LMFDB - Embedded newform 152.2.o.c.27.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(27,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.27"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-3,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.3
Character	$\chi$	$=$	152.27
Dual form			152.2.o.c.107.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34230 + 0.445227i) q^{2} +(0.705625 + 0.407393i) q^{3} +(1.60355 - 1.19526i) q^{4} +(-3.59735 - 2.07693i) q^{5} +(-1.12854 - 0.232681i) q^{6} -3.24695i q^{7} +(-1.62028 + 2.31834i) q^{8} +(-1.16806 - 2.02314i) q^{9} +(5.75343 + 1.18623i) q^{10} -1.21833 q^{11} +(1.61844 - 0.190130i) q^{12} +(2.01425 + 3.48878i) q^{13} +(1.44563 + 4.35839i) q^{14} +(-1.69225 - 2.93107i) q^{15} +(1.14272 - 3.83330i) q^{16} +(1.50282 - 2.60296i) q^{17} +(2.46865 + 2.19562i) q^{18} +(-2.16355 - 3.78405i) q^{19} +(-8.25097 + 0.969300i) q^{20} +(1.32279 - 2.29113i) q^{21} +(1.63536 - 0.542432i) q^{22} +(3.01328 - 1.73972i) q^{23} +(-2.08779 + 0.975785i) q^{24} +(6.12726 + 10.6127i) q^{25} +(-4.25703 - 3.78620i) q^{26} -4.34780i q^{27} +(-3.88094 - 5.20664i) q^{28} +(2.35755 + 4.08339i) q^{29} +(3.57650 + 3.18094i) q^{30} -5.99801 q^{31} +(0.172808 + 5.65421i) q^{32} +(-0.859683 - 0.496338i) q^{33} +(-0.858329 + 4.16305i) q^{34} +(-6.74369 + 11.6804i) q^{35} +(-4.29122 - 1.84807i) q^{36} -1.34860 q^{37} +(4.58890 + 4.11607i) q^{38} +3.28236i q^{39} +(10.6437 - 4.97465i) q^{40} +(2.97093 + 1.71527i) q^{41} +(-0.755505 + 3.66433i) q^{42} +(-1.01615 + 1.76003i) q^{43} +(-1.95365 + 1.45621i) q^{44} +9.70392i q^{45} +(-3.27016 + 3.67682i) q^{46} +(8.37318 - 4.83426i) q^{47} +(2.36799 - 2.23934i) q^{48} -3.54271 q^{49} +(-12.9497 - 11.5175i) q^{50} +(2.12085 - 1.22448i) q^{51} +(7.39993 + 3.18688i) q^{52} +(-1.22182 - 2.11626i) q^{53} +(1.93576 + 5.83606i) q^{54} +(4.38275 + 2.53038i) q^{55} +(7.52753 + 5.26099i) q^{56} +(0.0149406 - 3.55154i) q^{57} +(-4.98257 - 4.43150i) q^{58} +(-9.35127 - 5.39896i) q^{59} +(-6.21698 - 2.67743i) q^{60} +(0.300922 - 0.173737i) q^{61} +(8.05114 - 2.67048i) q^{62} +(-6.56905 + 3.79264i) q^{63} +(-2.74937 - 7.51272i) q^{64} -16.7338i q^{65} +(1.37494 + 0.283482i) q^{66} +(8.31107 - 4.79840i) q^{67} +(-0.701363 - 5.97022i) q^{68} +2.83500 q^{69} +(3.85164 - 18.6811i) q^{70} +(0.581533 - 1.00725i) q^{71} +(6.58292 + 0.570103i) q^{72} +(1.46675 - 2.54048i) q^{73} +(1.81022 - 0.600431i) q^{74} +9.98482i q^{75} +(-7.99227 - 3.48191i) q^{76} +3.95586i q^{77} +(-1.46140 - 4.40592i) q^{78} +(2.57780 - 4.46489i) q^{79} +(-12.0723 + 11.4163i) q^{80} +(-1.73292 + 3.00151i) q^{81} +(-4.75157 - 0.979669i) q^{82} +11.7265 q^{83} +(-0.617343 - 5.25501i) q^{84} +(-10.8123 + 6.24249i) q^{85} +(0.580372 - 2.81491i) q^{86} +3.84179i q^{87} +(1.97404 - 2.82449i) q^{88} +(-12.1643 + 7.02306i) q^{89} +(-4.32044 - 13.0256i) q^{90} +(11.3279 - 6.54017i) q^{91} +(2.75253 - 6.39137i) q^{92} +(-4.23235 - 2.44355i) q^{93} +(-9.08699 + 10.2170i) q^{94} +(-0.0761686 + 18.1061i) q^{95} +(-2.18155 + 4.06016i) q^{96} +(12.1187 + 6.99673i) q^{97} +(4.75539 - 1.57731i) q^{98} +(1.42308 + 2.46485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) $ 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.34230	+	0.445227i	−0.949150	+	0.314823i
$2$	−1.34230	+	0.445227i	−0.949150	+	0.314823i
$3$	0.705625	+	0.407393i	0.407393	+	0.235208i	0.689669	−	0.724125i	$-0.257756\pi$
$3$	0.705625	+	0.407393i	0.407393	+	0.235208i	−0.282276	+	0.959333i	$0.591089\pi$
$4$	1.60355	−	1.19526i	0.801773	−	0.597628i
$5$	−3.59735	−	2.07693i	−1.60878	−	0.928831i	−0.989643	−	0.143549i	$-0.954149\pi$
$5$	−3.59735	−	2.07693i	−1.60878	−	0.928831i	−0.619139	−	0.785282i	$-0.712518\pi$
$6$	−1.12854	−	0.232681i	−0.460726	−	0.0949916i
$7$		−	3.24695i		−	1.22723i	−0.789604	−	0.613617i	$-0.789714\pi$
$7$		−	3.24695i		−	1.22723i	0.789604	−	0.613617i	$-0.210286\pi$
$8$	−1.62028	+	2.31834i	−0.572857	+	0.819656i
$9$	−1.16806	−	2.02314i	−0.389354	−	0.674381i
$10$	5.75343	+	1.18623i	1.81939	+	0.375119i
$11$	−1.21833			−0.367340			−0.183670	−	0.982988i	$-0.558798\pi$
$11$	−1.21833			−0.367340			−0.183670	+	0.982988i	$0.558798\pi$
$12$	1.61844	−	0.190130i	0.467204	−	0.0548857i
$13$	2.01425	+	3.48878i	0.558652	+	0.967614i	0.997609	+	0.0691058i	$0.0220146\pi$
$13$	2.01425	+	3.48878i	0.558652	+	0.967614i	−0.438957	+	0.898508i	$0.644652\pi$
$14$	1.44563	+	4.35839i	0.386361	+	1.16483i
$15$	−1.69225	−	2.93107i	−0.436938	−	0.756798i
$16$	1.14272	−	3.83330i	0.285681	−	0.958325i
$17$	1.50282	−	2.60296i	0.364487	−	0.631310i	−0.624207	−	0.781259i	$-0.714578\pi$
$17$	1.50282	−	2.60296i	0.364487	−	0.631310i	0.988694	+	0.149949i	$0.0479110\pi$
$18$	2.46865	+	2.19562i	0.581866	+	0.517511i
$19$	−2.16355	−	3.78405i	−0.496352	−	0.868121i
$19$	−2.16355	−	3.78405i	−0.496352	−	0.868121i
$20$	−8.25097	+	0.969300i	−1.84497	+	0.216742i
$21$	1.32279	−	2.29113i	0.288656	−	0.499966i
$22$	1.63536	−	0.542432i	0.348661	−	0.115647i
$23$	3.01328	−	1.73972i	0.628313	−	0.362756i	−0.151786	−	0.988413i	$-0.548502\pi$
$23$	3.01328	−	1.73972i	0.628313	−	0.362756i	0.780098	+	0.625657i	$0.215169\pi$
$24$	−2.08779	+	0.975785i	−0.426168	+	0.199181i
$25$	6.12726	+	10.6127i	1.22545	+	2.12255i
$26$	−4.25703	−	3.78620i	−0.834872	−	0.742535i
$27$		−	4.34780i		−	0.836734i
$28$	−3.88094	−	5.20664i	−0.733429	−	0.983963i
$29$	2.35755	+	4.08339i	0.437785	+	0.758266i	0.997518	−	0.0704067i	$-0.0224297\pi$
$29$	2.35755	+	4.08339i	0.437785	+	0.758266i	−0.559733	+	0.828673i	$0.689096\pi$
$30$	3.57650	+	3.18094i	0.652977	+	0.580757i
$31$	−5.99801			−1.07728			−0.538638	−	0.842538i	$-0.681061\pi$
$31$	−5.99801			−1.07728			−0.538638	+	0.842538i	$0.681061\pi$
$32$	0.172808	+	5.65421i	0.0305484	+	0.999533i
$33$	−0.859683	−	0.496338i	−0.149652	−	0.0864014i
$34$	−0.858329	+	4.16305i	−0.147202	+	0.713957i
$35$	−6.74369	+	11.6804i	−1.13989	+	1.97435i
$36$	−4.29122	−	1.84807i	−0.715203	−	0.308012i
$37$	−1.34860			−0.221708			−0.110854	−	0.993837i	$-0.535359\pi$
$37$	−1.34860			−0.221708			−0.110854	+	0.993837i	$0.535359\pi$
$38$	4.58890	+	4.11607i	0.744417	+	0.667715i
$39$			3.28236i			0.525599i
$40$	10.6437	−	4.97465i	1.68292	−	0.786560i
$41$	2.97093	+	1.71527i	0.463981	+	0.267880i	0.713717	−	0.700434i	$-0.247010\pi$
$41$	2.97093	+	1.71527i	0.463981	+	0.267880i	−0.249736	+	0.968314i	$0.580344\pi$
$42$	−0.755505	+	3.66433i	−0.116577	+	0.565419i
$43$	−1.01615	+	1.76003i	−0.154962	+	0.268402i	−0.933045	−	0.359759i	$-0.882859\pi$
$43$	−1.01615	+	1.76003i	−0.154962	+	0.268402i	0.778083	+	0.628161i	$0.216192\pi$
$44$	−1.95365	+	1.45621i	−0.294523	+	0.219533i
$45$			9.70392i			1.44658i
$46$	−3.27016	+	3.67682i	−0.482159	+	0.542118i
$47$	8.37318	−	4.83426i	1.22135	−	0.705149i	0.256147	−	0.966638i	$-0.417547\pi$
$47$	8.37318	−	4.83426i	1.22135	−	0.705149i	0.965207	+	0.261489i	$0.0842134\pi$
$48$	2.36799	−	2.23934i	0.341790	−	0.323220i
$49$	−3.54271			−0.506102
$50$	−12.9497	−	11.5175i	−1.83136	−	1.62882i
$51$	2.12085	−	1.22448i	0.296979	−	0.171461i
$52$	7.39993	+	3.18688i	1.02619	+	0.441941i
$53$	−1.22182	−	2.11626i	−0.167830	−	0.290690i	0.769827	−	0.638253i	$-0.220343\pi$
$53$	−1.22182	−	2.11626i	−0.167830	−	0.290690i	−0.937657	+	0.347563i	$0.887009\pi$
$54$	1.93576	+	5.83606i	0.263423	+	0.794187i
$55$	4.38275	+	2.53038i	0.590969	+	0.341196i
$56$	7.52753	+	5.26099i	1.00591	+	0.703029i
$57$	0.0149406	−	3.55154i	0.00197893	−	0.470413i
$58$	−4.98257	−	4.43150i	−0.654244	−	0.581884i
$59$	−9.35127	−	5.39896i	−1.21743	−	0.702885i	−0.253064	−	0.967450i	$-0.581438\pi$
$59$	−9.35127	−	5.39896i	−1.21743	−	0.702885i	−0.964368	+	0.264565i	$0.914772\pi$
$60$	−6.21698	−	2.67743i	−0.802609	−	0.345654i
$61$	0.300922	−	0.173737i	0.0385291	−	0.0222448i	−0.480612	−	0.876934i	$-0.659585\pi$
$61$	0.300922	−	0.173737i	0.0385291	−	0.0222448i	0.519141	+	0.854689i	$0.326252\pi$
$62$	8.05114	−	2.67048i	1.02250	−	0.339151i
$63$	−6.56905	+	3.79264i	−0.827623	+	0.477828i
$64$	−2.74937	−	7.51272i	−0.343671	−	0.939090i
$65$		−	16.7338i		−	2.07557i
$66$	1.37494	+	0.283482i	0.169243	+	0.0348942i
$67$	8.31107	−	4.79840i	1.01536	−	0.586218i	0.102603	−	0.994722i	$-0.467283\pi$
$67$	8.31107	−	4.79840i	1.01536	−	0.586218i	0.912756	+	0.408505i	$0.133950\pi$
$68$	−0.701363	−	5.97022i	−0.0850528	−	0.723995i
$69$	2.83500			0.341294
$70$	3.85164	−	18.6811i	0.460359	−	2.23282i
$71$	0.581533	−	1.00725i	0.0690153	−	0.119538i	−0.829453	−	0.558577i	$-0.811348\pi$
$71$	0.581533	−	1.00725i	0.0690153	−	0.119538i	0.898468	+	0.439039i	$0.144681\pi$
$72$	6.58292	+	0.570103i	0.775804	+	0.0671873i
$73$	1.46675	−	2.54048i	0.171670	−	0.297341i	−0.767334	−	0.641248i	$-0.778417\pi$
$73$	1.46675	−	2.54048i	0.171670	−	0.297341i	0.939004	+	0.343907i	$0.111750\pi$
$74$	1.81022	−	0.600431i	0.210434	−	0.0697987i
$75$			9.98482i			1.15295i
$76$	−7.99227	−	3.48191i	−0.916776	−	0.399402i
$77$			3.95586i			0.450812i
$78$	−1.46140	−	4.40592i	−0.165470	−	0.498872i
$79$	2.57780	−	4.46489i	0.290026	−	0.502339i	−0.683790	−	0.729679i	$-0.739670\pi$
$79$	2.57780	−	4.46489i	0.290026	−	0.502339i	0.973815	+	0.227340i	$0.0730029\pi$
$80$	−12.0723	+	11.4163i	−1.34972	+	1.27639i
$81$	−1.73292	+	3.00151i	−0.192547	+	0.333501i
$82$	−4.75157	−	0.979669i	−0.524723	−	0.108186i
$83$	11.7265			1.28715			0.643574	−	0.765384i	$-0.277451\pi$
$83$	11.7265			1.28715			0.643574	+	0.765384i	$0.277451\pi$
$84$	−0.617343	−	5.25501i	−0.0673576	−	0.573368i
$85$	−10.8123	+	6.24249i	−1.17276	+	0.677093i
$86$	0.580372	−	2.81491i	0.0625831	−	0.303539i
$87$			3.84179i			0.411883i
$88$	1.97404	−	2.82449i	0.210433	−	0.301092i
$89$	−12.1643	+	7.02306i	−1.28941	+	0.744443i	−0.978550	−	0.206011i	$-0.933952\pi$
$89$	−12.1643	+	7.02306i	−1.28941	+	0.744443i	−0.310864	+	0.950455i	$0.600618\pi$
$90$	−4.32044	−	13.0256i	−0.455415	−	1.37302i
$91$	11.3279	−	6.54017i	1.18749	−	0.685596i
$92$	2.75253	−	6.39137i	0.286971	−	0.666346i
$93$	−4.23235	−	2.44355i	−0.438874	−	0.253384i
$94$	−9.08699	+	10.2170i	−0.937252	+	1.05380i
$95$	−0.0761686	+	18.1061i	−0.00781474	+	1.85764i
$96$	−2.18155	+	4.06016i	−0.222653	+	0.414388i
$97$	12.1187	+	6.99673i	1.23047	+	0.710410i	0.967127	−	0.254293i	$-0.0818428\pi$
$97$	12.1187	+	6.99673i	1.23047	+	0.710410i	0.263339	+	0.964703i	$0.415176\pi$
$98$	4.75539	−	1.57731i	0.480367	−	0.159332i
$99$	1.42308	+	2.46485i	0.143025	+	0.247727i
$100$	22.5103	+	9.69436i	2.25103	+	0.969436i
$101$	17.3113	−	9.99467i	1.72254	−	0.994507i	0.808932	−	0.587903i	$-0.200046\pi$
$101$	17.3113	−	9.99467i	1.72254	−	0.994507i	0.913604	−	0.406604i	$-0.133287\pi$
$102$	−2.30166	+	2.58788i	−0.227898	+	0.256238i
$103$	1.87110			0.184365			0.0921826	−	0.995742i	$-0.470616\pi$
$103$	1.87110			0.184365			0.0921826	+	0.995742i	$0.470616\pi$
$104$	−11.3518	−	0.983106i	−1.11314	−	0.0964015i
$105$	−9.51704	+	5.49467i	−0.928768	+	0.536225i
$106$	2.58227	+	2.29667i	0.250812	+	0.223072i
$107$		−	4.39763i		−	0.425135i	−0.977146	−	0.212567i	$-0.931817\pi$
$107$		−	4.39763i		−	0.425135i	0.977146	−	0.212567i	$-0.0681825\pi$
$108$	−5.19674	−	6.97190i	−0.500056	−	0.670871i
$109$	1.94786	−	3.37379i	0.186571	−	0.323150i	−0.757534	−	0.652796i	$-0.773596\pi$
$109$	1.94786	−	3.37379i	0.186571	−	0.323150i	0.944105	+	0.329646i	$0.106929\pi$
$110$	−7.00956	−	1.44522i	−0.668335	−	0.137796i
$111$	−0.951604	−	0.549409i	−0.0903222	−	0.0521476i
$112$	−12.4465	−	3.71037i	−1.17609	−	0.350597i
$113$			0.221322i			0.0208202i	0.999946	+	0.0104101i	$0.00331369\pi$
$113$			0.221322i			0.0208202i	−0.999946	+	0.0104101i	$0.996686\pi$
$114$	1.56118	+	4.77389i	0.146218	+	0.447116i
$115$	−14.4531			−1.34776
$116$	8.66113	+	3.73003i	0.804166	+	0.346325i
$117$	4.70553	−	8.15022i	0.435027	−	0.753488i
$118$	14.9560	+	3.08360i	1.37681	+	0.283868i
$119$	−8.45169	−	4.87958i	−0.774765	−	0.447311i
$120$	9.53713	+	0.825948i	0.870617	+	0.0753984i
$121$	−9.51568			−0.865062
$122$	−0.326576	+	0.367187i	−0.0295668	+	0.0332435i
$123$	1.39758	+	2.42067i	0.126015	+	0.218265i
$124$	−9.61810	+	7.16917i	−0.863731	+	0.643810i
$125$		−	30.1343i		−	2.69529i
$126$	7.12906	−	8.01559i	0.635107	−	0.714085i
$127$	4.30308	+	7.45316i	0.381837	+	0.661361i	0.991325	−	0.131435i	$-0.0419583\pi$
$127$	4.30308	+	7.45316i	0.381837	+	0.661361i	−0.609488	+	0.792795i	$0.708625\pi$
$128$	7.03534	+	8.86025i	0.621842	+	0.783143i
$129$	−1.43405	+	0.827947i	−0.126261	+	0.0728967i
$130$	7.45033	+	22.4618i	0.653437	+	1.97003i
$131$	0.494676	−	0.856804i	0.0432201	−	0.0748593i	−0.843606	−	0.536962i	$-0.819572\pi$
$131$	0.494676	−	0.856804i	0.0432201	−	0.0748593i	0.886826	+	0.462103i	$0.152905\pi$
$132$	−1.97179	+	0.231640i	−0.171623	+	0.0201617i
$133$	−12.2866	+	7.02495i	−1.06539	+	0.609140i
$134$	−9.01959	+	10.1412i	−0.779174	+	0.876067i
$135$	−9.03007	+	15.6405i	−0.777184	+	1.34612i
$136$	3.59954	+	7.70157i	0.308658	+	0.660404i
$137$	9.20933	+	15.9510i	0.786806	+	1.36279i	0.927914	+	0.372794i	$0.121600\pi$
$137$	9.20933	+	15.9510i	0.786806	+	1.36279i	−0.141108	+	0.989994i	$0.545066\pi$
$138$	−3.80542	+	1.26222i	−0.323939	+	0.107447i
$139$	−5.46807	−	9.47098i	−0.463796	−	0.803318i	0.535350	−	0.844630i	$-0.320180\pi$
$139$	−5.46807	−	9.47098i	−0.463796	−	0.803318i	−0.999146	+	0.0413120i	$0.986846\pi$
$140$	3.14727	+	26.7905i	0.265993	+	2.26421i
$141$	7.87777			0.663428
$142$	−0.332141	+	1.61094i	−0.0278726	+	0.135187i
$143$	−2.45401	−	4.25048i	−0.205215	−	0.355443i
$144$	−9.09008	+	2.16564i	−0.757507	+	0.180470i
$145$		−	19.5858i		−	1.62651i
$146$	−0.837728	+	4.06313i	−0.0693308	+	0.336267i
$147$	−2.49983	−	1.44328i	−0.206182	−	0.119039i
$148$	−2.16254	+	1.61192i	−0.177759	+	0.132499i
$149$	0.679549	+	0.392338i	0.0556708	+	0.0321416i	0.527577	−	0.849507i	$-0.323101\pi$
$149$	0.679549	+	0.392338i	0.0556708	+	0.0321416i	−0.471906	+	0.881649i	$0.656434\pi$
$150$	−4.44551	−	13.4026i	−0.362974	−	1.09432i
$151$	−4.53858			−0.369344			−0.184672	−	0.982800i	$-0.559122\pi$
$151$	−4.53858			−0.369344			−0.184672	+	0.982800i	$0.559122\pi$
$152$	12.2783	+	1.11540i	0.995899	+	0.0904708i
$153$	−7.02154			−0.567658
$154$	−1.76125	−	5.30995i	−0.141926	−	0.427888i
$155$	21.5769	+	12.4574i	1.73310	+	1.00061i
$156$	3.92327	+	5.26342i	0.314113	+	0.421411i
$157$	−7.14123	−	4.12299i	−0.569932	−	0.329050i	0.187190	−	0.982324i	$-0.440062\pi$
$157$	−7.14123	−	4.12299i	−0.569932	−	0.329050i	−0.757122	+	0.653273i	$0.773395\pi$
$158$	−1.47230	+	7.14093i	−0.117130	+	0.568102i
$159$		−	1.99105i		−	0.157900i
$160$	11.1217	−	20.6991i	0.879251	−	1.63641i
$161$	−5.64879	−	9.78399i	−0.445187	−	0.771086i
$162$	0.989753	−	4.80048i	0.0777623	−	0.377161i
$163$	3.99098			0.312597			0.156299	−	0.987710i	$-0.450044\pi$
$163$	3.99098			0.312597			0.156299	+	0.987710i	$0.450044\pi$
$164$	6.81421	−	0.800513i	0.532100	−	0.0625095i
$165$	2.06172	+	3.57100i	0.160505	+	0.278002i
$166$	−15.7405	+	5.22094i	−1.22170	+	0.405223i
$167$	−9.24487	−	16.0126i	−0.715390	−	1.23909i	−0.962809	−	0.270183i	$-0.912916\pi$
$167$	−9.24487	−	16.0126i	−0.715390	−	1.23909i	0.247419	−	0.968909i	$-0.420418\pi$
$168$	3.16833	+	6.77895i	0.244442	+	0.523007i
$169$	−1.61439	+	2.79621i	−0.124184	+	0.215093i
$170$	11.7341	−	13.1932i	0.899961	−	1.01188i
$171$	−5.12852	+	8.79718i	−0.392187	+	0.672737i
$172$	0.474237	+	4.03685i	0.0361602	+	0.307807i
$173$	−1.81313	+	3.14044i	−0.137850	+	0.238763i	−0.926683	−	0.375845i	$-0.877353\pi$
$173$	−1.81313	+	3.14044i	−0.137850	+	0.238763i	0.788833	+	0.614608i	$0.210686\pi$
$174$	−1.71047	−	5.15684i	−0.129670	−	0.390939i
$175$	34.4591	−	19.8949i	2.60486	−	1.50392i
$176$	−1.39221	+	4.67022i	−0.104942	+	0.352031i
$177$	−4.39900	−	7.61928i	−0.330649	−	0.572700i
$178$	13.2013	−	14.8429i	0.989480	−	1.11253i
$179$			15.8678i			1.18601i	0.805197	+	0.593007i	$0.202060\pi$
$179$			15.8678i			1.18601i	−0.805197	+	0.593007i	$0.797940\pi$
$180$	11.5987	+	15.5607i	0.864515	+	1.15983i
$181$	−2.14373	−	3.71305i	−0.159342	−	0.275989i	0.775289	−	0.631606i	$-0.217604\pi$
$181$	−2.14373	−	3.71305i	−0.159342	−	0.275989i	−0.934632	+	0.355617i	$0.884271\pi$
$182$	−12.2936	+	13.8224i	−0.911263	+	1.02458i
$183$	0.283118			0.0209287
$184$	−0.849115	+	9.80464i	−0.0625976	+	0.722807i
$185$	4.85137	+	2.80094i	0.356680	+	0.205929i
$186$	6.76902	+	1.39562i	0.496329	+	0.102332i
$187$	−1.83093	+	3.17126i	−0.133891	+	0.231905i
$188$	7.64861	−	17.7601i	0.557832	−	1.29529i
$189$	−14.1171			−1.02687
$190$	−7.95907	−	24.3377i	−0.577411	−	1.76564i
$191$			1.84103i			0.133212i	0.997779	+	0.0666060i	$0.0212171\pi$
$191$			1.84103i			0.133212i	−0.997779	+	0.0666060i	$0.978783\pi$
$192$	1.12061	−	6.42124i	0.0808729	−	0.463413i
$193$	−10.8408	−	6.25891i	−0.780335	−	0.450526i	0.0562143	−	0.998419i	$-0.482097\pi$
$193$	−10.8408	−	6.25891i	−0.780335	−	0.450526i	−0.836549	+	0.547892i	$0.815430\pi$
$194$	−19.3821	−	3.99616i	−1.39155	−	0.286907i
$195$	6.81723	−	11.8078i	0.488192	−	0.845574i
$196$	−5.68091	+	4.23445i	−0.405779	+	0.302461i
$197$			10.5073i			0.748613i	0.927305	+	0.374307i	$0.122119\pi$
$197$			10.5073i			0.748613i	−0.927305	+	0.374307i	$0.877881\pi$
$198$	−3.00762	−	2.67498i	−0.213742	−	0.190102i
$199$	−5.21989	+	3.01371i	−0.370028	+	0.213636i	−0.673471	−	0.739214i	$-0.735197\pi$
$199$	−5.21989	+	3.01371i	−0.370028	+	0.213636i	0.303443	+	0.952850i	$0.401864\pi$
$200$	−34.5318	−	2.99057i	−2.44177	−	0.211465i
$201$	7.81934			0.551534
$202$	−18.7871	+	21.1233i	−1.32185	+	1.48623i
$203$	13.2586	−	7.65484i	0.930570	−	0.537265i
$204$	1.93733	−	4.49847i	0.135640	−	0.314956i
$205$	−7.12497	−	12.3408i	−0.497630	−	0.861920i
$206$	−2.51158	+	0.833064i	−0.174990	+	0.0580423i
$207$	−7.03940	−	4.06420i	−0.489272	−	0.282481i
$208$	15.6753	−	3.73451i	1.08688	−	0.258941i
$209$	2.63591	+	4.61022i	0.182330	+	0.318895i
$210$	10.3284	−	11.6127i	0.712725	−	0.801355i
$211$	12.6720	+	7.31618i	0.872377	+	0.503667i	0.868137	−	0.496324i	$-0.165317\pi$
$211$	12.6720	+	7.31618i	0.872377	+	0.503667i	0.00423928	+	0.999991i	$0.498651\pi$
$212$	−4.48872	−	1.93313i	−0.308286	−	0.132768i
$213$	0.820689	−	0.473825i	0.0562327	−	0.0324660i
$214$	1.95794	+	5.90295i	0.133842	+	0.403517i
$215$	7.31090	−	4.22095i	0.498599	−	0.287867i
$216$	10.0797	+	7.04466i	0.685834	+	0.479329i
$217$			19.4753i			1.32207i
$218$	−1.11251	+	5.39588i	−0.0753488	+	0.365455i
$219$	2.06995	−	1.19509i	0.139874	−	0.0807564i
$220$	10.0524	−	1.18092i	0.677732	−	0.0796179i
$221$	12.1082			0.814486
$222$	1.52195	+	0.313793i	0.102147	+	0.0210604i
$223$	−13.7578	+	23.8293i	−0.921294	+	1.59573i	−0.123878	+	0.992297i	$0.539533\pi$
$223$	−13.7578	+	23.8293i	−0.921294	+	1.59573i	−0.797416	+	0.603430i	$0.793800\pi$
$224$	18.3590	−	0.561099i	1.22666	−	0.0374900i
$225$	14.3140	−	24.7927i	0.954270	−	1.65284i
$226$	−0.0985382	−	0.297080i	−0.00655467	−	0.0197615i
$227$		−	18.4655i		−	1.22560i	−0.790239	−	0.612799i	$-0.790044\pi$
$227$		−	18.4655i		−	1.22560i	0.790239	−	0.612799i	$-0.209956\pi$
$228$	−4.22104	−	5.71292i	−0.279545	−	0.378347i
$229$			18.8145i			1.24330i	0.783295	+	0.621650i	$0.213537\pi$
$229$			18.8145i			1.24330i	−0.783295	+	0.621650i	$0.786463\pi$
$230$	19.4004	−	6.43490i	1.27922	−	0.424305i
$231$	−1.61159	+	2.79135i	−0.106035	+	0.183657i
$232$	−13.2866	−	1.15066i	−0.872305	−	0.0755446i
$233$	−0.339317	+	0.587714i	−0.0222294	+	0.0385024i	−0.876926	−	0.480625i	$-0.840410\pi$
$233$	−0.339317	+	0.587714i	−0.0222294	+	0.0385024i	0.854697	+	0.519128i	$0.173743\pi$
$234$	−2.68755	+	13.0351i	−0.175691	+	0.852130i
$235$	−40.1616			−2.61986
$236$	−21.4483	+	2.51969i	−1.39617	+	0.164018i
$237$	3.63793	−	2.10036i	0.236309	−	0.136433i
$238$	13.5172	+	2.78696i	0.876192	+	0.180652i
$239$			4.57846i			0.296156i	0.988976	+	0.148078i	$0.0473087\pi$
$239$			4.57846i			0.296156i	−0.988976	+	0.148078i	$0.952691\pi$
$240$	−13.1694	+	3.13751i	−0.850083	+	0.202525i
$241$	4.98480	−	2.87797i	0.321099	−	0.185387i	−0.330783	−	0.943707i	$-0.607313\pi$
$241$	4.98480	−	2.87797i	0.321099	−	0.185387i	0.651882	+	0.758320i	$0.273980\pi$
$242$	12.7729	−	4.23663i	0.821074	−	0.272341i
$243$	−13.7415	+	7.93366i	−0.881518	+	0.508945i
$244$	0.274882	−	0.638275i	0.0175975	−	0.0408614i
$245$	12.7444	+	7.35796i	0.814208	+	0.470083i
$246$	−2.95372	−	2.62703i	−0.188322	−	0.167494i
$247$	8.84380	−	15.1702i	0.562718	−	0.965255i
$248$	9.71848	−	13.9054i	0.617124	−	0.882995i
$249$	8.27450	+	4.77728i	0.524375	+	0.302748i
$250$	13.4166	+	40.4493i	0.848539	+	2.55824i
$251$	−7.52848	−	13.0397i	−0.475194	−	0.823059i	0.524403	−	0.851470i	$-0.324289\pi$
$251$	−7.52848	−	13.0397i	−0.475194	−	0.823059i	−0.999596	+	0.0284110i	$0.990955\pi$
$252$	−6.00060	+	13.9334i	−0.378002	+	0.877721i
$253$	−3.67116	+	2.11955i	−0.230804	+	0.133255i
$254$	−9.09438	−	8.08854i	−0.570632	−	0.507520i
$255$	−10.1726			−0.637032
$256$	−13.3884	−	8.76080i	−0.836773	−	0.547550i
$257$	−10.5279	+	6.07826i	−0.656709	+	0.379151i	−0.791022	−	0.611788i	$-0.790451\pi$
$257$	−10.5279	+	6.07826i	−0.656709	+	0.379151i	0.134313	+	0.990939i	$0.457117\pi$
$258$	1.55630	−	1.74983i	0.0968909	−	0.108940i
$259$			4.37883i			0.272087i
$260$	−20.0012	−	26.8334i	−1.24042	−	1.66414i
$261$	5.50752	−	9.53930i	0.340907	−	0.590468i
$262$	−0.282533	+	1.37033i	−0.0174549	+	0.0846594i
$263$	−8.19758	−	4.73288i	−0.505485	−	0.291842i	0.225491	−	0.974245i	$-0.427601\pi$
$263$	−8.19758	−	4.73288i	−0.505485	−	0.291842i	−0.730976	+	0.682404i	$0.760935\pi$
$264$	2.54361	−	1.18883i	0.156548	−	0.0731672i
$265$			10.1505i			0.623543i
$266$	13.3647	−	14.8999i	0.819442	−	0.913574i
$267$	−11.4446			−0.700397
$268$	7.59187	−	17.6283i	0.463747	−	1.07682i
$269$	1.65200	−	2.86135i	0.100724	−	0.174459i	−0.811259	−	0.584687i	$-0.801217\pi$
$269$	1.65200	−	2.86135i	0.100724	−	0.174459i	0.911983	+	0.410227i	$0.134551\pi$
$270$	5.15749	−	25.0147i	0.313875	−	1.52235i
$271$	−10.3868	−	5.99685i	−0.630956	−	0.364282i	0.150166	−	0.988661i	$-0.452019\pi$
$271$	−10.3868	−	5.99685i	−0.630956	−	0.364282i	−0.781122	+	0.624378i	$0.785352\pi$
$272$	−8.26061	−	8.73521i	−0.500873	−	0.529650i
$273$	10.6577			0.645032
$274$	−19.4635	−	17.3108i	−1.17583	−	1.04579i
$275$	−7.46502	−	12.9298i	−0.450157	−	0.779695i
$276$	4.54605	−	3.38855i	0.273640	−	0.203967i
$277$			12.2692i			0.737185i	0.929591	+	0.368592i	$0.120160\pi$
$277$			12.2692i			0.737185i	−0.929591	+	0.368592i	$0.879840\pi$
$278$	11.5565	+	10.2784i	0.693115	+	0.616456i
$279$	7.00605	+	12.1348i	0.419441	+	0.726494i
$280$	−16.1524	−	34.5597i	−0.965293	−	2.06534i
$281$	10.4906	−	6.05677i	0.625819	−	0.361317i	−0.153312	−	0.988178i	$-0.548994\pi$
$281$	10.4906	−	6.05677i	0.625819	−	0.361317i	0.779131	+	0.626861i	$0.215661\pi$
$282$	−10.5743	+	3.50739i	−0.629693	+	0.208862i
$283$	6.53976	−	11.3272i	0.388748	−	0.673332i	−0.603533	−	0.797338i	$-0.706241\pi$
$283$	6.53976	−	11.3272i	0.388748	−	0.673332i	0.992281	+	0.124006i	$0.0395742\pi$
$284$	−0.271401	−	2.31025i	−0.0161047	−	0.137088i
$285$	−7.43004	+	12.7451i	−0.440117	+	0.754953i
$286$	5.18645	+	4.61283i	0.306681	+	0.272762i
$287$	5.56939	−	9.64647i	0.328751	−	0.569413i
$288$	11.2374	−	6.95409i	0.662172	−	0.409773i
$289$	3.98307	+	6.89889i	0.234298	+	0.405817i
$290$	8.72013	+	26.2901i	0.512063	+	1.54381i
$291$	5.70084	+	9.87414i	0.334189	+	0.578832i
$292$	−0.684529	−	5.82692i	−0.0400590	−	0.340995i
$293$	11.8661			0.693224			0.346612	−	0.938009i	$-0.387332\pi$
$293$	11.8661			0.693224			0.346612	+	0.938009i	$0.387332\pi$
$294$	3.99811	+	0.824323i	0.233174	+	0.0480755i
$295$	22.4265	+	38.8438i	1.30572	+	2.26158i
$296$	2.18511	−	3.12650i	0.127007	−	0.181724i
$297$			5.29704i			0.307366i
$298$	−1.08684	−	0.224082i	−0.0629589	−	0.0129807i
$299$	12.1390	+	7.00845i	0.702016	+	0.405309i
$300$	11.9344	+	16.0111i	0.689034	+	0.924402i
$301$	5.71473	+	3.29940i	0.329392	+	0.190174i
$302$	6.09214	−	2.02070i	0.350563	−	0.116278i
$303$	16.2870			0.935666
$304$	−16.9777	+	3.96941i	−0.973740	+	0.227661i
$305$	−1.44336			−0.0826466
$306$	9.42502	−	3.12618i	0.538793	−	0.178712i
$307$	−16.1814	−	9.34236i	−0.923524	−	0.533197i	−0.0387664	−	0.999248i	$-0.512343\pi$
$307$	−16.1814	−	9.34236i	−0.923524	−	0.533197i	−0.884758	+	0.466051i	$0.845676\pi$
$308$	4.72826	+	6.34340i	0.269418	+	0.361449i
$309$	1.32030	+	0.762274i	0.0751091	+	0.0433642i
$310$	−34.5091	−	7.11503i	−1.95999	−	0.404106i
$311$		−	17.9447i		−	1.01755i	−0.860900	−	0.508774i	$-0.830099\pi$
$311$		−	17.9447i		−	1.01755i	0.860900	−	0.508774i	$-0.169901\pi$
$312$	−7.60962	−	5.31836i	−0.430810	−	0.301093i
$313$	15.8925	+	27.5267i	0.898300	+	1.55590i	0.829667	+	0.558259i	$0.188530\pi$
$313$	15.8925	+	27.5267i	0.898300	+	1.55590i	0.0686331	+	0.997642i	$0.478136\pi$
$314$	11.4213	+	2.35483i	0.644544	+	0.132891i
$315$	31.5082			1.77529
$316$	−1.20306	−	10.2408i	−0.0676773	−	0.576089i
$317$	4.48565	+	7.76938i	0.251939	+	0.436372i	0.964060	−	0.265686i	$-0.0855983\pi$
$317$	4.48565	+	7.76938i	0.251939	+	0.436372i	−0.712120	+	0.702057i	$0.752265\pi$
$318$	0.886467	+	2.67258i	0.0497106	+	0.149871i
$319$	−2.87226	−	4.97491i	−0.160816	−	0.278541i
$320$	−5.71296	+	32.7361i	−0.319364	+	1.83000i
$321$	1.79156	−	3.10308i	0.0999953	−	0.173197i
$322$	11.9385	+	10.6181i	0.665305	+	0.591722i
$323$	−13.1012	−	0.0551139i	−0.728968	−	0.00306662i
$324$	0.808753	+	6.88435i	0.0449307	+	0.382464i
$325$	−24.6837	+	42.7534i	−1.36920	+	2.37153i
$326$	−5.35709	+	1.77689i	−0.296702	+	0.0984128i
$327$	2.74892	−	1.58709i	0.152015	−	0.0877661i
$328$	−8.79031	+	4.10840i	−0.485364	+	0.226848i
$329$	−15.6966	−	27.1873i	−0.865382	−	1.49889i
$330$	−4.35735	−	3.87543i	−0.239864	−	0.213335i
$331$			29.7989i			1.63790i	0.573868	+	0.818948i	$0.305442\pi$
$331$			29.7989i			1.63790i	−0.573868	+	0.818948i	$0.694558\pi$
$332$	18.8039	−	14.0161i	1.03200	−	0.769236i
$333$	1.57524	+	2.72840i	0.0863228	+	0.149516i
$334$	19.5386	+	17.3777i	1.06911	+	0.950863i
$335$	−39.8637			−2.17799
$336$	−7.27102	−	7.68877i	−0.396667	−	0.419457i
$337$	−7.44373	−	4.29764i	−0.405486	−	0.234107i	0.283362	−	0.959013i	$-0.408550\pi$
$337$	−7.44373	−	4.29764i	−0.405486	−	0.234107i	−0.688848	+	0.724905i	$0.741883\pi$
$338$	0.922055	−	4.47213i	0.0501532	−	0.243252i
$339$	−0.0901649	+	0.156170i	−0.00489708	+	0.00848200i
$340$	−9.87667	+	22.9336i	−0.535638	+	1.24375i
$341$	7.30755			0.395726
$342$	2.96728	−	14.0918i	0.160452	−	0.761998i
$343$		−	11.2256i		−	0.606128i
$344$	−2.43388	−	5.20753i	−0.131226	−	0.280771i
$345$	−10.1985	−	5.88809i	−0.549067	−	0.317004i
$346$	1.03556	−	5.02267i	0.0556723	−	0.270020i
$347$	−7.95629	+	13.7807i	−0.427116	+	0.739787i	−0.996615	−	0.0822050i	$-0.973804\pi$
$347$	−7.95629	+	13.7807i	−0.427116	+	0.739787i	0.569499	+	0.821992i	$0.307137\pi$
$348$	4.59193	+	6.16049i	0.246153	+	0.330237i
$349$		−	11.3168i		−	0.605776i	−0.953026	−	0.302888i	$-0.902049\pi$
$349$		−	11.3168i		−	0.605776i	0.953026	−	0.302888i	$-0.0979507\pi$
$350$	−37.3967	+	42.0471i	−1.99894	+	2.24751i
$351$	15.1685	−	8.75755i	0.809636	−	0.467443i
$352$	−0.210536	−	6.88869i	−0.0112216	−	0.367168i
$353$	4.52158			0.240660			0.120330	−	0.992734i	$-0.461605\pi$
$353$	4.52158			0.240660			0.120330	+	0.992734i	$0.461605\pi$
$354$	9.29709	+	8.26883i	0.494135	+	0.439483i
$355$	−4.18395	+	2.41561i	−0.222061	+	0.128207i
$356$	−11.1117	+	25.8013i	−0.588917	+	1.36746i
$357$	−3.97582	−	6.88632i	−0.210422	−	0.364462i
$358$	−7.06477	−	21.2994i	−0.373384	−	1.12571i
$359$	29.7521	+	17.1774i	1.57026	+	0.906589i	0.996136	+	0.0878192i	$0.0279898\pi$
$359$	29.7521	+	17.1774i	1.57026	+	0.906589i	0.574122	+	0.818770i	$0.305344\pi$
$360$	−22.4970	−	15.7231i	−1.18569	−	0.828680i
$361$	−9.63810	+	16.3740i	−0.507269	+	0.861788i
$362$	4.53068	+	4.02959i	0.238127	+	0.211790i
$363$	−6.71450	−	3.87662i	−0.352420	−	0.203470i
$364$	10.3477	−	24.0272i	0.542364	−	1.25937i
$365$	−10.5528	+	6.09266i	−0.552359	+	0.318904i
$366$	−0.380029	+	0.126052i	−0.0198645	+	0.00658882i
$367$	24.5824	−	14.1927i	1.28319	−	0.740851i	0.305760	−	0.952108i	$-0.401089\pi$
$367$	24.5824	−	14.1927i	1.28319	−	0.740851i	0.977430	+	0.211258i	$0.0677560\pi$
$368$	−3.22552	−	13.5388i	−0.168142	−	0.705760i
$369$		−	8.01415i		−	0.417200i
$370$	−7.75905	−	1.59975i	−0.403374	−	0.0831668i
$371$	−6.87139	+	3.96720i	−0.356745	+	0.205967i
$372$	−9.70744	+	1.14040i	−0.503307	+	0.0591270i
$373$	−8.73811			−0.452442			−0.226221	−	0.974076i	$-0.572637\pi$
$373$	−8.73811			−0.452442			−0.226221	+	0.974076i	$0.572637\pi$
$374$	1.04573	−	5.07196i	0.0540732	−	0.262265i
$375$	12.2765	−	21.2635i	0.633955	−	1.09804i
$376$	−2.35949	+	27.2447i	−0.121681	+	1.40504i
$377$	−9.49737	+	16.4499i	−0.489139	+	0.847214i
$378$	18.9494	−	6.28531i	0.974653	−	0.323282i
$379$		−	12.0886i		−	0.620951i	−0.950581	−	0.310475i	$-0.899512\pi$
$379$		−	12.0886i		−	0.620951i	0.950581	−	0.310475i	$-0.100488\pi$
$380$	21.5193	+	29.1250i	1.10392	+	1.49408i
$381$			7.01218i			0.359245i
$382$	−0.819674	−	2.47121i	−0.0419382	−	0.126438i
$383$	−6.03554	+	10.4539i	−0.308402	+	0.534167i	−0.978013	−	0.208545i	$-0.933127\pi$
$383$	−6.03554	+	10.4539i	−0.308402	+	0.534167i	0.669611	+	0.742712i	$0.266461\pi$
$384$	1.35471	+	9.11816i	0.0691324	+	0.465309i
$385$	8.21603	−	14.2306i	0.418728	−	0.725257i
$386$	17.3382	+	3.57476i	0.882491	+	0.181950i
$387$	4.74772			0.241340
$388$	27.7958	−	3.26536i	1.41112	−	0.165774i
$389$	5.68110	−	3.27998i	0.288043	−	0.166302i	−0.349016	−	0.937117i	$-0.613484\pi$
$389$	5.68110	−	3.27998i	0.288043	−	0.166302i	0.637059	+	0.770815i	$0.280151\pi$
$390$	−3.89364	+	18.8848i	−0.197162	+	0.956271i
$391$		−	10.4579i		−	0.528880i
$392$	5.74020	−	8.21320i	0.289924	−	0.414829i
$393$	0.698112	−	0.403055i	0.0352151	−	0.0203314i
$394$	−4.67812	−	14.1039i	−0.235680	−	0.710546i
$395$	−18.5465	+	10.7078i	−0.933176	+	0.538769i
$396$	5.22811	+	2.25155i	0.262722	+	0.113145i
$397$	−16.0785	−	9.28295i	−0.806959	−	0.465898i	0.0389397	−	0.999242i	$-0.487602\pi$
$397$	−16.0785	−	9.28295i	−0.806959	−	0.465898i	−0.845899	+	0.533344i	$0.820935\pi$
$398$	5.66489	−	6.36934i	0.283955	−	0.319266i
$399$	−11.5317	−	0.0485115i	−0.577306	−	0.00242861i
$400$	47.6835	−	11.3602i	2.38418	−	0.568011i
$401$	−20.9710	−	12.1076i	−1.04724	−	0.604624i	−0.125365	−	0.992111i	$-0.540010\pi$
$401$	−20.9710	−	12.1076i	−1.04724	−	0.604624i	−0.921875	+	0.387486i	$0.873343\pi$
$402$	−10.4959	+	3.48138i	−0.523488	+	0.173635i
$403$	−12.0815	−	20.9258i	−0.601822	−	1.04239i
$404$	15.8132	−	36.7183i	0.786738	−	1.82681i
$405$	12.4678	−	7.19831i	0.619532	−	0.357687i
$406$	−14.3889	+	16.1782i	−0.714108	+	0.802910i
$407$	1.64303			0.0814421
$408$	−0.597637	+	6.90085i	−0.0295874	+	0.341643i
$409$	5.79614	−	3.34641i	0.286601	−	0.165469i	−0.349807	−	0.936822i	$-0.613753\pi$
$409$	5.79614	−	3.34641i	0.286601	−	0.165469i	0.636408	+	0.771353i	$0.280420\pi$
$410$	15.0583	+	13.3929i	0.743678	+	0.661427i
$411$			15.0073i			0.740254i
$412$	3.00040	−	2.23645i	0.147819	−	0.110182i
$413$	−17.5302	+	30.3631i	−0.862603	+	1.49407i
$414$	11.2585	+	2.32125i	0.553324	+	0.114083i
$415$	−42.1842	−	24.3550i	−2.07074	−	1.19554i
$416$	−19.3782	+	11.9919i	−0.950096	+	0.587950i
$417$		−	8.91062i		−	0.436355i
$418$	−5.59078	−	5.01472i	−0.273454	−	0.245278i
$419$	19.0537			0.930832			0.465416	−	0.885092i	$-0.345905\pi$
$419$	19.0537			0.930832			0.465416	+	0.885092i	$0.345905\pi$
$420$	−8.69348	+	20.1863i	−0.424199	+	0.984989i
$421$	17.3507	−	30.0523i	0.845622	−	1.46466i	−0.0394576	−	0.999221i	$-0.512563\pi$
$421$	17.3507	−	30.0523i	0.845622	−	1.46466i	0.885080	−	0.465439i	$-0.154104\pi$
$422$	−20.2670	−	4.17861i	−0.986582	−	0.203412i
$423$	−19.5608	−	11.2934i	−0.951078	−	0.549105i
$424$	6.88589	+	0.596342i	0.334408	+	0.0289609i
$425$	36.8327			1.78665
$426$	−0.890653	+	1.00141i	−0.0431523	+	0.0485184i
$427$	−0.564118	−	0.977080i	−0.0272996	−	0.0472842i
$428$	−5.25630	−	7.05180i	−0.254073	−	0.340862i
$429$		−	3.99899i		−	0.193073i
$430$	−7.93416	+	8.92080i	−0.382619	+	0.430199i
$431$	13.5200	+	23.4173i	0.651234	+	1.12797i	0.982824	+	0.184547i	$0.0590818\pi$
$431$	13.5200	+	23.4173i	0.651234	+	1.12797i	−0.331590	+	0.943424i	$0.607585\pi$
$432$	−16.6664	−	4.96833i	−0.801863	−	0.239039i
$433$	29.7946	−	17.2019i	1.43184	−	0.826670i	0.434574	−	0.900636i	$-0.356899\pi$
$433$	29.7946	−	17.2019i	1.43184	−	0.826670i	0.997261	+	0.0739655i	$0.0235655\pi$
$434$	−8.67091	−	26.1417i	−0.416217	−	1.25484i
$435$	7.97912	−	13.8202i	0.382570	−	0.662630i
$436$	−0.909063	−	7.73822i	−0.0435362	−	0.370593i
$437$	−13.1026	−	7.63845i	−0.626781	−	0.365396i
$438$	−2.24641	+	2.52576i	−0.107338	+	0.120686i
$439$	−0.606126	+	1.04984i	−0.0289288	+	0.0501062i	−0.880127	−	0.474738i	$-0.842543\pi$
$439$	−0.606126	+	1.04984i	−0.0289288	+	0.0501062i	0.851199	+	0.524844i	$0.175876\pi$
$440$	−12.9676	+	6.06075i	−0.618204	+	0.288935i
$441$	4.13811	+	7.16742i	0.197053	+	0.341306i
$442$	−16.2529	+	5.39089i	−0.773069	+	0.256419i
$443$	12.5887	+	21.8042i	0.598106	+	1.03595i	0.993100	+	0.117267i	$0.0374132\pi$
$443$	12.5887	+	21.8042i	0.598106	+	1.03595i	−0.394994	+	0.918684i	$0.629253\pi$
$444$	−2.18262	+	0.256408i	−0.103583	+	0.0121686i
$445$	58.3456			2.76585
$446$	7.85775	−	38.1115i	0.372075	−	1.80463i
$447$	0.319671	+	0.553687i	0.0151199	+	0.0261885i
$448$	−24.3935	+	8.92707i	−1.15248	+	0.421764i
$449$			21.4991i			1.01460i	0.861768	+	0.507302i	$0.169357\pi$
$449$			21.4991i			1.01460i	−0.861768	+	0.507302i	$0.830643\pi$
$450$	−8.17542	+	39.6522i	−0.385393	+	1.86922i
$451$	−3.61957	−	2.08976i	−0.170439	−	0.0984028i
$452$	0.264536	+	0.354899i	0.0124427	+	0.0166931i
$453$	−3.20254	−	1.84899i	−0.150468	−	0.0868729i
$454$	8.22132	+	24.7862i	0.385846	+	1.16328i
$455$	−54.3339			−2.54721
$456$	8.20945	+	5.78913i	0.384443	+	0.271101i
$457$	26.4299			1.23634			0.618168	−	0.786046i	$-0.287875\pi$
$457$	26.4299			1.23634			0.618168	+	0.786046i	$0.287875\pi$
$458$	−8.37674	−	25.2548i	−0.391419	−	1.18008i
$459$	−11.3171	−	6.53395i	−0.528239	−	0.304979i
$460$	−23.1762	+	17.2751i	−1.08060	+	0.805458i
$461$	−16.0782	−	9.28278i	−0.748839	−	0.432342i	0.0764354	−	0.997075i	$-0.475646\pi$
$461$	−16.0782	−	9.28278i	−0.748839	−	0.432342i	−0.825274	+	0.564732i	$0.808979\pi$
$462$	0.920453	−	4.46436i	0.0428233	−	0.207701i
$463$			18.5375i			0.861510i	0.902469	+	0.430755i	$0.141753\pi$
$463$			18.5375i			0.861510i	−0.902469	+	0.430755i	$0.858247\pi$
$464$	18.3469	−	4.37099i	0.851732	−	0.202918i
$465$	10.1502	+	17.5806i	0.470702	+	0.815280i
$466$	0.193799	−	0.939962i	0.00897759	−	0.0435429i
$467$	5.96750			0.276143			0.138072	−	0.990422i	$-0.455910\pi$
$467$	5.96750			0.276143			0.138072	+	0.990422i	$0.455910\pi$
$468$	−2.19607	−	18.6936i	−0.101513	−	0.864111i
$469$	−15.5802	−	26.9857i	−0.719426	−	1.24608i
$470$	53.9090	−	17.8810i	2.48664	−	0.824790i
$471$	−3.35935	−	5.81857i	−0.154791	−	0.268106i
$472$	27.6683	−	12.9315i	1.27354	−	0.595223i
$473$	1.23801	−	2.14429i	0.0569236	−	0.0985946i
$474$	−3.94806	+	4.43902i	−0.181340	+	0.203891i
$475$	26.9025	−	46.1471i	1.23437	−	2.11737i
$476$	−19.3850	+	2.27729i	−0.888511	+	0.104380i
$477$	−2.85433	+	4.94384i	−0.130691	+	0.226363i
$478$	−2.03845	−	6.14567i	−0.0932366	−	0.281097i
$479$	23.5115	−	13.5744i	1.07427	−	0.620229i	0.144924	−	0.989443i	$-0.453706\pi$
$479$	23.5115	−	13.5744i	1.07427	−	0.620229i	0.929344	+	0.369214i	$0.120373\pi$
$480$	16.2804	−	10.0749i	0.743097	−	0.459853i
$481$	−2.71641	−	4.70496i	−0.123858	−	0.214528i
$482$	−5.40975	+	6.08247i	−0.246407	+	0.277049i
$483$		−	9.20511i		−	0.418847i
$484$	−15.2588	+	11.3737i	−0.693583	+	0.516985i
$485$	−29.0634	−	50.3393i	−1.31970	−	2.28579i
$486$	14.9130	−	16.7674i	0.676466	−	0.760587i
$487$	35.4384			1.60587			0.802933	−	0.596070i	$-0.203272\pi$
$487$	35.4384			1.60587			0.802933	+	0.596070i	$0.203272\pi$
$488$	−0.0847971	+	0.979143i	−0.00383858	+	0.0443237i
$489$	2.81613	+	1.62590i	0.127350	+	0.0735255i
$490$	−20.3827	−	4.20248i	−0.920799	−	0.189848i
$491$	5.05769	−	8.76018i	0.228250	−	0.395341i	−0.729039	−	0.684472i	$-0.760033\pi$
$491$	5.05769	−	8.76018i	0.228250	−	0.395341i	0.957290	+	0.289131i	$0.0933662\pi$
$492$	5.13440	+	2.21120i	0.231477	+	0.0996885i
$493$	14.1719			0.638268
$494$	−5.11688	+	24.3004i	−0.230219	+	1.09333i
$495$		−	11.8226i		−	0.531385i
$496$	−6.85407	+	22.9922i	−0.307757	+	1.03238i
$497$	−3.27048	−	1.88821i	−0.146701	−	0.0846979i
$498$	−13.2338	−	2.72853i	−0.593023	−	0.122268i
$499$	5.83840	−	10.1124i	0.261363	−	0.452693i	−0.705242	−	0.708967i	$-0.749161\pi$
$499$	5.83840	−	10.1124i	0.261363	−	0.452693i	0.966604	+	0.256274i	$0.0824948\pi$
$500$	−36.0182	−	48.3217i	−1.61078	−	2.16101i
$501$		−	15.0652i		−	0.673063i
$502$	15.9111	+	14.1513i	0.710148	+	0.631605i
$503$	−26.1068	+	15.0728i	−1.16405	+	0.672062i	−0.952270	−	0.305256i	$-0.901258\pi$
$503$	−26.1068	+	15.0728i	−1.16405	+	0.672062i	−0.211776	+	0.977318i	$0.567925\pi$
$504$	1.85110	−	21.3744i	0.0824545	−	0.952093i
$505$	−83.0329			−3.69491
$506$	3.98413	−	4.47957i	0.177116	−	0.199141i
$507$	−2.27831	+	1.31539i	−0.101184	+	0.0584183i
$508$	15.8086	+	6.80820i	0.701394	+	0.302065i
$509$	3.66628	+	6.35018i	0.162505	+	0.281467i	0.935766	−	0.352620i	$-0.114709\pi$
$509$	3.66628	+	6.35018i	0.162505	+	0.281467i	−0.773261	+	0.634087i	$0.781376\pi$
$510$	13.6547	−	4.52911i	0.604640	−	0.200552i
$511$	−8.24883	−	4.76246i	−0.364907	−	0.210679i
$512$	21.8718	+	5.79878i	0.966605	+	0.256272i
$513$	−16.4523	+	9.40668i	−0.726387	+	0.415315i
$514$	11.4253	−	12.8461i	0.503951	−	0.566619i
$515$	−6.73100	−	3.88615i	−0.296603	−	0.171244i
$516$	−1.30995	+	3.04170i	−0.0576674	+	0.133904i
$517$	−10.2013	+	5.88971i	−0.448652	+	0.259029i
$518$	−1.94957	−	5.87771i	−0.0856593	−	0.258252i
$519$	−2.55879	+	1.47732i	−0.112318	+	0.0648469i
$520$	38.7946	+	27.1135i	1.70125	+	1.18901i
$521$		−	33.7736i		−	1.47965i	−0.672800	−	0.739825i	$-0.734908\pi$
$521$		−	33.7736i		−	1.47965i	0.672800	−	0.739825i	$-0.265092\pi$
$522$	−3.14560	+	15.2567i	−0.137679	+	0.667768i
$523$	−10.2580	+	5.92247i	−0.448552	+	0.258972i	−0.707219	−	0.706995i	$-0.750050\pi$
$523$	−10.2580	+	5.92247i	−0.448552	+	0.258972i	0.258666	+	0.965967i	$0.416717\pi$
$524$	−0.230865	−	1.96519i	−0.0100854	−	0.0858497i
$525$	32.4202			1.41494
$526$	13.1108	+	2.70317i	0.571659	+	0.117864i
$527$	−9.01393	+	15.6126i	−0.392653	+	0.680095i
$528$	−2.88499	+	2.72825i	−0.125553	+	0.118732i
$529$	−5.44676	+	9.43406i	−0.236815	+	0.410176i
$530$	−4.51929	−	13.6251i	−0.196305	−	0.591836i
$531$			25.2253i			1.09468i
$532$	−11.3056	+	25.9505i	−0.490160	+	1.12510i
$533$			13.8199i			0.598606i
$534$	15.3621	−	5.09543i	0.664782	−	0.220501i
$535$	−9.13356	+	15.8198i	−0.394878	+	0.683949i
$536$	−2.34198	+	27.0426i	−0.101158	+	1.16806i
$537$	−6.46443	+	11.1967i	−0.278961	+	0.483174i
$538$	−0.943534	+	4.57631i	−0.0406786	+	0.197299i
$539$	4.31619			0.185911
$540$	4.21432	+	35.8736i	0.181355	+	1.54375i
$541$	−2.24678	+	1.29718i	−0.0965967	+	0.0557701i	−0.547520	−	0.836792i	$-0.684428\pi$
$541$	−2.24678	+	1.29718i	−0.0965967	+	0.0557701i	0.450923	+	0.892563i	$0.351095\pi$
$542$	16.6122	+	3.42508i	0.713556	+	0.147120i
$543$		−	3.49336i		−	0.149915i
$544$	14.9774	+	8.04745i	0.642150	+	0.345031i
$545$	−14.0142	+	8.09112i	−0.600304	+	0.346586i
$546$	−14.3058	+	4.74508i	−0.612233	+	0.203071i
$547$	7.78965	−	4.49735i	0.333061	−	0.192293i	−0.324138	−	0.946010i	$-0.605074\pi$
$547$	7.78965	−	4.49735i	0.333061	−	0.192293i	0.657199	+	0.753717i	$0.271741\pi$
$548$	33.8332	+	14.5707i	1.44528	+	0.622430i
$549$	−0.702991	−	0.405872i	−0.0300029	−	0.0173222i
$550$	15.7770	+	14.0320i	0.672733	+	0.598329i
$551$	10.3511	−	17.7557i	0.440971	−	0.756418i
$552$	−4.59350	+	6.57248i	−0.195512	+	0.279743i
$553$	−14.4973	−	8.37001i	−0.616487	−	0.355929i
$554$	−5.46257	−	16.4690i	−0.232083	−	0.699699i
$555$	2.28216	+	3.95283i	0.0968725	+	0.167788i
$556$	−20.0886	−	8.65141i	−0.851945	−	0.366901i
$557$	−27.7574	+	16.0257i	−1.17612	+	0.679032i	−0.955113	−	0.296241i	$-0.904267\pi$
$557$	−27.7574	+	16.0257i	−1.17612	+	0.679032i	−0.221004	+	0.975273i	$0.570934\pi$
$558$	−14.8070	−	13.1693i	−0.626830	−	0.557502i
$559$	−8.18713			−0.346279
$560$	37.0684	+	39.1981i	1.56642	+	1.65642i
$561$	−2.58389	+	1.49181i	−0.109092	+	0.0629844i
$562$	−11.3850	+	12.8007i	−0.480246	+	0.539966i
$563$			30.9719i			1.30531i	0.757655	+	0.652656i	$0.226345\pi$
$563$			30.9719i			1.30531i	−0.757655	+	0.652656i	$0.773655\pi$
$564$	12.6324	−	9.41596i	0.531919	−	0.396483i
$565$	0.459669	−	0.796170i	0.0193384	−	0.0334951i
$566$	−3.73516	+	18.1162i	−0.157001	+	0.761480i
$567$	9.74577	+	5.62672i	0.409284	+	0.236300i
$568$	1.39288	+	2.98021i	0.0584441	+	0.125047i
$569$		−	9.72745i		−	0.407796i	−0.978992	−	0.203898i	$-0.934639\pi$
$569$		−	9.72745i		−	0.407796i	0.978992	−	0.203898i	$-0.0653611\pi$
$570$	4.29890	−	20.4158i	0.180061	−	0.855123i
$571$	41.7629			1.74772			0.873862	−	0.486174i	$-0.161608\pi$
$571$	41.7629			1.74772			0.873862	+	0.486174i	$0.161608\pi$
$572$	−9.01554	−	3.88266i	−0.376959	−	0.162342i
$573$	−0.750022	+	1.29908i	−0.0313326	+	0.0542697i
$574$	−3.18094	+	15.4281i	−0.132770	+	0.643957i
$575$	36.9263	+	21.3194i	1.53993	+	0.889082i
$576$	−11.9879	+	14.3377i	−0.499495	+	0.597403i
$577$	37.1247			1.54552			0.772761	−	0.634698i	$-0.218875\pi$
$577$	37.1247			1.54552			0.772761	+	0.634698i	$0.218875\pi$
$578$	−8.41805	−	7.48701i	−0.350145	−	0.311419i
$579$	−5.09967	−	8.83290i	−0.211935	−	0.367083i
$580$	−23.4101	−	31.4068i	−0.972050	−	1.30409i
$581$		−	38.0753i		−	1.57963i
$582$	−12.0485	−	10.7159i	−0.499425	−	0.444189i
$583$	1.48858	+	2.57829i	0.0616506	+	0.106782i
$584$	3.51314	+	7.51671i	0.145375	+	0.311044i
$585$	−33.8549	+	19.5461i	−1.39973	+	0.808132i
$586$	−15.9279	+	5.28309i	−0.657973	+	0.218243i
$587$	−20.9655	+	36.3133i	−0.865338	+	1.49881i	0.00137323	+	0.999999i	$0.499563\pi$
$587$	−20.9655	+	36.3133i	−0.865338	+	1.49881i	−0.866711	+	0.498810i	$0.833770\pi$
$588$	−5.73368	+	0.673575i	−0.236453	+	0.0277778i
$589$	12.9770	+	22.6968i	0.534708	+	0.935205i
$590$	−47.3974	−	42.1553i	−1.95132	−	1.73550i
$591$	−4.28059	+	7.41421i	−0.176080	+	0.304980i
$592$	−1.54107	+	5.16957i	−0.0633377	+	0.212468i
$593$	2.27252	+	3.93612i	0.0933212	+	0.161637i	0.908907	−	0.417000i	$-0.136918\pi$
$593$	2.27252	+	3.93612i	0.0933212	+	0.161637i	−0.815586	+	0.578637i	$0.803585\pi$
$594$	−2.35838	−	7.11023i	−0.0967657	−	0.291736i
$595$	20.2691	+	35.1071i	0.830952	+	1.43925i
$596$	1.55863	−	0.183103i	0.0638441	−	0.00750021i
$597$	−4.91105			−0.200996
$598$	−19.4145	−	4.00285i	−0.793920	−	0.163689i
$599$	17.1887	+	29.7716i	0.702309	+	1.21644i	0.967654	+	0.252282i	$0.0811810\pi$
$599$	17.1887	+	29.7716i	0.702309	+	1.21644i	−0.265344	+	0.964154i	$0.585486\pi$
$600$	−23.1482	−	16.1782i	−0.945020	−	0.660473i
$601$		−	43.0249i		−	1.75502i	−0.479554	−	0.877512i	$-0.659202\pi$
$601$		−	43.0249i		−	1.75502i	0.479554	−	0.877512i	$-0.340798\pi$
$602$	−9.13987	−	1.88444i	−0.372513	−	0.0768041i
$603$	−19.4157	−	11.2097i	−0.790668	−	0.456492i
$604$	−7.27782	+	5.42477i	−0.296130	+	0.220731i
$605$	34.2312	+	19.7634i	1.39170	+	0.803496i
$606$	−21.8621	+	7.25142i	−0.888087	+	0.294569i
$607$	38.5179			1.56339			0.781696	−	0.623660i	$-0.214355\pi$
$607$	38.5179			1.56339			0.781696	+	0.623660i	$0.214355\pi$
$608$	21.0220	−	12.8871i	0.852553	−	0.522640i
$609$	12.4741			0.505477
$610$	1.93743	−	0.642623i	0.0784441	−	0.0260190i
$611$	33.7313	+	19.4748i	1.36462	+	0.787866i
$612$	−11.2594	+	8.39254i	−0.455133	+	0.339248i
$613$	−8.20483	−	4.73706i	−0.331390	−	0.191328i	0.325068	−	0.945691i	$-0.394613\pi$
$613$	−8.20483	−	4.73706i	−0.331390	−	0.191328i	−0.656458	+	0.754362i	$0.727946\pi$
$614$	25.8799	+	5.33586i	1.04443	+	0.215338i
$615$		−	11.6107i		−	0.468187i
$616$	−9.17100	−	6.40960i	−0.369510	−	0.258250i
$617$	−10.5392	−	18.2545i	−0.424294	−	0.734899i	0.572060	−	0.820212i	$-0.306144\pi$
$617$	−10.5392	−	18.2545i	−0.424294	−	0.734899i	−0.996354	+	0.0853127i	$0.972811\pi$
$618$	−2.11162	−	0.435370i	−0.0849419	−	0.0175131i
$619$	2.62181			0.105380			0.0526898	−	0.998611i	$-0.483221\pi$
$619$	2.62181			0.105380			0.0526898	+	0.998611i	$0.483221\pi$
$620$	49.4895	−	5.81387i	1.98754	−	0.233491i
$621$	−7.56395	−	13.1011i	−0.303531	−	0.525731i
$622$	7.98944	+	24.0871i	0.320347	+	0.965806i
$623$	22.8036	+	39.4969i	0.913606	+	1.58241i
$624$	12.5823	+	3.75083i	0.503694	+	0.150153i
$625$	−31.9504	+	55.3397i	−1.27802	+	2.21359i
$626$	−33.5882	−	29.8733i	−1.34245	−	1.19398i
$627$	−0.0182026	+	4.32694i	−0.000726940	+	0.172801i
$628$	−16.3793	+	1.92419i	−0.653606	+	0.0767837i
$629$	−2.02669	+	3.51034i	−0.0808096	+	0.139966i
$630$	−42.2935	+	14.0283i	−1.68501	+	0.558900i
$631$	−37.2197	+	21.4888i	−1.48169	+	0.855455i	−0.999784	−	0.0207671i	$-0.993389\pi$
$631$	−37.2197	+	21.4888i	−1.48169	+	0.855455i	−0.481907	+	0.876222i	$0.660056\pi$
$632$	6.17434	+	13.2106i	0.245602	+	0.525489i
$633$	5.96112	+	10.3250i	0.236933	+	0.410381i
$634$	−9.48023	−	8.43172i	−0.376508	−	0.334866i
$635$		−	35.7488i		−	1.41865i
$636$	−2.37981	−	3.19273i	−0.0943656	−	0.126600i
$637$	−7.13591	−	12.3598i	−0.282735	−	0.489711i
$638$	6.07040	+	5.39902i	0.240330	+	0.213749i
$639$	−2.71707			−0.107486
$640$	−6.90646	−	46.4853i	−0.273002	−	1.83749i
$641$	−24.4261	−	14.1024i	−0.964773	−	0.557012i	−0.0671340	−	0.997744i	$-0.521386\pi$
$641$	−24.4261	−	14.1024i	−0.964773	−	0.557012i	−0.897639	+	0.440732i	$0.854719\pi$
$642$	−1.02325	+	4.96292i	−0.0403843	+	0.195871i
$643$	3.71938	−	6.44216i	0.146678	−	0.254054i	−0.783320	−	0.621619i	$-0.786475\pi$
$643$	3.71938	−	6.44216i	0.146678	−	0.254054i	0.929998	+	0.367565i	$0.119809\pi$
$644$	−20.7525	−	8.93733i	−0.817762	−	0.352180i
$645$	6.87835			0.270835
$646$	17.6102	−	5.75900i	0.692865	−	0.226585i
$647$			18.5510i			0.729316i	0.931141	+	0.364658i	$0.118814\pi$
$647$			18.5510i			0.729316i	−0.931141	+	0.364658i	$0.881186\pi$
$648$	−4.15069	−	8.88079i	−0.163054	−	0.348871i
$649$	11.3929	+	6.57770i	0.447211	+	0.258197i
$650$	14.0980	−	68.3777i	0.552969	−	2.68199i
$651$	−7.93409	+	13.7423i	−0.310962	+	0.538601i
$652$	6.39972	−	4.77024i	0.250632	−	0.186817i
$653$			23.6341i			0.924874i	0.886652	+	0.462437i	$0.153025\pi$
$653$			23.6341i			0.924874i	−0.886652	+	0.462437i	$0.846975\pi$
$654$	−2.98326	+	3.35424i	−0.116655	+	0.131161i
$655$	−3.55904	+	2.05481i	−0.139063	+	0.0802882i
$656$	9.97008	−	9.42839i	0.389266	−	0.368117i
$657$	−6.85301			−0.267361
$658$	33.1741	+	29.5051i	1.29326	+	1.15023i
$659$	−24.6089	+	14.2079i	−0.958625	+	0.553463i	−0.895750	−	0.444559i	$-0.853360\pi$
$659$	−24.6089	+	14.2079i	−0.958625	+	0.553463i	−0.0628757	+	0.998021i	$0.520027\pi$
$660$	7.57432	+	3.26198i	0.294830	+	0.126973i
$661$	18.8702	+	32.6841i	0.733964	+	1.27126i	0.955176	+	0.296038i	$0.0956654\pi$
$661$	18.8702	+	32.6841i	0.733964	+	1.27126i	−0.221212	+	0.975226i	$0.571001\pi$
$662$	−13.2673	−	39.9991i	−0.515647	−	1.55461i
$663$	8.54385	+	4.93280i	0.331816	+	0.191574i
$664$	−19.0002	+	27.1859i	−0.737351	+	1.05502i
$665$	58.7896	+	0.247316i	2.27976	+	0.00959051i
$666$	−3.32921	−	2.96100i	−0.129004	−	0.114736i
$667$	14.2079	+	8.20293i	0.550132	+	0.317619i
$668$	−33.9637	−	14.6269i	−1.31410	−	0.565933i
$669$	−19.4158	+	11.2097i	−0.750657	+	0.433392i
$670$	53.5091	−	17.7484i	2.06724	−	0.685680i
$671$	−0.366622	+	0.211669i	−0.0141533	+	0.00817140i
$672$	13.1831	+	7.08339i	0.508551	+	0.273248i
$673$			7.92449i			0.305467i	0.988267	+	0.152733i	$0.0488075\pi$
$673$			7.92449i			0.305467i	−0.988267	+	0.152733i	$0.951192\pi$
$674$	11.9052	+	2.45458i	0.458570	+	0.0945470i
$675$	46.1420	−	26.6401i	1.77601	−	1.02538i
$676$	0.753436	+	6.41347i	0.0289783	+	0.246672i
$677$	13.1739			0.506315			0.253158	−	0.967425i	$-0.418531\pi$
$677$	13.1739			0.506315			0.253158	+	0.967425i	$0.418531\pi$
$678$	0.0514973	−	0.249771i	0.00197774	−	0.00959240i
$679$	22.7181	−	39.3488i	0.871839	−	1.51007i
$680$	3.04681	−	35.1812i	0.116840	−	1.34914i
$681$	7.52271	−	13.0297i	0.288271	−	0.499300i
$682$	−9.80893	+	3.25351i	−0.375603	+	0.124584i
$683$		−	25.6624i		−	0.981945i	−0.871175	−	0.490972i	$-0.836642\pi$
$683$		−	25.6624i		−	0.981945i	0.871175	−	0.490972i	$-0.163358\pi$
$684$	2.29107	+	20.2366i	0.0876012	+	0.773765i
$685$		−	76.5085i		−	2.92324i
$686$	4.99796	+	15.0682i	0.190823	+	0.575307i
$687$	−7.66491	+	13.2760i	−0.292435	+	0.506512i
$688$	5.58553	+	5.90644i	0.212946	+	0.225181i
$689$	4.92210	−	8.52533i	0.187517	−	0.324789i
$690$	16.3109	+	3.36296i	0.620947	+	0.128026i
$691$	−42.3757			−1.61205			−0.806024	−	0.591883i	$-0.798385\pi$
$691$	−42.3757			−1.61205			−0.806024	+	0.591883i	$0.798385\pi$
$692$	0.846187	+	7.20300i	0.0321672	+	0.273817i
$693$	8.00326	−	4.62068i	0.304019	−	0.175525i
$694$	4.54421	−	22.0402i	0.172496	−	0.836635i
$695$			45.4272i			1.72315i
$696$	−8.90656	−	6.22479i	−0.337602	−	0.235950i
$697$	8.92954	−	5.15547i	0.338230	−	0.195277i
$698$	5.03855	+	15.1906i	0.190712	+	0.574972i
$699$	−0.478861	+	0.276470i	−0.0181122	+	0.0104571i
$700$	31.4771	−	73.0899i	1.18972	−	2.76254i
$701$	10.6725	+	6.16178i	0.403096	+	0.232727i	0.687819	−	0.725882i	$-0.258568\pi$
$701$	10.6725	+	6.16178i	0.403096	+	0.232727i	−0.284723	+	0.958610i	$0.591902\pi$
$702$	−16.4616	+	18.5087i	−0.621304	+	0.698566i
$703$	2.91776	+	5.10316i	0.110045	+	0.192469i
$704$	3.34963	+	9.15296i	0.126244	+	0.344965i
$705$	−28.3391	−	16.3616i	−1.06731	−	0.616212i
$706$	−6.06933	+	2.01313i	−0.228422	+	0.0757651i
$707$	−32.4522	−	56.2089i	−1.22049	−	2.11395i
$708$	−16.1610	−	6.95995i	−0.607367	−	0.261571i
$709$	8.81856	−	5.09140i	0.331188	−	0.191212i	−0.325180	−	0.945652i	$-0.605425\pi$
$709$	8.81856	−	5.09140i	0.331188	−	0.191212i	0.656368	+	0.754440i	$0.272092\pi$
$710$	4.54063	−	5.10528i	0.170407	−	0.191598i
$711$	−12.0441			−0.451690
$712$	3.42779	−	39.5803i	0.128462	−	1.48333i
$713$	−18.0737	+	10.4349i	−0.676866	+	0.390789i
$714$	8.40271	+	7.47337i	0.314464	+	0.279684i
$715$			20.3873i			0.762440i
$716$	18.9661	+	25.4448i	0.708796	+	0.950915i
$717$	−1.86523	+	3.23068i	−0.0696584	+	0.120652i
$718$	−47.5842	−	9.81082i	−1.77583	−	0.366136i
$719$	−43.2292	−	24.9584i	−1.61218	−	0.930791i	−0.988865	−	0.148817i	$-0.952453\pi$
$719$	−43.2292	−	24.9584i	−1.61218	−	0.930791i	−0.623312	−	0.781973i	$-0.714213\pi$
$720$	37.1980	+	11.0889i	1.38629	+	0.413259i
$721$		−	6.07538i		−	0.226259i
$722$	5.64711	−	26.2699i	0.210164	−	0.977666i
$723$	4.68987			0.174418
$724$	−7.87562	−	3.39174i	−0.292695	−	0.126053i
$725$	−28.8906	+	50.0400i	−1.07297	+	1.85844i
$726$	10.7389	+	2.21412i	0.398557	+	0.0821736i
$727$	−4.69030	−	2.70795i	−0.173954	−	0.100432i	0.410495	−	0.911863i	$-0.365356\pi$
$727$	−4.69030	−	2.70795i	−0.173954	−	0.100432i	−0.584449	+	0.811431i	$0.698689\pi$
$728$	−3.19210	+	36.8588i	−0.118307	+	1.36608i
$729$	−2.53093			−0.0937382
$730$	11.4524	−	12.8766i	0.423873	−	0.476583i
$731$	3.05419	+	5.29000i	0.112963	+	0.195658i
$732$	0.453992	−	0.338398i	0.0167800	−	0.0125076i
$733$		−	13.6183i		−	0.503003i	−0.967857	−	0.251502i	$-0.919076\pi$
$733$		−	13.6183i		−	0.503003i	0.967857	−	0.251502i	$-0.0809244\pi$
$734$	−26.6780	+	29.9956i	−0.984705	+	1.10716i
$735$	5.99517	+	10.3839i	0.221135	+	0.383017i
$736$	10.3575	+	16.7371i	0.381781	+	0.616938i
$737$	−10.1256	+	5.84602i	−0.372982	+	0.215341i
$738$	3.56811	+	10.7574i	0.131344	+	0.395986i
$739$	9.19703	−	15.9297i	0.338318	−	0.585984i	−0.645798	−	0.763508i	$-0.723475\pi$
$739$	9.19703	−	15.9297i	0.338318	−	0.585984i	0.984117	+	0.177524i	$0.0568086\pi$
$740$	11.1272	−	1.30719i	0.409045	−	0.0480534i
$741$	12.4206	−	7.10156i	0.456283	−	0.260882i
$742$	7.45717	−	8.38450i	0.273761	−	0.307805i
$743$	−1.99704	+	3.45898i	−0.0732643	+	0.126898i	−0.900330	−	0.435207i	$-0.856675\pi$
$743$	−1.99704	+	3.45898i	−0.0732643	+	0.126898i	0.827066	+	0.562105i	$0.190008\pi$
$744$	12.5226	−	5.85277i	0.459100	−	0.214573i
$745$	−1.62971	−	2.82275i	−0.0597081	−	0.103418i
$746$	11.7292	−	3.89044i	0.429436	−	0.142439i
$747$	−13.6972	−	23.7243i	−0.501156	−	0.868028i
$748$	0.854490	+	7.27368i	0.0312433	+	0.265952i
$749$	−14.2789			−0.521740
$750$	−7.01167	+	34.0079i	−0.256030	+	1.24179i
$751$	0.00116611	+	0.00201977i	4.25521e−5	+	7.37023e-5i	0.866047	−	0.499963i	$-0.166653\pi$
$751$	0.00116611	+	0.00201977i	4.25521e−5	+	7.37023e-5i	−0.866004	+	0.500037i	$0.833320\pi$
$752$	−8.96293	−	37.6211i	−0.326844	−	1.37190i
$753$		−	12.2682i		−	0.447078i
$754$	5.42439	−	26.3092i	0.197545	−	0.958126i
$755$	16.3268	+	9.42630i	0.594194	+	0.343058i
$756$	−22.6374	+	16.8736i	−0.823316	+	0.613686i
$757$	9.96007	+	5.75045i	0.362005	+	0.209004i	0.669960	−	0.742397i	$-0.266311\pi$
$757$	9.96007	+	5.75045i	0.362005	+	0.209004i	−0.307955	+	0.951401i	$0.599645\pi$
$758$	5.38218	+	16.2266i	0.195489	+	0.589376i
$759$	−3.45396			−0.125371
$760$	−41.8526	−	29.5136i	−1.51815	−	1.07057i
$761$	13.5383			0.490765			0.245382	−	0.969426i	$-0.421086\pi$
$761$	13.5383			0.490765			0.245382	+	0.969426i	$0.421086\pi$
$762$	−3.12201	−	9.41246i	−0.113098	−	0.340978i
$763$	−10.9545	−	6.32461i	−0.396581	−	0.228966i
$764$	2.20050	+	2.95217i	0.0796113	+	0.106806i
$765$	25.2589	+	14.5832i	0.913238	+	0.527258i
$766$	3.44718	−	16.7194i	0.124552	−	0.604097i
$767$		−	43.4994i		−	1.57067i
$768$	−5.87808	−	11.6362i	−0.212107	−	0.419884i
$769$	4.16442	+	7.21299i	0.150173	+	0.260107i	0.931291	−	0.364276i	$-0.118684\pi$
$769$	4.16442	+	7.21299i	0.150173	+	0.260107i	−0.781118	+	0.624383i	$0.785350\pi$
$770$	−4.69255	+	22.7597i	−0.169108	+	0.820203i
$771$	−9.90496			−0.356718
$772$	−24.8647	+	2.92103i	−0.894899	+	0.105130i
$773$	−0.0685585	−	0.118747i	−0.00246588	−	0.00427103i	0.864790	−	0.502134i	$-0.167452\pi$
$773$	−0.0685585	−	0.118747i	−0.00246588	−	0.00427103i	−0.867256	+	0.497863i	$0.834118\pi$
$774$	−6.37287	+	2.11381i	−0.229068	+	0.0759793i
$775$	−36.7514	−	63.6553i	−1.32015	−	2.28657i
$776$	−35.8565	+	16.7585i	−1.28717	+	0.601596i
$777$	−1.78390	+	3.08981i	−0.0639972	+	0.110846i
$778$	−6.16541	+	6.93210i	−0.221041	+	0.248528i
$779$	0.0629052	−	14.9532i	0.00225381	−	0.535755i
$780$	−3.18159	−	27.0827i	−0.113919	−	0.969716i
$781$	−0.708498	+	1.22715i	−0.0253521	+	0.0439111i
$782$	4.65615	+	14.0377i	0.166503	+	0.501987i
$783$	17.7538	−	10.2501i	0.634467	−	0.366310i
$784$	−4.04834	+	13.5803i	−0.144584	+	0.485010i
$785$	17.1263	+	29.6636i	0.611264	+	1.05874i
$786$	−0.757626	+	0.851840i	−0.0270236	+	0.0303841i
$787$			27.2431i			0.971113i	0.874205	+	0.485556i	$0.161383\pi$
$787$			27.2431i			0.971113i	−0.874205	+	0.485556i	$0.838617\pi$
$788$	12.5589	+	16.8489i	0.447392	+	0.600218i
$789$	−3.85628	−	6.67928i	−0.137287	−	0.237789i
$790$	20.1276	−	22.6305i	0.716107	−	0.805158i
$791$	0.718621			0.0255512
$792$	−8.02015	−	0.694572i	−0.284984	−	0.0246806i
$793$	1.21226	+	0.699901i	0.0430488	+	0.0248542i
$794$	25.7153	+	5.30193i	0.912601	+	0.188158i
$795$	−4.13526	+	7.16248i	−0.146663	+	0.254027i
$796$	−4.76819	+	11.0717i	−0.169004	+	0.392427i
$797$	−39.2885			−1.39167			−0.695835	−	0.718202i	$-0.744965\pi$
$797$	−39.2885			−1.39167			−0.695835	+	0.718202i	$0.744965\pi$
$798$	15.5006	−	5.06910i	0.548715	−	0.179444i
$799$		−	29.0600i		−	1.02807i
$800$	−58.9478	+	36.4788i	−2.08412	+	1.28972i
$801$	28.4173	+	16.4067i	1.00408	+	0.579704i
$802$	33.5400	+	6.91521i	1.18434	+	0.244185i
$803$	−1.78698	+	3.09514i	−0.0630611	+	0.109225i
$804$	12.5387	−	9.34611i	0.442205	−	0.329612i
$805$			46.9285i			1.65401i
$806$	25.5337	+	22.7097i	0.899387	+	0.799914i
$807$	2.33139	−	1.34603i	0.0820687	−	0.0473824i
$808$	−4.87816	+	56.3275i	−0.171613	+	1.98160i
$809$	41.6938			1.46588			0.732938	−	0.680295i	$-0.238148\pi$
$809$	41.6938			1.46588			0.732938	+	0.680295i	$0.238148\pi$
$810$	−13.5307	+	15.2133i	−0.475421	+	0.534542i
$811$	8.50428	−	4.90995i	0.298626	−	0.172412i	−0.343200	−	0.939262i	$-0.611511\pi$
$811$	8.50428	−	4.90995i	0.298626	−	0.172412i	0.641825	+	0.766851i	$0.278177\pi$
$812$	12.1112	−	28.1223i	0.425021	−	0.986899i
$813$	−4.88615	−	8.46305i	−0.171365	−	0.296812i
$814$	−2.20544	+	0.731522i	−0.0773008	+	0.0256398i
$815$	−14.3569	−	8.28897i	−0.502901	−	0.290350i
$816$	−2.27023	−	9.52910i	−0.0794740	−	0.333585i
$817$	8.85853	+	0.0372661i	0.309921	+	0.00130377i
$818$	−6.29026	+	7.07248i	−0.219934	+	0.247284i
$819$	−26.4634	−	15.2787i	−0.924706	−	0.533879i
$820$	−26.1757	−	11.2729i	−0.914094	−	0.393667i
$821$	22.9743	−	13.2642i	0.801809	−	0.462925i	−0.0422942	−	0.999105i	$-0.513467\pi$
$821$	22.9743	−	13.2642i	0.801809	−	0.462925i	0.844103	+	0.536180i	$0.180133\pi$
$822$	−6.68163	−	20.1443i	−0.233049	−	0.702612i
$823$	−33.1763	+	19.1543i	−1.15645	+	0.667678i	−0.950451	−	0.310874i	$-0.899378\pi$
$823$	−33.1763	+	19.1543i	−1.15645	+	0.667678i	−0.206001	+	0.978552i	$0.566045\pi$
$824$	−3.03171	+	4.33784i	−0.105615	+	0.151116i
$825$		−	12.1648i		−	0.423523i
$826$	10.0123	−	48.5614i	0.348372	−	1.68967i
$827$	39.0052	−	22.5196i	1.35634	−	0.783085i	0.367214	−	0.930137i	$-0.380312\pi$
$827$	39.0052	−	22.5196i	1.35634	−	0.783085i	0.989129	+	0.147052i	$0.0469785\pi$
$828$	−16.1458	+	1.89676i	−0.561104	+	0.0659168i
$829$	−24.9335			−0.865977			−0.432989	−	0.901399i	$-0.642541\pi$
$829$	−24.9335			−0.865977			−0.432989	+	0.901399i	$0.642541\pi$
$830$	67.4674	+	13.9103i	2.34183	+	0.482833i
$831$	−4.99839	+	8.65746i	−0.173392	+	0.300324i
$832$	20.6723	−	24.7244i	0.716684	−	0.857165i
$833$	−5.32406	+	9.22154i	−0.184468	+	0.319507i
$834$	3.96724	+	11.9607i	0.137374	+	0.414166i
$835$			76.8038i			2.65790i
$836$	9.73720	+	4.24210i	0.336768	+	0.146716i
$837$			26.0782i			0.901393i
$838$	−25.5758	+	8.48320i	−0.883500	+	0.293047i
$839$	9.87363	−	17.1016i	0.340876	−	0.590414i	−0.643720	−	0.765261i	$-0.722610\pi$
$839$	9.87363	−	17.1016i	0.340876	−	0.590414i	0.984596	+	0.174847i	$0.0559431\pi$
$840$	2.68181	−	30.9666i	0.0925314	−	1.06845i
$841$	3.38396	−	5.86119i	0.116688	−	0.202110i
$842$	−9.90980	+	48.0643i	−0.341514	+	1.65640i
$843$	9.86995			0.339939
$844$	29.0649	−	3.41445i	1.00045	−	0.117530i
$845$	11.6151	−	6.70596i	0.399570	−	0.230692i
$846$	31.2846	+	6.45020i	1.07559	+	0.221762i
$847$			30.8970i			1.06163i
$848$	−9.50845	+	2.26531i	−0.326521	+	0.0777911i
$849$	9.22924	−	5.32850i	0.316747	−	0.182874i
$850$	−49.4405	+	16.3989i	−1.69580	+	0.562477i
$851$	−4.06370	+	2.34618i	−0.139302	+	0.0804260i
$852$	0.749671	−	1.74074i	0.0256833	−	0.0596366i
$853$	6.13275	+	3.54074i	0.209981	+	0.121233i	0.601303	−	0.799021i	$-0.294649\pi$
$853$	6.13275	+	3.54074i	0.209981	+	0.121233i	−0.391321	+	0.920254i	$0.627982\pi$
$854$	1.19224	+	1.06038i	0.0407976	+	0.0362853i
$855$	36.7202	−	20.9949i	1.25580	−	0.718011i
$856$	10.1952	+	7.12540i	0.348464	+	0.243541i
$857$	10.7446	+	6.20337i	0.367027	+	0.211903i	0.672159	−	0.740407i	$-0.265367\pi$
$857$	10.7446	+	6.20337i	0.367027	+	0.211903i	−0.305132	+	0.952310i	$0.598701\pi$
$858$	1.78046	+	5.36786i	0.0607838	+	0.183256i
$859$	21.2782	+	36.8549i	0.726003	+	1.25747i	0.958560	+	0.284891i	$0.0919576\pi$
$859$	21.2782	+	36.8549i	0.726003	+	1.25747i	−0.232557	+	0.972583i	$0.574709\pi$
$860$	6.67825	−	15.5069i	0.227727	−	0.528781i
$861$	7.85981	−	4.53786i	0.267862	−	0.154650i
$862$	−28.5739	−	25.4136i	−0.973230	−	0.865591i
$863$	2.40464			0.0818549			0.0409275	−	0.999162i	$-0.486969\pi$
$863$	2.40464			0.0818549			0.0409275	+	0.999162i	$0.486969\pi$
$864$	24.5834	−	0.751333i	0.836344	−	0.0255609i
$865$	13.0449	−	7.53149i	0.443541	−	0.256078i
$866$	−32.3345	+	36.3555i	−1.09877	+	1.23541i
$867$			6.49071i			0.220436i
$868$	23.2780	+	31.2295i	0.790105	+	1.06000i
$869$	−3.14061	+	5.43969i	−0.106538	+	0.184529i
$870$	−4.55725	+	22.1035i	−0.154505	+	0.749377i
$871$	33.4811	+	19.3303i	1.13446	+	0.654984i
$872$	4.66550	+	9.98228i	0.157994	+	0.338043i
$873$		−	32.6904i		−	1.10640i
$874$	20.9884	+	4.41948i	0.709945	+	0.149491i
$875$	−97.8446			−3.30775
$876$	1.89083	−	4.39050i	0.0638851	−	0.148341i
$877$	19.4607	−	33.7069i	0.657141	−	1.13820i	−0.324212	−	0.945985i	$-0.605099\pi$
$877$	19.4607	−	33.7069i	0.657141	−	1.13820i	0.981353	−	0.192217i	$-0.0615676\pi$
$878$	0.346187	−	1.67907i	0.0116832	−	0.0566658i
$879$	8.37300	+	4.83416i	0.282414	+	0.163052i
$880$	14.7080	−	13.9089i	0.495806	−	0.468867i
$881$	−44.6764			−1.50519			−0.752593	−	0.658486i	$-0.771197\pi$
$881$	−44.6764			−1.50519			−0.752593	+	0.658486i	$0.771197\pi$
$882$	−8.74572	−	7.77844i	−0.294484	−	0.261914i
$883$	−4.20011	−	7.27481i	−0.141345	−	0.244817i	0.786658	−	0.617389i	$-0.211809\pi$
$883$	−4.20011	−	7.27481i	−0.141345	−	0.244817i	−0.928003	+	0.372572i	$0.878476\pi$
$884$	19.4161	−	14.4724i	0.653033	−	0.486760i
$885$			36.5456i			1.22847i
$886$	−26.6056	−	23.6630i	−0.893833	−	0.794975i
$887$	−21.0193	−	36.4065i	−0.705759	−	1.22241i	−0.966417	−	0.256979i	$-0.917273\pi$
$887$	−21.0193	−	36.4065i	−0.705759	−	1.22241i	0.260658	−	0.965431i	$-0.416060\pi$
$888$	2.81558	−	1.31594i	0.0944847	−	0.0441600i
$889$	24.2001	−	13.9719i	0.811644	−	0.468603i
$890$	−78.3174	+	25.9770i	−2.62520	+	0.870751i
$891$	2.11127	−	3.65682i	0.0707301	−	0.122508i
$892$	6.42077	+	54.6555i	0.214983	+	1.83000i
$893$	−36.4089	−	21.2254i	−1.21838	−	0.710281i
$894$	−0.675611	−	0.600889i	−0.0225958	−	0.0200967i
$895$	32.9563	−	57.0820i	1.10161	−	1.90804i
$896$	28.7688	−	22.8434i	0.961099	−	0.763146i
$897$	5.71039	+	9.89068i	0.190664	+	0.330240i
$898$	−9.57196	−	28.8582i	−0.319420	−	0.963012i
$899$	−14.1406	−	24.4922i	−0.471615	−	0.816862i
$900$	−6.68035	−	56.8651i	−0.222678	−	1.89550i
$901$	−7.34470			−0.244688
$902$	5.78896	+	1.19356i	0.192751	+	0.0397411i
$903$	2.68831	+	4.65628i	0.0894612	+	0.154951i
$904$	−0.513098	−	0.358604i	−0.0170654	−	0.0119270i
$905$			17.8095i			0.592008i
$906$	5.12199	+	1.05604i	0.170167	+	0.0350846i
$907$	−17.4703	−	10.0865i	−0.580092	−	0.334916i	0.181078	−	0.983469i	$-0.442041\pi$
$907$	−17.4703	−	10.0865i	−0.580092	−	0.334916i	−0.761170	+	0.648552i	$0.775375\pi$
$908$	−22.0710	−	29.6103i	−0.732452	−	0.982651i
$909$	−40.4413	−	23.3488i	−1.34135	−	0.774430i
$910$	72.9325	−	24.1909i	2.41769	−	0.801920i
$911$	−42.5350			−1.40925			−0.704623	−	0.709582i	$-0.748884\pi$
$911$	−42.5350			−1.40925			−0.704623	+	0.709582i	$0.748884\pi$
$912$	−13.5970	−	4.11570i	−0.450243	−	0.136284i
$913$	−14.2867			−0.472820
$914$	−35.4768	+	11.7673i	−1.17347	+	0.389227i
$915$	−1.01847	−	0.588015i	−0.0336697	−	0.0194392i
$916$	22.4882	+	30.1700i	0.743031	+	0.996845i
$917$	−2.78200	−	1.60619i	−0.0918699	−	0.0530411i
$918$	18.1001	+	3.73184i	0.597392	+	0.123169i
$919$		−	8.32732i		−	0.274693i	−0.990523	−	0.137346i	$-0.956143\pi$
$919$		−	8.32732i		−	0.274693i	0.990523	−	0.137346i	$-0.0438574\pi$
$920$	23.4181	−	33.5071i	0.772072	−	1.10470i
$921$	−7.61203	−	13.1844i	−0.250825	−	0.434441i
$922$	25.7148	+	5.30183i	0.846872	+	0.174606i
$923$	4.68541			0.154222
$924$	0.752126	+	6.40232i	0.0247431	+	0.210621i
$925$	−8.26320	−	14.3123i	−0.271692	−	0.470585i
$926$	−8.25338	−	24.8829i	−0.271223	−	0.817702i
$927$	−2.18556	−	3.78551i	−0.0717833	−	0.124332i
$928$	−22.6810	+	14.0357i	−0.744539	+	0.460745i
$929$	−6.55867	+	11.3599i	−0.215183	+	0.372708i	−0.953329	−	0.301933i	$-0.902368\pi$
$929$	−6.55867	+	11.3599i	−0.215183	+	0.372708i	0.738146	+	0.674641i	$0.235701\pi$
$930$	−21.4519	−	19.0793i	−0.703436	−	0.625636i
$931$	7.66484	+	13.4058i	0.251205	+	0.439358i
$932$	0.158359	+	1.34800i	0.00518721	+	0.0441551i
$933$	7.31053	−	12.6622i	0.239336	−	0.414542i
$934$	−8.01019	+	2.65689i	−0.262101	+	0.0869361i
$935$	13.1729	−	7.60540i	0.430801	−	0.248723i
$936$	11.2707	+	24.1147i	0.368393	+	0.788213i
$937$	−15.9089	−	27.5550i	−0.519721	−	0.900183i	−0.999737	−	0.0229235i	$-0.992703\pi$
$937$	−15.9089	−	27.5550i	−0.519721	−	0.900183i	0.480016	−	0.877260i	$-0.340631\pi$
$938$	32.9280	+	29.2862i	1.07514	+	0.956228i
$939$			25.8980i			0.845151i
$940$	−64.4010	+	48.0035i	−2.10053	+	1.56570i
$941$	20.6578	+	35.7804i	0.673426	+	1.16641i	0.976926	+	0.213577i	$0.0685114\pi$
$941$	20.6578	+	35.7804i	0.673426	+	1.16641i	−0.303500	+	0.952831i	$0.598155\pi$
$942$	7.09985	+	6.31460i	0.231326	+	0.205741i
$943$	11.9363			0.388700
$944$	−31.3817	+	29.6767i	−1.02139	+	0.965894i
$945$	50.7841	+	29.3202i	1.65201	+	0.953787i
$946$	−0.707083	+	3.42948i	−0.0229893	+	0.111502i
$947$	10.0389	−	17.3878i	0.326220	−	0.565029i	−0.655539	−	0.755161i	$-0.727558\pi$
$947$	10.0389	−	17.3878i	0.326220	−	0.565029i	0.981758	+	0.190133i	$0.0608918\pi$
$948$	3.32312	−	7.71628i	0.107930	−	0.250613i
$949$	11.8176			0.383615
$950$	−15.5654	+	73.9210i	−0.505007	+	2.39831i
$951$			7.30970i			0.237033i
$952$	25.0066	−	11.6875i	0.810470	−	0.378796i
$953$	−46.5493	−	26.8753i	−1.50788	−	0.870575i	−0.999958	−	0.00917274i	$-0.997080\pi$
$953$	−46.5493	−	26.8753i	−1.50788	−	0.870575i	−0.507923	−	0.861403i	$-0.669586\pi$
$954$	1.63024	−	7.90694i	0.0527809	−	0.255997i
$955$	3.82368	−	6.62281i	0.123731	−	0.214309i
$956$	5.47243	+	7.34177i	0.176991	+	0.237450i
$957$		−	4.68056i		−	0.151301i
$958$	−25.5159	+	28.6888i	−0.824380	+	0.926895i
$959$	51.7923	−	29.9023i	1.67246	−	0.965595i
$960$	−17.3677	+	20.7720i	−0.560539	+	0.670413i
$961$	4.97618			0.160522
$962$	5.74101	+	5.10605i	0.185098	+	0.164626i
$963$	−8.89703	+	5.13670i	−0.286703	+	0.165528i
$964$	4.55344	−	10.5731i	0.146656	−	0.340536i
$965$	25.9986	+	45.0309i	0.836925	+	1.44960i
$966$	4.09836	+	12.3560i	0.131863	+	0.397549i
$967$	37.3255	+	21.5499i	1.20031	+	0.692999i	0.960624	−	0.277852i	$-0.0896226\pi$
$967$	37.3255	+	21.5499i	1.20031	+	0.692999i	0.239685	+	0.970851i	$0.422956\pi$
$968$	15.4181	−	22.0605i	0.495556	−	0.709053i
$969$	−9.22205	−	5.37621i	−0.296255	−	0.172709i
$970$	61.4243	+	54.6307i	1.97221	+	1.75409i
$971$	−15.8067	−	9.12598i	−0.507260	−	0.292866i	0.224447	−	0.974486i	$-0.427942\pi$
$971$	−15.8067	−	9.12598i	−0.507260	−	0.292866i	−0.731706	+	0.681620i	$0.761276\pi$
$972$	−12.5524	+	29.1466i	−0.402618	+	0.934878i
$973$	−30.7518	+	17.7546i	−0.985859	+	0.569186i
$974$	−47.5690	+	15.7781i	−1.52421	+	0.505563i
$975$	−34.8348	+	20.1119i	−1.11561	+	0.644096i
$976$	−0.322117	−	1.35206i	−0.0103107	−	0.0432783i
$977$			1.36452i			0.0436550i	0.999762	+	0.0218275i	$0.00694846\pi$
$977$			1.36452i			0.0436550i	−0.999762	+	0.0218275i	$0.993052\pi$
$978$	−4.50399	−	0.928625i	−0.144022	−	0.0296941i
$979$	14.8201	−	8.55639i	0.473653	−	0.273463i
$980$	29.2308	−	3.43395i	0.933745	−	0.109694i
$981$	−9.10088			−0.290569
$982$	−2.88868	+	14.0106i	−0.0921815	+	0.447097i
$983$	25.1141	−	43.4988i	0.801014	−	1.38740i	−0.117935	−	0.993021i	$-0.537627\pi$
$983$	25.1141	−	43.4988i	0.801014	−	1.38740i	0.918949	−	0.394376i	$-0.129039\pi$
$984$	−7.87640	−	0.682123i	−0.251090	−	0.0217453i
$985$	21.8229	−	37.7983i	0.695335	−	1.20436i
$986$	−19.0229	+	6.30969i	−0.605812	+	0.200941i
$987$		−	25.5788i		−	0.814181i
$988$	−3.95080	−	34.8967i	−0.125692	−	1.11021i
$989$			7.07128i			0.224854i
$990$	5.26372	+	15.8694i	0.167292	+	0.504364i
$991$	−16.9365	+	29.3349i	−0.538007	+	0.931855i	0.461004	+	0.887398i	$0.347489\pi$
$991$	−16.9365	+	29.3349i	−0.538007	+	0.931855i	−0.999011	+	0.0444574i	$0.985844\pi$
$992$	−1.03650	−	33.9141i	−0.0329090	−	1.07677i
$993$	−12.1399	+	21.0269i	−0.385247	+	0.667267i
$994$	5.23065	+	1.07845i	0.165906	+	0.0342062i
$995$	25.0370			0.793726
$996$	18.9786	−	2.22955i	0.601361	−	0.0706460i
$997$	−9.16830	+	5.29332i	−0.290363	+	0.167641i	−0.638106	−	0.769949i	$-0.720282\pi$
$997$	−9.16830	+	5.29332i	−0.290363	+	0.167641i	0.347743	+	0.937590i	$0.386948\pi$
$998$	−3.33458	+	16.1733i	−0.105554	+	0.511957i
$999$			5.86342i			0.185511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.27.3	✓	28
4.3	odd	2		608.2.s.c.559.5		28
8.3	odd	2	inner	152.2.o.c.27.7	yes	28
8.5	even	2		608.2.s.c.559.6		28
19.12	odd	6	inner	152.2.o.c.107.7	yes	28
76.31	even	6		608.2.s.c.335.6		28
152.69	odd	6		608.2.s.c.335.5		28
152.107	even	6	inner	152.2.o.c.107.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.3	✓	28	1.1	even	1	trivial
152.2.o.c.27.7	yes	28	8.3	odd	2	inner
152.2.o.c.107.3	yes	28	152.107	even	6	inner
152.2.o.c.107.7	yes	28	19.12	odd	6	inner
608.2.s.c.335.5		28	152.69	odd	6
608.2.s.c.335.6		28	76.31	even	6
608.2.s.c.559.5		28	4.3	odd	2
608.2.s.c.559.6		28	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34230 + 0.445227i) q^{2} +(0.705625 + 0.407393i) q^{3} +(1.60355 - 1.19526i) q^{4} +(-3.59735 - 2.07693i) q^{5} +(-1.12854 - 0.232681i) q^{6} -3.24695i q^{7} +(-1.62028 + 2.31834i) q^{8} +(-1.16806 - 2.02314i) q^{9} +(5.75343 + 1.18623i) q^{10} -1.21833 q^{11} +(1.61844 - 0.190130i) q^{12} +(2.01425 + 3.48878i) q^{13} +(1.44563 + 4.35839i) q^{14} +(-1.69225 - 2.93107i) q^{15} +(1.14272 - 3.83330i) q^{16} +(1.50282 - 2.60296i) q^{17} +(2.46865 + 2.19562i) q^{18} +(-2.16355 - 3.78405i) q^{19} +(-8.25097 + 0.969300i) q^{20} +(1.32279 - 2.29113i) q^{21} +(1.63536 - 0.542432i) q^{22} +(3.01328 - 1.73972i) q^{23} +(-2.08779 + 0.975785i) q^{24} +(6.12726 + 10.6127i) q^{25} +(-4.25703 - 3.78620i) q^{26} -4.34780i q^{27} +(-3.88094 - 5.20664i) q^{28} +(2.35755 + 4.08339i) q^{29} +(3.57650 + 3.18094i) q^{30} -5.99801 q^{31} +(0.172808 + 5.65421i) q^{32} +(-0.859683 - 0.496338i) q^{33} +(-0.858329 + 4.16305i) q^{34} +(-6.74369 + 11.6804i) q^{35} +(-4.29122 - 1.84807i) q^{36} -1.34860 q^{37} +(4.58890 + 4.11607i) q^{38} +3.28236i q^{39} +(10.6437 - 4.97465i) q^{40} +(2.97093 + 1.71527i) q^{41} +(-0.755505 + 3.66433i) q^{42} +(-1.01615 + 1.76003i) q^{43} +(-1.95365 + 1.45621i) q^{44} +9.70392i q^{45} +(-3.27016 + 3.67682i) q^{46} +(8.37318 - 4.83426i) q^{47} +(2.36799 - 2.23934i) q^{48} -3.54271 q^{49} +(-12.9497 - 11.5175i) q^{50} +(2.12085 - 1.22448i) q^{51} +(7.39993 + 3.18688i) q^{52} +(-1.22182 - 2.11626i) q^{53} +(1.93576 + 5.83606i) q^{54} +(4.38275 + 2.53038i) q^{55} +(7.52753 + 5.26099i) q^{56} +(0.0149406 - 3.55154i) q^{57} +(-4.98257 - 4.43150i) q^{58} +(-9.35127 - 5.39896i) q^{59} +(-6.21698 - 2.67743i) q^{60} +(0.300922 - 0.173737i) q^{61} +(8.05114 - 2.67048i) q^{62} +(-6.56905 + 3.79264i) q^{63} +(-2.74937 - 7.51272i) q^{64} -16.7338i q^{65} +(1.37494 + 0.283482i) q^{66} +(8.31107 - 4.79840i) q^{67} +(-0.701363 - 5.97022i) q^{68} +2.83500 q^{69} +(3.85164 - 18.6811i) q^{70} +(0.581533 - 1.00725i) q^{71} +(6.58292 + 0.570103i) q^{72} +(1.46675 - 2.54048i) q^{73} +(1.81022 - 0.600431i) q^{74} +9.98482i q^{75} +(-7.99227 - 3.48191i) q^{76} +3.95586i q^{77} +(-1.46140 - 4.40592i) q^{78} +(2.57780 - 4.46489i) q^{79} +(-12.0723 + 11.4163i) q^{80} +(-1.73292 + 3.00151i) q^{81} +(-4.75157 - 0.979669i) q^{82} +11.7265 q^{83} +(-0.617343 - 5.25501i) q^{84} +(-10.8123 + 6.24249i) q^{85} +(0.580372 - 2.81491i) q^{86} +3.84179i q^{87} +(1.97404 - 2.82449i) q^{88} +(-12.1643 + 7.02306i) q^{89} +(-4.32044 - 13.0256i) q^{90} +(11.3279 - 6.54017i) q^{91} +(2.75253 - 6.39137i) q^{92} +(-4.23235 - 2.44355i) q^{93} +(-9.08699 + 10.2170i) q^{94} +(-0.0761686 + 18.1061i) q^{95} +(-2.18155 + 4.06016i) q^{96} +(12.1187 + 6.99673i) q^{97} +(4.75539 - 1.57731i) q^{98} +(1.42308 + 2.46485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

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