LMFDB - Embedded newform 666.2.k.a.175.5

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			175.5
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.24

$q$-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} +(-1.36870 + 1.06145i) q^{3} -1.00000 q^{4} +2.68401i q^{5} +(1.06145 + 1.36870i) q^{6} +(-1.22466 + 2.12118i) q^{7} +1.00000i q^{8} +(0.746656 - 2.90560i) q^{9} +2.68401 q^{10} +(1.18799 + 2.05767i) q^{11} +(1.36870 - 1.06145i) q^{12} -1.70111i q^{13} +(2.12118 + 1.22466i) q^{14} +(-2.84894 - 3.67360i) q^{15} +1.00000 q^{16} +(-3.71658 - 2.14577i) q^{17} +(-2.90560 - 0.746656i) q^{18} +(-2.63557 + 1.52164i) q^{19} -2.68401i q^{20} +(-0.575330 - 4.20317i) q^{21} +(2.05767 - 1.18799i) q^{22} +(-1.50343 - 0.868005i) q^{23} +(-1.06145 - 1.36870i) q^{24} -2.20394 q^{25} -1.70111 q^{26} +(2.06220 + 4.76942i) q^{27} +(1.22466 - 2.12118i) q^{28} +(1.92274 - 1.11009i) q^{29} +(-3.67360 + 2.84894i) q^{30} +(-7.93259 - 4.57988i) q^{31} -1.00000i q^{32} +(-3.81011 - 1.55533i) q^{33} +(-2.14577 + 3.71658i) q^{34} +(-5.69328 - 3.28702i) q^{35} +(-0.746656 + 2.90560i) q^{36} +(-5.64698 - 2.26088i) q^{37} +(1.52164 + 2.63557i) q^{38} +(1.80564 + 2.32831i) q^{39} -2.68401 q^{40} -4.96158 q^{41} +(-4.20317 + 0.575330i) q^{42} +(-4.16828 + 2.40656i) q^{43} +(-1.18799 - 2.05767i) q^{44} +(7.79867 + 2.00404i) q^{45} +(-0.868005 + 1.50343i) q^{46} +(3.30470 + 5.72391i) q^{47} +(-1.36870 + 1.06145i) q^{48} +(0.500396 + 0.866710i) q^{49} +2.20394i q^{50} +(7.36450 - 1.00805i) q^{51} +1.70111i q^{52} +(1.42518 - 2.46849i) q^{53} +(4.76942 - 2.06220i) q^{54} +(-5.52281 + 3.18860i) q^{55} +(-2.12118 - 1.22466i) q^{56} +(1.99214 - 4.88018i) q^{57} +(-1.11009 - 1.92274i) q^{58} +(10.2433 - 5.91398i) q^{59} +(2.84894 + 3.67360i) q^{60} +(-2.61487 - 1.50970i) q^{61} +(-4.57988 + 7.93259i) q^{62} +(5.24890 + 5.14218i) q^{63} -1.00000 q^{64} +4.56582 q^{65} +(-1.55533 + 3.81011i) q^{66} -7.61951 q^{67} +(3.71658 + 2.14577i) q^{68} +(2.97908 - 0.407777i) q^{69} +(-3.28702 + 5.69328i) q^{70} +(5.35309 + 9.27182i) q^{71} +(2.90560 + 0.746656i) q^{72} -8.21612 q^{73} +(-2.26088 + 5.64698i) q^{74} +(3.01652 - 2.33936i) q^{75} +(2.63557 - 1.52164i) q^{76} -5.81958 q^{77} +(2.32831 - 1.80564i) q^{78} +(1.63069 + 0.941477i) q^{79} +2.68401i q^{80} +(-7.88501 - 4.33897i) q^{81} +4.96158i q^{82} +1.81133 q^{83} +(0.575330 + 4.20317i) q^{84} +(5.75928 - 9.97537i) q^{85} +(2.40656 + 4.16828i) q^{86} +(-1.45334 + 3.56027i) q^{87} +(-2.05767 + 1.18799i) q^{88} +(-10.9819 - 6.34038i) q^{89} +(2.00404 - 7.79867i) q^{90} +(3.60837 + 2.08329i) q^{91} +(1.50343 + 0.868005i) q^{92} +(15.7186 - 2.15157i) q^{93} +(5.72391 - 3.30470i) q^{94} +(-4.08412 - 7.07390i) q^{95} +(1.06145 + 1.36870i) q^{96} +(-9.83416 + 5.67776i) q^{97} +(0.866710 - 0.500396i) q^{98} +(6.86578 - 1.91547i) 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
$3$	−1.36870	+	1.06145i	−0.790217	+	0.612827i
$3$	−1.36870	+	1.06145i	−0.790217	+	0.612827i
$4$	−1.00000			−0.500000
$5$			2.68401i			1.20033i	0.799877	+	0.600164i	$0.204898\pi$
$5$			2.68401i			1.20033i	−0.799877	+	0.600164i	$0.795102\pi$
$6$	1.06145	+	1.36870i	0.433334	+	0.558768i
$7$	−1.22466	+	2.12118i	−0.462880	+	0.801731i	−0.999103	−	0.0423452i	$-0.986517\pi$
$7$	−1.22466	+	2.12118i	−0.462880	+	0.801731i	0.536224	+	0.844076i	$0.319850\pi$
$8$			1.00000i			0.353553i
$9$	0.746656	−	2.90560i	0.248885	−	0.968533i
$10$	2.68401			0.848760
$11$	1.18799	+	2.05767i	0.358194	+	0.620410i	0.987659	−	0.156619i	$-0.0500593\pi$
$11$	1.18799	+	2.05767i	0.358194	+	0.620410i	−0.629465	+	0.777029i	$0.716726\pi$
$12$	1.36870	−	1.06145i	0.395108	−	0.306414i
$13$		−	1.70111i		−	0.471804i	−0.971777	−	0.235902i	$-0.924196\pi$
$13$		−	1.70111i		−	0.471804i	0.971777	−	0.235902i	$-0.0758045\pi$
$14$	2.12118	+	1.22466i	0.566909	+	0.327305i
$15$	−2.84894	−	3.67360i	−0.735594	−	0.948519i
$16$	1.00000			0.250000
$17$	−3.71658	−	2.14577i	−0.901404	−	0.520426i	−0.0237485	−	0.999718i	$-0.507560\pi$
$17$	−3.71658	−	2.14577i	−0.901404	−	0.520426i	−0.877655	+	0.479292i	$0.840893\pi$
$18$	−2.90560	−	0.746656i	−0.684856	−	0.175989i
$19$	−2.63557	+	1.52164i	−0.604640	+	0.349089i	−0.770865	−	0.636999i	$-0.780176\pi$
$19$	−2.63557	+	1.52164i	−0.604640	+	0.349089i	0.166225	+	0.986088i	$0.446842\pi$
$20$		−	2.68401i		−	0.600164i
$21$	−0.575330	−	4.20317i	−0.125547	−	0.917206i
$22$	2.05767	−	1.18799i	0.438696	−	0.253281i
$23$	−1.50343	−	0.868005i	−0.313487	−	0.180992i	0.334999	−	0.942218i	$-0.391264\pi$
$23$	−1.50343	−	0.868005i	−0.313487	−	0.180992i	−0.648486	+	0.761227i	$0.724597\pi$
$24$	−1.06145	−	1.36870i	−0.216667	−	0.279384i
$25$	−2.20394			−0.440787
$26$	−1.70111			−0.333616
$27$	2.06220	+	4.76942i	0.396870	+	0.917875i
$28$	1.22466	−	2.12118i	0.231440	−	0.400865i
$29$	1.92274	−	1.11009i	0.357044	−	0.206139i	−0.310739	−	0.950495i	$-0.600577\pi$
$29$	1.92274	−	1.11009i	0.357044	−	0.206139i	0.667783	+	0.744356i	$0.267243\pi$
$30$	−3.67360	+	2.84894i	−0.670704	+	0.520143i
$31$	−7.93259	−	4.57988i	−1.42474	−	0.822571i	−0.428037	−	0.903761i	$-0.640795\pi$
$31$	−7.93259	−	4.57988i	−1.42474	−	0.822571i	−0.996699	+	0.0811900i	$0.974128\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−3.81011	−	1.55533i	−0.663255	−	0.270747i
$34$	−2.14577	+	3.71658i	−0.367997	+	0.637389i
$35$	−5.69328	−	3.28702i	−0.962340	−	0.555607i
$36$	−0.746656	+	2.90560i	−0.124443	+	0.484266i
$37$	−5.64698	−	2.26088i	−0.928358	−	0.371686i
$37$	−5.64698	−	2.26088i	−0.928358	−	0.371686i
$38$	1.52164	+	2.63557i	0.246843	+	0.427545i
$39$	1.80564	+	2.32831i	0.289134	+	0.372828i
$40$	−2.68401			−0.424380
$41$	−4.96158			−0.774869			−0.387434	−	0.921897i	$-0.626639\pi$
$41$	−4.96158			−0.774869			−0.387434	+	0.921897i	$0.626639\pi$
$42$	−4.20317	+	0.575330i	−0.648563	+	0.0887754i
$43$	−4.16828	+	2.40656i	−0.635657	+	0.366997i	−0.782940	−	0.622098i	$-0.786281\pi$
$43$	−4.16828	+	2.40656i	−0.635657	+	0.366997i	0.147282	+	0.989094i	$0.452947\pi$
$44$	−1.18799	−	2.05767i	−0.179097	−	0.310205i
$45$	7.79867	+	2.00404i	1.16256	+	0.298744i
$46$	−0.868005	+	1.50343i	−0.127980	+	0.221669i
$47$	3.30470	+	5.72391i	0.482040	+	0.834918i	0.999787	−	0.0206158i	$-0.00656267\pi$
$47$	3.30470	+	5.72391i	0.482040	+	0.834918i	−0.517748	+	0.855533i	$0.673229\pi$
$48$	−1.36870	+	1.06145i	−0.197554	+	0.153207i
$49$	0.500396	+	0.866710i	0.0714851	+	0.123816i
$50$			2.20394i			0.311684i
$51$	7.36450	−	1.00805i	1.03124	−	0.141156i
$52$			1.70111i			0.235902i
$53$	1.42518	−	2.46849i	0.195764	−	0.339073i	−0.751387	−	0.659862i	$-0.770615\pi$
$53$	1.42518	−	2.46849i	0.195764	−	0.339073i	0.947151	+	0.320789i	$0.103948\pi$
$54$	4.76942	−	2.06220i	0.649036	−	0.280629i
$55$	−5.52281	+	3.18860i	−0.744696	+	0.429950i
$56$	−2.12118	−	1.22466i	−0.283455	−	0.163653i
$57$	1.99214	−	4.88018i	0.263865	−	0.646396i
$58$	−1.11009	−	1.92274i	−0.145763	−	0.252468i
$59$	10.2433	−	5.91398i	1.33357	−	0.769935i	0.347722	−	0.937598i	$-0.386955\pi$
$59$	10.2433	−	5.91398i	1.33357	−	0.769935i	0.985844	+	0.167663i	$0.0536221\pi$
$60$	2.84894	+	3.67360i	0.367797	+	0.474260i
$61$	−2.61487	−	1.50970i	−0.334800	−	0.193297i	0.323170	−	0.946341i	$-0.395251\pi$
$61$	−2.61487	−	1.50970i	−0.334800	−	0.193297i	−0.657970	+	0.753044i	$0.728585\pi$
$62$	−4.57988	+	7.93259i	−0.581646	+	1.00744i
$63$	5.24890	+	5.14218i	0.661299	+	0.647853i
$64$	−1.00000			−0.125000
$65$	4.56582			0.566320
$66$	−1.55533	+	3.81011i	−0.191447	+	0.468992i
$67$	−7.61951			−0.930871			−0.465436	−	0.885082i	$-0.654102\pi$
$67$	−7.61951			−0.930871			−0.465436	+	0.885082i	$0.654102\pi$
$68$	3.71658	+	2.14577i	0.450702	+	0.260213i
$69$	2.97908	−	0.407777i	0.358639	−	0.0490906i
$70$	−3.28702	+	5.69328i	−0.392874	+	0.680477i
$71$	5.35309	+	9.27182i	0.635294	+	1.10036i	0.986453	+	0.164046i	$0.0524546\pi$
$71$	5.35309	+	9.27182i	0.635294	+	1.10036i	−0.351158	+	0.936316i	$0.614212\pi$
$72$	2.90560	+	0.746656i	0.342428	+	0.0879943i
$73$	−8.21612			−0.961624			−0.480812	−	0.876824i	$-0.659658\pi$
$73$	−8.21612			−0.961624			−0.480812	+	0.876824i	$0.659658\pi$
$74$	−2.26088	+	5.64698i	−0.262822	+	0.656448i
$75$	3.01652	−	2.33936i	0.348317	−	0.270126i
$76$	2.63557	−	1.52164i	0.302320	−	0.174545i
$77$	−5.81958			−0.663203
$78$	2.32831	−	1.80564i	0.263629	−	0.204449i
$79$	1.63069	+	0.941477i	0.183467	+	0.105924i	0.588920	−	0.808191i	$-0.299553\pi$
$79$	1.63069	+	0.941477i	0.183467	+	0.105924i	−0.405454	+	0.914116i	$0.632886\pi$
$80$			2.68401i			0.300082i
$81$	−7.88501	−	4.33897i	−0.876112	−	0.482107i
$82$			4.96158i			0.547915i
$83$	1.81133			0.198820			0.0994098	−	0.995047i	$-0.468305\pi$
$83$	1.81133			0.198820			0.0994098	+	0.995047i	$0.468305\pi$
$84$	0.575330	+	4.20317i	0.0627737	+	0.458603i
$85$	5.75928	−	9.97537i	0.624682	−	1.08198i
$86$	2.40656	+	4.16828i	0.259506	+	0.449478i
$87$	−1.45334	+	3.56027i	−0.155814	+	0.381701i
$88$	−2.05767	+	1.18799i	−0.219348	+	0.126641i
$89$	−10.9819	−	6.34038i	−1.16408	−	0.672079i	−0.211798	−	0.977313i	$-0.567932\pi$
$89$	−10.9819	−	6.34038i	−1.16408	−	0.672079i	−0.952277	+	0.305234i	$0.901265\pi$
$90$	2.00404	−	7.79867i	0.211244	−	0.822052i
$91$	3.60837	+	2.08329i	0.378260	+	0.218388i
$92$	1.50343	+	0.868005i	0.156743	+	0.0904958i
$93$	15.7186	−	2.15157i	1.62994	−	0.223107i
$94$	5.72391	−	3.30470i	0.590376	−	0.340854i
$95$	−4.08412	−	7.07390i	−0.419021	−	0.725767i
$96$	1.06145	+	1.36870i	0.108334	+	0.139692i
$97$	−9.83416	+	5.67776i	−0.998508	+	0.576489i	−0.907806	−	0.419389i	$-0.862244\pi$
$97$	−9.83416	+	5.67776i	−0.998508	+	0.576489i	−0.0907015	+	0.995878i	$0.528911\pi$
$98$	0.866710	−	0.500396i	0.0875510	−	0.0505476i
$99$	6.86578	−	1.91547i	0.690037	−	0.192512i
$100$	2.20394			0.220394
$101$	0.824564	+	1.42819i	0.0820472	+	0.142110i	0.904129	−	0.427259i	$-0.140521\pi$
$101$	0.824564	+	1.42819i	0.0820472	+	0.142110i	−0.822082	+	0.569369i	$0.807188\pi$
$102$	−1.00805	−	7.36450i	−0.0998122	−	0.729194i
$103$	−9.91602	−	5.72502i	−0.977054	−	0.564103i	−0.0756748	−	0.997133i	$-0.524111\pi$
$103$	−9.91602	−	5.72502i	−0.977054	−	0.564103i	−0.901380	+	0.433030i	$0.857444\pi$
$104$	1.70111			0.166808
$105$	11.2814	−	1.54420i	1.10095	−	0.150698i
$106$	−2.46849	−	1.42518i	−0.239761	−	0.138426i
$107$	7.88827	+	13.6629i	0.762588	+	1.32084i	0.941513	+	0.336978i	$0.109405\pi$
$107$	7.88827	+	13.6629i	0.762588	+	1.32084i	−0.178925	+	0.983863i	$0.557262\pi$
$108$	−2.06220	−	4.76942i	−0.198435	−	0.458937i
$109$	5.75984	+	3.32544i	0.551692	+	0.318520i	0.749804	−	0.661660i	$-0.230148\pi$
$109$	5.75984	+	3.32544i	0.551692	+	0.318520i	−0.198112	+	0.980179i	$0.563481\pi$
$110$	3.18860	+	5.52281i	0.304021	+	0.526579i
$111$	10.1288	−	2.89952i	0.961384	−	0.275211i
$112$	−1.22466	+	2.12118i	−0.115720	+	0.200433i
$113$	12.1305	−	7.00356i	1.14114	−	0.658840i	0.194430	−	0.980916i	$-0.437714\pi$
$113$	12.1305	−	7.00356i	1.14114	−	0.658840i	0.946714	+	0.322077i	$0.104381\pi$
$114$	−4.88018	−	1.99214i	−0.457071	−	0.186581i
$115$	2.32974	−	4.03523i	0.217249	−	0.376287i
$116$	−1.92274	+	1.11009i	−0.178522	+	0.103070i
$117$	−4.94276	−	1.27015i	−0.456958	−	0.117425i
$118$	−5.91398	−	10.2433i	−0.544426	−	0.942973i
$119$	9.10313	−	5.25570i	0.834483	−	0.481789i
$120$	3.67360	−	2.84894i	0.335352	−	0.260072i
$121$	2.67734	−	4.63728i	0.243394	−	0.421571i
$122$	−1.50970	+	2.61487i	−0.136682	+	0.236740i
$123$	6.79090	−	5.26646i	0.612314	−	0.474861i
$124$	7.93259	+	4.57988i	0.712368	+	0.411286i
$125$			7.50468i			0.671239i
$126$	5.14218	−	5.24890i	0.458101	−	0.467609i
$127$	−7.67285	+	13.2898i	−0.680855	+	1.17928i	0.293865	+	0.955847i	$0.405058\pi$
$127$	−7.67285	+	13.2898i	−0.680855	+	1.17928i	−0.974720	+	0.223429i	$0.928275\pi$
$128$			1.00000i			0.0883883i
$129$	3.15067	−	7.71827i	0.277401	−	0.679555i
$130$		−	4.56582i		−	0.400449i
$131$	7.27820	−	4.20207i	0.635899	−	0.367137i	−0.147134	−	0.989117i	$-0.547005\pi$
$131$	7.27820	−	4.20207i	0.635899	−	0.367137i	0.783033	+	0.621980i	$0.213671\pi$
$132$	3.81011	+	1.55533i	0.331628	+	0.135374i
$133$		−	7.45401i		−	0.646345i
$134$			7.61951i			0.658225i
$135$	−12.8012	+	5.53497i	−1.10175	+	0.476374i
$136$	2.14577	−	3.71658i	0.183998	−	0.318694i
$137$	−0.708673	−	1.22746i	−0.0605461	−	0.104869i	0.834164	−	0.551517i	$-0.185951\pi$
$137$	−0.708673	−	1.22746i	−0.0605461	−	0.104869i	−0.894710	+	0.446648i	$0.852618\pi$
$138$	−0.407777	−	2.97908i	−0.0347123	−	0.253596i
$139$	5.08079	+	8.80019i	0.430947	+	0.746422i	0.996955	−	0.0779775i	$-0.0248462\pi$
$139$	5.08079	+	8.80019i	0.430947	+	0.746422i	−0.566008	+	0.824400i	$0.691513\pi$
$140$	5.69328	+	3.28702i	0.481170	+	0.277804i
$141$	−10.5988	−	4.32652i	−0.892576	−	0.364359i
$142$	9.27182	−	5.35309i	0.778074	−	0.449221i
$143$	3.50033	−	2.02091i	0.292712	−	0.168997i
$144$	0.746656	−	2.90560i	0.0622213	−	0.242133i
$145$	2.97951	+	5.16066i	0.247435	+	0.428570i
$146$			8.21612i			0.679971i
$147$	−1.60486	−	0.655119i	−0.132366	−	0.0540333i
$148$	5.64698	+	2.26088i	0.464179	+	0.185843i
$149$	3.36373	−	5.82616i	0.275568	−	0.477297i	−0.694711	−	0.719289i	$-0.744468\pi$
$149$	3.36373	−	5.82616i	0.275568	−	0.477297i	0.970278	+	0.241992i	$0.0778008\pi$
$150$	−2.33936	−	3.01652i	−0.191008	−	0.246298i
$151$	−3.20912	+	5.55836i	−0.261155	+	0.452333i	−0.966549	−	0.256482i	$-0.917437\pi$
$151$	−3.20912	+	5.55836i	−0.261155	+	0.452333i	0.705394	+	0.708815i	$0.250770\pi$
$152$	−1.52164	−	2.63557i	−0.123422	−	0.213773i
$153$	−9.00976	+	9.19675i	−0.728396	+	0.743513i
$154$			5.81958i			0.468955i
$155$	12.2925	−	21.2912i	0.987355	−	1.71015i
$156$	−1.80564	−	2.32831i	−0.144567	−	0.186414i
$157$	−6.99140	−	12.1095i	−0.557975	−	0.966441i	−0.997665	−	0.0682913i	$-0.978245\pi$
$157$	−6.99140	−	12.1095i	−0.557975	−	0.966441i	0.439691	−	0.898149i	$-0.355088\pi$
$158$	0.941477	−	1.63069i	0.0748999	−	0.129730i
$159$	0.669531	+	4.89137i	0.0530972	+	0.387910i
$160$	2.68401			0.212190
$161$	3.68239	−	2.12603i	0.290213	−	0.167555i
$162$	−4.33897	+	7.88501i	−0.340901	+	0.619505i
$163$	−16.8099	−	9.70519i	−1.31665	−	0.760169i	−0.333463	−	0.942763i	$-0.608217\pi$
$163$	−16.8099	−	9.70519i	−1.31665	−	0.760169i	−0.983188	+	0.182594i	$0.941551\pi$
$164$	4.96158			0.387434
$165$	4.17452	−	10.2264i	0.324986	−	0.796124i
$166$		−	1.81133i		−	0.140587i
$167$			21.4017i			1.65611i	0.560646	+	0.828056i	$0.310553\pi$
$167$			21.4017i			1.65611i	−0.560646	+	0.828056i	$0.689447\pi$
$168$	4.20317	−	0.575330i	0.324281	−	0.0443877i
$169$	10.1062			0.777401
$170$	−9.97537	−	5.75928i	−0.765076	−	0.441717i
$171$	2.45343	+	8.79404i	0.187618	+	0.672497i
$172$	4.16828	−	2.40656i	0.317829	−	0.183498i
$173$	−11.3031			−0.859356			−0.429678	−	0.902982i	$-0.641373\pi$
$173$	−11.3031			−0.859356			−0.429678	+	0.902982i	$0.641373\pi$
$174$	3.56027	+	1.45334i	0.269903	+	0.110177i
$175$	2.69908	−	4.67495i	0.204031	−	0.353393i
$176$	1.18799	+	2.05767i	0.0895485	+	0.155103i
$177$	−7.74260	+	18.9672i	−0.581969	+	1.42566i
$178$	−6.34038	+	10.9819i	−0.475232	+	0.823125i
$179$			9.61686i			0.718798i	0.933184	+	0.359399i	$0.117018\pi$
$179$			9.61686i			0.718798i	−0.933184	+	0.359399i	$0.882982\pi$
$180$	−7.79867	−	2.00404i	−0.581279	−	0.149372i
$181$	8.53789	+	14.7881i	0.634617	+	1.09919i	0.986596	+	0.163181i	$0.0521753\pi$
$181$	8.53789	+	14.7881i	0.634617	+	1.09919i	−0.351980	+	0.936008i	$0.614491\pi$
$182$	2.08329	−	3.60837i	0.154424	−	0.267470i
$183$	5.18144	−	0.709236i	0.383023	−	0.0524282i
$184$	0.868005	−	1.50343i	0.0639902	−	0.110834i
$185$	6.06824	−	15.1566i	0.446146	−	1.11433i
$186$	−2.15157	−	15.7186i	−0.157760	−	1.15254i
$187$		−	10.1967i		−	0.745653i
$188$	−3.30470	−	5.72391i	−0.241020	−	0.417459i
$189$	−12.6423	−	1.46664i	−0.919592	−	0.106683i
$190$	−7.07390	+	4.08412i	−0.513194	+	0.296293i
$191$	−11.4835	+	6.62998i	−0.830915	+	0.479729i	−0.854166	−	0.520001i	$-0.825932\pi$
$191$	−11.4835	+	6.62998i	−0.830915	+	0.479729i	0.0232511	+	0.999730i	$0.492598\pi$
$192$	1.36870	−	1.06145i	0.0987771	−	0.0766034i
$193$	16.8148	+	9.70804i	1.21036	+	0.698800i	0.962837	−	0.270082i	$-0.0870509\pi$
$193$	16.8148	+	9.70804i	1.21036	+	0.698800i	0.247520	+	0.968883i	$0.420384\pi$
$194$	5.67776	+	9.83416i	0.407639	+	0.706052i
$195$	−6.24921	+	4.84638i	−0.447515	+	0.347056i
$196$	−0.500396	−	0.866710i	−0.0357425	−	0.0619079i
$197$	−5.44571	+	9.43225i	−0.387991	+	0.672020i	−0.992179	−	0.124822i	$-0.960164\pi$
$197$	−5.44571	+	9.43225i	−0.387991	+	0.672020i	0.604188	+	0.796842i	$0.293497\pi$
$198$	−1.91547	−	6.86578i	−0.136126	−	0.487930i
$199$			1.68904i			0.119733i	0.998206	+	0.0598663i	$0.0190674\pi$
$199$			1.68904i			0.119733i	−0.998206	+	0.0598663i	$0.980933\pi$
$200$		−	2.20394i		−	0.155842i
$201$	10.4288	−	8.08771i	0.735590	−	0.570463i
$202$	1.42819	−	0.824564i	0.100487	−	0.0580161i
$203$			5.43797i			0.381671i
$204$	−7.36450	+	1.00805i	−0.515618	+	0.0705779i
$205$		−	13.3170i		−	0.930097i
$206$	−5.72502	+	9.91602i	−0.398881	+	0.690882i
$207$	−3.64462	+	3.72026i	−0.253319	+	0.258576i
$208$		−	1.70111i		−	0.117951i
$209$	−6.26208	−	3.61541i	−0.433157	−	0.250083i
$210$	−1.54420	−	11.2814i	−0.106560	−	0.778488i
$211$	7.46471	−	12.9293i	0.513892	−	0.890087i	−0.485978	−	0.873971i	$-0.661537\pi$
$211$	7.46471	−	12.9293i	0.513892	−	0.890087i	0.999870	−	0.0161161i	$-0.00513013\pi$
$212$	−1.42518	+	2.46849i	−0.0978819	+	0.169536i
$213$	−17.1683	−	7.00827i	−1.17635	−	0.480199i
$214$	13.6629	−	7.88827i	0.933975	−	0.539231i
$215$	−6.45924	−	11.1877i	−0.440517	−	0.762997i
$216$	−4.76942	+	2.06220i	−0.324518	+	0.140315i
$217$	19.4295	−	11.2176i	1.31896	−	0.761503i
$218$	3.32544	−	5.75984i	0.225227	−	0.390105i
$219$	11.2454	−	8.72099i	0.759892	−	0.589310i
$220$	5.52281	−	3.18860i	0.372348	−	0.214975i
$221$	−3.65020	+	6.32233i	−0.245539	+	0.425286i
$222$	−2.89952	−	10.1288i	−0.194603	−	0.679801i
$223$	8.24868	+	14.2871i	0.552372	+	0.956737i	0.998103	+	0.0615697i	$0.0196106\pi$
$223$	8.24868	+	14.2871i	0.552372	+	0.956737i	−0.445730	+	0.895167i	$0.647056\pi$
$224$	2.12118	+	1.22466i	0.141727	+	0.0818263i
$225$	−1.64558	+	6.40375i	−0.109705	+	0.426917i
$226$	−7.00356	−	12.1305i	−0.465870	−	0.806910i
$227$	−15.7235	−	9.07796i	−1.04360	−	0.602526i	−0.122753	−	0.992437i	$-0.539172\pi$
$227$	−15.7235	−	9.07796i	−1.04360	−	0.602526i	−0.920852	+	0.389912i	$0.872505\pi$
$228$	−1.99214	+	4.88018i	−0.131933	+	0.323198i
$229$	−9.39009			−0.620515			−0.310257	−	0.950653i	$-0.600415\pi$
$229$	−9.39009			−0.620515			−0.310257	+	0.950653i	$0.600415\pi$
$230$	−4.03523	−	2.32974i	−0.266075	−	0.153618i
$231$	7.96523	−	6.17718i	0.524074	−	0.406429i
$232$	1.11009	+	1.92274i	0.0728813	+	0.126234i
$233$	14.3014			0.936913			0.468457	−	0.883486i	$-0.344810\pi$
$233$	14.3014			0.936913			0.468457	+	0.883486i	$0.344810\pi$
$234$	−1.27015	+	4.94276i	−0.0830321	+	0.323118i
$235$	−15.3631	+	8.86986i	−1.00218	+	0.578606i
$236$	−10.2433	+	5.91398i	−0.666783	+	0.384967i
$237$	−3.23124	+	0.442293i	−0.209892	+	0.0287300i
$238$	−5.25570	−	9.10313i	−0.340676	−	0.590068i
$239$	−13.2361	+	7.64189i	−0.856174	+	0.494313i	−0.862729	−	0.505666i	$-0.831247\pi$
$239$	−13.2361	+	7.64189i	−0.856174	+	0.494313i	0.00655487	+	0.999979i	$0.497914\pi$
$240$	−2.84894	−	3.67360i	−0.183898	−	0.237130i
$241$	−3.27950	−	1.89342i	−0.211251	−	0.121966i	0.390642	−	0.920543i	$-0.372253\pi$
$241$	−3.27950	−	1.89342i	−0.211251	−	0.121966i	−0.601893	+	0.798577i	$0.705586\pi$
$242$	−4.63728	−	2.67734i	−0.298096	−	0.172106i
$243$	15.3978	−	2.43080i	0.987767	−	0.155936i
$244$	2.61487	+	1.50970i	0.167400	+	0.0966486i
$245$	−2.32626	+	1.34307i	−0.148620	+	0.0858055i
$246$	−5.26646	−	6.79090i	−0.335777	−	0.432972i
$247$	2.58849	+	4.48340i	0.164702	+	0.285272i
$248$	4.57988	−	7.93259i	0.290823	−	0.503720i
$249$	−2.47916	+	1.92264i	−0.157111	+	0.121842i
$250$	7.50468			0.474638
$251$			21.7343i			1.37185i	0.727670	+	0.685927i	$0.240603\pi$
$251$			21.7343i			1.37185i	−0.727670	+	0.685927i	$0.759397\pi$
$252$	−5.24890	−	5.14218i	−0.330649	−	0.323927i
$253$		−	4.12474i		−	0.259320i
$254$	13.2898	+	7.67285i	0.833874	+	0.481437i
$255$	2.70563	+	19.7664i	0.169433	+	1.23782i
$256$	1.00000			0.0625000
$257$	−13.1425	+	7.58782i	−0.819806	+	0.473315i	−0.850349	−	0.526218i	$-0.823609\pi$
$257$	−13.1425	+	7.58782i	−0.819806	+	0.473315i	0.0305437	+	0.999533i	$0.490276\pi$
$258$	−7.71827	−	3.15067i	−0.480518	−	0.196152i
$259$	11.7114	−	9.20945i	0.727711	−	0.572248i
$260$	−4.56582			−0.283160
$261$	−1.78986	−	6.41557i	−0.110790	−	0.397114i
$262$	−4.20207	−	7.27820i	−0.259605	−	0.449649i
$263$	−3.73623	+	6.47134i	−0.230386	+	0.399040i	−0.957922	−	0.287030i	$-0.907332\pi$
$263$	−3.73623	+	6.47134i	−0.230386	+	0.399040i	0.727536	+	0.686070i	$0.240665\pi$
$264$	1.55533	−	3.81011i	0.0957237	−	0.234496i
$265$	6.62546	+	3.82521i	0.406999	+	0.234981i
$266$	−7.45401			−0.457035
$267$	21.7608	−	2.97862i	1.33174	−	0.182289i
$268$	7.61951			0.465436
$269$	25.7826			1.57199			0.785997	−	0.618230i	$-0.212150\pi$
$269$	25.7826			1.57199			0.785997	+	0.618230i	$0.212150\pi$
$270$	5.53497	+	12.8012i	0.336847	+	0.779055i
$271$	−2.27532	+	3.94097i	−0.138216	+	0.239397i	−0.926821	−	0.375503i	$-0.877470\pi$
$271$	−2.27532	+	3.94097i	−0.138216	+	0.239397i	0.788606	+	0.614899i	$0.210803\pi$
$272$	−3.71658	−	2.14577i	−0.225351	−	0.130106i
$273$	−7.15007	+	0.978702i	−0.432742	+	0.0592338i
$274$	−1.22746	+	0.708673i	−0.0741535	+	0.0428125i
$275$	−2.61826	−	4.53497i	−0.157887	−	0.273469i
$276$	−2.97908	+	0.407777i	−0.179320	+	0.0245453i
$277$	15.3707	+	8.87428i	0.923537	+	0.533204i	0.884762	−	0.466044i	$-0.154321\pi$
$277$	15.3707	+	8.87428i	0.923537	+	0.533204i	0.0387749	+	0.999248i	$0.487654\pi$
$278$	8.80019	−	5.08079i	0.527800	−	0.304726i
$279$	−19.2302	+	19.6293i	−1.15128	+	1.17518i
$280$	3.28702	−	5.69328i	0.196437	−	0.340239i
$281$			0.996645i			0.0594548i	0.999558	+	0.0297274i	$0.00946393\pi$
$281$			0.996645i			0.0594548i	−0.999558	+	0.0297274i	$0.990536\pi$
$282$	−4.32652	+	10.5988i	−0.257641	+	0.631147i
$283$			13.2273i			0.786283i	0.919478	+	0.393141i	$0.128612\pi$
$283$			13.2273i			0.786283i	−0.919478	+	0.393141i	$0.871388\pi$
$284$	−5.35309	−	9.27182i	−0.317647	−	0.550181i
$285$	13.0985	+	5.34694i	0.775887	+	0.316725i
$286$	−2.02091	−	3.50033i	−0.119499	−	0.206979i
$287$	6.07627	−	10.5244i	0.358671	−	0.621236i
$288$	−2.90560	−	0.746656i	−0.171214	−	0.0439971i
$289$	0.708662	+	1.22744i	0.0416860	+	0.0722023i
$290$	5.16066	−	2.97951i	0.303045	−	0.174963i
$291$	7.43333	−	18.2096i	0.435750	−	1.06746i
$292$	8.21612			0.480812
$293$	2.37465			0.138729			0.0693644	−	0.997591i	$-0.477903\pi$
$293$	2.37465			0.138729			0.0693644	+	0.997591i	$0.477903\pi$
$294$	−0.655119	+	1.60486i	−0.0382073	+	0.0935972i
$295$	15.8732	+	27.4932i	0.924174	+	1.60072i
$296$	2.26088	−	5.64698i	0.131411	−	0.328224i
$297$	−7.36400	+	9.90936i	−0.427302	+	0.574999i
$298$	−5.82616	−	3.36373i	−0.337500	−	0.194856i
$299$	−1.47658	+	2.55750i	−0.0853926	+	0.147904i
$300$	−3.01652	+	2.33936i	−0.174159	+	0.135063i
$301$		−	11.7889i		−	0.679502i
$302$	5.55836	+	3.20912i	0.319848	+	0.184664i
$303$	−2.64452	−	1.07952i	−0.151924	−	0.0620169i
$304$	−2.63557	+	1.52164i	−0.151160	+	0.0872723i
$305$	4.05205	−	7.01836i	0.232020	−	0.401870i
$306$	9.19675	+	9.00976i	0.525743	+	0.515054i
$307$	−31.8595			−1.81832			−0.909158	−	0.416451i	$-0.863274\pi$
$307$	−31.8595			−1.81832			−0.909158	+	0.416451i	$0.863274\pi$
$308$	5.81958			0.331601
$309$	19.6488	−	2.68953i	1.11778	−	0.153002i
$310$	−21.2912	−	12.2925i	−1.20926	−	0.698166i
$311$	−29.8856	+	17.2545i	−1.69466	+	0.978410i	−0.743992	+	0.668189i	$0.767070\pi$
$311$	−29.8856	+	17.2545i	−1.69466	+	0.978410i	−0.950664	+	0.310222i	$0.899597\pi$
$312$	−2.32831	+	1.80564i	−0.131814	+	0.102224i
$313$			31.5906i			1.78561i	0.450448	+	0.892803i	$0.351264\pi$
$313$			31.5906i			1.78561i	−0.450448	+	0.892803i	$0.648736\pi$
$314$	−12.1095	+	6.99140i	−0.683377	+	0.394548i
$315$	−13.8017	+	14.0881i	−0.777636	+	0.793775i
$316$	−1.63069	−	0.941477i	−0.0917333	−	0.0529622i
$317$	−4.42230			−0.248381			−0.124190	−	0.992258i	$-0.539633\pi$
$317$	−4.42230			−0.248381			−0.124190	+	0.992258i	$0.539633\pi$
$318$	4.89137	−	0.669531i	0.274294	−	0.0375454i
$319$	4.56841	+	2.63757i	0.255782	+	0.147676i
$320$		−	2.68401i		−	0.150041i
$321$	−25.2991	−	10.3273i	−1.41206	−	0.576416i
$322$	−2.12603	−	3.68239i	−0.118479	−	0.205212i
$323$	13.0604			0.726700
$324$	7.88501	+	4.33897i	0.438056	+	0.241054i
$325$			3.74915i			0.207965i
$326$	−9.70519	+	16.8099i	−0.537521	+	0.931013i
$327$	−11.4133	+	1.56225i	−0.631154	+	0.0863925i
$328$		−	4.96158i		−	0.273958i
$329$	−16.1886			−0.892506
$330$	−10.2264	−	4.17452i	−0.562944	−	0.229800i
$331$		−	12.7092i		−	0.698559i	−0.937019	−	0.349279i	$-0.886426\pi$
$331$		−	12.7092i		−	0.698559i	0.937019	−	0.349279i	$-0.113574\pi$
$332$	−1.81133			−0.0994098
$333$	−10.7856	+	14.7198i	−0.591045	+	0.806638i
$334$	21.4017			1.17105
$335$		−	20.4509i		−	1.11735i
$336$	−0.575330	−	4.20317i	−0.0313868	−	0.229302i
$337$	24.1633			1.31626			0.658129	−	0.752905i	$-0.271348\pi$
$337$	24.1633			1.31626			0.658129	+	0.752905i	$0.271348\pi$
$338$		−	10.1062i		−	0.549705i
$339$	−9.16908	+	22.4617i	−0.497996	+	1.21995i
$340$	−5.75928	+	9.97537i	−0.312341	+	0.540990i
$341$		−	21.7635i		−	1.17856i
$342$	8.79404	−	2.45343i	0.475527	−	0.132666i
$343$	−19.5966			−1.05811
$344$	−2.40656	−	4.16828i	−0.129753	−	0.224739i
$345$	1.09448	+	7.99590i	0.0589248	+	0.430485i
$346$			11.3031i			0.607657i
$347$	−9.67388	−	5.58522i	−0.519321	−	0.299830i	0.217336	−	0.976097i	$-0.430263\pi$
$347$	−9.67388	−	5.58522i	−0.519321	−	0.299830i	−0.736657	+	0.676267i	$0.763597\pi$
$348$	1.45334	−	3.56027i	0.0779071	−	0.190851i
$349$	−18.9378			−1.01372			−0.506859	−	0.862029i	$-0.669194\pi$
$349$	−18.9378			−1.01372			−0.506859	+	0.862029i	$0.669194\pi$
$350$	−4.67495	−	2.69908i	−0.249886	−	0.144272i
$351$	8.11332	−	3.50803i	0.433057	−	0.187245i
$352$	2.05767	−	1.18799i	0.109674	−	0.0633203i
$353$			15.9374i			0.848260i	0.905601	+	0.424130i	$0.139420\pi$
$353$			15.9374i			0.848260i	−0.905601	+	0.424130i	$0.860580\pi$
$354$	18.9672	+	7.74260i	1.00809	+	0.411514i
$355$	−24.8857	+	14.3678i	−1.32080	+	0.762562i
$356$	10.9819	+	6.34038i	0.582038	+	0.336040i
$357$	−6.88077	+	16.8560i	−0.364169	+	0.892112i
$358$	9.61686			0.508267
$359$	11.1233			0.587068			0.293534	−	0.955949i	$-0.405169\pi$
$359$	11.1233			0.587068			0.293534	+	0.955949i	$0.405169\pi$
$360$	−2.00404	+	7.79867i	−0.105622	+	0.411026i
$361$	−4.86920	+	8.43370i	−0.256273	+	0.443879i
$362$	14.7881	−	8.53789i	0.777243	−	0.448742i
$363$	1.25778	+	9.18888i	0.0660161	+	0.482291i
$364$	−3.60837	−	2.08329i	−0.189130	−	0.109194i
$365$		−	22.0522i		−	1.15426i
$366$	−0.709236	−	5.18144i	−0.0370723	−	0.270838i
$367$	−0.583314	+	1.01033i	−0.0304487	+	0.0527388i	−0.880848	−	0.473399i	$-0.843027\pi$
$367$	−0.583314	+	1.01033i	−0.0304487	+	0.0527388i	0.850399	+	0.526138i	$0.176360\pi$
$368$	−1.50343	−	0.868005i	−0.0783717	−	0.0452479i
$369$	−3.70460	+	14.4164i	−0.192854	+	0.750486i
$370$	−15.1566	−	6.06824i	−0.787953	−	0.315473i
$371$	3.49074	+	6.04614i	0.181230	+	0.313900i
$372$	−15.7186	+	2.15157i	−0.814972	+	0.111554i
$373$	17.6524			0.914007			0.457003	−	0.889465i	$-0.348923\pi$
$373$	17.6524			0.914007			0.457003	+	0.889465i	$0.348923\pi$
$374$	−10.1967			−0.527257
$375$	−7.96583	−	10.2716i	−0.411353	−	0.530424i
$376$	−5.72391	+	3.30470i	−0.295188	+	0.170427i
$377$	−1.88840	−	3.27080i	−0.0972574	−	0.168455i
$378$	−1.46664	+	12.6423i	−0.0754359	+	0.650249i
$379$	6.25459	−	10.8333i	0.321277	−	0.556467i	−0.659475	−	0.751726i	$-0.729221\pi$
$379$	6.25459	−	10.8333i	0.321277	−	0.556467i	0.980752	+	0.195259i	$0.0625547\pi$
$380$	4.08412	+	7.07390i	0.209511	+	0.362883i
$381$	−3.60460	−	26.3340i	−0.184669	−	1.34913i
$382$	6.62998	+	11.4835i	0.339219	+	0.587545i
$383$		−	28.8112i		−	1.47219i	−0.676880	−	0.736093i	$-0.736669\pi$
$383$		−	28.8112i		−	1.47219i	0.676880	−	0.736093i	$-0.263331\pi$
$384$	−1.06145	−	1.36870i	−0.0541668	−	0.0698460i
$385$		−	15.6198i		−	0.796061i
$386$	9.70804	−	16.8148i	0.494126	−	0.855852i
$387$	3.88022	+	13.9082i	0.197243	+	0.706995i
$388$	9.83416	−	5.67776i	0.499254	−	0.288244i
$389$	12.1643	+	7.02304i	0.616752	+	0.356082i	0.775603	−	0.631220i	$-0.217446\pi$
$389$	12.1643	+	7.02304i	0.616752	+	0.356082i	−0.158851	+	0.987303i	$0.550779\pi$
$390$	4.84638	+	6.24921i	0.245406	+	0.316441i
$391$	3.72508	+	6.45203i	0.188385	+	0.326293i
$392$	−0.866710	+	0.500396i	−0.0437755	+	0.0252738i
$393$	−5.50136	+	13.4768i	−0.277507	+	0.679814i
$394$	9.43225	+	5.44571i	0.475190	+	0.274351i
$395$	−2.52694	+	4.37679i	−0.127144	+	0.220220i
$396$	−6.86578	+	1.91547i	−0.345018	+	0.0962558i
$397$	−22.5599			−1.13225			−0.566125	−	0.824319i	$-0.691558\pi$
$397$	−22.5599			−1.13225			−0.566125	+	0.824319i	$0.691558\pi$
$398$	1.68904			0.0846638
$399$	7.91205	+	10.2023i	0.396098	+	0.510753i
$400$	−2.20394			−0.110197
$401$	−13.8296	−	7.98455i	−0.690619	−	0.398729i	0.113225	−	0.993569i	$-0.463882\pi$
$401$	−13.8296	−	7.98455i	−0.690619	−	0.398729i	−0.803844	+	0.594840i	$0.797215\pi$
$402$	−8.08771	−	10.4288i	−0.403378	−	0.520141i
$403$	−7.79090	+	13.4942i	−0.388093	+	0.672196i
$404$	−0.824564	−	1.42819i	−0.0410236	−	0.0710549i
$405$	11.6458	−	21.1635i	0.578687	−	1.05162i
$406$	5.43797			0.269882
$407$	−2.05645	−	14.3055i	−0.101934	−	0.709099i
$408$	1.00805	+	7.36450i	0.0499061	+	0.364597i
$409$	16.4233	−	9.48200i	0.812080	−	0.468855i	−0.0355977	−	0.999366i	$-0.511333\pi$
$409$	16.4233	−	9.48200i	0.812080	−	0.468855i	0.847678	+	0.530512i	$0.178000\pi$
$410$	−13.3170			−0.657678
$411$	2.27284	+	0.927797i	0.112111	+	0.0457649i
$412$	9.91602	+	5.72502i	0.488527	+	0.282051i
$413$			28.9706i			1.42555i
$414$	3.72026	+	3.64462i	0.182841	+	0.179123i
$415$			4.86164i			0.238649i
$416$	−1.70111			−0.0834040
$417$	−16.2950	−	6.65178i	−0.797970	−	0.325739i
$418$	−3.61541	+	6.26208i	−0.176836	+	0.306288i
$419$	0.370601	+	0.641900i	0.0181051	+	0.0313589i	0.874936	−	0.484239i	$-0.160903\pi$
$419$	0.370601	+	0.641900i	0.0181051	+	0.0313589i	−0.856831	+	0.515597i	$0.827570\pi$
$420$	−11.2814	+	1.54420i	−0.550474	+	0.0753490i
$421$	−25.5538	+	14.7535i	−1.24542	+	0.719042i	−0.970192	−	0.242337i	$-0.922086\pi$
$421$	−25.5538	+	14.7535i	−1.24542	+	0.719042i	−0.275226	+	0.961380i	$0.588753\pi$
$422$	−12.9293	−	7.46471i	−0.629387	−	0.363377i
$423$	19.0989	−	5.32834i	0.928618	−	0.259073i
$424$	2.46849	+	1.42518i	0.119880	+	0.0692130i
$425$	8.19111	+	4.72914i	0.397327	+	0.229397i
$426$	−7.00827	+	17.1683i	−0.339552	+	0.831807i
$427$	6.40469	−	3.69775i	0.309945	−	0.178947i
$428$	−7.88827	−	13.6629i	−0.381294	−	0.660420i
$429$	−2.64579	+	6.48143i	−0.127740	+	0.312927i
$430$	−11.1877	+	6.45924i	−0.539521	+	0.311492i
$431$	15.9210	−	9.19198i	0.766887	−	0.442762i	−0.0648763	−	0.997893i	$-0.520665\pi$
$431$	15.9210	−	9.19198i	0.766887	−	0.442762i	0.831763	+	0.555131i	$0.187332\pi$
$432$	2.06220	+	4.76942i	0.0992175	+	0.229469i
$433$	0.767638			0.0368903			0.0184452	−	0.999830i	$-0.494128\pi$
$433$	0.767638			0.0368903			0.0184452	+	0.999830i	$0.494128\pi$
$434$	−11.2176	−	19.4295i	−0.538464	−	0.932647i
$435$	−9.55582	−	3.90078i	−0.458167	−	0.187028i
$436$	−5.75984	−	3.32544i	−0.275846	−	0.159260i
$437$	5.28318			0.252729
$438$	−8.72099	−	11.2454i	−0.416705	−	0.537325i
$439$	30.1223	+	17.3911i	1.43766	+	0.830032i	0.997687	−	0.0679798i	$-0.0216553\pi$
$439$	30.1223	+	17.3911i	1.43766	+	0.830032i	0.439971	+	0.898012i	$0.354989\pi$
$440$	−3.18860	−	5.52281i	−0.152010	−	0.263290i
$441$	2.89194	−	0.806814i	0.137711	−	0.0384197i
$442$	6.32233	+	3.65020i	0.300723	+	0.173622i
$443$	−10.9859	−	19.0281i	−0.521954	−	0.904050i	−0.999674	−	0.0255382i	$-0.991870\pi$
$443$	−10.9859	−	19.0281i	−0.521954	−	0.904050i	0.477720	−	0.878512i	$-0.341463\pi$
$444$	−10.1288	+	2.89952i	−0.480692	+	0.137605i
$445$	17.0177	−	29.4755i	0.806715	−	1.39727i
$446$	14.2871	−	8.24868i	0.676515	−	0.390586i
$447$	1.58023	+	11.5447i	0.0747425	+	0.546044i
$448$	1.22466	−	2.12118i	0.0578599	−	0.100216i
$449$	12.6696	−	7.31479i	0.597914	−	0.345206i	−0.170306	−	0.985391i	$-0.554476\pi$
$449$	12.6696	−	7.31479i	0.597914	−	0.345206i	0.768221	+	0.640185i	$0.221142\pi$
$450$	6.40375	+	1.64558i	0.301876	+	0.0775735i
$451$	−5.89433	−	10.2093i	−0.277553	−	0.480736i
$452$	−12.1305	+	7.00356i	−0.570572	+	0.329420i
$453$	−1.50760	−	11.0140i	−0.0708333	−	0.517484i
$454$	−9.07796	+	15.7235i	−0.426050	+	0.737940i
$455$	−5.59159	+	9.68492i	−0.262138	+	0.454036i
$456$	4.88018	+	1.99214i	0.228536	+	0.0932905i
$457$	−19.9253	−	11.5039i	−0.932067	−	0.538129i	−0.0446023	−	0.999005i	$-0.514202\pi$
$457$	−19.9253	−	11.5039i	−0.932067	−	0.538129i	−0.887465	+	0.460876i	$0.847535\pi$
$458$			9.39009i			0.438770i
$459$	2.56975	−	22.1509i	0.119946	−	1.03392i
$460$	−2.32974	+	4.03523i	−0.108625	+	0.188143i
$461$			25.8568i			1.20427i	0.798394	+	0.602135i	$0.205683\pi$
$461$			25.8568i			1.20427i	−0.798394	+	0.602135i	$0.794317\pi$
$462$	−6.17718	−	7.96523i	−0.287388	−	0.370576i
$463$			22.5548i			1.04821i	0.851653	+	0.524106i	$0.175600\pi$
$463$			22.5548i			1.04821i	−0.851653	+	0.524106i	$0.824400\pi$
$464$	1.92274	−	1.11009i	0.0892610	−	0.0515349i
$465$	5.77484	+	42.1890i	0.267802	+	1.95647i
$466$		−	14.3014i		−	0.662498i
$467$		−	27.8214i		−	1.28742i	−0.765269	−	0.643710i	$-0.777394\pi$
$467$		−	27.8214i		−	1.28742i	0.765269	−	0.643710i	$-0.222606\pi$
$468$	4.94276	+	1.27015i	0.228479	+	0.0587126i
$469$	9.33134	−	16.1624i	0.430881	−	0.746308i
$470$	8.86986	+	15.3631i	0.409136	+	0.708645i
$471$	22.4227	+	9.15316i	1.03318	+	0.421755i
$472$	5.91398	+	10.2433i	0.272213	+	0.471487i
$473$	−9.90380	−	5.71796i	−0.455377	−	0.262912i
$474$	0.442293	+	3.23124i	0.0203152	+	0.148416i
$475$	5.80862	−	3.35361i	0.266518	−	0.153874i
$476$	−9.10313	+	5.25570i	−0.417241	+	0.240894i
$477$	−6.10831	−	5.98412i	−0.279680	−	0.273994i
$478$	7.64189	+	13.2361i	0.349532	+	0.605407i
$479$		−	38.8746i		−	1.77622i	−0.459627	−	0.888112i	$-0.652017\pi$
$479$		−	38.8746i		−	1.77622i	0.459627	−	0.888112i	$-0.347983\pi$
$480$	−3.67360	+	2.84894i	−0.167676	+	0.130036i
$481$	−3.84601	+	9.60616i	−0.175363	+	0.438003i
$482$	−1.89342	+	3.27950i	−0.0862428	+	0.149377i
$483$	−2.78340	+	6.81856i	−0.126649	+	0.310255i
$484$	−2.67734	+	4.63728i	−0.121697	+	0.210786i
$485$	−15.2392	−	26.3950i	−0.691976	−	1.19854i
$486$	−2.43080	−	15.3978i	−0.110263	−	0.698457i
$487$		−	3.06171i		−	0.138739i	−0.997591	−	0.0693696i	$-0.977901\pi$
$487$		−	3.06171i		−	0.138739i	0.997591	−	0.0693696i	$-0.0220988\pi$
$488$	1.50970	−	2.61487i	0.0683409	−	0.118370i
$489$	33.3092	−	4.55936i	1.50629	−	0.206182i
$490$	1.34307	+	2.32626i	0.0606737	+	0.105090i
$491$	11.6019	−	20.0951i	0.523586	−	0.906877i	−0.476037	−	0.879425i	$-0.657927\pi$
$491$	11.6019	−	20.0951i	0.523586	−	0.906877i	0.999623	−	0.0274521i	$-0.00873938\pi$
$492$	−6.79090	+	5.26646i	−0.306157	+	0.237430i
$493$	−9.52803			−0.429121
$494$	4.48340	−	2.58849i	0.201718	−	0.116462i
$495$	5.14114	+	18.4279i	0.231077	+	0.828271i
$496$	−7.93259	−	4.57988i	−0.356184	−	0.205643i
$497$	−26.2229			−1.17626
$498$	1.92264	+	2.47916i	0.0861554	+	0.111094i
$499$		−	6.91284i		−	0.309461i	−0.987957	−	0.154731i	$-0.950549\pi$
$499$		−	6.91284i		−	0.309461i	0.987957	−	0.154731i	$-0.0494510\pi$
$500$		−	7.50468i		−	0.335619i
$501$	−22.7168	−	29.2924i	−1.01491	−	1.30869i
$502$	21.7343			0.970048
$503$	2.13459	+	1.23241i	0.0951767	+	0.0549503i	0.546833	−	0.837242i	$-0.315833\pi$
$503$	2.13459	+	1.23241i	0.0951767	+	0.0549503i	−0.451656	+	0.892192i	$0.649167\pi$
$504$	−5.14218	+	5.24890i	−0.229051	+	0.233804i
$505$	−3.83327	+	2.21314i	−0.170578	+	0.0984835i
$506$	−4.12474			−0.183367
$507$	−13.8323	+	10.7272i	−0.614315	+	0.476412i
$508$	7.67285	−	13.2898i	0.340427	−	0.589638i
$509$	9.22062	+	15.9706i	0.408697	+	0.707883i	0.994744	−	0.102393i	$-0.0326500\pi$
$509$	9.22062	+	15.9706i	0.408697	+	0.707883i	−0.586047	+	0.810277i	$0.699317\pi$
$510$	19.7664	−	2.70563i	0.875272	−	0.119807i
$511$	10.0620	−	17.4279i	0.445116	−	0.770964i
$512$		−	1.00000i		−	0.0441942i
$513$	−12.6924	−	9.43218i	−0.560384	−	0.416441i
$514$	7.58782	+	13.1425i	0.334684	+	0.579690i
$515$	15.3660	−	26.6147i	0.677108	−	1.17279i
$516$	−3.15067	+	7.71827i	−0.138701	+	0.339778i
$517$	−7.85193	+	13.5999i	−0.345328	+	0.598125i
$518$	−9.20945	−	11.7114i	−0.404640	−	0.514569i
$519$	15.4705	−	11.9976i	0.679078	−	0.526637i
$520$			4.56582i			0.200224i
$521$	−12.3189	−	21.3370i	−0.539702	−	0.934791i	−0.998920	−	0.0464671i	$-0.985204\pi$
$521$	−12.3189	−	21.3370i	−0.539702	−	0.934791i	0.459218	−	0.888323i	$-0.348130\pi$
$522$	−6.41557	+	1.78986i	−0.280802	+	0.0783402i
$523$	31.4590	−	18.1629i	1.37561	−	0.794207i	0.383979	−	0.923342i	$-0.374553\pi$
$523$	31.4590	−	18.1629i	1.37561	−	0.794207i	0.991627	+	0.129135i	$0.0412200\pi$
$524$	−7.27820	+	4.20207i	−0.317950	+	0.183568i
$525$	1.26799	+	9.26351i	0.0553397	+	0.404293i
$526$	6.47134	+	3.73623i	0.282164	+	0.162907i
$527$	19.6548	+	34.0430i	0.856175	+	1.48294i
$528$	−3.81011	−	1.55533i	−0.165814	−	0.0676869i
$529$	−9.99313	−	17.3086i	−0.434484	−	0.752548i
$530$	3.82521	−	6.62546i	0.166156	−	0.287791i
$531$	−9.53542	−	34.1787i	−0.413802	−	1.48323i
$532$			7.45401i			0.323172i
$533$			8.44022i			0.365586i
$534$	−2.97862	−	21.7608i	−0.128898	−	0.941682i
$535$	−36.6714	+	21.1722i	−1.58544	+	0.915355i
$536$		−	7.61951i		−	0.329113i
$537$	−10.2078	−	13.1626i	−0.440499	−	0.568006i
$538$		−	25.7826i		−	1.11157i
$539$	−1.18893	+	2.05930i	−0.0512110	+	0.0887001i
$540$	12.8012	−	5.53497i	0.550875	−	0.238187i
$541$		−	35.9811i		−	1.54695i	−0.633829	−	0.773474i	$-0.718518\pi$
$541$		−	35.9811i		−	1.54695i	0.633829	−	0.773474i	$-0.281482\pi$
$542$	3.94097	+	2.27532i	0.169279	+	0.0977333i
$543$	−27.3825	−	11.1778i	−1.17510	−	0.479687i
$544$	−2.14577	+	3.71658i	−0.0919992	+	0.159347i
$545$	−8.92554	+	15.4595i	−0.382328	+	0.662212i
$546$	0.978702	+	7.15007i	0.0418846	+	0.305995i
$547$	23.4683	−	13.5494i	1.00343	−	0.579332i	0.0941708	−	0.995556i	$-0.469980\pi$
$547$	23.4683	−	13.5494i	1.00343	−	0.579332i	0.909262	+	0.416224i	$0.136647\pi$
$548$	0.708673	+	1.22746i	0.0302730	+	0.0524344i
$549$	−6.33899	+	6.47055i	−0.270542	+	0.276156i
$550$	−4.53497	+	2.61826i	−0.193372	+	0.111643i
$551$	−3.37834	+	5.85146i	−0.143922	+	0.249280i
$552$	0.407777	+	2.97908i	0.0173561	+	0.126798i
$553$	−3.99409	+	2.30599i	−0.169846	+	0.0980605i
$554$	8.87428	−	15.3707i	0.377032	−	0.653039i
$555$	7.78236	+	27.1859i	0.330343	+	1.15398i
$556$	−5.08079	−	8.80019i	−0.215474	−	0.373211i
$557$	−17.6588	−	10.1953i	−0.748228	−	0.431989i	0.0768255	−	0.997045i	$-0.475522\pi$
$557$	−17.6588	−	10.1953i	−0.748228	−	0.431989i	−0.825053	+	0.565055i	$0.808855\pi$
$558$	19.6293	+	19.2302i	0.830976	+	0.814080i
$559$	4.09383	+	7.09073i	0.173151	+	0.299906i
$560$	−5.69328	−	3.28702i	−0.240585	−	0.138902i
$561$	10.8232	+	13.9561i	0.456957	+	0.589228i
$562$	0.996645			0.0420409
$563$	13.3295	+	7.69578i	0.561771	+	0.324339i	0.753856	−	0.657040i	$-0.228192\pi$
$563$	13.3295	+	7.69578i	0.561771	+	0.324339i	−0.192085	+	0.981378i	$0.561525\pi$
$564$	10.5988	+	4.32652i	0.446288	+	0.182179i
$565$	18.7977	+	32.5585i	0.790824	+	1.36975i
$566$	13.2273			0.555986
$567$	18.8602	−	11.4118i	0.792055	−	0.479249i
$568$	−9.27182	+	5.35309i	−0.389037	+	0.224611i
$569$	−13.5310	+	7.81215i	−0.567251	+	0.327503i	−0.756051	−	0.654513i	$-0.772874\pi$
$569$	−13.5310	+	7.81215i	−0.567251	+	0.327503i	0.188800	+	0.982016i	$0.439540\pi$
$570$	5.34694	−	13.0985i	0.223958	−	0.548635i
$571$	−21.1835	−	36.6909i	−0.886503	−	1.53547i	−0.843982	−	0.536372i	$-0.819794\pi$
$571$	−21.1835	−	36.6909i	−0.886503	−	1.53547i	−0.0425208	−	0.999096i	$-0.513539\pi$
$572$	−3.50033	+	2.02091i	−0.146356	+	0.0844987i
$573$	8.67999	−	21.2635i	0.362612	−	0.888297i
$574$	−10.5244	−	6.07627i	−0.439280	−	0.253619i
$575$	3.31346	+	1.91303i	0.138181	+	0.0797788i
$576$	−0.746656	+	2.90560i	−0.0311107	+	0.121067i
$577$	−37.9248	−	21.8959i	−1.57883	−	0.911538i	−0.995023	−	0.0996462i	$-0.968229\pi$
$577$	−37.9248	−	21.8959i	−1.57883	−	0.911538i	−0.583808	−	0.811892i	$-0.698438\pi$
$578$	1.22744	−	0.708662i	0.0510547	−	0.0294765i
$579$	−33.3190	+	4.56071i	−1.38469	+	0.189536i
$580$	−2.97951	−	5.16066i	−0.123717	−	0.214285i
$581$	−2.21827	+	3.84216i	−0.0920295	+	0.159400i
$582$	−18.2096	−	7.43333i	−0.754811	−	0.308122i
$583$	6.77244			0.280486
$584$		−	8.21612i		−	0.339986i
$585$	3.40909	−	13.2664i	0.140949	−	0.548499i
$586$		−	2.37465i		−	0.0980961i
$587$	4.58194	+	2.64538i	0.189117	+	0.109187i	0.591569	−	0.806254i	$-0.298509\pi$
$587$	4.58194	+	2.64538i	0.189117	+	0.109187i	−0.402452	+	0.915441i	$0.631842\pi$
$588$	1.60486	+	0.655119i	0.0661832	+	0.0270167i
$589$	27.8758			1.14860
$590$	27.4932	−	15.8732i	1.13188	−	0.653490i
$591$	−2.55832	−	18.6902i	−0.105235	−	0.768813i
$592$	−5.64698	−	2.26088i	−0.232090	−	0.0929216i
$593$	2.67327			0.109778			0.0548889	−	0.998492i	$-0.482520\pi$
$593$	2.67327			0.109778			0.0548889	+	0.998492i	$0.482520\pi$
$594$	9.90936	+	7.36400i	0.406586	+	0.302148i
$595$	14.1064	+	24.4329i	0.578305	+	1.00165i
$596$	−3.36373	+	5.82616i	−0.137784	+	0.238649i
$597$	−1.79283	−	2.31178i	−0.0733755	−	0.0946148i
$598$	2.55750	+	1.47658i	0.104584	+	0.0603817i
$599$	37.7455			1.54224			0.771120	−	0.636689i	$-0.219697\pi$
$599$	37.7455			1.54224			0.771120	+	0.636689i	$0.219697\pi$
$600$	2.33936	+	3.01652i	0.0955041	+	0.123149i
$601$	25.3511			1.03409			0.517047	−	0.855957i	$-0.327031\pi$
$601$	25.3511			1.03409			0.517047	+	0.855957i	$0.327031\pi$
$602$	−11.7889			−0.480480
$603$	−5.68915	+	22.1392i	−0.231680	+	0.901579i
$604$	3.20912	−	5.55836i	0.130577	−	0.226166i
$605$	12.4465	+	7.18601i	0.506024	+	0.292153i
$606$	−1.07952	+	2.64452i	−0.0438525	+	0.107426i
$607$	15.0068	−	8.66420i	0.609109	−	0.351669i	−0.163508	−	0.986542i	$-0.552281\pi$
$607$	15.0068	−	8.66420i	0.609109	−	0.351669i	0.772617	+	0.634873i	$0.218948\pi$
$608$	1.52164	+	2.63557i	0.0617108	+	0.106886i
$609$	−5.77213	−	7.44293i	−0.233898	−	0.301603i
$610$	−7.01836	−	4.05205i	−0.284165	−	0.164063i
$611$	9.73702	−	5.62167i	0.393918	−	0.227428i
$612$	9.00976	−	9.19675i	0.364198	−	0.371757i
$613$	5.43348	−	9.41107i	0.219456	−	0.380109i	−0.735186	−	0.677866i	$-0.762905\pi$
$613$	5.43348	−	9.41107i	0.219456	−	0.380109i	0.954642	+	0.297757i	$0.0962384\pi$
$614$			31.8595i			1.28574i
$615$	14.1353	+	18.2269i	0.569989	+	0.734978i
$616$		−	5.81958i		−	0.234478i
$617$	17.0538	+	29.5381i	0.686562	+	1.18916i	0.972943	+	0.231044i	$0.0742142\pi$
$617$	17.0538	+	29.5381i	0.686562	+	1.18916i	−0.286382	+	0.958116i	$0.592452\pi$
$618$	−2.68953	−	19.6488i	−0.108189	−	0.790391i
$619$	−5.14114	−	8.90472i	−0.206640	−	0.357911i	0.744014	−	0.668164i	$-0.232920\pi$
$619$	−5.14114	−	8.90472i	−0.206640	−	0.357911i	−0.950654	+	0.310253i	$0.899586\pi$
$620$	−12.2925	+	21.2912i	−0.493678	+	0.855075i
$621$	1.03951	−	8.96048i	0.0417142	−	0.359572i
$622$	17.2545	+	29.8856i	0.691840	+	1.19830i
$623$	26.8982	−	15.5297i	1.07765	−	0.622183i
$624$	1.80564	+	2.32831i	0.0722836	+	0.0932069i
$625$	−31.1623			−1.24649
$626$	31.5906			1.26261
$627$	12.4084	−	1.69847i	0.495546	−	0.0678304i
$628$	6.99140	+	12.1095i	0.278987	+	0.483220i
$629$	16.1362	+	20.5199i	0.643391	+	0.818181i
$630$	14.0881	+	13.8017i	0.561284	+	0.549872i
$631$	−1.79914	−	1.03873i	−0.0716226	−	0.0413513i	0.463761	−	0.885960i	$-0.346500\pi$
$631$	−1.79914	−	1.03873i	−0.0716226	−	0.0413513i	−0.535384	+	0.844609i	$0.679833\pi$
$632$	−0.941477	+	1.63069i	−0.0374499	+	0.0648652i
$633$	3.50682	+	25.6196i	0.139384	+	1.01829i
$634$			4.42230i			0.175632i
$635$	−35.6699	−	20.5940i	−1.41552	−	0.817249i
$636$	−0.669531	−	4.89137i	−0.0265486	−	0.193955i
$637$	1.47437	−	0.851230i	0.0584168	−	0.0337270i
$638$	2.63757	−	4.56841i	0.104423	−	0.180865i
$639$	30.9371	−	8.63106i	1.22385	−	0.341440i
$640$	−2.68401			−0.106095
$641$	−17.0595			−0.673812			−0.336906	−	0.941538i	$-0.609380\pi$
$641$	−17.0595			−0.673812			−0.336906	+	0.941538i	$0.609380\pi$
$642$	−10.3273	+	25.2991i	−0.407588	+	0.998475i
$643$	35.3796	+	20.4264i	1.39524	+	0.805540i	0.993889	−	0.110387i	$-0.0352089\pi$
$643$	35.3796	+	20.4264i	1.39524	+	0.805540i	0.401347	+	0.915926i	$0.368542\pi$
$644$	−3.68239	+	2.12603i	−0.145107	+	0.0837773i
$645$	20.7159	+	8.45646i	0.815689	+	0.332973i
$646$		−	13.0604i		−	0.513855i
$647$	−29.3898	+	16.9682i	−1.15543	+	0.667090i	−0.950205	−	0.311624i	$-0.899127\pi$
$647$	−29.3898	+	16.9682i	−1.15543	+	0.667090i	−0.205228	+	0.978714i	$0.565794\pi$
$648$	4.33897	−	7.88501i	0.170451	−	0.309752i
$649$	24.3380	+	14.0516i	0.955350	+	0.551572i
$650$	3.74915			0.147054
$651$	−14.6862	+	35.9770i	−0.575596	+	1.41005i
$652$	16.8099	+	9.70519i	0.658326	+	0.380085i
$653$			42.5162i			1.66379i	0.554935	+	0.831894i	$0.312743\pi$
$653$			42.5162i			1.66379i	−0.554935	+	0.831894i	$0.687257\pi$
$654$	1.56225	+	11.4133i	0.0610887	+	0.446293i
$655$	11.2784	+	19.5348i	0.440684	+	0.763288i
$656$	−4.96158			−0.193717
$657$	−6.13462	+	23.8728i	−0.239334	+	0.931365i
$658$			16.1886i			0.631097i
$659$	3.93871	−	6.82204i	0.153430	−	0.265749i	−0.779056	−	0.626954i	$-0.784301\pi$
$659$	3.93871	−	6.82204i	0.153430	−	0.265749i	0.932486	+	0.361205i	$0.117635\pi$
$660$	−4.17452	+	10.2264i	−0.162493	+	0.398062i
$661$		−	20.2243i		−	0.786632i	−0.919403	−	0.393316i	$-0.871328\pi$
$661$		−	20.2243i		−	0.786632i	0.919403	−	0.393316i	$-0.128672\pi$
$662$	−12.7092			−0.493955
$663$	−1.71481	−	12.5278i	−0.0665978	−	0.486541i
$664$			1.81133i			0.0702933i
$665$	20.0067			0.775826
$666$	14.7198	+	10.7856i	0.570379	+	0.417932i
$667$	−3.85427			−0.149238
$668$		−	21.4017i		−	0.828056i
$669$	−26.4550	−	10.7992i	−1.02281	−	0.417521i
$670$	−20.4509			−0.790086
$671$		−	7.17406i		−	0.276951i
$672$	−4.20317	+	0.575330i	−0.162141	+	0.0221938i
$673$	−17.7759	+	30.7888i	−0.685211	+	1.18682i	0.288160	+	0.957582i	$0.406957\pi$
$673$	−17.7759	+	30.7888i	−0.685211	+	1.18682i	−0.973371	+	0.229237i	$0.926377\pi$
$674$		−	24.1633i		−	0.930735i
$675$	−4.54495	−	10.5115i	−0.174935	−	0.404587i
$676$	−10.1062			−0.388700
$677$	6.61080	+	11.4502i	0.254074	+	0.440068i	0.964643	−	0.263558i	$-0.0848961\pi$
$677$	6.61080	+	11.4502i	0.254074	+	0.440068i	−0.710570	+	0.703627i	$0.751563\pi$
$678$	22.4617	+	9.16908i	0.862635	+	0.352136i
$679$		−	27.8134i		−	1.06738i
$680$	9.97537	+	5.75928i	0.382538	+	0.220858i
$681$	31.1565	−	4.26470i	1.19392	−	0.163424i
$682$	−21.7635			−0.833368
$683$	−32.1318	−	18.5513i	−1.22949	−	0.709846i	−0.262566	−	0.964914i	$-0.584569\pi$
$683$	−32.1318	−	18.5513i	−1.22949	−	0.709846i	−0.966923	+	0.255068i	$0.917902\pi$
$684$	−2.45343	−	8.79404i	−0.0938091	−	0.336249i
$685$	3.29452	−	1.90209i	0.125877	−	0.0726751i
$686$			19.5966i			0.748200i
$687$	12.8522	−	9.96709i	0.490341	−	0.380268i
$688$	−4.16828	+	2.40656i	−0.158914	+	0.0917492i
$689$	−4.19918	−	2.42440i	−0.159976	−	0.0923622i
$690$	7.99590	−	1.09448i	0.304399	−	0.0416661i
$691$	6.74213			0.256483			0.128241	−	0.991743i	$-0.459067\pi$
$691$	6.74213			0.256483			0.128241	+	0.991743i	$0.459067\pi$
$692$	11.3031			0.429678
$693$	−4.34522	+	16.9094i	−0.165061	+	0.642334i
$694$	−5.58522	+	9.67388i	−0.212012	+	0.367215i
$695$	−23.6198	+	13.6369i	−0.895951	+	0.517278i
$696$	−3.56027	−	1.45334i	−0.134952	−	0.0550887i
$697$	18.4401	+	10.6464i	0.698470	+	0.403262i
$698$			18.9378i			0.716808i
$699$	−19.5742	+	15.1802i	−0.740365	+	0.574166i
$700$	−2.69908	+	4.67495i	−0.102016	+	0.176696i
$701$	36.0167	+	20.7943i	1.36033	+	0.785388i	0.989668	−	0.143379i	$-0.0457968\pi$
$701$	36.0167	+	20.7943i	1.36033	+	0.785388i	0.370664	+	0.928767i	$0.379130\pi$
$702$	−3.50803	−	8.11332i	−0.132402	−	0.306218i
$703$	18.3233	−	2.63400i	0.691074	−	0.0993433i
$704$	−1.18799	−	2.05767i	−0.0447742	−	0.0775513i
$705$	11.6124	−	28.4472i	0.437350	−	1.07138i
$706$	15.9374			0.599810
$707$	−4.03926			−0.151912
$708$	7.74260	−	18.9672i	0.290985	−	0.712830i
$709$	34.4807	−	19.9074i	1.29495	−	0.747639i	0.315422	−	0.948952i	$-0.397854\pi$
$709$	34.4807	−	19.9074i	1.29495	−	0.747639i	0.979527	+	0.201313i	$0.0645207\pi$
$710$	14.3678	+	24.8857i	0.539213	+	0.933944i
$711$	3.95312	−	4.03516i	0.148253	−	0.151330i
$712$	6.34038	−	10.9819i	0.237616	−	0.411563i
$713$	7.95073	+	13.7711i	0.297757	+	0.515730i
$714$	16.8560	+	6.88077i	0.630818	+	0.257506i
$715$	5.42417	+	9.39493i	0.202852	+	0.351350i
$716$		−	9.61686i		−	0.359399i
$717$	10.0048	−	24.5089i	0.373635	−	0.915301i
$718$		−	11.1233i		−	0.415119i
$719$	12.6713	−	21.9474i	0.472562	−	0.818501i	−0.526945	−	0.849899i	$-0.676663\pi$
$719$	12.6713	−	21.9474i	0.472562	−	0.818501i	0.999507	+	0.0313985i	$0.00999610\pi$
$720$	7.79867	+	2.00404i	0.290639	+	0.0746860i
$721$	24.2876	−	14.0224i	0.904517	−	0.522223i
$722$	8.43370	+	4.86920i	0.313870	+	0.181213i
$723$	6.49840	−	0.889502i	0.241678	−	0.0330809i
$724$	−8.53789	−	14.7881i	−0.317308	−	0.549594i
$725$	−4.23760	+	2.44658i	−0.157380	+	0.0908636i
$726$	9.18888	−	1.25778i	0.341031	−	0.0466804i
$727$	11.3480	+	6.55180i	0.420876	+	0.242993i	0.695452	−	0.718573i	$-0.255204\pi$
$727$	11.3480	+	6.55180i	0.420876	+	0.242993i	−0.274576	+	0.961565i	$0.588538\pi$
$728$	−2.08329	+	3.60837i	−0.0772120	+	0.133735i
$729$	−18.4947	+	19.6710i	−0.684988	+	0.728554i
$730$	−22.0522			−0.816188
$731$	20.6557			0.763979
$732$	−5.18144	+	0.709236i	−0.191511	+	0.0262141i
$733$	−3.71484			−0.137211			−0.0686053	−	0.997644i	$-0.521855\pi$
$733$	−3.71484			−0.137211			−0.0686053	+	0.997644i	$0.521855\pi$
$734$	1.01033	+	0.583314i	0.0372919	+	0.0215305i
$735$	1.75835	−	4.30746i	0.0648577	−	0.158883i
$736$	−0.868005	+	1.50343i	−0.0319951	+	0.0554171i
$737$	−9.05194	−	15.6784i	−0.333432	−	0.577522i
$738$	14.4164	+	3.70460i	0.530674	+	0.136368i
$739$	−5.99157			−0.220404			−0.110202	−	0.993909i	$-0.535150\pi$
$739$	−5.99157			−0.220404			−0.110202	+	0.993909i	$0.535150\pi$
$740$	−6.06824	+	15.1566i	−0.223073	+	0.557167i
$741$	−8.30175	−	3.38886i	−0.304972	−	0.124493i
$742$	6.04614	−	3.49074i	0.221961	−	0.128149i
$743$	−46.0319			−1.68875			−0.844374	−	0.535754i	$-0.820027\pi$
$743$	−46.0319			−1.68875			−0.844374	+	0.535754i	$0.820027\pi$
$744$	2.15157	+	15.7186i	0.0788802	+	0.576272i
$745$	15.6375	+	9.02831i	0.572913	+	0.330772i
$746$		−	17.6524i		−	0.646300i
$747$	1.35244	−	5.26301i	0.0494833	−	0.192563i
$748$			10.1967i			0.372827i
$749$	−38.6419			−1.41194
$750$	−10.2716	+	7.96583i	−0.375067	+	0.290871i
$751$	13.4811	−	23.3499i	0.491931	−	0.852050i	−0.508026	−	0.861342i	$-0.669624\pi$
$751$	13.4811	−	23.3499i	0.491931	−	0.852050i	0.999957	+	0.00929202i	$0.00295778\pi$
$752$	3.30470	+	5.72391i	0.120510	+	0.208729i
$753$	−23.0698	−	29.7476i	−0.840710	−	1.08406i
$754$	−3.27080	+	1.88840i	−0.119116	+	0.0687714i
$755$	−14.9187	−	8.61333i	−0.542948	−	0.313471i
$756$	12.6423	+	1.46664i	0.459796	+	0.0533413i
$757$	32.9492	+	19.0232i	1.19756	+	0.691411i	0.960010	−	0.279964i	$-0.0903226\pi$
$757$	32.9492	+	19.0232i	1.19756	+	0.691411i	0.237549	+	0.971376i	$0.423656\pi$
$758$	−10.8333	−	6.25459i	−0.393482	−	0.227177i
$759$	4.37820	+	5.64552i	0.158919	+	0.204919i
$760$	7.07390	−	4.08412i	0.256597	−	0.148146i
$761$	0.857365	+	1.48500i	0.0310795	+	0.0538312i	0.881147	−	0.472843i	$-0.156772\pi$
$761$	0.857365	+	1.48500i	0.0310795	+	0.0538312i	−0.850067	+	0.526674i	$0.823439\pi$
$762$	−26.3340	+	3.60460i	−0.953979	+	0.130581i
$763$	−14.1077	+	8.14510i	−0.510734	+	0.294873i
$764$	11.4835	−	6.62998i	0.415457	−	0.239864i
$765$	−24.6842	−	24.1823i	−0.892459	−	0.874314i
$766$	−28.8112			−1.04099
$767$	−10.0604	−	17.4250i	−0.363258	−	0.629182i
$768$	−1.36870	+	1.06145i	−0.0493886	+	0.0383017i
$769$	−21.8215	−	12.5987i	−0.786904	−	0.454319i	0.0519672	−	0.998649i	$-0.483451\pi$
$769$	−21.8215	−	12.5987i	−0.786904	−	0.454319i	−0.838872	+	0.544329i	$0.816784\pi$
$770$	−15.6198			−0.562900
$771$	9.93399	−	24.3355i	0.357764	−	0.876421i
$772$	−16.8148	−	9.70804i	−0.605179	−	0.349400i
$773$	−10.7705	−	18.6551i	−0.387389	−	0.670977i	0.604709	−	0.796447i	$-0.293290\pi$
$773$	−10.7705	−	18.6551i	−0.387389	−	0.670977i	−0.992097	+	0.125470i	$0.959956\pi$
$774$	13.9082	−	3.88022i	0.499921	−	0.139472i
$775$	17.4829	+	10.0938i	0.628005	+	0.362579i
$776$	−5.67776	−	9.83416i	−0.203820	−	0.353026i
$777$	−6.25398	+	25.0360i	−0.224360	+	0.898161i
$778$	7.02304	−	12.1643i	0.251788	−	0.436110i
$779$	13.0766	−	7.54976i	0.468517	−	0.270498i
$780$	6.24921	−	4.84638i	0.223758	−	0.173528i
$781$	−12.7189	+	22.0297i	−0.455117	+	0.788286i
$782$	6.45203	−	3.72508i	0.230724	−	0.133209i
$783$	9.25958	+	6.88112i	0.330910	+	0.245911i
$784$	0.500396	+	0.866710i	0.0178713	+	0.0309539i
$785$	32.5020	−	18.7650i	1.16005	−	0.669753i
$786$	13.4768	+	5.50136i	0.480701	+	0.196227i
$787$	−21.6421	+	37.4851i	−0.771456	+	1.33620i	0.165309	+	0.986242i	$0.447138\pi$
$787$	−21.6421	+	37.4851i	−0.771456	+	1.33620i	−0.936765	+	0.349959i	$0.886195\pi$
$788$	5.44571	−	9.43225i	0.193995	−	0.336010i
$789$	−1.75523	−	12.8231i	−0.0624878	−	0.456515i
$790$	4.37679	+	2.52694i	0.155719	+	0.0899044i
$791$			34.3080i			1.21985i
$792$	1.91547	+	6.86578i	0.0680631	+	0.243965i
$793$	−2.56817	+	4.44820i	−0.0911984	+	0.157960i
$794$			22.5599i			0.800622i
$795$	−13.1285	+	1.79703i	−0.465620	+	0.0637341i
$796$		−	1.68904i		−	0.0598663i
$797$	17.7951	−	10.2740i	0.630336	−	0.363924i	−0.150546	−	0.988603i	$-0.548103\pi$
$797$	17.7951	−	10.2740i	0.630336	−	0.363924i	0.780882	+	0.624678i	$0.214770\pi$
$798$	10.2023	−	7.91205i	0.361157	−	0.280083i
$799$		−	28.3645i		−	1.00346i
$800$			2.20394i			0.0779209i
$801$	−26.6223	+	27.1748i	−0.940652	+	0.960174i
$802$	−7.98455	+	13.8296i	−0.281944	+	0.488342i
$803$	−9.76071	−	16.9060i	−0.344448	−	0.596601i
$804$	−10.4288	+	8.08771i	−0.367795	+	0.285232i
$805$	5.70630	+	9.88360i	0.201121	+	0.348351i
$806$	13.4942	+	7.79090i	0.475314	+	0.274423i
$807$	−35.2886	+	27.3669i	−1.24222	+	0.963361i
$808$	−1.42819	+	0.824564i	−0.0502434	+	0.0290081i
$809$	−0.357979	+	0.206679i	−0.0125859	+	0.00726645i	−0.506280	−	0.862369i	$-0.668980\pi$
$809$	−0.357979	+	0.206679i	−0.0125859	+	0.00726645i	0.493694	+	0.869636i	$0.335646\pi$
$810$	−21.1635	−	11.6458i	−0.743609	−	0.409193i
$811$	−11.3793	−	19.7095i	−0.399581	−	0.692095i	0.594093	−	0.804396i	$-0.297511\pi$
$811$	−11.3793	−	19.7095i	−0.399581	−	0.692095i	−0.993674	+	0.112301i	$0.964178\pi$
$812$		−	5.43797i		−	0.190835i
$813$	−1.06891	−	7.80912i	−0.0374884	−	0.273878i
$814$	−14.3055	+	2.05645i	−0.501408	+	0.0720785i
$815$	26.0489	−	45.1180i	0.912452	−	1.58041i
$816$	7.36450	−	1.00805i	0.257809	−	0.0352889i
$817$	7.32386	−	12.6853i	0.256229	−	0.443802i
$818$	−9.48200	−	16.4233i	−0.331530	−	0.574227i
$819$	8.74743	−	8.92897i	0.305660	−	0.312004i
$820$			13.3170i			0.465048i
$821$	2.36326	−	4.09329i	0.0824785	−	0.142857i	−0.821835	−	0.569725i	$-0.807050\pi$
$821$	2.36326	−	4.09329i	0.0824785	−	0.142857i	0.904314	+	0.426868i	$0.140383\pi$
$822$	0.927797	−	2.27284i	0.0323606	−	0.0792745i
$823$	3.24511	+	5.62070i	0.113118	+	0.195925i	0.917026	−	0.398828i	$-0.130583\pi$
$823$	3.24511	+	5.62070i	0.113118	+	0.195925i	−0.803908	+	0.594753i	$0.797250\pi$
$824$	5.72502	−	9.91602i	0.199440	−	0.345441i
$825$	8.39724	+	3.42784i	0.292354	+	0.119342i
$826$	28.9706			1.00801
$827$	14.2193	−	8.20952i	0.494454	−	0.285473i	−0.231966	−	0.972724i	$-0.574516\pi$
$827$	14.2193	−	8.20952i	0.494454	−	0.285473i	0.726420	+	0.687251i	$0.241183\pi$
$828$	3.64462	−	3.72026i	0.126659	−	0.129288i
$829$	15.8340	+	9.14174i	0.549936	+	0.317506i	0.749096	−	0.662461i	$-0.230488\pi$
$829$	15.8340	+	9.14174i	0.549936	+	0.317506i	−0.199160	+	0.979967i	$0.563821\pi$
$830$	4.86164			0.168750
$831$	−30.4574	+	4.16902i	−1.05656	+	0.144622i
$832$			1.70111i			0.0589755i
$833$		−	4.29494i		−	0.148811i
$834$	−6.65178	+	16.2950i	−0.230332	+	0.564250i
$835$	−57.4424			−1.98788
$836$	6.26208	+	3.61541i	0.216578	+	0.125042i
$837$	5.48481	−	47.2785i	0.189583	−	1.63418i
$838$	0.641900	−	0.370601i	0.0221741	−	0.0128022i
$839$	−8.51309			−0.293904			−0.146952	−	0.989144i	$-0.546946\pi$
$839$	−8.51309			−0.293904			−0.146952	+	0.989144i	$0.546946\pi$
$840$	1.54420	+	11.2814i	0.0532798	+	0.389244i
$841$	−12.0354	+	20.8459i	−0.415013	+	0.718824i
$842$	14.7535	+	25.5538i	0.508440	+	0.880643i
$843$	−1.05789	−	1.36410i	−0.0364356	−	0.0469822i
$844$	−7.46471	+	12.9293i	−0.256946	+	0.445044i
$845$			27.1252i			0.933136i
$846$	−5.32834	−	19.0989i	−0.183192	−	0.656632i
$847$	6.55768	+	11.3582i	0.225324	+	0.390273i
$848$	1.42518	−	2.46849i	0.0489410	−	0.0847682i
$849$	−14.0401	−	18.1042i	−0.481855	−	0.621334i
$850$	4.72914	−	8.19111i	0.162208	−	0.280953i
$851$	6.52739	+	8.30069i	0.223756	+	0.284544i
$852$	17.1683	+	7.00827i	0.588176	+	0.240100i
$853$		−	51.1356i		−	1.75085i	−0.483355	−	0.875424i	$-0.660582\pi$
$853$		−	51.1356i		−	1.75085i	0.483355	−	0.875424i	$-0.339418\pi$
$854$	−3.69775	−	6.40469i	−0.126534	−	0.219164i
$855$	−23.6033	+	6.58504i	−0.807217	+	0.225203i
$856$	−13.6629	+	7.88827i	−0.466988	+	0.269615i
$857$	45.9203	−	26.5121i	1.56861	−	0.905636i	0.572276	−	0.820061i	$-0.306061\pi$
$857$	45.9203	−	26.5121i	1.56861	−	0.905636i	0.996332	−	0.0855748i	$-0.0272727\pi$
$858$	6.48143	+	2.64579i	0.221272	+	0.0903257i
$859$	−6.02487	−	3.47846i	−0.205566	−	0.118684i	0.393683	−	0.919246i	$-0.371201\pi$
$859$	−6.02487	−	3.47846i	−0.205566	−	0.118684i	−0.599249	+	0.800563i	$0.704534\pi$
$860$	6.45924	+	11.1877i	0.220258	+	0.381499i
$861$	2.85455	+	20.8544i	0.0972827	+	0.710715i
$862$	−9.19198	−	15.9210i	−0.313080	−	0.542271i
$863$	−22.7321	+	39.3732i	−0.773811	+	1.34028i	0.161649	+	0.986848i	$0.448319\pi$
$863$	−22.7321	+	39.3732i	−0.773811	+	1.34028i	−0.935460	+	0.353432i	$0.885014\pi$
$864$	4.76942	−	2.06220i	0.162259	−	0.0701574i
$865$		−	30.3376i		−	1.03151i
$866$		−	0.767638i		−	0.0260854i
$867$	−2.27281	−	0.927782i	−0.0771885	−	0.0315091i
$868$	−19.4295	+	11.2176i	−0.659481	+	0.380751i
$869$			4.47388i			0.151766i
$870$	−3.90078	+	9.55582i	−0.132249	+	0.323973i
$871$			12.9617i			0.439189i
$872$	−3.32544	+	5.75984i	−0.112614	+	0.195053i
$873$	9.15455	+	32.8135i	0.309834	+	1.11057i
$874$		−	5.28318i		−	0.178706i
$875$	−15.9188	−	9.19071i	−0.538153	−	0.310703i
$876$	−11.2454	+	8.72099i	−0.379946	+	0.294655i
$877$	15.8749	−	27.4961i	0.536058	−	0.928479i	−0.463054	−	0.886330i	$-0.653246\pi$
$877$	15.8749	−	27.4961i	0.536058	−	0.928479i	0.999111	−	0.0421487i	$-0.0134203\pi$
$878$	17.3911	−	30.1223i	0.586921	−	1.01658i
$879$	−3.25018	+	2.52057i	−0.109626	+	0.0850168i
$880$	−5.52281	+	3.18860i	−0.186174	+	0.107488i
$881$	9.91394	+	17.1714i	0.334009	+	0.578521i	0.983294	−	0.182025i	$-0.0582650\pi$
$881$	9.91394	+	17.1714i	0.334009	+	0.578521i	−0.649285	+	0.760545i	$0.724932\pi$
$882$	−0.806814	−	2.89194i	−0.0271668	−	0.0973766i
$883$	−14.3326	+	8.27491i	−0.482329	+	0.278473i	−0.721387	−	0.692532i	$-0.756495\pi$
$883$	−14.3326	+	8.27491i	−0.482329	+	0.278473i	0.239057	+	0.971005i	$0.423162\pi$
$884$	3.65020	−	6.32233i	0.122770	−	0.212643i
$885$	−50.9082	−	20.7812i	−1.71126	−	0.698554i
$886$	−19.0281	+	10.9859i	−0.639260	+	0.369077i
$887$	−16.8661	+	29.2130i	−0.566310	+	0.980877i	0.430617	+	0.902535i	$0.358296\pi$
$887$	−16.8661	+	29.2130i	−0.566310	+	0.980877i	−0.996927	+	0.0783421i	$0.975037\pi$
$888$	2.89952	+	10.1288i	0.0973016	+	0.339901i
$889$	−18.7933	−	32.5510i	−0.630308	−	1.09172i
$890$	−29.4755	−	17.0177i	−0.988020	−	0.570434i
$891$	−0.439201	−	21.3794i	−0.0147138	−	0.716237i
$892$	−8.24868	−	14.2871i	−0.276186	−	0.478368i
$893$	−17.4195	−	10.0572i	−0.582921	−	0.336550i
$894$	11.5447	−	1.58023i	0.386111	−	0.0528510i
$895$	−25.8118			−0.862793
$896$	−2.12118	−	1.22466i	−0.0708637	−	0.0409132i
$897$	−0.693675	−	5.06776i	−0.0231611	−	0.169207i
$898$	−7.31479	−	12.6696i	−0.244098	−	0.422789i
$899$	−20.3364			−0.678258
$900$	1.64558	−	6.40375i	0.0548527	−	0.213458i
$901$	−10.5936	+	6.11623i	−0.352925	+	0.203761i
$902$	−10.2093	+	5.89433i	−0.339932	+	0.196260i
$903$	12.5133	+	16.1354i	0.416417	+	0.536954i
$904$	7.00356	+	12.1305i	0.232935	+	0.403455i
$905$	−39.6914	+	22.9158i	−1.31939	+	0.761748i
$906$	−11.0140	+	1.50760i	−0.365916	+	0.0500867i
$907$	−10.2269	−	5.90449i	−0.339578	−	0.196055i	0.320507	−	0.947246i	$-0.396147\pi$
$907$	−10.2269	−	5.90449i	−0.339578	−	0.196055i	−0.660085	+	0.751191i	$0.729480\pi$
$908$	15.7235	+	9.07796i	0.521802	+	0.301263i
$909$	4.76540	−	1.32949i	0.158058	−	0.0440963i
$910$	9.68492	+	5.59159i	0.321052	+	0.185359i
$911$	−44.4717	+	25.6757i	−1.47341	+	0.850675i	−0.999552	−	0.0299251i	$-0.990473\pi$
$911$	−44.4717	+	25.6757i	−1.47341	+	0.850675i	−0.473860	+	0.880600i	$0.657140\pi$
$912$	1.99214	−	4.88018i	0.0659664	−	0.161599i
$913$	2.15185	+	3.72712i	0.0712160	+	0.123350i
$914$	−11.5039	+	19.9253i	−0.380515	+	0.659071i
$915$	1.90360	+	13.9070i	0.0629310	+	0.459753i
$916$	9.39009			0.310257
$917$			20.5845i			0.679760i
$918$	−22.1509	−	2.56975i	−0.731090	−	0.0848143i
$919$			16.1532i			0.532845i	0.963856	+	0.266423i	$0.0858417\pi$
$919$			16.1532i			0.532845i	−0.963856	+	0.266423i	$0.914158\pi$
$920$	4.03523	+	2.32974i	0.133037	+	0.0768092i
$921$	43.6059	−	33.8172i	1.43686	−	1.11431i
$922$	25.8568			0.851548
$923$	15.7724	−	9.10621i	0.519155	−	0.299735i
$924$	−7.96523	+	6.17718i	−0.262037	+	0.203214i
$925$	12.4456	+	4.98283i	0.409208	+	0.163835i
$926$	22.5548			0.741198
$927$	−24.0385	+	24.5374i	−0.789526	+	0.805912i
$928$	−1.11009	−	1.92274i	−0.0364406	−	0.0631171i
$929$	−9.71068	+	16.8194i	−0.318597	+	0.551826i	−0.980196	−	0.198032i	$-0.936545\pi$
$929$	−9.71068	+	16.8194i	−0.318597	+	0.551826i	0.661599	+	0.749858i	$0.269878\pi$
$930$	42.1890	−	5.77484i	1.38343	−	0.189364i
$931$	−2.63765	−	1.52285i	−0.0864455	−	0.0499093i
$932$	−14.3014			−0.468457
$933$	22.5896	−	55.3381i	0.739549	−	1.81169i
$934$	−27.8214			−0.910344
$935$	27.3680			0.895029
$936$	1.27015	−	4.94276i	0.0415161	−	0.161559i
$937$	−26.6721	+	46.1974i	−0.871339	+	1.50920i	−0.0107260	+	0.999942i	$0.503414\pi$
$937$	−26.6721	+	46.1974i	−0.871339	+	1.50920i	−0.860613	+	0.509260i	$0.829919\pi$
$938$	−16.1624	−	9.33134i	−0.527720	−	0.304679i
$939$	−33.5318	−	43.2379i	−1.09427	−	1.41102i
$940$	15.3631	−	8.86986i	0.501088	−	0.289303i
$941$	19.5726	+	33.9008i	0.638049	+	1.10513i	0.985860	+	0.167569i	$0.0535916\pi$
$941$	19.5726	+	33.9008i	0.638049	+	1.10513i	−0.347811	+	0.937565i	$0.613075\pi$
$942$	9.15316	−	22.4227i	0.298226	−	0.730570i
$943$	7.45939	+	4.30668i	0.242911	+	0.140245i
$944$	10.2433	−	5.91398i	0.333391	−	0.192484i
$945$	3.93649	−	33.9321i	0.128054	−	1.10381i
$946$	−5.71796	+	9.90380i	−0.185907	+	0.322000i
$947$		−	47.7416i		−	1.55139i	−0.631106	−	0.775697i	$-0.717399\pi$
$947$		−	47.7416i		−	1.55139i	0.631106	−	0.775697i	$-0.282601\pi$
$948$	3.23124	−	0.442293i	0.104946	−	0.0143650i
$949$			13.9766i			0.453698i
$950$	−3.35361	−	5.80862i	−0.108805	−	0.188456i
$951$	6.05278	−	4.69404i	0.196275	−	0.152215i
$952$	5.25570	+	9.10313i	0.170338	+	0.295034i
$953$	−5.27791	+	9.14160i	−0.170968	+	0.296126i	−0.938759	−	0.344575i	$-0.888023\pi$
$953$	−5.27791	+	9.14160i	−0.170968	+	0.296126i	0.767790	+	0.640701i	$0.221356\pi$
$954$	−5.98412	+	6.10831i	−0.193743	+	0.197764i
$955$	−17.7950	−	30.8218i	−0.575832	−	0.997370i
$956$	13.2361	−	7.64189i	0.428087	−	0.247156i
$957$	−9.05241	+	1.23910i	−0.292623	+	0.0400543i
$958$	−38.8746			−1.25598
$959$	3.47155			0.112102
$960$	2.84894	+	3.67360i	0.0919492	+	0.118565i
$961$	26.4507	+	45.8139i	0.853247	+	1.47787i
$962$	9.60616	+	3.84601i	0.309715	+	0.124000i
$963$	45.5887	−	12.7187i	1.46907	−	0.409853i
$964$	3.27950	+	1.89342i	0.105625	+	0.0609829i
$965$	−26.0565	+	45.1312i	−0.838790	+	1.45283i
$966$	6.81856	+	2.78340i	0.219383	+	0.0895546i
$967$		−	59.3677i		−	1.90914i	−0.297994	−	0.954568i	$-0.596318\pi$
$967$		−	59.3677i		−	1.90914i	0.297994	−	0.954568i	$-0.403682\pi$
$968$	4.63728	+	2.67734i	0.149048	+	0.0860528i
$969$	−17.8757	+	13.8629i	−0.574251	+	0.445342i
$970$	−26.3950	+	15.2392i	−0.847494	+	0.489301i
$971$	−25.4424	+	44.0676i	−0.816487	+	1.41420i	0.0917686	+	0.995780i	$0.470748\pi$
$971$	−25.4424	+	44.0676i	−0.816487	+	1.41420i	−0.908255	+	0.418416i	$0.862585\pi$
$972$	−15.3978	+	2.43080i	−0.493884	+	0.0779680i
$973$	−24.8891			−0.797906
$974$	−3.06171			−0.0981034
$975$	−3.97952	−	5.13144i	−0.127447	−	0.164338i
$976$	−2.61487	−	1.50970i	−0.0837001	−	0.0483243i
$977$	−24.4110	+	14.0937i	−0.780978	+	0.450898i	−0.836777	−	0.547544i	$-0.815563\pi$
$977$	−24.4110	+	14.0937i	−0.780978	+	0.450898i	0.0557986	+	0.998442i	$0.482230\pi$
$978$	−4.55936	−	33.3092i	−0.145792	−	1.06511i
$979$		−	30.1294i		−	0.962939i
$980$	2.32626	−	1.34307i	0.0743098	−	0.0429028i
$981$	13.9630	−	14.2528i	0.445805	−	0.455057i
$982$	−20.0951	−	11.6019i	−0.641259	−	0.370231i
$983$	44.4059			1.41633			0.708164	−	0.706048i	$-0.249524\pi$
$983$	44.4059			1.41633			0.708164	+	0.706048i	$0.249524\pi$
$984$	5.26646	+	6.79090i	0.167889	+	0.216486i
$985$	−25.3163	−	14.6164i	−0.806644	−	0.465716i
$986$			9.52803i			0.303434i
$987$	22.1573	−	17.1833i	0.705273	−	0.546952i
$988$	−2.58849	−	4.48340i	−0.0823509	−	0.142636i
$989$	8.35563			0.265694
$990$	18.4279	−	5.14114i	0.585676	−	0.163396i
$991$			22.1297i			0.702973i	0.936193	+	0.351486i	$0.114324\pi$
$991$			22.1297i			0.702973i	−0.936193	+	0.351486i	$0.885676\pi$
$992$	−4.57988	+	7.93259i	−0.145411	+	0.251860i
$993$	13.4901	+	17.3950i	0.428096	+	0.552013i
$994$			26.2229i			0.831741i
$995$	−4.53340			−0.143718
$996$	2.47916	−	1.92264i	0.0785553	−	0.0609210i
$997$		−	22.0162i		−	0.697260i	−0.937260	−	0.348630i	$-0.886647\pi$
$997$		−	22.0162i		−	0.697260i	0.937260	−	0.348630i	$-0.113353\pi$
$998$	−6.91284			−0.218822
$999$	−0.862113	−	31.5952i	−0.0272760	−	0.999628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.5	✓	76
3.2	odd	2		1998.2.k.a.1063.36		76
9.2	odd	6		1998.2.t.a.397.35		76
9.7	even	3		666.2.t.a.619.18	yes	76
37.11	even	6		666.2.t.a.85.18	yes	76
111.11	odd	6		1998.2.t.a.307.35		76
333.11	odd	6		1998.2.k.a.1639.3		76
333.196	even	6	inner	666.2.k.a.529.24	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.5	✓	76	1.1	even	1	trivial
666.2.k.a.529.24	yes	76	333.196	even	6	inner
666.2.t.a.85.18	yes	76	37.11	even	6
666.2.t.a.619.18	yes	76	9.7	even	3
1998.2.k.a.1063.36		76	3.2	odd	2
1998.2.k.a.1639.3		76	333.11	odd	6
1998.2.t.a.307.35		76	111.11	odd	6
1998.2.t.a.397.35		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} +(-1.36870 + 1.06145i) q^{3} -1.00000 q^{4} +2.68401i q^{5} +(1.06145 + 1.36870i) q^{6} +(-1.22466 + 2.12118i) q^{7} +1.00000i q^{8} +(0.746656 - 2.90560i) q^{9} +2.68401 q^{10} +(1.18799 + 2.05767i) q^{11} +(1.36870 - 1.06145i) q^{12} -1.70111i q^{13} +(2.12118 + 1.22466i) q^{14} +(-2.84894 - 3.67360i) q^{15} +1.00000 q^{16} +(-3.71658 - 2.14577i) q^{17} +(-2.90560 - 0.746656i) q^{18} +(-2.63557 + 1.52164i) q^{19} -2.68401i q^{20} +(-0.575330 - 4.20317i) q^{21} +(2.05767 - 1.18799i) q^{22} +(-1.50343 - 0.868005i) q^{23} +(-1.06145 - 1.36870i) q^{24} -2.20394 q^{25} -1.70111 q^{26} +(2.06220 + 4.76942i) q^{27} +(1.22466 - 2.12118i) q^{28} +(1.92274 - 1.11009i) q^{29} +(-3.67360 + 2.84894i) q^{30} +(-7.93259 - 4.57988i) q^{31} -1.00000i q^{32} +(-3.81011 - 1.55533i) q^{33} +(-2.14577 + 3.71658i) q^{34} +(-5.69328 - 3.28702i) q^{35} +(-0.746656 + 2.90560i) q^{36} +(-5.64698 - 2.26088i) q^{37} +(1.52164 + 2.63557i) q^{38} +(1.80564 + 2.32831i) q^{39} -2.68401 q^{40} -4.96158 q^{41} +(-4.20317 + 0.575330i) q^{42} +(-4.16828 + 2.40656i) q^{43} +(-1.18799 - 2.05767i) q^{44} +(7.79867 + 2.00404i) q^{45} +(-0.868005 + 1.50343i) q^{46} +(3.30470 + 5.72391i) q^{47} +(-1.36870 + 1.06145i) q^{48} +(0.500396 + 0.866710i) q^{49} +2.20394i q^{50} +(7.36450 - 1.00805i) q^{51} +1.70111i q^{52} +(1.42518 - 2.46849i) q^{53} +(4.76942 - 2.06220i) q^{54} +(-5.52281 + 3.18860i) q^{55} +(-2.12118 - 1.22466i) q^{56} +(1.99214 - 4.88018i) q^{57} +(-1.11009 - 1.92274i) q^{58} +(10.2433 - 5.91398i) q^{59} +(2.84894 + 3.67360i) q^{60} +(-2.61487 - 1.50970i) q^{61} +(-4.57988 + 7.93259i) q^{62} +(5.24890 + 5.14218i) q^{63} -1.00000 q^{64} +4.56582 q^{65} +(-1.55533 + 3.81011i) q^{66} -7.61951 q^{67} +(3.71658 + 2.14577i) q^{68} +(2.97908 - 0.407777i) q^{69} +(-3.28702 + 5.69328i) q^{70} +(5.35309 + 9.27182i) q^{71} +(2.90560 + 0.746656i) q^{72} -8.21612 q^{73} +(-2.26088 + 5.64698i) q^{74} +(3.01652 - 2.33936i) q^{75} +(2.63557 - 1.52164i) q^{76} -5.81958 q^{77} +(2.32831 - 1.80564i) q^{78} +(1.63069 + 0.941477i) q^{79} +2.68401i q^{80} +(-7.88501 - 4.33897i) q^{81} +4.96158i q^{82} +1.81133 q^{83} +(0.575330 + 4.20317i) q^{84} +(5.75928 - 9.97537i) q^{85} +(2.40656 + 4.16828i) q^{86} +(-1.45334 + 3.56027i) q^{87} +(-2.05767 + 1.18799i) q^{88} +(-10.9819 - 6.34038i) q^{89} +(2.00404 - 7.79867i) q^{90} +(3.60837 + 2.08329i) q^{91} +(1.50343 + 0.868005i) q^{92} +(15.7186 - 2.15157i) q^{93} +(5.72391 - 3.30470i) q^{94} +(-4.08412 - 7.07390i) q^{95} +(1.06145 + 1.36870i) q^{96} +(-9.83416 + 5.67776i) q^{97} +(0.866710 - 0.500396i) q^{98} +(6.86578 - 1.91547i) 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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