LMFDB - Embedded newform 966.2.s.b.97.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(97,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

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

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

chi := DirichletCharacter("966.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.s (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			97.8
Character	$\chi$	$=$	966.97
Dual form			966.2.s.b.727.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.629097 - 4.37546i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(2.43657 - 1.03108i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.959493 + 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.629097 - 4.37546i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(2.43657 - 1.03108i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(1.83632 - 4.02099i) q^{10} +(0.640886 + 2.18266i) q^{11} +(-0.281733 - 0.959493i) q^{12} +(2.53056 + 1.15567i) q^{13} +(2.62836 - 0.302858i) q^{14} +(-3.34076 + 2.89478i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.308589 - 0.198318i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(0.503656 + 0.323680i) q^{19} +(2.89478 - 3.34076i) q^{20} +(-2.51665 - 0.816371i) q^{21} +2.27480i q^{22} +(1.80829 - 4.44186i) q^{23} -1.00000i q^{24} +(-13.9514 - 4.09651i) q^{25} +(2.10246 + 1.82179i) q^{26} +(0.540641 - 0.841254i) q^{27} +(2.60722 + 0.449905i) q^{28} +(5.84893 - 3.75888i) q^{29} +(-4.02099 + 1.83632i) q^{30} +(-3.12580 + 2.70852i) q^{31} +(0.142315 + 0.989821i) q^{32} +(0.944988 - 2.06923i) q^{33} +(0.351962 - 0.103345i) q^{34} +(-2.97863 - 11.3098i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(-7.27461 + 1.04593i) q^{37} +(0.392063 + 0.452465i) q^{38} +(-1.15567 - 2.53056i) q^{39} +(3.71872 - 2.38988i) q^{40} +(-8.40000 - 1.20774i) q^{41} +(-2.18471 - 1.49233i) q^{42} +(1.89482 + 1.64187i) q^{43} +(-0.640886 + 2.18266i) q^{44} +4.42046 q^{45} +(2.98646 - 3.75248i) q^{46} -1.69375i q^{47} +(0.281733 - 0.959493i) q^{48} +(4.87373 - 5.02462i) q^{49} +(-12.2322 - 7.86115i) q^{50} +(-0.363087 - 0.0522041i) q^{51} +(1.50404 + 2.34033i) q^{52} +(-7.14466 + 3.26286i) q^{53} +(0.755750 - 0.654861i) q^{54} +(9.95332 - 1.43107i) q^{55} +(2.37485 + 1.16622i) q^{56} +(-0.168672 - 0.574445i) q^{57} +(6.67101 - 1.95879i) q^{58} +(4.63113 + 2.11497i) q^{59} +(-4.37546 + 0.629097i) q^{60} +(0.685803 + 0.791459i) q^{61} +(-3.76226 + 1.71817i) q^{62} +(1.36735 + 2.26503i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(6.64854 - 10.3453i) q^{65} +(1.48968 - 1.71918i) q^{66} +(-2.96264 + 10.0898i) q^{67} +0.366821 q^{68} +(-4.27541 + 2.17275i) q^{69} +(0.328350 - 11.6908i) q^{70} +(7.82993 + 2.29908i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(1.70586 - 2.65438i) q^{73} +(-7.27461 - 1.04593i) q^{74} +(7.86115 + 12.2322i) q^{75} +(0.248708 + 0.544593i) q^{76} +(3.81207 + 4.65739i) q^{77} +(-0.395914 - 2.75364i) q^{78} +(6.36370 + 2.90620i) q^{79} +(4.24140 - 1.24539i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-7.71948 - 3.52537i) q^{82} +(-1.24843 - 8.68301i) q^{83} +(-1.67578 - 2.04738i) q^{84} +(-0.673602 - 1.47498i) q^{85} +(1.35550 + 2.10920i) q^{86} +(-6.88187 - 0.989464i) q^{87} +(-1.22985 + 1.91369i) q^{88} +(-6.85734 + 7.91379i) q^{89} +(4.24140 + 1.24539i) q^{90} +(7.35747 + 0.206643i) q^{91} +(3.92268 - 2.75909i) q^{92} +4.13603 q^{93} +(0.477184 - 1.62514i) q^{94} +(1.73310 - 2.00010i) q^{95} +(0.540641 - 0.841254i) q^{96} +(-1.74392 + 12.1292i) q^{97} +(6.09191 - 3.44799i) q^{98} +(-2.06923 + 0.944988i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9	$ 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9} + 22 q^{14} - 16 q^{16} - 16 q^{18} - 52 q^{23} - 48 q^{25} + 22 q^{28} - 12 q^{29} + 16 q^{32} + 22 q^{35} + 16 q^{36} + 22 q^{37} - 4 q^{39} + 154 q^{43} + 8 q^{46} + 4 q^{50} + 22 q^{51} + 88 q^{53} + 22 q^{57} + 56 q^{58} - 16 q^{64} + 16 q^{71} - 16 q^{72} + 22 q^{74} - 72 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} - 22 q^{84} - 68 q^{85} - 44 q^{86} + 44 q^{88} - 8 q^{92} - 8 q^{93} - 66 q^{95} + 66 q^{98} - 66 q^{99}+O(q^{100}) $ 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9 + 22 * q^14 - 16 * q^16 - 16 * q^18 - 52 * q^23 - 48 * q^25 + 22 * q^28 - 12 * q^29 + 16 * q^32 + 22 * q^35 + 16 * q^36 + 22 * q^37 - 4 * q^39 + 154 * q^43 + 8 * q^46 + 4 * q^50 + 22 * q^51 + 88 * q^53 + 22 * q^57 + 56 * q^58 - 16 * q^64 + 16 * q^71 - 16 * q^72 + 22 * q^74 - 72 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 - 22 * q^84 - 68 * q^85 - 44 * q^86 + 44 * q^88 - 8 * q^92 - 8 * q^93 - 66 * q^95 + 66 * q^98 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{22}\right)$

Coefficient data

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

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

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

$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$3$	−0.755750	−	0.654861i	−0.436332	−	0.378084i
$3$	−0.755750	−	0.654861i	−0.436332	−	0.378084i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.629097	−	4.37546i	0.281341	−	1.95677i	−0.00937271	−	0.999956i	$-0.502983\pi$
$5$	0.629097	−	4.37546i	0.281341	−	1.95677i	0.290713	−	0.956810i	$-0.406107\pi$
$6$	−0.540641	−	0.841254i	−0.220716	−	0.343440i
$7$	2.43657	−	1.03108i	0.920936	−	0.389713i
$7$	2.43657	−	1.03108i	0.920936	−	0.389713i
$8$	0.654861	+	0.755750i	0.231528	+	0.267198i
$9$	0.142315	+	0.989821i	0.0474383	+	0.329940i
$10$	1.83632	−	4.02099i	0.580697	−	1.27155i
$11$	0.640886	+	2.18266i	0.193234	+	0.658096i	0.997924	+	0.0644005i	$0.0205135\pi$
$11$	0.640886	+	2.18266i	0.193234	+	0.658096i	−0.804690	+	0.593696i	$0.797668\pi$
$12$	−0.281733	−	0.959493i	−0.0813292	−	0.276982i
$13$	2.53056	+	1.15567i	0.701850	+	0.320524i	0.734182	−	0.678953i	$-0.237566\pi$
$13$	2.53056	+	1.15567i	0.701850	+	0.320524i	−0.0323314	+	0.999477i	$0.510293\pi$
$14$	2.62836	−	0.302858i	0.702459	−	0.0809421i
$15$	−3.34076	+	2.89478i	−0.862580	+	0.747430i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	0.308589	−	0.198318i	0.0748439	−	0.0480993i	−0.502684	−	0.864470i	$-0.667654\pi$
$17$	0.308589	−	0.198318i	0.0748439	−	0.0480993i	0.577528	+	0.816371i	$0.304018\pi$
$18$	−0.142315	+	0.989821i	−0.0335439	+	0.233303i
$19$	0.503656	+	0.323680i	0.115547	+	0.0742572i	0.597138	−	0.802139i	$-0.296305\pi$
$19$	0.503656	+	0.323680i	0.115547	+	0.0742572i	−0.481591	+	0.876396i	$0.659941\pi$
$20$	2.89478	−	3.34076i	0.647293	−	0.747016i
$21$	−2.51665	−	0.816371i	−0.549179	−	0.178147i
$22$			2.27480i			0.484990i
$23$	1.80829	−	4.44186i	0.377054	−	0.926191i
$23$	1.80829	−	4.44186i	0.377054	−	0.926191i
$24$		−	1.00000i		−	0.204124i
$25$	−13.9514	−	4.09651i	−2.79029	−	0.819303i
$26$	2.10246	+	1.82179i	0.412327	+	0.357283i
$27$	0.540641	−	0.841254i	0.104046	−	0.161899i
$28$	2.60722	+	0.449905i	0.492718	+	0.0850240i
$29$	5.84893	−	3.75888i	1.08612	−	0.698007i	0.130157	−	0.991493i	$-0.458452\pi$
$29$	5.84893	−	3.75888i	1.08612	−	0.698007i	0.955963	+	0.293487i	$0.0948156\pi$
$30$	−4.02099	+	1.83632i	−0.734129	+	0.335265i
$31$	−3.12580	+	2.70852i	−0.561411	+	0.486465i	−0.888719	−	0.458452i	$-0.848404\pi$
$31$	−3.12580	+	2.70852i	−0.561411	+	0.486465i	0.327308	+	0.944918i	$0.393858\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$	0.944988	−	2.06923i	0.164501	−	0.360207i
$34$	0.351962	−	0.103345i	0.0603610	−	0.0177236i
$35$	−2.97863	−	11.3098i	−0.503481	−	1.91170i
$36$	−0.415415	+	0.909632i	−0.0692358	+	0.151605i
$37$	−7.27461	+	1.04593i	−1.19594	+	0.171950i	−0.711379	−	0.702809i	$-0.751929\pi$
$37$	−7.27461	+	1.04593i	−1.19594	+	0.171950i	−0.484559	+	0.874759i	$0.661020\pi$
$38$	0.392063	+	0.452465i	0.0636010	+	0.0733995i
$39$	−1.15567	−	2.53056i	−0.185055	−	0.405214i
$40$	3.71872	−	2.38988i	0.587982	−	0.377873i
$41$	−8.40000	−	1.20774i	−1.31186	−	0.188617i	−0.549349	−	0.835593i	$-0.685124\pi$
$41$	−8.40000	−	1.20774i	−1.31186	−	0.188617i	−0.762510	+	0.646976i	$0.776033\pi$
$42$	−2.18471	−	1.49233i	−0.337108	−	0.230271i
$43$	1.89482	+	1.64187i	0.288957	+	0.250383i	0.787261	−	0.616619i	$-0.211498\pi$
$43$	1.89482	+	1.64187i	0.288957	+	0.250383i	−0.498304	+	0.867002i	$0.666044\pi$
$44$	−0.640886	+	2.18266i	−0.0966172	+	0.329048i
$45$	4.42046			0.658963
$46$	2.98646	−	3.75248i	0.440329	−	0.553272i
$47$		−	1.69375i		−	0.247059i	−0.992341	−	0.123529i	$-0.960579\pi$
$47$		−	1.69375i		−	0.247059i	0.992341	−	0.123529i	$-0.0394213\pi$
$48$	0.281733	−	0.959493i	0.0406646	−	0.138491i
$49$	4.87373	−	5.02462i	0.696247	−	0.717802i
$50$	−12.2322	−	7.86115i	−1.72989	−	1.11173i
$51$	−0.363087	−	0.0522041i	−0.0508424	−	0.00731003i
$52$	1.50404	+	2.34033i	0.208573	+	0.324546i
$53$	−7.14466	+	3.26286i	−0.981394	+	0.448188i	−0.840485	−	0.541835i	$-0.817730\pi$
$53$	−7.14466	+	3.26286i	−0.981394	+	0.448188i	−0.140909	+	0.990023i	$0.545003\pi$
$54$	0.755750	−	0.654861i	0.102844	−	0.0891153i
$55$	9.95332	−	1.43107i	1.34211	−	0.192966i
$56$	2.37485	+	1.16622i	0.317353	+	0.155843i
$57$	−0.168672	−	0.574445i	−0.0223412	−	0.0760871i
$58$	6.67101	−	1.95879i	0.875947	−	0.257201i
$59$	4.63113	+	2.11497i	0.602922	+	0.275345i	0.693400	−	0.720553i	$-0.256112\pi$
$59$	4.63113	+	2.11497i	0.602922	+	0.275345i	−0.0904777	+	0.995898i	$0.528839\pi$
$60$	−4.37546	+	0.629097i	−0.564870	+	0.0812160i
$61$	0.685803	+	0.791459i	0.0878081	+	0.101336i	0.797953	−	0.602719i	$-0.205916\pi$
$61$	0.685803	+	0.791459i	0.0878081	+	0.101336i	−0.710145	+	0.704055i	$0.751371\pi$
$62$	−3.76226	+	1.71817i	−0.477808	+	0.218208i
$63$	1.36735	+	2.26503i	0.172270	+	0.285367i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	6.64854	−	10.3453i	0.824650	−	1.28318i
$66$	1.48968	−	1.71918i	0.183367	−	0.211617i
$67$	−2.96264	+	10.0898i	−0.361945	+	1.23267i	0.554390	+	0.832257i	$0.312952\pi$
$67$	−2.96264	+	10.0898i	−0.361945	+	1.23267i	−0.916335	+	0.400413i	$0.868867\pi$
$68$	0.366821			0.0444836
$69$	−4.27541	+	2.17275i	−0.514699	+	0.261569i
$70$	0.328350	−	11.6908i	0.0392453	−	1.39732i
$71$	7.82993	+	2.29908i	0.929242	+	0.272850i	0.711119	−	0.703071i	$-0.248189\pi$
$71$	7.82993	+	2.29908i	0.929242	+	0.272850i	0.218123	+	0.975921i	$0.430007\pi$
$72$	−0.654861	+	0.755750i	−0.0771761	+	0.0890659i
$73$	1.70586	−	2.65438i	0.199656	−	0.310671i	−0.726960	−	0.686680i	$-0.759067\pi$
$73$	1.70586	−	2.65438i	0.199656	−	0.310671i	0.926616	+	0.376009i	$0.122704\pi$
$74$	−7.27461	−	1.04593i	−0.845656	−	0.121587i
$75$	7.86115	+	12.2322i	0.907728	+	1.41245i
$76$	0.248708	+	0.544593i	0.0285287	+	0.0624692i
$77$	3.81207	+	4.65739i	0.434425	+	0.530759i
$78$	−0.395914	−	2.75364i	−0.0448284	−	0.311789i
$79$	6.36370	+	2.90620i	0.715972	+	0.326973i	0.739878	−	0.672741i	$-0.234883\pi$
$79$	6.36370	+	2.90620i	0.715972	+	0.326973i	−0.0239063	+	0.999714i	$0.507610\pi$
$80$	4.24140	−	1.24539i	0.474203	−	0.139238i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−7.71948	−	3.52537i	−0.852474	−	0.389312i
$83$	−1.24843	−	8.68301i	−0.137033	−	0.953084i	−0.936073	−	0.351806i	$-0.885568\pi$
$83$	−1.24843	−	8.68301i	−0.137033	−	0.953084i	0.799040	−	0.601278i	$-0.205342\pi$
$84$	−1.67578	−	2.04738i	−0.182842	−	0.223387i
$85$	−0.673602	−	1.47498i	−0.0730624	−	0.159984i
$86$	1.35550	+	2.10920i	0.146167	+	0.227440i
$87$	−6.88187	−	0.989464i	−0.737814	−	0.106082i
$88$	−1.22985	+	1.91369i	−0.131103	+	0.204000i
$89$	−6.85734	+	7.91379i	−0.726877	+	0.838861i	−0.992116	−	0.125322i	$-0.960004\pi$
$89$	−6.85734	+	7.91379i	−0.726877	+	0.838861i	0.265239	+	0.964183i	$0.414549\pi$
$90$	4.24140	+	1.24539i	0.447082	+	0.131275i
$91$	7.35747	+	0.206643i	0.771272	+	0.0216621i
$92$	3.92268	−	2.75909i	0.408968	−	0.287655i
$93$	4.13603			0.428886
$94$	0.477184	−	1.62514i	0.0492178	−	0.167620i
$95$	1.73310	−	2.00010i	0.177812	−	0.205206i
$96$	0.540641	−	0.841254i	0.0551789	−	0.0858601i
$97$	−1.74392	+	12.1292i	−0.177068	+	1.23154i	0.686434	+	0.727192i	$0.259175\pi$
$97$	−1.74392	+	12.1292i	−0.177068	+	1.23154i	−0.863502	+	0.504345i	$0.831734\pi$
$98$	6.09191	−	3.44799i	0.615376	−	0.348300i
$99$	−2.06923	+	0.944988i	−0.207966	+	0.0949748i
$100$	−9.52196	−	10.9889i	−0.952196	−	1.09889i
$101$	14.6834	−	2.11116i	1.46106	−	0.210068i	0.634500	−	0.772923i	$-0.281206\pi$
$101$	14.6834	−	2.11116i	1.46106	−	0.210068i	0.826556	+	0.562855i	$0.190297\pi$
$102$	−0.333672	−	0.152383i	−0.0330385	−	0.0150882i
$103$	−14.4344	+	4.23833i	−1.42227	+	0.417615i	−0.900269	−	0.435333i	$-0.856631\pi$
$103$	−14.4344	+	4.23833i	−1.42227	+	0.417615i	−0.521996	+	0.852948i	$0.674812\pi$
$104$	0.783768	+	2.66927i	0.0768548	+	0.261743i
$105$	−5.15522	+	10.4979i	−0.503098	+	1.02449i
$106$	−7.77450	+	1.11780i	−0.755126	+	0.108571i
$107$	9.08313	−	7.87058i	0.878099	−	0.760877i	−0.0939690	−	0.995575i	$-0.529955\pi$
$107$	9.08313	−	7.87058i	0.878099	−	0.760877i	0.972068	+	0.234698i	$0.0754100\pi$
$108$	0.909632	−	0.415415i	0.0875294	−	0.0399733i
$109$	3.17684	+	4.94325i	0.304286	+	0.473478i	0.959399	−	0.282053i	$-0.0910154\pi$
$109$	3.17684	+	4.94325i	0.304286	+	0.473478i	−0.655113	+	0.755531i	$0.727379\pi$
$110$	9.95332	+	1.43107i	0.949012	+	0.136447i
$111$	6.18272	+	3.97339i	0.586838	+	0.377138i
$112$	1.95009	+	1.78805i	0.184267	+	0.168955i
$113$	−2.22251	+	7.56916i	−0.209076	+	0.712047i	0.786458	+	0.617643i	$0.211912\pi$
$113$	−2.22251	+	7.56916i	−0.209076	+	0.712047i	−0.995534	+	0.0944032i	$0.969906\pi$
$114$		−	0.598696i		−	0.0560731i
$115$	−18.2976	−	10.7065i	−1.70626	−	0.998383i
$116$	6.95264			0.645537
$117$	−0.783768	+	2.66927i	−0.0724594	+	0.246774i
$118$	3.84768	+	3.33404i	0.354208	+	0.306923i
$119$	0.547416	−	0.801398i	0.0501816	−	0.0734641i
$120$	−4.37546	−	0.629097i	−0.399423	−	0.0574284i
$121$	4.90053	−	3.14938i	0.445503	−	0.286307i
$122$	0.435044	+	0.952613i	0.0393870	+	0.0862455i
$123$	5.55739	+	6.41358i	0.501093	+	0.578293i
$124$	−4.09393	+	0.588618i	−0.367646	+	0.0528595i
$125$	−17.5193	+	38.3620i	−1.56698	+	3.43120i
$126$	0.673830	+	2.55851i	0.0600295	+	0.227930i
$127$	15.4964	−	4.55016i	1.37508	−	0.403761i	0.491029	−	0.871143i	$-0.336621\pi$
$127$	15.4964	−	4.55016i	1.37508	−	0.403761i	0.884055	+	0.467382i	$0.154803\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$	−0.356812	−	2.48169i	−0.0314156	−	0.218500i
$130$	9.29385	−	8.05317i	0.815124	−	0.706309i
$131$	7.37599	−	3.36850i	0.644443	−	0.294307i	−0.0662567	−	0.997803i	$-0.521106\pi$
$131$	7.37599	−	3.36850i	0.644443	−	0.294307i	0.710700	+	0.703495i	$0.248378\pi$
$132$	1.91369	−	1.22985i	0.166565	−	0.107045i
$133$	1.56093	+	0.269356i	0.135350	+	0.0233562i
$134$	−5.68527	+	8.84646i	−0.491133	+	0.764218i
$135$	−3.34076	−	2.89478i	−0.287527	−	0.249143i
$136$	0.351962	+	0.103345i	0.0301805	+	0.00886180i
$137$		−	9.05149i		−	0.773321i	−0.922222	−	0.386661i	$-0.873628\pi$
$137$		−	9.05149i		−	0.773321i	0.922222	−	0.386661i	$-0.126372\pi$
$138$	−4.71436	+	0.880219i	−0.401313	+	0.0749292i
$139$			19.5552i			1.65865i	0.558765	+	0.829326i	$0.311275\pi$
$139$			19.5552i			1.65865i	−0.558765	+	0.829326i	$0.688725\pi$
$140$	3.60873	−	11.1248i	0.304994	−	0.940213i
$141$	−1.10917	+	1.28005i	−0.0934089	+	0.107800i
$142$	6.86504	+	4.41189i	0.576102	+	0.370238i
$143$	−0.900626	+	6.26399i	−0.0753142	+	0.523821i
$144$	−0.841254	+	0.540641i	−0.0701045	+	0.0450534i
$145$	−12.7673	−	27.9565i	−1.06027	−	2.32166i
$146$	2.38459	−	2.06626i	0.197350	−	0.171005i
$147$	−6.97374	+	0.605736i	−0.575185	+	0.0499603i
$148$	−6.68526	−	3.05306i	−0.549525	−	0.250960i
$149$	1.57860	+	5.37622i	0.129324	+	0.440437i	0.998541	−	0.0539932i	$-0.0171949\pi$
$149$	1.57860	+	5.37622i	0.129324	+	0.440437i	−0.869217	+	0.494430i	$0.835377\pi$
$150$	4.09651	+	13.9514i	0.334479	+	1.13913i
$151$	−3.78797	+	8.29450i	−0.308261	+	0.674997i	−0.998835	−	0.0482649i	$-0.984631\pi$
$151$	−3.78797	+	8.29450i	−0.308261	+	0.674997i	0.690574	+	0.723262i	$0.257358\pi$
$152$	0.0852034	+	0.592603i	0.00691091	+	0.0480664i
$153$	0.240217	+	0.277225i	0.0194204	+	0.0224123i
$154$	2.34551	+	5.54271i	0.189007	+	0.446645i
$155$	9.88461	+	15.3808i	0.793951	+	1.23541i
$156$	0.395914	−	2.75364i	0.0316985	−	0.220468i
$157$	−9.94832	−	6.39339i	−0.793962	−	0.510248i	0.0796784	−	0.996821i	$-0.474611\pi$
$157$	−9.94832	−	6.39339i	−0.793962	−	0.510248i	−0.873640	+	0.486572i	$0.838247\pi$
$158$	5.28715	+	4.58134i	0.420623	+	0.364472i
$159$	7.53629	+	2.21285i	0.597667	+	0.175491i
$160$	4.42046			0.349468
$161$	−0.173908	−	12.6874i	−0.0137058	−	0.999906i
$162$	−1.00000			−0.0785674
$163$	−22.5695	−	6.62701i	−1.76778	−	0.519068i	−0.774276	−	0.632848i	$-0.781886\pi$
$163$	−22.5695	−	6.62701i	−1.76778	−	0.519068i	−0.993506	+	0.113780i	$0.963704\pi$
$164$	−6.41358	−	5.55739i	−0.500816	−	0.433960i
$165$	−8.45937	−	5.43651i	−0.658561	−	0.423231i
$166$	1.24843	−	8.68301i	0.0968969	−	0.673933i
$167$	2.74984	+	4.27883i	0.212789	+	0.331106i	0.931197	−	0.364516i	$-0.118765\pi$
$167$	2.74984	+	4.27883i	0.212789	+	0.331106i	−0.718408	+	0.695622i	$0.755129\pi$
$168$	−1.03108	−	2.43657i	−0.0795499	−	0.187985i
$169$	−3.44503	−	3.97578i	−0.265003	−	0.305829i
$170$	−0.230766	−	1.60501i	−0.0176989	−	0.123099i
$171$	−0.248708	+	0.544593i	−0.0190191	+	0.0416461i
$172$	0.706361	+	2.40565i	0.0538595	+	0.183429i
$173$	0.559552	+	1.90566i	0.0425420	+	0.144885i	0.978025	−	0.208486i	$-0.0668536\pi$
$173$	0.559552	+	1.90566i	0.0425420	+	0.144885i	−0.935483	+	0.353371i	$0.885035\pi$
$174$	−6.32434	−	2.88823i	−0.479447	−	0.218956i
$175$	−38.2175	+	4.40368i	−2.88897	+	0.332887i
$176$	−1.71918	+	1.48968i	−0.129588	+	0.112289i
$177$	−2.11497	−	4.63113i	−0.158971	−	0.348097i
$178$	−8.80914	+	5.66129i	−0.660273	+	0.424332i
$179$	0.819136	−	5.69722i	0.0612251	−	0.425830i	−0.936038	−	0.351898i	$-0.885536\pi$
$179$	0.819136	−	5.69722i	0.0612251	−	0.425830i	0.997263	−	0.0739317i	$-0.0235547\pi$
$180$	3.71872	+	2.38988i	0.277177	+	0.178131i
$181$	−5.96690	+	6.88617i	−0.443516	+	0.511845i	−0.932857	−	0.360248i	$-0.882692\pi$
$181$	−5.96690	+	6.88617i	−0.443516	+	0.511845i	0.489340	+	0.872093i	$0.337238\pi$
$182$	7.00122	+	2.27111i	0.518965	+	0.168346i
$183$		−	1.04725i		−	0.0774150i
$184$	4.54111	−	1.54218i	0.334775	−	0.113691i
$185$			32.4878i			2.38855i
$186$	3.96849	+	1.16525i	0.290984	+	0.0854406i
$187$	0.630632	+	0.546446i	0.0461164	+	0.0399601i
$188$	0.915710	−	1.42487i	0.0667850	−	0.103919i
$189$	0.449905	−	2.60722i	0.0327258	−	0.189647i
$190$	2.22639	−	1.43081i	0.161519	−	0.103802i
$191$	−1.63446	+	0.746431i	−0.118265	+	0.0540098i	−0.473669	−	0.880703i	$-0.657071\pi$
$191$	−1.63446	+	0.746431i	−0.118265	+	0.0540098i	0.355404	+	0.934713i	$0.384343\pi$
$192$	0.755750	−	0.654861i	0.0545415	−	0.0472605i
$193$	−1.23974	−	8.62257i	−0.0892384	−	0.620666i	−0.984534	−	0.175194i	$-0.943945\pi$
$193$	−1.23974	−	8.62257i	−0.0892384	−	0.620666i	0.895296	−	0.445473i	$-0.146964\pi$
$194$	−5.09048	+	11.1466i	−0.365475	+	0.800279i
$195$	−11.7994	+	3.46461i	−0.844972	+	0.248106i
$196$	6.81655	−	1.59204i	0.486897	−	0.113717i
$197$	−9.83068	+	21.5262i	−0.700407	+	1.53368i	0.139071	+	0.990282i	$0.455589\pi$
$197$	−9.83068	+	21.5262i	−0.700407	+	1.53368i	−0.839477	+	0.543395i	$0.817139\pi$
$198$	−2.25165	+	0.323738i	−0.160018	+	0.0230071i
$199$	11.7083	+	13.5121i	0.829978	+	0.957846i	0.999617	−	0.0276603i	$-0.00880566\pi$
$199$	11.7083	+	13.5121i	0.829978	+	0.957846i	−0.169639	+	0.985506i	$0.554260\pi$
$200$	−6.04031	−	13.2264i	−0.427115	−	0.935251i
$201$	8.84646	−	5.68527i	0.623981	−	0.401008i
$202$	14.6834	+	2.11116i	1.03312	+	0.148541i
$203$	10.3756	−	15.1895i	0.728225	−	1.06610i
$204$	−0.277225	−	0.240217i	−0.0194096	−	0.0168185i
$205$	−10.5688	+	35.9941i	−0.738158	+	2.51394i
$206$	−15.0438			−1.04815
$207$	4.65399	+	1.15774i	0.323475	+	0.0804686i
$208$			2.78196i			0.192894i
$209$	−0.383696	+	1.30675i	−0.0265408	+	0.0903898i
$210$	−7.90401	+	8.62031i	−0.545428	+	0.594858i
$211$	−11.4473	−	7.35671i	−0.788062	−	0.506456i	0.0836385	−	0.996496i	$-0.473346\pi$
$211$	−11.4473	−	7.35671i	−0.788062	−	0.506456i	−0.871700	+	0.490040i	$0.836982\pi$
$212$	−7.77450	−	1.11780i	−0.533955	−	0.0767711i
$213$	−4.41189	−	6.86504i	−0.302298	−	0.470385i
$214$	10.9326	−	4.99275i	0.747337	−	0.341297i
$215$	8.37597	−	7.25782i	0.571236	−	0.494979i
$216$	0.989821	−	0.142315i	0.0673488	−	0.00968330i
$217$	−4.82352	+	9.82247i	−0.327442	+	0.666793i
$218$	1.65548	+	5.63803i	0.112123	+	0.381856i
$219$	−3.02745	+	0.888941i	−0.204576	+	0.0600691i
$220$	9.14696	+	4.17728i	0.616688	+	0.281632i
$221$	1.01009	−	0.145230i	0.0679463	−	0.00976920i
$222$	4.81284	+	5.55432i	0.323017	+	0.372781i
$223$	22.7450	−	10.3873i	1.52311	−	0.695583i	0.534378	−	0.845246i	$-0.320546\pi$
$223$	22.7450	−	10.3873i	1.52311	−	0.695583i	0.988737	+	0.149663i	$0.0478188\pi$
$224$	1.36735	+	2.26503i	0.0913599	+	0.151339i
$225$	2.06932	−	14.3924i	0.137955	−	0.959496i
$226$	−4.26496	+	6.63640i	−0.283701	+	0.441447i
$227$	17.4781	−	20.1708i	1.16006	−	1.33878i	0.229216	−	0.973376i	$-0.426384\pi$
$227$	17.4781	−	20.1708i	1.16006	−	1.33878i	0.930847	−	0.365408i	$-0.119071\pi$
$228$	0.168672	−	0.574445i	0.0111706	−	0.0380436i
$229$	−26.6582			−1.76163			−0.880813	−	0.473464i	$-0.843003\pi$
$229$	−26.6582			−1.76163			−0.880813	+	0.473464i	$0.843003\pi$
$230$	−14.5400	−	15.4278i	−0.958742	−	1.01728i
$231$	0.168972	−	6.01619i	0.0111175	−	0.395836i
$232$	6.67101	+	1.95879i	0.437973	+	0.128601i
$233$	10.0854	−	11.6392i	0.660716	−	0.762507i	−0.322178	−	0.946679i	$-0.604415\pi$
$233$	10.0854	−	11.6392i	0.660716	−	0.762507i	0.982894	+	0.184172i	$0.0589605\pi$
$234$	−1.50404	+	2.34033i	−0.0983222	+	0.152992i
$235$	−7.41093	−	1.06553i	−0.483436	−	0.0695076i
$236$	2.75252	+	4.28300i	0.179174	+	0.278800i
$237$	−2.90620	−	6.36370i	−0.188778	−	0.413367i
$238$	0.751022	−	0.614711i	0.0486815	−	0.0398458i
$239$	−1.48917	−	10.3574i	−0.0963266	−	0.669966i	−0.979578	−	0.201066i	$-0.935559\pi$
$239$	−1.48917	−	10.3574i	−0.0963266	−	0.669966i	0.883251	−	0.468900i	$-0.155350\pi$
$240$	−4.02099	−	1.83632i	−0.259554	−	0.118534i
$241$	23.4074	−	6.87303i	1.50780	−	0.442730i	0.579629	−	0.814881i	$-0.303198\pi$
$241$	23.4074	−	6.87303i	1.50780	−	0.442730i	0.928173	+	0.372150i	$0.121379\pi$
$242$	5.58930	−	1.64117i	0.359294	−	0.105498i
$243$	0.909632	+	0.415415i	0.0583529	+	0.0266489i
$244$	0.149039	+	1.03659i	0.00954127	+	0.0663610i
$245$	−18.9190	−	24.4858i	−1.20869	−	1.56434i
$246$	3.52537	+	7.71948i	0.224769	+	0.492176i
$247$	0.900463	+	1.40115i	0.0572951	+	0.0891529i
$248$	−4.09393	−	0.588618i	−0.259965	−	0.0373773i
$249$	−4.74266	+	7.37973i	−0.300554	+	0.467671i
$250$	−27.6175	+	31.8723i	−1.74668	+	2.01578i
$251$	11.0879	+	3.25569i	0.699860	+	0.205498i	0.612258	−	0.790658i	$-0.290261\pi$
$251$	11.0879	+	3.25569i	0.699860	+	0.205498i	0.0876022	+	0.996156i	$0.472080\pi$
$252$	−0.0742797	+	2.64471i	−0.00467918	+	0.166601i
$253$	10.8540	+	1.10015i	0.682383	+	0.0691661i
$254$	16.1506			1.01338
$255$	−0.456834	+	1.55583i	−0.0286081	+	0.0974301i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−0.973295	+	1.51448i	−0.0607125	+	0.0944705i	−0.870283	−	0.492553i	$-0.836064\pi$
$257$	−0.973295	+	1.51448i	−0.0607125	+	0.0944705i	0.809570	+	0.587023i	$0.199700\pi$
$258$	0.356812	−	2.48169i	0.0222142	−	0.154503i
$259$	−16.6466	+	10.0492i	−1.03437	+	0.624428i
$260$	11.1862	−	5.10858i	0.693740	−	0.316820i
$261$	4.55301	+	5.25446i	0.281824	+	0.325243i
$262$	8.02623	−	1.15400i	0.495862	−	0.0712942i
$263$	26.4356	+	12.0727i	1.63009	+	0.744437i	0.999498	−	0.0316780i	$-0.0100851\pi$
$263$	26.4356	+	12.0727i	1.63009	+	0.744437i	0.630591	+	0.776115i	$0.282812\pi$
$264$	2.18266	−	0.640886i	0.134333	−	0.0394438i
$265$	9.78182	+	33.3138i	0.600893	+	2.04645i
$266$	1.42182	+	0.698211i	0.0871772	+	0.0428101i
$267$	10.3649	−	1.49024i	0.634320	−	0.0912014i
$268$	−7.94732	+	6.88639i	−0.485460	+	0.420653i
$269$	−23.7742	+	10.8573i	−1.44954	+	0.661982i	−0.975796	−	0.218681i	$-0.929825\pi$
$269$	−23.7742	+	10.8573i	−1.44954	+	0.661982i	−0.473743	+	0.880663i	$0.657097\pi$
$270$	−2.38988	−	3.71872i	−0.145443	−	0.226314i
$271$	25.8725	+	3.71991i	1.57165	+	0.225968i	0.872356	−	0.488871i	$-0.162591\pi$
$271$	25.8725	+	3.71991i	1.57165	+	0.225968i	0.699289	+	0.714839i	$0.253500\pi$
$272$	0.308589	+	0.198318i	0.0187110	+	0.0120248i
$273$	−5.42508	−	4.97429i	−0.328341	−	0.301058i
$274$	2.55010	−	8.68484i	0.154057	−	0.524671i
$275$		−	33.0766i		−	1.99460i
$276$	−4.77138	−	0.483626i	−0.287204	−	0.0291108i
$277$	15.2217			0.914585			0.457293	−	0.889316i	$-0.348819\pi$
$277$	15.2217			0.914585			0.457293	+	0.889316i	$0.348819\pi$
$278$	−5.50934	+	18.7631i	−0.330428	+	1.12534i
$279$	−3.12580	−	2.70852i	−0.187137	−	0.162155i
$280$	6.59676	−	9.65742i	0.394232	−	0.577141i
$281$	25.7270	+	3.69898i	1.53474	+	0.220663i	0.857263	−	0.514879i	$-0.172163\pi$
$281$	25.7270	+	3.69898i	1.53474	+	0.220663i	0.677480	+	0.735542i	$0.263072\pi$
$282$	−1.42487	+	0.915710i	−0.0848499	+	0.0545297i
$283$	3.35656	+	7.34984i	0.199527	+	0.436903i	0.982775	−	0.184807i	$-0.0591659\pi$
$283$	3.35656	+	7.34984i	0.199527	+	0.436903i	−0.783248	+	0.621709i	$0.786439\pi$
$284$	5.34399	+	6.16729i	0.317107	+	0.365961i
$285$	−2.61957	+	0.376638i	−0.155170	+	0.0223101i
$286$	−2.62892	+	5.75652i	−0.155451	+	0.340390i
$287$	−21.7124	+	5.71837i	−1.28165	+	0.337545i
$288$	−0.959493	+	0.281733i	−0.0565387	+	0.0166013i
$289$	−7.00616	+	15.3413i	−0.412127	+	0.902432i
$290$	−4.37388	−	30.4210i	−0.256843	−	1.78638i
$291$	9.26092	−	8.02464i	0.542885	−	0.470412i
$292$	2.87013	−	1.31074i	0.167962	−	0.0767055i
$293$	−13.9867	+	8.98868i	−0.817109	+	0.525124i	−0.881158	−	0.472822i	$-0.843235\pi$
$293$	−13.9867	+	8.98868i	−0.817109	+	0.525124i	0.0640483	+	0.997947i	$0.479599\pi$
$294$	−6.86191	−	1.38353i	−0.400195	−	0.0806891i
$295$	12.1674	−	18.9328i	0.708412	−	1.10231i
$296$	−5.55432	−	4.81284i	−0.322838	−	0.279741i
$297$	2.18266	+	0.640886i	0.126651	+	0.0371880i
$298$			5.60319i			0.324584i
$299$	9.70929	−	9.15059i	0.561503	−	0.529193i
$300$			14.5404i			0.839492i
$301$	6.30976	+	2.04681i	0.363689	+	0.117976i
$302$	−5.97137	+	6.89132i	−0.343613	+	0.396551i
$303$	−12.4795	−	8.02009i	−0.716929	−	0.460742i
$304$	−0.0852034	+	0.592603i	−0.00488675	+	0.0339881i
$305$	3.89444	−	2.50280i	0.222995	−	0.143310i
$306$	0.152383	+	0.333672i	0.00871115	+	0.0190748i
$307$	−14.2262	+	12.3271i	−0.811933	+	0.703544i	−0.958324	−	0.285683i	$-0.907780\pi$
$307$	−14.2262	+	12.3271i	−0.811933	+	0.703544i	0.146391	+	0.989227i	$0.453234\pi$
$308$	0.688942	+	5.97900i	0.0392561	+	0.340685i
$309$	13.6843	+	6.24942i	0.778474	+	0.355517i
$310$	5.15096	+	17.5425i	0.292555	+	0.996349i
$311$	−2.00327	−	6.82252i	−0.113595	−	0.386870i	0.882995	−	0.469383i	$-0.155524\pi$
$311$	−2.00327	−	6.82252i	−0.113595	−	0.386870i	−0.996590	+	0.0825132i	$0.973705\pi$
$312$	1.15567	−	2.53056i	0.0654268	−	0.143265i
$313$	0.168064	+	1.16891i	0.00949953	+	0.0660707i	0.994020	−	0.109200i	$-0.0348290\pi$
$313$	0.168064	+	1.16891i	0.00949953	+	0.0660707i	−0.984520	+	0.175271i	$0.943920\pi$
$314$	−7.74411	−	8.93718i	−0.437025	−	0.504354i
$315$	10.7707	−	4.55786i	0.606863	−	0.256807i
$316$	3.78227	+	5.88533i	0.212769	+	0.331076i
$317$	−2.51225	+	17.4731i	−0.141102	+	0.981385i	0.789081	+	0.614289i	$0.210557\pi$
$317$	−2.51225	+	17.4731i	−0.141102	+	0.981385i	−0.930183	+	0.367096i	$0.880352\pi$
$318$	6.60758	+	4.24644i	0.370535	+	0.238128i
$319$	11.9529	+	10.3572i	0.669231	+	0.579892i
$320$	4.24140	+	1.24539i	0.237101	+	0.0696192i
$321$	−12.0187			−0.670819
$322$	3.40759	−	12.2225i	0.189897	−	0.681131i
$323$	0.219614			0.0122197
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−30.5707	−	26.4897i	−1.69576	−	1.46938i
$326$	−19.7883	−	12.7171i	−1.09597	−	0.704337i
$327$	0.836250	−	5.81625i	0.0462447	−	0.321639i
$328$	−4.58808	−	7.13919i	−0.253334	−	0.394196i
$329$	−1.74640	−	4.12693i	−0.0962820	−	0.227525i
$330$	−6.58506	−	7.59957i	−0.362496	−	0.418342i
$331$	−1.68596	−	11.7261i	−0.0926687	−	0.644525i	−0.982226	−	0.187702i	$-0.939896\pi$
$331$	−1.68596	−	11.7261i	−0.0926687	−	0.644525i	0.889557	−	0.456823i	$-0.151013\pi$
$332$	3.64415	−	7.97957i	0.199998	−	0.437936i
$333$	−2.07057	−	7.05171i	−0.113466	−	0.386431i
$334$	1.43296	+	4.88023i	0.0784083	+	0.267034i
$335$	42.2839	+	19.3104i	2.31022	+	1.05504i
$336$	−0.302858	−	2.62836i	−0.0165222	−	0.143389i
$337$	−12.1534	+	10.5309i	−0.662035	+	0.573657i	−0.919721	−	0.392572i	$-0.871585\pi$
$337$	−12.1534	+	10.5309i	−0.662035	+	0.573657i	0.257686	+	0.966229i	$0.417040\pi$
$338$	−2.18538	−	4.78531i	−0.118869	−	0.260287i
$339$	6.63640	−	4.26496i	0.360440	−	0.231641i
$340$	0.230766	−	1.60501i	0.0125150	−	0.0870440i
$341$	−7.91506	−	5.08670i	−0.428625	−	0.275460i
$342$	−0.392063	+	0.452465i	−0.0212003	+	0.0244665i
$343$	6.69437	−	17.2680i	0.361462	−	0.932387i
$344$			2.50721i			0.135179i
$345$	6.81715	+	20.0738i	0.367023	+	1.08074i
$346$			1.98611i			0.106774i
$347$	−17.2792	−	5.07363i	−0.927596	−	0.272367i	−0.217166	−	0.976135i	$-0.569681\pi$
$347$	−17.2792	−	5.07363i	−0.927596	−	0.272367i	−0.710430	+	0.703768i	$0.751499\pi$
$348$	−5.25446	−	4.55301i	−0.281668	−	0.244067i
$349$	−0.605944	+	0.942867i	−0.0324354	+	0.0504705i	−0.857093	−	0.515162i	$-0.827732\pi$
$349$	−0.605944	+	0.942867i	−0.0324354	+	0.0504705i	0.824657	+	0.565633i	$0.191368\pi$
$350$	−37.9101	−	6.54181i	−2.02638	−	0.349675i
$351$	2.34033	−	1.50404i	0.124918	−	0.0802797i
$352$	−2.06923	+	0.944988i	−0.110291	+	0.0503680i
$353$	17.4353	−	15.1078i	0.927987	−	0.804106i	−0.0529165	−	0.998599i	$-0.516852\pi$
$353$	17.4353	−	15.1078i	0.927987	−	0.804106i	0.980904	+	0.194493i	$0.0623063\pi$
$354$	−0.724555	−	5.03939i	−0.0385097	−	0.267841i
$355$	14.9853	−	32.8132i	0.795337	−	1.74155i
$356$	−10.0473	+	2.95015i	−0.532505	+	0.156358i
$357$	−0.938514	+	0.247175i	−0.0496714	+	0.0130819i
$358$	2.39105	−	5.23566i	0.126371	−	0.276713i
$359$	−8.80352	+	1.26576i	−0.464632	+	0.0668040i	−0.370656	−	0.928770i	$-0.620867\pi$
$359$	−8.80352	+	1.26576i	−0.464632	+	0.0668040i	−0.0939765	+	0.995574i	$0.529958\pi$
$360$	2.89478	+	3.34076i	0.152568	+	0.176073i
$361$	−7.74398	−	16.9570i	−0.407578	−	0.892472i
$362$	−7.66526	+	4.92616i	−0.402877	+	0.258913i
$363$	−5.76598	−	0.829022i	−0.302635	−	0.0435124i
$364$	6.07778	+	4.15159i	0.318562	+	0.217602i
$365$	−10.5410	−	9.13381i	−0.551740	−	0.478085i
$366$	0.295045	−	1.00483i	0.0154222	−	0.0525233i
$367$	21.4218			1.11821			0.559105	−	0.829097i	$-0.311145\pi$
$367$	21.4218			1.11821			0.559105	+	0.829097i	$0.311145\pi$
$368$	4.79165	−	0.200336i	0.249782	−	0.0104432i
$369$		−	8.48638i		−	0.441783i
$370$	−9.15286	+	31.1718i	−0.475835	+	1.62054i
$371$	−14.0442	+	15.3169i	−0.729137	+	0.795215i
$372$	3.47945	+	2.23611i	0.180401	+	0.115937i
$373$	3.32222	+	0.477663i	0.172018	+	0.0247325i	0.227786	−	0.973711i	$-0.426851\pi$
$373$	3.32222	+	0.477663i	0.172018	+	0.0247325i	−0.0557675	+	0.998444i	$0.517761\pi$
$374$	0.451135	+	0.701980i	0.0233277	+	0.0362985i
$375$	38.3620	−	17.5193i	1.98100	−	0.904694i
$376$	1.28005	−	1.10917i	0.0660135	−	0.0572010i
$377$	19.1451	−	2.75265i	0.986022	−	0.141769i
$378$	1.16622	−	2.37485i	0.0599838	−	0.122149i
$379$	1.21002	+	4.12096i	0.0621547	+	0.211679i	0.984715	−	0.174174i	$-0.0557254\pi$
$379$	1.21002	+	4.12096i	0.0621547	+	0.211679i	−0.922560	+	0.385853i	$0.873907\pi$
$380$	2.53931	−	0.745608i	0.130264	−	0.0382489i
$381$	−14.6911	−	6.70921i	−0.752649	−	0.343723i
$382$	−1.77854	+	0.255716i	−0.0909982	+	0.0130836i
$383$	−24.2166	−	27.9475i	−1.23741	−	1.42805i	−0.866347	−	0.499442i	$-0.833538\pi$
$383$	−24.2166	−	27.9475i	−1.23741	−	1.42805i	−0.371065	−	0.928607i	$-0.621007\pi$
$384$	0.909632	−	0.415415i	0.0464195	−	0.0211991i
$385$	22.7764	−	13.7496i	1.16079	−	0.700745i
$386$	1.23974	−	8.62257i	0.0631011	−	0.438877i
$387$	−1.35550	+	2.10920i	−0.0689038	+	0.107216i
$388$	−8.02464	+	9.26092i	−0.407389	+	0.470152i
$389$	−0.949799	+	3.23472i	−0.0481567	+	0.164007i	−0.980061	−	0.198698i	$-0.936329\pi$
$389$	−0.949799	+	3.23472i	−0.0481567	+	0.164007i	0.931904	+	0.362705i	$0.118147\pi$
$390$	−12.2975			−0.622709
$391$	−0.322883	−	1.72933i	−0.0163289	−	0.0874558i
$392$	6.98897	+	0.392896i	0.352996	+	0.0198442i
$393$	−7.78030	−	2.28450i	−0.392464	−	0.115238i
$394$	−15.4971	+	17.8846i	−0.780732	+	0.901013i
$395$	16.7194	−	26.0158i	0.841242	−	1.30900i
$396$	−2.25165	−	0.323738i	−0.113150	−	0.0162685i
$397$	1.20994	+	1.88270i	0.0607249	+	0.0944898i	0.870288	−	0.492543i	$-0.163932\pi$
$397$	1.20994	+	1.88270i	0.0607249	+	0.0944898i	−0.809563	+	0.587032i	$0.800296\pi$
$398$	7.42722	+	16.2634i	0.372293	+	0.815208i
$399$	−1.00328	−	1.22576i	−0.0502270	−	0.0613647i
$400$	−2.06932	−	14.3924i	−0.103466	−	0.719622i
$401$	−10.8772	−	4.96747i	−0.543184	−	0.248064i	0.124875	−	0.992173i	$-0.460147\pi$
$401$	−10.8772	−	4.96747i	−0.543184	−	0.248064i	−0.668058	+	0.744109i	$0.732874\pi$
$402$	10.0898	−	2.96264i	0.503236	−	0.147763i
$403$	−11.0402	+	3.24169i	−0.549950	+	0.161480i
$404$	13.4939	+	6.16244i	0.671345	+	0.306593i
$405$	0.629097	+	4.37546i	0.0312601	+	0.217418i
$406$	14.2347	−	11.6511i	0.706456	−	0.578234i
$407$	−6.94510	−	15.2077i	−0.344256	−	0.753816i
$408$	−0.198318	−	0.308589i	−0.00981822	−	0.0152775i
$409$	−13.5112	−	1.94262i	−0.668088	−	0.0960566i	−0.200078	−	0.979780i	$-0.564120\pi$
$409$	−13.5112	−	1.94262i	−0.668088	−	0.0960566i	−0.468010	+	0.883723i	$0.655029\pi$
$410$	−20.2814	+	31.5585i	−1.00163	+	1.55856i
$411$	−5.92747	+	6.84066i	−0.292380	+	0.337425i
$412$	−14.4344	−	4.23833i	−0.711133	−	0.208807i
$413$	13.4648	+	0.378174i	0.662558	+	0.0186087i
$414$	4.13930	+	2.42203i	0.203435	+	0.119036i
$415$	−38.7776			−1.90352
$416$	−0.783768	+	2.66927i	−0.0384274	+	0.130872i
$417$	12.8059	−	14.7788i	0.627110	−	0.723723i
$418$	−0.736308	+	1.14572i	−0.0360140	+	0.0560389i
$419$	−4.53929	+	31.5715i	−0.221759	+	1.54237i	0.509623	+	0.860398i	$0.329785\pi$
$419$	−4.53929	+	31.5715i	−0.221759	+	1.54237i	−0.731381	+	0.681969i	$0.761124\pi$
$420$	−10.0125	+	6.04431i	−0.488558	+	0.294932i
$421$	−30.6019	+	13.9754i	−1.49145	+	0.681121i	−0.983606	−	0.180329i	$-0.942284\pi$
$421$	−30.6019	+	13.9754i	−1.49145	+	0.681121i	−0.507841	+	0.861451i	$0.669556\pi$
$422$	−8.91094	−	10.2838i	−0.433778	−	0.500606i
$423$	1.67651	−	0.241046i	0.0815146	−	0.0117200i
$424$	−7.14466	−	3.26286i	−0.346975	−	0.158458i
$425$	−5.11768	+	1.50269i	−0.248244	+	0.0728910i
$426$	−2.29908	−	7.82993i	−0.111391	−	0.379362i
$427$	2.48707	+	1.22132i	0.120358	+	0.0591040i
$428$	11.8964	−	1.71044i	0.575033	−	0.0826772i
$429$	4.78269	−	4.14423i	0.230911	−	0.200085i
$430$	10.0814	−	4.60404i	0.486170	−	0.222027i
$431$	6.85375	+	10.6647i	0.330134	+	0.513698i	0.966151	−	0.257977i	$-0.0830557\pi$
$431$	6.85375	+	10.6647i	0.330134	+	0.513698i	−0.636017	+	0.771675i	$0.719419\pi$
$432$	0.989821	+	0.142315i	0.0476228	+	0.00684713i
$433$	13.1279	+	8.43677i	0.630885	+	0.405445i	0.816637	−	0.577151i	$-0.195836\pi$
$433$	13.1279	+	8.43677i	0.630885	+	0.405445i	−0.185752	+	0.982597i	$0.559472\pi$
$434$	−7.39544	+	8.06565i	−0.354992	+	0.387163i
$435$	−8.65872	+	29.4889i	−0.415154	+	1.41388i
$436$			5.87605i			0.281412i
$437$	2.34849	−	1.65186i	0.112344	−	0.0790191i
$438$	−3.15526			−0.150764
$439$	−0.967835	+	3.29614i	−0.0461923	+	0.157316i	−0.979360	−	0.202126i	$-0.935215\pi$
$439$	−0.967835	+	3.29614i	−0.0461923	+	0.157316i	0.933167	+	0.359442i	$0.117033\pi$
$440$	7.59957	+	6.58506i	0.362295	+	0.313931i
$441$	5.66708	+	4.10905i	0.269861	+	0.195669i
$442$	1.01009	+	0.145230i	0.0480453	+	0.00690786i
$443$	−18.3837	+	11.8145i	−0.873434	+	0.561322i	−0.898801	−	0.438356i	$-0.855561\pi$
$443$	−18.3837	+	11.8145i	−0.873434	+	0.561322i	0.0253674	+	0.999678i	$0.491924\pi$
$444$	3.05306	+	6.68526i	0.144892	+	0.317268i
$445$	30.3126	+	34.9826i	1.43695	+	1.65833i
$446$	24.7501	−	3.55852i	1.17195	−	0.168501i
$447$	2.32765	−	5.09684i	0.110094	−	0.241072i
$448$	0.673830	+	2.55851i	0.0318355	+	0.120878i
$449$	1.97947	−	0.581224i	0.0934169	−	0.0274297i	−0.234690	−	0.972070i	$-0.575408\pi$
$449$	1.97947	−	0.581224i	0.0934169	−	0.0274297i	0.328107	+	0.944641i	$0.393589\pi$
$450$	6.04031	−	13.2264i	0.284743	−	0.623501i
$451$	−2.74737	−	19.1083i	−0.129368	−	0.899777i
$452$	−5.96189	+	5.16600i	−0.280424	+	0.242988i
$453$	8.29450	−	3.78797i	0.389710	−	0.177974i
$454$	22.4529	−	14.4296i	1.05377	−	0.677215i
$455$	5.53272	−	32.0623i	0.259378	−	1.50310i
$456$	0.323680	−	0.503656i	0.0151577	−	0.0235858i
$457$	−3.79518	−	3.28854i	−0.177531	−	0.153832i	0.561562	−	0.827434i	$-0.310200\pi$
$457$	−3.79518	−	3.28854i	−0.177531	−	0.153832i	−0.739094	+	0.673603i	$0.764746\pi$
$458$	−25.5784	−	7.51049i	−1.19520	−	0.350942i
$459$		−	0.366821i		−	0.0171217i
$460$	−9.60456	−	18.8993i	−0.447815	−	0.881183i
$461$		−	5.08408i		−	0.236789i	−0.992967	−	0.118395i	$-0.962225\pi$
$461$		−	5.08408i		−	0.236789i	0.992967	−	0.118395i	$-0.0377748\pi$
$462$	1.85708	−	5.72489i	0.0863994	−	0.266346i
$463$	6.01007	−	6.93599i	0.279312	−	0.322343i	−0.598708	−	0.800967i	$-0.704319\pi$
$463$	6.01007	−	6.93599i	0.279312	−	0.322343i	0.878020	+	0.478624i	$0.158864\pi$
$464$	5.84893	+	3.75888i	0.271530	+	0.174502i
$465$	2.60196	−	18.0970i	0.120663	−	0.839230i
$466$	12.9560	−	8.32631i	0.600175	−	0.385709i
$467$	−2.03965	−	4.46621i	−0.0943836	−	0.206671i	0.856552	−	0.516061i	$-0.172602\pi$
$467$	−2.03965	−	4.46621i	−0.0943836	−	0.206671i	−0.950935	+	0.309390i	$0.899875\pi$
$468$	−2.10246	+	1.82179i	−0.0971864	+	0.0842125i
$469$	3.18479	+	27.6393i	0.147060	+	1.27627i
$470$	−6.81054	−	3.11027i	−0.314147	−	0.143466i
$471$	3.33165	+	11.3466i	0.153514	+	0.522822i
$472$	1.43436	+	4.88498i	0.0660218	+	0.224850i
$473$	−2.36928	+	5.18799i	−0.108940	+	0.238544i
$474$	−0.995621	−	6.92470i	−0.0457304	−	0.318062i
$475$	−5.70076	−	6.57903i	−0.261569	−	0.301867i
$476$	0.893784	−	0.378223i	0.0409665	−	0.0173358i
$477$	−4.24644	−	6.60758i	−0.194431	−	0.302540i
$478$	1.48917	−	10.3574i	0.0681132	−	0.473738i
$479$	−14.9647	−	9.61720i	−0.683753	−	0.439421i	0.152107	−	0.988364i	$-0.451394\pi$
$479$	−14.9647	−	9.61720i	−0.683753	−	0.439421i	−0.835860	+	0.548943i	$0.815030\pi$
$480$	−3.34076	−	2.89478i	−0.152484	−	0.132128i
$481$	−19.6176	−	5.76024i	−0.894484	−	0.262644i
$482$	24.3956			1.11119
$483$	−8.17704	+	9.70237i	−0.372068	+	0.441473i
$484$	5.82527			0.264785
$485$	51.9739	+	15.2609i	2.36001	+	0.692962i
$486$	0.755750	+	0.654861i	0.0342815	+	0.0297051i
$487$	−1.69824	−	1.09139i	−0.0769544	−	0.0494556i	0.501598	−	0.865101i	$-0.332746\pi$
$487$	−1.69824	−	1.09139i	−0.0769544	−	0.0494556i	−0.578552	+	0.815645i	$0.696382\pi$
$488$	−0.149039	+	1.03659i	−0.00674669	+	0.0469243i
$489$	12.7171	+	19.7883i	0.575089	+	0.894856i
$490$	−11.2542	−	28.8240i	−0.508412	−	1.30214i
$491$	−12.6095	−	14.5522i	−0.569060	−	0.656731i	0.396156	−	0.918183i	$-0.370344\pi$
$491$	−12.6095	−	14.5522i	−0.569060	−	0.656731i	−0.965216	+	0.261453i	$0.915798\pi$
$492$	1.20774	+	8.40000i	0.0544490	+	0.378701i
$493$	1.05946	−	2.31990i	0.0477159	−	0.104483i
$494$	0.469239	+	1.59808i	0.0211121	+	0.0719011i
$495$	2.83301	+	9.64834i	0.127334	+	0.433661i
$496$	−3.76226	−	1.71817i	−0.168931	−	0.0771481i
$497$	21.4487	−	2.47147i	0.962106	−	0.110860i
$498$	−6.62966	+	5.74464i	−0.297082	+	0.257423i
$499$	9.64865	+	21.1276i	0.431933	+	0.945801i	0.993009	+	0.118037i	$0.0376601\pi$
$499$	9.64865	+	21.1276i	0.431933	+	0.945801i	−0.561076	+	0.827764i	$0.689613\pi$
$500$	−35.4782	+	22.8005i	−1.58664	+	1.01967i
$501$	0.723850	−	5.03448i	0.0323392	−	0.224924i
$502$	9.72150	+	6.24763i	0.433892	+	0.278845i
$503$	−7.40235	+	8.54276i	−0.330054	+	0.380903i	−0.896386	−	0.443274i	$-0.853817\pi$
$503$	−7.40235	+	8.54276i	−0.330054	+	0.380903i	0.566332	+	0.824177i	$0.308362\pi$
$504$	−0.816371	+	2.51665i	−0.0363641	+	0.112101i
$505$		−	65.5749i		−	2.91804i
$506$	10.1044	+	4.11350i	0.449193	+	0.182868i
$507$			5.26071i			0.233636i
$508$	15.4964	+	4.55016i	0.687542	+	0.201881i
$509$	26.2757	+	22.7680i	1.16465	+	1.00918i	0.999739	+	0.0228673i	$0.00727952\pi$
$509$	26.2757	+	22.7680i	1.16465	+	1.00918i	0.164912	+	0.986308i	$0.447266\pi$
$510$	−0.876658	+	1.36411i	−0.0388191	+	0.0604036i
$511$	1.41957	−	8.22646i	0.0627980	−	0.363917i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$	0.544593	−	0.248708i	0.0240444	−	0.0109807i
$514$	−1.36055	+	1.17892i	−0.0600112	+	0.0520000i
$515$	9.46400	+	65.8236i	0.417034	+	2.90053i
$516$	1.04153	−	2.28063i	0.0458508	−	0.100399i
$517$	3.69687	−	1.08550i	0.162588	−	0.0477402i
$518$	−18.8035	+	4.95225i	−0.826179	+	0.217589i
$519$	0.825060	−	1.80663i	0.0362161	−	0.0793022i
$520$	12.1724	−	1.75012i	0.533793	−	0.0767478i
$521$	−5.42429	−	6.25996i	−0.237642	−	0.274254i	0.624384	−	0.781118i	$-0.285350\pi$
$521$	−5.42429	−	6.25996i	−0.237642	−	0.274254i	−0.862026	+	0.506864i	$0.830805\pi$
$522$	2.88823	+	6.32434i	0.126414	+	0.276809i
$523$	−4.13770	+	2.65914i	−0.180929	+	0.116276i	−0.627970	−	0.778237i	$-0.716114\pi$
$523$	−4.13770	+	2.65914i	−0.180929	+	0.116276i	0.447041	+	0.894513i	$0.352478\pi$
$524$	8.02623	+	1.15400i	0.350627	+	0.0504126i
$525$	31.7667	+	21.6991i	1.38641	+	0.947025i
$526$	21.9635	+	19.0315i	0.957654	+	0.829812i
$527$	−0.427440	+	1.45573i	−0.0186196	+	0.0634124i
$528$	2.27480			0.0989981
$529$	−16.4602	−	16.0643i	−0.715660	−	0.698449i
$530$			34.7202i			1.50815i
$531$	−1.43436	+	4.88498i	−0.0622459	+	0.211990i
$532$	1.16751	+	1.07050i	0.0506182	+	0.0464121i
$533$	−19.8609	−	12.7638i	−0.860273	−	0.552864i
$534$	10.3649	+	1.49024i	0.448532	+	0.0644891i
$535$	−28.7233	−	44.6943i	−1.24181	−	1.93230i
$536$	−9.56551	+	4.36842i	−0.413167	+	0.188687i
$537$	−4.34995	+	3.76925i	−0.187714	+	0.162655i
$538$	−25.8700	+	3.71955i	−1.11534	+	0.160361i
$539$	14.0905	+	7.41748i	0.606922	+	0.319493i
$540$	−1.24539	−	4.24140i	−0.0535929	−	0.182521i
$541$	−2.84414	+	0.835116i	−0.122279	+	0.0359044i	−0.342300	−	0.939591i	$-0.611206\pi$
$541$	−2.84414	+	0.835116i	−0.122279	+	0.0359044i	0.220020	+	0.975495i	$0.429388\pi$
$542$	23.7765	+	10.8584i	1.02129	+	0.466407i
$543$	9.01896	−	1.29673i	0.387041	−	0.0556481i
$544$	0.240217	+	0.277225i	0.0102992	+	0.0118859i
$545$	23.6275	−	10.7903i	1.01209	−	0.462207i
$546$	−3.80391	−	6.30121i	−0.162792	−	0.269667i
$547$	−1.57402	+	10.9476i	−0.0673004	+	0.468085i	0.928104	+	0.372322i	$0.121438\pi$
$547$	−1.57402	+	10.9476i	−0.0673004	+	0.468085i	−0.995404	+	0.0957630i	$0.969471\pi$
$548$	4.89361	−	7.61460i	0.209044	−	0.325280i
$549$	−0.685803	+	0.791459i	−0.0292694	+	0.0337787i
$550$	9.31876	−	31.7368i	0.397353	−	1.35326i
$551$	4.16252			0.177329
$552$	−4.44186	−	1.80829i	−0.189058	−	0.0769659i
$553$	18.5021	+	0.519653i	0.786790	+	0.0220979i
$554$	14.6051	+	4.28846i	0.620513	+	0.182199i
$555$	21.2750	−	24.5526i	0.903072	−	1.04220i
$556$	−10.5724	+	16.4509i	−0.448368	+	0.697674i
$557$	−45.7533	−	6.57832i	−1.93863	−	0.278733i	−0.940494	−	0.339809i	$-0.889637\pi$
$557$	−45.7533	−	6.57832i	−1.93863	−	0.278733i	−0.998133	+	0.0610768i	$0.980547\pi$
$558$	−2.23611	−	3.47945i	−0.0946619	−	0.147297i
$559$	2.89749	+	6.34463i	0.122551	+	0.268349i
$560$	9.05035	−	7.40771i	0.382447	−	0.313033i
$561$	−0.118754	−	0.825952i	−0.00501380	−	0.0348717i
$562$	23.6427	+	10.7973i	0.997308	+	0.455455i
$563$	30.7190	−	9.01993i	1.29465	−	0.380145i	0.439371	−	0.898306i	$-0.355202\pi$
$563$	30.7190	−	9.01993i	1.29465	−	0.380145i	0.855283	+	0.518161i	$0.173383\pi$
$564$	−1.62514	+	0.477184i	−0.0684307	+	0.0200931i
$565$	31.7204	+	14.4862i	1.33449	+	0.609440i
$566$	1.14991	+	7.99777i	0.0483342	+	0.336171i
$567$	−2.04738	+	1.67578i	−0.0859819	+	0.0703761i
$568$	3.38999	+	7.42304i	0.142241	+	0.311464i
$569$	−19.5313	−	30.3913i	−0.818796	−	1.27407i	−0.958846	−	0.283927i	$-0.908363\pi$
$569$	−19.5313	−	30.3913i	−0.818796	−	1.27407i	0.140050	−	0.990144i	$-0.455274\pi$
$570$	−2.61957	−	0.376638i	−0.109722	−	0.0157756i
$571$	7.03705	−	10.9499i	0.294491	−	0.458238i	−0.662206	−	0.749322i	$-0.730380\pi$
$571$	7.03705	−	10.9499i	0.294491	−	0.458238i	0.956697	+	0.291084i	$0.0940160\pi$
$572$	−4.14423	+	4.78269i	−0.173279	+	0.199974i
$573$	1.72405	+	0.506226i	0.0720231	+	0.0211479i
$574$	−22.4440	−	0.630365i	−0.936794	−	0.0263109i
$575$	−43.4244	+	54.5626i	−1.81092	+	2.27542i
$576$	−1.00000			−0.0416667
$577$	3.06505	−	10.4386i	0.127600	−	0.434565i	−0.870767	−	0.491696i	$-0.836377\pi$
$577$	3.06505	−	10.4386i	0.127600	−	0.434565i	0.998367	+	0.0571311i	$0.0181953\pi$
$578$	−11.0445	+	12.7461i	−0.459391	+	0.530166i
$579$	−4.70965	+	7.32836i	−0.195726	+	0.304556i
$580$	4.37388	−	30.4210i	0.181616	−	1.26316i
$581$	−11.9948	−	19.8695i	−0.497628	−	0.824327i
$582$	11.1466	−	5.09048i	0.462041	−	0.211007i
$583$	−11.7006	−	13.5032i	−0.484590	−	0.559246i
$584$	3.12315	−	0.449041i	0.129237	−	0.0185814i
$585$	11.1862	+	5.10858i	0.462493	+	0.211214i
$586$	−15.9525	+	4.68408i	−0.658992	+	0.193497i
$587$	−9.18294	−	31.2742i	−0.379020	−	1.29083i	−0.899489	−	0.436944i	$-0.856061\pi$
$587$	−9.18294	−	31.2742i	−0.379020	−	1.29083i	0.520468	−	0.853881i	$-0.325757\pi$
$588$	−6.19417	−	3.26071i	−0.255443	−	0.134469i
$589$	−2.45102	+	0.352404i	−0.100993	+	0.0145205i
$590$	17.0085	−	14.7380i	0.700229	−	0.606752i
$591$	21.5262	−	9.83068i	0.885469	−	0.404380i
$592$	−3.97339	−	6.18272i	−0.163305	−	0.254108i
$593$	−0.838032	−	0.120491i	−0.0344139	−	0.00494797i	0.125086	−	0.992146i	$-0.460079\pi$
$593$	−0.838032	−	0.120491i	−0.0344139	−	0.00494797i	−0.159500	+	0.987198i	$0.550988\pi$
$594$	1.91369	+	1.22985i	0.0785195	+	0.0504614i
$595$	−3.16211	−	2.89936i	−0.129634	−	0.118862i
$596$	−1.57860	+	5.37622i	−0.0646620	+	0.220219i
$597$		−	17.8790i		−	0.731741i
$598$	11.8940	−	6.04451i	0.486382	−	0.247178i
$599$	0.327390			0.0133768			0.00668840	−	0.999978i	$-0.497871\pi$
$599$	0.327390			0.0133768			0.00668840	+	0.999978i	$0.497871\pi$
$600$	−4.09651	+	13.9514i	−0.167239	+	0.569565i
$601$	−26.1536	−	22.6622i	−1.06683	−	0.924410i	−0.0695071	−	0.997581i	$-0.522143\pi$
$601$	−26.1536	−	22.6622i	−1.06683	−	0.924410i	−0.997319	+	0.0731710i	$0.976688\pi$
$602$	5.47752	+	3.74157i	0.223247	+	0.152495i
$603$	−10.4088	−	1.49656i	−0.423878	−	0.0609444i
$604$	−7.67099	+	4.92985i	−0.312128	+	0.200593i
$605$	−10.6971	−	23.4233i	−0.434898	−	0.952294i
$606$	−9.71448	−	11.2111i	−0.394624	−	0.455420i
$607$	38.0345	−	5.46853i	1.54377	−	0.221961i	0.682797	−	0.730608i	$-0.260763\pi$
$607$	38.0345	−	5.46853i	1.54377	−	0.221961i	0.860975	+	0.508647i	$0.169854\pi$
$608$	−0.248708	+	0.544593i	−0.0100864	+	0.0220862i
$609$	−17.7884	+	4.68490i	−0.720821	+	0.189842i
$610$	4.44181	−	1.30423i	0.179843	−	0.0528068i
$611$	1.95741	−	4.28613i	0.0791883	−	0.173398i
$612$	0.0522041	+	0.363087i	0.00211022	+	0.0146769i
$613$	17.6338	−	15.2798i	0.712224	−	0.617146i	−0.221491	−	0.975162i	$-0.571092\pi$
$613$	17.6338	−	15.2798i	0.712224	−	0.617146i	0.933715	+	0.358016i	$0.116547\pi$
$614$	−17.1229	+	7.81977i	−0.691024	+	0.315580i
$615$	31.5585	−	20.2814i	1.27256	−	0.817826i
$616$	−1.02345	+	5.93091i	−0.0412358	+	0.238963i
$617$	−18.3928	+	28.6198i	−0.740467	+	1.15219i	0.242810	+	0.970074i	$0.421931\pi$
$617$	−18.3928	+	28.6198i	−0.740467	+	1.15219i	−0.983277	+	0.182116i	$0.941706\pi$
$618$	11.3693	+	9.85159i	0.457342	+	0.396289i
$619$	−3.98910	−	1.17131i	−0.160335	−	0.0470787i	0.200580	−	0.979677i	$-0.435717\pi$
$619$	−3.98910	−	1.17131i	−0.160335	−	0.0470787i	−0.360915	+	0.932599i	$0.617536\pi$
$620$			18.2831i			0.734268i
$621$	−2.75909	−	3.92268i	−0.110719	−	0.157412i
$622$		−	7.11055i		−	0.285107i
$623$	−8.54859	+	26.3530i	−0.342492	+	1.05581i
$624$	1.82179	−	2.10246i	0.0729302	−	0.0841659i
$625$	95.6691	+	61.4828i	3.82676	+	2.45931i
$626$	−0.168064	+	1.16891i	−0.00671718	+	0.0467190i
$627$	1.14572	−	0.736308i	0.0457555	−	0.0294053i
$628$	−4.91253	−	10.7569i	−0.196031	−	0.429248i
$629$	−2.03744	+	1.76545i	−0.0812381	+	0.0703932i
$630$	11.6186	−	1.33877i	0.462894	−	0.0533378i
$631$	−26.1839	−	11.9578i	−1.04237	−	0.476033i	−0.180716	−	0.983535i	$-0.557841\pi$
$631$	−26.1839	−	11.9578i	−1.04237	−	0.476033i	−0.861650	+	0.507503i	$0.830569\pi$
$632$	1.97097	+	6.71252i	0.0784011	+	0.267010i
$633$	3.83364	+	13.0562i	0.152374	+	0.518937i
$634$	−7.33321	+	16.0575i	−0.291239	+	0.637725i
$635$	−10.1603	−	70.6664i	−0.403199	−	2.80431i
$636$	5.14357	+	5.93600i	0.203956	+	0.235378i
$637$	18.1400	−	7.08267i	0.718734	−	0.280626i
$638$	8.55072	+	13.3052i	0.338526	+	0.526757i
$639$	−1.16136	+	8.07743i	−0.0459426	+	0.319538i
$640$	3.71872	+	2.38988i	0.146995	+	0.0944683i
$641$	−3.48421	−	3.01908i	−0.137618	−	0.119247i	0.583332	−	0.812234i	$-0.301749\pi$
$641$	−3.48421	−	3.01908i	−0.137618	−	0.119247i	−0.720950	+	0.692987i	$0.756294\pi$
$642$	−11.5319	−	3.38606i	−0.455126	−	0.133637i
$643$	−21.3290			−0.841132			−0.420566	−	0.907262i	$-0.638168\pi$
$643$	−21.3290			−0.841132			−0.420566	+	0.907262i	$0.638168\pi$
$644$	6.71302	−	10.7673i	0.264530	−	0.424292i
$645$	−11.0830			−0.436392
$646$	0.210719	+	0.0618725i	0.00829061	+	0.00243434i
$647$	2.98727	+	2.58848i	0.117442	+	0.101764i	0.711602	−	0.702583i	$-0.247970\pi$
$647$	2.98727	+	2.58848i	0.117442	+	0.101764i	−0.594160	+	0.804347i	$0.702515\pi$
$648$	−0.841254	−	0.540641i	−0.0330476	−	0.0212384i
$649$	−1.64822	+	11.4636i	−0.0646983	+	0.449987i
$650$	−21.8694	−	34.0294i	−0.857788	−	1.33474i
$651$	10.0777	−	4.26460i	0.394977	−	0.167143i
$652$	−15.4039	−	17.7770i	−0.603262	−	0.696201i
$653$	−4.83011	−	33.5941i	−0.189017	−	1.31464i	−0.834560	−	0.550917i	$-0.814278\pi$
$653$	−4.83011	−	33.5941i	−0.189017	−	1.31464i	0.645544	−	0.763723i	$-0.276631\pi$
$654$	2.44100	−	5.34505i	0.0954507	−	0.209008i
$655$	−10.0985	−	34.3925i	−0.394583	−	1.34383i
$656$	−2.39089	−	8.14262i	−0.0933485	−	0.317916i
$657$	2.87013	+	1.31074i	0.111974	+	0.0511370i
$658$	−0.512965	−	4.45178i	−0.0199974	−	0.173548i
$659$	−37.7724	+	32.7300i	−1.47140	+	1.27498i	−0.585869	+	0.810406i	$0.699247\pi$
$659$	−37.7724	+	32.7300i	−1.47140	+	1.27498i	−0.885535	+	0.464573i	$0.846208\pi$
$660$	−4.17728	−	9.14696i	−0.162600	−	0.356045i
$661$	25.2249	−	16.2110i	0.981133	−	0.630536i	0.0513643	−	0.998680i	$-0.483643\pi$
$661$	25.2249	−	16.2110i	0.981133	−	0.630536i	0.929769	+	0.368144i	$0.120007\pi$
$662$	1.68596	−	11.7261i	0.0655267	−	0.455748i
$663$	−0.858483	−	0.551713i	−0.0333407	−	0.0214268i
$664$	5.74464	−	6.62966i	0.222935	−	0.257281i
$665$	2.16054	−	6.66035i	0.0837820	−	0.258277i
$666$		−	7.34941i		−	0.284784i
$667$	−6.11985	−	32.7773i	−0.236961	−	1.26914i
$668$			5.08626i			0.196793i
$669$	−23.9917	−	7.04460i	−0.927573	−	0.272360i
$670$	35.1308	+	30.4410i	1.35722	+	1.17604i
$671$	−1.28796	+	2.00411i	−0.0497213	+	0.0773678i
$672$	0.449905	−	2.60722i	0.0173555	−	0.100576i
$673$	22.6309	−	14.5440i	0.872358	−	0.560631i	−0.0261150	−	0.999659i	$-0.508314\pi$
$673$	22.6309	−	14.5440i	0.872358	−	0.560631i	0.898473	+	0.439028i	$0.144677\pi$
$674$	−14.6280	+	6.68037i	−0.563448	+	0.257318i
$675$	−10.9889	+	9.52196i	−0.422964	+	0.366500i
$676$	−0.748677	−	5.20716i	−0.0287953	−	0.200276i
$677$	−12.2594	+	26.8444i	−0.471168	+	1.03171i	0.513630	+	0.858012i	$0.328301\pi$
$677$	−12.2594	+	26.8444i	−0.471168	+	1.03171i	−0.984798	+	0.173703i	$0.944427\pi$
$678$	7.56916	−	2.22251i	0.290692	−	0.0853548i
$679$	8.25708	+	31.3518i	0.316878	+	1.20317i
$680$	0.673602	−	1.47498i	0.0258315	−	0.0565630i
$681$	−26.4181	+	3.79836i	−1.01235	+	0.145553i
$682$	−6.16136	−	7.11059i	−0.235931	−	0.272278i
$683$	1.18877	+	2.60303i	0.0454869	+	0.0996023i	0.931011	−	0.364991i	$-0.118928\pi$
$683$	1.18877	+	2.60303i	0.0454869	+	0.0996023i	−0.885524	+	0.464593i	$0.846201\pi$
$684$	−0.503656	+	0.323680i	−0.0192578	+	0.0123762i
$685$	−39.6045	−	5.69426i	−1.51321	−	0.217567i
$686$	11.2882	−	14.6825i	0.430984	−	0.560582i
$687$	20.1470	+	17.4574i	0.768654	+	0.666043i
$688$	−0.706361	+	2.40565i	−0.0269298	+	0.0917144i
$689$	−21.8507			−0.832447
$690$	0.885575	+	21.1813i	0.0337133	+	0.806357i
$691$			28.9038i			1.09955i	0.835312	+	0.549776i	$0.185287\pi$
$691$			28.9038i			1.09955i	−0.835312	+	0.549776i	$0.814713\pi$
$692$	−0.559552	+	1.90566i	−0.0212710	+	0.0724423i
$693$	−4.06747	+	4.43608i	−0.154510	+	0.168513i
$694$	−15.1499	−	9.73622i	−0.575081	−	0.369582i
$695$	85.5631	+	12.3021i	3.24559	+	0.466646i
$696$	−3.75888	−	5.84893i	−0.142480	−	0.221703i
$697$	−2.83167	+	1.29318i	−0.107257	+	0.0489827i
$698$	−0.847035	+	0.733960i	−0.0320607	+	0.0277808i
$699$	−15.2441	+	2.19176i	−0.576583	+	0.0829001i
$700$	−34.5314	−	16.9573i	−1.30516	−	0.640927i
$701$	−8.90002	−	30.3107i	−0.336149	−	1.14482i	−0.938123	−	0.346303i	$-0.887437\pi$
$701$	−8.90002	−	30.3107i	−0.336149	−	1.14482i	0.601974	−	0.798516i	$-0.294381\pi$
$702$	2.66927	−	0.783768i	0.100745	−	0.0295814i
$703$	−4.00244	−	1.82785i	−0.150955	−	0.0689388i
$704$	−2.25165	+	0.323738i	−0.0848622	+	0.0122013i
$705$	4.90303	+	5.65840i	0.184659	+	0.213108i
$706$	20.9854	−	9.58371i	0.789796	−	0.360688i
$707$	33.6004	−	20.2838i	1.26367	−	0.762852i
$708$	0.724555	−	5.03939i	0.0272305	−	0.189392i
$709$	14.8927	−	23.1735i	0.559307	−	0.870298i	−0.440314	−	0.897844i	$-0.645133\pi$
$709$	14.8927	−	23.1735i	0.559307	−	0.870298i	0.999621	+	0.0275458i	$0.00876921\pi$
$710$	23.6229	−	27.2622i	0.886550	−	1.02313i
$711$	−1.97097	+	6.71252i	−0.0739173	+	0.251739i
$712$	−10.4715			−0.392434
$713$	6.37852	+	18.7822i	0.238877	+	0.703397i
$714$	−0.970135	−	0.0272473i	−0.0363064	−	0.00101971i
$715$	26.8413	+	7.88131i	1.00381	+	0.294744i
$716$	3.76925	−	4.34995i	0.140863	−	0.162565i
$717$	−5.65723	+	8.80282i	−0.211273	+	0.328747i
$718$	−8.80352	−	1.26576i	−0.328545	−	0.0472376i
$719$	−15.5250	−	24.1573i	−0.578984	−	0.900916i	0.420997	−	0.907062i	$-0.361680\pi$
$719$	−15.5250	−	24.1573i	−0.578984	−	0.900916i	−0.999981	+	0.00614569i	$0.998044\pi$
$720$	1.83632	+	4.02099i	0.0684358	+	0.149853i
$721$	−30.8004	+	25.2101i	−1.14707	+	0.938872i
$722$	−2.65297	−	18.4518i	−0.0987334	−	0.686706i
$723$	−22.1910	−	10.1343i	−0.825292	−	0.376898i
$724$	−8.74262	+	2.56706i	−0.324917	+	0.0954042i
$725$	−96.9994	+	28.4816i	−3.60247	+	1.05778i
$726$	−5.29885	−	2.41990i	−0.196659	−	0.0898111i
$727$	−4.98909	−	34.6999i	−0.185035	−	1.28695i	−0.844640	−	0.535335i	$-0.820185\pi$
$727$	−4.98909	−	34.6999i	−0.185035	−	1.28695i	0.659605	−	0.751613i	$-0.270724\pi$
$728$	4.66195	+	5.69573i	0.172783	+	0.211098i
$729$	−0.415415	−	0.909632i	−0.0153857	−	0.0336901i
$730$	−7.54070	−	11.7336i	−0.279094	−	0.434279i
$731$	0.910334	+	0.130886i	0.0336699	+	0.00484101i
$732$	0.566187	−	0.881003i	0.0209269	−	0.0325628i
$733$	7.49557	−	8.65035i	0.276855	−	0.319508i	−0.600244	−	0.799817i	$-0.704930\pi$
$733$	7.49557	−	8.65035i	0.276855	−	0.319508i	0.877099	+	0.480309i	$0.159475\pi$
$734$	20.5541	+	6.03523i	0.758666	+	0.222764i
$735$	−1.73678	+	30.8944i	−0.0640621	+	1.13956i
$736$	4.65399	+	1.15774i	0.171548	+	0.0426749i
$737$	−23.9214			−0.881156
$738$	2.39089	−	8.14262i	0.0880098	−	0.299734i
$739$	−2.33303	+	2.69246i	−0.0858217	+	0.0990436i	−0.797036	−	0.603932i	$-0.793600\pi$
$739$	−2.33303	+	2.69246i	−0.0858217	+	0.0990436i	0.711214	+	0.702975i	$0.248145\pi$
$740$	−17.5642	+	27.3304i	−0.645673	+	1.00469i
$741$	0.237032	−	1.64860i	0.00870760	−	0.0605627i
$742$	−17.7906	+	10.7398i	−0.653112	+	0.394270i
$743$	−14.0035	+	6.39518i	−0.513738	+	0.234616i	−0.655377	−	0.755302i	$-0.727490\pi$
$743$	−14.0035	+	6.39518i	−0.513738	+	0.234616i	0.141638	+	0.989918i	$0.454763\pi$
$744$	2.70852	+	3.12580i	0.0992993	+	0.114597i
$745$	24.5165	−	3.52495i	0.898216	−	0.129144i
$746$	3.05308	+	1.39429i	0.111781	+	0.0510487i
$747$	8.41696	−	2.47144i	0.307961	−	0.0904254i
$748$	0.235091	+	0.800645i	0.00859576	+	0.0292745i
$749$	14.0164	−	28.5427i	0.512149	−	1.04293i
$750$	41.7438	−	6.00185i	1.52427	−	0.219157i
$751$	−17.7692	+	15.3971i	−0.648407	+	0.561848i	−0.915747	−	0.401754i	$-0.868401\pi$
$751$	−17.7692	+	15.3971i	−0.648407	+	0.561848i	0.267341	+	0.963602i	$0.413855\pi$
$752$	1.54069	−	0.703609i	0.0561831	−	0.0256580i
$753$	−6.24763	−	9.72150i	−0.227676	−	0.354271i
$754$	19.1451	+	2.75265i	0.697223	+	0.100245i
$755$	33.9093	+	21.7922i	1.23409	+	0.793099i
$756$	1.78805	−	1.95009i	0.0650308	−	0.0709242i
$757$	14.9116	−	50.7842i	0.541971	−	1.84578i	0.00850200	−	0.999964i	$-0.497294\pi$
$757$	14.9116	−	50.7842i	0.541971	−	1.84578i	0.533469	−	0.845820i	$-0.320888\pi$
$758$			4.29493i			0.155999i
$759$	−7.48243	−	7.93927i	−0.271595	−	0.288177i
$760$	2.64651			0.0959991
$761$	4.79186	−	16.3196i	0.173705	−	0.591584i	−0.825909	−	0.563803i	$-0.809338\pi$
$761$	4.79186	−	16.3196i	0.173705	−	0.591584i	0.999614	−	0.0277811i	$-0.00884413\pi$
$762$	−12.2058	−	10.5764i	−0.442170	−	0.383143i
$763$	12.8375	+	8.76899i	0.464748	+	0.317459i
$764$	−1.77854	−	0.255716i	−0.0643454	−	0.00925147i
$765$	1.36411	−	0.876658i	0.0493194	−	0.0316956i
$766$	−15.3620	−	33.6380i	−0.555051	−	1.21539i
$767$	9.27515	+	10.7041i	0.334906	+	0.386502i
$768$	0.989821	−	0.142315i	0.0357171	−	0.00513534i
$769$	−13.8061	+	30.2312i	−0.497862	+	1.09017i	0.479296	+	0.877653i	$0.340892\pi$
$769$	−13.8061	+	30.2312i	−0.497862	+	1.09017i	−0.977158	+	0.212513i	$0.931835\pi$
$770$	25.7275	−	6.77581i	0.927154	−	0.244183i
$771$	1.72734	−	0.507193i	0.0622086	−	0.0182661i
$772$	3.61878	−	7.92402i	0.130243	−	0.285192i
$773$	−5.55048	−	38.6045i	−0.199637	−	1.38851i	−0.805339	−	0.592815i	$-0.798017\pi$
$773$	−5.55048	−	38.6045i	−0.199637	−	1.38851i	0.605702	−	0.795692i	$-0.292892\pi$
$774$	−1.89482	+	1.64187i	−0.0681079	+	0.0590158i
$775$	54.7050	−	24.9829i	1.96506	−	0.897413i
$776$	−10.3087	+	6.62499i	−0.370060	+	0.237823i
$777$	19.1615	+	3.30654i	0.687416	+	0.118621i
$778$	−1.82265	+	2.83610i	−0.0653452	+	0.101679i
$779$	−3.83979	−	3.32719i	−0.137575	−	0.119209i
$780$	−11.7994	−	3.46461i	−0.422486	−	0.124053i
$781$			18.5635i			0.664255i
$782$	0.177404	−	1.75024i	0.00634396	−	0.0625886i
$783$		−	6.95264i		−	0.248467i
$784$	6.59517	+	2.34600i	0.235542	+	0.0837857i
$785$	−34.2325	+	39.5064i	−1.22181	+	1.41004i
$786$	−6.82153	−	4.38393i	−0.243316	−	0.156370i
$787$	−2.53377	+	17.6228i	−0.0903192	+	0.628184i	0.893506	+	0.449052i	$0.148238\pi$
$787$	−2.53377	+	17.6228i	−0.0903192	+	0.628184i	−0.983825	+	0.179132i	$0.942671\pi$
$788$	−19.9080	+	12.7941i	−0.709194	+	0.455771i
$789$	−12.0727	−	26.4356i	−0.429801	−	0.941133i
$790$	23.3716	−	20.2516i	0.831525	−	0.720520i
$791$	2.38916	+	20.7344i	0.0849486	+	0.737229i
$792$	−2.06923	−	0.944988i	−0.0735270	−	0.0335787i
$793$	0.820802	+	2.79539i	0.0291475	+	0.0992674i
$794$	0.630508	+	2.14731i	0.0223759	+	0.0762053i
$795$	14.4233	−	31.5826i	0.511542	−	1.12012i
$796$	2.54445	+	17.6971i	0.0901858	+	0.627256i
$797$	−27.2053	−	31.3966i	−0.963662	−	1.11213i	−0.993643	−	0.112575i	$-0.964090\pi$
$797$	−27.2053	−	31.3966i	−0.963662	−	1.11213i	0.0299810	−	0.999550i	$-0.490455\pi$
$798$	−0.617307	−	1.45876i	−0.0218524	−	0.0516397i
$799$	−0.335902	−	0.522673i	−0.0118833	−	0.0184908i
$800$	2.06932	−	14.3924i	0.0731615	−	0.508849i
$801$	−8.80914	−	5.66129i	−0.311256	−	0.200032i
$802$	−9.03714	−	7.83073i	−0.319113	−	0.276513i
$803$	6.88686	+	2.02217i	0.243032	+	0.0713607i
$804$	10.5158			0.370864
$805$	−55.6226	−	7.22066i	−1.96044	−	0.254495i
$806$	−11.5063			−0.405291
$807$	25.0774	+	7.36338i	0.882766	+	0.259203i
$808$	11.2111	+	9.71448i	0.394405	+	0.341754i
$809$	−5.24464	−	3.37053i	−0.184392	−	0.118501i	0.445188	−	0.895437i	$-0.353137\pi$
$809$	−5.24464	−	3.37053i	−0.184392	−	0.118501i	−0.629580	+	0.776936i	$0.716773\pi$
$810$	−0.629097	+	4.37546i	−0.0221042	+	0.153738i
$811$	23.6088	+	36.7360i	0.829017	+	1.28998i	0.954599	+	0.297893i	$0.0962838\pi$
$811$	23.6088	+	36.7360i	0.829017	+	1.28998i	−0.125582	+	0.992083i	$0.540080\pi$
$812$	16.9406	−	7.16876i	0.594498	−	0.251574i
$813$	−17.1171	−	19.7542i	−0.600324	−	0.692811i
$814$	−2.37929	−	16.5483i	−0.0833940	−	0.580018i
$815$	−43.1947	+	94.5831i	−1.51304	+	3.31310i
$816$	−0.103345	−	0.351962i	−0.00361781	−	0.0123211i
$817$	0.422896	+	1.44025i	0.0147953	+	0.0503880i
$818$	−12.4166	−	5.67049i	−0.434138	−	0.198264i
$819$	0.842537	+	7.31199i	0.0294406	+	0.255502i
$820$	−28.3509	+	24.5662i	−0.990057	+	0.857890i
$821$	0.0377405	+	0.0826402i	0.00131715	+	0.00288416i	0.910289	−	0.413972i	$-0.135859\pi$
$821$	0.0377405	+	0.0826402i	0.00131715	+	0.00288416i	−0.908972	+	0.416857i	$0.863132\pi$
$822$	−7.61460	+	4.89361i	−0.265590	+	0.170684i
$823$	0.345083	−	2.40010i	0.0120288	−	0.0836624i	−0.982923	−	0.184019i	$-0.941089\pi$
$823$	0.345083	−	2.40010i	0.0120288	−	0.0836624i	0.994952	+	0.100357i	$0.0319983\pi$
$824$	−12.6556	−	8.13329i	−0.440880	−	0.283337i
$825$	−21.6606	+	24.9976i	−0.754125	+	0.870306i
$826$	12.8128	+	4.15632i	0.445815	+	0.144617i
$827$			18.1421i			0.630863i	0.948948	+	0.315431i	$0.102149\pi$
$827$			18.1421i			0.630863i	−0.948948	+	0.315431i	$0.897851\pi$
$828$	3.28926	+	3.49009i	0.114310	+	0.121289i
$829$			51.6127i			1.79258i	0.443467	+	0.896291i	$0.353748\pi$
$829$			51.6127i			1.79258i	−0.443467	+	0.896291i	$0.646252\pi$
$830$	−37.2068	−	10.9249i	−1.29147	−	0.379209i
$831$	−11.5038	−	9.96811i	−0.399063	−	0.345790i
$832$	−1.50404	+	2.34033i	−0.0521432	+	0.0811364i
$833$	0.507508	−	2.51709i	0.0175841	−	0.0872121i
$834$	16.4509	−	10.5724i	0.569648	−	0.366091i
$835$	20.4518	−	9.34001i	0.707763	−	0.323224i
$836$	−1.02927	+	0.891866i	−0.0355980	+	0.0308458i
$837$	0.588618	+	4.09393i	0.0203456	+	0.141507i
$838$	−13.2501	+	29.0137i	−0.457718	+	1.00226i
$839$	−42.6492	+	12.5229i	−1.47241	+	0.432340i	−0.916883	−	0.399156i	$-0.869303\pi$
$839$	−42.6492	+	12.5229i	−1.47241	+	0.432340i	−0.555531	+	0.831496i	$0.687485\pi$
$840$	−11.3098	+	2.97863i	−0.390224	+	0.102773i
$841$	8.03380	−	17.5916i	0.277028	−	0.606606i
$842$	−33.2997	+	4.78777i	−1.14758	+	0.164998i
$843$	−17.0208	−	19.6431i	−0.586229	−	0.676544i
$844$	−5.65271	−	12.3777i	−0.194574	−	0.426058i
$845$	−19.5631	+	12.5725i	−0.672992	+	0.432506i
$846$	1.67651	+	0.241046i	0.0576396	+	0.00828732i
$847$	8.69320	−	12.7265i	0.298702	−	0.437289i
$848$	−5.93600	−	5.14357i	−0.203843	−	0.176631i
$849$	2.27640	−	7.75272i	0.0781260	−	0.266073i
$850$	−5.33374			−0.182946
$851$	−8.50872	+	34.2041i	−0.291675	+	1.17250i
$852$		−	8.16049i		−	0.279574i
$853$	−11.3998	+	38.8240i	−0.390320	+	1.32931i	0.496837	+	0.867844i	$0.334495\pi$
$853$	−11.3998	+	38.8240i	−0.390320	+	1.32931i	−0.887158	+	0.461466i	$0.847324\pi$
$854$	2.04224	+	1.87254i	0.0698839	+	0.0640770i
$855$	2.22639	+	1.43081i	0.0761408	+	0.0489327i
$856$	11.8964	+	1.71044i	0.406610	+	0.0584616i
$857$	3.97064	+	6.17844i	0.135635	+	0.211052i	0.902426	−	0.430845i	$-0.141784\pi$
$857$	3.97064	+	6.17844i	0.135635	+	0.211052i	−0.766791	+	0.641896i	$0.778148\pi$
$858$	5.75652	−	2.62892i	0.196524	−	0.0897497i
$859$	−18.5983	+	16.1156i	−0.634567	+	0.549856i	−0.911638	−	0.410994i	$-0.865182\pi$
$859$	−18.5983	+	16.1156i	−0.634567	+	0.549856i	0.277071	+	0.960849i	$0.410636\pi$
$860$	10.9702	−	1.57727i	0.374080	−	0.0537846i
$861$	20.1539	+	9.89697i	0.686843	+	0.337288i
$862$	3.57155	+	12.1636i	0.121647	+	0.414293i
$863$	4.99951	−	1.46799i	0.170185	−	0.0499709i	−0.195530	−	0.980698i	$-0.562643\pi$
$863$	4.99951	−	1.46799i	0.170185	−	0.0499709i	0.365715	+	0.930727i	$0.380824\pi$
$864$	0.909632	+	0.415415i	0.0309463	+	0.0141327i
$865$	8.69015	−	1.24946i	0.295474	−	0.0424828i
$866$	10.2192	+	11.7936i	0.347262	+	0.400762i
$867$	15.3413	−	7.00616i	0.521019	−	0.237942i
$868$	−9.36823	+	5.65540i	−0.317978	+	0.191957i
$869$	−2.26484	+	15.7523i	−0.0768295	+	0.534361i
$870$	−16.6160	+	25.8550i	−0.563334	+	0.876565i
$871$	−19.1576	+	22.1091i	−0.649132	+	0.749138i
$872$	−1.65548	+	5.63803i	−0.0560615	+	0.190928i
$873$	−12.2540			−0.414734
$874$	2.71875	−	0.923300i	0.0919630	−	0.0312311i
$875$	−3.13260	+	111.535i	−0.105901	+	3.77059i
$876$	−3.02745	−	0.888941i	−0.102288	−	0.0300345i
$877$	−30.4737	+	35.1685i	−1.02902	+	1.18755i	−0.0469794	+	0.998896i	$0.514960\pi$
$877$	−30.4737	+	35.1685i	−1.02902	+	1.18755i	−0.982043	+	0.188659i	$0.939586\pi$
$878$	−1.85726	+	2.88996i	−0.0626796	+	0.0975313i
$879$	16.4567	+	2.36612i	0.555072	+	0.0798073i
$880$	5.43651	+	8.45937i	0.183265	+	0.285165i
$881$	−8.16437	−	17.8775i	−0.275065	−	0.602307i	0.720801	−	0.693142i	$-0.243774\pi$
$881$	−8.16437	−	17.8775i	−0.275065	−	0.602307i	−0.995866	+	0.0908342i	$0.971047\pi$
$882$	4.27987	+	5.53920i	0.144111	+	0.186515i
$883$	1.25172	+	8.70588i	0.0421236	+	0.292976i	0.999984	+	0.00574042i	$0.00182724\pi$
$883$	1.25172	+	8.70588i	0.0421236	+	0.292976i	−0.957860	+	0.287236i	$0.907264\pi$
$884$	0.928262	+	0.423923i	0.0312208	+	0.0142581i
$885$	−21.5939	+	6.34053i	−0.725869	+	0.213135i
$886$	−20.9675	+	6.15662i	−0.704417	+	0.206836i
$887$	19.4980	+	8.90444i	0.654679	+	0.298982i	0.714924	−	0.699202i	$-0.246461\pi$
$887$	19.4980	+	8.90444i	0.654679	+	0.298982i	−0.0602456	+	0.998184i	$0.519188\pi$
$888$	1.04593	+	7.27461i	0.0350991	+	0.244120i
$889$	33.0665	−	27.0649i	1.10901	−	0.907727i
$890$	19.2290	+	42.1056i	0.644557	+	1.41138i
$891$	−1.22985	−	1.91369i	−0.0412016	−	0.0641109i
$892$	24.7501	+	3.55852i	0.828693	+	0.119148i
$893$	0.548232	−	0.853066i	0.0183459	−	0.0285468i
$894$	3.66931	−	4.23461i	0.122720	−	0.141626i
$895$	−24.4127	−	7.16820i	−0.816025	−	0.239607i
$896$	−0.0742797	+	2.64471i	−0.00248151	+	0.0883535i
$897$	−13.3302	+	0.557325i	−0.445081	+	0.0186086i
$898$	2.06304			0.0688444
$899$	−8.10159	+	27.5915i	−0.270203	+	0.920228i
$900$	9.52196	−	10.9889i	0.317399	−	0.366298i
$901$	−1.55768	+	2.42380i	−0.0518939	+	0.0807485i
$902$	2.74737	−	19.1083i	0.0914773	−	0.636238i
$903$	−3.42823	−	5.67889i	−0.114084	−	0.188982i
$904$	−7.17582	+	3.27709i	−0.238664	+	0.108994i
$905$	26.3764	+	30.4400i	0.876782	+	1.01186i
$906$	9.02571	−	1.29770i	0.299859	−	0.0431133i
$907$	14.6333	+	6.68279i	0.485890	+	0.221898i	0.643270	−	0.765640i	$-0.277577\pi$
$907$	14.6333	+	6.68279i	0.485890	+	0.221898i	−0.157380	+	0.987538i	$0.550305\pi$
$908$	25.6087	−	7.51939i	0.849854	−	0.249540i
$909$	4.17934	+	14.2335i	0.138620	+	0.472096i
$910$	14.3416	−	29.2048i	0.475419	−	0.968131i
$911$	42.2870	−	6.07995i	1.40103	−	0.201438i	0.599971	−	0.800022i	$-0.295179\pi$
$911$	42.2870	−	6.07995i	1.40103	−	0.201438i	0.801060	+	0.598584i	$0.204270\pi$
$912$	0.452465	−	0.392063i	0.0149826	−	0.0129825i
$913$	18.1519	−	8.28972i	0.600742	−	0.274350i
$914$	−2.71496	−	4.22456i	−0.0898029	−	0.139736i
$915$	−4.58221	−	0.658822i	−0.151483	−	0.0217800i
$916$	−22.4263	−	14.4125i	−0.740987	−	0.476203i
$917$	14.4989	−	15.8129i	0.478796	−	0.522186i
$918$	0.103345	−	0.351962i	0.00341091	−	0.0116165i
$919$			20.6220i			0.680258i	0.940379	+	0.340129i	$0.110471\pi$
$919$			20.6220i			0.680258i	−0.940379	+	0.340129i	$0.889529\pi$
$920$	−3.89097	−	20.8396i	−0.128281	−	0.687062i
$921$	18.8240			0.620272
$922$	1.43235	−	4.87814i	0.0471720	−	0.160653i
$923$	17.1571	+	14.8667i	0.564734	+	0.489345i
$924$	3.39475	−	4.96979i	0.111679	−	0.163494i
$925$	105.776	+	15.2083i	3.47789	+	0.500045i
$926$	7.72072	−	4.96180i	0.253719	−	0.163055i
$927$	−6.24942	−	13.6843i	−0.205258	−	0.449452i
$928$	4.55301	+	5.25446i	0.149460	+	0.172486i
$929$	3.62599	−	0.521339i	0.118965	−	0.0171046i	−0.0825752	−	0.996585i	$-0.526314\pi$
$929$	3.62599	−	0.521339i	0.118965	−	0.0171046i	0.201540	+	0.979480i	$0.435405\pi$
$930$	7.59509	−	16.6309i	0.249053	−	0.545350i
$931$	4.08105	−	0.953148i	0.133751	−	0.0312381i
$932$	14.7770	−	4.33891i	0.484036	−	0.142126i
$933$	−2.95383	+	6.46798i	−0.0967040	+	0.211752i
$934$	−0.698752	−	4.85993i	−0.0228639	−	0.159022i
$935$	2.78768	−	2.41554i	0.0911669	−	0.0789966i
$936$	−2.53056	+	1.15567i	−0.0827139	+	0.0377742i
$937$	30.1903	−	19.4021i	0.986274	−	0.633840i	0.0551256	−	0.998479i	$-0.482444\pi$
$937$	30.1903	−	19.4021i	0.986274	−	0.633840i	0.931149	+	0.364639i	$0.118808\pi$
$938$	−4.73111	+	27.4170i	−0.154476	+	0.895197i
$939$	0.638459	−	0.993461i	0.0208353	−	0.0324204i
$940$	−5.65840	−	4.90303i	−0.184557	−	0.159919i
$941$	−13.4015	−	3.93502i	−0.436875	−	0.128278i	0.0558969	−	0.998437i	$-0.482198\pi$
$941$	−13.4015	−	3.93502i	−0.436875	−	0.128278i	−0.492772	+	0.870158i	$0.664016\pi$
$942$			11.8256i			0.385298i
$943$	−20.5542	+	35.1276i	−0.669338	+	1.14391i
$944$			5.09121i			0.165705i
$945$	−11.1248	−	3.60873i	−0.361888	−	0.117392i
$946$	−3.73493	+	4.31034i	−0.121433	+	0.140141i
$947$	−35.4755	−	22.7987i	−1.15280	−	0.740859i	−0.182605	−	0.983186i	$-0.558453\pi$
$947$	−35.4755	−	22.7987i	−1.15280	−	0.740859i	−0.970195	+	0.242327i	$0.922089\pi$
$948$	0.995621	−	6.92470i	0.0323363	−	0.224904i
$949$	7.38437	−	4.74564i	0.239707	−	0.154050i
$950$	−3.61632	−	7.91863i	−0.117329	−	0.256914i
$951$	13.3411	−	11.5601i	0.432613	−	0.374861i
$952$	0.964138	−	0.111095i	0.0312479	−	0.00360060i
$953$	−39.9948	−	18.2650i	−1.29556	−	0.591662i	−0.356140	−	0.934433i	$-0.615907\pi$
$953$	−39.9948	−	18.2650i	−1.29556	−	0.591662i	−0.939419	+	0.342770i	$0.888635\pi$
$954$	−2.21285	−	7.53629i	−0.0716438	−	0.243996i
$955$	2.23775	+	7.62108i	0.0724119	+	0.246612i
$956$	4.34687	−	9.51833i	0.140588	−	0.307845i
$957$	−2.25084	−	15.6549i	−0.0727592	−	0.506051i
$958$	−11.6490	−	13.4437i	−0.376362	−	0.434345i
$959$	−9.33285	−	22.0546i	−0.301374	−	0.712180i
$960$	−2.38988	−	3.71872i	−0.0771330	−	0.120021i
$961$	−1.97722	+	13.7518i	−0.0637812	+	0.443608i
$962$	−17.2001	−	11.0538i	−0.554552	−	0.356389i
$963$	9.08313	+	7.87058i	0.292700	+	0.253626i
$964$	23.4074	+	6.87303i	0.753901	+	0.221365i
$965$	−38.5077			−1.23961
$966$	−10.5793	+	7.00562i	−0.340383	+	0.225402i
$967$	−4.78191			−0.153776			−0.0768880	−	0.997040i	$-0.524498\pi$
$967$	−4.78191			−0.153776			−0.0768880	+	0.997040i	$0.524498\pi$
$968$	5.58930	+	1.64117i	0.179647	+	0.0527491i
$969$	−0.165974	−	0.143817i	−0.00533184	−	0.00462006i
$970$	45.5691	+	29.2855i	1.46314	+	0.940300i
$971$	−1.35233	+	9.40565i	−0.0433983	+	0.301842i	0.956549	+	0.291572i	$0.0941782\pi$
$971$	−1.35233	+	9.40565i	−0.0433983	+	0.301842i	−0.999947	+	0.0102699i	$0.996731\pi$
$972$	0.540641	+	0.841254i	0.0173411	+	0.0269832i
$973$	20.1631	+	47.6476i	0.646399	+	1.52751i
$974$	−1.32197	−	1.52563i	−0.0423585	−	0.0488843i
$975$	5.75676	+	40.0391i	0.184364	+	1.28228i
$976$	−0.435044	+	0.952613i	−0.0139254	+	0.0304924i
$977$	−11.6082	−	39.5338i	−0.371379	−	1.26480i	−0.907283	−	0.420520i	$-0.861847\pi$
$977$	−11.6082	−	39.5338i	−0.371379	−	1.26480i	0.535905	−	0.844279i	$-0.319971\pi$
$978$	6.62701	+	22.5695i	0.211908	+	0.721694i
$979$	−21.6679	−	9.89539i	−0.692509	−	0.316258i
$980$	−2.67763	−	30.8271i	−0.0855338	−	0.984736i
$981$	−4.44083	+	3.84800i	−0.141785	+	0.122857i
$982$	−7.99894	−	17.5152i	−0.255256	−	0.558933i
$983$	−9.93860	+	6.38715i	−0.316992	+	0.203718i	−0.689455	−	0.724329i	$-0.742150\pi$
$983$	−9.93860	+	6.38715i	−0.316992	+	0.203718i	0.372463	+	0.928047i	$0.378513\pi$
$984$	−1.20774	+	8.40000i	−0.0385013	+	0.267782i
$985$	88.0026	+	56.5558i	2.80399	+	1.80202i
$986$	1.67014	−	1.92744i	0.0531881	−	0.0613823i
$987$	−1.38273	+	4.26258i	−0.0440127	+	0.135679i
$988$			1.66555i			0.0529882i
$989$	10.7193	−	5.44754i	0.340855	−	0.173222i
$990$			10.0557i			0.319590i
$991$	−35.8942	−	10.5395i	−1.14022	−	0.334798i	−0.343502	−	0.939152i	$-0.611613\pi$
$991$	−35.8942	−	10.5395i	−1.14022	−	0.334798i	−0.796716	+	0.604354i	$0.793431\pi$
$992$	−3.12580	−	2.70852i	−0.0992443	−	0.0859957i
$993$	−6.40480	+	9.96607i	−0.203250	+	0.316264i
$994$	21.2762	+	3.67144i	0.674839	+	0.116451i
$995$	66.4872	−	42.7288i	2.10779	−	1.35459i
$996$	−7.97957	+	3.64415i	−0.252842	+	0.115469i
$997$	20.0948	−	17.4122i	0.636409	−	0.551451i	−0.275780	−	0.961221i	$-0.588936\pi$
$997$	20.0948	−	17.4122i	0.636409	−	0.551451i	0.912189	+	0.409769i	$0.134391\pi$
$998$	3.30548	+	22.9901i	0.104633	+	0.727739i
$999$	−3.05306	+	6.68526i	−0.0965944	+	0.211512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.b.97.8	✓	160
7.6	odd	2	inner	966.2.s.b.97.9	yes	160
23.14	odd	22	inner	966.2.s.b.727.9	yes	160
161.83	even	22	inner	966.2.s.b.727.8	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.b.97.8	✓	160	1.1	even	1	trivial
966.2.s.b.97.9	yes	160	7.6	odd	2	inner
966.2.s.b.727.8	yes	160	161.83	even	22	inner
966.2.s.b.727.9	yes	160	23.14	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.629097 - 4.37546i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(2.43657 - 1.03108i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.959493 + 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.629097 - 4.37546i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(2.43657 - 1.03108i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(1.83632 - 4.02099i) q^{10} +(0.640886 + 2.18266i) q^{11} +(-0.281733 - 0.959493i) q^{12} +(2.53056 + 1.15567i) q^{13} +(2.62836 - 0.302858i) q^{14} +(-3.34076 + 2.89478i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.308589 - 0.198318i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(0.503656 + 0.323680i) q^{19} +(2.89478 - 3.34076i) q^{20} +(-2.51665 - 0.816371i) q^{21} +2.27480i q^{22} +(1.80829 - 4.44186i) q^{23} -1.00000i q^{24} +(-13.9514 - 4.09651i) q^{25} +(2.10246 + 1.82179i) q^{26} +(0.540641 - 0.841254i) q^{27} +(2.60722 + 0.449905i) q^{28} +(5.84893 - 3.75888i) q^{29} +(-4.02099 + 1.83632i) q^{30} +(-3.12580 + 2.70852i) q^{31} +(0.142315 + 0.989821i) q^{32} +(0.944988 - 2.06923i) q^{33} +(0.351962 - 0.103345i) q^{34} +(-2.97863 - 11.3098i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(-7.27461 + 1.04593i) q^{37} +(0.392063 + 0.452465i) q^{38} +(-1.15567 - 2.53056i) q^{39} +(3.71872 - 2.38988i) q^{40} +(-8.40000 - 1.20774i) q^{41} +(-2.18471 - 1.49233i) q^{42} +(1.89482 + 1.64187i) q^{43} +(-0.640886 + 2.18266i) q^{44} +4.42046 q^{45} +(2.98646 - 3.75248i) q^{46} -1.69375i q^{47} +(0.281733 - 0.959493i) q^{48} +(4.87373 - 5.02462i) q^{49} +(-12.2322 - 7.86115i) q^{50} +(-0.363087 - 0.0522041i) q^{51} +(1.50404 + 2.34033i) q^{52} +(-7.14466 + 3.26286i) q^{53} +(0.755750 - 0.654861i) q^{54} +(9.95332 - 1.43107i) q^{55} +(2.37485 + 1.16622i) q^{56} +(-0.168672 - 0.574445i) q^{57} +(6.67101 - 1.95879i) q^{58} +(4.63113 + 2.11497i) q^{59} +(-4.37546 + 0.629097i) q^{60} +(0.685803 + 0.791459i) q^{61} +(-3.76226 + 1.71817i) q^{62} +(1.36735 + 2.26503i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(6.64854 - 10.3453i) q^{65} +(1.48968 - 1.71918i) q^{66} +(-2.96264 + 10.0898i) q^{67} +0.366821 q^{68} +(-4.27541 + 2.17275i) q^{69} +(0.328350 - 11.6908i) q^{70} +(7.82993 + 2.29908i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(1.70586 - 2.65438i) q^{73} +(-7.27461 - 1.04593i) q^{74} +(7.86115 + 12.2322i) q^{75} +(0.248708 + 0.544593i) q^{76} +(3.81207 + 4.65739i) q^{77} +(-0.395914 - 2.75364i) q^{78} +(6.36370 + 2.90620i) q^{79} +(4.24140 - 1.24539i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-7.71948 - 3.52537i) q^{82} +(-1.24843 - 8.68301i) q^{83} +(-1.67578 - 2.04738i) q^{84} +(-0.673602 - 1.47498i) q^{85} +(1.35550 + 2.10920i) q^{86} +(-6.88187 - 0.989464i) q^{87} +(-1.22985 + 1.91369i) q^{88} +(-6.85734 + 7.91379i) q^{89} +(4.24140 + 1.24539i) q^{90} +(7.35747 + 0.206643i) q^{91} +(3.92268 - 2.75909i) q^{92} +4.13603 q^{93} +(0.477184 - 1.62514i) q^{94} +(1.73310 - 2.00010i) q^{95} +(0.540641 - 0.841254i) q^{96} +(-1.74392 + 12.1292i) q^{97} +(6.09191 - 3.44799i) q^{98} +(-2.06923 + 0.944988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9	\( 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9} + 22 q^{14} - 16 q^{16} - 16 q^{18} - 52 q^{23} - 48 q^{25} + 22 q^{28} - 12 q^{29} + 16 q^{32} + 22 q^{35} + 16 q^{36} + 22 q^{37} - 4 q^{39} + 154 q^{43} + 8 q^{46} + 4 q^{50} + 22 q^{51} + 88 q^{53} + 22 q^{57} + 56 q^{58} - 16 q^{64} + 16 q^{71} - 16 q^{72} + 22 q^{74} - 72 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} - 22 q^{84} - 68 q^{85} - 44 q^{86} + 44 q^{88} - 8 q^{92} - 8 q^{93} - 66 q^{95} + 66 q^{98} - 66 q^{99}+O(q^{100}) \) 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9 + 22 * q^14 - 16 * q^16 - 16 * q^18 - 52 * q^23 - 48 * q^25 + 22 * q^28 - 12 * q^29 + 16 * q^32 + 22 * q^35 + 16 * q^36 + 22 * q^37 - 4 * q^39 + 154 * q^43 + 8 * q^46 + 4 * q^50 + 22 * q^51 + 88 * q^53 + 22 * q^57 + 56 * q^58 - 16 * q^64 + 16 * q^71 - 16 * q^72 + 22 * q^74 - 72 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 - 22 * q^84 - 68 * q^85 - 44 * q^86 + 44 * q^88 - 8 * q^92 - 8 * q^93 - 66 * q^95 + 66 * q^98 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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