LMFDB - Embedded newform 133.2.g.a.102.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(30,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("133.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			102.5
Character	$\chi$	$=$	133.102
Dual form			133.2.g.a.30.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.545630 + 0.945059i) q^{2} +2.31954 q^{3} +(0.404576 + 0.700746i) q^{4} +(-1.44449 + 2.50193i) q^{5} +(-1.26561 + 2.19210i) q^{6} +(-0.319979 - 2.62633i) q^{7} -3.06551 q^{8} +2.38028 q^{9} +O(q^{10})$	\(q+(-0.545630 + 0.945059i) q^{2} +2.31954 q^{3} +(0.404576 + 0.700746i) q^{4} +(-1.44449 + 2.50193i) q^{5} +(-1.26561 + 2.19210i) q^{6} +(-0.319979 - 2.62633i) q^{7} -3.06551 q^{8} +2.38028 q^{9} +(-1.57631 - 2.73025i) q^{10} +(0.431542 - 0.747453i) q^{11} +(0.938430 + 1.62541i) q^{12} +(2.92030 - 5.05811i) q^{13} +(2.65663 + 1.13061i) q^{14} +(-3.35055 + 5.80333i) q^{15} +(0.863486 - 1.49560i) q^{16} -0.331892 q^{17} +(-1.29875 + 2.24950i) q^{18} +(-0.317404 + 4.34733i) q^{19} -2.33762 q^{20} +(-0.742206 - 6.09189i) q^{21} +(0.470925 + 0.815666i) q^{22} +5.17496 q^{23} -7.11059 q^{24} +(-1.67309 - 2.89788i) q^{25} +(3.18681 + 5.51972i) q^{26} -1.43747 q^{27} +(1.71093 - 1.28677i) q^{28} +(1.73240 - 3.00061i) q^{29} +(-3.65632 - 6.33294i) q^{30} +(-0.741791 + 1.28482i) q^{31} +(-2.12323 - 3.67754i) q^{32} +(1.00098 - 1.73375i) q^{33} +(0.181090 - 0.313658i) q^{34} +(7.03310 + 2.99314i) q^{35} +(0.963002 + 1.66797i) q^{36} +(-3.58470 - 6.20888i) q^{37} +(-3.93530 - 2.67200i) q^{38} +(6.77377 - 11.7325i) q^{39} +(4.42810 - 7.66970i) q^{40} +(0.760720 + 1.31761i) q^{41} +(6.16216 + 2.62249i) q^{42} +(0.0304489 + 0.0527391i) q^{43} +0.698366 q^{44} +(-3.43828 + 5.95528i) q^{45} +(-2.82361 + 4.89064i) q^{46} -10.5519 q^{47} +(2.00289 - 3.46911i) q^{48} +(-6.79523 + 1.68074i) q^{49} +3.65156 q^{50} -0.769838 q^{51} +4.72594 q^{52} +(3.39174 + 5.87466i) q^{53} +(0.784329 - 1.35850i) q^{54} +(1.24672 + 2.15937i) q^{55} +(0.980902 + 8.05106i) q^{56} +(-0.736232 + 10.0838i) q^{57} +(1.89050 + 3.27444i) q^{58} -13.9220 q^{59} -5.42221 q^{60} -11.1700 q^{61} +(-0.809487 - 1.40207i) q^{62} +(-0.761640 - 6.25139i) q^{63} +8.08793 q^{64} +(8.43669 + 14.6128i) q^{65} +(1.09233 + 1.89197i) q^{66} +(6.65954 + 11.5347i) q^{67} +(-0.134276 - 0.232572i) q^{68} +12.0035 q^{69} +(-6.66616 + 5.01354i) q^{70} +(-0.725991 - 1.25745i) q^{71} -7.29677 q^{72} +4.93298 q^{73} +7.82368 q^{74} +(-3.88081 - 6.72176i) q^{75} +(-3.17478 + 1.53640i) q^{76} +(-2.10114 - 0.894203i) q^{77} +(7.39194 + 12.8032i) q^{78} +(6.33822 - 10.9781i) q^{79} +(2.49459 + 4.32076i) q^{80} -10.4751 q^{81} -1.66029 q^{82} -5.88748 q^{83} +(3.96858 - 2.98473i) q^{84} +(0.479414 - 0.830370i) q^{85} -0.0664554 q^{86} +(4.01838 - 6.96004i) q^{87} +(-1.32290 + 2.29133i) q^{88} +15.6704 q^{89} +(-3.75206 - 6.49876i) q^{90} +(-14.2187 - 6.05119i) q^{91} +(2.09366 + 3.62633i) q^{92} +(-1.72062 + 2.98019i) q^{93} +(5.75742 - 9.97214i) q^{94} +(-10.4182 - 7.07379i) q^{95} +(-4.92492 - 8.53020i) q^{96} +(1.21410 + 2.10288i) q^{97} +(2.11928 - 7.33895i) q^{98} +(1.02719 - 1.77915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.545630	+	0.945059i	−0.385819	+	0.668258i	−0.991882	−	0.127158i	$-0.959414\pi$
$2$	−0.545630	+	0.945059i	−0.385819	+	0.668258i	0.606064	+	0.795416i	$0.292748\pi$
$3$	2.31954			1.33919			0.669594	−	0.742727i	$-0.266468\pi$
$3$	2.31954			1.33919			0.669594	+	0.742727i	$0.266468\pi$
$4$	0.404576	+	0.700746i	0.202288	+	0.350373i
$5$	−1.44449	+	2.50193i	−0.645995	+	1.11890i	0.338076	+	0.941119i	$0.390224\pi$
$5$	−1.44449	+	2.50193i	−0.645995	+	1.11890i	−0.984071	+	0.177777i	$0.943109\pi$
$6$	−1.26561	+	2.19210i	−0.516684	+	0.894923i
$7$	−0.319979	−	2.62633i	−0.120941	−	0.992660i
$7$	−0.319979	−	2.62633i	−0.120941	−	0.992660i
$8$	−3.06551			−1.08382
$9$	2.38028			0.793426
$10$	−1.57631	−	2.73025i	−0.498474	−	0.863382i
$11$	0.431542	−	0.747453i	0.130115	−	0.225366i	−0.793606	−	0.608432i	$-0.791799\pi$
$11$	0.431542	−	0.747453i	0.130115	−	0.225366i	0.923721	+	0.383067i	$0.125132\pi$
$12$	0.938430	+	1.62541i	0.270902	+	0.469215i
$13$	2.92030	−	5.05811i	0.809947	−	1.40287i	−0.102954	−	0.994686i	$-0.532829\pi$
$13$	2.92030	−	5.05811i	0.809947	−	1.40287i	0.912900	−	0.408182i	$-0.133837\pi$
$14$	2.65663	+	1.13061i	0.710014	+	0.302167i
$15$	−3.35055	+	5.80333i	−0.865109	+	1.49841i
$16$	0.863486	−	1.49560i	0.215871	−	0.373900i
$17$	−0.331892			−0.0804957			−0.0402478	−	0.999190i	$-0.512815\pi$
$17$	−0.331892			−0.0804957			−0.0402478	+	0.999190i	$0.512815\pi$
$18$	−1.29875	+	2.24950i	−0.306118	+	0.530213i
$19$	−0.317404	+	4.34733i	−0.0728174	+	0.997345i
$19$	−0.317404	+	4.34733i	−0.0728174	+	0.997345i
$20$	−2.33762			−0.522708
$21$	−0.742206	−	6.09189i	−0.161963	−	1.32936i
$22$	0.470925	+	0.815666i	0.100402	+	0.173901i
$23$	5.17496			1.07905			0.539527	−	0.841968i	$-0.318603\pi$
$23$	5.17496			1.07905			0.539527	+	0.841968i	$0.318603\pi$
$24$	−7.11059			−1.45144
$25$	−1.67309	−	2.89788i	−0.334619	−	0.579577i
$26$	3.18681	+	5.51972i	0.624985	+	1.08251i
$27$	−1.43747			−0.276642
$28$	1.71093	−	1.28677i	0.323336	−	0.243177i
$29$	1.73240	−	3.00061i	0.321699	−	0.557199i	−0.659140	−	0.752020i	$-0.729079\pi$
$29$	1.73240	−	3.00061i	0.321699	−	0.557199i	0.980839	+	0.194822i	$0.0624128\pi$
$30$	−3.65632	−	6.33294i	−0.667550	−	1.15623i
$31$	−0.741791	+	1.28482i	−0.133230	+	0.230760i	−0.924920	−	0.380162i	$-0.875868\pi$
$31$	−0.741791	+	1.28482i	−0.133230	+	0.230760i	0.791690	+	0.610923i	$0.209201\pi$
$32$	−2.12323	−	3.67754i	−0.375337	−	0.650103i
$33$	1.00098	−	1.73375i	0.174248	−	0.301807i
$34$	0.181090	−	0.313658i	0.0310567	−	0.0537919i
$35$	7.03310	+	2.99314i	1.18881	+	0.505933i
$36$	0.963002	+	1.66797i	0.160500	+	0.277995i
$37$	−3.58470	−	6.20888i	−0.589321	−	1.02073i	−0.994322	−	0.106418i	$-0.966062\pi$
$37$	−3.58470	−	6.20888i	−0.589321	−	1.02073i	0.405000	−	0.914317i	$-0.367271\pi$
$38$	−3.93530	−	2.67200i	−0.638389	−	0.433455i
$39$	6.77377	−	11.7325i	1.08467	−	1.87871i
$40$	4.42810	−	7.66970i	0.700144	−	1.21269i
$41$	0.760720	+	1.31761i	0.118805	+	0.205775i	0.919294	−	0.393571i	$-0.128760\pi$
$41$	0.760720	+	1.31761i	0.118805	+	0.205775i	−0.800490	+	0.599347i	$0.795427\pi$
$42$	6.16216	+	2.62249i	0.950842	+	0.404659i
$43$	0.0304489	+	0.0527391i	0.00464342	+	0.00804264i	0.868338	−	0.495973i	$-0.165189\pi$
$43$	0.0304489	+	0.0527391i	0.00464342	+	0.00804264i	−0.863694	+	0.504016i	$0.831855\pi$
$44$	0.698366			0.105283
$45$	−3.43828	+	5.95528i	−0.512549	+	0.887761i
$46$	−2.82361	+	4.89064i	−0.416319	+	0.721086i
$47$	−10.5519			−1.53915			−0.769574	−	0.638557i	$-0.779532\pi$
$47$	−10.5519			−1.53915			−0.769574	+	0.638557i	$0.779532\pi$
$48$	2.00289	−	3.46911i	0.289093	−	0.500723i
$49$	−6.79523	+	1.68074i	−0.970747	+	0.240106i
$50$	3.65156			0.516409
$51$	−0.769838			−0.107799
$52$	4.72594			0.655369
$53$	3.39174	+	5.87466i	0.465891	+	0.806947i	0.999241	−	0.0389478i	$-0.0124006\pi$
$53$	3.39174	+	5.87466i	0.465891	+	0.806947i	−0.533350	+	0.845894i	$0.679067\pi$
$54$	0.784329	−	1.35850i	0.106734	−	0.184868i
$55$	1.24672	+	2.15937i	0.168107	+	0.291170i
$56$	0.980902	+	8.05106i	0.131079	+	1.07587i
$57$	−0.736232	+	10.0838i	−0.0975163	+	1.33563i
$58$	1.89050	+	3.27444i	0.248235	+	0.429955i
$59$	−13.9220			−1.81249			−0.906246	−	0.422751i	$-0.861065\pi$
$59$	−13.9220			−1.81249			−0.906246	+	0.422751i	$0.861065\pi$
$60$	−5.42221			−0.700004
$61$	−11.1700			−1.43018			−0.715088	−	0.699034i	$-0.753613\pi$
$61$	−11.1700			−1.43018			−0.715088	+	0.699034i	$0.753613\pi$
$62$	−0.809487	−	1.40207i	−0.102805	−	0.178063i
$63$	−0.761640	−	6.25139i	−0.0959576	−	0.787602i
$64$	8.08793			1.01099
$65$	8.43669	+	14.6128i	1.04644	+	1.81249i
$66$	1.09233	+	1.89197i	0.134457	+	0.232886i
$67$	6.65954	+	11.5347i	0.813593	+	1.40918i	0.910334	+	0.413875i	$0.135825\pi$
$67$	6.65954	+	11.5347i	0.813593	+	1.40918i	−0.0967410	+	0.995310i	$0.530842\pi$
$68$	−0.134276	−	0.232572i	−0.0162833	−	0.0282035i
$69$	12.0035			1.44506
$70$	−6.66616	+	5.01354i	−0.796759	+	0.599233i
$71$	−0.725991	−	1.25745i	−0.0861593	−	0.149232i	0.819725	−	0.572757i	$-0.194126\pi$
$71$	−0.725991	−	1.25745i	−0.0861593	−	0.149232i	−0.905885	+	0.423525i	$0.860793\pi$
$72$	−7.29677			−0.859933
$73$	4.93298			0.577361			0.288681	−	0.957425i	$-0.406783\pi$
$73$	4.93298			0.577361			0.288681	+	0.957425i	$0.406783\pi$
$74$	7.82368			0.909485
$75$	−3.88081	−	6.72176i	−0.448117	−	0.776162i
$76$	−3.17478	+	1.53640i	−0.364173	+	0.176238i
$77$	−2.10114	−	0.894203i	−0.239448	−	0.101904i
$78$	7.39194	+	12.8032i	0.836973	+	1.44968i
$79$	6.33822	−	10.9781i	0.713105	−	1.23513i	−0.250581	−	0.968096i	$-0.580622\pi$
$79$	6.33822	−	10.9781i	0.713105	−	1.23513i	0.963686	−	0.267039i	$-0.0860451\pi$
$80$	2.49459	+	4.32076i	0.278904	+	0.483075i
$81$	−10.4751			−1.16390
$82$	−1.66029			−0.183348
$83$	−5.88748			−0.646235			−0.323117	−	0.946359i	$-0.604731\pi$
$83$	−5.88748			−0.646235			−0.323117	+	0.946359i	$0.604731\pi$
$84$	3.96858	−	2.98473i	0.433008	−	0.325660i
$85$	0.479414	−	0.830370i	0.0519998	−	0.0900663i
$86$	−0.0664554			−0.00716608
$87$	4.01838	−	6.96004i	0.430815	−	0.746194i
$88$	−1.32290	+	2.29133i	−0.141022	+	0.244256i
$89$	15.6704			1.66106			0.830530	−	0.556974i	$-0.188038\pi$
$89$	15.6704			1.66106			0.830530	+	0.556974i	$0.188038\pi$
$90$	−3.75206	−	6.49876i	−0.395502	−	0.685029i
$91$	−14.2187	−	6.05119i	−1.49053	−	0.634337i
$92$	2.09366	+	3.62633i	0.218279	+	0.378071i
$93$	−1.72062	+	2.98019i	−0.178419	+	0.309032i
$94$	5.75742	−	9.97214i	0.593832	−	1.02855i
$95$	−10.4182	−	7.07379i	−1.06889	−	0.725755i
$96$	−4.92492	−	8.53020i	−0.502647	−	0.870610i
$97$	1.21410	+	2.10288i	0.123273	+	0.213515i	0.921057	−	0.389429i	$-0.127328\pi$
$97$	1.21410	+	2.10288i	0.123273	+	0.213515i	−0.797784	+	0.602944i	$0.793994\pi$
$98$	2.11928	−	7.33895i	0.214079	−	0.741346i
$99$	1.02719	−	1.77915i	0.103236	−	0.178811i
$100$	1.35379	−	2.34483i	0.135379	−	0.234483i
$101$	−0.408111	−	0.706869i	−0.0406086	−	0.0703361i	0.845007	−	0.534756i	$-0.179596\pi$
$101$	−0.408111	−	0.706869i	−0.0406086	−	0.0703361i	−0.885615	+	0.464420i	$0.846263\pi$
$102$	0.420047	−	0.727542i	0.0415908	−	0.0720374i
$103$	3.33267	+	5.77236i	0.328378	+	0.568768i	0.982190	−	0.187889i	$-0.0601646\pi$
$103$	3.33267	+	5.77236i	0.328378	+	0.568768i	−0.653812	+	0.756657i	$0.726831\pi$
$104$	−8.95223	+	15.5057i	−0.877839	+	1.52046i
$105$	16.3136	+	6.94271i	1.59204	+	0.677539i
$106$	−7.40253			−0.718998
$107$	2.74500	+	4.75449i	0.265370	+	0.459634i	0.967660	−	0.252257i	$-0.0811727\pi$
$107$	2.74500	+	4.75449i	0.265370	+	0.459634i	−0.702291	+	0.711890i	$0.747839\pi$
$108$	−0.581567	−	1.00730i	−0.0559613	−	0.0969278i
$109$	3.83653			0.367473			0.183737	−	0.982976i	$-0.441181\pi$
$109$	3.83653			0.367473			0.183737	+	0.982976i	$0.441181\pi$
$110$	−2.72098			−0.259435
$111$	−8.31487	−	14.4018i	−0.789212	−	1.36696i
$112$	−4.20424	−	1.78924i	−0.397263	−	0.169067i
$113$	9.03417			0.849863			0.424932	−	0.905225i	$-0.360298\pi$
$113$	9.03417			0.849863			0.424932	+	0.905225i	$0.360298\pi$
$114$	−9.12809	−	6.19781i	−0.854924	−	0.580478i
$115$	−7.47517	+	12.9474i	−0.697063	+	1.20735i
$116$	2.80355			0.260303
$117$	6.95113	−	12.0397i	0.642632	−	1.11307i
$118$	7.59627	−	13.1571i	0.699293	−	1.21121i
$119$	0.106199	+	0.871659i	0.00973522	+	0.0799048i
$120$	10.2712	−	17.7902i	0.937625	−	1.62401i
$121$	5.12754	+	8.88116i	0.466140	+	0.807379i
$122$	6.09471	−	10.5563i	0.551789	−	0.955726i
$123$	1.76452	+	3.05624i	0.159102	+	0.275572i
$124$	−1.20044			−0.107803
$125$	−4.77783			−0.427342
$126$	6.32351	+	2.69115i	0.563343	+	0.239747i
$127$	1.50695	−	2.61011i	0.133720	−	0.231610i	−0.791388	−	0.611314i	$-0.790641\pi$
$127$	1.50695	−	2.61011i	0.133720	−	0.231610i	0.925108	+	0.379705i	$0.123974\pi$
$128$	−0.166564	+	0.288497i	−0.0147223	+	0.0254997i
$129$	0.0706276	+	0.122331i	0.00621842	+	0.0107706i
$130$	−18.4132			−1.61495
$131$	−4.65317	+	8.05953i	−0.406550	+	0.704165i	−0.994500	−	0.104732i	$-0.966602\pi$
$131$	−4.65317	+	8.05953i	−0.406550	+	0.704165i	0.587951	+	0.808897i	$0.299935\pi$
$132$	1.61989			0.140993
$133$	11.5191	−	0.557448i	0.998831	−	0.0483369i
$134$	−14.5346			−1.25560
$135$	2.07641	−	3.59645i	0.178709	−	0.309534i
$136$	1.01742			0.0872431
$137$	−2.82911	−	4.90017i	−0.241708	−	0.418650i	0.719493	−	0.694499i	$-0.244374\pi$
$137$	−2.82911	−	4.90017i	−0.241708	−	0.418650i	−0.961201	+	0.275850i	$0.911041\pi$
$138$	−6.54949	+	11.3440i	−0.557530	+	0.965670i
$139$	−8.37365	+	14.5036i	−0.710244	+	1.23018i	0.254522	+	0.967067i	$0.418082\pi$
$139$	−8.37365	+	14.5036i	−0.710244	+	1.23018i	−0.964766	+	0.263111i	$0.915251\pi$
$140$	0.747990	+	6.13936i	0.0632167	+	0.518871i
$141$	−24.4755			−2.06121
$142$	1.58449			0.132968
$143$	−2.52047	−	4.36558i	−0.210772	−	0.365068i
$144$	2.05534	−	3.55995i	0.171278	−	0.296662i
$145$	5.00487	+	8.66869i	0.415632	+	0.719895i
$146$	−2.69158	+	4.66195i	−0.222757	+	0.385826i
$147$	−15.7618	+	3.89856i	−1.30001	+	0.321548i
$148$	2.90057	−	5.02393i	0.238425	−	0.412964i
$149$	−1.35019	+	2.33860i	−0.110612	+	0.191586i	−0.916017	−	0.401139i	$-0.868614\pi$
$149$	−1.35019	+	2.33860i	−0.110612	+	0.191586i	0.805405	+	0.592725i	$0.201948\pi$
$150$	8.46995			0.691568
$151$	−6.07964	+	10.5302i	−0.494754	+	0.856939i	−0.999982	−	0.00604692i	$-0.998075\pi$
$151$	−6.07964	+	10.5302i	−0.494754	+	0.856939i	0.505228	+	0.862986i	$0.331409\pi$
$152$	0.973006	−	13.3268i	0.0789212	−	1.08095i
$153$	−0.789995			−0.0638673
$154$	1.99152	−	1.49780i	0.160481	−	0.120696i
$155$	−2.14302	−	3.71181i	−0.172131	−	0.298140i
$156$	10.9620			0.877663
$157$	14.3179			1.14270			0.571348	−	0.820708i	$-0.306421\pi$
$157$	14.3179			1.14270			0.571348	+	0.820708i	$0.306421\pi$
$158$	6.91664	+	11.9800i	0.550259	+	0.953076i
$159$	7.86728	+	13.6265i	0.623916	+	1.08065i
$160$	12.2679			0.969863
$161$	−1.65588	−	13.5912i	−0.130502	−	1.07113i
$162$	5.71554	−	9.89960i	0.449055	−	0.777786i
$163$	−6.96699	−	12.0672i	−0.545697	−	0.945174i	−0.998563	−	0.0535956i	$-0.982932\pi$
$163$	−6.96699	−	12.0672i	−0.545697	−	0.945174i	0.452866	−	0.891578i	$-0.350402\pi$
$164$	−0.615538	+	1.06614i	−0.0480654	+	0.0832517i
$165$	2.89181	+	5.00876i	0.225127	+	0.389931i
$166$	3.21239	−	5.56402i	0.249330	−	0.431851i
$167$	6.30446	−	10.9196i	0.487854	−	0.844987i	−0.512049	−	0.858956i	$-0.671113\pi$
$167$	6.30446	−	10.9196i	0.487854	−	0.844987i	0.999902	+	0.0139690i	$0.00444663\pi$
$168$	2.27524	+	18.6748i	0.175539	+	1.44079i
$169$	−10.5563	−	18.2841i	−0.812027	−	1.40647i
$170$	0.523166	+	0.906150i	0.0401250	+	0.0694985i
$171$	−0.755509	+	10.3478i	−0.0577752	+	0.791319i
$172$	−0.0246378	+	0.0426739i	−0.00187862	+	0.00325386i
$173$	7.51952	−	13.0242i	0.571698	−	0.990211i	−0.424693	−	0.905337i	$-0.639618\pi$
$173$	7.51952	−	13.0242i	0.571698	−	0.990211i	0.996392	−	0.0848735i	$-0.0270486\pi$
$174$	4.38510	+	7.59521i	0.332433	+	0.575791i
$175$	−7.07544	+	5.32136i	−0.534853	+	0.402257i
$176$	−0.745261	−	1.29083i	−0.0561762	−	0.0973000i
$177$	−32.2927			−2.42727
$178$	−8.55024	+	14.8095i	−0.640868	+	1.11002i
$179$	12.4122	−	21.4986i	0.927733	−	1.60688i	0.140626	−	0.990063i	$-0.455088\pi$
$179$	12.4122	−	21.4986i	0.927733	−	1.60688i	0.787106	−	0.616817i	$-0.211578\pi$
$180$	−5.56418			−0.414730
$181$	−7.90938	+	13.6995i	−0.587900	+	1.01827i	0.406607	+	0.913603i	$0.366712\pi$
$181$	−7.90938	+	13.6995i	−0.587900	+	1.01827i	−0.994507	+	0.104669i	$0.966622\pi$
$182$	13.4769	−	10.1358i	0.998974	−	0.751317i
$183$	−25.9094			−1.91528
$184$	−15.8639			−1.16950
$185$	20.7122			1.52279
$186$	−1.87764	−	3.25217i	−0.137675	−	0.238460i
$187$	−0.143225	+	0.248074i	−0.0104737	+	0.0181410i
$188$	−4.26903	−	7.39418i	−0.311351	−	0.539276i
$189$	0.459962	+	3.77528i	0.0334573	+	0.274611i
$190$	12.3696	−	5.98615i	0.897388	−	0.434281i
$191$	0.343690	+	0.595289i	0.0248686	+	0.0430736i	0.878192	−	0.478309i	$-0.158750\pi$
$191$	0.343690	+	0.595289i	0.0248686	+	0.0430736i	−0.853323	+	0.521382i	$0.825417\pi$
$192$	18.7603			1.35391
$193$	14.0794			1.01345			0.506727	−	0.862106i	$-0.330855\pi$
$193$	14.0794			1.01345			0.506727	+	0.862106i	$0.330855\pi$
$194$	−2.64979			−0.190244
$195$	19.5693	+	33.8950i	1.40138	+	2.42727i
$196$	−3.92696	−	4.08174i	−0.280497	−	0.291553i
$197$	8.27494			0.589565			0.294783	−	0.955564i	$-0.404753\pi$
$197$	8.27494			0.589565			0.294783	+	0.955564i	$0.404753\pi$
$198$	1.12093	+	1.94151i	0.0796611	+	0.137977i
$199$	−8.68642	−	15.0453i	−0.615764	−	1.06653i	−0.990250	−	0.139302i	$-0.955514\pi$
$199$	−8.68642	−	15.0453i	−0.615764	−	1.06653i	0.374486	−	0.927233i	$-0.377819\pi$
$200$	5.12889	+	8.88350i	0.362667	+	0.628158i
$201$	15.4471	+	26.7552i	1.08955	+	1.88716i
$202$	0.890711			0.0626702
$203$	−8.43492	−	3.58973i	−0.592015	−	0.251949i
$204$	−0.311458	−	0.539461i	−0.0218064	−	0.0377698i
$205$	−4.39540			−0.306988
$206$	−7.27363			−0.506778
$207$	12.3178			0.856149
$208$	−5.04328	−	8.73522i	−0.349689	−	0.605679i
$209$	3.11245	+	2.11330i	0.215293	+	0.146180i
$210$	−15.4624	+	11.6291i	−1.06701	+	0.802486i
$211$	5.07948	+	8.79791i	0.349685	+	0.605673i	0.986193	−	0.165597i	$-0.0529551\pi$
$211$	5.07948	+	8.79791i	0.349685	+	0.605673i	−0.636508	+	0.771270i	$0.719622\pi$
$212$	−2.74443	+	4.75349i	−0.188488	+	0.326471i
$213$	−1.68397	−	2.91672i	−0.115384	−	0.199850i
$214$	−5.99103			−0.409538
$215$	−0.175933			−0.0119985
$216$	4.40660			0.299831
$217$	3.61172	+	1.53707i	0.245179	+	0.104343i
$218$	−2.09333	+	3.62575i	−0.141778	+	0.245567i
$219$	11.4422			0.773196
$220$	−1.00878	+	1.74726i	−0.0680120	+	0.117800i
$221$	−0.969226	+	1.67875i	−0.0651972	+	0.112925i
$222$	18.1474			1.21797
$223$	5.00995	+	8.67749i	0.335491	+	0.581088i	0.983579	−	0.180478i	$-0.0577644\pi$
$223$	5.00995	+	8.67749i	0.335491	+	0.581088i	−0.648088	+	0.761566i	$0.724431\pi$
$224$	−8.97904	+	6.75303i	−0.599937	+	0.451206i
$225$	−3.98243	−	6.89776i	−0.265495	−	0.459851i
$226$	−4.92931	+	8.53782i	−0.327893	+	0.567928i
$227$	−0.827042	+	1.43248i	−0.0548927	+	0.0950770i	−0.892166	−	0.451708i	$-0.850815\pi$
$227$	−0.827042	+	1.43248i	−0.0548927	+	0.0950770i	0.837273	+	0.546785i	$0.184148\pi$
$228$	−7.36405	+	3.56375i	−0.487696	+	0.236015i
$229$	11.9622	+	20.7191i	0.790481	+	1.36915i	0.925669	+	0.378334i	$0.123503\pi$
$229$	11.9622	+	20.7191i	0.790481	+	1.36915i	−0.135188	+	0.990820i	$0.543164\pi$
$230$	−8.15735	−	14.1289i	−0.537880	−	0.931635i
$231$	−4.87369	−	2.07414i	−0.320665	−	0.136468i
$232$	−5.31070	+	9.19841i	−0.348665	+	0.603905i
$233$	−3.45893	+	5.99103i	−0.226602	+	0.392486i	−0.956799	−	0.290751i	$-0.906095\pi$
$233$	−3.45893	+	5.99103i	−0.226602	+	0.392486i	0.730197	+	0.683237i	$0.239428\pi$
$234$	7.58549	+	13.1385i	0.495879	+	0.858888i
$235$	15.2421	−	26.4000i	0.994282	−	1.72215i
$236$	−5.63251	−	9.75579i	−0.366645	−	0.635048i
$237$	14.7018	−	25.4642i	0.954982	−	1.65408i
$238$	−0.881714	−	0.375239i	−0.0571530	−	0.0243231i
$239$	−25.6394			−1.65848			−0.829239	−	0.558894i	$-0.811226\pi$
$239$	−25.6394			−1.65848			−0.829239	+	0.558894i	$0.811226\pi$
$240$	5.78631	+	10.0222i	0.373505	+	0.646929i
$241$	2.69441	+	4.66685i	0.173562	+	0.300618i	0.939663	−	0.342102i	$-0.111139\pi$
$241$	2.69441	+	4.66685i	0.173562	+	0.300618i	−0.766101	+	0.642721i	$0.777806\pi$
$242$	−11.1910			−0.719383
$243$	−19.9850			−1.28204
$244$	−4.51912	−	7.82735i	−0.289307	−	0.501095i
$245$	5.61053	−	19.4290i	0.358443	−	1.24127i
$246$	−3.85111			−0.245538
$247$	21.0624	+	14.3010i	1.34017	+	0.909950i
$248$	2.27397	−	3.93863i	0.144397	−	0.250103i
$249$	−13.6563			−0.865430
$250$	2.60693	−	4.51533i	0.164877	−	0.285575i
$251$	5.90996	−	10.2364i	0.373034	−	0.646113i	−0.616997	−	0.786965i	$-0.711651\pi$
$251$	5.90996	−	10.2364i	0.373034	−	0.646113i	0.990031	+	0.140852i	$0.0449843\pi$
$252$	4.07250	−	3.06288i	0.256543	−	0.192943i
$253$	2.23321	−	3.86804i	0.140401	−	0.243181i
$254$	1.64447	+	2.84831i	0.103183	+	0.178719i
$255$	1.11202	−	1.92608i	0.0696375	−	0.120616i
$256$	7.90617	+	13.6939i	0.494135	+	0.855868i
$257$	−11.6780			−0.728453			−0.364226	−	0.931310i	$-0.618667\pi$
$257$	−11.6780			−0.728453			−0.364226	+	0.931310i	$0.618667\pi$
$258$	−0.154146			−0.00959673
$259$	−15.1596	+	11.4013i	−0.941969	+	0.708444i
$260$	−6.82656	+	11.8239i	−0.423365	+	0.733290i
$261$	4.12360	−	7.14228i	0.255244	−	0.442096i
$262$	−5.07782	−	8.79505i	−0.313709	−	0.543360i
$263$	6.22885			0.384087			0.192044	−	0.981386i	$-0.438488\pi$
$263$	6.22885			0.384087			0.192044	+	0.981386i	$0.438488\pi$
$264$	−3.06852	+	5.31483i	−0.188854	+	0.327105i
$265$	−19.5973			−1.20385
$266$	−5.75834	+	11.1904i	−0.353066	+	0.686126i
$267$	36.3482			2.22447
$268$	−5.38858	+	9.33329i	−0.329160	+	0.570122i
$269$	−6.23165			−0.379951			−0.189975	−	0.981789i	$-0.560841\pi$
$269$	−6.23165			−0.379951			−0.189975	+	0.981789i	$0.560841\pi$
$270$	2.26591	+	3.92467i	0.137899	+	0.238848i
$271$	8.74099	−	15.1398i	0.530977	−	0.919680i	−0.468369	−	0.883533i	$-0.655158\pi$
$271$	8.74099	−	15.1398i	0.530977	−	0.919680i	0.999346	−	0.0361467i	$-0.0115084\pi$
$272$	−0.286584	+	0.496378i	−0.0173767	+	0.0300974i
$273$	−32.9809	−	14.0360i	−1.99610	−	0.849497i
$274$	6.17460			0.373021
$275$	−2.88804			−0.174155
$276$	4.85634	+	8.41142i	0.292317	+	0.506308i
$277$	4.08665	−	7.07828i	0.245543	−	0.425293i	−0.716741	−	0.697339i	$-0.754367\pi$
$277$	4.08665	−	7.07828i	0.245543	−	0.425293i	0.962284	+	0.272047i	$0.0877005\pi$
$278$	−9.13783	−	15.8272i	−0.548051	−	0.949252i
$279$	−1.76567	+	3.05823i	−0.105708	+	0.183091i
$280$	−21.5601	−	9.17551i	−1.28846	−	0.548342i
$281$	6.61418	−	11.4561i	0.394569	−	0.683413i	−0.598477	−	0.801140i	$-0.704227\pi$
$281$	6.61418	−	11.4561i	0.394569	−	0.683413i	0.993046	+	0.117727i	$0.0375607\pi$
$282$	13.3546	−	23.1308i	0.795253	−	1.37742i
$283$	4.36799			0.259650			0.129825	−	0.991537i	$-0.458558\pi$
$283$	4.36799			0.259650			0.129825	+	0.991537i	$0.458558\pi$
$284$	0.587437	−	1.01747i	0.0348580	−	0.0603758i
$285$	−24.1655	−	16.4079i	−1.43144	−	0.971923i
$286$	5.50097			0.325279
$287$	3.21705	−	2.41951i	0.189897	−	0.142819i
$288$	−5.05387	−	8.75356i	−0.297802	−	0.515808i
$289$	−16.8898			−0.993520
$290$	−10.9232			−0.641434
$291$	2.81615	+	4.87772i	0.165086	+	0.285937i
$292$	1.99576	+	3.45676i	0.116793	+	0.202292i
$293$	2.59327			0.151501			0.0757504	−	0.997127i	$-0.475865\pi$
$293$	2.59327			0.151501			0.0757504	+	0.997127i	$0.475865\pi$
$294$	4.91575	−	17.0230i	0.286693	−	0.992802i
$295$	20.1102	−	34.8319i	1.17086	−	2.02799i
$296$	10.9890	+	19.0334i	0.638720	+	1.10630i
$297$	−0.620331	+	1.07444i	−0.0359952	+	0.0623456i
$298$	−1.47341	−	2.55202i	−0.0853524	−	0.147835i
$299$	15.1125	−	26.1755i	0.873976	−	1.51377i
$300$	3.14016	−	5.43892i	0.181297	−	0.314016i
$301$	0.128767	−	0.0968444i	0.00742203	−	0.00558202i
$302$	−6.63447	−	11.4912i	−0.381771	−	0.661246i
$303$	−0.946631	−	1.63961i	−0.0543825	−	0.0941933i
$304$	6.22780	+	4.22857i	0.357189	+	0.242525i
$305$	16.1350	−	27.9466i	0.923887	−	1.60022i
$306$	0.431045	−	0.746592i	0.0246412	−	0.0426798i
$307$	3.81419	+	6.60637i	0.217687	+	0.377046i	0.954101	−	0.299486i	$-0.0968153\pi$
$307$	3.81419	+	6.60637i	0.217687	+	0.377046i	−0.736413	+	0.676532i	$0.763482\pi$
$308$	−0.223463	−	1.83414i	−0.0127330	−	0.104510i
$309$	7.73028	+	13.3892i	0.439760	+	0.761687i
$310$	4.67718			0.265646
$311$	−4.51348	+	7.81758i	−0.255936	+	0.443294i	−0.965149	−	0.261700i	$-0.915717\pi$
$311$	−4.51348	+	7.81758i	−0.255936	+	0.443294i	0.709213	+	0.704994i	$0.249050\pi$
$312$	−20.7651	+	35.9662i	−1.17559	+	2.03618i
$313$	14.1377			0.799108			0.399554	−	0.916710i	$-0.369165\pi$
$313$	14.1377			0.799108			0.399554	+	0.916710i	$0.369165\pi$
$314$	−7.81230	+	13.5313i	−0.440874	+	0.763615i
$315$	16.7407	+	7.12450i	0.943232	+	0.401420i
$316$	10.2572			0.577010
$317$	−9.31755			−0.523326			−0.261663	−	0.965159i	$-0.584271\pi$
$317$	−9.31755			−0.523326			−0.261663	+	0.965159i	$0.584271\pi$
$318$	−17.1705			−0.962873
$319$	−1.49521	−	2.58978i	−0.0837156	−	0.145000i
$320$	−11.6829	+	20.2354i	−0.653095	+	1.13119i
$321$	6.36715	+	11.0282i	0.355380	+	0.615536i
$322$	13.7479	+	5.85084i	0.766143	+	0.326054i
$323$	0.105344	−	1.44284i	0.00586149	−	0.0802820i
$324$	−4.23798	−	7.34039i	−0.235443	−	0.407799i
$325$	−19.5438			−1.08409
$326$	15.2056			0.842160
$327$	8.89900			0.492116
$328$	−2.33200	−	4.03914i	−0.128763	−	0.223024i
$329$	3.37638	+	27.7127i	0.186146	+	1.52785i
$330$	−6.31143			−0.347433
$331$	−0.165094	−	0.285951i	−0.00907438	−	0.0157173i	0.861453	−	0.507838i	$-0.169555\pi$
$331$	−0.165094	−	0.285951i	−0.00907438	−	0.0157173i	−0.870527	+	0.492121i	$0.836222\pi$
$332$	−2.38193	−	4.12563i	−0.130725	−	0.226423i
$333$	−8.53258	−	14.7789i	−0.467583	−	0.809877i
$334$	6.87980	+	11.9162i	0.376446	+	0.652024i
$335$	−38.4785			−2.10231
$336$	−9.75192	−	4.15021i	−0.532011	−	0.226413i
$337$	2.28337	+	3.95491i	0.124383	+	0.215438i	0.921492	−	0.388398i	$-0.126972\pi$
$337$	2.28337	+	3.95491i	0.124383	+	0.215438i	−0.797109	+	0.603836i	$0.793638\pi$
$338$	23.0394			1.25318
$339$	20.9551			1.13813
$340$	0.775838			0.0420757
$341$	0.640228	+	1.10891i	0.0346703	+	0.0600507i
$342$	−9.36709	−	6.36010i	−0.506514	−	0.343915i
$343$	6.58852	+	17.3087i	0.355747	+	0.934582i
$344$	−0.0933417	−	0.161673i	−0.00503265	−	0.00871680i
$345$	−17.3390	+	30.0320i	−0.933499	+	1.61687i
$346$	8.20575	+	14.2128i	0.441144	+	0.764084i
$347$	−13.5201			−0.725796			−0.362898	−	0.931829i	$-0.618213\pi$
$347$	−13.5201			−0.725796			−0.362898	+	0.931829i	$0.618213\pi$
$348$	6.50295			0.348595
$349$	15.3481			0.821566			0.410783	−	0.911733i	$-0.365255\pi$
$349$	15.3481			0.821566			0.410783	+	0.911733i	$0.365255\pi$
$350$	−1.16842	−	9.59020i	−0.0624549	−	0.512618i
$351$	−4.19786	+	7.27091i	−0.224065	+	0.388092i
$352$	−3.66505			−0.195348
$353$	8.44456	−	14.6264i	0.449459	−	0.778485i	−0.548892	−	0.835893i	$-0.684950\pi$
$353$	8.44456	−	14.6264i	0.449459	−	0.778485i	0.998351	+	0.0574080i	$0.0182836\pi$
$354$	17.6199	−	30.5185i	0.936485	−	1.62204i
$355$	4.19474			0.222634
$356$	6.33986	+	10.9810i	0.336012	+	0.581990i
$357$	0.246332	+	2.02185i	0.0130373	+	0.107008i
$358$	13.5450	+	23.4606i	0.715873	+	1.23993i
$359$	−4.15464	+	7.19605i	−0.219274	+	0.379793i	−0.954586	−	0.297935i	$-0.903702\pi$
$359$	−4.15464	+	7.19605i	−0.219274	+	0.379793i	0.735312	+	0.677728i	$0.237035\pi$
$360$	10.5401	−	18.2560i	0.555512	−	0.962176i
$361$	−18.7985	−	2.75972i	−0.989395	−	0.145248i
$362$	−8.63120	−	14.9497i	−0.453646	−	0.785737i
$363$	11.8936	+	20.6002i	0.624250	+	1.08123i
$364$	−1.51220	−	12.4119i	−0.0792609	−	0.650559i
$365$	−7.12563	+	12.3419i	−0.372972	+	0.646007i
$366$	14.1369	−	24.4859i	0.738949	−	1.27990i
$367$	−3.19032	−	5.52579i	−0.166533	−	0.288444i	0.770666	−	0.637240i	$-0.219924\pi$
$367$	−3.19032	−	5.52579i	−0.166533	−	0.288444i	−0.937199	+	0.348796i	$0.886591\pi$
$368$	4.46850	−	7.73967i	0.232937	−	0.403458i
$369$	1.81072	+	3.13627i	0.0942625	+	0.163268i
$370$	−11.3012	+	19.5743i	−0.587522	+	1.01762i
$371$	14.3435	−	10.7876i	0.744678	−	0.560064i
$372$	−2.78448			−0.144368
$373$	−14.1709	−	24.5447i	−0.733742	−	1.27088i	−0.955273	−	0.295725i	$-0.904439\pi$
$373$	−14.1709	−	24.5447i	−0.733742	−	1.27088i	0.221532	−	0.975153i	$-0.428894\pi$
$374$	−0.156296	−	0.270713i	−0.00808189	−	0.0139982i
$375$	−11.0824			−0.572291
$376$	32.3469			1.66816
$377$	−10.1183	−	17.5254i	−0.521118	−	0.902603i
$378$	−3.81883	−	1.62522i	−0.196420	−	0.0835921i
$379$	−0.233212			−0.0119793			−0.00598964	−	0.999982i	$-0.501907\pi$
$379$	−0.233212			−0.0119793			−0.00598964	+	0.999982i	$0.501907\pi$
$380$	0.741969	−	10.1624i	0.0380622	−	0.521320i
$381$	3.49543	−	6.05426i	0.179076	−	0.310169i
$382$	−0.750111			−0.0383790
$383$	−8.79279	+	15.2296i	−0.449291	+	0.778194i	−0.998340	−	0.0575956i	$-0.981657\pi$
$383$	−8.79279	+	15.2296i	−0.449291	+	0.778194i	0.549049	+	0.835790i	$0.314990\pi$
$384$	−0.386351	+	0.669180i	−0.0197159	+	0.0341490i
$385$	5.27231	−	3.96524i	0.268702	−	0.202087i
$386$	−7.68212	+	13.3058i	−0.391010	+	0.677249i
$387$	0.0724769	+	0.125534i	0.00368421	+	0.00638124i
$388$	−0.982389	+	1.70155i	−0.0498733	+	0.0863830i
$389$	12.3271	+	21.3512i	0.625009	+	1.08255i	0.988539	+	0.150965i	$0.0482380\pi$
$389$	12.3271	+	21.3512i	0.625009	+	1.08255i	−0.363530	+	0.931582i	$0.618429\pi$
$390$	−42.7103			−2.16272
$391$	−1.71753			−0.0868591
$392$	20.8309	−	5.15235i	1.05212	−	0.260233i
$393$	−10.7932	+	18.6944i	−0.544447	+	0.943009i
$394$	−4.51506	+	7.82031i	−0.227465	+	0.393981i
$395$	18.3110	+	31.7155i	0.921324	+	1.59578i
$396$	1.66230			0.0835339
$397$	−4.22589	+	7.31945i	−0.212091	+	0.367353i	−0.952369	−	0.304949i	$-0.901361\pi$
$397$	−4.22589	+	7.31945i	−0.212091	+	0.367353i	0.740278	+	0.672301i	$0.234694\pi$
$398$	18.9583			0.950293
$399$	26.7190	−	1.29302i	1.33762	−	0.0647322i
$400$	−5.77877			−0.288938
$401$	2.71343	−	4.69980i	0.135502	−	0.234697i	−0.790287	−	0.612737i	$-0.790069\pi$
$401$	2.71343	−	4.69980i	0.135502	−	0.234697i	0.925789	+	0.378040i	$0.123402\pi$
$402$	−33.7136			−1.68148
$403$	4.33251	+	7.50412i	0.215818	+	0.373807i
$404$	0.330224	−	0.571964i	0.0164292	−	0.0284563i
$405$	15.1312	−	26.2080i	0.751874	−	1.30228i
$406$	7.99485	−	6.01284i	0.396778	−	0.298412i
$407$	−6.18780			−0.306718
$408$	2.35995			0.116835
$409$	−6.80989	−	11.7951i	−0.336727	−	0.583229i	0.647088	−	0.762416i	$-0.275987\pi$
$409$	−6.80989	−	11.7951i	−0.336727	−	0.583229i	−0.983815	+	0.179187i	$0.942653\pi$
$410$	2.39827	−	4.15392i	0.118442	−	0.205147i
$411$	−6.56225	−	11.3662i	−0.323692	−	0.560651i
$412$	−2.69664	+	4.67071i	−0.132854	+	0.230110i
$413$	4.45476	+	36.5638i	0.219204	+	1.79919i
$414$	−6.72098	+	11.6411i	−0.330318	+	0.572128i
$415$	8.50440	−	14.7300i	0.417464	−	0.723070i
$416$	−24.8019			−1.21601
$417$	−19.4230	+	33.6417i	−0.951150	+	1.64744i
$418$	−3.69544	+	1.78837i	−0.180750	+	0.0874720i
$419$	−7.84926			−0.383461			−0.191731	−	0.981448i	$-0.561410\pi$
$419$	−7.84926			−0.383461			−0.191731	+	0.981448i	$0.561410\pi$
$420$	1.73499	+	14.2405i	0.0846591	+	0.694866i
$421$	5.38356	+	9.32459i	0.262378	+	0.454453i	0.966873	−	0.255256i	$-0.0821598\pi$
$421$	5.38356	+	9.32459i	0.262378	+	0.454453i	−0.704495	+	0.709709i	$0.748826\pi$
$422$	−11.0861			−0.539661
$423$	−25.1164			−1.22120
$424$	−10.3974	−	18.0089i	−0.504943	−	0.874587i
$425$	0.555287	+	0.961785i	0.0269354	+	0.0466534i
$426$	3.67529			0.178069
$427$	3.57418	+	29.3362i	0.172967	+	1.41968i
$428$	−2.22112	+	3.84710i	−0.107362	+	0.185957i
$429$	−5.84633	−	10.1261i	−0.282264	−	0.488895i
$430$	0.0959941	−	0.166267i	0.00462925	−	0.00801809i
$431$	1.03267	+	1.78864i	0.0497420	+	0.0861557i	0.889824	−	0.456303i	$-0.150827\pi$
$431$	1.03267	+	1.78864i	0.0497420	+	0.0861557i	−0.840082	+	0.542459i	$0.817493\pi$
$432$	−1.24124	+	2.14989i	−0.0597191	+	0.103437i
$433$	8.71951	−	15.1026i	0.419033	−	0.725786i	−0.576810	−	0.816879i	$-0.695703\pi$
$433$	8.71951	−	15.1026i	0.419033	−	0.725786i	0.995842	+	0.0910924i	$0.0290359\pi$
$434$	−3.42329	+	2.57461i	−0.164323	+	0.123585i
$435$	11.6090	+	20.1074i	0.556609	+	0.964075i
$436$	1.55217	+	2.68843i	0.0743353	+	0.128753i
$437$	−1.64255	+	22.4972i	−0.0785739	+	1.07619i
$438$	−6.24324	+	10.8136i	−0.298313	+	0.516694i
$439$	7.09651	−	12.2915i	0.338698	−	0.586642i	−0.645490	−	0.763769i	$-0.723347\pi$
$439$	7.09651	−	12.2915i	0.338698	−	0.586642i	0.984188	+	0.177127i	$0.0566802\pi$
$440$	−3.82182	−	6.61959i	−0.182198	−	0.315577i
$441$	−16.1745	+	4.00064i	−0.770215	+	0.190506i
$442$	−1.05768	−	1.83195i	−0.0503086	−	0.0871371i
$443$	36.6832			1.74287			0.871437	−	0.490508i	$-0.163189\pi$
$443$	36.6832			1.74287			0.871437	+	0.490508i	$0.163189\pi$
$444$	6.72798	−	11.6532i	0.319296	−	0.553037i
$445$	−22.6357	+	39.2062i	−1.07304	+	1.85855i
$446$	−10.9343			−0.517755
$447$	−3.13183	+	5.42448i	−0.148130	+	0.256569i
$448$	−2.58797	−	21.2416i	−0.122270	−	1.00357i
$449$	34.1399			1.61116			0.805580	−	0.592487i	$-0.201854\pi$
$449$	34.1399			1.61116			0.805580	+	0.592487i	$0.201854\pi$
$450$	8.69172			0.409732
$451$	1.31313			0.0618329
$452$	3.65500	+	6.33065i	0.171917	+	0.297769i
$453$	−14.1020	+	24.4254i	−0.662569	+	1.14760i
$454$	−0.902518	−	1.56321i	−0.0423573	−	0.0733649i
$455$	35.6784	−	26.8333i	1.67263	−	1.25797i
$456$	2.25693	−	30.9121i	0.105690	−	1.44759i
$457$	−14.1283	−	24.4709i	−0.660892	−	1.14470i	−0.980382	−	0.197109i	$-0.936845\pi$
$457$	−14.1283	−	24.4709i	−0.660892	−	1.14470i	0.319489	−	0.947590i	$-0.396489\pi$
$458$	−26.1076			−1.21993
$459$	0.477086			0.0222685
$460$	−12.0971			−0.564029
$461$	−11.5129	−	19.9410i	−0.536211	−	0.928745i	−0.999104	−	0.0423305i	$-0.986522\pi$
$461$	−11.5129	−	19.9410i	−0.536211	−	0.928745i	0.462893	−	0.886414i	$-0.346812\pi$
$462$	4.61942	−	3.47421i	0.214915	−	0.161635i
$463$	−34.4692			−1.60192			−0.800960	−	0.598718i	$-0.795677\pi$
$463$	−34.4692			−1.60192			−0.800960	+	0.598718i	$0.795677\pi$
$464$	−2.99181	−	5.18196i	−0.138891	−	0.240567i
$465$	−4.97082	−	8.60971i	−0.230516	−	0.399266i
$466$	−3.77459	−	6.53778i	−0.174854	−	0.302857i
$467$	7.44733	+	12.8992i	0.344622	+	0.596902i	0.985285	−	0.170920i	$-0.0546739\pi$
$467$	7.44733	+	12.8992i	0.344622	+	0.596902i	−0.640663	+	0.767822i	$0.721341\pi$
$468$	11.2490			0.519987
$469$	28.1629	−	21.1810i	1.30044	−	0.978049i
$470$	16.6330	+	28.8093i	0.767225	+	1.32887i
$471$	33.2111			1.53029
$472$	42.6781			1.96442
$473$	0.0525600			0.00241671
$474$	16.0434	+	27.7881i	0.736900	+	1.27635i
$475$	13.1291	−	6.35368i	0.602404	−	0.291527i
$476$	−0.567846	+	0.427070i	−0.0260272	+	0.0195747i
$477$	8.07327	+	13.9833i	0.369650	+	0.640252i
$478$	13.9897	−	24.2308i	0.639872	−	1.10829i
$479$	4.61297	+	7.98990i	0.210772	+	0.365068i	0.951956	−	0.306234i	$-0.0990689\pi$
$479$	4.61297	+	7.98990i	0.210772	+	0.365068i	−0.741184	+	0.671302i	$0.765736\pi$
$480$	28.4559			1.29883
$481$	−41.8737			−1.90927
$482$	−5.88060			−0.267854
$483$	−3.84088	−	31.5253i	−0.174766	−	1.43445i
$484$	−4.14896	+	7.18621i	−0.188589	+	0.326646i
$485$	−7.01501			−0.318535
$486$	10.9044	−	18.8870i	0.494636	−	0.856734i
$487$	−7.55001	+	13.0770i	−0.342124	+	0.592576i	−0.984827	−	0.173540i	$-0.944480\pi$
$487$	−7.55001	+	13.0770i	−0.342124	+	0.592576i	0.642703	+	0.766115i	$0.277813\pi$
$488$	34.2419			1.55006
$489$	−16.1602	−	27.9903i	−0.730790	−	1.26577i
$490$	15.3003	+	15.9033i	0.691195	+	0.718438i
$491$	−5.57058	−	9.64852i	−0.251397	−	0.435432i	0.712514	−	0.701658i	$-0.247556\pi$
$491$	−5.57058	−	9.64852i	−0.251397	−	0.435432i	−0.963911	+	0.266226i	$0.914223\pi$
$492$	−1.42777	+	2.47296i	−0.0643686	+	0.111490i
$493$	−0.574971	+	0.995878i	−0.0258954	+	0.0448521i
$494$	−25.0075	+	12.1021i	−1.12514	+	0.544501i
$495$	2.96753	+	5.13991i	0.133380	+	0.231022i
$496$	1.28105	+	2.21885i	0.0575209	+	0.0996291i
$497$	−3.07019	+	2.30905i	−0.137717	+	0.103575i
$498$	7.45127	−	12.9060i	0.333899	−	0.578330i
$499$	−11.7440	+	20.3412i	−0.525734	+	0.910598i	0.473817	+	0.880623i	$0.342876\pi$
$499$	−11.7440	+	20.3412i	−0.525734	+	0.910598i	−0.999551	+	0.0299743i	$0.990457\pi$
$500$	−1.93299	−	3.34804i	−0.0864461	−	0.149729i
$501$	14.6235	−	25.3286i	0.653328	−	1.13160i
$502$	6.44931	+	11.1705i	0.287847	+	0.498565i
$503$	11.6852	−	20.2394i	0.521018	−	0.902430i	−0.478683	−	0.877988i	$-0.658886\pi$
$503$	11.6852	−	20.2394i	0.521018	−	0.902430i	0.999701	−	0.0244425i	$-0.00778107\pi$
$504$	2.33482	+	19.1637i	0.104001	+	0.853621i
$505$	2.35805			0.104932
$506$	2.43702	+	4.22104i	0.108339	+	0.187648i
$507$	−24.4859	−	42.4108i	−1.08746	−	1.88353i
$508$	2.43870			0.108200
$509$	−7.69340			−0.341004			−0.170502	−	0.985357i	$-0.554539\pi$
$509$	−7.69340			−0.341004			−0.170502	+	0.985357i	$0.554539\pi$
$510$	1.21351	+	2.10185i	0.0537349	+	0.0930716i
$511$	−1.57845	−	12.9556i	−0.0698266	−	0.573123i
$512$	−17.9216			−0.792031
$513$	0.456260	−	6.24917i	0.0201444	−	0.275908i
$514$	6.37186	−	11.0364i	0.281051	−	0.486794i
$515$	−19.2560			−0.848522
$516$	−0.0571484	+	0.0989840i	−0.00251582	+	0.00435753i
$517$	−4.55358	+	7.88703i	−0.200266	+	0.346871i
$518$	−2.50342	−	20.5476i	−0.109994	−	0.902809i
$519$	17.4418	−	30.2102i	0.765612	−	1.32608i
$520$	−25.8628	−	44.7957i	−1.13416	−	1.96442i
$521$	9.89676	−	17.1417i	0.433585	−	0.750991i	−0.563594	−	0.826052i	$-0.690582\pi$
$521$	9.89676	−	17.1417i	0.433585	−	0.750991i	0.997179	+	0.0750609i	$0.0239151\pi$
$522$	4.49992	+	7.79408i	0.196956	+	0.341138i
$523$	−34.8684			−1.52469			−0.762344	−	0.647172i	$-0.775952\pi$
$523$	−34.8684			−1.52469			−0.762344	+	0.647172i	$0.775952\pi$
$524$	−7.53024			−0.328960
$525$	−16.4118	+	12.3431i	−0.716269	+	0.538698i
$526$	−3.39865	+	5.88663i	−0.148188	+	0.256669i
$527$	0.246195	−	0.426421i	0.0107244	−	0.0185752i
$528$	−1.72866	−	2.99414i	−0.0752305	−	0.130303i
$529$	3.78019			0.164356
$530$	10.6929	−	18.5206i	0.464469	−	0.804483i
$531$	−33.1382			−1.43808
$532$	5.05097	+	7.84642i	0.218987	+	0.340185i
$533$	8.88613			0.384901
$534$	−19.8327	+	34.3512i	−0.858243	+	1.48652i
$535$	−15.8605			−0.685709
$536$	−20.4149	−	35.3597i	−0.881791	−	1.52731i
$537$	28.7907	−	49.8669i	1.24241	−	2.15192i
$538$	3.40018	−	5.88928i	0.146592	−	0.253905i
$539$	−1.67615	+	5.80442i	−0.0721969	+	0.250014i
$540$	3.36027			0.144603
$541$	−10.8993			−0.468597			−0.234298	−	0.972165i	$-0.575279\pi$
$541$	−10.8993			−0.468597			−0.234298	+	0.972165i	$0.575279\pi$
$542$	9.53869	+	16.5215i	0.409722	+	0.709659i
$543$	−18.3462	+	31.7765i	−0.787309	+	1.36366i
$544$	0.704683	+	1.22055i	0.0302130	+	0.0523305i
$545$	−5.54182	+	9.59872i	−0.237386	+	0.411164i
$546$	31.2602	−	23.5105i	1.33781	−	1.00615i
$547$	−17.1530	+	29.7099i	−0.733411	+	1.27030i	0.222006	+	0.975045i	$0.428739\pi$
$547$	−17.1530	+	29.7099i	−0.733411	+	1.27030i	−0.955417	+	0.295259i	$0.904594\pi$
$548$	2.28918	−	3.96498i	0.0977890	−	0.169376i
$549$	−26.5878			−1.13474
$550$	1.57580	−	2.72937i	0.0671924	−	0.116381i
$551$	12.4948	+	8.48372i	0.532294	+	0.361419i
$552$	−36.7970			−1.56618
$553$	−30.8603	−	13.1335i	−1.31231	−	0.558493i
$554$	4.45959	+	7.72424i	0.189470	+	0.328172i
$555$	48.0429			2.03931
$556$	−13.5511			−0.574695
$557$	8.90588	+	15.4254i	0.377354	+	0.653597i	0.990676	−	0.136236i	$-0.0435006\pi$
$557$	8.90588	+	15.4254i	0.377354	+	0.653597i	−0.613322	+	0.789833i	$0.710167\pi$
$558$	−1.92680	−	3.33732i	−0.0815681	−	0.141280i
$559$	0.355681			0.0150437
$560$	10.5495	−	7.93417i	0.445799	−	0.335280i
$561$	−0.332218	+	0.575418i	−0.0140262	+	0.0242942i
$562$	7.21779	+	12.5016i	0.304464	+	0.527347i
$563$	1.14374	−	1.98102i	0.0482029	−	0.0834899i	−0.840917	−	0.541164i	$-0.817984\pi$
$563$	1.14374	−	1.98102i	0.0482029	−	0.0834899i	0.889120	+	0.457674i	$0.151317\pi$
$564$	−9.90220	−	17.1511i	−0.416958	−	0.722192i
$565$	−13.0498	+	22.6028i	−0.549007	+	0.950908i
$566$	−2.38331	+	4.12801i	−0.100178	+	0.173513i
$567$	3.35182	+	27.5111i	0.140763	+	1.15536i
$568$	2.22554	+	3.85474i	0.0933815	+	0.161741i
$569$	−3.40444	−	5.89667i	−0.142722	−	0.247201i	0.785799	−	0.618482i	$-0.212252\pi$
$569$	−3.40444	−	5.89667i	−0.142722	−	0.247201i	−0.928521	+	0.371281i	$0.878919\pi$
$570$	28.6919	−	13.8851i	1.20177	−	0.581584i
$571$	5.92163	−	10.2566i	0.247813	−	0.429224i	−0.715106	−	0.699016i	$-0.753622\pi$
$571$	5.92163	−	10.2566i	0.247813	−	0.429224i	0.962919	+	0.269792i	$0.0869549\pi$
$572$	2.03944	−	3.53241i	0.0852733	−	0.147698i
$573$	0.797205	+	1.38080i	0.0333037	+	0.0576837i
$574$	0.531258	+	4.36046i	0.0221743	+	0.182002i
$575$	−8.65819	−	14.9964i	−0.361071	−	0.625394i
$576$	19.2515			0.802146
$577$	18.7267	−	32.4355i	0.779601	−	1.35031i	−0.152571	−	0.988293i	$-0.548755\pi$
$577$	18.7267	−	32.4355i	0.779601	−	1.35031i	0.932172	−	0.362016i	$-0.117911\pi$
$578$	9.21561	−	15.9619i	0.383319	−	0.663928i
$579$	32.6577			1.35721
$580$	−4.04970	+	7.01428i	−0.168154	+	0.291252i
$581$	1.88387	+	15.4625i	0.0781562	+	0.641491i
$582$	−6.14631			−0.254773
$583$	5.85471			0.242477
$584$	−15.1221			−0.625758
$585$	20.0817	+	34.7825i	0.830274	+	1.43808i
$586$	−1.41497	+	2.45080i	−0.0584518	+	0.101242i
$587$	16.0525	+	27.8037i	0.662557	+	1.14758i	0.979941	+	0.199286i	$0.0638623\pi$
$587$	16.0525	+	27.8037i	0.662557	+	1.14758i	−0.317384	+	0.948297i	$0.602804\pi$
$588$	−9.10874	−	9.46776i	−0.375638	−	0.390444i
$589$	−5.35008	−	3.63261i	−0.220446	−	0.149679i
$590$	21.9454	+	38.0106i	0.903480	+	1.56487i
$591$	19.1941			0.789539
$592$	−12.3814			−0.508871
$593$	−7.61005			−0.312507			−0.156254	−	0.987717i	$-0.549942\pi$
$593$	−7.61005			−0.312507			−0.156254	+	0.987717i	$0.549942\pi$
$594$	−0.676942	−	1.17250i	−0.0277753	−	0.0481082i
$595$	−2.33423	−	0.993399i	−0.0956941	−	0.0407254i
$596$	−2.18502			−0.0895018
$597$	−20.1485	−	34.8983i	−0.824624	−	1.42829i
$598$	16.4916	+	28.5643i	0.674392	+	1.16808i
$599$	−18.4778	−	32.0045i	−0.754982	−	1.30767i	−0.945383	−	0.325961i	$-0.894312\pi$
$599$	−18.4778	−	32.0045i	−0.754982	−	1.30767i	0.190401	−	0.981706i	$-0.439021\pi$
$600$	11.8967	+	20.6057i	0.485680	+	0.841223i
$601$	27.2405			1.11116			0.555581	−	0.831463i	$-0.312496\pi$
$601$	27.2405			1.11116			0.555581	+	0.831463i	$0.312496\pi$
$602$	0.0212644	+	0.174534i	0.000866671	+	0.00711347i
$603$	15.8516	+	27.4557i	0.645526	+	1.11808i
$604$	−9.83870			−0.400331
$605$	−29.6267			−1.20450
$606$	2.06604			0.0839272
$607$	3.14488	+	5.44710i	0.127647	+	0.221091i	0.922764	−	0.385364i	$-0.125924\pi$
$607$	3.14488	+	5.44710i	0.127647	+	0.221091i	−0.795118	+	0.606455i	$0.792591\pi$
$608$	16.6614	−	8.06310i	0.675708	−	0.327002i
$609$	−19.5652	−	8.32652i	−0.792820	−	0.337408i
$610$	17.6075	+	30.4970i	0.712905	+	1.23479i
$611$	−30.8147	+	53.3726i	−1.24663	+	2.15922i
$612$	−0.319613	−	0.553586i	−0.0129196	−	0.0223774i
$613$	−3.99269			−0.161263			−0.0806316	−	0.996744i	$-0.525694\pi$
$613$	−3.99269			−0.161263			−0.0806316	+	0.996744i	$0.525694\pi$
$614$	−8.32455			−0.335951
$615$	−10.1953			−0.411115
$616$	6.44109	+	2.74119i	0.259519	+	0.110446i
$617$	14.2324	−	24.6512i	0.572973	−	0.992419i	−0.423285	−	0.905996i	$-0.639123\pi$
$617$	14.2324	−	24.6512i	0.572973	−	0.992419i	0.996259	−	0.0864223i	$-0.0275434\pi$
$618$	−16.8715			−0.678671
$619$	−19.5255	+	33.8192i	−0.784798	+	1.35931i	0.144322	+	0.989531i	$0.453900\pi$
$619$	−19.5255	+	33.8192i	−0.784798	+	1.35931i	−0.929120	+	0.369779i	$0.879433\pi$
$620$	1.73402	−	3.00342i	0.0696401	−	0.120620i
$621$	−7.43887			−0.298511
$622$	−4.92538	−	8.53101i	−0.197490	−	0.342062i
$623$	−5.01421	−	41.1557i	−0.200890	−	1.64887i
$624$	−11.6981	−	20.2617i	−0.468299	−	0.811118i
$625$	15.2670	−	26.4432i	0.610679	−	1.05773i
$626$	−7.71393	+	13.3609i	−0.308311	+	0.534010i
$627$	7.21946	+	4.90189i	0.288317	+	0.195763i
$628$	5.79269	+	10.0332i	0.231154	+	0.400370i
$629$	1.18973	+	2.06068i	0.0474378	+	0.0821647i
$630$	−15.8673	+	11.9336i	−0.632169	+	0.475447i
$631$	6.17121	−	10.6889i	0.245672	−	0.425516i	−0.716648	−	0.697435i	$-0.754325\pi$
$631$	6.17121	−	10.6889i	0.245672	−	0.425516i	0.962320	+	0.271918i	$0.0876580\pi$
$632$	−19.4299	+	33.6536i	−0.772880	+	1.33867i
$633$	11.7821	+	20.4071i	0.468295	+	0.811110i
$634$	5.08393	−	8.80563i	0.201909	−	0.349716i
$635$	4.35353	+	7.54054i	0.172765	+	0.299237i
$636$	−6.36582	+	11.0259i	−0.252421	+	0.437206i
$637$	−11.3427	+	39.2793i	−0.449415	+	1.55630i
$638$	3.26332			0.129196
$639$	−1.72806	−	2.99309i	−0.0683610	−	0.118405i
$640$	−0.481198	−	0.833460i	−0.0190210	−	0.0329454i
$641$	45.2272			1.78637			0.893183	−	0.449693i	$-0.148467\pi$
$641$	45.2272			1.78637			0.893183	+	0.449693i	$0.148467\pi$
$642$	−13.8964			−0.548449
$643$	2.15938	+	3.74015i	0.0851575	+	0.147497i	0.905458	−	0.424435i	$-0.139527\pi$
$643$	2.15938	+	3.74015i	0.0851575	+	0.147497i	−0.820301	+	0.571932i	$0.806194\pi$
$644$	8.85401	−	6.65900i	0.348897	−	0.262401i
$645$	−0.408083			−0.0160683
$646$	1.30609	+	0.886815i	0.0513876	+	0.0348913i
$647$	−18.5030	+	32.0481i	−0.727426	+	1.25994i	0.230541	+	0.973063i	$0.425950\pi$
$647$	−18.5030	+	32.0481i	−0.727426	+	1.25994i	−0.957967	+	0.286877i	$0.907383\pi$
$648$	32.1116			1.26146
$649$	−6.00794	+	10.4061i	−0.235832	+	0.408473i
$650$	10.6637	−	18.4700i	0.418263	−	0.724453i
$651$	8.37753	+	3.56530i	0.328341	+	0.139735i
$652$	5.63735	−	9.76417i	0.220776	−	0.382394i
$653$	14.3405	+	24.8384i	0.561185	+	0.972001i	0.997393	+	0.0721556i	$0.0229878\pi$
$653$	14.3405	+	24.8384i	0.561185	+	0.972001i	−0.436208	+	0.899846i	$0.643679\pi$
$654$	−4.85556	+	8.41008i	−0.189867	+	0.328860i
$655$	−13.4429	−	23.2838i	−0.525258	−	0.909774i
$656$	2.62748			0.102586
$657$	11.7419			0.458093
$658$	−28.0324	−	11.9300i	−1.09282	−	0.465080i
$659$	−12.3874	+	21.4557i	−0.482546	+	0.835794i	−0.999799	−	0.0200383i	$-0.993621\pi$
$659$	−12.3874	+	21.4557i	−0.482546	+	0.835794i	0.517253	+	0.855832i	$0.326955\pi$
$660$	−2.33991	+	4.05284i	−0.0910809	+	0.157757i
$661$	−5.71261	−	9.89453i	−0.222195	−	0.384853i	0.733279	−	0.679927i	$-0.237989\pi$
$661$	−5.71261	−	9.89453i	−0.222195	−	0.384853i	−0.955474	+	0.295075i	$0.904655\pi$
$662$	0.360321			0.0140043
$663$	−2.24816	+	3.89393i	−0.0873113	+	0.151228i
$664$	18.0482			0.700404
$665$	−15.2445	+	29.6251i	−0.591156	+	1.14881i
$666$	18.6225			0.721608
$667$	8.96511	−	15.5280i	0.347130	−	0.601247i
$668$	10.2025			0.394747
$669$	11.6208	+	20.1278i	0.449286	+	0.778186i
$670$	20.9950	−	36.3645i	0.811110	−	1.40488i
$671$	−4.82034	+	8.34908i	−0.186087	+	0.322313i
$672$	−20.8273	+	15.6639i	−0.803429	+	0.604250i
$673$	−31.7573			−1.22415			−0.612077	−	0.790799i	$-0.709666\pi$
$673$	−31.7573			−1.22415			−0.612077	+	0.790799i	$0.709666\pi$
$674$	−4.98350			−0.191957
$675$	2.40503	+	4.16563i	0.0925696	+	0.160335i
$676$	8.54168	−	14.7946i	0.328526	−	0.569024i
$677$	−14.8197	−	25.6685i	−0.569569	−	0.986522i	−0.996608	−	0.0822891i	$-0.973777\pi$
$677$	−14.8197	−	25.6685i	−0.569569	−	0.986522i	0.427040	−	0.904233i	$-0.359556\pi$
$678$	−11.4338	+	19.8038i	−0.439111	+	0.760562i
$679$	5.13437	−	3.86150i	0.197039	−	0.148191i
$680$	−1.46965	+	2.54551i	−0.0563586	+	0.0976159i
$681$	−1.91836	+	3.32270i	−0.0735117	+	0.127326i
$682$	−1.39731			−0.0535058
$683$	7.61536	−	13.1902i	0.291394	−	0.504708i	−0.682746	−	0.730656i	$-0.739214\pi$
$683$	7.61536	−	13.1902i	0.291394	−	0.504708i	0.974140	+	0.225947i	$0.0725477\pi$
$684$	−7.55687	+	3.65707i	−0.288944	+	0.139831i
$685$	16.3465			0.624567
$686$	−19.9526	−	3.21761i	−0.761796	−	0.122849i
$687$	27.7467	+	48.0587i	1.05860	+	1.83355i
$688$	0.105169			0.00400953
$689$	39.6196			1.50939
$690$	−18.9213	−	32.7727i	−0.720322	−	1.24764i
$691$	−19.9121	−	34.4888i	−0.757493	−	1.31202i	−0.944125	−	0.329587i	$-0.893090\pi$
$691$	−19.9121	−	34.4888i	−0.757493	−	1.31202i	0.186632	−	0.982430i	$-0.440243\pi$
$692$	12.1689			0.462591
$693$	−5.00130	−	2.12845i	−0.189984	−	0.0808532i
$694$	7.37696	−	12.7773i	0.280026	−	0.485019i
$695$	−24.1913	−	41.9005i	−0.917627	−	1.58938i
$696$	−12.3184	+	21.3361i	−0.466928	+	0.808743i
$697$	−0.252477	−	0.437303i	−0.00956325	−	0.0165640i
$698$	−8.37439	+	14.5049i	−0.316976	+	0.549018i
$699$	−8.02312	+	13.8965i	−0.303462	+	0.525612i
$700$	−6.59147	−	2.80519i	−0.249134	−	0.106026i
$701$	24.7904	+	42.9383i	0.936322	+	1.62176i	0.772260	+	0.635307i	$0.219126\pi$
$701$	24.7904	+	42.9383i	0.936322	+	1.62176i	0.164062	+	0.986450i	$0.447540\pi$
$702$	−4.58096	−	7.93445i	−0.172897	−	0.299467i
$703$	28.1298	−	13.6131i	1.06094	−	0.513429i
$704$	3.49028	−	6.04535i	0.131545	−	0.227843i
$705$	35.3546	−	61.2359i	1.33153	−	2.30628i
$706$	9.21521	+	15.9612i	0.346819	+	0.600708i
$707$	−1.72588	+	1.29802i	−0.0649086	+	0.0488170i
$708$	−13.0648	−	22.6290i	−0.491007	−	0.850449i
$709$	43.3911			1.62959			0.814793	−	0.579752i	$-0.196850\pi$
$709$	43.3911			1.62959			0.814793	+	0.579752i	$0.196850\pi$
$710$	−2.28878	+	3.96428i	−0.0858963	+	0.148777i
$711$	15.0867	−	26.1310i	0.565796	−	0.979987i
$712$	−48.0379			−1.80029
$713$	−3.83874	+	6.64889i	−0.143762	+	0.249003i
$714$	−2.04517	−	0.870383i	−0.0765387	−	0.0325733i
$715$	14.5632			0.544631
$716$	20.0867			0.750676
$717$	−59.4718			−2.22101
$718$	−4.53380	−	7.85277i	−0.169200	−	0.293063i
$719$	−12.2055	+	21.1405i	−0.455187	+	0.788408i	−0.998699	−	0.0509939i	$-0.983761\pi$
$719$	−12.2055	+	21.1405i	−0.455187	+	0.788408i	0.543512	+	0.839402i	$0.317094\pi$
$720$	5.93782	+	10.2846i	0.221289	+	0.383284i
$721$	14.0937	−	10.5997i	0.524878	−	0.394755i
$722$	12.8651	−	16.2599i	0.478790	−	0.605131i
$723$	6.24979	+	10.8250i	0.232432	+	0.402585i
$724$	−12.7998			−0.475700
$725$	−11.5939			−0.430586
$726$	−25.9579			−0.963389
$727$	−2.87267	−	4.97561i	−0.106541	−	0.184535i	0.807825	−	0.589422i	$-0.200644\pi$
$727$	−2.87267	−	4.97561i	−0.106541	−	0.184535i	−0.914367	+	0.404886i	$0.867311\pi$
$728$	43.5877	+	18.5500i	1.61547	+	0.687509i
$729$	−14.9308			−0.552994
$730$	−7.77591	−	13.4683i	−0.287799	−	0.498483i
$731$	−0.0101058	−	0.0175037i	−0.000373775	−	0.000647398i
$732$	−10.4823	−	18.1559i	−0.387437	−	0.671060i
$733$	9.04881	+	15.6730i	0.334226	+	0.578896i	0.983336	−	0.181799i	$-0.0581919\pi$
$733$	9.04881	+	15.6730i	0.334226	+	0.578896i	−0.649110	+	0.760694i	$0.724859\pi$
$734$	6.96293			0.257006
$735$	13.0139	−	45.0663i	0.480023	−	1.66230i
$736$	−10.9876	−	19.0311i	−0.405009	−	0.701496i
$737$	11.4955			0.423442
$738$	−3.95194			−0.145473
$739$	25.0907			0.922976			0.461488	−	0.887146i	$-0.347316\pi$
$739$	25.0907			0.922976			0.461488	+	0.887146i	$0.347316\pi$
$740$	8.37966	+	14.5140i	0.308043	+	0.533545i
$741$	48.8550	+	33.1717i	1.79474	+	1.21859i
$742$	2.36866	+	19.4415i	0.0869562	+	0.713720i
$743$	−23.9612	−	41.5021i	−0.879053	−	1.52256i	−0.852382	−	0.522919i	$-0.824843\pi$
$743$	−23.9612	−	41.5021i	−0.879053	−	1.52256i	−0.0266704	−	0.999644i	$-0.508490\pi$
$744$	5.27457	−	9.13582i	0.193375	−	0.334936i
$745$	−3.90067	−	6.75616i	−0.142910	−	0.247527i
$746$	30.9283			1.13237
$747$	−14.0138			−0.512739
$748$	−0.231782			−0.00847480
$749$	11.6085	−	8.73063i	0.424166	−	0.319010i
$750$	6.04688	−	10.4735i	0.220801	−	0.382438i
$751$	−0.854043			−0.0311645			−0.0155822	−	0.999879i	$-0.504960\pi$
$751$	−0.854043			−0.0311645			−0.0155822	+	0.999879i	$0.504960\pi$
$752$	−9.11139	+	15.7814i	−0.332258	+	0.575488i
$753$	13.7084	−	23.7437i	0.499562	−	0.865267i
$754$	22.0833			0.804228
$755$	−17.5639	−	30.4216i	−0.639217	−	1.10716i
$756$	−2.45942	+	1.84970i	−0.0894483	+	0.0672731i
$757$	−20.8523	−	36.1173i	−0.757890	−	1.31270i	−0.943925	−	0.330161i	$-0.892897\pi$
$757$	−20.8523	−	36.1173i	−0.757890	−	1.31270i	0.186034	−	0.982543i	$-0.440436\pi$
$758$	0.127247	−	0.220399i	0.00462183	−	0.00800525i
$759$	5.18003	−	8.97208i	0.188023	−	0.325666i
$760$	31.9372	+	21.6848i	1.15848	+	0.786590i
$761$	−5.79726	−	10.0411i	−0.210151	−	0.363991i	0.741611	−	0.670830i	$-0.234062\pi$
$761$	−5.79726	−	10.0411i	−0.210151	−	0.363991i	−0.951761	+	0.306839i	$0.900729\pi$
$762$	3.81442	+	6.60677i	0.138182	+	0.239338i
$763$	−1.22761	−	10.0760i	−0.0444425	−	0.364776i
$764$	−0.278098	+	0.481679i	−0.0100612	+	0.0174265i
$765$	1.14114	−	1.97651i	0.0412580	−	0.0714609i
$766$	−9.59523	−	16.6194i	−0.346690	−	0.600484i
$767$	−40.6565	+	70.4191i	−1.46802	+	2.54269i
$768$	18.3387	+	31.7635i	0.661740	+	1.14617i
$769$	15.9801	−	27.6784i	0.576258	−	0.998108i	−0.419646	−	0.907688i	$-0.637846\pi$
$769$	15.9801	−	27.6784i	0.576258	−	0.998108i	0.995904	−	0.0904200i	$-0.0288209\pi$
$770$	0.870658	+	7.14620i	0.0313763	+	0.257531i
$771$	−27.0876			−0.975536
$772$	5.69617	+	9.86605i	0.205009	+	0.355087i
$773$	7.23104	+	12.5245i	0.260083	+	0.450476i	0.966264	−	0.257555i	$-0.0829169\pi$
$773$	7.23104	+	12.5245i	0.260083	+	0.450476i	−0.706181	+	0.708031i	$0.749584\pi$
$774$	−0.158182			−0.00568575
$775$	4.96434			0.178324
$776$	−3.72184	−	6.44641i	−0.133606	−	0.231413i
$777$	−35.1632	+	26.4459i	−1.26147	+	0.948740i
$778$	−26.9041			−0.964560
$779$	−5.96952	+	2.88889i	−0.213880	+	0.103505i
$780$	−15.8345	+	27.4261i	−0.566966	+	0.982013i
$781$	−1.25318			−0.0448424
$782$	0.937135	−	1.62317i	0.0335119	−	0.0580443i
$783$	−2.49028	+	4.31329i	−0.0889954	+	0.154145i
$784$	−3.35386	+	11.6142i	−0.119781	+	0.414795i
$785$	−20.6821	+	35.8224i	−0.738176	+	1.27856i
$786$	−11.7782	−	20.4005i	−0.420115	−	0.727661i
$787$	−8.58885	+	14.8763i	−0.306160	+	0.530284i	−0.977519	−	0.210848i	$-0.932377\pi$
$787$	−8.58885	+	14.8763i	−0.306160	+	0.530284i	0.671359	+	0.741132i	$0.265711\pi$
$788$	3.34784	+	5.79863i	0.119262	+	0.206568i
$789$	14.4481			0.514365
$790$	−39.9640			−1.42186
$791$	−2.89075	−	23.7267i	−0.102783	−	0.843625i
$792$	−3.14887	+	5.45400i	−0.111890	+	0.193799i
$793$	−32.6199	+	56.4993i	−1.15837	+	2.00635i
$794$	−4.61154	−	7.98743i	−0.163658	−	0.283463i
$795$	−45.4568			−1.61219
$796$	7.02863	−	12.1739i	0.249123	−	0.431494i
$797$	−18.2853			−0.647698			−0.323849	−	0.946109i	$-0.604977\pi$
$797$	−18.2853			−0.647698			−0.323849	+	0.946109i	$0.604977\pi$
$798$	−13.3567	+	25.9565i	−0.472822	+	0.918852i
$799$	3.50208			0.123895
$800$	−7.10471	+	12.3057i	−0.251190	+	0.435073i
$801$	37.2999			1.31793
$802$	2.96106	+	5.12870i	0.104559	+	0.181101i
$803$	2.12879	−	3.68717i	0.0751233	−	0.130117i
$804$	−12.4990	+	21.6490i	−0.440807	+	0.763500i
$805$	36.3960	+	15.4894i	1.28279	+	0.545928i
$806$	−9.45579			−0.333066
$807$	−14.4546			−0.508825
$808$	1.25107	+	2.16692i	0.0440125	+	0.0762319i
$809$	−15.6564	+	27.1177i	−0.550451	+	0.953408i	0.447791	+	0.894138i	$0.352211\pi$
$809$	−15.6564	+	27.1177i	−0.550451	+	0.953408i	−0.998242	+	0.0592702i	$0.981123\pi$
$810$	16.5121	+	28.5997i	0.580174	+	1.00489i
$811$	21.0751	−	36.5032i	0.740048	−	1.28180i	−0.212425	−	0.977177i	$-0.568136\pi$
$811$	21.0751	−	36.5032i	0.740048	−	1.28180i	0.952473	−	0.304623i	$-0.0985304\pi$
$812$	−0.897078	−	7.36305i	−0.0314813	−	0.258392i
$813$	20.2751	−	35.1175i	0.711079	−	1.23162i
$814$	3.37625	−	5.84783i	0.118337	−	0.204966i
$815$	40.2549			1.41007
$816$	−0.664744	+	1.15137i	−0.0232707	+	0.0403060i
$817$	−0.238939	+	0.115632i	−0.00835941	+	0.00404545i
$818$	14.8627			0.519663
$819$	−33.8445	−	14.4035i	−1.18262	−	0.503299i
$820$	−1.77827	−	3.08006i	−0.0621000	−	0.107560i
$821$	−20.8868			−0.728956			−0.364478	−	0.931212i	$-0.618753\pi$
$821$	−20.8868			−0.728956			−0.364478	+	0.931212i	$0.618753\pi$
$822$	14.3222			0.499546
$823$	0.423893	+	0.734205i	0.0147760	+	0.0255928i	0.873319	−	0.487149i	$-0.161963\pi$
$823$	0.423893	+	0.734205i	0.0147760	+	0.0255928i	−0.858543	+	0.512742i	$0.828630\pi$
$824$	−10.2164	−	17.6953i	−0.355904	−	0.616444i
$825$	−6.69893			−0.233227
$826$	−36.9856	−	15.7403i	−1.28689	−	0.547675i
$827$	21.6401	−	37.4817i	0.752500	−	1.30337i	−0.194108	−	0.980980i	$-0.562181\pi$
$827$	21.6401	−	37.4817i	0.752500	−	1.30337i	0.946608	−	0.322388i	$-0.104485\pi$
$828$	4.98350	+	8.63167i	0.173188	+	0.299971i
$829$	−2.97527	+	5.15332i	−0.103335	+	0.178982i	−0.913057	−	0.407832i	$-0.866285\pi$
$829$	−2.97527	+	5.15332i	−0.103335	+	0.178982i	0.809721	+	0.586814i	$0.199618\pi$
$830$	9.28051	+	16.0743i	0.322131	+	0.557948i
$831$	9.47915	−	16.4184i	0.328828	−	0.569547i
$832$	23.6192	−	40.9097i	0.818849	−	1.41829i
$833$	2.25528	−	0.557826i	0.0781409	−	0.0193275i
$834$	−21.1956	−	36.7118i	−0.733943	−	1.27123i
$835$	18.2134	+	31.5466i	0.630302	+	1.09171i
$836$	−0.221664	+	3.03602i	−0.00766641	+	0.105003i
$837$	1.06630	−	1.84689i	0.0368569	−	0.0638380i
$838$	4.28279	−	7.41801i	0.147947	−	0.256251i
$839$	12.0596	+	20.8879i	0.416344	+	0.721129i	0.995569	−	0.0940388i	$-0.0299778\pi$
$839$	12.0596	+	20.8879i	0.416344	+	0.721129i	−0.579224	+	0.815168i	$0.696644\pi$
$840$	−50.0095	−	21.2830i	−1.72549	−	0.734333i
$841$	8.49757	+	14.7182i	0.293020	+	0.507525i
$842$	−11.7497			−0.404922
$843$	15.3419	−	26.5729i	0.528402	−	0.915219i
$844$	−4.11006	+	7.11884i	−0.141474	+	0.245041i
$845$	60.9941			2.09826
$846$	13.7043	−	23.7365i	0.471162	−	0.816076i
$847$	21.6842	−	16.3084i	0.745077	−	0.560364i
$848$	11.7149			0.402290
$849$	10.1317			0.347720
$850$	−1.21192			−0.0415687
$851$	−18.5507	−	32.1307i	−0.635909	−	1.10143i
$852$	1.36258	−	2.36007i	0.0466814	−	0.0808545i
$853$	−18.6142	−	32.2408i	−0.637338	−	1.10390i	−0.986015	−	0.166659i	$-0.946702\pi$
$853$	−18.6142	−	32.2408i	−0.637338	−	1.10390i	0.348676	−	0.937243i	$-0.386631\pi$
$854$	−29.6746	−	12.6289i	−1.01544	−	0.432152i
$855$	−24.7982	−	16.8376i	−0.848081	−	0.575833i
$856$	−8.41485	−	14.5749i	−0.287614	−	0.498162i
$857$	−9.85092			−0.336501			−0.168251	−	0.985744i	$-0.553812\pi$
$857$	−9.85092			−0.336501			−0.168251	+	0.985744i	$0.553812\pi$
$858$	12.7597			0.435610
$859$	−26.5841			−0.907036			−0.453518	−	0.891247i	$-0.649831\pi$
$859$	−26.5841			−0.907036			−0.453518	+	0.891247i	$0.649831\pi$
$860$	−0.0711780	−	0.123284i	−0.00242715	−	0.00420395i
$861$	7.46209	−	5.61215i	0.254307	−	0.191262i
$862$	−2.25383			−0.0767656
$863$	−6.10810	−	10.5795i	−0.207922	−	0.360132i	0.743138	−	0.669139i	$-0.233337\pi$
$863$	−6.10810	−	10.5795i	−0.207922	−	0.360132i	−0.951060	+	0.309007i	$0.900003\pi$
$864$	3.05208	+	5.28636i	0.103834	+	0.179846i
$865$	21.7237	+	37.6266i	0.738629	+	1.27934i
$866$	9.51525	+	16.4809i	0.323341	+	0.560044i
$867$	−39.1767			−1.33051
$868$	0.384117	+	3.15276i	0.0130378	+	0.107012i
$869$	−5.47042	−	9.47504i	−0.185571	−	0.321419i
$870$	−25.3369			−0.859001
$871$	77.7916			2.63587
$872$	−11.7609			−0.398276
$873$	2.88989	+	5.00544i	0.0978080	+	0.169408i
$874$	−20.3650	−	13.8275i	−0.688856	−	0.467721i
$875$	1.52881	+	12.5482i	0.0516831	+	0.424205i
$876$	4.62926	+	8.01811i	0.156408	+	0.270907i
$877$	10.5539	−	18.2799i	0.356380	−	0.617269i	−0.630973	−	0.775805i	$-0.717344\pi$
$877$	10.5539	−	18.2799i	0.356380	−	0.617269i	0.987353	+	0.158536i	$0.0506774\pi$
$878$	7.74414	+	13.4132i	0.261352	+	0.452675i
$879$	6.01521			0.202888
$880$	4.30608			0.145158
$881$	−36.1374			−1.21750			−0.608751	−	0.793362i	$-0.708329\pi$
$881$	−36.1374			−1.21750			−0.608751	+	0.793362i	$0.708329\pi$
$882$	5.04447	−	17.4687i	0.169856	−	0.588203i
$883$	−9.27130	+	16.0584i	−0.312004	+	0.540407i	−0.978796	−	0.204837i	$-0.934334\pi$
$883$	−9.27130	+	16.0584i	−0.312004	+	0.540407i	0.666792	+	0.745244i	$0.267667\pi$
$884$	−1.56850			−0.0527544
$885$	46.6464	−	80.7940i	1.56800	−	2.71586i
$886$	−20.0155	+	34.6678i	−0.672433	+	1.16469i
$887$	−11.3341			−0.380561			−0.190280	−	0.981730i	$-0.560940\pi$
$887$	−11.3341			−0.380561			−0.190280	+	0.981730i	$0.560940\pi$
$888$	25.4893	+	44.1488i	0.855366	+	1.48154i
$889$	−7.33720	−	3.12256i	−0.246082	−	0.104727i
$890$	−24.7015	−	42.7842i	−0.827995	−	1.43413i
$891$	−4.52045	+	7.82965i	−0.151441	+	0.262303i
$892$	−4.05381	+	7.02140i	−0.135732	+	0.235094i
$893$	3.34920	−	45.8724i	0.112077	−	1.53506i
$894$	−3.41764	−	5.91952i	−0.114303	−	0.197978i
$895$	35.8586	+	62.1089i	1.19862	+	2.07607i
$896$	0.810984	+	0.345138i	0.0270931	+	0.0115303i
$897$	35.0540	−	60.7153i	1.17042	−	2.02722i
$898$	−18.6277	+	32.2642i	−0.621616	+	1.07667i
$899$	2.57016	+	4.45165i	0.0857196	+	0.148471i
$900$	3.22238	−	5.58133i	0.107413	−	0.186044i
$901$	−1.12569	−	1.94975i	−0.0375022	−	0.0649557i
$902$	−0.716484	+	1.24099i	−0.0238563	+	0.0413203i
$903$	0.298681	−	0.224635i	0.00993949	−	0.00747538i
$904$	−27.6944			−0.921101
$905$	−22.8500	−	39.5774i	−0.759561	−	1.31560i
$906$	−15.3889	−	26.6544i	−0.511263	−	0.885534i
$907$	−3.73104			−0.123887			−0.0619436	−	0.998080i	$-0.519730\pi$
$907$	−3.73104			−0.123887			−0.0619436	+	0.998080i	$0.519730\pi$
$908$	−1.33840			−0.0444165
$909$	−0.971417	−	1.68254i	−0.0322199	−	0.0558065i
$910$	5.89186	+	48.3593i	0.195313	+	1.60309i
$911$	18.0710			0.598720			0.299360	−	0.954140i	$-0.403227\pi$
$911$	18.0710			0.598720			0.299360	+	0.954140i	$0.403227\pi$
$912$	14.4456	+	9.80834i	0.478343	+	0.324786i
$913$	−2.54070	+	4.40061i	−0.0840848	+	0.145639i
$914$	30.8352			1.01994
$915$	37.4258	−	64.8234i	1.23726	−	2.14299i
$916$	−9.67919	+	16.7649i	−0.319809	+	0.553926i
$917$	22.6559	+	9.64189i	0.748164	+	0.318403i
$918$	−0.260313	+	0.450875i	−0.00859160	+	0.0148811i
$919$	8.82879	+	15.2919i	0.291235	+	0.504434i	0.974102	−	0.226109i	$-0.0726005\pi$
$919$	8.82879	+	15.2919i	0.291235	+	0.504434i	−0.682867	+	0.730543i	$0.739267\pi$
$920$	22.9152	−	39.6904i	0.755493	−	1.30855i
$921$	8.84718	+	15.3238i	0.291524	+	0.504935i
$922$	25.1272			0.827521
$923$	−8.48046			−0.279138
$924$	−0.518331	−	4.25436i	−0.0170518	−	0.139958i
$925$	−11.9951	+	20.7761i	−0.394396	+	0.683113i
$926$	18.8074	−	32.5754i	0.618051	−	1.07050i
$927$	7.93269	+	13.7398i	0.260544	+	0.451275i
$928$	−14.7131			−0.482982
$929$	−21.2689	+	36.8388i	−0.697810	+	1.20864i	0.271414	+	0.962463i	$0.412509\pi$
$929$	−21.2689	+	36.8388i	−0.697810	+	1.20864i	−0.969224	+	0.246180i	$0.920825\pi$
$930$	10.8489			0.355750
$931$	−5.14991	−	30.0745i	−0.168782	−	0.985653i
$932$	−5.59759			−0.183355
$933$	−10.4692	+	18.1332i	−0.342746	+	0.593654i
$934$	−16.2540			−0.531846
$935$	−0.413775	−	0.716680i	−0.0135319	−	0.0234379i
$936$	−21.3088	+	36.9079i	−0.696500	+	1.20637i
$937$	6.33352	−	10.9700i	0.206907	−	0.358374i	−0.743832	−	0.668367i	$-0.766994\pi$
$937$	6.33352	−	10.9700i	0.206907	−	0.358374i	0.950739	+	0.309993i	$0.100327\pi$
$938$	4.65077	+	38.1726i	0.151853	+	1.24638i
$939$	32.7929			1.07016
$940$	24.6663			0.804525
$941$	25.5236	+	44.2081i	0.832045	+	1.44114i	0.896414	+	0.443218i	$0.146163\pi$
$941$	25.5236	+	44.2081i	0.832045	+	1.44114i	−0.0643693	+	0.997926i	$0.520504\pi$
$942$	−18.1210	+	31.3864i	−0.590413	+	1.02262i
$943$	3.93669	+	6.81855i	0.128196	+	0.222043i
$944$	−12.0215	+	20.8218i	−0.391265	+	0.677691i
$945$	−10.1099	−	4.30256i	−0.328875	−	0.139962i
$946$	−0.0286783	+	0.0496723i	−0.000932413	+	0.00161499i
$947$	−26.4253	+	45.7700i	−0.858708	+	1.48733i	0.0144542	+	0.999896i	$0.495399\pi$
$947$	−26.4253	+	45.7700i	−0.858708	+	1.48733i	−0.873162	+	0.487430i	$0.837934\pi$
$948$	23.7919			0.772725
$949$	14.4058	−	24.9516i	0.467632	−	0.809962i
$950$	−1.15902	+	15.8745i	−0.0376035	+	0.515038i
$951$	−21.6124			−0.700832
$952$	−0.325554	−	2.67208i	−0.0105513	−	0.0866027i
$953$	−14.0068	−	24.2605i	−0.453724	−	0.785873i	0.544890	−	0.838508i	$-0.316572\pi$
$953$	−14.0068	−	24.2605i	−0.453724	−	0.785873i	−0.998614	+	0.0526345i	$0.983238\pi$
$954$	−17.6201			−0.570471
$955$	−1.98583			−0.0642599
$956$	−10.3731	−	17.9667i	−0.335490	−	0.581085i
$957$	−3.46820	−	6.00710i	−0.112111	−	0.194182i
$958$	−10.0679			−0.325279
$959$	−11.9642	+	8.99814i	−0.386344	+	0.290565i
$960$	−27.0990	+	46.9369i	−0.874617	+	1.51488i
$961$	14.3995	+	24.9407i	0.464500	+	0.804537i
$962$	22.8475	−	39.5731i	0.736634	−	1.27589i
$963$	6.53387	+	11.3170i	0.210551	+	0.364685i
$964$	−2.18018	+	3.77619i	−0.0702190	+	0.121623i
$965$	−20.3375	+	35.2255i	−0.654686	+	1.13395i
$966$	31.8889	+	13.5713i	1.02601	+	0.436648i
$967$	8.59595	+	14.8886i	0.276427	+	0.478786i	0.970494	−	0.241124i	$-0.0775162\pi$
$967$	8.59595	+	14.8886i	0.276427	+	0.478786i	−0.694067	+	0.719910i	$0.744183\pi$
$968$	−15.7186	−	27.2253i	−0.505214	−	0.875056i
$969$	0.244350	−	3.34674i	0.00784964	−	0.107513i
$970$	3.82760	−	6.62959i	0.122897	−	0.212863i
$971$	−15.4665	+	26.7888i	−0.496344	+	0.859693i	−0.999991	−	0.00421640i	$-0.998658\pi$
$971$	−15.4665	+	26.7888i	−0.496344	+	0.859693i	0.503647	+	0.863910i	$0.331991\pi$
$972$	−8.08546	−	14.0044i	−0.259341	−	0.449192i
$973$	40.7706	+	17.3511i	1.30705	+	0.556251i
$974$	−8.23903	−	14.2704i	−0.263995	−	0.457254i
$975$	−45.3326			−1.45180
$976$	−9.64517	+	16.7059i	−0.308734	+	0.534743i
$977$	−6.78168	+	11.7462i	−0.216965	+	0.375795i	−0.953879	−	0.300192i	$-0.902949\pi$
$977$	−6.78168	+	11.7462i	−0.216965	+	0.375795i	0.736914	+	0.675987i	$0.236282\pi$
$978$	35.2700			1.12781
$979$	6.76244	−	11.7129i	0.216129	−	0.374346i
$980$	15.8847	−	3.92894i	0.507417	−	0.125505i
$981$	9.13201			0.291563
$982$	12.1579			0.387974
$983$	3.23643			0.103226			0.0516130	−	0.998667i	$-0.483564\pi$
$983$	3.23643			0.103226			0.0516130	+	0.998667i	$0.483564\pi$
$984$	−5.40917	−	9.36896i	−0.172438	−	0.298671i
$985$	−11.9531	+	20.7033i	−0.380856	+	0.659662i
$986$	−0.627443	−	1.08676i	−0.0199818	−	0.0346096i
$987$	7.83166	+	64.2808i	0.249285	+	2.04608i
$988$	−1.50003	+	20.5452i	−0.0477223	+	0.653629i
$989$	0.157572	+	0.272923i	0.00501050	+	0.00867844i
$990$	−6.47669			−0.205843
$991$	−39.2015			−1.24528			−0.622638	−	0.782510i	$-0.713939\pi$
$991$	−39.2015			−1.24528			−0.622638	+	0.782510i	$0.713939\pi$
$992$	6.29996			0.200024
$993$	−0.382942	−	0.663275i	−0.0121523	−	0.0210484i
$994$	−0.507005	−	4.16140i	−0.0160812	−	0.131991i
$995$	50.1897			1.59112
$996$	−5.52499	−	9.56956i	−0.175066	−	0.303223i
$997$	−19.8164	−	34.3231i	−0.627593	−	1.08702i	−0.988033	−	0.154241i	$-0.950707\pi$
$997$	−19.8164	−	34.3231i	−0.627593	−	1.08702i	0.360440	−	0.932782i	$-0.382627\pi$
$998$	−12.8158	−	22.1976i	−0.405676	−	0.702651i
$999$	5.15291	+	8.92511i	0.163031	+	0.282378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.g.a.102.5	yes	24
7.2	even	3		133.2.h.a.121.8	yes	24
7.3	odd	6		931.2.e.e.197.5		24
7.4	even	3		931.2.e.f.197.5		24
7.5	odd	6		931.2.h.h.520.8		24
7.6	odd	2		931.2.g.h.900.5		24
19.11	even	3		133.2.h.a.11.8	yes	24
133.11	even	3		931.2.e.f.638.5		24
133.30	even	3	inner	133.2.g.a.30.5	✓	24
133.68	odd	6		931.2.g.h.30.5		24
133.87	odd	6		931.2.e.e.638.5		24
133.125	odd	6		931.2.h.h.410.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.g.a.30.5	✓	24	133.30	even	3	inner
133.2.g.a.102.5	yes	24	1.1	even	1	trivial
133.2.h.a.11.8	yes	24	19.11	even	3
133.2.h.a.121.8	yes	24	7.2	even	3
931.2.e.e.197.5		24	7.3	odd	6
931.2.e.e.638.5		24	133.87	odd	6
931.2.e.f.197.5		24	7.4	even	3
931.2.e.f.638.5		24	133.11	even	3
931.2.g.h.30.5		24	133.68	odd	6
931.2.g.h.900.5		24	7.6	odd	2
931.2.h.h.410.8		24	133.125	odd	6
931.2.h.h.520.8		24	7.5	odd	6

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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.545630 + 0.945059i) q^{2} +2.31954 q^{3} +(0.404576 + 0.700746i) q^{4} +(-1.44449 + 2.50193i) q^{5} +(-1.26561 + 2.19210i) q^{6} +(-0.319979 - 2.62633i) q^{7} -3.06551 q^{8} +2.38028 q^{9} +O(q^{10})\)	\(q+(-0.545630 + 0.945059i) q^{2} +2.31954 q^{3} +(0.404576 + 0.700746i) q^{4} +(-1.44449 + 2.50193i) q^{5} +(-1.26561 + 2.19210i) q^{6} +(-0.319979 - 2.62633i) q^{7} -3.06551 q^{8} +2.38028 q^{9} +(-1.57631 - 2.73025i) q^{10} +(0.431542 - 0.747453i) q^{11} +(0.938430 + 1.62541i) q^{12} +(2.92030 - 5.05811i) q^{13} +(2.65663 + 1.13061i) q^{14} +(-3.35055 + 5.80333i) q^{15} +(0.863486 - 1.49560i) q^{16} -0.331892 q^{17} +(-1.29875 + 2.24950i) q^{18} +(-0.317404 + 4.34733i) q^{19} -2.33762 q^{20} +(-0.742206 - 6.09189i) q^{21} +(0.470925 + 0.815666i) q^{22} +5.17496 q^{23} -7.11059 q^{24} +(-1.67309 - 2.89788i) q^{25} +(3.18681 + 5.51972i) q^{26} -1.43747 q^{27} +(1.71093 - 1.28677i) q^{28} +(1.73240 - 3.00061i) q^{29} +(-3.65632 - 6.33294i) q^{30} +(-0.741791 + 1.28482i) q^{31} +(-2.12323 - 3.67754i) q^{32} +(1.00098 - 1.73375i) q^{33} +(0.181090 - 0.313658i) q^{34} +(7.03310 + 2.99314i) q^{35} +(0.963002 + 1.66797i) q^{36} +(-3.58470 - 6.20888i) q^{37} +(-3.93530 - 2.67200i) q^{38} +(6.77377 - 11.7325i) q^{39} +(4.42810 - 7.66970i) q^{40} +(0.760720 + 1.31761i) q^{41} +(6.16216 + 2.62249i) q^{42} +(0.0304489 + 0.0527391i) q^{43} +0.698366 q^{44} +(-3.43828 + 5.95528i) q^{45} +(-2.82361 + 4.89064i) q^{46} -10.5519 q^{47} +(2.00289 - 3.46911i) q^{48} +(-6.79523 + 1.68074i) q^{49} +3.65156 q^{50} -0.769838 q^{51} +4.72594 q^{52} +(3.39174 + 5.87466i) q^{53} +(0.784329 - 1.35850i) q^{54} +(1.24672 + 2.15937i) q^{55} +(0.980902 + 8.05106i) q^{56} +(-0.736232 + 10.0838i) q^{57} +(1.89050 + 3.27444i) q^{58} -13.9220 q^{59} -5.42221 q^{60} -11.1700 q^{61} +(-0.809487 - 1.40207i) q^{62} +(-0.761640 - 6.25139i) q^{63} +8.08793 q^{64} +(8.43669 + 14.6128i) q^{65} +(1.09233 + 1.89197i) q^{66} +(6.65954 + 11.5347i) q^{67} +(-0.134276 - 0.232572i) q^{68} +12.0035 q^{69} +(-6.66616 + 5.01354i) q^{70} +(-0.725991 - 1.25745i) q^{71} -7.29677 q^{72} +4.93298 q^{73} +7.82368 q^{74} +(-3.88081 - 6.72176i) q^{75} +(-3.17478 + 1.53640i) q^{76} +(-2.10114 - 0.894203i) q^{77} +(7.39194 + 12.8032i) q^{78} +(6.33822 - 10.9781i) q^{79} +(2.49459 + 4.32076i) q^{80} -10.4751 q^{81} -1.66029 q^{82} -5.88748 q^{83} +(3.96858 - 2.98473i) q^{84} +(0.479414 - 0.830370i) q^{85} -0.0664554 q^{86} +(4.01838 - 6.96004i) q^{87} +(-1.32290 + 2.29133i) q^{88} +15.6704 q^{89} +(-3.75206 - 6.49876i) q^{90} +(-14.2187 - 6.05119i) q^{91} +(2.09366 + 3.62633i) q^{92} +(-1.72062 + 2.98019i) q^{93} +(5.75742 - 9.97214i) q^{94} +(-10.4182 - 7.07379i) q^{95} +(-4.92492 - 8.53020i) q^{96} +(1.21410 + 2.10288i) q^{97} +(2.11928 - 7.33895i) q^{98} +(1.02719 - 1.77915i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more