LMFDB - Embedded newform 385.2.u.a.241.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(131,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("385.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.u (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.17
Character	$\chi$	$=$	385.241
Dual form			385.2.u.a.131.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0679871 - 0.0392524i) q^{2} +(2.45941 + 1.41994i) q^{3} +(-0.996918 + 1.72671i) q^{4} +(0.866025 - 0.500000i) q^{5} +0.222944 q^{6} +(-2.62999 + 0.288317i) q^{7} +0.313535i q^{8} +(2.53247 + 4.38636i) q^{9} +O(q^{10})$	\(q+(0.0679871 - 0.0392524i) q^{2} +(2.45941 + 1.41994i) q^{3} +(-0.996918 + 1.72671i) q^{4} +(0.866025 - 0.500000i) q^{5} +0.222944 q^{6} +(-2.62999 + 0.288317i) q^{7} +0.313535i q^{8} +(2.53247 + 4.38636i) q^{9} +(0.0392524 - 0.0679871i) q^{10} +(3.09300 + 1.19724i) q^{11} +(-4.90366 + 2.83113i) q^{12} -2.80916 q^{13} +(-0.167489 + 0.122835i) q^{14} +2.83988 q^{15} +(-1.98153 - 3.43211i) q^{16} +(2.02490 - 3.50724i) q^{17} +(0.344351 + 0.198811i) q^{18} +(3.78631 + 6.55809i) q^{19} +1.99384i q^{20} +(-6.87763 - 3.02535i) q^{21} +(0.257278 - 0.0400106i) q^{22} +(1.30169 + 2.25459i) q^{23} +(-0.445202 + 0.771112i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.190986 + 0.110266i) q^{26} +5.86418i q^{27} +(2.12405 - 4.82868i) q^{28} -7.66908i q^{29} +(0.193076 - 0.111472i) q^{30} +(-7.06497 - 4.07896i) q^{31} +(-0.812496 - 0.469095i) q^{32} +(5.90694 + 7.33637i) q^{33} -0.317929i q^{34} +(-2.13348 + 1.56469i) q^{35} -10.0987 q^{36} +(-1.19237 - 2.06525i) q^{37} +(0.514841 + 0.297244i) q^{38} +(-6.90887 - 3.98884i) q^{39} +(0.156768 + 0.271530i) q^{40} +3.55350 q^{41} +(-0.586343 + 0.0642787i) q^{42} +1.36196i q^{43} +(-5.15075 + 4.14717i) q^{44} +(4.38636 + 2.53247i) q^{45} +(0.176996 + 0.102189i) q^{46} +(5.55688 - 3.20827i) q^{47} -11.2546i q^{48} +(6.83375 - 1.51654i) q^{49} -0.0785048i q^{50} +(9.96014 - 5.75049i) q^{51} +(2.80050 - 4.85061i) q^{52} +(-0.0842735 + 0.145966i) q^{53} +(0.230183 + 0.398689i) q^{54} +(3.27723 - 0.509658i) q^{55} +(-0.0903976 - 0.824596i) q^{56} +21.5054i q^{57} +(-0.301030 - 0.521399i) q^{58} +(5.82244 + 3.36159i) q^{59} +(-2.83113 + 4.90366i) q^{60} +(1.87765 + 3.25219i) q^{61} -0.640436 q^{62} +(-7.92504 - 10.8060i) q^{63} +7.85247 q^{64} +(-2.43280 + 1.40458i) q^{65} +(0.689566 + 0.266918i) q^{66} +(3.69637 - 6.40230i) q^{67} +(4.03733 + 6.99286i) q^{68} +7.39328i q^{69} +(-0.0836317 + 0.190123i) q^{70} +1.02817 q^{71} +(-1.37528 + 0.794018i) q^{72} +(4.61135 - 7.98709i) q^{73} +(-0.162132 - 0.0936071i) q^{74} +(2.45941 - 1.41994i) q^{75} -15.0986 q^{76} +(-8.47975 - 2.25697i) q^{77} -0.626286 q^{78} +(-0.143561 + 0.0828847i) q^{79} +(-3.43211 - 1.98153i) q^{80} +(-0.729385 + 1.26333i) q^{81} +(0.241592 - 0.139483i) q^{82} -11.1743 q^{83} +(12.0803 - 8.85967i) q^{84} -4.04981i q^{85} +(0.0534602 + 0.0925957i) q^{86} +(10.8897 - 18.8614i) q^{87} +(-0.375377 + 0.969763i) q^{88} +(-7.39726 + 4.27081i) q^{89} +0.397622 q^{90} +(7.38807 - 0.809927i) q^{91} -5.19070 q^{92} +(-11.5838 - 20.0637i) q^{93} +(0.251864 - 0.436242i) q^{94} +(6.55809 + 3.78631i) q^{95} +(-1.33217 - 2.30739i) q^{96} -17.4903i q^{97} +(0.405079 - 0.371346i) q^{98} +(2.58139 + 16.5990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 28 q^{4} + 36 q^{9}+O(q^{10}) $ 64 * q + 28 * q^4 + 36 * q^9	$ 64 q + 28 q^{4} + 36 q^{9} - 20 q^{14} - 8 q^{15} - 48 q^{16} + 16 q^{22} + 20 q^{23} + 32 q^{25} - 60 q^{26} + 24 q^{33} + 16 q^{36} - 8 q^{37} + 84 q^{38} - 132 q^{42} + 12 q^{44} + 12 q^{47} + 12 q^{49} + 20 q^{53} + 32 q^{56} + 24 q^{58} + 36 q^{59} - 44 q^{60} - 120 q^{64} + 12 q^{66} + 44 q^{67} + 16 q^{70} - 72 q^{71} + 44 q^{77} - 120 q^{78} - 24 q^{80} - 48 q^{81} - 96 q^{82} + 76 q^{86} + 64 q^{88} + 60 q^{89} - 108 q^{91} - 40 q^{92} - 68 q^{93} - 64 q^{99}+O(q^{100}) $ 64 * q + 28 * q^4 + 36 * q^9 - 20 * q^14 - 8 * q^15 - 48 * q^16 + 16 * q^22 + 20 * q^23 + 32 * q^25 - 60 * q^26 + 24 * q^33 + 16 * q^36 - 8 * q^37 + 84 * q^38 - 132 * q^42 + 12 * q^44 + 12 * q^47 + 12 * q^49 + 20 * q^53 + 32 * q^56 + 24 * q^58 + 36 * q^59 - 44 * q^60 - 120 * q^64 + 12 * q^66 + 44 * q^67 + 16 * q^70 - 72 * q^71 + 44 * q^77 - 120 * q^78 - 24 * q^80 - 48 * q^81 - 96 * q^82 + 76 * q^86 + 64 * q^88 + 60 * q^89 - 108 * q^91 - 40 * q^92 - 68 * q^93 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.0679871	−	0.0392524i	0.0480742	−	0.0277556i	−0.475770	−	0.879570i	$-0.657831\pi$
$2$	0.0679871	−	0.0392524i	0.0480742	−	0.0277556i	0.523844	+	0.851814i	$0.324497\pi$
$3$	2.45941	+	1.41994i	1.41994	+	0.819804i	0.996293	−	0.0860231i	$-0.0274159\pi$
$3$	2.45941	+	1.41994i	1.41994	+	0.819804i	0.423648	+	0.905827i	$0.360749\pi$
$4$	−0.996918	+	1.72671i	−0.498459	+	0.863357i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	0.222944			0.0910167
$7$	−2.62999	+	0.288317i	−0.994045	+	0.108974i
$7$	−2.62999	+	0.288317i	−0.994045	+	0.108974i
$8$			0.313535i			0.110851i
$9$	2.53247	+	4.38636i	0.844156	+	1.46212i
$10$	0.0392524	−	0.0679871i	0.0124127	−	0.0214994i
$11$	3.09300	+	1.19724i	0.932573	+	0.360981i
$11$	3.09300	+	1.19724i	0.932573	+	0.360981i
$12$	−4.90366	+	2.83113i	−1.41557	+	0.817277i
$13$	−2.80916			−0.779120			−0.389560	−	0.921001i	$-0.627373\pi$
$13$	−2.80916			−0.779120			−0.389560	+	0.921001i	$0.627373\pi$
$14$	−0.167489	+	0.122835i	−0.0447632	+	0.0328292i
$15$	2.83988			0.733255
$16$	−1.98153	−	3.43211i	−0.495382	−	0.858028i
$17$	2.02490	−	3.50724i	0.491111	−	0.850629i	−0.508836	−	0.860863i	$-0.669924\pi$
$17$	2.02490	−	3.50724i	0.491111	−	0.850629i	0.999948	+	0.0102337i	$0.00325755\pi$
$18$	0.344351	+	0.198811i	0.0811642	+	0.0468602i
$19$	3.78631	+	6.55809i	0.868640	+	1.50453i	0.863387	+	0.504542i	$0.168339\pi$
$19$	3.78631	+	6.55809i	0.868640	+	1.50453i	0.00525248	+	0.999986i	$0.498328\pi$
$20$			1.99384i			0.445836i
$21$	−6.87763	−	3.02535i	−1.50082	−	0.660185i
$22$	0.257278	−	0.0400106i	0.0548519	−	0.00853029i
$23$	1.30169	+	2.25459i	0.271420	+	0.470114i	0.969226	−	0.246173i	$-0.0791733\pi$
$23$	1.30169	+	2.25459i	0.271420	+	0.470114i	−0.697805	+	0.716287i	$0.745840\pi$
$24$	−0.445202	+	0.771112i	−0.0908764	+	0.157403i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.190986	+	0.110266i	−0.0374555	+	0.0216250i
$27$			5.86418i			1.12856i
$28$	2.12405	−	4.82868i	0.401408	−	0.912534i
$29$		−	7.66908i		−	1.42411i	−0.702122	−	0.712057i	$-0.747764\pi$
$29$		−	7.66908i		−	1.42411i	0.702122	−	0.712057i	$-0.252236\pi$
$30$	0.193076	−	0.111472i	0.0352506	−	0.0203519i
$31$	−7.06497	−	4.07896i	−1.26891	−	0.732603i	−0.294125	−	0.955767i	$-0.595028\pi$
$31$	−7.06497	−	4.07896i	−1.26891	−	0.732603i	−0.974781	+	0.223163i	$0.928362\pi$
$32$	−0.812496	−	0.469095i	−0.143630	−	0.0829250i
$33$	5.90694	+	7.33637i	1.02827	+	1.27710i
$34$		−	0.317929i		−	0.0545244i
$35$	−2.13348	+	1.56469i	−0.360625	+	0.264480i
$36$	−10.0987			−1.68311
$37$	−1.19237	−	2.06525i	−0.196025	−	0.339525i	0.751211	−	0.660062i	$-0.229470\pi$
$37$	−1.19237	−	2.06525i	−0.196025	−	0.339525i	−0.947236	+	0.320537i	$0.896137\pi$
$38$	0.514841	+	0.297244i	0.0835183	+	0.0482193i
$39$	−6.90887	−	3.98884i	−1.10630	−	0.638725i
$40$	0.156768	+	0.271530i	0.0247871	+	0.0429326i
$41$	3.55350			0.554963			0.277481	−	0.960731i	$-0.410500\pi$
$41$	3.55350			0.554963			0.277481	+	0.960731i	$0.410500\pi$
$42$	−0.586343	+	0.0642787i	−0.0904746	+	0.00991841i
$43$			1.36196i			0.207697i	0.994593	+	0.103848i	$0.0331157\pi$
$43$			1.36196i			0.207697i	−0.994593	+	0.103848i	$0.966884\pi$
$44$	−5.15075	+	4.14717i	−0.776505	+	0.625209i
$45$	4.38636	+	2.53247i	0.653880	+	0.377518i
$46$	0.176996	+	0.102189i	0.0260966	+	0.0150669i
$47$	5.55688	−	3.20827i	0.810555	−	0.467974i	−0.0365938	−	0.999330i	$-0.511651\pi$
$47$	5.55688	−	3.20827i	0.810555	−	0.467974i	0.847148	+	0.531356i	$0.178317\pi$
$48$		−	11.2546i		−	1.62447i
$49$	6.83375	−	1.51654i	0.976250	−	0.216649i
$50$		−	0.0785048i		−	0.0111023i
$51$	9.96014	−	5.75049i	1.39470	−	0.805229i
$52$	2.80050	−	4.85061i	0.388359	−	0.672658i
$53$	−0.0842735	+	0.145966i	−0.0115759	+	0.0200500i	−0.871755	−	0.489942i	$-0.837018\pi$
$53$	−0.0842735	+	0.145966i	−0.0115759	+	0.0200500i	0.860179	+	0.509991i	$0.170351\pi$
$54$	0.230183	+	0.398689i	0.0313239	+	0.0542547i
$55$	3.27723	−	0.509658i	0.441902	−	0.0687223i
$56$	−0.0903976	−	0.824596i	−0.0120799	−	0.110191i
$57$			21.5054i			2.84846i
$58$	−0.301030	−	0.521399i	−0.0395272	−	0.0684631i
$59$	5.82244	+	3.36159i	0.758017	+	0.437641i	0.828583	−	0.559866i	$-0.189147\pi$
$59$	5.82244	+	3.36159i	0.758017	+	0.437641i	−0.0705662	+	0.997507i	$0.522481\pi$
$60$	−2.83113	+	4.90366i	−0.365498	+	0.633060i
$61$	1.87765	+	3.25219i	0.240409	+	0.416401i	0.960831	−	0.277135i	$-0.0893851\pi$
$61$	1.87765	+	3.25219i	0.240409	+	0.416401i	−0.720422	+	0.693536i	$0.756052\pi$
$62$	−0.640436			−0.0813355
$63$	−7.92504	−	10.8060i	−0.998461	−	1.36142i
$64$	7.85247			0.981558
$65$	−2.43280	+	1.40458i	−0.301752	+	0.174216i
$66$	0.689566	+	0.266918i	0.0848797	+	0.0328553i
$67$	3.69637	−	6.40230i	0.451584	−	0.782166i	−0.546901	−	0.837197i	$-0.684193\pi$
$67$	3.69637	−	6.40230i	0.451584	−	0.782166i	0.998485	+	0.0550313i	$0.0175259\pi$
$68$	4.03733	+	6.99286i	0.489598	+	0.848008i
$69$			7.39328i			0.890046i
$70$	−0.0836317	+	0.190123i	−0.00999591	+	0.0227240i
$71$	1.02817			0.122021			0.0610105	−	0.998137i	$-0.480568\pi$
$71$	1.02817			0.122021			0.0610105	+	0.998137i	$0.480568\pi$
$72$	−1.37528	+	0.794018i	−0.162078	+	0.0935759i
$73$	4.61135	−	7.98709i	0.539718	−	0.934819i	−0.459201	−	0.888332i	$-0.651864\pi$
$73$	4.61135	−	7.98709i	0.539718	−	0.934819i	0.998919	−	0.0464863i	$-0.0148024\pi$
$74$	−0.162132	−	0.0936071i	−0.0188475	−	0.0108816i
$75$	2.45941	−	1.41994i	0.283988	−	0.163961i
$76$	−15.0986			−1.73193
$77$	−8.47975	−	2.25697i	−0.966357	−	0.257205i
$78$	−0.626286			−0.0709129
$79$	−0.143561	+	0.0828847i	−0.0161518	+	0.00932526i	−0.508054	−	0.861325i	$-0.669635\pi$
$79$	−0.143561	+	0.0828847i	−0.0161518	+	0.00932526i	0.491902	+	0.870650i	$0.336302\pi$
$80$	−3.43211	−	1.98153i	−0.383722	−	0.221542i
$81$	−0.729385	+	1.26333i	−0.0810428	+	0.140370i
$82$	0.241592	−	0.139483i	0.0266794	−	0.0154033i
$83$	−11.1743			−1.22654			−0.613268	−	0.789875i	$-0.710145\pi$
$83$	−11.1743			−1.22654			−0.613268	+	0.789875i	$0.710145\pi$
$84$	12.0803	−	8.85967i	1.31807	−	0.966670i
$85$		−	4.04981i		−	0.439263i
$86$	0.0534602	+	0.0925957i	0.00576476	+	0.00998485i
$87$	10.8897	−	18.8614i	1.16749	−	2.02216i
$88$	−0.375377	+	0.969763i	−0.0400153	+	0.103377i
$89$	−7.39726	+	4.27081i	−0.784108	+	0.452705i	−0.837884	−	0.545848i	$-0.816208\pi$
$89$	−7.39726	+	4.27081i	−0.784108	+	0.452705i	0.0537764	+	0.998553i	$0.482874\pi$
$90$	0.397622			0.0419130
$91$	7.38807	−	0.809927i	0.774480	−	0.0849035i
$92$	−5.19070			−0.541168
$93$	−11.5838	−	20.0637i	−1.20118	−	2.08051i
$94$	0.251864	−	0.436242i	0.0259778	−	0.0449949i
$95$	6.55809	+	3.78631i	0.672845	+	0.388467i
$96$	−1.33217	−	2.30739i	−0.135965	−	0.235497i
$97$		−	17.4903i		−	1.77587i	−0.459972	−	0.887934i	$-0.652140\pi$
$97$		−	17.4903i		−	1.77587i	0.459972	−	0.887934i	$-0.347860\pi$
$98$	0.405079	−	0.371346i	0.0409191	−	0.0375117i
$99$	2.58139	+	16.5990i	0.259439	+	1.66826i
$100$	0.996918	+	1.72671i	0.0996918	+	0.172671i
$101$	−6.21853	+	10.7708i	−0.618767	+	1.07174i	0.370945	+	0.928655i	$0.379034\pi$
$101$	−6.21853	+	10.7708i	−0.618767	+	1.07174i	−0.989711	+	0.143080i	$0.954299\pi$
$102$	0.451441	−	0.781919i	0.0446993	−	0.0774215i
$103$	−11.7344	+	6.77484i	−1.15622	+	0.667544i	−0.950395	−	0.311044i	$-0.899321\pi$
$103$	−11.7344	+	6.77484i	−1.15622	+	0.667544i	−0.205825	+	0.978589i	$0.565988\pi$
$104$		−	0.880770i		−	0.0863666i
$105$	−7.46888	+	0.818787i	−0.728888	+	0.0799054i
$106$			0.0132317i			0.00128518i
$107$	2.96422	−	1.71139i	0.286562	−	0.165447i	−0.349828	−	0.936814i	$-0.613760\pi$
$107$	2.96422	−	1.71139i	0.286562	−	0.165447i	0.636390	+	0.771367i	$0.280427\pi$
$108$	−10.1258	−	5.84611i	−0.974351	−	0.562542i
$109$	1.97239	+	1.13876i	0.188921	+	0.109074i	0.591477	−	0.806322i	$-0.298545\pi$
$109$	1.97239	+	1.13876i	0.188921	+	0.109074i	−0.402556	+	0.915395i	$0.631878\pi$
$110$	0.202804	−	0.163289i	0.0193366	−	0.0155690i
$111$		−	6.77241i		−	0.642808i
$112$	6.20095	+	8.45512i	0.585935	+	0.798934i
$113$	−13.8827			−1.30598			−0.652990	−	0.757367i	$-0.726485\pi$
$113$	−13.8827			−1.30598			−0.652990	+	0.757367i	$0.726485\pi$
$114$	0.844137	+	1.46209i	0.0790607	+	0.136937i
$115$	2.25459	+	1.30169i	0.210241	+	0.121383i
$116$	13.2423	+	7.64545i	1.22952	+	0.709862i
$117$	−7.11410	−	12.3220i	−0.657699	−	1.13917i
$118$	0.527801			0.0485881
$119$	−4.31429	+	9.80782i	−0.395490	+	0.899082i
$120$			0.890404i			0.0812824i
$121$	8.13324	+	7.40611i	0.739385	+	0.673282i
$122$	0.255313	+	0.147405i	0.0231149	+	0.0133454i
$123$	8.73951	+	5.04576i	0.788015	+	0.454960i
$124$	14.0864	−	8.13279i	1.26500	−	0.730346i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.962961	−	0.423589i	−0.0857874	−	0.0377363i
$127$			6.66938i			0.591812i	0.955217	+	0.295906i	$0.0956215\pi$
$127$			6.66938i			0.591812i	−0.955217	+	0.295906i	$0.904379\pi$
$128$	2.15886	−	1.24642i	0.190818	−	0.110169i
$129$	−1.93390	+	3.34962i	−0.170271	+	0.294917i
$130$	−0.110266	+	0.190986i	−0.00967098	+	0.0167506i
$131$	−10.9435	−	18.9546i	−0.956135	−	1.65607i	−0.731748	−	0.681575i	$-0.761295\pi$
$131$	−10.9435	−	18.9546i	−0.956135	−	1.65607i	−0.224387	−	0.974500i	$-0.572038\pi$
$132$	−18.5566	+	2.88582i	−1.61514	+	0.251178i
$133$	−11.8488	−	16.1561i	−1.02742	−	1.40091i
$134$		−	0.580366i		−	0.0501360i
$135$	2.93209	+	5.07853i	0.252354	+	0.437090i
$136$	1.09964	+	0.634879i	0.0942935	+	0.0544404i
$137$	−3.41625	+	5.91712i	−0.291870	+	0.505534i	−0.974252	−	0.225462i	$-0.927611\pi$
$137$	−3.41625	+	5.91712i	−0.291870	+	0.505534i	0.682382	+	0.730996i	$0.260944\pi$
$138$	0.290204	+	0.502648i	0.0247038	+	0.0427882i
$139$	−15.5603			−1.31981			−0.659903	−	0.751350i	$-0.729403\pi$
$139$	−15.5603			−1.31981			−0.659903	+	0.751350i	$0.729403\pi$
$140$	−0.574857	−	5.24378i	−0.0485843	−	0.443180i
$141$	18.2222			1.53459
$142$	0.0699022	−	0.0403580i	0.00586606	−	0.00338677i
$143$	−8.68871	−	3.36323i	−0.726586	−	0.281247i
$144$	10.0363	−	17.3834i	0.836360	−	1.44862i
$145$	−3.83454	−	6.64162i	−0.318441	−	0.551557i
$146$		−	0.724026i		−	0.0599208i
$147$	18.9604	+	5.97372i	1.56383	+	0.492704i
$148$	4.75480			0.390842
$149$	9.52819	−	5.50110i	0.780579	−	0.450668i	−0.0560562	−	0.998428i	$-0.517853\pi$
$149$	9.52819	−	5.50110i	0.780579	−	0.450668i	0.836636	+	0.547760i	$0.184519\pi$
$150$	0.111472	−	0.193076i	0.00910167	−	0.0157646i
$151$	15.3849	+	8.88248i	1.25201	+	0.722846i	0.971507	−	0.237009i	$-0.0761671\pi$
$151$	15.3849	+	8.88248i	1.25201	+	0.722846i	0.280498	+	0.959855i	$0.409500\pi$
$152$	−2.05619	+	1.18714i	−0.166779	+	0.0962900i
$153$	20.5120			1.65830
$154$	−0.665105	+	0.179405i	−0.0535957	+	0.0144569i
$155$	−8.15793			−0.655260
$156$	13.7752	−	7.95309i	1.10290	−	0.636757i
$157$	−5.45321	−	3.14841i	−0.435213	−	0.251271i	0.266352	−	0.963876i	$-0.414182\pi$
$157$	−5.45321	−	3.14841i	−0.435213	−	0.251271i	−0.701565	+	0.712605i	$0.747515\pi$
$158$	−0.00650685	+	0.0112702i	−0.000517657	+	0.000896608i
$159$	−0.414526	+	0.239327i	−0.0328741	+	0.0189799i
$160$	−0.938190			−0.0741704
$161$	−4.07347	−	5.55426i	−0.321034	−	0.437737i
$162$			0.114520i			0.00899758i
$163$	5.10108	+	8.83533i	0.399547	+	0.692036i	0.993670	−	0.112338i	$-0.0358340\pi$
$163$	5.10108	+	8.83533i	0.399547	+	0.692036i	−0.594123	+	0.804374i	$0.702501\pi$
$164$	−3.54255	+	6.13587i	−0.276626	+	0.479131i
$165$	8.78375	+	3.40002i	0.683814	+	0.264691i
$166$	−0.759707	+	0.438617i	−0.0589647	+	0.0340433i
$167$	−6.04744			−0.467965			−0.233983	−	0.972241i	$-0.575176\pi$
$167$	−6.04744			−0.467965			−0.233983	+	0.972241i	$0.575176\pi$
$168$	0.948554	−	2.15638i	0.0731825	−	0.166368i
$169$	−5.10864			−0.392972
$170$	−0.158965	−	0.275335i	−0.0121920	−	0.0211172i
$171$	−19.1774	+	33.2163i	−1.46653	+	2.54011i
$172$	−2.35171	−	1.35776i	−0.179317	−	0.103528i
$173$	−8.98219	−	15.5576i	−0.682903	−	1.18282i	−0.974091	−	0.226157i	$-0.927384\pi$
$173$	−8.98219	−	15.5576i	−0.682903	−	1.18282i	0.291188	−	0.956666i	$-0.405950\pi$
$174$		−	1.70978i		−	0.129618i
$175$	−1.06531	+	2.42180i	−0.0805297	+	0.183071i
$176$	−2.01981	−	12.9879i	−0.152249	−	0.978997i
$177$	9.54652	+	16.5350i	0.717560	+	1.24285i
$178$	−0.335279	+	0.580720i	−0.0251302	+	0.0435268i
$179$	−10.2929	+	17.8279i	−0.769330	+	1.33252i	0.168596	+	0.985685i	$0.446077\pi$
$179$	−10.2929	+	17.8279i	−0.769330	+	1.33252i	−0.937926	+	0.346834i	$0.887257\pi$
$180$	−8.74569	+	5.04933i	−0.651866	+	0.376355i
$181$			16.4524i			1.22290i	0.791283	+	0.611450i	$0.209413\pi$
$181$			16.4524i			1.22290i	−0.791283	+	0.611450i	$0.790587\pi$
$182$	0.470502	−	0.345064i	0.0348759	−	0.0255778i
$183$			10.6646i			0.788353i
$184$	−0.706893	+	0.408125i	−0.0521128	+	0.0300874i
$185$	−2.06525	−	1.19237i	−0.151840	−	0.0876651i
$186$	−1.57510	−	0.909382i	−0.115492	−	0.0666791i
$187$	10.4620	−	8.42357i	0.765058	−	0.615992i
$188$			12.7935i			0.933064i
$189$	−1.69074	−	15.4228i	−0.122983	−	1.12184i
$190$	0.594487			0.0431286
$191$	0.284564	+	0.492880i	0.0205904	+	0.0356635i	0.876137	−	0.482062i	$-0.160112\pi$
$191$	0.284564	+	0.492880i	0.0205904	+	0.0356635i	−0.855547	+	0.517726i	$0.826779\pi$
$192$	19.3124	+	11.1500i	1.39376	+	0.804685i
$193$	−5.46677	−	3.15624i	−0.393507	−	0.227191i	0.290172	−	0.956975i	$-0.406288\pi$
$193$	−5.46677	−	3.15624i	−0.393507	−	0.227191i	−0.683678	+	0.729783i	$0.739621\pi$
$194$	−0.686535	−	1.18911i	−0.0492903	−	0.0853733i
$195$	−7.97768			−0.571293
$196$	−4.19405	+	13.3118i	−0.299575	+	0.950842i
$197$			5.47268i			0.389912i	0.980812	+	0.194956i	$0.0624565\pi$
$197$			5.47268i			0.389912i	−0.980812	+	0.194956i	$0.937544\pi$
$198$	0.827050	+	1.02719i	0.0587759	+	0.0729993i
$199$	22.1780	+	12.8045i	1.57216	+	0.907687i	0.995904	+	0.0904177i	$0.0288202\pi$
$199$	22.1780	+	12.8045i	1.57216	+	0.907687i	0.576256	+	0.817269i	$0.304513\pi$
$200$	0.271530	+	0.156768i	0.0192000	+	0.0110851i
$201$	18.1818	−	10.4973i	1.28245	−	0.740420i
$202$			0.976368i			0.0686970i
$203$	2.21113	+	20.1697i	0.155191	+	1.41563i
$204$			22.9311i			1.60550i
$205$	3.07742	−	1.77675i	0.214936	−	0.124093i
$206$	−0.531857	+	0.921203i	−0.0370562	+	0.0641833i
$207$	−6.59296	+	11.4193i	−0.458242	+	0.793699i
$208$	5.56643	+	9.64134i	0.385962	+	0.668506i
$209$	3.85945	+	24.8172i	0.266964	+	1.71664i
$210$	−0.475648	+	0.348838i	−0.0328229	+	0.0240721i
$211$		−	10.4184i		−	0.717231i	−0.933485	−	0.358615i	$-0.883249\pi$
$211$		−	10.4184i		−	0.717231i	0.933485	−	0.358615i	$-0.116751\pi$
$212$	−0.168028	−	0.291032i	−0.0115402	−	0.0199882i
$213$	2.52869	+	1.45994i	0.173263	+	0.100033i
$214$	0.134353	−	0.232706i	0.00918416	−	0.0159074i
$215$	0.680980	+	1.17949i	0.0464424	+	0.0804407i
$216$	−1.83863			−0.125103
$217$	19.7569	+	8.69070i	1.34118	+	0.589963i
$218$	0.178797			0.0121096
$219$	22.6824	−	13.0957i	1.53274	−	0.884925i
$220$	−2.38710	+	6.16693i	−0.160938	+	0.415774i
$221$	−5.68827	+	9.85237i	−0.382634	+	0.662742i
$222$	−0.265833	−	0.460437i	−0.0178416	−	0.0309025i
$223$		−	0.711510i		−	0.0476462i	−0.999716	−	0.0238231i	$-0.992416\pi$
$223$		−	0.711510i		−	0.0476462i	0.999716	−	0.0238231i	$-0.00758385\pi$
$224$	2.27211	+	0.999461i	0.151812	+	0.0667793i
$225$	5.06494			0.337662
$226$	−0.943848	+	0.544931i	−0.0627839	+	0.0362483i
$227$	3.16058	−	5.47428i	0.209775	−	0.363341i	−0.741869	−	0.670545i	$-0.766060\pi$
$227$	3.16058	−	5.47428i	0.209775	−	0.363341i	0.951644	+	0.307204i	$0.0993935\pi$
$228$	−37.1336	−	21.4391i	−2.45923	−	1.41984i
$229$	−2.85983	+	1.65112i	−0.188983	+	0.109109i	−0.591506	−	0.806300i	$-0.701467\pi$
$229$	−2.85983	+	1.65112i	−0.188983	+	0.109109i	0.402523	+	0.915410i	$0.368133\pi$
$230$	0.204377			0.0134762
$231$	−17.6504	−	17.5916i	−1.16131	−	1.15744i
$232$	2.40453			0.157865
$233$	−12.3470	+	7.12853i	−0.808878	+	0.467006i	−0.846566	−	0.532284i	$-0.821334\pi$
$233$	−12.3470	+	7.12853i	−0.808878	+	0.467006i	0.0376883	+	0.999290i	$0.488001\pi$
$234$	−0.967334	−	0.558491i	−0.0632366	−	0.0365097i
$235$	3.20827	−	5.55688i	0.209284	−	0.362491i
$236$	−11.6090	+	6.70246i	−0.755681	+	0.436293i
$237$	−0.470766			−0.0305795
$238$	0.0916644	+	0.836152i	0.00594172	+	0.0541997i
$239$			14.8576i			0.961057i	0.876979	+	0.480529i	$0.159555\pi$
$239$			14.8576i			0.961057i	−0.876979	+	0.480529i	$0.840445\pi$
$240$	−5.62731	−	9.74679i	−0.363242	−	0.629153i
$241$	−9.67014	+	16.7492i	−0.622908	+	1.07891i	0.366033	+	0.930602i	$0.380716\pi$
$241$	−9.67014	+	16.7492i	−0.622908	+	1.07891i	−0.988941	+	0.148307i	$0.952618\pi$
$242$	0.843663	+	0.184271i	0.0542327	+	0.0118454i
$243$	11.6479	−	6.72490i	0.747211	−	0.431402i
$244$	−7.48747			−0.479336
$245$	5.15993	−	4.73024i	0.329656	−	0.302204i
$246$	0.792232			0.0505109
$247$	−10.6363	−	18.4227i	−0.676774	−	1.17221i
$248$	1.27890	−	2.21512i	0.0812102	−	0.140660i
$249$	−27.4821	−	15.8668i	−1.74161	−	1.00552i
$250$	−0.0392524	−	0.0679871i	−0.00248254	−	0.00429988i
$251$		−	17.9154i		−	1.13081i	−0.824813	−	0.565405i	$-0.808720\pi$
$251$		−	17.9154i		−	1.13081i	0.824813	−	0.565405i	$-0.191280\pi$
$252$	26.5594	−	2.91161i	1.67309	−	0.183414i
$253$	1.32683	+	8.53186i	0.0834172	+	0.536393i
$254$	0.261789	+	0.453432i	0.0164261	+	0.0284509i
$255$	5.75049	−	9.96014i	0.360110	−	0.623728i
$256$	−7.75462	+	13.4314i	−0.484664	+	0.839462i
$257$	−14.9403	+	8.62579i	−0.931951	+	0.538062i	−0.887428	−	0.460946i	$-0.847510\pi$
$257$	−14.9403	+	8.62579i	−0.931951	+	0.538062i	−0.0445229	+	0.999008i	$0.514177\pi$
$258$			0.303641i			0.0189039i
$259$	3.73139	+	5.08782i	0.231857	+	0.316142i
$260$		−	5.60100i		−	0.347359i
$261$	33.6394	−	19.4217i	2.08223	−	1.20217i
$262$	−1.48803	−	0.859115i	−0.0919308	−	0.0530763i
$263$	25.2349	+	14.5694i	1.55605	+	0.898385i	0.997629	+	0.0688256i	$0.0219252\pi$
$263$	25.2349	+	14.5694i	1.55605	+	0.898385i	0.558419	+	0.829559i	$0.311408\pi$
$264$	−2.30021	+	1.85203i	−0.141568	+	0.113985i
$265$			0.168547i			0.0103538i
$266$	−1.43973	−	0.633312i	−0.0882755	−	0.0388308i
$267$	−24.2572			−1.48452
$268$	7.36996	+	12.7652i	0.450192	+	0.779756i
$269$	−19.6579	−	11.3495i	−1.19856	−	0.691991i	−0.238329	−	0.971185i	$-0.576600\pi$
$269$	−19.6579	−	11.3495i	−1.19856	−	0.691991i	−0.960235	+	0.279194i	$0.909933\pi$
$270$	0.398689	+	0.230183i	0.0242634	+	0.0140085i
$271$	−9.27844	−	16.0707i	−0.563625	−	0.976227i	−0.997176	−	0.0750979i	$-0.976073\pi$
$271$	−9.27844	−	16.0707i	−0.563625	−	0.976227i	0.433551	−	0.901129i	$-0.357260\pi$
$272$	−16.0496			−0.973151
$273$	19.3203	+	8.49868i	1.16932	+	0.514363i
$274$			0.536384i			0.0324042i
$275$	2.58334	−	2.07999i	0.155781	−	0.125428i
$276$	−12.7661	−	7.37049i	−0.768427	−	0.443652i
$277$	−19.7152	−	11.3826i	−1.18457	−	0.683914i	−0.227506	−	0.973777i	$-0.573057\pi$
$277$	−19.7152	−	11.3826i	−1.18457	−	0.683914i	−0.957068	+	0.289862i	$0.906390\pi$
$278$	−1.05790	+	0.610779i	−0.0634486	+	0.0366321i
$279$		−	41.3194i		−	2.47373i
$280$	−0.490585	−	0.668923i	−0.0293180	−	0.0399758i
$281$			16.9709i			1.01240i	0.862417	+	0.506199i	$0.168950\pi$
$281$			16.9709i			1.01240i	−0.862417	+	0.506199i	$0.831050\pi$
$282$	1.23888	−	0.715265i	0.0737740	−	0.0425934i
$283$	14.8738	−	25.7622i	0.884157	−	1.53141i	0.0374811	−	0.999297i	$-0.488067\pi$
$283$	14.8738	−	25.7622i	0.884157	−	1.53141i	0.846676	−	0.532108i	$-0.178600\pi$
$284$	−1.02500	+	1.77535i	−0.0608225	+	0.105348i
$285$	10.7527	+	18.6242i	0.636934	+	1.10320i
$286$	−0.722735	+	0.112396i	−0.0427362	+	0.00664612i
$287$	−9.34568	+	1.02453i	−0.551658	+	0.0604763i
$288$		−	4.75187i		−	0.280007i
$289$	0.299534	+	0.518808i	0.0176197	+	0.0305181i
$290$	−0.521399	−	0.301030i	−0.0306176	−	0.0176771i
$291$	24.8352	−	43.0157i	1.45586	−	2.52163i
$292$	9.19428	+	15.9250i	0.538055	+	0.931938i
$293$	17.8387			1.04215			0.521074	−	0.853512i	$-0.325532\pi$
$293$	17.8387			1.04215			0.521074	+	0.853512i	$0.325532\pi$
$294$	1.52355	−	0.338105i	0.0888550	−	0.0197187i
$295$	6.72317			0.391438
$296$	0.647530	−	0.373851i	0.0376369	−	0.0217297i
$297$	−7.02082	+	18.1379i	−0.407389	+	1.05247i
$298$	0.431863	−	0.748008i	0.0250171	−	0.0433309i
$299$	−3.65664	−	6.33349i	−0.211469	−	0.366275i
$300$			5.66226i			0.326911i
$301$	−0.392676	−	3.58195i	−0.0226335	−	0.206460i
$302$	1.39463			0.0802521
$303$	−30.5878	+	17.6599i	−1.75722	+	1.01453i
$304$	15.0054	−	25.9901i	0.860618	−	1.49063i
$305$	3.25219	+	1.87765i	0.186220	+	0.107514i
$306$	1.39455	−	0.805146i	0.0797213	−	0.0460271i
$307$	−23.5897			−1.34633			−0.673166	−	0.739491i	$-0.735066\pi$
$307$	−23.5897			−1.34633			−0.673166	+	0.739491i	$0.735066\pi$
$308$	12.3508	−	12.3921i	0.703750	−	0.706104i
$309$	−38.4795			−2.18902
$310$	−0.554634	+	0.320218i	−0.0315011	+	0.0181872i
$311$	11.3662	+	6.56229i	0.644519	+	0.372113i	0.786353	−	0.617777i	$-0.211967\pi$
$311$	11.3662	+	6.56229i	0.644519	+	0.372113i	−0.141834	+	0.989890i	$0.545300\pi$
$312$	1.25064	−	2.16617i	0.0708036	−	0.122635i
$313$	−2.30438	+	1.33043i	−0.130251	+	0.0752006i	−0.563710	−	0.825973i	$-0.690626\pi$
$313$	−2.30438	+	1.33043i	−0.130251	+	0.0752006i	0.433459	+	0.901173i	$0.357293\pi$
$314$	−0.494331			−0.0278967
$315$	−12.2663	−	5.39572i	−0.691126	−	0.304014i
$316$		−	0.330517i		−	0.0185930i
$317$	−3.84758	−	6.66421i	−0.216102	−	0.374299i	0.737511	−	0.675335i	$-0.236001\pi$
$317$	−3.84758	−	6.66421i	−0.216102	−	0.374299i	−0.953613	+	0.301036i	$0.902668\pi$
$318$	−0.0187883	+	0.0325423i	−0.00105360	+	0.00182488i
$319$	9.18172	−	23.7204i	0.514078	−	1.32809i
$320$	6.80044	−	3.92623i	0.380156	−	0.219483i
$321$	9.72032			0.542535
$322$	−0.494961	−	0.217725i	−0.0275831	−	0.0121333i
$323$	30.6677			1.70639
$324$	−1.45428	−	2.51888i	−0.0807931	−	0.139938i
$325$	−1.40458	+	2.43280i	−0.0779120	+	0.134948i
$326$	0.693615	+	0.400459i	0.0384158	+	0.0221794i
$327$	3.23395	+	5.60137i	0.178838	+	0.309756i
$328$			1.11415i			0.0615184i
$329$	−13.6896	+	10.0399i	−0.754731	+	0.553516i
$330$	0.730641	−	0.113626i	0.0402204	−	0.00625488i
$331$	−3.15766	−	5.46922i	−0.173560	−	0.300616i	0.766102	−	0.642719i	$-0.222194\pi$
$331$	−3.15766	−	5.46922i	−0.173560	−	0.300616i	−0.939662	+	0.342104i	$0.888861\pi$
$332$	11.1398	−	19.2948i	0.611378	−	1.05894i
$333$	6.03930	−	10.4604i	0.330952	−	0.573225i
$334$	−0.411148	+	0.237377i	−0.0224970	+	0.0129887i
$335$		−	7.39274i		−	0.403909i
$336$	3.24490	+	29.5996i	0.177024	+	1.61479i
$337$		−	21.9414i		−	1.19522i	−0.801786	−	0.597612i	$-0.796116\pi$
$337$		−	21.9414i		−	1.19522i	0.801786	−	0.597612i	$-0.203884\pi$
$338$	−0.347322	+	0.200526i	−0.0188918	+	0.0109072i
$339$	−34.1434	−	19.7127i	−1.85441	−	1.07065i
$340$	6.99286	+	4.03733i	0.379241	+	0.218955i
$341$	−16.9684	−	21.0747i	−0.918892	−	1.14126i
$342$			3.01104i			0.162818i
$343$	−17.5355	+	5.95879i	−0.946827	+	0.321744i
$344$	−0.427022			−0.0230235
$345$	3.69664	+	6.40277i	0.199020	+	0.344713i
$346$	−1.22135	−	0.705145i	−0.0656600	−	0.0379088i
$347$	22.1423	+	12.7839i	1.18866	+	0.686273i	0.958002	−	0.286761i	$-0.0925787\pi$
$347$	22.1423	+	12.7839i	1.18866	+	0.686273i	0.230658	+	0.973035i	$0.425912\pi$
$348$	21.7122	+	37.6066i	1.16390	+	2.01593i
$349$	24.5471			1.31398			0.656988	−	0.753901i	$-0.271830\pi$
$349$	24.5471			1.31398			0.656988	+	0.753901i	$0.271830\pi$
$350$	0.0226343	+	0.206467i	0.00120985	+	0.0110361i
$351$		−	16.4734i		−	0.879285i
$352$	−1.95143	−	2.42366i	−0.104011	−	0.129182i
$353$	11.1923	+	6.46189i	0.595708	+	0.343932i	0.767351	−	0.641227i	$-0.221574\pi$
$353$	11.1923	+	6.46189i	0.595708	+	0.343932i	−0.171644	+	0.985159i	$0.554908\pi$
$354$	1.29808	+	0.749447i	0.0689922	+	0.0398327i
$355$	0.890419	−	0.514084i	0.0472585	−	0.0272847i
$356$		−	17.0306i		−	0.902619i
$357$	−24.5371	+	17.9954i	−1.29864	+	0.952419i
$358$			1.61609i			0.0854130i
$359$	−0.0110443	+	0.00637644i	−0.000582897	+	0.000336536i	−0.500291	−	0.865857i	$-0.666774\pi$
$359$	−0.0110443	+	0.00637644i	−0.000582897	+	0.000336536i	0.499709	+	0.866194i	$0.333440\pi$
$360$	−0.794018	+	1.37528i	−0.0418484	+	0.0724836i
$361$	−19.1723	+	33.2074i	−1.00907	+	1.74776i
$362$	0.645798	+	1.11855i	0.0339424	+	0.0587899i
$363$	9.48674	+	29.7634i	0.497925	+	1.56217i
$364$	−5.96679	+	13.5645i	−0.312745	+	0.710973i
$365$		−	9.22270i		−	0.482738i
$366$	0.418613	+	0.725058i	0.0218812	+	0.0378994i
$367$	−20.0790	−	11.5926i	−1.04812	−	0.605130i	−0.125995	−	0.992031i	$-0.540212\pi$
$367$	−20.0790	−	11.5926i	−1.04812	−	0.605130i	−0.922121	+	0.386901i	$0.873546\pi$
$368$	5.15866	−	8.93507i	0.268914	−	0.465772i
$369$	8.99911	+	15.5869i	0.468475	+	0.811423i
$370$	−0.187214			−0.00973280
$371$	0.179554	−	0.408187i	0.00932200	−	0.0211920i
$372$	46.1923			2.39496
$373$	−12.1915	+	7.03878i	−0.631253	+	0.364454i	−0.781237	−	0.624234i	$-0.785411\pi$
$373$	−12.1915	+	7.03878i	−0.631253	+	0.364454i	0.149984	+	0.988688i	$0.452078\pi$
$374$	0.380637	−	0.983353i	0.0196823	−	0.0508480i
$375$	1.41994	−	2.45941i	0.0733255	−	0.127003i
$376$	1.00591	+	1.74228i	0.0518756	+	0.0898512i
$377$			21.5437i			1.10955i
$378$	−0.720329	−	0.982183i	−0.0370497	−	0.0505181i
$379$	−2.69083			−0.138219			−0.0691093	−	0.997609i	$-0.522016\pi$
$379$	−2.69083			−0.138219			−0.0691093	+	0.997609i	$0.522016\pi$
$380$	−13.0758	+	7.54929i	−0.670772	+	0.387270i
$381$	−9.47013	+	16.4027i	−0.485169	+	0.840338i
$382$	0.0386934	+	0.0223397i	0.00197973	+	0.00114300i
$383$	−4.14827	+	2.39501i	−0.211967	+	0.122379i	−0.602225	−	0.798326i	$-0.705719\pi$
$383$	−4.14827	+	2.39501i	−0.211967	+	0.122379i	0.390258	+	0.920705i	$0.372386\pi$
$384$	7.07936			0.361267
$385$	−8.47216	+	2.28528i	−0.431781	+	0.116469i
$386$	−0.495560			−0.0252233
$387$	−5.97405	+	3.44912i	−0.303678	+	0.175329i
$388$	30.2007	+	17.4364i	1.53321	+	0.885197i
$389$	−11.6043	+	20.0993i	−0.588362	+	1.01907i	0.406085	+	0.913835i	$0.366894\pi$
$389$	−11.6043	+	20.0993i	−0.588362	+	1.01907i	−0.994447	+	0.105238i	$0.966440\pi$
$390$	−0.542379	+	0.313143i	−0.0274644	+	0.0158566i
$391$	10.5432			0.533190
$392$	0.475490	+	2.14262i	0.0240159	+	0.108219i
$393$		−	62.1563i		−	3.13537i
$394$	0.214816	+	0.372072i	0.0108223	+	0.0187447i
$395$	−0.0828847	+	0.143561i	−0.00417038	+	0.00722331i
$396$	−31.2351	−	12.0905i	−1.56962	−	0.607571i
$397$	−0.979519	+	0.565525i	−0.0491606	+	0.0283829i	−0.524379	−	0.851485i	$-0.675702\pi$
$397$	−0.979519	+	0.565525i	−0.0491606	+	0.0283829i	0.475218	+	0.879868i	$0.342369\pi$
$398$	2.01043			0.100774
$399$	−6.20036	−	56.5590i	−0.310406	−	2.83149i
$400$	−3.96306			−0.198153
$401$	8.95972	+	15.5187i	0.447427	+	0.774966i	0.998218	−	0.0596770i	$-0.0190071\pi$
$401$	8.95972	+	15.5187i	0.447427	+	0.774966i	−0.550791	+	0.834643i	$0.685674\pi$
$402$	0.824086	−	1.42736i	0.0411017	−	0.0711902i
$403$	19.8466	+	11.4584i	0.988630	+	0.570786i
$404$	−12.3987	−	21.4752i	−0.616860	−	1.06843i
$405$			1.45877i			0.0724869i
$406$	0.942035	+	1.28448i	0.0467524	+	0.0637479i
$407$	−1.21541	−	7.81537i	−0.0602455	−	0.387394i
$408$	1.80298	+	3.12286i	0.0892609	+	0.154604i
$409$	−1.37167	+	2.37580i	−0.0678247	+	0.117476i	−0.897944	−	0.440111i	$-0.854939\pi$
$409$	−1.37167	+	2.37580i	−0.0678247	+	0.117476i	0.830119	+	0.557587i	$0.188273\pi$
$410$	0.139483	−	0.241592i	0.00688858	−	0.0119314i
$411$	−16.8039	+	9.70176i	−0.828877	+	0.478552i
$412$		−	27.0158i		−	1.33097i
$413$	−16.2822	−	7.16225i	−0.801194	−	0.352431i
$414$			1.03516i			0.0508752i
$415$	−9.67720	+	5.58714i	−0.475035	+	0.274262i
$416$	2.28243	+	1.31776i	0.111905	+	0.0646085i
$417$	−38.2692	−	22.0947i	−1.87405	−	1.08198i
$418$	1.23653	+	1.53576i	0.0604806	+	0.0751165i
$419$		−	21.3341i		−	1.04224i	−0.853483	−	0.521120i	$-0.825514\pi$
$419$		−	21.3341i		−	1.04224i	0.853483	−	0.521120i	$-0.174486\pi$
$420$	6.03205	−	13.7129i	0.294334	−	0.669120i
$421$	−26.1368			−1.27383			−0.636915	−	0.770934i	$-0.719790\pi$
$421$	−26.1368			−1.27383			−0.636915	+	0.770934i	$0.719790\pi$
$422$	−0.408946	−	0.708316i	−0.0199072	−	0.0344803i
$423$	28.1453	+	16.2497i	1.36847	+	0.790086i
$424$	−0.0457655	−	0.0264227i	−0.00222257	−	0.00128320i
$425$	−2.02490	−	3.50724i	−0.0982222	−	0.170126i
$426$	0.229224			0.0111059
$427$	−5.87588	−	8.01189i	−0.284354	−	0.387723i
$428$			6.82448i			0.329874i
$429$	−16.5935	−	20.6090i	−0.801142	−	0.995013i
$430$	0.0925957	+	0.0534602i	0.00446536	+	0.00257808i
$431$	28.2436	+	16.3065i	1.36045	+	0.785454i	0.989683	−	0.143273i	$-0.0457626\pi$
$431$	28.2436	+	16.3065i	1.36045	+	0.785454i	0.370764	+	0.928727i	$0.379096\pi$
$432$	20.1265	−	11.6200i	0.968337	−	0.559070i
$433$		−	16.0082i		−	0.769305i	−0.923062	−	0.384652i	$-0.874321\pi$
$433$		−	16.0082i		−	0.769305i	0.923062	−	0.384652i	$-0.125679\pi$
$434$	1.68434	−	0.184649i	0.0808511	−	0.00886342i
$435$		−	21.7793i		−	1.04424i
$436$	−3.93263	+	2.27051i	−0.188339	+	0.108738i
$437$	−9.85719	+	17.0731i	−0.471533	+	0.816719i
$438$	1.02807	−	1.78068i	0.0491233	−	0.0850841i
$439$	2.20348	+	3.81654i	0.105166	+	0.182153i	0.913806	−	0.406151i	$-0.133129\pi$
$439$	2.20348	+	3.81654i	0.105166	+	0.182153i	−0.808640	+	0.588304i	$0.799796\pi$
$440$	0.159796	+	1.02753i	0.00761797	+	0.0489855i
$441$	23.9584	+	26.1347i	1.14087	+	1.24451i
$442$			0.893113i			0.0424810i
$443$	3.32627	+	5.76127i	0.158036	+	0.273726i	0.934160	−	0.356854i	$-0.116151\pi$
$443$	3.32627	+	5.76127i	0.158036	+	0.273726i	−0.776124	+	0.630580i	$0.782817\pi$
$444$	11.6940	+	6.75154i	0.554973	+	0.320414i
$445$	−4.27081	+	7.39726i	−0.202456	+	0.350664i
$446$	−0.0279285	−	0.0483735i	−0.00132245	−	0.00229055i
$447$	31.2450			1.47784
$448$	−20.6519	+	2.26400i	−0.975713	+	0.106964i
$449$	36.0111			1.69947			0.849734	−	0.527211i	$-0.176762\pi$
$449$	36.0111			1.69947			0.849734	+	0.527211i	$0.176762\pi$
$450$	0.344351	−	0.198811i	0.0162328	−	0.00937203i
$451$	10.9909	+	4.25438i	0.517543	+	0.200331i
$452$	13.8400	−	23.9715i	0.650977	−	1.12753i
$453$	25.2252	+	43.6913i	1.18518	+	2.05280i
$454$		−	0.496241i		−	0.0232897i
$455$	5.99329	−	4.39545i	0.280970	−	0.206062i
$456$	−6.74269			−0.315756
$457$	31.0927	−	17.9514i	1.45445	−	0.839730i	0.455725	−	0.890121i	$-0.349380\pi$
$457$	31.0927	−	17.9514i	1.45445	−	0.839730i	0.998730	+	0.0503912i	$0.0160468\pi$
$458$	−0.129621	+	0.224510i	−0.00605679	+	0.0104907i
$459$	20.5671	+	11.8744i	0.959988	+	0.554249i
$460$	−4.49528	+	2.59535i	−0.209594	+	0.121009i
$461$	4.01759			0.187118			0.0935589	−	0.995614i	$-0.470176\pi$
$461$	4.01759			0.187118			0.0935589	+	0.995614i	$0.470176\pi$
$462$	−1.89051	−	0.503179i	−0.0879546	−	0.0234100i
$463$	−8.85949			−0.411736			−0.205868	−	0.978580i	$-0.566002\pi$
$463$	−8.85949			−0.411736			−0.205868	+	0.978580i	$0.566002\pi$
$464$	−26.3211	+	15.1965i	−1.22193	+	0.705481i
$465$	−20.0637	−	11.5838i	−0.930432	−	0.537185i
$466$	−0.559624	+	0.969297i	−0.0259241	+	0.0449018i
$467$	14.5462	−	8.39826i	0.673119	−	0.388625i	−0.124139	−	0.992265i	$-0.539617\pi$
$467$	14.5462	−	8.39826i	0.673119	−	0.388625i	0.797257	+	0.603640i	$0.206283\pi$
$468$	28.3687			1.31134
$469$	−7.87555	+	17.9038i	−0.363659	+	0.826719i
$470$		−	0.503729i		−	0.0232353i
$471$	−8.94112	−	15.4865i	−0.411985	−	0.713579i
$472$	−1.05398	+	1.82554i	−0.0485132	+	0.0840273i
$473$	−1.63059	+	4.21253i	−0.0749746	+	0.193693i
$474$	−0.0320060	+	0.0184787i	−0.00147008	+	0.000848754i
$475$	7.57263			0.347456
$476$	−12.6343	−	17.2271i	−0.579093	−	0.789605i
$477$	−0.853680			−0.0390873
$478$	0.583196	+	1.01012i	0.0266748	+	0.0462020i
$479$	7.73287	−	13.3937i	0.353324	−	0.611975i	−0.633506	−	0.773738i	$-0.718385\pi$
$479$	7.73287	−	13.3937i	0.353324	−	0.611975i	0.986830	+	0.161763i	$0.0517180\pi$
$480$	−2.30739	−	1.33217i	−0.105318	−	0.0608052i
$481$	3.34957	+	5.80162i	0.152727	+	0.264531i
$482$			1.51830i			0.0691569i
$483$	−2.13161	−	19.4443i	−0.0969915	−	0.884745i
$484$	−20.8964	+	6.66049i	−0.949836	+	0.302749i
$485$	−8.74513	−	15.1470i	−0.397096	−	0.687790i
$486$	0.527937	−	0.914413i	0.0239477	−	0.0414786i
$487$	14.0027	−	24.2534i	0.634523	−	1.09903i	−0.352093	−	0.935965i	$-0.614530\pi$
$487$	14.0027	−	24.2534i	0.634523	−	1.09903i	0.986616	−	0.163061i	$-0.0521368\pi$
$488$	−1.01968	+	0.588711i	−0.0461586	+	0.0266497i
$489$			28.9729i			1.31020i
$490$	0.165135	−	0.524135i	0.00746006	−	0.0236780i
$491$			4.29159i			0.193677i	0.995300	+	0.0968385i	$0.0308730\pi$
$491$			4.29159i			0.193677i	−0.995300	+	0.0968385i	$0.969127\pi$
$492$	−17.4251	+	10.0604i	−0.785586	+	0.453559i
$493$	−26.8973	−	15.5292i	−1.21139	−	0.699398i
$494$	−1.44627	−	0.835004i	−0.0650707	−	0.0375686i
$495$	10.5350	+	13.0844i	0.473514	+	0.588102i
$496$			32.3304i			1.45168i
$497$	−2.70408	+	0.296438i	−0.121294	+	0.0132971i
$498$	−2.49124			−0.111635
$499$	−9.57917	−	16.5916i	−0.428823	−	0.742742i	0.567946	−	0.823066i	$-0.307738\pi$
$499$	−9.57917	−	16.5916i	−0.428823	−	0.742742i	−0.996769	+	0.0803231i	$0.974405\pi$
$500$	1.72671	+	0.996918i	0.0772210	+	0.0445836i
$501$	−14.8731	−	8.58702i	−0.664483	−	0.383640i
$502$	−0.703223	−	1.21802i	−0.0313864	−	0.0543628i
$503$	−29.3566			−1.30895			−0.654473	−	0.756085i	$-0.727109\pi$
$503$	−29.3566			−1.30895			−0.654473	+	0.756085i	$0.727109\pi$
$504$	3.38805	−	2.48478i	0.150916	−	0.110681i
$505$			12.4371i			0.553442i
$506$	0.425103	+	0.527975i	0.0188981	+	0.0234714i
$507$	−12.5642	−	7.25397i	−0.557998	−	0.322160i
$508$	−11.5161	−	6.64883i	−0.510945	−	0.294994i
$509$	−9.20901	+	5.31682i	−0.408182	+	0.235664i	−0.690008	−	0.723801i	$-0.742393\pi$
$509$	−9.20901	+	5.31682i	−0.408182	+	0.235664i	0.281826	+	0.959465i	$0.409060\pi$
$510$		−	0.902882i		−	0.0399803i
$511$	−9.82502	+	22.3355i	−0.434633	+	0.988066i
$512$			6.20322i			0.274146i
$513$	−38.4578	+	22.2036i	−1.69795	+	0.980313i
$514$	−0.677166	+	1.17289i	−0.0298685	+	0.0517338i
$515$	−6.77484	+	11.7344i	−0.298535	+	0.517078i
$516$	−3.85589	−	6.67859i	−0.169746	−	0.294009i
$517$	21.0285	−	3.27024i	0.924831	−	0.143825i
$518$	0.453395	+	0.199441i	0.0199210	+	0.00876292i
$519$		−	51.0167i		−	2.23939i
$520$	−0.440385	−	0.762769i	−0.0193122	−	0.0334496i
$521$	−3.84050	−	2.21732i	−0.168256	−	0.0971424i	0.413507	−	0.910501i	$-0.364304\pi$
$521$	−3.84050	−	2.21732i	−0.168256	−	0.0971424i	−0.581763	+	0.813358i	$0.697637\pi$
$522$	1.52470	−	2.64085i	0.0667342	−	0.115587i
$523$	−8.49562	−	14.7148i	−0.371487	−	0.643435i	0.618307	−	0.785937i	$-0.287819\pi$
$523$	−8.49562	−	14.7148i	−0.371487	−	0.643435i	−0.989795	+	0.142501i	$0.954485\pi$
$524$	43.6390			1.90638
$525$	−6.05885	+	4.44353i	−0.264430	+	0.193932i
$526$	2.28753			0.0997409
$527$	−28.6118	+	16.5190i	−1.24635	+	0.719579i
$528$	13.4745	−	34.8105i	0.586401	−	1.51493i
$529$	8.11122	−	14.0491i	0.352662	−	0.610828i
$530$	0.00661587	+	0.0114590i	0.000287375	+	0.000497748i
$531$			34.0525i			1.47775i
$532$	39.7092	−	4.35318i	1.72161	−	0.188734i
$533$	−9.98232			−0.432382
$534$	−1.64918	+	0.952153i	−0.0713669	+	0.0412037i
$535$	1.71139	−	2.96422i	0.0739900	−	0.128154i
$536$	2.00735	+	1.15894i	0.0867043	+	0.0500587i
$537$	−50.6291	+	29.2307i	−2.18481	+	1.26140i
$538$	−1.78198			−0.0768266
$539$	22.9524	+	3.49096i	0.988630	+	0.150366i
$540$	−11.6922			−0.503153
$541$	0.866501	−	0.500274i	0.0372538	−	0.0215085i	−0.481257	−	0.876579i	$-0.659820\pi$
$541$	0.866501	−	0.500274i	0.0372538	−	0.0215085i	0.518511	+	0.855071i	$0.326486\pi$
$542$	−1.26163	−	0.728402i	−0.0541916	−	0.0312875i
$543$	−23.3615	+	40.4633i	−1.00254	+	1.73645i
$544$	−3.29045	+	1.89974i	−0.141077	+	0.0814508i
$545$	2.27753			0.0975585
$546$	1.64713	−	0.180569i	0.0704906	−	0.00772763i
$547$			4.75456i			0.203290i	0.994821	+	0.101645i	$0.0324107\pi$
$547$			4.75456i			0.203290i	−0.994821	+	0.101645i	$0.967589\pi$
$548$	−6.81145	−	11.7978i	−0.290971	−	0.503976i
$549$	−9.51020	+	16.4722i	−0.405886	+	0.703014i
$550$	0.0939890	−	0.242815i	0.00400770	−	0.0103537i
$551$	50.2945	−	29.0376i	2.14262	−	1.23704i
$552$	−2.31805			−0.0986629
$553$	0.353666	−	0.259377i	0.0150394	−	0.0110298i
$554$	−1.78718			−0.0759299
$555$	−3.38620	−	5.86508i	−0.143736	−	0.248959i
$556$	15.5123	−	26.8682i	0.657870	−	1.13946i
$557$	13.9386	+	8.04744i	0.590596	+	0.340981i	0.765333	−	0.643634i	$-0.222574\pi$
$557$	13.9386	+	8.04744i	0.590596	+	0.340981i	−0.174737	+	0.984615i	$0.555908\pi$
$558$	−1.62188	−	2.80919i	−0.0686598	−	0.118922i
$559$		−	3.82596i		−	0.161821i
$560$	9.59774	+	4.22188i	0.405579	+	0.178407i
$561$	37.6914	−	5.86157i	1.59133	−	0.247476i
$562$	0.666147	+	1.15380i	0.0280997	+	0.0486701i
$563$	−5.56137	+	9.63258i	−0.234384	+	0.405965i	−0.959093	−	0.283090i	$-0.908641\pi$
$563$	−5.56137	+	9.63258i	−0.234384	+	0.405965i	0.724710	+	0.689054i	$0.241974\pi$
$564$	−18.1661	+	31.4645i	−0.764929	+	1.32490i
$565$	−12.0228	+	6.94137i	−0.505804	+	0.292026i
$566$		−	2.33533i		−	0.0981614i
$567$	1.55404	−	3.53285i	0.0652635	−	0.148366i
$568$			0.322367i			0.0135262i
$569$	−15.6978	+	9.06314i	−0.658087	+	0.379947i	−0.791548	−	0.611108i	$-0.790724\pi$
$569$	−15.6978	+	9.06314i	−0.658087	+	0.379947i	0.133461	+	0.991054i	$0.457391\pi$
$570$	1.46209	+	0.844137i	0.0612402	+	0.0353570i
$571$	−11.1049	−	6.41139i	−0.464724	−	0.268308i	0.249305	−	0.968425i	$-0.419798\pi$
$571$	−11.1049	−	6.41139i	−0.464724	−	0.268308i	−0.714028	+	0.700117i	$0.753131\pi$
$572$	14.4693	−	11.6500i	0.604991	−	0.487113i
$573$			1.61626i			0.0675202i
$574$	−0.595170	+	0.436495i	−0.0248419	+	0.0182190i
$575$	2.60337			0.108568
$576$	19.8861	+	34.4438i	0.828588	+	1.43516i
$577$	16.8292	+	9.71633i	0.700608	+	0.404496i	0.807574	−	0.589766i	$-0.200780\pi$
$577$	16.8292	+	9.71633i	0.700608	+	0.404496i	−0.106966	+	0.994263i	$0.534114\pi$
$578$	0.0407289	+	0.0235149i	0.00169410	+	0.000978089i
$579$	−8.96335	−	15.5250i	−0.372504	−	0.645196i
$580$	15.2909			0.634920
$581$	29.3883	−	3.22173i	1.21923	−	0.133660i
$582$		−	3.89936i		−	0.161634i
$583$	−0.435414	+	0.350577i	−0.0180330	+	0.0145194i
$584$	2.50424	+	1.44582i	0.103626	+	0.0598285i
$585$	−12.3220	−	7.11410i	−0.509451	−	0.294132i
$586$	1.21280	−	0.700211i	0.0501004	−	0.0289255i
$587$			26.7842i			1.10550i	0.833347	+	0.552751i	$0.186422\pi$
$587$			26.7842i			1.10550i	−0.833347	+	0.552751i	$0.813578\pi$
$588$	−29.2169	+	26.7839i	−1.20488	+	1.10455i
$589$		−	61.7769i		−	2.54547i
$590$	0.457089	−	0.263901i	0.0188181	−	0.0108646i
$591$	−7.77089	+	13.4596i	−0.319652	+	0.553653i
$592$	−4.72545	+	8.18472i	−0.194215	+	0.336390i
$593$	2.73092	+	4.73010i	0.112146	+	0.194242i	0.916635	−	0.399725i	$-0.130894\pi$
$593$	2.73092	+	4.73010i	0.112146	+	0.194242i	−0.804490	+	0.593967i	$0.797561\pi$
$594$	0.234629	+	1.50873i	0.00962696	+	0.0619038i
$595$	1.16763	+	10.6510i	0.0478681	+	0.436647i
$596$			21.9366i			0.898558i
$597$	36.3633	+	62.9831i	1.48825	+	2.57772i
$598$	−0.497209	−	0.287064i	−0.0203324	−	0.0117389i
$599$	19.2942	−	33.4186i	0.788340	−	1.36545i	−0.138643	−	0.990342i	$-0.544274\pi$
$599$	19.2942	−	33.4186i	0.788340	−	1.36545i	0.926983	−	0.375103i	$-0.122393\pi$
$600$	0.445202	+	0.771112i	0.0181753	+	0.0314805i
$601$	−45.2838			−1.84716			−0.923582	−	0.383400i	$-0.874753\pi$
$601$	−45.2838			−1.84716			−0.923582	+	0.383400i	$0.874753\pi$
$602$	−0.167297	−	0.228113i	−0.00681851	−	0.00929719i
$603$	37.4438			1.52483
$604$	−30.6750	+	17.7102i	−1.24815	+	0.720618i
$605$	10.7466	+	2.34726i	0.436913	+	0.0954296i
$606$	−1.38639	+	2.40129i	−0.0563181	+	0.0975458i
$607$	0.790988	+	1.37003i	0.0321052	+	0.0556079i	0.881632	−	0.471938i	$-0.156445\pi$
$607$	0.790988	+	1.37003i	0.0321052	+	0.0556079i	−0.849526	+	0.527546i	$0.823112\pi$
$608$		−	7.10456i		−	0.288128i
$609$	−23.2017	+	52.7451i	−0.940179	+	2.13734i
$610$	0.294810			0.0119365
$611$	−15.6102	+	9.01253i	−0.631519	+	0.364608i
$612$	−20.4488	+	35.4184i	−0.826594	+	1.43170i
$613$	21.4751	+	12.3987i	0.867371	+	0.500777i	0.866474	−	0.499222i	$-0.166381\pi$
$613$	21.4751	+	12.3987i	0.867371	+	0.500777i	0.000897552		1.00000i	$0.499714\pi$
$614$	−1.60379	+	0.925950i	−0.0647238	+	0.0373683i
$615$	10.0915			0.406929
$616$	0.707639	−	2.65870i	0.0285116	−	0.107122i
$617$	−23.1854			−0.933410			−0.466705	−	0.884413i	$-0.654559\pi$
$617$	−23.1854			−0.933410			−0.466705	+	0.884413i	$0.654559\pi$
$618$	−2.61611	+	1.51041i	−0.105235	+	0.0607577i
$619$	1.69588	+	0.979118i	0.0681632	+	0.0393541i	0.533694	−	0.845677i	$-0.320803\pi$
$619$	1.69588	+	0.979118i	0.0681632	+	0.0393541i	−0.465531	+	0.885032i	$0.654137\pi$
$620$	8.13279	−	14.0864i	0.326621	−	0.565724i
$621$	−13.2213	+	7.63332i	−0.530553	+	0.306315i
$622$	1.03034			0.0413130
$623$	18.2234	−	13.3650i	0.730105	−	0.535456i
$624$			31.6160i			1.26565i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.104445	+	0.180905i	−0.00417448	+	0.00723041i
$627$	−25.7471	+	66.5160i	−1.02824	+	2.65639i
$628$	10.8728	−	6.27742i	0.433872	−	0.250496i
$629$	−9.65777			−0.385080
$630$	−1.04574	+	0.114641i	−0.0416634	+	0.00456741i
$631$	42.5260			1.69293			0.846467	−	0.532441i	$-0.178725\pi$
$631$	42.5260			1.69293			0.846467	+	0.532441i	$0.178725\pi$
$632$	−0.0259873	−	0.0450113i	−0.00103372	−	0.00179045i
$633$	14.7935	−	25.6231i	0.587988	−	1.01843i
$634$	−0.523172	−	0.302054i	−0.0207778	−	0.0119961i
$635$	3.33469	+	5.77585i	0.132333	+	0.229208i
$636$		−	0.954357i		−	0.0378427i
$637$	−19.1971	+	4.26021i	−0.760615	+	0.168796i
$638$	−0.306845	−	1.97309i	−0.0121481	−	0.0781154i
$639$	2.60380	+	4.50992i	0.103005	+	0.178410i
$640$	1.24642	−	2.15886i	0.0492690	−	0.0853364i
$641$	21.2453	−	36.7979i	0.839139	−	1.45343i	−0.0514770	−	0.998674i	$-0.516393\pi$
$641$	21.2453	−	36.7979i	0.839139	−	1.45343i	0.890616	−	0.454757i	$-0.150274\pi$
$642$	0.660857	−	0.381546i	0.0260819	−	0.0150584i
$643$		−	3.01884i		−	0.119051i	−0.998227	−	0.0595257i	$-0.981041\pi$
$643$		−	3.01884i		−	0.119051i	0.998227	−	0.0595257i	$-0.0189588\pi$
$644$	13.6515	−	1.49657i	0.537945	−	0.0589730i
$645$			3.86781i			0.152295i
$646$	2.08501	−	1.20378i	0.0820335	−	0.0473621i
$647$	30.0088	+	17.3256i	1.17977	+	0.681138i	0.955961	−	0.293495i	$-0.0948185\pi$
$647$	30.0088	+	17.3256i	1.17977	+	0.681138i	0.223806	+	0.974634i	$0.428152\pi$
$648$	−0.396099	−	0.228688i	−0.0155603	−	0.00898372i
$649$	13.9842	+	17.3682i	0.548926	+	0.681762i
$650$			0.220532i			0.00864999i
$651$	36.2500	+	49.4276i	1.42075	+	1.93722i
$652$	−20.3414			−0.796632
$653$	−13.1294	−	22.7408i	−0.513794	−	0.889918i	−0.999872	−	0.0160021i	$-0.994906\pi$
$653$	−13.1294	−	22.7408i	−0.513794	−	0.889918i	0.486078	−	0.873916i	$-0.338427\pi$
$654$	0.439734	+	0.253881i	0.0171950	+	0.00992752i
$655$	−18.9546	−	10.9435i	−0.740619	−	0.427597i
$656$	−7.04136	−	12.1960i	−0.274919	−	0.476173i
$657$	46.7124			1.82242
$658$	−0.536626	+	1.21993i	−0.0209199	+	0.0475579i
$659$		−	26.8160i		−	1.04460i	−0.852761	−	0.522302i	$-0.825073\pi$
$659$		−	26.8160i		−	1.04460i	0.852761	−	0.522302i	$-0.174927\pi$
$660$	−14.6275	+	11.7775i	−0.569376	+	0.458437i
$661$	8.60684	+	4.96916i	0.334767	+	0.193278i	0.657956	−	0.753057i	$-0.271421\pi$
$661$	8.60684	+	4.96916i	0.334767	+	0.193278i	−0.323188	+	0.946335i	$0.604755\pi$
$662$	−0.429360	−	0.247891i	−0.0166876	−	0.00963456i
$663$	−27.9796	+	16.1540i	−1.08664	+	0.627370i
$664$		−	3.50353i		−	0.135963i
$665$	−18.3394	−	8.06718i	−0.711171	−	0.312832i
$666$		−	0.948228i		−	0.0367431i
$667$	17.2906	−	9.98275i	0.669496	−	0.386533i
$668$	6.02881	−	10.4422i	0.233262	−	0.404021i
$669$	1.01030	−	1.74989i	0.0390605	−	0.0676548i
$670$	−0.290183	−	0.502612i	−0.0112107	−	0.0194176i
$671$	1.91393	+	12.3070i	0.0738863	+	0.475107i
$672$	4.16887	+	5.68435i	0.160818	+	0.219278i
$673$			37.8329i			1.45835i	0.684328	+	0.729175i	$0.260096\pi$
$673$			37.8329i			1.45835i	−0.684328	+	0.729175i	$0.739904\pi$
$674$	−0.861252	−	1.49173i	−0.0331742	−	0.0574594i
$675$	5.07853	+	2.93209i	0.195473	+	0.112856i
$676$	5.09290	−	8.82116i	0.195881	−	0.339275i
$677$	−24.5180	−	42.4664i	−0.942304	−	1.63212i	−0.761062	−	0.648679i	$-0.775322\pi$
$677$	−24.5180	−	42.4664i	−0.942304	−	1.63212i	−0.181242	−	0.983439i	$-0.558012\pi$
$678$	−3.09508			−0.118866
$679$	5.04274	+	45.9993i	0.193523	+	1.76529i
$680$	1.26976			0.0486930
$681$	15.5463	−	8.97567i	0.595736	−	0.343948i
$682$	−1.98087	−	0.766755i	−0.0758513	−	0.0293606i
$683$	−20.4413	+	35.4054i	−0.782166	+	1.35475i	0.148512	+	0.988911i	$0.452552\pi$
$683$	−20.4413	+	35.4054i	−0.782166	+	1.35475i	−0.930678	+	0.365840i	$0.880782\pi$
$684$	−38.2367	−	66.2279i	−1.46202	−	2.53229i
$685$			6.83250i			0.261057i
$686$	−0.958290	+	1.09343i	−0.0365877	+	0.0417474i
$687$	−9.37799			−0.357793
$688$	4.67440	−	2.69876i	0.178210	−	0.102889i
$689$	0.236737	−	0.410041i	0.00901898	−	0.0156213i
$690$	0.502648	+	0.290204i	0.0191355	+	0.0110479i
$691$	21.0232	−	12.1378i	0.799761	−	0.461742i	−0.0436269	−	0.999048i	$-0.513891\pi$
$691$	21.0232	−	12.1378i	0.799761	−	0.461742i	0.843387	+	0.537306i	$0.180558\pi$
$692$	35.8180			1.36160
$693$	−11.5748	−	42.9109i	−0.439690	−	1.63005i
$694$	2.00719			0.0761918
$695$	−13.4756	+	7.78015i	−0.511159	+	0.295118i
$696$	5.91372	+	3.41429i	0.224159	+	0.129418i
$697$	7.19548	−	12.4629i	0.272548	−	0.472068i
$698$	1.66889	−	0.963532i	0.0631683	−	0.0364702i
$699$	−40.4884			−1.53141
$700$	−3.11973	−	4.25382i	−0.117915	−	0.160779i
$701$			16.3890i			0.619005i	0.950899	+	0.309503i	$0.100163\pi$
$701$			16.3890i			0.619005i	−0.950899	+	0.309503i	$0.899837\pi$
$702$	−0.646620	−	1.11998i	−0.0244051	−	0.0422709i
$703$	9.02940	−	15.6394i	0.340550	−	0.589851i
$704$	24.2876	+	9.40128i	0.915375	+	0.354324i
$705$	15.7809	−	9.11111i	0.594343	−	0.343144i
$706$	1.01458			0.0381842
$707$	13.2493	−	30.1201i	0.498291	−	1.13278i
$708$	−38.0684			−1.43070
$709$	12.1045	+	20.9656i	0.454593	+	0.787379i	0.998665	−	0.0516601i	$-0.0164512\pi$
$709$	12.1045	+	20.9656i	0.454593	+	0.787379i	−0.544071	+	0.839039i	$0.683118\pi$
$710$	0.0403580	−	0.0699022i	0.00151461	−	0.00262338i
$711$	−0.727125	−	0.419806i	−0.0272693	−	0.0157439i
$712$	−1.33905	−	2.31930i	−0.0501830	−	0.0869195i
$713$		−	21.2381i		−	0.795374i
$714$	−0.961847	+	2.18660i	−0.0359962	+	0.0818314i
$715$	−9.20626	+	1.43171i	−0.344294	+	0.0535429i
$716$	−20.5224	−	35.5459i	−0.766960	−	1.32841i
$717$	−21.0969	+	36.5409i	−0.787878	+	1.36465i
$718$	−0.000500581	0	0.000867032i	−1.86815e−5	0	3.23573e-5i
$719$	30.0658	−	17.3585i	1.12126	−	0.647362i	0.179541	−	0.983750i	$-0.442539\pi$
$719$	30.0658	−	17.3585i	1.12126	−	0.647362i	0.941723	+	0.336388i	$0.109205\pi$
$720$		−	20.0726i		−	0.748063i
$721$	28.9080	−	21.2010i	1.07659	−	0.789566i
$722$			3.01024i			0.112029i
$723$	−47.5657	+	27.4621i	−1.76899	+	1.02132i
$724$	−28.4086	−	16.4017i	−1.05580	−	0.609566i
$725$	−6.64162	−	3.83454i	−0.246664	−	0.142411i
$726$	1.81326	+	1.65115i	0.0672964	+	0.0612799i
$727$		−	19.7276i		−	0.731655i	−0.930683	−	0.365828i	$-0.880786\pi$
$727$		−	19.7276i		−	0.731655i	0.930683	−	0.365828i	$-0.119214\pi$
$728$	0.253941	+	2.31642i	0.00941167	+	0.0858522i
$729$	42.5722			1.57675
$730$	−0.362013	−	0.627025i	−0.0133987	−	0.0232072i
$731$	4.77671	+	2.75784i	0.176673	+	0.102002i
$732$	−18.4148	−	10.6318i	−0.680630	−	0.392962i
$733$	9.24476	+	16.0124i	0.341463	+	0.591431i	0.984705	−	0.174232i	$-0.0557443\pi$
$733$	9.24476	+	16.0124i	0.341463	+	0.591431i	−0.643242	+	0.765663i	$0.722411\pi$
$734$	−1.82015			−0.0671831
$735$	19.4070	−	4.30681i	0.715840	−	0.158859i
$736$		−	2.44246i		−	0.0900302i
$737$	19.0979	−	15.3769i	0.703482	−	0.566414i
$738$	1.22365	+	0.706474i	0.0450431	+	0.0260056i
$739$	−1.43709	−	0.829705i	−0.0528643	−	0.0305212i	0.473335	−	0.880883i	$-0.343050\pi$
$739$	−1.43709	−	0.829705i	−0.0528643	−	0.0305212i	−0.526199	+	0.850361i	$0.676383\pi$
$740$	4.11778	−	2.37740i	0.151372	−	0.0873949i
$741$		−	60.4119i		−	2.21929i
$742$	−0.00381494	−	0.0347994i	−0.000140051	−	0.00127753i
$743$		−	23.0302i		−	0.844895i	−0.906387	−	0.422448i	$-0.861171\pi$
$743$		−	23.0302i		−	0.844895i	0.906387	−	0.422448i	$-0.138829\pi$
$744$	6.29068	−	3.63192i	0.230627	−	0.133153i
$745$	5.50110	−	9.52819i	0.201545	−	0.349086i
$746$	−0.552578	+	0.957093i	−0.0202313	+	0.0350417i
$747$	−28.2985	−	49.0144i	−1.03539	−	1.79334i
$748$	4.11532	+	26.4625i	0.150471	+	0.967565i
$749$	−7.30246	+	5.35559i	−0.266826	+	0.195689i
$750$		−	0.222944i		−	0.00814078i
$751$	2.93980	+	5.09188i	0.107275	+	0.185805i	0.914665	−	0.404212i	$-0.132454\pi$
$751$	2.93980	+	5.09188i	0.107275	+	0.185805i	−0.807391	+	0.590017i	$0.799121\pi$
$752$	−22.0223	−	12.7146i	−0.803069	−	0.463652i
$753$	25.4388	−	44.0614i	0.927043	−	1.60569i
$754$	0.845640	+	1.46469i	0.0307964	+	0.0533409i
$755$	17.7650			0.646533
$756$	28.3162	+	12.4558i	1.02985	+	0.453013i
$757$	37.8936			1.37726			0.688632	−	0.725111i	$-0.258211\pi$
$757$	37.8936			1.37726			0.688632	+	0.725111i	$0.258211\pi$
$758$	−0.182942	+	0.105621i	−0.00664474	+	0.00383634i
$759$	−8.85152	+	22.8674i	−0.321290	+	0.830033i
$760$	−1.18714	+	2.05619i	−0.0430622	+	0.0745859i
$761$	−3.06814	−	5.31418i	−0.111220	−	0.192639i	0.805042	−	0.593217i	$-0.202143\pi$
$761$	−3.06814	−	5.31418i	−0.111220	−	0.192639i	−0.916262	+	0.400578i	$0.868809\pi$
$762$			1.48690i			0.0538647i
$763$	−5.51571	−	2.42626i	−0.199682	−	0.0878367i
$764$	−1.13475			−0.0410538
$765$	17.7639	−	10.2560i	0.642256	−	0.370807i
$766$	−0.188020	+	0.325659i	−0.00679342	+	0.0117666i
$767$	−16.3561	−	9.44322i	−0.590586	−	0.340975i
$768$	−38.1436	+	22.0222i	−1.37639	+	0.794658i
$769$	−0.787896			−0.0284123			−0.0142061	−	0.999899i	$-0.504522\pi$
$769$	−0.787896			−0.0284123			−0.0142061	+	0.999899i	$0.504522\pi$
$770$	−0.486295	+	0.487922i	−0.0175249	+	0.0175835i
$771$	−48.9925			−1.76442
$772$	10.8998	−	6.29303i	0.392294	−	0.226491i
$773$	−6.66382	−	3.84736i	−0.239681	−	0.138380i	0.375349	−	0.926884i	$-0.377523\pi$
$773$	−6.66382	−	3.84736i	−0.239681	−	0.138380i	−0.615030	+	0.788504i	$0.710856\pi$
$774$	−0.270772	+	0.468991i	−0.00973271	+	0.0168576i
$775$	−7.06497	+	4.07896i	−0.253781	+	0.146521i
$776$	5.48382			0.196858
$777$	1.95260	+	17.8114i	0.0700491	+	0.638980i
$778$			1.82199i			0.0653215i
$779$	13.4546	+	23.3041i	0.482063	+	0.834957i
$780$	7.95309	−	13.7752i	0.284766	−	0.493230i
$781$	3.18012	+	1.23096i	0.113794	+	0.0440473i
$782$	0.716799	−	0.413844i	0.0256327	−	0.0147990i
$783$	44.9729			1.60720
$784$	−18.7462	−	20.4491i	−0.669508	−	0.730325i
$785$	−6.29682			−0.224743
$786$	−2.43979	−	4.22583i	−0.0870243	−	0.150730i
$787$	−19.5046	+	33.7830i	−0.695266	+	1.20424i	0.274825	+	0.961494i	$0.411380\pi$
$787$	−19.5046	+	33.7830i	−0.695266	+	1.20424i	−0.970091	+	0.242741i	$0.921953\pi$
$788$	−9.44976	−	5.45582i	−0.336634	−	0.194355i
$789$	41.3753	+	71.6640i	1.47300	+	2.55131i
$790$			0.0130137i			0.000463006i
$791$	36.5116	−	4.00263i	1.29820	−	0.142317i
$792$	−5.20436	+	0.809356i	−0.184929	+	0.0287592i
$793$	−5.27463	−	9.13592i	−0.187307	−	0.324426i
$794$	−0.0443964	+	0.0768969i	−0.00157557	+	0.00272897i
$795$	−0.239327	+	0.414526i	−0.00848805	+	0.0147017i
$796$	−44.2194	+	25.5301i	−1.56732	+	0.904890i
$797$		−	3.25392i		−	0.115260i	−0.998338	−	0.0576298i	$-0.981646\pi$
$797$		−	3.25392i		−	0.115260i	0.998338	−	0.0576298i	$-0.0183543\pi$
$798$	−2.64162	−	3.60191i	−0.0935124	−	0.127506i
$799$		−	25.9857i		−	0.919309i
$800$	−0.812496	+	0.469095i	−0.0287261	+	0.0165850i
$801$	−37.4666	−	21.6314i	−1.32382	−	0.764307i
$802$	1.21829	+	0.703381i	0.0430194	+	0.0248372i
$803$	23.8253	−	19.1832i	0.840778	−	0.676959i
$804$			41.8597i			1.47628i
$805$	−6.30485	−	2.77339i	−0.222217	−	0.0977493i
$806$	1.79909			0.0633701
$807$	−32.2312	−	55.8261i	−1.13459	−	1.96517i
$808$	−3.37703	−	1.94973i	−0.118803	−	0.0685912i
$809$	−9.81365	−	5.66591i	−0.345029	−	0.199203i	0.317464	−	0.948270i	$-0.397169\pi$
$809$	−9.81365	−	5.66591i	−0.345029	−	0.199203i	−0.662494	+	0.749067i	$0.730502\pi$
$810$	0.0572602	+	0.0991776i	0.00201192	+	0.00348475i
$811$	−26.6367			−0.935340			−0.467670	−	0.883903i	$-0.654906\pi$
$811$	−26.6367			−0.935340			−0.467670	+	0.883903i	$0.654906\pi$
$812$	−37.0315	−	16.2895i	−1.29955	−	0.571650i
$813$		−	52.6993i		−	1.84825i
$814$	−0.389404	−	0.483637i	−0.0136486	−	0.0169515i
$815$	8.83533	+	5.10108i	0.309488	+	0.178683i
$816$	−39.4726	−	22.7895i	−1.38182	−	0.797793i
$817$	−8.93185	+	5.15680i	−0.312486	+	0.180414i
$818$			0.215365i			0.00753007i
$819$	22.2627	+	30.3556i	0.777921	+	1.06071i
$820$			7.08509i			0.247422i
$821$	15.7945	−	9.11895i	0.551232	−	0.318254i	−0.198387	−	0.980124i	$-0.563570\pi$
$821$	15.7945	−	9.11895i	0.551232	−	0.318254i	0.749619	+	0.661870i	$0.230237\pi$
$822$	−0.761634	+	1.31919i	−0.0265650	+	0.0460120i
$823$	0.786320	−	1.36195i	0.0274094	−	0.0474744i	−0.851995	−	0.523549i	$-0.824608\pi$
$823$	0.786320	−	1.36195i	0.0274094	−	0.0474744i	0.879405	+	0.476075i	$0.157941\pi$
$824$	−2.12415	−	3.67914i	−0.0739983	−	0.128169i
$825$	9.30696	−	1.44737i	0.324027	−	0.0503910i
$826$	−1.38811	+	0.152174i	−0.0482987	+	0.00529481i
$827$			4.04047i			0.140501i	0.997529	+	0.0702504i	$0.0223798\pi$
$827$			4.04047i			0.140501i	−0.997529	+	0.0702504i	$0.977620\pi$
$828$	−13.1453	−	22.7683i	−0.456830	−	0.791253i
$829$	20.8028	+	12.0105i	0.722513	+	0.417143i	0.815677	−	0.578508i	$-0.196365\pi$
$829$	20.8028	+	12.0105i	0.722513	+	0.417143i	−0.0931641	+	0.995651i	$0.529698\pi$
$830$	−0.438617	+	0.759707i	−0.0152246	+	0.0263698i
$831$	−32.3253	−	55.9890i	−1.12135	−	1.94224i
$832$	−22.0588			−0.764752
$833$	8.51880	−	27.0384i	0.295159	−	0.936825i
$834$	−3.46908			−0.120124
$835$	−5.23724	+	3.02372i	−0.181242	+	0.104640i
$836$	−46.6998	−	18.0766i	−1.61515	−	0.625192i
$837$	23.9198	−	41.4303i	0.826788	−	1.43204i
$838$	−0.837415	−	1.45045i	−0.0289280	−	0.0501048i
$839$		−	2.15493i		−	0.0743966i	−0.999308	−	0.0371983i	$-0.988157\pi$
$839$		−	2.15493i		−	0.0743966i	0.999308	−	0.0371983i	$-0.0118433\pi$
$840$	−0.256718	−	2.34176i	−0.00885763	−	0.0807983i
$841$	−29.8149			−1.02810
$842$	−1.77697	+	1.02593i	−0.0612383	+	0.0353560i
$843$	−24.0976	+	41.7383i	−0.829967	+	1.43754i
$844$	17.9896	+	10.3863i	0.619226	+	0.357510i
$845$	−4.42421	+	2.55432i	−0.152198	+	0.0878713i
$846$	2.55135			0.0877174
$847$	−23.5257	−	17.1331i	−0.808352	−	0.588699i
$848$	0.667962			0.0229379
$849$	73.1617	−	42.2399i	2.51090	−	1.44967i
$850$	−0.275335	−	0.158965i	−0.00944390	−	0.00545244i
$851$	3.10420	−	5.37662i	0.106410	−	0.184308i
$852$	−5.04179	+	2.91088i	−0.172729	+	0.0997250i
$853$	−2.32952			−0.0797611			−0.0398805	−	0.999204i	$-0.512698\pi$
$853$	−2.32952			−0.0797611			−0.0398805	+	0.999204i	$0.512698\pi$
$854$	−0.713971	−	0.314063i	−0.0244316	−	0.0107470i
$855$			38.3549i			1.31171i
$856$	0.536582	+	0.929388i	0.0183400	+	0.0317658i
$857$	−21.0847	+	36.5197i	−0.720238	+	1.24749i	0.240666	+	0.970608i	$0.422634\pi$
$857$	−21.0847	+	36.5197i	−0.720238	+	1.24749i	−0.960904	+	0.276881i	$0.910699\pi$
$858$	−1.93710	−	0.749814i	−0.0661315	−	0.0255982i
$859$	−25.2111	+	14.5556i	−0.860190	+	0.496631i	−0.864076	−	0.503361i	$-0.832096\pi$
$859$	−25.2111	+	14.5556i	−0.860190	+	0.496631i	0.00388583	+	0.999992i	$0.498763\pi$
$860$	−2.71553			−0.0925986
$861$	−24.4396	−	10.7506i	−0.832900	−	0.366378i
$862$	2.56027			0.0872031
$863$	2.14216	+	3.71033i	0.0729200	+	0.126301i	0.900180	−	0.435518i	$-0.143435\pi$
$863$	2.14216	+	3.71033i	0.0729200	+	0.126301i	−0.827260	+	0.561819i	$0.810102\pi$
$864$	2.75086	−	4.76462i	0.0935860	−	0.162096i
$865$	−15.5576	−	8.98219i	−0.528974	−	0.305404i
$866$	−0.628360	−	1.08835i	−0.0213525	−	0.0369837i
$867$			1.70128i			0.0577786i
$868$	−34.7023	+	25.4505i	−1.17787	+	0.863848i
$869$	−0.543265	+	0.0844858i	−0.0184290	+	0.00286598i
$870$	−0.854890	−	1.48071i	−0.0289835	−	0.0502009i
$871$	−10.3837	+	17.9851i	−0.351838	+	0.609401i
$872$	−0.357042	+	0.618415i	−0.0120910	+	0.0209422i
$873$	76.7187	−	44.2935i	2.59653	−	1.49911i
$874$			1.54767i			0.0523508i
$875$	0.288317	+	2.62999i	0.00974689	+	0.0889101i
$876$			52.2214i			1.76440i
$877$	35.2208	−	20.3347i	1.18932	−	0.686655i	0.231169	−	0.972914i	$-0.425745\pi$
$877$	35.2208	−	20.3347i	1.18932	−	0.686655i	0.958152	+	0.286259i	$0.0924117\pi$
$878$	0.299616	+	0.172984i	0.0101116	+	0.00583791i
$879$	43.8727	+	25.3299i	1.47979	+	0.854356i
$880$	−8.24314	−	10.2379i	−0.277876	−	0.345120i
$881$		−	10.4521i		−	0.352139i	−0.984378	−	0.176070i	$-0.943662\pi$
$881$		−	10.4521i		−	0.352139i	0.984378	−	0.176070i	$-0.0563384\pi$
$882$	2.65471	+	0.836400i	0.0893887	+	0.0281631i
$883$	12.1824			0.409972			0.204986	−	0.978765i	$-0.434285\pi$
$883$	12.1824			0.409972			0.204986	+	0.978765i	$0.434285\pi$
$884$	−11.3415	−	19.6440i	−0.381455	−	0.660700i
$885$	16.5350	+	9.54652i	0.555820	+	0.320903i
$886$	0.452287	+	0.261128i	0.0151949	+	0.00877277i
$887$	8.72489	+	15.1119i	0.292953	+	0.507410i	0.974507	−	0.224359i	$-0.0720287\pi$
$887$	8.72489	+	15.1119i	0.292953	+	0.507410i	−0.681554	+	0.731768i	$0.738695\pi$
$888$	2.12339			0.0712563
$889$	−1.92289	−	17.5404i	−0.0644918	−	0.588287i
$890$			0.670558i			0.0224771i
$891$	−3.76850	+	3.03423i	−0.126249	+	0.101651i
$892$	1.22857	+	0.709317i	0.0411357	+	0.0237497i
$893$	42.0802	+	24.2950i	1.40816	+	0.813002i
$894$	2.12426	−	1.22644i	0.0710457	−	0.0410183i
$895$			20.5859i			0.688110i
$896$	−5.31843	+	3.90051i	−0.177676	+	0.130307i
$897$		−	20.7689i		−	0.693452i
$898$	2.44829	−	1.41352i	0.0817005	−	0.0471698i
$899$	−31.2819	+	54.1819i	−1.04331	+	1.80707i
$900$	−5.04933	+	8.74569i	−0.168311	+	0.291523i
$901$	0.341291	+	0.591134i	0.0113701	+	0.0196935i
$902$	0.914238	−	0.142178i	0.0304408	−	0.00473400i
$903$	4.12040	−	9.36706i	0.137118	−	0.311716i
$904$		−	4.35273i		−	0.144770i
$905$	8.22622	+	14.2482i	0.273449	+	0.473627i
$906$	3.42998	+	1.98030i	0.113953	+	0.0657910i
$907$	−0.359197	+	0.622148i	−0.0119270	+	0.0206581i	−0.871927	−	0.489635i	$-0.837130\pi$
$907$	−0.359197	+	0.622148i	−0.0119270	+	0.0206581i	0.860000	+	0.510293i	$0.170463\pi$
$908$	6.30168	+	10.9148i	0.209128	+	0.362221i
$909$	−62.9929			−2.08934
$910$	0.234935	−	0.534085i	0.00778801	−	0.0177047i
$911$	−24.3393			−0.806398			−0.403199	−	0.915112i	$-0.632102\pi$
$911$	−24.3393			−0.806398			−0.403199	+	0.915112i	$0.632102\pi$
$912$	73.8088	−	42.6135i	2.44405	−	1.41108i
$913$	−34.5620	−	13.3783i	−1.14383	−	0.442756i
$914$	1.40927	−	2.44092i	0.0466145	−	0.0807386i
$915$	5.33232	+	9.23585i	0.176281	+	0.305328i
$916$		−	6.58414i		−	0.217546i
$917$	34.2462	+	46.6954i	1.13091	+	1.54202i
$918$	1.86439			0.0615341
$919$	12.3704	−	7.14207i	0.408063	−	0.235595i	−0.281894	−	0.959445i	$-0.590963\pi$
$919$	12.3704	−	7.14207i	0.408063	−	0.235595i	0.689957	+	0.723850i	$0.257629\pi$
$920$	−0.408125	+	0.706893i	−0.0134555	+	0.0233056i
$921$	−58.0167	−	33.4959i	−1.91171	−	1.10373i
$922$	0.273144	−	0.157700i	0.00899553	−	0.00519357i
$923$	−2.88828			−0.0950690
$924$	47.9716	−	12.9399i	1.57815	−	0.425690i
$925$	−2.38475			−0.0784100
$926$	−0.602332	+	0.347756i	−0.0197938	+	0.0114280i
$927$	−59.4338	−	34.3141i	−1.95206	−	1.12702i
$928$	−3.59753	+	6.23110i	−0.118095	+	0.204546i
$929$	−4.18313	+	2.41513i	−0.137244	+	0.0792378i	−0.567050	−	0.823683i	$-0.691915\pi$
$929$	−4.18313	+	2.41513i	−0.137244	+	0.0792378i	0.429806	+	0.902921i	$0.358582\pi$
$930$	−1.81876			−0.0596396
$931$	35.8203	+	39.0742i	1.17396	+	1.28060i
$932$		−	28.4263i		−	0.931133i
$933$	18.6361	+	32.2787i	0.610120	+	1.05676i
$934$	0.659304	−	1.14195i	0.0215731	−	0.0373657i
$935$	4.84859	−	12.5260i	0.158566	−	0.409645i
$936$	3.86338	−	2.23052i	0.126278	−	0.0729069i
$937$	20.4314			0.667466			0.333733	−	0.942668i	$-0.391692\pi$
$937$	20.4314			0.667466			0.333733	+	0.942668i	$0.391692\pi$
$938$	0.167329	+	1.52636i	0.00546350	+	0.0498374i
$939$	−7.55655			−0.246599
$940$	6.39676	+	11.0795i	0.208639	+	0.361374i
$941$	10.4441	−	18.0897i	0.340468	−	0.589707i	−0.644052	−	0.764982i	$-0.722748\pi$
$941$	10.4441	−	18.0897i	0.340468	−	0.589707i	0.984520	+	0.175275i	$0.0560813\pi$
$942$	−1.21576	−	0.701921i	−0.0396117	−	0.0228698i
$943$	4.62554	+	8.01167i	0.150628	+	0.260896i
$944$		−	26.6443i		−	0.867200i
$945$	−9.17560	−	12.5111i	−0.298482	−	0.406987i
$946$	0.0544929	+	0.350403i	0.00177172	+	0.0113926i
$947$	24.8826	+	43.0980i	0.808576	+	1.40050i	0.913850	+	0.406052i	$0.133095\pi$
$947$	24.8826	+	43.0980i	0.808576	+	1.40050i	−0.105274	+	0.994443i	$0.533572\pi$
$948$	0.469315	−	0.812878i	0.0152426	−	0.0264010i
$949$	−12.9540	+	22.4370i	−0.420505	+	0.728336i
$950$	0.514841	−	0.297244i	0.0167037	−	0.00964386i
$951$		−	21.8534i		−	0.708644i
$952$	−3.07510	−	1.35268i	−0.0996645	−	0.0438407i
$953$			14.8187i			0.480023i	0.970770	+	0.240012i	$0.0771513\pi$
$953$			14.8187i			0.480023i	−0.970770	+	0.240012i	$0.922849\pi$
$954$	−0.0580392	+	0.0335090i	−0.00187909	+	0.00108489i
$955$	0.492880	+	0.284564i	0.0159492	+	0.00920829i
$956$	−25.6548	−	14.8118i	−0.829735	−	0.479048i
$957$	56.2633	−	45.3008i	1.81873	−	1.46437i
$958$		−	1.21414i		−	0.0392269i
$959$	7.27872	−	16.5470i	0.235042	−	0.534329i
$960$	22.3001			0.719732
$961$	17.7759	+	30.7887i	0.573416	+	0.993185i
$962$	0.455455	+	0.262957i	0.0146844	+	0.00847807i
$963$	15.0136	+	8.66810i	0.483806	+	0.279326i
$964$	−19.2807	−	33.3951i	−0.620989	−	1.07558i
$965$	−6.31248			−0.203206
$966$	−0.908156	−	1.23829i	−0.0292195	−	0.0398413i
$967$			19.4642i			0.625925i	0.949765	+	0.312963i	$0.101321\pi$
$967$			19.4642i			0.625925i	−0.949765	+	0.312963i	$0.898679\pi$
$968$	−2.32208	+	2.55006i	−0.0746344	+	0.0819620i
$969$	75.4244	+	43.5463i	2.42298	+	1.39891i
$970$	−1.18911	−	0.686535i	−0.0381801	−	0.0220433i
$971$	−11.1754	+	6.45211i	−0.358635	+	0.207058i	−0.668482	−	0.743728i	$-0.733056\pi$
$971$	−11.1754	+	6.45211i	−0.358635	+	0.207058i	0.309847	+	0.950787i	$0.399722\pi$
$972$			26.8167i			0.860146i
$973$	40.9235	−	4.48630i	1.31195	−	0.143824i
$974$		−	2.19856i		−	0.0704464i
$975$	−6.90887	+	3.98884i	−0.221261	+	0.127745i
$976$	7.44126	−	12.8886i	0.238189	−	0.412555i
$977$	−16.4565	+	28.5035i	−0.526491	+	0.911909i	0.473033	+	0.881045i	$0.343159\pi$
$977$	−16.4565	+	28.5035i	−0.526491	+	0.911909i	−0.999524	+	0.0308642i	$0.990174\pi$
$978$	1.13726	+	1.96979i	0.0363655	+	0.0629868i
$979$	−27.9929	+	4.35331i	−0.894656	+	0.139132i
$980$	3.02374	+	13.6254i	0.0965899	+	0.435247i
$981$			11.5355i			0.368301i
$982$	0.168455	+	0.291773i	0.00537563	+	0.00931086i
$983$	4.35068	+	2.51187i	0.138765	+	0.0801161i	0.567775	−	0.823184i	$-0.307804\pi$
$983$	4.35068	+	2.51187i	0.138765	+	0.0801161i	−0.429010	+	0.903300i	$0.641138\pi$
$984$	−1.58202	+	2.74014i	−0.0504330	+	0.0873526i
$985$	2.73634	+	4.73948i	0.0871871	+	0.151012i
$986$	−2.43823			−0.0776489
$987$	−47.9243	+	5.25377i	−1.52545	+	0.167229i
$988$	42.4143			1.34938
$989$	−3.07066	+	1.77284i	−0.0976412	+	0.0563732i
$990$	1.22984	+	0.476048i	0.0390869	+	0.0151298i
$991$	−15.7412	+	27.2646i	−0.500037	+	0.866089i	0.499963	+	0.866047i	$0.333347\pi$
$991$	−15.7412	+	27.2646i	−0.500037	+	0.866089i	−1.00000		4.22238e-5i	$0.999987\pi$
$992$	3.82684	+	6.62828i	0.121502	+	0.210448i
$993$		−	17.9348i		−	0.569142i
$994$	−0.172206	+	0.126295i	−0.00546206	+	0.00400585i
$995$	25.6090			0.811860
$996$	54.7949	−	31.6358i	1.73624	−	1.00242i
$997$	−23.1260	+	40.0554i	−0.732407	+	1.26857i	0.223445	+	0.974717i	$0.428270\pi$
$997$	−23.1260	+	40.0554i	−0.732407	+	1.26857i	−0.955852	+	0.293850i	$0.905063\pi$
$998$	−1.30252	−	0.752011i	−0.0412306	−	0.0238045i
$999$	12.1110	−	6.99229i	0.383175	−	0.221226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.u.a.241.17	yes	64
7.5	odd	6	inner	385.2.u.a.131.16	✓	64
11.10	odd	2	inner	385.2.u.a.241.16	yes	64
77.54	even	6	inner	385.2.u.a.131.17	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.u.a.131.16	✓	64	7.5	odd	6	inner
385.2.u.a.131.17	yes	64	77.54	even	6	inner
385.2.u.a.241.16	yes	64	11.10	odd	2	inner
385.2.u.a.241.17	yes	64	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0679871 - 0.0392524i) q^{2} +(2.45941 + 1.41994i) q^{3} +(-0.996918 + 1.72671i) q^{4} +(0.866025 - 0.500000i) q^{5} +0.222944 q^{6} +(-2.62999 + 0.288317i) q^{7} +0.313535i q^{8} +(2.53247 + 4.38636i) q^{9} +O(q^{10})\)	\(q+(0.0679871 - 0.0392524i) q^{2} +(2.45941 + 1.41994i) q^{3} +(-0.996918 + 1.72671i) q^{4} +(0.866025 - 0.500000i) q^{5} +0.222944 q^{6} +(-2.62999 + 0.288317i) q^{7} +0.313535i q^{8} +(2.53247 + 4.38636i) q^{9} +(0.0392524 - 0.0679871i) q^{10} +(3.09300 + 1.19724i) q^{11} +(-4.90366 + 2.83113i) q^{12} -2.80916 q^{13} +(-0.167489 + 0.122835i) q^{14} +2.83988 q^{15} +(-1.98153 - 3.43211i) q^{16} +(2.02490 - 3.50724i) q^{17} +(0.344351 + 0.198811i) q^{18} +(3.78631 + 6.55809i) q^{19} +1.99384i q^{20} +(-6.87763 - 3.02535i) q^{21} +(0.257278 - 0.0400106i) q^{22} +(1.30169 + 2.25459i) q^{23} +(-0.445202 + 0.771112i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.190986 + 0.110266i) q^{26} +5.86418i q^{27} +(2.12405 - 4.82868i) q^{28} -7.66908i q^{29} +(0.193076 - 0.111472i) q^{30} +(-7.06497 - 4.07896i) q^{31} +(-0.812496 - 0.469095i) q^{32} +(5.90694 + 7.33637i) q^{33} -0.317929i q^{34} +(-2.13348 + 1.56469i) q^{35} -10.0987 q^{36} +(-1.19237 - 2.06525i) q^{37} +(0.514841 + 0.297244i) q^{38} +(-6.90887 - 3.98884i) q^{39} +(0.156768 + 0.271530i) q^{40} +3.55350 q^{41} +(-0.586343 + 0.0642787i) q^{42} +1.36196i q^{43} +(-5.15075 + 4.14717i) q^{44} +(4.38636 + 2.53247i) q^{45} +(0.176996 + 0.102189i) q^{46} +(5.55688 - 3.20827i) q^{47} -11.2546i q^{48} +(6.83375 - 1.51654i) q^{49} -0.0785048i q^{50} +(9.96014 - 5.75049i) q^{51} +(2.80050 - 4.85061i) q^{52} +(-0.0842735 + 0.145966i) q^{53} +(0.230183 + 0.398689i) q^{54} +(3.27723 - 0.509658i) q^{55} +(-0.0903976 - 0.824596i) q^{56} +21.5054i q^{57} +(-0.301030 - 0.521399i) q^{58} +(5.82244 + 3.36159i) q^{59} +(-2.83113 + 4.90366i) q^{60} +(1.87765 + 3.25219i) q^{61} -0.640436 q^{62} +(-7.92504 - 10.8060i) q^{63} +7.85247 q^{64} +(-2.43280 + 1.40458i) q^{65} +(0.689566 + 0.266918i) q^{66} +(3.69637 - 6.40230i) q^{67} +(4.03733 + 6.99286i) q^{68} +7.39328i q^{69} +(-0.0836317 + 0.190123i) q^{70} +1.02817 q^{71} +(-1.37528 + 0.794018i) q^{72} +(4.61135 - 7.98709i) q^{73} +(-0.162132 - 0.0936071i) q^{74} +(2.45941 - 1.41994i) q^{75} -15.0986 q^{76} +(-8.47975 - 2.25697i) q^{77} -0.626286 q^{78} +(-0.143561 + 0.0828847i) q^{79} +(-3.43211 - 1.98153i) q^{80} +(-0.729385 + 1.26333i) q^{81} +(0.241592 - 0.139483i) q^{82} -11.1743 q^{83} +(12.0803 - 8.85967i) q^{84} -4.04981i q^{85} +(0.0534602 + 0.0925957i) q^{86} +(10.8897 - 18.8614i) q^{87} +(-0.375377 + 0.969763i) q^{88} +(-7.39726 + 4.27081i) q^{89} +0.397622 q^{90} +(7.38807 - 0.809927i) q^{91} -5.19070 q^{92} +(-11.5838 - 20.0637i) q^{93} +(0.251864 - 0.436242i) q^{94} +(6.55809 + 3.78631i) q^{95} +(-1.33217 - 2.30739i) q^{96} -17.4903i q^{97} +(0.405079 - 0.371346i) q^{98} +(2.58139 + 16.5990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 28 q^{4} + 36 q^{9}+O(q^{10}) \) 64 * q + 28 * q^4 + 36 * q^9	\( 64 q + 28 q^{4} + 36 q^{9} - 20 q^{14} - 8 q^{15} - 48 q^{16} + 16 q^{22} + 20 q^{23} + 32 q^{25} - 60 q^{26} + 24 q^{33} + 16 q^{36} - 8 q^{37} + 84 q^{38} - 132 q^{42} + 12 q^{44} + 12 q^{47} + 12 q^{49} + 20 q^{53} + 32 q^{56} + 24 q^{58} + 36 q^{59} - 44 q^{60} - 120 q^{64} + 12 q^{66} + 44 q^{67} + 16 q^{70} - 72 q^{71} + 44 q^{77} - 120 q^{78} - 24 q^{80} - 48 q^{81} - 96 q^{82} + 76 q^{86} + 64 q^{88} + 60 q^{89} - 108 q^{91} - 40 q^{92} - 68 q^{93} - 64 q^{99}+O(q^{100}) \) 64 * q + 28 * q^4 + 36 * q^9 - 20 * q^14 - 8 * q^15 - 48 * q^16 + 16 * q^22 + 20 * q^23 + 32 * q^25 - 60 * q^26 + 24 * q^33 + 16 * q^36 - 8 * q^37 + 84 * q^38 - 132 * q^42 + 12 * q^44 + 12 * q^47 + 12 * q^49 + 20 * q^53 + 32 * q^56 + 24 * q^58 + 36 * q^59 - 44 * q^60 - 120 * q^64 + 12 * q^66 + 44 * q^67 + 16 * q^70 - 72 * q^71 + 44 * q^77 - 120 * q^78 - 24 * q^80 - 48 * q^81 - 96 * q^82 + 76 * q^86 + 64 * q^88 + 60 * q^89 - 108 * q^91 - 40 * q^92 - 68 * q^93 - 64 * q^99

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