LMFDB - Embedded newform 700.2.p.c.551.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(451,700)] 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("700.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.8
Character	$\chi$	$=$	700.551
Dual form			700.2.p.c.451.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.288532 + 1.38447i) q^{2} +(0.450639 + 0.780530i) q^{3} +(-1.83350 - 0.798926i) q^{4} +(-1.21064 + 0.398687i) q^{6} +(2.29962 + 1.30833i) q^{7} +(1.63511 - 2.30790i) q^{8} +(1.09385 - 1.89460i) q^{9} +(3.24107 - 1.87123i) q^{11} +(-0.202661 - 1.79113i) q^{12} -2.41990i q^{13} +(-2.47486 + 2.80626i) q^{14} +(2.72344 + 2.92966i) q^{16} +(0.505515 - 0.291859i) q^{17} +(2.30740 + 2.06105i) q^{18} +(3.07977 - 5.33433i) q^{19} +(0.0151060 + 2.38451i) q^{21} +(1.65551 + 5.02706i) q^{22} +(-3.73439 - 2.15605i) q^{23} +(2.53823 + 0.236220i) q^{24} +(3.35028 + 0.698219i) q^{26} +4.67556 q^{27} +(-3.17109 - 4.23606i) q^{28} -0.435463 q^{29} +(1.26933 + 2.19854i) q^{31} +(-4.84181 + 2.92521i) q^{32} +(2.92110 + 1.68650i) q^{33} +(0.258212 + 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} +(-5.65039 + 9.78676i) q^{37} +(6.49659 + 5.80297i) q^{38} +(1.88881 - 1.09050i) q^{39} +7.35068i q^{41} +(-3.30563 - 0.667093i) q^{42} +5.80096i q^{43} +(-7.43747 + 0.841528i) q^{44} +(4.06247 - 4.54805i) q^{46} +(5.78826 - 10.0256i) q^{47} +(-1.05940 + 3.44594i) q^{48} +(3.57652 + 6.01735i) q^{49} +(0.455610 + 0.263046i) q^{51} +(-1.93332 + 4.43689i) q^{52} +(-1.55746 - 2.69759i) q^{53} +(-1.34905 + 6.47316i) q^{54} +(6.77964 - 3.16804i) q^{56} +5.55147 q^{57} +(0.125645 - 0.602884i) q^{58} +(1.73534 + 3.00569i) q^{59} +(-8.99597 - 5.19383i) q^{61} +(-3.41004 + 1.12299i) q^{62} +(4.99421 - 2.92575i) q^{63} +(-2.65284 - 7.54735i) q^{64} +(-3.17773 + 3.55756i) q^{66} +(8.52602 - 4.92250i) q^{67} +(-1.16004 + 0.131255i) q^{68} -3.88640i q^{69} +9.96771i q^{71} +(-2.58400 - 5.62238i) q^{72} +(-8.48612 + 4.89946i) q^{73} +(-11.9191 - 10.6466i) q^{74} +(-9.90849 + 7.31997i) q^{76} +(9.90142 - 0.0627260i) q^{77} +(0.964785 + 2.92964i) q^{78} +(0.397549 + 0.229525i) q^{79} +(-1.17456 - 2.03439i) q^{81} +(-10.1768 - 2.12091i) q^{82} -2.59747 q^{83} +(1.87735 - 4.38406i) q^{84} +(-8.03123 - 1.67376i) q^{86} +(-0.196236 - 0.339892i) q^{87} +(0.980878 - 10.5397i) q^{88} +(-8.55647 - 4.94008i) q^{89} +(3.16604 - 5.56486i) q^{91} +(5.12447 + 6.93662i) q^{92} +(-1.14402 + 1.98149i) q^{93} +(12.2100 + 10.9064i) q^{94} +(-4.46512 - 2.46097i) q^{96} -4.54044i q^{97} +(-9.36276 + 3.21538i) q^{98} -8.18738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 16 q^{9} + 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} + 8 q^{22} + 36 q^{24} + 30 q^{26} - 2 q^{28} - 40 q^{29} - 2 q^{32} + 60 q^{36} - 8 q^{37} + 60 q^{38} + 62 q^{42}+ \cdots - 78 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 16 * q^9 + 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 + 8 * q^22 + 36 * q^24 + 30 * q^26 - 2 * q^28 - 40 * q^29 - 2 * q^32 + 60 * q^36 - 8 * q^37 + 60 * q^38 + 62 * q^42 - 18 * q^44 + 2 * q^46 - 16 * q^49 + 36 * q^52 + 8 * q^53 + 12 * q^54 - 4 * q^56 - 48 * q^57 - 2 * q^58 + 24 * q^61 + 4 * q^64 + 24 * q^66 - 60 * q^68 - 4 * q^72 + 72 * q^73 + 38 * q^74 + 40 * q^77 - 120 * q^78 - 36 * q^81 - 42 * q^82 - 20 * q^84 + 28 * q^86 - 4 * q^88 - 60 * q^89 + 4 * q^92 + 8 * q^93 + 18 * q^94 - 60 * q^96 - 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	−0.288532	+	1.38447i	−0.204023	+	0.978966i
$2$	−0.288532	+	1.38447i	−0.204023	+	0.978966i
$3$	0.450639	+	0.780530i	0.260177	+	0.450639i	0.966289	−	0.257461i	$-0.0828859\pi$
$3$	0.450639	+	0.780530i	0.260177	+	0.450639i	−0.706112	+	0.708100i	$0.749553\pi$
$4$	−1.83350	−	0.798926i	−0.916749	−	0.399463i
$5$		0			0
$5$		0			0
$6$	−1.21064	+	0.398687i	−0.494242	+	0.162763i
$7$	2.29962	+	1.30833i	0.869175	+	0.494504i
$7$	2.29962	+	1.30833i	0.869175	+	0.494504i
$8$	1.63511	−	2.30790i	0.578098	−	0.815967i
$9$	1.09385	−	1.89460i	0.364616	−	0.631534i
$10$		0			0
$11$	3.24107	−	1.87123i	0.977218	−	0.564197i	0.0757892	−	0.997124i	$-0.475852\pi$
$11$	3.24107	−	1.87123i	0.977218	−	0.564197i	0.901429	+	0.432927i	$0.142519\pi$
$12$	−0.202661	−	1.79113i	−0.0585032	−	0.517054i
$13$		−	2.41990i		−	0.671161i	−0.942012	−	0.335580i	$-0.891068\pi$
$13$		−	2.41990i		−	0.671161i	0.942012	−	0.335580i	$-0.108932\pi$
$14$	−2.47486	+	2.80626i	−0.661434	+	0.750003i
$15$		0			0
$16$	2.72344	+	2.92966i	0.680859	+	0.732415i
$17$	0.505515	−	0.291859i	0.122605	−	0.0707863i	−0.437443	−	0.899246i	$-0.644116\pi$
$17$	0.505515	−	0.291859i	0.122605	−	0.0707863i	0.560048	+	0.828460i	$0.310782\pi$
$18$	2.30740	+	2.06105i	0.543860	+	0.485794i
$19$	3.07977	−	5.33433i	0.706549	−	1.22378i	−0.259581	−	0.965721i	$-0.583584\pi$
$19$	3.07977	−	5.33433i	0.706549	−	1.22378i	0.966130	−	0.258057i	$-0.0830822\pi$
$20$		0			0
$21$	0.0151060	+	2.38451i	0.00329639	+	0.520343i
$22$	1.65551	+	5.02706i	0.352955	+	1.07177i
$23$	−3.73439	−	2.15605i	−0.778674	−	0.449568i	0.0572861	−	0.998358i	$-0.481755\pi$
$23$	−3.73439	−	2.15605i	−0.778674	−	0.449568i	−0.835960	+	0.548790i	$0.815089\pi$
$24$	2.53823	+	0.236220i	0.518114	+	0.0482182i
$25$		0			0
$26$	3.35028	+	0.698219i	0.657043	+	0.136932i
$27$	4.67556			0.899812
$28$	−3.17109	−	4.23606i	−0.599280	−	0.800539i
$29$	−0.435463			−0.0808634			−0.0404317	−	0.999182i	$-0.512873\pi$
$29$	−0.435463			−0.0808634			−0.0404317	+	0.999182i	$0.512873\pi$
$30$		0			0
$31$	1.26933	+	2.19854i	0.227978	+	0.394869i	0.957209	−	0.289399i	$-0.0934554\pi$
$31$	1.26933	+	2.19854i	0.227978	+	0.394869i	−0.729231	+	0.684268i	$0.760122\pi$
$32$	−4.84181	+	2.92521i	−0.855920	+	0.517109i
$33$	2.92110	+	1.68650i	0.508499	+	0.293582i
$34$	0.258212	+	0.784080i	0.0442831	+	0.134469i
$35$		0			0
$36$	−3.51922	+	2.59985i	−0.586536	+	0.433308i
$37$	−5.65039	+	9.78676i	−0.928918	+	1.60893i	−0.143782	+	0.989609i	$0.545927\pi$
$37$	−5.65039	+	9.78676i	−0.928918	+	1.60893i	−0.785136	+	0.619324i	$0.787407\pi$
$38$	6.49659	+	5.80297i	1.05389	+	0.941366i
$39$	1.88881	−	1.09050i	0.302451	−	0.174620i
$40$		0			0
$41$			7.35068i			1.14798i	0.818861	+	0.573992i	$0.194606\pi$
$41$			7.35068i			1.14798i	−0.818861	+	0.573992i	$0.805394\pi$
$42$	−3.30563	−	0.667093i	−0.510070	−	0.102935i
$43$			5.80096i			0.884637i	0.896858	+	0.442319i	$0.145844\pi$
$43$			5.80096i			0.884637i	−0.896858	+	0.442319i	$0.854156\pi$
$44$	−7.43747	+	0.841528i	−1.12124	+	0.126865i
$45$		0			0
$46$	4.06247	−	4.54805i	0.598979	−	0.670573i
$47$	5.78826	−	10.0256i	0.844305	−	1.46238i	−0.0419181	−	0.999121i	$-0.513347\pi$
$47$	5.78826	−	10.0256i	0.844305	−	1.46238i	0.886223	−	0.463258i	$-0.153320\pi$
$48$	−1.05940	+	3.44594i	−0.152911	+	0.497379i
$49$	3.57652	+	6.01735i	0.510932	+	0.859621i
$50$		0			0
$51$	0.455610	+	0.263046i	0.0637981	+	0.0368339i
$52$	−1.93332	+	4.43689i	−0.268104	+	0.615286i
$53$	−1.55746	−	2.69759i	−0.213933	−	0.370543i	0.739009	−	0.673696i	$-0.235294\pi$
$53$	−1.55746	−	2.69759i	−0.213933	−	0.370543i	−0.952942	+	0.303153i	$0.901961\pi$
$54$	−1.34905	+	6.47316i	−0.183582	+	0.880885i
$55$		0			0
$56$	6.77964	−	3.16804i	0.905968	−	0.423347i
$57$	5.55147			0.735310
$58$	0.125645	−	0.602884i	0.0164980	−	0.0791625i
$59$	1.73534	+	3.00569i	0.225922	+	0.391308i	0.956596	−	0.291419i	$-0.0941273\pi$
$59$	1.73534	+	3.00569i	0.225922	+	0.391308i	−0.730674	+	0.682727i	$0.760794\pi$
$60$		0			0
$61$	−8.99597	−	5.19383i	−1.15182	−	0.665001i	−0.202487	−	0.979285i	$-0.564902\pi$
$61$	−8.99597	−	5.19383i	−1.15182	−	0.665001i	−0.949329	+	0.314284i	$0.898236\pi$
$62$	−3.41004	+	1.12299i	−0.433076	+	0.142620i
$63$	4.99421	−	2.92575i	0.629211	−	0.368610i
$64$	−2.65284	−	7.54735i	−0.331605	−	0.943418i
$65$		0			0
$66$	−3.17773	+	3.55756i	−0.391152	+	0.437906i
$67$	8.52602	−	4.92250i	1.04162	−	0.601379i	0.121327	−	0.992613i	$-0.461285\pi$
$67$	8.52602	−	4.92250i	1.04162	−	0.601379i	0.920291	+	0.391234i	$0.127952\pi$
$68$	−1.16004	+	0.131255i	−0.140675	+	0.0159170i
$69$		−	3.88640i		−	0.467868i
$70$		0			0
$71$			9.96771i			1.18295i	0.806324	+	0.591475i	$0.201454\pi$
$71$			9.96771i			1.18295i	−0.806324	+	0.591475i	$0.798546\pi$
$72$	−2.58400	−	5.62238i	−0.304527	−	0.662604i
$73$	−8.48612	+	4.89946i	−0.993225	+	0.573439i	−0.906237	−	0.422771i	$-0.861058\pi$
$73$	−8.48612	+	4.89946i	−0.993225	+	0.573439i	−0.0869881	+	0.996209i	$0.527724\pi$
$74$	−11.9191	−	10.6466i	−1.38557	−	1.23764i
$75$		0			0
$76$	−9.90849	+	7.31997i	−1.13658	+	0.839658i
$77$	9.90142	−	0.0627260i	1.12837	−	0.00714829i
$78$	0.964785	+	2.92964i	0.109240	+	0.331716i
$79$	0.397549	+	0.229525i	0.0447278	+	0.0258236i	0.522197	−	0.852825i	$-0.325113\pi$
$79$	0.397549	+	0.229525i	0.0447278	+	0.0258236i	−0.477469	+	0.878648i	$0.658446\pi$
$80$		0			0
$81$	−1.17456	−	2.03439i	−0.130506	−	0.226044i
$82$	−10.1768	−	2.12091i	−1.12384	−	0.234215i
$83$	−2.59747			−0.285109			−0.142554	−	0.989787i	$-0.545532\pi$
$83$	−2.59747			−0.285109			−0.142554	+	0.989787i	$0.545532\pi$
$84$	1.87735	−	4.38406i	0.204836	−	0.478341i
$85$		0			0
$86$	−8.03123	−	1.67376i	−0.866030	−	0.180486i
$87$	−0.196236	−	0.339892i	−0.0210388	−	0.0364402i
$88$	0.980878	−	10.5397i	0.104562	−	1.12354i
$89$	−8.55647	−	4.94008i	−0.906984	−	0.523648i	−0.0275247	−	0.999621i	$-0.508763\pi$
$89$	−8.55647	−	4.94008i	−0.906984	−	0.523648i	−0.879460	+	0.475973i	$0.842096\pi$
$90$		0			0
$91$	3.16604	−	5.56486i	0.331891	−	0.583356i
$92$	5.12447	+	6.93662i	0.534263	+	0.723192i
$93$	−1.14402	+	1.98149i	−0.118629	+	0.205471i
$94$	12.2100	+	10.9064i	1.25936	+	1.12490i
$95$		0			0
$96$	−4.46512	−	2.46097i	−0.455720	−	0.251171i
$97$		−	4.54044i		−	0.461011i	−0.973071	−	0.230506i	$-0.925962\pi$
$97$		−	4.54044i		−	0.461011i	0.973071	−	0.230506i	$-0.0740380\pi$
$98$	−9.36276	+	3.21538i	−0.945782	+	0.324803i
$99$		−	8.18738i		−	0.822862i
$100$		0			0
$101$	7.91930	−	4.57221i	0.787999	−	0.454952i	−0.0512584	−	0.998685i	$-0.516323\pi$
$101$	7.91930	−	4.57221i	0.787999	−	0.454952i	0.839258	+	0.543734i	$0.182990\pi$
$102$	−0.495637	+	0.554880i	−0.0490754	+	0.0549413i
$103$	−5.11597	+	8.86113i	−0.504092	+	0.873113i	0.495897	+	0.868381i	$0.334839\pi$
$103$	−5.11597	+	8.86113i	−0.504092	+	0.873113i	−0.999989	+	0.00473128i	$0.998494\pi$
$104$	−5.58490	−	3.95681i	−0.547645	−	0.387997i
$105$		0			0
$106$	4.18410	−	1.37790i	0.406396	−	0.133834i
$107$	−5.48368	−	3.16601i	−0.530128	−	0.306069i	0.210941	−	0.977499i	$-0.432347\pi$
$107$	−5.48368	−	3.16601i	−0.530128	−	0.306069i	−0.741068	+	0.671430i	$0.765681\pi$
$108$	−8.57263	−	3.73542i	−0.824902	−	0.359441i
$109$	9.38027	+	16.2471i	0.898467	+	1.55619i	0.829454	+	0.558575i	$0.188652\pi$
$109$	9.38027	+	16.2471i	0.898467	+	1.55619i	0.0690134	+	0.997616i	$0.478015\pi$
$110$		0			0
$111$	−10.1851			−0.966731
$112$	2.42990	+	10.3003i	0.229604	+	0.973284i
$113$	−4.17847			−0.393077			−0.196539	−	0.980496i	$-0.562970\pi$
$113$	−4.17847			−0.393077			−0.196539	+	0.980496i	$0.562970\pi$
$114$	−1.60177	+	7.68582i	−0.150020	+	0.719843i
$115$		0			0
$116$	0.798420	+	0.347902i	0.0741315	+	0.0323019i
$117$	−4.58475	−	2.64701i	−0.423861	−	0.244716i
$118$	−4.66198	+	1.53528i	−0.429170	+	0.141334i
$119$	1.54434	−	0.00978348i	0.141570	−	0.000896851i
$120$		0			0
$121$	1.50301	−	2.60329i	0.136637	−	0.236663i
$122$	9.78631	−	10.9560i	0.886010	−	0.991913i
$123$	−5.73743	+	3.31250i	−0.517326	+	0.298678i
$124$	−0.570840	−	5.04511i	−0.0512629	−	0.453064i
$125$		0			0
$126$	2.60961	+	7.75849i	0.232483	+	0.691182i
$127$			4.91036i			0.435724i	0.975980	+	0.217862i	$0.0699083\pi$
$127$			4.91036i			0.435724i	−0.975980	+	0.217862i	$0.930092\pi$
$128$	11.2145	−	1.49512i	0.991230	−	0.132151i
$129$	−4.52782	+	2.61414i	−0.398652	+	0.230162i
$130$		0			0
$131$	7.93723	−	13.7477i	0.693479	−	1.20114i	−0.277212	−	0.960809i	$-0.589410\pi$
$131$	7.93723	−	13.7477i	0.693479	−	1.20114i	0.970691	−	0.240332i	$-0.0772564\pi$
$132$	−4.00845	−	5.42594i	−0.348891	−	0.472267i
$133$	14.0614	−	8.23756i	1.21928	−	0.714287i
$134$	4.35501	+	13.2243i	0.376216	+	1.14240i
$135$		0			0
$136$	0.152989	−	1.64390i	0.0131187	−	0.140963i
$137$	−3.92110	−	6.79155i	−0.335002	−	0.580241i	0.648483	−	0.761229i	$-0.275404\pi$
$137$	−3.92110	−	6.79155i	−0.335002	−	0.580241i	−0.983485	+	0.180988i	$0.942070\pi$
$138$	5.38060	+	1.12135i	0.458027	+	0.0954557i
$139$	17.4044			1.47623			0.738113	−	0.674677i	$-0.235717\pi$
$139$	17.4044			1.47623			0.738113	+	0.674677i	$0.235717\pi$
$140$		0			0
$141$	10.4337			0.878674
$142$	−13.8000	−	2.87600i	−1.15807	−	0.241349i
$143$	−4.52820	−	7.84307i	−0.378667	−	0.655871i
$144$	8.52956	−	1.95522i	0.710797	−	0.162935i
$145$		0			0
$146$	−4.33463	−	13.1624i	−0.358736	−	1.08933i
$147$	−3.08500	+	5.50324i	−0.254446	+	0.453899i
$148$	18.1789	−	13.4298i	1.49429	−	1.10392i
$149$	−0.825776	+	1.43029i	−0.0676502	+	0.117174i	−0.897867	−	0.440268i	$-0.854884\pi$
$149$	−0.825776	+	1.43029i	−0.0676502	+	0.117174i	0.830216	+	0.557441i	$0.188217\pi$
$150$		0			0
$151$	−6.37060	+	3.67807i	−0.518432	+	0.299317i	−0.736293	−	0.676663i	$-0.763425\pi$
$151$	−6.37060	+	3.67807i	−0.518432	+	0.299317i	0.217861	+	0.975980i	$0.430092\pi$
$152$	−7.27534	−	15.8300i	−0.590108	−	1.28398i
$153$		−	1.27700i		−	0.103239i
$154$	−2.77003	+	13.7263i	−0.223216	+	1.10610i
$155$		0			0
$156$	−4.33436	+	0.490420i	−0.347026	+	0.0392650i
$157$	2.66953	−	1.54125i	0.213052	−	0.123005i	−0.389677	−	0.920952i	$-0.627413\pi$
$157$	2.66953	−	1.54125i	0.213052	−	0.123005i	0.602729	+	0.797946i	$0.294080\pi$
$158$	−0.432476	+	0.484169i	−0.0344059	+	0.0385184i
$159$	1.40370	−	2.43128i	0.111321	−	0.192813i
$160$		0			0
$161$	−5.76685	−	9.84393i	−0.454491	−	0.775810i
$162$	3.15545	−	1.03915i	0.247915	−	0.0816433i
$163$	3.91284	+	2.25908i	0.306477	+	0.176945i	0.645349	−	0.763888i	$-0.276712\pi$
$163$	3.91284	+	2.25908i	0.306477	+	0.176945i	−0.338872	+	0.940833i	$0.610045\pi$
$164$	5.87265	−	13.4775i	0.458577	−	1.05241i
$165$		0			0
$166$	0.749452	−	3.59611i	0.0581687	−	0.279112i
$167$	−16.9358			−1.31053			−0.655266	−	0.755398i	$-0.727444\pi$
$167$	−16.9358			−1.31053			−0.655266	+	0.755398i	$0.727444\pi$
$168$	5.52792	+	3.86407i	0.426488	+	0.298119i
$169$	7.14406			0.549543
$170$		0			0
$171$	−6.73762	−	11.6699i	−0.515238	−	0.892419i
$172$	4.63453	−	10.6360i	0.353380	−	0.810991i
$173$	−0.114919	−	0.0663486i	−0.00873715	−	0.00504439i	0.495625	−	0.868537i	$-0.334939\pi$
$173$	−0.114919	−	0.0663486i	−0.00873715	−	0.00504439i	−0.504362	+	0.863492i	$0.668272\pi$
$174$	0.527189	−	0.173613i	0.0399661	−	0.0131616i
$175$		0			0
$176$	14.3089	+	4.39904i	1.07857	+	0.331590i
$177$	−1.56402	+	2.70897i	−0.117559	+	0.203618i
$178$	9.30820	−	10.4208i	0.697679	−	0.781071i
$179$	−13.9422	+	8.04953i	−1.04209	+	0.601650i	−0.920424	−	0.390921i	$-0.872157\pi$
$179$	−13.9422	+	8.04953i	−1.04209	+	0.601650i	−0.121664	+	0.992571i	$0.538823\pi$
$180$		0			0
$181$			3.99317i			0.296810i	0.988927	+	0.148405i	$0.0474139\pi$
$181$			3.99317i			0.296810i	−0.988927	+	0.148405i	$0.952586\pi$
$182$	6.79087	+	5.98892i	0.503373	+	0.443928i
$183$		−	9.36216i		−	0.692071i
$184$	−11.0821	+	5.09323i	−0.816983	+	0.375478i
$185$		0			0
$186$	−2.41323	−	2.15558i	−0.176946	−	0.158054i
$187$	1.09227	−	1.89187i	0.0798749	−	0.138347i
$188$	−18.6225	+	13.7575i	−1.35818	+	1.00337i
$189$	10.7520	+	6.11719i	0.782094	+	0.444960i
$190$		0			0
$191$	−17.3638	−	10.0250i	−1.25640	−	0.725385i	−0.284030	−	0.958815i	$-0.591671\pi$
$191$	−17.3638	−	10.0250i	−1.25640	−	0.725385i	−0.972373	+	0.233431i	$0.925005\pi$
$192$	4.69546	−	5.47175i	0.338865	−	0.394889i
$193$	9.66959	+	16.7482i	0.696032	+	1.20556i	0.969832	+	0.243776i	$0.0783862\pi$
$193$	9.66959	+	16.7482i	0.696032	+	1.20556i	−0.273799	+	0.961787i	$0.588280\pi$
$194$	6.28608	+	1.31006i	0.451315	+	0.0940568i
$195$		0			0
$196$	−1.75014	−	13.8902i	−0.125010	−	0.992155i
$197$	1.63738			0.116659			0.0583293	−	0.998297i	$-0.481423\pi$
$197$	1.63738			0.116659			0.0583293	+	0.998297i	$0.481423\pi$
$198$	11.3352	+	2.36232i	0.805554	+	0.167883i
$199$	−0.391632	−	0.678326i	−0.0277621	−	0.0480853i	0.851811	−	0.523850i	$-0.175505\pi$
$199$	−0.391632	−	0.678326i	−0.0277621	−	0.0480853i	−0.879573	+	0.475765i	$0.842171\pi$
$200$		0			0
$201$	7.68431	+	4.43654i	0.542009	+	0.312929i
$202$	4.04510	+	12.2832i	0.284612	+	0.864245i
$203$	−1.00140	−	0.569731i	−0.0702845	−	0.0399873i
$204$	−0.625205	−	0.846294i	−0.0437731	−	0.0592524i
$205$		0			0
$206$	−10.7918	−	9.63961i	−0.751901	−	0.671624i
$207$	−8.16972	+	4.71679i	−0.567835	+	0.327839i
$208$	7.08949	−	6.59045i	0.491568	−	0.456966i
$209$		−	23.0519i		−	1.59453i
$210$		0			0
$211$			9.22534i			0.635099i	0.948242	+	0.317549i	$0.102860\pi$
$211$			9.22534i			0.635099i	−0.948242	+	0.317549i	$0.897140\pi$
$212$	0.700417	+	6.19032i	0.0481048	+	0.425153i
$213$	−7.78009	+	4.49184i	−0.533083	+	0.307776i
$214$	5.96545	−	6.67849i	0.407790	−	0.456532i
$215$		0			0
$216$	7.64505	−	10.7907i	0.520180	−	0.734217i
$217$	0.0425494	+	6.71651i	0.00288844	+	0.455946i
$218$	−25.2001	+	8.29887i	−1.70677	+	0.562071i
$219$	−7.64835	−	4.41578i	−0.516828	−	0.298391i
$220$		0			0
$221$	−0.706272	−	1.22330i	−0.0475090	−	0.0822880i
$222$	2.93874	−	14.1010i	0.197235	−	0.946397i
$223$	24.2380			1.62310			0.811550	−	0.584284i	$-0.198624\pi$
$223$	24.2380			1.62310			0.811550	+	0.584284i	$0.198624\pi$
$224$	−14.9615	+	0.392163i	−0.999657	+	0.0262025i
$225$		0			0
$226$	1.20562	−	5.78495i	0.0801967	−	0.384809i
$227$	5.31623	+	9.20798i	0.352851	+	0.611155i	0.986748	−	0.162262i	$-0.0518791\pi$
$227$	5.31623	+	9.20798i	0.352851	+	0.611155i	−0.633897	+	0.773417i	$0.718546\pi$
$228$	−10.1786	−	4.43521i	−0.674095	−	0.293729i
$229$	−25.5589	−	14.7564i	−1.68898	−	0.975132i	−0.955302	−	0.295633i	$-0.904470\pi$
$229$	−25.5589	−	14.7564i	−1.68898	−	0.975132i	−0.733676	−	0.679499i	$-0.762197\pi$
$230$		0			0
$231$	4.51093	+	7.70009i	0.296797	+	0.506629i
$232$	−0.712029	+	1.00501i	−0.0467470	+	0.0659819i
$233$	14.0351	−	24.3096i	0.919472	−	1.59257i	0.119254	−	0.992864i	$-0.461950\pi$
$233$	14.0351	−	24.3096i	0.919472	−	1.59257i	0.800218	−	0.599709i	$-0.204717\pi$
$234$	4.98755	−	5.58370i	0.326046	−	0.365018i
$235$		0			0
$236$	−0.780415	−	6.89734i	−0.0508007	−	0.448979i
$237$			0.413732i			0.0268748i
$238$	−0.432047	+	2.14092i	−0.0280055	+	0.138775i
$239$			13.6279i			0.881512i	0.897627	+	0.440756i	$0.145290\pi$
$239$			13.6279i			0.881512i	−0.897627	+	0.440756i	$0.854710\pi$
$240$		0			0
$241$	−3.64372	+	2.10370i	−0.234713	+	0.135512i	−0.612744	−	0.790281i	$-0.709934\pi$
$241$	−3.64372	+	2.10370i	−0.234713	+	0.135512i	0.378031	+	0.925793i	$0.376601\pi$
$242$	3.17050	+	2.83200i	0.203808	+	0.182048i
$243$	8.07194	−	13.9810i	0.517815	−	0.896882i
$244$	12.3446	+	16.7100i	0.790283	+	1.06975i
$245$		0			0
$246$	−2.93062	−	8.89904i	−0.186850	−	0.567382i
$247$	−12.9086	−	7.45276i	−0.821352	−	0.474208i
$248$	7.14950	+	0.665366i	0.453993	+	0.0422508i
$249$	−1.17052	−	2.02740i	−0.0741787	−	0.128481i
$250$		0			0
$251$	18.8826			1.19186			0.595928	−	0.803038i	$-0.296784\pi$
$251$	18.8826			1.19186			0.595928	+	0.803038i	$0.296784\pi$
$252$	−11.4943	+	1.37435i	−0.724075	+	0.0865761i
$253$	−16.1379			−1.01458
$254$	−6.79824	−	1.41680i	−0.426559	−	0.0888977i
$255$		0			0
$256$	−1.16580	+	15.9575i	−0.0728623	+	0.997342i
$257$	−22.3734	−	12.9173i	−1.39561	−	0.805757i	−0.401682	−	0.915779i	$-0.631574\pi$
$257$	−22.3734	−	12.9173i	−1.39561	−	0.805757i	−0.993929	+	0.110022i	$0.964908\pi$
$258$	−2.31277	−	7.02288i	−0.143987	−	0.437225i
$259$	−25.7981	+	15.1133i	−1.60302	+	0.939092i
$260$		0			0
$261$	−0.476330	+	0.825028i	−0.0294841	+	0.0510680i
$262$	16.7431	+	14.9555i	1.03439	+	0.923953i
$263$	−9.26400	+	5.34857i	−0.571243	+	0.329807i	−0.757645	−	0.652666i	$-0.773650\pi$
$263$	−9.26400	+	5.34857i	−0.571243	+	0.329807i	0.186403	+	0.982473i	$0.440317\pi$
$264$	8.66860	−	3.98401i	0.533515	−	0.245199i
$265$		0			0
$266$	7.34747	+	21.8443i	0.450502	+	1.33936i
$267$		−	8.90478i		−	0.544963i
$268$	−19.5651	+	2.21374i	−1.19513	+	0.135226i
$269$	−7.24441	+	4.18256i	−0.441699	+	0.255015i	−0.704318	−	0.709884i	$-0.748747\pi$
$269$	−7.24441	+	4.18256i	−0.441699	+	0.255015i	0.262619	+	0.964900i	$0.415414\pi$
$270$		0			0
$271$	−13.5557	+	23.4791i	−0.823448	+	1.42625i	0.0796525	+	0.996823i	$0.474619\pi$
$271$	−13.5557	+	23.4791i	−0.823448	+	1.42625i	−0.903100	+	0.429430i	$0.858714\pi$
$272$	2.23179	+	0.686127i	0.135322	+	0.0416025i
$273$	5.77028	−	0.0365550i	0.349234	−	0.00221241i
$274$	10.5340	−	3.46906i	0.636385	−	0.209574i
$275$		0			0
$276$	−3.10495	+	7.12571i	−0.186896	+	0.428918i
$277$	1.67991	+	2.90970i	0.100936	+	0.174827i	0.912071	−	0.410033i	$-0.134483\pi$
$277$	1.67991	+	2.90970i	0.100936	+	0.174827i	−0.811134	+	0.584860i	$0.801150\pi$
$278$	−5.02173	+	24.0959i	−0.301184	+	1.44517i
$279$	5.55380			0.332497
$280$		0			0
$281$	−7.33947			−0.437836			−0.218918	−	0.975743i	$-0.570253\pi$
$281$	−7.33947			−0.437836			−0.218918	+	0.975743i	$0.570253\pi$
$282$	−3.01045	+	14.4451i	−0.179269	+	0.860192i
$283$	−3.60282	−	6.24027i	−0.214165	−	0.370945i	0.738849	−	0.673871i	$-0.235370\pi$
$283$	−3.60282	−	6.24027i	−0.214165	−	0.370945i	−0.953014	+	0.302926i	$0.902036\pi$
$284$	7.96346	−	18.2758i	0.472544	−	1.08447i
$285$		0			0
$286$	12.1650	−	4.00617i	0.719332	−	0.236890i
$287$	−9.61715	+	16.9038i	−0.567682	+	0.997799i
$288$	0.245892	+	12.3730i	0.0144893	+	0.729089i
$289$	−8.32964	+	14.4274i	−0.489979	+	0.848668i
$290$		0			0
$291$	3.54395	−	2.04610i	0.207750	−	0.119944i
$292$	19.4736	−	2.20338i	1.13961	−	0.128943i
$293$		−	8.47879i		−	0.495336i	−0.968845	−	0.247668i	$-0.920336\pi$
$293$		−	8.47879i		−	0.495336i	0.968845	−	0.247668i	$-0.0796642\pi$
$294$	−6.72893	−	5.85894i	−0.392439	−	0.341700i
$295$		0			0
$296$	13.3479	+	29.0430i	0.775831	+	1.68809i
$297$	15.1538	−	8.74905i	0.879312	−	0.507671i
$298$	−1.74192	−	1.55594i	−0.100907	−	0.0901333i
$299$	−5.21744	+	9.03686i	−0.301732	+	0.522615i
$300$		0			0
$301$	−7.58959	+	13.3400i	−0.437457	+	0.768905i
$302$	−3.25404	−	9.88112i	−0.187249	−	0.568595i
$303$	7.13749	+	4.12083i	0.410038	+	0.236736i
$304$	24.0153	−	5.50501i	1.37737	−	0.315734i
$305$		0			0
$306$	1.76796	+	0.368455i	0.101068	+	0.0210632i
$307$	10.4271			0.595104			0.297552	−	0.954706i	$-0.403830\pi$
$307$	10.4271			0.595104			0.297552	+	0.954706i	$0.403830\pi$
$308$	−18.2044	−	7.79549i	−1.03729	−	0.444189i
$309$	−9.22183			−0.524612
$310$		0			0
$311$	3.96296	+	6.86404i	0.224719	+	0.389224i	0.956235	−	0.292600i	$-0.0945203\pi$
$311$	3.96296	+	6.86404i	0.224719	+	0.389224i	−0.731516	+	0.681824i	$0.761187\pi$
$312$	0.571629	−	6.14228i	0.0323621	−	0.347738i
$313$	−12.5285	−	7.23333i	−0.708152	−	0.408852i	0.102224	−	0.994761i	$-0.467404\pi$
$313$	−12.5285	−	7.23333i	−0.708152	−	0.408852i	−0.810376	+	0.585910i	$0.800737\pi$
$314$	1.36357	+	4.14058i	0.0769507	+	0.233666i
$315$		0			0
$316$	−0.545533	−	0.738447i	−0.0306886	−	0.0415409i
$317$	1.76853	−	3.06318i	0.0993305	−	0.172046i	−0.812077	−	0.583550i	$-0.801663\pi$
$317$	1.76853	−	3.06318i	0.0993305	−	0.172046i	0.911408	+	0.411504i	$0.134997\pi$
$318$	2.96101	+	2.64488i	0.166045	+	0.148317i
$319$	−1.41136	+	0.814851i	−0.0790212	+	0.0456229i
$320$		0			0
$321$		−	5.70690i		−	0.318528i
$322$	15.2925	−	5.14373i	0.852219	−	0.286649i
$323$		−	3.59544i		−	0.200056i
$324$	0.528221	+	4.66844i	0.0293456	+	0.259358i
$325$		0			0
$326$	−4.25660	+	4.76538i	−0.235751	+	0.263930i
$327$	−8.45423	+	14.6432i	−0.467520	+	0.809769i
$328$	16.9647	+	12.0192i	0.936717	+	0.663648i
$329$	26.4276	−	15.4820i	1.45700	−	0.853552i
$330$		0			0
$331$	20.3773	+	11.7649i	1.12004	+	0.646655i	0.941411	−	0.337261i	$-0.109501\pi$
$331$	20.3773	+	11.7649i	1.12004	+	0.646655i	0.178629	+	0.983917i	$0.442834\pi$
$332$	4.76245	+	2.07518i	0.261373	+	0.113890i
$333$	12.3613	+	21.4105i	0.677397	+	1.17329i
$334$	4.88652	−	23.4471i	0.267378	−	1.28297i
$335$		0			0
$336$	−6.94466	+	6.53831i	−0.378862	+	0.356694i
$337$	−5.10057			−0.277846			−0.138923	−	0.990303i	$-0.544364\pi$
$337$	−5.10057			−0.277846			−0.138923	+	0.990303i	$0.544364\pi$
$338$	−2.06129	+	9.89072i	−0.112119	+	0.537984i
$339$	−1.88298	−	3.26142i	−0.102269	−	0.177136i
$340$		0			0
$341$	8.22794	+	4.75040i	0.445568	+	0.257249i
$342$	18.1006	−	5.96087i	0.978768	−	0.322327i
$343$	0.351954	+	18.5169i	0.0190037	+	0.999819i
$344$	13.3880	+	9.48520i	0.721835	+	0.511407i
$345$		0			0
$346$	0.125015	−	0.139958i	0.00672087	−	0.00752420i
$347$	−1.44316	+	0.833209i	−0.0774729	+	0.0447290i	−0.538236	−	0.842794i	$-0.680909\pi$
$347$	−1.44316	+	0.833209i	−0.0774729	+	0.0447290i	0.460763	+	0.887523i	$0.347576\pi$
$348$	0.0882513	+	0.779969i	0.00473077	+	0.0418107i
$349$		−	27.6081i		−	1.47783i	−0.673801	−	0.738913i	$-0.735339\pi$
$349$		−	27.6081i		−	1.47783i	0.673801	−	0.738913i	$-0.264661\pi$
$350$		0			0
$351$		−	11.3144i		−	0.603918i
$352$	−10.2189	+	18.5409i	−0.544669	+	0.988236i
$353$	−23.5193	+	13.5789i	−1.25180	+	0.722730i	−0.971468	−	0.237172i	$-0.923779\pi$
$353$	−23.5193	+	13.5789i	−1.25180	+	0.722730i	−0.280337	+	0.959902i	$0.590446\pi$
$354$	−3.29920	−	2.94696i	−0.175351	−	0.156629i
$355$		0			0
$356$	11.7415	+	15.8936i	0.622300	+	0.842360i
$357$	0.703578	+	1.20100i	0.0372373	+	0.0635635i
$358$	−7.12154	−	21.6251i	−0.376385	−	1.14292i
$359$	−14.5102	−	8.37747i	−0.765819	−	0.442146i	0.0655619	−	0.997849i	$-0.479116\pi$
$359$	−14.5102	−	8.37747i	−0.765819	−	0.442146i	−0.831381	+	0.555703i	$0.812449\pi$
$360$		0			0
$361$	−9.47002	−	16.4026i	−0.498422	−	0.863293i
$362$	−5.52841	−	1.15216i	−0.290567	−	0.0605560i
$363$	2.70926			0.142199
$364$	−10.2508	+	7.67374i	−0.537290	+	0.402213i
$365$		0			0
$366$	12.9616	+	2.70128i	0.677514	+	0.141198i
$367$	4.22213	+	7.31294i	0.220393	+	0.381732i	0.954927	−	0.296839i	$-0.0959326\pi$
$367$	4.22213	+	7.31294i	0.220393	+	0.381732i	−0.734534	+	0.678572i	$0.762599\pi$
$368$	−3.85388	−	16.8124i	−0.200897	−	0.876404i
$369$	13.9266	+	8.04054i	0.724991	+	0.418574i
$370$		0			0
$371$	−0.0522078	−	8.24111i	−0.00271049	−	0.427857i
$372$	3.68062	−	2.71908i	0.190831	−	0.140978i
$373$	−5.18861	+	8.98694i	−0.268656	+	0.465326i	−0.968515	−	0.248955i	$-0.919913\pi$
$373$	−5.18861	+	8.98694i	−0.268656	+	0.465326i	0.699859	+	0.714281i	$0.253246\pi$
$374$	2.30408	+	2.05808i	0.119141	+	0.106421i
$375$		0			0
$376$	−13.6736	−	29.7517i	−0.705162	−	1.53432i
$377$			1.05378i			0.0542723i
$378$	−11.5714	+	13.1208i	−0.595166	+	0.674862i
$379$			11.7976i			0.606002i	0.952990	+	0.303001i	$0.0979886\pi$
$379$			11.7976i			0.606002i	−0.952990	+	0.303001i	$0.902011\pi$
$380$		0			0
$381$	−3.83268	+	2.21280i	−0.196354	+	0.113365i
$382$	18.8893	−	21.1471i	0.966462	−	1.08198i
$383$	−0.478522	+	0.828825i	−0.0244514	+	0.0423510i	−0.877992	−	0.478675i	$-0.841117\pi$
$383$	−0.478522	+	0.828825i	−0.0244514	+	0.0423510i	0.853541	+	0.521026i	$0.174451\pi$
$384$	6.22067	+	8.07948i	0.317447	+	0.412304i
$385$		0			0
$386$	−25.9773	+	8.55483i	−1.32221	+	0.435430i
$387$	10.9905	+	6.34537i	0.558679	+	0.322553i
$388$	−3.62747	+	8.32488i	−0.184157	+	0.422632i
$389$	15.0820	+	26.1228i	0.764689	+	1.32448i	0.940411	+	0.340041i	$0.110441\pi$
$389$	15.0820	+	26.1228i	0.764689	+	1.32448i	−0.175722	+	0.984440i	$0.556226\pi$
$390$		0			0
$391$	−2.51705			−0.127293
$392$	19.7355	+	1.58475i	0.996792	+	0.0800418i
$393$	14.3073			0.721708
$394$	−0.472436	+	2.26690i	−0.0238010	+	0.114205i
$395$		0			0
$396$	−6.54110	+	15.0115i	−0.328703	+	0.754358i
$397$	5.37540	+	3.10349i	0.269783	+	0.155760i	0.628789	−	0.777576i	$-0.283551\pi$
$397$	5.37540	+	3.10349i	0.269783	+	0.155760i	−0.359006	+	0.933335i	$0.616884\pi$
$398$	1.05212	−	0.346483i	0.0527380	−	0.0173676i
$399$	12.7663	+	7.26317i	0.639113	+	0.363613i
$400$		0			0
$401$	−13.1565	+	22.7877i	−0.657004	+	1.13796i	0.324384	+	0.945926i	$0.394843\pi$
$401$	−13.1565	+	22.7877i	−0.657004	+	1.13796i	−0.981387	+	0.192038i	$0.938490\pi$
$402$	−8.35941	+	9.35859i	−0.416930	+	0.466764i
$403$	5.32025	−	3.07165i	0.265020	−	0.153010i
$404$	−18.1729	+	2.05621i	−0.904134	+	0.102300i
$405$		0			0
$406$	1.07771	−	1.22202i	0.0534858	−	0.0606478i
$407$			42.2927i			2.09637i
$408$	1.35206	−	0.621394i	0.0669368	−	0.0307636i
$409$	−15.9374	+	9.20148i	−0.788055	+	0.454984i	−0.839277	−	0.543703i	$-0.817022\pi$
$409$	−15.9374	+	9.20148i	−0.788055	+	0.454984i	0.0512223	+	0.998687i	$0.483688\pi$
$410$		0			0
$411$	3.53400	−	6.12107i	0.174320	−	0.301930i
$412$	16.4595	−	12.1596i	0.810902	−	0.599060i
$413$	0.0581707	+	9.18236i	0.00286239	+	0.451834i
$414$	−4.17302	−	12.6716i	−0.205093	−	0.622777i
$415$		0			0
$416$	7.07872	+	11.7167i	0.347063	+	0.574460i
$417$	7.84312	+	13.5847i	0.384079	+	0.665245i
$418$	31.9146	+	6.65120i	1.56099	+	0.325321i
$419$	−35.2426			−1.72171			−0.860856	−	0.508848i	$-0.830072\pi$
$419$	−35.2426			−1.72171			−0.860856	+	0.508848i	$0.830072\pi$
$420$		0			0
$421$	−15.6669			−0.763558			−0.381779	−	0.924254i	$-0.624688\pi$
$421$	−15.6669			−0.763558			−0.381779	+	0.924254i	$0.624688\pi$
$422$	−12.7722	−	2.66181i	−0.621740	−	0.129575i
$423$	−12.6630	−	21.9329i	−0.615695	−	1.06641i
$424$	−8.77239	−	0.816400i	−0.426025	−	0.0396479i
$425$		0			0
$426$	−3.97400	−	12.0673i	−0.192541	−	0.584664i
$427$	−13.8921	−	23.7136i	−0.672285	−	1.14758i
$428$	7.52492	+	10.1859i	0.363731	+	0.492355i
$429$	4.08117	−	7.06879i	0.197041	−	0.341284i
$430$		0			0
$431$	1.73673	−	1.00270i	0.0836555	−	0.0482985i	−0.457589	−	0.889164i	$-0.651287\pi$
$431$	1.73673	−	1.00270i	0.0836555	−	0.0482985i	0.541244	+	0.840865i	$0.317953\pi$
$432$	12.7336	+	13.6978i	0.612645	+	0.659035i
$433$		−	13.5978i		−	0.653469i	−0.945116	−	0.326734i	$-0.894052\pi$
$433$		−	13.5978i		−	0.653469i	0.945116	−	0.326734i	$-0.105948\pi$
$434$	−9.31106	−	1.87902i	−0.446945	−	0.0901957i
$435$		0			0
$436$	−4.21849	−	37.2832i	−0.202029	−	1.78554i
$437$	−23.0022	+	13.2803i	−1.10034	+	0.635283i
$438$	8.32029	−	9.31480i	0.397559	−	0.445078i
$439$	14.5247	−	25.1574i	0.693224	−	1.20070i	−0.277552	−	0.960711i	$-0.589523\pi$
$439$	14.5247	−	25.1574i	0.693224	−	1.20070i	0.970776	−	0.239989i	$-0.0771437\pi$
$440$		0			0
$441$	15.3127	−	0.194020i	0.729174	−	0.00923907i
$442$	1.89740	−	0.624849i	0.0902500	−	0.0297211i
$443$	12.6757	+	7.31831i	0.602240	+	0.347703i	0.769922	−	0.638138i	$-0.220295\pi$
$443$	12.6757	+	7.31831i	0.602240	+	0.347703i	−0.167683	+	0.985841i	$0.553628\pi$
$444$	18.6744	+	8.13717i	0.886250	+	0.386173i
$445$		0			0
$446$	−6.99345	+	33.5568i	−0.331149	+	1.58896i
$447$	−1.48851			−0.0704040
$448$	3.77393	−	20.8268i	0.178301	−	0.983976i
$449$	−27.0699			−1.27751			−0.638754	−	0.769411i	$-0.720550\pi$
$449$	−27.0699			−1.27751			−0.638754	+	0.769411i	$0.720550\pi$
$450$		0			0
$451$	13.7548	+	23.8241i	0.647689	+	1.12183i
$452$	7.66122	+	3.33829i	0.360353	+	0.157020i
$453$	−5.74168	−	3.31496i	−0.269768	−	0.155750i
$454$	−14.2820	+	4.70335i	−0.670290	+	0.220739i
$455$		0			0
$456$	9.07725	−	12.8122i	0.425081	−	0.599989i
$457$	−3.80306	+	6.58709i	−0.177900	+	0.308131i	−0.941161	−	0.337959i	$-0.890264\pi$
$457$	−3.80306	+	6.58709i	−0.177900	+	0.308131i	0.763261	+	0.646090i	$0.223597\pi$
$458$	27.8043	−	31.1277i	1.29921	−	1.45450i
$459$	2.36357	−	1.36461i	0.110322	−	0.0636943i
$460$		0			0
$461$			12.7953i			0.595936i	0.954576	+	0.297968i	$0.0963089\pi$
$461$			12.7953i			0.595936i	−0.954576	+	0.297968i	$0.903691\pi$
$462$	−11.9621	+	4.02351i	−0.556526	+	0.187191i
$463$			27.9178i			1.29745i	0.761024	+	0.648724i	$0.224697\pi$
$463$			27.9178i			1.29745i	−0.761024	+	0.648724i	$0.775303\pi$
$464$	−1.18595	−	1.27576i	−0.0550566	−	0.0592255i
$465$		0			0
$466$	29.6062	+	26.4453i	1.37148	+	1.22505i
$467$	11.3054	−	19.5815i	0.523152	−	0.906126i	−0.476485	−	0.879183i	$-0.658089\pi$
$467$	11.3054	−	19.5815i	0.523152	−	0.906126i	0.999637	−	0.0269432i	$-0.00857731\pi$
$468$	6.29138	+	8.51617i	0.290819	+	0.393660i
$469$	26.0469	−	0.165008i	1.20273	−	0.00761937i
$470$		0			0
$471$	2.40599	+	1.38910i	0.110862	+	0.0640062i
$472$	9.77432	+	0.909644i	0.449899	+	0.0418698i
$473$	10.8549	+	18.8013i	0.499110	+	0.864484i
$474$	−0.572798	−	0.119375i	−0.0263095	−	0.00548307i
$475$		0			0
$476$	−2.83937	−	1.21588i	−0.130142	−	0.0557297i
$477$	−6.81448			−0.312014
$478$	−18.8673	−	3.93207i	−0.862971	−	0.179849i
$479$	−10.9907	−	19.0365i	−0.502180	−	0.869801i	−0.999997	−	0.00251901i	$-0.999198\pi$
$479$	−10.9907	−	19.0365i	−0.502180	−	0.869801i	0.497817	−	0.867282i	$-0.334135\pi$
$480$		0			0
$481$	23.6830	+	13.6734i	1.07985	+	0.623453i
$482$	−1.86118	−	5.65160i	−0.0847744	−	0.257423i
$483$	5.08471	−	8.93726i	0.231362	−	0.406659i
$484$	−4.83560	+	3.57234i	−0.219800	+	0.162379i
$485$		0			0
$486$	17.0272	+	15.2093i	0.772371	+	0.689908i
$487$	−21.9822	+	12.6914i	−0.996108	+	0.575103i	−0.907095	−	0.420927i	$-0.861705\pi$
$487$	−21.9822	+	12.6914i	−0.996108	+	0.575103i	−0.0890138	+	0.996030i	$0.528372\pi$
$488$	−26.6962	+	12.2694i	−1.20848	+	0.555408i
$489$			4.07212i			0.184147i
$490$		0			0
$491$		−	36.4635i		−	1.64557i	−0.568350	−	0.822787i	$-0.692418\pi$
$491$		−	36.4635i		−	1.64557i	0.568350	−	0.822787i	$-0.307582\pi$
$492$	13.1660	−	1.48970i	0.593570	−	0.0671607i
$493$	−0.220133	+	0.127094i	−0.00991429	+	0.00572402i
$494$	14.0426	−	15.7211i	0.631808	−	0.707326i
$495$		0			0
$496$	−2.98403	+	9.70626i	−0.133987	+	0.435824i
$497$	−13.0411	+	22.9220i	−0.584973	+	1.02819i
$498$	3.14460	−	1.03558i	0.140913	−	0.0464053i
$499$	10.2874	+	5.93945i	0.460528	+	0.265886i	0.712266	−	0.701909i	$-0.247669\pi$
$499$	10.2874	+	5.93945i	0.460528	+	0.265886i	−0.251738	+	0.967795i	$0.581002\pi$
$500$		0			0
$501$	−7.63194	−	13.2189i	−0.340970	−	0.590577i
$502$	−5.44822	+	26.1423i	−0.243166	+	1.16679i
$503$	−17.3055			−0.771614			−0.385807	−	0.922580i	$-0.626077\pi$
$503$	−17.3055			−0.771614			−0.385807	+	0.922580i	$0.626077\pi$
$504$	1.41373	−	16.3101i	0.0629727	−	0.726509i
$505$		0			0
$506$	4.65629	−	22.3424i	0.206997	−	0.993239i
$507$	3.21939	+	5.57615i	0.142978	+	0.247646i
$508$	3.92301	−	9.00314i	0.174056	−	0.399450i
$509$	−11.8717	−	6.85414i	−0.526205	−	0.303805i	0.213265	−	0.976994i	$-0.431590\pi$
$509$	−11.8717	−	6.85414i	−0.526205	−	0.303805i	−0.739470	+	0.673190i	$0.764924\pi$
$510$		0			0
$511$	−25.9250	+	0.164236i	−1.14685	+	0.00726537i
$512$	−21.7562	−	6.21824i	−0.961498	−	0.274810i
$513$	14.3997	−	24.9410i	0.635761	−	1.10117i
$514$	24.3389	−	27.2481i	1.07355	−	1.20186i
$515$		0			0
$516$	10.3903	−	1.17563i	0.457405	−	0.0517541i
$517$		−	43.3247i		−	1.90542i
$518$	−13.4802	−	40.0773i	−0.592287	−	1.76089i
$519$		−	0.119597i		−	0.00524973i
$520$		0			0
$521$	31.4817	−	18.1760i	1.37924	−	0.796304i	0.387171	−	0.922008i	$-0.373452\pi$
$521$	31.4817	−	18.1760i	1.37924	−	0.796304i	0.992068	+	0.125704i	$0.0401190\pi$
$522$	−1.00479	−	0.897511i	−0.0439784	−	0.0392830i
$523$	2.13211	−	3.69292i	0.0932306	−	0.161480i	−0.815638	−	0.578562i	$-0.803614\pi$
$523$	2.13211	−	3.69292i	0.0932306	−	0.161480i	0.908869	+	0.417082i	$0.136947\pi$
$524$	−25.5363	+	18.8651i	−1.11556	+	0.824126i
$525$		0			0
$526$	−4.73196	−	14.3689i	−0.206323	−	0.626515i
$527$	1.28333	+	0.740929i	0.0559026	+	0.0322754i
$528$	3.01457	+	13.1509i	0.131192	+	0.572320i
$529$	−2.20289	−	3.81552i	−0.0957778	−	0.165892i
$530$		0			0
$531$	7.59279			0.329499
$532$	−32.3628	+	3.86955i	−1.40310	+	0.167766i
$533$	17.7879			0.770482
$534$	12.3284	+	2.56931i	0.533501	+	0.111185i
$535$		0			0
$536$	2.58032	−	27.7260i	0.111453	−	1.19758i
$537$	−12.5658	−	7.25487i	−0.542254	−	0.313071i
$538$	−3.70038	−	11.2364i	−0.159535	−	0.484438i
$539$	22.8516	+	12.8101i	0.984288	+	0.551771i
$540$		0			0
$541$	3.34133	−	5.78736i	0.143655	−	0.248818i	−0.785215	−	0.619223i	$-0.787448\pi$
$541$	3.34133	−	5.78736i	0.143655	−	0.248818i	0.928870	+	0.370405i	$0.120781\pi$
$542$	−28.5948	−	25.5418i	−1.22825	−	1.09712i
$543$	−3.11679	+	1.79948i	−0.133754	+	0.0772229i
$544$	−1.59386	+	2.89187i	−0.0683362	+	0.123988i
$545$		0			0
$546$	−1.61430	+	7.99932i	−0.0690857	+	0.342339i
$547$		−	45.6888i		−	1.95351i	−0.214353	−	0.976756i	$-0.568764\pi$
$547$		−	45.6888i		−	1.95351i	0.214353	−	0.976756i	$-0.431236\pi$
$548$	1.76339	+	15.5850i	0.0753285	+	0.665757i
$549$	−19.6805	+	11.3625i	−0.839942	+	0.484941i
$550$		0			0
$551$	−1.34113	+	2.32290i	−0.0571339	+	0.0989589i
$552$	−8.96944	−	6.35469i	−0.381765	−	0.270474i
$553$	0.613918	+	1.04795i	0.0261064	+	0.0445633i
$554$	−4.51309	+	1.48625i	−0.191743	+	0.0631445i
$555$		0			0
$556$	−31.9110	−	13.9049i	−1.35333	−	0.589697i
$557$	2.44203	+	4.22972i	0.103472	+	0.179219i	0.913113	−	0.407707i	$-0.133671\pi$
$557$	2.44203	+	4.22972i	0.103472	+	0.179219i	−0.809641	+	0.586926i	$0.800338\pi$
$558$	−1.60245	+	7.68906i	−0.0678371	+	0.325504i
$559$	14.0378			0.593734
$560$		0			0
$561$	1.96888			0.0831263
$562$	2.11767	−	10.1613i	0.0893286	−	0.428627i
$563$	1.36792	+	2.36931i	0.0576509	+	0.0998543i	0.893410	−	0.449241i	$-0.148306\pi$
$563$	1.36792	+	2.36931i	0.0576509	+	0.0998543i	−0.835760	+	0.549096i	$0.814972\pi$
$564$	−19.1301	−	8.33573i	−0.805524	−	0.350997i
$565$		0			0
$566$	9.67897	−	3.18747i	0.406838	−	0.133979i
$567$	−0.0393726	−	6.21505i	−0.00165349	−	0.261008i
$568$	23.0045	+	16.2983i	0.965248	+	0.683861i
$569$	−2.29674	+	3.97807i	−0.0962843	+	0.166769i	−0.910144	−	0.414292i	$-0.864029\pi$
$569$	−2.29674	+	3.97807i	−0.0962843	+	0.166769i	0.813860	+	0.581062i	$0.197362\pi$
$570$		0			0
$571$	4.86573	−	2.80923i	0.203625	−	0.117563i	−0.394720	−	0.918801i	$-0.629159\pi$
$571$	4.86573	−	2.80923i	0.203625	−	0.117563i	0.598345	+	0.801239i	$0.295825\pi$
$572$	2.03642	+	17.9980i	0.0851469	+	0.752532i
$573$		−	18.0707i		−	0.754912i
$574$	−20.6279	−	18.1919i	−0.860992	−	0.759316i
$575$		0			0
$576$	−17.2010	−	3.22959i	−0.716709	−	0.134566i
$577$	29.7446	−	17.1731i	1.23828	−	0.714924i	0.269541	−	0.962989i	$-0.413128\pi$
$577$	29.7446	−	17.1731i	1.23828	−	0.714924i	0.968743	+	0.248065i	$0.0797948\pi$
$578$	−17.5708	−	15.6949i	−0.730850	−	0.652820i
$579$	−8.71499	+	15.0948i	−0.362182	+	0.627318i
$580$		0			0
$581$	−5.97319	−	3.39835i	−0.247810	−	0.140987i
$582$	1.81021	+	5.49684i	0.0750358	+	0.227851i
$583$	−10.0956	−	5.82872i	−0.418118	−	0.241401i
$584$	−2.56824	+	27.5963i	−0.106275	+	1.14194i
$585$		0			0
$586$	11.7386	+	2.44640i	0.484917	+	0.101060i
$587$	40.1422			1.65685			0.828423	−	0.560103i	$-0.189238\pi$
$587$	40.1422			1.65685			0.828423	+	0.560103i	$0.189238\pi$
$588$	10.0530	−	7.62549i	0.414579	−	0.314470i
$589$	15.6369			0.644309
$590$		0			0
$591$	0.737868	+	1.27802i	0.0303518	+	0.0525709i
$592$	−44.0603	+	10.0999i	−1.81087	+	0.415103i
$593$	−9.46884	−	5.46684i	−0.388839	−	0.224496i	0.292818	−	0.956168i	$-0.405407\pi$
$593$	−9.46884	−	5.46684i	−0.388839	−	0.224496i	−0.681657	+	0.731672i	$0.738740\pi$
$594$	7.74042	+	23.5043i	0.317593	+	0.964394i
$595$		0			0
$596$	2.65675	−	1.96269i	0.108825	−	0.0803951i
$597$	0.352969	−	0.611361i	0.0144461	−	0.0250213i
$598$	−11.0058	−	9.83079i	−0.450063	−	0.402011i
$599$	4.51466	−	2.60654i	0.184464	−	0.106500i	−0.404924	−	0.914350i	$-0.632702\pi$
$599$	4.51466	−	2.60654i	0.184464	−	0.106500i	0.589388	+	0.807850i	$0.299369\pi$
$600$		0			0
$601$		−	16.1103i		−	0.657154i	−0.944477	−	0.328577i	$-0.893431\pi$
$601$		−	16.1103i		−	0.657154i	0.944477	−	0.328577i	$-0.106569\pi$
$602$	−16.2790	−	14.3566i	−0.663481	−	0.585129i
$603$		−	21.5379i		−	0.877090i
$604$	14.6190	−	1.65410i	0.594838	−	0.0673042i
$605$		0			0
$606$	−7.76455	+	8.69263i	−0.315413	+	0.353114i
$607$	−4.82810	+	8.36252i	−0.195967	+	0.339424i	−0.947217	−	0.320593i	$-0.896118\pi$
$607$	−4.82810	+	8.36252i	−0.195967	+	0.339424i	0.751250	+	0.660017i	$0.229451\pi$
$608$	0.692317	+	34.8368i	0.0280772	+	1.41282i
$609$	−0.00657809	−	1.03837i	−0.000266558	−	0.0420767i
$610$		0			0
$611$	−24.2609	−	14.0070i	−0.981491	−	0.566664i
$612$	−1.02023	+	2.34138i	−0.0412403	+	0.0946446i
$613$	3.92388	+	6.79635i	0.158484	+	0.274502i	0.934322	−	0.356430i	$-0.116006\pi$
$613$	3.92388	+	6.79635i	0.158484	+	0.274502i	−0.775838	+	0.630932i	$0.782673\pi$
$614$	−3.00854	+	14.4359i	−0.121415	+	0.582586i
$615$		0			0
$616$	16.0451	−	22.9541i	0.646477	−	0.924847i
$617$	28.8434			1.16119			0.580597	−	0.814191i	$-0.302819\pi$
$617$	28.8434			1.16119			0.580597	+	0.814191i	$0.302819\pi$
$618$	2.66079	−	12.7673i	0.107033	−	0.513577i
$619$	1.24278	+	2.15256i	0.0499517	+	0.0865189i	0.889920	−	0.456116i	$-0.150760\pi$
$619$	1.24278	+	2.15256i	0.0499517	+	0.0865189i	−0.839968	+	0.542635i	$0.817427\pi$
$620$		0			0
$621$	−17.4604	−	10.0807i	−0.700660	−	0.404526i
$622$	−10.6465	+	3.50609i	−0.426885	+	0.140581i
$623$	−13.2134	−	22.5550i	−0.529383	−	0.903649i
$624$	8.33885	+	2.56364i	0.333821	+	0.102628i
$625$		0			0
$626$	13.6292	−	15.2582i	0.544731	−	0.609842i
$627$	17.9927	−	10.3881i	0.718558	−	0.414860i
$628$	−6.12592	+	0.693131i	−0.244451	+	0.0276589i
$629$			6.59647i			0.263019i
$630$		0			0
$631$			8.90728i			0.354593i	0.984157	+	0.177297i	$0.0567352\pi$
$631$			8.90728i			0.354593i	−0.984157	+	0.177297i	$0.943265\pi$
$632$	1.17976	−	0.542207i	0.0469283	−	0.0215678i
$633$	−7.20066	+	4.15730i	−0.286200	+	0.165238i
$634$	3.73060	+	3.33230i	0.148161	+	0.132342i
$635$		0			0
$636$	−4.51609	+	3.33630i	−0.179075	+	0.132293i
$637$	14.5614	−	8.65485i	0.576944	−	0.342917i
$638$	−0.720911	−	2.18910i	−0.0285412	−	0.0866672i
$639$	18.8848	+	10.9032i	0.747073	+	0.431323i
$640$		0			0
$641$	−7.31652	−	12.6726i	−0.288985	−	0.500537i	0.684583	−	0.728935i	$-0.259984\pi$
$641$	−7.31652	−	12.6726i	−0.288985	−	0.500537i	−0.973568	+	0.228398i	$0.926651\pi$
$642$	7.90102	+	1.64662i	0.311828	+	0.0649870i
$643$	−24.2513			−0.956380			−0.478190	−	0.878256i	$-0.658707\pi$
$643$	−24.2513			−0.956380			−0.478190	+	0.878256i	$0.658707\pi$
$644$	2.70894	+	22.6561i	0.106747	+	0.892776i
$645$		0			0
$646$	4.97777	+	1.03740i	0.195848	+	0.0408160i
$647$	−14.9578	−	25.9077i	−0.588053	−	1.01854i	−0.994487	−	0.104857i	$-0.966561\pi$
$647$	−14.9578	−	25.9077i	−0.588053	−	1.01854i	0.406435	−	0.913680i	$-0.366772\pi$
$648$	−6.61571	−	0.615690i	−0.259890	−	0.0241866i
$649$	11.2487	+	6.49444i	0.441550	+	0.254929i
$650$		0			0
$651$	−5.22326	+	3.05993i	−0.204716	+	0.119928i
$652$	−5.36935	−	7.26808i	−0.210280	−	0.284640i
$653$	−7.78155	+	13.4780i	−0.304516	+	0.527436i	−0.977153	−	0.212535i	$-0.931828\pi$
$653$	−7.78155	+	13.4780i	−0.304516	+	0.527436i	0.672638	+	0.739972i	$0.265161\pi$
$654$	−17.8337	−	15.9296i	−0.697351	−	0.622898i
$655$		0			0
$656$	−21.5350	+	20.0191i	−0.840800	+	0.781615i
$657$			21.4371i			0.836340i
$658$	13.8092	+	41.0552i	0.538337	+	1.60050i
$659$		−	30.2702i		−	1.17916i	−0.807710	−	0.589580i	$-0.799293\pi$
$659$		−	30.2702i		−	1.17916i	0.807710	−	0.589580i	$-0.200707\pi$
$660$		0			0
$661$	15.5209	−	8.96099i	0.603693	−	0.348542i	−0.166800	−	0.985991i	$-0.553344\pi$
$661$	15.5209	−	8.96099i	0.603693	−	0.348542i	0.770493	+	0.637449i	$0.220010\pi$
$662$	−22.1676	+	24.8172i	−0.861567	+	0.964549i
$663$	0.636547	−	1.10253i	0.0247214	−	0.0428188i
$664$	−4.24714	+	5.99470i	−0.164821	+	0.232640i
$665$		0			0
$666$	−33.2087	+	10.9363i	−1.28681	+	0.423772i
$667$	1.62619	+	0.938880i	0.0629662	+	0.0363536i
$668$	31.0518	+	13.5305i	1.20143	+	0.523509i
$669$	10.9226	+	18.9185i	0.422292	+	0.731432i
$670$		0			0
$671$	−38.8754			−1.50077
$672$	−7.04833	−	11.5012i	−0.271895	−	0.443667i
$673$	−21.1876			−0.816723			−0.408362	−	0.912820i	$-0.633900\pi$
$673$	−21.1876			−0.816723			−0.408362	+	0.912820i	$0.633900\pi$
$674$	1.47168	−	7.06157i	0.0566868	−	0.272001i
$675$		0			0
$676$	−13.0986	−	5.70758i	−0.503794	−	0.219522i
$677$	21.8732	+	12.6285i	0.840657	+	0.485353i	0.857487	−	0.514505i	$-0.172024\pi$
$677$	21.8732	+	12.6285i	0.840657	+	0.485353i	−0.0168308	+	0.999858i	$0.505358\pi$
$678$	5.05863	−	1.66590i	0.194275	−	0.0639786i
$679$	5.94041	−	10.4413i	0.227972	−	0.400700i
$680$		0			0
$681$	−4.79140	+	8.29895i	−0.183607	+	0.318016i
$682$	−8.95080	+	10.0207i	−0.342744	+	0.383711i
$683$	19.1391	−	11.0499i	0.732336	−	0.422814i	−0.0869404	−	0.996214i	$-0.527709\pi$
$683$	19.1391	−	11.0499i	0.732336	−	0.422814i	0.819276	+	0.573399i	$0.194376\pi$
$684$	3.03003	+	26.7796i	0.115856	+	1.02394i
$685$		0			0
$686$	−25.7376	−	4.85545i	−0.982667	−	0.185382i
$687$		−	26.5993i		−	1.01483i
$688$	−16.9948	+	15.7985i	−0.647921	+	0.602313i
$689$	−6.52791	+	3.76889i	−0.248694	+	0.143583i
$690$		0			0
$691$	−9.05508	+	15.6839i	−0.344471	+	0.596642i	−0.985258	−	0.171077i	$-0.945275\pi$
$691$	−9.05508	+	15.6839i	−0.344471	+	0.596642i	0.640786	+	0.767719i	$0.278609\pi$
$692$	0.157697	+	0.213462i	0.00599473	+	0.00811461i
$693$	10.7118	−	18.8279i	0.406908	−	0.715212i
$694$	−0.737153	−	2.23841i	−0.0279819	−	0.0849691i
$695$		0			0
$696$	−1.10530	−	0.102865i	−0.0418965	−	0.00389908i
$697$	2.14537	+	3.71588i	0.0812615	+	0.140749i
$698$	38.2225	+	7.96581i	1.44674	+	0.301510i
$699$	25.2991			0.956901
$700$		0			0
$701$	14.4315			0.545070			0.272535	−	0.962146i	$-0.412138\pi$
$701$	14.4315			0.545070			0.272535	+	0.962146i	$0.412138\pi$
$702$	15.6644	+	3.26456i	0.591215	+	0.123213i
$703$	34.8038	+	60.2820i	1.31265	+	2.27358i
$704$	−22.7209	−	19.4974i	−0.856324	−	0.734835i
$705$		0			0
$706$	−12.0134	−	36.4796i	−0.452131	−	1.37293i
$707$	24.1934	−	0.153266i	0.909885	−	0.00576416i
$708$	5.03189	−	3.71735i	0.189110	−	0.139706i
$709$	18.5131	−	32.0657i	0.695275	−	1.20425i	−0.274814	−	0.961498i	$-0.588616\pi$
$709$	18.5131	−	32.0657i	0.695275	−	1.20425i	0.970088	−	0.242753i	$-0.0780505\pi$
$710$		0			0
$711$	0.869718	−	0.502132i	0.0326170	−	0.0188314i
$712$	−25.3920	+	11.6699i	−0.951605	+	0.437350i
$713$		−	10.9469i		−	0.409965i
$714$	−1.86575	+	0.627554i	−0.0698238	+	0.0234856i
$715$		0			0
$716$	31.9940	−	3.62003i	1.19567	−	0.135287i
$717$	−10.6369	+	6.14124i	−0.397244	+	0.229349i
$718$	15.7850	−	17.6717i	0.589091	−	0.659503i
$719$	10.0975	−	17.4894i	0.376573	−	0.652243i	−0.613988	−	0.789315i	$-0.710436\pi$
$719$	10.0975	−	17.4894i	0.376573	−	0.652243i	0.990561	+	0.137072i	$0.0437692\pi$
$720$		0			0
$721$	−23.3581	+	13.6838i	−0.869902	+	0.509613i
$722$	25.4412	−	8.37828i	0.946824	−	0.311807i
$723$	−3.28401	−	1.89602i	−0.122134	−	0.0705138i
$724$	3.19024	−	7.32147i	0.118564	−	0.272100i
$725$		0			0
$726$	−0.781708	+	3.75088i	−0.0290119	+	0.139208i
$727$	10.7925			0.400272			0.200136	−	0.979768i	$-0.435862\pi$
$727$	10.7925			0.400272			0.200136	+	0.979768i	$0.435862\pi$
$728$	−7.66635	−	16.4061i	−0.284134	−	0.608050i
$729$	7.50278			0.277881
$730$		0			0
$731$	1.69306	+	2.93247i	0.0626202	+	0.108461i
$732$	−7.47967	+	17.1655i	−0.276457	+	0.634456i
$733$	−6.26329	−	3.61611i	−0.231340	−	0.133564i	0.379850	−	0.925048i	$-0.375976\pi$
$733$	−6.26329	−	3.61611i	−0.231340	−	0.133564i	−0.611190	+	0.791484i	$0.709309\pi$
$734$	−11.3427	+	3.73538i	−0.418668	+	0.137875i
$735$		0			0
$736$	24.3881	−	0.484669i	0.898958	−	0.0178651i
$737$	18.4223	−	31.9083i	0.678593	−	1.17536i
$738$	−15.1501	+	16.9610i	−0.557684	+	0.624343i
$739$	−1.71927	+	0.992622i	−0.0632444	+	0.0365142i	−0.531289	−	0.847191i	$-0.678292\pi$
$739$	−1.71927	+	0.992622i	−0.0632444	+	0.0365142i	0.468044	+	0.883705i	$0.344959\pi$
$740$		0			0
$741$		−	13.4340i		−	0.493511i
$742$	11.4246	+	2.30554i	0.419411	+	0.0846391i
$743$		−	19.8225i		−	0.727216i	−0.931552	−	0.363608i	$-0.881545\pi$
$743$		−	19.8225i		−	0.727216i	0.931552	−	0.363608i	$-0.118455\pi$
$744$	2.70250	+	5.88023i	0.0990786	+	0.215580i
$745$		0			0
$746$	−10.9450	−	9.77648i	−0.400727	−	0.357942i
$747$	−2.84124	+	4.92116i	−0.103955	+	0.180056i
$748$	−3.51414	+	2.59610i	−0.128490	+	0.0949228i
$749$	−8.46821	−	14.4551i	−0.309421	−	0.528178i
$750$		0			0
$751$	20.8718	+	12.0504i	0.761624	+	0.439724i	0.829879	−	0.557944i	$-0.188410\pi$
$751$	20.8718	+	12.0504i	0.761624	+	0.439724i	−0.0682545	+	0.997668i	$0.521743\pi$
$752$	45.1355	−	10.3464i	1.64592	−	0.377293i
$753$	8.50921	+	14.7384i	0.310093	+	0.537097i
$754$	−1.45892	−	0.304048i	−0.0531308	−	0.0110728i
$755$		0			0
$756$	−14.8266	−	19.8059i	−0.539239	−	0.720335i
$757$	−34.8711			−1.26741			−0.633706	−	0.773574i	$-0.718467\pi$
$757$	−34.8711			−1.26741			−0.633706	+	0.773574i	$0.718467\pi$
$758$	−16.3334	−	3.40398i	−0.593256	−	0.123638i
$759$	−7.27236	−	12.5961i	−0.263970	−	0.457209i
$760$		0			0
$761$	7.76620	+	4.48382i	0.281524	+	0.162538i	0.634113	−	0.773240i	$-0.281365\pi$
$761$	7.76620	+	4.48382i	0.281524	+	0.162538i	−0.352589	+	0.935778i	$0.614699\pi$
$762$	−1.95770	−	5.94469i	−0.0709200	−	0.215353i
$763$	0.314438	+	49.6347i	0.0113834	+	1.79690i
$764$	23.8273	+	32.2533i	0.862043	+	1.16688i
$765$		0			0
$766$	−1.00941	−	0.901641i	−0.0364715	−	0.0325776i
$767$	7.27349	−	4.19935i	0.262631	−	0.151630i
$768$	−12.9806	+	6.28112i	−0.468398	+	0.226650i
$769$		−	0.573577i		−	0.0206837i	−0.999947	−	0.0103419i	$-0.996708\pi$
$769$		−	0.573577i		−	0.0206837i	0.999947	−	0.0103419i	$-0.00329197\pi$
$770$		0			0
$771$		−	23.2841i		−	0.838556i
$772$	−4.34860	−	38.4331i	−0.156509	−	1.38324i
$773$	3.76591	−	2.17425i	0.135450	−	0.0782023i	−0.430744	−	0.902474i	$-0.641749\pi$
$773$	3.76591	−	2.17425i	0.135450	−	0.0782023i	0.566194	+	0.824272i	$0.308415\pi$
$774$	−11.9561	+	13.3851i	−0.429752	+	0.481119i
$775$		0			0
$776$	−10.4789	−	7.42411i	−0.376170	−	0.266510i
$777$	−23.4220	−	13.3256i	−0.840259	−	0.478052i
$778$	−40.5179	+	13.3433i	−1.45264	+	0.478381i
$779$	39.2109	+	22.6384i	1.40488	+	0.811107i
$780$		0			0
$781$	18.6519	+	32.3060i	0.667417	+	1.15600i
$782$	0.726250	−	3.48478i	0.0259707	−	0.124615i
$783$	−2.03603			−0.0727618
$784$	−7.88834	+	26.8659i	−0.281726	+	0.959495i
$785$		0			0
$786$	−4.12811	+	19.8080i	−0.147245	+	0.706528i
$787$	−10.5248	−	18.2295i	−0.375168	−	0.649811i	0.615184	−	0.788384i	$-0.289082\pi$
$787$	−10.5248	−	18.2295i	−0.375168	−	0.649811i	−0.990352	+	0.138573i	$0.955748\pi$
$788$	−3.00214	−	1.30815i	−0.106947	−	0.0466008i
$789$	−8.34944	−	4.82055i	−0.297248	−	0.171616i
$790$		0			0
$791$	−9.60890	−	5.46683i	−0.341653	−	0.194378i
$792$	−18.8957	−	13.3873i	−0.671428	−	0.475695i
$793$	−12.5686	+	21.7694i	−0.446323	+	0.773054i
$794$	−5.84765	+	6.54661i	−0.207525	+	0.232330i
$795$		0			0
$796$	0.176124	+	1.55660i	0.00624256	+	0.0551721i
$797$			14.7349i			0.521938i	0.965347	+	0.260969i	$0.0840420\pi$
$797$			14.7349i			0.521938i	−0.965347	+	0.260969i	$0.915958\pi$
$798$	−13.7391	+	15.5788i	−0.486359	+	0.551485i
$799$		−	6.75744i		−	0.239061i
$800$		0			0
$801$	−18.7190	+	10.8074i	−0.661403	+	0.381861i
$802$	−27.7528	−	24.7897i	−0.979984	−	0.875355i
$803$	−18.3360	+	31.7590i	−0.647065	+	1.12075i
$804$	−10.5447	−	14.2736i	−0.371883	−	0.503390i
$805$		0			0
$806$	2.71753	+	8.25198i	0.0957210	+	0.290663i
$807$	−6.52923	−	3.76965i	−0.229840	−	0.132698i
$808$	2.39670	−	25.7530i	0.0843156	−	0.905988i
$809$	7.23808	+	12.5367i	0.254477	+	0.440768i	0.964753	−	0.263156i	$-0.0847632\pi$
$809$	7.23808	+	12.5367i	0.254477	+	0.440768i	−0.710276	+	0.703923i	$0.751430\pi$
$810$		0			0
$811$	18.5825			0.652521			0.326260	−	0.945280i	$-0.394211\pi$
$811$	18.5825			0.652521			0.326260	+	0.945280i	$0.394211\pi$
$812$	1.38089	+	1.84464i	0.0484598	+	0.0647343i
$813$	−24.4348			−0.856967
$814$	−58.5529	−	12.2028i	−2.05228	−	0.427708i
$815$		0			0
$816$	0.470188	+	2.05117i	0.0164599	+	0.0718054i
$817$	30.9442	+	17.8656i	1.08260	+	0.625040i
$818$	−8.14069	−	24.7198i	−0.284633	−	0.864306i
$819$	−7.08003	−	12.0855i	−0.247396	−	0.422302i
$820$		0			0
$821$	8.20275	−	14.2076i	0.286278	−	0.495848i	−0.686640	−	0.726997i	$-0.740915\pi$
$821$	8.20275	−	14.2076i	0.286278	−	0.495848i	0.972918	+	0.231149i	$0.0742486\pi$
$822$	7.45475	+	6.65884i	0.260014	+	0.232254i
$823$	−38.0161	+	21.9486i	−1.32516	+	0.765081i	−0.984547	−	0.175123i	$-0.943968\pi$
$823$	−38.0161	+	21.9486i	−1.32516	+	0.765081i	−0.340612	+	0.940204i	$0.610634\pi$
$824$	12.0854	+	26.2961i	0.421017	+	0.916067i
$825$		0			0
$826$	−12.7295	−	2.56887i	−0.442915	−	0.0893823i
$827$			8.10796i			0.281941i	0.990014	+	0.140971i	$0.0450224\pi$
$827$			8.10796i			0.281941i	−0.990014	+	0.140971i	$0.954978\pi$
$828$	18.7475	−	2.12123i	0.651522	−	0.0737178i
$829$	−36.5657	+	21.1112i	−1.26998	+	0.733223i	−0.974984	−	0.222276i	$-0.928651\pi$
$829$	−36.5657	+	21.1112i	−1.26998	+	0.733223i	−0.294995	+	0.955499i	$0.595318\pi$
$830$		0			0
$831$	−1.51407	+	2.62245i	−0.0525225	+	0.0909716i
$832$	−18.2639	+	6.41961i	−0.633185	+	0.222560i
$833$	3.56421	+	1.99802i	0.123492	+	0.0692273i
$834$	−21.0705	+	6.93893i	−0.729613	+	0.240275i
$835$		0			0
$836$	−18.4167	+	42.2656i	−0.636956	+	1.46179i
$837$	5.93481	+	10.2794i	0.205137	+	0.355308i
$838$	10.1686	−	48.7922i	0.351269	−	1.68550i
$839$	31.8404			1.09925			0.549627	−	0.835410i	$-0.314770\pi$
$839$	31.8404			1.09925			0.549627	+	0.835410i	$0.314770\pi$
$840$		0			0
$841$	−28.8104			−0.993461
$842$	4.52040	−	21.6903i	0.155783	−	0.747497i
$843$	−3.30745	−	5.72868i	−0.113915	−	0.197306i
$844$	7.37036	−	16.9147i	0.253698	−	0.582227i
$845$		0			0
$846$	34.0191	−	11.2031i	1.16960	−	0.385171i
$847$	6.86233	−	4.02014i	0.235792	−	0.138134i
$848$	3.66139	−	11.9095i	0.125733	−	0.408975i
$849$	3.24714	−	5.62422i	0.111442	−	0.193023i
$850$		0			0
$851$	42.2015	−	24.3650i	1.44665	−	0.835223i
$852$	17.8534	−	2.02007i	0.611649	−	0.0692063i
$853$		−	16.2023i		−	0.554755i	−0.960761	−	0.277378i	$-0.910535\pi$
$853$		−	16.2023i		−	0.554755i	0.960761	−	0.277378i	$-0.0894653\pi$
$854$	36.8390	−	12.3910i	1.26060	−	0.424011i
$855$		0			0
$856$	−16.2733	+	7.47905i	−0.556208	+	0.255629i
$857$	−35.4659	+	20.4762i	−1.21149	+	0.699455i	−0.963084	−	0.269201i	$-0.913240\pi$
$857$	−35.4659	+	20.4762i	−1.21149	+	0.699455i	−0.248407	+	0.968656i	$0.579907\pi$
$858$	8.60896	+	7.68981i	0.293905	+	0.262526i
$859$	6.02640	−	10.4380i	0.205618	−	0.356141i	−0.744711	−	0.667387i	$-0.767413\pi$
$859$	6.02640	−	10.4380i	0.205618	−	0.356141i	0.950329	+	0.311246i	$0.100746\pi$
$860$		0			0
$861$	−17.5278	+	0.111039i	−0.597345	+	0.00378421i
$862$	0.887107	+	2.69376i	0.0302150	+	0.0917499i
$863$	−0.494372	−	0.285426i	−0.0168286	−	0.00971602i	0.491562	−	0.870843i	$-0.336426\pi$
$863$	−0.494372	−	0.285426i	−0.0168286	−	0.00971602i	−0.508391	+	0.861127i	$0.669759\pi$
$864$	−22.6382	+	13.6770i	−0.770167	+	0.465300i
$865$		0			0
$866$	18.8257	+	3.92340i	0.639724	+	0.133323i
$867$	−15.0146			−0.509924
$868$	5.28797	−	12.3487i	0.179486	−	0.419142i
$869$	1.71798			0.0582784
$870$		0			0
$871$	−11.9120	−	20.6321i	−0.403622	−	0.699093i
$872$	52.8345	+	4.91703i	1.78920	+	0.166512i
$873$	−8.60232	−	4.96655i	−0.291144	−	0.168092i
$874$	−11.7493	−	35.6775i	−0.397426	−	1.20681i
$875$		0			0
$876$	10.4954	+	14.2068i	0.354605	+	0.480003i
$877$	9.47193	−	16.4059i	0.319844	−	0.553987i	−0.660611	−	0.750728i	$-0.729703\pi$
$877$	9.47193	−	16.4059i	0.319844	−	0.553987i	0.980455	+	0.196742i	$0.0630361\pi$
$878$	30.6388	+	27.3676i	1.03401	+	0.923613i
$879$	6.61794	−	3.82087i	0.223218	−	0.128875i
$880$		0			0
$881$			35.7695i			1.20511i	0.798079	+	0.602553i	$0.205850\pi$
$881$			35.7695i			1.20511i	−0.798079	+	0.602553i	$0.794150\pi$
$882$	−4.14957	+	21.2559i	−0.139723	+	0.715722i
$883$		−	25.4594i		−	0.856776i	−0.903595	−	0.428388i	$-0.859082\pi$
$883$		−	25.4594i		−	0.856776i	0.903595	−	0.428388i	$-0.140918\pi$
$884$	0.317624	+	2.80717i	0.0106828	+	0.0944155i
$885$		0			0
$886$	−13.7893	+	15.4375i	−0.463260	+	0.518633i
$887$	−5.30243	+	9.18408i	−0.178038	+	0.308371i	−0.941209	−	0.337826i	$-0.890308\pi$
$887$	−5.30243	+	9.18408i	−0.178038	+	0.308371i	0.763170	+	0.646197i	$0.223642\pi$
$888$	−16.6538	+	23.5063i	−0.558865	+	0.788821i
$889$	−6.42439	+	11.2920i	−0.215467	+	0.378721i
$890$		0			0
$891$	−7.61364	−	4.39574i	−0.255067	−	0.147263i
$892$	−44.4404	−	19.3644i	−1.48798	−	0.648368i
$893$	−35.6531	−	61.7530i	−1.19309	−	2.06648i
$894$	0.429482	−	2.06079i	0.0143640	−	0.0689231i
$895$		0			0
$896$	27.7452	+	11.2341i	0.926902	+	0.375305i
$897$	−9.40472			−0.314014
$898$	7.81053	−	37.4774i	0.260641	−	1.25064i
$899$	−0.552744	−	0.957381i	−0.0184350	−	0.0319304i
$900$		0			0
$901$	−1.57463	−	0.909116i	−0.0524587	−	0.0302870i
$902$	−36.9523	+	12.1691i	−1.23038	+	0.405187i
$903$	−13.8324	+	0.0876291i	−0.460315	+	0.00291611i
$904$	−6.83225	+	9.64350i	−0.227237	+	0.320738i
$905$		0			0
$906$	6.24611	−	6.99269i	0.207513	−	0.232317i
$907$	13.3054	−	7.68190i	0.441800	−	0.255073i	−0.262561	−	0.964915i	$-0.584567\pi$
$907$	13.3054	−	7.68190i	0.441800	−	0.255073i	0.704361	+	0.709842i	$0.251234\pi$
$908$	−2.39081	−	21.1301i	−0.0793418	−	0.701227i
$909$		−	20.0052i		−	0.663531i
$910$		0			0
$911$			22.0734i			0.731324i	0.930748	+	0.365662i	$0.119157\pi$
$911$			22.0734i			0.731324i	−0.930748	+	0.365662i	$0.880843\pi$
$912$	15.1191	+	16.2639i	0.500642	+	0.538552i
$913$	−8.41856	+	4.86046i	−0.278614	+	0.160858i
$914$	−8.02231	−	7.16579i	−0.265354	−	0.237023i
$915$		0			0
$916$	35.0729	+	47.4755i	1.15884	+	1.56864i
$917$	36.2392	−	21.2299i	1.19672	−	0.701074i
$918$	1.20729	+	3.66601i	0.0398464	+	0.120996i
$919$	−45.1598	−	26.0730i	−1.48968	−	0.860069i	−0.489753	−	0.871861i	$-0.662913\pi$
$919$	−45.1598	−	26.0730i	−1.48968	−	0.860069i	−0.999930	+	0.0117923i	$0.996246\pi$
$920$		0			0
$921$	4.69884	+	8.13863i	0.154832	+	0.268177i
$922$	−17.7147	−	3.69185i	−0.583401	−	0.121585i
$923$	24.1209			0.793949
$924$	−2.11898	−	17.7220i	−0.0697094	−	0.583011i
$925$		0			0
$926$	−38.6512	−	8.05516i	−1.27016	−	0.264709i
$927$	11.1922	+	19.3855i	0.367600	+	0.636702i
$928$	2.10843	−	1.27382i	0.0692126	−	0.0418152i
$929$	24.8707	+	14.3591i	0.815982	+	0.471107i	0.849029	−	0.528346i	$-0.177188\pi$
$929$	24.8707	+	14.3591i	0.815982	+	0.471107i	−0.0330469	+	0.999454i	$0.510521\pi$
$930$		0			0
$931$	43.1134	−	0.546272i	1.41298	−	0.0179033i
$932$	−45.1549	+	33.3585i	−1.47910	+	1.09270i
$933$	−3.57173	+	6.18641i	−0.116933	+	0.202534i
$934$	23.8480	+	21.3019i	0.780332	+	0.697018i
$935$		0			0
$936$	−13.6056	+	6.25302i	−0.444713	+	0.204386i
$937$			44.9045i			1.46697i	0.679707	+	0.733484i	$0.262107\pi$
$937$			44.9045i			1.46697i	−0.679707	+	0.733484i	$0.737893\pi$
$938$	−7.28691	+	36.1087i	−0.237926	+	1.17899i
$939$		−	13.0385i		−	0.425495i
$940$		0			0
$941$	15.3727	−	8.87541i	0.501134	−	0.289330i	−0.228048	−	0.973650i	$-0.573234\pi$
$941$	15.3727	−	8.87541i	0.501134	−	0.289330i	0.729182	+	0.684320i	$0.239901\pi$
$942$	−2.61736	+	2.93021i	−0.0852783	+	0.0954715i
$943$	15.8484	−	27.4503i	0.516096	−	0.893905i
$944$	−4.07957	+	13.2698i	−0.132779	+	0.431894i
$945$		0			0
$946$	−29.1618	+	9.60352i	−0.948130	+	0.312237i
$947$	32.1100	+	18.5387i	1.04344	+	0.602428i	0.920804	−	0.390025i	$-0.127533\pi$
$947$	32.1100	+	18.5387i	1.04344	+	0.602428i	0.122631	+	0.992452i	$0.460867\pi$
$948$	0.330541	−	0.758577i	0.0107355	−	0.0246374i
$949$	11.8562	+	20.5356i	0.384869	+	0.666613i
$950$		0			0
$951$	3.18787			0.103374
$952$	2.50259	−	3.58019i	0.0811094	−	0.116035i
$953$	28.5420			0.924567			0.462283	−	0.886732i	$-0.347030\pi$
$953$	28.5420			0.924567			0.462283	+	0.886732i	$0.347030\pi$
$954$	1.96619	−	9.43443i	0.0636579	−	0.305451i
$955$		0			0
$956$	10.8876	−	24.9866i	0.352131	−	0.808126i
$957$	−1.27203	−	0.734408i	−0.0411189	−	0.0237400i
$958$	29.5266	−	9.72368i	0.953962	−	0.314158i
$959$	−0.131440	−	20.7481i	−0.00424442	−	0.669991i
$960$		0			0
$961$	12.2776	−	21.2655i	0.396052	−	0.685983i
$962$	−25.7637	+	28.8431i	−0.830654	+	0.929940i
$963$	−11.9966	+	6.92626i	−0.386586	+	0.223196i
$964$	8.36146	−	0.946076i	0.269305	−	0.0304711i
$965$		0			0
$966$	10.9062	+	9.61830i	0.350902	+	0.309464i
$967$		−	5.33936i		−	0.171702i	−0.996308	−	0.0858510i	$-0.972639\pi$
$967$		−	5.33936i		−	0.171702i	0.996308	−	0.0858510i	$-0.0273609\pi$
$968$	−3.55056	−	7.72546i	−0.114119	−	0.248306i
$969$	2.80635	−	1.62025i	0.0901530	−	0.0520498i
$970$		0			0
$971$	5.49906	−	9.52465i	0.176473	−	0.305660i	−0.764197	−	0.644983i	$-0.776864\pi$
$971$	5.49906	−	9.52465i	0.176473	−	0.305660i	0.940670	+	0.339323i	$0.110198\pi$
$972$	−25.9697	+	19.1853i	−0.832978	+	0.615368i
$973$	40.0236	+	22.7708i	1.28310	+	0.729999i
$974$	−11.2283	−	34.0955i	−0.359778	−	1.09249i
$975$		0			0
$976$	−9.28381	−	40.5002i	−0.297168	−	1.29638i
$977$	−15.7434	−	27.2684i	−0.503676	−	0.872392i	−0.999991	−	0.00424979i	$-0.998647\pi$
$977$	−15.7434	−	27.2684i	−0.503676	−	0.872392i	0.496315	−	0.868142i	$-0.334686\pi$
$978$	−5.63771	−	1.17493i	−0.180274	−	0.0375703i
$979$	−36.9761			−1.18176
$980$		0			0
$981$	41.0424			1.31038
$982$	50.4825	+	10.5209i	1.61096	+	0.335735i
$983$	−17.2762	−	29.9232i	−0.551025	−	0.954402i	−0.998201	−	0.0599567i	$-0.980904\pi$
$983$	−17.2762	−	29.9232i	−0.551025	−	0.954402i	0.447176	−	0.894446i	$-0.352430\pi$
$984$	−1.73638	+	18.6577i	−0.0553537	+	0.594787i
$985$		0			0
$986$	−0.112442	−	0.341438i	−0.00358088	−	0.0108736i
$987$	23.9935	+	13.6507i	0.763722	+	0.434507i
$988$	17.7136	+	23.9776i	0.563545	+	0.762829i
$989$	12.5072	−	21.6630i	0.397704	−	0.688844i
$990$		0			0
$991$	−47.8668	+	27.6359i	−1.52054	+	0.877884i	−0.520833	+	0.853659i	$0.674378\pi$
$991$	−47.8668	+	27.6359i	−1.52054	+	0.877884i	−0.999707	+	0.0242247i	$0.992288\pi$
$992$	−12.5770	−	6.93186i	−0.399321	−	0.220087i
$993$			21.2068i			0.672978i
$994$	−27.9719	−	24.6687i	−0.887216	−	0.782443i
$995$		0			0
$996$	0.526405	+	4.65239i	0.0166798	+	0.147417i
$997$	−13.2344	+	7.64087i	−0.419137	+	0.241989i	−0.694708	−	0.719292i	$-0.744466\pi$
$997$	−13.2344	+	7.64087i	−0.419137	+	0.241989i	0.275571	+	0.961281i	$0.411133\pi$
$998$	−11.1912	+	12.5289i	−0.354252	+	0.396595i
$999$	−26.4187	+	45.7586i	−0.835851	+	1.44774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.p.c.551.8		32
4.3	odd	2	inner	700.2.p.c.551.4		32
5.2	odd	4		700.2.t.c.299.1		32
5.3	odd	4		700.2.t.d.299.16		32
5.4	even	2		140.2.o.a.131.9	yes	32
7.3	odd	6	inner	700.2.p.c.451.4		32
20.3	even	4		700.2.t.d.299.11		32
20.7	even	4		700.2.t.c.299.6		32
20.19	odd	2		140.2.o.a.131.13	yes	32
28.3	even	6	inner	700.2.p.c.451.8		32
35.3	even	12		700.2.t.c.199.6		32
35.4	even	6		980.2.o.f.31.13		32
35.9	even	6		980.2.g.a.391.8		32
35.17	even	12		700.2.t.d.199.11		32
35.19	odd	6		980.2.g.a.391.7		32
35.24	odd	6		140.2.o.a.31.13	yes	32
35.34	odd	2		980.2.o.f.411.9		32
140.3	odd	12		700.2.t.c.199.1		32
140.19	even	6		980.2.g.a.391.6		32
140.39	odd	6		980.2.o.f.31.9		32
140.59	even	6		140.2.o.a.31.9	✓	32
140.79	odd	6		980.2.g.a.391.5		32
140.87	odd	12		700.2.t.d.199.16		32
140.139	even	2		980.2.o.f.411.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.9	✓	32	140.59	even	6
140.2.o.a.31.13	yes	32	35.24	odd	6
140.2.o.a.131.9	yes	32	5.4	even	2
140.2.o.a.131.13	yes	32	20.19	odd	2
700.2.p.c.451.4		32	7.3	odd	6	inner
700.2.p.c.451.8		32	28.3	even	6	inner
700.2.p.c.551.4		32	4.3	odd	2	inner
700.2.p.c.551.8		32	1.1	even	1	trivial
700.2.t.c.199.1		32	140.3	odd	12
700.2.t.c.199.6		32	35.3	even	12
700.2.t.c.299.1		32	5.2	odd	4
700.2.t.c.299.6		32	20.7	even	4
700.2.t.d.199.11		32	35.17	even	12
700.2.t.d.199.16		32	140.87	odd	12
700.2.t.d.299.11		32	20.3	even	4
700.2.t.d.299.16		32	5.3	odd	4
980.2.g.a.391.5		32	140.79	odd	6
980.2.g.a.391.6		32	140.19	even	6
980.2.g.a.391.7		32	35.19	odd	6
980.2.g.a.391.8		32	35.9	even	6
980.2.o.f.31.9		32	140.39	odd	6
980.2.o.f.31.13		32	35.4	even	6
980.2.o.f.411.9		32	35.34	odd	2
980.2.o.f.411.13		32	140.139	even	2

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.288532 + 1.38447i) q^{2} +(0.450639 + 0.780530i) q^{3} +(-1.83350 - 0.798926i) q^{4} +(-1.21064 + 0.398687i) q^{6} +(2.29962 + 1.30833i) q^{7} +(1.63511 - 2.30790i) q^{8} +(1.09385 - 1.89460i) q^{9} +(3.24107 - 1.87123i) q^{11} +(-0.202661 - 1.79113i) q^{12} -2.41990i q^{13} +(-2.47486 + 2.80626i) q^{14} +(2.72344 + 2.92966i) q^{16} +(0.505515 - 0.291859i) q^{17} +(2.30740 + 2.06105i) q^{18} +(3.07977 - 5.33433i) q^{19} +(0.0151060 + 2.38451i) q^{21} +(1.65551 + 5.02706i) q^{22} +(-3.73439 - 2.15605i) q^{23} +(2.53823 + 0.236220i) q^{24} +(3.35028 + 0.698219i) q^{26} +4.67556 q^{27} +(-3.17109 - 4.23606i) q^{28} -0.435463 q^{29} +(1.26933 + 2.19854i) q^{31} +(-4.84181 + 2.92521i) q^{32} +(2.92110 + 1.68650i) q^{33} +(0.258212 + 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} +(-5.65039 + 9.78676i) q^{37} +(6.49659 + 5.80297i) q^{38} +(1.88881 - 1.09050i) q^{39} +7.35068i q^{41} +(-3.30563 - 0.667093i) q^{42} +5.80096i q^{43} +(-7.43747 + 0.841528i) q^{44} +(4.06247 - 4.54805i) q^{46} +(5.78826 - 10.0256i) q^{47} +(-1.05940 + 3.44594i) q^{48} +(3.57652 + 6.01735i) q^{49} +(0.455610 + 0.263046i) q^{51} +(-1.93332 + 4.43689i) q^{52} +(-1.55746 - 2.69759i) q^{53} +(-1.34905 + 6.47316i) q^{54} +(6.77964 - 3.16804i) q^{56} +5.55147 q^{57} +(0.125645 - 0.602884i) q^{58} +(1.73534 + 3.00569i) q^{59} +(-8.99597 - 5.19383i) q^{61} +(-3.41004 + 1.12299i) q^{62} +(4.99421 - 2.92575i) q^{63} +(-2.65284 - 7.54735i) q^{64} +(-3.17773 + 3.55756i) q^{66} +(8.52602 - 4.92250i) q^{67} +(-1.16004 + 0.131255i) q^{68} -3.88640i q^{69} +9.96771i q^{71} +(-2.58400 - 5.62238i) q^{72} +(-8.48612 + 4.89946i) q^{73} +(-11.9191 - 10.6466i) q^{74} +(-9.90849 + 7.31997i) q^{76} +(9.90142 - 0.0627260i) q^{77} +(0.964785 + 2.92964i) q^{78} +(0.397549 + 0.229525i) q^{79} +(-1.17456 - 2.03439i) q^{81} +(-10.1768 - 2.12091i) q^{82} -2.59747 q^{83} +(1.87735 - 4.38406i) q^{84} +(-8.03123 - 1.67376i) q^{86} +(-0.196236 - 0.339892i) q^{87} +(0.980878 - 10.5397i) q^{88} +(-8.55647 - 4.94008i) q^{89} +(3.16604 - 5.56486i) q^{91} +(5.12447 + 6.93662i) q^{92} +(-1.14402 + 1.98149i) q^{93} +(12.2100 + 10.9064i) q^{94} +(-4.46512 - 2.46097i) q^{96} -4.54044i q^{97} +(-9.36276 + 3.21538i) q^{98} -8.18738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 16 q^{9} + 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} + 8 q^{22} + 36 q^{24} + 30 q^{26} - 2 q^{28} - 40 q^{29} - 2 q^{32} + 60 q^{36} - 8 q^{37} + 60 q^{38} + 62 q^{42}+ \cdots - 78 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 16 * q^9 + 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 + 8 * q^22 + 36 * q^24 + 30 * q^26 - 2 * q^28 - 40 * q^29 - 2 * q^32 + 60 * q^36 - 8 * q^37 + 60 * q^38 + 62 * q^42 - 18 * q^44 + 2 * q^46 - 16 * q^49 + 36 * q^52 + 8 * q^53 + 12 * q^54 - 4 * q^56 - 48 * q^57 - 2 * q^58 + 24 * q^61 + 4 * q^64 + 24 * q^66 - 60 * q^68 - 4 * q^72 + 72 * q^73 + 38 * q^74 + 40 * q^77 - 120 * q^78 - 36 * q^81 - 42 * q^82 - 20 * q^84 + 28 * q^86 - 4 * q^88 - 60 * q^89 + 4 * q^92 + 8 * q^93 + 18 * q^94 - 60 * q^96 - 78 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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