LMFDB - Embedded newform 966.2.s.a.181.14

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			181.14
Character	$\chi$	$=$	966.181
Dual form			966.2.s.a.475.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.30557 - 1.50670i) q^{5} +(0.281733 - 0.959493i) q^{6} +(-2.33235 + 1.24906i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.30557 - 1.50670i) q^{5} +(0.281733 - 0.959493i) q^{6} +(-2.33235 + 1.24906i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-1.67717 - 1.07785i) q^{10} +(-5.59475 - 0.804403i) q^{11} +(-0.989821 - 0.142315i) q^{12} +(-2.36808 + 3.68480i) q^{13} +(1.56827 + 2.13085i) q^{14} +(1.81349 - 0.828195i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-6.51798 - 1.91385i) q^{17} +(0.654861 - 0.755750i) q^{18} +(0.721432 - 0.211831i) q^{19} +(-0.828195 + 1.81349i) q^{20} +(-2.64046 + 0.167293i) q^{21} +5.65228i q^{22} +(-4.47709 - 1.71920i) q^{23} +1.00000i q^{24} +(0.145921 + 1.01490i) q^{25} +(3.98430 + 1.81957i) q^{26} +(0.281733 + 0.959493i) q^{27} +(1.88597 - 1.85556i) q^{28} +(-8.03505 - 2.35930i) q^{29} +(-1.07785 - 1.67717i) q^{30} +(6.73834 - 3.07730i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-4.75500 - 3.05585i) q^{33} +(-0.966766 + 6.72401i) q^{34} +(-1.16307 + 5.14489i) q^{35} +(-0.841254 - 0.540641i) q^{36} +(1.80754 - 1.56625i) q^{37} +(-0.312346 - 0.683942i) q^{38} +(-3.68480 + 2.36808i) q^{39} +(1.91290 + 0.561678i) q^{40} +(8.72376 + 7.55918i) q^{41} +(0.541367 + 2.58977i) q^{42} +(-8.11086 - 3.70410i) q^{43} +(5.59475 - 0.804403i) q^{44} +1.99366 q^{45} +(-1.06454 + 4.67619i) q^{46} -8.92364i q^{47} +(0.989821 - 0.142315i) q^{48} +(3.87969 - 5.82649i) q^{49} +(0.983803 - 0.288871i) q^{50} +(-5.13392 - 4.44857i) q^{51} +(1.23402 - 4.20270i) q^{52} +(2.91021 + 4.52838i) q^{53} +(0.909632 - 0.415415i) q^{54} +(-8.51632 + 7.37943i) q^{55} +(-2.10508 - 1.60270i) q^{56} +(0.744235 + 0.107005i) q^{57} +(-1.19178 + 8.28903i) q^{58} +(5.04989 - 7.85779i) q^{59} +(-1.50670 + 1.30557i) q^{60} +(2.86290 + 6.26888i) q^{61} +(-4.00494 - 6.23181i) q^{62} +(-2.47134 - 0.944710i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(2.46022 + 8.37874i) q^{65} +(-2.34804 + 5.14150i) q^{66} +(-6.35909 + 0.914298i) q^{67} +6.79315 q^{68} +(-3.35833 - 3.42369i) q^{69} +(5.25805 + 0.419038i) q^{70} +(-0.385612 - 2.68199i) q^{71} +(-0.415415 + 0.909632i) q^{72} +(0.959829 + 3.26888i) q^{73} +(-1.80754 - 1.56625i) q^{74} +(-0.288871 + 0.983803i) q^{75} +(-0.632529 + 0.406502i) q^{76} +(14.0536 - 5.11203i) q^{77} +(2.86837 + 3.31028i) q^{78} +(-9.34521 + 14.5414i) q^{79} +(0.283727 - 1.97336i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(6.24072 - 9.71075i) q^{82} +(-2.98441 - 3.44419i) q^{83} +(2.48637 - 0.904419i) q^{84} +(-11.3933 + 7.32201i) q^{85} +(-2.51211 + 8.55545i) q^{86} +(-6.32885 - 5.48398i) q^{87} +(-1.59243 - 5.42332i) q^{88} +(-2.71978 + 5.95548i) q^{89} +(-0.283727 - 1.97336i) q^{90} +(0.920640 - 11.5521i) q^{91} +(4.78009 + 0.388216i) q^{92} +7.40777 q^{93} +(-8.83281 + 1.26997i) q^{94} +(0.622710 - 1.36354i) q^{95} +(-0.281733 - 0.959493i) q^{96} +(-2.35988 + 2.72345i) q^{97} +(-6.31932 - 3.01101i) q^{98} +(-3.05585 - 4.75500i) 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} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 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 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	1.30557	−	1.50670i	0.583867	−	0.673819i	−0.384564	−	0.923098i	$-0.625648\pi$
$5$	1.30557	−	1.50670i	0.583867	−	0.673819i	0.968432	+	0.249279i	$0.0801938\pi$
$6$	0.281733	−	0.959493i	0.115017	−	0.391711i
$7$	−2.33235	+	1.24906i	−0.881545	+	0.472101i
$7$	−2.33235	+	1.24906i	−0.881545	+	0.472101i
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	−1.67717	−	1.07785i	−0.530368	−	0.340847i
$11$	−5.59475	−	0.804403i	−1.68688	−	0.242537i	−0.768959	−	0.639299i	$-0.779225\pi$
$11$	−5.59475	−	0.804403i	−1.68688	−	0.242537i	−0.917922	+	0.396762i	$0.870134\pi$
$12$	−0.989821	−	0.142315i	−0.285737	−	0.0410828i
$13$	−2.36808	+	3.68480i	−0.656786	+	1.02198i	0.339886	+	0.940467i	$0.389611\pi$
$13$	−2.36808	+	3.68480i	−0.656786	+	1.02198i	−0.996672	+	0.0815125i	$0.974025\pi$
$14$	1.56827	+	2.13085i	0.419139	+	0.569493i
$15$	1.81349	−	0.828195i	0.468242	−	0.213839i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−6.51798	−	1.91385i	−1.58084	−	0.464177i	−0.630709	−	0.776019i	$-0.717236\pi$
$17$	−6.51798	−	1.91385i	−1.58084	−	0.464177i	−0.950134	+	0.311842i	$0.899054\pi$
$18$	0.654861	−	0.755750i	0.154352	−	0.178132i
$19$	0.721432	−	0.211831i	0.165508	−	0.0485975i	−0.197929	−	0.980216i	$-0.563421\pi$
$19$	0.721432	−	0.211831i	0.165508	−	0.0485975i	0.363437	+	0.931619i	$0.381603\pi$
$20$	−0.828195	+	1.81349i	−0.185190	+	0.405509i
$21$	−2.64046	+	0.167293i	−0.576195	+	0.0365064i
$22$			5.65228i			1.20507i
$23$	−4.47709	−	1.71920i	−0.933538	−	0.358478i
$23$	−4.47709	−	1.71920i	−0.933538	−	0.358478i
$24$			1.00000i			0.204124i
$25$	0.145921	+	1.01490i	0.0291841	+	0.202980i
$26$	3.98430	+	1.81957i	0.781386	+	0.356847i
$27$	0.281733	+	0.959493i	0.0542195	+	0.184655i
$28$	1.88597	−	1.85556i	0.356415	−	0.350669i
$29$	−8.03505	−	2.35930i	−1.49207	−	0.438112i	−0.568870	−	0.822428i	$-0.692619\pi$
$29$	−8.03505	−	2.35930i	−1.49207	−	0.438112i	−0.923202	+	0.384316i	$0.874437\pi$
$30$	−1.07785	−	1.67717i	−0.196788	−	0.306208i
$31$	6.73834	−	3.07730i	1.21024	−	0.552699i	0.294959	−	0.955510i	$-0.404694\pi$
$31$	6.73834	−	3.07730i	1.21024	−	0.552699i	0.915283	+	0.402811i	$0.131967\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	−4.75500	−	3.05585i	−0.827739	−	0.531956i
$34$	−0.966766	+	6.72401i	−0.165799	+	1.15316i
$35$	−1.16307	+	5.14489i	−0.196595	+	0.869645i
$36$	−0.841254	−	0.540641i	−0.140209	−	0.0901068i
$37$	1.80754	−	1.56625i	0.297158	−	0.257489i	−0.493501	−	0.869745i	$-0.664283\pi$
$37$	1.80754	−	1.56625i	0.297158	−	0.257489i	0.790660	+	0.612256i	$0.209738\pi$
$38$	−0.312346	−	0.683942i	−0.0506692	−	0.110950i
$39$	−3.68480	+	2.36808i	−0.590040	+	0.379196i
$40$	1.91290	+	0.561678i	0.302456	+	0.0888091i
$41$	8.72376	+	7.55918i	1.36242	+	1.18055i	0.964796	+	0.262998i	$0.0847112\pi$
$41$	8.72376	+	7.55918i	1.36242	+	1.18055i	0.397626	+	0.917548i	$0.369834\pi$
$42$	0.541367	+	2.58977i	0.0835347	+	0.399611i
$43$	−8.11086	−	3.70410i	−1.23689	−	0.564871i	−0.313816	−	0.949484i	$-0.601608\pi$
$43$	−8.11086	−	3.70410i	−1.23689	−	0.564871i	−0.923078	+	0.384613i	$0.874335\pi$
$44$	5.59475	−	0.804403i	0.843440	−	0.121268i
$45$	1.99366			0.297197
$46$	−1.06454	+	4.67619i	−0.156958	+	0.689467i
$47$		−	8.92364i		−	1.30165i	−0.759229	−	0.650823i	$-0.774424\pi$
$47$		−	8.92364i		−	1.30165i	0.759229	−	0.650823i	$-0.225576\pi$
$48$	0.989821	−	0.142315i	0.142868	−	0.0205414i
$49$	3.87969	−	5.82649i	0.554242	−	0.832356i
$50$	0.983803	−	0.288871i	0.139131	−	0.0408525i
$51$	−5.13392	−	4.44857i	−0.718893	−	0.622924i
$52$	1.23402	−	4.20270i	0.171128	−	0.582810i
$53$	2.91021	+	4.52838i	0.399748	+	0.622020i	0.981526	−	0.191327i	$-0.0612791\pi$
$53$	2.91021	+	4.52838i	0.399748	+	0.622020i	−0.581778	+	0.813348i	$0.697643\pi$
$54$	0.909632	−	0.415415i	0.123785	−	0.0565308i
$55$	−8.51632	+	7.37943i	−1.14834	+	0.995042i
$56$	−2.10508	−	1.60270i	−0.281303	−	0.214170i
$57$	0.744235	+	0.107005i	0.0985764	+	0.0141731i
$58$	−1.19178	+	8.28903i	−0.156489	+	1.08840i
$59$	5.04989	−	7.85779i	0.657440	−	1.02300i	−0.339170	−	0.940725i	$-0.610146\pi$
$59$	5.04989	−	7.85779i	0.657440	−	1.02300i	0.996610	−	0.0822715i	$-0.0262175\pi$
$60$	−1.50670	+	1.30557i	−0.194515	+	0.168548i
$61$	2.86290	+	6.26888i	0.366557	+	0.802648i	0.999593	+	0.0285256i	$0.00908120\pi$
$61$	2.86290	+	6.26888i	0.366557	+	0.802648i	−0.633036	+	0.774122i	$0.718192\pi$
$62$	−4.00494	−	6.23181i	−0.508628	−	0.791441i
$63$	−2.47134	−	0.944710i	−0.311360	−	0.119022i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	2.46022	+	8.37874i	0.305153	+	1.03925i
$66$	−2.34804	+	5.14150i	−0.289024	+	0.632874i
$67$	−6.35909	+	0.914298i	−0.776886	+	0.111699i	−0.519341	−	0.854567i	$-0.673823\pi$
$67$	−6.35909	+	0.914298i	−0.776886	+	0.111699i	−0.257545	+	0.966266i	$0.582913\pi$
$68$	6.79315			0.823791
$69$	−3.35833	−	3.42369i	−0.404295	−	0.412164i
$70$	5.25805	+	0.419038i	0.628457	+	0.0500846i
$71$	−0.385612	−	2.68199i	−0.0457638	−	0.318294i	−0.999825	−	0.0186837i	$-0.994052\pi$
$71$	−0.385612	−	2.68199i	−0.0457638	−	0.318294i	0.954062	−	0.299610i	$-0.0968566\pi$
$72$	−0.415415	+	0.909632i	−0.0489571	+	0.107201i
$73$	0.959829	+	3.26888i	0.112339	+	0.382593i	0.996400	−	0.0847798i	$-0.0270187\pi$
$73$	0.959829	+	3.26888i	0.112339	+	0.382593i	−0.884060	+	0.467373i	$0.845201\pi$
$74$	−1.80754	−	1.56625i	−0.210123	−	0.182072i
$75$	−0.288871	+	0.983803i	−0.0333559	+	0.113600i
$76$	−0.632529	+	0.406502i	−0.0725560	+	0.0466289i
$77$	14.0536	−	5.11203i	1.60156	−	0.582570i
$78$	2.86837	+	3.31028i	0.324779	+	0.374815i
$79$	−9.34521	+	14.5414i	−1.05142	+	1.63604i	−0.329362	+	0.944204i	$0.606834\pi$
$79$	−9.34521	+	14.5414i	−1.05142	+	1.63604i	−0.722056	+	0.691835i	$0.756803\pi$
$80$	0.283727	−	1.97336i	0.0317216	−	0.220629i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	6.24072	−	9.71075i	0.689172	−	1.07237i
$83$	−2.98441	−	3.44419i	−0.327581	−	0.378049i	0.567938	−	0.823071i	$-0.307741\pi$
$83$	−2.98441	−	3.44419i	−0.327581	−	0.378049i	−0.895520	+	0.445022i	$0.853196\pi$
$84$	2.48637	−	0.904419i	0.271285	−	0.0986802i
$85$	−11.3933	+	7.32201i	−1.23577	+	0.794184i
$86$	−2.51211	+	8.55545i	−0.270887	+	0.922558i
$87$	−6.32885	−	5.48398i	−0.678524	−	0.587944i
$88$	−1.59243	−	5.42332i	−0.169754	−	0.578128i
$89$	−2.71978	+	5.95548i	−0.288296	+	0.631279i	−0.997261	−	0.0739639i	$-0.976435\pi$
$89$	−2.71978	+	5.95548i	−0.288296	+	0.631279i	0.708965	+	0.705243i	$0.249162\pi$
$90$	−0.283727	−	1.97336i	−0.0299074	−	0.208011i
$91$	0.920640	−	11.5521i	0.0965093	−	1.21099i
$92$	4.78009	+	0.388216i	0.498359	+	0.0404743i
$93$	7.40777			0.768150
$94$	−8.83281	+	1.26997i	−0.911035	+	0.130987i
$95$	0.622710	−	1.36354i	0.0638887	−	0.139897i
$96$	−0.281733	−	0.959493i	−0.0287542	−	0.0979278i
$97$	−2.35988	+	2.72345i	−0.239610	+	0.276524i	−0.862799	−	0.505546i	$-0.831291\pi$
$97$	−2.35988	+	2.72345i	−0.239610	+	0.276524i	0.623190	+	0.782071i	$0.285836\pi$
$98$	−6.31932	−	3.01101i	−0.638348	−	0.304158i
$99$	−3.05585	−	4.75500i	−0.307125	−	0.477896i
$100$	−0.425940	−	0.932679i	−0.0425940	−	0.0932679i
$101$	−2.44827	+	2.12144i	−0.243612	+	0.211091i	−0.768105	−	0.640323i	$-0.778800\pi$
$101$	−2.44827	+	2.12144i	−0.243612	+	0.211091i	0.524493	+	0.851415i	$0.324255\pi$
$102$	−3.67266	+	5.71476i	−0.363647	+	0.565846i
$103$	−0.524155	+	3.64558i	−0.0516465	+	0.359210i	0.947567	+	0.319557i	$0.103534\pi$
$103$	−0.524155	+	3.64558i	−0.0516465	+	0.359210i	−0.999214	+	0.0396524i	$0.987375\pi$
$104$	−4.33554	−	0.623357i	−0.425135	−	0.0611252i
$105$	−3.19523	+	4.19680i	−0.311823	+	0.409566i
$106$	4.06812	−	3.52504i	0.395131	−	0.342383i
$107$	2.72713	−	1.24544i	0.263642	−	0.120401i	−0.279209	−	0.960230i	$-0.590072\pi$
$107$	2.72713	−	1.24544i	0.263642	−	0.120401i	0.542851	+	0.839829i	$0.317345\pi$
$108$	−0.540641	−	0.841254i	−0.0520232	−	0.0809497i
$109$	0.481994	−	1.64152i	0.0461667	−	0.157229i	−0.933184	−	0.359400i	$-0.882981\pi$
$109$	0.481994	−	1.64152i	0.0461667	−	0.157229i	0.979350	+	0.202171i	$0.0647996\pi$
$110$	8.51632	+	7.37943i	0.811999	+	0.703601i
$111$	2.29484	−	0.673826i	0.217817	−	0.0639567i
$112$	−1.28680	+	2.31174i	−0.121591	+	0.218439i
$113$	−1.53569	+	0.220799i	−0.144466	+	0.0207711i	−0.214168	−	0.976797i	$-0.568704\pi$
$113$	−1.53569	+	0.220799i	−0.144466	+	0.0207711i	0.0697025	+	0.997568i	$0.477795\pi$
$114$		−	0.751889i		−	0.0704208i
$115$	−8.43547	+	4.50113i	−0.786611	+	0.419732i
$116$	8.37427			0.777531
$117$	−4.33554	+	0.623357i	−0.400821	+	0.0576294i
$118$	−8.49648	−	3.88021i	−0.782164	−	0.357202i
$119$	17.5927	−	3.67759i	1.61272	−	0.337124i
$120$	1.50670	+	1.30557i	0.137543	+	0.119181i
$121$	20.0997	+	5.90181i	1.82725	+	0.536528i
$122$	5.79764	−	3.72592i	0.524894	−	0.337329i
$123$	4.79521	+	10.5001i	0.432370	+	0.946758i
$124$	−5.59842	+	4.85106i	−0.502753	+	0.435638i
$125$	10.1055	+	6.49442i	0.903865	+	0.580879i
$126$	−0.583386	+	2.58063i	−0.0519722	+	0.229901i
$127$	1.51306	−	10.5236i	0.134262	−	0.933816i	−0.805648	−	0.592395i	$-0.798183\pi$
$127$	1.51306	−	10.5236i	0.134262	−	0.933816i	0.939910	−	0.341421i	$-0.110908\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	−5.83916	−	6.73874i	−0.514109	−	0.593313i
$130$	7.94333	−	3.62760i	0.696676	−	0.318161i
$131$	2.43810	+	3.79376i	0.213018	+	0.331463i	0.931276	−	0.364314i	$-0.118697\pi$
$131$	2.43810	+	3.79376i	0.213018	+	0.331463i	−0.718258	+	0.695777i	$0.755060\pi$
$132$	5.42332	+	1.59243i	0.472040	+	0.138603i
$133$	−1.41804	+	1.39518i	−0.122960	+	0.120977i
$134$	1.80998	+	6.16424i	0.156359	+	0.532509i
$135$	1.81349	+	0.828195i	0.156081	+	0.0712796i
$136$	−0.966766	−	6.72401i	−0.0828995	−	0.576579i
$137$		−	6.63603i		−	0.566954i	−0.958979	−	0.283477i	$-0.908512\pi$
$137$		−	6.63603i		−	0.566954i	0.958979	−	0.283477i	$-0.0914880\pi$
$138$	−2.91090	+	3.81138i	−0.247792	+	0.324447i
$139$		−	0.321449i		−	0.0272649i	−0.999907	−	0.0136325i	$-0.995661\pi$
$139$		−	0.321449i		−	0.0272649i	0.999907	−	0.0136325i	$-0.00433948\pi$
$140$	−0.333525	−	5.26416i	−0.0281880	−	0.444903i
$141$	3.70701	−	8.11723i	0.312187	−	0.683594i
$142$	−2.59982	+	0.763375i	−0.218172	+	0.0640610i
$143$	16.2129	−	18.7106i	1.35579	−	1.56466i
$144$	0.959493	+	0.281733i	0.0799577	+	0.0234777i
$145$	−14.0451	+	9.02622i	−1.16638	+	0.749587i
$146$	3.09901	−	1.41527i	0.256476	−	0.117129i
$147$	5.94951	−	3.68828i	0.490707	−	0.304204i
$148$	−1.29306	+	2.01205i	−0.106289	+	0.165389i
$149$	−17.3867	−	2.49983i	−1.42437	−	0.204794i	−0.613353	−	0.789809i	$-0.710179\pi$
$149$	−17.3867	−	2.49983i	−1.42437	−	0.204794i	−0.811022	+	0.585015i	$0.801089\pi$
$150$	1.01490	+	0.145921i	0.0828662	+	0.0119144i
$151$	8.49205	+	5.45751i	0.691073	+	0.444126i	0.838467	−	0.544952i	$-0.183452\pi$
$151$	8.49205	+	5.45751i	0.691073	+	0.444126i	−0.147394	+	0.989078i	$0.547089\pi$
$152$	0.492382	+	0.568239i	0.0399375	+	0.0460903i
$153$	−2.82198	−	6.17927i	−0.228143	−	0.499564i
$154$	−7.06004	−	13.1831i	−0.568914	−	1.06232i
$155$	4.16078	−	14.1703i	0.334202	−	1.13819i
$156$	2.86837	−	3.31028i	0.229654	−	0.265034i
$157$	−9.19179	+	2.69895i	−0.733585	+	0.215400i	−0.627127	−	0.778917i	$-0.715769\pi$
$157$	−9.19179	+	2.69895i	−0.733585	+	0.215400i	−0.106458	+	0.994317i	$0.533951\pi$
$158$	15.7234	+	7.18063i	1.25088	+	0.571260i
$159$	0.766065	+	5.32810i	0.0607529	+	0.422546i
$160$	−1.99366			−0.157612
$161$	12.5895	−	1.58239i	0.992193	−	0.124710i
$162$	1.00000			0.0785674
$163$	−1.52676	−	10.6188i	−0.119585	−	0.831732i	−0.958014	−	0.286721i	$-0.907435\pi$
$163$	−1.52676	−	10.6188i	−0.119585	−	0.831732i	0.838429	−	0.545011i	$-0.183474\pi$
$164$	−10.5001	−	4.79521i	−0.819916	−	0.374443i
$165$	−10.8122	+	3.17476i	−0.841732	+	0.247155i
$166$	−2.98441	+	3.44419i	−0.231635	+	0.267321i
$167$	−3.30370	+	11.2514i	−0.255648	+	0.870658i	0.727229	+	0.686395i	$0.240808\pi$
$167$	−3.30370	+	11.2514i	−0.255648	+	0.870658i	−0.982877	+	0.184263i	$0.941010\pi$
$168$	−1.24906	−	2.33235i	−0.0963671	−	0.179945i
$169$	−2.56956	−	5.62655i	−0.197658	−	0.432811i
$170$	8.86892	+	10.2353i	0.680215	+	0.785010i
$171$	0.632529	+	0.406502i	0.0483707	+	0.0310860i
$172$	8.82588	+	1.26897i	0.672967	+	0.0967580i
$173$	7.56161	+	1.08719i	0.574898	+	0.0826579i	0.423631	−	0.905835i	$-0.360755\pi$
$173$	7.56161	+	1.08719i	0.574898	+	0.0826579i	0.151268	+	0.988493i	$0.451664\pi$
$174$	−4.52747	+	7.04488i	−0.343227	+	0.534071i
$175$	−1.60801	−	2.18484i	−0.121554	−	0.165158i
$176$	−5.14150	+	2.34804i	−0.387555	+	0.176990i
$177$	7.85779	−	5.04989i	0.590627	−	0.379573i
$178$	6.28193	+	1.84454i	0.470850	+	0.138254i
$179$	−12.6908	+	14.6459i	−0.948553	+	1.09469i	0.0468488	+	0.998902i	$0.485082\pi$
$179$	−12.6908	+	14.6459i	−0.948553	+	1.09469i	−0.995402	+	0.0957866i	$0.969463\pi$
$180$	−1.91290	+	0.561678i	−0.142579	+	0.0418650i
$181$	−1.79138	+	3.92257i	−0.133152	+	0.291562i	−0.964450	−	0.264264i	$-0.914871\pi$
$181$	−1.79138	+	3.92257i	−0.133152	+	0.291562i	0.831298	+	0.555826i	$0.187598\pi$
$182$	−11.5655	+	0.732766i	−0.857295	+	0.0543162i
$183$			6.89167i			0.509447i
$184$	−0.296014	−	4.78669i	−0.0218224	−	0.352879i
$185$		−	4.76827i		−	0.350570i
$186$	−1.05424	−	7.33237i	−0.0773003	−	0.537635i
$187$	34.9270	+	15.9506i	2.55411	+	1.16642i
$188$	2.51408	+	8.56217i	0.183358	+	0.624460i
$189$	−1.85556	−	1.88597i	−0.134972	−	0.137184i
$190$	−1.43829	−	0.422319i	−0.104344	−	0.0306382i
$191$	−11.8527	−	18.4432i	−0.857635	−	1.33451i	−0.941147	−	0.337999i	$-0.890250\pi$
$191$	−11.8527	−	18.4432i	−0.857635	−	1.33451i	0.0835119	−	0.996507i	$-0.473386\pi$
$192$	−0.909632	+	0.415415i	−0.0656470	+	0.0299800i
$193$	−7.87126	−	9.08392i	−0.566586	−	0.653875i	0.398080	−	0.917351i	$-0.369677\pi$
$193$	−7.87126	−	9.08392i	−0.566586	−	0.653875i	−0.964666	+	0.263476i	$0.915131\pi$
$194$	3.03158	+	1.94828i	0.217654	+	0.139878i
$195$	−1.24276	+	8.64358i	−0.0889959	+	0.618980i
$196$	−2.08103	+	6.68351i	−0.148645	+	0.477394i
$197$	11.3599	+	7.30059i	0.809363	+	0.520146i	0.878659	−	0.477450i	$-0.158439\pi$
$197$	11.3599	+	7.30059i	0.809363	+	0.520146i	−0.0692962	+	0.997596i	$0.522075\pi$
$198$	−4.27171	+	3.70146i	−0.303577	+	0.263051i
$199$	−3.32999	−	7.29166i	−0.236057	−	0.516892i	0.754116	−	0.656741i	$-0.228066\pi$
$199$	−3.32999	−	7.29166i	−0.236057	−	0.516892i	−0.990173	+	0.139849i	$0.955338\pi$
$200$	−0.862568	+	0.554339i	−0.0609928	+	0.0391977i
$201$	−6.16424	−	1.80998i	−0.434792	−	0.127666i
$202$	2.44827	+	2.12144i	0.172260	+	0.149264i
$203$	21.6874	−	4.53355i	1.52216	−	0.318193i
$204$	6.17927	+	2.82198i	0.432635	+	0.197578i
$205$	22.7789	−	3.27511i	1.59095	−	0.228744i
$206$	3.68307			0.256611
$207$	−1.63259	−	4.50940i	−0.113473	−	0.313425i
$208$			4.38013i			0.303707i
$209$	−4.20663	+	0.604822i	−0.290978	+	0.0418364i
$210$	4.60881	+	2.56544i	0.318038	+	0.177032i
$211$	6.99203	−	2.05305i	0.481351	−	0.141337i	−0.0320498	−	0.999486i	$-0.510204\pi$
$211$	6.99203	−	2.05305i	0.481351	−	0.141337i	0.513401	+	0.858149i	$0.328385\pi$
$212$	−4.06812	−	3.52504i	−0.279400	−	0.242101i
$213$	0.763375	−	2.59982i	0.0523056	−	0.178136i
$214$	−1.62087	−	2.52213i	−0.110801	−	0.172409i
$215$	−16.1703	+	7.38471i	−1.10280	+	0.503633i
$216$	−0.755750	+	0.654861i	−0.0514222	+	0.0445576i
$217$	−11.8724	+	15.5939i	−0.805953	+	1.05858i
$218$	−1.69341	−	0.243475i	−0.114692	−	0.0164902i
$219$	−0.484850	+	3.37220i	−0.0327631	+	0.227872i
$220$	6.09232	−	9.47984i	0.410744	−	0.639130i
$221$	22.4872	−	19.4853i	1.51266	−	1.31072i
$222$	−0.993557	−	2.17559i	−0.0666832	−	0.146016i
$223$	−7.29450	−	11.3505i	−0.488476	−	0.760083i	0.506279	−	0.862370i	$-0.331021\pi$
$223$	−7.29450	−	11.3505i	−0.488476	−	0.760083i	−0.994755	+	0.102286i	$0.967384\pi$
$224$	2.47134	+	0.944710i	0.165123	+	0.0631211i
$225$	−0.671453	+	0.774898i	−0.0447635	+	0.0516598i
$226$	0.437104	+	1.48864i	0.0290757	+	0.0990228i
$227$	−4.39638	+	9.62674i	−0.291798	+	0.638949i	−0.997584	−	0.0694766i	$-0.977867\pi$
$227$	−4.39638	+	9.62674i	−0.291798	+	0.638949i	0.705785	+	0.708426i	$0.250594\pi$
$228$	−0.744235	+	0.107005i	−0.0492882	+	0.00708657i
$229$	11.3543			0.750312			0.375156	−	0.926962i	$-0.377589\pi$
$229$	11.3543			0.750312			0.375156	+	0.926962i	$0.377589\pi$
$230$	5.65580	+	7.70903i	0.372933	+	0.508318i
$231$	14.9073	+	1.18803i	0.980826	+	0.0781666i
$232$	−1.19178	−	8.28903i	−0.0782444	−	0.544201i
$233$	5.70870	−	12.5003i	0.373989	−	0.818922i	−0.625269	−	0.780409i	$-0.715011\pi$
$233$	5.70870	−	12.5003i	0.373989	−	0.818922i	0.999258	−	0.0385128i	$-0.0122620\pi$
$234$	1.23402	+	4.20270i	0.0806707	+	0.274739i
$235$	−13.4453	−	11.6504i	−0.877074	−	0.759989i
$236$	−2.63154	+	8.96221i	−0.171299	+	0.583390i
$237$	−14.5414	+	9.34521i	−0.944567	+	0.607036i
$238$	−6.14386	−	16.8903i	−0.398247	−	1.09483i
$239$	−0.227837	−	0.262937i	−0.0147375	−	0.0170080i	0.748333	−	0.663323i	$-0.230855\pi$
$239$	−0.227837	−	0.262937i	−0.0147375	−	0.0170080i	−0.763070	+	0.646315i	$0.776309\pi$
$240$	1.07785	−	1.67717i	0.0695750	−	0.108261i
$241$	2.14494	−	14.9184i	0.138168	−	0.960978i	−0.796293	−	0.604912i	$-0.793208\pi$
$241$	2.14494	−	14.9184i	0.138168	−	0.960978i	0.934461	−	0.356067i	$-0.115882\pi$
$242$	2.98125	−	20.7351i	0.191642	−	1.33290i
$243$	−0.540641	+	0.841254i	−0.0346821	+	0.0539664i
$244$	−4.51308	−	5.20837i	−0.288920	−	0.333432i
$245$	−3.71360	−	13.4524i	−0.237253	−	0.859444i
$246$	9.71075	−	6.24072i	0.619135	−	0.397894i
$247$	−0.927849	+	3.15996i	−0.0590376	+	0.201064i
$248$	5.59842	+	4.85106i	0.355500	+	0.308042i
$249$	−1.28394	−	4.37271i	−0.0813667	−	0.277110i
$250$	4.99015	−	10.9269i	0.315605	−	0.691078i
$251$	3.24222	+	22.5501i	0.204647	+	1.42335i	0.790266	+	0.612764i	$0.209943\pi$
$251$	3.24222	+	22.5501i	0.204647	+	1.42335i	−0.585619	+	0.810587i	$0.699148\pi$
$252$	2.63739	+	0.210186i	0.166140	+	0.0132405i
$253$	23.6653	+	13.2199i	1.48782	+	0.831126i
$254$	−10.6318			−0.667098
$255$	−13.4054	+	1.92740i	−0.839476	+	0.120698i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−8.21357	−	27.9728i	−0.512348	−	1.74490i	−0.655498	−	0.755197i	$-0.727541\pi$
$257$	−8.21357	−	27.9728i	−0.512348	−	1.74490i	0.143149	−	0.989701i	$-0.454277\pi$
$258$	−5.83916	+	6.73874i	−0.363530	+	0.419536i
$259$	−2.25948	+	5.91076i	−0.140398	+	0.367277i
$260$	−4.72113	−	7.34622i	−0.292792	−	0.455593i
$261$	−3.47880	−	7.61750i	−0.215332	−	0.471512i
$262$	3.40817	−	2.95320i	0.210558	−	0.182449i
$263$	13.6196	−	21.1926i	0.839823	−	1.30679i	−0.109977	−	0.993934i	$-0.535078\pi$
$263$	13.6196	−	21.1926i	0.839823	−	1.30679i	0.949800	−	0.312856i	$-0.101286\pi$
$264$	0.804403	−	5.59475i	0.0495076	−	0.344333i
$265$	10.6224	+	1.52727i	0.652529	+	0.0938195i
$266$	1.58278	+	1.20505i	0.0970467	+	0.0738865i
$267$	−4.94799	+	4.28746i	−0.302812	+	0.262388i
$268$	5.84391	−	2.66882i	0.356974	−	0.163024i
$269$	−14.7559	−	22.9606i	−0.899681	−	1.39993i	−0.916483	−	0.400072i	$-0.868985\pi$
$269$	−14.7559	−	22.9606i	−0.899681	−	1.39993i	0.0168023	−	0.999859i	$-0.494651\pi$
$270$	0.561678	−	1.91290i	0.0341826	−	0.116415i
$271$	−22.1386	−	19.1832i	−1.34482	−	1.16529i	−0.971350	−	0.237653i	$-0.923622\pi$
$271$	−22.1386	−	19.1832i	−1.34482	−	1.16529i	−0.373471	−	0.927642i	$-0.621833\pi$
$272$	−6.51798	+	1.91385i	−0.395211	+	0.116044i
$273$	5.63636	−	10.1257i	0.341128	−	0.612836i
$274$	−6.56848	+	0.944405i	−0.396816	+	0.0570536i
$275$		−	5.79549i		−	0.349481i
$276$	4.18685	+	2.33886i	0.252019	+	0.140783i
$277$	−26.5187			−1.59336			−0.796678	−	0.604404i	$-0.793411\pi$
$277$	−26.5187			−1.59336			−0.796678	+	0.604404i	$0.793411\pi$
$278$	−0.318177	+	0.0457469i	−0.0190830	+	0.00274372i
$279$	6.73834	+	3.07730i	0.403414	+	0.184233i
$280$	−5.16312	+	1.07930i	−0.308555	+	0.0645004i
$281$	16.4393	+	14.2447i	0.980686	+	0.849770i	0.988656	−	0.150199i	$-0.0479913\pi$
$281$	16.4393	+	14.2447i	0.980686	+	0.849770i	−0.00796935	+	0.999968i	$0.502537\pi$
$282$	−8.56217	−	2.51408i	−0.509870	−	0.149711i
$283$	1.68007	−	1.07972i	0.0998698	−	0.0641824i	−0.489753	−	0.871861i	$-0.662913\pi$
$283$	1.68007	−	1.07972i	0.0998698	−	0.0641824i	0.589622	+	0.807679i	$0.299277\pi$
$284$	1.12560	+	2.46471i	0.0667919	+	0.146254i
$285$	1.13287	−	0.981641i	0.0671057	−	0.0581474i
$286$	−20.8275	−	13.3850i	−1.23156	−	0.791473i
$287$	−29.7887	−	6.73413i	−1.75837	−	0.397503i
$288$	0.142315	−	0.989821i	0.00838598	−	0.0583258i
$289$	24.5200	+	15.7580i	1.44235	+	0.926942i
$290$	10.9332	+	12.6175i	0.642018	+	0.740928i
$291$	−3.27799	+	1.49701i	−0.192159	+	0.0877561i
$292$	−1.84190	−	2.86605i	−0.107789	−	0.167723i
$293$	−18.7140	−	5.49492i	−1.09328	−	0.321017i	−0.315102	−	0.949058i	$-0.602039\pi$
$293$	−18.7140	−	5.49492i	−1.09328	−	0.321017i	−0.778180	+	0.628041i	$0.783857\pi$
$294$	−4.49744	−	5.36405i	−0.262296	−	0.312838i
$295$	−5.24639	−	17.8676i	−0.305457	−	1.04029i
$296$	2.17559	+	0.993557i	0.126453	+	0.0577494i
$297$	−0.804403	−	5.59475i	−0.0466762	−	0.324640i
$298$			17.5655i			1.01754i
$299$	16.9370	−	12.4260i	0.979492	−	0.718614i
$300$		−	1.02534i		−	0.0591978i
$301$	23.5440	−	1.49169i	1.35705	−	0.0859798i
$302$	4.19341	−	9.18230i	0.241304	−	0.528382i
$303$	−3.10831	+	0.912682i	−0.178568	+	0.0524322i
$304$	0.492382	−	0.568239i	0.0282401	−	0.0325908i
$305$	13.1831	+	3.87090i	0.754860	+	0.221647i
$306$	−5.71476	+	3.67266i	−0.326691	+	0.209952i
$307$	−13.5705	+	6.19744i	−0.774510	+	0.353707i	−0.763144	−	0.646229i	$-0.776345\pi$
$307$	−13.5705	+	6.19744i	−0.774510	+	0.353707i	−0.0113660	+	0.999935i	$0.503618\pi$
$308$	−12.0442	+	8.86433i	−0.686279	+	0.505092i
$309$	−1.99122	+	3.09839i	−0.113276	+	0.176261i
$310$	−14.6182	−	2.10178i	−0.830259	−	0.119373i
$311$	2.61272	+	0.375653i	0.148154	+	0.0213013i	0.215993	−	0.976395i	$-0.430701\pi$
$311$	2.61272	+	0.375653i	0.148154	+	0.0213013i	−0.0678388	+	0.997696i	$0.521610\pi$
$312$	−3.68480	−	2.36808i	−0.208611	−	0.134066i
$313$	−3.10213	−	3.58005i	−0.175343	−	0.202356i	0.661275	−	0.750144i	$-0.270016\pi$
$313$	−3.10213	−	3.58005i	−0.175343	−	0.202356i	−0.836618	+	0.547787i	$0.815470\pi$
$314$	3.97961	+	8.71413i	0.224582	+	0.491767i
$315$	−4.64990	+	2.49020i	−0.261992	+	0.140307i
$316$	4.86987	−	16.5852i	0.273951	−	0.932993i
$317$	−12.4747	+	14.3966i	−0.700648	+	0.808591i	−0.988840	−	0.148982i	$-0.952400\pi$
$317$	−12.4747	+	14.3966i	−0.700648	+	0.808591i	0.288192	+	0.957573i	$0.406946\pi$
$318$	5.16485	−	1.51654i	0.289630	−	0.0850431i
$319$	43.0563	+	19.6631i	2.41069	+	1.10092i
$320$	0.283727	+	1.97336i	0.0158608	+	0.110314i
$321$	2.99806			0.167335
$322$	−3.35796	−	12.2362i	−0.187132	−	0.681896i
$323$	−5.10769			−0.284200
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	−4.08525	−	1.86567i	−0.226609	−	0.103489i
$326$	−10.2935	+	3.02244i	−0.570103	+	0.167397i
$327$	1.12035	−	1.29295i	0.0619555	−	0.0715005i
$328$	−3.25209	+	11.0756i	−0.179567	+	0.611548i
$329$	11.1462	+	20.8130i	0.614508	+	1.14746i
$330$	4.68119	+	10.2504i	0.257691	+	0.564264i
$331$	−10.9301	−	12.6140i	−0.600774	−	0.693330i	0.371164	−	0.928567i	$-0.378959\pi$
$331$	−10.9301	−	12.6140i	−0.600774	−	0.693330i	−0.971938	+	0.235237i	$0.924413\pi$
$332$	3.83386	+	2.46387i	0.210410	+	0.135223i
$333$	2.36738	+	0.340378i	0.129732	+	0.0186526i
$334$	11.6070	+	1.66884i	0.635108	+	0.0913147i
$335$	−6.92463	+	10.7749i	−0.378333	+	0.588698i
$336$	−2.13085	+	1.56827i	−0.116247	+	0.0855564i
$337$	12.3146	−	5.62390i	0.670820	−	0.306353i	−0.0507331	−	0.998712i	$-0.516156\pi$
$337$	12.3146	−	5.62390i	0.670820	−	0.306353i	0.721553	+	0.692359i	$0.243428\pi$
$338$	−5.20359	+	3.34414i	−0.283038	+	0.181897i
$339$	−1.48864	−	0.437104i	−0.0808518	−	0.0237402i
$340$	8.86892	−	10.2353i	0.480984	−	0.555086i
$341$	−40.1747	+	11.7964i	−2.17558	+	0.638809i
$342$	0.312346	−	0.683942i	0.0168897	−	0.0369833i
$343$	−1.77116	+	18.4354i	−0.0956336	+	0.995417i
$344$		−	8.91664i		−	0.480753i
$345$	−9.54301	+	0.590150i	−0.513778	+	0.0317726i
$346$		−	7.63936i		−	0.410695i
$347$	−1.82270	−	12.6771i	−0.0978475	−	0.680544i	−0.978419	−	0.206631i	$-0.933750\pi$
$347$	−1.82270	−	12.6771i	−0.0978475	−	0.680544i	0.880571	−	0.473913i	$-0.157159\pi$
$348$	7.61750	+	3.47880i	0.408341	+	0.186483i
$349$	6.32581	+	21.5437i	0.338613	+	1.15321i	0.936218	+	0.351420i	$0.114301\pi$
$349$	6.32581	+	21.5437i	0.338613	+	1.15321i	−0.597605	+	0.801791i	$0.703881\pi$
$350$	−1.93375	+	1.90258i	−0.103364	+	0.101697i
$351$	−4.20270	−	1.23402i	−0.224324	−	0.0658674i
$352$	3.05585	+	4.75500i	0.162878	+	0.253442i
$353$	−1.98431	+	0.906206i	−0.105614	+	0.0482325i	−0.467522	−	0.883982i	$-0.654853\pi$
$353$	−1.98431	+	0.906206i	−0.105614	+	0.0482325i	0.361907	+	0.932214i	$0.382126\pi$
$354$	−6.11677	−	7.05913i	−0.325103	−	0.375189i
$355$	−4.54441	−	2.92052i	−0.241192	−	0.155005i
$356$	0.931754	−	6.48049i	0.0493828	−	0.343465i
$357$	17.5306	+	3.96303i	0.927819	+	0.209746i
$358$	16.3029	+	10.4773i	0.861637	+	0.553741i
$359$	−23.7178	+	20.5516i	−1.25178	+	1.08467i	−0.258856	+	0.965916i	$0.583345\pi$
$359$	−23.7178	+	20.5516i	−1.25178	+	1.08467i	−0.992923	+	0.118757i	$0.962109\pi$
$360$	0.828195	+	1.81349i	0.0436497	+	0.0955795i
$361$	−15.5082	+	9.96653i	−0.816222	+	0.524554i
$362$	4.13758	+	1.21490i	0.217466	+	0.0638539i
$363$	15.8317	+	13.7182i	0.830946	+	0.720019i
$364$	2.37126	+	11.3435i	0.124288	+	0.594563i
$365$	6.17835	+	2.82156i	0.323390	+	0.147687i
$366$	6.82152	−	0.980786i	0.356567	−	0.0512665i
$367$	0.544838			0.0284403			0.0142201	−	0.999899i	$-0.495473\pi$
$367$	0.544838			0.0284403			0.0142201	+	0.999899i	$0.495473\pi$
$368$	−4.69584	+	0.974218i	−0.244788	+	0.0507846i
$369$			11.5432i			0.600914i
$370$	−4.71974	+	0.678596i	−0.245367	+	0.0352785i
$371$	−12.4438	−	6.92672i	−0.646052	−	0.359617i
$372$	−7.10770	+	2.08701i	−0.368517	+	0.108206i
$373$	3.78615	+	3.28072i	0.196039	+	0.169869i	0.747349	−	0.664432i	$-0.231326\pi$
$373$	3.78615	+	3.28072i	0.196039	+	0.169869i	−0.551310	+	0.834301i	$0.685872\pi$
$374$	10.8176	−	36.8415i	0.559366	−	1.90503i
$375$	6.49442	+	10.1055i	0.335370	+	0.521846i
$376$	8.11723	−	3.70701i	0.418614	−	0.191175i
$377$	27.7212	−	24.0205i	1.42771	−	1.23712i
$378$	−1.60270	+	2.10508i	−0.0824340	+	0.108274i
$379$	7.31040	+	1.05108i	0.375510	+	0.0539902i	0.327486	−	0.944856i	$-0.393799\pi$
$379$	7.31040	+	1.05108i	0.375510	+	0.0539902i	0.0480238	+	0.998846i	$0.484708\pi$
$380$	−0.213331	+	1.48375i	−0.0109436	+	0.0761147i
$381$	5.74798	−	8.94403i	0.294478	−	0.458217i
$382$	−16.5687	+	14.3568i	−0.847728	+	0.734560i
$383$	12.7245	+	27.8628i	0.650193	+	1.42372i	0.891385	+	0.453247i	$0.149734\pi$
$383$	12.7245	+	27.8628i	0.650193	+	1.42372i	−0.241192	+	0.970477i	$0.577538\pi$
$384$	0.540641	+	0.841254i	0.0275895	+	0.0429300i
$385$	10.6457	−	27.8488i	0.542553	−	1.41931i
$386$	−7.87126	+	9.08392i	−0.400637	+	0.462360i
$387$	−2.51211	−	8.55545i	−0.127698	−	0.434898i
$388$	1.49701	−	3.27799i	0.0759990	−	0.166415i
$389$	15.7904	−	2.27032i	0.800606	−	0.115110i	0.270146	−	0.962819i	$-0.412928\pi$
$389$	15.7904	−	2.27032i	0.800606	−	0.115110i	0.530461	+	0.847710i	$0.322019\pi$
$390$	8.73247			0.442186
$391$	25.8913	+	19.7742i	1.30938	+	1.00002i
$392$	6.91164	+	1.10868i	0.349091	+	0.0559970i
$393$	0.641791	+	4.46375i	0.0323741	+	0.225167i
$394$	5.60959	−	12.2833i	0.282607	−	0.618824i
$395$	9.70884	+	33.0653i	0.488505	+	1.66369i
$396$	4.27171	+	3.70146i	0.214661	+	0.186005i
$397$	0.569560	−	1.93974i	0.0285854	−	0.0973529i	−0.943965	−	0.330046i	$-0.892936\pi$
$397$	0.569560	−	1.93974i	0.0285854	−	0.0973529i	0.972550	+	0.232693i	$0.0747538\pi$
$398$	−6.74353	+	4.33381i	−0.338023	+	0.217234i
$399$	−1.86947	+	0.680023i	−0.0935906	+	0.0340437i
$400$	0.671453	+	0.774898i	0.0335726	+	0.0387449i
$401$	−7.74744	+	12.0553i	−0.386889	+	0.602011i	−0.979004	−	0.203843i	$-0.934657\pi$
$401$	−7.74744	+	12.0553i	−0.386889	+	0.602011i	0.592115	+	0.805854i	$0.298293\pi$
$402$	−0.914298	+	6.35909i	−0.0456011	+	0.317162i
$403$	−4.61768	+	32.1167i	−0.230023	+	1.59985i
$404$	1.75142	−	2.72527i	0.0871366	−	0.135587i
$405$	1.30557	+	1.50670i	0.0648741	+	0.0748688i
$406$	−7.57385	−	20.8215i	−0.375884	−	1.03335i
$407$	−11.3726	+	7.30875i	−0.563721	+	0.362281i
$408$	1.91385	−	6.51798i	0.0947498	−	0.322688i
$409$	5.02564	+	4.35474i	0.248502	+	0.215328i	0.770201	−	0.637802i	$-0.220156\pi$
$409$	5.02564	+	4.35474i	0.248502	+	0.215328i	−0.521699	+	0.853130i	$0.674701\pi$
$410$	−6.48355	−	22.0809i	−0.320200	−	1.09050i
$411$	2.75670	−	6.03634i	0.135978	−	0.297751i
$412$	−0.524155	−	3.64558i	−0.0258233	−	0.179605i
$413$	−1.96325	+	24.6347i	−0.0966054	+	1.21220i
$414$	−4.23116	+	2.25773i	−0.207950	+	0.110961i
$415$	−9.08572			−0.446001
$416$	4.33554	−	0.623357i	0.212568	−	0.0305626i
$417$	0.133535	−	0.292400i	0.00653922	−	0.0143189i
$418$	1.19733	+	4.07773i	0.0585634	+	0.199449i
$419$	17.7800	−	20.5193i	0.868612	−	1.00243i	−0.131326	−	0.991339i	$-0.541924\pi$
$419$	17.7800	−	20.5193i	0.868612	−	1.00243i	0.999938	−	0.0110928i	$-0.00353102\pi$
$420$	1.88343	−	4.92700i	0.0919018	−	0.240413i
$421$	−6.05626	−	9.42373i	−0.295164	−	0.459284i	0.661721	−	0.749750i	$-0.269826\pi$
$421$	−6.05626	−	9.42373i	−0.295164	−	0.459284i	−0.956885	+	0.290465i	$0.906190\pi$
$422$	−3.02722	−	6.62868i	−0.147363	−	0.322679i
$423$	6.74404	−	5.84374i	0.327906	−	0.284132i
$424$	−2.91021	+	4.52838i	−0.141332	+	0.219917i
$425$	0.991261	−	6.89437i	0.0480832	−	0.334426i
$426$	−2.68199	−	0.385612i	−0.129943	−	0.0186830i
$427$	−14.5075	−	11.0453i	−0.702067	−	0.534518i
$428$	−2.26578	+	1.96331i	−0.109521	+	0.0949002i
$429$	22.5204	−	10.2847i	1.08730	−	0.496551i
$430$	9.61081	+	14.9547i	0.463475	+	0.721180i
$431$	10.5237	−	35.8406i	0.506911	−	1.72638i	−0.165508	−	0.986209i	$-0.552926\pi$
$431$	10.5237	−	35.8406i	0.506911	−	1.72638i	0.672418	−	0.740171i	$-0.265256\pi$
$432$	0.755750	+	0.654861i	0.0363610	+	0.0315070i
$433$	0.717927	−	0.210803i	0.0345014	−	0.0101305i	−0.264436	−	0.964403i	$-0.585186\pi$
$433$	0.717927	−	0.210803i	0.0345014	−	0.0101305i	0.298938	+	0.954273i	$0.403368\pi$
$434$	17.1248	+	9.53233i	0.822018	+	0.457567i
$435$	−16.5255	+	2.37600i	−0.792336	+	0.113921i
$436$			1.71082i			0.0819335i
$437$	−3.59410	−	0.291895i	−0.171929	−	0.0139632i
$438$	3.40688			0.162787
$439$	−13.0120	+	1.87085i	−0.621031	+	0.0892908i	−0.445646	−	0.895209i	$-0.647026\pi$
$439$	−13.0120	+	1.87085i	−0.621031	+	0.0892908i	−0.175385	+	0.984500i	$0.556117\pi$
$440$	−10.2504	−	4.68119i	−0.488667	−	0.223167i
$441$	6.94403	−	0.883461i	0.330668	−	0.0420696i
$442$	−22.4872	−	19.4853i	−1.06961	−	0.926821i
$443$	30.9200	+	9.07893i	1.46905	+	0.431353i	0.915791	−	0.401654i	$-0.131565\pi$
$443$	30.9200	+	9.07893i	1.46905	+	0.431353i	0.553262	+	0.833007i	$0.313383\pi$
$444$	−2.01205	+	1.29306i	−0.0954874	+	0.0613660i
$445$	5.42230	+	11.8732i	0.257042	+	0.562842i
$446$	−10.1968	+	8.83559i	−0.482833	+	0.418377i
$447$	−14.7770	−	9.49663i	−0.698930	−	0.449175i
$448$	0.583386	−	2.58063i	0.0275624	−	0.121923i
$449$	−1.06903	+	7.43528i	−0.0504507	+	0.350892i	0.948923	+	0.315508i	$0.102175\pi$
$449$	−1.06903	+	7.43528i	−0.0504507	+	0.350892i	−0.999374	+	0.0353848i	$0.988734\pi$
$450$	0.862568	+	0.554339i	0.0406618	+	0.0261318i
$451$	−42.7266	−	49.3091i	−2.01192	−	2.32188i
$452$	1.41128	−	0.644510i	0.0663810	−	0.0303152i
$453$	5.45751	+	8.49205i	0.256416	+	0.398991i
$454$	10.1544	+	2.98161i	0.476571	+	0.139934i
$455$	−16.2036	−	16.4692i	−0.759639	−	0.772087i
$456$	0.211831	+	0.721432i	0.00991992	+	0.0337841i
$457$	3.87620	+	1.77020i	0.181321	+	0.0828066i	0.504007	−	0.863699i	$-0.331859\pi$
$457$	3.87620	+	1.77020i	0.181321	+	0.0828066i	−0.322686	+	0.946506i	$0.604586\pi$
$458$	−1.61588	−	11.2387i	−0.0755052	−	0.525150i
$459$		−	6.79315i		−	0.317077i
$460$	6.82566	−	6.69535i	0.318248	−	0.312172i
$461$			35.2401i			1.64129i	0.571436	+	0.820646i	$0.306386\pi$
$461$			35.2401i			1.64129i	−0.571436	+	0.820646i	$0.693614\pi$
$462$	−0.945588	−	14.9246i	−0.0439928	−	0.694355i
$463$	−15.6832	+	34.3413i	−0.728859	+	1.59598i	0.0721989	+	0.997390i	$0.476998\pi$
$463$	−15.6832	+	34.3413i	−0.728859	+	1.59598i	−0.801058	+	0.598587i	$0.795729\pi$
$464$	−8.03505	+	2.35930i	−0.373018	+	0.109528i
$465$	9.67133	−	11.1613i	0.448497	−	0.517594i
$466$	−13.1855	−	3.87161i	−0.610807	−	0.179349i
$467$	−16.0445	+	10.3112i	−0.742450	+	0.477144i	−0.856381	−	0.516345i	$-0.827292\pi$
$467$	−16.0445	+	10.3112i	−0.742450	+	0.477144i	0.113931	+	0.993489i	$0.463656\pi$
$468$	3.98430	−	1.81957i	0.184175	−	0.0841097i
$469$	13.6896	−	10.0753i	0.632126	−	0.465236i
$470$	−9.61836	+	14.9665i	−0.443662	+	0.690351i
$471$	−9.48233	−	1.36335i	−0.436923	−	0.0628200i
$472$	9.24549	+	1.32930i	0.425558	+	0.0611861i
$473$	42.3986	+	27.2479i	1.94949	+	1.25286i
$474$	11.3195	+	13.0635i	0.519924	+	0.600024i
$475$	0.320259	+	0.701270i	0.0146945	+	0.0321765i
$476$	−15.8440	+	8.48506i	−0.726208	+	0.388912i
$477$	−1.51654	+	5.16485i	−0.0694374	+	0.236482i
$478$	−0.227837	+	0.262937i	−0.0104210	+	0.0120265i
$479$	−20.4435	+	6.00277i	−0.934089	+	0.274273i	−0.713148	−	0.701014i	$-0.752731\pi$
$479$	−20.4435	+	6.00277i	−0.934089	+	0.274273i	−0.220942	+	0.975287i	$0.570913\pi$
$480$	−1.81349	−	0.828195i	−0.0827743	−	0.0378017i
$481$	1.49090	+	10.3694i	0.0679791	+	0.472805i
$482$	−15.0718			−0.686502
$483$	12.1092	+	3.79048i	0.550987	+	0.172473i
$484$	−20.9483			−0.952194
$485$	1.02245	+	7.11129i	0.0464270	+	0.322907i
$486$	0.909632	+	0.415415i	0.0412617	+	0.0188436i
$487$	−38.4126	+	11.2790i	−1.74064	+	0.511098i	−0.988929	−	0.148392i	$-0.952590\pi$
$487$	−38.4126	+	11.2790i	−1.74064	+	0.511098i	−0.751713	+	0.659491i	$0.770772\pi$
$488$	−4.51308	+	5.20837i	−0.204298	+	0.235772i
$489$	3.02244	−	10.2935i	0.136679	−	0.465487i
$490$	−12.7870	+	5.59028i	−0.577658	+	0.252543i
$491$	16.7438	+	36.6637i	0.755635	+	1.65461i	0.755967	+	0.654610i	$0.227167\pi$
$491$	16.7438	+	36.6637i	0.755635	+	1.65461i	−0.000331542		1.00000i	$0.500106\pi$
$492$	−7.55918	−	8.72376i	−0.340794	−	0.393297i
$493$	47.8570	+	30.7558i	2.15537	+	1.38517i
$494$	3.25985	+	0.468695i	0.146667	+	0.0210876i
$495$	−11.1540	−	1.60370i	−0.501335	−	0.0720811i
$496$	4.00494	−	6.23181i	0.179827	−	0.279817i
$497$	4.24935	+	5.77369i	0.190610	+	0.258985i
$498$	−4.14548	+	1.89318i	−0.185764	+	0.0848354i
$499$	−1.16810	+	0.750690i	−0.0522912	+	0.0336055i	−0.566525	−	0.824044i	$-0.691713\pi$
$499$	−1.16810	+	0.750690i	−0.0522912	+	0.0336055i	0.514234	+	0.857650i	$0.328076\pi$
$500$	−11.5259	−	3.38430i	−0.515452	−	0.151350i
$501$	−7.67914	+	8.86220i	−0.343079	+	0.395934i
$502$	21.8592	−	6.41843i	0.975623	−	0.286469i
$503$	−7.44550	+	16.3034i	−0.331978	+	0.726931i	−0.999850	−	0.0173458i	$-0.994478\pi$
$503$	−7.44550	+	16.3034i	−0.331978	+	0.726931i	0.667871	+	0.744277i	$0.267206\pi$
$504$	−0.167293	−	2.64046i	−0.00745183	−	0.117615i
$505$			6.45851i			0.287400i
$506$	9.71739	−	25.3058i	0.431991	−	1.12498i
$507$		−	6.18552i		−	0.274709i
$508$	1.51306	+	10.5236i	0.0671312	+	0.466908i
$509$	−25.8685	−	11.8137i	−1.14660	−	0.523635i	−0.250777	−	0.968045i	$-0.580686\pi$
$509$	−25.8685	−	11.8137i	−1.14660	−	0.523635i	−0.895824	+	0.444410i	$0.853413\pi$
$510$	3.81556	+	12.9946i	0.168956	+	0.575411i
$511$	−6.32168	−	6.42528i	−0.279655	−	0.284237i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	0.406502	+	0.632529i	0.0179475	+	0.0279268i
$514$	−26.5192	+	12.1109i	−1.16971	+	0.534190i
$515$	4.80849	+	5.54930i	0.211887	+	0.244531i
$516$	7.50115	+	4.82070i	0.330220	+	0.212219i
$517$	−7.17821	+	49.9255i	−0.315697	+	2.19572i
$518$	6.17216	+	1.39530i	0.271189	+	0.0613059i
$519$	6.42664	+	4.13015i	0.282098	+	0.181294i
$520$	−6.59956	+	5.71855i	−0.289410	+	0.250775i
$521$	8.94027	+	19.5765i	0.391680	+	0.857661i	0.998047	+	0.0624749i	$0.0198993\pi$
$521$	8.94027	+	19.5765i	0.391680	+	0.857661i	−0.606366	+	0.795186i	$0.707373\pi$
$522$	−7.04488	+	4.52747i	−0.308346	+	0.198162i
$523$	−20.3267	−	5.96846i	−0.888825	−	0.260982i	−0.194722	−	0.980858i	$-0.562380\pi$
$523$	−20.3267	−	5.96846i	−0.888825	−	0.260982i	−0.694103	+	0.719876i	$0.744199\pi$
$524$	−3.40817	−	2.95320i	−0.148887	−	0.129011i
$525$	−0.555083	−	2.65539i	−0.0242258	−	0.115891i
$526$	−22.9151	−	10.4650i	−0.999148	−	0.456296i
$527$	−49.8099	+	7.16158i	−2.16975	+	0.311963i
$528$	−5.65228			−0.245984
$529$	17.0887	+	15.3940i	0.742988	+	0.669305i
$530$		−	10.7316i		−	0.466152i
$531$	9.24549	−	1.32930i	0.401220	−	0.0576868i
$532$	0.967532	−	1.73817i	0.0419478	−	0.0753592i
$533$	−48.5126	+	14.2446i	−2.10131	+	0.617001i
$534$	4.94799	+	4.28746i	0.214120	+	0.185536i
$535$	1.68394	−	5.73498i	0.0728032	−	0.247945i
$536$	−3.47333	−	5.40461i	−0.150025	−	0.233444i
$537$	−17.6281	+	8.05047i	−0.760708	+	0.347404i
$538$	−20.6269	+	17.8733i	−0.889289	+	0.770573i
$539$	−26.3928	+	29.4769i	−1.13682	+	1.26966i
$540$	−1.97336	−	0.283727i	−0.0849200	−	0.0122097i
$541$	−2.61040	+	18.1557i	−0.112230	+	0.780574i	0.853513	+	0.521072i	$0.174468\pi$
$541$	−2.61040	+	18.1557i	−0.112230	+	0.780574i	−0.965742	+	0.259502i	$0.916441\pi$
$542$	−15.8373	+	24.6433i	−0.680269	+	1.05852i
$543$	−3.25899	+	2.82393i	−0.139856	+	0.121186i
$544$	2.82198	+	6.17927i	0.120991	+	0.264934i
$545$	−1.84401	−	2.86934i	−0.0789888	−	0.122909i
$546$	−10.8248	−	4.13795i	−0.463258	−	0.177088i
$547$	8.71991	−	10.0633i	0.372837	−	0.430276i	−0.538063	−	0.842905i	$-0.680844\pi$
$547$	8.71991	−	10.0633i	0.372837	−	0.430276i	0.910899	+	0.412628i	$0.135389\pi$
$548$	1.86958	+	6.36722i	0.0798647	+	0.271994i
$549$	−2.86290	+	6.26888i	−0.122186	+	0.267549i
$550$	−5.73650	+	0.824784i	−0.244605	+	0.0351689i
$551$	−6.29652			−0.268241
$552$	1.71920	−	4.47709i	0.0731739	−	0.190558i
$553$	3.63315	−	45.5884i	0.154497	−	1.93862i
$554$	3.77401	+	26.2488i	0.160342	+	1.11520i
$555$	1.98081	−	4.33737i	0.0840808	−	0.184111i
$556$	0.0905626	+	0.308428i	0.00384071	+	0.0130803i
$557$	−25.7160	−	22.2830i	−1.08962	−	0.944163i	−0.0909591	−	0.995855i	$-0.528993\pi$
$557$	−25.7160	−	22.2830i	−1.08962	−	0.944163i	−0.998663	+	0.0516916i	$0.983539\pi$
$558$	2.08701	−	7.10770i	0.0883501	−	0.300893i
$559$	32.8560	−	21.1153i	1.38966	−	0.893081i
$560$	1.80310	+	4.95696i	0.0761949	+	0.209470i
$561$	25.1446	+	29.0184i	1.06160	+	1.22516i
$562$	11.7602	−	18.2992i	0.496074	−	0.771906i
$563$	−1.19638	+	8.32100i	−0.0504214	+	0.350688i	0.948956	+	0.315408i	$0.102141\pi$
$563$	−1.19638	+	8.32100i	−0.0504214	+	0.350688i	−0.999377	+	0.0352801i	$0.988768\pi$
$564$	−1.26997	+	8.83281i	−0.0534752	+	0.371928i
$565$	−1.67227	+	2.60210i	−0.0703530	+	0.109471i
$566$	−1.30782	−	1.50931i	−0.0549720	−	0.0634410i
$567$	−0.904419	−	2.48637i	−0.0379820	−	0.104418i
$568$	2.27944	−	1.46491i	0.0956430	−	0.0614661i
$569$	1.85007	−	6.30076i	0.0775590	−	0.264142i	−0.911580	−	0.411122i	$-0.865137\pi$
$569$	1.85007	−	6.30076i	0.0775590	−	0.264142i	0.989139	+	0.146980i	$0.0469553\pi$
$570$	−1.13287	−	0.981641i	−0.0474509	−	0.0411164i
$571$	−4.40069	−	14.9874i	−0.184163	−	0.627202i	−0.998879	−	0.0473414i	$-0.984925\pi$
$571$	−4.40069	−	14.9874i	−0.184163	−	0.627202i	0.814716	−	0.579861i	$-0.196893\pi$
$572$	−10.2847	+	22.5204i	−0.430026	+	0.941625i
$573$	−3.12004	−	21.7004i	−0.130342	−	0.906546i
$574$	−2.42621	+	30.4439i	−0.101268	+	1.27070i
$575$	1.09151	−	4.79467i	0.0455193	−	0.199951i
$576$	−1.00000			−0.0416667
$577$	40.7399	−	5.85751i	1.69602	−	0.243851i	0.774612	−	0.632437i	$-0.217945\pi$
$577$	40.7399	−	5.85751i	1.69602	−	0.243851i	0.921413	+	0.388586i	$0.127036\pi$
$578$	12.1081	−	26.5130i	0.503629	−	1.10279i
$579$	−3.38636	−	11.5329i	−0.140732	−	0.479290i
$580$	10.9332	−	12.6175i	0.453975	−	0.523915i
$581$	11.2627	+	4.30534i	0.467255	+	0.178616i
$582$	1.94828	+	3.03158i	0.0807586	+	0.125663i
$583$	−12.6393	−	27.6761i	−0.523465	−	1.14623i
$584$	−2.57475	+	2.23103i	−0.106544	+	0.0923208i
$585$	−4.72113	+	7.34622i	−0.195195	+	0.303729i
$586$	−2.77571	+	19.3055i	−0.114664	+	0.797503i
$587$	−6.19017	−	0.890012i	−0.255496	−	0.0367347i	0.0133768	−	0.999911i	$-0.495742\pi$
$587$	−6.19017	−	0.890012i	−0.255496	−	0.0367347i	−0.268872	+	0.963176i	$0.586651\pi$
$588$	−4.66940	+	5.21505i	−0.192563	+	0.215065i
$589$	4.20938	−	3.64745i	0.173445	−	0.150291i
$590$	−16.9391	+	7.73581i	−0.697370	+	0.318478i
$591$	7.30059	+	11.3599i	0.300306	+	0.467286i
$592$	0.673826	−	2.29484i	0.0276941	−	0.0943174i
$593$	−4.37623	−	3.79203i	−0.179710	−	0.155720i	0.560361	−	0.828249i	$-0.310663\pi$
$593$	−4.37623	−	3.79203i	−0.179710	−	0.155720i	−0.740071	+	0.672529i	$0.765208\pi$
$594$	−5.42332	+	1.59243i	−0.222522	+	0.0653383i
$595$	17.4274	−	31.3084i	0.714455	−	1.28352i
$596$	17.3867	−	2.49983i	0.712187	−	0.102397i
$597$		−	8.01605i		−	0.328075i
$598$	−14.7099	−	14.9962i	−0.601532	−	0.613240i
$599$	−20.4023			−0.833616			−0.416808	−	0.908994i	$-0.636851\pi$
$599$	−20.4023			−0.833616			−0.416808	+	0.908994i	$0.636851\pi$
$600$	−1.01490	+	0.145921i	−0.0414331	+	0.00595718i
$601$	−13.7990	−	6.30177i	−0.562871	−	0.257055i	0.113597	−	0.993527i	$-0.463763\pi$
$601$	−13.7990	−	6.30177i	−0.562871	−	0.257055i	−0.676468	+	0.736472i	$0.736490\pi$
$602$	−4.82717	−	23.0921i	−0.196741	−	0.941162i
$603$	−4.85530	−	4.20714i	−0.197723	−	0.171328i
$604$	−9.68562	−	2.84395i	−0.394102	−	0.115719i
$605$	35.1338	−	22.5791i	1.42839	−	0.917972i
$606$	1.34575	+	2.94678i	0.0546674	+	0.119705i
$607$	−14.9240	+	12.9317i	−0.605747	+	0.524883i	−0.902846	−	0.429964i	$-0.858526\pi$
$607$	−14.9240	+	12.9317i	−0.605747	+	0.524883i	0.297099	+	0.954847i	$0.403981\pi$
$608$	−0.632529	−	0.406502i	−0.0256524	−	0.0164858i
$609$	21.6109	+	4.88543i	0.875718	+	0.197968i
$610$	1.95535	−	13.5998i	0.0791698	−	0.550638i
$611$	32.8818	+	21.1319i	1.33026	+	0.854903i
$612$	4.44857	+	5.13392i	0.179823	+	0.207527i
$613$	−11.8467	+	5.41020i	−0.478483	+	0.218516i	−0.640031	−	0.768349i	$-0.721079\pi$
$613$	−11.8467	+	5.41020i	−0.478483	+	0.218516i	0.161548	+	0.986865i	$0.448351\pi$
$614$	8.06565	+	12.5504i	0.325503	+	0.506493i
$615$	22.0809	+	6.48355i	0.890390	+	0.261442i
$616$	10.4882	+	10.6600i	0.422580	+	0.429505i
$617$	−9.42261	−	32.0904i	−0.379340	−	1.29191i	−0.899154	−	0.437633i	$-0.855817\pi$
$617$	−9.42261	−	32.0904i	−0.379340	−	1.29191i	0.519814	−	0.854280i	$-0.326001\pi$
$618$	3.35024	+	1.53000i	0.134766	+	0.0615457i
$619$	−3.85551	−	26.8157i	−0.154966	−	1.07781i	−0.907740	−	0.419533i	$-0.862194\pi$
$619$	−3.85551	−	26.8157i	−0.154966	−	1.07781i	0.752774	−	0.658279i	$-0.228715\pi$
$620$			14.7685i			0.593119i
$621$	0.388216	−	4.78009i	0.0155786	−	0.191819i
$622$		−	2.63959i		−	0.105838i
$623$	−1.09529	−	17.2874i	−0.0438819	−	0.692606i
$624$	−1.81957	+	3.98430i	−0.0728411	+	0.159500i
$625$	18.0596	−	5.30277i	0.722383	−	0.212111i
$626$	−3.10213	+	3.58005i	−0.123986	+	0.143088i
$627$	−4.07773	−	1.19733i	−0.162849	−	0.0478168i
$628$	8.05908	−	5.17925i	0.321592	−	0.206675i
$629$	−14.7791	+	6.74939i	−0.589281	+	0.269116i
$630$	3.12660	+	4.24818i	0.124567	+	0.169251i
$631$	−7.18378	+	11.1782i	−0.285982	+	0.444996i	−0.954287	−	0.298890i	$-0.903383\pi$
$631$	−7.18378	+	11.1782i	−0.285982	+	0.444996i	0.668306	+	0.743887i	$0.267020\pi$
$632$	−17.1095	−	2.45997i	−0.680579	−	0.0978525i
$633$	7.21304	+	1.03708i	0.286693	+	0.0412202i
$634$	16.0254	+	10.2989i	0.636448	+	0.409020i
$635$	−13.8805	−	16.0190i	−0.550831	−	0.635693i
$636$	−2.23613	−	4.89645i	−0.0886685	−	0.194157i
$637$	12.2820	+	28.0935i	0.486631	+	1.11310i
$638$	13.3354	−	45.4164i	0.527955	−	1.79805i
$639$	1.77439	−	2.04776i	0.0701939	−	0.0810080i
$640$	1.91290	−	0.561678i	0.0756140	−	0.0222023i
$641$	−19.2953	−	8.81189i	−0.762120	−	0.348049i	−0.00385305	−	0.999993i	$-0.501226\pi$
$641$	−19.2953	−	8.81189i	−0.762120	−	0.348049i	−0.758267	+	0.651944i	$0.773954\pi$
$642$	−0.426668	−	2.96754i	−0.0168393	−	0.117120i
$643$	12.4208			0.489829			0.244915	−	0.969545i	$-0.421240\pi$
$643$	12.4208			0.489829			0.244915	+	0.969545i	$0.421240\pi$
$644$	−11.6337	+	5.06517i	−0.458434	+	0.199596i
$645$	−17.7767			−0.699957
$646$	0.726901	+	5.05570i	0.0285995	+	0.198914i
$647$	−14.7287	−	6.72639i	−0.579046	−	0.264442i	0.104288	−	0.994547i	$-0.466744\pi$
$647$	−14.7287	−	6.72639i	−0.579046	−	0.264442i	−0.683334	+	0.730106i	$0.739471\pi$
$648$	−0.959493	+	0.281733i	−0.0376924	+	0.0110675i
$649$	−34.5737	+	39.9002i	−1.35714	+	1.56622i
$650$	−1.26529	+	4.30918i	−0.0496288	+	0.169020i
$651$	−17.2775	+	9.25275i	−0.677158	+	0.362644i
$652$	4.45659	+	9.75857i	0.174533	+	0.382175i
$653$	−17.5737	−	20.2811i	−0.687711	−	0.793660i	0.299327	−	0.954151i	$-0.403238\pi$
$653$	−17.5737	−	20.2811i	−0.687711	−	0.793660i	−0.987037	+	0.160490i	$0.948692\pi$
$654$	−1.43924	−	0.924940i	−0.0562785	−	0.0361680i
$655$	8.89919	+	1.27951i	0.347720	+	0.0499946i
$656$	11.4257	+	1.64277i	0.446098	+	0.0641393i
$657$	−1.84190	+	2.86605i	−0.0718593	+	0.111815i
$658$	19.0149	−	13.9947i	0.741279	−	0.545571i
$659$	31.1005	−	14.2031i	1.21150	−	0.553274i	0.295845	−	0.955236i	$-0.404399\pi$
$659$	31.1005	−	14.2031i	1.21150	−	0.553274i	0.915657	+	0.401961i	$0.131671\pi$
$660$	9.47984	−	6.09232i	0.369002	−	0.237143i
$661$	31.4742	+	9.24166i	1.22421	+	0.359459i	0.829060	−	0.559160i	$-0.188876\pi$
$661$	31.4742	+	9.24166i	1.22421	+	0.359459i	0.395145	+	0.918619i	$0.370694\pi$
$662$	−10.9301	+	12.6140i	−0.424811	+	0.490258i
$663$	28.5496	−	8.38292i	1.10877	−	0.325566i
$664$	1.89318	−	4.14548i	0.0734696	−	0.160876i
$665$	0.250774	+	3.95806i	0.00972459	+	0.153487i
$666$		−	2.39172i		−	0.0926774i
$667$	31.9176	+	24.3767i	1.23585	+	0.943868i
$668$		−	11.7264i		−	0.453707i
$669$	−1.92016	−	13.3550i	−0.0742376	−	0.516334i
$670$	11.6507	+	5.32072i	0.450108	+	0.205557i
$671$	−10.9745	−	37.3757i	−0.423666	−	1.44287i
$672$	1.85556	+	1.88597i	0.0715799	+	0.0727529i
$673$	22.9538	+	6.73984i	0.884803	+	0.259802i	0.692400	−	0.721514i	$-0.256554\pi$
$673$	22.9538	+	6.73984i	0.884803	+	0.259802i	0.192404	+	0.981316i	$0.438372\pi$
$674$	−7.31921	−	11.3889i	−0.281925	−	0.438685i
$675$	−0.932679	+	0.425940i	−0.0358988	+	0.0163944i
$676$	4.05065	+	4.67470i	0.155794	+	0.179796i
$677$	−10.8159	−	6.95092i	−0.415687	−	0.267146i	0.316037	−	0.948747i	$-0.397648\pi$
$677$	−10.8159	−	6.95092i	−0.415687	−	0.267146i	−0.731724	+	0.681601i	$0.761284\pi$
$678$	−0.220799	+	1.53569i	−0.00847975	+	0.0589779i
$679$	2.10231	−	9.29967i	0.0806794	−	0.356889i
$680$	−11.3933	−	7.32201i	−0.436912	−	0.280786i
$681$	−7.99818	+	6.93047i	−0.306491	+	0.265576i
$682$	17.3937	+	38.0870i	0.666041	+	1.45843i
$683$	−8.09085	+	5.19968i	−0.309588	+	0.198960i	−0.686204	−	0.727410i	$-0.740724\pi$
$683$	−8.09085	+	5.19968i	−0.309588	+	0.198960i	0.376616	+	0.926370i	$0.377088\pi$
$684$	−0.721432	−	0.211831i	−0.0275846	−	0.00809958i
$685$	−9.99853	−	8.66378i	−0.382024	−	0.331026i
$686$	18.4998	−	0.870496i	0.706325	−	0.0332357i
$687$	10.3282	+	4.71674i	0.394046	+	0.179955i
$688$	−8.82588	+	1.26897i	−0.336483	+	0.0483790i
$689$	−23.5778			−0.898241
$690$	1.94225	+	9.36189i	0.0739404	+	0.356401i
$691$			6.61531i			0.251658i	0.992052	+	0.125829i	$0.0401591\pi$
$691$			6.61531i			0.251658i	−0.992052	+	0.125829i	$0.959841\pi$
$692$	−7.56161	+	1.08719i	−0.287449	+	0.0413290i
$693$	13.0666	+	7.27337i	0.496359	+	0.276292i
$694$	−12.2887	+	3.60829i	−0.466473	+	0.136969i
$695$	−0.484328	−	0.419673i	−0.0183716	−	0.0159191i
$696$	2.35930	−	8.03505i	0.0894292	−	0.304568i
$697$	−42.3941	−	65.9666i	−1.60579	−	2.49866i
$698$	20.4242	−	9.32742i	0.773068	−	0.353048i
$699$	10.3856	−	8.99920i	0.392821	−	0.340381i
$700$	2.15841	+	1.64331i	0.0815803	+	0.0621111i
$701$	−42.7656	−	6.14877i	−1.61523	−	0.232236i	−0.725337	−	0.688394i	$-0.758316\pi$
$701$	−42.7656	−	6.14877i	−1.61523	−	0.232236i	−0.889898	+	0.456159i	$0.849225\pi$
$702$	−0.623357	+	4.33554i	−0.0235271	+	0.163635i
$703$	0.972239	−	1.51283i	0.0366687	−	0.0570576i
$704$	4.27171	−	3.70146i	0.160996	−	0.139504i
$705$	−7.39051	−	16.1830i	−0.278343	−	0.609485i
$706$	1.17938	+	1.83515i	0.0443865	+	0.0690668i
$707$	3.06042	−	8.00599i	0.115099	−	0.301096i
$708$	−6.11677	+	7.05913i	−0.229882	+	0.265298i
$709$	2.40707	+	8.19774i	0.0903995	+	0.307873i	0.992264	−	0.124147i	$-0.0396194\pi$
$709$	2.40707	+	8.19774i	0.0903995	+	0.307873i	−0.901864	+	0.432019i	$0.857801\pi$
$710$	−2.24405	+	4.91379i	−0.0842178	+	0.184411i
$711$	−17.1095	+	2.45997i	−0.641656	+	0.0922562i
$712$	−6.54713			−0.245364
$713$	−35.4587	+	2.19280i	−1.32794	+	0.0821211i
$714$	1.42782	−	17.9162i	0.0534350	−	0.670496i
$715$	−7.02443	−	48.8560i	−0.262699	−	1.82711i
$716$	8.05047	−	17.6281i	0.300860	−	0.658792i
$717$	−0.0980193	−	0.333823i	−0.00366060	−	0.0124669i
$718$	23.7178	+	20.5516i	0.885142	+	0.766980i
$719$	2.03363	−	6.92590i	0.0758415	−	0.258293i	−0.912841	−	0.408315i	$-0.866116\pi$
$719$	2.03363	−	6.92590i	0.0758415	−	0.258293i	0.988683	+	0.150023i	$0.0479346\pi$
$720$	1.67717	−	1.07785i	0.0625044	−	0.0401692i
$721$	−3.33104	−	9.15746i	−0.124054	−	0.341042i
$722$	12.0721	+	13.9320i	0.449278	+	0.518495i
$723$	8.14843	−	12.6792i	0.303043	−	0.471545i
$724$	0.613698	−	4.26836i	0.0228079	−	0.158632i
$725$	1.22198	−	8.49904i	0.0453831	−	0.315647i
$726$	11.3255	−	17.6228i	0.420328	−	0.654044i
$727$	10.2211	+	11.7958i	0.379081	+	0.437483i	0.912942	−	0.408089i	$-0.133805\pi$
$727$	10.2211	+	11.7958i	0.379081	+	0.437483i	−0.533861	+	0.845572i	$0.679259\pi$
$728$	10.8906	−	3.96147i	0.403633	−	0.146822i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	1.91357	−	6.51702i	0.0708244	−	0.241206i
$731$	45.7773	+	39.6663i	1.69314	+	1.46711i
$732$	−1.94161	−	6.61251i	−0.0717639	−	0.244405i
$733$	6.07735	−	13.3075i	0.224472	−	0.491526i	−0.763567	−	0.645729i	$-0.776554\pi$
$733$	6.07735	−	13.3075i	0.224472	−	0.491526i	0.988039	+	0.154203i	$0.0492810\pi$
$734$	−0.0775385	−	0.539292i	−0.00286200	−	0.0199056i
$735$	2.21033	−	13.7794i	0.0815294	−	0.508262i
$736$	1.63259	+	4.50940i	0.0601780	+	0.166219i
$737$	36.3129			1.33760
$738$	11.4257	−	1.64277i	0.420586	−	0.0604711i
$739$	19.4734	−	42.6408i	0.716340	−	1.56857i	−0.102624	−	0.994720i	$-0.532724\pi$
$739$	19.4734	−	42.6408i	0.716340	−	1.56857i	0.818964	−	0.573846i	$-0.194549\pi$
$740$	1.34338	+	4.57512i	0.0493835	+	0.168185i
$741$	−2.15670	+	2.48896i	−0.0792283	+	0.0914343i
$742$	−5.08527	+	13.3030i	−0.186686	+	0.488367i
$743$	3.71784	+	5.78507i	0.136394	+	0.212234i	0.902731	−	0.430206i	$-0.141559\pi$
$743$	3.71784	+	5.78507i	0.136394	+	0.212234i	−0.766337	+	0.642439i	$0.777923\pi$
$744$	3.07730	+	6.73834i	0.112819	+	0.247040i
$745$	−26.4660	+	22.9329i	−0.969640	+	0.840198i
$746$	2.70850	−	4.21451i	0.0991652	−	0.154304i
$747$	0.648574	−	4.51093i	0.0237301	−	0.165046i
$748$	−38.0060	−	5.46444i	−1.38964	−	0.199800i
$749$	−4.80499	+	6.31115i	−0.175570	+	0.230604i
$750$	9.07840	−	7.86648i	0.331496	−	0.287243i
$751$	34.2356	−	15.6349i	1.24927	−	0.570525i	0.322652	−	0.946518i	$-0.395426\pi$
$751$	34.2356	−	15.6349i	1.24927	−	0.570525i	0.926622	+	0.375993i	$0.122698\pi$
$752$	−4.82448	−	7.50704i	−0.175931	−	0.273754i
$753$	−6.41843	+	21.8592i	−0.233901	+	0.796593i
$754$	−27.7212	−	24.0205i	−1.00955	−	0.874776i
$755$	19.3098	−	5.66987i	0.702755	−	0.206348i
$756$	2.31174	+	1.28680i	0.0840771	+	0.0468006i
$757$	−25.1172	+	3.61131i	−0.912901	+	0.131255i	−0.582730	−	0.812666i	$-0.698016\pi$
$757$	−25.1172	+	3.61131i	−0.912901	+	0.131255i	−0.330171	+	0.943921i	$0.607106\pi$
$758$		−	7.38557i		−	0.268256i
$759$	16.0350	+	21.8561i	0.582032	+	0.793327i
$760$	1.49901			0.0543747
$761$	45.2021	−	6.49908i	1.63857	−	0.235591i	0.739427	−	0.673237i	$-0.235097\pi$
$761$	45.2021	−	6.49908i	1.63857	−	0.235591i	0.899147	+	0.437646i	$0.144188\pi$
$762$	−9.67101	−	4.41660i	−0.350344	−	0.159997i
$763$	0.926182	+	4.43064i	0.0335300	+	0.160400i
$764$	16.5687	+	14.3568i	0.599434	+	0.519413i
$765$	−12.9946	−	3.81556i	−0.469821	−	0.137952i
$766$	25.7683	−	16.5603i	0.931048	−	0.598348i
$767$	16.9958	+	37.2157i	0.613684	+	1.34378i
$768$	0.755750	−	0.654861i	0.0272708	−	0.0236303i
$769$	27.2302	+	17.4998i	0.981947	+	0.631059i	0.929988	−	0.367591i	$-0.119817\pi$
$769$	27.2302	+	17.4998i	0.981947	+	0.631059i	0.0519588	+	0.998649i	$0.483454\pi$
$770$	−29.0804	−	6.57400i	−1.04798	−	0.236911i
$771$	4.14902	−	28.8570i	0.149423	−	1.03926i
$772$	10.1117	+	6.49837i	0.363927	+	0.233881i
$773$	9.25044	+	10.6756i	0.332715	+	0.383974i	0.897315	−	0.441391i	$-0.145515\pi$
$773$	9.25044	+	10.6756i	0.332715	+	0.383974i	−0.564600	+	0.825365i	$0.690969\pi$
$774$	−8.11086	+	3.70410i	−0.291539	+	0.133141i
$775$	4.10641	+	6.38970i	0.147507	+	0.229525i
$776$	−3.45767	−	1.01526i	−0.124123	−	0.0364458i
$777$	−4.51072	+	4.43799i	−0.161821	+	0.159212i
$778$	−4.49442	−	15.3066i	−0.161133	−	0.548768i
$779$	7.89487	+	3.60547i	0.282863	+	0.129179i
$780$	−1.24276	−	8.64358i	−0.0444979	−	0.309490i
$781$			15.3153i			0.548023i
$782$	15.8882	−	28.4419i	0.568161	−	1.01708i
$783$		−	8.37427i		−	0.299272i
$784$	0.113769	−	6.99908i	0.00406318	−	0.249967i
$785$	−7.93397	+	17.3730i	−0.283176	+	0.620068i
$786$	4.32698	−	1.27052i	0.154338	−	0.0453178i
$787$	2.09324	−	2.41573i	0.0746159	−	0.0861114i	−0.717214	−	0.696853i	$-0.754583\pi$
$787$	2.09324	−	2.41573i	0.0746159	−	0.0861114i	0.791830	+	0.610741i	$0.209129\pi$
$788$	−12.9566	−	3.80440i	−0.461560	−	0.135526i
$789$	21.1926	−	13.6196i	0.754476	−	0.484872i
$790$	31.3470	−	14.3157i	1.11528	−	0.509330i
$791$	3.30598	−	2.43315i	0.117547	−	0.0865130i
$792$	3.05585	−	4.75500i	0.108585	−	0.168962i
$793$	−29.8791	−	4.29597i	−1.06104	−	0.152554i
$794$	−2.00106	−	0.287708i	−0.0710148	−	0.0102104i
$795$	9.02803	+	5.80196i	0.320191	+	0.205774i
$796$	5.24940	+	6.05813i	0.186060	+	0.214725i
$797$	−0.858162	−	1.87911i	−0.0303977	−	0.0665616i	0.893824	−	0.448418i	$-0.148012\pi$
$797$	−0.858162	−	1.87911i	−0.0303977	−	0.0665616i	−0.924222	+	0.381856i	$0.875285\pi$
$798$	0.939154	+	1.75367i	0.0332457	+	0.0620791i
$799$	−17.0785	+	58.1641i	−0.604195	+	2.05770i
$800$	0.671453	−	0.774898i	0.0237394	−	0.0273968i
$801$	−6.28193	+	1.84454i	−0.221961	+	0.0651736i
$802$	13.0351	+	5.95294i	0.460286	+	0.210206i
$803$	−2.74051	−	19.0606i	−0.0967104	−	0.672635i
$804$	6.42448			0.226574
$805$	14.0523	−	21.0346i	0.495277	−	0.741373i
$806$	32.4470			1.14290
$807$	−3.88424	−	27.0155i	−0.136732	−	0.950990i
$808$	−2.94678	−	1.34575i	−0.103667	−	0.0473433i
$809$	53.8131	−	15.8010i	1.89197	−	0.555532i	0.898875	−	0.438204i	$-0.144385\pi$
$809$	53.8131	−	15.8010i	1.89197	−	0.555532i	0.993093	−	0.117328i	$-0.0374328\pi$
$810$	1.30557	−	1.50670i	0.0458729	−	0.0529402i
$811$	−0.453665	+	1.54504i	−0.0159303	+	0.0542537i	−0.967075	−	0.254493i	$-0.918091\pi$
$811$	−0.453665	+	1.54504i	−0.0159303	+	0.0542537i	0.951144	+	0.308747i	$0.0999096\pi$
$812$	−19.5317	+	10.4600i	−0.685428	+	0.367073i
$813$	−12.1690	−	26.6463i	−0.426784	−	0.934527i
$814$	8.85286	+	10.2167i	0.310292	+	0.358097i
$815$	−17.9927	−	11.5632i	−0.630258	−	0.405042i
$816$	−6.72401	−	0.966766i	−0.235387	−	0.0338436i
$817$	−6.63608	−	0.954124i	−0.232167	−	0.0333806i
$818$	3.59519	−	5.59423i	0.125703	−	0.195598i
$819$	9.33339	−	6.86924i	0.326135	−	0.240031i
$820$	−20.9335	+	9.56000i	−0.731029	+	0.333850i
$821$	−29.4354	+	18.9170i	−1.02730	+	0.660207i	−0.941815	−	0.336132i	$-0.890881\pi$
$821$	−29.4354	+	18.9170i	−1.02730	+	0.660207i	−0.0854873	+	0.996339i	$0.527245\pi$
$822$	−6.36722	−	1.86958i	−0.222082	−	0.0652092i
$823$	−30.1374	+	34.7805i	−1.05053	+	1.21237i	−0.0739347	+	0.997263i	$0.523556\pi$
$823$	−30.1374	+	34.7805i	−1.05053	+	1.21237i	−0.976590	+	0.215107i	$0.930990\pi$
$824$	−3.53388	+	1.03764i	−0.123108	+	0.0361479i
$825$	2.40753	−	5.27176i	0.0838195	−	0.183539i
$826$	24.6634	−	1.56261i	0.858148	−	0.0543703i
$827$		−	30.0747i		−	1.04580i	−0.852394	−	0.522899i	$-0.824850\pi$
$827$		−	30.0747i		−	1.04580i	0.852394	−	0.522899i	$-0.175150\pi$
$828$	2.83690	+	3.86678i	0.0985891	+	0.134380i
$829$			6.98616i			0.242640i	0.992613	+	0.121320i	$0.0387126\pi$
$829$			6.98616i			0.242640i	−0.992613	+	0.121320i	$0.961287\pi$
$830$	1.29303	+	8.99324i	0.0448818	+	0.312160i
$831$	−24.1223	−	11.0163i	−0.836793	−	0.382150i
$832$	−1.23402	−	4.20270i	−0.0427821	−	0.145702i
$833$	−36.4388	+	30.5518i	−1.26253	+	1.05856i
$834$	−0.308428	−	0.0905626i	−0.0106800	−	0.00313593i
$835$	12.6393	+	19.6671i	0.437401	+	0.680609i
$836$	3.86583	−	1.76547i	0.133703	−	0.0610599i
$837$	4.85106	+	5.59842i	0.167677	+	0.193510i
$838$	−22.8408	−	14.6789i	−0.789022	−	0.507073i
$839$	−2.24230	+	15.5955i	−0.0774127	+	0.538417i	0.913803	+	0.406159i	$0.133132\pi$
$839$	−2.24230	+	15.5955i	−0.0774127	+	0.538417i	−0.991215	+	0.132259i	$0.957777\pi$
$840$	−5.14489	−	1.16307i	−0.177516	−	0.0401298i
$841$	34.5994	+	22.2357i	1.19308	+	0.766747i
$842$	−8.46591	+	7.33576i	−0.291755	+	0.252807i
$843$	9.03624	+	19.7866i	0.311225	+	0.681487i
$844$	−6.13040	+	3.93977i	−0.211017	+	0.135612i
$845$	−11.8323	−	3.47427i	−0.407043	−	0.119518i
$846$	−6.74404	−	5.84374i	−0.231865	−	0.200912i
$847$	−54.2513	+	11.3407i	−1.86410	+	0.389671i
$848$	4.89645	+	2.23613i	0.168145	+	0.0767892i
$849$	1.97678	−	0.284218i	0.0678428	−	0.00975432i
$850$	−6.96527			−0.238907
$851$	−10.7852	+	3.90470i	−0.369713	+	0.133851i
$852$			2.70957i			0.0928284i
$853$	−21.0167	+	3.02175i	−0.719599	+	0.103463i	−0.492379	−	0.870381i	$-0.663873\pi$
$853$	−21.0167	+	3.02175i	−0.719599	+	0.103463i	−0.227220	+	0.973844i	$0.572964\pi$
$854$	−8.86822	+	15.9317i	−0.303464	+	0.545173i
$855$	1.43829	−	0.422319i	0.0491884	−	0.0144430i
$856$	2.26578	+	1.96331i	0.0774428	+	0.0671046i
$857$	6.76447	−	23.0377i	0.231070	−	0.786952i	−0.759567	−	0.650429i	$-0.774589\pi$
$857$	6.76447	−	23.0377i	0.231070	−	0.786952i	0.990637	−	0.136523i	$-0.0435928\pi$
$858$	−13.3850	−	20.8275i	−0.456957	−	0.711040i
$859$	−20.6848	+	9.44642i	−0.705756	+	0.322308i	−0.735760	−	0.677242i	$-0.763175\pi$
$859$	−20.6848	+	9.44642i	−0.705756	+	0.322308i	0.0300047	+	0.999550i	$0.490448\pi$
$860$	13.4347	−	11.6413i	0.458121	−	0.396964i
$861$	−24.2993	−	18.5003i	−0.828118	−	0.630487i
$862$	−36.9735	−	5.31598i	−1.25932	−	0.181063i
$863$	3.44788	−	23.9805i	0.117367	−	0.816306i	−0.843069	−	0.537805i	$-0.819253\pi$
$863$	3.44788	−	23.9805i	0.117367	−	0.816306i	0.960436	−	0.278501i	$-0.0898374\pi$
$864$	0.540641	−	0.841254i	0.0183930	−	0.0286200i
$865$	11.5103	−	9.97370i	0.391361	−	0.339116i
$866$	−0.310829	−	0.680620i	−0.0105624	−	0.0231284i
$867$	15.7580	+	24.5200i	0.535170	+	0.832741i
$868$	6.99819	−	18.3071i	0.237534	−	0.621384i
$869$	63.9813	−	73.8383i	2.17042	−	2.50479i
$870$	4.70364	+	16.0191i	0.159468	+	0.543099i
$871$	11.6898	−	25.5971i	0.396093	−	0.867324i
$872$	1.69341	−	0.243475i	0.0573460	−	0.00824512i
$873$	−3.60364			−0.121965
$874$	0.222569	+	3.59906i	0.00752853	+	0.121740i
$875$	−31.6815	−	2.52485i	−1.07103	−	0.0853554i
$876$	−0.484850	−	3.37220i	−0.0163816	−	0.113936i
$877$	14.3014	−	31.3158i	0.482926	−	1.05746i	−0.498723	−	0.866761i	$-0.666198\pi$
$877$	14.3014	−	31.3158i	0.482926	−	1.05746i	0.981649	−	0.190698i	$-0.0610752\pi$
$878$	3.70362	+	12.6134i	0.124991	+	0.425680i
$879$	−14.7402	−	12.7724i	−0.497173	−	0.430803i
$880$	−3.17476	+	10.8122i	−0.107021	+	0.364481i
$881$	2.57499	−	1.65485i	0.0867538	−	0.0557533i	−0.496545	−	0.868011i	$-0.665398\pi$
$881$	2.57499	−	1.65485i	0.0867538	−	0.0557533i	0.583299	+	0.812258i	$0.301762\pi$
$882$	−1.86271	−	6.74762i	−0.0627206	−	0.227204i
$883$	34.6779	+	40.0205i	1.16701	+	1.34680i	0.926566	+	0.376132i	$0.122746\pi$
$883$	34.6779	+	40.0205i	1.16701	+	1.34680i	0.240439	+	0.970664i	$0.422708\pi$
$884$	−16.0867	+	25.0314i	−0.541054	+	0.841897i
$885$	2.65017	−	18.4323i	0.0890845	−	0.619596i
$886$	4.58614	−	31.8973i	0.154075	−	1.07161i
$887$	−9.10555	+	14.1685i	−0.305735	+	0.475732i	−0.959792	−	0.280713i	$-0.909429\pi$
$887$	−9.10555	+	14.1685i	−0.305735	+	0.475732i	0.654057	+	0.756445i	$0.273066\pi$
$888$	1.56625	+	1.80754i	0.0525597	+	0.0606572i
$889$	9.61560	+	26.4345i	0.322497	+	0.886586i
$890$	10.9806	−	7.05684i	0.368072	−	0.236546i
$891$	1.59243	−	5.42332i	0.0533485	−	0.181688i
$892$	10.1968	+	8.83559i	0.341415	+	0.295838i
$893$	−1.89031	−	6.43780i	−0.0632567	−	0.215433i
$894$	−7.29697	+	15.9781i	−0.244047	+	0.534389i
$895$	5.49844	+	38.2425i	0.183793	+	1.27831i
$896$	−2.63739	−	0.210186i	−0.0881090	−	0.00702181i
$897$	20.5684	−	4.26720i	0.686758	−	0.142478i
$898$	7.51174			0.250670
$899$	−61.4032	+	8.82845i	−2.04791	+	0.294445i
$900$	0.425940	−	0.932679i	0.0141980	−	0.0310893i
$901$	−10.3021	−	35.0856i	−0.343211	−	1.16887i
$902$	−42.7266	+	49.3091i	−1.42264	+	1.64181i
$903$	22.0360	+	8.42364i	0.733314	+	0.280321i
$904$	−0.838796	−	1.30519i	−0.0278979	−	0.0434100i
$905$	3.57139	+	7.82025i	0.118717	+	0.259954i
$906$	7.62893	−	6.61050i	0.253454	−	0.219619i
$907$	−20.5736	+	32.0131i	−0.683134	+	1.06298i	0.310528	+	0.950564i	$0.399494\pi$
$907$	−20.5736	+	32.0131i	−0.683134	+	1.06298i	−0.993662	+	0.112413i	$0.964142\pi$
$908$	1.50613	−	10.4754i	0.0499828	−	0.347638i
$909$	−3.20656	−	0.461033i	−0.106355	−	0.0152915i
$910$	−13.9955	+	18.3825i	−0.463947	+	0.609375i
$911$	23.0741	−	19.9938i	0.764479	−	0.662425i	−0.182686	−	0.983171i	$-0.558479\pi$
$911$	23.0741	−	19.9938i	0.764479	−	0.662425i	0.947165	+	0.320746i	$0.103934\pi$
$912$	0.683942	−	0.312346i	0.0226476	−	0.0103428i
$913$	13.9265	+	21.6701i	0.460900	+	0.717174i
$914$	1.20054	−	4.08867i	0.0397104	−	0.135241i
$915$	10.3837	+	8.99753i	0.343275	+	0.297449i
$916$	−10.8943	+	3.19887i	−0.359959	+	0.105694i
$917$	−10.4252	−	5.80304i	−0.344269	−	0.191633i
$918$	−6.72401	+	0.966766i	−0.221925	+	0.0319080i
$919$		−	22.7415i		−	0.750174i	−0.926990	−	0.375087i	$-0.877613\pi$
$919$		−	22.7415i		−	0.750174i	0.926990	−	0.375087i	$-0.122387\pi$
$920$	−7.59859	−	5.80334i	−0.250518	−	0.191330i
$921$	−14.9187			−0.491587
$922$	34.8814	−	5.01518i	1.14876	−	0.165166i
$923$	10.7958	+	4.93026i	0.355347	+	0.162281i
$924$	−14.6381	+	3.05996i	−0.481559	+	0.100665i
$925$	1.85334	+	1.60593i	0.0609374	+	0.0528026i
$926$	36.2237	+	10.6363i	1.19039	+	0.349529i
$927$	−3.09839	+	1.99122i	−0.101765	+	0.0654001i
$928$	3.47880	+	7.61750i	0.114197	+	0.250057i
$929$	15.3065	−	13.2632i	0.502190	−	0.435150i	−0.366565	−	0.930393i	$-0.619466\pi$
$929$	15.3065	−	13.2632i	0.502190	−	0.435150i	0.868755	+	0.495242i	$0.164921\pi$
$930$	−12.4241	−	7.98447i	−0.407402	−	0.261821i
$931$	1.56470	−	5.02526i	0.0512810	−	0.164696i
$932$	−1.95571	+	13.6023i	−0.0640615	+	0.445557i
$933$	2.22056	+	1.42707i	0.0726980	+	0.0467201i
$934$	12.4896	+	14.4137i	0.408671	+	0.471632i
$935$	69.6323	−	31.8000i	2.27722	−	1.03997i
$936$	−2.36808	−	3.68480i	−0.0774030	−	0.120441i
$937$	24.0126	+	7.05075i	0.784459	+	0.230338i	0.649347	−	0.760493i	$-0.275042\pi$
$937$	24.0126	+	7.05075i	0.784459	+	0.230338i	0.135112	+	0.990830i	$0.456861\pi$
$938$	−11.9210	−	12.1164i	−0.389235	−	0.395614i
$939$	−1.33459	−	4.54520i	−0.0435527	−	0.148327i
$940$	16.1830	+	7.39051i	0.527830	+	0.241052i
$941$	−6.01892	−	41.8625i	−0.196211	−	1.36468i	−0.815155	−	0.579244i	$-0.803348\pi$
$941$	−6.01892	−	41.8625i	−0.196211	−	1.36468i	0.618943	−	0.785436i	$-0.287561\pi$
$942$			9.57984i			0.312128i
$943$	−26.0613	−	48.8410i	−0.848674	−	1.59048i
$944$		−	9.34057i		−	0.304010i
$945$	−5.26416	+	0.333525i	−0.171243	+	0.0108496i
$946$	20.9366	−	45.8448i	0.680709	−	1.49054i
$947$	−36.5109	+	10.7206i	−1.18644	+	0.348372i	−0.814655	−	0.579945i	$-0.803074\pi$
$947$	−36.5109	+	10.7206i	−1.18644	+	0.348372i	−0.371790	+	0.928317i	$0.621256\pi$
$948$	11.3195	−	13.0635i	0.367642	−	0.424281i
$949$	−14.3181	−	4.20417i	−0.464785	−	0.136473i
$950$	0.648555	−	0.416801i	0.0210419	−	0.0135228i
$951$	−17.3279	+	7.91339i	−0.561896	+	0.256609i
$952$	10.6535	+	14.4752i	0.345283	+	0.469143i
$953$	−12.6411	+	19.6699i	−0.409485	+	0.637171i	−0.983338	−	0.181787i	$-0.941812\pi$
$953$	−12.6411	+	19.6699i	−0.409485	+	0.637171i	0.573853	+	0.818958i	$0.305448\pi$
$954$	5.32810	+	0.766065i	0.172504	+	0.0248023i
$955$	−43.2631	−	6.22029i	−1.39996	−	0.201284i
$956$	0.292686	+	0.188098i	0.00946613	+	0.00608351i
$957$	30.9970	+	35.7724i	1.00199	+	1.15636i
$958$	8.85109	+	19.3812i	0.285966	+	0.626177i
$959$	8.28880	+	15.4775i	0.267659	+	0.499795i
$960$	−0.561678	+	1.91290i	−0.0181281	+	0.0617385i
$961$	15.6348	−	18.0435i	0.504348	−	0.582049i
$962$	10.0517	−	2.95144i	0.324080	−	0.0951584i
$963$	2.72713	+	1.24544i	0.0878806	+	0.0401337i
$964$	2.14494	+	14.9184i	0.0690839	+	0.480489i
$965$	−23.9633			−0.771404
$966$	2.02858	−	12.5254i	0.0652686	−	0.402997i
$967$	27.1601			0.873409			0.436705	−	0.899605i	$-0.356146\pi$
$967$	27.1601			0.873409			0.436705	+	0.899605i	$0.356146\pi$
$968$	2.98125	+	20.7351i	0.0958210	+	0.666450i
$969$	−4.64612	−	2.12181i	−0.149255	−	0.0681624i
$970$	6.89340	−	2.02408i	0.221334	−	0.0649894i
$971$	−28.1224	+	32.4550i	−0.902491	+	1.04153i	0.0964420	+	0.995339i	$0.469254\pi$
$971$	−28.1224	+	32.4550i	−0.902491	+	1.04153i	−0.998933	+	0.0461911i	$0.985292\pi$
$972$	0.281733	−	0.959493i	0.00903658	−	0.0307758i
$973$	0.401509	+	0.749730i	0.0128718	+	0.0240353i
$974$	16.6308	+	36.4165i	0.532886	+	1.16686i
$975$	−2.94105	−	3.39415i	−0.0941889	−	0.108700i
$976$	5.79764	+	3.72592i	0.185578	+	0.119264i
$977$	4.71152	+	0.677414i	0.150735	+	0.0216724i	0.217269	−	0.976112i	$-0.430285\pi$
$977$	4.71152	+	0.677414i	0.150735	+	0.0216724i	−0.0665343	+	0.997784i	$0.521194\pi$
$978$	−10.6188	−	1.52676i	−0.339553	−	0.0488204i
$979$	20.0071	−	31.1316i	0.639429	−	0.994971i
$980$	7.35316	+	11.8613i	0.234888	+	0.378894i
$981$	1.55622	−	0.710701i	0.0496862	−	0.0226909i
$982$	33.9076	−	21.7911i	1.08204	−	0.695383i
$983$	−17.2412	−	5.06246i	−0.549908	−	0.161467i	−0.00503657	−	0.999987i	$-0.501603\pi$
$983$	−17.2412	−	5.06246i	−0.549908	−	0.161467i	−0.544871	+	0.838520i	$0.683421\pi$
$984$	−7.55918	+	8.72376i	−0.240978	+	0.278103i
$985$	25.8310	−	7.58467i	0.823044	−	0.241668i
$986$	23.6320	−	51.7469i	0.752596	−	1.64796i
$987$	1.49286	+	23.5625i	0.0475184	+	0.750002i
$988$		−	3.29337i		−	0.104776i
$989$	29.9450	+	30.5278i	0.952195	+	0.970727i
$990$			11.2687i			0.358143i
$991$	−4.94785	−	34.4130i	−0.157174	−	1.09317i	−0.903810	−	0.427934i	$-0.859242\pi$
$991$	−4.94785	−	34.4130i	−0.157174	−	1.09317i	0.746637	−	0.665232i	$-0.231667\pi$
$992$	−6.73834	−	3.07730i	−0.213943	−	0.0977043i
$993$	−4.70233	−	16.0147i	−0.149224	−	0.508210i
$994$	5.11017	−	5.02778i	0.162085	−	0.159472i
$995$	−15.3339	−	4.50244i	−0.486117	−	0.142737i
$996$	2.46387	+	3.83386i	0.0780708	+	0.121481i
$997$	17.8789	−	8.16504i	0.566232	−	0.258589i	−0.111666	−	0.993746i	$-0.535619\pi$
$997$	17.8789	−	8.16504i	0.566232	−	0.258589i	0.677897	+	0.735156i	$0.262891\pi$
$998$	0.909286	+	1.04937i	0.0287830	+	0.0332173i
$999$	2.01205	+	1.29306i	0.0636583	+	0.0409107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.a.181.14	yes	160
7.6	odd	2	inner	966.2.s.a.181.3	✓	160
23.15	odd	22	inner	966.2.s.a.475.3	yes	160
161.153	even	22	inner	966.2.s.a.475.14	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.181.3	✓	160	7.6	odd	2	inner
966.2.s.a.181.14	yes	160	1.1	even	1	trivial
966.2.s.a.475.3	yes	160	23.15	odd	22	inner
966.2.s.a.475.14	yes	160	161.153	even	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)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.30557 - 1.50670i) q^{5} +(0.281733 - 0.959493i) q^{6} +(-2.33235 + 1.24906i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.30557 - 1.50670i) q^{5} +(0.281733 - 0.959493i) q^{6} +(-2.33235 + 1.24906i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-1.67717 - 1.07785i) q^{10} +(-5.59475 - 0.804403i) q^{11} +(-0.989821 - 0.142315i) q^{12} +(-2.36808 + 3.68480i) q^{13} +(1.56827 + 2.13085i) q^{14} +(1.81349 - 0.828195i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-6.51798 - 1.91385i) q^{17} +(0.654861 - 0.755750i) q^{18} +(0.721432 - 0.211831i) q^{19} +(-0.828195 + 1.81349i) q^{20} +(-2.64046 + 0.167293i) q^{21} +5.65228i q^{22} +(-4.47709 - 1.71920i) q^{23} +1.00000i q^{24} +(0.145921 + 1.01490i) q^{25} +(3.98430 + 1.81957i) q^{26} +(0.281733 + 0.959493i) q^{27} +(1.88597 - 1.85556i) q^{28} +(-8.03505 - 2.35930i) q^{29} +(-1.07785 - 1.67717i) q^{30} +(6.73834 - 3.07730i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-4.75500 - 3.05585i) q^{33} +(-0.966766 + 6.72401i) q^{34} +(-1.16307 + 5.14489i) q^{35} +(-0.841254 - 0.540641i) q^{36} +(1.80754 - 1.56625i) q^{37} +(-0.312346 - 0.683942i) q^{38} +(-3.68480 + 2.36808i) q^{39} +(1.91290 + 0.561678i) q^{40} +(8.72376 + 7.55918i) q^{41} +(0.541367 + 2.58977i) q^{42} +(-8.11086 - 3.70410i) q^{43} +(5.59475 - 0.804403i) q^{44} +1.99366 q^{45} +(-1.06454 + 4.67619i) q^{46} -8.92364i q^{47} +(0.989821 - 0.142315i) q^{48} +(3.87969 - 5.82649i) q^{49} +(0.983803 - 0.288871i) q^{50} +(-5.13392 - 4.44857i) q^{51} +(1.23402 - 4.20270i) q^{52} +(2.91021 + 4.52838i) q^{53} +(0.909632 - 0.415415i) q^{54} +(-8.51632 + 7.37943i) q^{55} +(-2.10508 - 1.60270i) q^{56} +(0.744235 + 0.107005i) q^{57} +(-1.19178 + 8.28903i) q^{58} +(5.04989 - 7.85779i) q^{59} +(-1.50670 + 1.30557i) q^{60} +(2.86290 + 6.26888i) q^{61} +(-4.00494 - 6.23181i) q^{62} +(-2.47134 - 0.944710i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(2.46022 + 8.37874i) q^{65} +(-2.34804 + 5.14150i) q^{66} +(-6.35909 + 0.914298i) q^{67} +6.79315 q^{68} +(-3.35833 - 3.42369i) q^{69} +(5.25805 + 0.419038i) q^{70} +(-0.385612 - 2.68199i) q^{71} +(-0.415415 + 0.909632i) q^{72} +(0.959829 + 3.26888i) q^{73} +(-1.80754 - 1.56625i) q^{74} +(-0.288871 + 0.983803i) q^{75} +(-0.632529 + 0.406502i) q^{76} +(14.0536 - 5.11203i) q^{77} +(2.86837 + 3.31028i) q^{78} +(-9.34521 + 14.5414i) q^{79} +(0.283727 - 1.97336i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(6.24072 - 9.71075i) q^{82} +(-2.98441 - 3.44419i) q^{83} +(2.48637 - 0.904419i) q^{84} +(-11.3933 + 7.32201i) q^{85} +(-2.51211 + 8.55545i) q^{86} +(-6.32885 - 5.48398i) q^{87} +(-1.59243 - 5.42332i) q^{88} +(-2.71978 + 5.95548i) q^{89} +(-0.283727 - 1.97336i) q^{90} +(0.920640 - 11.5521i) q^{91} +(4.78009 + 0.388216i) q^{92} +7.40777 q^{93} +(-8.83281 + 1.26997i) q^{94} +(0.622710 - 1.36354i) q^{95} +(-0.281733 - 0.959493i) q^{96} +(-2.35988 + 2.72345i) q^{97} +(-6.31932 - 3.01101i) q^{98} +(-3.05585 - 4.75500i) 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	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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