LMFDB - Embedded newform 633.2.k.a.23.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [633,2,Mod(23,633)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(633, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("633.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 633 = 3 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	633.k (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.05453044795$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			23.14
Character	$\chi$	$=$	633.23
Dual form			633.2.k.a.578.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.575669 + 1.77173i) q^{2} +(-0.528679 - 1.64939i) q^{3} +(-1.18959 - 0.864285i) q^{4} +(-0.832701 + 1.14612i) q^{5} +(3.22662 + 0.0128300i) q^{6} +(2.59824 - 0.844220i) q^{7} +(-0.798157 + 0.579895i) q^{8} +(-2.44100 + 1.74400i) q^{9} +O(q^{10})$	\(q+(-0.575669 + 1.77173i) q^{2} +(-0.528679 - 1.64939i) q^{3} +(-1.18959 - 0.864285i) q^{4} +(-0.832701 + 1.14612i) q^{5} +(3.22662 + 0.0128300i) q^{6} +(2.59824 - 0.844220i) q^{7} +(-0.798157 + 0.579895i) q^{8} +(-2.44100 + 1.74400i) q^{9} +(-1.55124 - 2.13510i) q^{10} +(-0.737463 + 1.01503i) q^{11} +(-0.796637 + 2.41902i) q^{12} +(-0.610128 - 1.87778i) q^{13} +5.08937i q^{14} +(2.33063 + 0.767525i) q^{15} +(-1.47670 - 4.54483i) q^{16} +(1.20538 + 3.70979i) q^{17} +(-1.68468 - 5.32875i) q^{18} +(0.838196 + 2.57970i) q^{19} +(1.98114 - 0.643711i) q^{20} +(-2.76609 - 3.83920i) q^{21} +(-1.37382 - 1.89091i) q^{22} +(-0.901785 + 2.77541i) q^{23} +(1.37844 + 1.00990i) q^{24} +(0.924897 + 2.84654i) q^{25} +3.67815 q^{26} +(4.16704 + 3.10415i) q^{27} +(-3.82048 - 1.24135i) q^{28} +(-0.137517 - 0.423233i) q^{29} +(-2.70151 + 3.68739i) q^{30} +9.47388i q^{31} +6.92913 q^{32} +(2.06407 + 0.679742i) q^{33} -7.26664 q^{34} +(-1.19599 + 3.68087i) q^{35} +(4.41109 + 0.0350802i) q^{36} +(-3.62889 + 2.63654i) q^{37} -5.05305 q^{38} +(-2.77464 + 1.99909i) q^{39} -1.39766i q^{40} +(-7.86258 - 5.71250i) q^{41} +(8.39437 - 2.69064i) q^{42} -12.1782 q^{43} +(1.75455 - 0.570089i) q^{44} +(0.0337983 - 4.24989i) q^{45} +(-4.39814 - 3.19543i) q^{46} +(4.33230 - 1.40765i) q^{47} +(-6.71551 + 4.83842i) q^{48} +(0.375036 - 0.272479i) q^{49} -5.57572 q^{50} +(5.48165 - 3.94944i) q^{51} +(-0.897138 + 2.76111i) q^{52} +(3.72793 + 5.13105i) q^{53} +(-7.89854 + 5.59590i) q^{54} +(-0.549256 - 1.69044i) q^{55} +(-1.58425 + 2.18053i) q^{56} +(3.81181 - 2.74635i) q^{57} +0.829018 q^{58} +(-4.17393 + 5.74492i) q^{59} +(-2.10912 - 2.92736i) q^{60} +(2.08249 + 2.86630i) q^{61} +(-16.7851 - 5.45382i) q^{62} +(-4.86998 + 6.59207i) q^{63} +(-1.03548 + 3.18687i) q^{64} +(2.66021 + 0.864354i) q^{65} +(-2.39254 + 3.26566i) q^{66} -1.25080i q^{67} +(1.77241 - 5.45491i) q^{68} +(5.05450 + 0.0200982i) q^{69} +(-5.83300 - 4.23792i) q^{70} +(3.12120 + 4.29596i) q^{71} +(0.936963 - 2.80751i) q^{72} +12.5814 q^{73} +(-2.58219 - 7.94717i) q^{74} +(4.20609 - 3.03042i) q^{75} +(1.23249 - 3.79322i) q^{76} +(-1.05920 + 3.25988i) q^{77} +(-1.94456 - 6.06671i) q^{78} +(-0.782707 - 0.568670i) q^{79} +(6.43855 + 2.09201i) q^{80} +(2.91694 - 8.51419i) q^{81} +(14.6472 - 10.6418i) q^{82} +(-9.26354 + 12.7502i) q^{83} +(-0.0276661 + 6.95775i) q^{84} +(-5.25558 - 1.70764i) q^{85} +(7.01064 - 21.5765i) q^{86} +(-0.625376 + 0.450574i) q^{87} -1.23781i q^{88} +(-0.656054 - 2.01913i) q^{89} +(7.51019 + 2.50641i) q^{90} +(-3.17052 - 4.36385i) q^{91} +(3.47150 - 2.52219i) q^{92} +(15.6262 - 5.00864i) q^{93} +8.48599i q^{94} +(-3.65460 - 1.18745i) q^{95} +(-3.66329 - 11.4289i) q^{96} +(4.01730 + 5.52933i) q^{97} +(0.266862 + 0.821318i) q^{98} +(0.0299327 - 3.76382i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9}+O(q^{10}) $ 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9	$ 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9} - 20 q^{10} + 6 q^{13} - 46 q^{16} - 20 q^{18} + 6 q^{19} - 3 q^{21} - 10 q^{22} + 23 q^{24} + 50 q^{25} - 40 q^{27} + 80 q^{28} - q^{30} + 12 q^{34} + 13 q^{36} - 42 q^{37} + 25 q^{39} - 10 q^{42} + 40 q^{43} - 23 q^{45} - 2 q^{46} - 15 q^{48} + 30 q^{49} - 11 q^{51} - 34 q^{52} + 128 q^{54} + 14 q^{55} + 20 q^{57} + 60 q^{58} + 30 q^{60} - 10 q^{61} - 108 q^{64} - 73 q^{66} + 40 q^{69} + 70 q^{70} - 105 q^{72} - 20 q^{73} - 10 q^{75} - 12 q^{76} - 82 q^{78} - 30 q^{79} - 42 q^{81} - 106 q^{82} + 121 q^{84} - 110 q^{85} - 11 q^{87} + 60 q^{90} - 40 q^{91} - 45 q^{93} - 114 q^{96} - 80 q^{97} - 18 q^{99}+O(q^{100}) $ 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9 - 20 * q^10 + 6 * q^13 - 46 * q^16 - 20 * q^18 + 6 * q^19 - 3 * q^21 - 10 * q^22 + 23 * q^24 + 50 * q^25 - 40 * q^27 + 80 * q^28 - q^30 + 12 * q^34 + 13 * q^36 - 42 * q^37 + 25 * q^39 - 10 * q^42 + 40 * q^43 - 23 * q^45 - 2 * q^46 - 15 * q^48 + 30 * q^49 - 11 * q^51 - 34 * q^52 + 128 * q^54 + 14 * q^55 + 20 * q^57 + 60 * q^58 + 30 * q^60 - 10 * q^61 - 108 * q^64 - 73 * q^66 + 40 * q^69 + 70 * q^70 - 105 * q^72 - 20 * q^73 - 10 * q^75 - 12 * q^76 - 82 * q^78 - 30 * q^79 - 42 * q^81 - 106 * q^82 + 121 * q^84 - 110 * q^85 - 11 * q^87 + 60 * q^90 - 40 * q^91 - 45 * q^93 - 114 * q^96 - 80 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/633\mathbb{Z}\right)^\times$.

$n$	$212$	$424$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.575669	+	1.77173i	−0.407059	+	1.25280i	0.512104	+	0.858923i	$0.328866\pi$
$2$	−0.575669	+	1.77173i	−0.407059	+	1.25280i	−0.919163	+	0.393876i	$0.871134\pi$
$3$	−0.528679	−	1.64939i	−0.305233	−	0.952278i
$3$	−0.528679	−	1.64939i	−0.305233	−	0.952278i
$4$	−1.18959	−	0.864285i	−0.594793	−	0.432142i
$5$	−0.832701	+	1.14612i	−0.372395	+	0.512558i	−0.953550	−	0.301235i	$-0.902601\pi$
$5$	−0.832701	+	1.14612i	−0.372395	+	0.512558i	0.581155	+	0.813793i	$0.302601\pi$
$6$	3.22662	+	0.0128300i	1.31726	+	0.00523783i
$7$	2.59824	−	0.844220i	0.982043	−	0.319085i	0.226375	−	0.974040i	$-0.427312\pi$
$7$	2.59824	−	0.844220i	0.982043	−	0.319085i	0.755668	+	0.654955i	$0.227312\pi$
$8$	−0.798157	+	0.579895i	−0.282191	+	0.205024i
$9$	−2.44100	+	1.74400i	−0.813666	+	0.581333i
$10$	−1.55124	−	2.13510i	−0.490546	−	0.675178i
$11$	−0.737463	+	1.01503i	−0.222354	+	0.306043i	−0.905590	−	0.424153i	$-0.860572\pi$
$11$	−0.737463	+	1.01503i	−0.222354	+	0.306043i	0.683237	+	0.730197i	$0.260572\pi$
$12$	−0.796637	+	2.41902i	−0.229969	+	0.698312i
$13$	−0.610128	−	1.87778i	−0.169219	−	0.520803i	0.830103	−	0.557610i	$-0.188281\pi$
$13$	−0.610128	−	1.87778i	−0.169219	−	0.520803i	−0.999322	+	0.0368067i	$0.988281\pi$
$14$			5.08937i			1.36019i
$15$	2.33063	+	0.767525i	0.601765	+	0.198174i
$16$	−1.47670	−	4.54483i	−0.369176	−	1.13621i
$17$	1.20538	+	3.70979i	0.292349	+	0.899757i	0.984099	+	0.177620i	$0.0568399\pi$
$17$	1.20538	+	3.70979i	0.292349	+	0.899757i	−0.691750	+	0.722137i	$0.743160\pi$
$18$	−1.68468	−	5.32875i	−0.397084	−	1.25600i
$19$	0.838196	+	2.57970i	0.192295	+	0.591824i	0.999998	+	0.00223342i	$0.000710919\pi$
$19$	0.838196	+	2.57970i	0.192295	+	0.591824i	−0.807702	+	0.589591i	$0.799289\pi$
$20$	1.98114	−	0.643711i	0.442996	−	0.143938i
$21$	−2.76609	−	3.83920i	−0.603610	−	0.837783i
$22$	−1.37382	−	1.89091i	−0.292900	−	0.403142i
$23$	−0.901785	+	2.77541i	−0.188035	+	0.578713i	−0.999987	−	0.00501100i	$-0.998405\pi$
$23$	−0.901785	+	2.77541i	−0.188035	+	0.578713i	0.811952	+	0.583724i	$0.198405\pi$
$24$	1.37844	+	1.00990i	0.281374	+	0.206144i
$25$	0.924897	+	2.84654i	0.184979	+	0.569308i
$26$	3.67815			0.721344
$27$	4.16704	+	3.10415i	0.801948	+	0.597394i
$28$	−3.82048	−	1.24135i	−0.722003	−	0.234593i
$29$	−0.137517	−	0.423233i	−0.0255362	−	0.0785925i	0.937476	−	0.348049i	$-0.113156\pi$
$29$	−0.137517	−	0.423233i	−0.0255362	−	0.0785925i	−0.963012	+	0.269457i	$0.913156\pi$
$30$	−2.70151	+	3.68739i	−0.493227	+	0.673223i
$31$			9.47388i			1.70156i	0.525523	+	0.850779i	$0.323870\pi$
$31$			9.47388i			1.70156i	−0.525523	+	0.850779i	$0.676130\pi$
$32$	6.92913			1.22491
$33$	2.06407	+	0.679742i	0.359308	+	0.118328i
$34$	−7.26664			−1.24622
$35$	−1.19599	+	3.68087i	−0.202159	+	0.622180i
$36$	4.41109	+	0.0350802i	0.735181	+	0.00584670i
$37$	−3.62889	+	2.63654i	−0.596585	+	0.433445i	−0.844665	−	0.535295i	$-0.820200\pi$
$37$	−3.62889	+	2.63654i	−0.596585	+	0.433445i	0.248080	+	0.968740i	$0.420200\pi$
$38$	−5.05305			−0.819713
$39$	−2.77464	+	1.99909i	−0.444298	+	0.320110i
$40$		−	1.39766i		−	0.220989i
$41$	−7.86258	−	5.71250i	−1.22793	−	0.892143i	−0.231196	−	0.972907i	$-0.574264\pi$
$41$	−7.86258	−	5.71250i	−1.22793	−	0.892143i	−0.996733	+	0.0807642i	$0.974264\pi$
$42$	8.39437	−	2.69064i	1.29528	−	0.415175i
$43$	−12.1782			−1.85717			−0.928583	−	0.371125i	$-0.878972\pi$
$43$	−12.1782			−1.85717			−0.928583	+	0.371125i	$0.878972\pi$
$44$	1.75455	−	0.570089i	0.264509	−	0.0859441i
$45$	0.0337983	−	4.24989i	0.00503835	−	0.633537i
$46$	−4.39814	−	3.19543i	−0.648470	−	0.471141i
$47$	4.33230	−	1.40765i	0.631931	−	0.205327i	0.0245008	−	0.999700i	$-0.492200\pi$
$47$	4.33230	−	1.40765i	0.631931	−	0.205327i	0.607430	+	0.794373i	$0.292200\pi$
$48$	−6.71551	+	4.83842i	−0.969300	+	0.698366i
$49$	0.375036	−	0.272479i	0.0535765	−	0.0389256i
$50$	−5.57572			−0.788526
$51$	5.48165	−	3.94944i	0.767584	−	0.553033i
$52$	−0.897138	+	2.76111i	−0.124411	+	0.382897i
$53$	3.72793	+	5.13105i	0.512070	+	0.704804i	0.984267	−	0.176689i	$-0.0565387\pi$
$53$	3.72793	+	5.13105i	0.512070	+	0.704804i	−0.472196	+	0.881493i	$0.656539\pi$
$54$	−7.89854	+	5.59590i	−1.07486	+	0.761506i
$55$	−0.549256	−	1.69044i	−0.0740617	−	0.227938i
$56$	−1.58425	+	2.18053i	−0.211704	+	0.291385i
$57$	3.81181	−	2.74635i	0.504886	−	0.363763i
$58$	0.829018			0.108855
$59$	−4.17393	+	5.74492i	−0.543399	+	0.747924i	−0.989098	−	0.147258i	$-0.952955\pi$
$59$	−4.17393	+	5.74492i	−0.543399	+	0.747924i	0.445699	+	0.895183i	$0.352955\pi$
$60$	−2.10912	−	2.92736i	−0.272286	−	0.377921i
$61$	2.08249	+	2.86630i	0.266635	+	0.366992i	0.921250	−	0.388970i	$-0.127169\pi$
$61$	2.08249	+	2.86630i	0.266635	+	0.366992i	−0.654615	+	0.755963i	$0.727169\pi$
$62$	−16.7851	−	5.45382i	−2.13171	−	0.692635i
$63$	−4.86998	+	6.59207i	−0.613560	+	0.830523i
$64$	−1.03548	+	3.18687i	−0.129435	+	0.398359i
$65$	2.66021	+	0.864354i	0.329958	+	0.107210i
$66$	−2.39254	+	3.26566i	−0.294501	+	0.401975i
$67$		−	1.25080i		−	0.152809i	−0.997077	−	0.0764045i	$-0.975656\pi$
$67$		−	1.25080i		−	0.152809i	0.997077	−	0.0764045i	$-0.0243440\pi$
$68$	1.77241	−	5.45491i	0.214936	−	0.661505i
$69$	5.05450	+	0.0200982i	0.608490	+	0.00241954i
$70$	−5.83300	−	4.23792i	−0.697177	−	0.506529i
$71$	3.12120	+	4.29596i	0.370418	+	0.509837i	0.953014	−	0.302925i	$-0.0979631\pi$
$71$	3.12120	+	4.29596i	0.370418	+	0.509837i	−0.582596	+	0.812762i	$0.697963\pi$
$72$	0.936963	−	2.80751i	0.110422	−	0.330868i
$73$	12.5814			1.47255			0.736273	−	0.676684i	$-0.236584\pi$
$73$	12.5814			1.47255			0.736273	+	0.676684i	$0.236584\pi$
$74$	−2.58219	−	7.94717i	−0.300174	−	0.923840i
$75$	4.20609	−	3.03042i	0.485677	−	0.349923i
$76$	1.23249	−	3.79322i	0.141376	−	0.435112i
$77$	−1.05920	+	3.25988i	−0.120707	+	0.371498i
$78$	−1.94456	−	6.06671i	−0.220178	−	0.686920i
$79$	−0.782707	−	0.568670i	−0.0880615	−	0.0639804i	0.542883	−	0.839808i	$-0.317333\pi$
$79$	−0.782707	−	0.568670i	−0.0880615	−	0.0639804i	−0.630945	+	0.775828i	$0.717333\pi$
$80$	6.43855	+	2.09201i	0.719852	+	0.233894i
$81$	2.91694	−	8.51419i	0.324104	−	0.946021i
$82$	14.6472	−	10.6418i	1.61752	−	1.17519i
$83$	−9.26354	+	12.7502i	−1.01681	+	1.39951i	−0.102386	+	0.994745i	$0.532648\pi$
$83$	−9.26354	+	12.7502i	−1.01681	+	1.39951i	−0.914420	+	0.404768i	$0.867352\pi$
$84$	−0.0276661	+	6.95775i	−0.00301862	+	0.759153i
$85$	−5.25558	−	1.70764i	−0.570047	−	0.185220i
$86$	7.01064	−	21.5765i	0.755977	−	2.32666i
$87$	−0.625376	+	0.450574i	−0.0670474	+	0.0483066i
$88$		−	1.23781i		−	0.131951i
$89$	−0.656054	−	2.01913i	−0.0695416	−	0.214027i	0.910246	−	0.414068i	$-0.135892\pi$
$89$	−0.656054	−	2.01913i	−0.0695416	−	0.214027i	−0.979788	+	0.200041i	$0.935892\pi$
$90$	7.51019	+	2.50641i	0.791644	+	0.264199i
$91$	−3.17052	−	4.36385i	−0.332361	−	0.457456i
$92$	3.47150	−	2.52219i	0.361928	−	0.262956i
$93$	15.6262	−	5.00864i	1.62036	−	0.519372i
$94$			8.48599i			0.875263i
$95$	−3.65460	−	1.18745i	−0.374954	−	0.121830i
$96$	−3.66329	−	11.4289i	−0.373883	−	1.16645i
$97$	4.01730	+	5.52933i	0.407895	+	0.561419i	0.962703	−	0.270559i	$-0.0872086\pi$
$97$	4.01730	+	5.52933i	0.407895	+	0.561419i	−0.554809	+	0.831978i	$0.687209\pi$
$98$	0.266862	+	0.821318i	0.0269572	+	0.0829657i
$99$	0.0299327	−	3.76382i	0.00300835	−	0.378279i
$100$	1.35998	−	4.18558i	0.135998	−	0.418558i
$101$		−	17.5690i		−	1.74818i	−0.485761	−	0.874092i	$-0.661457\pi$
$101$		−	17.5690i		−	1.74818i	0.485761	−	0.874092i	$-0.338543\pi$
$102$	3.84172	+	11.9855i	0.380387	+	1.18675i
$103$	3.45707	−	10.6398i	0.340635	−	1.04837i	−0.623244	−	0.782027i	$-0.714186\pi$
$103$	3.45707	−	10.6398i	0.340635	−	1.04837i	0.963879	−	0.266339i	$-0.0858142\pi$
$104$	1.57590	+	1.14495i	0.154529	+	0.112272i
$105$	6.70349	+	0.0266551i	0.654194	+	0.00260127i
$106$	−11.2369	+	3.65108i	−1.09142	+	0.354624i
$107$	5.81584	−	8.00481i	0.562238	−	0.773854i	−0.429371	−	0.903128i	$-0.641265\pi$
$107$	5.81584	−	8.00481i	0.562238	−	0.773854i	0.991609	+	0.129274i	$0.0412646\pi$
$108$	−2.27419	−	7.29417i	−0.218834	−	0.701881i
$109$	9.98973	−	7.25796i	0.956842	−	0.695187i	0.00442713	−	0.999990i	$-0.498591\pi$
$109$	9.98973	−	7.25796i	0.956842	−	0.695187i	0.952415	+	0.304804i	$0.0985908\pi$
$110$	3.31118			0.315709
$111$	6.26721	+	4.59158i	0.594857	+	0.435813i
$112$	−7.67367	−	10.5619i	−0.725094	−	0.998006i
$113$	−6.34215	+	2.06069i	−0.596619	+	0.193853i	−0.591732	−	0.806135i	$-0.701556\pi$
$113$	−6.34215	+	2.06069i	−0.596619	+	0.193853i	−0.00488702	+	0.999988i	$0.501556\pi$
$114$	2.67144	+	8.33446i	0.250203	+	0.780594i
$115$	−2.43002	−	3.34464i	−0.226601	−	0.311889i
$116$	−0.202206	+	0.622326i	−0.0187744	+	0.0577816i
$117$	4.76417	+	3.51960i	0.440448	+	0.325387i
$118$	−7.77562	−	10.7022i	−0.715804	−	0.985220i
$119$	6.26376	+	8.62133i	0.574198	+	0.790316i
$120$	−2.30529	+	0.738913i	−0.210443	+	0.0674532i
$121$	2.91275	+	8.96452i	0.264796	+	0.814957i
$122$	−6.27712	+	2.03956i	−0.568304	+	0.184653i
$123$	−5.26538	+	15.9886i	−0.474763	+	1.44164i
$124$	8.18813	−	11.2700i	0.735316	−	1.01208i
$125$	−10.7693	−	3.49916i	−0.963237	−	0.312975i
$126$	−8.87585	−	12.4231i	−0.790723	−	1.10674i
$127$	7.16452	−	2.32789i	0.635749	−	0.206567i	0.0266287	−	0.999645i	$-0.491523\pi$
$127$	7.16452	−	2.32789i	0.635749	−	0.206567i	0.609120	+	0.793078i	$0.291523\pi$
$128$	6.16140	+	4.47652i	0.544596	+	0.395672i
$129$	6.43838	+	20.0867i	0.566868	+	1.76854i
$130$	−3.06280	+	4.21558i	−0.268625	+	0.369731i
$131$	−1.34770	+	4.14778i	−0.117749	+	0.362393i	−0.992510	−	0.122160i	$-0.961018\pi$
$131$	−1.34770	+	4.14778i	−0.117749	+	0.362393i	0.874762	+	0.484553i	$0.161018\pi$
$132$	−1.86790	−	2.59255i	−0.162579	−	0.225653i
$133$	4.35567	+	5.99507i	0.377685	+	0.519838i
$134$	2.21607	+	0.720044i	0.191439	+	0.0622023i
$135$	−7.02762	+	2.19108i	−0.604841	+	0.188578i
$136$	−3.11338	−	2.26200i	−0.266970	−	0.193965i
$137$	14.4701	−	4.70163i	1.23627	−	0.401687i	0.383285	−	0.923630i	$-0.374793\pi$
$137$	14.4701	−	4.70163i	1.23627	−	0.401687i	0.852980	+	0.521943i	$0.174793\pi$
$138$	−2.94532	+	8.94362i	−0.250723	+	0.761331i
$139$	0.140411	+	0.432140i	0.0119095	+	0.0366536i	0.956835	−	0.290633i	$-0.0938658\pi$
$139$	0.140411	+	0.432140i	0.0119095	+	0.0366536i	−0.944925	+	0.327286i	$0.893866\pi$
$140$	4.60405	−	3.34504i	0.389113	−	0.282707i
$141$	−4.61217	−	6.40148i	−0.388414	−	0.539101i
$142$	−9.40805	+	3.05686i	−0.789506	+	0.256526i
$143$	2.35596	+	0.765496i	0.197015	+	0.0640140i
$144$	11.5308	+	8.51854i	0.960901	+	0.709879i
$145$	0.599585	+	0.194817i	0.0497928	+	0.0161787i
$146$	−7.24275	+	22.2909i	−0.599414	+	1.84481i
$147$	−0.647699	−	0.474527i	−0.0534213	−	0.0391383i
$148$	6.59560			0.542155
$149$	5.72545	−	17.6211i	0.469047	−	1.44358i	−0.384773	−	0.923011i	$-0.625720\pi$
$149$	5.72545	−	17.6211i	0.469047	−	1.44358i	0.853820	−	0.520568i	$-0.174280\pi$
$150$	2.94777	+	9.19656i	0.240684	+	0.750896i
$151$	3.06587	+	2.22748i	0.249497	+	0.181270i	0.705504	−	0.708706i	$-0.250721\pi$
$151$	3.06587	+	2.22748i	0.249497	+	0.181270i	−0.456007	+	0.889976i	$0.650721\pi$
$152$	−2.16497	−	1.57294i	−0.175602	−	0.127582i
$153$	−9.41222	−	6.95340i	−0.760933	−	0.562149i
$154$	−5.16587	−	3.75322i	−0.416277	−	0.302443i
$155$	−10.8582	−	7.88891i	−0.872148	−	0.633653i
$156$	5.02845	+	0.0199947i	0.402598	+	0.00160085i
$157$			20.1584i			1.60881i	0.594079	+	0.804406i	$0.297517\pi$
$157$			20.1584i			1.60881i	−0.594079	+	0.804406i	$0.702483\pi$
$158$	1.45811	−	1.05938i	0.116001	−	0.0842796i
$159$	6.49225	−	8.86150i	0.514869	−	0.702763i
$160$	−5.76990	+	7.94158i	−0.456150	+	0.627837i
$161$			7.97249i			0.628320i
$162$	13.4056	+	10.0694i	1.05325	+	0.791124i
$163$	−1.55631	−	1.13073i	−0.121900	−	0.0885654i	0.525165	−	0.851000i	$-0.324004\pi$
$163$	−1.55631	−	1.13073i	−0.121900	−	0.0885654i	−0.647065	+	0.762435i	$0.724004\pi$
$164$	4.41599	+	13.5910i	0.344831	+	1.06128i
$165$	−2.49781	+	1.79964i	−0.194455	+	0.140102i
$166$	−17.2571	−	23.7523i	−1.33941	−	1.84354i
$167$	0.541598	+	1.66687i	0.0419101	+	0.128986i	0.969822	−	0.243813i	$-0.0783982\pi$
$167$	0.541598	+	1.66687i	0.0419101	+	0.128986i	−0.927912	+	0.372799i	$0.878398\pi$
$168$	4.43411	+	1.46025i	0.342099	+	0.112660i
$169$	7.36341	−	5.34983i	0.566416	−	0.411526i
$170$	6.05094	−	8.32841i	0.464086	−	0.638760i
$171$	−6.54503	−	4.83523i	−0.500511	−	0.369759i
$172$	14.4871	+	10.5255i	1.10463	+	0.802560i
$173$			16.9069i			1.28541i	0.766114	+	0.642705i	$0.222188\pi$
$173$			16.9069i			1.28541i	−0.766114	+	0.642705i	$0.777812\pi$
$174$	−0.438284	−	1.36738i	−0.0332263	−	0.103661i
$175$	4.80621	+	6.61518i	0.363315	+	0.500061i
$176$	5.70216	+	1.85274i	0.429816	+	0.139656i
$177$	11.6823	+	3.84723i	0.878095	+	0.289176i
$178$	3.95501			0.296441
$179$		−	4.42921i		−	0.331055i	−0.986205	−	0.165527i	$-0.947067\pi$
$179$		−	4.42921i		−	0.331055i	0.986205	−	0.165527i	$-0.0529326\pi$
$180$	−3.71333	+	5.02640i	−0.276775	+	0.374646i
$181$	0.356211	+	0.115740i	0.0264770	+	0.00860289i	0.322226	−	0.946663i	$-0.395569\pi$
$181$	0.356211	+	0.115740i	0.0264770	+	0.00860289i	−0.295749	+	0.955266i	$0.595569\pi$
$182$	9.55672	−	3.10517i	0.708391	−	0.230170i
$183$	3.62669	−	4.95020i	0.268093	−	0.365929i
$184$	−0.889680	−	2.73815i	−0.0655881	−	0.201859i
$185$		−	6.35457i		−	0.467198i
$186$	−0.121550	+	30.5686i	−0.00891248	+	2.24140i
$187$	−4.65448	−	1.51233i	−0.340370	−	0.110593i
$188$	−6.37026	−	2.06982i	−0.464599	−	0.150957i
$189$	13.4476	+	4.54743i	0.978167	+	0.330777i
$190$	4.20768	−	5.79138i	0.305257	−	0.420151i
$191$	−1.63339	−	5.02707i	−0.118188	−	0.363746i	0.874410	−	0.485187i	$-0.161248\pi$
$191$	−1.63339	−	5.02707i	−0.118188	−	0.363746i	−0.992599	+	0.121441i	$0.961248\pi$
$192$	5.80384	+	0.0230778i	0.418856	+	0.00166550i
$193$	−8.63664	−	6.27489i	−0.621679	−	0.451676i	0.231829	−	0.972757i	$-0.425529\pi$
$193$	−8.63664	−	6.27489i	−0.621679	−	0.451676i	−0.853508	+	0.521080i	$0.825529\pi$
$194$	−12.1091	+	3.93449i	−0.869383	+	0.282480i
$195$	0.0192640	−	4.84470i	0.00137952	−	0.346936i
$196$	−0.681637			−0.0486883
$197$	−5.20596			−0.370910			−0.185455	−	0.982653i	$-0.559376\pi$
$197$	−5.20596			−0.370910			−0.185455	+	0.982653i	$0.559376\pi$
$198$	6.65124	+	2.21975i	0.472683	+	0.157751i
$199$	6.87786			0.487559			0.243779	−	0.969831i	$-0.421613\pi$
$199$	6.87786			0.487559			0.243779	+	0.969831i	$0.421613\pi$
$200$	−2.38891	−	1.73564i	−0.168921	−	0.122728i
$201$	−2.06305	+	0.661269i	−0.145517	+	0.0466423i
$202$	31.1275	+	10.1139i	2.19012	+	0.711614i
$203$	−0.714604	−	0.983568i	−0.0501554	−	0.0690330i
$204$	−9.93433	−	0.0395019i	−0.695542	−	0.00276569i
$205$	13.0944	−	4.25462i	0.914550	−	0.297155i
$206$	16.8606	+	12.2500i	1.17473	+	0.853495i
$207$	−2.63906	−	8.34748i	−0.183427	−	0.580190i
$208$	−7.63322	+	5.54586i	−0.529268	+	0.384536i
$209$	−3.23662	−	1.05164i	−0.223881	−	0.0727435i
$210$	−3.90622	+	11.8614i	−0.269555	+	0.818515i
$211$	−3.60148	−	14.0723i	−0.247936	−	0.968776i
$211$	−3.60148	−	14.0723i	−0.247936	−	0.968776i
$212$		−	9.32582i		−	0.640500i
$213$	5.43562	−	7.41927i	0.372443	−	0.508360i
$214$	10.8343	+	14.9122i	0.740620	+	1.01938i
$215$	10.1408	−	13.9577i	0.691600	−	0.951906i
$216$	−5.12604	−	0.0611506i	−0.348783	−	0.00416077i
$217$	7.99804	+	24.6154i	0.542942	+	1.67100i
$218$	7.10835	+	21.8772i	0.481438	+	1.48171i
$219$	−6.65154	−	20.7518i	−0.449470	−	1.40227i
$220$	−0.807631	+	2.48563i	−0.0544505	+	0.167581i
$221$	6.23074	−	4.52690i	0.419125	−	0.304512i
$222$	−11.7429	+	8.46055i	−0.788129	+	0.567835i
$223$		−	0.223640i		−	0.0149760i	−0.999972	−	0.00748802i	$-0.997616\pi$
$223$		−	0.223640i		−	0.0149760i	0.999972	−	0.00748802i	$-0.00238353\pi$
$224$	18.0036	−	5.84971i	1.20291	−	0.390850i
$225$	−7.22203	−	5.33538i	−0.481469	−	0.355692i
$226$		−	12.4228i		−	0.826354i
$227$	14.3091	−	4.64931i	0.949728	−	0.308585i	0.207123	−	0.978315i	$-0.433590\pi$
$227$	14.3091	−	4.64931i	0.949728	−	0.308585i	0.742605	+	0.669730i	$0.233590\pi$
$228$	−6.90810	−	0.0274687i	−0.457500	−	0.00181916i
$229$	8.13489	−	11.1967i	0.537568	−	0.739899i	−0.450692	−	0.892680i	$-0.648823\pi$
$229$	8.13489	−	11.1967i	0.537568	−	0.739899i	0.988260	+	0.152780i	$0.0488227\pi$
$230$	7.32467	−	2.37993i	0.482974	−	0.156928i
$231$	5.93680	+	0.0236065i	0.390613	+	0.00155319i
$232$	0.355191	+	0.258061i	0.0233194	+	0.0169426i
$233$	0.421238	−	0.306048i	0.0275962	−	0.0200498i	−0.573902	−	0.818924i	$-0.694571\pi$
$233$	0.421238	−	0.306048i	0.0275962	−	0.0200498i	0.601498	+	0.798874i	$0.294571\pi$
$234$	−8.97835	+	6.41469i	−0.586933	+	0.419341i
$235$	−1.99418	+	6.13747i	−0.130086	+	0.400364i
$236$	9.93049	−	3.22661i	0.646420	−	0.210034i
$237$	−0.524160	+	1.59164i	−0.0340479	+	0.103388i
$238$	−18.8805	+	6.13464i	−1.22384	+	0.397650i
$239$	−3.73244	+	11.4873i	−0.241431	+	0.743049i	0.754772	+	0.655988i	$0.227748\pi$
$239$	−3.73244	+	11.4873i	−0.241431	+	0.743049i	−0.996203	+	0.0870616i	$0.972252\pi$
$240$	0.0466250	−	11.7257i	0.00300963	−	0.756891i
$241$	−1.00378	+	3.08933i	−0.0646594	+	0.199001i	−0.978167	−	0.207821i	$-0.933363\pi$
$241$	−1.00378	+	3.08933i	−0.0646594	+	0.199001i	0.913508	+	0.406822i	$0.133363\pi$
$242$	−17.5595			−1.12877
$243$	−15.5854	−	0.309900i	−0.999802	−	0.0198801i
$244$		−	5.20957i		−	0.333509i
$245$			0.656728i			0.0419568i
$246$	−25.2963	−	18.5329i	−1.61283	−	1.18162i
$247$	4.33271	−	3.14790i	0.275684	−	0.200296i
$248$	−5.49386	−	7.56164i	−0.348860	−	0.480165i
$249$	25.9275	+	8.53847i	1.64309	+	0.541104i
$250$	12.3991	−	17.0659i	0.784189	−	1.07934i
$251$	−2.32267			−0.146606			−0.0733029	−	0.997310i	$-0.523354\pi$
$251$	−2.32267			−0.146606			−0.0733029	+	0.997310i	$0.523354\pi$
$252$	11.4907	−	3.63278i	0.723845	−	0.228844i
$253$	−2.15209	−	2.96210i	−0.135301	−	0.186226i
$254$			14.0337i			0.880551i
$255$	−0.0380584	+	9.57130i	−0.00238331	+	0.599378i
$256$	−16.8999	+	12.2785i	−1.05625	+	0.767407i
$257$	−2.82698	+	3.89100i	−0.176342	+	0.242714i	−0.888034	−	0.459778i	$-0.847929\pi$
$257$	−2.82698	+	3.89100i	−0.176342	+	0.242714i	0.711692	+	0.702492i	$0.247929\pi$
$258$	−39.2946	−	0.156247i	−2.44637	−	0.00972752i
$259$	−7.20291	+	9.91395i	−0.447567	+	0.616023i
$260$	−2.41750	−	3.32740i	−0.149927	−	0.206357i
$261$	1.07380	+	0.793282i	0.0664664	+	0.0491029i
$262$	−6.57291	−	4.77550i	−0.406076	−	0.295031i
$263$	−12.2383	−	3.97646i	−0.754646	−	0.245199i	−0.0936666	−	0.995604i	$-0.529859\pi$
$263$	−12.2383	−	3.97646i	−0.754646	−	0.245199i	−0.660979	+	0.750404i	$0.729859\pi$
$264$	−2.04163	+	0.654402i	−0.125654	+	0.0402757i
$265$	−8.98503			−0.551946
$266$	−13.1290	+	4.26588i	−0.804993	+	0.261558i
$267$	−2.98349	+	2.14956i	−0.182587	+	0.131551i
$268$	−1.08104	+	1.48793i	−0.0660352	+	0.0908897i
$269$		−	23.5285i		−	1.43456i	−0.696785	−	0.717280i	$-0.745387\pi$
$269$		−	23.5285i		−	1.43456i	0.696785	−	0.717280i	$-0.254613\pi$
$270$	0.163580	−	13.7124i	0.00995518	−	0.834507i
$271$	1.06295	−	1.46302i	0.0645695	−	0.0888723i	−0.775511	−	0.631334i	$-0.782508\pi$
$271$	1.06295	−	1.46302i	0.0645695	−	0.0888723i	0.840080	+	0.542462i	$0.182508\pi$
$272$	15.0804	−	10.9565i	0.914382	−	0.664337i
$273$	−5.52152	+	7.53651i	−0.334177	+	0.456131i
$274$			28.3437i			1.71230i
$275$	−3.57140	−	1.16042i	−0.215364	−	0.0699759i
$276$	−5.99539	−	4.39243i	−0.360880	−	0.264393i
$277$	−4.46644	+	13.7463i	−0.268363	+	0.825935i	0.722537	+	0.691332i	$0.242976\pi$
$277$	−4.46644	+	13.7463i	−0.268363	+	0.825935i	−0.990900	+	0.134603i	$0.957024\pi$
$278$	−0.846463			−0.0507675
$279$	−16.5224	−	23.1257i	−0.989172	−	1.38450i
$280$	−1.17993	−	3.63146i	−0.0705144	−	0.217021i
$281$	12.5714	−	17.3031i	0.749948	−	1.03222i	−0.248036	−	0.968751i	$-0.579785\pi$
$281$	12.5714	−	17.3031i	0.749948	−	1.03222i	0.997984	−	0.0634644i	$-0.0202149\pi$
$282$	13.9967	−	4.48637i	0.833494	−	0.267159i
$283$	−11.8152	+	3.83901i	−0.702344	+	0.228205i	−0.638351	−	0.769745i	$-0.720383\pi$
$283$	−11.8152	+	3.83901i	−0.702344	+	0.228205i	−0.0639922	+	0.997950i	$0.520383\pi$
$284$		−	7.80802i		−	0.463321i
$285$	−0.0264649	+	6.65566i	−0.00156765	+	0.394247i
$286$	−2.71250	+	3.73344i	−0.160393	+	0.220763i
$287$	−25.2515	−	8.20471i	−1.49055	−	0.484309i
$288$	−16.9140	+	12.0844i	−0.996667	+	0.712080i
$289$	1.44368	−	1.04889i	0.0849222	−	0.0616996i
$290$	−0.690325	+	0.950150i	−0.0405373	+	0.0557947i
$291$	6.99619	−	9.54934i	0.410124	−	0.559792i
$292$	−14.9667	−	10.8740i	−0.875860	−	0.636350i
$293$	−9.87993	−	13.5986i	−0.577192	−	0.794437i	0.416192	−	0.909277i	$-0.363364\pi$
$293$	−9.87993	−	13.5986i	−0.577192	−	0.794437i	−0.993384	+	0.114840i	$0.963364\pi$
$294$	1.21359	−	0.874375i	0.0707781	−	0.0509946i
$295$	−3.10870	−	9.56760i	−0.180996	−	0.557047i
$296$	1.36751	−	4.20875i	0.0794846	−	0.244629i
$297$	−6.22385	+	1.94048i	−0.361144	+	0.112598i
$298$	27.9239	+	20.2879i	1.61759	+	1.17524i
$299$	5.76182			0.333215
$300$	−7.62265	−	0.0303100i	−0.440094	−	0.00174995i
$301$	−31.6420	+	10.2811i	−1.82382	+	0.592594i
$302$	−5.71142	+	4.14959i	−0.328655	+	0.238782i
$303$	−28.9782	+	9.28837i	−1.66476	+	0.533603i
$304$	10.4865	−	7.61891i	0.601444	−	0.436975i
$305$	−5.01920			−0.287399
$306$	17.7378	−	12.6730i	1.01401	−	0.724468i
$307$	14.3065	−	10.3943i	0.816514	−	0.593232i	−0.0991976	−	0.995068i	$-0.531628\pi$
$307$	14.3065	−	10.3943i	0.816514	−	0.593232i	0.915712	+	0.401835i	$0.131628\pi$
$308$	4.07747	−	2.96246i	0.232335	−	0.168802i
$309$	−19.3768	−	0.0770482i	−1.10231	−	0.00438312i
$310$	20.2277	−	14.6963i	1.14886	−	0.834693i
$311$	−28.6456	−	9.30753i	−1.62434	−	0.527781i	−0.651383	−	0.758749i	$-0.725811\pi$
$311$	−28.6456	−	9.30753i	−1.62434	−	0.527781i	−0.972961	+	0.230968i	$0.925811\pi$
$312$	1.05534	−	3.20458i	0.0597468	−	0.181424i
$313$	9.08364	+	12.5026i	0.513438	+	0.706687i	0.984494	−	0.175416i	$-0.0561272\pi$
$313$	9.08364	+	12.5026i	0.513438	+	0.706687i	−0.471056	+	0.882103i	$0.656127\pi$
$314$	−35.7151	−	11.6045i	−2.01552	−	0.654882i
$315$	−3.50003	−	11.0708i	−0.197204	−	0.623768i
$316$	0.439605	+	1.35296i	0.0247297	+	0.0761102i
$317$	5.79365	+	17.8310i	0.325404	+	1.00149i	0.971258	+	0.238029i	$0.0765012\pi$
$317$	5.79365	+	17.8310i	0.325404	+	1.00149i	−0.645855	+	0.763460i	$0.723499\pi$
$318$	11.9628	+	16.6038i	0.670839	+	0.931094i
$319$	0.531009	+	0.172535i	0.0297308	+	0.00966012i
$320$	−2.79028	−	3.84049i	−0.155981	−	0.214690i
$321$	−16.2778	−	5.36063i	−0.908538	−	0.299201i
$322$	−14.1251	−	4.58951i	−0.787160	−	0.255764i
$323$	−8.55981	+	6.21907i	−0.476281	+	0.346038i
$324$	−10.8286	+	7.60730i	−0.601591	+	0.422628i
$325$	4.78088	−	3.47351i	0.265195	−	0.192676i
$326$	2.89926	−	2.10644i	0.160575	−	0.116665i
$327$	−17.2526	−	12.6399i	−0.954071	−	0.698986i
$328$	9.58823			0.529422
$329$	10.0680	−	7.31483i	0.555067	−	0.403280i
$330$	−1.75055	−	5.46144i	−0.0963646	−	0.300642i
$331$	−2.78188	+	2.02116i	−0.152906	+	0.111093i	−0.661608	−	0.749850i	$-0.730126\pi$
$331$	−2.78188	+	2.02116i	−0.152906	+	0.111093i	0.508702	+	0.860943i	$0.330126\pi$
$332$	22.0395	−	7.16108i	1.20958	−	0.393015i
$333$	4.25998	−	12.7646i	0.233445	−	0.699494i
$334$	−3.26501			−0.178654
$335$	1.43356	+	1.04154i	0.0783235	+	0.0569054i
$336$	−13.3638	+	18.2408i	−0.729056	+	0.995115i
$337$	−10.5176	+	32.3699i	−0.572931	+	1.76330i	0.0701880	+	0.997534i	$0.477640\pi$
$337$	−10.5176	+	32.3699i	−0.572931	+	1.76330i	−0.643119	+	0.765766i	$0.722360\pi$
$338$	5.23955	+	16.1257i	0.284994	+	0.877121i
$339$	6.75184	+	9.37125i	0.366710	+	0.508977i
$340$	4.77607	+	6.57370i	0.259019	+	0.356509i
$341$	−9.61628	−	6.98664i	−0.520751	−	0.378348i
$342$	12.3345	−	8.81251i	0.666972	−	0.476526i
$343$	−10.4962	+	14.4468i	−0.566742	+	0.780054i
$344$	9.72016	−	7.06211i	0.524076	−	0.380763i
$345$	−4.23192	+	5.77630i	−0.227839	+	0.310986i
$346$	−29.9544	−	9.73279i	−1.61036	−	0.523238i
$347$	10.7523	−	14.7992i	0.577212	−	0.794464i	−0.416174	−	0.909285i	$-0.636629\pi$
$347$	10.7523	−	14.7992i	0.577212	−	0.794464i	0.993386	+	0.114821i	$0.0366294\pi$
$348$	1.13336	+	0.00450660i	0.0607546	+	0.000241579i
$349$		−	13.7796i		−	0.737603i	−0.929508	−	0.368801i	$-0.879768\pi$
$349$		−	13.7796i		−	0.737603i	0.929508	−	0.368801i	$-0.120232\pi$
$350$	−14.4871	+	4.70714i	−0.774367	+	0.251607i
$351$	3.28648	−	9.71873i	0.175420	−	0.518747i
$352$	−5.10998	+	7.03329i	−0.272363	+	0.374875i
$353$	4.35529	+	13.4042i	0.231809	+	0.713434i	0.997529	+	0.0702596i	$0.0223828\pi$
$353$	4.35529	+	13.4042i	0.231809	+	0.713434i	−0.765720	+	0.643174i	$0.777617\pi$
$354$	−13.5414	+	18.4831i	−0.719716	+	0.982366i
$355$	−7.52269			−0.399263
$356$	−0.964668	+	2.96894i	−0.0511273	+	0.157354i
$357$	10.9084	−	14.8893i	0.577336	−	0.788027i
$358$	7.84734	+	2.54976i	0.414745	+	0.134759i
$359$			26.5872i			1.40322i	0.712562	+	0.701609i	$0.247535\pi$
$359$			26.5872i			1.40322i	−0.712562	+	0.701609i	$0.752465\pi$
$360$	2.43752	+	3.41168i	0.128468	+	0.179812i
$361$	9.41904	−	6.84333i	0.495739	−	0.360175i
$362$	−0.410119	+	0.564481i	−0.0215554	+	0.0296685i
$363$	13.2461	−	9.54363i	0.695241	−	0.500910i
$364$			7.93141i			0.415719i
$365$	−10.4766	+	14.4198i	−0.548370	+	0.754766i
$366$	6.68262	+	9.27517i	0.349306	+	0.484821i
$367$	−18.1033	+	5.88212i	−0.944985	+	0.307044i	−0.740676	−	0.671862i	$-0.765495\pi$
$367$	−18.1033	+	5.88212i	−0.944985	+	0.307044i	−0.204309	+	0.978907i	$0.565495\pi$
$368$	13.9454			0.726956
$369$	29.1551	+	0.231863i	1.51776	+	0.0120703i
$370$	11.2586	+	3.65813i	0.585305	+	0.190177i
$371$	14.0178	+	10.1845i	0.727768	+	0.528754i
$372$	−22.9175	−	7.54724i	−1.18822	−	0.391306i
$373$	18.4146	+	25.3455i	0.953470	+	1.31234i	0.949969	+	0.312344i	$0.101114\pi$
$373$	18.4146	+	25.3455i	0.953470	+	1.31234i	0.00350066	+	0.999994i	$0.498886\pi$
$374$	5.35888	−	7.37587i	0.277101	−	0.381397i
$375$	−0.0779864	+	19.6128i	−0.00402720	+	1.01280i
$376$	−2.64157	+	3.63581i	−0.136228	+	0.187502i
$377$	−0.710837	+	0.516454i	−0.0366100	+	0.0265987i
$378$	−15.7982	+	21.2076i	−0.812569	+	1.09080i
$379$		−	30.2843i		−	1.55560i	−0.628512	−	0.777800i	$-0.716336\pi$
$379$		−	30.2843i		−	1.55560i	0.628512	−	0.777800i	$-0.283664\pi$
$380$	3.32117	+	4.57119i	0.170372	+	0.234497i
$381$	−7.62734	−	10.5864i	−0.390761	−	0.542358i
$382$	9.84689			0.503811
$383$	14.9158	−	20.5299i	0.762164	−	1.04903i	−0.234867	−	0.972027i	$-0.575465\pi$
$383$	14.9158	−	20.5299i	0.762164	−	1.04903i	0.997031	−	0.0770011i	$-0.0245345\pi$
$384$	4.12614	−	12.5292i	0.210561	−	0.639379i
$385$	−2.85420	−	3.92847i	−0.145463	−	0.200213i
$386$	16.0892	−	11.6895i	0.818920	−	0.594980i
$387$	29.7271	−	21.2389i	1.51111	−	1.07963i
$388$		−	10.0497i		−	0.510197i
$389$			24.9144i			1.26321i	0.775289	+	0.631606i	$0.217604\pi$
$389$			24.9144i			1.26321i	−0.775289	+	0.631606i	$0.782396\pi$
$390$	8.57239	+	2.82307i	0.434080	+	0.142952i
$391$	−11.3832			−0.575673
$392$	−0.141328	+	0.434963i	−0.00713814	+	0.0219689i
$393$	7.55382	+	0.0300363i	0.381040	+	0.00151513i
$394$	2.99691	−	9.22354i	0.150982	−	0.464675i
$395$	1.30352	−	0.423540i	0.0655874	−	0.0213106i
$396$	−3.28862	+	4.45152i	−0.165260	+	0.223697i
$397$	−0.142532	+	0.0463113i	−0.00715346	+	0.00232430i	−0.312592	−	0.949888i	$-0.601197\pi$
$397$	−0.142532	+	0.0463113i	−0.00715346	+	0.00232430i	0.305438	+	0.952212i	$0.401197\pi$
$398$	−3.95937	+	12.1857i	−0.198465	+	0.610814i
$399$	7.58547	−	10.3537i	0.379749	−	0.518332i
$400$	11.5712	−	8.40699i	0.578562	−	0.420350i
$401$	8.17084	+	5.93646i	0.408032	+	0.296453i	0.772805	−	0.634644i	$-0.218853\pi$
$401$	8.17084	+	5.93646i	0.408032	+	0.296453i	−0.364773	+	0.931097i	$0.618853\pi$
$402$	0.0160477	−	4.03584i	0.000800387	−	0.201289i
$403$	17.7899	−	5.78028i	0.886177	−	0.287936i
$404$	−15.1846	+	20.8999i	−0.755464	+	1.03981i
$405$	7.32931	+	10.4329i	0.364196	+	0.518416i
$406$	2.15399	−	0.699874i	0.106901	−	0.0347341i
$407$		−	5.62779i		−	0.278959i
$408$	−2.08495	+	6.33106i	−0.103221	+	0.313434i
$409$	−29.9711	+	9.73819i	−1.48197	+	0.481523i	−0.934702	−	0.355432i	$-0.884334\pi$
$409$	−29.9711	+	9.73819i	−1.48197	+	0.481523i	−0.547272	+	0.836955i	$0.684334\pi$
$410$			25.6489i			1.26671i
$411$	−15.4049	−	21.3813i	−0.759866	−	1.05466i
$412$	−13.3083	+	9.66902i	−0.655651	+	0.476358i
$413$	−5.99490	+	18.4504i	−0.294990	+	0.907885i
$414$	16.3087	+	0.129699i	0.801528	+	0.00637433i
$415$	−6.89940	−	21.2342i	−0.338678	−	1.04234i
$416$	−4.22766	−	13.0114i	−0.207278	−	0.637936i
$417$	0.638536	−	0.460055i	0.0312692	−	0.0225290i
$418$	3.72644	−	5.12900i	0.182266	−	0.250868i
$419$	−7.36784	−	10.1410i	−0.359942	−	0.495418i	0.590190	−	0.807264i	$-0.299053\pi$
$419$	−7.36784	−	10.1410i	−0.359942	−	0.495418i	−0.950133	+	0.311846i	$0.899053\pi$
$420$	−7.95134	−	5.82543i	−0.387986	−	0.284252i
$421$		−	36.8779i		−	1.79732i	−0.438645	−	0.898660i	$-0.644541\pi$
$421$		−	36.8779i		−	1.79732i	0.438645	−	0.898660i	$-0.355459\pi$
$422$	27.0055	+	1.72015i	1.31461	+	0.0837354i
$423$	−8.12020	+	10.9916i	−0.394817	+	0.534430i
$424$	−5.95095	−	1.93358i	−0.289004	−	0.0939029i
$425$	−9.44521	+	6.86235i	−0.458160	+	0.332873i
$426$	10.0158	+	13.9015i	0.485267	+	0.673529i
$427$	7.83060	+	5.68926i	0.378949	+	0.275323i
$428$	−13.8369	+	4.49587i	−0.668831	+	0.217316i
$429$	0.0170607	−	4.29060i	0.000823699	−	0.207152i
$430$	18.8914	+	26.0018i	0.911025	+	1.25392i
$431$	26.9269	+	8.74909i	1.29702	+	0.421429i	0.874545	−	0.484944i	$-0.161160\pi$
$431$	26.9269	+	8.74909i	1.29702	+	0.421429i	0.422479	+	0.906373i	$0.361160\pi$
$432$	7.95433	−	23.5224i	0.382703	−	1.13172i
$433$	−6.31061	−	4.58492i	−0.303268	−	0.220337i	0.425734	−	0.904848i	$-0.360016\pi$
$433$	−6.31061	−	4.58492i	−0.303268	−	0.220337i	−0.729003	+	0.684511i	$0.760016\pi$
$434$	−48.2160			−2.31444
$435$	0.00434191	−	1.09195i	0.000208179	−	0.0523548i
$436$	−18.1566			−0.869543
$437$	−7.91560			−0.378655
$438$	40.5955	+	0.161420i	1.93973	+	0.00771295i
$439$	−15.3481	+	4.98690i	−0.732524	+	0.238012i	−0.651445	−	0.758696i	$-0.725837\pi$
$439$	−15.3481	+	4.98690i	−0.732524	+	0.238012i	−0.0810795	+	0.996708i	$0.525837\pi$
$440$	1.41867	+	1.03072i	0.0676324	+	0.0491378i
$441$	−0.440257	+	1.31918i	−0.0209646	+	0.0628182i
$442$	4.43358	+	13.6452i	0.210884	+	0.649034i
$443$	−14.3802	+	19.7926i	−0.683222	+	0.940374i	−0.999967	−	0.00813668i	$-0.997410\pi$
$443$	−14.3802	+	19.7926i	−0.683222	+	0.940374i	0.316745	+	0.948511i	$0.397410\pi$
$444$	−3.48695	−	10.8787i	−0.165483	−	0.516282i
$445$	2.86045	+	0.929417i	0.135598	+	0.0440586i
$446$	0.396229	+	0.128743i	0.0187620	+	0.00609614i
$447$	−32.0911	−	0.127604i	−1.51786	−	0.00603546i
$448$			9.15443i			0.432506i
$449$	2.04027	+	6.27931i	0.0962864	+	0.296339i	0.987587	−	0.157074i	$-0.0502062\pi$
$449$	2.04027	+	6.27931i	0.0962864	+	0.296339i	−0.891300	+	0.453413i	$0.850206\pi$
$450$	13.6103	−	9.72405i	0.641597	−	0.458396i
$451$	11.5967	−	3.76801i	0.546069	−	0.177429i
$452$	9.32555	+	3.03005i	0.438637	+	0.142522i
$453$	2.05314	−	6.23445i	0.0964648	−	0.292920i
$454$			28.0283i			1.31543i
$455$	7.64157			0.358242
$456$	−1.44983	+	4.40247i	−0.0678943	+	0.206164i
$457$	21.1946	+	6.88655i	0.991443	+	0.322139i	0.759441	−	0.650576i	$-0.225472\pi$
$457$	21.1946	+	6.88655i	0.991443	+	0.322139i	0.232002	+	0.972715i	$0.425472\pi$
$458$	15.1545	+	20.8584i	0.708124	+	0.974648i
$459$	−6.49286	+	19.2006i	−0.303061	+	0.896206i
$460$			6.07896i			0.283433i
$461$	24.7541	+	17.9849i	1.15292	+	0.837642i	0.988866	−	0.148810i	$-0.0475443\pi$
$461$	24.7541	+	17.9849i	1.15292	+	0.837642i	0.164050	+	0.986452i	$0.447544\pi$
$462$	−3.45945	+	10.5048i	−0.160948	+	0.488727i
$463$	−15.4826	+	21.3100i	−0.719537	+	0.990358i	0.280002	+	0.960000i	$0.409665\pi$
$463$	−15.4826	+	21.3100i	−0.719537	+	0.990358i	−0.999539	+	0.0303587i	$0.990335\pi$
$464$	−1.72045	+	1.24998i	−0.0798700	+	0.0580289i
$465$	−7.27144	+	22.0801i	−0.337205	+	1.02394i
$466$	0.299739	+	0.922501i	0.0138851	+	0.0427340i
$467$	6.81185	+	9.37571i	0.315215	+	0.433856i	0.936999	−	0.349333i	$-0.113592\pi$
$467$	6.81185	+	9.37571i	0.315215	+	0.433856i	−0.621784	+	0.783189i	$0.713592\pi$
$468$	−2.62546	−	8.30447i	−0.121362	−	0.383874i
$469$	−1.05595	−	3.24987i	−0.0487591	−	0.150065i
$470$	−9.72593	−	7.06630i	−0.448624	−	0.325944i
$471$	33.2491	−	10.6573i	1.53204	−	0.491063i
$472$		−	7.00579i		−	0.322467i
$473$	8.98101	−	12.3613i	0.412947	−	0.568373i
$474$	−2.51820	−	1.84492i	−0.115665	−	0.0847402i
$475$	−6.56798	+	4.77191i	−0.301359	+	0.218950i
$476$		−	15.6695i		−	0.718210i
$477$	−18.0484	−	6.02338i	−0.826380	−	0.275792i
$478$	−18.2036	−	13.2257i	−0.832615	−	0.604930i
$479$	−17.7299	−	12.8815i	−0.810100	−	0.588572i	0.103760	−	0.994602i	$-0.466913\pi$
$479$	−17.7299	−	12.8815i	−0.810100	−	0.588572i	−0.913860	+	0.406030i	$0.866913\pi$
$480$	16.1492	+	5.31828i	0.737108	+	0.242745i
$481$	7.16494	+	5.20563i	0.326693	+	0.237356i
$482$	−4.89560	−	3.55686i	−0.222989	−	0.162011i
$483$	13.1498	−	4.21489i	0.598335	−	0.191784i
$484$	4.28294	−	13.1815i	0.194679	−	0.599160i
$485$	−9.68246			−0.439658
$486$	9.52107	−	27.4346i	0.431885	−	1.24446i
$487$	−0.543426	+	1.67249i	−0.0246250	+	0.0757879i	−0.962614	−	0.270878i	$-0.912686\pi$
$487$	−0.543426	+	1.67249i	−0.0246250	+	0.0757879i	0.937989	+	0.346666i	$0.112686\pi$
$488$	−3.32431	−	1.08013i	−0.150484	−	0.0488953i
$489$	−1.04222	+	3.16476i	−0.0471310	+	0.143115i
$490$	−1.16354	−	0.378058i	−0.0525635	−	0.0170789i
$491$	18.1663	−	5.90260i	0.819835	−	0.266381i	0.131078	−	0.991372i	$-0.458156\pi$
$491$	18.1663	−	5.90260i	0.819835	−	0.266381i	0.688758	+	0.724991i	$0.258156\pi$
$492$	20.0823	−	14.4690i	0.905380	−	0.652313i
$493$	1.40435	−	1.02032i	0.0632486	−	0.0459528i
$494$	3.08301	+	9.48852i	0.138711	+	0.426909i
$495$	4.28885	+	3.16845i	0.192770	+	0.142411i
$496$	43.0571	−	13.9901i	1.93332	−	0.628175i
$497$	11.7364	+	8.52697i	0.526448	+	0.382487i
$498$	−30.0535	+	41.0211i	−1.34673	+	1.83820i
$499$	−15.5384	−	5.04873i	−0.695594	−	0.226012i	−0.0601843	−	0.998187i	$-0.519169\pi$
$499$	−15.5384	−	5.04873i	−0.695594	−	0.226012i	−0.635410	+	0.772175i	$0.719169\pi$
$500$	9.78676	+	13.4703i	0.437677	+	0.602411i
$501$	2.46299	−	1.77454i	0.110038	−	0.0792808i
$502$	1.33709	−	4.11514i	0.0596773	−	0.183668i
$503$	−3.51929	+	4.84388i	−0.156917	+	0.215978i	−0.880236	−	0.474536i	$-0.842616\pi$
$503$	−3.51929	+	4.84388i	−0.156917	+	0.215978i	0.723319	+	0.690514i	$0.242616\pi$
$504$	0.0643025	−	8.08559i	0.00286426	−	0.360161i
$505$	20.1361	+	14.6298i	0.896046	+	0.651016i
$506$	6.48693	−	2.10773i	0.288379	−	0.0937001i
$507$	−12.7169	−	9.31682i	−0.564775	−	0.413774i
$508$	−10.5348	−	3.42296i	−0.467405	−	0.151869i
$509$	−14.7500	+	20.3017i	−0.653783	+	0.899856i	−0.999256	−	0.0385733i	$-0.987719\pi$
$509$	−14.7500	+	20.3017i	−0.653783	+	0.899856i	0.345472	+	0.938429i	$0.387719\pi$
$510$	−16.9358	−	5.57733i	−0.749931	−	0.246968i
$511$	32.6896	−	10.6215i	1.44610	−	0.469868i
$512$	−7.31851	−	22.5241i	−0.323436	−	0.995433i
$513$	−4.51498	+	13.3516i	−0.199341	+	0.589488i
$514$	−5.26639	−	7.24856i	−0.232290	−	0.319720i
$515$	9.31568	+	12.8219i	0.410498	+	0.565002i
$516$	9.70164	−	29.4595i	0.427091	−	1.29688i
$517$	−1.76611	+	5.43551i	−0.0776732	+	0.239054i
$518$	−13.4183	−	18.4687i	−0.589567	−	0.811470i
$519$	27.8862	−	8.93833i	1.22407	−	0.392349i
$520$	−2.62450	+	0.852752i	−0.115092	+	0.0373956i
$521$	7.08536	+	9.75216i	0.310415	+	0.427250i	0.935511	−	0.353298i	$-0.114940\pi$
$521$	7.08536	+	9.75216i	0.310415	+	0.427250i	−0.625095	+	0.780548i	$0.714940\pi$
$522$	−2.02363	+	1.44581i	−0.0885719	+	0.0632812i
$523$	−3.77313			−0.164987			−0.0824937	−	0.996592i	$-0.526288\pi$
$523$	−3.77313			−0.164987			−0.0824937	+	0.996592i	$0.526288\pi$
$524$	5.18807	−	3.76935i	0.226642	−	0.164665i
$525$	8.37010	−	11.4246i	0.365301	−	0.498612i
$526$	14.0904	−	19.3938i	0.614371	−	0.845609i
$527$	−35.1461	+	11.4197i	−1.53099	+	0.497449i
$528$	0.0412924	−	10.3846i	0.00179702	−	0.451932i
$529$	11.7177	+	8.51341i	0.509466	+	0.370148i
$530$	5.17240	−	15.9190i	0.224675	−	0.691478i
$531$	0.169414	−	21.3026i	0.00735195	−	0.924456i
$532$		−	10.8962i		−	0.472410i
$533$	−5.92965	+	18.2496i	−0.256842	+	0.790477i
$534$	−2.09093	−	6.52337i	−0.0904834	−	0.282294i
$535$	4.33158	+	13.3312i	0.187271	+	0.576360i
$536$	0.725330	+	0.998331i	0.0313295	+	0.0431213i
$537$	−7.30551	+	2.34163i	−0.315256	+	0.101049i
$538$	41.6861	+	13.5446i	1.79722	+	0.583951i
$539$			0.581616i			0.0250520i
$540$	10.2537	+	3.46738i	0.441248	+	0.149212i
$541$	−8.96520	+	6.51360i	−0.385444	+	0.280042i	−0.763586	−	0.645706i	$-0.776563\pi$
$541$	−8.96520	+	6.51360i	−0.385444	+	0.280042i	0.378142	+	0.925748i	$0.376563\pi$
$542$	1.98017	+	2.72547i	0.0850555	+	0.117069i
$543$	0.00257951	−	0.648722i	0.000110698	−	0.0278393i
$544$	8.35227	+	25.7056i	0.358101	+	1.10212i
$545$			17.4931i			0.749322i
$546$	−10.1741	−	14.1212i	−0.435410	−	0.604330i
$547$	−9.68507	+	29.8076i	−0.414104	+	1.27448i	0.498946	+	0.866633i	$0.333720\pi$
$547$	−9.68507	+	29.8076i	−0.414104	+	1.27448i	−0.913050	+	0.407847i	$0.866280\pi$
$548$	−21.2770	−	6.91331i	−0.908908	−	0.295322i
$549$	−10.0822	−	3.36477i	−0.430297	−	0.143605i
$550$	4.11189	−	5.65953i	0.175332	−	0.241323i
$551$	0.976550	−	0.709505i	0.0416024	−	0.0302259i
$552$	−4.04594	+	2.91504i	−0.172207	+	0.124072i
$553$	−2.51375	−	0.816766i	−0.106895	−	0.0347324i
$554$	−21.7835	−	15.8266i	−0.925492	−	0.672409i
$555$	−10.4812	+	3.35953i	−0.444902	+	0.142604i
$556$	0.206461	−	0.635422i	0.00875590	−	0.0269479i
$557$	−0.870989	+	2.68063i	−0.0369050	+	0.113582i	−0.967812	−	0.251675i	$-0.919019\pi$
$557$	−0.870989	+	2.68063i	−0.0369050	+	0.113582i	0.930907	+	0.365257i	$0.119019\pi$
$558$	50.4839	−	15.9605i	2.13715	−	0.675661i
$559$	7.43030	+	22.8681i	0.314268	+	0.967218i
$560$	18.4950			0.781558
$561$	−0.0337056	+	8.47661i	−0.00142305	+	0.357883i
$562$	23.4193	+	32.2340i	0.987886	+	1.35971i
$563$	−6.58830	−	4.78668i	−0.277664	−	0.201734i	0.440234	−	0.897883i	$-0.354895\pi$
$563$	−6.58830	−	4.78668i	−0.277664	−	0.201734i	−0.717898	+	0.696149i	$0.754895\pi$
$564$	−0.0461304	+	11.6013i	−0.00194244	+	0.488504i
$565$	2.91933	−	8.98477i	0.122817	−	0.377992i
$566$		−	23.1434i		−	0.972789i
$567$	0.391052	−	24.5845i	0.0164226	−	1.03245i
$568$	−4.98242	−	1.61888i	−0.209058	−	0.0679269i
$569$	8.14961	−	25.0819i	0.341649	−	1.05149i	−0.621704	−	0.783252i	$-0.713559\pi$
$569$	8.14961	−	25.0819i	0.341649	−	1.05149i	0.963353	−	0.268236i	$-0.0864407\pi$
$570$	−11.7768	−	3.87834i	−0.493275	−	0.162446i
$571$	−1.47155	−	0.478136i	−0.0615824	−	0.0200093i	0.278064	−	0.960563i	$-0.410307\pi$
$571$	−1.47155	−	0.478136i	−0.0615824	−	0.0200093i	−0.339646	+	0.940553i	$0.610307\pi$
$572$	−2.14100	−	2.94684i	−0.0895199	−	0.123214i
$573$	−7.42808	+	5.35182i	−0.310312	+	0.223575i
$574$	29.0730	−	40.0156i	1.21348	−	1.67022i
$575$	−8.73437			−0.364248
$576$	−3.03030	−	9.58501i	−0.126263	−	0.399375i
$577$	−13.8538	+	19.0681i	−0.576740	+	0.793815i	−0.993333	−	0.115278i	$-0.963224\pi$
$577$	−13.8538	+	19.0681i	−0.576740	+	0.793815i	0.416593	+	0.909093i	$0.363224\pi$
$578$	1.02727	+	3.16162i	0.0427289	+	0.131506i
$579$	−5.78375	+	17.5626i	−0.240364	+	0.729877i
$580$	−0.544880	−	0.749963i	−0.0226249	−	0.0311405i
$581$	−13.3050	+	40.9485i	−0.551983	+	1.69883i
$582$	12.8913	+	17.8926i	0.534363	+	0.741672i
$583$	−7.95739			−0.329561
$584$	−10.0420	+	7.29592i	−0.415540	+	0.301907i
$585$	−8.00100	+	2.52952i	−0.330801	+	0.104583i
$586$	29.7805	−	9.67627i	1.23022	−	0.399723i
$587$	31.3957	+	22.8103i	1.29584	+	0.941484i	0.999906	−	0.0137245i	$-0.00436877\pi$
$587$	31.3957	+	22.8103i	1.29584	+	0.941484i	0.295935	+	0.955208i	$0.404369\pi$
$588$	0.360367	+	1.12429i	0.0148613	+	0.0463648i
$589$	−24.4398	+	7.94096i	−1.00702	+	0.327202i
$590$	18.7408			0.771545
$591$	2.75228	+	8.58668i	0.113214	+	0.353209i
$592$	17.3414	+	12.5993i	0.712728	+	0.517827i
$593$		−	12.9963i		−	0.533694i	−0.963739	−	0.266847i	$-0.914018\pi$
$593$		−	12.9963i		−	0.533694i	0.963739	−	0.266847i	$-0.0859819\pi$
$594$	0.144871	−	12.1440i	0.00594414	−	0.498276i
$595$	−15.0969			−0.618912
$596$	−22.0406	+	16.0134i	−0.902818	+	0.655936i
$597$	−3.63618	−	11.3443i	−0.148819	−	0.464291i
$598$	−3.31690	+	10.2084i	−0.135638	+	0.417451i
$599$	16.5843			0.677615			0.338807	−	0.940856i	$-0.389977\pi$
$599$	16.5843			0.677615			0.338807	+	0.940856i	$0.389977\pi$
$600$	−1.59979	+	4.85785i	−0.0653113	+	0.198321i
$601$	39.1434			1.59669			0.798346	−	0.602200i	$-0.205709\pi$
$601$	39.1434			1.59669			0.798346	+	0.602200i	$0.205709\pi$
$602$		−	61.9796i		−	2.52610i
$603$	2.18139	+	3.05319i	0.0888329	+	0.124335i
$604$	−1.72193	−	5.29957i	−0.0700645	−	0.215636i
$605$	−12.6998	−	4.12642i	−0.516321	−	0.167763i
$606$	0.225411	−	56.6885i	0.00915669	−	2.30281i
$607$	13.6696			0.554834			0.277417	−	0.960750i	$-0.410522\pi$
$607$	13.6696			0.554834			0.277417	+	0.960750i	$0.410522\pi$
$608$	5.80797	+	17.8751i	0.235544	+	0.724931i
$609$	−1.24450	+	1.69866i	−0.0504295	+	0.0688330i
$610$	2.88940	−	8.89265i	0.116988	−	0.360053i
$611$	−5.28652	−	7.27627i	−0.213870	−	0.294366i
$612$	5.18692	+	16.4065i	0.209669	+	0.663194i
$613$	40.6198	−	13.1982i	1.64062	−	0.533069i	0.663942	−	0.747784i	$-0.268882\pi$
$613$	40.6198	−	13.1982i	1.64062	−	0.533069i	0.976677	+	0.214714i	$0.0688821\pi$
$614$	10.1800	+	31.3308i	0.410832	+	1.26441i
$615$	−13.9403	−	19.3484i	−0.562125	−	0.780204i
$616$	−1.04498	−	3.21612i	−0.0421035	−	0.129581i
$617$	−10.8014	−	33.2433i	−0.434847	−	1.33832i	−0.893243	−	0.449575i	$-0.851576\pi$
$617$	−10.8014	−	33.2433i	−0.434847	−	1.33832i	0.458395	−	0.888748i	$-0.348424\pi$
$618$	11.2911	−	34.2861i	0.454196	−	1.37919i
$619$		−	10.6446i		−	0.427843i	−0.976851	−	0.213922i	$-0.931376\pi$
$619$		−	10.6446i		−	0.427843i	0.976851	−	0.213922i	$-0.0686237\pi$
$620$	6.09844	+	18.7691i	0.244919	+	0.753784i
$621$	−12.3731	+	8.76598i	−0.496514	+	0.351767i
$622$	32.9808	−	45.3942i	1.32241	−	1.82014i
$623$	−3.40918	−	4.69233i	−0.136586	−	0.187994i
$624$	13.1828	+	9.65820i	0.527735	+	0.386638i
$625$	0.871019	−	0.632832i	0.0348407	−	0.0253133i
$626$	−27.3803	+	8.89640i	−1.09434	+	0.355571i
$627$	−0.0234381	+	5.89443i	−0.000936026	+	0.235401i
$628$	17.4226	−	23.9801i	0.695236	−	0.956911i
$629$	−14.1552	−	10.2844i	−0.564406	−	0.410065i
$630$	21.6293	+	0.172012i	0.861731	+	0.00685311i
$631$	−14.2334	+	43.8060i	−0.566623	+	1.74389i	0.0964546	+	0.995337i	$0.469250\pi$
$631$	−14.2334	+	43.8060i	−0.566623	+	1.74389i	−0.663078	+	0.748550i	$0.730750\pi$
$632$	0.954493			0.0379677
$633$	−21.3067	+	13.3800i	−0.846866	+	0.531806i
$634$	−34.9269			−1.38712
$635$	−3.29787	+	10.1498i	−0.130872	+	0.402783i
$636$	−15.3819	+	4.93037i	−0.609934	+	0.195502i
$637$	−0.740477	−	0.537988i	−0.0293387	−	0.0213158i
$638$	−0.611371	+	0.841479i	−0.0242044	+	0.0333145i
$639$	−15.1110	−	5.04306i	−0.597782	−	0.199501i
$640$	−10.2612	+	3.33407i	−0.405610	+	0.131791i
$641$	24.6577	−	17.9149i	0.973921	−	0.707595i	0.0175793	−	0.999845i	$-0.494404\pi$
$641$	24.6577	−	17.9149i	0.973921	−	0.707595i	0.956342	+	0.292250i	$0.0944041\pi$
$642$	18.8682	−	25.7539i	0.744668	−	1.01642i
$643$	−26.0176	−	35.8102i	−1.02604	−	1.41222i	−0.907884	−	0.419221i	$-0.862303\pi$
$643$	−26.0176	−	35.8102i	−1.02604	−	1.41222i	−0.118151	−	0.992996i	$-0.537697\pi$
$644$	6.89050	−	9.48396i	0.271524	−	0.373721i
$645$	−28.3829	−	9.34711i	−1.11758	−	0.368042i
$646$	−6.09087	−	18.7458i	−0.239642	−	0.737542i
$647$			23.2436i			0.913799i	0.889518	+	0.456899i	$0.151040\pi$
$647$			23.2436i			0.913799i	−0.889518	+	0.456899i	$0.848960\pi$
$648$	2.60917	+	8.48718i	0.102498	+	0.333408i
$649$	−2.75315	−	8.47333i	−0.108071	−	0.332607i
$650$	3.40191	+	10.4700i	0.133434	+	0.410667i
$651$	36.3721	−	26.2056i	1.42554	−	1.02708i
$652$	0.874097	+	2.69019i	0.0342323	+	0.105356i
$653$	−3.43618	+	1.11648i	−0.134468	+	0.0436913i	−0.375478	−	0.926831i	$-0.622521\pi$
$653$	−3.43618	+	1.11648i	−0.134468	+	0.0436913i	0.241010	+	0.970523i	$0.422521\pi$
$654$	32.3262	−	23.2905i	1.26405	−	0.910731i
$655$	−3.63161	−	4.99848i	−0.141899	−	0.195307i
$656$	−14.3516	+	44.1698i	−0.560337	+	1.72454i
$657$	−30.7113	+	21.9420i	−1.19816	+	0.856040i
$658$	7.16405	+	22.0487i	0.279284	+	0.859547i
$659$	−2.50133			−0.0974379			−0.0487189	−	0.998813i	$-0.515514\pi$
$659$	−2.50133			−0.0974379			−0.0487189	+	0.998813i	$0.515514\pi$
$660$	4.52676	+	0.0179998i	0.176204	+	0.000700641i
$661$	−24.5387	−	7.97312i	−0.954446	−	0.310118i	−0.209925	−	0.977717i	$-0.567322\pi$
$661$	−24.5387	−	7.97312i	−0.954446	−	0.310118i	−0.744521	+	0.667599i	$0.767322\pi$
$662$	−1.97949	−	6.09225i	−0.0769351	−	0.236782i
$663$	−10.7607	−	7.88367i	−0.417911	−	0.306176i
$664$		−	15.5485i		−	0.603399i
$665$	−10.4980			−0.407095
$666$	20.1630	+	14.8957i	0.781300	+	0.577196i
$667$	1.29866			0.0502842
$668$	0.796370	−	2.45098i	0.0308125	−	0.0948311i
$669$	−0.368870	+	0.118234i	−0.0142614	+	0.00457118i
$670$	−2.67058	+	1.94029i	−0.103173	+	0.0749598i
$671$	−4.44514			−0.171603
$672$	−19.1666	−	26.6023i	−0.739367	−	1.02621i
$673$		−	37.9980i		−	1.46471i	−0.680921	−	0.732357i	$-0.738420\pi$
$673$		−	37.9980i		−	1.46471i	0.680921	−	0.732357i	$-0.261580\pi$
$674$	−51.2959	−	37.2687i	−1.97585	−	1.43554i
$675$	−4.98200	+	14.7327i	−0.191757	+	0.567061i
$676$	−13.3832			−0.514738
$677$	37.5932	−	12.2148i	1.44482	−	0.469451i	0.521425	−	0.853297i	$-0.325401\pi$
$677$	37.5932	−	12.2148i	1.44482	−	0.469451i	0.923397	+	0.383846i	$0.125401\pi$
$678$	−20.4901	+	6.56768i	−0.786918	+	0.252230i
$679$	15.1059	+	10.9751i	0.579711	+	0.421184i
$680$	5.18503	−	1.68472i	0.198837	−	0.0646060i
$681$	−15.2335	−	21.1433i	−0.583747	−	0.810214i
$682$	17.9142	−	13.0154i	0.685970	−	0.498387i
$683$	45.9749			1.75918			0.879590	−	0.475732i	$-0.157817\pi$
$683$	45.9749			1.75918			0.879590	+	0.475732i	$0.157817\pi$
$684$	3.60686	+	11.4087i	0.137912	+	0.436222i
$685$	−6.66068	+	20.4995i	−0.254492	+	0.783244i
$686$	−19.5534	−	26.9130i	−0.746553	−	1.02754i
$687$	−22.7685	−	7.49816i	−0.868673	−	0.286073i
$688$	17.9837	+	55.3481i	0.685621	+	2.11012i
$689$	7.36049	−	10.1308i	0.280412	−	0.385954i
$690$	−7.79784	−	10.8230i	−0.296859	−	0.412026i
$691$	8.66018			0.329449			0.164724	−	0.986340i	$-0.447327\pi$
$691$	8.66018			0.329449			0.164724	+	0.986340i	$0.447327\pi$
$692$	14.6124	−	20.1122i	0.555480	−	0.764552i
$693$	−3.09972	−	9.80460i	−0.117749	−	0.372446i
$694$	20.0304	+	27.5695i	0.760345	+	1.04652i
$695$	−0.612202	−	0.198916i	−0.0232221	−	0.00754533i
$696$	0.237863	−	0.722282i	0.00901617	−	0.0273780i
$697$	11.7148	−	36.0543i	0.443728	−	1.36565i
$698$	24.4136	+	7.93246i	0.924069	+	0.300248i
$699$	−0.727493	−	0.532987i	−0.0275163	−	0.0201594i
$700$		−	12.0233i		−	0.454437i
$701$	−1.72805	+	5.31840i	−0.0652677	+	0.200873i	−0.978372	−	0.206852i	$-0.933678\pi$
$701$	−1.72805	+	5.31840i	−0.0652677	+	0.200873i	0.913104	+	0.407726i	$0.133678\pi$
$702$	15.3270	+	11.4175i	0.578481	+	0.430927i
$703$	−9.84321	−	7.15151i	−0.371244	−	0.269724i
$704$	−2.47115	−	3.40124i	−0.0931348	−	0.128189i
$705$	11.1774	+	0.0444447i	0.420965	+	0.00167388i
$706$	−26.2558			−0.988149
$707$	−14.8321	−	45.6486i	−0.557819	−	1.71679i
$708$	−10.5720	−	14.6734i	−0.397320	−	0.551462i
$709$	4.24028	−	13.0502i	0.159247	−	0.490112i	−0.839319	−	0.543639i	$-0.817046\pi$
$709$	4.24028	−	13.0502i	0.159247	−	0.490112i	0.998566	+	0.0535268i	$0.0170462\pi$
$710$	4.33058	−	13.3282i	0.162524	−	0.500197i
$711$	2.90235	+	0.0230816i	0.108847	+	0.000865627i
$712$	1.69452	+	1.23114i	0.0635047	+	0.0461389i
$713$	−26.2939	−	8.54340i	−0.984714	−	0.319953i
$714$	20.1002	+	27.8981i	0.752229	+	1.04406i
$715$	−2.83915	+	2.06277i	−0.106178	+	0.0771431i
$716$	−3.82810	+	5.26892i	−0.143063	+	0.196909i
$717$	20.9203	+	0.0831854i	0.781282	+	0.00310662i
$718$	−47.1052	−	15.3054i	−1.75795	−	0.571193i
$719$	2.17787	−	6.70279i	0.0812207	−	0.249972i	−0.902198	−	0.431323i	$-0.858047\pi$
$719$	2.17787	−	6.70279i	0.0812207	−	0.249972i	0.983418	+	0.181351i	$0.0580470\pi$
$720$	−19.3649	+	6.12223i	−0.721689	+	0.228162i
$721$		−	30.5632i		−	1.13823i
$722$	6.70226	+	20.6274i	0.249432	+	0.767674i
$723$	5.62620	+	0.0223715i	0.209241	+	0.000832004i
$724$	−0.323712	−	0.445551i	−0.0120306	−	0.0165588i
$725$	1.07756	−	0.782894i	0.0400196	−	0.0290760i
$726$	9.28332	+	28.9625i	0.344536	+	1.07490i
$727$			42.7765i			1.58649i	0.608901	+	0.793246i	$0.291611\pi$
$727$			42.7765i			1.58649i	−0.608901	+	0.793246i	$0.708389\pi$
$728$	5.06115	+	1.64447i	0.187579	+	0.0609480i
$729$	7.72851	+	25.8703i	0.286241	+	0.958158i
$730$	−19.5169	−	26.8627i	−0.722352	−	0.994232i
$731$	−14.6795	−	45.1788i	−0.542940	−	1.67100i
$732$	−8.59264	+	2.75419i	−0.317593	+	0.101798i
$733$	−9.98475	+	30.7299i	−0.368795	+	1.13503i	0.578775	+	0.815487i	$0.303531\pi$
$733$	−9.98475	+	30.7299i	−0.368795	+	1.13503i	−0.947570	+	0.319548i	$0.896469\pi$
$734$		−	35.4602i		−	1.30886i
$735$	1.08320	−	0.347198i	0.0399545	−	0.0128066i
$736$	−6.24859	+	19.2312i	−0.230326	+	0.708871i
$737$	1.26960	+	0.922416i	0.0467662	+	0.0339776i
$738$	−17.1945	+	51.5215i	−0.632939	+	1.89653i
$739$	30.3082	−	9.84774i	1.11491	−	0.362255i	0.307084	−	0.951682i	$-0.400647\pi$
$739$	30.3082	−	9.84774i	1.11491	−	0.362255i	0.807821	+	0.589427i	$0.200647\pi$
$740$	−5.49216	+	7.55931i	−0.201896	+	0.277886i
$741$	−7.48274	−	5.48212i	−0.274885	−	0.201391i
$742$	−26.1138	+	18.9728i	−0.958668	+	0.696513i
$743$	23.1201			0.848195			0.424098	−	0.905616i	$-0.360591\pi$
$743$	23.1201			0.848195			0.424098	+	0.905616i	$0.360591\pi$
$744$	−9.56764	+	13.0592i	−0.350767	+	0.478774i
$745$	15.4283	+	21.2352i	0.565248	+	0.777996i
$746$	−55.5059	+	18.0350i	−2.03222	+	0.660307i
$747$	0.375995	−	47.2787i	0.0137569	−	1.72984i
$748$	4.22982	+	5.82185i	0.154658	+	0.212868i
$749$	8.35313	−	25.7083i	0.305217	−	0.939360i
$750$	−34.7036	−	11.4286i	−1.26720	−	0.417315i
$751$	−12.3969	−	17.0629i	−0.452370	−	0.622634i	0.520535	−	0.853841i	$-0.325733\pi$
$751$	−12.3969	−	17.0629i	−0.452370	−	0.622634i	−0.972905	+	0.231207i	$0.925733\pi$
$752$	−12.7951	−	17.6109i	−0.466588	−	0.642203i
$753$	1.22795	+	3.83100i	0.0447489	+	0.139610i
$754$	−0.505808	−	1.55672i	−0.0184204	−	0.0566922i
$755$	−5.10591	+	1.65901i	−0.185823	+	0.0603776i
$756$	−12.0668	−	17.0321i	−0.438864	−	0.619451i
$757$	−7.94525	+	10.9357i	−0.288775	+	0.397465i	−0.928616	−	0.371043i	$-0.879000\pi$
$757$	−7.94525	+	10.9357i	−0.288775	+	0.397465i	0.639841	+	0.768507i	$0.279000\pi$
$758$	53.6555	+	17.4337i	1.94886	+	0.633222i
$759$	−3.74791	+	5.11565i	−0.136040	+	0.185686i
$760$	3.60554	−	1.17151i	0.130787	−	0.0424952i
$761$	−15.0546	−	10.9378i	−0.545729	−	0.396496i	0.280479	−	0.959860i	$-0.409507\pi$
$761$	−15.0546	−	10.9378i	−0.545729	−	0.396496i	−0.826208	+	0.563365i	$0.809507\pi$
$762$	23.1470	−	7.41930i	0.838529	−	0.268773i
$763$	19.8284	−	27.2915i	0.717837	−	0.988018i
$764$	−2.40176	+	7.39185i	−0.0868926	+	0.267428i
$765$	15.8070	−	4.99737i	0.571502	−	0.180680i
$766$	27.7868	+	38.2452i	1.00398	+	1.38186i
$767$	13.3343	+	4.33259i	0.481475	+	0.156441i
$768$	29.1867	+	21.3832i	1.05319	+	0.771601i
$769$	18.6045	+	13.5170i	0.670895	+	0.487434i	0.870325	−	0.492478i	$-0.163909\pi$
$769$	18.6045	+	13.5170i	0.670895	+	0.487434i	−0.199430	+	0.979912i	$0.563909\pi$
$770$	8.60325	−	2.79536i	0.310039	−	0.100738i
$771$	7.91235	+	2.60571i	0.284957	+	0.0938423i
$772$	4.85074	+	14.9290i	0.174582	+	0.537308i
$773$	−30.8622	+	22.4227i	−1.11004	+	0.806488i	−0.982669	−	0.185368i	$-0.940652\pi$
$773$	−30.8622	+	22.4227i	−1.11004	+	0.806488i	−0.127366	+	0.991856i	$0.540652\pi$
$774$	20.5165	+	64.8948i	0.737450	+	2.33259i
$775$	−26.9678	+	8.76236i	−0.968711	+	0.314753i
$776$	−6.41287	−	2.08367i	−0.230209	−	0.0747993i
$777$	20.1600	+	6.63913i	0.723237	+	0.238178i
$778$	−44.1416	−	14.3425i	−1.58255	−	0.514202i
$779$	8.14616	−	25.0713i	0.291867	−	0.898273i
$780$	−4.21012	+	5.74654i	−0.150746	+	0.205759i
$781$	−6.66231			−0.238396
$782$	6.55295	−	20.1679i	0.234333	−	0.721203i
$783$	0.740741	−	2.19051i	0.0264719	−	0.0782823i
$784$	−1.79219	−	1.30210i	−0.0640067	−	0.0465036i
$785$	−23.1038	−	16.7859i	−0.824610	−	0.599114i
$786$	−4.40172	+	13.3660i	−0.157004	+	0.476750i
$787$	3.95090	+	2.87049i	0.140834	+	0.102322i	0.655972	−	0.754786i	$-0.272259\pi$
$787$	3.95090	+	2.87049i	0.140834	+	0.102322i	−0.515137	+	0.857108i	$0.672259\pi$
$788$	6.19294	+	4.49944i	0.220614	+	0.160286i
$789$	−0.0886240	+	22.2880i	−0.00315510	+	0.793475i
$790$			2.55331i			0.0908425i
$791$	−14.7388	+	10.7083i	−0.524050	+	0.380745i
$792$	2.15873	+	3.02148i	0.0767072	+	0.107364i
$793$	4.11170	−	5.65927i	0.146011	−	0.200967i
$794$		−	0.279187i		−	0.00990798i
$795$	4.75020	+	14.8198i	0.168472	+	0.525606i
$796$	−8.18181	−	5.94443i	−0.289997	−	0.210695i
$797$	−10.4382	−	32.1253i	−0.369738	−	1.13794i	−0.946960	−	0.321351i	$-0.895863\pi$
$797$	−10.4382	−	32.1253i	−0.369738	−	1.13794i	0.577222	−	0.816587i	$-0.304137\pi$
$798$	13.9772	+	19.3997i	0.494786	+	0.686741i
$799$	10.4442	+	14.3752i	0.369489	+	0.508557i
$800$	6.40873	+	19.7240i	0.226583	+	0.697350i
$801$	5.12278	+	3.78453i	0.181005	+	0.133720i
$802$	−15.2215	+	11.0591i	−0.537489	+	0.390509i
$803$	−9.27836	+	12.7706i	−0.327426	+	0.450663i
$804$	3.02570	+	0.996429i	0.106708	+	0.0351414i
$805$	−9.13739	−	6.63870i	−0.322051	−	0.233984i
$806$			34.8463i			1.22741i
$807$	−38.8078	+	12.4390i	−1.36610	+	0.437875i
$808$	10.1882	+	14.0228i	0.358419	+	0.493322i
$809$	33.6915	+	10.9470i	1.18453	+	0.384878i	0.834048	−	0.551692i	$-0.186017\pi$
$809$	33.6915	+	10.9470i	1.18453	+	0.384878i	0.350483	+	0.936569i	$0.386017\pi$
$810$	−22.7035	+	6.97962i	−0.797721	+	0.245239i
$811$	−25.1454			−0.882976			−0.441488	−	0.897267i	$-0.645549\pi$
$811$	−25.1454			−0.882976			−0.441488	+	0.897267i	$0.645549\pi$
$812$			1.78766i			0.0627346i
$813$	−2.97506	−	0.979750i	−0.104340	−	0.0343613i
$814$	9.97090	+	3.23974i	0.349480	+	0.113553i
$815$	2.59189	−	0.842155i	0.0907898	−	0.0294994i
$816$	−26.0443	−	19.0810i	−0.911733	−	0.667968i
$817$	−10.2078	−	31.4162i	−0.357124	−	1.09912i
$818$		−	58.7065i		−	2.05263i
$819$	15.3498	+	5.12276i	0.536365	+	0.179004i
$820$	−19.2541	−	6.25603i	−0.672382	−	0.218470i
$821$	26.9645	+	8.76130i	0.941068	+	0.305771i	0.739081	−	0.673617i	$-0.235260\pi$
$821$	26.9645	+	8.76130i	0.941068	+	0.305771i	0.201987	+	0.979388i	$0.435260\pi$
$822$	46.7499	−	14.9847i	1.63059	−	0.522651i
$823$	−6.17526	+	8.49951i	−0.215256	+	0.296274i	−0.902967	−	0.429710i	$-0.858616\pi$
$823$	−6.17526	+	8.49951i	−0.215256	+	0.296274i	0.687711	+	0.725985i	$0.258616\pi$
$824$	3.41066	+	10.4969i	0.118816	+	0.365678i
$825$	−0.0258624	+	6.50414i	−0.000900414	+	0.226445i
$826$	−29.2380	−	21.2426i	−1.01732	−	0.739126i
$827$	−39.7794	+	12.9251i	−1.38327	+	0.449451i	−0.903742	−	0.428078i	$-0.859191\pi$
$827$	−39.7794	+	12.9251i	−1.38327	+	0.449451i	−0.479525	+	0.877528i	$0.659191\pi$
$828$	−4.07522	+	12.2109i	−0.141624	+	0.424360i
$829$	−31.8815			−1.10729			−0.553645	−	0.832753i	$-0.686764\pi$
$829$	−31.8815			−1.10729			−0.553645	+	0.832753i	$0.686764\pi$
$830$	41.5929			1.44371
$831$	25.0344	+	0.0995443i	0.868433	+	0.00345315i
$832$	6.61602			0.229369
$833$	1.46290	+	1.06286i	0.0506866	+	0.0368260i
$834$	0.447507	+	1.39615i	0.0154959	+	0.0483447i
$835$	−2.36141	−	0.767269i	−0.0817200	−	0.0265524i
$836$	2.94132	+	4.04837i	0.101728	+	0.140016i
$837$	−29.4083	+	39.4781i	−1.01650	+	1.36456i
$838$	22.2084	−	7.21596i	0.767178	−	0.249271i
$839$	−4.42189	−	3.21269i	−0.152661	−	0.110914i	0.508833	−	0.860865i	$-0.330077\pi$
$839$	−4.42189	−	3.21269i	−0.152661	−	0.110914i	−0.661494	+	0.749951i	$0.730077\pi$
$840$	−5.36590	+	3.86605i	−0.185141	+	0.133391i
$841$	23.3013	−	16.9294i	0.803492	−	0.583771i
$842$	65.3376	+	21.2295i	2.25168	+	0.731616i
$843$	−35.1858	−	11.5875i	−1.21186	−	0.399093i
$844$	−7.87820	+	19.8529i	−0.271179	+	0.683365i
$845$			12.8941i			0.443572i
$846$	−14.7996	−	20.7143i	−0.508819	−	0.712172i
$847$	15.1361	+	20.8330i	0.520081	+	0.715830i
$848$	17.8147	−	24.5198i	0.611760	−	0.842015i
$849$	12.5785	+	17.4584i	0.431693	+	0.599170i
$850$	−6.72089	−	20.6848i	−0.230525	−	0.709482i
$851$	−4.04500	−	12.4492i	−0.138661	−	0.426755i
$852$	−12.8785	+	4.12794i	−0.441210	+	0.141421i
$853$	16.2125	−	49.8969i	0.555105	−	1.70844i	−0.140561	−	0.990072i	$-0.544891\pi$
$853$	16.2125	−	49.8969i	0.555105	−	1.70844i	0.695666	−	0.718365i	$-0.255109\pi$
$854$	−14.5876	+	10.5985i	−0.499179	+	0.362675i
$855$	10.9918	−	3.47505i	0.375911	−	0.118844i
$856$			9.76167i			0.333647i
$857$	−0.317271	+	0.103088i	−0.0108378	+	0.00352141i	−0.314431	−	0.949280i	$-0.601814\pi$
$857$	−0.317271	+	0.103088i	−0.0108378	+	0.00352141i	0.303593	+	0.952802i	$0.401814\pi$
$858$	7.59195	+	2.50019i	0.259185	+	0.0853551i
$859$		−	52.4081i		−	1.78814i	−0.447927	−	0.894070i	$-0.647838\pi$
$859$		−	52.4081i		−	1.78814i	0.447927	−	0.894070i	$-0.352162\pi$
$860$	−24.1268	+	7.83928i	−0.822718	+	0.267317i
$861$	−0.182860	+	45.9873i	−0.00623184	+	1.56724i
$862$	−31.0020	+	42.6706i	−1.05593	+	1.45337i
$863$	36.7716	−	11.9478i	1.25172	−	0.406709i	0.393184	−	0.919460i	$-0.371374\pi$
$863$	36.7716	−	11.9478i	1.25172	−	0.406709i	0.858537	+	0.512751i	$0.171374\pi$
$864$	28.8740	+	21.5091i	0.982313	+	0.731753i
$865$	−19.3773	−	14.0784i	−0.658847	−	0.478681i
$866$	11.7561	−	8.54127i	0.399487	−	0.290244i
$867$	−2.49328	−	1.82667i	−0.0846762	−	0.0620368i
$868$	11.7604	−	36.1948i	0.399174	−	1.22853i
$869$	1.15444	−	0.375099i	0.0391616	−	0.0127244i
$870$	1.93213	+	0.636292i	0.0655054	+	0.0215723i
$871$	−2.34872	+	0.763146i	−0.0795834	+	0.0258582i
$872$	−3.76452	+	11.5860i	−0.127483	+	0.392351i
$873$	−19.4494	−	6.49093i	−0.658261	−	0.219685i
$874$	4.55676	−	14.0243i	0.154135	−	0.474378i
$875$	−30.9354			−1.04581
$876$	−10.0228	+	30.4348i	−0.338640	+	1.02830i
$877$		−	32.9966i		−	1.11422i	−0.830440	−	0.557108i	$-0.811911\pi$
$877$		−	32.9966i		−	1.11422i	0.830440	−	0.557108i	$-0.188089\pi$
$878$		−	30.0634i		−	1.01459i
$879$	−17.2061	+	23.4852i	−0.580346	+	0.792135i
$880$	−6.87165	+	4.99255i	−0.231643	+	0.168299i
$881$	21.1777	+	29.1485i	0.713493	+	0.982039i	0.999715	+	0.0238759i	$0.00760067\pi$
$881$	21.1777	+	29.1485i	0.713493	+	0.982039i	−0.286222	+	0.958163i	$0.592399\pi$
$882$	−2.08379	−	1.53943i	−0.0701648	−	0.0518352i
$883$	11.5775	−	15.9350i	0.389612	−	0.536256i	−0.568487	−	0.822693i	$-0.692471\pi$
$883$	11.5775	−	15.9350i	0.389612	−	0.536256i	0.958099	+	0.286437i	$0.0924709\pi$
$884$	−11.3245			−0.380885
$885$	−14.1372	+	10.1857i	−0.475218	+	0.342387i
$886$	−26.7888	−	36.8717i	−0.899989	−	1.23873i
$887$			48.1335i			1.61616i	0.589070	+	0.808082i	$0.299494\pi$
$887$			48.1335i			1.61616i	−0.589070	+	0.808082i	$0.700506\pi$
$888$	−7.66485	−	0.0304778i	−0.257216	−	0.00102277i
$889$	16.6499	−	12.0969i	0.558420	−	0.405716i
$890$	−3.29334	+	4.53290i	−0.110393	+	0.151943i
$891$	6.49104	+	9.23969i	0.217458	+	0.309541i
$892$	−0.193289	+	0.266039i	−0.00647178	+	0.00890764i
$893$	7.26263	+	9.99616i	0.243035	+	0.334509i
$894$	18.6999	−	56.7832i	0.625419	−	1.89911i
$895$	5.07638	+	3.68821i	0.169685	+	0.123283i
$896$	19.7880	+	6.42950i	0.661070	+	0.214795i
$897$	−3.04615	−	9.50351i	−0.101708	−	0.317313i
$898$	−12.2997			−0.410448
$899$	4.00966	−	1.30282i	0.133730	−	0.0434514i
$900$	3.97994	+	12.5888i	0.132665	+	0.419626i
$901$	−14.5416	+	20.0147i	−0.484450	+	0.666788i
$902$			22.7154i			0.756339i
$903$	33.6861	+	46.7548i	1.12100	+	1.55590i
$904$	3.86705	−	5.32253i	0.128616	−	0.177025i
$905$	−0.429269	+	0.311882i	−0.0142694	+	0.0103673i
$906$	9.86381	+	7.22658i	0.327703	+	0.240087i
$907$			37.9335i			1.25956i	0.776773	+	0.629780i	$0.216855\pi$
$907$			37.9335i			1.25956i	−0.776773	+	0.629780i	$0.783145\pi$
$908$	−21.0402	−	6.83638i	−0.698244	−	0.226873i
$909$	30.6404	+	42.8859i	1.01628	+	1.42244i
$910$	−4.39902	+	13.5388i	−0.145826	+	0.448806i
$911$	42.0599			1.39351			0.696754	−	0.717310i	$-0.254627\pi$
$911$	42.0599			1.39351			0.696754	+	0.717310i	$0.254627\pi$
$912$	−18.1106	−	13.2685i	−0.599702	−	0.439363i
$913$	−6.11030	−	18.8056i	−0.202221	−	0.622373i
$914$	−24.4022	+	33.5867i	−0.807152	+	1.11095i
$915$	2.65355	+	8.27864i	0.0877235	+	0.273683i
$916$	−19.3543	+	6.28859i	−0.639484	+	0.207781i
$917$			11.9147i			0.393458i
$918$	−30.2804	−	22.5567i	−0.999402	−	0.744483i
$919$	−19.8162	+	27.2747i	−0.653678	+	0.899710i	−0.999252	−	0.0386814i	$-0.987684\pi$
$919$	−19.8162	+	27.2747i	−0.653678	+	0.899710i	0.345574	+	0.938392i	$0.387684\pi$
$920$	3.87908	+	1.26039i	0.127889	+	0.0415538i
$921$	−24.7078	−	18.1018i	−0.814149	−	0.596474i
$922$	−46.1146	+	33.5042i	−1.51870	+	1.10340i
$923$	6.16255	−	8.48202i	0.202843	−	0.279189i
$924$	−7.04193	−	5.15917i	−0.231662	−	0.169724i
$925$	−10.8614	−	7.89124i	−0.357119	−	0.259462i
$926$	−28.8426	−	39.6984i	−0.947826	−	1.30457i
$927$	10.1170	+	32.0007i	0.332287	+	1.05104i
$928$	−0.952873	−	2.93264i	−0.0312796	−	0.0962686i
$929$	−1.21274	+	3.73242i	−0.0397886	+	0.122457i	−0.968978	−	0.247148i	$-0.920507\pi$
$929$	−1.21274	+	3.73242i	−0.0397886	+	0.122457i	0.929189	+	0.369604i	$0.120507\pi$
$930$	−34.9339	−	25.5938i	−1.14553	−	0.839254i
$931$	1.01727	+	0.739089i	0.0333396	+	0.0242227i
$932$	−0.765611			−0.0250784
$933$	−0.207438	+	52.1686i	−0.00679122	+	1.70792i
$934$	−20.5326	+	6.67144i	−0.671846	+	0.218296i
$935$	5.60910	−	4.07525i	0.183437	−	0.133275i
$936$	−5.84356	−	0.0464722i	−0.191003	−	0.00151899i
$937$	3.54151	−	2.57306i	0.115696	−	0.0840582i	−0.528433	−	0.848975i	$-0.677220\pi$
$937$	3.54151	−	2.57306i	0.115696	−	0.0840582i	0.644129	+	0.764917i	$0.277220\pi$
$938$	6.36575			0.207849
$939$	15.8193	−	21.5923i	0.516244	−	0.704639i
$940$	7.67678	−	5.57750i	0.250389	−	0.181918i
$941$	31.4248	−	22.8315i	1.02442	−	0.744285i	0.0572360	−	0.998361i	$-0.481771\pi$
$941$	31.4248	−	22.8315i	1.02442	−	0.744285i	0.967184	+	0.254076i	$0.0817713\pi$
$942$	−0.258632	+	65.0433i	−0.00842669	+	2.11923i
$943$	22.9449	−	16.6704i	0.747189	−	0.542864i
$944$	32.2733	+	10.4862i	1.05041	+	0.341298i
$945$	−16.4097	+	11.6258i	−0.533807	+	0.378188i
$946$	16.7308	+	23.0279i	0.543964	+	0.748702i
$947$	−8.16011	−	2.65138i	−0.265168	−	0.0861583i	0.173416	−	0.984849i	$-0.444520\pi$
$947$	−8.16011	−	2.65138i	−0.265168	−	0.0861583i	−0.438583	+	0.898690i	$0.644520\pi$
$948$	1.99916	−	1.44036i	0.0649297	−	0.0467809i
$949$	−7.67630	−	23.6252i	−0.249183	−	0.766907i
$950$	−4.67355	−	14.3837i	−0.151630	−	0.466669i
$951$	26.3474	−	18.9829i	0.854372	−	0.615562i
$952$	−9.99894	−	3.24885i	−0.324067	−	0.105296i
$953$	26.0126	+	35.8033i	0.842632	+	1.15978i	0.985438	+	0.170032i	$0.0543872\pi$
$953$	26.0126	+	35.8033i	0.842632	+	1.15978i	−0.142807	+	0.989751i	$0.545613\pi$
$954$	21.0617	−	28.5094i	0.681898	−	0.923025i
$955$	7.12173	+	2.31399i	0.230454	+	0.0748790i
$956$	14.3683	−	10.4392i	0.464705	−	0.337628i
$957$	0.00384532	−	0.967058i	0.000124301	−	0.0312606i
$958$	33.0291	−	23.9970i	1.06712	−	0.775309i
$959$	33.6277	−	24.4319i	1.08589	−	0.788948i
$960$	−4.85931	+	6.63265i	−0.156834	+	0.214068i
$961$	−58.7544			−1.89530
$962$	−13.3476	+	9.69759i	−0.430343	+	0.312663i
$963$	−0.236057	+	29.6825i	−0.00760684	+	0.956506i
$964$	3.86415	−	2.80747i	0.124456	−	0.0904225i
$965$	14.3835	−	4.67348i	0.463021	−	0.150445i
$966$	−0.102287	+	25.7242i	−0.00329104	+	0.827662i
$967$	−0.421838			−0.0135654			−0.00678270	−	0.999977i	$-0.502159\pi$
$967$	−0.421838			−0.0135654			−0.00678270	+	0.999977i	$0.502159\pi$
$968$	−7.52332	−	5.46601i	−0.241809	−	0.175684i
$969$	14.7831	+	10.8306i	0.474901	+	0.347929i
$970$	5.57389	−	17.1547i	0.178967	−	0.550803i
$971$	7.61943	+	23.4502i	0.244519	+	0.752553i	0.995715	+	0.0924735i	$0.0294773\pi$
$971$	7.61943	+	23.4502i	0.244519	+	0.752553i	−0.751196	+	0.660079i	$0.770523\pi$
$972$	18.2723	+	13.8389i	0.586084	+	0.443882i
$973$	0.729642	+	1.00427i	0.0233912	+	0.0321953i
$974$	−2.65037	−	1.92561i	−0.0849233	−	0.0617004i
$975$	−8.25673	−	6.04917i	−0.264427	−	0.193729i
$976$	9.95162	−	13.6972i	0.318544	−	0.438438i
$977$	42.6265	−	30.9700i	1.36374	−	0.990817i	0.365546	−	0.930793i	$-0.380882\pi$
$977$	42.6265	−	30.9700i	1.36374	−	0.990817i	0.998197	−	0.0600242i	$-0.0191178\pi$
$978$	−5.00712	−	3.66839i	−0.160110	−	0.117302i
$979$	2.53329	+	0.823117i	0.0809644	+	0.0263069i
$980$	0.567600	−	0.781234i	0.0181313	−	0.0249556i
$981$	−11.7270	+	35.1387i	−0.374415	+	1.12189i
$982$			35.5837i			1.13552i
$983$	0.404583	−	0.131457i	0.0129042	−	0.00419282i	−0.302558	−	0.953131i	$-0.597841\pi$
$983$	0.404583	−	0.131457i	0.0129042	−	0.00419282i	0.315462	+	0.948938i	$0.397841\pi$
$984$	−5.06910	−	15.8148i	−0.161597	−	0.504156i
$985$	4.33501	−	5.96663i	0.138125	−	0.190113i
$986$	0.999286	+	3.07549i	0.0318237	+	0.0979434i
$987$	−17.3878	−	12.7389i	−0.553459	−	0.405484i
$988$	−7.87481			−0.250531
$989$	10.9822	−	33.7996i	0.349213	−	1.07477i
$990$	−8.08258	+	5.77469i	−0.256881	+	0.183532i
$991$	29.9826	+	9.74194i	0.952429	+	0.309463i	0.743702	−	0.668511i	$-0.233068\pi$
$991$	29.9826	+	9.74194i	0.952429	+	0.309463i	0.208727	+	0.977974i	$0.433068\pi$
$992$			65.6457i			2.08425i
$993$	4.80440	+	3.51988i	0.152463	+	0.111700i
$994$	−21.8637	+	15.8849i	−0.693475	+	0.503839i
$995$	−5.72721	+	7.88282i	−0.181565	+	0.249902i
$996$	−23.4633	−	32.5660i	−0.743463	−	1.03189i
$997$			59.4625i			1.88320i	0.336739	+	0.941598i	$0.390676\pi$
$997$			59.4625i			1.88320i	−0.336739	+	0.941598i	$0.609324\pi$
$998$	17.8899	−	24.6234i	0.566296	−	0.779440i
$999$	−23.3060	−	0.278026i	−0.737368	−	0.00879636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	633.2.k.a.23.14	✓	272
3.2	odd	2	inner	633.2.k.a.23.55	yes	272
211.156	odd	10	inner	633.2.k.a.578.55	yes	272
633.578	even	10	inner	633.2.k.a.578.14	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.2.k.a.23.14	✓	272	1.1	even	1	trivial
633.2.k.a.23.55	yes	272	3.2	odd	2	inner
633.2.k.a.578.14	yes	272	633.578	even	10	inner
633.2.k.a.578.55	yes	272	211.156	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	633.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.575669 + 1.77173i) q^{2} +(-0.528679 - 1.64939i) q^{3} +(-1.18959 - 0.864285i) q^{4} +(-0.832701 + 1.14612i) q^{5} +(3.22662 + 0.0128300i) q^{6} +(2.59824 - 0.844220i) q^{7} +(-0.798157 + 0.579895i) q^{8} +(-2.44100 + 1.74400i) q^{9} +O(q^{10})\)	\(q+(-0.575669 + 1.77173i) q^{2} +(-0.528679 - 1.64939i) q^{3} +(-1.18959 - 0.864285i) q^{4} +(-0.832701 + 1.14612i) q^{5} +(3.22662 + 0.0128300i) q^{6} +(2.59824 - 0.844220i) q^{7} +(-0.798157 + 0.579895i) q^{8} +(-2.44100 + 1.74400i) q^{9} +(-1.55124 - 2.13510i) q^{10} +(-0.737463 + 1.01503i) q^{11} +(-0.796637 + 2.41902i) q^{12} +(-0.610128 - 1.87778i) q^{13} +5.08937i q^{14} +(2.33063 + 0.767525i) q^{15} +(-1.47670 - 4.54483i) q^{16} +(1.20538 + 3.70979i) q^{17} +(-1.68468 - 5.32875i) q^{18} +(0.838196 + 2.57970i) q^{19} +(1.98114 - 0.643711i) q^{20} +(-2.76609 - 3.83920i) q^{21} +(-1.37382 - 1.89091i) q^{22} +(-0.901785 + 2.77541i) q^{23} +(1.37844 + 1.00990i) q^{24} +(0.924897 + 2.84654i) q^{25} +3.67815 q^{26} +(4.16704 + 3.10415i) q^{27} +(-3.82048 - 1.24135i) q^{28} +(-0.137517 - 0.423233i) q^{29} +(-2.70151 + 3.68739i) q^{30} +9.47388i q^{31} +6.92913 q^{32} +(2.06407 + 0.679742i) q^{33} -7.26664 q^{34} +(-1.19599 + 3.68087i) q^{35} +(4.41109 + 0.0350802i) q^{36} +(-3.62889 + 2.63654i) q^{37} -5.05305 q^{38} +(-2.77464 + 1.99909i) q^{39} -1.39766i q^{40} +(-7.86258 - 5.71250i) q^{41} +(8.39437 - 2.69064i) q^{42} -12.1782 q^{43} +(1.75455 - 0.570089i) q^{44} +(0.0337983 - 4.24989i) q^{45} +(-4.39814 - 3.19543i) q^{46} +(4.33230 - 1.40765i) q^{47} +(-6.71551 + 4.83842i) q^{48} +(0.375036 - 0.272479i) q^{49} -5.57572 q^{50} +(5.48165 - 3.94944i) q^{51} +(-0.897138 + 2.76111i) q^{52} +(3.72793 + 5.13105i) q^{53} +(-7.89854 + 5.59590i) q^{54} +(-0.549256 - 1.69044i) q^{55} +(-1.58425 + 2.18053i) q^{56} +(3.81181 - 2.74635i) q^{57} +0.829018 q^{58} +(-4.17393 + 5.74492i) q^{59} +(-2.10912 - 2.92736i) q^{60} +(2.08249 + 2.86630i) q^{61} +(-16.7851 - 5.45382i) q^{62} +(-4.86998 + 6.59207i) q^{63} +(-1.03548 + 3.18687i) q^{64} +(2.66021 + 0.864354i) q^{65} +(-2.39254 + 3.26566i) q^{66} -1.25080i q^{67} +(1.77241 - 5.45491i) q^{68} +(5.05450 + 0.0200982i) q^{69} +(-5.83300 - 4.23792i) q^{70} +(3.12120 + 4.29596i) q^{71} +(0.936963 - 2.80751i) q^{72} +12.5814 q^{73} +(-2.58219 - 7.94717i) q^{74} +(4.20609 - 3.03042i) q^{75} +(1.23249 - 3.79322i) q^{76} +(-1.05920 + 3.25988i) q^{77} +(-1.94456 - 6.06671i) q^{78} +(-0.782707 - 0.568670i) q^{79} +(6.43855 + 2.09201i) q^{80} +(2.91694 - 8.51419i) q^{81} +(14.6472 - 10.6418i) q^{82} +(-9.26354 + 12.7502i) q^{83} +(-0.0276661 + 6.95775i) q^{84} +(-5.25558 - 1.70764i) q^{85} +(7.01064 - 21.5765i) q^{86} +(-0.625376 + 0.450574i) q^{87} -1.23781i q^{88} +(-0.656054 - 2.01913i) q^{89} +(7.51019 + 2.50641i) q^{90} +(-3.17052 - 4.36385i) q^{91} +(3.47150 - 2.52219i) q^{92} +(15.6262 - 5.00864i) q^{93} +8.48599i q^{94} +(-3.65460 - 1.18745i) q^{95} +(-3.66329 - 11.4289i) q^{96} +(4.01730 + 5.52933i) q^{97} +(0.266862 + 0.821318i) q^{98} +(0.0299327 - 3.76382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9}+O(q^{10}) \) 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9	\( 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9} - 20 q^{10} + 6 q^{13} - 46 q^{16} - 20 q^{18} + 6 q^{19} - 3 q^{21} - 10 q^{22} + 23 q^{24} + 50 q^{25} - 40 q^{27} + 80 q^{28} - q^{30} + 12 q^{34} + 13 q^{36} - 42 q^{37} + 25 q^{39} - 10 q^{42} + 40 q^{43} - 23 q^{45} - 2 q^{46} - 15 q^{48} + 30 q^{49} - 11 q^{51} - 34 q^{52} + 128 q^{54} + 14 q^{55} + 20 q^{57} + 60 q^{58} + 30 q^{60} - 10 q^{61} - 108 q^{64} - 73 q^{66} + 40 q^{69} + 70 q^{70} - 105 q^{72} - 20 q^{73} - 10 q^{75} - 12 q^{76} - 82 q^{78} - 30 q^{79} - 42 q^{81} - 106 q^{82} + 121 q^{84} - 110 q^{85} - 11 q^{87} + 60 q^{90} - 40 q^{91} - 45 q^{93} - 114 q^{96} - 80 q^{97} - 18 q^{99}+O(q^{100}) \) 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9 - 20 * q^10 + 6 * q^13 - 46 * q^16 - 20 * q^18 + 6 * q^19 - 3 * q^21 - 10 * q^22 + 23 * q^24 + 50 * q^25 - 40 * q^27 + 80 * q^28 - q^30 + 12 * q^34 + 13 * q^36 - 42 * q^37 + 25 * q^39 - 10 * q^42 + 40 * q^43 - 23 * q^45 - 2 * q^46 - 15 * q^48 + 30 * q^49 - 11 * q^51 - 34 * q^52 + 128 * q^54 + 14 * q^55 + 20 * q^57 + 60 * q^58 + 30 * q^60 - 10 * q^61 - 108 * q^64 - 73 * q^66 + 40 * q^69 + 70 * q^70 - 105 * q^72 - 20 * q^73 - 10 * q^75 - 12 * q^76 - 82 * q^78 - 30 * q^79 - 42 * q^81 - 106 * q^82 + 121 * q^84 - 110 * q^85 - 11 * q^87 + 60 * q^90 - 40 * q^91 - 45 * q^93 - 114 * q^96 - 80 * q^97 - 18 * q^99

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