LMFDB - Embedded newform 33.3.h.b.14.3

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			14.3
Root			$0.974642 + 1.34148i$ of defining polynomial
Character	$\chi$	$=$	33.14
Dual form			33.3.h.b.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.974642 + 1.34148i) q^{2} +(-1.09751 + 2.79204i) q^{3} +(0.386428 - 1.18930i) q^{4} +(-0.410570 + 0.565101i) q^{5} +(-4.81514 + 1.24895i) q^{6} +(0.806259 - 2.48141i) q^{7} +(8.28007 - 2.69036i) q^{8} +(-6.59095 - 6.12857i) q^{9} +O(q^{10})$	\(q+(0.974642 + 1.34148i) q^{2} +(-1.09751 + 2.79204i) q^{3} +(0.386428 - 1.18930i) q^{4} +(-0.410570 + 0.565101i) q^{5} +(-4.81514 + 1.24895i) q^{6} +(0.806259 - 2.48141i) q^{7} +(8.28007 - 2.69036i) q^{8} +(-6.59095 - 6.12857i) q^{9} -1.15823 q^{10} +(4.26126 - 10.1411i) q^{11} +(2.89647 + 2.38419i) q^{12} +(-13.8479 + 10.0611i) q^{13} +(4.11458 - 1.33691i) q^{14} +(-1.12718 - 1.76653i) q^{15} +(7.63243 + 5.54529i) q^{16} +(-9.47072 + 13.0353i) q^{17} +(1.79754 - 14.8148i) q^{18} +(-4.92151 - 15.1469i) q^{19} +(0.513421 + 0.706663i) q^{20} +(6.04332 + 4.97448i) q^{21} +(17.7573 - 4.16754i) q^{22} +23.1295i q^{23} +(-1.57587 + 26.0710i) q^{24} +(7.57465 + 23.3124i) q^{25} +(-26.9935 - 8.77071i) q^{26} +(24.3448 - 11.6760i) q^{27} +(-2.63959 - 1.91777i) q^{28} +(-5.10329 - 1.65816i) q^{29} +(1.27117 - 3.23382i) q^{30} +(3.28671 - 2.38793i) q^{31} -19.1813i q^{32} +(23.6375 + 23.0275i) q^{33} -26.7172 q^{34} +(1.07122 + 1.47441i) q^{35} +(-9.83565 + 5.47038i) q^{36} +(19.6322 - 60.4217i) q^{37} +(15.5225 - 21.3649i) q^{38} +(-12.8927 - 49.7060i) q^{39} +(-1.87922 + 5.78366i) q^{40} +(-64.1371 + 20.8394i) q^{41} +(-0.783092 + 12.9553i) q^{42} -22.6622 q^{43} +(-10.4142 - 8.98672i) q^{44} +(6.16931 - 1.20834i) q^{45} +(-31.0277 + 22.5429i) q^{46} +(70.2078 - 22.8119i) q^{47} +(-23.8593 + 15.2240i) q^{48} +(34.1345 + 24.8002i) q^{49} +(-23.8905 + 32.8825i) q^{50} +(-26.0009 - 40.7490i) q^{51} +(6.61446 + 20.3572i) q^{52} +(25.1873 + 34.6673i) q^{53} +(39.3906 + 21.2782i) q^{54} +(3.98120 + 6.57167i) q^{55} -22.7154i q^{56} +(47.6920 + 2.88277i) q^{57} +(-2.74949 - 8.46207i) q^{58} +(27.3316 + 8.88056i) q^{59} +(-2.53651 + 0.657920i) q^{60} +(37.4585 + 27.2152i) q^{61} +(6.40673 + 2.08167i) q^{62} +(-20.5215 + 11.4136i) q^{63} +(56.2610 - 40.8760i) q^{64} -11.9562i q^{65} +(-7.85282 + 54.1529i) q^{66} -77.2821 q^{67} +(11.8432 + 16.3008i) q^{68} +(-64.5783 - 25.3848i) q^{69} +(-0.933834 + 2.87405i) q^{70} +(-24.2537 + 33.3824i) q^{71} +(-71.0615 - 33.0130i) q^{72} +(-17.5438 + 53.9942i) q^{73} +(100.189 - 32.5533i) q^{74} +(-73.4023 - 4.43685i) q^{75} -19.9160 q^{76} +(-21.7285 - 18.7503i) q^{77} +(54.1137 - 65.7409i) q^{78} +(41.1994 - 29.9331i) q^{79} +(-6.26730 + 2.03637i) q^{80} +(5.88115 + 80.7862i) q^{81} +(-90.4664 - 65.7277i) q^{82} +(34.8026 - 47.9017i) q^{83} +(8.25147 - 5.26505i) q^{84} +(-3.47788 - 10.7038i) q^{85} +(-22.0875 - 30.4009i) q^{86} +(10.2306 - 12.4287i) q^{87} +(8.00033 - 95.4332i) q^{88} -38.1909i q^{89} +(7.63383 + 7.09830i) q^{90} +(13.8007 + 42.4742i) q^{91} +(27.5079 + 8.93786i) q^{92} +(3.06001 + 11.7974i) q^{93} +(99.0291 + 71.9489i) q^{94} +(10.5801 + 3.43769i) q^{95} +(53.5549 + 21.0516i) q^{96} +(-13.1808 + 9.57644i) q^{97} +69.9620i q^{98} +(-90.2361 + 40.7240i) 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 $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	0.974642	+	1.34148i	0.487321	+	0.670740i	0.979891	−	0.199533i	$-0.0639425\pi$
$2$	0.974642	+	1.34148i	0.487321	+	0.670740i	−0.492570	+	0.870273i	$0.663943\pi$
$3$	−1.09751	+	2.79204i	−0.365836	+	0.930679i
$3$	−1.09751	+	2.79204i	−0.365836	+	0.930679i
$4$	0.386428	−	1.18930i	0.0966070	−	0.297326i
$5$	−0.410570	+	0.565101i	−0.0821140	+	0.113020i	−0.848098	−	0.529839i	$-0.822252\pi$
$5$	−0.410570	+	0.565101i	−0.0821140	+	0.113020i	0.765984	+	0.642860i	$0.222252\pi$
$6$	−4.81514	+	1.24895i	−0.802523	+	0.208158i
$7$	0.806259	−	2.48141i	0.115180	−	0.354487i	−0.876805	−	0.480847i	$-0.840329\pi$
$7$	0.806259	−	2.48141i	0.115180	−	0.354487i	0.991985	+	0.126360i	$0.0403293\pi$
$8$	8.28007	−	2.69036i	1.03501	−	0.336295i
$9$	−6.59095	−	6.12857i	−0.732327	−	0.680953i
$10$	−1.15823			−0.115823
$11$	4.26126	−	10.1411i	0.387387	−	0.921917i
$11$	4.26126	−	10.1411i	0.387387	−	0.921917i
$12$	2.89647	+	2.38419i	0.241372	+	0.198683i
$13$	−13.8479	+	10.0611i	−1.06522	+	0.773930i	−0.975048	−	0.221996i	$-0.928743\pi$
$13$	−13.8479	+	10.0611i	−1.06522	+	0.773930i	−0.0901753	+	0.995926i	$0.528743\pi$
$14$	4.11458	−	1.33691i	0.293898	−	0.0954933i
$15$	−1.12718	−	1.76653i	−0.0751453	−	0.117769i
$16$	7.63243	+	5.54529i	0.477027	+	0.346580i
$17$	−9.47072	+	13.0353i	−0.557101	+	0.766784i	−0.990954	−	0.134200i	$-0.957154\pi$
$17$	−9.47072	+	13.0353i	−0.557101	+	0.766784i	0.433853	+	0.900984i	$0.357154\pi$
$18$	1.79754	−	14.8148i	0.0998636	−	0.823043i
$19$	−4.92151	−	15.1469i	−0.259027	−	0.797203i	−0.993009	−	0.118035i	$-0.962341\pi$
$19$	−4.92151	−	15.1469i	−0.259027	−	0.797203i	0.733983	−	0.679168i	$-0.237659\pi$
$20$	0.513421	+	0.706663i	0.0256710	+	0.0353331i
$21$	6.04332	+	4.97448i	0.287777	+	0.236880i
$22$	17.7573	−	4.16754i	0.807148	−	0.189434i
$23$			23.1295i			1.00563i	0.864395	+	0.502814i	$0.167702\pi$
$23$			23.1295i			1.00563i	−0.864395	+	0.502814i	$0.832298\pi$
$24$	−1.57587	+	26.0710i	−0.0656614	+	1.08629i
$25$	7.57465	+	23.3124i	0.302986	+	0.932495i
$26$	−26.9935	−	8.77071i	−1.03821	−	0.337335i
$27$	24.3448	−	11.6760i	0.901661	−	0.432444i
$28$	−2.63959	−	1.91777i	−0.0942710	−	0.0684919i
$29$	−5.10329	−	1.65816i	−0.175976	−	0.0571779i	0.219704	−	0.975567i	$-0.429491\pi$
$29$	−5.10329	−	1.65816i	−0.175976	−	0.0571779i	−0.395679	+	0.918389i	$0.629491\pi$
$30$	1.27117	−	3.23382i	0.0423723	−	0.107794i
$31$	3.28671	−	2.38793i	0.106023	−	0.0770301i	−0.533511	−	0.845793i	$-0.679128\pi$
$31$	3.28671	−	2.38793i	0.106023	−	0.0770301i	0.639533	+	0.768763i	$0.279128\pi$
$32$		−	19.1813i		−	0.599415i
$33$	23.6375	+	23.0275i	0.716289	+	0.697804i
$34$	−26.7172			−0.785799
$35$	1.07122	+	1.47441i	0.0306064	+	0.0421260i
$36$	−9.83565	+	5.47038i	−0.273213	+	0.151955i
$37$	19.6322	−	60.4217i	0.530600	−	1.63302i	−0.222368	−	0.974963i	$-0.571379\pi$
$37$	19.6322	−	60.4217i	0.530600	−	1.63302i	0.752968	−	0.658057i	$-0.228621\pi$
$38$	15.5225	−	21.3649i	0.408486	−	0.562233i
$39$	−12.8927	−	49.7060i	−0.330583	−	1.27451i
$40$	−1.87922	+	5.78366i	−0.0469806	+	0.144591i
$41$	−64.1371	+	20.8394i	−1.56432	+	0.508278i	−0.957958	−	0.286910i	$-0.907372\pi$
$41$	−64.1371	+	20.8394i	−1.56432	+	0.508278i	−0.606362	+	0.795188i	$0.707372\pi$
$42$	−0.783092	+	12.9553i	−0.0186450	+	0.308460i
$43$	−22.6622			−0.527028			−0.263514	−	0.964656i	$-0.584882\pi$
$43$	−22.6622			−0.527028			−0.263514	+	0.964656i	$0.584882\pi$
$44$	−10.4142	−	8.98672i	−0.236685	−	0.204244i
$45$	6.16931	−	1.20834i	0.137096	−	0.0268521i
$46$	−31.0277	+	22.5429i	−0.674515	+	0.490064i
$47$	70.2078	−	22.8119i	1.49378	−	0.485360i	0.555585	−	0.831460i	$-0.312494\pi$
$47$	70.2078	−	22.8119i	1.49378	−	0.485360i	0.938198	+	0.346100i	$0.112494\pi$
$48$	−23.8593	+	15.2240i	−0.497069	+	0.317167i
$49$	34.1345	+	24.8002i	0.696622	+	0.506126i
$50$	−23.8905	+	32.8825i	−0.477810	+	0.657649i
$51$	−26.0009	−	40.7490i	−0.509822	−	0.799000i
$52$	6.61446	+	20.3572i	0.127201	+	0.391485i
$53$	25.1873	+	34.6673i	0.475232	+	0.654100i	0.977580	−	0.210565i	$-0.0675304\pi$
$53$	25.1873	+	34.6673i	0.475232	+	0.654100i	−0.502348	+	0.864666i	$0.667530\pi$
$54$	39.3906	+	21.2782i	0.729456	+	0.394040i
$55$	3.98120	+	6.57167i	0.0723854	+	0.119485i
$56$		−	22.7154i		−	0.405632i
$57$	47.6920	+	2.88277i	0.836702	+	0.0505749i
$58$	−2.74949	−	8.46207i	−0.0474051	−	0.145898i
$59$	27.3316	+	8.88056i	0.463247	+	0.150518i	0.531336	−	0.847161i	$-0.321690\pi$
$59$	27.3316	+	8.88056i	0.463247	+	0.150518i	−0.0680891	+	0.997679i	$0.521690\pi$
$60$	−2.53651	+	0.657920i	−0.0422752	+	0.0109653i
$61$	37.4585	+	27.2152i	0.614074	+	0.446151i	0.850847	−	0.525414i	$-0.176090\pi$
$61$	37.4585	+	27.2152i	0.614074	+	0.446151i	−0.236772	+	0.971565i	$0.576090\pi$
$62$	6.40673	+	2.08167i	0.103334	+	0.0335753i
$63$	−20.5215	+	11.4136i	−0.325739	+	0.181169i
$64$	56.2610	−	40.8760i	0.879079	−	0.638688i
$65$		−	11.9562i		−	0.183942i
$66$	−7.85282	+	54.1529i	−0.118982	+	0.820498i
$67$	−77.2821			−1.15346			−0.576732	−	0.816933i	$-0.695672\pi$
$67$	−77.2821			−1.15346			−0.576732	+	0.816933i	$0.695672\pi$
$68$	11.8432	+	16.3008i	0.174165	+	0.239717i
$69$	−64.5783	−	25.3848i	−0.935917	−	0.367896i
$70$	−0.933834	+	2.87405i	−0.0133405	+	0.0410578i
$71$	−24.2537	+	33.3824i	−0.341601	+	0.470174i	−0.944908	−	0.327335i	$-0.893849\pi$
$71$	−24.2537	+	33.3824i	−0.341601	+	0.470174i	0.603307	+	0.797509i	$0.293849\pi$
$72$	−71.0615	−	33.0130i	−0.986966	−	0.458514i
$73$	−17.5438	+	53.9942i	−0.240326	+	0.739647i	0.756044	+	0.654521i	$0.227129\pi$
$73$	−17.5438	+	53.9942i	−0.240326	+	0.739647i	−0.996370	+	0.0851266i	$0.972871\pi$
$74$	100.189	−	32.5533i	1.35390	−	0.439910i
$75$	−73.4023	−	4.43685i	−0.978697	−	0.0591579i
$76$	−19.9160			−0.262053
$77$	−21.7285	−	18.7503i	−0.282189	−	0.243510i
$78$	54.1137	−	65.7409i	0.693766	−	0.842831i
$79$	41.1994	−	29.9331i	0.521512	−	0.378901i	−0.295661	−	0.955293i	$-0.595540\pi$
$79$	41.1994	−	29.9331i	0.521512	−	0.378901i	0.817173	+	0.576392i	$0.195540\pi$
$80$	−6.26730	+	2.03637i	−0.0783412	+	0.0254546i
$81$	5.88115	+	80.7862i	0.0726068	+	0.997361i
$82$	−90.4664	−	65.7277i	−1.10325	−	0.801557i
$83$	34.8026	−	47.9017i	0.419309	−	0.577129i	−0.546149	−	0.837688i	$-0.683907\pi$
$83$	34.8026	−	47.9017i	0.419309	−	0.577129i	0.965458	+	0.260559i	$0.0839068\pi$
$84$	8.25147	−	5.26505i	0.0982317	−	0.0626792i
$85$	−3.47788	−	10.7038i	−0.0409163	−	0.125927i
$86$	−22.0875	−	30.4009i	−0.256832	−	0.353499i
$87$	10.2306	−	12.4287i	0.117593	−	0.142859i
$88$	8.00033	−	95.4332i	0.0909128	−	1.08447i
$89$		−	38.1909i		−	0.429112i	−0.976712	−	0.214556i	$-0.931170\pi$
$89$		−	38.1909i		−	0.429112i	0.976712	−	0.214556i	$-0.0688304\pi$
$90$	7.63383	+	7.09830i	0.0848204	+	0.0788700i
$91$	13.8007	+	42.4742i	0.151656	+	0.466749i
$92$	27.5079	+	8.93786i	0.298999	+	0.0971507i
$93$	3.06001	+	11.7974i	0.0329033	+	0.126854i
$94$	99.0291	+	71.9489i	1.05350	+	0.765414i
$95$	10.5801	+	3.43769i	0.111370	+	0.0361862i
$96$	53.5549	+	21.0516i	0.557863	+	0.219288i
$97$	−13.1808	+	9.57644i	−0.135885	+	0.0987262i	−0.653651	−	0.756796i	$-0.726764\pi$
$97$	−13.1808	+	9.57644i	−0.135885	+	0.0987262i	0.517766	+	0.855522i	$0.326764\pi$
$98$			69.9620i			0.713898i
$99$	−90.2361	+	40.7240i	−0.911476	+	0.411353i
$100$	30.6525			0.306525
$101$	−61.2440	−	84.2951i	−0.606376	−	0.834605i	0.389897	−	0.920858i	$-0.372510\pi$
$101$	−61.2440	−	84.2951i	−0.606376	−	0.834605i	−0.996273	+	0.0862537i	$0.972510\pi$
$102$	29.3224	−	74.5954i	0.287474	−	0.731327i
$103$	16.8125	−	51.7437i	0.163229	−	0.502366i	−0.835673	−	0.549227i	$-0.814922\pi$
$103$	16.8125	−	51.7437i	0.163229	−	0.502366i	0.998901	+	0.0468618i	$0.0149220\pi$
$104$	−87.5936	+	120.562i	−0.842246	+	1.15925i
$105$	−5.29229	+	1.37271i	−0.0504027	+	0.0130735i
$106$	−21.9569	+	67.5764i	−0.207141	+	0.637514i
$107$	−27.0164	+	8.77818i	−0.252490	+	0.0820390i	−0.432527	−	0.901621i	$-0.642378\pi$
$107$	−27.0164	+	8.77818i	−0.252490	+	0.0820390i	0.180037	+	0.983660i	$0.442378\pi$
$108$	−4.47878	−	33.4653i	−0.0414702	−	0.309864i
$109$	−41.2540			−0.378477			−0.189238	−	0.981931i	$-0.560602\pi$
$109$	−41.2540			−0.378477			−0.189238	+	0.981931i	$0.560602\pi$
$110$	−4.93551	+	11.7457i	−0.0448683	+	0.106779i
$111$	147.153	+	121.127i	1.32570	+	1.09124i
$112$	19.9139	−	14.4683i	0.177802	−	0.129181i
$113$	−138.072	+	44.8625i	−1.22188	+	0.397013i	−0.847766	−	0.530370i	$-0.822053\pi$
$113$	−138.072	+	44.8625i	−1.22188	+	0.397013i	−0.374114	+	0.927383i	$0.622053\pi$
$114$	42.6154	+	66.7875i	0.373820	+	0.585855i
$115$	−13.0705	−	9.49626i	−0.113656	−	0.0825762i
$116$	−3.94411	+	5.42860i	−0.0340009	+	0.0467983i
$117$	152.931	+	18.5558i	1.30710	+	0.158596i
$118$	14.7254	+	45.3201i	0.124791	+	0.384069i
$119$	24.7101	+	34.0106i	0.207648	+	0.285803i
$120$	−14.0857	−	11.5945i	−0.117381	−	0.0966207i
$121$	−84.6834	−	86.4275i	−0.699863	−	0.714277i
$122$			76.7749i			0.629303i
$123$	12.2067	−	201.945i	0.0992412	−	1.64183i
$124$	−1.56990	−	4.83165i	−0.0126605	−	0.0389650i
$125$	−32.8917	−	10.6872i	−0.263134	−	0.0854973i
$126$	−35.3123	−	16.4050i	−0.280256	−	0.130198i
$127$	147.873	+	107.436i	1.16436	+	0.845955i	0.990323	−	0.138785i	$-0.0443197\pi$
$127$	147.873	+	107.436i	1.16436	+	0.845955i	0.174034	+	0.984740i	$0.444320\pi$
$128$	36.6987	+	11.9241i	0.286709	+	0.0931574i
$129$	24.8720	−	63.2737i	0.192806	−	0.490494i
$130$	16.0391	−	11.6531i	0.123377	−	0.0896389i
$131$		−	84.5109i		−	0.645121i	−0.946549	−	0.322561i	$-0.895456\pi$
$131$		−	84.5109i		−	0.645121i	0.946549	−	0.322561i	$-0.104544\pi$
$132$	36.5209	−	19.2137i	0.276673	−	0.145558i
$133$	−41.5536			−0.312433
$134$	−75.3223	−	103.672i	−0.562107	−	0.773674i
$135$	−3.39714	+	18.5511i	−0.0251640	+	0.137416i
$136$	−43.3485	+	133.413i	−0.318739	+	0.980978i
$137$	120.127	−	165.341i	0.876841	−	1.20687i	−0.100445	−	0.994943i	$-0.532027\pi$
$137$	120.127	−	165.341i	0.876841	−	1.20687i	0.977286	−	0.211925i	$-0.0679733\pi$
$138$	−28.8875	−	111.372i	−0.209330	−	0.807040i
$139$	−15.5254	+	47.7824i	−0.111694	+	0.343758i	−0.991243	−	0.132050i	$-0.957844\pi$
$139$	−15.5254	+	47.7824i	−0.111694	+	0.343758i	0.879549	+	0.475808i	$0.157844\pi$
$140$	2.16747	−	0.704254i	0.0154819	−	0.00503039i
$141$	−13.3620	+	221.059i	−0.0947663	+	1.56779i
$142$	−68.4204			−0.481834
$143$	43.0210	+	183.306i	0.300846	+	1.28186i
$144$	−16.3203	−	83.3246i	−0.113335	−	0.578643i
$145$	3.03229	−	2.20308i	0.0209123	−	0.0151937i
$146$	−89.5311	+	29.0904i	−0.613227	+	0.199249i
$147$	−106.706	+	68.0864i	−0.725890	+	0.463172i
$148$	−64.2733	−	46.6973i	−0.434279	−	0.315522i
$149$	92.5187	−	127.341i	0.620931	−	0.854638i	−0.376490	−	0.926421i	$-0.622869\pi$
$149$	92.5187	−	127.341i	0.620931	−	0.854638i	0.997420	+	0.0717830i	$0.0228689\pi$
$150$	−65.5890	−	102.792i	−0.437260	−	0.685280i
$151$	−52.9598	−	162.993i	−0.350727	−	1.07943i	−0.958446	−	0.285274i	$-0.907915\pi$
$151$	−52.9598	−	162.993i	−0.350727	−	1.07943i	0.607719	−	0.794152i	$-0.292085\pi$
$152$	−81.5009	−	112.176i	−0.536190	−	0.738002i
$153$	142.309	−	27.8731i	0.930124	−	0.182177i
$154$	3.97557	−	47.4232i	0.0258154	−	0.307943i
$155$			2.83774i			0.0183080i
$156$	−64.0976	−	3.87442i	−0.410882	−	0.0248360i
$157$	−20.1905	−	62.1401i	−0.128602	−	0.395797i	0.865938	−	0.500151i	$-0.166722\pi$
$157$	−20.1905	−	62.1401i	−0.128602	−	0.395797i	−0.994540	+	0.104355i	$0.966722\pi$
$158$	80.3094	+	26.0941i	0.508287	+	0.165153i
$159$	−124.436	+	32.2761i	−0.782615	+	0.202995i
$160$	10.8394	+	7.87526i	0.0677461	+	0.0492204i
$161$	57.3937	+	18.6483i	0.356483	+	0.115828i
$162$	−102.641	+	86.6271i	−0.633587	+	0.534735i
$163$	12.4900	−	9.07449i	0.0766256	−	0.0556717i	−0.548813	−	0.835945i	$-0.684920\pi$
$163$	12.4900	−	9.07449i	0.0766256	−	0.0556717i	0.625439	+	0.780273i	$0.284920\pi$
$164$			84.3314i			0.514216i
$165$	−22.7177	+	3.90319i	−0.137683	+	0.0236557i
$166$	98.1792			0.591441
$167$	90.5798	+	124.672i	0.542394	+	0.746542i	0.988956	−	0.148211i	$-0.0473516\pi$
$167$	90.5798	+	124.672i	0.542394	+	0.746542i	−0.446561	+	0.894753i	$0.647352\pi$
$168$	63.4222	+	24.9303i	0.377513	+	0.148395i
$169$	38.3149	−	117.921i	0.226715	−	0.697758i
$170$	10.9693	−	15.0979i	0.0645251	−	0.0888112i
$171$	−60.3912	+	129.994i	−0.353165	+	0.760199i
$172$	−8.75731	+	26.9522i	−0.0509146	+	0.156699i
$173$	−23.8744	+	7.75725i	−0.138002	+	0.0448396i	−0.377204	−	0.926130i	$-0.623114\pi$
$173$	−23.8744	+	7.75725i	−0.138002	+	0.0448396i	0.239202	+	0.970970i	$0.423114\pi$
$174$	26.6440	+	1.61051i	0.153127	+	0.00925582i
$175$	63.9548			0.365456
$176$	88.7590	−	53.7713i	0.504312	−	0.305519i
$177$	−54.7915	+	66.5642i	−0.309556	+	0.376069i
$178$	51.2323	−	37.2225i	0.287822	−	0.209115i
$179$	58.7800	−	19.0988i	0.328380	−	0.106697i	−0.140187	−	0.990125i	$-0.544770\pi$
$179$	58.7800	−	19.0988i	0.328380	−	0.106697i	0.468567	+	0.883428i	$0.344770\pi$
$180$	0.946908	−	7.80411i	0.00526060	−	0.0433562i
$181$	120.062	+	87.2301i	0.663325	+	0.481934i	0.867784	−	0.496941i	$-0.165544\pi$
$181$	120.062	+	87.2301i	0.663325	+	0.481934i	−0.204459	+	0.978875i	$0.565544\pi$
$182$	−43.5275	+	59.9104i	−0.239162	+	0.329178i
$183$	−117.097	+	74.7167i	−0.639874	+	0.408288i
$184$	62.2265	+	191.513i	0.338187	+	1.04083i
$185$	26.0840	+	35.9015i	0.140995	+	0.194062i
$186$	−12.8435	+	15.6032i	−0.0690513	+	0.0838880i
$187$	91.8353	+	151.590i	0.491098	+	0.810643i
$188$		−	92.3135i		−	0.491029i
$189$	−9.34471	−	69.8234i	−0.0494429	−	0.369436i
$190$	5.70024	+	17.5435i	0.0300013	+	0.0923344i
$191$	53.4521	+	17.3676i	0.279854	+	0.0909301i	0.445581	−	0.895242i	$-0.352997\pi$
$191$	53.4521	+	17.3676i	0.279854	+	0.0909301i	−0.165727	+	0.986172i	$0.552997\pi$
$192$	52.3804	+	201.945i	0.272815	+	1.05180i
$193$	−122.139	−	88.7392i	−0.632844	−	0.459788i	0.224540	−	0.974465i	$-0.427912\pi$
$193$	−122.139	−	88.7392i	−0.632844	−	0.459788i	−0.857384	+	0.514676i	$0.827912\pi$
$194$	−25.6932	−	8.34822i	−0.132439	−	0.0430321i
$195$	33.3823	+	13.1221i	0.171191	+	0.0672928i
$196$	42.6854	−	31.0128i	0.217783	−	0.158228i
$197$			22.3374i			0.113388i	0.998392	+	0.0566938i	$0.0180559\pi$
$197$			22.3374i			0.113388i	−0.998392	+	0.0566938i	$0.981944\pi$
$198$	−142.578	−	81.3586i	−0.720092	−	0.410902i
$199$	−150.930			−0.758444			−0.379222	−	0.925306i	$-0.623808\pi$
$199$	−150.930			−0.758444			−0.379222	+	0.925306i	$0.623808\pi$
$200$	125.437	+	172.650i	0.627186	+	0.863248i
$201$	84.8178	−	215.774i	0.421979	−	1.07350i
$202$	53.3892	−	164.315i	0.264303	−	0.813441i
$203$	−8.22915	+	11.3265i	−0.0405377	+	0.0557954i
$204$	−58.5104	+	15.1764i	−0.286815	+	0.0743942i
$205$	14.5564	−	44.8000i	0.0710068	−	0.218537i
$206$	85.7993	−	27.8779i	0.416501	−	0.135329i
$207$	141.751	−	152.445i	0.684785	−	0.736449i
$208$	−161.485			−0.776369
$209$	−174.577	−	14.6351i	−0.835299	−	0.0700245i
$210$	−6.99955	−	5.76159i	−0.0333312	−	0.0274362i
$211$	−146.900	+	106.729i	−0.696207	+	0.505824i	−0.878695	−	0.477384i	$-0.841585\pi$
$211$	−146.900	+	106.729i	−0.696207	+	0.505824i	0.182488	+	0.983208i	$0.441585\pi$
$212$	50.9630	−	16.5589i	0.240392	−	0.0781079i
$213$	−66.5861	−	104.355i	−0.312611	−	0.489928i
$214$	−38.1071	−	27.6864i	−0.178071	−	0.129376i
$215$	9.30442	−	12.8064i	0.0432764	−	0.0595648i
$216$	170.164	−	162.174i	0.787798	−	0.750807i
$217$	−3.27551	−	10.0810i	−0.0150945	−	0.0464561i
$218$	−40.2078	−	55.3414i	−0.184440	−	0.253859i
$219$	−131.499	−	108.242i	−0.600454	−	0.494256i
$220$	9.35415	−	2.19537i	0.0425189	−	0.00997897i
$221$		−	275.798i		−	1.24795i
$222$	−19.0681	+	315.459i	−0.0858923	+	1.42098i
$223$	58.1059	+	178.831i	0.260564	+	0.801935i	0.992682	+	0.120757i	$0.0385321\pi$
$223$	58.1059	+	178.831i	0.260564	+	0.801935i	−0.732118	+	0.681178i	$0.761468\pi$
$224$	−47.5967	−	15.4651i	−0.212485	−	0.0690406i
$225$	92.9476	−	200.073i	0.413100	−	0.889211i
$226$	−194.753	−	141.497i	−0.861740	−	0.626091i
$227$	−408.219	−	132.638i	−1.79832	−	0.584310i	−0.798478	−	0.602024i	$-0.794361\pi$
$227$	−408.219	−	132.638i	−1.79832	−	0.584310i	−0.999843	+	0.0177135i	$0.994361\pi$
$228$	21.8580	−	55.6062i	0.0958684	−	0.243887i
$229$	−109.845	+	79.8068i	−0.479671	+	0.348501i	−0.801198	−	0.598399i	$-0.795804\pi$
$229$	−109.845	+	79.8068i	−0.479671	+	0.348501i	0.321527	+	0.946900i	$0.395804\pi$
$230$		−	26.7892i		−	0.116475i
$231$	76.1987	−	40.0883i	0.329865	−	0.173542i
$232$	−46.7166			−0.201365
$233$	192.141	+	264.459i	0.824638	+	1.13502i	0.988897	+	0.148600i	$0.0474768\pi$
$233$	192.141	+	264.459i	0.824638	+	1.13502i	−0.164259	+	0.986417i	$0.552523\pi$
$234$	124.161	+	223.239i	0.530601	+	0.954012i
$235$	−15.9342	+	49.0404i	−0.0678051	+	0.208683i
$236$	21.1233	−	29.0738i	0.0895057	−	0.123194i
$237$	38.3577	+	147.882i	0.161847	+	0.623976i
$238$	−21.5410	+	66.2963i	−0.0905083	+	0.278556i
$239$	−88.8791	+	28.8786i	−0.371879	+	0.120831i	−0.488993	−	0.872288i	$-0.662636\pi$
$239$	−88.8791	+	28.8786i	−0.371879	+	0.120831i	0.117114	+	0.993118i	$0.462636\pi$
$240$	1.19280	−	19.7335i	0.00497000	−	0.0822227i
$241$	206.766			0.857952			0.428976	−	0.903316i	$-0.358875\pi$
$241$	206.766			0.857952			0.428976	+	0.903316i	$0.358875\pi$
$242$	33.4048	−	197.837i	0.138036	−	0.817508i
$243$	−232.013	−	72.2432i	−0.954785	−	0.297297i
$244$	46.8421	−	34.0328i	0.191976	−	0.139479i
$245$	−28.0292	+	9.10724i	−0.114405	+	0.0371724i
$246$	282.802	−	180.449i	1.14960	−	0.733531i
$247$	220.546	+	160.236i	0.892900	+	0.648730i
$248$	20.7898	−	28.6147i	0.0838297	−	0.115382i
$249$	95.5472	+	149.743i	0.383724	+	0.601377i
$250$	−17.7210	−	54.5397i	−0.0708841	−	0.218159i
$251$	1.64009	+	2.25739i	0.00653422	+	0.00899358i	0.812272	−	0.583279i	$-0.198231\pi$
$251$	1.64009	+	2.25739i	0.00653422	+	0.00899358i	−0.805737	+	0.592273i	$0.798231\pi$
$252$	5.64417	+	28.8168i	0.0223975	+	0.114353i
$253$	234.558	+	98.5605i	0.927106	+	0.389567i
$254$			303.081i			1.19323i
$255$	33.7025	+	2.03717i	0.132167	+	0.00798889i
$256$	−66.1871	−	203.703i	−0.258543	−	0.795714i
$257$	−380.619	−	123.671i	−1.48101	−	0.481208i	−0.546593	−	0.837398i	$-0.684076\pi$
$257$	−380.619	−	123.671i	−1.48101	−	0.481208i	−0.934414	+	0.356190i	$0.884076\pi$
$258$	109.122	−	28.3040i	0.422952	−	0.109705i
$259$	−134.103	−	97.4312i	−0.517770	−	0.376182i
$260$	−14.2196	−	4.62022i	−0.0546907	−	0.0177701i
$261$	23.4734	+	42.2047i	0.0899362	+	0.161704i
$262$	113.370	−	82.3678i	0.432708	−	0.314381i
$263$			379.212i			1.44187i	0.693003	+	0.720935i	$0.256287\pi$
$263$			379.212i			1.44187i	−0.693003	+	0.720935i	$0.743713\pi$
$264$	257.673	+	127.076i	0.976033	+	0.481349i
$265$	−29.9317			−0.112950
$266$	−40.4999	−	55.7433i	−0.152255	−	0.209561i
$267$	106.631	+	41.9149i	0.399365	+	0.156985i
$268$	−29.8639	+	91.9118i	−0.111433	+	0.342954i
$269$	−18.3393	+	25.2419i	−0.0681760	+	0.0938362i	−0.841743	−	0.539878i	$-0.818470\pi$
$269$	−18.3393	+	25.2419i	−0.0681760	+	0.0938362i	0.773567	+	0.633714i	$0.218470\pi$
$270$	−28.1969	+	13.5235i	−0.104433	+	0.0500870i
$271$	160.104	−	492.748i	0.590788	−	1.81826i	0.0161246	−	0.999870i	$-0.494867\pi$
$271$	160.104	−	492.748i	0.590788	−	1.81826i	0.574664	−	0.818390i	$-0.305133\pi$
$272$	−144.569	+	46.9734i	−0.531505	+	0.172696i
$273$	−133.736	−	8.08374i	−0.489875	−	0.0296108i
$274$	338.882			1.23680
$275$	268.691	+	22.5248i	0.977056	+	0.0819083i
$276$	−55.1450	+	66.9937i	−0.199801	+	0.242731i
$277$	−297.684	+	216.280i	−1.07467	+	0.780795i	−0.976746	−	0.214399i	$-0.931221\pi$
$277$	−297.684	+	216.280i	−1.07467	+	0.780795i	−0.0979254	+	0.995194i	$0.531221\pi$
$278$	−79.2308	+	25.7436i	−0.285003	+	0.0926031i
$279$	−36.2971	−	4.40410i	−0.130097	−	0.0157853i
$280$	12.8365	+	9.32625i	0.0458446	+	0.0333081i
$281$	−188.322	+	259.203i	−0.670184	+	0.922429i	−0.999765	−	0.0216982i	$-0.993093\pi$
$281$	−188.322	+	259.203i	−0.670184	+	0.922429i	0.329580	+	0.944127i	$0.393093\pi$
$282$	−309.569	+	197.528i	−1.09776	+	0.700456i
$283$	−49.6883	−	152.925i	−0.175577	−	0.540371i	0.824082	−	0.566470i	$-0.191691\pi$
$283$	−49.6883	−	152.925i	−0.175577	−	0.540371i	−0.999659	+	0.0260993i	$0.991691\pi$
$284$	30.3294	+	41.7449i	0.106794	+	0.146989i
$285$	−21.2100	+	25.7672i	−0.0744209	+	0.0904113i
$286$	−203.971	+	236.369i	−0.713184	+	0.826465i
$287$			175.953i			0.613075i
$288$	−117.554	+	126.423i	−0.408174	+	0.438968i
$289$	9.08071	+	27.9475i	0.0314211	+	0.0967043i
$290$	5.91079	+	1.92053i	0.0203820	+	0.00662252i
$291$	−12.2717	−	47.3116i	−0.0421707	−	0.162583i
$292$	57.4361	+	41.7298i	0.196699	+	0.142910i
$293$	276.702	+	89.9060i	0.944377	+	0.306847i	0.740429	−	0.672135i	$-0.234623\pi$
$293$	276.702	+	89.9060i	0.944377	+	0.306847i	0.203948	+	0.978982i	$0.434623\pi$
$294$	−195.336	−	76.7839i	−0.664410	−	0.261170i
$295$	−16.2399	+	11.7990i	−0.0550506	+	0.0399966i
$296$		−	553.114i		−	1.86863i
$297$	−14.6678	−	296.638i	−0.0493866	−	0.998780i
$298$	260.998			0.875832
$299$	−232.707	−	320.294i	−0.778286	−	1.07122i
$300$	−33.6414	+	85.5830i	−0.112138	+	0.285277i
$301$	−18.2716	+	56.2343i	−0.0607030	+	0.186825i
$302$	167.035	−	229.905i	0.553097	−	0.761273i
$303$	302.571	−	78.4808i	0.998583	−	0.259012i
$304$	46.4306	−	142.899i	0.152732	−	0.470061i
$305$	−30.7587	+	9.99411i	−0.100848	+	0.0327676i
$306$	176.091	+	163.738i	0.575462	+	0.535092i
$307$	−281.800			−0.917915			−0.458957	−	0.888458i	$-0.651777\pi$
$307$	−281.800			−0.917915			−0.458957	+	0.888458i	$0.651777\pi$
$308$	−30.6963	+	18.5962i	−0.0996632	+	0.0603772i
$309$	126.018	+	103.730i	0.407826	+	0.335697i
$310$	−3.80676	+	2.76578i	−0.0122799	+	0.00892186i
$311$	450.565	−	146.398i	1.44876	−	0.470732i	0.524146	−	0.851628i	$-0.324385\pi$
$311$	450.565	−	146.398i	1.44876	−	0.470732i	0.924618	+	0.380897i	$0.124385\pi$
$312$	−240.480	−	376.883i	−0.770768	−	1.20796i
$313$	24.2496	+	17.6184i	0.0774748	+	0.0562887i	0.625848	−	0.779945i	$-0.284753\pi$
$313$	24.2496	+	17.6184i	0.0774748	+	0.0562887i	−0.548374	+	0.836233i	$0.684753\pi$
$314$	63.6811	−	87.6495i	0.202806	−	0.279139i
$315$	1.97567	−	16.2828i	0.00627197	−	0.0516915i
$316$	−19.6790	−	60.5656i	−0.0622752	−	0.191663i
$317$	93.6204	+	128.857i	0.295333	+	0.406490i	0.930737	−	0.365689i	$-0.119167\pi$
$317$	93.6204	+	128.857i	0.295333	+	0.406490i	−0.635405	+	0.772179i	$0.719167\pi$
$318$	−164.578	−	135.470i	−0.517541	−	0.426007i
$319$	−38.5620	+	44.6871i	−0.120884	+	0.140085i
$320$			48.5757i			0.151799i
$321$	5.14181	−	85.0651i	0.0160181	−	0.265000i
$322$	30.9219	+	95.1679i	0.0960308	+	0.295552i
$323$	244.054	+	79.2981i	0.755586	+	0.245505i
$324$	98.3519	+	24.2236i	0.303555	+	0.0747641i
$325$	−339.441	−	246.618i	−1.04443	−	0.758825i
$326$	24.3465	+	7.91065i	0.0746825	+	0.0242658i
$327$	45.2766	−	115.183i	0.138461	−	0.352241i
$328$	−474.994	+	345.103i	−1.44815	+	1.05214i
$329$		−	192.607i		−	0.585431i
$330$	−27.3777	−	26.6712i	−0.0829628	−	0.0808217i
$331$	332.709			1.00516			0.502582	−	0.864530i	$-0.332384\pi$
$331$	332.709			1.00516			0.502582	+	0.864530i	$0.332384\pi$
$332$	−43.5209	−	59.9014i	−0.131087	−	0.180426i
$333$	−499.694	+	277.919i	−1.50058	+	0.834591i
$334$	−78.9626	+	243.022i	−0.236415	+	0.727611i
$335$	31.7297	−	43.6722i	0.0947155	−	0.130365i
$336$	18.5403	+	71.4793i	0.0551794	+	0.212736i
$337$	17.1212	−	52.6936i	0.0508047	−	0.156361i	−0.922435	−	0.386152i	$-0.873804\pi$
$337$	17.1212	−	52.6936i	0.0508047	−	0.156361i	0.973240	+	0.229791i	$0.0738042\pi$
$338$	195.532	−	63.5322i	0.578497	−	0.187965i
$339$	26.2782	−	434.741i	0.0775167	−	1.28242i
$340$	−14.0740			−0.0413942
$341$	−10.2107	−	43.5064i	−0.0299435	−	0.127585i
$342$	−233.244	+	45.6840i	−0.682000	+	0.133579i
$343$	192.491	−	139.853i	0.561197	−	0.407733i
$344$	−187.645	+	60.9694i	−0.545478	+	0.177237i
$345$	40.8589	−	26.0710i	0.118432	−	0.0755682i
$346$	−33.6751	−	24.4664i	−0.0973270	−	0.0707122i
$347$	−81.4326	+	112.082i	−0.234676	+	0.323004i	−0.910071	−	0.414452i	$-0.863973\pi$
$347$	−81.4326	+	112.082i	−0.234676	+	0.323004i	0.675395	+	0.737456i	$0.263973\pi$
$348$	−10.8282	−	16.9700i	−0.0311154	−	0.0487645i
$349$	69.9974	+	215.430i	0.200566	+	0.617277i	0.999866	+	0.0163462i	$0.00520338\pi$
$349$	69.9974	+	215.430i	0.200566	+	0.617277i	−0.799301	+	0.600931i	$0.794797\pi$
$350$	62.3330	+	85.7940i	0.178094	+	0.245126i
$351$	−219.652	+	406.624i	−0.625788	+	1.15847i
$352$	−194.519	−	81.7364i	−0.552611	−	0.232206i
$353$			258.939i			0.733538i	0.930312	+	0.366769i	$0.119536\pi$
$353$			258.939i			0.733538i	−0.930312	+	0.366769i	$0.880464\pi$
$354$	−142.697	−	8.62538i	−0.403098	−	0.0243655i
$355$	−8.90657	−	27.4116i	−0.0250889	−	0.0772157i
$356$	−45.4206	−	14.7580i	−0.127586	−	0.0414552i
$357$	−122.078	+	31.6647i	−0.341957	+	0.0886967i
$358$	82.9101	+	60.2377i	0.231592	+	0.168262i
$359$	246.358	+	80.0466i	0.686234	+	0.222971i	0.631323	−	0.775520i	$-0.282512\pi$
$359$	246.358	+	80.0466i	0.686234	+	0.222971i	0.0549113	+	0.998491i	$0.482512\pi$
$360$	47.8314	−	26.6028i	0.132865	−	0.0738967i
$361$	86.8492	−	63.0996i	0.240580	−	0.174791i
$362$			246.079i			0.679775i
$363$	334.250	−	141.584i	0.920798	−	0.390039i
$364$	55.8476			0.153428
$365$	−23.3093	−	32.0824i	−0.0638610	−	0.0878971i
$366$	−214.358	−	84.2612i	−0.585679	−	0.230222i
$367$	−61.4255	+	189.048i	−0.167372	+	0.515118i	−0.999203	−	0.0399105i	$-0.987293\pi$
$367$	−61.4255	+	189.048i	−0.167372	+	0.515118i	0.831831	+	0.555029i	$0.187293\pi$
$368$	−128.259	+	176.534i	−0.348531	+	0.479712i
$369$	550.440	+	255.718i	1.49171	+	0.693002i
$370$	−22.7386	+	69.9823i	−0.0614557	+	0.189141i
$371$	106.331	−	34.5492i	0.286607	−	0.0931244i
$372$	15.2131	+	0.919567i	0.0408955	+	0.00247195i
$373$	670.467			1.79750			0.898750	−	0.438462i	$-0.144477\pi$
$373$	670.467			1.79750			0.898750	+	0.438462i	$0.144477\pi$
$374$	−113.849	+	270.941i	−0.304408	+	0.724442i
$375$	65.9379	−	80.1056i	0.175834	−	0.213615i
$376$	519.953	−	377.768i	1.38285	−	1.00470i
$377$	87.3527	−	28.3826i	0.231705	−	0.0752855i
$378$	84.5590	−	80.5886i	0.223701	−	0.213197i
$379$	−317.451	−	230.642i	−0.837601	−	0.608553i	0.0840983	−	0.996457i	$-0.473199\pi$
$379$	−317.451	−	230.642i	−0.837601	−	0.608553i	−0.921700	+	0.387905i	$0.873199\pi$
$380$	8.17691	−	11.2546i	0.0215182	−	0.0296173i
$381$	−462.258	+	294.956i	−1.21328	+	0.774161i
$382$	28.7983	+	88.6321i	0.0753883	+	0.232021i
$383$	−292.542	−	402.649i	−0.763817	−	1.05130i	−0.996887	−	0.0788436i	$-0.974877\pi$
$383$	−292.542	−	402.649i	−0.763817	−	1.05130i	0.233070	−	0.972460i	$-0.425123\pi$
$384$	−73.5699	+	89.3774i	−0.191588	+	0.232754i
$385$	19.5169	−	4.58052i	0.0506932	−	0.0118975i
$386$		−	250.336i		−	0.648538i
$387$	149.365	+	138.887i	0.385957	+	0.358881i
$388$	6.29584	+	19.3766i	0.0162264	+	0.0499397i
$389$	392.101	+	127.401i	1.00797	+	0.327510i	0.766047	−	0.642785i	$-0.222221\pi$
$389$	392.101	+	127.401i	1.00797	+	0.327510i	0.241926	+	0.970295i	$0.422221\pi$
$390$	14.9328	+	57.5710i	0.0382891	+	0.147618i
$391$	−301.500	−	219.053i	−0.771100	−	0.560237i
$392$	349.357	+	113.513i	0.891217	+	0.289574i
$393$	235.958	+	92.7515i	0.600401	+	0.236009i
$394$	−29.9651	+	21.7709i	−0.0760535	+	0.0552561i
$395$			35.5715i			0.0900544i
$396$	13.5634	+	123.055i	0.0342509	+	0.310745i
$397$	171.230			0.431310			0.215655	−	0.976470i	$-0.430811\pi$
$397$	171.230			0.431310			0.215655	+	0.976470i	$0.430811\pi$
$398$	−147.103	−	202.470i	−0.369605	−	0.508718i
$399$	45.6055	−	116.019i	0.114299	−	0.290775i
$400$	−71.4608	+	219.934i	−0.178652	+	0.549835i
$401$	−426.743	+	587.361i	−1.06420	+	1.46474i	−0.188382	+	0.982096i	$0.560324\pi$
$401$	−426.743	+	587.361i	−1.06420	+	1.46474i	−0.875816	+	0.482646i	$0.839676\pi$
$402$	372.124	−	96.5215i	0.925681	−	0.240103i
$403$	−21.4888	+	66.1357i	−0.0533221	+	0.164108i
$404$	−123.919	+	40.2636i	−0.306729	+	0.0996624i
$405$	−48.0670	−	29.8450i	−0.118684	−	0.0736912i
$406$	−23.2147			−0.0571790
$407$	−529.084	−	456.564i	−1.29996	−	1.12178i
$408$	−324.919	−	267.453i	−0.796369	−	0.655521i
$409$	−243.830	+	177.153i	−0.596161	+	0.433137i	−0.844514	−	0.535533i	$-0.820111\pi$
$409$	−243.830	+	177.153i	−0.596161	+	0.433137i	0.248353	+	0.968670i	$0.420111\pi$
$410$	74.2855	−	24.1368i	0.181184	−	0.0588703i
$411$	329.797	+	516.863i	0.802426	+	1.25757i
$412$	−55.0420	−	39.9904i	−0.133597	−	0.0970640i
$413$	44.0727	−	60.6608i	0.106713	−	0.146878i
$414$	342.658	+	41.5762i	0.827676	+	0.100426i
$415$	12.7804	+	39.3340i	0.0307961	+	0.0947808i
$416$	192.985	+	265.621i	0.463905	+	0.638511i
$417$	−116.371	−	95.7892i	−0.279067	−	0.229710i
$418$	−150.518	−	248.456i	−0.360090	−	0.594392i
$419$		−	573.195i		−	1.36801i	−0.729478	−	0.684004i	$-0.760237\pi$
$419$		−	573.195i		−	1.36801i	0.729478	−	0.684004i	$-0.239763\pi$
$420$	−0.412516	+	6.82459i	−0.000982181	+	0.0162490i
$421$	−172.827	−	531.908i	−0.410516	−	1.26344i	−0.916200	−	0.400721i	$-0.868760\pi$
$421$	−172.827	−	531.908i	−0.410516	−	1.26344i	0.505684	−	0.862719i	$-0.331240\pi$
$422$	−286.349	−	93.0404i	−0.678552	−	0.220475i
$423$	−602.540	−	279.922i	−1.42445	−	0.661754i
$424$	301.820	+	219.285i	0.711839	+	0.517182i
$425$	−375.622	−	122.047i	−0.883816	−	0.287169i
$426$	75.0920	−	191.032i	0.176272	−	0.448433i
$427$	97.7334	−	71.0075i	0.228884	−	0.166294i
$428$			35.5229i			0.0829973i
$429$	−559.012	−	81.0635i	−1.30306	−	0.188959i
$430$	26.2480			0.0610420
$431$	−117.467	−	161.680i	−0.272546	−	0.375127i	0.650701	−	0.759334i	$-0.274475\pi$
$431$	−117.467	−	161.680i	−0.272546	−	0.375127i	−0.923247	+	0.384207i	$0.874475\pi$
$432$	250.557	+	45.8828i	0.579993	+	0.106210i
$433$	−31.9791	+	98.4214i	−0.0738547	+	0.227301i	−0.981169	−	0.193152i	$-0.938129\pi$
$433$	−31.9791	+	98.4214i	−0.0738547	+	0.227301i	0.907314	+	0.420453i	$0.138129\pi$
$434$	10.3310	−	14.2194i	0.0238041	−	0.0327635i
$435$	2.82313	+	10.8842i	0.00648996	+	0.0250211i
$436$	−15.9417	+	49.0635i	−0.0365635	+	0.112531i
$437$	350.338	−	113.832i	0.801690	−	0.260485i
$438$	17.0397	−	281.901i	0.0389034	−	0.643610i
$439$	−662.550			−1.50923			−0.754613	−	0.656171i	$-0.772175\pi$
$439$	−662.550			−1.50923			−0.754613	+	0.656171i	$0.772175\pi$
$440$	50.6447	+	43.7030i	0.115102	+	0.0993250i
$441$	−72.9890	−	372.652i	−0.165508	−	0.845016i
$442$	369.977	−	268.804i	0.837051	−	0.608153i
$443$	−200.511	+	65.1499i	−0.452620	+	0.147065i	−0.526451	−	0.850206i	$-0.676478\pi$
$443$	−200.511	+	65.1499i	−0.452620	+	0.147065i	0.0738308	+	0.997271i	$0.476478\pi$
$444$	200.921	−	128.203i	0.452525	−	0.288745i
$445$	21.5817	+	15.6801i	0.0484983	+	0.0352361i
$446$	−183.266	+	252.244i	−0.410911	+	0.565570i
$447$	254.001	+	398.074i	0.568235	+	0.890545i
$448$	−56.0693	−	172.563i	−0.125155	−	0.385186i
$449$	140.640	+	193.574i	0.313229	+	0.431123i	0.936385	−	0.350975i	$-0.114150\pi$
$449$	140.640	+	193.574i	0.313229	+	0.431123i	−0.623156	+	0.782098i	$0.714150\pi$
$450$	358.984	−	70.3118i	0.797742	−	0.156248i
$451$	−61.9703	+	739.222i	−0.137406	+	1.63907i
$452$			181.546i			0.401651i
$453$	513.207	+	31.0211i	1.13291	+	0.0684793i
$454$	−219.936	−	676.892i	−0.484440	−	1.49095i
$455$	−29.6684	−	9.63983i	−0.0652052	−	0.0211864i
$456$	402.649	−	104.439i	0.883001	−	0.229033i
$457$	−21.5908	−	15.6866i	−0.0472446	−	0.0343252i	0.563912	−	0.825835i	$-0.309296\pi$
$457$	−21.5908	−	15.6866i	−0.0472446	−	0.0343252i	−0.611157	+	0.791509i	$0.709296\pi$
$458$	−214.118	−	69.5713i	−0.467507	−	0.151902i
$459$	−78.3626	+	427.923i	−0.170725	+	0.932294i
$460$	−16.3447	+	11.8751i	−0.0355320	+	0.0258155i
$461$		−	393.125i		−	0.852766i	−0.904543	−	0.426383i	$-0.859788\pi$
$461$		−	393.125i		−	0.852766i	0.904543	−	0.426383i	$-0.140212\pi$
$462$	128.044	+	63.1473i	0.277152	+	0.136683i
$463$	106.954			0.231002			0.115501	−	0.993307i	$-0.463153\pi$
$463$	106.954			0.231002			0.115501	+	0.993307i	$0.463153\pi$
$464$	−29.7556	−	40.9550i	−0.0641283	−	0.0882651i
$465$	−7.92307	−	3.11444i	−0.0170389	−	0.00669772i
$466$	−167.498	+	515.506i	−0.359438	+	1.10624i
$467$	−248.580	+	342.141i	−0.532291	+	0.732636i	−0.987477	−	0.157760i	$-0.949573\pi$
$467$	−248.580	+	342.141i	−0.532291	+	0.732636i	0.455186	+	0.890396i	$0.349573\pi$
$468$	81.1652	−	174.711i	0.173430	−	0.373313i
$469$	−62.3094	+	191.769i	−0.132856	+	0.408888i
$470$	−81.3168	+	26.4214i	−0.173014	+	0.0562158i
$471$	195.657	+	11.8266i	0.415407	+	0.0251095i
$472$	250.199			0.530083
$473$	−96.5694	+	229.819i	−0.204164	+	0.485876i
$474$	−160.996	+	195.588i	−0.339654	+	0.412634i
$475$	315.831	−	229.464i	0.664906	−	0.483083i
$476$	49.9976	−	16.2452i	0.105037	−	0.0341286i
$477$	46.4532	−	382.853i	0.0973862	−	0.802626i
$478$	−125.365	−	91.0832i	−0.262270	−	0.190551i
$479$	317.236	−	436.638i	0.662289	−	0.911562i	−0.337266	−	0.941409i	$-0.609502\pi$
$479$	317.236	−	436.638i	0.662289	−	0.911562i	0.999554	+	0.0298475i	$0.00950216\pi$
$480$	−33.8843	+	21.6208i	−0.0705924	+	0.0450432i
$481$	336.043	+	1034.24i	0.698635	+	2.15018i
$482$	201.523	+	277.373i	0.418098	+	0.575462i
$483$	−115.057	+	139.779i	−0.238213	+	0.289397i
$484$	−135.513	+	67.3162i	−0.279985	+	0.139083i
$485$		−	11.3803i		−	0.0234645i
$486$	−129.217	−	381.652i	−0.265878	−	0.785291i
$487$	188.700	+	580.759i	0.387474	+	1.19252i	0.934669	+	0.355518i	$0.115696\pi$
$487$	188.700	+	580.759i	0.387474	+	1.19252i	−0.547195	+	0.837005i	$0.684304\pi$
$488$	383.378	+	124.567i	0.785610	+	0.255260i
$489$	11.6285	+	44.8318i	0.0237801	+	0.0916805i
$490$	−39.5356	−	28.7243i	−0.0806849	−	0.0586210i
$491$	54.0905	+	17.5751i	0.110164	+	0.0357944i	0.363580	−	0.931563i	$-0.381554\pi$
$491$	54.0905	+	17.5751i	0.110164	+	0.0357944i	−0.253416	+	0.967357i	$0.581554\pi$
$492$	−235.456	−	92.5545i	−0.478570	−	0.188119i
$493$	69.9465	−	50.8191i	0.141879	−	0.103081i
$494$			452.031i			0.915043i
$495$	14.0351	−	67.7126i	0.0283537	−	0.136793i
$496$	38.3274			0.0772729
$497$	63.2806	+	87.0983i	0.127325	+	0.175248i
$498$	−107.753	+	274.120i	−0.216371	+	0.550442i
$499$	144.891	−	445.930i	0.290363	−	0.893646i	−0.694376	−	0.719612i	$-0.744320\pi$
$499$	144.891	−	445.930i	0.290363	−	0.893646i	0.984740	−	0.174034i	$-0.0556804\pi$
$500$	−25.4205	+	34.9884i	−0.0508411	+	0.0699767i
$501$	−447.502	+	116.073i	−0.893218	+	0.231683i
$502$	−1.42974	+	4.40029i	−0.00284809	+	0.00876552i
$503$	−435.748	+	141.583i	−0.866297	+	0.281477i	−0.708256	−	0.705955i	$-0.750518\pi$
$503$	−435.748	+	141.583i	−0.866297	+	0.281477i	−0.158041	+	0.987433i	$0.550518\pi$
$504$	−139.213	+	149.716i	−0.276216	+	0.297055i
$505$	72.7802			0.144119
$506$	96.3930	+	410.716i	0.190500	+	0.811691i
$507$	287.189	+	236.396i	0.566448	+	0.466265i
$508$	184.917	−	134.350i	0.364009	−	0.264468i
$509$	−261.397	+	84.9330i	−0.513550	+	0.166862i	−0.554316	−	0.832306i	$-0.687020\pi$
$509$	−261.397	+	84.9330i	−0.513550	+	0.166862i	0.0407663	+	0.999169i	$0.487020\pi$
$510$	30.1150	+	47.1967i	0.0590491	+	0.0925426i
$511$	119.837	+	87.0667i	0.234515	+	0.170385i
$512$	299.479	−	412.197i	0.584920	−	0.805073i
$513$	−296.668	−	311.284i	−0.578300	−	0.606792i
$514$	−205.065	−	631.127i	−0.398960	−	1.22787i
$515$	22.3377	+	30.7452i	0.0433741	+	0.0596994i
$516$	−65.6404	−	54.0310i	−0.127210	−	0.104711i
$517$	67.8358	−	809.191i	0.131211	−	1.56517i
$518$		−	274.856i		−	0.530610i
$519$	4.54380	−	75.1717i	0.00875491	−	0.144840i
$520$	−32.1666	−	98.9985i	−0.0618588	−	0.190382i
$521$	236.239	+	76.7587i	0.453434	+	0.147330i	0.526825	−	0.849974i	$-0.323382\pi$
$521$	236.239	+	76.7587i	0.453434	+	0.147330i	−0.0733915	+	0.997303i	$0.523382\pi$
$522$	−33.7387	+	72.6235i	−0.0646335	+	0.139126i
$523$	−113.737	−	82.6347i	−0.217470	−	0.158001i	0.473717	−	0.880677i	$-0.342912\pi$
$523$	−113.737	−	82.6347i	−0.217470	−	0.158001i	−0.691187	+	0.722676i	$0.742912\pi$
$524$	−100.509	−	32.6574i	−0.191811	−	0.0623232i
$525$	−70.1909	+	178.564i	−0.133697	+	0.340122i
$526$	−508.705	+	369.596i	−0.967119	+	0.702653i
$527$			65.4587i			0.124210i
$528$	52.7177	+	306.833i	0.0998441	+	0.581123i
$529$	−5.97152			−0.0112883
$530$	−29.1727	−	40.1527i	−0.0550428	−	0.0757599i
$531$	−125.716	−	226.035i	−0.236753	−	0.425678i
$532$	−16.0575	+	49.4198i	−0.0301832	+	0.0928943i
$533$	678.497	−	933.871i	1.27298	−	1.75210i
$534$	47.6986	+	183.895i	0.0893232	+	0.344372i
$535$	6.13159	−	18.8711i	0.0114609	−	0.0352731i
$536$	−639.901	+	207.916i	−1.19384	+	0.387904i
$537$	−11.1871	+	185.077i	−0.0208326	+	0.344650i
$538$	−51.7358			−0.0961633
$539$	396.956	−	240.481i	0.736468	−	0.446162i
$540$	20.7501	+	11.2089i	0.0384262	+	0.0207572i
$541$	−486.149	+	353.208i	−0.898612	+	0.652880i	−0.938109	−	0.346340i	$-0.887424\pi$
$541$	−486.149	+	353.208i	−0.898612	+	0.652880i	0.0394969	+	0.999220i	$0.487424\pi$
$542$	817.055	−	265.477i	1.50748	−	0.489811i
$543$	−375.319	+	239.481i	−0.691195	+	0.441034i
$544$	250.034	+	181.661i	0.459622	+	0.333935i
$545$	16.9376	−	23.3127i	0.0310782	−	0.0427755i
$546$	−119.500	−	187.283i	−0.218865	−	0.343009i
$547$	−191.860	−	590.485i	−0.350750	−	1.07950i	−0.958433	−	0.285318i	$-0.907901\pi$
$547$	−191.860	−	590.485i	−0.350750	−	1.07950i	0.607683	−	0.794180i	$-0.292099\pi$
$548$	−150.220	−	206.760i	−0.274124	−	0.377299i
$549$	−80.0967	−	408.941i	−0.145896	−	0.744884i
$550$	231.660	+	382.396i	0.421201	+	0.695266i
$551$			85.4594i			0.155099i
$552$	−603.007	−	36.4491i	−1.09240	−	0.0660310i
$553$	−41.0590	−	126.367i	−0.0742478	−	0.228511i
$554$	−580.271	−	188.541i	−1.04742	−	0.340327i
$555$	−128.866	+	33.4252i	−0.232191	+	0.0602256i
$556$	50.8282	+	36.9289i	0.0914177	+	0.0664188i
$557$	513.595	+	166.877i	0.922074	+	0.299600i	0.731317	−	0.682037i	$-0.238906\pi$
$557$	513.595	+	166.877i	0.922074	+	0.299600i	0.190757	+	0.981637i	$0.438906\pi$
$558$	−29.4687	−	52.9843i	−0.0528113	−	0.0949539i
$559$	313.824	−	228.006i	0.561402	−	0.407883i
$560$			17.1936i			0.0307028i
$561$	−524.036	+	90.0358i	−0.934110	+	0.160492i
$562$	−531.261			−0.945305
$563$	163.796	+	225.446i	0.290934	+	0.400437i	0.929317	−	0.369282i	$-0.120396\pi$
$563$	163.796	+	225.446i	0.290934	+	0.400437i	−0.638383	+	0.769719i	$0.720396\pi$
$564$	257.743	+	101.315i	0.456991	+	0.179636i
$565$	31.3366	−	96.4441i	0.0554630	−	0.170698i
$566$	156.717	−	215.703i	0.276886	−	0.381101i
$567$	205.206	+	50.5411i	0.361915	+	0.0891377i
$568$	−111.012	+	341.659i	−0.195443	+	0.601513i
$569$	1017.22	−	330.514i	1.78773	−	0.580869i	0.788321	−	0.615264i	$-0.210950\pi$
$569$	1017.22	−	330.514i	1.78773	−	0.580869i	0.999408	+	0.0343952i	$0.0109505\pi$
$570$	−55.2383	−	3.33891i	−0.0969093	−	0.00585774i
$571$	470.660			0.824274			0.412137	−	0.911122i	$-0.364783\pi$
$571$	470.660			0.824274			0.412137	+	0.911122i	$0.364783\pi$
$572$	234.630	+	19.6695i	0.410193	+	0.0343872i
$573$	−107.155	+	130.179i	−0.187007	+	0.227189i
$574$	−236.037	+	171.491i	−0.411214	+	0.298764i
$575$	−539.203	+	175.198i	−0.937744	+	0.304691i
$576$	−621.325	−	75.3882i	−1.07869	−	0.130882i
$577$	−185.383	−	134.689i	−0.321288	−	0.233429i	0.415437	−	0.909622i	$-0.363629\pi$
$577$	−185.383	−	134.689i	−0.321288	−	0.233429i	−0.736725	+	0.676193i	$0.763629\pi$
$578$	−28.6406	+	39.4204i	−0.0495512	+	0.0682014i
$579$	381.812	−	243.625i	0.659433	−	0.420768i
$580$	−1.44837	−	4.45764i	−0.00249720	−	0.00768558i
$581$	−90.8039	−	124.981i	−0.156289	−	0.215113i
$582$	51.5071	−	62.5741i	0.0885001	−	0.107516i
$583$	458.894	−	107.700i	0.787125	−	0.184734i
$584$			494.275i			0.846361i
$585$	−73.2747	+	78.8030i	−0.125256	+	0.134706i
$586$	149.079	+	458.817i	0.254400	+	0.782964i
$587$	0.704580	+	0.228932i	0.00120031	+	0.000390003i	0.309617	−	0.950861i	$-0.399799\pi$
$587$	0.704580	+	0.228932i	0.00120031	+	0.000390003i	−0.308417	+	0.951251i	$0.599799\pi$
$588$	39.7412	+	153.216i	0.0675870	+	0.260571i
$589$	−52.3452	−	38.0310i	−0.0888714	−	0.0645688i
$590$	−31.6562	−	10.2857i	−0.0536546	−	0.0174334i
$591$	−62.3667	−	24.5155i	−0.105527	−	0.0414813i
$592$	484.897	−	352.299i	0.819083	−	0.595099i
$593$		−	498.413i		−	0.840494i	−0.907410	−	0.420247i	$-0.861943\pi$
$593$		−	498.413i		−	0.840494i	0.907410	−	0.420247i	$-0.138057\pi$
$594$	383.637	−	308.792i	0.645854	−	0.519852i
$595$	−29.3647			−0.0493524
$596$	−115.695	−	159.241i	−0.194120	−	0.267183i
$597$	165.647	−	421.403i	0.277466	−	0.705868i
$598$	202.862	−	624.344i	0.339234	−	1.04405i
$599$	−112.504	+	154.848i	−0.187819	+	0.258511i	−0.892534	−	0.450979i	$-0.851075\pi$
$599$	−112.504	+	154.848i	−0.187819	+	0.258511i	0.704715	+	0.709490i	$0.251075\pi$
$600$	−619.713	+	160.741i	−1.03285	+	0.267902i
$601$	256.922	−	790.726i	0.427491	−	1.31568i	−0.473097	−	0.881010i	$-0.656864\pi$
$601$	256.922	−	790.726i	0.427491	−	1.31568i	0.900588	−	0.434673i	$-0.143136\pi$
$602$	−93.2454	+	30.2973i	−0.154893	+	0.0503277i
$603$	509.362	+	473.629i	0.844713	+	0.785454i
$604$	−214.314			−0.354824
$605$	83.6088	−	12.3701i	0.138196	−	0.0204465i
$606$	400.178	+	329.402i	0.660361	+	0.543567i
$607$	−638.876	+	464.171i	−1.05251	+	0.764697i	−0.972689	−	0.232112i	$-0.925436\pi$
$607$	−638.876	+	464.171i	−1.05251	+	0.764697i	−0.0798256	+	0.996809i	$0.525436\pi$
$608$	−290.536	+	94.4010i	−0.477856	+	0.155265i
$609$	−22.5923	−	35.4070i	−0.0370974	−	0.0581396i
$610$	−43.3856	−	31.5215i	−0.0711239	−	0.0516746i
$611$	−742.718	+	1022.26i	−1.21558	+	1.67310i
$612$	21.8426	−	180.019i	0.0356905	−	0.294149i
$613$	−85.6583	−	263.629i	−0.139736	−	0.430064i	0.856560	−	0.516047i	$-0.172597\pi$
$613$	−85.6583	−	263.629i	−0.139736	−	0.430064i	−0.996297	+	0.0859829i	$0.972597\pi$
$614$	−274.654	−	378.029i	−0.447319	−	0.615682i
$615$	109.107	+	89.8104i	0.177411	+	0.146033i
$616$	−230.359	−	96.7960i	−0.373959	−	0.157136i
$617$			928.547i			1.50494i	0.658628	+	0.752469i	$0.271137\pi$
$617$			928.547i			1.50494i	−0.658628	+	0.752469i	$0.728863\pi$
$618$	−16.3294	+	270.151i	−0.0264230	+	0.437137i
$619$	295.319	+	908.900i	0.477091	+	1.46834i	0.843117	+	0.537731i	$0.180718\pi$
$619$	295.319	+	908.900i	0.477091	+	1.46834i	−0.366025	+	0.930605i	$0.619282\pi$
$620$	3.37493	+	1.09658i	0.00544343	+	0.00176868i
$621$	270.060	+	563.083i	0.434878	+	0.906735i
$622$	635.529	+	461.739i	1.02175	+	0.742346i
$623$	−94.7674	−	30.7918i	−0.152115	−	0.0494250i
$624$	177.231	−	450.871i	0.284024	−	0.722550i
$625$	−476.224	+	345.997i	−0.761958	+	0.553595i
$626$			49.7019i			0.0793961i
$627$	232.462	−	471.365i	0.370753	−	0.751778i
$628$	−81.7055			−0.130104
$629$	601.686	+	828.149i	0.956575	+	1.31661i
$630$	23.7687	−	13.2196i	0.0377280	−	0.0209835i
$631$	−1.62527	+	5.00208i	−0.00257571	+	0.00792722i	−0.952336	−	0.305051i	$-0.901327\pi$
$631$	−1.62527	+	5.00208i	−0.00257571	+	0.00792722i	0.949760	+	0.312978i	$0.101327\pi$
$632$	260.603	−	358.690i	0.412347	−	0.567547i
$633$	−136.767	−	527.285i	−0.216062	−	0.832994i
$634$	−81.6132	+	251.180i	−0.128728	+	0.396183i
$635$	−121.425	+	39.4533i	−0.191220	+	0.0621311i
$636$	−9.69935	+	160.464i	−0.0152506	+	0.252302i
$637$	−722.207			−1.13376
$638$	−97.5309	−	8.17618i	−0.152870	−	0.0128153i
$639$	364.441	−	71.3807i	0.570330	−	0.111707i
$640$	−21.8058	+	15.8428i	−0.0340715	+	0.0247544i
$641$	−462.217	+	150.183i	−0.721087	+	0.234296i	−0.646495	−	0.762919i	$-0.723766\pi$
$641$	−462.217	+	150.183i	−0.721087	+	0.234296i	−0.0745928	+	0.997214i	$0.523766\pi$
$642$	119.124	−	76.0103i	0.185552	−	0.118396i
$643$	597.765	+	434.302i	0.929650	+	0.675430i	0.945907	−	0.324437i	$-0.105175\pi$
$643$	597.765	+	434.302i	0.929650	+	0.675430i	−0.0162570	+	0.999868i	$0.505175\pi$
$644$	44.3570	−	61.0522i	0.0688774	−	0.0948016i
$645$	25.5444	+	40.0335i	0.0396037	+	0.0620674i
$646$	131.489	+	404.681i	0.203543	+	0.626441i
$647$	−676.121	−	930.601i	−1.04501	−	1.43833i	−0.893057	−	0.449945i	$-0.851444\pi$
$647$	−676.121	−	930.601i	−1.04501	−	1.43833i	−0.151953	−	0.988388i	$-0.548556\pi$
$648$	266.040	+	653.093i	0.410556	+	1.00786i
$649$	206.525	−	239.329i	0.318221	−	0.368766i
$650$		−	695.717i		−	1.07033i
$651$	31.7413	+	1.91862i	0.0487578	+	0.00294720i
$652$	−5.96585	−	18.3610i	−0.00915007	−	0.0281610i
$653$	−575.439	−	186.971i	−0.881224	−	0.286327i	−0.166758	−	0.985998i	$-0.553330\pi$
$653$	−575.439	−	186.971i	−0.881224	−	0.286327i	−0.714465	+	0.699671i	$0.753330\pi$
$654$	198.644	−	51.5242i	0.303736	−	0.0787831i
$655$	47.7572	+	34.6976i	0.0729117	+	0.0529735i
$656$	−605.083	−	196.603i	−0.922382	−	0.299700i
$657$	446.538	−	248.355i	0.679662	−	0.378013i
$658$	258.378	−	187.723i	0.392672	−	0.285293i
$659$			956.314i			1.45116i	0.688138	+	0.725580i	$0.258428\pi$
$659$			956.314i			1.45116i	−0.688138	+	0.725580i	$0.741572\pi$
$660$	−4.13670	+	28.5266i	−0.00626772	+	0.0432221i
$661$	57.8747			0.0875563			0.0437781	−	0.999041i	$-0.486061\pi$
$661$	57.8747			0.0875563			0.0437781	+	0.999041i	$0.486061\pi$
$662$	324.272	+	446.323i	0.489837	+	0.674203i
$663$	770.037	+	302.690i	1.16144	+	0.456547i
$664$	159.295	−	490.261i	0.239903	−	0.738345i
$665$	17.0607	−	23.4820i	0.0256551	−	0.0353113i
$666$	−859.845	−	399.458i	−1.29106	−	0.599786i
$667$	38.3523	−	118.036i	0.0574997	−	0.176966i
$668$	183.276	−	59.5499i	0.274365	−	0.0891466i
$669$	−563.076	−	34.0355i	−0.841668	−	0.0508751i
$670$	89.5104			0.133598
$671$	435.612	−	263.899i	0.649199	−	0.393293i
$672$	95.4169	−	115.919i	0.141989	−	0.172498i
$673$	−688.997	+	500.586i	−1.02377	+	0.743813i	−0.967052	−	0.254578i	$-0.918064\pi$
$673$	−688.997	+	500.586i	−1.02377	+	0.743813i	−0.0567178	+	0.998390i	$0.518064\pi$
$674$	87.3744	−	28.3897i	0.129636	−	0.0421212i
$675$	456.599	+	479.095i	0.676443	+	0.709770i
$676$	−125.438	−	91.1361i	−0.185559	−	0.134817i
$677$	158.543	−	218.215i	0.234184	−	0.322327i	−0.675710	−	0.737168i	$-0.736163\pi$
$677$	158.543	−	218.215i	0.234184	−	0.322327i	0.909894	+	0.414841i	$0.136163\pi$
$678$	608.807	−	388.465i	0.897946	−	0.572957i
$679$	13.1359	+	40.4282i	0.0193460	+	0.0595408i
$680$	−57.5942	−	79.2717i	−0.0846974	−	0.116576i
$681$	818.355	−	994.191i	1.20170	−	1.45990i
$682$	48.4111	−	56.1006i	0.0709840	−	0.0822590i
$683$		−	254.016i		−	0.371913i	−0.982558	−	0.185956i	$-0.940462\pi$
$683$		−	254.016i		−	0.371913i	0.982558	−	0.185956i	$-0.0595383\pi$
$684$	131.265	+	122.057i	0.191908	+	0.178445i
$685$	44.1137	+	135.768i	0.0643996	+	0.198201i
$686$	375.219	+	121.916i	0.546966	+	0.177720i
$687$	−102.268	−	394.279i	−0.148862	−	0.573914i
$688$	−172.968	−	125.668i	−0.251407	−	0.182658i
$689$	−697.582	−	226.658i	−1.01246	−	0.328967i
$690$	74.7965	+	29.4014i	0.108401	+	0.0426108i
$691$	306.290	−	222.532i	0.443256	−	0.322044i	−0.343672	−	0.939090i	$-0.611671\pi$
$691$	306.290	−	222.532i	0.443256	−	0.322044i	0.786927	+	0.617046i	$0.211671\pi$
$692$			31.3914i			0.0453634i
$693$	28.2992	+	256.747i	0.0408357	+	0.370486i
$694$	−229.724			−0.331014
$695$	−20.6276	−	28.3915i	−0.0296800	−	0.0408510i
$696$	51.2719	−	130.435i	0.0736666	−	0.187406i
$697$	335.776	−	1033.41i	0.481745	−	1.48266i
$698$	−220.772	+	303.867i	−0.316293	+	0.435339i
$699$	−949.256	+	246.218i	−1.35802	+	0.352243i
$700$	24.7139	−	76.0616i	0.0353056	−	0.108659i
$701$	304.289	−	98.8694i	0.434078	−	0.141040i	−0.0838238	−	0.996481i	$-0.526713\pi$
$701$	304.289	−	98.8694i	0.434078	−	0.141040i	0.517902	+	0.855440i	$0.326713\pi$
$702$	−759.559	+	101.654i	−1.08199	+	0.144807i
$703$	−1011.82			−1.43929
$704$	−174.785	−	744.731i	−0.248274	−	1.05786i
$705$	−119.435	−	98.3111i	−0.169411	−	0.139448i
$706$	−347.361	+	252.373i	−0.492013	+	0.357468i
$707$	−258.549	+	84.0077i	−0.365699	+	0.118823i
$708$	57.9921	+	90.8859i	0.0819097	+	0.128370i
$709$	184.876	+	134.320i	0.260755	+	0.189450i	0.710480	−	0.703717i	$-0.248478\pi$
$709$	184.876	+	134.320i	0.260755	+	0.189450i	−0.449725	+	0.893167i	$0.648478\pi$
$710$	28.0914	−	38.6645i	0.0395653	−	0.0544570i
$711$	−454.991	−	55.2061i	−0.639931	−	0.0776457i
$712$	−102.747	−	316.223i	−0.144308	−	0.444134i
$713$	55.2316	+	76.0198i	0.0774636	+	0.106620i
$714$	−161.460	−	132.904i	−0.226135	−	0.186140i
$715$	−121.249	−	50.9486i	−0.169579	−	0.0712568i
$716$		−	77.2875i		−	0.107943i
$717$	16.9156	−	279.848i	0.0235922	−	0.390304i
$718$	132.730	+	408.501i	0.184861	+	0.568943i
$719$	−765.742	−	248.805i	−1.06501	−	0.346043i	−0.276467	−	0.961023i	$-0.589164\pi$
$719$	−765.742	−	248.805i	−1.06501	−	0.346043i	−0.788542	+	0.614981i	$0.789164\pi$
$720$	53.7874	+	24.9880i	0.0747048	+	0.0347056i
$721$	−114.842	−	83.4376i	−0.159282	−	0.115725i
$722$	169.294	+	55.0069i	0.234479	+	0.0761868i
$723$	−226.928	+	577.300i	−0.313870	+	0.798478i
$724$	150.138	−	109.082i	0.207373	−	0.150665i
$725$		−	131.530i		−	0.181420i
$726$	515.706	+	310.395i	0.710339	+	0.427542i
$727$	−1002.31			−1.37869			−0.689345	−	0.724434i	$-0.742101\pi$
$727$	−1002.31			−1.37869			−0.689345	+	0.724434i	$0.742101\pi$
$728$	228.541	+	314.560i	0.313930	+	0.432088i
$729$	456.342	−	568.501i	0.625984	−	0.779836i
$730$	20.3198	−	62.5378i	0.0278353	−	0.0856682i
$731$	214.627	−	295.409i	0.293608	−	0.404117i
$732$	43.6112	+	168.136i	0.0595781	+	0.229694i
$733$	−223.915	+	689.141i	−0.305478	+	0.940165i	0.674020	+	0.738713i	$0.264566\pi$
$733$	−223.915	+	689.141i	−0.305478	+	0.940165i	−0.979498	+	0.201452i	$0.935434\pi$
$734$	−313.472	+	101.853i	−0.427074	+	0.138765i
$735$	5.33456	−	88.2538i	0.00725790	−	0.120073i
$736$	443.653			0.602789
$737$	−329.319	+	783.724i	−0.446837	+	1.06340i
$738$	193.442	+	987.637i	0.262117	+	1.33826i
$739$	696.026	−	505.693i	0.941849	−	0.684293i	−0.00701624	−	0.999975i	$-0.502233\pi$
$739$	696.026	−	505.693i	0.941849	−	0.684293i	0.948865	+	0.315682i	$0.102233\pi$
$740$	52.7774	−	17.1484i	0.0713208	−	0.0231735i
$741$	−689.438	+	439.913i	−0.930415	+	0.593675i
$742$	149.982	+	108.968i	0.202132	+	0.146858i
$743$	229.421	−	315.771i	0.308776	−	0.424994i	−0.626223	−	0.779644i	$-0.715400\pi$
$743$	229.421	−	315.771i	0.308776	−	0.424994i	0.934999	+	0.354650i	$0.115400\pi$
$744$	57.0762	+	89.4507i	0.0767154	+	0.120229i
$745$	33.9752	+	104.565i	0.0456043	+	0.140355i
$746$	653.465	+	899.418i	0.875959	+	1.20565i
$747$	−522.951	+	102.427i	−0.700069	+	0.137118i
$748$	215.774	−	50.6412i	0.288468	−	0.0677022i
$749$			74.1164i			0.0989538i
$750$	171.726	+	10.3801i	0.228968	+	0.0138401i
$751$	−266.909	−	821.461i	−0.355405	−	1.09382i	−0.955774	−	0.294101i	$-0.904980\pi$
$751$	−266.909	−	821.461i	−0.355405	−	1.09382i	0.600370	−	0.799722i	$-0.295020\pi$
$752$	662.355	+	215.212i	0.880791	+	0.286186i
$753$	−8.10273	+	2.10168i	−0.0107606	+	0.00279108i
$754$	123.212	+	89.5190i	0.163412	+	0.118725i
$755$	113.851	+	36.9926i	0.150797	+	0.0489968i
$756$	−86.6523	−	15.8680i	−0.114619	−	0.0209895i
$757$	683.966	−	496.931i	0.903522	−	0.656447i	−0.0358461	−	0.999357i	$-0.511413\pi$
$757$	683.966	−	496.931i	0.903522	−	0.656447i	0.939368	+	0.342910i	$0.111413\pi$
$758$		−	650.647i		−	0.858373i
$759$	−532.614	+	546.723i	−0.701731	+	0.720320i
$760$	96.8528			0.127438
$761$	−103.379	−	142.289i	−0.135847	−	0.186977i	0.735674	−	0.677336i	$-0.236866\pi$
$761$	−103.379	−	142.289i	−0.135847	−	0.186977i	−0.871521	+	0.490359i	$0.836866\pi$
$762$	−846.213	−	332.634i	−1.11052	−	0.436528i
$763$	−33.2614	+	102.368i	−0.0435929	+	0.134165i
$764$	41.3108	−	56.8594i	0.0540717	−	0.0744233i
$765$	−42.6767	+	91.8628i	−0.0557865	+	0.120082i
$766$	255.022	−	784.878i	0.332927	−	1.02464i
$767$	−467.833	+	152.008i	−0.609951	+	0.198185i
$768$	641.387	+	38.7690i	0.835139	+	0.0504805i
$769$	1341.04			1.74388			0.871941	−	0.489611i	$-0.162861\pi$
$769$	1341.04			1.74388			0.871941	+	0.489611i	$0.162861\pi$
$770$	25.1667	+	21.7171i	0.0326840	+	0.0282041i
$771$	763.025	−	926.972i	0.989657	−	1.20230i
$772$	−152.736	+	110.969i	−0.197844	+	0.143742i
$773$	746.230	−	242.465i	0.965368	−	0.313667i	0.216424	−	0.976300i	$-0.430561\pi$
$773$	746.230	−	242.465i	0.965368	−	0.313667i	0.748945	+	0.662632i	$0.230561\pi$
$774$	−40.7363	+	335.736i	−0.0526309	+	0.433767i
$775$	80.5641	+	58.5332i	0.103954	+	0.0755268i
$776$	−83.3742	+	114.755i	−0.107441	+	0.147880i
$777$	419.210	−	267.488i	0.539524	−	0.344257i
$778$	211.252	+	650.167i	0.271532	+	0.835690i
$779$	631.303	+	868.914i	0.810402	+	1.11542i
$780$	28.5060	−	34.6309i	0.0365461	−	0.0443986i
$781$	235.182	+	388.210i	0.301130	+	0.497068i
$782$		−	617.954i		−	0.790222i
$783$	−143.599	+	19.2184i	−0.183396	+	0.0245446i
$784$	123.005	+	378.571i	0.156894	+	0.482871i
$785$	43.4051	+	14.1032i	0.0552931	+	0.0179658i
$786$	105.550	+	406.932i	0.134287	+	0.517725i
$787$	1171.82	+	851.375i	1.48897	+	1.08180i	0.974526	+	0.224273i	$0.0720007\pi$
$787$	1171.82	+	851.375i	1.48897	+	1.08180i	0.514442	+	0.857525i	$0.327999\pi$
$788$	26.5659	+	8.63178i	0.0337130	+	0.0109540i
$789$	−1058.77	−	416.189i	−1.34192	−	0.527489i
$790$	−47.7184	+	34.6695i	−0.0604031	+	0.0438854i
$791$			378.785i			0.478869i
$792$	−637.599	+	579.965i	−0.805050	+	0.732278i
$793$	−792.536			−0.999415
$794$	166.888	+	229.702i	0.210186	+	0.289297i
$795$	32.8503	−	83.5704i	0.0413211	−	0.105120i
$796$	−58.3237	+	179.502i	−0.0732709	+	0.225505i
$797$	−203.605	+	280.238i	−0.255464	+	0.351616i	−0.917416	−	0.397931i	$-0.869728\pi$
$797$	−203.605	+	280.238i	−0.255464	+	0.351616i	0.661951	+	0.749547i	$0.269728\pi$
$798$	200.086	−	51.8984i	0.250735	−	0.0650355i
$799$	−367.558	+	1131.23i	−0.460022	+	1.41580i
$800$	447.162	−	145.292i	0.558952	−	0.181615i
$801$	−234.056	+	251.714i	−0.292205	+	0.314250i
$802$	−1203.85			−1.50107
$803$	472.802	+	407.996i	0.588794	+	0.508090i
$804$	−223.845	−	184.255i	−0.278414	−	0.229173i
$805$	−34.1023	+	24.7768i	−0.0423631	+	0.0307786i
$806$	−109.664	+	35.6318i	−0.136059	+	0.0442082i
$807$	−50.3488	−	78.9074i	−0.0623901	−	0.0977787i
$808$	−733.888	−	533.201i	−0.908277	−	0.659902i
$809$	307.526	−	423.274i	0.380131	−	0.523206i	−0.575488	−	0.817810i	$-0.695188\pi$
$809$	307.526	−	423.274i	0.380131	−	0.523206i	0.955619	+	0.294604i	$0.0951878\pi$
$810$	−6.81172	−	93.5690i	−0.00840954	−	0.115517i
$811$	−319.359	−	982.886i	−0.393784	−	1.21194i	−0.929904	−	0.367802i	$-0.880111\pi$
$811$	−319.359	−	982.886i	−0.393784	−	1.21194i	0.536120	−	0.844142i	$-0.319889\pi$
$812$	10.2906	+	14.1638i	0.0126732	+	0.0174431i
$813$	1200.06	+	987.811i	1.47608	+	1.21502i
$814$	96.8040	−	1154.74i	0.118924	−	1.41860i
$815$			10.7838i			0.0132317i
$816$	27.5146	−	455.196i	0.0337189	−	0.557839i
$817$	111.532	+	343.261i	0.136514	+	0.420148i
$818$	−475.294	−	154.432i	−0.581044	−	0.188793i
$819$	169.346	−	364.524i	0.206772	−	0.445084i
$820$	−47.6558	−	34.6239i	−0.0581168	−	0.0422243i
$821$	92.9928	+	30.2152i	0.113268	+	0.0368029i	0.365102	−	0.930967i	$-0.381034\pi$
$821$	92.9928	+	30.2152i	0.113268	+	0.0368029i	−0.251835	+	0.967770i	$0.581034\pi$
$822$	−371.927	+	946.172i	−0.452465	+	1.15106i
$823$	−583.839	+	424.184i	−0.709404	+	0.515412i	−0.882981	−	0.469408i	$-0.844467\pi$
$823$	−583.839	+	424.184i	−0.709404	+	0.515412i	0.173578	+	0.984820i	$0.444467\pi$
$824$		−	473.673i		−	0.574846i
$825$	−357.780	+	725.473i	−0.433673	+	0.879361i
$826$	124.330			0.150521
$827$	−722.545	−	994.498i	−0.873694	−	1.20254i	−0.978128	−	0.208005i	$-0.933303\pi$
$827$	−722.545	−	994.498i	−0.873694	−	1.20254i	0.104433	−	0.994532i	$-0.466697\pi$
$828$	−126.527	−	227.493i	−0.152810	−	0.274750i
$829$	−59.7651	+	183.938i	−0.0720930	+	0.221879i	−0.980610	−	0.195968i	$-0.937215\pi$
$829$	−59.7651	+	183.938i	−0.0720930	+	0.221879i	0.908517	+	0.417847i	$0.137215\pi$
$830$	−40.3095	+	55.4812i	−0.0485656	+	0.0668448i
$831$	−277.151	−	1068.51i	−0.333515	−	1.28582i
$832$	−367.840	+	1132.09i	−0.442115	+	1.36069i
$833$	−646.556	+	210.079i	−0.776178	+	0.252195i
$834$	15.0793	−	249.469i	0.0180807	−	0.299124i
$835$	−107.642			−0.128912
$836$	−84.8672	+	201.970i	−0.101516	+	0.241591i
$837$	52.1329	−	96.5094i	0.0622854	−	0.115304i
$838$	768.930	−	558.660i	0.917577	−	0.666659i
$839$	554.741	−	180.246i	0.661193	−	0.214835i	0.0408501	−	0.999165i	$-0.486993\pi$
$839$	554.741	−	180.246i	0.661193	−	0.214835i	0.620343	+	0.784331i	$0.286993\pi$
$840$	−40.1274	+	25.6043i	−0.0477707	+	0.0304813i
$841$	−657.089	−	477.403i	−0.781319	−	0.567661i
$842$	545.099	−	750.264i	0.647386	−	0.891050i
$843$	−517.019	−	810.279i	−0.613308	−	0.961185i
$844$	70.1668	+	215.951i	0.0831360	+	0.255866i
$845$	50.9064	+	70.0667i	0.0602443	+	0.0829192i
$846$	−211.752	−	1081.12i	−0.250297	−	1.27792i
$847$	−282.739	+	140.451i	−0.333812	+	0.165822i
$848$			404.267i			0.476730i
$849$	481.506	+	29.1049i	0.567144	+	0.0342814i
$850$	−202.373	−	622.841i	−0.238086	−	0.732754i
$851$	1397.52	+	454.082i	1.64221	+	0.533587i
$852$	−149.840	+	38.8655i	−0.175869	+	0.0456168i
$853$	348.868	+	253.468i	0.408990	+	0.297148i	0.773193	−	0.634171i	$-0.218659\pi$
$853$	348.868	+	253.468i	0.408990	+	0.297148i	−0.364203	+	0.931320i	$0.618659\pi$
$854$	190.510	+	61.9005i	0.223080	+	0.0724830i
$855$	−48.6649	−	87.4988i	−0.0569180	−	0.102338i
$856$	−200.082	+	145.368i	−0.233740	+	0.169822i
$857$			580.461i			0.677317i	0.940909	+	0.338659i	$0.109973\pi$
$857$			580.461i			0.677317i	−0.940909	+	0.338659i	$0.890027\pi$
$858$	−436.091	−	828.911i	−0.508265	−	0.966097i
$859$	−812.241			−0.945566			−0.472783	−	0.881179i	$-0.656751\pi$
$859$	−812.241			−0.945566			−0.472783	+	0.881179i	$0.656751\pi$
$860$	−11.6352	−	16.0145i	−0.0135294	−	0.0186216i
$861$	−491.266	−	193.110i	−0.570576	−	0.224285i
$862$	102.402	−	315.160i	0.118795	−	0.365614i
$863$	369.257	−	508.239i	0.427876	−	0.588921i	−0.539588	−	0.841929i	$-0.681420\pi$
$863$	369.257	−	508.239i	0.427876	−	0.588921i	0.967464	+	0.253008i	$0.0814199\pi$
$864$	−223.961	−	466.965i	−0.259214	−	0.540469i
$865$	5.41846	−	16.6763i	0.00626412	−	0.0192790i
$866$	−163.198	+	53.0264i	−0.188451	+	0.0612314i
$867$	−87.9967	−	5.31902i	−0.101496	−	0.00613497i
$868$	−13.2551			−0.0152708
$869$	−127.993	−	545.360i	−0.147288	−	0.627572i
$870$	−11.8493	+	14.3953i	−0.0136199	+	0.0165464i
$871$	1070.19	−	777.542i	1.22870	−	0.892700i
$872$	−341.586	+	110.988i	−0.391727	+	0.127280i
$873$	145.564	+	17.6619i	0.166740	+	0.0202313i
$874$	494.158	+	359.026i	0.565398	+	0.410785i
$875$	−53.0385	+	73.0012i	−0.0606154	+	0.0834299i
$876$	−179.548	+	114.565i	−0.204963	+	0.130782i
$877$	371.068	+	1142.03i	0.423111	+	1.30220i	0.904791	+	0.425855i	$0.140027\pi$
$877$	371.068	+	1142.03i	0.423111	+	1.30220i	−0.481680	+	0.876347i	$0.659973\pi$
$878$	−645.749	−	888.797i	−0.735477	−	1.01230i
$879$	−554.704	+	673.891i	−0.631063	+	0.766656i
$880$	−6.05556	+	72.2347i	−0.00688132	+	0.0820849i
$881$		−	131.219i		−	0.148943i	−0.997223	−	0.0744714i	$-0.976273\pi$
$881$		−	131.219i		−	0.148943i	0.997223	−	0.0744714i	$-0.0237269\pi$
$882$	428.767	−	461.116i	0.486131	−	0.522807i
$883$	−39.2451	−	120.784i	−0.0444452	−	0.136788i	0.926371	−	0.376611i	$-0.122911\pi$
$883$	−39.2451	−	120.784i	−0.0444452	−	0.136788i	−0.970817	+	0.239823i	$0.922911\pi$
$884$	−328.007	−	106.576i	−0.371048	−	0.120561i
$885$	−15.1198	−	58.2920i	−0.0170845	−	0.0658667i
$886$	−282.823	−	205.483i	−0.319214	−	0.231922i
$887$	1136.31	+	369.209i	1.28107	+	0.416245i	0.868957	−	0.494888i	$-0.164791\pi$
$887$	1136.31	+	369.209i	1.28107	+	0.416245i	0.412113	+	0.911133i	$0.364791\pi$
$888$	1544.31	+	607.047i	1.73909	+	0.683612i
$889$	385.818	−	280.313i	0.433991	−	0.315313i
$890$			44.2339i			0.0497010i
$891$	844.321	+	284.609i	0.947611	+	0.319427i
$892$	235.138			0.263608
$893$	−691.057	−	951.158i	−0.773860	−	1.06513i
$894$	−286.448	+	728.716i	−0.320411	+	0.815119i
$895$	−13.3406	+	41.0580i	−0.0149057	+	0.0458749i
$896$	59.1774	−	81.4507i	0.0660462	−	0.0909048i
$897$	1149.67	−	298.202i	1.28169	−	0.332443i
$898$	−122.602	+	377.331i	−0.136528	+	0.420190i
$899$	−20.7326	+	6.73643i	−0.0230618	+	0.00749325i
$900$	−202.029	−	187.856i	−0.224477	−	0.208729i
$901$	−690.442			−0.766306
$902$	−1052.05	+	637.345i	−1.16635	+	0.706591i
$903$	−136.955	−	112.733i	−0.151667	−	0.124842i
$904$	−1022.55	+	742.929i	−1.13114	+	0.821824i
$905$	−98.5876	+	32.0331i	−0.108937	+	0.0353956i
$906$	458.579	+	718.692i	0.506158	+	0.793258i
$907$	−424.397	−	308.342i	−0.467913	−	0.339958i	0.328715	−	0.944429i	$-0.393385\pi$
$907$	−424.397	−	308.342i	−0.467913	−	0.339958i	−0.796627	+	0.604471i	$0.793385\pi$
$908$	−315.494	+	434.241i	−0.347461	+	0.478239i
$909$	−112.953	+	930.922i	−0.124261	+	1.02412i
$910$	−15.9844	−	49.1949i	−0.0175653	−	0.0540603i
$911$	103.220	+	142.070i	0.113304	+	0.155950i	0.861903	−	0.507074i	$-0.169273\pi$
$911$	103.220	+	142.070i	0.113304	+	0.155950i	−0.748598	+	0.663024i	$0.769273\pi$
$912$	348.020	+	286.468i	0.381601	+	0.314110i
$913$	−337.473	−	557.058i	−0.369631	−	0.610140i
$914$		−	44.2524i		−	0.0484162i
$915$	5.85404	−	96.8481i	0.00639786	−	0.105845i
$916$	52.4674	+	161.478i	0.0572788	+	0.176286i
$917$	−209.706	−	68.1377i	−0.228687	−	0.0743050i
$918$	−650.425	+	311.950i	−0.708524	+	0.339815i
$919$	1055.86	+	767.124i	1.14892	+	0.834738i	0.988337	−	0.152285i	$-0.0486631\pi$
$919$	1055.86	+	767.124i	1.14892	+	0.834738i	0.160581	+	0.987023i	$0.448663\pi$
$920$	−133.773	−	43.4654i	−0.145405	−	0.0472450i
$921$	309.278	−	786.796i	0.335807	−	0.854284i
$922$	527.369	−	383.156i	0.571984	−	0.415571i
$923$		−	706.294i		−	0.765216i
$924$	−18.2318	−	106.115i	−0.0197314	−	0.114843i
$925$	1557.28			1.68355
$926$	104.242	+	143.476i	0.112572	+	0.154942i
$927$	−427.925	+	238.003i	−0.461624	+	0.256745i
$928$	−31.8056	+	97.8877i	−0.0342733	+	0.105482i
$929$	−916.652	+	1261.66i	−0.986708	+	1.35809i	−0.0535724	+	0.998564i	$0.517061\pi$
$929$	−916.652	+	1261.66i	−0.986708	+	1.35809i	−0.933136	+	0.359524i	$0.882939\pi$
$930$	−3.54419	−	13.6641i	−0.00381096	−	0.0146926i
$931$	207.651	−	639.084i	0.223041	−	0.686449i
$932$	388.770	−	126.319i	0.417136	−	0.135536i
$933$	−85.7523	+	1418.67i	−0.0919102	+	1.52054i
$934$	−701.251			−0.750804
$935$	−123.369	−	10.3422i	−0.131945	−	0.0110612i
$936$	1316.20	−	257.795i	1.40620	−	0.275422i
$937$	581.968	−	422.824i	0.621097	−	0.451253i	−0.232208	−	0.972666i	$-0.574595\pi$
$937$	581.968	−	422.824i	0.621097	−	0.451253i	0.853305	+	0.521413i	$0.174595\pi$
$938$	−317.983	+	103.319i	−0.339001	+	0.110148i
$939$	−75.8053	+	48.3695i	−0.0807298	+	0.0515117i
$940$	52.1664	+	37.9011i	0.0554962	+	0.0403204i
$941$	−689.641	+	949.209i	−0.732881	+	1.00872i	0.266116	+	0.963941i	$0.414260\pi$
$941$	−689.641	+	949.209i	−0.732881	+	1.00872i	−0.998997	+	0.0447831i	$0.985740\pi$
$942$	174.830	+	273.996i	0.185595	+	0.290866i
$943$	−482.004	−	1483.46i	−0.511139	−	1.57312i
$944$	159.361	+	219.342i	0.168815	+	0.232353i
$945$	43.2940	+	23.3867i	0.0458137	+	0.0247478i
$946$	−402.419	+	94.4457i	−0.425390	+	0.0998369i
$947$			266.119i			0.281013i	0.990080	+	0.140506i	$0.0448730\pi$
$947$			266.119i			0.281013i	−0.990080	+	0.140506i	$0.955127\pi$
$948$	190.699	+	11.5269i	0.201160	+	0.0121592i
$949$	−300.296	−	924.216i	−0.316434	−	0.973884i
$950$	615.643	+	200.035i	0.648046	+	0.210563i
$951$	−462.524	+	119.969i	−0.486356	+	0.126151i
$952$	296.102	+	215.131i	0.311032	+	0.225978i
$953$	121.881	+	39.6016i	0.127892	+	0.0415547i	0.372264	−	0.928127i	$-0.378582\pi$
$953$	121.881	+	39.6016i	0.127892	+	0.0415547i	−0.244372	+	0.969682i	$0.578582\pi$
$954$	558.864	−	310.828i	0.585811	−	0.325816i
$955$	−31.7603	+	23.0752i	−0.0332569	+	0.0241625i
$956$			116.864i			0.122242i
$957$	−82.4459	−	156.711i	−0.0861504	−	0.163752i
$958$	894.933			0.934168
$959$	−313.425	−	431.393i	−0.326825	−	0.449836i
$960$	−135.625	−	53.3122i	−0.141276	−	0.0555336i
$961$	−291.865	+	898.268i	−0.303710	+	0.934723i
$962$	−1059.88	+	1458.80i	−1.10175	+	1.51643i
$963$	231.862	+	107.716i	0.240770	+	0.111854i
$964$	79.9003	−	245.908i	0.0828841	−	0.255091i
$965$	100.293	−	32.5872i	0.103931	−	0.0337692i
$966$	−299.649	−	18.1125i	−0.310196	−	0.0187500i
$967$	1324.17			1.36936			0.684682	−	0.728842i	$-0.259941\pi$
$967$	1324.17			1.36936			0.684682	+	0.728842i	$0.259941\pi$
$968$	−933.705	−	487.797i	−0.964572	−	0.503923i
$969$	−489.255	+	594.379i	−0.504907	+	0.613394i
$970$	15.2664	−	11.0917i	0.0157386	−	0.0114348i
$971$	556.252	−	180.737i	0.572865	−	0.186135i	−0.00823681	−	0.999966i	$-0.502622\pi$
$971$	556.252	−	180.737i	0.572865	−	0.186135i	0.581102	+	0.813831i	$0.302622\pi$
$972$	−175.575	+	248.017i	−0.180633	+	0.255161i
$973$	106.050	+	77.0500i	0.108993	+	0.0791881i
$974$	−595.161	+	819.169i	−0.611048	+	0.841036i
$975$	1061.11	−	677.066i	1.08831	−	0.694427i
$976$	134.984	+	415.437i	0.138303	+	0.425652i
$977$	−406.363	−	559.311i	−0.415930	−	0.572478i	0.548722	−	0.836005i	$-0.315114\pi$
$977$	−406.363	−	559.311i	−0.415930	−	0.572478i	−0.964652	+	0.263526i	$0.915114\pi$
$978$	−48.8073	+	59.2943i	−0.0499052	+	0.0606281i
$979$	−387.298	−	162.741i	−0.395605	−	0.166232i
$980$			36.8545i			0.0376066i
$981$	271.903	+	252.828i	0.277169	+	0.257725i
$982$	29.1423	+	89.6907i	0.0296764	+	0.0913347i
$983$	−623.407	−	202.557i	−0.634188	−	0.206060i	−0.0257588	−	0.999668i	$-0.508200\pi$
$983$	−623.407	−	202.557i	−0.634188	−	0.206060i	−0.608430	+	0.793608i	$0.708200\pi$
$984$	−442.231	−	1704.96i	−0.449422	−	1.73268i
$985$	−12.6229	−	9.17105i	−0.0128151	−	0.00931071i
$986$	136.346	+	44.3013i	0.138281	+	0.0449304i
$987$	537.765	+	211.388i	0.544848	+	0.214172i
$988$	275.795	−	200.377i	0.279144	−	0.202810i
$989$		−	524.164i		−	0.529994i
$990$	104.514	−	47.1677i	0.105570	−	0.0476442i
$991$	95.0559			0.0959192			0.0479596	−	0.998849i	$-0.484728\pi$
$991$	95.0559			0.0959192			0.0479596	+	0.998849i	$0.484728\pi$
$992$	−45.8036	−	63.0433i	−0.0461730	−	0.0635517i
$993$	−365.151	+	928.937i	−0.367726	+	0.935485i
$994$	−55.1646	+	169.779i	−0.0554976	+	0.170804i
$995$	61.9675	−	85.2909i	0.0622789	−	0.0857195i
$996$	215.012	−	55.7697i	0.215875	−	0.0559937i
$997$	−241.467	+	743.158i	−0.242193	+	0.745394i	0.753892	+	0.656998i	$0.228174\pi$
$997$	−241.467	+	743.158i	−0.242193	+	0.745394i	−0.996085	+	0.0883960i	$0.971826\pi$
$998$	739.422	−	240.253i	0.740904	−	0.240734i
$999$	−227.541	−	1700.18i	−0.227769	−	1.70188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.3.h.b.14.3	yes	16
3.2	odd	2	inner	33.3.h.b.14.2	✓	16
11.2	odd	10		363.3.b.l.122.5		8
11.3	even	5		363.3.h.o.269.3		16
11.4	even	5	inner	33.3.h.b.26.2	yes	16
11.5	even	5		363.3.h.o.251.2		16
11.6	odd	10		363.3.h.n.251.3		16
11.7	odd	10		363.3.h.j.323.3		16
11.8	odd	10		363.3.h.n.269.2		16
11.9	even	5		363.3.b.m.122.4		8
11.10	odd	2		363.3.h.j.245.2		16
33.2	even	10		363.3.b.l.122.4		8
33.5	odd	10		363.3.h.o.251.3		16
33.8	even	10		363.3.h.n.269.3		16
33.14	odd	10		363.3.h.o.269.2		16
33.17	even	10		363.3.h.n.251.2		16
33.20	odd	10		363.3.b.m.122.5		8
33.26	odd	10	inner	33.3.h.b.26.3	yes	16
33.29	even	10		363.3.h.j.323.2		16
33.32	even	2		363.3.h.j.245.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.14.2	✓	16	3.2	odd	2	inner
33.3.h.b.14.3	yes	16	1.1	even	1	trivial
33.3.h.b.26.2	yes	16	11.4	even	5	inner
33.3.h.b.26.3	yes	16	33.26	odd	10	inner
363.3.b.l.122.4		8	33.2	even	10
363.3.b.l.122.5		8	11.2	odd	10
363.3.b.m.122.4		8	11.9	even	5
363.3.b.m.122.5		8	33.20	odd	10
363.3.h.j.245.2		16	11.10	odd	2
363.3.h.j.245.3		16	33.32	even	2
363.3.h.j.323.2		16	33.29	even	10
363.3.h.j.323.3		16	11.7	odd	10
363.3.h.n.251.2		16	33.17	even	10
363.3.h.n.251.3		16	11.6	odd	10
363.3.h.n.269.2		16	11.8	odd	10
363.3.h.n.269.3		16	33.8	even	10
363.3.h.o.251.2		16	11.5	even	5
363.3.h.o.251.3		16	33.5	odd	10
363.3.h.o.269.2		16	33.14	odd	10
363.3.h.o.269.3		16	11.3	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)

\(f(q)\)	\(=\)	\(q+(0.974642 + 1.34148i) q^{2} +(-1.09751 + 2.79204i) q^{3} +(0.386428 - 1.18930i) q^{4} +(-0.410570 + 0.565101i) q^{5} +(-4.81514 + 1.24895i) q^{6} +(0.806259 - 2.48141i) q^{7} +(8.28007 - 2.69036i) q^{8} +(-6.59095 - 6.12857i) q^{9} +O(q^{10})\)	\(q+(0.974642 + 1.34148i) q^{2} +(-1.09751 + 2.79204i) q^{3} +(0.386428 - 1.18930i) q^{4} +(-0.410570 + 0.565101i) q^{5} +(-4.81514 + 1.24895i) q^{6} +(0.806259 - 2.48141i) q^{7} +(8.28007 - 2.69036i) q^{8} +(-6.59095 - 6.12857i) q^{9} -1.15823 q^{10} +(4.26126 - 10.1411i) q^{11} +(2.89647 + 2.38419i) q^{12} +(-13.8479 + 10.0611i) q^{13} +(4.11458 - 1.33691i) q^{14} +(-1.12718 - 1.76653i) q^{15} +(7.63243 + 5.54529i) q^{16} +(-9.47072 + 13.0353i) q^{17} +(1.79754 - 14.8148i) q^{18} +(-4.92151 - 15.1469i) q^{19} +(0.513421 + 0.706663i) q^{20} +(6.04332 + 4.97448i) q^{21} +(17.7573 - 4.16754i) q^{22} +23.1295i q^{23} +(-1.57587 + 26.0710i) q^{24} +(7.57465 + 23.3124i) q^{25} +(-26.9935 - 8.77071i) q^{26} +(24.3448 - 11.6760i) q^{27} +(-2.63959 - 1.91777i) q^{28} +(-5.10329 - 1.65816i) q^{29} +(1.27117 - 3.23382i) q^{30} +(3.28671 - 2.38793i) q^{31} -19.1813i q^{32} +(23.6375 + 23.0275i) q^{33} -26.7172 q^{34} +(1.07122 + 1.47441i) q^{35} +(-9.83565 + 5.47038i) q^{36} +(19.6322 - 60.4217i) q^{37} +(15.5225 - 21.3649i) q^{38} +(-12.8927 - 49.7060i) q^{39} +(-1.87922 + 5.78366i) q^{40} +(-64.1371 + 20.8394i) q^{41} +(-0.783092 + 12.9553i) q^{42} -22.6622 q^{43} +(-10.4142 - 8.98672i) q^{44} +(6.16931 - 1.20834i) q^{45} +(-31.0277 + 22.5429i) q^{46} +(70.2078 - 22.8119i) q^{47} +(-23.8593 + 15.2240i) q^{48} +(34.1345 + 24.8002i) q^{49} +(-23.8905 + 32.8825i) q^{50} +(-26.0009 - 40.7490i) q^{51} +(6.61446 + 20.3572i) q^{52} +(25.1873 + 34.6673i) q^{53} +(39.3906 + 21.2782i) q^{54} +(3.98120 + 6.57167i) q^{55} -22.7154i q^{56} +(47.6920 + 2.88277i) q^{57} +(-2.74949 - 8.46207i) q^{58} +(27.3316 + 8.88056i) q^{59} +(-2.53651 + 0.657920i) q^{60} +(37.4585 + 27.2152i) q^{61} +(6.40673 + 2.08167i) q^{62} +(-20.5215 + 11.4136i) q^{63} +(56.2610 - 40.8760i) q^{64} -11.9562i q^{65} +(-7.85282 + 54.1529i) q^{66} -77.2821 q^{67} +(11.8432 + 16.3008i) q^{68} +(-64.5783 - 25.3848i) q^{69} +(-0.933834 + 2.87405i) q^{70} +(-24.2537 + 33.3824i) q^{71} +(-71.0615 - 33.0130i) q^{72} +(-17.5438 + 53.9942i) q^{73} +(100.189 - 32.5533i) q^{74} +(-73.4023 - 4.43685i) q^{75} -19.9160 q^{76} +(-21.7285 - 18.7503i) q^{77} +(54.1137 - 65.7409i) q^{78} +(41.1994 - 29.9331i) q^{79} +(-6.26730 + 2.03637i) q^{80} +(5.88115 + 80.7862i) q^{81} +(-90.4664 - 65.7277i) q^{82} +(34.8026 - 47.9017i) q^{83} +(8.25147 - 5.26505i) q^{84} +(-3.47788 - 10.7038i) q^{85} +(-22.0875 - 30.4009i) q^{86} +(10.2306 - 12.4287i) q^{87} +(8.00033 - 95.4332i) q^{88} -38.1909i q^{89} +(7.63383 + 7.09830i) q^{90} +(13.8007 + 42.4742i) q^{91} +(27.5079 + 8.93786i) q^{92} +(3.06001 + 11.7974i) q^{93} +(99.0291 + 71.9489i) q^{94} +(10.5801 + 3.43769i) q^{95} +(53.5549 + 21.0516i) q^{96} +(-13.1808 + 9.57644i) q^{97} +69.9620i q^{98} +(-90.2361 + 40.7240i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more