LMFDB - Embedded newform 726.2.i.b.265.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(67,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 20])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.i (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [50,5] 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:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			265.1
Character	$\chi$	$=$	726.265
Dual form			726.2.i.b.463.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.415415 + 0.909632i) q^{2} -1.00000 q^{3} +(-0.654861 - 0.755750i) q^{4} +(-2.63232 - 0.772918i) q^{5} +(0.415415 - 0.909632i) q^{6} +(0.388005 + 2.69864i) q^{7} +(0.959493 - 0.281733i) q^{8} +1.00000 q^{9} +(1.79657 - 2.07336i) q^{10} +(0.854530 + 3.20465i) q^{11} +(0.654861 + 0.755750i) q^{12} +(-2.20171 - 2.54091i) q^{13} +(-2.61595 - 0.768112i) q^{14} +(2.63232 + 0.772918i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-5.40901 - 3.47616i) q^{17} +(-0.415415 + 0.909632i) q^{18} +(1.58244 - 1.01697i) q^{19} +(1.13967 + 2.49553i) q^{20} +(-0.388005 - 2.69864i) q^{21} +(-3.27004 - 0.553951i) q^{22} +(-0.419470 + 2.91748i) q^{23} +(-0.959493 + 0.281733i) q^{24} +(2.12542 + 1.36593i) q^{25} +(3.22591 - 0.947214i) q^{26} -1.00000 q^{27} +(1.78540 - 2.06047i) q^{28} +(3.91549 - 2.51633i) q^{29} +(-1.79657 + 2.07336i) q^{30} +(5.39910 - 6.23090i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.854530 - 3.20465i) q^{33} +(5.40901 - 3.47616i) q^{34} +(1.06447 - 7.40356i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(5.39749 - 6.22903i) q^{37} +(0.267702 + 1.86191i) q^{38} +(2.20171 + 2.54091i) q^{39} -2.74345 q^{40} +(-0.722174 + 1.58134i) q^{41} +(2.61595 + 0.768112i) q^{42} +(6.73652 - 1.97802i) q^{43} +(1.86231 - 2.74441i) q^{44} +(-2.63232 - 0.772918i) q^{45} +(-2.47958 - 1.59353i) q^{46} +(-3.35158 - 7.33893i) q^{47} +(0.142315 - 0.989821i) q^{48} +(-0.415640 + 0.122043i) q^{49} +(-2.12542 + 1.36593i) q^{50} +(5.40901 + 3.47616i) q^{51} +(-0.478477 + 3.32788i) q^{52} +(-1.76572 - 12.2808i) q^{53} +(0.415415 - 0.909632i) q^{54} +(0.227536 - 9.09613i) q^{55} +(1.13258 + 2.48001i) q^{56} +(-1.58244 + 1.01697i) q^{57} +(0.662384 + 4.60698i) q^{58} +(0.0574855 + 0.125876i) q^{59} +(-1.13967 - 2.49553i) q^{60} +(2.73198 + 5.98220i) q^{61} +(3.42496 + 7.49961i) q^{62} +(0.388005 + 2.69864i) q^{63} +(0.841254 - 0.540641i) q^{64} +(3.83168 + 8.39021i) q^{65} +(3.27004 + 0.553951i) q^{66} +(1.16385 - 2.54849i) q^{67} +(0.915043 + 6.36426i) q^{68} +(0.419470 - 2.91748i) q^{69} +(6.29232 + 4.04383i) q^{70} +(-8.72300 + 5.60593i) q^{71} +(0.959493 - 0.281733i) q^{72} +(-0.249675 + 1.73653i) q^{73} +(3.42393 + 7.49736i) q^{74} +(-2.12542 - 1.36593i) q^{75} +(-1.80486 - 0.529954i) q^{76} +(-8.31662 + 3.54949i) q^{77} +(-3.22591 + 0.947214i) q^{78} +(-2.10226 - 0.617280i) q^{79} +(1.13967 - 2.49553i) q^{80} +1.00000 q^{81} +(-1.13844 - 1.31382i) q^{82} +(-2.03572 - 14.1588i) q^{83} +(-1.78540 + 2.06047i) q^{84} +(11.5514 + 13.3311i) q^{85} +(-0.999181 + 6.94945i) q^{86} +(-3.91549 + 2.51633i) q^{87} +(1.72277 + 2.83409i) q^{88} +(-10.3181 - 6.63107i) q^{89} +(1.79657 - 2.07336i) q^{90} +(6.00271 - 6.92750i) q^{91} +(2.47958 - 1.59353i) q^{92} +(-5.39910 + 6.23090i) q^{93} +8.06802 q^{94} +(-4.95153 + 1.45390i) q^{95} +(0.841254 + 0.540641i) q^{96} +(-10.2102 + 2.99800i) q^{97} +(0.0616489 - 0.428778i) q^{98} +(0.854530 + 3.20465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{2} - 50 q^{3} - 5 q^{4} - 5 q^{6} - q^{7} + 5 q^{8} + 50 q^{9} - 11 q^{11} + 5 q^{12} - 21 q^{13} - 10 q^{14} - 5 q^{16} - 12 q^{17} + 5 q^{18} + q^{21} - 11 q^{22} + 22 q^{23} - 5 q^{24}+ \cdots - 11 q^{99}+O(q^{100}) $ 50 * q + 5 * q^2 - 50 * q^3 - 5 * q^4 - 5 * q^6 - q^7 + 5 * q^8 + 50 * q^9 - 11 * q^11 + 5 * q^12 - 21 * q^13 - 10 * q^14 - 5 * q^16 - 12 * q^17 + 5 * q^18 + q^21 - 11 * q^22 + 22 * q^23 - 5 * q^24 - 3 * q^25 - q^26 - 50 * q^27 - q^28 + 36 * q^31 + 5 * q^32 + 11 * q^33 + 12 * q^34 - 11 * q^35 - 5 * q^36 - 19 * q^37 + 22 * q^38 + 21 * q^39 + 23 * q^41 + 10 * q^42 - 44 * q^43 + 11 * q^44 + 11 * q^46 + 20 * q^47 + 5 * q^48 - 24 * q^49 + 3 * q^50 + 12 * q^51 + q^52 - 11 * q^53 - 5 * q^54 - 33 * q^55 + 12 * q^56 + q^59 + 38 * q^61 - 14 * q^62 - q^63 - 5 * q^64 + 26 * q^65 + 11 * q^66 - 64 * q^67 - q^68 - 22 * q^69 + 24 * q^71 + 5 * q^72 + 35 * q^73 - 14 * q^74 + 3 * q^75 + 22 * q^76 - 77 * q^77 + q^78 - 32 * q^79 + 50 * q^81 - 12 * q^82 - 8 * q^83 + q^84 - 5 * q^85 - 11 * q^88 - 12 * q^89 - 11 * q^92 - 36 * q^93 + 46 * q^94 + 57 * q^95 - 5 * q^96 + 33 * q^97 - 42 * q^98 - 11 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$

Coefficient data

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

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

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

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−2.63232	−	0.772918i	−1.17721	−	0.345659i	−0.366111	−	0.930571i	$-0.619311\pi$
$5$	−2.63232	−	0.772918i	−1.17721	−	0.345659i	−0.811097	+	0.584912i	$0.801129\pi$
$6$	0.415415	−	0.909632i	0.169592	−	0.371356i
$7$	0.388005	+	2.69864i	0.146652	+	1.01999i	0.921649	+	0.388024i	$0.126842\pi$
$7$	0.388005	+	2.69864i	0.146652	+	1.01999i	−0.774997	+	0.631965i	$0.782249\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	1.00000			0.333333
$10$	1.79657	−	2.07336i	0.568127	−	0.655653i
$11$	0.854530	+	3.20465i	0.257651	+	0.966238i
$11$	0.854530	+	3.20465i	0.257651	+	0.966238i
$12$	0.654861	+	0.755750i	0.189042	+	0.218166i
$13$	−2.20171	−	2.54091i	−0.610644	−	0.704721i	0.363258	−	0.931688i	$-0.381664\pi$
$13$	−2.20171	−	2.54091i	−0.610644	−	0.704721i	−0.973902	+	0.226968i	$0.927119\pi$
$14$	−2.61595	−	0.768112i	−0.699142	−	0.205287i
$15$	2.63232	+	0.772918i	0.679661	+	0.199567i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−5.40901	−	3.47616i	−1.31188	−	0.843093i	−0.317426	−	0.948283i	$-0.602819\pi$
$17$	−5.40901	−	3.47616i	−1.31188	−	0.843093i	−0.994452	+	0.105190i	$0.966455\pi$
$18$	−0.415415	+	0.909632i	−0.0979143	+	0.214402i
$19$	1.58244	−	1.01697i	0.363037	−	0.233310i	−0.346387	−	0.938092i	$-0.612591\pi$
$19$	1.58244	−	1.01697i	0.363037	−	0.233310i	0.709424	+	0.704782i	$0.248955\pi$
$20$	1.13967	+	2.49553i	0.254838	+	0.558017i
$21$	−0.388005	−	2.69864i	−0.0846697	−	0.588891i
$22$	−3.27004	−	0.553951i	−0.697174	−	0.118103i
$23$	−0.419470	+	2.91748i	−0.0874656	+	0.608337i	0.898195	+	0.439597i	$0.144879\pi$
$23$	−0.419470	+	2.91748i	−0.0874656	+	0.608337i	−0.985661	+	0.168740i	$0.946030\pi$
$24$	−0.959493	+	0.281733i	−0.195856	+	0.0575084i
$25$	2.12542	+	1.36593i	0.425084	+	0.273185i
$26$	3.22591	−	0.947214i	0.632654	−	0.185764i
$27$	−1.00000			−0.192450
$28$	1.78540	−	2.06047i	0.337410	−	0.389391i
$29$	3.91549	−	2.51633i	0.727088	−	0.467271i	−0.124008	−	0.992281i	$-0.539575\pi$
$29$	3.91549	−	2.51633i	0.727088	−	0.467271i	0.851096	+	0.525010i	$0.175938\pi$
$30$	−1.79657	+	2.07336i	−0.328008	+	0.378542i
$31$	5.39910	−	6.23090i	0.969708	−	1.11910i	−0.0231419	−	0.999732i	$-0.507367\pi$
$31$	5.39910	−	6.23090i	0.969708	−	1.11910i	0.992850	−	0.119370i	$-0.0380876\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	−0.854530	−	3.20465i	−0.148755	−	0.557858i
$34$	5.40901	−	3.47616i	0.927638	−	0.596157i
$35$	1.06447	−	7.40356i	0.179929	−	1.25143i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	5.39749	−	6.22903i	0.887342	−	1.02405i	−0.112197	−	0.993686i	$-0.535789\pi$
$37$	5.39749	−	6.22903i	0.887342	−	1.02405i	0.999539	−	0.0303608i	$-0.00966564\pi$
$38$	0.267702	+	1.86191i	0.0434270	+	0.302041i
$39$	2.20171	+	2.54091i	0.352556	+	0.406871i
$40$	−2.74345			−0.433777
$41$	−0.722174	+	1.58134i	−0.112785	+	0.246964i	−0.957604	−	0.288088i	$-0.906981\pi$
$41$	−0.722174	+	1.58134i	−0.112785	+	0.246964i	0.844819	+	0.535051i	$0.179708\pi$
$42$	2.61595	+	0.768112i	0.403650	+	0.118522i
$43$	6.73652	−	1.97802i	1.02731	−	0.301645i	0.275693	−	0.961246i	$-0.411093\pi$
$43$	6.73652	−	1.97802i	1.02731	−	0.301645i	0.751616	+	0.659600i	$0.229274\pi$
$44$	1.86231	−	2.74441i	0.280754	−	0.413735i
$45$	−2.63232	−	0.772918i	−0.392403	−	0.115220i
$46$	−2.47958	−	1.59353i	−0.365594	−	0.234953i
$47$	−3.35158	−	7.33893i	−0.488878	−	1.07049i	−0.979926	−	0.199360i	$-0.936114\pi$
$47$	−3.35158	−	7.33893i	−0.488878	−	1.07049i	0.491049	−	0.871132i	$-0.336614\pi$
$48$	0.142315	−	0.989821i	0.0205414	−	0.142868i
$49$	−0.415640	+	0.122043i	−0.0593771	+	0.0174347i
$50$	−2.12542	+	1.36593i	−0.300580	+	0.193171i
$51$	5.40901	+	3.47616i	0.757413	+	0.486760i
$52$	−0.478477	+	3.32788i	−0.0663528	+	0.461494i
$53$	−1.76572	−	12.2808i	−0.242540	−	1.68690i	−0.639283	−	0.768971i	$-0.720769\pi$
$53$	−1.76572	−	12.2808i	−0.242540	−	1.68690i	0.396743	−	0.917930i	$-0.370140\pi$
$54$	0.415415	−	0.909632i	0.0565308	−	0.123785i
$55$	0.227536	−	9.09613i	0.0306810	−	1.22652i
$56$	1.13258	+	2.48001i	0.151348	+	0.331405i
$57$	−1.58244	+	1.01697i	−0.209600	+	0.134702i
$58$	0.662384	+	4.60698i	0.0869752	+	0.604926i
$59$	0.0574855	+	0.125876i	0.00748398	+	0.0163876i	0.913337	−	0.407204i	$-0.133496\pi$
$59$	0.0574855	+	0.125876i	0.00748398	+	0.0163876i	−0.905853	+	0.423592i	$0.860769\pi$
$60$	−1.13967	−	2.49553i	−0.147131	−	0.322171i
$61$	2.73198	+	5.98220i	0.349794	+	0.765942i	0.999981	+	0.00616764i	$0.00196323\pi$
$61$	2.73198	+	5.98220i	0.349794	+	0.765942i	−0.650187	+	0.759774i	$0.725309\pi$
$62$	3.42496	+	7.49961i	0.434970	+	0.952451i
$63$	0.388005	+	2.69864i	0.0488841	+	0.339996i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	3.83168	+	8.39021i	0.475262	+	1.04068i
$66$	3.27004	+	0.553951i	0.402514	+	0.0681867i
$67$	1.16385	−	2.54849i	0.142187	−	0.311347i	−0.825118	−	0.564960i	$-0.808892\pi$
$67$	1.16385	−	2.54849i	0.142187	−	0.311347i	0.967306	+	0.253613i	$0.0816189\pi$
$68$	0.915043	+	6.36426i	0.110965	+	0.771780i
$69$	0.419470	−	2.91748i	0.0504983	−	0.351223i
$70$	6.29232	+	4.04383i	0.752076	+	0.483330i
$71$	−8.72300	+	5.60593i	−1.03523	+	0.665302i	−0.943803	−	0.330510i	$-0.892779\pi$
$71$	−8.72300	+	5.60593i	−1.03523	+	0.665302i	−0.0914275	+	0.995812i	$0.529143\pi$
$72$	0.959493	−	0.281733i	0.113077	−	0.0332025i
$73$	−0.249675	+	1.73653i	−0.0292223	+	0.203245i	−0.999202	−	0.0399402i	$-0.987283\pi$
$73$	−0.249675	+	1.73653i	−0.0292223	+	0.203245i	0.969980	+	0.243185i	$0.0781924\pi$
$74$	3.42393	+	7.49736i	0.398024	+	0.871551i
$75$	−2.12542	−	1.36593i	−0.245423	−	0.157723i
$76$	−1.80486	−	0.529954i	−0.207031	−	0.0607899i
$77$	−8.31662	+	3.54949i	−0.947767	+	0.404502i
$78$	−3.22591	+	0.947214i	−0.365263	+	0.107251i
$79$	−2.10226	−	0.617280i	−0.236523	−	0.0694494i	0.161323	−	0.986902i	$-0.448424\pi$
$79$	−2.10226	−	0.617280i	−0.236523	−	0.0694494i	−0.397846	+	0.917452i	$0.630242\pi$
$80$	1.13967	−	2.49553i	0.127419	−	0.279008i
$81$	1.00000			0.111111
$82$	−1.13844	−	1.31382i	−0.125719	−	0.145088i
$83$	−2.03572	−	14.1588i	−0.223450	−	1.55413i	−0.724847	−	0.688910i	$-0.758090\pi$
$83$	−2.03572	−	14.1588i	−0.223450	−	1.55413i	0.501397	−	0.865217i	$-0.332819\pi$
$84$	−1.78540	+	2.06047i	−0.194804	+	0.224815i
$85$	11.5514	+	13.3311i	1.25293	+	1.44596i
$86$	−0.999181	+	6.94945i	−0.107744	+	0.749379i
$87$	−3.91549	+	2.51633i	−0.419785	+	0.269779i
$88$	1.72277	+	2.83409i	0.183648	+	0.302115i
$89$	−10.3181	−	6.63107i	−1.09372	−	0.702892i	−0.136035	−	0.990704i	$-0.543436\pi$
$89$	−10.3181	−	6.63107i	−1.09372	−	0.702892i	−0.957687	+	0.287812i	$0.907072\pi$
$90$	1.79657	−	2.07336i	0.189376	−	0.218551i
$91$	6.00271	−	6.92750i	0.629255	−	0.726199i
$92$	2.47958	−	1.59353i	0.258514	−	0.166137i
$93$	−5.39910	+	6.23090i	−0.559861	+	0.646114i
$94$	8.06802			0.832153
$95$	−4.95153	+	1.45390i	−0.508016	+	0.149167i
$96$	0.841254	+	0.540641i	0.0858601	+	0.0551789i
$97$	−10.2102	+	2.99800i	−1.03669	+	0.304401i	−0.755429	−	0.655230i	$-0.772572\pi$
$97$	−10.2102	+	2.99800i	−1.03669	+	0.304401i	−0.281264	+	0.959631i	$0.590754\pi$
$98$	0.0616489	−	0.428778i	0.00622748	−	0.0433131i
$99$	0.854530	+	3.20465i	0.0858835	+	0.322079i
$100$	−0.359558	−	2.50078i	−0.0359558	−	0.250078i
$101$	2.44429	+	5.35226i	0.243216	+	0.532569i	0.991391	−	0.130932i	$-0.0417970\pi$
$101$	2.44429	+	5.35226i	0.243216	+	0.532569i	−0.748175	+	0.663501i	$0.769070\pi$
$102$	−5.40901	+	3.47616i	−0.535572	+	0.344191i
$103$	−0.836508	+	1.83170i	−0.0824236	+	0.180482i	−0.946356	−	0.323125i	$-0.895267\pi$
$103$	−0.836508	+	1.83170i	−0.0824236	+	0.180482i	0.863933	+	0.503607i	$0.167994\pi$
$104$	−2.82838	−	1.81769i	−0.277345	−	0.178239i
$105$	−1.06447	+	7.40356i	−0.103882	+	0.722514i
$106$	11.9045	+	3.49549i	1.15627	+	0.339512i
$107$	−1.14905	−	0.337390i	−0.111082	−	0.0326167i	0.225719	−	0.974192i	$-0.427527\pi$
$107$	−1.14905	−	0.337390i	−0.111082	−	0.0326167i	−0.336801	+	0.941576i	$0.609345\pi$
$108$	0.654861	+	0.755750i	0.0630140	+	0.0727220i
$109$	4.61647	+	5.32769i	0.442178	+	0.510301i	0.932465	−	0.361260i	$-0.117653\pi$
$109$	4.61647	+	5.32769i	0.442178	+	0.510301i	−0.490287	+	0.871561i	$0.663108\pi$
$110$	8.17961	+	3.98564i	0.779895	+	0.380016i
$111$	−5.39749	+	6.22903i	−0.512307	+	0.591234i
$112$	−2.72639			−0.257619
$113$	10.3721	−	3.04552i	0.975723	−	0.286498i	0.245265	−	0.969456i	$-0.421125\pi$
$113$	10.3721	−	3.04552i	0.975723	−	0.286498i	0.730458	+	0.682958i	$0.239307\pi$
$114$	−0.267702	−	1.86191i	−0.0250726	−	0.174384i
$115$	3.35915	−	7.35552i	0.313243	−	0.685905i
$116$	−4.46582	−	1.31128i	−0.414641	−	0.121750i
$117$	−2.20171	−	2.54091i	−0.203548	−	0.234907i
$118$	−0.138381			−0.0127390
$119$	7.28217	−	15.9457i	0.667556	−	1.46174i
$120$	2.74345			0.250441
$121$	−9.53956	+	5.47694i	−0.867232	+	0.497904i
$122$	−6.57650			−0.595409
$123$	0.722174	−	1.58134i	0.0651162	−	0.142585i
$124$	−8.24466			−0.740392
$125$	4.44384	+	5.12846i	0.397469	+	0.458704i
$126$	−2.61595	−	0.768112i	−0.233047	−	0.0684289i
$127$	6.42462	−	14.0679i	0.570093	−	1.24833i	−0.376656	−	0.926353i	$-0.622926\pi$
$127$	6.42462	−	14.0679i	0.570093	−	1.24833i	0.946748	−	0.321975i	$-0.104347\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	−6.73652	+	1.97802i	−0.593118	+	0.174155i
$130$	−9.22374			−0.808976
$131$	−9.33675	+	10.7752i	−0.815755	+	0.941432i	−0.999134	−	0.0416106i	$-0.986751\pi$
$131$	−9.33675	+	10.7752i	−0.815755	+	0.941432i	0.183379	+	0.983042i	$0.441297\pi$
$132$	−1.86231	+	2.74441i	−0.162094	+	0.238870i
$133$	3.35844	+	3.87585i	0.291214	+	0.336079i
$134$	1.83470	+	2.11736i	0.158494	+	0.182912i
$135$	2.63232	+	0.772918i	0.226554	+	0.0665222i
$136$	−6.16926	−	1.81146i	−0.529010	−	0.155331i
$137$	−0.564835	+	3.92851i	−0.0482571	+	0.335636i	0.951363	+	0.308072i	$0.0996839\pi$
$137$	−0.564835	+	3.92851i	−0.0482571	+	0.335636i	−0.999620	+	0.0275633i	$0.991225\pi$
$138$	2.47958	+	1.59353i	0.211076	+	0.135650i
$139$	6.29234	−	13.7783i	0.533710	−	1.16866i	−0.430274	−	0.902698i	$-0.641583\pi$
$139$	6.29234	−	13.7783i	0.533710	−	1.16866i	0.963983	−	0.265963i	$-0.0856897\pi$
$140$	−6.29232	+	4.04383i	−0.531798	+	0.341766i
$141$	3.35158	+	7.33893i	0.282254	+	0.618049i
$142$	−1.47567	−	10.2635i	−0.123835	−	0.861295i
$143$	6.26129	−	9.22699i	0.523595	−	0.771599i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	−12.2517	+	3.59743i	−1.01745	+	0.298751i
$146$	−1.47588	−	0.948492i	−0.122145	−	0.0784978i
$147$	0.415640	−	0.122043i	0.0342814	−	0.0100659i
$148$	−8.24219			−0.677504
$149$	11.1953	−	12.9200i	0.917151	−	1.05845i	−0.0809422	−	0.996719i	$-0.525793\pi$
$149$	11.1953	−	12.9200i	0.917151	−	1.05845i	0.998093	−	0.0617295i	$-0.0196616\pi$
$150$	2.12542	−	1.36593i	0.173540	−	0.111527i
$151$	−12.6597	+	14.6100i	−1.03023	+	1.18895i	−0.0484685	+	0.998825i	$0.515434\pi$
$151$	−12.6597	+	14.6100i	−1.03023	+	1.18895i	−0.981760	+	0.190123i	$0.939111\pi$
$152$	1.23183	−	1.42161i	0.0999145	−	0.115307i
$153$	−5.40901	−	3.47616i	−0.437293	−	0.281031i
$154$	0.226121	−	9.03958i	0.0182214	−	0.728430i
$155$	−19.0281	+	12.2286i	−1.52838	+	0.982228i
$156$	0.478477	−	3.32788i	0.0383088	−	0.266444i
$157$	0.251776	+	0.290564i	0.0200939	+	0.0231896i	0.765708	−	0.643189i	$-0.222389\pi$
$157$	0.251776	+	0.290564i	0.0200939	+	0.0231896i	−0.745614	+	0.666378i	$0.767844\pi$
$158$	1.43481	−	1.65586i	0.114147	−	0.131733i
$159$	1.76572	+	12.2808i	0.140030	+	0.973933i
$160$	1.79657	+	2.07336i	0.142032	+	0.163913i
$161$	−8.03598			−0.633324
$162$	−0.415415	+	0.909632i	−0.0326381	+	0.0714674i
$163$	−6.41806	−	1.88451i	−0.502701	−	0.147606i	0.0205435	−	0.999789i	$-0.493460\pi$
$163$	−6.41806	−	1.88451i	−0.502701	−	0.147606i	−0.523244	+	0.852183i	$0.675279\pi$
$164$	1.66802	−	0.489775i	0.130250	−	0.0382450i
$165$	−0.227536	+	9.09613i	−0.0177137	+	0.708133i
$166$	13.7249	+	4.03001i	1.06526	+	0.312789i
$167$	−0.819212	−	0.526476i	−0.0633925	−	0.0407399i	0.508561	−	0.861026i	$-0.330178\pi$
$167$	−0.819212	−	0.526476i	−0.0633925	−	0.0407399i	−0.571953	+	0.820286i	$0.693814\pi$
$168$	−1.13258	−	2.48001i	−0.0873806	−	0.191337i
$169$	0.241405	−	1.67901i	0.0185696	−	0.129154i
$170$	−16.9250	+	4.96964i	−1.29809	+	0.381154i
$171$	1.58244	−	1.01697i	0.121012	−	0.0777700i
$172$	−5.90637	−	3.79579i	−0.450357	−	0.289427i
$173$	−0.743099	+	5.16837i	−0.0564968	+	0.392944i	0.941878	+	0.335955i	$0.109059\pi$
$173$	−0.743099	+	5.16837i	−0.0564968	+	0.392944i	−0.998375	+	0.0569887i	$0.981850\pi$
$174$	−0.662384	−	4.60698i	−0.0502152	−	0.349254i
$175$	−2.86146	+	6.26573i	−0.216306	+	0.473644i
$176$	−3.29364	+	0.389763i	−0.248268	+	0.0293795i
$177$	−0.0574855	−	0.125876i	−0.00432088	−	0.00946140i
$178$	10.3181	−	6.63107i	0.773378	−	0.497020i
$179$	0.876978	+	6.09952i	0.0655484	+	0.455899i	0.995990	+	0.0894601i	$0.0285142\pi$
$179$	0.876978	+	6.09952i	0.0655484	+	0.455899i	−0.930442	+	0.366439i	$0.880577\pi$
$180$	1.13967	+	2.49553i	0.0849459	+	0.186006i
$181$	−10.3105	−	22.5768i	−0.766371	−	1.67812i	−0.734483	−	0.678627i	$-0.762575\pi$
$181$	−10.3105	−	22.5768i	−0.766371	−	1.67812i	−0.0318882	−	0.999491i	$-0.510152\pi$
$182$	3.80786	+	8.33804i	0.282257	+	0.618057i
$183$	−2.73198	−	5.98220i	−0.201954	−	0.442217i
$184$	0.419470	+	2.91748i	0.0309238	+	0.215080i
$185$	−19.0224	+	12.2250i	−1.39856	+	0.898798i
$186$	−3.42496	−	7.49961i	−0.251130	−	0.549898i
$187$	6.51771	−	20.3045i	0.476622	−	1.48481i
$188$	−3.35158	+	7.33893i	−0.244439	+	0.535246i
$189$	−0.388005	−	2.69864i	−0.0282232	−	0.196297i
$190$	0.734426	−	5.10804i	0.0532808	−	0.370576i
$191$	22.8622	+	14.6927i	1.65425	+	1.06312i	0.925790	+	0.378039i	$0.123401\pi$
$191$	22.8622	+	14.6927i	1.65425	+	1.06312i	0.728463	+	0.685085i	$0.240235\pi$
$192$	−0.841254	+	0.540641i	−0.0607122	+	0.0390174i
$193$	−19.2708	+	5.65842i	−1.38714	+	0.407302i	−0.888249	−	0.459362i	$-0.848078\pi$
$193$	−19.2708	+	5.65842i	−1.38714	+	0.407302i	−0.498893	+	0.866663i	$0.666260\pi$
$194$	1.51441	−	10.5330i	0.108729	−	0.756224i
$195$	−3.83168	−	8.39021i	−0.274392	−	0.600836i
$196$	0.364420	+	0.234199i	0.0260300	+	0.0167285i
$197$	22.6882	+	6.66186i	1.61647	+	0.474638i	0.960066	−	0.279774i	$-0.0902595\pi$
$197$	22.6882	+	6.66186i	1.61647	+	0.474638i	0.656402	+	0.754412i	$0.272078\pi$
$198$	−3.27004	−	0.553951i	−0.232391	−	0.0393676i
$199$	−17.0808	+	5.01537i	−1.21082	+	0.355530i	−0.823982	−	0.566616i	$-0.808252\pi$
$199$	−17.0808	+	5.01537i	−1.21082	+	0.355530i	−0.386842	+	0.922146i	$0.626434\pi$
$200$	2.42415	+	0.711796i	0.171413	+	0.0503315i
$201$	−1.16385	+	2.54849i	−0.0820920	+	0.179756i
$202$	−5.88398			−0.413995
$203$	8.30990	+	9.59014i	0.583241	+	0.673096i
$204$	−0.915043	−	6.36426i	−0.0640658	−	0.445587i
$205$	3.12324	−	3.60441i	0.218136	−	0.251743i
$206$	−1.31867	−	1.52183i	−0.0918762	−	0.106031i
$207$	−0.419470	+	2.91748i	−0.0291552	+	0.202779i
$208$	2.82838	−	1.81769i	0.196113	−	0.126034i
$209$	4.61129	+	4.20214i	0.318970	+	0.290668i
$210$	−6.29232	−	4.04383i	−0.434211	−	0.279051i
$211$	−0.647211	+	0.746921i	−0.0445558	+	0.0514202i	−0.777590	−	0.628772i	$-0.783558\pi$
$211$	−0.647211	+	0.746921i	−0.0445558	+	0.0514202i	0.733034	+	0.680192i	$0.238103\pi$
$212$	−8.12493	+	9.37667i	−0.558022	+	0.643992i
$213$	8.72300	−	5.60593i	0.597690	−	0.384112i
$214$	0.784231	−	0.905051i	0.0536090	−	0.0618680i
$215$	−19.2615			−1.31362
$216$	−0.959493	+	0.281733i	−0.0652852	+	0.0191695i
$217$	18.9098	+	12.1526i	1.28368	+	0.824972i
$218$	−6.76399	+	1.98609i	−0.458115	+	0.134515i
$219$	0.249675	−	1.73653i	0.0168715	−	0.117344i
$220$	−7.02340	+	5.78474i	−0.473518	+	0.390007i
$221$	3.07647	+	21.3973i	0.206946	+	1.43934i
$222$	−3.42393	−	7.49736i	−0.229799	−	0.503190i
$223$	14.0565	−	9.03356i	0.941292	−	0.604932i	0.0225313	−	0.999746i	$-0.492827\pi$
$223$	14.0565	−	9.03356i	0.941292	−	0.604932i	0.918761	+	0.394814i	$0.129191\pi$
$224$	1.13258	−	2.48001i	0.0756738	−	0.165703i
$225$	2.12542	+	1.36593i	0.141695	+	0.0910617i
$226$	−1.53842	+	10.6999i	−0.102334	+	0.711748i
$227$	−12.8649	−	3.77746i	−0.853871	−	0.250719i	−0.174630	−	0.984634i	$-0.555873\pi$
$227$	−12.8649	−	3.77746i	−0.853871	−	0.250719i	−0.679241	+	0.733915i	$0.737691\pi$
$228$	1.80486	+	0.529954i	0.119530	+	0.0350971i
$229$	−10.6640	−	12.3069i	−0.704699	−	0.813266i	0.284680	−	0.958622i	$-0.408113\pi$
$229$	−10.6640	−	12.3069i	−0.704699	−	0.813266i	−0.989379	+	0.145357i	$0.953567\pi$
$230$	5.29537	+	6.11118i	0.349166	+	0.402960i
$231$	8.31662	−	3.54949i	0.547194	−	0.233539i
$232$	3.04795	−	3.51753i	0.200108	−	0.230937i
$233$	9.24022			0.605347			0.302673	−	0.953094i	$-0.402121\pi$
$233$	9.24022			0.605347			0.302673	+	0.953094i	$0.402121\pi$
$234$	3.22591	−	0.947214i	0.210885	−	0.0619213i
$235$	3.15002	+	21.9089i	0.205485	+	1.42918i
$236$	0.0574855	−	0.125876i	0.00374199	−	0.00819381i
$237$	2.10226	+	0.617280i	0.136557	+	0.0400966i
$238$	11.4796	+	13.2482i	0.744114	+	0.858753i
$239$	5.02897			0.325297			0.162649	−	0.986684i	$-0.447996\pi$
$239$	5.02897			0.325297			0.162649	+	0.986684i	$0.447996\pi$
$240$	−1.13967	+	2.49553i	−0.0735653	+	0.161086i
$241$	−14.7756			−0.951780			−0.475890	−	0.879505i	$-0.657874\pi$
$241$	−14.7756			−0.951780			−0.475890	+	0.879505i	$0.657874\pi$
$242$	−1.01913	−	10.9527i	−0.0655119	−	0.704065i
$243$	−1.00000			−0.0641500
$244$	2.73198	−	5.98220i	0.174897	−	0.382971i
$245$	1.18843			0.0759257
$246$	1.13844	+	1.31382i	0.0725840	+	0.0837664i
$247$	−6.06812	−	1.78176i	−0.386105	−	0.113371i
$248$	3.42496	−	7.49961i	0.217485	−	0.476226i
$249$	2.03572	+	14.1588i	0.129009	+	0.897276i
$250$	−6.51105	+	1.91182i	−0.411795	+	0.120914i
$251$	12.6810			0.800418			0.400209	−	0.916424i	$-0.368938\pi$
$251$	12.6810			0.800418			0.400209	+	0.916424i	$0.368938\pi$
$252$	1.78540	−	2.06047i	0.112470	−	0.129797i
$253$	−9.70795	+	1.14882i	−0.610334	+	0.0722257i
$254$	10.1278	+	11.6881i	0.635473	+	0.733375i
$255$	−11.5514	−	13.3311i	−0.723380	−	0.834825i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−19.4136	−	5.70034i	−1.21099	−	0.355577i	−0.386942	−	0.922104i	$-0.626469\pi$
$257$	−19.4136	−	5.70034i	−1.21099	−	0.355577i	−0.824043	+	0.566527i	$0.808287\pi$
$258$	0.999181	−	6.94945i	0.0622063	−	0.432654i
$259$	18.9042	+	12.1490i	1.17465	+	0.754900i
$260$	3.83168	−	8.39021i	0.237631	−	0.520339i
$261$	3.91549	−	2.51633i	0.242363	−	0.155757i
$262$	−5.92282	−	12.9692i	−0.365913	−	0.801238i
$263$	−4.17816	−	29.0597i	−0.257636	−	1.79190i	−0.549556	−	0.835457i	$-0.685203\pi$
$263$	−4.17816	−	29.0597i	−0.257636	−	1.79190i	0.291919	−	0.956443i	$-0.405706\pi$
$264$	−1.72277	−	2.83409i	−0.106029	−	0.174426i
$265$	−4.84415	+	33.6918i	−0.297574	+	2.06967i
$266$	−4.92074	+	1.44486i	−0.301710	+	0.0885901i
$267$	10.3181	+	6.63107i	0.631460	+	0.405815i
$268$	−2.68818	+	0.789321i	−0.164207	+	0.0482154i
$269$	8.51787			0.519343			0.259672	−	0.965697i	$-0.416386\pi$
$269$	8.51787			0.519343			0.259672	+	0.965697i	$0.416386\pi$
$270$	−1.79657	+	2.07336i	−0.109336	+	0.126181i
$271$	15.6503	−	10.0578i	0.950689	−	0.610971i	0.0292827	−	0.999571i	$-0.490678\pi$
$271$	15.6503	−	10.0578i	0.950689	−	0.610971i	0.921406	+	0.388600i	$0.127041\pi$
$272$	4.21056	−	4.85925i	0.255303	−	0.294635i
$273$	−6.00271	+	6.92750i	−0.363301	+	0.419271i
$274$	−3.33886	−	2.14576i	−0.201708	−	0.129630i
$275$	−2.56108	+	7.97846i	−0.154439	+	0.481119i
$276$	−2.47958	+	1.59353i	−0.149253	+	0.0959192i
$277$	−0.179600	+	1.24915i	−0.0107911	+	0.0750539i	−0.994505	−	0.104686i	$-0.966616\pi$
$277$	−0.179600	+	1.24915i	−0.0107911	+	0.0750539i	0.983714	+	0.179739i	$0.0575255\pi$
$278$	9.91926	+	11.4474i	0.594918	+	0.686571i
$279$	5.39910	−	6.23090i	0.323236	−	0.373034i
$280$	−1.06447	−	7.40356i	−0.0636143	−	0.442447i
$281$	−13.3226	−	15.3751i	−0.794761	−	0.917203i	0.203321	−	0.979112i	$-0.434827\pi$
$281$	−13.3226	−	15.3751i	−0.794761	−	0.917203i	−0.998082	+	0.0619092i	$0.980281\pi$
$282$	−8.06802			−0.480443
$283$	4.44352	−	9.72996i	0.264140	−	0.578386i	−0.730367	−	0.683055i	$-0.760651\pi$
$283$	4.44352	−	9.72996i	0.264140	−	0.578386i	0.994507	+	0.104669i	$0.0333783\pi$
$284$	9.94903	+	2.92130i	0.590367	+	0.173347i
$285$	4.95153	−	1.45390i	0.293303	−	0.0861216i
$286$	5.79213	+	9.52850i	0.342496	+	0.563432i
$287$	−4.54767	−	1.33532i	−0.268440	−	0.0788212i
$288$	−0.841254	−	0.540641i	−0.0495713	−	0.0318576i
$289$	10.1117	+	22.1415i	0.594804	+	1.30244i
$290$	1.81721	−	12.6390i	0.106710	−	0.742187i
$291$	10.2102	−	2.99800i	0.598535	−	0.175746i
$292$	1.47588	−	0.948492i	0.0863695	−	0.0555063i
$293$	8.22002	+	5.28268i	0.480218	+	0.308618i	0.758261	−	0.651951i	$-0.226049\pi$
$293$	8.22002	+	5.28268i	0.480218	+	0.308618i	−0.278043	+	0.960569i	$0.589686\pi$
$294$	−0.0616489	+	0.428778i	−0.00359544	+	0.0250068i
$295$	−0.0540285	−	0.375776i	−0.00314566	−	0.0218785i
$296$	3.42393	−	7.49736i	0.199012	−	0.435775i
$297$	−0.854530	−	3.20465i	−0.0495849	−	0.185953i
$298$	7.10178	+	15.5507i	0.411395	+	0.900829i
$299$	8.33660	−	5.35761i	0.482118	−	0.309838i
$300$	0.359558	+	2.50078i	0.0207591	+	0.144382i
$301$	7.95176	+	17.4119i	0.458332	+	1.00361i
$302$	−8.03074	−	17.5849i	−0.462117	−	1.01190i
$303$	−2.44429	−	5.35226i	−0.140421	−	0.307479i
$304$	0.781418	+	1.71107i	0.0448174	+	0.0981364i
$305$	−2.56768	−	17.8586i	−0.147025	−	1.02258i
$306$	5.40901	−	3.47616i	0.309213	−	0.198719i
$307$	−3.20338	−	7.01443i	−0.182827	−	0.400335i	0.795922	−	0.605400i	$-0.206987\pi$
$307$	−3.20338	−	7.01443i	−0.182827	−	0.400335i	−0.978748	+	0.205065i	$0.934259\pi$
$308$	8.12875	+	3.96086i	0.463179	+	0.225691i
$309$	0.836508	−	1.83170i	0.0475873	−	0.104202i
$310$	−3.21899	−	22.3886i	−0.182826	−	1.27158i
$311$	0.618174	−	4.29949i	0.0350534	−	0.243802i	−0.964760	−	0.263132i	$-0.915244\pi$
$311$	0.618174	−	4.29949i	0.0350534	−	0.243802i	0.999813	+	0.0193305i	$0.00615347\pi$
$312$	2.82838	+	1.81769i	0.160125	+	0.102906i
$313$	−9.80784	+	6.30312i	−0.554372	+	0.356273i	−0.787637	−	0.616140i	$-0.788696\pi$
$313$	−9.80784	+	6.30312i	−0.554372	+	0.356273i	0.233265	+	0.972413i	$0.425059\pi$
$314$	−0.368898	+	0.108318i	−0.0208181	+	0.00611275i
$315$	1.06447	−	7.40356i	0.0599762	−	0.417143i
$316$	0.910179	+	1.99302i	0.0512016	+	0.112116i
$317$	−25.4911	−	16.3821i	−1.43172	−	0.920112i	−0.999835	−	0.0181849i	$-0.994211\pi$
$317$	−25.4911	−	16.3821i	−1.43172	−	0.920112i	−0.431888	−	0.901927i	$-0.642152\pi$
$318$	−11.9045	−	3.49549i	−0.667573	−	0.196017i
$319$	11.4099	+	10.3975i	0.638830	+	0.582148i
$320$	−2.63232	+	0.772918i	−0.147151	+	0.0432074i
$321$	1.14905	+	0.337390i	0.0641335	+	0.0188313i
$322$	3.33826	−	7.30978i	0.186034	−	0.407358i
$323$	−12.0946			−0.672963
$324$	−0.654861	−	0.755750i	−0.0363812	−	0.0419861i
$325$	−1.20887	−	8.40787i	−0.0670560	−	0.466385i
$326$	4.38037	−	5.05521i	0.242606	−	0.279982i
$327$	−4.61647	−	5.32769i	−0.255292	−	0.294622i
$328$	−0.247406	+	1.72074i	−0.0136607	+	0.0950122i
$329$	18.5047	−	11.8922i	1.02020	−	0.655640i
$330$	−8.17961	−	3.98564i	−0.450273	−	0.219403i
$331$	−15.9399	−	10.2440i	−0.876137	−	0.563059i	0.0234868	−	0.999724i	$-0.492523\pi$
$331$	−15.9399	−	10.2440i	−0.876137	−	0.563059i	−0.899624	+	0.436665i	$0.856160\pi$
$332$	−9.36737	+	10.8105i	−0.514101	+	0.593304i
$333$	5.39749	−	6.22903i	0.295781	−	0.341349i
$334$	0.819212	−	0.526476i	0.0448253	−	0.0288075i
$335$	−5.03340	+	5.80886i	−0.275004	+	0.317372i
$336$	2.72639			0.148737
$337$	−1.87600	+	0.550844i	−0.102192	+	0.0300064i	−0.332429	−	0.943128i	$-0.607868\pi$
$337$	−1.87600	+	0.550844i	−0.102192	+	0.0300064i	0.230237	+	0.973135i	$0.426050\pi$
$338$	1.42699	+	0.917074i	0.0776183	+	0.0498822i
$339$	−10.3721	+	3.04552i	−0.563334	+	0.165410i
$340$	2.51037	−	17.4600i	0.136144	−	0.946902i
$341$	24.5815	+	11.9777i	1.33117	+	0.648631i
$342$	0.267702	+	1.86191i	0.0144757	+	0.100680i
$343$	7.43746	+	16.2858i	0.401585	+	0.879348i
$344$	5.90637	−	3.79579i	0.318450	−	0.204655i
$345$	−3.35915	+	7.35552i	−0.180851	+	0.396008i
$346$	−4.39262	−	2.82296i	−0.236149	−	0.151763i
$347$	4.44334	−	30.9041i	0.238531	−	1.65902i	−0.420791	−	0.907158i	$-0.638247\pi$
$347$	4.44334	−	30.9041i	0.238531	−	1.65902i	0.659322	−	0.751861i	$-0.270844\pi$
$348$	4.46582	+	1.31128i	0.239393	+	0.0702921i
$349$	25.9557	+	7.62128i	1.38938	+	0.407958i	0.889023	−	0.457863i	$-0.151385\pi$
$349$	25.9557	+	7.62128i	1.38938	+	0.407958i	0.500354	+	0.865821i	$0.333203\pi$
$350$	−4.51081	−	5.20575i	−0.241113	−	0.278259i
$351$	2.20171	+	2.54091i	0.117519	+	0.135624i
$352$	1.01369	−	3.15792i	0.0540297	−	0.168318i
$353$	2.07548	−	2.39523i	0.110467	−	0.127485i	−0.697823	−	0.716270i	$-0.745848\pi$
$353$	2.07548	−	2.39523i	0.110467	−	0.127485i	0.808290	+	0.588785i	$0.200393\pi$
$354$	0.138381			0.00735486
$355$	27.2946	−	8.01443i	1.44865	−	0.425362i
$356$	1.74552	+	12.1404i	0.0925124	+	0.643438i
$357$	−7.28217	+	15.9457i	−0.385413	+	0.843938i
$358$	−5.91263	−	1.73610i	−0.312492	−	0.0917560i
$359$	15.0223	+	17.3367i	0.792847	+	0.914994i	0.997966	−	0.0637432i	$-0.0203039\pi$
$359$	15.0223	+	17.3367i	0.792847	+	0.914994i	−0.205120	+	0.978737i	$0.565758\pi$
$360$	−2.74345			−0.144592
$361$	−6.42300	+	14.0644i	−0.338052	+	0.740231i
$362$	24.8197			1.30449
$363$	9.53956	−	5.47694i	0.500697	−	0.287465i
$364$	−9.16639			−0.480449
$365$	1.99942	−	4.37811i	0.104654	−	0.229161i
$366$	6.57650			0.343759
$367$	14.5402	+	16.7803i	0.758991	+	0.875922i	0.995407	−	0.0957295i	$-0.0305184\pi$
$367$	14.5402	+	16.7803i	0.758991	+	0.875922i	−0.236416	+	0.971652i	$0.575973\pi$
$368$	−2.82809	−	0.830401i	−0.147424	−	0.0432877i
$369$	−0.722174	+	1.58134i	−0.0375949	+	0.0823212i
$370$	−3.21802	−	22.3818i	−0.167297	−	1.16358i
$371$	32.4564	−	9.53005i	1.68505	−	0.494776i
$372$	8.24466			0.427466
$373$	−1.96955	+	2.27299i	−0.101980	+	0.117691i	−0.804445	−	0.594027i	$-0.797537\pi$
$373$	−1.96955	+	2.27299i	−0.101980	+	0.117691i	0.702465	+	0.711718i	$0.252083\pi$
$374$	15.7620	+	14.3635i	0.815036	+	0.742719i
$375$	−4.44384	−	5.12846i	−0.229479	−	0.264833i
$376$	−5.28343	−	6.09740i	−0.272472	−	0.314449i
$377$	−15.0145	−	4.40867i	−0.773288	−	0.227058i
$378$	2.61595	+	0.768112i	0.134550	+	0.0395074i
$379$	2.91662	−	20.2855i	0.149817	−	1.04200i	−0.766701	−	0.642004i	$-0.778103\pi$
$379$	2.91662	−	20.2855i	0.149817	−	1.04200i	0.916518	−	0.399994i	$-0.130988\pi$
$380$	4.34135	+	2.79002i	0.222706	+	0.143125i
$381$	−6.42462	+	14.0679i	−0.329143	+	0.720723i
$382$	−22.8622	+	14.6927i	−1.16973	+	0.751742i
$383$	−3.01113	−	6.59345i	−0.153861	−	0.336910i	0.816967	−	0.576684i	$-0.195654\pi$
$383$	−3.01113	−	6.59345i	−0.153861	−	0.336910i	−0.970829	+	0.239775i	$0.922926\pi$
$384$	−0.142315	−	0.989821i	−0.00726247	−	0.0505116i
$385$	24.6354	−	2.91531i	1.25554	−	0.148578i
$386$	2.85830	−	19.8799i	0.145484	−	1.01186i
$387$	6.73652	−	1.97802i	0.342437	−	0.100548i
$388$	8.95202	+	5.75312i	0.454470	+	0.292070i
$389$	−11.5007	+	3.37691i	−0.583109	+	0.171216i	−0.559966	−	0.828516i	$-0.689186\pi$
$389$	−11.5007	+	3.37691i	−0.583109	+	0.171216i	−0.0231437	+	0.999732i	$0.507368\pi$
$390$	9.22374			0.467062
$391$	12.4106	−	14.3225i	0.627629	−	0.724322i
$392$	−0.364420	+	0.234199i	−0.0184060	+	0.0118288i
$393$	9.33675	−	10.7752i	0.470977	−	0.543536i
$394$	−15.4849	+	17.8705i	−0.780116	+	0.900302i
$395$	5.05671	+	3.24975i	0.254431	+	0.163513i
$396$	1.86231	−	2.74441i	0.0935848	−	0.137912i
$397$	−7.23462	+	4.64941i	−0.363095	+	0.233347i	−0.709449	−	0.704757i	$-0.751056\pi$
$397$	−7.23462	+	4.64941i	−0.363095	+	0.233347i	0.346354	+	0.938104i	$0.387420\pi$
$398$	2.53347	−	17.6207i	0.126991	−	0.883245i
$399$	−3.35844	−	3.87585i	−0.168132	−	0.194035i
$400$	−1.65450	+	1.90940i	−0.0827251	+	0.0954698i
$401$	1.37613	+	9.57118i	0.0687206	+	0.477962i	0.994899	+	0.100876i	$0.0321647\pi$
$401$	1.37613	+	9.57118i	0.0687206	+	0.477962i	−0.926178	+	0.377086i	$0.876926\pi$
$402$	−1.83470	−	2.11736i	−0.0915066	−	0.105604i
$403$	−27.7194			−1.38080
$404$	2.44429	−	5.35226i	0.121608	−	0.266285i
$405$	−2.63232	−	0.772918i	−0.130801	−	0.0384066i
$406$	−12.1756	+	3.57506i	−0.604263	+	0.177427i
$407$	24.5742	+	11.9742i	1.21810	+	0.593537i
$408$	6.16926	+	1.81146i	0.305424	+	0.0896805i
$409$	−5.43213	−	3.49102i	−0.268601	−	0.172620i	0.399406	−	0.916774i	$-0.369216\pi$
$409$	−5.43213	−	3.49102i	−0.268601	−	0.172620i	−0.668008	+	0.744154i	$0.732853\pi$
$410$	1.98124	+	4.33832i	0.0978467	+	0.214254i
$411$	0.564835	−	3.92851i	0.0278613	−	0.193779i
$412$	1.93210	−	0.567316i	0.0951877	−	0.0279496i
$413$	−0.317388	+	0.203973i	−0.0156176	+	0.0100369i
$414$	−2.47958	−	1.59353i	−0.121865	−	0.0783177i
$415$	−5.58490	+	38.8438i	−0.274152	+	1.90677i
$416$	0.478477	+	3.32788i	0.0234593	+	0.163163i
$417$	−6.29234	+	13.7783i	−0.308137	+	0.674727i
$418$	−5.73800	+	2.44895i	−0.280655	+	0.119782i
$419$	14.5287	+	31.8134i	0.709773	+	1.55419i	0.827704	+	0.561165i	$0.189647\pi$
$419$	14.5287	+	31.8134i	0.709773	+	1.55419i	−0.117931	+	0.993022i	$0.537626\pi$
$420$	6.29232	−	4.04383i	0.307034	−	0.197319i
$421$	0.0333959	+	0.232273i	0.00162761	+	0.0113203i	0.990619	−	0.136652i	$-0.0436343\pi$
$421$	0.0333959	+	0.232273i	0.00162761	+	0.0113203i	−0.988991	+	0.147973i	$0.952725\pi$
$422$	−0.410562	−	0.899006i	−0.0199859	−	0.0437629i
$423$	−3.35158	−	7.33893i	−0.162959	−	0.356831i
$424$	−5.15410	−	11.2859i	−0.250305	−	0.548092i
$425$	−6.74826	−	14.7766i	−0.327339	−	0.716771i
$426$	1.47567	+	10.2635i	0.0714965	+	0.497269i
$427$	−15.0838	+	9.69374i	−0.729954	+	0.469113i
$428$	0.497482	+	1.08933i	0.0240467	+	0.0526549i
$429$	−6.26129	+	9.22699i	−0.302298	+	0.445483i
$430$	8.00152	−	17.5209i	0.385867	−	0.844932i
$431$	2.82041	+	19.6164i	0.135854	+	0.944888i	0.937722	+	0.347386i	$0.112931\pi$
$431$	2.82041	+	19.6164i	0.135854	+	0.944888i	−0.801868	+	0.597501i	$0.796160\pi$
$432$	0.142315	−	0.989821i	0.00684713	−	0.0476228i
$433$	−0.294013	−	0.188950i	−0.0141293	−	0.00908038i	0.533557	−	0.845764i	$-0.320855\pi$
$433$	−0.294013	−	0.188950i	−0.0141293	−	0.00908038i	−0.547686	+	0.836684i	$0.684491\pi$
$434$	−18.9098	+	12.1526i	−0.907700	+	0.583343i
$435$	12.2517	−	3.59743i	0.587426	−	0.172484i
$436$	1.00326	−	6.97780i	0.0480472	−	0.334176i
$437$	2.30322	+	5.04334i	0.110178	+	0.241256i
$438$	1.47588	+	0.948492i	0.0705204	+	0.0453207i
$439$	−7.96543	−	2.33886i	−0.380169	−	0.111628i	0.0860640	−	0.996290i	$-0.472571\pi$
$439$	−7.96543	−	2.33886i	−0.380169	−	0.111628i	−0.466233	+	0.884662i	$0.654389\pi$
$440$	−2.34436	−	8.79178i	−0.111763	−	0.419132i
$441$	−0.415640	+	0.122043i	−0.0197924	+	0.00581157i
$442$	−20.7417	−	6.09031i	−0.986581	−	0.289686i
$443$	0.882974	−	1.93344i	0.0419513	−	0.0918606i	−0.887496	−	0.460815i	$-0.847557\pi$
$443$	0.882974	−	1.93344i	0.0419513	−	0.0918606i	0.929447	+	0.368955i	$0.120284\pi$
$444$	8.24219			0.391157
$445$	22.0354	+	25.4302i	1.04458	+	1.20551i
$446$	2.37794	+	16.5389i	0.112599	+	0.783140i
$447$	−11.1953	+	12.9200i	−0.529517	+	0.611095i
$448$	1.78540	+	2.06047i	0.0843524	+	0.0973479i
$449$	3.15331	−	21.9318i	0.148814	−	1.03502i	−0.769351	−	0.638826i	$-0.779420\pi$
$449$	3.15331	−	21.9318i	0.148814	−	1.03502i	0.918165	−	0.396198i	$-0.129671\pi$
$450$	−2.12542	+	1.36593i	−0.100193	+	0.0643903i
$451$	−5.68476	−	0.963010i	−0.267685	−	0.0453464i
$452$	−9.09391	−	5.84430i	−0.427742	−	0.274893i
$453$	12.6597	−	14.6100i	0.594803	−	0.686439i
$454$	8.78036	−	10.1331i	0.412083	−	0.475569i
$455$	−21.1554	+	13.5958i	−0.991781	+	0.637379i
$456$	−1.23183	+	1.42161i	−0.0576857	+	0.0665728i
$457$	−18.5299			−0.866790			−0.433395	−	0.901204i	$-0.642685\pi$
$457$	−18.5299			−0.866790			−0.433395	+	0.901204i	$0.642685\pi$
$458$	15.6248	−	4.58785i	0.730099	−	0.214376i
$459$	5.40901	+	3.47616i	0.252471	+	0.162253i
$460$	−7.75870	+	2.27816i	−0.361751	+	0.106220i
$461$	5.84758	−	40.6708i	0.272349	−	1.89423i	−0.151439	−	0.988467i	$-0.548391\pi$
$461$	5.84758	−	40.6708i	0.272349	−	1.89423i	0.423788	−	0.905762i	$-0.360700\pi$
$462$	−0.226121	+	9.03958i	−0.0105201	+	0.420559i
$463$	−5.21494	−	36.2707i	−0.242359	−	1.68564i	−0.640217	−	0.768194i	$-0.721156\pi$
$463$	−5.21494	−	36.2707i	−0.242359	−	1.68564i	0.397858	−	0.917447i	$-0.369754\pi$
$464$	1.93349	+	4.23375i	0.0897599	+	0.196547i
$465$	19.0281	−	12.2286i	0.882408	−	0.567089i
$466$	−3.83853	+	8.40520i	−0.177816	+	0.389363i
$467$	−10.0420	−	6.45359i	−0.464688	−	0.298637i	0.287268	−	0.957850i	$-0.407253\pi$
$467$	−10.0420	−	6.45359i	−0.464688	−	0.298637i	−0.751956	+	0.659214i	$0.770889\pi$
$468$	−0.478477	+	3.32788i	−0.0221176	+	0.153831i
$469$	7.32902	+	2.15199i	0.338423	+	0.0993699i
$470$	−21.2376	−	6.23592i	−0.979616	−	0.287641i
$471$	−0.251776	−	0.290564i	−0.0116012	−	0.0133885i
$472$	0.0906202	+	0.104581i	0.00417113	+	0.00481375i
$473$	12.0954	+	19.8979i	0.556148	+	0.914907i
$474$	−1.43481	+	1.65586i	−0.0659029	+	0.0760560i
$475$	4.75247			0.218058
$476$	−16.8198	+	4.93874i	−0.770934	+	0.226367i
$477$	−1.76572	−	12.2808i	−0.0808466	−	0.562300i
$478$	−2.08911	+	4.57451i	−0.0955536	+	0.209233i
$479$	15.7840	+	4.63461i	0.721191	+	0.211761i	0.621675	−	0.783275i	$-0.286452\pi$
$479$	15.7840	+	4.63461i	0.721191	+	0.211761i	0.0995157	+	0.995036i	$0.468271\pi$
$480$	−1.79657	−	2.07336i	−0.0820020	−	0.0946354i
$481$	−27.7111			−1.26352
$482$	6.13801	−	13.4404i	0.279578	−	0.612192i
$483$	8.03598			0.365650
$484$	10.3863	+	3.62288i	0.472103	+	0.164676i
$485$	29.1938			1.32562
$486$	0.415415	−	0.909632i	0.0188436	−	0.0412617i
$487$	−34.5127			−1.56392			−0.781960	−	0.623329i	$-0.785780\pi$
$487$	−34.5127			−1.56392			−0.781960	+	0.623329i	$0.785780\pi$
$488$	4.30669	+	4.97019i	0.194955	+	0.224990i
$489$	6.41806	+	1.88451i	0.290235	+	0.0852205i
$490$	−0.493690	+	1.08103i	−0.0223026	+	0.0488359i
$491$	−4.39715	−	30.5828i	−0.198440	−	1.38018i	−0.808812	−	0.588068i	$-0.799889\pi$
$491$	−4.39715	−	30.5828i	−0.198440	−	1.38018i	0.610371	−	0.792116i	$-0.291020\pi$
$492$	−1.66802	+	0.489775i	−0.0752001	+	0.0220808i
$493$	−29.9261			−1.34781
$494$	4.14153	−	4.77958i	0.186336	−	0.215044i
$495$	0.227536	−	9.09613i	0.0102270	−	0.408841i
$496$	5.39910	+	6.23090i	0.242427	+	0.279776i
$497$	−18.5129	−	21.3651i	−0.830419	−	0.958355i
$498$	−13.7249	−	4.03001i	−0.615029	−	0.180589i
$499$	−12.8289	−	3.76691i	−0.574301	−	0.168630i	−0.0183304	−	0.999832i	$-0.505835\pi$
$499$	−12.8289	−	3.76691i	−0.574301	−	0.168630i	−0.555970	+	0.831202i	$0.687653\pi$
$500$	0.965739	−	6.71686i	0.0431891	−	0.300387i
$501$	0.819212	+	0.526476i	0.0365997	+	0.0235212i
$502$	−5.26788	+	11.5350i	−0.235117	+	0.514834i
$503$	19.4543	−	12.5025i	0.867424	−	0.557459i	−0.0295400	−	0.999564i	$-0.509404\pi$
$503$	19.4543	−	12.5025i	0.867424	−	0.557459i	0.896964	+	0.442104i	$0.145768\pi$
$504$	1.13258	+	2.48001i	0.0504492	+	0.110468i
$505$	−2.29730	−	15.9781i	−0.102228	−	0.711015i
$506$	2.98783	−	9.30790i	0.132825	−	0.413787i
$507$	−0.241405	+	1.67901i	−0.0107212	+	0.0745673i
$508$	−14.8391	+	4.35715i	−0.658377	+	0.193317i
$509$	−29.7349	−	19.1095i	−1.31798	−	0.847012i	−0.322930	−	0.946423i	$-0.604668\pi$
$509$	−29.7349	−	19.1095i	−1.31798	−	0.847012i	−0.995046	+	0.0994110i	$0.968304\pi$
$510$	16.9250	−	4.96964i	0.749453	−	0.220059i
$511$	−4.78313			−0.211593
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−1.58244	+	1.01697i	−0.0698666	+	0.0449005i
$514$	13.2499	−	15.2912i	0.584428	−	0.674466i
$515$	3.61770	−	4.17505i	0.159415	−	0.183975i
$516$	5.90637	+	3.79579i	0.260013	+	0.167101i
$517$	20.6547	−	17.0120i	0.908391	−	0.748185i
$518$	−18.9042	+	12.1490i	−0.830601	+	0.533795i
$519$	0.743099	−	5.16837i	0.0326184	−	0.226866i
$520$	6.04027	+	6.97084i	0.264883	+	0.305692i
$521$	16.4978	−	19.0395i	0.722782	−	0.834135i	−0.268857	−	0.963180i	$-0.586646\pi$
$521$	16.4978	−	19.0395i	0.722782	−	0.834135i	0.991639	+	0.129045i	$0.0411913\pi$
$522$	0.662384	+	4.60698i	0.0289917	+	0.201642i
$523$	13.3897	+	15.4525i	0.585490	+	0.675691i	0.968776	−	0.247938i	$-0.0797531\pi$
$523$	13.3897	+	15.4525i	0.585490	+	0.675691i	−0.383286	+	0.923630i	$0.625208\pi$
$524$	14.2576			0.622846
$525$	2.86146	−	6.26573i	0.124884	−	0.273459i
$526$	28.1693	+	8.27126i	1.22824	+	0.360644i
$527$	−50.8634	+	14.9349i	−2.21565	+	0.650573i
$528$	3.29364	−	0.389763i	0.143337	−	0.0169623i
$529$	13.7326	+	4.03226i	0.597070	+	0.175315i
$530$	−28.6348	−	18.4025i	−1.24382	−	0.799352i
$531$	0.0574855	+	0.125876i	0.00249466	+	0.00546254i
$532$	0.729859	−	5.07628i	0.0316434	−	0.220085i
$533$	5.60805	−	1.64667i	0.242912	−	0.0713253i
$534$	−10.3181	+	6.63107i	−0.446510	+	0.286955i
$535$	2.76388	+	1.77624i	0.119493	+	0.0767934i
$536$	0.398719	−	2.77315i	0.0172220	−	0.119782i
$537$	−0.876978	−	6.09952i	−0.0378444	−	0.263214i
$538$	−3.53845	+	7.74812i	−0.152553	+	0.334045i
$539$	−0.746282	−	1.22769i	−0.0321446	−	0.0528804i
$540$	−1.13967	−	2.49553i	−0.0490435	−	0.107390i
$541$	29.9422	−	19.2427i	1.28731	−	0.827306i	0.295543	−	0.955330i	$-0.404500\pi$
$541$	29.9422	−	19.2427i	1.28731	−	0.827306i	0.991771	+	0.128023i	$0.0408632\pi$
$542$	2.64756	+	18.4142i	0.113723	+	0.790958i
$543$	10.3105	+	22.5768i	0.442465	+	0.968862i
$544$	2.67100	+	5.84867i	0.114518	+	0.250760i
$545$	−8.03415	−	17.5923i	−0.344145	−	0.753573i
$546$	−3.80786	−	8.33804i	−0.162961	−	0.356835i
$547$	3.87659	+	26.9623i	0.165751	+	1.15282i	0.887546	+	0.460718i	$0.152408\pi$
$547$	3.87659	+	26.9623i	0.165751	+	1.15282i	−0.721795	+	0.692107i	$0.756683\pi$
$548$	3.33886	−	2.14576i	0.142629	−	0.0916621i
$549$	2.73198	+	5.98220i	0.116598	+	0.255314i
$550$	−6.19355	−	5.64401i	−0.264094	−	0.240661i
$551$	3.63700	−	7.96391i	0.154941	−	0.339274i
$552$	−0.419470	−	2.91748i	−0.0178538	−	0.124176i
$553$	0.850125	−	5.91275i	0.0361510	−	0.251436i
$554$	−1.06165	−	0.682283i	−0.0451053	−	0.0289874i
$555$	19.0224	−	12.2250i	0.807457	−	0.518921i
$556$	−14.5336	+	4.26744i	−0.616360	+	0.180980i
$557$	−3.37412	+	23.4675i	−0.142966	+	0.994350i	0.784416	+	0.620235i	$0.212963\pi$
$557$	−3.37412	+	23.4675i	−0.142966	+	0.994350i	−0.927382	+	0.374116i	$0.877946\pi$
$558$	3.42496	+	7.49961i	0.144990	+	0.317484i
$559$	−19.8578	−	12.7618i	−0.839896	−	0.539769i
$560$	7.17671	+	2.10727i	0.303272	+	0.0890486i
$561$	−6.51771	+	20.3045i	−0.275178	+	0.857256i
$562$	19.5201	−	5.73162i	0.823407	−	0.241774i
$563$	2.88564	+	0.847302i	0.121615	+	0.0357095i	0.341974	−	0.939709i	$-0.388905\pi$
$563$	2.88564	+	0.847302i	0.121615	+	0.0357095i	−0.220359	+	0.975419i	$0.570723\pi$
$564$	3.35158	−	7.33893i	0.141127	−	0.309025i
$565$	−29.6565			−1.24766
$566$	7.00477	+	8.08394i	0.294433	+	0.339793i
$567$	0.388005	+	2.69864i	0.0162947	+	0.113332i
$568$	−6.79029	+	7.83641i	−0.284914	+	0.328808i
$569$	−12.6994	−	14.6559i	−0.532386	−	0.614406i	0.424303	−	0.905520i	$-0.360519\pi$
$569$	−12.6994	−	14.6559i	−0.532386	−	0.614406i	−0.956688	+	0.291115i	$0.905974\pi$
$570$	−0.734426	+	5.10804i	−0.0307617	+	0.213952i
$571$	−12.8583	+	8.26354i	−0.538104	+	0.345818i	−0.781297	−	0.624160i	$-0.785441\pi$
$571$	−12.8583	+	8.26354i	−0.538104	+	0.345818i	0.243193	+	0.969978i	$0.421805\pi$
$572$	−11.0736	+	1.31042i	−0.463009	+	0.0547916i
$573$	−22.8622	−	14.6927i	−0.955083	−	0.613795i
$574$	3.10382	−	3.58199i	0.129551	−	0.149510i
$575$	−4.87661	+	5.62791i	−0.203369	+	0.234700i
$576$	0.841254	−	0.540641i	0.0350522	−	0.0225267i
$577$	−28.1000	+	32.4292i	−1.16982	+	1.35004i	−0.245052	+	0.969510i	$0.578805\pi$
$577$	−28.1000	+	32.4292i	−1.16982	+	1.35004i	−0.924767	+	0.380534i	$0.875740\pi$
$578$	−24.3411			−1.01246
$579$	19.2708	−	5.65842i	0.800867	−	0.235156i
$580$	10.7419	+	6.90342i	0.446035	+	0.286649i
$581$	37.4195	−	10.9874i	1.55242	−	0.455832i
$582$	−1.51441	+	10.5330i	−0.0627745	+	0.436606i
$583$	37.8469	−	16.1528i	1.56746	−	0.668982i
$584$	0.249675	+	1.73653i	0.0103316	+	0.0718580i
$585$	3.83168	+	8.39021i	0.158421	+	0.346893i
$586$	−8.22002	+	5.28268i	−0.339566	+	0.218226i
$587$	−17.2446	+	37.7604i	−0.711761	+	1.55854i	0.113341	+	0.993556i	$0.463845\pi$
$587$	−17.2446	+	37.7604i	−0.711761	+	1.55854i	−0.825102	+	0.564983i	$0.808883\pi$
$588$	−0.364420	−	0.234199i	−0.0150284	−	0.00965819i
$589$	2.20711	−	15.3508i	0.0909425	−	0.632519i
$590$	0.364262	+	0.106957i	0.0149964	+	0.00440335i
$591$	−22.6882	−	6.66186i	−0.933268	−	0.274032i
$592$	5.39749	+	6.22903i	0.221835	+	0.256012i
$593$	21.5251	+	24.8412i	0.883928	+	1.02011i	0.999640	+	0.0268246i	$0.00853956\pi$
$593$	21.5251	+	24.8412i	0.883928	+	1.02011i	−0.115712	+	0.993283i	$0.536915\pi$
$594$	3.27004	+	0.553951i	0.134171	+	0.0227289i
$595$	−31.4937	+	36.3457i	−1.29112	+	1.49003i
$596$	−17.0956			−0.700264
$597$	17.0808	−	5.01537i	0.699070	−	0.205265i
$598$	1.41030	+	9.80887i	0.0576715	+	0.401114i
$599$	−15.3127	+	33.5302i	−0.625661	+	1.37001i	0.285668	+	0.958329i	$0.407785\pi$
$599$	−15.3127	+	33.5302i	−0.625661	+	1.37001i	−0.911329	+	0.411679i	$0.864943\pi$
$600$	−2.42415	−	0.711796i	−0.0989656	−	0.0290589i
$601$	24.6156	+	28.4079i	1.00409	+	1.15878i	0.987291	+	0.158925i	$0.0508027\pi$
$601$	24.6156	+	28.4079i	1.00409	+	1.15878i	0.0168008	+	0.999859i	$0.494652\pi$
$602$	−19.1417			−0.780159
$603$	1.16385	−	2.54849i	0.0473958	−	0.103782i
$604$	19.3318			0.786601
$605$	29.3444	−	7.04375i	1.19302	−	0.286369i
$606$	5.88398			0.239020
$607$	0.967374	−	2.11825i	0.0392645	−	0.0859772i	−0.888983	−	0.457939i	$-0.848588\pi$
$607$	0.967374	−	2.11825i	0.0392645	−	0.0859772i	0.928248	+	0.371962i	$0.121315\pi$
$608$	−1.88105			−0.0762868
$609$	−8.30990	−	9.59014i	−0.336734	−	0.388612i
$610$	17.3114	+	5.08310i	0.700920	+	0.205809i
$611$	−11.2683	+	24.6742i	−0.455868	+	0.998212i
$612$	0.915043	+	6.36426i	0.0369884	+	0.257260i
$613$	−18.2601	+	5.36166i	−0.737520	+	0.216555i	−0.628854	−	0.777523i	$-0.716476\pi$
$613$	−18.2601	+	5.36166i	−0.737520	+	0.216555i	−0.108665	+	0.994078i	$0.534658\pi$
$614$	7.71128			0.311202
$615$	−3.12324	+	3.60441i	−0.125941	+	0.145344i
$616$	−6.97973	+	5.74877i	−0.281221	+	0.231625i
$617$	−10.7651	−	12.4236i	−0.433386	−	0.500154i	0.496482	−	0.868047i	$-0.334625\pi$
$617$	−10.7651	−	12.4236i	−0.433386	−	0.500154i	−0.929868	+	0.367893i	$0.880079\pi$
$618$	1.31867	+	1.52183i	0.0530448	+	0.0612169i
$619$	2.28014	+	0.669509i	0.0916465	+	0.0269098i	0.327234	−	0.944943i	$-0.393883\pi$
$619$	2.28014	+	0.669509i	0.0916465	+	0.0269098i	−0.235588	+	0.971853i	$0.575702\pi$
$620$	21.7026	+	6.37245i	0.871596	+	0.255924i
$621$	0.419470	−	2.91748i	0.0168328	−	0.117074i
$622$	3.65416	+	2.34839i	0.146518	+	0.0941617i
$623$	13.8914	−	30.4178i	0.556545	−	1.21866i
$624$	−2.82838	+	1.81769i	−0.113226	+	0.0727658i
$625$	−12.9814	−	28.4254i	−0.519257	−	1.13701i
$626$	−1.65919	−	11.5399i	−0.0663147	−	0.461229i
$627$	−4.61129	−	4.20214i	−0.184157	−	0.167817i
$628$	0.0547161	−	0.380559i	0.00218341	−	0.0151859i
$629$	−50.8482	+	14.9304i	−2.02745	+	0.595313i
$630$	6.29232	+	4.04383i	0.250692	+	0.161110i
$631$	−21.0612	+	6.18412i	−0.838433	+	0.246186i	−0.672636	−	0.739974i	$-0.734838\pi$
$631$	−21.0612	+	6.18412i	−0.838433	+	0.246186i	−0.165797	+	0.986160i	$0.553020\pi$
$632$	−2.19101			−0.0871538
$633$	0.647211	−	0.746921i	0.0257243	−	0.0296874i
$634$	25.4911	−	16.3821i	1.01238	−	0.650618i
$635$	−27.7850	+	32.0656i	−1.10261	+	1.27248i
$636$	8.12493	−	9.37667i	0.322174	−	0.371809i
$637$	1.22522	+	0.787400i	0.0485449	+	0.0311979i
$638$	−14.1977	+	6.05951i	−0.562093	+	0.239898i
$639$	−8.72300	+	5.60593i	−0.345077	+	0.221767i
$640$	0.390433	−	2.71552i	0.0154332	−	0.107340i
$641$	−17.4564	−	20.1458i	−0.689488	−	0.795712i	0.297804	−	0.954627i	$-0.403746\pi$
$641$	−17.4564	−	20.1458i	−0.689488	−	0.795712i	−0.987292	+	0.158915i	$0.949200\pi$
$642$	−0.784231	+	0.905051i	−0.0309511	+	0.0357195i
$643$	−2.59622	−	18.0571i	−0.102385	−	0.712103i	−0.974758	−	0.223263i	$-0.928329\pi$
$643$	−2.59622	−	18.0571i	−0.102385	−	0.712103i	0.872373	−	0.488840i	$-0.162580\pi$
$644$	5.26244	+	6.07319i	0.207369	+	0.239317i
$645$	19.2615			0.758421
$646$	5.02429	−	11.0017i	0.197678	−	0.432855i
$647$	9.95668	+	2.92355i	0.391438	+	0.114936i	0.471528	−	0.881851i	$-0.343703\pi$
$647$	9.95668	+	2.92355i	0.391438	+	0.114936i	−0.0800902	+	0.996788i	$0.525521\pi$
$648$	0.959493	−	0.281733i	0.0376924	−	0.0110675i
$649$	−0.354264	+	0.291786i	−0.0139061	+	0.0114536i
$650$	8.15025	+	2.39313i	0.319679	+	0.0938662i
$651$	−18.9098	−	12.1526i	−0.741134	−	0.476298i
$652$	2.77871	+	6.08454i	0.108823	+	0.238289i
$653$	−3.19362	+	22.2121i	−0.124976	+	0.869228i	0.826813	+	0.562476i	$0.190151\pi$
$653$	−3.19362	+	22.2121i	−0.124976	+	0.869228i	−0.951790	+	0.306752i	$0.900758\pi$
$654$	6.76399	−	1.98609i	0.264493	−	0.0776622i
$655$	32.9056	−	21.1471i	1.28573	−	0.826287i
$656$	−1.46247	−	0.939871i	−0.0570998	−	0.0366958i
$657$	−0.249675	+	1.73653i	−0.00974075	+	0.0677484i
$658$	3.13043	+	21.7726i	0.122037	+	0.848786i
$659$	18.6334	−	40.8015i	0.725856	−	1.58940i	−0.0796561	−	0.996822i	$-0.525382\pi$
$659$	18.6334	−	40.8015i	0.725856	−	1.58940i	0.805512	−	0.592580i	$-0.201891\pi$
$660$	7.02340	−	5.78474i	0.273386	−	0.225171i
$661$	−18.3848	−	40.2571i	−0.715086	−	1.56582i	−0.820665	−	0.571409i	$-0.806397\pi$
$661$	−18.3848	−	40.2571i	−0.715086	−	1.56582i	0.105579	−	0.994411i	$-0.466330\pi$
$662$	15.9399	−	10.2440i	0.619523	−	0.398143i
$663$	−3.07647	−	21.3973i	−0.119480	−	0.831002i
$664$	−5.94225	−	13.0117i	−0.230604	−	0.504952i
$665$	−5.84477	−	12.7983i	−0.226650	−	0.496295i
$666$	3.42393	+	7.49736i	0.132675	+	0.290517i
$667$	5.69892	+	12.4789i	0.220663	+	0.483185i
$668$	0.138586	+	0.963887i	0.00536206	+	0.0372939i
$669$	−14.0565	+	9.03356i	−0.543455	+	0.349258i
$670$	−3.19297	−	6.99163i	−0.123355	−	0.270110i
$671$	−16.8363	+	13.8670i	−0.649958	+	0.535330i
$672$	−1.13258	+	2.48001i	−0.0436903	+	0.0956684i
$673$	0.377274	+	2.62400i	0.0145428	+	0.101148i	0.995800	−	0.0915551i	$-0.0291838\pi$
$673$	0.377274	+	2.62400i	0.0145428	+	0.101148i	−0.981257	+	0.192703i	$0.938275\pi$
$674$	0.278254	−	1.93530i	0.0107180	−	0.0745450i
$675$	−2.12542	−	1.36593i	−0.0818075	−	0.0525745i
$676$	−1.42699	+	0.917074i	−0.0548844	+	0.0352721i
$677$	2.30462	−	0.676698i	0.0885738	−	0.0260076i	−0.237145	−	0.971474i	$-0.576212\pi$
$677$	2.30462	−	0.676698i	0.0885738	−	0.0260076i	0.325719	+	0.945467i	$0.394394\pi$
$678$	1.53842	−	10.6999i	0.0590825	−	0.410928i
$679$	−12.0521	−	26.3905i	−0.462518	−	1.01277i
$680$	14.8393	+	9.53666i	0.569063	+	0.365714i
$681$	12.8649	+	3.77746i	0.492983	+	0.144753i
$682$	−21.1069	+	17.3844i	−0.808224	+	0.665684i
$683$	−15.2630	+	4.48162i	−0.584023	+	0.171484i	−0.560379	−	0.828236i	$-0.689345\pi$
$683$	−15.2630	+	4.48162i	−0.584023	+	0.171484i	−0.0236430	+	0.999720i	$0.507527\pi$
$684$	−1.80486	−	0.529954i	−0.0690105	−	0.0202633i
$685$	4.52324	−	9.90452i	0.172824	−	0.378432i
$686$	−17.9037			−0.683565
$687$	10.6640	+	12.3069i	0.406858	+	0.469539i
$688$	0.999181	+	6.94945i	0.0380934	+	0.264945i
$689$	−27.3168	+	31.5253i	−1.04069	+	1.20102i
$690$	−5.29537	−	6.11118i	−0.201591	−	0.232649i
$691$	−4.34887	+	30.2470i	−0.165439	+	1.15065i	0.722729	+	0.691132i	$0.242888\pi$
$691$	−4.34887	+	30.2470i	−0.165439	+	1.15065i	−0.888167	+	0.459520i	$0.848021\pi$
$692$	4.39262	−	2.82296i	0.166982	−	0.107313i
$693$	−8.31662	+	3.54949i	−0.315922	+	0.134834i
$694$	26.2655	+	16.8798i	0.997026	+	0.640749i
$695$	−27.2129	+	31.4054i	−1.03225	+	1.19128i
$696$	−3.04795	+	3.51753i	−0.115532	+	0.133331i
$697$	9.40324	−	6.04310i	0.356173	−	0.228899i
$698$	−17.7149	+	20.4441i	−0.670520	+	0.773822i
$699$	−9.24022			−0.349497
$700$	6.60918	−	1.94063i	0.249803	−	0.0733489i
$701$	3.39716	+	2.18322i	0.128309	+	0.0824592i	0.603221	−	0.797574i	$-0.293884\pi$
$701$	3.39716	+	2.18322i	0.128309	+	0.0824592i	−0.474912	+	0.880033i	$0.657520\pi$
$702$	−3.22591	+	0.947214i	−0.121754	+	0.0357503i
$703$	2.20645	−	15.3462i	0.0832179	−	0.578793i
$704$	2.45144	+	2.23393i	0.0923922	+	0.0841944i
$705$	−3.15002	−	21.9089i	−0.118637	−	0.825136i
$706$	1.31659	+	2.88294i	0.0495506	+	0.108501i
$707$	−13.4954	+	8.67296i	−0.507546	+	0.326180i
$708$	−0.0574855	+	0.125876i	−0.00216044	+	0.00473070i
$709$	−11.0641	−	7.11047i	−0.415521	−	0.267039i	0.316134	−	0.948715i	$-0.397615\pi$
$709$	−11.0641	−	7.11047i	−0.415521	−	0.267039i	−0.731655	+	0.681676i	$0.761252\pi$
$710$	−4.04842	+	28.1574i	−0.151935	+	1.05673i
$711$	−2.10226	−	0.617280i	−0.0788410	−	0.0231498i
$712$	−11.7684	−	3.45551i	−0.441039	−	0.129501i
$713$	15.9138	+	18.3655i	0.595975	+	0.687792i
$714$	−11.4796	−	13.2482i	−0.429614	−	0.495801i
$715$	−23.6134	+	19.4489i	−0.883091	+	0.727347i
$716$	4.03541	−	4.65711i	0.150810	−	0.174044i
$717$	−5.02897			−0.187810
$718$	−22.0105	+	6.46286i	−0.821423	+	0.241192i
$719$	−0.381536	−	2.65364i	−0.0142289	−	0.0989640i	0.981469	−	0.191619i	$-0.0613738\pi$
$719$	−0.381536	−	2.65364i	−0.0142289	−	0.0989640i	−0.995698	+	0.0926549i	$0.970465\pi$
$720$	1.13967	−	2.49553i	0.0424729	−	0.0930028i
$721$	−5.26765	−	1.54672i	−0.196178	−	0.0576030i
$722$	−10.1252	−	11.6851i	−0.376822	−	0.434875i
$723$	14.7756			0.549510
$724$	−10.3105	+	22.5768i	−0.383186	+	0.839059i
$725$	11.7592			0.436726
$726$	1.01913	+	10.9527i	0.0378233	+	0.406492i
$727$	38.1184			1.41373			0.706867	−	0.707347i	$-0.250108\pi$
$727$	38.1184			1.41373			0.706867	+	0.707347i	$0.250108\pi$
$728$	3.80786	−	8.33804i	0.141129	−	0.309028i
$729$	1.00000			0.0370370
$730$	3.15188	+	3.63747i	0.116656	+	0.134629i
$731$	−43.3139	−	12.7181i	−1.60202	−	0.470396i
$732$	−2.73198	+	5.98220i	−0.100977	+	0.221108i
$733$	5.71509	+	39.7493i	0.211092	+	1.46817i	0.769521	+	0.638622i	$0.220495\pi$
$733$	5.71509	+	39.7493i	0.211092	+	1.46817i	−0.558429	+	0.829552i	$0.688596\pi$
$734$	−21.3041	+	6.25544i	−0.786348	+	0.230892i
$735$	−1.18843			−0.0438357
$736$	1.93019	−	2.22756i	0.0711477	−	0.0821089i
$737$	9.16155	+	1.55199i	0.337470	+	0.0571682i
$738$	−1.13844	−	1.31382i	−0.0419064	−	0.0483625i
$739$	23.9734	+	27.6668i	0.881875	+	1.01774i	0.999695	+	0.0247029i	$0.00786399\pi$
$739$	23.9734	+	27.6668i	0.881875	+	1.01774i	−0.117820	+	0.993035i	$0.537591\pi$
$740$	21.6961	+	6.37054i	0.797563	+	0.234186i
$741$	6.06812	+	1.78176i	0.222918	+	0.0654546i
$742$	−4.81403	+	33.4823i	−0.176728	+	1.22917i
$743$	−28.5828	−	18.3691i	−1.04860	−	0.673896i	−0.101503	−	0.994835i	$-0.532365\pi$
$743$	−28.5828	−	18.3691i	−1.04860	−	0.673896i	−0.947100	+	0.320939i	$0.896002\pi$
$744$	−3.42496	+	7.49961i	−0.125565	+	0.274949i
$745$	−39.4556	+	25.3565i	−1.44554	+	0.928992i
$746$	−1.24940	−	2.73580i	−0.0457437	−	0.100165i
$747$	−2.03572	−	14.1588i	−0.0744832	−	0.518042i
$748$	−19.6133	+	8.37085i	−0.717133	+	0.306068i
$749$	0.464658	−	3.23176i	0.0169782	−	0.118086i
$750$	6.51105	−	1.91182i	0.237750	−	0.0698097i
$751$	−16.8609	−	10.8359i	−0.615263	−	0.395406i	0.195564	−	0.980691i	$-0.437346\pi$
$751$	−16.8609	−	10.8359i	−0.615263	−	0.395406i	−0.810828	+	0.585285i	$0.800983\pi$
$752$	7.74121	−	2.27302i	0.282293	−	0.0828886i
$753$	−12.6810			−0.462122
$754$	10.2475	−	11.8263i	0.373193	−	0.430688i
$755$	44.6166	−	28.6733i	1.62376	−	1.04353i
$756$	−1.78540	+	2.06047i	−0.0649345	+	0.0749384i
$757$	−24.6890	+	28.4926i	−0.897336	+	1.03558i	0.101832	+	0.994802i	$0.467529\pi$
$757$	−24.6890	+	28.4926i	−0.897336	+	1.03558i	−0.999168	+	0.0407790i	$0.987016\pi$
$758$	17.2408	+	11.0800i	0.626213	+	0.402442i
$759$	9.70795	−	1.14882i	0.352376	−	0.0416995i
$760$	−4.34135	+	2.79002i	−0.157477	+	0.101204i
$761$	−0.668421	+	4.64897i	−0.0242302	+	0.168525i	−0.998343	−	0.0575358i	$-0.981676\pi$
$761$	−0.668421	+	4.64897i	−0.0242302	+	0.168525i	0.974113	+	0.226061i	$0.0725848\pi$
$762$	−10.1278	−	11.6881i	−0.366891	−	0.423414i
$763$	−12.5863	+	14.5254i	−0.455654	+	0.525853i
$764$	−3.86760	−	26.8998i	−0.139925	−	0.973199i
$765$	11.5514	+	13.3311i	0.417644	+	0.481986i
$766$	7.24848			0.261898
$767$	0.193272	−	0.423207i	0.00697865	−	0.0152811i
$768$	0.959493	+	0.281733i	0.0346227	+	0.0101661i
$769$	24.8284	−	7.29026i	0.895333	−	0.262894i	0.198478	−	0.980105i	$-0.436400\pi$
$769$	24.8284	−	7.29026i	0.895333	−	0.262894i	0.696855	+	0.717212i	$0.254582\pi$
$770$	−7.58207	+	23.6203i	−0.273239	+	0.851215i
$771$	19.4136	+	5.70034i	0.699163	+	0.205293i
$772$	16.8960	+	10.8584i	0.608102	+	0.390803i
$773$	16.3972	+	35.9050i	0.589768	+	1.29141i	0.935582	+	0.353109i	$0.114875\pi$
$773$	16.3972	+	35.9050i	0.589768	+	1.29141i	−0.345815	+	0.938303i	$0.612397\pi$
$774$	−0.999181	+	6.94945i	−0.0359148	+	0.249793i
$775$	19.9863	−	5.86851i	0.717930	−	0.210803i
$776$	−8.95202	+	5.75312i	−0.321359	+	0.206525i
$777$	−18.9042	−	12.1490i	−0.678183	−	0.435842i
$778$	1.70582	−	11.8642i	0.0611566	−	0.425354i
$779$	0.465383	+	3.23681i	0.0166741	+	0.115971i
$780$	−3.83168	+	8.39021i	−0.137196	+	0.300418i
$781$	−25.4191	−	23.1637i	−0.909568	−	0.828863i
$782$	7.87271	+	17.2388i	0.281528	+	0.616460i
$783$	−3.91549	+	2.51633i	−0.139928	+	0.0899264i
$784$	−0.0616489	−	0.428778i	−0.00220175	−	0.0153135i
$785$	−0.438171	−	0.959460i	−0.0156390	−	0.0342446i
$786$	5.92282	+	12.9692i	0.211260	+	0.462595i
$787$	2.68169	+	5.87208i	0.0955919	+	0.209317i	0.951387	−	0.307998i	$-0.0996589\pi$
$787$	2.68169	+	5.87208i	0.0955919	+	0.209317i	−0.855795	+	0.517315i	$0.826932\pi$
$788$	−9.82292	−	21.5092i	−0.349927	−	0.766233i
$789$	4.17816	+	29.0597i	0.148746	+	1.03455i
$790$	−5.05671	+	3.24975i	−0.179910	+	0.115621i
$791$	12.2432	+	26.8088i	0.435317	+	0.953211i
$792$	1.72277	+	2.83409i	0.0612160	+	0.100705i
$793$	9.18519	−	20.1128i	0.326176	−	0.714225i
$794$	−1.22388	−	8.51228i	−0.0434339	−	0.302090i
$795$	4.84415	−	33.6918i	0.171804	−	1.19492i
$796$	14.9759	+	9.62442i	0.530806	+	0.341129i
$797$	−11.8486	+	7.61461i	−0.419697	+	0.269723i	−0.733399	−	0.679798i	$-0.762067\pi$
$797$	−11.8486	+	7.61461i	−0.419697	+	0.269723i	0.313701	+	0.949522i	$0.398431\pi$
$798$	4.92074	−	1.44486i	0.174192	−	0.0511475i
$799$	−7.38258	+	51.3470i	−0.261177	+	1.81653i
$800$	−1.04954	−	2.29818i	−0.0371070	−	0.0812529i
$801$	−10.3181	−	6.63107i	−0.364574	−	0.234297i
$802$	−9.27792	−	2.72424i	−0.327615	−	0.0961964i
$803$	−5.77832	+	0.683795i	−0.203912	+	0.0241306i
$804$	2.68818	−	0.789321i	0.0948048	−	0.0278372i
$805$	21.1532	+	6.21115i	0.745554	+	0.218914i
$806$	11.5151	−	25.2144i	0.405600	−	0.888141i
$807$	−8.51787			−0.299843
$808$	3.85319	+	4.44681i	0.135555	+	0.156438i
$809$	−4.95187	−	34.4410i	−0.174098	−	1.21088i	−0.870113	−	0.492853i	$-0.835954\pi$
$809$	−4.95187	−	34.4410i	−0.174098	−	1.21088i	0.696014	−	0.718028i	$-0.254955\pi$
$810$	1.79657	−	2.07336i	0.0631252	−	0.0728504i
$811$	−9.80013	−	11.3100i	−0.344129	−	0.397146i	0.557131	−	0.830425i	$-0.311902\pi$
$811$	−9.80013	−	11.3100i	−0.344129	−	0.397146i	−0.901260	+	0.433279i	$0.857357\pi$
$812$	1.80591	−	12.5604i	0.0633752	−	0.440784i
$813$	−15.6503	+	10.0578i	−0.548881	+	0.352744i
$814$	−21.1006	+	17.3792i	−0.739574	+	0.609141i
$815$	15.4378	+	9.92126i	0.540762	+	0.347527i
$816$	−4.21056	+	4.85925i	−0.147399	+	0.170108i
$817$	8.64857	−	9.98098i	0.302575	−	0.349190i
$818$	5.43213	−	3.49102i	0.189930	−	0.122061i
$819$	6.00271	−	6.92750i	0.209752	−	0.242066i
$820$	−4.76931			−0.166552
$821$	23.4609	−	6.88875i	0.818792	−	0.240419i	0.154596	−	0.987978i	$-0.450592\pi$
$821$	23.4609	−	6.88875i	0.818792	−	0.240419i	0.664196	+	0.747559i	$0.268774\pi$
$822$	3.33886	+	2.14576i	0.116456	+	0.0748418i
$823$	25.6198	−	7.52266i	0.893051	−	0.262223i	0.197160	−	0.980371i	$-0.436828\pi$
$823$	25.6198	−	7.52266i	0.893051	−	0.262223i	0.695891	+	0.718148i	$0.255010\pi$
$824$	−0.286575	+	1.99317i	−0.00998331	+	0.0694354i
$825$	2.56108	−	7.97846i	0.0891652	−	0.277774i
$826$	−0.0536925	−	0.373440i	−0.00186820	−	0.0129936i
$827$	15.2292	+	33.3473i	0.529572	+	1.15960i	0.965687	+	0.259709i	$0.0836267\pi$
$827$	15.2292	+	33.3473i	0.529572	+	1.15960i	−0.436115	+	0.899891i	$0.643646\pi$
$828$	2.47958	−	1.59353i	0.0861713	−	0.0553790i
$829$	22.6018	−	49.4910i	0.784992	−	1.71889i	0.0945328	−	0.995522i	$-0.469864\pi$
$829$	22.6018	−	49.4910i	0.784992	−	1.71889i	0.690459	−	0.723371i	$-0.257408\pi$
$830$	−33.0135	−	21.2165i	−1.14592	−	0.736436i
$831$	0.179600	−	1.24915i	0.00623025	−	0.0433324i
$832$	−3.22591	−	0.947214i	−0.111838	−	0.0328387i
$833$	2.67244	+	0.784700i	0.0925947	+	0.0271882i
$834$	−9.91926	−	11.4474i	−0.343476	−	0.396392i
$835$	1.74950	+	2.01903i	0.0605440	+	0.0698716i
$836$	0.156011	−	6.23680i	0.00539576	−	0.215704i
$837$	−5.39910	+	6.23090i	−0.186620	+	0.215371i
$838$	−34.9739			−1.20815
$839$	52.9145	−	15.5371i	1.82681	−	0.536401i	0.827141	−	0.561995i	$-0.189966\pi$
$839$	52.9145	−	15.5371i	1.82681	−	0.536401i	0.999672	+	0.0255944i	$0.00814785\pi$
$840$	1.06447	+	7.40356i	0.0367278	+	0.255447i
$841$	−3.04790	+	6.67396i	−0.105100	+	0.230137i
$842$	−0.225156	−	0.0661119i	−0.00775940	−	0.00227837i
$843$	13.3226	+	15.3751i	0.458855	+	0.529547i
$844$	0.988318			0.0340193
$845$	−1.93319	+	4.23309i	−0.0665037	+	0.145623i
$846$	8.06802			0.277384
$847$	−18.4817	−	23.6187i	−0.635038	−	0.811548i
$848$	12.4071			0.426062
$849$	−4.44352	+	9.72996i	−0.152501	+	0.333931i
$850$	16.2446			0.557186
$851$	15.9090	+	18.3600i	0.545353	+	0.629371i
$852$	−9.94903	−	2.92130i	−0.340848	−	0.100082i
$853$	17.4745	−	38.2637i	0.598314	−	1.31013i	−0.331971	−	0.943289i	$-0.607714\pi$
$853$	17.4745	−	38.2637i	0.598314	−	1.31013i	0.930286	−	0.366836i	$-0.119559\pi$
$854$	−2.55172	−	17.7476i	−0.0873180	−	0.607310i
$855$	−4.95153	+	1.45390i	−0.169339	+	0.0497224i
$856$	−1.19755			−0.0409316
$857$	13.5560	−	15.6444i	0.463063	−	0.534403i	−0.475406	−	0.879766i	$-0.657699\pi$
$857$	13.5560	−	15.6444i	0.463063	−	0.534403i	0.938469	+	0.345364i	$0.112244\pi$
$858$	−5.79213	−	9.52850i	−0.197740	−	0.325298i
$859$	−20.0716	−	23.1638i	−0.684833	−	0.790339i	0.301787	−	0.953375i	$-0.402417\pi$
$859$	−20.0716	−	23.1638i	−0.684833	−	0.790339i	−0.986620	+	0.163036i	$0.947871\pi$
$860$	12.6136	+	14.5569i	0.430120	+	0.496385i
$861$	4.54767	+	1.33532i	0.154984	+	0.0455074i
$862$	−19.0153	−	5.58340i	−0.647664	−	0.190171i
$863$	2.14714	−	14.9337i	0.0730894	−	0.508348i	−0.920086	−	0.391717i	$-0.871881\pi$
$863$	2.14714	−	14.9337i	0.0730894	−	0.508348i	0.993175	−	0.116631i	$-0.0372096\pi$
$864$	0.841254	+	0.540641i	0.0286200	+	0.0183930i
$865$	5.95079	−	13.0304i	0.202333	−	0.443048i
$866$	0.294013	−	0.188950i	0.00999096	−	0.00642080i
$867$	−10.1117	−	22.1415i	−0.343410	−	0.751964i
$868$	−3.19897	−	22.2493i	−0.108580	−	0.755192i
$869$	0.181718	−	7.26449i	0.00616438	−	0.246431i
$870$	−1.81721	+	12.6390i	−0.0616093	+	0.428502i
$871$	−9.03793	+	2.65378i	−0.306239	+	0.0899198i
$872$	5.93046	+	3.81127i	0.200831	+	0.129066i
$873$	−10.2102	+	2.99800i	−0.345564	+	0.101467i
$874$	−5.54437			−0.187541
$875$	−12.1156	+	13.9822i	−0.409583	+	0.472684i
$876$	−1.47588	+	0.948492i	−0.0498655	+	0.0320466i
$877$	22.3497	−	25.7929i	0.754696	−	0.870966i	−0.240319	−	0.970694i	$-0.577252\pi$
$877$	22.3497	−	25.7929i	0.754696	−	0.870966i	0.995015	+	0.0997284i	$0.0317974\pi$
$878$	5.43646	−	6.27401i	0.183472	−	0.211738i
$879$	−8.22002	−	5.28268i	−0.277254	−	0.178180i
$880$	8.97117	+	1.51974i	0.302418	+	0.0512303i
$881$	48.1974	−	30.9746i	1.62381	−	1.04356i	0.670349	−	0.742046i	$-0.266144\pi$
$881$	48.1974	−	30.9746i	1.62381	−	1.04356i	0.953462	−	0.301514i	$-0.0974921\pi$
$882$	0.0616489	−	0.428778i	0.00207583	−	0.0144377i
$883$	−5.29621	−	6.11215i	−0.178232	−	0.205690i	0.659603	−	0.751614i	$-0.270724\pi$
$883$	−5.29621	−	6.11215i	−0.178232	−	0.205690i	−0.837835	+	0.545924i	$0.816179\pi$
$884$	14.1563	−	16.3373i	0.476129	−	0.549482i
$885$	0.0540285	+	0.375776i	0.00181615	+	0.0126316i
$886$	1.39192	+	1.60636i	0.0467625	+	0.0539668i
$887$	−3.54978			−0.119190			−0.0595950	−	0.998223i	$-0.518981\pi$
$887$	−3.54978			−0.119190			−0.0595950	+	0.998223i	$0.518981\pi$
$888$	−3.42393	+	7.49736i	−0.114900	+	0.251595i
$889$	40.4571	+	11.8793i	1.35689	+	0.398418i
$890$	−32.2859	+	9.48000i	−1.08223	+	0.317770i
$891$	0.854530	+	3.20465i	0.0286278	+	0.107360i
$892$	−16.0322	−	4.70746i	−0.536796	−	0.157618i
$893$	−12.7672	−	8.20497i	−0.427238	−	0.274569i
$894$	−7.10178	−	15.5507i	−0.237519	−	0.520094i
$895$	2.40594	−	16.7337i	0.0804218	−	0.559346i
$896$	−2.61595	+	0.768112i	−0.0873927	+	0.0256608i
$897$	−8.33660	+	5.35761i	−0.278351	+	0.178885i
$898$	18.6399	+	11.9791i	0.622021	+	0.399749i
$899$	5.46113	−	37.9830i	0.182139	−	1.26680i
$900$	−0.359558	−	2.50078i	−0.0119853	−	0.0833593i
$901$	−33.1394	+	72.5651i	−1.10403	+	2.41749i
$902$	3.23752	−	4.77099i	0.107798	−	0.158857i
$903$	−7.95176	−	17.4119i	−0.264618	−	0.579433i
$904$	9.09391	−	5.84430i	0.302459	−	0.194379i
$905$	9.69042	+	67.3984i	0.322121	+	2.24040i
$906$	8.03074	+	17.5849i	0.266803	+	0.584218i
$907$	3.73585	+	8.18037i	0.124047	+	0.271625i	0.961460	−	0.274946i	$-0.0886601\pi$
$907$	3.73585	+	8.18037i	0.124047	+	0.271625i	−0.837413	+	0.546571i	$0.815933\pi$
$908$	5.56988	+	12.1963i	0.184843	+	0.404749i
$909$	2.44429	+	5.35226i	0.0810721	+	0.177523i
$910$	−3.57886	−	24.8915i	−0.118638	−	0.825146i
$911$	27.2078	−	17.4854i	0.901434	−	0.579316i	−0.00578125	−	0.999983i	$-0.501840\pi$
$911$	27.2078	−	17.4854i	0.901434	−	0.579316i	0.907215	+	0.420667i	$0.138204\pi$
$912$	−0.781418	−	1.71107i	−0.0258753	−	0.0566591i
$913$	43.6343	−	18.6229i	1.44408	−	0.616327i
$914$	7.69758	−	16.8554i	0.254613	−	0.557526i
$915$	2.56768	+	17.8586i	0.0848850	+	0.590388i
$916$	−2.31752	+	16.1187i	−0.0765729	+	0.532576i
$917$	−32.7010	−	21.0157i	−1.07988	−	0.693998i
$918$	−5.40901	+	3.47616i	−0.178524	+	0.114730i
$919$	24.6933	−	7.25062i	0.814558	−	0.239176i	0.152187	−	0.988352i	$-0.451368\pi$
$919$	24.6933	−	7.25062i	0.814558	−	0.239176i	0.662371	+	0.749176i	$0.269550\pi$
$920$	1.15079	−	8.00395i	0.0379406	−	0.263882i
$921$	3.20338	+	7.01443i	0.105555	+	0.231133i
$922$	34.5663	+	22.2144i	1.13838	+	0.731593i
$923$	33.4497	+	9.82171i	1.10101	+	0.323285i
$924$	−8.12875	−	3.96086i	−0.267416	−	0.130303i
$925$	19.9803	−	5.86676i	0.656949	−	0.192898i
$926$	35.1593	+	10.3237i	1.15541	+	0.339258i
$927$	−0.836508	+	1.83170i	−0.0274745	+	0.0601608i
$928$	−4.65435			−0.152787
$929$	29.3484	+	33.8698i	0.962888	+	1.11123i	0.993741	+	0.111708i	$0.0356322\pi$
$929$	29.3484	+	33.8698i	0.962888	+	1.11123i	−0.0308529	+	0.999524i	$0.509822\pi$
$930$	3.21899	+	22.3886i	0.105555	+	0.734150i
$931$	−0.533612	+	0.615821i	−0.0174884	+	0.0201827i
$932$	−6.05106	−	6.98329i	−0.198209	−	0.228745i
$933$	−0.618174	+	4.29949i	−0.0202381	+	0.140759i
$934$	10.0420	−	6.45359i	0.328584	−	0.211168i
$935$	−32.8504	+	48.4102i	−1.07432	+	1.58318i
$936$	−2.82838	−	1.81769i	−0.0924485	−	0.0594130i
$937$	−15.0369	+	17.3536i	−0.491236	+	0.566916i	−0.946195	−	0.323596i	$-0.895108\pi$
$937$	−15.0369	+	17.3536i	−0.491236	+	0.566916i	0.454960	+	0.890512i	$0.349654\pi$
$938$	−5.00211	+	5.77274i	−0.163325	+	0.188487i
$939$	9.80784	−	6.30312i	0.320067	−	0.205694i
$940$	14.4948	−	16.7279i	0.472768	−	0.545604i
$941$	−14.4366			−0.470619			−0.235309	−	0.971921i	$-0.575610\pi$
$941$	−14.4366			−0.470619			−0.235309	+	0.971921i	$0.575610\pi$
$942$	0.368898	−	0.108318i	0.0120193	−	0.00352920i
$943$	−4.31060	−	2.77025i	−0.140372	−	0.0902118i
$944$	−0.132776	+	0.0389864i	−0.00432147	+	0.00126890i
$945$	−1.06447	+	7.40356i	−0.0346273	+	0.240838i
$946$	−23.1244	+	2.73650i	−0.751839	+	0.0889712i
$947$	3.72250	+	25.8906i	0.120965	+	0.841330i	0.956467	+	0.291842i	$0.0942681\pi$
$947$	3.72250	+	25.8906i	0.120965	+	0.841330i	−0.835502	+	0.549488i	$0.814823\pi$
$948$	−0.910179	−	1.99302i	−0.0295613	−	0.0647301i
$949$	4.96207	−	3.18893i	0.161076	−	0.103517i
$950$	−1.97425	+	4.32300i	−0.0640531	+	0.140257i
$951$	25.4911	+	16.3821i	0.826605	+	0.531227i
$952$	2.49476	−	17.3514i	0.0808557	−	0.562363i
$953$	−26.0709	−	7.65512i	−0.844520	−	0.247974i	−0.169277	−	0.985569i	$-0.554143\pi$
$953$	−26.0709	−	7.65512i	−0.844520	−	0.247974i	−0.675243	+	0.737595i	$0.735961\pi$
$954$	11.9045	+	3.49549i	0.385424	+	0.113171i
$955$	−48.8244	−	56.3464i	−1.57992	−	1.82333i
$956$	−3.29327	−	3.80064i	−0.106512	−	0.122922i
$957$	−11.4099	−	10.3975i	−0.368829	−	0.336103i
$958$	−10.7727	+	12.4324i	−0.348051	+	0.401672i
$959$	−10.8208			−0.349421
$960$	2.63232	−	0.772918i	0.0849577	−	0.0249458i
$961$	−5.26201	−	36.5981i	−0.169742	−	1.18058i
$962$	11.5116	−	25.2069i	0.371149	−	0.812703i
$963$	−1.14905	−	0.337390i	−0.0370275	−	0.0108722i
$964$	9.67596	+	11.1667i	0.311642	+	0.359654i
$965$	55.1003			1.77374
$966$	−3.33826	+	7.30978i	−0.107407	+	0.235188i
$967$	−42.5175			−1.36727			−0.683635	−	0.729824i	$-0.739602\pi$
$967$	−42.5175			−1.36727			−0.683635	+	0.729824i	$0.739602\pi$
$968$	−7.61010	+	7.94269i	−0.244598	+	0.255288i
$969$	12.0946			0.388535
$970$	−12.1275	+	26.5556i	−0.389392	+	0.852649i
$971$	−52.3237			−1.67915			−0.839574	−	0.543246i	$-0.817195\pi$
$971$	−52.3237			−1.67915			−0.839574	+	0.543246i	$0.817195\pi$
$972$	0.654861	+	0.755750i	0.0210047	+	0.0242407i
$973$	39.6241	+	11.6347i	1.27029	+	0.372991i
$974$	14.3371	−	31.3939i	0.459390	−	1.00592i
$975$	1.20887	+	8.40787i	0.0387148	+	0.269267i
$976$	−6.31011	+	1.85281i	−0.201982	+	0.0593072i
$977$	−50.2555			−1.60782			−0.803909	−	0.594753i	$-0.797250\pi$
$977$	−50.2555			−1.60782			−0.803909	+	0.594753i	$0.797250\pi$
$978$	−4.38037	+	5.05521i	−0.140069	+	0.161648i
$979$	12.4331	−	38.7325i	0.397363	−	1.23790i
$980$	−0.778253	−	0.898152i	−0.0248604	−	0.0286904i
$981$	4.61647	+	5.32769i	0.147393	+	0.170100i
$982$	29.6458	+	8.70478i	0.946034	+	0.277781i
$983$	−17.7098	−	5.20008i	−0.564856	−	0.165857i	−0.0131769	−	0.999913i	$-0.504194\pi$
$983$	−17.7098	−	5.20008i	−0.564856	−	0.165857i	−0.551679	+	0.834057i	$0.686013\pi$
$984$	0.247406	−	1.72074i	0.00788700	−	0.0548553i
$985$	−54.5735	−	35.0722i	−1.73886	−	1.11749i
$986$	12.4318	−	27.2218i	0.395908	−	0.866918i
$987$	−18.5047	+	11.8922i	−0.589010	+	0.378534i
$988$	2.62721	+	5.75278i	0.0835826	+	0.183020i
$989$	2.94507	+	20.4834i	0.0936477	+	0.651334i
$990$	8.17961	+	3.98564i	0.259965	+	0.126672i
$991$	3.23658	−	22.5109i	0.102813	−	0.715083i	−0.871583	−	0.490248i	$-0.836906\pi$
$991$	3.23658	−	22.5109i	0.102813	−	0.715083i	0.974397	−	0.224836i	$-0.0721846\pi$
$992$	−7.91069	+	2.32279i	−0.251165	+	0.0737486i
$993$	15.9399	+	10.2440i	0.505838	+	0.325082i
$994$	27.1249	−	7.96460i	0.860350	−	0.252622i
$995$	48.8385			1.54828
$996$	9.36737	−	10.8105i	0.296816	−	0.342544i
$997$	34.8989	−	22.4281i	1.10526	−	0.710306i	0.145003	−	0.989431i	$-0.453681\pi$
$997$	34.8989	−	22.4281i	1.10526	−	0.710306i	0.960255	+	0.279125i	$0.0900444\pi$
$998$	8.75582	−	10.1048i	0.277161	−	0.319860i
$999$	−5.39749	+	6.22903i	−0.170769	+	0.197078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.i.b.265.1	✓	50
121.100	even	11	inner	726.2.i.b.463.1	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
726.2.i.b.265.1	✓	50	1.1	even	1	trivial
726.2.i.b.463.1	yes	50	121.100	even	11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} -1.00000 q^{3} +(-0.654861 - 0.755750i) q^{4} +(-2.63232 - 0.772918i) q^{5} +(0.415415 - 0.909632i) q^{6} +(0.388005 + 2.69864i) q^{7} +(0.959493 - 0.281733i) q^{8} +1.00000 q^{9} +(1.79657 - 2.07336i) q^{10} +(0.854530 + 3.20465i) q^{11} +(0.654861 + 0.755750i) q^{12} +(-2.20171 - 2.54091i) q^{13} +(-2.61595 - 0.768112i) q^{14} +(2.63232 + 0.772918i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-5.40901 - 3.47616i) q^{17} +(-0.415415 + 0.909632i) q^{18} +(1.58244 - 1.01697i) q^{19} +(1.13967 + 2.49553i) q^{20} +(-0.388005 - 2.69864i) q^{21} +(-3.27004 - 0.553951i) q^{22} +(-0.419470 + 2.91748i) q^{23} +(-0.959493 + 0.281733i) q^{24} +(2.12542 + 1.36593i) q^{25} +(3.22591 - 0.947214i) q^{26} -1.00000 q^{27} +(1.78540 - 2.06047i) q^{28} +(3.91549 - 2.51633i) q^{29} +(-1.79657 + 2.07336i) q^{30} +(5.39910 - 6.23090i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.854530 - 3.20465i) q^{33} +(5.40901 - 3.47616i) q^{34} +(1.06447 - 7.40356i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(5.39749 - 6.22903i) q^{37} +(0.267702 + 1.86191i) q^{38} +(2.20171 + 2.54091i) q^{39} -2.74345 q^{40} +(-0.722174 + 1.58134i) q^{41} +(2.61595 + 0.768112i) q^{42} +(6.73652 - 1.97802i) q^{43} +(1.86231 - 2.74441i) q^{44} +(-2.63232 - 0.772918i) q^{45} +(-2.47958 - 1.59353i) q^{46} +(-3.35158 - 7.33893i) q^{47} +(0.142315 - 0.989821i) q^{48} +(-0.415640 + 0.122043i) q^{49} +(-2.12542 + 1.36593i) q^{50} +(5.40901 + 3.47616i) q^{51} +(-0.478477 + 3.32788i) q^{52} +(-1.76572 - 12.2808i) q^{53} +(0.415415 - 0.909632i) q^{54} +(0.227536 - 9.09613i) q^{55} +(1.13258 + 2.48001i) q^{56} +(-1.58244 + 1.01697i) q^{57} +(0.662384 + 4.60698i) q^{58} +(0.0574855 + 0.125876i) q^{59} +(-1.13967 - 2.49553i) q^{60} +(2.73198 + 5.98220i) q^{61} +(3.42496 + 7.49961i) q^{62} +(0.388005 + 2.69864i) q^{63} +(0.841254 - 0.540641i) q^{64} +(3.83168 + 8.39021i) q^{65} +(3.27004 + 0.553951i) q^{66} +(1.16385 - 2.54849i) q^{67} +(0.915043 + 6.36426i) q^{68} +(0.419470 - 2.91748i) q^{69} +(6.29232 + 4.04383i) q^{70} +(-8.72300 + 5.60593i) q^{71} +(0.959493 - 0.281733i) q^{72} +(-0.249675 + 1.73653i) q^{73} +(3.42393 + 7.49736i) q^{74} +(-2.12542 - 1.36593i) q^{75} +(-1.80486 - 0.529954i) q^{76} +(-8.31662 + 3.54949i) q^{77} +(-3.22591 + 0.947214i) q^{78} +(-2.10226 - 0.617280i) q^{79} +(1.13967 - 2.49553i) q^{80} +1.00000 q^{81} +(-1.13844 - 1.31382i) q^{82} +(-2.03572 - 14.1588i) q^{83} +(-1.78540 + 2.06047i) q^{84} +(11.5514 + 13.3311i) q^{85} +(-0.999181 + 6.94945i) q^{86} +(-3.91549 + 2.51633i) q^{87} +(1.72277 + 2.83409i) q^{88} +(-10.3181 - 6.63107i) q^{89} +(1.79657 - 2.07336i) q^{90} +(6.00271 - 6.92750i) q^{91} +(2.47958 - 1.59353i) q^{92} +(-5.39910 + 6.23090i) q^{93} +8.06802 q^{94} +(-4.95153 + 1.45390i) q^{95} +(0.841254 + 0.540641i) q^{96} +(-10.2102 + 2.99800i) q^{97} +(0.0616489 - 0.428778i) q^{98} +(0.854530 + 3.20465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{2} - 50 q^{3} - 5 q^{4} - 5 q^{6} - q^{7} + 5 q^{8} + 50 q^{9} - 11 q^{11} + 5 q^{12} - 21 q^{13} - 10 q^{14} - 5 q^{16} - 12 q^{17} + 5 q^{18} + q^{21} - 11 q^{22} + 22 q^{23} - 5 q^{24}+ \cdots - 11 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 50 * q^3 - 5 * q^4 - 5 * q^6 - q^7 + 5 * q^8 + 50 * q^9 - 11 * q^11 + 5 * q^12 - 21 * q^13 - 10 * q^14 - 5 * q^16 - 12 * q^17 + 5 * q^18 + q^21 - 11 * q^22 + 22 * q^23 - 5 * q^24 - 3 * q^25 - q^26 - 50 * q^27 - q^28 + 36 * q^31 + 5 * q^32 + 11 * q^33 + 12 * q^34 - 11 * q^35 - 5 * q^36 - 19 * q^37 + 22 * q^38 + 21 * q^39 + 23 * q^41 + 10 * q^42 - 44 * q^43 + 11 * q^44 + 11 * q^46 + 20 * q^47 + 5 * q^48 - 24 * q^49 + 3 * q^50 + 12 * q^51 + q^52 - 11 * q^53 - 5 * q^54 - 33 * q^55 + 12 * q^56 + q^59 + 38 * q^61 - 14 * q^62 - q^63 - 5 * q^64 + 26 * q^65 + 11 * q^66 - 64 * q^67 - q^68 - 22 * q^69 + 24 * q^71 + 5 * q^72 + 35 * q^73 - 14 * q^74 + 3 * q^75 + 22 * q^76 - 77 * q^77 + q^78 - 32 * q^79 + 50 * q^81 - 12 * q^82 - 8 * q^83 + q^84 - 5 * q^85 - 11 * q^88 - 12 * q^89 - 11 * q^92 - 36 * q^93 + 46 * q^94 + 57 * q^95 - 5 * q^96 + 33 * q^97 - 42 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

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Database

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