LMFDB - Embedded newform 555.2.bb.a.454.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(454,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("555.454");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			454.6
Character	$\chi$	$=$	555.454
Dual form			555.2.bb.a.544.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73475 - 1.00156i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.00624 + 1.74286i) q^{4} +(-1.32535 - 1.80096i) q^{5} -2.00312 q^{6} +(-3.12135 + 1.80211i) q^{7} -0.0249930i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.73475 - 1.00156i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.00624 + 1.74286i) q^{4} +(-1.32535 - 1.80096i) q^{5} -2.00312 q^{6} +(-3.12135 + 1.80211i) q^{7} -0.0249930i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.495375 + 4.45163i) q^{10} +0.0942816 q^{11} +(1.74286 + 1.00624i) q^{12} +(-3.67144 + 2.11971i) q^{13} +7.21969 q^{14} +(-2.04826 - 0.897005i) q^{15} +(1.98745 - 3.44236i) q^{16} +(6.14920 + 3.55024i) q^{17} +(-1.73475 + 1.00156i) q^{18} +(3.58934 + 6.21692i) q^{19} +(1.80520 - 4.12208i) q^{20} +(-1.80211 + 3.12135i) q^{21} +(-0.163555 - 0.0944286i) q^{22} -7.68394i q^{23} +(-0.0124965 - 0.0216445i) q^{24} +(-1.48692 + 4.77379i) q^{25} +8.49204 q^{26} -1.00000i q^{27} +(-6.28165 - 3.62671i) q^{28} +1.15153 q^{29} +(2.65482 + 3.60753i) q^{30} -1.14652 q^{31} +(-6.93873 + 4.00608i) q^{32} +(0.0816503 - 0.0471408i) q^{33} +(-7.11155 - 12.3176i) q^{34} +(7.38240 + 3.23301i) q^{35} +2.01248 q^{36} +(0.333504 + 6.07361i) q^{37} -14.3797i q^{38} +(-2.11971 + 3.67144i) q^{39} +(-0.0450113 + 0.0331243i) q^{40} +(0.851748 + 1.47527i) q^{41} +(6.25243 - 3.60984i) q^{42} +0.758158i q^{43} +(0.0948698 + 0.164319i) q^{44} +(-2.22235 + 0.247302i) q^{45} +(-7.69591 + 13.3297i) q^{46} +8.58221i q^{47} -3.97489i q^{48} +(2.99522 - 5.18788i) q^{49} +(7.36066 - 6.79210i) q^{50} +7.10049 q^{51} +(-7.38868 - 4.26586i) q^{52} +(-5.83344 - 3.36794i) q^{53} +(-1.00156 + 1.73475i) q^{54} +(-0.124956 - 0.169798i) q^{55} +(0.0450401 + 0.0780118i) q^{56} +(6.21692 + 3.58934i) q^{57} +(-1.99762 - 1.15333i) q^{58} +(-1.05402 + 1.82562i) q^{59} +(-0.497690 - 4.47243i) q^{60} +(1.45039 + 2.51214i) q^{61} +(1.98892 + 1.14831i) q^{62} +3.60423i q^{63} +8.09950 q^{64} +(8.68343 + 3.80277i) q^{65} -0.188857 q^{66} +(11.5629 - 6.67582i) q^{67} +14.2896i q^{68} +(-3.84197 - 6.65448i) q^{69} +(-9.56858 - 13.0024i) q^{70} +(1.33937 + 2.31985i) q^{71} +(-0.0216445 - 0.0124965i) q^{72} -5.07509i q^{73} +(5.50453 - 10.8702i) q^{74} +(1.09918 + 4.87768i) q^{75} +(-7.22347 + 12.5114i) q^{76} +(-0.294286 + 0.169906i) q^{77} +(7.35432 - 4.24602i) q^{78} +(7.82480 + 13.5530i) q^{79} +(-8.83360 + 0.982999i) q^{80} +(-0.500000 - 0.866025i) q^{81} -3.41230i q^{82} +(9.00711 + 5.20026i) q^{83} -7.25342 q^{84} +(-1.75597 - 15.7798i) q^{85} +(0.759340 - 1.31522i) q^{86} +(0.997255 - 0.575766i) q^{87} -0.00235638i q^{88} +(-4.77622 + 8.27265i) q^{89} +(4.10291 + 1.79681i) q^{90} +(7.63990 - 13.2327i) q^{91} +(13.3920 - 7.73187i) q^{92} +(-0.992915 + 0.573259i) q^{93} +(8.59558 - 14.8880i) q^{94} +(6.43932 - 14.7038i) q^{95} +(-4.00608 + 6.93873i) q^{96} +8.05406i q^{97} +(-10.3919 + 5.99979i) q^{98} +(0.0471408 - 0.0816503i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.73475	−	1.00156i	−1.22665	−	0.708209i	−0.260325	−	0.965521i	$-0.583830\pi$
$2$	−1.73475	−	1.00156i	−1.22665	−	0.708209i	−0.966328	+	0.257312i	$0.917163\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	1.00624	+	1.74286i	0.503119	+	0.871428i
$5$	−1.32535	−	1.80096i	−0.592712	−	0.805414i
$5$	−1.32535	−	1.80096i	−0.592712	−	0.805414i
$6$	−2.00312			−0.817769
$7$	−3.12135	+	1.80211i	−1.17976	+	0.681135i	−0.955959	−	0.293500i	$-0.905180\pi$
$7$	−3.12135	+	1.80211i	−1.17976	+	0.681135i	−0.223801	+	0.974635i	$0.571847\pi$
$8$		−	0.0249930i		−	0.00883635i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.495375	+	4.45163i	0.156651	+	1.40773i
$11$	0.0942816			0.0284270			0.0142135	−	0.999899i	$-0.495476\pi$
$11$	0.0942816			0.0284270			0.0142135	+	0.999899i	$0.495476\pi$
$12$	1.74286	+	1.00624i	0.503119	+	0.290476i
$13$	−3.67144	+	2.11971i	−1.01827	+	0.587901i	−0.913603	−	0.406606i	$-0.866712\pi$
$13$	−3.67144	+	2.11971i	−1.01827	+	0.587901i	−0.104670	+	0.994507i	$0.533379\pi$
$14$	7.21969			1.92954
$15$	−2.04826	−	0.897005i	−0.528859	−	0.231606i
$16$	1.98745	−	3.44236i	0.496861	−	0.860589i
$17$	6.14920	+	3.55024i	1.49140	+	0.861061i	0.999952	−	0.00984576i	$-0.00313405\pi$
$17$	6.14920	+	3.55024i	1.49140	+	0.861061i	0.491449	+	0.870906i	$0.336467\pi$
$18$	−1.73475	+	1.00156i	−0.408885	+	0.236070i
$19$	3.58934	+	6.21692i	0.823452	+	1.42626i	0.903097	+	0.429437i	$0.141288\pi$
$19$	3.58934	+	6.21692i	0.823452	+	1.42626i	−0.0796455	+	0.996823i	$0.525379\pi$
$20$	1.80520	−	4.12208i	0.403656	−	0.921726i
$21$	−1.80211	+	3.12135i	−0.393253	+	0.681135i
$22$	−0.163555	−	0.0944286i	−0.0348701	−	0.0201322i
$23$		−	7.68394i		−	1.60221i	−0.598523	−	0.801106i	$-0.704245\pi$
$23$		−	7.68394i		−	1.60221i	0.598523	−	0.801106i	$-0.295755\pi$
$24$	−0.0124965	−	0.0216445i	−0.00255083	−	0.00441817i
$25$	−1.48692	+	4.77379i	−0.297384	+	0.954758i
$26$	8.49204			1.66543
$27$		−	1.00000i		−	0.192450i
$28$	−6.28165	−	3.62671i	−1.18712	−	0.685384i
$29$	1.15153			0.213834			0.106917	−	0.994268i	$-0.465902\pi$
$29$	1.15153			0.213834			0.106917	+	0.994268i	$0.465902\pi$
$30$	2.65482	+	3.60753i	0.484702	+	0.658643i
$31$	−1.14652			−0.205921			−0.102960	−	0.994685i	$-0.532832\pi$
$31$	−1.14652			−0.205921			−0.102960	+	0.994685i	$0.532832\pi$
$32$	−6.93873	+	4.00608i	−1.22661	+	0.708181i
$33$	0.0816503	−	0.0471408i	0.0142135	−	0.00820616i
$34$	−7.11155	−	12.3176i	−1.21962	−	2.11245i
$35$	7.38240	+	3.23301i	1.24785	+	0.546478i
$36$	2.01248			0.335413
$37$	0.333504	+	6.07361i	0.0548278	+	0.998496i
$37$	0.333504	+	6.07361i	0.0548278	+	0.998496i
$38$		−	14.3797i		−	2.33270i
$39$	−2.11971	+	3.67144i	−0.339425	+	0.587901i
$40$	−0.0450113	+	0.0331243i	−0.00711692	+	0.00523741i
$41$	0.851748	+	1.47527i	0.133021	+	0.230399i	0.924840	−	0.380357i	$-0.124199\pi$
$41$	0.851748	+	1.47527i	0.133021	+	0.230399i	−0.791819	+	0.610756i	$0.790866\pi$
$42$	6.25243	−	3.60984i	0.964771	−	0.557011i
$43$			0.758158i			0.115618i	0.998328	+	0.0578090i	$0.0184115\pi$
$43$			0.758158i			0.115618i	−0.998328	+	0.0578090i	$0.981589\pi$
$44$	0.0948698	+	0.164319i	0.0143022	+	0.0247721i
$45$	−2.22235	+	0.247302i	−0.331288	+	0.0368656i
$46$	−7.69591	+	13.3297i	−1.13470	+	1.96536i
$47$			8.58221i			1.25184i	0.779886	+	0.625922i	$0.215277\pi$
$47$			8.58221i			1.25184i	−0.779886	+	0.625922i	$0.784723\pi$
$48$		−	3.97489i		−	0.573726i
$49$	2.99522	−	5.18788i	0.427889	−	0.741126i
$50$	7.36066	−	6.79210i	1.04096	−	0.960547i
$51$	7.10049			0.994267
$52$	−7.38868	−	4.26586i	−1.02463	−	0.591568i
$53$	−5.83344	−	3.36794i	−0.801285	−	0.462622i	0.0426353	−	0.999091i	$-0.486425\pi$
$53$	−5.83344	−	3.36794i	−0.801285	−	0.462622i	−0.843920	+	0.536469i	$0.819758\pi$
$54$	−1.00156	+	1.73475i	−0.136295	+	0.236070i
$55$	−0.124956	−	0.169798i	−0.0168490	−	0.0228955i
$56$	0.0450401	+	0.0780118i	0.00601874	+	0.0104248i
$57$	6.21692	+	3.58934i	0.823452	+	0.475420i
$58$	−1.99762	−	1.15333i	−0.262300	−	0.151439i
$59$	−1.05402	+	1.82562i	−0.137222	+	0.237675i	−0.926444	−	0.376433i	$-0.877151\pi$
$59$	−1.05402	+	1.82562i	−0.137222	+	0.237675i	0.789222	+	0.614108i	$0.210484\pi$
$60$	−0.497690	−	4.47243i	−0.0642515	−	0.577388i
$61$	1.45039	+	2.51214i	0.185703	+	0.321647i	0.943813	−	0.330479i	$-0.107210\pi$
$61$	1.45039	+	2.51214i	0.185703	+	0.321647i	−0.758110	+	0.652127i	$0.773877\pi$
$62$	1.98892	+	1.14831i	0.252594	+	0.145835i
$63$			3.60423i			0.454090i
$64$	8.09950			1.01244
$65$	8.68343	+	3.80277i	1.07705	+	0.471676i
$66$	−0.188857			−0.0232467
$67$	11.5629	−	6.67582i	1.41263	−	0.815581i	0.416992	−	0.908910i	$-0.363084\pi$
$67$	11.5629	−	6.67582i	1.41263	−	0.815581i	0.995635	+	0.0933289i	$0.0297508\pi$
$68$			14.2896i			1.73286i
$69$	−3.84197	−	6.65448i	−0.462519	−	0.801106i
$70$	−9.56858	−	13.0024i	−1.14366	−	1.55408i
$71$	1.33937	+	2.31985i	0.158954	+	0.275316i	0.934492	−	0.355985i	$-0.115855\pi$
$71$	1.33937	+	2.31985i	0.158954	+	0.275316i	−0.775538	+	0.631301i	$0.782521\pi$
$72$	−0.0216445	−	0.0124965i	−0.00255083	−	0.00147272i
$73$		−	5.07509i		−	0.593994i	−0.954878	−	0.296997i	$-0.904015\pi$
$73$		−	5.07509i		−	0.593994i	0.954878	−	0.296997i	$-0.0959851\pi$
$74$	5.50453	−	10.8702i	0.639889	−	1.26364i
$75$	1.09918	+	4.87768i	0.126923	+	0.563226i
$76$	−7.22347	+	12.5114i	−0.828589	+	1.43516i
$77$	−0.294286	+	0.169906i	−0.0335370	+	0.0193626i
$78$	7.35432	−	4.24602i	0.832713	−	0.480767i
$79$	7.82480	+	13.5530i	0.880359	+	1.52483i	0.850942	+	0.525259i	$0.176032\pi$
$79$	7.82480	+	13.5530i	0.880359	+	1.52483i	0.0294164	+	0.999567i	$0.490635\pi$
$80$	−8.83360	+	0.982999i	−0.987626	+	0.109903i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	3.41230i		−	0.376826i
$83$	9.00711	+	5.20026i	0.988659	+	0.570803i	0.904873	−	0.425681i	$-0.139965\pi$
$83$	9.00711	+	5.20026i	0.988659	+	0.570803i	0.0837859	+	0.996484i	$0.473299\pi$
$84$	−7.25342			−0.791413
$85$	−1.75597	−	15.7798i	−0.190461	−	1.71156i
$86$	0.759340	−	1.31522i	0.0818817	−	0.141823i
$87$	0.997255	−	0.575766i	0.106917	−	0.0617286i
$88$		−	0.00235638i		−	0.000251191i
$89$	−4.77622	+	8.27265i	−0.506278	+	0.876899i	0.493696	+	0.869635i	$0.335646\pi$
$89$	−4.77622	+	8.27265i	−0.506278	+	0.876899i	−0.999974	+	0.00726420i	$0.997688\pi$
$90$	4.10291	+	1.79681i	0.432485	+	0.189400i
$91$	7.63990	−	13.2327i	0.800879	−	1.38716i
$92$	13.3920	−	7.73187i	1.39621	−	0.806103i
$93$	−0.992915	+	0.573259i	−0.102960	+	0.0594442i
$94$	8.59558	−	14.8880i	0.886567	−	1.53558i
$95$	6.43932	−	14.7038i	0.660660	−	1.50858i
$96$	−4.00608	+	6.93873i	−0.408869	+	0.708181i
$97$			8.05406i			0.817766i	0.912587	+	0.408883i	$0.134082\pi$
$97$			8.05406i			0.817766i	−0.912587	+	0.408883i	$0.865918\pi$
$98$	−10.3919	+	5.99979i	−1.04974	+	0.606070i
$99$	0.0471408	−	0.0816503i	0.00473783	−	0.00820616i
$100$	−9.81623	+	2.21208i	−0.981623	+	0.221208i
$101$	−7.68045			−0.764233			−0.382117	−	0.924114i	$-0.624805\pi$
$101$	−7.68045			−0.764233			−0.382117	+	0.924114i	$0.624805\pi$
$102$	−12.3176	−	7.11155i	−1.21962	−	0.704149i
$103$			13.5467i			1.33480i	0.744701	+	0.667398i	$0.232592\pi$
$103$			13.5467i			1.33480i	−0.744701	+	0.667398i	$0.767408\pi$
$104$	0.0529777	+	0.0917601i	0.00519489	+	0.00899782i
$105$	8.00985	−	0.891334i	0.781682	−	0.0869852i
$106$	6.74638	+	11.6851i	0.655266	+	1.13495i
$107$	1.77091	−	1.02244i	0.171200	−	0.0988426i	−0.411951	−	0.911206i	$-0.635153\pi$
$107$	1.77091	−	1.02244i	0.171200	−	0.0988426i	0.583152	+	0.812363i	$0.301819\pi$
$108$	1.74286	−	1.00624i	0.167706	−	0.0968253i
$109$	−7.56660	+	13.1057i	−0.724749	+	1.25530i	0.234329	+	0.972157i	$0.424711\pi$
$109$	−7.56660	+	13.1057i	−0.724749	+	1.25530i	−0.959077	+	0.283144i	$0.908623\pi$
$110$	0.0467048	+	0.419707i	0.00445313	+	0.0400175i
$111$	3.32563	+	5.09315i	0.315655	+	0.483420i
$112$			14.3264i			1.35372i
$113$	−12.0748	−	6.97141i	−1.13590	−	0.655815i	−0.190491	−	0.981689i	$-0.561008\pi$
$113$	−12.0748	−	6.97141i	−1.13590	−	0.655815i	−0.945413	+	0.325874i	$0.894341\pi$
$114$	−7.18987	−	12.4532i	−0.673393	−	1.16635i
$115$	−13.8385	+	10.1839i	−1.29044	+	0.949651i
$116$	1.15872	+	2.00695i	0.107584	+	0.186341i
$117$			4.23941i			0.391934i
$118$	3.65693	−	2.11133i	0.336647	−	0.194363i
$119$	−25.5918			−2.34599
$120$	−0.0224188	+	0.0511922i	−0.00204655	+	0.00467318i
$121$	−10.9911			−0.999192
$122$		−	5.81059i		−	0.526066i
$123$	1.47527	+	0.851748i	0.133021	+	0.0767995i
$124$	−1.15367	−	1.99822i	−0.103603	−	0.179445i
$125$	10.5681	−	3.64904i	0.945239	−	0.326380i
$126$	3.60984	−	6.25243i	0.321590	−	0.557011i
$127$	−17.0681	−	9.85424i	−1.51454	−	0.874423i	−0.999855	−	0.0170465i	$-0.994574\pi$
$127$	−17.0681	−	9.85424i	−1.51454	−	0.874423i	−0.514690	−	0.857376i	$-0.672093\pi$
$128$	−0.173153	−	0.0999699i	−0.0153047	−	0.00883617i
$129$	0.379079	+	0.656584i	0.0333761	+	0.0578090i
$130$	−11.2549	−	15.2938i	−0.987118	−	1.34136i
$131$	−5.76563	+	9.98637i	−0.503746	+	0.872513i	0.496245	+	0.868183i	$0.334712\pi$
$131$	−5.76563	+	9.98637i	−0.503746	+	0.872513i	−0.999991	+	0.00433071i	$0.998621\pi$
$132$	0.164319	+	0.0948698i	0.0143022	+	0.00825736i
$133$	−22.4072	−	12.9368i	−1.94295	−	1.12176i
$134$	−26.7449			−2.31041
$135$	−1.80096	+	1.32535i	−0.155002	+	0.114068i
$136$	0.0887311	−	0.153687i	0.00760863	−	0.0131785i
$137$		−	8.24239i		−	0.704195i	−0.935963	−	0.352098i	$-0.885469\pi$
$137$		−	8.24239i		−	0.704195i	0.935963	−	0.352098i	$-0.114531\pi$
$138$			15.3918i			1.31024i
$139$	6.19594	−	10.7317i	0.525532	−	0.910249i	−0.474025	−	0.880511i	$-0.657199\pi$
$139$	6.19594	−	10.7317i	0.525532	−	0.910249i	0.999558	−	0.0297376i	$-0.00946718\pi$
$140$	1.79379	+	16.1196i	0.151603	+	1.36236i
$141$	4.29110	+	7.43241i	0.361376	+	0.625922i
$142$		−	5.36582i		−	0.450290i
$143$	−0.346149	+	0.199849i	−0.0289464	+	0.0167122i
$144$	−1.98745	−	3.44236i	−0.165620	−	0.286863i
$145$	−1.52618	−	2.07386i	−0.126742	−	0.172225i
$146$	−5.08300	+	8.80401i	−0.420672	+	0.728625i
$147$		−	5.99045i		−	0.494084i
$148$	−10.2498	+	6.69275i	−0.842532	+	0.550141i
$149$	−12.7960			−1.04829			−0.524144	−	0.851630i	$-0.675615\pi$
$149$	−12.7960			−1.04829			−0.524144	+	0.851630i	$0.675615\pi$
$150$	2.97847	−	9.56246i	0.243191	−	0.780771i
$151$	0.952789	+	1.65028i	0.0775369	+	0.134298i	0.902187	−	0.431346i	$-0.141961\pi$
$151$	0.952789	+	1.65028i	0.0775369	+	0.134298i	−0.824650	+	0.565644i	$0.808628\pi$
$152$	0.155379	−	0.0897083i	0.0126029	−	0.00727630i
$153$	6.14920	−	3.55024i	0.497134	−	0.287020i
$154$	0.680684			0.0548511
$155$	1.51953	+	2.06484i	0.122052	+	0.165852i
$156$	−8.53172			−0.683084
$157$	12.2653	+	7.08137i	0.978877	+	0.565155i	0.901931	−	0.431880i	$-0.142150\pi$
$157$	12.2653	+	7.08137i	0.978877	+	0.565155i	0.0769460	+	0.997035i	$0.475483\pi$
$158$		−	31.3480i		−	2.49391i
$159$	−6.73588			−0.534190
$160$	16.4110	+	7.18694i	1.29740	+	0.568178i
$161$	13.8473	+	23.9843i	1.09132	+	1.89023i
$162$			2.00312i			0.157380i
$163$	1.14304	+	0.659933i	0.0895296	+	0.0516899i	0.544096	−	0.839023i	$-0.316873\pi$
$163$	1.14304	+	0.659933i	0.0895296	+	0.0516899i	−0.454567	+	0.890713i	$0.650206\pi$
$164$	−1.71412	+	2.96895i	−0.133851	+	0.231836i
$165$	−0.193114	−	0.0845711i	−0.0150339	−	0.00658385i
$166$	−10.4167	−	18.0423i	−0.808495	−	1.40035i
$167$	−12.9799	+	7.49394i	−1.00441	+	0.579899i	−0.909551	−	0.415592i	$-0.863574\pi$
$167$	−12.9799	+	7.49394i	−1.00441	+	0.579899i	−0.0948626	+	0.995490i	$0.530241\pi$
$168$	0.0780118	+	0.0450401i	0.00601874	+	0.00347492i
$169$	2.48630	−	4.30640i	0.191254	−	0.331262i
$170$	−12.7582	+	29.1327i	−0.978509	+	2.23437i
$171$	7.17868			0.548968
$172$	−1.32136	+	0.762888i	−0.100753	+	0.0581697i
$173$	1.75722	+	1.01453i	0.133599	+	0.0771333i	0.565310	−	0.824879i	$-0.308757\pi$
$173$	1.75722	+	1.01453i	0.133599	+	0.0771333i	−0.431711	+	0.902012i	$0.642090\pi$
$174$	−2.30665			−0.174867
$175$	−3.96171	−	17.5803i	−0.299477	−	1.32894i
$176$	0.187380	−	0.324551i	0.0141243	−	0.0244639i
$177$			2.10804i			0.158450i
$178$	16.5711	−	9.56732i	1.24205	−	0.717101i
$179$	−8.80639			−0.658221			−0.329110	−	0.944291i	$-0.606749\pi$
$179$	−8.80639			−0.658221			−0.329110	+	0.944291i	$0.606749\pi$
$180$	−2.66723	−	3.62439i	−0.198803	−	0.270146i
$181$	2.82742	+	4.89724i	0.210161	+	0.364009i	0.951765	−	0.306829i	$-0.0992679\pi$
$181$	2.82742	+	4.89724i	0.210161	+	0.364009i	−0.741604	+	0.670838i	$0.765935\pi$
$182$	−26.5066	+	15.3036i	−1.96480	+	1.13438i
$183$	2.51214	+	1.45039i	0.185703	+	0.107216i
$184$	−0.192044			−0.0141577
$185$	10.4963	−	8.65026i	0.771706	−	0.635980i
$186$	2.29661			0.168396
$187$	0.579757	+	0.334723i	0.0423960	+	0.0244773i
$188$	−14.9576	+	8.63575i	−1.09089	+	0.629827i
$189$	1.80211	+	3.12135i	0.131084	+	0.227045i
$190$	−25.8974	+	19.0581i	−1.87879	+	1.38262i
$191$	19.1207			1.38353			0.691764	−	0.722123i	$-0.256834\pi$
$191$	19.1207			1.38353			0.691764	+	0.722123i	$0.256834\pi$
$192$	7.01438	−	4.04975i	0.506219	−	0.292266i
$193$			15.6815i			1.12878i	0.825508	+	0.564391i	$0.190889\pi$
$193$			15.6815i			1.12878i	−0.825508	+	0.564391i	$0.809111\pi$
$194$	8.06661	−	13.9718i	0.579149	−	1.00312i
$195$	9.42146	−	1.04842i	0.674685	−	0.0750786i
$196$	12.0556			0.861117
$197$	−2.44017	−	1.40883i	−0.173855	−	0.100375i	0.410547	−	0.911839i	$-0.365338\pi$
$197$	−2.44017	−	1.40883i	−0.173855	−	0.100375i	−0.584402	+	0.811464i	$0.698671\pi$
$198$	−0.163555	+	0.0944286i	−0.0116234	+	0.00671075i
$199$	22.7275			1.61111			0.805554	−	0.592523i	$-0.201868\pi$
$199$	22.7275			1.61111			0.805554	+	0.592523i	$0.201868\pi$
$200$	0.119311	+	0.0371625i	0.00843657	+	0.00262779i
$201$	6.67582	−	11.5629i	0.470876	−	0.815581i
$202$	13.3237	+	7.69242i	0.937449	+	0.541237i
$203$	−3.59433	+	2.07519i	−0.252273	+	0.145650i
$204$	7.14478	+	12.3751i	0.500235	+	0.866432i
$205$	1.52804	−	3.48921i	0.106723	−	0.243697i
$206$	13.5678	−	23.5001i	0.945314	−	1.63733i
$207$	−6.65448	−	3.84197i	−0.462519	−	0.267035i
$208$			16.8512i			1.16842i
$209$	0.338409	+	0.586142i	0.0234082	+	0.0405443i
$210$	−14.7878	−	6.47610i	−1.02046	−	0.446893i
$211$	−5.04237			−0.347131			−0.173566	−	0.984822i	$-0.555529\pi$
$211$	−5.04237			−0.347131			−0.173566	+	0.984822i	$0.555529\pi$
$212$		−	13.5558i		−	0.931016i
$213$	2.31985	+	1.33937i	0.158954	+	0.0917720i
$214$	−4.09612			−0.280005
$215$	1.36541	−	1.00482i	0.0931204	−	0.0685283i
$216$	−0.0249930			−0.00170056
$217$	3.57869	−	2.06616i	0.242937	−	0.140260i
$218$	26.2523	−	15.1568i	1.77803	−	1.02655i
$219$	−2.53754	−	4.39515i	−0.171471	−	0.296997i
$220$	0.170197	−	0.388637i	0.0114747	−	0.0262019i
$221$	−30.1019			−2.02487
$222$	−0.668048	−	12.1662i	−0.0448365	−	0.816539i
$223$		−	23.7185i		−	1.58831i	−0.607717	−	0.794154i	$-0.707914\pi$
$223$		−	23.7185i		−	1.58831i	0.607717	−	0.794154i	$-0.292086\pi$
$224$	14.4388	−	25.0088i	0.964734	−	1.67097i
$225$	3.39076	+	3.67461i	0.226051	+	0.244974i
$226$	13.9645	+	24.1873i	0.928908	+	1.60892i
$227$	−2.49692	+	1.44160i	−0.165726	+	0.0956822i	−0.580569	−	0.814211i	$-0.697170\pi$
$227$	−2.49692	+	1.44160i	−0.165726	+	0.0956822i	0.414843	+	0.909893i	$0.363837\pi$
$228$			14.4469i			0.956772i
$229$	2.43671	+	4.22050i	0.161022	+	0.278898i	0.935235	−	0.354026i	$-0.115188\pi$
$229$	2.43671	+	4.22050i	0.161022	+	0.278898i	−0.774213	+	0.632925i	$0.781854\pi$
$230$	34.2060	−	3.80643i	2.25548	−	0.250989i
$231$	−0.169906	+	0.294286i	−0.0111790	+	0.0193626i
$232$		−	0.0287802i		−	0.00188951i
$233$		−	15.1128i		−	0.990075i	−0.868872	−	0.495038i	$-0.835154\pi$
$233$		−	15.1128i		−	0.990075i	0.868872	−	0.495038i	$-0.164846\pi$
$234$	4.24602	−	7.35432i	0.277571	−	0.480767i
$235$	15.4562	−	11.3744i	1.00825	−	0.741983i
$236$	−4.24239			−0.276156
$237$	13.5530	+	7.82480i	0.880359	+	0.508275i
$238$	44.3953	+	25.6316i	2.87772	+	1.66145i
$239$	5.60816	−	9.71362i	0.362762	−	0.628322i	−0.625653	−	0.780102i	$-0.715167\pi$
$239$	5.60816	−	9.71362i	0.362762	−	0.628322i	0.988414	+	0.151780i	$0.0485005\pi$
$240$	−7.15862	+	5.26810i	−0.462087	+	0.340055i
$241$	−3.13560	−	5.43101i	−0.201981	−	0.349842i	0.747185	−	0.664616i	$-0.231405\pi$
$241$	−3.13560	−	5.43101i	−0.201981	−	0.349842i	−0.949167	+	0.314774i	$0.898071\pi$
$242$	19.0668	+	11.0082i	1.22566	+	0.707636i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−2.91887	+	5.05563i	−0.186862	+	0.323654i
$245$	−13.3129	+	1.48145i	−0.850529	+	0.0946465i
$246$	−1.70615	−	2.95514i	−0.108780	−	0.188413i
$247$	−26.3561	−	15.2167i	−1.67700	−	0.968215i
$248$			0.0286549i			0.00181959i
$249$	10.4005			0.659106
$250$	−21.9877	−	4.25439i	−1.39063	−	0.269072i
$251$	−24.1081			−1.52169			−0.760846	−	0.648933i	$-0.775216\pi$
$251$	−24.1081			−1.52169			−0.760846	+	0.648933i	$0.775216\pi$
$252$	−6.28165	+	3.62671i	−0.395707	+	0.228461i
$253$		−	0.724454i		−	0.0455460i
$254$	19.7392	+	34.1893i	1.23855	+	2.14523i
$255$	−9.41060	−	12.7877i	−0.589314	−	0.800797i
$256$	−7.89925	−	13.6819i	−0.493703	−	0.855119i
$257$	1.23159	+	0.711060i	0.0768246	+	0.0443547i	0.537920	−	0.842996i	$-0.319210\pi$
$257$	1.23159	+	0.711060i	0.0768246	+	0.0443547i	−0.461096	+	0.887350i	$0.652543\pi$
$258$		−	1.51868i		−	0.0945489i
$259$	−11.9863	−	18.3569i	−0.744794	−	1.14064i
$260$	2.10991	+	18.9605i	0.130851	+	1.17588i
$261$	0.575766	−	0.997255i	0.0356390	−	0.0617286i
$262$	20.0039	−	11.5492i	1.23584	−	0.713514i
$263$	24.8995	−	14.3757i	1.53537	−	0.886446i	0.536269	−	0.844047i	$-0.319833\pi$
$263$	24.8995	−	14.3757i	1.53537	−	0.886446i	0.999101	−	0.0423985i	$-0.0134999\pi$
$264$	−0.00117819	−	0.00204068i	−7.25125e−5	−	0.000125595i
$265$	1.66580	+	14.9695i	0.102329	+	0.919568i
$266$	25.9139	+	44.8842i	1.58888	+	2.75203i
$267$			9.55243i			0.584599i
$268$	23.2700	+	13.4349i	1.42144	+	0.820669i
$269$	−8.80899			−0.537093			−0.268547	−	0.963267i	$-0.586543\pi$
$269$	−8.80899			−0.537093			−0.268547	+	0.963267i	$0.586543\pi$
$270$	4.45163	−	0.495375i	0.270917	−	0.0301476i
$271$	8.93986	−	15.4843i	0.543058	−	0.940604i	−0.455668	−	0.890150i	$-0.650600\pi$
$271$	8.93986	−	15.4843i	0.543058	−	0.940604i	0.998726	−	0.0504545i	$-0.0160670\pi$
$272$	24.4424	−	14.1118i	1.48204	−	0.855655i
$273$		−	15.2798i		−	0.924775i
$274$	−8.25524	+	14.2985i	−0.498717	+	0.863804i
$275$	−0.140189	+	0.450081i	−0.00845373	+	0.0271409i
$276$	7.73187	−	13.3920i	0.465404	−	0.806103i
$277$	−4.56108	+	2.63334i	−0.274049	+	0.158222i	−0.630726	−	0.776006i	$-0.717243\pi$
$277$	−4.56108	+	2.63334i	−0.274049	+	0.158222i	0.356678	+	0.934228i	$0.383909\pi$
$278$	−21.4968	+	12.4112i	−1.28929	+	0.744373i
$279$	−0.573259	+	0.992915i	−0.0343201	+	0.0594442i
$280$	0.0808025	−	0.184508i	0.00482887	−	0.0110265i
$281$	4.24123	−	7.34603i	0.253011	−	0.438227i	−0.711343	−	0.702845i	$-0.751913\pi$
$281$	4.24123	−	7.34603i	0.253011	−	0.438227i	0.964353	+	0.264618i	$0.0852459\pi$
$282$		−	17.1912i		−	1.02372i
$283$	−6.29197	+	3.63267i	−0.374019	+	0.215940i	−0.675213	−	0.737623i	$-0.735948\pi$
$283$	−6.29197	+	3.63267i	−0.374019	+	0.215940i	0.301194	+	0.953563i	$0.402615\pi$
$284$	−2.69545	+	4.66865i	−0.159945	+	0.277034i
$285$	−1.77531	−	15.9536i	−0.105160	−	0.945007i
$286$	0.800643			0.0473430
$287$	−5.31721	−	3.06989i	−0.313865	−	0.181210i
$288$			8.01216i			0.472121i
$289$	16.7085	+	28.9399i	0.982851	+	1.70235i
$290$	0.570440	+	5.12619i	0.0334974	+	0.301020i
$291$	4.02703	+	6.97502i	0.236069	+	0.408883i
$292$	8.84515	−	5.10675i	0.517623	−	0.298850i
$293$	−14.1496	+	8.16928i	−0.826629	+	0.477255i	−0.852697	−	0.522406i	$-0.825035\pi$
$293$	−14.1496	+	8.16928i	−0.826629	+	0.477255i	0.0260680	+	0.999660i	$0.491701\pi$
$294$	−5.99979	+	10.3919i	−0.349915	+	0.606070i
$295$	4.68481	−	0.521324i	0.272760	−	0.0303526i
$296$	0.151798	−	0.00833526i	0.00882305	−	0.000484477i
$297$		−	0.0942816i		−	0.00547077i
$298$	22.1978	+	12.8159i	1.28589	+	0.742406i
$299$	16.2877	+	28.2111i	0.941941	+	1.63149i
$300$	−7.39506	+	6.82383i	−0.426954	+	0.393974i
$301$	−1.36629	−	2.36648i	−0.0787515	−	0.136402i
$302$		−	3.81709i		−	0.219649i
$303$	−6.65146	+	3.84022i	−0.382117	+	0.220615i
$304$	28.5345			1.63656
$305$	2.60201	−	5.94155i	0.148991	−	0.340212i
$306$	−14.2231			−0.813081
$307$		−	3.08977i		−	0.176343i	−0.996105	−	0.0881713i	$-0.971898\pi$
$307$		−	3.08977i		−	0.176343i	0.996105	−	0.0881713i	$-0.0281023\pi$
$308$	−0.592244	−	0.341932i	−0.0337462	−	0.0194834i
$309$	6.77335	+	11.7318i	0.385322	+	0.667398i
$310$	−0.567957	−	5.10388i	−0.0322578	−	0.289881i
$311$	3.10553	−	5.37894i	0.176098	−	0.305012i	−0.764442	−	0.644692i	$-0.776986\pi$
$311$	3.10553	−	5.37894i	0.176098	−	0.305012i	0.940541	+	0.339681i	$0.110319\pi$
$312$	0.0917601	+	0.0529777i	0.00519489	+	0.00299927i
$313$	16.9425	+	9.78176i	0.957647	+	0.552898i	0.895448	−	0.445166i	$-0.146855\pi$
$313$	16.9425	+	9.78176i	0.957647	+	0.552898i	0.0621988	+	0.998064i	$0.480189\pi$
$314$	−14.1848	−	24.5688i	−0.800495	−	1.38650i
$315$	6.49107	−	4.77684i	0.365730	−	0.269145i
$316$	−15.7472	+	27.2750i	−0.885851	+	1.53434i
$317$	4.64191	+	2.68001i	0.260716	+	0.150524i	0.624661	−	0.780896i	$-0.285237\pi$
$317$	4.64191	+	2.68001i	0.260716	+	0.150524i	−0.363945	+	0.931420i	$0.618570\pi$
$318$	11.6851	+	6.74638i	0.655266	+	0.378318i
$319$	0.108568			0.00607865
$320$	−10.7346	−	14.5869i	−0.600085	−	0.815432i
$321$	1.02244	−	1.77091i	0.0570668	−	0.0988426i
$322$		−	55.4756i		−	3.09153i
$323$			50.9722i			2.83617i
$324$	1.00624	−	1.74286i	0.0559021	−	0.0968253i
$325$	−4.65990	−	20.6785i	−0.258485	−	1.14704i
$326$	−1.32192	−	2.28964i	−0.0732145	−	0.126811i
$327$			15.1332i			0.836868i
$328$	0.0368714	−	0.0212877i	0.00203588	−	0.00117542i
$329$	−15.4661	−	26.7881i	−0.852674	−	1.47688i
$330$	0.250301	+	0.340124i	0.0137786	+	0.0187232i
$331$	8.24875	−	14.2872i	0.453392	−	0.785298i	−0.545202	−	0.838305i	$-0.683547\pi$
$331$	8.24875	−	14.2872i	0.453392	−	0.785298i	0.998594	+	0.0530066i	$0.0168804\pi$
$332$			20.9308i			1.14873i
$333$	5.42666	+	2.74798i	0.297379	+	0.150589i
$334$	30.0225			1.64276
$335$	−27.3477	−	11.9765i	−1.49416	−	0.654345i
$336$	7.16320	+	12.4070i	0.390785	+	0.676859i
$337$	−12.4501	+	7.18809i	−0.678202	+	0.391560i	−0.799177	−	0.601095i	$-0.794731\pi$
$337$	−12.4501	+	7.18809i	−0.678202	+	0.391560i	0.120975	+	0.992656i	$0.461398\pi$
$338$	−8.62623	+	4.98035i	−0.469205	+	0.270896i
$339$	−13.9428			−0.757270
$340$	25.7350	−	18.9386i	1.39567	−	1.02709i
$341$	−0.108096			−0.00585371
$342$	−12.4532	−	7.18987i	−0.673393	−	0.388784i
$343$		−	3.63865i		−	0.196469i
$344$	0.0189486			0.00102164
$345$	−6.89253	+	15.7387i	−0.371081	+	0.847344i
$346$	−2.03222	−	3.51991i	−0.109253	−	0.189232i
$347$			34.0396i			1.82734i	0.406458	+	0.913670i	$0.366764\pi$
$347$			34.0396i			1.82734i	−0.406458	+	0.913670i	$0.633236\pi$
$348$	2.00695	+	1.15872i	0.107584	+	0.0621136i
$349$	−15.9112	+	27.5591i	−0.851709	+	1.47520i	0.0279563	+	0.999609i	$0.491100\pi$
$349$	−15.9112	+	27.5591i	−0.851709	+	1.47520i	−0.879665	+	0.475594i	$0.842233\pi$
$350$	−10.7351	+	34.4653i	−0.573815	+	1.84225i
$351$	2.11971	+	3.67144i	0.113142	+	0.195967i
$352$	−0.654195	+	0.377700i	−0.0348687	+	0.0201315i
$353$	−5.83409	−	3.36832i	−0.310517	−	0.179277i	0.336641	−	0.941633i	$-0.390709\pi$
$353$	−5.83409	−	3.36832i	−0.310517	−	0.179277i	−0.647158	+	0.762356i	$0.724043\pi$
$354$	2.11133	−	3.65693i	0.112216	−	0.194363i
$355$	2.40284	−	5.48676i	0.127530	−	0.291207i
$356$	−19.2240			−1.01887
$357$	−22.1631	+	12.7959i	−1.17300	+	0.677230i
$358$	15.2769	+	8.82012i	0.807409	+	0.466158i
$359$	21.6968			1.14511			0.572556	−	0.819866i	$-0.305952\pi$
$359$	21.6968			1.14511			0.572556	+	0.819866i	$0.305952\pi$
$360$	0.00618082	+	0.0555431i	0.000325758	+	0.00292738i
$361$	−16.2668	+	28.1748i	−0.856145	+	1.48289i
$362$		−	11.3273i		−	0.595351i
$363$	−9.51858	+	5.49556i	−0.499596	+	0.288442i
$364$	30.7502			1.61175
$365$	−9.14003	+	6.72624i	−0.478411	+	0.352068i
$366$	−2.90529	−	5.03212i	−0.151862	−	0.263033i
$367$	−1.63326	+	0.942964i	−0.0852556	+	0.0492223i	−0.542022	−	0.840364i	$-0.682341\pi$
$367$	−1.63326	+	0.942964i	−0.0852556	+	0.0492223i	0.456766	+	0.889587i	$0.349008\pi$
$368$	−26.4508	−	15.2714i	−1.37885	−	0.796077i
$369$	1.70350			0.0886805
$370$	−26.8723	+	4.49336i	−1.39702	+	0.233598i
$371$	24.2776			1.26043
$372$	−1.99822	−	1.15367i	−0.103603	−	0.0598151i
$373$	24.6532	−	14.2335i	1.27649	−	0.736983i	0.300291	−	0.953848i	$-0.402916\pi$
$373$	24.6532	−	14.2335i	1.27649	−	0.736983i	0.976202	+	0.216864i	$0.0695829\pi$
$374$	−0.670489	−	1.16132i	−0.0346701	−	0.0600505i
$375$	7.32772	−	8.44420i	0.378402	−	0.436057i
$376$	0.214495			0.0110617
$377$	−4.22777	+	2.44091i	−0.217741	+	0.125713i
$378$		−	7.21969i		−	0.371341i
$379$	2.49282	−	4.31770i	0.128048	−	0.221785i	−0.794872	−	0.606777i	$-0.792462\pi$
$379$	2.49282	−	4.31770i	0.128048	−	0.221785i	0.922920	+	0.384991i	$0.125796\pi$
$380$	32.1062	−	3.57276i	1.64701	−	0.183279i
$381$	−19.7085			−1.00970
$382$	−33.1697	−	19.1505i	−1.69711	−	0.979827i
$383$	−8.13939	+	4.69928i	−0.415903	+	0.240122i	−0.693323	−	0.720627i	$-0.743854\pi$
$383$	−8.13939	+	4.69928i	−0.415903	+	0.240122i	0.277420	+	0.960749i	$0.410521\pi$
$384$	−0.199940			−0.0102031
$385$	0.696025	+	0.304813i	0.0354727	+	0.0155347i
$386$	15.7060	−	27.2036i	0.799413	−	1.38462i
$387$	0.656584	+	0.379079i	0.0333761	+	0.0192697i
$388$	−14.0371	+	8.10431i	−0.712624	+	0.411434i
$389$	−9.23835	−	16.0013i	−0.468403	−	0.811298i	0.530945	−	0.847406i	$-0.321837\pi$
$389$	−9.23835	−	16.0013i	−0.468403	−	0.811298i	−0.999348	+	0.0361085i	$0.988504\pi$
$390$	−17.3939	−	7.61740i	−0.880776	−	0.385722i
$391$	27.2798	−	47.2501i	1.37960	−	2.38954i
$392$	−0.129661	−	0.0748595i	−0.00654884	−	0.00378098i
$393$			11.5313i			0.581676i
$394$	2.82205	+	4.88794i	0.142173	+	0.246251i
$395$	14.0378	−	32.0545i	0.706317	−	1.61284i
$396$	0.189740			0.00953477
$397$			9.71107i			0.487385i	0.969853	+	0.243692i	$0.0783587\pi$
$397$			9.71107i			0.487385i	−0.969853	+	0.243692i	$0.921641\pi$
$398$	−39.4265	−	22.7629i	−1.97627	−	1.14100i
$399$	−25.8736			−1.29530
$400$	13.4779	+	14.6062i	0.673896	+	0.730308i
$401$	28.9716			1.44677			0.723387	−	0.690442i	$-0.242584\pi$
$401$	28.9716			1.44677			0.723387	+	0.690442i	$0.242584\pi$
$402$	−23.1618	+	13.3724i	−1.15520	+	0.666957i
$403$	4.20937	−	2.43028i	0.209684	−	0.121061i
$404$	−7.72836	−	13.3859i	−0.384500	−	0.665974i
$405$	−0.897005	+	2.04826i	−0.0445725	+	0.101779i
$406$	8.31369			0.412602
$407$	0.0314433	+	0.572630i	0.00155859	+	0.0283842i
$408$		−	0.177462i		−	0.00878569i
$409$	10.0530	−	17.4124i	0.497091	−	0.860986i	−0.502904	−	0.864342i	$-0.667735\pi$
$409$	10.0530	−	17.4124i	0.497091	−	0.860986i	0.999994	+	0.00335618i	$0.00106831\pi$
$410$	−6.14542	+	4.52248i	−0.303501	+	0.223349i
$411$	−4.12120	−	7.13812i	−0.203284	−	0.352098i
$412$	−23.6099	+	13.6312i	−1.16318	+	0.671561i
$413$		−	7.59786i		−	0.373866i
$414$	7.69591	+	13.3297i	0.378233	+	0.655119i
$415$	−2.57207	−	23.1136i	−0.126258	−	1.13460i
$416$	16.9834	−	29.4161i	0.832680	−	1.44224i
$417$		−	12.3919i		−	0.606833i
$418$		−	1.35575i		−	0.0663117i
$419$	8.33064	−	14.4291i	0.406978	−	0.704907i	−0.587571	−	0.809172i	$-0.699916\pi$
$419$	8.33064	−	14.4291i	0.406978	−	0.704907i	0.994550	+	0.104265i	$0.0332491\pi$
$420$	9.61329	+	13.0631i	0.469081	+	0.637416i
$421$	−18.1463			−0.884396			−0.442198	−	0.896917i	$-0.645801\pi$
$421$	−18.1463			−0.884396			−0.442198	+	0.896917i	$0.645801\pi$
$422$	8.74726	+	5.05023i	0.425810	+	0.245841i
$423$	7.43241	+	4.29110i	0.361376	+	0.208641i
$424$	−0.0841748	+	0.145795i	−0.00408789	+	0.00708043i
$425$	−26.0915	+	24.0761i	−1.26562	+	1.16786i
$426$	−2.68291	−	4.64694i	−0.129987	−	0.225145i
$427$	−9.05434	−	5.22752i	−0.438170	−	0.252978i
$428$	3.56392	+	2.05763i	0.172269	+	0.0994593i
$429$	−0.199849	+	0.346149i	−0.00964881	+	0.0167122i
$430$	−3.37504	+	0.375573i	−0.162759	+	0.0181117i
$431$	−3.33540	−	5.77709i	−0.160661	−	0.278273i	0.774445	−	0.632641i	$-0.218029\pi$
$431$	−3.33540	−	5.77709i	−0.160661	−	0.278273i	−0.935106	+	0.354369i	$0.884696\pi$
$432$	−3.44236	−	1.98745i	−0.165620	−	0.0956210i
$433$		−	7.40835i		−	0.356023i	−0.984028	−	0.178011i	$-0.943034\pi$
$433$		−	7.40835i		−	0.356023i	0.984028	−	0.178011i	$-0.0569664\pi$
$434$	−8.27751			−0.397333
$435$	−2.35864	−	1.03293i	−0.113088	−	0.0495252i
$436$	−30.4552			−1.45854
$437$	47.7704	−	27.5803i	2.28517	−	1.31934i
$438$			10.1660i			0.485750i
$439$	−14.7002	−	25.4614i	−0.701600	−	1.21521i	−0.967905	−	0.251318i	$-0.919136\pi$
$439$	−14.7002	−	25.4614i	−0.701600	−	1.21521i	0.266304	−	0.963889i	$-0.414197\pi$
$440$	−0.00424374	+	0.00312301i	−0.000202312	+	0.000148884i
$441$	−2.99522	−	5.18788i	−0.142630	−	0.247042i
$442$	52.2192	+	30.1488i	2.48382	+	1.43403i
$443$			9.98142i			0.474232i	0.971481	+	0.237116i	$0.0762021\pi$
$443$			9.98142i			0.474232i	−0.971481	+	0.237116i	$0.923798\pi$
$444$	−5.53025	+	10.9210i	−0.262454	+	0.518289i
$445$	21.2288	−	2.36234i	1.00634	−	0.111986i
$446$	−23.7555	+	41.1456i	−1.12485	+	1.94830i
$447$	−11.0816	+	6.39799i	−0.524144	+	0.302614i
$448$	−25.2814	+	14.5962i	−1.19443	+	0.689607i
$449$	12.3162	+	21.3322i	0.581236	+	1.00673i	0.995333	+	0.0964979i	$0.0307641\pi$
$449$	12.3162	+	21.3322i	0.581236	+	1.00673i	−0.414097	+	0.910233i	$0.635903\pi$
$450$	−2.20180	−	9.77057i	−0.103794	−	0.460589i
$451$	0.0803042	+	0.139091i	0.00378138	+	0.00654954i
$452$		−	28.0596i		−	1.31981i
$453$	1.65028	+	0.952789i	0.0775369	+	0.0447659i
$454$	5.77538			0.271052
$455$	−33.9571	+	3.77873i	−1.59193	+	0.177150i
$456$	0.0897083	−	0.155379i	0.00420097	−	0.00727630i
$457$	−25.1197	+	14.5029i	−1.17505	+	0.678416i	−0.954865	−	0.297042i	$-0.904000\pi$
$457$	−25.1197	+	14.5029i	−1.17505	+	0.678416i	−0.220187	+	0.975458i	$0.570667\pi$
$458$		−	9.76201i		−	0.456149i
$459$	3.55024	−	6.14920i	0.165711	−	0.287020i
$460$	−31.6738	−	13.8711i	−1.47680	−	0.646741i
$461$	13.6641	−	23.6669i	0.636400	−	1.10228i	−0.349816	−	0.936818i	$-0.613756\pi$
$461$	13.6641	−	23.6669i	0.636400	−	1.10228i	0.986217	−	0.165459i	$-0.0529106\pi$
$462$	0.589489	−	0.340342i	0.0274255	−	0.0158341i
$463$	28.1853	−	16.2728i	1.30988	−	0.756260i	0.327805	−	0.944745i	$-0.393691\pi$
$463$	28.1853	−	16.2728i	1.30988	−	0.756260i	0.982076	+	0.188485i	$0.0603578\pi$
$464$	2.28861	−	3.96398i	0.106246	−	0.184023i
$465$	2.34837	+	1.02843i	0.108903	+	0.0476925i
$466$	−15.1364	+	26.2170i	−0.701180	+	1.21448i
$467$		−	3.37552i		−	0.156201i	−0.996946	−	0.0781003i	$-0.975115\pi$
$467$		−	3.37552i		−	0.156201i	0.996946	−	0.0781003i	$-0.0248854\pi$
$468$	−7.38868	+	4.26586i	−0.341542	+	0.197189i
$469$	−24.0612	+	41.6752i	−1.11104	+	1.92438i
$470$	−38.2048	+	4.25142i	−1.76226	+	0.196103i
$471$	14.1627			0.652585
$472$	0.0456276	+	0.0263431i	0.00210018	+	0.00121254i
$473$			0.0714804i			0.00328667i
$474$	−15.6740	−	27.1481i	−0.719930	−	1.24696i
$475$	−35.0153	+	7.89070i	−1.60661	+	0.362050i
$476$	−25.7514	−	44.6028i	−1.18031	−	2.04436i
$477$	−5.83344	+	3.36794i	−0.267095	+	0.154207i
$478$	−19.4575	+	11.2338i	−0.889966	+	0.513822i
$479$	17.9960	−	31.1700i	0.822259	−	1.42419i	−0.0817374	−	0.996654i	$-0.526047\pi$
$479$	17.9960	−	31.1700i	0.822259	−	1.42419i	0.903996	−	0.427540i	$-0.140620\pi$
$480$	17.8058	−	1.98142i	0.812721	−	0.0904392i
$481$	−14.0987	−	21.5920i	−0.642846	−	0.984509i
$482$			12.5619i			0.572180i
$483$	23.9843	+	13.8473i	1.09132	+	0.630075i
$484$	−11.0597	−	19.1559i	−0.502713	−	0.870724i
$485$	14.5050	−	10.6744i	0.658640	−	0.484700i
$486$	1.00156	+	1.73475i	0.0454316	+	0.0786899i
$487$			14.9745i			0.678558i	0.940686	+	0.339279i	$0.110183\pi$
$487$			14.9745i			0.678558i	−0.940686	+	0.339279i	$0.889817\pi$
$488$	0.0627859	−	0.0362495i	0.00284218	−	0.00164094i
$489$	1.31987			0.0596864
$490$	24.5783	+	10.7637i	1.11033	+	0.486253i
$491$	−31.9345			−1.44118			−0.720591	−	0.693360i	$-0.756130\pi$
$491$	−31.9345			−1.44118			−0.720591	+	0.693360i	$0.756130\pi$
$492$			3.42825i			0.154557i
$493$	7.08100	+	4.08822i	0.318912	+	0.184124i
$494$	30.4808	+	52.7943i	1.37140	+	2.37533i
$495$	−0.209527	+	0.0233161i	−0.00941753	+	0.00104798i
$496$	−2.27864	+	3.94673i	−0.102314	+	0.177213i
$497$	−8.36128	−	4.82739i	−0.375055	−	0.216538i
$498$	−18.0423	−	10.4167i	−0.808495	−	0.466785i
$499$	8.26030	+	14.3073i	0.369782	+	0.640481i	0.989531	−	0.144319i	$-0.0460991\pi$
$499$	8.26030	+	14.3073i	0.369782	+	0.640481i	−0.619749	+	0.784800i	$0.712766\pi$
$500$	16.9938	+	14.7469i	0.759984	+	0.659500i
$501$	−7.49394	+	12.9799i	−0.334805	+	0.579899i
$502$	41.8216	+	24.1457i	1.86659	+	1.07768i
$503$	15.5359	+	8.96968i	0.692713	+	0.399938i	0.804628	−	0.593780i	$-0.202365\pi$
$503$	15.5359	+	8.96968i	0.692713	+	0.399938i	−0.111914	+	0.993718i	$0.535698\pi$
$504$	0.0900803			0.00401249
$505$	10.1792	+	13.8322i	0.452971	+	0.615524i
$506$	−0.725583	+	1.25675i	−0.0322561	+	0.0558692i
$507$		−	4.97261i		−	0.220841i
$508$		−	39.6629i		−	1.75976i
$509$	−6.25380	+	10.8319i	−0.277195	+	0.480116i	−0.970687	−	0.240349i	$-0.922738\pi$
$509$	−6.25380	+	10.8319i	−0.277195	+	0.480116i	0.693492	+	0.720465i	$0.256071\pi$
$510$	3.51741	+	31.6087i	0.155753	+	1.39966i
$511$	9.14588	+	15.8411i	0.404590	+	0.700770i
$512$			32.0461i			1.41625i
$513$	6.21692	−	3.58934i	0.274484	−	0.158473i
$514$	−1.42434	−	2.46702i	−0.0628248	−	0.108816i
$515$	24.3971	−	17.9541i	1.07506	−	0.791150i
$516$	−0.762888	+	1.32136i	−0.0335843	+	0.0581697i
$517$			0.809145i			0.0355861i
$518$	2.40780	+	43.8496i	0.105793	+	1.92664i
$519$	2.02906			0.0890659
$520$	0.0950426	−	0.217025i	0.00416789	−	0.00951716i
$521$	7.07206	+	12.2492i	0.309833	+	0.536646i	0.978326	−	0.207073i	$-0.0663936\pi$
$521$	7.07206	+	12.2492i	0.309833	+	0.536646i	−0.668493	+	0.743719i	$0.733060\pi$
$522$	−1.99762	+	1.15333i	−0.0874334	+	0.0504797i
$523$	6.69867	−	3.86748i	0.292912	−	0.169113i	−0.346342	−	0.938108i	$-0.612576\pi$
$523$	6.69867	−	3.86748i	0.292912	−	0.169113i	0.639254	+	0.768995i	$0.279243\pi$
$524$	−23.2064			−1.01378
$525$	−12.2211	−	13.2441i	−0.533372	−	0.578020i
$526$	−57.5926			−2.51115
$527$	−7.05018	−	4.07042i	−0.307111	−	0.177310i
$528$		−	0.374759i		−	0.0163093i
$529$	−36.0429			−1.56708
$530$	12.1031	−	27.6367i	0.525724	−	1.20046i
$531$	1.05402	+	1.82562i	0.0457406	+	0.0792251i
$532$		−	52.0700i		−	2.25752i
$533$	−6.25428	−	3.61091i	−0.270903	−	0.156406i
$534$	9.56732	−	16.5711i	0.414018	−	0.717101i
$535$	−4.18844	−	1.83426i	−0.181082	−	0.0793020i
$536$	−0.166848	−	0.288990i	−0.00720676	−	0.0124825i
$537$	−7.62656	+	4.40320i	−0.329110	+	0.190012i
$538$	15.2814	+	8.82271i	0.658827	+	0.380374i
$539$	0.282395	−	0.489122i	0.0121636	−	0.0210680i
$540$	−4.12208	−	1.80520i	−0.177386	−	0.0776835i
$541$	−1.11972			−0.0481407			−0.0240703	−	0.999710i	$-0.507663\pi$
$541$	−1.11972			−0.0481407			−0.0240703	+	0.999710i	$0.507663\pi$
$542$	−31.0169	+	17.9076i	−1.33229	+	0.769197i
$543$	4.89724	+	2.82742i	0.210161	+	0.121336i
$544$	−56.8902			−2.43915
$545$	33.6313	−	3.74247i	1.44061	−	0.160310i
$546$	−15.3036	+	26.5066i	−0.654934	+	1.13438i
$547$			11.5267i			0.492846i	0.969162	+	0.246423i	$0.0792553\pi$
$547$			11.5267i			0.492846i	−0.969162	+	0.246423i	$0.920745\pi$
$548$	14.3653	−	8.29381i	0.613656	−	0.354294i
$549$	2.90077			0.123802
$550$	0.693975	−	0.640370i	0.0295912	−	0.0273055i
$551$	4.13324	+	7.15898i	0.176082	+	0.304983i
$552$	−0.166315	+	0.0960221i	−0.00707885	+	0.00408697i
$553$	−48.8479	−	28.2024i	−2.07722	−	1.19929i
$554$	10.5498			0.448217
$555$	4.76496	−	12.7395i	0.202261	−	0.540762i
$556$	24.9384			1.05762
$557$	−7.90855	−	4.56601i	−0.335096	−	0.193468i	0.323005	−	0.946397i	$-0.395307\pi$
$557$	−7.90855	−	4.56601i	−0.335096	−	0.193468i	−0.658101	+	0.752929i	$0.728640\pi$
$558$	1.98892	−	1.14831i	0.0841979	−	0.0486117i
$559$	−1.60707	−	2.78353i	−0.0679719	−	0.117731i
$560$	25.8013	−	18.9874i	1.09030	−	0.802366i
$561$	0.669445			0.0282640
$562$	−14.7150	+	8.49568i	−0.620713	+	0.358369i
$563$		−	14.2018i		−	0.598533i	−0.954170	−	0.299267i	$-0.903258\pi$
$563$		−	14.2018i		−	0.598533i	0.954170	−	0.299267i	$-0.0967420\pi$
$564$	−8.63575	+	14.9576i	−0.363631	+	0.629827i
$565$	3.44809	+	30.9858i	0.145062	+	1.30358i
$566$	14.5533			0.611722
$567$	3.12135	+	1.80211i	0.131084	+	0.0756816i
$568$	0.0579800	−	0.0334748i	0.00243279	−	0.00140457i
$569$	−17.6054			−0.738058			−0.369029	−	0.929418i	$-0.620310\pi$
$569$	−17.6054			−0.738058			−0.369029	+	0.929418i	$0.620310\pi$
$570$	−12.8987	+	29.4535i	−0.540267	+	1.23367i
$571$	−0.490669	+	0.849864i	−0.0205339	+	0.0355657i	−0.876110	−	0.482112i	$-0.839870\pi$
$571$	−0.490669	+	0.849864i	−0.0205339	+	0.0355657i	0.855576	+	0.517677i	$0.173203\pi$
$572$	−0.696617	−	0.402192i	−0.0291270	−	0.0168165i
$573$	16.5590	−	9.56037i	0.691764	−	0.399390i
$574$	6.14935	+	10.6510i	0.256669	+	0.444564i
$575$	36.6815	+	11.4254i	1.52972	+	0.476472i
$576$	4.04975	−	7.01438i	0.168740	−	0.292266i
$577$	5.71839	+	3.30151i	0.238060	+	0.137444i	0.614285	−	0.789085i	$-0.289445\pi$
$577$	5.71839	+	3.30151i	0.238060	+	0.137444i	−0.376225	+	0.926528i	$0.622778\pi$
$578$		−	66.9380i		−	2.78425i
$579$	7.84077	+	13.5806i	0.325851	+	0.564391i
$580$	2.07875	−	4.74671i	0.0863153	−	0.197096i
$581$	−37.4858			−1.55517
$582$		−	16.1332i		−	0.668744i
$583$	−0.549986	−	0.317535i	−0.0227781	−	0.0131509i
$584$	−0.126841			−0.00524874
$585$	7.63501	−	5.61868i	0.315669	−	0.232304i
$586$	32.7281			1.35198
$587$	41.3262	−	23.8597i	1.70571	−	0.984794i	0.765995	−	0.642847i	$-0.222247\pi$
$587$	41.3262	−	23.8597i	1.70571	−	0.984794i	0.939719	−	0.341947i	$-0.111086\pi$
$588$	10.4405	−	6.02782i	0.430559	−	0.248583i
$589$	−4.11525	−	7.12782i	−0.169566	−	0.293697i
$590$	−8.64911	−	3.78774i	−0.356078	−	0.155939i
$591$	−2.81766			−0.115903
$592$	21.5704	+	10.9229i	0.886536	+	0.448930i
$593$			1.03949i			0.0426866i	0.999772	+	0.0213433i	$0.00679431\pi$
$593$			1.03949i			0.0426866i	−0.999772	+	0.0213433i	$0.993206\pi$
$594$	−0.0944286	+	0.163555i	−0.00387445	+	0.00671075i
$595$	33.9179	+	46.0898i	1.39050	+	1.88950i
$596$	−12.8758	−	22.3015i	−0.527414	−	0.913507i
$597$	19.6826	−	11.3637i	0.805554	−	0.465087i
$598$		−	65.2523i		−	2.66836i
$599$	6.94974	+	12.0373i	0.283959	+	0.491831i	0.972356	−	0.233503i	$-0.0750188\pi$
$599$	6.94974	+	12.0373i	0.283959	+	0.491831i	−0.688397	+	0.725334i	$0.741686\pi$
$600$	0.121908	−	0.0274719i	0.00497686	−	0.00112153i
$601$	14.8464	−	25.7148i	0.605599	−	1.04893i	−0.386357	−	0.922349i	$-0.626267\pi$
$601$	14.8464	−	25.7148i	0.605599	−	1.04893i	0.991957	−	0.126579i	$-0.0403998\pi$
$602$			5.47367i			0.223090i
$603$		−	13.3516i		−	0.543721i
$604$	−1.91747	+	3.32115i	−0.0780206	+	0.135136i
$605$	14.5670	+	19.7946i	0.592233	+	0.804763i
$606$	15.3848			0.624966
$607$	38.1050	+	21.9999i	1.54664	+	0.892950i	0.998395	+	0.0566293i	$0.0180353\pi$
$607$	38.1050	+	21.9999i	1.54664	+	0.892950i	0.548240	+	0.836321i	$0.315298\pi$
$608$	−49.8110	−	28.7584i	−2.02010	−	1.16631i
$609$	−2.07519	+	3.59433i	−0.0840909	+	0.145650i
$610$	−10.4646	+	7.70104i	−0.423701	+	0.311806i
$611$	−18.1918	−	31.5090i	−0.735960	−	1.27472i
$612$	12.3751	+	7.14478i	0.500235	+	0.288811i
$613$	28.8246	+	16.6419i	1.16421	+	0.672159i	0.952310	−	0.305132i	$-0.0987007\pi$
$613$	28.8246	+	16.6419i	1.16421	+	0.672159i	0.211903	+	0.977291i	$0.432034\pi$
$614$	−3.09459	+	5.35998i	−0.124887	+	0.216311i
$615$	−0.421278	−	3.78576i	−0.0169876	−	0.152657i
$616$	0.00424646	+	0.00735508i	0.000171095	+	0.000296345i
$617$	1.53876	+	0.888405i	0.0619483	+	0.0357658i	0.530654	−	0.847588i	$-0.321946\pi$
$617$	1.53876	+	0.888405i	0.0619483	+	0.0357658i	−0.468706	+	0.883354i	$0.655280\pi$
$618$		−	27.1356i		−	1.09155i
$619$	−35.3048			−1.41902			−0.709509	−	0.704696i	$-0.751083\pi$
$619$	−35.3048			−1.41902			−0.709509	+	0.704696i	$0.751083\pi$
$620$	−2.06970	+	4.72605i	−0.0831211	+	0.189803i
$621$	−7.68394			−0.308346
$622$	−10.7746	+	6.22074i	−0.432024	+	0.249429i
$623$		−	34.4291i		−	1.37937i
$624$	8.42560	+	14.5936i	0.337294	+	0.584210i
$625$	−20.5781	−	14.1965i	−0.823126	−	0.567859i
$626$	−19.5940	−	33.9378i	−0.783134	−	1.35643i
$627$	0.586142	+	0.338409i	0.0234082	+	0.0135148i
$628$			28.5022i			1.13736i
$629$	−19.5120	+	38.5319i	−0.777995	+	1.53637i
$630$	−16.0447	+	1.78545i	−0.639235	+	0.0711338i
$631$	−9.73240	+	16.8570i	−0.387441	+	0.671067i	−0.992105	−	0.125414i	$-0.959974\pi$
$631$	−9.73240	+	16.8570i	−0.387441	+	0.671067i	0.604664	+	0.796481i	$0.293308\pi$
$632$	0.338728	−	0.195565i	0.0134739	−	0.00777915i
$633$	−4.36682	+	2.52119i	−0.173566	+	0.100208i
$634$	−5.36837	−	9.29829i	−0.213205	−	0.369282i
$635$	4.87395	+	43.7992i	0.193417	+	1.73812i
$636$	−6.77790	−	11.7397i	−0.268761	−	0.465508i
$637$			25.3960i			1.00623i
$638$	−0.188339	−	0.108737i	−0.00745640	−	0.00430496i
$639$	2.67874			0.105969
$640$	0.0494456	+	0.444336i	0.00195451	+	0.0175639i
$641$	20.4929	−	35.4947i	0.809421	−	1.40196i	−0.103845	−	0.994593i	$-0.533115\pi$
$641$	20.4929	−	35.4947i	0.809421	−	1.40196i	0.913266	−	0.407364i	$-0.133552\pi$
$642$	−3.54734	+	2.04806i	−0.140002	+	0.0808305i
$643$		−	13.1039i		−	0.516768i	−0.966042	−	0.258384i	$-0.916810\pi$
$643$		−	13.1039i		−	0.516768i	0.966042	−	0.258384i	$-0.0831899\pi$
$644$	−27.8674	+	48.2678i	−1.09813	+	1.90202i
$645$	0.680072	−	1.55291i	0.0267778	−	0.0611457i
$646$	51.0516	−	88.4239i	2.00860	−	3.47899i
$647$	16.1490	−	9.32363i	0.634883	−	0.366550i	−0.147758	−	0.989024i	$-0.547206\pi$
$647$	16.1490	−	9.32363i	0.634883	−	0.366550i	0.782641	+	0.622474i	$0.213872\pi$
$648$	−0.0216445	+	0.0124965i	−0.000850278	+	0.000490908i
$649$	−0.0993748	+	0.172122i	−0.00390080	+	0.00675639i
$650$	−12.6270	+	40.5392i	−0.495271	+	1.59008i
$651$	2.06616	−	3.57869i	0.0809791	−	0.140260i
$652$			2.65620i			0.104025i
$653$	−10.6957	+	6.17517i	−0.418555	+	0.241653i	−0.694459	−	0.719532i	$-0.744356\pi$
$653$	−10.6957	+	6.17517i	−0.418555	+	0.241653i	0.275904	+	0.961185i	$0.411023\pi$
$654$	15.1568	−	26.2523i	0.592677	−	1.02655i
$655$	25.6265	−	2.85171i	1.00131	−	0.111425i
$656$	6.77121			0.264371
$657$	−4.39515	−	2.53754i	−0.171471	−	0.0989990i
$658$			61.9609i			2.41549i
$659$	10.1421	+	17.5666i	0.395079	+	0.684297i	0.993111	−	0.117175i	$-0.0373839\pi$
$659$	10.1421	+	17.5666i	0.395079	+	0.684297i	−0.598032	+	0.801472i	$0.704051\pi$
$660$	−0.0469230	−	0.421668i	−0.00182648	−	0.0164134i
$661$	−8.42433	−	14.5914i	−0.327668	−	0.567538i	0.654380	−	0.756166i	$-0.272930\pi$
$661$	−8.42433	−	14.5914i	−0.327668	−	0.567538i	−0.982049	+	0.188627i	$0.939596\pi$
$662$	−28.6190	+	16.5232i	−1.11231	+	0.642192i
$663$	−26.0690	+	15.0509i	−1.01244	+	0.584530i
$664$	0.129970	−	0.225114i	0.00504381	−	0.00873613i
$665$	6.39860	+	57.5002i	0.248127	+	2.22976i
$666$	−6.66163	−	10.2022i	−0.258133	−	0.395326i
$667$		−	8.84829i		−	0.342607i
$668$	−26.1217	−	15.0814i	−1.01068	−	0.583516i
$669$	−11.8592	−	20.5408i	−0.458505	−	0.794154i
$670$	35.4462	+	48.1665i	1.36941	+	1.86083i
$671$	0.136745	+	0.236849i	0.00527898	+	0.00914346i
$672$		−	28.8776i		−	1.11398i
$673$	9.10488	−	5.25671i	0.350968	−	0.202631i	−0.314144	−	0.949375i	$-0.601717\pi$
$673$	9.10488	−	5.25671i	0.350968	−	0.202631i	0.665111	+	0.746744i	$0.268384\pi$
$674$	28.7972			1.10923
$675$	4.77379	+	1.48692i	0.183743	+	0.0572316i
$676$	10.0073			0.384894
$677$			17.5417i			0.674181i	0.941472	+	0.337090i	$0.109443\pi$
$677$			17.5417i			0.674181i	−0.941472	+	0.337090i	$0.890557\pi$
$678$	24.1873	+	13.9645i	0.928908	+	0.536305i
$679$	−14.5143	−	25.1396i	−0.557009	−	0.964768i
$680$	−0.394383	+	0.0438868i	−0.0151239	+	0.00168298i
$681$	−1.44160	+	2.49692i	−0.0552421	+	0.0956822i
$682$	0.187519	+	0.108264i	0.00718047	+	0.00414565i
$683$	1.09967	+	0.634893i	0.0420776	+	0.0242935i	0.520891	−	0.853623i	$-0.325600\pi$
$683$	1.09967	+	0.634893i	0.0420776	+	0.0242935i	−0.478814	+	0.877917i	$0.658933\pi$
$684$	7.22347	+	12.5114i	0.276196	+	0.478386i
$685$	−14.8442	+	10.9240i	−0.567169	+	0.417385i
$686$	−3.64432	+	6.31214i	−0.139141	+	0.240999i
$687$	4.22050	+	2.43671i	0.161022	+	0.0929661i
$688$	2.60985	+	1.50680i	0.0994996	+	0.0574461i
$689$	28.5562			1.08790
$690$	27.7201	−	20.3995i	1.05528	−	0.776595i
$691$	8.92353	−	15.4560i	0.339467	−	0.587974i	−0.644865	−	0.764296i	$-0.723087\pi$
$691$	8.92353	−	15.4560i	0.339467	−	0.587974i	0.984333	+	0.176322i	$0.0564199\pi$
$692$			4.08344i			0.155229i
$693$			0.339812i			0.0129084i
$694$	34.0926	−	59.0501i	1.29414	−	2.24151i
$695$	−27.5391	+	3.06454i	−1.04462	+	0.116245i
$696$	−0.0143901	−	0.0249244i	−0.000545455	−	0.000944755i
$697$			12.0957i			0.458155i
$698$	55.2040	−	31.8721i	2.08950	−	1.20638i
$699$	−7.55642	−	13.0881i	−0.285810	−	0.495038i
$700$	26.6535	−	24.5946i	1.00741	−	0.929590i
$701$	−8.16129	+	14.1358i	−0.308248	+	0.533900i	−0.977979	−	0.208703i	$-0.933076\pi$
$701$	−8.16129	+	14.1358i	−0.308248	+	0.533900i	0.669732	+	0.742603i	$0.266409\pi$
$702$		−	8.49204i		−	0.320511i
$703$	−36.5621	+	23.8736i	−1.37897	+	0.900412i
$704$	0.763634			0.0287805
$705$	7.69829	−	17.5786i	0.289934	−	0.662049i
$706$	6.74713	+	11.6864i	0.253932	+	0.439822i
$707$	23.9734	−	13.8410i	0.901612	−	0.520546i
$708$	−3.67402	+	2.12119i	−0.138078	+	0.0797193i
$709$	8.40611			0.315698			0.157849	−	0.987463i	$-0.449544\pi$
$709$	8.40611			0.315698			0.157849	+	0.987463i	$0.449544\pi$
$710$	−9.66363	+	7.11157i	−0.362670	+	0.266892i
$711$	15.6496			0.586906
$712$	0.206758	+	0.119372i	0.00774858	+	0.00447365i
$713$			8.80978i			0.329929i
$714$	51.2633			1.91848
$715$	0.818688	+	0.358532i	0.0306172	+	0.0134083i
$716$	−8.86133	−	15.3483i	−0.331163	−	0.573592i
$717$		−	11.2163i		−	0.418881i
$718$	−37.6385	−	21.7306i	−1.40465	−	0.810978i
$719$	13.2433	−	22.9380i	0.493891	−	0.855444i	−0.506085	−	0.862484i	$-0.668908\pi$
$719$	13.2433	−	22.9380i	0.493891	−	0.855444i	0.999975	+	0.00704019i	$0.00224098\pi$
$720$	−3.56550	+	8.14162i	−0.132878	+	0.303420i
$721$	−24.4127	−	42.2840i	−0.909176	−	1.57474i
$722$	56.4375	−	32.5842i	2.10039	−	1.21266i
$723$	−5.43101	−	3.13560i	−0.201981	−	0.116614i
$724$	−5.69013	+	9.85559i	−0.211472	+	0.366280i
$725$	−1.71223	+	5.49717i	−0.0635908	+	0.204160i
$726$	22.0165			0.817108
$727$	19.6473	−	11.3434i	0.728679	−	0.420703i	−0.0892599	−	0.996008i	$-0.528450\pi$
$727$	19.6473	−	11.3434i	0.728679	−	0.420703i	0.817939	+	0.575306i	$0.195117\pi$
$728$	−0.330724	−	0.190944i	−0.0122575	−	0.00707684i
$729$	−1.00000			−0.0370370
$730$	22.5924	−	2.51407i	0.836182	−	0.0930500i
$731$	−2.69165	+	4.66207i	−0.0995542	+	0.172433i
$732$			5.83774i			0.215769i
$733$	−35.0247	+	20.2215i	−1.29367	+	0.746900i	−0.979302	−	0.202402i	$-0.935125\pi$
$733$	−35.0247	+	20.2215i	−1.29367	+	0.746900i	−0.314366	+	0.949302i	$0.601792\pi$
$734$	3.77773			0.139439
$735$	−10.7886	+	7.93941i	−0.397942	+	0.292850i
$736$	30.7824	+	53.3168i	1.13466	+	1.96528i
$737$	1.09016	−	0.629407i	0.0401567	−	0.0231845i
$738$	−2.95514	−	1.70615i	−0.108780	−	0.0628043i
$739$	5.34576			0.196647			0.0983235	−	0.995155i	$-0.468652\pi$
$739$	5.34576			0.196647			0.0983235	+	0.995155i	$0.468652\pi$
$740$	25.6380	+	9.58937i	0.942471	+	0.352512i
$741$	−30.4334			−1.11800
$742$	−42.1156	−	24.3155i	−1.54611	−	0.892649i
$743$	−18.6037	+	10.7408i	−0.682503	+	0.394044i	−0.800798	−	0.598935i	$-0.795591\pi$
$743$	−18.6037	+	10.7408i	−0.682503	+	0.394044i	0.118294	+	0.992979i	$0.462257\pi$
$744$	0.0143275	+	0.0248159i	0.000525270	+	0.000909794i
$745$	16.9591	+	23.0451i	0.621333	+	0.844305i
$746$	−57.0228			−2.08775
$747$	9.00711	−	5.20026i	0.329553	−	0.190268i
$748$			1.34724i			0.0492601i
$749$	−3.68509	+	6.38277i	−0.134650	+	0.233221i
$750$	−21.1691	+	7.30945i	−0.772987	+	0.266903i
$751$	12.8924			0.470452			0.235226	−	0.971941i	$-0.424417\pi$
$751$	12.8924			0.470452			0.235226	+	0.971941i	$0.424417\pi$
$752$	29.5430	+	17.0567i	1.07732	+	0.621993i
$753$	−20.8783	+	12.0541i	−0.760846	+	0.439275i
$754$	9.77884			0.356124
$755$	1.70931	−	3.90312i	0.0622083	−	0.142049i
$756$	−3.62671	+	6.28165i	−0.131902	+	0.228461i
$757$	−34.0666	−	19.6683i	−1.23817	−	0.714858i	−0.269450	−	0.963014i	$-0.586842\pi$
$757$	−34.0666	−	19.6683i	−1.23817	−	0.714858i	−0.968720	+	0.248156i	$0.920175\pi$
$758$	−8.64885	+	4.99341i	−0.314140	+	0.181369i
$759$	−0.362227	−	0.627395i	−0.0131480	−	0.0227730i
$760$	−0.367492	−	0.160938i	−0.0133303	−	0.00583782i
$761$	−19.2989	+	33.4267i	−0.699584	+	1.21172i	0.269026	+	0.963133i	$0.413298\pi$
$761$	−19.2989	+	33.4267i	−0.699584	+	1.21172i	−0.968611	+	0.248583i	$0.920035\pi$
$762$	34.1893	+	19.7392i	1.23855	+	0.715076i
$763$		−	54.5435i		−	1.97461i
$764$	19.2400	+	33.3247i	0.696080	+	1.20565i
$765$	−14.5437	−	6.36917i	−0.525827	−	0.230278i
$766$	18.8264			0.680226
$767$		−	8.93686i		−	0.322691i
$768$	−13.6819	−	7.89925i	−0.493703	−	0.285040i
$769$	−22.9343			−0.827031			−0.413516	−	0.910497i	$-0.635699\pi$
$769$	−22.9343			−0.827031			−0.413516	+	0.910497i	$0.635699\pi$
$770$	−0.902141	−	1.22588i	−0.0325109	−	0.0441778i
$771$	1.42212			0.0512164
$772$	−27.3307	+	15.7794i	−0.983653	+	0.567912i
$773$	−8.35426	+	4.82333i	−0.300482	+	0.173483i	−0.642659	−	0.766152i	$-0.722169\pi$
$773$	−8.35426	+	4.82333i	−0.300482	+	0.173483i	0.342178	+	0.939635i	$0.388836\pi$
$774$	−0.759340	−	1.31522i	−0.0272939	−	0.0472744i
$775$	1.70478	−	5.47324i	0.0612376	−	0.196605i
$776$	0.201295			0.00722606
$777$	−19.5589	−	9.90435i	−0.701671	−	0.355317i
$778$			37.0110i			1.32691i
$779$	−6.11443	+	10.5905i	−0.219072	+	0.379444i
$780$	11.3075	+	15.3653i	0.404872	+	0.550166i
$781$	0.126278	+	0.218720i	0.00451857	+	0.00782640i
$782$	−94.6474	+	54.6447i	−3.38458	+	1.95409i
$783$		−	1.15153i		−	0.0411524i
$784$	−11.9057	−	20.6213i	−0.425203	−	0.736474i
$785$	−3.50248	−	31.4746i	−0.125009	−	1.12338i
$786$	11.5492	−	20.0039i	0.411948	−	0.713514i
$787$		−	45.6788i		−	1.62827i	−0.580674	−	0.814137i	$-0.697211\pi$
$787$		−	45.6788i		−	1.62827i	0.580674	−	0.814137i	$-0.302789\pi$
$788$		−	5.67048i		−	0.202003i
$789$	14.3757	−	24.8995i	0.511790	−	0.886446i
$790$	−56.4565	+	41.5469i	−2.00863	+	1.47817i
$791$	50.2531			1.78679
$792$	−0.00204068	−	0.00117819i	−7.25125e−5	−	4.18651e-5i
$793$	−10.6500	−	6.14879i	−0.378193	−	0.218350i
$794$	9.72620	−	16.8463i	0.345170	−	0.597852i
$795$	8.92737	+	12.1311i	0.316621	+	0.430244i
$796$	22.8692	+	39.6107i	0.810579	+	1.40396i
$797$	13.2240	+	7.63488i	0.468418	+	0.270441i	0.715577	−	0.698534i	$-0.246164\pi$
$797$	13.2240	+	7.63488i	0.468418	+	0.270441i	−0.247159	+	0.968975i	$0.579497\pi$
$798$	44.8842	+	25.9139i	1.58888	+	0.917343i
$799$	−30.4689	+	52.7737i	−1.07791	+	1.86700i
$800$	−8.80684	−	39.0808i	−0.311369	−	1.38171i
$801$	4.77622	+	8.27265i	0.168759	+	0.292300i
$802$	−50.2586	−	29.0168i	−1.77469	−	1.02462i
$803$		−	0.478487i		−	0.0168855i
$804$	26.8699			0.947627
$805$	24.8422	−	56.7259i	0.875574	−	1.99933i
$806$	−9.73628			−0.342946
$807$	−7.62881	+	4.40449i	−0.268547	+	0.155045i
$808$			0.191957i			0.00675303i
$809$	−16.1697	−	28.0068i	−0.568497	−	0.984666i	−0.996715	−	0.0809902i	$-0.974192\pi$
$809$	−16.1697	−	28.0068i	−0.568497	−	0.984666i	0.428218	−	0.903676i	$-0.359142\pi$
$810$	3.60753	−	2.65482i	0.126756	−	0.0932809i
$811$	0.167243	+	0.289673i	0.00587269	+	0.0101718i	0.868947	−	0.494905i	$-0.164797\pi$
$811$	0.167243	+	0.289673i	0.00587269	+	0.0101718i	−0.863074	+	0.505077i	$0.831464\pi$
$812$	−7.23351	−	4.17627i	−0.253847	−	0.146558i
$813$		−	17.8797i		−	0.627069i
$814$	0.518976	−	1.02486i	0.0181901	−	0.0359214i
$815$	−0.326406	−	2.93320i	−0.0114335	−	0.102746i
$816$	14.1118	−	24.4424i	0.494013	−	0.855655i
$817$	−4.71341	+	2.72129i	−0.164901	+	0.0952059i
$818$	−34.8790	+	20.1374i	−1.21952	+	0.704088i
$819$	−7.63990	−	13.2327i	−0.266960	−	0.462388i
$820$	7.61877	−	0.847813i	0.266059	−	0.0296069i
$821$	6.88677	+	11.9282i	0.240350	+	0.416298i	0.960814	−	0.277194i	$-0.0894045\pi$
$821$	6.88677	+	11.9282i	0.240350	+	0.416298i	−0.720464	+	0.693492i	$0.756071\pi$
$822$			16.5105i			0.575869i
$823$	32.2386	+	18.6130i	1.12377	+	0.648808i	0.942360	−	0.334600i	$-0.108601\pi$
$823$	32.2386	+	18.6130i	1.12377	+	0.648808i	0.181408	+	0.983408i	$0.441935\pi$
$824$	0.338572			0.0117947
$825$	0.103633	+	0.459876i	0.00360804	+	0.0160108i
$826$	−7.60970	+	13.1804i	−0.264775	+	0.458605i
$827$	−22.3354	+	12.8954i	−0.776679	+	0.448416i	−0.835252	−	0.549867i	$-0.814678\pi$
$827$	−22.3354	+	12.8954i	−0.776679	+	0.448416i	0.0585728	+	0.998283i	$0.481345\pi$
$828$		−	15.4637i		−	0.537402i
$829$	3.47716	−	6.02263i	0.120767	−	0.209174i	−0.799303	−	0.600928i	$-0.794798\pi$
$829$	3.47716	−	6.02263i	0.120767	−	0.209174i	0.920070	+	0.391753i	$0.128131\pi$
$830$	−18.6877	+	42.6724i	−0.648660	+	1.48118i
$831$	−2.63334	+	4.56108i	−0.0913495	+	0.158222i
$832$	−29.7368	+	17.1686i	−1.03094	+	0.595213i
$833$	36.8365	−	21.2676i	1.27631	−	0.736877i
$834$	−12.4112	+	21.4968i	−0.429764	+	0.744373i
$835$	30.6991	+	13.4442i	1.06239	+	0.465256i
$836$	−0.681040	+	1.17960i	−0.0235543	+	0.0407972i
$837$			1.14652i			0.0396295i
$838$	−28.9032	+	16.6872i	−0.998443	+	0.576451i
$839$	−15.7786	+	27.3293i	−0.544738	+	0.943513i	0.453886	+	0.891060i	$0.350037\pi$
$839$	−15.7786	+	27.3293i	−0.544738	+	0.943513i	−0.998623	+	0.0524533i	$0.983296\pi$
$840$	−0.0222771	−	0.200190i	−0.000768632	−	0.00690721i
$841$	−27.6740			−0.954275
$842$	31.4793	+	18.1746i	1.08485	+	0.626337i
$843$		−	8.48246i		−	0.292152i
$844$	−5.07383	−	8.78813i	−0.174648	−	0.302500i
$845$	−11.0509	+	1.22974i	−0.380162	+	0.0423042i
$846$	−8.59558	−	14.8880i	−0.295522	−	0.511860i
$847$	34.3071	−	19.8072i	1.17881	−	0.680584i
$848$	−23.1873	+	13.3872i	−0.796255	+	0.459718i
$849$	−3.63267	+	6.29197i	−0.124673	+	0.215940i
$850$	69.3758	−	15.6338i	2.37957	−	0.536236i
$851$	46.6693	−	2.56263i	1.59980	−	0.0878457i
$852$			5.39089i			0.184689i
$853$	−12.7627	−	7.36856i	−0.436987	−	0.252295i	0.265332	−	0.964157i	$-0.414519\pi$
$853$	−12.7627	−	7.36856i	−0.436987	−	0.252295i	−0.702319	+	0.711862i	$0.747852\pi$
$854$	10.4713	+	18.1369i	0.358322	+	0.620632i
$855$	−9.51424	−	12.9285i	−0.325380	−	0.442146i
$856$	−0.0255537	−	0.0442603i	−0.000873408	−	0.00151279i
$857$		−	47.3285i		−	1.61671i	−0.588694	−	0.808356i	$-0.700358\pi$
$857$		−	47.3285i		−	1.61671i	0.588694	−	0.808356i	$-0.299642\pi$
$858$	0.693377	−	0.400321i	0.0236715	−	0.0136667i
$859$	28.5508			0.974142			0.487071	−	0.873362i	$-0.338065\pi$
$859$	28.5508			0.974142			0.487071	+	0.873362i	$0.338065\pi$
$860$	3.12519	+	1.36863i	0.106568	+	0.0466699i
$861$	−6.13979			−0.209243
$862$			13.3624i			0.455125i
$863$	−17.0143	−	9.82319i	−0.579172	−	0.334385i	0.181632	−	0.983367i	$-0.441862\pi$
$863$	−17.0143	−	9.82319i	−0.579172	−	0.334385i	−0.760804	+	0.648981i	$0.775195\pi$
$864$	4.00608	+	6.93873i	0.136290	+	0.236060i
$865$	−0.501791	−	4.50928i	−0.0170614	−	0.153320i
$866$	−7.41990	+	12.8516i	−0.252138	+	0.436716i
$867$	28.9399	+	16.7085i	0.982851	+	0.567449i
$868$	7.20203	+	4.15809i	0.244453	+	0.141135i
$869$	0.737735	+	1.27779i	0.0250259	+	0.0433462i
$870$	3.05711	+	4.15419i	0.103646	+	0.140840i
$871$	−28.3015	+	49.0197i	−0.958961	+	1.66097i
$872$	0.327551	+	0.189112i	0.0110923	+	0.00640413i
$873$	6.97502	+	4.02703i	0.236069	+	0.136294i
$874$	−110.493			−3.73748
$875$	−26.4108	+	30.4348i	−0.892846	+	1.02888i
$876$	5.10675	−	8.84515i	0.172541	−	0.298850i
$877$			34.2882i			1.15783i	0.815387	+	0.578916i	$0.196524\pi$
$877$			34.2882i			1.15783i	−0.815387	+	0.578916i	$0.803476\pi$
$878$			58.8923i			1.98752i
$879$	−8.16928	+	14.1496i	−0.275543	+	0.477255i
$880$	−0.832846	+	0.0926788i	−0.0280752	+	0.00312420i
$881$	28.4686	+	49.3090i	0.959131	+	1.66126i	0.724618	+	0.689151i	$0.242016\pi$
$881$	28.4686	+	49.3090i	0.959131	+	1.66126i	0.234513	+	0.972113i	$0.424650\pi$
$882$			11.9996i			0.404047i
$883$	−37.1812	+	21.4666i	−1.25125	+	0.722409i	−0.971357	−	0.237623i	$-0.923632\pi$
$883$	−37.1812	+	21.4666i	−1.25125	+	0.722409i	−0.279891	+	0.960032i	$0.590298\pi$
$884$	−30.2897	−	52.4633i	−1.01875	−	1.76453i
$885$	3.79650	−	2.79388i	0.127618	−	0.0939154i
$886$	9.99697	−	17.3153i	0.335855	−	0.581718i
$887$			40.2706i			1.35215i	0.736831	+	0.676077i	$0.236321\pi$
$887$			40.2706i			1.35215i	−0.736831	+	0.676077i	$0.763679\pi$
$888$	0.127293	−	0.0831173i	0.00427167	−	0.00278923i
$889$	71.0339			2.38240
$890$	−39.1928	−	17.1639i	−1.31374	−	0.575334i
$891$	−0.0471408	−	0.0816503i	−0.00157928	−	0.00273539i
$892$	41.3379	−	23.8665i	1.38410	−	0.799108i
$893$	−53.3549	+	30.8045i	−1.78545	+	1.03083i
$894$	25.6318			0.857257
$895$	11.6715	+	15.8600i	0.390136	+	0.530140i
$896$	0.720628			0.0240745
$897$	28.2111	+	16.2877i	0.941941	+	0.543830i
$898$		−	49.3415i		−	1.64655i
$899$	−1.32025			−0.0440329
$900$	−2.99239	+	9.60714i	−0.0997464	+	0.320238i
$901$	−23.9140	−	41.4203i	−0.796691	−	1.37991i
$902$		−	0.321717i		−	0.0107120i
$903$	−2.36648	−	1.36629i	−0.0787515	−	0.0454672i
$904$	−0.174236	+	0.301786i	−0.00579501	+	0.0100372i
$905$	5.07243	−	11.5826i	0.168613	−	0.385019i
$906$	−1.90855	−	3.30570i	−0.0634072	−	0.109825i
$907$	5.94470	−	3.43217i	0.197391	−	0.113963i	−0.398047	−	0.917365i	$-0.630312\pi$
$907$	5.94470	−	3.43217i	0.197391	−	0.113963i	0.595438	+	0.803401i	$0.296979\pi$
$908$	−5.02499	−	2.90118i	−0.166760	−	0.0962791i
$909$	−3.84022	+	6.65146i	−0.127372	+	0.220615i
$910$	62.6916	+	27.4548i	2.07821	+	0.910119i
$911$	36.9502			1.22422			0.612108	−	0.790774i	$-0.290322\pi$
$911$	36.9502			1.22422			0.612108	+	0.790774i	$0.290322\pi$
$912$	24.7116	−	14.2672i	0.818282	−	0.472436i
$913$	0.849205	+	0.490289i	0.0281046	+	0.0162262i
$914$	58.1019			1.92184
$915$	−0.717368	−	6.44654i	−0.0237155	−	0.213116i
$916$	−4.90381	+	8.49365i	−0.162027	+	0.280638i
$917$		−	41.5613i		−	1.37248i
$918$	−12.3176	+	7.11155i	−0.406540	+	0.234716i
$919$	−34.0760			−1.12406			−0.562031	−	0.827116i	$-0.689980\pi$
$919$	−34.0760			−1.12406			−0.562031	+	0.827116i	$0.689980\pi$
$920$	0.254525	+	0.345864i	0.00839144	+	0.0114028i
$921$	−1.54489	−	2.67582i	−0.0509057	−	0.0881713i
$922$	−47.4076	+	27.3708i	−1.56129	+	0.901408i
$923$	−9.83481	−	5.67813i	−0.323717	−	0.186898i
$924$	−0.683865			−0.0224975
$925$	−29.4900	−	7.43889i	−0.969627	−	0.244589i
$926$	−65.1925			−2.14236
$927$	11.7318	+	6.77335i	0.385322	+	0.222466i
$928$	−7.99016	+	4.61312i	−0.262290	+	0.151433i
$929$	10.3865	+	17.9900i	0.340771	+	0.590233i	0.984576	−	0.174957i	$-0.0559785\pi$
$929$	10.3865	+	17.9900i	0.340771	+	0.590233i	−0.643805	+	0.765190i	$0.722645\pi$
$930$	−3.04380	−	4.13611i	−0.0998102	−	0.135628i
$931$	43.0035			1.40938
$932$	26.3395	−	15.2071i	0.862780	−	0.498126i
$933$		−	6.21106i		−	0.203341i
$934$	−3.38078	+	5.85569i	−0.110623	+	0.191604i
$935$	−0.165555	−	1.48774i	−0.00541424	−	0.0486544i
$936$	0.105955			0.00346326
$937$	−0.948677	−	0.547719i	−0.0309919	−	0.0178932i	0.484424	−	0.874833i	$-0.339029\pi$
$937$	−0.948677	−	0.547719i	−0.0309919	−	0.0178932i	−0.515416	+	0.856940i	$0.672363\pi$
$938$	83.4802	−	48.1973i	2.72573	−	1.57370i
$939$	19.5635			0.638431
$940$	35.3766	+	15.4926i	1.15386	+	0.505314i
$941$	0.106139	−	0.183838i	0.00346003	−	0.00599295i	−0.864290	−	0.502993i	$-0.832232\pi$
$941$	0.106139	−	0.183838i	0.00346003	−	0.00599295i	0.867750	+	0.497001i	$0.165565\pi$
$942$	−24.5688	−	14.1848i	−0.800495	−	0.462166i
$943$	11.3359	−	6.54478i	0.369147	−	0.213127i
$944$	4.18962	+	7.25663i	0.136360	+	0.236183i
$945$	3.23301	−	7.38240i	0.105170	−	0.240150i
$946$	0.0715918	−	0.124001i	0.00232765	−	0.00403161i
$947$	−34.7043	−	20.0365i	−1.12774	−	0.651100i	−0.184374	−	0.982856i	$-0.559026\pi$
$947$	−34.7043	−	20.0365i	−1.12774	−	0.651100i	−0.943365	+	0.331756i	$0.892359\pi$
$948$			31.4945i			1.02289i
$949$	10.7577	+	18.6329i	0.349209	+	0.604848i
$950$	68.6459	+	21.3815i	2.22717	+	0.693708i
$951$	5.36002			0.173811
$952$			0.639614i			0.0207300i
$953$	48.4093	+	27.9491i	1.56813	+	0.905360i	0.996387	+	0.0849275i	$0.0270659\pi$
$953$	48.4093	+	27.9491i	1.56813	+	0.905360i	0.571743	+	0.820433i	$0.306267\pi$
$954$	13.4928			0.436844
$955$	−25.3416	−	34.4357i	−0.820034	−	1.11431i
$956$	22.5726			0.730050
$957$	0.0940228	−	0.0542841i	0.00303933	−	0.00175476i
$958$	−62.4372	+	36.0481i	−2.01725	+	1.16466i
$959$	14.8537	+	25.7274i	0.479652	+	0.830781i
$960$	−16.5899	−	7.26530i	−0.535437	−	0.234486i
$961$	−29.6855			−0.957597
$962$	2.83213	+	51.5773i	0.0913116	+	1.66292i
$963$		−	2.04487i		−	0.0658951i
$964$	6.31031	−	10.9298i	0.203242	−	0.352025i
$965$	28.2418	−	20.7835i	0.909137	−	0.669043i
$966$	−27.7378	−	48.0433i	−0.892449	−	1.54577i
$967$	7.83505	−	4.52357i	0.251958	−	0.145468i	−0.368702	−	0.929548i	$-0.620198\pi$
$967$	7.83505	−	4.52357i	0.251958	−	0.145468i	0.620661	+	0.784079i	$0.286864\pi$
$968$			0.274700i			0.00882920i
$969$	25.4861	+	44.1432i	0.818731	+	1.41808i
$970$	−35.8537	+	3.98978i	−1.15119	+	0.128104i
$971$	2.89772	−	5.01899i	0.0929921	−	0.161067i	−0.815777	−	0.578367i	$-0.803690\pi$
$971$	2.89772	−	5.01899i	0.0929921	−	0.161067i	0.908769	+	0.417300i	$0.137024\pi$
$972$		−	2.01248i		−	0.0645502i
$973$			44.6631i			1.43183i
$974$	14.9978	−	25.9770i	0.480561	−	0.832355i
$975$	−14.3748	−	15.5782i	−0.460363	−	0.498900i
$976$	11.5303			0.369075
$977$	−9.43643	−	5.44812i	−0.301898	−	0.174301i	0.341397	−	0.939919i	$-0.389100\pi$
$977$	−9.43643	−	5.44812i	−0.301898	−	0.174301i	−0.643295	+	0.765618i	$0.722433\pi$
$978$	−2.28964	−	1.32192i	−0.0732145	−	0.0422704i
$979$	−0.450309	+	0.779959i	−0.0143919	+	0.0249276i
$980$	−15.9779	−	21.7117i	−0.510395	−	0.693556i
$981$	7.56660	+	13.1057i	0.241583	+	0.418434i
$982$	55.3983	+	31.9842i	1.76783	+	1.02066i
$983$	−6.89670	−	3.98181i	−0.219971	−	0.127000i	0.385966	−	0.922513i	$-0.373868\pi$
$983$	−6.89670	−	3.98181i	−0.219971	−	0.127000i	−0.605937	+	0.795513i	$0.707202\pi$
$984$	0.0212877	−	0.0368714i	0.000678627	−	0.00117542i
$985$	0.696814	+	6.26183i	0.0222024	+	0.199519i
$986$	−8.18917	−	14.1841i	−0.260796	−	0.451713i
$987$	−26.7881	−	15.4661i	−0.852674	−	0.492292i
$988$		−	61.2465i		−	1.94851i
$989$	5.82564			0.185245
$990$	0.386829	+	0.169406i	0.0122942	+	0.00538407i
$991$	−16.0500			−0.509845			−0.254922	−	0.966962i	$-0.582050\pi$
$991$	−16.0500			−0.509845			−0.254922	+	0.966962i	$0.582050\pi$
$992$	7.95539	−	4.59304i	0.252584	−	0.145829i
$993$		−	16.4975i		−	0.523532i
$994$	9.66982	+	16.7486i	0.306708	+	0.531234i
$995$	−30.1217	−	40.9313i	−0.954923	−	1.29761i
$996$	10.4654	+	18.1266i	0.331609	+	0.574364i
$997$	6.63587	+	3.83122i	0.210160	+	0.121336i	0.601386	−	0.798959i	$-0.294615\pi$
$997$	6.63587	+	3.83122i	0.210160	+	0.121336i	−0.391226	+	0.920295i	$0.627949\pi$
$998$		−	33.0927i		−	1.04753i
$999$	6.07361	−	0.333504i	0.192161	−	0.0105516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bb.a.454.6	✓	72
5.4	even	2	inner	555.2.bb.a.454.31	yes	72
37.26	even	3	inner	555.2.bb.a.544.31	yes	72
185.174	even	6	inner	555.2.bb.a.544.6	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bb.a.454.6	✓	72	1.1	even	1	trivial
555.2.bb.a.454.31	yes	72	5.4	even	2	inner
555.2.bb.a.544.6	yes	72	185.174	even	6	inner
555.2.bb.a.544.31	yes	72	37.26	even	3	inner

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:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73475 - 1.00156i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.00624 + 1.74286i) q^{4} +(-1.32535 - 1.80096i) q^{5} -2.00312 q^{6} +(-3.12135 + 1.80211i) q^{7} -0.0249930i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.73475 - 1.00156i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.00624 + 1.74286i) q^{4} +(-1.32535 - 1.80096i) q^{5} -2.00312 q^{6} +(-3.12135 + 1.80211i) q^{7} -0.0249930i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.495375 + 4.45163i) q^{10} +0.0942816 q^{11} +(1.74286 + 1.00624i) q^{12} +(-3.67144 + 2.11971i) q^{13} +7.21969 q^{14} +(-2.04826 - 0.897005i) q^{15} +(1.98745 - 3.44236i) q^{16} +(6.14920 + 3.55024i) q^{17} +(-1.73475 + 1.00156i) q^{18} +(3.58934 + 6.21692i) q^{19} +(1.80520 - 4.12208i) q^{20} +(-1.80211 + 3.12135i) q^{21} +(-0.163555 - 0.0944286i) q^{22} -7.68394i q^{23} +(-0.0124965 - 0.0216445i) q^{24} +(-1.48692 + 4.77379i) q^{25} +8.49204 q^{26} -1.00000i q^{27} +(-6.28165 - 3.62671i) q^{28} +1.15153 q^{29} +(2.65482 + 3.60753i) q^{30} -1.14652 q^{31} +(-6.93873 + 4.00608i) q^{32} +(0.0816503 - 0.0471408i) q^{33} +(-7.11155 - 12.3176i) q^{34} +(7.38240 + 3.23301i) q^{35} +2.01248 q^{36} +(0.333504 + 6.07361i) q^{37} -14.3797i q^{38} +(-2.11971 + 3.67144i) q^{39} +(-0.0450113 + 0.0331243i) q^{40} +(0.851748 + 1.47527i) q^{41} +(6.25243 - 3.60984i) q^{42} +0.758158i q^{43} +(0.0948698 + 0.164319i) q^{44} +(-2.22235 + 0.247302i) q^{45} +(-7.69591 + 13.3297i) q^{46} +8.58221i q^{47} -3.97489i q^{48} +(2.99522 - 5.18788i) q^{49} +(7.36066 - 6.79210i) q^{50} +7.10049 q^{51} +(-7.38868 - 4.26586i) q^{52} +(-5.83344 - 3.36794i) q^{53} +(-1.00156 + 1.73475i) q^{54} +(-0.124956 - 0.169798i) q^{55} +(0.0450401 + 0.0780118i) q^{56} +(6.21692 + 3.58934i) q^{57} +(-1.99762 - 1.15333i) q^{58} +(-1.05402 + 1.82562i) q^{59} +(-0.497690 - 4.47243i) q^{60} +(1.45039 + 2.51214i) q^{61} +(1.98892 + 1.14831i) q^{62} +3.60423i q^{63} +8.09950 q^{64} +(8.68343 + 3.80277i) q^{65} -0.188857 q^{66} +(11.5629 - 6.67582i) q^{67} +14.2896i q^{68} +(-3.84197 - 6.65448i) q^{69} +(-9.56858 - 13.0024i) q^{70} +(1.33937 + 2.31985i) q^{71} +(-0.0216445 - 0.0124965i) q^{72} -5.07509i q^{73} +(5.50453 - 10.8702i) q^{74} +(1.09918 + 4.87768i) q^{75} +(-7.22347 + 12.5114i) q^{76} +(-0.294286 + 0.169906i) q^{77} +(7.35432 - 4.24602i) q^{78} +(7.82480 + 13.5530i) q^{79} +(-8.83360 + 0.982999i) q^{80} +(-0.500000 - 0.866025i) q^{81} -3.41230i q^{82} +(9.00711 + 5.20026i) q^{83} -7.25342 q^{84} +(-1.75597 - 15.7798i) q^{85} +(0.759340 - 1.31522i) q^{86} +(0.997255 - 0.575766i) q^{87} -0.00235638i q^{88} +(-4.77622 + 8.27265i) q^{89} +(4.10291 + 1.79681i) q^{90} +(7.63990 - 13.2327i) q^{91} +(13.3920 - 7.73187i) q^{92} +(-0.992915 + 0.573259i) q^{93} +(8.59558 - 14.8880i) q^{94} +(6.43932 - 14.7038i) q^{95} +(-4.00608 + 6.93873i) q^{96} +8.05406i q^{97} +(-10.3919 + 5.99979i) q^{98} +(0.0471408 - 0.0816503i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

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