LMFDB - Embedded newform 150.2.l.a.47.7

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			47.7
Character	$\chi$	$=$	150.47
Dual form			150.2.l.a.83.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.453990 + 0.891007i) q^{2} +(-0.666690 + 1.59860i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.35023 + 1.78238i) q^{5} +(-1.72703 + 0.131724i) q^{6} +(-1.51403 - 1.51403i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(-2.11105 - 2.13154i) q^{9} +O(q^{10})$	\(q+(0.453990 + 0.891007i) q^{2} +(-0.666690 + 1.59860i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.35023 + 1.78238i) q^{5} +(-1.72703 + 0.131724i) q^{6} +(-1.51403 - 1.51403i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(-2.11105 - 2.13154i) q^{9} +(-2.20110 - 0.393876i) q^{10} +(5.62798 + 1.82864i) q^{11} +(-0.901424 - 1.47900i) q^{12} +(0.941310 + 0.479621i) q^{13} +(0.661655 - 2.03636i) q^{14} +(-1.94913 - 3.34677i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.899945 + 5.68203i) q^{17} +(0.940823 - 2.84866i) q^{18} +(3.16950 + 4.36244i) q^{19} +(-0.648334 - 2.14001i) q^{20} +(3.42972 - 1.41094i) 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} +(4.81490 - 1.95364i) q^{27} +(2.11480 - 0.334951i) q^{28} +(-3.67723 - 2.67167i) q^{29} +(2.09711 - 3.25609i) q^{30} +(8.62475 - 6.26624i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.67539 + 7.77776i) q^{33} +(-5.47129 + 1.77773i) q^{34} +(4.74286 - 0.654296i) q^{35} +(2.96530 - 0.454984i) q^{36} +(0.100380 - 0.197006i) q^{37} +(-2.44804 + 4.80455i) q^{38} +(-1.39429 + 1.18502i) q^{39} +(1.61243 - 1.54922i) q^{40} +(-1.54235 + 0.501139i) q^{41} +(2.81421 + 2.41535i) q^{42} +(1.33532 - 1.33532i) q^{43} +(-4.78745 + 3.47829i) q^{44} +(6.64962 - 0.884628i) q^{45} +(-1.25240 - 0.909919i) q^{46} +(4.75083 - 0.752458i) q^{47} +(1.72638 + 0.140065i) 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} +(3.92663 + 3.40317i) q^{54} +(-10.8584 + 7.56214i) q^{55} +(1.25854 + 1.73224i) q^{56} +(-9.08688 + 2.15837i) q^{57} +(0.711043 - 4.48935i) q^{58} +(-2.24119 - 6.89769i) q^{59} +(3.85327 + 0.390300i) q^{60} +(-1.30934 + 4.02973i) q^{61} +(9.49882 + 4.83989i) q^{62} +(-0.0310298 + 6.42341i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-2.12585 + 1.03018i) q^{65} +(-9.96060 - 2.41679i) q^{66} +(-1.28043 - 0.202800i) q^{67} +(-4.06788 - 4.06788i) q^{68} +(-0.203915 - 2.67353i) q^{69} +(2.73620 + 3.92888i) q^{70} +(-2.39892 + 3.30183i) q^{71} +(1.75161 + 2.43554i) q^{72} +(0.141918 + 0.278530i) q^{73} +0.221105 q^{74} +(8.59700 + 1.04480i) q^{75} -5.39228 q^{76} +(-5.75231 - 11.2895i) q^{77} +(-1.68885 - 0.704330i) q^{78} +(0.555462 - 0.764528i) q^{79} +(2.11239 + 0.733356i) q^{80} +(-0.0869513 + 8.99958i) q^{81} +(-1.14673 - 1.14673i) q^{82} +(7.47149 + 1.18337i) q^{83} +(-0.874463 + 3.60403i) q^{84} +(-8.91242 - 9.27607i) q^{85} +(1.79600 + 0.583556i) q^{86} +(6.72250 - 4.09725i) q^{87} +(-5.27263 - 2.68654i) q^{88} +(-2.67429 + 8.23061i) q^{89} +(3.80707 + 5.52324i) q^{90} +(-0.699010 - 2.15133i) q^{91} +(0.242168 - 1.52899i) q^{92} +(4.26719 + 17.9652i) q^{93} +(2.82728 + 3.89142i) q^{94} +(-12.0551 - 0.241026i) q^{95} +(0.658960 + 1.60180i) 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{17}{20}\right)$

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
$3$	−0.666690	+	1.59860i	−0.384914	+	0.922953i
$3$	−0.666690	+	1.59860i	−0.384914	+	0.922953i
$4$	−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
$6$	−1.72703	+	0.131724i	−0.705059	+	0.0537762i
$7$	−1.51403	−	1.51403i	−0.572249	−	0.572249i	0.360507	−	0.932756i	$-0.382604\pi$
$7$	−1.51403	−	1.51403i	−0.572249	−	0.572249i	−0.932756	+	0.360507i	$0.882604\pi$
$8$	−0.987688	−	0.156434i	−0.349201	−	0.0553079i
$9$	−2.11105	−	2.13154i	−0.703683	−	0.710514i
$10$	−2.20110	−	0.393876i	−0.696050	−	0.124555i
$11$	5.62798	+	1.82864i	1.69690	+	0.551357i	0.988068	−	0.154020i	$-0.0492219\pi$
$11$	5.62798	+	1.82864i	1.69690	+	0.551357i	0.708833	+	0.705376i	$0.249222\pi$
$12$	−0.901424	−	1.47900i	−0.260219	−	0.426950i
$13$	0.941310	+	0.479621i	0.261072	+	0.133023i	0.579628	−	0.814881i	$-0.303198\pi$
$13$	0.941310	+	0.479621i	0.261072	+	0.133023i	−0.318556	+	0.947904i	$0.603198\pi$
$14$	0.661655	−	2.03636i	0.176835	−	0.544241i
$15$	−1.94913	−	3.34677i	−0.503264	−	0.864132i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−0.899945	+	5.68203i	−0.218269	+	1.37809i	0.598497	+	0.801125i	$0.295765\pi$
$17$	−0.899945	+	5.68203i	−0.218269	+	1.37809i	−0.816766	+	0.576969i	$0.804235\pi$
$18$	0.940823	−	2.84866i	0.221754	−	0.671435i
$19$	3.16950	+	4.36244i	0.727133	+	1.00081i	0.999257	+	0.0385508i	$0.0122742\pi$
$19$	3.16950	+	4.36244i	0.727133	+	1.00081i	−0.272123	+	0.962262i	$0.587726\pi$
$20$	−0.648334	−	2.14001i	−0.144972	−	0.478522i
$21$	3.42972	−	1.41094i	0.748425	−	0.307892i
$22$	0.925718	+	5.84476i	0.197364	+	1.24611i
$23$	−1.37932	+	0.702799i	−0.287608	+	0.146544i	−0.591843	−	0.806054i	$-0.701599\pi$
$23$	−1.37932	+	0.702799i	−0.287608	+	0.146544i	0.304235	+	0.952597i	$0.401599\pi$
$24$	0.908558	−	1.47463i	0.185459	−	0.301007i
$25$	−1.35377	−	4.81324i	−0.270755	−	0.962648i
$26$			1.05646i			0.207188i
$27$	4.81490	−	1.95364i	0.926628	−	0.375979i
$28$	2.11480	−	0.334951i	0.399659	−	0.0632998i
$29$	−3.67723	−	2.67167i	−0.682845	−	0.496116i	0.191455	−	0.981501i	$-0.438679\pi$
$29$	−3.67723	−	2.67167i	−0.682845	−	0.496116i	−0.874300	+	0.485386i	$0.838679\pi$
$30$	2.09711	−	3.25609i	0.382877	−	0.594479i
$31$	8.62475	−	6.26624i	1.54905	−	1.12545i	0.604726	−	0.796433i	$-0.293282\pi$
$31$	8.62475	−	6.26624i	1.54905	−	1.12545i	0.944324	−	0.329017i	$-0.106718\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−6.67539	+	7.77776i	−1.16204	+	1.35393i
$34$	−5.47129	+	1.77773i	−0.938319	+	0.304878i
$35$	4.74286	−	0.654296i	0.801690	−	0.110596i
$36$	2.96530	−	0.454984i	0.494216	−	0.0758307i
$37$	0.100380	−	0.197006i	0.0165023	−	0.0323876i	−0.882608	−	0.470109i	$-0.844214\pi$
$37$	0.100380	−	0.197006i	0.0165023	−	0.0323876i	0.899111	+	0.437722i	$0.144214\pi$
$38$	−2.44804	+	4.80455i	−0.397125	+	0.779402i
$39$	−1.39429	+	1.18502i	−0.223264	+	0.189755i
$40$	1.61243	−	1.54922i	0.254947	−	0.244953i
$41$	−1.54235	+	0.501139i	−0.240874	+	0.0782648i	−0.426966	−	0.904268i	$-0.640418\pi$
$41$	−1.54235	+	0.501139i	−0.240874	+	0.0782648i	0.186092	+	0.982532i	$0.440418\pi$
$42$	2.81421	+	2.41535i	0.434243	+	0.372696i
$43$	1.33532	−	1.33532i	0.203634	−	0.203634i	−0.597921	−	0.801555i	$-0.704006\pi$
$43$	1.33532	−	1.33532i	0.203634	−	0.203634i	0.801555	+	0.597921i	$0.204006\pi$
$44$	−4.78745	+	3.47829i	−0.721735	+	0.524371i
$45$	6.64962	−	0.884628i	0.991267	−	0.131873i
$46$	−1.25240	−	0.909919i	−0.184656	−	0.134160i
$47$	4.75083	−	0.752458i	0.692980	−	0.109757i	0.199998	−	0.979796i	$-0.435907\pi$
$47$	4.75083	−	0.752458i	0.692980	−	0.109757i	0.492983	+	0.870039i	$0.335907\pi$
$48$	1.72638	+	0.140065i	0.249181	+	0.0202167i
$49$		−	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	−0.962950	−	0.269680i	$-0.913082\pi$
$53$	−0.949805	−	5.99683i	−0.130466	−	0.823728i	0.832484	−	0.554049i	$-0.186918\pi$
$54$	3.92663	+	3.40317i	0.534347	+	0.463113i
$55$	−10.8584	+	7.56214i	−1.46415	+	1.01968i
$56$	1.25854	+	1.73224i	0.168180	+	0.231480i
$57$	−9.08688	+	2.15837i	−1.20359	+	0.285883i
$58$	0.711043	−	4.48935i	0.0933645	−	0.589480i
$59$	−2.24119	−	6.89769i	−0.291779	−	0.898002i	−0.984285	−	0.176590i	$-0.943493\pi$
$59$	−2.24119	−	6.89769i	−0.291779	−	0.898002i	0.692506	−	0.721412i	$-0.256507\pi$
$60$	3.85327	+	0.390300i	0.497455	+	0.0503874i
$61$	−1.30934	+	4.02973i	−0.167644	+	0.515954i	−0.999221	−	0.0394543i	$-0.987438\pi$
$61$	−1.30934	+	4.02973i	−0.167644	+	0.515954i	0.831578	+	0.555408i	$0.187438\pi$
$62$	9.49882	+	4.83989i	1.20635	+	0.614667i
$63$	−0.0310298	+	6.42341i	−0.00390939	+	0.809273i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−2.12585	+	1.03018i	−0.263679	+	0.127778i
$66$	−9.96060	−	2.41679i	−1.22607	−	0.297486i
$67$	−1.28043	−	0.202800i	−0.156429	−	0.0247759i	0.0777287	−	0.996975i	$-0.475233\pi$
$67$	−1.28043	−	0.202800i	−0.156429	−	0.0247759i	−0.234158	+	0.972199i	$0.575233\pi$
$68$	−4.06788	−	4.06788i	−0.493303	−	0.493303i
$69$	−0.203915	−	2.67353i	−0.0245485	−	0.321855i
$70$	2.73620	+	3.92888i	0.327038	+	0.469591i
$71$	−2.39892	+	3.30183i	−0.284700	+	0.391856i	−0.927283	−	0.374360i	$-0.877862\pi$
$71$	−2.39892	+	3.30183i	−0.284700	+	0.391856i	0.642584	+	0.766215i	$0.277862\pi$
$72$	1.75161	+	2.43554i	0.206429	+	0.287031i
$73$	0.141918	+	0.278530i	0.0166102	+	0.0325994i	0.899163	−	0.437615i	$-0.144177\pi$
$73$	0.141918	+	0.278530i	0.0166102	+	0.0325994i	−0.882552	+	0.470214i	$0.844177\pi$
$74$	0.221105			0.0257030
$75$	8.59700	+	1.04480i	0.992696	+	0.120643i
$76$	−5.39228			−0.618537
$77$	−5.75231	−	11.2895i	−0.655537	−	1.28656i
$78$	−1.68885	−	0.704330i	−0.191225	−	0.0797496i
$79$	0.555462	−	0.764528i	0.0624944	−	0.0860162i	−0.776626	−	0.629962i	$-0.783070\pi$
$79$	0.555462	−	0.764528i	0.0624944	−	0.0860162i	0.839120	+	0.543946i	$0.183070\pi$
$80$	2.11239	+	0.733356i	0.236172	+	0.0819917i
$81$	−0.0869513	+	8.99958i	−0.00966125	+	0.999953i
$82$	−1.14673	−	1.14673i	−0.126635	−	0.126635i
$83$	7.47149	+	1.18337i	0.820102	+	0.129891i	0.552367	−	0.833601i	$-0.313725\pi$
$83$	7.47149	+	1.18337i	0.820102	+	0.129891i	0.267735	+	0.963493i	$0.413725\pi$
$84$	−0.874463	+	3.60403i	−0.0954117	+	0.393232i
$85$	−8.91242	−	9.27607i	−0.966687	−	1.00613i
$86$	1.79600	+	0.583556i	0.193668	+	0.0629264i
$87$	6.72250	−	4.09725i	0.720728	−	0.439272i
$88$	−5.27263	−	2.68654i	−0.562064	−	0.286386i
$89$	−2.67429	+	8.23061i	−0.283474	+	0.872443i	0.703378	+	0.710816i	$0.251674\pi$
$89$	−2.67429	+	8.23061i	−0.283474	+	0.872443i	−0.986852	+	0.161627i	$0.948326\pi$
$90$	3.80707	+	5.52324i	0.401301	+	0.582201i
$91$	−0.699010	−	2.15133i	−0.0732762	−	0.225521i
$92$	0.242168	−	1.52899i	0.0252477	−	0.159408i
$93$	4.26719	+	17.9652i	0.442487	+	1.86290i
$94$	2.82728	+	3.89142i	0.291612	+	0.401369i
$95$	−12.0551	−	0.241026i	−1.23683	−	0.0247288i
$96$	0.658960	+	1.60180i	0.0672548	+	0.163483i
$97$	1.88725	+	11.9156i	0.191621	+	1.20985i	0.876577	+	0.481262i	$0.159821\pi$
$97$	1.88725	+	11.9156i	0.191621	+	1.20985i	−0.684956	+	0.728584i	$0.740179\pi$
$98$	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	$0.995086\pi$
$102$	0.805776	−	9.93161i	0.0797837	−	0.983375i
$103$	−8.72553	+	1.38199i	−0.859752	+	0.136171i	−0.570717	−	0.821147i	$-0.693335\pi$
$103$	−8.72553	+	1.38199i	−0.859752	+	0.136171i	−0.289035	+	0.957318i	$0.593335\pi$
$104$	−0.854692	−	0.620970i	−0.0838094	−	0.0608911i
$105$	−2.11606	+	8.01815i	−0.206506	+	0.782492i
$106$	4.91201	−	3.56879i	0.477097	−	0.346631i
$107$	−4.19190	+	4.19190i	−0.405246	+	0.405246i	−0.880077	−	0.474831i	$-0.842509\pi$
$107$	−4.19190	+	4.19190i	−0.405246	+	0.405246i	0.474831	+	0.880077i	$0.342509\pi$
$108$	−1.24960	+	5.04366i	−0.120243	+	0.485326i
$109$	1.79521	−	0.583300i	0.171950	−	0.0558700i	−0.221777	−	0.975098i	$-0.571186\pi$
$109$	1.79521	−	0.583300i	0.171950	−	0.0558700i	0.393727	+	0.919227i	$0.371186\pi$
$110$	−11.6675	−	6.24176i	−1.11245	−	0.595129i
$111$	0.248012	+	0.291809i	0.0235403	+	0.0276973i
$112$	−0.972066	+	1.90779i	−0.0918516	+	0.180269i
$113$	3.85086	−	7.55774i	0.362258	−	0.710972i	−0.635891	−	0.771779i	$-0.719367\pi$
$113$	3.85086	−	7.55774i	0.362258	−	0.710972i	0.998150	+	0.0608066i	$0.0193673\pi$
$114$	−6.04848	−	7.11659i	−0.566492	−	0.666530i
$115$	0.609739	−	3.40741i	0.0568585	−	0.317743i
$116$	4.32285	−	1.40458i	0.401366	−	0.130412i
$117$	−0.964817	−	3.01895i	−0.0891974	−	0.279102i
$118$	5.12840	−	5.12840i	0.472108	−	0.472108i
$119$	9.96530	−	7.24021i	0.913517	−	0.663709i
$120$	1.40159	+	3.61048i	0.127947	+	0.329590i
$121$	19.4311	+	14.1175i	1.76646	+	1.28341i
$122$	−4.18494	+	0.662830i	−0.378887	+	0.0600098i
$123$	0.227147	−	2.79970i	0.0204811	−	0.252441i
$124$			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	0.0112913	−	0.999936i	$-0.496406\pi$
$127$	9.31862	−	4.74807i	0.826894	−	0.421323i	0.815602	+	0.578613i	$0.196406\pi$
$128$	0.156434	+	0.987688i	0.0138270	+	0.0873001i
$129$	1.24440	+	3.02489i	0.109563	+	0.266326i
$130$	−1.88301	−	1.42646i	−0.165151	−	0.125109i
$131$	−11.4805	−	15.8015i	−1.00306	−	1.38059i	−0.923432	−	0.383762i	$-0.874628\pi$
$131$	−11.4805	−	15.8015i	−1.00306	−	1.38059i	−0.0796236	−	0.996825i	$-0.525372\pi$
$132$	−2.36864	−	9.97216i	−0.206164	−	0.867965i
$133$	1.80615	−	11.4036i	0.156613	−	0.988816i
$134$	−0.400605	−	1.23294i	−0.0346070	−	0.106510i
$135$	−3.01907	+	11.2199i	−0.259840	+	0.965652i
$136$	1.77773	−	5.47129i	0.152439	−	0.469159i
$137$	−10.6831	−	5.44330i	−0.912717	−	0.465053i	−0.0664369	−	0.997791i	$-0.521163\pi$
$137$	−10.6831	−	5.44330i	−0.912717	−	0.465053i	−0.846280	+	0.532738i	$0.821163\pi$
$138$	2.28956	−	1.39545i	0.194900	−	0.118788i
$139$	22.1318	+	7.19107i	1.87720	+	0.609939i	0.988451	+	0.151540i	$0.0484232\pi$
$139$	22.1318	+	7.19107i	1.87720	+	0.609939i	0.888747	+	0.458399i	$0.151577\pi$
$140$	−2.25845	+	4.22164i	−0.190874	+	0.356794i
$141$	−1.96445	+	8.09634i	−0.165437	+	0.681835i
$142$	−4.03104	−	0.638455i	−0.338278	−	0.0535779i
$143$	4.42062	+	4.42062i	0.369671	+	0.369671i
$144$	−1.37487	+	2.66641i	−0.114572	+	0.222201i
$145$	9.72703	−	2.94688i	0.807786	−	0.244725i
$146$	−0.183742	+	0.252900i	−0.0152066	+	0.0209301i
$147$	3.86131	+	1.61035i	0.318476	+	0.132819i
$148$	0.100380	+	0.197006i	0.00825116	+	0.0161938i
$149$	14.7140			1.20542			0.602711	−	0.797960i	$-0.294087\pi$
$149$	14.7140			1.20542			0.602711	+	0.797960i	$0.294087\pi$
$150$	2.97204	+	8.13431i	0.242666	+	0.664164i
$151$	−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
$153$	14.0113	−	10.0768i	1.13275	−	0.814658i
$154$	7.44757	−	10.2507i	0.600142	−	0.826025i
$155$	−0.476520	+	23.8334i	−0.0382750	+	1.91435i
$156$	−0.139161	−	1.82454i	−0.0111418	−	0.146080i
$157$	−17.5864	−	17.5864i	−1.40355	−	1.40355i	−0.788446	−	0.615104i	$-0.789114\pi$
$157$	−17.5864	−	17.5864i	−1.40355	−	1.40355i	−0.615104	−	0.788446i	$-0.710886\pi$
$158$	0.933375	+	0.147832i	0.0742553	+	0.0117609i
$159$	10.2198	+	2.47967i	0.810480	+	0.196651i
$160$	0.305580	+	2.21509i	0.0241582	+	0.175118i
$161$	3.15239	+	1.02427i	0.248443	+	0.0807240i
$162$	−8.05816	+	4.00825i	−0.633109	+	0.314918i
$163$	1.79029	+	0.912200i	0.140227	+	0.0714490i	0.522696	−	0.852519i	$-0.324926\pi$
$163$	1.79029	+	0.912200i	0.140227	+	0.0714490i	−0.382469	+	0.923968i	$0.624926\pi$
$164$	0.501139	−	1.54235i	0.0391324	−	0.120437i
$165$	−4.84965	−	22.3998i	−0.377545	−	1.74383i
$166$	2.33760	+	7.19438i	0.181433	+	0.558392i
$167$	2.32146	−	14.6571i	0.179640	−	1.13420i	−0.718837	−	0.695179i	$-0.755325\pi$
$167$	2.32146	−	14.6571i	0.179640	−	1.13420i	0.898477	−	0.439021i	$-0.144675\pi$
$168$	−3.60821	+	0.857043i	−0.278379	+	0.0661223i
$169$	−6.98518	−	9.61428i	−0.537322	−	0.739560i
$170$	4.21889	−	12.1523i	0.323574	−	0.932037i
$171$	2.60777	−	15.9653i	0.199421	−	1.22089i
$172$	0.295415	+	1.86518i	0.0225252	+	0.142218i
$173$	4.46800	−	2.27656i	0.339696	−	0.173084i	−0.275818	−	0.961210i	$-0.588949\pi$
$173$	4.46800	−	2.27656i	0.339696	−	0.173084i	0.615514	+	0.788126i	$0.288949\pi$
$174$	6.70263	+	4.12968i	0.508125	+	0.313070i
$175$	−5.23773	+	9.33704i	−0.395935	+	0.705814i
$176$		−	5.91761i		−	0.446057i
$177$	12.5208	+	1.01585i	0.941123	+	0.0763556i
$178$	−8.54762	+	1.35381i	−0.640672	+	0.101472i
$179$	2.56353	+	1.86252i	0.191607	+	0.139211i	0.679453	−	0.733719i	$-0.262217\pi$
$179$	2.56353	+	1.86252i	0.191607	+	0.139211i	−0.487846	+	0.872930i	$0.662217\pi$
$180$	−3.19287	+	5.89963i	−0.237982	+	0.439732i
$181$	−5.04884	+	3.66820i	−0.375278	+	0.272655i	−0.759396	−	0.650629i	$-0.774505\pi$
$181$	−5.04884	+	3.66820i	−0.375278	+	0.272655i	0.384118	+	0.923284i	$0.374505\pi$
$182$	1.59951	−	1.59951i	0.118563	−	0.118563i
$183$	−5.56901	−	4.77969i	−0.411673	−	0.353325i
$184$	1.47228	−	0.478373i	0.108538	−	0.0352661i
$185$	0.215605	+	0.444918i	0.0158516	+	0.0327110i
$186$	−14.0698	+	11.9581i	−1.03165	+	0.876811i
$187$	−15.4553	+	30.3327i	−1.13020	+	2.21815i
$188$	−2.18372	+	4.28579i	−0.159264	+	0.312573i
$189$	−10.2478	−	4.33203i	−0.745416	−	0.315109i
$190$	−5.25814	−	10.8506i	−0.381466	−	0.787184i
$191$	−19.9806	+	6.49209i	−1.44574	+	0.469751i	−0.923683	−	0.383157i	$-0.874837\pi$
$191$	−19.9806	+	6.49209i	−1.44574	+	0.469751i	−0.522062	+	0.852908i	$0.674837\pi$
$192$	−1.12805	+	1.31434i	−0.0814103	+	0.0948544i
$193$	7.00922	−	7.00922i	0.504535	−	0.504535i	−0.408309	−	0.912844i	$-0.633881\pi$
$193$	7.00922	−	7.00922i	0.504535	−	0.504535i	0.912844	+	0.408309i	$0.133881\pi$
$194$	−9.76009	+	7.09112i	−0.700734	+	0.509113i
$195$	−0.229557	−	4.08520i	−0.0164389	−	0.292547i
$196$	1.95413	+	1.41976i	0.139580	+	0.101411i
$197$	10.0821	−	1.59685i	0.718320	−	0.113771i	0.213435	−	0.976957i	$-0.431535\pi$
$197$	10.0821	−	1.59685i	0.718320	−	0.113771i	0.504885	+	0.863186i	$0.331535\pi$
$198$	10.5041	−	14.3118i	0.746495	−	1.01709i
$199$			15.1147i			1.07146i	0.844391	+	0.535728i	$0.179963\pi$
$199$			15.1147i			1.07146i	−0.844391	+	0.535728i	$0.820037\pi$
$200$	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
$204$	9.21494	−	3.79090i	0.645175	−	0.265416i
$205$	1.18930	−	3.42570i	0.0830642	−	0.239262i
$206$	−5.19267	−	7.14709i	−0.361790	−	0.497962i
$207$	4.40986	+	1.45644i	0.306506	+	0.101229i
$208$	0.165266	−	1.04345i	0.0114592	−	0.0723503i
$209$	9.86055	+	30.3476i	0.682068	+	2.09919i
$210$	−8.10490	+	1.75474i	−0.559291	+	0.121089i
$211$	−1.22728	+	3.77719i	−0.0844897	+	0.260033i	−0.984372	−	0.176099i	$-0.943652\pi$
$211$	−1.22728	+	3.77719i	−0.0844897	+	0.260033i	0.899883	+	0.436132i	$0.143652\pi$
$212$	5.40982	+	2.75644i	0.371548	+	0.189313i
$213$	−3.67898	−	6.03622i	−0.252079	−	0.413595i
$214$	−5.63809	−	1.83193i	−0.385412	−	0.125228i
$215$	0.577065	+	4.18303i	0.0393555	+	0.285280i
$216$	−5.06124	+	1.17637i	−0.344374	+	0.0800422i
$217$	−22.5454	−	3.57084i	−1.53048	−	0.242404i
$218$	1.33473	+	1.33473i	0.0903996	+	0.0903996i
$219$	−0.539873	+	0.0411771i	−0.0364812	+	0.00278249i
$220$	0.264508	−	13.2295i	0.0178331	−	0.891935i
$221$	−3.57235	+	4.91692i	−0.240302	+	0.330748i
$222$	−0.147409	+	0.353459i	−0.00989342	+	0.0237226i
$223$	−6.07755	−	11.9279i	−0.406983	−	0.798748i	0.592996	−	0.805205i	$-0.297945\pi$
$223$	−6.07755	−	11.9279i	−0.406983	−	0.798748i	−0.999979	+	0.00645660i	$0.997945\pi$
$224$	−2.14116			−0.143062
$225$	−7.40175	+	13.0466i	−0.493450	+	0.869774i
$226$	8.48225			0.564231
$227$	0.388579	+	0.762629i	0.0257909	+	0.0506175i	0.903542	−	0.428499i	$-0.140957\pi$
$227$	0.388579	+	0.762629i	0.0257909	+	0.0506175i	−0.877752	+	0.479116i	$0.840957\pi$
$228$	3.59498	−	8.62010i	0.238083	−	0.570880i
$229$	−9.72545	+	13.3859i	−0.642676	+	0.884567i	−0.998755	−	0.0498887i	$-0.984113\pi$
$229$	−9.72545	+	13.3859i	−0.642676	+	0.884567i	0.356079	+	0.934456i	$0.384113\pi$
$230$	3.31284	−	1.00365i	0.218442	−	0.0661788i
$231$	21.8825	−	1.66902i	1.43976	−	0.109813i
$232$	3.21402	+	3.21402i	0.211011	+	0.211011i
$233$	−5.38346	−	0.852656i	−0.352682	−	0.0558593i	−0.0224200	−	0.999749i	$-0.507137\pi$
$233$	−5.38346	−	0.852656i	−0.352682	−	0.0558593i	−0.330262	+	0.943889i	$0.607137\pi$
$234$	2.25188	−	2.23023i	0.147210	−	0.145795i
$235$	−5.07354	+	9.48379i	−0.330961	+	0.618654i
$236$	6.89769	+	2.24119i	0.449001	+	0.145889i
$237$	0.851854	+	1.39767i	0.0553339	+	0.0907882i
$238$	10.9752	+	5.59216i	0.711418	+	0.362486i
$239$	−2.69306	+	8.28837i	−0.174199	+	0.536130i	−0.999596	−	0.0284230i	$-0.990951\pi$
$239$	−2.69306	+	8.28837i	−0.174199	+	0.536130i	0.825397	+	0.564553i	$0.190951\pi$
$240$	−2.58065	+	2.88795i	−0.166580	+	0.186416i
$241$	−7.85699	−	24.1813i	−0.506113	−	1.55766i	−0.798892	−	0.601475i	$-0.794580\pi$
$241$	−7.85699	−	24.1813i	−0.506113	−	1.55766i	0.292779	−	0.956180i	$-0.405420\pi$
$242$	−3.75726	+	23.7224i	−0.241526	+	1.52494i
$243$	−14.3288	−	6.13893i	−0.919191	−	0.393813i
$244$	−2.49051	−	3.42789i	−0.159439	−	0.219448i
$245$	4.30522	+	3.26138i	0.275051	+	0.208362i
$246$	2.59768	−	1.06865i	0.165622	−	0.0681346i
$247$	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	$0.768131\pi$
$252$	−5.17841	−	3.80069i	−0.326209	−	0.239421i
$253$	−9.04796	+	1.43306i	−0.568840	+	0.0900954i
$254$	8.46113	+	6.14737i	0.530898	+	0.385720i
$255$	20.7706	−	8.06313i	1.30070	−	0.504933i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−11.8588	+	11.8588i	−0.739734	+	0.739734i	−0.972526	−	0.232792i	$-0.925214\pi$
$257$	−11.8588	+	11.8588i	−0.739734	+	0.739734i	0.232792	+	0.972526i	$0.425214\pi$
$258$	−2.13025	+	2.48204i	−0.132623	+	0.154525i
$259$	−0.450251	+	0.146295i	−0.0279772	+	0.00909035i
$260$	0.416113	−	2.32537i	0.0258063	−	0.144213i
$261$	2.06804	+	13.4782i	0.128009	+	0.834279i
$262$	8.86724	−	17.4029i	0.547820	−	1.07516i
$263$	10.3291	−	20.2720i	0.636919	−	1.25002i	−0.316562	−	0.948572i	$-0.602529\pi$
$263$	10.3291	−	20.2720i	0.636919	−	1.25002i	0.953481	−	0.301453i	$-0.0974715\pi$
$264$	7.80992	−	6.63774i	0.480667	−	0.408525i
$265$	11.9711	+	6.40417i	0.735379	+	0.393405i
$266$	10.9806	−	3.56783i	0.673266	−	0.218757i
$267$	−11.3745	−	9.76238i	−0.696110	−	0.597448i
$268$	0.916684	−	0.916684i	0.0559954	−	0.0559954i
$269$	8.37684	−	6.08613i	0.510745	−	0.371078i	−0.302361	−	0.953193i	$-0.597775\pi$
$269$	8.37684	−	6.08613i	0.510745	−	0.371078i	0.813106	+	0.582115i	$0.197775\pi$
$270$	−11.3676	+	2.40370i	−0.691810	+	0.146284i
$271$	−0.517312	−	0.375849i	−0.0314245	−	0.0228312i	0.571962	−	0.820280i	$-0.306182\pi$
$271$	−0.517312	−	0.375849i	−0.0314245	−	0.0228312i	−0.603387	+	0.797449i	$0.706182\pi$
$272$	5.68203	−	0.899945i	0.344524	−	0.0545672i
$273$	3.90514	+	0.316834i	0.236350	+	0.0191757i
$274$		−	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	0.626616	−	0.779328i	$-0.284440\pi$
$277$	27.0524	−	13.7839i	1.62542	−	0.828193i	0.998805	−	0.0488650i	$-0.0155604\pi$
$278$	3.64035	+	22.9843i	0.218334	+	1.37851i
$279$	−31.5640	−	5.15567i	−1.88969	−	0.308662i
$280$	−4.78682	−	0.0957066i	−0.286067	−	0.00571956i
$281$	−12.7646	−	17.5690i	−0.761473	−	1.04808i	−0.997090	−	0.0762322i	$-0.975711\pi$
$281$	−12.7646	−	17.5690i	−0.761473	−	1.04808i	0.235617	−	0.971846i	$-0.424289\pi$
$282$	−8.10574	+	1.92532i	−0.482690	+	0.114651i
$283$	0.541258	−	3.41737i	0.0321745	−	0.203142i	−0.966365	−	0.257176i	$-0.917208\pi$
$283$	0.541258	−	3.41737i	0.0321745	−	0.203142i	0.998539	+	0.0540343i	$0.0172080\pi$
$284$	−1.26119	−	3.88154i	−0.0748378	−	0.230327i
$285$	8.42232	−	19.1106i	0.498895	−	1.13201i
$286$	−1.93188	+	5.94572i	−0.114235	+	0.351578i
$287$	3.09390	+	1.57642i	0.182627	+	0.0930531i
$288$	−2.99996	−	0.0144920i	−0.176775	−	0.000853952i
$289$	−15.3076	−	4.97374i	−0.900446	−	0.292573i
$290$	7.04167	+	7.32899i	0.413501	+	0.430373i
$291$	−20.3065	−	4.92706i	−1.19039	−	0.288830i
$292$	−0.308752	−	0.0489016i	−0.0180684	−	0.00286175i
$293$	−12.2527	−	12.2527i	−0.715808	−	0.715808i	0.251936	−	0.967744i	$-0.418933\pi$
$293$	−12.2527	−	12.2527i	−0.715808	−	0.715808i	−0.967744	+	0.251936i	$0.918933\pi$
$294$	0.318171	+	4.17154i	0.0185561	+	0.243289i
$295$	15.3204	+	5.31878i	0.891990	+	0.309671i
$296$	−0.129962	+	0.178878i	−0.00755391	+	0.0103971i
$297$	30.6707	−	2.19034i	1.77969	−	0.127097i
$298$	6.68004	+	13.1103i	0.386964	+	0.759460i
$299$	−1.63544			−0.0945802
$300$	−5.89845	+	6.34100i	−0.340547	+	0.366098i
$301$	−4.04342			−0.233059
$302$	−3.88107	−	7.61703i	−0.223330	−	0.438311i
$303$	−0.496017	−	0.206862i	−0.0284954	−	0.0118839i
$304$	3.16950	−	4.36244i	0.181783	−	0.250203i
$305$	−5.41462	−	7.77479i	−0.310040	−	0.445183i
$306$	15.3395	+	7.90942i	0.876899	+	0.452151i
$307$	16.8133	+	16.8133i	0.959588	+	0.959588i	0.999215	−	0.0396263i	$-0.0126167\pi$
$307$	16.8133	+	16.8133i	0.959588	+	0.959588i	−0.0396263	+	0.999215i	$0.512617\pi$
$308$	12.5146	+	1.98211i	0.713083	+	0.112941i
$309$	3.60798	−	14.8700i	0.205251	−	0.845924i
$310$	−21.4521	+	10.3956i	−1.21840	+	0.590429i
$311$	−7.39905	−	2.40410i	−0.419562	−	0.136324i	0.0916250	−	0.995794i	$-0.470794\pi$
$311$	−7.39905	−	2.40410i	−0.419562	−	0.136324i	−0.511187	+	0.859470i	$0.670794\pi$
$312$	1.56250	−	0.952316i	0.0884590	−	0.0539143i
$313$	18.5326	+	9.44284i	1.04753	+	0.533741i	0.891033	−	0.453939i	$-0.149981\pi$
$313$	18.5326	+	9.44284i	1.04753	+	0.533741i	0.156492	+	0.987679i	$0.449981\pi$
$314$	7.68555	−	23.6537i	0.433721	−	1.33486i
$315$	−11.4071	−	8.72836i	−0.642716	−	0.491788i
$316$	0.292024	+	0.898757i	0.0164276	+	0.0505590i
$317$	−0.0339077	+	0.214085i	−0.00190445	+	0.0120242i	−0.988622	−	0.150419i	$-0.951938\pi$
$317$	−0.0339077	+	0.214085i	−0.00190445	+	0.0120242i	0.986718	+	0.162444i	$0.0519376\pi$
$318$	2.43027	+	10.2316i	0.136283	+	0.573761i
$319$	−15.8099	−	21.7604i	−0.885183	−	1.21835i
$320$	−1.83493	+	1.27790i	−0.102576	+	0.0714370i
$321$	−3.90647	−	9.49587i	−0.218038	−	0.530008i
$322$	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
$327$	−0.264387	+	3.25871i	−0.0146207	+	0.180207i
$328$	1.60175	−	0.253693i	0.0884421	−	0.0140078i
$329$	−8.33214	−	6.05366i	−0.459366	−	0.333749i
$330$	17.7567	−	14.4904i	0.977475	−	0.797669i
$331$	5.81535	−	4.22510i	0.319640	−	0.232232i	−0.416382	−	0.909190i	$-0.636702\pi$
$331$	5.81535	−	4.22510i	0.319640	−	0.232232i	0.736022	+	0.676958i	$0.236702\pi$
$332$	−5.34899	+	5.34899i	−0.293564	+	0.293564i
$333$	−0.631833	+	0.201926i	−0.0346243	+	0.0110655i
$334$	14.1135	−	4.58575i	0.772255	−	0.250921i
$335$	2.09033	−	2.00838i	0.114207	−	0.109730i
$336$	−2.40172	−	2.82585i	−0.131025	−	0.154163i
$337$	3.06621	−	6.01777i	0.167027	−	0.327809i	−0.792288	−	0.610147i	$-0.791110\pi$
$337$	3.06621	−	6.01777i	0.167027	−	0.327809i	0.959315	+	0.282339i	$0.0911102\pi$
$338$	5.39518	−	10.5886i	0.293459	−	0.575946i
$339$	9.51447	+	11.1947i	0.516755	+	0.608010i
$340$	12.7431	−	1.75796i	0.691091	−	0.0953387i
$341$	59.9987	−	19.4947i	3.24911	−	1.05570i
$342$	15.4090	−	4.92454i	0.833226	−	0.266288i
$343$	−14.2552	+	14.2552i	−0.769710	+	0.769710i
$344$	−1.52777	+	1.10999i	−0.0823718	+	0.0598466i
$345$	5.04059	+	3.24642i	0.271376	+	0.174781i
$346$	4.05686	+	2.94748i	0.218098	+	0.158458i
$347$	−4.52113	+	0.716076i	−0.242707	+	0.0384410i	−0.276603	−	0.960984i	$-0.589209\pi$
$347$	−4.52113	+	0.716076i	−0.242707	+	0.0384410i	0.0338958	+	0.999425i	$0.489209\pi$
$348$	−0.636640	+	7.84692i	−0.0341275	+	0.420639i
$349$			9.78119i			0.523575i	0.965126	+	0.261787i	$0.0843120\pi$
$349$			9.78119i			0.523575i	−0.965126	+	0.261787i	$0.915688\pi$
$350$	−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	0.990827	+	0.135136i	$0.0431471\pi$
$353$	1.69571	+	10.7063i	0.0902538	+	0.569840i	−0.900573	+	0.434704i	$0.856853\pi$
$354$	4.77921	+	11.6173i	0.254012	+	0.617454i
$355$	−2.64604	−	8.73402i	−0.140437	−	0.463554i
$356$	−5.08679	−	7.00137i	−0.269600	−	0.371072i
$357$	4.93044	+	20.7575i	0.260947	+	1.09860i
$358$	−0.495694	+	3.12969i	−0.0261982	+	0.165409i
$359$	−6.51044	−	20.0371i	−0.343608	−	1.05752i	−0.962325	−	0.271902i	$-0.912347\pi$
$359$	−6.51044	−	20.0371i	−0.343608	−	1.05752i	0.618717	−	0.785614i	$-0.287653\pi$
$360$	−6.70614	−	0.166493i	−0.353444	−	0.00877493i
$361$	−3.11386	+	9.58347i	−0.163887	+	0.504393i
$362$	−5.56052	−	2.83323i	−0.292254	−	0.148911i
$363$	−35.5228	+	21.6505i	−1.86446	+	1.13636i
$364$	2.15133	+	0.699010i	0.112760	+	0.0366381i
$365$	−0.688068	−	0.123126i	−0.0360151	−	0.00644472i
$366$	1.73046	−	7.13196i	0.0904526	−	0.372793i
$367$	26.6770	+	4.22522i	1.39253	+	0.220555i	0.807218	−	0.590254i	$-0.200972\pi$
$367$	26.6770	+	4.22522i	1.39253	+	0.220555i	0.585311	+	0.810809i	$0.300972\pi$
$368$	1.09463	+	1.09463i	0.0570618	+	0.0570618i
$369$	4.32417	+	2.22965i	0.225107	+	0.116071i
$370$	−0.298542	+	0.394094i	−0.0155205	+	0.0204880i
$371$	−7.64135	+	10.5174i	−0.396719	+	0.546037i
$372$	−17.0423	−	7.10743i	−0.883603	−	0.368503i
$373$	12.1464	+	23.8387i	0.628917	+	1.23432i	0.957114	+	0.289711i	$0.0935590\pi$
$373$	12.1464	+	23.8387i	0.628917	+	1.23432i	−0.328197	+	0.944609i	$0.606441\pi$
$374$	−34.0432			−1.76033
$375$	−13.4701	+	13.9124i	−0.695594	+	0.718435i
$376$	−4.81005			−0.248060
$377$	−2.18003	−	4.27854i	−0.112277	−	0.220356i
$378$	−0.792528	−	11.0975i	−0.0407632	−	0.570795i
$379$	9.28018	−	12.7731i	0.476691	−	0.656109i	−0.501174	−	0.865347i	$-0.667098\pi$
$379$	9.28018	−	12.7731i	0.476691	−	0.656109i	0.977865	+	0.209238i	$0.0670983\pi$
$380$	7.28080	−	9.61110i	0.373497	−	0.493039i
$381$	1.37764	+	18.0622i	0.0705787	+	0.925357i
$382$	−14.8555	−	14.8555i	−0.760073	−	0.760073i
$383$	15.7705	+	2.49780i	0.805836	+	0.127632i	0.545744	−	0.837952i	$-0.316247\pi$
$383$	15.7705	+	2.49780i	0.805836	+	0.127632i	0.260092	+	0.965584i	$0.416247\pi$
$384$	−1.68321	−	0.408406i	−0.0858961	−	0.0208414i
$385$	27.8892	+	4.99063i	1.42137	+	0.254346i
$386$	9.42739	+	3.06314i	0.479841	+	0.155910i
$387$	−5.66521	−	0.0273672i	−0.287979	−	0.00139115i
$388$	−10.7492	−	5.47700i	−0.545709	−	0.278053i
$389$	−3.56490	+	10.9716i	−0.180748	+	0.556284i	−0.999849	−	0.0173647i	$-0.994472\pi$
$389$	−3.56490	+	10.9716i	−0.180748	+	0.556284i	0.819102	+	0.573648i	$0.194472\pi$
$390$	3.53572	−	2.05918i	0.179038	−	0.104270i
$391$	−2.75201	−	8.46982i	−0.139175	−	0.428337i
$392$	−0.377857	+	2.38569i	−0.0190847	+	0.120496i
$393$	32.9143	−	7.81799i	1.66031	−	0.394365i
$394$	5.99998	+	8.25827i	0.302275	+	0.416046i
$395$	0.612682	+	2.02233i	0.0308274	+	0.101755i
$396$	17.5206	+	2.86183i	0.880446	+	0.143812i
$397$	−3.27643	−	20.6866i	−0.164439	−	1.03823i	−0.922486	−	0.386030i	$-0.873846\pi$
$397$	−3.27643	−	20.6866i	−0.164439	−	1.03823i	0.758047	−	0.652200i	$-0.226154\pi$
$398$	−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	$0.791080\pi$
$402$	2.23805	+	0.181579i	0.111624	+	0.00905633i
$403$	11.1240	−	1.76187i	0.554125	−	0.0877648i
$404$	−0.251023	−	0.182379i	−0.0124889	−	0.00907370i
$405$	−15.9233	−	12.3065i	−0.791235	−	0.611513i
$406$	−7.87354	+	5.72046i	−0.390757	+	0.283902i
$407$	0.925189	−	0.925189i	0.0458599	−	0.0458599i
$408$	7.56121	+	6.48954i	0.374336	+	0.321280i
$409$	−9.31361	+	3.02618i	−0.460528	+	0.149635i	−0.530087	−	0.847943i	$-0.677841\pi$
$409$	−9.31361	+	3.02618i	−0.460528	+	0.149635i	0.0695588	+	0.997578i	$0.477841\pi$
$410$	3.59226	−	0.495565i	0.177409	−	0.0244742i
$411$	15.8240	−	13.4490i	0.780539	−	0.663389i
$412$	4.01069	−	7.87141i	0.197592	−	0.387797i
$413$	−7.05006	+	13.8365i	−0.346911	+	0.680851i
$414$	0.704337	+	4.59042i	0.0346163	+	0.225607i
$415$	−12.1974	+	11.7192i	−0.598747	+	0.575274i
$416$	1.00475	−	0.326463i	0.0492619	−	0.0160062i
$417$	−26.2507	+	30.5858i	−1.28550	+	1.49779i
$418$	−22.5634	+	22.5634i	−1.10361	+	1.10361i
$419$	20.8723	−	15.1646i	1.01968	−	0.740840i	0.0534618	−	0.998570i	$-0.482974\pi$
$419$	20.8723	−	15.1646i	1.01968	−	0.740840i	0.966217	+	0.257730i	$0.0829745\pi$
$420$	−5.24303	−	6.42488i	−0.255834	−	0.313502i
$421$	−31.8859	−	23.1664i	−1.55402	−	1.12906i	−0.940705	−	0.339225i	$-0.889835\pi$
$421$	−31.8859	−	23.1664i	−1.55402	−	1.12906i	−0.613316	−	0.789837i	$-0.710165\pi$
$422$	−3.92268	+	0.621291i	−0.190953	+	0.0302440i
$423$	−11.6331	−	8.53813i	−0.565623	−	0.415138i
$424$			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
$429$	−10.0140	+	4.11962i	−0.483480	+	0.198897i
$430$	−3.46513	+	2.41323i	−0.167103	+	0.116376i
$431$	3.61295	+	4.97279i	0.174030	+	0.239531i	0.887118	−	0.461543i	$-0.152704\pi$
$431$	3.61295	+	4.97279i	0.174030	+	0.239531i	−0.713088	+	0.701074i	$0.752704\pi$
$432$	−3.34591	−	3.97553i	−0.160980	−	0.191273i
$433$	−2.61783	+	16.5283i	−0.125805	+	0.794299i	0.841421	+	0.540380i	$0.181720\pi$
$433$	−2.61783	+	16.5283i	−0.125805	+	0.794299i	−0.967225	+	0.253919i	$0.918280\pi$
$434$	−7.05375	−	21.7092i	−0.338591	−	1.04208i
$435$	−1.77403	+	17.5143i	−0.0850583	+	0.839746i
$436$	−0.583300	+	1.79521i	−0.0279350	+	0.0859752i
$437$	−7.43768	−	3.78968i	−0.355792	−	0.181285i
$438$	−0.281786	−	0.462336i	−0.0134643	−	0.0220913i
$439$	−19.1311	−	6.21606i	−0.913076	−	0.296676i	−0.185453	−	0.982653i	$-0.559375\pi$
$439$	−19.1311	−	6.21606i	−0.913076	−	0.296676i	−0.727623	+	0.685977i	$0.759375\pi$
$440$	11.9077	−	5.77041i	0.567677	−	0.275093i
$441$	−5.14860	+	5.09909i	−0.245171	+	0.242814i
$442$	−6.00282	−	0.950753i	−0.285525	−	0.0452227i
$443$	−17.1571	−	17.1571i	−0.815159	−	0.815159i	0.170243	−	0.985402i	$-0.445545\pi$
$443$	−17.1571	−	17.1571i	−0.815159	−	0.815159i	−0.985402	+	0.170243i	$0.945545\pi$
$444$	−0.381856	+	0.0291249i	−0.0181221	+	0.00138221i
$445$	−11.0592	−	15.8798i	−0.524256	−	0.752774i
$446$	7.86865	−	10.8303i	0.372591	−	0.512828i
$447$	−9.80971	+	23.5219i	−0.463984	+	1.11255i
$448$	−0.972066	−	1.90779i	−0.0459258	−	0.0901345i
$449$	−15.9242			−0.751511			−0.375755	−	0.926719i	$-0.622617\pi$
$449$	−15.9242			−0.751511			−0.375755	+	0.926719i	$0.622617\pi$
$450$	−14.9849	−	0.671968i	−0.706397	−	0.0316769i
$451$	−9.59671			−0.451891
$452$	3.85086	+	7.55774i	0.181129	+	0.355486i
$453$	5.69940	−	13.6661i	0.267781	−	0.642089i
$454$	−0.503096	+	0.692453i	−0.0236115	+	0.0324984i
$455$	4.77832	+	1.65888i	0.224011	+	0.0777696i
$456$	9.31265	−	0.710293i	0.436105	−	0.0332625i
$457$	2.30257	+	2.30257i	0.107710	+	0.107710i	0.758908	−	0.651198i	$-0.225733\pi$
$457$	2.30257	+	2.30257i	0.107710	+	0.107710i	−0.651198	+	0.758908i	$0.725733\pi$
$458$	−16.3422	−	2.58835i	−0.763621	−	0.120946i
$459$	6.76752	+	29.1166i	0.315881	+	1.35905i
$460$	2.39826	+	2.49612i	0.111819	+	0.116382i
$461$	−9.43135	−	3.06443i	−0.439262	−	0.142725i	0.0810333	−	0.996711i	$-0.474178\pi$
$461$	−9.43135	−	3.06443i	−0.439262	−	0.142725i	−0.520295	+	0.853987i	$0.674178\pi$
$462$	11.4215	+	18.7397i	0.531379	+	0.871851i
$463$	−20.5992	−	10.4958i	−0.957328	−	0.487783i	−0.0957485	−	0.995406i	$-0.530524\pi$
$463$	−20.5992	−	10.4958i	−0.957328	−	0.487783i	−0.861580	+	0.507623i	$0.830524\pi$
$464$	−1.40458	+	4.32285i	−0.0652059	+	0.200683i
$465$	−37.7825	−	16.6513i	−1.75212	−	0.772185i
$466$	−1.68432	−	5.18379i	−0.0780245	−	0.240135i
$467$	0.726976	−	4.58995i	0.0336405	−	0.212397i	−0.965142	−	0.261726i	$-0.915708\pi$
$467$	0.726976	−	4.58995i	0.0336405	−	0.212397i	0.998783	+	0.0493288i	$0.0157082\pi$
$468$	3.00948	+	0.993939i	0.139113	+	0.0459448i
$469$	1.63156	+	2.24565i	0.0753383	+	0.103694i
$470$	−10.7535	−	0.215002i	−0.496020	−	0.00991730i
$471$	39.8384	−	16.3890i	1.83566	−	0.755164i
$472$	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
$477$	−10.7774	+	14.6842i	−0.493464	+	0.672341i
$478$	−8.60761	+	1.36331i	−0.393703	+	0.0623564i
$479$	−12.7801	−	9.28530i	−0.583939	−	0.424256i	0.256203	−	0.966623i	$-0.417528\pi$
$479$	−12.7801	−	9.28530i	−0.583939	−	0.424256i	−0.840142	+	0.542367i	$0.817528\pi$
$480$	−3.74477	−	0.988278i	−0.170925	−	0.0451085i
$481$	0.188977	−	0.137300i	0.00861660	−	0.00626032i
$482$	17.9787	−	17.9787i	0.818908	−	0.818908i
$483$	−3.73907	+	4.35654i	−0.170134	+	0.198229i
$484$	−22.8426	+	7.42201i	−1.03830	+	0.337364i
$485$	−23.7864	−	12.7250i	−1.08008	−	0.577811i
$486$	−1.03529	−	15.5540i	−0.0469619	−	0.705546i
$487$	0.0615473	−	0.120793i	0.00278898	−	0.00547367i	−0.889608	−	0.456725i	$-0.849022\pi$
$487$	0.0615473	−	0.120793i	0.00278898	−	0.00547367i	0.892397	+	0.451252i	$0.149022\pi$
$488$	1.92361	−	3.77529i	0.0870776	−	0.170899i
$489$	−2.65182	+	2.25381i	−0.119919	+	0.101921i
$490$	−0.951382	+	5.31662i	−0.0429790	+	0.240180i
$491$	−8.65368	+	2.81175i	−0.390535	+	0.126893i	−0.497701	−	0.867349i	$-0.665822\pi$
$491$	−8.65368	+	2.81175i	−0.390535	+	0.126893i	0.107166	+	0.994241i	$0.465822\pi$
$492$	2.13149	+	1.82939i	0.0960951	+	0.0824752i
$493$	18.4898	−	18.4898i	0.832738	−	0.832738i
$494$	−4.60873	+	3.34844i	−0.207357	+	0.150654i
$495$	39.0416	+	7.18110i	1.75479	+	0.322767i
$496$	−8.62475	−	6.26624i	−0.387263	−	0.281363i
$497$	8.63111	−	1.36703i	0.387158	−	0.0613198i
$498$	−13.0594	−	1.05954i	−0.585205	−	0.0474792i
$499$		−	27.5900i		−	1.23510i	−0.786532	−	0.617549i	$-0.788126\pi$
$499$		−	27.5900i		−	1.23510i	0.786532	−	0.617549i	$-0.211874\pi$
$500$	−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	0.995993	+	0.0894274i	$0.0285037\pi$
$503$	1.71307	+	10.8159i	0.0763820	+	0.482257i	−0.919611	+	0.392829i	$0.871496\pi$
$504$	1.03549	−	6.33947i	0.0461244	−	0.282382i
$505$	−0.553041	−	0.418951i	−0.0246100	−	0.0186431i
$506$	−5.38455	−	7.41120i	−0.239372	−	0.329468i
$507$	20.0263	−	4.75677i	0.889401	−	0.211256i
$508$	−1.63607	+	10.3298i	−0.0725891	+	0.458309i
$509$	2.83257	+	8.71775i	0.125551	+	0.386407i	0.994001	−	0.109370i	$-0.0348833\pi$
$509$	2.83257	+	8.71775i	0.125551	+	0.386407i	−0.868450	+	0.495777i	$0.834883\pi$
$510$	16.6139	+	14.8461i	0.735678	+	0.657397i
$511$	0.206834	−	0.636570i	0.00914980	−	0.0281602i
$512$	−0.891007	−	0.453990i	−0.0393773	−	0.0200637i
$513$	23.7835	+	14.8127i	1.05007	+	0.653995i
$514$	−15.9501	−	5.18250i	−0.703529	−	0.228590i
$515$	9.31821	−	17.4182i	0.410610	−	0.767539i
$516$	−3.17862	−	0.771244i	−0.139931	−	0.0339521i
$517$	28.1136	+	4.45276i	1.23643	+	0.195832i
$518$	−0.334760	−	0.334760i	−0.0147085	−	0.0147085i
$519$	0.660538	+	8.66031i	0.0289944	+	0.380146i
$520$	2.26083	−	0.684937i	0.0991441	−	0.0300365i
$521$	−13.3932	+	18.4342i	−0.586767	+	0.807615i	−0.994417	−	0.105523i	$-0.966348\pi$
$521$	−13.3932	+	18.4342i	−0.586767	+	0.807615i	0.407650	+	0.913138i	$0.366348\pi$
$522$	−11.0703	+	7.96161i	−0.484533	+	0.348470i
$523$	16.3751	+	32.1380i	0.716035	+	1.40530i	0.905902	+	0.423488i	$0.139194\pi$
$523$	16.3751	+	32.1380i	0.716035	+	1.40530i	−0.189867	+	0.981810i	$0.560806\pi$
$524$	19.5318			0.853250
$525$	−11.4343	−	14.5980i	−0.499032	−	0.637107i
$526$	22.7518			0.992025
$527$	27.8432	+	54.6453i	1.21287	+	2.38039i
$528$	9.45990	+	3.94521i	0.411689	+	0.171693i
$529$	−12.1105	+	16.6686i	−0.526542	+	0.724723i
$530$	−0.271390	+	13.5738i	−0.0117884	+	0.589606i
$531$	−9.97144	+	19.3385i	−0.432724	+	0.839221i
$532$	8.16406	+	8.16406i	0.353957	+	0.353957i
$533$	−1.69218	−	0.268016i	−0.0732966	−	0.0116090i
$534$	3.53442	−	14.5668i	0.152949	−	0.630368i
$535$	−1.81155	−	13.1316i	−0.0783202	−	0.567728i
$536$	1.23294	+	0.400605i	0.0532548	+	0.0173035i
$537$	−4.68650	+	2.85634i	−0.202237	+	0.123260i
$538$	9.22579	+	4.70077i	0.397752	+	0.202665i
$539$	4.41696	−	13.5940i	0.190252	−	0.585536i
$540$	−7.30249	−	9.03735i	−0.314249	−	0.388905i
$541$	10.6711	+	32.8422i	0.458786	+	1.41200i	0.866633	+	0.498947i	$0.166280\pi$
$541$	10.6711	+	32.8422i	0.458786	+	1.41200i	−0.407847	+	0.913050i	$0.633720\pi$
$542$	0.100029	−	0.631560i	0.00429663	−	0.0271278i
$543$	−2.49797	−	10.5166i	−0.107198	−	0.451312i
$544$	3.38144	+	4.65416i	0.144978	+	0.199545i
$545$	−1.38428	+	3.98735i	−0.0592961	+	0.170799i
$546$	1.49060	+	3.62335i	0.0637917	+	0.155065i
$547$	−3.53445	−	22.3156i	−0.151122	−	0.954148i	−0.940390	−	0.340098i	$-0.889540\pi$
$547$	−3.53445	−	22.3156i	−0.151122	−	0.954148i	0.789268	−	0.614049i	$-0.210460\pi$
$548$	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
$552$	−0.216828	+	2.67251i	−0.00922880	+	0.113750i
$553$	−1.99850	+	0.316532i	−0.0849851	+	0.0134603i
$554$	24.5631	+	17.8461i	1.04358	+	0.758209i
$555$	−0.854988	+	0.0480438i	−0.0362922	+	0.00203935i
$556$	−18.8265	+	13.6782i	−0.798420	+	0.580086i
$557$	3.76017	−	3.76017i	0.159323	−	0.159323i	−0.622943	−	0.782267i	$-0.714063\pi$
$557$	3.76017	−	3.76017i	0.159323	−	0.159323i	0.782267	+	0.622943i	$0.214063\pi$
$558$	−9.73603	−	30.4644i	−0.412159	−	1.28966i
$559$	1.89740	−	0.616502i	0.0802513	−	0.0260752i
$560$	−2.08790	−	4.30854i	−0.0882298	−	0.182069i
$561$	−38.1860	−	44.9293i	−1.61221	−	1.89692i
$562$	9.85907	−	19.3495i	0.415880	−	0.816210i
$563$	11.0089	−	21.6061i	0.463969	−	0.910590i	−0.533913	−	0.845539i	$-0.679279\pi$
$563$	11.0089	−	21.6061i	0.463969	−	0.910590i	0.997882	−	0.0650508i	$-0.0207209\pi$
$564$	−5.39540	−	6.34819i	−0.227187	−	0.267307i
$565$	8.27124	+	17.0684i	0.347974	+	0.718071i
$566$	3.29063	−	1.06919i	0.138315	−	0.0449414i
$567$	13.7573	−	13.4940i	0.577751	−	0.566694i
$568$	2.88591	−	2.88591i	0.121090	−	0.121090i
$569$	−24.5934	+	17.8681i	−1.03101	+	0.749071i	−0.968510	−	0.248974i	$-0.919907\pi$
$569$	−24.5934	+	17.8681i	−1.03101	+	0.749071i	−0.0624977	+	0.998045i	$0.519907\pi$
$570$	20.8513	−	1.17169i	0.873365	−	0.0490765i
$571$	4.57335	+	3.32274i	0.191389	+	0.139052i	0.679353	−	0.733811i	$-0.262260\pi$
$571$	4.57335	+	3.32274i	0.191389	+	0.139052i	−0.487964	+	0.872864i	$0.662260\pi$
$572$	−6.17473	+	0.977982i	−0.258179	+	0.0408915i
$573$	2.94261	−	36.2692i	0.122929	−	1.51517i
$574$			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	−0.860223	−	0.509919i	$-0.829676\pi$
$577$	−22.8994	+	11.6678i	−0.953316	+	0.485739i	−0.0930933	+	0.995657i	$0.529676\pi$
$578$	−2.51787	−	15.8972i	−0.104729	−	0.661236i
$579$	6.53197	+	15.8779i	0.271459	+	0.659864i
$580$	−3.33333	+	9.60146i	−0.138409	+	0.398679i
$581$	−9.52039	−	13.1037i	−0.394972	−	0.543633i
$582$	−4.82891	−	20.3301i	−0.200165	−	0.842708i
$583$	5.62058	−	35.4869i	0.232781	−	1.46972i
$584$	−0.0965991	−	0.297301i	−0.00399730	−	0.0123024i
$585$	6.68364	+	2.35659i	0.276335	+	0.0974330i
$586$	5.35461	−	16.4798i	0.221197	−	0.680773i
$587$	12.8802	+	6.56280i	0.531623	+	0.270876i	0.699129	−	0.714995i	$-0.253571\pi$
$587$	12.8802	+	6.56280i	0.531623	+	0.270876i	−0.167506	+	0.985871i	$0.553571\pi$
$588$	−3.57242	+	2.17733i	−0.147324	+	0.0897916i
$589$	54.6723	+	17.7641i	2.25273	+	0.731957i
$590$	2.21627	+	16.0653i	0.0912423	+	0.661397i
$591$	−4.16892	+	17.1819i	−0.171486	+	0.706768i
$592$	−0.218383	−	0.0345885i	−0.00897549	−	0.00142158i
$593$	−27.1124	−	27.1124i	−1.11337	−	1.11337i	−0.992691	−	0.120680i	$-0.961492\pi$
$593$	−27.1124	−	27.1124i	−1.11337	−	1.11337i	−0.120680	−	0.992691i	$-0.538508\pi$
$594$	15.8758	+	26.3334i	0.651393	+	1.08047i
$595$	−0.550586	+	27.5379i	−0.0225718	+	1.12894i
$596$	−8.64870	+	11.9039i	−0.354265	+	0.487603i
$597$	−24.1624	−	10.0769i	−0.988903	−	0.412418i
$598$	−0.742476	−	1.45719i	−0.0303621	−	0.0595890i
$599$	22.2597			0.909506			0.454753	−	0.890618i	$-0.349728\pi$
$599$	22.2597			0.909506			0.454753	+	0.890618i	$0.349728\pi$
$600$	−8.32771	−	2.37680i	−0.339977	−	0.0970325i
$601$	−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
$603$	2.27076	+	3.15740i	0.0924727	+	0.128579i
$604$	5.02485	−	6.91612i	0.204458	−	0.281413i
$605$	−51.3992	+	15.5718i	−2.08967	+	0.633083i
$606$	−0.0408716	−	0.535868i	−0.00166030	−	0.0217681i
$607$	−25.2285	−	25.2285i	−1.02399	−	1.02399i	−0.999705	−	0.0242876i	$-0.992268\pi$
$607$	−25.2285	−	25.2285i	−1.02399	−	1.02399i	−0.0242876	−	0.999705i	$-0.507732\pi$
$608$	5.32589	+	0.843538i	0.215993	+	0.0342100i
$609$	−16.3814	−	3.97470i	−0.663809	−	0.161063i
$610$	4.46921	−	8.35414i	0.180953	−	0.338249i
$611$	4.83290	+	1.57031i	0.195518	+	0.0635278i
$612$	−0.0833706	+	17.2584i	−0.00337006	+	0.697628i
$613$	−22.2583	−	11.3412i	−0.899003	−	0.458065i	−0.0575173	−	0.998345i	$-0.518318\pi$
$613$	−22.2583	−	11.3412i	−0.899003	−	0.458065i	−0.841485	+	0.540280i	$0.818318\pi$
$614$	−7.34770	+	22.6139i	−0.296529	+	0.912623i
$615$	4.68344	+	4.18510i	0.188855	+	0.168759i
$616$	3.91542	+	12.0504i	0.157757	+	0.485525i
$617$	4.87738	−	30.7946i	0.196356	−	1.23974i	−0.670775	−	0.741661i	$-0.734038\pi$
$617$	4.87738	−	30.7946i	0.196356	−	1.23974i	0.867131	−	0.498081i	$-0.165962\pi$
$618$	14.8873	−	3.53610i	0.598853	−	0.142243i
$619$	2.12975	+	2.93135i	0.0856019	+	0.117821i	0.849670	−	0.527314i	$-0.176801\pi$
$619$	2.12975	+	2.93135i	0.0856019	+	0.117821i	−0.764068	+	0.645135i	$0.776801\pi$
$620$	−19.0016	−	14.3945i	−0.763122	−	0.578096i
$621$	−5.26827	+	6.07861i	−0.211408	+	0.243926i
$622$	−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
$627$	−55.0877	−	4.46940i	−2.19999	−	0.178491i
$628$	24.5648	−	3.89068i	0.980241	−	0.155255i
$629$	1.02906	+	0.747655i	0.0410312	+	0.0298109i
$630$	2.59833	−	14.1264i	0.103520	−	0.562808i
$631$	4.12680	−	2.99829i	0.164285	−	0.119360i	−0.502605	−	0.864516i	$-0.667625\pi$
$631$	4.12680	−	2.99829i	0.164285	−	0.119360i	0.666890	+	0.745156i	$0.267625\pi$
$632$	−0.668222	+	0.668222i	−0.0265805	+	0.0265805i
$633$	−5.22000	−	4.48015i	−0.207477	−	0.178070i
$634$	−0.206145	+	0.0669805i	−0.00818706	+	0.00266014i
$635$	−4.11937	+	23.0203i	−0.163472	+	0.913533i
$636$	−8.01312	+	6.81045i	−0.317741	+	0.270052i
$637$	1.15849	−	2.27367i	0.0459012	−	0.0900861i
$638$	12.2112	−	23.9657i	0.483444	−	0.948813i
$639$	12.1022	−	1.85692i	0.478757	−	0.0734587i
$640$	−1.97166	−	1.05478i	−0.0779367	−	0.0416937i
$641$	45.1681	−	14.6760i	1.78403	−	0.579668i	0.784836	−	0.619703i	$-0.212747\pi$
$641$	45.1681	−	14.6760i	1.78403	−	0.579668i	0.999198	+	0.0400355i	$0.0127471\pi$
$642$	6.68738	−	7.79173i	0.263930	−	0.307515i
$643$	−17.9186	+	17.9186i	−0.706639	+	0.706639i	−0.965827	−	0.259188i	$-0.916545\pi$
$643$	−17.9186	+	17.9186i	−0.706639	+	0.706639i	0.259188	+	0.965827i	$0.416545\pi$
$644$	−2.68158	+	1.94828i	−0.105669	+	0.0767731i
$645$	−7.07172	−	1.86629i	−0.278449	−	0.0734851i
$646$	−25.0965	−	18.2337i	−0.987409	−	0.717395i
$647$	−7.06356	+	1.11876i	−0.277697	+	0.0439829i	−0.293730	−	0.955889i	$-0.594897\pi$
$647$	−7.06356	+	1.11876i	−0.277697	+	0.0439829i	0.0160323	+	0.999871i	$0.494897\pi$
$648$	1.49373	−	8.87518i	0.0586791	−	0.348650i
$649$		−	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	0.950583	+	0.310470i	$0.100486\pi$
$653$	3.64054	+	22.9855i	0.142465	+	0.899490i	−0.808118	+	0.589021i	$0.799514\pi$
$654$	−3.02356	+	1.24385i	−0.118231	+	0.0486385i
$655$	43.6657	+	0.873041i	1.70616	+	0.0341125i
$656$	0.953223	+	1.31200i	0.0372171	+	0.0512250i
$657$	0.294102	−	0.890494i	0.0114740	−	0.0347415i
$658$	1.61113	−	10.1723i	0.0628085	−	0.396557i
$659$	1.14382	+	3.52031i	0.0445568	+	0.137132i	0.970860	−	0.239647i	$-0.0770317\pi$
$659$	1.14382	+	3.52031i	0.0445568	+	0.137132i	−0.926303	+	0.376779i	$0.877032\pi$
$660$	20.9724	+	9.24285i	0.816350	+	0.359777i
$661$	−11.4157	+	35.1339i	−0.444019	+	1.36655i	0.439537	+	0.898224i	$0.355143\pi$
$661$	−11.4157	+	35.1339i	−0.444019	+	1.36655i	−0.883556	+	0.468326i	$0.844857\pi$
$662$	6.40470	+	3.26336i	0.248926	+	0.126834i
$663$	−5.47854	−	8.98882i	−0.212769	−	0.349097i
$664$	−7.19438	−	2.33760i	−0.279196	−	0.0907163i
$665$	17.8868	+	18.6167i	0.693622	+	0.721924i
$666$	−0.466764	−	0.471295i	−0.0180867	−	0.0182623i
$667$	6.94972	+	1.10073i	0.269094	+	0.0426203i
$668$	10.4933	+	10.4933i	0.405999	+	0.405999i
$669$	23.1197	−	1.76338i	0.893860	−	0.0681764i
$670$	2.73847	+	0.950713i	0.105796	+	0.0367292i
$671$	−14.7379	+	20.2849i	−0.568949	+	0.783092i
$672$	1.42749	−	3.42286i	0.0550667	−	0.132040i
$673$	−0.542210	−	1.06415i	−0.0209006	−	0.0410198i	0.880320	−	0.474380i	$-0.157328\pi$
$673$	−0.542210	−	1.06415i	−0.0209006	−	0.0410198i	−0.901221	+	0.433360i	$0.857328\pi$
$674$	6.75390			0.260151
$675$	−15.9217	−	20.5305i	−0.612825	−	0.790219i
$676$	11.8839			0.457073
$677$	−15.6087	−	30.6338i	−0.599892	−	1.17735i	−0.968790	−	0.247884i	$-0.920265\pi$
$677$	−15.6087	−	30.6338i	−0.599892	−	1.17735i	0.368898	−	0.929470i	$-0.379735\pi$
$678$	−5.65503	+	13.5597i	−0.217180	+	0.520758i
$679$	15.1832	−	20.8979i	0.582679	−	0.801988i
$680$	7.35159	+	10.5561i	0.281921	+	0.404807i
$681$	−1.47820	+	0.112745i	−0.0566448	+	0.00432040i
$682$	44.6088	+	44.6088i	1.70816	+	1.70816i
$683$	44.5125	+	7.05008i	1.70322	+	0.269764i	0.930849	−	0.365405i	$-0.119070\pi$
$683$	44.5125	+	7.05008i	1.70322	+	0.269764i	0.772373	+	0.635169i	$0.219070\pi$
$684$	11.3834	+	11.4939i	0.435254	+	0.439479i
$685$	24.1266	−	11.6916i	0.921831	−	0.446715i
$686$	−19.1733	−	6.22977i	−0.732038	−	0.237854i
$687$	−14.9149	−	24.4714i	−0.569039	−	0.933641i
$688$	−1.68260	−	0.857327i	−0.0641485	−	0.0326853i
$689$	1.98215	−	6.10043i	0.0755138	−	0.232408i
$690$	−0.604202	+	5.96504i	−0.0230016	+	0.227085i
$691$	1.10289	+	3.39434i	0.0419558	+	0.129127i	0.969840	−	0.243741i	$-0.0783746\pi$
$691$	1.10289	+	3.39434i	0.0419558	+	0.129127i	−0.927885	+	0.372867i	$0.878375\pi$
$692$	−0.784450	+	4.95282i	−0.0298203	+	0.188278i
$693$	−11.9207	+	36.0941i	−0.452832	+	1.37110i
$694$	−2.69058	−	3.70326i	−0.102133	−	0.140574i
$695$	−42.7002	+	29.7378i	−1.61971	+	1.12802i
$696$	−7.28069	+	2.99518i	−0.275974	+	0.113532i
$697$	−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	$-0.120781\pi$
$702$	2.06394	+	5.08674i	0.0778984	+	0.191986i
$703$	1.17758	−	0.186511i	0.0444133	−	0.00703438i
$704$	4.78745	+	3.47829i	0.180434	+	0.131093i
$705$	−11.7783	−	14.4333i	−0.443597	−	0.543590i
$706$	−8.76956	+	6.37146i	−0.330047	+	0.239793i
$707$	0.469776	−	0.469776i	0.0176677	−	0.0176677i
$708$	−8.18139	+	9.53246i	−0.307476	+	0.358252i
$709$	−22.4237	+	7.28590i	−0.842140	+	0.273628i	−0.698150	−	0.715951i	$-0.745993\pi$
$709$	−22.4237	+	7.28590i	−0.842140	+	0.273628i	−0.143990	+	0.989579i	$0.545993\pi$
$710$	6.58079	−	6.32280i	0.246973	−	0.237291i
$711$	−2.80223	+	0.429964i	−0.105092	+	0.0161249i
$712$	3.92891	−	7.71092i	0.147242	−	0.288979i
$713$	−7.49238	+	14.7046i	−0.280592	+	0.550692i
$714$	−16.2567	+	13.8168i	−0.608392	+	0.517080i
$715$	−13.8481	+	1.91040i	−0.517889	+	0.0714447i
$716$	−3.01361	+	0.979183i	−0.112624	+	0.0365938i
$717$	−11.4544	−	9.83090i	−0.427771	−	0.367142i
$718$	14.8975	−	14.8975i	0.555969	−	0.555969i
$719$	−30.2210	+	21.9569i	−1.12705	+	0.818853i	−0.985263	−	0.171044i	$-0.945286\pi$
$719$	−30.2210	+	21.9569i	−1.12705	+	0.818853i	−0.141791	+	0.989897i	$0.545286\pi$
$720$	−2.89618	−	6.05080i	−0.107934	−	0.225500i
$721$	15.3031	+	11.1183i	0.569916	+	0.414068i
$722$	−9.95259	+	1.57634i	−0.370397	+	0.0586651i
$723$	43.8944	+	3.56127i	1.63245	+	0.132445i
$724$		−	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	−0.981597	−	0.190964i	$-0.938839\pi$
$727$	−37.8579	+	19.2896i	−1.40407	+	0.715411i	−0.422476	+	0.906374i	$0.638839\pi$
$728$	0.353862	+	2.23419i	0.0131150	+	0.0828047i
$729$	19.3666	−	18.8132i	0.717280	−	0.696785i
$730$	−0.202670	−	0.668971i	−0.00750115	−	0.0247597i
$731$	6.38561	+	8.78903i	0.236180	+	0.325074i
$732$	7.14023	−	1.69599i	0.263911	−	0.0626855i
$733$	−6.98056	+	44.0735i	−0.257833	+	1.62789i	0.430565	+	0.902559i	$0.358314\pi$
$733$	−6.98056	+	44.0735i	−0.257833	+	1.62789i	−0.688398	+	0.725333i	$0.741686\pi$
$734$	8.34641	+	25.6876i	0.308072	+	0.948147i
$735$	−8.08390	+	4.70800i	−0.298179	+	0.173657i
$736$	−0.478373	+	1.47228i	−0.0176331	+	0.0542690i
$737$	−6.83537	−	3.48279i	−0.251784	−	0.128290i
$738$	−0.0235020	+	4.86510i	−0.000865122	+	0.179087i
$739$	−8.01855	−	2.60538i	−0.294967	−	0.0958406i	0.157795	−	0.987472i	$-0.449561\pi$
$739$	−8.01855	−	2.60538i	−0.294967	−	0.0958406i	−0.452762	+	0.891631i	$0.649561\pi$
$740$	−0.486676	−	0.0870881i	−0.0178906	−	0.00320142i
$741$	−9.58877	−	2.32657i	−0.352252	−	0.0854687i
$742$	−12.8402	−	2.03368i	−0.471378	−	0.0746589i
$743$	24.9192	+	24.9192i	0.914196	+	0.914196i	0.996599	−	0.0824029i	$-0.0262594\pi$
$743$	24.9192	+	24.9192i	0.914196	+	0.914196i	−0.0824029	+	0.996599i	$0.526259\pi$
$744$	−1.40428	−	18.4115i	−0.0514834	−	0.674999i
$745$	−19.8673	+	26.2261i	−0.727882	+	0.960849i
$746$	−15.7261	+	21.6451i	−0.575772	+	0.792482i
$747$	−13.2503	−	18.4239i	−0.484802	−	0.674097i
$748$	−15.4553	−	30.3327i	−0.565101	−	1.10907i
$749$	12.6933			0.463804
$750$	−18.5114	−	5.68586i	−0.675940	−	0.207618i
$751$	−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
$753$	−33.7201	−	14.0628i	−1.22883	−	0.512478i
$754$	2.82250	−	3.88484i	0.102789	−	0.141477i
$755$	11.5428	−	15.2372i	0.420086	−	0.554539i
$756$	9.52817	−	5.74432i	0.346536	−	0.208919i
$757$	5.57829	+	5.57829i	0.202746	+	0.202746i	0.801176	−	0.598429i	$-0.204208\pi$
$757$	5.57829	+	5.57829i	0.202746	+	0.202746i	−0.598429	+	0.801176i	$0.704208\pi$
$758$	15.5940	+	2.46985i	0.566400	+	0.0897089i
$759$	3.74130	−	15.4195i	0.135801	−	0.559691i
$760$	11.8690	+	2.12389i	0.430533	+	0.0770416i
$761$	5.92036	+	1.92364i	0.214613	+	0.0697320i	0.414350	−	0.910118i	$-0.364009\pi$
$761$	5.92036	+	1.92364i	0.214613	+	0.0697320i	−0.199737	+	0.979849i	$0.564009\pi$
$762$	−15.4681	+	9.42757i	−0.560352	+	0.341525i
$763$	−3.60114	−	1.83487i	−0.130370	−	0.0664268i
$764$	6.49209	−	19.9806i	0.234875	−	0.722872i
$765$	−0.957807	+	38.5794i	−0.0346296	+	1.39484i
$766$	4.93411	+	15.1856i	0.178276	+	0.548679i
$767$	1.19862	−	7.56779i	0.0432796	−	0.273257i
$768$	−0.400270	−	1.68517i	−0.0144435	−	0.0608082i
$769$	−2.22958	−	3.06876i	−0.0804008	−	0.110662i	0.766922	−	0.641740i	$-0.221787\pi$
$769$	−2.22958	−	3.06876i	−0.0804008	−	0.110662i	−0.847323	+	0.531078i	$0.821787\pi$
$770$	8.21475	+	27.1152i	0.296039	+	0.977163i
$771$	−11.0514	−	26.8637i	−0.398006	−	0.967473i
$772$	1.55066	+	9.79050i	0.0558096	+	0.352368i
$773$	−30.3587	+	15.4685i	−1.09193	+	0.556364i	−0.904742	−	0.425960i	$-0.859936\pi$
$773$	−30.3587	+	15.4685i	−1.09193	+	0.556364i	−0.187185	+	0.982325i	$0.559936\pi$
$774$	−2.54757	−	5.06017i	−0.0915704	−	0.181884i
$775$	−41.8369	−	33.0299i	−1.50283	−	1.18647i
$776$		−	12.0641i		−	0.433077i
$777$	0.0663100	−	0.817305i	0.00237886	−	0.0293206i
$778$	−11.3942	+	1.80467i	−0.408503	+	0.0647005i
$779$	−7.07466	−	5.14004i	−0.253476	−	0.184161i
$780$	3.43992	+	2.21550i	0.123169	+	0.0793277i
$781$	−19.5390	+	14.1959i	−0.699159	+	0.507969i
$782$	6.29727	−	6.29727i	0.225190	−	0.225190i
$783$	−22.9250	−	5.67980i	−0.819272	−	0.202980i
$784$	−2.29721	+	0.746410i	−0.0820433	+	0.0266575i
$785$	55.0914	−	7.60007i	1.96630	−	0.271258i
$786$	21.9087	+	25.7776i	0.781456	+	0.919455i
$787$	14.2544	−	27.9758i	0.508114	−	0.997230i	−0.484371	−	0.874863i	$-0.660951\pi$
$787$	14.2544	−	27.9758i	0.508114	−	0.997230i	0.992485	−	0.122367i	$-0.0390486\pi$
$788$	−4.63424	+	9.09520i	−0.165088	+	0.324003i
$789$	25.5205	+	30.0272i	0.908554	+	1.06900i
$790$	−1.52376	+	1.46402i	−0.0542130	+	0.0520876i
$791$	−17.2729	+	5.61232i	−0.614155	+	0.199551i
$792$	5.40430	+	16.9103i	0.192034	+	0.600880i
$793$	−3.16524	+	3.16524i	−0.112401	+	0.112401i
$794$	16.9444	−	12.3108i	0.601334	−	0.436895i
$795$	−18.2187	+	14.8674i	−0.646152	+	0.527293i
$796$	−12.2281	−	8.88422i	−0.433413	−	0.314893i
$797$	−10.4366	+	1.65300i	−0.369685	+	0.0585523i	−0.338513	−	0.940962i	$-0.609924\pi$
$797$	−10.4366	+	1.65300i	−0.369685	+	0.0585523i	−0.0311718	+	0.999514i	$0.509924\pi$
$798$	−1.61716	+	19.9323i	−0.0572467	+	0.705596i
$799$			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
$804$	0.854267	+	2.07656i	0.0301277	+	0.0732345i
$805$	−6.08208	+	4.23576i	−0.214365	+	0.149291i
$806$	6.62002	+	9.11167i	0.233180	+	0.320945i
$807$	4.14454	+	17.4488i	0.145895	+	0.614227i
$808$	0.0485388	−	0.306462i	0.00170759	−	0.0107813i
$809$	−4.15772	−	12.7961i	−0.146178	−	0.449889i	0.850983	−	0.525193i	$-0.176007\pi$
$809$	−4.15772	−	12.7961i	−0.146178	−	0.449889i	−0.997161	+	0.0753048i	$0.976007\pi$
$810$	3.73611	−	19.7748i	0.131274	−	0.694815i
$811$	6.32531	−	19.4673i	0.222112	−	0.683590i	−0.776460	−	0.630166i	$-0.782987\pi$
$811$	6.32531	−	19.4673i	0.222112	−	0.683590i	0.998572	−	0.0534235i	$-0.0170133\pi$
$812$	−8.67148	−	4.41834i	−0.304309	−	0.155053i
$813$	0.945720	−	0.576400i	0.0331678	−	0.0202152i
$814$	1.24438	+	0.404322i	0.0436154	+	0.0141715i
$815$	−4.04319	+	1.95931i	−0.141627	+	0.0686317i
$816$	−2.34950	+	9.68328i	−0.0822490	+	0.338983i
$817$	10.0575	+	1.59296i	0.351869	+	0.0557306i
$818$	−6.92463	−	6.92463i	−0.242114	−	0.242114i
$819$	−3.11001	+	6.03153i	−0.108673	+	0.210759i
$820$	2.07240	+	2.97574i	0.0723714	+	0.103917i
$821$	−11.1279	+	15.3163i	−0.388368	+	0.534543i	−0.957777	−	0.287512i	$-0.907172\pi$
$821$	−11.1279	+	15.3163i	−0.388368	+	0.534543i	0.569409	+	0.822054i	$0.307172\pi$
$822$	19.1671	+	7.99355i	0.668528	+	0.278807i
$823$	−7.17013	−	14.0722i	−0.249935	−	0.490525i	0.731618	−	0.681715i	$-0.238765\pi$
$823$	−7.17013	−	14.0722i	−0.249935	−	0.490525i	−0.981553	+	0.191190i	$0.938765\pi$
$824$	8.83429			0.307757
$825$	46.4732	+	21.6009i	1.61799	+	0.752048i
$826$	−15.5291			−0.540326
$827$	3.08387	+	6.05244i	0.107237	+	0.210464i	0.938389	−	0.345581i	$-0.112318\pi$
$827$	3.08387	+	6.05244i	0.107237	+	0.210464i	−0.831152	+	0.556045i	$0.812318\pi$
$828$	−3.77033	+	2.71158i	−0.131028	+	0.0942338i
$829$	11.0240	−	15.1733i	0.382880	−	0.526989i	−0.573465	−	0.819230i	$-0.694401\pi$
$829$	11.0240	−	15.1733i	0.382880	−	0.526989i	0.956345	+	0.292241i	$0.0944010\pi$
$830$	−15.9794	−	5.54756i	−0.554654	−	0.192558i
$831$	3.99936	+	52.4356i	0.138736	+	1.81897i
$832$	0.747028	+	0.747028i	0.0258985	+	0.0258985i
$833$	13.7246	+	2.17376i	0.475528	+	0.0753162i
$834$	−39.1697	−	9.50393i	−1.35634	−	0.329094i
$835$	22.9901	+	23.9281i	0.795604	+	0.828067i
$836$	−30.3476	−	9.86055i	−1.04960	−	0.341034i
$837$	29.2853	−	47.0210i	1.01225	−	1.62528i
$838$	22.9876	+	11.7128i	0.794093	+	0.404611i
$839$	5.00273	−	15.3968i	0.172713	−	0.531557i	−0.826808	−	0.562484i	$-0.809846\pi$
$839$	5.00273	−	15.3968i	0.172713	−	0.531557i	0.999522	+	0.0309268i	$0.00984587\pi$
$840$	3.34433	−	7.58841i	0.115390	−	0.261825i
$841$	−2.57725	−	7.93197i	−0.0888709	−	0.273516i
$842$	6.16556	−	38.9278i	0.212479	−	1.34154i
$843$	36.5959	−	8.69245i	1.26043	−	0.299384i
$844$	−2.33443	−	3.21307i	−0.0803545	−	0.110598i
$845$	26.5679	+	0.531192i	0.913963	+	0.0182736i
$846$	2.32620	−	14.2414i	0.0799763	−	0.489631i
$847$	−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
$852$	7.04585	+	0.571647i	0.241387	+	0.0195843i
$853$	−32.4823	+	5.14470i	−1.11217	+	0.176151i	−0.685371	−	0.728194i	$-0.740360\pi$
$853$	−32.4823	+	5.14470i	−1.11217	+	0.176151i	−0.426803	+	0.904345i	$0.640360\pi$
$854$	7.33967	+	5.33258i	0.251158	+	0.182477i
$855$	24.9351	+	26.2048i	0.852763	+	0.896184i
$856$	4.79605	−	3.48453i	0.163926	−	0.119099i
$857$	14.2417	−	14.2417i	0.486489	−	0.486489i	−0.420708	−	0.907196i	$-0.638218\pi$
$857$	14.2417	−	14.2417i	0.486489	−	0.486489i	0.907196	+	0.420708i	$0.138218\pi$
$858$	−8.21687	−	7.05226i	−0.280519	−	0.240760i
$859$	29.9968	−	9.74655i	1.02348	−	0.332548i	0.251269	−	0.967917i	$-0.419152\pi$
$859$	29.9968	−	9.74655i	1.02348	−	0.332548i	0.772208	+	0.635369i	$0.219152\pi$
$860$	−3.72333	−	1.99187i	−0.126965	−	0.0679222i
$861$	−4.58274	+	3.89492i	−0.156179	+	0.132739i
$862$	−2.79055	+	5.47676i	−0.0950465	+	0.186539i
$863$	9.85205	−	19.3357i	0.335368	−	0.658196i	−0.660318	−	0.750986i	$-0.729579\pi$
$863$	9.85205	−	19.3357i	0.335368	−	0.658196i	0.995686	+	0.0927901i	$0.0295785\pi$
$864$	2.02321	−	4.78608i	0.0688312	−	0.162826i
$865$	−1.97512	+	11.0376i	−0.0671559	+	0.375288i
$866$	−15.9153	+	5.17119i	−0.540824	+	0.175724i
$867$	18.1564	−	21.1548i	0.616625	−	0.718454i
$868$	16.1407	−	16.1407i	0.547852	−	0.547852i
$869$	4.52418	−	3.28701i	0.153472	−	0.111504i
$870$	−16.4107	+	6.37065i	−0.556376	+	0.215985i
$871$	−1.10801	−	0.805017i	−0.0375435	−	0.0272770i
$872$	−1.86436	+	0.295286i	−0.0631352	+	0.00999963i
$873$	21.4146	−	29.1772i	0.724773	−	0.987497i
$874$		−	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	−0.564092	−	0.825712i	$-0.690774\pi$
$877$	−6.74142	+	3.43493i	−0.227642	+	0.115989i	0.336450	+	0.941701i	$0.390774\pi$
$878$	−3.14677	−	19.8679i	−0.106198	−	0.670510i
$879$	27.7558	−	11.4184i	0.936181	−	0.385132i
$880$	10.5474	+	7.99012i	0.355554	+	0.269347i
$881$	−18.8656	−	25.9662i	−0.635597	−	0.874825i	0.362774	−	0.931877i	$-0.381830\pi$
$881$	−18.8656	−	25.9662i	−0.635597	−	0.874825i	−0.998371	+	0.0570525i	$0.981830\pi$
$882$	−6.88074	−	2.27249i	−0.231687	−	0.0765189i
$883$	−4.49099	+	28.3550i	−0.151134	+	0.954222i	0.789241	+	0.614083i	$0.210474\pi$
$883$	−4.49099	+	28.3550i	−0.151134	+	0.954222i	−0.940375	+	0.340139i	$0.889526\pi$
$884$	−1.87810	−	5.78018i	−0.0631672	−	0.194409i
$885$	−18.7166	+	20.9453i	−0.629151	+	0.704068i
$886$	7.49794	−	23.0763i	0.251898	−	0.775263i
$887$	−10.8136	−	5.50981i	−0.363086	−	0.185001i	0.262924	−	0.964816i	$-0.415313\pi$
$887$	−10.8136	−	5.50981i	−0.363086	−	0.185001i	−0.626010	+	0.779815i	$0.715313\pi$
$888$	−0.199310	−	0.327014i	−0.00668839	−	0.0109739i
$889$	−21.2974	−	6.91994i	−0.714291	−	0.232087i
$890$	9.12822	−	17.0631i	0.305979	−	0.571956i
$891$	−16.9464	+	50.4905i	−0.567725	+	1.69149i
$892$	13.2221	+	2.09418i	0.442710	+	0.0701183i
$893$	18.3403	+	18.3403i	0.613736	+	0.613736i
$894$	−25.4117	+	1.93820i	−0.849893	+	0.0648230i
$895$	−6.78107	+	2.05438i	−0.226666	+	0.0686703i
$896$	1.25854	−	1.73224i	0.0420450	−	0.0578699i
$897$	1.09034	−	2.61442i	0.0364052	−	0.0872931i
$898$	−7.22945	−	14.1886i	−0.241250	−	0.473479i
$899$	−48.4565			−1.61611
$900$	−6.20429	−	13.6567i	−0.206810	−	0.455225i
$901$	34.9289			1.16365
$902$	−4.35682	−	8.55073i	−0.145066	−	0.284708i
$903$	2.69571	−	6.46382i	0.0897076	−	0.215102i
$904$	−4.98574	+	6.86228i	−0.165823	+	0.228236i
$905$	0.278950	−	13.9519i	0.00927262	−	0.463776i
$906$	14.7641	−	1.12608i	0.490503	−	0.0374116i
$907$	18.7112	+	18.7112i	0.621295	+	0.621295i	0.945863	−	0.324567i	$-0.105219\pi$
$907$	18.7112	+	18.7112i	0.621295	+	0.621295i	−0.324567	+	0.945863i	$0.605219\pi$
$908$	−0.845381	−	0.133895i	−0.0280549	−	0.00444347i
$909$	0.661379	−	0.655020i	0.0219366	−	0.0217257i
$910$	0.691235	+	5.01063i	0.0229142	+	0.166101i
$911$	37.0222	+	12.0293i	1.22660	+	0.398547i	0.849482	−	0.527618i	$-0.176915\pi$
$911$	37.0222	+	12.0293i	1.22660	+	0.398547i	0.377119	+	0.926165i	$0.376915\pi$
$912$	4.86073	+	7.97517i	0.160955	+	0.264084i
$913$	39.8854	+	20.3226i	1.32002	+	0.672581i
$914$	−1.00626	+	3.09695i	−0.0332842	+	0.102438i
$915$	16.0387	−	3.47243i	0.530222	−	0.114795i
$916$	−5.11297	−	15.7361i	−0.168937	−	0.519935i
$917$	−6.54220	+	41.3058i	−0.216042	+	1.36404i
$918$	−22.8707	+	19.2486i	−0.754845	+	0.635297i
$919$	13.4831	+	18.5579i	0.444766	+	0.612168i	0.971263	−	0.238009i	$-0.0764948\pi$
$919$	13.4831	+	18.5579i	0.444766	+	0.612168i	−0.526497	+	0.850177i	$0.676495\pi$
$920$	−1.13527	+	3.27008i	−0.0374287	+	0.107811i
$921$	−38.0871	+	15.6685i	−1.25501	+	0.516296i
$922$	−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
$927$	21.3658	+	15.6814i	0.701744	+	0.515045i
$928$	−4.48935	+	0.711043i	−0.147370	+	0.0233411i
$929$	−0.473139	−	0.343755i	−0.0155232	−	0.0112782i	0.579997	−	0.814619i	$-0.303054\pi$
$929$	−0.473139	−	0.343755i	−0.0155232	−	0.0112782i	−0.595520	+	0.803341i	$0.703054\pi$
$930$	−2.31647	−	41.2240i	−0.0759602	−	1.35179i
$931$	10.5372	−	7.65572i	0.345342	−	0.250906i
$932$	3.85413	−	3.85413i	0.126246	−	0.126246i
$933$	8.77606	−	10.2253i	0.287315	−	0.334763i
$934$	4.41971	−	1.43605i	0.144617	−	0.0469891i
$935$	−33.1963	−	68.5032i	−1.08564	−	2.24029i
$936$	0.480671	+	3.13271i	0.0157112	+	0.102396i
$937$	−25.3343	+	49.7213i	−0.827634	+	1.62432i	−0.0473659	+	0.998878i	$0.515083\pi$
$937$	−25.3343	+	49.7213i	−0.827634	+	1.62432i	−0.780268	+	0.625445i	$0.784917\pi$
$938$	−1.26017	+	2.47323i	−0.0411461	+	0.0807538i
$939$	−27.4508	+	23.3308i	−0.895824	+	0.761372i
$940$	−4.69040	−	9.67901i	−0.152984	−	0.315695i
$941$	12.5712	−	4.08462i	0.409808	−	0.133155i	−0.0968556	−	0.995298i	$-0.530879\pi$
$941$	12.5712	−	4.08462i	0.409808	−	0.133155i	0.506664	+	0.862144i	$0.330879\pi$
$942$	32.6889	+	28.0558i	1.06506	+	0.914108i
$943$	1.77519	−	1.77519i	0.0578082	−	0.0578082i
$944$	−5.86752	+	4.26300i	−0.190972	+	0.138749i
$945$	21.5581	−	12.4162i	0.701287	−	0.403900i
$946$	9.04074	+	6.56848i	0.293940	+	0.213560i
$947$	−17.8550	+	2.82795i	−0.580210	+	0.0918962i	−0.439639	−	0.898174i	$-0.644894\pi$
$947$	−17.8550	+	2.82795i	−0.580210	+	0.0918962i	−0.140571	+	0.990071i	$0.544894\pi$
$948$	−1.63144	−	0.132363i	−0.0529868	−	0.00429895i
$949$			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	−0.657671	−	0.753305i	$-0.728458\pi$
$953$	−8.17990	−	51.6458i	−0.264973	−	1.67297i	0.392698	−	0.919667i	$-0.371542\pi$
$954$	−17.9765	−	2.93629i	−0.582011	−	0.0950658i
$955$	15.4070	−	44.3788i	0.498557	−	1.43607i
$956$	−5.12250	−	7.05051i	−0.165673	−	0.228030i
$957$	45.3265	−	10.7662i	1.46520	−	0.348022i
$958$	2.47121	−	15.6026i	0.0798412	−	0.504097i
$959$	7.93318	+	24.4158i	0.256176	+	0.788428i
$960$	−0.819528	−	3.78528i	−0.0264502	−	0.122170i
$961$	25.5409	−	78.6068i	0.823900	−	2.53570i
$962$	0.208129	+	0.106047i	0.00671033	+	0.00341909i
$963$	17.7845	+	0.0859123i	0.573098	+	0.00276849i
$964$	24.1813	+	7.85699i	0.778828	+	0.253056i
$965$	3.02907	+	21.9572i	0.0975094	+	0.706826i
$966$	−5.57920	−	1.35371i	−0.179508	−	0.0435549i
$967$	−30.7047	−	4.86314i	−0.987395	−	0.156388i	−0.358208	−	0.933642i	$-0.616612\pi$
$967$	−30.7047	−	4.86314i	−0.987395	−	0.156388i	−0.629187	+	0.777254i	$0.716612\pi$
$968$	−16.9834	−	16.9834i	−0.545867	−	0.545867i
$969$	−4.08621	−	53.5743i	−0.131268	−	1.72106i
$970$	0.539248	−	26.9708i	0.0173142	−	0.865981i
$971$	25.2468	−	34.7493i	0.810210	−	1.11516i	−0.181081	−	0.983468i	$-0.557960\pi$
$971$	25.2468	−	34.7493i	0.810210	−	1.11516i	0.991291	−	0.131690i	$-0.0420404\pi$
$972$	13.3887	−	7.98384i	0.429444	−	0.256082i
$973$	−22.6208	−	44.3957i	−0.725188	−	1.42326i
$974$	0.135570			0.00434393
$975$	7.59134	+	5.10678i	0.243117	+	0.163548i
$976$	4.23711			0.135627
$977$	26.9394	+	52.8715i	0.861867	+	1.69151i	0.711276	+	0.702912i	$0.248117\pi$
$977$	26.9394	+	52.8715i	0.861867	+	1.69151i	0.150590	+	0.988596i	$0.451883\pi$
$978$	−3.21206	−	1.33958i	−0.102710	−	0.0428349i
$979$	−30.1017	+	41.4314i	−0.962054	+	1.32415i
$980$	−5.16906	+	1.56601i	−0.165120	+	0.0500243i
$981$	−5.03311	−	2.59520i	−0.160695	−	0.0828584i
$982$	−6.43398	−	6.43398i	−0.205317	−	0.205317i
$983$	−37.5537	−	5.94792i	−1.19778	−	0.189709i	−0.474492	−	0.880260i	$-0.657368\pi$
$983$	−37.5537	−	5.94792i	−1.19778	−	0.189709i	−0.723284	+	0.690550i	$0.757368\pi$
$984$	−0.662320	+	2.72970i	−0.0211140	+	0.0870197i
$985$	−10.7669	+	20.1263i	−0.343063	+	0.641277i
$986$	24.8687	+	8.08033i	0.791981	+	0.257330i
$987$	15.2323	−	9.28386i	0.484851	−	0.295508i
$988$	−5.07580	−	2.58625i	−0.161483	−	0.0822796i
$989$	−0.903372	+	2.78029i	−0.0287255	+	0.0884081i
$990$	11.3261	+	38.0465i	0.359967	+	1.20920i
$991$	9.31171	+	28.6585i	0.295796	+	0.910367i	0.982953	+	0.183858i	$0.0588585\pi$
$991$	9.31171	+	28.6585i	0.295796	+	0.910367i	−0.687157	+	0.726509i	$0.741141\pi$
$992$	1.66771	−	10.5295i	0.0529499	−	0.334313i
$993$	2.87721	+	12.1132i	0.0913054	+	0.384402i
$994$	5.13648	+	7.06976i	0.162919	+	0.224239i
$995$	−26.9403	−	20.4083i	−0.854063	−	0.646988i
$996$	−4.98478	−	12.1170i	−0.157949	−	0.383943i
$997$	5.29952	+	33.4599i	0.167838	+	1.05968i	0.917463	+	0.397822i	$0.130234\pi$
$997$	5.29952	+	33.4599i	0.167838	+	1.05968i	−0.749625	+	0.661863i	$0.769766\pi$
$998$	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.47.7	yes	80
3.2	odd	2	inner	150.2.l.a.47.1	✓	80
5.2	odd	4		750.2.l.a.743.5		80
5.3	odd	4		750.2.l.c.743.6		80
5.4	even	2		750.2.l.b.257.4		80
15.2	even	4		750.2.l.a.743.6		80
15.8	even	4		750.2.l.c.743.5		80
15.14	odd	2		750.2.l.b.257.10		80
25.6	even	5		750.2.l.c.107.5		80
25.8	odd	20	inner	150.2.l.a.83.1	yes	80
25.17	odd	20		750.2.l.b.143.10		80
25.19	even	10		750.2.l.a.107.6		80
75.8	even	20	inner	150.2.l.a.83.7	yes	80
75.17	even	20		750.2.l.b.143.4		80
75.44	odd	10		750.2.l.a.107.5		80
75.56	odd	10		750.2.l.c.107.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.1	✓	80	3.2	odd	2	inner
150.2.l.a.47.7	yes	80	1.1	even	1	trivial
150.2.l.a.83.1	yes	80	25.8	odd	20	inner
150.2.l.a.83.7	yes	80	75.8	even	20	inner
750.2.l.a.107.5		80	75.44	odd	10
750.2.l.a.107.6		80	25.19	even	10
750.2.l.a.743.5		80	5.2	odd	4
750.2.l.a.743.6		80	15.2	even	4
750.2.l.b.143.4		80	75.17	even	20
750.2.l.b.143.10		80	25.17	odd	20
750.2.l.b.257.4		80	5.4	even	2
750.2.l.b.257.10		80	15.14	odd	2
750.2.l.c.107.5		80	25.6	even	5
750.2.l.c.107.6		80	75.56	odd	10
750.2.l.c.743.5		80	15.8	even	4
750.2.l.c.743.6		80	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.453990 + 0.891007i) q^{2} +(-0.666690 + 1.59860i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.35023 + 1.78238i) q^{5} +(-1.72703 + 0.131724i) q^{6} +(-1.51403 - 1.51403i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(-2.11105 - 2.13154i) q^{9} +O(q^{10})\)	\(q+(0.453990 + 0.891007i) q^{2} +(-0.666690 + 1.59860i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.35023 + 1.78238i) q^{5} +(-1.72703 + 0.131724i) q^{6} +(-1.51403 - 1.51403i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(-2.11105 - 2.13154i) q^{9} +(-2.20110 - 0.393876i) q^{10} +(5.62798 + 1.82864i) q^{11} +(-0.901424 - 1.47900i) q^{12} +(0.941310 + 0.479621i) q^{13} +(0.661655 - 2.03636i) q^{14} +(-1.94913 - 3.34677i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.899945 + 5.68203i) q^{17} +(0.940823 - 2.84866i) q^{18} +(3.16950 + 4.36244i) q^{19} +(-0.648334 - 2.14001i) q^{20} +(3.42972 - 1.41094i) 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} +(4.81490 - 1.95364i) q^{27} +(2.11480 - 0.334951i) q^{28} +(-3.67723 - 2.67167i) q^{29} +(2.09711 - 3.25609i) q^{30} +(8.62475 - 6.26624i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.67539 + 7.77776i) q^{33} +(-5.47129 + 1.77773i) q^{34} +(4.74286 - 0.654296i) q^{35} +(2.96530 - 0.454984i) q^{36} +(0.100380 - 0.197006i) q^{37} +(-2.44804 + 4.80455i) q^{38} +(-1.39429 + 1.18502i) q^{39} +(1.61243 - 1.54922i) q^{40} +(-1.54235 + 0.501139i) q^{41} +(2.81421 + 2.41535i) q^{42} +(1.33532 - 1.33532i) q^{43} +(-4.78745 + 3.47829i) q^{44} +(6.64962 - 0.884628i) q^{45} +(-1.25240 - 0.909919i) q^{46} +(4.75083 - 0.752458i) q^{47} +(1.72638 + 0.140065i) 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} +(3.92663 + 3.40317i) q^{54} +(-10.8584 + 7.56214i) q^{55} +(1.25854 + 1.73224i) q^{56} +(-9.08688 + 2.15837i) q^{57} +(0.711043 - 4.48935i) q^{58} +(-2.24119 - 6.89769i) q^{59} +(3.85327 + 0.390300i) q^{60} +(-1.30934 + 4.02973i) q^{61} +(9.49882 + 4.83989i) q^{62} +(-0.0310298 + 6.42341i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-2.12585 + 1.03018i) q^{65} +(-9.96060 - 2.41679i) q^{66} +(-1.28043 - 0.202800i) q^{67} +(-4.06788 - 4.06788i) q^{68} +(-0.203915 - 2.67353i) q^{69} +(2.73620 + 3.92888i) q^{70} +(-2.39892 + 3.30183i) q^{71} +(1.75161 + 2.43554i) q^{72} +(0.141918 + 0.278530i) q^{73} +0.221105 q^{74} +(8.59700 + 1.04480i) q^{75} -5.39228 q^{76} +(-5.75231 - 11.2895i) q^{77} +(-1.68885 - 0.704330i) q^{78} +(0.555462 - 0.764528i) q^{79} +(2.11239 + 0.733356i) q^{80} +(-0.0869513 + 8.99958i) q^{81} +(-1.14673 - 1.14673i) q^{82} +(7.47149 + 1.18337i) q^{83} +(-0.874463 + 3.60403i) q^{84} +(-8.91242 - 9.27607i) q^{85} +(1.79600 + 0.583556i) q^{86} +(6.72250 - 4.09725i) q^{87} +(-5.27263 - 2.68654i) q^{88} +(-2.67429 + 8.23061i) q^{89} +(3.80707 + 5.52324i) q^{90} +(-0.699010 - 2.15133i) q^{91} +(0.242168 - 1.52899i) q^{92} +(4.26719 + 17.9652i) q^{93} +(2.82728 + 3.89142i) q^{94} +(-12.0551 - 0.241026i) q^{95} +(0.658960 + 1.60180i) 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

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