LMFDB - Embedded newform 385.2.u.a.131.16

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			131.16
Character	$\chi$	$=$	385.131
Dual form			385.2.u.a.241.16

$q$-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} +(-2.58334 + 2.07999i) 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} +(-3.40002 + 8.78375i) 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} +(6.16693 + 2.38710i) 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} +(0.575941 - 0.463723i) 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} +(-7.39386 + 4.72555i) 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} +(-0.652151 - 0.809967i) 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 $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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	$-0.342169\pi$
$2$	−0.0679871	−	0.0392524i	−0.0480742	−	0.0277556i	−0.523844	+	0.851814i	$0.675503\pi$
$3$	2.45941	−	1.41994i	1.41994	−	0.819804i	0.423648	−	0.905827i	$-0.360749\pi$
$3$	2.45941	−	1.41994i	1.41994	−	0.819804i	0.996293	+	0.0860231i	$0.0274159\pi$
$4$	−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
$11$	−2.58334	+	2.07999i	−0.778905	+	0.627142i
$11$	−2.58334	+	2.07999i	−0.778905	+	0.627142i
$12$	−4.90366	−	2.83113i	−1.41557	−	0.817277i
$13$	2.80916			0.779120			0.389560	−	0.921001i	$-0.372627\pi$
$13$	2.80916			0.779120			0.389560	+	0.921001i	$0.372627\pi$
$14$	−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	$-0.330076\pi$
$17$	−2.02490	−	3.50724i	−0.491111	−	0.850629i	−0.999948	+	0.0102337i	$0.996742\pi$
$18$	−0.344351	+	0.198811i	−0.0811642	+	0.0468602i
$19$	−3.78631	+	6.55809i	−0.868640	+	1.50453i	−0.00525248	+	0.999986i	$0.501672\pi$
$19$	−3.78631	+	6.55809i	−0.868640	+	1.50453i	−0.863387	+	0.504542i	$0.831661\pi$
$20$		−	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	−0.697805	−	0.716287i	$-0.745840\pi$
$23$	1.30169	−	2.25459i	0.271420	−	0.470114i	0.969226	+	0.246173i	$0.0791733\pi$
$24$	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	−0.974781	−	0.223163i	$-0.928362\pi$
$31$	−7.06497	+	4.07896i	−1.26891	+	0.732603i	−0.294125	+	0.955767i	$0.595028\pi$
$32$	0.812496	−	0.469095i	0.143630	−	0.0829250i
$33$	−3.40002	+	8.78375i	−0.591867	+	1.52905i
$34$			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	−0.947236	−	0.320537i	$-0.896137\pi$
$37$	−1.19237	+	2.06525i	−0.196025	+	0.339525i	0.751211	+	0.660062i	$0.229470\pi$
$38$	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	$-0.589500\pi$
$41$	−3.55350			−0.554963			−0.277481	+	0.960731i	$0.589500\pi$
$42$	−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	$0.966884\pi$
$44$	6.16693	+	2.38710i	0.929699	+	0.359869i
$45$	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	0.847148	−	0.531356i	$-0.178317\pi$
$47$	5.55688	+	3.20827i	0.810555	+	0.467974i	−0.0365938	+	0.999330i	$0.511651\pi$
$48$			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	0.860179	−	0.509991i	$-0.170351\pi$
$53$	−0.0842735	−	0.145966i	−0.0115759	−	0.0200500i	−0.871755	+	0.489942i	$0.837018\pi$
$54$	−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	−0.0705662	−	0.997507i	$-0.522481\pi$
$59$	5.82244	−	3.36159i	0.758017	−	0.437641i	0.828583	+	0.559866i	$0.189147\pi$
$60$	−2.83113	−	4.90366i	−0.365498	−	0.633060i
$61$	−1.87765	+	3.25219i	−0.240409	+	0.416401i	−0.960831	−	0.277135i	$-0.910615\pi$
$61$	−1.87765	+	3.25219i	−0.240409	+	0.416401i	0.720422	+	0.693536i	$0.243948\pi$
$62$	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
$66$	0.575941	−	0.463723i	0.0708934	−	0.0570803i
$67$	3.69637	+	6.40230i	0.451584	+	0.782166i	0.998485	−	0.0550313i	$-0.0175259\pi$
$67$	3.69637	+	6.40230i	0.451584	+	0.782166i	−0.546901	+	0.837197i	$0.684193\pi$
$68$	−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	−0.998919	−	0.0464863i	$-0.985198\pi$
$73$	−4.61135	−	7.98709i	−0.539718	−	0.934819i	0.459201	−	0.888332i	$-0.348136\pi$
$74$	0.162132	−	0.0936071i	0.0188475	−	0.0108816i
$75$	2.45941	+	1.41994i	0.283988	+	0.163961i
$76$	15.0986			1.73193
$77$	−7.39386	+	4.72555i	−0.842609	+	0.538527i
$78$	−0.626286			−0.0709129
$79$	0.143561	+	0.0828847i	0.0161518	+	0.00932526i	0.508054	−	0.861325i	$-0.330365\pi$
$79$	0.143561	+	0.0828847i	0.0161518	+	0.00932526i	−0.491902	+	0.870650i	$0.663698\pi$
$80$	−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	$-0.289855\pi$
$83$	11.1743			1.22654			0.613268	+	0.789875i	$0.289855\pi$
$84$	−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
$88$	−0.652151	−	0.809967i	−0.0695196	−	0.0863428i
$89$	−7.39726	−	4.27081i	−0.784108	−	0.452705i	0.0537764	−	0.998553i	$-0.482874\pi$
$89$	−7.39726	−	4.27081i	−0.784108	−	0.452705i	−0.837884	+	0.545848i	$0.816208\pi$
$90$	−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	$0.347860\pi$
$97$			17.4903i			1.77587i	−0.459972	+	0.887934i	$0.652140\pi$
$98$	−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	0.989711	+	0.143080i	$0.0457006\pi$
$101$	6.21853	+	10.7708i	0.618767	+	1.07174i	−0.370945	+	0.928655i	$0.620966\pi$
$102$	0.451441	+	0.781919i	0.0446993	+	0.0774215i
$103$	−11.7344	−	6.77484i	−1.15622	−	0.667544i	−0.205825	−	0.978589i	$-0.565988\pi$
$103$	−11.7344	−	6.77484i	−1.15622	−	0.667544i	−0.950395	+	0.311044i	$0.899321\pi$
$104$			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	$-0.386240\pi$
$107$	−2.96422	−	1.71139i	−0.286562	−	0.165447i	−0.636390	+	0.771367i	$0.719573\pi$
$108$	−10.1258	+	5.84611i	−0.974351	+	0.562542i
$109$	−1.97239	+	1.13876i	−0.188921	+	0.109074i	−0.591477	−	0.806322i	$-0.701455\pi$
$109$	−1.97239	+	1.13876i	−0.188921	+	0.109074i	0.402556	+	0.915395i	$0.368122\pi$
$110$	0.242815	+	0.0939890i	0.0231515	+	0.00896150i
$111$			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
$121$	2.34726	−	10.7466i	0.213387	−	0.976968i
$122$	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	0.224387	−	0.974500i	$-0.427962\pi$
$131$	10.9435	−	18.9546i	0.956135	−	1.65607i	0.731748	−	0.681575i	$-0.238705\pi$
$132$	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	0.682382	−	0.730996i	$-0.260944\pi$
$137$	−3.41625	−	5.91712i	−0.291870	−	0.505534i	−0.974252	+	0.225462i	$0.927611\pi$
$138$	−0.290204	+	0.502648i	−0.0247038	+	0.0427882i
$139$	15.5603			1.31981			0.659903	−	0.751350i	$-0.270597\pi$
$139$	15.5603			1.31981			0.659903	+	0.751350i	$0.270597\pi$
$140$	0.574857	−	5.24378i	0.0485843	−	0.443180i
$141$	18.2222			1.53459
$142$	−0.0699022	−	0.0403580i	−0.00586606	−	0.00338677i
$143$	−7.25700	+	5.84303i	−0.606861	+	0.488618i
$144$	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	$-0.482147\pi$
$149$	−9.52819	−	5.50110i	−0.780579	−	0.450668i	−0.836636	+	0.547760i	$0.815481\pi$
$150$	−0.111472	−	0.193076i	−0.00910167	−	0.0157646i
$151$	−15.3849	+	8.88248i	−1.25201	+	0.722846i	−0.971507	−	0.237009i	$-0.923833\pi$
$151$	−15.3849	+	8.88248i	−1.25201	+	0.722846i	−0.280498	+	0.959855i	$0.590500\pi$
$152$	−2.05619	−	1.18714i	−0.166779	−	0.0962900i
$153$	−20.5120			−1.65830
$154$	0.688177	−	0.0310500i	0.0554548	−	0.00250208i
$155$	−8.15793			−0.655260
$156$	−13.7752	−	7.95309i	−1.10290	−	0.636757i
$157$	−5.45321	+	3.14841i	−0.435213	+	0.251271i	−0.701565	−	0.712605i	$-0.747515\pi$
$157$	−5.45321	+	3.14841i	−0.435213	+	0.251271i	0.266352	+	0.963876i	$0.414182\pi$
$158$	−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	−0.594123	−	0.804374i	$-0.702501\pi$
$163$	5.10108	−	8.83533i	0.399547	−	0.692036i	0.993670	+	0.112338i	$0.0358340\pi$
$164$	3.54255	+	6.13587i	0.276626	+	0.479131i
$165$	−7.33637	+	5.90694i	−0.571136	+	0.459854i
$166$	−0.759707	−	0.438617i	−0.0589647	−	0.0340433i
$167$	6.04744			0.467965			0.233983	−	0.972241i	$-0.424824\pi$
$167$	6.04744			0.467965			0.233983	+	0.972241i	$0.424824\pi$
$168$	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	−0.291188	−	0.956666i	$-0.594050\pi$
$173$	8.98219	−	15.5576i	0.682903	−	1.18282i	0.974091	−	0.226157i	$-0.0726162\pi$
$174$			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	−0.937926	−	0.346834i	$-0.887257\pi$
$179$	−10.2929	−	17.8279i	−0.769330	−	1.33252i	0.168596	−	0.985685i	$-0.446077\pi$
$180$	−8.74569	−	5.04933i	−0.651866	−	0.376355i
$181$		−	16.4524i		−	1.22290i	−0.791283	−	0.611450i	$-0.790587\pi$
$181$		−	16.4524i		−	1.22290i	0.791283	−	0.611450i	$-0.209413\pi$
$182$	−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
$187$	12.5260	+	4.84859i	0.915994	+	0.354564i
$188$		−	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	−0.855547	−	0.517726i	$-0.826779\pi$
$191$	0.284564	−	0.492880i	0.0205904	−	0.0356635i	0.876137	+	0.482062i	$0.160112\pi$
$192$	19.3124	−	11.1500i	1.39376	−	0.804685i
$193$	5.46677	−	3.15624i	0.393507	−	0.227191i	−0.290172	−	0.956975i	$-0.593712\pi$
$193$	5.46677	−	3.15624i	0.393507	−	0.227191i	0.683678	+	0.729783i	$0.260379\pi$
$194$	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	$0.937544\pi$
$198$	0.476048	−	1.22984i	0.0338313	−	0.0874011i
$199$	22.1780	−	12.8045i	1.57216	−	0.907687i	0.576256	−	0.817269i	$-0.304513\pi$
$199$	22.1780	−	12.8045i	1.57216	−	0.907687i	0.995904	−	0.0904177i	$-0.0288202\pi$
$200$	−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
$220$	4.14717	+	5.15075i	0.279602	+	0.347264i
$221$	−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	$0.00758385\pi$
$223$			0.711510i			0.0476462i	−0.999716	+	0.0238231i	$0.992416\pi$
$224$	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	$-0.233940\pi$
$227$	−3.16058	−	5.47428i	−0.209775	−	0.363341i	−0.951644	+	0.307204i	$0.900606\pi$
$228$	37.1336	−	21.4391i	2.45923	−	1.41984i
$229$	−2.85983	−	1.65112i	−0.188983	−	0.109109i	0.402523	−	0.915410i	$-0.368133\pi$
$229$	−2.85983	−	1.65112i	−0.188983	−	0.109109i	−0.591506	+	0.806300i	$0.701467\pi$
$230$	−0.204377			−0.0134762
$231$	−11.4745	+	22.1209i	−0.754969	+	1.45545i
$232$	2.40453			0.157865
$233$	12.3470	+	7.12853i	0.808878	+	0.467006i	0.846566	−	0.532284i	$-0.178666\pi$
$233$	12.3470	+	7.12853i	0.808878	+	0.467006i	−0.0376883	+	0.999290i	$0.511999\pi$
$234$	−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	0.988941	+	0.148307i	$0.0473824\pi$
$241$	9.67014	+	16.7492i	0.622908	+	1.07891i	−0.366033	+	0.930602i	$0.619284\pi$
$242$	−0.581415	+	0.638498i	−0.0373748	+	0.0410442i
$243$	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	$0.191280\pi$
$251$			17.9154i			1.13081i	−0.824813	+	0.565405i	$0.808720\pi$
$252$	−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	−0.0445229	−	0.999008i	$-0.514177\pi$
$257$	−14.9403	−	8.62579i	−0.931951	−	0.538062i	−0.887428	+	0.460946i	$0.847510\pi$
$258$		−	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	−0.558419	+	0.829559i	$0.688592\pi$
$263$	−25.2349	+	14.5694i	−1.55605	+	0.898385i	−0.997629	+	0.0688256i	$0.978075\pi$
$264$	−2.75401	−	1.06603i	−0.169498	−	0.0656093i
$265$		−	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	−0.960235	−	0.279194i	$-0.909933\pi$
$269$	−19.6579	+	11.3495i	−1.19856	+	0.691991i	−0.238329	+	0.971185i	$0.576600\pi$
$270$	−0.398689	+	0.230183i	−0.0242634	+	0.0140085i
$271$	9.27844	−	16.0707i	0.563625	−	0.976227i	−0.433551	−	0.901129i	$-0.642740\pi$
$271$	9.27844	−	16.0707i	0.563625	−	0.976227i	0.997176	−	0.0750979i	$-0.0239269\pi$
$272$	16.0496			0.973151
$273$	19.3203	−	8.49868i	1.16932	−	0.514363i
$274$			0.536384i			0.0324042i
$275$	−3.09300	−	1.19724i	−0.186515	−	0.0721962i
$276$	−12.7661	+	7.37049i	−0.768427	+	0.443652i
$277$	19.7152	−	11.3826i	1.18457	−	0.683914i	0.227506	−	0.973777i	$-0.426943\pi$
$277$	19.7152	−	11.3826i	1.18457	−	0.683914i	0.957068	+	0.289862i	$0.0936095\pi$
$278$	−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	−0.846676	−	0.532108i	$-0.821400\pi$
$283$	−14.8738	−	25.7622i	−0.884157	−	1.53141i	−0.0374811	−	0.999297i	$-0.511933\pi$
$284$	−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	$-0.674468\pi$
$293$	−17.8387			−1.04215			−0.521074	+	0.853512i	$0.674468\pi$
$294$	−1.52355	−	0.338105i	−0.0888550	−	0.0197187i
$295$	6.72317			0.391438
$296$	−0.647530	−	0.373851i	−0.0376369	−	0.0217297i
$297$	12.1974	+	15.1491i	0.707768	+	0.879043i
$298$	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	$-0.264934\pi$
$307$	23.5897			1.34633			0.673166	+	0.739491i	$0.264934\pi$
$308$	15.5307	+	8.05609i	0.884947	+	0.459038i
$309$	−38.4795			−2.18902
$310$	0.554634	+	0.320218i	0.0315011	+	0.0181872i
$311$	11.3662	−	6.56229i	0.644519	−	0.372113i	−0.141834	−	0.989890i	$-0.545300\pi$
$311$	11.3662	−	6.56229i	0.644519	−	0.372113i	0.786353	+	0.617777i	$0.211967\pi$
$312$	1.25064	+	2.16617i	0.0708036	+	0.122635i
$313$	−2.30438	−	1.33043i	−0.130251	−	0.0752006i	0.433459	−	0.901173i	$-0.357293\pi$
$313$	−2.30438	−	1.33043i	−0.130251	−	0.0752006i	−0.563710	+	0.825973i	$0.690626\pi$
$314$	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	−0.953613	−	0.301036i	$-0.902668\pi$
$317$	−3.84758	+	6.66421i	−0.216102	+	0.374299i	0.737511	+	0.675335i	$0.236001\pi$
$318$	0.0187883	+	0.0325423i	0.00105360	+	0.00182488i
$319$	15.9516	+	19.8118i	0.893121	+	1.10925i
$320$	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	−0.939662	−	0.342104i	$-0.888861\pi$
$331$	−3.15766	+	5.46922i	−0.173560	+	0.300616i	0.766102	+	0.642719i	$0.222194\pi$
$332$	−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
$341$	9.76699	−	25.2324i	0.528912	−	1.36641i
$342$		−	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	$-0.907421\pi$
$347$	−22.1423	+	12.7839i	−1.18866	+	0.686273i	−0.230658	+	0.973035i	$0.574088\pi$
$348$	−21.7122	+	37.6066i	−1.16390	+	2.01593i
$349$	−24.5471			−1.31398			−0.656988	−	0.753901i	$-0.728170\pi$
$349$	−24.5471			−1.31398			−0.656988	+	0.753901i	$0.728170\pi$
$350$	0.0226343	−	0.206467i	0.00120985	−	0.0110361i
$351$		−	16.4734i		−	0.879285i
$352$	−1.12324	+	2.90182i	−0.0598687	+	0.154667i
$353$	11.1923	−	6.46189i	0.595708	−	0.343932i	−0.171644	−	0.985159i	$-0.554908\pi$
$353$	11.1923	−	6.46189i	0.595708	−	0.343932i	0.767351	+	0.641227i	$0.221574\pi$
$354$	−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	$-0.333226\pi$
$359$	0.0110443	+	0.00637644i	0.000582897	+	0.000336536i	−0.499709	+	0.866194i	$0.666560\pi$
$360$	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	−0.922121	−	0.386901i	$-0.873546\pi$
$367$	−20.0790	+	11.5926i	−1.04812	+	0.605130i	−0.125995	+	0.992031i	$0.540212\pi$
$368$	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	$-0.214589\pi$
$373$	12.1915	+	7.03878i	0.631253	+	0.364454i	−0.149984	+	0.988688i	$0.547922\pi$
$374$	−0.661290	−	0.821318i	−0.0341945	−	0.0424693i
$375$	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	0.390258	−	0.920705i	$-0.372386\pi$
$383$	−4.14827	−	2.39501i	−0.211967	−	0.122379i	−0.602225	+	0.798326i	$0.705719\pi$
$384$	−7.07936			−0.361267
$385$	−8.76605	+	0.395518i	−0.446759	+	0.0201574i
$386$	−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	−0.994447	−	0.105238i	$-0.966440\pi$
$389$	−11.6043	−	20.0993i	−0.588362	−	1.01907i	0.406085	−	0.913835i	$-0.366894\pi$
$390$	−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
$396$	26.0882	−	21.0051i	1.31098	−	1.05555i
$397$	−0.979519	−	0.565525i	−0.0491606	−	0.0283829i	0.475218	−	0.879868i	$-0.342369\pi$
$397$	−0.979519	−	0.565525i	−0.0491606	−	0.0283829i	−0.524379	+	0.851485i	$0.675702\pi$
$398$	−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	−0.550791	−	0.834643i	$-0.685674\pi$
$401$	8.95972	−	15.5187i	0.447427	−	0.774966i	0.998218	+	0.0596770i	$0.0190071\pi$
$402$	−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	$-0.145061\pi$
$409$	1.37167	+	2.37580i	0.0678247	+	0.117476i	−0.830119	+	0.557587i	$0.811727\pi$
$410$	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
$418$	−0.711743	+	1.83875i	−0.0348125	+	0.0899360i
$419$			21.3341i			1.04224i	0.853483	+	0.521120i	$0.174486\pi$
$419$			21.3341i			1.04224i	−0.853483	+	0.521120i	$0.825514\pi$
$420$	−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
$429$	−9.55118	+	24.6749i	−0.461135	+	1.19132i
$430$	0.0925957	−	0.0534602i	0.00446536	−	0.00257808i
$431$	−28.2436	+	16.3065i	−1.36045	+	0.785454i	−0.989683	−	0.143273i	$-0.954237\pi$
$431$	−28.2436	+	16.3065i	−1.36045	+	0.785454i	−0.370764	+	0.928727i	$0.620904\pi$
$432$	20.1265	+	11.6200i	0.968337	+	0.559070i
$433$			16.0082i			0.769305i	0.923062	+	0.384652i	$0.125679\pi$
$433$			16.0082i			0.769305i	−0.923062	+	0.384652i	$0.874321\pi$
$434$	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	$-0.866871\pi$
$439$	−2.20348	+	3.81654i	−0.105166	+	0.182153i	0.808640	+	0.588304i	$0.200204\pi$
$440$	−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	−0.776124	−	0.630580i	$-0.782817\pi$
$443$	3.32627	−	5.76127i	0.158036	−	0.273726i	0.934160	+	0.356854i	$0.116151\pi$
$444$	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
$451$	9.17988	−	7.39125i	0.432263	−	0.348040i
$452$	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	$-0.650620\pi$
$457$	−31.0927	−	17.9514i	−1.45445	−	0.839730i	−0.998730	+	0.0503912i	$0.983953\pi$
$458$	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	$-0.529824\pi$
$461$	−4.01759			−0.187118			−0.0935589	+	0.995614i	$0.529824\pi$
$462$	1.64842	−	1.05354i	0.0766914	−	0.0490149i
$463$	−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	0.797257	−	0.603640i	$-0.206283\pi$
$467$	14.5462	+	8.39826i	0.673119	+	0.388625i	−0.124139	+	0.992265i	$0.539617\pi$
$468$	−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
$473$	−2.83287	−	3.51840i	−0.130255	−	0.161776i
$474$	−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	$-0.281615\pi$
$479$	−7.73287	−	13.3937i	−0.353324	−	0.611975i	−0.986830	+	0.161763i	$0.948282\pi$
$480$	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	0.986616	+	0.163061i	$0.0521368\pi$
$487$	14.0027	+	24.2534i	0.634523	+	1.09903i	−0.352093	+	0.935965i	$0.614530\pi$
$488$	−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
$495$	−6.06394	+	15.6658i	−0.272554	+	0.704126i
$496$		−	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	−0.996769	−	0.0803231i	$-0.974405\pi$
$499$	−9.57917	+	16.5916i	−0.428823	+	0.742742i	0.567946	+	0.823066i	$0.307738\pi$
$500$	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	$-0.272891\pi$
$503$	29.3566			1.30895			0.654473	+	0.756085i	$0.272891\pi$
$504$	3.38805	+	2.48478i	0.150916	+	0.110681i
$505$			12.4371i			0.553442i
$506$	0.244688	−	0.632138i	0.0108777	−	0.0281020i
$507$	−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	0.281826	−	0.959465i	$-0.409060\pi$
$509$	−9.20901	−	5.31682i	−0.408182	−	0.235664i	−0.690008	+	0.723801i	$0.742393\pi$
$510$			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	−0.581763	−	0.813358i	$-0.697637\pi$
$521$	−3.84050	+	2.21732i	−0.168256	+	0.0971424i	0.413507	+	0.910501i	$0.364304\pi$
$522$	1.52470	+	2.64085i	0.0667342	+	0.115587i
$523$	8.49562	−	14.7148i	0.371487	−	0.643435i	−0.618307	−	0.785937i	$-0.712181\pi$
$523$	8.49562	−	14.7148i	0.371487	−	0.643435i	0.989795	+	0.142501i	$0.0455146\pi$
$524$	−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
$528$	−23.4095	−	29.0745i	−1.01877	−	1.26530i
$529$	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
$539$	−20.8083	+	10.2964i	−0.896276	+	0.443497i
$540$	−11.6922			−0.503153
$541$	−0.866501	−	0.500274i	−0.0372538	−	0.0215085i	0.481257	−	0.876579i	$-0.340180\pi$
$541$	−0.866501	−	0.500274i	−0.0372538	−	0.0215085i	−0.518511	+	0.855071i	$0.673514\pi$
$542$	−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
$550$	0.163289	+	0.202804i	0.00696268	+	0.00864760i
$551$	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	$-0.777426\pi$
$557$	−13.9386	+	8.04744i	−0.590596	+	0.340981i	0.174737	+	0.984615i	$0.444092\pi$
$558$	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	$-0.0913594\pi$
$563$	5.56137	+	9.63258i	0.234384	+	0.405965i	−0.724710	+	0.689054i	$0.758026\pi$
$564$	−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	$-0.209276\pi$
$569$	15.6978	+	9.06314i	0.658087	+	0.379947i	−0.133461	+	0.991054i	$0.542609\pi$
$570$	1.46209	−	0.844137i	0.0612402	−	0.0353570i
$571$	11.1049	−	6.41139i	0.464724	−	0.268308i	−0.249305	−	0.968425i	$-0.580202\pi$
$571$	11.1049	−	6.41139i	0.464724	−	0.268308i	0.714028	+	0.700117i	$0.246869\pi$
$572$	17.3239	+	6.70573i	0.724347	+	0.280381i
$573$		−	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	−0.106966	−	0.994263i	$-0.534114\pi$
$577$	16.8292	−	9.71633i	0.700608	−	0.404496i	0.807574	+	0.589766i	$0.200780\pi$
$578$	−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
$583$	0.521315	+	0.201791i	0.0215907	+	0.00835733i
$584$	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	$-0.813578\pi$
$587$		−	26.7842i		−	1.10550i	0.833347	−	0.552751i	$-0.186422\pi$
$588$	−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	$-0.869106\pi$
$593$	−2.73092	+	4.73010i	−0.112146	+	0.194242i	0.804490	+	0.593967i	$0.202439\pi$
$594$	−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	0.926983	+	0.375103i	$0.122393\pi$
$599$	19.2942	+	33.4186i	0.788340	+	1.36545i	−0.138643	+	0.990342i	$0.544274\pi$
$600$	−0.445202	+	0.771112i	−0.0181753	+	0.0314805i
$601$	45.2838			1.84716			0.923582	−	0.383400i	$-0.125247\pi$
$601$	45.2838			1.84716			0.923582	+	0.383400i	$0.125247\pi$
$602$	0.167297	−	0.228113i	0.00681851	−	0.00929719i
$603$	37.4438			1.52483
$604$	30.6750	+	17.7102i	1.24815	+	0.720618i
$605$	7.40611	−	8.13324i	0.301101	−	0.330663i
$606$	−1.38639	−	2.40129i	−0.0563181	−	0.0975458i
$607$	−0.790988	+	1.37003i	−0.0321052	+	0.0556079i	−0.881632	−	0.471938i	$-0.843555\pi$
$607$	−0.790988	+	1.37003i	−0.0321052	+	0.0556079i	0.849526	+	0.527546i	$0.176888\pi$
$608$			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	$-0.833619\pi$
$613$	−21.4751	+	12.3987i	−0.867371	+	0.500777i	−0.000897552		1.00000i	$0.500286\pi$
$614$	−1.60379	−	0.925950i	−0.0647238	−	0.0373683i
$615$	−10.0915			−0.406929
$616$	−1.48163	−	2.31824i	−0.0596965	−	0.0934044i
$617$	−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	−0.465531	−	0.885032i	$-0.654137\pi$
$619$	1.69588	−	0.979118i	0.0681632	−	0.0393541i	0.533694	+	0.845677i	$0.320803\pi$
$620$	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
$627$	−44.7310	−	55.5556i	−1.78638	−	2.21868i
$628$	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	0.890616	+	0.454757i	$0.150274\pi$
$641$	21.2453	+	36.7979i	0.839139	+	1.45343i	−0.0514770	+	0.998674i	$0.516393\pi$
$642$	0.660857	+	0.381546i	0.0260819	+	0.0150584i
$643$			3.01884i			0.119051i	0.998227	+	0.0595257i	$0.0189588\pi$
$643$			3.01884i			0.119051i	−0.998227	+	0.0595257i	$0.981041\pi$
$644$	−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	0.223806	−	0.974634i	$-0.428152\pi$
$647$	30.0088	−	17.3256i	1.17977	−	0.681138i	0.955961	+	0.293495i	$0.0948185\pi$
$648$	0.396099	−	0.228688i	0.0155603	−	0.00898372i
$649$	−8.04924	+	20.7947i	−0.315961	+	0.816265i
$650$		−	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	0.486078	+	0.873916i	$0.338427\pi$
$653$	−13.1294	+	22.7408i	−0.513794	+	0.889918i	−0.999872	+	0.0160021i	$0.994906\pi$
$654$	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	$-0.174927\pi$
$660$	17.5134	+	6.77908i	0.681706	+	0.263875i
$661$	8.60684	−	4.96916i	0.334767	−	0.193278i	−0.323188	−	0.946335i	$-0.604755\pi$
$661$	8.60684	−	4.96916i	0.334767	−	0.193278i	0.657956	+	0.753057i	$0.271421\pi$
$662$	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	0.181242	−	0.983439i	$-0.441988\pi$
$677$	24.5180	−	42.4664i	0.942304	−	1.63212i	0.761062	−	0.648679i	$-0.224678\pi$
$678$	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
$682$	−1.65446	+	1.33210i	−0.0633526	+	0.0510089i
$683$	−20.4413	−	35.4054i	−0.782166	−	1.35475i	−0.930678	−	0.365840i	$-0.880782\pi$
$683$	−20.4413	−	35.4054i	−0.782166	−	1.35475i	0.148512	−	0.988911i	$-0.452552\pi$
$684$	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	0.843387	−	0.537306i	$-0.180558\pi$
$691$	21.0232	+	12.1378i	0.799761	+	0.461742i	−0.0436269	+	0.999048i	$0.513891\pi$
$692$	−35.8180			−1.36160
$693$	2.00327	+	44.3995i	0.0760980	+	1.68660i
$694$	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
$704$	−20.2856	+	16.3331i	−0.764541	+	0.615576i
$705$	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	−0.544071	−	0.839039i	$-0.683118\pi$
$709$	12.1045	−	20.9656i	0.454593	−	0.787379i	0.998665	+	0.0516601i	$0.0164512\pi$
$710$	−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	0.941723	−	0.336388i	$-0.109205\pi$
$719$	30.0658	+	17.3585i	1.12126	+	0.647362i	0.179541	+	0.983750i	$0.442539\pi$
$720$			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
$726$	−0.523308	+	2.39590i	−0.0194218	+	0.0889204i
$727$			19.7276i			0.731655i	0.930683	+	0.365828i	$0.119214\pi$
$727$			19.7276i			0.731655i	−0.930683	+	0.365828i	$0.880786\pi$
$728$	−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	$-0.944256\pi$
$733$	−9.24476	+	16.0124i	−0.341463	+	0.591431i	0.643242	+	0.765663i	$0.277589\pi$
$734$	1.82015			0.0671831
$735$	19.4070	+	4.30681i	0.715840	+	0.158859i
$736$		−	2.44246i		−	0.0900302i
$737$	−22.8657	−	8.85088i	−0.842270	−	0.326026i
$738$	1.22365	−	0.706474i	0.0450431	−	0.0260056i
$739$	1.43709	−	0.829705i	0.0528643	−	0.0305212i	−0.473335	−	0.880883i	$-0.656950\pi$
$739$	1.43709	−	0.829705i	0.0528643	−	0.0305212i	0.526199	+	0.850361i	$0.323617\pi$
$740$	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	−0.807391	−	0.590017i	$-0.799121\pi$
$751$	2.93980	−	5.09188i	0.107275	−	0.185805i	0.914665	+	0.404212i	$0.132454\pi$
$752$	−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
$759$	15.3780	+	19.0993i	0.558185	+	0.693261i
$760$	−1.18714	−	2.05619i	−0.0430622	−	0.0745859i
$761$	3.06814	−	5.31418i	0.111220	−	0.192639i	−0.805042	−	0.593217i	$-0.797857\pi$
$761$	3.06814	−	5.31418i	0.111220	−	0.192639i	0.916262	+	0.400578i	$0.131191\pi$
$762$		−	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	$-0.495478\pi$
$769$	0.787896			0.0284123			0.0142061	+	0.999899i	$0.495478\pi$
$770$	0.611503	+	0.317198i	0.0220371	+	0.0114310i
$771$	−48.9925			−1.76442
$772$	−10.8998	−	6.29303i	−0.392294	−	0.226491i
$773$	−6.66382	+	3.84736i	−0.239681	+	0.138380i	−0.615030	−	0.788504i	$-0.710856\pi$
$773$	−6.66382	+	3.84736i	−0.239681	+	0.138380i	0.375349	+	0.926884i	$0.377523\pi$
$774$	−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
$781$	−2.65610	+	2.13858i	−0.0950428	+	0.0765245i
$782$	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	0.970091	+	0.242741i	$0.0780466\pi$
$787$	19.5046	+	33.7830i	0.695266	+	1.20424i	−0.274825	+	0.961494i	$0.588620\pi$
$788$	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	$0.0183543\pi$
$797$			3.25392i			0.115260i	−0.998338	+	0.0576298i	$0.981646\pi$
$798$	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
$803$	28.5258	+	11.0418i	1.00665	+	0.389656i
$804$		−	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	$-0.602831\pi$
$809$	9.81365	−	5.66591i	0.345029	−	0.199203i	0.662494	+	0.749067i	$0.269498\pi$
$810$	−0.0572602	+	0.0991776i	−0.00201192	+	0.00348475i
$811$	26.6367			0.935340			0.467670	−	0.883903i	$-0.345094\pi$
$811$	26.6367			0.935340			0.467670	+	0.883903i	$0.345094\pi$
$812$	−37.0315	+	16.2895i	−1.29955	+	0.571650i
$813$		−	52.6993i		−	1.84825i
$814$	−0.224140	+	0.579052i	−0.00785610	+	0.0202958i
$815$	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	$-0.436430\pi$
$821$	−15.7945	−	9.11895i	−0.551232	−	0.318254i	−0.749619	+	0.661870i	$0.769763\pi$
$822$	0.761634	+	1.31919i	0.0265650	+	0.0460120i
$823$	0.786320	+	1.36195i	0.0274094	+	0.0474744i	0.879405	−	0.476075i	$-0.157941\pi$
$823$	0.786320	+	1.36195i	0.0274094	+	0.0474744i	−0.851995	+	0.523549i	$0.824608\pi$
$824$	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	−0.0931641	−	0.995651i	$-0.529698\pi$
$829$	20.8028	−	12.0105i	0.722513	−	0.417143i	0.815677	+	0.578508i	$0.196365\pi$
$830$	−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
$836$	−39.0047	+	31.4049i	−1.34901	+	1.08616i
$837$	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	$0.0118433\pi$
$839$			2.15493i			0.0743966i	−0.999308	+	0.0371983i	$0.988157\pi$
$840$	−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
$847$	9.27172	−	27.5869i	0.318580	−	0.947896i
$848$	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	$-0.487302\pi$
$853$	2.32952			0.0797611			0.0398805	+	0.999204i	$0.487302\pi$
$854$	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	0.960904	+	0.276881i	$0.0893007\pi$
$857$	21.0847	+	36.5197i	0.720238	+	1.24749i	−0.240666	+	0.970608i	$0.577366\pi$
$858$	1.61791	−	1.30267i	0.0552344	−	0.0444724i
$859$	−25.2111	−	14.5556i	−0.860190	−	0.496631i	0.00388583	−	0.999992i	$-0.498763\pi$
$859$	−25.2111	−	14.5556i	−0.860190	−	0.496631i	−0.864076	+	0.503361i	$0.832096\pi$
$860$	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	−0.827260	−	0.561819i	$-0.810102\pi$
$863$	2.14216	−	3.71033i	0.0729200	−	0.126301i	0.900180	+	0.435518i	$0.143435\pi$
$864$	−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	$-0.574255\pi$
$877$	−35.2208	−	20.3347i	−1.18932	−	0.686655i	−0.958152	+	0.286259i	$0.907588\pi$
$878$	0.299616	−	0.172984i	0.0101116	−	0.00583791i
$879$	−43.8727	+	25.3299i	−1.47979	+	0.854356i
$880$	4.74473	−	12.2577i	0.159945	−	0.413208i
$881$			10.4521i			0.352139i	0.984378	+	0.176070i	$0.0563384\pi$
$881$			10.4521i			0.352139i	−0.984378	+	0.176070i	$0.943662\pi$
$882$	−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	$-0.927971\pi$
$887$	−8.72489	+	15.1119i	−0.292953	+	0.507410i	0.681554	+	0.731768i	$0.261305\pi$
$888$	−2.12339			−0.0712563
$889$	−1.92289	+	17.5404i	−0.0644918	+	0.588287i
$890$			0.670558i			0.0224771i
$891$	4.51197	+	1.74650i	0.151157	+	0.0585098i
$892$	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	0.860000	−	0.510293i	$-0.170463\pi$
$907$	−0.359197	−	0.622148i	−0.0119270	−	0.0206581i	−0.871927	+	0.489635i	$0.837130\pi$
$908$	−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
$913$	−28.8669	+	23.2424i	−0.955355	+	0.769211i
$914$	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	$-0.409037\pi$
$919$	−12.3704	−	7.14207i	−0.408063	−	0.235595i	−0.689957	+	0.723850i	$0.742371\pi$
$920$	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
$924$	49.6357	−	2.23953i	1.63289	−	0.0736750i
$925$	−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	0.429806	−	0.902921i	$-0.358582\pi$
$929$	−4.18313	−	2.41513i	−0.137244	−	0.0792378i	−0.567050	+	0.823683i	$0.691915\pi$
$930$	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
$935$	8.42357	+	10.4620i	0.275480	+	0.342144i
$936$	3.86338	+	2.23052i	0.126278	+	0.0729069i
$937$	−20.4314			−0.667466			−0.333733	−	0.942668i	$-0.608308\pi$
$937$	−20.4314			−0.667466			−0.333733	+	0.942668i	$0.608308\pi$
$938$	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	$-0.277252\pi$
$941$	−10.4441	−	18.0897i	−0.340468	−	0.589707i	−0.984520	+	0.175275i	$0.943919\pi$
$942$	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	−0.105274	−	0.994443i	$-0.533572\pi$
$947$	24.8826	−	43.0980i	0.808576	−	1.40050i	0.913850	−	0.406052i	$-0.133095\pi$
$948$	−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
$957$	67.3633	+	26.0750i	2.17755	+	0.842886i
$958$			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	$0.898679\pi$
$968$	3.36945	+	0.735948i	0.108298	+	0.0236543i
$969$	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	0.309847	−	0.950787i	$-0.399722\pi$
$971$	−11.1754	−	6.45211i	−0.358635	−	0.207058i	−0.668482	+	0.743728i	$0.733056\pi$
$972$		−	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	−0.999524	−	0.0308642i	$-0.990174\pi$
$977$	−16.4565	−	28.5035i	−0.526491	−	0.911909i	0.473033	−	0.881045i	$-0.343159\pi$
$978$	−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	−0.429010	−	0.903300i	$-0.641138\pi$
$983$	4.35068	−	2.51187i	0.138765	−	0.0801161i	0.567775	+	0.823184i	$0.307804\pi$
$984$	−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
$990$	1.02719	−	0.827050i	0.0326463	−	0.0262854i
$991$	−15.7412	−	27.2646i	−0.500037	−	0.866089i	−1.00000		4.22238e-5i	$-0.999987\pi$
$991$	−15.7412	−	27.2646i	−0.500037	−	0.866089i	0.499963	−	0.866047i	$-0.333347\pi$
$992$	−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	0.955852	+	0.293850i	$0.0949365\pi$
$997$	23.1260	+	40.0554i	0.732407	+	1.26857i	−0.223445	+	0.974717i	$0.571730\pi$
$998$	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.131.16	✓	64
7.3	odd	6	inner	385.2.u.a.241.17	yes	64
11.10	odd	2	inner	385.2.u.a.131.17	yes	64
77.10	even	6	inner	385.2.u.a.241.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.u.a.131.16	✓	64	1.1	even	1	trivial
385.2.u.a.131.17	yes	64	11.10	odd	2	inner
385.2.u.a.241.16	yes	64	77.10	even	6	inner
385.2.u.a.241.17	yes	64	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
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} +(-2.58334 + 2.07999i) 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} +(-3.40002 + 8.78375i) 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} +(6.16693 + 2.38710i) 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} +(0.575941 - 0.463723i) 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} +(-7.39386 + 4.72555i) 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} +(-0.652151 - 0.809967i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more