LMFDB - Embedded newform 735.2.u.b.106.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(106,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("735.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.u (of order $7$, degree $6$, 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			106.7
Character	$\chi$	$=$	735.106
Dual form			735.2.u.b.631.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.02388 + 1.28391i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-0.155040 + 0.679276i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(-1.47955 - 0.712514i) q^{6} +(-0.516929 - 2.59476i) q^{7} +(1.92823 - 0.928588i) q^{8} +(0.623490 - 0.781831i) q^{9} +(-1.47955 - 0.712514i) q^{10} +(-2.66856 - 3.34627i) q^{11} +(-0.155040 - 0.679276i) q^{12} +(-0.474147 - 0.594561i) q^{13} +(2.80215 - 3.32041i) q^{14} +(0.623490 - 0.781831i) q^{15} +(4.42199 + 2.12952i) q^{16} +(-0.265960 - 1.16525i) q^{17} +1.64218 q^{18} +1.64829 q^{19} +(-0.155040 - 0.679276i) q^{20} +(1.59156 + 2.11351i) q^{21} +(1.56401 - 6.85237i) q^{22} +(1.20642 - 5.28568i) q^{23} +(-1.33438 + 1.67326i) q^{24} +(0.623490 - 0.781831i) q^{25} +(0.277891 - 1.21752i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(1.84270 + 0.0511547i) q^{28} +(-2.07721 - 9.10087i) q^{29} +1.64218 q^{30} +4.21465 q^{31} +(0.841020 + 3.68475i) q^{32} +(3.85619 + 1.85704i) q^{33} +(1.22376 - 1.53454i) q^{34} +(1.59156 + 2.11351i) q^{35} +(0.434413 + 0.544737i) q^{36} +(1.27496 + 5.58596i) q^{37} +(1.68766 + 2.11625i) q^{38} +(0.685162 + 0.329957i) q^{39} +(-1.33438 + 1.67326i) q^{40} +(-6.12140 + 2.94791i) q^{41} +(-1.08398 + 4.20740i) q^{42} +(4.61262 + 2.22132i) q^{43} +(2.68678 - 1.29388i) q^{44} +(-0.222521 + 0.974928i) q^{45} +(8.02155 - 3.86298i) q^{46} +(4.12724 + 5.17540i) q^{47} -4.90804 q^{48} +(-6.46557 + 2.68262i) q^{49} +1.64218 q^{50} +(0.745203 + 0.934455i) q^{51} +(0.477383 - 0.229895i) q^{52} +(-0.137882 + 0.604101i) q^{53} +(-1.47955 + 0.712514i) q^{54} +(3.85619 + 1.85704i) q^{55} +(-3.40622 - 4.52329i) q^{56} +(-1.48506 + 0.715168i) q^{57} +(9.55784 - 11.9851i) q^{58} +(-3.28641 - 1.58265i) q^{59} +(0.434413 + 0.544737i) q^{60} +(0.132325 + 0.579753i) q^{61} +(4.31530 + 5.41122i) q^{62} +(-2.35097 - 1.21366i) q^{63} +(2.25045 - 2.82198i) q^{64} +(0.685162 + 0.329957i) q^{65} +(1.56401 + 6.85237i) q^{66} -2.44386 q^{67} +0.832758 q^{68} +(1.20642 + 5.28568i) q^{69} +(-1.08398 + 4.20740i) q^{70} +(2.71208 - 11.8824i) q^{71} +(0.476234 - 2.08652i) q^{72} +(1.62378 - 2.03616i) q^{73} +(-5.86644 + 7.35629i) q^{74} +(-0.222521 + 0.974928i) q^{75} +(-0.255552 + 1.11965i) q^{76} +(-7.30332 + 8.65407i) q^{77} +(0.277891 + 1.21752i) q^{78} -1.93434 q^{79} -4.90804 q^{80} +(-0.222521 - 0.974928i) q^{81} +(-10.0524 - 4.84099i) q^{82} +(7.50590 - 9.41211i) q^{83} +(-1.68241 + 0.753430i) q^{84} +(0.745203 + 0.934455i) q^{85} +(1.87080 + 8.19653i) q^{86} +(5.82022 + 7.29833i) q^{87} +(-8.25292 - 3.97439i) q^{88} +(-5.60526 + 7.02877i) q^{89} +(-1.47955 + 0.712514i) q^{90} +(-1.29764 + 1.53764i) q^{91} +(3.40339 + 1.63899i) q^{92} +(-3.79727 + 1.82867i) q^{93} +(-2.41892 + 10.5980i) q^{94} +(-1.48506 + 0.715168i) q^{95} +(-2.35649 - 2.95494i) q^{96} -4.69981 q^{97} +(-10.0642 - 5.55450i) q^{98} -4.28004 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 8 q^{3} - q^{4} - 8 q^{5} + q^{6} - q^{7} + 15 q^{8} - 8 q^{9} + q^{10} + 10 q^{11} - q^{12} + 20 q^{13} - q^{14} - 8 q^{15} - 15 q^{16} + 7 q^{17} - 6 q^{18} - 2 q^{19} - q^{20}+ \cdots - 32 q^{99}+O(q^{100}) $ 48 * q + q^2 - 8 * q^3 - q^4 - 8 * q^5 + q^6 - q^7 + 15 * q^8 - 8 * q^9 + q^10 + 10 * q^11 - q^12 + 20 * q^13 - q^14 - 8 * q^15 - 15 * q^16 + 7 * q^17 - 6 * q^18 - 2 * q^19 - q^20 - q^21 - 17 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 - 12 * q^26 - 8 * q^27 + 29 * q^28 + 12 * q^29 - 6 * q^30 - 58 * q^31 + 9 * q^32 + 3 * q^33 + 36 * q^34 - q^35 - q^36 - 15 * q^37 - 5 * q^38 - 8 * q^39 - 6 * q^40 - 2 * q^41 + 6 * q^42 + 30 * q^43 + 33 * q^44 - 8 * q^45 + 52 * q^46 + 6 * q^47 + 6 * q^48 + 13 * q^49 - 6 * q^50 - 7 * q^51 + 3 * q^53 + q^54 + 3 * q^55 - 67 * q^56 + 19 * q^57 + 36 * q^58 + 9 * q^59 - q^60 - 7 * q^61 + 14 * q^62 - 15 * q^63 + 19 * q^64 - 8 * q^65 - 17 * q^66 + 14 * q^67 + 22 * q^68 + 12 * q^69 + 6 * q^70 - 24 * q^71 - 6 * q^72 + 2 * q^73 + 2 * q^74 - 8 * q^75 + 62 * q^76 + 42 * q^77 - 12 * q^78 + 22 * q^79 + 6 * q^80 - 8 * q^81 - 51 * q^82 + 53 * q^83 + 50 * q^84 - 7 * q^85 - 35 * q^86 + 19 * q^87 + 11 * q^88 - 51 * q^89 + q^90 - q^91 + 29 * q^92 + 26 * q^93 - 4 * q^94 + 19 * q^95 + 9 * q^96 - 102 * q^97 + 90 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$	$1$

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 $

$2$	1.02388	+	1.28391i	0.723993	+	0.907858i	0.998557	−	0.0537106i	$-0.0171049\pi$
$2$	1.02388	+	1.28391i	0.723993	+	0.907858i	−0.274564	+	0.961569i	$0.588533\pi$
$3$	−0.900969	+	0.433884i	−0.520175	+	0.250503i
$3$	−0.900969	+	0.433884i	−0.520175	+	0.250503i
$4$	−0.155040	+	0.679276i	−0.0775201	+	0.339638i
$5$	−0.900969	+	0.433884i	−0.402926	+	0.194039i
$5$	−0.900969	+	0.433884i	−0.402926	+	0.194039i
$6$	−1.47955	−	0.712514i	−0.604024	−	0.290883i
$7$	−0.516929	−	2.59476i	−0.195381	−	0.980727i
$7$	−0.516929	−	2.59476i	−0.195381	−	0.980727i
$8$	1.92823	−	0.928588i	0.681733	−	0.328305i
$9$	0.623490	−	0.781831i	0.207830	−	0.260610i
$10$	−1.47955	−	0.712514i	−0.467875	−	0.225317i
$11$	−2.66856	−	3.34627i	−0.804602	−	1.00894i	−0.999604	−	0.0281362i	$-0.991043\pi$
$11$	−2.66856	−	3.34627i	−0.804602	−	1.00894i	0.195002	−	0.980803i	$-0.437529\pi$
$12$	−0.155040	−	0.679276i	−0.0447563	−	0.196090i
$13$	−0.474147	−	0.594561i	−0.131505	−	0.164902i	0.711719	−	0.702464i	$-0.247917\pi$
$13$	−0.474147	−	0.594561i	−0.131505	−	0.164902i	−0.843224	+	0.537562i	$0.819345\pi$
$14$	2.80215	−	3.32041i	0.748907	−	0.887418i
$15$	0.623490	−	0.781831i	0.160984	−	0.201868i
$16$	4.42199	+	2.12952i	1.10550	+	0.532379i
$17$	−0.265960	−	1.16525i	−0.0645048	−	0.282614i	0.932381	−	0.361478i	$-0.117728\pi$
$17$	−0.265960	−	1.16525i	−0.0645048	−	0.282614i	−0.996885	+	0.0788642i	$0.974871\pi$
$18$	1.64218			0.387065
$19$	1.64829			0.378145			0.189072	−	0.981963i	$-0.439452\pi$
$19$	1.64829			0.378145			0.189072	+	0.981963i	$0.439452\pi$
$20$	−0.155040	−	0.679276i	−0.0346680	−	0.151891i
$21$	1.59156	+	2.11351i	0.347307	+	0.461206i
$22$	1.56401	−	6.85237i	0.333448	−	1.46093i
$23$	1.20642	−	5.28568i	0.251557	−	1.10214i	−0.678464	−	0.734634i	$-0.737354\pi$
$23$	1.20642	−	5.28568i	0.251557	−	1.10214i	0.930020	−	0.367508i	$-0.119789\pi$
$24$	−1.33438	+	1.67326i	−0.272379	+	0.341552i
$25$	0.623490	−	0.781831i	0.124698	−	0.156366i
$26$	0.277891	−	1.21752i	0.0544989	−	0.238775i
$27$	−0.222521	+	0.974928i	−0.0428242	+	0.187625i
$28$	1.84270	+	0.0511547i	0.348238	+	0.00966733i
$29$	−2.07721	−	9.10087i	−0.385729	−	1.68999i	−0.679145	−	0.734004i	$-0.737649\pi$
$29$	−2.07721	−	9.10087i	−0.385729	−	1.68999i	0.293416	−	0.955985i	$-0.405208\pi$
$30$	1.64218			0.299819
$31$	4.21465			0.756974			0.378487	−	0.925607i	$-0.376444\pi$
$31$	4.21465			0.756974			0.378487	+	0.925607i	$0.376444\pi$
$32$	0.841020	+	3.68475i	0.148673	+	0.651378i
$33$	3.85619	+	1.85704i	0.671276	+	0.323269i
$34$	1.22376	−	1.53454i	0.209872	−	0.263172i
$35$	1.59156	+	2.11351i	0.269023	+	0.357249i
$36$	0.434413	+	0.544737i	0.0724022	+	0.0907894i
$37$	1.27496	+	5.58596i	0.209602	+	0.918327i	0.964832	+	0.262867i	$0.0846680\pi$
$37$	1.27496	+	5.58596i	0.209602	+	0.918327i	−0.755230	+	0.655460i	$0.772475\pi$
$38$	1.68766	+	2.11625i	0.273774	+	0.343302i
$39$	0.685162	+	0.329957i	0.109714	+	0.0528354i
$40$	−1.33438	+	1.67326i	−0.210984	+	0.264565i
$41$	−6.12140	+	2.94791i	−0.956002	+	0.460386i	−0.845787	−	0.533521i	$-0.820868\pi$
$41$	−6.12140	+	2.94791i	−0.956002	+	0.460386i	−0.110216	+	0.993908i	$0.535154\pi$
$42$	−1.08398	+	4.20740i	−0.167262	+	0.649216i
$43$	4.61262	+	2.22132i	0.703418	+	0.338748i	0.751168	−	0.660111i	$-0.229491\pi$
$43$	4.61262	+	2.22132i	0.703418	+	0.338748i	−0.0477503	+	0.998859i	$0.515205\pi$
$44$	2.68678	−	1.29388i	0.405047	−	0.195060i
$45$	−0.222521	+	0.974928i	−0.0331715	+	0.145334i
$46$	8.02155	−	3.86298i	1.18271	−	0.569565i
$47$	4.12724	+	5.17540i	0.602020	+	0.754910i	0.985691	−	0.168560i	$-0.0539118\pi$
$47$	4.12724	+	5.17540i	0.602020	+	0.754910i	−0.383671	+	0.923470i	$0.625340\pi$
$48$	−4.90804			−0.708414
$49$	−6.46557	+	2.68262i	−0.923653	+	0.383231i
$50$	1.64218			0.232239
$51$	0.745203	+	0.934455i	0.104349	+	0.130850i
$52$	0.477383	−	0.229895i	0.0662011	−	0.0318808i
$53$	−0.137882	+	0.604101i	−0.0189396	+	0.0829797i	−0.983514	−	0.180830i	$-0.942122\pi$
$53$	−0.137882	+	0.604101i	−0.0189396	+	0.0829797i	0.964575	+	0.263809i	$0.0849789\pi$
$54$	−1.47955	+	0.712514i	−0.201341	+	0.0969608i
$55$	3.85619	+	1.85704i	0.519968	+	0.250403i
$56$	−3.40622	−	4.52329i	−0.455176	−	0.604450i
$57$	−1.48506	+	0.715168i	−0.196701	+	0.0947263i
$58$	9.55784	−	11.9851i	1.25501	−	1.57373i
$59$	−3.28641	−	1.58265i	−0.427854	−	0.206043i	0.207549	−	0.978225i	$-0.433451\pi$
$59$	−3.28641	−	1.58265i	−0.427854	−	0.206043i	−0.635402	+	0.772181i	$0.719166\pi$
$60$	0.434413	+	0.544737i	0.0560825	+	0.0703252i
$61$	0.132325	+	0.579753i	0.0169425	+	0.0742298i	0.982692	−	0.185245i	$-0.0593078\pi$
$61$	0.132325	+	0.579753i	0.0169425	+	0.0742298i	−0.965750	+	0.259475i	$0.916451\pi$
$62$	4.31530	+	5.41122i	0.548044	+	0.687225i
$63$	−2.35097	−	1.21366i	−0.296194	−	0.152906i
$64$	2.25045	−	2.82198i	0.281307	−	0.352748i
$65$	0.685162	+	0.329957i	0.0849839	+	0.0409261i
$66$	1.56401	+	6.85237i	0.192516	+	0.843468i
$67$	−2.44386			−0.298565			−0.149282	−	0.988795i	$-0.547696\pi$
$67$	−2.44386			−0.298565			−0.149282	+	0.988795i	$0.547696\pi$
$68$	0.832758			0.100987
$69$	1.20642	+	5.28568i	0.145236	+	0.636322i
$70$	−1.08398	+	4.20740i	−0.129560	+	0.502880i
$71$	2.71208	−	11.8824i	0.321865	−	1.41018i	−0.512366	−	0.858767i	$-0.671231\pi$
$71$	2.71208	−	11.8824i	0.321865	−	1.41018i	0.834231	−	0.551415i	$-0.185912\pi$
$72$	0.476234	−	2.08652i	0.0561247	−	0.245898i
$73$	1.62378	−	2.03616i	0.190049	−	0.238314i	−0.677673	−	0.735363i	$-0.737012\pi$
$73$	1.62378	−	2.03616i	0.190049	−	0.238314i	0.867722	+	0.497049i	$0.165583\pi$
$74$	−5.86644	+	7.35629i	−0.681960	+	0.855151i
$75$	−0.222521	+	0.974928i	−0.0256945	+	0.112575i
$76$	−0.255552	+	1.11965i	−0.0293138	+	0.128432i
$77$	−7.30332	+	8.65407i	−0.832290	+	0.986223i
$78$	0.277891	+	1.21752i	0.0314649	+	0.137857i
$79$	−1.93434			−0.217630			−0.108815	−	0.994062i	$-0.534706\pi$
$79$	−1.93434			−0.217630			−0.108815	+	0.994062i	$0.534706\pi$
$80$	−4.90804			−0.548735
$81$	−0.222521	−	0.974928i	−0.0247245	−	0.108325i
$82$	−10.0524	−	4.84099i	−1.11010	−	0.534598i
$83$	7.50590	−	9.41211i	0.823880	−	1.03311i	−0.174941	−	0.984579i	$-0.555974\pi$
$83$	7.50590	−	9.41211i	0.823880	−	1.03311i	0.998822	−	0.0485341i	$-0.0154549\pi$
$84$	−1.68241	+	0.753430i	−0.183566	+	0.0822059i
$85$	0.745203	+	0.934455i	0.0808287	+	0.101356i
$86$	1.87080	+	8.19653i	0.201734	+	0.883855i
$87$	5.82022	+	7.29833i	0.623994	+	0.782463i
$88$	−8.25292	−	3.97439i	−0.879764	−	0.423672i
$89$	−5.60526	+	7.02877i	−0.594156	+	0.745049i	−0.984454	−	0.175640i	$-0.943801\pi$
$89$	−5.60526	+	7.02877i	−0.594156	+	0.745049i	0.390298	+	0.920689i	$0.372372\pi$
$90$	−1.47955	+	0.712514i	−0.155958	+	0.0751055i
$91$	−1.29764	+	1.53764i	−0.136030	+	0.161189i
$92$	3.40339	+	1.63899i	0.354828	+	0.170876i
$93$	−3.79727	+	1.82867i	−0.393759	+	0.189624i
$94$	−2.41892	+	10.5980i	−0.249493	+	1.09310i
$95$	−1.48506	+	0.715168i	−0.152364	+	0.0733747i
$96$	−2.35649	−	2.95494i	−0.240508	−	0.301587i
$97$	−4.69981			−0.477194			−0.238597	−	0.971119i	$-0.576687\pi$
$97$	−4.69981			−0.477194			−0.238597	+	0.971119i	$0.576687\pi$
$98$	−10.0642	−	5.55450i	−1.01664	−	0.561089i
$99$	−4.28004			−0.430160
$100$	0.434413	+	0.544737i	0.0434413	+	0.0544737i
$101$	−5.04199	+	2.42809i	−0.501697	+	0.241604i	−0.667576	−	0.744542i	$-0.732668\pi$
$101$	−5.04199	+	2.42809i	−0.501697	+	0.241604i	0.165879	+	0.986146i	$0.446954\pi$
$102$	−0.436753	+	1.91354i	−0.0432450	+	0.189469i
$103$	8.84936	−	4.26163i	0.871954	−	0.419911i	0.0562745	−	0.998415i	$-0.482078\pi$
$103$	8.84936	−	4.26163i	0.871954	−	0.419911i	0.815679	+	0.578505i	$0.196364\pi$
$104$	−1.46637	−	0.706165i	−0.143789	−	0.0692452i
$105$	−2.35097	−	1.21366i	−0.229431	−	0.118441i
$106$	−0.916783	+	0.441500i	−0.0890459	+	0.0428822i
$107$	−9.26671	+	11.6201i	−0.895846	+	1.12336i	0.0959320	+	0.995388i	$0.469417\pi$
$107$	−9.26671	+	11.6201i	−0.895846	+	1.12336i	−0.991778	+	0.127968i	$0.959155\pi$
$108$	−0.627745	−	0.302306i	−0.0604048	−	0.0290894i
$109$	−3.43143	−	4.30288i	−0.328672	−	0.412141i	0.589849	−	0.807513i	$-0.299187\pi$
$109$	−3.43143	−	4.30288i	−0.328672	−	0.412141i	−0.918521	+	0.395372i	$0.870616\pi$
$110$	1.56401	+	6.85237i	0.149122	+	0.653347i
$111$	−3.57236	−	4.47959i	−0.339073	−	0.425184i
$112$	3.23973	−	12.5748i	0.306126	−	1.18821i
$113$	9.62972	−	12.0753i	0.905888	−	1.13595i	−0.0843327	−	0.996438i	$-0.526876\pi$
$113$	9.62972	−	12.0753i	0.905888	−	1.13595i	0.990221	−	0.139510i	$-0.0445527\pi$
$114$	−2.43873	−	1.17443i	−0.228408	−	0.109996i
$115$	1.20642	+	5.28568i	0.112500	+	0.492893i
$116$	6.50405			0.603886
$117$	−0.760473			−0.0703057
$118$	−1.33291	−	5.83988i	−0.122705	−	0.537605i
$119$	−2.88605	+	1.29245i	−0.264564	+	0.118479i
$120$	0.476234	−	2.08652i	0.0434740	−	0.190472i
$121$	−1.62858	+	7.13527i	−0.148053	+	0.648661i
$122$	−0.608864	+	0.763491i	−0.0551239	+	0.0691232i
$123$	4.23614	−	5.31195i	0.381960	−	0.478963i
$124$	−0.653441	+	2.86291i	−0.0586807	+	0.257097i
$125$	−0.222521	+	0.974928i	−0.0199029	+	0.0872002i
$126$	−0.848890	−	4.26106i	−0.0756251	−	0.379605i
$127$	2.89031	+	12.6633i	0.256474	+	1.12369i	0.924991	+	0.379989i	$0.124072\pi$
$127$	2.89031	+	12.6633i	0.256474	+	1.12369i	−0.668517	+	0.743697i	$0.733071\pi$
$128$	13.4864			1.19204
$129$	−5.11962			−0.450757
$130$	0.277891	+	1.21752i	0.0243726	+	0.106784i
$131$	−12.6839	−	6.10825i	−1.10820	−	0.533681i	−0.211972	−	0.977276i	$-0.567989\pi$
$131$	−12.6839	−	6.10825i	−1.10820	−	0.533681i	−0.896227	+	0.443595i	$0.853703\pi$
$132$	−1.85931	+	2.33150i	−0.161832	+	0.202931i
$133$	−0.852052	−	4.27693i	−0.0738823	−	0.370857i
$134$	−2.50222	−	3.13768i	−0.216159	−	0.271054i
$135$	−0.222521	−	0.974928i	−0.0191516	−	0.0839084i
$136$	−1.59487	−	1.99990i	−0.136759	−	0.171490i
$137$	−0.823368	−	0.396513i	−0.0703451	−	0.0338764i	0.398380	−	0.917220i	$-0.369572\pi$
$137$	−0.823368	−	0.396513i	−0.0703451	−	0.0338764i	−0.468726	+	0.883344i	$0.655287\pi$
$138$	−5.55109	+	6.96084i	−0.472540	+	0.592546i
$139$	−3.90161	+	1.87891i	−0.330930	+	0.159367i	−0.591969	−	0.805961i	$-0.701649\pi$
$139$	−3.90161	+	1.87891i	−0.330930	+	0.159367i	0.261039	+	0.965328i	$0.415935\pi$
$140$	−1.68241	+	0.753430i	−0.142190	+	0.0636764i
$141$	−5.96404	−	2.87213i	−0.502263	−	0.241877i
$142$	18.0327	−	8.68411i	1.51327	−	0.728754i
$143$	−0.724273	+	3.17325i	−0.0605668	+	0.265360i
$144$	4.42199	−	2.12952i	0.368499	−	0.177460i
$145$	5.82022	+	7.29833i	0.483343	+	0.606093i
$146$	4.27679			0.353949
$147$	4.66133	−	5.22226i	0.384460	−	0.430725i
$148$	−3.99208			−0.328147
$149$	−1.04741	−	1.31341i	−0.0858074	−	0.107599i	0.737075	−	0.675811i	$-0.236207\pi$
$149$	−1.04741	−	1.31341i	−0.0858074	−	0.107599i	−0.822882	+	0.568212i	$0.807635\pi$
$150$	−1.47955	+	0.712514i	−0.120805	+	0.0581765i
$151$	0.370792	−	1.62455i	0.0301747	−	0.132204i	−0.957597	−	0.288111i	$-0.906973\pi$
$151$	0.370792	−	1.62455i	0.0301747	−	0.132204i	0.987772	+	0.155907i	$0.0498300\pi$
$152$	3.17829	−	1.53059i	0.257794	−	0.124147i
$153$	−1.07685	−	0.518584i	−0.0870582	−	0.0419250i
$154$	−18.5887	−	0.516036i	−1.49792	−	0.0415834i
$155$	−3.79727	+	1.82867i	−0.305004	+	0.146882i
$156$	−0.330359	+	0.414257i	−0.0264499	+	0.0331671i
$157$	12.3619	+	5.95316i	0.986583	+	0.475114i	0.856365	−	0.516372i	$-0.172718\pi$
$157$	12.3619	+	5.95316i	0.986583	+	0.475114i	0.130219	+	0.991485i	$0.458432\pi$
$158$	−1.98053	−	2.48350i	−0.157562	−	0.197577i
$159$	−0.137882	−	0.604101i	−0.0109348	−	0.0479083i
$160$	−2.35649	−	2.95494i	−0.186297	−	0.233609i
$161$	−14.3387	−	0.398053i	−1.13005	−	0.0313710i
$162$	1.02388	−	1.28391i	0.0804436	−	0.100873i
$163$	12.6990	+	6.11553i	0.994664	+	0.479005i	0.859124	−	0.511767i	$-0.171009\pi$
$163$	12.6990	+	6.11553i	0.994664	+	0.479005i	0.135540	+	0.990772i	$0.456723\pi$
$164$	−1.05338	−	4.61516i	−0.0822552	−	0.360384i
$165$	−4.28004			−0.333201
$166$	19.7694			1.53440
$167$	4.36044	+	19.1043i	0.337421	+	1.47834i	0.804410	+	0.594075i	$0.202482\pi$
$167$	4.36044	+	19.1043i	0.337421	+	1.47834i	−0.466989	+	0.884263i	$0.654661\pi$
$168$	5.03148	+	2.59744i	0.388187	+	0.200397i
$169$	2.76408	−	12.1102i	0.212622	−	0.931557i
$170$	−0.436753	+	1.91354i	−0.0334975	+	0.146762i
$171$	1.02769	−	1.28869i	0.0785898	−	0.0985485i
$172$	−2.22403	+	2.78884i	−0.169581	+	0.212647i
$173$	−0.731876	+	3.20656i	−0.0556435	+	0.243790i	−0.995099	−	0.0988797i	$-0.968474\pi$
$173$	−0.731876	+	3.20656i	−0.0556435	+	0.243790i	0.939456	+	0.342670i	$0.111331\pi$
$174$	−3.41115	+	14.9452i	−0.258599	+	1.13300i
$175$	−2.35097	−	1.21366i	−0.177716	−	0.0917437i
$176$	−4.67441	−	20.4799i	−0.352347	−	1.54373i
$177$	3.64764			0.274173
$178$	−14.7634			−1.10656
$179$	5.17919	+	22.6915i	0.387111	+	1.69604i	0.674536	+	0.738242i	$0.264344\pi$
$179$	5.17919	+	22.6915i	0.387111	+	1.69604i	−0.287425	+	0.957803i	$0.592799\pi$
$180$	−0.627745	−	0.302306i	−0.0467893	−	0.0225326i
$181$	−10.9593	+	13.7426i	−0.814601	+	1.02148i	0.184651	+	0.982804i	$0.440885\pi$
$181$	−10.9593	+	13.7426i	−0.814601	+	1.02148i	−0.999252	+	0.0386732i	$0.987687\pi$
$182$	−3.30282	−	0.0916886i	−0.244821	−	0.00679641i
$183$	−0.370766	−	0.464926i	−0.0274078	−	0.0343683i
$184$	−2.58196	−	11.3123i	−0.190344	−	0.833954i
$185$	−3.57236	−	4.47959i	−0.262645	−	0.329346i
$186$	−6.23579	−	3.00300i	−0.457230	−	0.220191i
$187$	−3.18950	+	3.99951i	−0.233240	+	0.292473i
$188$	−4.15541	+	2.00114i	−0.303064	+	0.145948i
$189$	2.64473	+	0.0734196i	0.192376	+	0.00534049i
$190$	−2.43873	−	1.17443i	−0.176924	−	0.0852023i
$191$	−0.0312913	+	0.0150691i	−0.00226416	+	0.00109036i	−0.435015	−	0.900423i	$-0.643257\pi$
$191$	−0.0312913	+	0.0150691i	−0.00226416	+	0.00109036i	0.432751	+	0.901513i	$0.357543\pi$
$192$	−0.803178	+	3.51895i	−0.0579644	+	0.253958i
$193$	11.8626	−	5.71275i	0.853891	−	0.411212i	0.0448709	−	0.998993i	$-0.485712\pi$
$193$	11.8626	−	5.71275i	0.853891	−	0.411212i	0.809021	+	0.587780i	$0.199998\pi$
$194$	−4.81205	−	6.03412i	−0.345485	−	0.433224i
$195$	−0.760473			−0.0544586
$196$	−0.819813	−	4.80782i	−0.0585581	−	0.343415i
$197$	−14.8541			−1.05831			−0.529155	−	0.848525i	$-0.677491\pi$
$197$	−14.8541			−1.05831			−0.529155	+	0.848525i	$0.677491\pi$
$198$	−4.38225	−	5.49517i	−0.311433	−	0.390525i
$199$	−2.07546	+	0.999487i	−0.147125	+	0.0708517i	−0.505998	−	0.862535i	$-0.668876\pi$
$199$	−2.07546	+	0.999487i	−0.147125	+	0.0708517i	0.358873	+	0.933387i	$0.383161\pi$
$200$	0.476234	−	2.08652i	0.0336748	−	0.147539i
$201$	2.20184	−	1.06035i	0.155306	−	0.0747913i
$202$	−8.27984	−	3.98736i	−0.582567	−	0.280550i
$203$	−22.5408	+	10.0944i	−1.58205	+	0.708487i
$204$	−0.750289	+	0.361320i	−0.0525308	+	0.0252975i
$205$	4.23614	−	5.31195i	0.295865	−	0.371003i
$206$	14.5322	+	6.99835i	1.01251	+	0.487598i
$207$	−3.38032	−	4.23879i	−0.234949	−	0.294616i
$208$	−0.830543	−	3.63885i	−0.0575878	−	0.252309i
$209$	−4.39858	−	5.51564i	−0.304256	−	0.381525i
$210$	−0.848890	−	4.26106i	−0.0585789	−	0.294041i
$211$	1.46948	−	1.84267i	0.101163	−	0.126855i	−0.728673	−	0.684862i	$-0.759862\pi$
$211$	1.46948	−	1.84267i	0.101163	−	0.126855i	0.829836	+	0.558007i	$0.188434\pi$
$212$	−0.388974	−	0.187320i	−0.0267148	−	0.0128652i
$213$	2.71208	+	11.8824i	0.185829	+	0.814169i
$214$	−24.4071			−1.66843
$215$	−5.11962			−0.349155
$216$	0.476234	+	2.08652i	0.0324036	+	0.141970i
$217$	−2.17868	−	10.9360i	−0.147898	−	0.742385i
$218$	2.01112	−	8.81127i	0.136210	−	0.596775i
$219$	−0.579520	+	2.53904i	−0.0391604	+	0.171573i
$220$	−1.85931	+	2.33150i	−0.125354	+	0.157189i
$221$	−0.566707	+	0.710628i	−0.0381208	+	0.0478020i
$222$	2.09371	−	9.17314i	0.140521	−	0.615661i
$223$	5.01642	−	21.9784i	0.335924	−	1.47178i	−0.471530	−	0.881850i	$-0.656298\pi$
$223$	5.01642	−	21.9784i	0.335924	−	1.47178i	0.807454	−	0.589930i	$-0.200845\pi$
$224$	9.12630	−	4.08700i	0.609776	−	0.273074i
$225$	−0.222521	−	0.974928i	−0.0148347	−	0.0649952i
$226$	25.3632			1.68714
$227$	24.5246			1.62776			0.813878	−	0.581036i	$-0.197353\pi$
$227$	24.5246			1.62776			0.813878	+	0.581036i	$0.197353\pi$
$228$	−0.255552	−	1.11965i	−0.0169243	−	0.0741504i
$229$	14.6450	+	7.05264i	0.967767	+	0.466052i	0.849881	−	0.526975i	$-0.176674\pi$
$229$	14.6450	+	7.05264i	0.967767	+	0.466052i	0.117886	+	0.993027i	$0.462388\pi$
$230$	−5.55109	+	6.96084i	−0.366028	+	0.458984i
$231$	2.82520	−	10.9658i	0.185885	−	0.721499i
$232$	−12.4563	−	15.6197i	−0.817796	−	1.02548i
$233$	5.69114	+	24.9345i	0.372839	+	1.63352i	0.718765	+	0.695254i	$0.244708\pi$
$233$	5.69114	+	24.9345i	0.372839	+	1.63352i	−0.345925	+	0.938262i	$0.612435\pi$
$234$	−0.778633	−	0.976375i	−0.0509008	−	0.0638276i
$235$	−5.96404	−	2.87213i	−0.389051	−	0.187357i
$236$	1.58458	−	1.98700i	0.103147	−	0.129343i
$237$	1.74278	−	0.839277i	0.113206	−	0.0545169i
$238$	−4.61436	−	2.38210i	−0.299105	−	0.154409i
$239$	17.2284	+	8.29676i	1.11441	+	0.536673i	0.898162	−	0.439665i	$-0.144903\pi$
$239$	17.2284	+	8.29676i	1.11441	+	0.536673i	0.216251	+	0.976338i	$0.430617\pi$
$240$	4.42199	−	2.12952i	0.285438	−	0.137460i
$241$	3.32204	−	14.5548i	0.213992	−	0.937558i	−0.747832	−	0.663888i	$-0.768905\pi$
$241$	3.32204	−	14.5548i	0.213992	−	0.937558i	0.961824	−	0.273670i	$-0.0882377\pi$
$242$	−10.8285	+	5.21472i	−0.696081	+	0.335215i
$243$	0.623490	+	0.781831i	0.0399969	+	0.0501545i
$244$	−0.414328			−0.0265246
$245$	4.66133	−	5.22226i	0.297802	−	0.333638i
$246$	11.1573			0.711366
$247$	−0.781534	−	0.980012i	−0.0497278	−	0.0623567i
$248$	8.12683	−	3.91367i	0.516054	−	0.248519i
$249$	−2.67883	+	11.7367i	−0.169764	+	0.743783i
$250$	−1.47955	+	0.712514i	−0.0935750	+	0.0450633i
$251$	6.36921	+	3.06725i	0.402021	+	0.193603i	0.623958	−	0.781458i	$-0.285524\pi$
$251$	6.36921	+	3.06725i	0.402021	+	0.193603i	−0.221937	+	0.975061i	$0.571238\pi$
$252$	1.18890	−	1.40879i	0.0748937	−	0.0887453i
$253$	−20.9068	+	10.0682i	−1.31440	+	0.632980i
$254$	−13.2991	+	16.6766i	−0.834462	+	1.04638i
$255$	−1.07685	−	0.518584i	−0.0674350	−	0.0324750i
$256$	9.30752	+	11.6713i	0.581720	+	0.729454i
$257$	−3.74485	−	16.4072i	−0.233597	−	1.02346i	−0.946629	−	0.322325i	$-0.895536\pi$
$257$	−3.74485	−	16.4072i	−0.233597	−	1.02346i	0.713032	−	0.701131i	$-0.247321\pi$
$258$	−5.24188	−	6.57311i	−0.326345	−	0.409224i
$259$	13.8352	−	6.19576i	0.859676	−	0.384986i
$260$	−0.330359	+	0.414257i	−0.0204880	+	0.0256911i
$261$	−8.41047	−	4.05027i	−0.520595	−	0.250705i
$262$	−5.14440	−	22.5391i	−0.317822	−	1.39247i
$263$	31.3411			1.93258			0.966289	−	0.257460i	$-0.0828856\pi$
$263$	31.3411			1.93258			0.966289	+	0.257460i	$0.0828856\pi$
$264$	9.16004			0.563762
$265$	−0.137882	−	0.604101i	−0.00847003	−	0.0371096i
$266$	4.61877	−	5.47302i	0.283195	−	0.335572i
$267$	2.00049	−	8.76474i	0.122428	−	0.536393i
$268$	0.378896	−	1.66005i	0.0231448	−	0.101404i
$269$	−0.922755	+	1.15710i	−0.0562614	+	0.0705495i	−0.809166	−	0.587580i	$-0.800081\pi$
$269$	−0.922755	+	1.15710i	−0.0562614	+	0.0705495i	0.752905	+	0.658130i	$0.228652\pi$
$270$	1.02388	−	1.28391i	0.0623114	−	0.0781360i
$271$	−5.09474	+	22.3215i	−0.309484	+	1.35594i	0.545860	+	0.837876i	$0.316203\pi$
$271$	−5.09474	+	22.3215i	−0.309484	+	1.35594i	−0.855344	+	0.518060i	$0.826654\pi$
$272$	1.30534	−	5.71907i	0.0791479	−	0.346770i
$273$	0.501978	−	1.94840i	0.0303811	−	0.117922i
$274$	−0.333945	−	1.46311i	−0.0201744	−	0.0883896i
$275$	−4.28004			−0.258096
$276$	−3.77748			−0.227378
$277$	0.695212	+	3.04592i	0.0417713	+	0.183012i	0.991510	−	0.130033i	$-0.0415082\pi$
$277$	0.695212	+	3.04592i	0.0417713	+	0.183012i	−0.949738	+	0.313045i	$0.898651\pi$
$278$	−6.40713	−	3.08551i	−0.384274	−	0.185057i
$279$	2.62779	−	3.29515i	0.157322	−	0.197275i
$280$	5.03148	+	2.59744i	0.300689	+	0.155226i
$281$	4.58355	+	5.74760i	0.273432	+	0.342873i	0.899520	−	0.436880i	$-0.143916\pi$
$281$	4.58355	+	5.74760i	0.273432	+	0.342873i	−0.626088	+	0.779752i	$0.715345\pi$
$282$	−2.41892	−	10.5980i	−0.144045	−	0.631100i
$283$	15.9901	+	20.0510i	0.950515	+	1.19191i	0.981320	+	0.192382i	$0.0616214\pi$
$283$	15.9901	+	20.0510i	0.950515	+	1.19191i	−0.0308052	+	0.999525i	$0.509807\pi$
$284$	7.65095	+	3.68450i	0.454000	+	0.218635i
$285$	1.02769	−	1.28869i	0.0608754	−	0.0763353i
$286$	−4.81572	+	2.31913i	−0.284760	+	0.137133i
$287$	10.8135	+	14.3597i	0.638298	+	0.847627i
$288$	3.40522	+	1.63987i	0.200655	+	0.0966302i
$289$	14.0294	−	6.75621i	0.825259	−	0.397424i
$290$	−3.41115	+	14.9452i	−0.200310	+	0.877614i
$291$	4.23439	−	2.03917i	0.248224	−	0.119538i
$292$	1.13136	+	1.41868i	0.0662078	+	0.0830220i
$293$	−32.5010			−1.89873			−0.949363	−	0.314180i	$-0.898270\pi$
$293$	−32.5010			−1.89873			−0.949363	+	0.314180i	$0.898270\pi$
$294$	11.4775	+	0.637740i	0.669383	+	0.0371938i
$295$	3.64764			0.212374
$296$	7.64547	+	9.58712i	0.444384	+	0.557240i
$297$	3.85619	−	1.85704i	0.223759	−	0.107756i
$298$	0.613874	−	2.68956i	0.0355608	−	0.155802i
$299$	−3.71469	+	1.78890i	−0.214826	+	0.103455i
$300$	−0.627745	−	0.302306i	−0.0362429	−	0.0174536i
$301$	3.37940	−	13.1169i	0.194785	−	0.756046i
$302$	2.46541	−	1.18728i	0.141869	−	0.0683203i
$303$	3.48917	−	4.37528i	0.200447	−	0.251353i
$304$	7.28874	+	3.51007i	0.418038	+	0.201316i
$305$	−0.370766	−	0.464926i	−0.0212300	−	0.0266216i
$306$	−0.436753	−	1.91354i	−0.0249675	−	0.109390i
$307$	−10.7883	−	13.5281i	−0.615721	−	0.772089i	0.372015	−	0.928227i	$-0.378667\pi$
$307$	−10.7883	−	13.5281i	−0.615721	−	0.772089i	−0.987735	+	0.156138i	$0.950096\pi$
$308$	−4.74619	−	6.30269i	−0.270439	−	0.359129i
$309$	−6.12395	+	7.67919i	−0.348379	+	0.436854i
$310$	−6.23579	−	3.00300i	−0.354169	−	0.170559i
$311$	−5.28078	−	23.1366i	−0.299445	−	1.31196i	−0.870956	−	0.491361i	$-0.836499\pi$
$311$	−5.28078	−	23.1366i	−0.299445	−	1.31196i	0.571510	−	0.820595i	$-0.306358\pi$
$312$	1.62755			0.0921416
$313$	−20.0206			−1.13163			−0.565816	−	0.824531i	$-0.691439\pi$
$313$	−20.0206			−1.13163			−0.565816	+	0.824531i	$0.691439\pi$
$314$	5.01377	+	21.9668i	0.282944	+	1.23966i
$315$	2.64473	+	0.0734196i	0.149014	+	0.00413673i
$316$	0.299900	−	1.31395i	0.0168707	−	0.0739153i
$317$	−1.18916	+	5.21003i	−0.0667896	+	0.292624i	−0.997281	−	0.0736886i	$-0.976523\pi$
$317$	−1.18916	+	5.21003i	−0.0667896	+	0.292624i	0.930492	+	0.366313i	$0.119380\pi$
$318$	0.634434	−	0.795555i	0.0355773	−	0.0446125i
$319$	−24.9108	+	31.2372i	−1.39474	+	1.74895i
$320$	−0.803178	+	3.51895i	−0.0448990	+	0.196715i
$321$	3.30725	−	14.4900i	0.184593	−	0.808753i
$322$	−14.1701	−	18.8171i	−0.789667	−	1.04864i
$323$	−0.438380	−	1.92067i	−0.0243921	−	0.106869i
$324$	0.696744			0.0387080
$325$	−0.760473			−0.0421834
$326$	5.15052	+	22.5659i	0.285261	+	1.24981i
$327$	4.95856	+	2.38792i	0.274209	+	0.132052i
$328$	−9.06609	+	11.3685i	−0.500591	+	0.627721i
$329$	11.2954	−	13.3845i	0.622737	−	0.737913i
$330$	−4.38225	−	5.49517i	−0.241235	−	0.302499i
$331$	1.96337	+	8.60211i	0.107917	+	0.472815i	0.999789	+	0.0205275i	$0.00653458\pi$
$331$	1.96337	+	8.60211i	0.107917	+	0.472815i	−0.891872	+	0.452287i	$0.850608\pi$
$332$	5.22970	+	6.55783i	0.287017	+	0.359908i
$333$	5.16221	+	2.48599i	0.282887	+	0.136231i
$334$	−20.0636	+	25.1590i	−1.09783	+	1.37664i
$335$	2.20184	−	1.06035i	0.120299	−	0.0579331i
$336$	2.53711	+	12.7352i	0.138411	+	0.694761i
$337$	22.9629	+	11.0583i	1.25087	+	0.602386i	0.937744	−	0.347326i	$-0.112910\pi$
$337$	22.9629	+	11.0583i	1.25087	+	0.602386i	0.313124	+	0.949712i	$0.398625\pi$
$338$	18.3785	−	8.85062i	0.999659	−	0.481410i
$339$	−3.43681	+	15.0576i	−0.186662	+	0.817819i
$340$	−0.750289	+	0.361320i	−0.0406901	+	0.0195953i
$341$	−11.2471	−	14.1034i	−0.609063	−	0.763741i
$342$	2.70679			0.146366
$343$	10.3030	+	15.3899i	0.556309	+	0.830975i
$344$	10.9569			0.590756
$345$	−3.38032	−	4.23879i	−0.181990	−	0.228209i
$346$	−4.86627	+	2.34347i	−0.261612	+	0.125986i
$347$	−5.85534	+	25.6539i	−0.314331	+	1.37718i	0.533002	+	0.846114i	$0.321064\pi$
$347$	−5.85534	+	25.6539i	−0.314331	+	1.37718i	−0.847333	+	0.531062i	$0.821793\pi$
$348$	−5.85995	+	2.82200i	−0.314126	+	0.151275i
$349$	11.4025	+	5.49115i	0.610361	+	0.293934i	0.713415	−	0.700741i	$-0.247147\pi$
$349$	11.4025	+	5.49115i	0.610361	+	0.293934i	−0.103054	+	0.994676i	$0.532862\pi$
$350$	−0.848890	−	4.26106i	−0.0453751	−	0.227763i
$351$	0.685162	−	0.329957i	0.0365712	−	0.0176118i
$352$	10.0859	−	12.6473i	0.537578	−	0.674102i
$353$	24.2154	+	11.6615i	1.28886	+	0.620681i	0.947651	−	0.319307i	$-0.103450\pi$
$353$	24.2154	+	11.6615i	1.28886	+	0.620681i	0.341206	+	0.939988i	$0.389165\pi$
$354$	3.73474	+	4.68322i	0.198499	+	0.248910i
$355$	2.71208	+	11.8824i	0.143942	+	0.630653i
$356$	−3.90543	−	4.89726i	−0.206988	−	0.259554i
$357$	2.03947	−	2.41667i	0.107940	−	0.127904i
$358$	−23.8309	+	29.8830i	−1.25950	+	1.57937i
$359$	−14.4565	−	6.96188i	−0.762984	−	0.367434i	0.0115769	−	0.999933i	$-0.496315\pi$
$359$	−14.4565	−	6.96188i	−0.762984	−	0.367434i	−0.774561	+	0.632499i	$0.782029\pi$
$360$	0.476234	+	2.08652i	0.0250997	+	0.109969i
$361$	−16.2831			−0.857007
$362$	−28.8652			−1.51712
$363$	−1.62858	−	7.13527i	−0.0854782	−	0.374504i
$364$	−0.843297	−	1.11985i	−0.0442008	−	0.0586963i
$365$	−0.579520	+	2.53904i	−0.0303335	+	0.132900i
$366$	0.217301	−	0.952057i	0.0113585	−	0.0497648i
$367$	22.5003	−	28.2144i	1.17450	−	1.47278i	0.324594	−	0.945854i	$-0.394772\pi$
$367$	22.5003	−	28.2144i	1.17450	−	1.47278i	0.849910	−	0.526928i	$-0.176656\pi$
$368$	16.5907	−	20.8041i	0.864852	−	1.08449i
$369$	−1.51186	+	6.62390i	−0.0787044	+	0.344826i
$370$	2.09371	−	9.17314i	0.108847	−	0.476889i
$371$	1.63877	+	0.0454935i	0.0850808	+	0.00236190i
$372$	−0.653441	−	2.86291i	−0.0338793	−	0.148435i
$373$	15.8744			0.821944			0.410972	−	0.911648i	$-0.365189\pi$
$373$	15.8744			0.821944			0.410972	+	0.911648i	$0.365189\pi$
$374$	−8.40066			−0.434388
$375$	−0.222521	−	0.974928i	−0.0114909	−	0.0503451i
$376$	12.7641	+	6.14686i	0.658258	+	0.317000i
$377$	−4.42612	+	5.55018i	−0.227957	+	0.285849i
$378$	2.61363	+	3.47076i	0.134430	+	0.178517i
$379$	−2.61771	−	3.28250i	−0.134463	−	0.168611i	0.710041	−	0.704160i	$-0.248676\pi$
$379$	−2.61771	−	3.28250i	−0.134463	−	0.168611i	−0.844504	+	0.535549i	$0.820105\pi$
$380$	−0.255552	−	1.11965i	−0.0131095	−	0.0574366i
$381$	−8.09848	−	10.1552i	−0.414898	−	0.520265i
$382$	−0.0513858	−	0.0247461i	−0.00262913	−	0.00126612i
$383$	4.37676	−	5.48829i	0.223642	−	0.280438i	−0.657334	−	0.753600i	$-0.728316\pi$
$383$	4.37676	−	5.48829i	0.223642	−	0.280438i	0.880976	+	0.473161i	$0.156887\pi$
$384$	−12.1508	+	5.85152i	−0.620068	+	0.298609i
$385$	2.82520	−	10.9658i	0.143986	−	0.558871i
$386$	19.4805	+	9.38134i	0.991534	+	0.477498i
$387$	4.61262	−	2.22132i	0.234473	−	0.112916i
$388$	0.728660	−	3.19247i	0.0369921	−	0.162073i
$389$	1.97075	−	0.949061i	0.0999208	−	0.0481193i	−0.383256	−	0.923642i	$-0.625197\pi$
$389$	1.97075	−	0.949061i	0.0999208	−	0.0481193i	0.483177	+	0.875523i	$0.339483\pi$
$390$	−0.778633	−	0.976375i	−0.0394276	−	0.0494407i
$391$	−6.47999			−0.327707
$392$	−9.97607	+	11.1766i	−0.503868	+	0.564501i
$393$	14.0781			0.710146
$394$	−15.2088	−	19.0712i	−0.766209	−	0.960795i
$395$	1.74278	−	0.839277i	0.0876886	−	0.0422286i
$396$	0.663579	−	2.90733i	0.0333461	−	0.146099i
$397$	−14.0092	+	6.74647i	−0.703101	+	0.338596i	−0.751042	−	0.660254i	$-0.770448\pi$
$397$	−14.0092	+	6.74647i	−0.703101	+	0.338596i	0.0479406	+	0.998850i	$0.484734\pi$
$398$	−3.40826	−	1.64133i	−0.170841	−	0.0822726i
$399$	2.62336	+	3.48369i	0.131332	+	0.174403i
$400$	4.42199	−	2.12952i	0.221099	−	0.106476i
$401$	−4.28726	+	5.37606i	−0.214096	+	0.268467i	−0.877270	−	0.479998i	$-0.840637\pi$
$401$	−4.28726	+	5.37606i	−0.214096	+	0.268467i	0.663174	+	0.748465i	$0.269209\pi$
$402$	3.61581	+	1.74128i	0.180340	+	0.0868473i
$403$	−1.99836	−	2.50587i	−0.0995456	−	0.124826i
$404$	−0.867634	−	3.80135i	−0.0431664	−	0.189124i
$405$	0.623490	+	0.781831i	0.0309815	+	0.0388495i
$406$	−36.0393	−	18.6048i	−1.78860	−	0.923342i
$407$	15.2898	−	19.1729i	0.757889	−	0.950363i
$408$	2.30465	+	1.10986i	0.114097	+	0.0549463i
$409$	4.18934	+	18.3547i	0.207150	+	0.907581i	0.966453	+	0.256844i	$0.0826828\pi$
$409$	4.18934	+	18.3547i	0.207150	+	0.907581i	−0.759303	+	0.650737i	$0.774460\pi$
$410$	11.1573			0.551022
$411$	0.913869			0.0450778
$412$	1.52281	+	6.67188i	0.0750236	+	0.328700i
$413$	−2.40776	+	9.34556i	−0.118478	+	0.459865i
$414$	1.98116	−	8.68003i	0.0973687	−	0.426600i
$415$	−2.67883	+	11.7367i	−0.131498	+	0.576132i
$416$	1.79204	−	2.24715i	0.0878621	−	0.110176i
$417$	2.70000	−	3.38569i	0.132219	−	0.165798i
$418$	2.57794	−	11.2947i	0.126091	−	0.552443i
$419$	6.90471	−	30.2515i	0.337317	−	1.47788i	−0.467305	−	0.884096i	$-0.654775\pi$
$419$	6.90471	−	30.2515i	0.337317	−	1.47788i	0.804622	−	0.593787i	$-0.202368\pi$
$420$	1.18890	−	1.40879i	0.0580124	−	0.0687418i
$421$	2.67146	+	11.7044i	0.130199	+	0.570439i	0.997373	+	0.0724340i	$0.0230767\pi$
$421$	2.67146	+	11.7044i	0.130199	+	0.570439i	−0.867174	+	0.498005i	$0.834066\pi$
$422$	3.87039			0.188408
$423$	6.61958			0.321855
$424$	0.295092	+	1.29288i	0.0143309	+	0.0627879i
$425$	−1.07685	−	0.518584i	−0.0522349	−	0.0251550i
$426$	−12.4790	+	15.6482i	−0.604612	+	0.758159i
$427$	1.43592	−	0.643043i	0.0694890	−	0.0311190i
$428$	−6.45653	−	8.09623i	−0.312088	−	0.391346i
$429$	−0.724273	−	3.17325i	−0.0349682	−	0.153206i
$430$	−5.24188	−	6.57311i	−0.252786	−	0.316983i
$431$	11.8934	+	5.72757i	0.572886	+	0.275887i	0.697815	−	0.716278i	$-0.254156\pi$
$431$	11.8934	+	5.72757i	0.572886	+	0.275887i	−0.124929	+	0.992166i	$0.539870\pi$
$432$	−3.06011	+	3.83726i	−0.147230	+	0.184620i
$433$	10.2659	−	4.94378i	0.493346	−	0.237583i	−0.170632	−	0.985335i	$-0.554581\pi$
$433$	10.2659	−	4.94378i	0.493346	−	0.237583i	0.663978	+	0.747752i	$0.268867\pi$
$434$	11.8101	−	13.9944i	0.566903	−	0.671752i
$435$	−8.41047	−	4.05027i	−0.403251	−	0.194195i
$436$	3.45485	−	1.66377i	0.165457	−	0.0796801i
$437$	1.98854	−	8.71236i	0.0951248	−	0.416769i
$438$	−3.85325	+	1.85563i	−0.184116	+	0.0886654i
$439$	17.5696	+	22.0316i	0.838550	+	1.05151i	0.997931	+	0.0642917i	$0.0204788\pi$
$439$	17.5696	+	22.0316i	0.838550	+	1.05151i	−0.159381	+	0.987217i	$0.550950\pi$
$440$	9.16004			0.436688
$441$	−1.93386	+	6.72757i	−0.0920886	+	0.320360i
$442$	−1.49262			−0.0709966
$443$	−17.2506	−	21.6316i	−0.819601	−	1.02775i	−0.999033	−	0.0439770i	$-0.985997\pi$
$443$	−17.2506	−	21.6316i	−0.819601	−	1.02775i	0.179431	−	0.983771i	$-0.442574\pi$
$444$	3.59674	−	1.73210i	0.170694	−	0.0822017i
$445$	2.00049	−	8.76474i	0.0948325	−	0.415488i
$446$	33.3544	−	16.0626i	1.57937	−	0.760587i
$447$	1.51356	+	0.728890i	0.0715887	+	0.0344753i
$448$	−8.48569	−	4.38063i	−0.400911	−	0.206965i
$449$	21.5578	−	10.3817i	1.01737	−	0.489942i	0.150575	−	0.988599i	$-0.451887\pi$
$449$	21.5578	−	10.3817i	1.01737	−	0.489942i	0.866800	+	0.498657i	$0.166173\pi$
$450$	1.02388	−	1.28391i	0.0482662	−	0.0605239i
$451$	26.1999	+	12.6172i	1.23370	+	0.594120i
$452$	6.70945	+	8.41339i	0.315586	+	0.395733i
$453$	0.370792	+	1.62455i	0.0174213	+	0.0763279i
$454$	25.1103	+	31.4873i	1.17848	+	1.47777i
$455$	0.501978	−	1.94840i	0.0235331	−	0.0913422i
$456$	−2.19945	+	2.75802i	−0.102999	+	0.129156i
$457$	−35.8462	−	17.2626i	−1.67681	−	0.807511i	−0.997267	−	0.0738801i	$-0.976462\pi$
$457$	−35.8462	−	17.2626i	−1.67681	−	0.807511i	−0.679548	−	0.733631i	$-0.737824\pi$
$458$	5.93977	+	26.0238i	0.277547	+	1.21601i
$459$	1.19521			0.0557878
$460$	−3.77748			−0.176126
$461$	0.410476	+	1.79841i	0.0191178	+	0.0837605i	0.983587	−	0.180435i	$-0.0577506\pi$
$461$	0.410476	+	1.79841i	0.0191178	+	0.0837605i	−0.964469	+	0.264196i	$0.914893\pi$
$462$	16.9718	−	7.60042i	0.789598	−	0.353603i
$463$	−7.34055	+	32.1611i	−0.341144	+	1.49465i	0.455518	+	0.890227i	$0.349454\pi$
$463$	−7.34055	+	32.1611i	−0.341144	+	1.49465i	−0.796662	+	0.604425i	$0.793403\pi$
$464$	10.1950	−	44.6674i	0.473293	−	2.07363i
$465$	2.62779	−	3.29515i	0.121861	−	0.152809i
$466$	−26.1865	+	32.8369i	−1.21307	+	1.52114i
$467$	1.70138	−	7.45424i	0.0787305	−	0.344941i	−0.920186	−	0.391482i	$-0.871963\pi$
$467$	1.70138	−	7.45424i	0.0787305	−	0.344941i	0.998916	+	0.0465408i	$0.0148198\pi$
$468$	0.117904	−	0.516570i	0.00545011	−	0.0238785i
$469$	1.26330	+	6.34123i	0.0583339	+	0.292811i
$470$	−2.41892	−	10.5980i	−0.111576	−	0.488848i
$471$	−13.7206			−0.632213
$472$	−7.80658			−0.359327
$473$	−4.87592	−	21.3628i	−0.224195	−	0.982263i
$474$	2.86195	+	1.37824i	0.131454	+	0.0633047i
$475$	1.02769	−	1.28869i	0.0471539	−	0.0591291i
$476$	−0.430477	−	2.16081i	−0.0197309	−	0.0990405i
$477$	0.386337	+	0.484451i	0.0176892	+	0.0221815i
$478$	6.98757	+	30.6145i	0.319604	+	1.40028i
$479$	−19.9202	−	24.9792i	−0.910178	−	1.14133i	−0.989508	−	0.144479i	$-0.953849\pi$
$479$	−19.9202	−	24.9792i	−0.910178	−	1.14133i	0.0793295	−	0.996848i	$-0.474722\pi$
$480$	3.40522	+	1.63987i	0.155426	+	0.0748494i
$481$	2.71668	−	3.40661i	0.123870	−	0.155328i
$482$	22.0884	−	10.6372i	1.00610	−	0.484511i
$483$	13.0915	−	5.86271i	0.595682	−	0.266762i
$484$	−4.59432	−	2.21251i	−0.208833	−	0.100569i
$485$	4.23439	−	2.03917i	0.192274	−	0.0925941i
$486$	−0.365419	+	1.60100i	−0.0165757	+	0.0726230i
$487$	16.0109	−	7.71046i	0.725525	−	0.349394i	−0.0343973	−	0.999408i	$-0.510951\pi$
$487$	16.0109	−	7.71046i	0.725525	−	0.349394i	0.759922	+	0.650014i	$0.225237\pi$
$488$	0.793505	+	0.995024i	0.0359203	+	0.0450426i
$489$	−14.0948			−0.637391
$490$	11.4775	+	0.637740i	0.518502	+	0.0288102i
$491$	38.3745			1.73182			0.865909	−	0.500201i	$-0.166740\pi$
$491$	38.3745			1.73182			0.865909	+	0.500201i	$0.166740\pi$
$492$	2.95151	+	3.70107i	0.133064	+	0.166857i
$493$	−10.0523	+	4.84093i	−0.452733	+	0.218025i
$494$	0.458046	−	2.00683i	0.0206085	−	0.0902916i
$495$	3.85619	−	1.85704i	0.173323	−	0.0834678i
$496$	18.6371	+	8.97518i	0.836832	+	0.402997i
$497$	−32.2340	−	0.894837i	−1.44589	−	0.0401389i
$498$	−17.8116	+	8.57762i	−0.798158	+	0.384372i
$499$	9.18810	−	11.5215i	0.411316	−	0.515774i	−0.532417	−	0.846482i	$-0.678716\pi$
$499$	9.18810	−	11.5215i	0.411316	−	0.515774i	0.943733	+	0.330708i	$0.107288\pi$
$500$	−0.627745	−	0.302306i	−0.0280736	−	0.0135195i
$501$	−12.2177	−	15.3205i	−0.545846	−	0.684469i
$502$	2.58325	+	11.3180i	0.115296	+	0.505145i
$503$	−19.4817	−	24.4292i	−0.868645	−	1.08925i	−0.995256	−	0.0972936i	$-0.968981\pi$
$503$	−19.4817	−	24.4292i	−0.868645	−	1.08925i	0.126611	−	0.991952i	$-0.459590\pi$
$504$	−5.66019	−	0.157131i	−0.252125	−	0.00699917i
$505$	3.48917	−	4.37528i	0.155266	−	0.194697i
$506$	−34.3326	−	16.5337i	−1.52627	−	0.735013i
$507$	2.76408	+	12.1102i	0.122757	+	0.537835i
$508$	−9.04998			−0.401528
$509$	−33.6542			−1.49170			−0.745848	−	0.666117i	$-0.767955\pi$
$509$	−33.6542			−1.49170			−0.745848	+	0.666117i	$0.767955\pi$
$510$	−0.436753	−	1.91354i	−0.0193398	−	0.0847330i
$511$	−6.12272	−	3.16077i	−0.270853	−	0.139824i
$512$	0.546990	−	2.39652i	0.0241738	−	0.105912i
$513$	−0.366780	+	1.60697i	−0.0161937	+	0.0709494i
$514$	17.2311	−	21.6071i	0.760030	−	0.953048i
$515$	−6.12395	+	7.67919i	−0.269853	+	0.338386i
$516$	0.793747	−	3.47763i	0.0349428	−	0.153094i
$517$	6.30449	−	27.6218i	0.277271	−	1.21480i
$518$	22.1203	+	11.4193i	0.971912	+	0.501737i
$519$	−0.731876	−	3.20656i	−0.0321258	−	0.140752i
$520$	1.62755			0.0713726
$521$	13.0605			0.572190			0.286095	−	0.958201i	$-0.407643\pi$
$521$	13.0605			0.572190			0.286095	+	0.958201i	$0.407643\pi$
$522$	−3.41115	−	14.9452i	−0.149302	−	0.654135i
$523$	11.8952	+	5.72841i	0.520139	+	0.250486i	0.675484	−	0.737375i	$-0.263935\pi$
$523$	11.8952	+	5.72841i	0.520139	+	0.250486i	−0.155345	+	0.987860i	$0.549649\pi$
$524$	6.11571	−	7.66885i	0.267166	−	0.335015i
$525$	2.64473	+	0.0734196i	0.115426	+	0.00320430i
$526$	32.0896	+	40.2391i	1.39917	+	1.75451i
$527$	−1.12093	−	4.91111i	−0.0488284	−	0.213931i
$528$	13.0974	+	16.4236i	0.569991	+	0.714746i
$529$	−5.76072	−	2.77422i	−0.250466	−	0.120618i
$530$	0.634434	−	0.795555i	0.0275580	−	0.0345567i
$531$	−3.28641	+	1.58265i	−0.142618	+	0.0686812i
$532$	3.03732	+	0.0843180i	0.131684	+	0.00365565i
$533$	4.65516	+	2.24181i	0.201637	+	0.0971034i
$534$	13.3014	−	6.40560i	0.575606	−	0.277197i
$535$	3.30725	−	14.4900i	0.142985	−	0.626458i
$536$	−4.71232	+	2.26934i	−0.203541	+	0.0980204i
$537$	−14.5118	−	18.1972i	−0.626230	−	0.785267i
$538$	−2.43040			−0.104782
$539$	26.2305	+	14.4768i	1.12983	+	0.623561i
$540$	0.696744			0.0299831
$541$	7.09770	+	8.90023i	0.305154	+	0.382651i	0.910637	−	0.413207i	$-0.135591\pi$
$541$	7.09770	+	8.90023i	0.305154	+	0.382651i	−0.605483	+	0.795858i	$0.707020\pi$
$542$	−33.8751	+	16.3134i	−1.45506	+	0.700721i
$543$	3.91134	−	17.1367i	0.167852	−	0.735407i
$544$	4.06997	−	1.95999i	0.174498	−	0.0840340i
$545$	4.95856	+	2.38792i	0.212402	+	0.102287i
$546$	3.01552	−	1.35043i	0.129052	−	0.0577932i
$547$	−33.8004	+	16.2774i	−1.44520	+	0.695972i	−0.981755	−	0.190153i	$-0.939102\pi$
$547$	−33.8004	+	16.2774i	−1.44520	+	0.695972i	−0.463447	+	0.886125i	$0.653387\pi$
$548$	0.396997	−	0.497818i	0.0169589	−	0.0212657i
$549$	0.535773	+	0.258014i	0.0228662	+	0.0110118i
$550$	−4.38225	−	5.49517i	−0.186860	−	0.234315i
$551$	−3.42386	−	15.0009i	−0.145861	−	0.639060i
$552$	7.23449	+	9.07176i	0.307920	+	0.386120i
$553$	0.999915	+	5.01914i	0.0425207	+	0.213436i
$554$	−3.19886	+	4.01125i	−0.135907	+	0.170422i
$555$	5.16221	+	2.48599i	0.219123	+	0.105524i
$556$	−0.671395	−	2.94157i	−0.0284735	−	0.124750i
$557$	7.28491			0.308672			0.154336	−	0.988018i	$-0.450676\pi$
$557$	7.28491			0.308672			0.154336	+	0.988018i	$0.450676\pi$
$558$	6.92121			0.292998
$559$	−0.866347	−	3.79572i	−0.0366426	−	0.160542i
$560$	2.53711	+	12.7352i	0.107212	+	0.538160i
$561$	1.13832	−	4.98731i	0.0480599	−	0.210564i
$562$	−2.68636	+	11.7697i	−0.113317	+	0.496475i
$563$	28.1936	−	35.3536i	1.18822	−	1.48998i	0.356934	−	0.934130i	$-0.383822\pi$
$563$	28.1936	−	35.3536i	1.18822	−	1.48998i	0.831284	−	0.555848i	$-0.187606\pi$
$564$	2.87563	−	3.60593i	0.121086	−	0.151837i
$565$	−3.43681	+	15.0576i	−0.144588	+	0.633480i
$566$	−9.37160	+	41.0596i	−0.393918	+	1.72587i
$567$	−2.41468	+	1.08136i	−0.101407	+	0.0454128i
$568$	−5.80433	−	25.4304i	−0.243544	−	1.06704i
$569$	−40.2428			−1.68706			−0.843532	−	0.537079i	$-0.819528\pi$
$569$	−40.2428			−1.68706			−0.843532	+	0.537079i	$0.819528\pi$
$570$	2.70679			0.113375
$571$	5.28705	+	23.1641i	0.221256	+	0.969387i	0.956534	+	0.291621i	$0.0941946\pi$
$571$	5.28705	+	23.1641i	0.221256	+	0.969387i	−0.735278	+	0.677766i	$0.762948\pi$
$572$	−2.04322	−	0.983962i	−0.0854313	−	0.0411415i
$573$	0.0216542	−	0.0271535i	0.000904619	−	0.00113436i
$574$	−7.36482	+	28.5861i	−0.307402	+	1.19316i
$575$	−3.38032	−	4.23879i	−0.140969	−	0.176770i
$576$	−0.803178	−	3.51895i	−0.0334657	−	0.146623i
$577$	−12.2658	−	15.3808i	−0.510631	−	0.640312i	0.457959	−	0.888973i	$-0.348581\pi$
$577$	−12.2658	−	15.3808i	−0.510631	−	0.640312i	−0.968590	+	0.248662i	$0.920009\pi$
$578$	23.0388	+	11.0949i	0.958286	+	0.461486i
$579$	−8.20920	+	10.2940i	−0.341163	+	0.427805i
$580$	−5.85995	+	2.82200i	−0.243321	+	0.117177i
$581$	−28.3022	−	14.6106i	−1.17417	−	0.606151i
$582$	6.95361	+	3.34868i	0.288236	+	0.138807i
$583$	2.38943	−	1.15069i	0.0989602	−	0.0476567i
$584$	1.24028	−	5.43400i	0.0513230	−	0.224861i
$585$	0.685162	−	0.329957i	0.0283280	−	0.0136420i
$586$	−33.2771	−	41.7282i	−1.37466	−	1.72377i
$587$	−6.30244			−0.260130			−0.130065	−	0.991505i	$-0.541519\pi$
$587$	−6.30244			−0.260130			−0.130065	+	0.991505i	$0.541519\pi$
$588$	2.82466	+	3.97599i	0.116487	+	0.163967i
$589$	6.94699			0.286246
$590$	3.73474	+	4.68322i	0.153757	+	0.192805i
$591$	13.3831	−	6.44495i	0.550506	−	0.265110i
$592$	−6.25755	+	27.4161i	−0.257184	+	1.12680i
$593$	−33.6198	+	16.1904i	−1.38060	+	0.664862i	−0.969127	−	0.246561i	$-0.920699\pi$
$593$	−33.6198	+	16.1904i	−1.38060	+	0.664862i	−0.411472	+	0.911422i	$0.634985\pi$
$594$	6.33254	+	3.04959i	0.259827	+	0.125126i
$595$	2.03947	−	2.41667i	0.0836102	−	0.0990739i
$596$	1.05456	−	0.507850i	0.0431965	−	0.0208024i
$597$	1.43626	−	1.80101i	0.0587822	−	0.0737105i
$598$	−6.10017	−	2.93769i	−0.249455	−	0.120131i
$599$	12.2652	+	15.3800i	0.501141	+	0.628411i	0.966486	−	0.256718i	$-0.0826413\pi$
$599$	12.2652	+	15.3800i	0.501141	+	0.628411i	−0.465345	+	0.885129i	$0.654070\pi$
$600$	0.476234	+	2.08652i	0.0194422	+	0.0851817i
$601$	−27.7810	−	34.8363i	−1.13321	−	1.42100i	−0.892870	−	0.450314i	$-0.851312\pi$
$601$	−27.7810	−	34.8363i	−1.13321	−	1.42100i	−0.240341	−	0.970688i	$-0.577259\pi$
$602$	20.3010	−	9.09132i	0.827405	−	0.370534i
$603$	−1.52372	+	1.91068i	−0.0620507	+	0.0778091i
$604$	1.04603	+	0.503740i	0.0425623	+	0.0204969i
$605$	−1.62858	−	7.13527i	−0.0662111	−	0.290090i
$606$	9.18993			0.373315
$607$	33.2369			1.34905			0.674523	−	0.738254i	$-0.264350\pi$
$607$	33.2369			1.34905			0.674523	+	0.738254i	$0.264350\pi$
$608$	1.38625	+	6.07355i	0.0562198	+	0.246315i
$609$	15.9288	−	18.8748i	0.645467	−	0.764846i
$610$	0.217301	−	0.952057i	0.00879826	−	0.0385477i
$611$	1.12017	−	4.90780i	0.0453173	−	0.198548i
$612$	0.519216	−	0.651077i	0.0209881	−	0.0263182i
$613$	4.27947	−	5.36629i	0.172846	−	0.216742i	−0.687861	−	0.725842i	$-0.741450\pi$
$613$	4.27947	−	5.36629i	0.172846	−	0.216742i	0.860707	+	0.509100i	$0.170022\pi$
$614$	6.32287	−	27.7023i	0.255170	−	1.11797i
$615$	−1.51186	+	6.62390i	−0.0609641	+	0.267101i
$616$	−6.04643	+	23.4688i	−0.243618	+	0.945586i
$617$	2.71213	+	11.8826i	0.109186	+	0.478377i	0.999725	+	0.0234683i	$0.00747087\pi$
$617$	2.71213	+	11.8826i	0.109186	+	0.478377i	−0.890538	+	0.454908i	$0.849672\pi$
$618$	−16.1295			−0.648825
$619$	−36.7219			−1.47598			−0.737989	−	0.674812i	$-0.764225\pi$
$619$	−36.7219			−1.47598			−0.737989	+	0.674812i	$0.764225\pi$
$620$	−0.653441	−	2.86291i	−0.0262428	−	0.114977i
$621$	4.88471	+	2.35235i	0.196017	+	0.0943966i
$622$	24.2983	−	30.4691i	0.974274	−	1.22170i
$623$	21.1355	+	10.9109i	0.846776	+	0.437137i
$624$	2.32713	+	2.91813i	0.0931598	+	0.116819i
$625$	−0.222521	−	0.974928i	−0.00890084	−	0.0389971i
$626$	−20.4987	−	25.7046i	−0.819294	−	1.02736i
$627$	6.35613	+	3.06095i	0.253839	+	0.122243i
$628$	−5.96042	+	7.47413i	−0.237847	+	0.298250i
$629$	6.16994	−	2.97129i	0.246012	−	0.118473i
$630$	2.61363	+	3.47076i	0.104129	+	0.138278i
$631$	−7.79060	−	3.75176i	−0.310139	−	0.149355i	0.272339	−	0.962201i	$-0.412203\pi$
$631$	−7.79060	−	3.75176i	−0.310139	−	0.149355i	−0.582478	+	0.812846i	$0.697917\pi$
$632$	−3.72985	+	1.79620i	−0.148365	+	0.0714490i
$633$	−0.524452	+	2.29777i	−0.0208451	+	0.0913284i
$634$	−7.90674	+	3.80768i	−0.314017	+	0.151222i
$635$	−8.09848	−	10.1552i	−0.321378	−	0.402996i
$636$	0.431728			0.0171191
$637$	4.66061	+	2.57222i	0.184660	+	0.101915i
$638$	−65.6113			−2.59757
$639$	−7.59909	−	9.52895i	−0.300615	−	0.376960i
$640$	−12.1508	+	5.85152i	−0.480303	+	0.231302i
$641$	10.4091	−	45.6052i	0.411134	−	1.80130i	−0.167683	−	0.985841i	$-0.553629\pi$
$641$	10.4091	−	45.6052i	0.411134	−	1.80130i	0.578818	−	0.815457i	$-0.303514\pi$
$642$	21.9900	−	10.5898i	0.867877	−	0.417948i
$643$	−41.3320	−	19.9045i	−1.62998	−	0.784955i	−0.999965	−	0.00836976i	$-0.997336\pi$
$643$	−41.3320	−	19.9045i	−1.62998	−	0.784955i	−0.630012	−	0.776586i	$-0.716950\pi$
$644$	2.49347	−	9.67823i	0.0982563	−	0.381376i
$645$	4.61262	−	2.22132i	0.181622	−	0.0874644i
$646$	2.01711	−	2.52938i	0.0793621	−	0.0995169i
$647$	26.6570	+	12.8373i	1.04799	+	0.504687i	0.876953	−	0.480576i	$-0.159573\pi$
$647$	26.6570	+	12.8373i	1.04799	+	0.504687i	0.171041	+	0.985264i	$0.445287\pi$
$648$	−1.33438	−	1.67326i	−0.0524193	−	0.0657317i
$649$	3.47401	+	15.2206i	0.136367	+	0.597461i
$650$	−0.778633	−	0.976375i	−0.0305405	−	0.0382966i
$651$	6.70788	+	8.90772i	0.262903	+	0.349121i
$652$	−6.12299	+	7.67798i	−0.239795	+	0.300693i
$653$	−22.1144	−	10.6498i	−0.865405	−	0.416757i	−0.0521327	−	0.998640i	$-0.516602\pi$
$653$	−22.1144	−	10.6498i	−0.865405	−	0.416757i	−0.813273	+	0.581883i	$0.802316\pi$
$654$	2.01112	+	8.81127i	0.0786408	+	0.344548i
$655$	14.0781			0.550076
$656$	−33.3464			−1.30196
$657$	−0.579520	−	2.53904i	−0.0226092	−	0.0990576i
$658$	28.7496	+	0.798110i	1.12078	+	0.0311136i
$659$	10.9953	−	48.1736i	0.428317	−	1.87658i	−0.0506024	−	0.998719i	$-0.516114\pi$
$659$	10.9953	−	48.1736i	0.428317	−	1.87658i	0.478919	−	0.877859i	$-0.341029\pi$
$660$	0.663579	−	2.90733i	0.0258298	−	0.113168i
$661$	13.2035	−	16.5567i	0.513556	−	0.643979i	−0.455671	−	0.890148i	$-0.650601\pi$
$661$	13.2035	−	16.5567i	0.513556	−	0.643979i	0.969227	+	0.246169i	$0.0791719\pi$
$662$	−9.03403	+	11.3283i	−0.351118	+	0.440288i
$663$	0.202255	−	0.886138i	0.00785494	−	0.0344148i
$664$	5.73316	−	25.1186i	0.222490	−	0.974791i
$665$	2.62336	+	3.48369i	0.101730	+	0.135092i
$666$	2.09371	+	9.17314i	0.0811296	+	0.355452i
$667$	−50.6103			−1.95964
$668$	−13.6532			−0.528256
$669$	5.01642	+	21.9784i	0.193946	+	0.849733i
$670$	3.61581	+	1.74128i	0.139691	+	0.0672716i
$671$	1.58689	−	1.98990i	0.0612614	−	0.0768194i
$672$	−6.44923	+	7.64201i	−0.248784	+	0.294797i
$673$	13.6910	+	17.1680i	0.527750	+	0.661778i	0.972234	−	0.234009i	$-0.0751845\pi$
$673$	13.6910	+	17.1680i	0.527750	+	0.661778i	−0.444484	+	0.895787i	$0.646613\pi$
$674$	9.31338	+	40.8046i	0.358738	+	1.57173i
$675$	0.623490	+	0.781831i	0.0239981	+	0.0300927i
$676$	7.79765	+	3.75515i	0.299910	+	0.144429i
$677$	−12.6593	+	15.8743i	−0.486537	+	0.610097i	−0.963133	−	0.269025i	$-0.913299\pi$
$677$	−12.6593	+	15.8743i	−0.486537	+	0.610097i	0.476597	+	0.879122i	$0.341870\pi$
$678$	−22.8515	+	11.0047i	−0.877605	+	0.422632i
$679$	2.42947	+	12.1949i	0.0932346	+	0.467997i
$680$	2.30465	+	1.10986i	0.0883792	+	0.0425612i
$681$	−22.0959	+	10.6408i	−0.846717	+	0.407757i
$682$	6.59175	−	28.8803i	0.252411	−	1.10589i
$683$	−2.62611	+	1.26467i	−0.100485	+	0.0483912i	−0.483451	−	0.875371i	$-0.660617\pi$
$683$	−2.62611	+	1.26467i	−0.100485	+	0.0483912i	0.382966	+	0.923762i	$0.374903\pi$
$684$	0.716040	+	0.897886i	0.0273785	+	0.0343315i
$685$	0.913869			0.0349171
$686$	−9.21012	+	28.9855i	−0.351644	+	1.10667i
$687$	−16.2547			−0.620155
$688$	15.6666	+	19.6453i	0.597284	+	0.748970i
$689$	0.424551	−	0.204453i	0.0161741	−	0.00778905i
$690$	1.98116	−	8.68003i	0.0754215	−	0.330443i
$691$	−2.67182	+	1.28668i	−0.101641	+	0.0489477i	−0.484013	−	0.875061i	$-0.660821\pi$
$691$	−2.67182	+	1.28668i	−0.101641	+	0.0489477i	0.382372	+	0.924008i	$0.375107\pi$
$692$	−2.06467	−	0.994291i	−0.0784869	−	0.0377973i
$693$	2.21248	+	11.1057i	0.0840452	+	0.421870i
$694$	−38.9324	+	18.7489i	−1.47785	+	0.711697i
$695$	2.70000	−	3.38569i	0.102417	−	0.128426i
$696$	17.9999	+	8.66829i	0.682284	+	0.328571i
$697$	5.06309	+	6.34892i	0.191778	+	0.240482i
$698$	4.62467	+	20.2620i	0.175046	+	0.766928i
$699$	−15.9462	−	19.9959i	−0.603142	−	0.756316i
$700$	1.18890	−	1.40879i	0.0449362	−	0.0532472i
$701$	−29.6933	+	37.2342i	−1.12150	+	1.40632i	−0.218950	+	0.975736i	$0.570263\pi$
$701$	−29.6933	+	37.2342i	−1.12150	+	1.40632i	−0.902551	+	0.430582i	$0.858308\pi$
$702$	1.12516	+	0.541847i	0.0424663	+	0.0204507i
$703$	2.10151	+	9.20731i	0.0792599	+	0.347260i
$704$	−15.4486			−0.582241
$705$	6.61958			0.249308
$706$	9.82140	+	43.0303i	0.369633	+	1.61947i
$707$	8.90668	+	11.8276i	0.334970	+	0.444823i
$708$	−0.565530	+	2.47775i	−0.0212539	+	0.0931196i
$709$	1.53871	−	6.74153i	0.0577875	−	0.253184i	−0.937780	−	0.347229i	$-0.887123\pi$
$709$	1.53871	−	6.74153i	0.0577875	−	0.253184i	0.995568	+	0.0940453i	$0.0299798\pi$
$710$	−12.4790	+	15.6482i	−0.468330	+	0.587267i
$711$	−1.20604	+	1.51232i	−0.0452300	+	0.0567166i
$712$	−4.28141	+	18.7581i	−0.160453	+	0.702989i
$713$	5.08465	−	22.2773i	0.190422	−	0.834293i
$714$	5.19095	+	0.144104i	0.194267	+	0.00539297i
$715$	−0.724273	−	3.17325i	−0.0270863	−	0.118673i
$716$	−16.2168			−0.606050
$717$	−19.1221			−0.714127
$718$	−5.86332	−	25.6889i	−0.218817	−	0.958701i
$719$	21.3176	+	10.2660i	0.795013	+	0.382858i	0.786878	−	0.617109i	$-0.211696\pi$
$719$	21.3176	+	10.2660i	0.795013	+	0.382858i	0.00813519	+	0.999967i	$0.497410\pi$
$720$	−3.06011	+	3.83726i	−0.114044	+	0.143006i
$721$	−15.6324	−	20.7590i	−0.582181	−	0.773106i
$722$	−16.6720	−	20.9060i	−0.620467	−	0.778041i
$723$	3.32204	+	14.5548i	0.123548	+	0.541300i
$724$	−7.63586	−	9.57506i	−0.283784	−	0.355854i
$725$	−8.41047	−	4.05027i	−0.312357	−	0.150423i
$726$	7.49354	−	9.39660i	0.278111	−	0.348741i
$727$	−17.0123	+	8.19269i	−0.630951	+	0.303850i	−0.721892	−	0.692006i	$-0.756727\pi$
$727$	−17.0123	+	8.19269i	−0.630951	+	0.303850i	0.0909401	+	0.995856i	$0.471013\pi$
$728$	−1.07432	+	4.16991i	−0.0398170	+	0.154547i
$729$	−0.900969	−	0.433884i	−0.0333692	−	0.0160698i
$730$	−3.85325	+	1.85563i	−0.142615	+	0.0686799i
$731$	1.36161	−	5.96562i	0.0503611	−	0.220646i
$732$	0.373297	−	0.179770i	0.0137974	−	0.00664450i
$733$	7.77893	+	9.75447i	0.287321	+	0.360290i	0.904455	−	0.426569i	$-0.140278\pi$
$733$	7.77893	+	9.75447i	0.287321	+	0.360290i	−0.617134	+	0.786858i	$0.711706\pi$
$734$	59.2622			2.18741
$735$	−1.93386	+	6.72757i	−0.0713315	+	0.248150i
$736$	20.4911			0.755310
$737$	6.52159	+	8.17781i	0.240226	+	0.301234i
$738$	−10.0524	+	4.84099i	−0.370035	+	0.178199i
$739$	−4.24728	+	18.6085i	−0.156239	+	0.684526i	0.834755	+	0.550621i	$0.185609\pi$
$739$	−4.24728	+	18.6085i	−0.156239	+	0.684526i	−0.990994	+	0.133905i	$0.957248\pi$
$740$	3.59674	−	1.73210i	0.132219	−	0.0636732i
$741$	1.12935	+	0.543866i	0.0414877	+	0.0199794i
$742$	1.61950	+	2.15061i	0.0594536	+	0.0789514i
$743$	−18.5313	+	8.92421i	−0.679848	+	0.327398i	−0.741742	−	0.670685i	$-0.766000\pi$
$743$	−18.5313	+	8.92421i	−0.679848	+	0.327398i	0.0618942	+	0.998083i	$0.480286\pi$
$744$	−5.62394	+	7.05220i	−0.206184	+	0.258546i
$745$	1.51356	+	0.728890i	0.0554524	+	0.0267045i
$746$	16.2535	+	20.3812i	0.595082	+	0.746209i
$747$	−2.67883	−	11.7367i	−0.0980131	−	0.429424i
$748$	−2.22227	−	2.78664i	−0.0812542	−	0.101889i
$749$	34.9416	+	18.0381i	1.27674	+	0.659099i
$750$	1.02388	−	1.28391i	0.0373868	−	0.0468816i
$751$	−33.9485	−	16.3487i	−1.23880	−	0.596573i	−0.304311	−	0.952573i	$-0.598426\pi$
$751$	−33.9485	−	16.3487i	−1.23880	−	0.596573i	−0.934486	+	0.356000i	$0.884140\pi$
$752$	7.22952	+	31.6746i	0.263633	+	1.15505i
$753$	−7.06929			−0.257619
$754$	−11.6577			−0.424549
$755$	0.370792	+	1.62455i	0.0134945	+	0.0591234i
$756$	−0.459912	+	1.78512i	−0.0167268	+	0.0649241i
$757$	−10.6938	+	46.8525i	−0.388672	+	1.70288i	0.280566	+	0.959835i	$0.409478\pi$
$757$	−10.6938	+	46.8525i	−0.388672	+	1.70288i	−0.669238	+	0.743048i	$0.733379\pi$
$758$	1.53420	−	6.72178i	0.0557248	−	0.244146i
$759$	14.4679	−	18.1422i	0.525152	−	0.658520i
$760$	−2.19945	+	2.75802i	−0.0797823	+	0.100044i
$761$	−1.84194	+	8.07008i	−0.0667704	+	0.292540i	−0.997278	−	0.0737322i	$-0.976509\pi$
$761$	−1.84194	+	8.07008i	−0.0667704	+	0.292540i	0.930508	+	0.366272i	$0.119366\pi$
$762$	4.74641	−	20.7954i	0.171944	−	0.753337i
$763$	−9.39114	+	11.1280i	−0.339982	+	0.402862i
$764$	−0.00538465	−	0.0235917i	−0.000194810	−	0.000853518i
$765$	1.19521			0.0432130
$766$	11.5277			0.416514
$767$	0.617257	+	2.70438i	0.0222879	+	0.0976495i
$768$	−13.4498	−	6.47706i	−0.485327	−	0.233721i
$769$	13.8212	−	17.3313i	0.498407	−	0.624983i	−0.467462	−	0.884013i	$-0.654832\pi$
$769$	13.8212	−	17.3313i	0.498407	−	0.624983i	0.965869	+	0.259030i	$0.0834030\pi$
$770$	16.9718	−	7.60042i	0.611620	−	0.273900i
$771$	10.4928	+	13.1576i	0.377890	+	0.473859i
$772$	2.04134	+	8.94371i	0.0734695	+	0.321891i
$773$	−16.9203	−	21.2174i	−0.608581	−	0.763137i	0.378107	−	0.925762i	$-0.376575\pi$
$773$	−16.9203	−	21.2174i	−0.608581	−	0.763137i	−0.986688	+	0.162625i	$0.948004\pi$
$774$	7.57473	+	3.64780i	0.272268	+	0.131117i
$775$	2.62779	−	3.29515i	0.0943931	−	0.118365i
$776$	−9.06233	+	4.36419i	−0.325319	+	0.156665i
$777$	−9.77682	+	11.5850i	−0.350741	+	0.415611i
$778$	3.23631	+	1.55853i	0.116027	+	0.0558759i
$779$	−10.0899	+	4.85903i	−0.361507	+	0.174093i
$780$	0.117904	−	0.516570i	0.00422163	−	0.0184962i
$781$	−46.9991	+	22.6336i	−1.68176	+	0.809894i
$782$	−6.63473	−	8.31969i	−0.237258	−	0.297512i
$783$	9.33491			0.333603
$784$	−34.3033	−	1.90604i	−1.22512	−	0.0680728i
$785$	−13.7206			−0.489710
$786$	14.4143	+	18.0749i	0.514140	+	0.644712i
$787$	−15.3820	+	7.40760i	−0.548311	+	0.264052i	−0.687464	−	0.726218i	$-0.741276\pi$
$787$	−15.3820	+	7.40760i	−0.548311	+	0.264052i	0.139154	+	0.990271i	$0.455562\pi$
$788$	2.30298	−	10.0900i	0.0820403	−	0.359442i
$789$	−28.2374	+	13.5984i	−1.00528	+	0.484116i
$790$	2.86195	+	1.37824i	0.101824	+	0.0490356i
$791$	−36.3104	−	18.7448i	−1.29105	−	0.666487i
$792$	−8.25292	+	3.97439i	−0.293255	+	0.141224i
$793$	0.281957	−	0.353563i	0.0100126	−	0.0125554i
$794$	−23.0056	−	11.0789i	−0.816437	−	0.393175i
$795$	0.386337	+	0.484451i	0.0137020	+	0.0171817i
$796$	−0.357148	−	1.56477i	−0.0126588	−	0.0554617i
$797$	−11.5858	−	14.5281i	−0.410390	−	0.514613i	0.533083	−	0.846063i	$-0.321033\pi$
$797$	−11.5858	−	14.5281i	−0.410390	−	0.514613i	−0.943473	+	0.331450i	$0.892462\pi$
$798$	−1.78672	+	6.93503i	−0.0632491	+	0.245497i
$799$	4.93294	−	6.18571i	0.174515	−	0.218835i
$800$	3.40522	+	1.63987i	0.120393	+	0.0579781i
$801$	2.00049	+	8.76474i	0.0706840	+	0.309687i
$802$	−11.2920			−0.398734
$803$	−11.1467			−0.393358
$804$	0.378896	+	1.66005i	0.0133626	+	0.0585455i
$805$	13.0915	−	5.86271i	0.461413	−	0.206633i
$806$	1.17121	−	5.13142i	0.0412542	−	0.180747i
$807$	0.329327	−	1.44288i	0.0115929	−	0.0507917i
$808$	−7.46743	+	9.36386i	−0.262703	+	0.329419i
$809$	15.3734	−	19.2777i	0.540502	−	0.677768i	−0.434319	−	0.900759i	$-0.643011\pi$
$809$	15.3734	−	19.2777i	0.540502	−	0.677768i	0.974820	+	0.222992i	$0.0715823\pi$
$810$	−0.365419	+	1.60100i	−0.0128395	+	0.0562535i
$811$	11.8453	−	51.8976i	0.415944	−	1.82237i	−0.138765	−	0.990325i	$-0.544313\pi$
$811$	11.8453	−	51.8976i	0.415944	−	1.82237i	0.554709	−	0.832044i	$-0.312829\pi$
$812$	−3.36213	−	16.8765i	−0.117988	−	0.592247i
$813$	−5.09474	−	22.3215i	−0.178680	−	0.782850i
$814$	40.2711			1.41150
$815$	−14.0948			−0.493721
$816$	1.30534	+	5.71907i	0.0456961	+	0.200208i
$817$	7.60295	+	3.66139i	0.265994	+	0.128096i
$818$	−19.2763	+	24.1717i	−0.673981	+	0.845145i
$819$	0.393111	+	1.97324i	0.0137364	+	0.0689507i
$820$	2.95151	+	3.70107i	0.103071	+	0.129247i
$821$	5.34701	+	23.4268i	0.186612	+	0.817600i	0.978386	+	0.206786i	$0.0663005\pi$
$821$	5.34701	+	23.4268i	0.186612	+	0.817600i	−0.791774	+	0.610814i	$0.790842\pi$
$822$	0.935693	+	1.17332i	0.0326360	+	0.0409243i
$823$	−21.5579	−	10.3817i	−0.751461	−	0.361885i	0.0186234	−	0.999827i	$-0.494072\pi$
$823$	−21.5579	−	10.3817i	−0.751461	−	0.361885i	−0.770084	+	0.637942i	$0.779786\pi$
$824$	13.1063	−	16.4348i	0.456581	−	0.572534i
$825$	3.85619	−	1.85704i	0.134255	−	0.0646539i
$826$	−14.4641	+	6.47740i	−0.503269	+	0.225378i
$827$	37.7519	+	18.1804i	1.31276	+	0.632194i	0.953599	−	0.301080i	$-0.0973472\pi$
$827$	37.7519	+	18.1804i	1.31276	+	0.632194i	0.359165	+	0.933274i	$0.383062\pi$
$828$	3.40339	−	1.63899i	0.118276	−	0.0569587i
$829$	−2.72475	+	11.9379i	−0.0946347	+	0.414621i	−0.999949	−	0.0101212i	$-0.996778\pi$
$829$	−2.72475	+	11.9379i	−0.0946347	+	0.414621i	0.905314	+	0.424743i	$0.139635\pi$
$830$	−17.8116	+	8.57762i	−0.618250	+	0.297734i
$831$	−1.94794	−	2.44264i	−0.0675734	−	0.0847343i
$832$	−2.74489			−0.0951618
$833$	4.84549	+	6.82051i	0.167886	+	0.236317i
$834$	7.11138			0.246247
$835$	−12.2177	−	15.3205i	−0.422810	−	0.530187i
$836$	4.42860	−	2.13270i	0.153166	−	0.0737610i
$837$	−0.937849	+	4.10898i	−0.0324168	+	0.142027i
$838$	45.9097	−	22.1089i	1.58592	−	0.763741i
$839$	12.4333	+	5.98756i	0.429245	+	0.206714i	0.636016	−	0.771676i	$-0.280581\pi$
$839$	12.4333	+	5.98756i	0.429245	+	0.206714i	−0.206771	+	0.978389i	$0.566295\pi$
$840$	−5.66019	−	0.157131i	−0.195295	−	0.00542153i
$841$	−52.3829	+	25.2263i	−1.80631	+	0.869872i
$842$	−12.2921	+	15.4138i	−0.423615	+	0.531196i
$843$	−6.62343	−	3.18968i	−0.228123	−	0.109858i
$844$	1.02385	+	1.28387i	0.0352425	+	0.0441927i
$845$	2.76408	+	12.1102i	0.0950874	+	0.416605i
$846$	6.77766	+	8.49892i	0.233021	+	0.292199i
$847$	19.3562	+	0.537341i	0.665086	+	0.0184633i
$848$	−1.89616	+	2.37770i	−0.0651143	+	0.0816507i
$849$	−23.1064	−	11.1275i	−0.793010	−	0.381894i
$850$	−0.436753	−	1.91354i	−0.0149805	−	0.0656339i
$851$	31.0638			1.06485
$852$	−8.49191			−0.290928
$853$	6.68844	+	29.3040i	0.229008	+	1.00335i	0.950451	+	0.310875i	$0.100622\pi$
$853$	6.68844	+	29.3040i	0.229008	+	1.00335i	−0.721443	+	0.692474i	$0.756521\pi$
$854$	2.29582	+	1.18518i	0.0785612	+	0.0405562i
$855$	−0.366780	+	1.60697i	−0.0125436	+	0.0549571i
$856$	−7.07810	+	31.0112i	−0.241924	+	1.05994i
$857$	2.33819	−	2.93200i	0.0798711	−	0.100155i	−0.740291	−	0.672287i	$-0.765312\pi$
$857$	2.33819	−	2.93200i	0.0798711	−	0.100155i	0.820162	+	0.572132i	$0.193883\pi$
$858$	3.33258	−	4.17893i	0.113772	−	0.142666i
$859$	3.67519	−	16.1021i	0.125396	−	0.549395i	−0.872730	−	0.488203i	$-0.837653\pi$
$859$	3.67519	−	16.1021i	0.125396	−	0.549395i	0.998126	−	0.0611921i	$-0.0194902\pi$
$860$	0.793747	−	3.47763i	0.0270665	−	0.118586i
$861$	−15.9730	−	8.24587i	−0.544360	−	0.281018i
$862$	4.82378	+	21.1344i	0.164299	+	0.719839i
$863$	23.6914			0.806466			0.403233	−	0.915097i	$-0.367886\pi$
$863$	23.6914			0.806466			0.403233	+	0.915097i	$0.367886\pi$
$864$	−3.77951			−0.128582
$865$	−0.731876	−	3.20656i	−0.0248845	−	0.109026i
$866$	16.8584	+	8.11856i	0.572871	+	0.275880i
$867$	−9.70865	+	12.1743i	−0.329723	+	0.413460i
$868$	7.76635	+	0.215599i	0.263607	+	0.00731792i
$869$	5.16190	+	6.47281i	0.175105	+	0.219575i
$870$	−3.41115	−	14.9452i	−0.115649	−	0.506691i
$871$	1.15875	+	1.45302i	0.0392627	+	0.0492338i
$872$	−10.6122	−	5.11057i	−0.359374	−	0.173066i
$873$	−2.93029	+	3.67446i	−0.0991752	+	0.124362i
$874$	13.2219	−	6.36732i	0.447237	−	0.215378i
$875$	2.64473	+	0.0734196i	0.0894083	+	0.00248204i
$876$	−1.63486	−	0.787308i	−0.0552369	−	0.0266007i
$877$	12.9514	−	6.23709i	0.437339	−	0.210611i	−0.202241	−	0.979336i	$-0.564822\pi$
$877$	12.9514	−	6.23709i	0.437339	−	0.210611i	0.639580	+	0.768724i	$0.279108\pi$
$878$	−10.2973	+	45.1154i	−0.347517	+	1.52257i
$879$	29.2824	−	14.1016i	0.987669	−	0.475637i
$880$	13.0974	+	16.4236i	0.441513	+	0.553640i
$881$	38.5746			1.29961			0.649806	−	0.760100i	$-0.274850\pi$
$881$	38.5746			1.29961			0.649806	+	0.760100i	$0.274850\pi$
$882$	−10.6176	+	4.40533i	−0.357513	+	0.148335i
$883$	−50.7871			−1.70912			−0.854560	−	0.519352i	$-0.826173\pi$
$883$	−50.7871			−1.70912			−0.854560	+	0.519352i	$0.826173\pi$
$884$	−0.394850	−	0.495126i	−0.0132802	−	0.0166529i
$885$	−3.28641	+	1.58265i	−0.110471	+	0.0532002i
$886$	10.1103	−	44.2963i	0.339664	−	1.48816i
$887$	−1.54053	+	0.741880i	−0.0517259	+	0.0249099i	−0.459568	−	0.888143i	$-0.651996\pi$
$887$	−1.54053	+	0.741880i	−0.0517259	+	0.0249099i	0.407842	+	0.913053i	$0.366281\pi$
$888$	−11.0480	−	5.32045i	−0.370748	−	0.178543i
$889$	31.3641	−	14.0457i	1.05192	−	0.471078i
$890$	13.3014	−	6.40560i	0.445863	−	0.214716i
$891$	−2.66856	+	3.34627i	−0.0894002	+	0.112104i
$892$	14.1516	+	6.81506i	0.473831	+	0.228185i
$893$	6.80291	+	8.53058i	0.227651	+	0.285465i
$894$	0.613874	+	2.68956i	0.0205310	+	0.0899523i
$895$	−14.5118	−	18.1972i	−0.485075	−	0.608265i
$896$	−6.97150	−	34.9939i	−0.232902	−	1.16906i
$897$	2.57064	−	3.22348i	0.0858313	−	0.107629i
$898$	35.4017	+	17.0486i	1.18137	+	0.568918i
$899$	−8.75474	−	38.3570i	−0.291987	−	1.27928i
$900$	0.696744			0.0232248
$901$	0.740598			0.0246729
$902$	10.6262	+	46.5566i	0.353815	+	1.55017i
$903$	2.64648	+	13.2842i	0.0880694	+	0.442070i
$904$	7.35537	−	32.2260i	0.244636	−	1.07182i
$905$	3.91134	−	17.1367i	0.130017	−	0.569643i
$906$	−1.70612	+	2.13941i	−0.0566820	+	0.0710770i
$907$	25.1752	−	31.5687i	0.835930	−	1.04822i	−0.162179	−	0.986761i	$-0.551852\pi$
$907$	25.1752	−	31.5687i	0.835930	−	1.04822i	0.998109	−	0.0614617i	$-0.0195762\pi$
$908$	−3.80230	+	16.6590i	−0.126184	+	0.552847i
$909$	−1.24527	+	5.45588i	−0.0413030	+	0.180960i
$910$	3.01552	−	1.35043i	0.0999636	−	0.0447664i
$911$	3.44536	+	15.0951i	0.114150	+	0.500123i	0.999388	+	0.0349848i	$0.0111383\pi$
$911$	3.44536	+	15.0951i	0.114150	+	0.500123i	−0.885238	+	0.465138i	$0.846005\pi$
$912$	−8.08989			−0.267883
$913$	−51.5254			−1.70524
$914$	−14.5387	−	63.6980i	−0.480896	−	2.10694i
$915$	0.535773	+	0.258014i	0.0177121	+	0.00852970i
$916$	−7.06125	+	8.85452i	−0.233310	+	0.292562i
$917$	−9.29277	+	36.0693i	−0.306874	+	1.19111i
$918$	1.22376	+	1.53454i	0.0403900	+	0.0506474i
$919$	−4.08482	−	17.8968i	−0.134746	−	0.590360i	−0.996541	−	0.0831035i	$-0.973517\pi$
$919$	−4.08482	−	17.8968i	−0.134746	−	0.590360i	0.861795	−	0.507257i	$-0.169340\pi$
$920$	7.23449	+	9.07176i	0.238514	+	0.299087i
$921$	15.5895	+	7.50753i	0.513693	+	0.247381i
$922$	−1.88871	+	2.36837i	−0.0622015	+	0.0779982i
$923$	−8.35075	+	4.02151i	−0.274868	+	0.132370i
$924$	7.01081	+	3.61924i	0.230639	+	0.119064i
$925$	5.16221	+	2.48599i	0.169732	+	0.0817388i
$926$	−48.8076	+	23.5045i	−1.60392	+	0.772406i
$927$	2.18561	−	9.57579i	0.0717849	−	0.314510i
$928$	31.7874	−	15.3080i	1.04347	−	0.502511i
$929$	0.274881	+	0.344690i	0.00901856	+	0.0113089i	0.786320	−	0.617819i	$-0.211984\pi$
$929$	0.274881	+	0.344690i	0.00901856	+	0.0113089i	−0.777302	+	0.629128i	$0.783412\pi$
$930$	6.92121			0.226955
$931$	−10.6572	+	4.42174i	−0.349274	+	0.144917i
$932$	−17.8198			−0.583706
$933$	14.7964	+	18.5541i	0.484413	+	0.607434i
$934$	11.3125	−	5.44783i	0.370158	−	0.178259i
$935$	1.13832	−	4.98731i	0.0372271	−	0.163102i
$936$	−1.46637	+	0.706165i	−0.0479297	+	0.0230817i
$937$	22.3666	+	10.7712i	0.730685	+	0.351879i	0.761953	−	0.647632i	$-0.224241\pi$
$937$	22.3666	+	10.7712i	0.730685	+	0.351879i	−0.0312688	+	0.999511i	$0.509955\pi$
$938$	−6.84806	+	8.11462i	−0.223597	+	0.264952i
$939$	18.0380	−	8.68662i	0.588646	−	0.283477i
$940$	2.87563	−	3.60593i	0.0937928	−	0.117612i
$941$	27.3569	+	13.1744i	0.891810	+	0.429473i	0.822924	−	0.568152i	$-0.192341\pi$
$941$	27.3569	+	13.1744i	0.891810	+	0.429473i	0.0688857	+	0.997625i	$0.478056\pi$
$942$	−14.0483	−	17.6160i	−0.457718	−	0.573960i
$943$	8.19673	+	35.9122i	0.266922	+	1.16946i
$944$	−11.1622	−	13.9969i	−0.363298	−	0.455561i
$945$	−2.41468	+	1.08136i	−0.0785495	+	0.0351766i
$946$	22.4355	−	28.1332i	0.729440	−	0.914689i
$947$	−0.733660	−	0.353312i	−0.0238407	−	0.0114811i	0.421925	−	0.906631i	$-0.361354\pi$
$947$	−0.733660	−	0.353312i	−0.0238407	−	0.0114811i	−0.445766	+	0.895149i	$0.647069\pi$
$948$	0.299900	+	1.31395i	0.00974029	+	0.0426750i
$949$	−1.98053			−0.0642907
$950$	2.70679			0.0878199
$951$	−1.18916	−	5.21003i	−0.0385610	−	0.168947i
$952$	−4.36483	+	5.17210i	−0.141465	+	0.167629i
$953$	−4.75803	+	20.8463i	−0.154128	+	0.675278i	0.837531	+	0.546389i	$0.183998\pi$
$953$	−4.75803	+	20.8463i	−0.154128	+	0.675278i	−0.991659	+	0.128888i	$0.958859\pi$
$954$	−0.226427	+	0.992041i	−0.00733084	+	0.0321185i
$955$	0.0216542	−	0.0271535i	0.000700714	−	0.000878668i
$956$	−8.30688	+	10.4165i	−0.268664	+	0.336894i
$957$	8.89056	−	38.9521i	0.287391	−	1.25914i
$958$	11.6750	−	51.1514i	0.377201	−	1.65263i
$959$	−0.603233	+	2.34141i	−0.0194794	+	0.0756081i
$960$	−0.803178	−	3.51895i	−0.0259225	−	0.113574i
$961$	−13.2367			−0.426990
$962$	7.15532			0.230697
$963$	3.30725	+	14.4900i	0.106575	+	0.466934i
$964$	9.37168	+	4.51316i	0.301842	+	0.145359i
$965$	−8.20920	+	10.2940i	−0.264264	+	0.331376i
$966$	20.9312	+	10.8055i	0.673452	+	0.347661i
$967$	27.6775	+	34.7065i	0.890049	+	1.11609i	0.992609	+	0.121360i	$0.0387255\pi$
$967$	27.6775	+	34.7065i	0.890049	+	1.11609i	−0.102559	+	0.994727i	$0.532703\pi$
$968$	3.48544	+	15.2707i	0.112026	+	0.490820i
$969$	1.22831	+	1.54026i	0.0394591	+	0.0494802i
$970$	6.95361	+	3.34868i	0.223267	+	0.107520i
$971$	0.354852	−	0.444971i	0.0113878	−	0.0142798i	−0.776105	−	0.630604i	$-0.782807\pi$
$971$	0.354852	−	0.444971i	0.0113878	−	0.0142798i	0.787493	+	0.616324i	$0.211379\pi$
$972$	−0.627745	+	0.302306i	−0.0201349	+	0.00969647i
$973$	6.89219	+	9.15247i	0.220953	+	0.293415i
$974$	26.2928	+	12.6619i	0.842476	+	0.405715i
$975$	0.685162	−	0.329957i	0.0219427	−	0.0105671i
$976$	−0.649455	+	2.84545i	−0.0207886	+	0.0910806i
$977$	7.60386	−	3.66183i	0.243269	−	0.117152i	−0.308277	−	0.951297i	$-0.599752\pi$
$977$	7.60386	−	3.66183i	0.243269	−	0.117152i	0.551546	+	0.834144i	$0.314038\pi$
$978$	−14.4314	−	18.0965i	−0.461467	−	0.578661i
$979$	38.4782			1.22977
$980$	2.82466	+	3.97599i	0.0902304	+	0.127008i
$981$	−5.50359			−0.175716
$982$	39.2909	+	49.2693i	1.25382	+	1.57225i
$983$	−3.50957	+	1.69012i	−0.111938	+	0.0539064i	−0.489015	−	0.872276i	$-0.662644\pi$
$983$	−3.50957	+	1.69012i	−0.111938	+	0.0539064i	0.377077	+	0.926182i	$0.376929\pi$
$984$	3.23565	−	14.1763i	0.103149	−	0.451924i
$985$	13.3831	−	6.44495i	0.426420	−	0.205353i
$986$	−16.5077	−	7.94967i	−0.525711	−	0.253169i
$987$	−4.36950	+	16.9599i	−0.139083	+	0.539841i
$988$	0.786867	−	0.378935i	0.0250336	−	0.0120555i
$989$	17.3060	−	21.7010i	0.550298	−	0.690051i
$990$	6.33254	+	3.04959i	0.201261	+	0.0969223i
$991$	−15.7557	−	19.7570i	−0.500495	−	0.627601i	0.465846	−	0.884866i	$-0.345750\pi$
$991$	−15.7557	−	19.7570i	−0.500495	−	0.627601i	−0.966341	+	0.257265i	$0.917179\pi$
$992$	3.54461	+	15.5299i	0.112541	+	0.493076i
$993$	−5.50125	−	6.89835i	−0.174577	−	0.218913i
$994$	−31.8548	−	42.3016i	−1.01037	−	1.34172i
$995$	1.43626	−	1.80101i	0.0455325	−	0.0570959i
$996$	−7.55713	−	3.63932i	−0.239457	−	0.115316i
$997$	−1.45199	−	6.36159i	−0.0459850	−	0.201474i	0.946717	−	0.322067i	$-0.104378\pi$
$997$	−1.45199	−	6.36159i	−0.0459850	−	0.201474i	−0.992702	+	0.120593i	$0.961520\pi$
$998$	24.2001			0.766039
$999$	−5.72962			−0.181277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.u.b.106.7	✓	48
49.43	even	7	inner	735.2.u.b.631.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.u.b.106.7	✓	48	1.1	even	1	trivial
735.2.u.b.631.7	yes	48	49.43	even	7	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02388 + 1.28391i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-0.155040 + 0.679276i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(-1.47955 - 0.712514i) q^{6} +(-0.516929 - 2.59476i) q^{7} +(1.92823 - 0.928588i) q^{8} +(0.623490 - 0.781831i) q^{9} +(-1.47955 - 0.712514i) q^{10} +(-2.66856 - 3.34627i) q^{11} +(-0.155040 - 0.679276i) q^{12} +(-0.474147 - 0.594561i) q^{13} +(2.80215 - 3.32041i) q^{14} +(0.623490 - 0.781831i) q^{15} +(4.42199 + 2.12952i) q^{16} +(-0.265960 - 1.16525i) q^{17} +1.64218 q^{18} +1.64829 q^{19} +(-0.155040 - 0.679276i) q^{20} +(1.59156 + 2.11351i) q^{21} +(1.56401 - 6.85237i) q^{22} +(1.20642 - 5.28568i) q^{23} +(-1.33438 + 1.67326i) q^{24} +(0.623490 - 0.781831i) q^{25} +(0.277891 - 1.21752i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(1.84270 + 0.0511547i) q^{28} +(-2.07721 - 9.10087i) q^{29} +1.64218 q^{30} +4.21465 q^{31} +(0.841020 + 3.68475i) q^{32} +(3.85619 + 1.85704i) q^{33} +(1.22376 - 1.53454i) q^{34} +(1.59156 + 2.11351i) q^{35} +(0.434413 + 0.544737i) q^{36} +(1.27496 + 5.58596i) q^{37} +(1.68766 + 2.11625i) q^{38} +(0.685162 + 0.329957i) q^{39} +(-1.33438 + 1.67326i) q^{40} +(-6.12140 + 2.94791i) q^{41} +(-1.08398 + 4.20740i) q^{42} +(4.61262 + 2.22132i) q^{43} +(2.68678 - 1.29388i) q^{44} +(-0.222521 + 0.974928i) q^{45} +(8.02155 - 3.86298i) q^{46} +(4.12724 + 5.17540i) q^{47} -4.90804 q^{48} +(-6.46557 + 2.68262i) q^{49} +1.64218 q^{50} +(0.745203 + 0.934455i) q^{51} +(0.477383 - 0.229895i) q^{52} +(-0.137882 + 0.604101i) q^{53} +(-1.47955 + 0.712514i) q^{54} +(3.85619 + 1.85704i) q^{55} +(-3.40622 - 4.52329i) q^{56} +(-1.48506 + 0.715168i) q^{57} +(9.55784 - 11.9851i) q^{58} +(-3.28641 - 1.58265i) q^{59} +(0.434413 + 0.544737i) q^{60} +(0.132325 + 0.579753i) q^{61} +(4.31530 + 5.41122i) q^{62} +(-2.35097 - 1.21366i) q^{63} +(2.25045 - 2.82198i) q^{64} +(0.685162 + 0.329957i) q^{65} +(1.56401 + 6.85237i) q^{66} -2.44386 q^{67} +0.832758 q^{68} +(1.20642 + 5.28568i) q^{69} +(-1.08398 + 4.20740i) q^{70} +(2.71208 - 11.8824i) q^{71} +(0.476234 - 2.08652i) q^{72} +(1.62378 - 2.03616i) q^{73} +(-5.86644 + 7.35629i) q^{74} +(-0.222521 + 0.974928i) q^{75} +(-0.255552 + 1.11965i) q^{76} +(-7.30332 + 8.65407i) q^{77} +(0.277891 + 1.21752i) q^{78} -1.93434 q^{79} -4.90804 q^{80} +(-0.222521 - 0.974928i) q^{81} +(-10.0524 - 4.84099i) q^{82} +(7.50590 - 9.41211i) q^{83} +(-1.68241 + 0.753430i) q^{84} +(0.745203 + 0.934455i) q^{85} +(1.87080 + 8.19653i) q^{86} +(5.82022 + 7.29833i) q^{87} +(-8.25292 - 3.97439i) q^{88} +(-5.60526 + 7.02877i) q^{89} +(-1.47955 + 0.712514i) q^{90} +(-1.29764 + 1.53764i) q^{91} +(3.40339 + 1.63899i) q^{92} +(-3.79727 + 1.82867i) q^{93} +(-2.41892 + 10.5980i) q^{94} +(-1.48506 + 0.715168i) q^{95} +(-2.35649 - 2.95494i) q^{96} -4.69981 q^{97} +(-10.0642 - 5.55450i) q^{98} -4.28004 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 8 q^{3} - q^{4} - 8 q^{5} + q^{6} - q^{7} + 15 q^{8} - 8 q^{9} + q^{10} + 10 q^{11} - q^{12} + 20 q^{13} - q^{14} - 8 q^{15} - 15 q^{16} + 7 q^{17} - 6 q^{18} - 2 q^{19} - q^{20}+ \cdots - 32 q^{99}+O(q^{100}) \) 48 * q + q^2 - 8 * q^3 - q^4 - 8 * q^5 + q^6 - q^7 + 15 * q^8 - 8 * q^9 + q^10 + 10 * q^11 - q^12 + 20 * q^13 - q^14 - 8 * q^15 - 15 * q^16 + 7 * q^17 - 6 * q^18 - 2 * q^19 - q^20 - q^21 - 17 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 - 12 * q^26 - 8 * q^27 + 29 * q^28 + 12 * q^29 - 6 * q^30 - 58 * q^31 + 9 * q^32 + 3 * q^33 + 36 * q^34 - q^35 - q^36 - 15 * q^37 - 5 * q^38 - 8 * q^39 - 6 * q^40 - 2 * q^41 + 6 * q^42 + 30 * q^43 + 33 * q^44 - 8 * q^45 + 52 * q^46 + 6 * q^47 + 6 * q^48 + 13 * q^49 - 6 * q^50 - 7 * q^51 + 3 * q^53 + q^54 + 3 * q^55 - 67 * q^56 + 19 * q^57 + 36 * q^58 + 9 * q^59 - q^60 - 7 * q^61 + 14 * q^62 - 15 * q^63 + 19 * q^64 - 8 * q^65 - 17 * q^66 + 14 * q^67 + 22 * q^68 + 12 * q^69 + 6 * q^70 - 24 * q^71 - 6 * q^72 + 2 * q^73 + 2 * q^74 - 8 * q^75 + 62 * q^76 + 42 * q^77 - 12 * q^78 + 22 * q^79 + 6 * q^80 - 8 * q^81 - 51 * q^82 + 53 * q^83 + 50 * q^84 - 7 * q^85 - 35 * q^86 + 19 * q^87 + 11 * q^88 - 51 * q^89 + q^90 - q^91 + 29 * q^92 + 26 * q^93 - 4 * q^94 + 19 * q^95 + 9 * q^96 - 102 * q^97 + 90 * q^98 - 32 * q^99

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