LMFDB - Embedded newform 105.2.s.c.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(26,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("105.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.s (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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$-2.06288i$ of defining polynomial
Character	$\chi$	$=$	105.101
Dual form			105.2.s.c.26.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78651 - 1.03144i) q^{2} +(-0.627739 + 1.61429i) q^{3} +(1.12774 - 1.95330i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.543588 + 3.53142i) q^{6} +(-0.00953166 - 2.64573i) q^{7} -0.527019i q^{8} +(-2.21189 - 2.02671i) q^{9} +O(q^{10})$	\(q+(1.78651 - 1.03144i) q^{2} +(-0.627739 + 1.61429i) q^{3} +(1.12774 - 1.95330i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.543588 + 3.53142i) q^{6} +(-0.00953166 - 2.64573i) q^{7} -0.527019i q^{8} +(-2.21189 - 2.02671i) q^{9} +(1.78651 + 1.03144i) q^{10} +(-4.06348 - 2.34605i) q^{11} +(2.44528 + 3.04666i) q^{12} +0.638688i q^{13} +(-2.74595 - 4.71679i) q^{14} +(-1.71189 + 0.263509i) q^{15} +(1.71189 + 2.96508i) q^{16} +(-2.07462 + 3.59334i) q^{17} +(-6.04198 - 1.33930i) q^{18} +(-0.776975 + 0.448587i) q^{19} +2.25548 q^{20} +(4.27698 + 1.64544i) q^{21} -9.67925 q^{22} +(5.89275 - 3.40218i) q^{23} +(0.850763 + 0.330830i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.658769 + 1.14102i) q^{26} +(4.66019 - 2.29839i) q^{27} +(-5.17866 - 2.96508i) q^{28} -2.14740i q^{29} +(-2.78651 + 2.23647i) q^{30} +(-2.02453 - 1.16886i) q^{31} +(7.02943 + 4.05844i) q^{32} +(6.33802 - 5.08695i) q^{33} +8.55938i q^{34} +(2.28651 - 1.33112i) q^{35} +(-6.45320 + 2.03489i) q^{36} +(5.69122 + 9.85748i) q^{37} +(-0.925382 + 1.60281i) q^{38} +(-1.03103 - 0.400929i) q^{39} +(0.456412 - 0.263509i) q^{40} -4.10624 q^{41} +(9.33802 - 1.47185i) q^{42} +3.14924 q^{43} +(-9.16509 + 5.29147i) q^{44} +(0.649237 - 2.92891i) q^{45} +(7.01829 - 12.1560i) q^{46} +(-3.40471 - 5.89714i) q^{47} +(-5.86113 + 0.902197i) q^{48} +(-6.99982 + 0.0504365i) q^{49} +2.06288i q^{50} +(-4.49840 - 5.60472i) q^{51} +(1.24755 + 0.720273i) q^{52} +(1.96187 + 1.13269i) q^{53} +(5.95481 - 8.91281i) q^{54} -4.69211i q^{55} +(-1.39435 + 0.00502336i) q^{56} +(-0.236414 - 1.53586i) q^{57} +(-2.21492 - 3.83635i) q^{58} +(-0.254055 + 0.440035i) q^{59} +(-1.41585 + 3.64100i) q^{60} +(4.48946 - 2.59199i) q^{61} -4.82244 q^{62} +(-5.34105 + 5.87139i) q^{63} +9.89660 q^{64} +(-0.553120 + 0.319344i) q^{65} +(6.07604 - 15.6252i) q^{66} +(-2.41425 + 4.18160i) q^{67} +(4.67925 + 8.10471i) q^{68} +(1.79301 + 11.6483i) q^{69} +(2.71189 - 4.73645i) q^{70} +1.22800i q^{71} +(-1.06811 + 1.16571i) q^{72} +(12.5197 + 7.22826i) q^{73} +(20.3348 + 11.7403i) q^{74} +(-1.08415 - 1.35078i) q^{75} +2.02356i q^{76} +(-6.16830 + 10.7733i) q^{77} +(-2.25548 + 0.347183i) q^{78} +(-4.54056 - 7.86448i) q^{79} +(-1.71189 + 2.96508i) q^{80} +(0.784903 + 8.96571i) q^{81} +(-7.33583 + 4.23534i) q^{82} +2.76359 q^{83} +(8.03735 - 6.49859i) q^{84} -4.14924 q^{85} +(5.62613 - 3.24825i) q^{86} +(3.46653 + 1.34801i) q^{87} +(-1.23641 + 2.14153i) q^{88} +(-6.90067 - 11.9523i) q^{89} +(-1.86113 - 5.90216i) q^{90} +(1.68980 - 0.00608775i) q^{91} -15.3471i q^{92} +(3.15776 - 2.53444i) q^{93} +(-12.1651 - 7.02352i) q^{94} +(-0.776975 - 0.448587i) q^{95} +(-10.9642 + 8.79992i) q^{96} -12.9085i q^{97} +(-12.4532 + 7.31000i) q^{98} +(4.23321 + 13.4247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 2 q^{7} - 5 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 2 * q^7 - 5 * q^9	$ 8 q - 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 2 q^{7} - 5 q^{9} - 3 q^{10} - 9 q^{12} - 12 q^{14} - q^{15} + q^{16} - 12 q^{17} - 19 q^{18} + 9 q^{19} + 6 q^{20} + 19 q^{21} - 40 q^{22} + 27 q^{23} + 16 q^{24} - 4 q^{25} - 6 q^{26} + 4 q^{27} + 3 q^{28} - 5 q^{30} - 21 q^{31} + 21 q^{32} + 2 q^{33} + q^{35} + 9 q^{36} + 7 q^{37} - 12 q^{38} - 3 q^{39} + 3 q^{40} - 30 q^{41} + 26 q^{42} + 16 q^{43} - 4 q^{45} - 7 q^{46} - 6 q^{47} - 25 q^{48} - 4 q^{49} - 6 q^{51} + 30 q^{52} + 24 q^{53} + 17 q^{54} - 21 q^{56} + 6 q^{57} - 13 q^{58} - 12 q^{59} - 18 q^{60} + 15 q^{61} + 24 q^{62} - 2 q^{63} + 38 q^{64} - 3 q^{65} + 22 q^{66} + 4 q^{67} - 13 q^{69} + 9 q^{70} - 14 q^{72} + 15 q^{73} + 54 q^{74} - 2 q^{75} - 36 q^{77} - 6 q^{78} - 29 q^{79} - q^{80} - 41 q^{81} + 27 q^{82} + 30 q^{83} - 3 q^{84} - 24 q^{85} + 9 q^{86} + 32 q^{87} - 2 q^{88} - 3 q^{89} + 7 q^{90} - 3 q^{91} - 9 q^{93} - 24 q^{94} + 9 q^{95} - 3 q^{96} - 39 q^{98} - 34 q^{99}+O(q^{100}) $ 8 * q - 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 2 * q^7 - 5 * q^9 - 3 * q^10 - 9 * q^12 - 12 * q^14 - q^15 + q^16 - 12 * q^17 - 19 * q^18 + 9 * q^19 + 6 * q^20 + 19 * q^21 - 40 * q^22 + 27 * q^23 + 16 * q^24 - 4 * q^25 - 6 * q^26 + 4 * q^27 + 3 * q^28 - 5 * q^30 - 21 * q^31 + 21 * q^32 + 2 * q^33 + q^35 + 9 * q^36 + 7 * q^37 - 12 * q^38 - 3 * q^39 + 3 * q^40 - 30 * q^41 + 26 * q^42 + 16 * q^43 - 4 * q^45 - 7 * q^46 - 6 * q^47 - 25 * q^48 - 4 * q^49 - 6 * q^51 + 30 * q^52 + 24 * q^53 + 17 * q^54 - 21 * q^56 + 6 * q^57 - 13 * q^58 - 12 * q^59 - 18 * q^60 + 15 * q^61 + 24 * q^62 - 2 * q^63 + 38 * q^64 - 3 * q^65 + 22 * q^66 + 4 * q^67 - 13 * q^69 + 9 * q^70 - 14 * q^72 + 15 * q^73 + 54 * q^74 - 2 * q^75 - 36 * q^77 - 6 * q^78 - 29 * q^79 - q^80 - 41 * q^81 + 27 * q^82 + 30 * q^83 - 3 * q^84 - 24 * q^85 + 9 * q^86 + 32 * q^87 - 2 * q^88 - 3 * q^89 + 7 * q^90 - 3 * q^91 - 9 * q^93 - 24 * q^94 + 9 * q^95 - 3 * q^96 - 39 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.78651	−	1.03144i	1.26325	−	0.729338i	0.289549	−	0.957163i	$-0.406495\pi$
$2$	1.78651	−	1.03144i	1.26325	−	0.729338i	0.973702	+	0.227825i	$0.0731613\pi$
$3$	−0.627739	+	1.61429i	−0.362425	+	0.932013i
$3$	−0.627739	+	1.61429i	−0.362425	+	0.932013i
$4$	1.12774	−	1.95330i	0.563869	−	0.976650i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.543588	+	3.53142i	0.221919	+	1.44170i
$7$	−0.00953166	−	2.64573i	−0.00360263	−	0.999994i
$7$	−0.00953166	−	2.64573i	−0.00360263	−	0.999994i
$8$		−	0.527019i		−	0.186329i
$9$	−2.21189	−	2.02671i	−0.737296	−	0.675570i
$10$	1.78651	+	1.03144i	0.564943	+	0.326170i
$11$	−4.06348	−	2.34605i	−1.22519	−	0.707362i	−0.259167	−	0.965833i	$-0.583448\pi$
$11$	−4.06348	−	2.34605i	−1.22519	−	0.707362i	−0.966019	+	0.258471i	$0.916781\pi$
$12$	2.44528	+	3.04666i	0.705890	+	0.879496i
$13$			0.638688i			0.177140i	0.996070	+	0.0885701i	$0.0282297\pi$
$13$			0.638688i			0.177140i	−0.996070	+	0.0885701i	$0.971770\pi$
$14$	−2.74595	−	4.71679i	−0.733885	−	1.26062i
$15$	−1.71189	+	0.263509i	−0.442008	+	0.0680378i
$16$	1.71189	+	2.96508i	0.427972	+	0.741270i
$17$	−2.07462	+	3.59334i	−0.503169	+	0.871514i	0.496824	+	0.867851i	$0.334499\pi$
$17$	−2.07462	+	3.59334i	−0.503169	+	0.871514i	−0.999993	+	0.00366299i	$0.998834\pi$
$18$	−6.04198	−	1.33930i	−1.42411	−	0.315676i
$19$	−0.776975	+	0.448587i	−0.178250	+	0.102913i	−0.586470	−	0.809971i	$-0.699483\pi$
$19$	−0.776975	+	0.448587i	−0.178250	+	0.102913i	0.408220	+	0.912884i	$0.366150\pi$
$20$	2.25548			0.504340
$21$	4.27698	+	1.64544i	0.933313	+	0.359065i
$22$	−9.67925			−2.06362
$23$	5.89275	−	3.40218i	1.22872	−	0.709403i	0.261960	−	0.965079i	$-0.415631\pi$
$23$	5.89275	−	3.40218i	1.22872	−	0.709403i	0.966763	+	0.255675i	$0.0822978\pi$
$24$	0.850763	+	0.330830i	0.173661	+	0.0675304i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.658769	+	1.14102i	0.129195	+	0.223773i
$27$	4.66019	−	2.29839i	0.896854	−	0.442326i
$28$	−5.17866	−	2.96508i	−0.978675	−	0.560347i
$29$		−	2.14740i		−	0.398762i	−0.979922	−	0.199381i	$-0.936107\pi$
$29$		−	2.14740i		−	0.398762i	0.979922	−	0.199381i	$-0.0638932\pi$
$30$	−2.78651	+	2.23647i	−0.508744	+	0.408322i
$31$	−2.02453	−	1.16886i	−0.363615	−	0.209933i	0.307050	−	0.951693i	$-0.400658\pi$
$31$	−2.02453	−	1.16886i	−0.363615	−	0.209933i	−0.670666	+	0.741760i	$0.733991\pi$
$32$	7.02943	+	4.05844i	1.24264	+	0.717438i
$33$	6.33802	−	5.08695i	1.10331	−	0.885524i
$34$			8.55938i			1.46792i
$35$	2.28651	−	1.33112i	0.386490	−	0.225001i
$36$	−6.45320	+	2.03489i	−1.07553	+	0.339148i
$37$	5.69122	+	9.85748i	0.935631	+	1.62056i	0.773505	+	0.633790i	$0.218502\pi$
$37$	5.69122	+	9.85748i	0.935631	+	1.62056i	0.162126	+	0.986770i	$0.448165\pi$
$38$	−0.925382	+	1.60281i	−0.150117	+	0.260010i
$39$	−1.03103	−	0.400929i	−0.165097	−	0.0642000i
$40$	0.456412	−	0.263509i	0.0721650	−	0.0416645i
$41$	−4.10624			−0.641287			−0.320643	−	0.947200i	$-0.603899\pi$
$41$	−4.10624			−0.641287			−0.320643	+	0.947200i	$0.603899\pi$
$42$	9.33802	−	1.47185i	1.44089	−	0.227111i
$43$	3.14924			0.480254			0.240127	−	0.970741i	$-0.422811\pi$
$43$	3.14924			0.480254			0.240127	+	0.970741i	$0.422811\pi$
$44$	−9.16509	+	5.29147i	−1.38169	+	0.797719i
$45$	0.649237	−	2.92891i	0.0967825	−	0.436616i
$46$	7.01829	−	12.1560i	1.03479	−	1.79231i
$47$	−3.40471	−	5.89714i	−0.496629	−	0.860186i	0.503364	−	0.864075i	$-0.332096\pi$
$47$	−3.40471	−	5.89714i	−0.496629	−	0.860186i	−0.999992	+	0.00388861i	$0.998762\pi$
$48$	−5.86113	+	0.902197i	−0.845981	+	0.130221i
$49$	−6.99982	+	0.0504365i	−0.999974	+	0.00720521i
$50$			2.06288i			0.291735i
$51$	−4.49840	−	5.60472i	−0.629901	−	0.784818i
$52$	1.24755	+	0.720273i	0.173004	+	0.0998839i
$53$	1.96187	+	1.13269i	0.269484	+	0.155587i	0.628653	−	0.777686i	$-0.283607\pi$
$53$	1.96187	+	1.13269i	0.269484	+	0.155587i	−0.359169	+	0.933272i	$0.616940\pi$
$54$	5.95481	−	8.91281i	0.810347	−	1.21288i
$55$		−	4.69211i		−	0.632683i
$56$	−1.39435	+	0.00502336i	−0.186328	+	0.000671275i
$57$	−0.236414	−	1.53586i	−0.0313138	−	0.203430i
$58$	−2.21492	−	3.83635i	−0.290833	−	0.503737i
$59$	−0.254055	+	0.440035i	−0.0330751	+	0.0572877i	−0.882089	−	0.471083i	$-0.843863\pi$
$59$	−0.254055	+	0.440035i	−0.0330751	+	0.0572877i	0.849014	+	0.528370i	$0.177197\pi$
$60$	−1.41585	+	3.64100i	−0.182785	+	0.470051i
$61$	4.48946	−	2.59199i	0.574816	−	0.331870i	−0.184255	−	0.982879i	$-0.558987\pi$
$61$	4.48946	−	2.59199i	0.574816	−	0.331870i	0.759070	+	0.651008i	$0.225654\pi$
$62$	−4.82244			−0.612450
$63$	−5.34105	+	5.87139i	−0.672909	+	0.739725i
$64$	9.89660			1.23708
$65$	−0.553120	+	0.319344i	−0.0686061	+	0.0396097i
$66$	6.07604	−	15.6252i	0.747909	−	1.92332i
$67$	−2.41425	+	4.18160i	−0.294947	+	0.510863i	−0.974973	−	0.222325i	$-0.928635\pi$
$67$	−2.41425	+	4.18160i	−0.294947	+	0.510863i	0.680026	+	0.733188i	$0.261969\pi$
$68$	4.67925	+	8.10471i	0.567443	+	0.982840i
$69$	1.79301	+	11.6483i	0.215853	+	1.40229i
$70$	2.71189	−	4.73645i	0.324133	−	0.566115i
$71$			1.22800i			0.145737i	0.997342	+	0.0728686i	$0.0232154\pi$
$71$			1.22800i			0.145737i	−0.997342	+	0.0728686i	$0.976785\pi$
$72$	−1.06811	+	1.16571i	−0.125878	+	0.137380i
$73$	12.5197	+	7.22826i	1.46532	+	0.846004i	0.999249	−	0.0387429i	$-0.0123353\pi$
$73$	12.5197	+	7.22826i	1.46532	+	0.846004i	0.466072	+	0.884747i	$0.345669\pi$
$74$	20.3348	+	11.7403i	2.36387	+	1.36478i
$75$	−1.08415	−	1.35078i	−0.125187	−	0.155975i
$76$			2.02356i			0.232118i
$77$	−6.16830	+	10.7733i	−0.702943	+	1.22773i
$78$	−2.25548	+	0.347183i	−0.255382	+	0.0393108i
$79$	−4.54056	−	7.86448i	−0.510853	−	0.884824i	−0.999921	−	0.0125778i	$-0.995996\pi$
$79$	−4.54056	−	7.86448i	−0.510853	−	0.884824i	0.489068	−	0.872246i	$-0.337337\pi$
$80$	−1.71189	+	2.96508i	−0.191395	+	0.331506i
$81$	0.784903	+	8.96571i	0.0872114	+	0.996190i
$82$	−7.33583	+	4.23534i	−0.810107	+	0.467715i
$83$	2.76359			0.303343			0.151671	−	0.988431i	$-0.451534\pi$
$83$	2.76359			0.303343			0.151671	+	0.988431i	$0.451534\pi$
$84$	8.03735	−	6.49859i	0.876947	−	0.709054i
$85$	−4.14924			−0.450048
$86$	5.62613	−	3.24825i	0.606682	−	0.350268i
$87$	3.46653	+	1.34801i	0.371652	+	0.144521i
$88$	−1.23641	+	2.14153i	−0.131802	+	0.228288i
$89$	−6.90067	−	11.9523i	−0.731470	−	1.26694i	−0.956255	−	0.292535i	$-0.905501\pi$
$89$	−6.90067	−	11.9523i	−0.731470	−	1.26694i	0.224785	−	0.974408i	$-0.427832\pi$
$90$	−1.86113	−	5.90216i	−0.196180	−	0.622142i
$91$	1.68980	−	0.00608775i	0.177139	−	0.000638170i
$92$		−	15.3471i		−	1.60004i
$93$	3.15776	−	2.53444i	0.327444	−	0.262809i
$94$	−12.1651	−	7.02352i	−1.25473	−	0.724421i
$95$	−0.776975	−	0.448587i	−0.0797160	−	0.0460241i
$96$	−10.9642	+	8.79992i	−1.11902	+	0.898138i
$97$		−	12.9085i		−	1.31066i	−0.755344	−	0.655329i	$-0.772530\pi$
$97$		−	12.9085i		−	1.31066i	0.755344	−	0.655329i	$-0.227470\pi$
$98$	−12.4532	+	7.31000i	−1.25796	+	0.738422i
$99$	4.23321	+	13.4247i	0.425453	+	1.34923i
$100$	1.12774	+	1.95330i	0.112774	+	0.195330i
$101$	−4.51989	+	7.82869i	−0.449746	+	0.778983i	−0.998369	−	0.0570865i	$-0.981819\pi$
$101$	−4.51989	+	7.82869i	−0.449746	+	0.778983i	0.548623	+	0.836070i	$0.315152\pi$
$102$	−13.8174	−	5.37305i	−1.36812	−	0.532012i
$103$	−13.4412	+	7.76030i	−1.32440	+	0.764645i	−0.984428	−	0.175789i	$-0.943752\pi$
$103$	−13.4412	+	7.76030i	−1.32440	+	0.764645i	−0.339976	+	0.940434i	$0.610419\pi$
$104$	0.336601			0.0330064
$105$	0.713493	+	4.52669i	0.0696298	+	0.441760i
$106$	4.67320			0.453901
$107$	−4.64012	+	2.67897i	−0.448577	+	0.258986i	−0.707229	−	0.706985i	$-0.750055\pi$
$107$	−4.64012	+	2.67897i	−0.448577	+	0.258986i	0.258652	+	0.965971i	$0.416722\pi$
$108$	0.766021	−	11.6947i	0.0737104	−	1.12533i
$109$	−0.679436	+	1.17682i	−0.0650782	+	0.112719i	−0.896729	−	0.442581i	$-0.854063\pi$
$109$	−0.679436	+	1.17682i	−0.0650782	+	0.112719i	0.831650	+	0.555299i	$0.187396\pi$
$110$	−4.83963	−	8.38248i	−0.461440	−	0.799238i
$111$	−19.4855	+	2.99938i	−1.84948	+	0.284689i
$112$	7.82849	−	4.55746i	0.739723	−	0.430640i
$113$		−	11.9390i		−	1.12312i	−0.827435	−	0.561562i	$-0.810201\pi$
$113$		−	11.9390i		−	1.12312i	0.827435	−	0.561562i	$-0.189799\pi$
$114$	−2.00650	−	2.49998i	−0.187926	−	0.234145i
$115$	5.89275	+	3.40218i	0.549502	+	0.317255i
$116$	−4.19452	−	2.42171i	−0.389451	−	0.224850i
$117$	1.29443	−	1.41271i	0.119671	−	0.130605i
$118$			1.04817i			0.0964917i
$119$	9.52681	+	5.45464i	0.873321	+	0.500026i
$120$	0.138874	+	0.902197i	0.0126774	+	0.0823590i
$121$	5.50793	+	9.54001i	0.500721	+	0.867274i
$122$	5.34696	−	9.26121i	0.484091	−	0.838471i
$123$	2.57765	−	6.62868i	0.232418	−	0.597688i
$124$	−4.56627	+	2.63634i	−0.410063	+	0.236750i
$125$	−1.00000			−0.0894427
$126$	−3.48584	+	15.9982i	−0.310543	+	1.42524i
$127$	−16.8492			−1.49513			−0.747563	−	0.664191i	$-0.768776\pi$
$127$	−16.8492			−1.49513			−0.747563	+	0.664191i	$0.768776\pi$
$128$	3.62150	−	2.09088i	0.320099	−	0.184809i
$129$	−1.97690	+	5.08379i	−0.174056	+	0.447603i
$130$	−0.658769	+	1.14102i	−0.0577778	+	0.100074i
$131$	6.93473	+	12.0113i	0.605890	+	1.04943i	0.991910	+	0.126942i	$0.0405163\pi$
$131$	6.93473	+	12.0113i	0.605890	+	1.04943i	−0.386020	+	0.922490i	$0.626150\pi$
$132$	−2.78870	−	18.1168i	−0.242725	−	1.57687i
$133$	1.19425	+	2.05139i	0.103554	+	0.177878i
$134$			9.96060i			0.860465i
$135$	4.32056	+	2.88665i	0.371855	+	0.248443i
$136$	1.89376	+	1.09336i	0.162389	+	0.0937551i
$137$	−3.75708	−	2.16915i	−0.320989	−	0.185323i	0.330844	−	0.943685i	$-0.392667\pi$
$137$	−3.75708	−	2.16915i	−0.320989	−	0.185323i	−0.651833	+	0.758362i	$0.726000\pi$
$138$	15.2178	+	18.9604i	1.29542	+	1.61402i
$139$		−	10.9631i		−	0.929881i	−0.885342	−	0.464941i	$-0.846076\pi$
$139$		−	10.9631i		−	0.929881i	0.885342	−	0.464941i	$-0.153924\pi$
$140$	−0.0214984	−	5.96739i	−0.00181695	−	0.504337i
$141$	11.6570	−	1.79435i	0.981695	−	0.151111i
$142$	1.26661	+	2.19384i	0.106292	+	0.184103i
$143$	1.49840	−	2.59530i	0.125302	−	0.217030i
$144$	2.22284	−	10.0279i	0.185237	−	0.835660i
$145$	1.85970	−	1.07370i	0.154440	−	0.0891659i
$146$	29.8221			2.46809
$147$	4.31264	−	11.3314i	0.355700	−	0.934600i
$148$	25.6728			2.11029
$149$	7.50546	−	4.33328i	0.614871	−	0.354996i	−0.159998	−	0.987117i	$-0.551149\pi$
$149$	7.50546	−	4.33328i	0.614871	−	0.354996i	0.774870	+	0.632121i	$0.217816\pi$
$150$	−3.33010	−	1.29495i	−0.271901	−	0.105732i
$151$	−6.73018	+	11.6570i	−0.547694	+	0.948634i	0.450738	+	0.892656i	$0.351161\pi$
$151$	−6.73018	+	11.6570i	−0.547694	+	0.948634i	−0.998432	+	0.0559778i	$0.982172\pi$
$152$	0.236414	+	0.409481i	0.0191757	+	0.0332133i
$153$	11.8715	−	3.74343i	0.959753	−	0.302638i
$154$	0.0922593	+	25.6087i	0.00743447	+	2.06361i
$155$		−	2.33772i		−	0.187770i
$156$	−1.94587	+	1.56177i	−0.155794	+	0.125042i
$157$	−6.76643	−	3.90660i	−0.540020	−	0.311781i	0.205067	−	0.978748i	$-0.434259\pi$
$157$	−6.76643	−	3.90660i	−0.540020	−	0.311781i	−0.745087	+	0.666967i	$0.767592\pi$
$158$	−16.2235	−	9.36664i	−1.29067	−	0.745170i
$159$	−3.06003	+	2.45601i	−0.242677	+	0.194774i
$160$			8.11688i			0.641696i
$161$	−9.05743	−	15.5582i	−0.713825	−	1.22616i
$162$	10.6498	+	15.2077i	0.836730	+	1.19483i
$163$	−8.33945	−	14.4443i	−0.653196	−	1.13137i	−0.982343	−	0.187090i	$-0.940095\pi$
$163$	−8.33945	−	14.4443i	−0.653196	−	1.13137i	0.329147	−	0.944279i	$-0.393239\pi$
$164$	−4.63077	+	8.02072i	−0.361602	+	0.626313i
$165$	7.57444	+	2.94542i	0.589669	+	0.229300i
$166$	4.93717	−	2.85047i	0.383198	−	0.221240i
$167$	0.465112			0.0359915			0.0179957	−	0.999838i	$-0.494271\pi$
$167$	0.465112			0.0359915			0.0179957	+	0.999838i	$0.494271\pi$
$168$	0.867179	−	2.25405i	0.0669043	−	0.173903i
$169$	12.5921			0.968621
$170$	−7.41264	+	4.27969i	−0.568524	+	0.328237i
$171$	2.62774	+	0.582479i	0.200948	+	0.0445432i
$172$	3.55152	−	6.15141i	0.270801	−	0.469040i
$173$	5.59208	+	9.68576i	0.425158	+	0.736395i	0.996435	−	0.0843622i	$-0.0268853\pi$
$173$	5.59208	+	9.68576i	0.425158	+	0.736395i	−0.571277	+	0.820757i	$0.693552\pi$
$174$	7.58338	−	1.16730i	0.574894	−	0.0884929i
$175$	2.29604	+	1.31461i	0.173564	+	0.0993754i
$176$		−	16.0647i		−	1.21092i
$177$	−0.550867	−	0.686346i	−0.0414057	−	0.0515889i
$178$	−24.6562	−	14.2353i	−1.84806	−	1.06698i
$179$	−0.214505	−	0.123845i	−0.0160329	−	0.00925660i	0.491962	−	0.870617i	$-0.336280\pi$
$179$	−0.214505	−	0.123845i	−0.0160329	−	0.00925660i	−0.507995	+	0.861360i	$0.669613\pi$
$180$	−4.98886	−	4.57120i	−0.371848	−	0.340717i
$181$		−	14.3385i		−	1.06578i	−0.846186	−	0.532888i	$-0.821107\pi$
$181$		−	14.3385i		−	1.06578i	0.846186	−	0.532888i	$-0.178893\pi$
$182$	3.01256	−	1.75380i	0.223306	−	0.130000i
$183$	1.36603	+	8.87439i	0.100980	+	0.656014i
$184$	−1.79301	−	3.10559i	−0.132183	−	0.228947i
$185$	−5.69122	+	9.85748i	−0.418427	+	0.724737i
$186$	3.02723	−	7.78483i	0.221967	−	0.570812i
$187$	16.8604	−	9.73433i	1.23295	−	0.711845i
$188$	−15.3585			−1.12013
$189$	−6.12536	−	12.3077i	−0.445554	−	0.895255i
$190$	−1.85076			−0.134268
$191$	14.7572	−	8.52006i	1.06779	−	0.616490i	0.140214	−	0.990121i	$-0.455221\pi$
$191$	14.7572	−	8.52006i	1.06779	−	0.616490i	0.927577	+	0.373632i	$0.121888\pi$
$192$	−6.21248	+	15.9760i	−0.448347	+	1.15297i
$193$	−1.41181	+	2.44533i	−0.101624	+	0.176019i	−0.912354	−	0.409402i	$-0.865737\pi$
$193$	−1.41181	+	2.44533i	−0.101624	+	0.176019i	0.810730	+	0.585421i	$0.199071\pi$
$194$	−13.3143	−	23.0611i	−0.955913	−	1.65569i
$195$	−0.168300	−	1.09336i	−0.0120522	−	0.0782973i
$196$	−7.79545	+	13.7296i	−0.556818	+	0.980688i
$197$			9.59675i			0.683740i	0.939747	+	0.341870i	$0.111060\pi$
$197$			9.59675i			0.683740i	−0.939747	+	0.341870i	$0.888940\pi$
$198$	21.4094	+	19.6170i	1.52150	+	1.39412i
$199$	10.5777	+	6.10706i	0.749836	+	0.432918i	0.825635	−	0.564205i	$-0.190817\pi$
$199$	10.5777	+	6.10706i	0.749836	+	0.432918i	−0.0757989	+	0.997123i	$0.524151\pi$
$200$	0.456412	+	0.263509i	0.0322732	+	0.0186329i
$201$	−5.23481	−	6.52225i	−0.369235	−	0.460044i
$202$			18.6480i			1.31207i
$203$	−5.68145	+	0.0204683i	−0.398760	+	0.00143659i
$204$	−16.0207	+	2.46605i	−1.12168	+	0.172658i
$205$	−2.05312	−	3.55611i	−0.143396	−	0.248369i
$206$	−16.0086	+	27.7277i	−1.11537	+	1.93188i
$207$	−19.9293	−	4.41764i	−1.38518	−	0.307047i
$208$	−1.89376	+	1.09336i	−0.131309	+	0.0758111i
$209$	4.20964			0.291187
$210$	5.94367	+	7.35104i	0.410152	+	0.507270i
$211$	5.64113			0.388351			0.194176	−	0.980967i	$-0.437797\pi$
$211$	5.64113			0.388351			0.194176	+	0.980967i	$0.437797\pi$
$212$	4.42496	−	2.55475i	0.303908	−	0.175461i
$213$	−1.98236	−	0.770865i	−0.135829	−	0.0528188i
$214$	−5.52640	+	9.57200i	−0.377777	+	0.654329i
$215$	1.57462	+	2.72732i	0.107388	+	0.186002i
$216$	−1.21130	−	2.45601i	−0.0824183	−	0.167110i
$217$	−3.07320	+	5.36750i	−0.208622	+	0.364369i
$218$			2.80319i			0.189856i
$219$	−19.5276	+	15.6730i	−1.31956	+	1.05909i
$220$	−9.16509	−	5.29147i	−0.617910	−	0.356751i
$221$	−2.29503	−	1.32503i	−0.154380	−	0.0891314i
$222$	−31.7173	+	25.4565i	−2.12872	+	1.70853i
$223$		−	0.392378i		−	0.0262755i	−0.999914	−	0.0131378i	$-0.995818\pi$
$223$		−	0.392378i		−	0.0262755i	0.999914	−	0.0131378i	$-0.00418200\pi$
$224$	10.6706	−	18.6367i	0.712956	−	1.24522i
$225$	2.86113	−	0.902197i	0.190742	−	0.0601465i
$226$	−12.3143	−	21.3290i	−0.819137	−	1.41879i
$227$	11.7125	−	20.2867i	0.777388	−	1.34648i	−0.156054	−	0.987749i	$-0.549877\pi$
$227$	11.7125	−	20.2867i	0.777388	−	1.34648i	0.933442	−	0.358728i	$-0.116789\pi$
$228$	−3.26661	−	1.27026i	−0.216337	−	0.0841253i
$229$	6.69286	−	3.86412i	0.442276	−	0.255348i	−0.262286	−	0.964990i	$-0.584477\pi$
$229$	6.69286	−	3.86412i	0.442276	−	0.255348i	0.704563	+	0.709642i	$0.251143\pi$
$230$	14.0366			0.925545
$231$	−13.5191	−	16.7202i	−0.889493	−	1.10011i
$232$	−1.13172			−0.0743011
$233$	3.53323	−	2.03991i	0.231469	−	0.133639i	−0.379780	−	0.925077i	$-0.624000\pi$
$233$	3.53323	−	2.03991i	0.231469	−	0.133639i	0.611250	+	0.791438i	$0.290667\pi$
$234$	0.855394	−	3.85894i	0.0559188	−	0.252267i
$235$	3.40471	−	5.89714i	0.222099	−	0.384687i
$236$	0.573014	+	0.992490i	0.0373001	+	0.0646056i
$237$	15.5459	−	2.39296i	1.00981	−	0.155440i
$238$	22.6458	−	0.0815851i	1.46791	−	0.00528837i
$239$			5.76281i			0.372765i	0.982477	+	0.186383i	$0.0596764\pi$
$239$			5.76281i			0.372765i	−0.982477	+	0.186383i	$0.940324\pi$
$240$	−3.71189	−	4.62479i	−0.239601	−	0.298529i
$241$	−17.6840	−	10.2098i	−1.13912	−	0.657674i	−0.192911	−	0.981216i	$-0.561793\pi$
$241$	−17.6840	−	10.2098i	−1.13912	−	0.657674i	−0.946214	+	0.323542i	$0.895126\pi$
$242$	19.6799	+	11.3622i	1.26507	+	0.730390i
$243$	−14.9660	−	4.36106i	−0.960069	−	0.279762i
$244$		−	11.6923i		−	0.748525i
$245$	−3.54359	−	6.03680i	−0.226392	−	0.385677i
$246$	−2.23210	−	14.5009i	−0.142314	−	0.924542i
$247$	−0.286507	−	0.496245i	−0.0182300	−	0.0315753i
$248$	−0.616011	+	1.06696i	−0.0391167	+	0.0677522i
$249$	−1.73481	+	4.46124i	−0.109939	+	0.282720i
$250$	−1.78651	+	1.03144i	−0.112989	+	0.0652340i
$251$	4.42544			0.279331			0.139666	−	0.990199i	$-0.455397\pi$
$251$	4.42544			0.279331			0.139666	+	0.990199i	$0.455397\pi$
$252$	5.44528	+	17.0541i	0.343020	+	1.07431i
$253$	−31.9268			−2.00722
$254$	−30.1012	+	17.3790i	−1.88872	+	1.09045i
$255$	2.60464	−	6.69809i	0.163109	−	0.419450i
$256$	−5.58338	+	9.67069i	−0.348961	+	0.604418i
$257$	12.7539	+	22.0904i	0.795565	+	1.37796i	0.922480	+	0.386045i	$0.126159\pi$
$257$	12.7539	+	22.0904i	0.795565	+	1.37796i	−0.126915	+	0.991914i	$0.540508\pi$
$258$	1.71189	+	11.1213i	0.106578	+	0.692381i
$259$	26.0260	−	15.1514i	1.61718	−	0.941463i
$260$			1.44055i			0.0893389i
$261$	−4.35215	+	4.74981i	−0.269392	+	0.294006i
$262$	24.7779	+	14.3055i	1.53078	+	0.883798i
$263$	0.310020	+	0.178990i	0.0191166	+	0.0110370i	0.509528	−	0.860454i	$-0.329820\pi$
$263$	0.310020	+	0.178990i	0.0191166	+	0.0110370i	−0.490411	+	0.871491i	$0.663153\pi$
$264$	−2.68092	−	3.34026i	−0.164999	−	0.205579i
$265$			2.26538i			0.139161i
$266$	4.24942	+	2.43304i	0.260549	+	0.149179i
$267$	23.6264	−	3.63678i	1.44591	−	0.222568i
$268$	5.44528	+	9.43149i	0.332623	+	0.576120i
$269$	4.26905	−	7.39421i	0.260288	−	0.450833i	−0.706030	−	0.708182i	$-0.749516\pi$
$269$	4.26905	−	7.39421i	0.260288	−	0.450833i	0.966319	+	0.257349i	$0.0828490\pi$
$270$	10.6961	+	0.700610i	0.650945	+	0.0426378i
$271$	−7.30474	+	4.21739i	−0.443731	+	0.256188i	−0.705179	−	0.709029i	$-0.749133\pi$
$271$	−7.30474	+	4.21739i	−0.443731	+	0.256188i	0.261448	+	0.965218i	$0.415800\pi$
$272$	−14.2061			−0.861369
$273$	−1.05092	+	2.73165i	−0.0636048	+	0.165327i
$274$	−8.94940			−0.540653
$275$	4.06348	−	2.34605i	0.245037	−	0.141472i
$276$	24.7747	+	9.63395i	1.49126	+	0.579896i
$277$	−5.05294	+	8.75195i	−0.303602	+	0.525853i	−0.976949	−	0.213473i	$-0.931523\pi$
$277$	−5.05294	+	8.75195i	−0.303602	+	0.525853i	0.673347	+	0.739326i	$0.264856\pi$
$278$	−11.3078	−	19.5857i	−0.678198	−	1.17467i
$279$	2.10909	+	6.68851i	0.126268	+	0.400431i
$280$	−0.701526	−	1.20503i	−0.0419242	−	0.0720144i
$281$			15.1554i			0.904094i	0.891994	+	0.452047i	$0.149306\pi$
$281$			15.1554i			0.904094i	−0.891994	+	0.452047i	$0.850694\pi$
$282$	18.9745	−	15.2291i	1.12992	−	0.906880i
$283$	20.7322	+	11.9697i	1.23240	+	0.711527i	0.967530	−	0.252757i	$-0.0813373\pi$
$283$	20.7322	+	11.9697i	1.23240	+	0.711527i	0.264871	+	0.964284i	$0.414671\pi$
$284$	2.39866	+	1.38487i	0.142334	+	0.0821768i
$285$	1.21189	−	0.972671i	0.0717861	−	0.0576161i
$286$		−	6.18202i		−	0.365551i
$287$	0.0391393	+	10.8640i	0.00231032	+	0.641283i
$288$	−7.32303	−	23.2234i	−0.431514	−	1.36845i
$289$	−0.108084	−	0.187206i	−0.00635786	−	0.0110121i
$290$	2.21492	−	3.83635i	0.130064	−	0.225278i
$291$	20.8381	+	8.10315i	1.22155	+	0.475015i
$292$	28.2379	−	16.3032i	1.65250	−	0.954071i
$293$	−21.2223			−1.23982			−0.619909	−	0.784673i	$-0.712831\pi$
$293$	−21.2223			−1.23982			−0.619909	+	0.784673i	$0.712831\pi$
$294$	−3.98313	−	24.6919i	−0.232301	−	1.44006i
$295$	−0.508109			−0.0295833
$296$	5.19508	−	2.99938i	0.301958	−	0.174335i
$297$	−24.3288	−	1.59357i	−1.41170	−	0.0924681i
$298$	8.93904	−	15.4829i	0.517825	−	0.896899i
$299$	2.17293	+	3.76363i	0.125664	+	0.217656i
$300$	−3.86113	+	0.594339i	−0.222922	+	0.0343142i
$301$	−0.0300174	−	8.33204i	−0.00173018	−	0.480251i
$302$			27.7671i			1.59782i
$303$	−9.80049	−	12.2108i	−0.563023	−	0.701492i
$304$	−2.66019	−	1.53586i	−0.152572	−	0.0880877i
$305$	4.48946	+	2.59199i	0.257065	+	0.148417i
$306$	17.3474	−	18.9324i	0.991683	−	1.08229i
$307$			24.2817i			1.38583i	0.721019	+	0.692916i	$0.243674\pi$
$307$			24.2817i			1.38583i	−0.721019	+	0.692916i	$0.756326\pi$
$308$	14.0872	+	24.1980i	0.802691	+	1.37881i
$309$	−4.08982	−	26.5695i	−0.232662	−	1.51149i
$310$	−2.41122	−	4.17635i	−0.136948	−	0.237201i
$311$	3.55858	−	6.16364i	0.201789	−	0.349508i	−0.747316	−	0.664469i	$-0.768658\pi$
$311$	3.55858	−	6.16364i	0.201789	−	0.349508i	0.949105	+	0.314960i	$0.101991\pi$
$312$	−0.211297	+	0.543372i	−0.0119623	+	0.0307624i
$313$	3.07200	−	1.77362i	0.173640	−	0.100251i	−0.410661	−	0.911788i	$-0.634702\pi$
$313$	3.07200	−	1.77362i	0.173640	−	0.100251i	0.584301	+	0.811537i	$0.301369\pi$
$314$	−16.1177			−0.909575
$315$	−7.75530	−	1.68979i	−0.436961	−	0.0952089i
$316$	−20.4823			−1.15222
$317$	−18.2527	+	10.5382i	−1.02517	+	0.591885i	−0.915599	−	0.402093i	$-0.868283\pi$
$317$	−18.2527	+	10.5382i	−1.02517	+	0.591885i	−0.109576	+	0.993978i	$0.534949\pi$
$318$	−2.93355	+	7.54392i	−0.164505	+	0.423042i
$319$	−5.03791	+	8.72592i	−0.282069	+	0.488558i
$320$	4.94830	+	8.57071i	0.276619	+	0.479117i
$321$	−1.41187	−	9.17220i	−0.0788028	−	0.511942i
$322$	−32.2285	−	18.4527i	−1.79603	−	1.02833i
$323$		−	3.72259i		−	0.207130i
$324$	18.3979	+	8.57782i	1.02210	+	0.476546i
$325$	−0.553120	−	0.319344i	−0.0306816	−	0.0177140i
$326$	−29.7970	−	17.2033i	−1.65030	−	0.952802i
$327$	−1.47322	−	1.83554i	−0.0814693	−	0.101506i
$328$			2.16407i			0.119491i
$329$	−15.5698	+	9.06418i	−0.858391	+	0.499724i
$330$	16.5698	−	2.55057i	0.912138	−	0.140404i
$331$	7.40412	+	12.8243i	0.406967	+	0.704888i	0.994548	−	0.104277i	$-0.0332529\pi$
$331$	7.40412	+	12.8243i	0.406967	+	0.704888i	−0.587581	+	0.809165i	$0.699920\pi$
$332$	3.11660	−	5.39811i	0.171046	−	0.296260i
$333$	7.38990	−	33.3381i	0.404964	−	1.82692i
$334$	0.830926	−	0.479736i	0.0454663	−	0.0262500i
$335$	−4.82849			−0.263809
$336$	2.44284	+	15.4984i	0.133268	+	0.845506i
$337$	20.5062			1.11704			0.558522	−	0.829490i	$-0.311369\pi$
$337$	20.5062			1.11704			0.558522	+	0.829490i	$0.311369\pi$
$338$	22.4958	−	12.9880i	1.22361	−	0.706453i
$339$	19.2730	+	7.49455i	1.04677	+	0.407048i
$340$	−4.67925	+	8.10471i	−0.253768	+	0.439539i
$341$	5.48442	+	9.49929i	0.296998	+	0.514415i
$342$	5.29527	−	1.66975i	0.286335	−	0.0902899i
$343$	0.200161	+	18.5192i	0.0108077	+	0.999942i
$344$		−	1.65971i		−	0.0894854i
$345$	−9.19122	+	7.37695i	−0.494839	+	0.397161i
$346$	19.9806	+	11.5358i	1.07416	+	0.620168i
$347$	13.7103	+	7.91567i	0.736010	+	0.424935i	0.820617	−	0.571479i	$-0.193630\pi$
$347$	13.7103	+	7.91567i	0.736010	+	0.424935i	−0.0846070	+	0.996414i	$0.526963\pi$
$348$	6.54241	−	5.25099i	0.350710	−	0.281482i
$349$		−	8.96019i		−	0.479628i	−0.970819	−	0.239814i	$-0.922914\pi$
$349$		−	8.96019i		−	0.479628i	0.970819	−	0.239814i	$-0.0770865\pi$
$350$	5.45783	−	0.0196627i	0.291734	−	0.00105101i
$351$	1.46796	+	2.97641i	0.0783538	+	0.158869i
$352$	−19.0426	−	32.9828i	−1.01498	−	1.75799i
$353$	6.72876	−	11.6545i	0.358136	−	0.620309i	−0.629514	−	0.776989i	$-0.716746\pi$
$353$	6.72876	−	11.6545i	0.358136	−	0.620309i	0.987649	+	0.156680i	$0.0500792\pi$
$354$	−1.69205	−	0.657976i	−0.0899316	−	0.0349710i
$355$	−1.06348	+	0.614002i	−0.0564438	+	0.0325878i
$356$	−31.1286			−1.64981
$357$	−14.7857	+	11.9550i	−0.782544	+	0.632725i
$358$	−0.510954			−0.0270048
$359$	−4.85824	+	2.80491i	−0.256408	+	0.148037i	−0.622695	−	0.782465i	$-0.713962\pi$
$359$	−4.85824	+	2.80491i	−0.256408	+	0.148037i	0.366287	+	0.930502i	$0.380629\pi$
$360$	−1.54359	−	0.342160i	−0.0813543	−	0.0180334i
$361$	−9.09754	+	15.7574i	−0.478818	+	0.829337i
$362$	−14.7894	−	25.6159i	−0.777311	−	1.34634i
$363$	−18.8579	+	2.90278i	−0.989784	+	0.152356i
$364$	1.89376	−	3.30755i	0.0992600	−	0.173363i
$365$			14.4565i			0.756689i
$366$	11.5938	+	14.4452i	0.606019	+	0.755062i
$367$	−1.71154	−	0.988156i	−0.0893415	−	0.0515813i	0.454664	−	0.890663i	$-0.349759\pi$
$367$	−1.71154	−	0.988156i	−0.0893415	−	0.0515813i	−0.544005	+	0.839082i	$0.683093\pi$
$368$	20.1755	+	11.6483i	1.05172	+	0.607210i
$369$	9.08255	+	8.32215i	0.472818	+	0.433234i
$370$			23.4806i			1.22070i
$371$	2.97809	−	5.20139i	0.154615	−	0.270043i
$372$	−1.38940	−	9.02623i	−0.0720370	−	0.467988i
$373$	11.5467	+	19.9995i	0.597866	+	1.03553i	0.993136	+	0.116969i	$0.0373177\pi$
$373$	11.5467	+	19.9995i	0.597866	+	1.03553i	−0.395270	+	0.918565i	$0.629349\pi$
$374$	20.0808	−	34.7809i	1.03835	−	1.79848i
$375$	0.627739	−	1.61429i	0.0324163	−	0.0833618i
$376$	−3.10790	+	1.79435i	−0.160278	+	0.0925364i
$377$	1.37152			0.0706368
$378$	−23.6377	−	15.6699i	−1.21579	−	0.805972i
$379$	−17.0645			−0.876547			−0.438273	−	0.898842i	$-0.644410\pi$
$379$	−17.0645			−0.876547			−0.438273	+	0.898842i	$0.644410\pi$
$380$	−1.75245	+	1.01178i	−0.0898988	+	0.0519031i
$381$	10.5769	−	27.1996i	0.541871	−	1.39348i
$382$	17.5759	−	30.4423i	0.899259	−	1.55756i
$383$	13.3056	+	23.0460i	0.679886	+	1.17760i	0.975015	+	0.222139i	$0.0713040\pi$
$383$	13.3056	+	23.0460i	0.679886	+	1.17760i	−0.295129	+	0.955457i	$0.595363\pi$
$384$	1.10193	+	7.15869i	0.0562327	+	0.365316i
$385$	−12.4141	+	0.0447235i	−0.632679	+	0.00227932i
$386$			5.82479i			0.296474i
$387$	−6.96576	−	6.38259i	−0.354090	−	0.324445i
$388$	−25.2141	−	14.5574i	−1.28005	−	0.739040i
$389$	8.20951	+	4.73976i	0.416239	+	0.240316i	0.693467	−	0.720489i	$-0.256082\pi$
$389$	8.20951	+	4.73976i	0.416239	+	0.240316i	−0.277228	+	0.960804i	$0.589416\pi$
$390$	−1.42841	−	1.77971i	−0.0723303	−	0.0901191i
$391$			28.2329i			1.42780i
$392$	0.0265810	+	3.68904i	0.00134254	+	0.186324i
$393$	−23.7430	+	3.65473i	−1.19767	+	0.184357i
$394$	9.89848	+	17.1447i	0.498678	+	0.863736i
$395$	4.54056	−	7.86448i	0.228460	−	0.395705i
$396$	30.9964	+	6.87083i	1.55763	+	0.345272i
$397$	10.7042	−	6.18009i	0.537230	−	0.310170i	−0.206726	−	0.978399i	$-0.566281\pi$
$397$	10.7042	−	6.18009i	0.537230	−	0.310170i	0.743956	+	0.668229i	$0.232947\pi$
$398$	25.1963			1.26297
$399$	−4.06123	+	0.640127i	−0.203316	+	0.0320464i
$400$	−3.42378			−0.171189
$401$	7.11494	−	4.10781i	0.355303	−	0.205134i	−0.311715	−	0.950176i	$-0.600904\pi$
$401$	7.11494	−	4.10781i	0.355303	−	0.205134i	0.667019	+	0.745041i	$0.267570\pi$
$402$	−16.0793	−	6.25265i	−0.801964	−	0.311854i
$403$	0.746537	−	1.29304i	0.0371877	−	0.0644109i
$404$	10.1945	+	17.6574i	0.507196	+	0.878490i
$405$	−7.37208	+	5.16260i	−0.366322	+	0.256532i
$406$	−10.1288	+	5.89664i	−0.502686	+	0.292646i
$407$		−	53.4076i		−	2.64732i
$408$	−2.95379	+	2.37074i	−0.146235	+	0.117369i
$409$	−17.9575	−	10.3678i	−0.887942	−	0.512653i	−0.0146731	−	0.999892i	$-0.504671\pi$
$409$	−17.9575	−	10.3678i	−0.887942	−	0.512653i	−0.873269	+	0.487239i	$0.838004\pi$
$410$	−7.33583	−	4.23534i	−0.362291	−	0.209169i
$411$	5.86011	−	4.70337i	0.289058	−	0.232000i
$412$			35.0064i			1.72464i
$413$	1.16664	+	0.667967i	0.0574065	+	0.0328685i
$414$	−40.1604	+	12.6638i	−1.97378	+	0.622390i
$415$	1.38179	+	2.39334i	0.0678296	+	0.117484i
$416$	−2.59208	+	4.48961i	−0.127087	+	0.220121i
$417$	17.6977	+	6.88198i	0.866661	+	0.337012i
$418$	7.52054	−	4.34199i	0.367842	−	0.212374i
$419$	6.93924			0.339004			0.169502	−	0.985530i	$-0.445784\pi$
$419$	6.93924			0.339004			0.169502	+	0.985530i	$0.445784\pi$
$420$	9.64662	+	3.71126i	0.470707	+	0.181091i
$421$	−15.2162			−0.741594			−0.370797	−	0.928714i	$-0.620915\pi$
$421$	−15.2162			−0.741594			−0.370797	+	0.928714i	$0.620915\pi$
$422$	10.0779	−	5.81849i	0.490585	−	0.283240i
$423$	−4.42093	+	19.9442i	−0.214953	+	0.969719i
$424$	0.596948	−	1.03394i	0.0289904	−	0.0502128i
$425$	−2.07462	−	3.59334i	−0.100634	−	0.174303i
$426$	−4.33660	+	0.667529i	−0.210109	+	0.0323419i
$427$	−6.90050	−	11.8532i	−0.333939	−	0.573617i
$428$			12.0847i			0.584137i
$429$	3.24897	+	4.04802i	0.156862	+	0.195440i
$430$	5.62613	+	3.24825i	0.271316	+	0.156645i
$431$	−26.9043	−	15.5332i	−1.29594	−	0.748209i	−0.316236	−	0.948681i	$-0.602419\pi$
$431$	−26.9043	−	15.5332i	−1.29594	−	0.748209i	−0.979699	+	0.200472i	$0.935752\pi$
$432$	14.7926	+	9.88323i	0.711712	+	0.475507i
$433$		−	22.3083i		−	1.07207i	−0.844196	−	0.536034i	$-0.819922\pi$
$433$		−	22.3083i		−	1.07207i	0.844196	−	0.536034i	$-0.180078\pi$
$434$	0.0459658	+	12.7589i	0.00220643	+	0.612446i
$435$	0.565860	+	3.67611i	0.0271309	+	0.176256i
$436$	1.53245	+	2.65429i	0.0733912	+	0.127117i
$437$	−3.05235	+	5.28682i	−0.146014	+	0.252903i
$438$	−18.7205	+	48.1416i	−0.894498	+	2.30029i
$439$	−22.4126	+	12.9399i	−1.06970	+	0.617590i	−0.928099	−	0.372334i	$-0.878557\pi$
$439$	−22.4126	+	12.9399i	−1.06970	+	0.617590i	−0.141598	+	0.989924i	$0.545224\pi$
$440$	−2.47283			−0.117887
$441$	15.5850	+	14.0750i	0.742145	+	0.670240i
$442$	−5.46677			−0.260028
$443$	−26.8166	+	15.4826i	−1.27409	+	0.735599i	−0.975756	−	0.218862i	$-0.929766\pi$
$443$	−26.8166	+	15.4826i	−1.27409	+	0.735599i	−0.298338	+	0.954460i	$0.596432\pi$
$444$	−16.1158	+	41.4435i	−0.764823	+	1.96682i
$445$	6.90067	−	11.9523i	0.327123	−	0.566594i
$446$	−0.404714	−	0.700985i	−0.0191638	−	0.0331926i
$447$	2.28372	+	14.8362i	0.108016	+	0.701728i
$448$	−0.0943310	−	26.1838i	−0.00445672	−	1.23707i
$449$		−	24.2032i		−	1.14222i	−0.820874	−	0.571110i	$-0.806513\pi$
$449$		−	24.2032i		−	1.14222i	0.820874	−	0.571110i	$-0.193487\pi$
$450$	4.18086	−	4.56286i	0.197088	−	0.215095i
$451$	16.6856	+	9.63346i	0.785696	+	0.453622i
$452$	−23.3204	−	13.4640i	−1.09690	−	0.633295i
$453$	−14.5930	−	18.1820i	−0.685641	−	0.854267i
$454$		−	48.3231i		−	2.26792i
$455$	0.850172	+	1.46036i	0.0398567	+	0.0684630i
$456$	−0.809428	+	0.124594i	−0.0379049	+	0.00583467i
$457$	1.20726	+	2.09103i	0.0564731	+	0.0978143i	0.892880	−	0.450295i	$-0.148681\pi$
$457$	1.20726	+	2.09103i	0.0564731	+	0.0978143i	−0.836407	+	0.548109i	$0.815348\pi$
$458$	7.97122	−	13.8066i	0.372471	−	0.645138i
$459$	−1.40919	+	21.5140i	−0.0657755	+	1.00419i
$460$	13.2910	−	7.67354i	0.619694	−	0.357781i
$461$	7.45376			0.347156			0.173578	−	0.984820i	$-0.444467\pi$
$461$	7.45376			0.347156			0.173578	+	0.984820i	$0.444467\pi$
$462$	−41.3979	−	15.9267i	−1.92601	−	0.740975i
$463$	13.8862			0.645345			0.322672	−	0.946511i	$-0.395419\pi$
$463$	13.8862			0.645345			0.322672	+	0.946511i	$0.395419\pi$
$464$	6.36721	−	3.67611i	0.295590	−	0.170659i
$465$	3.77377	+	1.46748i	0.175004	+	0.0680526i
$466$	4.20809	−	7.28862i	0.194936	−	0.337639i
$467$	−10.0692	−	17.4404i	−0.465948	−	0.807045i	0.533296	−	0.845929i	$-0.320953\pi$
$467$	−10.0692	−	17.4404i	−0.465948	−	0.807045i	−0.999244	+	0.0388836i	$0.987620\pi$
$468$	−1.29966	−	4.12158i	−0.0600767	−	0.190520i
$469$	11.0864	+	6.34759i	0.511923	+	0.293105i
$470$		−	14.0470i		−	0.647942i
$471$	10.5540	−	8.47068i	0.486300	−	0.390309i
$472$	0.231907	+	0.133892i	0.0106744	+	0.00616286i
$473$	−12.7969	−	7.38828i	−0.588401	−	0.339713i
$474$	25.3046	−	20.3097i	1.16228	−	0.932855i
$475$		−	0.897174i		−	0.0411652i
$476$	21.3983	−	12.4573i	0.980789	−	0.570980i
$477$	−2.04382	−	6.48153i	−0.0935799	−	0.296769i
$478$	5.94399	+	10.2953i	0.271872	+	0.470896i
$479$	−16.6189	+	28.7847i	−0.759335	+	1.31521i	0.183855	+	0.982953i	$0.441142\pi$
$479$	−16.6189	+	28.7847i	−0.759335	+	1.31521i	−0.943190	+	0.332253i	$0.892191\pi$
$480$	−13.1030	−	5.09528i	−0.598069	−	0.232567i
$481$	−6.29586	+	3.63491i	−0.287066	+	0.165738i
$482$	−42.1234			−1.91867
$483$	30.8012	−	4.85486i	1.40150	−	0.220904i
$484$	24.8460			1.12936
$485$	11.1791	−	6.45424i	0.507616	−	0.293072i
$486$	−31.2350	+	7.64548i	−1.41685	+	0.346806i
$487$	16.1039	−	27.8927i	0.729736	−	1.26394i	−0.227259	−	0.973834i	$-0.572976\pi$
$487$	16.1039	−	27.8927i	0.729736	−	1.26394i	0.956995	−	0.290105i	$-0.0936902\pi$
$488$	−1.36603	−	2.36603i	−0.0618371	−	0.107105i
$489$	28.5524	−	4.39504i	1.29118	−	0.198751i
$490$	−12.5572	−	7.12979i	−0.567279	−	0.322091i
$491$			22.5003i			1.01542i	0.861527	+	0.507712i	$0.169509\pi$
$491$			22.5003i			1.01542i	−0.861527	+	0.507712i	$0.830491\pi$
$492$	−10.0409	−	12.5103i	−0.452678	−	0.564009i
$493$	7.71635	+	4.45504i	0.347527	+	0.200645i
$494$	−1.02369	−	0.591030i	−0.0460582	−	0.0265917i
$495$	−9.50953	+	10.3784i	−0.427422	+	0.466475i
$496$		−	8.00383i		−	0.359383i
$497$	3.24897	−	0.0117049i	0.145736	−	0.000525037i
$498$	1.50225	+	9.75939i	0.0673176	+	0.437329i
$499$	−3.20702	−	5.55472i	−0.143566	−	0.248663i	0.785271	−	0.619152i	$-0.212524\pi$
$499$	−3.20702	−	5.55472i	−0.143566	−	0.248663i	−0.928837	+	0.370489i	$0.879190\pi$
$500$	−1.12774	+	1.95330i	−0.0504340	+	0.0873543i
$501$	−0.291969	+	0.750828i	−0.0130442	+	0.0335445i
$502$	7.90608	−	4.56458i	0.352866	−	0.203727i
$503$	38.0103			1.69479			0.847397	−	0.530960i	$-0.178169\pi$
$503$	38.0103			1.69479			0.847397	+	0.530960i	$0.178169\pi$
$504$	3.09433	+	2.81483i	0.137832	+	0.125383i
$505$	−9.03979			−0.402265
$506$	−57.0374	+	32.9306i	−2.53562	+	1.46394i
$507$	−7.90453	+	20.3273i	−0.351053	+	0.902768i
$508$	−19.0015	+	32.9116i	−0.843056	+	1.46022i
$509$	−6.34981	−	10.9982i	−0.281450	−	0.487486i	0.690292	−	0.723531i	$-0.257482\pi$
$509$	−6.34981	−	10.9982i	−0.281450	−	0.487486i	−0.971742	+	0.236045i	$0.924149\pi$
$510$	−2.25548	−	14.6527i	−0.0998742	−	0.648833i
$511$	19.0047	−	33.1927i	0.840719	−	1.46836i
$512$			31.3992i			1.38766i
$513$	−2.58982	+	3.87630i	−0.114344	+	0.171143i
$514$	45.5698	+	26.3097i	2.01000	+	1.16047i
$515$	−13.4412	−	7.76030i	−0.592292	−	0.341960i
$516$	7.70075	+	9.59466i	0.339007	+	0.422382i
$517$			31.9506i			1.40518i
$518$	30.8679	−	53.9124i	1.35626	−	2.36878i
$519$	−19.1460	+	2.94713i	−0.840417	+	0.129365i
$520$	0.168300	+	0.291505i	0.00738046	+	0.0127833i
$521$	18.0970	−	31.3449i	0.792843	−	1.37324i	−0.131357	−	0.991335i	$-0.541933\pi$
$521$	18.0970	−	31.3449i	0.792843	−	1.37324i	0.924200	−	0.381909i	$-0.124733\pi$
$522$	−2.87601	+	12.9746i	−0.125880	+	0.567881i
$523$	−4.27382	+	2.46749i	−0.186881	+	0.107896i	−0.590522	−	0.807022i	$-0.701078\pi$
$523$	−4.27382	+	2.46749i	−0.186881	+	0.107896i	0.403640	+	0.914918i	$0.367745\pi$
$524$	31.2823			1.36657
$525$	−3.56348	+	2.88125i	−0.155523	+	0.125748i
$526$	0.738470			0.0321988
$527$	8.40023	−	4.84988i	0.365920	−	0.211264i
$528$	25.9332	+	10.0844i	1.12860	+	0.438869i
$529$	11.6496	−	20.1778i	0.506506	−	0.877295i
$530$	2.33660	+	4.04711i	0.101495	+	0.175795i
$531$	1.45376	−	0.458415i	0.0630880	−	0.0198935i
$532$	5.35379	−	0.0192878i	0.232116	−	0.000836234i
$533$		−	2.62261i		−	0.113598i
$534$	38.4576	−	30.8663i	1.66422	−	1.33572i
$535$	−4.64012	−	2.67897i	−0.200610	−	0.115822i
$536$	2.20378	+	1.27235i	0.0951888	+	0.0549573i
$537$	0.334575	−	0.268533i	0.0144380	−	0.0115880i
$538$		−	17.6131i		−	0.759354i
$539$	28.5620	+	16.2170i	1.23025	+	0.698515i
$540$	10.5110	−	5.18398i	0.452319	−	0.223083i
$541$	−8.32849	−	14.4254i	−0.358070	−	0.620195i	0.629569	−	0.776945i	$-0.283232\pi$
$541$	−8.32849	−	14.4254i	−0.358070	−	0.620195i	−0.987638	+	0.156750i	$0.949898\pi$
$542$	−8.69998	+	15.0688i	−0.373696	+	0.647261i
$543$	23.1466	+	9.00086i	0.993317	+	0.386264i
$544$	−29.1668	+	16.8394i	−1.25051	+	0.721985i
$545$	−1.35887			−0.0582077
$546$	0.940053	+	5.96408i	0.0402306	+	0.255239i
$547$	21.2868			0.910159			0.455079	−	0.890451i	$-0.349611\pi$
$547$	21.2868			0.910159			0.455079	+	0.890451i	$0.349611\pi$
$548$	−8.47401	+	4.89247i	−0.361992	+	0.208996i
$549$	−15.1834	−	3.36563i	−0.648011	−	0.143642i
$550$	4.83963	−	8.38248i	0.206362	−	0.357430i
$551$	0.963296	+	1.66848i	0.0410378	+	0.0710795i
$552$	6.13887	−	0.944951i	0.261288	−	0.0402198i
$553$	−20.7641	+	12.0881i	−0.882977	+	0.514037i
$554$			20.8472i			0.885713i
$555$	−12.3403	−	15.3752i	−0.523816	−	0.652642i
$556$	−21.4143	−	12.3636i	−0.908169	−	0.524331i
$557$	−16.5937	−	9.58040i	−0.703099	−	0.405935i	0.105401	−	0.994430i	$-0.466387\pi$
$557$	−16.5937	−	9.58040i	−0.703099	−	0.405935i	−0.808501	+	0.588495i	$0.799721\pi$
$558$	10.6667	+	9.77368i	0.451557	+	0.413753i
$559$			2.01138i			0.0850723i
$560$	7.86113	+	4.50094i	0.332193	+	0.190199i
$561$	5.13017	+	33.3282i	0.216596	+	1.40712i
$562$	15.6319	+	27.0752i	0.659390	+	1.14210i
$563$	−13.6243	+	23.5981i	−0.574198	+	0.994540i	0.421930	+	0.906628i	$0.361353\pi$
$563$	−13.6243	+	23.5981i	−0.574198	+	0.994540i	−0.996128	+	0.0879116i	$0.971981\pi$
$564$	9.64113	−	24.7931i	0.405965	−	1.04398i
$565$	10.3394	−	5.96948i	0.434984	−	0.251138i
$566$	49.3843			2.07578
$567$	23.7134	−	2.16210i	0.995869	−	0.0907998i
$568$	0.647181			0.0271551
$569$	22.7124	−	13.1130i	0.952153	−	0.549726i	0.0584038	−	0.998293i	$-0.481399\pi$
$569$	22.7124	−	13.1130i	0.952153	−	0.549726i	0.893749	+	0.448567i	$0.148066\pi$
$570$	1.16180	−	2.98768i	0.0486622	−	0.125140i
$571$	13.4388	−	23.2767i	0.562397	−	0.974101i	−0.434889	−	0.900484i	$-0.643212\pi$
$571$	13.4388	−	23.2767i	0.562397	−	0.974101i	0.997287	−	0.0736170i	$-0.0234542\pi$
$572$	−3.37960	−	5.85363i	−0.141308	−	0.244753i
$573$	4.49023	+	29.1708i	0.187582	+	1.21863i
$574$	11.2755	+	19.3683i	0.470631	+	0.808416i
$575$			6.80436i			0.283761i
$576$	−21.8902	−	20.0575i	−0.912091	−	0.835731i
$577$	−8.93069	−	5.15614i	−0.371790	−	0.214653i	0.302450	−	0.953165i	$-0.402195\pi$
$577$	−8.93069	−	5.15614i	−0.371790	−	0.214653i	−0.674240	+	0.738512i	$0.735529\pi$
$578$	−0.386185	−	0.222964i	−0.0160632	−	0.00927407i
$579$	−3.06123	−	3.81410i	−0.127220	−	0.158509i
$580$		−	4.84341i		−	0.201112i
$581$	−0.0263416	−	7.31171i	−0.00109283	−	0.303341i
$582$	45.5853	−	7.01690i	1.88957	−	0.290860i
$583$	−5.31469	−	9.20532i	−0.220112	−	0.381245i
$584$	3.80943	−	6.59812i	0.157635	−	0.273032i
$585$	1.87066	+	0.414660i	0.0773422	+	0.0171441i
$586$	−37.9138	+	21.8895i	−1.56620	+	0.904248i
$587$	22.1492			0.914197			0.457098	−	0.889416i	$-0.348889\pi$
$587$	22.1492			0.914197			0.457098	+	0.889416i	$0.348889\pi$
$588$	−17.2701	−	21.2028i	−0.712209	−	0.874387i
$589$	2.09734			0.0864195
$590$	−0.907741	+	0.524084i	−0.0373711	+	0.0215762i
$591$	−15.4920	−	6.02425i	−0.637255	−	0.247805i
$592$	−19.4855	+	33.7498i	−0.800848	+	1.38711i
$593$	1.45861	+	2.52638i	0.0598978	+	0.103746i	0.894419	−	0.447229i	$-0.147589\pi$
$593$	1.45861	+	2.52638i	0.0598978	+	0.103746i	−0.834522	+	0.550975i	$0.814256\pi$
$594$	−45.1072	+	22.2467i	−1.85077	+	0.912795i
$595$	0.0395491	+	10.9778i	0.00162135	+	0.450045i
$596$		−	19.5472i		−	0.800686i
$597$	−16.4986	+	13.2419i	−0.675244	+	0.541956i
$598$	7.76391	+	4.48250i	0.317490	+	0.183303i
$599$	−31.4551	−	18.1606i	−1.28522	−	0.742023i	−0.307424	−	0.951573i	$-0.599467\pi$
$599$	−31.4551	−	18.1606i	−1.28522	−	0.742023i	−0.977798	+	0.209550i	$0.932800\pi$
$600$	−0.711889	+	0.571367i	−0.0290627	+	0.0233260i
$601$			7.15198i			0.291735i	0.989304	+	0.145868i	$0.0465974\pi$
$601$			7.15198i			0.291735i	−0.989304	+	0.145868i	$0.953403\pi$
$602$	−8.64763	−	14.8543i	−0.352451	−	0.605416i
$603$	13.8149	−	4.35625i	0.562587	−	0.177400i
$604$	15.1798	+	26.2921i	0.617656	+	1.06981i
$605$	−5.50793	+	9.54001i	−0.223929	+	0.387857i
$606$	−30.1034	−	11.7061i	−1.22287	−	0.475527i
$607$	−37.8248	+	21.8382i	−1.53526	+	0.886384i	−0.536156	+	0.844119i	$0.680124\pi$
$607$	−37.8248	+	21.8382i	−1.53526	+	0.886384i	−0.999106	+	0.0422651i	$0.986543\pi$
$608$	−7.28226			−0.295334
$609$	3.53342	−	9.18438i	0.143182	−	0.372170i
$610$	10.6939			0.432984
$611$	3.76643	−	2.17455i	0.152373	−	0.0879729i
$612$	6.07589	−	27.4102i	0.245603	−	1.10799i
$613$	7.27926	−	12.6080i	0.294007	−	0.509234i	−0.680747	−	0.732519i	$-0.738345\pi$
$613$	7.27926	−	12.6080i	0.294007	−	0.509234i	0.974753	+	0.223285i	$0.0716779\pi$
$614$	25.0452	+	43.3795i	1.01074	+	1.75065i
$615$	7.02943	−	1.08203i	0.283454	−	0.0436318i
$616$	5.67771	+	3.25081i	0.228761	+	0.130979i
$617$		−	4.68442i		−	0.188588i	−0.995544	−	0.0942938i	$-0.969941\pi$
$617$		−	4.68442i		−	0.188588i	0.995544	−	0.0942938i	$-0.0300593\pi$
$618$	−34.7114	−	43.2483i	−1.39630	−	1.73970i
$619$	−33.0429	−	19.0773i	−1.32810	−	0.766782i	−0.343098	−	0.939299i	$-0.611476\pi$
$619$	−33.0429	−	19.0773i	−1.32810	−	0.766782i	−0.985006	+	0.172518i	$0.944810\pi$
$620$	−4.56627	−	2.63634i	−0.183386	−	0.105878i
$621$	19.6418	−	29.3987i	0.788197	−	1.17973i
$622$		−	14.6819i		−	0.588689i
$623$	−31.5569	+	18.3713i	−1.26430	+	0.736030i
$624$	−0.576223	−	3.74343i	−0.0230674	−	0.149857i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	3.65877	−	6.33717i	0.146234	−	0.253284i
$627$	−2.64255	+	6.79559i	−0.105533	+	0.271390i
$628$	−15.2615	+	8.81125i	−0.609001	+	0.351607i
$629$	−47.2285			−1.88312
$630$	−15.5978	+	4.98030i	−0.621432	+	0.198420i
$631$	23.9959			0.955264			0.477632	−	0.878560i	$-0.341495\pi$
$631$	23.9959			0.955264			0.477632	+	0.878560i	$0.341495\pi$
$632$	−4.14473	+	2.39296i	−0.164869	+	0.0951869i
$633$	−3.54115	+	9.10644i	−0.140748	+	0.361948i
$634$	−21.7391	+	37.6532i	−0.863369	+	1.49540i
$635$	−8.42461	−	14.5918i	−0.334320	−	0.579060i
$636$	1.34640	+	8.74690i	0.0533883	+	0.346837i
$637$	−0.0322132	−	4.47070i	−0.00127633	−	0.177136i
$638$			20.7852i			0.822895i
$639$	2.48881	−	2.71621i	0.0984557	−	0.107452i
$640$	3.62150	+	2.09088i	0.143152	+	0.0826491i
$641$	20.0037	+	11.5491i	0.790099	+	0.456164i	0.839997	−	0.542590i	$-0.182556\pi$
$641$	20.0037	+	11.5491i	0.790099	+	0.456164i	−0.0498985	+	0.998754i	$0.515890\pi$
$642$	−11.9829	−	14.9299i	−0.472927	−	0.589238i
$643$		−	22.7592i		−	0.897536i	−0.893648	−	0.448768i	$-0.851863\pi$
$643$		−	22.7592i		−	0.897536i	0.893648	−	0.448768i	$-0.148137\pi$
$644$	−40.6043	+	0.146283i	−1.60003	+	0.00576436i
$645$	−5.39114	+	0.829853i	−0.212276	+	0.0326754i
$646$	−3.83963	−	6.65043i	−0.151068	−	0.261658i
$647$	1.21349	−	2.10183i	0.0477073	−	0.0826315i	−0.841186	−	0.540746i	$-0.818142\pi$
$647$	1.21349	−	2.10183i	0.0477073	−	0.0826315i	0.888893	+	0.458115i	$0.151475\pi$
$648$	4.72510	−	0.413659i	0.185619	−	0.0162500i
$649$	2.06469	−	1.19205i	0.0810463	−	0.0467921i
$650$	−1.31754			−0.0516781
$651$	−6.73555	−	8.33043i	−0.263987	−	0.326495i
$652$	−37.6189			−1.47327
$653$	−34.7760	+	20.0779i	−1.36089	+	0.785709i	−0.989742	−	0.142865i	$-0.954368\pi$
$653$	−34.7760	+	20.0779i	−1.36089	+	0.785709i	−0.371146	+	0.928574i	$0.621035\pi$
$654$	−4.52517	−	1.75967i	−0.176948	−	0.0688086i
$655$	−6.93473	+	12.0113i	−0.270962	+	0.469321i
$656$	−7.02943	−	12.1753i	−0.274453	−	0.475366i
$657$	−13.0426	−	41.3619i	−0.508842	−	1.61368i
$658$	−18.4664	+	32.2525i	−0.719896	+	1.25734i
$659$		−	0.627454i		−	0.0244421i	−0.999925	−	0.0122211i	$-0.996110\pi$
$659$		−	0.627454i		−	0.0244421i	0.999925	−	0.0122211i	$-0.00389018\pi$
$660$	14.2953	−	11.4735i	0.556442	−	0.446605i
$661$	−28.5745	−	16.4975i	−1.11142	−	0.641678i	−0.172222	−	0.985058i	$-0.555095\pi$
$661$	−28.5745	−	16.4975i	−1.11142	−	0.641678i	−0.939197	+	0.343380i	$0.888428\pi$
$662$	26.4550	+	15.2738i	1.02820	+	0.593634i
$663$	3.57967	−	2.87307i	0.139023	−	0.111581i
$664$		−	1.45646i		−	0.0565217i
$665$	−1.17944	+	2.05995i	−0.0457366	+	0.0798813i
$666$	−21.1842	−	67.1810i	−0.820869	−	2.60321i
$667$	−7.30584	−	12.6541i	−0.282883	−	0.489968i
$668$	0.524525	−	0.908504i	0.0202945	−	0.0351511i
$669$	0.633413	+	0.246310i	0.0244891	+	0.00952291i
$670$	−8.62613	+	4.98030i	−0.333257	+	0.192406i
$671$	−24.3238			−0.939009
$672$	23.3868	+	28.9244i	0.902164	+	1.11578i
$673$	1.14437			0.0441121			0.0220560	−	0.999757i	$-0.492979\pi$
$673$	1.14437			0.0441121			0.0220560	+	0.999757i	$0.492979\pi$
$674$	36.6345	−	21.1509i	1.41111	−	0.814703i
$675$	−0.339627	+	5.18504i	−0.0130723	+	0.199572i
$676$	14.2006	−	24.5961i	0.546176	−	0.946004i
$677$	7.98910	+	13.8375i	0.307046	+	0.531820i	0.977715	−	0.209938i	$-0.0673261\pi$
$677$	7.98910	+	13.8375i	0.307046	+	0.531820i	−0.670669	+	0.741757i	$0.733993\pi$
$678$	42.1615	−	6.48988i	1.61920	−	0.249242i
$679$	−34.1524	+	0.123039i	−1.31065	+	0.00472181i
$680$			2.18673i			0.0838571i
$681$	25.3963	+	31.6422i	0.973188	+	1.21253i
$682$	19.5959	+	11.3137i	0.750366	+	0.433224i
$683$	−1.96122	−	1.13231i	−0.0750442	−	0.0433268i	0.462008	−	0.886876i	$-0.347129\pi$
$683$	−1.96122	−	1.13231i	−0.0750442	−	0.0433268i	−0.537053	+	0.843549i	$0.680462\pi$
$684$	4.10116	−	4.47588i	0.156812	−	0.171140i
$685$		−	4.33830i		−	0.165758i
$686$	19.4590	+	32.8782i	0.742949	+	1.25530i
$687$	2.03646	+	13.2299i	0.0776960	+	0.504752i
$688$	5.39114	+	9.33773i	0.205535	+	0.355998i
$689$	−0.723434	+	1.25303i	−0.0275607	+	0.0477365i
$690$	−8.81130	+	22.6592i	−0.335441	+	0.862620i
$691$	−2.40044	+	1.38589i	−0.0913169	+	0.0527218i	−0.544963	−	0.838460i	$-0.683456\pi$
$691$	−2.40044	+	1.38589i	−0.0913169	+	0.0527218i	0.453646	+	0.891182i	$0.350123\pi$
$692$	25.2256			0.958934
$693$	35.4778	−	11.3279i	1.34769	−	0.430311i
$694$	32.6582			1.23969
$695$	9.49436	−	5.48157i	0.360141	−	0.207928i
$696$	0.710424	−	1.82693i	0.0269286	−	0.0692496i
$697$	8.51888	−	14.7551i	0.322676	−	0.558891i
$698$	−9.24191	−	16.0075i	−0.349811	−	0.605891i
$699$	1.07507	+	6.98419i	0.0406629	+	0.264166i
$700$	5.15716	−	3.00231i	0.194922	−	0.113477i
$701$			23.1184i			0.873169i	0.899663	+	0.436585i	$0.143812\pi$
$701$			23.1184i			0.873169i	−0.899663	+	0.436585i	$0.856188\pi$
$702$	5.69250	+	3.80326i	0.214850	+	0.143545i
$703$	−8.84388	−	5.10602i	−0.333553	−	0.192577i
$704$	−40.2147	−	23.2180i	−1.51565	−	0.875060i
$705$	7.38244	+	9.19807i	0.278039	+	0.346419i
$706$		−	27.7612i		−	1.04481i
$707$	20.7557	+	11.8838i	0.780599	+	0.446937i
$708$	−1.96187	+	0.301989i	−0.0737317	+	0.0113495i
$709$	18.0134	+	31.2002i	0.676508	+	1.17175i	0.976026	+	0.217656i	$0.0698410\pi$
$709$	18.0134	+	31.2002i	0.676508	+	1.17175i	−0.299517	+	0.954091i	$0.596826\pi$
$710$	−1.26661	+	2.19384i	−0.0475351	+	0.0823333i
$711$	−5.89580	+	26.5978i	−0.221110	+	0.997494i
$712$	−6.29910	+	3.63678i	−0.236069	+	0.136294i
$713$	−15.9067			−0.595710
$714$	−14.0840	+	36.6083i	−0.527079	+	1.37003i
$715$	2.99679			0.112074
$716$	−0.483812	+	0.279329i	−0.0180809	+	0.0104390i
$717$	−9.30287	−	3.61754i	−0.347422	−	0.135099i
$718$	−5.78619	+	10.0220i	−0.215939	+	0.374017i
$719$	8.57099	+	14.8454i	0.319644	+	0.553640i	0.980414	−	0.196949i	$-0.0631034\pi$
$719$	8.57099	+	14.8454i	0.319644	+	0.553640i	−0.660770	+	0.750589i	$0.729770\pi$
$720$	9.79586	−	3.08892i	0.365070	−	0.115117i
$721$	20.6598	+	35.4880i	0.769412	+	1.32164i
$722$			37.5343i			1.39688i
$723$	27.5826	−	22.1380i	1.02581	−	0.823322i
$724$	−28.0075	−	16.1701i	−1.04089	−	0.600958i
$725$	1.85970	+	1.07370i	0.0690676	+	0.0398762i
$726$	−30.6958	+	24.6367i	−1.13923	+	0.914352i
$727$		−	16.6832i		−	0.618747i	−0.950941	−	0.309374i	$-0.899881\pi$
$727$		−	16.6832i		−	0.618747i	0.950941	−	0.309374i	$-0.100119\pi$
$728$	−0.00320836	−	0.890556i	−0.000118910	−	0.0330062i
$729$	16.4348	−	21.4219i	0.608695	−	0.793404i
$730$	14.9110	+	25.8267i	0.551882	+	0.955888i
$731$	−6.53347	+	11.3163i	−0.241649	+	0.418548i
$732$	18.8749	+	7.33973i	0.697635	+	0.271284i
$733$	32.9814	−	19.0418i	1.21820	−	0.703326i	0.253664	−	0.967292i	$-0.418364\pi$
$733$	32.9814	−	19.0418i	1.21820	−	0.703326i	0.964532	+	0.263967i	$0.0850309\pi$
$734$	−4.07690			−0.150481
$735$	11.9696	−	1.93086i	0.441506	−	0.0712208i
$736$	55.2302			2.03581
$737$	19.6205	−	11.3279i	0.722730	−	0.417268i
$738$	24.8098	+	5.49948i	0.913263	+	0.202439i
$739$	11.2186	−	19.4312i	0.412684	−	0.714790i	−0.582498	−	0.812832i	$-0.697925\pi$
$739$	11.2186	−	19.4312i	0.412684	−	0.714790i	0.995182	+	0.0980422i	$0.0312580\pi$
$740$	12.8364	+	22.2333i	0.471876	+	0.817313i
$741$	0.980937	−	0.150995i	0.0360356	−	0.00554693i
$742$	−0.0445433	−	12.3640i	−0.00163524	−	0.453898i
$743$		−	6.39189i		−	0.234496i	−0.993103	−	0.117248i	$-0.962593\pi$
$743$		−	6.39189i		−	0.234496i	0.993103	−	0.117248i	$-0.0374072\pi$
$744$	−1.33570	−	1.66420i	−0.0489690	−	0.0610124i
$745$	7.50546	+	4.33328i	0.274979	+	0.158759i
$746$	41.2565	+	23.8195i	1.51051	+	0.872093i
$747$	−6.11275	−	5.60098i	−0.223654	−	0.204929i
$748$		−	43.9111i		−	1.60555i
$749$	7.13207	+	12.2510i	0.260600	+	0.447641i
$750$	−0.543588	−	3.53142i	−0.0198490	−	0.128949i
$751$	5.49944	+	9.52531i	0.200677	+	0.347583i	0.948747	−	0.316037i	$-0.102352\pi$
$751$	5.49944	+	9.52531i	0.200677	+	0.347583i	−0.748069	+	0.663620i	$0.769019\pi$
$752$	11.6570	−	20.1905i	0.425086	−	0.736271i
$753$	−2.77802	+	7.14396i	−0.101237	+	0.260340i
$754$	2.45023	−	1.41464i	0.0892320	−	0.0515181i
$755$	−13.4604			−0.489873
$756$	−30.9485	−	1.91522i	−1.12559	−	0.0696558i
$757$	−27.8216			−1.01119			−0.505597	−	0.862770i	$-0.668728\pi$
$757$	−27.8216			−1.01119			−0.505597	+	0.862770i	$0.668728\pi$
$758$	−30.4859	+	17.6011i	−1.10730	+	0.639299i
$759$	20.0417	−	51.5392i	0.727466	−	1.87075i
$760$	−0.236414	+	0.409481i	−0.00857563	+	0.0148534i
$761$	−6.54766	−	11.3409i	−0.237352	−	0.411106i	0.722601	−	0.691265i	$-0.242946\pi$
$761$	−6.54766	−	11.3409i	−0.237352	−	0.411106i	−0.959954	+	0.280159i	$0.909613\pi$
$762$	−9.15904	−	59.5017i	−0.331797	−	2.15552i
$763$	3.12002	+	1.78639i	0.112952	+	0.0646717i
$764$		−	38.4336i		−	1.39048i
$765$	9.17765	+	8.40930i	0.331819	+	0.304039i
$766$	47.5412	+	27.4479i	1.71773	+	0.991734i
$767$	−0.281045	−	0.162262i	−0.0101480	−	0.00585893i
$768$	−12.1064	−	15.0839i	−0.436853	−	0.544293i
$769$		−	7.74247i		−	0.279201i	−0.990208	−	0.139600i	$-0.955418\pi$
$769$		−	7.74247i		−	0.279201i	0.990208	−	0.139600i	$-0.0445818\pi$
$770$	−22.1317	+	12.8843i	−0.797571	+	0.464317i
$771$	−43.6664	+	6.72153i	−1.57261	+	0.242070i
$772$	3.18431	+	5.51538i	0.114606	+	0.198503i
$773$	19.1733	−	33.2091i	0.689614	−	1.19445i	−0.282349	−	0.959312i	$-0.591113\pi$
$773$	19.1733	−	33.2091i	0.689614	−	1.19445i	0.971963	−	0.235135i	$-0.0755532\pi$
$774$	−19.0276	−	4.21777i	−0.683934	−	0.151605i
$775$	2.02453	−	1.16886i	0.0727231	−	0.0419867i
$776$	−6.80301			−0.244214
$777$	8.12129	+	51.5248i	0.291350	+	1.84844i
$778$	19.5551			0.701086
$779$	3.19045	−	1.84201i	0.114310	−	0.0659967i
$780$	−2.32546	−	0.904286i	−0.0832650	−	0.0323786i
$781$	2.88096	−	4.98997i	0.103089	−	0.178555i
$782$	29.1205	+	50.4383i	1.04135	+	1.80367i
$783$	−4.93557	−	10.0073i	−0.176383	−	0.357632i
$784$	−12.1325	−	20.6687i	−0.433302	−	0.738167i
$785$		−	7.81320i		−	0.278865i
$786$	−38.6474	+	31.0187i	−1.37851	+	1.10640i
$787$	−21.6178	−	12.4811i	−0.770592	−	0.444901i	0.0624938	−	0.998045i	$-0.480095\pi$
$787$	−21.6178	−	12.4811i	−0.770592	−	0.444901i	−0.833086	+	0.553144i	$0.813428\pi$
$788$	18.7453	+	10.8226i	0.667775	+	0.385540i
$789$	−0.483554	+	0.388104i	−0.0172150	+	0.0138169i
$790$		−	18.7333i		−	0.666500i
$791$	−31.5873	+	0.113798i	−1.12312	+	0.00404619i
$792$	7.07507	−	2.23098i	0.251402	−	0.0792744i
$793$	1.65547	+	2.86736i	0.0587875	+	0.101823i
$794$	12.7488	−	22.0816i	0.452438	−	0.783645i
$795$	−3.65698	−	1.42206i	−0.129700	−	0.0504354i
$796$	23.8578	−	13.7743i	0.845619	−	0.488218i
$797$	5.81191			0.205868			0.102934	−	0.994688i	$-0.467177\pi$
$797$	5.81191			0.205868			0.102934	+	0.994688i	$0.467177\pi$
$798$	−6.59516	+	5.33251i	−0.233466	+	0.188769i
$799$	28.2539			0.999552
$800$	−7.02943	+	4.05844i	−0.248528	+	0.143488i
$801$	−8.96035	+	40.4229i	−0.316598	+	1.42827i
$802$	8.47393	−	14.6773i	0.299225	−	0.518273i
$803$	−33.9158	−	58.7438i	−1.19686	−	2.07302i
$804$	−18.6434	+	2.86976i	−0.657502	+	0.101209i
$805$	8.94509	−	15.6231i	0.315273	−	0.550641i
$806$		−	3.08003i		−	0.108490i
$807$	9.25658	+	11.5331i	0.325847	+	0.405985i
$808$	4.12586	+	2.38207i	0.145147	+	0.0838009i
$809$	1.51563	+	0.875048i	0.0532866	+	0.0307650i	0.526407	−	0.850233i	$-0.323539\pi$
$809$	1.51563	+	0.875048i	0.0532866	+	0.0307650i	−0.473120	+	0.880998i	$0.656872\pi$
$810$	−7.84536	+	16.8269i	−0.275658	+	0.591236i
$811$			28.4479i			0.998940i	0.866331	+	0.499470i	$0.166472\pi$
$811$			28.4479i			0.998940i	−0.866331	+	0.499470i	$0.833528\pi$
$812$	−6.36721	+	11.1207i	−0.223445	+	0.390259i
$813$	−2.22265	−	14.4394i	−0.0779516	−	0.506412i
$814$	−55.0868	−	95.4131i	−1.93079	−	3.34423i
$815$	8.33945	−	14.4443i	0.292118	−	0.505963i
$816$	8.91769	−	22.9328i	0.312182	−	0.802807i
$817$	−2.44688	+	1.41271i	−0.0856055	+	0.0494244i
$818$	−42.7750			−1.49559
$819$	−3.74998	−	3.41126i	−0.131035	−	0.119199i
$820$	−9.26153			−0.323427
$821$	25.9378	−	14.9752i	0.905236	−	0.522638i	0.0263407	−	0.999653i	$-0.491615\pi$
$821$	25.9378	−	14.9752i	0.905236	−	0.522638i	0.878895	+	0.477015i	$0.158281\pi$
$822$	5.61789	−	14.4470i	0.195946	−	0.503896i
$823$	−8.06283	+	13.9652i	−0.281053	+	0.486798i	−0.971644	−	0.236447i	$-0.924017\pi$
$823$	−8.06283	+	13.9652i	−0.281053	+	0.486798i	0.690592	+	0.723245i	$0.257350\pi$
$824$	4.08982	+	7.08378i	0.142476	+	0.246775i
$825$	1.23641	+	8.03236i	0.0430464	+	0.279651i
$826$	2.77318	−	0.00999078i	0.0964911	−	0.000347624i
$827$		−	15.9844i		−	0.555831i	−0.960605	−	0.277916i	$-0.910356\pi$
$827$		−	15.9844i		−	0.555831i	0.960605	−	0.277916i	$-0.0896436\pi$
$828$	−31.1041	+	33.9460i	−1.08094	+	1.17971i
$829$	18.0763	+	10.4363i	0.627815	+	0.362469i	0.779905	−	0.625898i	$-0.215267\pi$
$829$	18.0763	+	10.4363i	0.627815	+	0.362469i	−0.152091	+	0.988367i	$0.548601\pi$
$830$	4.93717	+	2.85047i	0.171372	+	0.0989414i
$831$	−10.9563	−	13.6509i	−0.380069	−	0.473543i
$832$			6.32084i			0.219136i
$833$	14.3407	−	25.2574i	0.496876	−	0.875117i
$834$	38.7155	−	5.95943i	1.34061	−	0.206358i
$835$	0.232556	+	0.402799i	0.00804794	+	0.0139394i
$836$	4.74737	−	8.22268i	0.164191	−	0.284387i
$837$	−12.1212	−	0.793953i	−0.418969	−	0.0274430i
$838$	12.3970	−	7.15741i	0.428247	−	0.247249i
$839$	−14.2504			−0.491977			−0.245989	−	0.969273i	$-0.579113\pi$
$839$	−14.2504			−0.491977			−0.245989	+	0.969273i	$0.579113\pi$
$840$	2.38565	−	0.376024i	0.0823128	−	0.0129741i
$841$	24.3887			0.840989
$842$	−27.1839	+	15.6946i	−0.936819	+	0.540873i
$843$	−24.4652	−	9.51361i	−0.842627	−	0.327666i
$844$	6.36172	−	11.0188i	0.218979	−	0.379283i
$845$	6.29604	+	10.9051i	0.216590	+	0.375145i
$846$	12.6732	+	40.1903i	0.435714	+	1.38177i
$847$	25.1878	−	14.6634i	0.865464	−	0.503842i
$848$			7.75614i			0.266347i
$849$	−32.3371	+	25.9540i	−1.10981	+	0.890738i
$850$	−7.41264	−	4.27969i	−0.254252	−	0.146792i
$851$	67.0739	+	38.7251i	2.29926	+	1.32748i
$852$	−3.74131	+	3.00281i	−0.128175	+	0.102875i
$853$			49.6034i			1.69839i	0.528081	+	0.849194i	$0.322912\pi$
$853$			49.6034i			1.69839i	−0.528081	+	0.849194i	$0.677088\pi$
$854$	−24.5537	−	14.0584i	−0.840209	−	0.481067i
$855$	0.809428	+	2.56693i	0.0276819	+	0.0877871i
$856$	1.41187	+	2.44543i	0.0482567	+	0.0835830i
$857$	2.62252	−	4.54233i	0.0895834	−	0.155163i	−0.817752	−	0.575571i	$-0.804780\pi$
$857$	2.62252	−	4.54233i	0.0895834	−	0.155163i	0.907335	+	0.420408i	$0.138113\pi$
$858$	9.97960	+	3.88069i	0.340698	+	0.132485i
$859$	−10.1722	+	5.87292i	−0.347071	+	0.200382i	−0.663394	−	0.748270i	$-0.730885\pi$
$859$	−10.1722	+	5.87292i	−0.347071	+	0.200382i	0.316323	+	0.948651i	$0.397552\pi$
$860$	7.10303			0.242211
$861$	−17.5623	−	6.75658i	−0.598521	−	0.230264i
$862$	−64.0863			−2.18279
$863$	30.3896	−	17.5454i	1.03447	−	0.597254i	0.116211	−	0.993225i	$-0.462925\pi$
$863$	30.3896	−	17.5454i	1.03447	−	0.597254i	0.918263	+	0.395971i	$0.129592\pi$
$864$	42.0864	+	2.75671i	1.43181	+	0.0937853i
$865$	−5.59208	+	9.68576i	−0.190136	+	0.329326i
$866$	−23.0097	−	39.8539i	−0.781901	−	1.35429i
$867$	0.370054	−	0.0569621i	0.0125677	−	0.00193454i
$868$	7.01857	+	12.0560i	0.238226	+	0.409208i
$869$			42.6096i			1.44543i
$870$	4.80260	+	5.98375i	0.162823	+	0.202868i
$871$	−2.67074	−	1.54195i	−0.0904944	−	0.0522470i
$872$	0.620205	+	0.358076i	0.0210028	+	0.0121260i
$873$	−26.1617	+	28.5521i	−0.885440	+	0.966343i
$874$			12.5933i			0.425973i
$875$	0.00953166	+	2.64573i	0.000322229	+	0.0894421i
$876$	8.59208	+	55.8184i	0.290299	+	1.88593i
$877$	8.42662	+	14.5953i	0.284547	+	0.492850i	0.972499	−	0.232906i	$-0.0748235\pi$
$877$	8.42662	+	14.5953i	0.284547	+	0.492850i	−0.687952	+	0.725756i	$0.741490\pi$
$878$	−26.6936	+	46.2346i	−0.900864	+	1.56034i
$879$	13.3220	−	34.2590i	0.449341	−	1.15553i
$880$	13.9125	−	8.03236i	0.468989	−	0.270771i
$881$	−51.9437			−1.75003			−0.875015	−	0.484096i	$-0.839148\pi$
$881$	−51.9437			−1.75003			−0.875015	+	0.484096i	$0.839148\pi$
$882$	42.3603	+	9.07011i	1.42635	+	0.305406i
$883$	14.9096			0.501748			0.250874	−	0.968020i	$-0.419282\pi$
$883$	14.9096			0.501748			0.250874	+	0.968020i	$0.419282\pi$
$884$	−5.17638	+	2.98858i	−0.174100	+	0.100517i
$885$	0.318960	−	0.820237i	0.0107217	−	0.0275720i
$886$	−31.9387	+	55.3194i	−1.07300	+	1.85849i
$887$	−6.59427	−	11.4216i	−0.221414	−	0.383500i	0.733824	−	0.679340i	$-0.237734\pi$
$887$	−6.59427	−	11.4216i	−0.221414	−	0.383500i	−0.955238	+	0.295840i	$0.904401\pi$
$888$	1.58073	+	10.2692i	0.0530458	+	0.344612i
$889$	0.160601	+	44.5785i	0.00538638	+	1.49512i
$890$		−	28.4705i		−	0.954335i
$891$	17.8446	−	38.2734i	0.597816	−	1.28221i
$892$	−0.766431	−	0.442499i	−0.0256620	−	0.0148160i
$893$	5.29076	+	3.05462i	0.177048	+	0.102219i
$894$	19.3825	+	24.1494i	0.648249	+	0.807678i
$895$		−	0.247690i		−	0.00827935i
$896$	−5.56642	−	9.56161i	−0.185961	−	0.319431i
$897$	−7.43963	+	1.14518i	−0.248402	+	0.0382363i
$898$	−24.9642	−	43.2392i	−0.833065	−	1.44291i
$899$	−2.51001	+	4.34747i	−0.0837135	+	0.144996i
$900$	1.46434	−	6.60608i	0.0488113	−	0.220203i
$901$	−8.14028	+	4.69979i	−0.271192	+	0.156573i
$902$	39.7453			1.32338
$903$	13.4692	+	5.18189i	0.448227	+	0.172442i
$904$	−6.29206			−0.209271
$905$	12.4175	−	7.16927i	0.412773	−	0.238315i
$906$	−44.8243	−	17.4305i	−1.48919	−	0.579089i
$907$	−23.4709	+	40.6527i	−0.779337	+	1.34985i	0.152987	+	0.988228i	$0.451111\pi$
$907$	−23.4709	+	40.6527i	−0.779337	+	1.34985i	−0.932324	+	0.361623i	$0.882223\pi$
$908$	−26.4174	−	45.7562i	−0.876691	−	1.51847i
$909$	25.8640	−	8.15567i	0.857854	−	0.270507i
$910$	3.02512	+	1.73205i	0.100282	+	0.0574169i
$911$		−	45.2977i		−	1.50078i	−0.660996	−	0.750389i	$-0.729866\pi$
$911$		−	45.2977i		−	1.50078i	0.660996	−	0.750389i	$-0.270134\pi$
$912$	4.14924	−	3.33021i	0.137395	−	0.110274i
$913$	−11.2298	−	6.48352i	−0.371652	−	0.214573i
$914$	4.31355	+	2.49043i	0.142680	+	0.0823761i
$915$	−7.00244	+	5.62021i	−0.231493	+	0.185798i
$916$		−	17.4309i		−	0.575932i
$917$	31.7126	−	18.4619i	1.04724	−	0.609667i
$918$	19.6728	+	39.8884i	0.649300	+	1.31651i
$919$	−21.5911	−	37.3969i	−0.712225	−	1.23361i	−0.964020	−	0.265830i	$-0.914354\pi$
$919$	−21.5911	−	37.3969i	−0.712225	−	1.23361i	0.251795	−	0.967781i	$-0.418979\pi$
$920$	1.79301	−	3.10559i	0.0591139	−	0.102388i
$921$	−39.1978	−	15.2426i	−1.29161	−	0.502260i
$922$	13.3162	−	7.68811i	0.438546	−	0.253195i
$923$	−0.784311			−0.0258159
$924$	−47.9057	+	7.55085i	−1.57598	+	0.248405i
$925$	−11.3824			−0.374252
$926$	24.8077	−	14.3227i	0.815232	−	0.470675i
$927$	45.4584	+	10.0765i	1.49305	+	0.330957i
$928$	8.71510	−	15.0950i	0.286087	−	0.495517i
$929$	−4.50570	−	7.80410i	−0.147827	−	0.256044i	0.782597	−	0.622529i	$-0.213895\pi$
$929$	−4.50570	−	7.80410i	−0.147827	−	0.256044i	−0.930424	+	0.366484i	$0.880561\pi$
$930$	8.25548	−	1.27076i	0.270708	−	0.0416698i
$931$	5.41606	−	3.17922i	0.177504	−	0.104195i
$932$		−	9.20194i		−	0.301419i
$933$	7.71607	+	9.61375i	0.252613	+	0.314740i
$934$	−35.9774	−	20.7716i	−1.17722	−	0.679667i
$935$	16.8604	+	9.73433i	0.551392	+	0.318347i
$936$	−0.744523	−	0.682191i	−0.0243355	−	0.0222981i
$937$			21.9677i			0.717654i	0.933404	+	0.358827i	$0.116823\pi$
$937$			21.9677i			0.717654i	−0.933404	+	0.358827i	$0.883177\pi$
$938$	26.3531	−	0.0949410i	0.860459	−	0.00309993i
$939$	0.934731	+	6.07248i	0.0305038	+	0.198168i
$940$	−7.67925	−	13.3009i	−0.250470	−	0.433826i
$941$	0.823861	−	1.42697i	0.0268571	−	0.0465178i	−0.852284	−	0.523079i	$-0.824783\pi$
$941$	0.823861	−	1.42697i	0.0268571	−	0.0465178i	0.879142	+	0.476561i	$0.158117\pi$
$942$	10.1177	−	26.0187i	0.329653	−	0.847735i
$943$	−24.1970	+	13.9702i	−0.787964	+	0.454931i
$944$	−1.73965			−0.0566209
$945$	7.59612	−	11.4586i	0.247102	−	0.372748i
$946$	−30.4823			−0.991064
$947$	−23.6645	+	13.6627i	−0.768994	+	0.443979i	−0.832516	−	0.554002i	$-0.813100\pi$
$947$	−23.6645	+	13.6627i	−0.768994	+	0.443979i	0.0635217	+	0.997980i	$0.479767\pi$
$948$	12.8575	−	33.0644i	0.417592	−	1.07388i
$949$	−4.61660	+	7.99619i	−0.149861	+	0.259567i
$950$	−0.925382	−	1.60281i	−0.0300233	−	0.0520020i
$951$	−5.55384	−	36.0805i	−0.180095	−	1.16999i
$952$	2.87470	−	5.02081i	0.0931695	−	0.162725i
$953$			55.2380i			1.78933i	0.446734	+	0.894667i	$0.352587\pi$
$953$			55.2380i			1.78933i	−0.446734	+	0.894667i	$0.647413\pi$
$954$	−10.3366	−	9.47122i	−0.334660	−	0.306642i
$955$	14.7572	+	8.52006i	0.477531	+	0.275703i
$956$	11.2565	+	6.49894i	0.364061	+	0.210191i
$957$	−10.9237	−	13.6103i	−0.353113	−	0.439958i
$958$			68.5654i			2.21525i
$959$	−5.70319	+	9.96091i	−0.184166	+	0.321655i
$960$	−16.9419	+	2.60785i	−0.546797	+	0.0841679i
$961$	−12.7675	−	22.1140i	−0.411856	−	0.713355i
$962$	−7.49840	+	12.9876i	−0.241758	+	0.418737i
$963$	15.6929	+	3.47857i	0.505697	+	0.112096i
$964$	−39.8858	+	23.0281i	−1.28464	+	0.741684i
$965$	−2.82362			−0.0908956
$966$	50.0191	−	40.4429i	1.60934	−	1.30123i
$967$	−34.5930			−1.11244			−0.556218	−	0.831036i	$-0.687748\pi$
$967$	−34.5930			−1.11244			−0.556218	+	0.831036i	$0.687748\pi$
$968$	5.02776	−	2.90278i	0.161598	−	0.0932989i
$969$	6.00935	+	2.33681i	0.193048	+	0.0750692i
$970$	13.3143	−	23.0611i	0.427497	−	0.740447i
$971$	2.12246	+	3.67621i	0.0681129	+	0.117975i	0.898071	−	0.439851i	$-0.144969\pi$
$971$	2.12246	+	3.67621i	0.0681129	+	0.117975i	−0.829958	+	0.557826i	$0.811636\pi$
$972$	−25.3962	+	24.3150i	−0.814583	+	0.779903i
$973$	−29.0056	+	0.104497i	−0.929875	+	0.00335002i
$974$		−	66.4407i		−	2.12890i
$975$	0.862730	−	0.692434i	0.0276295	−	0.0221756i
$976$	15.3709	+	8.87439i	0.492010	+	0.284062i
$977$	−33.6806	−	19.4455i	−1.07754	−	0.622118i	−0.147308	−	0.989091i	$-0.547061\pi$
$977$	−33.6806	−	19.4455i	−1.07754	−	0.622118i	−0.930232	+	0.366973i	$0.880394\pi$
$978$	46.4758	−	37.3019i	1.48613	−	1.19278i
$979$			64.7574i			2.06966i
$980$	−15.7879	+	0.113758i	−0.504327	+	0.00363387i
$981$	3.88790	−	1.22597i	0.124131	−	0.0391422i
$982$	23.2077	+	40.1970i	0.740588	+	1.28274i
$983$	−13.1884	+	22.8429i	−0.420644	+	0.728577i	−0.996003	−	0.0893246i	$-0.971529\pi$
$983$	−13.1884	+	22.8429i	−0.420644	+	0.728577i	0.575359	+	0.817901i	$0.304862\pi$
$984$	−3.49344	−	1.35847i	−0.111367	−	0.0433064i
$985$	−8.31103	+	4.79838i	−0.264812	+	0.152889i
$986$	18.3804			0.585352
$987$	−4.85848	−	30.8242i	−0.154647	−	0.981144i
$988$	−1.29242			−0.0411174
$989$	18.5577	−	10.7143i	0.590099	−	0.340694i
$990$	−6.28413	+	28.3496i	−0.199723	+	0.901010i
$991$	6.90833	−	11.9656i	0.219450	−	0.380099i	−0.735190	−	0.677861i	$-0.762907\pi$
$991$	6.90833	−	11.9656i	0.219450	−	0.380099i	0.954640	+	0.297762i	$0.0962403\pi$
$992$	−9.48750	−	16.4328i	−0.301228	−	0.521743i
$993$	−25.3501	+	3.90211i	−0.804460	+	0.123830i
$994$	5.79224	−	3.37203i	0.183719	−	0.106954i
$995$			12.2141i			0.387213i
$996$	6.75773	+	8.41972i	0.214127	+	0.266789i
$997$	53.1001	+	30.6574i	1.68170	+	0.970929i	0.960533	+	0.278166i	$0.0897265\pi$
$997$	53.1001	+	30.6574i	1.68170	+	0.970929i	0.721165	+	0.692763i	$0.243607\pi$
$998$	−11.4587	−	6.61570i	−0.362720	−	0.209416i
$999$	49.1786	+	32.8571i	1.55594	+	1.03955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.s.c.101.4	yes	8
3.2	odd	2		105.2.s.d.101.1	yes	8
5.2	odd	4		525.2.q.f.374.7		16
5.3	odd	4		525.2.q.f.374.2		16
5.4	even	2		525.2.t.g.101.1		8
7.2	even	3		735.2.s.l.656.1		8
7.3	odd	6		735.2.b.c.146.7		8
7.4	even	3		735.2.b.d.146.7		8
7.5	odd	6		105.2.s.d.26.1	yes	8
7.6	odd	2		735.2.s.k.521.4		8
15.2	even	4		525.2.q.e.374.2		16
15.8	even	4		525.2.q.e.374.7		16
15.14	odd	2		525.2.t.f.101.4		8
21.2	odd	6		735.2.s.k.656.4		8
21.5	even	6	inner	105.2.s.c.26.4	✓	8
21.11	odd	6		735.2.b.c.146.2		8
21.17	even	6		735.2.b.d.146.2		8
21.20	even	2		735.2.s.l.521.1		8
35.12	even	12		525.2.q.e.299.7		16
35.19	odd	6		525.2.t.f.26.4		8
35.33	even	12		525.2.q.e.299.2		16
105.47	odd	12		525.2.q.f.299.2		16
105.68	odd	12		525.2.q.f.299.7		16
105.89	even	6		525.2.t.g.26.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.4	✓	8	21.5	even	6	inner
105.2.s.c.101.4	yes	8	1.1	even	1	trivial
105.2.s.d.26.1	yes	8	7.5	odd	6
105.2.s.d.101.1	yes	8	3.2	odd	2
525.2.q.e.299.2		16	35.33	even	12
525.2.q.e.299.7		16	35.12	even	12
525.2.q.e.374.2		16	15.2	even	4
525.2.q.e.374.7		16	15.8	even	4
525.2.q.f.299.2		16	105.47	odd	12
525.2.q.f.299.7		16	105.68	odd	12
525.2.q.f.374.2		16	5.3	odd	4
525.2.q.f.374.7		16	5.2	odd	4
525.2.t.f.26.4		8	35.19	odd	6
525.2.t.f.101.4		8	15.14	odd	2
525.2.t.g.26.1		8	105.89	even	6
525.2.t.g.101.1		8	5.4	even	2
735.2.b.c.146.2		8	21.11	odd	6
735.2.b.c.146.7		8	7.3	odd	6
735.2.b.d.146.2		8	21.17	even	6
735.2.b.d.146.7		8	7.4	even	3
735.2.s.k.521.4		8	7.6	odd	2
735.2.s.k.656.4		8	21.2	odd	6
735.2.s.l.521.1		8	21.20	even	2
735.2.s.l.656.1		8	7.2	even	3

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.78651 - 1.03144i) q^{2} +(-0.627739 + 1.61429i) q^{3} +(1.12774 - 1.95330i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.543588 + 3.53142i) q^{6} +(-0.00953166 - 2.64573i) q^{7} -0.527019i q^{8} +(-2.21189 - 2.02671i) q^{9} +O(q^{10})\)	\(q+(1.78651 - 1.03144i) q^{2} +(-0.627739 + 1.61429i) q^{3} +(1.12774 - 1.95330i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.543588 + 3.53142i) q^{6} +(-0.00953166 - 2.64573i) q^{7} -0.527019i q^{8} +(-2.21189 - 2.02671i) q^{9} +(1.78651 + 1.03144i) q^{10} +(-4.06348 - 2.34605i) q^{11} +(2.44528 + 3.04666i) q^{12} +0.638688i q^{13} +(-2.74595 - 4.71679i) q^{14} +(-1.71189 + 0.263509i) q^{15} +(1.71189 + 2.96508i) q^{16} +(-2.07462 + 3.59334i) q^{17} +(-6.04198 - 1.33930i) q^{18} +(-0.776975 + 0.448587i) q^{19} +2.25548 q^{20} +(4.27698 + 1.64544i) q^{21} -9.67925 q^{22} +(5.89275 - 3.40218i) q^{23} +(0.850763 + 0.330830i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.658769 + 1.14102i) q^{26} +(4.66019 - 2.29839i) q^{27} +(-5.17866 - 2.96508i) q^{28} -2.14740i q^{29} +(-2.78651 + 2.23647i) q^{30} +(-2.02453 - 1.16886i) q^{31} +(7.02943 + 4.05844i) q^{32} +(6.33802 - 5.08695i) q^{33} +8.55938i q^{34} +(2.28651 - 1.33112i) q^{35} +(-6.45320 + 2.03489i) q^{36} +(5.69122 + 9.85748i) q^{37} +(-0.925382 + 1.60281i) q^{38} +(-1.03103 - 0.400929i) q^{39} +(0.456412 - 0.263509i) q^{40} -4.10624 q^{41} +(9.33802 - 1.47185i) q^{42} +3.14924 q^{43} +(-9.16509 + 5.29147i) q^{44} +(0.649237 - 2.92891i) q^{45} +(7.01829 - 12.1560i) q^{46} +(-3.40471 - 5.89714i) q^{47} +(-5.86113 + 0.902197i) q^{48} +(-6.99982 + 0.0504365i) q^{49} +2.06288i q^{50} +(-4.49840 - 5.60472i) q^{51} +(1.24755 + 0.720273i) q^{52} +(1.96187 + 1.13269i) q^{53} +(5.95481 - 8.91281i) q^{54} -4.69211i q^{55} +(-1.39435 + 0.00502336i) q^{56} +(-0.236414 - 1.53586i) q^{57} +(-2.21492 - 3.83635i) q^{58} +(-0.254055 + 0.440035i) q^{59} +(-1.41585 + 3.64100i) q^{60} +(4.48946 - 2.59199i) q^{61} -4.82244 q^{62} +(-5.34105 + 5.87139i) q^{63} +9.89660 q^{64} +(-0.553120 + 0.319344i) q^{65} +(6.07604 - 15.6252i) q^{66} +(-2.41425 + 4.18160i) q^{67} +(4.67925 + 8.10471i) q^{68} +(1.79301 + 11.6483i) q^{69} +(2.71189 - 4.73645i) q^{70} +1.22800i q^{71} +(-1.06811 + 1.16571i) q^{72} +(12.5197 + 7.22826i) q^{73} +(20.3348 + 11.7403i) q^{74} +(-1.08415 - 1.35078i) q^{75} +2.02356i q^{76} +(-6.16830 + 10.7733i) q^{77} +(-2.25548 + 0.347183i) q^{78} +(-4.54056 - 7.86448i) q^{79} +(-1.71189 + 2.96508i) q^{80} +(0.784903 + 8.96571i) q^{81} +(-7.33583 + 4.23534i) q^{82} +2.76359 q^{83} +(8.03735 - 6.49859i) q^{84} -4.14924 q^{85} +(5.62613 - 3.24825i) q^{86} +(3.46653 + 1.34801i) q^{87} +(-1.23641 + 2.14153i) q^{88} +(-6.90067 - 11.9523i) q^{89} +(-1.86113 - 5.90216i) q^{90} +(1.68980 - 0.00608775i) q^{91} -15.3471i q^{92} +(3.15776 - 2.53444i) q^{93} +(-12.1651 - 7.02352i) q^{94} +(-0.776975 - 0.448587i) q^{95} +(-10.9642 + 8.79992i) q^{96} -12.9085i q^{97} +(-12.4532 + 7.31000i) q^{98} +(4.23321 + 13.4247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 2 q^{7} - 5 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 2 * q^7 - 5 * q^9	\( 8 q - 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 2 q^{7} - 5 q^{9} - 3 q^{10} - 9 q^{12} - 12 q^{14} - q^{15} + q^{16} - 12 q^{17} - 19 q^{18} + 9 q^{19} + 6 q^{20} + 19 q^{21} - 40 q^{22} + 27 q^{23} + 16 q^{24} - 4 q^{25} - 6 q^{26} + 4 q^{27} + 3 q^{28} - 5 q^{30} - 21 q^{31} + 21 q^{32} + 2 q^{33} + q^{35} + 9 q^{36} + 7 q^{37} - 12 q^{38} - 3 q^{39} + 3 q^{40} - 30 q^{41} + 26 q^{42} + 16 q^{43} - 4 q^{45} - 7 q^{46} - 6 q^{47} - 25 q^{48} - 4 q^{49} - 6 q^{51} + 30 q^{52} + 24 q^{53} + 17 q^{54} - 21 q^{56} + 6 q^{57} - 13 q^{58} - 12 q^{59} - 18 q^{60} + 15 q^{61} + 24 q^{62} - 2 q^{63} + 38 q^{64} - 3 q^{65} + 22 q^{66} + 4 q^{67} - 13 q^{69} + 9 q^{70} - 14 q^{72} + 15 q^{73} + 54 q^{74} - 2 q^{75} - 36 q^{77} - 6 q^{78} - 29 q^{79} - q^{80} - 41 q^{81} + 27 q^{82} + 30 q^{83} - 3 q^{84} - 24 q^{85} + 9 q^{86} + 32 q^{87} - 2 q^{88} - 3 q^{89} + 7 q^{90} - 3 q^{91} - 9 q^{93} - 24 q^{94} + 9 q^{95} - 3 q^{96} - 39 q^{98} - 34 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 2 * q^7 - 5 * q^9 - 3 * q^10 - 9 * q^12 - 12 * q^14 - q^15 + q^16 - 12 * q^17 - 19 * q^18 + 9 * q^19 + 6 * q^20 + 19 * q^21 - 40 * q^22 + 27 * q^23 + 16 * q^24 - 4 * q^25 - 6 * q^26 + 4 * q^27 + 3 * q^28 - 5 * q^30 - 21 * q^31 + 21 * q^32 + 2 * q^33 + q^35 + 9 * q^36 + 7 * q^37 - 12 * q^38 - 3 * q^39 + 3 * q^40 - 30 * q^41 + 26 * q^42 + 16 * q^43 - 4 * q^45 - 7 * q^46 - 6 * q^47 - 25 * q^48 - 4 * q^49 - 6 * q^51 + 30 * q^52 + 24 * q^53 + 17 * q^54 - 21 * q^56 + 6 * q^57 - 13 * q^58 - 12 * q^59 - 18 * q^60 + 15 * q^61 + 24 * q^62 - 2 * q^63 + 38 * q^64 - 3 * q^65 + 22 * q^66 + 4 * q^67 - 13 * q^69 + 9 * q^70 - 14 * q^72 + 15 * q^73 + 54 * q^74 - 2 * q^75 - 36 * q^77 - 6 * q^78 - 29 * q^79 - q^80 - 41 * q^81 + 27 * q^82 + 30 * q^83 - 3 * q^84 - 24 * q^85 + 9 * q^86 + 32 * q^87 - 2 * q^88 - 3 * q^89 + 7 * q^90 - 3 * q^91 - 9 * q^93 - 24 * q^94 + 9 * q^95 - 3 * q^96 - 39 * q^98 - 34 * q^99

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