LMFDB - Embedded newform 33.3.h.b.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,3,Mod(5,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("33.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	33.h (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:	$0.899184872389$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 180x^{12} - 2562x^{10} + 25179x^{8} - 96398x^{6} + 239275x^{4} - 536393x^{2} + 1771561 $ x^16 - 12x^14 + 180x^12 - 2562x^10 + 25179x^8 - 96398x^6 + 239275x^4 - 536393*x^2 + 1771561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			5.2
Root			$-1.90610 + 0.619331i$ of defining polynomial
Character	$\chi$	$=$	33.5
Dual form			33.3.h.b.20.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90610 + 0.619331i) q^{2} +(-2.89787 - 0.776113i) q^{3} +(0.0135968 - 0.00987866i) q^{4} +(-5.21596 - 1.69477i) q^{5} +(6.00431 - 0.315387i) q^{6} +(-4.52308 + 3.28621i) q^{7} +(4.69235 - 6.45847i) q^{8} +(7.79530 + 4.49815i) q^{9} +O(q^{10})$	\(q+(-1.90610 + 0.619331i) q^{2} +(-2.89787 - 0.776113i) q^{3} +(0.0135968 - 0.00987866i) q^{4} +(-5.21596 - 1.69477i) q^{5} +(6.00431 - 0.315387i) q^{6} +(-4.52308 + 3.28621i) q^{7} +(4.69235 - 6.45847i) q^{8} +(7.79530 + 4.49815i) q^{9} +10.9918 q^{10} +(-2.23693 + 10.7702i) q^{11} +(-0.0470687 + 0.0180744i) q^{12} +(-3.00265 - 9.24122i) q^{13} +(6.58622 - 9.06515i) q^{14} +(13.7998 + 8.95939i) q^{15} +(-4.96496 + 15.2806i) q^{16} +(-16.9969 - 5.52262i) q^{17} +(-17.6445 - 3.74608i) q^{18} +(-15.0954 - 10.9674i) q^{19} +(-0.0876624 + 0.0284832i) q^{20} +(15.6578 - 6.01259i) q^{21} +(-2.40646 - 21.9144i) q^{22} +12.3649i q^{23} +(-18.6103 + 15.0740i) q^{24} +(4.10855 + 2.98503i) q^{25} +(11.4467 + 15.7551i) q^{26} +(-19.0987 - 19.0851i) q^{27} +(-0.0290361 + 0.0893640i) q^{28} +(1.45613 + 2.00420i) q^{29} +(-31.8528 - 8.53087i) q^{30} +(15.2132 + 46.8213i) q^{31} -0.268903i q^{32} +(14.8412 - 29.4744i) q^{33} +35.8182 q^{34} +(29.1616 - 9.47517i) q^{35} +(0.150427 - 0.0158466i) q^{36} +(31.8192 - 23.1180i) q^{37} +(35.5658 + 11.5560i) q^{38} +(1.52907 + 29.1102i) q^{39} +(-35.4207 + 25.7346i) q^{40} +(33.2237 - 45.7285i) q^{41} +(-26.1216 + 21.1580i) q^{42} -43.9060 q^{43} +(0.0759795 + 0.168537i) q^{44} +(-33.0366 - 36.6734i) q^{45} +(-7.65794 - 23.5687i) q^{46} +(-33.9646 + 46.7482i) q^{47} +(26.2473 - 40.4277i) q^{48} +(-5.48274 + 16.8741i) q^{49} +(-9.68004 - 3.14524i) q^{50} +(44.9686 + 29.1954i) q^{51} +(-0.132117 - 0.0959889i) q^{52} +(-41.0056 + 13.3235i) q^{53} +(48.2241 + 24.5498i) q^{54} +(29.9206 - 52.3856i) q^{55} +44.6323i q^{56} +(35.2324 + 43.4979i) q^{57} +(-4.01681 - 2.91838i) q^{58} +(-52.9190 - 72.8367i) q^{59} +(0.276140 - 0.0145048i) q^{60} +(-9.53920 + 29.3587i) q^{61} +(-57.9958 - 79.8244i) q^{62} +(-50.0407 + 5.27149i) q^{63} +(-19.6933 - 60.6097i) q^{64} +53.2906i q^{65} +(-10.0345 + 65.3729i) q^{66} +34.0775 q^{67} +(-0.285659 + 0.0928164i) q^{68} +(9.59653 - 35.8318i) q^{69} +(-49.7168 + 36.1213i) q^{70} +(35.7561 + 11.6179i) q^{71} +(65.6294 - 29.2388i) q^{72} +(9.81022 - 7.12754i) q^{73} +(-46.3331 + 63.7720i) q^{74} +(-9.58931 - 11.8389i) q^{75} -0.313592 q^{76} +(-25.2752 - 56.0653i) q^{77} +(-20.9434 - 54.5402i) q^{78} +(-19.5128 - 60.0542i) q^{79} +(51.7940 - 71.2884i) q^{80} +(40.5333 + 70.1288i) q^{81} +(-35.0068 + 107.740i) q^{82} +(9.22665 + 2.99792i) q^{83} +(0.153499 - 0.236430i) q^{84} +(79.2955 + 57.6115i) q^{85} +(83.6893 - 27.1923i) q^{86} +(-2.66420 - 6.93803i) q^{87} +(59.0622 + 64.9845i) q^{88} +34.1289i q^{89} +(85.6842 + 49.4427i) q^{90} +(43.9499 + 31.9315i) q^{91} +(0.122148 + 0.168123i) q^{92} +(-7.74713 - 147.489i) q^{93} +(35.7874 - 110.142i) q^{94} +(60.1495 + 82.7887i) q^{95} +(-0.208700 + 0.779247i) q^{96} +(-11.6879 - 35.9715i) q^{97} -35.5595i q^{98} +(-65.8833 + 73.8945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{3} + 8 q^{4} - 33 q^{6} + 6 q^{7} - 28 q^{9}+O(q^{10}) $ 16 * q - 10 * q^3 + 8 * q^4 - 33 * q^6 + 6 * q^7 - 28 * q^9	$ 16 q - 10 q^{3} + 8 q^{4} - 33 q^{6} + 6 q^{7} - 28 q^{9} - 12 q^{10} + 106 q^{12} - 42 q^{13} + 82 q^{15} - 88 q^{16} - 43 q^{18} - 134 q^{19} - 12 q^{21} + 78 q^{22} + 41 q^{24} + 134 q^{25} + 80 q^{27} + 264 q^{28} - 120 q^{30} + 124 q^{31} - 79 q^{33} - 132 q^{34} - 219 q^{36} + 90 q^{37} - 174 q^{39} - 284 q^{40} - 102 q^{42} - 156 q^{43} - 72 q^{45} - 22 q^{46} + 30 q^{48} - 30 q^{49} + 111 q^{51} + 326 q^{52} + 1046 q^{54} - 172 q^{55} + 281 q^{57} - 116 q^{58} + 54 q^{60} - 126 q^{61} - 138 q^{63} + 236 q^{64} - 236 q^{66} + 368 q^{67} + 198 q^{69} - 322 q^{70} - 562 q^{72} + 24 q^{73} - 21 q^{75} - 900 q^{76} - 492 q^{78} - 314 q^{79} - 388 q^{81} + 270 q^{84} + 318 q^{85} + 132 q^{87} + 1064 q^{88} + 176 q^{90} + 374 q^{91} - 10 q^{93} + 990 q^{94} - 332 q^{96} + 72 q^{97} - 530 q^{99}+O(q^{100}) $ 16 * q - 10 * q^3 + 8 * q^4 - 33 * q^6 + 6 * q^7 - 28 * q^9 - 12 * q^10 + 106 * q^12 - 42 * q^13 + 82 * q^15 - 88 * q^16 - 43 * q^18 - 134 * q^19 - 12 * q^21 + 78 * q^22 + 41 * q^24 + 134 * q^25 + 80 * q^27 + 264 * q^28 - 120 * q^30 + 124 * q^31 - 79 * q^33 - 132 * q^34 - 219 * q^36 + 90 * q^37 - 174 * q^39 - 284 * q^40 - 102 * q^42 - 156 * q^43 - 72 * q^45 - 22 * q^46 + 30 * q^48 - 30 * q^49 + 111 * q^51 + 326 * q^52 + 1046 * q^54 - 172 * q^55 + 281 * q^57 - 116 * q^58 + 54 * q^60 - 126 * q^61 - 138 * q^63 + 236 * q^64 - 236 * q^66 + 368 * q^67 + 198 * q^69 - 322 * q^70 - 562 * q^72 + 24 * q^73 - 21 * q^75 - 900 * q^76 - 492 * q^78 - 314 * q^79 - 388 * q^81 + 270 * q^84 + 318 * q^85 + 132 * q^87 + 1064 * q^88 + 176 * q^90 + 374 * q^91 - 10 * q^93 + 990 * q^94 - 332 * q^96 + 72 * q^97 - 530 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.90610	+	0.619331i	−0.953052	+	0.309666i	−0.743955	−	0.668229i	$-0.767052\pi$
$2$	−1.90610	+	0.619331i	−0.953052	+	0.309666i	−0.209097	+	0.977895i	$0.567052\pi$
$3$	−2.89787	−	0.776113i	−0.965957	−	0.258704i
$3$	−2.89787	−	0.776113i	−0.965957	−	0.258704i
$4$	0.0135968	−	0.00987866i	0.00339920	−	0.00246966i
$5$	−5.21596	−	1.69477i	−1.04319	−	0.338953i	−0.263198	−	0.964742i	$-0.584777\pi$
$5$	−5.21596	−	1.69477i	−1.04319	−	0.338953i	−0.779993	+	0.625788i	$0.784777\pi$
$6$	6.00431	−	0.315387i	1.00072	−	0.0525645i
$7$	−4.52308	+	3.28621i	−0.646155	+	0.469459i	−0.861959	−	0.506978i	$-0.830763\pi$
$7$	−4.52308	+	3.28621i	−0.646155	+	0.469459i	0.215804	+	0.976437i	$0.430763\pi$
$8$	4.69235	−	6.45847i	0.586544	−	0.807308i
$9$	7.79530	+	4.49815i	0.866144	+	0.499794i
$10$	10.9918			1.09918
$11$	−2.23693	+	10.7702i	−0.203357	+	0.979105i
$11$	−2.23693	+	10.7702i	−0.203357	+	0.979105i
$12$	−0.0470687	+	0.0180744i	−0.00392239	+	0.00150620i
$13$	−3.00265	−	9.24122i	−0.230973	−	0.710863i	−0.997630	−	0.0688058i	$-0.978081\pi$
$13$	−3.00265	−	9.24122i	−0.230973	−	0.710863i	0.766657	−	0.642057i	$-0.221919\pi$
$14$	6.58622	−	9.06515i	0.470444	−	0.647511i
$15$	13.7998	+	8.95939i	0.919989	+	0.597293i
$16$	−4.96496	+	15.2806i	−0.310310	+	0.955036i
$17$	−16.9969	−	5.52262i	−0.999817	−	0.324860i	−0.237024	−	0.971504i	$-0.576172\pi$
$17$	−16.9969	−	5.52262i	−0.999817	−	0.324860i	−0.762792	+	0.646643i	$0.776172\pi$
$18$	−17.6445	−	3.74608i	−0.980250	−	0.208115i
$19$	−15.0954	−	10.9674i	−0.794493	−	0.577233i	0.114801	−	0.993389i	$-0.463377\pi$
$19$	−15.0954	−	10.9674i	−0.794493	−	0.577233i	−0.909293	+	0.416156i	$0.863377\pi$
$20$	−0.0876624	+	0.0284832i	−0.00438312	+	0.00142416i
$21$	15.6578	−	6.01259i	0.745609	−	0.286314i
$22$	−2.40646	−	21.9144i	−0.109385	−	0.996111i
$23$			12.3649i			0.537603i	0.963196	+	0.268801i	$0.0866275\pi$
$23$			12.3649i			0.537603i	−0.963196	+	0.268801i	$0.913372\pi$
$24$	−18.6103	+	15.0740i	−0.775430	+	0.628083i
$25$	4.10855	+	2.98503i	0.164342	+	0.119401i
$26$	11.4467	+	15.7551i	0.440260	+	0.605965i
$27$	−19.0987	−	19.0851i	−0.707358	−	0.706855i
$28$	−0.0290361	+	0.0893640i	−0.00103700	+	0.00319157i
$29$	1.45613	+	2.00420i	0.0502115	+	0.0691102i	0.833384	−	0.552694i	$-0.186400\pi$
$29$	1.45613	+	2.00420i	0.0502115	+	0.0691102i	−0.783173	+	0.621804i	$0.786400\pi$
$30$	−31.8528	−	8.53087i	−1.06176	−	0.284362i
$31$	15.2132	+	46.8213i	0.490747	+	1.51037i	0.823481	+	0.567344i	$0.192029\pi$
$31$	15.2132	+	46.8213i	0.490747	+	1.51037i	−0.332733	+	0.943021i	$0.607971\pi$
$32$		−	0.268903i		−	0.00840323i
$33$	14.8412	−	29.4744i	0.449733	−	0.893163i
$34$	35.8182			1.05348
$35$	29.1616	−	9.47517i	0.833188	−	0.270719i
$36$	0.150427	−	0.0158466i	0.00417852	−	0.000440183i
$37$	31.8192	−	23.1180i	0.859979	−	0.624811i	−0.0679003	−	0.997692i	$-0.521630\pi$
$37$	31.8192	−	23.1180i	0.859979	−	0.624811i	0.927879	+	0.372881i	$0.121630\pi$
$38$	35.5658	+	11.5560i	0.935942	+	0.304106i
$39$	1.52907	+	29.1102i	0.0392068	+	0.746417i
$40$	−35.4207	+	25.7346i	−0.885518	+	0.643366i
$41$	33.2237	−	45.7285i	0.810335	−	1.11533i	−0.180937	−	0.983495i	$-0.557913\pi$
$41$	33.2237	−	45.7285i	0.810335	−	1.11533i	0.991272	−	0.131835i	$-0.0420870\pi$
$42$	−26.1216	+	21.1580i	−0.621943	+	0.503761i
$43$	−43.9060			−1.02107			−0.510534	−	0.859857i	$-0.670552\pi$
$43$	−43.9060			−1.02107			−0.510534	+	0.859857i	$0.670552\pi$
$44$	0.0759795	+	0.168537i	0.00172681	+	0.00383040i
$45$	−33.0366	−	36.6734i	−0.734147	−	0.814964i
$46$	−7.65794	−	23.5687i	−0.166477	−	0.512364i
$47$	−33.9646	+	46.7482i	−0.722651	+	0.994643i	0.276781	+	0.960933i	$0.410732\pi$
$47$	−33.9646	+	46.7482i	−0.722651	+	0.994643i	−0.999432	+	0.0337102i	$0.989268\pi$
$48$	26.2473	−	40.4277i	0.546818	−	0.842244i
$49$	−5.48274	+	16.8741i	−0.111893	+	0.344370i
$50$	−9.68004	−	3.14524i	−0.193601	−	0.0629047i
$51$	44.9686	+	29.1954i	0.881737	+	0.572458i
$52$	−0.132117	−	0.0959889i	−0.00254072	−	0.00184594i
$53$	−41.0056	+	13.3235i	−0.773690	+	0.251387i	−0.669144	−	0.743133i	$-0.733339\pi$
$53$	−41.0056	+	13.3235i	−0.773690	+	0.251387i	−0.104546	+	0.994520i	$0.533339\pi$
$54$	48.2241	+	24.5498i	0.893038	+	0.454625i
$55$	29.9206	−	52.3856i	0.544012	−	0.952465i
$56$			44.6323i			0.797005i
$57$	35.2324	+	43.4979i	0.618113	+	0.763121i
$58$	−4.01681	−	2.91838i	−0.0692553	−	0.0503169i
$59$	−52.9190	−	72.8367i	−0.896932	−	1.23452i	−0.971436	−	0.237300i	$-0.923738\pi$
$59$	−52.9190	−	72.8367i	−0.896932	−	1.23452i	0.0745046	−	0.997221i	$-0.476262\pi$
$60$	0.276140	−	0.0145048i	0.00460234	−	0.000241746i
$61$	−9.53920	+	29.3587i	−0.156380	+	0.481289i	−0.998298	−	0.0583165i	$-0.981427\pi$
$61$	−9.53920	+	29.3587i	−0.156380	+	0.481289i	0.841918	+	0.539606i	$0.181427\pi$
$62$	−57.9958	−	79.8244i	−0.935416	−	1.28749i
$63$	−50.0407	+	5.27149i	−0.794296	+	0.0836745i
$64$	−19.6933	−	60.6097i	−0.307708	−	0.947027i
$65$			53.2906i			0.819855i
$66$	−10.0345	+	65.3729i	−0.152037	+	0.990498i
$67$	34.0775			0.508620			0.254310	−	0.967123i	$-0.418152\pi$
$67$	34.0775			0.508620			0.254310	+	0.967123i	$0.418152\pi$
$68$	−0.285659	+	0.0928164i	−0.00420087	+	0.00136495i
$69$	9.59653	−	35.8318i	0.139080	−	0.519301i
$70$	−49.7168	+	36.1213i	−0.710240	+	0.516019i
$71$	35.7561	+	11.6179i	0.503607	+	0.163632i	0.549793	−	0.835301i	$-0.314707\pi$
$71$	35.7561	+	11.6179i	0.503607	+	0.163632i	−0.0461856	+	0.998933i	$0.514707\pi$
$72$	65.6294	−	29.2388i	0.911520	−	0.406094i
$73$	9.81022	−	7.12754i	0.134387	−	0.0976375i	−0.518561	−	0.855041i	$-0.673532\pi$
$73$	9.81022	−	7.12754i	0.134387	−	0.0976375i	0.652948	+	0.757403i	$0.273532\pi$
$74$	−46.3331	+	63.7720i	−0.626123	+	0.861784i
$75$	−9.58931	−	11.8389i	−0.127857	−	0.157852i
$76$	−0.313592			−0.00412621
$77$	−25.2752	−	56.0653i	−0.328249	−	0.728121i
$78$	−20.9434	−	54.5402i	−0.268506	−	0.699233i
$79$	−19.5128	−	60.0542i	−0.246997	−	0.760180i	−0.995302	−	0.0968240i	$-0.969132\pi$
$79$	−19.5128	−	60.0542i	−0.246997	−	0.760180i	0.748304	−	0.663356i	$-0.230868\pi$
$80$	51.7940	−	71.2884i	0.647425	−	0.891104i
$81$	40.5333	+	70.1288i	0.500411	+	0.865788i
$82$	−35.0068	+	107.740i	−0.426912	+	1.31390i
$83$	9.22665	+	2.99792i	0.111164	+	0.0361195i	0.364071	−	0.931371i	$-0.381387\pi$
$83$	9.22665	+	2.99792i	0.111164	+	0.0361195i	−0.252907	+	0.967491i	$0.581387\pi$
$84$	0.153499	−	0.236430i	0.00182737	−	0.00281464i
$85$	79.2955	+	57.6115i	0.932888	+	0.677783i
$86$	83.6893	−	27.1923i	0.973132	−	0.316190i
$87$	−2.66420	−	6.93803i	−0.0306230	−	0.0797474i
$88$	59.0622	+	64.9845i	0.671161	+	0.738460i
$89$			34.1289i			0.383471i	0.981447	+	0.191735i	$0.0614115\pi$
$89$			34.1289i			0.383471i	−0.981447	+	0.191735i	$0.938588\pi$
$90$	85.6842	+	49.4427i	0.952047	+	0.549363i
$91$	43.9499	+	31.9315i	0.482966	+	0.350895i
$92$	0.122148	+	0.168123i	0.00132770	+	0.00182742i
$93$	−7.74713	−	147.489i	−0.0833025	−	1.58591i
$94$	35.7874	−	110.142i	0.380717	−	1.17173i
$95$	60.1495	+	82.7887i	0.633153	+	0.871460i
$96$	−0.208700	+	0.779247i	−0.00217395	+	0.00811716i
$97$	−11.6879	−	35.9715i	−0.120493	−	0.370841i	0.872560	−	0.488507i	$-0.162458\pi$
$97$	−11.6879	−	35.9715i	−0.120493	−	0.370841i	−0.993053	+	0.117667i	$0.962458\pi$
$98$		−	35.5595i		−	0.362852i
$99$	−65.8833	+	73.8945i	−0.665488	+	0.746409i
$100$	0.0853512			0.000853512
$101$	−44.6091	+	14.4944i	−0.441674	+	0.143509i	−0.521408	−	0.853308i	$-0.674593\pi$
$101$	−44.6091	+	14.4944i	−0.441674	+	0.143509i	0.0797339	+	0.996816i	$0.474593\pi$
$102$	−103.796	−	27.7990i	−1.01761	−	0.272539i
$103$	−84.7824	+	61.5980i	−0.823130	+	0.598039i	−0.917607	−	0.397488i	$-0.869882\pi$
$103$	−84.7824	+	61.5980i	−0.823130	+	0.598039i	0.0944773	+	0.995527i	$0.469882\pi$
$104$	−73.7736	−	23.9705i	−0.709362	−	0.230486i
$105$	−91.8603	+	4.82512i	−0.874860	+	0.0459535i
$106$	69.9092	−	50.7920i	0.659521	−	0.479170i
$107$	27.4085	−	37.7246i	0.256154	−	0.352566i	−0.661500	−	0.749945i	$-0.730080\pi$
$107$	27.4085	−	37.7246i	0.256154	−	0.352566i	0.917655	+	0.397378i	$0.130080\pi$
$108$	−0.448216	−	0.0708269i	−0.00415015	−	0.000655805i
$109$	−168.413			−1.54507			−0.772537	−	0.634969i	$-0.781013\pi$
$109$	−168.413			−1.54507			−0.772537	+	0.634969i	$0.781013\pi$
$110$	−24.5879	+	118.383i	−0.223526	+	1.07621i
$111$	−110.150	+	42.2977i	−0.992344	+	0.381060i
$112$	−27.7583	−	85.4312i	−0.247842	−	0.762779i
$113$	−27.2263	+	37.4738i	−0.240941	+	0.331627i	−0.912313	−	0.409494i	$-0.865705\pi$
$113$	−27.2263	+	37.4738i	−0.240941	+	0.331627i	0.671372	+	0.741121i	$0.265705\pi$
$114$	−94.0963	−	61.0910i	−0.825406	−	0.535886i
$115$	20.9556	−	64.4946i	0.182222	−	0.560822i
$116$	0.0395975	+	0.0128660i	0.000341358	+	0.000110914i
$117$	18.1618	−	85.5444i	0.155229	−	0.731149i
$118$	145.979	+	106.060i	1.23711	+	0.898814i
$119$	95.0269	−	30.8761i	0.798545	−	0.259463i
$120$	122.618	−	47.0852i	1.02181	−	0.392376i
$121$	−110.992	−	48.1842i	−0.917292	−	0.398216i
$122$		−	61.8686i		−	0.507120i
$123$	−131.769	+	106.730i	−1.07129	+	0.867723i
$124$	0.669382	+	0.486335i	0.00539824	+	0.00392205i
$125$	64.2199	+	88.3911i	0.513759	+	0.707129i
$126$	92.1180	−	41.0398i	0.731095	−	0.325712i
$127$	−21.1024	+	64.9465i	−0.166161	+	0.511390i	−0.999120	−	0.0419443i	$-0.986645\pi$
$127$	−21.1024	+	64.9465i	−0.166161	+	0.511390i	0.832959	+	0.553334i	$0.186645\pi$
$128$	75.7072	+	104.202i	0.591462	+	0.814078i
$129$	127.234	+	34.0760i	0.986308	+	0.264155i
$130$	−33.0045	−	101.577i	−0.253881	−	0.781365i
$131$		−	162.272i		−	1.23872i	−0.785109	−	0.619358i	$-0.787393\pi$
$131$		−	162.272i		−	1.23872i	0.785109	−	0.619358i	$-0.212607\pi$
$132$	−0.0893745	−	0.547368i	−0.000677079	−	0.00414673i
$133$	104.319			0.784353
$134$	−64.9553	+	21.1053i	−0.484741	+	0.157502i
$135$	67.2731	+	131.915i	0.498319	+	0.977147i
$136$	−115.423	+	83.8598i	−0.848699	+	0.616616i
$137$	50.2796	+	16.3368i	0.367004	+	0.119247i	0.486713	−	0.873562i	$-0.338196\pi$
$137$	50.2796	+	16.3368i	0.367004	+	0.119247i	−0.119708	+	0.992809i	$0.538196\pi$
$138$	3.89972	+	74.2425i	0.0282588	+	0.537989i
$139$	70.0088	−	50.8644i	0.503661	−	0.365931i	−0.306753	−	0.951789i	$-0.599242\pi$
$139$	70.0088	−	50.8644i	0.503661	−	0.365931i	0.810414	+	0.585858i	$0.199242\pi$
$140$	0.302902	−	0.416909i	0.00216359	−	0.00297792i
$141$	134.707	−	109.110i	0.955368	−	0.773829i
$142$	−75.3502			−0.530635
$143$	106.246	−	11.6671i	0.742979	−	0.0815879i
$144$	−107.438	+	96.7835i	−0.746095	+	0.672107i
$145$	−4.19849	−	12.9216i	−0.0289551	−	0.0891146i
$146$	−14.2850	+	19.6616i	−0.0978424	+	0.134669i
$147$	28.9845	−	44.6438i	0.197173	−	0.303699i
$148$	0.204265	−	0.628662i	0.00138017	−	0.00424772i
$149$	61.2955	+	19.9161i	0.411379	+	0.133665i	0.507393	−	0.861715i	$-0.330609\pi$
$149$	61.2955	+	19.9161i	0.411379	+	0.133665i	−0.0960136	+	0.995380i	$0.530609\pi$
$150$	25.6104	+	16.6273i	0.170736	+	0.110849i
$151$	−36.1103	−	26.2357i	−0.239141	−	0.173746i	0.461760	−	0.887005i	$-0.347218\pi$
$151$	−36.1103	−	26.2357i	−0.239141	−	0.173746i	−0.700901	+	0.713259i	$0.747218\pi$
$152$	−141.666	+	46.0299i	−0.932010	+	0.302828i
$153$	−107.654	−	119.505i	−0.703622	−	0.781079i
$154$	82.9002	+	91.2127i	0.538313	+	0.592290i
$155$		−	270.001i		−	1.74194i
$156$	0.308361	+	0.380701i	0.00197667	+	0.00244039i
$157$	114.125	+	82.9166i	0.726910	+	0.528131i	0.888584	−	0.458713i	$-0.151689\pi$
$157$	114.125	+	82.9166i	0.726910	+	0.528131i	−0.161675	+	0.986844i	$0.551689\pi$
$158$	74.3869	+	102.385i	0.470803	+	0.648005i
$159$	129.169	−	6.78485i	0.812386	−	0.0426720i
$160$	−0.455729	+	1.40259i	−0.00284830	+	0.00876618i
$161$	−40.6336	−	55.9273i	−0.252382	−	0.347375i
$162$	−120.694	−	108.569i	−0.745023	−	0.670181i
$163$	37.3801	+	115.044i	0.229326	+	0.705793i	0.997824	+	0.0659401i	$0.0210046\pi$
$163$	37.3801	+	115.044i	0.229326	+	0.705793i	−0.768498	+	0.639853i	$0.778995\pi$
$164$		−	0.949967i		−	0.00579248i
$165$	−127.363	+	128.585i	−0.771898	+	0.779301i
$166$	−19.4437			−0.117130
$167$	102.174	−	33.1982i	0.611819	−	0.198792i	0.0133141	−	0.999911i	$-0.495762\pi$
$167$	102.174	−	33.1982i	0.611819	−	0.198792i	0.598504	+	0.801119i	$0.295762\pi$
$168$	34.6397	−	129.338i	0.206189	−	0.769872i
$169$	60.3397	−	43.8393i	0.357039	−	0.259404i
$170$	−186.826	−	60.7035i	−1.09898	−	0.357079i
$171$	−68.3397	−	153.396i	−0.399647	−	0.897050i
$172$	−0.596981	+	0.433732i	−0.00347082	+	0.00252170i
$173$	−193.272	+	266.016i	−1.11718	+	1.53767i	−0.306787	+	0.951778i	$0.599254\pi$
$173$	−193.272	+	266.016i	−1.11718	+	1.53767i	−0.810393	+	0.585887i	$0.800746\pi$
$174$	9.37519	+	11.5746i	0.0538804	+	0.0665206i
$175$	−28.3928			−0.162244
$176$	−153.468	−	87.6549i	−0.871976	−	0.498039i
$177$	96.8227	+	252.142i	0.547021	+	1.42453i
$178$	−21.1371	−	65.0533i	−0.118748	−	0.365468i
$179$	28.3892	−	39.0743i	0.158599	−	0.218292i	−0.722321	−	0.691558i	$-0.756925\pi$
$179$	28.3892	−	39.0743i	0.158599	−	0.218292i	0.880920	+	0.473265i	$0.156925\pi$
$180$	−0.811476	−	0.172283i	−0.00450820	−	0.000957129i
$181$	0.0205705	−	0.0633093i	0.000113649	−	0.000349775i	−0.951000	−	0.309192i	$-0.899941\pi$
$181$	0.0205705	−	0.0633093i	0.000113649	−	0.000349775i	0.951113	+	0.308842i	$0.0999415\pi$
$182$	−103.549	−	33.6452i	−0.568952	−	0.184864i
$183$	50.4290	−	77.6740i	0.275568	−	0.424448i
$184$	79.8581	+	58.0203i	0.434011	+	0.315328i
$185$	−205.147	+	66.6564i	−1.10890	+	0.360305i
$186$	106.111	+	276.332i	0.570492	+	1.48566i
$187$	97.5003	−	170.705i	0.521392	−	0.912863i
$188$			0.971151i			0.00516570i
$189$	149.103	+	23.5611i	0.788903	+	0.124662i
$190$	−165.925	−	120.552i	−0.873289	−	0.634482i
$191$	−116.037	−	159.711i	−0.607523	−	0.836183i	0.388848	−	0.921302i	$-0.372873\pi$
$191$	−116.037	−	159.711i	−0.607523	−	0.836183i	−0.996371	+	0.0851188i	$0.972873\pi$
$192$	10.0286	+	190.923i	0.0522322	+	0.994392i
$193$	0.470837	−	1.44909i	0.00243957	−	0.00750823i	−0.949829	−	0.312769i	$-0.898744\pi$
$193$	0.470837	−	1.44909i	0.00243957	−	0.00750823i	0.952269	+	0.305260i	$0.0987435\pi$
$194$	44.5566	+	61.3269i	0.229673	+	0.316118i
$195$	41.3595	−	154.429i	0.212100	−	0.791945i
$196$	0.0921460	+	0.283596i	0.000470133	+	0.00144692i
$197$			215.460i			1.09370i	0.837229	+	0.546852i	$0.184174\pi$
$197$			215.460i			1.09370i	−0.837229	+	0.546852i	$0.815826\pi$
$198$	79.8153	−	181.654i	0.403108	−	0.917445i
$199$	−106.663			−0.535993			−0.267997	−	0.963420i	$-0.586362\pi$
$199$	−106.663			−0.535993			−0.267997	+	0.963420i	$0.586362\pi$
$200$	38.5575	−	12.5281i	0.192787	−	0.0626404i
$201$	−98.7522	−	26.4480i	−0.491305	−	0.131582i
$202$	76.0527	−	55.2555i	0.376499	−	0.273542i
$203$	−13.1724	−	4.27999i	−0.0648889	−	0.0210837i
$204$	0.899840	−	0.0472657i	0.00441098	−	0.000231694i
$205$	−250.793	+	182.212i	−1.22338	+	0.888837i
$206$	123.455	−	169.921i	0.599294	−	0.824858i
$207$	−55.6190	+	96.3878i	−0.268691	+	0.465641i
$208$	156.119			0.750573
$209$	151.888	−	138.046i	0.726737	−	0.660507i
$210$	172.107	−	66.0891i	0.819557	−	0.314710i
$211$	66.3847	+	204.311i	0.314619	+	0.968299i	0.975911	+	0.218170i	$0.0700086\pi$
$211$	66.3847	+	204.311i	0.314619	+	0.968299i	−0.661291	+	0.750129i	$0.729991\pi$
$212$	−0.425926	+	0.586237i	−0.00200909	+	0.00276527i
$213$	−94.5998	−	61.4179i	−0.444131	−	0.288347i
$214$	−28.8795	+	88.8820i	−0.134951	+	0.415336i
$215$	229.012	+	74.4104i	1.06517	+	0.346095i
$216$	−212.878	+	33.7943i	−0.985547	+	0.156455i
$217$	−222.675	−	161.783i	−1.02615	−	0.745544i
$218$	321.013	−	104.303i	1.47254	−	0.478456i
$219$	−33.9605	+	13.0408i	−0.155071	+	0.0595472i
$220$	−0.110674	−	1.00785i	−0.000503064	−	0.00458114i
$221$			173.654i			0.785767i
$222$	183.761	−	148.843i	0.827754	−	0.670465i
$223$	−36.2187	−	26.3144i	−0.162416	−	0.118002i	0.503609	−	0.863932i	$-0.332005\pi$
$223$	−36.2187	−	26.3144i	−0.162416	−	0.118002i	−0.666024	+	0.745930i	$0.732005\pi$
$224$	0.883674	+	1.21627i	0.00394497	+	0.00542979i
$225$	18.6002	+	41.7501i	0.0826676	+	0.185556i
$226$	28.6875	−	88.2911i	0.126936	−	0.390669i
$227$	−131.960	−	181.627i	−0.581322	−	0.800121i	0.412518	−	0.910950i	$-0.364649\pi$
$227$	−131.960	−	181.627i	−0.581322	−	0.800121i	−0.993840	+	0.110829i	$0.964649\pi$
$228$	0.908749	+	0.243383i	0.00398574	+	0.00106747i
$229$	−32.1689	−	99.0057i	−0.140476	−	0.432339i	0.855926	−	0.517099i	$-0.172988\pi$
$229$	−32.1689	−	99.0057i	−0.140476	−	0.432339i	−0.996401	+	0.0847591i	$0.972988\pi$
$230$			135.912i			0.590921i
$231$	29.7311	+	182.086i	0.128706	+	0.788253i
$232$	19.7767			0.0852446
$233$	−58.5176	+	19.0135i	−0.251148	+	0.0816030i	−0.431886	−	0.901928i	$-0.642152\pi$
$233$	−58.5176	+	19.0135i	−0.251148	+	0.0816030i	0.180737	+	0.983531i	$0.442152\pi$
$234$	18.3620	+	174.305i	0.0784701	+	0.744892i
$235$	256.385	−	186.275i	1.09100	−	0.792658i
$236$	−1.43906	−	0.467578i	−0.00609770	−	0.00198126i
$237$	9.93666	+	189.173i	0.0419269	+	0.798200i
$238$	−162.009	+	117.706i	−0.680709	+	0.494564i
$239$	−87.7330	+	120.754i	−0.367084	+	0.505247i	−0.952105	−	0.305770i	$-0.901086\pi$
$239$	−87.7330	+	120.754i	−0.367084	+	0.505247i	0.585022	+	0.811018i	$0.301086\pi$
$240$	−205.420	+	166.386i	−0.855917	+	0.693276i
$241$	358.881			1.48913			0.744567	−	0.667548i	$-0.232656\pi$
$241$	358.881			1.48913			0.744567	+	0.667548i	$0.232656\pi$
$242$	241.405	+	23.1031i	0.997541	+	0.0954674i
$243$	−63.0323	−	234.683i	−0.259392	−	0.965772i
$244$	0.160321	+	0.493418i	0.000657055	+	0.00202221i
$245$	57.1954	−	78.7227i	0.233451	−	0.321317i
$246$	185.063	−	285.047i	0.752290	−	1.15873i
$247$	−56.0262	+	172.431i	−0.226827	+	0.698101i
$248$	373.780	+	121.448i	1.50718	+	0.489711i
$249$	−24.4109	−	15.8485i	−0.0980357	−	0.0636486i
$250$	−177.153	−	128.709i	−0.708613	−	0.514837i
$251$	−339.548	+	110.326i	−1.35278	+	0.439545i	−0.893627	−	0.448811i	$-0.851848\pi$
$251$	−339.548	+	110.326i	−1.35278	+	0.439545i	−0.459155	+	0.888356i	$0.651848\pi$
$252$	−0.628318	+	0.566010i	−0.00249332	+	0.00224607i
$253$	−133.171	−	27.6593i	−0.526369	−	0.109325i
$254$		−	136.864i		−	0.538836i
$255$	−185.075	−	228.493i	−0.725784	−	0.896051i
$256$	−2.61054	−	1.89667i	−0.0101974	−	0.00740886i
$257$	38.8488	+	53.4707i	0.151162	+	0.208057i	0.877882	−	0.478877i	$-0.158956\pi$
$257$	38.8488	+	53.4707i	0.151162	+	0.208057i	−0.726720	+	0.686934i	$0.758956\pi$
$258$	−263.625	+	13.8474i	−1.02180	+	0.0536720i
$259$	−67.9503	+	209.130i	−0.262356	+	0.807450i
$260$	0.526440	+	0.724582i	0.00202477	+	0.00278685i
$261$	2.33582	+	22.1732i	0.00894950	+	0.0849549i
$262$	100.500	+	309.307i	0.383587	+	1.18056i
$263$			85.4194i			0.324789i	0.986726	+	0.162394i	$0.0519216\pi$
$263$			85.4194i			0.324789i	−0.986726	+	0.162394i	$0.948078\pi$
$264$	−120.719	−	234.156i	−0.457270	−	0.886953i
$265$	236.464			0.892315
$266$	−198.843	+	64.6079i	−0.747529	+	0.242887i
$267$	26.4879	−	98.9011i	0.0992056	−	0.370416i
$268$	0.463345	−	0.336640i	0.00172890	−	0.00125612i
$269$	153.866	+	49.9940i	0.571991	+	0.185851i	0.580710	−	0.814111i	$-0.302775\pi$
$269$	153.866	+	49.9940i	0.571991	+	0.185851i	−0.00871848	+	0.999962i	$0.502775\pi$
$270$	−209.929	−	209.779i	−0.777513	−	0.776960i
$271$	210.339	−	152.820i	0.776160	−	0.563913i	−0.127664	−	0.991817i	$-0.540748\pi$
$271$	210.339	−	152.820i	0.776160	−	0.563913i	0.903824	+	0.427904i	$0.140748\pi$
$272$	168.778	−	232.303i	0.620506	−	0.854053i
$273$	−102.579	−	126.643i	−0.375746	−	0.463895i
$274$	−105.956			−0.386701
$275$	−41.3398	+	37.5723i	−0.150327	+	0.136627i
$276$	−0.223487	−	0.581998i	−0.000809737	−	0.00210869i
$277$	−26.8202	−	82.5441i	−0.0968239	−	0.297993i	0.890901	−	0.454198i	$-0.150074\pi$
$277$	−26.8202	−	82.5441i	−0.0968239	−	0.297993i	−0.987725	+	0.156205i	$0.950074\pi$
$278$	−101.942	+	140.312i	−0.366699	+	0.504718i
$279$	−92.0182	+	433.417i	−0.329814	+	1.55347i
$280$	75.6413	−	232.800i	0.270147	−	0.831429i
$281$	−460.991	−	149.785i	−1.64054	−	0.533043i	−0.663880	−	0.747839i	$-0.731091\pi$
$281$	−460.991	−	149.785i	−1.64054	−	0.533043i	−0.976659	+	0.214796i	$0.931091\pi$
$282$	−189.190	+	291.403i	−0.670887	+	1.03334i
$283$	−349.554	−	253.966i	−1.23517	−	0.897406i	−0.237906	−	0.971288i	$-0.576461\pi$
$283$	−349.554	−	253.966i	−1.23517	−	0.897406i	−0.997267	+	0.0738826i	$0.976461\pi$
$284$	0.600938	−	0.195257i	0.00211598	−	0.000687523i
$285$	−110.052	−	286.594i	−0.386148	−	1.00559i
$286$	−195.290	+	88.0401i	−0.682833	+	0.307833i
$287$			316.014i			1.10109i
$288$	1.20957	−	2.09618i	0.00419989	−	0.00727841i
$289$	24.5889	+	17.8649i	0.0850826	+	0.0618161i
$290$	16.0055	+	22.0297i	0.0551914	+	0.0759645i
$291$	5.95191	+	113.312i	0.0204533	+	0.389388i
$292$	0.0629771	−	0.193823i	0.000215675	−	0.000663779i
$293$	−3.25020	−	4.47352i	−0.0110928	−	0.0152680i	0.803435	−	0.595393i	$-0.203004\pi$
$293$	−3.25020	−	4.47352i	−0.0110928	−	0.0152680i	−0.814527	+	0.580125i	$0.803004\pi$
$294$	−27.5982	+	103.047i	−0.0938714	+	0.350499i
$295$	152.582	+	469.599i	0.517227	+	1.59186i
$296$		−	313.981i		−	1.06075i
$297$	248.272	−	163.004i	0.835932	−	0.548834i
$298$	−129.170			−0.433458
$299$	114.266	−	37.1274i	0.382162	−	0.124172i
$300$	−0.247337	−	0.0662422i	−0.000824456	−	0.000220807i
$301$	198.590	−	144.284i	0.659769	−	0.479350i
$302$	85.0786	+	27.6437i	0.281717	+	0.0915354i
$303$	140.520	−	7.38108i	0.463764	−	0.0243600i
$304$	242.536	−	176.213i	0.797817	−	0.579648i
$305$	99.5122	−	136.967i	0.326269	−	0.449071i
$306$	279.213	+	161.116i	0.912462	+	0.526521i
$307$	219.257			0.714191			0.357095	−	0.934068i	$-0.383767\pi$
$307$	219.257			0.714191			0.357095	+	0.934068i	$0.383767\pi$
$308$	−0.897512	−	0.512625i	−0.00291400	−	0.00166437i
$309$	293.495	−	112.702i	0.949823	−	0.364732i
$310$	167.220	+	514.650i	0.539419	+	1.66016i
$311$	83.5538	−	115.002i	0.268662	−	0.369781i	−0.653276	−	0.757120i	$-0.726606\pi$
$311$	83.5538	−	115.002i	0.268662	−	0.369781i	0.921937	+	0.387339i	$0.126606\pi$
$312$	195.183	+	126.720i	0.625585	+	0.406154i
$313$	29.1359	−	89.6710i	0.0930859	−	0.286489i	−0.893664	−	0.448736i	$-0.851874\pi$
$313$	29.1359	−	89.6710i	0.0930859	−	0.286489i	0.986750	+	0.162247i	$0.0518743\pi$
$314$	−268.887	−	87.3666i	−0.856327	−	0.278238i
$315$	269.944	+	57.3114i	0.856965	+	0.181941i
$316$	−0.858566	−	0.623785i	−0.00271698	−	0.00197400i
$317$	476.684	−	154.884i	1.50373	−	0.488593i	0.562630	−	0.826709i	$-0.309790\pi$
$317$	476.684	−	154.884i	1.50373	−	0.488593i	0.941104	+	0.338116i	$0.109790\pi$
$318$	−242.008	+	92.9312i	−0.761032	+	0.292237i
$319$	−24.8428	+	11.1995i	−0.0778770	+	0.0351083i
$320$			349.513i			1.09223i
$321$	−108.705	+	88.0489i	−0.338645	+	0.274295i
$322$	112.089	+	81.4377i	0.348104	+	0.252912i
$323$	196.005	+	269.778i	0.606827	+	0.835226i
$324$	1.24390	+	0.553114i	0.00383920	+	0.00170714i
$325$	15.2488	−	46.9310i	0.0469194	−	0.144403i
$326$	−142.501	−	196.136i	−0.437119	−	0.601643i
$327$	488.039	+	130.708i	1.49247	+	0.399718i
$328$	−139.439	−	429.149i	−0.425118	−	1.30838i
$329$		−	323.061i		−	0.981948i
$330$	163.131	−	323.976i	0.494337	−	0.981745i
$331$	−653.489			−1.97429			−0.987143	−	0.159839i	$-0.948903\pi$
$331$	−653.489			−1.97429			−0.987143	+	0.159839i	$0.948903\pi$
$332$	0.155068	−	0.0503847i	0.000467073	−	0.000151761i
$333$	352.029	−	37.0841i	1.05714	−	0.111364i
$334$	−174.193	+	126.559i	−0.521536	+	0.378918i
$335$	−177.747	−	57.7535i	−0.530588	−	0.172398i
$336$	14.1356	+	269.112i	0.0420702	+	0.800929i
$337$	−533.438	+	387.565i	−1.58290	+	1.15005i	−0.669629	+	0.742696i	$0.733547\pi$
$337$	−533.438	+	387.565i	−1.58290	+	1.15005i	−0.913272	+	0.407349i	$0.866453\pi$
$338$	−87.8627	+	120.933i	−0.259949	+	0.357789i
$339$	107.982	−	87.4635i	0.318532	−	0.258004i
$340$	1.64729			0.00484497
$341$	−538.303	+	59.1120i	−1.57860	+	0.173349i
$342$	225.265	+	250.063i	0.658670	+	0.731179i
$343$	−115.309	−	354.884i	−0.336177	−	1.03465i
$344$	−206.022	+	283.565i	−0.598902	+	0.824317i
$345$	−110.782	+	170.633i	−0.321106	+	0.494588i
$346$	203.645	−	626.754i	0.588569	−	1.81143i
$347$	−264.279	−	85.8695i	−0.761611	−	0.247463i	−0.0976413	−	0.995222i	$-0.531130\pi$
$347$	−264.279	−	85.8695i	−0.761611	−	0.247463i	−0.663970	+	0.747759i	$0.731130\pi$
$348$	−0.104763	−	0.0680162i	−0.000301043	−	0.000195449i
$349$	204.499	+	148.578i	0.585958	+	0.425724i	0.840867	−	0.541242i	$-0.182046\pi$
$349$	204.499	+	148.578i	0.585958	+	0.425724i	−0.254909	+	0.966965i	$0.582046\pi$
$350$	54.1196	−	17.5845i	0.154627	−	0.0502415i
$351$	−119.023	+	233.801i	−0.339096	+	0.666100i
$352$	2.89613	+	0.601518i	0.00822764	+	0.00170886i
$353$		−	560.803i		−	1.58868i	−0.607476	−	0.794338i	$-0.707818\pi$
$353$		−	560.803i		−	1.58868i	0.607476	−	0.794338i	$-0.292182\pi$
$354$	−340.714	−	420.645i	−0.962469	−	1.18826i
$355$	−166.813	−	121.197i	−0.469895	−	0.341399i
$356$	0.337148	+	0.464044i	0.000947044	+	0.00130349i
$357$	−299.339	+	15.7233i	−0.838484	+	0.0440428i
$358$	−29.9128	+	92.0620i	−0.0835552	+	0.257157i
$359$	174.022	+	239.520i	0.484740	+	0.667187i	0.979407	−	0.201895i	$-0.0647100\pi$
$359$	174.022	+	239.520i	0.484740	+	0.667187i	−0.494667	+	0.869083i	$0.664710\pi$
$360$	−391.873	+	41.2815i	−1.08854	+	0.114671i
$361$	−3.96952	−	12.2169i	−0.0109959	−	0.0338419i
$362$			0.133414i			0.000368547i
$363$	284.245	+	225.774i	0.783043	+	0.621967i
$364$	0.913018			0.00250829
$365$	−63.2492	+	20.5509i	−0.173285	+	0.0563038i
$366$	−48.0170	+	179.287i	−0.131194	+	0.489856i
$367$	−68.6514	+	49.8782i	−0.187061	+	0.135908i	−0.677375	−	0.735638i	$-0.736882\pi$
$367$	−68.6514	+	49.8782i	−0.187061	+	0.135908i	0.490313	+	0.871546i	$0.336882\pi$
$368$	−188.942	−	61.3910i	−0.513430	−	0.166823i
$369$	464.683	−	207.022i	1.25930	−	0.561036i
$370$	349.750	−	254.108i	0.945270	−	0.686779i
$371$	141.688	−	195.016i	0.381908	−	0.525651i
$372$	−1.56233	−	1.92885i	−0.00419982	−	0.00518508i
$373$	316.098			0.847447			0.423724	−	0.905792i	$-0.360723\pi$
$373$	316.098			0.847447			0.423724	+	0.905792i	$0.360723\pi$
$374$	−80.1228	+	385.767i	−0.214232	+	1.03146i
$375$	−117.499	−	305.988i	−0.313332	−	0.815968i
$376$	142.548	+	438.718i	0.379118	+	1.16680i
$377$	14.1490	−	19.4744i	0.0375304	−	0.0516562i
$378$	−298.797	+	47.4339i	−0.790469	+	0.125486i
$379$	−33.6016	+	103.415i	−0.0886586	+	0.272863i	−0.985549	−	0.169389i	$-0.945820\pi$
$379$	−33.6016	+	103.415i	−0.0886586	+	0.272863i	0.896891	+	0.442253i	$0.145820\pi$
$380$	1.63568	+	0.531466i	0.00430443	+	0.00139859i
$381$	111.558	−	171.829i	0.292803	−	0.450994i
$382$	320.092	+	232.561i	0.837938	+	0.608797i
$383$	−420.380	+	136.590i	−1.09760	+	0.356631i	−0.801178	−	0.598426i	$-0.795793\pi$
$383$	−420.380	+	136.590i	−1.09760	+	0.356631i	−0.296420	+	0.955058i	$0.595793\pi$
$384$	−138.517	−	360.721i	−0.360721	−	0.939378i
$385$	36.8166	+	335.270i	0.0956275	+	0.870831i
$386$			3.05372i			0.00791119i
$387$	−342.260	−	197.496i	−0.884393	−	0.510324i
$388$	−0.514268	−	0.373638i	−0.00132543	−	0.000962983i
$389$	−299.534	−	412.273i	−0.770010	−	1.05983i	−0.996315	−	0.0857708i	$-0.972665\pi$
$389$	−299.534	−	412.273i	−0.770010	−	1.05983i	0.226305	−	0.974056i	$-0.427335\pi$
$390$	16.8072	+	319.974i	0.0430953	+	0.820445i
$391$	68.2865	−	210.164i	0.174646	−	0.537504i
$392$	83.2541	+	114.589i	0.212383	+	0.292320i
$393$	−125.941	+	470.242i	−0.320461	+	1.19655i
$394$	−133.441	−	410.689i	−0.338682	−	1.04236i
$395$			346.310i			0.876734i
$396$	−0.165824	+	1.65557i	−0.000418748	+	0.00418072i
$397$	13.0481			0.0328668			0.0164334	−	0.999865i	$-0.494769\pi$
$397$	13.0481			0.0328668			0.0164334	+	0.999865i	$0.494769\pi$
$398$	203.310	−	66.0595i	0.510830	−	0.165979i
$399$	−302.303	−	80.9633i	−0.757651	−	0.202916i
$400$	−66.0118	+	47.9604i	−0.165029	+	0.119901i
$401$	522.706	+	169.837i	1.30351	+	0.423535i	0.876800	−	0.480855i	$-0.159674\pi$
$401$	522.706	+	169.837i	1.30351	+	0.423535i	0.426706	+	0.904390i	$0.359674\pi$
$402$	204.612	−	10.7476i	0.508986	−	0.0267354i
$403$	387.006	−	281.176i	0.960313	−	0.697708i
$404$	−0.463356	+	0.637754i	−0.00114692	+	0.00157860i
$405$	−92.5678	−	434.483i	−0.228563	−	1.07280i
$406$	27.7588			0.0683714
$407$	177.807	+	394.411i	0.436873	+	0.969069i
$408$	399.566	−	153.433i	0.979327	−	0.376062i
$409$	191.024	+	587.911i	0.467051	+	1.43744i	0.856385	+	0.516339i	$0.172705\pi$
$409$	191.024	+	587.911i	0.467051	+	1.43744i	−0.389334	+	0.921097i	$0.627295\pi$
$410$	365.188	−	502.638i	0.890702	−	1.22595i
$411$	−133.024	−	86.3646i	−0.323660	−	0.210133i
$412$	−0.544264	+	1.67507i	−0.00132103	+	0.00406571i
$413$	478.714	+	155.544i	1.15911	+	0.376619i
$414$	46.3197	−	218.172i	0.111883	−	0.526985i
$415$	−43.0450	−	31.2740i	−0.103723	−	0.0753591i
$416$	−2.48500	+	0.807424i	−0.00597355	+	0.00194092i
$417$	−242.353	+	93.0636i	−0.581182	+	0.223174i
$418$	−204.018	+	357.199i	−0.488082	+	0.854543i
$419$			440.342i			1.05094i	0.850814	+	0.525468i	$0.176110\pi$
$419$			440.342i			1.05094i	−0.850814	+	0.525468i	$0.823890\pi$
$420$	−1.20134	+	0.973062i	−0.00286033	+	0.00231681i
$421$	−464.562	−	337.524i	−1.10347	−	0.801719i	−0.121849	−	0.992549i	$-0.538882\pi$
$421$	−464.562	−	337.524i	−1.10347	−	0.801719i	−0.981623	+	0.190829i	$0.938882\pi$
$422$	−253.072	−	348.324i	−0.599697	−	0.825413i
$423$	−475.044	+	211.639i	−1.12304	+	0.500327i
$424$	−106.363	+	327.352i	−0.250856	+	0.772056i
$425$	−53.3473	−	73.4262i	−0.125523	−	0.172768i
$426$	218.355	+	58.4803i	0.512571	+	0.137278i
$427$	−53.3322	−	164.140i	−0.124900	−	0.384402i
$428$		−	0.783693i		−	0.00183106i
$429$	−316.942	−	48.6493i	−0.738793	−	0.113402i
$430$	−482.605			−1.12234
$431$	629.106	−	204.409i	1.45964	−	0.474267i	0.531682	−	0.846944i	$-0.321560\pi$
$431$	629.106	−	204.409i	1.45964	−	0.474267i	0.927961	+	0.372677i	$0.121560\pi$
$432$	386.455	−	197.082i	0.894572	−	0.456208i
$433$	−172.144	+	125.070i	−0.397560	+	0.288845i	−0.768547	−	0.639794i	$-0.779020\pi$
$433$	−172.144	+	125.070i	−0.397560	+	0.288845i	0.370986	+	0.928638i	$0.379020\pi$
$434$	524.640	+	170.466i	1.20885	+	0.392778i
$435$	2.13803	+	40.7037i	0.00491501	+	0.0935716i
$436$	−2.28988	+	1.66370i	−0.00525202	+	0.00381581i
$437$	135.611	−	186.652i	0.310322	−	0.427121i
$438$	56.6557	−	45.8900i	0.129351	−	0.104772i
$439$	−103.815			−0.236482			−0.118241	−	0.992985i	$-0.537725\pi$
$439$	−103.815			−0.236482			−0.118241	+	0.992985i	$0.537725\pi$
$440$	−197.932	−	439.053i	−0.449846	−	0.997848i
$441$	−118.642	+	106.877i	−0.269029	+	0.242351i
$442$	−107.550	−	331.004i	−0.243325	−	0.748877i
$443$	−162.680	+	223.910i	−0.367225	+	0.505441i	−0.952144	−	0.305650i	$-0.901126\pi$
$443$	−162.680	+	223.910i	−0.367225	+	0.505441i	0.584919	+	0.811092i	$0.301126\pi$
$444$	−1.07985	+	1.66325i	−0.00243209	+	0.00374606i
$445$	57.8405	−	178.015i	0.129979	−	0.400033i
$446$	85.3340	+	27.7267i	0.191332	+	0.0621675i
$447$	−162.169	−	105.287i	−0.362795	−	0.235541i
$448$	288.251	+	209.427i	0.643417	+	0.467470i
$449$	473.509	−	153.852i	1.05459	−	0.342656i	0.270119	−	0.962827i	$-0.412937\pi$
$449$	473.509	−	153.852i	1.05459	−	0.342656i	0.784466	+	0.620171i	$0.212937\pi$
$450$	−61.3111	−	68.0603i	−0.136247	−	0.151245i
$451$	418.184	+	460.116i	0.927237	+	1.02021i
$452$			0.778483i			0.00172231i
$453$	84.2811	+	104.053i	0.186051	+	0.229698i
$454$	364.017	+	264.474i	0.801800	+	0.582542i
$455$	−175.124	−	241.038i	−0.384889	−	0.529754i
$456$	446.253	−	23.4402i	0.978624	−	0.0514039i
$457$	250.649	−	771.417i	0.548465	−	1.68800i	−0.164140	−	0.986437i	$-0.552485\pi$
$457$	250.649	−	771.417i	0.548465	−	1.68800i	0.712605	−	0.701565i	$-0.247515\pi$
$458$	122.635	+	168.792i	0.267761	+	0.368542i
$459$	219.218	+	429.862i	0.477600	+	0.936518i
$460$	−0.352191	−	1.08393i	−0.000765633	−	0.00235638i
$461$			790.057i			1.71379i	0.515492	+	0.856894i	$0.327609\pi$
$461$			790.057i			1.71379i	−0.515492	+	0.856894i	$0.672391\pi$
$462$	−169.442	−	328.662i	−0.366759	−	0.711391i
$463$	540.381			1.16713			0.583565	−	0.812067i	$-0.301658\pi$
$463$	540.381			1.16713			0.583565	+	0.812067i	$0.301658\pi$
$464$	−37.8549	+	12.2998i	−0.0815839	+	0.0265082i
$465$	−209.551	+	782.427i	−0.450648	+	1.68264i
$466$	99.7650	−	72.4835i	0.214088	−	0.155544i
$467$	−264.267	−	85.8654i	−0.565881	−	0.183866i	0.0120845	−	0.999927i	$-0.496153\pi$
$467$	−264.267	−	85.8654i	−0.565881	−	0.183866i	−0.577966	+	0.816061i	$0.696153\pi$
$468$	−0.598121	−	1.34255i	−0.00127804	−	0.00286869i
$469$	−154.136	+	111.986i	−0.328647	+	0.238776i
$470$	−373.331	+	513.846i	−0.794322	+	1.09329i
$471$	−266.366	−	328.855i	−0.565533	−	0.698206i
$472$	−718.728			−1.52273
$473$	98.2146	−	472.874i	0.207642	−	0.999733i
$474$	−136.101	−	354.430i	−0.287133	−	0.747743i
$475$	−29.2819	−	90.1203i	−0.0616460	−	0.189727i
$476$	0.987047	−	1.35855i	0.00207363	−	0.00285411i
$477$	−379.582	−	80.5885i	−0.795769	−	0.168949i
$478$	92.4415	−	284.506i	0.193392	−	0.595200i
$479$	−447.212	−	145.308i	−0.933636	−	0.303357i	−0.197587	−	0.980285i	$-0.563311\pi$
$479$	−447.212	−	145.308i	−0.933636	−	0.303357i	−0.736049	+	0.676929i	$0.763311\pi$
$480$	2.40921	−	3.71082i	0.00501919	−	0.00773088i
$481$	−309.181	−	224.633i	−0.642787	−	0.467012i
$482$	−684.065	+	222.266i	−1.41922	+	0.461133i
$483$	74.3449	+	193.606i	0.153923	+	0.400841i
$484$	−1.98513	+	0.441304i	−0.00410152	+	0.000911785i
$485$			207.434i			0.427699i
$486$	265.492	+	408.292i	0.546280	+	0.840107i
$487$	−205.651	−	149.414i	−0.422282	−	0.306806i	0.356274	−	0.934382i	$-0.384047\pi$
$487$	−205.651	−	149.414i	−0.422282	−	0.306806i	−0.778555	+	0.627576i	$0.784047\pi$
$488$	144.851	+	199.370i	0.296825	+	0.408545i
$489$	−19.0354	−	362.394i	−0.0389272	−	0.741093i
$490$	−60.2650	+	185.477i	−0.122990	+	0.378524i
$491$	72.3701	+	99.6089i	0.147393	+	0.202869i	0.876329	−	0.481712i	$-0.159985\pi$
$491$	72.3701	+	99.6089i	0.147393	+	0.202869i	−0.728936	+	0.684582i	$0.759985\pi$
$492$	−0.737282	+	2.75288i	−0.00149854	+	0.00559529i
$493$	−13.6813	−	42.1068i	−0.0277512	−	0.0854093i
$494$		−	363.370i		−	0.735567i
$495$	468.878	−	273.773i	0.947229	−	0.553078i
$496$	−790.989			−1.59474
$497$	−199.907	+	64.9537i	−0.402227	+	0.130691i
$498$	56.3452	+	15.0905i	0.113143	+	0.0303022i
$499$	−52.8516	+	38.3990i	−0.105915	+	0.0769518i	−0.639482	−	0.768806i	$-0.720851\pi$
$499$	−52.8516	+	38.3990i	−0.105915	+	0.0769518i	0.533567	+	0.845758i	$0.320851\pi$
$500$	1.74637	+	0.567430i	0.00349274	+	0.00113486i
$501$	−321.852	+	16.9058i	−0.642418	+	0.0337442i
$502$	578.886	−	420.585i	1.15316	−	0.837820i
$503$	−250.337	+	344.560i	−0.497688	+	0.685009i	−0.981783	−	0.190007i	$-0.939149\pi$
$503$	−250.337	+	344.560i	−0.497688	+	0.685009i	0.484095	+	0.875016i	$0.339149\pi$
$504$	−200.763	+	347.922i	−0.398339	+	0.690321i
$505$	257.243			0.509393
$506$	270.969	−	29.7556i	0.535512	−	0.0588055i
$507$	−208.881	+	80.2103i	−0.411994	+	0.158206i
$508$	0.354659	+	1.09153i	0.000698148	+	0.00214868i
$509$	41.0633	−	56.5188i	0.0806745	−	0.111039i	−0.766772	−	0.641919i	$-0.778139\pi$
$509$	41.0633	−	56.5188i	0.0806745	−	0.111039i	0.847447	+	0.530880i	$0.178139\pi$
$510$	494.285	+	320.909i	0.969186	+	0.629233i
$511$	−20.9498	+	64.4769i	−0.0409977	+	0.126178i
$512$	−483.837	−	157.208i	−0.944993	−	0.307047i
$513$	78.9872	+	497.560i	0.153971	+	0.969902i
$514$	−107.166	−	77.8606i	−0.208494	−	0.151480i
$515$	546.616	−	177.606i	1.06139	−	0.344866i
$516$	2.06660	−	0.793574i	0.00400503	−	0.00153793i
$517$	−427.509	−	470.376i	−0.826903	−	0.909818i
$518$		−	440.706i		−	0.850785i
$519$	766.536	−	620.879i	1.47695	−	1.19630i
$520$	344.176	+	250.058i	0.661876	+	0.480881i
$521$	−59.1550	−	81.4198i	−0.113541	−	0.156276i	0.748464	−	0.663175i	$-0.230792\pi$
$521$	−59.1550	−	81.4198i	−0.113541	−	0.156276i	−0.862005	+	0.506899i	$0.830792\pi$
$522$	−18.1849	−	40.8178i	−0.0348369	−	0.0781951i
$523$	−263.265	+	810.248i	−0.503376	+	1.54923i	0.300109	+	0.953905i	$0.402977\pi$
$523$	−263.265	+	810.248i	−0.503376	+	1.54923i	−0.803484	+	0.595326i	$0.797023\pi$
$524$	−1.60303	−	2.20638i	−0.00305921	−	0.00421064i
$525$	82.2785	+	22.0360i	0.156721	+	0.0419733i
$526$	−52.9029	−	162.818i	−0.100576	−	0.309541i
$527$		−	879.833i		−	1.66951i
$528$	376.699	+	373.121i	0.713446	+	0.706669i
$529$	376.110			0.710983
$530$	−450.724	+	146.449i	−0.850423	+	0.276319i
$531$	−84.8886	−	805.821i	−0.159865	−	1.51755i
$532$	1.41840	−	1.03053i	0.00266617	−	0.00193709i
$533$	−522.347	−	169.721i	−0.980013	−	0.318425i
$534$	10.7638	+	204.921i	0.0201570	+	0.383747i
$535$	−206.896	+	150.319i	−0.386722	+	0.280970i
$536$	159.904	−	220.089i	0.298328	−	0.410613i
$537$	−112.594	+	91.1991i	−0.209673	+	0.169831i
$538$	−324.247			−0.602689
$539$	−169.472	−	96.7961i	−0.314420	−	0.179585i
$540$	2.21784	+	1.12905i	0.00410711	+	0.00209084i
$541$	226.023	+	695.627i	0.417787	+	1.28582i	0.909734	+	0.415192i	$0.136285\pi$
$541$	226.023	+	695.627i	0.417787	+	1.28582i	−0.491947	+	0.870625i	$0.663715\pi$
$542$	−306.282	+	421.561i	−0.565096	+	0.777788i
$543$	−0.108746	+	0.167497i	−0.000200268	+	0.000308466i
$544$	−1.48505	+	4.57052i	−0.00272988	+	0.00840169i
$545$	878.436	+	285.421i	1.61181	+	0.523708i
$546$	273.960	+	177.865i	0.501758	+	0.325761i
$547$	99.7347	+	72.4615i	0.182330	+	0.132471i	0.675207	−	0.737629i	$-0.264054\pi$
$547$	99.7347	+	72.4615i	0.182330	+	0.132471i	−0.492876	+	0.870099i	$0.664054\pi$
$548$	0.845027	−	0.274566i	0.00154202	−	0.000501033i
$549$	−206.421	+	185.951i	−0.375994	+	0.338708i
$550$	55.5283	−	97.2198i	0.100960	−	0.176763i
$551$		−	46.2241i		−	0.0838913i
$552$	−186.388	−	230.114i	−0.337659	−	0.416873i
$553$	285.609	+	207.507i	0.516472	+	0.375239i
$554$	102.244	+	140.727i	0.184556	+	0.254020i
$555$	646.223	−	33.9440i	1.16437	−	0.0611604i
$556$	0.449425	−	1.38319i	0.000808318	−	0.00248775i
$557$	−118.600	−	163.240i	−0.212927	−	0.293069i	0.689172	−	0.724598i	$-0.257974\pi$
$557$	−118.600	−	163.240i	−0.212927	−	0.293069i	−0.902099	+	0.431529i	$0.857974\pi$
$558$	−93.0324	−	883.128i	−0.166725	−	1.58267i
$559$	131.834	+	405.745i	0.235840	+	0.725840i
$560$			492.649i			0.879731i
$561$	−415.030	+	419.010i	−0.739804	+	0.746899i
$562$	971.465			1.72858
$563$	−460.414	+	149.597i	−0.817786	+	0.265715i	−0.687892	−	0.725813i	$-0.741464\pi$
$563$	−460.414	+	149.597i	−0.817786	+	0.265715i	−0.129894	+	0.991528i	$0.541464\pi$
$564$	0.753723	−	2.81427i	0.00133639	−	0.00498984i
$565$	205.521	−	149.319i	0.363753	−	0.264282i
$566$	823.575	+	267.596i	1.45508	+	0.472784i
$567$	−413.794	−	183.998i	−0.729795	−	0.324511i
$568$	242.814	−	176.415i	0.427489	−	0.310589i
$569$	274.742	−	378.150i	0.482850	−	0.664586i	−0.496199	−	0.868209i	$-0.665271\pi$
$569$	274.742	−	378.150i	0.482850	−	0.664586i	0.979050	+	0.203622i	$0.0652714\pi$
$570$	387.267	+	478.119i	0.679416	+	0.838806i
$571$	656.796			1.15026			0.575128	−	0.818064i	$-0.304952\pi$
$571$	656.796			1.15026			0.575128	+	0.818064i	$0.304952\pi$
$572$	1.32935	−	1.20820i	0.00232404	−	0.00211224i
$573$	212.306	+	552.879i	0.370516	+	0.964885i
$574$	−195.717	−	602.356i	−0.340971	−	1.04940i
$575$	−36.9095	+	50.8016i	−0.0641905	+	0.0883506i
$576$	119.117	−	561.054i	0.206800	−	0.974052i
$577$	−269.912	+	830.704i	−0.467785	+	1.43969i	0.387660	+	0.921802i	$0.373283\pi$
$577$	−269.912	+	830.704i	−0.467785	+	1.43969i	−0.855446	+	0.517893i	$0.826717\pi$
$578$	−57.9332	−	18.8236i	−0.100230	−	0.0325669i
$579$	−2.48908	+	3.83385i	−0.00429893	+	0.00662149i
$580$	−0.184734	−	0.134217i	−0.000318507	−	0.000231409i
$581$	−51.5847	+	16.7609i	−0.0887861	+	0.0288483i
$582$	−81.5225	−	212.298i	−0.140073	−	0.364774i
$583$	−51.7696	−	471.440i	−0.0887987	−	0.808645i
$584$		−	96.8039i		−	0.165760i
$585$	−239.709	+	415.416i	−0.409759	+	0.710113i
$586$	8.96581	+	6.51405i	0.0153000	+	0.0111161i
$587$	464.705	+	639.611i	0.791661	+	1.08963i	0.993899	+	0.110291i	$0.0351783\pi$
$587$	464.705	+	639.611i	0.791661	+	1.08963i	−0.202239	+	0.979336i	$0.564822\pi$
$588$	−0.0469243	−	0.893341i	−7.98032e−5	−	0.00151929i
$589$	283.861	−	873.634i	0.481937	−	1.48325i
$590$	−581.674	−	800.605i	−0.985888	−	1.35696i
$591$	167.221	−	624.374i	0.282946	−	1.05647i
$592$	195.275	+	600.996i	0.329857	+	1.01520i
$593$		−	928.634i		−	1.56599i	−0.622026	−	0.782997i	$-0.713690\pi$
$593$		−	928.634i		−	1.56599i	0.622026	−	0.782997i	$-0.286310\pi$
$594$	−372.279	+	464.464i	−0.626732	+	0.781926i
$595$	−547.984			−0.920981
$596$	1.03017	−	0.334722i	0.00172847	−	0.000561614i
$597$	309.094	+	82.7823i	0.517746	+	0.138664i
$598$	−194.810	+	141.537i	−0.325769	+	0.236685i
$599$	−872.469	−	283.482i	−1.45654	−	0.473259i	−0.529530	−	0.848291i	$-0.677632\pi$
$599$	−872.469	−	283.482i	−1.45654	−	0.473259i	−0.927012	+	0.375032i	$0.877632\pi$
$600$	−121.458	+	6.37978i	−0.202430	+	0.0106330i
$601$	−773.147	+	561.724i	−1.28643	+	0.934649i	−0.999727	−	0.0233687i	$-0.992561\pi$
$601$	−773.147	+	561.724i	−1.28643	+	0.934649i	−0.286708	+	0.958018i	$0.592561\pi$
$602$	−289.174	+	398.014i	−0.480356	+	0.661153i
$603$	265.644	+	153.286i	0.440538	+	0.254205i
$604$	−0.750158			−0.00124198
$605$	497.270	+	439.433i	0.821934	+	0.726335i
$606$	−263.275	+	101.098i	−0.434448	+	0.166828i
$607$	−241.534	−	743.364i	−0.397914	−	1.22465i	−0.926669	−	0.375878i	$-0.877341\pi$
$607$	−241.534	−	743.364i	−0.397914	−	1.22465i	0.528756	−	0.848774i	$-0.322659\pi$
$608$	−2.94918	+	4.05919i	−0.00485062	+	0.00667631i
$609$	34.8503	+	22.6261i	0.0572254	+	0.0371529i
$610$	−104.853	+	322.704i	−0.171890	+	0.529023i
$611$	533.995	+	173.505i	0.873968	+	0.283969i
$612$	−2.64430	−	0.561408i	−0.00432075	−	0.000917333i
$613$	−69.5578	−	50.5367i	−0.113471	−	0.0824416i	0.529603	−	0.848246i	$-0.322341\pi$
$613$	−69.5578	−	50.5367i	−0.113471	−	0.0824416i	−0.643074	+	0.765804i	$0.722341\pi$
$614$	−417.926	+	135.792i	−0.680661	+	0.221160i
$615$	868.181	−	333.382i	1.41168	−	0.542084i
$616$	−480.696	−	99.8393i	−0.780351	−	0.162077i
$617$			7.47837i			0.0121205i	0.999982	+	0.00606027i	$0.00192905\pi$
$617$			7.47837i			0.0121205i	−0.999982	+	0.00606027i	$0.998071\pi$
$618$	−489.633	+	396.593i	−0.792286	+	0.641736i
$619$	−263.047	−	191.115i	−0.424955	−	0.308748i	0.354674	−	0.934990i	$-0.384592\pi$
$619$	−263.047	−	191.115i	−0.424955	−	0.308748i	−0.779628	+	0.626243i	$0.784592\pi$
$620$	−2.66724	−	3.67115i	−0.00430201	−	0.00592121i
$621$	235.984	−	236.152i	0.380007	−	0.380278i
$622$	−88.0380	+	270.953i	−0.141540	+	0.435616i
$623$	−112.155	−	154.368i	−0.180024	−	0.247782i
$624$	−452.413	−	121.166i	−0.725021	−	0.194177i
$625$	−224.399	−	690.629i	−0.359038	−	1.10501i
$626$			188.967i			0.301864i
$627$	−547.291	+	282.157i	−0.872873	+	0.450011i
$628$	2.37084			0.00377522
$629$	−668.500	+	217.209i	−1.06280	+	0.345324i
$630$	−550.036	+	57.9431i	−0.873073	+	0.0919732i
$631$	554.612	−	402.949i	0.878941	−	0.638588i	−0.0540299	−	0.998539i	$-0.517207\pi$
$631$	554.612	−	402.949i	0.878941	−	0.638588i	0.932971	+	0.359951i	$0.117207\pi$
$632$	−479.419	−	155.773i	−0.758574	−	0.246476i
$633$	−33.8056	−	643.589i	−0.0534054	−	1.01673i
$634$	−812.685	+	590.450i	−1.28184	+	0.931309i
$635$	220.139	−	302.995i	0.346675	−	0.477157i
$636$	1.68927	−	1.36827i	0.00265608	−	0.00215137i
$637$	172.400			0.270644
$638$	40.4167	−	36.7334i	0.0633491	−	0.0575759i
$639$	226.471	+	251.401i	0.354414	+	0.393429i
$640$	−218.287	−	671.819i	−0.341074	−	1.04972i
$641$	−160.641	+	221.104i	−0.250610	+	0.344935i	−0.915725	−	0.401806i	$-0.868383\pi$
$641$	−160.641	+	221.104i	−0.250610	+	0.344935i	0.665115	+	0.746741i	$0.268383\pi$
$642$	152.672	−	235.155i	0.237806	−	0.366285i
$643$	57.0519	−	175.588i	0.0887277	−	0.273076i	−0.896841	−	0.442354i	$-0.854144\pi$
$643$	57.0519	−	175.588i	0.0887277	−	0.273076i	0.985568	+	0.169278i	$0.0541436\pi$
$644$	−1.10497	−	0.359028i	−0.00171580	−	0.000557496i
$645$	−605.895	−	393.370i	−0.939372	−	0.609877i
$646$	−540.688	−	392.833i	−0.836979	−	0.608101i
$647$	342.473	−	111.276i	0.529325	−	0.171988i	−0.0321480	−	0.999483i	$-0.510235\pi$
$647$	342.473	−	111.276i	0.529325	−	0.171988i	0.561473	+	0.827495i	$0.310235\pi$
$648$	643.121	+	67.2862i	0.992471	+	0.103837i
$649$	902.839	−	407.015i	1.39112	−	0.627141i
$650$			98.8995i			0.152153i
$651$	519.722	+	641.648i	0.798344	+	0.985634i
$652$	1.64473	+	1.19497i	0.00252260	+	0.00183277i
$653$	605.633	+	833.583i	0.927463	+	1.27654i	0.960841	+	0.277101i	$0.0893735\pi$
$653$	605.633	+	833.583i	0.927463	+	1.27654i	−0.0333778	+	0.999443i	$0.510626\pi$
$654$	−1011.21	+	53.1153i	−1.54619	+	0.0812161i
$655$	−275.013	+	846.402i	−0.419867	+	1.29222i
$656$	533.804	+	734.718i	0.813725	+	1.12000i
$657$	108.534	−	11.4335i	0.165197	−	0.0174025i
$658$	200.082	+	615.788i	0.304076	+	0.935848i
$659$			1071.63i			1.62614i	0.582166	+	0.813070i	$0.302205\pi$
$659$			1071.63i			1.62614i	−0.582166	+	0.813070i	$0.697795\pi$
$660$	−0.461488	+	3.00652i	−0.000699225	+	0.00455533i
$661$	441.357			0.667712			0.333856	−	0.942624i	$-0.391650\pi$
$661$	441.357			0.667712			0.333856	+	0.942624i	$0.391650\pi$
$662$	1245.62	−	404.726i	1.88160	−	0.611368i
$663$	134.776	−	503.228i	0.203281	−	0.759017i
$664$	62.6566	−	45.5227i	0.0943624	−	0.0685583i
$665$	−544.123	−	176.796i	−0.818230	−	0.265859i
$666$	−648.036	+	288.708i	−0.973027	+	0.433496i
$667$	−24.7816	+	18.0049i	−0.0371539	+	0.0269939i
$668$	1.06128	−	1.46073i	0.00158874	−	0.00218672i
$669$	84.5342	+	104.366i	0.126359	+	0.156003i
$670$	374.573			0.559064
$671$	−294.859	−	168.412i	−0.439432	−	0.250987i
$672$	−1.61681	−	4.21043i	−0.00240596	−	0.00626552i
$673$	−114.553	−	352.559i	−0.170213	−	0.523861i	0.829170	−	0.558997i	$-0.188814\pi$
$673$	−114.553	−	352.559i	−0.170213	−	0.523861i	−0.999383	+	0.0351357i	$0.988814\pi$
$674$	776.757	−	1069.11i	1.15246	−	1.58622i
$675$	−21.4982	−	135.422i	−0.0318491	−	0.200625i
$676$	0.387353	−	1.19215i	0.000573007	−	0.00176353i
$677$	71.5458	+	23.2466i	0.105681	+	0.0343377i	0.361380	−	0.932419i	$-0.382306\pi$
$677$	71.5458	+	23.2466i	0.105681	+	0.0343377i	−0.255699	+	0.966756i	$0.582306\pi$
$678$	−151.657	+	233.591i	−0.223682	+	0.344530i
$679$	171.075	+	124.294i	0.251952	+	0.183054i
$680$	744.164	−	241.794i	1.09436	−	0.355579i
$681$	241.440	+	628.749i	0.354537	+	0.923272i
$682$	989.453	−	446.062i	1.45081	−	0.654050i
$683$		−	987.234i		−	1.44544i	−0.691142	−	0.722719i	$-0.742892\pi$
$683$		−	987.234i		−	1.44544i	0.691142	−	0.722719i	$-0.257108\pi$
$684$	−2.44454	−	1.41058i	−0.00357389	−	0.00206226i
$685$	−234.569	−	170.424i	−0.342436	−	0.248795i
$686$	439.581	+	605.031i	0.640788	+	0.881970i
$687$	16.3816	+	311.872i	0.0238452	+	0.453963i
$688$	217.991	−	670.908i	0.316848	−	0.975157i
$689$	246.251	+	338.936i	0.357404	+	0.491924i
$690$	105.483	−	393.855i	0.152874	−	0.570804i
$691$	317.299	+	976.547i	0.459188	+	1.41324i	0.866147	+	0.499790i	$0.166589\pi$
$691$	317.299	+	976.547i	0.459188	+	1.41324i	−0.406958	+	0.913447i	$0.633411\pi$
$692$			5.52624i			0.00798589i
$693$	55.1628	−	550.737i	0.0796000	−	0.794715i
$694$	556.925			0.802486
$695$	−451.366	+	146.658i	−0.649448	+	0.211018i
$696$	−57.3104	−	15.3490i	−0.0823425	−	0.0220531i
$697$	−817.241	+	593.760i	−1.17251	+	0.851880i
$698$	−481.816	−	156.551i	−0.690281	−	0.224286i
$699$	184.333	−	9.68241i	0.263709	−	0.0138518i
$700$	−0.386051	+	0.280482i	−0.000551501	+	0.000400689i
$701$	−109.885	+	151.244i	−0.156754	+	0.215754i	−0.880170	−	0.474659i	$-0.842571\pi$
$701$	−109.885	+	151.244i	−0.156754	+	0.215754i	0.723415	+	0.690413i	$0.242571\pi$
$702$	82.0696	−	519.364i	0.116908	−	0.739834i
$703$	−733.868			−1.04391
$704$	696.828	−	76.5200i	0.989813	−	0.108693i
$705$	−887.541	+	340.816i	−1.25892	+	0.483427i
$706$	347.322	+	1068.95i	0.491958	+	1.51409i
$707$	154.139	−	212.154i	0.218018	−	0.300077i
$708$	3.80731	+	2.47185i	0.00537755	+	0.00349132i
$709$	−220.538	+	678.745i	−0.311055	+	0.957327i	0.666294	+	0.745690i	$0.267880\pi$
$709$	−220.538	+	678.745i	−0.311055	+	0.957327i	−0.977348	+	0.211638i	$0.932120\pi$
$710$	393.024	+	127.701i	0.553554	+	0.179861i
$711$	118.025	−	555.912i	0.165998	−	0.781873i
$712$	220.420	+	160.145i	0.309579	+	0.224922i
$713$	−578.939	+	188.109i	−0.811976	+	0.263827i
$714$	560.833	−	215.360i	0.785481	−	0.301625i
$715$	−573.948	−	119.207i	−0.802724	−	0.166724i
$716$		−	0.811733i		−	0.00113370i
$717$	347.958	−	281.839i	0.485297	−	0.393081i
$718$	−480.046	−	348.774i	−0.668588	−	0.485757i
$719$	−293.142	−	403.475i	−0.407708	−	0.561162i	0.554950	−	0.831884i	$-0.312738\pi$
$719$	−293.142	−	403.475i	−0.407708	−	0.561162i	−0.962658	+	0.270722i	$0.912738\pi$
$720$	724.415	−	322.737i	1.00613	−	0.448245i
$721$	181.054	−	557.226i	0.251115	−	0.772852i
$722$	15.1326	+	20.8283i	0.0209593	+	0.0288480i
$723$	−1039.99	−	278.533i	−1.43844	−	0.385246i
$724$	−0.000345719	−	0.00106401i	−4.77512e−7	−	1.46963e-6i
$725$			12.5809i			0.0173530i
$726$	−681.629	−	254.307i	−0.938883	−	0.350286i
$727$	427.838			0.588498			0.294249	−	0.955729i	$-0.404930\pi$
$727$	427.838			0.588498			0.294249	+	0.955729i	$0.404930\pi$
$728$	412.457	−	134.015i	0.566561	−	0.184087i
$729$	0.518938	+	729.000i	0.000711849	+	1.00000i
$730$	107.832	−	78.3444i	0.147715	−	0.107321i
$731$	746.264	+	242.476i	1.02088	+	0.331705i
$732$	−0.0816418	−	1.55429i	−0.000111532	−	0.00212335i
$733$	−774.572	+	562.759i	−1.05671	+	0.767748i	−0.973478	−	0.228782i	$-0.926526\pi$
$733$	−774.572	+	562.759i	−1.05671	+	0.767748i	−0.0832370	+	0.996530i	$0.526526\pi$
$734$	99.9657	−	137.591i	0.136193	−	0.187454i
$735$	−226.843	+	183.738i	−0.308629	+	0.249984i
$736$	3.32495			0.00451760
$737$	−76.2291	+	367.020i	−0.103432	+	0.497992i
$738$	−757.518	+	682.398i	−1.02645	+	0.924659i
$739$	−350.729	−	1079.43i	−0.474599	−	1.46067i	−0.846498	−	0.532392i	$-0.821293\pi$
$739$	−350.729	−	1079.43i	−0.474599	−	1.46067i	0.371899	−	0.928273i	$-0.378707\pi$
$740$	−2.13087	+	2.93289i	−0.00287956	+	0.00396337i
$741$	296.183	−	456.200i	0.399707	−	0.615654i
$742$	−149.292	+	459.473i	−0.201202	+	0.619236i
$743$	−824.458	−	267.883i	−1.10963	−	0.360542i	−0.303831	−	0.952726i	$-0.598266\pi$
$743$	−824.458	−	267.883i	−1.10963	−	0.360542i	−0.805803	+	0.592184i	$0.798266\pi$
$744$	−988.907	−	642.037i	−1.32918	−	0.862953i
$745$	−285.962	−	207.763i	−0.383841	−	0.278877i
$746$	−602.516	+	195.769i	−0.807662	+	0.262425i
$747$	58.4393	+	64.8725i	0.0782321	+	0.0868441i
$748$	−0.360646	−	3.28422i	−0.000482147	−	0.00439067i
$749$			260.702i			0.348067i
$750$	413.474	+	510.474i	0.551299	+	0.680632i
$751$	936.412	+	680.343i	1.24689	+	0.905916i	0.998037	−	0.0626258i	$-0.0199475\pi$
$751$	936.412	+	680.343i	1.24689	+	0.905916i	0.248850	+	0.968542i	$0.419947\pi$
$752$	−545.707	−	751.101i	−0.725674	−	0.998805i
$753$	1069.59	−	56.1822i	1.42044	−	0.0746111i
$754$	−14.9083	+	45.8831i	−0.0197723	+	0.0608529i
$755$	143.886	+	198.043i	0.190578	+	0.262308i
$756$	2.26007	−	1.15258i	0.00298951	−	0.00152457i
$757$	−126.788	−	390.214i	−0.167488	−	0.515474i	0.831723	−	0.555190i	$-0.187355\pi$
$757$	−126.788	−	390.214i	−0.167488	−	0.515474i	−0.999211	+	0.0397163i	$0.987355\pi$
$758$		−	217.931i		−	0.287508i
$759$	364.447	+	183.509i	0.480167	+	0.241778i
$760$	816.931			1.07491
$761$	−241.083	+	78.3326i	−0.316798	+	0.102934i	−0.463100	−	0.886306i	$-0.653263\pi$
$761$	−241.083	+	78.3326i	−0.316798	+	0.102934i	0.146302	+	0.989240i	$0.453263\pi$
$762$	−106.222	+	396.615i	−0.139399	+	0.520492i
$763$	761.747	−	553.442i	0.998358	−	0.725349i
$764$	−3.15546	−	1.02527i	−0.00413018	−	0.00134198i
$765$	358.986	+	805.782i	0.469263	+	1.05331i
$766$	716.694	−	520.709i	0.935632	−	0.679776i
$767$	−514.203	+	707.739i	−0.670408	+	0.922737i
$768$	6.09298	+	7.52237i	0.00793356	+	0.00979476i
$769$	−788.887			−1.02586			−0.512931	−	0.858430i	$-0.671440\pi$
$769$	−788.887			−1.02586			−0.512931	+	0.858430i	$0.671440\pi$
$770$	−277.819	−	616.258i	−0.360804	−	0.800335i
$771$	−71.0793	−	185.102i	−0.0921910	−	0.240081i
$772$	−0.00791316	−	0.0243542i	−1.02502e−5	−	3.15469e-5i
$773$	−201.817	+	277.778i	−0.261083	+	0.359350i	−0.919354	−	0.393431i	$-0.871288\pi$
$773$	−201.817	+	277.778i	−0.261083	+	0.359350i	0.658271	+	0.752781i	$0.271288\pi$
$774$	774.698	+	164.475i	1.00090	+	0.212500i
$775$	−77.2592	+	237.779i	−0.0996893	+	0.306812i
$776$	−287.165	−	93.3054i	−0.370057	−	0.120239i
$777$	359.219	−	553.293i	0.462316	−	0.712089i
$778$	826.276	+	600.325i	1.06205	+	0.771625i
$779$	−1003.05	+	325.910i	−1.28761	+	0.418370i
$780$	−0.963195	−	2.50832i	−0.00123487	−	0.00321580i
$781$	−205.110	+	359.111i	−0.262625	+	0.459809i
$782$			442.887i			0.566351i
$783$	10.4400	−	66.0680i	0.0133334	−	0.0843780i
$784$	−230.625	−	167.559i	−0.294164	−	0.213723i
$785$	−454.746	−	625.904i	−0.579294	−	0.797330i
$786$	−51.1784	−	974.330i	−0.0651125	−	1.23961i
$787$	−59.7777	+	183.977i	−0.0759564	+	0.233770i	−0.981825	−	0.189789i	$-0.939219\pi$
$787$	−59.7777	+	183.977i	−0.0759564	+	0.233770i	0.905868	+	0.423559i	$0.139219\pi$
$788$	2.12845	+	2.92956i	0.00270108	+	0.00371772i
$789$	66.2951	−	247.534i	0.0840243	−	0.313732i
$790$	−214.480	−	660.103i	−0.271494	−	0.835573i
$791$		−	258.969i		−	0.327394i
$792$	168.097	+	772.244i	0.212244	+	0.975055i
$793$	299.953			0.378251
$794$	−24.8711	+	8.08110i	−0.0313238	+	0.0101777i
$795$	−685.241	−	183.523i	−0.861938	−	0.230846i
$796$	−1.45027	+	1.05368i	−0.00182195	+	0.00132372i
$797$	505.892	+	164.374i	0.634745	+	0.206241i	0.608676	−	0.793419i	$-0.291701\pi$
$797$	505.892	+	164.374i	0.634745	+	0.206241i	0.0260694	+	0.999660i	$0.491701\pi$
$798$	626.363	−	32.9008i	0.784917	−	0.0412291i
$799$	835.465	−	607.001i	1.04564	−	0.759701i
$800$	0.802686	−	1.10480i	0.00100336	−	0.00138100i
$801$	−153.517	+	266.045i	−0.191657	+	0.332141i
$802$	−1101.52			−1.37346
$803$	54.8199	+	121.601i	0.0682689	+	0.151434i
$804$	−1.60399	+	0.615931i	−0.00199501	+	0.000766083i
$805$	117.159	+	360.579i	0.145539	+	0.447924i
$806$	−563.533	+	775.637i	−0.699173	+	0.962328i
$807$	−407.081	−	264.293i	−0.504438	−	0.327501i
$808$	−115.710	+	356.119i	−0.143205	+	0.440741i
$809$	−276.212	−	89.7467i	−0.341424	−	0.110935i	0.133286	−	0.991078i	$-0.457447\pi$
$809$	−276.212	−	89.7467i	−0.341424	−	0.110935i	−0.474710	+	0.880142i	$0.657447\pi$
$810$	445.533	+	770.841i	0.550041	+	0.951655i
$811$	−311.109	−	226.034i	−0.383611	−	0.278710i	0.379221	−	0.925306i	$-0.376192\pi$
$811$	−311.109	−	226.034i	−0.383611	−	0.278710i	−0.762833	+	0.646596i	$0.776192\pi$
$812$	−0.221384	+	0.0719319i	−0.000272640	+	8.85861e-5i
$813$	−728.142	+	279.607i	−0.895623	+	0.343919i
$814$	−583.190	−	641.668i	−0.716450	−	0.788289i
$815$		−	663.416i		−	0.814008i
$816$	−669.389	+	542.192i	−0.820329	+	0.664451i
$817$	662.776	+	481.535i	0.811232	+	0.589394i
$818$	−728.223	−	1002.31i	−0.890248	−	1.22532i
$819$	198.970	+	446.608i	0.242942	+	0.545309i
$820$	−1.60997	+	4.95499i	−0.00196338	+	0.00604267i
$821$	−365.440	−	502.985i	−0.445116	−	0.612650i	0.526223	−	0.850346i	$-0.323608\pi$
$821$	−365.440	−	502.985i	−0.445116	−	0.612650i	−0.971339	+	0.237697i	$0.923608\pi$
$822$	307.047	+	82.2339i	0.373536	+	0.100041i
$823$	−88.4972	−	272.366i	−0.107530	−	0.330943i	0.882786	−	0.469776i	$-0.155665\pi$
$823$	−88.4972	−	272.366i	−0.107530	−	0.330943i	−0.990316	+	0.138832i	$0.955665\pi$
$824$			836.604i			1.01530i
$825$	148.958	−	76.7954i	0.180555	−	0.0930853i
$826$	−1008.81			−1.22132
$827$	397.074	−	129.017i	0.480138	−	0.156006i	−0.0589412	−	0.998261i	$-0.518772\pi$
$827$	397.074	−	129.017i	0.480138	−	0.156006i	0.539079	+	0.842255i	$0.318772\pi$
$828$	0.195941	+	1.86001i	0.000236643	+	0.00224638i
$829$	−300.030	+	217.984i	−0.361918	+	0.262949i	−0.753852	−	0.657045i	$-0.771806\pi$
$829$	−300.030	+	217.984i	−0.361918	+	0.262949i	0.391934	+	0.919993i	$0.371806\pi$
$830$	101.417	+	32.9525i	0.122189	+	0.0397018i
$831$	13.6579	+	260.018i	0.0164355	+	0.312897i
$832$	−500.976	+	363.980i	−0.602134	+	0.437476i
$833$	186.379	−	256.528i	0.223744	−	0.307957i
$834$	404.313	−	327.486i	0.484788	−	0.392669i
$835$	−589.197			−0.705625
$836$	0.701484	−	3.37743i	0.000839096	−	0.00403999i
$837$	603.038	−	1184.57i	0.720475	−	1.41526i
$838$	−272.717	−	839.338i	−0.325438	−	1.00160i
$839$	508.937	−	700.492i	0.606599	−	0.834912i	−0.389693	−	0.920945i	$-0.627419\pi$
$839$	508.937	−	700.492i	0.606599	−	0.834912i	0.996292	+	0.0860324i	$0.0274189\pi$
$840$	−399.878	+	615.918i	−0.476045	+	0.733235i
$841$	257.987	−	794.002i	0.306762	−	0.944116i
$842$	1094.54	+	355.638i	1.29993	+	0.422373i
$843$	1219.64	+	791.840i	1.44679	+	0.939311i
$844$	2.92094	+	2.12219i	0.00346083	+	0.00251444i
$845$	−389.027	+	126.402i	−0.460386	+	0.149589i
$846$	774.410	−	697.615i	0.915379	−	0.824604i
$847$	660.371	−	146.803i	0.779659	−	0.173321i
$848$		−	692.739i		−	0.816910i
$849$	815.855	+	1007.25i	0.960960	+	1.18640i
$850$	147.161	+	106.918i	0.173130	+	0.125786i
$851$	285.851	+	393.440i	0.335900	+	0.462327i
$852$	−1.89298	+	0.0994321i	−0.00222181	+	0.000116704i
$853$	−416.202	+	1280.94i	−0.487927	+	1.50169i	0.339768	+	0.940509i	$0.389651\pi$
$853$	−416.202	+	1280.94i	−0.487927	+	1.50169i	−0.827696	+	0.561177i	$0.810349\pi$
$854$	203.313	+	279.837i	0.238072	+	0.327678i
$855$	96.4873	+	915.924i	0.112851	+	1.07126i
$856$	−115.033	−	354.034i	−0.134384	−	0.413591i
$857$		−	770.599i		−	0.899182i	−0.893235	−	0.449591i	$-0.851570\pi$
$857$		−	770.599i		−	0.899182i	0.893235	−	0.449591i	$-0.148430\pi$
$858$	634.255	−	103.561i	0.739225	−	0.120701i
$859$	−549.532			−0.639735			−0.319867	−	0.947462i	$-0.603638\pi$
$859$	−549.532			−0.639735			−0.319867	+	0.947462i	$0.603638\pi$
$860$	3.84890	−	1.25058i	0.00447546	−	0.00145417i
$861$	245.263	−	915.768i	0.284858	−	1.06361i
$862$	−1072.55	+	779.250i	−1.24425	+	0.904002i
$863$	1042.29	+	338.660i	1.20775	+	0.392422i	0.842607	−	0.538530i	$-0.181020\pi$
$863$	1042.29	+	338.660i	1.20775	+	0.392422i	0.365143	+	0.930951i	$0.381020\pi$
$864$	−5.13204	+	5.13570i	−0.00593987	+	0.00594410i
$865$	1458.93	−	1059.98i	1.68663	−	1.22541i
$866$	250.664	−	345.010i	0.289451	−	0.398395i
$867$	−57.3902	−	70.8538i	−0.0661940	−	0.0817229i
$868$	−4.62587			−0.00532935
$869$	690.442	−	75.8186i	0.794524	−	0.0872481i
$870$	−29.2843	−	76.2613i	−0.0336602	−	0.0876567i
$871$	−102.323	−	314.918i	−0.117478	−	0.361559i
$872$	−790.254	+	1087.69i	−0.906254	+	1.24735i
$873$	70.6950	−	332.983i	0.0809794	−	0.381423i
$874$	−142.889	+	439.766i	−0.163488	+	0.503165i
$875$	−580.944	−	188.760i	−0.663936	−	0.215726i
$876$	−0.332928	+	0.512798i	−0.000380055	+	0.000585386i
$877$	1167.54	+	848.264i	1.33128	+	0.967234i	0.999717	+	0.0238017i	$0.00757702\pi$
$877$	1167.54	+	848.264i	1.33128	+	0.967234i	0.331566	+	0.943432i	$0.392423\pi$
$878$	197.883	−	64.2961i	0.225379	−	0.0732302i
$879$	5.94670	+	15.4862i	0.00676531	+	0.0176180i
$880$	651.927	+	717.297i	0.740826	+	0.815110i
$881$			162.080i			0.183973i	0.995760	+	0.0919866i	$0.0293217\pi$
$881$			162.080i			0.183973i	−0.995760	+	0.0919866i	$0.970678\pi$
$882$	159.952	−	277.197i	0.181351	−	0.314282i
$883$	70.4786	+	51.2057i	0.0798172	+	0.0579906i	0.626978	−	0.779037i	$-0.284291\pi$
$883$	70.4786	+	51.2057i	0.0798172	+	0.0579906i	−0.547161	+	0.837027i	$0.684291\pi$
$884$	1.71547	+	2.36115i	0.00194058	+	0.00267098i
$885$	−77.7005	−	1479.26i	−0.0877972	−	1.67148i
$886$	171.411	−	527.550i	0.193467	−	0.595429i
$887$	479.767	+	660.342i	0.540887	+	0.744467i	0.988741	−	0.149640i	$-0.0478114\pi$
$887$	479.767	+	660.342i	0.540887	+	0.744467i	−0.447853	+	0.894107i	$0.647811\pi$
$888$	−243.685	+	909.877i	−0.274420	+	1.02464i
$889$	−117.980	−	363.106i	−0.132711	−	0.408443i
$890$			375.137i			0.421503i
$891$	−845.968	+	279.676i	−0.949459	+	0.313890i
$892$	−0.752410			−0.000843509
$893$	1025.42	−	333.178i	1.14828	−	0.373099i
$894$	374.319	+	100.251i	0.418701	+	0.112137i
$895$	−214.298	+	155.697i	−0.239440	+	0.173963i
$896$	−684.860	−	222.525i	−0.764353	−	0.248353i
$897$	−359.944	+	18.9067i	−0.401276	+	0.0210777i
$898$	−807.272	+	586.517i	−0.898967	+	0.653137i
$899$	−71.6867	+	98.6683i	−0.0797405	+	0.109753i
$900$	0.665338	+	0.383923i	0.000739264	+	0.000426581i
$901$	770.548			0.855214
$902$	−1082.07	−	618.035i	−1.19963	−	0.685183i
$903$	−687.470	+	263.989i	−0.761318	+	0.292346i
$904$	114.268	+	351.681i	0.126403	+	0.389027i
$905$	−0.214589	+	0.295357i	−0.000237115	+	0.000326361i
$906$	−225.092	−	146.138i	−0.248446	−	0.161301i
$907$	172.604	−	531.221i	0.190302	−	0.585691i	−0.809697	−	0.586848i	$-0.800368\pi$
$907$	172.604	−	531.221i	0.190302	−	0.585691i	0.999999	+	0.00115761i	$0.000368480\pi$
$908$	−3.58847	−	1.16596i	−0.00395206	−	0.00128410i
$909$	−412.939	−	87.6704i	−0.454278	−	0.0964471i
$910$	483.088	+	350.984i	0.530865	+	0.385696i
$911$	1547.41	−	502.785i	1.69859	−	0.551904i	0.710217	−	0.703982i	$-0.248597\pi$
$911$	1547.41	−	502.785i	1.69859	−	0.551904i	0.988368	+	0.152078i	$0.0485966\pi$
$912$	−839.600	+	322.407i	−0.920614	+	0.353516i
$913$	−52.9274	+	92.6662i	−0.0579709	+	0.101496i
$914$			1625.64i			1.77860i
$915$	−394.675	+	319.679i	−0.431339	+	0.349376i
$916$	−1.41544	−	1.02838i	−0.00154524	−	0.00112268i
$917$	533.259	+	733.969i	0.581526	+	0.800402i
$918$	−684.080	−	683.593i	−0.745185	−	0.744655i
$919$	17.7957	−	54.7694i	0.0193642	−	0.0595967i	−0.940908	−	0.338664i	$-0.890025\pi$
$919$	17.7957	−	54.7694i	0.0193642	−	0.0595967i	0.960272	+	0.279067i	$0.0900251\pi$
$920$	−318.205	−	437.972i	−0.345875	−	0.476057i
$921$	−635.377	−	170.168i	−0.689877	−	0.184764i
$922$	−489.307	−	1505.93i	−0.530701	−	1.63333i
$923$		−	365.315i		−	0.395791i
$924$	2.20302	+	2.18209i	0.00238422	+	0.00236157i
$925$	199.739			0.215934
$926$	−1030.02	+	334.675i	−1.11234	+	0.361420i
$927$	−937.981	+	98.8108i	−1.01185	+	0.106592i
$928$	0.538935	−	0.391560i	0.000580749	−	0.000421939i
$929$	−20.4483	−	6.64405i	−0.0220111	−	0.00715183i	0.297991	−	0.954569i	$-0.403684\pi$
$929$	−20.4483	−	6.64405i	−0.0220111	−	0.00715183i	−0.320002	+	0.947417i	$0.603684\pi$
$930$	−85.1548	−	1621.17i	−0.0915643	−	1.74319i
$931$	267.830	−	194.590i	0.287679	−	0.209011i
$932$	−0.607824	+	0.836598i	−0.000652172	+	0.000897637i
$933$	−331.383	+	268.413i	−0.355180	+	0.287689i
$934$	556.899			0.596251
$935$	−797.863	+	725.151i	−0.853330	+	0.775563i
$936$	−467.264	−	518.702i	−0.499214	−	0.554169i
$937$	−70.7518	−	217.752i	−0.0755089	−	0.232393i	0.906177	−	0.422898i	$-0.138987\pi$
$937$	−70.7518	−	217.752i	−0.0755089	−	0.232393i	−0.981686	+	0.190506i	$0.938987\pi$
$938$	224.442	−	308.918i	0.239277	−	0.329337i
$939$	−154.027	+	237.242i	−0.164033	+	0.252654i
$940$	1.64587	−	5.06548i	0.00175093	−	0.00538881i
$941$	−820.918	−	266.732i	−0.872389	−	0.283456i	−0.161596	−	0.986857i	$-0.551664\pi$
$941$	−820.918	−	266.732i	−0.872389	−	0.283456i	−0.710794	+	0.703401i	$0.751664\pi$
$942$	711.392	+	461.864i	0.755193	+	0.490301i
$943$	565.427	+	410.807i	0.599604	+	0.435638i
$944$	1375.73	−	447.001i	1.45734	−	0.473518i
$945$	−737.782	−	375.588i	−0.780722	−	0.397448i
$946$	105.658	+	962.174i	0.111689	+	1.01710i
$947$			1155.70i			1.22038i	0.792253	+	0.610192i	$0.208908\pi$
$947$			1155.70i			1.22038i	−0.792253	+	0.610192i	$0.791092\pi$
$948$	2.00389	+	2.47399i	0.00211380	+	0.00260970i
$949$	−95.3238	−	69.2568i	−0.100447	−	0.0729787i
$950$	111.629	+	153.644i	0.117504	+	0.161730i
$951$	−1501.57	+	78.8728i	−1.57894	+	0.0829367i
$952$	246.487	−	758.610i	0.258915	−	0.796859i
$953$	−1056.31	−	1453.89i	−1.10841	−	1.52559i	−0.823739	−	0.566969i	$-0.808116\pi$
$953$	−1056.31	−	1453.89i	−1.10841	−	1.52559i	−0.284670	−	0.958626i	$-0.591884\pi$
$954$	773.434	−	81.4767i	0.810727	−	0.0854053i
$955$	334.570	+	1029.70i	0.350335	+	1.07822i
$956$			2.50855i			0.00262401i
$957$	80.6832	−	13.1740i	0.0843085	−	0.0137659i
$958$	942.426			0.983743
$959$	−281.105	+	91.3366i	−0.293123	+	0.0952415i
$960$	271.262	−	1012.84i	0.282564	−	1.05505i
$961$	−1183.33	+	859.740i	−1.23135	+	0.894630i
$962$	728.453	+	236.689i	0.757228	+	0.246038i
$963$	383.349	−	170.787i	0.398077	−	0.177349i
$964$	4.87964	−	3.54526i	0.00506186	−	0.00367766i
$965$	−4.91173	+	6.76042i	−0.00508988	+	0.00700562i
$966$	−261.615	−	322.990i	−0.270823	−	0.334358i
$967$	−1767.36			−1.82767			−0.913835	−	0.406085i	$-0.866894\pi$
$967$	−1767.36			−1.82767			−0.913835	+	0.406085i	$0.866894\pi$
$968$	−832.011	+	490.743i	−0.859515	+	0.506966i
$969$	−358.619	−	933.904i	−0.370092	−	0.963781i
$970$	−128.470	−	395.391i	−0.132444	−	0.407620i
$971$	299.023	−	411.570i	0.307954	−	0.423862i	−0.626788	−	0.779190i	$-0.715631\pi$
$971$	299.023	−	411.570i	0.307954	−	0.423862i	0.934742	+	0.355328i	$0.115631\pi$
$972$	−3.17539	−	2.56826i	−0.00326686	−	0.00264224i
$973$	−149.505	+	460.128i	−0.153653	+	0.472896i
$974$	484.530	+	157.433i	0.497464	+	0.161636i
$975$	−80.6128	+	124.165i	−0.0826798	+	0.127349i
$976$	−401.255	−	291.529i	−0.411122	−	0.298698i
$977$	1345.28	−	437.107i	1.37695	−	0.447397i	0.475281	−	0.879834i	$-0.342346\pi$
$977$	1345.28	−	437.107i	1.37695	−	0.447397i	0.901664	+	0.432437i	$0.142346\pi$
$978$	260.726	+	678.972i	0.266590	+	0.694246i
$979$	−367.573	−	76.3440i	−0.375458	−	0.0779816i
$980$		−	1.63539i		−	0.00166877i
$981$	−1312.83	−	757.548i	−1.33826	−	0.772220i
$982$	−199.636	−	145.044i	−0.203295	−	0.147703i
$983$	−0.659524	−	0.907756i	−0.000670929	−	0.000923455i	0.808681	−	0.588247i	$-0.200182\pi$
$983$	−0.659524	−	0.907756i	−0.000670929	−	0.000923455i	−0.809352	+	0.587323i	$0.800182\pi$
$984$	71.0076	+	1351.84i	0.0721622	+	1.37382i
$985$	365.154	−	1123.83i	0.370715	−	1.14094i
$986$	52.1561	+	71.7867i	0.0528966	+	0.0728060i
$987$	−250.732	+	936.189i	−0.254034	+	0.948520i
$988$	0.941609	+	2.89797i	0.000953045	+	0.00293317i
$989$		−	542.891i		−	0.548929i
$990$	−724.175	+	812.232i	−0.731490	+	0.820436i
$991$	−1431.64			−1.44464			−0.722320	−	0.691559i	$-0.756924\pi$
$991$	−1431.64			−1.44464			−0.722320	+	0.691559i	$0.756924\pi$
$992$	12.5904	−	4.09087i	0.0126919	−	0.00412386i
$993$	1893.73	+	507.181i	1.90707	+	0.510757i
$994$	340.816	−	247.617i	0.342873	−	0.249112i
$995$	556.348	+	180.768i	0.559144	+	0.181677i
$996$	−0.488472	+	0.0256578i	−0.000490434	+	2.57609e-5i
$997$	943.609	−	685.572i	0.946448	−	0.687635i	−0.00351594	−	0.999994i	$-0.501119\pi$
$997$	943.609	−	685.572i	0.946448	−	0.687635i	0.949964	+	0.312359i	$0.101119\pi$
$998$	76.9591	−	105.925i	0.0771133	−	0.106137i
$999$	−1048.91	−	165.749i	−1.04996	−	0.165915i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.3.h.b.5.2	✓	16
3.2	odd	2	inner	33.3.h.b.5.3	yes	16
11.2	odd	10		363.3.h.j.251.2		16
11.3	even	5		363.3.b.m.122.6		8
11.4	even	5		363.3.h.o.245.2		16
11.5	even	5		363.3.h.o.323.3		16
11.6	odd	10		363.3.h.n.323.2		16
11.7	odd	10		363.3.h.n.245.3		16
11.8	odd	10		363.3.b.l.122.3		8
11.9	even	5	inner	33.3.h.b.20.3	yes	16
11.10	odd	2		363.3.h.j.269.3		16
33.2	even	10		363.3.h.j.251.3		16
33.5	odd	10		363.3.h.o.323.2		16
33.8	even	10		363.3.b.l.122.6		8
33.14	odd	10		363.3.b.m.122.3		8
33.17	even	10		363.3.h.n.323.3		16
33.20	odd	10	inner	33.3.h.b.20.2	yes	16
33.26	odd	10		363.3.h.o.245.3		16
33.29	even	10		363.3.h.n.245.2		16
33.32	even	2		363.3.h.j.269.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.5.2	✓	16	1.1	even	1	trivial
33.3.h.b.5.3	yes	16	3.2	odd	2	inner
33.3.h.b.20.2	yes	16	33.20	odd	10	inner
33.3.h.b.20.3	yes	16	11.9	even	5	inner
363.3.b.l.122.3		8	11.8	odd	10
363.3.b.l.122.6		8	33.8	even	10
363.3.b.m.122.3		8	33.14	odd	10
363.3.b.m.122.6		8	11.3	even	5
363.3.h.j.251.2		16	11.2	odd	10
363.3.h.j.251.3		16	33.2	even	10
363.3.h.j.269.2		16	33.32	even	2
363.3.h.j.269.3		16	11.10	odd	2
363.3.h.n.245.2		16	33.29	even	10
363.3.h.n.245.3		16	11.7	odd	10
363.3.h.n.323.2		16	11.6	odd	10
363.3.h.n.323.3		16	33.17	even	10
363.3.h.o.245.2		16	11.4	even	5
363.3.h.o.245.3		16	33.26	odd	10
363.3.h.o.323.2		16	33.5	odd	10
363.3.h.o.323.3		16	11.5	even	5

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	33.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.90610 + 0.619331i) q^{2} +(-2.89787 - 0.776113i) q^{3} +(0.0135968 - 0.00987866i) q^{4} +(-5.21596 - 1.69477i) q^{5} +(6.00431 - 0.315387i) q^{6} +(-4.52308 + 3.28621i) q^{7} +(4.69235 - 6.45847i) q^{8} +(7.79530 + 4.49815i) q^{9} +O(q^{10})\)	\(q+(-1.90610 + 0.619331i) q^{2} +(-2.89787 - 0.776113i) q^{3} +(0.0135968 - 0.00987866i) q^{4} +(-5.21596 - 1.69477i) q^{5} +(6.00431 - 0.315387i) q^{6} +(-4.52308 + 3.28621i) q^{7} +(4.69235 - 6.45847i) q^{8} +(7.79530 + 4.49815i) q^{9} +10.9918 q^{10} +(-2.23693 + 10.7702i) q^{11} +(-0.0470687 + 0.0180744i) q^{12} +(-3.00265 - 9.24122i) q^{13} +(6.58622 - 9.06515i) q^{14} +(13.7998 + 8.95939i) q^{15} +(-4.96496 + 15.2806i) q^{16} +(-16.9969 - 5.52262i) q^{17} +(-17.6445 - 3.74608i) q^{18} +(-15.0954 - 10.9674i) q^{19} +(-0.0876624 + 0.0284832i) q^{20} +(15.6578 - 6.01259i) q^{21} +(-2.40646 - 21.9144i) q^{22} +12.3649i q^{23} +(-18.6103 + 15.0740i) q^{24} +(4.10855 + 2.98503i) q^{25} +(11.4467 + 15.7551i) q^{26} +(-19.0987 - 19.0851i) q^{27} +(-0.0290361 + 0.0893640i) q^{28} +(1.45613 + 2.00420i) q^{29} +(-31.8528 - 8.53087i) q^{30} +(15.2132 + 46.8213i) q^{31} -0.268903i q^{32} +(14.8412 - 29.4744i) q^{33} +35.8182 q^{34} +(29.1616 - 9.47517i) q^{35} +(0.150427 - 0.0158466i) q^{36} +(31.8192 - 23.1180i) q^{37} +(35.5658 + 11.5560i) q^{38} +(1.52907 + 29.1102i) q^{39} +(-35.4207 + 25.7346i) q^{40} +(33.2237 - 45.7285i) q^{41} +(-26.1216 + 21.1580i) q^{42} -43.9060 q^{43} +(0.0759795 + 0.168537i) q^{44} +(-33.0366 - 36.6734i) q^{45} +(-7.65794 - 23.5687i) q^{46} +(-33.9646 + 46.7482i) q^{47} +(26.2473 - 40.4277i) q^{48} +(-5.48274 + 16.8741i) q^{49} +(-9.68004 - 3.14524i) q^{50} +(44.9686 + 29.1954i) q^{51} +(-0.132117 - 0.0959889i) q^{52} +(-41.0056 + 13.3235i) q^{53} +(48.2241 + 24.5498i) q^{54} +(29.9206 - 52.3856i) q^{55} +44.6323i q^{56} +(35.2324 + 43.4979i) q^{57} +(-4.01681 - 2.91838i) q^{58} +(-52.9190 - 72.8367i) q^{59} +(0.276140 - 0.0145048i) q^{60} +(-9.53920 + 29.3587i) q^{61} +(-57.9958 - 79.8244i) q^{62} +(-50.0407 + 5.27149i) q^{63} +(-19.6933 - 60.6097i) q^{64} +53.2906i q^{65} +(-10.0345 + 65.3729i) q^{66} +34.0775 q^{67} +(-0.285659 + 0.0928164i) q^{68} +(9.59653 - 35.8318i) q^{69} +(-49.7168 + 36.1213i) q^{70} +(35.7561 + 11.6179i) q^{71} +(65.6294 - 29.2388i) q^{72} +(9.81022 - 7.12754i) q^{73} +(-46.3331 + 63.7720i) q^{74} +(-9.58931 - 11.8389i) q^{75} -0.313592 q^{76} +(-25.2752 - 56.0653i) q^{77} +(-20.9434 - 54.5402i) q^{78} +(-19.5128 - 60.0542i) q^{79} +(51.7940 - 71.2884i) q^{80} +(40.5333 + 70.1288i) q^{81} +(-35.0068 + 107.740i) q^{82} +(9.22665 + 2.99792i) q^{83} +(0.153499 - 0.236430i) q^{84} +(79.2955 + 57.6115i) q^{85} +(83.6893 - 27.1923i) q^{86} +(-2.66420 - 6.93803i) q^{87} +(59.0622 + 64.9845i) q^{88} +34.1289i q^{89} +(85.6842 + 49.4427i) q^{90} +(43.9499 + 31.9315i) q^{91} +(0.122148 + 0.168123i) q^{92} +(-7.74713 - 147.489i) q^{93} +(35.7874 - 110.142i) q^{94} +(60.1495 + 82.7887i) q^{95} +(-0.208700 + 0.779247i) q^{96} +(-11.6879 - 35.9715i) q^{97} -35.5595i q^{98} +(-65.8833 + 73.8945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{3} + 8 q^{4} - 33 q^{6} + 6 q^{7} - 28 q^{9}+O(q^{10}) \) 16 * q - 10 * q^3 + 8 * q^4 - 33 * q^6 + 6 * q^7 - 28 * q^9	\( 16 q - 10 q^{3} + 8 q^{4} - 33 q^{6} + 6 q^{7} - 28 q^{9} - 12 q^{10} + 106 q^{12} - 42 q^{13} + 82 q^{15} - 88 q^{16} - 43 q^{18} - 134 q^{19} - 12 q^{21} + 78 q^{22} + 41 q^{24} + 134 q^{25} + 80 q^{27} + 264 q^{28} - 120 q^{30} + 124 q^{31} - 79 q^{33} - 132 q^{34} - 219 q^{36} + 90 q^{37} - 174 q^{39} - 284 q^{40} - 102 q^{42} - 156 q^{43} - 72 q^{45} - 22 q^{46} + 30 q^{48} - 30 q^{49} + 111 q^{51} + 326 q^{52} + 1046 q^{54} - 172 q^{55} + 281 q^{57} - 116 q^{58} + 54 q^{60} - 126 q^{61} - 138 q^{63} + 236 q^{64} - 236 q^{66} + 368 q^{67} + 198 q^{69} - 322 q^{70} - 562 q^{72} + 24 q^{73} - 21 q^{75} - 900 q^{76} - 492 q^{78} - 314 q^{79} - 388 q^{81} + 270 q^{84} + 318 q^{85} + 132 q^{87} + 1064 q^{88} + 176 q^{90} + 374 q^{91} - 10 q^{93} + 990 q^{94} - 332 q^{96} + 72 q^{97} - 530 q^{99}+O(q^{100}) \) 16 * q - 10 * q^3 + 8 * q^4 - 33 * q^6 + 6 * q^7 - 28 * q^9 - 12 * q^10 + 106 * q^12 - 42 * q^13 + 82 * q^15 - 88 * q^16 - 43 * q^18 - 134 * q^19 - 12 * q^21 + 78 * q^22 + 41 * q^24 + 134 * q^25 + 80 * q^27 + 264 * q^28 - 120 * q^30 + 124 * q^31 - 79 * q^33 - 132 * q^34 - 219 * q^36 + 90 * q^37 - 174 * q^39 - 284 * q^40 - 102 * q^42 - 156 * q^43 - 72 * q^45 - 22 * q^46 + 30 * q^48 - 30 * q^49 + 111 * q^51 + 326 * q^52 + 1046 * q^54 - 172 * q^55 + 281 * q^57 - 116 * q^58 + 54 * q^60 - 126 * q^61 - 138 * q^63 + 236 * q^64 - 236 * q^66 + 368 * q^67 + 198 * q^69 - 322 * q^70 - 562 * q^72 + 24 * q^73 - 21 * q^75 - 900 * q^76 - 492 * q^78 - 314 * q^79 - 388 * q^81 + 270 * q^84 + 318 * q^85 + 132 * q^87 + 1064 * q^88 + 176 * q^90 + 374 * q^91 - 10 * q^93 + 990 * q^94 - 332 * q^96 + 72 * q^97 - 530 * q^99

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