LMFDB - Embedded newform 490.2.p.a.239.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(29,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("490.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.p (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			239.21
Character	$\chi$	$=$	490.239
Dual form			490.2.p.a.449.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 + 0.623490i) q^{2} +(0.0985255 - 0.204590i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.593468 - 2.15587i) q^{5} +(0.204590 - 0.0985255i) q^{6} +(0.719254 + 2.54611i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(1.83832 + 2.30518i) q^{9} +O(q^{10})$	\(q+(0.781831 + 0.623490i) q^{2} +(0.0985255 - 0.204590i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.593468 - 2.15587i) q^{5} +(0.204590 - 0.0985255i) q^{6} +(0.719254 + 2.54611i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(1.83832 + 2.30518i) q^{9} +(0.880174 - 2.05555i) q^{10} +(1.14712 - 1.43845i) q^{11} +(0.221385 + 0.0505296i) q^{12} +(0.208379 + 0.166177i) q^{13} +(-1.02514 + 2.43908i) q^{14} +(-0.499543 - 0.0909909i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(3.36872 + 0.768887i) q^{17} +2.94844i q^{18} +8.08129 q^{19} +(1.96976 - 1.05832i) q^{20} +(0.591774 + 0.103704i) q^{21} +(1.79371 - 0.409403i) q^{22} +(-5.46583 + 1.24754i) q^{23} +(0.141581 + 0.177537i) q^{24} +(-4.29559 + 2.55888i) q^{25} +(0.0593079 + 0.259845i) q^{26} +(1.31689 - 0.300572i) q^{27} +(-2.32222 + 1.26778i) q^{28} +(1.12883 - 4.94571i) q^{29} +(-0.333826 - 0.382599i) q^{30} +5.34663 q^{31} +(-0.974928 - 0.222521i) q^{32} +(-0.181271 - 0.376413i) q^{33} +(2.15437 + 2.70150i) q^{34} +(5.06224 - 3.06166i) q^{35} +(-1.83832 + 2.30518i) q^{36} +(-4.72628 - 1.07874i) q^{37} +(6.31821 + 5.03860i) q^{38} +(0.0545289 - 0.0262597i) q^{39} +(2.19987 + 0.400703i) q^{40} +(-2.20582 - 1.06227i) q^{41} +(0.398009 + 0.450044i) q^{42} +(2.42518 + 5.03594i) q^{43} +(1.65764 + 0.798277i) q^{44} +(3.87870 - 5.33124i) q^{45} +(-5.05119 - 2.43252i) q^{46} +(-6.10038 - 4.86489i) q^{47} +0.227078i q^{48} +(-5.96535 + 3.66260i) q^{49} +(-4.95387 - 0.677642i) q^{50} +(0.489211 - 0.613451i) q^{51} +(-0.115642 + 0.240133i) q^{52} +(-9.46838 + 2.16109i) q^{53} +(1.21699 + 0.586072i) q^{54} +(-3.78189 - 1.61938i) q^{55} +(-2.60604 - 0.456690i) q^{56} +(0.796213 - 1.65335i) q^{57} +(3.96615 - 3.16290i) q^{58} +(-13.5792 + 6.53941i) q^{59} +(-0.0224492 - 0.507265i) q^{60} +(2.66439 - 11.6734i) q^{61} +(4.18017 + 3.33357i) q^{62} +(-4.54702 + 6.33857i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(0.234590 - 0.547860i) q^{65} +(0.0929665 - 0.407313i) q^{66} +0.326381i q^{67} +3.45535i q^{68} +(-0.283289 + 1.24117i) q^{69} +(5.86673 + 0.762556i) q^{70} +(-1.48356 - 6.49988i) q^{71} +(-2.87451 + 0.656089i) q^{72} +(-7.02441 + 5.60178i) q^{73} +(-3.02257 - 3.79018i) q^{74} +(0.100298 + 1.13095i) q^{75} +(1.79826 + 7.87868i) q^{76} +(4.48751 + 1.88609i) q^{77} +(0.0590051 + 0.0134675i) q^{78} +8.81712 q^{79} +(1.47009 + 1.68488i) q^{80} +(-1.90001 + 8.32450i) q^{81} +(-1.06227 - 2.20582i) q^{82} +(12.8722 - 10.2653i) q^{83} +(0.0305779 + 0.600013i) q^{84} +(-0.341599 - 7.71884i) q^{85} +(-1.24377 + 5.44933i) q^{86} +(-0.900626 - 0.718225i) q^{87} +(0.798277 + 1.65764i) q^{88} +(-5.39558 - 6.76584i) q^{89} +(6.35646 - 1.74980i) q^{90} +(-0.273227 + 0.650080i) q^{91} +(-2.43252 - 5.05119i) q^{92} +(0.526780 - 1.09387i) q^{93} +(-1.73626 - 7.60705i) q^{94} +(-4.79599 - 17.4223i) q^{95} +(-0.141581 + 0.177537i) q^{96} -11.7351i q^{97} +(-6.94749 - 0.855798i) q^{98} +5.42465 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$-1$

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 $

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$	0.0985255	−	0.204590i	0.0568837	−	0.118120i	−0.870589	−	0.492011i	$-0.836262\pi$
$3$	0.0985255	−	0.204590i	0.0568837	−	0.118120i	0.927473	+	0.373890i	$0.121976\pi$
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−0.593468	−	2.15587i	−0.265407	−	0.964137i
$5$	−0.593468	−	2.15587i	−0.265407	−	0.964137i
$6$	0.204590	−	0.0985255i	0.0835236	−	0.0402229i
$7$	0.719254	+	2.54611i	0.271852	+	0.962339i
$7$	0.719254	+	2.54611i	0.271852	+	0.962339i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$	1.83832	+	2.30518i	0.612773	+	0.768393i
$10$	0.880174	−	2.05555i	0.278336	−	0.650023i
$11$	1.14712	−	1.43845i	0.345870	−	0.433708i	−0.578221	−	0.815880i	$-0.696253\pi$
$11$	1.14712	−	1.43845i	0.345870	−	0.433708i	0.924091	+	0.382173i	$0.124824\pi$
$12$	0.221385	+	0.0505296i	0.0639083	+	0.0145866i
$13$	0.208379	+	0.166177i	0.0577940	+	0.0460892i	0.651961	−	0.758253i	$-0.273947\pi$
$13$	0.208379	+	0.166177i	0.0577940	+	0.0460892i	−0.594167	+	0.804342i	$0.702518\pi$
$14$	−1.02514	+	2.43908i	−0.273980	+	0.651871i
$15$	−0.499543	−	0.0909909i	−0.128981	−	0.0234937i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	3.36872	+	0.768887i	0.817034	+	0.186483i	0.610560	−	0.791970i	$-0.290944\pi$
$17$	3.36872	+	0.768887i	0.817034	+	0.186483i	0.206473	+	0.978452i	$0.433801\pi$
$18$			2.94844i			0.694953i
$19$	8.08129			1.85398			0.926988	−	0.375092i	$-0.122389\pi$
$19$	8.08129			1.85398			0.926988	+	0.375092i	$0.122389\pi$
$20$	1.96976	−	1.05832i	0.440453	−	0.236647i
$21$	0.591774	+	0.103704i	0.129136	+	0.0226301i
$22$	1.79371	−	0.409403i	0.382421	−	0.0872850i
$23$	−5.46583	+	1.24754i	−1.13970	+	0.260130i	−0.750403	−	0.660980i	$-0.770141\pi$
$23$	−5.46583	+	1.24754i	−1.13970	+	0.260130i	−0.389301	+	0.921110i	$0.627284\pi$
$24$	0.141581	+	0.177537i	0.0289001	+	0.0362395i
$25$	−4.29559	+	2.55888i	−0.859118	+	0.511777i
$26$	0.0593079	+	0.259845i	0.0116312	+	0.0509598i
$27$	1.31689	−	0.300572i	0.253436	−	0.0578451i
$28$	−2.32222	+	1.26778i	−0.438859	+	0.239589i
$29$	1.12883	−	4.94571i	0.209618	−	0.918395i	−0.755204	−	0.655490i	$-0.772462\pi$
$29$	1.12883	−	4.94571i	0.209618	−	0.918395i	0.964822	−	0.262905i	$-0.0846807\pi$
$30$	−0.333826	−	0.382599i	−0.0609481	−	0.0698528i
$31$	5.34663			0.960284			0.480142	−	0.877191i	$-0.340585\pi$
$31$	5.34663			0.960284			0.480142	+	0.877191i	$0.340585\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$	−0.181271	−	0.376413i	−0.0315553	−	0.0655252i
$34$	2.15437	+	2.70150i	0.369472	+	0.463303i
$35$	5.06224	−	3.06166i	0.855675	−	0.517514i
$36$	−1.83832	+	2.30518i	−0.306387	+	0.384197i
$37$	−4.72628	−	1.07874i	−0.776996	−	0.177344i	−0.184408	−	0.982850i	$-0.559037\pi$
$37$	−4.72628	−	1.07874i	−0.776996	−	0.177344i	−0.592588	+	0.805505i	$0.701894\pi$
$38$	6.31821	+	5.03860i	1.02495	+	0.817369i
$39$	0.0545289	−	0.0262597i	0.00873161	−	0.00420492i
$40$	2.19987	+	0.400703i	0.347830	+	0.0633567i
$41$	−2.20582	−	1.06227i	−0.344492	−	0.165899i	0.253635	−	0.967300i	$-0.418374\pi$
$41$	−2.20582	−	1.06227i	−0.344492	−	0.165899i	−0.598127	+	0.801401i	$0.704088\pi$
$42$	0.398009	+	0.450044i	0.0614141	+	0.0694434i
$43$	2.42518	+	5.03594i	0.369837	+	0.767974i	0.999964	−	0.00851827i	$-0.00271148\pi$
$43$	2.42518	+	5.03594i	0.369837	+	0.767974i	−0.630127	+	0.776492i	$0.716997\pi$
$44$	1.65764	+	0.798277i	0.249899	+	0.120345i
$45$	3.87870	−	5.33124i	0.578202	−	0.794734i
$46$	−5.05119	−	2.43252i	−0.744757	−	0.358656i
$47$	−6.10038	−	4.86489i	−0.889832	−	0.709617i	0.0677736	−	0.997701i	$-0.478410\pi$
$47$	−6.10038	−	4.86489i	−0.889832	−	0.709617i	−0.957605	+	0.288084i	$0.906982\pi$
$48$			0.227078i			0.0327759i
$49$	−5.96535	+	3.66260i	−0.852192	+	0.523228i
$50$	−4.95387	−	0.677642i	−0.700583	−	0.0958330i
$51$	0.489211	−	0.613451i	0.0685033	−	0.0859004i
$52$	−0.115642	+	0.240133i	−0.0160366	+	0.0333004i
$53$	−9.46838	+	2.16109i	−1.30058	+	0.296849i	−0.816079	−	0.577941i	$-0.803857\pi$
$53$	−9.46838	+	2.16109i	−1.30058	+	0.296849i	−0.484503	+	0.874790i	$0.660999\pi$
$54$	1.21699	+	0.586072i	0.165612	+	0.0797544i
$55$	−3.78189	−	1.61938i	−0.509950	−	0.218357i
$56$	−2.60604	−	0.456690i	−0.348246	−	0.0610278i
$57$	0.796213	−	1.65335i	0.105461	−	0.218992i
$58$	3.96615	−	3.16290i	0.520781	−	0.415309i
$59$	−13.5792	+	6.53941i	−1.76787	+	0.851359i	−0.799957	+	0.600057i	$0.795144\pi$
$59$	−13.5792	+	6.53941i	−1.76787	+	0.851359i	−0.967909	+	0.251302i	$0.919141\pi$
$60$	−0.0224492	−	0.507265i	−0.00289818	−	0.0654877i
$61$	2.66439	−	11.6734i	0.341140	−	1.49463i	−0.455532	−	0.890220i	$-0.650551\pi$
$61$	2.66439	−	11.6734i	0.341140	−	1.49463i	0.796672	−	0.604412i	$-0.206592\pi$
$62$	4.18017	+	3.33357i	0.530882	+	0.423364i
$63$	−4.54702	+	6.33857i	−0.572871	+	0.798585i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	0.234590	−	0.547860i	0.0290974	−	0.0679537i
$66$	0.0929665	−	0.407313i	0.0114434	−	0.0501367i
$67$			0.326381i			0.0398738i	0.999801	+	0.0199369i	$0.00634654\pi$
$67$			0.326381i			0.0398738i	−0.999801	+	0.0199369i	$0.993653\pi$
$68$			3.45535i			0.419023i
$69$	−0.283289	+	1.24117i	−0.0341040	+	0.149419i
$70$	5.86673	+	0.762556i	0.701208	+	0.0911429i
$71$	−1.48356	−	6.49988i	−0.176066	−	0.771394i	−0.983422	−	0.181330i	$-0.941960\pi$
$71$	−1.48356	−	6.49988i	−0.176066	−	0.771394i	0.807357	−	0.590064i	$-0.200897\pi$
$72$	−2.87451	+	0.656089i	−0.338765	+	0.0773208i
$73$	−7.02441	+	5.60178i	−0.822144	+	0.655638i	−0.941425	−	0.337222i	$-0.890513\pi$
$73$	−7.02441	+	5.60178i	−0.822144	+	0.655638i	0.119281	+	0.992861i	$0.461941\pi$
$74$	−3.02257	−	3.79018i	−0.351367	−	0.440600i
$75$	0.100298	+	1.13095i	0.0115814	+	0.130591i
$76$	1.79826	+	7.87868i	0.206274	+	0.903746i
$77$	4.48751	+	1.88609i	0.511399	+	0.214940i
$78$	0.0590051	+	0.0134675i	0.00668101	+	0.00152490i
$79$	8.81712			0.992004			0.496002	−	0.868321i	$-0.334801\pi$
$79$	8.81712			0.992004			0.496002	+	0.868321i	$0.334801\pi$
$80$	1.47009	+	1.68488i	0.164362	+	0.188375i
$81$	−1.90001	+	8.32450i	−0.211113	+	0.924944i
$82$	−1.06227	−	2.20582i	−0.117308	−	0.243593i
$83$	12.8722	−	10.2653i	1.41291	−	1.12676i	0.439357	−	0.898313i	$-0.355206\pi$
$83$	12.8722	−	10.2653i	1.41291	−	1.12676i	0.973556	−	0.228448i	$-0.0733650\pi$
$84$	0.0305779	+	0.600013i	0.00333632	+	0.0654668i
$85$	−0.341599	−	7.71884i	−0.0370516	−	0.837226i
$86$	−1.24377	+	5.44933i	−0.134120	+	0.587617i
$87$	−0.900626	−	0.718225i	−0.0965573	−	0.0770018i
$88$	0.798277	+	1.65764i	0.0850966	+	0.176705i
$89$	−5.39558	−	6.76584i	−0.571930	−	0.717178i	0.408783	−	0.912632i	$-0.365953\pi$
$89$	−5.39558	−	6.76584i	−0.571930	−	0.717178i	−0.980713	+	0.195454i	$0.937382\pi$
$90$	6.35646	−	1.74980i	0.670029	−	0.184445i
$91$	−0.273227	+	0.650080i	−0.0286420	+	0.0681469i
$92$	−2.43252	−	5.05119i	−0.253608	−	0.526623i
$93$	0.526780	−	1.09387i	0.0546245	−	0.113429i
$94$	−1.73626	−	7.60705i	−0.179081	−	0.784607i
$95$	−4.79599	−	17.4223i	−0.492058	−	1.78749i
$96$	−0.141581	+	0.177537i	−0.0144500	+	0.0181198i
$97$		−	11.7351i		−	1.19152i	−0.803163	−	0.595760i	$-0.796851\pi$
$97$		−	11.7351i		−	1.19152i	0.803163	−	0.595760i	$-0.203149\pi$
$98$	−6.94749	−	0.855798i	−0.701802	−	0.0864487i
$99$	5.42465			0.545198
$100$	−3.45059	−	3.61849i	−0.345059	−	0.361849i
$101$	0.211069	+	0.101645i	0.0210021	+	0.0101141i	0.444355	−	0.895851i	$-0.353433\pi$
$101$	0.211069	+	0.101645i	0.0210021	+	0.0101141i	−0.423353	+	0.905965i	$0.639147\pi$
$102$	0.764961	−	0.174597i	0.0757425	−	0.0172877i
$103$	−0.296603	+	0.615902i	−0.0292252	+	0.0606867i	−0.915070	−	0.403294i	$-0.867865\pi$
$103$	−0.296603	+	0.615902i	−0.0292252	+	0.0606867i	0.885845	+	0.463981i	$0.153579\pi$
$104$	−0.240133	+	0.115642i	−0.0235469	+	0.0113396i
$105$	−0.127625	−	1.33734i	−0.0124550	−	0.130511i
$106$	−8.75009	−	4.21382i	−0.849884	−	0.409283i
$107$	13.2107	−	10.5352i	1.27712	−	1.01847i	0.278815	−	0.960345i	$-0.410058\pi$
$107$	13.2107	−	10.5352i	1.27712	−	1.01847i	0.998309	−	0.0581277i	$-0.0185131\pi$
$108$	0.586072	+	1.21699i	0.0563949	+	0.117105i
$109$	−7.29307	+	9.14523i	−0.698550	+	0.875954i	−0.996914	−	0.0784983i	$-0.974987\pi$
$109$	−7.29307	+	9.14523i	−0.698550	+	0.875954i	0.298364	+	0.954452i	$0.403559\pi$
$110$	−1.94713	−	3.62405i	−0.185652	−	0.345540i
$111$	−0.686360	+	0.860668i	−0.0651464	+	0.0816910i
$112$	−1.75274	−	1.98189i	−0.165618	−	0.187271i
$113$	−6.59189	+	5.25686i	−0.620113	+	0.494524i	−0.882421	−	0.470461i	$-0.844088\pi$
$113$	−6.59189	+	5.25686i	−0.620113	+	0.494524i	0.262308	+	0.964984i	$0.415516\pi$
$114$	1.65335	−	0.796213i	0.154851	−	0.0745722i
$115$	5.93334	+	11.0433i	0.553286	+	1.02979i
$116$	5.07290			0.471007
$117$			0.785838i			0.0726508i
$118$	−14.6939	−	3.35379i	−1.35269	−	0.308742i
$119$	0.465291	+	9.13014i	0.0426531	+	0.836959i
$120$	0.298723	−	0.410593i	0.0272696	−	0.0374818i
$121$	1.69449	+	7.42406i	0.154045	+	0.674915i
$122$	9.36138	−	7.46545i	0.847540	−	0.675890i
$123$	−0.434660	+	0.346630i	−0.0391919	+	0.0312545i
$124$	1.18974	+	5.21258i	0.106842	+	0.468104i
$125$	8.06593	+	7.74214i	0.721439	+	0.692478i
$126$	−7.50704	+	2.12067i	−0.668780	+	0.188925i
$127$	−10.5475	−	2.40740i	−0.935939	−	0.213622i	−0.272759	−	0.962082i	$-0.587936\pi$
$127$	−10.5475	−	2.40740i	−0.935939	−	0.213622i	−0.663179	+	0.748460i	$0.730793\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.26925			0.111751
$130$	0.524996	−	0.282070i	0.0460452	−	0.0247392i
$131$	6.73981	−	3.24572i	0.588860	−	0.283580i	−0.115632	−	0.993292i	$-0.536889\pi$
$131$	6.73981	−	3.24572i	0.588860	−	0.283580i	0.704492	+	0.709712i	$0.251175\pi$
$132$	0.326639	−	0.260486i	0.0284303	−	0.0226724i
$133$	5.81250	+	20.5759i	0.504008	+	1.78415i
$134$	−0.203496	+	0.255175i	−0.0175793	+	0.0220438i
$135$	−1.42953	−	2.66068i	−0.123034	−	0.228995i
$136$	−2.15437	+	2.70150i	−0.184736	+	0.231652i
$137$	−2.26477	−	4.70284i	−0.193492	−	0.401790i	0.781540	−	0.623855i	$-0.214435\pi$
$137$	−2.26477	−	4.70284i	−0.193492	−	0.401790i	−0.975032	+	0.222065i	$0.928720\pi$
$138$	−0.995341	+	0.793758i	−0.0847291	+	0.0675692i
$139$	−6.49443	−	3.12755i	−0.550851	−	0.265276i	0.137688	−	0.990476i	$-0.456033\pi$
$139$	−6.49443	−	3.12755i	−0.550851	−	0.265276i	−0.688538	+	0.725200i	$0.741747\pi$
$140$	4.11135	+	4.25404i	0.347472	+	0.359532i
$141$	−1.59635	+	0.768762i	−0.134437	+	0.0647415i
$142$	2.89272	−	6.00679i	0.242752	−	0.504079i
$143$	0.478073	−	0.109117i	0.0399785	−	0.00912483i
$144$	−2.65645	−	1.27928i	−0.221371	−	0.106607i
$145$	−11.3323	+	0.501512i	−0.941092	+	0.0416483i
$146$	−8.98455			−0.743567
$147$	0.161593	+	1.58131i	0.0133280	+	0.130424i
$148$		−	4.84783i		−	0.398489i
$149$	−0.659194	+	0.826603i	−0.0540033	+	0.0677180i	−0.808100	−	0.589046i	$-0.799504\pi$
$149$	−0.659194	+	0.826603i	−0.0540033	+	0.0677180i	0.754096	+	0.656764i	$0.228075\pi$
$150$	−0.626721	+	0.946748i	−0.0511716	+	0.0773017i
$151$	−3.52368	−	15.4382i	−0.286753	−	1.25635i	−0.888952	−	0.458001i	$-0.848566\pi$
$151$	−3.52368	−	15.4382i	−0.286753	−	1.25635i	0.602199	−	0.798346i	$-0.294291\pi$
$152$	−3.50634	+	7.28099i	−0.284402	+	0.590566i
$153$	4.42035	+	9.17896i	0.357364	+	0.742075i
$154$	2.33252	+	4.27252i	0.187960	+	0.344290i
$155$	−3.17306	−	11.5267i	−0.254866	−	0.925845i
$156$	0.0377352	+	0.0473184i	0.00302123	+	0.00378850i
$157$	3.21417	+	6.67429i	0.256519	+	0.532667i	0.988963	−	0.148160i	$-0.0473350\pi$
$157$	3.21417	+	6.67429i	0.256519	+	0.532667i	−0.732445	+	0.680827i	$0.761621\pi$
$158$	6.89351	+	5.49739i	0.548418	+	0.437349i
$159$	−0.490737	+	2.15006i	−0.0389180	+	0.170511i
$160$	0.0988610	+	2.23388i	0.00781565	+	0.176604i
$161$	−7.10770	−	13.0193i	−0.560165	−	1.02607i
$162$	−6.67573	+	5.32372i	−0.524495	+	0.418271i
$163$	−5.62834	−	11.6874i	−0.440846	−	0.915425i	−0.996467	−	0.0839896i	$-0.973234\pi$
$163$	−5.62834	−	11.6874i	−0.440846	−	0.915425i	0.555621	−	0.831436i	$-0.312481\pi$
$164$	0.544794	−	2.38690i	0.0425412	−	0.186385i
$165$	−0.703922	+	0.614187i	−0.0548002	+	0.0478144i
$166$	16.4642			1.27787
$167$	5.48359	+	1.25159i	0.424333	+	0.0968512i	0.429354	−	0.903136i	$-0.358741\pi$
$167$	5.48359	+	1.25159i	0.424333	+	0.0968512i	−0.00502129	+	0.999987i	$0.501598\pi$
$168$	−0.350195	+	0.488174i	−0.0270182	+	0.0376635i
$169$	−2.87696	−	12.6048i	−0.221305	−	0.969601i
$170$	4.54554	−	6.24781i	0.348627	−	0.479186i
$171$	14.8560	+	18.6288i	1.13607	+	1.42458i
$172$	−4.37003	+	3.48498i	−0.333211	+	0.265727i
$173$	2.25840	−	0.515464i	0.171703	−	0.0391900i	−0.135805	−	0.990736i	$-0.543362\pi$
$173$	2.25840	−	0.515464i	0.171703	−	0.0391900i	0.307508	+	0.951546i	$0.400505\pi$
$174$	−0.256332	−	1.12306i	−0.0194325	−	0.0851391i
$175$	−9.60482	−	9.09656i	−0.726056	−	0.687635i
$176$	−0.409403	+	1.79371i	−0.0308599	+	0.135206i
$177$			3.42248i			0.257249i
$178$		−	8.65384i		−	0.648632i
$179$	−1.26495	+	5.54212i	−0.0945470	+	0.414237i	−0.999947	−	0.0103228i	$-0.996714\pi$
$179$	−1.26495	+	5.54212i	−0.0945470	+	0.414237i	0.905400	+	0.424560i	$0.139571\pi$
$180$	6.06066	+	2.59514i	0.451735	+	0.193430i
$181$	−5.37141	−	6.73553i	−0.399254	−	0.500648i	0.541047	−	0.840992i	$-0.318028\pi$
$181$	−5.37141	−	6.73553i	−0.399254	−	0.500648i	−0.940301	+	0.340344i	$0.889457\pi$
$182$	−0.618936	+	0.337899i	−0.0458786	+	0.0250467i
$183$	−2.12576	−	1.69524i	−0.157141	−	0.125316i
$184$	1.24754	−	5.46583i	0.0919699	−	0.402946i
$185$	0.479261	+	10.8295i	0.0352360	+	0.796199i
$186$	1.09387	−	0.526780i	0.0802064	−	0.0386254i
$187$	4.97033	−	3.96371i	0.363467	−	0.289855i
$188$	3.38545	−	7.02997i	0.246910	−	0.512713i
$189$	1.71247	+	3.13677i	0.124564	+	0.228166i
$190$	7.11294	−	16.6115i	0.516027	−	1.20513i
$191$	18.8797	+	9.09198i	1.36609	+	0.657873i	0.965985	−	0.258598i	$-0.0832605\pi$
$191$	18.8797	+	9.09198i	1.36609	+	0.657873i	0.400102	+	0.916471i	$0.368975\pi$
$192$	−0.221385	+	0.0505296i	−0.0159771	+	0.00364666i
$193$	−10.2987	+	21.3854i	−0.741315	+	1.53936i	0.0976808	+	0.995218i	$0.468858\pi$
$193$	−10.2987	+	21.3854i	−0.741315	+	1.53936i	−0.838996	+	0.544138i	$0.816857\pi$
$194$	7.31672	−	9.17487i	0.525310	−	0.658717i
$195$	−0.0889738	−	0.101973i	−0.00637155	−	0.00730245i
$196$	−4.89818	−	5.00078i	−0.349870	−	0.357198i
$197$			9.58477i			0.682887i	0.939902	+	0.341443i	$0.110916\pi$
$197$			9.58477i			0.682887i	−0.939902	+	0.341443i	$0.889084\pi$
$198$	4.24116	+	3.38221i	0.301406	+	0.240364i
$199$	9.86175	+	4.74917i	0.699081	+	0.336660i	0.749441	−	0.662071i	$-0.230322\pi$
$199$	9.86175	+	4.74917i	0.699081	+	0.336660i	−0.0503596	+	0.998731i	$0.516037\pi$
$200$	−0.441688	−	4.98045i	−0.0312320	−	0.352171i
$201$	0.0667745	+	0.0321569i	0.00470991	+	0.00226817i
$202$	0.101645	+	0.211069i	0.00715175	+	0.0148508i
$203$	13.4042	−	0.683107i	0.940793	−	0.0479447i
$204$	0.706931	+	0.340440i	0.0494950	+	0.0238356i
$205$	−0.981033	+	5.38590i	−0.0685183	+	0.376168i
$206$	−0.615902	+	0.296603i	−0.0429120	+	0.0206653i
$207$	−12.9237	−	10.3063i	−0.898263	−	0.716341i
$208$	−0.259845	−	0.0593079i	−0.0180170	−	0.00411226i
$209$	9.27023	−	11.6245i	0.641235	−	0.804083i
$210$	0.734034	−	1.12514i	0.0506531	−	0.0776423i
$211$	4.63465	+	5.81167i	0.319062	+	0.400092i	0.915337	−	0.402689i	$-0.131924\pi$
$211$	4.63465	+	5.81167i	0.319062	+	0.400092i	−0.596274	+	0.802781i	$0.703353\pi$
$212$	−4.21382	−	8.75009i	−0.289407	−	0.600959i
$213$	−1.47598	−	0.336883i	−0.101133	−	0.0230828i
$214$	16.8971			1.15506
$215$	9.41759	−	8.21706i	0.642274	−	0.560399i
$216$	−0.300572	+	1.31689i	−0.0204513	+	0.0896032i
$217$	3.84559	+	13.6131i	0.261056	+	0.924119i
$218$	−11.4039	+	2.60287i	−0.772370	+	0.176288i
$219$	0.453986	+	1.98904i	0.0306775	+	0.134407i
$220$	0.737230	−	4.04741i	0.0497040	−	0.272877i
$221$	0.574199	+	0.720023i	0.0386248	+	0.0484340i
$222$	−1.07324	+	0.244959i	−0.0720308	+	0.0164406i
$223$	−12.4775	+	2.84790i	−0.835554	+	0.190710i	−0.618832	−	0.785523i	$-0.712394\pi$
$223$	−12.4775	+	2.84790i	−0.835554	+	0.190710i	−0.216722	+	0.976233i	$0.569537\pi$
$224$	−0.134658	−	2.64232i	−0.00899722	−	0.176548i
$225$	−13.7954	−	5.19806i	−0.919691	−	0.346538i
$226$	−8.43135			−0.560845
$227$			4.67589i			0.310350i	0.987887	+	0.155175i	$0.0495941\pi$
$227$			4.67589i			0.310350i	−0.987887	+	0.155175i	$0.950406\pi$
$228$	1.78907	+	0.408345i	0.118484	+	0.0270433i
$229$	−24.0357	+	11.5750i	−1.58832	+	0.764896i	−0.999073	−	0.0430538i	$-0.986291\pi$
$229$	−24.0357	+	11.5750i	−1.58832	+	0.764896i	−0.589251	+	0.807950i	$0.700577\pi$
$230$	−2.24650	+	12.3334i	−0.148130	+	0.813237i
$231$	0.828010	−	0.732273i	0.0544791	−	0.0481800i
$232$	3.96615	+	3.16290i	0.260391	+	0.207655i
$233$	16.8030	+	3.83519i	1.10080	+	0.251251i	0.734070	−	0.679074i	$-0.237619\pi$
$233$	16.8030	+	3.83519i	1.10080	+	0.251251i	0.366735	+	0.930326i	$0.380476\pi$
$234$	−0.489962	+	0.614393i	−0.0320298	+	0.0401641i
$235$	−6.86771	+	16.0388i	−0.448000	+	1.04626i
$236$	−9.39712	−	11.7836i	−0.611701	−	0.767048i
$237$	0.868711	−	1.80390i	0.0564289	−	0.117176i
$238$	−5.32877	+	7.42834i	−0.345413	+	0.481508i
$239$	1.39279	−	0.670733i	0.0900922	−	0.0433861i	−0.388295	−	0.921535i	$-0.626936\pi$
$239$	1.39279	−	0.670733i	0.0900922	−	0.0433861i	0.478387	+	0.878149i	$0.341222\pi$
$240$	0.489552	−	0.134764i	0.0316004	−	0.00869895i
$241$	1.69090	+	7.40831i	0.108920	+	0.477211i	0.999739	+	0.0228519i	$0.00727463\pi$
$241$	1.69090	+	7.40831i	0.108920	+	0.477211i	−0.890819	+	0.454359i	$0.849868\pi$
$242$	−3.30402	+	6.86087i	−0.212390	+	0.441033i
$243$	4.68411	+	3.73545i	0.300486	+	0.239629i
$244$	11.9737			0.766535
$245$	11.4363	+	10.6869i	0.730641	+	0.682761i
$246$	−0.555951			−0.0354461
$247$	1.68397	+	1.34292i	0.107149	+	0.0854483i
$248$	−2.31982	+	4.81715i	−0.147309	+	0.305889i
$249$	−0.831931	−	3.64493i	−0.0527215	−	0.230988i
$250$	1.47905	+	11.0821i	0.0935434	+	0.700892i
$251$	16.9868	−	8.18040i	1.07220	−	0.516342i	0.187382	−	0.982287i	$-0.440000\pi$
$251$	16.9868	−	8.18040i	1.07220	−	0.516342i	0.884814	+	0.465945i	$0.154285\pi$
$252$	−7.19146	−	3.02255i	−0.453019	−	0.190403i
$253$	−4.47546	+	9.29338i	−0.281370	+	0.584270i
$254$	−6.74538	−	8.45843i	−0.423243	−	0.530729i
$255$	−1.61286	−	0.690614i	−0.101001	−	0.0432480i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−11.2053	−	2.55754i	−0.698968	−	0.159535i	−0.141752	−	0.989902i	$-0.545274\pi$
$257$	−11.2053	−	2.55754i	−0.698968	−	0.159535i	−0.557217	+	0.830367i	$0.688131\pi$
$258$	0.992337	+	0.791362i	0.0617802	+	0.0492681i
$259$	−0.652799	−	12.8095i	−0.0405630	−	0.795945i
$260$	0.586326	+	0.106798i	0.0363624	+	0.00662335i
$261$	13.4759	−	6.48965i	0.834137	−	0.401699i
$262$	7.29307	+	1.66460i	0.450568	+	0.102839i
$263$			18.2178i			1.12336i	0.827356	+	0.561679i	$0.189844\pi$
$263$			18.2178i			1.12336i	−0.827356	+	0.561679i	$0.810156\pi$
$264$	0.417787			0.0257130
$265$	10.2782	+	19.1301i	0.631386	+	1.17515i
$266$	−8.28444	+	19.7109i	−0.507952	+	1.20855i
$267$	−1.91583	+	0.437275i	−0.117247	+	0.0267608i
$268$	−0.318198	+	0.0726267i	−0.0194371	+	0.00443638i
$269$	−13.8280	−	17.3398i	−0.843108	−	1.05722i	−0.997601	−	0.0692297i	$-0.977946\pi$
$269$	−13.8280	−	17.3398i	−0.843108	−	1.05722i	0.154493	−	0.987994i	$-0.450626\pi$
$270$	0.541253	−	2.97150i	0.0329396	−	0.180840i
$271$	−1.04121	−	4.56183i	−0.0632489	−	0.277112i	0.933408	−	0.358818i	$-0.116820\pi$
$271$	−1.04121	−	4.56183i	−0.0632489	−	0.277112i	−0.996656	+	0.0817064i	$0.973963\pi$
$272$	−3.36872	+	0.768887i	−0.204258	+	0.0466206i
$273$	0.106080	+	0.119949i	0.00642027	+	0.00725965i
$274$	1.16150	−	5.08889i	0.0701691	−	0.307431i
$275$	−1.24675	+	9.11433i	−0.0751820	+	0.549615i
$276$	−1.27309			−0.0766310
$277$	30.7558	+	7.01982i	1.84794	+	0.421780i	0.994969	−	0.100182i	$-0.0319425\pi$
$277$	30.7558	+	7.01982i	1.84794	+	0.421780i	0.852969	+	0.521962i	$0.174800\pi$
$278$	−3.12755	−	6.49443i	−0.187578	−	0.389510i
$279$	9.82882	+	12.3250i	0.588436	+	0.737876i
$280$	0.562033	+	5.88932i	0.0335879	+	0.351954i
$281$	−1.18506	+	1.48601i	−0.0706945	+	0.0886481i	−0.815921	−	0.578163i	$-0.803770\pi$
$281$	−1.18506	+	1.48601i	−0.0706945	+	0.0886481i	0.745227	+	0.666811i	$0.232341\pi$
$282$	−1.72739	−	0.394266i	−0.102865	−	0.0234782i
$283$	−10.6742	−	8.51238i	−0.634515	−	0.506009i	0.252592	−	0.967573i	$-0.418717\pi$
$283$	−10.6742	−	8.51238i	−0.634515	−	0.506009i	−0.887107	+	0.461564i	$0.847288\pi$
$284$	6.00679	−	2.89272i	0.356438	−	0.171651i
$285$	−4.03695	−	0.735324i	−0.239128	−	0.0435568i
$286$	0.441806	+	0.212763i	0.0261245	+	0.0125809i
$287$	1.11811	−	6.38031i	0.0659997	−	0.376618i
$288$	−1.27928	−	2.65645i	−0.0753822	−	0.156533i
$289$	−4.55941	−	2.19570i	−0.268201	−	0.129159i
$290$	−9.17260	−	6.67345i	−0.538634	−	0.391878i
$291$	−2.40089	−	1.15621i	−0.140743	−	0.0677780i
$292$	−7.02441	−	5.60178i	−0.411072	−	0.327819i
$293$		−	8.31529i		−	0.485785i	−0.970053	−	0.242892i	$-0.921904\pi$
$293$		−	8.31529i		−	0.485785i	0.970053	−	0.242892i	$-0.0780962\pi$
$294$	−0.859593	+	1.33707i	−0.0501325	+	0.0779796i
$295$	22.1570	+	25.3942i	1.29003	+	1.47851i
$296$	3.02257	−	3.79018i	0.175683	−	0.220300i
$297$	1.07828	−	2.23907i	0.0625681	−	0.129924i
$298$	−1.03076	+	0.235264i	−0.0597102	+	0.0136285i
$299$	−1.34628	−	0.648334i	−0.0778573	−	0.0374941i
$300$	−1.08028	+	0.349443i	−0.0623699	+	0.0201751i
$301$	−11.0777	+	9.79690i	−0.638510	+	0.564684i
$302$	6.87067	−	14.2671i	0.395362	−	0.820978i
$303$	0.0415913	−	0.0331680i	0.00238936	−	0.00190545i
$304$	−7.28099	+	3.50634i	−0.417594	+	0.201102i
$305$	−26.7477	+	1.18373i	−1.53157	+	0.0677800i
$306$	−2.26701	+	9.93244i	−0.129597	+	0.567800i
$307$	12.8637	+	10.2584i	0.734168	+	0.585479i	0.917577	−	0.397557i	$-0.130142\pi$
$307$	12.8637	+	10.2584i	0.734168	+	0.585479i	−0.183410	+	0.983037i	$0.558713\pi$
$308$	−0.840237	+	4.79469i	−0.0478769	+	0.273203i
$309$	0.0967847	+	0.121364i	0.00550589	+	0.00690417i
$310$	4.70597	−	10.9903i	0.267281	−	0.624206i
$311$	−1.67102	+	7.32123i	−0.0947551	+	0.415149i	−0.999952	−	0.00984429i	$-0.996866\pi$
$311$	−1.67102	+	7.32123i	−0.0947551	+	0.415149i	0.905196	+	0.424993i	$0.139724\pi$
$312$			0.0605225i			0.00342641i
$313$		−	14.6410i		−	0.827556i	−0.910378	−	0.413778i	$-0.864209\pi$
$313$		−	14.6410i		−	0.827556i	0.910378	−	0.413778i	$-0.135791\pi$
$314$	−1.64841	+	7.22217i	−0.0930254	+	0.407571i
$315$	16.3637	+	6.04107i	0.921989	+	0.340376i
$316$	1.96199	+	8.59606i	0.110371	+	0.483566i
$317$	−11.3095	+	2.58131i	−0.635203	+	0.144981i	−0.527984	−	0.849254i	$-0.677052\pi$
$317$	−11.3095	+	2.58131i	−0.635203	+	0.144981i	−0.107219	+	0.994235i	$0.534195\pi$
$318$	−1.72421	+	1.37502i	−0.0966891	+	0.0771070i
$319$	−5.81923	−	7.29709i	−0.325814	−	0.408558i
$320$	−1.31551	+	1.80816i	−0.0735392	+	0.101079i
$321$	−0.853803	−	3.74076i	−0.0476547	−	0.208789i
$322$	2.56039	−	14.6105i	0.142685	−	0.814210i
$323$	27.2236	+	6.21360i	1.51476	+	0.345734i
$324$	−8.53858			−0.474365
$325$	−1.32034	−	0.180610i	−0.0732393	−	0.0100184i
$326$	2.88654	−	12.6468i	0.159871	−	0.700439i
$327$	1.15247	+	2.39313i	0.0637318	+	0.132340i
$328$	1.91414	−	1.52648i	0.105691	−	0.0842856i
$329$	7.99882	−	19.0313i	0.440989	−	1.04923i
$330$	−0.933288	+	0.0413029i	−0.0513758	+	0.00227365i
$331$	−4.76459	+	20.8750i	−0.261885	+	1.14739i	0.657319	+	0.753613i	$0.271691\pi$
$331$	−4.76459	+	20.8750i	−0.261885	+	1.14739i	−0.919204	+	0.393782i	$0.871167\pi$
$332$	12.8722	+	10.2653i	0.706456	+	0.563380i
$333$	−6.20172	−	12.8780i	−0.339852	−	0.705710i
$334$	3.50689	+	4.39750i	0.191888	+	0.240620i
$335$	0.703638	−	0.193697i	0.0384438	−	0.0105828i
$336$	−0.578166	+	0.163327i	−0.0315415	+	0.00891021i
$337$	2.21490	+	4.59928i	0.120653	+	0.250539i	0.952544	−	0.304400i	$-0.0984560\pi$
$337$	2.21490	+	4.59928i	0.120653	+	0.250539i	−0.831891	+	0.554939i	$0.812742\pi$
$338$	5.60967	−	11.6486i	0.305126	−	0.633600i
$339$	0.426033	+	1.86657i	0.0231389	+	0.101378i
$340$	7.44930	−	2.05064i	0.403995	−	0.111211i
$341$	6.13324	−	7.69084i	0.332134	−	0.416482i
$342$			23.8272i			1.28843i
$343$	−13.6160	−	12.5541i	−0.735194	−	0.677857i
$344$	−5.58947			−0.301364
$345$	2.84393	−	0.125859i	0.153112	−	0.00677602i
$346$	2.08707	+	1.00508i	0.112202	+	0.0540335i
$347$	−14.1791	+	3.23629i	−0.761175	+	0.173733i	−0.585453	−	0.810706i	$-0.699083\pi$
$347$	−14.1791	+	3.23629i	−0.761175	+	0.173733i	−0.175722	+	0.984440i	$0.556226\pi$
$348$	0.499810	−	1.03787i	0.0267926	−	0.0556354i
$349$	4.84731	−	2.33434i	0.259470	−	0.124954i	−0.299627	−	0.954056i	$-0.596862\pi$
$349$	4.84731	−	2.33434i	0.259470	−	0.124954i	0.559097	+	0.829102i	$0.311148\pi$
$350$	−1.83774	−	13.1005i	−0.0982313	−	0.700250i
$351$	0.324361	+	0.156204i	0.0173131	+	0.00833757i
$352$	−1.43845	+	1.14712i	−0.0766694	+	0.0611418i
$353$	1.77916	+	3.69446i	0.0946950	+	0.196636i	0.942936	−	0.332974i	$-0.108052\pi$
$353$	1.77916	+	3.69446i	0.0946950	+	0.196636i	−0.848241	+	0.529611i	$0.822338\pi$
$354$	−2.13388	+	2.67580i	−0.113414	+	0.142217i
$355$	−13.1325	+	7.05583i	−0.697000	+	0.374485i
$356$	5.39558	−	6.76584i	0.285965	−	0.358589i
$357$	1.91378	+	0.804358i	0.101288	+	0.0425711i
$358$	−4.44443	+	3.54432i	−0.234896	+	0.187323i
$359$	16.0125	−	7.71121i	0.845107	−	0.406982i	0.0393479	−	0.999226i	$-0.487472\pi$
$359$	16.0125	−	7.71121i	0.845107	−	0.406982i	0.805759	+	0.592244i	$0.201758\pi$
$360$	3.12038	+	5.80772i	0.164458	+	0.306094i
$361$	46.3073			2.43722
$362$		−	8.61507i		−	0.452798i
$363$	1.68584	+	0.384782i	0.0884837	+	0.0201958i
$364$	−0.694580	−	0.121720i	−0.0364059	−	0.00637988i
$365$	16.2455	+	11.8193i	0.850328	+	0.618649i
$366$	−0.605024	−	2.65078i	−0.0316251	−	0.138559i
$367$	−2.82422	+	2.25224i	−0.147423	+	0.117566i	−0.694424	−	0.719566i	$-0.744341\pi$
$367$	−2.82422	+	2.25224i	−0.147423	+	0.117566i	0.547001	+	0.837132i	$0.315769\pi$
$368$	4.38326	−	3.49553i	0.228493	−	0.182217i
$369$	−1.60629	−	7.03761i	−0.0836200	−	0.366363i
$370$	−6.37737	+	8.76564i	−0.331543	+	0.455704i
$371$	−12.3126	−	22.5531i	−0.639236	−	1.17090i
$372$	1.18366	+	0.270163i	0.0613701	+	0.0140073i
$373$		−	25.6973i		−	1.33056i	−0.746596	−	0.665278i	$-0.768313\pi$
$373$		−	25.6973i		−	1.33056i	0.746596	−	0.665278i	$-0.231687\pi$
$374$	6.35729			0.328728
$375$	2.37867	−	0.887412i	0.122834	−	0.0458258i
$376$	7.02997	−	3.38545i	0.362543	−	0.174591i
$377$	1.05709	−	0.842999i	0.0544428	−	0.0434167i
$378$	−0.616878	+	3.52013i	−0.0317288	+	0.181056i
$379$	7.60688	−	9.53873i	0.390739	−	0.489972i	−0.547087	−	0.837076i	$-0.684263\pi$
$379$	7.60688	−	9.53873i	0.390739	−	0.489972i	0.937827	+	0.347104i	$0.112835\pi$
$380$	15.9182	−	8.55256i	0.816588	−	0.438737i
$381$	−1.53173	+	1.92072i	−0.0784727	+	0.0984017i
$382$	9.09198	+	18.8797i	0.465186	+	0.965969i
$383$	17.5968	−	14.0329i	0.899152	−	0.717050i	−0.0605212	−	0.998167i	$-0.519276\pi$
$383$	17.5968	−	14.0329i	0.899152	−	0.717050i	0.959674	+	0.281117i	$0.0907048\pi$
$384$	−0.204590	−	0.0985255i	−0.0104405	−	0.00502786i
$385$	1.40298	−	10.7938i	0.0715026	−	0.550105i
$386$	−21.3854	+	10.2987i	−1.08849	+	0.524189i
$387$	−7.15049	+	14.8481i	−0.363480	+	0.754774i
$388$	11.4409	−	2.61131i	0.580823	−	0.132569i
$389$	−28.7119	−	13.8269i	−1.45575	−	0.701052i	−0.472166	−	0.881510i	$-0.656528\pi$
$389$	−28.7119	−	13.8269i	−1.45575	−	0.701052i	−0.983583	+	0.180458i	$0.942242\pi$
$390$	−0.00598331	−	0.135200i	−0.000302977	−	0.00684612i
$391$	−19.3720			−0.979687
$392$	−0.711620	−	6.96373i	−0.0359423	−	0.351722i
$393$		−	1.69869i		−	0.0856874i
$394$	−5.97601	+	7.49368i	−0.301067	+	0.377526i
$395$	−5.23268	−	19.0086i	−0.263285	−	0.956427i
$396$	1.20710	+	5.28864i	0.0606590	+	0.265764i
$397$	7.38130	−	15.3274i	0.370457	−	0.769261i	−0.629513	−	0.776990i	$-0.716746\pi$
$397$	7.38130	−	15.3274i	0.370457	−	0.769261i	0.999970	+	0.00772840i	$0.00246005\pi$
$398$	4.74917	+	9.86175i	0.238054	+	0.494325i
$399$	4.78230	+	0.838065i	0.239414	+	0.0419557i
$400$	2.75994	−	4.16926i	0.137997	−	0.208463i
$401$	1.57202	+	1.97126i	0.0785032	+	0.0984398i	0.819532	−	0.573033i	$-0.194233\pi$
$401$	1.57202	+	1.97126i	0.0785032	+	0.0984398i	−0.741029	+	0.671473i	$0.765662\pi$
$402$	0.0321569	+	0.0667745i	0.00160384	+	0.00333041i
$403$	1.11413	+	0.888488i	0.0554987	+	0.0442587i
$404$	−0.0521297	+	0.228395i	−0.00259355	+	0.0113631i
$405$	19.0742	−	0.844133i	0.947803	−	0.0419453i
$406$	10.9058	+	7.82333i	0.541244	+	0.388265i
$407$	−6.97334	+	5.56105i	−0.345655	+	0.275651i
$408$	0.340440	+	0.706931i	0.0168543	+	0.0349983i
$409$	−3.45558	+	15.1399i	−0.170868	+	0.748620i	0.814775	+	0.579777i	$0.196860\pi$
$409$	−3.45558	+	15.1399i	−0.170868	+	0.748620i	−0.985643	+	0.168843i	$0.945997\pi$
$410$	−4.12506	+	3.59920i	−0.203722	+	0.177752i
$411$	−1.18529			−0.0584661
$412$	−0.666461	−	0.152115i	−0.0328342	−	0.00749418i
$413$	−26.4170	−	29.8707i	−1.29989	−	1.46984i
$414$	−3.67829	−	16.1157i	−0.180778	−	0.792041i
$415$	−29.7699	−	21.6588i	−1.46135	−	1.06319i
$416$	−0.166177	−	0.208379i	−0.00814750	−	0.0102166i
$417$	−1.27973	+	1.02055i	−0.0626689	+	0.0499767i
$418$	14.4955	−	3.30851i	0.708999	−	0.161824i
$419$	7.49071	+	32.8190i	0.365945	+	1.60331i	0.737800	+	0.675020i	$0.235865\pi$
$419$	7.49071	+	32.8190i	0.365945	+	1.60331i	−0.371855	+	0.928291i	$0.621278\pi$
$420$	1.27541	−	0.422011i	0.0622335	−	0.0205920i
$421$	−5.39292	+	23.6279i	−0.262835	+	1.15155i	0.655326	+	0.755346i	$0.272531\pi$
$421$	−5.39292	+	23.6279i	−0.262835	+	1.15155i	−0.918161	+	0.396209i	$0.870326\pi$
$422$			7.43340i			0.361852i
$423$		−	23.0057i		−	1.11857i
$424$	2.16109	−	9.46838i	0.104952	−	0.459825i
$425$	−16.4381	+	5.31733i	−0.797366	+	0.257928i
$426$	−0.943925	−	1.18364i	−0.0457333	−	0.0573478i
$427$	31.6383	−	1.61235i	1.53108	−	0.0780271i
$428$	13.2107	+	10.5352i	0.638562	+	0.509236i
$429$	0.0247781	−	0.108560i	0.00119630	−	0.00524132i
$430$	12.4862	−	0.552581i	0.602139	−	0.0266478i
$431$	4.30152	−	2.07150i	0.207197	−	0.0997808i	−0.327407	−	0.944883i	$-0.606175\pi$
$431$	4.30152	−	2.07150i	0.207197	−	0.0997808i	0.534604	+	0.845102i	$0.320461\pi$
$432$	−1.05607	+	0.842185i	−0.0508100	+	0.0405196i
$433$	11.6918	−	24.2783i	0.561873	−	1.16674i	−0.405666	−	0.914021i	$-0.632960\pi$
$433$	11.6918	−	24.2783i	0.561873	−	1.16674i	0.967539	−	0.252720i	$-0.0813253\pi$
$434$	−5.48104	+	13.0408i	−0.263098	+	0.625981i
$435$	−1.01391	+	2.36788i	−0.0486133	+	0.113531i
$436$	−10.5388	−	5.07522i	−0.504717	−	0.243059i
$437$	−44.1710	+	10.0817i	−2.11298	+	0.482275i
$438$	−0.885207	+	1.83815i	−0.0422968	+	0.0878303i
$439$	−11.0783	+	13.8918i	−0.528740	+	0.663019i	−0.972439	−	0.233157i	$-0.925094\pi$
$439$	−11.0783	+	13.8918i	−0.528740	+	0.663019i	0.443699	+	0.896176i	$0.353666\pi$
$440$	3.09991	−	2.70474i	0.147782	−	0.128943i
$441$	−19.4092	−	7.01817i	−0.924246	−	0.334199i
$442$			0.920944i			0.0438049i
$443$	−1.04643	−	0.834501i	−0.0497175	−	0.0396484i	0.598316	−	0.801260i	$-0.295837\pi$
$443$	−1.04643	−	0.834501i	−0.0497175	−	0.0396484i	−0.648033	+	0.761612i	$0.724408\pi$
$444$	−0.991819	−	0.477635i	−0.0470696	−	0.0226675i
$445$	−11.3842	+	15.6475i	−0.539663	+	0.741763i
$446$	−11.5309	−	5.55300i	−0.546005	−	0.262942i
$447$	0.104168	+	0.216306i	0.00492696	+	0.0102309i
$448$	1.54218	−	2.14981i	0.0728612	−	0.101569i
$449$	−8.70678	−	4.19296i	−0.410898	−	0.197878i	0.217003	−	0.976171i	$-0.430372\pi$
$449$	−8.70678	−	4.19296i	−0.410898	−	0.197878i	−0.627902	+	0.778293i	$0.716086\pi$
$450$	−7.54471	−	12.6653i	−0.355661	−	0.597047i
$451$	−4.05836	+	1.95441i	−0.191101	+	0.0920294i
$452$	−6.59189	−	5.25686i	−0.310057	−	0.247262i
$453$	−3.50569	−	0.800150i	−0.164712	−	0.0375943i
$454$	−2.91537	+	3.65576i	−0.136825	+	0.171573i
$455$	1.56364	+	0.203242i	0.0733047	+	0.00952813i
$456$	1.14416	+	1.43473i	0.0535800	+	0.0671872i
$457$	3.97532	+	8.25483i	0.185957	+	0.386145i	0.973017	−	0.230732i	$-0.0741121\pi$
$457$	3.97532	+	8.25483i	0.185957	+	0.386145i	−0.787060	+	0.616877i	$0.788398\pi$
$458$	−26.0087	−	5.93633i	−1.21531	−	0.277386i
$459$	4.66734			0.217853
$460$	−9.44610	+	8.24193i	−0.440427	+	0.384282i
$461$	7.02472	−	30.7773i	0.327174	−	1.43344i	−0.497318	−	0.867568i	$-0.665682\pi$
$461$	7.02472	−	30.7773i	0.327174	−	1.43344i	0.824492	−	0.565874i	$-0.191461\pi$
$462$	1.10393	−	0.0562585i	0.0513594	−	0.00261738i
$463$	19.4205	−	4.43261i	0.902549	−	0.206001i	0.254027	−	0.967197i	$-0.418245\pi$
$463$	19.4205	−	4.43261i	0.902549	−	0.206001i	0.648522	+	0.761196i	$0.275387\pi$
$464$	1.12883	+	4.94571i	0.0524044	+	0.229599i
$465$	−2.67087	−	0.486495i	−0.123859	−	0.0225607i
$466$	10.7460	+	13.4750i	0.497797	+	0.624217i
$467$	−23.0356	+	5.25772i	−1.06596	+	0.243298i	−0.719305	−	0.694694i	$-0.755540\pi$
$467$	−23.0356	+	5.25772i	−1.06596	+	0.243298i	−0.346655	+	0.937993i	$0.612683\pi$
$468$	−0.766136	+	0.174865i	−0.0354146	+	0.00808316i
$469$	−0.831003	+	0.234751i	−0.0383722	+	0.0108398i
$470$	−15.3694	+	8.25769i	−0.708939	+	0.380899i
$471$	1.68217			0.0775104
$472$		−	15.0718i		−	0.693736i
$473$	10.0259	+	2.28835i	0.460992	+	0.105218i
$474$	1.80390	−	0.868711i	0.0828558	−	0.0399012i
$475$	−34.7139	+	20.6791i	−1.59278	+	0.948822i
$476$	−8.79770	+	2.48527i	−0.403242	+	0.113912i
$477$	−22.3876	−	17.8535i	−1.02506	−	0.817457i
$478$	1.50712	+	0.343991i	0.0689342	+	0.0157338i
$479$	−11.8474	+	14.8561i	−0.541320	+	0.678793i	−0.974982	−	0.222282i	$-0.928649\pi$
$479$	−11.8474	+	14.8561i	−0.541320	+	0.678793i	0.433663	+	0.901075i	$0.357221\pi$
$480$	0.466771	+	0.199868i	0.0213051	+	0.00912270i
$481$	−0.805598	−	1.01019i	−0.0367321	−	0.0460606i
$482$	−3.29701	+	6.84631i	−0.150175	+	0.311841i
$483$	−3.36391	+	0.171432i	−0.153063	+	0.00780042i
$484$	−6.86087	+	3.30402i	−0.311858	+	0.150183i
$485$	−25.2994	+	6.96440i	−1.14879	+	0.316237i
$486$	1.33317	+	5.84099i	0.0604737	+	0.264953i
$487$	17.0490	−	35.4026i	0.772563	−	1.60424i	−0.0240176	−	0.999712i	$-0.507646\pi$
$487$	17.0490	−	35.4026i	0.772563	−	1.60424i	0.796581	−	0.604532i	$-0.206640\pi$
$488$	9.36138	+	7.46545i	0.423770	+	0.337945i
$489$	−2.94566			−0.133207
$490$	2.27812	+	15.4858i	0.102915	+	0.699577i
$491$	−12.7542			−0.575589			−0.287795	−	0.957692i	$-0.592922\pi$
$491$	−12.7542			−0.575589			−0.287795	+	0.957692i	$0.592922\pi$
$492$	−0.434660	−	0.346630i	−0.0195960	−	0.0156273i
$493$	7.60539	−	15.7928i	0.342529	−	0.711270i
$494$	0.479284	+	2.09988i	0.0215640	+	0.0944781i
$495$	−3.21936	−	11.6949i	−0.144699	−	0.525645i
$496$	−4.81715	+	2.31982i	−0.216296	+	0.104163i
$497$	15.4824	−	8.45236i	0.694479	−	0.379140i
$498$	1.62215	−	3.36842i	0.0726901	−	0.150943i
$499$	15.0883	+	18.9201i	0.675443	+	0.846979i	0.994926	−	0.100613i	$-0.0320805\pi$
$499$	15.0883	+	18.9201i	0.675443	+	0.846979i	−0.319482	+	0.947592i	$0.603509\pi$
$500$	−5.75319	+	9.58649i	−0.257291	+	0.428721i
$501$	0.796337	−	0.998575i	0.0355777	−	0.0446131i
$502$	18.3812	+	4.19539i	0.820393	+	0.187249i
$503$	−21.2435	−	16.9411i	−0.947202	−	0.755368i	0.0224781	−	0.999747i	$-0.492844\pi$
$503$	−21.2435	−	16.9411i	−0.947202	−	0.755368i	−0.969680	+	0.244379i	$0.921416\pi$
$504$	−3.73798	−	6.84693i	−0.166503	−	0.304986i
$505$	0.0938722	−	0.515361i	0.00417726	−	0.0229333i
$506$	−9.29338	+	4.47546i	−0.413141	+	0.198958i
$507$	−2.86228	−	0.653296i	−0.127118	−	0.0290139i
$508$		−	10.8187i		−	0.480004i
$509$	−9.46690			−0.419613			−0.209807	−	0.977743i	$-0.567283\pi$
$509$	−9.46690			−0.419613			−0.209807	+	0.977743i	$0.567283\pi$
$510$	−0.830390	−	1.54554i	−0.0367703	−	0.0684378i
$511$	−19.3151	−	13.8558i	−0.854448	−	0.612945i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$	10.6422	−	2.42901i	0.469864	−	0.107243i
$514$	−7.16607	−	8.98597i	−0.316082	−	0.396354i
$515$	1.50383	+	0.273921i	0.0662668	+	0.0120704i
$516$	0.282434	+	1.23742i	0.0124335	+	0.0544746i
$517$	−13.9958	+	3.19444i	−0.615533	+	0.140491i
$518$	7.47623	−	10.4219i	0.328487	−	0.457912i
$519$	0.117051	−	0.512832i	0.00513795	−	0.0225108i
$520$	0.391820	+	0.449066i	0.0171825	+	0.0196929i
$521$	37.5150			1.64356			0.821781	−	0.569803i	$-0.192981\pi$
$521$	37.5150			1.64356			0.821781	+	0.569803i	$0.192981\pi$
$522$	14.5821	+	3.32827i	0.638242	+	0.145674i
$523$	0.982559	+	2.04031i	0.0429643	+	0.0892163i	0.921346	−	0.388743i	$-0.127091\pi$
$523$	0.982559	+	2.04031i	0.0429643	+	0.0892163i	−0.878382	+	0.477960i	$0.841376\pi$
$524$	4.66410	+	5.84859i	0.203752	+	0.255497i
$525$	−2.80739	+	1.06881i	−0.122524	+	0.0466467i
$526$	−11.3586	+	14.2432i	−0.495259	+	0.621035i
$527$	18.0113	+	4.11096i	0.784584	+	0.179076i
$528$	0.326639	+	0.260486i	0.0142152	+	0.0113362i
$529$	7.59667	−	3.65836i	0.330290	−	0.159059i
$530$	−3.89158	+	21.3649i	−0.169039	+	0.928031i
$531$	−40.0375	−	19.2810i	−1.73748	−	0.836726i
$532$	−18.7666	+	10.2453i	−0.813634	+	0.444191i
$533$	−0.283124	−	0.587912i	−0.0122634	−	0.0254653i
$534$	−1.77049	−	0.852623i	−0.0766166	−	0.0368966i
$535$	−30.5526	−	22.2283i	−1.32090	−	0.961012i
$536$	−0.294060	−	0.141612i	−0.0127014	−	0.00611669i
$537$	1.00923	+	0.804837i	0.0435516	+	0.0347313i
$538$		−	22.1784i		−	0.956178i
$539$	−1.57453	+	12.7823i	−0.0678199	+	0.550571i
$540$	2.27587	−	1.98574i	0.0979377	−	0.0854528i
$541$	−23.4396	+	29.3924i	−1.00775	+	1.26368i	−0.0433945	+	0.999058i	$0.513817\pi$
$541$	−23.4396	+	29.3924i	−1.00775	+	1.26368i	−0.964353	+	0.264618i	$0.914754\pi$
$542$	2.03021	−	4.21577i	0.0872049	−	0.181083i
$543$	−1.90725	+	0.435316i	−0.0818477	+	0.0186812i
$544$	−3.11316	−	1.49922i	−0.133476	−	0.0642785i
$545$	24.0442	+	10.2956i	1.02994	+	0.441013i
$546$	0.00814984	+	0.159920i	0.000348781	+	0.00684394i
$547$	−0.436606	+	0.906621i	−0.0186679	+	0.0387643i	−0.910094	−	0.414401i	$-0.863991\pi$
$547$	−0.436606	+	0.906621i	−0.0186679	+	0.0387643i	0.891426	+	0.453165i	$0.149705\pi$
$548$	4.08097	−	3.25446i	0.174330	−	0.139024i
$549$	31.8074	−	15.3176i	1.35751	−	0.653741i
$550$	−6.65744	+	6.34853i	−0.283874	+	0.270702i
$551$	9.12237	−	39.9677i	0.388626	−	1.70268i
$552$	−0.995341	−	0.793758i	−0.0423645	−	0.0337846i
$553$	6.34175	+	22.4494i	0.269679	+	0.954644i
$554$	19.6691	+	24.6643i	0.835659	+	1.04788i
$555$	2.26282	+	0.968927i	0.0960516	+	0.0411287i
$556$	1.60399	−	7.02755i	0.0680244	−	0.298034i
$557$		−	4.15112i		−	0.175888i	−0.996125	−	0.0879442i	$-0.971970\pi$
$557$		−	4.15112i		−	0.175888i	0.996125	−	0.0879442i	$-0.0280297\pi$
$558$			15.7642i			0.667352i
$559$	−0.331500	+	1.45240i	−0.0140209	+	0.0614298i
$560$	−3.23252	+	4.95488i	−0.136599	+	0.209382i
$561$	−0.321231	−	1.40741i	−0.0135624	−	0.0594208i
$562$	−1.85303	+	0.422942i	−0.0781653	+	0.0178407i
$563$	−17.9450	+	14.3107i	−0.756293	+	0.603124i	−0.923857	−	0.382738i	$-0.874981\pi$
$563$	−17.9450	+	14.3107i	−0.756293	+	0.603124i	0.167564	+	0.985861i	$0.446410\pi$
$564$	−1.10471	−	1.38526i	−0.0465167	−	0.0583301i
$565$	15.2452	+	11.0915i	0.641371	+	0.466624i
$566$	−3.03803	−	13.3105i	−0.127698	−	0.559482i
$567$	−22.5617	+	1.14979i	−0.947501	+	0.0482866i
$568$	6.49988	+	1.48356i	0.272729	+	0.0622486i
$569$	−40.1415			−1.68282			−0.841410	−	0.540398i	$-0.818274\pi$
$569$	−40.1415			−1.68282			−0.841410	+	0.540398i	$0.818274\pi$
$570$	−2.69775	−	3.09190i	−0.112996	−	0.129505i
$571$	8.05593	−	35.2953i	0.337130	−	1.47706i	−0.467875	−	0.883795i	$-0.654980\pi$
$571$	8.05593	−	35.2953i	0.337130	−	1.47706i	0.805005	−	0.593268i	$-0.202163\pi$
$572$	0.212763	+	0.441806i	0.00889605	+	0.0184728i
$573$	3.72026	−	2.96681i	0.155416	−	0.123940i
$574$	4.85223	−	4.29120i	0.202528	−	0.179111i
$575$	20.2867	−	19.3454i	0.846013	−	0.806757i
$576$	0.656089	−	2.87451i	0.0273370	−	0.119771i
$577$	0.310015	+	0.247229i	0.0129061	+	0.0102923i	0.629922	−	0.776659i	$-0.283087\pi$
$577$	0.310015	+	0.247229i	0.0129061	+	0.0102923i	−0.617016	+	0.786951i	$0.711658\pi$
$578$	−2.19570	−	4.55941i	−0.0913290	−	0.189647i
$579$	3.36057	+	4.21402i	0.139660	+	0.175129i
$580$	−3.01060	−	10.9365i	−0.125008	−	0.454115i
$581$	35.3949	+	25.3908i	1.46843	+	1.05339i
$582$	−1.15621	−	2.40089i	−0.0479263	−	0.0995200i
$583$	−7.75276	+	16.0988i	−0.321087	+	0.666743i
$584$	−1.99925	−	8.75929i	−0.0827296	−	0.362462i
$585$	1.69417	−	0.466370i	0.0700453	−	0.0192820i
$586$	5.18450	−	6.50116i	0.214170	−	0.268560i
$587$		−	27.6587i		−	1.14160i	−0.821090	−	0.570799i	$-0.806634\pi$
$587$		−	27.6587i		−	1.14160i	0.821090	−	0.570799i	$-0.193366\pi$
$588$	−1.50571	+	0.509417i	−0.0620943	+	0.0210080i
$589$	43.2077			1.78034
$590$	1.49001	+	33.6686i	0.0613429	+	1.38612i
$591$	1.96095	+	0.944345i	0.0806628	+	0.0388451i
$592$	4.72628	−	1.07874i	0.194249	−	0.0443361i
$593$	6.75647	−	14.0300i	0.277455	−	0.576141i	−0.714947	−	0.699179i	$-0.753549\pi$
$593$	6.75647	−	14.0300i	0.277455	−	0.576141i	0.992402	+	0.123037i	$0.0392635\pi$
$594$	2.23907	−	1.07828i	0.0918702	−	0.0442424i
$595$	19.4073	−	6.42155i	0.795622	−	0.263258i
$596$	−0.952563	−	0.458730i	−0.0390185	−	0.0187903i
$597$	1.94327	−	1.54970i	0.0795327	−	0.0634252i
$598$	−0.648334	−	1.34628i	−0.0265123	−	0.0550534i
$599$	−2.67508	+	3.35445i	−0.109301	+	0.137059i	−0.833473	−	0.552561i	$-0.813651\pi$
$599$	−2.67508	+	3.35445i	−0.109301	+	0.137059i	0.724172	+	0.689620i	$0.242222\pi$
$600$	−1.06247	−	0.400337i	−0.0433751	−	0.0163437i
$601$	10.1158	−	12.6848i	0.412632	−	0.517424i	−0.531471	−	0.847077i	$-0.678360\pi$
$601$	10.1158	−	12.6848i	0.412632	−	0.517424i	0.944102	+	0.329653i	$0.106932\pi$
$602$	−14.7692	+	0.752668i	−0.601947	+	0.0306765i
$603$	−0.752368	+	0.599993i	−0.0306388	+	0.0244336i
$604$	14.2671	−	6.87067i	0.580519	−	0.279563i
$605$	14.9997	−	8.05906i	0.609825	−	0.327647i
$606$	0.0531973			0.00216099
$607$			35.5085i			1.44125i	0.693327	+	0.720623i	$0.256144\pi$
$607$			35.5085i			1.44125i	−0.693327	+	0.720623i	$0.743856\pi$
$608$	−7.87868	−	1.79826i	−0.319523	−	0.0729289i
$609$	1.18090	−	2.80968i	0.0478525	−	0.113854i
$610$	−21.6503	−	15.7515i	−0.876593	−	0.637758i
$611$	−0.462760	−	2.02748i	−0.0187213	−	0.0820233i
$612$	−7.96520	+	6.35203i	−0.321974	+	0.256766i
$613$	13.2802	−	10.5906i	0.536381	−	0.427749i	−0.317469	−	0.948269i	$-0.602833\pi$
$613$	13.2802	−	10.5906i	0.536381	−	0.427749i	0.853850	+	0.520519i	$0.174262\pi$
$614$	3.66119	+	16.0407i	0.147754	+	0.647351i
$615$	1.00525	+	0.731358i	0.0405355	+	0.0294912i
$616$	−3.64637	+	3.22476i	−0.146916	+	0.129929i
$617$	−16.0196	−	3.65637i	−0.644925	−	0.147200i	−0.112466	−	0.993656i	$-0.535875\pi$
$617$	−16.0196	−	3.65637i	−0.644925	−	0.147200i	−0.532459	+	0.846456i	$0.678732\pi$
$618$			0.155231i			0.00624429i
$619$	−3.77685			−0.151805			−0.0759023	−	0.997115i	$-0.524184\pi$
$619$	−3.77685			−0.151805			−0.0759023	+	0.997115i	$0.524184\pi$
$620$	10.5316	−	5.65843i	0.422959	−	0.227248i
$621$	−6.82294	+	3.28575i	−0.273795	+	0.131853i
$622$	−5.87117	+	4.68210i	−0.235413	+	0.187735i
$623$	13.3458	−	18.6041i	0.534687	−	0.745357i
$624$	−0.0377352	+	0.0473184i	−0.00151062	+	0.00189425i
$625$	11.9042	−	21.9838i	0.476169	−	0.879354i
$626$	9.12849	−	11.4468i	0.364848	−	0.457505i
$627$	−1.46491	−	3.04191i	−0.0585027	−	0.121482i
$628$	−5.79173	+	4.61875i	−0.231115	+	0.184308i
$629$	−15.0921	−	7.26796i	−0.601760	−	0.289792i
$630$	9.02709	+	14.9257i	0.359648	+	0.594654i
$631$	−25.7692	+	12.4098i	−1.02586	+	0.494026i	−0.869635	−	0.493696i	$-0.835646\pi$
$631$	−25.7692	+	12.4098i	−1.02586	+	0.494026i	−0.156222	+	0.987722i	$0.549931\pi$
$632$	−3.82561	+	7.94395i	−0.152174	+	0.315994i
$633$	1.64564	−	0.375607i	0.0654084	−	0.0149290i
$634$	−10.4515	−	5.03319i	−0.415083	−	0.199893i
$635$	1.06955	+	24.1678i	0.0424439	+	0.959069i
$636$	−2.20535			−0.0874479
$637$	−1.85169	−	0.228093i	−0.0733668	−	0.00903739i
$638$		−	9.33333i		−	0.369510i
$639$	12.2561	−	15.3687i	0.484846	−	0.607977i
$640$	−2.15587	+	0.593468i	−0.0852184	+	0.0234589i
$641$	7.44052	+	32.5990i	0.293883	+	1.28758i	0.879073	+	0.476688i	$0.158163\pi$
$641$	7.44052	+	32.5990i	0.293883	+	1.28758i	−0.585190	+	0.810896i	$0.698980\pi$
$642$	1.66479	−	3.45698i	0.0657042	−	0.136436i
$643$	10.6301	+	22.0735i	0.419208	+	0.870495i	0.998467	+	0.0553513i	$0.0176279\pi$
$643$	10.6301	+	22.0735i	0.419208	+	0.870495i	−0.579259	+	0.815144i	$0.696658\pi$
$644$	11.1113	−	9.82656i	0.437846	−	0.387221i
$645$	−0.753257	−	2.73634i	−0.0296595	−	0.107743i
$646$	17.4101	+	21.8316i	0.684992	+	0.858953i
$647$	−0.514289	−	1.06793i	−0.0202188	−	0.0419848i	0.890615	−	0.454758i	$-0.150274\pi$
$647$	−0.514289	−	1.06793i	−0.0202188	−	0.0419848i	−0.910834	+	0.412774i	$0.864560\pi$
$648$	−6.67573	−	5.32372i	−0.262247	−	0.209135i
$649$	−6.17045	+	27.0345i	−0.242211	+	1.06120i
$650$	−0.919675	−	0.964425i	−0.0360726	−	0.0378279i
$651$	3.16400	+	0.554469i	0.124007	+	0.0217314i
$652$	10.1419	−	8.08791i	0.397188	−	0.316747i
$653$	−0.583199	−	1.21102i	−0.0228223	−	0.0473910i	0.889246	−	0.457429i	$-0.151230\pi$
$653$	−0.583199	−	1.21102i	−0.0228223	−	0.0473910i	−0.912068	+	0.410038i	$0.865515\pi$
$654$	−0.591054	+	2.58958i	−0.0231120	+	0.101261i
$655$	−10.9972	−	12.6040i	−0.429698	−	0.492478i
$656$	2.44828			0.0955893
$657$	−25.8262	−	5.89466i	−1.00758	−	0.229973i
$658$	18.1196	−	9.89210i	0.706374	−	0.385634i
$659$	7.68756	+	33.6814i	0.299465	+	1.31204i	0.870927	+	0.491413i	$0.163519\pi$
$659$	7.68756	+	33.6814i	0.299465	+	1.31204i	−0.571462	+	0.820629i	$0.693624\pi$
$660$	−0.755426	−	0.549603i	−0.0294049	−	0.0213933i
$661$	2.32784	+	2.91902i	0.0905426	+	0.113537i	0.825039	−	0.565076i	$-0.191153\pi$
$661$	2.32784	+	2.91902i	0.0905426	+	0.113537i	−0.734497	+	0.678612i	$0.762582\pi$
$662$	−16.7405	+	13.3501i	−0.650636	+	0.518865i
$663$	0.203883	−	0.0465350i	0.00791816	−	0.00180727i
$664$	3.66363	+	16.0514i	0.142177	+	0.622916i
$665$	40.9094	−	24.7421i	1.58640	−	0.959459i
$666$	3.18061	−	13.9351i	0.123246	−	0.539976i
$667$			28.4407i			1.10123i
$668$			5.62461i			0.217623i
$669$	−0.646697	+	2.83336i	−0.0250027	+	0.109544i
$670$	0.670894	+	0.287273i	0.0259189	+	0.0110983i
$671$	−13.7352	−	17.2234i	−0.530243	−	0.664904i
$672$	−0.553861	−	0.232786i	−0.0213656	−	0.00897993i
$673$	19.0971	+	15.2295i	0.736141	+	0.587053i	0.918145	−	0.396245i	$-0.129687\pi$
$673$	19.0971	+	15.2295i	0.736141	+	0.587053i	−0.182004	+	0.983298i	$0.558258\pi$
$674$	−1.13593	+	4.97683i	−0.0437543	+	0.191700i
$675$	−4.88771	+	4.66091i	−0.188128	+	0.179399i
$676$	11.6486	−	5.60967i	0.448023	−	0.215756i
$677$	−16.3037	+	13.0018i	−0.626604	+	0.499700i	−0.884541	−	0.466462i	$-0.845529\pi$
$677$	−16.3037	+	13.0018i	−0.626604	+	0.499700i	0.257938	+	0.966162i	$0.416957\pi$
$678$	−0.830703	+	1.72497i	−0.0319029	+	0.0662471i
$679$	29.8789	−	8.44052i	1.14665	−	0.323917i
$680$	7.10265	+	3.04131i	0.272374	+	0.116629i
$681$	0.956642	+	0.460695i	0.0366586	+	0.0176539i
$682$	9.59032	−	2.18893i	0.367232	−	0.0838184i
$683$	13.7606	−	28.5743i	0.526536	−	1.09336i	−0.452891	−	0.891566i	$-0.649607\pi$
$683$	13.7606	−	28.5743i	0.526536	−	1.09336i	0.979427	−	0.201798i	$-0.0646783\pi$
$684$	−14.8560	+	18.6288i	−0.568033	+	0.712291i
$685$	−8.79466	+	7.67354i	−0.336027	+	0.293191i
$686$	−2.81805	−	18.3046i	−0.107594	−	0.698873i
$687$			6.05790i			0.231123i
$688$	−4.37003	−	3.48498i	−0.166606	−	0.132864i
$689$	−2.33214	−	1.12310i	−0.0888474	−	0.0427866i
$690$	2.30195	+	1.67476i	0.0876336	+	0.0637571i
$691$	6.48370	+	3.12239i	0.246652	+	0.118781i	0.553126	−	0.833098i	$-0.313435\pi$
$691$	6.48370	+	3.12239i	0.246652	+	0.118781i	−0.306474	+	0.951879i	$0.599149\pi$
$692$	1.00508	+	2.08707i	0.0382074	+	0.0793386i
$693$	3.90170	+	13.8118i	0.148213	+	0.524665i
$694$	−13.1035	−	6.31030i	−0.497401	−	0.239536i
$695$	−2.88838	+	15.8573i	−0.109562	+	0.601501i
$696$	1.03787	−	0.499810i	0.0393402	−	0.0189452i
$697$	−6.61403	−	5.27451i	−0.250524	−	0.199786i
$698$	5.24521	+	1.19719i	0.198534	+	0.0453142i
$699$	2.44017	−	3.05988i	0.0922957	−	0.115735i
$700$	6.73122	−	11.3882i	0.254416	−	0.430433i
$701$	25.8338	+	32.3946i	0.975730	+	1.22353i	0.974698	+	0.223527i	$0.0717572\pi$
$701$	25.8338	+	32.3946i	0.975730	+	1.22353i	0.00103252	+	0.999999i	$0.499671\pi$
$702$	0.156204	+	0.324361i	0.00589555	+	0.0122422i
$703$	−38.1945	−	8.71764i	−1.44053	−	0.328792i
$704$	−1.83984			−0.0693416
$705$	2.60474	+	2.98530i	0.0981001	+	0.112433i
$706$	−0.912456	+	3.99773i	−0.0343407	+	0.150457i
$707$	−0.106988	+	0.610513i	−0.00402371	+	0.0229607i
$708$	−3.33667	+	0.761573i	−0.125400	+	0.0286217i
$709$	−9.42922	−	41.3121i	−0.354122	−	1.55151i	−0.767560	−	0.640977i	$-0.778530\pi$
$709$	−9.42922	−	41.3121i	−0.354122	−	1.55151i	0.413439	−	0.910532i	$-0.364328\pi$
$710$	−14.6666	−	2.67150i	−0.550429	−	0.100260i
$711$	16.2087	+	20.3251i	0.607873	+	0.762249i
$712$	8.43687	−	1.92566i	0.316185	−	0.0721671i
$713$	−29.2238	+	6.67014i	−1.09444	+	0.249799i
$714$	0.994746	+	1.82210i	0.0372274	+	0.0681902i
$715$	−0.518964	−	0.965908i	−0.0194081	−	0.0361229i
$716$	−5.68464			−0.212445
$717$		−	0.351036i		−	0.0131097i
$718$	17.3269	+	3.95476i	0.646635	+	0.147590i
$719$	22.6261	−	10.8962i	0.843812	−	0.406358i	0.0385349	−	0.999257i	$-0.487731\pi$
$719$	22.6261	−	10.8962i	0.843812	−	0.406358i	0.805277	+	0.592899i	$0.202017\pi$
$720$	−1.18145	+	6.48618i	−0.0440299	+	0.241726i
$721$	−1.78149	−	0.312193i	−0.0663461	−	0.0116267i
$722$	36.2045	+	28.8721i	1.34739	+	1.07451i
$723$	1.68226	+	0.383966i	0.0625641	+	0.0142798i
$724$	5.37141	−	6.73553i	0.199627	−	0.250324i
$725$	7.80652	+	24.1333i	0.289927	+	0.896288i
$726$	1.07814	+	1.35194i	0.0400134	+	0.0501752i
$727$	4.41197	−	9.16155i	0.163631	−	0.339783i	−0.802991	−	0.595992i	$-0.796759\pi$
$727$	4.41197	−	9.16155i	0.163631	−	0.339783i	0.966622	+	0.256209i	$0.0824734\pi$
$728$	−0.467153	−	0.528228i	−0.0173138	−	0.0195774i
$729$	−21.8532	+	10.5240i	−0.809379	+	0.389777i
$730$	5.33204	+	19.3696i	0.197348	+	0.716900i
$731$	4.29767	+	18.8293i	0.158955	+	0.696428i
$732$	1.17971	−	2.44969i	0.0436033	−	0.0905433i
$733$	14.4662	+	11.5364i	0.534320	+	0.426106i	0.853119	−	0.521716i	$-0.174708\pi$
$733$	14.4662	+	11.5364i	0.534320	+	0.426106i	−0.318799	+	0.947822i	$0.603279\pi$
$734$	−3.61231			−0.133333
$735$	3.31321	−	1.28683i	0.122210	−	0.0474655i
$736$	5.60640			0.206654
$737$	0.469482	+	0.374399i	0.0172936	+	0.0137912i
$738$	3.13203	−	6.50373i	0.115292	−	0.239406i
$739$	9.05406	+	39.6684i	0.333059	+	1.45923i	0.813174	+	0.582021i	$0.197738\pi$
$739$	9.05406	+	39.6684i	0.333059	+	1.45923i	−0.480115	+	0.877206i	$0.659405\pi$
$740$	−10.4513	+	2.87703i	−0.384198	+	0.105762i
$741$	0.440664	−	0.212212i	0.0161882	−	0.00779582i
$742$	4.43532	−	25.3095i	0.162826	−	0.929141i
$743$	11.2090	−	23.2758i	0.411220	−	0.853906i	−0.587773	−	0.809026i	$-0.699995\pi$
$743$	11.2090	−	23.2758i	0.411220	−	0.853906i	0.998992	−	0.0448802i	$-0.0142906\pi$
$744$	0.756981	+	0.949224i	0.0277523	+	0.0348003i
$745$	2.17326	+	0.930578i	0.0796222	+	0.0340937i
$746$	16.0220	−	20.0910i	0.586607	−	0.735582i
$747$	47.3266	+	10.8020i	1.73159	+	0.395224i
$748$	4.97033	+	3.96371i	0.181733	+	0.144927i
$749$	36.3255	+	26.0584i	1.32731	+	0.952152i
$750$	2.41301	+	0.789268i	0.0881106	+	0.0288200i
$751$	−14.1974	+	6.83711i	−0.518070	+	0.249490i	−0.674600	−	0.738184i	$-0.735684\pi$
$751$	−14.1974	+	6.83711i	−0.518070	+	0.249490i	0.156529	+	0.987673i	$0.449969\pi$
$752$	7.60705	+	1.73626i	0.277400	+	0.0633148i
$753$		−	4.28131i		−	0.156020i
$754$	1.35207			0.0492393
$755$	−31.1917	+	16.7587i	−1.13518	+	0.609912i
$756$	−2.67706	+	2.36753i	−0.0973637	+	0.0861063i
$757$	24.7603	−	5.65139i	0.899930	−	0.205403i	0.252562	−	0.967581i	$-0.418727\pi$
$757$	24.7603	−	5.65139i	0.899930	−	0.205403i	0.647368	+	0.762178i	$0.275870\pi$
$758$	11.8946	−	2.71487i	0.432031	−	0.0986084i
$759$	1.46039	+	1.83127i	0.0530088	+	0.0664709i
$760$	17.7778	+	3.23820i	0.644869	+	0.117462i
$761$	−4.99956	−	21.9045i	−0.181234	−	0.794038i	−0.981044	−	0.193785i	$-0.937924\pi$
$761$	−4.99956	−	21.9045i	−0.181234	−	0.794038i	0.799810	−	0.600253i	$-0.204933\pi$
$762$	−2.39510	+	0.546667i	−0.0867655	+	0.0198037i
$763$	−28.5303	−	11.9912i	−1.03287	−	0.434111i
$764$	−4.66290	+	20.4295i	−0.168698	+	0.739113i
$765$	17.1653	−	14.9771i	0.620614	−	0.541500i
$766$	22.5071			0.813215
$767$	−3.91633	−	0.893877i	−0.141411	−	0.0322760i
$768$	−0.0985255	−	0.204590i	−0.00355523	−	0.00738252i
$769$	−22.4036	−	28.0932i	−0.807895	−	1.01307i	−0.999501	−	0.0315961i	$-0.989941\pi$
$769$	−22.4036	−	28.0932i	−0.807895	−	1.01307i	0.191606	−	0.981472i	$-0.438630\pi$
$770$	7.82675	−	7.56422i	0.282056	−	0.272596i
$771$	−1.62726	+	2.04052i	−0.0586042	+	0.0734874i
$772$	−23.1409	−	5.28176i	−0.832860	−	0.190095i
$773$	30.2137	+	24.0946i	1.08671	+	0.866623i	0.991664	−	0.128850i	$-0.0411286\pi$
$773$	30.2137	+	24.0946i	1.08671	+	0.866623i	0.0950464	+	0.995473i	$0.469700\pi$
$774$	−14.8481	+	7.15049i	−0.533706	+	0.257019i
$775$	−22.9670	+	13.6814i	−0.824998	+	0.491451i
$776$	10.5730	+	5.09167i	0.379547	+	0.182780i
$777$	−2.68502	−	1.12851i	−0.0963246	−	0.0404850i
$778$	−13.8269	−	28.7119i	−0.495718	−	1.02937i
$779$	−17.8259	−	8.58450i	−0.638679	−	0.307572i
$780$	0.0796179	−	0.109434i	0.00285078	−	0.00391837i
$781$	−11.0515	−	5.32214i	−0.395455	−	0.190441i
$782$	−15.1457	−	12.0783i	−0.541608	−	0.431918i
$783$		−	6.85226i		−	0.244880i
$784$	3.78545	−	5.88815i	0.135195	−	0.210291i
$785$	12.4814	−	10.8903i	0.445481	−	0.388692i
$786$	1.05911	−	1.32809i	0.0377773	−	0.0473713i
$787$	3.10489	−	6.44738i	0.110677	−	0.229824i	−0.838272	−	0.545252i	$-0.816434\pi$
$787$	3.10489	−	6.44738i	0.110677	−	0.229824i	0.948949	+	0.315428i	$0.102148\pi$
$788$	−9.34446	+	2.13281i	−0.332883	+	0.0759783i
$789$	3.72718	+	1.79492i	0.132691	+	0.0639007i
$790$	7.76060	−	18.1241i	0.276110	−	0.644825i
$791$	−18.1258	−	13.0027i	−0.644479	−	0.462322i
$792$	−2.35367	+	4.88744i	−0.0836340	+	0.173668i
$793$	2.49506	−	1.98975i	0.0886023	−	0.0706579i
$794$	15.3274	−	7.38130i	0.543950	−	0.261952i
$795$	4.92650	−	0.218023i	0.174725	−	0.00773249i
$796$	−2.43565	+	10.6713i	−0.0863294	+	0.378234i
$797$	34.9361	+	27.8606i	1.23750	+	0.986872i	0.999880	+	0.0155137i	$0.00493836\pi$
$797$	34.9361	+	27.8606i	1.23750	+	0.986872i	0.237619	+	0.971358i	$0.423633\pi$
$798$	3.21643	+	3.63694i	0.113860	+	0.128746i
$799$	−16.8099	−	21.0789i	−0.594691	−	0.745719i
$800$	4.75730	−	1.53887i	0.168196	−	0.0544072i
$801$	5.67768	−	24.8756i	0.200611	−	0.878935i
$802$			2.52133i			0.0890313i
$803$			16.5301i			0.583336i
$804$	−0.0164919	+	0.0722559i	−0.000581626	+	0.00254827i
$805$	−23.8498	+	23.0498i	−0.840595	+	0.812400i
$806$	0.317098	+	1.38930i	0.0111693	+	0.0489358i
$807$	−4.90995	+	1.12067i	−0.172839	+	0.0394493i
$808$	−0.183159	+	0.146064i	−0.00644350	+	0.00513852i
$809$	32.9266	+	41.2887i	1.15764	+	1.45163i	0.869424	+	0.494066i	$0.164490\pi$
$809$	32.9266	+	41.2887i	1.15764	+	1.45163i	0.288214	+	0.957566i	$0.406939\pi$
$810$	15.4391	+	11.2326i	0.542475	+	0.394673i
$811$	3.93631	+	17.2461i	0.138222	+	0.605592i	0.995825	+	0.0912796i	$0.0290957\pi$
$811$	3.93631	+	17.2461i	0.138222	+	0.605592i	−0.857603	+	0.514312i	$0.828047\pi$
$812$	3.64870	+	12.9162i	0.128044	+	0.453268i
$813$	−1.03589	−	0.236436i	−0.0363303	−	0.00829216i
$814$	−8.91923			−0.312619
$815$	−21.8563	+	19.0701i	−0.765591	+	0.667995i
$816$	−0.174597	+	0.764961i	−0.00611213	+	0.0267790i
$817$	19.5986	+	40.6969i	0.685668	+	1.42380i
$818$	−12.1413	+	9.68233i	−0.424509	+	0.338535i
$819$	−2.00083	+	0.565217i	−0.0699147	+	0.0197503i
$820$	−5.46917	+	0.242039i	−0.190992	+	0.00845238i
$821$	−5.18095	+	22.6992i	−0.180816	+	0.792208i	0.800426	+	0.599431i	$0.204606\pi$
$821$	−5.18095	+	22.6992i	−0.180816	+	0.792208i	−0.981243	+	0.192777i	$0.938251\pi$
$822$	−0.926699	−	0.739017i	−0.0323223	−	0.0257762i
$823$	12.2270	+	25.3897i	0.426208	+	0.885030i	0.997913	+	0.0645705i	$0.0205678\pi$
$823$	12.2270	+	25.3897i	0.426208	+	0.885030i	−0.571705	+	0.820459i	$0.693718\pi$
$824$	−0.426218	−	0.534460i	−0.0148480	−	0.0186188i
$825$	1.74187	+	1.15307i	0.0606440	+	0.0401446i
$826$	−2.02954	−	39.8246i	−0.0706168	−	1.38567i
$827$	−3.48398	−	7.23456i	−0.121150	−	0.251570i	0.831570	−	0.555420i	$-0.187442\pi$
$827$	−3.48398	−	7.23456i	−0.121150	−	0.251570i	−0.952720	+	0.303849i	$0.901728\pi$
$828$	7.17214	−	14.8931i	0.249249	−	0.517571i
$829$	−5.14446	−	22.5394i	−0.178675	−	0.782825i	−0.982243	−	0.187612i	$-0.939925\pi$
$829$	−5.14446	−	22.5394i	−0.178675	−	0.782825i	0.803569	−	0.595212i	$-0.202932\pi$
$830$	−9.77099	−	35.4948i	−0.339156	−	1.23204i
$831$	4.46642	−	5.60071i	0.154938	−	0.194287i
$832$		−	0.266527i		−	0.00924017i
$833$	−22.9117	+	7.75157i	−0.793843	+	0.268576i
$834$	−1.63684			−0.0566792
$835$	−0.556055	−	12.5647i	−0.0192431	−	0.434820i
$836$	13.3959	+	6.45111i	0.463306	+	0.223116i
$837$	7.04095	−	1.60705i	0.243371	−	0.0555478i
$838$	−14.6058	+	30.3293i	−0.504549	+	1.04771i
$839$	11.2356	−	5.41076i	0.387894	−	0.186800i	−0.229764	−	0.973246i	$-0.573796\pi$
$839$	11.2356	−	5.41076i	0.387894	−	0.186800i	0.617659	+	0.786446i	$0.288081\pi$
$840$	1.26027	+	0.465262i	0.0434835	+	0.0160531i
$841$	2.94229	+	1.41693i	0.101458	+	0.0488598i
$842$	−18.9481	+	15.1106i	−0.652996	+	0.520747i
$843$	0.187266	+	0.388861i	0.00644977	+	0.0133931i
$844$	−4.63465	+	5.81167i	−0.159531	+	0.200046i
$845$	−25.4670	+	13.6829i	−0.876091	+	0.470707i
$846$	14.3438	−	17.9866i	0.493150	−	0.618391i
$847$	−17.6837	+	9.65415i	−0.607619	+	0.331721i
$848$	7.59305	−	6.05525i	0.260746	−	0.207938i
$849$	−2.79323	+	1.34515i	−0.0958634	+	0.0461654i
$850$	−16.1671	−	6.09175i	−0.554528	−	0.208945i
$851$	27.1788			0.931679
$852$		−	1.51394i		−	0.0518667i
$853$	11.9685	+	2.73172i	0.409792	+	0.0935324i	0.422447	−	0.906388i	$-0.361171\pi$
$853$	11.9685	+	2.73172i	0.409792	+	0.0935324i	−0.0126550	+	0.999920i	$0.504028\pi$
$854$	25.7411	+	18.4655i	0.880841	+	0.631878i
$855$	31.3449	−	43.0833i	1.07197	−	1.47342i
$856$	3.75996	+	16.4734i	0.128513	+	0.563051i
$857$	−17.2767	+	13.7777i	−0.590160	+	0.470637i	−0.872458	−	0.488690i	$-0.837475\pi$
$857$	−17.2767	+	13.7777i	−0.590160	+	0.470637i	0.282297	+	0.959327i	$0.408904\pi$
$858$	0.0870583	−	0.0694267i	0.00297212	−	0.00237019i
$859$	−1.07246	−	4.69874i	−0.0365917	−	0.160319i	0.953331	−	0.301927i	$-0.0976299\pi$
$859$	−1.07246	−	4.69874i	−0.0365917	−	0.160319i	−0.989923	+	0.141608i	$0.954773\pi$
$860$	10.1066	+	7.35301i	0.344634	+	0.250735i
$861$	−1.19519	−	0.857377i	−0.0407319	−	0.0292193i
$862$	4.65463	+	1.06239i	0.158537	+	0.0361851i
$863$			46.8942i			1.59630i	0.602461	+	0.798148i	$0.294187\pi$
$863$			46.8942i			1.59630i	−0.602461	+	0.798148i	$0.705813\pi$
$864$	−1.35076			−0.0459538
$865$	−2.45156	−	4.56291i	−0.0833556	−	0.155144i
$866$	24.2783	−	11.6918i	0.825011	−	0.397304i
$867$	−0.898437	+	0.716480i	−0.0305125	+	0.0243329i
$868$	−12.4161	+	6.77837i	−0.421429	+	0.230073i
$869$	10.1143	−	12.6830i	0.343105	−	0.430240i
$870$	−2.26906	+	1.21912i	−0.0769282	+	0.0413320i
$871$	−0.0542371	+	0.0680112i	−0.00183775	+	0.00230447i
$872$	−5.07522	−	10.5388i	−0.171869	−	0.356889i
$873$	27.0515	−	21.5729i	0.915555	−	0.730131i
$874$	−40.8201	−	19.6579i	−1.38076	−	0.664940i
$875$	−13.9109	+	26.1053i	−0.470274	+	0.882520i
$876$	−1.83815	+	0.885207i	−0.0621054	+	0.0299084i
$877$	24.0979	−	50.0398i	0.813728	−	1.68972i	0.0938887	−	0.995583i	$-0.470070\pi$
$877$	24.0979	−	50.0398i	0.813728	−	1.68972i	0.719839	−	0.694141i	$-0.244215\pi$
$878$	−17.3228	+	3.95381i	−0.584616	+	0.133435i
$879$	−1.70123	−	0.819268i	−0.0573810	−	0.0276332i
$880$	4.10999	−	0.181889i	0.138548	−	0.00613146i
$881$	−30.3857			−1.02372			−0.511859	−	0.859069i	$-0.671043\pi$
$881$	−30.3857			−1.02372			−0.511859	+	0.859069i	$0.671043\pi$
$882$	−10.7989	−	17.5884i	−0.363619	−	0.592234i
$883$			19.0256i			0.640263i	0.947373	+	0.320132i	$0.103727\pi$
$883$			19.0256i			0.640263i	−0.947373	+	0.320132i	$0.896273\pi$
$884$	−0.574199	+	0.720023i	−0.0193124	+	0.0242170i
$885$	7.37843	−	2.03113i	0.248023	−	0.0682757i
$886$	−0.297830	−	1.30488i	−0.0100058	−	0.0438383i
$887$	−16.1343	+	33.5033i	−0.541738	+	1.12493i	0.432962	+	0.901412i	$0.357468\pi$
$887$	−16.1343	+	33.5033i	−0.541738	+	1.12493i	−0.974700	+	0.223518i	$0.928246\pi$
$888$	−0.477635	−	0.991819i	−0.0160284	−	0.0332833i
$889$	−1.45683	−	28.5866i	−0.0488606	−	0.958764i
$890$	−18.6566	+	5.13577i	−0.625370	+	0.172151i
$891$	9.79479	+	12.2823i	0.328138	+	0.411472i
$892$	−5.55300	−	11.5309i	−0.185928	−	0.386084i
$893$	−49.2989	−	39.3146i	−1.64973	−	1.31561i
$894$	−0.0534232	+	0.234062i	−0.00178674	+	0.00782822i
$895$	12.6988	−	0.561990i	0.424475	−	0.0187852i
$896$	2.54611	−	0.719254i	0.0850595	−	0.0240286i
$897$	−0.265286	+	0.211558i	−0.00885763	+	0.00706372i
$898$	−4.19296	−	8.70678i	−0.139921	−	0.290549i
$899$	6.03542	−	26.4429i	0.201293	−	0.881920i
$900$	1.99798	−	14.6062i	0.0665994	−	0.486872i
$901$	−33.5579			−1.11798
$902$	−4.39151	−	1.00233i	−0.146221	−	0.0333740i
$903$	0.912911	+	3.23164i	0.0303798	+	0.107542i
$904$	−1.87615	−	8.21996i	−0.0623999	−	0.273392i
$905$	−11.3332	+	15.5774i	−0.376729	+	0.517811i
$906$	−2.24197	−	2.81134i	−0.0744845	−	0.0934006i
$907$	31.4299	−	25.0645i	1.04361	−	0.832253i	0.0575021	−	0.998345i	$-0.481686\pi$
$907$	31.4299	−	25.0645i	1.04361	−	0.832253i	0.986110	+	0.166092i	$0.0531150\pi$
$908$	−4.55866	+	1.04048i	−0.151284	+	0.0345297i
$909$	0.153701	+	0.673408i	0.00509794	+	0.0223355i
$910$	1.09579	+	1.13382i	0.0363250	+	0.0375856i
$911$	−2.43123	+	10.6519i	−0.0805501	+	0.352913i	−0.999101	−	0.0423893i	$-0.986503\pi$
$911$	−2.43123	+	10.6519i	−0.0805501	+	0.352913i	0.918551	+	0.395302i	$0.129360\pi$
$912$			1.83508i			0.0607657i
$913$		−	30.2915i		−	1.00250i
$914$	−2.03877	+	8.93245i	−0.0674366	+	0.295459i
$915$	−2.39315	+	5.58895i	−0.0791152	+	0.184765i
$916$	−16.6332	−	20.8574i	−0.549577	−	0.689148i
$917$	13.1116	+	14.8258i	0.432983	+	0.489591i
$918$	3.64908	+	2.91004i	0.120437	+	0.0960457i
$919$	−5.27870	+	23.1275i	−0.174128	+	0.762906i	0.810141	+	0.586234i	$0.199390\pi$
$919$	−5.27870	+	23.1275i	−0.174128	+	0.762906i	−0.984270	+	0.176672i	$0.943467\pi$
$920$	−12.5240	+	0.554254i	−0.412905	+	0.0182732i
$921$	3.36617	−	1.62106i	0.110919	−	0.0534158i
$922$	24.6815	−	19.6828i	0.812842	−	0.648220i
$923$	0.770988	−	1.60097i	0.0253774	−	0.0526967i
$924$	0.898163	+	0.644304i	0.0295474	+	0.0211960i
$925$	23.0626	−	7.46017i	0.758292	−	0.245289i
$926$	17.9473	+	8.64296i	0.589784	+	0.284025i
$927$	−1.96502	+	0.448502i	−0.0645396	+	0.0147307i
$928$	−2.20105	+	4.57052i	−0.0722529	+	0.150035i
$929$	11.5384	−	14.4687i	0.378563	−	0.474703i	−0.555651	−	0.831415i	$-0.687531\pi$
$929$	11.5384	−	14.4687i	0.378563	−	0.474703i	0.934214	+	0.356713i	$0.116102\pi$
$930$	−1.78485	−	2.04562i	−0.0585275	−	0.0670785i
$931$	−48.2077	+	29.5985i	−1.57994	+	0.970053i
$932$			17.2352i			0.564557i
$933$	1.33321	+	1.06320i	0.0436475	+	0.0348077i
$934$	−21.2881	−	10.2518i	−0.696568	−	0.335449i
$935$	−11.4950	−	8.36308i	−0.375926	−	0.273502i
$936$	−0.708016	−	0.340962i	−0.0231422	−	0.0111447i
$937$	−2.23879	−	4.64889i	−0.0731379	−	0.151872i	0.861194	−	0.508276i	$-0.169717\pi$
$937$	−2.23879	−	4.64889i	−0.0731379	−	0.151872i	−0.934332	+	0.356404i	$0.884003\pi$
$938$	−0.796069	−	0.334586i	−0.0259926	−	0.0109246i
$939$	−2.99540	−	1.44251i	−0.0977512	−	0.0470745i
$940$	−17.1649	−	3.12656i	−0.559857	−	0.101977i
$941$	13.2124	−	6.36278i	0.430713	−	0.207421i	−0.205950	−	0.978563i	$-0.566028\pi$
$941$	13.2124	−	6.36278i	0.430713	−	0.207421i	0.636663	+	0.771142i	$0.280314\pi$
$942$	1.31518	+	1.04882i	0.0428507	+	0.0341723i
$943$	13.3819	+	3.05433i	0.435774	+	0.0994626i
$944$	9.39712	−	11.7836i	0.305850	−	0.383524i
$945$	5.74618	−	5.55344i	0.186923	−	0.180653i
$946$	6.41181	+	8.04015i	0.208466	+	0.261408i
$947$	17.9010	+	37.1719i	0.581706	+	1.20792i	0.959414	+	0.282000i	$0.0909978\pi$
$947$	17.9010	+	37.1719i	0.581706	+	1.20792i	−0.377709	+	0.925925i	$0.623288\pi$
$948$	1.95198	+	0.445526i	0.0633973	+	0.0144700i
$949$	−2.39463			−0.0777329
$950$	−40.0336	−	5.47622i	−1.29886	−	0.177672i
$951$	−0.586160	+	2.56813i	−0.0190075	+	0.0832774i
$952$	−8.42786	−	3.54221i	−0.273148	−	0.114804i
$953$	21.6029	−	4.93072i	0.699787	−	0.159722i	0.142197	−	0.989838i	$-0.454583\pi$
$953$	21.6029	−	4.93072i	0.699787	−	0.159722i	0.557590	+	0.830117i	$0.311726\pi$
$954$	−6.37185	−	27.9169i	−0.206296	−	0.903843i
$955$	8.39668	−	46.0981i	0.271710	−	1.49170i
$956$	0.963841	+	1.20862i	0.0311729	+	0.0390895i
$957$	−2.06626	+	0.471609i	−0.0667926	+	0.0152450i
$958$	−18.5253	+	4.22827i	−0.598525	+	0.136609i
$959$	10.3450	−	9.14888i	0.334057	−	0.295433i
$960$	0.240320	+	0.447290i	0.00775630	+	0.0144362i
$961$	−2.41350			−0.0778548
$962$		−	1.29208i		−	0.0416583i
$963$	48.5709	+	11.0860i	1.56517	+	0.357241i
$964$	−6.84631	+	3.29701i	−0.220505	+	0.106189i
$965$	52.2162	+	9.51110i	1.68090	+	0.306173i
$966$	−2.73690	−	1.96333i	−0.0880583	−	0.0631692i
$967$	4.12618	+	3.29052i	0.132689	+	0.105816i	0.687585	−	0.726104i	$-0.258671\pi$
$967$	4.12618	+	3.29052i	0.132689	+	0.105816i	−0.554896	+	0.831919i	$0.687242\pi$
$968$	−7.42406	−	1.69449i	−0.238618	−	0.0544631i
$969$	3.95346	−	4.95748i	0.127003	−	0.159257i
$970$	−24.1221	−	10.3289i	−0.774514	−	0.331642i
$971$	4.53070	+	5.68132i	0.145397	+	0.182322i	0.849197	−	0.528076i	$-0.177086\pi$
$971$	4.53070	+	5.68132i	0.145397	+	0.182322i	−0.703800	+	0.710398i	$0.748515\pi$
$972$	−2.59949	+	5.39789i	−0.0833785	+	0.173137i
$973$	3.29195	−	18.7850i	0.105535	−	0.602221i
$974$	35.4026	−	17.0490i	1.13437	−	0.546285i
$975$	−0.167038	+	0.252334i	−0.00534950	+	0.00808116i
$976$	2.66439	+	11.6734i	0.0852850	+	0.373658i
$977$	−3.45465	+	7.17365i	−0.110524	+	0.229505i	−0.948893	−	0.315597i	$-0.897795\pi$
$977$	−3.45465	+	7.17365i	−0.110524	+	0.229505i	0.838369	+	0.545103i	$0.183509\pi$
$978$	−2.30301	−	1.83659i	−0.0736420	−	0.0587276i
$979$	−15.9217			−0.508859
$980$	−7.87414	+	13.5277i	−0.251530	+	0.432126i
$981$	−34.4884			−1.10113
$982$	−9.97164	−	7.95212i	−0.318208	−	0.253762i
$983$	2.93843	−	6.10172i	0.0937215	−	0.194615i	−0.848838	−	0.528653i	$-0.822697\pi$
$983$	2.93843	−	6.10172i	0.0937215	−	0.194615i	0.942559	+	0.334038i	$0.108412\pi$
$984$	−0.123711	−	0.542012i	−0.00394375	−	0.0172787i
$985$	20.6636	−	5.68825i	0.658396	−	0.181243i
$986$	15.7928	−	7.60539i	0.502944	−	0.242205i
$987$	−3.10554	−	3.51155i	−0.0988503	−	0.111774i
$988$	−0.934535	+	1.94058i	−0.0297315	+	0.0617382i
$989$	−19.5382	−	24.5001i	−0.621278	−	0.779058i
$990$	4.77464	−	11.1507i	0.151748	−	0.354391i
$991$	−14.5121	+	18.1975i	−0.460991	+	0.578064i	−0.956939	−	0.290288i	$-0.906249\pi$
$991$	−14.5121	+	18.1975i	−0.460991	+	0.578064i	0.495949	+	0.868352i	$0.334820\pi$
$992$	−5.21258	−	1.18974i	−0.165500	−	0.0377742i
$993$	3.80139	+	3.03151i	0.120634	+	0.0962020i
$994$	17.3746	+	3.04477i	0.551087	+	0.0965742i
$995$	4.38598	−	24.0792i	0.139045	−	0.763362i
$996$	3.36842	−	1.62215i	0.106732	−	0.0513997i
$997$	38.4130	+	8.76753i	1.21655	+	0.277670i	0.782174	−	0.623060i	$-0.214111\pi$
$997$	38.4130	+	8.76753i	1.21655	+	0.277670i	0.434379	+	0.900730i	$0.356968\pi$
$998$			24.1997i			0.766028i
$999$	−6.54825			−0.207177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.p.a.239.21	yes	168
5.4	even	2	inner	490.2.p.a.239.8	✓	168
49.8	even	7	inner	490.2.p.a.449.8	yes	168
245.204	even	14	inner	490.2.p.a.449.21	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.p.a.239.8	✓	168	5.4	even	2	inner
490.2.p.a.239.21	yes	168	1.1	even	1	trivial
490.2.p.a.449.8	yes	168	49.8	even	7	inner
490.2.p.a.449.21	yes	168	245.204	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.p (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(0.0985255 - 0.204590i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.593468 - 2.15587i) q^{5} +(0.204590 - 0.0985255i) q^{6} +(0.719254 + 2.54611i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(1.83832 + 2.30518i) q^{9} +O(q^{10})\)	\(q+(0.781831 + 0.623490i) q^{2} +(0.0985255 - 0.204590i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.593468 - 2.15587i) q^{5} +(0.204590 - 0.0985255i) q^{6} +(0.719254 + 2.54611i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(1.83832 + 2.30518i) q^{9} +(0.880174 - 2.05555i) q^{10} +(1.14712 - 1.43845i) q^{11} +(0.221385 + 0.0505296i) q^{12} +(0.208379 + 0.166177i) q^{13} +(-1.02514 + 2.43908i) q^{14} +(-0.499543 - 0.0909909i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(3.36872 + 0.768887i) q^{17} +2.94844i q^{18} +8.08129 q^{19} +(1.96976 - 1.05832i) q^{20} +(0.591774 + 0.103704i) q^{21} +(1.79371 - 0.409403i) q^{22} +(-5.46583 + 1.24754i) q^{23} +(0.141581 + 0.177537i) q^{24} +(-4.29559 + 2.55888i) q^{25} +(0.0593079 + 0.259845i) q^{26} +(1.31689 - 0.300572i) q^{27} +(-2.32222 + 1.26778i) q^{28} +(1.12883 - 4.94571i) q^{29} +(-0.333826 - 0.382599i) q^{30} +5.34663 q^{31} +(-0.974928 - 0.222521i) q^{32} +(-0.181271 - 0.376413i) q^{33} +(2.15437 + 2.70150i) q^{34} +(5.06224 - 3.06166i) q^{35} +(-1.83832 + 2.30518i) q^{36} +(-4.72628 - 1.07874i) q^{37} +(6.31821 + 5.03860i) q^{38} +(0.0545289 - 0.0262597i) q^{39} +(2.19987 + 0.400703i) q^{40} +(-2.20582 - 1.06227i) q^{41} +(0.398009 + 0.450044i) q^{42} +(2.42518 + 5.03594i) q^{43} +(1.65764 + 0.798277i) q^{44} +(3.87870 - 5.33124i) q^{45} +(-5.05119 - 2.43252i) q^{46} +(-6.10038 - 4.86489i) q^{47} +0.227078i q^{48} +(-5.96535 + 3.66260i) q^{49} +(-4.95387 - 0.677642i) q^{50} +(0.489211 - 0.613451i) q^{51} +(-0.115642 + 0.240133i) q^{52} +(-9.46838 + 2.16109i) q^{53} +(1.21699 + 0.586072i) q^{54} +(-3.78189 - 1.61938i) q^{55} +(-2.60604 - 0.456690i) q^{56} +(0.796213 - 1.65335i) q^{57} +(3.96615 - 3.16290i) q^{58} +(-13.5792 + 6.53941i) q^{59} +(-0.0224492 - 0.507265i) q^{60} +(2.66439 - 11.6734i) q^{61} +(4.18017 + 3.33357i) q^{62} +(-4.54702 + 6.33857i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(0.234590 - 0.547860i) q^{65} +(0.0929665 - 0.407313i) q^{66} +0.326381i q^{67} +3.45535i q^{68} +(-0.283289 + 1.24117i) q^{69} +(5.86673 + 0.762556i) q^{70} +(-1.48356 - 6.49988i) q^{71} +(-2.87451 + 0.656089i) q^{72} +(-7.02441 + 5.60178i) q^{73} +(-3.02257 - 3.79018i) q^{74} +(0.100298 + 1.13095i) q^{75} +(1.79826 + 7.87868i) q^{76} +(4.48751 + 1.88609i) q^{77} +(0.0590051 + 0.0134675i) q^{78} +8.81712 q^{79} +(1.47009 + 1.68488i) q^{80} +(-1.90001 + 8.32450i) q^{81} +(-1.06227 - 2.20582i) q^{82} +(12.8722 - 10.2653i) q^{83} +(0.0305779 + 0.600013i) q^{84} +(-0.341599 - 7.71884i) q^{85} +(-1.24377 + 5.44933i) q^{86} +(-0.900626 - 0.718225i) q^{87} +(0.798277 + 1.65764i) q^{88} +(-5.39558 - 6.76584i) q^{89} +(6.35646 - 1.74980i) q^{90} +(-0.273227 + 0.650080i) q^{91} +(-2.43252 - 5.05119i) q^{92} +(0.526780 - 1.09387i) q^{93} +(-1.73626 - 7.60705i) q^{94} +(-4.79599 - 17.4223i) q^{95} +(-0.141581 + 0.177537i) q^{96} -11.7351i q^{97} +(-6.94749 - 0.855798i) q^{98} +5.42465 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Introduction

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