LMFDB - Embedded newform 666.2.k.a.175.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.14
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(1.29891 + 1.14579i) q^{3} -1.00000 q^{4} -2.07510i q^{5} +(1.14579 - 1.29891i) q^{6} +(-1.46218 + 2.53257i) q^{7} +1.00000i q^{8} +(0.374317 + 2.97656i) q^{9} -2.07510 q^{10} +(1.24729 + 2.16036i) q^{11} +(-1.29891 - 1.14579i) q^{12} -0.965976i q^{13} +(2.53257 + 1.46218i) q^{14} +(2.37763 - 2.69536i) q^{15} +1.00000 q^{16} +(5.51981 + 3.18686i) q^{17} +(2.97656 - 0.374317i) q^{18} +(5.19406 - 2.99879i) q^{19} +2.07510i q^{20} +(-4.80103 + 1.61422i) q^{21} +(2.16036 - 1.24729i) q^{22} +(6.10692 + 3.52583i) q^{23} +(-1.14579 + 1.29891i) q^{24} +0.693968 q^{25} -0.965976 q^{26} +(-2.92431 + 4.29516i) q^{27} +(1.46218 - 2.53257i) q^{28} +(1.39694 - 0.806522i) q^{29} +(-2.69536 - 2.37763i) q^{30} +(-4.44527 - 2.56648i) q^{31} -1.00000i q^{32} +(-0.855220 + 4.23524i) q^{33} +(3.18686 - 5.51981i) q^{34} +(5.25533 + 3.03416i) q^{35} +(-0.374317 - 2.97656i) q^{36} +(-5.41023 - 2.78018i) q^{37} +(-2.99879 - 5.19406i) q^{38} +(1.10681 - 1.25471i) q^{39} +2.07510 q^{40} -7.84678 q^{41} +(1.61422 + 4.80103i) q^{42} +(0.286819 - 0.165595i) q^{43} +(-1.24729 - 2.16036i) q^{44} +(6.17665 - 0.776745i) q^{45} +(3.52583 - 6.10692i) q^{46} +(-4.35223 - 7.53829i) q^{47} +(1.29891 + 1.14579i) q^{48} +(-0.775932 - 1.34395i) q^{49} -0.693968i q^{50} +(3.51823 + 10.4640i) q^{51} +0.965976i q^{52} +(-6.29300 + 10.8998i) q^{53} +(4.29516 + 2.92431i) q^{54} +(4.48297 - 2.58824i) q^{55} +(-2.53257 - 1.46218i) q^{56} +(10.1826 + 2.05617i) q^{57} +(-0.806522 - 1.39694i) q^{58} +(5.26958 - 3.04240i) q^{59} +(-2.37763 + 2.69536i) q^{60} +(3.32949 + 1.92228i) q^{61} +(-2.56648 + 4.44527i) q^{62} +(-8.08565 - 3.40427i) q^{63} -1.00000 q^{64} -2.00450 q^{65} +(4.23524 + 0.855220i) q^{66} +9.83943 q^{67} +(-5.51981 - 3.18686i) q^{68} +(3.89244 + 11.5770i) q^{69} +(3.03416 - 5.25533i) q^{70} +(1.55554 + 2.69428i) q^{71} +(-2.97656 + 0.374317i) q^{72} -12.3747 q^{73} +(-2.78018 + 5.41023i) q^{74} +(0.901400 + 0.795144i) q^{75} +(-5.19406 + 2.99879i) q^{76} -7.29502 q^{77} +(-1.25471 - 1.10681i) q^{78} +(1.65079 + 0.953087i) q^{79} -2.07510i q^{80} +(-8.71977 + 2.22835i) q^{81} +7.84678i q^{82} +10.8429 q^{83} +(4.80103 - 1.61422i) q^{84} +(6.61306 - 11.4541i) q^{85} +(-0.165595 - 0.286819i) q^{86} +(2.73860 + 0.553004i) q^{87} +(-2.16036 + 1.24729i) q^{88} +(-11.9327 - 6.88934i) q^{89} +(-0.776745 - 6.17665i) q^{90} +(2.44640 + 1.41243i) q^{91} +(-6.10692 - 3.52583i) q^{92} +(-2.83334 - 8.42697i) q^{93} +(-7.53829 + 4.35223i) q^{94} +(-6.22279 - 10.7782i) q^{95} +(1.14579 - 1.29891i) q^{96} +(4.24112 - 2.44861i) q^{97} +(-1.34395 + 0.775932i) q^{98} +(-5.96356 + 4.52128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.29891	+	1.14579i	0.749924	+	0.661524i
$3$	1.29891	+	1.14579i	0.749924	+	0.661524i
$4$	−1.00000			−0.500000
$5$		−	2.07510i		−	0.928012i	−0.885832	−	0.464006i	$-0.846412\pi$
$5$		−	2.07510i		−	0.928012i	0.885832	−	0.464006i	$-0.153588\pi$
$6$	1.14579	−	1.29891i	0.467768	−	0.530276i
$7$	−1.46218	+	2.53257i	−0.552652	+	0.957221i	0.445431	+	0.895316i	$0.353051\pi$
$7$	−1.46218	+	2.53257i	−0.552652	+	0.957221i	−0.998082	+	0.0619040i	$0.980283\pi$
$8$			1.00000i			0.353553i
$9$	0.374317	+	2.97656i	0.124772	+	0.992185i
$10$	−2.07510			−0.656204
$11$	1.24729	+	2.16036i	0.376071	+	0.651374i	0.990487	−	0.137608i	$-0.0439415\pi$
$11$	1.24729	+	2.16036i	0.376071	+	0.651374i	−0.614416	+	0.788982i	$0.710608\pi$
$12$	−1.29891	−	1.14579i	−0.374962	−	0.330762i
$13$		−	0.965976i		−	0.267914i	−0.990987	−	0.133957i	$-0.957232\pi$
$13$		−	0.965976i		−	0.267914i	0.990987	−	0.133957i	$-0.0427683\pi$
$14$	2.53257	+	1.46218i	0.676857	+	0.390784i
$15$	2.37763	−	2.69536i	0.613902	−	0.695939i
$16$	1.00000			0.250000
$17$	5.51981	+	3.18686i	1.33875	+	0.772928i	0.986622	−	0.163024i	$-0.0521247\pi$
$17$	5.51981	+	3.18686i	1.33875	+	0.772928i	0.352129	+	0.935952i	$0.385458\pi$
$18$	2.97656	−	0.374317i	0.701581	−	0.0882275i
$19$	5.19406	−	2.99879i	1.19160	−	0.687970i	0.232930	−	0.972494i	$-0.425169\pi$
$19$	5.19406	−	2.99879i	1.19160	−	0.687970i	0.958669	+	0.284523i	$0.0918354\pi$
$20$			2.07510i			0.464006i
$21$	−4.80103	+	1.61422i	−1.04767	+	0.352251i
$22$	2.16036	−	1.24729i	0.460591	−	0.265922i
$23$	6.10692	+	3.52583i	1.27338	+	0.735186i	0.975623	−	0.219455i	$-0.0704280\pi$
$23$	6.10692	+	3.52583i	1.27338	+	0.735186i	0.297757	+	0.954642i	$0.403761\pi$
$24$	−1.14579	+	1.29891i	−0.233884	+	0.265138i
$25$	0.693968			0.138794
$26$	−0.965976			−0.189444
$27$	−2.92431	+	4.29516i	−0.562784	+	0.826604i
$28$	1.46218	−	2.53257i	0.276326	−	0.478610i
$29$	1.39694	−	0.806522i	0.259405	−	0.149767i	−0.364658	−	0.931141i	$-0.618814\pi$
$29$	1.39694	−	0.806522i	0.259405	−	0.149767i	0.624063	+	0.781374i	$0.285481\pi$
$30$	−2.69536	−	2.37763i	−0.492103	−	0.434094i
$31$	−4.44527	−	2.56648i	−0.798393	−	0.460953i	0.0445157	−	0.999009i	$-0.485826\pi$
$31$	−4.44527	−	2.56648i	−0.798393	−	0.460953i	−0.842909	+	0.538056i	$0.819159\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.855220	+	4.23524i	−0.148875	+	0.737261i
$34$	3.18686	−	5.51981i	0.546543	−	0.946640i
$35$	5.25533	+	3.03416i	0.888312	+	0.512867i
$36$	−0.374317	−	2.97656i	−0.0623862	−	0.496093i
$37$	−5.41023	−	2.78018i	−0.889436	−	0.457060i
$37$	−5.41023	−	2.78018i	−0.889436	−	0.457060i
$38$	−2.99879	−	5.19406i	−0.486468	−	0.842588i
$39$	1.10681	−	1.25471i	0.177231	−	0.200915i
$40$	2.07510			0.328102
$41$	−7.84678			−1.22546			−0.612730	−	0.790292i	$-0.709929\pi$
$41$	−7.84678			−1.22546			−0.612730	+	0.790292i	$0.709929\pi$
$42$	1.61422	+	4.80103i	0.249079	+	0.740815i
$43$	0.286819	−	0.165595i	0.0437395	−	0.0252530i	−0.477971	−	0.878376i	$-0.658628\pi$
$43$	0.286819	−	0.165595i	0.0437395	−	0.0252530i	0.521710	+	0.853123i	$0.325294\pi$
$44$	−1.24729	−	2.16036i	−0.188036	−	0.325687i
$45$	6.17665	−	0.776745i	0.920760	−	0.115790i
$46$	3.52583	−	6.10692i	0.519855	−	0.900416i
$47$	−4.35223	−	7.53829i	−0.634838	−	1.09957i	−0.986549	−	0.163463i	$-0.947733\pi$
$47$	−4.35223	−	7.53829i	−0.634838	−	1.09957i	0.351711	−	0.936109i	$-0.385600\pi$
$48$	1.29891	+	1.14579i	0.187481	+	0.165381i
$49$	−0.775932	−	1.34395i	−0.110847	−	0.191993i
$50$		−	0.693968i		−	0.0981419i
$51$	3.51823	+	10.4640i	0.492651	+	1.46525i
$52$			0.965976i			0.133957i
$53$	−6.29300	+	10.8998i	−0.864410	+	1.49720i	0.00322093	+	0.999995i	$0.498975\pi$
$53$	−6.29300	+	10.8998i	−0.864410	+	1.49720i	−0.867631	+	0.497208i	$0.834359\pi$
$54$	4.29516	+	2.92431i	0.584497	+	0.397949i
$55$	4.48297	−	2.58824i	0.604483	−	0.348998i
$56$	−2.53257	−	1.46218i	−0.338429	−	0.195392i
$57$	10.1826	+	2.05617i	1.34872	+	0.272346i
$58$	−0.806522	−	1.39694i	−0.105902	−	0.183427i
$59$	5.26958	−	3.04240i	0.686041	−	0.396086i	−0.116086	−	0.993239i	$-0.537035\pi$
$59$	5.26958	−	3.04240i	0.686041	−	0.396086i	0.802127	+	0.597153i	$0.203701\pi$
$60$	−2.37763	+	2.69536i	−0.306951	+	0.347969i
$61$	3.32949	+	1.92228i	0.426298	+	0.246123i	0.697768	−	0.716324i	$-0.254177\pi$
$61$	3.32949	+	1.92228i	0.426298	+	0.246123i	−0.271470	+	0.962447i	$0.587510\pi$
$62$	−2.56648	+	4.44527i	−0.325943	+	0.564549i
$63$	−8.08565	−	3.40427i	−1.01870	−	0.428898i
$64$	−1.00000			−0.125000
$65$	−2.00450			−0.248627
$66$	4.23524	+	0.855220i	0.521322	+	0.105270i
$67$	9.83943			1.20208			0.601039	−	0.799220i	$-0.294754\pi$
$67$	9.83943			1.20208			0.601039	+	0.799220i	$0.294754\pi$
$68$	−5.51981	−	3.18686i	−0.669375	−	0.386464i
$69$	3.89244	+	11.5770i	0.468595	+	1.39371i
$70$	3.03416	−	5.25533i	0.362652	−	0.628132i
$71$	1.55554	+	2.69428i	0.184609	+	0.319752i	0.943445	−	0.331530i	$-0.107565\pi$
$71$	1.55554	+	2.69428i	0.184609	+	0.319752i	−0.758836	+	0.651282i	$0.774231\pi$
$72$	−2.97656	+	0.374317i	−0.350791	+	0.0441137i
$73$	−12.3747			−1.44835			−0.724177	−	0.689614i	$-0.757780\pi$
$73$	−12.3747			−1.44835			−0.724177	+	0.689614i	$0.757780\pi$
$74$	−2.78018	+	5.41023i	−0.323190	+	0.628926i
$75$	0.901400	+	0.795144i	0.104085	+	0.0918153i
$76$	−5.19406	+	2.99879i	−0.595800	+	0.343985i
$77$	−7.29502			−0.831345
$78$	−1.25471	−	1.10681i	−0.142068	−	0.125321i
$79$	1.65079	+	0.953087i	0.185729	+	0.107231i	0.589982	−	0.807417i	$-0.299135\pi$
$79$	1.65079	+	0.953087i	0.185729	+	0.107231i	−0.404253	+	0.914647i	$0.632468\pi$
$80$		−	2.07510i		−	0.232003i
$81$	−8.71977	+	2.22835i	−0.968864	+	0.247595i
$82$			7.84678i			0.866531i
$83$	10.8429			1.19016			0.595082	−	0.803665i	$-0.297120\pi$
$83$	10.8429			1.19016			0.595082	+	0.803665i	$0.297120\pi$
$84$	4.80103	−	1.61422i	0.523835	−	0.176125i
$85$	6.61306	−	11.4541i	0.717287	−	1.24238i
$86$	−0.165595	−	0.286819i	−0.0178566	−	0.0309285i
$87$	2.73860	+	0.553004i	0.293609	+	0.0592882i
$88$	−2.16036	+	1.24729i	−0.230296	+	0.132961i
$89$	−11.9327	−	6.88934i	−1.26486	−	0.730269i	−0.290851	−	0.956768i	$-0.593939\pi$
$89$	−11.9327	−	6.88934i	−1.26486	−	0.730269i	−0.974011	+	0.226499i	$0.927272\pi$
$90$	−0.776745	−	6.17665i	−0.0818762	−	0.651076i
$91$	2.44640	+	1.41243i	0.256452	+	0.148063i
$92$	−6.10692	−	3.52583i	−0.636690	−	0.367593i
$93$	−2.83334	−	8.42697i	−0.293803	−	0.873836i
$94$	−7.53829	+	4.35223i	−0.777515	+	0.448898i
$95$	−6.22279	−	10.7782i	−0.638444	−	1.10582i
$96$	1.14579	−	1.29891i	0.116942	−	0.132569i
$97$	4.24112	−	2.44861i	0.430620	−	0.248619i	−0.268991	−	0.963143i	$-0.586690\pi$
$97$	4.24112	−	2.44861i	0.430620	−	0.248619i	0.699611	+	0.714524i	$0.253357\pi$
$98$	−1.34395	+	0.775932i	−0.135760	+	0.0783810i
$99$	−5.96356	+	4.52128i	−0.599361	+	0.454406i
$100$	−0.693968			−0.0693968
$101$	0.280230	+	0.485372i	0.0278839	+	0.0482963i	0.879631	−	0.475657i	$-0.157790\pi$
$101$	0.280230	+	0.485372i	0.0278839	+	0.0482963i	−0.851747	+	0.523954i	$0.824456\pi$
$102$	10.4640	−	3.51823i	1.03609	−	0.348357i
$103$	−8.90739	−	5.14268i	−0.877671	−	0.506724i	−0.00778126	−	0.999970i	$-0.502477\pi$
$103$	−8.90739	−	5.14268i	−0.877671	−	0.506724i	−0.869890	+	0.493246i	$0.835810\pi$
$104$	0.965976			0.0947218
$105$	3.34965	+	9.96261i	0.326893	+	0.972251i
$106$	10.8998	+	6.29300i	1.05868	+	0.611230i
$107$	9.12887	+	15.8117i	0.882521	+	1.52857i	0.848529	+	0.529149i	$0.177489\pi$
$107$	9.12887	+	15.8117i	0.882521	+	1.52857i	0.0339922	+	0.999422i	$0.489178\pi$
$108$	2.92431	−	4.29516i	0.281392	−	0.413302i
$109$	−12.4302	−	7.17656i	−1.19059	−	0.687389i	−0.232152	−	0.972679i	$-0.574577\pi$
$109$	−12.4302	−	7.17656i	−1.19059	−	0.687389i	−0.958441	+	0.285290i	$0.907910\pi$
$110$	−2.58824	−	4.48297i	−0.246779	−	0.427434i
$111$	−3.84187	−	9.81020i	−0.364654	−	0.931143i
$112$	−1.46218	+	2.53257i	−0.138163	+	0.239305i
$113$	4.10371	−	2.36928i	0.386045	−	0.222883i	−0.294400	−	0.955682i	$-0.595120\pi$
$113$	4.10371	−	2.36928i	0.386045	−	0.222883i	0.680445	+	0.732799i	$0.261787\pi$
$114$	2.05617	−	10.1826i	0.192578	−	0.953687i
$115$	7.31644	−	12.6724i	0.682262	−	1.18171i
$116$	−1.39694	+	0.806522i	−0.129702	+	0.0748837i
$117$	2.87528	−	0.361582i	0.265820	−	0.0334283i
$118$	−3.04240	−	5.26958i	−0.280075	−	0.485104i
$119$	−16.1419	+	9.31953i	−1.47973	+	0.854320i
$120$	2.69536	+	2.37763i	0.246051	+	0.217047i
$121$	2.38855	−	4.13709i	0.217141	−	0.376099i
$122$	1.92228	−	3.32949i	0.174035	−	0.301438i
$123$	−10.1922	−	8.99078i	−0.919002	−	0.810671i
$124$	4.44527	+	2.56648i	0.399197	+	0.230476i
$125$		−	11.8155i		−	1.05681i
$126$	−3.40427	+	8.08565i	−0.303277	+	0.720327i
$127$	6.78495	−	11.7519i	0.602067	−	1.04281i	−0.390441	−	0.920628i	$-0.627677\pi$
$127$	6.78495	−	11.7519i	0.602067	−	1.04281i	0.992508	−	0.122182i	$-0.0389893\pi$
$128$			1.00000i			0.0883883i
$129$	0.562289	+	0.113543i	0.0495068	+	0.00999688i
$130$			2.00450i			0.175806i
$131$	−11.3418	+	6.54821i	−0.990940	+	0.572120i	−0.905555	−	0.424228i	$-0.860545\pi$
$131$	−11.3418	+	6.54821i	−0.990940	+	0.572120i	−0.0853850	+	0.996348i	$0.527212\pi$
$132$	0.855220	−	4.23524i	0.0744374	−	0.368631i
$133$			17.5391i			1.52083i
$134$		−	9.83943i		−	0.849997i
$135$	8.91288	+	6.06824i	0.767098	+	0.522271i
$136$	−3.18686	+	5.51981i	−0.273271	+	0.473320i
$137$	4.51361	+	7.81780i	0.385624	+	0.667920i	0.991856	−	0.127368i	$-0.0406529\pi$
$137$	4.51361	+	7.81780i	0.385624	+	0.667920i	−0.606232	+	0.795288i	$0.707320\pi$
$138$	11.5770	−	3.89244i	0.985498	−	0.331347i
$139$	−11.4771	−	19.8788i	−0.973471	−	1.68610i	−0.684890	−	0.728646i	$-0.740150\pi$
$139$	−11.4771	−	19.8788i	−0.973471	−	1.68610i	−0.288581	−	0.957455i	$-0.593183\pi$
$140$	−5.25533	−	3.03416i	−0.444156	−	0.256434i
$141$	2.98417	−	14.7783i	0.251313	−	1.24456i
$142$	2.69428	−	1.55554i	0.226099	−	0.130538i
$143$	2.08686	−	1.20485i	0.174512	−	0.100755i
$144$	0.374317	+	2.97656i	0.0311931	+	0.248046i
$145$	−1.67361	−	2.89878i	−0.138986	−	0.240731i
$146$			12.3747i			1.02414i
$147$	0.532029	−	2.63473i	0.0438810	−	0.217309i
$148$	5.41023	+	2.78018i	0.444718	+	0.228530i
$149$	−1.77169	+	3.06866i	−0.145143	+	0.251394i	−0.929426	−	0.369008i	$-0.879697\pi$
$149$	−1.77169	+	3.06866i	−0.145143	+	0.251394i	0.784284	+	0.620403i	$0.213031\pi$
$150$	0.795144	−	0.901400i	0.0649232	−	0.0735990i
$151$	−5.11404	+	8.85777i	−0.416175	+	0.720835i	−0.995551	−	0.0942247i	$-0.969963\pi$
$151$	−5.11404	+	8.85777i	−0.416175	+	0.720835i	0.579376	+	0.815060i	$0.303296\pi$
$152$	2.99879	+	5.19406i	0.243234	+	0.421294i
$153$	−7.41972	+	17.6229i	−0.599849	+	1.42473i
$154$			7.29502i			0.587850i
$155$	−5.32569	+	9.22436i	−0.427770	+	0.740919i
$156$	−1.10681	+	1.25471i	−0.0886156	+	0.100457i
$157$	−1.98168	−	3.43237i	−0.158155	−	0.273933i	0.776048	−	0.630674i	$-0.217221\pi$
$157$	−1.98168	−	3.43237i	−0.158155	−	0.273933i	−0.934203	+	0.356741i	$0.883888\pi$
$158$	0.953087	−	1.65079i	0.0758235	−	0.131330i
$159$	−20.6629	+	6.94735i	−1.63868	+	0.550960i
$160$	−2.07510			−0.164051
$161$	−17.8588	+	10.3108i	−1.40747	+	0.812604i
$162$	2.22835	+	8.71977i	0.175076	+	0.685090i
$163$	−12.9105	−	7.45388i	−1.01123	−	0.583833i	−0.0996771	−	0.995020i	$-0.531781\pi$
$163$	−12.9105	−	7.45388i	−1.01123	−	0.583833i	−0.911551	+	0.411187i	$0.865114\pi$
$164$	7.84678			0.612730
$165$	8.78854	+	1.77467i	0.684187	+	0.138158i
$166$		−	10.8429i		−	0.841573i
$167$		−	5.38912i		−	0.417023i	−0.978020	−	0.208511i	$-0.933138\pi$
$167$		−	5.38912i		−	0.417023i	0.978020	−	0.208511i	$-0.0668618\pi$
$168$	−1.61422	−	4.80103i	−0.124539	−	0.370408i
$169$	12.0669			0.928222
$170$	−11.4541	−	6.61306i	−0.878493	−	0.507198i
$171$	10.8703	+	14.3379i	0.831273	+	1.09645i
$172$	−0.286819	+	0.165595i	−0.0218698	+	0.0126265i
$173$	−2.77645			−0.211089			−0.105545	−	0.994415i	$-0.533659\pi$
$173$	−2.77645			−0.211089			−0.105545	+	0.994415i	$0.533659\pi$
$174$	0.553004	−	2.73860i	0.0419231	−	0.207613i
$175$	−1.01471	+	1.75752i	−0.0767045	+	0.132856i
$176$	1.24729	+	2.16036i	0.0940178	+	0.162844i
$177$	10.3307	+	2.08606i	0.776499	+	0.156798i
$178$	−6.88934	+	11.9327i	−0.516378	+	0.894393i
$179$		−	6.05390i		−	0.452490i	−0.974070	−	0.226245i	$-0.927355\pi$
$179$		−	6.05390i		−	0.452490i	0.974070	−	0.226245i	$-0.0726450\pi$
$180$	−6.17665	+	0.776745i	−0.460380	+	0.0578952i
$181$	3.93255	+	6.81137i	0.292304	+	0.506286i	0.974354	−	0.225020i	$-0.0722447\pi$
$181$	3.93255	+	6.81137i	0.292304	+	0.506286i	−0.682050	+	0.731305i	$0.738911\pi$
$182$	1.41243	−	2.44640i	0.104696	−	0.181339i
$183$	2.12216	+	6.31178i	0.156875	+	0.466580i
$184$	−3.52583	+	6.10692i	−0.259928	+	0.450208i
$185$	−5.76916	+	11.2268i	−0.424157	+	0.825407i
$186$	−8.42697	+	2.83334i	−0.617895	+	0.207750i
$187$			15.8997i			1.16270i
$188$	4.35223	+	7.53829i	0.317419	+	0.549786i
$189$	−6.60191	−	13.6863i	−0.480218	−	0.995533i
$190$	−10.7782	+	6.22279i	−0.781932	+	0.451448i
$191$	7.53550	−	4.35062i	0.545249	−	0.314800i	−0.201954	−	0.979395i	$-0.564729\pi$
$191$	7.53550	−	4.35062i	0.545249	−	0.314800i	0.747204	+	0.664595i	$0.231396\pi$
$192$	−1.29891	−	1.14579i	−0.0937405	−	0.0826905i
$193$	−8.34933	−	4.82049i	−0.600998	−	0.346986i	0.168436	−	0.985713i	$-0.446128\pi$
$193$	−8.34933	−	4.82049i	−0.600998	−	0.346986i	−0.769434	+	0.638726i	$0.779462\pi$
$194$	−2.44861	−	4.24112i	−0.175800	−	0.304495i
$195$	−2.60365	−	2.29674i	−0.186451	−	0.164473i
$196$	0.775932	+	1.34395i	0.0554237	+	0.0959967i
$197$	5.57481	−	9.65586i	0.397189	−	0.687951i	−0.596189	−	0.802844i	$-0.703319\pi$
$197$	5.57481	−	9.65586i	0.397189	−	0.687951i	0.993378	+	0.114893i	$0.0366524\pi$
$198$	4.52128	+	5.96356i	0.321313	+	0.423812i
$199$			6.78425i			0.480923i	0.970659	+	0.240461i	$0.0772987\pi$
$199$			6.78425i			0.480923i	−0.970659	+	0.240461i	$0.922701\pi$
$200$			0.693968i			0.0490710i
$201$	12.7805	+	11.2739i	0.901467	+	0.795203i
$202$	0.485372	−	0.280230i	0.0341507	−	0.0197169i
$203$			4.71712i			0.331077i
$204$	−3.51823	−	10.4640i	−0.246326	−	0.732626i
$205$			16.2828i			1.13724i
$206$	−5.14268	+	8.90739i	−0.358308	+	0.620607i
$207$	−8.20890	+	19.4974i	−0.570558	+	1.35516i
$208$		−	0.965976i		−	0.0669784i
$209$	12.9570	+	7.48071i	0.896252	+	0.517451i
$210$	9.96261	−	3.34965i	0.687485	−	0.231148i
$211$	8.45706	−	14.6480i	0.582208	−	1.00841i	−0.413010	−	0.910727i	$-0.635522\pi$
$211$	8.45706	−	14.6480i	0.582208	−	1.00841i	0.995217	−	0.0976866i	$-0.0311443\pi$
$212$	6.29300	−	10.8998i	0.432205	−	0.748601i
$213$	−1.06658	+	5.28195i	−0.0730810	+	0.361913i
$214$	15.8117	−	9.12887i	1.08086	−	0.624037i
$215$	−0.343626	−	0.595178i	−0.0234351	−	0.0405908i
$216$	−4.29516	−	2.92431i	−0.292249	−	0.198974i
$217$	12.9995	−	7.50529i	0.882467	−	0.509492i
$218$	−7.17656	+	12.4302i	−0.486058	+	0.841877i
$219$	−16.0736	−	14.1789i	−1.08616	−	0.958121i
$220$	−4.48297	+	2.58824i	−0.302242	+	0.174499i
$221$	3.07844	−	5.33201i	0.207078	−	0.358670i
$222$	−9.81020	+	3.84187i	−0.658418	+	0.257849i
$223$	−10.7054	−	18.5423i	−0.716886	−	1.24168i	−0.962227	−	0.272247i	$-0.912233\pi$
$223$	−10.7054	−	18.5423i	−0.716886	−	1.24168i	0.245341	−	0.969437i	$-0.421100\pi$
$224$	2.53257	+	1.46218i	0.169214	+	0.0976959i
$225$	0.259764	+	2.06564i	0.0173176	+	0.137709i
$226$	−2.36928	−	4.10371i	−0.157602	−	0.272975i
$227$	21.7648	+	12.5659i	1.44458	+	0.834028i	0.998150	−	0.0607919i	$-0.0193626\pi$
$227$	21.7648	+	12.5659i	1.44458	+	0.834028i	0.446428	+	0.894820i	$0.352696\pi$
$228$	−10.1826	−	2.05617i	−0.674359	−	0.136173i
$229$	−6.45385			−0.426482			−0.213241	−	0.977000i	$-0.568402\pi$
$229$	−6.45385			−0.426482			−0.213241	+	0.977000i	$0.568402\pi$
$230$	−12.6724	−	7.31644i	−0.835597	−	0.482432i
$231$	−9.47555	−	8.35858i	−0.623446	−	0.549954i
$232$	0.806522	+	1.39694i	0.0529508	+	0.0917134i
$233$	−20.1699			−1.32137			−0.660686	−	0.750662i	$-0.729735\pi$
$233$	−20.1699			−1.32137			−0.660686	+	0.750662i	$0.729735\pi$
$234$	−0.361582	−	2.87528i	−0.0236373	−	0.187963i
$235$	−15.6427	+	9.03131i	−1.02042	+	0.589138i
$236$	−5.26958	+	3.04240i	−0.343021	+	0.198043i
$237$	1.05219	+	3.12944i	0.0683470	+	0.203279i
$238$	9.31953	+	16.1419i	0.604095	+	1.04632i
$239$	4.12334	−	2.38061i	0.266716	−	0.153989i	−0.360678	−	0.932690i	$-0.617455\pi$
$239$	4.12334	−	2.38061i	0.266716	−	0.153989i	0.627395	+	0.778702i	$0.284121\pi$
$240$	2.37763	−	2.69536i	0.153476	−	0.173985i
$241$	−5.64101	−	3.25684i	−0.363369	−	0.209791i	0.307188	−	0.951649i	$-0.400612\pi$
$241$	−5.64101	−	3.25684i	−0.363369	−	0.209791i	−0.670558	+	0.741857i	$0.733945\pi$
$242$	−4.13709	−	2.38855i	−0.265942	−	0.153542i
$243$	−13.8794	−	7.09663i	−0.890364	−	0.455249i
$244$	−3.32949	−	1.92228i	−0.213149	−	0.123062i
$245$	−2.78884	+	1.61013i	−0.178172	+	0.102868i
$246$	−8.99078	+	10.1922i	−0.573231	+	0.649833i
$247$	−2.89676	−	5.01734i	−0.184317	−	0.319246i
$248$	2.56648	−	4.44527i	0.162971	−	0.282275i
$249$	14.0839	+	12.4237i	0.892533	+	0.787322i
$250$	−11.8155			−0.747280
$251$		−	5.22002i		−	0.329485i	−0.986337	−	0.164742i	$-0.947321\pi$
$251$		−	5.22002i		−	0.329485i	0.986337	−	0.164742i	$-0.0526793\pi$
$252$	8.08565	+	3.40427i	0.509348	+	0.214449i
$253$			17.5909i			1.10593i
$254$	−11.7519	−	6.78495i	−0.737378	−	0.425726i
$255$	21.7138	−	7.30068i	1.35977	−	0.457186i
$256$	1.00000			0.0625000
$257$	1.04659	−	0.604249i	0.0652844	−	0.0376920i	−0.467002	−	0.884256i	$-0.654666\pi$
$257$	1.04659	−	0.604249i	0.0652844	−	0.0376920i	0.532287	+	0.846564i	$0.321333\pi$
$258$	0.113543	−	0.562289i	0.00706886	−	0.0350066i
$259$	14.9517	−	9.63664i	0.929055	−	0.598792i
$260$	2.00450			0.124314
$261$	2.92356	+	3.85617i	0.180964	+	0.238691i
$262$	6.54821	+	11.3418i	0.404550	+	0.700701i
$263$	12.0489	−	20.8694i	0.742970	−	1.28686i	−0.208168	−	0.978093i	$-0.566750\pi$
$263$	12.0489	−	20.8694i	0.742970	−	1.28686i	0.951137	−	0.308768i	$-0.0999167\pi$
$264$	−4.23524	−	0.855220i	−0.260661	−	0.0526352i
$265$	22.6182	+	13.0586i	1.38942	+	0.802183i
$266$	17.5391			1.07539
$267$	−7.60569	−	22.6210i	−0.465461	−	1.38438i
$268$	−9.83943			−0.601039
$269$	15.0540			0.917857			0.458928	−	0.888473i	$-0.348233\pi$
$269$	15.0540			0.917857			0.458928	+	0.888473i	$0.348233\pi$
$270$	6.06824	−	8.91288i	0.369301	−	0.542420i
$271$	−6.82535	+	11.8219i	−0.414611	+	0.718127i	−0.995387	−	0.0959361i	$-0.969416\pi$
$271$	−6.82535	+	11.8219i	−0.414611	+	0.718127i	0.580777	+	0.814063i	$0.302749\pi$
$272$	5.51981	+	3.18686i	0.334688	+	0.193232i
$273$	1.55929	+	4.63768i	0.0943728	+	0.280685i
$274$	7.81780	−	4.51361i	0.472291	−	0.272677i
$275$	0.865577	+	1.49922i	0.0521963	+	0.0904066i
$276$	−3.89244	−	11.5770i	−0.234298	−	0.696853i
$277$	−0.428527	−	0.247410i	−0.0257477	−	0.0148654i	0.487071	−	0.873362i	$-0.338065\pi$
$277$	−0.428527	−	0.247410i	−0.0257477	−	0.0148654i	−0.512819	+	0.858497i	$0.671399\pi$
$278$	−19.8788	+	11.4771i	−1.19225	+	0.688348i
$279$	5.97532	−	14.1923i	0.357733	−	0.849668i
$280$	−3.03416	+	5.25533i	−0.181326	+	0.314066i
$281$		−	32.4144i		−	1.93368i	−0.255385	−	0.966839i	$-0.582202\pi$
$281$		−	32.4144i		−	1.93368i	0.255385	−	0.966839i	$-0.417798\pi$
$282$	−14.7783	−	2.98417i	−0.880034	−	0.177705i
$283$		−	23.2720i		−	1.38338i	−0.722197	−	0.691688i	$-0.756867\pi$
$283$		−	23.2720i		−	1.38338i	0.722197	−	0.691688i	$-0.243133\pi$
$284$	−1.55554	−	2.69428i	−0.0923046	−	0.159876i
$285$	4.26675	−	21.1299i	0.252740	−	1.25163i
$286$	−1.20485	−	2.08686i	−0.0712442	−	0.123399i
$287$	11.4734	−	19.8725i	0.677253	−	1.17304i
$288$	2.97656	−	0.374317i	0.175395	−	0.0220569i
$289$	11.8122	+	20.4593i	0.694836	+	1.20349i
$290$	−2.89878	+	1.67361i	−0.170222	+	0.0982779i
$291$	8.31442	+	1.67893i	0.487400	+	0.0984204i
$292$	12.3747			0.724177
$293$	−16.4919			−0.963466			−0.481733	−	0.876318i	$-0.659993\pi$
$293$	−16.4919			−0.963466			−0.481733	+	0.876318i	$0.659993\pi$
$294$	−2.63473	−	0.532029i	−0.153660	−	0.0310286i
$295$	−6.31327	−	10.9349i	−0.367573	−	0.636655i
$296$	2.78018	−	5.41023i	0.161595	−	0.314463i
$297$	−12.9266	−	0.960286i	−0.750075	−	0.0557214i
$298$	3.06866	+	1.77169i	0.177763	+	0.102631i
$299$	3.40587	−	5.89914i	0.196966	−	0.341156i
$300$	−0.901400	−	0.795144i	−0.0520423	−	0.0459076i
$301$			0.968519i			0.0558245i
$302$	8.85777	+	5.11404i	0.509708	+	0.294280i
$303$	−0.192144	+	0.951538i	−0.0110384	+	0.0546644i
$304$	5.19406	−	2.99879i	0.297900	−	0.171993i
$305$	3.98893	−	6.90903i	0.228405	−	0.395610i
$306$	17.6229	+	7.41972i	1.00744	+	0.424157i
$307$	19.9087			1.13625			0.568125	−	0.822942i	$-0.307669\pi$
$307$	19.9087			1.13625			0.568125	+	0.822942i	$0.307669\pi$
$308$	7.29502			0.415672
$309$	−5.67742	−	16.8859i	−0.322977	−	0.960605i
$310$	9.22436	+	5.32569i	0.523909	+	0.302479i
$311$	−7.25454	+	4.18841i	−0.411367	+	0.237503i	−0.691377	−	0.722494i	$-0.742996\pi$
$311$	−7.25454	+	4.18841i	−0.411367	+	0.237503i	0.280010	+	0.959997i	$0.409662\pi$
$312$	1.25471	+	1.10681i	0.0710342	+	0.0626607i
$313$		−	2.70871i		−	0.153105i	−0.997066	−	0.0765526i	$-0.975609\pi$
$313$		−	2.70871i		−	0.153105i	0.997066	−	0.0765526i	$-0.0243913\pi$
$314$	−3.43237	+	1.98168i	−0.193700	+	0.111833i
$315$	−7.06420	+	16.7785i	−0.398022	+	0.945362i
$316$	−1.65079	−	0.953087i	−0.0928645	−	0.0536153i
$317$	−7.39929			−0.415586			−0.207793	−	0.978173i	$-0.566628\pi$
$317$	−7.39929			−0.415586			−0.207793	+	0.978173i	$0.566628\pi$
$318$	6.94735	+	20.6629i	0.389588	+	1.15872i
$319$	3.48476	+	2.01193i	0.195109	+	0.112646i
$320$			2.07510i			0.116002i
$321$	−6.25934	+	30.9977i	−0.349362	+	1.73012i
$322$	10.3108	+	17.8588i	0.574598	+	0.995232i
$323$	38.2270			2.12701
$324$	8.71977	−	2.22835i	0.484432	−	0.123797i
$325$		−	0.670357i		−	0.0371847i
$326$	−7.45388	+	12.9105i	−0.412832	+	0.715046i
$327$	−7.92277	−	23.5641i	−0.438130	−	1.30310i
$328$		−	7.84678i		−	0.433266i
$329$	25.4550			1.40338
$330$	1.77467	−	8.78854i	0.0976922	−	0.483793i
$331$		−	0.437608i		−	0.0240531i	−0.999928	−	0.0120266i	$-0.996172\pi$
$331$		−	0.437608i		−	0.0240531i	0.999928	−	0.0120266i	$-0.00382826\pi$
$332$	−10.8429			−0.595082
$333$	6.25023	−	17.1445i	0.342511	−	0.939514i
$334$	−5.38912			−0.294880
$335$		−	20.4178i		−	1.11554i
$336$	−4.80103	+	1.61422i	−0.261918	+	0.0880627i
$337$	2.65082			0.144400			0.0721998	−	0.997390i	$-0.476998\pi$
$337$	2.65082			0.144400			0.0721998	+	0.997390i	$0.476998\pi$
$338$		−	12.0669i		−	0.656352i
$339$	8.04504	+	1.62453i	0.436946	+	0.0882324i
$340$	−6.61306	+	11.4541i	−0.358643	+	0.621188i
$341$		−	12.8045i		−	0.693404i
$342$	14.3379	−	10.8703i	0.775305	−	0.587798i
$343$	−15.9323			−0.860263
$344$	0.165595	+	0.286819i	0.00892829	+	0.0154643i
$345$	24.0234	−	8.07720i	1.29338	−	0.434862i
$346$			2.77645i			0.149263i
$347$	1.84812	+	1.06701i	0.0992125	+	0.0572804i	0.548785	−	0.835963i	$-0.315090\pi$
$347$	1.84812	+	1.06701i	0.0992125	+	0.0572804i	−0.449573	+	0.893244i	$0.648424\pi$
$348$	−2.73860	−	0.553004i	−0.146804	−	0.0296441i
$349$	−0.0108863			−0.000582733			−0.000291366	−	1.00000i	$-0.500093\pi$
$349$	−0.0108863			−0.000582733			−0.000291366		1.00000i	$0.500093\pi$
$350$	1.75752	+	1.01471i	0.0939435	+	0.0542383i
$351$	4.14902	+	2.82482i	0.221458	+	0.150778i
$352$	2.16036	−	1.24729i	0.115148	−	0.0664806i
$353$			29.4755i			1.56882i	0.620240	+	0.784412i	$0.287035\pi$
$353$			29.4755i			1.56882i	−0.620240	+	0.784412i	$0.712965\pi$
$354$	2.08606	−	10.3307i	0.110873	−	0.549068i
$355$	5.59090	−	3.22791i	0.296734	−	0.171320i
$356$	11.9327	+	6.88934i	0.632431	+	0.365134i
$357$	−31.6451	−	6.39007i	−1.67483	−	0.338198i
$358$	−6.05390			−0.319959
$359$	18.3714			0.969608			0.484804	−	0.874623i	$-0.338891\pi$
$359$	18.3714			0.969608			0.484804	+	0.874623i	$0.338891\pi$
$360$	0.776745	+	6.17665i	0.0409381	+	0.325538i
$361$	8.48551	−	14.6973i	0.446606	−	0.773544i
$362$	6.81137	−	3.93255i	0.357998	−	0.206690i
$363$	7.84276	−	2.63691i	0.411638	−	0.138402i
$364$	−2.44640	−	1.41243i	−0.128226	−	0.0740314i
$365$			25.6788i			1.34409i
$366$	6.31178	−	2.12216i	0.329922	−	0.110927i
$367$	−12.8321	+	22.2258i	−0.669829	+	1.16018i	0.308123	+	0.951347i	$0.400299\pi$
$367$	−12.8321	+	22.2258i	−0.669829	+	1.16018i	−0.977952	+	0.208831i	$0.933034\pi$
$368$	6.10692	+	3.52583i	0.318345	+	0.183797i
$369$	−2.93719	−	23.3564i	−0.152904	−	1.21588i
$370$	11.2268	+	5.76916i	0.583651	+	0.299924i
$371$	−18.4030	−	31.8749i	−0.955436	−	1.65486i
$372$	2.83334	+	8.42697i	0.146902	+	0.436918i
$373$	27.9016			1.44469			0.722346	−	0.691532i	$-0.243064\pi$
$373$	27.9016			1.44469			0.722346	+	0.691532i	$0.243064\pi$
$374$	15.8997			0.822156
$375$	13.5382	−	15.3473i	0.699108	−	0.792531i
$376$	7.53829	−	4.35223i	0.388757	−	0.224449i
$377$	−0.779081	−	1.34941i	−0.0401247	−	0.0694981i
$378$	−13.6863	+	6.60191i	−0.703948	+	0.339566i
$379$	−8.28061	+	14.3424i	−0.425346	+	0.736722i	−0.996453	−	0.0841544i	$-0.973181\pi$
$379$	−8.28061	+	14.3424i	−0.425346	+	0.736722i	0.571106	+	0.820876i	$0.306514\pi$
$380$	6.22279	+	10.7782i	0.319222	+	0.552909i
$381$	22.2782	−	7.49045i	1.14135	−	0.383747i
$382$	−4.35062	−	7.53550i	−0.222597	−	0.385550i
$383$			20.4913i			1.04705i	0.852009	+	0.523527i	$0.175384\pi$
$383$			20.4913i			1.04705i	−0.852009	+	0.523527i	$0.824616\pi$
$384$	−1.14579	+	1.29891i	−0.0584710	+	0.0662846i
$385$			15.1379i			0.771498i
$386$	−4.82049	+	8.34933i	−0.245356	+	0.424970i
$387$	0.600265	+	0.791748i	0.0305132	+	0.0402468i
$388$	−4.24112	+	2.44861i	−0.215310	+	0.124309i
$389$	22.4403	+	12.9559i	1.13777	+	0.656890i	0.945877	−	0.324526i	$-0.105205\pi$
$389$	22.4403	+	12.9559i	1.13777	+	0.656890i	0.191891	+	0.981416i	$0.438538\pi$
$390$	−2.29674	+	2.60365i	−0.116300	+	0.131841i
$391$	22.4727	+	38.9238i	1.13649	+	1.96846i
$392$	1.34395	−	0.775932i	0.0678799	−	0.0391905i
$393$	−22.2349	−	4.48987i	−1.12160	−	0.226484i
$394$	−9.65586	−	5.57481i	−0.486455	−	0.280855i
$395$	1.97775	−	3.42556i	0.0995113	−	0.172359i
$396$	5.96356	−	4.52128i	0.299680	−	0.227203i
$397$	−9.32207			−0.467861			−0.233931	−	0.972253i	$-0.575159\pi$
$397$	−9.32207			−0.467861			−0.233931	+	0.972253i	$0.575159\pi$
$398$	6.78425			0.340064
$399$	−20.0961	+	22.7816i	−1.00607	+	1.14051i
$400$	0.693968			0.0346984
$401$	6.01297	+	3.47159i	0.300274	+	0.173363i	0.642566	−	0.766231i	$-0.277870\pi$
$401$	6.01297	+	3.47159i	0.300274	+	0.173363i	−0.342292	+	0.939594i	$0.611203\pi$
$402$	11.2739	−	12.7805i	0.562293	−	0.637433i
$403$	−2.47916	+	4.29402i	−0.123496	+	0.213900i
$404$	−0.280230	−	0.485372i	−0.0139419	−	0.0241482i
$405$	4.62405	+	18.0944i	0.229771	+	0.899117i
$406$	4.71712			0.234107
$407$	−0.741895	−	15.1557i	−0.0367744	−	0.751243i
$408$	−10.4640	+	3.51823i	−0.518045	+	0.174178i
$409$	−28.0121	+	16.1728i	−1.38511	+	0.799693i	−0.992759	−	0.120122i	$-0.961671\pi$
$409$	−28.0121	+	16.1728i	−1.38511	+	0.799693i	−0.392351	+	0.919816i	$0.628338\pi$
$410$	16.2828			0.804152
$411$	−3.09482	+	15.3263i	−0.152656	+	0.755989i
$412$	8.90739	+	5.14268i	0.438836	+	0.253362i
$413$			17.7941i			0.875590i
$414$	19.4974	+	8.20890i	0.958243	+	0.403446i
$415$		−	22.5001i		−	1.10449i
$416$	−0.965976			−0.0473609
$417$	7.86941	−	38.9711i	0.385367	−	1.90842i
$418$	7.48071	−	12.9570i	0.365893	−	0.633746i
$419$	−17.0524	−	29.5355i	−0.833062	−	1.44291i	−0.895599	−	0.444863i	$-0.853252\pi$
$419$	−17.0524	−	29.5355i	−0.833062	−	1.44291i	0.0625364	−	0.998043i	$-0.480081\pi$
$420$	−3.34965	−	9.96261i	−0.163446	−	0.486126i
$421$	−1.49015	+	0.860340i	−0.0726256	+	0.0419304i	−0.535873	−	0.844299i	$-0.680017\pi$
$421$	−1.49015	+	0.860340i	−0.0726256	+	0.0419304i	0.463247	+	0.886229i	$0.346684\pi$
$422$	−14.6480	−	8.45706i	−0.713056	−	0.411683i
$423$	20.8090	−	15.7764i	1.01177	−	0.767074i
$424$	−10.8998	−	6.29300i	−0.529341	−	0.305615i
$425$	3.83057	+	2.21158i	0.185810	+	0.107277i
$426$	5.28195	+	1.06658i	0.255911	+	0.0516761i
$427$	−9.73663	+	5.62145i	−0.471189	+	0.272041i
$428$	−9.12887	−	15.8117i	−0.441261	−	0.764286i
$429$	4.09114	+	0.826123i	0.197522	+	0.0398856i
$430$	−0.595178	+	0.343626i	−0.0287020	+	0.0165711i
$431$	−7.18439	+	4.14791i	−0.346060	+	0.199798i	−0.662949	−	0.748665i	$-0.730695\pi$
$431$	−7.18439	+	4.14791i	−0.346060	+	0.199798i	0.316889	+	0.948463i	$0.397362\pi$
$432$	−2.92431	+	4.29516i	−0.140696	+	0.206651i
$433$	−17.3517			−0.833867			−0.416934	−	0.908937i	$-0.636895\pi$
$433$	−17.3517			−0.833867			−0.416934	+	0.908937i	$0.636895\pi$
$434$	−7.50529	−	12.9995i	−0.360265	−	0.623998i
$435$	1.14754	−	5.68286i	0.0550202	−	0.272472i
$436$	12.4302	+	7.17656i	0.595297	+	0.343695i
$437$	42.2929			2.02314
$438$	−14.1789	+	16.0736i	−0.677494	+	0.768028i
$439$	−27.8441	−	16.0758i	−1.32893	−	0.767257i	−0.343794	−	0.939045i	$-0.611712\pi$
$439$	−27.8441	−	16.0758i	−1.32893	−	0.767257i	−0.985134	+	0.171789i	$0.945045\pi$
$440$	2.58824	+	4.48297i	0.123390	+	0.213717i
$441$	3.70991	−	2.81267i	0.176662	−	0.133937i
$442$	−5.33201	−	3.07844i	−0.253618	−	0.146426i
$443$	9.47241	+	16.4067i	0.450048	+	0.779506i	0.998388	−	0.0567494i	$-0.0180736\pi$
$443$	9.47241	+	16.4067i	0.450048	+	0.779506i	−0.548341	+	0.836255i	$0.684740\pi$
$444$	3.84187	+	9.81020i	0.182327	+	0.465572i
$445$	−14.2961	+	24.7615i	−0.677698	+	1.17381i
$446$	−18.5423	+	10.7054i	−0.878003	+	0.506915i
$447$	−5.81731	+	1.95591i	−0.275149	+	0.0925114i
$448$	1.46218	−	2.53257i	0.0690814	−	0.119653i
$449$	−11.7990	+	6.81218i	−0.556832	+	0.321487i	−0.751873	−	0.659308i	$-0.770849\pi$
$449$	−11.7990	+	6.81218i	−0.556832	+	0.321487i	0.195041	+	0.980795i	$0.437516\pi$
$450$	2.06564	−	0.259764i	0.0973750	−	0.0122454i
$451$	−9.78718	−	16.9519i	−0.460860	−	0.798233i
$452$	−4.10371	+	2.36928i	−0.193022	+	0.111441i
$453$	−16.7918	+	5.64579i	−0.788949	+	0.265263i
$454$	12.5659	−	21.7648i	0.589747	−	1.02147i
$455$	2.93093	−	5.07652i	0.137404	−	0.237991i
$456$	−2.05617	+	10.1826i	−0.0962888	+	0.476844i
$457$	8.61765	+	4.97540i	0.403117	+	0.232740i	0.687828	−	0.725874i	$-0.258564\pi$
$457$	8.61765	+	4.97540i	0.403117	+	0.232740i	−0.284711	+	0.958613i	$0.591898\pi$
$458$			6.45385i			0.301569i
$459$	−29.8297	+	14.3891i	−1.39233	+	0.671625i
$460$	−7.31644	+	12.6724i	−0.341131	+	0.590856i
$461$		−	22.0486i		−	1.02691i	−0.858117	−	0.513454i	$-0.828366\pi$
$461$		−	22.0486i		−	1.02691i	0.858117	−	0.513454i	$-0.171634\pi$
$462$	−8.35858	+	9.47555i	−0.388877	+	0.440843i
$463$		−	13.4512i		−	0.625129i	−0.949897	−	0.312565i	$-0.898812\pi$
$463$		−	13.4512i		−	0.625129i	0.949897	−	0.312565i	$-0.101188\pi$
$464$	1.39694	−	0.806522i	0.0648512	−	0.0374418i
$465$	−17.4868	+	5.87945i	−0.810930	+	0.272653i
$466$			20.1699i			0.934352i
$467$			11.8425i			0.548005i	0.961729	+	0.274003i	$0.0883477\pi$
$467$			11.8425i			0.548005i	−0.961729	+	0.274003i	$0.911652\pi$
$468$	−2.87528	+	0.361582i	−0.132910	+	0.0167141i
$469$	−14.3870	+	24.9190i	−0.664330	+	1.15065i
$470$	9.03131	+	15.6427i	0.416583	+	0.721543i
$471$	1.35877	−	6.72892i	0.0626087	−	0.310052i
$472$	3.04240	+	5.26958i	0.140038	+	0.242552i
$473$	0.715492	+	0.413089i	0.0328983	+	0.0189939i
$474$	3.12944	−	1.05219i	0.143740	−	0.0483286i
$475$	3.60451	−	2.08107i	0.165386	−	0.0954859i
$476$	16.1419	−	9.31953i	0.739863	−	0.427160i
$477$	−34.7995	−	14.6515i	−1.59336	−	0.670846i
$478$	−2.38061	−	4.12334i	−0.108887	−	0.188597i
$479$		−	9.31385i		−	0.425561i	−0.977100	−	0.212780i	$-0.931748\pi$
$479$		−	9.31385i		−	0.425561i	0.977100	−	0.212780i	$-0.0682519\pi$
$480$	−2.69536	−	2.37763i	−0.123026	−	0.108524i
$481$	−2.68559	+	5.22615i	−0.122453	+	0.238292i
$482$	−3.25684	+	5.64101i	−0.148345	+	0.256941i
$483$	−35.0109	−	7.06974i	−1.59305	−	0.321684i
$484$	−2.38855	+	4.13709i	−0.108571	+	0.188050i
$485$	−5.08111	−	8.80074i	−0.230721	−	0.399621i
$486$	−7.09663	+	13.8794i	−0.321910	+	0.629583i
$487$		−	28.3740i		−	1.28575i	−0.765972	−	0.642874i	$-0.777742\pi$
$487$		−	28.3740i		−	1.28575i	0.765972	−	0.642874i	$-0.222258\pi$
$488$	−1.92228	+	3.32949i	−0.0870177	+	0.150719i
$489$	−8.22893	−	24.4746i	−0.372125	−	1.10678i
$490$	1.61013	+	2.78884i	0.0727385	+	0.125987i
$491$	−16.0415	+	27.7847i	−0.723942	+	1.25390i	0.235466	+	0.971883i	$0.424338\pi$
$491$	−16.0415	+	27.7847i	−0.723942	+	1.25390i	−0.959408	+	0.282022i	$0.908995\pi$
$492$	10.1922	+	8.99078i	0.459501	+	0.405336i
$493$	10.2811			0.463038
$494$	−5.01734	+	2.89676i	−0.225741	+	0.130331i
$495$	9.38210	+	12.3750i	0.421694	+	0.556214i
$496$	−4.44527	−	2.56648i	−0.199598	−	0.115238i
$497$	−9.09794			−0.408098
$498$	12.4237	−	14.0839i	0.556721	−	0.631116i
$499$			17.8888i			0.800812i	0.916338	+	0.400406i	$0.131131\pi$
$499$			17.8888i			0.800812i	−0.916338	+	0.400406i	$0.868869\pi$
$500$			11.8155i			0.528407i
$501$	6.17482	−	6.99997i	0.275871	−	0.312736i
$502$	−5.22002			−0.232981
$503$	20.1448	+	11.6306i	0.898212	+	0.518583i	0.876620	−	0.481184i	$-0.159793\pi$
$503$	20.1448	+	11.6306i	0.898212	+	0.518583i	0.0215923	+	0.999767i	$0.493126\pi$
$504$	3.40427	−	8.08565i	0.151638	−	0.360163i
$505$	1.00719	−	0.581504i	0.0448196	−	0.0258766i
$506$	17.5909			0.782010
$507$	15.6738	+	13.8262i	0.696096	+	0.614041i
$508$	−6.78495	+	11.7519i	−0.301033	+	0.521405i
$509$	11.2233	+	19.4393i	0.497462	+	0.861630i	0.999996	−	0.00292796i	$-0.000932001\pi$
$509$	11.2233	+	19.4393i	0.497462	+	0.861630i	−0.502534	+	0.864558i	$0.667599\pi$
$510$	−7.30068	−	21.7138i	−0.323279	−	0.961504i
$511$	18.0941	−	31.3399i	0.800436	−	1.38639i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.30877	+	31.0787i	−0.101935	+	1.37216i
$514$	−0.604249	−	1.04659i	−0.0266523	−	0.0461631i
$515$	−10.6716	+	18.4837i	−0.470246	+	0.814489i
$516$	−0.562289	−	0.113543i	−0.0247534	−	0.00499844i
$517$	10.8570	−	18.8048i	0.477489	−	0.827034i
$518$	−9.63664	−	14.9517i	−0.423410	−	0.656941i
$519$	−3.60634	−	3.18123i	−0.158301	−	0.139641i
$520$		−	2.00450i		−	0.0879030i
$521$	−4.75508	−	8.23605i	−0.208324	−	0.360828i	0.742863	−	0.669444i	$-0.233468\pi$
$521$	−4.75508	−	8.23605i	−0.208324	−	0.360828i	−0.951187	+	0.308616i	$0.900134\pi$
$522$	3.85617	−	2.92356i	0.168780	−	0.127961i
$523$	−8.58415	+	4.95606i	−0.375359	+	0.216713i	−0.675797	−	0.737088i	$-0.736200\pi$
$523$	−8.58415	+	4.95606i	−0.375359	+	0.216713i	0.300438	+	0.953801i	$0.402867\pi$
$524$	11.3418	−	6.54821i	0.495470	−	0.286060i
$525$	−3.33176	+	1.12021i	−0.145410	+	0.0488901i
$526$	−20.8694	−	12.0489i	−0.909948	−	0.525359i
$527$	−16.3580	−	28.3329i	−0.712566	−	1.23420i
$528$	−0.855220	+	4.23524i	−0.0372187	+	0.184315i
$529$	13.3629	+	23.1453i	0.580998	+	1.00632i
$530$	13.0586	−	22.6182i	0.567229	−	0.982470i
$531$	11.0284	+	14.5464i	0.478590	+	0.631260i
$532$		−	17.5391i		−	0.760415i
$533$			7.57980i			0.328318i
$534$	−22.6210	+	7.60569i	−0.978907	+	0.329131i
$535$	32.8108	−	18.9433i	1.41853	−	0.818990i
$536$			9.83943i			0.424999i
$537$	6.93652	−	7.86345i	0.299333	−	0.339333i
$538$		−	15.0540i		−	0.649023i
$539$	1.93562	−	3.35259i	0.0833730	−	0.144406i
$540$	−8.91288	−	6.06824i	−0.383549	−	0.261135i
$541$			30.8724i			1.32731i	0.748040	+	0.663653i	$0.230995\pi$
$541$			30.8724i			1.32731i	−0.748040	+	0.663653i	$0.769005\pi$
$542$	11.8219	+	6.82535i	0.507792	+	0.293174i
$543$	−2.69641	+	13.3532i	−0.115714	+	0.573042i
$544$	3.18686	−	5.51981i	0.136636	−	0.236660i
$545$	−14.8921	+	25.7938i	−0.637906	+	1.10489i
$546$	4.63768	−	1.55929i	0.198475	−	0.0667316i
$547$	−3.81046	+	2.19997i	−0.162924	+	0.0940640i	−0.579245	−	0.815154i	$-0.696652\pi$
$547$	−3.81046	+	2.19997i	−0.162924	+	0.0940640i	0.416321	+	0.909218i	$0.363319\pi$
$548$	−4.51361	−	7.81780i	−0.192812	−	0.333960i
$549$	−4.47550	+	10.6300i	−0.191010	+	0.453676i
$550$	1.49922	−	0.865577i	0.0639271	−	0.0369083i
$551$	4.83718	−	8.37825i	0.206071	−	0.356925i
$552$	−11.5770	+	3.89244i	−0.492749	+	0.165673i
$553$	−4.82751	+	2.78717i	−0.205287	+	0.118522i
$554$	−0.247410	+	0.428527i	−0.0105114	+	0.0182064i
$555$	−20.3571	+	7.97225i	−0.864112	+	0.338403i
$556$	11.4771	+	19.8788i	0.486736	+	0.843051i
$557$	3.30729	+	1.90946i	0.140134	+	0.0809065i	0.568428	−	0.822733i	$-0.307552\pi$
$557$	3.30729	+	1.90946i	0.140134	+	0.0809065i	−0.428294	+	0.903640i	$0.640885\pi$
$558$	−14.1923	−	5.97532i	−0.600806	−	0.252955i
$559$	−0.159961	−	0.277061i	−0.00676563	−	0.0117184i
$560$	5.25533	+	3.03416i	0.222078	+	0.128217i
$561$	−18.2178	+	20.6523i	−0.769156	+	0.871939i
$562$	−32.4144			−1.36732
$563$	−9.90220	−	5.71704i	−0.417328	−	0.240945i	0.276605	−	0.960984i	$-0.410791\pi$
$563$	−9.90220	−	5.71704i	−0.417328	−	0.240945i	−0.693934	+	0.720039i	$0.744124\pi$
$564$	−2.98417	+	14.7783i	−0.125656	+	0.622278i
$565$	−4.91648	−	8.51560i	−0.206838	−	0.358254i
$566$	−23.2720			−0.978194
$567$	7.10641	−	25.3417i	0.298441	−	1.06425i
$568$	−2.69428	+	1.55554i	−0.113050	+	0.0652692i
$569$	26.2859	−	15.1762i	1.10196	−	0.636217i	0.165226	−	0.986256i	$-0.447165\pi$
$569$	26.2859	−	15.1762i	1.10196	−	0.636217i	0.936735	+	0.350038i	$0.113831\pi$
$570$	−21.1299	−	4.26675i	−0.885033	−	0.178714i
$571$	−12.1777	−	21.0923i	−0.509619	−	0.882686i	−0.999938	−	0.0111430i	$-0.996453\pi$
$571$	−12.1777	−	21.0923i	−0.509619	−	0.882686i	0.490319	−	0.871543i	$-0.336880\pi$
$572$	−2.08686	+	1.20485i	−0.0872560	+	0.0503773i
$573$	14.7728	+	2.98307i	0.617143	+	0.124619i
$574$	−19.8725	−	11.4734i	−0.829462	−	0.478890i
$575$	4.23800	+	2.44681i	0.176737	+	0.102039i
$576$	−0.374317	−	2.97656i	−0.0155966	−	0.124023i
$577$	−5.16764	−	2.98354i	−0.215132	−	0.124206i	0.388562	−	0.921422i	$-0.372972\pi$
$577$	−5.16764	−	2.98354i	−0.215132	−	0.124206i	−0.603694	+	0.797216i	$0.706305\pi$
$578$	20.4593	−	11.8122i	0.850996	−	0.491323i
$579$	−5.32172	−	15.8280i	−0.221163	−	0.657788i
$580$	1.67361	+	2.89878i	0.0694930	+	0.120365i
$581$	−15.8543	+	27.4604i	−0.657746	+	1.13925i
$582$	1.67893	−	8.31442i	0.0695937	−	0.344644i
$583$	−31.3967			−1.30032
$584$		−	12.3747i		−	0.512071i
$585$	−0.750318	−	5.96649i	−0.0310218	−	0.246684i
$586$			16.4919i			0.681273i
$587$	18.6025	+	10.7401i	0.767806	+	0.443293i	0.832091	−	0.554639i	$-0.187143\pi$
$587$	18.6025	+	10.7401i	0.767806	+	0.443293i	−0.0642855	+	0.997932i	$0.520477\pi$
$588$	−0.532029	+	2.63473i	−0.0219405	+	0.108654i
$589$	−30.7853			−1.26849
$590$	−10.9349	+	6.31327i	−0.450183	+	0.259913i
$591$	18.3048	−	6.15448i	0.752958	−	0.253161i
$592$	−5.41023	−	2.78018i	−0.222359	−	0.114265i
$593$	14.6839			0.602995			0.301497	−	0.953467i	$-0.402514\pi$
$593$	14.6839			0.602995			0.301497	+	0.953467i	$0.402514\pi$
$594$	−0.960286	+	12.9266i	−0.0394010	+	0.530383i
$595$	19.3389	+	33.4960i	0.792819	+	1.37320i
$596$	1.77169	−	3.06866i	0.0725713	−	0.125697i
$597$	−7.77334	+	8.81211i	−0.318142	+	0.360656i
$598$	−5.89914	−	3.40587i	−0.241234	−	0.139276i
$599$	37.2774			1.52311			0.761557	−	0.648098i	$-0.224435\pi$
$599$	37.2774			1.52311			0.761557	+	0.648098i	$0.224435\pi$
$600$	−0.795144	+	0.901400i	−0.0324616	+	0.0367995i
$601$	21.2614			0.867272			0.433636	−	0.901088i	$-0.357230\pi$
$601$	21.2614			0.867272			0.433636	+	0.901088i	$0.357230\pi$
$602$	0.968519			0.0394739
$603$	3.68307	+	29.2876i	0.149986	+	1.19268i
$604$	5.11404	−	8.85777i	0.208087	−	0.360418i
$605$	−8.58488	−	4.95648i	−0.349025	−	0.201510i
$606$	0.951538	+	0.192144i	0.0386536	+	0.00780530i
$607$	30.9306	−	17.8578i	1.25543	−	0.724824i	0.283250	−	0.959046i	$-0.408588\pi$
$607$	30.9306	−	17.8578i	1.25543	−	0.724824i	0.972183	+	0.234222i	$0.0752542\pi$
$608$	−2.99879	−	5.19406i	−0.121617	−	0.210647i
$609$	−5.40484	+	6.12709i	−0.219015	+	0.248282i
$610$	−6.90903	−	3.98893i	−0.279738	−	0.161507i
$611$	−7.28181	+	4.20415i	−0.294590	+	0.170082i
$612$	7.41972	−	17.6229i	0.299924	−	0.712365i
$613$	−4.63356	+	8.02556i	−0.187148	+	0.324149i	−0.944298	−	0.329091i	$-0.893258\pi$
$613$	−4.63356	+	8.02556i	−0.187148	+	0.324149i	0.757151	+	0.653240i	$0.226591\pi$
$614$		−	19.9087i		−	0.803450i
$615$	−18.6567	+	21.1499i	−0.752313	+	0.852845i
$616$		−	7.29502i		−	0.293925i
$617$	10.6162	+	18.3879i	0.427393	+	0.740267i	0.996641	−	0.0818993i	$-0.0260986\pi$
$617$	10.6162	+	18.3879i	0.427393	+	0.740267i	−0.569247	+	0.822166i	$0.692765\pi$
$618$	−16.8859	+	5.67742i	−0.679250	+	0.228379i
$619$	15.2987	+	26.4981i	0.614907	+	1.06505i	0.990401	+	0.138225i	$0.0441397\pi$
$619$	15.2987	+	26.4981i	0.614907	+	1.06505i	−0.375494	+	0.926825i	$0.622527\pi$
$620$	5.32569	−	9.22436i	0.213885	−	0.370459i
$621$	−33.0025	+	15.9195i	−1.32435	+	0.638829i
$622$	4.18841	+	7.25454i	0.167940	+	0.290881i
$623$	34.8955	−	20.1469i	1.39806	−	0.807168i
$624$	1.10681	−	1.25471i	0.0443078	−	0.0502287i
$625$	−21.0486			−0.841943
$626$	−2.70871			−0.108262
$627$	8.25855	+	24.5627i	0.329815	+	0.980941i
$628$	1.98168	+	3.43237i	0.0790776	+	0.136966i
$629$	−21.0034	−	32.5878i	−0.837459	−	1.29936i
$630$	16.7785	+	7.06420i	0.668472	+	0.281444i
$631$	−24.2862	−	14.0216i	−0.966817	−	0.558192i	−0.0685526	−	0.997648i	$-0.521838\pi$
$631$	−24.2862	−	14.0216i	−0.966817	−	0.558192i	−0.898264	+	0.439455i	$0.855171\pi$
$632$	−0.953087	+	1.65079i	−0.0379118	+	0.0656651i
$633$	27.7686	−	9.33642i	1.10370	−	0.371089i
$634$			7.39929i			0.293863i
$635$	−24.3863	−	14.0794i	−0.967741	−	0.558725i
$636$	20.6629	−	6.94735i	0.819339	−	0.275480i
$637$	−1.29823	+	0.749532i	−0.0514376	+	0.0296975i
$638$	2.01193	−	3.48476i	0.0796530	−	0.137963i
$639$	−7.43742	+	5.63868i	−0.294220	+	0.223063i
$640$	2.07510			0.0820255
$641$	−29.6377			−1.17062			−0.585310	−	0.810810i	$-0.699027\pi$
$641$	−29.6377			−1.17062			−0.585310	+	0.810810i	$0.699027\pi$
$642$	30.9977	+	6.25934i	1.22338	+	0.247037i
$643$	28.4800	+	16.4429i	1.12314	+	0.648445i	0.942201	−	0.335049i	$-0.108753\pi$
$643$	28.4800	+	16.4429i	1.12314	+	0.648445i	0.180940	+	0.983494i	$0.442086\pi$
$644$	17.8588	−	10.3108i	0.703735	−	0.406302i
$645$	0.235612	−	1.16681i	0.00927723	−	0.0459429i
$646$		−	38.2270i		−	1.50402i
$647$	27.5906	−	15.9294i	1.08470	−	0.626250i	0.152538	−	0.988298i	$-0.451255\pi$
$647$	27.5906	−	15.9294i	1.08470	−	0.626250i	0.932160	+	0.362047i	$0.117922\pi$
$648$	−2.22835	−	8.71977i	−0.0875380	−	0.342545i
$649$	13.1454	+	7.58948i	0.516001	+	0.297913i
$650$	−0.670357			−0.0262936
$651$	25.4847	+	5.14611i	0.998824	+	0.201692i
$652$	12.9105	+	7.45388i	0.505614	+	0.291916i
$653$			7.38487i			0.288992i	0.989505	+	0.144496i	$0.0461561\pi$
$653$			7.38487i			0.288992i	−0.989505	+	0.144496i	$0.953844\pi$
$654$	−23.5641	+	7.92277i	−0.921428	+	0.309805i
$655$	13.5882	+	23.5354i	0.530934	+	0.919604i
$656$	−7.84678			−0.306365
$657$	−4.63208	−	36.8341i	−0.180715	−	1.43704i
$658$		−	25.4550i		−	0.992338i
$659$	−22.1651	+	38.3911i	−0.863431	+	1.49551i	0.00516561	+	0.999987i	$0.498356\pi$
$659$	−22.1651	+	38.3911i	−0.863431	+	1.49551i	−0.868597	+	0.495520i	$0.834978\pi$
$660$	−8.78854	−	1.77467i	−0.342094	−	0.0690788i
$661$		−	18.8130i		−	0.731741i	−0.930666	−	0.365870i	$-0.880771\pi$
$661$		−	18.8130i		−	0.731741i	0.930666	−	0.365870i	$-0.119229\pi$
$662$	−0.437608			−0.0170081
$663$	10.1080	−	3.39853i	0.392561	−	0.131988i
$664$			10.8429i			0.420787i
$665$	36.3953			1.41135
$666$	−17.1445	−	6.25023i	−0.664337	−	0.242192i
$667$	11.3746			0.440428
$668$			5.38912i			0.208511i
$669$	7.34031	−	36.3509i	0.283793	−	1.40541i
$670$	−20.4178			−0.788807
$671$			9.59056i			0.370239i
$672$	1.61422	+	4.80103i	0.0622697	+	0.185204i
$673$	22.9828	−	39.8073i	0.885921	−	1.53446i	0.0412668	−	0.999148i	$-0.486861\pi$
$673$	22.9828	−	39.8073i	0.885921	−	1.53446i	0.844654	−	0.535312i	$-0.179806\pi$
$674$		−	2.65082i		−	0.102106i
$675$	−2.02938	+	2.98070i	−0.0781109	+	0.114727i
$676$	−12.0669			−0.464111
$677$	−24.4206	−	42.2977i	−0.938561	−	1.62563i	−0.768158	−	0.640260i	$-0.778827\pi$
$677$	−24.4206	−	42.2977i	−0.938561	−	1.62563i	−0.170402	−	0.985375i	$-0.554507\pi$
$678$	1.62453	−	8.04504i	0.0623897	−	0.308968i
$679$			14.3212i			0.549598i
$680$	11.4541	+	6.61306i	0.439247	+	0.253599i
$681$	13.8725	+	41.2598i	0.531595	+	1.58108i
$682$	−12.8045			−0.490310
$683$	25.0780	+	14.4788i	0.959582	+	0.554015i	0.896044	−	0.443965i	$-0.146428\pi$
$683$	25.0780	+	14.4788i	0.959582	+	0.554015i	0.0635373	+	0.997979i	$0.479762\pi$
$684$	−10.8703	−	14.3379i	−0.415636	−	0.548224i
$685$	16.2227	−	9.36619i	0.619838	−	0.357864i
$686$			15.9323i			0.608298i
$687$	−8.38295	−	7.39477i	−0.319829	−	0.282128i
$688$	0.286819	−	0.165595i	0.0109349	−	0.00631326i
$689$	10.5290	+	6.07889i	0.401121	+	0.231587i
$690$	−8.07720	−	24.0234i	−0.307494	−	0.914554i
$691$	−20.9594			−0.797334			−0.398667	−	0.917096i	$-0.630527\pi$
$691$	−20.9594			−0.797334			−0.398667	+	0.917096i	$0.630527\pi$
$692$	2.77645			0.105545
$693$	−2.73065	−	21.7140i	−0.103729	−	0.824848i
$694$	1.06701	−	1.84812i	0.0405033	−	0.0701538i
$695$	−41.2506	+	23.8160i	−1.56472	+	0.903393i
$696$	−0.553004	+	2.73860i	−0.0209615	+	0.103806i
$697$	−43.3127	−	25.0066i	−1.64059	−	0.947193i
$698$			0.0108863i			0.000412054i
$699$	−26.1988	−	23.1105i	−0.990929	−	0.874120i
$700$	1.01471	−	1.75752i	0.0383523	−	0.0664281i
$701$	−31.9608	−	18.4526i	−1.20714	−	0.696945i	−0.245009	−	0.969521i	$-0.578791\pi$
$701$	−31.9608	−	18.4526i	−1.20714	−	0.696945i	−0.962134	+	0.272576i	$0.912124\pi$
$702$	2.82482	−	4.14902i	0.106616	−	0.156595i
$703$	−36.4382	+	1.78370i	−1.37429	+	0.0672736i
$704$	−1.24729	−	2.16036i	−0.0470089	−	0.0814218i
$705$	−30.6664	−	6.19245i	−1.15496	−	0.233221i
$706$	29.4755			1.10933
$707$	−1.63898			−0.0616403
$708$	−10.3307	−	2.08606i	−0.388250	−	0.0783991i
$709$	−39.8517	+	23.0084i	−1.49666	+	0.864099i	−0.999993	−	0.00384026i	$-0.998778\pi$
$709$	−39.8517	+	23.0084i	−1.49666	+	0.864099i	−0.496671	+	0.867939i	$0.665444\pi$
$710$	−3.22791	−	5.59090i	−0.121141	−	0.209823i
$711$	−2.21900	+	5.27044i	−0.0832188	+	0.197657i
$712$	6.88934	−	11.9327i	0.258189	−	0.447197i
$713$	−18.0979	−	31.3465i	−0.677772	−	1.17394i
$714$	−6.39007	+	31.6451i	−0.239142	+	1.18429i
$715$	−2.50018	−	4.33044i	−0.0935015	−	0.161949i
$716$			6.05390i			0.226245i
$717$	8.08351	+	1.63230i	0.301884	+	0.0609594i
$718$		−	18.3714i		−	0.685616i
$719$	−15.5745	+	26.9759i	−0.580832	+	1.00603i	0.414549	+	0.910027i	$0.363939\pi$
$719$	−15.5745	+	26.9759i	−0.580832	+	1.00603i	−0.995381	+	0.0960034i	$0.969394\pi$
$720$	6.17665	−	0.776745i	0.230190	−	0.0289476i
$721$	26.0484	−	15.0390i	0.970093	−	0.560083i
$722$	−14.6973	−	8.48551i	−0.546978	−	0.315798i
$723$	−3.59548	−	10.6938i	−0.133717	−	0.397705i
$724$	−3.93255	−	6.81137i	−0.146152	−	0.253143i
$725$	0.969430	−	0.559701i	0.0360037	−	0.0207868i
$726$	−2.63691	−	7.84276i	−0.0978650	−	0.291072i
$727$	22.5417	+	13.0144i	0.836025	+	0.482679i	0.855911	−	0.517123i	$-0.172997\pi$
$727$	22.5417	+	13.0144i	0.836025	+	0.482679i	−0.0198862	+	0.999802i	$0.506330\pi$
$728$	−1.41243	+	2.44640i	−0.0523481	+	0.0906696i
$729$	−9.89678	−	25.1208i	−0.366548	−	0.930399i
$730$	25.6788			0.950416
$731$	2.11092			0.0780751
$732$	−2.12216	−	6.31178i	−0.0784374	−	0.233290i
$733$	14.0275			0.518116			0.259058	−	0.965862i	$-0.416588\pi$
$733$	14.0275			0.518116			0.259058	+	0.965862i	$0.416588\pi$
$734$	22.2258	+	12.8321i	0.820370	+	0.473641i
$735$	−5.46732	−	1.10401i	−0.201665	−	0.0407221i
$736$	3.52583	−	6.10692i	0.129964	−	0.225104i
$737$	12.2726	+	21.2567i	0.452066	+	0.783002i
$738$	−23.3564	+	2.93719i	−0.859760	+	0.108119i
$739$	−31.7058			−1.16632			−0.583158	−	0.812359i	$-0.698183\pi$
$739$	−31.7058			−1.16632			−0.583158	+	0.812359i	$0.698183\pi$
$740$	5.76916	−	11.2268i	0.212078	−	0.412704i
$741$	1.98621	−	9.83615i	0.0729652	−	0.361340i
$742$	−31.8749	+	18.4030i	−1.17016	+	0.675595i
$743$	39.9145			1.46432			0.732160	−	0.681133i	$-0.238512\pi$
$743$	39.9145			1.46432			0.732160	+	0.681133i	$0.238512\pi$
$744$	8.42697	−	2.83334i	0.308948	−	0.103875i
$745$	6.36777	+	3.67643i	0.233297	+	0.134694i
$746$		−	27.9016i		−	1.02155i
$747$	4.05869	+	32.2745i	0.148500	+	1.18086i
$748$		−	15.8997i		−	0.581352i
$749$	−53.3921			−1.95091
$750$	−15.3473	−	13.5382i	−0.560404	−	0.494344i
$751$	−21.5366	+	37.3024i	−0.785880	+	1.36118i	0.142592	+	0.989782i	$0.454456\pi$
$751$	−21.5366	+	37.3024i	−0.785880	+	1.36118i	−0.928472	+	0.371402i	$0.878877\pi$
$752$	−4.35223	−	7.53829i	−0.158710	−	0.274893i
$753$	5.98107	−	6.78032i	0.217962	−	0.247089i
$754$	−1.34941	+	0.779081i	−0.0491425	+	0.0283725i
$755$	18.3807	+	10.6121i	0.668944	+	0.386215i
$756$	6.60191	+	13.6863i	0.240109	+	0.497766i
$757$	39.2580	+	22.6656i	1.42686	+	0.823797i	0.996872	−	0.0790390i	$-0.0251852\pi$
$757$	39.2580	+	22.6656i	1.42686	+	0.823797i	0.429986	+	0.902836i	$0.358519\pi$
$758$	14.3424	+	8.28061i	0.520941	+	0.300765i
$759$	−20.1555	+	22.8489i	−0.731598	+	0.829363i
$760$	10.7782	−	6.22279i	0.390966	−	0.225724i
$761$	−21.3517	−	36.9823i	−0.774000	−	1.34061i	−0.935355	−	0.353710i	$-0.884920\pi$
$761$	−21.3517	−	36.9823i	−0.774000	−	1.34061i	0.161355	−	0.986896i	$-0.448413\pi$
$762$	−7.49045	−	22.2782i	−0.271350	−	0.807055i
$763$	36.3502	−	20.9868i	1.31597	−	0.759774i
$764$	−7.53550	+	4.35062i	−0.272625	+	0.157400i
$765$	36.5693	+	15.3966i	1.32217	+	0.556667i
$766$	20.4913			0.740379
$767$	−2.93888	−	5.09029i	−0.106117	−	0.183800i
$768$	1.29891	+	1.14579i	0.0468703	+	0.0413452i
$769$	−27.2910	−	15.7565i	−0.984139	−	0.568193i	−0.0806222	−	0.996745i	$-0.525691\pi$
$769$	−27.2910	−	15.7565i	−0.984139	−	0.568193i	−0.903517	+	0.428552i	$0.859024\pi$
$770$	15.1379			0.545532
$771$	2.05177	+	0.414312i	0.0738925	+	0.0149211i
$772$	8.34933	+	4.82049i	0.300499	+	0.173493i
$773$	−17.8946	−	30.9944i	−0.643626	−	1.11479i	−0.984617	−	0.174726i	$-0.944096\pi$
$773$	−17.8946	−	30.9944i	−0.643626	−	1.11479i	0.340991	−	0.940066i	$-0.389237\pi$
$774$	0.791748	−	0.600265i	0.0284588	−	0.0215761i
$775$	−3.08487	−	1.78105i	−0.110812	−	0.0639773i
$776$	2.44861	+	4.24112i	0.0879000	+	0.152247i
$777$	30.4625	+	4.61448i	1.09284	+	0.165544i
$778$	12.9559	−	22.4403i	0.464492	−	0.804523i
$779$	−40.7566	+	23.5308i	−1.46026	+	0.843080i
$780$	2.60365	+	2.29674i	0.0932257	+	0.0822364i
$781$	−3.88042	+	6.72108i	−0.138852	+	0.240499i
$782$	38.9238	−	22.4727i	1.39191	−	0.803621i
$783$	−0.620941	+	8.35859i	−0.0221906	+	0.298712i
$784$	−0.775932	−	1.34395i	−0.0277119	−	0.0479983i
$785$	−7.12250	+	4.11218i	−0.254213	+	0.146770i
$786$	−4.48987	+	22.2349i	−0.160149	+	0.793091i
$787$	−14.4367	+	25.0050i	−0.514611	+	0.891332i	0.485245	+	0.874378i	$0.338730\pi$
$787$	−14.4367	+	25.0050i	−0.514611	+	0.891332i	−0.999856	+	0.0169544i	$0.994603\pi$
$788$	−5.57481	+	9.65586i	−0.198594	+	0.343976i
$789$	39.5624	−	13.3018i	1.40846	−	0.473556i
$790$	−3.42556	−	1.97775i	−0.121876	−	0.0703651i
$791$			13.8572i			0.492706i
$792$	−4.52128	−	5.96356i	−0.160657	−	0.211906i
$793$	1.85688	−	3.21621i	0.0659398	−	0.114211i
$794$			9.32207i			0.330828i
$795$	14.4164	+	42.8776i	0.511298	+	1.52071i
$796$		−	6.78425i		−	0.240461i
$797$	−7.45836	+	4.30608i	−0.264189	+	0.152529i	−0.626244	−	0.779627i	$-0.715409\pi$
$797$	−7.45836	+	4.30608i	−0.264189	+	0.152529i	0.362055	+	0.932157i	$0.382075\pi$
$798$	22.7816	+	20.0961i	0.806461	+	0.711396i
$799$		−	55.4799i		−	1.96274i
$800$		−	0.693968i		−	0.0245355i
$801$	16.0399	−	38.0971i	0.566742	−	1.34610i
$802$	3.47159	−	6.01297i	0.122586	−	0.212325i
$803$	−15.4349	−	26.7340i	−0.544684	−	0.943421i
$804$	−12.7805	−	11.2739i	−0.450733	−	0.397601i
$805$	21.3959	+	37.0588i	0.754106	+	1.30615i
$806$	4.29402	+	2.47916i	0.151250	+	0.0873245i
$807$	19.5537	+	17.2487i	0.688323	+	0.607184i
$808$	−0.485372	+	0.280230i	−0.0170753	+	0.00985845i
$809$	−32.9827	+	19.0426i	−1.15961	+	0.669500i	−0.951210	−	0.308544i	$-0.900158\pi$
$809$	−32.9827	+	19.0426i	−1.15961	+	0.669500i	−0.208399	+	0.978044i	$0.566825\pi$
$810$	18.0944	−	4.62405i	0.635772	−	0.162473i
$811$	−1.25518	−	2.17403i	−0.0440752	−	0.0763405i	0.843146	−	0.537684i	$-0.180701\pi$
$811$	−1.25518	−	2.17403i	−0.0440752	−	0.0763405i	−0.887221	+	0.461344i	$0.847367\pi$
$812$		−	4.71712i		−	0.165538i
$813$	−22.4109	+	7.53505i	−0.785984	+	0.264266i
$814$	−15.1557	+	0.741895i	−0.531209	+	0.0260034i
$815$	−15.4675	+	26.7905i	−0.541804	+	0.938432i
$816$	3.51823	+	10.4640i	0.123163	+	0.366313i
$817$	0.993171	−	1.72022i	0.0347467	−	0.0601830i
$818$	16.1728	+	28.0121i	0.565469	+	0.979420i
$819$	−3.28845	+	7.81055i	−0.114908	+	0.272923i
$820$		−	16.2828i		−	0.568621i
$821$	−7.37137	+	12.7676i	−0.257262	+	0.445592i	−0.965508	−	0.260375i	$-0.916154\pi$
$821$	−7.37137	+	12.7676i	−0.257262	+	0.445592i	0.708245	+	0.705967i	$0.249487\pi$
$822$	15.3263	+	3.09482i	0.534565	+	0.107944i
$823$	−7.35430	−	12.7380i	−0.256355	−	0.444020i	0.708908	−	0.705301i	$-0.249188\pi$
$823$	−7.35430	−	12.7380i	−0.256355	−	0.444020i	−0.965263	+	0.261282i	$0.915855\pi$
$824$	5.14268	−	8.90739i	0.179154	−	0.310304i
$825$	−0.593496	+	2.93912i	−0.0206629	+	0.102327i
$826$	17.7941			0.619136
$827$	−6.22156	+	3.59202i	−0.216345	+	0.124907i	−0.604257	−	0.796790i	$-0.706530\pi$
$827$	−6.22156	+	3.59202i	−0.216345	+	0.124907i	0.387912	+	0.921697i	$0.373197\pi$
$828$	8.20890	−	19.4974i	0.285279	−	0.677580i
$829$	47.5246	+	27.4384i	1.65060	+	0.952974i	0.976826	+	0.214035i	$0.0686606\pi$
$829$	47.5246	+	27.4384i	1.65060	+	0.952974i	0.673773	+	0.738939i	$0.264673\pi$
$830$	−22.5001			−0.780990
$831$	−0.273136	−	0.812365i	−0.00947497	−	0.0281806i
$832$			0.965976i			0.0334892i
$833$		−	9.89116i		−	0.342708i
$834$	−38.9711	−	7.86941i	−1.34946	−	0.272495i
$835$	−11.1830			−0.387002
$836$	−12.9570	−	7.48071i	−0.448126	−	0.258726i
$837$	24.0228	−	11.5879i	0.830348	−	0.400538i
$838$	−29.5355	+	17.0524i	−1.02029	+	0.589064i
$839$	−18.4848			−0.638165			−0.319082	−	0.947727i	$-0.603375\pi$
$839$	−18.4848			−0.638165			−0.319082	+	0.947727i	$0.603375\pi$
$840$	−9.96261	+	3.34965i	−0.343743	+	0.115574i
$841$	−13.1990	+	22.8614i	−0.455139	+	0.788325i
$842$	0.860340	+	1.49015i	0.0296493	+	0.0513540i
$843$	37.1401	−	42.1032i	1.27917	−	1.45011i
$844$	−8.45706	+	14.6480i	−0.291104	+	0.504207i
$845$		−	25.0400i		−	0.861401i
$846$	−15.7764	−	20.8090i	−0.542403	−	0.715429i
$847$	6.98498	+	12.0983i	0.240007	+	0.415704i
$848$	−6.29300	+	10.8998i	−0.216103	+	0.374301i
$849$	26.6649	−	30.2281i	0.915136	−	1.03743i
$850$	2.21158	−	3.83057i	0.0758566	−	0.131388i
$851$	−23.2374	−	36.0539i	−0.796566	−	1.23591i
$852$	1.06658	−	5.28195i	0.0365405	−	0.180957i
$853$			31.2396i			1.06962i	0.844971	+	0.534812i	$0.179618\pi$
$853$			31.2396i			1.06962i	−0.844971	+	0.534812i	$0.820382\pi$
$854$	5.62145	+	9.73663i	0.192362	+	0.333181i
$855$	29.7526	−	22.5569i	1.01752	−	0.771431i
$856$	−15.8117	+	9.12887i	−0.540432	+	0.312018i
$857$	5.55472	−	3.20702i	0.189746	−	0.109550i	−0.402118	−	0.915588i	$-0.631726\pi$
$857$	5.55472	−	3.20702i	0.189746	−	0.109550i	0.591864	+	0.806038i	$0.298392\pi$
$858$	0.826123	−	4.09114i	0.0282034	−	0.139669i
$859$	9.71896	+	5.61125i	0.331607	+	0.191453i	0.656554	−	0.754279i	$-0.272013\pi$
$859$	9.71896	+	5.61125i	0.331607	+	0.191453i	−0.324947	+	0.945732i	$0.605347\pi$
$860$	0.343626	+	0.595178i	0.0117176	+	0.0202954i
$861$	37.6726	−	12.6664i	1.28388	−	0.431669i
$862$	4.14791	+	7.18439i	0.141278	+	0.244701i
$863$	−10.1464	+	17.5740i	−0.345386	+	0.598226i	−0.985424	−	0.170117i	$-0.945585\pi$
$863$	−10.1464	+	17.5740i	−0.345386	+	0.598226i	0.640038	+	0.768344i	$0.278919\pi$
$864$	4.29516	+	2.92431i	0.146124	+	0.0994872i
$865$			5.76140i			0.195893i
$866$			17.3517i			0.589633i
$867$	−8.09921	+	40.1091i	−0.275064	+	1.36218i
$868$	−12.9995	+	7.50529i	−0.441233	+	0.254746i
$869$			4.75509i			0.161305i
$870$	−5.68286	−	1.14754i	−0.192667	−	0.0389051i
$871$		−	9.50465i		−	0.322053i
$872$	7.17656	−	12.4302i	0.243029	−	0.420938i
$873$	8.87595	+	11.7074i	0.300406	+	0.396234i
$874$		−	42.2929i		−	1.43058i
$875$	29.9237	+	17.2764i	1.01160	+	0.584050i
$876$	16.0736	+	14.1789i	0.543078	+	0.479061i
$877$	8.83272	−	15.2987i	0.298260	−	0.516601i	−0.677478	−	0.735543i	$-0.736927\pi$
$877$	8.83272	−	15.2987i	0.298260	−	0.516601i	0.975738	+	0.218942i	$0.0702605\pi$
$878$	−16.0758	+	27.8441i	−0.542532	+	0.939694i
$879$	−21.4214	−	18.8963i	−0.722527	−	0.637356i
$880$	4.48297	−	2.58824i	0.151121	−	0.0872496i
$881$	20.2235	+	35.0281i	0.681347	+	1.18013i	0.974570	+	0.224083i	$0.0719387\pi$
$881$	20.2235	+	35.0281i	0.681347	+	1.18013i	−0.293223	+	0.956044i	$0.594728\pi$
$882$	−2.81267	−	3.70991i	−0.0947075	−	0.124919i
$883$	−11.9594	+	6.90475i	−0.402465	+	0.232363i	−0.687547	−	0.726140i	$-0.741312\pi$
$883$	−11.9594	+	6.90475i	−0.402465	+	0.232363i	0.285082	+	0.958503i	$0.407979\pi$
$884$	−3.07844	+	5.33201i	−0.103539	+	0.179335i
$885$	4.32879	−	21.4371i	0.145511	−	0.720601i
$886$	16.4067	−	9.47241i	0.551194	−	0.318232i
$887$	8.37557	−	14.5069i	0.281224	−	0.487094i	−0.690462	−	0.723368i	$-0.742593\pi$
$887$	8.37557	−	14.5069i	0.281224	−	0.487094i	0.971687	+	0.236274i	$0.0759262\pi$
$888$	9.81020	−	3.84187i	0.329209	−	0.128925i
$889$	19.8416	+	34.3667i	0.665466	+	1.15262i
$890$	24.7615	+	14.2961i	0.830008	+	0.479205i
$891$	−15.6901	−	16.0585i	−0.525638	−	0.537979i
$892$	10.7054	+	18.5423i	0.358443	+	0.620842i
$893$	−45.2115	−	26.1029i	−1.51295	−	0.873499i
$894$	1.95591	+	5.81731i	0.0654155	+	0.194560i
$895$	−12.5624			−0.419916
$896$	−2.53257	−	1.46218i	−0.0846071	−	0.0488480i
$897$	11.1831	−	3.76001i	0.373393	−	0.125543i
$898$	6.81218	+	11.7990i	0.227326	+	0.393739i
$899$	−8.27968			−0.276143
$900$	−0.259764	−	2.06564i	−0.00865881	−	0.0688545i
$901$	−69.4724	+	40.1099i	−2.31446	+	1.33625i
$902$	−16.9519	+	9.78718i	−0.564436	+	0.325877i
$903$	−1.10972	+	1.25802i	−0.0369292	+	0.0418641i
$904$	2.36928	+	4.10371i	0.0788010	+	0.136487i
$905$	14.1343	−	8.16043i	0.469839	−	0.271262i
$906$	5.64579	+	16.7918i	0.187569	+	0.557871i
$907$	−5.95086	−	3.43573i	−0.197595	−	0.114082i	0.397938	−	0.917412i	$-0.369726\pi$
$907$	−5.95086	−	3.43573i	−0.197595	−	0.114082i	−0.595533	+	0.803331i	$0.703059\pi$
$908$	−21.7648	−	12.5659i	−0.722289	−	0.417014i
$909$	−1.33984	+	1.01580i	−0.0444398	+	0.0336920i
$910$	−5.07652	−	2.93093i	−0.168285	−	0.0971594i
$911$	−23.7057	+	13.6865i	−0.785406	+	0.453455i	−0.838343	−	0.545143i	$-0.816475\pi$
$911$	−23.7057	+	13.6865i	−0.785406	+	0.453455i	0.0529365	+	0.998598i	$0.483142\pi$
$912$	10.1826	+	2.05617i	0.337179	+	0.0680865i
$913$	13.5242	+	23.4246i	0.447586	+	0.775242i
$914$	4.97540	−	8.61765i	0.164572	−	0.285047i
$915$	13.0976	−	4.40370i	0.432992	−	0.145582i
$916$	6.45385			0.213241
$917$		−	38.2986i		−	1.26473i
$918$	14.3891	+	29.8297i	0.474910	+	0.984528i
$919$			23.1609i			0.764009i	0.924161	+	0.382004i	$0.124766\pi$
$919$			23.1609i			0.764009i	−0.924161	+	0.382004i	$0.875234\pi$
$920$	12.6724	+	7.31644i	0.417798	+	0.241216i
$921$	25.8596	+	22.8113i	0.852102	+	0.751657i
$922$	−22.0486			−0.726133
$923$	2.60261	−	1.50262i	0.0856661	−	0.0494593i
$924$	9.47555	+	8.35858i	0.311723	+	0.274977i
$925$	−3.75453	−	1.92936i	−0.123448	−	0.0634370i
$926$	−13.4512			−0.442033
$927$	11.9733	−	28.4383i	0.393255	−	0.934038i
$928$	−0.806522	−	1.39694i	−0.0264754	−	0.0458567i
$929$	11.7720	−	20.3898i	0.386228	−	0.668966i	−0.605711	−	0.795685i	$-0.707111\pi$
$929$	11.7720	−	20.3898i	0.386228	−	0.668966i	0.991939	+	0.126719i	$0.0404445\pi$
$930$	5.87945	+	17.4868i	0.192795	+	0.573414i
$931$	−8.06047	−	4.65372i	−0.264171	−	0.152519i
$932$	20.1699			0.660686
$933$	−14.2220	−	2.87185i	−0.465608	−	0.0940200i
$934$	11.8425			0.387498
$935$	32.9935			1.07900
$936$	0.361582	+	2.87528i	0.0118187	+	0.0939816i
$937$	12.5828	−	21.7940i	0.411061	−	0.711978i	−0.583945	−	0.811793i	$-0.698492\pi$
$937$	12.5828	−	21.7940i	0.411061	−	0.711978i	0.995006	+	0.0998150i	$0.0318251\pi$
$938$	24.9190	+	14.3870i	0.813635	+	0.469752i
$939$	3.10362	−	3.51836i	0.101283	−	0.114817i
$940$	15.6427	−	9.03131i	0.510208	−	0.294569i
$941$	−8.26816	−	14.3209i	−0.269534	−	0.466847i	0.699207	−	0.714919i	$-0.253536\pi$
$941$	−8.26816	−	14.3209i	−0.269534	−	0.466847i	−0.968742	+	0.248072i	$0.920203\pi$
$942$	−6.72892	−	1.35877i	−0.219240	−	0.0442710i
$943$	−47.9196	−	27.6664i	−1.56048	−	0.900942i
$944$	5.26958	−	3.04240i	0.171510	−	0.0990215i
$945$	−28.4004	+	13.6996i	−0.923866	+	0.445649i
$946$	0.413089	−	0.715492i	0.0134307	−	0.0232626i
$947$		−	18.2880i		−	0.594281i	−0.954834	−	0.297141i	$-0.903967\pi$
$947$		−	18.2880i		−	0.594281i	0.954834	−	0.297141i	$-0.0960330\pi$
$948$	−1.05219	−	3.12944i	−0.0341735	−	0.101639i
$949$			11.9537i			0.388034i
$950$	−2.08107	−	3.60451i	−0.0675187	−	0.116946i
$951$	−9.61099	−	8.47806i	−0.311658	−	0.274920i
$952$	−9.31953	−	16.1419i	−0.302048	−	0.523162i
$953$	−19.9492	+	34.5531i	−0.646219	+	1.11928i	0.337799	+	0.941218i	$0.390317\pi$
$953$	−19.9492	+	34.5531i	−0.646219	+	1.11928i	−0.984018	+	0.178066i	$0.943016\pi$
$954$	−14.6515	+	34.7995i	−0.474360	+	1.12667i
$955$	−9.02797	−	15.6369i	−0.292138	−	0.505998i
$956$	−4.12334	+	2.38061i	−0.133358	+	0.0769944i
$957$	2.22113	+	6.60612i	0.0717989	+	0.213546i
$958$	−9.31385			−0.300917
$959$	−26.3988			−0.852462
$960$	−2.37763	+	2.69536i	−0.0767378	+	0.0869923i
$961$	−2.32641	−	4.02945i	−0.0750453	−	0.129982i
$962$	5.22615	+	2.68559i	0.168498	+	0.0865870i
$963$	−43.6472	+	33.0912i	−1.40651	+	1.06635i
$964$	5.64101	+	3.25684i	0.181685	+	0.104896i
$965$	−10.0030	+	17.3257i	−0.322007	+	0.557733i
$966$	−7.06974	+	35.0109i	−0.227465	+	1.12646i
$967$			10.2031i			0.328111i	0.986451	+	0.164055i	$0.0524576\pi$
$967$			10.2031i			0.328111i	−0.986451	+	0.164055i	$0.947542\pi$
$968$	4.13709	+	2.38855i	0.132971	+	0.0767710i
$969$	49.6533	+	43.8002i	1.59509	+	1.40706i
$970$	−8.80074	+	5.08111i	−0.282575	+	0.163145i
$971$	−18.9059	+	32.7460i	−0.606720	+	1.05087i	0.385057	+	0.922893i	$0.374182\pi$
$971$	−18.9059	+	32.7460i	−0.606720	+	1.05087i	−0.991777	+	0.127977i	$0.959152\pi$
$972$	13.8794	+	7.09663i	0.445182	+	0.227624i
$973$	67.1260			2.15196
$974$	−28.3740			−0.909161
$975$	0.768090	−	0.870731i	0.0245986	−	0.0278857i
$976$	3.32949	+	1.92228i	0.106575	+	0.0615308i
$977$	−10.4748	+	6.04761i	−0.335118	+	0.193480i	−0.658111	−	0.752921i	$-0.728644\pi$
$977$	−10.4748	+	6.04761i	−0.335118	+	0.193480i	0.322993	+	0.946401i	$0.395311\pi$
$978$	−24.4746	+	8.22893i	−0.782613	+	0.263132i
$979$		−	34.3719i		−	1.09853i
$980$	2.78884	−	1.61013i	0.0890861	−	0.0514339i
$981$	16.7086	−	39.6854i	0.533464	−	1.26706i
$982$	27.7847	+	16.0415i	0.886644	+	0.511904i
$983$	28.1841			0.898933			0.449467	−	0.893297i	$-0.351614\pi$
$983$	28.1841			0.898933			0.449467	+	0.893297i	$0.351614\pi$
$984$	8.99078	−	10.1922i	0.286616	−	0.324916i
$985$	−20.0369	−	11.5683i	−0.638427	−	0.368596i
$986$		−	10.2811i		−	0.327417i
$987$	33.0636	+	29.1661i	1.05243	+	0.928367i
$988$	2.89676	+	5.01734i	0.0921583	+	0.159623i
$989$	2.33544			0.0742627
$990$	12.3750	−	9.38210i	0.393303	−	0.298183i
$991$		−	0.284061i		−	0.00902349i	−0.999990	−	0.00451174i	$-0.998564\pi$
$991$		−	0.284061i		−	0.00902349i	0.999990	−	0.00451174i	$-0.00143614\pi$
$992$	−2.56648	+	4.44527i	−0.0814857	+	0.141137i
$993$	0.501408	−	0.568412i	0.0159117	−	0.0180380i
$994$			9.09794i			0.288569i
$995$	14.0780			0.446302
$996$	−14.0839	−	12.4237i	−0.446266	−	0.393661i
$997$			43.4781i			1.37697i	0.725253	+	0.688483i	$0.241723\pi$
$997$			43.4781i			1.37697i	−0.725253	+	0.688483i	$0.758277\pi$
$998$	17.8888			0.566260
$999$	27.7625	−	15.1077i	0.878368	−	0.477985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.14	✓	76
3.2	odd	2		1998.2.k.a.1063.24		76
9.2	odd	6		1998.2.t.a.397.24		76
9.7	even	3		666.2.t.a.619.12	yes	76
37.11	even	6		666.2.t.a.85.12	yes	76
111.11	odd	6		1998.2.t.a.307.24		76
333.11	odd	6		1998.2.k.a.1639.15		76
333.196	even	6	inner	666.2.k.a.529.33	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.14	✓	76	1.1	even	1	trivial
666.2.k.a.529.33	yes	76	333.196	even	6	inner
666.2.t.a.85.12	yes	76	37.11	even	6
666.2.t.a.619.12	yes	76	9.7	even	3
1998.2.k.a.1063.24		76	3.2	odd	2
1998.2.k.a.1639.15		76	333.11	odd	6
1998.2.t.a.307.24		76	111.11	odd	6
1998.2.t.a.397.24		76	9.2	odd	6

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.29891 + 1.14579i) q^{3} -1.00000 q^{4} -2.07510i q^{5} +(1.14579 - 1.29891i) q^{6} +(-1.46218 + 2.53257i) q^{7} +1.00000i q^{8} +(0.374317 + 2.97656i) q^{9} -2.07510 q^{10} +(1.24729 + 2.16036i) q^{11} +(-1.29891 - 1.14579i) q^{12} -0.965976i q^{13} +(2.53257 + 1.46218i) q^{14} +(2.37763 - 2.69536i) q^{15} +1.00000 q^{16} +(5.51981 + 3.18686i) q^{17} +(2.97656 - 0.374317i) q^{18} +(5.19406 - 2.99879i) q^{19} +2.07510i q^{20} +(-4.80103 + 1.61422i) q^{21} +(2.16036 - 1.24729i) q^{22} +(6.10692 + 3.52583i) q^{23} +(-1.14579 + 1.29891i) q^{24} +0.693968 q^{25} -0.965976 q^{26} +(-2.92431 + 4.29516i) q^{27} +(1.46218 - 2.53257i) q^{28} +(1.39694 - 0.806522i) q^{29} +(-2.69536 - 2.37763i) q^{30} +(-4.44527 - 2.56648i) q^{31} -1.00000i q^{32} +(-0.855220 + 4.23524i) q^{33} +(3.18686 - 5.51981i) q^{34} +(5.25533 + 3.03416i) q^{35} +(-0.374317 - 2.97656i) q^{36} +(-5.41023 - 2.78018i) q^{37} +(-2.99879 - 5.19406i) q^{38} +(1.10681 - 1.25471i) q^{39} +2.07510 q^{40} -7.84678 q^{41} +(1.61422 + 4.80103i) q^{42} +(0.286819 - 0.165595i) q^{43} +(-1.24729 - 2.16036i) q^{44} +(6.17665 - 0.776745i) q^{45} +(3.52583 - 6.10692i) q^{46} +(-4.35223 - 7.53829i) q^{47} +(1.29891 + 1.14579i) q^{48} +(-0.775932 - 1.34395i) q^{49} -0.693968i q^{50} +(3.51823 + 10.4640i) q^{51} +0.965976i q^{52} +(-6.29300 + 10.8998i) q^{53} +(4.29516 + 2.92431i) q^{54} +(4.48297 - 2.58824i) q^{55} +(-2.53257 - 1.46218i) q^{56} +(10.1826 + 2.05617i) q^{57} +(-0.806522 - 1.39694i) q^{58} +(5.26958 - 3.04240i) q^{59} +(-2.37763 + 2.69536i) q^{60} +(3.32949 + 1.92228i) q^{61} +(-2.56648 + 4.44527i) q^{62} +(-8.08565 - 3.40427i) q^{63} -1.00000 q^{64} -2.00450 q^{65} +(4.23524 + 0.855220i) q^{66} +9.83943 q^{67} +(-5.51981 - 3.18686i) q^{68} +(3.89244 + 11.5770i) q^{69} +(3.03416 - 5.25533i) q^{70} +(1.55554 + 2.69428i) q^{71} +(-2.97656 + 0.374317i) q^{72} -12.3747 q^{73} +(-2.78018 + 5.41023i) q^{74} +(0.901400 + 0.795144i) q^{75} +(-5.19406 + 2.99879i) q^{76} -7.29502 q^{77} +(-1.25471 - 1.10681i) q^{78} +(1.65079 + 0.953087i) q^{79} -2.07510i q^{80} +(-8.71977 + 2.22835i) q^{81} +7.84678i q^{82} +10.8429 q^{83} +(4.80103 - 1.61422i) q^{84} +(6.61306 - 11.4541i) q^{85} +(-0.165595 - 0.286819i) q^{86} +(2.73860 + 0.553004i) q^{87} +(-2.16036 + 1.24729i) q^{88} +(-11.9327 - 6.88934i) q^{89} +(-0.776745 - 6.17665i) q^{90} +(2.44640 + 1.41243i) q^{91} +(-6.10692 - 3.52583i) q^{92} +(-2.83334 - 8.42697i) q^{93} +(-7.53829 + 4.35223i) q^{94} +(-6.22279 - 10.7782i) q^{95} +(1.14579 - 1.29891i) q^{96} +(4.24112 - 2.44861i) q^{97} +(-1.34395 + 0.775932i) q^{98} +(-5.96356 + 4.52128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Introduction

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