LMFDB - Embedded newform 841.2.e.m.267.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			267.9
Character	$\chi$	$=$	841.267
Dual form			841.2.e.m.63.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0327942 + 0.0261525i) q^{2} +(2.95182 + 0.673734i) q^{3} +(-0.444650 - 1.94814i) q^{4} +(1.08614 - 1.36198i) q^{5} +(0.0791828 + 0.0992921i) q^{6} +(-0.456981 + 2.00217i) q^{7} +(0.0727657 - 0.151099i) q^{8} +(5.55642 + 2.67583i) q^{9} +(0.0712384 - 0.0162597i) q^{10} +(-0.803488 - 1.66846i) q^{11} -6.05014i q^{12} +(2.32260 - 1.11851i) q^{13} +(-0.0673480 + 0.0537083i) q^{14} +(4.12371 - 3.28855i) q^{15} +(-3.59437 + 1.73096i) q^{16} -5.23359i q^{17} +(0.112239 + 0.233066i) q^{18} +(-0.369537 + 0.0843444i) q^{19} +(-3.13628 - 1.51035i) q^{20} +(-2.69785 + 5.60215i) q^{21} +(0.0172847 - 0.0757291i) q^{22} +(2.26357 + 2.83842i) q^{23} +(0.316592 - 0.396994i) q^{24} +(0.437322 + 1.91603i) q^{25} +(0.105420 + 0.0240614i) q^{26} +(7.49723 + 5.97884i) q^{27} +4.10370 q^{28} +0.221238 q^{30} +(-1.84952 - 1.47494i) q^{31} +(-0.490149 - 0.111873i) q^{32} +(-1.24765 - 5.46633i) q^{33} +(0.136872 - 0.171631i) q^{34} +(2.23056 + 2.79704i) q^{35} +(2.74223 - 12.0145i) q^{36} +(-2.84946 + 5.91697i) q^{37} +(-0.0143245 - 0.00689831i) q^{38} +(7.60949 - 1.73682i) q^{39} +(-0.126760 - 0.263221i) q^{40} +9.44586i q^{41} +(-0.234984 + 0.113163i) q^{42} +(-0.778328 + 0.620696i) q^{43} +(-2.89312 + 2.30719i) q^{44} +(9.67949 - 4.66140i) q^{45} +0.152282i q^{46} +(-4.41153 - 9.16063i) q^{47} +(-11.7761 + 2.68782i) q^{48} +(2.50694 + 1.20728i) q^{49} +(-0.0357675 + 0.0742719i) q^{50} +(3.52605 - 15.4486i) q^{51} +(-3.21176 - 4.02742i) q^{52} +(6.19127 - 7.76360i) q^{53} +(0.0895040 + 0.392143i) q^{54} +(-3.14511 - 0.717851i) q^{55} +(0.269274 + 0.214739i) q^{56} -1.14763 q^{57} -6.24449 q^{59} +(-8.24016 - 6.57131i) q^{60} +(-7.78508 - 1.77689i) q^{61} +(-0.0220801 - 0.0967392i) q^{62} +(-7.89664 + 9.90207i) q^{63} +(4.96161 + 6.22166i) q^{64} +(0.999295 - 4.37820i) q^{65} +(0.102042 - 0.211893i) q^{66} +(-3.72841 - 1.79551i) q^{67} +(-10.1958 + 2.32712i) q^{68} +(4.76930 + 9.90355i) q^{69} +0.150061i q^{70} +(-2.05682 + 0.990512i) q^{71} +(0.808633 - 0.644863i) q^{72} +(7.08653 - 5.65132i) q^{73} +(-0.248190 + 0.119522i) q^{74} +5.95042i q^{75} +(0.328629 + 0.682406i) q^{76} +(3.70771 - 0.846262i) q^{77} +(0.294969 + 0.142050i) q^{78} +(-4.45891 + 9.25903i) q^{79} +(-1.54647 + 6.77552i) q^{80} +(6.56684 + 8.23455i) q^{81} +(-0.247033 + 0.309770i) q^{82} +(3.47592 + 15.2290i) q^{83} +(12.1134 + 2.76480i) q^{84} +(-7.12804 - 5.68442i) q^{85} -0.0417574 q^{86} -0.310570 q^{88} +(7.51879 + 5.99604i) q^{89} +(0.439339 + 0.100276i) q^{90} +(1.17805 + 5.16138i) q^{91} +(4.52315 - 5.67185i) q^{92} +(-4.46573 - 5.59985i) q^{93} +(0.0949009 - 0.415788i) q^{94} +(-0.286494 + 0.594912i) q^{95} +(-1.37146 - 0.660460i) q^{96} +(5.04795 - 1.15216i) q^{97} +(0.0506399 + 0.105155i) q^{98} -11.4207i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} - 2 q^{5} + 6 q^{6} + 16 q^{9} - 8 q^{13} + 4 q^{16} + 14 q^{20} + 50 q^{22} + 14 q^{23} - 50 q^{24} + 26 q^{25} - 300 q^{28} - 312 q^{30} + 24 q^{34} - 10 q^{35} + 38 q^{36} - 28 q^{38}+ \cdots - 4 q^{96}+O(q^{100}) $ 96 * q + 12 * q^4 - 2 * q^5 + 6 * q^6 + 16 * q^9 - 8 * q^13 + 4 * q^16 + 14 * q^20 + 50 * q^22 + 14 * q^23 - 50 * q^24 + 26 * q^25 - 300 * q^28 - 312 * q^30 + 24 * q^34 - 10 * q^35 + 38 * q^36 - 28 * q^38 + 30 * q^42 + 2 * q^45 - 8 * q^49 + 46 * q^51 - 4 * q^52 - 38 * q^53 + 92 * q^54 + 72 * q^57 - 12 * q^59 - 24 * q^62 - 20 * q^63 + 2 * q^64 + 34 * q^65 + 4 * q^67 - 24 * q^71 + 54 * q^74 - 12 * q^78 - 82 * q^80 - 24 * q^81 + 44 * q^82 + 6 * q^83 + 60 * q^86 - 180 * q^88 - 8 * q^92 + 4 * q^93 - 26 * q^94 - 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{14}\right)$

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 $

$2$	0.0327942	+	0.0261525i	0.0231890	+	0.0184926i	0.635016	−	0.772499i	$-0.280994\pi$
$2$	0.0327942	+	0.0261525i	0.0231890	+	0.0184926i	−0.611827	+	0.790992i	$0.709565\pi$
$3$	2.95182	+	0.673734i	1.70423	+	0.388980i	0.960233	−	0.279198i	$-0.0900687\pi$
$3$	2.95182	+	0.673734i	1.70423	+	0.388980i	0.744001	+	0.668179i	$0.232926\pi$
$4$	−0.444650	−	1.94814i	−0.222325	−	0.974070i
$5$	1.08614	−	1.36198i	0.485738	−	0.609096i	−0.477208	−	0.878790i	$-0.658351\pi$
$5$	1.08614	−	1.36198i	0.485738	−	0.609096i	0.962946	+	0.269695i	$0.0869227\pi$
$6$	0.0791828	+	0.0992921i	0.0323262	+	0.0405358i
$7$	−0.456981	+	2.00217i	−0.172723	+	0.756748i	0.812147	+	0.583453i	$0.198299\pi$
$7$	−0.456981	+	2.00217i	−0.172723	+	0.756748i	−0.984870	+	0.173295i	$0.944559\pi$
$8$	0.0727657	−	0.151099i	0.0257265	−	0.0534217i
$9$	5.55642	+	2.67583i	1.85214	+	0.891944i
$10$	0.0712384	−	0.0162597i	0.0225276	−	0.00514177i
$11$	−0.803488	−	1.66846i	−0.242261	−	0.503060i	0.744016	−	0.668162i	$-0.232919\pi$
$11$	−0.803488	−	1.66846i	−0.242261	−	0.503060i	−0.986276	+	0.165102i	$0.947205\pi$
$12$		−	6.05014i		−	1.74652i
$13$	2.32260	−	1.11851i	0.644175	−	0.310218i	−0.0831241	−	0.996539i	$-0.526490\pi$
$13$	2.32260	−	1.11851i	0.644175	−	0.310218i	0.727299	+	0.686321i	$0.240775\pi$
$14$	−0.0673480	+	0.0537083i	−0.0179995	+	0.0143541i
$15$	4.12371	−	3.28855i	1.06474	−	0.849099i
$16$	−3.59437	+	1.73096i	−0.898592	+	0.432739i
$17$		−	5.23359i		−	1.26933i	−0.772787	−	0.634666i	$-0.781138\pi$
$17$		−	5.23359i		−	1.26933i	0.772787	−	0.634666i	$-0.218862\pi$
$18$	0.112239	+	0.233066i	0.0264549	+	0.0549342i
$19$	−0.369537	+	0.0843444i	−0.0847776	+	0.0193499i	−0.264699	−	0.964331i	$-0.585273\pi$
$19$	−0.369537	+	0.0843444i	−0.0847776	+	0.0193499i	0.179922	+	0.983681i	$0.442416\pi$
$20$	−3.13628	−	1.51035i	−0.701294	−	0.337725i
$21$	−2.69785	+	5.60215i	−0.588720	+	1.22249i
$22$	0.0172847	−	0.0757291i	0.00368510	−	0.0161455i
$23$	2.26357	+	2.83842i	0.471986	+	0.591852i	0.959656	−	0.281176i	$-0.0907245\pi$
$23$	2.26357	+	2.83842i	0.471986	+	0.591852i	−0.487670	+	0.873028i	$0.662153\pi$
$24$	0.316592	−	0.396994i	0.0646241	−	0.0810360i
$25$	0.437322	+	1.91603i	0.0874644	+	0.383207i
$26$	0.105420	+	0.0240614i	0.0206745	+	0.00471883i
$27$	7.49723	+	5.97884i	1.44284	+	1.15063i
$28$	4.10370			0.775526
$29$		0			0
$29$		0			0
$30$	0.221238			0.0403923
$31$	−1.84952	−	1.47494i	−0.332184	−	0.264908i	0.443166	−	0.896439i	$-0.353855\pi$
$31$	−1.84952	−	1.47494i	−0.332184	−	0.264908i	−0.775350	+	0.631532i	$0.782427\pi$
$32$	−0.490149	−	0.111873i	−0.0866470	−	0.0197766i
$33$	−1.24765	−	5.46633i	−0.217189	−	0.951566i
$34$	0.136872	−	0.171631i	0.0234733	−	0.0294346i
$35$	2.23056	+	2.79704i	0.377034	+	0.472785i
$36$	2.74223	−	12.0145i	0.457038	−	2.00242i
$37$	−2.84946	+	5.91697i	−0.468449	+	0.972744i	0.524186	+	0.851604i	$0.324369\pi$
$37$	−2.84946	+	5.91697i	−0.468449	+	0.972744i	−0.992635	+	0.121141i	$0.961345\pi$
$38$	−0.0143245	−	0.00689831i	−0.00232374	−	0.00111905i
$39$	7.60949	−	1.73682i	1.21849	−	0.278113i
$40$	−0.126760	−	0.263221i	−0.0200426	−	0.0416189i
$41$			9.44586i			1.47520i	0.675240	+	0.737598i	$0.264040\pi$
$41$			9.44586i			1.47520i	−0.675240	+	0.737598i	$0.735960\pi$
$42$	−0.234984	+	0.113163i	−0.0362589	+	0.0174614i
$43$	−0.778328	+	0.620696i	−0.118694	+	0.0946553i	−0.681038	−	0.732248i	$-0.738471\pi$
$43$	−0.778328	+	0.620696i	−0.118694	+	0.0946553i	0.562344	+	0.826903i	$0.309900\pi$
$44$	−2.89312	+	2.30719i	−0.436155	+	0.347822i
$45$	9.67949	−	4.66140i	1.44293	−	0.694880i
$46$			0.152282i			0.0224527i
$47$	−4.41153	−	9.16063i	−0.643487	−	1.33621i	−0.926208	−	0.377013i	$-0.876951\pi$
$47$	−4.41153	−	9.16063i	−0.643487	−	1.33621i	0.282721	−	0.959202i	$-0.408763\pi$
$48$	−11.7761	+	2.68782i	−1.69974	+	0.387954i
$49$	2.50694	+	1.20728i	0.358135	+	0.172469i
$50$	−0.0357675	+	0.0742719i	−0.00505828	+	0.0105036i
$51$	3.52605	−	15.4486i	0.493745	−	2.16324i
$52$	−3.21176	−	4.02742i	−0.445391	−	0.558502i
$53$	6.19127	−	7.76360i	0.850436	−	1.06641i	−0.146579	−	0.989199i	$-0.546826\pi$
$53$	6.19127	−	7.76360i	0.850436	−	1.06641i	0.997015	−	0.0772140i	$-0.0246025\pi$
$54$	0.0895040	+	0.392143i	0.0121800	+	0.0533639i
$55$	−3.14511	−	0.717851i	−0.424087	−	0.0967950i
$56$	0.269274	+	0.214739i	0.0359832	+	0.0286956i
$57$	−1.14763			−0.152008
$58$		0			0
$59$	−6.24449			−0.812963			−0.406482	−	0.913659i	$-0.633244\pi$
$59$	−6.24449			−0.812963			−0.406482	+	0.913659i	$0.633244\pi$
$60$	−8.24016	−	6.57131i	−1.06380	−	0.848352i
$61$	−7.78508	−	1.77689i	−0.996777	−	0.227508i	−0.307141	−	0.951664i	$-0.599372\pi$
$61$	−7.78508	−	1.77689i	−0.996777	−	0.227508i	−0.689636	+	0.724156i	$0.742229\pi$
$62$	−0.0220801	−	0.0967392i	−0.00280417	−	0.0122859i
$63$	−7.89664	+	9.90207i	−0.994883	+	1.24754i
$64$	4.96161	+	6.22166i	0.620201	+	0.777708i
$65$	0.999295	−	4.37820i	0.123947	−	0.543049i
$66$	0.102042	−	0.211893i	0.0125606	−	0.0260823i
$67$	−3.72841	−	1.79551i	−0.455498	−	0.219356i	0.192044	−	0.981386i	$-0.438489\pi$
$67$	−3.72841	−	1.79551i	−0.455498	−	0.219356i	−0.647542	+	0.762030i	$0.724203\pi$
$68$	−10.1958	+	2.32712i	−1.23642	+	0.282204i
$69$	4.76930	+	9.90355i	0.574156	+	1.19225i
$70$			0.150061i			0.0179358i
$71$	−2.05682	+	0.990512i	−0.244100	+	0.117552i	−0.551934	−	0.833888i	$-0.686110\pi$
$71$	−2.05682	+	0.990512i	−0.244100	+	0.117552i	0.307834	+	0.951440i	$0.400396\pi$
$72$	0.808633	−	0.644863i	0.0952983	−	0.0759979i
$73$	7.08653	−	5.65132i	0.829416	−	0.661437i	−0.113842	−	0.993499i	$-0.536316\pi$
$73$	7.08653	−	5.65132i	0.829416	−	0.661437i	0.943258	+	0.332062i	$0.107744\pi$
$74$	−0.248190	+	0.119522i	−0.0288515	+	0.0138941i
$75$			5.95042i			0.687096i
$76$	0.328629	+	0.682406i	0.0376964	+	0.0782774i
$77$	3.70771	−	0.846262i	0.422533	−	0.0964405i
$78$	0.294969	+	0.142050i	0.0333987	+	0.0160840i
$79$	−4.45891	+	9.25903i	−0.501667	+	1.04172i	0.484318	+	0.874892i	$0.339068\pi$
$79$	−4.45891	+	9.25903i	−0.501667	+	1.04172i	−0.985986	+	0.166831i	$0.946647\pi$
$80$	−1.54647	+	6.77552i	−0.172900	+	0.757526i
$81$	6.56684	+	8.23455i	0.729648	+	0.914950i
$82$	−0.247033	+	0.309770i	−0.0272802	+	0.0342083i
$83$	3.47592	+	15.2290i	0.381532	+	1.67160i	0.692685	+	0.721240i	$0.256428\pi$
$83$	3.47592	+	15.2290i	0.381532	+	1.67160i	−0.311153	+	0.950360i	$0.600715\pi$
$84$	12.1134	+	2.76480i	1.32168	+	0.301664i
$85$	−7.12804	−	5.68442i	−0.773145	−	0.616562i
$86$	−0.0417574			−0.00450282
$87$		0			0
$88$	−0.310570			−0.0331069
$89$	7.51879	+	5.99604i	0.796990	+	0.635578i	0.934918	−	0.354864i	$-0.115473\pi$
$89$	7.51879	+	5.99604i	0.796990	+	0.635578i	−0.137928	+	0.990442i	$0.544044\pi$
$90$	0.439339	+	0.100276i	0.0463103	+	0.0105700i
$91$	1.17805	+	5.16138i	0.123493	+	0.541059i
$92$	4.52315	−	5.67185i	0.471571	−	0.591331i
$93$	−4.46573	−	5.59985i	−0.463075	−	0.580677i
$94$	0.0949009	−	0.415788i	0.00978828	−	0.0428853i
$95$	−0.286494	+	0.594912i	−0.0293937	+	0.0610367i
$96$	−1.37146	−	0.660460i	−0.139974	−	0.0674079i
$97$	5.04795	−	1.15216i	0.512542	−	0.116984i	0.0415754	−	0.999135i	$-0.486762\pi$
$97$	5.04795	−	1.15216i	0.512542	−	0.116984i	0.470967	+	0.882151i	$0.343905\pi$
$98$	0.0506399	+	0.105155i	0.00511540	+	0.0106222i
$99$		−	11.4207i		−	1.14782i
$100$	3.53825	−	1.70393i	0.353825	−	0.170393i
$101$	−6.61542	+	5.27562i	−0.658259	+	0.524944i	−0.894681	−	0.446706i	$-0.852597\pi$
$101$	−6.61542	+	5.27562i	−0.658259	+	0.524944i	0.236421	+	0.971651i	$0.424025\pi$
$102$	0.519654	−	0.414410i	0.0514534	−	0.0410327i
$103$	−3.16609	+	1.52471i	−0.311964	+	0.150234i	−0.583314	−	0.812247i	$-0.698244\pi$
$103$	−3.16609	+	1.52471i	−0.311964	+	0.150234i	0.271350	+	0.962481i	$0.412530\pi$
$104$		−	0.432333i		−	0.0423938i
$105$	4.69976	+	9.75915i	0.458650	+	0.952396i
$106$	0.406076	−	0.0926841i	0.0394415	−	0.00900228i
$107$	4.00371	+	1.92808i	0.387053	+	0.186395i	0.617283	−	0.786741i	$-0.288234\pi$
$107$	4.00371	+	1.92808i	0.387053	+	0.186395i	−0.230230	+	0.973136i	$0.573948\pi$
$108$	8.31397	−	17.2641i	0.800012	−	1.66124i
$109$	−2.61746	+	11.4679i	−0.250708	+	1.09842i	0.680159	+	0.733064i	$0.261911\pi$
$109$	−2.61746	+	11.4679i	−0.250708	+	1.09842i	−0.930867	+	0.365358i	$0.880947\pi$
$110$	−0.0843679	−	0.105794i	−0.00804416	−	0.0100871i
$111$	−12.3976	+	15.5461i	−1.17673	+	1.47557i
$112$	−1.82310	−	7.98753i	−0.172267	−	0.754751i
$113$	−11.1334	−	2.54113i	−1.04734	−	0.239049i	−0.335977	−	0.941870i	$-0.609066\pi$
$113$	−11.1334	−	2.54113i	−1.04734	−	0.239049i	−0.711367	+	0.702821i	$0.751923\pi$
$114$	−0.0376357	−	0.0300135i	−0.00352491	−	0.00281102i
$115$	6.32443			0.589756
$116$		0			0
$117$	15.8983			1.46980
$118$	−0.204783	−	0.163309i	−0.0188518	−	0.0150338i
$119$	10.4785	+	2.39165i	0.960564	+	0.219242i
$120$	−0.196833	−	0.862383i	−0.0179683	−	0.0787245i
$121$	4.72022	−	5.91897i	0.429111	−	0.538088i
$122$	−0.208835	−	0.261871i	−0.0189071	−	0.0237087i
$123$	−6.36400	+	27.8825i	−0.573822	+	2.51408i
$124$	−2.05101	+	4.25896i	−0.184186	+	0.382466i
$125$	10.9322	+	5.26467i	0.977805	+	0.470886i
$126$	−0.517928	+	0.118214i	−0.0461407	+	0.0105313i
$127$	−5.22667	−	10.8533i	−0.463792	−	0.963074i	−0.993386	−	0.114823i	$-0.963370\pi$
$127$	−5.22667	−	10.8533i	−0.463792	−	0.963074i	0.529594	−	0.848251i	$-0.322344\pi$
$128$			1.33930i			0.118379i
$129$	−2.71567	+	1.30780i	−0.239101	+	0.115145i
$130$	0.147272	−	0.117446i	0.0129166	−	0.0103007i
$131$	−11.4103	+	9.09941i	−0.996922	+	0.795019i	−0.978800	−	0.204817i	$-0.934340\pi$
$131$	−11.4103	+	9.09941i	−0.996922	+	0.795019i	−0.0181218	+	0.999836i	$0.505769\pi$
$132$	−10.0944	+	4.86121i	−0.878606	+	0.423114i
$133$		−	0.778418i		−	0.0674974i
$134$	−0.0753133	−	0.156390i	−0.00650608	−	0.0135100i
$135$	16.2861	−	3.71720i	1.40169	−	0.319925i
$136$	−0.790793	−	0.380826i	−0.0678099	−	0.0326555i
$137$	1.24195	−	2.57894i	0.106107	−	0.220334i	−0.841155	−	0.540795i	$-0.818124\pi$
$137$	1.24195	−	2.57894i	0.106107	−	0.220334i	0.947262	+	0.320461i	$0.103838\pi$
$138$	−0.102597	+	0.449509i	−0.00873367	+	0.0382647i
$139$	−13.8841	−	17.4101i	−1.17763	−	1.47670i	−0.845910	−	0.533326i	$-0.820942\pi$
$139$	−13.8841	−	17.4101i	−1.17763	−	1.47670i	−0.331722	−	0.943377i	$-0.607630\pi$
$140$	4.45720	−	5.58915i	0.376702	−	0.472370i
$141$	−6.85021	−	30.0127i	−0.576892	−	2.52753i
$142$	−0.0933562	−	0.0213079i	−0.00783428	−	0.00178812i
$143$	−3.73237	−	2.97647i	−0.312117	−	0.248905i
$144$	−24.6036			−2.05030
$145$		0			0
$146$	0.380194			0.0314650
$147$	6.58666	+	5.25269i	0.543259	+	0.433235i
$148$	12.7941	+	2.92017i	1.05167	+	0.240037i
$149$	0.942652	+	4.13003i	0.0772250	+	0.338345i	0.998751	−	0.0499728i	$-0.0159134\pi$
$149$	0.942652	+	4.13003i	0.0772250	+	0.338345i	−0.921526	+	0.388318i	$0.873056\pi$
$150$	−0.155619	+	0.195140i	−0.0127062	+	0.0159331i
$151$	−4.85985	−	6.09406i	−0.395489	−	0.495927i	0.543723	−	0.839265i	$-0.317014\pi$
$151$	−4.85985	−	6.09406i	−0.395489	−	0.495927i	−0.939212	+	0.343337i	$0.888443\pi$
$152$	−0.0141452	+	0.0619742i	−0.00114733	+	0.00502677i
$153$	14.0042	−	29.0800i	1.13217	−	2.35098i
$154$	0.143723	+	0.0692136i	0.0115816	+	0.00557739i
$155$	−4.01768	+	0.917010i	−0.322708	+	0.0736560i
$156$	−6.76712	−	14.0521i	−0.541803	−	1.12507i
$157$			6.32741i			0.504982i	0.967599	+	0.252491i	$0.0812498\pi$
$157$			6.32741i			0.504982i	−0.967599	+	0.252491i	$0.918750\pi$
$158$	−0.388374	+	0.187031i	−0.0308973	+	0.0148794i
$159$	23.5061	−	18.7455i	1.86416	−	1.48661i
$160$	−0.684741	+	0.546063i	−0.0541335	+	0.0431700i
$161$	−6.71740	+	3.23493i	−0.529405	+	0.254948i
$162$			0.441785i			0.0347099i
$163$	0.763393	+	1.58520i	0.0597936	+	0.124163i	0.928724	−	0.370771i	$-0.120907\pi$
$163$	0.763393	+	1.58520i	0.0597936	+	0.124163i	−0.868931	+	0.494934i	$0.835192\pi$
$164$	18.4019	−	4.20011i	1.43694	−	0.327973i
$165$	−8.80016	−	4.23793i	−0.685092	−	0.329923i
$166$	−0.284287	+	0.590327i	−0.0220649	+	0.0458183i
$167$	−3.09755	+	13.5713i	−0.239696	+	1.05018i	0.701594	+	0.712577i	$0.252472\pi$
$167$	−3.09755	+	13.5713i	−0.239696	+	1.05018i	−0.941290	+	0.337600i	$0.890385\pi$
$168$	0.650171	+	0.815288i	0.0501618	+	0.0629009i
$169$	−3.96193	+	4.96811i	−0.304764	+	0.382162i
$170$	−0.0850966	−	0.372832i	−0.00652661	−	0.0285949i
$171$	−2.27899	−	0.520165i	−0.174279	−	0.0397780i
$172$	1.55529	+	1.24030i	0.118590	+	0.0945720i
$173$	8.38553			0.637540			0.318770	−	0.947832i	$-0.396730\pi$
$173$	8.38553			0.637540			0.318770	+	0.947832i	$0.396730\pi$
$174$		0			0
$175$	−4.03606			−0.305098
$176$	5.77606	+	4.60626i	0.435387	+	0.347210i
$177$	−18.4326	−	4.20712i	−1.38548	−	0.316227i
$178$	0.0897614	+	0.393271i	0.00672790	+	0.0294769i
$179$	12.2675	−	15.3829i	0.916914	−	1.14977i	−0.0714156	−	0.997447i	$-0.522752\pi$
$179$	12.2675	−	15.3829i	0.916914	−	1.14977i	0.988330	−	0.152328i	$-0.0486769\pi$
$180$	−13.3850	−	16.7843i	−0.997662	−	1.25103i
$181$	−2.68216	+	11.7513i	−0.199364	+	0.873469i	0.771953	+	0.635679i	$0.219280\pi$
$181$	−2.68216	+	11.7513i	−0.199364	+	0.873469i	−0.971317	+	0.237789i	$0.923577\pi$
$182$	−0.0963498	+	0.200072i	−0.00714192	+	0.0148303i
$183$	−21.7830	−	10.4901i	−1.61025	−	0.775453i
$184$	0.593594	−	0.135484i	0.0437603	−	0.00998801i
$185$	4.96387	+	10.3076i	0.364951	+	0.757829i
$186$		−	0.300433i		−	0.0220288i
$187$	−8.73204	+	4.20513i	−0.638550	+	0.307509i
$188$	−15.8846	+	12.6675i	−1.15850	+	0.923876i
$189$	−15.3967	+	12.2785i	−1.11995	+	0.893128i
$190$	−0.0249538	+	0.0120171i	−0.00181034	+	0.000871813i
$191$		−	11.6202i		−	0.840810i	−0.907337	−	0.420405i	$-0.861888\pi$
$191$		−	11.6202i		−	0.840810i	0.907337	−	0.420405i	$-0.138112\pi$
$192$	10.4540	+	21.7080i	0.754455	+	1.56664i
$193$	−18.5748	+	4.23958i	−1.33704	+	0.305172i	−0.830489	−	0.557035i	$-0.811939\pi$
$193$	−18.5748	+	4.23958i	−1.33704	+	0.305172i	−0.506556	+	0.862207i	$0.669082\pi$
$194$	0.195676	+	0.0942324i	0.0140487	+	0.00676549i
$195$	5.89948	−	12.2504i	0.422470	−	0.877269i
$196$	1.23724	−	5.42070i	0.0883742	−	0.387193i
$197$	10.4165	+	13.0618i	0.742142	+	0.930616i	0.999361	−	0.0357368i	$-0.0113778\pi$
$197$	10.4165	+	13.0618i	0.742142	+	0.930616i	−0.257220	+	0.966353i	$0.582806\pi$
$198$	0.298679	−	0.374532i	0.0212262	−	0.0266168i
$199$	1.98233	+	8.68517i	0.140524	+	0.615676i	0.995313	+	0.0967009i	$0.0308290\pi$
$199$	1.98233	+	8.68517i	0.140524	+	0.615676i	−0.854790	+	0.518975i	$0.826314\pi$
$200$	0.321334	+	0.0733423i	0.0227217	+	0.00518608i
$201$	−9.79591	−	7.81197i	−0.690950	−	0.551014i
$202$	−0.354918			−0.0249720
$203$		0			0
$204$	−31.6639			−2.21692
$205$	12.8651	+	10.2596i	0.898536	+	0.716558i
$206$	−0.143704	−	0.0327996i	−0.0100124	−	0.00228526i
$207$	4.98219	+	21.8284i	0.346286	+	1.51718i
$208$	−6.41221	+	8.04065i	−0.444607	+	0.557519i
$209$	0.437644	+	0.548788i	0.0302725	+	0.0379605i
$210$	−0.101101	+	0.442954i	−0.00697666	+	0.0305668i
$211$	0.110300	−	0.229041i	0.00759339	−	0.0157678i	−0.897138	−	0.441751i	$-0.854357\pi$
$211$	0.110300	−	0.229041i	0.00759339	−	0.0157678i	0.904731	+	0.425983i	$0.140072\pi$
$212$	−17.8775	−	8.60937i	−1.22783	−	0.591294i
$213$	−6.73870	+	1.53807i	−0.461728	+	0.105386i
$214$	0.0808742	+	0.167937i	0.00552844	+	0.0114799i
$215$			1.73423i			0.118274i
$216$	1.44894	−	0.697773i	0.0985879	−	0.0474774i
$217$	3.79828	−	3.02902i	0.257844	−	0.205624i
$218$	−0.385751	+	0.307626i	−0.0261264	+	0.0208351i
$219$	24.7257	−	11.9072i	1.67080	−	0.804617i
$220$			6.44631i			0.434610i
$221$	−5.85381	−	12.1556i	−0.393770	−	0.817671i
$222$	−0.813137	+	0.185593i	−0.0545742	+	0.0124562i
$223$	−8.24994	−	3.97296i	−0.552457	−	0.266049i	0.136760	−	0.990604i	$-0.456331\pi$
$223$	−8.24994	−	3.97296i	−0.552457	−	0.266049i	−0.689217	+	0.724555i	$0.742045\pi$
$224$	0.447978	−	0.930236i	0.0299318	−	0.0621540i
$225$	−2.69704	+	11.8165i	−0.179802	+	0.787766i
$226$	−0.298655	−	0.374501i	−0.0198662	−	0.0249114i
$227$	−3.00177	+	3.76410i	−0.199234	+	0.249832i	−0.871405	−	0.490564i	$-0.836791\pi$
$227$	−3.00177	+	3.76410i	−0.199234	+	0.249832i	0.672171	+	0.740396i	$0.265362\pi$
$228$	0.510295	+	2.23575i	0.0337951	+	0.148066i
$229$	6.69386	+	1.52783i	0.442343	+	0.100962i	0.437891	−	0.899028i	$-0.355726\pi$
$229$	6.69386	+	1.52783i	0.442343	+	0.100962i	0.00445223	+	0.999990i	$0.498583\pi$
$230$	0.207405	+	0.165400i	0.0136759	+	0.0109061i
$231$	11.5147			0.757609
$232$		0			0
$233$	17.2302			1.12879			0.564393	−	0.825507i	$-0.309110\pi$
$233$	17.2302			1.12879			0.564393	+	0.825507i	$0.309110\pi$
$234$	0.521372	+	0.415781i	0.0340832	+	0.0271804i
$235$	−17.2681	−	3.94134i	−1.12645	−	0.257105i
$236$	2.77661	+	12.1651i	0.180742	+	0.791883i
$237$	−19.4000	+	24.3269i	−1.26017	+	1.58020i
$238$	0.281087	+	0.352472i	0.0182202	+	0.0228474i
$239$	4.74062	−	20.7700i	0.306645	−	1.34350i	−0.553244	−	0.833019i	$-0.686610\pi$
$239$	4.74062	−	20.7700i	0.306645	−	1.34350i	0.859889	−	0.510481i	$-0.170533\pi$
$240$	−9.12979	+	18.9582i	−0.589325	+	1.22375i
$241$	−8.10252	−	3.90197i	−0.521929	−	0.251348i	0.154320	−	0.988021i	$-0.450681\pi$
$241$	−8.10252	−	3.90197i	−0.521929	−	0.251348i	−0.676249	+	0.736673i	$0.736396\pi$
$242$	0.309592	−	0.0706623i	0.0199013	−	0.00454235i
$243$	1.35428	+	2.81220i	0.0868773	+	0.180402i
$244$			15.9565i			1.02151i
$245$	4.36719	−	2.10313i	0.279010	−	0.134364i
$246$	−0.937900	+	0.747950i	−0.0597983	+	0.0476876i
$247$	−0.763948	+	0.609229i	−0.0486089	+	0.0387643i
$248$	−0.357445	+	0.172136i	−0.0226978	+	0.0109307i
$249$			47.2951i			2.99721i
$250$	0.220829	+	0.458555i	0.0139664	+	0.0290016i
$251$	6.33959	−	1.44697i	0.400151	−	0.0913319i	−0.0177090	−	0.999843i	$-0.505637\pi$
$251$	6.33959	−	1.44697i	0.400151	−	0.0913319i	0.417860	+	0.908511i	$0.362780\pi$
$252$	22.8019	+	10.9808i	1.43638	+	0.691725i
$253$	2.91705	−	6.05731i	0.183393	−	0.380820i
$254$	0.112436	−	0.492616i	0.00705488	−	0.0309095i
$255$	−17.2109	−	21.5818i	−1.07779	−	1.35150i
$256$	9.88819	−	12.3994i	0.618012	−	0.774963i
$257$	1.28785	+	5.64245i	0.0803341	+	0.351966i	0.999080	−	0.0428824i	$-0.0136541\pi$
$257$	1.28785	+	5.64245i	0.0803341	+	0.351966i	−0.918746	+	0.394849i	$0.870797\pi$
$258$	−0.123260	−	0.0281334i	−0.00767386	−	0.00175151i
$259$	−10.5446	−	8.40905i	−0.655210	−	0.522513i
$260$	−8.97368			−0.556524
$261$		0			0
$262$	−0.612164			−0.0378196
$263$	−23.6479	−	18.8585i	−1.45819	−	1.16287i	−0.954205	−	0.299155i	$-0.903295\pi$
$263$	−23.6479	−	18.8585i	−1.45819	−	1.16287i	−0.503985	−	0.863712i	$-0.668133\pi$
$264$	−0.916746	−	0.209241i	−0.0564218	−	0.0128779i
$265$	−3.84927	−	16.8648i	−0.236459	−	1.03599i
$266$	0.0203576	−	0.0255276i	0.00124820	−	0.00156520i
$267$	18.1544	+	22.7649i	1.11103	+	1.39319i
$268$	−1.84006	+	8.06184i	−0.112400	+	0.492455i
$269$	5.17894	−	10.7542i	0.315766	−	0.655695i	−0.681320	−	0.731986i	$-0.738594\pi$
$269$	5.17894	−	10.7542i	0.315766	−	0.655695i	0.997086	+	0.0762914i	$0.0243079\pi$
$270$	0.631304	+	0.304020i	0.0384200	+	0.0185021i
$271$	−17.1169	+	3.90683i	−1.03978	+	0.237323i	−0.708132	−	0.706080i	$-0.750462\pi$
$271$	−17.1169	+	3.90683i	−1.03978	+	0.237323i	−0.331648	+	0.943403i	$0.607605\pi$
$272$	9.05911	+	18.8114i	0.549289	+	1.14061i
$273$			16.0292i			0.970128i
$274$	0.108175	−	0.0520941i	0.00653506	−	0.00314712i
$275$	2.84544	−	2.26916i	0.171587	−	0.136836i
$276$	17.1728	−	13.6949i	1.03368	−	0.824335i
$277$	−0.968331	+	0.466324i	−0.0581814	+	0.0280187i	−0.462748	−	0.886490i	$-0.653137\pi$
$277$	−0.968331	+	0.466324i	−0.0581814	+	0.0280187i	0.404567	+	0.914508i	$0.367422\pi$
$278$		−	0.934053i		−	0.0560208i
$279$	−6.33001	−	13.1444i	−0.378968	−	0.786935i
$280$	0.584939	−	0.133509i	0.0349568	−	0.00797866i
$281$	26.9268	+	12.9673i	1.60632	+	0.773563i	0.999769	−	0.0214813i	$-0.00683824\pi$
$281$	26.9268	+	12.9673i	1.60632	+	0.773563i	0.606551	+	0.795044i	$0.292553\pi$
$282$	0.560261	−	1.16339i	0.0333631	−	0.0692791i
$283$	5.95247	−	26.0795i	0.353837	−	1.55026i	−0.414398	−	0.910096i	$-0.636008\pi$
$283$	5.95247	−	26.0795i	0.353837	−	1.55026i	0.768236	−	0.640167i	$-0.221135\pi$
$284$	2.84422	+	3.56654i	0.168774	+	0.211635i
$285$	−1.24649	+	1.56305i	−0.0738358	+	0.0925872i
$286$	−0.0445581	−	0.195222i	−0.00263478	−	0.0115437i
$287$	−18.9122	−	4.31658i	−1.11635	−	0.254800i
$288$	−2.42412	−	1.93317i	−0.142843	−	0.113913i
$289$	−10.3905			−0.611204
$290$		0			0
$291$	15.6769			0.918996
$292$	−14.1606	−	11.2927i	−0.828686	−	0.660855i
$293$	−5.66470	−	1.29293i	−0.330935	−	0.0755338i	0.0538251	−	0.998550i	$-0.482859\pi$
$293$	−5.66470	−	1.29293i	−0.330935	−	0.0755338i	−0.384760	+	0.923017i	$0.625716\pi$
$294$	0.0786335	+	0.344516i	0.00458600	+	0.0200926i
$295$	−6.78240	+	8.50486i	−0.394887	+	0.495172i
$296$	0.686708	+	0.861105i	0.0399141	+	0.0500507i
$297$	3.95152	−	17.3128i	0.229291	−	1.00459i
$298$	−0.0770971	+	0.160094i	−0.00446611	+	0.00927398i
$299$	8.43217	+	4.06072i	0.487645	+	0.234837i
$300$	11.5923	−	2.64586i	0.669280	−	0.152759i
$301$	−0.887055	−	1.84199i	−0.0511290	−	0.106171i
$302$		−	0.326947i		−	0.0188137i
$303$	−23.0819	+	11.1157i	−1.32602	+	0.638578i
$304$	1.18226	−	0.942817i	0.0678070	−	0.0540743i
$305$	−10.8758	+	8.67316i	−0.622746	+	0.496623i
$306$	1.21977	−	0.587412i	0.0697298	−	0.0335801i
$307$		−	5.15345i		−	0.294123i	−0.989127	−	0.147061i	$-0.953018\pi$
$307$		−	5.15345i		−	0.294123i	0.989127	−	0.147061i	$-0.0469815\pi$
$308$	−3.29727	−	6.84686i	−0.187880	−	0.390136i
$309$	−10.3730	+	2.36756i	−0.590098	+	0.134686i
$310$	−0.155739	−	0.0749999i	−0.00884538	−	0.00425971i
$311$	4.60974	−	9.57223i	0.261395	−	0.542792i	−0.728424	−	0.685127i	$-0.759747\pi$
$311$	4.60974	−	9.57223i	0.261395	−	0.542792i	0.989819	+	0.142335i	$0.0454611\pi$
$312$	0.291277	−	1.27617i	0.0164903	−	0.0722489i
$313$	10.4187	+	13.0647i	0.588902	+	0.738460i	0.983603	−	0.180350i	$-0.0577230\pi$
$313$	10.4187	+	13.0647i	0.588902	+	0.738460i	−0.394700	+	0.918810i	$0.629152\pi$
$314$	−0.165478	+	0.207502i	−0.00933844	+	0.0117100i
$315$	4.90954	+	21.5101i	0.276621	+	1.21196i
$316$	20.0206	+	4.56956i	1.12624	+	0.257058i
$317$	−1.16590	−	0.929772i	−0.0654833	−	0.0522212i	0.590201	−	0.807256i	$-0.299048\pi$
$317$	−1.16590	−	0.929772i	−0.0654833	−	0.0522212i	−0.655684	+	0.755035i	$0.727620\pi$
$318$	1.26111			0.0707193
$319$		0			0
$320$	13.8628			0.774954
$321$	10.5192	+	8.38879i	0.587125	+	0.468216i
$322$	−0.304893	−	0.0695899i	−0.0169910	−	0.00387810i
$323$	0.441424	+	1.93400i	0.0245615	+	0.107611i
$324$	13.1221	−	16.4546i	0.729006	−	0.914145i
$325$	3.15882	+	3.96104i	0.175220	+	0.219719i
$326$	−0.0164222	+	0.0719501i	−0.000909539	+	0.00398495i
$327$	−15.4526	+	32.0876i	−0.854529	+	1.77445i
$328$	1.42726	+	0.687335i	0.0788075	+	0.0379517i
$329$	20.3571	−	4.64637i	1.12232	−	0.256163i
$330$	−0.177762	−	0.369126i	−0.00978546	−	0.0203197i
$331$		−	29.8803i		−	1.64237i	−0.570663	−	0.821184i	$-0.693314\pi$
$331$		−	29.8803i		−	1.64237i	0.570663	−	0.821184i	$-0.306686\pi$
$332$	28.1227	−	13.5432i	1.54343	−	0.743278i
$333$	−31.6656	+	25.2525i	−1.73527	+	1.38383i
$334$	−0.456505	+	0.364050i	−0.0249788	+	0.0199200i
$335$	−6.49503	+	3.12784i	−0.354861	+	0.170892i
$336$		−	24.8061i		−	1.35328i
$337$	0.408434	+	0.848122i	0.0222488	+	0.0462002i	0.911797	−	0.410641i	$-0.134695\pi$
$337$	0.408434	+	0.848122i	0.0222488	+	0.0462002i	−0.889548	+	0.456841i	$0.848981\pi$
$338$	−0.259857	+	0.0593107i	−0.0141344	+	0.00322608i
$339$	−31.1518	−	15.0019i	−1.69193	−	0.814792i
$340$	−7.90457	+	16.4140i	−0.428685	+	0.890174i
$341$	−0.974816	+	4.27095i	−0.0527893	+	0.231285i
$342$	−0.0611342	−	0.0766598i	−0.00330576	−	0.00414529i
$343$	−12.5258	+	15.7069i	−0.676332	+	0.848093i
$344$	0.0371513	+	0.162770i	0.00200306	+	0.00877599i
$345$	18.6686	+	4.26098i	1.00508	+	0.229403i
$346$	0.274997	+	0.219303i	0.0147839	+	0.0117898i
$347$	8.65358			0.464548			0.232274	−	0.972650i	$-0.425383\pi$
$347$	8.65358			0.464548			0.232274	+	0.972650i	$0.425383\pi$
$348$		0			0
$349$	−34.5616			−1.85004			−0.925021	−	0.379916i	$-0.875953\pi$
$349$	−34.5616			−1.85004			−0.925021	+	0.379916i	$0.875953\pi$
$350$	−0.132360	−	0.105553i	−0.00707492	−	0.00564206i
$351$	24.1005	+	5.50077i	1.28639	+	0.293610i
$352$	0.207173	+	0.907684i	0.0110423	+	0.0483797i
$353$	8.99264	−	11.2764i	0.478630	−	0.600183i	−0.482631	−	0.875824i	$-0.660319\pi$
$353$	8.99264	−	11.2764i	0.478630	−	0.600183i	0.961261	+	0.275641i	$0.0888901\pi$
$354$	−0.494456	−	0.620028i	−0.0262801	−	0.0329541i
$355$	−0.884942	+	3.87718i	−0.0469678	+	0.205780i
$356$	8.33789	−	17.3138i	0.441907	−	0.917630i
$357$	29.3194	+	14.1195i	1.55175	+	0.747281i
$358$	0.804605	−	0.183646i	0.0425247	−	0.00970598i
$359$	9.67167	+	20.0834i	0.510451	+	1.05996i	0.983830	+	0.179104i	$0.0573199\pi$
$359$	9.67167	+	20.0834i	0.510451	+	1.05996i	−0.473379	+	0.880859i	$0.656966\pi$
$360$		−	1.80175i		−	0.0949608i
$361$	−16.9890	+	8.18145i	−0.894156	+	0.430603i
$362$	−0.395286	+	0.315230i	−0.0207758	+	0.0165681i
$363$	17.9211	−	14.2916i	0.940611	−	0.750113i
$364$	9.53127	−	4.59002i	0.499574	−	0.240582i
$365$		−	15.7898i		−	0.826478i
$366$	−0.440013	−	0.913696i	−0.0229998	−	0.0477597i
$367$	4.95309	−	1.13051i	0.258549	−	0.0590121i	−0.0912815	−	0.995825i	$-0.529096\pi$
$367$	4.95309	−	1.13051i	0.258549	−	0.0590121i	0.349831	+	0.936813i	$0.386239\pi$
$368$	−13.0493	−	6.28420i	−0.680240	−	0.327586i
$369$	−25.2755	+	52.4852i	−1.31579	+	2.73227i
$370$	−0.106783	+	0.467847i	−0.00555138	+	0.0243222i
$371$	12.7147	+	15.9438i	0.660116	+	0.827759i
$372$	−8.92361	+	11.1898i	−0.462667	+	0.580167i
$373$	−5.67645	−	24.8702i	−0.293916	−	1.28773i	−0.879026	−	0.476774i	$-0.841806\pi$
$373$	−5.67645	−	24.8702i	−0.293916	−	1.28773i	0.585110	−	0.810954i	$-0.301051\pi$
$374$	−0.396335	−	0.0904609i	−0.0204940	−	0.00467762i
$375$	28.7229	+	22.9057i	1.48324	+	1.18285i
$376$	−1.70517			−0.0879376
$377$		0			0
$378$	−0.826036			−0.0424867
$379$	6.50423	+	5.18695i	0.334100	+	0.266436i	0.776141	−	0.630559i	$-0.217174\pi$
$379$	6.50423	+	5.18695i	0.334100	+	0.266436i	−0.442042	+	0.896994i	$0.645746\pi$
$380$	1.28636	+	0.293604i	0.0659889	+	0.0150615i
$381$	−8.11596	−	35.5584i	−0.415793	−	1.82171i
$382$	0.303898	−	0.381076i	0.0155488	−	0.0194976i
$383$	−15.7882	−	19.7978i	−0.806741	−	1.01162i	−0.999538	−	0.0303822i	$-0.990328\pi$
$383$	−15.7882	−	19.7978i	−0.806741	−	1.01162i	0.192798	−	0.981239i	$-0.438244\pi$
$384$	−0.902333	+	3.95338i	−0.0460470	+	0.201745i
$385$	2.87451	−	5.96899i	0.146499	−	0.304208i
$386$	−0.720022	−	0.346745i	−0.0366482	−	0.0176488i
$387$	−5.98560	+	1.36617i	−0.304265	+	0.0694465i
$388$	−4.48915	−	9.32181i	−0.227902	−	0.473243i
$389$		−	27.3249i		−	1.38543i	−0.721212	−	0.692714i	$-0.756415\pi$
$389$		−	27.3249i		−	1.38543i	0.721212	−	0.692714i	$-0.243585\pi$
$390$	0.513848	−	0.247456i	0.0260197	−	0.0125304i
$391$	14.8551	−	11.8466i	0.751257	−	0.599107i
$392$	0.364839	−	0.290949i	0.0184272	−	0.0146952i
$393$	−39.8117	+	19.1723i	−2.00824	+	0.967115i
$394$			0.700769i			0.0353042i
$395$	7.76759	+	16.1296i	0.390830	+	0.811567i
$396$	−22.2491	+	5.07820i	−1.11806	+	0.255189i
$397$	−10.1136	−	4.87046i	−0.507588	−	0.244441i	0.162520	−	0.986705i	$-0.448038\pi$
$397$	−10.1136	−	4.87046i	−0.507588	−	0.244441i	−0.670108	+	0.742264i	$0.733752\pi$
$398$	−0.162130	+	0.336667i	−0.00812685	+	0.0168756i
$399$	0.524447	−	2.29775i	0.0262552	−	0.115031i
$400$	−4.88846	−	6.12994i	−0.244423	−	0.306497i
$401$	20.7632	−	26.0362i	1.03686	−	1.30019i	0.0841055	−	0.996457i	$-0.473197\pi$
$401$	20.7632	−	26.0362i	1.03686	−	1.30019i	0.952758	−	0.303729i	$-0.0982319\pi$
$402$	−0.116946	−	0.512375i	−0.00583275	−	0.0255550i
$403$	−5.94544	−	1.35701i	−0.296163	−	0.0675974i
$404$	13.2192	+	10.5420i	0.657680	+	0.524482i
$405$	18.3478			0.911710
$406$		0			0
$407$	12.1617			0.602835
$408$	−2.07770	−	1.65691i	−0.102862	−	0.0820294i
$409$	15.6788	+	3.57858i	0.775266	+	0.176949i	0.591809	−	0.806078i	$-0.298414\pi$
$409$	15.6788	+	3.57858i	0.775266	+	0.176949i	0.183457	+	0.983028i	$0.441271\pi$
$410$	0.153587	+	0.672908i	0.00758512	+	0.0332326i
$411$	5.40353	−	6.77582i	0.266537	−	0.334226i
$412$	4.37815	+	5.49002i	0.215696	+	0.270474i
$413$	2.85362	−	12.5025i	0.140417	−	0.615208i
$414$	−0.407480	+	0.846142i	−0.0200266	+	0.0415856i
$415$	24.5169	+	11.8067i	1.20349	+	0.579570i
$416$	−1.26355	+	0.288398i	−0.0619508	+	0.0141399i
$417$	−29.2535	−	60.7456i	−1.43255	−	2.97472i
$418$			0.0294426i			0.00144008i
$419$	25.2958	−	12.1818i	1.23578	−	0.595120i	0.302116	−	0.953271i	$-0.402307\pi$
$419$	25.2958	−	12.1818i	1.23578	−	0.595120i	0.933664	+	0.358151i	$0.116593\pi$
$420$	16.9225	−	13.4952i	0.825731	−	0.658499i
$421$	23.8443	−	19.0152i	1.16210	−	0.926745i	0.163888	−	0.986479i	$-0.447597\pi$
$421$	23.8443	−	19.0152i	1.16210	−	0.926745i	0.998214	+	0.0597337i	$0.0190252\pi$
$422$	0.00960722	−	0.00462659i	0.000467672	−	0.000225219i
$423$		−	62.7048i		−	3.04881i
$424$	−0.722565	−	1.50042i	−0.0350908	−	0.0728669i
$425$	10.0277	−	2.28876i	0.486416	−	0.111021i
$426$	−0.261215	−	0.125794i	−0.0126559	−	0.00609476i
$427$	7.11527	−	14.7750i	0.344332	−	0.715013i
$428$	1.97593	−	8.65710i	0.0955101	−	0.418457i
$429$	−9.01194	−	11.3006i	−0.435101	−	0.545599i
$430$	−0.0453545	+	0.0568728i	−0.00218719	+	0.00274265i
$431$	2.16416	+	9.48182i	0.104244	+	0.456723i	0.999928	+	0.0120313i	$0.00382976\pi$
$431$	2.16416	+	9.48182i	0.104244	+	0.456723i	−0.895683	+	0.444692i	$0.853313\pi$
$432$	−37.2969	−	8.51277i	−1.79445	−	0.409571i
$433$	18.1617	+	14.4835i	0.872796	+	0.696032i	0.953722	−	0.300688i	$-0.0972164\pi$
$433$	18.1617	+	14.4835i	0.872796	+	0.696032i	−0.0809262	+	0.996720i	$0.525788\pi$
$434$	0.203778			0.00978166
$435$		0			0
$436$	23.5049			1.12568
$437$	−1.07588	−	0.857983i	−0.0514661	−	0.0410429i
$438$	1.12226	+	0.256149i	0.0536238	+	0.0122393i
$439$	−3.03245	−	13.2860i	−0.144731	−	0.634107i	−0.994299	−	0.106628i	$-0.965995\pi$
$439$	−3.03245	−	13.2860i	−0.144731	−	0.634107i	0.849568	−	0.527479i	$-0.176863\pi$
$440$	−0.337323	+	0.422990i	−0.0160812	+	0.0201652i
$441$	10.6992	+	13.4163i	0.509484	+	0.638872i
$442$	0.125927	−	0.551724i	0.00598976	−	0.0262428i
$443$	3.98012	−	8.26480i	0.189101	−	0.392673i	−0.784766	−	0.619793i	$-0.787217\pi$
$443$	3.98012	−	8.26480i	0.189101	−	0.392673i	0.973867	+	0.227120i	$0.0729310\pi$
$444$	35.7985	+	17.2396i	1.69892	+	0.818157i
$445$	16.3330	−	3.72789i	0.774256	−	0.176719i
$446$	−0.166647	−	0.346047i	−0.00789098	−	0.0163858i
$447$			12.8262i			0.606658i
$448$	−14.7242	+	7.09078i	−0.695651	+	0.335008i
$449$	13.8731	−	11.0635i	0.654714	−	0.522117i	−0.238848	−	0.971057i	$-0.576770\pi$
$449$	13.8731	−	11.0635i	0.654714	−	0.522117i	0.893562	+	0.448940i	$0.148198\pi$
$450$	−0.397478	+	0.316978i	−0.0187373	+	0.0149425i
$451$	15.7601	−	7.58964i	0.742112	−	0.357382i
$452$			22.8194i			1.07333i
$453$	−10.2396	−	21.2628i	−0.481100	−	0.999014i
$454$	−0.196881	+	0.0449368i	−0.00924009	+	0.00210899i
$455$	8.30922	+	4.00151i	0.389542	+	0.187594i
$456$	−0.0835082	+	0.173407i	−0.00391063	+	0.00812051i
$457$	0.561526	−	2.46020i	0.0262671	−	0.115084i	−0.960095	−	0.279675i	$-0.909773\pi$
$457$	0.561526	−	2.46020i	0.0262671	−	0.115084i	0.986362	+	0.164591i	$0.0526305\pi$
$458$	0.179563	+	0.225165i	0.00839045	+	0.0105213i
$459$	31.2908	−	39.2374i	1.46053	−	1.83145i
$460$	−2.81216	−	12.3209i	−0.131118	−	0.574464i
$461$	−9.76174	−	2.22805i	−0.454649	−	0.103771i	−0.0109374	−	0.999940i	$-0.503482\pi$
$461$	−9.76174	−	2.22805i	−0.454649	−	0.103771i	−0.443712	+	0.896169i	$0.646339\pi$
$462$	0.377614	+	0.301137i	0.0175682	+	0.0140102i
$463$	−27.8485			−1.29423			−0.647115	−	0.762393i	$-0.724024\pi$
$463$	−27.8485			−1.29423			−0.647115	+	0.762393i	$0.724024\pi$
$464$		0			0
$465$	−12.4773			−0.578621
$466$	0.565050	+	0.450612i	0.0261754	+	0.0208742i
$467$	19.8182	+	4.52337i	0.917076	+	0.209317i	0.654911	−	0.755706i	$-0.272706\pi$
$467$	19.8182	+	4.52337i	0.917076	+	0.209317i	0.262165	+	0.965023i	$0.415563\pi$
$468$	−7.06919	−	30.9721i	−0.326773	−	1.43169i
$469$	5.29872	−	6.64439i	0.244672	−	0.306809i
$470$	−0.463219	−	0.580858i	−0.0213667	−	0.0267930i
$471$	−4.26299	+	18.6774i	−0.196428	+	0.860608i
$472$	−0.454384	+	0.943539i	−0.0209147	+	0.0434299i
$473$	1.66098	+	0.799888i	0.0763722	+	0.0367789i
$474$	−1.27242	+	0.290421i	−0.0584441	+	0.0133395i
$475$	−0.323213	−	0.671159i	−0.0148300	−	0.0307949i
$476$		−	21.4771i		−	0.984400i
$477$	55.1754	−	26.5711i	2.52631	−	1.21661i
$478$	0.698653	−	0.557157i	0.0319557	−	0.0254838i
$479$	−16.7710	+	13.3745i	−0.766288	+	0.611094i	−0.926633	−	0.375967i	$-0.877311\pi$
$479$	−16.7710	+	13.3745i	−0.766288	+	0.611094i	0.160345	+	0.987061i	$0.448739\pi$
$480$	−2.38913	+	1.15055i	−0.109049	+	0.0525150i
$481$			16.9299i			0.771939i
$482$	−0.163670	−	0.339863i	−0.00745495	−	0.0154804i
$483$	−22.0080	+	5.02319i	−1.00140	+	0.228563i
$484$	−13.6298	−	6.56378i	−0.619538	−	0.298354i
$485$	3.91357	−	8.12662i	0.177706	−	0.369011i
$486$	−0.0291334	+	0.127642i	−0.00132152	+	0.00578994i
$487$	10.2229	+	12.8192i	0.463245	+	0.580891i	0.957503	−	0.288424i	$-0.0931314\pi$
$487$	10.2229	+	12.8192i	0.463245	+	0.580891i	−0.494257	+	0.869316i	$0.664560\pi$
$488$	−0.834974	+	1.04702i	−0.0377975	+	0.0473966i
$489$	1.18540	+	5.19356i	0.0536054	+	0.234861i
$490$	0.198221	+	0.0452426i	0.00895470	+	0.00204385i
$491$	22.8879	+	18.2525i	1.03292	+	0.823723i	0.984550	−	0.175106i	$-0.0560269\pi$
$491$	22.8879	+	18.2525i	1.03292	+	0.823723i	0.0483669	+	0.998830i	$0.484598\pi$
$492$	57.1488			2.57647
$493$		0			0
$494$	−0.0409860			−0.00184405
$495$	−15.5547	−	12.4045i	−0.699132	−	0.557539i
$496$	9.20091	+	2.10005i	0.413133	+	0.0942950i
$497$	−1.04324	−	4.57074i	−0.0467958	−	0.205026i
$498$	−1.23689	+	1.55101i	−0.0554262	+	0.0695023i
$499$	2.91420	+	3.65430i	0.130458	+	0.163589i	0.842770	−	0.538274i	$-0.180923\pi$
$499$	2.91420	+	3.65430i	0.130458	+	0.163589i	−0.712312	+	0.701863i	$0.752352\pi$
$500$	5.39531	−	23.6384i	0.241286	−	1.05714i
$501$	−18.2868	+	37.9730i	−0.816996	+	1.69651i
$502$	0.245744	+	0.118344i	0.0109681	+	0.00528195i
$503$	10.8288	−	2.47160i	0.482831	−	0.110203i	0.0258248	−	0.999666i	$-0.491779\pi$
$503$	10.8288	−	2.47160i	0.482831	−	0.110203i	0.457006	+	0.889463i	$0.348922\pi$
$504$	0.921593	+	1.91371i	0.0410510	+	0.0852433i
$505$			14.7401i			0.655928i
$506$	0.254076	−	0.122357i	0.0112951	−	0.00543942i
$507$	−15.0421	+	11.9957i	−0.668043	+	0.532747i
$508$	−18.8197	+	15.0082i	−0.834989	+	0.665882i
$509$	29.9589	−	14.4274i	1.32790	−	0.639484i	0.370660	−	0.928769i	$-0.379132\pi$
$509$	29.9589	−	14.4274i	1.32790	−	0.639484i	0.957243	+	0.289284i	$0.0934174\pi$
$510$		−	1.15787i		−	0.0512712i
$511$	8.07647	+	16.7710i	0.357282	+	0.741904i
$512$	3.26000	−	0.744073i	0.144073	−	0.0328837i
$513$	−3.27478	−	1.57705i	−0.144585	−	0.0696286i
$514$	−0.105330	+	0.218720i	−0.00464592	+	0.00964734i
$515$	−1.36220	+	5.96820i	−0.0600258	+	0.262990i
$516$	3.75530	+	4.70899i	0.165318	+	0.207302i
$517$	−11.7395	+	14.7209i	−0.516304	+	0.647425i
$518$	−0.125885	−	0.551536i	−0.00553105	−	0.0242331i
$519$	24.7526	+	5.64962i	1.08652	+	0.247991i
$520$	−0.588829	−	0.469575i	−0.0258219	−	0.0205922i
$521$	11.6310			0.509565			0.254783	−	0.966998i	$-0.417996\pi$
$521$	11.6310			0.509565			0.254783	+	0.966998i	$0.417996\pi$
$522$		0			0
$523$	−0.747202			−0.0326728			−0.0163364	−	0.999867i	$-0.505200\pi$
$523$	−0.747202			−0.0326728			−0.0163364	+	0.999867i	$0.505200\pi$
$524$	22.8005	+	18.1828i	0.996045	+	0.794319i
$525$	−11.9137	−	2.71923i	−0.519958	−	0.118677i
$526$	−0.282315	−	1.23690i	−0.0123095	−	0.0539315i
$527$	−7.71925	+	9.67963i	−0.336256	+	0.421651i
$528$	13.9465	+	17.4884i	0.606944	+	0.761084i
$529$	2.18507	−	9.57343i	0.0950031	−	0.416236i
$530$	0.314822	−	0.653735i	0.0136750	−	0.0283964i
$531$	−34.6970	−	16.7092i	−1.50572	−	0.725117i
$532$	−1.51647	+	0.346124i	−0.0657472	+	0.0150064i
$533$	10.5653	+	21.9390i	0.457633	+	0.950284i
$534$			1.22134i			0.0528525i
$535$	6.97460	−	3.35879i	0.301538	−	0.145213i
$536$	−0.542601	+	0.432710i	−0.0234368	+	0.0186902i
$537$	46.5754	−	37.1426i	2.00988	−	1.60282i
$538$	0.451089	−	0.217233i	0.0194478	−	0.00936557i
$539$		−	5.15277i		−	0.221946i
$540$	−14.4832	−	30.0748i	−0.623260	−	1.29421i
$541$	−18.7646	+	4.28290i	−0.806753	+	0.184136i	−0.605957	−	0.795497i	$-0.707210\pi$
$541$	−18.7646	+	4.28290i	−0.806753	+	0.184136i	−0.200795	+	0.979633i	$0.564353\pi$
$542$	−0.663510	−	0.319530i	−0.0285002	−	0.0137250i
$543$	−15.8345	+	32.8807i	−0.679524	+	1.41105i
$544$	−0.585499	+	2.56524i	−0.0251031	+	0.109984i
$545$	12.7761	+	16.0207i	0.547266	+	0.686250i
$546$	−0.419203	+	0.525664i	−0.0179402	+	0.0224963i
$547$	5.62909	+	24.6627i	0.240683	+	1.05450i	0.940398	+	0.340077i	$0.110453\pi$
$547$	5.62909	+	24.6627i	0.240683	+	1.05450i	−0.699715	+	0.714422i	$0.746690\pi$
$548$	−5.57637	−	1.27277i	−0.238211	−	0.0543700i
$549$	−38.5025	−	30.7047i	−1.64325	−	1.31045i
$550$	0.152658			0.00650938
$551$		0			0
$552$	1.84346			0.0784630
$553$	−16.5005	−	13.1587i	−0.701672	−	0.559565i
$554$	−0.0439512	−	0.0100316i	−0.00186731	−	0.000426201i
$555$	7.70789	+	33.7705i	0.327182	+	1.43348i
$556$	−27.7437	+	34.7895i	−1.17660	+	1.47540i
$557$	−22.5353	−	28.2584i	−0.954851	−	1.19735i	−0.980269	−	0.197668i	$-0.936663\pi$
$557$	−22.5353	−	28.2584i	−0.954851	−	1.19735i	0.0254181	−	0.999677i	$-0.491908\pi$
$558$	0.136171	−	0.596606i	0.00576460	−	0.0252564i
$559$	−1.11350	+	2.31220i	−0.0470959	+	0.0977956i
$560$	−12.8590	−	6.19257i	−0.543392	−	0.261684i
$561$	−28.6085	+	6.52971i	−1.20785	+	0.275685i
$562$	0.543918	+	1.12946i	0.0229438	+	0.0476432i
$563$			8.84332i			0.372701i	0.982483	+	0.186351i	$0.0596661\pi$
$563$			8.84332i			0.372701i	−0.982483	+	0.186351i	$0.940334\pi$
$564$	−55.4230	+	26.6903i	−2.33373	+	1.12387i
$565$	−15.5534	+	12.4034i	−0.654338	+	0.521817i
$566$	0.877250	−	0.699584i	0.0368736	−	0.0294057i
$567$	−19.4879	+	9.38486i	−0.818413	+	0.394127i
$568$			0.382860i			0.0160644i
$569$	7.15474	+	14.8570i	0.299942	+	0.622837i	0.995408	−	0.0957226i	$-0.0305162\pi$
$569$	7.15474	+	14.8570i	0.299942	+	0.622837i	−0.695466	+	0.718559i	$0.744802\pi$
$570$	−0.0817555	+	0.0186602i	−0.00342436	+	0.000781588i
$571$	20.3900	+	9.81931i	0.853295	+	0.410925i	0.808800	−	0.588084i	$-0.200118\pi$
$571$	20.3900	+	9.81931i	0.853295	+	0.410925i	0.0444957	+	0.999010i	$0.485832\pi$
$572$	−4.13898	+	8.59467i	−0.173059	+	0.359361i
$573$	7.82894	−	34.3008i	0.327058	−	1.43294i
$574$	−0.507321	−	0.636160i	−0.0211752	−	0.0265528i
$575$	−4.44860	+	5.57837i	−0.185520	+	0.232634i
$576$	10.9207	+	47.8466i	0.455028	+	1.99361i
$577$	40.1086	+	9.15453i	1.66974	+	0.381108i	0.949784	−	0.312907i	$-0.101303\pi$
$577$	40.1086	+	9.15453i	1.66974	+	0.381108i	0.719960	+	0.694015i	$0.244160\pi$
$578$	−0.340747	−	0.271737i	−0.0141732	−	0.0113028i
$579$	−57.6859			−2.39734
$580$		0			0
$581$	−32.0794			−1.33088
$582$	0.514112	+	0.409991i	0.0213106	+	0.0169947i
$583$	−17.9279	−	4.09192i	−0.742497	−	0.169470i
$584$	−0.338255	−	1.48199i	−0.0139971	−	0.0613253i
$585$	17.2678	−	21.6532i	0.713936	−	0.895248i
$586$	−0.151956	−	0.190547i	−0.00627724	−	0.00787141i
$587$	5.82733	−	25.5312i	0.240520	−	1.05379i	−0.700026	−	0.714118i	$-0.746828\pi$
$587$	5.82733	−	25.5312i	0.240520	−	1.05379i	0.940545	−	0.339668i	$-0.110315\pi$
$588$	7.30422	−	15.1674i	0.301221	−	0.625491i
$589$	0.807869	+	0.389049i	0.0332877	+	0.0160305i
$590$	−0.444847	+	0.101533i	−0.0183141	+	0.00418007i
$591$	21.9473	+	45.5741i	0.902792	+	1.87467i
$592$		−	26.2001i		−	1.07682i
$593$	−28.3677	+	13.6611i	−1.16492	+	0.560996i	−0.913483	−	0.406877i	$-0.866618\pi$
$593$	−28.3677	+	13.6611i	−1.16492	+	0.560996i	−0.251438	+	0.967873i	$0.580903\pi$
$594$	0.582359	−	0.464416i	0.0238945	−	0.0190552i
$595$	14.6385	−	11.6738i	0.600122	−	0.478581i
$596$	7.62672	−	3.67284i	0.312403	−	0.150445i
$597$			26.9726i			1.10392i
$598$	0.170328	+	0.353690i	0.00696524	+	0.0144635i
$599$	−13.8236	+	3.15514i	−0.564816	+	0.128916i	−0.495389	−	0.868671i	$-0.664974\pi$
$599$	−13.8236	+	3.15514i	−0.564816	+	0.128916i	−0.0694275	+	0.997587i	$0.522117\pi$
$600$	0.899106	+	0.432987i	0.0367058	+	0.0176766i
$601$	6.08447	−	12.6345i	0.248191	−	0.515373i	−0.739237	−	0.673445i	$-0.764814\pi$
$601$	6.08447	−	12.6345i	0.248191	−	0.515373i	0.987428	+	0.158072i	$0.0505280\pi$
$602$	0.0190824	−	0.0836053i	0.000777740	−	0.00340750i
$603$	−15.9121	−	19.9532i	−0.647993	−	0.812557i
$604$	−9.71115	+	12.1774i	−0.395141	+	0.495491i
$605$	−2.93468	−	12.8577i	−0.119312	−	0.522739i
$606$	−1.04766	−	0.239121i	−0.0425581	−	0.00971361i
$607$	14.3075	+	11.4099i	0.580725	+	0.463113i	0.869259	−	0.494357i	$-0.164596\pi$
$607$	14.3075	+	11.4099i	0.580725	+	0.463113i	−0.288534	+	0.957470i	$0.593168\pi$
$608$	0.190564			0.00772840
$609$		0			0
$610$	−0.583488			−0.0236247
$611$	−20.4925	−	16.3422i	−0.829036	−	0.661134i
$612$	−62.8789	−	14.3517i	−2.54173	−	0.580133i
$613$	6.64203	+	29.1006i	0.268269	+	1.17536i	0.912026	+	0.410133i	$0.134518\pi$
$613$	6.64203	+	29.1006i	0.268269	+	1.17536i	−0.643757	+	0.765230i	$0.722625\pi$
$614$	0.134776	−	0.169003i	0.00543911	−	0.00682042i
$615$	31.0632	+	38.9520i	1.25259	+	1.57070i
$616$	0.141925	−	0.621812i	0.00571831	−	0.0250535i
$617$	1.99315	−	4.13882i	0.0802412	−	0.166623i	−0.856988	−	0.515336i	$-0.827667\pi$
$617$	1.99315	−	4.13882i	0.0802412	−	0.166623i	0.937229	+	0.348714i	$0.113381\pi$
$618$	−0.402091	−	0.193637i	−0.0161745	−	0.00778922i
$619$	6.12797	−	1.39867i	0.246304	−	0.0562173i	−0.0975864	−	0.995227i	$-0.531112\pi$
$619$	6.12797	−	1.39867i	0.246304	−	0.0562173i	0.343891	+	0.939010i	$0.388255\pi$
$620$	3.57293	+	7.41926i	0.143492	+	0.297965i
$621$			34.8138i			1.39703i
$622$	0.401511	−	0.193357i	0.0160991	−	0.00775293i
$623$	−15.4410	+	12.3138i	−0.618631	+	0.493342i
$624$	−24.3449	+	19.4144i	−0.974578	+	0.777200i
$625$	10.1909	−	4.90767i	0.407635	−	0.196307i
$626$			0.700923i			0.0280145i
$627$	0.922109	+	1.91478i	0.0368255	+	0.0764689i
$628$	12.3267	−	2.81348i	0.491888	−	0.112270i
$629$	30.9670	+	14.9129i	1.23474	+	0.594617i
$630$	−0.401539	+	0.833804i	−0.0159977	+	0.0332196i
$631$	2.15554	−	9.44402i	0.0858105	−	0.375961i	−0.913728	−	0.406326i	$-0.866810\pi$
$631$	2.15554	−	9.44402i	0.0858105	−	0.375961i	0.999539	+	0.0303651i	$0.00966700\pi$
$632$	1.07458	+	1.34748i	0.0427444	+	0.0535998i
$633$	0.479900	−	0.601775i	0.0190743	−	0.0239184i
$634$	−0.0139188	−	0.0609823i	−0.000552787	−	0.00242192i
$635$	−20.4589	−	4.66960i	−0.811885	−	0.185308i
$636$	−46.9709	−	37.4580i	−1.86252	−	1.48531i
$637$	7.17299			0.284204
$638$		0			0
$639$	−14.0790			−0.556956
$640$	1.82410	+	1.45467i	0.0721039	+	0.0575010i
$641$	−4.67849	−	1.06783i	−0.184789	−	0.0421769i	0.129125	−	0.991628i	$-0.458783\pi$
$641$	−4.67849	−	1.06783i	−0.184789	−	0.0421769i	−0.313914	+	0.949451i	$0.601640\pi$
$642$	0.125581	+	0.550207i	0.00495630	+	0.0217150i
$643$	−7.65128	+	9.59440i	−0.301737	+	0.378366i	−0.909466	−	0.415778i	$-0.863509\pi$
$643$	−7.65128	+	9.59440i	−0.301737	+	0.378366i	0.607729	+	0.794144i	$0.292081\pi$
$644$	9.28899	+	11.6480i	0.366038	+	0.458997i
$645$	−1.16841	+	5.11914i	−0.0460061	+	0.201566i
$646$	−0.0361029	+	0.0749685i	−0.00142045	+	0.00294960i
$647$	−9.57683	−	4.61196i	−0.376504	−	0.181315i	0.236055	−	0.971740i	$-0.424146\pi$
$647$	−9.57683	−	4.61196i	−0.376504	−	0.181315i	−0.612559	+	0.790425i	$0.709860\pi$
$648$	1.72208	−	0.393053i	0.0676495	−	0.0154406i
$649$	5.01737	+	10.4187i	0.196949	+	0.408969i
$650$			0.212510i			0.00833534i
$651$	13.2526	−	6.38211i	0.519410	−	0.250135i
$652$	2.74875	−	2.19206i	0.107650	−	0.0858476i
$653$	−21.9246	+	17.4843i	−0.857974	+	0.684212i	−0.950239	−	0.311523i	$-0.899161\pi$
$653$	−21.9246	+	17.4843i	−0.857974	+	0.684212i	0.0922642	+	0.995735i	$0.470590\pi$
$654$	−1.34593	+	0.648164i	−0.0526299	+	0.0253452i
$655$			25.4238i			0.993391i
$656$	−16.3504	−	33.9519i	−0.638375	−	1.32560i
$657$	54.4977	−	12.4387i	2.12616	−	0.485282i
$658$	0.789109	+	0.380015i	0.0307627	+	0.0148145i
$659$	8.79977	−	18.2729i	0.342790	−	0.711812i	−0.656298	−	0.754502i	$-0.727879\pi$
$659$	8.79977	−	18.2729i	0.342790	−	0.711812i	0.999088	+	0.0426903i	$0.0135929\pi$
$660$	−4.34310	+	19.0284i	−0.169055	+	0.740678i
$661$	−19.5336	−	24.4943i	−0.759768	−	0.952719i	0.240069	−	0.970756i	$-0.422830\pi$
$661$	−19.5336	−	24.4943i	−0.759768	−	0.952719i	−0.999837	+	0.0180369i	$0.994258\pi$
$662$	0.781444	−	0.979900i	0.0303717	−	0.0380849i
$663$	−9.08978	−	39.8249i	−0.353018	−	1.54667i
$664$	2.55402	+	0.582939i	0.0991153	+	0.0226224i
$665$	−1.06019	−	0.845473i	−0.0411124	−	0.0327860i
$666$	−1.69887			−0.0658297
$667$		0			0
$668$	27.8161			1.07624
$669$	−21.6756	−	17.2857i	−0.838028	−	0.668305i
$670$	−0.294800	−	0.0672863i	−0.0113891	−	0.00259950i
$671$	3.29054	+	14.4168i	0.127030	+	0.556555i
$672$	1.94908	−	2.44407i	0.0751875	−	0.0942821i
$673$	−25.3813	−	31.8271i	−0.978376	−	1.22685i	−0.973929	−	0.226855i	$-0.927156\pi$
$673$	−25.3813	−	31.8271i	−0.978376	−	1.22685i	−0.00444768	−	0.999990i	$-0.501416\pi$
$674$	−0.00878626	+	0.0384951i	−0.000338434	+	0.00148278i
$675$	−8.17695	+	16.9796i	−0.314731	+	0.653546i
$676$	11.4402	+	5.50933i	0.440009	+	0.211897i
$677$	8.07381	−	1.84280i	0.310302	−	0.0708244i	−0.0645342	−	0.997915i	$-0.520556\pi$
$677$	8.07381	−	1.84280i	0.310302	−	0.0708244i	0.374836	+	0.927091i	$0.377699\pi$
$678$	−0.629261	−	1.30667i	−0.0241666	−	0.0501825i
$679$			10.6334i			0.408071i
$680$	−1.37759	+	0.663412i	−0.0528282	+	0.0254407i
$681$	−11.3967	+	9.08854i	−0.436721	+	0.348274i
$682$	−0.143664	+	0.114569i	−0.00550120	+	0.00438706i
$683$	−3.03215	+	1.46021i	−0.116022	+	0.0558733i	−0.490994	−	0.871163i	$-0.663366\pi$
$683$	−3.03215	+	1.46021i	−0.116022	+	0.0558733i	0.374972	+	0.927036i	$0.377652\pi$
$684$			4.67109i			0.178604i
$685$	−2.16352	−	4.49260i	−0.0826640	−	0.171654i
$686$	−0.821550	+	0.187513i	−0.0313669	+	0.00715930i
$687$	18.7297	+	9.01976i	0.714584	+	0.344125i
$688$	1.72320	−	3.57826i	0.0656964	−	0.136420i
$689$	5.69622	−	24.9568i	0.217009	−	0.950777i
$690$	0.500786	+	0.627966i	0.0190646	+	0.0239062i
$691$	0.657864	−	0.824935i	0.0250263	−	0.0313820i	−0.769161	−	0.639055i	$-0.779326\pi$
$691$	0.657864	−	0.824935i	0.0250263	−	0.0313820i	0.794187	+	0.607673i	$0.207897\pi$
$692$	−3.72863	−	16.3362i	−0.141741	−	0.621009i
$693$	22.8661	+	5.21903i	0.868610	+	0.198255i
$694$	0.283787	+	0.226313i	0.0107724	+	0.00859072i
$695$	−38.7922			−1.47147
$696$		0			0
$697$	49.4358			1.87251
$698$	−1.13342	−	0.903874i	−0.0429007	−	0.0342121i
$699$	50.8603	+	11.6085i	1.92371	+	0.439075i
$700$	1.79464	+	7.86282i	0.0678309	+	0.297187i
$701$	−8.76970	+	10.9969i	−0.331227	+	0.415345i	−0.919359	−	0.393419i	$-0.871292\pi$
$701$	−8.76970	+	10.9969i	−0.331227	+	0.415345i	0.588132	+	0.808765i	$0.299863\pi$
$702$	0.646497	+	0.810682i	0.0244005	+	0.0305972i
$703$	0.553919	−	2.42688i	0.0208914	−	0.0915314i
$704$	6.39400	−	13.2773i	0.240983	−	0.500406i
$705$	−48.3170	−	23.2682i	−1.81972	−	0.876333i
$706$	0.589813	−	0.134621i	0.0221979	−	0.00506653i
$707$	−7.53955	−	15.6560i	−0.283554	−	0.588806i
$708$			37.7800i			1.41986i
$709$	3.67395	−	1.76928i	0.137978	−	0.0664467i	−0.363621	−	0.931547i	$-0.618460\pi$
$709$	3.67395	−	1.76928i	0.137978	−	0.0664467i	0.501599	+	0.865100i	$0.332745\pi$
$710$	−0.130419	+	0.104006i	−0.00489454	+	0.00390327i
$711$	−49.5512	+	39.5158i	−1.85832	+	1.48196i
$712$	1.45311	−	0.699780i	0.0544575	−	0.0262253i
$713$		−	8.58835i		−	0.321636i
$714$	0.592246	+	1.22981i	0.0221643	+	0.0460245i
$715$	−8.10777	+	1.85055i	−0.303213	+	0.0692065i
$716$	−35.4229	−	17.0587i	−1.32381	−	0.637515i
$717$	27.9869	−	58.1154i	1.04519	−	2.17036i
$718$	−0.208057	+	0.911559i	−0.00776463	+	0.0340191i
$719$	5.19082	+	6.50908i	0.193585	+	0.242748i	0.869145	−	0.494557i	$-0.164670\pi$
$719$	5.19082	+	6.50908i	0.193585	+	0.242748i	−0.675560	+	0.737305i	$0.736098\pi$
$720$	−26.7230	+	33.5095i	−0.995906	+	1.24883i
$721$	−1.60588	−	7.03580i	−0.0598059	−	0.262027i
$722$	−0.771106	−	0.176000i	−0.0286976	−	0.00655003i
$723$	−21.2883	−	16.9769i	−0.791720	−	0.631376i
$724$	24.0858			0.895144
$725$		0			0
$726$	0.961467			0.0356834
$727$	28.8392	+	22.9985i	1.06959	+	0.852968i	0.989603	−	0.143828i	$-0.0459411\pi$
$727$	28.8392	+	22.9985i	1.06959	+	0.852968i	0.0799858	+	0.996796i	$0.474513\pi$
$728$	0.865603	+	0.197568i	0.0320814	+	0.00732237i
$729$	−4.92810	−	21.5914i	−0.182522	−	0.799682i
$730$	0.412944	−	0.517816i	0.0152838	−	0.0191652i
$731$	3.24847	+	4.07345i	0.120149	+	0.150662i
$732$	−10.7504	+	47.1008i	−0.397348	+	1.74090i
$733$	−4.39963	+	9.13593i	−0.162504	+	0.337443i	−0.966282	−	0.257486i	$-0.917106\pi$
$733$	−4.39963	+	9.13593i	−0.162504	+	0.337443i	0.803778	+	0.594930i	$0.202820\pi$
$734$	0.191998	+	0.0924615i	0.00708679	+	0.00341282i
$735$	14.3081	−	3.26573i	0.527763	−	0.120458i
$736$	−0.791941	−	1.64448i	−0.0291913	−	0.0606165i
$737$			7.66338i			0.282284i
$738$	−2.20151	+	1.06019i	−0.0810387	+	0.0390262i
$739$	9.53463	−	7.60362i	0.350737	−	0.279704i	−0.432234	−	0.901761i	$-0.642275\pi$
$739$	9.53463	−	7.60362i	0.350737	−	0.279704i	0.782971	+	0.622058i	$0.213703\pi$
$740$	17.8734	−	14.2536i	0.657041	−	0.523972i
$741$	−2.66550	+	1.28364i	−0.0979195	+	0.0471555i
$742$			0.855386i			0.0314022i
$743$	14.2079	+	29.5030i	0.521237	+	1.08236i	0.980944	+	0.194289i	$0.0622400\pi$
$743$	14.2079	+	29.5030i	0.521237	+	1.08236i	−0.459707	+	0.888070i	$0.652046\pi$
$744$	−1.17109	+	0.267293i	−0.0429341	+	0.00979943i
$745$	6.64887	+	3.20192i	0.243596	+	0.117309i
$746$	0.464263	−	0.964051i	0.0169979	−	0.0352964i
$747$	−21.4366	+	93.9197i	−0.784323	+	3.43634i
$748$	12.0749	+	15.1414i	0.441501	+	0.553625i
$749$	−5.68996	+	7.13499i	−0.207907	+	0.260707i
$750$	0.342902	+	1.50235i	0.0125210	+	0.0548581i
$751$	−46.6110	−	10.6387i	−1.70086	−	0.388210i	−0.741624	−	0.670816i	$-0.765944\pi$
$751$	−46.6110	−	10.6387i	−1.70086	−	0.388210i	−0.959236	+	0.282605i	$0.908801\pi$
$752$	31.7133	+	25.2905i	1.15646	+	0.922250i
$753$	19.6882			0.717478
$754$		0			0
$755$	−13.5785			−0.494171
$756$	30.7664	+	24.5353i	1.11896	+	0.892342i
$757$	−14.4846	−	3.30601i	−0.526450	−	0.120159i	−0.0489682	−	0.998800i	$-0.515593\pi$
$757$	−14.4846	−	3.30601i	−0.526450	−	0.120159i	−0.477482	+	0.878641i	$0.658450\pi$
$758$	0.0776493	+	0.340204i	0.00282035	+	0.0123568i
$759$	12.6916	−	15.9148i	0.460676	−	0.577670i
$760$	0.0690439	+	0.0865783i	0.00250448	+	0.00314052i
$761$	−4.08433	+	17.8946i	−0.148057	+	0.648680i	0.845367	+	0.534186i	$0.179382\pi$
$761$	−4.08433	+	17.8946i	−0.148057	+	0.648680i	−0.993424	+	0.114494i	$0.963475\pi$
$762$	0.663784	−	1.37836i	0.0240464	−	0.0499328i
$763$	−21.7644	−	10.4812i	−0.787925	−	0.379445i
$764$	−22.6378	+	5.16694i	−0.819008	+	0.186933i
$765$	−24.3958	−	50.6585i	−0.882033	−	1.83156i
$766$		−	1.06216i		−	0.0383772i
$767$	−14.5035	+	6.98451i	−0.523690	+	0.252196i
$768$	37.5421	−	29.9388i	1.35468	−	1.08032i
$769$	10.2099	−	8.14215i	0.368180	−	0.293614i	−0.421870	−	0.906656i	$-0.638626\pi$
$769$	10.2099	−	8.14215i	0.368180	−	0.293614i	0.790050	+	0.613043i	$0.210055\pi$
$770$	0.250372	−	0.120573i	0.00902277	−	0.00434513i
$771$			17.5232i			0.631082i
$772$	16.5186	+	34.3012i	0.594517	+	1.23453i
$773$	29.5266	−	6.73926i	1.06200	−	0.242394i	0.344380	−	0.938830i	$-0.388089\pi$
$773$	29.5266	−	6.73926i	1.06200	−	0.242394i	0.717619	+	0.696436i	$0.245232\pi$
$774$	−0.232022	−	0.111736i	−0.00833985	−	0.00401626i
$775$	2.01720	−	4.18877i	0.0724601	−	0.150465i
$776$	0.193227	−	0.846581i	0.00693643	−	0.0303905i
$777$	−25.4603	−	31.9262i	−0.913384	−	1.14535i
$778$	0.714615	−	0.896099i	0.0256202	−	0.0321267i
$779$	−0.796706	−	3.49060i	−0.0285449	−	0.125064i
$780$	−26.4887	−	6.04587i	−0.948447	−	0.216477i
$781$	3.30526	+	2.63586i	0.118272	+	0.0943184i
$782$	0.796981			0.0285000
$783$		0			0
$784$	−11.1006			−0.396451
$785$	8.61780	+	6.87246i	0.307582	+	0.245289i
$786$	−1.80700	−	0.412436i	−0.0644535	−	0.0147111i
$787$	−0.659533	−	2.88960i	−0.0235098	−	0.103003i	0.961812	−	0.273712i	$-0.0882515\pi$
$787$	−0.659533	−	2.88960i	−0.0235098	−	0.103003i	−0.985322	+	0.170709i	$0.945394\pi$
$788$	20.8146	−	26.1007i	0.741489	−	0.929798i
$789$	−57.0986	−	71.5994i	−2.03276	−	2.54901i
$790$	−0.167097	+	0.732099i	−0.00594504	+	0.0260469i
$791$	10.1755	−	21.1297i	0.361800	−	0.751285i
$792$	−1.72566	−	0.831032i	−0.0613185	−	0.0295294i
$793$	−20.0691	+	4.58065i	−0.712676	+	0.162664i
$794$	−0.204293	−	0.424219i	−0.00725010	−	0.0150550i
$795$		−	52.3751i		−	1.85755i
$796$	16.0385	−	7.72373i	0.568469	−	0.273760i
$797$	18.7344	−	14.9402i	0.663607	−	0.529209i	−0.232753	−	0.972536i	$-0.574773\pi$
$797$	18.7344	−	14.9402i	0.663607	−	0.529209i	0.896360	+	0.443327i	$0.146202\pi$
$798$	0.0772908	−	0.0616373i	0.00273606	−	0.00218194i
$799$	−47.9430	+	23.0881i	−1.69610	+	0.816799i
$800$		−	0.988067i		−	0.0349334i
$801$	25.7332	+	53.4355i	0.909237	+	1.88805i
$802$	1.36182	−	0.310828i	0.0480877	−	0.0109757i
$803$	−15.1229	−	7.28283i	−0.533677	−	0.257005i
$804$	−10.8631	+	22.5574i	−0.383111	+	0.795538i
$805$	−2.89015	+	12.6626i	−0.101864	+	0.446296i
$806$	−0.159487	−	0.199990i	−0.00561768	−	0.00704435i
$807$	22.5328	−	28.2552i	0.793191	−	0.994630i
$808$	0.315768	+	1.38347i	0.0111087	+	0.0486703i
$809$	47.5397	+	10.8506i	1.67141	+	0.381487i	0.950299	−	0.311337i	$-0.100777\pi$
$809$	47.5397	+	10.8506i	1.67141	+	0.381487i	0.721106	+	0.692825i	$0.243634\pi$
$810$	0.601702	+	0.479841i	0.0211417	+	0.0168599i
$811$	−23.3346			−0.819389			−0.409695	−	0.912223i	$-0.634365\pi$
$811$	−23.3346			−0.819389			−0.409695	+	0.912223i	$0.634365\pi$
$812$		0			0
$813$	−53.1583			−1.86434
$814$	0.398835	+	0.318060i	0.0139792	+	0.0111480i
$815$	2.98817	+	0.682030i	0.104671	+	0.0238905i
$816$	14.0670	+	61.6314i	0.492443	+	2.15753i
$817$	0.235269	−	0.295018i	0.00823102	−	0.0103214i
$818$	0.420585	+	0.527396i	0.0147054	+	0.0184400i
$819$	−7.26523	+	31.8310i	−0.253868	+	1.11227i
$820$	14.2666	−	29.6249i	0.498211	−	1.03455i
$821$	33.0050	+	15.8944i	1.15188	+	0.554718i	0.909599	−	0.415487i	$-0.136389\pi$
$821$	33.0050	+	15.8944i	1.15188	+	0.554718i	0.242284	+	0.970205i	$0.422103\pi$
$822$	0.354409	−	0.0808916i	0.0123614	−	0.00282142i
$823$	−11.6578	−	24.2077i	−0.406366	−	0.843828i	−0.999257	−	0.0385451i	$-0.987728\pi$
$823$	−11.6578	−	24.2077i	−0.406366	−	0.843828i	0.592891	−	0.805283i	$-0.297987\pi$
$824$			0.589341i			0.0205307i
$825$	9.92805	−	4.78110i	0.345650	−	0.166456i
$826$	0.420554	−	0.335381i	0.0146329	−	0.0116694i
$827$	−1.99392	+	1.59010i	−0.0693355	+	0.0552932i	−0.657544	−	0.753416i	$-0.728405\pi$
$827$	−1.99392	+	1.59010i	−0.0693355	+	0.0552932i	0.588209	+	0.808709i	$0.299833\pi$
$828$	40.3094	−	19.4120i	1.40085	−	0.674614i
$829$		−	29.2663i		−	1.01646i	−0.861221	−	0.508230i	$-0.830300\pi$
$829$		−	29.2663i		−	1.01646i	0.861221	−	0.508230i	$-0.169700\pi$
$830$	0.495238	+	1.02837i	0.0171900	+	0.0356953i
$831$	−3.17252	+	0.724106i	−0.110053	+	0.0251190i
$832$	18.4828	+	8.90086i	0.640777	+	0.308582i
$833$	6.31841	−	13.1203i	0.218920	−	0.454592i
$834$	0.629303	−	2.75716i	0.0217910	−	0.0954726i
$835$	15.1194	+	18.9591i	0.523229	+	0.656108i
$836$	0.874518	−	1.09661i	0.0302458	−	0.0379271i
$837$	−5.04782	−	22.1160i	−0.174478	−	0.764439i
$838$	1.14814	+	0.262056i	0.0396619	+	0.00905256i
$839$	−36.2667	−	28.9217i	−1.25206	−	0.998488i	−0.999522	−	0.0309019i	$-0.990162\pi$
$839$	−36.2667	−	28.9217i	−1.25206	−	0.998488i	−0.252542	−	0.967586i	$-0.581267\pi$
$840$	1.81658			0.0626781
$841$		0			0
$842$	1.27925			0.0440860
$843$	70.7467	+	56.4186i	2.43665	+	1.94316i
$844$	−0.495249	−	0.113037i	−0.0170472	−	0.00389091i
$845$	2.46324	+	10.7921i	0.0847379	+	0.371261i
$846$	1.63989	−	2.05635i	0.0563805	−	0.0706989i
$847$	9.69371	+	12.1555i	0.333080	+	0.417669i
$848$	−8.81523	+	38.6221i	−0.302716	+	1.32629i
$849$	35.1412	−	72.9715i	1.20604	−	2.50438i
$850$	0.388709	+	0.187192i	0.0133326	+	0.00642064i
$851$	−23.2448	+	5.30548i	−0.796822	+	0.181869i
$852$	5.99273	+	12.4440i	0.205308	+	0.426326i
$853$		−	51.5353i		−	1.76453i	−0.470749	−	0.882267i	$-0.656016\pi$
$853$		−	51.5353i		−	1.76453i	0.470749	−	0.882267i	$-0.343984\pi$
$854$	0.619744	−	0.298453i	0.0212072	−	0.0102128i
$855$	−3.18377	+	2.53897i	−0.108882	+	0.0868309i
$856$	0.582665	−	0.464659i	0.0199151	−	0.0158817i
$857$	−15.5150	+	7.47163i	−0.529982	+	0.255226i	−0.679684	−	0.733505i	$-0.737883\pi$
$857$	−15.5150	+	7.47163i	−0.529982	+	0.255226i	0.149701	+	0.988731i	$0.452169\pi$
$858$		−	0.606280i		−	0.0206981i
$859$	−6.13784	−	12.7454i	−0.209420	−	0.434866i	0.769628	−	0.638492i	$-0.220442\pi$
$859$	−6.13784	−	12.7454i	−0.209420	−	0.434866i	−0.979049	+	0.203626i	$0.934727\pi$
$860$	3.37853	−	0.771127i	0.115207	−	0.0262952i
$861$	−52.9172	−	25.4836i	−1.80341	−	0.868477i
$862$	−0.177001	+	0.367547i	−0.00602869	+	0.0125187i
$863$	−4.14122	+	18.1439i	−0.140969	+	0.617624i	0.854242	+	0.519875i	$0.174021\pi$
$863$	−4.14122	+	18.1439i	−0.140969	+	0.617624i	−0.995211	+	0.0977493i	$0.968836\pi$
$864$	−3.00589	−	3.76926i	−0.102262	−	0.128233i
$865$	9.10788	−	11.4209i	0.309677	−	0.388323i
$866$	0.216820	+	0.949949i	0.00736783	+	0.0322806i
$867$	−30.6708	−	7.00040i	−1.04163	−	0.237746i
$868$	−7.58987	−	6.05272i	−0.257617	−	0.205443i
$869$	19.0310			0.645583
$870$		0			0
$871$	−10.6679			−0.361469
$872$	1.54233	+	1.22996i	0.0522298	+	0.0416518i
$873$	31.1315	+	7.10557i	1.05364	+	0.240487i
$874$	−0.0128441	−	0.0562738i	−0.000434459	−	0.00190349i
$875$	−15.5366	+	19.4822i	−0.525231	+	0.658619i
$876$	−34.1913	−	42.8745i	−1.15522	−	1.44859i
$877$	−1.89286	+	8.29317i	−0.0639174	+	0.280041i	−0.996779	−	0.0801937i	$-0.974446\pi$
$877$	−1.89286	+	8.29317i	−0.0639174	+	0.280041i	0.932862	+	0.360234i	$0.117303\pi$
$878$	0.248016	−	0.515010i	0.00837013	−	0.0173808i
$879$	−15.8501	−	7.63299i	−0.534610	−	0.257454i
$880$	12.5473	−	2.86383i	0.422968	−	0.0965396i
$881$	−13.5226	−	28.0800i	−0.455588	−	0.946038i	−0.994604	−	0.103743i	$-0.966918\pi$
$881$	−13.5226	−	28.0800i	−0.455588	−	0.946038i	0.539016	−	0.842295i	$-0.318796\pi$
$882$			0.719788i			0.0242365i
$883$	18.3332	−	8.82880i	0.616961	−	0.297113i	−0.0991789	−	0.995070i	$-0.531622\pi$
$883$	18.3332	−	8.82880i	0.616961	−	0.297113i	0.716140	+	0.697957i	$0.245907\pi$
$884$	−21.0778	+	16.8090i	−0.708925	+	0.565348i
$885$	−25.7505	+	20.5353i	−0.865592	+	0.690287i
$886$	0.346670	−	0.166948i	0.0116466	−	0.00560871i
$887$		−	11.2240i		−	0.376866i	−0.982086	−	0.188433i	$-0.939659\pi$
$887$		−	11.2240i		−	0.376866i	0.982086	−	0.188433i	$-0.0603408\pi$
$888$	1.44688	+	3.00448i	0.0485542	+	0.100824i
$889$	24.1186	−	5.50491i	0.808911	−	0.184629i
$890$	0.633120	+	0.304895i	0.0212222	+	0.0102201i
$891$	8.46265	−	17.5729i	0.283509	−	0.588713i
$892$	−4.07155	+	17.8386i	−0.136325	+	0.597281i
$893$	2.40287	+	3.01310i	0.0804089	+	0.100830i
$894$	−0.335437	+	0.420625i	−0.0112187	+	0.0140678i
$895$	−7.62701	−	33.4161i	−0.254943	−	1.11698i
$896$	−2.68150	−	0.612036i	−0.0895828	−	0.0204467i
$897$	22.1544	+	17.6675i	0.739714	+	0.589902i
$898$	0.744296			0.0248375
$899$		0			0
$900$	24.2194			0.807314
$901$	−40.6315	−	32.4026i	−1.35363	−	1.07949i
$902$	0.715327	+	0.163269i	0.0238178	+	0.00543625i
$903$	−1.37742	−	6.03486i	−0.0458376	−	0.200828i
$904$	−1.19409	+	1.49735i	−0.0397149	+	0.0498010i
$905$	13.0918	+	16.4167i	0.435188	+	0.545708i
$906$	0.220275	−	0.965089i	0.00731816	−	0.0320629i
$907$	−17.7000	+	36.7544i	−0.587718	+	1.22041i	0.369011	+	0.929425i	$0.379697\pi$
$907$	−17.7000	+	36.7544i	−0.587718	+	1.22041i	−0.956728	+	0.290983i	$0.906018\pi$
$908$	8.66772	+	4.17416i	0.287648	+	0.138524i
$909$	−50.8747	+	11.6118i	−1.68741	+	0.385140i
$910$	0.167845	+	0.348533i	0.00556400	+	0.0115538i
$911$			30.2991i			1.00385i	0.864910	+	0.501926i	$0.167375\pi$
$911$			30.2991i			1.00385i	−0.864910	+	0.501926i	$0.832625\pi$
$912$	4.12501	−	1.98650i	0.136593	−	0.0657796i
$913$	22.6161	−	18.0358i	0.748485	−	0.596897i
$914$	0.0827553	−	0.0659952i	0.00273730	−	0.00218293i
$915$	−37.9468	+	18.2742i	−1.25448	+	0.604127i
$916$		−	13.7199i		−	0.453320i
$917$	−13.0042	−	27.0036i	−0.429438	−	0.891736i
$918$	2.05231	−	0.468427i	0.0677365	−	0.0154604i
$919$	−23.9089	−	11.5139i	−0.788680	−	0.379808i	−0.00422290	−	0.999991i	$-0.501344\pi$
$919$	−23.9089	−	11.5139i	−0.788680	−	0.379808i	−0.784457	+	0.620183i	$0.787058\pi$
$920$	0.460201	−	0.955618i	0.0151724	−	0.0315058i
$921$	3.47205	−	15.2121i	0.114408	−	0.501254i
$922$	−0.261859	−	0.328361i	−0.00862388	−	0.0108140i
$923$	−3.66928	+	4.60114i	−0.120776	+	0.151448i
$924$	−5.12000	−	22.4322i	−0.168436	−	0.737964i
$925$	−12.5832	−	2.87204i	−0.413735	−	0.0944322i
$926$	−0.913270	−	0.728308i	−0.0300119	−	0.0239337i
$927$	−21.6720			−0.711801
$928$		0			0
$929$	4.73988			0.155510			0.0777551	−	0.996972i	$-0.475225\pi$
$929$	4.73988			0.155510			0.0777551	+	0.996972i	$0.475225\pi$
$930$	−0.409183	−	0.326313i	−0.0134176	−	0.0107002i
$931$	−1.02824	−	0.234688i	−0.0336991	−	0.00769159i
$932$	−7.66140	−	33.5668i	−0.250957	−	1.09952i
$933$	20.0563	−	25.1498i	0.656613	−	0.823367i
$934$	0.531624	+	0.666636i	0.0173953	+	0.0218130i
$935$	−3.75694	+	16.4602i	−0.122865	+	0.538307i
$936$	1.15685	−	2.40222i	0.0378128	−	0.0785192i
$937$	−16.8106	−	8.09556i	−0.549179	−	0.264471i	0.138653	−	0.990341i	$-0.455723\pi$
$937$	−16.8106	−	8.09556i	−0.549179	−	0.264471i	−0.687831	+	0.725871i	$0.741437\pi$
$938$	0.347535	−	0.0793226i	0.0113474	−	0.00258997i
$939$	21.9521	+	45.5841i	0.716381	+	1.48758i
$940$			35.3933i			1.15440i
$941$	−20.3307	+	9.79076i	−0.662762	+	0.319170i	−0.734851	−	0.678229i	$-0.762748\pi$
$941$	−20.3307	+	9.79076i	−0.662762	+	0.319170i	0.0720885	+	0.997398i	$0.477034\pi$
$942$	−0.628261	+	0.501022i	−0.0204699	+	0.0163242i
$943$	−26.8114	+	21.3813i	−0.873098	+	0.696272i
$944$	22.4450	−	10.8089i	0.730522	−	0.351801i
$945$			34.3062i			1.11598i
$946$	0.0335516	+	0.0696706i	0.00109086	+	0.00226519i
$947$	−26.9443	+	6.14987i	−0.875573	+	0.199844i	−0.636611	−	0.771185i	$-0.719664\pi$
$947$	−26.9443	+	6.14987i	−0.875573	+	0.199844i	−0.238962	+	0.971029i	$0.576807\pi$
$948$	56.0184	+	26.9770i	1.81939	+	0.876174i
$949$	10.1382	−	21.0521i	0.329099	−	0.683381i
$950$	0.00695298	−	0.0304630i	0.000225584	−	0.000988350i
$951$	−2.81510	−	3.53003i	−0.0912859	−	0.114469i
$952$	1.12385	−	1.40927i	0.0364243	−	0.0456746i
$953$	8.31233	+	36.4187i	0.269263	+	1.17972i	0.910873	+	0.412687i	$0.135410\pi$
$953$	8.31233	+	36.4187i	0.269263	+	1.17972i	−0.641610	+	0.767031i	$0.721733\pi$
$954$	2.50433	+	0.571598i	0.0810808	+	0.0185062i
$955$	−15.8265	−	12.6212i	−0.512134	−	0.408413i
$956$	−42.5708			−1.37684
$957$		0			0
$958$	−0.899769			−0.0290702
$959$	4.59591	+	3.66512i	0.148410	+	0.118353i
$960$	40.9205	+	9.33983i	1.32070	+	0.301442i
$961$	−5.65288	−	24.7669i	−0.182351	−	0.798932i
$962$	−0.442760	+	0.555204i	−0.0142752	+	0.0179005i
$963$	17.0870	+	21.4265i	0.550622	+	0.690458i
$964$	−3.99879	+	17.5199i	−0.128792	+	0.564277i
$965$	−14.4007	+	29.9033i	−0.463574	+	0.962621i
$966$	−0.853106	−	0.410834i	−0.0274482	−	0.0132184i
$967$	38.9506	−	8.89021i	1.25257	−	0.285890i	0.455747	−	0.890109i	$-0.349372\pi$
$967$	38.9506	−	8.89021i	1.25257	−	0.285890i	0.796818	+	0.604219i	$0.206515\pi$
$968$	−0.550883	−	1.14392i	−0.0177061	−	0.0367670i
$969$			6.00624i			0.192948i
$970$	0.340874	−	0.164156i	0.0109448	−	0.00527074i
$971$	11.5571	−	9.21647i	0.370885	−	0.295771i	−0.420255	−	0.907406i	$-0.638059\pi$
$971$	11.5571	−	9.21647i	0.370885	−	0.295771i	0.791140	+	0.611635i	$0.209488\pi$
$972$	4.87637	−	3.88878i	0.156410	−	0.124733i
$973$	41.2026	−	19.8421i	1.32090	−	0.636110i
$974$			0.687749i			0.0220369i
$975$	6.65559	+	13.8205i	0.213150	+	0.442610i
$976$	31.0582	−	7.08882i	0.994147	−	0.226908i
$977$	8.85513	+	4.26441i	0.283301	+	0.136430i	0.570138	−	0.821549i	$-0.306890\pi$
$977$	8.85513	+	4.26441i	0.283301	+	0.136430i	−0.286837	+	0.957979i	$0.592604\pi$
$978$	−0.0969505	+	0.201320i	−0.00310013	+	0.00643750i
$979$	3.96289	−	17.3625i	0.126654	−	0.554909i
$980$	−6.03906	−	7.57274i	−0.192911	−	0.241902i
$981$	−45.2298	+	56.7164i	−1.44408	+	1.81081i
$982$	0.273242	+	1.19715i	0.00871951	+	0.0382027i
$983$	46.1811	+	10.5405i	1.47295	+	0.336191i	0.882280	−	0.470724i	$-0.156007\pi$
$983$	46.1811	+	10.5405i	1.47295	+	0.336191i	0.590667	+	0.806915i	$0.298865\pi$
$984$	3.74995	+	2.99048i	0.119544	+	0.0953332i
$985$	29.1037			0.927320
$986$		0			0
$987$	63.2209			2.01234
$988$	1.52655	+	1.21739i	0.0485661	+	0.0387302i
$989$	−3.52360	−	0.804238i	−0.112044	−	0.0255733i
$990$	−0.185697	−	0.813590i	−0.00590182	−	0.0258576i
$991$	30.5393	−	38.2950i	0.970112	−	1.21648i	−0.00617090	−	0.999981i	$-0.501964\pi$
$991$	30.5393	−	38.2950i	0.970112	−	1.21648i	0.976283	−	0.216501i	$-0.0694643\pi$
$992$	0.741534	+	0.929854i	0.0235437	+	0.0295229i
$993$	20.1313	−	88.2012i	0.638849	−	2.79898i
$994$	0.0853241	−	0.177177i	0.00270632	−	0.00561972i
$995$	13.9821	+	6.73344i	0.443263	+	0.213464i
$996$	92.1376	−	21.0298i	2.91949	−	0.666355i
$997$	−0.504144	−	1.04687i	−0.0159664	−	0.0331546i	0.892833	−	0.450388i	$-0.148714\pi$
$997$	−0.504144	−	1.04687i	−0.0159664	−	0.0331546i	−0.908800	+	0.417233i	$0.863000\pi$
$998$			0.196054i			0.00620597i
$999$	−56.7397	+	27.3244i	−1.79516	+	0.864506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.m.267.9		96
29.2	odd	28		841.2.d.q.778.5		48
29.3	odd	28		841.2.d.q.605.4		48
29.4	even	14	inner	841.2.e.m.270.9		96
29.5	even	14	inner	841.2.e.m.63.9		96
29.6	even	14	inner	841.2.e.m.651.8		96
29.7	even	7	inner	841.2.e.m.236.8		96
29.8	odd	28		841.2.d.p.645.5		48
29.9	even	14	inner	841.2.e.m.196.8		96
29.10	odd	28		841.2.d.p.571.5		48
29.11	odd	28		841.2.a.i.1.5	✓	8
29.12	odd	4		841.2.d.p.574.4		48
29.13	even	14		841.2.b.f.840.8		16
29.14	odd	28		841.2.d.q.190.4		48
29.15	odd	28		841.2.d.p.190.5		48
29.16	even	7		841.2.b.f.840.9		16
29.17	odd	4		841.2.d.q.574.5		48
29.18	odd	28		841.2.a.j.1.4	yes	8
29.19	odd	28		841.2.d.q.571.4		48
29.20	even	7	inner	841.2.e.m.196.9		96
29.21	odd	28		841.2.d.q.645.4		48
29.22	even	14	inner	841.2.e.m.236.9		96
29.23	even	7	inner	841.2.e.m.651.9		96
29.24	even	7	inner	841.2.e.m.63.8		96
29.25	even	7	inner	841.2.e.m.270.8		96
29.26	odd	28		841.2.d.p.605.5		48
29.27	odd	28		841.2.d.p.778.4		48
29.28	even	2	inner	841.2.e.m.267.8		96
87.11	even	28		7569.2.a.bi.1.4		8
87.47	even	28		7569.2.a.bd.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.i.1.5	✓	8	29.11	odd	28
841.2.a.j.1.4	yes	8	29.18	odd	28
841.2.b.f.840.8		16	29.13	even	14
841.2.b.f.840.9		16	29.16	even	7
841.2.d.p.190.5		48	29.15	odd	28
841.2.d.p.571.5		48	29.10	odd	28
841.2.d.p.574.4		48	29.12	odd	4
841.2.d.p.605.5		48	29.26	odd	28
841.2.d.p.645.5		48	29.8	odd	28
841.2.d.p.778.4		48	29.27	odd	28
841.2.d.q.190.4		48	29.14	odd	28
841.2.d.q.571.4		48	29.19	odd	28
841.2.d.q.574.5		48	29.17	odd	4
841.2.d.q.605.4		48	29.3	odd	28
841.2.d.q.645.4		48	29.21	odd	28
841.2.d.q.778.5		48	29.2	odd	28
841.2.e.m.63.8		96	29.24	even	7	inner
841.2.e.m.63.9		96	29.5	even	14	inner
841.2.e.m.196.8		96	29.9	even	14	inner
841.2.e.m.196.9		96	29.20	even	7	inner
841.2.e.m.236.8		96	29.7	even	7	inner
841.2.e.m.236.9		96	29.22	even	14	inner
841.2.e.m.267.8		96	29.28	even	2	inner
841.2.e.m.267.9		96	1.1	even	1	trivial
841.2.e.m.270.8		96	29.25	even	7	inner
841.2.e.m.270.9		96	29.4	even	14	inner
841.2.e.m.651.8		96	29.6	even	14	inner
841.2.e.m.651.9		96	29.23	even	7	inner
7569.2.a.bd.1.5		8	87.47	even	28
7569.2.a.bi.1.4		8	87.11	even	28

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0327942 + 0.0261525i) q^{2} +(2.95182 + 0.673734i) q^{3} +(-0.444650 - 1.94814i) q^{4} +(1.08614 - 1.36198i) q^{5} +(0.0791828 + 0.0992921i) q^{6} +(-0.456981 + 2.00217i) q^{7} +(0.0727657 - 0.151099i) q^{8} +(5.55642 + 2.67583i) q^{9} +(0.0712384 - 0.0162597i) q^{10} +(-0.803488 - 1.66846i) q^{11} -6.05014i q^{12} +(2.32260 - 1.11851i) q^{13} +(-0.0673480 + 0.0537083i) q^{14} +(4.12371 - 3.28855i) q^{15} +(-3.59437 + 1.73096i) q^{16} -5.23359i q^{17} +(0.112239 + 0.233066i) q^{18} +(-0.369537 + 0.0843444i) q^{19} +(-3.13628 - 1.51035i) q^{20} +(-2.69785 + 5.60215i) q^{21} +(0.0172847 - 0.0757291i) q^{22} +(2.26357 + 2.83842i) q^{23} +(0.316592 - 0.396994i) q^{24} +(0.437322 + 1.91603i) q^{25} +(0.105420 + 0.0240614i) q^{26} +(7.49723 + 5.97884i) q^{27} +4.10370 q^{28} +0.221238 q^{30} +(-1.84952 - 1.47494i) q^{31} +(-0.490149 - 0.111873i) q^{32} +(-1.24765 - 5.46633i) q^{33} +(0.136872 - 0.171631i) q^{34} +(2.23056 + 2.79704i) q^{35} +(2.74223 - 12.0145i) q^{36} +(-2.84946 + 5.91697i) q^{37} +(-0.0143245 - 0.00689831i) q^{38} +(7.60949 - 1.73682i) q^{39} +(-0.126760 - 0.263221i) q^{40} +9.44586i q^{41} +(-0.234984 + 0.113163i) q^{42} +(-0.778328 + 0.620696i) q^{43} +(-2.89312 + 2.30719i) q^{44} +(9.67949 - 4.66140i) q^{45} +0.152282i q^{46} +(-4.41153 - 9.16063i) q^{47} +(-11.7761 + 2.68782i) q^{48} +(2.50694 + 1.20728i) q^{49} +(-0.0357675 + 0.0742719i) q^{50} +(3.52605 - 15.4486i) q^{51} +(-3.21176 - 4.02742i) q^{52} +(6.19127 - 7.76360i) q^{53} +(0.0895040 + 0.392143i) q^{54} +(-3.14511 - 0.717851i) q^{55} +(0.269274 + 0.214739i) q^{56} -1.14763 q^{57} -6.24449 q^{59} +(-8.24016 - 6.57131i) q^{60} +(-7.78508 - 1.77689i) q^{61} +(-0.0220801 - 0.0967392i) q^{62} +(-7.89664 + 9.90207i) q^{63} +(4.96161 + 6.22166i) q^{64} +(0.999295 - 4.37820i) q^{65} +(0.102042 - 0.211893i) q^{66} +(-3.72841 - 1.79551i) q^{67} +(-10.1958 + 2.32712i) q^{68} +(4.76930 + 9.90355i) q^{69} +0.150061i q^{70} +(-2.05682 + 0.990512i) q^{71} +(0.808633 - 0.644863i) q^{72} +(7.08653 - 5.65132i) q^{73} +(-0.248190 + 0.119522i) q^{74} +5.95042i q^{75} +(0.328629 + 0.682406i) q^{76} +(3.70771 - 0.846262i) q^{77} +(0.294969 + 0.142050i) q^{78} +(-4.45891 + 9.25903i) q^{79} +(-1.54647 + 6.77552i) q^{80} +(6.56684 + 8.23455i) q^{81} +(-0.247033 + 0.309770i) q^{82} +(3.47592 + 15.2290i) q^{83} +(12.1134 + 2.76480i) q^{84} +(-7.12804 - 5.68442i) q^{85} -0.0417574 q^{86} -0.310570 q^{88} +(7.51879 + 5.99604i) q^{89} +(0.439339 + 0.100276i) q^{90} +(1.17805 + 5.16138i) q^{91} +(4.52315 - 5.67185i) q^{92} +(-4.46573 - 5.59985i) q^{93} +(0.0949009 - 0.415788i) q^{94} +(-0.286494 + 0.594912i) q^{95} +(-1.37146 - 0.660460i) q^{96} +(5.04795 - 1.15216i) q^{97} +(0.0506399 + 0.105155i) q^{98} -11.4207i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} - 2 q^{5} + 6 q^{6} + 16 q^{9} - 8 q^{13} + 4 q^{16} + 14 q^{20} + 50 q^{22} + 14 q^{23} - 50 q^{24} + 26 q^{25} - 300 q^{28} - 312 q^{30} + 24 q^{34} - 10 q^{35} + 38 q^{36} - 28 q^{38}+ \cdots - 4 q^{96}+O(q^{100}) \) 96 * q + 12 * q^4 - 2 * q^5 + 6 * q^6 + 16 * q^9 - 8 * q^13 + 4 * q^16 + 14 * q^20 + 50 * q^22 + 14 * q^23 - 50 * q^24 + 26 * q^25 - 300 * q^28 - 312 * q^30 + 24 * q^34 - 10 * q^35 + 38 * q^36 - 28 * q^38 + 30 * q^42 + 2 * q^45 - 8 * q^49 + 46 * q^51 - 4 * q^52 - 38 * q^53 + 92 * q^54 + 72 * q^57 - 12 * q^59 - 24 * q^62 - 20 * q^63 + 2 * q^64 + 34 * q^65 + 4 * q^67 - 24 * q^71 + 54 * q^74 - 12 * q^78 - 82 * q^80 - 24 * q^81 + 44 * q^82 + 6 * q^83 + 60 * q^86 - 180 * q^88 - 8 * q^92 + 4 * q^93 - 26 * q^94 - 4 * q^96

Introduction

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