LMFDB - Embedded newform 966.2.k.b.367.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(229,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("966.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			367.1
Character	$\chi$	$=$	966.367
Dual form			966.2.k.b.229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.02969 - 3.51552i) q^{5} -1.00000i q^{6} +(2.03303 - 1.69316i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.02969 - 3.51552i) q^{5} -1.00000i q^{6} +(2.03303 - 1.69316i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.02969 - 3.51552i) q^{10} +(-4.89939 - 2.82867i) q^{11} +(0.866025 - 0.500000i) q^{12} +1.68666i q^{13} +(2.48284 + 0.914071i) q^{14} +4.05937i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.577549 + 1.00034i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(3.27848 + 5.67849i) q^{19} +4.05937 q^{20} +(-2.60723 + 0.449810i) q^{21} -5.65733i q^{22} +(-3.50171 + 3.27690i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-5.73924 + 9.94066i) q^{25} +(-1.46069 + 0.843329i) q^{26} -1.00000i q^{27} +(0.449810 + 2.60723i) q^{28} -6.42612 q^{29} +(-3.51552 + 2.02969i) q^{30} +(-2.49704 - 1.44167i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.82867 + 4.89939i) q^{33} -1.15510 q^{34} +(-10.0788 - 3.71055i) q^{35} -1.00000 q^{36} +(1.89767 - 1.09562i) q^{37} +(-3.27848 + 5.67849i) q^{38} +(0.843329 - 1.46069i) q^{39} +(2.02969 + 3.51552i) q^{40} +5.70186i q^{41} +(-1.69316 - 2.03303i) q^{42} -1.32493i q^{43} +(4.89939 - 2.82867i) q^{44} +(2.02969 - 3.51552i) q^{45} +(-4.58873 - 1.39412i) q^{46} +(3.82275 - 2.20707i) q^{47} +1.00000i q^{48} +(1.26639 - 6.88449i) q^{49} -11.4785 q^{50} +(1.00034 - 0.577549i) q^{51} +(-1.46069 - 0.843329i) q^{52} +(-1.85774 - 1.07256i) q^{53} +(0.866025 - 0.500000i) q^{54} +22.9652i q^{55} +(-2.03303 + 1.69316i) q^{56} -6.55695i q^{57} +(-3.21306 - 5.56519i) q^{58} +(6.54465 + 3.77855i) q^{59} +(-3.51552 - 2.02969i) q^{60} +(-5.20534 - 9.01591i) q^{61} -2.88334i q^{62} +(2.48284 + 0.914071i) q^{63} +1.00000 q^{64} +(5.92947 - 3.42338i) q^{65} +(-2.82867 + 4.89939i) q^{66} +(-4.92805 - 2.84521i) q^{67} +(-0.577549 - 1.00034i) q^{68} +(4.67101 - 1.08702i) q^{69} +(-1.82594 - 10.5837i) q^{70} -7.18784 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-9.62590 - 5.55752i) q^{73} +(1.89767 + 1.09562i) q^{74} +(9.94066 - 5.73924i) q^{75} -6.55695 q^{76} +(-14.7500 + 2.54472i) q^{77} +1.68666 q^{78} +(-9.79501 + 5.65515i) q^{79} +(-2.02969 + 3.51552i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.93795 + 2.85093i) q^{82} -0.847910 q^{83} +(0.914071 - 2.48284i) q^{84} +4.68897 q^{85} +(1.14742 - 0.662464i) q^{86} +(5.56519 + 3.21306i) q^{87} +(4.89939 + 2.82867i) q^{88} +(6.80960 + 11.7946i) q^{89} +4.05937 q^{90} +(2.85579 + 3.42902i) q^{91} +(-1.08702 - 4.67101i) q^{92} +(1.44167 + 2.49704i) q^{93} +(3.82275 + 2.20707i) q^{94} +(13.3085 - 23.0511i) q^{95} +(-0.866025 + 0.500000i) q^{96} +4.92590 q^{97} +(6.59534 - 2.34552i) q^{98} -5.65733i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.02969	−	3.51552i	−0.907703	−	1.57219i	−0.817248	−	0.576287i	$-0.804501\pi$
$5$	−2.02969	−	3.51552i	−0.907703	−	1.57219i	−0.0904552	−	0.995901i	$-0.528832\pi$
$6$		−	1.00000i		−	0.408248i
$7$	2.03303	−	1.69316i	0.768412	−	0.639956i
$7$	2.03303	−	1.69316i	0.768412	−	0.639956i
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.02969	−	3.51552i	0.641843	−	1.11170i
$11$	−4.89939	−	2.82867i	−1.47722	−	0.852875i	−0.477554	−	0.878603i	$-0.658476\pi$
$11$	−4.89939	−	2.82867i	−1.47722	−	0.852875i	−0.999669	+	0.0257278i	$0.991810\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$			1.68666i			0.467795i	0.972261	+	0.233897i	$0.0751480\pi$
$13$			1.68666i			0.467795i	−0.972261	+	0.233897i	$0.924852\pi$
$14$	2.48284	+	0.914071i	0.663566	+	0.244296i
$15$			4.05937i			1.04812i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.577549	+	1.00034i	−0.140076	+	0.242619i	−0.927525	−	0.373761i	$-0.878068\pi$
$17$	−0.577549	+	1.00034i	−0.140076	+	0.242619i	0.787449	+	0.616380i	$0.211401\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	3.27848	+	5.67849i	0.752134	+	1.30273i	0.946787	+	0.321862i	$0.104309\pi$
$19$	3.27848	+	5.67849i	0.752134	+	1.30273i	−0.194653	+	0.980872i	$0.562358\pi$
$20$	4.05937			0.907703
$21$	−2.60723	+	0.449810i	−0.568945	+	0.0981565i
$22$		−	5.65733i		−	1.20615i
$23$	−3.50171	+	3.27690i	−0.730156	+	0.683280i
$23$	−3.50171	+	3.27690i	−0.730156	+	0.683280i
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−5.73924	+	9.94066i	−1.14785	+	1.98813i
$26$	−1.46069	+	0.843329i	−0.286465	+	0.165390i
$27$		−	1.00000i		−	0.192450i
$28$	0.449810	+	2.60723i	0.0850061	+	0.492721i
$29$	−6.42612			−1.19330			−0.596651	−	0.802501i	$-0.703502\pi$
$29$	−6.42612			−1.19330			−0.596651	+	0.802501i	$0.703502\pi$
$30$	−3.51552	+	2.02969i	−0.641843	+	0.370568i
$31$	−2.49704	−	1.44167i	−0.448482	−	0.258931i	0.258707	−	0.965956i	$-0.416704\pi$
$31$	−2.49704	−	1.44167i	−0.448482	−	0.258931i	−0.707189	+	0.707025i	$0.750037\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.82867	+	4.89939i	0.492408	+	0.852875i
$34$	−1.15510			−0.198098
$35$	−10.0788	−	3.71055i	−1.70362	−	0.627198i
$36$	−1.00000			−0.166667
$37$	1.89767	−	1.09562i	0.311975	−	0.180119i	−0.335835	−	0.941921i	$-0.609018\pi$
$37$	1.89767	−	1.09562i	0.311975	−	0.180119i	0.647810	+	0.761802i	$0.275685\pi$
$38$	−3.27848	+	5.67849i	−0.531839	+	0.921172i
$39$	0.843329	−	1.46069i	0.135041	−	0.233897i
$40$	2.02969	+	3.51552i	0.320921	+	0.555852i
$41$			5.70186i			0.890480i	0.895411	+	0.445240i	$0.146882\pi$
$41$			5.70186i			0.890480i	−0.895411	+	0.445240i	$0.853118\pi$
$42$	−1.69316	−	2.03303i	−0.261261	−	0.313703i
$43$		−	1.32493i		−	0.202049i	−0.994884	−	0.101025i	$-0.967788\pi$
$43$		−	1.32493i		−	0.202049i	0.994884	−	0.101025i	$-0.0322121\pi$
$44$	4.89939	−	2.82867i	0.738611	−	0.426437i
$45$	2.02969	−	3.51552i	0.302568	−	0.524062i
$46$	−4.58873	−	1.39412i	−0.676571	−	0.205551i
$47$	3.82275	−	2.20707i	0.557606	−	0.321934i	−0.194578	−	0.980887i	$-0.562334\pi$
$47$	3.82275	−	2.20707i	0.557606	−	0.321934i	0.752184	+	0.658953i	$0.229000\pi$
$48$			1.00000i			0.144338i
$49$	1.26639	−	6.88449i	0.180913	−	0.983499i
$50$	−11.4785			−1.62330
$51$	1.00034	−	0.577549i	0.140076	−	0.0808731i
$52$	−1.46069	−	0.843329i	−0.202561	−	0.116949i
$53$	−1.85774	−	1.07256i	−0.255180	−	0.147328i	0.366954	−	0.930239i	$-0.380401\pi$
$53$	−1.85774	−	1.07256i	−0.255180	−	0.147328i	−0.622134	+	0.782911i	$0.713734\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$			22.9652i			3.09663i
$56$	−2.03303	+	1.69316i	−0.271675	+	0.226259i
$57$		−	6.55695i		−	0.868489i
$58$	−3.21306	−	5.56519i	−0.421896	−	0.730745i
$59$	6.54465	+	3.77855i	0.852041	+	0.491926i	0.861339	−	0.508031i	$-0.169626\pi$
$59$	6.54465	+	3.77855i	0.852041	+	0.491926i	−0.00929818	+	0.999957i	$0.502960\pi$
$60$	−3.51552	−	2.02969i	−0.453851	−	0.262031i
$61$	−5.20534	−	9.01591i	−0.666476	−	1.15437i	−0.978883	−	0.204421i	$-0.934469\pi$
$61$	−5.20534	−	9.01591i	−0.666476	−	1.15437i	0.312407	−	0.949948i	$-0.398865\pi$
$62$		−	2.88334i		−	0.366184i
$63$	2.48284	+	0.914071i	0.312808	+	0.115162i
$64$	1.00000			0.125000
$65$	5.92947	−	3.42338i	0.735461	−	0.424618i
$66$	−2.82867	+	4.89939i	−0.348185	+	0.603074i
$67$	−4.92805	−	2.84521i	−0.602057	−	0.347598i	0.167793	−	0.985822i	$-0.446336\pi$
$67$	−4.92805	−	2.84521i	−0.602057	−	0.347598i	−0.769851	+	0.638224i	$0.779669\pi$
$68$	−0.577549	−	1.00034i	−0.0700381	−	0.121310i
$69$	4.67101	−	1.08702i	0.562324	−	0.130862i
$70$	−1.82594	−	10.5837i	−0.218242	−	1.26500i
$71$	−7.18784			−0.853040			−0.426520	−	0.904478i	$-0.640261\pi$
$71$	−7.18784			−0.853040			−0.426520	+	0.904478i	$0.640261\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−9.62590	−	5.55752i	−1.12663	−	0.650458i	−0.183542	−	0.983012i	$-0.558756\pi$
$73$	−9.62590	−	5.55752i	−1.12663	−	0.650458i	−0.943084	+	0.332554i	$0.892090\pi$
$74$	1.89767	+	1.09562i	0.220600	+	0.127363i
$75$	9.94066	−	5.73924i	1.14785	−	0.662711i
$76$	−6.55695			−0.752134
$77$	−14.7500	+	2.54472i	−1.68092	+	0.289998i
$78$	1.68666			0.190976
$79$	−9.79501	+	5.65515i	−1.10202	+	0.636254i	−0.936752	−	0.349994i	$-0.886184\pi$
$79$	−9.79501	+	5.65515i	−1.10202	+	0.636254i	−0.165272	+	0.986248i	$0.552850\pi$
$80$	−2.02969	+	3.51552i	−0.226926	+	0.393047i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.93795	+	2.85093i	−0.545306	+	0.314832i
$83$	−0.847910			−0.0930702			−0.0465351	−	0.998917i	$-0.514818\pi$
$83$	−0.847910			−0.0930702			−0.0465351	+	0.998917i	$0.514818\pi$
$84$	0.914071	−	2.48284i	0.0997333	−	0.270900i
$85$	4.68897			0.508591
$86$	1.14742	−	0.662464i	0.123730	−	0.0714353i
$87$	5.56519	+	3.21306i	0.596651	+	0.344476i
$88$	4.89939	+	2.82867i	0.522277	+	0.301537i
$89$	6.80960	+	11.7946i	0.721817	+	1.25022i	0.960271	+	0.279069i	$0.0900259\pi$
$89$	6.80960	+	11.7946i	0.721817	+	1.25022i	−0.238454	+	0.971154i	$0.576641\pi$
$90$	4.05937			0.427895
$91$	2.85579	+	3.42902i	0.299368	+	0.359459i
$92$	−1.08702	−	4.67101i	−0.113330	−	0.486987i
$93$	1.44167	+	2.49704i	0.149494	+	0.258931i
$94$	3.82275	+	2.20707i	0.394287	+	0.227642i
$95$	13.3085	−	23.0511i	1.36543	−	2.36499i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	4.92590			0.500149			0.250075	−	0.968227i	$-0.419545\pi$
$97$	4.92590			0.500149			0.250075	+	0.968227i	$0.419545\pi$
$98$	6.59534	−	2.34552i	0.666230	−	0.236933i
$99$		−	5.65733i		−	0.568583i
$100$	−5.73924	−	9.94066i	−0.573924	−	0.994066i
$101$	−6.94536	−	4.00991i	−0.691089	−	0.399001i	0.112931	−	0.993603i	$-0.463976\pi$
$101$	−6.94536	−	4.00991i	−0.691089	−	0.399001i	−0.804020	+	0.594602i	$0.797310\pi$
$102$	1.00034	+	0.577549i	0.0990489	+	0.0571859i
$103$	3.81453	+	6.60696i	0.375857	+	0.651003i	0.990455	−	0.137837i	$-0.0440150\pi$
$103$	3.81453	+	6.60696i	0.375857	+	0.651003i	−0.614598	+	0.788841i	$0.710682\pi$
$104$		−	1.68666i		−	0.165390i
$105$	6.87318	+	8.25281i	0.670754	+	0.805391i
$106$		−	2.14513i		−	0.208353i
$107$	6.14656	−	3.54872i	0.594210	−	0.343067i	−0.172550	−	0.985001i	$-0.555201\pi$
$107$	6.14656	−	3.54872i	0.594210	−	0.343067i	0.766761	+	0.641933i	$0.221867\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−15.1271	−	8.73364i	−1.44891	−	0.836531i	−0.450497	−	0.892778i	$-0.648753\pi$
$109$	−15.1271	−	8.73364i	−1.44891	−	0.836531i	−0.998417	+	0.0562469i	$0.982087\pi$
$110$	−19.8884	+	11.4826i	−1.89629	+	1.09482i
$111$	−2.19124			−0.207983
$112$	−2.48284	−	0.914071i	−0.234606	−	0.0863715i
$113$		−	8.83766i		−	0.831377i	−0.909507	−	0.415688i	$-0.863541\pi$
$113$		−	8.83766i		−	0.831377i	0.909507	−	0.415688i	$-0.136459\pi$
$114$	5.67849	−	3.27848i	0.531839	−	0.307057i
$115$	18.6274	+	5.65923i	1.73701	+	0.527726i
$116$	3.21306	−	5.56519i	0.298325	−	0.516715i
$117$	−1.46069	+	0.843329i	−0.135041	+	0.0779658i
$118$			7.55711i			0.695688i
$119$	0.519575	+	3.01161i	0.0476293	+	0.276074i
$120$		−	4.05937i		−	0.370568i
$121$	10.5027	+	18.1912i	0.954791	+	1.65375i
$122$	5.20534	−	9.01591i	0.471269	−	0.816262i
$123$	2.85093	−	4.93795i	0.257060	−	0.445240i
$124$	2.49704	−	1.44167i	0.224241	−	0.129466i
$125$	26.2986			2.35222
$126$	0.449810	+	2.60723i	0.0400722	+	0.232271i
$127$	−6.74682			−0.598683			−0.299342	−	0.954146i	$-0.596767\pi$
$127$	−6.74682			−0.598683			−0.299342	+	0.954146i	$0.596767\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−0.662464	+	1.14742i	−0.0583267	+	0.101025i
$130$	5.92947	+	3.42338i	0.520049	+	0.300251i
$131$	4.79326	−	2.76739i	0.418789	−	0.241788i	−0.275770	−	0.961224i	$-0.588933\pi$
$131$	4.79326	−	2.76739i	0.418789	−	0.241788i	0.694559	+	0.719436i	$0.255600\pi$
$132$	−5.65733			−0.492408
$133$	16.2798	+	5.99352i	1.41164	+	0.519704i
$134$		−	5.69042i		−	0.491578i
$135$	−3.51552	+	2.02969i	−0.302568	+	0.174687i
$136$	0.577549	−	1.00034i	0.0495244	−	0.0857789i
$137$	−15.9415	−	9.20385i	−1.36198	−	0.786338i	−0.372090	−	0.928197i	$-0.621359\pi$
$137$	−15.9415	−	9.20385i	−1.36198	−	0.786338i	−0.989887	+	0.141859i	$0.954692\pi$
$138$	3.27690	+	3.50171i	0.278948	+	0.298085i
$139$		−	20.4754i		−	1.73670i	−0.495950	−	0.868351i	$-0.665180\pi$
$139$		−	20.4754i		−	1.73670i	0.495950	−	0.868351i	$-0.334820\pi$
$140$	8.25281	−	6.87318i	0.697489	−	0.580890i
$141$	−4.41413			−0.371737
$142$	−3.59392	−	6.22486i	−0.301595	−	0.522378i
$143$	4.77099	−	8.26360i	0.398970	−	0.691037i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	13.0430	+	22.5912i	1.08316	+	1.87609i
$146$		−	11.1150i		−	0.919887i
$147$	−4.53897	+	5.32895i	−0.374368	+	0.439524i
$148$			2.19124i			0.180119i
$149$	−13.7082	+	7.91446i	−1.12302	+	0.648378i	−0.942171	−	0.335132i	$-0.891219\pi$
$149$	−13.7082	+	7.91446i	−1.12302	+	0.648378i	−0.180852	+	0.983510i	$0.557886\pi$
$150$	9.94066	+	5.73924i	0.811652	+	0.468607i
$151$	7.74316	−	13.4115i	0.630129	−	1.09142i	−0.357396	−	0.933953i	$-0.616335\pi$
$151$	7.74316	−	13.4115i	0.630129	−	1.09142i	0.987525	−	0.157463i	$-0.0503314\pi$
$152$	−3.27848	−	5.67849i	−0.265919	−	0.460586i
$153$	−1.15510			−0.0933842
$154$	−9.57879	−	11.5015i	−0.771881	−	0.926818i
$155$			11.7045i			0.940130i
$156$	0.843329	+	1.46069i	0.0675203	+	0.116949i
$157$	2.07407	−	3.59239i	0.165529	−	0.286704i	−0.771314	−	0.636455i	$-0.780400\pi$
$157$	2.07407	−	3.59239i	0.165529	−	0.286704i	0.936843	+	0.349750i	$0.113734\pi$
$158$	−9.79501	−	5.65515i	−0.779249	−	0.449900i
$159$	1.07256	+	1.85774i	0.0850599	+	0.147328i
$160$	−4.05937			−0.320921
$161$	−1.57073	+	12.5910i	−0.123791	+	0.992308i
$162$	−1.00000			−0.0785674
$163$	10.4256	+	18.0576i	0.816593	+	1.41438i	0.908178	+	0.418584i	$0.137473\pi$
$163$	10.4256	+	18.0576i	0.816593	+	1.41438i	−0.0915851	+	0.995797i	$0.529193\pi$
$164$	−4.93795	−	2.85093i	−0.385589	−	0.222620i
$165$	11.4826	−	19.8884i	0.893919	−	1.54831i
$166$	−0.423955	−	0.734312i	−0.0329053	−	0.0569936i
$167$			10.9872i			0.850212i	0.905144	+	0.425106i	$0.139763\pi$
$167$			10.9872i			0.850212i	−0.905144	+	0.425106i	$0.860237\pi$
$168$	2.60723	−	0.449810i	0.201153	−	0.0347036i
$169$	10.1552			0.781168
$170$	2.34449	+	4.06077i	0.179814	+	0.311447i
$171$	−3.27848	+	5.67849i	−0.250711	+	0.434245i
$172$	1.14742	+	0.662464i	0.0874900	+	0.0505124i
$173$	1.79243	−	1.03486i	0.136276	−	0.0786789i	−0.430312	−	0.902680i	$-0.641596\pi$
$173$	1.79243	−	1.03486i	0.136276	−	0.0786789i	0.566588	+	0.824001i	$0.308263\pi$
$174$			6.42612i			0.487163i
$175$	5.16313	+	29.9271i	0.390296	+	2.26228i
$176$			5.65733i			0.426437i
$177$	−3.77855	−	6.54465i	−0.284014	−	0.491926i
$178$	−6.80960	+	11.7946i	−0.510401	+	0.884041i
$179$	2.79957	−	4.84900i	0.209250	−	0.362431i	−0.742229	−	0.670147i	$-0.766231\pi$
$179$	2.79957	−	4.84900i	0.209250	−	0.362431i	0.951478	+	0.307715i	$0.0995645\pi$
$180$	2.02969	+	3.51552i	0.151284	+	0.262031i
$181$	−22.5958			−1.67954			−0.839768	−	0.542946i	$-0.817309\pi$
$181$	−22.5958			−1.67954			−0.839768	+	0.542946i	$0.817309\pi$
$182$	−1.54172	+	4.18769i	−0.114280	+	0.310413i
$183$			10.4107i			0.769580i
$184$	3.50171	−	3.27690i	0.258149	−	0.241576i
$185$	−7.70334	−	4.44753i	−0.566361	−	0.326989i
$186$	−1.44167	+	2.49704i	−0.105708	+	0.183092i
$187$	5.65928	−	3.26739i	0.413848	−	0.238935i
$188$			4.41413i			0.321934i
$189$	−1.69316	−	2.03303i	−0.123160	−	0.147881i
$190$	26.6171			1.93101
$191$	4.57461	−	2.64115i	0.331007	−	0.191107i	−0.325281	−	0.945617i	$-0.605459\pi$
$191$	4.57461	−	2.64115i	0.331007	−	0.191107i	0.656288	+	0.754510i	$0.272126\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−13.3588	+	23.1381i	−0.961587	+	1.66552i	−0.243071	+	0.970009i	$0.578155\pi$
$193$	−13.3588	+	23.1381i	−0.961587	+	1.66552i	−0.718517	+	0.695510i	$0.755179\pi$
$194$	2.46295	+	4.26595i	0.176829	+	0.306278i
$195$	−6.84677			−0.490307
$196$	5.32895	+	4.53897i	0.380639	+	0.324212i
$197$	14.1605			1.00889			0.504447	−	0.863443i	$-0.331696\pi$
$197$	14.1605			1.00889			0.504447	+	0.863443i	$0.331696\pi$
$198$	4.89939	−	2.82867i	0.348185	−	0.201025i
$199$	−11.6374	+	20.1566i	−0.824955	+	1.42886i	0.0769991	+	0.997031i	$0.475466\pi$
$199$	−11.6374	+	20.1566i	−0.824955	+	1.42886i	−0.901954	+	0.431832i	$0.857867\pi$
$200$	5.73924	−	9.94066i	0.405826	−	0.702911i
$201$	2.84521	+	4.92805i	0.200686	+	0.347598i
$202$		−	8.01981i		−	0.564272i
$203$	−13.0645	+	10.8805i	−0.916947	+	0.763660i
$204$			1.15510i			0.0808731i
$205$	20.0450	−	11.5730i	1.40000	−	0.808292i
$206$	−3.81453	+	6.60696i	−0.265771	+	0.460329i
$207$	−4.58873	−	1.39412i	−0.318939	−	0.0968978i
$208$	1.46069	−	0.843329i	0.101281	−	0.0584743i
$209$		−	37.0948i		−	2.56590i
$210$	−3.71055	+	10.0788i	−0.256052	+	0.695500i
$211$	−2.59509			−0.178653			−0.0893266	−	0.996002i	$-0.528471\pi$
$211$	−2.59509			−0.178653			−0.0893266	+	0.996002i	$0.528471\pi$
$212$	1.85774	−	1.07256i	0.127590	−	0.0736640i
$213$	6.22486	+	3.59392i	0.426520	+	0.246251i
$214$	6.14656	+	3.54872i	0.420170	+	0.242585i
$215$	−4.65780	+	2.68918i	−0.317660	+	0.183401i
$216$			1.00000i			0.0680414i
$217$	−7.51753	+	1.29695i	−0.510323	+	0.0880429i
$218$		−	17.4673i		−	1.18303i
$219$	5.55752	+	9.62590i	0.375542	+	0.650458i
$220$	−19.8884	−	11.4826i	−1.34088	−	0.774157i
$221$	−1.68724	−	0.974128i	−0.113496	−	0.0655269i
$222$	−1.09562	−	1.89767i	−0.0735332	−	0.127363i
$223$		−	11.5831i		−	0.775664i	−0.921730	−	0.387832i	$-0.873224\pi$
$223$		−	11.5831i		−	0.775664i	0.921730	−	0.387832i	$-0.126776\pi$
$224$	−0.449810	−	2.60723i	−0.0300542	−	0.174203i
$225$	−11.4785			−0.765232
$226$	7.65364	−	4.41883i	0.509112	−	0.293936i
$227$	3.86164	−	6.68855i	0.256306	−	0.443935i	−0.708943	−	0.705265i	$-0.750828\pi$
$227$	3.86164	−	6.68855i	0.256306	−	0.443935i	0.965249	+	0.261330i	$0.0841612\pi$
$228$	5.67849	+	3.27848i	0.376067	+	0.217122i
$229$	−11.0002	−	19.0529i	−0.726912	−	1.25905i	−0.958182	−	0.286158i	$-0.907622\pi$
$229$	−11.0002	−	19.0529i	−0.726912	−	1.25905i	0.231271	−	0.972889i	$-0.425712\pi$
$230$	4.41263	+	18.9614i	0.290961	+	1.25028i
$231$	14.0462	+	5.17120i	0.924174	+	0.340240i
$232$	6.42612			0.421896
$233$	−11.7283	−	20.3141i	−0.768350	−	1.33082i	−0.938457	−	0.345395i	$-0.887745\pi$
$233$	−11.7283	−	20.3141i	−0.768350	−	1.33082i	0.170108	−	0.985425i	$-0.445588\pi$
$234$	−1.46069	−	0.843329i	−0.0954882	−	0.0551301i
$235$	−15.5180	−	8.95930i	−1.01228	−	0.584440i
$236$	−6.54465	+	3.77855i	−0.426020	+	0.245963i
$237$	11.3103			0.734683
$238$	−2.34835	+	1.95577i	−0.152221	+	0.126774i
$239$	14.2154			0.919516			0.459758	−	0.888044i	$-0.347936\pi$
$239$	14.2154			0.919516			0.459758	+	0.888044i	$0.347936\pi$
$240$	3.51552	−	2.02969i	0.226926	−	0.131016i
$241$	8.10166	−	14.0325i	0.521874	−	0.903912i	−0.477802	−	0.878467i	$-0.658566\pi$
$241$	8.10166	−	14.0325i	0.521874	−	0.903912i	0.999676	−	0.0254449i	$-0.00810022\pi$
$242$	−10.5027	+	18.1912i	−0.675139	+	1.16938i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	10.4107			0.666476
$245$	−26.7729	+	9.52133i	−1.71046	+	0.608295i
$246$	5.70186			0.363537
$247$	−9.57766	+	5.52967i	−0.609412	+	0.351844i
$248$	2.49704	+	1.44167i	0.158562	+	0.0915460i
$249$	0.734312	+	0.423955i	0.0465351	+	0.0268671i
$250$	13.1493	+	22.7752i	0.831634	+	1.44043i
$251$	10.0678			0.635475			0.317737	−	0.948179i	$-0.397077\pi$
$251$	10.0678			0.635475			0.317737	+	0.948179i	$0.397077\pi$
$252$	−2.03303	+	1.69316i	−0.128069	+	0.106659i
$253$	26.4255	−	6.14966i	1.66136	−	0.386626i
$254$	−3.37341	−	5.84292i	−0.211667	−	0.366617i
$255$	−4.06077	−	2.34449i	−0.254295	−	0.146817i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−17.1515	+	9.90240i	−1.06988	+	0.617695i	−0.928148	−	0.372211i	$-0.878600\pi$
$257$	−17.1515	+	9.90240i	−1.06988	+	0.617695i	−0.141730	+	0.989905i	$0.545267\pi$
$258$	−1.32493			−0.0824864
$259$	2.00295	−	5.44049i	0.124457	−	0.338055i
$260$			6.84677i			0.424618i
$261$	−3.21306	−	5.56519i	−0.198884	−	0.344476i
$262$	4.79326	+	2.76739i	0.296128	+	0.170970i
$263$	−11.6562	−	6.72970i	−0.718750	−	0.414971i	0.0955421	−	0.995425i	$-0.469542\pi$
$263$	−11.6562	−	6.72970i	−0.718750	−	0.414971i	−0.814293	+	0.580455i	$0.802875\pi$
$264$	−2.82867	−	4.89939i	−0.174092	−	0.301537i
$265$			8.70787i			0.534920i
$266$	2.94938	+	17.0955i	0.180838	+	1.04819i
$267$		−	13.6192i		−	0.833482i
$268$	4.92805	−	2.84521i	0.301029	−	0.173799i
$269$	−14.9189	−	8.61345i	−0.909624	−	0.525171i	−0.0293136	−	0.999570i	$-0.509332\pi$
$269$	−14.9189	−	8.61345i	−0.909624	−	0.525171i	−0.880310	+	0.474399i	$0.842665\pi$
$270$	−3.51552	−	2.02969i	−0.213948	−	0.123523i
$271$	17.3001	−	9.98824i	1.05091	−	0.606743i	0.128005	−	0.991773i	$-0.459143\pi$
$271$	17.3001	−	9.98824i	1.05091	−	0.606743i	0.922904	+	0.385031i	$0.125809\pi$
$272$	1.15510			0.0700381
$273$	−0.758675	−	4.39751i	−0.0459171	−	0.266150i
$274$		−	18.4077i		−	1.11205i
$275$	56.2376	−	32.4688i	3.39126	−	1.95794i
$276$	−1.39412	+	4.58873i	−0.0839160	+	0.276209i
$277$	−4.94088	+	8.55786i	−0.296869	+	0.514192i	−0.975418	−	0.220363i	$-0.929276\pi$
$277$	−4.94088	+	8.55786i	−0.296869	+	0.514192i	0.678549	+	0.734555i	$0.262609\pi$
$278$	17.7322	−	10.2377i	1.06351	−	0.614017i
$279$		−	2.88334i		−	0.172621i
$280$	10.0788	+	3.71055i	0.602321	+	0.221748i
$281$			19.4586i			1.16080i	0.814331	+	0.580400i	$0.197104\pi$
$281$			19.4586i			1.16080i	−0.814331	+	0.580400i	$0.802896\pi$
$282$	−2.20707	−	3.82275i	−0.131429	−	0.227642i
$283$	15.2174	−	26.3573i	0.904581	−	1.56678i	0.0831017	−	0.996541i	$-0.473517\pi$
$283$	15.2174	−	26.3573i	0.904581	−	1.56678i	0.821479	−	0.570239i	$-0.193149\pi$
$284$	3.59392	−	6.22486i	0.213260	−	0.369377i
$285$	−23.0511	+	13.3085i	−1.36543	+	0.788330i
$286$	9.54198			0.564229
$287$	9.65418	+	11.5920i	0.569868	+	0.684256i
$288$	1.00000			0.0589256
$289$	7.83287	+	13.5669i	0.460757	+	0.798055i
$290$	−13.0430	+	22.5912i	−0.765912	+	1.32660i
$291$	−4.26595	−	2.46295i	−0.250075	−	0.144381i
$292$	9.62590	−	5.55752i	0.563313	−	0.325229i
$293$	−15.7604			−0.920733			−0.460367	−	0.887729i	$-0.652282\pi$
$293$	−15.7604			−0.920733			−0.460367	+	0.887729i	$0.652282\pi$
$294$	−6.88449	−	1.26639i	−0.401512	−	0.0738575i
$295$		−	30.6771i		−	1.78609i
$296$	−1.89767	+	1.09562i	−0.110300	+	0.0636816i
$297$	−2.82867	+	4.89939i	−0.164136	+	0.284292i
$298$	−13.7082	−	7.91446i	−0.794097	−	0.458472i
$299$	−5.52701	−	5.90618i	−0.319635	−	0.341563i
$300$			11.4785i			0.662711i
$301$	−2.24332	−	2.69361i	−0.129303	−	0.155257i
$302$	15.4863			0.891137
$303$	4.00991	+	6.94536i	0.230363	+	0.399001i
$304$	3.27848	−	5.67849i	0.188033	−	0.325684i
$305$	−21.1304	+	36.5989i	−1.20992	+	2.09565i
$306$	−0.577549	−	1.00034i	−0.0330163	−	0.0571859i
$307$			7.88200i			0.449849i	0.974376	+	0.224925i	$0.0722136\pi$
$307$			7.88200i			0.449849i	−0.974376	+	0.224925i	$0.927786\pi$
$308$	5.17120	−	14.0462i	0.294656	−	0.800358i
$309$		−	7.62906i		−	0.434002i
$310$	−10.1364	+	5.85226i	−0.575710	+	0.332386i
$311$	15.8777	+	9.16702i	0.900345	+	0.519814i	0.877312	−	0.479921i	$-0.159335\pi$
$311$	15.8777	+	9.16702i	0.900345	+	0.519814i	0.0230326	+	0.999735i	$0.492668\pi$
$312$	−0.843329	+	1.46069i	−0.0477441	+	0.0826952i
$313$	−6.20167	−	10.7416i	−0.350539	−	0.607152i	0.635805	−	0.771850i	$-0.280668\pi$
$313$	−6.20167	−	10.7416i	−0.350539	−	0.607152i	−0.986344	+	0.164698i	$0.947335\pi$
$314$	4.14814			0.234093
$315$	−1.82594	−	10.5837i	−0.102880	−	0.596326i
$316$		−	11.3103i		−	0.636254i
$317$	1.83984	+	3.18670i	0.103336	+	0.178983i	0.913057	−	0.407832i	$-0.133715\pi$
$317$	1.83984	+	3.18670i	0.103336	+	0.178983i	−0.809721	+	0.586815i	$0.800382\pi$
$318$	−1.07256	+	1.85774i	−0.0601464	+	0.104177i
$319$	31.4841	+	18.1774i	1.76277	+	1.01774i
$320$	−2.02969	−	3.51552i	−0.113463	−	0.196523i
$321$	−7.09744			−0.396140
$322$	−11.6895	+	4.93520i	−0.651429	+	0.275028i
$323$	−7.57393			−0.421424
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−16.7665	−	9.68014i	−0.930038	−	0.536957i
$326$	−10.4256	+	18.0576i	−0.577419	+	1.00012i
$327$	8.73364	+	15.1271i	0.482971	+	0.836531i
$328$		−	5.70186i		−	0.314832i
$329$	4.03483	−	10.9596i	0.222447	−	0.604221i
$330$	22.9652			1.26419
$331$	−2.45413	−	4.25068i	−0.134891	−	0.233638i	0.790665	−	0.612249i	$-0.209735\pi$
$331$	−2.45413	−	4.25068i	−0.134891	−	0.233638i	−0.925556	+	0.378611i	$0.876402\pi$
$332$	0.423955	−	0.734312i	0.0232676	−	0.0403006i
$333$	1.89767	+	1.09562i	0.103992	+	0.0600396i
$334$	−9.51516	+	5.49358i	−0.520647	+	0.300595i
$335$			23.0995i			1.26206i
$336$	1.69316	+	2.03303i	0.0923697	+	0.110911i
$337$			17.4280i			0.949365i	0.880157	+	0.474682i	$0.157437\pi$
$337$			17.4280i			0.949365i	−0.880157	+	0.474682i	$0.842563\pi$
$338$	5.07759	+	8.79465i	0.276185	+	0.478366i
$339$	−4.41883	+	7.65364i	−0.239998	+	0.415688i
$340$	−2.34449	+	4.06077i	−0.127148	+	0.220226i
$341$	8.15599	+	14.1266i	0.441672	+	0.764998i
$342$	−6.55695			−0.354559
$343$	−9.08197	−	16.1406i	−0.490380	−	0.871509i
$344$			1.32493i			0.0714353i
$345$	−13.3021	−	14.2147i	−0.716163	−	0.765295i
$346$	1.79243	+	1.03486i	0.0963615	+	0.0556344i
$347$	5.46035	−	9.45761i	0.293127	−	0.507711i	−0.681420	−	0.731892i	$-0.738637\pi$
$347$	5.46035	−	9.45761i	0.293127	−	0.507711i	0.974547	+	0.224181i	$0.0719708\pi$
$348$	−5.56519	+	3.21306i	−0.298325	+	0.172238i
$349$		−	35.9929i		−	1.92665i	−0.268332	−	0.963327i	$-0.586472\pi$
$349$		−	35.9929i		−	1.92665i	0.268332	−	0.963327i	$-0.413528\pi$
$350$	−23.3361	+	19.4350i	−1.24737	+	1.03884i
$351$	1.68666			0.0900271
$352$	−4.89939	+	2.82867i	−0.261139	+	0.150768i
$353$	−4.71527	−	2.72237i	−0.250969	−	0.144897i	0.369239	−	0.929334i	$-0.379618\pi$
$353$	−4.71527	−	2.72237i	−0.250969	−	0.144897i	−0.620208	+	0.784438i	$0.712952\pi$
$354$	3.77855	−	6.54465i	0.200828	−	0.347844i
$355$	14.5891	+	25.2690i	0.774307	+	1.34114i
$356$	−13.6192			−0.721817
$357$	1.05584	−	2.86792i	0.0558811	−	0.151786i
$358$	5.59914			0.295924
$359$	11.5930	−	6.69322i	0.611855	−	0.353255i	−0.161836	−	0.986818i	$-0.551742\pi$
$359$	11.5930	−	6.69322i	0.611855	−	0.353255i	0.773691	+	0.633563i	$0.218408\pi$
$360$	−2.02969	+	3.51552i	−0.106974	+	0.185284i
$361$	−11.9968	+	20.7791i	−0.631411	+	1.09364i
$362$	−11.2979	−	19.5686i	−0.593805	−	1.02850i
$363$		−	21.0054i		−	1.10250i
$364$	−4.39751	+	0.758675i	−0.230492	+	0.0397654i
$365$			45.1200i			2.36169i
$366$	−9.01591	+	5.20534i	−0.471269	+	0.272087i
$367$	6.26456	−	10.8505i	0.327007	−	0.566393i	−0.654909	−	0.755708i	$-0.727293\pi$
$367$	6.26456	−	10.8505i	0.327007	−	0.566393i	0.981917	+	0.189314i	$0.0606265\pi$
$368$	4.58873	+	1.39412i	0.239204	+	0.0726733i
$369$	−4.93795	+	2.85093i	−0.257060	+	0.148413i
$370$		−	8.89505i		−	0.462432i
$371$	−5.59285	+	0.964899i	−0.290366	+	0.0500951i
$372$	−2.88334			−0.149494
$373$	−8.52214	+	4.92026i	−0.441260	+	0.254761i	−0.704132	−	0.710069i	$-0.748664\pi$
$373$	−8.52214	+	4.92026i	−0.441260	+	0.254761i	0.262872	+	0.964831i	$0.415330\pi$
$374$	5.65928	+	3.26739i	0.292635	+	0.168953i
$375$	−22.7752	−	13.1493i	−1.17611	−	0.679026i
$376$	−3.82275	+	2.20707i	−0.197143	+	0.113821i
$377$		−	10.8387i		−	0.558220i
$378$	0.914071	−	2.48284i	0.0470147	−	0.127703i
$379$		−	10.2772i		−	0.527903i	−0.964536	−	0.263951i	$-0.914974\pi$
$379$		−	10.2772i		−	0.527903i	0.964536	−	0.263951i	$-0.0850258\pi$
$380$	13.3085	+	23.0511i	0.682714	+	1.18250i
$381$	5.84292	+	3.37341i	0.299342	+	0.172825i
$382$	4.57461	+	2.64115i	0.234057	+	0.135133i
$383$	−8.84461	−	15.3193i	−0.451939	−	0.782781i	0.546568	−	0.837415i	$-0.315934\pi$
$383$	−8.84461	−	15.3193i	−0.451939	−	0.782781i	−0.998506	+	0.0546341i	$0.982601\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	38.8839	+	46.6889i	1.98170	+	2.37948i
$386$	−26.7176			−1.35989
$387$	1.14742	−	0.662464i	0.0583267	−	0.0336749i
$388$	−2.46295	+	4.26595i	−0.125037	+	0.216571i
$389$	−27.8127	−	16.0577i	−1.41016	−	0.814156i	−0.414757	−	0.909932i	$-0.636133\pi$
$389$	−27.8127	−	16.0577i	−1.41016	−	0.814156i	−0.995403	+	0.0957759i	$0.969467\pi$
$390$	−3.42338	−	5.92947i	−0.173350	−	0.300251i
$391$	−1.25562	−	5.39548i	−0.0634995	−	0.272861i
$392$	−1.26639	+	6.88449i	−0.0639625	+	0.347719i
$393$	−5.53478			−0.279193
$394$	7.08025	+	12.2634i	0.356698	+	0.617819i
$395$	39.7616	+	22.9563i	2.00062	+	1.15506i
$396$	4.89939	+	2.82867i	0.246204	+	0.142146i
$397$	−16.1963	+	9.35091i	−0.812867	+	0.469309i	−0.847950	−	0.530075i	$-0.822164\pi$
$397$	−16.1963	+	9.35091i	−0.812867	+	0.469309i	0.0350835	+	0.999384i	$0.488830\pi$
$398$	−23.2748			−1.16666
$399$	−11.1020	−	13.3305i	−0.555795	−	0.667357i
$400$	11.4785			0.573924
$401$	−14.8691	+	8.58467i	−0.742527	+	0.428698i	−0.822987	−	0.568060i	$-0.807694\pi$
$401$	−14.8691	+	8.58467i	−0.742527	+	0.428698i	0.0804605	+	0.996758i	$0.474361\pi$
$402$	−2.84521	+	4.92805i	−0.141906	+	0.245789i
$403$	2.43160	−	4.21165i	0.121127	−	0.209797i
$404$	6.94536	−	4.00991i	0.345545	−	0.199500i
$405$	4.05937			0.201712
$406$	−15.9550	−	5.87393i	−0.791834	−	0.291518i
$407$	−12.3966			−0.614475
$408$	−1.00034	+	0.577549i	−0.0495244	+	0.0285930i
$409$	−8.69664	−	5.02101i	−0.430021	−	0.248273i	0.269334	−	0.963047i	$-0.413196\pi$
$409$	−8.69664	−	5.02101i	−0.430021	−	0.248273i	−0.699356	+	0.714774i	$0.746530\pi$
$410$	20.0450	+	11.5730i	0.989951	+	0.571548i
$411$	9.20385	+	15.9415i	0.453992	+	0.786338i
$412$	−7.62906			−0.375857
$413$	19.7032	−	3.39926i	0.969529	−	0.167267i
$414$	−1.08702	−	4.67101i	−0.0534243	−	0.229568i
$415$	1.72099	+	2.98084i	0.0844801	+	0.146324i
$416$	1.46069	+	0.843329i	0.0716161	+	0.0413476i
$417$	−10.2377	+	17.7322i	−0.501343	+	0.868351i
$418$	32.1251	−	18.5474i	1.57129	−	0.907184i
$419$	36.7063			1.79322			0.896610	−	0.442821i	$-0.146022\pi$
$419$	36.7063			1.79322			0.896610	+	0.442821i	$0.146022\pi$
$420$	−10.5837	+	1.82594i	−0.516433	+	0.0890970i
$421$		−	1.74437i		−	0.0850155i	−0.999096	−	0.0425077i	$-0.986465\pi$
$421$		−	1.74437i		−	0.0850155i	0.999096	−	0.0425077i	$-0.0135347\pi$
$422$	−1.29754	−	2.24741i	−0.0631634	−	0.109402i
$423$	3.82275	+	2.20707i	0.185869	+	0.107311i
$424$	1.85774	+	1.07256i	0.0902196	+	0.0520883i
$425$	−6.62939	−	11.4824i	−0.321573	−	0.556980i
$426$			7.18784i			0.348252i
$427$	−25.8480	−	9.51610i	−1.25087	−	0.460516i
$428$			7.09744i			0.343067i
$429$	−8.26360	+	4.77099i	−0.398970	+	0.230346i
$430$	−4.65780	−	2.68918i	−0.224619	−	0.129684i
$431$	−12.3926	−	7.15487i	−0.596931	−	0.344638i	0.170903	−	0.985288i	$-0.445332\pi$
$431$	−12.3926	−	7.15487i	−0.596931	−	0.344638i	−0.767833	+	0.640650i	$0.778665\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	17.9359			0.861943			0.430972	−	0.902365i	$-0.358171\pi$
$433$	17.9359			0.861943			0.430972	+	0.902365i	$0.358171\pi$
$434$	−4.88196	−	5.86190i	−0.234342	−	0.281380i
$435$		−	26.0860i		−	1.25073i
$436$	15.1271	−	8.73364i	0.724457	−	0.418265i
$437$	−30.0881	−	9.14115i	−1.43931	−	0.437281i
$438$	−5.55752	+	9.62590i	−0.265548	+	0.459943i
$439$	−28.0581	+	16.1994i	−1.33914	+	0.773154i	−0.986680	−	0.162672i	$-0.947989\pi$
$439$	−28.0581	+	16.1994i	−1.33914	+	0.773154i	−0.352462	+	0.935826i	$0.614655\pi$
$440$		−	22.9652i		−	1.09482i
$441$	6.59534	−	2.34552i	0.314064	−	0.111691i
$442$		−	1.94826i		−	0.0926691i
$443$	−19.0976	−	33.0780i	−0.907355	−	1.57159i	−0.817724	−	0.575610i	$-0.804765\pi$
$443$	−19.0976	−	33.0780i	−0.907355	−	1.57159i	−0.0896309	−	0.995975i	$-0.528569\pi$
$444$	1.09562	−	1.89767i	0.0519958	−	0.0900594i
$445$	27.6427	−	47.8786i	1.31039	−	2.26966i
$446$	10.0313	−	5.79156i	0.474995	−	0.274239i
$447$	15.8289			0.748682
$448$	2.03303	−	1.69316i	0.0960515	−	0.0799945i
$449$	14.0922			0.665052			0.332526	−	0.943094i	$-0.392099\pi$
$449$	14.0922			0.665052			0.332526	+	0.943094i	$0.392099\pi$
$450$	−5.73924	−	9.94066i	−0.270551	−	0.468607i
$451$	16.1286	−	27.9356i	0.759468	−	1.31544i
$452$	7.65364	+	4.41883i	0.359997	+	0.207844i
$453$	−13.4115	+	7.74316i	−0.630129	+	0.363805i
$454$	7.72328			0.362471
$455$	6.25843	−	16.9994i	0.293400	−	0.796944i
$456$			6.55695i			0.307057i
$457$	−3.70638	+	2.13988i	−0.173377	+	0.100099i	−0.584177	−	0.811626i	$-0.698583\pi$
$457$	−3.70638	+	2.13988i	−0.173377	+	0.100099i	0.410800	+	0.911725i	$0.365249\pi$
$458$	11.0002	−	19.0529i	0.514004	−	0.890281i
$459$	1.00034	+	0.577549i	0.0466921	+	0.0269577i
$460$	−14.2147	+	13.3021i	−0.662765	+	0.620216i
$461$		−	7.14597i		−	0.332821i	−0.986057	−	0.166410i	$-0.946782\pi$
$461$		−	7.14597i		−	0.332821i	0.986057	−	0.166410i	$-0.0532177\pi$
$462$	2.54472	+	14.7500i	0.118391	+	0.686232i
$463$	2.83540			0.131772			0.0658861	−	0.997827i	$-0.479013\pi$
$463$	2.83540			0.131772			0.0658861	+	0.997827i	$0.479013\pi$
$464$	3.21306	+	5.56519i	0.149163	+	0.258357i
$465$	5.85226	−	10.1364i	0.271392	−	0.470065i
$466$	11.7283	−	20.3141i	0.543305	−	0.941032i
$467$	12.7367	+	22.0606i	0.589384	+	1.02084i	0.994313	+	0.106495i	$0.0339628\pi$
$467$	12.7367	+	22.0606i	0.589384	+	1.02084i	−0.404929	+	0.914348i	$0.632704\pi$
$468$		−	1.68666i		−	0.0779658i
$469$	−14.8363	+	2.55961i	−0.685075	+	0.118192i
$470$		−	17.9186i		−	0.826523i
$471$	−3.59239	+	2.07407i	−0.165529	+	0.0955680i
$472$	−6.54465	−	3.77855i	−0.301242	−	0.173922i
$473$	−3.74778	+	6.49134i	−0.172323	+	0.298472i
$474$	5.65515	+	9.79501i	0.259750	+	0.449900i
$475$	−75.2639			−3.45334
$476$	−2.86792	−	1.05584i	−0.131451	−	0.0483944i
$477$		−	2.14513i		−	0.0982187i
$478$	7.10768	+	12.3109i	0.325098	+	0.563086i
$479$	9.60900	−	16.6433i	0.439046	−	0.760450i	−0.558570	−	0.829457i	$-0.688650\pi$
$479$	9.60900	−	16.6433i	0.439046	−	0.760450i	0.997616	+	0.0690070i	$0.0219831\pi$
$480$	3.51552	+	2.02969i	0.160461	+	0.0926420i
$481$	1.84794	+	3.20072i	0.0842586	+	0.145940i
$482$	16.2033			0.738041
$483$	7.65579	−	10.1187i	0.348350	−	0.460419i
$484$	−21.0054			−0.954791
$485$	−9.99802	−	17.3171i	−0.453987	−	0.786328i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−15.1812	+	26.2947i	−0.687927	+	1.19152i	0.284580	+	0.958652i	$0.408146\pi$
$487$	−15.1812	+	26.2947i	−0.687927	+	1.19152i	−0.972507	+	0.232872i	$0.925188\pi$
$488$	5.20534	+	9.01591i	0.235635	+	0.408131i
$489$		−	20.8511i		−	0.942921i
$490$	−21.6322	−	18.4254i	−0.977242	−	0.832374i
$491$	8.50669			0.383902			0.191951	−	0.981405i	$-0.438519\pi$
$491$	8.50669			0.383902			0.191951	+	0.981405i	$0.438519\pi$
$492$	2.85093	+	4.93795i	0.128530	+	0.222620i
$493$	3.71140	−	6.42834i	0.167153	−	0.289518i
$494$	−9.57766	−	5.52967i	−0.430919	−	0.248791i
$495$	−19.8884	+	11.4826i	−0.893919	+	0.516105i
$496$			2.88334i			0.129466i
$497$	−14.6131	+	12.1702i	−0.655486	+	0.545908i
$498$			0.847910i			0.0379958i
$499$	−6.28157	−	10.8800i	−0.281202	−	0.487056i	0.690479	−	0.723352i	$-0.257400\pi$
$499$	−6.28157	−	10.8800i	−0.281202	−	0.487056i	−0.971681	+	0.236297i	$0.924066\pi$
$500$	−13.1493	+	22.7752i	−0.588054	+	1.01854i
$501$	5.49358	−	9.51516i	0.245435	−	0.425106i
$502$	5.03391	+	8.71899i	0.224674	+	0.389147i
$503$	−5.00925			−0.223351			−0.111676	−	0.993745i	$-0.535622\pi$
$503$	−5.00925			−0.223351			−0.111676	+	0.993745i	$0.535622\pi$
$504$	−2.48284	−	0.914071i	−0.110594	−	0.0407159i
$505$			32.5554i			1.44870i
$506$	18.5385	+	19.8103i	0.824137	+	0.880676i
$507$	−8.79465	−	5.07759i	−0.390584	−	0.225504i
$508$	3.37341	−	5.84292i	0.149671	−	0.259238i
$509$	16.2344	−	9.37291i	0.719575	−	0.415447i	−0.0950210	−	0.995475i	$-0.530292\pi$
$509$	16.2344	−	9.37291i	0.719575	−	0.415447i	0.814596	+	0.580028i	$0.196958\pi$
$510$		−	4.68897i		−	0.207631i
$511$	−28.9795	+	4.99965i	−1.28198	+	0.221172i
$512$	−1.00000			−0.0441942
$513$	5.67849	−	3.27848i	0.250711	−	0.144748i
$514$	−17.1515	−	9.90240i	−0.756518	−	0.436776i
$515$	15.4846	−	26.8201i	0.682333	−	1.18184i
$516$	−0.662464	−	1.14742i	−0.0291633	−	0.0505124i
$517$	−24.9722			−1.09828
$518$	5.71307	−	0.985641i	0.251018	−	0.0433066i
$519$	−2.06972			−0.0908505
$520$	−5.92947	+	3.42338i	−0.260025	+	0.150125i
$521$	−2.62697	+	4.55004i	−0.115090	+	0.199341i	−0.917816	−	0.397007i	$-0.870049\pi$
$521$	−2.62697	+	4.55004i	−0.115090	+	0.199341i	0.802726	+	0.596348i	$0.203382\pi$
$522$	3.21306	−	5.56519i	0.140632	−	0.243582i
$523$	9.66808	+	16.7456i	0.422755	+	0.732234i	0.996208	−	0.0870049i	$-0.0277296\pi$
$523$	9.66808	+	16.7456i	0.422755	+	0.732234i	−0.573452	+	0.819239i	$0.694396\pi$
$524$			5.53478i			0.241788i
$525$	10.4921	−	28.4992i	0.457915	−	1.24381i
$526$		−	13.4594i		−	0.586857i
$527$	2.88433	−	1.66527i	0.125643	−	0.0725402i
$528$	2.82867	−	4.89939i	0.123102	−	0.213219i
$529$	1.52388	−	22.9495i	0.0662555	−	0.997803i
$530$	−7.54124	+	4.35393i	−0.327570	+	0.189123i
$531$			7.55711i			0.327951i
$532$	−13.3305	+	11.1020i	−0.577948	+	0.481332i
$533$	−9.61708			−0.416562
$534$	11.7946	−	6.80960i	0.510401	−	0.294680i
$535$	−24.9512	−	14.4056i	−1.07873	−	0.622807i
$536$	4.92805	+	2.84521i	0.212859	+	0.122894i
$537$	−4.84900	+	2.79957i	−0.209250	+	0.120810i
$538$		−	17.2269i		−	0.742705i
$539$	−25.6785	+	30.1476i	−1.10605	+	1.29855i
$540$		−	4.05937i		−	0.174687i
$541$	−4.36382	−	7.55835i	−0.187615	−	0.324959i	0.756840	−	0.653601i	$-0.226742\pi$
$541$	−4.36382	−	7.55835i	−0.187615	−	0.324959i	−0.944455	+	0.328642i	$0.893409\pi$
$542$	17.3001	+	9.98824i	0.743105	+	0.429032i
$543$	19.5686	+	11.2979i	0.839768	+	0.484840i
$544$	0.577549	+	1.00034i	0.0247622	+	0.0428894i
$545$			70.9062i			3.03729i
$546$	3.42902	−	2.85579i	0.146748	−	0.122216i
$547$	−25.3827			−1.08529			−0.542643	−	0.839963i	$-0.682577\pi$
$547$	−25.3827			−1.08529			−0.542643	+	0.839963i	$0.682577\pi$
$548$	15.9415	−	9.20385i	0.680988	−	0.393169i
$549$	5.20534	−	9.01591i	0.222159	−	0.384790i
$550$	56.2376	+	32.4688i	2.39798	+	1.38447i
$551$	−21.0679	−	36.4907i	−0.897522	−	1.55455i
$552$	−4.67101	+	1.08702i	−0.198812	+	0.0462668i
$553$	−10.3384	+	28.0816i	−0.439634	+	1.19415i
$554$	−9.88176			−0.419836
$555$	4.44753	+	7.70334i	0.188787	+	0.326989i
$556$	17.7322	+	10.2377i	0.752014	+	0.434176i
$557$	−0.975085	−	0.562966i	−0.0413157	−	0.0238536i	0.479200	−	0.877706i	$-0.340927\pi$
$557$	−0.975085	−	0.562966i	−0.0413157	−	0.0238536i	−0.520516	+	0.853852i	$0.674260\pi$
$558$	2.49704	−	1.44167i	0.105708	−	0.0610307i
$559$	2.23470			0.0945177
$560$	1.82594	+	10.5837i	0.0771602	+	0.447244i
$561$	−6.53478			−0.275898
$562$	−16.8516	+	9.72928i	−0.710842	+	0.410405i
$563$	−21.1487	+	36.6307i	−0.891313	+	1.54380i	−0.0530108	+	0.998594i	$0.516882\pi$
$563$	−21.1487	+	36.6307i	−0.891313	+	1.54380i	−0.838302	+	0.545206i	$0.816452\pi$
$564$	2.20707	−	3.82275i	0.0929343	−	0.160967i
$565$	−31.0689	+	17.9377i	−1.30708	+	0.754643i
$566$	30.4348			1.27927
$567$	0.449810	+	2.60723i	0.0188902	+	0.109494i
$568$	7.18784			0.301595
$569$	25.2638	−	14.5861i	1.05911	−	0.611479i	0.133926	−	0.990991i	$-0.457242\pi$
$569$	25.2638	−	14.5861i	1.05911	−	0.611479i	0.925187	+	0.379512i	$0.123908\pi$
$570$	−23.0511	−	13.3085i	−0.965503	−	0.557434i
$571$	11.9062	+	6.87403i	0.498257	+	0.287669i	0.727994	−	0.685584i	$-0.240453\pi$
$571$	11.9062	+	6.87403i	0.498257	+	0.287669i	−0.229736	+	0.973253i	$0.573786\pi$
$572$	4.77099	+	8.26360i	0.199485	+	0.345518i
$573$	−5.28230			−0.220671
$574$	−5.21190	+	14.1568i	−0.217540	+	0.590892i
$575$	−12.4774	−	53.6162i	−0.520343	−	2.23595i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	24.2748	+	14.0150i	1.01057	+	0.583454i	0.911359	−	0.411613i	$-0.135034\pi$
$577$	24.2748	+	14.0150i	1.01057	+	0.583454i	0.0992124	+	0.995066i	$0.468368\pi$
$578$	−7.83287	+	13.5669i	−0.325805	+	0.564310i
$579$	23.1381	−	13.3588i	0.961587	−	0.555173i
$580$	−26.0860			−1.08316
$581$	−1.72382	+	1.43565i	−0.0715163	+	0.0595608i
$582$		−	4.92590i		−	0.204185i
$583$	6.06785	+	10.5098i	0.251305	+	0.435272i
$584$	9.62590	+	5.55752i	0.398323	+	0.229972i
$585$	5.92947	+	3.42338i	0.245154	+	0.141539i
$586$	−7.88021	−	13.6489i	−0.325528	−	0.563832i
$587$		−	1.89303i		−	0.0781337i	−0.999237	−	0.0390668i	$-0.987561\pi$
$587$		−	1.89303i		−	0.0781337i	0.999237	−	0.0390668i	$-0.0124385\pi$
$588$	−2.34552	−	6.59534i	−0.0967276	−	0.271987i
$589$		−	18.9059i		−	0.779004i
$590$	26.5672	−	15.3386i	1.09375	−	0.631478i
$591$	−12.2634	−	7.08025i	−0.504447	−	0.291243i
$592$	−1.89767	−	1.09562i	−0.0779937	−	0.0450297i
$593$	6.51640	−	3.76224i	0.267596	−	0.154497i	−0.360198	−	0.932876i	$-0.617291\pi$
$593$	6.51640	−	3.76224i	0.267596	−	0.154497i	0.627795	+	0.778379i	$0.283958\pi$
$594$	−5.65733			−0.232123
$595$	9.53281	−	7.93920i	0.390807	−	0.325475i
$596$		−	15.8289i		−	0.648378i
$597$	20.1566	−	11.6374i	0.824955	−	0.476288i
$598$	2.35140	−	7.73962i	0.0961558	−	0.316496i
$599$	23.1928	−	40.1711i	0.947631	−	1.64135i	0.197236	−	0.980356i	$-0.436803\pi$
$599$	23.1928	−	40.1711i	0.947631	−	1.64135i	0.750395	−	0.660990i	$-0.229863\pi$
$600$	−9.94066	+	5.73924i	−0.405826	+	0.234304i
$601$		−	5.74340i		−	0.234278i	−0.993116	−	0.117139i	$-0.962628\pi$
$601$		−	5.74340i		−	0.234278i	0.993116	−	0.117139i	$-0.0373723\pi$
$602$	1.21108	−	3.28958i	0.0493598	−	0.134073i
$603$		−	5.69042i		−	0.231732i
$604$	7.74316	+	13.4115i	0.315065	+	0.545708i
$605$	42.6344	−	73.8449i	1.73333	−	3.00222i
$606$	−4.00991	+	6.94536i	−0.162891	+	0.282136i
$607$	20.9112	−	12.0731i	0.848761	−	0.490033i	−0.0114715	−	0.999934i	$-0.503652\pi$
$607$	20.9112	−	12.0731i	0.848761	−	0.490033i	0.860233	+	0.509902i	$0.170318\pi$
$608$	6.55695			0.265919
$609$	16.7544	−	2.89053i	0.678923	−	0.117130i
$610$	−42.2608			−1.71109
$611$	3.72257	+	6.44767i	0.150599	+	0.260845i
$612$	0.577549	−	1.00034i	0.0233460	−	0.0404365i
$613$	2.02156	+	1.16715i	0.0816501	+	0.0471407i	0.540269	−	0.841492i	$-0.318322\pi$
$613$	2.02156	+	1.16715i	0.0816501	+	0.0471407i	−0.458619	+	0.888633i	$0.651656\pi$
$614$	−6.82601	+	3.94100i	−0.275475	+	0.159046i
$615$	−23.1459			−0.933335
$616$	14.7500	−	2.54472i	0.594294	−	0.102530i
$617$		−	3.06512i		−	0.123397i	−0.998095	−	0.0616986i	$-0.980348\pi$
$617$		−	3.06512i		−	0.123397i	0.998095	−	0.0616986i	$-0.0196518\pi$
$618$	6.60696	−	3.81453i	0.265771	−	0.153443i
$619$	−4.41751	+	7.65135i	−0.177555	+	0.307534i	−0.941042	−	0.338289i	$-0.890152\pi$
$619$	−4.41751	+	7.65135i	−0.177555	+	0.307534i	0.763488	+	0.645822i	$0.223485\pi$
$620$	−10.1364	−	5.85226i	−0.407088	−	0.235033i
$621$	3.27690	+	3.50171i	0.131497	+	0.140519i
$622$			18.3340i			0.735128i
$623$	33.8143	+	12.4489i	1.35474	+	0.498755i
$624$	−1.68666			−0.0675203
$625$	−24.6816	−	42.7498i	−0.987264	−	1.70999i
$626$	6.20167	−	10.7416i	0.247869	−	0.429321i
$627$	−18.5474	+	32.1251i	−0.740713	+	1.28295i
$628$	2.07407	+	3.59239i	0.0827643	+	0.143352i
$629$			2.53110i			0.100921i
$630$	8.25281	−	6.87318i	0.328800	−	0.273834i
$631$			5.70623i			0.227162i	0.993529	+	0.113581i	$0.0362321\pi$
$631$			5.70623i			0.227162i	−0.993529	+	0.113581i	$0.963768\pi$
$632$	9.79501	−	5.65515i	0.389624	−	0.224950i
$633$	2.24741	+	1.29754i	0.0893266	+	0.0515727i
$634$	−1.83984	+	3.18670i	−0.0730696	+	0.126560i
$635$	13.6939	+	23.7186i	0.543427	+	0.941242i
$636$	−2.14513			−0.0850599
$637$	11.6118	+	2.13597i	0.460076	+	0.0846302i
$638$			36.3547i			1.43930i
$639$	−3.59392	−	6.22486i	−0.142173	−	0.246251i
$640$	2.02969	−	3.51552i	0.0802303	−	0.138963i
$641$	5.46662	+	3.15616i	0.215919	+	0.124661i	0.604059	−	0.796940i	$-0.293549\pi$
$641$	5.46662	+	3.15616i	0.215919	+	0.124661i	−0.388140	+	0.921600i	$0.626882\pi$
$642$	−3.54872	−	6.14656i	−0.140057	−	0.242585i
$643$	−29.5677			−1.16604			−0.583019	−	0.812458i	$-0.698129\pi$
$643$	−29.5677			−1.16604			−0.583019	+	0.812458i	$0.698129\pi$
$644$	−10.1187	−	7.65579i	−0.398734	−	0.301680i
$645$	5.37837			0.211773
$646$	−3.78696	−	6.55921i	−0.148996	−	0.258069i
$647$	38.1119	+	22.0039i	1.49833	+	0.865063i	0.999998	−	0.00192095i	$-0.000611456\pi$
$647$	38.1119	+	22.0039i	1.49833	+	0.865063i	0.498335	+	0.866984i	$0.333945\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−21.3765	−	37.0252i	−0.839102	−	1.45337i
$650$		−	19.3603i		−	0.759372i
$651$	7.15885	+	2.63557i	0.280577	+	0.103296i
$652$	−20.8511			−0.816593
$653$	−8.76586	−	15.1829i	−0.343035	−	0.594154i	0.641960	−	0.766738i	$-0.278122\pi$
$653$	−8.76586	−	15.1829i	−0.343035	−	0.594154i	−0.984995	+	0.172585i	$0.944788\pi$
$654$	−8.73364	+	15.1271i	−0.341512	+	0.591517i
$655$	−19.4576	−	11.2339i	−0.760271	−	0.438943i
$656$	4.93795	−	2.85093i	0.192795	−	0.111310i
$657$		−	11.1150i		−	0.433639i
$658$	11.5087	−	1.98552i	0.448655	−	0.0774036i
$659$			46.8252i			1.82405i	0.410132	+	0.912026i	$0.365483\pi$
$659$			46.8252i			1.82405i	−0.410132	+	0.912026i	$0.634517\pi$
$660$	11.4826	+	19.8884i	0.446960	+	0.774157i
$661$	−19.0305	+	32.9619i	−0.740202	+	1.28207i	0.212201	+	0.977226i	$0.431937\pi$
$661$	−19.0305	+	32.9619i	−0.740202	+	1.28207i	−0.952403	+	0.304842i	$0.901396\pi$
$662$	2.45413	−	4.25068i	0.0953824	−	0.165207i
$663$	0.974128	+	1.68724i	0.0378320	+	0.0655269i
$664$	0.847910			0.0329053
$665$	−11.9726	−	69.3970i	−0.464279	−	2.69110i
$666$			2.19124i			0.0849088i
$667$	22.5024	−	21.0578i	0.871296	−	0.815360i
$668$	−9.51516	−	5.49358i	−0.368153	−	0.212553i
$669$	−5.79156	+	10.0313i	−0.223915	+	0.387832i
$670$	−20.0048	+	11.5498i	−0.772852	+	0.446206i
$671$			58.8967i			2.27368i
$672$	−0.914071	+	2.48284i	−0.0352610	+	0.0957775i
$673$	−45.8997			−1.76930			−0.884651	−	0.466254i	$-0.845603\pi$
$673$	−45.8997			−1.76930			−0.884651	+	0.466254i	$0.845603\pi$
$674$	−15.0931	+	8.71401i	−0.581365	+	0.335651i
$675$	9.94066	+	5.73924i	0.382616	+	0.220904i
$676$	−5.07759	+	8.79465i	−0.195292	+	0.338256i
$677$	7.26567	+	12.5845i	0.279242	+	0.483662i	0.971197	−	0.238279i	$-0.0765834\pi$
$677$	7.26567	+	12.5845i	0.279242	+	0.483662i	−0.691954	+	0.721941i	$0.743250\pi$
$678$	−8.83766			−0.339408
$679$	10.0145	−	8.34035i	0.384320	−	0.320073i
$680$	−4.68897			−0.179814
$681$	−6.68855	+	3.86164i	−0.256306	+	0.147978i
$682$	−8.15599	+	14.1266i	−0.312309	+	0.540935i
$683$	−23.3505	+	40.4443i	−0.893482	+	1.54756i	−0.0578106	+	0.998328i	$0.518412\pi$
$683$	−23.3505	+	40.4443i	−0.893482	+	1.54756i	−0.835672	+	0.549229i	$0.814921\pi$
$684$	−3.27848	−	5.67849i	−0.125356	−	0.217122i
$685$			74.7236i			2.85504i
$686$	9.43716	−	15.9355i	0.360312	−	0.608420i
$687$			22.0003i			0.839365i
$688$	−1.14742	+	0.662464i	−0.0437450	+	0.0252562i
$689$	1.80905	−	3.13336i	0.0689192	−	0.119372i
$690$	5.65923	−	18.6274i	0.215443	−	0.709131i
$691$	−0.0941465	+	0.0543555i	−0.00358150	+	0.00206778i	−0.501790	−	0.864990i	$-0.667325\pi$
$691$	−0.0941465	+	0.0543555i	−0.00358150	+	0.00206778i	0.498208	+	0.867057i	$0.333992\pi$
$692$			2.06972i			0.0786789i
$693$	−9.57879	−	11.5015i	−0.363868	−	0.436906i
$694$	10.9207			0.414544
$695$	−71.9817	+	41.5587i	−2.73042	+	1.57641i
$696$	−5.56519	−	3.21306i	−0.210948	−	0.121791i
$697$	−5.70382	−	3.29310i	−0.216048	−	0.124735i
$698$	31.1707	−	17.9964i	1.17983	−	0.681175i
$699$			23.4567i			0.887214i
$700$	−28.4992	−	10.4921i	−1.07717	−	0.396566i
$701$			21.6443i			0.817495i	0.912648	+	0.408747i	$0.134034\pi$
$701$			21.6443i			0.817495i	−0.912648	+	0.408747i	$0.865966\pi$
$702$	0.843329	+	1.46069i	0.0318294	+	0.0551301i
$703$	12.4429	+	7.18392i	0.469294	+	0.270947i
$704$	−4.89939	−	2.82867i	−0.184653	−	0.106609i
$705$	8.95930	+	15.5180i	0.337427	+	0.584440i
$706$		−	5.44473i		−	0.204915i
$707$	−20.9095	+	3.60739i	−0.786384	+	0.135670i
$708$	7.55711			0.284014
$709$	13.6161	−	7.86128i	0.511365	−	0.295237i	−0.222030	−	0.975040i	$-0.571268\pi$
$709$	13.6161	−	7.86128i	0.511365	−	0.295237i	0.733394	+	0.679803i	$0.237935\pi$
$710$	−14.5891	+	25.2690i	−0.547518	+	0.948328i
$711$	−9.79501	−	5.65515i	−0.367341	−	0.212085i
$712$	−6.80960	−	11.7946i	−0.255201	−	0.442021i
$713$	13.4681	−	3.13426i	0.504384	−	0.117379i
$714$	3.01161	−	0.519575i	0.112707	−	0.0194446i
$715$	−38.7344			−1.44859
$716$	2.79957	+	4.84900i	0.104625	+	0.181216i
$717$	−12.3109	−	7.10768i	−0.459758	−	0.265441i
$718$	11.5930	+	6.69322i	0.432647	+	0.249789i
$719$	19.1661	−	11.0655i	0.714775	−	0.412675i	−0.0980518	−	0.995181i	$-0.531261\pi$
$719$	19.1661	−	11.0655i	0.714775	−	0.412675i	0.812826	+	0.582506i	$0.197928\pi$
$720$	−4.05937			−0.151284
$721$	18.9417	+	6.97350i	0.705426	+	0.259707i
$722$	−23.9936			−0.892950
$723$	−14.0325	+	8.10166i	−0.521874	+	0.301304i
$724$	11.2979	−	19.5686i	0.419884	−	0.727260i
$725$	36.8811	−	63.8799i	1.36973	−	2.37244i
$726$	18.1912	−	10.5027i	0.675139	−	0.389792i
$727$	−5.61811			−0.208364			−0.104182	−	0.994558i	$-0.533222\pi$
$727$	−5.61811			−0.208364			−0.104182	+	0.994558i	$0.533222\pi$
$728$	−2.85579	−	3.42902i	−0.105843	−	0.127088i
$729$	−1.00000			−0.0370370
$730$	−39.0751	+	22.5600i	−1.44623	+	0.834984i
$731$	1.32538	+	0.765211i	0.0490211	+	0.0283023i
$732$	−9.01591	−	5.20534i	−0.333238	−	0.192395i
$733$	13.2866	+	23.0130i	0.490751	+	0.850006i	0.999943	−	0.0106469i	$-0.00338909\pi$
$733$	13.2866	+	23.0130i	0.490751	+	0.850006i	−0.509192	+	0.860653i	$0.670056\pi$
$734$	12.5291			0.462458
$735$	27.9467	+	5.14076i	1.03083	+	0.189620i
$736$	1.08702	+	4.67101i	0.0400683	+	0.172176i
$737$	16.0963	+	27.8796i	0.592915	+	1.02696i
$738$	−4.93795	−	2.85093i	−0.181769	−	0.104944i
$739$	−9.73154	+	16.8555i	−0.357981	+	0.620041i	−0.987623	−	0.156844i	$-0.949868\pi$
$739$	−9.73154	+	16.8555i	−0.357981	+	0.620041i	0.629643	+	0.776885i	$0.283201\pi$
$740$	7.70334	−	4.44753i	0.283180	−	0.163494i
$741$	11.0593			0.406275
$742$	−3.63205	−	4.36110i	−0.133337	−	0.160101i
$743$			45.3501i			1.66373i	0.554975	+	0.831867i	$0.312728\pi$
$743$			45.3501i			1.66373i	−0.554975	+	0.831867i	$0.687272\pi$
$744$	−1.44167	−	2.49704i	−0.0528541	−	0.0915460i
$745$	55.6468	+	32.1277i	2.03874	+	1.17707i
$746$	−8.52214	−	4.92026i	−0.312018	−	0.180144i
$747$	−0.423955	−	0.734312i	−0.0155117	−	0.0268671i
$748$			6.53478i			0.238935i
$749$	6.48756	−	17.6218i	0.237050	−	0.643885i
$750$		−	26.2986i		−	0.960288i
$751$	29.0897	−	16.7950i	1.06150	−	0.612857i	0.135652	−	0.990756i	$-0.456687\pi$
$751$	29.0897	−	16.7950i	1.06150	−	0.612857i	0.925847	+	0.377900i	$0.123354\pi$
$752$	−3.82275	−	2.20707i	−0.139401	−	0.0804834i
$753$	−8.71899	−	5.03391i	−0.317737	−	0.183446i
$754$	9.38657	−	5.41934i	0.341839	−	0.197361i
$755$	−62.8647			−2.28788
$756$	2.60723	−	0.449810i	0.0948242	−	0.0163594i
$757$		−	12.3995i		−	0.450669i	−0.974281	−	0.225335i	$-0.927652\pi$
$757$		−	12.3995i		−	0.450669i	0.974281	−	0.225335i	$-0.0723475\pi$
$758$	8.90029	−	5.13858i	0.323273	−	0.186642i
$759$	−25.9600	−	7.88698i	−0.942287	−	0.286279i
$760$	−13.3085	+	23.0511i	−0.482752	+	0.836150i
$761$	−3.23071	+	1.86525i	−0.117113	+	0.0676152i	−0.557412	−	0.830236i	$-0.688206\pi$
$761$	−3.23071	+	1.86525i	−0.117113	+	0.0676152i	0.440299	+	0.897851i	$0.354872\pi$
$762$			6.74682i			0.244411i
$763$	−45.5413	+	7.85695i	−1.64871	+	0.284441i
$764$			5.28230i			0.191107i
$765$	2.34449	+	4.06077i	0.0847651	+	0.146817i
$766$	8.84461	−	15.3193i	0.319569	−	0.553510i
$767$	−6.37313	+	11.0386i	−0.230120	+	0.398580i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	22.5407			0.812837			0.406418	−	0.913687i	$-0.366778\pi$
$769$	22.5407			0.812837			0.406418	+	0.913687i	$0.366778\pi$
$770$	−20.9918	+	57.0188i	−0.756493	+	2.05482i
$771$	19.8048			0.713252
$772$	−13.3588	−	23.1381i	−0.480794	−	0.832759i
$773$	−1.13116	+	1.95922i	−0.0406850	+	0.0704684i	−0.885651	−	0.464352i	$-0.846287\pi$
$773$	−1.13116	+	1.95922i	−0.0406850	+	0.0704684i	0.844966	+	0.534820i	$0.179621\pi$
$774$	1.14742	+	0.662464i	0.0412432	+	0.0238118i
$775$	28.6623	−	16.5482i	1.02958	−	0.594428i
$776$	−4.92590			−0.176829
$777$	−4.45485	+	3.71013i	−0.159817	+	0.133100i
$778$		−	32.1153i		−	1.15139i
$779$	−32.3779	+	18.6934i	−1.16006	+	0.669761i
$780$	3.42338	−	5.92947i	0.122577	−	0.212309i
$781$	35.2161	+	20.3320i	1.26013	+	0.727536i
$782$	4.04481	−	3.78514i	0.144642	−	0.135356i
$783$			6.42612i			0.229651i
$784$	−6.59534	+	2.34552i	−0.235548	+	0.0837685i
$785$	−16.8388			−0.601003
$786$	−2.76739	−	4.79326i	−0.0987095	−	0.170970i
$787$	−5.09861	+	8.83105i	−0.181746	+	0.314793i	−0.942475	−	0.334276i	$-0.891508\pi$
$787$	−5.09861	+	8.83105i	−0.181746	+	0.314793i	0.760729	+	0.649069i	$0.224841\pi$
$788$	−7.08025	+	12.2634i	−0.252224	+	0.436864i
$789$	6.72970	+	11.6562i	0.239583	+	0.414971i
$790$			45.9127i			1.63350i
$791$	−14.9636	−	17.9672i	−0.532045	−	0.638840i
$792$			5.65733i			0.201025i
$793$	15.2068	−	8.77963i	0.540008	−	0.311774i
$794$	−16.1963	−	9.35091i	−0.574784	−	0.331852i
$795$	4.35393	−	7.54124i	0.154418	−	0.267460i
$796$	−11.6374	−	20.1566i	−0.412477	−	0.714432i
$797$	−42.3104			−1.49871			−0.749355	−	0.662168i	$-0.769636\pi$
$797$	−42.3104			−1.49871			−0.749355	+	0.662168i	$0.769636\pi$
$798$	5.99352	−	16.2798i	0.212168	−	0.576300i
$799$			5.09876i			0.180381i
$800$	5.73924	+	9.94066i	0.202913	+	0.351455i
$801$	−6.80960	+	11.7946i	−0.240606	+	0.416741i
$802$	−14.8691	−	8.58467i	−0.525046	−	0.303135i
$803$	31.4407	+	54.4569i	1.10952	+	1.92174i
$804$	−5.69042			−0.200686
$805$	47.4519	−	20.0338i	1.67246	−	0.706098i
$806$	4.86320			0.171299
$807$	8.61345	+	14.9189i	0.303208	+	0.525171i
$808$	6.94536	+	4.00991i	0.244337	+	0.141068i
$809$	5.12273	−	8.87283i	0.180106	−	0.311952i	−0.761811	−	0.647800i	$-0.775689\pi$
$809$	5.12273	−	8.87283i	0.180106	−	0.311952i	0.941916	+	0.335848i	$0.109023\pi$
$810$	2.02969	+	3.51552i	0.0713159	+	0.123523i
$811$			0.00263642i			9.25771e-5i	1.00000		4.62885e-5i	$1.47341e-5\pi$
$811$			0.00263642i			9.25771e-5i	−1.00000		4.62885e-5i	$0.999985\pi$
$812$	−2.89053	−	16.7544i	−0.101438	−	0.587965i
$813$	−19.9765			−0.700606
$814$	−6.19828	−	10.7357i	−0.217250	−	0.376288i
$815$	42.3212	−	73.3025i	1.48245	−	2.56767i
$816$	−1.00034	−	0.577549i	−0.0350191	−	0.0202183i
$817$	7.52358	−	4.34374i	0.263217	−	0.151968i
$818$		−	10.0420i		−	0.351111i
$819$	−1.54172	+	4.18769i	−0.0538722	+	0.146330i
$820$			23.1459i			0.808292i
$821$	15.5493	+	26.9322i	0.542675	+	0.939941i	0.998749	+	0.0499989i	$0.0159218\pi$
$821$	15.5493	+	26.9322i	0.542675	+	0.939941i	−0.456074	+	0.889942i	$0.650745\pi$
$822$	−9.20385	+	15.9415i	−0.321021	+	0.556025i
$823$	11.5987	−	20.0896i	0.404306	−	0.700278i	−0.589935	−	0.807451i	$-0.700847\pi$
$823$	11.5987	−	20.0896i	0.404306	−	0.700278i	0.994240	+	0.107173i	$0.0341799\pi$
$824$	−3.81453	−	6.60696i	−0.132886	−	0.230164i
$825$	−64.9376			−2.26084
$826$	12.7954	+	15.3638i	0.445210	+	0.534575i
$827$			50.8112i			1.76688i	0.468547	+	0.883439i	$0.344778\pi$
$827$			50.8112i			1.76688i	−0.468547	+	0.883439i	$0.655222\pi$
$828$	3.50171	−	3.27690i	0.121693	−	0.113880i
$829$	32.1953	+	18.5880i	1.11819	+	0.645587i	0.940938	−	0.338578i	$-0.109946\pi$
$829$	32.1953	+	18.5880i	1.11819	+	0.645587i	0.177252	+	0.984166i	$0.443279\pi$
$830$	−1.72099	+	2.98084i	−0.0597365	+	0.103467i
$831$	8.55786	−	4.94088i	0.296869	−	0.171397i
$832$			1.68666i			0.0584743i
$833$	6.15546	+	5.24296i	0.213274	+	0.181658i
$834$	−20.4754			−0.709006
$835$	38.6256	−	22.3005i	1.33669	−	0.771740i
$836$	32.1251	+	18.5474i	1.11107	+	0.641476i
$837$	−1.44167	+	2.49704i	−0.0498313	+	0.0863104i
$838$	18.3532	+	31.7886i	0.633999	+	1.09812i
$839$	32.6237			1.12629			0.563147	−	0.826357i	$-0.309590\pi$
$839$	32.6237			1.12629			0.563147	+	0.826357i	$0.309590\pi$
$840$	−6.87318	−	8.25281i	−0.237147	−	0.284749i
$841$	12.2951			0.423968
$842$	1.51067	−	0.872186i	0.0520611	−	0.0300575i
$843$	9.72928	−	16.8516i	0.335094	−	0.580400i
$844$	1.29754	−	2.24741i	0.0446633	−	0.0773591i
$845$	−20.6118	−	35.7007i	−0.709069	−	1.22814i
$846$			4.41413i			0.151761i
$847$	52.1530	+	19.2004i	1.79200	+	0.659734i
$848$			2.14513i			0.0736640i
$849$	−26.3573	+	15.2174i	−0.904581	+	0.522260i
$850$	6.62939	−	11.4824i	0.227386	−	0.393845i
$851$	−3.05484	+	10.0550i	−0.104719	+	0.344681i
$852$	−6.22486	+	3.59392i	−0.213260	+	0.123126i
$853$		−	19.3294i		−	0.661828i	−0.943661	−	0.330914i	$-0.892643\pi$
$853$		−	19.3294i		−	0.661828i	0.943661	−	0.330914i	$-0.107357\pi$
$854$	−4.68283	−	27.1431i	−0.160243	−	0.928817i
$855$	26.6171			0.910285
$856$	−6.14656	+	3.54872i	−0.210085	+	0.121293i
$857$	0.785476	+	0.453495i	0.0268314	+	0.0154911i	0.513356	−	0.858176i	$-0.328402\pi$
$857$	0.785476	+	0.453495i	0.0268314	+	0.0154911i	−0.486524	+	0.873667i	$0.661736\pi$
$858$	−8.26360	−	4.77099i	−0.282115	−	0.162879i
$859$	−40.8309	+	23.5737i	−1.39313	+	0.804324i	−0.993661	−	0.112422i	$-0.964139\pi$
$859$	−40.8309	+	23.5737i	−1.39313	+	0.804324i	−0.399470	+	0.916746i	$0.630806\pi$
$860$		−	5.37837i		−	0.183401i
$861$	−2.56475	−	14.8661i	−0.0874065	−	0.506635i
$862$		−	14.3097i		−	0.487392i
$863$	−7.34726	−	12.7258i	−0.250104	−	0.433192i	0.713450	−	0.700706i	$-0.247131\pi$
$863$	−7.34726	−	12.7258i	−0.250104	−	0.433192i	−0.963554	+	0.267513i	$0.913798\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−7.27613	−	4.20088i	−0.247396	−	0.142834i
$866$	8.96794	+	15.5329i	0.304743	+	0.527830i
$867$		−	15.6657i		−	0.532037i
$868$	2.63557	−	7.15885i	0.0894572	−	0.242987i
$869$	63.9861			2.17058
$870$	22.5912	−	13.0430i	0.765912	−	0.442199i
$871$	4.79890	−	8.31194i	0.162604	−	0.281639i
$872$	15.1271	+	8.73364i	0.512268	+	0.295758i
$873$	2.46295	+	4.26595i	0.0833582	+	0.144381i
$874$	−7.12757	−	30.6276i	−0.241094	−	1.03599i
$875$	53.4657	−	44.5278i	1.80747	−	1.50531i
$876$	−11.1150			−0.375542
$877$	9.56932	+	16.5746i	0.323133	+	0.559683i	0.981133	−	0.193335i	$-0.0619305\pi$
$877$	9.56932	+	16.5746i	0.323133	+	0.559683i	−0.658000	+	0.753018i	$0.728597\pi$
$878$	−28.0581	−	16.1994i	−0.946916	−	0.546702i
$879$	13.6489	+	7.88021i	0.460367	+	0.265793i
$880$	19.8884	−	11.4826i	0.670439	−	0.387078i
$881$	0.0981784			0.00330771			0.00165386	−	0.999999i	$-0.499474\pi$
$881$	0.0981784			0.00330771			0.00165386	+	0.999999i	$0.499474\pi$
$882$	5.32895	+	4.53897i	0.179435	+	0.152835i
$883$	−27.4328			−0.923186			−0.461593	−	0.887092i	$-0.652722\pi$
$883$	−27.4328			−0.923186			−0.461593	+	0.887092i	$0.652722\pi$
$884$	1.68724	−	0.974128i	0.0567480	−	0.0327635i
$885$	−15.3386	+	26.5672i	−0.515600	+	0.893045i
$886$	19.0976	−	33.0780i	0.641597	−	1.11128i
$887$	−29.6506	+	17.1188i	−0.995571	+	0.574793i	−0.906935	−	0.421271i	$-0.861584\pi$
$887$	−29.6506	+	17.1188i	−0.995571	+	0.574793i	−0.0886359	+	0.996064i	$0.528251\pi$
$888$	2.19124			0.0735332
$889$	−13.7165	+	11.4235i	−0.460035	+	0.383131i
$890$	55.2854			1.85317
$891$	4.89939	−	2.82867i	0.164136	−	0.0947639i
$892$	10.0313	+	5.79156i	0.335872	+	0.193916i
$893$	25.0656	+	14.4716i	0.838788	+	0.484275i
$894$	7.91446	+	13.7082i	0.264699	+	0.458472i
$895$	−22.7290			−0.759746
$896$	2.48284	+	0.914071i	0.0829457	+	0.0305370i
$897$	1.83344	+	7.87840i	0.0612167	+	0.263052i
$898$	7.04610	+	12.2042i	0.235131	+	0.407259i
$899$	16.0463	+	9.26434i	0.535174	+	0.308983i
$900$	5.73924	−	9.94066i	0.191308	−	0.331355i
$901$	2.14587	−	1.23892i	0.0714892	−	0.0412743i
$902$	32.2573			1.07405
$903$	0.595965	+	3.45440i	0.0198325	+	0.114955i
$904$			8.83766i			0.293936i
$905$	45.8624	+	79.4361i	1.52452	+	2.64054i
$906$	−13.4115	−	7.74316i	−0.445569	−	0.257249i
$907$	−28.9373	−	16.7069i	−0.960846	−	0.554745i	−0.0644125	−	0.997923i	$-0.520517\pi$
$907$	−28.9373	−	16.7069i	−0.960846	−	0.554745i	−0.896433	+	0.443179i	$0.853851\pi$
$908$	3.86164	+	6.68855i	0.128153	+	0.221967i
$909$		−	8.01981i		−	0.266000i
$910$	17.8511	−	3.07974i	0.591759	−	0.102092i
$911$			15.0207i			0.497659i	0.968547	+	0.248830i	$0.0800460\pi$
$911$			15.0207i			0.497659i	−0.968547	+	0.248830i	$0.919954\pi$
$912$	−5.67849	+	3.27848i	−0.188033	+	0.108561i
$913$	4.15424	+	2.39845i	0.137485	+	0.0793773i
$914$	−3.70638	−	2.13988i	−0.122596	−	0.0707809i
$915$	36.5989	−	21.1304i	1.20992	−	0.698550i
$916$	22.0003			0.726912
$917$	5.05918	−	13.7419i	0.167069	−	0.453799i
$918$			1.15510i			0.0381239i
$919$	41.5218	−	23.9726i	1.36968	−	0.790784i	0.378792	−	0.925482i	$-0.376340\pi$
$919$	41.5218	−	23.9726i	1.36968	−	0.790784i	0.990887	+	0.134698i	$0.0430064\pi$
$920$	−18.6274	−	5.65923i	−0.614126	−	0.186579i
$921$	3.94100	−	6.82601i	0.129860	−	0.224925i
$922$	6.18859	−	3.57298i	0.203810	−	0.117670i
$923$		−	12.1234i		−	0.399048i
$924$	−11.5015	+	9.57879i	−0.378372	+	0.315119i
$925$			25.1521i			0.826996i
$926$	1.41770	+	2.45553i	0.0465885	+	0.0806937i
$927$	−3.81453	+	6.60696i	−0.125286	+	0.217001i
$928$	−3.21306	+	5.56519i	−0.105474	+	0.182686i
$929$	35.9751	−	20.7702i	1.18030	−	0.681449i	0.224219	−	0.974539i	$-0.428017\pi$
$929$	35.9751	−	20.7702i	1.18030	−	0.681449i	0.956085	+	0.293090i	$0.0946836\pi$
$930$	11.7045			0.383807
$931$	43.2453	−	15.3795i	1.41731	−	0.504041i
$932$	23.4567			0.768350
$933$	−9.16702	−	15.8777i	−0.300115	−	0.519814i
$934$	−12.7367	+	22.0606i	−0.416757	+	0.721845i
$935$	−22.9731	−	13.2635i	−0.751301	−	0.433764i
$936$	1.46069	−	0.843329i	0.0477441	−	0.0275651i
$937$	1.07710			0.0351873			0.0175937	−	0.999845i	$-0.494399\pi$
$937$	1.07710			0.0351873			0.0175937	+	0.999845i	$0.494399\pi$
$938$	−9.63482	−	11.5688i	−0.314588	−	0.377734i
$939$			12.4033i			0.404768i
$940$	15.5180	−	8.95930i	0.506140	−	0.292220i
$941$	8.11695	−	14.0590i	0.264605	−	0.458309i	−0.702855	−	0.711333i	$-0.748092\pi$
$941$	8.11695	−	14.0590i	0.264605	−	0.458309i	0.967460	+	0.253024i	$0.0814251\pi$
$942$	−3.59239	−	2.07407i	−0.117046	−	0.0675768i
$943$	−18.6844	−	19.9662i	−0.608448	−	0.650190i
$944$		−	7.55711i		−	0.245963i
$945$	−3.71055	+	10.0788i	−0.120704	+	0.327862i
$946$	−7.49555			−0.243701
$947$	−2.86317	−	4.95916i	−0.0930405	−	0.161151i	0.815749	−	0.578407i	$-0.196325\pi$
$947$	−2.86317	−	4.95916i	−0.0930405	−	0.161151i	−0.908789	+	0.417256i	$0.862992\pi$
$948$	−5.65515	+	9.79501i	−0.183671	+	0.318127i
$949$	9.37363	−	16.2356i	0.304281	−	0.527030i
$950$	−37.6319	−	65.1804i	−1.22094	−	2.11473i
$951$		−	3.67969i		−	0.119322i
$952$	−0.519575	−	3.01161i	−0.0168395	−	0.0976069i
$953$		−	6.77880i		−	0.219587i	−0.993954	−	0.109793i	$-0.964981\pi$
$953$		−	6.77880i		−	0.219587i	0.993954	−	0.109793i	$-0.0350189\pi$
$954$	1.85774	−	1.07256i	0.0601464	−	0.0347255i
$955$	−18.5700	−	10.7214i	−0.600912	−	0.346936i
$956$	−7.10768	+	12.3109i	−0.229879	+	0.398162i
$957$	−18.1774	−	31.4841i	−0.587591	−	1.01774i
$958$	19.2180			0.620905
$959$	−47.9932	+	8.27996i	−1.54978	+	0.267374i
$960$			4.05937i			0.131016i
$961$	−11.3432	−	19.6470i	−0.365909	−	0.633773i
$962$	−1.84794	+	3.20072i	−0.0595798	+	0.103195i
$963$	6.14656	+	3.54872i	0.198070	+	0.114356i
$964$	8.10166	+	14.0325i	0.260937	+	0.451956i
$965$	108.457			3.49134
$966$	12.5910	+	1.57073i	0.405108	+	0.0505375i
$967$	−14.4508			−0.464705			−0.232353	−	0.972632i	$-0.574642\pi$
$967$	−14.4508			−0.464705			−0.232353	+	0.972632i	$0.574642\pi$
$968$	−10.5027	−	18.1912i	−0.337570	−	0.584688i
$969$	6.55921	+	3.78696i	0.210712	+	0.121655i
$970$	9.99802	−	17.3171i	0.321017	−	0.556018i
$971$	−8.92641	−	15.4610i	−0.286462	−	0.496167i	0.686501	−	0.727129i	$-0.259146\pi$
$971$	−8.92641	−	15.4610i	−0.286462	−	0.496167i	−0.972963	+	0.230962i	$0.925813\pi$
$972$			1.00000i			0.0320750i
$973$	−34.6682	−	41.6271i	−1.11141	−	1.33450i
$974$	−30.3625			−0.972876
$975$	9.68014	+	16.7665i	0.310013	+	0.536957i
$976$	−5.20534	+	9.01591i	−0.166619	+	0.288592i
$977$	−39.1189	−	22.5853i	−1.25152	−	0.722568i	−0.280112	−	0.959967i	$-0.590372\pi$
$977$	−39.1189	−	22.5853i	−1.25152	−	0.722568i	−0.971412	+	0.237400i	$0.923705\pi$
$978$	18.0576	−	10.4256i	0.577419	−	0.333373i
$979$		−	77.0484i		−	2.46248i
$980$	5.14076	−	27.9467i	0.164215	−	0.892725i
$981$		−	17.4673i		−	0.557687i
$982$	4.25335	+	7.36701i	0.135730	+	0.235091i
$983$	−10.9144	+	18.9044i	−0.348117	+	0.602956i	−0.985915	−	0.167248i	$-0.946512\pi$
$983$	−10.9144	+	18.9044i	−0.348117	+	0.602956i	0.637798	+	0.770204i	$0.279845\pi$
$984$	−2.85093	+	4.93795i	−0.0908843	+	0.157416i
$985$	−28.7414	−	49.7815i	−0.915776	−	1.58617i
$986$	7.42281			0.236390
$987$	−8.97405	+	7.47385i	−0.285647	+	0.237895i
$988$		−	11.0593i		−	0.351844i
$989$	4.34165	+	4.63950i	0.138056	+	0.147528i
$990$	−19.8884	−	11.4826i	−0.632096	−	0.364941i
$991$	−10.9207	+	18.9151i	−0.346906	+	0.600859i	−0.985698	−	0.168520i	$-0.946101\pi$
$991$	−10.9207	+	18.9151i	−0.346906	+	0.600859i	0.638792	+	0.769379i	$0.279434\pi$
$992$	−2.49704	+	1.44167i	−0.0792812	+	0.0457730i
$993$			4.90826i			0.155759i
$994$	−17.8462	−	6.57020i	−0.566048	−	0.208394i
$995$	94.4812			2.99525
$996$	−0.734312	+	0.423955i	−0.0232676	+	0.0134335i
$997$	49.4147	+	28.5296i	1.56498	+	0.903542i	0.996740	+	0.0806791i	$0.0257089\pi$
$997$	49.4147	+	28.5296i	1.56498	+	0.903542i	0.568240	+	0.822863i	$0.307624\pi$
$998$	6.28157	−	10.8800i	0.198840	−	0.344400i
$999$	−1.09562	−	1.89767i	−0.0346639	−	0.0600396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.b.367.1	yes	32
7.5	odd	6	inner	966.2.k.b.229.8	yes	32
23.22	odd	2	inner	966.2.k.b.367.8	yes	32
161.68	even	6	inner	966.2.k.b.229.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.b.229.1	✓	32	161.68	even	6	inner
966.2.k.b.229.8	yes	32	7.5	odd	6	inner
966.2.k.b.367.1	yes	32	1.1	even	1	trivial
966.2.k.b.367.8	yes	32	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.02969 - 3.51552i) q^{5} -1.00000i q^{6} +(2.03303 - 1.69316i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.02969 - 3.51552i) q^{5} -1.00000i q^{6} +(2.03303 - 1.69316i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.02969 - 3.51552i) q^{10} +(-4.89939 - 2.82867i) q^{11} +(0.866025 - 0.500000i) q^{12} +1.68666i q^{13} +(2.48284 + 0.914071i) q^{14} +4.05937i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.577549 + 1.00034i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(3.27848 + 5.67849i) q^{19} +4.05937 q^{20} +(-2.60723 + 0.449810i) q^{21} -5.65733i q^{22} +(-3.50171 + 3.27690i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-5.73924 + 9.94066i) q^{25} +(-1.46069 + 0.843329i) q^{26} -1.00000i q^{27} +(0.449810 + 2.60723i) q^{28} -6.42612 q^{29} +(-3.51552 + 2.02969i) q^{30} +(-2.49704 - 1.44167i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.82867 + 4.89939i) q^{33} -1.15510 q^{34} +(-10.0788 - 3.71055i) q^{35} -1.00000 q^{36} +(1.89767 - 1.09562i) q^{37} +(-3.27848 + 5.67849i) q^{38} +(0.843329 - 1.46069i) q^{39} +(2.02969 + 3.51552i) q^{40} +5.70186i q^{41} +(-1.69316 - 2.03303i) q^{42} -1.32493i q^{43} +(4.89939 - 2.82867i) q^{44} +(2.02969 - 3.51552i) q^{45} +(-4.58873 - 1.39412i) q^{46} +(3.82275 - 2.20707i) q^{47} +1.00000i q^{48} +(1.26639 - 6.88449i) q^{49} -11.4785 q^{50} +(1.00034 - 0.577549i) q^{51} +(-1.46069 - 0.843329i) q^{52} +(-1.85774 - 1.07256i) q^{53} +(0.866025 - 0.500000i) q^{54} +22.9652i q^{55} +(-2.03303 + 1.69316i) q^{56} -6.55695i q^{57} +(-3.21306 - 5.56519i) q^{58} +(6.54465 + 3.77855i) q^{59} +(-3.51552 - 2.02969i) q^{60} +(-5.20534 - 9.01591i) q^{61} -2.88334i q^{62} +(2.48284 + 0.914071i) q^{63} +1.00000 q^{64} +(5.92947 - 3.42338i) q^{65} +(-2.82867 + 4.89939i) q^{66} +(-4.92805 - 2.84521i) q^{67} +(-0.577549 - 1.00034i) q^{68} +(4.67101 - 1.08702i) q^{69} +(-1.82594 - 10.5837i) q^{70} -7.18784 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-9.62590 - 5.55752i) q^{73} +(1.89767 + 1.09562i) q^{74} +(9.94066 - 5.73924i) q^{75} -6.55695 q^{76} +(-14.7500 + 2.54472i) q^{77} +1.68666 q^{78} +(-9.79501 + 5.65515i) q^{79} +(-2.02969 + 3.51552i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.93795 + 2.85093i) q^{82} -0.847910 q^{83} +(0.914071 - 2.48284i) q^{84} +4.68897 q^{85} +(1.14742 - 0.662464i) q^{86} +(5.56519 + 3.21306i) q^{87} +(4.89939 + 2.82867i) q^{88} +(6.80960 + 11.7946i) q^{89} +4.05937 q^{90} +(2.85579 + 3.42902i) q^{91} +(-1.08702 - 4.67101i) q^{92} +(1.44167 + 2.49704i) q^{93} +(3.82275 + 2.20707i) q^{94} +(13.3085 - 23.0511i) q^{95} +(-0.866025 + 0.500000i) q^{96} +4.92590 q^{97} +(6.59534 - 2.34552i) q^{98} -5.65733i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more