	$0.147826\pi$
$284$	5.83332	−	10.6961i	0.346144	−	0.634699i
$285$	0.421088	+	0.421088i	0.0249431	+	0.0249431i
$286$	−7.89192	−	2.01211i	−0.466659	−	0.118978i
$287$	12.3982			0.731840
$288$	−10.4697	+	3.49978i	−0.616934	+	0.206226i
$289$	1.00000			0.0588235
$290$	0.244372	+	0.0623047i	0.0143500	+	0.00365866i
$291$	−12.9744	−	12.9744i	−0.760574	−	0.760574i
$292$	−12.9395	+	23.7262i	−0.757224	+	1.38847i
$293$	−6.90203	+	6.90203i	−0.403221	+	0.403221i	−0.879366	−	0.476146i	$-0.842033\pi$
$293$	−6.90203	+	6.90203i	−0.403221	+	0.403221i	0.476146	+	0.879366i	$0.342033\pi$
$294$	−0.0690495	−	0.116308i	−0.00402705	−	0.00678321i
$295$			1.29843i			0.0755972i
$296$	4.75000	−	0.173355i	0.276088	−	0.0100761i
$297$		−	13.8836i		−	0.805605i
$298$	17.7281	−	10.5248i	1.02696	−	0.609685i
$299$	7.95845	−	7.95845i	0.460249	−	0.460249i
$300$	−9.78415	+	2.87841i	−0.564888	+	0.166185i
$301$	−19.5590	−	19.5590i	−1.12736	−	1.12736i
$302$	2.20461	−	8.64695i	0.126861	−	0.497576i
$303$	12.7555			0.732785
$304$	−3.47780	+	16.0676i	−0.199466	+	0.921540i
$305$	0.262096			0.0150076
$306$	−0.681820	+	2.67425i	−0.0389771	+	0.152876i
$307$	3.04718	+	3.04718i	0.173912	+	0.173912i	0.788696	−	0.614784i	$-0.210757\pi$
$307$	3.04718	+	3.04718i	0.173912	+	0.173912i	−0.614784	+	0.788696i	$0.710757\pi$
$308$	−4.06203	−	13.8075i	−0.231456	−	0.786753i
$309$	0.541957	−	0.541957i	0.0308309	−	0.0308309i
$310$	−0.248522	+	0.147542i	−0.0141151	+	0.00837983i
$311$		−	20.0156i		−	1.13498i	−0.823381	−	0.567489i	$-0.807915\pi$
$311$		−	20.0156i		−	1.13498i	0.823381	−	0.567489i	$-0.192085\pi$
$312$	4.14717	−	4.46135i	0.234787	−	0.252574i
$313$		−	27.5542i		−	1.55746i	−0.627362	−	0.778728i	$-0.715865\pi$
$313$		−	27.5542i		−	1.55746i	0.627362	−	0.778728i	$-0.284135\pi$
$314$	9.27950	+	15.6305i	0.523672	+	0.882080i
$315$	−0.513149	+	0.513149i	−0.0289127	+	0.0289127i
$316$	−4.04663	−	2.20690i	−0.227641	−	0.124148i
$317$	21.4263	+	21.4263i	1.20342	+	1.20342i	0.973119	+	0.230302i	$0.0739714\pi$
$317$	21.4263	+	21.4263i	1.20342	+	1.20342i	0.230302	+	0.973119i	$0.426029\pi$
$318$	9.51087	+	2.42487i	0.533343	+	0.135980i
$319$	−3.45083			−0.193210
$320$	0.856680	+	0.739981i	0.0478898	+	0.0413662i
$321$	1.12568			0.0628291
$322$	19.2729	+	4.91379i	1.07404	+	0.273835i
$323$	2.90615	+	2.90615i	0.161702	+	0.161702i
$324$	−1.16351	−	0.634542i	−0.0646397	−	0.0352523i
$325$	−7.40593	+	7.40593i	−0.410807	+	0.410807i
$326$	−2.76810	−	4.66262i	−0.153311	−	0.258238i
$327$			0.670145i			0.0370591i
$328$	9.08489	−	9.77313i	0.501629	−	0.539631i
$329$			31.9553i			1.76175i
$330$	−0.482486	+	0.286442i	−0.0265600	+	0.0157681i
$331$	0.466937	−	0.466937i	0.0256652	−	0.0256652i	−0.694158	−	0.719823i	$-0.744223\pi$
$331$	0.466937	−	0.466937i	0.0256652	−	0.0256652i	0.719823	+	0.694158i	$0.244223\pi$
$332$	0.504845	+	1.71604i	0.0277070	+	0.0941801i
$333$	2.31891	+	2.31891i	0.127076	+	0.127076i
$334$	4.60916	−	18.0781i	0.252202	−	0.989191i
$335$	−0.563997			−0.0308145
$336$	10.5206	+	2.27716i	0.573945	+	0.124229i
$337$	13.5762			0.739541			0.369770	−	0.929123i	$-0.379436\pi$
$337$	13.5762			0.739541			0.369770	+	0.929123i	$0.379436\pi$
$338$	−2.99664	+	11.7535i	−0.162996	+	0.639304i
$339$	3.47610	+	3.47610i	0.188796	+	0.188796i
$340$	0.271500	−	0.0798729i	0.0147242	−	0.00433172i
$341$	2.79645	−	2.79645i	0.151436	−	0.151436i
$342$	−9.75323	+	5.79029i	−0.527394	+	0.313103i
$343$		−	18.6418i		−	1.00656i
$344$	−29.7499	+	1.08574i	−1.60401	+	0.0585394i
$345$		−	0.775410i		−	0.0417466i
$346$	−12.5024	−	21.0592i	−0.672132	−	1.13215i
$347$	−22.0844	+	22.0844i	−1.18555	+	1.18555i	−0.207266	+	0.978285i	$0.566457\pi$
$347$	−22.0844	+	22.0844i	−1.18555	+	1.18555i	−0.978285	+	0.207266i	$0.933543\pi$
$348$	1.23571	−	2.26583i	0.0662409	−	0.121461i
$349$	1.79835	+	1.79835i	0.0962633	+	0.0962633i	0.753598	−	0.657335i	$-0.228316\pi$
$349$	1.79835	+	1.79835i	0.0962633	+	0.0962633i	−0.657335	+	0.753598i	$0.728316\pi$
$350$	−17.9349	−	4.57264i	−0.958660	−	0.244418i
$351$	10.6633			0.569165
$352$	−13.8605	−	6.91558i	−0.738769	−	0.368602i
$353$	−2.22119			−0.118222			−0.0591110	−	0.998251i	$-0.518827\pi$
$353$	−2.22119			−0.118222			−0.0591110	+	0.998251i	$0.518827\pi$
$354$	12.8760	+	3.28285i	0.684354	+	0.174481i
$355$	−0.609520	−	0.609520i	−0.0323500	−	0.0323500i
$356$	−10.5695	+	19.3806i	−0.560183	+	1.02717i
$357$	1.90286	−	1.90286i	0.100710	−	0.100710i
$358$	−16.9198	−	28.4999i	−0.894238	−	1.50627i
$359$		−	1.52104i		−	0.0802776i	−0.999194	−	0.0401388i	$-0.987220\pi$
$359$		−	1.52104i		−	0.0802776i	0.999194	−	0.0401388i	$-0.0127800\pi$
$360$	0.0284856	+	0.780517i	0.00150132	+	0.0411369i
$361$		−	2.10859i		−	0.110978i
$362$	12.6594	−	7.51564i	0.665365	−	0.395013i
$363$	−2.53558	+	2.53558i	−0.133083	+	0.133083i
$364$	10.6049	−	3.11985i	0.555845	−	0.163525i
$365$	1.35204	+	1.35204i	0.0707688	+	0.0707688i
$366$	0.662666	−	2.59912i	0.0346381	−	0.135858i
$367$	33.3249			1.73955			0.869774	−	0.493451i	$-0.164265\pi$
$367$	33.3249			1.73955			0.869774	+	0.493451i	$0.164265\pi$
$368$	17.9959	−	11.5917i	0.938099	−	0.604259i
$369$	9.20634			0.479263
$370$	0.0830826	−	0.325868i	0.00431926	−	0.0169411i
$371$	12.5953	+	12.5953i	0.653914	+	0.653914i
$372$	0.834779	+	2.83754i	0.0432813	+	0.147120i
$373$	−24.8863	+	24.8863i	−1.28856	+	1.28856i	−0.352906	+	0.935659i	$0.614806\pi$
$373$	−24.8863	+	24.8863i	−1.28856	+	1.28856i	−0.935659	+	0.352906i	$0.885194\pi$
$374$	−3.32989	+	1.97688i	−0.172184	+	0.102222i
$375$			1.44605i			0.0746739i
$376$	25.1895	+	23.4156i	1.29905	+	1.20757i
$377$		−	2.65042i		−	0.136504i
$378$	9.61971	+	16.2036i	0.494784	+	0.833421i
$379$	12.4894	−	12.4894i	0.641536	−	0.641536i	−0.309397	−	0.950933i	$-0.600127\pi$
$379$	12.4894	−	12.4894i	0.641536	−	0.641536i	0.950933	+	0.309397i	$0.100127\pi$
$380$	1.02114	+	0.556897i	0.0523835	+	0.0285682i
$381$	−9.25219	−	9.25219i	−0.474004	−	0.474004i
$382$	21.5709	+	5.49967i	1.10366	+	0.281388i
$383$	−26.7131			−1.36498			−0.682488	−	0.730897i	$-0.739102\pi$
$383$	−26.7131			−1.36498			−0.682488	+	0.730897i	$0.739102\pi$
$384$	9.50411	−	6.62448i	0.485004	−	0.338054i
$385$	−1.01829			−0.0518970
$386$	23.8832	+	6.08921i	1.21562	+	0.309933i
$387$	−14.5237	−	14.5237i	−0.738279	−	0.738279i
$388$	−31.4631	−	17.1589i	−1.59730	−	0.871113i
$389$	−2.66266	+	2.66266i	−0.135002	+	0.135002i	−0.771379	−	0.636376i	$-0.780433\pi$
$389$	−2.66266	+	2.66266i	−0.135002	+	0.135002i	0.636376	+	0.771379i	$0.280433\pi$
$390$	−0.220002	−	0.370575i	−0.0111403	−	0.0187648i
$391$		−	5.35151i		−	0.270637i
$392$	−0.193497	−	0.179870i	−0.00977306	−	0.00908483i
$393$			13.4538i			0.678653i
$394$	−32.9693	+	19.5732i	−1.66097	+	0.986083i
$395$	−0.230597	+	0.230597i	−0.0116026	+	0.0116026i
$396$	−3.01629	−	10.2528i	−0.151574	−	0.515224i
$397$	12.2181	+	12.2181i	0.613209	+	0.613209i	0.943781	−	0.330572i	$-0.107241\pi$
$397$	12.2181	+	12.2181i	0.613209	+	0.613209i	−0.330572	+	0.943781i	$0.607241\pi$
$398$	7.13940	−	28.0023i	0.357866	−	1.40363i
$399$	11.0600			0.553693
$400$	−16.7465	+	10.7869i	−0.837324	+	0.539347i
$401$	−26.8473			−1.34069			−0.670346	−	0.742049i	$-0.733854\pi$
$401$	−26.8473			−1.34069			−0.670346	+	0.742049i	$0.733854\pi$
$402$	−1.42597	+	5.59297i	−0.0711210	+	0.278952i
$403$	2.14782	+	2.14782i	0.106991	+	0.106991i
$404$	23.9008	−	7.03142i	1.18911	−	0.349826i
$405$	−0.0663029	+	0.0663029i	−0.00329462	+	0.00329462i
$406$	4.02748	−	2.39103i	0.199881	−	0.118665i
$407$			4.60165i			0.228095i
$408$	−0.105630	−	2.89432i	−0.00522949	−	0.143290i
$409$		−	17.8962i		−	0.884910i	−0.896791	−	0.442455i	$-0.854108\pi$
$409$		−	17.8962i		−	0.884910i	0.896791	−	0.442455i	$-0.145892\pi$
$410$	−0.481942	−	0.811789i	−0.0238014	−	0.0400914i
$411$	6.20493	−	6.20493i	0.306067	−	0.306067i
$412$	0.716749	−	1.31425i	0.0353117	−	0.0647485i
$413$	17.0518	+	17.0518i	0.839063	+	0.839063i
$414$	14.3113	+	3.64877i	0.703360	+	0.179327i
$415$	0.126557			0.00621246
$416$	5.31153	−	10.6456i	0.260419	−	0.521945i
$417$	10.6159			0.519862
$418$	−15.4223	−	3.93203i	−0.754328	−	0.192322i
$419$	−17.1549	−	17.1549i	−0.838073	−	0.838073i	0.150533	−	0.988605i	$-0.451901\pi$
$419$	−17.1549	−	17.1549i	−0.838073	−	0.838073i	−0.988605	+	0.150533i	$0.951901\pi$
$420$	0.364640	−	0.668615i	0.0177926	−	0.0326251i
$421$	−28.2854	+	28.2854i	−1.37855	+	1.37855i	−0.531471	+	0.847077i	$0.678360\pi$
$421$	−28.2854	+	28.2854i	−1.37855	+	1.37855i	−0.847077	+	0.531471i	$0.821640\pi$
$422$	−2.93704	−	4.94719i	−0.142973	−	0.240825i
$423$			23.7287i			1.15373i
$424$	19.1578	−	0.699180i	0.930387	−	0.0339552i
$425$			4.97998i			0.241564i
$426$	−7.58547	+	4.50333i	−0.367517	+	0.218187i
$427$	3.44202	−	3.44202i	0.166571	−	0.166571i
$428$	2.10925	−	0.620524i	0.101955	−	0.0299941i
$429$	4.16983	+	4.16983i	0.201321	+	0.201321i
$430$	−0.520357	+	2.04095i	−0.0250939	+	0.0984235i
$431$	−11.5554			−0.556605			−0.278303	−	0.960493i	$-0.589772\pi$
$431$	−11.5554			−0.556605			−0.278303	+	0.960493i	$0.589772\pi$
$432$	19.8218	+	4.29038i	0.953675	+	0.206421i
$433$	0.357537			0.0171821			0.00859107	−	0.999963i	$-0.497265\pi$
$433$	0.357537			0.0171821			0.00859107	+	0.999963i	$0.497265\pi$
$434$	−1.32613	+	5.20137i	−0.0636563	+	0.249674i
$435$	−0.129118	−	0.129118i	−0.00619075	−	0.00619075i
$436$	0.369414	+	1.25569i	0.0176917	+	0.0601368i
$437$	15.5523	−	15.5523i	0.743967	−	0.743967i
$438$	16.8261	−	9.98928i	0.803980	−	0.477306i
$439$		−	7.54117i		−	0.359920i	−0.983674	−	0.179960i	$-0.942403\pi$
$439$		−	7.54117i		−	0.359920i	0.983674	−	0.179960i	$-0.0575969\pi$
$440$	−0.746166	+	0.802692i	−0.0355721	+	0.0382669i
$441$		−	0.182275i		−	0.00867976i
$442$	−1.51835	−	2.55753i	−0.0722206	−	0.121649i
$443$	−18.1559	+	18.1559i	−0.862613	+	0.862613i	−0.991641	−	0.129028i	$-0.958814\pi$
$443$	−18.1559	+	18.1559i	−0.862613	+	0.862613i	0.129028	+	0.991641i	$0.458814\pi$
$444$	−3.02146	−	1.64780i	−0.143392	−	0.0782013i
$445$	1.10440	+	1.10440i	0.0523537	+	0.0523537i
$446$	−10.9068	−	2.78077i	−0.516450	−	0.131673i
$447$	−14.9279			−0.706065
$448$	20.9684	−	1.53256i	0.990663	−	0.0724065i
$449$	18.0732			0.852927			0.426463	−	0.904505i	$-0.359759\pi$
$449$	18.0732			0.852927			0.426463	+	0.904505i	$0.359759\pi$
$450$	−13.3177	−	3.39545i	−0.627802	−	0.160063i
$451$	9.13453	+	9.13453i	0.430128	+	0.430128i
$452$	8.42958	+	4.59721i	0.396494	+	0.216235i
$453$	−4.56876	+	4.56876i	−0.214659	+	0.214659i
$454$	9.66609	+	16.2817i	0.453652	+	0.764137i
$455$		−	0.782103i		−	0.0366655i
$456$	8.10434	−	8.71830i	0.379521	−	0.408272i
$457$		−	37.4375i		−	1.75125i	−0.482991	−	0.875625i	$-0.660450\pi$
$457$		−	37.4375i		−	1.75125i	0.482991	−	0.875625i	$-0.339550\pi$
$458$	11.4274	−	6.78420i	0.533967	−	0.317005i
$459$	3.58517	−	3.58517i	0.167341	−	0.167341i
$460$	−0.427441	−	1.45294i	−0.0199295	−	0.0677435i
$461$	14.0370	+	14.0370i	0.653770	+	0.653770i	0.953899	−	0.300129i	$-0.0970297\pi$
$461$	14.0370	+	14.0370i	0.653770	+	0.653770i	−0.300129	+	0.953899i	$0.597030\pi$
$462$	−2.57458	+	10.0981i	−0.119780	+	0.469804i
$463$	−18.3120			−0.851030			−0.425515	−	0.904951i	$-0.639907\pi$
$463$	−18.3120			−0.851030			−0.425515	+	0.904951i	$0.639907\pi$
$464$	1.06640	−	4.92681i	0.0495063	−	0.228721i
$465$	0.209267			0.00970453
$466$	3.38626	−	13.2816i	0.156865	−	0.615259i
$467$	−8.99457	−	8.99457i	−0.416219	−	0.416219i	0.467679	−	0.883898i	$-0.345090\pi$
$467$	−8.99457	−	8.99457i	−0.416219	−	0.416219i	−0.883898	+	0.467679i	$0.845090\pi$
$468$	7.87471	−	2.31667i	0.364009	−	0.107088i
$469$	−7.40678	+	7.40678i	−0.342013	+	0.342013i
$470$	2.09233	−	1.24217i	0.0965118	−	0.0572970i
$471$		−	13.1616i		−	0.606456i
$472$	25.9363	−	0.946567i	1.19382	−	0.0435693i
$473$		−	28.8207i		−	1.32518i
$474$	1.70373	+	2.86978i	0.0782549	+	0.131813i
$475$	−14.4726	+	14.4726i	−0.664047	+	0.664047i
$476$	2.51657	−	4.61446i	0.115347	−	0.211503i
$477$	9.35271	+	9.35271i	0.428231	+	0.428231i
$478$	−32.9877	−	8.41047i	−1.50882	−	0.384686i
$479$	−6.50691			−0.297308			−0.148654	−	0.988889i	$-0.547494\pi$
$479$	−6.50691			−0.297308			−0.148654	+	0.988889i	$0.547494\pi$
$480$	−0.259856	−	0.777371i	−0.0118608	−	0.0354820i
$481$	−3.53431			−0.161151
$482$	−22.7246	−	5.79381i	−1.03508	−	0.263901i
$483$	−10.1832	−	10.1832i	−0.463351	−	0.463351i
$484$	−3.35335	+	6.14880i	−0.152425	+	0.279491i
$485$	−1.79293	+	1.79293i	−0.0814126	+	0.0814126i
$486$	11.4711	+	19.3221i	0.520340	+	0.876466i
$487$		−	19.6338i		−	0.889694i	−0.895606	−	0.444847i	$-0.853258\pi$
$487$		−	19.6338i		−	0.889694i	0.895606	−	0.444847i	$-0.146742\pi$
$488$	−0.191071	−	5.23543i	−0.00864938	−	0.236997i
$489$			3.92615i			0.177546i
$490$	−0.0160725	+	0.00954190i	−0.000726081	+	0.000431059i
$491$	7.46270	−	7.46270i	0.336787	−	0.336787i	−0.518370	−	0.855157i	$-0.673461\pi$
$491$	7.46270	−	7.46270i	0.336787	−	0.336787i	0.855157	+	0.518370i	$0.173461\pi$
$492$	−9.26875	+	2.72678i	−0.417867	+	0.122933i
$493$	−0.891113	−	0.891113i	−0.0401337	−	0.0401337i
$494$	3.02001	−	11.8451i	0.135877	−	0.532937i
$495$	−0.756141			−0.0339860
$496$	3.12836	+	4.85671i	0.140467	+	0.218073i
$497$	−16.0092			−0.718112
$498$	0.319979	−	1.25503i	0.0143386	−	0.0562390i
$499$	−29.7678	−	29.7678i	−1.33259	−	1.33259i	−0.903044	−	0.429548i	$-0.858673\pi$
$499$	−29.7678	−	29.7678i	−1.33259	−	1.33259i	−0.429548	−	0.903044i	$-0.641327\pi$
$500$	0.797130	+	2.70957i	0.0356487	+	0.121175i
$501$	−9.55189	+	9.55189i	−0.426747	+	0.426747i
$502$	14.8901	−	8.83996i	0.664579	−	0.394547i
$503$		−	2.48521i		−	0.110810i	−0.998464	−	0.0554051i	$-0.982355\pi$
$503$		−	2.48521i		−	0.110810i	0.998464	−	0.0554051i	$-0.0176450\pi$
$504$	10.6244	+	9.87617i	0.473246	+	0.439920i
$505$		−	1.76267i		−	0.0784380i
$506$	10.5793	+	17.8199i	0.470308	+	0.792192i
$507$	6.21015	−	6.21015i	0.275802	−	0.275802i
$508$	−22.4366	−	12.2362i	−0.995465	−	0.542894i
$509$	1.18351	+	1.18351i	0.0524581	+	0.0524581i	0.732849	−	0.680391i	$-0.238190\pi$
$509$	1.18351	+	1.18351i	0.0524581	+	0.0524581i	−0.680391	+	0.732849i	$0.738190\pi$
$510$	−0.198561	−	0.0506248i	−0.00879244	−	0.00224170i
$511$	35.5116			1.57094
$512$	14.1568	−	17.6518i	0.625646	−	0.780107i
$513$	20.8381			0.920023
$514$	2.72377	+	0.694448i	0.120141	+	0.0306308i
$515$	−0.0748926	−	0.0748926i	−0.00330016	−	0.00330016i
$516$	18.9238	+	10.3204i	0.833074	+	0.454331i
$517$	−23.5436	+	23.5436i	−1.03544	+	1.03544i
$518$	−3.18841	−	5.37060i	−0.140091	−	0.235971i
$519$			17.7328i			0.778385i
$520$	−0.616510	−	0.573094i	−0.0270358	−	0.0251319i
$521$		−	16.5566i		−	0.725358i	−0.931914	−	0.362679i	$-0.881862\pi$
$521$		−	16.5566i		−	0.725358i	0.931914	−	0.362679i	$-0.118138\pi$
$522$	2.99064	−	1.77548i	0.130897	−	0.0777105i
$523$	3.85369	−	3.85369i	0.168510	−	0.168510i	−0.617814	−	0.786324i	$-0.711982\pi$
$523$	3.85369	−	3.85369i	0.168510	−	0.168510i	0.786324	+	0.617814i	$0.211982\pi$
$524$	7.41632	+	25.2092i	0.323984	+	1.10127i
$525$	9.47621	+	9.47621i	0.413576	+	0.413576i
$526$	4.27775	−	16.7783i	0.186519	−	0.731567i
$527$	1.44426			0.0629131
$528$	6.07347	+	9.42894i	0.264314	+	0.410342i
$529$	−5.63864			−0.245158
$530$	0.335091	−	1.31430i	0.0145554	−	0.0570895i
$531$	12.6619	+	12.6619i	0.549480	+	0.549480i
$532$	20.7239	−	6.09677i	0.898493	−	0.264329i
$533$	−7.01580	+	7.01580i	−0.303888	+	0.303888i
$534$	13.7443	−	8.15968i	0.594773	−	0.353104i
$535$		−	0.155556i		−	0.00672529i
$536$	0.411160	+	11.2660i	0.0177594	+	0.486616i
$537$			23.9983i			1.03560i
$538$	−8.15014	−	13.7282i	−0.351377	−	0.591864i
$539$	0.180853	−	0.180853i	0.00778990	−	0.00778990i
$540$	0.687016	−	1.25973i	0.0295644	−	0.0542102i
$541$	−27.1691	−	27.1691i	−1.16809	−	1.16809i	−0.982657	−	0.185433i	$-0.940631\pi$
$541$	−27.1691	−	27.1691i	−1.16809	−	1.16809i	−0.185433	−	0.982657i	$-0.559369\pi$
$542$	−0.610678	−	0.155697i	−0.0262309	−	0.00668777i
$543$	−10.6599			−0.457458
$544$	−1.79341	−	5.36504i	−0.0768916	−	0.230024i
$545$	0.0926068			0.00396684
$546$	−7.75584	−	1.97741i	−0.331919	−	0.0846255i
$547$	−1.77642	−	1.77642i	−0.0759544	−	0.0759544i	0.668109	−	0.744063i	$-0.267104\pi$
$547$	−1.77642	−	1.77642i	−0.0759544	−	0.0759544i	−0.744063	+	0.668109i	$0.767104\pi$
$548$	8.20615	−	15.0470i	0.350549	−	0.642777i
$549$	2.55589	−	2.55589i	0.109083	−	0.109083i
$550$	−9.84484	−	16.5828i	−0.419785	−	0.707092i
$551$		−	5.17942i		−	0.220651i
$552$	−15.4890	+	0.565282i	−0.659254	+	0.0240600i
$553$			6.05671i			0.257558i
$554$	−38.1659	+	22.6583i	−1.62152	+	0.962659i
$555$	−0.172178	+	0.172178i	−0.00730854	+	0.00730854i
$556$	19.8917	−	5.85196i	0.843595	−	0.248178i
$557$	11.1562	+	11.1562i	0.472702	+	0.472702i	0.902788	−	0.430086i	$-0.141517\pi$
$557$	11.1562	+	11.1562i	0.472702	+	0.472702i	−0.430086	+	0.902788i	$0.641517\pi$
$558$	−0.984728	+	3.86231i	−0.0416868	+	0.163505i
$559$	22.1358			0.936246
$560$	0.314679	−	1.45383i	0.0132976	−	0.0614356i
$561$	2.80393			0.118382
$562$	−10.1906	+	39.9698i	−0.429865	+	1.68602i
$563$	−5.69060	−	5.69060i	−0.239830	−	0.239830i	0.576950	−	0.816780i	$-0.304243\pi$
$563$	−5.69060	−	5.69060i	−0.239830	−	0.239830i	−0.816780	+	0.576950i	$0.804243\pi$
$564$	−7.02808	−	23.8895i	−0.295935	−	1.00593i
$565$	0.480360	−	0.480360i	0.0202089	−	0.0202089i
$566$	−12.9088	+	7.66366i	−0.542596	+	0.322128i
$567$			1.74147i			0.0731347i
$568$	−11.7309	+	12.6196i	−0.492219	+	0.529508i
$569$			8.79716i			0.368796i	0.982852	+	0.184398i	$0.0590335\pi$
$569$			8.79716i			0.368796i	−0.982852	+	0.184398i	$0.940966\pi$
$570$	−0.429925	−	0.724172i	−0.0180076	−	0.0303322i
$571$	−1.80244	+	1.80244i	−0.0754297	+	0.0754297i	−0.743815	−	0.668385i	$-0.766986\pi$
$571$	−1.80244	+	1.80244i	−0.0754297	+	0.0754297i	0.668385	+	0.743815i	$0.266986\pi$
$572$	10.1119	+	5.51468i	0.422799	+	0.230581i
$573$	−11.3974	−	11.3974i	−0.476132	−	0.476132i
$574$	−16.9901	−	4.33177i	−0.709154	−	0.180805i
$575$	26.6504			1.11140
$576$	15.5702	−	1.13801i	0.648760	−	0.0474171i
$577$	−28.9174			−1.20385			−0.601924	−	0.798554i	$-0.705599\pi$
$577$	−28.9174			−1.20385			−0.601924	+	0.798554i	$0.705599\pi$
$578$	−1.37038	−	0.349388i	−0.0570001	−	0.0145326i
$579$	−12.6191	−	12.6191i	−0.524432	−	0.524432i
$580$	−0.313113	−	0.170762i	−0.0130013	−	0.00709049i
$581$	1.66203	−	1.66203i	0.0689528	−	0.0689528i
$582$	13.2467	+	22.3129i	0.549094	+	0.924901i
$583$			18.5595i			0.768656i
$584$	26.0215	−	27.9928i	1.07678	−	1.15835i
$585$		−	0.580756i		−	0.0240113i
$586$	11.8698	−	7.04688i	0.490339	−	0.291104i
$587$	−28.3756	+	28.3756i	−1.17119	+	1.17119i	−0.189258	+	0.981927i	$0.560608\pi$
$587$	−28.3756	+	28.3756i	−1.17119	+	1.17119i	−0.981927	+	0.189258i	$0.939392\pi$
$588$	0.0539872	+	0.183511i	0.00222639	+	0.00756785i
$589$	4.19724	+	4.19724i	0.172944	+	0.172944i
$590$	0.453654	−	1.77933i	0.0186767	−	0.0732538i
$591$	27.7617			1.14197
$592$	−6.56985	−	1.42203i	−0.270019	−	0.0584451i
$593$	−14.7813			−0.606995			−0.303498	−	0.952832i	$-0.598154\pi$
$593$	−14.7813			−0.606995			−0.303498	+	0.952832i	$0.598154\pi$
$594$	−4.85075	+	19.0257i	−0.199029	+	0.780633i
$595$	−0.262955	−	0.262955i	−0.0107801	−	0.0107801i
$596$	−27.9714	+	8.22893i	−1.14575	+	0.337070i
$597$	−14.7955	+	14.7955i	−0.605538	+	0.605538i
$598$	−13.6866	+	8.12547i	−0.559688	+	0.332275i
$599$		−	20.9554i		−	0.856213i	−0.903728	−	0.428106i	$-0.859181\pi$
$599$		−	20.9554i		−	0.856213i	0.903728	−	0.428106i	$-0.140819\pi$
$600$	14.4136	−	0.526037i	0.588434	−	0.0214754i
$601$			43.8547i			1.78887i	0.447199	+	0.894435i	$0.352422\pi$
$601$			43.8547i			1.78887i	−0.447199	+	0.894435i	$0.647578\pi$
$602$	19.9695	+	33.6368i	0.813894	+	1.37093i
$603$	−5.49996	+	5.49996i	−0.223976	+	0.223976i
$604$	−6.04228	+	11.0793i	−0.245857	+	0.450810i
$605$	0.350390	+	0.350390i	0.0142454	+	0.0142454i
$606$	−17.4798	−	4.45662i	−0.710070	−	0.181038i
$607$	−41.3621			−1.67884			−0.839418	−	0.543487i	$-0.817104\pi$
$607$	−41.3621			−1.67884			−0.839418	+	0.543487i	$0.817104\pi$
$608$	10.3797	−	20.8035i	0.420953	−	0.843694i
$609$	−3.39133			−0.137424
$610$	−0.359170	−	0.0915733i	−0.0145424	−	0.00370769i
$611$	−18.0827	−	18.0827i	−0.731548	−	0.731548i
$612$	1.86870	−	3.42650i	0.0755377	−	0.138508i
$613$	−26.7053	+	26.7053i	−1.07862	+	1.07862i	−0.0819848	+	0.996634i	$0.526126\pi$
$613$	−26.7053	+	26.7053i	−1.07862	+	1.07862i	−0.996634	+	0.0819848i	$0.973874\pi$
$614$	−3.11113	−	5.24043i	−0.125555	−	0.211487i
$615$			0.683565i			0.0275640i
$616$	0.742347	+	20.3406i	0.0299100	+	0.819547i
$617$			19.4571i			0.783314i	0.920111	+	0.391657i	$0.128098\pi$
$617$			19.4571i			0.783314i	−0.920111	+	0.391657i	$0.871902\pi$
$618$	−0.932038	+	0.553331i	−0.0374921	+	0.0222582i
$619$	9.08683	−	9.08683i	0.365231	−	0.365231i	−0.500504	−	0.865734i	$-0.666852\pi$
$619$	9.08683	−	9.08683i	0.365231	−	0.365231i	0.865734	+	0.500504i	$0.166852\pi$
$620$	0.392117	−	0.115357i	0.0157478	−	0.00463287i
$621$	−19.1861	−	19.1861i	−0.769910	−	0.769910i
$622$	−6.99319	+	27.4288i	−0.280402	+	1.09980i
$623$	29.0075			1.16216
$624$	−7.24192	+	4.66475i	−0.289909	+	0.186739i
$625$	−24.7001			−0.988002
$626$	−9.62711	+	37.7596i	−0.384777	+	1.50918i
$627$	8.14863	+	8.14863i	0.325425	+	0.325425i
$628$	−7.25528	−	24.6618i	−0.289517	−	0.984113i
$629$	−1.18829	+	1.18829i	−0.0473802	+	0.0473802i
$630$	0.882495	−	0.523919i	0.0351594	−	0.0208734i
$631$		−	17.7992i		−	0.708577i	−0.935136	−	0.354288i	$-0.884723\pi$
$631$		−	17.7992i		−	0.708577i	0.935136	−	0.354288i	$-0.115277\pi$
$632$	4.77434	+	4.43812i	0.189913	+	0.176539i
$633$			4.16577i			0.165574i
$634$	−21.8760	−	36.8482i	−0.868806	−	1.46343i
$635$	−1.27855	+	1.27855i	−0.0507378	+	0.0507378i
$636$	−12.1862	−	6.64597i	−0.483216	−	0.263530i
$637$	0.138905	+	0.138905i	0.00550361	+	0.00550361i
$638$	4.72894	+	1.20568i	0.187220	+	0.0477333i
$639$	−11.8878			−0.470273
$640$	−0.915432	−	1.31337i	−0.0361856	−	0.0519153i
$641$	−3.54239			−0.139916			−0.0699580	−	0.997550i	$-0.522287\pi$
$641$	−3.54239			−0.139916			−0.0699580	+	0.997550i	$0.522287\pi$
$642$	−1.54260	−	0.393298i	−0.0608815	−	0.0155222i
$643$	−6.39752	−	6.39752i	−0.252294	−	0.252294i	0.569617	−	0.821910i	$-0.307092\pi$
$643$	−6.39752	−	6.39752i	−0.252294	−	0.252294i	−0.821910	+	0.569617i	$0.807092\pi$
$644$	−24.6943	−	13.4675i	−0.973093	−	0.530692i
$645$	1.07837	−	1.07837i	0.0424609	−	0.0424609i
$646$	−2.96714	−	4.99789i	−0.116741	−	0.196639i
$647$		−	2.11694i		−	0.0832255i	−0.999134	−	0.0416127i	$-0.986750\pi$
$647$		−	2.11694i		−	0.0832255i	0.999134	−	0.0416127i	$-0.0132496\pi$
$648$	1.37275	+	1.27608i	0.0539267	+	0.0501291i
$649$			25.1263i			0.986293i
$650$	12.7364	−	7.56136i	0.499564	−	0.296581i
$651$	2.74823	−	2.74823i	0.107712	−	0.107712i
$652$	2.16427	+	7.35667i	0.0847593	+	0.288110i
$653$	19.0110	+	19.0110i	0.743958	+	0.743958i	0.973337	−	0.229379i	$-0.0736695\pi$
$653$	19.0110	+	19.0110i	0.743958	+	0.743958i	−0.229379	+	0.973337i	$0.573670\pi$
$654$	0.234141	−	0.918350i	0.00915562	−	0.0359103i
$655$	1.85917			0.0726436
$656$	−15.8643	+	10.2187i	−0.619398	+	0.398973i
$657$	26.3694			1.02877
$658$	11.1648	−	43.7908i	0.435249	−	1.70714i
$659$	−4.51444	−	4.51444i	−0.175858	−	0.175858i	0.613690	−	0.789547i	$-0.289685\pi$
$659$	−4.51444	−	4.51444i	−0.175858	−	0.175858i	−0.789547	+	0.613690i	$0.789685\pi$
$660$	0.761266	−	0.223958i	0.0296322	−	0.00871754i
$661$	9.76412	−	9.76412i	0.379780	−	0.379780i	−0.491243	−	0.871023i	$-0.663457\pi$
$661$	9.76412	−	9.76412i	0.379780	−	0.379780i	0.871023	+	0.491243i	$0.163457\pi$
$662$	−0.803021	+	0.476737i	−0.0312103	+	0.0185289i
$663$			2.15356i			0.0836374i
$664$	−0.0922617	−	2.52801i	−0.00358045	−	0.0981058i
$665$		−	1.52837i		−	0.0592678i
$666$	−2.36758	−	3.98798i	−0.0917419	−	0.154531i
$667$	−4.76880	+	4.76880i	−0.184649	+	0.184649i
$668$	−12.6326	+	23.1634i	−0.488769	+	0.896220i
$669$	5.76278	+	5.76278i	0.222802	+	0.222802i
$670$	0.772888	+	0.197054i	0.0298593	+	0.00761286i
$671$	5.07192			0.195799
$672$	−13.6215	−	6.79634i	−0.525462	−	0.262174i
$673$	21.9260			0.845186			0.422593	−	0.906319i	$-0.361120\pi$
$673$	21.9260			0.845186			0.422593	+	0.906319i	$0.361120\pi$
$674$	−18.6044	−	4.74335i	−0.716616	−	0.182707i
$675$	17.8541	+	17.8541i	0.687203	+	0.687203i
$676$	8.21304	−	15.0597i	0.315886	−	0.579218i
$677$	23.4977	−	23.4977i	0.903088	−	0.903088i	−0.0926137	−	0.995702i	$-0.529522\pi$
$677$	23.4977	−	23.4977i	0.903088	−	0.903088i	0.995702	+	0.0926137i	$0.0295222\pi$
$678$	−3.54905	−	5.97807i	−0.136301	−	0.229586i
$679$			47.0917i			1.80722i
$680$	−0.399964	+	0.0145970i	−0.0153379	+	0.000559769i
$681$		−	13.7100i		−	0.525367i
$682$	−4.80923	+	2.85514i	−0.184155	+	0.109329i
$683$	23.6192	−	23.6192i	0.903765	−	0.903765i	−0.0919944	−	0.995760i	$-0.529324\pi$
$683$	23.6192	−	23.6192i	0.903765	−	0.903765i	0.995760	+	0.0919944i	$0.0293242\pi$
$684$	15.3886	−	4.52720i	0.588400	−	0.173102i
$685$	−0.857455	−	0.857455i	−0.0327617	−	0.0327617i
$686$	−6.51321	+	25.5462i	−0.248675	+	0.975358i
$687$	−9.62241			−0.367118
$688$	41.1478	+	8.90637i	1.56875	+	0.339552i
$689$	−14.2547			−0.543060
$690$	−0.270919	+	1.06260i	−0.0103137	+	0.0404526i
$691$	−26.2542	−	26.2542i	−0.998755	−	0.998755i	0.00124381	−	0.999999i	$-0.499604\pi$
$691$	−26.2542	−	26.2542i	−0.998755	−	0.998755i	−0.999999	+	0.00124381i	$0.999604\pi$
$692$	9.77513	+	33.2271i	0.371595	+	1.26311i
$693$	−9.93013	+	9.93013i	−0.377215	+	0.377215i
$694$	37.9799	−	22.5478i	1.44170	−	0.855905i
$695$		−	1.46700i		−	0.0556466i
$696$	−2.48504	+	2.67329i	−0.0941951	+	0.101331i
$697$			4.71764i			0.178694i
$698$	−1.83609	−	3.09273i	−0.0694970	−	0.117062i
$699$	−7.01757	+	7.01757i	−0.265429	+	0.265429i
$700$	22.9799	+	12.5325i	0.868559	+	0.473683i
$701$	−10.9200	−	10.9200i	−0.412444	−	0.412444i	0.470145	−	0.882589i	$-0.344202\pi$
$701$	−10.9200	−	10.9200i	−0.412444	−	0.412444i	−0.882589	+	0.470145i	$0.844202\pi$
$702$	−14.6127	−	3.72563i	−0.551522	−	0.140615i
$703$	−6.90670			−0.260491
$704$	16.5779	+	14.3196i	0.624804	+	0.539692i
$705$	−1.76184			−0.0663547
$706$	3.04386	+	0.776058i	0.114557	+	0.0292073i
$707$	−23.1486	−	23.1486i	−0.870593	−	0.870593i
$708$	−16.4980	−	8.99747i	−0.620033	−	0.338146i
$709$	33.1421	−	33.1421i	1.24468	−	1.24468i	0.286638	−	0.958039i	$-0.407462\pi$
$709$	33.1421	−	33.1421i	1.24468	−	1.24468i	0.958039	−	0.286638i	$-0.0925377\pi$
$710$	0.622312	+	1.04823i	0.0233550	+	0.0393394i
$711$			4.49745i			0.168668i
$712$	21.2555	−	22.8658i	0.796585	−	0.856931i
$713$		−	7.72898i		−	0.289453i
$714$	−3.27247	+	1.94280i	−0.122469	+	0.0727074i
$715$	0.576226	−	0.576226i	0.0215496	−	0.0215496i
$716$	13.2289	+	44.9671i	0.494388	+	1.68050i
$717$	17.4296	+	17.4296i	0.650921	+	0.650921i
$718$	−0.531435	+	2.08440i	−0.0198330	+	0.0777891i
$719$	9.31625			0.347437			0.173719	−	0.984795i	$-0.444422\pi$
$719$	9.31625			0.347437			0.173719	+	0.984795i	$0.444422\pi$
$720$	0.233667	−	1.07955i	0.00870827	−	0.0402326i
$721$	−1.96708			−0.0732578
$722$	−0.736716	+	2.88956i	−0.0274177	+	0.107538i
$723$	12.0069	+	12.0069i	0.446542	+	0.446542i
$724$	−19.9741	+	5.87619i	−0.742330	+	0.218387i
$725$	4.43772	−	4.43772i	0.164813	−	0.164813i
$726$	4.36059	−	2.58879i	0.161837	−	0.0960791i
$727$		−	50.6097i		−	1.87701i	−0.345266	−	0.938505i	$-0.612211\pi$
$727$		−	50.6097i		−	1.87701i	0.345266	−	0.938505i	$-0.387789\pi$
$728$	−15.6227	+	0.570161i	−0.579014	+	0.0211316i
$729$		−	14.2822i		−	0.528969i
$730$	−1.38041	−	2.32518i	−0.0510913	−	0.0860588i
$731$	7.44242	−	7.44242i	0.275268	−	0.275268i
$732$	−1.81620	+	3.33024i	−0.0671287	+	0.123089i
$733$	27.4040	+	27.4040i	1.01219	+	1.01219i	0.999925	+	0.0122657i	$0.00390438\pi$
$733$	27.4040	+	27.4040i	1.01219	+	1.01219i	0.0122657	+	0.999925i	$0.496096\pi$
$734$	−45.6677	−	11.6433i	−1.68562	−	0.429763i
$735$	0.0135338			0.000499202
$736$	−28.7111	+	9.59742i	−1.05830	+	0.353766i
$737$	−10.9141			−0.402027
$738$	−12.6161	−	3.21659i	−0.464407	−	0.118404i
$739$	−13.2619	−	13.2619i	−0.487848	−	0.487848i	0.419779	−	0.907626i	$-0.362108\pi$
$739$	−13.2619	−	13.2619i	−0.487848	−	0.487848i	−0.907626	+	0.419779i	$0.862108\pi$
$740$	−0.227709	+	0.417533i	−0.00837074	+	0.0153488i
$741$	−6.25857	+	6.25857i	−0.229914	+	0.229914i
$742$	−12.8596	−	21.6609i	−0.472091	−	0.795196i
$743$			23.9937i			0.880244i	0.897938	+	0.440122i	$0.145065\pi$
$743$			23.9937i			0.880244i	−0.897938	+	0.440122i	$0.854935\pi$
$744$	−0.152558	−	4.18016i	−0.00559305	−	0.153252i
$745$			2.06287i			0.0755779i
$746$	42.7986	−	25.4086i	1.56697	−	0.930275i
$747$	1.23416	−	1.23416i	0.0451554	−	0.0451554i
$748$	5.25390	−	1.54565i	0.192101	−	0.0565146i
$749$	−2.04287	−	2.04287i	−0.0746448	−	0.0746448i
$750$	0.505234	−	1.98164i	0.0184485	−	0.0723591i
$751$	28.4233			1.03718			0.518590	−	0.855023i	$-0.326457\pi$
$751$	28.4233			1.03718			0.518590	+	0.855023i	$0.326457\pi$
$752$	−26.3379	−	40.8891i	−0.960445	−	1.49107i
$753$	−12.5382			−0.456918
$754$	−0.926026	+	3.63207i	−0.0337239	+	0.132272i
$755$	0.631354	+	0.631354i	0.0229773	+	0.0229773i
$756$	−7.52128	−	25.5660i	−0.273546	−	0.929825i
$757$	24.5037	−	24.5037i	0.890602	−	0.890602i	−0.103977	−	0.994580i	$-0.533157\pi$
$757$	24.5037	−	24.5037i	0.890602	−	0.890602i	0.994580	+	0.103977i	$0.0331570\pi$
$758$	−21.4788	+	12.7515i	−0.780143	+	0.463155i
$759$		−	15.0052i		−	0.544655i
$760$	−1.20478	−	1.11993i	−0.0437018	−	0.0406242i
$761$		−	9.53970i		−	0.345814i	−0.984938	−	0.172907i	$-0.944684\pi$
$761$		−	9.53970i		−	0.345814i	0.984938	−	0.172907i	$-0.0553160\pi$
$762$	9.44636	+	15.9116i	0.342206	+	0.576415i
$763$	1.21617	−	1.21617i	0.0440284	−	0.0440284i
$764$	−27.6387	−	15.0732i	−0.999934	−	0.545331i
$765$	−0.195259	−	0.195259i	−0.00705961	−	0.00705961i
$766$	36.6070	+	9.33324i	1.32266	+	0.337224i
$767$	−19.2983			−0.696822
$768$	−15.3387	+	5.75740i	−0.553488	+	0.207752i
$769$	25.2175			0.909366			0.454683	−	0.890653i	$-0.349753\pi$
$769$	25.2175			0.909366			0.454683	+	0.890653i	$0.349753\pi$
$770$	1.39544	+	0.355779i	0.0502883	+	0.0128214i
$771$	−1.43915	−	1.43915i	−0.0518298	−	0.0518298i
$772$	−30.6015	−	16.6890i	−1.10137	−	0.600651i
$773$	33.4601	−	33.4601i	1.20348	−	1.20348i	0.230375	−	0.973102i	$-0.426005\pi$
$773$	33.4601	−	33.4601i	1.20348	−	1.20348i	0.973102	−	0.230375i	$-0.0739954\pi$
$774$	14.8285	+	24.9772i	0.532998	+	0.897789i
$775$			7.19239i			0.258358i
$776$	37.1211	+	34.5070i	1.33257	+	1.23873i
$777$			4.52230i			0.162237i
$778$	4.57914	−	2.71854i	0.164170	−	0.0974644i
$779$	−13.7102	+	13.7102i	−0.491218	+	0.491218i
$780$	0.172011	+	0.584692i	0.00615899	+	0.0209353i
$781$	−11.7950	−	11.7950i	−0.422060	−	0.422060i
$782$	−1.86975	+	7.33357i	−0.0668622	+	0.262248i
$783$	−6.38958			−0.228345
$784$	0.202319	+	0.314095i	0.00722566	+	0.0112177i
$785$	−1.81880			−0.0649156
$786$	4.70059	−	18.4367i	0.167664	−	0.657616i
$787$	25.7204	+	25.7204i	0.916832	+	0.916832i	0.996798	−	0.0799660i	$-0.0254812\pi$
$787$	25.7204	+	25.7204i	0.916832	+	0.916832i	−0.0799660	+	0.996798i	$0.525481\pi$
$788$	52.0190	−	15.3035i	1.85310	−	0.545166i
$789$	−8.86508	+	8.86508i	−0.315605	+	0.315605i
$790$	0.396573	−	0.235437i	0.0141094	−	0.00837647i
$791$		−	12.6168i		−	0.448601i
$792$	0.551235	+	15.1041i	0.0195873	+	0.536700i
$793$			3.89550i			0.138333i
$794$	−12.4745	−	21.0123i	−0.442705	−	0.745697i
$795$	−0.694433	+	0.694433i	−0.0246290	+	0.0246290i
$796$	−19.5673	+	35.8792i	−0.693545	+	1.27170i
$797$	31.1741	+	31.1741i	1.10424	+	1.10424i	0.993893	+	0.110352i	$0.0351978\pi$
$797$	31.1741	+	31.1741i	1.10424	+	1.10424i	0.110352	+	0.993893i	$0.464802\pi$
$798$	−15.1564	−	3.86423i	−0.536529	−	0.136792i
$799$	−12.1594			−0.430168
$800$	26.7178	−	8.93112i	0.944617	−	0.315763i
$801$	21.5397			0.761068
$802$	36.7909	+	9.38014i	1.29913	+	0.331224i
$803$	26.1637	+	26.1637i	0.923298	+	0.923298i
$804$	3.90823	−	7.16624i	0.137833	−	0.252734i
$805$	−1.40721	+	1.40721i	−0.0495975	+	0.0495975i
$806$	−2.19290	−	3.69374i	−0.0772415	−	0.130107i
$807$			11.5598i			0.406924i
$808$	−35.2098	+	1.28501i	−1.23868	+	0.0452065i
$809$		−	23.8830i		−	0.839681i	−0.907598	−	0.419840i	$-0.862086\pi$
$809$		−	23.8830i		−	0.839681i	0.907598	−	0.419840i	$-0.137914\pi$
$810$	0.114025	−	0.0676944i	0.00400644	−	0.00237854i
$811$	29.5247	−	29.5247i	1.03675	−	1.03675i	0.0374533	−	0.999298i	$-0.488075\pi$
$811$	29.5247	−	29.5247i	1.03675	−	1.03675i	0.999298	−	0.0374533i	$-0.0119246\pi$
$812$	−6.35456	+	1.86946i	−0.223001	+	0.0656050i
$813$	0.322662	+	0.322662i	0.0113163	+	0.0113163i
$814$	1.60776	−	6.30599i	0.0563520	−	0.221025i
$815$	0.542551			0.0190047
$816$	−0.866487	+	4.00321i	−0.0303331	+	0.140140i
$817$	43.2576			1.51339
$818$	−6.25272	+	24.5245i	−0.218621	+	0.857479i
$819$	−7.62687	−	7.62687i	−0.266504	−	0.266504i
$820$	0.376812	+	1.28084i	0.0131588	+	0.0447289i
$821$	−10.1861	+	10.1861i	−0.355496	+	0.355496i	−0.862150	−	0.506654i	$-0.830882\pi$
$821$	−10.1861	+	10.1861i	−0.355496	+	0.355496i	0.506654	+	0.862150i	$0.330882\pi$
$822$	−10.6710	+	6.33516i	−0.372194	+	0.220964i
$823$			55.6252i			1.93897i	0.245148	+	0.969486i	$0.421163\pi$
$823$			55.6252i			1.93897i	−0.245148	+	0.969486i	$0.578837\pi$
$824$	−1.44140	+	1.55059i	−0.0502135	+	0.0540175i
$825$			13.9635i			0.486146i
$826$	−17.4096	−	29.3250i	−0.605759	−	1.02035i
$827$	−18.1650	+	18.1650i	−0.631660	+	0.631660i	−0.948484	−	0.316824i	$-0.897383\pi$
$827$	−18.1650	+	18.1650i	−0.631660	+	0.631660i	0.316824	+	0.948484i	$0.397383\pi$
$828$	−18.3369	−	10.0004i	−0.637253	−	0.347537i
$829$	−10.1346	−	10.1346i	−0.351989	−	0.351989i	0.508860	−	0.860849i	$-0.330067\pi$
$829$	−10.1346	−	10.1346i	−0.351989	−	0.351989i	−0.860849	+	0.508860i	$0.830067\pi$
$830$	−0.173431	−	0.0442176i	−0.00601988	−	0.00153482i
$831$	32.1375			1.11484
$832$	−10.9982	+	12.7327i	−0.381295	+	0.441427i
$833$	0.0934039			0.00323625
$834$	−14.5478	−	3.70907i	−0.503748	−	0.128434i
$835$	1.31997	+	1.31997i	0.0456794	+	0.0456794i
$836$	19.7605	+	10.7767i	0.683431	+	0.372721i
$837$	5.17792	−	5.17792i	0.178975	−	0.178975i
$838$	17.5149	+	29.5024i	0.605044	+	1.01914i
$839$		−	44.9141i		−	1.55061i	−0.631589	−	0.775303i	$-0.717597\pi$
$839$		−	44.9141i		−	1.55061i	0.631589	−	0.775303i	$-0.282403\pi$
$840$	−0.733300	+	0.788852i	−0.0253012	+	0.0272180i
$841$		−	27.4118i		−	0.945236i
$842$	48.6442	−	28.8791i	1.67639	−	0.995238i
$843$	21.1187	−	21.1187i	0.727367	−	0.727367i
$844$	2.29636	+	7.80567i	0.0790439	+	0.268682i
$845$	−0.858176	−	0.858176i	−0.0295221	−	0.0295221i
$846$	8.29051	−	32.5172i	0.285034	−	1.11796i
$847$	9.20309			0.316222
$848$	−26.4977	−	5.73538i	−0.909935	−	0.196954i
$849$	10.8698			0.373050
$850$	1.73994	−	6.82444i	0.0596796	−	0.234076i
$851$	6.35914	+	6.35914i	0.217989	+	0.217989i
$852$	11.9683	−	3.52098i	0.410029	−	0.120627i
$853$	23.6486	−	23.6486i	0.809714	−	0.809714i	−0.174876	−	0.984590i	$-0.555953\pi$
$853$	23.6486	−	23.6486i	0.809714	−	0.809714i	0.984590	+	0.174876i	$0.0559526\pi$
$854$	−5.91945	+	3.51425i	−0.202560	+	0.120255i
$855$		−	1.13491i		−	0.0388129i
$856$	−3.10727	+	0.113402i	−0.106204	+	0.00387601i
$857$		−	33.0162i		−	1.12781i	−0.825839	−	0.563906i	$-0.809298\pi$
$857$		−	33.0162i		−	1.12781i	0.825839	−	0.563906i	$-0.190702\pi$
$858$	−4.25734	−	7.17112i	−0.145343	−	0.244818i
$859$	−5.16428	+	5.16428i	−0.176203	+	0.176203i	−0.789698	−	0.613495i	$-0.789763\pi$
$859$	−5.16428	+	5.16428i	−0.176203	+	0.176203i	0.613495	+	0.789698i	$0.289763\pi$
$860$	1.42617	−	2.61506i	0.0486320	−	0.0891730i
$861$	8.97703	+	8.97703i	0.305936	+	0.305936i
$862$	15.8353	+	4.03733i	0.539352	+	0.137512i
$863$	6.25192			0.212818			0.106409	−	0.994322i	$-0.466065\pi$
$863$	6.25192			0.212818			0.106409	+	0.994322i	$0.466065\pi$
$864$	−25.6642	−	12.8049i	−0.873115	−	0.435632i
$865$	2.45049			0.0833190
$866$	−0.489960	−	0.124919i	−0.0166495	−	0.00424493i
$867$	0.724061	+	0.724061i	0.0245904	+	0.0245904i
$868$	3.63459	−	6.66449i	0.123366	−	0.226208i
$869$	−4.46237	+	4.46237i	−0.151376	+	0.151376i
$870$	0.131828	+	0.222053i	0.00446939	+	0.00752830i
$871$		−	8.38261i		−	0.284034i
$872$	−0.0675114	−	1.84984i	−0.00228622	−	0.0626435i
$873$			34.9683i			1.18350i
$874$	−26.7462	+	15.8787i	−0.904705	+	0.537104i
$875$	2.62429	−	2.62429i	0.0887171	−	0.0887171i
$876$	−26.5482	+	7.81023i	−0.896979	+	0.263883i
$877$	5.65049	+	5.65049i	0.190804	+	0.190804i	0.796043	−	0.605240i	$-0.206923\pi$
$877$	5.65049	+	5.65049i	0.190804	+	0.190804i	−0.605240	+	0.796043i	$0.706923\pi$
$878$	−2.63480	+	10.3342i	−0.0889200	+	0.348763i
$879$	−9.99498			−0.337122
$880$	1.30298	−	0.839288i	0.0439234	−	0.0282924i
$881$	−4.36508			−0.147063			−0.0735316	−	0.997293i	$-0.523427\pi$
$881$	−4.36508			−0.147063			−0.0735316	+	0.997293i	$0.523427\pi$
$882$	−0.0636847	+	0.249785i	−0.00214438	+	0.00841070i
$883$	29.4447	+	29.4447i	0.990893	+	0.990893i	0.999959	−	0.00906586i	$-0.00288579\pi$
$883$	29.4447	+	29.4447i	0.990893	+	0.990893i	−0.00906586	+	0.999959i	$0.502886\pi$
$884$	1.18714	+	4.03527i	0.0399279	+	0.135721i
$885$	−0.940140	+	0.940140i	−0.0316024	+	0.0316024i
$886$	31.2239	−	18.5369i	1.04899	−	0.622761i
$887$		−	44.5674i		−	1.49643i	−0.663458	−	0.748214i	$-0.730912\pi$
$887$		−	44.5674i		−	1.49643i	0.663458	−	0.748214i	$-0.269088\pi$
$888$	3.56481	+	3.31377i	0.119627	+	0.111203i
$889$			33.5816i			1.12629i
$890$	−1.12758	−	1.89931i	−0.0377966	−	0.0636650i
$891$	−1.28305	+	1.28305i	−0.0429838	+	0.0429838i
$892$	13.9748	+	7.62139i	0.467911	+	0.255183i
$893$	−35.3369	−	35.3369i	−1.18251	−	1.18251i
$894$	20.4568	+	5.21563i	0.684178	+	0.174437i
$895$	3.31630			0.110852
$896$	−29.2700	−	5.22593i	−0.977843	−	0.174586i
$897$	11.5248			0.384802
$898$	−24.7671	−	6.31456i	−0.826487	−	0.210720i
$899$	−1.28700	−	1.28700i	−0.0429239	−	0.0429239i
$900$	17.0639	+	9.30608i	0.568797	+	0.310203i
$901$	−4.79265	+	4.79265i	−0.159666	+	0.159666i
$902$	−9.32624	−	15.7092i	−0.310530	−	0.523060i
$903$		−	28.3238i		−	0.942557i
$904$	−9.94547	−	9.24510i	−0.330781	−	0.307487i
$905$			1.47308i			0.0489667i
$906$	7.85719	−	4.66465i	0.261038	−	0.154973i
$907$	34.7519	−	34.7519i	1.15392	−	1.15392i	0.168157	−	0.985760i	$-0.446219\pi$
$907$	34.7519	−	34.7519i	1.15392	−	1.15392i	0.985760	−	0.168157i	$-0.0537814\pi$
$908$	−7.55754	−	25.6892i	−0.250806	−	0.852527i
$909$	−17.1892	−	17.1892i	−0.570128	−	0.570128i
$910$	−0.273257	+	1.07177i	−0.00905839	+	0.0355290i
$911$	−40.9415			−1.35645			−0.678226	−	0.734853i	$-0.737251\pi$
$911$	−40.9415			−1.35645			−0.678226	+	0.734853i	$0.737251\pi$
$912$	−14.1521	+	9.11578i	−0.468622	+	0.301854i
$913$	2.44906			0.0810520
$914$	−13.0802	+	51.3034i	−0.432655	+	1.69696i
$915$	0.189774	+	0.189774i	0.00627372	+	0.00627372i
$916$	−18.0301	+	5.30431i	−0.595732	+	0.175259i
$917$	24.4158	−	24.4158i	0.806280	−	0.806280i
$918$	−6.16564	+	3.66041i	−0.203496	+	0.120812i
$919$			17.6406i			0.581911i	0.956737	+	0.290956i	$0.0939732\pi$
$919$			17.6406i			0.581911i	−0.956737	+	0.290956i	$0.906027\pi$
$920$	0.0781159	+	2.14041i	0.00257541	+	0.0705672i
$921$			4.41269i			0.145403i
$922$	−14.3316	−	24.1404i	−0.471987	−	0.795021i
$923$	9.05921	−	9.05921i	0.298188	−	0.298188i
$924$	7.05628	−	12.9386i	0.232135	−	0.425649i
$925$	−5.91766	−	5.91766i	−0.194571	−	0.194571i
$926$	25.0943	+	6.39799i	0.824649	+	0.210251i
$927$	−1.46067			−0.0479746
$928$	−3.18273	+	6.37899i	−0.104478	+	0.209401i
$929$	−8.34203			−0.273693			−0.136847	−	0.990592i	$-0.543697\pi$
$929$	−8.34203			−0.273693			−0.136847	+	0.990592i	$0.543697\pi$
$930$	−0.286774	−	0.0731154i	−0.00940371	−	0.00239755i
$931$	0.271446	+	0.271446i	0.00889628	+	0.00889628i
$932$	−9.28088	+	17.0177i	−0.304005	+	0.557433i
$933$	14.4925	−	14.4925i	0.474463	−	0.474463i
$934$	9.18334	+	15.4685i	0.300488	+	0.506146i
$935$		−	0.387472i		−	0.0126717i
$936$	−11.6007	+	0.423377i	−0.379181	+	0.0138385i
$937$		−	14.1664i		−	0.462796i	−0.972859	−	0.231398i	$-0.925670\pi$
$937$		−	14.1664i		−	0.462796i	0.972859	−	0.231398i	$-0.0743300\pi$
$938$	12.7379	−	7.56223i	0.415907	−	0.246915i
$939$	19.9509	−	19.9509i	0.651074	−	0.651074i
$940$	−3.30127	+	0.971205i	−0.107676	+	0.0316772i
$941$	−22.4415	−	22.4415i	−0.731572	−	0.731572i	0.239359	−	0.970931i	$-0.423063\pi$
$941$	−22.4415	−	22.4415i	−0.731572	−	0.731572i	−0.970931	+	0.239359i	$0.923063\pi$
$942$	−4.59852	+	18.0364i	−0.149828	+	0.587657i
$943$	25.2465			0.822140
$944$	−35.8732	−	7.76469i	−1.16757	−	0.252719i
$945$	−1.88548			−0.0613346
$946$	−10.0696	+	39.4952i	−0.327392	+	1.28410i
$947$	31.2571	+	31.2571i	1.01572	+	1.01572i	0.999874	+	0.0158460i	$0.00504415\pi$
$947$	31.2571	+	31.2571i	1.01572	+	1.01572i	0.0158460	+	0.999874i	$0.494956\pi$
$948$	−1.33208	−	4.52794i	−0.0432639	−	0.147061i
$949$	−20.0951	+	20.0951i	−0.652315	+	0.652315i
$950$	24.8894	−	14.7763i	0.807518	−	0.479406i
$951$			31.0279i			1.00615i
$952$	−5.06089	+	5.44428i	−0.164024	+	0.176450i
$953$		−	54.5167i		−	1.76597i	−0.469402	−	0.882985i	$-0.655530\pi$
$953$		−	54.5167i		−	1.76597i	0.469402	−	0.882985i	$-0.344470\pi$
$954$	−9.54900	−	16.0844i	−0.309160	−	0.520753i
$955$	−1.57499	+	1.57499i	−0.0509656	+	0.0509656i
$956$	42.2670	+	23.0510i	1.36701	+	0.745523i
$957$	−2.49862	−	2.49862i	−0.0807688	−	0.0807688i
$958$	8.91691	+	2.27344i	0.288092	+	0.0734514i
$959$	−22.5213			−0.727251
$960$	0.0844967	+	1.15608i	0.00272712	+	0.0373123i
$961$	−28.9141			−0.932713
$962$	4.84333	+	1.23485i	0.156155	+	0.0398130i
$963$	−1.51695	−	1.51695i	−0.0488829	−	0.0488829i
$964$	29.1169	+	15.8794i	0.937792	+	0.511440i
$965$	−1.74382	+	1.74382i	−0.0561357	+	0.0561357i
$966$	10.3969	+	17.5127i	0.334515	+	0.563461i
$967$			6.88781i			0.221497i	0.993848	+	0.110749i	$0.0353248\pi$
$967$			6.88781i			0.221497i	−0.993848	+	0.110749i	$0.964675\pi$
$968$	6.74367	−	7.25455i	0.216750	−	0.233170i
$969$			4.20846i			0.135195i
$970$	3.08341	−	1.83055i	0.0990023	−	0.0587755i
$971$	25.1974	−	25.1974i	0.808623	−	0.808623i	−0.175803	−	0.984425i	$-0.556252\pi$
$971$	25.1974	−	25.1974i	0.808623	−	0.808623i	0.984425	+	0.175803i	$0.0562521\pi$
$972$	−8.96881	−	30.4863i	−0.287675	−	0.977850i
$973$	−19.2656	−	19.2656i	−0.617628	−	0.617628i
$974$	−6.85983	+	26.9057i	−0.219803	+	0.862115i
$975$	−10.7247			−0.343465
$976$	−1.56736	+	7.24125i	−0.0501698	+	0.231787i
$977$	−8.31259			−0.265943			−0.132972	−	0.991120i	$-0.542452\pi$
$977$	−8.31259			−0.265943			−0.132972	+	0.991120i	$0.542452\pi$
$978$	1.37175	−	5.38029i	0.0438637	−	0.172043i
$979$	21.3717	+	21.3717i	0.683042	+	0.683042i
$980$	0.0253592	−	0.00746045i	0.000810069	−	0.000238315i
$981$	0.903078	−	0.903078i	0.0288331	−	0.0288331i
$982$	−12.8341	+	7.61932i	−0.409552	+	0.243142i
$983$			38.9586i			1.24259i	0.783578	+	0.621293i	$0.213392\pi$
$983$			38.9586i			1.24259i	−0.783578	+	0.621293i	$0.786608\pi$
$984$	13.6544	−	0.498327i	0.435285	−	0.0158861i
$985$		−	3.83637i		−	0.122237i
$986$	0.909815	+	1.53250i	0.0289744	+	0.0488049i
$987$	−23.1376	+	23.1376i	−0.736478	+	0.736478i
$988$	−8.27709	+	15.1771i	−0.263329	+	0.482848i
$989$	−39.8282	−	39.8282i	−1.26646	−	1.26646i
$990$	1.03620	+	0.264187i	0.0329325	+	0.00839640i
$991$	−60.2776			−1.91478			−0.957391	−	0.288796i	$-0.906745\pi$
$991$	−60.2776			−1.91478			−0.957391	+	0.288796i	$0.906745\pi$
$992$	−2.59015	−	7.74853i	−0.0822373	−	0.246016i
$993$	0.676182			0.0214580
$994$	21.9386	+	5.59343i	0.695852	+	0.177413i
$995$	2.04458	+	2.04458i	0.0648174	+	0.0648174i
$996$	−0.876982	+	1.60806i	−0.0277882	+	0.0509533i
$997$	−8.55785	+	8.55785i	−0.271030	+	0.271030i	−0.829515	−	0.558485i	$-0.811383\pi$
$997$	−8.55785	+	8.55785i	−0.271030	+	0.271030i	0.558485	+	0.829515i	$0.311383\pi$
$998$	30.3926	+	51.1936i	0.962060	+	1.62051i
$999$			8.52044i			0.269575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.c.205.3	yes	32
4.3	odd	2		1088.2.l.c.273.6		32
16.5	even	4	inner	272.2.l.c.69.3	✓	32
16.11	odd	4		1088.2.l.c.817.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.c.69.3	✓	32	16.5	even	4	inner
272.2.l.c.205.3	yes	32	1.1	even	1	trivial
1088.2.l.c.273.6		32	4.3	odd	2
1088.2.l.c.817.6		32	16.11	odd	4

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:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37038 - 0.349388i) q^{2} +(0.724061 + 0.724061i) q^{3} +(1.75586 + 0.957585i) q^{4} +(0.100057 - 0.100057i) q^{5} +(-0.739257 - 1.24521i) q^{6} -2.62804i q^{7} +(-2.07161 - 1.92573i) q^{8} -1.95147i q^{9} +(-0.172075 + 0.102157i) q^{10} +(1.93625 - 1.93625i) q^{11} +(0.577997 + 1.96470i) q^{12} +(1.48714 + 1.48714i) q^{13} +(-0.918206 + 3.60140i) q^{14} +0.144896 q^{15} +(2.16606 + 3.36276i) q^{16} +1.00000 q^{17} +(-0.681820 + 2.67425i) q^{18} +(2.90615 + 2.90615i) q^{19} +(0.271500 - 0.0798729i) q^{20} +(1.90286 - 1.90286i) q^{21} +(-3.32989 + 1.97688i) q^{22} -5.35151i q^{23} +(-0.105630 - 2.89432i) q^{24} +4.97998i q^{25} +(-1.51835 - 2.55753i) q^{26} +(3.58517 - 3.58517i) q^{27} +(2.51657 - 4.61446i) q^{28} +(-0.891113 - 0.891113i) q^{29} +(-0.198561 - 0.0506248i) q^{30} +1.44426 q^{31} +(-1.79341 - 5.36504i) q^{32} +2.80393 q^{33} +(-1.37038 - 0.349388i) q^{34} +(-0.262955 - 0.262955i) q^{35} +(1.86870 - 3.42650i) q^{36} +(-1.18829 + 1.18829i) q^{37} +(-2.96714 - 4.99789i) q^{38} +2.15356i q^{39} +(-0.399964 + 0.0145970i) q^{40} +4.71764i q^{41} +(-3.27247 + 1.94280i) q^{42} +(7.44242 - 7.44242i) q^{43} +(5.25390 - 1.54565i) q^{44} +(-0.195259 - 0.195259i) q^{45} +(-1.86975 + 7.33357i) q^{46} -12.1594 q^{47} +(-0.866487 + 4.00321i) q^{48} +0.0934039 q^{49} +(1.73994 - 6.82444i) q^{50} +(0.724061 + 0.724061i) q^{51} +(1.18714 + 4.03527i) q^{52} +(-4.79265 + 4.79265i) q^{53} +(-6.16564 + 3.66041i) q^{54} -0.387472i q^{55} +(-5.06089 + 5.44428i) q^{56} +4.20846i q^{57} +(0.909815 + 1.53250i) q^{58} +(-6.48840 + 6.48840i) q^{59} +(0.254416 + 0.138750i) q^{60} +(1.30973 + 1.30973i) q^{61} +(-1.97918 - 0.504608i) q^{62} -5.12854 q^{63} +(0.583156 + 7.97872i) q^{64} +0.297599 q^{65} +(-3.84243 - 0.979658i) q^{66} +(-2.81837 - 2.81837i) q^{67} +(1.75586 + 0.957585i) q^{68} +(3.87482 - 3.87482i) q^{69} +(0.268474 + 0.452221i) q^{70} -6.09170i q^{71} +(-3.75800 + 4.04269i) q^{72} +13.5126i q^{73} +(2.04358 - 1.21323i) q^{74} +(-3.60581 + 3.60581i) q^{75} +(2.31989 + 7.88567i) q^{76} +(-5.08854 - 5.08854i) q^{77} +(0.752429 - 2.95119i) q^{78} -2.30465 q^{79} +(0.553200 + 0.119739i) q^{80} -0.662648 q^{81} +(1.64829 - 6.46494i) q^{82} +(0.632423 + 0.632423i) q^{83} +(5.16331 - 1.51900i) q^{84} +(0.100057 - 0.100057i) q^{85} +(-12.7992 + 7.59861i) q^{86} -1.29044i q^{87} +(-7.73984 + 0.282472i) q^{88} +11.0377i q^{89} +(0.199357 + 0.335800i) q^{90} +(3.90827 - 3.90827i) q^{91} +(5.12453 - 9.39648i) q^{92} +(1.04573 + 1.04573i) q^{93} +(16.6629 + 4.24834i) q^{94} +0.581564 q^{95} +(2.58609 - 5.18316i) q^{96} -17.9190 q^{97} +(-0.127998 - 0.0326342i) q^{98} +(-3.77853 - 3.77853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{4} - 16 q^{6} - 18 q^{8} - 6 q^{10} - 4 q^{11} + 2 q^{12} + 14 q^{14} + 24 q^{15} + 26 q^{16} + 32 q^{17} + 10 q^{18} - 14 q^{20} - 8 q^{22} - 50 q^{24} - 6 q^{26} + 12 q^{27} - 8 q^{29} + 36 q^{30}+ \cdots - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^4 - 16 * q^6 - 18 * q^8 - 6 * q^10 - 4 * q^11 + 2 * q^12 + 14 * q^14 + 24 * q^15 + 26 * q^16 + 32 * q^17 + 10 * q^18 - 14 * q^20 - 8 * q^22 - 50 * q^24 - 6 * q^26 + 12 * q^27 - 8 * q^29 + 36 * q^30 - 24 * q^31 + 10 * q^32 + 12 * q^35 + 16 * q^36 - 8 * q^37 - 34 * q^38 - 38 * q^40 - 12 * q^42 - 12 * q^43 + 38 * q^44 - 40 * q^45 + 26 * q^46 + 32 * q^47 + 30 * q^48 - 32 * q^49 - 2 * q^50 - 54 * q^52 + 8 * q^53 - 52 * q^54 - 36 * q^56 - 26 * q^58 - 12 * q^59 + 28 * q^60 + 6 * q^62 - 40 * q^63 + 10 * q^64 + 28 * q^66 + 8 * q^67 - 2 * q^68 - 32 * q^70 - 32 * q^72 - 14 * q^74 + 8 * q^75 + 30 * q^76 + 56 * q^77 + 108 * q^78 + 48 * q^79 + 90 * q^80 - 64 * q^81 + 32 * q^82 + 4 * q^83 - 8 * q^84 - 54 * q^86 - 66 * q^88 - 66 * q^90 - 28 * q^91 + 24 * q^92 - 24 * q^93 + 12 * q^94 - 40 * q^95 + 70 * q^96 + 12 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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