LMFDB - Embedded newform 240.2.bl.a.229.19

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			229.19
Character	$\chi$	$=$	240.229
Dual form			240.2.bl.a.109.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06224 - 0.933621i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.256702 - 1.98346i) q^{4} +(-1.24079 - 1.86022i) q^{5} +(-1.41129 - 0.0909462i) q^{6} -1.58988 q^{7} +(-1.57912 - 2.34657i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(1.06224 - 0.933621i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.256702 - 1.98346i) q^{4} +(-1.24079 - 1.86022i) q^{5} +(-1.41129 - 0.0909462i) q^{6} -1.58988 q^{7} +(-1.57912 - 2.34657i) q^{8} +1.00000i q^{9} +(-3.05476 - 0.817572i) 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} +(-4.00819 + 1.98353i) 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} +(1.58193 + 2.73815i) q^{30} -1.50391 q^{31} +(-5.05968 + 2.52975i) q^{32} -5.54525i q^{33} +(-1.38499 - 1.57579i) q^{34} +(1.97271 + 2.95754i) q^{35} +(1.98346 + 0.256702i) q^{36} +(2.14771 - 2.14771i) q^{37} +(0.635482 - 9.86128i) q^{38} +4.39055i q^{39} +(-2.40578 + 5.84912i) q^{40} +6.84881i q^{41} +(2.24378 + 0.144594i) q^{42} +(-0.322458 + 0.322458i) q^{43} +(8.78386 - 6.77076i) q^{44} +(1.86022 - 1.24079i) q^{45} +(7.03111 - 6.17977i) q^{46} +13.3031i q^{47} +(2.01518 + 3.45529i) q^{48} -4.47227 q^{49} +(2.26946 + 6.69698i) 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} +(4.23679 + 1.43165i) 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} +(4.85672 + 1.29984i) q^{70} -2.26233i q^{71} +(2.34657 - 1.57912i) q^{72} +5.27105 q^{73} +(0.276233 - 4.28653i) q^{74} +(4.62248 - 1.90596i) q^{75} +(-8.53167 - 11.0683i) q^{76} +(-6.23407 - 6.23407i) q^{77} +(4.09911 + 4.66381i) q^{78} -6.52058 q^{79} +(2.90534 + 8.45925i) q^{80} -1.00000 q^{81} +(6.39419 + 7.27507i) q^{82} +(0.973359 + 0.973359i) q^{83} +(2.51843 - 1.94125i) q^{84} +(-2.75957 + 1.84067i) q^{85} +(-0.0414737 + 0.643581i) q^{86} -6.25941 q^{87} +(3.00923 - 15.3930i) q^{88} -6.83613i q^{89} +(0.817572 - 3.05476i) 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 $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

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

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
$5$	−1.24079	−	1.86022i	−0.554899	−	0.831918i
$5$	−1.24079	−	1.86022i	−0.554899	−	0.831918i
$6$	−1.41129	−	0.0909462i	−0.576155	−	0.0371286i
$7$	−1.58988			−0.600919			−0.300460	−	0.953795i	$-0.597140\pi$
$7$	−1.58988			−0.600919			−0.300460	+	0.953795i	$0.597140\pi$
$8$	−1.57912	−	2.34657i	−0.558303	−	0.829637i
$9$			1.00000i			0.333333i
$10$	−3.05476	−	0.817572i	−0.966001	−	0.258539i
$11$	3.92109	+	3.92109i	1.18225	+	1.18225i	0.979160	+	0.203093i	$0.0650993\pi$
$11$	3.92109	+	3.92109i	1.18225	+	1.18225i	0.203093	+	0.979160i	$0.434901\pi$
$12$	−1.58403	+	1.22100i	−0.457271	+	0.352472i
$13$	−3.10459	−	3.10459i	−0.861057	−	0.861057i	0.130404	−	0.991461i	$-0.458373\pi$
$13$	−3.10459	−	3.10459i	−0.861057	−	0.861057i	−0.991461	+	0.130404i	$0.958373\pi$
$14$	−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	0.143924	−	0.989589i	$-0.454028\pi$
$19$	4.94087	−	4.94087i	1.13351	−	1.13351i	0.989589	−	0.143924i	$-0.0459721\pi$
$20$	−4.00819	+	1.98353i	−0.896259	+	0.443532i
$21$	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	$-0.257569\pi$
$23$	6.61914			1.38019			0.690094	+	0.723720i	$0.257569\pi$
$24$	−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	−0.164480	−	0.986380i	$-0.552594\pi$
$29$	4.42607	−	4.42607i	0.821901	−	0.821901i	0.986380	+	0.164480i	$0.0525945\pi$
$30$	1.58193	+	2.73815i	0.288820	+	0.499916i
$31$	−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
$35$	1.97271	+	2.95754i	0.333450	+	0.499915i
$36$	1.98346	+	0.256702i	0.330576	+	0.0427837i
$37$	2.14771	−	2.14771i	0.353082	−	0.353082i	−0.508173	−	0.861255i	$-0.669679\pi$
$37$	2.14771	−	2.14771i	0.353082	−	0.353082i	0.861255	+	0.508173i	$0.169679\pi$
$38$	0.635482	−	9.86128i	0.103089	−	1.59971i
$39$			4.39055i			0.703050i
$40$	−2.40578	+	5.84912i	−0.380388	+	0.924827i
$41$			6.84881i			1.06960i	0.844977	+	0.534802i	$0.179614\pi$
$41$			6.84881i			1.06960i	−0.844977	+	0.534802i	$0.820386\pi$
$42$	2.24378	+	0.144594i	0.346223	+	0.0223113i
$43$	−0.322458	+	0.322458i	−0.0491744	+	0.0491744i	−0.731266	−	0.682092i	$-0.761070\pi$
$43$	−0.322458	+	0.322458i	−0.0491744	+	0.0491744i	0.682092	+	0.731266i	$0.261070\pi$
$44$	8.78386	−	6.77076i	1.32422	−	1.02073i
$45$	1.86022	−	1.24079i	0.277306	−	0.184966i
$46$	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
$50$	2.26946	+	6.69698i	0.320950	+	0.947096i
$51$	−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	$-0.721157\pi$
$53$	0.931646	−	0.931646i	0.127971	−	0.127971i	0.768192	+	0.640220i	$0.221157\pi$
$54$	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	0.777600	−	0.628760i	$-0.216437\pi$
$59$	1.14326	+	1.14326i	0.148840	+	0.148840i	−0.628760	+	0.777600i	$0.716437\pi$
$60$	4.23679	+	1.43165i	0.546967	+	0.184825i
$61$	2.67458	−	2.67458i	0.342445	−	0.342445i	−0.514841	−	0.857286i	$-0.672149\pi$
$61$	2.67458	−	2.67458i	0.342445	−	0.342445i	0.857286	+	0.514841i	$0.172149\pi$
$62$	−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	$-0.0945250\pi$
$67$	5.43194	+	5.43194i	0.663617	+	0.663617i	−0.292614	+	0.956231i	$0.594525\pi$
$68$	−2.94239	−	0.380808i	−0.356817	−	0.0461798i
$69$	−4.68044	−	4.68044i	−0.563459	−	0.563459i
$70$	4.85672	+	1.29984i	0.580488	+	0.155361i
$71$		−	2.26233i		−	0.268489i	−0.990948	−	0.134245i	$-0.957139\pi$
$71$		−	2.26233i		−	0.268489i	0.990948	−	0.134245i	$-0.0428608\pi$
$72$	2.34657	−	1.57912i	0.276546	−	0.186101i
$73$	5.27105			0.616930			0.308465	−	0.951236i	$-0.400185\pi$
$73$	5.27105			0.616930			0.308465	+	0.951236i	$0.400185\pi$
$74$	0.276233	−	4.28653i	0.0321115	−	0.498299i
$75$	4.62248	−	1.90596i	0.533758	−	0.220081i
$76$	−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	$0.619550\pi$
$80$	2.90534	+	8.45925i	0.324827	+	0.945773i
$81$	−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	$-0.225930\pi$
$83$	0.973359	+	0.973359i	0.106840	+	0.106840i	−0.651666	+	0.758506i	$0.725930\pi$
$84$	2.51843	−	1.94125i	0.274783	−	0.211807i
$85$	−2.75957	+	1.84067i	−0.299318	+	0.199649i
$86$	−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	$-0.881987\pi$
$89$		−	6.83613i		−	0.724629i	0.932056	−	0.362314i	$-0.118013\pi$
$90$	0.817572	−	3.05476i	0.0861797	−	0.322000i
$91$	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
$100$	8.66315	+	4.99498i	0.866315	+	0.499498i
$101$	2.18050	+	2.18050i	0.216968	+	0.216968i	0.807220	−	0.590251i	$-0.200971\pi$
$101$	2.18050	+	2.18050i	0.216968	+	0.216968i	−0.590251	+	0.807220i	$0.700971\pi$
$102$	−0.134915	+	2.09359i	−0.0133586	+	0.207296i
$103$	−8.09580			−0.797703			−0.398851	−	0.917016i	$-0.630591\pi$
$103$	−8.09580			−0.797703			−0.398851	+	0.917016i	$0.630591\pi$
$104$	−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	$-0.961144\pi$
$107$	−9.00752	+	9.00752i	−0.870790	+	0.870790i	0.121768	+	0.992559i	$0.461144\pi$
$108$	−1.22100	−	1.58403i	−0.117491	−	0.152424i
$109$	−9.91170	+	9.91170i	−0.949369	+	0.949369i	−0.998779	−	0.0494097i	$-0.984266\pi$
$109$	−9.91170	+	9.91170i	−0.949369	+	0.949369i	0.0494097	+	0.998779i	$0.484266\pi$
$110$	−8.77222	−	15.1838i	−0.836398	−	1.44771i
$111$	−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
$115$	−8.21298	−	12.3131i	−0.765865	−	1.14820i
$116$	−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
$120$	5.83710	−	2.43481i	0.532852	−	0.222266i
$121$			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
$125$	10.9708	−	2.15462i	0.981255	−	0.192716i
$126$	−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
$130$	6.94555	+	12.0220i	0.609165	+	1.05440i
$131$	0.701725	−	0.701725i	0.0613100	−	0.0613100i	−0.675787	−	0.737097i	$-0.736196\pi$
$131$	0.701725	−	0.701725i	0.0613100	−	0.0613100i	0.737097	+	0.675787i	$0.236196\pi$
$132$	−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	$-0.247078\pi$
$137$	16.7042			1.42714			0.713568	+	0.700586i	$0.247078\pi$
$138$	−9.34151	−	0.601986i	−0.795202	−	0.0512445i
$139$	−5.03646	−	5.03646i	−0.427187	−	0.427187i	0.460482	−	0.887669i	$-0.347677\pi$
$139$	−5.03646	−	5.03646i	−0.427187	−	0.427187i	−0.887669	+	0.460482i	$0.847677\pi$
$140$	6.37255	−	3.15359i	0.538579	−	0.266527i
$141$	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	−0.999998	−	0.00178156i	$-0.999433\pi$
$149$	−12.2283	−	12.2283i	−1.00178	−	1.00178i	−0.00178156	−	0.999998i	$-0.500567\pi$
$150$	3.13073	−	6.34023i	0.255623	−	0.517678i
$151$			0.567736i			0.0462017i	0.999733	+	0.0231008i	$0.00735388\pi$
$151$			0.567736i			0.0462017i	−0.999733	+	0.0231008i	$0.992646\pi$
$152$	−19.3963	−	3.79186i	−1.57325	−	0.307561i
$153$	1.48346			0.119931
$154$	−12.4423	−	0.801810i	−1.00263	−	0.0646117i
$155$	1.86604	+	2.79761i	0.149884	+	0.224709i
$156$	8.70847	+	1.12706i	0.697235	+	0.0902373i
$157$	8.06109	+	8.06109i	0.643345	+	0.643345i	0.951376	−	0.308031i	$-0.0996702\pi$
$157$	8.06109	+	8.06109i	0.643345	+	0.643345i	−0.308031	+	0.951376i	$0.599670\pi$
$158$	−6.92641	+	6.08775i	−0.551036	+	0.484315i
$159$	−1.31755			−0.104488
$160$	10.9839	+	6.27326i	0.868354	+	0.495944i
$161$	−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	$-0.251708\pi$
$163$	−0.0969036	−	0.0969036i	−0.00759008	−	0.00759008i	−0.710892	+	0.703302i	$0.751708\pi$
$164$	13.5843	+	1.75811i	1.06076	+	0.137285i
$165$	−10.3154	+	6.88051i	−0.803054	+	0.535647i
$166$	1.94269	+	0.125191i	0.150782	+	0.00971670i
$167$	14.9619			1.15779			0.578894	−	0.815403i	$-0.303484\pi$
$167$	14.9619			1.15779			0.578894	+	0.815403i	$0.303484\pi$
$168$	0.862779	−	4.41332i	0.0665649	−	0.340495i
$169$			6.27691i			0.482839i
$170$	−1.21284	+	4.53163i	−0.0930205	+	0.347560i
$171$	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	$-0.499801\pi$
$173$	−13.1447	−	13.1447i	−0.999374	−	0.999374i	−1.00000		0.000626029i	$0.999801\pi$
$174$	−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	−0.561349	−	0.827579i	$-0.689717\pi$
$179$	3.56192	−	3.56192i	0.266230	−	0.266230i	0.827579	+	0.561349i	$0.189717\pi$
$180$	−1.98353	−	4.00819i	−0.147844	−	0.298753i
$181$	5.89499	+	5.89499i	0.438171	+	0.438171i	0.891396	−	0.453225i	$-0.149727\pi$
$181$	5.89499	+	5.89499i	0.438171	+	0.438171i	−0.453225	+	0.891396i	$0.649727\pi$
$182$	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
$190$	−19.1327	+	11.0537i	−1.38803	+	0.801917i
$191$	−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
$195$	8.16740	−	5.44776i	0.584880	−	0.390122i
$196$	−1.14804	+	8.87056i	−0.0820031	+	0.633612i
$197$	3.90642	−	3.90642i	0.278321	−	0.278321i	−0.554118	−	0.832438i	$-0.686944\pi$
$197$	3.90642	−	3.90642i	0.278321	−	0.278321i	0.832438	+	0.554118i	$0.186944\pi$
$198$	−0.504320	+	7.82594i	−0.0358405	+	0.556165i
$199$			3.84627i			0.272655i	0.990664	+	0.136328i	$0.0435300\pi$
$199$			3.84627i			0.272655i	−0.990664	+	0.136328i	$0.956470\pi$
$200$	13.8658	−	2.78224i	0.980457	−	0.196734i
$201$		−	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
$205$	12.7403	−	8.49795i	0.889823	−	0.593523i
$206$	−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
$210$	−2.51509	−	4.35334i	−0.173558	−	0.300409i
$211$	8.77616	−	8.77616i	0.604176	−	0.604176i	−0.337242	−	0.941418i	$-0.609494\pi$
$211$	8.77616	−	8.77616i	0.604176	−	0.604176i	0.941418	+	0.337242i	$0.109494\pi$
$212$	−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
$220$	−23.4941	−	7.93885i	−1.58397	−	0.535237i
$221$	−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	−0.996913	−	0.0785084i	$-0.974984\pi$
$227$	−16.2029	−	16.2029i	−1.07542	−	1.07542i	−0.0785084	−	0.996913i	$-0.525016\pi$
$228$	−1.79369	+	13.8593i	−0.118790	+	0.917854i
$229$	1.34898	+	1.34898i	0.0891433	+	0.0891433i	0.750272	−	0.661129i	$-0.229922\pi$
$229$	1.34898	+	1.34898i	0.0891433	+	0.0891433i	−0.661129	+	0.750272i	$0.729922\pi$
$230$	−20.2199	−	5.41163i	−1.33326	−	0.356832i
$231$			8.81631i			0.580070i
$232$	−17.3754	−	3.39678i	−1.14075	−	0.223010i
$233$	13.0887			0.857470			0.428735	−	0.903430i	$-0.358959\pi$
$233$	13.0887			0.857470			0.428735	+	0.903430i	$0.358959\pi$
$234$	0.399304	−	6.19632i	0.0261033	−	0.405066i
$235$	24.7468	−	16.5064i	1.61430	−	1.07676i
$236$	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	$0.383846\pi$
$240$	3.92721	−	8.03598i	0.253500	−	0.518721i
$241$	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
$245$	5.54916	+	8.31943i	0.354523	+	0.531509i
$246$	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
$250$	9.64196	−	12.5313i	0.609811	−	0.792547i
$251$	15.0055	+	15.0055i	0.947138	+	0.947138i	0.998671	−	0.0515329i	$-0.0164107\pi$
$251$	15.0055	+	15.0055i	0.947138	+	0.947138i	−0.0515329	+	0.998671i	$0.516411\pi$
$252$	−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
$260$	18.6018	+	6.28572i	1.15364	+	0.389824i
$261$	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	$-0.451325\pi$
$263$	4.94045			0.304641			0.152320	+	0.988331i	$0.451325\pi$
$264$	−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	−0.965896	−	0.258929i	$-0.916630\pi$
$269$	−11.5951	+	11.5951i	−0.706967	+	0.706967i	0.258929	+	0.965896i	$0.416630\pi$
$270$	−2.73815	+	1.58193i	−0.166639	+	0.0962733i
$271$	−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
$275$	−25.6328	+	10.5690i	−1.54572	+	0.637337i
$276$	−10.4849	+	8.08198i	−0.631119	+	0.486478i
$277$	11.2957	−	11.2957i	0.678690	−	0.678690i	−0.281014	−	0.959704i	$-0.590671\pi$
$277$	11.2957	−	11.2957i	0.678690	−	0.678690i	0.959704	+	0.281014i	$0.0906707\pi$
$278$	−10.0521	−	0.647777i	−0.602884	−	0.0388511i
$279$		−	1.50391i		−	0.0900366i
$280$	3.82492	−	9.29942i	0.228582	−	0.555746i
$281$		−	4.72775i		−	0.282034i	−0.990007	−	0.141017i	$-0.954963\pi$
$281$		−	4.72775i		−	0.282034i	0.990007	−	0.141017i	$-0.0450372\pi$
$282$	1.20987	−	18.7745i	0.0720466	−	1.11801i
$283$	−6.51882	+	6.51882i	−0.387504	+	0.387504i	−0.873796	−	0.486292i	$-0.838349\pi$
$283$	−6.51882	+	6.51882i	−0.387504	+	0.387504i	0.486292	+	0.873796i	$0.338349\pi$
$284$	−4.48724	−	0.580746i	−0.266268	−	0.0344609i
$285$	8.66996	+	12.9982i	0.513564	+	0.769948i
$286$	−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
$290$	−17.1392	+	9.90196i	−1.00645	+	0.581463i
$291$	−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	$-0.784340\pi$
$293$	−2.60652	+	2.60652i	−0.152274	+	0.152274i	0.626859	+	0.779133i	$0.284340\pi$
$294$	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
$300$	−2.59379	−	9.65776i	−0.149752	−	0.557591i
$301$	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	$-0.127848\pi$
$307$	9.27735	+	9.27735i	0.529486	+	0.529486i	−0.390933	+	0.920419i	$0.627848\pi$
$308$	−13.9653	+	10.7647i	−0.795747	+	0.613376i
$309$	5.72459	+	5.72459i	0.325661	+	0.325661i
$310$	4.59408	+	1.22955i	0.260926	+	0.0698339i
$311$		−	8.87398i		−	0.503197i	−0.967832	−	0.251599i	$-0.919044\pi$
$311$		−	8.87398i		−	0.503197i	0.967832	−	0.251599i	$-0.0809563\pi$
$312$	10.3027	−	6.93320i	0.583277	−	0.392515i
$313$	−25.6160			−1.44790			−0.723952	−	0.689850i	$-0.757676\pi$
$313$	−25.6160			−1.44790			−0.723952	+	0.689850i	$0.757676\pi$
$314$	16.0888	+	1.03680i	0.907944	+	0.0585098i
$315$	−2.95754	+	1.97271i	−0.166638	+	0.111150i
$316$	−1.67385	+	12.9333i	−0.0941613	+	0.727554i
$317$	−19.5425	−	19.5425i	−1.09762	−	1.09762i	−0.994689	−	0.102929i	$-0.967179\pi$
$317$	−19.5425	−	19.5425i	−1.09762	−	1.09762i	−0.102929	−	0.994689i	$-0.532821\pi$
$318$	−1.39955	+	1.23009i	−0.0784828	+	0.0689800i
$319$	34.7100			1.94339
$320$	17.5244	−	3.59112i	0.979643	−	0.200750i
$321$	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
$325$	20.2952	−	8.36821i	1.12578	−	0.464185i
$326$	−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
$330$	−4.53365	+	16.9394i	−0.249569	+	0.932485i
$331$	−17.9546	−	17.9546i	−0.986875	−	0.986875i	0.0130395	−	0.999915i	$-0.495849\pi$
$331$	−17.9546	−	17.9546i	−0.986875	−	0.986875i	−0.999915	+	0.0130395i	$0.995849\pi$
$332$	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
$340$	2.94250	+	5.94600i	0.159579	+	0.322467i
$341$	−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	$-0.976031\pi$
$347$	−17.1738	+	17.1738i	−0.921936	+	0.921936i	0.0752299	+	0.997166i	$0.476031\pi$
$348$	−1.60681	+	12.4153i	−0.0861338	+	0.665529i
$349$	−11.7155	+	11.7155i	−0.627115	+	0.627115i	−0.947341	−	0.320226i	$-0.896241\pi$
$349$	−11.7155	+	11.7155i	−0.627115	+	0.627115i	0.320226	+	0.947341i	$0.396241\pi$
$350$	−3.60817	−	10.6474i	−0.192865	−	0.569128i
$351$	−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
$355$	−4.20844	+	2.80708i	−0.223361	+	0.148984i
$356$	−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	$0.272620\pi$
$359$			28.6304i			1.51106i	−0.655116	+	0.755529i	$0.727380\pi$
$360$	−5.84912	−	2.40578i	−0.308276	−	0.126796i
$361$		−	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
$365$	−6.54028	−	9.80534i	−0.342334	−	0.513235i
$366$	−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
$370$	−8.31666	+	4.80484i	−0.432363	+	0.249792i
$371$	−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	$-0.876798\pi$
$373$	−10.5946	+	10.5946i	−0.548568	+	0.548568i	0.377458	+	0.926027i	$0.376798\pi$
$374$	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	−0.906320	−	0.422593i	$-0.861120\pi$
$379$	−25.8712	−	25.8712i	−1.32891	−	1.32891i	−0.422593	−	0.906320i	$-0.638880\pi$
$380$	−10.0036	+	29.6043i	−0.513172	+	1.51867i
$381$	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	0.991505	+	0.130071i	$0.0415205\pi$
$389$	22.1209	+	22.1209i	1.12158	+	1.12158i	0.130071	+	0.991505i	$0.458480\pi$
$390$	3.58959	−	13.4121i	0.181766	−	0.679147i
$391$		−	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
$395$	8.09068	+	12.1297i	0.407086	+	0.610313i
$396$	6.77076	+	8.78386i	0.340243	+	0.441406i
$397$	−12.9968	−	12.9968i	−0.652290	−	0.652290i	0.301254	−	0.953544i	$-0.402595\pi$
$397$	−12.9968	−	12.9968i	−0.652290	−	0.652290i	−0.953544	+	0.301254i	$0.902595\pi$
$398$	3.59096	+	4.08566i	0.179999	+	0.204796i
$399$	11.1092			0.556156
$400$	12.1312	−	15.9008i	0.606559	−	0.795038i
$401$	−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
$405$	1.24079	+	1.86022i	0.0616555	+	0.0924353i
$406$	−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	$-0.763169\pi$
$409$		−	27.3933i		−	1.35451i	0.735747	−	0.677256i	$-0.236831\pi$
$410$	5.59940	−	20.9215i	0.276535	−	1.03324i
$411$	−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	−0.610561	−	0.791969i	$-0.709056\pi$
$419$	3.71334	−	3.71334i	0.181409	−	0.181409i	0.791969	+	0.610561i	$0.209056\pi$
$420$	−6.73600	−	2.27615i	−0.328683	−	0.111065i
$421$	−10.7755	−	10.7755i	−0.525167	−	0.525167i	0.393960	−	0.919127i	$-0.371105\pi$
$421$	−10.7755	−	10.7755i	−0.525167	−	0.525167i	−0.919127	+	0.393960i	$0.871105\pi$
$422$	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
$430$	1.24867	−	0.721400i	0.0602160	−	0.0347890i
$431$	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
$435$	7.76663	+	11.6439i	0.372381	+	0.558283i
$436$	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	$0.233734\pi$
$439$			28.0789i			1.34013i	−0.742302	+	0.670065i	$0.766266\pi$
$440$	−32.3682	+	13.5016i	−1.54309	+	0.643664i
$441$		−	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	$-0.715300\pi$
$443$	3.23844	−	3.23844i	0.153863	−	0.153863i	0.779841	+	0.625978i	$0.215300\pi$
$444$	−0.779688	+	6.02440i	−0.0370024	+	0.285906i
$445$	−12.7167	+	8.48222i	−0.602831	+	0.402096i
$446$	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	$0.492035\pi$
$450$	−6.69698	+	2.26946i	−0.315699	+	0.106983i
$451$	−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	$-0.470486\pi$
$457$	3.95861			0.185176			0.0925880	+	0.995705i	$0.470486\pi$
$458$	2.69238	+	0.173503i	0.125807	+	0.00810725i
$459$	−1.04897	−	1.04897i	−0.0489616	−	0.0489616i
$460$	−26.5308	+	13.1293i	−1.23700	+	0.612157i
$461$	−17.2310	+	17.2310i	−0.802526	+	0.802526i	−0.983490	−	0.180963i	$-0.942078\pi$
$461$	−17.2310	+	17.2310i	−0.802526	+	0.802526i	0.180963	+	0.983490i	$0.442078\pi$
$462$	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	0.972576	+	0.232585i	$0.0747183\pi$
$467$	26.0437	+	26.0437i	1.20516	+	1.20516i	0.232585	+	0.972576i	$0.425282\pi$
$468$	−5.36086	−	6.95477i	−0.247806	−	0.321484i
$469$	−8.63615	−	8.63615i	−0.398780	−	0.398780i
$470$	10.8763	−	40.6379i	0.501684	−	1.87448i
$471$		−	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
$475$	13.3178	+	32.2993i	0.611062	+	1.48199i
$476$	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	$0.639126\pi$
$480$	−3.33094	−	12.2027i	−0.152036	−	0.556973i
$481$	−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
$485$	−29.4340	+	19.6328i	−1.33653	+	0.891481i
$486$	1.41129	+	0.0909462i	0.0640172	+	0.00412541i
$487$	−4.16579			−0.188770			−0.0943851	−	0.995536i	$-0.530088\pi$
$487$	−4.16579			−0.188770			−0.0943851	+	0.995536i	$0.530088\pi$
$488$	−10.4996	−	2.05261i	−0.475293	−	0.0929171i
$489$			0.137042i			0.00619727i
$490$	13.6617	+	3.65641i	0.617174	+	0.165180i
$491$	−20.2554	−	20.2554i	−0.914115	−	0.914115i	0.0824778	−	0.996593i	$-0.473717\pi$
$491$	−20.2554	−	20.2554i	−0.914115	−	0.914115i	−0.996593	+	0.0824778i	$0.973717\pi$
$492$	−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	−0.575518	−	0.817789i	$-0.695200\pi$
$499$	5.41192	−	5.41192i	0.242271	−	0.242271i	0.817789	+	0.575518i	$0.195200\pi$
$500$	−1.45739	−	22.3131i	−0.0651763	−	0.997874i
$501$	−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	$-0.514869\pi$
$503$	−2.09459			−0.0933934			−0.0466967	+	0.998909i	$0.514869\pi$
$504$	−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	−0.180638	+	0.983550i	$0.557816\pi$
$509$	−26.2653	+	26.2653i	−1.16419	+	1.16419i	−0.983550	+	0.180638i	$0.942184\pi$
$510$	4.06195	−	2.34674i	0.179866	−	0.103915i
$511$	−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
$515$	10.0452	+	15.0600i	0.442644	+	0.663623i
$516$	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
$520$	25.6281	−	10.6901i	1.12386	−	0.468793i
$521$			10.2533i			0.449205i	0.974450	+	0.224602i	$0.0721083\pi$
$521$			10.2533i			0.449205i	−0.974450	+	0.224602i	$0.927892\pi$
$522$	8.83382	+	0.569270i	0.386646	+	0.0249163i
$523$	−7.87557	+	7.87557i	−0.344375	+	0.344375i	−0.858009	−	0.513634i	$-0.828299\pi$
$523$	−7.87557	+	7.87557i	−0.344375	+	0.344375i	0.513634	+	0.858009i	$0.328299\pi$
$524$	−1.21171	−	1.57198i	−0.0529337	−	0.0686721i
$525$	−7.34920	+	3.03025i	−0.320745	+	0.132251i
$526$	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
$530$	−3.60765	+	2.08427i	−0.156706	+	0.0905349i
$531$	−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
$540$	−1.43165	+	4.23679i	−0.0616083	+	0.182322i
$541$	23.6782	−	23.6782i	1.01800	−	1.01800i	0.0181698	−	0.999835i	$-0.494216\pi$
$541$	23.6782	−	23.6782i	1.01800	−	1.01800i	0.999835	−	0.0181698i	$-0.00578394\pi$
$542$	−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	$-0.186018\pi$
$547$	6.60366	+	6.60366i	0.282352	+	0.282352i	−0.551694	+	0.834046i	$0.686018\pi$
$548$	4.28801	−	33.1321i	0.183175	−	1.41533i
$549$	2.67458	+	2.67458i	0.114148	+	0.114148i
$550$	−17.3607	+	35.1582i	−0.740263	+	1.49915i
$551$		−	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
$555$	3.76869	+	5.65010i	0.159972	+	0.239834i
$556$	−11.2825	+	8.69674i	−0.478484	+	0.368824i
$557$	11.5466	+	11.5466i	0.489245	+	0.489245i	0.908068	−	0.418823i	$-0.137557\pi$
$557$	11.5466	+	11.5466i	0.489245	+	0.489245i	−0.418823	+	0.908068i	$0.637557\pi$
$558$	−1.40408	−	1.59751i	−0.0594395	−	0.0676279i
$559$	2.00220			0.0846840
$560$	−4.61916	−	13.4492i	−0.195195	−	0.568333i
$561$	−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	$-0.380071\pi$
$563$	−13.3335	−	13.3335i	−0.561940	−	0.561940i	−0.929858	+	0.367918i	$0.880071\pi$
$564$	−16.2431	−	21.0726i	−0.683958	−	0.887315i
$565$	19.4599	−	12.9800i	0.818685	−	0.546073i
$566$	−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	$0.0935887\pi$
$569$			13.8256i			0.579600i	−0.957087	+	0.289800i	$0.906411\pi$
$570$	21.3450	+	5.71274i	0.894043	+	0.239280i
$571$	17.8448	+	17.8448i	0.746781	+	0.746781i	0.973873	−	0.227092i	$-0.0729218\pi$
$571$	17.8448	+	17.8448i	0.746781	+	0.746781i	−0.227092	+	0.973873i	$0.572922\pi$
$572$	−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
$580$	−8.96127	+	26.5198i	−0.372097	+	1.10117i
$581$	−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	$-0.843980\pi$
$587$	−9.96994	+	9.96994i	−0.411504	+	0.411504i	0.470758	+	0.882262i	$0.343980\pi$
$588$	7.08422	−	5.46065i	0.292148	−	0.225193i
$589$	−7.43061	+	7.43061i	−0.306173	+	0.306173i
$590$	−2.55769	−	4.42709i	−0.105299	−	0.182261i
$591$	−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
$595$	4.38740	−	2.92645i	0.179866	−	0.119973i
$596$	−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	$0.0507841\pi$
$599$			7.77638i			0.317734i	−0.987300	+	0.158867i	$0.949216\pi$
$600$	−11.7719	−	7.83723i	−0.480586	−	0.319953i
$601$		−	31.7530i		−	1.29523i	−0.761966	−	0.647617i	$-0.775766\pi$
$601$		−	31.7530i		−	1.29523i	0.761966	−	0.647617i	$-0.224234\pi$
$602$	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
$605$	36.7391	−	24.5055i	1.49366	−	0.996288i
$606$	−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
$610$	−10.3569	+	5.98355i	−0.419338	+	0.242267i
$611$	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	$-0.576609\pi$
$613$	18.1437	−	18.1437i	0.732818	−	0.732818i	0.971177	+	0.238359i	$0.0766094\pi$
$614$	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	$-0.403619\pi$
$617$	14.8136			0.596372			0.298186	+	0.954508i	$0.403619\pi$
$618$	11.4255	+	0.736282i	0.459600	+	0.0296176i
$619$	6.05155	+	6.05155i	0.243232	+	0.243232i	0.818186	−	0.574954i	$-0.194980\pi$
$619$	6.05155	+	6.05155i	0.243232	+	0.243232i	−0.574954	+	0.818186i	$0.694980\pi$
$620$	6.02795	−	2.98305i	0.242088	−	0.119802i
$621$	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
$630$	−1.29984	+	4.85672i	−0.0517870	+	0.193496i
$631$			35.8534i			1.42730i	0.700502	+	0.713650i	$0.252959\pi$
$631$			35.8534i			1.42730i	−0.700502	+	0.713650i	$0.747041\pi$
$632$	10.2968	+	15.3010i	0.409583	+	0.608640i
$633$	−12.4114			−0.493307
$634$	−39.0042	−	2.51351i	−1.54905	−	0.0998242i
$635$	3.50212	−	2.33596i	0.138978	−	0.0926997i
$636$	−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
$640$	15.2623	−	20.1758i	0.603297	−	0.797517i
$641$	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	$-0.145057\pi$
$643$	11.6098	+	11.6098i	0.457847	+	0.457847i	−0.440101	+	0.897948i	$0.645057\pi$
$644$	−2.70145	+	20.8732i	−0.106452	+	0.822521i
$645$	−0.565832	−	0.848308i	−0.0222796	−	0.0334021i
$646$	−14.6288	−	0.942714i	−0.575564	−	0.0370906i
$647$	−18.0688			−0.710357			−0.355178	−	0.934799i	$-0.615580\pi$
$647$	−18.0688			−0.710357			−0.355178	+	0.934799i	$0.615580\pi$
$648$	1.57912	+	2.34657i	0.0620337	+	0.0921819i
$649$			8.96566i			0.351933i
$650$	13.7456	−	27.8371i	0.539148	−	1.09186i
$651$	−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	$-0.282189\pi$
$653$	−3.64829	−	3.64829i	−0.142769	−	0.142769i	−0.774879	+	0.632110i	$0.782189\pi$
$654$	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	−0.984148	−	0.177351i	$-0.943247\pi$
$659$	−20.7113	+	20.7113i	−0.806796	+	0.806796i	0.177351	+	0.984148i	$0.443247\pi$
$660$	10.9992	+	22.2264i	0.428143	+	0.865163i
$661$	11.7363	+	11.7363i	0.456488	+	0.456488i	0.897501	−	0.441013i	$-0.145381\pi$
$661$	11.7363	+	11.7363i	0.456488	+	0.456488i	−0.441013	+	0.897501i	$0.645381\pi$
$662$	−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
$670$	−12.1523	−	21.0343i	−0.469484	−	0.812626i
$671$	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
$675$	1.90596	+	4.62248i	0.0733604	+	0.177919i
$676$	12.4500	+	1.61130i	0.478846	+	0.0619730i
$677$	−16.5124	+	16.5124i	−0.634623	+	0.634623i	−0.949224	−	0.314601i	$-0.898129\pi$
$677$	−16.5124	+	16.5124i	−0.634623	+	0.634623i	0.314601	+	0.949224i	$0.398129\pi$
$678$	0.951394	−	14.7636i	0.0365381	−	0.566991i
$679$			25.1564i			0.965416i
$680$	8.67695	+	3.56889i	0.332746	+	0.136861i
$681$			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	$-0.586270\pi$
$683$	18.1836	−	18.1836i	0.695777	−	0.695777i	0.963497	+	0.267720i	$0.0862702\pi$
$684$	11.0683	−	8.53167i	0.423208	−	0.326217i
$685$	−20.7264	−	31.0736i	−0.791917	−	1.18726i
$686$	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
$690$	10.4710	+	18.1242i	0.398626	+	0.689978i
$691$	−13.9630	+	13.9630i	−0.531178	+	0.531178i	−0.920923	−	0.389745i	$-0.872563\pi$
$691$	−13.9630	+	13.9630i	−0.531178	+	0.531178i	0.389745	+	0.920923i	$0.372563\pi$
$692$	−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
$700$	−13.7734	−	7.94143i	−0.520585	−	0.300158i
$701$	−15.7918	+	15.7918i	−0.596448	+	0.596448i	−0.939365	−	0.342918i	$-0.888585\pi$
$701$	−15.7918	+	15.7918i	−0.596448	+	0.596448i	0.342918	+	0.939365i	$0.388585\pi$
$702$	−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	0.432606	−	0.901583i	$-0.357594\pi$
$709$	−12.4875	−	12.4875i	−0.468977	−	0.468977i	−0.901583	+	0.432606i	$0.857594\pi$
$710$	−1.84962	+	6.91088i	−0.0694150	+	0.259361i
$711$		−	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
$715$	−45.2903	+	30.2092i	−1.69376	+	1.12976i
$716$	−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	$0.334782\pi$
$720$	−8.45925	+	2.90534i	−0.315258	+	0.108276i
$721$	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
$725$	11.9302	+	28.9340i	0.443076	+	1.07458i
$726$	1.79617	−	27.8727i	0.0666623	−	1.03445i
$727$	−5.84475			−0.216770			−0.108385	−	0.994109i	$-0.534568\pi$
$727$	−5.84475			−0.216770			−0.108385	+	0.994109i	$0.534568\pi$
$728$	3.78807	−	19.3769i	0.140395	−	0.718156i
$729$		−	1.00000i		−	0.0370370i
$730$	−16.1018	−	4.30947i	−0.595955	−	0.159501i
$731$	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	−0.945260	−	0.326318i	$-0.894192\pi$
$733$	−34.4267	−	34.4267i	−1.27158	−	1.27158i	−0.326318	−	0.945260i	$-0.605808\pi$
$734$	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	−0.839329	−	0.543624i	$-0.817052\pi$
$739$	−8.03861	+	8.03861i	−0.295705	+	0.295705i	0.543624	+	0.839329i	$0.317052\pi$
$740$	−4.34838	+	12.8685i	−0.159850	+	0.473056i
$741$	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	$-0.524208\pi$
$743$	−4.14206			−0.151957			−0.0759787	+	0.997109i	$0.524208\pi$
$744$	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
$750$	−15.6788	+	2.04304i	−0.572510	+	0.0746014i
$751$	−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
$755$	1.05612	−	0.704442i	0.0384360	−	0.0256373i
$756$	1.94125	+	2.51843i	0.0706025	+	0.0915943i
$757$	4.39557	−	4.39557i	0.159760	−	0.159760i	−0.622701	−	0.782460i	$-0.713965\pi$
$757$	4.39557	−	4.39557i	0.159760	−	0.159760i	0.782460	+	0.622701i	$0.213965\pi$
$758$	−51.6352	−	3.32748i	−1.87548	−	0.120860i
$759$		−	36.7048i		−	1.33230i
$760$	17.0131	+	40.7864i	0.617129	+	1.47948i
$761$			17.0961i			0.619732i	0.950780	+	0.309866i	$0.100284\pi$
$761$			17.0961i			0.619732i	−0.950780	+	0.309866i	$0.899716\pi$
$762$	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
$765$	−1.84067	−	2.75957i	−0.0665495	−	0.0997726i
$766$	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	$0.294468\pi$
$770$	13.9468	+	24.1404i	0.502608	+	0.869960i
$771$	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	$-0.949395\pi$
$773$	−23.0507	+	23.0507i	−0.829078	+	0.829078i	0.158312	+	0.987389i	$0.449395\pi$
$774$	−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
$780$	−8.70880	−	17.5982i	−0.311825	−	0.630115i
$781$	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	$-0.167596\pi$
$787$	10.1563	+	10.1563i	0.362034	+	0.362034i	−0.502527	+	0.864561i	$0.667596\pi$
$788$	−6.74543	−	8.75100i	−0.240296	−	0.311741i
$789$	−3.49342	−	3.49342i	−0.124369	−	0.124369i
$790$	19.9188	+	5.33104i	0.708680	+	0.189670i
$791$		−	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
$795$	1.63480	+	2.45093i	0.0579804	+	0.0869256i
$796$	7.62892	+	0.987348i	0.270400	+	0.0349956i
$797$	24.6189	+	24.6189i	0.872046	+	0.872046i	0.992695	−	0.120649i	$-0.0384975\pi$
$797$	24.6189	+	24.6189i	0.872046	+	0.872046i	−0.120649	+	0.992695i	$0.538498\pi$
$798$	11.8006	−	10.3718i	0.417738	−	0.367158i
$799$	19.7347			0.698163
$800$	−1.95909	−	28.2163i	−0.0692642	−	0.997598i
$801$	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
$805$	13.0577	+	19.5764i	0.460223	+	0.689977i
$806$	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	$-0.857958\pi$
$809$		−	24.5505i		−	0.863150i	0.902077	−	0.431575i	$-0.142042\pi$
$810$	3.05476	+	0.817572i	0.107333	+	0.0287266i
$811$	13.4539	+	13.4539i	0.472430	+	0.472430i	0.902700	−	0.430270i	$-0.141582\pi$
$811$	13.4539	+	13.4539i	0.472430	+	0.472430i	−0.430270	+	0.902700i	$0.641582\pi$
$812$	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
$820$	−13.5849	−	27.4513i	−0.474404	−	0.958642i
$821$	−7.23091	−	7.23091i	−0.252360	−	0.252360i	0.569577	−	0.821938i	$-0.307107\pi$
$821$	−7.23091	−	7.23091i	−0.252360	−	0.252360i	−0.821938	+	0.569577i	$0.807107\pi$
$822$	−23.5744	−	1.51918i	−0.822252	−	0.0529876i
$823$	−42.5825			−1.48433			−0.742167	−	0.670215i	$-0.766202\pi$
$823$	−42.5825			−1.48433			−0.742167	+	0.670215i	$0.766202\pi$
$824$	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	$-0.600512\pi$
$827$	18.4053	−	18.4053i	0.640014	−	0.640014i	0.950559	+	0.310545i	$0.100512\pi$
$828$	13.1288	+	1.69915i	0.456257	+	0.0590495i
$829$	10.8176	−	10.8176i	0.375710	−	0.375710i	−0.493842	−	0.869552i	$-0.664408\pi$
$829$	10.8176	−	10.8176i	0.375710	−	0.375710i	0.869552	+	0.493842i	$0.164408\pi$
$830$	−2.17759	−	3.76917i	−0.0755852	−	0.130830i
$831$	−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
$835$	−18.5646	−	27.8325i	−0.642456	−	0.963185i
$836$	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	$0.0598771\pi$
$839$			10.8332i			0.374004i	−0.982360	+	0.187002i	$0.940123\pi$
$840$	−9.28030	+	3.87106i	−0.320201	+	0.133564i
$841$		−	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
$845$	11.6765	−	7.78834i	0.401683	−	0.267927i
$846$	−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
$850$	9.93473	−	3.36666i	0.340758	−	0.115475i
$851$	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	0.0903009	−	0.995915i	$-0.471217\pi$
$853$	31.7242	−	31.7242i	1.08622	−	1.08622i	0.995915	−	0.0903009i	$-0.0287829\pi$
$854$	−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	$-0.739086\pi$
$857$	−39.9570			−1.36490			−0.682452	+	0.730930i	$0.739086\pi$
$858$	−2.21424	+	34.3602i	−0.0755930	+	1.17304i
$859$	23.9624	+	23.9624i	0.817587	+	0.817587i	0.985758	−	0.168171i	$-0.0537861\pi$
$859$	23.9624	+	23.9624i	0.817587	+	0.817587i	−0.168171	+	0.985758i	$0.553786\pi$
$860$	0.652867	−	1.93208i	0.0222626	−	0.0658834i
$861$	−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
$870$	19.1210	+	5.11752i	0.648263	+	0.173500i
$871$		−	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
$875$	−17.4422	+	3.42560i	−0.589655	+	0.115806i
$876$	−8.34952	+	6.43596i	−0.282104	+	0.217451i
$877$	22.4582	+	22.4582i	0.758358	+	0.758358i	0.976023	−	0.217666i	$-0.0698442\pi$
$877$	22.4582	+	22.4582i	0.758358	+	0.758358i	−0.217666	+	0.976023i	$0.569844\pi$
$878$	26.2150	+	29.8264i	0.884714	+	1.00659i
$879$	3.68618			0.124332
$880$	−21.7774	+	44.5616i	−0.734115	+	1.50217i
$881$	−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	−0.928771	−	0.370653i	$-0.879134\pi$
$883$	−38.6128	−	38.6128i	−1.29942	−	1.29942i	−0.370653	−	0.928771i	$-0.620866\pi$
$884$	7.95264	+	10.3171i	0.267476	+	0.347003i
$885$	−3.00764	+	2.00613i	−0.101101	+	0.0674354i
$886$	0.416520	−	6.46348i	0.0139933	−	0.217145i
$887$	27.1077			0.910186			0.455093	−	0.890444i	$-0.349606\pi$
$887$	27.1077			0.910186			0.455093	+	0.890444i	$0.349606\pi$
$888$	4.79630	+	7.12729i	0.160953	+	0.239176i
$889$		−	2.99317i		−	0.100388i
$890$	−5.58903	+	20.8828i	−0.187345	+	0.699992i
$891$	−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
$900$	−4.99498	+	8.66315i	−0.166499	+	0.288772i
$901$	−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	$-0.695220\pi$
$907$	7.29362	−	7.29362i	0.242181	−	0.242181i	0.817752	+	0.575571i	$0.195220\pi$
$908$	−36.2970	+	27.9784i	−1.20456	+	0.928495i
$909$	−2.18050	+	2.18050i	−0.0723228	+	0.0723228i
$910$	−11.0426	−	19.1136i	−0.366059	−	0.633609i
$911$	−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
$915$	4.69321	+	7.03617i	0.155153	+	0.232609i
$916$	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	$-0.849756\pi$
$919$		−	27.5668i		−	0.909346i	0.890659	−	0.454673i	$-0.150244\pi$
$920$	−15.9242	+	38.7162i	−0.525007	+	1.27643i
$921$		−	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
$925$	5.78902	+	14.0400i	0.190342	+	0.461631i
$926$	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	$0.445623\pi$
$930$	−2.37908	−	4.11793i	−0.0780131	−	0.135032i
$931$	−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	$-0.199195\pi$
$937$	49.6196			1.62100			0.810501	+	0.585738i	$0.199195\pi$
$938$	−17.2365	−	1.11076i	−0.562793	−	0.0362676i
$939$	18.1133	+	18.1133i	0.591104	+	0.591104i
$940$	−26.3872	−	53.3214i	−0.860655	−	1.73915i
$941$	24.3629	−	24.3629i	0.794208	−	0.794208i	−0.187967	−	0.982175i	$-0.560190\pi$
$941$	24.3629	−	24.3629i	0.794208	−	0.794208i	0.982175	+	0.187967i	$0.0601898\pi$
$942$	−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	−0.993762	−	0.111518i	$-0.964429\pi$
$947$	−34.0132	−	34.0132i	−1.10528	−	1.10528i	−0.111518	−	0.993762i	$-0.535571\pi$
$948$	10.3288	−	7.96163i	0.335464	−	0.258582i
$949$	−16.3644	−	16.3644i	−0.531212	−	0.531212i
$950$	44.3020	+	21.8758i	1.43735	+	0.709745i
$951$			27.6373i			0.896201i
$952$	5.53446	−	3.72440i	0.179373	−	0.120709i
$953$	21.9707			0.711700			0.355850	−	0.934543i	$-0.384191\pi$
$953$	21.9707			0.711700			0.355850	+	0.934543i	$0.384191\pi$
$954$	1.85944	+	0.119826i	0.0602014	+	0.00387951i
$955$	0.862594	+	1.29322i	0.0279129	+	0.0418476i
$956$	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
$960$	−14.9309	−	9.85230i	−0.481893	−	0.317982i
$961$	−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
$965$	44.3479	−	29.5806i	1.42761	−	0.952233i
$966$	14.8519	+	0.957088i	0.477852	+	0.0307938i
$967$	−20.8251			−0.669690			−0.334845	−	0.942273i	$-0.608684\pi$
$967$	−20.8251			−0.669690			−0.334845	+	0.942273i	$0.608684\pi$
$968$	46.3444	−	31.1874i	1.48956	−	1.00240i
$969$			10.3656i			0.332991i
$970$	−12.9363	+	48.3350i	−0.415360	+	1.55194i
$971$	27.3561	+	27.3561i	0.877898	+	0.877898i	0.993317	−	0.115418i	$-0.0368209\pi$
$971$	27.3561	+	27.3561i	0.877898	+	0.877898i	−0.115418	+	0.993317i	$0.536821\pi$
$972$	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
$980$	17.9257	−	8.87091i	0.572616	−	0.283371i
$981$	−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	$-0.636351\pi$
$983$	−26.0467			−0.830760			−0.415380	+	0.909648i	$0.636351\pi$
$984$	−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
$990$	15.1838	−	8.77222i	0.482572	−	0.278799i
$991$	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
$995$	7.15493	−	4.77243i	0.226827	−	0.151296i
$996$	−2.73030	−	0.353360i	−0.0865130	−	0.0111967i
$997$	−32.7172	+	32.7172i	−1.03617	+	1.03617i	−0.0368444	+	0.999321i	$0.511731\pi$
$997$	−32.7172	+	32.7172i	−1.03617	+	1.03617i	−0.999321	+	0.0368444i	$0.988269\pi$
$998$	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.229.19	yes	48
3.2	odd	2		720.2.bm.h.469.6		48
4.3	odd	2		960.2.bl.a.49.16		48
5.4	even	2	inner	240.2.bl.a.229.6	yes	48
8.3	odd	2		1920.2.bl.b.1249.5		48
8.5	even	2		1920.2.bl.a.1249.20		48
15.14	odd	2		720.2.bm.h.469.19		48
16.3	odd	4		960.2.bl.a.529.3		48
16.5	even	4		1920.2.bl.a.289.5		48
16.11	odd	4		1920.2.bl.b.289.20		48
16.13	even	4	inner	240.2.bl.a.109.6	✓	48
20.19	odd	2		960.2.bl.a.49.3		48
40.19	odd	2		1920.2.bl.b.1249.20		48
40.29	even	2		1920.2.bl.a.1249.5		48
48.29	odd	4		720.2.bm.h.109.19		48
80.19	odd	4		960.2.bl.a.529.16		48
80.29	even	4	inner	240.2.bl.a.109.19	yes	48
80.59	odd	4		1920.2.bl.b.289.5		48
80.69	even	4		1920.2.bl.a.289.20		48
240.29	odd	4		720.2.bm.h.109.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.6	✓	48	16.13	even	4	inner
240.2.bl.a.109.19	yes	48	80.29	even	4	inner
240.2.bl.a.229.6	yes	48	5.4	even	2	inner
240.2.bl.a.229.19	yes	48	1.1	even	1	trivial
720.2.bm.h.109.6		48	240.29	odd	4
720.2.bm.h.109.19		48	48.29	odd	4
720.2.bm.h.469.6		48	3.2	odd	2
720.2.bm.h.469.19		48	15.14	odd	2
960.2.bl.a.49.3		48	20.19	odd	2
960.2.bl.a.49.16		48	4.3	odd	2
960.2.bl.a.529.3		48	16.3	odd	4
960.2.bl.a.529.16		48	80.19	odd	4
1920.2.bl.a.289.5		48	16.5	even	4
1920.2.bl.a.289.20		48	80.69	even	4
1920.2.bl.a.1249.5		48	40.29	even	2
1920.2.bl.a.1249.20		48	8.5	even	2
1920.2.bl.b.289.5		48	80.59	odd	4
1920.2.bl.b.289.20		48	16.11	odd	4
1920.2.bl.b.1249.5		48	8.3	odd	2
1920.2.bl.b.1249.20		48	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.06224 - 0.933621i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.256702 - 1.98346i) q^{4} +(-1.24079 - 1.86022i) q^{5} +(-1.41129 - 0.0909462i) q^{6} -1.58988 q^{7} +(-1.57912 - 2.34657i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(1.06224 - 0.933621i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.256702 - 1.98346i) q^{4} +(-1.24079 - 1.86022i) q^{5} +(-1.41129 - 0.0909462i) q^{6} -1.58988 q^{7} +(-1.57912 - 2.34657i) q^{8} +1.00000i q^{9} +(-3.05476 - 0.817572i) 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} +(-4.00819 + 1.98353i) 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} +(1.58193 + 2.73815i) q^{30} -1.50391 q^{31} +(-5.05968 + 2.52975i) q^{32} -5.54525i q^{33} +(-1.38499 - 1.57579i) q^{34} +(1.97271 + 2.95754i) q^{35} +(1.98346 + 0.256702i) q^{36} +(2.14771 - 2.14771i) q^{37} +(0.635482 - 9.86128i) q^{38} +4.39055i q^{39} +(-2.40578 + 5.84912i) q^{40} +6.84881i q^{41} +(2.24378 + 0.144594i) q^{42} +(-0.322458 + 0.322458i) q^{43} +(8.78386 - 6.77076i) q^{44} +(1.86022 - 1.24079i) q^{45} +(7.03111 - 6.17977i) q^{46} +13.3031i q^{47} +(2.01518 + 3.45529i) q^{48} -4.47227 q^{49} +(2.26946 + 6.69698i) 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} +(4.23679 + 1.43165i) 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} +(4.85672 + 1.29984i) q^{70} -2.26233i q^{71} +(2.34657 - 1.57912i) q^{72} +5.27105 q^{73} +(0.276233 - 4.28653i) q^{74} +(4.62248 - 1.90596i) q^{75} +(-8.53167 - 11.0683i) q^{76} +(-6.23407 - 6.23407i) q^{77} +(4.09911 + 4.66381i) q^{78} -6.52058 q^{79} +(2.90534 + 8.45925i) q^{80} -1.00000 q^{81} +(6.39419 + 7.27507i) q^{82} +(0.973359 + 0.973359i) q^{83} +(2.51843 - 1.94125i) q^{84} +(-2.75957 + 1.84067i) q^{85} +(-0.0414737 + 0.643581i) q^{86} -6.25941 q^{87} +(3.00923 - 15.3930i) q^{88} -6.83613i q^{89} +(0.817572 - 3.05476i) 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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