LMFDB - Embedded newform 240.2.bb.a.173.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(173,240)]

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, 2, 3]))

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

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

chi := DirichletCharacter("240.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bb (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:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			173.12
Character	$\chi$	$=$	240.173
Dual form			240.2.bb.a.197.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.917499 + 1.07619i) q^{2} +(-1.42603 + 0.983076i) q^{3} +(-0.316391 - 1.97482i) q^{4} +(-0.322899 - 2.21263i) q^{5} +(0.250400 - 2.43666i) q^{6} +(1.41445 + 1.41445i) q^{7} +(2.41558 + 1.47139i) q^{8} +(1.06712 - 2.80379i) q^{9} +O(q^{10})$	\(q+(-0.917499 + 1.07619i) q^{2} +(-1.42603 + 0.983076i) q^{3} +(-0.316391 - 1.97482i) q^{4} +(-0.322899 - 2.21263i) q^{5} +(0.250400 - 2.43666i) q^{6} +(1.41445 + 1.41445i) q^{7} +(2.41558 + 1.47139i) q^{8} +(1.06712 - 2.80379i) q^{9} +(2.67748 + 1.68258i) q^{10} +(1.88279 + 1.88279i) q^{11} +(2.39258 + 2.50511i) q^{12} -1.62357i q^{13} +(-2.81998 + 0.224468i) q^{14} +(2.63565 + 2.83784i) q^{15} +(-3.79979 + 1.24963i) q^{16} +(4.72536 + 4.72536i) q^{17} +(2.03834 + 3.72091i) q^{18} +(2.66392 - 2.66392i) q^{19} +(-4.26738 + 1.33772i) q^{20} +(-3.40756 - 0.626537i) q^{21} +(-3.75370 + 0.298791i) q^{22} +(2.05128 + 2.05128i) q^{23} +(-4.89117 + 0.276443i) q^{24} +(-4.79147 + 1.42891i) q^{25} +(1.74727 + 1.48962i) q^{26} +(1.23459 + 5.04735i) q^{27} +(2.34576 - 3.24080i) q^{28} +(-1.64683 - 1.64683i) q^{29} +(-5.47228 + 0.232751i) q^{30} +4.31752 q^{31} +(2.14146 - 5.23585i) q^{32} +(-4.53584 - 0.833989i) q^{33} +(-9.42092 + 0.749896i) q^{34} +(2.67293 - 3.58638i) q^{35} +(-5.87460 - 1.22028i) q^{36} +0.432675i q^{37} +(0.422753 + 5.31104i) q^{38} +(1.59609 + 2.31525i) q^{39} +(2.47566 - 5.81989i) q^{40} +11.7342 q^{41} +(3.80071 - 3.09235i) q^{42} +7.25937 q^{43} +(3.12246 - 4.31386i) q^{44} +(-6.54833 - 1.45581i) q^{45} +(-4.08963 + 0.325530i) q^{46} +(-2.84866 - 2.84866i) q^{47} +(4.19014 - 5.51749i) q^{48} -2.99866i q^{49} +(2.85838 - 6.46758i) q^{50} +(-11.3839 - 2.09312i) q^{51} +(-3.20624 + 0.513682i) q^{52} -14.2471i q^{53} +(-6.56467 - 3.30228i) q^{54} +(3.55797 - 4.77386i) q^{55} +(1.33550 + 5.49793i) q^{56} +(-1.18000 + 6.41767i) q^{57} +(3.28327 - 0.261345i) q^{58} +(-6.71026 + 6.71026i) q^{59} +(4.77032 - 6.10279i) q^{60} +(2.46306 + 2.46306i) q^{61} +(-3.96132 + 4.64649i) q^{62} +(5.47522 - 2.45643i) q^{63} +(3.67001 + 7.10852i) q^{64} +(-3.59235 + 0.524248i) q^{65} +(5.05916 - 4.11626i) q^{66} -7.75965 q^{67} +(7.83666 - 10.8268i) q^{68} +(-4.94176 - 0.908625i) q^{69} +(1.40723 + 6.16710i) q^{70} -1.94196 q^{71} +(6.70320 - 5.20261i) q^{72} +(-10.6976 + 10.6976i) q^{73} +(-0.465642 - 0.396979i) q^{74} +(5.42806 - 6.74805i) q^{75} +(-6.10359 - 4.41791i) q^{76} +5.32622i q^{77} +(-3.95608 - 0.406541i) q^{78} +1.94859i q^{79} +(3.99191 + 8.00404i) q^{80} +(-6.72249 - 5.98398i) q^{81} +(-10.7661 + 12.6283i) q^{82} -9.36248 q^{83} +(-0.159173 + 6.92754i) q^{84} +(8.92967 - 11.9813i) q^{85} +(-6.66047 + 7.81250i) q^{86} +(3.96738 + 0.729470i) q^{87} +(1.77769 + 7.31834i) q^{88} -0.0668446i q^{89} +(7.57482 - 5.71157i) q^{90} +(2.29646 - 2.29646i) q^{91} +(3.40190 - 4.69992i) q^{92} +(-6.15691 + 4.24444i) q^{93} +(5.67936 - 0.452071i) q^{94} +(-6.75445 - 5.03410i) q^{95} +(2.09345 + 9.57170i) q^{96} +(0.253450 - 0.253450i) q^{97} +(3.22714 + 2.75126i) q^{98} +(7.28811 - 3.26978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) $ 88 * q - 4 * q^4 - 4 * q^6	$ 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) $ 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.917499	+	1.07619i	−0.648770	+	0.760985i
$2$	−0.917499	+	1.07619i	−0.648770	+	0.760985i
$3$	−1.42603	+	0.983076i	−0.823319	+	0.567579i
$3$	−1.42603	+	0.983076i	−0.823319	+	0.567579i
$4$	−0.316391	−	1.97482i	−0.158196	−	0.987408i
$5$	−0.322899	−	2.21263i	−0.144405	−	0.989519i
$5$	−0.322899	−	2.21263i	−0.144405	−	0.989519i
$6$	0.250400	−	2.43666i	0.102225	−	0.994761i
$7$	1.41445	+	1.41445i	0.534612	+	0.534612i	0.921941	−	0.387329i	$-0.126602\pi$
$7$	1.41445	+	1.41445i	0.534612	+	0.534612i	−0.387329	+	0.921941i	$0.626602\pi$
$8$	2.41558	+	1.47139i	0.854035	+	0.520216i
$9$	1.06712	−	2.80379i	0.355708	−	0.934597i
$10$	2.67748	+	1.68258i	0.846694	+	0.532080i
$11$	1.88279	+	1.88279i	0.567682	+	0.567682i	0.931478	−	0.363797i	$-0.118520\pi$
$11$	1.88279	+	1.88279i	0.567682	+	0.567682i	−0.363797	+	0.931478i	$0.618520\pi$
$12$	2.39258	+	2.50511i	0.690677	+	0.723163i
$13$		−	1.62357i		−	0.450296i	−0.974325	−	0.225148i	$-0.927713\pi$
$13$		−	1.62357i		−	0.450296i	0.974325	−	0.225148i	$-0.0722866\pi$
$14$	−2.81998	+	0.224468i	−0.753672	+	0.0599915i
$15$	2.63565	+	2.83784i	0.680521	+	0.732728i
$16$	−3.79979	+	1.24963i	−0.949948	+	0.312407i
$17$	4.72536	+	4.72536i	1.14607	+	1.14607i	0.987319	+	0.158750i	$0.0507463\pi$
$17$	4.72536	+	4.72536i	1.14607	+	1.14607i	0.158750	+	0.987319i	$0.449254\pi$
$18$	2.03834	+	3.72091i	0.480442	+	0.877027i
$19$	2.66392	−	2.66392i	0.611146	−	0.611146i	−0.332099	−	0.943245i	$-0.607757\pi$
$19$	2.66392	−	2.66392i	0.611146	−	0.611146i	0.943245	+	0.332099i	$0.107757\pi$
$20$	−4.26738	+	1.33772i	−0.954214	+	0.299124i
$21$	−3.40756	−	0.626537i	−0.743591	−	0.136722i
$22$	−3.75370	+	0.298791i	−0.800292	+	0.0637024i
$23$	2.05128	+	2.05128i	0.427722	+	0.427722i	0.887852	−	0.460130i	$-0.152197\pi$
$23$	2.05128	+	2.05128i	0.427722	+	0.427722i	−0.460130	+	0.887852i	$0.652197\pi$
$24$	−4.89117	+	0.276443i	−0.998407	+	0.0564287i
$25$	−4.79147	+	1.42891i	−0.958295	+	0.285782i
$26$	1.74727	+	1.48962i	0.342669	+	0.292139i
$27$	1.23459	+	5.04735i	0.237597	+	0.971364i
$28$	2.34576	−	3.24080i	0.443307	−	0.612454i
$29$	−1.64683	−	1.64683i	−0.305808	−	0.305808i	0.537473	−	0.843281i	$-0.319379\pi$
$29$	−1.64683	−	1.64683i	−0.305808	−	0.305808i	−0.843281	+	0.537473i	$0.819379\pi$
$30$	−5.47228	+	0.232751i	−0.999097	+	0.0424943i
$31$	4.31752			0.775449			0.387724	−	0.921775i	$-0.373261\pi$
$31$	4.31752			0.775449			0.387724	+	0.921775i	$0.373261\pi$
$32$	2.14146	−	5.23585i	0.378561	−	0.925576i
$33$	−4.53584	−	0.833989i	−0.789588	−	0.145179i
$34$	−9.42092	+	0.749896i	−1.61568	+	0.128606i
$35$	2.67293	−	3.58638i	0.451808	−	0.606209i
$36$	−5.87460	−	1.22028i	−0.979100	−	0.203380i
$37$			0.432675i			0.0711313i	0.999367	+	0.0355656i	$0.0113233\pi$
$37$			0.432675i			0.0711313i	−0.999367	+	0.0355656i	$0.988677\pi$
$38$	0.422753	+	5.31104i	0.0685797	+	0.861565i
$39$	1.59609	+	2.31525i	0.255579	+	0.370737i
$40$	2.47566	−	5.81989i	0.391437	−	0.920205i
$41$	11.7342			1.83257			0.916286	−	0.400524i	$-0.131172\pi$
$41$	11.7342			1.83257			0.916286	+	0.400524i	$0.131172\pi$
$42$	3.80071	−	3.09235i	0.586462	−	0.477161i
$43$	7.25937			1.10704			0.553522	−	0.832835i	$-0.313283\pi$
$43$	7.25937			1.10704			0.553522	+	0.832835i	$0.313283\pi$
$44$	3.12246	−	4.31386i	0.470729	−	0.650338i
$45$	−6.54833	−	1.45581i	−0.976167	−	0.217019i
$46$	−4.08963	+	0.325530i	−0.602983	+	0.0479968i
$47$	−2.84866	−	2.84866i	−0.415520	−	0.415520i	0.468136	−	0.883656i	$-0.344926\pi$
$47$	−2.84866	−	2.84866i	−0.415520	−	0.415520i	−0.883656	+	0.468136i	$0.844926\pi$
$48$	4.19014	−	5.51749i	0.604795	−	0.796381i
$49$		−	2.99866i		−	0.428379i
$50$	2.85838	−	6.46758i	0.404237	−	0.914654i
$51$	−11.3839	−	2.09312i	−1.59406	−	0.293095i
$52$	−3.20624	+	0.513682i	−0.444626	+	0.0712349i
$53$		−	14.2471i		−	1.95700i	−0.206258	−	0.978498i	$-0.566129\pi$
$53$		−	14.2471i		−	1.95700i	0.206258	−	0.978498i	$-0.433871\pi$
$54$	−6.56467	−	3.30228i	−0.893339	−	0.449384i
$55$	3.55797	−	4.77386i	0.479756	−	0.643708i
$56$	1.33550	+	5.49793i	0.178464	+	0.734691i
$57$	−1.18000	+	6.41767i	−0.156294	+	0.850041i
$58$	3.28327	−	0.261345i	0.431115	−	0.0343163i
$59$	−6.71026	+	6.71026i	−0.873602	+	0.873602i	−0.992863	−	0.119261i	$-0.961947\pi$
$59$	−6.71026	+	6.71026i	−0.873602	+	0.873602i	0.119261	+	0.992863i	$0.461947\pi$
$60$	4.77032	−	6.10279i	0.615846	−	0.787866i
$61$	2.46306	+	2.46306i	0.315362	+	0.315362i	0.846983	−	0.531620i	$-0.178417\pi$
$61$	2.46306	+	2.46306i	0.315362	+	0.315362i	−0.531620	+	0.846983i	$0.678417\pi$
$62$	−3.96132	+	4.64649i	−0.503088	+	0.590105i
$63$	5.47522	−	2.45643i	0.689813	−	0.309481i
$64$	3.67001	+	7.10852i	0.458751	+	0.888565i
$65$	−3.59235	+	0.524248i	−0.445577	+	0.0650249i
$66$	5.05916	−	4.11626i	0.622739	−	0.506676i
$67$	−7.75965			−0.947992			−0.473996	−	0.880527i	$-0.657189\pi$
$67$	−7.75965			−0.947992			−0.473996	+	0.880527i	$0.657189\pi$
$68$	7.83666	−	10.8268i	0.950334	−	1.31294i
$69$	−4.94176	−	0.908625i	−0.594918	−	0.109386i
$70$	1.40723	+	6.16710i	0.168196	+	0.737110i
$71$	−1.94196			−0.230468			−0.115234	−	0.993338i	$-0.536762\pi$
$71$	−1.94196			−0.230468			−0.115234	+	0.993338i	$0.536762\pi$
$72$	6.70320	−	5.20261i	0.789979	−	0.613134i
$73$	−10.6976	+	10.6976i	−1.25206	+	1.25206i	−0.297259	+	0.954797i	$0.596072\pi$
$73$	−10.6976	+	10.6976i	−1.25206	+	1.25206i	−0.954797	+	0.297259i	$0.903928\pi$
$74$	−0.465642	−	0.396979i	−0.0541298	−	0.0461478i
$75$	5.42806	−	6.74805i	0.626778	−	0.779198i
$76$	−6.10359	−	4.41791i	−0.700130	−	0.506769i
$77$			5.32622i			0.606979i
$78$	−3.95608	−	0.406541i	−0.447937	−	0.0460317i
$79$			1.94859i			0.219234i	0.993974	+	0.109617i	$0.0349624\pi$
$79$			1.94859i			0.219234i	−0.993974	+	0.109617i	$0.965038\pi$
$80$	3.99191	+	8.00404i	0.446310	+	0.894879i
$81$	−6.72249	−	5.98398i	−0.746944	−	0.664887i
$82$	−10.7661	+	12.6283i	−1.18892	+	1.39456i
$83$	−9.36248			−1.02767			−0.513833	−	0.857890i	$-0.671775\pi$
$83$	−9.36248			−1.02767			−0.513833	+	0.857890i	$0.671775\pi$
$84$	−0.159173	+	6.92754i	−0.0173672	+	0.755856i
$85$	8.92967	−	11.9813i	0.968559	−	1.29955i
$86$	−6.66047	+	7.81250i	−0.718217	+	0.842444i
$87$	3.96738	+	0.729470i	0.425348	+	0.0782074i
$88$	1.77769	+	7.31834i	0.189503	+	0.780137i
$89$		−	0.0668446i		−	0.00708551i	−0.999994	−	0.00354276i	$-0.998872\pi$
$89$		−	0.0668446i		−	0.00708551i	0.999994	−	0.00354276i	$-0.00112770\pi$
$90$	7.57482	−	5.71157i	0.798456	−	0.602053i
$91$	2.29646	−	2.29646i	0.240734	−	0.240734i
$92$	3.40190	−	4.69992i	0.354673	−	0.490000i
$93$	−6.15691	+	4.24444i	−0.638441	+	0.440128i
$94$	5.67936	−	0.452071i	0.585781	−	0.0466276i
$95$	−6.75445	−	5.03410i	−0.692992	−	0.516488i
$96$	2.09345	+	9.57170i	0.213662	+	0.976908i
$97$	0.253450	−	0.253450i	0.0257340	−	0.0257340i	−0.694123	−	0.719857i	$-0.744208\pi$
$97$	0.253450	−	0.253450i	0.0257340	−	0.0257340i	0.719857	+	0.694123i	$0.244208\pi$
$98$	3.22714	+	2.75126i	0.325990	+	0.277920i
$99$	7.28811	−	3.26978i	0.732483	−	0.328625i
$100$	4.33782	+	9.01018i	0.433782	+	0.901018i
$101$	3.15639	+	3.15639i	0.314073	+	0.314073i	0.846485	−	0.532412i	$-0.178714\pi$
$101$	3.15639	+	3.15639i	0.314073	+	0.314073i	−0.532412	+	0.846485i	$0.678714\pi$
$102$	12.6973	−	10.3309i	1.25722	−	1.02291i
$103$	−10.5085	+	10.5085i	−1.03543	+	1.03543i	−0.0360836	+	0.999349i	$0.511488\pi$
$103$	−10.5085	+	10.5085i	−1.03543	+	1.03543i	−0.999349	+	0.0360836i	$0.988512\pi$
$104$	2.38890	−	3.92185i	0.234251	−	0.384569i
$105$	−0.285998	+	7.74199i	−0.0279105	+	0.755541i
$106$	15.3327	+	13.0717i	1.48924	+	1.26964i
$107$	−5.96559			−0.576715			−0.288358	−	0.957523i	$-0.593109\pi$
$107$	−5.96559			−0.576715			−0.288358	+	0.957523i	$0.593109\pi$
$108$	9.57698	−	4.03502i	0.921546	−	0.388270i
$109$	11.0573	−	11.0573i	1.05909	−	1.05909i	0.0609528	−	0.998141i	$-0.480586\pi$
$109$	11.0573	−	11.0573i	1.05909	−	1.05909i	0.998141	−	0.0609528i	$-0.0194139\pi$
$110$	1.87318	+	8.20908i	0.178601	+	0.782705i
$111$	−0.425352	−	0.617007i	−0.0403726	−	0.0585637i
$112$	−7.14216	−	3.60708i	−0.674871	−	0.340837i
$113$	1.60678	−	1.60678i	0.151153	−	0.151153i	−0.627480	−	0.778633i	$-0.715913\pi$
$113$	1.60678	−	1.60678i	0.151153	−	0.151153i	0.778633	+	0.627480i	$0.215913\pi$
$114$	−5.82402	−	7.15811i	−0.545469	−	0.670418i
$115$	3.87638	−	5.20109i	0.361474	−	0.485004i
$116$	−2.73114	+	3.77323i	−0.253580	+	0.350335i
$117$	−4.55214	−	1.73255i	−0.420846	−	0.160174i
$118$	−1.06489	−	13.3782i	−0.0980312	−	1.23156i
$119$			13.3676i			1.22540i
$120$	2.19102	+	10.7331i	0.200012	+	0.979793i
$121$		−	3.91022i		−	0.355474i
$122$	−4.91059	+	0.390877i	−0.444584	+	0.0353884i
$123$	−16.7333	+	11.5356i	−1.50879	+	1.04013i
$124$	−1.36602	−	8.52630i	−0.122673	−	0.765684i
$125$	4.70881	+	10.1404i	0.421169	+	0.906982i
$126$	−2.37991	+	8.14618i	−0.212019	+	0.725719i
$127$	12.6245	−	12.6245i	1.12024	−	1.12024i	0.128540	−	0.991704i	$-0.458971\pi$
$127$	12.6245	−	12.6245i	1.12024	−	1.12024i	0.991704	−	0.128540i	$-0.0410291\pi$
$128$	−11.0174	−	2.57242i	−0.973808	−	0.227372i
$129$	−10.3521	+	7.13651i	−0.911450	+	0.628335i
$130$	2.73179	−	4.34707i	0.239594	−	0.381263i
$131$	−12.2658	+	12.2658i	−1.07167	+	1.07167i	−0.0744403	+	0.997225i	$0.523717\pi$
$131$	−12.2658	+	12.2658i	−1.07167	+	1.07167i	−0.997225	+	0.0744403i	$0.976283\pi$
$132$	−0.211876	+	9.22131i	−0.0184415	+	0.802612i
$133$	7.53597			0.653452
$134$	7.11947	−	8.35089i	0.615029	−	0.721407i
$135$	10.7693	−	4.36148i	0.926873	−	0.375376i
$136$	4.46160	+	18.3673i	0.382579	+	1.57499i
$137$	−6.60357	+	6.60357i	−0.564181	+	0.564181i	−0.930492	−	0.366311i	$-0.880621\pi$
$137$	−6.60357	+	6.60357i	−0.564181	+	0.564181i	0.366311	+	0.930492i	$0.380621\pi$
$138$	5.51192	−	4.48464i	0.469206	−	0.381757i
$139$	−2.41837	−	2.41837i	−0.205123	−	0.205123i	0.597068	−	0.802191i	$-0.296332\pi$
$139$	−2.41837	−	2.41837i	−0.205123	−	0.205123i	−0.802191	+	0.597068i	$0.796332\pi$
$140$	−7.92814	−	4.14385i	−0.670050	−	0.350219i
$141$	6.86273	+	1.26183i	0.577946	+	0.106265i
$142$	1.78174	−	2.08992i	0.149521	−	0.175383i
$143$	3.05683	−	3.05683i	0.255625	−	0.255625i
$144$	−0.551153	+	11.9873i	−0.0459294	+	0.998945i
$145$	−3.11207	+	4.17558i	−0.258443	+	0.346763i
$146$	−1.69766	−	21.3277i	−0.140499	−	1.76509i
$147$	2.94791	+	4.27617i	0.243139	+	0.352693i
$148$	0.854453	−	0.136894i	0.0702356	−	0.0112527i
$149$	−0.363374	+	0.363374i	−0.0297687	+	0.0297687i	−0.721834	−	0.692066i	$-0.756701\pi$
$149$	−0.363374	+	0.363374i	−0.0297687	+	0.0297687i	0.692066	+	0.721834i	$0.256701\pi$
$150$	2.28198	+	12.0330i	0.186323	+	0.982489i
$151$		−	1.99308i		−	0.162195i	−0.996706	−	0.0810974i	$-0.974158\pi$
$151$		−	1.99308i		−	0.162195i	0.996706	−	0.0810974i	$-0.0258425\pi$
$152$	10.3546	−	2.51523i	0.839867	−	0.204012i
$153$	18.2915	−	8.20638i	1.47878	−	0.663447i
$154$	−5.73205	−	4.88680i	−0.461902	−	0.393790i
$155$	−1.39412	−	9.55307i	−0.111978	−	0.767321i
$156$	4.06721	−	3.88451i	0.325638	−	0.311009i
$157$	−10.6841			−0.852680			−0.426340	−	0.904563i	$-0.640197\pi$
$157$	−10.6841			−0.852680			−0.426340	+	0.904563i	$0.640197\pi$
$158$	−2.09707	−	1.78783i	−0.166834	−	0.142232i
$159$	14.0060	+	20.3169i	1.11075	+	1.61123i
$160$	−12.2765	−	3.04762i	−0.970541	−	0.240935i
$161$			5.80288i			0.457331i
$162$	12.6078	−	1.74441i	0.990564	−	0.137054i
$163$			20.2762i			1.58815i	0.607818	+	0.794076i	$0.292045\pi$
$163$			20.2762i			1.58815i	−0.607818	+	0.794076i	$0.707955\pi$
$164$	−3.71259	−	23.1729i	−0.289905	−	1.80950i
$165$	−0.380694	+	10.3054i	−0.0296370	+	0.802276i
$166$	8.59007	−	10.0759i	0.666718	−	0.782038i
$167$	11.4257	−	11.4257i	0.884144	−	0.884144i	−0.109809	−	0.993953i	$-0.535024\pi$
$167$	11.4257	−	11.4257i	0.884144	−	0.884144i	0.993953	+	0.109809i	$0.0350238\pi$
$168$	−7.30934	−	6.52731i	−0.563928	−	0.503593i
$169$	10.3640			0.797233
$170$	4.70125	+	20.6029i	0.360569	+	1.58017i
$171$	−4.62635	−	10.3118i	−0.353786	−	0.788564i
$172$	−2.29680	−	14.3359i	−0.175129	−	1.09310i
$173$	−13.4579			−1.02318			−0.511592	−	0.859228i	$-0.670944\pi$
$173$	−13.4579			−1.02318			−0.511592	+	0.859228i	$0.670944\pi$
$174$	−4.42512	+	3.60039i	−0.335468	+	0.272945i
$175$	−8.79843	−	4.75618i	−0.665099	−	0.359533i
$176$	−9.50699	−	4.80142i	−0.716616	−	0.361921i
$177$	2.97234	−	16.1657i	0.223415	−	1.21509i
$178$	0.0719378	+	0.0613299i	0.00539197	+	0.00459687i
$179$	1.91445	+	1.91445i	0.143093	+	0.143093i	0.775024	−	0.631931i	$-0.217738\pi$
$179$	1.91445	+	1.91445i	0.143093	+	0.143093i	−0.631931	+	0.775024i	$0.717738\pi$
$180$	−0.803124	+	13.3923i	−0.0598613	+	0.998207i
$181$	−5.05100	+	5.05100i	−0.375438	+	0.375438i	−0.869453	−	0.494015i	$-0.835529\pi$
$181$	−5.05100	+	5.05100i	−0.375438	+	0.375438i	0.494015	+	0.869453i	$0.335529\pi$
$182$	0.364438	+	4.57843i	0.0270139	+	0.339376i
$183$	−5.93377	−	1.09102i	−0.438637	−	0.0806507i
$184$	1.93679	+	7.97328i	0.142782	+	0.587798i
$185$	0.957350	−	0.139710i	0.0703857	−	0.0102717i
$186$	1.08111	−	10.5203i	0.0792705	−	0.771386i
$187$			17.7937i			1.30120i
$188$	−4.72429	+	6.52687i	−0.344554	+	0.476021i
$189$	−5.39297	+	8.88550i	−0.392281	+	0.646325i
$190$	11.6149	−	2.65033i	0.842632	−	0.192275i
$191$		−	16.3823i		−	1.18538i	−0.805431	−	0.592690i	$-0.798066\pi$
$191$		−	16.3823i		−	1.18538i	0.805431	−	0.592690i	$-0.201934\pi$
$192$	−12.2218	−	6.52907i	−0.882029	−	0.471195i
$193$	−0.728053	−	0.728053i	−0.0524064	−	0.0524064i	0.680418	−	0.732824i	$-0.261798\pi$
$193$	−0.728053	−	0.728053i	−0.0524064	−	0.0524064i	−0.732824	+	0.680418i	$0.761798\pi$
$194$	0.0402215	+	0.505302i	0.00288773	+	0.0362786i
$195$	4.60743	−	4.27915i	0.329945	−	0.306436i
$196$	−5.92179	+	0.948748i	−0.422985	+	0.0677677i
$197$	12.3151			0.877414			0.438707	−	0.898630i	$-0.355437\pi$
$197$	12.3151			0.877414			0.438707	+	0.898630i	$0.355437\pi$
$198$	−3.16792	+	10.8434i	−0.225134	+	0.770610i
$199$	−17.1531			−1.21595			−0.607975	−	0.793956i	$-0.708018\pi$
$199$	−17.1531			−1.21595			−0.607975	+	0.793956i	$0.708018\pi$
$200$	−13.6767	−	3.59850i	−0.967085	−	0.254452i
$201$	11.0655	−	7.62832i	0.780500	−	0.538060i
$202$	−6.29288	+	0.500907i	−0.442766	+	0.0352437i
$203$		−	4.65872i		−	0.326978i
$204$	−0.531761	+	23.1433i	−0.0372307	+	1.62036i
$205$	−3.78895	−	25.9634i	−0.264632	−	1.81336i
$206$	−1.66765	−	20.9507i	−0.116191	−	1.45971i
$207$	7.94035	−	3.56240i	0.551892	−	0.247604i
$208$	2.02885	+	6.16922i	0.140676	+	0.427758i
$209$	10.0312			0.693873
$210$	−8.06948	−	7.41105i	−0.556847	−	0.511411i
$211$	−4.08378	−	4.08378i	−0.281139	−	0.281139i	0.552424	−	0.833563i	$-0.313703\pi$
$211$	−4.08378	−	4.08378i	−0.281139	−	0.281139i	−0.833563	+	0.552424i	$0.813703\pi$
$212$	−28.1355	+	4.50767i	−1.93235	+	0.309588i
$213$	2.76929	−	1.90909i	0.189749	−	0.130809i
$214$	5.47342	−	6.42014i	0.374155	−	0.438871i
$215$	−2.34404	−	16.0623i	−0.159862	−	1.09544i
$216$	−4.44440	+	14.0088i	−0.302403	+	0.953180i
$217$	6.10691	+	6.10691i	0.414564	+	0.414564i
$218$	1.75474	+	22.0448i	0.118846	+	1.49306i
$219$	4.73853	−	25.7716i	0.320200	−	1.74148i
$220$	−10.5532	−	5.51592i	−0.711497	−	0.371883i
$221$	7.67194	−	7.67194i	0.516070	−	0.516070i
$222$	1.05428	+	0.108342i	0.0707587	+	0.00727142i
$223$	−12.6308	−	12.6308i	−0.845820	−	0.845820i	0.143788	−	0.989608i	$-0.454072\pi$
$223$	−12.6308	−	12.6308i	−0.845820	−	0.845820i	−0.989608	+	0.143788i	$0.954072\pi$
$224$	10.4348	−	4.37686i	0.697208	−	0.292441i
$225$	−1.10672	+	14.9591i	−0.0737816	+	0.997274i
$226$	0.254990	+	3.20343i	0.0169617	+	0.213089i
$227$		−	13.0830i		−	0.868347i	−0.900829	−	0.434174i	$-0.857040\pi$
$227$		−	13.0830i		−	0.868347i	0.900829	−	0.434174i	$-0.142960\pi$
$228$	13.0471	+	0.299780i	0.864062	+	0.0198534i
$229$	15.5485	+	15.5485i	1.02748	+	1.02748i	0.999612	+	0.0278647i	$0.00887077\pi$
$229$	15.5485	+	15.5485i	1.02748	+	1.02748i	0.0278647	+	0.999612i	$0.491129\pi$
$230$	2.04082	+	8.94373i	0.134567	+	0.589732i
$231$	−5.23608	−	7.59535i	−0.344509	−	0.499738i
$232$	−1.55491	−	6.40117i	−0.102085	−	0.420257i
$233$	−7.61200	−	7.61200i	−0.498678	−	0.498678i	0.412348	−	0.911026i	$-0.364709\pi$
$233$	−7.61200	−	7.61200i	−0.498678	−	0.498678i	−0.911026	+	0.412348i	$0.864709\pi$
$234$	6.04114	−	3.30938i	0.394922	−	0.216341i
$235$	−5.38321	+	7.22287i	−0.351162	+	0.471168i
$236$	15.3746	+	11.1285i	1.00080	+	0.724401i
$237$	−1.91561	−	2.77875i	−0.124433	−	0.180499i
$238$	−14.3861	−	12.2647i	−0.932514	−	0.795005i
$239$	−8.26623			−0.534698			−0.267349	−	0.963600i	$-0.586148\pi$
$239$	−8.26623			−0.534698			−0.267349	+	0.963600i	$0.586148\pi$
$240$	−13.5612	−	7.48964i	−0.875370	−	0.483454i
$241$	8.65591			0.557576			0.278788	−	0.960353i	$-0.410067\pi$
$241$	8.65591			0.557576			0.278788	+	0.960353i	$0.410067\pi$
$242$	4.20816	+	3.58762i	0.270511	+	0.230621i
$243$	15.4692	+	1.92462i	0.992349	+	0.123465i
$244$	4.08480	−	5.64338i	0.261502	−	0.361280i
$245$	−6.63492	+	0.968262i	−0.423890	+	0.0618600i
$246$	2.93824	−	28.5922i	0.187335	−	1.82297i
$247$	−4.32505	−	4.32505i	−0.275197	−	0.275197i
$248$	10.4293	+	6.35276i	0.662260	+	0.403401i
$249$	13.3512	−	9.20403i	0.846097	−	0.583282i
$250$	−15.2333	−	4.23617i	−0.963441	−	0.267919i
$251$	12.2110	+	12.2110i	0.770750	+	0.770750i	0.978238	−	0.207487i	$-0.0665285\pi$
$251$	12.2110	+	12.2110i	0.770750	+	0.770750i	−0.207487	+	0.978238i	$0.566529\pi$
$252$	−6.58331	−	10.0354i	−0.414710	−	0.632168i
$253$			7.72427i			0.485620i
$254$	2.00346	+	25.1694i	0.125708	+	1.57927i
$255$	−0.955454	+	25.8642i	−0.0598329	+	1.61968i
$256$	12.8769	−	9.49666i	0.804804	−	0.593541i
$257$	−0.143632	−	0.143632i	−0.00895954	−	0.00895954i	0.702613	−	0.711572i	$-0.252017\pi$
$257$	−0.143632	−	0.143632i	−0.00895954	−	0.00895954i	−0.711572	+	0.702613i	$0.752017\pi$
$258$	1.81775	−	17.6886i	0.113168	−	1.10124i
$259$	−0.611997	+	0.611997i	−0.0380277	+	0.0380277i
$260$	2.17188	+	6.92837i	0.134694	+	0.429679i
$261$	−6.37473	+	2.85999i	−0.394586	+	0.177029i
$262$	−1.94653	−	24.4542i	−0.120257	−	1.51079i
$263$	1.14108	+	1.14108i	0.0703619	+	0.0703619i	0.741412	−	0.671050i	$-0.234156\pi$
$263$	1.14108	+	1.14108i	0.0703619	+	0.0703619i	−0.671050	+	0.741412i	$0.734156\pi$
$264$	−9.72953	−	8.68856i	−0.598811	−	0.534744i
$265$	−31.5237	+	4.60038i	−1.93648	+	0.282599i
$266$	−6.91425	+	8.11018i	−0.423940	+	0.497267i
$267$	0.0657133	+	0.0953224i	0.00402159	+	0.00583364i
$268$	2.45508	+	15.3239i	0.149968	+	0.936055i
$269$	5.00762	+	5.00762i	0.305320	+	0.305320i	0.843091	−	0.537771i	$-0.180733\pi$
$269$	5.00762	+	5.00762i	0.305320	+	0.305320i	−0.537771	+	0.843091i	$0.680733\pi$
$270$	−5.18701	+	15.5915i	−0.315672	+	0.948869i
$271$	−30.2387			−1.83687			−0.918435	−	0.395571i	$-0.870547\pi$
$271$	−30.2387			−1.83687			−0.918435	+	0.395571i	$0.870547\pi$
$272$	−23.8603	−	12.0505i	−1.44675	−	0.730666i
$273$	−1.01722	+	5.53240i	−0.0615652	+	0.334836i
$274$	−1.04796	−	13.1655i	−0.0633096	−	0.795357i
$275$	−11.7117	−	6.33099i	−0.706240	−	0.381773i
$276$	−0.230838	+	10.0465i	−0.0138948	+	0.604731i
$277$			10.1541i			0.610104i	0.952336	+	0.305052i	$0.0986738\pi$
$277$			10.1541i			0.610104i	−0.952336	+	0.305052i	$0.901326\pi$
$278$	4.82148	−	0.383785i	0.289173	−	0.0230179i
$279$	4.60732	−	12.1054i	0.275833	−	0.724732i
$280$	11.7337	−	4.73024i	0.701220	−	0.282686i
$281$	6.16277			0.367640			0.183820	−	0.982960i	$-0.441154\pi$
$281$	6.16277			0.367640			0.183820	+	0.982960i	$0.441154\pi$
$282$	−7.65452	+	6.22791i	−0.455820	+	0.370867i
$283$	17.7500			1.05513			0.527564	−	0.849515i	$-0.323105\pi$
$283$	17.7500			1.05513			0.527564	+	0.849515i	$0.323105\pi$
$284$	0.614418	+	3.83501i	0.0364590	+	0.227566i
$285$	14.5810	+	0.538637i	0.863701	+	0.0319061i
$286$	0.485107	+	6.09439i	0.0286850	+	0.360369i
$287$	16.5974	+	16.5974i	0.979716	+	0.979716i
$288$	−12.3950	−	11.5915i	−0.730384	−	0.683037i
$289$			27.6581i			1.62695i
$290$	−1.63842	−	7.18028i	−0.0962116	−	0.421641i
$291$	−0.112267	+	0.610588i	−0.00658120	+	0.0357933i
$292$	24.5103	+	17.7411i	1.43436	+	1.03822i
$293$			19.4435i			1.13590i	0.823063	+	0.567951i	$0.192264\pi$
$293$			19.4435i			1.13590i	−0.823063	+	0.567951i	$0.807736\pi$
$294$	−7.30670	−	0.750863i	−0.426135	−	0.0437912i
$295$	17.0141	+	12.6806i	0.990597	+	0.738293i
$296$	−0.636635	+	1.04516i	−0.0370036	+	0.0607486i
$297$	−7.17863	+	11.8276i	−0.416546	+	0.686305i
$298$	−0.0576659	−	0.724456i	−0.00334050	−	0.0419666i
$299$	3.33040	−	3.33040i	0.192602	−	0.192602i
$300$	−15.0435	−	8.58439i	−0.868540	−	0.495620i
$301$	10.2680	+	10.2680i	0.591839	+	0.591839i
$302$	2.14495	+	1.82865i	0.123428	+	0.105227i
$303$	−7.60409	−	1.39814i	−0.436843	−	0.0803209i
$304$	−6.79344	+	13.4513i	−0.389631	+	0.771483i
$305$	4.65452	−	6.24516i	0.266517	−	0.357597i
$306$	−7.95074	+	27.2145i	−0.454514	+	1.55575i
$307$	−10.7063			−0.611040			−0.305520	−	0.952186i	$-0.598830\pi$
$307$	−10.7063			−0.611040			−0.305520	+	0.952186i	$0.598830\pi$
$308$	10.5183	−	1.68517i	0.599336	−	0.0960214i
$309$	4.65478	−	25.3161i	0.264801	−	1.44018i
$310$	11.5601	+	7.26459i	0.656568	+	0.412601i
$311$	−25.8823			−1.46765			−0.733827	−	0.679337i	$-0.762268\pi$
$311$	−25.8823			−1.46765			−0.733827	+	0.679337i	$0.762268\pi$
$312$	0.448823	+	7.94114i	0.0254096	+	0.449579i
$313$	13.5598	−	13.5598i	0.766448	−	0.766448i	−0.211032	−	0.977479i	$-0.567682\pi$
$313$	13.5598	−	13.5598i	0.766448	−	0.766448i	0.977479	+	0.211032i	$0.0676823\pi$
$314$	9.80261	−	11.4981i	0.553193	−	0.648877i
$315$	−7.20312	−	11.3215i	−0.405850	−	0.637892i
$316$	3.84811	−	0.616517i	0.216473	−	0.0346818i
$317$		−	24.7042i		−	1.38753i	−0.720203	−	0.693764i	$-0.755951\pi$
$317$		−	24.7042i		−	1.38753i	0.720203	−	0.693764i	$-0.244049\pi$
$318$	−34.7154	−	3.56748i	−1.94674	−	0.200055i
$319$		−	6.20126i		−	0.347204i
$320$	14.5435	−	10.4157i	0.813006	−	0.582255i
$321$	8.50711	−	5.86463i	0.474820	−	0.327331i
$322$	−6.24503	−	5.32414i	−0.348022	−	0.296703i
$323$	25.1760			1.40083
$324$	−9.69033	+	15.1690i	−0.538352	+	0.842720i
$325$	2.31993	+	7.77927i	0.128687	+	0.431516i
$326$	−21.8211	−	18.6034i	−1.20856	−	1.03035i
$327$	−4.89786	+	26.6381i	−0.270852	+	1.47309i
$328$	28.3448	+	17.2656i	1.56508	+	0.953333i
$329$		−	8.05859i		−	0.444284i
$330$	−10.7414	−	9.86492i	−0.591292	−	0.543046i
$331$	14.7213	−	14.7213i	0.809154	−	0.809154i	−0.175352	−	0.984506i	$-0.556106\pi$
$331$	14.7213	−	14.7213i	0.809154	−	0.809154i	0.984506	+	0.175352i	$0.0561062\pi$
$332$	2.96220	+	18.4892i	0.162572	+	1.01473i
$333$	1.21313	+	0.461717i	0.0664791	+	0.0253020i
$334$	1.81321	+	22.7793i	0.0992142	+	1.24643i
$335$	2.50558	+	17.1692i	0.136895	+	0.938056i
$336$	13.7310	−	1.87747i	0.749086	−	0.102425i
$337$	−6.76440	+	6.76440i	−0.368480	+	0.368480i	−0.866923	−	0.498443i	$-0.833905\pi$
$337$	−6.76440	+	6.76440i	−0.368480	+	0.368480i	0.498443	+	0.866923i	$0.333905\pi$
$338$	−9.50899	+	11.1537i	−0.517221	+	0.606682i
$339$	−0.711731	+	3.87091i	−0.0386559	+	0.210239i
$340$	−26.4861	−	13.8437i	−1.43641	−	0.750779i
$341$	8.12897	+	8.12897i	0.440208	+	0.440208i
$342$	15.3422	+	4.48223i	0.829611	+	0.242371i
$343$	14.1426	−	14.1426i	0.763629	−	0.763629i
$344$	17.5356	+	10.6814i	0.945454	+	0.575902i
$345$	−0.414764	+	11.2277i	−0.0223301	+	0.604478i
$346$	12.3476	−	14.4833i	0.663811	−	0.778627i
$347$	−12.7582			−0.684896			−0.342448	−	0.939537i	$-0.611256\pi$
$347$	−12.7582			−0.684896			−0.342448	+	0.939537i	$0.611256\pi$
$348$	0.185323	−	8.06565i	0.00993436	−	0.432364i
$349$	6.16742	−	6.16742i	0.330134	−	0.330134i	−0.522503	−	0.852637i	$-0.675002\pi$
$349$	6.16742	−	6.16742i	0.330134	−	0.330134i	0.852637	+	0.522503i	$0.175002\pi$
$350$	13.1911	−	5.10504i	0.705095	−	0.272876i
$351$	8.19472	−	2.00444i	0.437402	−	0.106989i
$352$	13.8899	−	5.82608i	0.740335	−	0.310531i
$353$	1.09708	−	1.09708i	0.0583915	−	0.0583915i	−0.677308	−	0.735700i	$-0.736854\pi$
$353$	1.09708	−	1.09708i	0.0583915	−	0.0583915i	0.735700	+	0.677308i	$0.236854\pi$
$354$	14.6704	+	18.0309i	0.779721	+	0.958329i
$355$	0.627056	+	4.29684i	0.0332807	+	0.228052i
$356$	−0.132006	+	0.0211490i	−0.00699629	+	0.00112090i
$357$	−13.1414	−	19.0626i	−0.695514	−	1.00890i
$358$	−3.81683	+	0.303816i	−0.201726	+	0.0160572i
$359$			18.8168i			0.993111i	0.868005	+	0.496556i	$0.165402\pi$
$359$			18.8168i			0.993111i	−0.868005	+	0.496556i	$0.834598\pi$
$360$	−13.6759	−	13.1518i	−0.720784	−	0.693160i
$361$			4.80704i			0.253002i
$362$	−0.801573	−	10.0702i	−0.0421298	−	0.529275i
$363$	3.84404	+	5.57609i	0.201760	+	0.292669i
$364$	−5.26165	−	3.80850i	−0.275786	−	0.199620i
$365$	27.1240	+	20.2155i	1.41974	+	1.05813i
$366$	6.61838	−	5.38488i	0.345948	−	0.281472i
$367$	11.1879	−	11.1879i	0.584005	−	0.584005i	−0.351996	−	0.936001i	$-0.614497\pi$
$367$	11.1879	−	11.1879i	0.584005	−	0.584005i	0.936001	+	0.351996i	$0.114497\pi$
$368$	−10.3578	−	5.23111i	−0.539938	−	0.272691i
$369$	12.5218	−	32.9002i	0.651861	−	1.71272i
$370$	−0.728012	+	1.15848i	−0.0378475	+	0.0602264i
$371$	20.1519	−	20.1519i	1.04623	−	1.04623i
$372$	10.3300	+	10.8159i	0.535585	+	0.560776i
$373$	−32.0831			−1.66120			−0.830599	−	0.556871i	$-0.812002\pi$
$373$	−32.0831			−1.66120			−0.830599	+	0.556871i	$0.812002\pi$
$374$	−19.1495	−	16.3257i	−0.990197	−	0.844182i
$375$	−16.6837	−	9.83135i	−0.861541	−	0.507689i
$376$	−2.68966	−	11.0727i	−0.138708	−	0.571029i
$377$	−2.67374	+	2.67374i	−0.137704	+	0.137704i
$378$	−4.61449	−	13.9563i	−0.237344	−	0.717836i
$379$	−2.25076	−	2.25076i	−0.115614	−	0.115614i	0.646933	−	0.762547i	$-0.276051\pi$
$379$	−2.25076	−	2.25076i	−0.115614	−	0.115614i	−0.762547	+	0.646933i	$0.776051\pi$
$380$	−7.80437	+	14.9315i	−0.400356	+	0.765972i
$381$	−5.59208	+	30.4138i	−0.286491	+	1.55815i
$382$	17.6305	+	15.0307i	0.902056	+	0.769039i
$383$	−1.27686	+	1.27686i	−0.0652443	+	0.0652443i	−0.738976	−	0.673732i	$-0.764690\pi$
$383$	−1.27686	+	1.27686i	−0.0652443	+	0.0652443i	0.673732	+	0.738976i	$0.264690\pi$
$384$	18.2400	−	7.16257i	0.930806	−	0.365514i
$385$	11.7850	−	1.71983i	0.600617	−	0.0876507i
$386$	1.45151	−	0.115539i	0.0738801	−	0.00588078i
$387$	7.74665	−	20.3538i	0.393784	−	1.03464i
$388$	−0.580707	−	0.420328i	−0.0294809	−	0.0213389i
$389$	−18.1320	+	18.1320i	−0.919327	+	0.919327i	−0.996980	−	0.0776537i	$-0.975257\pi$
$389$	−18.1320	+	18.1320i	−0.919327	+	0.919327i	0.0776537	+	0.996980i	$0.475257\pi$
$390$	0.377887	+	8.88461i	0.0191350	+	0.449890i
$391$			19.3861i			0.980398i
$392$	4.41220	−	7.24348i	0.222850	−	0.365851i
$393$	5.43318	−	29.5496i	0.274068	−	1.49058i
$394$	−11.2991	+	13.2534i	−0.569240	+	0.667699i
$395$	4.31152	−	0.629198i	0.216936	−	0.0316584i
$396$	−8.76310	−	13.3581i	−0.440362	−	0.671272i
$397$	−8.35929			−0.419541			−0.209770	−	0.977751i	$-0.567272\pi$
$397$	−8.35929			−0.419541			−0.209770	+	0.977751i	$0.567272\pi$
$398$	15.7379	−	18.4601i	0.788872	−	0.925319i
$399$	−10.7465	+	7.40843i	−0.537999	+	0.370886i
$400$	16.4210	−	11.4171i	0.821050	−	0.570856i
$401$		−	5.19524i		−	0.259438i	−0.991551	−	0.129719i	$-0.958593\pi$
$401$		−	5.19524i		−	0.259438i	0.991551	−	0.129719i	$-0.0414075\pi$
$402$	−1.94302	+	18.9076i	−0.0969088	+	0.943026i
$403$		−	7.00977i		−	0.349182i
$404$	5.23464	−	7.23195i	0.260433	−	0.359803i
$405$	−11.0697	+	16.8066i	−0.550056	+	0.835128i
$406$	5.01369	+	4.27437i	0.248825	+	0.212133i
$407$	−0.814635	+	0.814635i	−0.0403799	+	0.0403799i
$408$	−24.4189	−	21.8063i	−1.20891	−	1.07957i
$409$	−26.3796			−1.30439			−0.652193	−	0.758053i	$-0.726151\pi$
$409$	−26.3796			−1.30439			−0.652193	+	0.758053i	$0.726151\pi$
$410$	31.4181	+	19.7438i	1.55163	+	0.975075i
$411$	2.92508	−	15.9087i	0.144284	−	0.784719i
$412$	24.0771	+	17.4275i	1.18619	+	0.858593i
$413$	−18.9827			−0.934076
$414$	−3.45142	+	11.8139i	−0.169628	+	0.580619i
$415$	3.02313	+	20.7157i	0.148400	+	1.01689i
$416$	−8.50075	−	3.47681i	−0.416784	−	0.170465i
$417$	5.82610	+	1.07123i	0.285305	+	0.0524581i
$418$	−9.20361	+	10.7955i	−0.450164	+	0.528026i
$419$	5.42844	+	5.42844i	0.265196	+	0.265196i	0.827161	−	0.561965i	$-0.189954\pi$
$419$	5.42844	+	5.42844i	0.265196	+	0.265196i	−0.561965	+	0.827161i	$0.689954\pi$
$420$	15.3795	−	1.88470i	0.750442	−	0.0919641i
$421$	1.51850	−	1.51850i	0.0740071	−	0.0740071i	−0.669134	−	0.743141i	$-0.733335\pi$
$421$	1.51850	−	1.51850i	0.0740071	−	0.0740071i	0.743141	+	0.669134i	$0.233335\pi$
$422$	8.14180	−	0.648079i	0.396337	−	0.0315480i
$423$	−11.0269	+	4.94718i	−0.536148	+	0.240540i
$424$	20.9631	−	34.4150i	1.01806	−	1.67134i
$425$	−29.3936	−	15.8893i	−1.42580	−	0.770745i
$426$	−0.486266	+	4.73189i	−0.0235597	+	0.229261i
$427$			6.96775i			0.337193i
$428$	1.88746	+	11.7809i	0.0912338	+	0.569453i
$429$	−1.35404	+	7.36423i	−0.0653735	+	0.355548i
$430$	19.4368	+	12.2145i	0.937328	+	0.589036i
$431$			11.2608i			0.542413i	0.962521	+	0.271206i	$0.0874226\pi$
$431$			11.2608i			0.542413i	−0.962521	+	0.271206i	$0.912577\pi$
$432$	−10.9985	−	17.6361i	−0.529166	−	0.848519i
$433$	−19.1798	−	19.1798i	−0.921723	−	0.921723i	0.0754279	−	0.997151i	$-0.475968\pi$
$433$	−19.1798	−	19.1798i	−0.921723	−	0.921723i	−0.997151	+	0.0754279i	$0.975968\pi$
$434$	−12.1753	+	0.969142i	−0.584434	+	0.0465203i
$435$	0.332984	−	9.01390i	0.0159654	−	0.432184i
$436$	−25.3345	−	18.3376i	−1.21330	−	0.878213i
$437$	10.9289			0.522801
$438$	23.3876	+	28.7450i	1.11750	+	1.37349i
$439$	3.24124			0.154696			0.0773480	−	0.997004i	$-0.475355\pi$
$439$	3.24124			0.154696			0.0773480	+	0.997004i	$0.475355\pi$
$440$	15.6188	−	6.29646i	0.744595	−	0.300172i
$441$	−8.40761	−	3.19994i	−0.400362	−	0.152378i
$442$	1.21751	+	15.2955i	0.0579108	+	0.727533i
$443$			4.98192i			0.236698i	0.992972	+	0.118349i	$0.0377602\pi$
$443$			4.98192i			0.236698i	−0.992972	+	0.118349i	$0.962240\pi$
$444$	−1.08390	+	1.03521i	−0.0514395	+	0.0491288i
$445$	−0.147902	+	0.0215840i	−0.00701125	+	0.00102318i
$446$	25.1819	−	2.00445i	1.19240	−	0.0949136i
$447$	0.160958	−	0.875405i	0.00761305	−	0.0414053i
$448$	−4.86361	+	15.2457i	−0.229784	+	0.720291i
$449$	−11.3136			−0.533920			−0.266960	−	0.963708i	$-0.586019\pi$
$449$	−11.3136			−0.533920			−0.266960	+	0.963708i	$0.586019\pi$
$450$	−15.0835	−	14.9160i	−0.711043	−	0.703148i
$451$	22.0930	+	22.0930i	1.04032	+	1.04032i
$452$	−3.68147	−	2.66473i	−0.173162	−	0.125338i
$453$	1.95935	+	2.84220i	0.0920584	+	0.133538i
$454$	14.0798	+	12.0036i	0.660799	+	0.563357i
$455$	−5.82273	−	4.33969i	−0.272974	−	0.203448i
$456$	−12.2933	+	13.7661i	−0.575686	+	0.644658i
$457$	−5.76979	−	5.76979i	−0.269899	−	0.269899i	0.559160	−	0.829060i	$-0.311124\pi$
$457$	−5.76979	−	5.76979i	−0.269899	−	0.269899i	−0.829060	+	0.559160i	$0.811124\pi$
$458$	−30.9990	+	2.46749i	−1.44849	+	0.115298i
$459$	−18.0167	+	29.6845i	−0.840947	+	1.38555i
$460$	−11.4976	−	6.00955i	−0.536081	−	0.280197i
$461$	10.8815	−	10.8815i	0.506804	−	0.506804i	−0.406740	−	0.913544i	$-0.633334\pi$
$461$	10.8815	−	10.8815i	0.506804	−	0.506804i	0.913544	+	0.406740i	$0.133334\pi$
$462$	12.9782	+	1.33369i	0.603800	+	0.0620487i
$463$	−2.85892	−	2.85892i	−0.132865	−	0.132865i	0.637547	−	0.770412i	$-0.279949\pi$
$463$	−2.85892	−	2.85892i	−0.132865	−	0.132865i	−0.770412	+	0.637547i	$0.779949\pi$
$464$	8.31553	+	4.19969i	0.386039	+	0.194966i
$465$	11.3794	+	12.2524i	0.527709	+	0.568193i
$466$	15.1760	−	1.20799i	0.703014	−	0.0559592i
$467$			6.28883i			0.291012i	0.989357	+	0.145506i	$0.0464811\pi$
$467$			6.28883i			0.291012i	−0.989357	+	0.145506i	$0.953519\pi$
$468$	−1.98120	+	9.53780i	−0.0915811	+	0.440885i
$469$	−10.9756	−	10.9756i	−0.506808	−	0.506808i
$470$	−2.83413	−	12.4204i	−0.130728	−	0.572908i
$471$	15.2358	−	10.5032i	0.702028	−	0.483963i
$472$	−26.0826	+	6.33571i	−1.20055	+	0.291625i
$473$	13.6679	+	13.6679i	0.628449	+	0.628449i
$474$	4.74805	+	0.487927i	0.218085	+	0.0224113i
$475$	−8.95760	+	16.5706i	−0.411003	+	0.760312i
$476$	26.3985	−	4.22938i	1.20997	−	0.193854i
$477$	−39.9460	−	15.2035i	−1.82900	−	0.696119i
$478$	7.58426	−	8.89607i	0.346896	−	0.406897i
$479$	−33.1385			−1.51414			−0.757068	−	0.653336i	$-0.773369\pi$
$479$	−33.1385			−1.51414			−0.757068	+	0.653336i	$0.773369\pi$
$480$	20.5027	−	7.72272i	0.935815	−	0.352492i
$481$	0.702476			0.0320302
$482$	−7.94179	+	9.31545i	−0.361739	+	0.424307i
$483$	−5.70467	−	8.27508i	−0.259572	−	0.376529i
$484$	−7.72196	+	1.23716i	−0.350998	+	0.0562345i
$485$	−0.642630	−	0.478953i	−0.0291803	−	0.0217481i
$486$	−16.2642	+	14.8820i	−0.737761	+	0.675062i
$487$	−30.3731	−	30.3731i	−1.37634	−	1.37634i	−0.850724	−	0.525612i	$-0.823836\pi$
$487$	−30.3731	−	30.3731i	−1.37634	−	1.37634i	−0.525612	−	0.850724i	$-0.676164\pi$
$488$	2.32558	+	9.57383i	0.105274	+	0.433387i
$489$	−19.9330	−	28.9144i	−0.901402	−	1.30756i
$490$	5.04549	−	8.02885i	0.227932	−	0.362706i
$491$	−1.85249	−	1.85249i	−0.0836017	−	0.0836017i	0.664069	−	0.747671i	$-0.268828\pi$
$491$	−1.85249	−	1.85249i	−0.0836017	−	0.0836017i	−0.747671	+	0.664069i	$0.768828\pi$
$492$	28.0749	+	29.3954i	1.26572	+	1.32525i
$493$		−	15.5637i		−	0.700955i
$494$	8.62283	−	0.686368i	0.387960	−	0.0308812i
$495$	−9.58813	−	15.0701i	−0.430955	−	0.677351i
$496$	−16.4057	+	5.39529i	−0.736636	+	0.242256i
$497$	−2.74680	−	2.74680i	−0.123211	−	0.123211i
$498$	−2.34436	+	22.8132i	−0.105053	+	1.02228i
$499$	−17.1309	+	17.1309i	−0.766884	+	0.766884i	−0.977557	−	0.210673i	$-0.932435\pi$
$499$	−17.1309	+	17.1309i	−0.766884	+	0.766884i	0.210673	+	0.977557i	$0.432435\pi$
$500$	18.5355	−	12.5074i	0.828934	−	0.559346i
$501$	−5.06104	+	27.5256i	−0.226111	+	1.22975i
$502$	−24.3450	+	1.93783i	−1.08657	+	0.0864897i
$503$	25.3410	+	25.3410i	1.12990	+	1.12990i	0.990193	+	0.139707i	$0.0446162\pi$
$503$	25.3410	+	25.3410i	1.12990	+	1.12990i	0.139707	+	0.990193i	$0.455384\pi$
$504$	16.8402	+	2.12251i	0.750121	+	0.0945439i
$505$	5.96474	−	8.00313i	0.265427	−	0.356135i
$506$	−8.31282	−	7.08701i	−0.369550	−	0.315056i
$507$	−14.7794	+	10.1886i	−0.656377	+	0.452493i
$508$	−28.9254	−	20.9368i	−1.28336	−	0.928920i
$509$	−17.6883	−	17.6883i	−0.784022	−	0.784022i	0.196485	−	0.980507i	$-0.437047\pi$
$509$	−17.6883	−	17.6883i	−0.784022	−	0.784022i	−0.980507	+	0.196485i	$0.937047\pi$
$510$	−26.9583	−	24.7587i	−1.19373	−	1.09633i
$511$	−30.2624			−1.33873
$512$	−1.59425	+	22.5712i	−0.0704566	+	0.997515i
$513$	16.7346	+	10.1569i	0.738851	+	0.448438i
$514$	0.286359	−	0.0227939i	0.0126308	−	0.00100539i
$515$	26.6446	+	19.8582i	1.17410	+	0.875058i
$516$	17.3686	+	18.1855i	0.764610	+	0.800573i
$517$		−	10.7269i		−	0.471767i
$518$	−0.0971215	−	1.22014i	−0.00426727	−	0.0536097i
$519$	19.1914	−	13.2301i	0.842407	−	0.580738i
$520$	−9.44897	−	4.01940i	−0.414365	−	0.176263i
$521$	−24.9035			−1.09104			−0.545521	−	0.838097i	$-0.683668\pi$
$521$	−24.9035			−1.09104			−0.545521	+	0.838097i	$0.683668\pi$
$522$	2.77090	−	9.48450i	0.121279	−	0.415125i
$523$	31.2522			1.36656			0.683281	−	0.730155i	$-0.260552\pi$
$523$	31.2522			1.36656			0.683281	+	0.730155i	$0.260552\pi$
$524$	28.1034	+	20.3419i	1.22770	+	0.888638i
$525$	17.2225	−	1.86707i	0.751652	−	0.0814856i
$526$	−2.27496	+	0.181084i	−0.0991930	+	0.00789565i
$527$	20.4018	+	20.4018i	0.888717	+	0.888717i
$528$	18.2774	−	2.49912i	0.795422	−	0.108760i
$529$		−	14.5845i		−	0.634107i
$530$	23.9720	−	38.1465i	1.04128	−	1.65698i
$531$	11.6535	+	25.9749i	0.505719	+	1.12721i
$532$	−2.38431	−	14.8822i	−0.103373	−	0.645223i
$533$		−	19.0512i		−	0.825201i
$534$	−0.162877	−	0.0167379i	−0.00704840	−	0.000724319i
$535$	1.92628	+	13.1996i	0.0832804	+	0.570670i
$536$	−18.7440	−	11.4175i	−0.809618	−	0.493161i
$537$	−4.61212	−	0.848015i	−0.199028	−	0.0365945i
$538$	−9.98367	+	0.794689i	−0.430427	+	0.0342615i
$539$	5.64583	−	5.64583i	0.243183	−	0.243183i
$540$	−12.0204	−	19.8874i	−0.517276	−	0.855818i
$541$	4.09787	+	4.09787i	0.176181	+	0.176181i	0.789689	−	0.613508i	$-0.210242\pi$
$541$	4.09787	+	4.09787i	0.176181	+	0.176181i	−0.613508	+	0.789689i	$0.710242\pi$
$542$	27.7440	−	32.5427i	1.19171	−	1.39783i
$543$	2.23736	−	12.1684i	0.0960144	−	0.522196i
$544$	34.8605	−	14.6221i	1.49463	−	0.626917i
$545$	−28.0360	−	20.8953i	−1.20093	−	0.895055i
$546$	−5.02064	−	6.17071i	−0.214864	−	0.264082i
$547$	−0.999021			−0.0427151			−0.0213575	−	0.999772i	$-0.506799\pi$
$547$	−0.999021			−0.0427151			−0.0213575	+	0.999772i	$0.506799\pi$
$548$	15.1302	+	10.9515i	0.646328	+	0.467826i
$549$	9.53429	−	4.27752i	0.406914	−	0.182560i
$550$	17.5588	−	6.79536i	0.748711	−	0.289755i
$551$	−8.77405			−0.373787
$552$	−10.6002	−	9.46612i	−0.451177	−	0.402905i
$553$	−2.75619	+	2.75619i	−0.117205	+	0.117205i
$554$	−10.9278	−	9.31642i	−0.464280	−	0.395817i
$555$	−1.22786	+	1.14038i	−0.0521199	+	0.0484064i
$556$	−4.01068	+	5.54098i	−0.170091	+	0.234990i
$557$			3.30644i			0.140098i	0.997544	+	0.0700491i	$0.0223156\pi$
$557$			3.30644i			0.140098i	−0.997544	+	0.0700491i	$0.977684\pi$
$558$	8.80057	+	16.0651i	0.372558	+	0.680089i
$559$		−	11.7861i		−	0.498498i
$560$	−5.67495	+	16.9677i	−0.239810	+	0.717016i
$561$	−17.4926	−	25.3744i	−0.738537	−	1.07131i
$562$	−5.65434	+	6.63234i	−0.238514	+	0.279768i
$563$	−6.88483			−0.290161			−0.145080	−	0.989420i	$-0.546344\pi$
$563$	−6.88483			−0.290161			−0.145080	+	0.989420i	$0.546344\pi$
$564$	0.320569	−	13.9519i	0.0134984	−	0.587479i
$565$	−4.07405	−	3.03639i	−0.171396	−	0.127742i
$566$	−16.2856	+	19.1025i	−0.684536	+	0.802937i
$567$	−1.04458	−	17.9727i	−0.0438684	−	0.754782i
$568$	−4.69094	−	2.85738i	−0.196828	−	0.119893i
$569$			19.3379i			0.810687i	0.914165	+	0.405343i	$0.132848\pi$
$569$			19.3379i			0.810687i	−0.914165	+	0.405343i	$0.867152\pi$
$570$	−13.9577	+	15.1977i	−0.584623	+	0.636564i
$571$	4.87138	−	4.87138i	0.203861	−	0.203861i	−0.597791	−	0.801652i	$-0.703955\pi$
$571$	4.87138	−	4.87138i	0.203861	−	0.203861i	0.801652	+	0.597791i	$0.203955\pi$
$572$	−7.00383	−	5.06952i	−0.292845	−	0.211967i
$573$	16.1050	+	23.3616i	0.672797	+	0.975946i
$574$	−33.0902	+	2.63395i	−1.38116	+	0.109939i
$575$	−12.7598	−	6.89757i	−0.532119	−	0.287648i
$576$	23.8472	−	2.70426i	0.993632	−	0.112678i
$577$	3.59569	−	3.59569i	0.149691	−	0.149691i	−0.628289	−	0.777980i	$-0.716245\pi$
$577$	3.59569	−	3.59569i	0.149691	−	0.149691i	0.777980	+	0.628289i	$0.216245\pi$
$578$	−29.7655	−	25.3763i	−1.23808	−	1.05551i
$579$	1.75396	+	0.322494i	0.0728919	+	0.0134024i
$580$	9.23064	+	4.82464i	0.383281	+	0.200332i
$581$	−13.2428	−	13.2428i	−0.549403	−	0.549403i
$582$	−0.554107	−	0.681035i	−0.0229685	−	0.0282298i
$583$	26.8243	−	26.8243i	1.11095	−	1.11095i
$584$	−41.5811	+	10.1005i	−1.72064	+	0.417960i
$585$	−2.36360	+	10.6316i	−0.0977230	+	0.439565i
$586$	−20.9250	−	17.8394i	−0.864403	−	0.736938i
$587$	20.8867			0.862087			0.431043	−	0.902331i	$-0.358146\pi$
$587$	20.8867			0.862087			0.431043	+	0.902331i	$0.358146\pi$
$588$	7.51196	−	7.17452i	0.309788	−	0.295872i
$589$	11.5015	−	11.5015i	0.473912	−	0.473912i
$590$	−29.2572	+	6.67602i	−1.20450	+	0.274847i
$591$	−17.5617	+	12.1067i	−0.722391	+	0.498002i
$592$	−0.540682	−	1.64407i	−0.0222219	−	0.0675710i
$593$	16.1559	−	16.1559i	0.663443	−	0.663443i	−0.292747	−	0.956190i	$-0.594569\pi$
$593$	16.1559	−	16.1559i	0.663443	−	0.663443i	0.956190	+	0.292747i	$0.0945693\pi$
$594$	−6.14238	−	18.5774i	−0.252025	−	0.762239i
$595$	29.5775	−	4.31638i	1.21256	−	0.176954i
$596$	0.832564	+	0.602628i	0.0341031	+	0.0246846i
$597$	24.4608	−	16.8628i	1.00111	−	0.690148i
$598$	0.528520	+	6.63979i	0.0216128	+	0.271521i
$599$		−	24.9140i		−	1.01796i	−0.860779	−	0.508978i	$-0.830023\pi$
$599$		−	24.9140i		−	1.01796i	0.860779	−	0.508978i	$-0.169977\pi$
$600$	23.0409	−	8.31362i	0.940641	−	0.339402i
$601$		−	23.1908i		−	0.945971i	−0.881070	−	0.472986i	$-0.843176\pi$
$601$		−	23.1908i		−	0.945971i	0.881070	−	0.472986i	$-0.156824\pi$
$602$	−20.4713	+	1.62949i	−0.834348	+	0.0664132i
$603$	−8.28051	+	21.7564i	−0.337208	+	0.885991i
$604$	−3.93597	+	0.630594i	−0.160152	+	0.0256585i
$605$	−8.65187	+	1.26260i	−0.351749	+	0.0513322i
$606$	8.48141	−	6.90069i	0.344534	−	0.280321i
$607$	−1.89299	+	1.89299i	−0.0768341	+	0.0768341i	−0.744479	−	0.667645i	$-0.767302\pi$
$607$	−1.89299	+	1.89299i	−0.0768341	+	0.0768341i	0.667645	+	0.744479i	$0.267302\pi$
$608$	−8.24321	−	19.6526i	−0.334306	−	0.797018i
$609$	4.57987	+	6.64347i	0.185586	+	0.269207i
$610$	2.45049	+	10.7391i	0.0992174	+	0.434814i
$611$	−4.62499	+	4.62499i	−0.187107	+	0.187107i
$612$	−21.9934	−	33.5259i	−0.889029	−	1.35520i
$613$	−7.33619			−0.296306			−0.148153	−	0.988964i	$-0.547333\pi$
$613$	−7.33619			−0.296306			−0.148153	+	0.988964i	$0.547333\pi$
$614$	9.82301	−	11.5221i	0.396424	−	0.464992i
$615$	30.9272	+	33.2998i	1.24710	+	1.34278i
$616$	−7.83697	+	12.8659i	−0.315760	+	0.518382i
$617$	9.49571	−	9.49571i	0.382283	−	0.382283i	−0.489641	−	0.871924i	$-0.662872\pi$
$617$	9.49571	−	9.49571i	0.382283	−	0.382283i	0.871924	+	0.489641i	$0.162872\pi$
$618$	22.9743	+	28.2369i	0.924161	+	1.13586i
$619$	−9.91632	−	9.91632i	−0.398571	−	0.398571i	0.479158	−	0.877729i	$-0.340942\pi$
$619$	−9.91632	−	9.91632i	−0.398571	−	0.398571i	−0.877729	+	0.479158i	$0.840942\pi$
$620$	−18.4245	+	5.77564i	−0.739944	+	0.231955i
$621$	−7.82106	+	12.8861i	−0.313849	+	0.517099i
$622$	23.7470	−	27.8545i	0.952169	−	1.11686i
$623$	0.0945484	−	0.0945484i	0.00378800	−	0.00378800i
$624$	−8.95801	−	6.80297i	−0.358608	−	0.272337i
$625$	20.9164	−	13.6932i	0.836657	−	0.547727i
$626$	2.15189	+	27.0342i	0.0860069	+	1.08050i
$627$	−14.3048	+	9.86143i	−0.571278	+	0.393828i
$628$	3.38034	+	21.0990i	0.134890	+	0.841943i
$629$	−2.04454	+	2.04454i	−0.0815213	+	0.0815213i
$630$	18.7930	+	2.63547i	0.748729	+	0.105000i
$631$		−	8.08758i		−	0.321962i	−0.986958	−	0.160981i	$-0.948534\pi$
$631$		−	8.08758i		−	0.321962i	0.986958	−	0.160981i	$-0.0514657\pi$
$632$	−2.86715	+	4.70697i	−0.114049	+	0.187233i
$633$	9.83825	+	1.80893i	0.391036	+	0.0718984i
$634$	26.5866	+	22.6661i	1.05589	+	0.900186i
$635$	−32.0098	−	23.8570i	−1.27027	−	0.946734i
$636$	35.6907	−	34.0874i	1.41523	−	1.35165i
$637$	−4.86852			−0.192898
$638$	6.67376	+	5.68965i	0.264217	+	0.225255i
$639$	−2.07231	+	5.44484i	−0.0819793	+	0.215395i
$640$	−2.13432	+	25.2080i	−0.0843662	+	0.996435i
$641$			24.2848i			0.959191i	0.877490	+	0.479596i	$0.159217\pi$
$641$			24.2848i			0.959191i	−0.877490	+	0.479596i	$0.840783\pi$
$642$	−1.49378	+	14.5361i	−0.0589549	+	0.573694i
$643$		−	2.64120i		−	0.104159i	−0.998643	−	0.0520793i	$-0.983415\pi$
$643$		−	2.64120i		−	0.104159i	0.998643	−	0.0520793i	$-0.0165849\pi$
$644$	11.4596	−	1.83598i	0.451572	−	0.0723477i
$645$	19.1332	+	20.6010i	0.753367	+	0.811163i
$646$	−23.0989	+	27.0943i	−0.908816	+	1.06601i
$647$	31.4871	−	31.4871i	1.23788	−	1.23788i	0.277020	−	0.960864i	$-0.410653\pi$
$647$	31.4871	−	31.4871i	1.23788	−	1.23788i	0.960864	−	0.277020i	$-0.0893467\pi$
$648$	−7.43390	−	24.3462i	−0.292031	−	0.956409i
$649$	−25.2680			−0.991856
$650$	−10.5006	−	4.64078i	−0.411866	−	0.182026i
$651$	−14.7122	−	2.70508i	−0.576617	−	0.106021i
$652$	40.0417	−	6.41520i	1.56815	−	0.251239i
$653$	14.7890			0.578737			0.289369	−	0.957218i	$-0.406555\pi$
$653$	14.7890			0.578737			0.289369	+	0.957218i	$0.406555\pi$
$654$	−24.1740	−	29.7115i	−0.945279	−	1.16181i
$655$	31.1002	+	23.1790i	1.21519	+	0.905680i
$656$	−44.5875	+	14.6634i	−1.74085	+	0.572508i
$657$	18.5781	+	41.4094i	0.724802	+	1.61553i
$658$	8.67261	+	7.39375i	0.338094	+	0.288238i
$659$	2.94228	+	2.94228i	0.114615	+	0.114615i	0.762088	−	0.647473i	$-0.224174\pi$
$659$	2.94228	+	2.94228i	0.114615	+	0.114615i	−0.647473	+	0.762088i	$0.724174\pi$
$660$	20.4718	−	2.50874i	0.796862	−	0.0976527i
$661$	−10.3487	+	10.3487i	−0.402516	+	0.402516i	−0.879119	−	0.476603i	$-0.841868\pi$
$661$	−10.3487	+	10.3487i	−0.402516	+	0.402516i	0.476603	+	0.879119i	$0.341868\pi$
$662$	2.33621	+	29.3497i	0.0907992	+	1.14071i
$663$	−3.39832	+	18.4825i	−0.131980	+	0.717801i
$664$	−22.6158	−	13.7759i	−0.877662	−	0.534608i
$665$	−2.43336	−	16.6743i	−0.0943615	−	0.646603i
$666$	−1.60994	+	0.881939i	−0.0623840	+	0.0341744i
$667$		−	6.75623i		−	0.261602i
$668$	−26.1785	−	18.9486i	−1.01288	−	0.733143i
$669$	30.4289	+	5.59486i	1.17645	+	0.216310i
$670$	−20.7763	−	13.0563i	−0.802659	−	0.504408i
$671$			9.27484i			0.358051i
$672$	−10.5776	+	16.4998i	−0.408041	+	0.636493i
$673$	22.2442	+	22.2442i	0.857451	+	0.857451i	0.991037	−	0.133586i	$-0.0426494\pi$
$673$	22.2442	+	22.2442i	0.857451	+	0.857451i	−0.133586	+	0.991037i	$0.542649\pi$
$674$	−1.07348	−	13.4861i	−0.0413490	−	0.519467i
$675$	−13.1277	−	22.4201i	−0.505286	−	0.862952i
$676$	−3.27909	−	20.4671i	−0.126119	−	0.787194i
$677$	4.12740			0.158629			0.0793144	−	0.996850i	$-0.474727\pi$
$677$	4.12740			0.158629			0.0793144	+	0.996850i	$0.474727\pi$
$678$	−3.51284	−	4.31752i	−0.134910	−	0.165813i
$679$	0.716985			0.0275154
$680$	39.1995	−	15.8027i	1.50323	−	0.606005i
$681$	12.8615	+	18.6567i	0.492856	+	0.714926i
$682$	−16.2067	+	1.29003i	−0.620585	+	0.0493979i
$683$		−	18.8780i		−	0.722346i	−0.932499	−	0.361173i	$-0.882376\pi$
$683$		−	18.8780i		−	0.722346i	0.932499	−	0.361173i	$-0.117624\pi$
$684$	−18.9002	+	12.3987i	−0.722667	+	0.474078i
$685$	16.7436	+	12.4790i	0.639738	+	0.476798i
$686$	2.24437	+	28.1960i	0.0856906	+	1.07653i
$687$	−37.4581	−	6.88729i	−1.42911	−	0.262767i
$688$	−27.5841	+	9.07152i	−1.05163	+	0.345848i
$689$	−23.1312			−0.881228
$690$	−11.7026	−	10.7478i	−0.445512	−	0.409160i
$691$	−8.59887	−	8.59887i	−0.327116	−	0.327116i	0.524372	−	0.851489i	$-0.324300\pi$
$691$	−8.59887	−	8.59887i	−0.327116	−	0.327116i	−0.851489	+	0.524372i	$0.824300\pi$
$692$	4.25795	+	26.5768i	0.161863	+	1.01030i
$693$	14.9336	+	5.68374i	0.567281	+	0.215907i
$694$	11.7056	−	13.7303i	0.444340	−	0.521195i
$695$	−4.57006	+	6.13184i	−0.173352	+	0.232594i
$696$	8.51018	+	7.59967i	0.322578	+	0.288065i
$697$	55.4483	+	55.4483i	2.10025	+	2.10025i
$698$	0.978744	+	12.2959i	0.0370460	+	0.465408i
$699$	18.3381	+	3.37177i	0.693611	+	0.127532i
$700$	−6.60883	+	18.8801i	−0.249790	+	0.713600i
$701$	−26.3416	+	26.3416i	−0.994910	+	0.994910i	−0.999987	−	0.00507760i	$-0.998384\pi$
$701$	−26.3416	+	26.3416i	−0.994910	+	0.994910i	0.00507760	+	0.999987i	$0.498384\pi$
$702$	−5.36148	+	10.6582i	−0.202356	+	0.402267i
$703$	1.15261	+	1.15261i	0.0434716	+	0.0434716i
$704$	−6.47399	+	20.2937i	−0.243998	+	0.764847i
$705$	0.575991	−	15.5921i	0.0216931	−	0.587234i
$706$	0.174101	+	2.18723i	0.00655239	+	0.0823176i
$707$			8.92913i			0.335814i
$708$	−32.8648	−	0.755128i	−1.23513	−	0.0283795i
$709$	25.4750	+	25.4750i	0.956734	+	0.956734i	0.999102	−	0.0423679i	$-0.0134902\pi$
$709$	25.4750	+	25.4750i	0.956734	+	0.956734i	−0.0423679	+	0.999102i	$0.513490\pi$
$710$	−5.19956	−	3.26751i	−0.195136	−	0.122627i
$711$	5.46345	+	2.07939i	0.204895	+	0.0779832i
$712$	0.0983547	−	0.161468i	0.00368600	−	0.00605128i
$713$	8.85645	+	8.85645i	0.331677	+	0.331677i
$714$	32.5722	+	3.34724i	1.21898	+	0.125267i
$715$	−7.75069	−	5.77659i	−0.289859	−	0.216032i
$716$	3.17497	−	4.38641i	0.118654	−	0.163928i
$717$	11.7879	−	8.12633i	0.440227	−	0.303483i
$718$	−20.2505	−	17.2644i	−0.755743	−	0.644301i
$719$	33.5054			1.24954			0.624770	−	0.780809i	$-0.285193\pi$
$719$	33.5054			1.24954			0.624770	+	0.780809i	$0.285193\pi$
$720$	26.7015	−	2.65120i	0.995107	−	0.0988043i
$721$	−29.7275			−1.10711
$722$	−5.17332	−	4.41046i	−0.192531	−	0.164140i
$723$	−12.3436	+	8.50942i	−0.459063	+	0.316469i
$724$	11.5729	+	8.37671i	0.430103	+	0.311318i
$725$	10.2439	+	5.53756i	0.380449	+	0.205660i
$726$	−9.52787	−	0.979119i	−0.353612	−	0.0363385i
$727$	18.5082	+	18.5082i	0.686431	+	0.686431i	0.961441	−	0.275010i	$-0.0886813\pi$
$727$	18.5082	+	18.5082i	0.686431	+	0.686431i	−0.275010	+	0.961441i	$0.588681\pi$
$728$	8.92625	−	2.16827i	0.330829	−	0.0803615i
$729$	−23.9516	+	12.4628i	−0.887096	+	0.461586i
$730$	−46.6421	+	10.6430i	−1.72630	+	0.393914i
$731$	34.3032	+	34.3032i	1.26875	+	1.26875i
$732$	−0.277176	+	12.0633i	−0.0102447	+	0.445872i
$733$			32.0871i			1.18516i	0.805510	+	0.592582i	$0.201891\pi$
$733$			32.0871i			1.18516i	−0.805510	+	0.592582i	$0.798109\pi$
$734$	1.77548	+	22.3053i	0.0655341	+	0.823304i
$735$	8.50972	−	7.90340i	0.313886	−	0.291521i
$736$	15.1330	−	6.34747i	0.557809	−	0.233971i
$737$	−14.6098	−	14.6098i	−0.538158	−	0.538158i
$738$	23.9183	+	43.6619i	0.880444	+	1.60721i
$739$	−1.40142	+	1.40142i	−0.0515520	+	0.0515520i	−0.732413	−	0.680861i	$-0.761606\pi$
$739$	−1.40142	+	1.40142i	−0.0515520	+	0.0515520i	0.680861	+	0.732413i	$0.261606\pi$
$740$	−0.578799	−	1.84639i	−0.0212771	−	0.0678745i
$741$	10.4195	+	1.91580i	0.382770	+	0.0703787i
$742$	3.19802	+	40.1767i	0.117403	+	1.47493i
$743$	−37.8661	−	37.8661i	−1.38917	−	1.38917i	−0.827064	−	0.562107i	$-0.809991\pi$
$743$	−37.8661	−	37.8661i	−1.38917	−	1.38917i	−0.562107	−	0.827064i	$-0.690009\pi$
$744$	−21.1177	+	1.19355i	−0.774213	+	0.0437575i
$745$	0.921344	+	0.686679i	0.0337554	+	0.0251580i
$746$	29.4362	−	34.5276i	1.07774	−	1.26415i
$747$	−9.99092	+	26.2504i	−0.365549	+	0.960453i
$748$	35.1393	−	5.62977i	1.28482	−	0.205845i
$749$	−8.43803	−	8.43803i	−0.308319	−	0.308319i
$750$	25.8877	−	8.93462i	0.945285	−	0.326246i
$751$	34.0117			1.24110			0.620552	−	0.784165i	$-0.286909\pi$
$751$	34.0117			1.24110			0.620552	+	0.784165i	$0.286909\pi$
$752$	14.3841	+	7.26456i	0.524534	+	0.264911i
$753$	−29.4176	−	5.40891i	−1.07204	−	0.197112i
$754$	−0.424311	−	5.33061i	−0.0154525	−	0.194129i
$755$	−4.40996	+	0.643564i	−0.160495	+	0.0234217i
$756$	19.2535	+	7.83883i	0.700244	+	0.285095i
$757$		−	35.5017i		−	1.29033i	−0.764042	−	0.645166i	$-0.776788\pi$
$757$		−	35.5017i		−	1.29033i	0.764042	−	0.645166i	$-0.223212\pi$
$758$	4.48733	−	0.357187i	0.162987	−	0.0129736i
$759$	−7.59354	−	11.0150i	−0.275628	−	0.399820i
$760$	−8.90875	−	22.0987i	−0.323154	−	0.801604i
$761$	24.7463			0.897051			0.448526	−	0.893770i	$-0.351949\pi$
$761$	24.7463			0.897051			0.448526	+	0.893770i	$0.351949\pi$
$762$	−27.6004	−	33.9228i	−0.999858	−	1.22889i
$763$	31.2799			1.13241
$764$	−32.3520	+	5.18321i	−1.17045	+	0.187522i
$765$	−24.0640	−	37.8225i	−0.870036	−	1.36747i
$766$	−0.202632	−	2.54566i	−0.00732139	−	0.0919785i
$767$	10.8946	+	10.8946i	0.393380	+	0.393380i
$768$	−9.02685	+	26.2014i	−0.325729	+	0.945463i
$769$			16.1521i			0.582460i	0.956653	+	0.291230i	$0.0940646\pi$
$769$			16.1521i			0.582460i	−0.956653	+	0.291230i	$0.905935\pi$
$770$	−8.96182	+	14.2609i	−0.322962	+	0.513926i
$771$	0.346026	+	0.0636226i	0.0124618	+	0.00229131i
$772$	−1.20742	+	1.66812i	−0.0434560	+	0.0600369i
$773$			14.7157i			0.529288i	0.964346	+	0.264644i	$0.0852545\pi$
$773$			14.7157i			0.529288i	−0.964346	+	0.264644i	$0.914745\pi$
$774$	14.7971	+	27.0115i	0.531870	+	0.970907i
$775$	−20.6873	+	6.16935i	−0.743108	+	0.221610i
$776$	0.985152	−	0.239303i	0.0353649	−	0.00859048i
$777$	0.271087	−	1.47437i	0.00972518	−	0.0528926i
$778$	−2.87747	−	36.1496i	−0.103162	−	1.29603i
$779$	31.2590	−	31.2590i	1.11997	−	1.11997i
$780$	−9.90828	−	7.74494i	−0.354773	−	0.277313i
$781$	−3.65629	−	3.65629i	−0.130832	−	0.130832i
$782$	−20.8632	−	17.7867i	−0.746068	−	0.636053i
$783$	6.27897	−	10.3453i	0.224392	−	0.369710i
$784$	3.74721	+	11.3943i	0.133829	+	0.406938i
$785$	3.44987	+	23.6399i	0.123131	+	0.843743i
$786$	26.8161	+	32.9588i	0.956500	+	1.17560i
$787$	21.5793			0.769220			0.384610	−	0.923079i	$-0.374336\pi$
$787$	21.5793			0.769220			0.384610	+	0.923079i	$0.374336\pi$
$788$	−3.89638	−	24.3200i	−0.138803	−	0.866365i
$789$	−2.74898	−	0.505445i	−0.0978662	−	0.0179943i
$790$	−3.27867	+	5.21732i	−0.116650	+	0.185624i
$791$	4.54543			0.161617
$792$	22.4161	+	2.82528i	0.796522	+	0.100392i
$793$	3.99894	−	3.99894i	0.142007	−	0.142007i
$794$	7.66964	−	8.99623i	0.272185	−	0.319264i
$795$	40.4312	−	37.5504i	1.43395	−	1.33178i
$796$	5.42708	+	33.8742i	0.192358	+	1.20064i
$797$			11.8350i			0.419216i	0.977786	+	0.209608i	$0.0672188\pi$
$797$			11.8350i			0.419216i	−0.977786	+	0.209608i	$0.932781\pi$
$798$	1.88701	−	18.3626i	0.0667993	−	0.650028i
$799$		−	26.9219i		−	0.952429i
$800$	−2.77919	+	28.1474i	−0.0982594	+	0.995161i
$801$	−0.187418	−	0.0713315i	−0.00662210	−	0.00252037i
$802$	5.59109	+	4.76662i	0.197428	+	0.168315i
$803$	−40.2825			−1.42154
$804$	−18.5656	−	19.4388i	−0.654757	−	0.685553i
$805$	12.8396	−	1.87374i	0.452538	−	0.0660408i
$806$	7.54388	+	6.43146i	0.265722	+	0.226538i
$807$	−12.0639	−	2.21815i	−0.424669	−	0.0780825i
$808$	2.98021	+	12.2688i	0.104843	+	0.431615i
$809$		−	10.6342i		−	0.373878i	−0.982371	−	0.186939i	$-0.940143\pi$
$809$		−	10.6342i		−	0.373878i	0.982371	−	0.186939i	$-0.0598567\pi$
$810$	−7.93079	−	27.3332i	−0.278660	−	0.960390i
$811$	−36.5074	+	36.5074i	−1.28195	+	1.28195i	−0.342389	+	0.939558i	$0.611236\pi$
$811$	−36.5074	+	36.5074i	−1.28195	+	1.28195i	−0.939558	+	0.342389i	$0.888764\pi$
$812$	−9.20011	+	1.47398i	−0.322860	+	0.0517264i
$813$	43.1213	−	29.7269i	1.51233	−	1.04257i
$814$	−0.129279	−	1.62413i	−0.00453123	−	0.0569258i
$815$	44.8637	−	6.54715i	1.57151	−	0.229337i
$816$	45.8721	−	6.27222i	1.60584	−	0.219572i
$817$	19.3384	−	19.3384i	0.676565	−	0.676565i
$818$	24.2032	−	28.3896i	0.846247	−	0.992618i
$819$	−3.98818	−	8.88938i	−0.139358	−	0.310620i
$820$	−50.0742	+	15.6971i	−1.74867	+	0.548166i
$821$	−27.1998	−	27.1998i	−0.949281	−	0.949281i	0.0494932	−	0.998774i	$-0.484239\pi$
$821$	−27.1998	−	27.1998i	−0.949281	−	0.949281i	−0.998774	+	0.0494932i	$0.984239\pi$
$822$	14.4371	+	17.7442i	0.503552	+	0.618899i
$823$	−22.0656	+	22.0656i	−0.769157	+	0.769157i	−0.977958	−	0.208801i	$-0.933044\pi$
$823$	−22.0656	+	22.0656i	−0.769157	+	0.769157i	0.208801	+	0.977958i	$0.433044\pi$
$824$	−40.8462	+	9.92193i	−1.42294	+	0.345647i
$825$	22.9250	−	2.48527i	0.798147	−	0.0865261i
$826$	17.4166	−	20.4291i	0.606000	−	0.710818i
$827$	−29.2398			−1.01677			−0.508384	−	0.861130i	$-0.669757\pi$
$827$	−29.2398			−1.01677			−0.508384	+	0.861130i	$0.669757\pi$
$828$	−9.54734	−	14.5536i	−0.331793	−	0.505773i
$829$	−29.1649	+	29.1649i	−1.01294	+	1.01294i	−0.0130228	+	0.999915i	$0.504145\pi$
$829$	−29.1649	+	29.1649i	−1.01294	+	1.01294i	−0.999915	+	0.0130228i	$0.995855\pi$
$830$	−25.0679	−	15.7532i	−0.870118	−	0.546800i
$831$	−9.98230	−	14.4801i	−0.346282	−	0.502310i
$832$	11.5412	−	5.95850i	0.400118	−	0.206574i
$833$	14.1697	−	14.1697i	0.490952	−	0.490952i
$834$	−6.49829	+	5.28717i	−0.225017	+	0.183080i
$835$	−28.9701	−	21.5914i	−1.00255	−	0.747202i
$836$	−3.17378	−	19.8098i	−0.109768	−	0.685135i
$837$	5.33036	+	21.7920i	0.184244	+	0.753243i
$838$	−10.8226	+	0.861471i	−0.373862	+	0.0297590i
$839$			23.9692i			0.827509i	0.910388	+	0.413755i	$0.135783\pi$
$839$			23.9692i			0.827509i	−0.910388	+	0.413755i	$0.864217\pi$
$840$	−12.0824	+	18.2805i	−0.416881	+	0.630738i
$841$		−	23.5759i		−	0.812962i
$842$	0.240980	+	3.02742i	0.00830471	+	0.104332i
$843$	−8.78830	+	6.05847i	−0.302685	+	0.208665i
$844$	−6.77264	+	9.35678i	−0.233124	+	0.322074i
$845$	−3.34653	−	22.9318i	−0.115124	−	0.788877i
$846$	4.79307	−	16.4062i	0.164789	−	0.564055i
$847$	5.53081	−	5.53081i	0.190041	−	0.190041i
$848$	17.8036	+	54.1362i	0.611379	+	1.85904i
$849$	−25.3121	+	17.4496i	−0.868707	+	0.598869i
$850$	44.0686	−	17.0548i	1.51154	−	0.584974i
$851$	−0.887539	+	0.887539i	−0.0304244	+	0.0304244i
$852$	−4.64628	−	4.86482i	−0.159179	−	0.166666i
$853$	−5.63640			−0.192987			−0.0964934	−	0.995334i	$-0.530763\pi$
$853$	−5.63640			−0.192987			−0.0964934	+	0.995334i	$0.530763\pi$
$854$	−7.49866	−	6.39291i	−0.256599	−	0.218761i
$855$	−21.3224	+	13.5661i	−0.729211	+	0.463950i
$856$	−14.4103	−	8.77772i	−0.492535	−	0.300016i
$857$	−13.0493	+	13.0493i	−0.445755	+	0.445755i	−0.893940	−	0.448186i	$-0.852070\pi$
$857$	−13.0493	+	13.0493i	−0.445755	+	0.445755i	0.448186	+	0.893940i	$0.352070\pi$
$858$	−6.68302	−	8.21388i	−0.228155	−	0.280417i
$859$	−16.2754	−	16.2754i	−0.555310	−	0.555310i	0.372659	−	0.927969i	$-0.378446\pi$
$859$	−16.2754	−	16.2754i	−0.555310	−	0.555310i	−0.927969	+	0.372659i	$0.878446\pi$
$860$	−30.9785	+	9.71103i	−1.05636	+	0.331143i
$861$	−39.9850	−	7.35190i	−1.36268	−	0.250552i
$862$	−12.1188	−	10.3318i	−0.412768	−	0.351901i
$863$	15.5543	−	15.5543i	0.529475	−	0.529475i	−0.390941	−	0.920416i	$-0.627850\pi$
$863$	15.5543	−	15.5543i	0.529475	−	0.529475i	0.920416	+	0.390941i	$0.127850\pi$
$864$	29.0710	+	4.34460i	0.989016	+	0.147806i
$865$	4.34553	+	29.7773i	0.147753	+	1.01246i
$866$	38.2387	−	3.04376i	1.29940	−	0.103431i
$867$	−27.1900	−	39.4413i	−0.923421	−	1.33950i
$868$	10.1279	−	13.9922i	0.343762	−	0.474926i
$869$	−3.66879	+	3.66879i	−0.124455	+	0.124455i
$870$	9.39521	+	8.62860i	0.318527	+	0.292537i
$871$			12.5983i			0.426877i
$872$	42.9792	−	10.4401i	1.45546	−	0.353545i
$873$	−0.440159	−	0.981084i	−0.0148971	−	0.0332047i
$874$	−10.0273	+	11.7616i	−0.339178	+	0.397844i
$875$	−7.68267	+	21.0034i	−0.259722	+	0.710046i
$876$	−52.3933	−	1.20383i	−1.77021	−	0.0406738i
$877$	−9.97271			−0.336755			−0.168377	−	0.985723i	$-0.553853\pi$
$877$	−9.97271			−0.336755			−0.168377	+	0.985723i	$0.553853\pi$
$878$	−2.97384	+	3.48821i	−0.100362	+	0.117721i
$879$	−19.1144	−	27.7270i	−0.644714	−	0.935209i
$880$	−7.55398	+	22.5858i	−0.254645	+	0.761368i
$881$			23.4290i			0.789344i	0.918822	+	0.394672i	$0.129142\pi$
$881$			23.4290i			0.789344i	−0.918822	+	0.394672i	$0.870858\pi$
$882$	11.1577	−	6.11229i	0.375700	−	0.205811i
$883$		−	25.8137i		−	0.868702i	−0.900744	−	0.434351i	$-0.856978\pi$
$883$		−	25.8137i		−	0.868702i	0.900744	−	0.434351i	$-0.143022\pi$
$884$	−17.5780	−	12.7233i	−0.591212	−	0.427932i
$885$	−36.7286	−	1.35679i	−1.23462	−	0.0456082i
$886$	−5.36152	−	4.57091i	−0.180124	−	0.153563i
$887$	−35.6374	+	35.6374i	−1.19659	+	1.19659i	−0.221404	+	0.975182i	$0.571064\pi$
$887$	−35.6374	+	35.6374i	−1.19659	+	1.19659i	−0.975182	+	0.221404i	$0.928936\pi$
$888$	−0.119610	−	2.11629i	−0.00401384	−	0.0710179i
$889$	35.7135			1.19779
$890$	0.112472	−	0.178975i	0.00377006	−	0.00599926i
$891$	−1.39046	−	23.9236i	−0.0465820	−	0.801471i
$892$	−20.9472	+	28.9397i	−0.701364	+	0.968974i
$893$	−15.1772			−0.507887
$894$	0.794428	+	0.976406i	0.0265697	+	0.0326559i
$895$	3.61780	−	4.85415i	0.120930	−	0.162256i
$896$	−11.9450	−	19.2221i	−0.399054	−	0.642165i
$897$	−1.47521	+	8.02328i	−0.0492559	+	0.267889i
$898$	10.3802	−	12.1756i	0.346391	−	0.406305i
$899$	−7.11021	−	7.11021i	−0.237139	−	0.237139i
$900$	29.8917	−	2.54736i	0.996388	−	0.0849118i
$901$	67.3229	−	67.3229i	2.24285	−	2.24285i
$902$	−44.0467	+	3.50607i	−1.46659	+	0.116739i
$903$	−24.7368	−	4.54827i	−0.823188	−	0.151357i
$904$	6.24551	−	1.51710i	0.207723	−	0.0504578i
$905$	12.8070	+	9.54504i	0.425718	+	0.317288i
$906$	−4.85646	−	0.499068i	−0.161345	−	0.0165804i
$907$		−	48.3645i		−	1.60592i	−0.596036	−	0.802958i	$-0.703258\pi$
$907$		−	48.3645i		−	1.60592i	0.596036	−	0.802958i	$-0.296742\pi$
$908$	−25.8364	+	4.13933i	−0.857413	+	0.137369i
$909$	12.2181	−	5.48161i	0.405250	−	0.181813i
$910$	10.0127	−	2.28474i	0.331918	−	0.0757383i
$911$		−	39.4428i		−	1.30680i	−0.757014	−	0.653399i	$-0.773342\pi$
$911$		−	39.4428i		−	1.30680i	0.757014	−	0.653399i	$-0.226658\pi$
$912$	−3.53596	−	25.8604i	−0.117087	−	0.856323i
$913$	−17.6276	−	17.6276i	−0.583387	−	0.583387i
$914$	11.5032	−	0.915642i	0.380492	−	0.0302867i
$915$	−0.498023	+	13.4815i	−0.0164641	+	0.445686i
$916$	25.7861	−	35.6249i	0.851996	−	1.17708i
$917$	−34.6987			−1.14585
$918$	−15.4160	−	46.6249i	−0.508803	−	1.53885i
$919$	1.97224			0.0650583			0.0325292	−	0.999471i	$-0.489644\pi$
$919$	1.97224			0.0650583			0.0325292	+	0.999471i	$0.489644\pi$
$920$	17.0165	−	6.85995i	0.561018	−	0.226166i
$921$	15.2675	−	10.5251i	0.503081	−	0.346814i
$922$	1.72686	+	21.6945i	0.0568710	+	0.714469i
$923$			3.15290i			0.103779i
$924$	−13.3428	+	12.7434i	−0.438945	+	0.419227i
$925$	−0.618254	−	2.07315i	−0.0203281	−	0.0681647i
$926$	5.69981	−	0.453699i	0.187307	−	0.0149095i
$927$	18.2498	+	40.6775i	0.599401	+	1.33602i
$928$	−12.1492	+	5.09593i	−0.398816	+	0.167282i
$929$	24.5340			0.804936			0.402468	−	0.915434i	$-0.368153\pi$
$929$	24.5340			0.804936			0.402468	+	0.915434i	$0.368153\pi$
$930$	−23.6266	+	1.00491i	−0.774748	+	0.0329522i
$931$	−7.98819	−	7.98819i	−0.261802	−	0.261802i
$932$	−12.6239	+	17.4407i	−0.413510	+	0.571288i
$933$	36.9090	−	25.4443i	1.20835	−	0.833009i
$934$	−6.76801	−	5.76999i	−0.221456	−	0.188800i
$935$	39.3709	−	5.74557i	1.28757	−	0.187900i
$936$	−8.44678	−	10.8831i	−0.276092	−	0.355725i
$937$	10.0537	+	10.0537i	0.328438	+	0.328438i	0.851992	−	0.523554i	$-0.175394\pi$
$937$	10.0537	+	10.0537i	0.328438	+	0.328438i	−0.523554	+	0.851992i	$0.675394\pi$
$938$	21.8821	−	1.74179i	0.714475	−	0.0568715i
$939$	−6.00639	+	32.6671i	−0.196011	+	1.06605i
$940$	15.9670	+	8.34560i	0.520787	+	0.272203i
$941$	37.0081	−	37.0081i	1.20643	−	1.20643i	0.234256	−	0.972175i	$-0.424735\pi$
$941$	37.0081	−	37.0081i	1.20643	−	1.20643i	0.972175	−	0.234256i	$-0.0752653\pi$
$942$	−2.67529	+	26.0334i	−0.0871655	+	0.848213i
$943$	24.0702	+	24.0702i	0.783832	+	0.783832i
$944$	17.1123	−	33.8829i	0.556957	−	1.10280i
$945$	21.4017	+	9.06354i	0.696198	+	0.294837i
$946$	−27.2495	+	2.16903i	−0.885959	+	0.0705214i
$947$		−	25.2337i		−	0.819984i	−0.912089	−	0.409992i	$-0.865532\pi$
$947$		−	25.2337i		−	0.819984i	0.912089	−	0.409992i	$-0.134468\pi$
$948$	−4.88144	+	4.66216i	−0.158542	+	0.151420i
$949$	17.3682	+	17.3682i	0.563796	+	0.563796i
$950$	−9.61462	−	24.8436i	−0.311940	−	0.806034i
$951$	24.2861	+	35.2290i	0.787532	+	1.14238i
$952$	−19.6690	+	32.2904i	−0.637475	+	1.04654i
$953$	27.3854	+	27.3854i	0.887101	+	0.887101i	0.994244	−	0.107142i	$-0.0341701\pi$
$953$	27.3854	+	27.3854i	0.887101	+	0.887101i	−0.107142	+	0.994244i	$0.534170\pi$
$954$	53.0123	−	29.0405i	1.71634	−	0.940222i
$955$	−36.2479	+	5.28982i	−1.17296	+	0.171174i
$956$	2.61536	+	16.3243i	0.0845868	+	0.527965i
$957$	6.09631	+	8.84318i	0.197066	+	0.285859i
$958$	30.4045	−	35.6635i	0.982326	−	1.15223i
$959$	−18.6809			−0.603237
$960$	−10.5000	+	29.1505i	−0.338887	+	0.940827i
$961$	−12.3591			−0.398679
$962$	−0.644521	+	0.756001i	−0.0207802	+	0.0243745i
$963$	−6.36602	+	16.7263i	−0.205142	+	0.538996i
$964$	−2.73865	−	17.0938i	−0.0882061	−	0.550555i
$965$	−1.37582	+	1.84600i	−0.0442894	+	0.0594248i
$966$	14.1396	+	1.45304i	0.454935	+	0.0467508i
$967$	−4.24153	−	4.24153i	−0.136398	−	0.136398i	0.635611	−	0.772009i	$-0.280748\pi$
$967$	−4.24153	−	4.24153i	−0.136398	−	0.136398i	−0.772009	+	0.635611i	$0.780748\pi$
$968$	5.75347	−	9.44543i	0.184923	−	0.303588i
$969$	−35.9017	+	24.7499i	−1.15333	+	0.795081i
$970$	1.10506	−	0.252157i	0.0354813	−	0.00809626i
$971$	30.3827	+	30.3827i	0.975028	+	0.975028i	0.999696	−	0.0246676i	$-0.00785274\pi$
$971$	30.3827	+	30.3827i	0.975028	+	0.975028i	−0.0246676	+	0.999696i	$0.507853\pi$
$972$	−1.09354	−	31.1577i	−0.0350754	−	0.999385i
$973$		−	6.84132i		−	0.219323i
$974$	60.5547	−	4.82009i	1.94030	−	0.154446i
$975$	−10.9559	−	8.81281i	−0.350870	−	0.282236i
$976$	−12.4370	−	6.28121i	−0.398099	−	0.201057i
$977$	−1.87914	−	1.87914i	−0.0601190	−	0.0601190i	0.676408	−	0.736527i	$-0.263536\pi$
$977$	−1.87914	−	1.87914i	−0.0601190	−	0.0601190i	−0.736527	+	0.676408i	$0.763536\pi$
$978$	49.4061	+	5.07715i	1.57983	+	0.162349i
$979$	0.125854	−	0.125854i	0.00402232	−	0.00402232i
$980$	4.01137	+	12.7964i	0.128138	+	0.408766i
$981$	−19.2028	−	42.8017i	−0.613098	−	1.36655i
$982$	3.69330	−	0.293983i	0.117858	−	0.00938136i
$983$	7.79666	+	7.79666i	0.248675	+	0.248675i	0.820427	−	0.571752i	$-0.193736\pi$
$983$	7.79666	+	7.79666i	0.248675	+	0.248675i	−0.571752	+	0.820427i	$0.693736\pi$
$984$	−57.3940	+	3.24383i	−1.82965	+	0.103410i
$985$	−3.97653	−	27.2488i	−0.126703	−	0.868217i
$986$	16.7496	+	14.2797i	0.533416	+	0.454758i
$987$	7.92220	+	11.4918i	0.252166	+	0.365788i
$988$	−7.17277	+	9.90959i	−0.228196	+	0.315266i
$989$	14.8910	+	14.8910i	0.473507	+	0.473507i
$990$	25.0155	+	3.50810i	0.795044	+	0.111495i
$991$	−0.555822			−0.0176563			−0.00882813	−	0.999961i	$-0.502810\pi$
$991$	−0.555822			−0.0176563			−0.00882813	+	0.999961i	$0.502810\pi$
$992$	9.24580	−	22.6059i	0.293554	−	0.717737i
$993$	−6.52085	+	35.4651i	−0.206933	+	1.12545i
$994$	5.47629	−	0.435907i	0.173697	−	0.0138261i
$995$	5.53871	+	37.9535i	0.175589	+	1.20321i
$996$	−22.4005	−	23.4540i	−0.709785	−	0.743170i
$997$			49.2942i			1.56116i	0.625053	+	0.780582i	$0.285077\pi$
$997$			49.2942i			1.56116i	−0.625053	+	0.780582i	$0.714923\pi$
$998$	−2.71860	−	34.1538i	−0.0860559	−	1.08112i
$999$	−2.18386	+	0.534176i	−0.0690944	+	0.0169006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bb.a.173.12	✓	88
3.2	odd	2	inner	240.2.bb.a.173.33	yes	88
4.3	odd	2		960.2.bb.a.593.36		88
5.2	odd	4		240.2.bf.a.77.11	yes	88
12.11	even	2		960.2.bb.a.593.9		88
15.2	even	4		240.2.bf.a.77.34	yes	88
16.5	even	4		240.2.bf.a.53.34	yes	88
16.11	odd	4		960.2.bf.a.113.13		88
20.7	even	4		960.2.bf.a.17.13		88
48.5	odd	4		240.2.bf.a.53.11	yes	88
48.11	even	4		960.2.bf.a.113.14		88
60.47	odd	4		960.2.bf.a.17.14		88
80.27	even	4		960.2.bb.a.497.9		88
80.37	odd	4	inner	240.2.bb.a.197.33	yes	88
240.107	odd	4		960.2.bb.a.497.36		88
240.197	even	4	inner	240.2.bb.a.197.12	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.12	✓	88	1.1	even	1	trivial
240.2.bb.a.173.33	yes	88	3.2	odd	2	inner
240.2.bb.a.197.12	yes	88	240.197	even	4	inner
240.2.bb.a.197.33	yes	88	80.37	odd	4	inner
240.2.bf.a.53.11	yes	88	48.5	odd	4
240.2.bf.a.53.34	yes	88	16.5	even	4
240.2.bf.a.77.11	yes	88	5.2	odd	4
240.2.bf.a.77.34	yes	88	15.2	even	4
960.2.bb.a.497.9		88	80.27	even	4
960.2.bb.a.497.36		88	240.107	odd	4
960.2.bb.a.593.9		88	12.11	even	2
960.2.bb.a.593.36		88	4.3	odd	2
960.2.bf.a.17.13		88	20.7	even	4
960.2.bf.a.17.14		88	60.47	odd	4
960.2.bf.a.113.13		88	16.11	odd	4
960.2.bf.a.113.14		88	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.917499 + 1.07619i) q^{2} +(-1.42603 + 0.983076i) q^{3} +(-0.316391 - 1.97482i) q^{4} +(-0.322899 - 2.21263i) q^{5} +(0.250400 - 2.43666i) q^{6} +(1.41445 + 1.41445i) q^{7} +(2.41558 + 1.47139i) q^{8} +(1.06712 - 2.80379i) q^{9} +O(q^{10})\)	\(q+(-0.917499 + 1.07619i) q^{2} +(-1.42603 + 0.983076i) q^{3} +(-0.316391 - 1.97482i) q^{4} +(-0.322899 - 2.21263i) q^{5} +(0.250400 - 2.43666i) q^{6} +(1.41445 + 1.41445i) q^{7} +(2.41558 + 1.47139i) q^{8} +(1.06712 - 2.80379i) q^{9} +(2.67748 + 1.68258i) q^{10} +(1.88279 + 1.88279i) q^{11} +(2.39258 + 2.50511i) q^{12} -1.62357i q^{13} +(-2.81998 + 0.224468i) q^{14} +(2.63565 + 2.83784i) q^{15} +(-3.79979 + 1.24963i) q^{16} +(4.72536 + 4.72536i) q^{17} +(2.03834 + 3.72091i) q^{18} +(2.66392 - 2.66392i) q^{19} +(-4.26738 + 1.33772i) q^{20} +(-3.40756 - 0.626537i) q^{21} +(-3.75370 + 0.298791i) q^{22} +(2.05128 + 2.05128i) q^{23} +(-4.89117 + 0.276443i) q^{24} +(-4.79147 + 1.42891i) q^{25} +(1.74727 + 1.48962i) q^{26} +(1.23459 + 5.04735i) q^{27} +(2.34576 - 3.24080i) q^{28} +(-1.64683 - 1.64683i) q^{29} +(-5.47228 + 0.232751i) q^{30} +4.31752 q^{31} +(2.14146 - 5.23585i) q^{32} +(-4.53584 - 0.833989i) q^{33} +(-9.42092 + 0.749896i) q^{34} +(2.67293 - 3.58638i) q^{35} +(-5.87460 - 1.22028i) q^{36} +0.432675i q^{37} +(0.422753 + 5.31104i) q^{38} +(1.59609 + 2.31525i) q^{39} +(2.47566 - 5.81989i) q^{40} +11.7342 q^{41} +(3.80071 - 3.09235i) q^{42} +7.25937 q^{43} +(3.12246 - 4.31386i) q^{44} +(-6.54833 - 1.45581i) q^{45} +(-4.08963 + 0.325530i) q^{46} +(-2.84866 - 2.84866i) q^{47} +(4.19014 - 5.51749i) q^{48} -2.99866i q^{49} +(2.85838 - 6.46758i) q^{50} +(-11.3839 - 2.09312i) q^{51} +(-3.20624 + 0.513682i) q^{52} -14.2471i q^{53} +(-6.56467 - 3.30228i) q^{54} +(3.55797 - 4.77386i) q^{55} +(1.33550 + 5.49793i) q^{56} +(-1.18000 + 6.41767i) q^{57} +(3.28327 - 0.261345i) q^{58} +(-6.71026 + 6.71026i) q^{59} +(4.77032 - 6.10279i) q^{60} +(2.46306 + 2.46306i) q^{61} +(-3.96132 + 4.64649i) q^{62} +(5.47522 - 2.45643i) q^{63} +(3.67001 + 7.10852i) q^{64} +(-3.59235 + 0.524248i) q^{65} +(5.05916 - 4.11626i) q^{66} -7.75965 q^{67} +(7.83666 - 10.8268i) q^{68} +(-4.94176 - 0.908625i) q^{69} +(1.40723 + 6.16710i) q^{70} -1.94196 q^{71} +(6.70320 - 5.20261i) q^{72} +(-10.6976 + 10.6976i) q^{73} +(-0.465642 - 0.396979i) q^{74} +(5.42806 - 6.74805i) q^{75} +(-6.10359 - 4.41791i) q^{76} +5.32622i q^{77} +(-3.95608 - 0.406541i) q^{78} +1.94859i q^{79} +(3.99191 + 8.00404i) q^{80} +(-6.72249 - 5.98398i) q^{81} +(-10.7661 + 12.6283i) q^{82} -9.36248 q^{83} +(-0.159173 + 6.92754i) q^{84} +(8.92967 - 11.9813i) q^{85} +(-6.66047 + 7.81250i) q^{86} +(3.96738 + 0.729470i) q^{87} +(1.77769 + 7.31834i) q^{88} -0.0668446i q^{89} +(7.57482 - 5.71157i) q^{90} +(2.29646 - 2.29646i) q^{91} +(3.40190 - 4.69992i) q^{92} +(-6.15691 + 4.24444i) q^{93} +(5.67936 - 0.452071i) q^{94} +(-6.75445 - 5.03410i) q^{95} +(2.09345 + 9.57170i) q^{96} +(0.253450 - 0.253450i) q^{97} +(3.22714 + 2.75126i) q^{98} +(7.28811 - 3.26978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) \) 88 * q - 4 * q^4 - 4 * q^6	\( 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) \) 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

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