LMFDB - Embedded newform 35.3.i.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(19,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("35.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.i (of order $6$, degree $2$, 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:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 180x^{8} - 669x^{6} + 1980x^{4} - 135x^{2} + 9 $ x^12 - 15x^10 + 180x^8 - 669x^6 + 1980x^4 - 135*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Root			$0.226181 + 0.130586i$ of defining polynomial
Character	$\chi$	$=$	35.19
Dual form			35.3.i.a.24.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.226181 + 0.130586i) q^{2} +(1.88157 + 3.25898i) q^{3} +(-1.96589 - 3.40503i) q^{4} +(2.11218 + 4.53196i) q^{5} +0.982826i q^{6} +(-1.66053 - 6.80019i) q^{7} -2.07156i q^{8} +(-2.58064 + 4.46979i) q^{9} +O(q^{10})$	\(q+(0.226181 + 0.130586i) q^{2} +(1.88157 + 3.25898i) q^{3} +(-1.96589 - 3.40503i) q^{4} +(2.11218 + 4.53196i) q^{5} +0.982826i q^{6} +(-1.66053 - 6.80019i) q^{7} -2.07156i q^{8} +(-2.58064 + 4.46979i) q^{9} +(-0.114075 + 1.30086i) q^{10} +(-3.04653 - 5.27675i) q^{11} +(7.39795 - 12.8136i) q^{12} -13.0886 q^{13} +(0.512426 - 1.75492i) q^{14} +(-10.7954 + 15.4108i) q^{15} +(-7.59306 + 13.1516i) q^{16} +(-5.05373 - 8.75332i) q^{17} +(-1.16738 + 0.673989i) q^{18} +(19.5373 + 11.2799i) q^{19} +(11.2792 - 16.1014i) q^{20} +(19.0373 - 18.2067i) q^{21} -1.59133i q^{22} +(30.2957 + 17.4912i) q^{23} +(6.75116 - 3.89779i) q^{24} +(-16.0774 + 19.1446i) q^{25} +(-2.96039 - 1.70918i) q^{26} +14.4457 q^{27} +(-19.8904 + 19.0226i) q^{28} -16.3474 q^{29} +(-4.45413 + 2.07590i) q^{30} +(-23.4907 + 13.5624i) q^{31} +(-10.6109 + 6.12620i) q^{32} +(11.4645 - 19.8572i) q^{33} -2.63978i q^{34} +(27.3109 - 21.8887i) q^{35} +20.2930 q^{36} +(-14.4349 - 8.33401i) q^{37} +(2.94598 + 5.10258i) q^{38} +(-24.6272 - 42.6555i) q^{39} +(9.38822 - 4.37550i) q^{40} +19.7267i q^{41} +(6.68341 - 1.63202i) q^{42} -53.4739i q^{43} +(-11.9783 + 20.7471i) q^{44} +(-25.7077 - 2.25436i) q^{45} +(4.56821 + 7.91237i) q^{46} +(-18.3385 + 31.7632i) q^{47} -57.1476 q^{48} +(-43.4852 + 22.5839i) q^{49} +(-6.13642 + 2.23067i) q^{50} +(19.0179 - 32.9400i) q^{51} +(25.7308 + 44.5671i) q^{52} +(31.9730 - 18.4596i) q^{53} +(3.26734 + 1.88640i) q^{54} +(17.4792 - 24.9522i) q^{55} +(-14.0870 + 3.43989i) q^{56} +84.8955i q^{57} +(-3.69747 - 2.13474i) q^{58} +(92.4861 - 53.3969i) q^{59} +(73.6967 + 6.46260i) q^{60} +(-18.4211 - 10.6354i) q^{61} -7.08422 q^{62} +(34.6807 + 10.1266i) q^{63} +57.5445 q^{64} +(-27.6455 - 59.3171i) q^{65} +(5.18613 - 2.99421i) q^{66} +(5.33016 - 3.07737i) q^{67} +(-19.8702 + 34.4162i) q^{68} +131.644i q^{69} +(9.03556 - 1.38440i) q^{70} -48.1133 q^{71} +(9.25943 + 5.34594i) q^{72} +(-2.82277 - 4.88919i) q^{73} +(-2.17660 - 3.76999i) q^{74} +(-92.6428 - 16.3739i) q^{75} -88.7000i q^{76} +(-30.8240 + 29.4792i) q^{77} -12.8638i q^{78} +(19.1607 - 33.1873i) q^{79} +(-75.6404 - 6.63304i) q^{80} +(50.4064 + 87.3064i) q^{81} +(-2.57602 + 4.46180i) q^{82} +102.359 q^{83} +(-99.4197 - 29.0300i) q^{84} +(28.9953 - 41.3919i) q^{85} +(6.98292 - 12.0948i) q^{86} +(-30.7588 - 53.2759i) q^{87} +(-10.9311 + 6.31106i) q^{88} +(-34.1003 - 19.6878i) q^{89} +(-5.52021 - 3.86695i) q^{90} +(21.7341 + 89.0050i) q^{91} -137.544i q^{92} +(-88.3991 - 51.0373i) q^{93} +(-8.29564 + 4.78949i) q^{94} +(-9.85369 + 112.367i) q^{95} +(-39.9304 - 23.0538i) q^{96} +33.5609 q^{97} +(-12.7847 - 0.570497i) q^{98} +31.4480 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 18 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 - 18 * q^9	$ 12 q + 6 q^{4} - 18 q^{9} - 54 q^{10} + 6 q^{11} - 66 q^{14} + 48 q^{15} - 6 q^{16} + 18 q^{19} + 12 q^{21} + 216 q^{24} + 18 q^{25} + 18 q^{26} + 48 q^{30} - 108 q^{31} + 222 q^{35} - 204 q^{36} - 240 q^{39} - 162 q^{40} - 42 q^{44} - 216 q^{45} + 114 q^{46} - 324 q^{49} - 192 q^{50} + 180 q^{51} + 252 q^{54} + 336 q^{56} + 396 q^{59} + 384 q^{60} - 108 q^{61} + 372 q^{64} - 54 q^{65} - 108 q^{66} + 300 q^{70} + 192 q^{71} - 594 q^{74} - 216 q^{75} - 192 q^{79} - 504 q^{80} + 294 q^{81} - 1200 q^{84} - 192 q^{85} - 384 q^{86} + 684 q^{89} - 72 q^{91} + 990 q^{94} + 288 q^{95} - 540 q^{96} + 396 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 - 18 * q^9 - 54 * q^10 + 6 * q^11 - 66 * q^14 + 48 * q^15 - 6 * q^16 + 18 * q^19 + 12 * q^21 + 216 * q^24 + 18 * q^25 + 18 * q^26 + 48 * q^30 - 108 * q^31 + 222 * q^35 - 204 * q^36 - 240 * q^39 - 162 * q^40 - 42 * q^44 - 216 * q^45 + 114 * q^46 - 324 * q^49 - 192 * q^50 + 180 * q^51 + 252 * q^54 + 336 * q^56 + 396 * q^59 + 384 * q^60 - 108 * q^61 + 372 * q^64 - 54 * q^65 - 108 * q^66 + 300 * q^70 + 192 * q^71 - 594 * q^74 - 216 * q^75 - 192 * q^79 - 504 * q^80 + 294 * q^81 - 1200 * q^84 - 192 * q^85 - 384 * q^86 + 684 * q^89 - 72 * q^91 + 990 * q^94 + 288 * q^95 - 540 * q^96 + 396 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.226181	+	0.130586i	0.113091	+	0.0652929i	0.555478	−	0.831531i	$-0.312535\pi$
$2$	0.226181	+	0.130586i	0.113091	+	0.0652929i	−0.442388	+	0.896824i	$0.645869\pi$
$3$	1.88157	+	3.25898i	0.627191	+	1.08633i	0.988113	+	0.153731i	$0.0491288\pi$
$3$	1.88157	+	3.25898i	0.627191	+	1.08633i	−0.360922	+	0.932596i	$0.617538\pi$
$4$	−1.96589	−	3.40503i	−0.491474	−	0.851257i
$5$	2.11218	+	4.53196i	0.422436	+	0.906393i
$5$	2.11218	+	4.53196i	0.422436	+	0.906393i
$6$			0.982826i			0.163804i
$7$	−1.66053	−	6.80019i	−0.237219	−	0.971456i
$7$	−1.66053	−	6.80019i	−0.237219	−	0.971456i
$8$		−	2.07156i		−	0.258945i
$9$	−2.58064	+	4.46979i	−0.286737	+	0.496644i
$10$	−0.114075	+	1.30086i	−0.0114075	+	0.130086i
$11$	−3.04653	−	5.27675i	−0.276957	−	0.479704i	0.693670	−	0.720293i	$-0.255993\pi$
$11$	−3.04653	−	5.27675i	−0.276957	−	0.479704i	−0.970627	+	0.240589i	$0.922659\pi$
$12$	7.39795	−	12.8136i	0.616496	−	1.06780i
$13$	−13.0886			−1.00682			−0.503408	−	0.864049i	$-0.667921\pi$
$13$	−13.0886			−1.00682			−0.503408	+	0.864049i	$0.667921\pi$
$14$	0.512426	−	1.75492i	0.0366019	−	0.125351i
$15$	−10.7954	+	15.4108i	−0.719691	+	1.02738i
$16$	−7.59306	+	13.1516i	−0.474566	+	0.821973i
$17$	−5.05373	−	8.75332i	−0.297278	−	0.514901i	0.678234	−	0.734846i	$-0.262746\pi$
$17$	−5.05373	−	8.75332i	−0.297278	−	0.514901i	−0.975512	+	0.219945i	$0.929412\pi$
$18$	−1.16738	+	0.673989i	−0.0648546	+	0.0374438i
$19$	19.5373	+	11.2799i	1.02828	+	0.593676i	0.916491	−	0.400056i	$-0.131009\pi$
$19$	19.5373	+	11.2799i	1.02828	+	0.593676i	0.111787	+	0.993732i	$0.464343\pi$
$20$	11.2792	−	16.1014i	0.563958	−	0.805070i
$21$	19.0373	−	18.2067i	0.906537	−	0.866986i
$22$		−	1.59133i		−	0.0723334i
$23$	30.2957	+	17.4912i	1.31720	+	0.760488i	0.983278	−	0.182111i	$-0.0582929\pi$
$23$	30.2957	+	17.4912i	1.31720	+	0.760488i	0.333927	+	0.942599i	$0.391626\pi$
$24$	6.75116	−	3.89779i	0.281298	−	0.162408i
$25$	−16.0774	+	19.1446i	−0.643096	+	0.765785i
$26$	−2.96039	−	1.70918i	−0.113861	−	0.0657379i
$27$	14.4457			0.535026
$28$	−19.8904	+	19.0226i	−0.710372	+	0.679380i
$29$	−16.3474			−0.563703			−0.281852	−	0.959458i	$-0.590949\pi$
$29$	−16.3474			−0.563703			−0.281852	+	0.959458i	$0.590949\pi$
$30$	−4.45413	+	2.07590i	−0.148471	+	0.0691968i
$31$	−23.4907	+	13.5624i	−0.757766	+	0.437496i	−0.828493	−	0.559999i	$-0.810801\pi$
$31$	−23.4907	+	13.5624i	−0.757766	+	0.437496i	0.0707270	+	0.997496i	$0.477468\pi$
$32$	−10.6109	+	6.12620i	−0.331591	+	0.191444i
$33$	11.4645	−	19.8572i	0.347410	−	0.601733i
$34$		−	2.63978i		−	0.0776406i
$35$	27.3109	−	21.8887i	0.780311	−	0.625391i
$36$	20.2930			0.563696
$37$	−14.4349	−	8.33401i	−0.390133	−	0.225243i	0.292085	−	0.956392i	$-0.405651\pi$
$37$	−14.4349	−	8.33401i	−0.390133	−	0.225243i	−0.682218	+	0.731149i	$0.738984\pi$
$38$	2.94598	+	5.10258i	0.0775257	+	0.134278i
$39$	−24.6272	−	42.6555i	−0.631466	−	1.09373i
$40$	9.38822	−	4.37550i	0.234706	−	0.109387i
$41$			19.7267i			0.481139i	0.970632	+	0.240569i	$0.0773341\pi$
$41$			19.7267i			0.481139i	−0.970632	+	0.240569i	$0.922666\pi$
$42$	6.68341	−	1.63202i	0.159129	−	0.0388576i
$43$		−	53.4739i		−	1.24358i	−0.783185	−	0.621789i	$-0.786406\pi$
$43$		−	53.4739i		−	1.24358i	0.783185	−	0.621789i	$-0.213594\pi$
$44$	−11.9783	+	20.7471i	−0.272235	+	0.471524i
$45$	−25.7077	−	2.25436i	−0.571283	−	0.0500968i
$46$	4.56821	+	7.91237i	0.0993089	+	0.172008i
$47$	−18.3385	+	31.7632i	−0.390181	+	0.675813i	−0.992473	−	0.122463i	$-0.960921\pi$
$47$	−18.3385	+	31.7632i	−0.390181	+	0.675813i	0.602293	+	0.798275i	$0.294254\pi$
$48$	−57.1476			−1.19058
$49$	−43.4852	+	22.5839i	−0.887454	+	0.460896i
$50$	−6.13642	+	2.23067i	−0.122728	+	0.0446135i
$51$	19.0179	−	32.9400i	0.372901	−	0.645883i
$52$	25.7308	+	44.5671i	0.494823	+	0.857059i
$53$	31.9730	−	18.4596i	0.603264	−	0.348294i	−0.167061	−	0.985947i	$-0.553428\pi$
$53$	31.9730	−	18.4596i	0.603264	−	0.348294i	0.770324	+	0.637652i	$0.220094\pi$
$54$	3.26734	+	1.88640i	0.0605063	+	0.0349333i
$55$	17.4792	−	24.9522i	0.317804	−	0.453676i
$56$	−14.0870	+	3.43989i	−0.251553	+	0.0614266i
$57$			84.8955i			1.48939i
$58$	−3.69747	−	2.13474i	−0.0637495	−	0.0368058i
$59$	92.4861	−	53.3969i	1.56756	−	0.905032i	0.571108	−	0.820875i	$-0.306514\pi$
$59$	92.4861	−	53.3969i	1.56756	−	0.905032i	0.996452	−	0.0841571i	$-0.0268198\pi$
$60$	73.6967	+	6.46260i	1.22828	+	0.107710i
$61$	−18.4211	−	10.6354i	−0.301985	−	0.174351i	0.341349	−	0.939937i	$-0.389116\pi$
$61$	−18.4211	−	10.6354i	−0.301985	−	0.174351i	−0.643334	+	0.765585i	$0.722450\pi$
$62$	−7.08422			−0.114262
$63$	34.6807	+	10.1266i	0.550487	+	0.160739i
$64$	57.5445			0.899133
$65$	−27.6455	−	59.3171i	−0.425315	−	0.912571i
$66$	5.18613	−	2.99421i	0.0785777	−	0.0453668i
$67$	5.33016	−	3.07737i	0.0795546	−	0.0459309i	−0.459695	−	0.888077i	$-0.652041\pi$
$67$	5.33016	−	3.07737i	0.0795546	−	0.0459309i	0.539250	+	0.842146i	$0.318708\pi$
$68$	−19.8702	+	34.4162i	−0.292209	+	0.506121i
$69$			131.644i			1.90789i
$70$	9.03556	−	1.38440i	0.129079	−	0.0197771i
$71$	−48.1133			−0.677652			−0.338826	−	0.940849i	$-0.610030\pi$
$71$	−48.1133			−0.677652			−0.338826	+	0.940849i	$0.610030\pi$
$72$	9.25943	+	5.34594i	0.128603	+	0.0742491i
$73$	−2.82277	−	4.88919i	−0.0386681	−	0.0669752i	0.846044	−	0.533114i	$-0.178978\pi$
$73$	−2.82277	−	4.88919i	−0.0386681	−	0.0669752i	−0.884712	+	0.466138i	$0.845645\pi$
$74$	−2.17660	−	3.76999i	−0.0294136	−	0.0509458i
$75$	−92.6428	−	16.3739i	−1.23524	−	0.218319i
$76$		−	88.7000i		−	1.16711i
$77$	−30.8240	+	29.4792i	−0.400312	+	0.382847i
$78$		−	12.8638i		−	0.164921i
$79$	19.1607	−	33.1873i	0.242540	−	0.420092i	−0.718897	−	0.695117i	$-0.755353\pi$
$79$	19.1607	−	33.1873i	0.242540	−	0.420092i	0.961437	+	0.275024i	$0.0886860\pi$
$80$	−75.6404	−	6.63304i	−0.945504	−	0.0829130i
$81$	50.4064	+	87.3064i	0.622301	+	1.07786i
$82$	−2.57602	+	4.46180i	−0.0314149	+	0.0544122i
$83$	102.359			1.23325			0.616623	−	0.787259i	$-0.288500\pi$
$83$	102.359			1.23325			0.616623	+	0.787259i	$0.288500\pi$
$84$	−99.4197	−	29.0300i	−1.18357	−	0.345595i
$85$	28.9953	−	41.3919i	0.341122	−	0.486963i
$86$	6.98292	−	12.0948i	0.0811968	−	0.140637i
$87$	−30.7588	−	53.2759i	−0.353550	−	0.612366i
$88$	−10.9311	+	6.31106i	−0.124217	+	0.0717166i
$89$	−34.1003	−	19.6878i	−0.383149	−	0.221211i	0.296038	−	0.955176i	$-0.404334\pi$
$89$	−34.1003	−	19.6878i	−0.383149	−	0.221211i	−0.679187	+	0.733965i	$0.737668\pi$
$90$	−5.52021	−	3.86695i	−0.0613357	−	0.0429661i
$91$	21.7341	+	89.0050i	0.238836	+	0.978077i
$92$		−	137.544i		−	1.49504i
$93$	−88.3991	−	51.0373i	−0.950528	−	0.548788i
$94$	−8.29564	+	4.78949i	−0.0882515	+	0.0509520i
$95$	−9.85369	+	112.367i	−0.103723	+	1.18281i
$96$	−39.9304	−	23.0538i	−0.415941	−	0.240144i
$97$	33.5609			0.345989			0.172994	−	0.984923i	$-0.444656\pi$
$97$	33.5609			0.345989			0.172994	+	0.984923i	$0.444656\pi$
$98$	−12.7847	−	0.570497i	−0.130456	−	0.00582140i
$99$	31.4480			0.317656
$100$	96.7945	+	17.1077i	0.967945	+	0.171077i
$101$	−16.5905	+	9.57851i	−0.164262	+	0.0948367i	−0.579877	−	0.814704i	$-0.696900\pi$
$101$	−16.5905	+	9.57851i	−0.164262	+	0.0948367i	0.415615	+	0.909540i	$0.363566\pi$
$102$	8.60299	−	4.96694i	0.0843430	−	0.0486955i
$103$	−11.1967	+	19.3933i	−0.108706	+	0.188285i	−0.915246	−	0.402895i	$-0.868004\pi$
$103$	−11.1967	+	19.3933i	−0.108706	+	0.188285i	0.806540	+	0.591179i	$0.201337\pi$
$104$			27.1138i			0.260709i
$105$	122.722	+	47.8205i	1.16878	+	0.455433i
$106$	9.64224			0.0909646
$107$	−44.9916	−	25.9759i	−0.420482	−	0.242766i	0.274801	−	0.961501i	$-0.411388\pi$
$107$	−44.9916	−	25.9759i	−0.420482	−	0.242766i	−0.695284	+	0.718735i	$0.744721\pi$
$108$	−28.3987	−	49.1880i	−0.262951	−	0.455444i
$109$	−90.8644	−	157.382i	−0.833619	−	1.44387i	−0.895150	−	0.445765i	$-0.852932\pi$
$109$	−90.8644	−	157.382i	−0.833619	−	1.44387i	0.0615316	−	0.998105i	$-0.480401\pi$
$110$	7.21187	−	3.36118i	0.0655624	−	0.0305562i
$111$		−	62.7242i		−	0.565083i
$112$	102.042	+	29.7957i	0.911087	+	0.266033i
$113$			195.000i			1.72566i	0.505492	+	0.862831i	$0.331311\pi$
$113$			195.000i			1.72566i	−0.505492	+	0.862831i	$0.668689\pi$
$114$	−11.0861	+	19.2018i	−0.0972468	+	0.168436i
$115$	−15.2797	+	174.244i	−0.132867	+	1.51516i
$116$	32.1373	+	55.6634i	0.277045	+	0.479857i
$117$	33.7769	−	58.5034i	0.288692	−	0.500029i
$118$	27.8915			0.236368
$119$	−51.1323	+	48.9015i	−0.429684	+	0.410937i
$120$	31.9243	+	22.3632i	0.266036	+	0.186360i
$121$	41.9373	−	72.6375i	0.346589	−	0.600310i
$122$	−2.77767	−	4.81107i	−0.0227678	−	0.0394350i
$123$	−64.2889	+	37.1172i	−0.522674	+	0.301766i
$124$	92.3607	+	53.3245i	0.744844	+	0.430036i
$125$	−120.721	−	32.4254i	−0.965769	−	0.259403i
$126$	6.52173	+	6.81924i	0.0517598	+	0.0541210i
$127$		−	67.3739i		−	0.530503i	−0.964179	−	0.265252i	$-0.914545\pi$
$127$		−	67.3739i		−	0.530503i	0.964179	−	0.265252i	$-0.0854550\pi$
$128$	55.4591	+	32.0193i	0.433274	+	0.250151i
$129$	174.270	−	100.615i	1.35093	−	0.779961i
$130$	1.49308	−	17.0265i	0.0114853	−	0.130973i
$131$	82.1026	+	47.4019i	0.626737	+	0.361847i	0.779487	−	0.626418i	$-0.215480\pi$
$131$	82.1026	+	47.4019i	0.626737	+	0.361847i	−0.152750	+	0.988265i	$0.548813\pi$
$132$	−90.1524			−0.682972
$133$	44.2628	−	151.588i	0.332803	−	1.13976i
$134$	1.60744			0.0119958
$135$	30.5119	+	65.4674i	0.226014	+	0.484943i
$136$	−18.1330	+	10.4691i	−0.133331	+	0.0769786i
$137$	141.017	−	81.4160i	1.02932	−	0.594278i	0.112529	−	0.993648i	$-0.464105\pi$
$137$	141.017	−	81.4160i	1.02932	−	0.594278i	0.916789	+	0.399371i	$0.130771\pi$
$138$	−17.1908	+	29.7754i	−0.124571	+	0.215764i
$139$			120.304i			0.865495i	0.901515	+	0.432747i	$0.142456\pi$
$139$			120.304i			0.865495i	−0.901515	+	0.432747i	$0.857544\pi$
$140$	−128.222	−	49.9635i	−0.915872	−	0.356882i
$141$	−138.021			−0.978871
$142$	−10.8823	−	6.28290i	−0.0766360	−	0.0442458i
$143$	39.8748	+	69.0653i	0.278845	+	0.482974i
$144$	−39.1899	−	67.8789i	−0.272152	−	0.471381i
$145$	−34.5286	−	74.0858i	−0.238128	−	0.510937i
$146$		−	1.47446i		−	0.0100990i
$147$	−155.421	−	99.2243i	−1.05729	−	0.674995i
$148$			65.5351i			0.442805i
$149$	−107.789	+	186.696i	−0.723414	+	1.25299i	0.236209	+	0.971702i	$0.424095\pi$
$149$	−107.789	+	186.696i	−0.723414	+	1.25299i	−0.959623	+	0.281288i	$0.909238\pi$
$150$	−18.8158	−	15.8013i	−0.125439	−	0.105342i
$151$	−58.8121	−	101.866i	−0.389484	−	0.674607i	0.602896	−	0.797820i	$-0.294013\pi$
$151$	−58.8121	−	101.866i	−0.389484	−	0.674607i	−0.992380	+	0.123213i	$0.960680\pi$
$152$	23.3669	−	40.4726i	0.153729	−	0.266267i
$153$	52.1674			0.340963
$154$	−10.8214	+	2.64247i	−0.0702687	+	0.0171589i
$155$	−111.081	−	77.8131i	−0.716651	−	0.502020i
$156$	−96.8288	+	167.712i	−0.620698	+	1.07508i
$157$	−12.4693	−	21.5974i	−0.0794222	−	0.137563i	0.823579	−	0.567202i	$-0.191974\pi$
$157$	−12.4693	−	21.5974i	−0.0794222	−	0.137563i	−0.903001	+	0.429639i	$0.858641\pi$
$158$	8.66757	−	5.00423i	0.0548581	−	0.0316723i
$159$	120.319	+	69.4662i	0.756723	+	0.436894i
$160$	−50.1758	−	35.1486i	−0.313599	−	0.219679i
$161$	68.6367	−	235.061i	0.426315	−	1.46001i
$162$			26.3294i			0.162527i
$163$	−112.324	−	64.8502i	−0.689103	−	0.397854i	0.114173	−	0.993461i	$-0.463578\pi$
$163$	−112.324	−	64.8502i	−0.689103	−	0.397854i	−0.803276	+	0.595607i	$0.796912\pi$
$164$	67.1699	−	38.7806i	0.409573	−	0.236467i
$165$	114.207	+	10.0150i	0.692165	+	0.0606972i
$166$	23.1518	+	13.3667i	0.139468	+	0.0805222i
$167$	−65.7030			−0.393431			−0.196716	−	0.980461i	$-0.563028\pi$
$167$	−65.7030			−0.393431			−0.196716	+	0.980461i	$0.563028\pi$
$168$	−37.7162	−	39.4368i	−0.224501	−	0.234743i
$169$	2.31155			0.0136778
$170$	11.9634	−	5.57568i	0.0703729	−	0.0327981i
$171$	−100.837	+	58.2184i	−0.589692	+	0.340459i
$172$	−182.080	+	105.124i	−1.05860	+	0.611186i
$173$	49.9582	−	86.5301i	0.288775	−	0.500174i	−0.684742	−	0.728785i	$-0.740085\pi$
$173$	49.9582	−	86.5301i	0.288775	−	0.500174i	0.973518	+	0.228612i	$0.0734185\pi$
$174$		−	16.0667i		−	0.0923371i
$175$	156.884	+	77.5392i	0.896482	+	0.443081i
$176$	92.5300			0.525739
$177$	348.039	+	200.940i	1.96632	+	1.13526i
$178$	−5.14189	−	8.90601i	−0.0288870	−	0.0500338i
$179$	−72.1529	−	124.972i	−0.403089	−	0.698170i	0.591008	−	0.806665i	$-0.298730\pi$
$179$	−72.1529	−	124.972i	−0.403089	−	0.698170i	−0.994097	+	0.108495i	$0.965397\pi$
$180$	42.8625	+	91.9674i	0.238125	+	0.510930i
$181$			62.7672i			0.346780i	0.984853	+	0.173390i	$0.0554722\pi$
$181$			62.7672i			0.346780i	−0.984853	+	0.173390i	$0.944528\pi$
$182$	−6.70695	+	22.9694i	−0.0368514	+	0.126206i
$183$		−	80.0454i		−	0.437407i
$184$	36.2341	−	62.7593i	0.196924	−	0.341083i
$185$	7.28030	−	83.0215i	0.0393530	−	0.448765i
$186$	−13.3295	−	23.0873i	−0.0716638	−	0.124125i
$187$	−30.7927	+	53.3345i	−0.164667	+	0.285211i
$188$	144.206			0.767054
$189$	−23.9876	−	98.2335i	−0.126918	−	0.519754i
$190$	−16.9023	+	24.1286i	−0.0889594	+	0.126993i
$191$	28.7734	−	49.8369i	0.150646	−	0.260926i	−0.780819	−	0.624757i	$-0.785198\pi$
$191$	28.7734	−	49.8369i	0.150646	−	0.260926i	0.931465	+	0.363831i	$0.118531\pi$
$192$	108.274	+	187.537i	0.563928	+	0.976753i
$193$	−213.940	+	123.518i	−1.10850	+	0.639991i	−0.938440	−	0.345444i	$-0.887728\pi$
$193$	−213.940	+	123.518i	−1.10850	+	0.639991i	−0.170057	+	0.985434i	$0.554395\pi$
$194$	7.59084	+	4.38258i	0.0391281	+	0.0225906i
$195$	141.296	−	201.705i	0.724596	−	1.03439i
$196$	162.386	+	103.671i	0.828502	+	0.528933i
$197$			225.394i			1.14413i	0.820207	+	0.572067i	$0.193858\pi$
$197$			225.394i			1.14413i	−0.820207	+	0.572067i	$0.806142\pi$
$198$	7.11294	+	4.10666i	0.0359239	+	0.0207407i
$199$	−159.406	+	92.0330i	−0.801034	+	0.462477i	−0.843833	−	0.536606i	$-0.819706\pi$
$199$	−159.406	+	92.0330i	−0.801034	+	0.462477i	0.0427985	+	0.999084i	$0.486373\pi$
$200$	39.6592	+	33.3053i	0.198296	+	0.166526i
$201$	20.0582	+	11.5806i	0.0997919	+	0.0576149i
$202$	−5.00327			−0.0247686
$203$	27.1454	+	111.165i	0.133721	+	0.547613i
$204$	−149.549			−0.733083
$205$	−89.4006	+	41.6663i	−0.436101	+	0.203250i
$206$	−5.06498	+	2.92427i	−0.0245873	+	0.0141955i
$207$	−156.364	+	90.2771i	−0.755384	+	0.436121i
$208$	99.3826	−	172.136i	0.477801	−	0.827576i
$209$		−	137.458i		−	0.657692i
$210$	21.5128	+	26.8419i	0.102442	+	0.127818i
$211$	189.894			0.899972			0.449986	−	0.893036i	$-0.351429\pi$
$211$	189.894			0.899972			0.449986	+	0.893036i	$0.351429\pi$
$212$	−125.711	−	72.5793i	−0.592977	−	0.342355i
$213$	−90.5286	−	156.800i	−0.425017	−	0.736151i
$214$	−6.78416	−	11.7505i	−0.0317017	−	0.0549090i
$215$	242.342	−	112.946i	1.12717	−	0.525332i
$216$		−	29.9251i		−	0.138542i
$217$	131.234	+	137.221i	0.604765	+	0.632354i
$218$		−	47.4624i		−	0.217717i
$219$	10.6225	−	18.3987i	0.0485046	−	0.0840125i
$220$	−119.325	−	10.4638i	−0.542388	−	0.0475630i
$221$	66.1463	+	114.569i	0.299304	+	0.518410i
$222$	8.19088	−	14.1870i	0.0368959	−	0.0639055i
$223$	−310.730			−1.39341			−0.696703	−	0.717360i	$-0.745350\pi$
$223$	−310.730			−1.39341			−0.696703	+	0.717360i	$0.745350\pi$
$224$	59.2791	+	61.9834i	0.264639	+	0.276711i
$225$	−44.0826	−	121.268i	−0.195923	−	0.538969i
$226$	−25.4642	+	44.1053i	−0.112673	+	0.195156i
$227$	−81.9716	−	141.979i	−0.361108	−	0.625458i	0.627035	−	0.778991i	$-0.284268\pi$
$227$	−81.9716	−	141.979i	−0.361108	−	0.625458i	−0.988144	+	0.153533i	$0.950935\pi$
$228$	289.072	−	166.896i	1.26786	−	0.731998i
$229$	−13.5862	−	7.84399i	−0.0593283	−	0.0342532i	0.470042	−	0.882644i	$-0.344239\pi$
$229$	−13.5862	−	7.84399i	−0.0593283	−	0.0342532i	−0.529371	+	0.848391i	$0.677572\pi$
$230$	−26.2097	+	37.4153i	−0.113955	+	0.162675i
$231$	−154.070	−	44.9876i	−0.666969	−	0.194751i
$232$			33.8646i			0.145968i
$233$	236.940	+	136.798i	1.01691	+	0.587114i	0.913208	−	0.407494i	$-0.133597\pi$
$233$	236.940	+	136.798i	1.01691	+	0.587114i	0.103704	+	0.994608i	$0.466931\pi$
$234$	15.2794	−	8.82157i	0.0652966	−	0.0376990i
$235$	−182.684	−	16.0199i	−0.777378	−	0.0681697i
$236$	−363.636	−	209.945i	−1.54083	−	0.889599i
$237$	144.209			0.608477
$238$	−17.9510	+	4.38345i	−0.0754244	+	0.0184178i
$239$	87.2116			0.364902			0.182451	−	0.983215i	$-0.441597\pi$
$239$	87.2116			0.364902			0.182451	+	0.983215i	$0.441597\pi$
$240$	−120.706	−	258.991i	−0.502941	−	1.07913i
$241$	−121.507	+	70.1522i	−0.504179	+	0.291088i	−0.730438	−	0.682979i	$-0.760684\pi$
$241$	−121.507	+	70.1522i	−0.504179	+	0.291088i	0.226259	+	0.974067i	$0.427351\pi$
$242$	18.9708	−	10.9528i	0.0783919	−	0.0452596i
$243$	−124.681	+	215.954i	−0.513090	+	0.888698i
$244$			83.6326i			0.342756i
$245$	−194.198	−	149.372i	−0.792645	−	0.609683i
$246$	−19.3879			−0.0788126
$247$	−255.716	−	147.638i	−1.03529	−	0.597723i
$248$	28.0953	+	48.6624i	0.113287	+	0.196219i
$249$	192.597	+	333.587i	0.773481	+	1.33971i
$250$	−23.0705	−	23.0985i	−0.0922822	−	0.0923939i
$251$			252.962i			1.00782i	0.863757	+	0.503909i	$0.168105\pi$
$251$			252.962i			1.00782i	−0.863757	+	0.503909i	$0.831895\pi$
$252$	−33.6973	−	137.997i	−0.133719	−	0.547606i
$253$		−	213.150i		−	0.842492i
$254$	8.79807	−	15.2387i	0.0346381	−	0.0599949i
$255$	189.452	+	16.6134i	0.742950	+	0.0651506i
$256$	−106.727	−	184.856i	−0.416900	−	0.722093i
$257$	−188.929	+	327.234i	−0.735132	+	1.27329i	0.219534	+	0.975605i	$0.429546\pi$
$257$	−188.929	+	327.234i	−0.735132	+	1.27329i	−0.954666	+	0.297680i	$0.903787\pi$
$258$	52.5555			0.203704
$259$	−32.7032	+	111.999i	−0.126267	+	0.432429i
$260$	−147.628	+	210.745i	−0.567802	+	0.810557i
$261$	42.1867	−	73.0695i	0.161635	−	0.279960i
$262$	12.3800	+	21.4428i	0.0472520	+	0.0818429i
$263$	194.747	−	112.437i	0.740484	−	0.427518i	−0.0817614	−	0.996652i	$-0.526055\pi$
$263$	194.747	−	112.437i	0.740484	−	0.427518i	0.822245	+	0.569133i	$0.192721\pi$
$264$	−41.1353	−	23.7495i	−0.155815	−	0.0899601i
$265$	151.191	+	105.910i	0.570532	+	0.399662i
$266$	29.8066	−	28.5062i	0.112055	−	0.107166i
$267$		−	148.176i		−	0.554967i
$268$	−20.9571	−	12.0996i	−0.0781980	−	0.0451476i
$269$	224.966	−	129.884i	0.836305	−	0.482841i	−0.0197015	−	0.999806i	$-0.506272\pi$
$269$	224.966	−	129.884i	0.836305	−	0.482841i	0.856007	+	0.516965i	$0.172938\pi$
$270$	−1.64789	+	18.7919i	−0.00610331	+	0.0695996i
$271$	142.862	+	82.4817i	0.527168	+	0.304360i	0.739862	−	0.672758i	$-0.234891\pi$
$271$	142.862	+	82.4817i	0.527168	+	0.304360i	−0.212695	+	0.977119i	$0.568224\pi$
$272$	153.493			0.564313
$273$	−249.171	+	238.300i	−0.912716	+	0.872895i
$274$	42.5271			0.155208
$275$	150.002	+	26.5117i	0.545461	+	0.0964062i
$276$	448.252	−	258.799i	1.62410	−	0.937676i
$277$	437.005	−	252.305i	1.57764	−	0.910848i	0.582447	−	0.812869i	$-0.302095\pi$
$277$	437.005	−	252.305i	1.57764	−	0.910848i	0.995188	−	0.0979797i	$-0.0312380\pi$
$278$	−15.7100	+	27.2104i	−0.0565106	+	0.0978793i
$279$		−	139.998i		−	0.501786i
$280$	−45.3437	−	56.5761i	−0.161942	−	0.202057i
$281$	119.284			0.424498			0.212249	−	0.977216i	$-0.431921\pi$
$281$	119.284			0.424498			0.212249	+	0.977216i	$0.431921\pi$
$282$	−31.2177	−	18.0235i	−0.110701	−	0.0639133i
$283$	194.704	+	337.236i	0.687998	+	1.19165i	0.972484	+	0.232968i	$0.0748437\pi$
$283$	194.704	+	337.236i	0.687998	+	1.19165i	−0.284486	+	0.958680i	$0.591823\pi$
$284$	94.5856	+	163.827i	0.333048	+	0.576856i
$285$	−384.743	+	179.314i	−1.34998	+	0.629173i
$286$			20.8283i			0.0728264i
$287$	134.145	−	32.7569i	0.467405	−	0.114135i
$288$		−	63.2380i		−	0.219577i
$289$	93.4196	−	161.808i	0.323251	−	0.559888i
$290$	1.86483	−	21.2658i	0.00643046	−	0.0733302i
$291$	63.1473	+	109.374i	0.217001	+	0.375857i
$292$	−11.0986	+	19.2233i	−0.0380088	+	0.0658331i
$293$	−482.593			−1.64708			−0.823538	−	0.567261i	$-0.808003\pi$
$293$	−482.593			−1.64708			−0.823538	+	0.567261i	$0.808003\pi$
$294$	−22.1961	−	42.7384i	−0.0754968	−	0.145369i
$295$	437.340	+	306.360i	1.48251	+	1.03851i
$296$	−17.2644	+	29.9028i	−0.0583256	+	0.101023i
$297$	−44.0093	−	76.2263i	−0.148179	−	0.256654i
$298$	−48.7595	+	28.1513i	−0.163623	+	0.0944675i
$299$	−396.529	−	228.936i	−1.32618	−	0.765672i
$300$	126.372	+	347.641i	0.421241	+	1.15880i
$301$	−363.633	+	88.7952i	−1.20808	+	0.295001i
$302$		−	30.7201i		−	0.101722i
$303$	−62.4324	−	36.0453i	−0.206047	−	0.118962i
$304$	−296.696	+	171.297i	−0.975972	+	0.563478i
$305$	9.29075	−	105.948i	0.0304615	−	0.347370i
$306$	11.7993	+	6.81231i	0.0385597	+	0.0222625i
$307$	−87.6642			−0.285551			−0.142776	−	0.989755i	$-0.545603\pi$
$307$	−87.6642			−0.285551			−0.142776	+	0.989755i	$0.545603\pi$
$308$	160.974	+	47.0037i	0.522644	+	0.152609i
$309$	−84.2700			−0.272718
$310$	−14.9631	−	32.1054i	−0.0482681	−	0.103566i
$311$	−149.803	+	86.4888i	−0.481681	+	0.278099i	−0.721117	−	0.692813i	$-0.756371\pi$
$311$	−149.803	+	86.4888i	−0.481681	+	0.278099i	0.239435	+	0.970912i	$0.423038\pi$
$312$	−88.3633	+	51.0166i	−0.283216	+	0.163515i
$313$	31.1714	−	53.9905i	0.0995891	−	0.172493i	−0.811926	−	0.583761i	$-0.801580\pi$
$313$	31.1714	−	53.9905i	0.0995891	−	0.172493i	0.911515	+	0.411268i	$0.134914\pi$
$314$		−	6.51324i		−	0.0207428i
$315$	27.3585	+	178.561i	0.0868524	+	0.566860i
$316$	−150.672			−0.476809
$317$	−143.150	−	82.6479i	−0.451578	−	0.260719i	0.256918	−	0.966433i	$-0.417293\pi$
$317$	−143.150	−	82.6479i	−0.451578	−	0.260719i	−0.708497	+	0.705714i	$0.750626\pi$
$318$	18.1426	+	31.4239i	0.0570522	+	0.0988173i
$319$	49.8029	+	86.2611i	0.156122	+	0.270411i
$320$	121.544	+	260.790i	0.379826	+	0.814968i
$321$		−	195.502i		−	0.609041i
$322$	46.2200	−	44.2035i	0.143540	−	0.137278i
$323$		−	228.021i		−	0.705948i
$324$	198.187	−	343.270i	0.611689	−	1.05948i
$325$	210.431	−	250.576i	0.647480	−	0.771005i
$326$	−16.9370	−	29.3358i	−0.0519541	−	0.0899871i
$327$	341.936	−	592.251i	1.04568	−	1.81116i
$328$	40.8649			0.124588
$329$	246.448	+	71.9614i	0.749081	+	0.218728i
$330$	24.5237	+	17.1790i	0.0743142	+	0.0520577i
$331$	166.380	−	288.178i	0.502657	−	0.870628i	−0.497338	−	0.867557i	$-0.665689\pi$
$331$	166.380	−	288.178i	0.502657	−	0.870628i	0.999995	−	0.00307088i	$-0.000977494\pi$
$332$	−201.228	−	348.537i	−0.606108	−	1.04981i
$333$	74.5026	−	43.0141i	0.223732	−	0.129171i
$334$	−14.8608	−	8.57988i	−0.0444934	−	0.0256882i
$335$	25.2048	+	17.6561i	0.0752381	+	0.0527049i
$336$	94.8956	+	388.615i	0.282427	+	1.15659i
$337$		−	313.978i		−	0.931685i	−0.884868	−	0.465842i	$-0.845751\pi$
$337$		−	313.978i		−	0.931685i	0.884868	−	0.465842i	$-0.154249\pi$
$338$	0.522828	+	0.301855i	0.00154683	+	0.000893062i
$339$	−635.501	+	366.907i	−1.87463	+	1.08232i
$340$	−197.942	−	17.3579i	−0.582184	−	0.0510527i
$341$	143.131	+	82.6365i	0.419738	+	0.242336i
$342$	−30.4100			−0.0889180
$343$	225.784	+	258.207i	0.658262	+	0.752789i
$344$	−110.774			−0.322018
$345$	−596.607	+	278.056i	−1.72929	+	0.805959i
$346$	22.5992	−	13.0476i	0.0653156	−	0.0377100i
$347$	−188.880	+	109.050i	−0.544322	+	0.314264i	−0.746829	−	0.665017i	$-0.768424\pi$
$347$	−188.880	+	109.050i	−0.544322	+	0.314264i	0.202507	+	0.979281i	$0.435091\pi$
$348$	−120.937	+	209.469i	−0.347521	+	0.601924i
$349$		−	452.923i		−	1.29777i	−0.760885	−	0.648886i	$-0.775235\pi$
$349$		−	452.923i		−	1.29777i	0.760885	−	0.648886i	$-0.224765\pi$
$350$	25.3587	+	38.0247i	0.0724536	+	0.108642i
$351$	−189.074			−0.538672
$352$	64.6529	+	37.3274i	0.183673	+	0.106044i
$353$	−113.487	−	196.565i	−0.321493	−	0.556842i	0.659304	−	0.751877i	$-0.270851\pi$
$353$	−113.487	−	196.565i	−0.321493	−	0.556842i	−0.980796	+	0.195035i	$0.937518\pi$
$354$	52.4799	+	90.8978i	0.148248	+	0.256773i
$355$	−101.624	−	218.048i	−0.286264	−	0.614219i
$356$			154.817i			0.434878i
$357$	−255.578	−	74.6275i	−0.715906	−	0.209041i
$358$		−	37.6885i		−	0.105275i
$359$	−124.724	+	216.028i	−0.347420	+	0.601748i	−0.985790	−	0.167981i	$-0.946275\pi$
$359$	−124.724	+	216.028i	−0.347420	+	0.601748i	0.638371	+	0.769729i	$0.279609\pi$
$360$	−4.67003	+	53.2550i	−0.0129723	+	0.147931i
$361$	73.9702	+	128.120i	0.204904	+	0.354903i
$362$	−8.19650	+	14.1968i	−0.0226423	+	0.0392176i
$363$	315.632			0.869511
$364$	260.338	−	248.980i	0.715214	−	0.684010i
$365$	16.1954	−	23.1196i	0.0443710	−	0.0633412i
$366$	10.4528	−	18.1048i	0.0285595	−	0.0494665i
$367$	152.029	+	263.322i	0.414247	+	0.717497i	0.995349	−	0.0963334i	$-0.0307115\pi$
$367$	152.029	+	263.322i	0.414247	+	0.717497i	−0.581102	+	0.813831i	$0.697378\pi$
$368$	−460.074	+	265.624i	−1.25020	+	0.721805i
$369$	−88.1742	−	50.9074i	−0.238955	−	0.137960i
$370$	12.4881	−	17.8272i	0.0337516	−	0.0481816i
$371$	−178.621	−	186.770i	−0.481459	−	0.503422i
$372$			401.336i			1.07886i
$373$	306.192	+	176.780i	0.820889	+	0.473940i	0.850723	−	0.525614i	$-0.176165\pi$
$373$	306.192	+	176.780i	0.820889	+	0.473940i	−0.0298340	+	0.999555i	$0.509498\pi$
$374$	−13.9294	+	8.04217i	−0.0372445	+	0.0215031i
$375$	−121.472	−	454.439i	−0.323925	−	1.21184i
$376$	65.7993	+	37.9892i	0.174998	+	0.101035i
$377$	213.965			0.567545
$378$	7.40235	−	25.3510i	0.0195829	−	0.0670661i
$379$	435.916			1.15017			0.575087	−	0.818092i	$-0.304968\pi$
$379$	435.916			1.15017			0.575087	+	0.818092i	$0.304968\pi$
$380$	401.985	−	187.350i	1.05786	−	0.493027i
$381$	219.570	−	126.769i	0.576300	−	0.332727i
$382$	13.0160	−	7.51478i	0.0340733	−	0.0196722i
$383$	104.085	−	180.281i	0.271764	−	0.470708i	−0.697550	−	0.716536i	$-0.745726\pi$
$383$	104.085	−	180.281i	0.271764	−	0.470708i	0.969314	+	0.245828i	$0.0790598\pi$
$384$			240.987i			0.627570i
$385$	−198.705	−	77.4280i	−0.516116	−	0.201112i
$386$	−64.5188			−0.167147
$387$	239.017	+	137.997i	0.617615	+	0.356580i
$388$	−65.9772	−	114.276i	−0.170044	−	0.294525i
$389$	284.349	+	492.507i	0.730975	+	1.26609i	0.956467	+	0.291840i	$0.0942675\pi$
$389$	284.349	+	492.507i	0.730975	+	1.26609i	−0.225493	+	0.974245i	$0.572399\pi$
$390$	58.2984	−	27.1707i	0.149483	−	0.0696684i
$391$		−	353.584i		−	0.904307i
$392$	46.7839	+	90.0822i	0.119347	+	0.229801i
$393$			356.761i			0.907789i
$394$	−29.4333	+	50.9799i	−0.0747038	+	0.129391i
$395$	190.874	+	16.7381i	0.483226	+	0.0423750i
$396$	−61.8234	−	107.081i	−0.156120	−	0.270407i
$397$	−142.678	+	247.125i	−0.359390	+	0.622482i	−0.987859	−	0.155353i	$-0.950349\pi$
$397$	−142.678	+	247.125i	−0.359390	+	0.622482i	0.628469	+	0.777835i	$0.283682\pi$
$398$	−48.0728			−0.120786
$399$	577.306	−	140.972i	1.44688	−	0.353313i
$400$	−129.705	−	356.810i	−0.324263	−	0.892024i
$401$	−140.086	+	242.635i	−0.349341	+	0.605076i	−0.986132	−	0.165960i	$-0.946928\pi$
$401$	−140.086	+	242.635i	−0.349341	+	0.605076i	0.636792	+	0.771036i	$0.280261\pi$
$402$	3.02452	+	5.23862i	0.00752368	+	0.0130314i
$403$	307.461	−	177.513i	0.762931	−	0.440478i
$404$	65.2302	+	37.6607i	0.161461	+	0.0932195i
$405$	−289.202	+	412.846i	−0.714080	+	1.01937i
$406$	−8.37684	+	28.6883i	−0.0206326	+	0.0706609i
$407$			101.559i			0.249531i
$408$	−68.2371	−	39.3967i	−0.167248	−	0.0965606i
$409$	−62.2921	+	35.9644i	−0.152303	+	0.0879325i	−0.574215	−	0.818705i	$-0.694693\pi$
$409$	−62.2921	+	35.9644i	−0.152303	+	0.0879325i	0.421911	+	0.906637i	$0.361359\pi$
$410$	−25.6618	−	2.25033i	−0.0625896	−	0.00548860i
$411$	530.666	+	306.380i	1.29116	+	0.745451i
$412$	88.0465			0.213705
$413$	−516.685	−	540.256i	−1.25105	−	1.30813i
$414$	−47.1556			−0.113902
$415$	216.201	+	463.889i	0.520967	+	1.11781i
$416$	138.882	−	80.1835i	0.333851	−	0.192749i
$417$	−392.068	+	226.360i	−0.940210	+	0.542831i
$418$	17.9500	−	31.0903i	0.0429426	−	0.0743788i
$419$		−	465.475i		−	1.11092i	−0.831544	−	0.555459i	$-0.812542\pi$
$419$		−	465.475i		−	1.11092i	0.831544	−	0.555459i	$-0.187458\pi$
$420$	−78.4290	−	511.883i	−0.186736	−	1.21877i
$421$	−368.126			−0.874410			−0.437205	−	0.899362i	$-0.644032\pi$
$421$	−368.126			−0.874410			−0.437205	+	0.899362i	$0.644032\pi$
$422$	42.9505	+	24.7975i	0.101778	+	0.0587618i
$423$	−94.6500	−	163.939i	−0.223759	−	0.387562i
$424$	−38.2401	−	66.2338i	−0.0901890	−	0.156212i
$425$	248.830	+	43.9789i	0.585482	+	0.103480i
$426$		−	47.2870i		−	0.111002i
$427$	−41.7341	+	142.928i	−0.0977379	+	0.334725i
$428$			204.264i			0.477251i
$429$	−150.055	+	259.903i	−0.349778	+	0.605834i
$430$	69.5623	+	6.10004i	0.161773	+	0.0141861i
$431$	−379.314	−	656.992i	−0.880080	−	1.52434i	−0.851251	−	0.524758i	$-0.824156\pi$
$431$	−379.314	−	656.992i	−0.880080	−	1.52434i	−0.0288283	−	0.999584i	$-0.509178\pi$
$432$	−109.687	+	189.984i	−0.253905	+	0.439777i
$433$	423.683			0.978482			0.489241	−	0.872149i	$-0.337274\pi$
$433$	423.683			0.978482			0.489241	+	0.872149i	$0.337274\pi$
$434$	11.7636	+	48.1740i	0.0271050	+	0.111000i
$435$	176.476	−	251.926i	0.405692	−	0.579140i
$436$	−357.260	+	618.792i	−0.819403	+	1.41925i
$437$	394.597	+	683.462i	0.902968	+	1.56399i
$438$	4.80522	−	2.77430i	0.0109708	−	0.00633401i
$439$	−63.4357	−	36.6246i	−0.144500	−	0.0834273i	0.426007	−	0.904720i	$-0.359920\pi$
$439$	−63.4357	−	36.6246i	−0.144500	−	0.0834273i	−0.570507	+	0.821293i	$0.693253\pi$
$440$	−51.6899	−	36.2092i	−0.117477	−	0.0822936i
$441$	11.2742	−	252.651i	0.0255650	−	0.572905i
$442$			34.5510i			0.0781697i
$443$	−499.601	−	288.445i	−1.12777	−	0.651117i	−0.184395	−	0.982852i	$-0.559032\pi$
$443$	−499.601	−	288.445i	−1.12777	−	0.651117i	−0.943372	+	0.331736i	$0.892366\pi$
$444$	−213.578	+	123.309i	−0.481031	+	0.277723i
$445$	17.1986	−	196.125i	0.0386485	−	0.440731i
$446$	−70.2811	−	40.5768i	−0.157581	−	0.0909794i
$447$	−811.249			−1.81488
$448$	−95.5547	−	391.314i	−0.213292	−	0.873469i
$449$	−652.932			−1.45419			−0.727095	−	0.686537i	$-0.759130\pi$
$449$	−652.932			−1.45419			−0.727095	+	0.686537i	$0.759130\pi$
$450$	5.86522	−	33.1851i	0.0130338	−	0.0737447i
$451$	104.093	−	60.0980i	0.230804	−	0.133255i
$452$	663.980	−	383.349i	1.46898	−	0.848118i
$453$	221.319	−	383.335i	0.488562	−	0.846215i
$454$		−	42.8173i		−	0.0943112i
$455$	−357.461	+	286.493i	−0.785629	+	0.629654i
$456$	175.866			0.385671
$457$	−108.778	−	62.8031i	−0.238027	−	0.137425i	0.376243	−	0.926521i	$-0.377216\pi$
$457$	−108.778	−	62.8031i	−0.238027	−	0.137425i	−0.614269	+	0.789096i	$0.710549\pi$
$458$	−2.04863	−	3.54832i	−0.00447298	−	0.00774743i
$459$	−73.0046	−	126.448i	−0.159051	−	0.275485i
$460$	623.343	−	290.517i	1.35509	−	0.631558i
$461$			695.270i			1.50818i	0.656773	+	0.754089i	$0.271921\pi$
$461$			695.270i			1.50818i	−0.656773	+	0.754089i	$0.728079\pi$
$462$	−28.9730	−	30.2947i	−0.0627120	−	0.0655729i
$463$			438.632i			0.947370i	0.880694	+	0.473685i	$0.157076\pi$
$463$			438.632i			0.947370i	−0.880694	+	0.473685i	$0.842924\pi$
$464$	124.127	−	214.994i	0.267515	−	0.463349i
$465$	44.5844	−	508.422i	0.0958804	−	1.09338i
$466$	35.7276	+	61.8821i	0.0766687	+	0.132794i
$467$	41.6921	−	72.2129i	0.0892765	−	0.154631i	−0.817929	−	0.575319i	$-0.804878\pi$
$467$	41.6921	−	72.2129i	0.0892765	−	0.154631i	0.907206	+	0.420688i	$0.138211\pi$
$468$	−265.608			−0.567538
$469$	−29.7776	−	31.1360i	−0.0634917	−	0.0663881i
$470$	−39.2277	−	27.4793i	−0.0834631	−	0.0584666i
$471$	46.9237	−	81.2743i	0.0996258	−	0.172557i
$472$	−110.615	−	191.590i	−0.234353	−	0.405911i
$473$	−282.168	+	162.910i	−0.596550	+	0.344418i
$474$	32.6174	+	18.8316i	0.0688130	+	0.0397292i
$475$	−530.057	+	192.683i	−1.11591	+	0.405649i
$476$	267.032	+	77.9719i	0.560991	+	0.163807i
$477$			190.550i			0.399476i
$478$	19.7256	+	11.3886i	0.0412670	+	0.0238255i
$479$	−270.669	+	156.271i	−0.565071	+	0.326244i	−0.755178	−	0.655520i	$-0.772450\pi$
$479$	−270.669	+	156.271i	−0.565071	+	0.326244i	0.190108	+	0.981763i	$0.439116\pi$
$480$	20.1390	−	229.657i	0.0419563	−	0.478452i
$481$	188.933	+	109.081i	0.392792	+	0.226779i
$482$	−36.6435			−0.0760239
$483$	895.206	−	218.600i	1.85343	−	0.452587i
$484$	−329.777			−0.681358
$485$	70.8866	+	152.097i	0.146158	+	0.313602i
$486$	−56.4009	+	32.5631i	−0.116051	+	0.0670022i
$487$	−425.683	+	245.768i	−0.874093	+	0.504658i	−0.868706	−	0.495328i	$-0.835048\pi$
$487$	−425.683	+	245.768i	−0.874093	+	0.504658i	−0.00538659	+	0.999985i	$0.501715\pi$
$488$	−22.0319	+	38.1604i	−0.0451473	+	0.0781975i
$489$		−	488.082i		−	0.998122i
$490$	−24.4180	−	59.1447i	−0.0498327	−	0.120703i
$491$	693.987			1.41342			0.706708	−	0.707506i	$-0.250180\pi$
$491$	693.987			1.41342			0.706708	+	0.707506i	$0.250180\pi$
$492$	252.770	+	145.937i	0.513761	+	0.296620i
$493$	82.6153	+	143.094i	0.167577	+	0.290251i
$494$	−38.5587	−	66.7856i	−0.0780541	−	0.135194i
$495$	66.4237	+	142.521i	0.134189	+	0.287921i
$496$		−	411.920i		−	0.830485i
$497$	79.8938	+	327.179i	0.160752	+	0.658309i
$498$			100.602i			0.202011i
$499$	35.7821	−	61.9763i	0.0717075	−	0.124201i	−0.827942	−	0.560813i	$-0.810489\pi$
$499$	35.7821	−	61.9763i	0.0717075	−	0.124201i	0.899650	+	0.436612i	$0.143822\pi$
$500$	126.916	+	474.804i	0.253831	+	0.949608i
$501$	−123.625	−	214.125i	−0.246757	−	0.427395i
$502$	−33.0333	+	57.2153i	−0.0658033	+	0.113975i
$503$	573.959			1.14107			0.570535	−	0.821273i	$-0.306736\pi$
$503$	573.959			1.14107			0.570535	+	0.821273i	$0.306736\pi$
$504$	20.9778	−	71.8430i	0.0416226	−	0.142546i
$505$	−78.4515	−	54.9559i	−0.155349	−	0.108824i
$506$	27.8344	−	48.2106i	0.0550087	−	0.0952778i
$507$	4.34935	+	7.53329i	0.00857859	+	0.0148586i
$508$	−229.410	+	132.450i	−0.451595	+	0.260728i
$509$	394.898	+	227.995i	0.775832	+	0.447927i	0.834951	−	0.550324i	$-0.185496\pi$
$509$	394.898	+	227.995i	0.775832	+	0.447927i	−0.0591192	+	0.998251i	$0.518829\pi$
$510$	40.6810	+	28.4974i	0.0797667	+	0.0558772i
$511$	−28.5601	+	27.3141i	−0.0558906	+	0.0534522i
$512$		−	311.902i		−	0.609184i
$513$	282.229	+	162.945i	0.550155	+	0.317632i
$514$	−85.4642	+	49.3428i	−0.166273	+	0.0959977i
$515$	−111.539	−	9.78109i	−0.216581	−	0.0189924i
$516$	−685.194	−	395.597i	−1.32790	−	0.766661i
$517$	223.475			0.432254
$518$	−22.0223	+	21.0615i	−0.0425142	+	0.0406593i
$519$	376.000			0.724470
$520$	−122.879	+	57.2691i	−0.236305	+	0.110133i
$521$	−318.552	+	183.916i	−0.611424	+	0.353006i	−0.773523	−	0.633769i	$-0.781507\pi$
$521$	−318.552	+	183.916i	−0.611424	+	0.353006i	0.162098	+	0.986775i	$0.448174\pi$
$522$	19.0837	−	11.0180i	0.0365588	−	0.0211072i
$523$	−329.927	+	571.450i	−0.630835	+	1.09264i	0.356546	+	0.934278i	$0.383954\pi$
$523$	−329.927	+	571.450i	−0.630835	+	1.09264i	−0.987381	+	0.158361i	$0.949379\pi$
$524$		−	372.749i		−	0.711353i
$525$	42.4907	+	657.178i	0.0809346	+	1.25177i
$526$	58.7308			0.111656
$527$	237.432	+	137.081i	0.450535	+	0.260116i
$528$	174.102	+	301.554i	0.329739	+	0.571124i
$529$	347.387	+	601.691i	0.656685	+	1.13741i
$530$	20.3661	+	43.6983i	0.0384267	+	0.0824496i
$531$			551.192i			1.03803i
$532$	−603.177	+	147.289i	−1.13379	+	0.276860i
$533$		−	258.195i		−	0.484418i
$534$	19.3497	−	33.5146i	0.0362354	−	0.0627615i
$535$	22.6917	−	258.766i	0.0424143	−	0.483675i
$536$	−6.37494	−	11.0417i	−0.0118935	−	0.0206002i
$537$	271.522	−	470.290i	0.505627	−	0.875772i
$538$	67.8441			0.126104
$539$	251.649	+	160.658i	0.466881	+	0.298067i
$540$	162.935	−	232.596i	0.301732	−	0.430733i
$541$	237.101	−	410.672i	0.438265	−	0.759098i	−0.559291	−	0.828972i	$-0.688926\pi$
$541$	237.101	−	410.672i	0.438265	−	0.759098i	0.997556	+	0.0698740i	$0.0222597\pi$
$542$	21.5419	+	37.3116i	0.0397451	+	0.0688406i
$543$	−204.557	+	118.101i	−0.376717	+	0.217498i
$544$	107.249	+	61.9204i	0.197149	+	0.113824i
$545$	521.327	−	744.213i	0.956563	−	1.36553i
$546$	−87.4765	+	21.3608i	−0.160213	+	0.0391224i
$547$		−	401.484i		−	0.733975i	−0.930226	−	0.366987i	$-0.880389\pi$
$547$		−	401.484i		−	0.733975i	0.930226	−	0.366987i	$-0.119611\pi$
$548$	−554.448	−	320.111i	−1.01177	−	0.584144i
$549$	95.0764	−	54.8924i	0.173181	−	0.0999861i
$550$	30.4655	+	25.5845i	0.0553918	+	0.0465173i
$551$	−319.384	−	184.396i	−0.579644	−	0.334657i
$552$	272.708			0.494037
$553$	−257.497	−	75.1878i	−0.465637	−	0.135963i
$554$	131.790			0.237888
$555$	284.264	−	132.485i	0.512187	−	0.238711i
$556$	409.638	−	236.505i	0.736759	−	0.425368i
$557$	−35.2935	+	20.3767i	−0.0633636	+	0.0365830i	−0.531347	−	0.847154i	$-0.678314\pi$
$557$	−35.2935	+	20.3767i	−0.0633636	+	0.0365830i	0.467984	+	0.883737i	$0.344981\pi$
$558$	18.2818	−	31.6650i	0.0327631	−	0.0567473i
$559$			699.898i			1.25205i
$560$	80.4975	+	525.383i	0.143746	+	0.938185i
$561$	−231.755			−0.413110
$562$	26.9797	+	15.5768i	0.0480067	+	0.0277167i
$563$	−368.838	−	638.845i	−0.655129	−	1.13472i	−0.981861	−	0.189600i	$-0.939281\pi$
$563$	−368.838	−	638.845i	−0.655129	−	1.13472i	0.326733	−	0.945117i	$-0.394052\pi$
$564$	271.334	+	469.965i	0.481089	+	0.833271i
$565$	−883.733	+	411.874i	−1.56413	+	0.728981i
$566$			101.702i			0.179685i
$567$	509.999	−	487.748i	0.899469	−	0.860226i
$568$			99.6694i			0.175474i
$569$	255.233	−	442.077i	0.448564	−	0.776936i	−0.549729	−	0.835343i	$-0.685269\pi$
$569$	255.233	−	442.077i	0.448564	−	0.776936i	0.998293	+	0.0584072i	$0.0186022\pi$
$570$	−110.438	−	9.68447i	−0.193750	−	0.0169903i
$571$	328.855	+	569.594i	0.575928	+	0.997537i	0.995940	+	0.0900183i	$0.0286925\pi$
$571$	328.855	+	569.594i	0.575928	+	0.997537i	−0.420012	+	0.907519i	$0.637974\pi$
$572$	156.779	−	271.550i	0.274090	−	0.474738i
$573$	216.557			0.377935
$574$	34.6187	+	10.1085i	0.0603113	+	0.0176106i
$575$	−821.940	+	298.786i	−1.42946	+	0.519628i
$576$	−148.502	+	257.212i	−0.257815	+	0.446549i
$577$	−517.946	−	897.109i	−0.897654	−	1.55478i	−0.830485	−	0.557041i	$-0.811937\pi$
$577$	−517.946	−	897.109i	−0.897654	−	1.55478i	−0.0671686	−	0.997742i	$-0.521397\pi$
$578$	42.2595	−	24.3985i	0.0731133	−	0.0422120i
$579$	−805.087	−	464.817i	−1.39048	−	0.802793i
$580$	−184.385	+	263.216i	−0.317905	+	0.453821i
$581$	−169.971	−	696.064i	−0.292550	−	1.19804i
$582$			32.9845i			0.0566745i
$583$	−194.813	−	112.476i	−0.334157	−	0.192925i
$584$	−10.1282	+	5.84754i	−0.0173429	+	0.0100129i
$585$	336.478	+	29.5064i	0.575176	+	0.0504382i
$586$	−109.153	−	63.0198i	−0.186269	−	0.107542i
$587$	−18.0678			−0.0307799			−0.0153900	−	0.999882i	$-0.504899\pi$
$587$	−18.0678			−0.0307799			−0.0153900	+	0.999882i	$0.504899\pi$
$588$	−32.3198	+	724.278i	−0.0549657	+	1.23177i
$589$	−611.927			−1.03893
$590$	58.9117	+	126.403i	0.0998504	+	0.214243i
$591$	−734.556	+	424.096i	−1.24290	+	0.717591i
$592$	219.211	−	126.561i	0.370288	−	0.213786i
$593$	−1.41323	+	2.44778i	−0.00238318	+	0.00412779i	−0.867215	−	0.497935i	$-0.834092\pi$
$593$	−1.41323	+	2.44778i	−0.00238318	+	0.00412779i	0.864831	+	0.502062i	$0.167425\pi$
$594$		−	22.9879i		−	0.0387002i
$595$	−329.621	−	128.441i	−0.553984	−	0.215868i
$596$	847.605			1.42216
$597$	−599.867	−	346.334i	−1.00480	−	0.580123i
$598$	−59.7915	−	103.562i	−0.0999858	−	0.173180i
$599$	−158.480	−	274.495i	−0.264574	−	0.458256i	0.702878	−	0.711310i	$-0.251898\pi$
$599$	−158.480	−	274.495i	−0.264574	−	0.458256i	−0.967452	+	0.253055i	$0.918565\pi$
$600$	−33.9195	+	191.915i	−0.0565326	+	0.319858i
$601$			479.510i			0.797854i	0.916983	+	0.398927i	$0.130617\pi$
$601$			479.510i			0.797854i	−0.916983	+	0.398927i	$0.869383\pi$
$602$	−93.8422	−	27.4014i	−0.155884	−	0.0455173i
$603$			31.7663i			0.0526804i
$604$	−231.237	+	400.514i	−0.382843	+	0.663103i
$605$	417.770	+	36.6350i	0.690528	+	0.0605537i
$606$	−9.41401	−	16.3055i	−0.0155347	−	0.0269068i
$607$	−142.302	+	246.475i	−0.234436	+	0.406054i	−0.959108	−	0.283039i	$-0.908658\pi$
$607$	−142.302	+	246.475i	−0.234436	+	0.406054i	0.724673	+	0.689093i	$0.241991\pi$
$608$	−276.411			−0.454623
$609$	−311.210	+	297.632i	−0.511018	+	0.488723i
$610$	15.9367	−	22.7501i	0.0261257	−	0.0372953i
$611$	240.025	−	415.736i	0.392840	−	0.680419i
$612$	−102.556	−	177.631i	−0.167574	−	0.290247i
$613$	820.234	−	473.562i	1.33807	−	0.772533i	0.351545	−	0.936171i	$-0.385656\pi$
$613$	820.234	−	473.562i	1.33807	−	0.772533i	0.986520	+	0.163638i	$0.0523230\pi$
$614$	−19.8280	−	11.4477i	−0.0322931	−	0.0186444i
$615$	−304.003	−	212.957i	−0.494315	−	0.346271i
$616$	61.0679	+	63.8537i	0.0991362	+	0.103659i
$617$		−	626.960i		−	1.01614i	−0.861315	−	0.508071i	$-0.830359\pi$
$617$		−	626.960i		−	1.01614i	0.861315	−	0.508071i	$-0.169641\pi$
$618$	−19.0603	−	11.0045i	−0.0308419	−	0.0178066i
$619$	826.701	−	477.296i	1.33554	−	0.771076i	0.349399	−	0.936974i	$-0.386386\pi$
$619$	826.701	−	477.296i	1.33554	−	0.771076i	0.986143	+	0.165898i	$0.0530523\pi$
$620$	−46.5824	+	531.206i	−0.0751329	+	0.856784i
$621$	437.642	+	252.673i	0.704738	+	0.406881i
$622$	−45.1768			−0.0726315
$623$	−77.2561	+	264.581i	−0.124007	+	0.424688i
$624$	747.983			1.19869
$625$	−108.034	−	615.592i	−0.172854	−	0.984947i
$626$	14.1008	−	8.14108i	0.0225252	−	0.0130049i
$627$	447.972	−	258.637i	0.714469	−	0.412499i
$628$	−49.0266	+	84.9166i	−0.0780678	+	0.135217i
$629$			168.471i			0.267840i
$630$	−17.1295	+	43.9597i	−0.0271897	+	0.0697773i
$631$	−773.291			−1.22550			−0.612751	−	0.790276i	$-0.709937\pi$
$631$	−773.291			−1.22550			−0.612751	+	0.790276i	$0.709937\pi$
$632$	−68.7494	−	39.6925i	−0.108781	−	0.0628045i
$633$	357.300	+	618.861i	0.564455	+	0.977664i
$634$	−21.5853	−	37.3868i	−0.0340462	−	0.0589697i
$635$	305.336	−	142.306i	0.480844	−	0.224103i
$636$		−	546.253i		−	0.858888i
$637$	569.161	−	295.592i	0.893503	−	0.464038i
$638$			26.0142i			0.0407746i
$639$	124.163	−	215.056i	0.194308	−	0.336551i
$640$	−27.9710	+	318.969i	−0.0437046	+	0.498389i
$641$	85.9409	+	148.854i	0.134073	+	0.232222i	0.925243	−	0.379375i	$-0.123861\pi$
$641$	85.9409	+	148.854i	0.134073	+	0.232222i	−0.791170	+	0.611597i	$0.790528\pi$
$642$	25.5298	−	44.2189i	0.0397661	−	0.0688768i
$643$	−301.390			−0.468725			−0.234363	−	0.972149i	$-0.575300\pi$
$643$	−301.390			−0.468725			−0.234363	+	0.972149i	$0.575300\pi$
$644$	−935.324	+	228.396i	−1.45237	+	0.354652i
$645$	824.073	+	577.270i	1.27763	+	0.894992i
$646$	29.7763	−	51.5741i	0.0460934	−	0.0798361i
$647$	347.837	+	602.471i	0.537615	+	0.931177i	0.999032	+	0.0439931i	$0.0140080\pi$
$647$	347.837	+	602.471i	0.537615	+	0.931177i	−0.461417	+	0.887184i	$0.652659\pi$
$648$	180.860	−	104.420i	0.279105	−	0.161141i
$649$	−563.524	−	325.351i	−0.868295	−	0.501311i
$650$	80.3172	−	29.1964i	0.123565	−	0.0449175i
$651$	−200.273	+	685.880i	−0.307640	+	1.05358i
$652$			509.955i			0.782139i
$653$	522.355	+	301.582i	0.799930	+	0.461840i	0.843447	−	0.537213i	$-0.180523\pi$
$653$	522.355	+	301.582i	0.799930	+	0.461840i	−0.0435164	+	0.999053i	$0.513856\pi$
$654$	154.679	−	89.3040i	0.236512	−	0.136550i
$655$	−41.4087	+	472.207i	−0.0632194	+	0.720927i
$656$	−259.437	−	149.786i	−0.395483	−	0.228332i
$657$	29.1382			0.0443504
$658$	46.3446	+	48.4588i	0.0704326	+	0.0736456i
$659$	403.838			0.612804			0.306402	−	0.951902i	$-0.400875\pi$
$659$	403.838			0.612804			0.306402	+	0.951902i	$0.400875\pi$
$660$	−190.418	−	408.567i	−0.288512	−	0.619041i
$661$	680.021	−	392.610i	1.02878	−	0.593964i	0.112142	−	0.993692i	$-0.464229\pi$
$661$	680.021	−	392.610i	1.02878	−	0.593964i	0.916634	+	0.399728i	$0.130896\pi$
$662$	75.2638	−	43.4536i	0.113692	−	0.0656398i
$663$	−248.918	+	431.139i	−0.375442	+	0.650285i
$664$		−	212.043i		−	0.319342i
$665$	780.482	−	119.583i	1.17366	−	0.179824i
$666$	22.4681			0.0337359
$667$	−495.256	−	285.936i	−0.742513	−	0.428690i
$668$	129.165	+	223.721i	0.193361	+	0.334911i
$669$	−584.660	−	1012.66i	−0.873932	−	1.51369i
$670$	3.39520	+	7.28487i	0.00506746	+	0.0108729i
$671$			129.605i			0.193152i
$672$	−90.4646	+	309.816i	−0.134620	+	0.461035i
$673$			374.318i			0.556193i	0.960553	+	0.278096i	$0.0897035\pi$
$673$			374.318i			0.556193i	−0.960553	+	0.278096i	$0.910297\pi$
$674$	41.0010	−	71.0158i	0.0608324	−	0.105365i
$675$	−232.249	+	276.557i	−0.344073	+	0.409715i
$676$	−4.54426	−	7.87089i	−0.00672228	−	0.0116433i
$677$	−470.298	+	814.579i	−0.694679	+	1.20322i	0.275610	+	0.961270i	$0.411120\pi$
$677$	−470.298	+	814.579i	−0.694679	+	1.20322i	−0.970289	+	0.241950i	$0.922213\pi$
$678$	−191.651			−0.282671
$679$	−55.7291	−	228.221i	−0.0820752	−	0.336113i
$680$	−85.7456	−	60.0655i	−0.126097	−	0.0883316i
$681$	308.471	−	534.288i	0.452968	−	0.784563i
$682$	21.5823	+	37.3816i	0.0316456	+	0.0548118i
$683$	0.311813	−	0.180026i	0.000456535	−	0.000263581i	−0.499772	−	0.866157i	$-0.666583\pi$
$683$	0.311813	−	0.180026i	0.000456535	−	0.000263581i	0.500228	+	0.865894i	$0.333249\pi$
$684$	396.471	+	228.903i	0.579636	+	0.334653i
$685$	666.827	+	467.118i	0.973470	+	0.681923i
$686$	17.3499	+	87.8856i	0.0252914	+	0.128113i
$687$		−	59.0362i		−	0.0859333i
$688$	703.265	+	406.030i	1.02219	+	0.590160i
$689$	−418.482	+	241.610i	−0.607375	+	0.350668i
$690$	−171.251	−	15.0173i	−0.248190	−	0.0217643i
$691$	−64.7660	−	37.3927i	−0.0937280	−	0.0541139i	0.452403	−	0.891813i	$-0.350567\pi$
$691$	−64.7660	−	37.3927i	−0.0937280	−	0.0541139i	−0.546131	+	0.837700i	$0.683900\pi$
$692$	−392.850			−0.567702
$693$	−52.2205	−	213.852i	−0.0753542	−	0.308589i
$694$	−56.9613			−0.0820768
$695$	−545.212	+	254.103i	−0.784478	+	0.365616i
$696$	−110.364	+	63.7187i	−0.158569	+	0.0915498i
$697$	172.674	−	99.6933i	0.247739	−	0.143032i
$698$	59.1452	−	102.443i	0.0847353	−	0.146766i
$699$			1029.58i			1.47293i
$700$	−44.3948	−	686.629i	−0.0634212	−	0.980899i
$701$	661.374			0.943472			0.471736	−	0.881740i	$-0.343628\pi$
$701$	661.374			0.943472			0.471736	+	0.881740i	$0.343628\pi$
$702$	−42.7649	−	24.6904i	−0.0609187	−	0.0351714i
$703$	−188.013	−	325.648i	−0.267444	−	0.463226i
$704$	−175.311	−	303.648i	−0.249022	−	0.431318i
$705$	−291.525	−	625.506i	−0.413510	−	0.887242i
$706$		−	59.2791i		−	0.0839647i
$707$	92.6848	+	96.9129i	0.131096	+	0.137076i
$708$		−	1580.11i		−	2.23179i
$709$	−33.3002	+	57.6776i	−0.0469678	+	0.0813506i	−0.888554	−	0.458773i	$-0.848289\pi$
$709$	−33.3002	+	57.6776i	−0.0469678	+	0.0813506i	0.841586	+	0.540124i	$0.181622\pi$
$710$	5.48853	−	62.5889i	0.00773032	−	0.0881533i
$711$	98.8936	+	171.289i	0.139091	+	0.240912i
$712$	−40.7844	+	70.6406i	−0.0572814	+	0.0992144i
$713$	−948.892			−1.33084
$714$	−48.0617	−	50.2542i	−0.0673133	−	0.0703841i
$715$	−228.779	+	326.589i	−0.319970	+	0.456769i
$716$	−283.690	+	491.365i	−0.396215	+	0.686264i
$717$	164.095	+	284.221i	0.228863	+	0.396403i
$718$	−56.4202	+	32.5742i	−0.0785797	+	0.0453680i
$719$	963.069	+	556.028i	1.33946	+	0.773336i	0.986727	−	0.162390i	$-0.0519201\pi$
$719$	963.069	+	556.028i	1.33946	+	0.773336i	0.352730	+	0.935725i	$0.385253\pi$
$720$	224.849	−	320.979i	0.312290	−	0.445805i
$721$	150.471	+	43.9367i	0.208698	+	0.0609386i
$722$			38.6378i			0.0535150i
$723$	−457.249	−	263.993i	−0.632433	−	0.365136i
$724$	213.724	−	123.394i	0.295199	−	0.170433i
$725$	262.824	−	312.965i	0.362516	−	0.431676i
$726$	71.3901	+	41.2171i	0.0983334	+	0.0567728i
$727$	1077.98			1.48278			0.741391	−	0.671073i	$-0.234166\pi$
$727$	1077.98			1.48278			0.741391	+	0.671073i	$0.234166\pi$
$728$	184.379	−	45.0234i	0.253268	−	0.0618453i
$729$	−31.0708			−0.0426211
$730$	6.68218	−	3.11431i	0.00915368	−	0.00426618i
$731$	−468.074	+	270.242i	−0.640320	+	0.369689i
$732$	−272.557	+	157.361i	−0.372346	+	0.214974i
$733$	414.302	−	717.592i	0.565214	−	0.978980i	−0.431815	−	0.901962i	$-0.642127\pi$
$733$	414.302	−	717.592i	0.565214	−	0.978980i	0.997030	−	0.0770179i	$-0.0245398\pi$
$734$			79.4111i			0.108190i
$735$	121.404	−	913.943i	0.165175	−	1.24346i
$736$	−428.620			−0.582363
$737$	−32.4770	−	18.7506i	−0.0440665	−	0.0254418i
$738$	−13.2956	−	23.0286i	−0.0180157	−	0.0312040i
$739$	22.9967	+	39.8315i	0.0311187	+	0.0538992i	0.881165	−	0.472808i	$-0.156760\pi$
$739$	22.9967	+	39.8315i	0.0311187	+	0.0538992i	−0.850047	+	0.526707i	$0.823426\pi$
$740$	−297.003	+	138.422i	−0.401355	+	0.187057i
$741$		−	1111.16i		−	1.49955i
$742$	−16.0113	−	65.5691i	−0.0215785	−	0.0883681i
$743$		−	1104.41i		−	1.48642i	−0.669060	−	0.743209i	$-0.733303\pi$
$743$		−	1104.41i		−	1.48642i	0.669060	−	0.743209i	$-0.266697\pi$
$744$	−105.727	+	183.124i	−0.142106	+	0.246134i
$745$	−1073.77	−	94.1605i	−1.44130	−	0.126390i
$746$	46.1698	+	79.9685i	0.0618899	+	0.107196i
$747$	−264.153	+	457.526i	−0.353618	+	0.612484i
$748$	242.141			0.323718
$749$	−101.931	+	349.085i	−0.136090	+	0.466069i
$750$	31.8685	−	118.648i	0.0424914	−	0.158197i
$751$	−78.7995	+	136.485i	−0.104926	+	0.181737i	−0.913708	−	0.406371i	$-0.866794\pi$
$751$	−78.7995	+	136.485i	−0.104926	+	0.181737i	0.808782	+	0.588109i	$0.200127\pi$
$752$	−278.491	−	482.360i	−0.370333	−	0.641436i
$753$	−824.400	+	475.967i	−1.09482	+	0.632095i
$754$	48.3948	+	27.9407i	0.0641840	+	0.0370567i
$755$	337.430	−	481.693i	0.446927	−	0.638004i
$756$	−287.331	+	274.795i	−0.380067	+	0.363486i
$757$			1148.34i			1.51696i	0.651695	+	0.758481i	$0.274058\pi$
$757$			1148.34i			1.51696i	−0.651695	+	0.758481i	$0.725942\pi$
$758$	98.5960	+	56.9244i	0.130074	+	0.0750982i
$759$	694.653	−	401.058i	0.915221	−	0.528403i
$760$	232.775	+	20.4125i	0.306283	+	0.0268585i
$761$	−761.832	−	439.844i	−1.00109	−	0.577981i	−0.0925215	−	0.995711i	$-0.529493\pi$
$761$	−761.832	−	439.844i	−1.00109	−	0.577981i	−0.908571	+	0.417729i	$0.862826\pi$
$762$	66.2169			0.0868988
$763$	−919.343	+	879.234i	−1.20491	+	1.15234i
$764$	−226.262			−0.296154
$765$	110.187	+	236.421i	0.144035	+	0.309047i
$766$	47.0843	−	27.1841i	0.0614678	−	0.0354884i
$767$	−1210.51	+	698.890i	−1.57824	+	0.911200i
$768$	401.628	−	695.639i	0.522953	−	0.905780i
$769$			725.749i			0.943757i	0.881664	+	0.471879i	$0.156424\pi$
$769$			725.749i			0.943757i	−0.881664	+	0.471879i	$0.843576\pi$
$770$	−34.8322	−	43.4607i	−0.0452367	−	0.0564425i
$771$	−1421.93			−1.84427
$772$	841.166	+	485.648i	1.08959	+	0.629077i
$773$	82.5496	+	142.980i	0.106791	+	0.184968i	0.914469	−	0.404657i	$-0.132609\pi$
$773$	82.5496	+	142.980i	0.106791	+	0.184968i	−0.807677	+	0.589625i	$0.799276\pi$
$774$	36.0408	+	62.4244i	0.0465643	+	0.0806517i
$775$	118.023	−	667.770i	0.152288	−	0.861638i
$776$		−	69.5233i		−	0.0895919i
$777$	−426.537	+	104.156i	−0.548953	+	0.134049i
$778$			148.528i			0.190910i
$779$	−222.514	+	385.406i	−0.285641	+	0.494744i
$780$	−964.587	−	84.5863i	−1.23665	−	0.108444i
$781$	146.579	+	253.882i	0.187681	+	0.325072i
$782$	46.1730	−	79.9740i	0.0590448	−	0.102269i
$783$	−236.149			−0.301596
$784$	33.1722	−	743.380i	0.0423115	−	0.948189i
$785$	71.5415	−	102.128i	0.0911356	−	0.130099i
$786$	−46.5879	+	80.6926i	−0.0592721	+	0.102662i
$787$	99.1839	+	171.792i	0.126028	+	0.218287i	0.922134	−	0.386870i	$-0.126444\pi$
$787$	99.1839	+	171.792i	0.126028	+	0.218287i	−0.796106	+	0.605157i	$0.793110\pi$
$788$	767.474	−	443.102i	0.973952	−	0.562312i
$789$	732.862	+	423.118i	0.928850	+	0.536272i
$790$	40.9864	+	28.7113i	0.0518816	+	0.0363434i
$791$	1326.04	−	323.804i	1.67641	−	0.409360i
$792$		−	65.1462i		−	0.0822554i
$793$	241.107	+	139.203i	0.304044	+	0.175540i
$794$	−64.5420	+	37.2634i	−0.0812872	+	0.0469312i
$795$	−60.6833	+	692.007i	−0.0763312	+	0.870448i
$796$	626.750	+	361.854i	0.787374	+	0.454591i
$797$	−266.357			−0.334199			−0.167100	−	0.985940i	$-0.553440\pi$
$797$	−266.357			−0.334199			−0.167100	+	0.985940i	$0.553440\pi$
$798$	148.985	+	43.5027i	0.186697	+	0.0545146i
$799$	370.711			0.463969
$800$	53.3118	−	301.635i	0.0666398	−	0.377044i
$801$	176.001	−	101.614i	0.219726	−	0.126859i
$802$	−63.3694	+	36.5863i	−0.0790142	+	0.0456189i
$803$	−17.1993	+	29.7901i	−0.0214189	+	0.0370986i
$804$		−	91.0649i		−	0.113265i
$805$	1210.26	−	185.433i	1.50343	−	0.230351i
$806$	92.7225			0.115040
$807$	846.580	+	488.773i	1.04905	+	0.605667i
$808$	19.8424	+	34.3681i	0.0245575	+	0.0425348i
$809$	−472.741	−	818.812i	−0.584352	−	1.01213i	−0.994956	−	0.100314i	$-0.968015\pi$
$809$	−472.741	−	818.812i	−0.584352	−	1.01213i	0.410603	−	0.911814i	$-0.365318\pi$
$810$	−119.324	+	55.6124i	−0.147313	+	0.0686572i
$811$		−	1402.01i		−	1.72875i	−0.502850	−	0.864374i	$-0.667715\pi$
$811$		−	1402.01i		−	1.72875i	0.502850	−	0.864374i	$-0.332285\pi$
$812$	325.157	−	310.971i	0.400439	−	0.382969i
$813$			620.781i			0.763569i
$814$	−13.2622	+	22.9708i	−0.0162926	+	0.0282196i
$815$	56.6509	−	646.023i	0.0695103	−	0.792666i
$816$	288.809	+	500.231i	0.353932	+	0.613028i
$817$	603.177	−	1044.73i	0.738283	−	1.27874i
$818$	−18.7857			−0.0229654
$819$	−453.922	−	132.543i	−0.554239	−	0.161835i
$820$	317.627	+	222.500i	0.387350	+	0.271342i
$821$	−224.015	+	388.005i	−0.272856	+	0.472601i	−0.969592	−	0.244727i	$-0.921302\pi$
$821$	−224.015	+	388.005i	−0.272856	+	0.472601i	0.696736	+	0.717328i	$0.254635\pi$
$822$	80.0178	+	138.595i	0.0973453	+	0.168607i
$823$	325.923	−	188.172i	0.396018	−	0.228641i	−0.288746	−	0.957406i	$-0.593238\pi$
$823$	325.923	−	188.172i	0.396018	−	0.228641i	0.684764	+	0.728765i	$0.259905\pi$
$824$	40.1744	+	23.1947i	0.0487553	+	0.0281489i
$825$	195.838	+	538.736i	0.237380	+	0.653014i
$826$	−46.3148	−	189.667i	−0.0560711	−	0.229622i
$827$			1506.52i			1.82166i	0.412778	+	0.910832i	$0.364559\pi$
$827$			1506.52i			1.82166i	−0.412778	+	0.910832i	$0.635441\pi$
$828$	614.792	+	354.950i	0.742503	+	0.428684i
$829$	1072.01	−	618.925i	1.29313	−	0.746592i	0.313926	−	0.949447i	$-0.398356\pi$
$829$	1072.01	−	618.925i	1.29313	−	0.746592i	0.979209	+	0.202856i	$0.0650222\pi$
$830$	−11.6767	+	133.156i	−0.0140683	+	0.160429i
$831$	1644.51	+	949.461i	1.97896	+	1.14255i
$832$	−753.178			−0.905261
$833$	417.447	+	266.507i	0.501137	+	0.319937i
$834$	−118.238			−0.141772
$835$	−138.776	−	297.764i	−0.166199	−	0.356603i
$836$	−468.048	+	270.227i	−0.559866	+	0.323239i
$837$	−339.340	+	195.918i	−0.405424	+	0.234072i
$838$	60.7844	−	105.282i	0.0725350	−	0.125634i
$839$			158.707i			0.189162i	0.995517	+	0.0945808i	$0.0301511\pi$
$839$			158.707i			0.189162i	−0.995517	+	0.0945808i	$0.969849\pi$
$840$	99.0628	−	254.226i	0.117932	−	0.302650i
$841$	−573.762			−0.682238
$842$	−83.2632	−	48.0721i	−0.0988875	−	0.0570927i
$843$	224.441	+	388.744i	0.266241	+	0.461143i
$844$	−373.312	−	646.595i	−0.442313	−	0.766108i
$845$	4.88240	+	10.4758i	0.00577799	+	0.0123975i
$846$		−	49.4397i		−	0.0584394i
$847$	−563.587	−	164.565i	−0.665393	−	0.194291i
$848$			560.660i			0.661156i
$849$	−732.698	+	1269.07i	−0.863013	+	1.49478i
$850$	50.5376	+	42.4408i	0.0594560	+	0.0499304i
$851$	−291.544	−	504.969i	−0.342590	−	0.593384i
$852$	−355.940	+	616.505i	−0.417769	+	0.723598i
$853$	−329.313			−0.386064			−0.193032	−	0.981192i	$-0.561832\pi$
$853$	−329.313			−0.386064			−0.193032	+	0.981192i	$0.561832\pi$
$854$	−28.1038	+	26.8776i	−0.0329084	+	0.0314727i
$855$	−476.830	−	334.023i	−0.557696	−	0.390670i
$856$	−53.8106	+	93.2026i	−0.0628628	+	0.108882i
$857$	−336.964	−	583.639i	−0.393190	−	0.681025i	0.599678	−	0.800241i	$-0.295295\pi$
$857$	−336.964	−	583.639i	−0.393190	−	0.681025i	−0.992868	+	0.119216i	$0.961962\pi$
$858$	−67.8792	+	39.1900i	−0.0791132	+	0.0456760i
$859$	−717.735	−	414.384i	−0.835547	−	0.482403i	0.0202012	−	0.999796i	$-0.493569\pi$
$859$	−717.735	−	414.384i	−0.835547	−	0.482403i	−0.855748	+	0.517393i	$0.826903\pi$
$860$	−861.004	−	603.140i	−1.00117	−	0.701325i
$861$	359.158	+	375.542i	0.417141	+	0.436170i
$862$		−	198.132i		−	0.229852i
$863$	89.2709	+	51.5406i	0.103443	+	0.0597226i	0.550829	−	0.834618i	$-0.314312\pi$
$863$	89.2709	+	51.5406i	0.103443	+	0.0597226i	−0.447386	+	0.894341i	$0.647645\pi$
$864$	−153.282	+	88.4972i	−0.177409	+	0.102427i
$865$	497.672	+	43.6417i	0.575343	+	0.0504529i
$866$	95.8290	+	55.3269i	0.110657	+	0.0638879i
$867$	703.104			0.810961
$868$	209.248	−	716.618i	0.241070	−	0.825596i
$869$	−233.495			−0.268694
$870$	72.8135	−	33.9356i	0.0836937	−	0.0390065i
$871$	−69.7643	+	40.2784i	−0.0800968	+	0.0462439i
$872$	−326.025	+	188.231i	−0.373882	+	0.215861i
$873$	−86.6085	+	150.010i	−0.0992079	+	0.171833i
$874$			206.115i			0.235829i
$875$	−20.0373	+	874.771i	−0.0228997	+	0.999738i
$876$	−83.5310			−0.0953550
$877$	−46.5819	−	26.8941i	−0.0531151	−	0.0306660i	0.473207	−	0.880951i	$-0.343096\pi$
$877$	−46.5819	−	26.8941i	−0.0531151	−	0.0306660i	−0.526322	+	0.850285i	$0.676429\pi$
$878$	−9.56530	−	16.5676i	−0.0108944	−	0.0188697i
$879$	−908.035	−	1572.76i	−1.03303	−	1.78926i
$880$	195.440	+	419.343i	0.222091	+	0.476526i
$881$			1300.77i			1.47647i	0.674545	+	0.738234i	$0.264340\pi$
$881$			1300.77i			1.47647i	−0.674545	+	0.738234i	$0.735660\pi$
$882$	35.5426	−	55.6726i	0.0402977	−	0.0631209i
$883$		−	525.467i		−	0.595093i	−0.954707	−	0.297546i	$-0.903832\pi$
$883$		−	525.467i		−	0.595093i	0.954707	−	0.297546i	$-0.0961683\pi$
$884$	260.073	−	450.460i	0.294200	−	0.509570i
$885$	−175.535	+	2001.72i	−0.198344	+	2.26183i
$886$	−75.3335	−	130.481i	−0.0850265	−	0.147270i
$887$	698.419	−	1209.70i	0.787395	−	1.36381i	−0.140164	−	0.990128i	$-0.544763\pi$
$887$	698.419	−	1209.70i	0.787395	−	1.36381i	0.927558	−	0.373679i	$-0.121904\pi$
$888$	−129.937			−0.146325
$889$	−458.156	+	111.877i	−0.515361	+	0.125846i
$890$	29.5012	−	42.1139i	0.0331474	−	0.0473190i
$891$	307.129	−	531.963i	0.344702	−	0.597041i
$892$	610.862	+	1058.04i	0.684822	+	1.18615i
$893$	−716.568	+	413.711i	−0.802428	+	0.463282i
$894$	−183.489	−	105.938i	−0.205245	−	0.118498i
$895$	413.971	−	590.958i	0.462537	−	0.660289i
$896$	125.646	−	430.302i	0.140230	−	0.480247i
$897$		−	1723.04i		−	1.92089i
$898$	−147.681	−	85.2635i	−0.164455	−	0.0949483i
$899$	384.013	−	221.710i	0.427155	−	0.246618i
$900$	−326.260	+	388.503i	−0.362511	+	0.431670i
$901$	−323.166	−	186.580i	−0.358674	−	0.207081i
$902$	31.3917			0.0348024
$903$	−973.583	−	1018.00i	−1.07817	−	1.12735i
$904$	403.953			0.446851
$905$	−284.459	+	132.576i	−0.314319	+	0.146492i
$906$	100.116	−	57.8021i	0.110504	−	0.0637992i
$907$	1436.20	−	829.191i	1.58346	−	0.914213i	0.589114	−	0.808050i	$-0.299477\pi$
$907$	1436.20	−	829.191i	1.58346	−	0.914213i	0.994349	−	0.106162i	$-0.0338564\pi$
$908$	−322.295	+	558.231i	−0.354950	+	0.614792i
$909$		−	98.8746i		−	0.108773i
$910$	−118.263	+	18.1198i	−0.129959	+	0.0199119i
$911$	891.683			0.978796			0.489398	−	0.872061i	$-0.337217\pi$
$911$	891.683			0.978796			0.489398	+	0.872061i	$0.337217\pi$
$912$	−1116.51	−	644.617i	−1.22424	−	0.706817i
$913$	−311.841	−	540.125i	−0.341557	−	0.591593i
$914$	−16.4024	−	28.4097i	−0.0179457	−	0.0310829i
$915$	362.763	−	169.070i	0.396462	−	0.184776i
$916$			61.6818i			0.0673383i
$917$	186.008	−	637.026i	0.202844	−	0.694685i
$918$		−	38.1334i		−	0.0415397i
$919$	−476.682	+	825.638i	−0.518697	+	0.898409i	0.481067	+	0.876684i	$0.340249\pi$
$919$	−476.682	+	825.638i	−0.518697	+	0.898409i	−0.999764	+	0.0217255i	$0.993084\pi$
$920$	360.956	+	31.6528i	0.392343	+	0.0344053i
$921$	−164.947	−	285.696i	−0.179095	−	0.310202i
$922$	−90.7923	+	157.257i	−0.0984732	+	0.170561i
$923$	629.735			0.682270
$924$	149.701	+	613.053i	0.162014	+	0.663478i
$925$	391.628	−	142.362i	0.423381	−	0.153905i
$926$	−57.2791	+	99.2103i	−0.0618565	+	0.107139i
$927$	−57.7895	−	100.094i	−0.0623403	−	0.107977i
$928$	173.461	−	100.148i	0.186919	−	0.107918i
$929$	1235.66	+	713.408i	1.33010	+	0.767931i	0.985314	−	0.170751i	$-0.0546195\pi$
$929$	1235.66	+	713.408i	1.33010	+	0.767931i	0.344782	+	0.938683i	$0.387953\pi$
$930$	76.4767	−	109.173i	0.0822330	−	0.117391i
$931$	−1104.33	−	49.2789i	−1.18617	−	0.0529312i
$932$		−	1075.72i		−	1.15420i
$933$	−563.730	−	325.470i	−0.604213	−	0.348842i
$934$	18.8599	−	10.8888i	0.0201927	−	0.0116582i
$935$	−306.750	−	26.8994i	−0.328075	−	0.0287695i
$936$	−121.193	−	69.9708i	−0.129480	−	0.0747552i
$937$	−1775.21			−1.89456			−0.947282	−	0.320400i	$-0.896183\pi$
$937$	−1775.21			−1.89456			−0.947282	+	0.320400i	$0.896183\pi$
$938$	−2.66921	−	10.9309i	−0.00284564	−	0.0116534i
$939$	234.605			0.249846
$940$	304.589	+	653.537i	0.324031	+	0.695252i
$941$	−1361.38	+	785.994i	−1.44674	+	0.835275i	−0.998286	−	0.0585313i	$-0.981358\pi$
$941$	−1361.38	+	785.994i	−1.44674	+	0.835275i	−0.448453	+	0.893806i	$0.648025\pi$
$942$	21.2265	−	12.2551i	0.0225335	−	0.0130097i
$943$	−345.044	+	597.634i	−0.365900	+	0.633758i
$944$			1621.78i			1.71799i
$945$	394.525	−	316.197i	0.417486	−	0.334600i
$946$	−85.0948			−0.0899522
$947$	477.980	+	275.962i	0.504731	+	0.291407i	0.730665	−	0.682736i	$-0.239210\pi$
$947$	477.980	+	275.962i	0.504731	+	0.291407i	−0.225934	+	0.974143i	$0.572543\pi$
$948$	−283.500	−	491.036i	−0.299050	−	0.517970i
$949$	36.9462	+	63.9927i	0.0389317	+	0.0674317i
$950$	−145.051	−	25.6366i	−0.152685	−	0.0269859i
$951$		−	622.032i		−	0.654082i
$952$	101.302	+	105.924i	0.106410	+	0.111264i
$953$			1328.92i			1.39446i	0.716846	+	0.697232i	$0.245585\pi$
$953$			1328.92i			1.39446i	−0.716846	+	0.697232i	$0.754415\pi$
$954$	−24.8831	+	43.0988i	−0.0260829	+	0.0451770i
$955$	286.634	+	25.1354i	0.300140	+	0.0263198i
$956$	−171.449	−	296.958i	−0.179340	−	0.310626i
$957$	−187.416	+	324.613i	−0.195836	+	0.339199i
$958$	−81.6269			−0.0852055
$959$	−787.808	−	823.747i	−0.821489	−	0.858964i
$960$	−621.214	+	886.806i	−0.647098	+	0.923756i
$961$	−112.623	+	195.069i	−0.117194	+	0.202986i
$962$	28.4887	+	49.3439i	0.0296141	+	0.0512930i
$963$	232.214	−	134.069i	0.241136	−	0.139220i
$964$	477.741	+	275.824i	0.495582	+	0.286124i
$965$	−1011.66	−	708.675i	−1.04835	−	0.734378i
$966$	231.025	+	67.4579i	0.239156	+	0.0698322i
$967$		−	380.091i		−	0.393062i	−0.980498	−	0.196531i	$-0.937032\pi$
$967$		−	380.091i		−	0.393062i	0.980498	−	0.196531i	$-0.0629676\pi$
$968$	−150.473	−	86.8755i	−0.155447	−	0.0897474i
$969$	743.117	−	429.039i	0.766891	−	0.442765i
$970$	−3.82847	+	43.6582i	−0.00394687	+	0.0450085i
$971$	−1539.11	−	888.604i	−1.58508	−	0.915144i	−0.994102	−	0.108453i	$-0.965410\pi$
$971$	−1539.11	−	888.604i	−1.58508	−	0.915144i	−0.590974	−	0.806691i	$-0.701256\pi$
$972$	980.438			1.00868
$973$	818.089	−	199.769i	0.840790	−	0.205312i
$974$	−128.375			−0.131802
$975$	1212.57	+	214.312i	1.24366	+	0.219807i
$976$	279.745	−	161.511i	0.286624	−	0.165483i
$977$	842.114	−	486.195i	0.861939	−	0.497641i	−0.00272235	−	0.999996i	$-0.500867\pi$
$977$	842.114	−	486.195i	0.861939	−	0.497641i	0.864661	+	0.502356i	$0.167533\pi$
$978$	63.7365	−	110.395i	0.0651702	−	0.112878i
$979$			239.918i			0.245064i
$980$	−126.844	+	954.901i	−0.129433	+	0.974388i
$981$	937.952			0.956119
$982$	156.967	+	90.6248i	0.159844	+	0.0922859i
$983$	693.763	+	1201.63i	0.705761	+	1.22241i	0.966416	+	0.256982i	$0.0827282\pi$
$983$	693.763	+	1201.63i	0.705761	+	1.22241i	−0.260655	+	0.965432i	$0.583939\pi$
$984$	76.8904	+	133.178i	0.0781406	+	0.135344i
$985$	−1021.48	+	476.073i	−1.03703	+	0.483323i
$986$			43.1535i			0.0437663i
$987$	229.188	+	938.568i	0.232207	+	0.950930i
$988$			1160.96i			1.17506i
$989$	935.324	−	1620.03i	0.945727	−	1.63805i
$990$	−3.58743	+	40.9096i	−0.00362367	+	0.0413228i
$991$	963.975	+	1669.65i	0.972730	+	1.68482i	0.687231	+	0.726439i	$0.258826\pi$
$991$	963.975	+	1669.65i	0.972730	+	1.68482i	0.285499	+	0.958379i	$0.407841\pi$
$992$	166.172	−	287.818i	0.167512	−	0.290139i
$993$	1252.22			1.26105
$994$	−24.6545	+	84.4348i	−0.0248033	+	0.0849445i
$995$	−753.784	−	528.031i	−0.757571	−	0.530685i
$996$	757.250	−	1311.60i	0.760291	−	1.31686i
$997$	−666.163	−	1153.83i	−0.668167	−	1.15730i	−0.978416	−	0.206644i	$-0.933746\pi$
$997$	−666.163	−	1153.83i	−0.668167	−	1.15730i	0.310249	−	0.950655i	$-0.399588\pi$
$998$	16.1864	−	9.34525i	0.0162189	−	0.00936398i
$999$	−208.522	−	120.391i	−0.208731	−	0.120511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.i.a.19.4	yes	12
3.2	odd	2		315.3.bi.c.19.3		12
4.3	odd	2		560.3.br.a.369.2		12
5.2	odd	4		175.3.i.c.26.3		12
5.3	odd	4		175.3.i.c.26.4		12
5.4	even	2	inner	35.3.i.a.19.3	✓	12
7.2	even	3		245.3.c.a.244.5		12
7.3	odd	6	inner	35.3.i.a.24.3	yes	12
7.4	even	3		245.3.i.d.129.3		12
7.5	odd	6		245.3.c.a.244.6		12
7.6	odd	2		245.3.i.d.19.4		12
15.14	odd	2		315.3.bi.c.19.4		12
20.19	odd	2		560.3.br.a.369.5		12
21.17	even	6		315.3.bi.c.199.4		12
28.3	even	6		560.3.br.a.129.5		12
35.3	even	12		175.3.i.c.101.4		12
35.4	even	6		245.3.i.d.129.4		12
35.9	even	6		245.3.c.a.244.8		12
35.17	even	12		175.3.i.c.101.3		12
35.19	odd	6		245.3.c.a.244.7		12
35.24	odd	6	inner	35.3.i.a.24.4	yes	12
35.34	odd	2		245.3.i.d.19.3		12
105.59	even	6		315.3.bi.c.199.3		12
140.59	even	6		560.3.br.a.129.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.i.a.19.3	✓	12	5.4	even	2	inner
35.3.i.a.19.4	yes	12	1.1	even	1	trivial
35.3.i.a.24.3	yes	12	7.3	odd	6	inner
35.3.i.a.24.4	yes	12	35.24	odd	6	inner
175.3.i.c.26.3		12	5.2	odd	4
175.3.i.c.26.4		12	5.3	odd	4
175.3.i.c.101.3		12	35.17	even	12
175.3.i.c.101.4		12	35.3	even	12
245.3.c.a.244.5		12	7.2	even	3
245.3.c.a.244.6		12	7.5	odd	6
245.3.c.a.244.7		12	35.19	odd	6
245.3.c.a.244.8		12	35.9	even	6
245.3.i.d.19.3		12	35.34	odd	2
245.3.i.d.19.4		12	7.6	odd	2
245.3.i.d.129.3		12	7.4	even	3
245.3.i.d.129.4		12	35.4	even	6
315.3.bi.c.19.3		12	3.2	odd	2
315.3.bi.c.19.4		12	15.14	odd	2
315.3.bi.c.199.3		12	105.59	even	6
315.3.bi.c.199.4		12	21.17	even	6
560.3.br.a.129.2		12	140.59	even	6
560.3.br.a.129.5		12	28.3	even	6
560.3.br.a.369.2		12	4.3	odd	2
560.3.br.a.369.5		12	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.226181 + 0.130586i) q^{2} +(1.88157 + 3.25898i) q^{3} +(-1.96589 - 3.40503i) q^{4} +(2.11218 + 4.53196i) q^{5} +0.982826i q^{6} +(-1.66053 - 6.80019i) q^{7} -2.07156i q^{8} +(-2.58064 + 4.46979i) q^{9} +O(q^{10})\)	\(q+(0.226181 + 0.130586i) q^{2} +(1.88157 + 3.25898i) q^{3} +(-1.96589 - 3.40503i) q^{4} +(2.11218 + 4.53196i) q^{5} +0.982826i q^{6} +(-1.66053 - 6.80019i) q^{7} -2.07156i q^{8} +(-2.58064 + 4.46979i) q^{9} +(-0.114075 + 1.30086i) q^{10} +(-3.04653 - 5.27675i) q^{11} +(7.39795 - 12.8136i) q^{12} -13.0886 q^{13} +(0.512426 - 1.75492i) q^{14} +(-10.7954 + 15.4108i) q^{15} +(-7.59306 + 13.1516i) q^{16} +(-5.05373 - 8.75332i) q^{17} +(-1.16738 + 0.673989i) q^{18} +(19.5373 + 11.2799i) q^{19} +(11.2792 - 16.1014i) q^{20} +(19.0373 - 18.2067i) q^{21} -1.59133i q^{22} +(30.2957 + 17.4912i) q^{23} +(6.75116 - 3.89779i) q^{24} +(-16.0774 + 19.1446i) q^{25} +(-2.96039 - 1.70918i) q^{26} +14.4457 q^{27} +(-19.8904 + 19.0226i) q^{28} -16.3474 q^{29} +(-4.45413 + 2.07590i) q^{30} +(-23.4907 + 13.5624i) q^{31} +(-10.6109 + 6.12620i) q^{32} +(11.4645 - 19.8572i) q^{33} -2.63978i q^{34} +(27.3109 - 21.8887i) q^{35} +20.2930 q^{36} +(-14.4349 - 8.33401i) q^{37} +(2.94598 + 5.10258i) q^{38} +(-24.6272 - 42.6555i) q^{39} +(9.38822 - 4.37550i) q^{40} +19.7267i q^{41} +(6.68341 - 1.63202i) q^{42} -53.4739i q^{43} +(-11.9783 + 20.7471i) q^{44} +(-25.7077 - 2.25436i) q^{45} +(4.56821 + 7.91237i) q^{46} +(-18.3385 + 31.7632i) q^{47} -57.1476 q^{48} +(-43.4852 + 22.5839i) q^{49} +(-6.13642 + 2.23067i) q^{50} +(19.0179 - 32.9400i) q^{51} +(25.7308 + 44.5671i) q^{52} +(31.9730 - 18.4596i) q^{53} +(3.26734 + 1.88640i) q^{54} +(17.4792 - 24.9522i) q^{55} +(-14.0870 + 3.43989i) q^{56} +84.8955i q^{57} +(-3.69747 - 2.13474i) q^{58} +(92.4861 - 53.3969i) q^{59} +(73.6967 + 6.46260i) q^{60} +(-18.4211 - 10.6354i) q^{61} -7.08422 q^{62} +(34.6807 + 10.1266i) q^{63} +57.5445 q^{64} +(-27.6455 - 59.3171i) q^{65} +(5.18613 - 2.99421i) q^{66} +(5.33016 - 3.07737i) q^{67} +(-19.8702 + 34.4162i) q^{68} +131.644i q^{69} +(9.03556 - 1.38440i) q^{70} -48.1133 q^{71} +(9.25943 + 5.34594i) q^{72} +(-2.82277 - 4.88919i) q^{73} +(-2.17660 - 3.76999i) q^{74} +(-92.6428 - 16.3739i) q^{75} -88.7000i q^{76} +(-30.8240 + 29.4792i) q^{77} -12.8638i q^{78} +(19.1607 - 33.1873i) q^{79} +(-75.6404 - 6.63304i) q^{80} +(50.4064 + 87.3064i) q^{81} +(-2.57602 + 4.46180i) q^{82} +102.359 q^{83} +(-99.4197 - 29.0300i) q^{84} +(28.9953 - 41.3919i) q^{85} +(6.98292 - 12.0948i) q^{86} +(-30.7588 - 53.2759i) q^{87} +(-10.9311 + 6.31106i) q^{88} +(-34.1003 - 19.6878i) q^{89} +(-5.52021 - 3.86695i) q^{90} +(21.7341 + 89.0050i) q^{91} -137.544i q^{92} +(-88.3991 - 51.0373i) q^{93} +(-8.29564 + 4.78949i) q^{94} +(-9.85369 + 112.367i) q^{95} +(-39.9304 - 23.0538i) q^{96} +33.5609 q^{97} +(-12.7847 - 0.570497i) q^{98} +31.4480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 18 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 - 18 * q^9	\( 12 q + 6 q^{4} - 18 q^{9} - 54 q^{10} + 6 q^{11} - 66 q^{14} + 48 q^{15} - 6 q^{16} + 18 q^{19} + 12 q^{21} + 216 q^{24} + 18 q^{25} + 18 q^{26} + 48 q^{30} - 108 q^{31} + 222 q^{35} - 204 q^{36} - 240 q^{39} - 162 q^{40} - 42 q^{44} - 216 q^{45} + 114 q^{46} - 324 q^{49} - 192 q^{50} + 180 q^{51} + 252 q^{54} + 336 q^{56} + 396 q^{59} + 384 q^{60} - 108 q^{61} + 372 q^{64} - 54 q^{65} - 108 q^{66} + 300 q^{70} + 192 q^{71} - 594 q^{74} - 216 q^{75} - 192 q^{79} - 504 q^{80} + 294 q^{81} - 1200 q^{84} - 192 q^{85} - 384 q^{86} + 684 q^{89} - 72 q^{91} + 990 q^{94} + 288 q^{95} - 540 q^{96} + 396 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 - 18 * q^9 - 54 * q^10 + 6 * q^11 - 66 * q^14 + 48 * q^15 - 6 * q^16 + 18 * q^19 + 12 * q^21 + 216 * q^24 + 18 * q^25 + 18 * q^26 + 48 * q^30 - 108 * q^31 + 222 * q^35 - 204 * q^36 - 240 * q^39 - 162 * q^40 - 42 * q^44 - 216 * q^45 + 114 * q^46 - 324 * q^49 - 192 * q^50 + 180 * q^51 + 252 * q^54 + 336 * q^56 + 396 * q^59 + 384 * q^60 - 108 * q^61 + 372 * q^64 - 54 * q^65 - 108 * q^66 + 300 * q^70 + 192 * q^71 - 594 * q^74 - 216 * q^75 - 192 * q^79 - 504 * q^80 + 294 * q^81 - 1200 * q^84 - 192 * q^85 - 384 * q^86 + 684 * q^89 - 72 * q^91 + 990 * q^94 + 288 * q^95 - 540 * q^96 + 396 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more