LMFDB - Embedded newform 1110.2.x.d.751.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 60x^{14} + 1362x^{12} + 15028x^{10} + 86441x^{8} + 260376x^{6} + 382684x^{4} + 224224x^{2} + 38416 $ x^16 + 60x^14 + 1362x^12 + 15028x^10 + 86441x^8 + 260376x^6 + 382684x^4 + 224224*x^2 + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.7
Root			$-2.16125i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.d.841.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.08063 - 1.87170i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.08063 - 1.87170i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +4.64319 q^{11} +(0.500000 + 0.866025i) q^{12} +(-4.51941 - 2.60928i) q^{13} -2.16125i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.73772 - 1.58063i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.178213 + 0.102891i) q^{19} +(0.866025 - 0.500000i) q^{20} +(1.08063 + 1.87170i) q^{21} +(4.02112 - 2.32159i) q^{22} +3.48652i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -5.21857 q^{26} +1.00000 q^{27} +(-1.08063 - 1.87170i) q^{28} -6.44199i q^{29} +(-0.500000 + 0.866025i) q^{30} -6.19187i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.32159 + 4.02112i) q^{33} +(1.58063 - 2.73772i) q^{34} +(1.87170 - 1.08063i) q^{35} -1.00000 q^{36} +(2.83833 + 5.37995i) q^{37} +0.205782 q^{38} +(4.51941 - 2.60928i) q^{39} +(0.500000 - 0.866025i) q^{40} +(1.61696 - 2.80066i) q^{41} +(1.87170 + 1.08063i) q^{42} +2.70535i q^{43} +(2.32159 - 4.02112i) q^{44} -1.00000i q^{45} +(1.74326 + 3.01941i) q^{46} +0.834167 q^{47} +1.00000 q^{48} +(1.16450 + 2.01696i) q^{49} +(0.866025 + 0.500000i) q^{50} +3.16125i q^{51} +(-4.51941 + 2.60928i) q^{52} +(0.578919 + 1.00272i) q^{53} +(0.866025 - 0.500000i) q^{54} +(4.02112 + 2.32159i) q^{55} +(-1.87170 - 1.08063i) q^{56} +(-0.178213 + 0.102891i) q^{57} +(-3.22099 - 5.57892i) q^{58} +(3.94537 - 2.27786i) q^{59} +1.00000i q^{60} +(9.21562 + 5.32064i) q^{61} +(-3.09594 - 5.36232i) q^{62} -2.16125 q^{63} -1.00000 q^{64} +(-2.60928 - 4.51941i) q^{65} +4.64319i q^{66} +(0.180274 - 0.312243i) q^{67} -3.16125i q^{68} +(-3.01941 - 1.74326i) q^{69} +(1.08063 - 1.87170i) q^{70} +(2.26228 - 3.91838i) q^{71} +(-0.866025 + 0.500000i) q^{72} +4.91562 q^{73} +(5.14804 + 3.24001i) q^{74} -1.00000 q^{75} +(0.178213 - 0.102891i) q^{76} +(5.01755 - 8.69065i) q^{77} +(2.60928 - 4.51941i) q^{78} +(2.06361 + 1.19143i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -3.23393i q^{82} +(-6.98079 - 12.0911i) q^{83} +2.16125 q^{84} +3.16125 q^{85} +(1.35268 + 2.34291i) q^{86} +(5.57892 + 3.22099i) q^{87} -4.64319i q^{88} +(-13.4453 + 7.76267i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-9.76759 + 5.63932i) q^{91} +(3.01941 + 1.74326i) q^{92} +(5.36232 + 3.09594i) q^{93} +(0.722410 - 0.417084i) q^{94} +(0.102891 + 0.178213i) q^{95} +(0.866025 - 0.500000i) q^{96} +0.153047i q^{97} +(2.01696 + 1.16450i) q^{98} +(-2.32159 - 4.02112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} + 16 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$			1.00000i			0.408248i
$7$	1.08063	−	1.87170i	0.408438	−	0.707436i	−0.586277	−	0.810111i	$-0.699407\pi$
$7$	1.08063	−	1.87170i	0.408438	−	0.707436i	0.994715	+	0.102675i	$0.0327402\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000			0.316228
$11$	4.64319			1.39997			0.699987	−	0.714156i	$-0.253189\pi$
$11$	4.64319			1.39997			0.699987	+	0.714156i	$0.253189\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−4.51941	−	2.60928i	−1.25346	−	0.723685i	−0.281664	−	0.959513i	$-0.590886\pi$
$13$	−4.51941	−	2.60928i	−1.25346	−	0.723685i	−0.971795	+	0.235828i	$0.924220\pi$
$14$		−	2.16125i		−	0.577619i
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.73772	−	1.58063i	0.663996	−	0.383358i	−0.129802	−	0.991540i	$-0.541434\pi$
$17$	2.73772	−	1.58063i	0.663996	−	0.383358i	0.793798	+	0.608182i	$0.208101\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	0.178213	+	0.102891i	0.0408848	+	0.0236048i	0.520303	−	0.853982i	$-0.325819\pi$
$19$	0.178213	+	0.102891i	0.0408848	+	0.0236048i	−0.479418	+	0.877587i	$0.659152\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	1.08063	+	1.87170i	0.235812	+	0.408438i
$22$	4.02112	−	2.32159i	0.857305	−	0.494965i
$23$			3.48652i			0.726989i	0.931596	+	0.363494i	$0.118416\pi$
$23$			3.48652i			0.726989i	−0.931596	+	0.363494i	$0.881584\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−5.21857			−1.02345
$27$	1.00000			0.192450
$28$	−1.08063	−	1.87170i	−0.204219	−	0.353718i
$29$		−	6.44199i		−	1.19625i	−0.801404	−	0.598123i	$-0.795913\pi$
$29$		−	6.44199i		−	1.19625i	0.801404	−	0.598123i	$-0.204087\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$		−	6.19187i		−	1.11209i	−0.831151	−	0.556046i	$-0.812318\pi$
$31$		−	6.19187i		−	1.11209i	0.831151	−	0.556046i	$-0.187682\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−2.32159	+	4.02112i	−0.404138	+	0.699987i
$34$	1.58063	−	2.73772i	0.271075	−	0.469516i
$35$	1.87170	−	1.08063i	0.316375	−	0.182659i
$36$	−1.00000			−0.166667
$37$	2.83833	+	5.37995i	0.466618	+	0.884459i
$37$	2.83833	+	5.37995i	0.466618	+	0.884459i
$38$	0.205782			0.0333823
$39$	4.51941	−	2.60928i	0.723685	−	0.417820i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	1.61696	−	2.80066i	0.252527	−	0.437390i	−0.711694	−	0.702490i	$-0.752072\pi$
$41$	1.61696	−	2.80066i	0.252527	−	0.437390i	0.964221	+	0.265100i	$0.0854050\pi$
$42$	1.87170	+	1.08063i	0.288809	+	0.166744i
$43$			2.70535i			0.412563i	0.978493	+	0.206281i	$0.0661362\pi$
$43$			2.70535i			0.412563i	−0.978493	+	0.206281i	$0.933864\pi$
$44$	2.32159	−	4.02112i	0.349993	−	0.606206i
$45$		−	1.00000i		−	0.149071i
$46$	1.74326	+	3.01941i	0.257029	+	0.445188i
$47$	0.834167			0.121676			0.0608379	−	0.998148i	$-0.480623\pi$
$47$	0.834167			0.121676			0.0608379	+	0.998148i	$0.480623\pi$
$48$	1.00000			0.144338
$49$	1.16450	+	2.01696i	0.166356	+	0.288138i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$			3.16125i			0.442664i
$52$	−4.51941	+	2.60928i	−0.626730	+	0.361843i
$53$	0.578919	+	1.00272i	0.0795207	+	0.137734i	0.903043	−	0.429550i	$-0.141328\pi$
$53$	0.578919	+	1.00272i	0.0795207	+	0.137734i	−0.823523	+	0.567284i	$0.807994\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	4.02112	+	2.32159i	0.542207	+	0.313044i
$56$	−1.87170	−	1.08063i	−0.250116	−	0.144405i
$57$	−0.178213	+	0.102891i	−0.0236048	+	0.0136283i
$58$	−3.22099	−	5.57892i	−0.422937	−	0.732549i
$59$	3.94537	−	2.27786i	0.513643	−	0.296552i	−0.220687	−	0.975345i	$-0.570830\pi$
$59$	3.94537	−	2.27786i	0.513643	−	0.296552i	0.734330	+	0.678793i	$0.237496\pi$
$60$			1.00000i			0.129099i
$61$	9.21562	+	5.32064i	1.17994	+	0.681238i	0.956001	−	0.293365i	$-0.0947751\pi$
$61$	9.21562	+	5.32064i	1.17994	+	0.681238i	0.223939	+	0.974603i	$0.428108\pi$
$62$	−3.09594	−	5.36232i	−0.393184	−	0.681015i
$63$	−2.16125			−0.272292
$64$	−1.00000			−0.125000
$65$	−2.60928	−	4.51941i	−0.323642	−	0.560564i
$66$			4.64319i			0.571537i
$67$	0.180274	−	0.312243i	0.0220239	−	0.0381465i	−0.854803	−	0.518952i	$-0.826322\pi$
$67$	0.180274	−	0.312243i	0.0220239	−	0.0381465i	0.876827	+	0.480805i	$0.159656\pi$
$68$		−	3.16125i		−	0.383358i
$69$	−3.01941	−	1.74326i	−0.363494	−	0.209864i
$70$	1.08063	−	1.87170i	0.129160	−	0.223711i
$71$	2.26228	−	3.91838i	0.268483	−	0.465027i	−0.699987	−	0.714155i	$-0.746811\pi$
$71$	2.26228	−	3.91838i	0.268483	−	0.465027i	0.968470	+	0.249129i	$0.0801443\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	4.91562			0.575329			0.287665	−	0.957731i	$-0.407121\pi$
$73$	4.91562			0.575329			0.287665	+	0.957731i	$0.407121\pi$
$74$	5.14804	+	3.24001i	0.598447	+	0.376644i
$75$	−1.00000			−0.115470
$76$	0.178213	−	0.102891i	0.0204424	−	0.0118024i
$77$	5.01755	−	8.69065i	0.571803	−	0.990391i
$78$	2.60928	−	4.51941i	0.295443	−	0.511723i
$79$	2.06361	+	1.19143i	0.232174	+	0.134046i	0.611575	−	0.791187i	$-0.290536\pi$
$79$	2.06361	+	1.19143i	0.232174	+	0.134046i	−0.379400	+	0.925233i	$0.623870\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		−	3.23393i		−	0.357127i
$83$	−6.98079	−	12.0911i	−0.766241	−	1.32717i	−0.939588	−	0.342308i	$-0.888791\pi$
$83$	−6.98079	−	12.0911i	−0.766241	−	1.32717i	0.173347	−	0.984861i	$-0.444542\pi$
$84$	2.16125			0.235812
$85$	3.16125			0.342886
$86$	1.35268	+	2.34291i	0.145863	+	0.252642i
$87$	5.57892	+	3.22099i	0.598123	+	0.345327i
$88$		−	4.64319i		−	0.494965i
$89$	−13.4453	+	7.76267i	−1.42520	+	0.822841i	−0.996737	−	0.0807166i	$-0.974279\pi$
$89$	−13.4453	+	7.76267i	−1.42520	+	0.822841i	−0.428466	+	0.903558i	$0.640946\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	−9.76759	+	5.63932i	−1.02392	+	0.591161i
$92$	3.01941	+	1.74326i	0.314795	+	0.181747i
$93$	5.36232	+	3.09594i	0.556046	+	0.321034i
$94$	0.722410	−	0.417084i	0.0745109	−	0.0430189i
$95$	0.102891	+	0.178213i	0.0105564	+	0.0182842i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$			0.153047i			0.0155396i	0.999970	+	0.00776981i	$0.00247323\pi$
$97$			0.153047i			0.0155396i	−0.999970	+	0.00776981i	$0.997527\pi$
$98$	2.01696	+	1.16450i	0.203744	+	0.117632i
$99$	−2.32159	−	4.02112i	−0.233329	−	0.404138i
$100$	1.00000			0.100000
$101$	8.43932			0.839744			0.419872	−	0.907583i	$-0.362075\pi$
$101$	8.43932			0.839744			0.419872	+	0.907583i	$0.362075\pi$
$102$	1.58063	+	2.73772i	0.156505	+	0.271075i
$103$		−	4.15256i		−	0.409164i	−0.978849	−	0.204582i	$-0.934417\pi$
$103$		−	4.15256i		−	0.409164i	0.978849	−	0.204582i	$-0.0655834\pi$
$104$	−2.60928	+	4.51941i	−0.255861	+	0.443165i
$105$			2.16125i			0.210917i
$106$	1.00272	+	0.578919i	0.0973926	+	0.0562296i
$107$	−8.48343	+	14.6937i	−0.820124	+	1.42050i	0.0854653	+	0.996341i	$0.472762\pi$
$107$	−8.48343	+	14.6937i	−0.820124	+	1.42050i	−0.905589	+	0.424155i	$0.860571\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−1.32344	+	0.764087i	−0.126762	+	0.0731863i	−0.562040	−	0.827110i	$-0.689983\pi$
$109$	−1.32344	+	0.764087i	−0.126762	+	0.0731863i	0.435278	+	0.900296i	$0.356650\pi$
$110$	4.64319			0.442711
$111$	−6.07834	−	0.231916i	−0.576930	−	0.0220125i
$112$	−2.16125			−0.204219
$113$	−17.1426	+	9.89727i	−1.61264	+	0.931057i	−0.623883	+	0.781518i	$0.714446\pi$
$113$	−17.1426	+	9.89727i	−1.61264	+	0.931057i	−0.988756	+	0.149539i	$0.952221\pi$
$114$	−0.102891	+	0.178213i	−0.00963663	+	0.0166911i
$115$	−1.74326	+	3.01941i	−0.162560	+	0.281562i
$116$	−5.57892	−	3.22099i	−0.517990	−	0.299062i
$117$			5.21857i			0.482457i
$118$	2.27786	−	3.94537i	0.209694	−	0.363201i
$119$		−	6.83226i		−	0.626312i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	10.5592			0.959926
$122$	10.6413			0.963416
$123$	1.61696	+	2.80066i	0.145797	+	0.252527i
$124$	−5.36232	−	3.09594i	−0.481550	−	0.278023i
$125$			1.00000i			0.0894427i
$126$	−1.87170	+	1.08063i	−0.166744	+	0.0962698i
$127$	−0.713592	−	1.23598i	−0.0633210	−	0.109675i	0.832627	−	0.553834i	$-0.186836\pi$
$127$	−0.713592	−	1.23598i	−0.0633210	−	0.109675i	−0.895948	+	0.444159i	$0.853503\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−2.34291	−	1.35268i	−0.206281	−	0.119097i
$130$	−4.51941	−	2.60928i	−0.396379	−	0.228849i
$131$	−13.7876	+	7.96026i	−1.20463	+	0.695491i	−0.961580	−	0.274524i	$-0.911480\pi$
$131$	−13.7876	+	7.96026i	−1.20463	+	0.695491i	−0.243045	+	0.970015i	$0.578146\pi$
$132$	2.32159	+	4.02112i	0.202069	+	0.349993i
$133$	0.385162	−	0.222373i	0.0333978	−	0.0192822i
$134$		−	0.360547i		−	0.0311465i
$135$	0.866025	+	0.500000i	0.0745356	+	0.0430331i
$136$	−1.58063	−	2.73772i	−0.135538	−	0.234758i
$137$	1.14116			0.0974958			0.0487479	−	0.998811i	$-0.484477\pi$
$137$	1.14116			0.0974958			0.0487479	+	0.998811i	$0.484477\pi$
$138$	−3.48652			−0.296792
$139$	1.38333	+	2.39599i	0.117332	+	0.203225i	0.918710	−	0.394934i	$-0.129232\pi$
$139$	1.38333	+	2.39599i	0.117332	+	0.203225i	−0.801377	+	0.598159i	$0.795899\pi$
$140$		−	2.16125i		−	0.182659i
$141$	−0.417084	+	0.722410i	−0.0351248	+	0.0608379i
$142$		−	4.52456i		−	0.379693i
$143$	−20.9845	−	12.1154i	−1.75481	−	1.01314i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	3.22099	−	5.57892i	0.267489	−	0.463304i
$146$	4.25705	−	2.45781i	0.352316	−	0.203410i
$147$	−2.32899			−0.192092
$148$	6.07834	+	0.231916i	0.499636	+	0.0190633i
$149$	10.1666			0.832881			0.416441	−	0.909163i	$-0.363277\pi$
$149$	10.1666			0.832881			0.416441	+	0.909163i	$0.363277\pi$
$150$	−0.866025	+	0.500000i	−0.0707107	+	0.0408248i
$151$	−1.21847	+	2.11046i	−0.0991580	+	0.171747i	−0.911336	−	0.411663i	$-0.864948\pi$
$151$	−1.21847	+	2.11046i	−0.0991580	+	0.171747i	0.812178	+	0.583409i	$0.198282\pi$
$152$	0.102891	−	0.178213i	0.00834557	−	0.0144549i
$153$	−2.73772	−	1.58063i	−0.221332	−	0.127786i
$154$		−	10.0351i		−	0.808651i
$155$	3.09594	−	5.36232i	0.248672	−	0.430712i
$156$		−	5.21857i		−	0.417820i
$157$	−0.705413	−	1.22181i	−0.0562981	−	0.0975111i	0.836503	−	0.547963i	$-0.184596\pi$
$157$	−0.705413	−	1.22181i	−0.0562981	−	0.0975111i	−0.892801	+	0.450451i	$0.851263\pi$
$158$	2.38285			0.189569
$159$	−1.15784			−0.0918226
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	6.52571	+	3.76762i	0.514298	+	0.296930i
$162$			1.00000i			0.0785674i
$163$	−8.49385	+	4.90393i	−0.665290	+	0.384105i	−0.794289	−	0.607539i	$-0.792157\pi$
$163$	−8.49385	+	4.90393i	−0.665290	+	0.384105i	0.129000	+	0.991645i	$0.458823\pi$
$164$	−1.61696	−	2.80066i	−0.126264	−	0.218695i
$165$	−4.02112	+	2.32159i	−0.313044	+	0.180736i
$166$	−12.0911	−	6.98079i	−0.938450	−	0.541814i
$167$	−13.2273	−	7.63680i	−1.02356	−	0.590953i	−0.108428	−	0.994104i	$-0.534582\pi$
$167$	−13.2273	−	7.63680i	−1.02356	−	0.590953i	−0.915134	+	0.403151i	$0.867915\pi$
$168$	1.87170	−	1.08063i	0.144405	−	0.0833721i
$169$	7.11672	+	12.3265i	0.547440	+	0.948194i
$170$	2.73772	−	1.58063i	0.209974	−	0.121228i
$171$		−	0.205782i		−	0.0157366i
$172$	2.34291	+	1.35268i	0.178645	+	0.103141i
$173$	1.38267	+	2.39485i	0.105122	+	0.182077i	0.913788	−	0.406191i	$-0.133143\pi$
$173$	1.38267	+	2.39485i	0.105122	+	0.182077i	−0.808666	+	0.588268i	$0.799810\pi$
$174$	6.44199			0.488366
$175$	2.16125			0.163375
$176$	−2.32159	−	4.02112i	−0.174997	−	0.303103i
$177$			4.55572i			0.342429i
$178$	−7.76267	+	13.4453i	−0.581837	+	1.00777i
$179$		−	1.17391i		−	0.0877424i	−0.999037	−	0.0438712i	$-0.986031\pi$
$179$		−	1.17391i		−	0.0877424i	0.999037	−	0.0438712i	$-0.0139691\pi$
$180$	−0.866025	−	0.500000i	−0.0645497	−	0.0372678i
$181$	−10.5795	+	18.3242i	−0.786366	+	1.36203i	0.141813	+	0.989893i	$0.454707\pi$
$181$	−10.5795	+	18.3242i	−0.786366	+	1.36203i	−0.928179	+	0.372133i	$0.878626\pi$
$182$	−5.63932	+	9.76759i	−0.418014	+	0.724022i
$183$	−9.21562	+	5.32064i	−0.681238	+	0.393313i
$184$	3.48652			0.257029
$185$	−0.231916	+	6.07834i	−0.0170508	+	0.446888i
$186$	6.19187			0.454010
$187$	12.7118	−	7.33914i	0.929577	−	0.536691i
$188$	0.417084	−	0.722410i	0.0304190	−	0.0526872i
$189$	1.08063	−	1.87170i	0.0786040	−	0.136146i
$190$	0.178213	+	0.102891i	0.0129289	+	0.00746450i
$191$		−	10.8527i		−	0.785274i	−0.919694	−	0.392637i	$-0.871563\pi$
$191$		−	10.8527i		−	0.785274i	0.919694	−	0.392637i	$-0.128437\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$			22.9744i			1.65373i	0.562399	+	0.826866i	$0.309878\pi$
$193$			22.9744i			1.65373i	−0.562399	+	0.826866i	$0.690122\pi$
$194$	0.0765237	+	0.132543i	0.00549408	+	0.00951603i
$195$	5.21857			0.373709
$196$	2.32899			0.166356
$197$	9.19854	+	15.9323i	0.655369	+	1.13513i	0.981801	+	0.189911i	$0.0608201\pi$
$197$	9.19854	+	15.9323i	0.655369	+	1.13513i	−0.326433	+	0.945221i	$0.605847\pi$
$198$	−4.02112	−	2.32159i	−0.285768	−	0.164988i
$199$			10.9340i			0.775090i	0.921851	+	0.387545i	$0.126677\pi$
$199$			10.9340i			0.775090i	−0.921851	+	0.387545i	$0.873323\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	0.180274	+	0.312243i	0.0127155	+	0.0220239i
$202$	7.30867	−	4.21966i	0.514236	−	0.296894i
$203$	−12.0575	−	6.96138i	−0.846268	−	0.488593i
$204$	2.73772	+	1.58063i	0.191679	+	0.110666i
$205$	2.80066	−	1.61696i	0.195607	−	0.112934i
$206$	−2.07628	−	3.59622i	−0.144661	−	0.250561i
$207$	3.01941	−	1.74326i	0.209864	−	0.121165i
$208$			5.21857i			0.361843i
$209$	0.827474	+	0.477742i	0.0572376	+	0.0330461i
$210$	1.08063	+	1.87170i	0.0745703	+	0.129160i
$211$	−5.36913			−0.369626			−0.184813	−	0.982774i	$-0.559168\pi$
$211$	−5.36913			−0.369626			−0.184813	+	0.982774i	$0.559168\pi$
$212$	1.15784			0.0795207
$213$	2.26228	+	3.91838i	0.155009	+	0.268483i
$214$			16.9669i			1.15983i
$215$	−1.35268	+	2.34291i	−0.0922518	+	0.159785i
$216$		−	1.00000i		−	0.0680414i
$217$	−11.5893	−	6.69110i	−0.786734	−	0.454221i
$218$	−0.764087	+	1.32344i	−0.0517505	+	0.0896345i
$219$	−2.45781	+	4.25705i	−0.166083	+	0.287665i
$220$	4.02112	−	2.32159i	0.271104	−	0.156522i
$221$	−16.4972			−1.10972
$222$	−5.37995	+	2.83833i	−0.361079	+	0.190496i
$223$	−23.1628			−1.55109			−0.775547	−	0.631289i	$-0.782526\pi$
$223$	−23.1628			−1.55109			−0.775547	+	0.631289i	$0.782526\pi$
$224$	−1.87170	+	1.08063i	−0.125058	+	0.0722024i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	−9.89727	+	17.1426i	−0.658357	+	1.14031i
$227$	−20.5859	−	11.8853i	−1.36634	−	0.788855i	−0.375879	−	0.926669i	$-0.622659\pi$
$227$	−20.5859	−	11.8853i	−1.36634	−	0.788855i	−0.990458	+	0.137814i	$0.955992\pi$
$228$			0.205782i			0.0136283i
$229$	−2.27891	+	3.94718i	−0.150594	+	0.260837i	−0.931446	−	0.363879i	$-0.881452\pi$
$229$	−2.27891	+	3.94718i	−0.150594	+	0.260837i	0.780852	+	0.624716i	$0.214785\pi$
$230$			3.48652i			0.229894i
$231$	5.01755	+	8.69065i	0.330130	+	0.571803i
$232$	−6.44199			−0.422937
$233$	−18.2804			−1.19759			−0.598793	−	0.800904i	$-0.704353\pi$
$233$	−18.2804			−1.19759			−0.598793	+	0.800904i	$0.704353\pi$
$234$	2.60928	+	4.51941i	0.170574	+	0.295443i
$235$	0.722410	+	0.417084i	0.0471248	+	0.0272075i
$236$		−	4.55572i		−	0.296552i
$237$	−2.06361	+	1.19143i	−0.134046	+	0.0773914i
$238$	−3.41613	−	5.91691i	−0.221435	−	0.383536i
$239$	17.6319	−	10.1798i	1.14051	−	0.658474i	0.193953	−	0.981011i	$-0.437869\pi$
$239$	17.6319	−	10.1798i	1.14051	−	0.658474i	0.946557	+	0.322537i	$0.104536\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	13.3225	+	7.69174i	0.858176	+	0.495468i	0.863401	−	0.504518i	$-0.168330\pi$
$241$	13.3225	+	7.69174i	0.858176	+	0.495468i	−0.00522493	+	0.999986i	$0.501663\pi$
$242$	9.14453	−	5.27959i	0.587832	−	0.339385i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	9.21562	−	5.32064i	0.589970	−	0.340619i
$245$			2.32899i			0.148794i
$246$	2.80066	+	1.61696i	0.178564	+	0.103094i
$247$	−0.536944	−	0.930014i	−0.0341649	−	0.0591754i
$248$	−6.19187			−0.393184
$249$	13.9616			0.884779
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$		−	13.2799i		−	0.838219i	−0.907936	−	0.419110i	$-0.862342\pi$
$251$		−	13.2799i		−	0.838219i	0.907936	−	0.419110i	$-0.137658\pi$
$252$	−1.08063	+	1.87170i	−0.0680730	+	0.117906i
$253$			16.1885i			1.01777i
$254$	−1.23598	−	0.713592i	−0.0775521	−	0.0447747i
$255$	−1.58063	+	2.73772i	−0.0989826	+	0.171443i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.52855	+	1.45986i	−0.157727	+	0.0910636i	−0.576786	−	0.816895i	$-0.695693\pi$
$257$	−2.52855	+	1.45986i	−0.157727	+	0.0910636i	0.419059	+	0.907959i	$0.362360\pi$
$258$	−2.70535			−0.168428
$259$	13.1368	+	0.501228i	0.816282	+	0.0311448i
$260$	−5.21857			−0.323642
$261$	−5.57892	+	3.22099i	−0.345327	+	0.199374i
$262$	−7.96026	+	13.7876i	−0.491786	+	0.851799i
$263$	−5.18381	+	8.97862i	−0.319647	+	0.553645i	−0.980414	−	0.196946i	$-0.936898\pi$
$263$	−5.18381	+	8.97862i	−0.319647	+	0.553645i	0.660767	+	0.750591i	$0.270231\pi$
$264$	4.02112	+	2.32159i	0.247483	+	0.142884i
$265$			1.15784i			0.0711255i
$266$	0.222373	−	0.385162i	0.0136346	−	0.0236158i
$267$		−	15.5253i		−	0.950135i
$268$	−0.180274	−	0.312243i	−0.0110120	−	0.0190733i
$269$	25.2440			1.53915			0.769577	−	0.638554i	$-0.220467\pi$
$269$	25.2440			1.53915			0.769577	+	0.638554i	$0.220467\pi$
$270$	1.00000			0.0608581
$271$	−8.17713	−	14.1632i	−0.496725	−	0.860353i	0.503268	−	0.864131i	$-0.332131\pi$
$271$	−8.17713	−	14.1632i	−0.496725	−	0.860353i	−0.999993	+	0.00377716i	$0.998798\pi$
$272$	−2.73772	−	1.58063i	−0.165999	−	0.0958395i
$273$		−	11.2786i		−	0.682614i
$274$	0.988273	−	0.570579i	0.0597037	−	0.0344700i
$275$	2.32159	+	4.02112i	0.139997	+	0.242483i
$276$	−3.01941	+	1.74326i	−0.181747	+	0.104932i
$277$	2.90340	+	1.67628i	0.174448	+	0.100718i	0.584682	−	0.811263i	$-0.301219\pi$
$277$	2.90340	+	1.67628i	0.174448	+	0.100718i	−0.410233	+	0.911981i	$0.634553\pi$
$278$	2.39599	+	1.38333i	0.143702	+	0.0829664i
$279$	−5.36232	+	3.09594i	−0.321034	+	0.185349i
$280$	−1.08063	−	1.87170i	−0.0645798	−	0.111855i
$281$	−2.92257	+	1.68735i	−0.174346	+	0.100659i	−0.584634	−	0.811297i	$-0.698762\pi$
$281$	−2.92257	+	1.68735i	−0.174346	+	0.100659i	0.410287	+	0.911956i	$0.365428\pi$
$282$			0.834167i			0.0496740i
$283$	18.0520	+	10.4223i	1.07308	+	0.619543i	0.929022	−	0.370026i	$-0.120651\pi$
$283$	18.0520	+	10.4223i	1.07308	+	0.619543i	0.144059	+	0.989569i	$0.453984\pi$
$284$	−2.26228	−	3.91838i	−0.134242	−	0.232513i
$285$	−0.205782			−0.0121895
$286$	−24.2308			−1.43280
$287$	−3.49466	−	6.05294i	−0.206283	−	0.357293i
$288$			1.00000i			0.0589256i
$289$	−3.50324	+	6.06780i	−0.206073	+	0.356929i
$290$		−	6.44199i		−	0.378286i
$291$	−0.132543	−	0.0765237i	−0.00776981	−	0.00448590i
$292$	2.45781	−	4.25705i	0.143832	−	0.249125i
$293$	1.12816	−	1.95403i	0.0659077	−	0.114156i	−0.831189	−	0.555991i	$-0.812339\pi$
$293$	1.12816	−	1.95403i	0.0659077	−	0.114156i	0.897096	+	0.441835i	$0.145672\pi$
$294$	−2.01696	+	1.16450i	−0.117632	+	0.0679147i
$295$	4.55572			0.265244
$296$	5.37995	−	2.83833i	0.312704	−	0.164974i
$297$	4.64319			0.269425
$298$	8.80454	−	5.08331i	0.510034	−	0.294468i
$299$	9.09731	−	15.7570i	0.526111	−	0.911251i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	5.06361	+	2.92348i	0.291862	+	0.168506i
$302$			2.43695i			0.140231i
$303$	−4.21966	+	7.30867i	−0.242413	+	0.419872i
$304$		−	0.205782i		−	0.0118024i
$305$	5.32064	+	9.21562i	0.304659	+	0.527685i
$306$	−3.16125			−0.180717
$307$	14.0079			0.799474			0.399737	−	0.916630i	$-0.369101\pi$
$307$	14.0079			0.799474			0.399737	+	0.916630i	$0.369101\pi$
$308$	−5.01755	−	8.69065i	−0.285901	−	0.495196i
$309$	3.59622	+	2.07628i	0.204582	+	0.118115i
$310$		−	6.19187i		−	0.351675i
$311$	17.2177	−	9.94062i	0.976323	−	0.563681i	0.0751653	−	0.997171i	$-0.476052\pi$
$311$	17.2177	−	9.94062i	0.976323	−	0.563681i	0.901158	+	0.433490i	$0.142718\pi$
$312$	−2.60928	−	4.51941i	−0.147722	−	0.255861i
$313$	−21.0731	+	12.1665i	−1.19112	+	0.687694i	−0.958561	−	0.284888i	$-0.908043\pi$
$313$	−21.0731	+	12.1665i	−1.19112	+	0.687694i	−0.232560	+	0.972582i	$0.574710\pi$
$314$	−1.22181	−	0.705413i	−0.0689508	−	0.0398087i
$315$	−1.87170	−	1.08063i	−0.105458	−	0.0608864i
$316$	2.06361	−	1.19143i	0.116087	−	0.0670229i
$317$	2.30160	+	3.98649i	0.129271	+	0.223903i	0.923394	−	0.383853i	$-0.125403\pi$
$317$	2.30160	+	3.98649i	0.129271	+	0.223903i	−0.794124	+	0.607756i	$0.792070\pi$
$318$	−1.00272	+	0.578919i	−0.0562296	+	0.0324642i
$319$		−	29.9113i		−	1.67471i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−8.48343	−	14.6937i	−0.473499	−	0.820124i
$322$	7.53524			0.419922
$323$	0.650529			0.0361964
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$		−	5.21857i		−	0.289474i
$326$	−4.90393	+	8.49385i	−0.271603	+	0.470431i
$327$		−	1.52817i		−	0.0845083i
$328$	−2.80066	−	1.61696i	−0.154641	−	0.0892818i
$329$	0.901423	−	1.56131i	0.0496971	−	0.0860778i
$330$	−2.32159	+	4.02112i	−0.127800	+	0.221355i
$331$	−22.7234	+	13.1193i	−1.24899	+	0.721105i	−0.970908	−	0.239453i	$-0.923032\pi$
$331$	−22.7234	+	13.1193i	−1.24899	+	0.721105i	−0.278082	+	0.960557i	$0.589699\pi$
$332$	−13.9616			−0.766241
$333$	3.24001	−	5.14804i	0.177552	−	0.282111i
$334$	−15.2736			−0.835734
$335$	0.312243	−	0.180274i	0.0170597	−	0.00984940i
$336$	1.08063	−	1.87170i	0.0589530	−	0.102110i
$337$	4.83436	−	8.37335i	0.263344	−	0.456126i	−0.703784	−	0.710414i	$-0.748508\pi$
$337$	4.83436	−	8.37335i	0.263344	−	0.456126i	0.967129	+	0.254288i	$0.0818412\pi$
$338$	12.3265	+	7.11672i	0.670474	+	0.387099i
$339$		−	19.7945i		−	1.07509i
$340$	1.58063	−	2.73772i	0.0857215	−	0.148474i
$341$		−	28.7500i		−	1.55690i
$342$	−0.102891	−	0.178213i	−0.00556371	−	0.00963663i
$343$	20.1623			1.08866
$344$	2.70535			0.145863
$345$	−1.74326	−	3.01941i	−0.0938539	−	0.162560i
$346$	2.39485	+	1.38267i	0.128748	+	0.0743327i
$347$			36.2192i			1.94435i	0.234259	+	0.972174i	$0.424734\pi$
$347$			36.2192i			1.94435i	−0.234259	+	0.972174i	$0.575266\pi$
$348$	5.57892	−	3.22099i	0.299062	−	0.172663i
$349$	4.27797	+	7.40967i	0.228995	+	0.396630i	0.957510	−	0.288399i	$-0.0931228\pi$
$349$	4.27797	+	7.40967i	0.228995	+	0.396630i	−0.728516	+	0.685029i	$0.759789\pi$
$350$	1.87170	−	1.08063i	0.100047	−	0.0577619i
$351$	−4.51941	−	2.60928i	−0.241228	−	0.139273i
$352$	−4.02112	−	2.32159i	−0.214326	−	0.123741i
$353$	29.7047	−	17.1500i	1.58102	−	0.912804i	0.586312	−	0.810085i	$-0.300579\pi$
$353$	29.7047	−	17.1500i	1.58102	−	0.912804i	0.994710	−	0.102719i	$-0.0327542\pi$
$354$	2.27786	+	3.94537i	0.121067	+	0.209694i
$355$	3.91838	−	2.26228i	0.207966	−	0.120069i
$356$			15.5253i			0.822841i
$357$	5.91691	+	3.41613i	0.313156	+	0.180801i
$358$	−0.586956	−	1.01664i	−0.0310216	−	0.0537310i
$359$	−0.531359			−0.0280441			−0.0140220	−	0.999902i	$-0.504464\pi$
$359$	−0.531359			−0.0280441			−0.0140220	+	0.999902i	$0.504464\pi$
$360$	−1.00000			−0.0527046
$361$	−9.47883	−	16.4178i	−0.498886	−	0.864095i
$362$			21.1590i			1.11209i
$363$	−5.27959	+	9.14453i	−0.277107	+	0.479963i
$364$			11.2786i			0.591161i
$365$	4.25705	+	2.45781i	0.222824	+	0.128648i
$366$	−5.32064	+	9.21562i	−0.278114	+	0.481708i
$367$	10.6682	−	18.4778i	0.556873	−	0.964533i	−0.440882	−	0.897565i	$-0.645334\pi$
$367$	10.6682	−	18.4778i	0.556873	−	0.964533i	0.997755	−	0.0669678i	$-0.0213325\pi$
$368$	3.01941	−	1.74326i	0.157398	−	0.0908736i
$369$	−3.23393			−0.168351
$370$	2.83833	+	5.37995i	0.147557	+	0.279691i
$371$	2.50238			0.129917
$372$	5.36232	−	3.09594i	0.278023	−	0.160517i
$373$	−12.0963	+	20.9513i	−0.626320	+	1.08482i	0.361964	+	0.932192i	$0.382106\pi$
$373$	−12.0963	+	20.9513i	−0.626320	+	1.08482i	−0.988284	+	0.152626i	$0.951227\pi$
$374$	7.33914	−	12.7118i	0.379498	−	0.657310i
$375$	−0.866025	−	0.500000i	−0.0447214	−	0.0258199i
$376$		−	0.834167i		−	0.0430189i
$377$	−16.8090	+	29.1140i	−0.865706	+	1.49945i
$378$		−	2.16125i		−	0.111163i
$379$	12.1357	+	21.0196i	0.623367	+	1.07970i	0.988854	+	0.148886i	$0.0475689\pi$
$379$	12.1357	+	21.0196i	0.623367	+	1.07970i	−0.365488	+	0.930816i	$0.619098\pi$
$380$	0.205782			0.0105564
$381$	1.42718			0.0731169
$382$	−5.42635	−	9.39872i	−0.277636	−	0.480880i
$383$	−11.1983	−	6.46534i	−0.572206	−	0.330363i	0.185824	−	0.982583i	$-0.440505\pi$
$383$	−11.1983	−	6.46534i	−0.572206	−	0.330363i	−0.758030	+	0.652220i	$0.773838\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	8.69065	−	5.01755i	0.442917	−	0.255718i
$386$	11.4872	+	19.8964i	0.584682	+	1.01270i
$387$	2.34291	−	1.35268i	0.119097	−	0.0687605i
$388$	0.132543	+	0.0765237i	0.00672885	+	0.00388490i
$389$	−10.9293	−	6.31001i	−0.554136	−	0.319930i	0.196653	−	0.980473i	$-0.436993\pi$
$389$	−10.9293	−	6.31001i	−0.554136	−	0.319930i	−0.750788	+	0.660543i	$0.770326\pi$
$390$	4.51941	−	2.60928i	0.228849	−	0.132126i
$391$	5.51088	+	9.54512i	0.278697	+	0.482718i
$392$	2.01696	−	1.16450i	0.101872	−	0.0588159i
$393$		−	15.9205i		−	0.803084i
$394$	15.9323	+	9.19854i	0.802659	+	0.463416i
$395$	1.19143	+	2.06361i	0.0599471	+	0.103831i
$396$	−4.64319			−0.233329
$397$	1.44241			0.0723926			0.0361963	−	0.999345i	$-0.488476\pi$
$397$	1.44241			0.0723926			0.0361963	+	0.999345i	$0.488476\pi$
$398$	5.46700	+	9.46911i	0.274036	+	0.474644i
$399$			0.444747i			0.0222652i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$		−	19.5163i		−	0.974597i	−0.873235	−	0.487299i	$-0.837982\pi$
$401$		−	19.5163i		−	0.974597i	0.873235	−	0.487299i	$-0.162018\pi$
$402$	0.312243	+	0.180274i	0.0155733	+	0.00899123i
$403$	−16.1563	+	27.9836i	−0.804805	+	1.39396i
$404$	4.21966	−	7.30867i	0.209936	−	0.363620i
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	−13.9228			−0.690975
$407$	13.1789	+	24.9801i	0.653253	+	1.23822i
$408$	3.16125			0.156505
$409$	−8.91730	+	5.14840i	−0.440932	+	0.254572i	−0.703993	−	0.710207i	$-0.748601\pi$
$409$	−8.91730	+	5.14840i	−0.440932	+	0.254572i	0.263061	+	0.964779i	$0.415268\pi$
$410$	1.61696	−	2.80066i	0.0798561	−	0.138315i
$411$	−0.570579	+	0.988273i	−0.0281446	+	0.0487479i
$412$	−3.59622	−	2.07628i	−0.177173	−	0.102291i
$413$		−	9.84606i		−	0.484493i
$414$	1.74326	−	3.01941i	0.0856765	−	0.148396i
$415$		−	13.9616i		−	0.685347i
$416$	2.60928	+	4.51941i	0.127931	+	0.221582i
$417$	−2.76665			−0.135484
$418$	0.955485			0.0467343
$419$	−3.05527	−	5.29188i	−0.149260	−	0.258525i	0.781694	−	0.623662i	$-0.214356\pi$
$419$	−3.05527	−	5.29188i	−0.149260	−	0.258525i	−0.930954	+	0.365136i	$0.881022\pi$
$420$	1.87170	+	1.08063i	0.0913296	+	0.0527291i
$421$			28.0074i			1.36500i	0.730888	+	0.682498i	$0.239106\pi$
$421$			28.0074i			1.36500i	−0.730888	+	0.682498i	$0.760894\pi$
$422$	−4.64980	+	2.68456i	−0.226349	+	0.130683i
$423$	−0.417084	−	0.722410i	−0.0202793	−	0.0351248i
$424$	1.00272	−	0.578919i	0.0486963	−	0.0281148i
$425$	2.73772	+	1.58063i	0.132799	+	0.0766716i
$426$	3.91838	+	2.26228i	0.189846	+	0.109608i
$427$	19.9173	−	11.4992i	0.963865	−	0.556487i
$428$	8.48343	+	14.6937i	0.410062	+	0.710248i
$429$	20.9845	−	12.1154i	1.01314	−	0.584937i
$430$			2.70535i			0.130464i
$431$	−13.3803	−	7.72513i	−0.644507	−	0.372106i	0.141842	−	0.989889i	$-0.454698\pi$
$431$	−13.3803	−	7.72513i	−0.644507	−	0.372106i	−0.786348	+	0.617783i	$0.788031\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	17.9207			0.861215			0.430607	−	0.902539i	$-0.358299\pi$
$433$	17.9207			0.861215			0.430607	+	0.902539i	$0.358299\pi$
$434$	−13.3822			−0.642366
$435$	3.22099	+	5.57892i	0.154435	+	0.267489i
$436$			1.52817i			0.0731863i
$437$	−0.358731	+	0.621341i	−0.0171604	+	0.0297228i
$438$			4.91562i			0.234877i
$439$	−3.25893	−	1.88155i	−0.155540	−	0.0898013i	0.420210	−	0.907427i	$-0.361957\pi$
$439$	−3.25893	−	1.88155i	−0.155540	−	0.0898013i	−0.575750	+	0.817626i	$0.695290\pi$
$440$	2.32159	−	4.02112i	0.110678	−	0.191699i
$441$	1.16450	−	2.01696i	0.0554522	−	0.0960460i
$442$	−14.2870	+	8.24860i	−0.679563	+	0.392346i
$443$	39.4966			1.87654			0.938271	−	0.345902i	$-0.112427\pi$
$443$	39.4966			1.87654			0.938271	+	0.345902i	$0.112427\pi$
$444$	−3.24001	+	5.14804i	−0.153764	+	0.244315i
$445$	−15.5253			−0.735972
$446$	−20.0596	+	11.5814i	−0.949848	+	0.548395i
$447$	−5.08331	+	8.80454i	−0.240432	+	0.416441i
$448$	−1.08063	+	1.87170i	−0.0510548	+	0.0884295i
$449$	−3.39675	−	1.96112i	−0.160303	−	0.0925508i	0.417703	−	0.908584i	$-0.362835\pi$
$449$	−3.39675	−	1.96112i	−0.160303	−	0.0925508i	−0.578005	+	0.816033i	$0.696169\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	7.50786	−	13.0040i	0.353531	−	0.612334i
$452$			19.7945i			0.931057i
$453$	−1.21847	−	2.11046i	−0.0572489	−	0.0991580i
$454$	−23.7706			−1.11561
$455$	−11.2786			−0.528751
$456$	0.102891	+	0.178213i	0.00481831	+	0.00834557i
$457$	−4.62565	−	2.67062i	−0.216379	−	0.124926i	0.387894	−	0.921704i	$-0.373203\pi$
$457$	−4.62565	−	2.67062i	−0.216379	−	0.124926i	−0.604272	+	0.796778i	$0.706536\pi$
$458$			4.55782i			0.212973i
$459$	2.73772	−	1.58063i	0.127786	−	0.0737773i
$460$	1.74326	+	3.01941i	0.0812798	+	0.140781i
$461$	22.9413	−	13.2452i	1.06848	−	0.616889i	0.140716	−	0.990050i	$-0.455059\pi$
$461$	22.9413	−	13.2452i	1.06848	−	0.616889i	0.927767	+	0.373161i	$0.121726\pi$
$462$	8.69065	+	5.01755i	0.404326	+	0.233437i
$463$	−29.0544	−	16.7746i	−1.35027	−	0.779580i	−0.361984	−	0.932184i	$-0.617901\pi$
$463$	−29.0544	−	16.7746i	−1.35027	−	0.779580i	−0.988287	+	0.152604i	$0.951234\pi$
$464$	−5.57892	+	3.22099i	−0.258995	+	0.149531i
$465$	3.09594	+	5.36232i	0.143571	+	0.248672i
$466$	−15.8313	+	9.14018i	−0.733369	+	0.423411i
$467$		−	19.4765i		−	0.901265i	−0.892709	−	0.450633i	$-0.851198\pi$
$467$		−	19.4765i		−	0.901265i	0.892709	−	0.450633i	$-0.148802\pi$
$468$	4.51941	+	2.60928i	0.208910	+	0.120614i
$469$	−0.389617	−	0.674836i	−0.0179908	−	0.0311610i
$470$	0.834167			0.0384773
$471$	1.41083			0.0650074
$472$	−2.27786	−	3.94537i	−0.104847	−	0.181600i
$473$			12.5615i			0.577577i
$474$	−1.19143	+	2.06361i	−0.0547240	+	0.0947847i
$475$			0.205782i			0.00944193i
$476$	−5.91691	−	3.41613i	−0.271201	−	0.156578i
$477$	0.578919	−	1.00272i	0.0265069	−	0.0459113i
$478$	10.1798	−	17.6319i	0.465611	−	0.806462i
$479$	11.0157	−	6.35989i	0.503318	−	0.290591i	−0.226765	−	0.973950i	$-0.572815\pi$
$479$	11.0157	−	6.35989i	0.503318	−	0.290591i	0.730083	+	0.683359i	$0.239482\pi$
$480$	1.00000			0.0456435
$481$	1.21027	−	31.7202i	0.0551834	−	1.44632i
$482$	15.3835			0.700698
$483$	−6.52571	+	3.76762i	−0.296930	+	0.171433i
$484$	5.27959	−	9.14453i	0.239982	−	0.415660i
$485$	−0.0765237	+	0.132543i	−0.00347476	+	0.00601847i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$		−	33.0632i		−	1.49824i	−0.662435	−	0.749119i	$-0.730477\pi$
$487$		−	33.0632i		−	1.49824i	0.662435	−	0.749119i	$-0.269523\pi$
$488$	5.32064	−	9.21562i	0.240854	−	0.417172i
$489$		−	9.80785i		−	0.443526i
$490$	1.16450	+	2.01696i	0.0526065	+	0.0911172i
$491$	18.4326			0.831853			0.415927	−	0.909398i	$-0.363457\pi$
$491$	18.4326			0.831853			0.415927	+	0.909398i	$0.363457\pi$
$492$	3.23393			0.145797
$493$	−10.1824	−	17.6364i	−0.458591	−	0.794303i
$494$	−0.930014	−	0.536944i	−0.0418433	−	0.0241582i
$495$		−	4.64319i		−	0.208696i
$496$	−5.36232	+	3.09594i	−0.240775	+	0.139012i
$497$	−4.88936	−	8.46861i	−0.219318	−	0.379869i
$498$	12.0911	−	6.98079i	0.541814	−	0.312817i
$499$	34.0311	+	19.6479i	1.52344	+	0.879559i	0.999615	+	0.0277344i	$0.00882925\pi$
$499$	34.0311	+	19.6479i	1.52344	+	0.879559i	0.523826	+	0.851825i	$0.324504\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	13.2273	−	7.63680i	0.590953	−	0.341187i
$502$	−6.63994	−	11.5007i	−0.296355	−	0.513302i
$503$	−25.6760	+	14.8240i	−1.14483	+	0.660970i	−0.947623	−	0.319391i	$-0.896522\pi$
$503$	−25.6760	+	14.8240i	−1.14483	+	0.660970i	−0.197211	+	0.980361i	$0.563188\pi$
$504$			2.16125i			0.0962698i
$505$	7.30867	+	4.21966i	0.325231	+	0.187772i
$506$	8.09427	+	14.0197i	0.359834	+	0.623251i
$507$	−14.2334			−0.632129
$508$	−1.42718			−0.0633210
$509$	−17.2652	−	29.9043i	−0.765268	−	1.32548i	−0.940105	−	0.340886i	$-0.889273\pi$
$509$	−17.2652	−	29.9043i	−0.765268	−	1.32548i	0.174836	−	0.984598i	$-0.444060\pi$
$510$			3.16125i			0.139983i
$511$	5.31194	−	9.20055i	0.234986	−	0.407008i
$512$			1.00000i			0.0441942i
$513$	0.178213	+	0.102891i	0.00786828	+	0.00454275i
$514$	−1.45986	+	2.52855i	−0.0643917	+	0.111530i
$515$	2.07628	−	3.59622i	0.0914918	−	0.158468i
$516$	−2.34291	+	1.35268i	−0.103141	+	0.0595483i
$517$	3.87320			0.170343
$518$	11.6274	−	6.13434i	0.510880	−	0.269527i
$519$	−2.76534			−0.121385
$520$	−4.51941	+	2.60928i	−0.198189	+	0.114425i
$521$	21.9354	−	37.9932i	0.961006	−	1.66451i	0.241023	−	0.970519i	$-0.422517\pi$
$521$	21.9354	−	37.9932i	0.961006	−	1.66451i	0.719983	−	0.693992i	$-0.244150\pi$
$522$	−3.22099	+	5.57892i	−0.140979	+	0.244183i
$523$	24.1241	+	13.9281i	1.05487	+	0.609031i	0.924010	−	0.382369i	$-0.124892\pi$
$523$	24.1241	+	13.9281i	1.05487	+	0.609031i	0.130864	+	0.991400i	$0.458225\pi$
$524$			15.9205i			0.695491i
$525$	−1.08063	+	1.87170i	−0.0471624	+	0.0816876i
$526$			10.3676i			0.452049i
$527$	−9.78703	−	16.9516i	−0.426330	−	0.738425i
$528$	4.64319			0.202069
$529$	10.8442			0.471487
$530$	0.578919	+	1.00272i	0.0251466	+	0.0435553i
$531$	−3.94537	−	2.27786i	−0.171214	−	0.0988507i
$532$		−	0.444747i		−	0.0192822i
$533$	−14.6154	+	8.43823i	−0.633065	+	0.365500i
$534$	−7.76267	−	13.4453i	−0.335924	−	0.581837i
$535$	−14.6937	+	8.48343i	−0.635265	+	0.366771i
$536$	−0.312243	−	0.180274i	−0.0134868	−	0.00778663i
$537$	1.01664	+	0.586956i	0.0438712	+	0.0253290i
$538$	21.8620	−	12.6220i	0.942536	−	0.544173i
$539$	5.40697	+	9.36515i	0.232895	+	0.403385i
$540$	0.866025	−	0.500000i	0.0372678	−	0.0215166i
$541$		−	9.84613i		−	0.423318i	−0.977344	−	0.211659i	$-0.932113\pi$
$541$		−	9.84613i		−	0.423318i	0.977344	−	0.211659i	$-0.0678866\pi$
$542$	−14.1632	−	8.17713i	−0.608362	−	0.351238i
$543$	−10.5795	−	18.3242i	−0.454009	−	0.786366i
$544$	−3.16125			−0.135538
$545$	−1.52817			−0.0654598
$546$	−5.63932	−	9.76759i	−0.241341	−	0.418014i
$547$		−	22.3203i		−	0.954348i	−0.878809	−	0.477174i	$-0.841661\pi$
$547$		−	22.3203i		−	0.954348i	0.878809	−	0.477174i	$-0.158339\pi$
$548$	0.570579	−	0.988273i	0.0243739	−	0.0422169i
$549$		−	10.6413i		−	0.454159i
$550$	4.02112	+	2.32159i	0.171461	+	0.0989931i
$551$	0.662823	−	1.14804i	0.0282372	−	0.0489083i
$552$	−1.74326	+	3.01941i	−0.0741980	+	0.128515i
$553$	4.45998	−	2.57497i	0.189658	−	0.109499i
$554$	3.35255			0.142436
$555$	−5.14804	−	3.24001i	−0.218522	−	0.137531i
$556$	2.76665			0.117332
$557$	−6.99456	+	4.03831i	−0.296369	+	0.171109i	−0.640811	−	0.767699i	$-0.721402\pi$
$557$	−6.99456	+	4.03831i	−0.296369	+	0.171109i	0.344441	+	0.938808i	$0.388068\pi$
$558$	−3.09594	+	5.36232i	−0.131061	+	0.227005i
$559$	7.05904	−	12.2266i	0.298565	−	0.517131i
$560$	−1.87170	−	1.08063i	−0.0790937	−	0.0456648i
$561$			14.6783i			0.619718i
$562$	−1.68735	+	2.92257i	−0.0711765	+	0.123281i
$563$		−	14.8077i		−	0.624069i	−0.950071	−	0.312034i	$-0.898990\pi$
$563$		−	14.8077i		−	0.624069i	0.950071	−	0.312034i	$-0.101010\pi$
$564$	0.417084	+	0.722410i	0.0175624	+	0.0304190i
$565$	−19.7945			−0.832763
$566$	20.8447			0.876167
$567$	1.08063	+	1.87170i	0.0453820	+	0.0786040i
$568$	−3.91838	−	2.26228i	−0.164412	−	0.0949232i
$569$			25.6916i			1.07705i	0.842611	+	0.538523i	$0.181018\pi$
$569$			25.6916i			1.07705i	−0.842611	+	0.538523i	$0.818982\pi$
$570$	−0.178213	+	0.102891i	−0.00746450	+	0.00430963i
$571$	−2.31582	−	4.01112i	−0.0969142	−	0.167860i	0.813492	−	0.581576i	$-0.197564\pi$
$571$	−2.31582	−	4.01112i	−0.0969142	−	0.167860i	−0.910406	+	0.413716i	$0.864231\pi$
$572$	−20.9845	+	12.1154i	−0.877405	+	0.506570i
$573$	9.39872	+	5.42635i	0.392637	+	0.226689i
$574$	−6.05294	−	3.49466i	−0.252645	−	0.145864i
$575$	−3.01941	+	1.74326i	−0.125918	+	0.0726989i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−26.8227	+	15.4861i	−1.11664	+	0.644694i	−0.940542	−	0.339678i	$-0.889682\pi$
$577$	−26.8227	+	15.4861i	−1.11664	+	0.644694i	−0.176101	+	0.984372i	$0.556349\pi$
$578$			7.00649i			0.291431i
$579$	−19.8964	−	11.4872i	−0.826866	−	0.477391i
$580$	−3.22099	−	5.57892i	−0.133744	−	0.231652i
$581$	−30.1745			−1.25185
$582$	−0.153047			−0.00634402
$583$	2.68803	+	4.65581i	0.111327	+	0.192824i
$584$		−	4.91562i		−	0.203410i
$585$	−2.60928	+	4.51941i	−0.107881	+	0.186855i
$586$		−	2.25632i		−	0.0932076i
$587$	−32.3952	−	18.7033i	−1.33709	−	0.771970i	−0.350716	−	0.936482i	$-0.614062\pi$
$587$	−32.3952	−	18.7033i	−1.33709	−	0.771970i	−0.986375	+	0.164512i	$0.947395\pi$
$588$	−1.16450	+	2.01696i	−0.0480230	+	0.0831782i
$589$	0.637088	−	1.10347i	0.0262508	−	0.0454676i
$590$	3.94537	−	2.27786i	0.162428	−	0.0937780i
$591$	−18.3971			−0.756755
$592$	3.24001	−	5.14804i	0.133164	−	0.211583i
$593$	−10.9308			−0.448876			−0.224438	−	0.974488i	$-0.572055\pi$
$593$	−10.9308			−0.448876			−0.224438	+	0.974488i	$0.572055\pi$
$594$	4.02112	−	2.32159i	0.164988	−	0.0952561i
$595$	3.41613	−	5.91691i	0.140048	−	0.242570i
$596$	5.08331	−	8.80454i	0.208220	−	0.360648i
$597$	−9.46911	−	5.46700i	−0.387545	−	0.223749i
$598$		−	18.1946i		−	0.744033i
$599$	−22.6620	+	39.2517i	−0.925943	+	1.60378i	−0.135906	+	0.990722i	$0.543394\pi$
$599$	−22.6620	+	39.2517i	−0.925943	+	1.60378i	−0.790037	+	0.613059i	$0.789939\pi$
$600$			1.00000i			0.0408248i
$601$	19.7964	+	34.2884i	0.807514	+	1.39865i	0.914581	+	0.404403i	$0.132521\pi$
$601$	19.7964	+	34.2884i	0.807514	+	1.39865i	−0.107067	+	0.994252i	$0.534146\pi$
$602$	5.84695			0.238304
$603$	−0.360547			−0.0146826
$604$	1.21847	+	2.11046i	0.0495790	+	0.0858733i
$605$	9.14453	+	5.27959i	0.371778	+	0.214646i
$606$			8.43932i			0.342824i
$607$	35.1813	−	20.3119i	1.42796	−	0.824435i	0.431004	−	0.902350i	$-0.358159\pi$
$607$	35.1813	−	20.3119i	1.42796	−	0.824435i	0.996960	+	0.0779145i	$0.0248261\pi$
$608$	−0.102891	−	0.178213i	−0.00417278	−	0.00722747i
$609$	12.0575	−	6.96138i	0.488593	−	0.282089i
$610$	9.21562	+	5.32064i	0.373130	+	0.215426i
$611$	−3.76995	−	2.17658i	−0.152516	−	0.0880550i
$612$	−2.73772	+	1.58063i	−0.110666	+	0.0638930i
$613$	−7.78583	−	13.4855i	−0.314467	−	0.544672i	0.664857	−	0.746970i	$-0.268492\pi$
$613$	−7.78583	−	13.4855i	−0.314467	−	0.544672i	−0.979324	+	0.202298i	$0.935159\pi$
$614$	12.1312	−	7.00396i	0.489576	−	0.282657i
$615$			3.23393i			0.130404i
$616$	−8.69065	−	5.01755i	−0.350156	−	0.202163i
$617$	10.5032	+	18.1921i	0.422843	+	0.732386i	0.996216	−	0.0869081i	$-0.0276987\pi$
$617$	10.5032	+	18.1921i	0.422843	+	0.732386i	−0.573373	+	0.819295i	$0.694365\pi$
$618$	4.15256			0.167040
$619$	−29.8151			−1.19837			−0.599186	−	0.800610i	$-0.704509\pi$
$619$	−29.8151			−1.19837			−0.599186	+	0.800610i	$0.704509\pi$
$620$	−3.09594	−	5.36232i	−0.124336	−	0.215356i
$621$			3.48652i			0.139909i
$622$	9.94062	−	17.2177i	0.398582	−	0.690365i
$623$			33.5542i			1.34432i
$624$	−4.51941	−	2.60928i	−0.180921	−	0.104455i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−12.1665	+	21.0731i	−0.486273	+	0.842249i
$627$	−0.827474	+	0.477742i	−0.0330461	+	0.0190792i
$628$	−1.41083			−0.0562981
$629$	16.2742	+	10.2425i	0.648897	+	0.408395i
$630$	−2.16125			−0.0861063
$631$	−19.1456	+	11.0537i	−0.762173	+	0.440041i	−0.830075	−	0.557651i	$-0.811703\pi$
$631$	−19.1456	+	11.0537i	−0.762173	+	0.440041i	0.0679026	+	0.997692i	$0.478369\pi$
$632$	1.19143	−	2.06361i	0.0473924	−	0.0820860i
$633$	2.68456	−	4.64980i	0.106702	−	0.184813i
$634$	3.98649	+	2.30160i	0.158324	+	0.0914081i
$635$		−	1.42718i		−	0.0566361i
$636$	−0.578919	+	1.00272i	−0.0229556	+	0.0397603i
$637$		−	12.1540i		−	0.481559i
$638$	−14.9557	−	25.9040i	−0.592101	−	1.02555i
$639$	−4.52456			−0.178989
$640$	−1.00000			−0.0395285
$641$	−2.21636	−	3.83886i	−0.0875411	−	0.151626i	0.818930	−	0.573893i	$-0.194568\pi$
$641$	−2.21636	−	3.83886i	−0.0875411	−	0.151626i	−0.906471	+	0.422268i	$0.861234\pi$
$642$	−14.6937	−	8.48343i	−0.579915	−	0.334814i
$643$			44.3817i			1.75024i	0.483902	+	0.875122i	$0.339219\pi$
$643$			44.3817i			1.75024i	−0.483902	+	0.875122i	$0.660781\pi$
$644$	6.52571	−	3.76762i	0.257149	−	0.148465i
$645$	−1.35268	−	2.34291i	−0.0532616	−	0.0922518i
$646$	0.563375	−	0.325265i	0.0221657	−	0.0127974i
$647$	−36.1565	−	20.8750i	−1.42146	−	0.820681i	−0.425037	−	0.905176i	$-0.639739\pi$
$647$	−36.1565	−	20.8750i	−1.42146	−	0.820681i	−0.996424	+	0.0844957i	$0.973072\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	18.3191	−	10.5765i	0.719087	−	0.415165i
$650$	−2.60928	−	4.51941i	−0.102345	−	0.177266i
$651$	11.5893	−	6.69110i	0.454221	−	0.262245i
$652$			9.80785i			0.384105i
$653$	15.9953	+	9.23488i	0.625944	+	0.361389i	0.779179	−	0.626801i	$-0.215636\pi$
$653$	15.9953	+	9.23488i	0.625944	+	0.361389i	−0.153236	+	0.988190i	$0.548969\pi$
$654$	−0.764087	−	1.32344i	−0.0298782	−	0.0517505i
$655$	−15.9205			−0.622066
$656$	−3.23393			−0.126264
$657$	−2.45781	−	4.25705i	−0.0958882	−	0.166083i
$658$		−	1.80285i		−	0.0702823i
$659$	3.89081	−	6.73909i	0.151565	−	0.262518i	−0.780238	−	0.625482i	$-0.784902\pi$
$659$	3.89081	−	6.73909i	0.151565	−	0.262518i	0.931803	+	0.362965i	$0.118236\pi$
$660$			4.64319i			0.180736i
$661$	24.6064	+	14.2065i	0.957077	+	0.552569i	0.895272	−	0.445520i	$-0.146981\pi$
$661$	24.6064	+	14.2065i	0.957077	+	0.552569i	0.0618049	+	0.998088i	$0.480314\pi$
$662$	−13.1193	+	22.7234i	−0.509898	+	0.883169i
$663$	8.24860	−	14.2870i	0.320349	−	0.554861i
$664$	−12.0911	+	6.98079i	−0.469225	+	0.270907i
$665$	0.444747			0.0172465
$666$	0.231916	−	6.07834i	0.00898655	−	0.235531i
$667$	22.4601			0.869658
$668$	−13.2273	+	7.63680i	−0.511781	+	0.295477i
$669$	11.5814	−	20.0596i	0.447763	−	0.775547i
$670$	0.180274	−	0.312243i	0.00696457	−	0.0120630i
$671$	42.7899	+	24.7047i	1.65188	+	0.953716i
$672$		−	2.16125i		−	0.0833721i
$673$	−11.5000	+	19.9185i	−0.443291	+	0.767803i	−0.997931	−	0.0642874i	$-0.979523\pi$
$673$	−11.5000	+	19.9185i	−0.443291	+	0.767803i	0.554640	+	0.832090i	$0.312856\pi$
$674$		−	9.66872i		−	0.372425i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	14.2334			0.547440
$677$	41.5752			1.59786			0.798932	−	0.601422i	$-0.205399\pi$
$677$	41.5752			1.59786			0.798932	+	0.601422i	$0.205399\pi$
$678$	−9.89727	−	17.1426i	−0.380103	−	0.658357i
$679$	0.286459	+	0.165387i	0.0109933	+	0.00634697i
$680$		−	3.16125i		−	0.121228i
$681$	20.5859	−	11.8853i	0.788855	−	0.455446i
$682$	−14.3750	−	24.8982i	−0.550448	−	0.953403i
$683$	−8.30680	+	4.79594i	−0.317851	+	0.183511i	−0.650434	−	0.759563i	$-0.725413\pi$
$683$	−8.30680	+	4.79594i	−0.317851	+	0.183511i	0.332583	+	0.943074i	$0.392080\pi$
$684$	−0.178213	−	0.102891i	−0.00681413	−	0.00393414i
$685$	0.988273	+	0.570579i	0.0377600	+	0.0218007i
$686$	17.4611	−	10.0811i	0.666666	−	0.384900i
$687$	−2.27891	−	3.94718i	−0.0869458	−	0.150594i
$688$	2.34291	−	1.35268i	0.0893224	−	0.0515703i
$689$		−	6.04226i		−	0.230192i
$690$	−3.01941	−	1.74326i	−0.114947	−	0.0663647i
$691$	−14.0821	−	24.3909i	−0.535709	−	0.927875i	−0.999129	−	0.0417362i	$-0.986711\pi$
$691$	−14.0821	−	24.3909i	−0.535709	−	0.927875i	0.463420	−	0.886139i	$-0.346622\pi$
$692$	2.76534			0.105122
$693$	−10.0351			−0.381202
$694$	18.1096	+	31.3667i	0.687431	+	1.19067i
$695$			2.76665i			0.104945i
$696$	3.22099	−	5.57892i	0.122091	−	0.211469i
$697$		−	10.2233i		−	0.387233i
$698$	7.40967	+	4.27797i	0.280460	+	0.161924i
$699$	9.14018	−	15.8313i	0.345713	−	0.598793i
$700$	1.08063	−	1.87170i	0.0408438	−	0.0707436i
$701$	23.6784	−	13.6707i	0.894319	−	0.516335i	0.0189664	−	0.999820i	$-0.493962\pi$
$701$	23.6784	−	13.6707i	0.894319	−	0.516335i	0.875353	+	0.483485i	$0.160629\pi$
$702$	−5.21857			−0.196962
$703$	−0.0477241	+	1.25081i	−0.00179995	+	0.0471753i
$704$	−4.64319			−0.174997
$705$	−0.722410	+	0.417084i	−0.0272075	+	0.0157083i
$706$	17.1500	−	29.7047i	0.645450	−	1.11795i
$707$	9.11975	−	15.7959i	0.342983	−	0.594065i
$708$	3.94537	+	2.27786i	0.148276	+	0.0856072i
$709$			1.92294i			0.0722174i	0.999348	+	0.0361087i	$0.0114963\pi$
$709$			1.92294i			0.0722174i	−0.999348	+	0.0361087i	$0.988504\pi$
$710$	2.26228	−	3.91838i	0.0849019	−	0.147054i
$711$		−	2.38285i		−	0.0893639i
$712$	7.76267	+	13.4453i	0.290918	+	0.503885i
$713$	21.5881			0.808479
$714$	6.83226			0.255691
$715$	−12.1154	−	20.9845i	−0.453090	−	0.784775i
$716$	−1.01664	−	0.586956i	−0.0379936	−	0.0219356i
$717$			20.3595i			0.760340i
$718$	−0.460171	+	0.265680i	−0.0171734	+	0.00991508i
$719$	10.1641	+	17.6047i	0.379056	+	0.656544i	0.990925	−	0.134415i	$-0.0429155\pi$
$719$	10.1641	+	17.6047i	0.379056	+	0.656544i	−0.611869	+	0.790959i	$0.709582\pi$
$720$	−0.866025	+	0.500000i	−0.0322749	+	0.0186339i
$721$	−7.77234	−	4.48736i	−0.289457	−	0.167118i
$722$	−16.4178	−	9.47883i	−0.611008	−	0.352765i
$723$	−13.3225	+	7.69174i	−0.495468	+	0.286059i
$724$	10.5795	+	18.3242i	0.393183	+	0.681013i
$725$	5.57892	−	3.22099i	0.207196	−	0.119625i
$726$			10.5592i			0.391888i
$727$	−35.6599	−	20.5883i	−1.32255	−	0.763576i	−0.338418	−	0.940996i	$-0.609892\pi$
$727$	−35.6599	−	20.5883i	−1.32255	−	0.763576i	−0.984135	+	0.177420i	$0.943225\pi$
$728$	5.63932	+	9.76759i	0.209007	+	0.362011i
$729$	1.00000			0.0370370
$730$	4.91562			0.181935
$731$	4.27615	+	7.40652i	0.158159	+	0.273940i
$732$			10.6413i			0.393313i
$733$	17.2131	−	29.8140i	0.635782	−	1.10121i	−0.350567	−	0.936538i	$-0.614011\pi$
$733$	17.2131	−	29.8140i	0.635782	−	1.10121i	0.986349	−	0.164669i	$-0.0526556\pi$
$734$		−	21.3363i		−	0.787538i
$735$	−2.01696	−	1.16450i	−0.0743969	−	0.0429531i
$736$	1.74326	−	3.01941i	0.0642573	−	0.111297i
$737$	0.837044	−	1.44980i	0.0308329	−	0.0534042i
$738$	−2.80066	+	1.61696i	−0.103094	+	0.0595212i
$739$	29.2229			1.07498			0.537490	−	0.843270i	$-0.319372\pi$
$739$	29.2229			1.07498			0.537490	+	0.843270i	$0.319372\pi$
$740$	5.14804	+	3.24001i	0.189246	+	0.119105i
$741$	1.07389			0.0394503
$742$	2.16713	−	1.25119i	0.0795577	−	0.0459326i
$743$	12.0985	−	20.9553i	0.443852	−	0.768774i	−0.554119	−	0.832437i	$-0.686945\pi$
$743$	12.0985	−	20.9553i	0.443852	−	0.768774i	0.997971	+	0.0636630i	$0.0202783\pi$
$744$	3.09594	−	5.36232i	0.113503	−	0.196592i
$745$	8.80454	+	5.08331i	0.322574	+	0.186238i
$746$			24.1925i			0.885750i
$747$	−6.98079	+	12.0911i	−0.255414	+	0.442390i
$748$		−	14.6783i		−	0.536691i
$749$	18.3348	+	31.7569i	0.669940	+	1.16037i
$750$	−1.00000			−0.0365148
$751$	17.0205			0.621085			0.310543	−	0.950559i	$-0.399489\pi$
$751$	17.0205			0.621085			0.310543	+	0.950559i	$0.399489\pi$
$752$	−0.417084	−	0.722410i	−0.0152095	−	0.0263436i
$753$	11.5007	+	6.63994i	0.419110	+	0.241973i
$754$			33.6179i			1.22429i
$755$	−2.11046	+	1.21847i	−0.0768074	+	0.0443448i
$756$	−1.08063	−	1.87170i	−0.0393020	−	0.0680730i
$757$	43.0684	−	24.8655i	1.56535	−	0.903753i	0.568646	−	0.822582i	$-0.307467\pi$
$757$	43.0684	−	24.8655i	1.56535	−	0.903753i	0.996700	−	0.0811706i	$-0.0258659\pi$
$758$	21.0196	+	12.1357i	0.763465	+	0.440787i
$759$	−14.0197	−	8.09427i	−0.508883	−	0.293804i
$760$	0.178213	−	0.102891i	0.00646445	−	0.00373225i
$761$	−2.37295	−	4.11007i	−0.0860193	−	0.148990i	0.819806	−	0.572642i	$-0.194081\pi$
$761$	−2.37295	−	4.11007i	−0.0860193	−	0.148990i	−0.905825	+	0.423652i	$0.860748\pi$
$762$	1.23598	−	0.713592i	0.0447747	−	0.0258507i
$763$			3.30277i			0.119568i
$764$	−9.39872	−	5.42635i	−0.340034	−	0.196319i
$765$	−1.58063	−	2.73772i	−0.0571477	−	0.0989826i
$766$	−12.9307			−0.467204
$767$	−23.7743			−0.858441
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	35.1897i		−	1.26897i	−0.772934	−	0.634486i	$-0.781212\pi$
$769$		−	35.1897i		−	1.26897i	0.772934	−	0.634486i	$-0.218788\pi$
$770$	5.01755	−	8.69065i	0.180820	−	0.313189i
$771$		−	2.91972i		−	0.105151i
$772$	19.8964	+	11.4872i	0.716087	+	0.413433i
$773$	−1.01203	+	1.75289i	−0.0364003	+	0.0630471i	−0.883652	−	0.468145i	$-0.844922\pi$
$773$	−1.01203	+	1.75289i	−0.0364003	+	0.0630471i	0.847251	+	0.531192i	$0.178256\pi$
$774$	1.35268	−	2.34291i	0.0486210	−	0.0842140i
$775$	5.36232	−	3.09594i	0.192620	−	0.111209i
$776$	0.153047			0.00549408
$777$	−7.00249	+	11.1262i	−0.251213	+	0.399151i
$778$	−12.6200			−0.452450
$779$	0.576326	−	0.332742i	0.0206490	−	0.0119217i
$780$	2.60928	−	4.51941i	0.0934273	−	0.161821i
$781$	10.5042	−	18.1938i	0.375869	−	0.651025i
$782$	9.54512	+	5.51088i	0.341333	+	0.197069i
$783$		−	6.44199i		−	0.230218i
$784$	1.16450	−	2.01696i	0.0415891	−	0.0720345i
$785$		−	1.41083i		−	0.0503545i
$786$	−7.96026	−	13.7876i	−0.283933	−	0.491786i
$787$	−9.32236			−0.332306			−0.166153	−	0.986100i	$-0.553135\pi$
$787$	−9.32236			−0.332306			−0.166153	+	0.986100i	$0.553135\pi$
$788$	18.3971			0.655369
$789$	−5.18381	−	8.97862i	−0.184548	−	0.319647i
$790$	2.06361	+	1.19143i	0.0734199	+	0.0423890i
$791$			42.7810i			1.52112i
$792$	−4.02112	+	2.32159i	−0.142884	+	0.0824942i
$793$	−27.7661	−	48.0923i	−0.986004	−	1.70781i
$794$	1.24917	−	0.721206i	0.0443312	−	0.0255946i
$795$	−1.00272	−	0.578919i	−0.0355627	−	0.0205322i
$796$	9.46911	+	5.46700i	0.335624	+	0.193773i
$797$	34.2858	−	19.7949i	1.21447	−	0.701172i	0.250737	−	0.968055i	$-0.419327\pi$
$797$	34.2858	−	19.7949i	1.21447	−	0.701172i	0.963729	+	0.266883i	$0.0859939\pi$
$798$	0.222373	+	0.385162i	0.00787194	+	0.0136346i
$799$	2.28372	−	1.31851i	0.0807922	−	0.0466454i
$800$		−	1.00000i		−	0.0353553i
$801$	13.4453	+	7.76267i	0.475068	+	0.274280i
$802$	−9.75814	−	16.9016i	−0.344572	−	0.596816i
$803$	22.8241			0.805446
$804$	0.360547			0.0127155
$805$	3.76762	+	6.52571i	0.132791	+	0.230001i
$806$			32.3127i			1.13817i
$807$	−12.6220	+	21.8620i	−0.444316	+	0.769577i
$808$		−	8.43932i		−	0.296894i
$809$	39.6420	+	22.8873i	1.39374	+	0.804675i	0.993727	−	0.111834i	$-0.0356726\pi$
$809$	39.6420	+	22.8873i	1.39374	+	0.804675i	0.400012	+	0.916510i	$0.369006\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−13.4039	+	23.2162i	−0.470674	+	0.815232i	−0.999437	−	0.0335375i	$-0.989323\pi$
$811$	−13.4039	+	23.2162i	−0.470674	+	0.815232i	0.528763	+	0.848769i	$0.322656\pi$
$812$	−12.0575	+	6.96138i	−0.423134	+	0.244296i
$813$	16.3543			0.573569
$814$	23.9033	+	15.0440i	0.837811	+	0.527292i
$815$	−9.80785			−0.343554
$816$	2.73772	−	1.58063i	0.0958395	−	0.0553330i
$817$	−0.278357	+	0.482128i	−0.00973847	+	0.0168675i
$818$	−5.14840	+	8.91730i	−0.180010	+	0.311786i
$819$	9.76759	+	5.63932i	0.341307	+	0.197054i
$820$		−	3.23393i		−	0.112934i
$821$	−5.62287	+	9.73910i	−0.196239	+	0.339897i	−0.947306	−	0.320330i	$-0.896206\pi$
$821$	−5.62287	+	9.73910i	−0.196239	+	0.339897i	0.751067	+	0.660226i	$0.229540\pi$
$822$			1.14116i			0.0398025i
$823$	1.35907	+	2.35398i	0.0473743	+	0.0820547i	0.888740	−	0.458411i	$-0.151581\pi$
$823$	1.35907	+	2.35398i	0.0473743	+	0.0820547i	−0.841366	+	0.540466i	$0.818248\pi$
$824$	−4.15256			−0.144661
$825$	−4.64319			−0.161655
$826$	−4.92303	−	8.52694i	−0.171294	−	0.296690i
$827$	−6.47438	−	3.73799i	−0.225136	−	0.129982i	0.383190	−	0.923670i	$-0.374825\pi$
$827$	−6.47438	−	3.73799i	−0.225136	−	0.129982i	−0.608326	+	0.793687i	$0.708159\pi$
$828$		−	3.48652i		−	0.121165i
$829$	−42.8830	+	24.7585i	−1.48939	+	0.859898i	−0.999926	−	0.0121269i	$-0.996140\pi$
$829$	−42.8830	+	24.7585i	−1.48939	+	0.859898i	−0.489461	+	0.872025i	$0.662806\pi$
$830$	−6.98079	−	12.0911i	−0.242307	−	0.419688i
$831$	−2.90340	+	1.67628i	−0.100718	+	0.0581494i
$832$	4.51941	+	2.60928i	0.156682	+	0.0904606i
$833$	6.37613	+	3.68126i	0.220920	+	0.127548i
$834$	−2.39599	+	1.38333i	−0.0829664	+	0.0479007i
$835$	−7.63680	−	13.2273i	−0.264282	−	0.457751i
$836$	0.827474	−	0.477742i	0.0286188	−	0.0165231i
$837$		−	6.19187i		−	0.214022i
$838$	−5.29188	−	3.05527i	−0.182805	−	0.105543i
$839$	16.9768	+	29.4047i	0.586105	+	1.01516i	0.994737	+	0.102464i	$0.0326727\pi$
$839$	16.9768	+	29.4047i	0.586105	+	1.01516i	−0.408632	+	0.912699i	$0.633994\pi$
$840$	2.16125			0.0745703
$841$	−12.4992			−0.431006
$842$	14.0037	+	24.2551i	0.482599	+	0.835885i
$843$		−	3.37470i		−	0.116231i
$844$	−2.68456	+	4.64980i	−0.0924065	+	0.160053i
$845$			14.2334i			0.489645i
$846$	−0.722410	−	0.417084i	−0.0248370	−	0.0143396i
$847$	11.4105	−	19.7636i	0.392071	−	0.679086i
$848$	0.578919	−	1.00272i	0.0198802	−	0.0344335i
$849$	−18.0520	+	10.4223i	−0.619543	+	0.357694i
$850$	3.16125			0.108430
$851$	−18.7573	+	9.89587i	−0.642992	+	0.339226i
$852$	4.52456			0.155009
$853$	−2.40473	+	1.38837i	−0.0823365	+	0.0475370i	−0.540603	−	0.841278i	$-0.681804\pi$
$853$	−2.40473	+	1.38837i	−0.0823365	+	0.0475370i	0.458266	+	0.888815i	$0.348471\pi$
$854$	11.4992	−	19.9173i	0.393496	−	0.681555i
$855$	0.102891	−	0.178213i	0.00351880	−	0.00609474i
$856$	14.6937	+	8.48343i	0.502221	+	0.289958i
$857$			44.3918i			1.51639i	0.652026	+	0.758197i	$0.273919\pi$
$857$			44.3918i			1.51639i	−0.652026	+	0.758197i	$0.726081\pi$
$858$	12.1154	−	20.9845i	0.413613	−	0.716398i
$859$		−	42.5097i		−	1.45041i	−0.688531	−	0.725207i	$-0.741744\pi$
$859$		−	42.5097i		−	1.45041i	0.688531	−	0.725207i	$-0.258256\pi$
$860$	1.35268	+	2.34291i	0.0461259	+	0.0798924i
$861$	6.98933			0.238196
$862$	−15.4503			−0.526238
$863$	3.12609	+	5.41454i	0.106413	+	0.184313i	0.914315	−	0.405004i	$-0.132730\pi$
$863$	3.12609	+	5.41454i	0.106413	+	0.184313i	−0.807901	+	0.589318i	$0.799397\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$			2.76534i			0.0940242i
$866$	15.5198	−	8.96036i	0.527384	−	0.304485i
$867$	−3.50324	−	6.06780i	−0.118976	−	0.206073i
$868$	−11.5893	+	6.69110i	−0.393367	+	0.227111i
$869$	9.58173	+	5.53201i	0.325038	+	0.187661i
$870$	5.57892	+	3.22099i	0.189143	+	0.109202i
$871$	−1.62946	+	0.940770i	−0.0552122	+	0.0318768i
$872$	0.764087	+	1.32344i	0.0258753	+	0.0448173i
$873$	0.132543	−	0.0765237i	0.00448590	−	0.00258994i
$874$			0.717463i			0.0242685i
$875$	1.87170	+	1.08063i	0.0632750	+	0.0365318i
$876$	2.45781	+	4.25705i	0.0830416	+	0.143832i
$877$	13.8626			0.468106			0.234053	−	0.972224i	$-0.424801\pi$
$877$	13.8626			0.468106			0.234053	+	0.972224i	$0.424801\pi$
$878$	−3.76309			−0.126998
$879$	1.12816	+	1.95403i	0.0380518	+	0.0659077i
$880$		−	4.64319i		−	0.156522i
$881$	−18.8071	+	32.5749i	−0.633628	+	1.09748i	0.353176	+	0.935557i	$0.385102\pi$
$881$	−18.8071	+	32.5749i	−0.633628	+	1.09748i	−0.986804	+	0.161919i	$0.948232\pi$
$882$		−	2.32899i		−	0.0784212i
$883$	51.3782	+	29.6632i	1.72901	+	0.998246i	0.894109	+	0.447850i	$0.147810\pi$
$883$	51.3782	+	29.6632i	1.72901	+	0.998246i	0.834904	+	0.550396i	$0.185523\pi$
$884$	−8.24860	+	14.2870i	−0.277431	+	0.480524i
$885$	−2.27786	+	3.94537i	−0.0765694	+	0.132622i
$886$	34.2051	−	19.7483i	1.14914	−	0.663457i
$887$	17.4623			0.586328			0.293164	−	0.956062i	$-0.405292\pi$
$887$	17.4623			0.586328			0.293164	+	0.956062i	$0.405292\pi$
$888$	−0.231916	+	6.07834i	−0.00778258	+	0.203976i
$889$	−3.08450			−0.103451
$890$	−13.4453	+	7.76267i	−0.450689	+	0.260205i
$891$	−2.32159	+	4.02112i	−0.0777763	+	0.134713i
$892$	−11.5814	+	20.0596i	−0.387774	+	0.671644i
$893$	0.148659	+	0.0858284i	0.00497469	+	0.00287214i
$894$			10.1666i			0.340022i
$895$	0.586956	−	1.01664i	0.0196198	−	0.0339825i
$896$			2.16125i			0.0722024i
$897$	9.09731	+	15.7570i	0.303750	+	0.526111i
$898$	−3.92223			−0.130887
$899$	−39.8879			−1.33034
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	3.16984	+	1.83011i	0.105603	+	0.0609698i
$902$		−	15.0157i		−	0.499969i
$903$	−5.06361	+	2.92348i	−0.168506	+	0.0972872i
$904$	9.89727	+	17.1426i	0.329178	+	0.570154i
$905$	−18.3242	+	10.5795i	−0.609117	+	0.351674i
$906$	−2.11046	−	1.21847i	−0.0701153	−	0.0404811i
$907$	−9.47092	−	5.46804i	−0.314477	−	0.181563i	0.334451	−	0.942413i	$-0.391449\pi$
$907$	−9.47092	−	5.46804i	−0.314477	−	0.181563i	−0.648928	+	0.760850i	$0.724782\pi$
$908$	−20.5859	+	11.8853i	−0.683168	+	0.394427i
$909$	−4.21966	−	7.30867i	−0.139957	−	0.242413i
$910$	−9.76759	+	5.63932i	−0.323792	+	0.186942i
$911$		−	33.5376i		−	1.11115i	−0.831467	−	0.555575i	$-0.812498\pi$
$911$		−	33.5376i		−	1.11115i	0.831467	−	0.555575i	$-0.187502\pi$
$912$	0.178213	+	0.102891i	0.00590121	+	0.00340706i
$913$	−32.4131	−	56.1412i	−1.07272	−	1.85800i
$914$	−5.34124			−0.176673
$915$	−10.6413			−0.351790
$916$	2.27891	+	3.94718i	0.0752972	+	0.130419i
$917$			34.4082i			1.13626i
$918$	1.58063	−	2.73772i	0.0521684	−	0.0903584i
$919$			35.6436i			1.17577i	0.808943	+	0.587887i	$0.200040\pi$
$919$			35.6436i			1.17577i	−0.808943	+	0.587887i	$0.799960\pi$
$920$	3.01941	+	1.74326i	0.0995471	+	0.0574735i
$921$	−7.00396	+	12.1312i	−0.230788	+	0.399737i
$922$	13.2452	−	22.9413i	0.436206	−	0.755532i
$923$	−20.4483	+	11.8059i	−0.673066	+	0.388595i
$924$	10.0351			0.330130
$925$	−3.24001	+	5.14804i	−0.106531	+	0.169266i
$926$	−33.5491			−1.10249
$927$	−3.59622	+	2.07628i	−0.118115	+	0.0681939i
$928$	−3.22099	+	5.57892i	−0.105734	+	0.183137i
$929$	−12.8356	+	22.2319i	−0.421123	+	0.729406i	−0.996050	−	0.0887990i	$-0.971697\pi$
$929$	−12.8356	+	22.2319i	−0.421123	+	0.729406i	0.574927	+	0.818205i	$0.305030\pi$
$930$	5.36232	+	3.09594i	0.175837	+	0.101520i
$931$			0.479265i			0.0157073i
$932$	−9.14018	+	15.8313i	−0.299396	+	0.518570i
$933$			19.8812i			0.650882i
$934$	−9.73826	−	16.8672i	−0.318645	−	0.551910i
$935$	14.6783			0.480031
$936$	5.21857			0.170574
$937$	−19.9104	−	34.4858i	−0.650443	−	1.12660i	−0.983015	−	0.183523i	$-0.941250\pi$
$937$	−19.9104	−	34.4858i	−0.650443	−	1.12660i	0.332572	−	0.943078i	$-0.392084\pi$
$938$	−0.674836	−	0.389617i	−0.0220342	−	0.0127214i
$939$		−	24.3331i		−	0.794080i
$940$	0.722410	−	0.417084i	0.0235624	−	0.0136038i
$941$	1.71512	+	2.97067i	0.0559113	+	0.0968411i	0.892626	−	0.450797i	$-0.148860\pi$
$941$	1.71512	+	2.97067i	0.0559113	+	0.0968411i	−0.836715	+	0.547638i	$0.815527\pi$
$942$	1.22181	−	0.705413i	0.0398087	−	0.0229836i
$943$	9.76455	+	5.63757i	0.317978	+	0.183584i
$944$	−3.94537	−	2.27786i	−0.128411	−	0.0741380i
$945$	1.87170	−	1.08063i	0.0608864	−	0.0351528i
$946$	6.28073	+	10.8786i	0.204204	+	0.353692i
$947$	−14.3872	+	8.30648i	−0.467523	+	0.269924i	−0.715202	−	0.698918i	$-0.753665\pi$
$947$	−14.3872	+	8.30648i	−0.467523	+	0.269924i	0.247679	+	0.968842i	$0.420332\pi$
$948$			2.38285i			0.0773914i
$949$	−22.2157	−	12.8262i	−0.721152	−	0.416357i
$950$	0.102891	+	0.178213i	0.00333823	+	0.00578198i
$951$	−4.60320			−0.149269
$952$	−6.83226			−0.221435
$953$	11.1748	+	19.3553i	0.361987	+	0.626980i	0.988288	−	0.152602i	$-0.0487651\pi$
$953$	11.1748	+	19.3553i	0.361987	+	0.626980i	−0.626301	+	0.779582i	$0.715432\pi$
$954$		−	1.15784i		−	0.0374864i
$955$	5.42635	−	9.39872i	0.175593	−	0.304135i
$956$		−	20.3595i		−	0.658474i
$957$	25.9040	+	14.9557i	0.837357	+	0.483448i
$958$	6.35989	−	11.0157i	0.205479	−	0.355900i
$959$	1.23317	−	2.13591i	0.0398210	−	0.0689720i
$960$	0.866025	−	0.500000i	0.0279508	−	0.0161374i
$961$	−7.33927			−0.236751
$962$	−14.8120	−	28.0757i	−0.477558	−	0.905195i
$963$	16.9669			0.546749
$964$	13.3225	−	7.69174i	0.429088	−	0.247734i
$965$	−11.4872	+	19.8964i	−0.369786	+	0.640487i
$966$	−3.76762	+	6.52571i	−0.121221	+	0.209961i
$967$	−4.23570	−	2.44549i	−0.136211	−	0.0786415i	0.430346	−	0.902664i	$-0.358392\pi$
$967$	−4.23570	−	2.44549i	−0.136211	−	0.0786415i	−0.566557	+	0.824023i	$0.691725\pi$
$968$		−	10.5592i		−	0.339385i
$969$	−0.325265	+	0.563375i	−0.0104490	+	0.0180982i
$970$			0.153047i			0.00491406i
$971$	13.3947	+	23.2002i	0.429855	+	0.744530i	0.996860	−	0.0791837i	$-0.0252314\pi$
$971$	13.3947	+	23.2002i	0.429855	+	0.744530i	−0.567005	+	0.823714i	$0.691898\pi$
$972$	−1.00000			−0.0320750
$973$	5.97943			0.191692
$974$	−16.5316	−	28.6336i	−0.529707	−	0.917480i
$975$	4.51941	+	2.60928i	0.144737	+	0.0835640i
$976$		−	10.6413i		−	0.340619i
$977$	−32.5426	+	18.7885i	−1.04113	+	0.601096i	−0.920153	−	0.391559i	$-0.871936\pi$
$977$	−32.5426	+	18.7885i	−1.04113	+	0.601096i	−0.120977	+	0.992655i	$0.538603\pi$
$978$	−4.90393	−	8.49385i	−0.156810	−	0.271603i
$979$	−62.4292	+	36.0435i	−1.99525	+	1.15196i
$980$	2.01696	+	1.16450i	0.0644296	+	0.0371984i
$981$	1.32344	+	0.764087i	0.0422541	+	0.0243954i
$982$	15.9631	−	9.21632i	0.509404	−	0.294105i
$983$	−16.6136	−	28.7756i	−0.529892	−	0.917801i	−0.999392	−	0.0348678i	$-0.988899\pi$
$983$	−16.6136	−	28.7756i	−0.529892	−	0.917801i	0.469500	−	0.882933i	$-0.344434\pi$
$984$	2.80066	−	1.61696i	0.0892818	−	0.0515469i
$985$			18.3971i			0.586180i
$986$	−17.6364	−	10.1824i	−0.561657	−	0.324273i
$987$	0.901423	+	1.56131i	0.0286926	+	0.0496971i
$988$	−1.07389			−0.0341649
$989$	−9.43226			−0.299929
$990$	−2.32159	−	4.02112i	−0.0737851	−	0.127800i
$991$			0.849371i			0.0269811i	0.999909	+	0.0134906i	$0.00429431\pi$
$991$			0.849371i			0.0269811i	−0.999909	+	0.0134906i	$0.995706\pi$
$992$	−3.09594	+	5.36232i	−0.0982960	+	0.170254i
$993$		−	26.2387i		−	0.832660i
$994$	−8.46861	−	4.88936i	−0.268608	−	0.155081i
$995$	−5.46700	+	9.46911i	−0.173315	+	0.300191i
$996$	6.98079	−	12.0911i	0.221195	−	0.383121i
$997$	−40.2264	+	23.2247i	−1.27398	+	0.735534i	−0.975735	−	0.218954i	$-0.929735\pi$
$997$	−40.2264	+	23.2247i	−1.27398	+	0.735534i	−0.298247	+	0.954489i	$0.596402\pi$
$998$	39.2957			1.24388
$999$	2.83833	+	5.37995i	0.0898006	+	0.170214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.d.751.7	✓	16
37.27	even	6	inner	1110.2.x.d.841.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.d.751.7	✓	16	1.1	even	1	trivial
1110.2.x.d.841.7	yes	16	37.27	even	6	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.08063 - 1.87170i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.08063 - 1.87170i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +4.64319 q^{11} +(0.500000 + 0.866025i) q^{12} +(-4.51941 - 2.60928i) q^{13} -2.16125i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.73772 - 1.58063i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.178213 + 0.102891i) q^{19} +(0.866025 - 0.500000i) q^{20} +(1.08063 + 1.87170i) q^{21} +(4.02112 - 2.32159i) q^{22} +3.48652i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -5.21857 q^{26} +1.00000 q^{27} +(-1.08063 - 1.87170i) q^{28} -6.44199i q^{29} +(-0.500000 + 0.866025i) q^{30} -6.19187i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.32159 + 4.02112i) q^{33} +(1.58063 - 2.73772i) q^{34} +(1.87170 - 1.08063i) q^{35} -1.00000 q^{36} +(2.83833 + 5.37995i) q^{37} +0.205782 q^{38} +(4.51941 - 2.60928i) q^{39} +(0.500000 - 0.866025i) q^{40} +(1.61696 - 2.80066i) q^{41} +(1.87170 + 1.08063i) q^{42} +2.70535i q^{43} +(2.32159 - 4.02112i) q^{44} -1.00000i q^{45} +(1.74326 + 3.01941i) q^{46} +0.834167 q^{47} +1.00000 q^{48} +(1.16450 + 2.01696i) q^{49} +(0.866025 + 0.500000i) q^{50} +3.16125i q^{51} +(-4.51941 + 2.60928i) q^{52} +(0.578919 + 1.00272i) q^{53} +(0.866025 - 0.500000i) q^{54} +(4.02112 + 2.32159i) q^{55} +(-1.87170 - 1.08063i) q^{56} +(-0.178213 + 0.102891i) q^{57} +(-3.22099 - 5.57892i) q^{58} +(3.94537 - 2.27786i) q^{59} +1.00000i q^{60} +(9.21562 + 5.32064i) q^{61} +(-3.09594 - 5.36232i) q^{62} -2.16125 q^{63} -1.00000 q^{64} +(-2.60928 - 4.51941i) q^{65} +4.64319i q^{66} +(0.180274 - 0.312243i) q^{67} -3.16125i q^{68} +(-3.01941 - 1.74326i) q^{69} +(1.08063 - 1.87170i) q^{70} +(2.26228 - 3.91838i) q^{71} +(-0.866025 + 0.500000i) q^{72} +4.91562 q^{73} +(5.14804 + 3.24001i) q^{74} -1.00000 q^{75} +(0.178213 - 0.102891i) q^{76} +(5.01755 - 8.69065i) q^{77} +(2.60928 - 4.51941i) q^{78} +(2.06361 + 1.19143i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -3.23393i q^{82} +(-6.98079 - 12.0911i) q^{83} +2.16125 q^{84} +3.16125 q^{85} +(1.35268 + 2.34291i) q^{86} +(5.57892 + 3.22099i) q^{87} -4.64319i q^{88} +(-13.4453 + 7.76267i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-9.76759 + 5.63932i) q^{91} +(3.01941 + 1.74326i) q^{92} +(5.36232 + 3.09594i) q^{93} +(0.722410 - 0.417084i) q^{94} +(0.102891 + 0.178213i) q^{95} +(0.866025 - 0.500000i) q^{96} +0.153047i q^{97} +(2.01696 + 1.16450i) q^{98} +(-2.32159 - 4.02112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} + 16 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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