LMFDB - Embedded newform 240.2.bl.a.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(109,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("240.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.6
Character	$\chi$	$=$	240.109
Dual form			240.2.bl.a.229.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06224 - 0.933621i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.256702 + 1.98346i) q^{4} +(-1.86022 + 1.24079i) q^{5} +(-1.41129 + 0.0909462i) q^{6} +1.58988 q^{7} +(1.57912 - 2.34657i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.06224 - 0.933621i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.256702 + 1.98346i) q^{4} +(-1.86022 + 1.24079i) q^{5} +(-1.41129 + 0.0909462i) q^{6} +1.58988 q^{7} +(1.57912 - 2.34657i) q^{8} -1.00000i q^{9} +(3.13443 + 0.418728i) q^{10} +(3.92109 - 3.92109i) q^{11} +(1.58403 + 1.22100i) q^{12} +(3.10459 - 3.10459i) q^{13} +(-1.68884 - 1.48435i) q^{14} +(-0.438005 + 2.19275i) q^{15} +(-3.86821 + 1.01832i) q^{16} -1.48346i q^{17} +(-0.933621 + 1.06224i) q^{18} +(4.94087 + 4.94087i) q^{19} +(-2.93858 - 3.37116i) q^{20} +(1.12422 - 1.12422i) q^{21} +(-7.82594 + 0.504320i) q^{22} -6.61914 q^{23} +(-0.542668 - 2.77588i) q^{24} +(1.92087 - 4.61630i) q^{25} +(-6.19632 + 0.399304i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.408127 + 3.15347i) q^{28} +(4.42607 + 4.42607i) q^{29} +(2.51246 - 1.92029i) q^{30} -1.50391 q^{31} +(5.05968 + 2.52975i) q^{32} -5.54525i q^{33} +(-1.38499 + 1.57579i) q^{34} +(-2.95754 + 1.97271i) q^{35} +(1.98346 - 0.256702i) q^{36} +(-2.14771 - 2.14771i) q^{37} +(-0.635482 - 9.86128i) q^{38} -4.39055i q^{39} +(-0.0259124 + 6.32450i) q^{40} -6.84881i q^{41} +(-2.24378 + 0.144594i) q^{42} +(0.322458 + 0.322458i) q^{43} +(8.78386 + 6.77076i) q^{44} +(1.24079 + 1.86022i) q^{45} +(7.03111 + 6.17977i) q^{46} +13.3031i q^{47} +(-2.01518 + 3.45529i) q^{48} -4.47227 q^{49} +(-6.35030 + 3.11025i) q^{50} +(-1.04897 - 1.04897i) q^{51} +(6.95477 + 5.36086i) q^{52} +(-0.931646 - 0.931646i) q^{53} +(0.0909462 + 1.41129i) q^{54} +(-2.42885 + 12.1594i) q^{55} +(2.51061 - 3.73077i) q^{56} +6.98744 q^{57} +(-0.569270 - 8.83382i) q^{58} +(1.14326 - 1.14326i) q^{59} +(-4.46166 - 0.305880i) q^{60} +(2.67458 + 2.67458i) q^{61} +(1.59751 + 1.40408i) q^{62} -1.58988i q^{63} +(-3.01277 - 7.41102i) q^{64} +(-1.92308 + 9.62737i) q^{65} +(-5.17717 + 5.89038i) q^{66} +(-5.43194 + 5.43194i) q^{67} +(2.94239 - 0.380808i) q^{68} +(-4.68044 + 4.68044i) q^{69} +(4.98338 + 0.665728i) q^{70} +2.26233i q^{71} +(-2.34657 - 1.57912i) q^{72} -5.27105 q^{73} +(0.276233 + 4.28653i) q^{74} +(-1.90596 - 4.62248i) q^{75} +(-8.53167 + 11.0683i) q^{76} +(6.23407 - 6.23407i) q^{77} +(-4.09911 + 4.66381i) q^{78} -6.52058 q^{79} +(5.93222 - 6.69394i) q^{80} -1.00000 q^{81} +(-6.39419 + 7.27507i) q^{82} +(-0.973359 + 0.973359i) q^{83} +(2.51843 + 1.94125i) q^{84} +(1.84067 + 2.75957i) q^{85} +(-0.0414737 - 0.643581i) q^{86} +6.25941 q^{87} +(-3.00923 - 15.3930i) q^{88} +6.83613i q^{89} +(0.418728 - 3.13443i) q^{90} +(4.93593 - 4.93593i) q^{91} +(-1.69915 - 13.1288i) q^{92} +(-1.06342 + 1.06342i) q^{93} +(12.4201 - 14.1311i) q^{94} +(-15.3217 - 3.06053i) q^{95} +(5.36654 - 1.78893i) q^{96} -15.8228i q^{97} +(4.75062 + 4.17541i) q^{98} +(-3.92109 - 3.92109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.06224	−	0.933621i	−0.751116	−	0.660170i
$2$	−1.06224	−	0.933621i	−0.751116	−	0.660170i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	0.256702	+	1.98346i	0.128351	+	0.991729i
$5$	−1.86022	+	1.24079i	−0.831918	+	0.554899i
$5$	−1.86022	+	1.24079i	−0.831918	+	0.554899i
$6$	−1.41129	+	0.0909462i	−0.576155	+	0.0371286i
$7$	1.58988			0.600919			0.300460	−	0.953795i	$-0.402860\pi$
$7$	1.58988			0.600919			0.300460	+	0.953795i	$0.402860\pi$
$8$	1.57912	−	2.34657i	0.558303	−	0.829637i
$9$		−	1.00000i		−	0.333333i
$10$	3.13443	+	0.418728i	0.991195	+	0.132413i
$11$	3.92109	−	3.92109i	1.18225	−	1.18225i	0.203093	−	0.979160i	$-0.434901\pi$
$11$	3.92109	−	3.92109i	1.18225	−	1.18225i	0.979160	−	0.203093i	$-0.0650993\pi$
$12$	1.58403	+	1.22100i	0.457271	+	0.352472i
$13$	3.10459	−	3.10459i	0.861057	−	0.861057i	−0.130404	−	0.991461i	$-0.541627\pi$
$13$	3.10459	−	3.10459i	0.861057	−	0.861057i	0.991461	+	0.130404i	$0.0416273\pi$
$14$	−1.68884	−	1.48435i	−0.451360	−	0.396709i
$15$	−0.438005	+	2.19275i	−0.113092	+	0.566166i
$16$	−3.86821	+	1.01832i	−0.967052	+	0.254579i
$17$		−	1.48346i		−	0.359793i	−0.983686	−	0.179896i	$-0.942424\pi$
$17$		−	1.48346i		−	0.359793i	0.983686	−	0.179896i	$-0.0575762\pi$
$18$	−0.933621	+	1.06224i	−0.220057	+	0.250372i
$19$	4.94087	+	4.94087i	1.13351	+	1.13351i	0.989589	+	0.143924i	$0.0459721\pi$
$19$	4.94087	+	4.94087i	1.13351	+	1.13351i	0.143924	+	0.989589i	$0.454028\pi$
$20$	−2.93858	−	3.37116i	−0.657087	−	0.753815i
$21$	1.12422	−	1.12422i	0.245324	−	0.245324i
$22$	−7.82594	+	0.504320i	−1.66850	+	0.107521i
$23$	−6.61914			−1.38019			−0.690094	−	0.723720i	$-0.742431\pi$
$23$	−6.61914			−1.38019			−0.690094	+	0.723720i	$0.742431\pi$
$24$	−0.542668	−	2.77588i	−0.110772	−	0.566624i
$25$	1.92087	−	4.61630i	0.384174	−	0.923261i
$26$	−6.19632	+	0.399304i	−1.21520	+	0.0783099i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	0.408127	+	3.15347i	0.0771287	+	0.595949i
$29$	4.42607	+	4.42607i	0.821901	+	0.821901i	0.986380	−	0.164480i	$-0.0525945\pi$
$29$	4.42607	+	4.42607i	0.821901	+	0.821901i	−0.164480	+	0.986380i	$0.552594\pi$
$30$	2.51246	−	1.92029i	0.458711	−	0.350596i
$31$	−1.50391			−0.270110			−0.135055	−	0.990838i	$-0.543121\pi$
$31$	−1.50391			−0.270110			−0.135055	+	0.990838i	$0.543121\pi$
$32$	5.05968	+	2.52975i	0.894434	+	0.447200i
$33$		−	5.54525i		−	0.965305i
$34$	−1.38499	+	1.57579i	−0.237524	+	0.270246i
$35$	−2.95754	+	1.97271i	−0.499915	+	0.333450i
$36$	1.98346	−	0.256702i	0.330576	−	0.0427837i
$37$	−2.14771	−	2.14771i	−0.353082	−	0.353082i	0.508173	−	0.861255i	$-0.330321\pi$
$37$	−2.14771	−	2.14771i	−0.353082	−	0.353082i	−0.861255	+	0.508173i	$0.830321\pi$
$38$	−0.635482	−	9.86128i	−0.103089	−	1.59971i
$39$		−	4.39055i		−	0.703050i
$40$	−0.0259124	+	6.32450i	−0.00409712	+	0.999992i
$41$		−	6.84881i		−	1.06960i	−0.844977	−	0.534802i	$-0.820386\pi$
$41$		−	6.84881i		−	1.06960i	0.844977	−	0.534802i	$-0.179614\pi$
$42$	−2.24378	+	0.144594i	−0.346223	+	0.0223113i
$43$	0.322458	+	0.322458i	0.0491744	+	0.0491744i	0.731266	−	0.682092i	$-0.238930\pi$
$43$	0.322458	+	0.322458i	0.0491744	+	0.0491744i	−0.682092	+	0.731266i	$0.738930\pi$
$44$	8.78386	+	6.77076i	1.32422	+	1.02073i
$45$	1.24079	+	1.86022i	0.184966	+	0.277306i
$46$	7.03111	+	6.17977i	1.03668	+	0.911158i
$47$			13.3031i			1.94046i	0.242188	+	0.970229i	$0.422135\pi$
$47$			13.3031i			1.94046i	−0.242188	+	0.970229i	$0.577865\pi$
$48$	−2.01518	+	3.45529i	−0.290866	+	0.498729i
$49$	−4.47227			−0.638896
$50$	−6.35030	+	3.11025i	−0.898068	+	0.439856i
$51$	−1.04897	−	1.04897i	−0.146885	−	0.146885i
$52$	6.95477	+	5.36086i	0.964453	+	0.743418i
$53$	−0.931646	−	0.931646i	−0.127971	−	0.127971i	0.640220	−	0.768192i	$-0.278843\pi$
$53$	−0.931646	−	0.931646i	−0.127971	−	0.127971i	−0.768192	+	0.640220i	$0.778843\pi$
$54$	0.0909462	+	1.41129i	0.0123762	+	0.192052i
$55$	−2.42885	+	12.1594i	−0.327506	+	1.63957i
$56$	2.51061	−	3.73077i	0.335495	−	0.498545i
$57$	6.98744			0.925509
$58$	−0.569270	−	8.83382i	−0.0747488	−	1.15994i
$59$	1.14326	−	1.14326i	0.148840	−	0.148840i	−0.628760	−	0.777600i	$-0.716437\pi$
$59$	1.14326	−	1.14326i	0.148840	−	0.148840i	0.777600	+	0.628760i	$0.216437\pi$
$60$	−4.46166	−	0.305880i	−0.575998	−	0.0394889i
$61$	2.67458	+	2.67458i	0.342445	+	0.342445i	0.857286	−	0.514841i	$-0.172149\pi$
$61$	2.67458	+	2.67458i	0.342445	+	0.342445i	−0.514841	+	0.857286i	$0.672149\pi$
$62$	1.59751	+	1.40408i	0.202884	+	0.178318i
$63$		−	1.58988i		−	0.200306i
$64$	−3.01277	−	7.41102i	−0.376596	−	0.926378i
$65$	−1.92308	+	9.62737i	−0.238529	+	1.19413i
$66$	−5.17717	+	5.89038i	−0.637265	+	0.725056i
$67$	−5.43194	+	5.43194i	−0.663617	+	0.663617i	−0.956231	−	0.292614i	$-0.905475\pi$
$67$	−5.43194	+	5.43194i	−0.663617	+	0.663617i	0.292614	+	0.956231i	$0.405475\pi$
$68$	2.94239	−	0.380808i	0.356817	−	0.0461798i
$69$	−4.68044	+	4.68044i	−0.563459	+	0.563459i
$70$	4.98338	+	0.665728i	0.595628	+	0.0795697i
$71$			2.26233i			0.268489i	0.990948	+	0.134245i	$0.0428608\pi$
$71$			2.26233i			0.268489i	−0.990948	+	0.134245i	$0.957139\pi$
$72$	−2.34657	−	1.57912i	−0.276546	−	0.186101i
$73$	−5.27105			−0.616930			−0.308465	−	0.951236i	$-0.599815\pi$
$73$	−5.27105			−0.616930			−0.308465	+	0.951236i	$0.599815\pi$
$74$	0.276233	+	4.28653i	0.0321115	+	0.498299i
$75$	−1.90596	−	4.62248i	−0.220081	−	0.533758i
$76$	−8.53167	+	11.0683i	−0.978650	+	1.26962i
$77$	6.23407	−	6.23407i	0.710438	−	0.710438i
$78$	−4.09911	+	4.66381i	−0.464133	+	0.528073i
$79$	−6.52058			−0.733622			−0.366811	−	0.930295i	$-0.619550\pi$
$79$	−6.52058			−0.733622			−0.366811	+	0.930295i	$0.619550\pi$
$80$	5.93222	−	6.69394i	0.663242	−	0.748405i
$81$	−1.00000			−0.111111
$82$	−6.39419	+	7.27507i	−0.706121	+	0.803397i
$83$	−0.973359	+	0.973359i	−0.106840	+	0.106840i	−0.758506	−	0.651666i	$-0.774070\pi$
$83$	−0.973359	+	0.973359i	−0.106840	+	0.106840i	0.651666	+	0.758506i	$0.274070\pi$
$84$	2.51843	+	1.94125i	0.274783	+	0.211807i
$85$	1.84067	+	2.75957i	0.199649	+	0.299318i
$86$	−0.0414737	−	0.643581i	−0.00447223	−	0.0693992i
$87$	6.25941			0.671079
$88$	−3.00923	−	15.3930i	−0.320786	−	1.64090i
$89$			6.83613i			0.724629i	0.932056	+	0.362314i	$0.118013\pi$
$89$			6.83613i			0.724629i	−0.932056	+	0.362314i	$0.881987\pi$
$90$	0.418728	−	3.13443i	0.0441378	−	0.330398i
$91$	4.93593	−	4.93593i	0.517426	−	0.517426i
$92$	−1.69915	−	13.1288i	−0.177149	−	1.36877i
$93$	−1.06342	+	1.06342i	−0.110272	+	0.110272i
$94$	12.4201	−	14.1311i	1.28103	−	1.45751i
$95$	−15.3217	−	3.06053i	−1.57197	−	0.314004i
$96$	5.36654	−	1.78893i	0.547720	−	0.182582i
$97$		−	15.8228i		−	1.60656i	−0.595599	−	0.803282i	$-0.703085\pi$
$97$		−	15.8228i		−	1.60656i	0.595599	−	0.803282i	$-0.296915\pi$
$98$	4.75062	+	4.17541i	0.479885	+	0.421780i
$99$	−3.92109	−	3.92109i	−0.394084	−	0.394084i
$100$	9.64933	+	2.62495i	0.964933	+	0.262495i
$101$	2.18050	−	2.18050i	0.216968	−	0.216968i	−0.590251	−	0.807220i	$-0.700971\pi$
$101$	2.18050	−	2.18050i	0.216968	−	0.216968i	0.807220	+	0.590251i	$0.200971\pi$
$102$	0.134915	+	2.09359i	0.0133586	+	0.207296i
$103$	8.09580			0.797703			0.398851	−	0.917016i	$-0.369409\pi$
$103$	8.09580			0.797703			0.398851	+	0.917016i	$0.369409\pi$
$104$	−2.38261	−	12.1876i	−0.233634	−	1.19510i
$105$	−0.696376	+	3.48622i	−0.0679594	+	0.340220i
$106$	0.119826	+	1.85944i	0.0116385	+	0.180604i
$107$	9.00752	+	9.00752i	0.870790	+	0.870790i	0.992559	−	0.121768i	$-0.0388565\pi$
$107$	9.00752	+	9.00752i	0.870790	+	0.870790i	−0.121768	+	0.992559i	$0.538856\pi$
$108$	1.22100	−	1.58403i	0.117491	−	0.152424i
$109$	−9.91170	−	9.91170i	−0.949369	−	0.949369i	0.0494097	−	0.998779i	$-0.484266\pi$
$109$	−9.91170	−	9.91170i	−0.949369	−	0.949369i	−0.998779	+	0.0494097i	$0.984266\pi$
$110$	13.9323	−	10.6485i	1.32839	−	1.01530i
$111$	−3.03732			−0.288290
$112$	−6.15000	+	1.61900i	−0.581120	+	0.152981i
$113$			10.4611i			0.984094i	0.870569	+	0.492047i	$0.163751\pi$
$113$			10.4611i			0.984094i	−0.870569	+	0.492047i	$0.836249\pi$
$114$	−7.42233	−	6.52363i	−0.695165	−	0.610993i
$115$	12.3131	−	8.21298i	1.14820	−	0.765865i
$116$	−7.64274	+	9.91511i	−0.709611	+	0.920595i
$117$	−3.10459	−	3.10459i	−0.287019	−	0.287019i
$118$	−2.28179	+	0.147043i	−0.210056	+	0.0135364i
$119$		−	2.35853i		−	0.216206i
$120$	4.45378	+	4.49042i	0.406572	+	0.409918i
$121$		−	19.7498i		−	1.79544i
$122$	−0.343998	−	5.33809i	−0.0311441	−	0.483288i
$123$	−4.84284	−	4.84284i	−0.436664	−	0.436664i
$124$	−0.386057	−	2.98294i	−0.0346689	−	0.267876i
$125$	2.15462	+	10.9708i	0.192716	+	0.981255i
$126$	−1.48435	+	1.68884i	−0.132236	+	0.150453i
$127$			1.88264i			0.167057i	0.996505	+	0.0835284i	$0.0266189\pi$
$127$			1.88264i			0.167057i	−0.996505	+	0.0835284i	$0.973381\pi$
$128$	−3.71881	+	10.6851i	−0.328700	+	0.944435i
$129$	0.456025			0.0401507
$130$	11.0311	−	8.43114i	0.967491	−	0.739460i
$131$	0.701725	+	0.701725i	0.0613100	+	0.0613100i	0.737097	−	0.675787i	$-0.236196\pi$
$131$	0.701725	+	0.701725i	0.0613100	+	0.0613100i	−0.675787	+	0.737097i	$0.736196\pi$
$132$	10.9988	−	1.42348i	0.957321	−	0.123898i
$133$	7.85540	+	7.85540i	0.681150	+	0.681150i
$134$	10.8414	−	0.698642i	0.936554	−	0.0603535i
$135$	2.19275	+	0.438005i	0.188722	+	0.0376974i
$136$	−3.48105	−	2.34257i	−0.298497	−	0.200873i
$137$	−16.7042			−1.42714			−0.713568	−	0.700586i	$-0.752922\pi$
$137$	−16.7042			−1.42714			−0.713568	+	0.700586i	$0.752922\pi$
$138$	9.34151	−	0.601986i	0.795202	−	0.0512445i
$139$	−5.03646	+	5.03646i	−0.427187	+	0.427187i	−0.887669	−	0.460482i	$-0.847677\pi$
$139$	−5.03646	+	5.03646i	−0.427187	+	0.427187i	0.460482	+	0.887669i	$0.347677\pi$
$140$	−4.67200	−	5.35975i	−0.394856	−	0.452982i
$141$	9.40672	+	9.40672i	0.792189	+	0.792189i
$142$	2.11216	−	2.40313i	0.177249	−	0.201667i
$143$		−	24.3467i		−	2.03597i
$144$	1.01832	+	3.86821i	0.0848597	+	0.322351i
$145$	−13.7253	−	2.74165i	−1.13983	−	0.227682i
$146$	5.59912	+	4.92117i	0.463386	+	0.407279i
$147$	−3.16237	+	3.16237i	−0.260828	+	0.260828i
$148$	3.70857	−	4.81122i	0.304843	−	0.395480i
$149$	−12.2283	+	12.2283i	−1.00178	+	1.00178i	−0.00178156	+	0.999998i	$0.500567\pi$
$149$	−12.2283	+	12.2283i	−1.00178	+	1.00178i	−0.999998	+	0.00178156i	$0.999433\pi$
$150$	−2.29106	+	6.68962i	−0.187064	+	0.546205i
$151$		−	0.567736i		−	0.0462017i	−0.999733	−	0.0231008i	$-0.992646\pi$
$151$		−	0.567736i		−	0.0462017i	0.999733	−	0.0231008i	$-0.00735388\pi$
$152$	19.3963	−	3.79186i	1.57325	−	0.307561i
$153$	−1.48346			−0.119931
$154$	−12.4423	+	0.801810i	−1.00263	+	0.0646117i
$155$	2.79761	−	1.86604i	0.224709	−	0.149884i
$156$	8.70847	−	1.12706i	0.697235	−	0.0902373i
$157$	−8.06109	+	8.06109i	−0.643345	+	0.643345i	−0.951376	−	0.308031i	$-0.900330\pi$
$157$	−8.06109	+	8.06109i	−0.643345	+	0.643345i	0.308031	+	0.951376i	$0.400330\pi$
$158$	6.92641	+	6.08775i	0.551036	+	0.484315i
$159$	−1.31755			−0.104488
$160$	−12.5510	+	1.57212i	−0.992246	+	0.124287i
$161$	−10.5237			−0.829381
$162$	1.06224	+	0.933621i	0.0834574	+	0.0733522i
$163$	0.0969036	−	0.0969036i	0.00759008	−	0.00759008i	−0.703302	−	0.710892i	$-0.748292\pi$
$163$	0.0969036	−	0.0969036i	0.00759008	−	0.00759008i	0.710892	+	0.703302i	$0.248292\pi$
$164$	13.5843	−	1.75811i	1.06076	−	0.137285i
$165$	6.88051	+	10.3154i	0.535647	+	0.803054i
$166$	1.94269	−	0.125191i	0.150782	−	0.00971670i
$167$	−14.9619			−1.15779			−0.578894	−	0.815403i	$-0.696516\pi$
$167$	−14.9619			−1.15779			−0.578894	+	0.815403i	$0.696516\pi$
$168$	−0.862779	−	4.41332i	−0.0665649	−	0.340495i
$169$		−	6.27691i		−	0.482839i
$170$	0.621167	−	4.64982i	0.0476413	−	0.356625i
$171$	4.94087	−	4.94087i	0.377838	−	0.377838i
$172$	−0.556806	+	0.722358i	−0.0424561	+	0.0550793i
$173$	13.1447	−	13.1447i	0.999374	−	0.999374i	−0.000626029	−	1.00000i	$-0.500199\pi$
$173$	13.1447	−	13.1447i	0.999374	−	0.999374i	1.00000		0.000626029i	$0.000199271\pi$
$174$	−6.64899	−	5.84392i	−0.504059	−	0.443026i
$175$	3.05396	−	7.33938i	0.230858	−	0.554805i
$176$	−11.1747	+	19.1605i	−0.842323	+	1.44428i
$177$		−	1.61682i		−	0.121527i
$178$	6.38236	−	7.26161i	0.478378	−	0.544280i
$179$	3.56192	+	3.56192i	0.266230	+	0.266230i	0.827579	−	0.561349i	$-0.189717\pi$
$179$	3.56192	+	3.56192i	0.266230	+	0.266230i	−0.561349	+	0.827579i	$0.689717\pi$
$180$	−3.37116	+	2.93858i	−0.251272	+	0.219029i
$181$	5.89499	−	5.89499i	0.438171	−	0.438171i	−0.453225	−	0.891396i	$-0.649727\pi$
$181$	5.89499	−	5.89499i	0.438171	−	0.438171i	0.891396	+	0.453225i	$0.149727\pi$
$182$	−9.85142	+	0.634846i	−0.730236	+	0.0470579i
$183$	3.78243			0.279605
$184$	−10.4524	+	15.5323i	−0.770562	+	1.14505i
$185$	6.66009	+	1.33036i	0.489660	+	0.0978102i
$186$	2.12244	−	0.136775i	0.155625	−	0.0100288i
$187$	−5.81679	−	5.81679i	−0.425366	−	0.425366i
$188$	−26.3862	+	3.41494i	−1.92441	+	0.249060i
$189$	−1.12422	−	1.12422i	−0.0817748	−	0.0817748i
$190$	13.4179	+	17.5557i	0.973440	+	1.27362i
$191$	−0.695196			−0.0503026			−0.0251513	−	0.999684i	$-0.508007\pi$
$191$	−0.695196			−0.0503026			−0.0251513	+	0.999684i	$0.508007\pi$
$192$	−7.37073	−	3.11004i	−0.531937	−	0.224448i
$193$			23.8401i			1.71605i	0.513611	+	0.858023i	$0.328307\pi$
$193$			23.8401i			1.71605i	−0.513611	+	0.858023i	$0.671693\pi$
$194$	−14.7725	+	16.8076i	−1.06061	+	1.20672i
$195$	5.44776	+	8.16740i	0.390122	+	0.584880i
$196$	−1.14804	−	8.87056i	−0.0820031	−	0.633612i
$197$	−3.90642	−	3.90642i	−0.278321	−	0.278321i	0.554118	−	0.832438i	$-0.313056\pi$
$197$	−3.90642	−	3.90642i	−0.278321	−	0.278321i	−0.832438	+	0.554118i	$0.813056\pi$
$198$	0.504320	+	7.82594i	0.0358405	+	0.556165i
$199$		−	3.84627i		−	0.272655i	−0.990664	−	0.136328i	$-0.956470\pi$
$199$		−	3.84627i		−	0.272655i	0.990664	−	0.136328i	$-0.0435300\pi$
$200$	−7.79919	−	11.7971i	−0.551486	−	0.834184i
$201$			7.68192i			0.541841i
$202$	−4.35198	+	0.280451i	−0.306204	+	0.0197324i
$203$	7.03694	+	7.03694i	0.493896	+	0.493896i
$204$	1.81131	−	2.34985i	0.126817	−	0.164523i
$205$	8.49795	+	12.7403i	0.593523	+	0.889823i
$206$	−8.59967	−	7.55841i	−0.599167	−	0.526619i
$207$			6.61914i			0.460062i
$208$	−8.84773	+	15.1706i	−0.613480	+	1.05189i
$209$	38.7471			2.68020
$210$	3.99452	−	3.05304i	0.275648	−	0.210680i
$211$	8.77616	+	8.77616i	0.604176	+	0.604176i	0.941418	−	0.337242i	$-0.109494\pi$
$211$	8.77616	+	8.77616i	0.604176	+	0.604176i	−0.337242	+	0.941418i	$0.609494\pi$
$212$	1.60873	−	2.08704i	0.110488	−	0.143338i
$213$	1.59971	+	1.59971i	0.109610	+	0.109610i
$214$	−1.15852	−	17.9778i	−0.0791951	−	1.22893i
$215$	−0.999948	−	0.199741i	−0.0681959	−	0.0136222i
$216$	−2.77588	+	0.542668i	−0.188875	+	0.0369239i
$217$	−2.39104			−0.162314
$218$	1.27482	+	19.7824i	0.0863415	+	1.33983i
$219$	−3.72720	+	3.72720i	−0.251861	+	0.251861i
$220$	−24.7411	−	1.69618i	−1.66804	−	0.114357i
$221$	−4.60554	−	4.60554i	−0.309802	−	0.309802i
$222$	3.22636	+	2.83571i	0.216539	+	0.190320i
$223$			13.4599i			0.901341i	0.892690	+	0.450671i	$0.148815\pi$
$223$			13.4599i			0.901341i	−0.892690	+	0.450671i	$0.851185\pi$
$224$	8.04430	+	4.02200i	0.537483	+	0.268731i
$225$	−4.61630	−	1.92087i	−0.307754	−	0.128058i
$226$	9.76667	−	11.1121i	0.649669	−	0.739169i
$227$	16.2029	−	16.2029i	1.07542	−	1.07542i	0.0785084	−	0.996913i	$-0.474984\pi$
$227$	16.2029	−	16.2029i	1.07542	−	1.07542i	0.996913	−	0.0785084i	$-0.0250157\pi$
$228$	1.79369	+	13.8593i	0.118790	+	0.917854i
$229$	1.34898	−	1.34898i	0.0891433	−	0.0891433i	−0.661129	−	0.750272i	$-0.729922\pi$
$229$	1.34898	−	1.34898i	0.0891433	−	0.0891433i	0.750272	+	0.661129i	$0.229922\pi$
$230$	−20.7473	−	2.77162i	−1.36803	−	0.182755i
$231$		−	8.81631i		−	0.580070i
$232$	17.3754	−	3.39678i	1.14075	−	0.223010i
$233$	−13.0887			−0.857470			−0.428735	−	0.903430i	$-0.641041\pi$
$233$	−13.0887			−0.857470			−0.428735	+	0.903430i	$0.641041\pi$
$234$	0.399304	+	6.19632i	0.0261033	+	0.405066i
$235$	−16.5064	−	24.7468i	−1.07676	−	1.61430i
$236$	2.56109	+	1.97413i	0.166713	+	0.128505i
$237$	−4.61074	+	4.61074i	−0.299500	+	0.299500i
$238$	−2.20198	+	2.50532i	−0.142733	+	0.162396i
$239$	11.0340			0.713730			0.356865	−	0.934156i	$-0.383846\pi$
$239$	11.0340			0.713730			0.356865	+	0.934156i	$0.383846\pi$
$240$	−0.538620	−	8.92804i	−0.0347678	−	0.576302i
$241$	8.31401			0.535553			0.267776	−	0.963481i	$-0.413711\pi$
$241$	8.31401			0.535553			0.267776	+	0.963481i	$0.413711\pi$
$242$	−18.4389	+	20.9791i	−1.18530	+	1.34858i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−4.61835	+	5.99149i	−0.295659	+	0.383566i
$245$	8.31943	−	5.54916i	0.531509	−	0.354523i
$246$	0.622873	+	9.66563i	0.0397130	+	0.616258i
$247$	30.6787			1.95204
$248$	−2.37485	+	3.52902i	−0.150803	+	0.224093i
$249$			1.37654i			0.0872345i
$250$	7.95381	−	13.6652i	0.503043	−	0.864261i
$251$	15.0055	−	15.0055i	0.947138	−	0.947138i	−0.0515329	−	0.998671i	$-0.516411\pi$
$251$	15.0055	−	15.0055i	0.947138	−	0.947138i	0.998671	+	0.0515329i	$0.0164107\pi$
$252$	3.15347	−	0.408127i	0.198650	−	0.0257096i
$253$	−25.9542	+	25.9542i	−1.63173	+	1.63173i
$254$	1.75767	−	1.99981i	0.110286	−	0.125479i
$255$	3.25286	+	0.649764i	0.203702	+	0.0406898i
$256$	13.9261	−	7.87812i	0.870379	−	0.492382i
$257$			14.3773i			0.896831i	0.893825	+	0.448415i	$0.148011\pi$
$257$			14.3773i			0.896831i	−0.893825	+	0.448415i	$0.851989\pi$
$258$	−0.484407	−	0.425754i	−0.0301579	−	0.0265063i
$259$	−3.41461	−	3.41461i	−0.212174	−	0.212174i
$260$	−19.5891	−	1.34298i	−1.21487	−	0.0832881i
$261$	4.42607	−	4.42607i	0.273967	−	0.273967i
$262$	−0.0902540	−	1.40054i	−0.00557591	−	0.0865259i
$263$	−4.94045			−0.304641			−0.152320	−	0.988331i	$-0.548675\pi$
$263$	−4.94045			−0.304641			−0.152320	+	0.988331i	$0.548675\pi$
$264$	−13.0123	−	8.75662i	−0.800853	−	0.538933i
$265$	2.88905	+	0.577092i	0.177473	+	0.0354505i
$266$	−1.01034	−	15.6783i	−0.0619480	−	0.961297i
$267$	4.83388	+	4.83388i	0.295828	+	0.295828i
$268$	−12.1684	−	9.37963i	−0.743304	−	0.572952i
$269$	−11.5951	−	11.5951i	−0.706967	−	0.706967i	0.258929	−	0.965896i	$-0.416630\pi$
$269$	−11.5951	−	11.5951i	−0.706967	−	0.706967i	−0.965896	+	0.258929i	$0.916630\pi$
$270$	−1.92029	−	2.51246i	−0.116865	−	0.152904i
$271$	−3.40933			−0.207102			−0.103551	−	0.994624i	$-0.533021\pi$
$271$	−3.40933			−0.207102			−0.103551	+	0.994624i	$0.533021\pi$
$272$	1.51063	+	5.73834i	0.0915957	+	0.347938i
$273$		−	6.98046i		−	0.422476i
$274$	17.7438	+	15.5954i	1.07195	+	0.942152i
$275$	−10.5690	−	25.6328i	−0.637337	−	1.54572i
$276$	−10.4849	−	8.08198i	−0.631119	−	0.486478i
$277$	−11.2957	−	11.2957i	−0.678690	−	0.678690i	0.281014	−	0.959704i	$-0.409329\pi$
$277$	−11.2957	−	11.2957i	−0.678690	−	0.678690i	−0.959704	+	0.281014i	$0.909329\pi$
$278$	10.0521	−	0.647777i	0.602884	−	0.0388511i
$279$			1.50391i			0.0900366i
$280$	−0.0411978	+	10.0552i	−0.00246204	+	0.600914i
$281$			4.72775i			0.282034i	0.990007	+	0.141017i	$0.0450372\pi$
$281$			4.72775i			0.282034i	−0.990007	+	0.141017i	$0.954963\pi$
$282$	−1.20987	−	18.7745i	−0.0720466	−	1.11801i
$283$	6.51882	+	6.51882i	0.387504	+	0.387504i	0.873796	−	0.486292i	$-0.161651\pi$
$283$	6.51882	+	6.51882i	0.387504	+	0.387504i	−0.486292	+	0.873796i	$0.661651\pi$
$284$	−4.48724	+	0.580746i	−0.266268	+	0.0344609i
$285$	−12.9982	+	8.66996i	−0.769948	+	0.513564i
$286$	−22.7306	+	25.8620i	−1.34409	+	1.52925i
$287$		−	10.8888i		−	0.642746i
$288$	2.52975	−	5.05968i	0.149067	−	0.298145i
$289$	14.7993			0.870549
$290$	12.0199	+	15.7265i	0.705833	+	0.923494i
$291$	−11.1884	−	11.1884i	−0.655877	−	0.655877i
$292$	−1.35309	−	10.4549i	−0.0791837	−	0.611827i
$293$	2.60652	+	2.60652i	0.152274	+	0.152274i	0.779133	−	0.626859i	$-0.215660\pi$
$293$	2.60652	+	2.60652i	0.152274	+	0.152274i	−0.626859	+	0.779133i	$0.715660\pi$
$294$	6.31166	−	0.406736i	0.368103	−	0.0237213i
$295$	−0.708173	+	3.54527i	−0.0412314	+	0.206414i
$296$	−8.43125	+	1.64826i	−0.490056	+	0.0958032i
$297$	−5.54525			−0.321768
$298$	24.4059	−	1.57277i	1.41380	−	0.0911081i
$299$	−20.5497	+	20.5497i	−1.18842	+	1.18842i
$300$	8.67923	−	4.96699i	0.501095	−	0.286769i
$301$	0.512671	+	0.512671i	0.0295499	+	0.0295499i
$302$	−0.530050	+	0.603071i	−0.0305010	+	0.0347028i
$303$		−	3.08370i		−	0.177154i
$304$	−24.1437	−	14.0809i	−1.38473	−	0.807597i
$305$	−8.29392	−	1.65672i	−0.474909	−	0.0948636i
$306$	1.57579	+	1.38499i	0.0900820	+	0.0791748i
$307$	−9.27735	+	9.27735i	−0.529486	+	0.529486i	−0.920419	−	0.390933i	$-0.872152\pi$
$307$	−9.27735	+	9.27735i	−0.529486	+	0.529486i	0.390933	+	0.920419i	$0.372152\pi$
$308$	13.9653	+	10.7647i	0.795747	+	0.613376i
$309$	5.72459	−	5.72459i	0.325661	−	0.325661i
$310$	−4.71390	−	0.629728i	−0.267731	−	0.0357661i
$311$			8.87398i			0.503197i	0.967832	+	0.251599i	$0.0809563\pi$
$311$			8.87398i			0.503197i	−0.967832	+	0.251599i	$0.919044\pi$
$312$	−10.3027	−	6.93320i	−0.583277	−	0.392515i
$313$	25.6160			1.44790			0.723952	−	0.689850i	$-0.242324\pi$
$313$	25.6160			1.44790			0.723952	+	0.689850i	$0.242324\pi$
$314$	16.0888	−	1.03680i	0.907944	−	0.0585098i
$315$	1.97271	+	2.95754i	0.111150	+	0.166638i
$316$	−1.67385	−	12.9333i	−0.0941613	−	0.727554i
$317$	19.5425	−	19.5425i	1.09762	−	1.09762i	0.102929	−	0.994689i	$-0.467179\pi$
$317$	19.5425	−	19.5425i	1.09762	−	1.09762i	0.994689	−	0.102929i	$-0.0328215\pi$
$318$	1.39955	+	1.23009i	0.0784828	+	0.0689800i
$319$	34.7100			1.94339
$320$	14.8000	+	10.0479i	0.827343	+	0.561697i
$321$	12.7386			0.710997
$322$	11.1786	+	9.82512i	0.622962	+	0.547532i
$323$	7.32960	−	7.32960i	0.407830	−	0.407830i
$324$	−0.256702	−	1.98346i	−0.0142612	−	0.110192i
$325$	−8.36821	−	20.2952i	−0.464185	−	1.12578i
$326$	−0.193406	+	0.0124635i	−0.0107118	+	0.000690289i
$327$	−14.0173			−0.775156
$328$	−16.0712	−	10.8151i	−0.887384	−	0.597163i
$329$			21.1504i			1.16606i
$330$	2.32195	−	17.3812i	0.127819	−	0.956805i
$331$	−17.9546	+	17.9546i	−0.986875	+	0.986875i	−0.999915	−	0.0130395i	$-0.995849\pi$
$331$	−17.9546	+	17.9546i	−0.986875	+	0.986875i	0.0130395	+	0.999915i	$0.495849\pi$
$332$	−2.18048	−	1.68075i	−0.119669	−	0.0922433i
$333$	−2.14771	+	2.14771i	−0.117694	+	0.117694i
$334$	15.8931	+	13.9688i	0.869634	+	0.764337i
$335$	3.36472	−	16.8445i	0.183834	−	0.920315i
$336$	−3.20390	+	5.49351i	−0.174787	+	0.299696i
$337$		−	30.1385i		−	1.64175i	−0.571108	−	0.820875i	$-0.693486\pi$
$337$		−	30.1385i		−	1.64175i	0.571108	−	0.820875i	$-0.306514\pi$
$338$	−5.86026	+	6.66758i	−0.318756	+	0.362668i
$339$	7.39709	+	7.39709i	0.401755	+	0.401755i
$340$	−5.00099	+	4.35928i	−0.271217	+	0.236415i
$341$	−5.89695	+	5.89695i	−0.319338	+	0.319338i
$342$	−9.86128	+	0.635482i	−0.533237	+	0.0343629i
$343$	−18.2396			−0.984844
$344$	1.26587	−	0.247470i	0.0682511	−	0.0133427i
$345$	2.89922	−	14.5141i	0.156089	−	0.781414i
$346$	−26.2350	+	1.69064i	−1.41040	+	0.0908893i
$347$	17.1738	+	17.1738i	0.921936	+	0.921936i	0.997166	−	0.0752299i	$-0.0239691\pi$
$347$	17.1738	+	17.1738i	0.921936	+	0.921936i	−0.0752299	+	0.997166i	$0.523969\pi$
$348$	1.60681	+	12.4153i	0.0861338	+	0.665529i
$349$	−11.7155	−	11.7155i	−0.627115	−	0.627115i	0.320226	−	0.947341i	$-0.396241\pi$
$349$	−11.7155	−	11.7155i	−0.627115	−	0.627115i	−0.947341	+	0.320226i	$0.896241\pi$
$350$	−10.0962	+	4.94494i	−0.539667	+	0.264318i
$351$	−4.39055			−0.234350
$352$	29.7588	−	9.92010i	1.58615	−	0.528743i
$353$			2.34745i			0.124942i	0.998047	+	0.0624712i	$0.0198982\pi$
$353$			2.34745i			0.124942i	−0.998047	+	0.0624712i	$0.980102\pi$
$354$	−1.50949	+	1.71745i	−0.0802287	+	0.0912812i
$355$	−2.80708	−	4.20844i	−0.148984	−	0.223361i
$356$	−13.5592	+	1.75485i	−0.718635	+	0.0930070i
$357$	−1.66773	−	1.66773i	−0.0882659	−	0.0882659i
$358$	−0.458124	−	7.10909i	−0.0242126	−	0.375727i
$359$		−	28.6304i		−	1.51106i	−0.655116	−	0.755529i	$-0.727380\pi$
$359$		−	28.6304i		−	1.51106i	0.655116	−	0.755529i	$-0.272620\pi$
$360$	6.32450	+	0.0259124i	0.333331	+	0.00136571i
$361$			29.8243i			1.56970i
$362$	−11.7656	+	0.758199i	−0.618385	+	0.0398500i
$363$	−13.9652	−	13.9652i	−0.732986	−	0.732986i
$364$	11.0573	+	8.52314i	0.579558	+	0.446734i
$365$	9.80534	−	6.54028i	0.513235	−	0.342334i
$366$	−4.01784	−	3.53136i	−0.210016	−	0.184587i
$367$			12.5964i			0.657527i	0.944412	+	0.328764i	$0.106632\pi$
$367$			12.5964i			0.657527i	−0.944412	+	0.328764i	$0.893368\pi$
$368$	25.6042	−	6.74038i	1.33471	−	0.351367i
$369$	−6.84881			−0.356535
$370$	−5.83255	−	7.63117i	−0.303220	−	0.396725i
$371$	−1.48121	−	1.48121i	−0.0769005	−	0.0769005i
$372$	−2.38224	−	1.83627i	−0.123513	−	0.0952063i
$373$	10.5946	+	10.5946i	0.548568	+	0.548568i	0.926027	−	0.377458i	$-0.123202\pi$
$373$	10.5946	+	10.5946i	0.548568	+	0.548568i	−0.377458	+	0.926027i	$0.623202\pi$
$374$	0.748140	+	11.6095i	0.0386854	+	0.600313i
$375$	9.28105	+	6.23395i	0.479271	+	0.321920i
$376$	31.2167	+	21.0072i	1.60988	+	1.08336i
$377$	27.4822			1.41541
$378$	0.144594	+	2.24378i	0.00743711	+	0.115408i
$379$	−25.8712	+	25.8712i	−1.32891	+	1.32891i	−0.422593	+	0.906320i	$0.638880\pi$
$379$	−25.8712	+	25.8712i	−1.32891	+	1.32891i	−0.906320	+	0.422593i	$0.861120\pi$
$380$	2.13732	−	31.1756i	0.109642	−	1.59928i
$381$	1.33122	+	1.33122i	0.0682007	+	0.0682007i
$382$	0.738464	+	0.649050i	0.0377831	+	0.0332083i
$383$			4.25894i			0.217622i	0.994062	+	0.108811i	$0.0347043\pi$
$383$			4.25894i			0.217622i	−0.994062	+	0.108811i	$0.965296\pi$
$384$	4.92588	+	10.1851i	0.251373	+	0.519755i
$385$	−3.86158	+	19.3320i	−0.196805	+	0.985247i
$386$	22.2576	−	25.3239i	1.13288	−	1.28895i
$387$	0.322458	−	0.322458i	0.0163915	−	0.0163915i
$388$	31.3839	−	4.06176i	1.59328	−	0.206204i
$389$	22.1209	−	22.1209i	1.12158	−	1.12158i	0.130071	−	0.991505i	$-0.458480\pi$
$389$	22.1209	−	22.1209i	1.12158	−	1.12158i	0.991505	−	0.130071i	$-0.0415205\pi$
$390$	1.83844	−	13.7619i	0.0930932	−	0.696860i
$391$			9.81926i			0.496581i
$392$	−7.06225	+	10.4945i	−0.356698	+	0.530052i
$393$	0.992388			0.0500594
$394$	0.502433	+	7.79666i	0.0253122	+	0.392790i
$395$	12.1297	−	8.09068i	0.610313	−	0.407086i
$396$	6.77076	−	8.78386i	0.340243	−	0.441406i
$397$	12.9968	−	12.9968i	0.652290	−	0.652290i	−0.301254	−	0.953544i	$-0.597405\pi$
$397$	12.9968	−	12.9968i	0.652290	−	0.652290i	0.953544	+	0.301254i	$0.0974053\pi$
$398$	−3.59096	+	4.08566i	−0.179999	+	0.204796i
$399$	11.1092			0.556156
$400$	−2.72947	+	19.8129i	−0.136473	+	0.990644i
$401$	−35.3598			−1.76578			−0.882892	−	0.469577i	$-0.844406\pi$
$401$	−35.3598			−1.76578			−0.882892	+	0.469577i	$0.844406\pi$
$402$	7.17201	−	8.16004i	0.357707	−	0.406986i
$403$	−4.66901	+	4.66901i	−0.232580	+	0.232580i
$404$	4.88468	+	3.76520i	0.243022	+	0.187326i
$405$	1.86022	−	1.24079i	0.0924353	−	0.0616555i
$406$	−0.905072	−	14.0447i	−0.0449180	−	0.697029i
$407$	−16.8427			−0.834863
$408$	−4.11792	+	0.805029i	−0.203867	+	0.0398549i
$409$			27.3933i			1.35451i	0.735747	+	0.677256i	$0.236831\pi$
$409$			27.3933i			1.35451i	−0.735747	+	0.677256i	$0.763169\pi$
$410$	2.86779	−	21.4671i	0.141630	−	1.06019i
$411$	−11.8117	+	11.8117i	−0.582626	+	0.582626i
$412$	2.07821	+	16.0577i	0.102386	+	0.791105i
$413$	1.81765	−	1.81765i	0.0894408	−	0.0894408i
$414$	6.17977	−	7.03111i	0.303719	−	0.345560i
$415$	0.602930	−	3.01840i	0.0295967	−	0.148168i
$416$	23.5620	−	7.85440i	1.15522	−	0.385094i
$417$			7.12264i			0.348797i
$418$	−41.1587	−	36.1752i	−2.01314	−	1.76938i
$419$	3.71334	+	3.71334i	0.181409	+	0.181409i	0.791969	−	0.610561i	$-0.209056\pi$
$419$	3.71334	+	3.71334i	0.181409	+	0.181409i	−0.610561	+	0.791969i	$0.709056\pi$
$420$	−7.09352	−	0.486313i	−0.346128	−	0.0237296i
$421$	−10.7755	+	10.7755i	−0.525167	+	0.525167i	−0.919127	−	0.393960i	$-0.871105\pi$
$421$	−10.7755	+	10.7755i	−0.525167	+	0.525167i	0.393960	+	0.919127i	$0.371105\pi$
$422$	−1.12877	−	17.5160i	−0.0549475	−	0.852665i
$423$	13.3031			0.646820
$424$	−3.65735	+	0.714991i	−0.177617	+	0.0347230i
$425$	−6.84812	−	2.84954i	−0.332182	−	0.138223i
$426$	−0.205750	−	3.19280i	−0.00996864	−	0.154691i
$427$	4.25227	+	4.25227i	0.205782	+	0.205782i
$428$	−15.5538	+	20.1783i	−0.751821	+	0.975355i
$429$	−17.2157	−	17.2157i	−0.831183	−	0.831183i
$430$	0.875701	+	1.14575i	0.0422301	+	0.0552528i
$431$	30.0581			1.44785			0.723924	−	0.689880i	$-0.242337\pi$
$431$	30.0581			1.44785			0.723924	+	0.689880i	$0.242337\pi$
$432$	3.45529	+	2.01518i	0.166243	+	0.0969553i
$433$		−	20.1636i		−	0.968999i	−0.874791	−	0.484500i	$-0.839002\pi$
$433$		−	20.1636i		−	0.968999i	0.874791	−	0.484500i	$-0.160998\pi$
$434$	2.53985	+	2.23232i	0.121917	+	0.107155i
$435$	−11.6439	+	7.76663i	−0.558283	+	0.372381i
$436$	17.1151	−	22.2038i	0.819664	−	1.06337i
$437$	−32.7043	−	32.7043i	−1.56446	−	1.56446i
$438$	7.43896	−	0.479382i	0.355447	−	0.0229058i
$439$		−	28.0789i		−	1.34013i	−0.742302	−	0.670065i	$-0.766266\pi$
$439$		−	28.0789i		−	1.34013i	0.742302	−	0.670065i	$-0.233734\pi$
$440$	24.6973	+	24.9005i	1.17740	+	1.18709i
$441$			4.47227i			0.212965i
$442$	0.592353	+	9.19201i	0.0281753	+	0.437219i
$443$	−3.23844	−	3.23844i	−0.153863	−	0.153863i	0.625978	−	0.779841i	$-0.284700\pi$
$443$	−3.23844	−	3.23844i	−0.153863	−	0.153863i	−0.779841	+	0.625978i	$0.784700\pi$
$444$	−0.779688	−	6.02440i	−0.0370024	−	0.285906i
$445$	−8.48222	−	12.7167i	−0.402096	−	0.602831i
$446$	12.5664	−	14.2976i	0.595039	−	0.677012i
$447$			17.2934i			0.817950i
$448$	−4.78994	−	11.7827i	−0.226304	−	0.556678i
$449$	1.06033			0.0500401			0.0250201	−	0.999687i	$-0.492035\pi$
$449$	1.06033			0.0500401			0.0250201	+	0.999687i	$0.492035\pi$
$450$	3.11025	+	6.35030i	0.146619	+	0.299356i
$451$	−26.8548	−	26.8548i	−1.26454	−	1.26454i
$452$	−20.7491	+	2.68538i	−0.975954	+	0.126310i
$453$	−0.401450	−	0.401450i	−0.0188618	−	0.0188618i
$454$	−32.3386	+	2.08397i	−1.51773	+	0.0978056i
$455$	−3.05747	+	15.3064i	−0.143337	+	0.717575i
$456$	11.0340	−	16.3965i	0.516715	−	0.767837i
$457$	−3.95861			−0.185176			−0.0925880	−	0.995705i	$-0.529514\pi$
$457$	−3.95861			−0.185176			−0.0925880	+	0.995705i	$0.529514\pi$
$458$	−2.69238	+	0.173503i	−0.125807	+	0.00810725i
$459$	−1.04897	+	1.04897i	−0.0489616	+	0.0489616i
$460$	19.4509	+	22.3142i	0.906903	+	1.04041i
$461$	−17.2310	−	17.2310i	−0.802526	−	0.802526i	0.180963	−	0.983490i	$-0.442078\pi$
$461$	−17.2310	−	17.2310i	−0.802526	−	0.802526i	−0.983490	+	0.180963i	$0.942078\pi$
$462$	−8.23109	+	9.36502i	−0.382945	+	0.435700i
$463$			14.4839i			0.673122i	0.941662	+	0.336561i	$0.109264\pi$
$463$			14.4839i			0.673122i	−0.941662	+	0.336561i	$0.890736\pi$
$464$	−21.6281	−	12.6138i	−1.00406	−	0.585582i
$465$	0.658719	−	3.29769i	0.0305473	−	0.152927i
$466$	13.9033	+	12.2199i	0.644059	+	0.566076i
$467$	−26.0437	+	26.0437i	−1.20516	+	1.20516i	−0.232585	+	0.972576i	$0.574718\pi$
$467$	−26.0437	+	26.0437i	−1.20516	+	1.20516i	−0.972576	+	0.232585i	$0.925282\pi$
$468$	5.36086	−	6.95477i	0.247806	−	0.321484i
$469$	−8.63615	+	8.63615i	−0.398780	+	0.398780i
$470$	−5.57038	+	41.6977i	−0.256943	+	1.92337i
$471$			11.4001i			0.525289i
$472$	−0.877395	−	4.48809i	−0.0403854	−	0.206581i
$473$	2.52877			0.116273
$474$	9.20240	−	0.593022i	0.422680	−	0.0272384i
$475$	32.2993	−	13.3178i	1.48199	−	0.611062i
$476$	4.67805	−	0.605441i	0.214418	−	0.0277503i
$477$	−0.931646	+	0.931646i	−0.0426572	+	0.0426572i
$478$	−11.7207	−	10.3016i	−0.536094	−	0.471183i
$479$	−18.5284			−0.846586			−0.423293	−	0.905993i	$-0.639126\pi$
$479$	−18.5284			−0.846586			−0.423293	+	0.905993i	$0.639126\pi$
$480$	−7.76327	+	9.98658i	−0.354343	+	0.455823i
$481$	−13.3355			−0.608047
$482$	−8.83147	−	7.76214i	−0.402262	−	0.353556i
$483$	−7.44135	+	7.44135i	−0.338593	+	0.338593i
$484$	39.1730	−	5.06983i	1.78059	−	0.230447i
$485$	19.6328	+	29.4340i	0.891481	+	1.33653i
$486$	1.41129	−	0.0909462i	0.0640172	−	0.00412541i
$487$	4.16579			0.188770			0.0943851	−	0.995536i	$-0.469912\pi$
$487$	4.16579			0.188770			0.0943851	+	0.995536i	$0.469912\pi$
$488$	10.4996	−	2.05261i	0.475293	−	0.0929171i
$489$		−	0.137042i		−	0.00619727i
$490$	−14.0180	−	1.87266i	−0.633270	−	0.0845984i
$491$	−20.2554	+	20.2554i	−0.914115	+	0.914115i	−0.996593	−	0.0824778i	$-0.973717\pi$
$491$	−20.2554	+	20.2554i	−0.914115	+	0.914115i	0.0824778	+	0.996593i	$0.473717\pi$
$492$	8.36240	−	10.8487i	0.377006	−	0.489099i
$493$	6.56591	−	6.56591i	0.295714	−	0.295714i
$494$	−32.5881	−	28.6423i	−1.46621	−	1.28868i
$495$	12.1594	+	2.42885i	0.546522	+	0.109169i
$496$	5.81743	−	1.53145i	0.261210	−	0.0687643i
$497$			3.59684i			0.161340i
$498$	1.28516	−	1.46221i	0.0575896	−	0.0655232i
$499$	5.41192	+	5.41192i	0.242271	+	0.242271i	0.817789	−	0.575518i	$-0.195200\pi$
$499$	5.41192	+	5.41192i	0.242271	+	0.242271i	−0.575518	+	0.817789i	$0.695200\pi$
$500$	−21.2069	+	7.08983i	−0.948403	+	0.317067i
$501$	−10.5797	+	10.5797i	−0.472665	+	0.472665i
$502$	−29.9489	+	1.92997i	−1.33668	+	0.0861387i
$503$	2.09459			0.0933934			0.0466967	−	0.998909i	$-0.485131\pi$
$503$	2.09459			0.0933934			0.0466967	+	0.998909i	$0.485131\pi$
$504$	−3.73077	−	2.51061i	−0.166182	−	0.111832i
$505$	−1.35067	+	6.76178i	−0.0601042	+	0.300895i
$506$	51.8010	−	3.33817i	2.30284	−	0.148400i
$507$	−4.43845	−	4.43845i	−0.197118	−	0.197118i
$508$	−3.73413	+	0.483277i	−0.165675	+	0.0214419i
$509$	−26.2653	−	26.2653i	−1.16419	−	1.16419i	−0.983550	−	0.180638i	$-0.942184\pi$
$509$	−26.2653	−	26.2653i	−1.16419	−	1.16419i	−0.180638	−	0.983550i	$-0.557816\pi$
$510$	−2.84868	−	3.72715i	−0.126142	−	0.165041i
$511$	−8.38036			−0.370725
$512$	−22.1480	−	4.63323i	−0.978812	−	0.204762i
$513$		−	6.98744i		−	0.308503i
$514$	13.4229	−	15.2721i	0.592061	−	0.673624i
$515$	−15.0600	+	10.0452i	−0.663623	+	0.442644i
$516$	0.117063	+	0.904506i	0.00515339	+	0.0398186i
$517$	52.1627	+	52.1627i	2.29411	+	2.29411i
$518$	0.439178	+	6.81509i	0.0192964	+	0.299438i
$519$		−	18.5894i		−	0.815985i
$520$	19.5545	+	19.7154i	0.857522	+	0.864578i
$521$		−	10.2533i		−	0.449205i	−0.974450	−	0.224602i	$-0.927892\pi$
$521$		−	10.2533i		−	0.449205i	0.974450	−	0.224602i	$-0.0721083\pi$
$522$	−8.83382	+	0.569270i	−0.386646	+	0.0249163i
$523$	7.87557	+	7.87557i	0.344375	+	0.344375i	0.858009	−	0.513634i	$-0.171701\pi$
$523$	7.87557	+	7.87557i	0.344375	+	0.344375i	−0.513634	+	0.858009i	$0.671701\pi$
$524$	−1.21171	+	1.57198i	−0.0529337	+	0.0686721i
$525$	−3.03025	−	7.34920i	−0.132251	−	0.320745i
$526$	5.24793	+	4.61251i	0.228821	+	0.201115i
$527$			2.23099i			0.0971835i
$528$	5.64682	+	21.4502i	0.245746	+	0.933500i
$529$	20.8131			0.904916
$530$	−2.53008	−	3.31029i	−0.109899	−	0.143790i
$531$	−1.14326	−	1.14326i	−0.0496133	−	0.0496133i
$532$	−13.5644	+	17.5974i	−0.588089	+	0.762942i
$533$	−21.2627	−	21.2627i	−0.920991	−	0.920991i
$534$	−0.621721	−	9.64774i	−0.0269045	−	0.417499i
$535$	−27.9325	−	5.57955i	−1.20763	−	0.241225i
$536$	4.16874	+	21.3241i	0.180062	+	0.921061i
$537$	5.03731			0.217376
$538$	1.49133	+	23.1422i	0.0642960	+	0.997733i
$539$	−17.5362	+	17.5362i	−0.755336	+	0.755336i
$540$	−0.305880	+	4.46166i	−0.0131630	+	0.191999i
$541$	23.6782	+	23.6782i	1.01800	+	1.01800i	0.999835	+	0.0181698i	$0.00578394\pi$
$541$	23.6782	+	23.6782i	1.01800	+	1.01800i	0.0181698	+	0.999835i	$0.494216\pi$
$542$	3.62152	+	3.18302i	0.155558	+	0.136723i
$543$		−	8.33678i		−	0.357765i
$544$	3.75279	−	7.50585i	0.160899	−	0.321811i
$545$	30.7364	+	6.13963i	1.31660	+	0.262993i
$546$	−6.51710	+	7.41491i	−0.278906	+	0.317329i
$547$	−6.60366	+	6.60366i	−0.282352	+	0.282352i	−0.834046	−	0.551694i	$-0.813982\pi$
$547$	−6.60366	+	6.60366i	−0.282352	+	0.282352i	0.551694	+	0.834046i	$0.313982\pi$
$548$	−4.28801	−	33.1321i	−0.183175	−	1.41533i
$549$	2.67458	−	2.67458i	0.114148	−	0.114148i
$550$	−12.7045	+	37.0957i	−0.541722	+	1.58176i
$551$			43.7373i			1.86327i
$552$	3.59200	+	18.3740i	0.152886	+	0.782047i
$553$	−10.3670			−0.440848
$554$	1.45282	+	22.5445i	0.0617243	+	0.957826i
$555$	5.65010	−	3.76869i	0.239834	−	0.159972i
$556$	−11.2825	−	8.69674i	−0.478484	−	0.368824i
$557$	−11.5466	+	11.5466i	−0.489245	+	0.489245i	−0.908068	−	0.418823i	$-0.862443\pi$
$557$	−11.5466	+	11.5466i	−0.489245	+	0.489245i	0.418823	+	0.908068i	$0.362443\pi$
$558$	1.40408	−	1.59751i	0.0594395	−	0.0676279i
$559$	2.00220			0.0846840
$560$	9.43153	−	10.6426i	0.398555	−	0.449731i
$561$	−8.22618			−0.347310
$562$	4.41393	−	5.02200i	0.186190	−	0.211840i
$563$	13.3335	−	13.3335i	0.561940	−	0.561940i	−0.367918	−	0.929858i	$-0.619929\pi$
$563$	13.3335	−	13.3335i	0.561940	−	0.561940i	0.929858	+	0.367918i	$0.119929\pi$
$564$	−16.2431	+	21.0726i	−0.683958	+	0.887315i
$565$	−12.9800	−	19.4599i	−0.546073	−	0.818685i
$566$	−0.838434	−	13.0107i	−0.0352420	−	0.546879i
$567$	−1.58988			−0.0667688
$568$	5.30871	+	3.57249i	0.222749	+	0.149898i
$569$		−	13.8256i		−	0.579600i	−0.957087	−	0.289800i	$-0.906411\pi$
$569$		−	13.8256i		−	0.579600i	0.957087	−	0.289800i	$-0.0935887\pi$
$570$	21.9017	+	2.92584i	0.917360	+	0.122550i
$571$	17.8448	−	17.8448i	0.746781	−	0.746781i	−0.227092	−	0.973873i	$-0.572922\pi$
$571$	17.8448	−	17.8448i	0.746781	−	0.746781i	0.973873	+	0.227092i	$0.0729218\pi$
$572$	48.2907	−	6.24986i	2.01913	−	0.261320i
$573$	−0.491578	+	0.491578i	−0.0205360	+	0.0205360i
$574$	−10.1660	+	11.5665i	−0.424322	+	0.482777i
$575$	−12.7145	+	30.5560i	−0.530232	+	1.27427i
$576$	−7.41102	+	3.01277i	−0.308793	+	0.125532i
$577$		−	22.6737i		−	0.943918i	−0.881620	−	0.471959i	$-0.843547\pi$
$577$		−	22.6737i		−	0.943918i	0.881620	−	0.471959i	$-0.156453\pi$
$578$	−15.7204	−	13.8170i	−0.653884	−	0.574710i
$579$	16.8575	+	16.8575i	0.700573	+	0.700573i
$580$	1.91463	−	27.9274i	0.0795006	−	1.15962i
$581$	−1.54753	+	1.54753i	−0.0642022	+	0.0642022i
$582$	1.43903	+	22.3305i	0.0596496	+	0.925630i
$583$	−7.30613			−0.302589
$584$	−8.32362	+	12.3689i	−0.344434	+	0.511828i
$585$	9.62737	+	1.92308i	0.398043	+	0.0795096i
$586$	−0.335244	−	5.20225i	−0.0138488	−	0.214903i
$587$	9.96994	+	9.96994i	0.411504	+	0.411504i	0.882262	−	0.470758i	$-0.156020\pi$
$587$	9.96994	+	9.96994i	0.411504	+	0.411504i	−0.470758	+	0.882262i	$0.656020\pi$
$588$	−7.08422	−	5.46065i	−0.292148	−	0.225193i
$589$	−7.43061	−	7.43061i	−0.306173	−	0.306173i
$590$	4.06219	−	3.10476i	0.167238	−	0.127821i
$591$	−5.52451			−0.227248
$592$	10.4948	+	6.12075i	0.431336	+	0.251561i
$593$		−	36.5396i		−	1.50050i	−0.661153	−	0.750251i	$-0.729933\pi$
$593$		−	36.5396i		−	1.50050i	0.661153	−	0.750251i	$-0.270067\pi$
$594$	5.89038	+	5.17717i	0.241685	+	0.212422i
$595$	2.92645	+	4.38740i	0.119973	+	0.179866i
$596$	−27.3933	−	21.1153i	−1.12207	−	0.864914i
$597$	−2.71973	−	2.71973i	−0.111311	−	0.111311i
$598$	41.0143	−	2.64305i	1.67720	−	0.108082i
$599$		−	7.77638i		−	0.317734i	−0.987300	−	0.158867i	$-0.949216\pi$
$599$		−	7.77638i		−	0.317734i	0.987300	−	0.158867i	$-0.0507841\pi$
$600$	−13.8567	−	2.82698i	−0.565697	−	0.115411i
$601$			31.7530i			1.29523i	0.761966	+	0.647617i	$0.224234\pi$
$601$			31.7530i			1.29523i	−0.761966	+	0.647617i	$0.775766\pi$
$602$	−0.0659384	−	1.02322i	−0.00268745	−	0.0417033i
$603$	5.43194	+	5.43194i	0.221206	+	0.221206i
$604$	1.12608	−	0.145739i	0.0458195	−	0.00593004i
$605$	24.5055	+	36.7391i	0.996288	+	1.49366i
$606$	−2.87901	+	3.27562i	−0.116952	+	0.133063i
$607$		−	30.7877i		−	1.24963i	−0.780771	−	0.624817i	$-0.785174\pi$
$607$		−	30.7877i		−	1.24963i	0.780771	−	0.624817i	$-0.214826\pi$
$608$	12.5001	+	37.4984i	0.506945	+	1.52076i
$609$	9.95173			0.403264
$610$	7.26337	+	9.50322i	0.294085	+	0.384774i
$611$	41.3007	+	41.3007i	1.67085	+	1.67085i
$612$	−0.380808	−	2.94239i	−0.0153933	−	0.118939i
$613$	−18.1437	−	18.1437i	−0.732818	−	0.732818i	0.238359	−	0.971177i	$-0.423391\pi$
$613$	−18.1437	−	18.1437i	−0.732818	−	0.732818i	−0.971177	+	0.238359i	$0.923391\pi$
$614$	18.5163	−	1.19323i	0.747257	−	0.0481548i
$615$	15.0177	+	2.99981i	0.605573	+	0.120964i
$616$	−4.78433	−	24.4730i	−0.192766	−	0.986046i
$617$	−14.8136			−0.596372			−0.298186	−	0.954508i	$-0.596381\pi$
$617$	−14.8136			−0.596372			−0.298186	+	0.954508i	$0.596381\pi$
$618$	−11.4255	+	0.736282i	−0.459600	+	0.0296176i
$619$	6.05155	−	6.05155i	0.243232	−	0.243232i	−0.574954	−	0.818186i	$-0.694980\pi$
$619$	6.05155	−	6.05155i	0.243232	−	0.243232i	0.818186	+	0.574954i	$0.194980\pi$
$620$	4.41936	+	5.06992i	0.177486	+	0.203613i
$621$	4.68044	+	4.68044i	0.187820	+	0.187820i
$622$	8.28494	−	9.42629i	0.332196	−	0.377960i
$623$			10.8687i			0.435443i
$624$	4.47097	+	16.9836i	0.178982	+	0.679886i
$625$	−17.6205	−	17.7346i	−0.704821	−	0.709385i
$626$	−27.2104	−	23.9157i	−1.08754	−	0.955863i
$627$	27.3984	−	27.3984i	1.09419	−	1.09419i
$628$	−18.0581	−	13.9195i	−0.720598	−	0.555449i
$629$	−3.18605	+	3.18605i	−0.127036	+	0.127036i
$630$	0.665728	−	4.98338i	0.0265232	−	0.198543i
$631$		−	35.8534i		−	1.42730i	−0.700502	−	0.713650i	$-0.747041\pi$
$631$		−	35.8534i		−	1.42730i	0.700502	−	0.713650i	$-0.252959\pi$
$632$	−10.2968	+	15.3010i	−0.409583	+	0.608640i
$633$	12.4114			0.493307
$634$	−39.0042	+	2.51351i	−1.54905	+	0.0998242i
$635$	−2.33596	−	3.50212i	−0.0926997	−	0.138978i
$636$	−0.338217	−	2.61330i	−0.0134112	−	0.103624i
$637$	−13.8846	+	13.8846i	−0.550126	+	0.550126i
$638$	−36.8703	−	32.4060i	−1.45971	−	1.28297i
$639$	2.26233			0.0894964
$640$	−6.34011	−	24.4909i	−0.250615	−	0.968087i
$641$	15.4688			0.610979			0.305490	−	0.952195i	$-0.401180\pi$
$641$	15.4688			0.610979			0.305490	+	0.952195i	$0.401180\pi$
$642$	−13.5314	−	11.8930i	−0.534042	−	0.469379i
$643$	−11.6098	+	11.6098i	−0.457847	+	0.457847i	−0.897948	−	0.440101i	$-0.854943\pi$
$643$	−11.6098	+	11.6098i	−0.457847	+	0.457847i	0.440101	+	0.897948i	$0.354943\pi$
$644$	−2.70145	−	20.8732i	−0.106452	−	0.822521i
$645$	−0.848308	+	0.565832i	−0.0334021	+	0.0222796i
$646$	−14.6288	+	0.942714i	−0.575564	+	0.0370906i
$647$	18.0688			0.710357			0.355178	−	0.934799i	$-0.384420\pi$
$647$	18.0688			0.710357			0.355178	+	0.934799i	$0.384420\pi$
$648$	−1.57912	+	2.34657i	−0.0620337	+	0.0921819i
$649$		−	8.96566i		−	0.351933i
$650$	−10.0590	+	29.3711i	−0.394547	+	1.15203i
$651$	−1.69072	+	1.69072i	−0.0662645	+	0.0662645i
$652$	0.217080	+	0.167329i	0.00850149	+	0.00655310i
$653$	3.64829	−	3.64829i	0.142769	−	0.142769i	−0.632110	−	0.774879i	$-0.717811\pi$
$653$	3.64829	−	3.64829i	0.142769	−	0.142769i	0.774879	+	0.632110i	$0.217811\pi$
$654$	14.8897	+	13.0868i	0.582233	+	0.511735i
$655$	−2.17606	−	0.434671i	−0.0850257	−	0.0169840i
$656$	6.97426	+	26.4926i	0.272299	+	1.03436i
$657$			5.27105i			0.205643i
$658$	19.7465	−	22.4668i	0.769797	−	0.875846i
$659$	−20.7113	−	20.7113i	−0.806796	−	0.806796i	0.177351	−	0.984148i	$-0.443247\pi$
$659$	−20.7113	−	20.7113i	−0.806796	−	0.806796i	−0.984148	+	0.177351i	$0.943247\pi$
$660$	−18.6940	+	16.2952i	−0.727661	+	0.634289i
$661$	11.7363	−	11.7363i	0.456488	−	0.456488i	−0.441013	−	0.897501i	$-0.645381\pi$
$661$	11.7363	−	11.7363i	0.456488	−	0.456488i	0.897501	+	0.441013i	$0.145381\pi$
$662$	35.8349	−	2.30928i	1.39276	−	0.0897526i
$663$	−6.51322			−0.252952
$664$	0.747003	+	3.82110i	0.0289894	+	0.148288i
$665$	−24.3597	−	4.86589i	−0.944630	−	0.188691i
$666$	4.28653	−	0.276233i	0.166100	−	0.0107038i
$667$	−29.2968	−	29.2968i	−1.13438	−	1.13438i
$668$	−3.84076	−	29.6763i	−0.148604	−	1.14821i
$669$	9.51759	+	9.51759i	0.367971	+	0.367971i
$670$	−19.3006	+	14.7515i	−0.745645	+	0.569902i
$671$	20.9745			0.809713
$672$	8.53216	−	2.84420i	0.329135	−	0.109717i
$673$			42.5085i			1.63858i	0.573379	+	0.819290i	$0.305632\pi$
$673$			42.5085i			1.63858i	−0.573379	+	0.819290i	$0.694368\pi$
$674$	−28.1380	+	32.0143i	−1.08383	+	1.23315i
$675$	−4.62248	+	1.90596i	−0.177919	+	0.0733604i
$676$	12.4500	−	1.61130i	0.478846	−	0.0619730i
$677$	16.5124	+	16.5124i	0.634623	+	0.634623i	0.949224	−	0.314601i	$-0.101871\pi$
$677$	16.5124	+	16.5124i	0.634623	+	0.634623i	−0.314601	+	0.949224i	$0.601871\pi$
$678$	−0.951394	−	14.7636i	−0.0365381	−	0.566991i
$679$		−	25.1564i		−	0.965416i
$680$	9.38217	+	0.0384402i	0.359790	+	0.00147411i
$681$		−	22.9143i		−	0.878078i
$682$	11.7695	−	0.758451i	0.450677	−	0.0290426i
$683$	−18.1836	−	18.1836i	−0.695777	−	0.695777i	0.267720	−	0.963497i	$-0.413730\pi$
$683$	−18.1836	−	18.1836i	−0.695777	−	0.695777i	−0.963497	+	0.267720i	$0.913730\pi$
$684$	11.0683	+	8.53167i	0.423208	+	0.326217i
$685$	31.0736	−	20.7264i	1.18726	−	0.791917i
$686$	19.3748	+	17.0289i	0.739732	+	0.650165i
$687$		−	1.90775i		−	0.0727852i
$688$	−1.57570	−	0.918971i	−0.0600730	−	0.0350354i
$689$	−5.78475			−0.220382
$690$	−16.6304	+	12.7107i	−0.633107	+	0.483888i
$691$	−13.9630	−	13.9630i	−0.531178	−	0.531178i	0.389745	−	0.920923i	$-0.372563\pi$
$691$	−13.9630	−	13.9630i	−0.531178	−	0.531178i	−0.920923	+	0.389745i	$0.872563\pi$
$692$	29.4463	+	22.6977i	1.11938	+	0.862837i
$693$	−6.23407	−	6.23407i	−0.236813	−	0.236813i
$694$	−2.20885	−	34.2764i	−0.0838466	−	1.30112i
$695$	3.11975	−	15.6182i	0.118339	−	0.592430i
$696$	9.88435	−	14.6881i	0.374666	−	0.556752i
$697$	−10.1600			−0.384836
$698$	1.50681	+	23.3824i	0.0570338	+	0.885039i
$699$	−9.25511	+	9.25511i	−0.350061	+	0.350061i
$700$	15.3413	+	4.17336i	0.579847	+	0.157738i
$701$	−15.7918	−	15.7918i	−0.596448	−	0.596448i	0.342918	−	0.939365i	$-0.388585\pi$
$701$	−15.7918	−	15.7918i	−0.596448	−	0.596448i	−0.939365	+	0.342918i	$0.888585\pi$
$702$	4.66381	+	4.09911i	0.176024	+	0.154711i
$703$		−	21.2231i		−	0.800445i
$704$	−40.8726	−	17.2459i	−1.54044	−	0.649981i
$705$	−29.1704	−	5.82683i	−1.09862	−	0.219451i
$706$	2.19163	−	2.49356i	0.0824832	−	0.0938463i
$707$	3.46675	−	3.46675i	0.130380	−	0.130380i
$708$	3.20689	−	0.415041i	0.120522	−	0.0155982i
$709$	−12.4875	+	12.4875i	−0.468977	+	0.468977i	−0.901583	−	0.432606i	$-0.857594\pi$
$709$	−12.4875	+	12.4875i	−0.468977	+	0.468977i	0.432606	+	0.901583i	$0.357594\pi$
$710$	−0.947300	+	7.09112i	−0.0355516	+	0.266125i
$711$			6.52058i			0.244541i
$712$	16.0415	+	10.7951i	0.601179	+	0.404562i
$713$	9.95458			0.372802
$714$	0.214500	+	3.32856i	0.00802745	+	0.124568i
$715$	30.2092	+	45.2903i	1.12976	+	1.69376i
$716$	−6.15056	+	7.97926i	−0.229857	+	0.298199i
$717$	7.80221	−	7.80221i	0.291379	−	0.291379i
$718$	−26.7300	+	30.4124i	−0.997555	+	1.13498i
$719$	26.6025			0.992107			0.496053	−	0.868292i	$-0.334782\pi$
$719$	26.6025			0.992107			0.496053	+	0.868292i	$0.334782\pi$
$720$	−6.69394	−	5.93222i	−0.249468	−	0.221081i
$721$	12.8714			0.479355
$722$	27.8446	−	31.6806i	1.03627	−	1.17903i
$723$	5.87890	−	5.87890i	0.218638	−	0.218638i
$724$	13.2057	+	10.1792i	0.490787	+	0.378307i
$725$	28.9340	−	11.9302i	1.07458	−	0.443076i
$726$	1.79617	+	27.8727i	0.0666623	+	1.03445i
$727$	5.84475			0.216770			0.108385	−	0.994109i	$-0.465432\pi$
$727$	5.84475			0.216770			0.108385	+	0.994109i	$0.465432\pi$
$728$	−3.78807	−	19.3769i	−0.140395	−	0.718156i
$729$			1.00000i			0.0370370i
$730$	−16.5218	−	2.20714i	−0.611498	−	0.0816898i
$731$	0.478355	−	0.478355i	0.0176926	−	0.0176926i
$732$	0.970959	+	7.50229i	0.0358877	+	0.277293i
$733$	34.4267	−	34.4267i	1.27158	−	1.27158i	0.326318	−	0.945260i	$-0.394192\pi$
$733$	34.4267	−	34.4267i	1.27158	−	1.27158i	0.945260	−	0.326318i	$-0.105808\pi$
$734$	11.7603	−	13.3804i	0.434080	−	0.493879i
$735$	1.95888	−	9.80657i	0.0722542	−	0.361721i
$736$	−33.4908	−	16.7448i	−1.23449	−	0.617220i
$737$			42.5982i			1.56913i
$738$	7.27507	+	6.39419i	0.267799	+	0.235374i
$739$	−8.03861	−	8.03861i	−0.295705	−	0.295705i	0.543624	−	0.839329i	$-0.317052\pi$
$739$	−8.03861	−	8.03861i	−0.295705	−	0.295705i	−0.839329	+	0.543624i	$0.817052\pi$
$740$	−0.929056	+	13.5515i	−0.0341528	+	0.498164i
$741$	21.6931	−	21.6931i	0.796917	−	0.796917i
$742$	0.190509	+	2.95628i	0.00699381	+	0.108529i
$743$	4.14206			0.151957			0.0759787	−	0.997109i	$-0.475792\pi$
$743$	4.14206			0.151957			0.0759787	+	0.997109i	$0.475792\pi$
$744$	0.816123	+	4.17467i	0.0299205	+	0.153051i
$745$	7.57459	−	37.9201i	0.277512	−	1.38929i
$746$	−1.36265	−	21.1454i	−0.0498902	−	0.774187i
$747$	0.973359	+	0.973359i	0.0356133	+	0.0356133i
$748$	10.0442	−	13.0305i	0.367251	−	0.476444i
$749$	14.3209	+	14.3209i	0.523275	+	0.523275i
$750$	−4.03854	−	15.2869i	−0.147467	−	0.558200i
$751$	−53.0366			−1.93533			−0.967667	−	0.252232i	$-0.918835\pi$
$751$	−53.0366			−1.93533			−0.967667	+	0.252232i	$0.918835\pi$
$752$	−13.5468	−	51.4592i	−0.494000	−	1.87652i
$753$		−	21.2210i		−	0.773335i
$754$	−29.1927	−	25.6580i	−1.06314	−	0.934410i
$755$	0.704442	+	1.05612i	0.0256373	+	0.0384360i
$756$	1.94125	−	2.51843i	0.0706025	−	0.0915943i
$757$	−4.39557	−	4.39557i	−0.159760	−	0.159760i	0.622701	−	0.782460i	$-0.286035\pi$
$757$	−4.39557	−	4.39557i	−0.159760	−	0.159760i	−0.782460	+	0.622701i	$0.786035\pi$
$758$	51.6352	−	3.32748i	1.87548	−	0.120860i
$759$			36.7048i			1.33230i
$760$	−31.3766	+	31.1205i	−1.13815	+	1.12886i
$761$		−	17.0961i		−	0.619732i	−0.950780	−	0.309866i	$-0.899716\pi$
$761$		−	17.0961i		−	0.619732i	0.950780	−	0.309866i	$-0.100284\pi$
$762$	−0.171219	−	2.65694i	−0.00620260	−	0.0962507i
$763$	−15.7584	−	15.7584i	−0.570494	−	0.570494i
$764$	−0.178458	−	1.37889i	−0.00645640	−	0.0498865i
$765$	2.75957	−	1.84067i	0.0997726	−	0.0665495i
$766$	3.97624	−	4.52401i	0.143667	−	0.163459i
$767$		−	7.09871i		−	0.256320i
$768$	4.27654	−	15.4179i	0.154316	−	0.556345i
$769$	33.3744			1.20351			0.601756	−	0.798680i	$-0.294468\pi$
$769$	33.3744			1.20351			0.601756	+	0.798680i	$0.294468\pi$
$770$	22.1506	−	16.9299i	0.798254	−	0.610111i
$771$	10.1663	+	10.1663i	0.366130	+	0.366130i
$772$	−47.2858	+	6.11980i	−1.70185	+	0.220257i
$773$	23.0507	+	23.0507i	0.829078	+	0.829078i	0.987389	−	0.158312i	$-0.0506051\pi$
$773$	23.0507	+	23.0507i	0.829078	+	0.829078i	−0.158312	+	0.987389i	$0.550605\pi$
$774$	−0.643581	+	0.0414737i	−0.0231331	+	0.00149074i
$775$	−2.88881	+	6.94249i	−0.103769	+	0.249382i
$776$	−37.1293	−	24.9861i	−1.33287	−	0.896950i
$777$	−4.82899			−0.173239
$778$	−44.1503	+	2.84514i	−1.58286	+	0.102003i
$779$	33.8391	−	33.8391i	1.21241	−	1.21241i
$780$	−14.8012	+	12.9020i	−0.529970	+	0.461965i
$781$	8.87079	+	8.87079i	0.317422	+	0.317422i
$782$	9.16747	−	10.4304i	0.327828	−	0.372990i
$783$		−	6.25941i		−	0.223693i
$784$	17.2997	−	4.55419i	0.617846	−	0.162650i
$785$	4.99330	−	24.9976i	0.178218	−	0.892201i
$786$	−1.05415	−	0.926515i	−0.0376004	−	0.0330477i
$787$	−10.1563	+	10.1563i	−0.362034	+	0.362034i	−0.864561	−	0.502527i	$-0.832404\pi$
$787$	−10.1563	+	10.1563i	−0.362034	+	0.362034i	0.502527	+	0.864561i	$0.332404\pi$
$788$	6.74543	−	8.75100i	0.240296	−	0.311741i
$789$	−3.49342	+	3.49342i	−0.124369	+	0.124369i
$790$	−20.4383	−	2.73035i	−0.727162	−	0.0971414i
$791$			16.6319i			0.591361i
$792$	−15.3930	+	3.00923i	−0.546965	+	0.106929i
$793$	16.6069			0.589730
$794$	−25.9398	+	1.67161i	−0.920567	+	0.0593233i
$795$	2.45093	−	1.63480i	0.0869256	−	0.0579804i
$796$	7.62892	−	0.987348i	0.270400	−	0.0349956i
$797$	−24.6189	+	24.6189i	−0.872046	+	0.872046i	−0.992695	−	0.120649i	$-0.961502\pi$
$797$	−24.6189	+	24.6189i	−0.872046	+	0.872046i	0.120649	+	0.992695i	$0.461502\pi$
$798$	−11.8006	−	10.3718i	−0.417738	−	0.367158i
$799$	19.7347			0.698163
$800$	21.3971	−	18.4977i	0.756501	−	0.653993i
$801$	6.83613			0.241543
$802$	37.5605	+	33.0126i	1.32631	+	1.16572i
$803$	−20.6683	+	20.6683i	−0.729367	+	0.729367i
$804$	−15.2368	+	1.97197i	−0.537359	+	0.0695459i
$805$	19.5764	−	13.0577i	0.689977	−	0.460223i
$806$	9.31869	−	0.600516i	0.328237	−	0.0211523i
$807$	−16.3980			−0.577236
$808$	−1.67343	−	8.55998i	−0.0588709	−	0.301139i
$809$			24.5505i			0.863150i	0.902077	+	0.431575i	$0.142042\pi$
$809$			24.5505i			0.863150i	−0.902077	+	0.431575i	$0.857958\pi$
$810$	−3.13443	−	0.418728i	−0.110133	−	0.0147126i
$811$	13.4539	−	13.4539i	0.472430	−	0.472430i	−0.430270	−	0.902700i	$-0.641582\pi$
$811$	13.4539	−	13.4539i	0.472430	−	0.472430i	0.902700	+	0.430270i	$0.141582\pi$
$812$	−12.1511	+	15.7639i	−0.426419	+	0.553203i
$813$	−2.41076	+	2.41076i	−0.0845491	+	0.0845491i
$814$	17.8910	+	15.7247i	0.627079	+	0.551152i
$815$	−0.0600252	+	0.300500i	−0.00210259	+	0.0105260i
$816$	5.12580	+	2.98944i	0.179439	+	0.104651i
$817$			3.18645i			0.111480i
$818$	25.5750	−	29.0982i	0.894209	−	1.01740i
$819$	−4.93593	−	4.93593i	−0.172475	−	0.172475i
$820$	−23.0884	+	20.1258i	−0.806283	+	0.702823i
$821$	−7.23091	+	7.23091i	−0.252360	+	0.252360i	−0.821938	−	0.569577i	$-0.807107\pi$
$821$	−7.23091	+	7.23091i	−0.252360	+	0.252360i	0.569577	+	0.821938i	$0.307107\pi$
$822$	23.5744	−	1.51918i	0.822252	−	0.0529876i
$823$	42.5825			1.48433			0.742167	−	0.670215i	$-0.233798\pi$
$823$	42.5825			1.48433			0.742167	+	0.670215i	$0.233798\pi$
$824$	12.7842	−	18.9973i	0.445360	−	0.661804i
$825$	−25.5986	−	10.6517i	−0.891228	−	0.370845i
$826$	−3.62778	+	0.233782i	−0.126227	+	0.00813431i
$827$	−18.4053	−	18.4053i	−0.640014	−	0.640014i	0.310545	−	0.950559i	$-0.399488\pi$
$827$	−18.4053	−	18.4053i	−0.640014	−	0.640014i	−0.950559	+	0.310545i	$0.899488\pi$
$828$	−13.1288	+	1.69915i	−0.456257	+	0.0590495i
$829$	10.8176	+	10.8176i	0.375710	+	0.375710i	0.869552	−	0.493842i	$-0.164408\pi$
$829$	10.8176	+	10.8176i	0.375710	+	0.375710i	−0.493842	+	0.869552i	$0.664408\pi$
$830$	−3.45850	+	2.64336i	−0.120046	+	0.0917522i
$831$	−15.9745			−0.554148
$832$	−32.3615	−	13.6548i	−1.12193	−	0.473394i
$833$			6.63445i			0.229870i
$834$	6.64984	−	7.56594i	0.230265	−	0.261987i
$835$	27.8325	−	18.5646i	0.963185	−	0.642456i
$836$	9.94648	+	76.8533i	0.344006	+	2.65803i
$837$	1.06342	+	1.06342i	0.0367573	+	0.0367573i
$838$	−0.477600	−	7.41131i	−0.0164984	−	0.256019i
$839$		−	10.8332i		−	0.374004i	−0.982360	−	0.187002i	$-0.940123\pi$
$839$		−	10.8332i		−	0.374004i	0.982360	−	0.187002i	$-0.0598771\pi$
$840$	7.08098	+	7.13924i	0.244317	+	0.246327i
$841$			10.1802i			0.351042i
$842$	21.5064	−	1.38592i	0.741161	−	0.0477620i
$843$	3.34302	+	3.34302i	0.115140	+	0.115140i
$844$	−15.1543	+	19.6600i	−0.521632	+	0.676725i
$845$	7.78834	+	11.6765i	0.267927	+	0.401683i
$846$	−14.1311	−	12.4201i	−0.485837	−	0.427011i
$847$		−	31.3999i		−	1.07891i
$848$	4.55251	+	2.65509i	0.156334	+	0.0911762i
$849$	9.21901			0.316396
$850$	4.61394	+	9.42044i	0.158257	+	0.323118i
$851$	14.2160	+	14.2160i	0.487319	+	0.487319i
$852$	−2.76231	+	3.58360i	−0.0946350	+	0.122772i
$853$	−31.7242	−	31.7242i	−1.08622	−	1.08622i	−0.995915	−	0.0903009i	$-0.971217\pi$
$853$	−31.7242	−	31.7242i	−1.08622	−	1.08622i	−0.0903009	−	0.995915i	$-0.528783\pi$
$854$	−0.546916	−	8.48694i	−0.0187151	−	0.290417i
$855$	−3.06053	+	15.3217i	−0.104668	+	0.523992i
$856$	35.3607	−	6.91282i	1.20860	−	0.236275i
$857$	39.9570			1.36490			0.682452	−	0.730930i	$-0.260914\pi$
$857$	39.9570			1.36490			0.682452	+	0.730930i	$0.260914\pi$
$858$	2.21424	+	34.3602i	0.0755930	+	1.17304i
$859$	23.9624	−	23.9624i	0.817587	−	0.817587i	−0.168171	−	0.985758i	$-0.553786\pi$
$859$	23.9624	−	23.9624i	0.817587	−	0.817587i	0.985758	+	0.168171i	$0.0537861\pi$
$860$	0.139489	−	2.03463i	0.00475653	−	0.0693803i
$861$	−7.69955	−	7.69955i	−0.262400	−	0.262400i
$862$	−31.9289	−	28.0629i	−1.08750	−	0.955826i
$863$			12.5202i			0.426192i	0.977031	+	0.213096i	$0.0683547\pi$
$863$			12.5202i			0.426192i	−0.977031	+	0.213096i	$0.931645\pi$
$864$	−1.78893	−	5.36654i	−0.0608608	−	0.182573i
$865$	−8.14226	+	40.7620i	−0.276845	+	1.38595i
$866$	−18.8251	+	21.4185i	−0.639704	+	0.727831i
$867$	10.4647	−	10.4647i	0.355400	−	0.355400i
$868$	−0.613785	−	4.74252i	−0.0208332	−	0.160972i
$869$	−25.5678	+	25.5678i	−0.867327	+	0.867327i
$870$	19.6197	+	2.62099i	0.665170	+	0.0888598i
$871$			33.7279i			1.14282i
$872$	−38.9102	+	7.60673i	−1.31767	+	0.257596i
$873$	−15.8228			−0.535522
$874$	4.20634	+	65.2732i	0.142282	+	2.20790i
$875$	3.42560	+	17.4422i	0.115806	+	0.589655i
$876$	−8.34952	−	6.43596i	−0.282104	−	0.217451i
$877$	−22.4582	+	22.4582i	−0.758358	+	0.758358i	−0.976023	−	0.217666i	$-0.930156\pi$
$877$	−22.4582	+	22.4582i	−0.758358	+	0.758358i	0.217666	+	0.976023i	$0.430156\pi$
$878$	−26.2150	+	29.8264i	−0.884714	+	1.00659i
$879$	3.68618			0.124332
$880$	−2.98678	−	49.5082i	−0.100684	−	1.66892i
$881$	−44.4416			−1.49728			−0.748638	−	0.662979i	$-0.769292\pi$
$881$	−44.4416			−1.49728			−0.748638	+	0.662979i	$0.769292\pi$
$882$	4.17541	−	4.75062i	0.140593	−	0.159962i
$883$	38.6128	−	38.6128i	1.29942	−	1.29942i	0.370653	−	0.928771i	$-0.379134\pi$
$883$	38.6128	−	38.6128i	1.29942	−	1.29942i	0.928771	−	0.370653i	$-0.120866\pi$
$884$	7.95264	−	10.3171i	0.267476	−	0.347003i
$885$	2.00613	+	3.00764i	0.0674354	+	0.101101i
$886$	0.416520	+	6.46348i	0.0139933	+	0.217145i
$887$	−27.1077			−0.910186			−0.455093	−	0.890444i	$-0.650394\pi$
$887$	−27.1077			−0.910186			−0.455093	+	0.890444i	$0.650394\pi$
$888$	−4.79630	+	7.12729i	−0.160953	+	0.239176i
$889$			2.99317i			0.100388i
$890$	−2.86248	+	21.4274i	−0.0959505	+	0.718248i
$891$	−3.92109	+	3.92109i	−0.131361	+	0.131361i
$892$	−26.6971	+	3.45519i	−0.893886	+	0.115688i
$893$	−65.7289	+	65.7289i	−2.19953	+	2.19953i
$894$	16.1455	−	18.3697i	0.539986	−	0.614375i
$895$	−11.0456	−	2.20637i	−0.369212	−	0.0737507i
$896$	−5.91248	+	16.9880i	−0.197522	+	0.567529i
$897$			29.0617i			0.970341i
$898$	−1.12632	−	0.989948i	−0.0375859	−	0.0330350i
$899$	−6.65640	−	6.65640i	−0.222003	−	0.222003i
$900$	2.62495	−	9.64933i	0.0874982	−	0.321644i
$901$	−1.38206	+	1.38206i	−0.0460432	+	0.0460432i
$902$	3.45399	+	53.5984i	0.115005	+	1.78463i
$903$	0.725026			0.0241274
$904$	24.5476	+	16.5193i	0.816441	+	0.549423i
$905$	−3.65155	+	18.2805i	−0.121382	+	0.607663i
$906$	0.0516334	+	0.801238i	0.00171541	+	0.0266193i
$907$	−7.29362	−	7.29362i	−0.242181	−	0.242181i	0.575571	−	0.817752i	$-0.304780\pi$
$907$	−7.29362	−	7.29362i	−0.242181	−	0.242181i	−0.817752	+	0.575571i	$0.804780\pi$
$908$	36.2970	+	27.9784i	1.20456	+	0.928495i
$909$	−2.18050	−	2.18050i	−0.0723228	−	0.0723228i
$910$	17.5381	−	13.4045i	0.581384	−	0.444356i
$911$	−32.2468			−1.06838			−0.534192	−	0.845363i	$-0.679384\pi$
$911$	−32.2468			−1.06838			−0.534192	+	0.845363i	$0.679384\pi$
$912$	−27.0289	+	7.11543i	−0.895016	+	0.235615i
$913$			7.63325i			0.252624i
$914$	4.20499	+	3.69584i	0.139089	+	0.122248i
$915$	−7.03617	+	4.69321i	−0.232609	+	0.155153i
$916$	3.02194	+	2.32936i	0.0998476	+	0.0769643i
$917$	1.11566	+	1.11566i	0.0368423	+	0.0368423i
$918$	2.09359	−	0.134915i	0.0690988	−	0.00445287i
$919$			27.5668i			0.909346i	0.890659	+	0.454673i	$0.150244\pi$
$919$			27.5668i			0.909346i	−0.890659	+	0.454673i	$0.849756\pi$
$920$	0.171518	−	41.8628i	0.00565479	−	1.38018i
$921$			13.1202i			0.432324i
$922$	2.21620	+	34.3906i	0.0729868	+	1.13259i
$923$	7.02360	+	7.02360i	0.231185	+	0.231185i
$924$	17.4868	−	2.26317i	0.575272	−	0.0744527i
$925$	−14.0400	+	5.78902i	−0.461631	+	0.190342i
$926$	13.5224	−	15.3853i	0.444375	−	0.505593i
$927$		−	8.09580i		−	0.265901i
$928$	11.1977	+	33.5914i	0.367582	+	1.10269i
$929$	10.3630			0.339999			0.169999	−	0.985444i	$-0.445623\pi$
$929$	10.3630			0.339999			0.169999	+	0.985444i	$0.445623\pi$
$930$	−3.77851	+	2.88794i	−0.123902	+	0.0946994i
$931$	−22.0969	−	22.0969i	−0.724197	−	0.724197i
$932$	−3.35990	−	25.9609i	−0.110057	−	0.850377i
$933$	6.27485	+	6.27485i	0.205430	+	0.205430i
$934$	51.9797	−	3.34968i	1.70083	−	0.109605i
$935$	18.0380	+	3.60311i	0.589904	+	0.117834i
$936$	−12.1876	+	2.38261i	−0.398365	+	0.0778781i
$937$	−49.6196			−1.62100			−0.810501	−	0.585738i	$-0.800805\pi$
$937$	−49.6196			−1.62100			−0.810501	+	0.585738i	$0.800805\pi$
$938$	17.2365	−	1.11076i	0.562793	−	0.0362676i
$939$	18.1133	−	18.1133i	0.591104	−	0.591104i
$940$	44.8470	−	39.0923i	1.46275	−	1.27505i
$941$	24.3629	+	24.3629i	0.794208	+	0.794208i	0.982175	−	0.187967i	$-0.0601898\pi$
$941$	24.3629	+	24.3629i	0.794208	+	0.794208i	−0.187967	+	0.982175i	$0.560190\pi$
$942$	10.6434	−	12.1096i	0.346780	−	0.394553i
$943$			45.3333i			1.47625i
$944$	−3.25817	+	5.58658i	−0.106044	+	0.181828i
$945$	3.48622	+	0.696376i	0.113407	+	0.0226531i
$946$	−2.68616	−	2.36092i	−0.0873346	−	0.0767600i
$947$	34.0132	−	34.0132i	1.10528	−	1.10528i	0.111518	−	0.993762i	$-0.464429\pi$
$947$	34.0132	−	34.0132i	1.10528	−	1.10528i	0.993762	−	0.111518i	$-0.0355714\pi$
$948$	−10.3288	−	7.96163i	−0.335464	−	0.258582i
$949$	−16.3644	+	16.3644i	−0.531212	+	0.531212i
$950$	−46.7433	−	16.0087i	−1.51655	−	0.519389i
$951$		−	27.6373i		−	0.896201i
$952$	−5.53446	−	3.72440i	−0.179373	−	0.120709i
$953$	−21.9707			−0.711700			−0.355850	−	0.934543i	$-0.615809\pi$
$953$	−21.9707			−0.711700			−0.355850	+	0.934543i	$0.615809\pi$
$954$	1.85944	−	0.119826i	0.0602014	−	0.00387951i
$955$	1.29322	−	0.862594i	0.0418476	−	0.0279129i
$956$	2.83245	+	21.8855i	0.0916081	+	0.707826i
$957$	24.5437	−	24.5437i	0.793385	−	0.793385i
$958$	19.6816	+	17.2985i	0.635884	+	0.558890i
$959$	−26.5577			−0.857594
$960$	17.5701	−	3.36018i	0.567073	−	0.108449i
$961$	−28.7383			−0.927041
$962$	14.1655	+	12.4503i	0.456714	+	0.401415i
$963$	9.00752	−	9.00752i	0.290263	−	0.290263i
$964$	2.13423	+	16.4905i	0.0687388	+	0.531123i
$965$	−29.5806	−	44.3479i	−0.952233	−	1.42761i
$966$	14.8519	−	0.957088i	0.477852	−	0.0307938i
$967$	20.8251			0.669690			0.334845	−	0.942273i	$-0.391316\pi$
$967$	20.8251			0.669690			0.334845	+	0.942273i	$0.391316\pi$
$968$	−46.3444	−	31.1874i	−1.48956	−	1.00240i
$969$		−	10.3656i		−	0.332991i
$970$	6.62546	−	49.5956i	0.212731	−	1.59242i
$971$	27.3561	−	27.3561i	0.877898	−	0.877898i	−0.115418	−	0.993317i	$-0.536821\pi$
$971$	27.3561	−	27.3561i	0.877898	−	0.877898i	0.993317	+	0.115418i	$0.0368209\pi$
$972$	−1.58403	−	1.22100i	−0.0508079	−	0.0391636i
$973$	−8.00739	+	8.00739i	−0.256705	+	0.256705i
$974$	−4.42507	−	3.88927i	−0.141788	−	0.124620i
$975$	−20.2681	−	8.43367i	−0.649099	−	0.270094i
$976$	−13.0694	−	7.62227i	−0.418342	−	0.243983i
$977$			25.5428i			0.817188i	0.912716	+	0.408594i	$0.133981\pi$
$977$			25.5428i			0.817188i	−0.912716	+	0.408594i	$0.866019\pi$
$978$	−0.127946	+	0.145572i	−0.00409125	+	0.00465487i
$979$	26.8051	+	26.8051i	0.856694	+	0.856694i
$980$	13.1421	+	15.0768i	0.419810	+	0.481609i
$981$	−9.91170	+	9.91170i	−0.316456	+	0.316456i
$982$	40.4270	−	2.60520i	1.29008	−	0.0831353i
$983$	26.0467			0.830760			0.415380	−	0.909648i	$-0.363649\pi$
$983$	26.0467			0.830760			0.415380	+	0.909648i	$0.363649\pi$
$984$	−19.0115	+	3.71663i	−0.606064	+	0.118482i
$985$	12.1139	+	2.41976i	0.385980	+	0.0771000i
$986$	−13.1046	+	0.844491i	−0.417337	+	0.0268941i
$987$	14.9556	+	14.9556i	0.476042	+	0.476042i
$988$	7.87529	+	60.8499i	0.250546	+	1.93589i
$989$	−2.13440	−	2.13440i	−0.0678699	−	0.0678699i
$990$	−10.6485	−	13.9323i	−0.338432	−	0.442796i
$991$	30.2000			0.959334			0.479667	−	0.877451i	$-0.340758\pi$
$991$	30.2000			0.959334			0.479667	+	0.877451i	$0.340758\pi$
$992$	−7.60929	−	3.80450i	−0.241595	−	0.120793i
$993$			25.3917i			0.805780i
$994$	3.35809	−	3.82070i	0.106512	−	0.121185i
$995$	4.77243	+	7.15493i	0.151296	+	0.226827i
$996$	−2.73030	+	0.353360i	−0.0865130	+	0.0111967i
$997$	32.7172	+	32.7172i	1.03617	+	1.03617i	0.999321	+	0.0368444i	$0.0117306\pi$
$997$	32.7172	+	32.7172i	1.03617	+	1.03617i	0.0368444	+	0.999321i	$0.488269\pi$
$998$	−0.696067	−	10.8014i	−0.0220336	−	0.341913i
$999$			3.03732i			0.0960967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.109.6	✓	48
3.2	odd	2		720.2.bm.h.109.19		48
4.3	odd	2		960.2.bl.a.529.3		48
5.4	even	2	inner	240.2.bl.a.109.19	yes	48
8.3	odd	2		1920.2.bl.b.289.20		48
8.5	even	2		1920.2.bl.a.289.5		48
15.14	odd	2		720.2.bm.h.109.6		48
16.3	odd	4		1920.2.bl.b.1249.5		48
16.5	even	4	inner	240.2.bl.a.229.19	yes	48
16.11	odd	4		960.2.bl.a.49.16		48
16.13	even	4		1920.2.bl.a.1249.20		48
20.19	odd	2		960.2.bl.a.529.16		48
40.19	odd	2		1920.2.bl.b.289.5		48
40.29	even	2		1920.2.bl.a.289.20		48
48.5	odd	4		720.2.bm.h.469.6		48
80.19	odd	4		1920.2.bl.b.1249.20		48
80.29	even	4		1920.2.bl.a.1249.5		48
80.59	odd	4		960.2.bl.a.49.3		48
80.69	even	4	inner	240.2.bl.a.229.6	yes	48
240.149	odd	4		720.2.bm.h.469.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.6	✓	48	1.1	even	1	trivial
240.2.bl.a.109.19	yes	48	5.4	even	2	inner
240.2.bl.a.229.6	yes	48	80.69	even	4	inner
240.2.bl.a.229.19	yes	48	16.5	even	4	inner
720.2.bm.h.109.6		48	15.14	odd	2
720.2.bm.h.109.19		48	3.2	odd	2
720.2.bm.h.469.6		48	48.5	odd	4
720.2.bm.h.469.19		48	240.149	odd	4
960.2.bl.a.49.3		48	80.59	odd	4
960.2.bl.a.49.16		48	16.11	odd	4
960.2.bl.a.529.3		48	4.3	odd	2
960.2.bl.a.529.16		48	20.19	odd	2
1920.2.bl.a.289.5		48	8.5	even	2
1920.2.bl.a.289.20		48	40.29	even	2
1920.2.bl.a.1249.5		48	80.29	even	4
1920.2.bl.a.1249.20		48	16.13	even	4
1920.2.bl.b.289.5		48	40.19	odd	2
1920.2.bl.b.289.20		48	8.3	odd	2
1920.2.bl.b.1249.5		48	16.3	odd	4
1920.2.bl.b.1249.20		48	80.19	odd	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06224 - 0.933621i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.256702 + 1.98346i) q^{4} +(-1.86022 + 1.24079i) q^{5} +(-1.41129 + 0.0909462i) q^{6} +1.58988 q^{7} +(1.57912 - 2.34657i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.06224 - 0.933621i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.256702 + 1.98346i) q^{4} +(-1.86022 + 1.24079i) q^{5} +(-1.41129 + 0.0909462i) q^{6} +1.58988 q^{7} +(1.57912 - 2.34657i) q^{8} -1.00000i q^{9} +(3.13443 + 0.418728i) q^{10} +(3.92109 - 3.92109i) q^{11} +(1.58403 + 1.22100i) q^{12} +(3.10459 - 3.10459i) q^{13} +(-1.68884 - 1.48435i) q^{14} +(-0.438005 + 2.19275i) q^{15} +(-3.86821 + 1.01832i) q^{16} -1.48346i q^{17} +(-0.933621 + 1.06224i) q^{18} +(4.94087 + 4.94087i) q^{19} +(-2.93858 - 3.37116i) q^{20} +(1.12422 - 1.12422i) q^{21} +(-7.82594 + 0.504320i) q^{22} -6.61914 q^{23} +(-0.542668 - 2.77588i) q^{24} +(1.92087 - 4.61630i) q^{25} +(-6.19632 + 0.399304i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.408127 + 3.15347i) q^{28} +(4.42607 + 4.42607i) q^{29} +(2.51246 - 1.92029i) q^{30} -1.50391 q^{31} +(5.05968 + 2.52975i) q^{32} -5.54525i q^{33} +(-1.38499 + 1.57579i) q^{34} +(-2.95754 + 1.97271i) q^{35} +(1.98346 - 0.256702i) q^{36} +(-2.14771 - 2.14771i) q^{37} +(-0.635482 - 9.86128i) q^{38} -4.39055i q^{39} +(-0.0259124 + 6.32450i) q^{40} -6.84881i q^{41} +(-2.24378 + 0.144594i) q^{42} +(0.322458 + 0.322458i) q^{43} +(8.78386 + 6.77076i) q^{44} +(1.24079 + 1.86022i) q^{45} +(7.03111 + 6.17977i) q^{46} +13.3031i q^{47} +(-2.01518 + 3.45529i) q^{48} -4.47227 q^{49} +(-6.35030 + 3.11025i) q^{50} +(-1.04897 - 1.04897i) q^{51} +(6.95477 + 5.36086i) q^{52} +(-0.931646 - 0.931646i) q^{53} +(0.0909462 + 1.41129i) q^{54} +(-2.42885 + 12.1594i) q^{55} +(2.51061 - 3.73077i) q^{56} +6.98744 q^{57} +(-0.569270 - 8.83382i) q^{58} +(1.14326 - 1.14326i) q^{59} +(-4.46166 - 0.305880i) q^{60} +(2.67458 + 2.67458i) q^{61} +(1.59751 + 1.40408i) q^{62} -1.58988i q^{63} +(-3.01277 - 7.41102i) q^{64} +(-1.92308 + 9.62737i) q^{65} +(-5.17717 + 5.89038i) q^{66} +(-5.43194 + 5.43194i) q^{67} +(2.94239 - 0.380808i) q^{68} +(-4.68044 + 4.68044i) q^{69} +(4.98338 + 0.665728i) q^{70} +2.26233i q^{71} +(-2.34657 - 1.57912i) q^{72} -5.27105 q^{73} +(0.276233 + 4.28653i) q^{74} +(-1.90596 - 4.62248i) q^{75} +(-8.53167 + 11.0683i) q^{76} +(6.23407 - 6.23407i) q^{77} +(-4.09911 + 4.66381i) q^{78} -6.52058 q^{79} +(5.93222 - 6.69394i) q^{80} -1.00000 q^{81} +(-6.39419 + 7.27507i) q^{82} +(-0.973359 + 0.973359i) q^{83} +(2.51843 + 1.94125i) q^{84} +(1.84067 + 2.75957i) q^{85} +(-0.0414737 - 0.643581i) q^{86} +6.25941 q^{87} +(-3.00923 - 15.3930i) q^{88} +6.83613i q^{89} +(0.418728 - 3.13443i) q^{90} +(4.93593 - 4.93593i) q^{91} +(-1.69915 - 13.1288i) q^{92} +(-1.06342 + 1.06342i) q^{93} +(12.4201 - 14.1311i) q^{94} +(-15.3217 - 3.06053i) q^{95} +(5.36654 - 1.78893i) q^{96} -15.8228i q^{97} +(4.75062 + 4.17541i) q^{98} +(-3.92109 - 3.92109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

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