LMFDB - Embedded newform 150.2.l.a.83.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			83.1
Character	$\chi$	$=$	150.83
Dual form			150.2.l.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-1.12805 + 1.31434i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.35023 + 1.78238i) q^{5} +(-0.658960 - 1.60180i) q^{6} +(-1.51403 + 1.51403i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-0.454984 - 2.96530i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.12805 + 1.31434i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.35023 + 1.78238i) q^{5} +(-0.658960 - 1.60180i) q^{6} +(-1.51403 + 1.51403i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-0.454984 - 2.96530i) q^{9} +(-2.20110 + 0.393876i) q^{10} +(-5.62798 + 1.82864i) q^{11} +(1.72638 + 0.140065i) q^{12} +(0.941310 - 0.479621i) q^{13} +(-0.661655 - 2.03636i) q^{14} +(-3.86579 - 0.235967i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(0.899945 + 5.68203i) q^{17} +(2.84866 + 0.940823i) q^{18} +(3.16950 - 4.36244i) q^{19} +(0.648334 - 2.14001i) q^{20} +(-0.282042 - 3.69786i) q^{21} +(0.925718 - 5.84476i) q^{22} +(1.37932 + 0.702799i) q^{23} +(-0.908558 + 1.47463i) q^{24} +(-1.35377 + 4.81324i) q^{25} +1.05646i q^{26} +(4.41066 + 2.74701i) q^{27} +(2.11480 + 0.334951i) q^{28} +(3.67723 - 2.67167i) q^{29} +(1.96528 - 3.33732i) q^{30} +(8.62475 + 6.26624i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.94521 - 9.45990i) q^{33} +(-5.47129 - 1.77773i) q^{34} +(-4.74286 - 0.654296i) q^{35} +(-2.13154 + 2.11105i) q^{36} +(0.100380 + 0.197006i) q^{37} +(2.44804 + 4.80455i) q^{38} +(-0.431463 + 1.77824i) q^{39} +(1.61243 + 1.54922i) q^{40} +(1.54235 + 0.501139i) q^{41} +(3.42286 + 1.42749i) q^{42} +(1.33532 + 1.33532i) q^{43} +(4.78745 + 3.47829i) q^{44} +(4.67096 - 4.81478i) q^{45} +(-1.25240 + 0.909919i) q^{46} +(-4.75083 - 0.752458i) q^{47} +(-0.901424 - 1.47900i) q^{48} +2.41543i q^{49} +(-3.67403 - 3.39139i) q^{50} +(-8.48331 - 5.22681i) q^{51} +(-0.941310 - 0.479621i) q^{52} +(0.949805 - 5.99683i) q^{53} +(-4.45000 + 2.68281i) q^{54} +(-10.8584 - 7.56214i) q^{55} +(-1.25854 + 1.73224i) q^{56} +(2.15837 + 9.08688i) q^{57} +(0.711043 + 4.48935i) q^{58} +(2.24119 - 6.89769i) q^{59} +(2.08135 + 3.26619i) q^{60} +(-1.30934 - 4.02973i) q^{61} +(-9.49882 + 4.83989i) q^{62} +(5.17841 + 3.80069i) q^{63} +(0.951057 - 0.309017i) q^{64} +(2.12585 + 1.03018i) q^{65} +(6.63774 + 7.80992i) q^{66} +(-1.28043 + 0.202800i) q^{67} +(4.06788 - 4.06788i) q^{68} +(-2.47967 + 1.02010i) q^{69} +(2.73620 - 3.92888i) q^{70} +(2.39892 + 3.30183i) q^{71} +(-0.913257 - 2.85761i) q^{72} +(0.141918 - 0.278530i) q^{73} -0.221105 q^{74} +(-4.79911 - 7.20892i) q^{75} -5.39228 q^{76} +(5.75231 - 11.2895i) q^{77} +(-1.38854 - 1.19174i) q^{78} +(0.555462 + 0.764528i) q^{79} +(-2.11239 + 0.733356i) q^{80} +(-8.58598 + 2.69833i) q^{81} +(-1.14673 + 1.14673i) q^{82} +(-7.47149 + 1.18337i) q^{83} +(-2.82585 + 2.40172i) q^{84} +(-8.91242 + 9.27607i) q^{85} +(-1.79600 + 0.583556i) q^{86} +(-0.636640 + 7.84692i) q^{87} +(-5.27263 + 2.68654i) q^{88} +(2.67429 + 8.23061i) q^{89} +(2.16943 + 6.34772i) q^{90} +(-0.699010 + 2.15133i) q^{91} +(-0.242168 - 1.52899i) q^{92} +(-17.9652 + 4.26719i) q^{93} +(2.82728 - 3.89142i) q^{94} +(12.0551 - 0.241026i) q^{95} +(1.72703 - 0.131724i) q^{96} +(1.88725 - 11.9156i) q^{97} +(-2.15217 - 1.09658i) q^{98} +(7.98311 + 15.8566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−1.12805	+	1.31434i	−0.651283	+	0.758835i
$3$	−1.12805	+	1.31434i	−0.651283	+	0.758835i
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	1.35023	+	1.78238i	0.603840	+	0.797106i
$5$	1.35023	+	1.78238i	0.603840	+	0.797106i
$6$	−0.658960	−	1.60180i	−0.269019	−	0.653933i
$7$	−1.51403	+	1.51403i	−0.572249	+	0.572249i	−0.932756	−	0.360507i	$-0.882604\pi$
$7$	−1.51403	+	1.51403i	−0.572249	+	0.572249i	0.360507	+	0.932756i	$0.382604\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−0.454984	−	2.96530i	−0.151661	−	0.988433i
$10$	−2.20110	+	0.393876i	−0.696050	+	0.124555i
$11$	−5.62798	+	1.82864i	−1.69690	+	0.551357i	−0.988068	−	0.154020i	$-0.950778\pi$
$11$	−5.62798	+	1.82864i	−1.69690	+	0.551357i	−0.708833	+	0.705376i	$0.750778\pi$
$12$	1.72638	+	0.140065i	0.498362	+	0.0404334i
$13$	0.941310	−	0.479621i	0.261072	−	0.133023i	−0.318556	−	0.947904i	$-0.603198\pi$
$13$	0.941310	−	0.479621i	0.261072	−	0.133023i	0.579628	+	0.814881i	$0.303198\pi$
$14$	−0.661655	−	2.03636i	−0.176835	−	0.544241i
$15$	−3.86579	−	0.235967i	−0.998142	−	0.0609263i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.899945	+	5.68203i	0.218269	+	1.37809i	0.816766	+	0.576969i	$0.195765\pi$
$17$	0.899945	+	5.68203i	0.218269	+	1.37809i	−0.598497	+	0.801125i	$0.704235\pi$
$18$	2.84866	+	0.940823i	0.671435	+	0.221754i
$19$	3.16950	−	4.36244i	0.727133	−	1.00081i	−0.272123	−	0.962262i	$-0.587726\pi$
$19$	3.16950	−	4.36244i	0.727133	−	1.00081i	0.999257	−	0.0385508i	$-0.0122742\pi$
$20$	0.648334	−	2.14001i	0.144972	−	0.478522i
$21$	−0.282042	−	3.69786i	−0.0615467	−	0.806939i
$22$	0.925718	−	5.84476i	0.197364	−	1.24611i
$23$	1.37932	+	0.702799i	0.287608	+	0.146544i	0.591843	−	0.806054i	$-0.298401\pi$
$23$	1.37932	+	0.702799i	0.287608	+	0.146544i	−0.304235	+	0.952597i	$0.598401\pi$
$24$	−0.908558	+	1.47463i	−0.185459	+	0.301007i
$25$	−1.35377	+	4.81324i	−0.270755	+	0.962648i
$26$			1.05646i			0.207188i
$27$	4.41066	+	2.74701i	0.848832	+	0.528663i
$28$	2.11480	+	0.334951i	0.399659	+	0.0632998i
$29$	3.67723	−	2.67167i	0.682845	−	0.496116i	−0.191455	−	0.981501i	$-0.561321\pi$
$29$	3.67723	−	2.67167i	0.682845	−	0.496116i	0.874300	+	0.485386i	$0.161321\pi$
$30$	1.96528	−	3.33732i	0.358809	−	0.609308i
$31$	8.62475	+	6.26624i	1.54905	+	1.12545i	0.944324	+	0.329017i	$0.106718\pi$
$31$	8.62475	+	6.26624i	1.54905	+	1.12545i	0.604726	+	0.796433i	$0.293282\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	3.94521	−	9.45990i	0.686774	−	1.64676i
$34$	−5.47129	−	1.77773i	−0.938319	−	0.304878i
$35$	−4.74286	−	0.654296i	−0.801690	−	0.110596i
$36$	−2.13154	+	2.11105i	−0.355257	+	0.351841i
$37$	0.100380	+	0.197006i	0.0165023	+	0.0323876i	0.899111	−	0.437722i	$-0.144214\pi$
$37$	0.100380	+	0.197006i	0.0165023	+	0.0323876i	−0.882608	+	0.470109i	$0.844214\pi$
$38$	2.44804	+	4.80455i	0.397125	+	0.779402i
$39$	−0.431463	+	1.77824i	−0.0690894	+	0.284747i
$40$	1.61243	+	1.54922i	0.254947	+	0.244953i
$41$	1.54235	+	0.501139i	0.240874	+	0.0782648i	0.426966	−	0.904268i	$-0.359582\pi$
$41$	1.54235	+	0.501139i	0.240874	+	0.0782648i	−0.186092	+	0.982532i	$0.559582\pi$
$42$	3.42286	+	1.42749i	0.528159	+	0.220267i
$43$	1.33532	+	1.33532i	0.203634	+	0.203634i	0.801555	−	0.597921i	$-0.204006\pi$
$43$	1.33532	+	1.33532i	0.203634	+	0.203634i	−0.597921	+	0.801555i	$0.704006\pi$
$44$	4.78745	+	3.47829i	0.721735	+	0.524371i
$45$	4.67096	−	4.81478i	0.696306	−	0.717745i
$46$	−1.25240	+	0.909919i	−0.184656	+	0.134160i
$47$	−4.75083	−	0.752458i	−0.692980	−	0.109757i	−0.199998	−	0.979796i	$-0.564093\pi$
$47$	−4.75083	−	0.752458i	−0.692980	−	0.109757i	−0.492983	+	0.870039i	$0.664093\pi$
$48$	−0.901424	−	1.47900i	−0.130109	−	0.213475i
$49$			2.41543i			0.345062i
$50$	−3.67403	−	3.39139i	−0.519586	−	0.479615i
$51$	−8.48331	−	5.22681i	−1.18790	−	0.731899i
$52$	−0.941310	−	0.479621i	−0.130536	−	0.0665115i
$53$	0.949805	−	5.99683i	0.130466	−	0.823728i	−0.832484	−	0.554049i	$-0.813082\pi$
$53$	0.949805	−	5.99683i	0.130466	−	0.823728i	0.962950	−	0.269680i	$-0.0869178\pi$
$54$	−4.45000	+	2.68281i	−0.605569	+	0.365084i
$55$	−10.8584	−	7.56214i	−1.46415	−	1.01968i
$56$	−1.25854	+	1.73224i	−0.168180	+	0.231480i
$57$	2.15837	+	9.08688i	0.285883	+	1.20359i
$58$	0.711043	+	4.48935i	0.0933645	+	0.589480i
$59$	2.24119	−	6.89769i	0.291779	−	0.898002i	−0.692506	−	0.721412i	$-0.743493\pi$
$59$	2.24119	−	6.89769i	0.291779	−	0.898002i	0.984285	−	0.176590i	$-0.0565066\pi$
$60$	2.08135	+	3.26619i	0.268701	+	0.421663i
$61$	−1.30934	−	4.02973i	−0.167644	−	0.515954i	0.831578	−	0.555408i	$-0.187438\pi$
$61$	−1.30934	−	4.02973i	−0.167644	−	0.515954i	−0.999221	+	0.0394543i	$0.987438\pi$
$62$	−9.49882	+	4.83989i	−1.20635	+	0.614667i
$63$	5.17841	+	3.80069i	0.652418	+	0.478842i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	2.12585	+	1.03018i	0.263679	+	0.127778i
$66$	6.63774	+	7.80992i	0.817050	+	0.961334i
$67$	−1.28043	+	0.202800i	−0.156429	+	0.0247759i	−0.234158	−	0.972199i	$-0.575233\pi$
$67$	−1.28043	+	0.202800i	−0.156429	+	0.0247759i	0.0777287	+	0.996975i	$0.475233\pi$
$68$	4.06788	−	4.06788i	0.493303	−	0.493303i
$69$	−2.47967	+	1.02010i	−0.298517	+	0.122806i
$70$	2.73620	−	3.92888i	0.327038	−	0.469591i
$71$	2.39892	+	3.30183i	0.284700	+	0.391856i	0.927283	−	0.374360i	$-0.122138\pi$
$71$	2.39892	+	3.30183i	0.284700	+	0.391856i	−0.642584	+	0.766215i	$0.722138\pi$
$72$	−0.913257	−	2.85761i	−0.107628	−	0.336773i
$73$	0.141918	−	0.278530i	0.0166102	−	0.0325994i	−0.882552	−	0.470214i	$-0.844177\pi$
$73$	0.141918	−	0.278530i	0.0166102	−	0.0325994i	0.899163	+	0.437615i	$0.144177\pi$
$74$	−0.221105			−0.0257030
$75$	−4.79911	−	7.20892i	−0.554153	−	0.832415i
$76$	−5.39228			−0.618537
$77$	5.75231	−	11.2895i	0.655537	−	1.28656i
$78$	−1.38854	−	1.19174i	−0.157222	−	0.134938i
$79$	0.555462	+	0.764528i	0.0624944	+	0.0860162i	0.839120	−	0.543946i	$-0.183070\pi$
$79$	0.555462	+	0.764528i	0.0624944	+	0.0860162i	−0.776626	+	0.629962i	$0.783070\pi$
$80$	−2.11239	+	0.733356i	−0.236172	+	0.0819917i
$81$	−8.58598	+	2.69833i	−0.953998	+	0.299814i
$82$	−1.14673	+	1.14673i	−0.126635	+	0.126635i
$83$	−7.47149	+	1.18337i	−0.820102	+	0.129891i	−0.552367	−	0.833601i	$-0.686275\pi$
$83$	−7.47149	+	1.18337i	−0.820102	+	0.129891i	−0.267735	+	0.963493i	$0.586275\pi$
$84$	−2.82585	+	2.40172i	−0.308325	+	0.262050i
$85$	−8.91242	+	9.27607i	−0.966687	+	1.00613i
$86$	−1.79600	+	0.583556i	−0.193668	+	0.0629264i
$87$	−0.636640	+	7.84692i	−0.0682550	+	0.841278i
$88$	−5.27263	+	2.68654i	−0.562064	+	0.286386i
$89$	2.67429	+	8.23061i	0.283474	+	0.872443i	0.986852	+	0.161627i	$0.0516741\pi$
$89$	2.67429	+	8.23061i	0.283474	+	0.872443i	−0.703378	+	0.710816i	$0.748326\pi$
$90$	2.16943	+	6.34772i	0.228678	+	0.669109i
$91$	−0.699010	+	2.15133i	−0.0732762	+	0.225521i
$92$	−0.242168	−	1.52899i	−0.0252477	−	0.159408i
$93$	−17.9652	+	4.26719i	−1.86290	+	0.442487i
$94$	2.82728	−	3.89142i	0.291612	−	0.401369i
$95$	12.0551	−	0.241026i	1.23683	−	0.0247288i
$96$	1.72703	−	0.131724i	0.176265	−	0.0134440i
$97$	1.88725	−	11.9156i	0.191621	−	1.20985i	−0.684956	−	0.728584i	$-0.740179\pi$
$97$	1.88725	−	11.9156i	0.191621	−	1.20985i	0.876577	−	0.481262i	$-0.159821\pi$
$98$	−2.15217	−	1.09658i	−0.217402	−	0.110772i
$99$	7.98311	+	15.8566i	0.802333	+	1.59365i
$100$	4.68972	−	1.73393i	0.468972	−	0.173393i
$101$			0.310282i			0.0308742i	0.999881	+	0.0154371i	$0.00491398\pi$
$101$			0.310282i			0.0308742i	−0.999881	+	0.0154371i	$0.995086\pi$
$102$	8.50846	−	5.18576i	0.842463	−	0.513467i
$103$	−8.72553	−	1.38199i	−0.859752	−	0.136171i	−0.289035	−	0.957318i	$-0.593335\pi$
$103$	−8.72553	−	1.38199i	−0.859752	−	0.136171i	−0.570717	+	0.821147i	$0.693335\pi$
$104$	0.854692	−	0.620970i	0.0838094	−	0.0608911i
$105$	6.21018	−	5.49566i	0.606051	−	0.536321i
$106$	4.91201	+	3.56879i	0.477097	+	0.346631i
$107$	4.19190	+	4.19190i	0.405246	+	0.405246i	0.880077	−	0.474831i	$-0.157491\pi$
$107$	4.19190	+	4.19190i	0.405246	+	0.405246i	−0.474831	+	0.880077i	$0.657491\pi$
$108$	−0.370140	−	5.18295i	−0.0356167	−	0.498730i
$109$	1.79521	+	0.583300i	0.171950	+	0.0558700i	0.393727	−	0.919227i	$-0.371186\pi$
$109$	1.79521	+	0.583300i	0.171950	+	0.0558700i	−0.221777	+	0.975098i	$0.571186\pi$
$110$	11.6675	−	6.24176i	1.11245	−	0.595129i
$111$	−0.372167	−	0.0903007i	−0.0353245	−	0.00857096i
$112$	−0.972066	−	1.90779i	−0.0918516	−	0.180269i
$113$	−3.85086	−	7.55774i	−0.362258	−	0.710972i	0.635891	−	0.771779i	$-0.280633\pi$
$113$	−3.85086	−	7.55774i	−0.362258	−	0.710972i	−0.998150	+	0.0608066i	$0.980633\pi$
$114$	−9.07635	−	2.20224i	−0.850078	−	0.206258i
$115$	0.609739	+	3.40741i	0.0568585	+	0.317743i
$116$	−4.32285	−	1.40458i	−0.401366	−	0.130412i
$117$	−1.85050	−	2.57304i	−0.171079	−	0.237878i
$118$	5.12840	+	5.12840i	0.472108	+	0.472108i
$119$	−9.96530	−	7.24021i	−0.913517	−	0.663709i
$120$	−3.85511	+	0.371681i	−0.351922	+	0.0339297i
$121$	19.4311	−	14.1175i	1.76646	−	1.28341i
$122$	4.18494	+	0.662830i	0.378887	+	0.0600098i
$123$	−2.39852	+	1.46186i	−0.216267	+	0.131811i
$124$		−	10.6608i		−	0.957366i
$125$	−10.4069	+	4.08603i	−0.930825	+	0.365465i
$126$	−5.73738	+	2.88852i	−0.511127	+	0.257330i
$127$	9.31862	+	4.74807i	0.826894	+	0.421323i	0.815602	−	0.578613i	$-0.196406\pi$
$127$	9.31862	+	4.74807i	0.826894	+	0.421323i	0.0112913	+	0.999936i	$0.496406\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	−3.26138	+	0.248751i	−0.287148	+	0.0219013i
$130$	−1.88301	+	1.42646i	−0.165151	+	0.125109i
$131$	11.4805	−	15.8015i	1.00306	−	1.38059i	0.0796236	−	0.996825i	$-0.474628\pi$
$131$	11.4805	−	15.8015i	1.00306	−	1.38059i	0.923432	−	0.383762i	$-0.125372\pi$
$132$	−9.97216	+	2.36864i	−0.867965	+	0.206164i
$133$	1.80615	+	11.4036i	0.156613	+	0.988816i
$134$	0.400605	−	1.23294i	0.0346070	−	0.106510i
$135$	1.05916	+	11.5706i	0.0911581	+	0.995836i
$136$	1.77773	+	5.47129i	0.152439	+	0.469159i
$137$	10.6831	−	5.44330i	0.912717	−	0.465053i	0.0664369	−	0.997791i	$-0.478837\pi$
$137$	10.6831	−	5.44330i	0.912717	−	0.465053i	0.846280	+	0.532738i	$0.178837\pi$
$138$	0.216828	−	2.67251i	0.0184576	−	0.227500i
$139$	22.1318	−	7.19107i	1.87720	−	0.609939i	0.888747	−	0.458399i	$-0.151577\pi$
$139$	22.1318	−	7.19107i	1.87720	−	0.609939i	0.988451	−	0.151540i	$-0.0484232\pi$
$140$	2.25845	+	4.22164i	0.190874	+	0.356794i
$141$	6.34819	−	5.39540i	0.534614	−	0.454375i
$142$	−4.03104	+	0.638455i	−0.338278	+	0.0535779i
$143$	−4.42062	+	4.42062i	−0.369671	+	0.369671i
$144$	2.96076	+	0.483612i	0.246730	+	0.0403010i
$145$	9.72703	+	2.94688i	0.807786	+	0.244725i
$146$	0.183742	+	0.252900i	0.0152066	+	0.0209301i
$147$	−3.17470	−	2.72474i	−0.261845	−	0.224733i
$148$	0.100380	−	0.197006i	0.00825116	−	0.0161938i
$149$	−14.7140			−1.20542			−0.602711	−	0.797960i	$-0.705913\pi$
$149$	−14.7140			−1.20542			−0.602711	+	0.797960i	$0.705913\pi$
$150$	8.60195	−	1.00326i	0.702346	−	0.0819155i
$151$	−8.54879			−0.695691			−0.347845	−	0.937552i	$-0.613087\pi$
$151$	−8.54879			−0.695691			−0.347845	+	0.937552i	$0.613087\pi$
$152$	2.44804	−	4.80455i	0.198562	−	0.389701i
$153$	16.4394	−	5.25384i	1.32905	−	0.424748i
$154$	7.44757	+	10.2507i	0.600142	+	0.826025i
$155$	0.476520	+	23.8334i	0.0382750	+	1.91435i
$156$	1.69224	−	0.696163i	0.135487	−	0.0557377i
$157$	−17.5864	+	17.5864i	−1.40355	+	1.40355i	−0.615104	+	0.788446i	$0.710886\pi$
$157$	−17.5864	+	17.5864i	−1.40355	+	1.40355i	−0.788446	+	0.615104i	$0.789114\pi$
$158$	−0.933375	+	0.147832i	−0.0742553	+	0.0117609i
$159$	6.81045	+	8.01312i	0.540104	+	0.635482i
$160$	0.305580	−	2.21509i	0.0241582	−	0.175118i
$161$	−3.15239	+	1.02427i	−0.248443	+	0.0807240i
$162$	1.49373	−	8.87518i	0.117358	−	0.697300i
$163$	1.79029	−	0.912200i	0.140227	−	0.0714490i	−0.382469	−	0.923968i	$-0.624926\pi$
$163$	1.79029	−	0.912200i	0.140227	−	0.0714490i	0.522696	+	0.852519i	$0.324926\pi$
$164$	−0.501139	−	1.54235i	−0.0391324	−	0.120437i
$165$	22.1881	−	5.74113i	1.72734	−	0.446946i
$166$	2.33760	−	7.19438i	0.181433	−	0.558392i
$167$	−2.32146	−	14.6571i	−0.179640	−	1.13420i	−0.898477	−	0.439021i	$-0.855325\pi$
$167$	−2.32146	−	14.6571i	−0.179640	−	1.13420i	0.718837	−	0.695179i	$-0.244675\pi$
$168$	−0.857043	−	3.60821i	−0.0661223	−	0.278379i
$169$	−6.98518	+	9.61428i	−0.537322	+	0.739560i
$170$	−4.21889	−	12.1523i	−0.323574	−	0.932037i
$171$	−14.3780	−	7.41367i	−1.09951	−	0.566937i
$172$	0.295415	−	1.86518i	0.0225252	−	0.142218i
$173$	−4.46800	−	2.27656i	−0.339696	−	0.173084i	0.275818	−	0.961210i	$-0.411051\pi$
$173$	−4.46800	−	2.27656i	−0.339696	−	0.173084i	−0.615514	+	0.788126i	$0.711051\pi$
$174$	−6.70263	−	4.12968i	−0.508125	−	0.313070i
$175$	−5.23773	−	9.33704i	−0.395935	−	0.705814i
$176$		−	5.91761i		−	0.446057i
$177$	6.53772	+	10.7267i	0.491405	+	0.806265i
$178$	−8.54762	−	1.35381i	−0.640672	−	0.101472i
$179$	−2.56353	+	1.86252i	−0.191607	+	0.139211i	−0.679453	−	0.733719i	$-0.737783\pi$
$179$	−2.56353	+	1.86252i	−0.191607	+	0.139211i	0.487846	+	0.872930i	$0.337783\pi$
$180$	−6.64076	−	0.948831i	−0.494973	−	0.0707217i
$181$	−5.04884	−	3.66820i	−0.375278	−	0.272655i	0.384118	−	0.923284i	$-0.374505\pi$
$181$	−5.04884	−	3.66820i	−0.375278	−	0.272655i	−0.759396	+	0.650629i	$0.774505\pi$
$182$	−1.59951	−	1.59951i	−0.118563	−	0.118563i
$183$	6.77345	+	2.82484i	0.500707	+	0.208818i
$184$	1.47228	+	0.478373i	0.108538	+	0.0352661i
$185$	−0.215605	+	0.444918i	−0.0158516	+	0.0327110i
$186$	4.35392	−	17.9443i	0.319245	−	1.31574i
$187$	−15.4553	−	30.3327i	−1.13020	−	2.21815i
$188$	2.18372	+	4.28579i	0.159264	+	0.312573i
$189$	−10.8369	+	2.51881i	−0.788270	+	0.183216i
$190$	−5.25814	+	10.8506i	−0.381466	+	0.787184i
$191$	19.9806	+	6.49209i	1.44574	+	0.469751i	0.923683	−	0.383157i	$-0.125163\pi$
$191$	19.9806	+	6.49209i	1.44574	+	0.469751i	0.522062	+	0.852908i	$0.325163\pi$
$192$	−0.666690	+	1.59860i	−0.0481142	+	0.115369i
$193$	7.00922	+	7.00922i	0.504535	+	0.504535i	0.912844	−	0.408309i	$-0.133881\pi$
$193$	7.00922	+	7.00922i	0.504535	+	0.504535i	−0.408309	+	0.912844i	$0.633881\pi$
$194$	9.76009	+	7.09112i	0.700734	+	0.509113i
$195$	−3.75208	+	1.63200i	−0.268692	+	0.116870i
$196$	1.95413	−	1.41976i	0.139580	−	0.101411i
$197$	−10.0821	−	1.59685i	−0.718320	−	0.113771i	−0.213435	−	0.976957i	$-0.568465\pi$
$197$	−10.0821	−	1.59685i	−0.718320	−	0.113771i	−0.504885	+	0.863186i	$0.668465\pi$
$198$	−17.7526	−	0.0857583i	−1.26162	−	0.00609458i
$199$		−	15.1147i		−	1.07146i	−0.844391	−	0.535728i	$-0.820037\pi$
$199$		−	15.1147i		−	1.07146i	0.844391	−	0.535728i	$-0.179963\pi$
$200$	−0.584150	+	4.96576i	−0.0413057	+	0.351132i
$201$	1.17784	−	1.91169i	0.0830786	−	0.134840i
$202$	−0.276463	−	0.140865i	−0.0194519	−	0.00991123i
$203$	−1.52246	+	9.61241i	−0.106856	+	0.674659i
$204$	0.757790	+	9.93538i	0.0530559	+	0.695616i
$205$	1.18930	+	3.42570i	0.0830642	+	0.239262i
$206$	5.19267	−	7.14709i	0.361790	−	0.497962i
$207$	1.45644	−	4.40986i	0.101229	−	0.306506i
$208$	0.165266	+	1.04345i	0.0114592	+	0.0723503i
$209$	−9.86055	+	30.3476i	−0.682068	+	2.09919i
$210$	2.07730	+	8.02828i	0.143348	+	0.554004i
$211$	−1.22728	−	3.77719i	−0.0844897	−	0.260033i	0.899883	−	0.436132i	$-0.143652\pi$
$211$	−1.22728	−	3.77719i	−0.0844897	−	0.260033i	−0.984372	+	0.176099i	$0.943652\pi$
$212$	−5.40982	+	2.75644i	−0.371548	+	0.189313i
$213$	−7.04585	−	0.571647i	−0.482774	−	0.0391686i
$214$	−5.63809	+	1.83193i	−0.385412	+	0.125228i
$215$	−0.577065	+	4.18303i	−0.0393555	+	0.285280i
$216$	4.78608	+	2.02321i	0.325652	+	0.137662i
$217$	−22.5454	+	3.57084i	−1.53048	+	0.242404i
$218$	−1.33473	+	1.33473i	−0.0903996	+	0.0903996i
$219$	0.205992	+	0.500725i	0.0139196	+	0.0338359i
$220$	0.264508	+	13.2295i	0.0178331	+	0.891935i
$221$	3.57235	+	4.91692i	0.240302	+	0.330748i
$222$	0.249419	−	0.290608i	0.0167399	−	0.0195043i
$223$	−6.07755	+	11.9279i	−0.406983	+	0.798748i	−0.999979	−	0.00645660i	$-0.997945\pi$
$223$	−6.07755	+	11.9279i	−0.406983	+	0.798748i	0.592996	+	0.805205i	$0.297945\pi$
$224$	2.14116			0.143062
$225$	14.8886	+	1.82439i	0.992576	+	0.121626i
$226$	8.48225			0.564231
$227$	−0.388579	+	0.762629i	−0.0257909	+	0.0506175i	−0.903542	−	0.428499i	$-0.859043\pi$
$227$	−0.388579	+	0.762629i	−0.0257909	+	0.0506175i	0.877752	+	0.479116i	$0.159043\pi$
$228$	6.08278	−	7.08729i	0.402842	−	0.469367i
$229$	−9.72545	−	13.3859i	−0.642676	−	0.884567i	0.356079	−	0.934456i	$-0.384113\pi$
$229$	−9.72545	−	13.3859i	−0.642676	−	0.884567i	−0.998755	+	0.0498887i	$0.984113\pi$
$230$	−3.31284	−	1.00365i	−0.218442	−	0.0661788i
$231$	8.34939	+	20.2957i	0.549350	+	1.33536i
$232$	3.21402	−	3.21402i	0.211011	−	0.211011i
$233$	5.38346	−	0.852656i	0.352682	−	0.0558593i	0.0224200	−	0.999749i	$-0.492863\pi$
$233$	5.38346	−	0.852656i	0.352682	−	0.0558593i	0.330262	+	0.943889i	$0.392863\pi$
$234$	3.13271	−	0.480671i	0.204792	−	0.0314225i
$235$	−5.07354	−	9.48379i	−0.330961	−	0.618654i
$236$	−6.89769	+	2.24119i	−0.449001	+	0.145889i
$237$	−1.63144	−	0.132363i	−0.105974	−	0.00859790i
$238$	10.9752	−	5.59216i	0.711418	−	0.362486i
$239$	2.69306	+	8.28837i	0.174199	+	0.536130i	0.999596	−	0.0284230i	$-0.00904853\pi$
$239$	2.69306	+	8.28837i	0.174199	+	0.536130i	−0.825397	+	0.564553i	$0.809049\pi$
$240$	1.41901	−	3.60367i	0.0915968	−	0.232616i
$241$	−7.85699	+	24.1813i	−0.506113	+	1.55766i	0.292779	+	0.956180i	$0.405420\pi$
$241$	−7.85699	+	24.1813i	−0.506113	+	1.55766i	−0.798892	+	0.601475i	$0.794580\pi$
$242$	3.75726	+	23.7224i	0.241526	+	1.52494i
$243$	6.13893	−	14.3288i	0.393813	−	0.919191i
$244$	−2.49051	+	3.42789i	−0.159439	+	0.219448i
$245$	−4.30522	+	3.26138i	−0.275051	+	0.208362i
$246$	−0.213620	−	2.80077i	−0.0136199	−	0.178570i
$247$	0.891162	−	5.62657i	0.0567033	−	0.358010i
$248$	9.49882	+	4.83989i	0.603176	+	0.307333i
$249$	6.87290	−	11.1550i	0.435552	−	0.706918i
$250$	1.08398	−	11.1277i	0.0685567	−	0.703776i
$251$			21.0935i			1.33141i	0.746215	+	0.665706i	$0.231869\pi$
$251$			21.0935i			1.33141i	−0.746215	+	0.665706i	$0.768131\pi$
$252$	0.0310298	−	6.42341i	0.00195469	−	0.404637i
$253$	−9.04796	−	1.43306i	−0.568840	−	0.0900954i
$254$	−8.46113	+	6.14737i	−0.530898	+	0.385720i
$255$	−2.13823	−	22.1779i	−0.133901	−	1.38883i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	11.8588	+	11.8588i	0.739734	+	0.739734i	0.972526	−	0.232792i	$-0.0747863\pi$
$257$	11.8588	+	11.8588i	0.739734	+	0.739734i	−0.232792	+	0.972526i	$0.574786\pi$
$258$	1.25900	−	3.01884i	0.0783816	−	0.187945i
$259$	−0.450251	−	0.146295i	−0.0279772	−	0.00909035i
$260$	−0.416113	−	2.32537i	−0.0258063	−	0.144213i
$261$	−9.59537	−	9.68852i	−0.593938	−	0.599704i
$262$	8.86724	+	17.4029i	0.547820	+	1.07516i
$263$	−10.3291	−	20.2720i	−0.636919	−	1.25002i	−0.953481	−	0.301453i	$-0.902529\pi$
$263$	−10.3291	−	20.2720i	−0.636919	−	1.25002i	0.316562	−	0.948572i	$-0.397471\pi$
$264$	2.41679	−	9.96060i	0.148743	−	0.613033i
$265$	11.9711	−	6.40417i	0.735379	−	0.393405i
$266$	−10.9806	−	3.56783i	−0.673266	−	0.218757i
$267$	−13.8346	−	5.76965i	−0.846662	−	0.353097i
$268$	0.916684	+	0.916684i	0.0559954	+	0.0559954i
$269$	−8.37684	−	6.08613i	−0.510745	−	0.371078i	0.302361	−	0.953193i	$-0.402225\pi$
$269$	−8.37684	−	6.08613i	−0.510745	−	0.371078i	−0.813106	+	0.582115i	$0.802225\pi$
$270$	−10.7903	−	4.30921i	−0.656677	−	0.262250i
$271$	−0.517312	+	0.375849i	−0.0314245	+	0.0228312i	−0.603387	−	0.797449i	$-0.706182\pi$
$271$	−0.517312	+	0.375849i	−0.0314245	+	0.0228312i	0.571962	+	0.820280i	$0.306182\pi$
$272$	−5.68203	−	0.899945i	−0.344524	−	0.0545672i
$273$	−2.03906	−	3.34556i	−0.123410	−	0.202482i
$274$			11.9899i			0.724336i
$275$	−1.18268	−	29.5644i	−0.0713183	−	1.78280i
$276$	2.28279	+	1.40649i	0.137408	+	0.0846608i
$277$	27.0524	+	13.7839i	1.62542	+	0.828193i	0.998805	+	0.0488650i	$0.0155604\pi$
$277$	27.0524	+	13.7839i	1.62542	+	0.828193i	0.626616	+	0.779328i	$0.284440\pi$
$278$	−3.64035	+	22.9843i	−0.218334	+	1.37851i
$279$	14.6572	−	28.4260i	0.877501	−	1.70182i
$280$	−4.78682	+	0.0957066i	−0.286067	+	0.00571956i
$281$	12.7646	−	17.5690i	0.761473	−	1.04808i	−0.235617	−	0.971846i	$-0.575711\pi$
$281$	12.7646	−	17.5690i	0.761473	−	1.04808i	0.997090	−	0.0762322i	$-0.0242890\pi$
$282$	1.92532	+	8.10574i	0.114651	+	0.482690i
$283$	0.541258	+	3.41737i	0.0321745	+	0.203142i	0.998539	−	0.0540343i	$-0.0172080\pi$
$283$	0.541258	+	3.41737i	0.0321745	+	0.203142i	−0.966365	+	0.257176i	$0.917208\pi$
$284$	1.26119	−	3.88154i	0.0748378	−	0.230327i
$285$	−13.2820	+	16.1164i	−0.786758	+	0.954652i
$286$	−1.93188	−	5.94572i	−0.114235	−	0.351578i
$287$	−3.09390	+	1.57642i	−0.182627	+	0.0930531i
$288$	−1.77506	+	2.41850i	−0.104596	+	0.142512i
$289$	−15.3076	+	4.97374i	−0.900446	+	0.292573i
$290$	−7.04167	+	7.32899i	−0.413501	+	0.430373i
$291$	13.5323	+	15.9219i	0.793275	+	0.933361i
$292$	−0.308752	+	0.0489016i	−0.0180684	+	0.00286175i
$293$	12.2527	−	12.2527i	0.715808	−	0.715808i	−0.251936	−	0.967744i	$-0.581067\pi$
$293$	12.2527	−	12.2527i	0.715808	−	0.715808i	0.967744	+	0.251936i	$0.0810673\pi$
$294$	3.86905	−	1.59167i	0.225647	−	0.0928283i
$295$	15.3204	−	5.31878i	0.891990	−	0.309671i
$296$	0.129962	+	0.178878i	0.00755391	+	0.0103971i
$297$	−29.8464	−	7.39463i	−1.73187	−	0.429080i
$298$	6.68004	−	13.1103i	0.386964	−	0.759460i
$299$	1.63544			0.0945802
$300$	−3.01129	+	8.11986i	−0.173857	+	0.468800i
$301$	−4.04342			−0.233059
$302$	3.88107	−	7.61703i	0.223330	−	0.438311i
$303$	−0.407816	−	0.350015i	−0.0234284	−	0.0201078i
$304$	3.16950	+	4.36244i	0.181783	+	0.250203i
$305$	5.41462	−	7.77479i	0.310040	−	0.445183i
$306$	−2.78215	+	17.0328i	−0.159045	+	0.973703i
$307$	16.8133	−	16.8133i	0.959588	−	0.959588i	−0.0396263	−	0.999215i	$-0.512617\pi$
$307$	16.8133	−	16.8133i	0.959588	−	0.959588i	0.999215	+	0.0396263i	$0.0126167\pi$
$308$	−12.5146	+	1.98211i	−0.713083	+	0.112941i
$309$	11.6593	−	9.90936i	0.663273	−	0.563724i
$310$	−21.4521	−	10.3956i	−1.21840	−	0.590429i
$311$	7.39905	−	2.40410i	0.419562	−	0.136324i	−0.0916250	−	0.995794i	$-0.529206\pi$
$311$	7.39905	−	2.40410i	0.419562	−	0.136324i	0.511187	+	0.859470i	$0.329206\pi$
$312$	−0.147973	+	1.82384i	−0.00837732	+	0.103255i
$313$	18.5326	−	9.44284i	1.04753	−	0.533741i	0.156492	−	0.987679i	$-0.449981\pi$
$313$	18.5326	−	9.44284i	1.04753	−	0.533741i	0.891033	+	0.453939i	$0.149981\pi$
$314$	−7.68555	−	23.6537i	−0.433721	−	1.33486i
$315$	0.217745	+	14.3617i	0.0122686	+	0.809190i
$316$	0.292024	−	0.898757i	0.0164276	−	0.0505590i
$317$	0.0339077	+	0.214085i	0.00190445	+	0.0120242i	0.988622	−	0.150419i	$-0.0480624\pi$
$317$	0.0339077	+	0.214085i	0.00190445	+	0.0120242i	−0.986718	+	0.162444i	$0.948062\pi$
$318$	−10.2316	+	2.43027i	−0.573761	+	0.136283i
$319$	−15.8099	+	21.7604i	−0.885183	+	1.21835i
$320$	1.83493	+	1.27790i	0.102576	+	0.0714370i
$321$	−10.2383	+	0.780892i	−0.571445	+	0.0435852i
$322$	0.518520	−	3.27381i	0.0288960	−	0.182442i
$323$	27.6399	+	14.0832i	1.53793	+	0.783612i
$324$	7.22970	+	5.36017i	0.401650	+	0.297787i
$325$	1.03421	+	5.18005i	0.0573678	+	0.287338i
$326$			2.00929i			0.111284i
$327$	−2.79176	+	1.70153i	−0.154384	+	0.0940947i
$328$	1.60175	+	0.253693i	0.0884421	+	0.0140078i
$329$	8.33214	−	6.05366i	0.459366	−	0.333749i
$330$	−4.95780	+	22.3762i	−0.272918	+	1.23177i
$331$	5.81535	+	4.22510i	0.319640	+	0.232232i	0.736022	−	0.676958i	$-0.236702\pi$
$331$	5.81535	+	4.22510i	0.319640	+	0.232232i	−0.416382	+	0.909190i	$0.636702\pi$
$332$	5.34899	+	5.34899i	0.293564	+	0.293564i
$333$	0.538511	−	0.387290i	0.0295102	−	0.0212234i
$334$	14.1135	+	4.58575i	0.772255	+	0.250921i
$335$	−2.09033	−	2.00838i	−0.114207	−	0.109730i
$336$	3.60403	+	0.874463i	0.196616	+	0.0477058i
$337$	3.06621	+	6.01777i	0.167027	+	0.327809i	0.959315	−	0.282339i	$-0.0911102\pi$
$337$	3.06621	+	6.01777i	0.167027	+	0.327809i	−0.792288	+	0.610147i	$0.791110\pi$
$338$	−5.39518	−	10.5886i	−0.293459	−	0.575946i
$339$	14.2774	+	3.46420i	0.775443	+	0.188150i
$340$	12.7431	+	1.75796i	0.691091	+	0.0953387i
$341$	−59.9987	−	19.4947i	−3.24911	−	1.05570i
$342$	13.1331	−	9.44517i	0.710157	−	0.510736i
$343$	−14.2552	−	14.2552i	−0.769710	−	0.769710i
$344$	1.52777	+	1.10999i	0.0823718	+	0.0598466i
$345$	−5.16632	−	3.04234i	−0.278145	−	0.163794i
$346$	4.05686	−	2.94748i	0.218098	−	0.158458i
$347$	4.52113	+	0.716076i	0.242707	+	0.0384410i	0.276603	−	0.960984i	$-0.410791\pi$
$347$	4.52113	+	0.716076i	0.242707	+	0.0384410i	−0.0338958	+	0.999425i	$0.510791\pi$
$348$	6.72250	−	4.09725i	0.360364	−	0.219636i
$349$		−	9.78119i		−	0.523575i	−0.965126	−	0.261787i	$-0.915688\pi$
$349$		−	9.78119i		−	0.523575i	0.965126	−	0.261787i	$-0.0843120\pi$
$350$	10.6972	−	0.427927i	0.571792	−	0.0228737i
$351$	5.46932	+	0.470345i	0.291931	+	0.0251052i
$352$	5.27263	+	2.68654i	0.281032	+	0.143193i
$353$	−1.69571	+	10.7063i	−0.0902538	+	0.569840i	0.900573	+	0.434704i	$0.143147\pi$
$353$	−1.69571	+	10.7063i	−0.0902538	+	0.569840i	−0.990827	+	0.135136i	$0.956853\pi$
$354$	−12.5256	+	0.955350i	−0.665727	+	0.0507763i
$355$	−2.64604	+	8.73402i	−0.140437	+	0.463554i
$356$	5.08679	−	7.00137i	0.269600	−	0.371072i
$357$	20.7575	−	4.93044i	1.09860	−	0.260947i
$358$	−0.495694	−	3.12969i	−0.0261982	−	0.165409i
$359$	6.51044	−	20.0371i	0.343608	−	1.05752i	−0.618717	−	0.785614i	$-0.712347\pi$
$359$	6.51044	−	20.0371i	0.343608	−	1.05752i	0.962325	−	0.271902i	$-0.0876527\pi$
$360$	3.86026	−	5.48620i	0.203453	−	0.289148i
$361$	−3.11386	−	9.58347i	−0.163887	−	0.504393i
$362$	5.56052	−	2.83323i	0.292254	−	0.148911i
$363$	−3.36411	+	41.4644i	−0.176570	+	2.17632i
$364$	2.15133	−	0.699010i	0.112760	−	0.0366381i
$365$	0.688068	−	0.123126i	0.0360151	−	0.00644472i
$366$	−5.59203	+	4.75273i	−0.292300	+	0.248429i
$367$	26.6770	−	4.22522i	1.39253	−	0.220555i	0.585311	−	0.810809i	$-0.300972\pi$
$367$	26.6770	−	4.22522i	1.39253	−	0.220555i	0.807218	+	0.590254i	$0.200972\pi$
$368$	−1.09463	+	1.09463i	−0.0570618	+	0.0570618i
$369$	0.784283	−	4.80153i	0.0408281	−	0.249958i
$370$	−0.298542	−	0.394094i	−0.0155205	−	0.0204880i
$371$	7.64135	+	10.5174i	0.396719	+	0.546037i
$372$	14.0119	+	12.0259i	0.726483	+	0.623516i
$373$	12.1464	−	23.8387i	0.628917	−	1.23432i	−0.328197	−	0.944609i	$-0.606441\pi$
$373$	12.1464	−	23.8387i	0.628917	−	1.23432i	0.957114	−	0.289711i	$-0.0935590\pi$
$374$	34.0432			1.76033
$375$	6.36917	−	18.2875i	0.328902	−	0.944364i
$376$	−4.81005			−0.248060
$377$	2.18003	−	4.27854i	0.112277	−	0.220356i
$378$	2.67559	−	10.7993i	0.137617	−	0.555455i
$379$	9.28018	+	12.7731i	0.476691	+	0.656109i	0.977865	−	0.209238i	$-0.0670983\pi$
$379$	9.28018	+	12.7731i	0.476691	+	0.656109i	−0.501174	+	0.865347i	$0.667098\pi$
$380$	−7.28080	−	9.61110i	−0.373497	−	0.493039i
$381$	−16.7525	+	6.89175i	−0.858257	+	0.353075i
$382$	−14.8555	+	14.8555i	−0.760073	+	0.760073i
$383$	−15.7705	+	2.49780i	−0.805836	+	0.127632i	−0.545744	−	0.837952i	$-0.683753\pi$
$383$	−15.7705	+	2.49780i	−0.805836	+	0.127632i	−0.260092	+	0.965584i	$0.583753\pi$
$384$	−1.12169	−	1.31977i	−0.0572411	−	0.0673495i
$385$	27.8892	−	4.99063i	1.42137	−	0.254346i
$386$	−9.42739	+	3.06314i	−0.479841	+	0.155910i
$387$	3.35207	−	4.56717i	0.170395	−	0.232162i
$388$	−10.7492	+	5.47700i	−0.545709	+	0.278053i
$389$	3.56490	+	10.9716i	0.180748	+	0.556284i	0.999849	−	0.0173647i	$-0.00552762\pi$
$389$	3.56490	+	10.9716i	0.180748	+	0.556284i	−0.819102	+	0.573648i	$0.805528\pi$
$390$	0.249289	−	4.08404i	0.0126232	−	0.206803i
$391$	−2.75201	+	8.46982i	−0.139175	+	0.428337i
$392$	0.377857	+	2.38569i	0.0190847	+	0.120496i
$393$	7.81799	+	32.9143i	0.394365	+	1.66031i
$394$	5.99998	−	8.25827i	0.302275	−	0.416046i
$395$	−0.612682	+	2.02233i	−0.0308274	+	0.101755i
$396$	8.13594	−	15.7788i	0.408846	−	0.792913i
$397$	−3.27643	+	20.6866i	−0.164439	+	1.03823i	0.758047	+	0.652200i	$0.226154\pi$
$397$	−3.27643	+	20.6866i	−0.164439	+	1.03823i	−0.922486	+	0.386030i	$0.873846\pi$
$398$	13.4673	+	6.86195i	0.675057	+	0.343958i
$399$	−17.0256	−	10.4900i	−0.852348	−	0.525155i
$400$	−4.15933	−	2.77489i	−0.207966	−	0.138744i
$401$			24.4394i			1.22045i	0.792229	+	0.610223i	$0.208920\pi$
$401$			24.4394i			1.22045i	−0.792229	+	0.610223i	$0.791080\pi$
$402$	1.16859	+	1.91735i	0.0582842	+	0.0956289i
$403$	11.1240	+	1.76187i	0.554125	+	0.0877648i
$404$	0.251023	−	0.182379i	0.0124889	−	0.00907370i
$405$	−16.4025	−	11.6601i	−0.815045	−	0.579397i
$406$	−7.87354	−	5.72046i	−0.390757	−	0.283902i
$407$	−0.925189	−	0.925189i	−0.0458599	−	0.0458599i
$408$	−9.19652	−	3.83537i	−0.455296	−	0.189879i
$409$	−9.31361	−	3.02618i	−0.460528	−	0.149635i	0.0695588	−	0.997578i	$-0.477841\pi$
$409$	−9.31361	−	3.02618i	−0.460528	−	0.149635i	−0.530087	+	0.847943i	$0.677841\pi$
$410$	−3.59226	−	0.495565i	−0.177409	−	0.0244742i
$411$	−4.89675	+	20.1816i	−0.241539	+	0.995483i
$412$	4.01069	+	7.87141i	0.197592	+	0.387797i
$413$	7.05006	+	13.8365i	0.346911	+	0.680851i
$414$	3.26800	+	3.29973i	0.160614	+	0.162173i
$415$	−12.1974	−	11.7192i	−0.598747	−	0.575274i
$416$	−1.00475	−	0.326463i	−0.0492619	−	0.0160062i
$417$	−15.5144	+	37.2007i	−0.759744	+	1.82173i
$418$	−22.5634	−	22.5634i	−1.10361	−	1.10361i
$419$	−20.8723	−	15.1646i	−1.01968	−	0.740840i	−0.0534618	−	0.998570i	$-0.517026\pi$
$419$	−20.8723	−	15.1646i	−1.01968	−	0.740840i	−0.966217	+	0.257730i	$0.917026\pi$
$420$	−8.09633	−	1.79387i	−0.395060	−	0.0875320i
$421$	−31.8859	+	23.1664i	−1.55402	+	1.12906i	−0.613316	+	0.789837i	$0.710165\pi$
$421$	−31.8859	+	23.1664i	−1.55402	+	1.12906i	−0.940705	+	0.339225i	$0.889835\pi$
$422$	3.92268	+	0.621291i	0.190953	+	0.0302440i
$423$	−0.0697075	+	14.4300i	−0.00338930	+	0.701610i
$424$		−	6.07158i		−	0.294862i
$425$	−28.5673	−	3.36053i	−1.38572	−	0.163010i
$426$	3.70809	−	6.01838i	0.179658	−	0.291591i
$427$	8.08350	+	4.11875i	0.391188	+	0.199320i
$428$	0.927381	−	5.85525i	0.0448267	−	0.283024i
$429$	−0.823500	−	10.7969i	−0.0397590	−	0.521280i
$430$	−3.46513	−	2.41323i	−0.167103	−	0.116376i
$431$	−3.61295	+	4.97279i	−0.174030	+	0.239531i	−0.887118	−	0.461543i	$-0.847296\pi$
$431$	−3.61295	+	4.97279i	−0.174030	+	0.239531i	0.713088	+	0.701074i	$0.247296\pi$
$432$	−3.97553	+	3.34591i	−0.191273	+	0.160980i
$433$	−2.61783	−	16.5283i	−0.125805	−	0.794299i	−0.967225	−	0.253919i	$-0.918280\pi$
$433$	−2.61783	−	16.5283i	−0.125805	−	0.794299i	0.841421	−	0.540380i	$-0.181720\pi$
$434$	7.05375	−	21.7092i	0.338591	−	1.04208i
$435$	−14.8458	+	9.46039i	−0.711803	+	0.453591i
$436$	−0.583300	−	1.79521i	−0.0279350	−	0.0859752i
$437$	7.43768	−	3.78968i	0.355792	−	0.181285i
$438$	−0.539668	−	0.0437846i	−0.0257863	−	0.00209211i
$439$	−19.1311	+	6.21606i	−0.913076	+	0.296676i	−0.727623	−	0.685977i	$-0.759375\pi$
$439$	−19.1311	+	6.21606i	−0.913076	+	0.296676i	−0.185453	+	0.982653i	$0.559375\pi$
$440$	−11.9077	−	5.77041i	−0.567677	−	0.275093i
$441$	7.16248	−	1.09898i	0.341070	−	0.0523326i
$442$	−6.00282	+	0.950753i	−0.285525	+	0.0452227i
$443$	17.1571	−	17.1571i	0.815159	−	0.815159i	−0.170243	−	0.985402i	$-0.554455\pi$
$443$	17.1571	−	17.1571i	0.815159	−	0.815159i	0.985402	+	0.170243i	$0.0544552\pi$
$444$	0.145699	+	0.354167i	0.00691459	+	0.0168080i
$445$	−11.0592	+	15.8798i	−0.524256	+	0.752774i
$446$	−7.86865	−	10.8303i	−0.372591	−	0.512828i
$447$	16.5983	−	19.3393i	0.785071	−	0.914716i
$448$	−0.972066	+	1.90779i	−0.0459258	+	0.0901345i
$449$	15.9242			0.751511			0.375755	−	0.926719i	$-0.377383\pi$
$449$	15.9242			0.751511			0.375755	+	0.926719i	$0.377383\pi$
$450$	−8.38485	+	12.4376i	−0.395266	+	0.586315i
$451$	−9.59671			−0.451891
$452$	−3.85086	+	7.55774i	−0.181129	+	0.355486i
$453$	9.64350	−	11.2360i	0.453091	−	0.527914i
$454$	−0.503096	−	0.692453i	−0.0236115	−	0.0324984i
$455$	−4.77832	+	1.65888i	−0.224011	+	0.0777696i
$456$	3.55330	+	8.63736i	0.166398	+	0.404482i
$457$	2.30257	−	2.30257i	0.107710	−	0.107710i	−0.651198	−	0.758908i	$-0.725733\pi$
$457$	2.30257	−	2.30257i	0.107710	−	0.107710i	0.758908	+	0.651198i	$0.225733\pi$
$458$	16.3422	−	2.58835i	0.763621	−	0.120946i
$459$	−11.6393	+	27.5337i	−0.543274	+	1.28516i
$460$	2.39826	−	2.49612i	0.111819	−	0.116382i
$461$	9.43135	−	3.06443i	0.439262	−	0.142725i	−0.0810333	−	0.996711i	$-0.525822\pi$
$461$	9.43135	−	3.06443i	0.439262	−	0.142725i	0.520295	+	0.853987i	$0.325822\pi$
$462$	−21.8742	−	1.77471i	−1.01768	−	0.0825668i
$463$	−20.5992	+	10.4958i	−0.957328	+	0.487783i	−0.861580	−	0.507623i	$-0.830524\pi$
$463$	−20.5992	+	10.4958i	−0.957328	+	0.487783i	−0.0957485	+	0.995406i	$0.530524\pi$
$464$	1.40458	+	4.32285i	0.0652059	+	0.200683i
$465$	−31.8628	−	26.2591i	−1.47760	−	1.21774i
$466$	−1.68432	+	5.18379i	−0.0780245	+	0.240135i
$467$	−0.726976	−	4.58995i	−0.0336405	−	0.212397i	0.965142	−	0.261726i	$-0.0842918\pi$
$467$	−0.726976	−	4.58995i	−0.0336405	−	0.212397i	−0.998783	+	0.0493288i	$0.984292\pi$
$468$	−0.993939	+	3.00948i	−0.0459448	+	0.139113i
$469$	1.63156	−	2.24565i	0.0753383	−	0.103694i
$470$	10.7535	−	0.215002i	0.496020	−	0.00991730i
$471$	−3.27611	−	42.9530i	−0.150955	−	1.97917i
$472$	1.13457	−	7.16336i	0.0522226	−	0.329721i
$473$	−9.95697	−	5.07333i	−0.457822	−	0.233272i
$474$	0.858596	−	1.39353i	0.0394366	−	0.0640072i
$475$	16.7067	+	21.1613i	0.766556	+	0.970949i
$476$			12.3178i			0.564585i
$477$	−18.2145	−	0.0879897i	−0.833986	−	0.00402877i
$478$	−8.60761	−	1.36331i	−0.393703	−	0.0623564i
$479$	12.7801	−	9.28530i	0.583939	−	0.424256i	−0.256203	−	0.966623i	$-0.582472\pi$
$479$	12.7801	−	9.28530i	0.583939	−	0.424256i	0.840142	+	0.542367i	$0.182472\pi$
$480$	2.56667	+	2.90038i	0.117152	+	0.132384i
$481$	0.188977	+	0.137300i	0.00861660	+	0.00626032i
$482$	−17.9787	−	17.9787i	−0.818908	−	0.818908i
$483$	2.20982	−	5.29875i	0.100550	−	0.241101i
$484$	−22.8426	−	7.42201i	−1.03830	−	0.337364i
$485$	23.7864	−	12.7250i	1.08008	−	0.577811i
$486$	9.98001	+	11.9750i	0.452702	+	0.543195i
$487$	0.0615473	+	0.120793i	0.00278898	+	0.00547367i	0.892397	−	0.451252i	$-0.149022\pi$
$487$	0.0615473	+	0.120793i	0.00278898	+	0.00547367i	−0.889608	+	0.456725i	$0.849022\pi$
$488$	−1.92361	−	3.77529i	−0.0870776	−	0.170899i
$489$	−0.820608	+	3.38207i	−0.0371092	+	0.152942i
$490$	−0.951382	−	5.31662i	−0.0429790	−	0.240180i
$491$	8.65368	+	2.81175i	0.390535	+	0.126893i	0.497701	−	0.867349i	$-0.334178\pi$
$491$	8.65368	+	2.81175i	0.390535	+	0.126893i	−0.107166	+	0.994241i	$0.534178\pi$
$492$	2.59248	+	1.08119i	0.116878	+	0.0487436i
$493$	18.4898	+	18.4898i	0.832738	+	0.832738i
$494$	4.60873	+	3.34844i	0.207357	+	0.150654i
$495$	−17.4836	+	35.6390i	−0.785829	+	1.60186i
$496$	−8.62475	+	6.26624i	−0.387263	+	0.281363i
$497$	−8.63111	−	1.36703i	−0.387158	−	0.0613198i
$498$	6.81893	+	11.1881i	0.305564	+	0.501349i
$499$			27.5900i			1.23510i	0.786532	+	0.617549i	$0.211874\pi$
$499$			27.5900i			1.23510i	−0.786532	+	0.617549i	$0.788126\pi$
$500$	9.42271	+	6.01769i	0.421396	+	0.269119i
$501$	21.8831	+	13.4828i	0.977667	+	0.602368i
$502$	−18.7945	−	9.57626i	−0.838838	−	0.427409i
$503$	−1.71307	+	10.8159i	−0.0763820	+	0.482257i	0.919611	+	0.392829i	$0.128504\pi$
$503$	−1.71307	+	10.8159i	−0.0763820	+	0.482257i	−0.995993	+	0.0894274i	$0.971496\pi$
$504$	5.70921	+	2.94381i	0.254308	+	0.131128i
$505$	−0.553041	+	0.418951i	−0.0246100	+	0.0186431i
$506$	5.38455	−	7.41120i	0.239372	−	0.329468i
$507$	−4.75677	−	20.0263i	−0.211256	−	0.889401i
$508$	−1.63607	−	10.3298i	−0.0725891	−	0.458309i
$509$	−2.83257	+	8.71775i	−0.125551	+	0.386407i	−0.994001	−	0.109370i	$-0.965117\pi$
$509$	−2.83257	+	8.71775i	−0.125551	+	0.386407i	0.868450	+	0.495777i	$0.165117\pi$
$510$	20.7314	+	8.16337i	0.918000	+	0.361480i
$511$	0.206834	+	0.636570i	0.00914980	+	0.0281602i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	25.9633	−	10.5346i	1.14631	−	0.465114i
$514$	−15.9501	+	5.18250i	−0.703529	+	0.228590i
$515$	−9.31821	−	17.4182i	−0.410610	−	0.767539i
$516$	2.11823	+	2.49230i	0.0932500	+	0.109717i
$517$	28.1136	−	4.45276i	1.23643	−	0.195832i
$518$	0.334760	−	0.334760i	0.0147085	−	0.0147085i
$519$	8.03233	−	3.30439i	0.352580	−	0.145047i
$520$	2.26083	+	0.684937i	0.0991441	+	0.0300365i
$521$	13.3932	+	18.4342i	0.586767	+	0.807615i	0.994417	−	0.105523i	$-0.0336517\pi$
$521$	13.3932	+	18.4342i	0.586767	+	0.807615i	−0.407650	+	0.913138i	$0.633652\pi$
$522$	12.9887	−	4.15104i	0.568502	−	0.181686i
$523$	16.3751	−	32.1380i	0.716035	−	1.40530i	−0.189867	−	0.981810i	$-0.560806\pi$
$523$	16.3751	−	32.1380i	0.716035	−	1.40530i	0.905902	−	0.423488i	$-0.139194\pi$
$524$	−19.5318			−0.853250
$525$	18.1805	+	3.64853i	0.793462	+	0.159235i
$526$	22.7518			0.992025
$527$	−27.8432	+	54.6453i	−1.21287	+	2.38039i
$528$	7.77776	+	6.67539i	0.338484	+	0.290509i
$529$	−12.1105	−	16.6686i	−0.526542	−	0.724723i
$530$	0.271390	+	13.5738i	0.0117884	+	0.589606i
$531$	−21.4734	−	3.50747i	−0.931866	−	0.152211i
$532$	8.16406	−	8.16406i	0.353957	−	0.353957i
$533$	1.69218	−	0.268016i	0.0732966	−	0.0116090i
$534$	11.4216	−	9.70732i	0.494259	−	0.420077i
$535$	−1.81155	+	13.1316i	−0.0783202	+	0.567728i
$536$	−1.23294	+	0.400605i	−0.0532548	+	0.0173035i
$537$	0.443825	−	5.47038i	0.0191525	−	0.236064i
$538$	9.22579	−	4.70077i	0.397752	−	0.202665i
$539$	−4.41696	−	13.5940i	−0.190252	−	0.585536i
$540$	8.73823	−	7.65789i	0.376034	−	0.329543i
$541$	10.6711	−	32.8422i	0.458786	−	1.41200i	−0.407847	−	0.913050i	$-0.633720\pi$
$541$	10.6711	−	32.8422i	0.458786	−	1.41200i	0.866633	−	0.498947i	$-0.166280\pi$
$542$	−0.100029	−	0.631560i	−0.00429663	−	0.0271278i
$543$	10.5166	−	2.49797i	0.451312	−	0.107198i
$544$	3.38144	−	4.65416i	0.144978	−	0.199545i
$545$	1.38428	+	3.98735i	0.0592961	+	0.170799i
$546$	3.90663	−	0.297966i	0.167188	−	0.0127518i
$547$	−3.53445	+	22.3156i	−0.151122	+	0.954148i	0.789268	+	0.614049i	$0.210460\pi$
$547$	−3.53445	+	22.3156i	−0.151122	+	0.954148i	−0.940390	+	0.340098i	$0.889540\pi$
$548$	−10.6831	−	5.44330i	−0.456359	−	0.232526i
$549$	−11.3536	+	5.71604i	−0.484561	+	0.243955i
$550$	26.8790	+	12.3682i	1.14612	+	0.527381i
$551$		−	24.5096i		−	1.04414i
$552$	−2.28956	+	1.39545i	−0.0974500	+	0.0593942i
$553$	−1.99850	−	0.316532i	−0.0849851	−	0.0134603i
$554$	−24.5631	+	17.8461i	−1.04358	+	0.758209i
$555$	−0.341560	−	0.785270i	−0.0144984	−	0.0333329i
$556$	−18.8265	−	13.6782i	−0.798420	−	0.580086i
$557$	−3.76017	−	3.76017i	−0.159323	−	0.159323i	0.622943	−	0.782267i	$-0.285937\pi$
$557$	−3.76017	−	3.76017i	−0.159323	−	0.159323i	−0.782267	+	0.622943i	$0.785937\pi$
$558$	18.6735	+	25.9647i	0.790513	+	1.09918i
$559$	1.89740	+	0.616502i	0.0802513	+	0.0260752i
$560$	2.08790	−	4.30854i	0.0882298	−	0.182069i
$561$	57.3019	+	13.9034i	2.41929	+	0.587003i
$562$	9.85907	+	19.3495i	0.415880	+	0.816210i
$563$	−11.0089	−	21.6061i	−0.463969	−	0.910590i	−0.997882	−	0.0650508i	$-0.979279\pi$
$563$	−11.0089	−	21.6061i	−0.463969	−	0.910590i	0.533913	−	0.845539i	$-0.320721\pi$
$564$	−8.09634	−	1.96445i	−0.340918	−	0.0827185i
$565$	8.27124	−	17.0684i	0.347974	−	0.718071i
$566$	−3.29063	−	1.06919i	−0.138315	−	0.0449414i
$567$	8.91407	−	17.0848i	0.374356	−	0.717493i
$568$	2.88591	+	2.88591i	0.121090	+	0.121090i
$569$	24.5934	+	17.8681i	1.03101	+	0.749071i	0.968510	−	0.248974i	$-0.0800934\pi$
$569$	24.5934	+	17.8681i	1.03101	+	0.749071i	0.0624977	+	0.998045i	$0.480093\pi$
$570$	−8.32990	−	19.1510i	−0.348901	−	0.802149i
$571$	4.57335	−	3.32274i	0.191389	−	0.139052i	−0.487964	−	0.872864i	$-0.662260\pi$
$571$	4.57335	−	3.32274i	0.191389	−	0.139052i	0.679353	+	0.733811i	$0.262260\pi$
$572$	6.17473	+	0.977982i	0.258179	+	0.0408915i
$573$	−31.0720	+	18.9379i	−1.29805	+	0.791141i
$574$		−	3.47236i		−	0.144934i
$575$	−5.25003	+	5.68757i	−0.218941	+	0.237188i
$576$	−1.34904	−	2.67957i	−0.0562101	−	0.111649i
$577$	−22.8994	−	11.6678i	−0.953316	−	0.485739i	−0.0930933	−	0.995657i	$-0.529676\pi$
$577$	−22.8994	−	11.6678i	−0.953316	−	0.485739i	−0.860223	+	0.509919i	$0.829676\pi$
$578$	2.51787	−	15.8972i	0.104729	−	0.661236i
$579$	−17.1193	+	1.30572i	−0.711454	+	0.0542639i
$580$	−3.33333	−	9.60146i	−0.138409	−	0.398679i
$581$	9.52039	−	13.1037i	0.394972	−	0.543633i
$582$	−20.3301	+	4.82891i	−0.842708	+	0.200165i
$583$	5.62058	+	35.4869i	0.232781	+	1.46972i
$584$	0.0965991	−	0.297301i	0.00399730	−	0.0123024i
$585$	2.08755	−	6.77250i	0.0863096	−	0.280008i
$586$	5.35461	+	16.4798i	0.221197	+	0.680773i
$587$	−12.8802	+	6.56280i	−0.531623	+	0.270876i	−0.699129	−	0.714995i	$-0.746429\pi$
$587$	−12.8802	+	6.56280i	−0.531623	+	0.270876i	0.167506	+	0.985871i	$0.446429\pi$
$588$	−0.338318	+	4.16995i	−0.0139520	+	0.171966i
$589$	54.6723	−	17.7641i	2.25273	−	0.731957i
$590$	−2.21627	+	16.0653i	−0.0912423	+	0.661397i
$591$	13.4720	−	11.4500i	0.554163	−	0.470990i
$592$	−0.218383	+	0.0345885i	−0.00897549	+	0.00142158i
$593$	27.1124	−	27.1124i	1.11337	−	1.11337i	0.120680	−	0.992691i	$-0.461492\pi$
$593$	27.1124	−	27.1124i	1.11337	−	1.11337i	0.992691	−	0.120680i	$-0.0385075\pi$
$594$	20.1387	−	23.2363i	0.826299	−	0.953396i
$595$	−0.550586	−	27.5379i	−0.0225718	−	1.12894i
$596$	8.64870	+	11.9039i	0.354265	+	0.487603i
$597$	19.8659	+	17.0503i	0.813058	+	0.697821i
$598$	−0.742476	+	1.45719i	−0.0303621	+	0.0595890i
$599$	−22.2597			−0.909506			−0.454753	−	0.890618i	$-0.650272\pi$
$599$	−22.2597			−0.909506			−0.454753	+	0.890618i	$0.650272\pi$
$600$	−5.86775	−	6.36942i	−0.239550	−	0.260031i
$601$	−0.661317			−0.0269757			−0.0134878	−	0.999909i	$-0.504293\pi$
$601$	−0.661317			−0.0269757			−0.0134878	+	0.999909i	$0.504293\pi$
$602$	1.83568	−	3.60272i	0.0748165	−	0.146836i
$603$	1.18393	+	3.70457i	0.0482135	+	0.150862i
$604$	5.02485	+	6.91612i	0.204458	+	0.281413i
$605$	51.3992	+	15.5718i	2.08967	+	0.633083i
$606$	0.497011	−	0.204463i	0.0201897	−	0.00830576i
$607$	−25.2285	+	25.2285i	−1.02399	+	1.02399i	−0.0242876	+	0.999705i	$0.507732\pi$
$607$	−25.2285	+	25.2285i	−1.02399	+	1.02399i	−0.999705	+	0.0242876i	$0.992268\pi$
$608$	−5.32589	+	0.843538i	−0.215993	+	0.0342100i
$609$	−10.9166	−	12.8444i	−0.442362	−	0.520480i
$610$	4.46921	+	8.35414i	0.180953	+	0.338249i
$611$	−4.83290	+	1.57031i	−0.195518	+	0.0635278i
$612$	−13.9133	−	10.2117i	−0.562412	−	0.412782i
$613$	−22.2583	+	11.3412i	−0.899003	+	0.458065i	−0.841485	−	0.540280i	$-0.818318\pi$
$613$	−22.2583	+	11.3412i	−0.899003	+	0.458065i	−0.0575173	+	0.998345i	$0.518318\pi$
$614$	7.34770	+	22.6139i	0.296529	+	0.912623i
$615$	−5.84414	−	2.30124i	−0.235658	−	0.0927950i
$616$	3.91542	−	12.0504i	0.157757	−	0.485525i
$617$	−4.87738	−	30.7946i	−0.196356	−	1.23974i	−0.867131	−	0.498081i	$-0.834038\pi$
$617$	−4.87738	−	30.7946i	−0.196356	−	1.23974i	0.670775	−	0.741661i	$-0.265962\pi$
$618$	3.53610	+	14.8873i	0.142243	+	0.598853i
$619$	2.12975	−	2.93135i	0.0856019	−	0.117821i	−0.764068	−	0.645135i	$-0.776801\pi$
$619$	2.12975	−	2.93135i	0.0856019	−	0.117821i	0.849670	+	0.527314i	$0.176801\pi$
$620$	19.0016	−	14.3945i	0.763122	−	0.578096i
$621$	4.15311	+	6.88882i	0.166659	+	0.276439i
$622$	−1.21703	+	7.68404i	−0.0487985	+	0.308102i
$623$	−16.5103	−	8.41243i	−0.661472	−	0.337037i
$624$	−1.55788	−	0.959853i	−0.0623651	−	0.0384249i
$625$	−21.3346	−	13.0321i	−0.853384	−	0.521283i
$626$			20.7996i			0.831321i
$627$	−28.7639	−	47.1939i	−1.14872	−	1.88474i
$628$	24.5648	+	3.89068i	0.980241	+	0.155255i
$629$	−1.02906	+	0.747655i	−0.0410312	+	0.0298109i
$630$	−12.8952	−	6.32606i	−0.513758	−	0.252036i
$631$	4.12680	+	2.99829i	0.164285	+	0.119360i	0.666890	−	0.745156i	$-0.267625\pi$
$631$	4.12680	+	2.99829i	0.164285	+	0.119360i	−0.502605	+	0.864516i	$0.667625\pi$
$632$	0.668222	+	0.668222i	0.0265805	+	0.0265805i
$633$	6.34896	+	2.64781i	0.252349	+	0.105241i
$634$	−0.206145	−	0.0669805i	−0.00818706	−	0.00266014i
$635$	4.11937	+	23.0203i	0.163472	+	0.913533i
$636$	2.47967	−	10.2198i	0.0983253	−	0.405240i
$637$	1.15849	+	2.27367i	0.0459012	+	0.0900861i
$638$	−12.2112	−	23.9657i	−0.483444	−	0.948813i
$639$	8.69945	−	8.61580i	0.344145	−	0.340836i
$640$	−1.97166	+	1.05478i	−0.0779367	+	0.0416937i
$641$	−45.1681	−	14.6760i	−1.78403	−	0.579668i	−0.784836	−	0.619703i	$-0.787253\pi$
$641$	−45.1681	−	14.6760i	−1.78403	−	0.579668i	−0.999198	+	0.0400355i	$0.987253\pi$
$642$	3.95230	−	9.47689i	0.155985	−	0.374023i
$643$	−17.9186	−	17.9186i	−0.706639	−	0.706639i	0.259188	−	0.965827i	$-0.416545\pi$
$643$	−17.9186	−	17.9186i	−0.706639	−	0.706639i	−0.965827	+	0.259188i	$0.916545\pi$
$644$	2.68158	+	1.94828i	0.105669	+	0.0767731i
$645$	−4.84697	−	5.47715i	−0.190849	−	0.215663i
$646$	−25.0965	+	18.2337i	−0.987409	+	0.717395i
$647$	7.06356	+	1.11876i	0.277697	+	0.0439829i	0.293730	−	0.955889i	$-0.405103\pi$
$647$	7.06356	+	1.11876i	0.277697	+	0.0439829i	−0.0160323	+	0.999871i	$0.505103\pi$
$648$	−8.05816	+	4.00825i	−0.316554	+	0.157459i
$649$			42.9184i			1.68469i
$650$	−5.08498	−	1.43020i	−0.199449	−	0.0560972i
$651$	20.7391	−	33.6604i	0.812831	−	1.31926i
$652$	−1.79029	−	0.912200i	−0.0701133	−	0.0357245i
$653$	−3.64054	+	22.9855i	−0.142465	+	0.899490i	0.808118	+	0.589021i	$0.200486\pi$
$653$	−3.64054	+	22.9855i	−0.142465	+	0.899490i	−0.950583	+	0.310470i	$0.899514\pi$
$654$	−0.248642	−	3.25995i	−0.00972269	−	0.127474i
$655$	43.6657	−	0.873041i	1.70616	−	0.0341125i
$656$	−0.953223	+	1.31200i	−0.0372171	+	0.0512250i
$657$	−0.890494	−	0.294102i	−0.0347415	−	0.0114740i
$658$	1.61113	+	10.1723i	0.0628085	+	0.396557i
$659$	−1.14382	+	3.52031i	−0.0445568	+	0.137132i	−0.970860	−	0.239647i	$-0.922968\pi$
$659$	−1.14382	+	3.52031i	−0.0445568	+	0.137132i	0.926303	+	0.376779i	$0.122968\pi$
$660$	−17.6865	−	14.5760i	−0.688446	−	0.567370i
$661$	−11.4157	−	35.1339i	−0.444019	−	1.36655i	−0.883556	−	0.468326i	$-0.844857\pi$
$661$	−11.4157	−	35.1339i	−0.444019	−	1.36655i	0.439537	−	0.898224i	$-0.355143\pi$
$662$	−6.40470	+	3.26336i	−0.248926	+	0.126834i
$663$	−10.4923	−	0.851267i	−0.407488	−	0.0330605i
$664$	−7.19438	+	2.33760i	−0.279196	+	0.0907163i
$665$	−17.8868	+	18.6167i	−0.693622	+	0.721924i
$666$	0.100599	+	0.655643i	0.00389815	+	0.0254056i
$667$	6.94972	−	1.10073i	0.269094	−	0.0426203i
$668$	−10.4933	+	10.4933i	−0.405999	+	0.405999i
$669$	−8.82147	−	21.4432i	−0.341058	−	0.829044i
$670$	2.73847	−	0.950713i	0.105796	−	0.0367292i
$671$	14.7379	+	20.2849i	0.568949	+	0.783092i
$672$	−2.41535	+	2.81421i	−0.0931740	+	0.108561i
$673$	−0.542210	+	1.06415i	−0.0209006	+	0.0410198i	−0.901221	−	0.433360i	$-0.857328\pi$
$673$	−0.542210	+	1.06415i	−0.0209006	+	0.0410198i	0.880320	+	0.474380i	$0.157328\pi$
$674$	−6.75390			−0.260151
$675$	−19.1931	+	17.5107i	−0.738742	+	0.673988i
$676$	11.8839			0.457073
$677$	15.6087	−	30.6338i	0.599892	−	1.17735i	−0.368898	−	0.929470i	$-0.620265\pi$
$677$	15.6087	−	30.6338i	0.599892	−	1.17735i	0.968790	−	0.247884i	$-0.0797351\pi$
$678$	−9.56844	+	11.1486i	−0.367474	+	0.428158i
$679$	15.1832	+	20.8979i	0.582679	+	0.801988i
$680$	−7.35159	+	10.5561i	−0.281921	+	0.404807i
$681$	−0.564016	−	1.37101i	−0.0216132	−	0.0525373i
$682$	44.6088	−	44.6088i	1.70816	−	1.70816i
$683$	−44.5125	+	7.05008i	−1.70322	+	0.269764i	−0.930849	−	0.365405i	$-0.880930\pi$
$683$	−44.5125	+	7.05008i	−1.70322	+	0.269764i	−0.772373	+	0.635169i	$0.780930\pi$
$684$	2.45340	+	15.9897i	0.0938081	+	0.611382i
$685$	24.1266	+	11.6916i	0.921831	+	0.446715i
$686$	19.1733	−	6.22977i	0.732038	−	0.237854i
$687$	28.5645	+	2.31751i	1.08980	+	0.0884185i
$688$	−1.68260	+	0.857327i	−0.0641485	+	0.0326853i
$689$	−1.98215	−	6.10043i	−0.0755138	−	0.232408i
$690$	5.05621	−	3.22203i	0.192487	−	0.122661i
$691$	1.10289	−	3.39434i	0.0419558	−	0.129127i	−0.927885	−	0.372867i	$-0.878375\pi$
$691$	1.10289	−	3.39434i	0.0419558	−	0.129127i	0.969840	+	0.243741i	$0.0783746\pi$
$692$	0.784450	+	4.95282i	0.0298203	+	0.188278i
$693$	−36.0941	−	11.9207i	−1.37110	−	0.452832i
$694$	−2.69058	+	3.70326i	−0.102133	+	0.140574i
$695$	42.7002	+	29.7378i	1.61971	+	1.12802i
$696$	0.598727	+	7.84991i	0.0226947	+	0.297550i
$697$	−1.45946	+	9.21466i	−0.0552809	+	0.349030i
$698$	8.71510	+	4.44057i	0.329871	+	0.168078i
$699$	−4.95215	+	8.03754i	−0.187308	+	0.304008i
$700$	−4.47516	+	9.72559i	−0.169145	+	0.367593i
$701$		−	19.6139i		−	0.740807i	−0.928871	−	0.370403i	$-0.879219\pi$
$701$		−	19.6139i		−	0.740807i	0.928871	−	0.370403i	$-0.120781\pi$
$702$	−2.90210	+	4.65967i	−0.109533	+	0.175868i
$703$	1.17758	+	0.186511i	0.0444133	+	0.00703438i
$704$	−4.78745	+	3.47829i	−0.180434	+	0.131093i
$705$	18.1882	+	4.02988i	0.685006	+	0.151774i
$706$	−8.76956	−	6.37146i	−0.330047	−	0.239793i
$707$	−0.469776	−	0.469776i	−0.0176677	−	0.0176677i
$708$	4.83527	−	11.5941i	0.181721	−	0.435733i
$709$	−22.4237	−	7.28590i	−0.842140	−	0.273628i	−0.143990	−	0.989579i	$-0.545993\pi$
$709$	−22.4237	−	7.28590i	−0.842140	−	0.273628i	−0.698150	+	0.715951i	$0.745993\pi$
$710$	−6.58079	−	6.32280i	−0.246973	−	0.237291i
$711$	2.01433	−	1.99496i	0.0755432	−	0.0748168i
$712$	3.92891	+	7.71092i	0.147242	+	0.288979i
$713$	7.49238	+	14.7046i	0.280592	+	0.550692i
$714$	−5.03066	+	20.7335i	−0.188268	+	0.775930i
$715$	−13.8481	−	1.91040i	−0.517889	−	0.0714447i
$716$	3.01361	+	0.979183i	0.112624	+	0.0365938i
$717$	−13.9317	−	5.81015i	−0.520287	−	0.216984i
$718$	14.8975	+	14.8975i	0.555969	+	0.555969i
$719$	30.2210	+	21.9569i	1.12705	+	0.818853i	0.985263	−	0.171044i	$-0.0547140\pi$
$719$	30.2210	+	21.9569i	1.12705	+	0.818853i	0.141791	+	0.989897i	$0.454714\pi$
$720$	3.13572	+	5.93020i	0.116861	+	0.221005i
$721$	15.3031	−	11.1183i	0.569916	−	0.414068i
$722$	9.95259	+	1.57634i	0.370397	+	0.0586651i
$723$	−22.9194	−	37.6046i	−0.852381	−	1.39853i
$724$			6.24071i			0.231934i
$725$	7.88123	+	21.3162i	0.292701	+	0.791665i
$726$	−35.4178	−	21.8219i	−1.31448	−	0.809886i
$727$	−37.8579	−	19.2896i	−1.40407	−	0.715411i	−0.422476	−	0.906374i	$-0.638839\pi$
$727$	−37.8579	−	19.2896i	−1.40407	−	0.715411i	−0.981597	+	0.190964i	$0.938839\pi$
$728$	−0.353862	+	2.23419i	−0.0131150	+	0.0828047i
$729$	11.9078	+	24.2323i	0.441031	+	0.897492i
$730$	−0.202670	+	0.668971i	−0.00750115	+	0.0247597i
$731$	−6.38561	+	8.78903i	−0.236180	+	0.325074i
$732$	−1.69599	−	7.14023i	−0.0626855	−	0.263911i
$733$	−6.98056	−	44.0735i	−0.257833	−	1.62789i	−0.688398	−	0.725333i	$-0.741686\pi$
$733$	−6.98056	−	44.0735i	−0.257833	−	1.62789i	0.430565	−	0.902559i	$-0.358314\pi$
$734$	−8.34641	+	25.6876i	−0.308072	+	0.948147i
$735$	0.569962	−	9.33755i	0.0210233	−	0.344421i
$736$	−0.478373	−	1.47228i	−0.0176331	−	0.0542690i
$737$	6.83537	−	3.48279i	0.251784	−	0.128290i
$738$	3.92214	+	2.87865i	0.144376	+	0.105965i
$739$	−8.01855	+	2.60538i	−0.294967	+	0.0958406i	−0.452762	−	0.891631i	$-0.649561\pi$
$739$	−8.01855	+	2.60538i	−0.294967	+	0.0958406i	0.157795	+	0.987472i	$0.449561\pi$
$740$	0.486676	−	0.0870881i	0.0178906	−	0.00320142i
$741$	6.38996	+	7.51837i	0.234741	+	0.276194i
$742$	−12.8402	+	2.03368i	−0.471378	+	0.0746589i
$743$	−24.9192	+	24.9192i	−0.914196	+	0.914196i	−0.996599	−	0.0824029i	$-0.973741\pi$
$743$	−24.9192	+	24.9192i	−0.914196	+	0.914196i	0.0824029	+	0.996599i	$0.473741\pi$
$744$	−17.0765	+	7.02502i	−0.626053	+	0.257550i
$745$	−19.8673	−	26.2261i	−0.727882	−	0.960849i
$746$	15.7261	+	21.6451i	0.575772	+	0.792482i
$747$	6.90844	+	21.6168i	0.252767	+	0.790916i
$748$	−15.4553	+	30.3327i	−0.565101	+	1.10907i
$749$	−12.6933			−0.463804
$750$	13.4028	+	13.9773i	0.489400	+	0.510380i
$751$	−8.40064			−0.306544			−0.153272	−	0.988184i	$-0.548981\pi$
$751$	−8.40064			−0.306544			−0.153272	+	0.988184i	$0.548981\pi$
$752$	2.18372	−	4.28579i	0.0796320	−	0.156287i
$753$	−27.7241	−	23.7946i	−1.01032	−	0.867125i
$754$	2.82250	+	3.88484i	0.102789	+	0.141477i
$755$	−11.5428	−	15.2372i	−0.420086	−	0.554539i
$756$	8.40754	+	7.28674i	0.305779	+	0.265016i
$757$	5.57829	−	5.57829i	0.202746	−	0.202746i	−0.598429	−	0.801176i	$-0.704208\pi$
$757$	5.57829	−	5.57829i	0.202746	−	0.202746i	0.801176	+	0.598429i	$0.204208\pi$
$758$	−15.5940	+	2.46985i	−0.566400	+	0.0897089i
$759$	12.0901	−	10.2755i	0.438843	−	0.372978i
$760$	11.8690	−	2.12389i	0.430533	−	0.0770416i
$761$	−5.92036	+	1.92364i	−0.214613	+	0.0697320i	−0.414350	−	0.910118i	$-0.635991\pi$
$761$	−5.92036	+	1.92364i	−0.214613	+	0.0697320i	0.199737	+	0.979849i	$0.435991\pi$
$762$	1.46488	−	18.0554i	0.0530669	−	0.654077i
$763$	−3.60114	+	1.83487i	−0.130370	+	0.0664268i
$764$	−6.49209	−	19.9806i	−0.234875	−	0.722872i
$765$	31.5613	+	22.2075i	1.14110	+	0.802914i
$766$	4.93411	−	15.1856i	0.178276	−	0.548679i
$767$	−1.19862	−	7.56779i	−0.0432796	−	0.273257i
$768$	1.68517	−	0.400270i	0.0608082	−	0.0144435i
$769$	−2.22958	+	3.06876i	−0.0804008	+	0.110662i	−0.847323	−	0.531078i	$-0.821787\pi$
$769$	−2.22958	+	3.06876i	−0.0804008	+	0.110662i	0.766922	+	0.641740i	$0.221787\pi$
$770$	−8.21475	+	27.1152i	−0.296039	+	0.977163i
$771$	−28.9640	+	2.20914i	−1.04311	+	0.0795601i
$772$	1.55066	−	9.79050i	0.0558096	−	0.352368i
$773$	30.3587	+	15.4685i	1.09193	+	0.556364i	0.904742	−	0.425960i	$-0.140064\pi$
$773$	30.3587	+	15.4685i	1.09193	+	0.556364i	0.187185	+	0.982325i	$0.440064\pi$
$774$	2.54757	+	5.06017i	0.0915704	+	0.181884i
$775$	−41.8369	+	33.0299i	−1.50283	+	1.18647i
$776$		−	12.0641i		−	0.433077i
$777$	0.700189	−	0.426754i	0.0251192	−	0.0153097i
$778$	−11.3942	−	1.80467i	−0.408503	−	0.0647005i
$779$	7.07466	−	5.14004i	0.253476	−	0.184161i
$780$	3.52573	+	2.07623i	0.126241	+	0.0743411i
$781$	−19.5390	−	14.1959i	−0.699159	−	0.507969i
$782$	−6.29727	−	6.29727i	−0.225190	−	0.225190i
$783$	23.5581	−	1.68240i	0.841898	−	0.0601240i
$784$	−2.29721	−	0.746410i	−0.0820433	−	0.0266575i
$785$	−55.0914	−	7.60007i	−1.96630	−	0.271258i
$786$	−32.8761	−	7.97690i	−1.17265	−	0.284527i
$787$	14.2544	+	27.9758i	0.508114	+	0.997230i	0.992485	+	0.122367i	$0.0390486\pi$
$787$	14.2544	+	27.9758i	0.508114	+	0.997230i	−0.484371	+	0.874863i	$0.660951\pi$
$788$	4.63424	+	9.09520i	0.165088	+	0.324003i
$789$	38.2961	+	9.29197i	1.36338	+	0.330803i
$790$	−1.52376	−	1.46402i	−0.0542130	−	0.0520876i
$791$	17.2729	+	5.61232i	0.614155	+	0.199551i
$792$	10.3654	+	14.4126i	0.368317	+	0.512129i
$793$	−3.16524	−	3.16524i	−0.112401	−	0.112401i
$794$	−16.9444	−	12.3108i	−0.601334	−	0.436895i
$795$	−5.08680	+	22.9584i	−0.180410	+	0.814249i
$796$	−12.2281	+	8.88422i	−0.433413	+	0.314893i
$797$	10.4366	+	1.65300i	0.369685	+	0.0585523i	0.338513	−	0.940962i	$-0.390076\pi$
$797$	10.4366	+	1.65300i	0.369685	+	0.0585523i	0.0311718	+	0.999514i	$0.490076\pi$
$798$	17.0761	−	10.4076i	0.604488	−	0.368425i
$799$		−	27.6716i		−	0.978949i
$800$	4.36074	−	2.44621i	0.154175	−	0.0864867i
$801$	23.1894	−	11.6749i	0.819358	−	0.412511i
$802$	−21.7757	−	11.0953i	−0.768926	−	0.391787i
$803$	−0.289381	+	1.82708i	−0.0102120	+	0.0644762i
$804$	−2.23890	+	0.170765i	−0.0789601	+	0.00602243i
$805$	−6.08208	−	4.23576i	−0.214365	−	0.149291i
$806$	−6.62002	+	9.11167i	−0.233180	+	0.320945i
$807$	17.4488	−	4.14454i	0.614227	−	0.145895i
$808$	0.0485388	+	0.306462i	0.00170759	+	0.0107813i
$809$	4.15772	−	12.7961i	0.146178	−	0.449889i	−0.850983	−	0.525193i	$-0.823993\pi$
$809$	4.15772	−	12.7961i	0.146178	−	0.449889i	0.997161	+	0.0753048i	$0.0239930\pi$
$810$	17.8358	−	9.32112i	0.626687	−	0.327511i
$811$	6.32531	+	19.4673i	0.222112	+	0.683590i	0.998572	+	0.0534235i	$0.0170133\pi$
$811$	6.32531	+	19.4673i	0.222112	+	0.683590i	−0.776460	+	0.630166i	$0.782987\pi$
$812$	8.67148	−	4.41834i	0.304309	−	0.155053i
$813$	0.0895624	−	1.10390i	0.00314109	−	0.0387156i
$814$	1.24438	−	0.404322i	0.0436154	−	0.0141715i
$815$	4.04319	+	1.95931i	0.141627	+	0.0686317i
$816$	7.59247	−	6.45294i	0.265790	−	0.225898i
$817$	10.0575	−	1.59296i	0.351869	−	0.0557306i
$818$	6.92463	−	6.92463i	0.242114	−	0.242114i
$819$	6.69738	+	1.09395i	0.234025	+	0.0382257i
$820$	2.07240	−	2.97574i	0.0723714	−	0.103917i
$821$	11.1279	+	15.3163i	0.388368	+	0.534543i	0.957777	−	0.287512i	$-0.0928280\pi$
$821$	11.1279	+	15.3163i	0.388368	+	0.534543i	−0.569409	+	0.822054i	$0.692828\pi$
$822$	−15.7588	−	13.5253i	−0.549652	−	0.471748i
$823$	−7.17013	+	14.0722i	−0.249935	+	0.490525i	−0.981553	−	0.191190i	$-0.938765\pi$
$823$	−7.17013	+	14.0722i	−0.249935	+	0.490525i	0.731618	+	0.681715i	$0.238765\pi$
$824$	−8.83429			−0.307757
$825$	40.1918	+	31.7958i	1.39930	+	1.10699i
$826$	−15.5291			−0.540326
$827$	−3.08387	+	6.05244i	−0.107237	+	0.210464i	−0.938389	−	0.345581i	$-0.887682\pi$
$827$	−3.08387	+	6.05244i	−0.107237	+	0.210464i	0.831152	+	0.556045i	$0.187682\pi$
$828$	−4.42372	+	1.41377i	−0.153735	+	0.0491317i
$829$	11.0240	+	15.1733i	0.382880	+	0.526989i	0.956345	−	0.292241i	$-0.0944010\pi$
$829$	11.0240	+	15.1733i	0.382880	+	0.526989i	−0.573465	+	0.819230i	$0.694401\pi$
$830$	15.9794	−	5.54756i	0.554654	−	0.192558i
$831$	−48.6333	+	20.0071i	−1.68707	+	0.694038i
$832$	0.747028	−	0.747028i	0.0258985	−	0.0258985i
$833$	−13.7246	+	2.17376i	−0.475528	+	0.0753162i
$834$	−26.1027	−	30.7122i	−0.903862	−	1.06348i
$835$	22.9901	−	23.9281i	0.795604	−	0.828067i
$836$	30.3476	−	9.86055i	1.04960	−	0.341034i
$837$	20.8274	+	51.3306i	0.719899	+	1.77424i
$838$	22.9876	−	11.7128i	0.794093	−	0.404611i
$839$	−5.00273	−	15.3968i	−0.172713	−	0.531557i	0.826808	−	0.562484i	$-0.190154\pi$
$839$	−5.00273	−	15.3968i	−0.172713	−	0.531557i	−0.999522	+	0.0309268i	$0.990154\pi$
$840$	5.27401	−	6.39948i	0.181971	−	0.220803i
$841$	−2.57725	+	7.93197i	−0.0888709	+	0.273516i
$842$	−6.16556	−	38.9278i	−0.212479	−	1.34154i
$843$	8.69245	+	36.5959i	0.299384	+	1.26043i
$844$	−2.33443	+	3.21307i	−0.0803545	+	0.110598i
$845$	−26.5679	+	0.531192i	−0.913963	+	0.0182736i
$846$	−12.8256	−	6.61319i	−0.440952	−	0.227366i
$847$	−8.04490	+	50.7935i	−0.276426	+	1.74529i
$848$	5.40982	+	2.75644i	0.185774	+	0.0946566i
$849$	−5.10216	−	3.14358i	−0.175106	−	0.107887i
$850$	15.9635	−	23.9280i	0.547545	−	0.820724i
$851$			0.342281i			0.0117332i
$852$	3.67898	+	6.03622i	0.126040	+	0.206797i
$853$	−32.4823	−	5.14470i	−1.11217	−	0.176151i	−0.426803	−	0.904345i	$-0.640360\pi$
$853$	−32.4823	−	5.14470i	−1.11217	−	0.176151i	−0.685371	+	0.728194i	$0.740360\pi$
$854$	−7.33967	+	5.33258i	−0.251158	+	0.182477i
$855$	−6.19959	−	35.6373i	−0.212022	−	1.21877i
$856$	4.79605	+	3.48453i	0.163926	+	0.119099i
$857$	−14.2417	−	14.2417i	−0.486489	−	0.486489i	0.420708	−	0.907196i	$-0.361782\pi$
$857$	−14.2417	−	14.2417i	−0.486489	−	0.486489i	−0.907196	+	0.420708i	$0.861782\pi$
$858$	9.99398	+	4.16795i	0.341189	+	0.142291i
$859$	29.9968	+	9.74655i	1.02348	+	0.332548i	0.772208	−	0.635369i	$-0.219152\pi$
$859$	29.9968	+	9.74655i	1.02348	+	0.332548i	0.251269	+	0.967917i	$0.419152\pi$
$860$	3.72333	−	1.99187i	0.126965	−	0.0679222i
$861$	1.41813	−	5.84472i	0.0483299	−	0.199188i
$862$	−2.79055	−	5.47676i	−0.0950465	−	0.186539i
$863$	−9.85205	−	19.3357i	−0.335368	−	0.658196i	0.660318	−	0.750986i	$-0.270421\pi$
$863$	−9.85205	−	19.3357i	−0.335368	−	0.658196i	−0.995686	+	0.0927901i	$0.970421\pi$
$864$	−1.17637	−	5.06124i	−0.0400211	−	0.172187i
$865$	−1.97512	−	11.0376i	−0.0671559	−	0.375288i
$866$	15.9153	+	5.17119i	0.540824	+	0.175724i
$867$	10.7306	−	25.7300i	0.364431	−	0.873838i
$868$	16.1407	+	16.1407i	0.547852	+	0.547852i
$869$	−4.52418	−	3.28701i	−0.153472	−	0.111504i
$870$	−1.68940	−	17.5227i	−0.0572762	−	0.594074i
$871$	−1.10801	+	0.805017i	−0.0375435	+	0.0272770i
$872$	1.86436	+	0.295286i	0.0631352	+	0.00999963i
$873$	−36.1920	−	0.174834i	−1.22491	−	0.00591723i
$874$			8.34750i			0.282358i
$875$	9.57005	−	21.9428i	0.323527	−	0.741801i
$876$	0.284016	−	0.460970i	0.00959602	−	0.0155747i
$877$	−6.74142	−	3.43493i	−0.227642	−	0.115989i	0.336450	−	0.941701i	$-0.390774\pi$
$877$	−6.74142	−	3.43493i	−0.227642	−	0.115989i	−0.564092	+	0.825712i	$0.690774\pi$
$878$	3.14677	−	19.8679i	0.106198	−	0.670510i
$879$	2.28250	+	29.9258i	0.0769868	+	1.00937i
$880$	10.5474	−	7.99012i	0.355554	−	0.269347i
$881$	18.8656	−	25.9662i	0.635597	−	0.874825i	−0.362774	−	0.931877i	$-0.618170\pi$
$881$	18.8656	−	25.9662i	0.635597	−	0.874825i	0.998371	+	0.0570525i	$0.0181702\pi$
$882$	−2.27249	+	6.88074i	−0.0765189	+	0.231687i
$883$	−4.49099	−	28.3550i	−0.151134	−	0.954222i	−0.940375	−	0.340139i	$-0.889526\pi$
$883$	−4.49099	−	28.3550i	−0.151134	−	0.954222i	0.789241	−	0.614083i	$-0.210474\pi$
$884$	1.87810	−	5.78018i	0.0631672	−	0.194409i
$885$	−10.2916	+	26.1361i	−0.345948	+	0.878557i
$886$	7.49794	+	23.0763i	0.251898	+	0.775263i
$887$	10.8136	−	5.50981i	0.363086	−	0.185001i	−0.262924	−	0.964816i	$-0.584687\pi$
$887$	10.8136	−	5.50981i	0.363086	−	0.185001i	0.626010	+	0.779815i	$0.284687\pi$
$888$	−0.381711	−	0.0309692i	−0.0128094	−	0.00103926i
$889$	−21.2974	+	6.91994i	−0.714291	+	0.232087i
$890$	−9.12822	−	17.0631i	−0.305979	−	0.571956i
$891$	43.3875	−	30.8868i	1.45353	−	1.03475i
$892$	13.2221	−	2.09418i	0.442710	−	0.0701183i
$893$	−18.3403	+	18.3403i	−0.613736	+	0.613736i
$894$	9.69597	+	23.5690i	0.324282	+	0.788265i
$895$	−6.78107	−	2.05438i	−0.226666	−	0.0686703i
$896$	−1.25854	−	1.73224i	−0.0420450	−	0.0578699i
$897$	−1.84487	+	2.14953i	−0.0615985	+	0.0717708i
$898$	−7.22945	+	14.1886i	−0.241250	+	0.473479i
$899$	48.4565			1.61611
$900$	−7.27536	−	13.1175i	−0.242512	−	0.437250i
$901$	34.9289			1.16365
$902$	4.35682	−	8.55073i	0.145066	−	0.284708i
$903$	4.56120	−	5.31444i	0.151787	−	0.176853i
$904$	−4.98574	−	6.86228i	−0.165823	−	0.228236i
$905$	−0.278950	−	13.9519i	−0.00927262	−	0.463776i
$906$	5.63331	+	13.6935i	0.187154	+	0.454935i
$907$	18.7112	−	18.7112i	0.621295	−	0.621295i	−0.324567	−	0.945863i	$-0.605219\pi$
$907$	18.7112	−	18.7112i	0.621295	−	0.621295i	0.945863	+	0.324567i	$0.105219\pi$
$908$	0.845381	−	0.133895i	0.0280549	−	0.00444347i
$909$	0.920078	−	0.141173i	0.0305171	−	0.00468243i
$910$	0.691235	−	5.01063i	0.0229142	−	0.166101i
$911$	−37.0222	+	12.0293i	−1.22660	+	0.398547i	−0.849482	−	0.527618i	$-0.823085\pi$
$911$	−37.0222	+	12.0293i	−1.22660	+	0.398547i	−0.377119	+	0.926165i	$0.623085\pi$
$912$	−9.30911	−	0.755271i	−0.308255	−	0.0250095i
$913$	39.8854	−	20.3226i	1.32002	−	0.672581i
$914$	1.00626	+	3.09695i	0.0332842	+	0.102438i
$915$	4.11074	+	15.8870i	0.135897	+	0.525209i
$916$	−5.11297	+	15.7361i	−0.168937	+	0.519935i
$917$	6.54220	+	41.3058i	0.216042	+	1.36404i
$918$	−19.2486	−	22.8707i	−0.635297	−	0.754845i
$919$	13.4831	−	18.5579i	0.444766	−	0.612168i	−0.526497	−	0.850177i	$-0.676495\pi$
$919$	13.4831	−	18.5579i	0.444766	−	0.612168i	0.971263	+	0.238009i	$0.0764948\pi$
$920$	1.13527	+	3.27008i	0.0374287	+	0.107811i
$921$	3.13209	+	41.0648i	0.103206	+	1.35313i
$922$	−1.55131	+	9.79461i	−0.0510898	+	0.322568i
$923$	3.84176	+	1.95747i	0.126453	+	0.0644311i
$924$	11.5119	−	18.6843i	0.378715	−	0.614669i
$925$	−1.08413	+	0.216450i	−0.0356460	+	0.00711682i
$926$		−	23.1191i		−	0.759740i
$927$	−0.128027	+	26.5026i	−0.00420496	+	0.870459i
$928$	−4.48935	−	0.711043i	−0.147370	−	0.0233411i
$929$	0.473139	−	0.343755i	0.0155232	−	0.0112782i	−0.579997	−	0.814619i	$-0.696946\pi$
$929$	0.473139	−	0.343755i	0.0155232	−	0.0112782i	0.595520	+	0.803341i	$0.296946\pi$
$930$	37.8625	−	16.4686i	1.24156	−	0.540026i
$931$	10.5372	+	7.65572i	0.345342	+	0.250906i
$932$	−3.85413	−	3.85413i	−0.126246	−	0.126246i
$933$	−5.18673	+	12.4368i	−0.169806	+	0.407163i
$934$	4.41971	+	1.43605i	0.144617	+	0.0469891i
$935$	33.1963	−	68.5032i	1.08564	−	2.24029i
$936$	−2.23023	−	2.25188i	−0.0728974	−	0.0736051i
$937$	−25.3343	−	49.7213i	−0.827634	−	1.62432i	−0.780268	−	0.625445i	$-0.784917\pi$
$937$	−25.3343	−	49.7213i	−0.827634	−	1.62432i	−0.0473659	−	0.998878i	$-0.515083\pi$
$938$	1.26017	+	2.47323i	0.0411461	+	0.0807538i
$939$	−8.49469	+	35.0102i	−0.277214	+	1.14251i
$940$	−4.69040	+	9.67901i	−0.152984	+	0.315695i
$941$	−12.5712	−	4.08462i	−0.409808	−	0.133155i	0.0968556	−	0.995298i	$-0.469121\pi$
$941$	−12.5712	−	4.08462i	−0.409808	−	0.133155i	−0.506664	+	0.862144i	$0.669121\pi$
$942$	39.7588	+	16.5812i	1.29541	+	0.540246i
$943$	1.77519	+	1.77519i	0.0578082	+	0.0578082i
$944$	5.86752	+	4.26300i	0.190972	+	0.138749i
$945$	−19.1218	−	15.9146i	−0.622032	−	0.517701i
$946$	9.04074	−	6.56848i	0.293940	−	0.213560i
$947$	17.8550	+	2.82795i	0.580210	+	0.0918962i	0.439639	−	0.898174i	$-0.355106\pi$
$947$	17.8550	+	2.82795i	0.580210	+	0.0918962i	0.140571	+	0.990071i	$0.455106\pi$
$948$	0.851854	+	1.39767i	0.0276669	+	0.0453941i
$949$		−	0.330250i		−	0.0107204i
$950$	−26.4396	+	5.27874i	−0.857813	+	0.171265i
$951$	−0.319630	−	0.196933i	−0.0103647	−	0.00638600i
$952$	−10.9752	−	5.59216i	−0.355709	−	0.181243i
$953$	8.17990	−	51.6458i	0.264973	−	1.67297i	−0.392698	−	0.919667i	$-0.628458\pi$
$953$	8.17990	−	51.6458i	0.264973	−	1.67297i	0.657671	−	0.753305i	$-0.271542\pi$
$954$	8.34763	−	16.1893i	0.270264	−	0.524149i
$955$	15.4070	+	44.3788i	0.498557	+	1.43607i
$956$	5.12250	−	7.05051i	0.165673	−	0.228030i
$957$	−10.7662	−	45.3265i	−0.348022	−	1.46520i
$958$	2.47121	+	15.6026i	0.0798412	+	0.504097i
$959$	−7.93318	+	24.4158i	−0.256176	+	0.788428i
$960$	−3.74950	+	0.970177i	−0.121015	+	0.0313123i
$961$	25.5409	+	78.6068i	0.823900	+	2.53570i
$962$	−0.208129	+	0.106047i	−0.00671033	+	0.00341909i
$963$	10.5230	−	14.3375i	0.339098	−	0.462019i
$964$	24.1813	−	7.85699i	0.778828	−	0.253056i
$965$	−3.02907	+	21.9572i	−0.0975094	+	0.706826i
$966$	3.71798	+	4.37455i	0.119624	+	0.140749i
$967$	−30.7047	+	4.86314i	−0.987395	+	0.156388i	−0.629187	−	0.777254i	$-0.716612\pi$
$967$	−30.7047	+	4.86314i	−0.987395	+	0.156388i	−0.358208	+	0.933642i	$0.616612\pi$
$968$	16.9834	−	16.9834i	0.545867	−	0.545867i
$969$	−49.6895	+	20.4416i	−1.59626	+	0.656679i
$970$	0.539248	+	26.9708i	0.0173142	+	0.865981i
$971$	−25.2468	−	34.7493i	−0.810210	−	1.11516i	−0.991291	−	0.131690i	$-0.957960\pi$
$971$	−25.2468	−	34.7493i	−0.810210	−	1.11516i	0.181081	−	0.983468i	$-0.442040\pi$
$972$	−15.2006	+	3.45574i	−0.487559	+	0.110843i
$973$	−22.6208	+	44.3957i	−0.725188	+	1.42326i
$974$	−0.135570			−0.00434393
$975$	−7.97500	−	4.48408i	−0.255405	−	0.143605i
$976$	4.23711			0.135627
$977$	−26.9394	+	52.8715i	−0.861867	+	1.69151i	−0.150590	+	0.988596i	$0.548117\pi$
$977$	−26.9394	+	52.8715i	−0.861867	+	1.69151i	−0.711276	+	0.702912i	$0.751883\pi$
$978$	−2.64090	−	2.26659i	−0.0844466	−	0.0724777i
$979$	−30.1017	−	41.4314i	−0.962054	−	1.32415i
$980$	5.16906	+	1.56601i	0.165120	+	0.0500243i
$981$	0.912865	−	5.58874i	0.0291455	−	0.178435i
$982$	−6.43398	+	6.43398i	−0.205317	+	0.205317i
$983$	37.5537	−	5.94792i	1.19778	−	0.189709i	0.474492	−	0.880260i	$-0.342632\pi$
$983$	37.5537	−	5.94792i	1.19778	−	0.189709i	0.723284	+	0.690550i	$0.242632\pi$
$984$	−2.14031	+	1.81907i	−0.0682305	+	0.0579899i
$985$	−10.7669	−	20.1263i	−0.343063	−	0.641277i
$986$	−24.8687	+	8.08033i	−0.791981	+	0.257330i
$987$	−1.44255	+	17.7801i	−0.0459168	+	0.565948i
$988$	−5.07580	+	2.58625i	−0.161483	+	0.0822796i
$989$	0.903372	+	2.78029i	0.0287255	+	0.0884081i
$990$	−23.8172	−	31.7578i	−0.756961	−	1.00933i
$991$	9.31171	−	28.6585i	0.295796	−	0.910367i	−0.687157	−	0.726509i	$-0.741141\pi$
$991$	9.31171	−	28.6585i	0.295796	−	0.910367i	0.982953	−	0.183858i	$-0.0588585\pi$
$992$	−1.66771	−	10.5295i	−0.0529499	−	0.334313i
$993$	−12.1132	+	2.87721i	−0.384402	+	0.0913054i
$994$	5.13648	−	7.06976i	0.162919	−	0.224239i
$995$	26.9403	−	20.4083i	0.854063	−	0.646988i
$996$	−13.0644	+	0.996443i	−0.413960	+	0.0315735i
$997$	5.29952	−	33.4599i	0.167838	−	1.05968i	−0.749625	−	0.661863i	$-0.769766\pi$
$997$	5.29952	−	33.4599i	0.167838	−	1.05968i	0.917463	−	0.397822i	$-0.130234\pi$
$998$	−24.5829	−	12.5256i	−0.778157	−	0.396491i
$999$	−0.0984382	+	1.14467i	−0.00311445	+	0.0362158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.83.1	yes	80
3.2	odd	2	inner	150.2.l.a.83.7	yes	80
5.2	odd	4		750.2.l.c.107.5		80
5.3	odd	4		750.2.l.a.107.6		80
5.4	even	2		750.2.l.b.143.10		80
15.2	even	4		750.2.l.c.107.6		80
15.8	even	4		750.2.l.a.107.5		80
15.14	odd	2		750.2.l.b.143.4		80
25.3	odd	20		750.2.l.b.257.4		80
25.4	even	10		750.2.l.a.743.5		80
25.21	even	5		750.2.l.c.743.6		80
25.22	odd	20	inner	150.2.l.a.47.7	yes	80
75.29	odd	10		750.2.l.a.743.6		80
75.47	even	20	inner	150.2.l.a.47.1	✓	80
75.53	even	20		750.2.l.b.257.10		80
75.71	odd	10		750.2.l.c.743.5		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.1	✓	80	75.47	even	20	inner
150.2.l.a.47.7	yes	80	25.22	odd	20	inner
150.2.l.a.83.1	yes	80	1.1	even	1	trivial
150.2.l.a.83.7	yes	80	3.2	odd	2	inner
750.2.l.a.107.5		80	15.8	even	4
750.2.l.a.107.6		80	5.3	odd	4
750.2.l.a.743.5		80	25.4	even	10
750.2.l.a.743.6		80	75.29	odd	10
750.2.l.b.143.4		80	15.14	odd	2
750.2.l.b.143.10		80	5.4	even	2
750.2.l.b.257.4		80	25.3	odd	20
750.2.l.b.257.10		80	75.53	even	20
750.2.l.c.107.5		80	5.2	odd	4
750.2.l.c.107.6		80	15.2	even	4
750.2.l.c.743.5		80	75.71	odd	10
750.2.l.c.743.6		80	25.21	even	5

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.12805 + 1.31434i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.35023 + 1.78238i) q^{5} +(-0.658960 - 1.60180i) q^{6} +(-1.51403 + 1.51403i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-0.454984 - 2.96530i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.12805 + 1.31434i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.35023 + 1.78238i) q^{5} +(-0.658960 - 1.60180i) q^{6} +(-1.51403 + 1.51403i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-0.454984 - 2.96530i) q^{9} +(-2.20110 + 0.393876i) q^{10} +(-5.62798 + 1.82864i) q^{11} +(1.72638 + 0.140065i) q^{12} +(0.941310 - 0.479621i) q^{13} +(-0.661655 - 2.03636i) q^{14} +(-3.86579 - 0.235967i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(0.899945 + 5.68203i) q^{17} +(2.84866 + 0.940823i) q^{18} +(3.16950 - 4.36244i) q^{19} +(0.648334 - 2.14001i) q^{20} +(-0.282042 - 3.69786i) q^{21} +(0.925718 - 5.84476i) q^{22} +(1.37932 + 0.702799i) q^{23} +(-0.908558 + 1.47463i) q^{24} +(-1.35377 + 4.81324i) q^{25} +1.05646i q^{26} +(4.41066 + 2.74701i) q^{27} +(2.11480 + 0.334951i) q^{28} +(3.67723 - 2.67167i) q^{29} +(1.96528 - 3.33732i) q^{30} +(8.62475 + 6.26624i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.94521 - 9.45990i) q^{33} +(-5.47129 - 1.77773i) q^{34} +(-4.74286 - 0.654296i) q^{35} +(-2.13154 + 2.11105i) q^{36} +(0.100380 + 0.197006i) q^{37} +(2.44804 + 4.80455i) q^{38} +(-0.431463 + 1.77824i) q^{39} +(1.61243 + 1.54922i) q^{40} +(1.54235 + 0.501139i) q^{41} +(3.42286 + 1.42749i) q^{42} +(1.33532 + 1.33532i) q^{43} +(4.78745 + 3.47829i) q^{44} +(4.67096 - 4.81478i) q^{45} +(-1.25240 + 0.909919i) q^{46} +(-4.75083 - 0.752458i) q^{47} +(-0.901424 - 1.47900i) q^{48} +2.41543i q^{49} +(-3.67403 - 3.39139i) q^{50} +(-8.48331 - 5.22681i) q^{51} +(-0.941310 - 0.479621i) q^{52} +(0.949805 - 5.99683i) q^{53} +(-4.45000 + 2.68281i) q^{54} +(-10.8584 - 7.56214i) q^{55} +(-1.25854 + 1.73224i) q^{56} +(2.15837 + 9.08688i) q^{57} +(0.711043 + 4.48935i) q^{58} +(2.24119 - 6.89769i) q^{59} +(2.08135 + 3.26619i) q^{60} +(-1.30934 - 4.02973i) q^{61} +(-9.49882 + 4.83989i) q^{62} +(5.17841 + 3.80069i) q^{63} +(0.951057 - 0.309017i) q^{64} +(2.12585 + 1.03018i) q^{65} +(6.63774 + 7.80992i) q^{66} +(-1.28043 + 0.202800i) q^{67} +(4.06788 - 4.06788i) q^{68} +(-2.47967 + 1.02010i) q^{69} +(2.73620 - 3.92888i) q^{70} +(2.39892 + 3.30183i) q^{71} +(-0.913257 - 2.85761i) q^{72} +(0.141918 - 0.278530i) q^{73} -0.221105 q^{74} +(-4.79911 - 7.20892i) q^{75} -5.39228 q^{76} +(5.75231 - 11.2895i) q^{77} +(-1.38854 - 1.19174i) q^{78} +(0.555462 + 0.764528i) q^{79} +(-2.11239 + 0.733356i) q^{80} +(-8.58598 + 2.69833i) q^{81} +(-1.14673 + 1.14673i) q^{82} +(-7.47149 + 1.18337i) q^{83} +(-2.82585 + 2.40172i) q^{84} +(-8.91242 + 9.27607i) q^{85} +(-1.79600 + 0.583556i) q^{86} +(-0.636640 + 7.84692i) q^{87} +(-5.27263 + 2.68654i) q^{88} +(2.67429 + 8.23061i) q^{89} +(2.16943 + 6.34772i) q^{90} +(-0.699010 + 2.15133i) q^{91} +(-0.242168 - 1.52899i) q^{92} +(-17.9652 + 4.26719i) q^{93} +(2.82728 - 3.89142i) q^{94} +(12.0551 - 0.241026i) q^{95} +(1.72703 - 0.131724i) q^{96} +(1.88725 - 11.9156i) q^{97} +(-2.15217 - 1.09658i) q^{98} +(7.98311 + 15.8566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more