LMFDB - Embedded newform 125.2.h.a.9.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			9.5
Character	$\chi$	$=$	125.9
Dual form			125.2.h.a.14.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.926191 - 0.435832i) q^{2} +(-1.75492 + 0.110410i) q^{3} +(-0.606968 - 0.733699i) q^{4} +(1.67095 + 1.48591i) q^{5} +(1.67351 + 0.662589i) q^{6} +(-3.38254 + 1.09905i) q^{7} +(0.751522 + 2.92699i) q^{8} +(0.0912001 - 0.0115212i) q^{9} +O(q^{10})$	\(q+(-0.926191 - 0.435832i) q^{2} +(-1.75492 + 0.110410i) q^{3} +(-0.606968 - 0.733699i) q^{4} +(1.67095 + 1.48591i) q^{5} +(1.67351 + 0.662589i) q^{6} +(-3.38254 + 1.09905i) q^{7} +(0.751522 + 2.92699i) q^{8} +(0.0912001 - 0.0115212i) q^{9} +(-0.900008 - 2.10449i) q^{10} +(-0.758354 + 1.61159i) q^{11} +(1.14619 + 1.22057i) q^{12} +(0.813049 + 6.43595i) q^{13} +(3.61188 + 0.456286i) q^{14} +(-3.09643 - 2.42316i) q^{15} +(0.222765 - 1.16778i) q^{16} +(-3.29203 - 2.72340i) q^{17} +(-0.0894900 - 0.0290771i) q^{18} +(0.144666 - 2.29939i) q^{19} +(0.0759995 - 2.12787i) q^{20} +(5.81473 - 2.30221i) q^{21} +(1.40476 - 1.16212i) q^{22} +(-3.72148 - 6.76935i) q^{23} +(-1.64203 - 5.05364i) q^{24} +(0.584131 + 4.96576i) q^{25} +(2.05196 - 6.31527i) q^{26} +(5.02295 - 0.958178i) q^{27} +(2.85947 + 1.81467i) q^{28} +(-0.198708 + 0.313114i) q^{29} +(1.81180 + 3.59384i) q^{30} +(-4.29518 + 5.19198i) q^{31} +(2.83721 - 3.90508i) q^{32} +(1.15291 - 2.91193i) q^{33} +(1.86210 + 3.95717i) q^{34} +(-7.28514 - 3.18969i) q^{35} +(-0.0638087 - 0.0599203i) q^{36} +(-4.25219 - 0.811148i) q^{37} +(-1.13614 + 2.06663i) q^{38} +(-2.13743 - 11.2048i) q^{39} +(-3.09349 + 6.00754i) q^{40} +(6.07250 + 3.33838i) q^{41} +(-6.38893 - 0.401957i) q^{42} +(2.91369 + 4.01035i) q^{43} +(1.64272 - 0.421778i) q^{44} +(0.169510 + 0.116264i) q^{45} +(0.496501 + 7.89165i) q^{46} +(-1.44821 + 5.64041i) q^{47} +(-0.262000 + 2.07395i) q^{48} +(4.57052 - 3.32068i) q^{49} +(1.62322 - 4.85383i) q^{50} +(6.07793 + 4.41588i) q^{51} +(4.22855 - 4.50295i) q^{52} +(-1.23959 - 3.13084i) q^{53} +(-5.06981 - 1.30171i) q^{54} +(-3.66184 + 1.56603i) q^{55} +(-5.75897 - 9.07468i) q^{56} +4.05122i q^{57} +(0.320507 - 0.203400i) q^{58} +(0.399398 - 0.375059i) q^{59} +(0.101566 + 3.74263i) q^{60} +(-2.72633 + 1.49881i) q^{61} +(6.24099 - 2.93679i) q^{62} +(-0.295825 + 0.139205i) q^{63} +(-6.41332 + 3.52575i) q^{64} +(-8.20469 + 11.9622i) q^{65} +(-2.33693 + 2.19452i) q^{66} +(-4.98886 + 3.16603i) q^{67} +4.06838i q^{68} +(7.27830 + 11.4688i) q^{69} +(5.35726 + 6.12936i) q^{70} +(2.43820 + 0.626023i) q^{71} +(0.102261 + 0.258283i) q^{72} +(9.79412 - 10.4297i) q^{73} +(3.58481 + 2.60452i) q^{74} +(-1.57337 - 8.65001i) q^{75} +(-1.77487 + 1.28952i) q^{76} +(0.793945 - 6.28472i) q^{77} +(-2.90374 + 11.3093i) q^{78} +(0.875507 + 13.9158i) q^{79} +(2.10744 - 1.62028i) q^{80} +(-8.97617 + 2.30469i) q^{81} +(-4.16932 - 5.73857i) q^{82} +(11.1655 + 0.702474i) q^{83} +(-5.21849 - 2.86889i) q^{84} +(-1.45407 - 9.44233i) q^{85} +(-0.950793 - 4.98423i) q^{86} +(0.314145 - 0.571428i) q^{87} +(-5.28701 - 1.00855i) q^{88} +(2.17706 + 2.04440i) q^{89} +(-0.106327 - 0.181561i) q^{90} +(-9.82362 - 20.8763i) q^{91} +(-2.70784 + 6.83923i) q^{92} +(6.96444 - 9.58573i) q^{93} +(3.79959 - 4.59292i) q^{94} +(3.65843 - 3.62721i) q^{95} +(-4.54791 + 7.16635i) q^{96} +(5.28023 + 3.35094i) q^{97} +(-5.68044 + 1.08360i) q^{98} +(-0.0505945 + 0.155714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{50}\right)$

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 $

$2$	−0.926191	−	0.435832i	−0.654916	−	0.308180i	0.0694606	−	0.997585i	$-0.477872\pi$
$2$	−0.926191	−	0.435832i	−0.654916	−	0.308180i	−0.724376	+	0.689405i	$0.757872\pi$
$3$	−1.75492	+	0.110410i	−1.01320	+	0.0637453i	−0.560701	−	0.828019i	$-0.689468\pi$
$3$	−1.75492	+	0.110410i	−1.01320	+	0.0637453i	−0.452501	+	0.891764i	$0.649468\pi$
$4$	−0.606968	−	0.733699i	−0.303484	−	0.366849i
$5$	1.67095	+	1.48591i	0.747270	+	0.664520i
$5$	1.67095	+	1.48591i	0.747270	+	0.664520i
$6$	1.67351	+	0.662589i	0.683207	+	0.270501i
$7$	−3.38254	+	1.09905i	−1.27848	+	0.415403i	−0.868044	−	0.496487i	$-0.834623\pi$
$7$	−3.38254	+	1.09905i	−1.27848	+	0.415403i	−0.410435	+	0.911890i	$0.634623\pi$
$8$	0.751522	+	2.92699i	0.265703	+	1.03485i
$9$	0.0912001	−	0.0115212i	0.0304000	−	0.00384042i
$10$	−0.900008	−	2.10449i	−0.284607	−	0.665498i
$11$	−0.758354	+	1.61159i	−0.228652	+	0.485911i	−0.985925	−	0.167188i	$-0.946531\pi$
$11$	−0.758354	+	1.61159i	−0.228652	+	0.485911i	0.757273	+	0.653099i	$0.226531\pi$
$12$	1.14619	+	1.22057i	0.330876	+	0.352347i
$13$	0.813049	+	6.43595i	0.225499	+	1.78501i	0.546023	+	0.837770i	$0.316141\pi$
$13$	0.813049	+	6.43595i	0.225499	+	1.78501i	−0.320524	+	0.947240i	$0.603859\pi$
$14$	3.61188	+	0.456286i	0.965315	+	0.121948i
$15$	−3.09643	−	2.42316i	−0.799496	−	0.625658i
$16$	0.222765	−	1.16778i	0.0556913	−	0.291944i
$17$	−3.29203	−	2.72340i	−0.798435	−	0.660523i	0.145977	−	0.989288i	$-0.453367\pi$
$17$	−3.29203	−	2.72340i	−0.798435	−	0.660523i	−0.944412	+	0.328765i	$0.893367\pi$
$18$	−0.0894900	−	0.0290771i	−0.0210930	−	0.00685353i
$19$	0.144666	−	2.29939i	0.0331886	−	0.527517i	−0.945949	−	0.324317i	$-0.894866\pi$
$19$	0.144666	−	2.29939i	0.0331886	−	0.527517i	0.979137	−	0.203201i	$-0.0651344\pi$
$20$	0.0759995	−	2.12787i	0.0169940	−	0.475807i
$21$	5.81473	−	2.30221i	1.26888	−	0.502384i
$22$	1.40476	−	1.16212i	0.299496	−	0.247765i
$23$	−3.72148	−	6.76935i	−0.775983	−	1.41151i	−0.907438	−	0.420185i	$-0.861965\pi$
$23$	−3.72148	−	6.76935i	−0.775983	−	1.41151i	0.131456	−	0.991322i	$-0.458035\pi$
$24$	−1.64203	−	5.05364i	−0.335178	−	1.03157i
$25$	0.584131	+	4.96576i	0.116826	+	0.993152i
$26$	2.05196	−	6.31527i	0.402422	−	1.23853i
$27$	5.02295	−	0.958178i	0.966667	−	0.184402i
$28$	2.85947	+	1.81467i	0.540388	+	0.342941i
$29$	−0.198708	+	0.313114i	−0.0368991	+	0.0581437i	−0.862277	−	0.506437i	$-0.830962\pi$
$29$	−0.198708	+	0.313114i	−0.0368991	+	0.0581437i	0.825378	+	0.564581i	$0.190962\pi$
$30$	1.81180	+	3.59384i	0.330787	+	0.656142i
$31$	−4.29518	+	5.19198i	−0.771437	+	0.932507i	−0.999150	−	0.0412209i	$-0.986875\pi$
$31$	−4.29518	+	5.19198i	−0.771437	+	0.932507i	0.227713	+	0.973728i	$0.426875\pi$
$32$	2.83721	−	3.90508i	0.501552	−	0.690328i
$33$	1.15291	−	2.91193i	0.200697	−	0.506902i
$34$	1.86210	+	3.95717i	0.319348	+	0.678648i
$35$	−7.28514	−	3.18969i	−1.23141	−	0.539157i
$36$	−0.0638087	−	0.0599203i	−0.0106348	−	0.00998672i
$37$	−4.25219	−	0.811148i	−0.699055	−	0.133352i	−0.174410	−	0.984673i	$-0.555802\pi$
$37$	−4.25219	−	0.811148i	−0.699055	−	0.133352i	−0.524645	+	0.851321i	$0.675802\pi$
$38$	−1.13614	+	2.06663i	−0.184306	+	0.335251i
$39$	−2.13743	−	11.2048i	−0.342262	−	1.79420i
$40$	−3.09349	+	6.00754i	−0.489124	+	0.949875i
$41$	6.07250	+	3.33838i	0.948365	+	0.521368i	0.879313	−	0.476245i	$-0.158002\pi$
$41$	6.07250	+	3.33838i	0.948365	+	0.521368i	0.0690523	+	0.997613i	$0.478002\pi$
$42$	−6.38893	−	0.401957i	−0.985833	−	0.0620233i
$43$	2.91369	+	4.01035i	0.444334	+	0.611573i	0.971168	−	0.238395i	$-0.0766212\pi$
$43$	2.91369	+	4.01035i	0.444334	+	0.611573i	−0.526834	+	0.849968i	$0.676621\pi$
$44$	1.64272	−	0.421778i	0.247649	−	0.0635854i
$45$	0.169510	+	0.116264i	0.0252691	+	0.0173316i
$46$	0.496501	+	7.89165i	0.0732050	+	1.16356i
$47$	−1.44821	+	5.64041i	−0.211243	+	0.822738i	0.771264	+	0.636515i	$0.219625\pi$
$47$	−1.44821	+	5.64041i	−0.211243	+	0.822738i	−0.982507	+	0.186223i	$0.940375\pi$
$48$	−0.262000	+	2.07395i	−0.0378165	+	0.299348i
$49$	4.57052	−	3.32068i	0.652932	−	0.474383i
$50$	1.62322	−	4.85383i	0.229558	−	0.686435i
$51$	6.07793	+	4.41588i	0.851081	+	0.618346i
$52$	4.22855	−	4.50295i	0.586395	−	0.624447i
$53$	−1.23959	−	3.13084i	−0.170271	−	0.430054i	0.819435	−	0.573172i	$-0.194287\pi$
$53$	−1.23959	−	3.13084i	−0.170271	−	0.430054i	−0.989706	+	0.143118i	$0.954287\pi$
$54$	−5.06981	−	1.30171i	−0.689914	−	0.177140i
$55$	−3.66184	+	1.56603i	−0.493763	+	0.211163i
$56$	−5.75897	−	9.07468i	−0.769574	−	1.21265i
$57$			4.05122i			0.536597i
$58$	0.320507	−	0.203400i	0.0420846	−	0.0267077i
$59$	0.399398	−	0.375059i	0.0519971	−	0.0488286i	−0.658113	−	0.752919i	$-0.728645\pi$
$59$	0.399398	−	0.375059i	0.0519971	−	0.0488286i	0.710110	+	0.704091i	$0.248645\pi$
$60$	0.101566	+	3.74263i	0.0131121	+	0.483172i
$61$	−2.72633	+	1.49881i	−0.349071	+	0.191903i	−0.646637	−	0.762798i	$-0.723825\pi$
$61$	−2.72633	+	1.49881i	−0.349071	+	0.191903i	0.297566	+	0.954701i	$0.403825\pi$
$62$	6.24099	−	2.93679i	0.792607	−	0.372972i
$63$	−0.295825	+	0.139205i	−0.0372705	+	0.0175382i
$64$	−6.41332	+	3.52575i	−0.801666	+	0.440719i
$65$	−8.20469	+	11.9622i	−1.01767	+	1.48373i
$66$	−2.33693	+	2.19452i	−0.287656	+	0.270127i
$67$	−4.98886	+	3.16603i	−0.609486	+	0.386792i	−0.804451	−	0.594019i	$-0.797541\pi$
$67$	−4.98886	+	3.16603i	−0.609486	+	0.386792i	0.194965	+	0.980810i	$0.437541\pi$
$68$			4.06838i			0.493363i
$69$	7.27830	+	11.4688i	0.876204	+	1.38068i
$70$	5.35726	+	6.12936i	0.640315	+	0.732599i
$71$	2.43820	+	0.626023i	0.289361	+	0.0742953i	0.390580	−	0.920569i	$-0.372274\pi$
$71$	2.43820	+	0.626023i	0.289361	+	0.0742953i	−0.101219	+	0.994864i	$0.532274\pi$
$72$	0.102261	+	0.258283i	0.0120516	+	0.0304389i
$73$	9.79412	−	10.4297i	1.14631	−	1.22070i	0.174575	−	0.984644i	$-0.444145\pi$
$73$	9.79412	−	10.4297i	1.14631	−	1.22070i	0.971739	−	0.236057i	$-0.0758553\pi$
$74$	3.58481	+	2.60452i	0.416726	+	0.302769i
$75$	−1.57337	−	8.65001i	−0.181677	−	0.998817i
$76$	−1.77487	+	1.28952i	−0.203592	+	0.147918i
$77$	0.793945	−	6.28472i	0.0904784	−	0.716210i
$78$	−2.90374	+	11.3093i	−0.328784	+	1.28053i
$79$	0.875507	+	13.9158i	0.0985023	+	1.56565i	0.668318	+	0.743876i	$0.267015\pi$
$79$	0.875507	+	13.9158i	0.0985023	+	1.56565i	−0.569816	+	0.821773i	$0.692985\pi$
$80$	2.10744	−	1.62028i	0.235619	−	0.181153i
$81$	−8.97617	+	2.30469i	−0.997353	+	0.256077i
$82$	−4.16932	−	5.73857i	−0.460424	−	0.633719i
$83$	11.1655	+	0.702474i	1.22557	+	0.0771066i	0.662348	−	0.749196i	$-0.269560\pi$
$83$	11.1655	+	0.702474i	1.22557	+	0.0771066i	0.563226	+	0.826303i	$0.309560\pi$
$84$	−5.21849	−	2.86889i	−0.569384	−	0.313021i
$85$	−1.45407	−	9.44233i	−0.157716	−	1.02416i
$86$	−0.950793	−	4.98423i	−0.102527	−	0.537464i
$87$	0.314145	−	0.571428i	0.0336799	−	0.0612635i
$88$	−5.28701	−	1.00855i	−0.563597	−	0.107512i
$89$	2.17706	+	2.04440i	0.230768	+	0.216706i	0.791302	−	0.611426i	$-0.209404\pi$
$89$	2.17706	+	2.04440i	0.230768	+	0.216706i	−0.560533	+	0.828132i	$0.689404\pi$
$90$	−0.106327	−	0.181561i	−0.0112079	−	0.0191382i
$91$	−9.82362	−	20.8763i	−1.02979	−	2.18843i
$92$	−2.70784	+	6.83923i	−0.282312	+	0.713039i
$93$	6.96444	−	9.58573i	0.722179	−	0.993994i
$94$	3.79959	−	4.59292i	0.391898	−	0.473723i
$95$	3.65843	−	3.62721i	0.375347	−	0.372144i
$96$	−4.54791	+	7.16635i	−0.464169	+	0.731413i
$97$	5.28023	+	3.35094i	0.536126	+	0.340236i	0.776168	−	0.630527i	$-0.217161\pi$
$97$	5.28023	+	3.35094i	0.536126	+	0.340236i	−0.240041	+	0.970763i	$0.577161\pi$
$98$	−5.68044	+	1.08360i	−0.573811	+	0.109460i
$99$	−0.0505945	+	0.155714i	−0.00508494	+	0.0156498i
$100$	3.28882	−	3.44264i	0.328882	−	0.344264i
$101$	−2.20585	−	6.78891i	−0.219490	−	0.675521i	−0.998804	−	0.0488879i	$-0.984432\pi$
$101$	−2.20585	−	6.78891i	−0.219490	−	0.675521i	0.779314	−	0.626634i	$-0.215568\pi$
$102$	−3.70474	−	6.73890i	−0.366824	−	0.667251i
$103$	−0.663829	+	0.549167i	−0.0654090	+	0.0541110i	−0.669554	−	0.742763i	$-0.733515\pi$
$103$	−0.663829	+	0.549167i	−0.0654090	+	0.0541110i	0.604145	+	0.796874i	$0.293515\pi$
$104$	−18.2269	+	7.21654i	−1.78729	+	0.707640i
$105$	13.1370	+	4.79330i	1.28204	+	0.467778i
$106$	−0.216427	+	3.44001i	−0.0210213	+	0.334123i
$107$	11.3247	+	3.67963i	1.09480	+	0.355723i	0.800100	−	0.599866i	$-0.204780\pi$
$107$	11.3247	+	3.67963i	1.09480	+	0.355723i	0.294702	+	0.955589i	$0.404780\pi$
$108$	−3.75178	−	3.10375i	−0.361016	−	0.298658i
$109$	−0.845347	+	4.43147i	−0.0809696	+	0.424458i	0.918602	+	0.395184i	$0.129319\pi$
$109$	−0.845347	+	4.43147i	−0.0809696	+	0.424458i	−0.999571	+	0.0292732i	$0.990681\pi$
$110$	4.07409	+	0.145511i	0.388449	+	0.0138739i
$111$	7.55179	+	0.954014i	0.716785	+	0.0905510i
$112$	0.529937	+	4.19488i	0.0500743	+	0.396379i
$113$	−7.85043	−	8.35986i	−0.738506	−	0.786429i	0.244569	−	0.969632i	$-0.421354\pi$
$113$	−7.85043	−	8.35986i	−0.738506	−	0.786429i	−0.983075	+	0.183203i	$0.941354\pi$
$114$	1.76565	−	3.75220i	0.165369	−	0.351426i
$115$	3.84026	−	16.8410i	0.358106	−	1.57043i
$116$	0.350341	−	0.0442583i	0.0325283	−	0.00410928i
$117$	0.148300	+	0.577592i	0.0137104	+	0.0533984i
$118$	−0.533381	+	0.173306i	−0.0491017	+	0.0159541i
$119$	14.1286	+	5.59390i	1.29517	+	0.512792i
$120$	4.76553	−	10.8843i	0.435031	−	0.993594i
$121$	4.98956	+	6.03134i	0.453596	+	0.548304i
$122$	3.17833	−	0.199964i	0.287753	−	0.0181039i
$123$	−11.0253	−	5.18812i	−0.994120	−	0.467797i
$124$	6.41639			0.576209
$125$	−6.40263	+	9.16549i	−0.572669	+	0.819787i
$126$	0.334661			0.0298139
$127$	−3.72154	−	1.75122i	−0.330233	−	0.155396i	0.253513	−	0.967332i	$-0.418414\pi$
$127$	−3.72154	−	1.75122i	−0.330233	−	0.155396i	−0.583747	+	0.811936i	$0.698414\pi$
$128$	−2.15824	+	0.135785i	−0.190764	+	0.0120018i
$129$	−5.55607	−	6.71614i	−0.489185	−	0.591323i
$130$	12.8126	−	7.50346i	1.12374	−	0.658097i
$131$	−2.01514	−	0.797851i	−0.176064	−	0.0697085i	0.278439	−	0.960454i	$-0.410183\pi$
$131$	−2.01514	−	0.797851i	−0.176064	−	0.0697085i	−0.454503	+	0.890745i	$0.650183\pi$
$132$	−2.83626	+	0.921557i	−0.246865	+	0.0802112i
$133$	2.03782	+	7.93679i	0.176701	+	0.688207i
$134$	6.00049	−	0.758038i	0.518363	−	0.0654845i
$135$	9.81685	+	5.86259i	0.844900	+	0.504572i
$136$	5.49733	−	11.6824i	0.471392	−	1.00176i
$137$	10.3882	+	11.0623i	0.887524	+	0.945117i	0.998815	−	0.0486709i	$-0.0154985\pi$
$137$	10.3882	+	11.0623i	0.887524	+	0.945117i	−0.111291	+	0.993788i	$0.535499\pi$
$138$	−1.74264	−	13.7944i	−0.148343	−	1.17426i
$139$	−9.64049	−	1.21788i	−0.817695	−	0.103299i	−0.294652	−	0.955605i	$-0.595204\pi$
$139$	−9.64049	−	1.21788i	−0.817695	−	0.103299i	−0.523044	+	0.852306i	$0.675204\pi$
$140$	2.08157	+	7.28114i	0.175925	+	0.615369i
$141$	1.91873	−	10.0583i	0.161586	−	0.847066i
$142$	−1.98540	−	1.64246i	−0.166611	−	0.137832i
$143$	−10.9887	−	3.57043i	−0.918918	−	0.298574i
$144$	0.00686197	−	0.109068i	0.000571831	−	0.00908899i
$145$	−0.797290	+	0.227934i	−0.0662113	+	0.0189289i
$146$	−13.6168	+	5.39128i	−1.12694	+	0.446185i
$147$	−7.65426	+	6.33215i	−0.631312	+	0.522267i
$148$	1.98580	+	3.61216i	0.163232	+	0.296918i
$149$	−2.91017	−	8.95659i	−0.238410	−	0.733752i	−0.996651	−	0.0817767i	$-0.973941\pi$
$149$	−2.91017	−	8.95659i	−0.238410	−	0.733752i	0.758240	−	0.651975i	$-0.226059\pi$
$150$	−2.31271	+	8.69728i	−0.188832	+	0.710130i
$151$	0.144723	−	0.445413i	0.0117774	−	0.0362472i	−0.944995	−	0.327084i	$-0.893934\pi$
$151$	0.144723	−	0.445413i	0.0117774	−	0.0362472i	0.956773	+	0.290837i	$0.0939338\pi$
$152$	6.83902	−	1.30461i	0.554717	−	0.105818i
$153$	−0.331610	−	0.210446i	−0.0268091	−	0.0170136i
$154$	−3.47443	+	5.47482i	−0.279977	+	0.441174i
$155$	−14.8918	+	2.29327i	−1.19614	+	0.184200i
$156$	−6.92359	+	8.36918i	−0.554331	+	0.670071i
$157$	−9.04363	+	12.4475i	−0.721760	+	0.993417i	0.277704	+	0.960667i	$0.410427\pi$
$157$	−9.04363	+	12.4475i	−0.721760	+	0.993417i	−0.999464	+	0.0327506i	$0.989573\pi$
$158$	5.25406	−	13.2703i	0.417991	−	1.05572i
$159$	2.52105	+	5.35751i	0.199932	+	0.424878i
$160$	10.5434	−	2.30935i	0.833532	−	0.182570i
$161$	20.0279	+	18.8075i	1.57842	+	1.48224i
$162$	9.31811	+	1.77752i	0.732100	+	0.139656i
$163$	−9.13183	+	16.6107i	−0.715260	+	1.30105i	0.229506	+	0.973307i	$0.426289\pi$
$163$	−9.13183	+	16.6107i	−0.715260	+	1.30105i	−0.944766	+	0.327746i	$0.893711\pi$
$164$	−1.23645	−	6.48168i	−0.0965502	−	0.506134i
$165$	6.25333	−	3.15255i	0.486821	−	0.245426i
$166$	−10.0352	−	5.51691i	−0.778885	−	0.428196i
$167$	−0.249344	−	0.0156874i	−0.0192948	−	0.00121393i	0.0531402	−	0.998587i	$-0.483077\pi$
$167$	−0.249344	−	0.0156874i	−0.0192948	−	0.00121393i	−0.0724350	+	0.997373i	$0.523077\pi$
$168$	11.1084	+	15.2895i	0.857035	+	1.17961i
$169$	−28.1688	+	7.23252i	−2.16683	+	0.556347i
$170$	−2.76853	+	9.37913i	−0.212336	+	0.719347i
$171$	−0.0132984	−	0.211372i	−0.00101695	−	0.0161640i
$172$	1.17387	−	4.57193i	0.0895069	−	0.348606i
$173$	1.78539	−	14.1328i	0.135741	−	1.07450i	−0.766189	−	0.642616i	$-0.777849\pi$
$173$	1.78539	−	14.1328i	0.135741	−	1.07450i	0.901930	−	0.431883i	$-0.142151\pi$
$174$	−0.540005	+	0.392337i	−0.0409377	+	0.0297430i
$175$	−7.43348	−	16.1549i	−0.561918	−	1.22119i
$176$	1.71304	+	1.24459i	0.129125	+	0.0938148i
$177$	−0.659500	+	0.702296i	−0.0495710	+	0.0527878i
$178$	−1.12536	−	2.84234i	−0.0843493	−	0.213042i
$179$	12.1636	+	3.12307i	0.909147	+	0.233429i	0.674174	−	0.738572i	$-0.264500\pi$
$179$	12.1636	+	3.12307i	0.909147	+	0.233429i	0.234973	+	0.972002i	$0.424500\pi$
$180$	−0.0175846	−	0.194938i	−0.00131068	−	0.0145298i
$181$	−4.93443	−	7.77542i	−0.366773	−	0.577942i	0.609951	−	0.792439i	$-0.291189\pi$
$181$	−4.93443	−	7.77542i	−0.366773	−	0.577942i	−0.976725	+	0.214497i	$0.931189\pi$
$182$			23.6168i			1.75060i
$183$	4.61900	−	2.93131i	0.341446	−	0.216688i
$184$	17.0170	−	15.9800i	1.25451	−	1.17806i
$185$	−5.89989	−	7.67376i	−0.433768	−	0.564186i
$186$	−10.6282	+	5.84289i	−0.779295	+	0.428421i
$187$	6.88552	−	3.24008i	0.503519	−	0.236938i
$188$	5.01738	−	2.36100i	0.365930	−	0.172194i
$189$	−15.9372	+	8.76156i	−1.15926	+	0.637310i
$190$	−4.96926	+	1.76503i	−0.360508	+	0.128048i
$191$	−11.1223	+	10.4445i	−0.804782	+	0.755741i	−0.973196	−	0.229976i	$-0.926135\pi$
$191$	−11.1223	+	10.4445i	−0.804782	+	0.755741i	0.168414	+	0.985716i	$0.446135\pi$
$192$	10.8656	−	6.89550i	0.784155	−	0.497640i
$193$			12.9507i			0.932212i	0.884729	+	0.466106i	$0.154344\pi$
$193$			12.9507i			0.932212i	−0.884729	+	0.466106i	$0.845656\pi$
$194$	−3.43005	−	5.40490i	−0.246264	−	0.388049i
$195$	13.0778	−	21.8986i	0.936521	−	1.56819i
$196$	−5.21054	−	1.33784i	−0.372182	−	0.0955600i
$197$	4.55367	+	11.5013i	0.324436	+	0.819431i	0.996854	+	0.0792595i	$0.0252556\pi$
$197$	4.55367	+	11.5013i	0.324436	+	0.819431i	−0.672418	+	0.740171i	$0.734744\pi$
$198$	0.114725	−	0.122170i	0.00815317	−	0.00868225i
$199$	5.83284	+	4.23781i	0.413479	+	0.300410i	0.775009	−	0.631950i	$-0.217745\pi$
$199$	5.83284	+	4.23781i	0.413479	+	0.300410i	−0.361530	+	0.932361i	$0.617745\pi$
$200$	−14.0957	+	5.44162i	−0.996718	+	0.384781i
$201$	8.40547	−	6.10693i	0.592876	−	0.430750i
$202$	−0.915787	+	7.24920i	−0.0644346	+	0.510052i
$203$	0.328009	−	1.27751i	0.0230217	−	0.0896636i
$204$	−0.449190	−	7.13967i	−0.0314496	−	0.499877i
$205$	5.18628	+	14.6015i	0.362226	+	1.01981i
$206$	0.854177	−	0.219315i	0.0595133	−	0.0152804i
$207$	−0.417391	−	0.574489i	−0.0290107	−	0.0399298i
$208$	7.69687	+	0.484246i	0.533682	+	0.0335764i
$209$	3.59596	+	1.97690i	0.248738	+	0.136745i
$210$	−10.0783	−	10.1650i	−0.695468	−	0.701454i
$211$	−0.196436	−	1.02976i	−0.0135232	−	0.0708913i	0.974886	−	0.222705i	$-0.0714886\pi$
$211$	−0.196436	−	1.02976i	−0.0135232	−	0.0708913i	−0.988409	+	0.151814i	$0.951489\pi$
$212$	−1.54470	+	2.80981i	−0.106091	+	0.192978i
$213$	−4.34796	−	0.829417i	−0.297917	−	0.0568307i
$214$	−8.88516	−	8.34372i	−0.607377	−	0.570365i
$215$	−1.09041	+	11.0306i	−0.0743650	+	0.752279i
$216$	6.57943	+	13.9820i	0.447674	+	0.951355i
$217$	8.82235	−	22.2827i	0.598900	−	1.51265i
$218$	2.71433	−	3.73595i	0.183838	−	0.253031i
$219$	−16.0363	+	19.3846i	−1.08363	+	1.30989i
$220$	3.37162	+	1.73616i	0.227314	+	0.117052i
$221$	14.8511	−	23.4016i	0.998993	−	1.57416i
$222$	−6.57861	−	4.17491i	−0.441528	−	0.280202i
$223$	1.45721	−	0.277978i	0.0975822	−	0.0186148i	−0.138359	−	0.990382i	$-0.544183\pi$
$223$	1.45721	−	0.277978i	0.0975822	−	0.0186148i	0.235941	+	0.971767i	$0.424183\pi$
$224$	−5.30507	+	16.3273i	−0.354460	+	1.09092i
$225$	0.110485	+	0.446148i	0.00736564	+	0.0297432i
$226$	3.62750	+	11.1643i	0.241298	+	0.742638i
$227$	−1.78837	−	3.25304i	−0.118699	−	0.215912i	0.810282	−	0.586040i	$-0.199314\pi$
$227$	−1.78837	−	3.25304i	−0.118699	−	0.215912i	−0.928981	+	0.370128i	$0.879314\pi$
$228$	2.97237	−	2.45896i	0.196850	−	0.162849i
$229$	19.3223	−	7.65025i	1.27686	−	0.505543i	0.370804	−	0.928711i	$-0.379082\pi$
$229$	19.3223	−	7.65025i	1.27686	−	0.505543i	0.906051	+	0.423168i	$0.139082\pi$
$230$	−10.8967	+	13.9243i	−0.718506	+	0.918141i
$231$	−0.699411	+	11.1168i	−0.0460179	+	0.731433i
$232$	−1.06581	−	0.346304i	−0.0699740	−	0.0227359i
$233$	−14.7392	−	12.1933i	−0.965596	−	0.798810i	0.0139765	−	0.999902i	$-0.495551\pi$
$233$	−14.7392	−	12.1933i	−0.965596	−	0.798810i	−0.979572	+	0.201092i	$0.935551\pi$
$234$	0.114379	−	0.599594i	0.00747717	−	0.0391967i
$235$	−10.8010	+	7.27291i	−0.704582	+	0.474433i
$236$	−0.517602	−	0.0653884i	−0.0336930	−	0.00425642i
$237$	−3.07289	−	24.3244i	−0.199605	−	1.58004i
$238$	−10.6478	−	11.3387i	−0.690192	−	0.734980i
$239$	2.67678	−	5.68844i	0.173146	−	0.367955i	−0.799353	−	0.600862i	$-0.794824\pi$
$239$	2.67678	−	5.68844i	0.173146	−	0.367955i	0.972499	+	0.232908i	$0.0748240\pi$
$240$	−3.51949	+	3.07615i	−0.227182	+	0.198564i
$241$	5.23095	−	0.660823i	0.336955	−	0.0425673i	0.0449648	−	0.998989i	$-0.485682\pi$
$241$	5.23095	−	0.660823i	0.336955	−	0.0425673i	0.291990	+	0.956421i	$0.405682\pi$
$242$	−1.99263	−	7.76078i	−0.128091	−	0.498882i
$243$	0.908239	−	0.295105i	0.0582636	−	0.0189310i
$244$	2.75447	+	1.09057i	0.176337	+	0.0698168i
$245$	12.5713	+	1.24271i	0.803154	+	0.0793941i
$246$	7.95040	+	9.61038i	0.506899	+	0.612736i
$247$	14.9164	−	0.938461i	0.949108	−	0.0597128i
$248$	−18.4248	−	8.67004i	−1.16997	−	0.550548i
$249$	−19.6721			−1.24667
$250$	9.92468	−	5.69852i	0.627692	−	0.360406i
$251$	−11.2202			−0.708216			−0.354108	−	0.935205i	$-0.615215\pi$
$251$	−11.2202			−0.708216			−0.354108	+	0.935205i	$0.615215\pi$
$252$	0.281691	+	0.132554i	0.0177449	+	0.00835010i
$253$	13.7316	−	0.863918i	0.863298	−	0.0543141i
$254$	2.68362	+	3.24394i	0.168385	+	0.203543i
$255$	3.59430	+	16.4100i	0.225084	+	1.02763i
$256$	15.6674	+	6.20317i	0.979214	+	0.387698i
$257$	−13.3411	+	4.33478i	−0.832194	+	0.270396i	−0.693969	−	0.720005i	$-0.744140\pi$
$257$	−13.3411	+	4.33478i	−0.832194	+	0.270396i	−0.138225	+	0.990401i	$0.544140\pi$
$258$	2.21887	+	8.64194i	0.138141	+	0.538024i
$259$	15.2747	−	1.92964i	0.949122	−	0.119902i
$260$	13.7567	−	1.24094i	0.853153	−	0.0769597i
$261$	−0.0145147	+	0.0308454i	−0.000898439	+	0.00190928i
$262$	1.51868	+	1.61723i	0.0938241	+	0.0999125i
$263$	1.56820	+	12.4136i	0.0966995	+	0.765456i	0.963670	+	0.267096i	$0.0860641\pi$
$263$	1.56820	+	12.4136i	0.0966995	+	0.765456i	−0.866970	+	0.498360i	$0.833936\pi$
$264$	9.38962	+	1.18618i	0.577891	+	0.0730046i
$265$	2.58087	−	7.07339i	0.158542	−	0.434515i
$266$	1.57170	−	8.23913i	0.0963669	−	0.505173i
$267$	−4.04629	−	3.34738i	−0.247629	−	0.204856i
$268$	5.35099	+	1.73864i	0.326864	+	0.106204i
$269$	0.312626	−	4.96904i	0.0190611	−	0.302968i	−0.976933	−	0.213547i	$-0.931498\pi$
$269$	0.312626	−	4.96904i	0.0190611	−	0.302968i	0.995994	−	0.0894209i	$-0.0285016\pi$
$270$	−6.53717	−	9.70838i	−0.397839	−	0.590833i
$271$	−16.8380	+	6.66662i	−1.02283	+	0.404968i	−0.818851	−	0.574006i	$-0.805388\pi$
$271$	−16.8380	+	6.66662i	−1.02283	+	0.404968i	−0.203982	+	0.978975i	$0.565388\pi$
$272$	−3.91368	+	3.23768i	−0.237302	+	0.196313i
$273$	19.5446	+	35.5515i	1.18289	+	2.15167i
$274$	−4.80014	−	14.7733i	−0.289987	−	0.892489i
$275$	−8.44573	−	2.82443i	−0.509297	−	0.170320i
$276$	3.99692	−	12.3013i	0.240586	−	0.740448i
$277$	−18.4147	+	3.51280i	−1.10643	+	0.211064i	−0.708055	−	0.706157i	$-0.750427\pi$
$277$	−18.4147	+	3.51280i	−1.10643	+	0.211064i	−0.398379	+	0.917221i	$0.630427\pi$
$278$	8.39814	+	5.32962i	0.503687	+	0.319650i
$279$	−0.331903	+	0.522995i	−0.0198705	+	0.0313109i
$280$	3.86124	−	23.7206i	0.230753	−	1.41758i
$281$	6.99168	−	8.45149i	0.417089	−	0.504174i	−0.519565	−	0.854431i	$-0.673906\pi$
$281$	6.99168	−	8.45149i	0.417089	−	0.504174i	0.936654	+	0.350257i	$0.113906\pi$
$282$	−6.16087	+	8.47970i	−0.366874	+	0.504959i
$283$	7.97885	−	20.1523i	0.474293	−	1.19793i	−0.473998	−	0.880526i	$-0.657189\pi$
$283$	7.97885	−	20.1523i	0.474293	−	1.19793i	0.948291	−	0.317402i	$-0.102811\pi$
$284$	−1.02060	−	2.16888i	−0.0605613	−	0.128699i
$285$	−6.01976	+	6.76938i	−0.356580	+	0.400983i
$286$	8.62148	+	8.09611i	0.509799	+	0.478733i
$287$	−24.2095	−	4.61821i	−1.42904	−	0.272604i
$288$	0.213762	−	0.388832i	0.0125961	−	0.0229121i
$289$	0.235051	+	1.23218i	0.0138265	+	0.0724811i
$290$	0.837784	+	0.136374i	0.0491963	+	0.00800818i
$291$	−9.63634	−	5.29763i	−0.564893	−	0.310552i
$292$	−13.5970	−	0.855448i	−0.795702	−	0.0500613i
$293$	0.862770	+	1.18750i	0.0504036	+	0.0693746i	0.833475	−	0.552557i	$-0.186348\pi$
$293$	0.862770	+	1.18750i	0.0504036	+	0.0693746i	−0.783071	+	0.621932i	$0.786348\pi$
$294$	9.84906	−	2.52881i	0.574409	−	0.147483i
$295$	1.22468	−	0.0332347i	0.0713035	−	0.00193500i
$296$	−0.821394	−	13.0557i	−0.0477426	−	0.758846i
$297$	−2.26499	+	8.82155i	−0.131428	+	0.511878i
$298$	−1.20820	+	9.56385i	−0.0699889	+	0.554019i
$299$	40.5414	−	29.4551i	2.34457	−	1.70343i
$300$	−5.39151	+	6.40466i	−0.311279	+	0.369773i
$301$	−14.2633	−	10.3629i	−0.822121	−	0.597306i
$302$	−0.328167	+	0.349462i	−0.0188839	+	0.0201093i
$303$	4.62065	+	11.6704i	0.265449	+	0.670448i
$304$	−2.65295	−	0.681163i	−0.152157	−	0.0390674i
$305$	−6.78266	−	1.54665i	−0.388374	−	0.0885609i
$306$	0.215415	+	0.339440i	0.0123145	+	0.0194045i
$307$		−	31.9865i		−	1.82557i	−0.408443	−	0.912784i	$-0.633928\pi$
$307$		−	31.9865i		−	1.82557i	0.408443	−	0.912784i	$-0.366072\pi$
$308$	−5.09299	+	3.23211i	−0.290200	+	0.184167i
$309$	1.10433	−	1.03704i	0.0628232	−	0.0589949i
$310$	14.7922	+	4.36635i	0.840139	+	0.247992i
$311$	5.42999	−	2.98516i	0.307907	−	0.169273i	−0.320307	−	0.947314i	$-0.603786\pi$
$311$	5.42999	−	2.98516i	0.307907	−	0.169273i	0.628214	+	0.778041i	$0.283786\pi$
$312$	31.1899	−	14.6769i	1.76578	−	0.830914i
$313$	−4.30153	+	2.02414i	−0.243137	+	0.114411i	−0.543487	−	0.839417i	$-0.682896\pi$
$313$	−4.30153	+	2.02414i	−0.243137	+	0.114411i	0.300351	+	0.953829i	$0.402896\pi$
$314$	13.8011	−	7.58724i	0.778843	−	0.428173i
$315$	−0.701154	−	0.206966i	−0.0395056	−	0.0116612i
$316$	9.67859	−	9.08880i	0.544463	−	0.511285i
$317$	3.96276	−	2.51485i	0.222571	−	0.141248i	−0.419867	−	0.907586i	$-0.637923\pi$
$317$	3.96276	−	2.51485i	0.222571	−	0.141248i	0.642438	+	0.766338i	$0.277923\pi$
$318$		−	6.06083i		−	0.339874i
$319$	−0.353918	−	0.557686i	−0.0198156	−	0.0312244i
$320$	−15.9553	−	3.63828i	−0.891928	−	0.203386i
$321$	−20.2802	−	5.20708i	−1.13193	−	0.290631i
$322$	−10.3528	−	26.1481i	−0.576938	−	1.45718i
$323$	−6.73843	+	7.17569i	−0.374936	+	0.399266i
$324$	7.13920	+	5.18693i	0.396622	+	0.288163i
$325$	−31.4845	+	7.79684i	−1.74644	+	0.432491i
$326$	15.6973	−	11.4048i	0.869394	−	0.631652i
$327$	0.994236	−	7.87019i	0.0549814	−	0.435223i
$328$	−5.20779	+	20.2830i	−0.287552	+	1.11994i
$329$	−1.30048	−	20.6706i	−0.0716978	−	1.13960i
$330$	−7.16576	+	0.194461i	−0.394462	+	0.0107047i
$331$	23.8756	−	6.13022i	1.31232	−	0.336947i	0.473231	−	0.880938i	$-0.343087\pi$
$331$	23.8756	−	6.13022i	1.31232	−	0.336947i	0.839091	+	0.543991i	$0.183087\pi$
$332$	−6.26171	−	8.61850i	−0.343656	−	0.473002i
$333$	−0.397145	−	0.0249863i	−0.0217634	−	0.00136924i
$334$	0.224103	+	0.123202i	0.0122624	+	0.00674131i
$335$	−13.0406	−	2.12274i	−0.712482	−	0.115978i
$336$	−1.39315	−	7.30316i	−0.0760027	−	0.398420i
$337$	−9.70136	+	17.6467i	−0.528467	+	0.961277i	0.468501	+	0.883463i	$0.344794\pi$
$337$	−9.70136	+	17.6467i	−0.528467	+	0.961277i	−0.996968	+	0.0778143i	$0.975206\pi$
$338$	29.2418	+	5.57818i	1.59055	+	0.303413i
$339$	14.6999	+	13.8041i	0.798387	+	0.749735i
$340$	−6.04525	+	6.79805i	−0.327850	+	0.368676i
$341$	−5.11005	−	10.8594i	−0.276725	−	0.588070i
$342$	−0.0798058	+	0.201566i	−0.00431540	+	0.0108995i
$343$	2.82329	−	3.88593i	0.152444	−	0.209821i
$344$	−9.54854	+	11.5422i	−0.514823	+	0.622314i
$345$	−4.87992	+	29.9786i	−0.262726	+	1.61399i
$346$	−7.81316	+	12.3116i	−0.420038	+	0.661874i
$347$	11.9832	+	7.60479i	0.643293	+	0.408246i	0.817070	−	0.576539i	$-0.195597\pi$
$347$	11.9832	+	7.60479i	0.643293	+	0.408246i	−0.173776	+	0.984785i	$0.555597\pi$
$348$	−0.609932	+	0.116351i	−0.0326958	+	0.00623706i
$349$	−7.81233	+	24.0439i	−0.418184	+	1.28704i	0.491187	+	0.871054i	$0.336563\pi$
$349$	−7.81233	+	24.0439i	−0.418184	+	1.28704i	−0.909371	+	0.415985i	$0.863437\pi$
$350$	−0.155999	+	18.2023i	−0.00833852	+	0.972952i
$351$	10.2507	+	31.5484i	0.547141	+	1.68393i
$352$	4.14176	+	7.53384i	0.220757	+	0.401555i
$353$	−25.8759	+	21.4064i	−1.37723	+	1.13935i	−0.402642	+	0.915358i	$0.631908\pi$
$353$	−25.8759	+	21.4064i	−1.37723	+	1.13935i	−0.974592	+	0.223989i	$0.928092\pi$
$354$	0.916906	−	0.363029i	0.0487330	−	0.0192948i
$355$	3.14389	+	4.66900i	0.166860	+	0.247805i
$356$	0.178564	−	2.83819i	0.00946387	−	0.150424i
$357$	−25.4121	−	8.25690i	−1.34495	−	0.437001i
$358$	−9.90464	−	8.19383i	−0.523477	−	0.433058i
$359$	−5.62944	+	29.5106i	−0.297110	+	1.55751i	0.450136	+	0.892960i	$0.351376\pi$
$359$	−5.62944	+	29.5106i	−0.297110	+	1.55751i	−0.747246	+	0.664547i	$0.768624\pi$
$360$	−0.212912	+	0.583529i	−0.0112215	+	0.0307547i
$361$	13.5839	+	1.71604i	0.714942	+	0.0903181i
$362$	1.18145	+	9.35210i	0.0620954	+	0.491536i
$363$	−9.42218	−	10.0336i	−0.494536	−	0.526628i
$364$	−9.35425	+	19.8788i	−0.490296	+	1.04193i
$365$	31.8630	−	2.87424i	1.66779	−	0.150445i
$366$	−5.55563	+	0.701840i	−0.290398	+	0.0366858i
$367$	2.60289	+	10.1376i	0.135870	+	0.529179i	0.999678	+	0.0253582i	$0.00807264\pi$
$367$	2.60289	+	10.1376i	0.135870	+	0.529179i	−0.863808	+	0.503820i	$0.831927\pi$
$368$	−8.73411	+	2.83788i	−0.455297	+	0.147935i
$369$	0.592275	+	0.234498i	0.0308326	+	0.0122075i
$370$	2.11995	+	9.67873i	0.110211	+	0.503173i
$371$	7.63392	+	9.22782i	0.396333	+	0.479085i
$372$	−11.2602	+	0.708434i	−0.583816	+	0.0367306i
$373$	12.8376	+	6.04094i	0.664708	+	0.312788i	0.728370	−	0.685184i	$-0.240278\pi$
$373$	12.8376	+	6.04094i	0.664708	+	0.312788i	−0.0636624	+	0.997971i	$0.520278\pi$
$374$	−7.78944			−0.402782
$375$	10.2241	−	16.7916i	0.527972	−	0.867114i
$376$	−17.5978			−0.907535
$377$	−2.17674	−	1.02430i	−0.112108	−	0.0527540i
$378$	18.5795	−	1.16892i	0.955625	−	0.0601228i
$379$	−12.6269	−	15.2633i	−0.648600	−	0.784023i	0.339038	−	0.940773i	$-0.389898\pi$
$379$	−12.6269	−	15.2633i	−0.648600	−	0.784023i	−0.987638	+	0.156750i	$0.949898\pi$
$380$	−4.88183	−	0.482583i	−0.250432	−	0.0247560i
$381$	6.72435	+	2.66236i	0.344499	+	0.136397i
$382$	14.8535	−	4.82618i	0.759969	−	0.246929i
$383$	7.81616	+	30.4419i	0.399387	+	1.55551i	0.776972	+	0.629535i	$0.216755\pi$
$383$	7.81616	+	30.4419i	0.399387	+	1.55551i	−0.377585	+	0.925975i	$0.623245\pi$
$384$	3.77255	−	0.476584i	0.192517	−	0.0243206i
$385$	10.6652	−	9.32170i	0.543548	−	0.475078i
$386$	5.64434	−	11.9948i	0.287289	−	0.610521i
$387$	0.311933	+	0.332175i	0.0158565	+	0.0168854i
$388$	−0.746355	−	5.90801i	−0.0378904	−	0.299934i
$389$	−5.89456	−	0.744656i	−0.298866	−	0.0377555i	−0.0255296	−	0.999674i	$-0.508127\pi$
$389$	−5.89456	−	0.744656i	−0.298866	−	0.0377555i	−0.273336	+	0.961919i	$0.588127\pi$
$390$	−21.6567	+	14.5826i	−1.09663	+	0.738418i
$391$	−6.18445	+	32.4200i	−0.312761	+	1.63955i
$392$	13.1544	+	10.8823i	0.664399	+	0.549639i
$393$	3.62450	+	1.17767i	0.182832	+	0.0594056i
$394$	0.795052	−	12.6370i	0.0400542	−	0.636643i
$395$	−19.2147	+	24.5535i	−0.966797	+	1.23542i
$396$	0.144956	−	0.0573923i	0.00728433	−	0.00288407i
$397$	8.52424	−	7.05187i	0.427819	−	0.353923i	−0.398458	−	0.917187i	$-0.630454\pi$
$397$	8.52424	−	7.05187i	0.427819	−	0.353923i	0.826277	+	0.563264i	$0.190454\pi$
$398$	−3.55535	−	6.46716i	−0.178214	−	0.324169i
$399$	−4.45251	−	13.7034i	−0.222904	−	0.686028i
$400$	5.92903	+	0.424065i	0.296451	+	0.0212032i
$401$	2.12277	−	6.53320i	0.106006	−	0.326253i	−0.883959	−	0.467564i	$-0.845132\pi$
$401$	2.12277	−	6.53320i	0.106006	−	0.326253i	0.989965	+	0.141311i	$0.0451318\pi$
$402$	−10.4467	+	1.99281i	−0.521033	+	0.0993923i
$403$	−36.9075	−	23.4222i	−1.83849	−	1.16674i
$404$	−3.64213	+	5.73908i	−0.181203	+	0.285530i
$405$	−18.4233	−	9.48679i	−0.915460	−	0.471402i
$406$	−0.860579	+	1.04026i	−0.0427098	+	0.0516273i
$407$	4.53190	−	6.23762i	0.224638	−	0.309188i
$408$	−8.35751	+	21.1087i	−0.413758	+	1.04503i
$409$	−16.7804	−	35.6603i	−0.829739	−	1.76329i	−0.618383	−	0.785877i	$-0.712212\pi$
$409$	−16.7804	−	35.6603i	−0.829739	−	1.76329i	−0.211356	−	0.977409i	$-0.567788\pi$
$410$	1.56030	−	15.7841i	0.0770579	−	0.779521i
$411$	−19.4518	−	18.2665i	−0.959488	−	0.901019i
$412$	0.805846	+	0.153723i	0.0397012	+	0.00757341i
$413$	−0.938767	+	1.70761i	−0.0461937	+	0.0840261i
$414$	0.136203	+	0.713999i	0.00669399	+	0.0350911i
$415$	17.6132	+	17.7648i	0.864596	+	0.872038i
$416$	27.4397	+	15.0851i	1.34534	+	0.739608i
$417$	17.0527	+	1.07287i	0.835075	+	0.0525385i
$418$	−2.46895	−	3.39822i	−0.120760	−	0.166212i
$419$	34.0611	−	8.74542i	1.66400	−	0.427241i	0.704668	−	0.709537i	$-0.251096\pi$
$419$	34.0611	−	8.74542i	1.66400	−	0.427241i	0.959328	+	0.282295i	$0.0910958\pi$
$420$	−4.45690	−	12.5480i	−0.217475	−	0.612278i
$421$	1.78582	+	28.3848i	0.0870356	+	1.38339i	0.762972	+	0.646432i	$0.223739\pi$
$421$	1.78582	+	28.3848i	0.0870356	+	1.38339i	−0.675936	+	0.736960i	$0.736261\pi$
$422$	−0.266863	+	1.03936i	−0.0129907	+	0.0505954i
$423$	−0.0670924	+	0.531091i	−0.00326214	+	0.0258225i
$424$	8.23236	−	5.98116i	0.399799	−	0.290471i
$425$	11.6008	−	17.9383i	0.562722	−	0.870134i
$426$	3.66555	+	2.66318i	0.177596	+	0.129031i
$427$	7.57464	−	8.06617i	0.366563	−	0.390349i
$428$	−4.17401	−	10.5424i	−0.201758	−	0.509584i
$429$	19.6784	+	5.05255i	0.950082	+	0.243940i
$430$	5.81741	−	9.74119i	0.280540	−	0.469762i
$431$	0.880059	+	1.38675i	0.0423910	+	0.0667975i	0.864863	−	0.502009i	$-0.167405\pi$
$431$	0.880059	+	1.38675i	0.0423910	+	0.0667975i	−0.822472	+	0.568806i	$0.807405\pi$
$432$		−	6.07913i		−	0.292482i
$433$	21.3168	−	13.5281i	1.02442	−	0.650118i	0.0862446	−	0.996274i	$-0.472513\pi$
$433$	21.3168	−	13.5281i	1.02442	−	0.650118i	0.938177	+	0.346156i	$0.112513\pi$
$434$	−17.8827	+	16.7930i	−0.858397	+	0.806089i
$435$	1.37401	−	0.488034i	0.0658788	−	0.0233994i
$436$	3.76446	−	2.06953i	0.180285	−	0.0991125i
$437$	−16.1038	+	7.57786i	−0.770348	+	0.362498i
$438$	23.3011	−	10.9647i	1.11337	−	0.523913i
$439$	−1.40012	+	0.769722i	−0.0668240	+	0.0367368i	−0.514815	−	0.857301i	$-0.672140\pi$
$439$	−1.40012	+	0.769722i	−0.0668240	+	0.0367368i	0.447991	+	0.894038i	$0.352140\pi$
$440$	−7.33569	−	9.54126i	−0.349716	−	0.454862i
$441$	0.378574	−	0.355504i	0.0180273	−	0.0169288i
$442$	−23.9541	+	15.2018i	−1.13938	+	0.723074i
$443$		−	13.5981i		−	0.646063i	−0.946388	−	0.323032i	$-0.895298\pi$
$443$		−	13.5981i		−	0.646063i	0.946388	−	0.323032i	$-0.104702\pi$
$444$	−3.88374	−	6.11980i	−0.184314	−	0.290433i
$445$	0.599962	+	6.65100i	0.0284409	+	0.315288i
$446$	−1.47081	−	0.377640i	−0.0696448	−	0.0178817i
$447$	6.09601	+	15.3968i	0.288331	+	0.728241i
$448$	17.8183	−	18.9746i	0.841836	−	0.896465i
$449$	−30.3593	−	22.0573i	−1.43274	−	1.04095i	−0.989498	−	0.144550i	$-0.953827\pi$
$449$	−30.3593	−	22.0573i	−1.43274	−	1.04095i	−0.443247	−	0.896400i	$-0.646173\pi$
$450$	0.0921159	−	0.461371i	0.00434239	−	0.0217492i
$451$	−9.98520	+	7.25467i	−0.470185	+	0.341609i
$452$	−1.36865	+	10.8340i	−0.0643761	+	0.509589i
$453$	−0.204800	+	0.797642i	−0.00962233	+	0.0374765i
$454$	0.238596	+	3.79237i	0.0111978	+	0.177985i
$455$	14.6055	−	49.4801i	0.684717	−	2.31967i
$456$	−11.8579	+	3.04458i	−0.555295	+	0.142576i
$457$	16.7529	+	23.0584i	0.783670	+	1.07863i	0.994868	+	0.101185i	$0.0322635\pi$
$457$	16.7529	+	23.0584i	0.783670	+	1.07863i	−0.211198	+	0.977443i	$0.567737\pi$
$458$	−21.2304	−	1.33570i	−0.992031	−	0.0624133i
$459$	−19.1452	−	10.5252i	−0.893622	−	0.491273i
$460$	−14.6872	+	7.40438i	−0.684792	+	0.345231i
$461$	2.07231	+	10.8634i	0.0965171	+	0.505960i	0.997410	+	0.0719198i	$0.0229125\pi$
$461$	2.07231	+	10.8634i	0.0965171	+	0.505960i	−0.900893	+	0.434041i	$0.857087\pi$
$462$	5.49286	−	9.99147i	0.255551	−	0.464845i
$463$	8.49420	+	1.62036i	0.394759	+	0.0753043i	0.380939	−	0.924600i	$-0.375601\pi$
$463$	8.49420	+	1.62036i	0.394759	+	0.0753043i	0.0138200	+	0.999904i	$0.495601\pi$
$464$	0.321382	+	0.301797i	0.0149198	+	0.0140106i
$465$	25.8808	−	5.66871i	1.20019	−	0.262880i
$466$	8.33706	+	17.7171i	0.386207	+	0.820731i
$467$	−8.80770	+	22.2457i	−0.407572	+	1.02941i	0.570529	+	0.821277i	$0.306738\pi$
$467$	−8.80770	+	22.2457i	−0.407572	+	1.02941i	−0.978101	+	0.208131i	$0.933262\pi$
$468$	0.333765	−	0.459388i	0.0154283	−	0.0212352i
$469$	13.3954	−	16.1922i	0.618541	−	0.747687i
$470$	13.1736	−	2.02866i	0.607652	−	0.0935753i
$471$	14.4965	−	22.8428i	0.667963	−	1.05254i
$472$	1.39795	+	0.887166i	0.0643459	+	0.0408351i
$473$	−8.67264	+	1.65439i	−0.398768	+	0.0760691i
$474$	−7.75528	+	23.8683i	−0.356212	+	1.09631i
$475$	11.5028	−	0.624773i	0.527782	−	0.0286665i
$476$	−4.47136	−	13.7614i	−0.204945	−	0.630755i
$477$	−0.149122	−	0.271252i	−0.00682782	−	0.0124198i
$478$	−4.95841	+	4.10196i	−0.226793	+	0.187619i
$479$	9.13962	−	3.61863i	0.417600	−	0.165340i	−0.149922	−	0.988698i	$-0.547902\pi$
$479$	9.13962	−	3.61863i	0.417600	−	0.165340i	0.567522	+	0.823358i	$0.307902\pi$
$480$	−18.2479	+	5.21681i	−0.832898	+	0.238114i
$481$	1.76327	−	28.0264i	0.0803981	−	1.27789i
$482$	−5.13287	−	1.66777i	−0.233796	−	0.0759648i
$483$	−37.2239	−	30.7943i	−1.69375	−	1.40119i
$484$	1.39668	−	7.32166i	0.0634856	−	0.332803i
$485$	3.84379	+	13.4452i	0.174538	+	0.610515i
$486$	−0.969819	−	0.122517i	−0.0439919	−	0.00555747i
$487$	−2.25015	−	17.8117i	−0.101964	−	0.807127i	−0.957309	−	0.289068i	$-0.906655\pi$
$487$	−2.25015	−	17.8117i	−0.101964	−	0.807127i	0.855345	−	0.518059i	$-0.173345\pi$
$488$	−6.43590	−	6.85354i	−0.291340	−	0.310245i
$489$	14.1916	−	30.1587i	0.641767	−	1.36382i
$490$	−11.1019	−	6.62999i	−0.501530	−	0.299512i
$491$	21.7656	−	2.74963i	0.982266	−	0.124089i	0.382234	−	0.924065i	$-0.375155\pi$
$491$	21.7656	−	2.74963i	0.982266	−	0.124089i	0.600032	+	0.799976i	$0.295155\pi$
$492$	2.88550	+	11.2383i	0.130089	+	0.506661i
$493$	1.50689	−	0.489618i	0.0678668	−	0.0220513i
$494$	−14.2244	−	5.63186i	−0.639988	−	0.253389i
$495$	−0.315918	+	0.185011i	−0.0141995	+	0.00831561i
$496$	5.10626	+	6.17241i	0.229278	+	0.277149i
$497$	−8.93533	+	0.562163i	−0.400804	+	0.0252165i
$498$	18.2201	+	8.57374i	0.816463	+	0.384198i
$499$	−19.4067			−0.868765			−0.434382	−	0.900729i	$-0.643033\pi$
$499$	−19.4067			−0.868765			−0.434382	+	0.900729i	$0.643033\pi$
$500$	10.6109	−	0.865562i	0.474534	−	0.0387091i
$501$	0.439311			0.0196270
$502$	10.3921	+	4.89015i	0.463822	+	0.218258i
$503$	31.9835	−	2.01223i	1.42607	−	0.0897210i	0.669103	−	0.743170i	$-0.266678\pi$
$503$	31.9835	−	2.01223i	1.42607	−	0.0897210i	0.756971	+	0.653449i	$0.226678\pi$
$504$	−0.629770	−	0.761261i	−0.0280522	−	0.0339093i
$505$	6.40186	−	14.6216i	0.284879	−	0.650653i
$506$	−13.0946	−	5.18452i	−0.582126	−	0.230480i
$507$	48.6353	−	15.8026i	2.15997	−	0.701817i
$508$	0.973987	+	3.79343i	0.0432137	+	0.168306i
$509$	4.10954	−	0.519156i	0.182152	−	0.0230112i	−0.0337279	−	0.999431i	$-0.510738\pi$
$509$	4.10954	−	0.519156i	0.182152	−	0.0230112i	0.215880	+	0.976420i	$0.430738\pi$
$510$	3.82299	−	16.7653i	0.169285	−	0.742379i
$511$	−21.6662	+	46.0430i	−0.958456	+	2.03682i
$512$	−8.84680	−	9.42088i	−0.390977	−	0.416348i
$513$	−1.47658	−	11.6884i	−0.0651927	−	0.516053i
$514$	14.2456	+	1.79964i	0.628348	+	0.0793788i
$515$	−1.92524	−	0.0687621i	−0.0848361	−	0.00303002i
$516$	−1.55526	+	8.15297i	−0.0684666	+	0.358914i
$517$	−7.99174	−	6.61134i	−0.351476	−	0.290767i
$518$	−14.9883	−	4.86998i	−0.658547	−	0.213975i
$519$	−1.57281	+	24.9991i	−0.0690386	+	1.09734i
$520$	−41.1793	−	15.0251i	−1.80583	−	0.658895i
$521$	13.4934	−	5.34242i	0.591158	−	0.234056i	−0.0534487	−	0.998571i	$-0.517021\pi$
$521$	13.4934	−	5.34242i	0.591158	−	0.234056i	0.644606	+	0.764515i	$0.277021\pi$
$522$	0.0268868	−	0.0222427i	0.00117680	−	0.000973536i
$523$	15.4248	+	28.0575i	0.674477	+	1.22687i	0.963027	+	0.269405i	$0.0868270\pi$
$523$	15.4248	+	28.0575i	0.674477	+	1.22687i	−0.288550	+	0.957465i	$0.593173\pi$
$524$	0.637745	+	1.96278i	0.0278600	+	0.0857443i
$525$	14.8288	+	27.5298i	0.647182	+	1.20150i
$526$	3.95780	−	12.1808i	0.172568	−	0.531110i
$527$	28.2797	−	5.39465i	1.23188	−	0.234995i
$528$	−3.14365	−	1.99502i	−0.136810	−	0.0868222i
$529$	−19.6507	+	30.9645i	−0.854377	+	1.34628i
$530$	−5.47319	+	5.42649i	−0.237740	+	0.235711i
$531$	0.0321039	−	0.0388070i	0.00139319	−	0.00168408i
$532$	4.58632	−	6.31252i	0.198842	−	0.273683i
$533$	−16.5484	+	41.7966i	−0.716792	+	1.81041i
$534$	2.28874	+	4.86381i	0.0990433	+	0.210478i
$535$	13.4554	+	22.9760i	0.581728	+	0.993339i
$536$	−13.0162	−	12.2230i	−0.562212	−	0.527952i
$537$	−21.6909	−	4.13775i	−0.936030	−	0.178557i
$538$	−2.45522	+	4.46603i	−0.105852	+	0.192544i
$539$	1.88548	+	9.88404i	0.0812135	+	0.425736i
$540$	−1.65714	−	10.7610i	−0.0713120	−	0.463080i
$541$	−7.25628	−	3.98917i	−0.311972	−	0.171508i	0.318074	−	0.948066i	$-0.396964\pi$
$541$	−7.25628	−	3.98917i	−0.311972	−	0.171508i	−0.630046	+	0.776558i	$0.716964\pi$
$542$	18.5007	+	1.16396i	0.794673	+	0.0499966i
$543$	9.51800	+	13.1004i	0.408456	+	0.562192i
$544$	−19.9753	+	5.12878i	−0.856434	+	0.219895i
$545$	−7.99730	+	6.14864i	−0.342567	+	0.263379i
$546$	−2.60754	−	41.4456i	−0.111592	−	1.77371i
$547$	0.569022	−	2.21620i	0.0243296	−	0.0947577i	−0.955259	−	0.295771i	$-0.904423\pi$
$547$	0.569022	−	2.21620i	0.0243296	−	0.0947577i	0.979589	+	0.201013i	$0.0644235\pi$
$548$	1.81109	−	14.3363i	0.0773661	−	0.612416i
$549$	−0.231373	+	0.168103i	−0.00987477	+	0.00717444i
$550$	6.59138	+	6.29688i	0.281057	+	0.268500i
$551$	0.691226	+	0.502205i	0.0294472	+	0.0213946i
$552$	−28.0991	+	29.9225i	−1.19598	+	1.27359i
$553$	−18.2556	−	46.1085i	−0.776308	−	1.96073i
$554$	18.5865	+	4.77221i	0.789666	+	0.202752i
$555$	11.2011	+	12.8154i	0.475459	+	0.543984i
$556$	4.95792	+	7.81243i	0.210262	+	0.331321i
$557$		−	29.8559i		−	1.26503i	−0.774546	−	0.632517i	$-0.782022\pi$
$557$		−	29.8559i		−	1.26503i	0.774546	−	0.632517i	$-0.217978\pi$
$558$	0.535343	−	0.339739i	0.0226629	−	0.0143823i
$559$	−23.4414	+	22.0130i	−0.991468	+	0.931050i
$560$	−5.34773	+	7.79686i	−0.225983	+	0.329478i
$561$	−11.7258	+	6.44631i	−0.495063	+	0.272163i
$562$	−10.1591	+	4.78049i	−0.428534	+	0.201653i
$563$	0.771190	−	0.362895i	0.0325018	−	0.0152942i	−0.409460	−	0.912328i	$-0.634283\pi$
$563$	0.771190	−	0.362895i	0.0325018	−	0.0152942i	0.441962	+	0.897034i	$0.354283\pi$
$564$	−8.54441	+	4.69733i	−0.359784	+	0.197793i
$565$	−0.695641	−	25.6339i	−0.0292659	−	1.07843i
$566$	−16.1730	+	15.1874i	−0.679800	+	0.638375i
$567$	27.8293	−	17.6610i	1.16872	−	0.741692i
$568$			7.60704i			0.319184i
$569$	−8.78305	−	13.8399i	−0.368205	−	0.580198i	0.608824	−	0.793305i	$-0.291642\pi$
$569$	−8.78305	−	13.8399i	−0.368205	−	0.580198i	−0.977029	+	0.213108i	$0.931642\pi$
$570$	8.52576	−	3.64613i	0.357105	−	0.152720i
$571$	16.0754	+	4.12746i	0.672734	+	0.172729i	0.569579	−	0.821937i	$-0.307106\pi$
$571$	16.0754	+	4.12746i	0.672734	+	0.172729i	0.103155	+	0.994665i	$0.467106\pi$
$572$	4.05015	+	10.2295i	0.169345	+	0.427717i
$573$	18.3655	−	19.5573i	0.767232	−	0.817019i
$574$	20.4099	+	14.8286i	0.851891	+	0.618935i
$575$	31.4412	−	22.4342i	1.31119	−	0.935570i
$576$	−0.544275	+	0.395439i	−0.0226781	+	0.0164766i
$577$	−5.08176	+	40.2263i	−0.211556	+	1.67464i	0.426373	+	0.904547i	$0.359791\pi$
$577$	−5.08176	+	40.2263i	−0.211556	+	1.67464i	−0.637930	+	0.770094i	$0.720209\pi$
$578$	0.319322	−	1.24368i	0.0132820	−	0.0517301i
$579$	−1.42989	−	22.7274i	−0.0594241	−	0.944519i
$580$	0.651165	+	0.446622i	0.0270381	+	0.0185450i
$581$	−38.5398	+	9.89534i	−1.59890	+	0.410528i
$582$	6.61622	+	9.10644i	0.274251	+	0.377474i
$583$	5.98567	+	0.376586i	0.247901	+	0.0155966i
$584$	37.8880	+	20.8291i	1.56782	+	0.861915i
$585$	−0.610448	+	1.18549i	−0.0252389	+	0.0490138i
$586$	−0.281538	−	1.47588i	−0.0116302	−	0.0609679i
$587$	−3.42206	+	6.22471i	−0.141244	+	0.256921i	−0.937462	−	0.348089i	$-0.886831\pi$
$587$	−3.42206	+	6.22471i	−0.141244	+	0.256921i	0.796218	+	0.605010i	$0.206831\pi$
$588$	9.29178	+	1.77250i	0.383187	+	0.0730968i
$589$	11.3171	+	10.6274i	0.466311	+	0.437895i
$590$	−1.14877	−	0.502972i	−0.0472941	−	0.0207070i
$591$	−9.26117	−	19.6810i	−0.380954	−	0.809568i
$592$	−1.89448	+	4.78491i	−0.0778626	+	0.196659i
$593$	22.6765	−	31.2115i	0.931212	−	1.28170i	−0.0281726	−	0.999603i	$-0.508969\pi$
$593$	22.6765	−	31.2115i	0.931212	−	1.28170i	0.959385	−	0.282101i	$-0.0910312\pi$
$594$	5.94253	−	7.18328i	0.243825	−	0.294734i
$595$	15.2961	+	30.3409i	0.627078	+	1.24386i
$596$	−4.80505	+	7.57155i	−0.196823	+	0.310143i
$597$	−10.7040	−	6.79300i	−0.438088	−	0.278019i
$598$	−50.3866	+	9.61176i	−2.06046	+	0.393054i
$599$	−9.96773	+	30.6775i	−0.407271	+	1.25345i	0.511714	+	0.859156i	$0.329011\pi$
$599$	−9.96773	+	30.6775i	−0.407271	+	1.25345i	−0.918984	+	0.394294i	$0.870989\pi$
$600$	24.1360	−	11.1059i	0.985349	−	0.453397i
$601$	−12.7199	−	39.1478i	−0.518855	−	1.59687i	−0.776157	−	0.630540i	$-0.782833\pi$
$601$	−12.7199	−	39.1478i	−0.518855	−	1.59687i	0.257302	−	0.966331i	$-0.417167\pi$
$602$	8.69403	+	15.8144i	0.354342	+	0.644546i
$603$	−0.418508	+	0.346220i	−0.0170430	+	0.0140992i
$604$	−0.414641	+	0.164168i	−0.0168715	+	0.00667991i
$605$	−0.624751	+	17.4921i	−0.0253997	+	0.711155i
$606$	0.806746	−	12.8229i	0.0327718	−	0.520893i
$607$	8.01970	+	2.60576i	0.325510	+	0.105764i	0.467213	−	0.884145i	$-0.345258\pi$
$607$	8.01970	+	2.60576i	0.325510	+	0.105764i	−0.141704	+	0.989909i	$0.545258\pi$
$608$	−8.56888	−	7.08879i	−0.347514	−	0.287489i
$609$	−0.434578	+	2.27814i	−0.0176100	+	0.0923148i
$610$	5.60796	+	4.38859i	0.227060	+	0.177689i
$611$	−37.4788	−	4.73468i	−1.51623	−	0.191545i
$612$	0.0468728	+	0.371036i	0.00189472	+	0.0149983i
$613$	28.6531	+	30.5124i	1.15729	+	1.23239i	0.968132	+	0.250439i	$0.0805750\pi$
$613$	28.6531	+	30.5124i	1.15729	+	1.23239i	0.189155	+	0.981947i	$0.439425\pi$
$614$	−13.9408	+	29.6256i	−0.562604	+	1.19559i
$615$	−10.7136	−	25.0517i	−0.432016	−	1.01018i
$616$	18.9920	−	2.39924i	0.765208	−	0.0966682i
$617$	−1.45367	−	5.66166i	−0.0585224	−	0.227930i	0.932594	−	0.360927i	$-0.117540\pi$
$617$	−1.45367	−	5.66166i	−0.0585224	−	0.227930i	−0.991116	+	0.132998i	$0.957540\pi$
$618$	−1.47479	+	0.479190i	−0.0593250	+	0.0192758i
$619$	−0.560715	−	0.222003i	−0.0225370	−	0.00892305i	0.356829	−	0.934170i	$-0.383858\pi$
$619$	−0.560715	−	0.222003i	−0.0225370	−	0.00892305i	−0.379366	+	0.925247i	$0.623858\pi$
$620$	10.7214	+	9.53419i	0.430584	+	0.382902i
$621$	−25.1791	−	30.4362i	−1.01040	−	1.22136i
$622$	−6.33024	+	0.398265i	−0.253819	+	0.0159690i
$623$	−9.61090	−	4.52254i	−0.385052	−	0.181192i
$624$	−13.5608			−0.542868
$625$	−24.3176	+	5.80131i	−0.972703	+	0.232052i
$626$	4.86622			0.194493
$627$	−6.52889	−	3.07226i	−0.260739	−	0.122694i
$628$	14.6219	−	0.919932i	0.583477	−	0.0367093i
$629$	11.7892	+	14.2507i	0.470068	+	0.568215i
$630$	0.559200	+	0.497276i	0.0222791	+	0.0198120i
$631$	8.91811	+	3.53093i	0.355024	+	0.140564i	0.538865	−	0.842392i	$-0.318853\pi$
$631$	8.91811	+	3.53093i	0.355024	+	0.140564i	−0.183841	+	0.982956i	$0.558853\pi$
$632$	−40.0734	+	13.0206i	−1.59403	+	0.517933i
$633$	0.458425	+	1.78545i	0.0182208	+	0.0709652i
$634$	−4.76633	+	0.602127i	−0.189295	+	0.0239135i
$635$	−3.61634	−	8.45609i	−0.143510	−	0.335570i
$636$	2.40060	−	5.10153i	0.0951899	−	0.202289i
$637$	25.0878	+	26.7158i	0.994014	+	1.05852i
$638$	0.0847383	+	0.670773i	0.00335482	+	0.0265561i
$639$	0.229576	+	0.0290023i	0.00908190	+	0.00114731i
$640$	−3.80808	−	2.98007i	−0.150527	−	0.117798i
$641$	−5.85697	+	30.7033i	−0.231337	+	1.21271i	0.657134	+	0.753774i	$0.271769\pi$
$641$	−5.85697	+	30.7033i	−0.231337	+	1.21271i	−0.888470	+	0.458934i	$0.848231\pi$
$642$	16.5139	+	13.6615i	0.651753	+	0.539177i
$643$	−46.1959	−	15.0100i	−1.82179	−	0.591936i	−0.999747	−	0.0225111i	$-0.992834\pi$
$643$	−46.1959	−	15.0100i	−1.82179	−	0.591936i	−0.822044	−	0.569424i	$-0.807166\pi$
$644$	1.64270	−	26.1100i	0.0647316	−	1.02888i
$645$	0.695685	−	19.4781i	0.0273926	−	0.766951i
$646$	9.36847	−	3.70924i	0.368597	−	0.145938i
$647$	22.1581	−	18.3308i	0.871124	−	0.720656i	−0.0902450	−	0.995920i	$-0.528765\pi$
$647$	22.1581	−	18.3308i	0.871124	−	0.720656i	0.961369	+	0.275263i	$0.0887650\pi$
$648$	−13.4916	−	24.5411i	−0.530000	−	0.964066i
$649$	0.301555	+	0.928091i	0.0118371	+	0.0364308i
$650$	32.5587	+	6.50058i	1.27706	+	0.254974i
$651$	−13.0223	+	40.0784i	−0.510382	+	1.57080i
$652$	17.7300	−	3.38218i	0.694361	−	0.132456i
$653$	−30.9671	−	19.6523i	−1.21184	−	0.769056i	−0.232759	−	0.972535i	$-0.574775\pi$
$653$	−30.9671	−	19.6523i	−1.21184	−	0.769056i	−0.979079	+	0.203479i	$0.934775\pi$
$654$	−4.35094	+	6.85598i	−0.170135	+	0.268090i
$655$	−2.18166	−	4.32749i	−0.0852445	−	0.169089i
$656$	5.25123	−	6.34765i	0.205026	−	0.247834i
$657$	0.773061	−	1.06403i	0.0301600	−	0.0415117i
$658$	−7.80440	+	19.7117i	−0.304247	+	0.768441i
$659$	5.40336	+	11.4827i	0.210485	+	0.447303i	0.981993	−	0.188916i	$-0.0604974\pi$
$659$	5.40336	+	11.4827i	0.210485	+	0.447303i	−0.771508	+	0.636219i	$0.780497\pi$
$660$	−6.10860	−	2.67456i	−0.237777	−	0.104107i
$661$	−15.4957	−	14.5514i	−0.602711	−	0.565983i	0.321959	−	0.946754i	$-0.395659\pi$
$661$	−15.4957	−	14.5514i	−0.602711	−	0.565983i	−0.924670	+	0.380770i	$0.875659\pi$
$662$	−24.7851	−	4.72801i	−0.963301	−	0.183760i
$663$	−23.4787	+	42.7076i	−0.911837	+	1.65862i
$664$	6.33500	+	33.2092i	0.245846	+	1.28877i
$665$	−8.38827	+	16.2900i	−0.325283	+	0.631698i
$666$	0.356942	+	0.196231i	0.0138312	+	0.00760379i
$667$	2.85906	+	0.179877i	0.110703	+	0.00696487i
$668$	0.139834	+	0.192465i	0.00541035	+	0.00744671i
$669$	−2.52660	+	0.648720i	−0.0976838	+	0.0250809i
$670$	11.1529	+	7.64956i	0.430873	+	0.295528i
$671$	−0.347940	−	5.53035i	−0.0134321	−	0.213497i
$672$	7.50726	−	29.2388i	0.289599	−	1.12791i
$673$	−1.91105	+	15.1275i	−0.0736655	+	0.583122i	0.911473	+	0.411360i	$0.134946\pi$
$673$	−1.91105	+	15.1275i	−0.0736655	+	0.583122i	−0.985138	+	0.171762i	$0.945054\pi$
$674$	16.6763	−	12.1160i	0.642348	−	0.466693i
$675$	7.69214	+	24.3831i	0.296071	+	0.938504i
$676$	22.4040	+	16.2775i	0.861694	+	0.626057i
$677$	10.3494	−	11.0210i	0.397759	−	0.423570i	−0.498647	−	0.866805i	$-0.666169\pi$
$677$	10.3494	−	11.0210i	0.397759	−	0.423570i	0.896405	+	0.443235i	$0.146169\pi$
$678$	−7.59861	−	19.1919i	−0.291823	−	0.737061i
$679$	−21.5434	−	5.53141i	−0.826761	−	0.212276i
$680$	26.5448	−	11.3522i	1.01795	−	0.435336i
$681$	3.49762	+	5.51136i	0.134029	+	0.211196i
$682$			12.2850i			0.470418i
$683$	13.0862	−	8.30474i	0.500728	−	0.317772i	−0.261364	−	0.965240i	$-0.584172\pi$
$683$	13.0862	−	8.30474i	0.500728	−	0.317772i	0.762092	+	0.647468i	$0.224172\pi$
$684$	−0.147011	+	0.138053i	−0.00562112	+	0.00527859i
$685$	0.920518	+	33.9205i	0.0351712	+	1.29604i
$686$	−4.30852	+	2.36863i	−0.164500	+	0.0904348i
$687$	−33.0644	+	15.5589i	−1.26149	+	0.593611i
$688$	5.33227	−	2.50917i	0.203291	−	0.0956614i
$689$	19.1421	−	10.5235i	0.729256	−	0.400912i
$690$	17.5854	−	25.6391i	0.669464	−	0.976063i
$691$	−1.64018	+	1.54023i	−0.0623955	+	0.0585932i	−0.715118	−	0.699004i	$-0.753627\pi$
$691$	−1.64018	+	1.54023i	−0.0623955	+	0.0585932i	0.652722	+	0.757597i	$0.273627\pi$
$692$	−11.4529	+	7.26824i	−0.435374	+	0.276297i
$693$		−	0.582314i		−	0.0221203i
$694$	−7.78434	−	12.2662i	−0.295490	−	0.465617i
$695$	−14.2991	−	16.3599i	−0.542395	−	0.620567i
$696$	1.90865	+	0.490058i	0.0723471	+	0.0185756i
$697$	−10.8991	−	27.5279i	−0.412832	−	1.04269i
$698$	17.7148	−	18.8644i	0.670515	−	0.714026i
$699$	27.2123	+	19.7709i	1.02926	+	0.747804i
$700$	−7.34093	+	15.2594i	−0.277461	+	0.576753i
$701$	−40.8949	+	29.7119i	−1.54458	+	1.12220i	−0.597201	+	0.802092i	$0.703721\pi$
$701$	−40.8949	+	29.7119i	−1.54458	+	1.12220i	−0.947380	+	0.320112i	$0.896279\pi$
$702$	4.25571	−	33.6874i	0.160621	−	1.27145i
$703$	−2.48029	+	9.66011i	−0.0935461	+	0.364338i
$704$	−0.818481	−	13.0094i	−0.0308477	−	0.490310i
$705$	18.1519	−	13.9559i	0.683641	−	0.525610i
$706$	33.2956	−	8.54885i	1.25310	−	0.321740i
$707$	14.9227	+	20.5394i	0.561227	+	0.772463i
$708$	0.915569	+	0.0576027i	0.0344092	+	0.00216484i
$709$	−38.8211	−	21.3421i	−1.45796	−	0.801518i	−0.461622	−	0.887077i	$-0.652732\pi$
$709$	−38.8211	−	21.3421i	−1.45796	−	0.801518i	−0.996333	+	0.0855589i	$0.972732\pi$
$710$	−0.876938	−	5.69459i	−0.0329109	−	0.213714i
$711$	0.240174	+	1.25903i	0.00900721	+	0.0472175i
$712$	−4.34781	+	7.90864i	−0.162941	+	0.296389i
$713$	51.1308	+	9.75372i	1.91486	+	0.365280i
$714$	19.9378	+	18.7229i	0.746155	+	0.700686i
$715$	−13.0561	−	22.2942i	−0.488271	−	0.833755i
$716$	−5.09150	−	10.8200i	−0.190278	−	0.404362i
$717$	−4.06946	+	10.2783i	−0.151977	+	0.383850i
$718$	18.0756	−	24.8789i	0.674575	−	0.928473i
$719$	4.89915	−	5.92205i	0.182707	−	0.220855i	−0.671205	−	0.741271i	$-0.734223\pi$
$719$	4.89915	−	5.92205i	0.182707	−	0.220855i	0.853913	+	0.520416i	$0.174223\pi$
$720$	0.173531	−	0.172050i	0.00646713	−	0.00641194i
$721$	1.64186	−	2.58716i	0.0611461	−	0.0963509i
$722$	−11.8334	−	7.50968i	−0.440392	−	0.279481i
$723$	−9.10693	+	1.73724i	−0.338690	+	0.0646086i
$724$	−2.70977	+	8.33982i	−0.100708	+	0.309947i
$725$	−1.67092	−	0.803837i	−0.0620564	−	0.0298538i
$726$	4.35377	+	13.3995i	0.161584	+	0.497303i
$727$	−0.0924307	−	0.168131i	−0.00342807	−	0.00623563i	0.874587	−	0.484868i	$-0.161133\pi$
$727$	−0.0924307	−	0.168131i	−0.00342807	−	0.00623563i	−0.878015	+	0.478633i	$0.841133\pi$
$728$	53.7218	−	44.4426i	1.99106	−	1.64715i
$729$	24.2883	−	9.61643i	0.899567	−	0.356164i
$730$	−30.7639	−	11.2248i	−1.13862	−	0.415450i
$731$	1.32985	−	21.1374i	0.0491863	−	0.781794i
$732$	−4.95428	−	1.60974i	−0.183116	−	0.0594978i
$733$	37.4071	+	30.9459i	1.38166	+	1.14301i	0.973127	+	0.230269i	$0.0739607\pi$
$733$	37.4071	+	30.9459i	1.38166	+	1.14301i	0.408536	+	0.912742i	$0.366039\pi$
$734$	2.00752	−	10.5238i	0.0740989	−	0.388440i
$735$	−22.1989	−	0.792859i	−0.818818	−	0.0292450i
$736$	−36.9935	−	4.67337i	−1.36360	−	0.172263i
$737$	−1.31900	−	10.4409i	−0.0485859	−	0.384597i
$738$	−0.446358	−	0.475322i	−0.0164306	−	0.0174969i
$739$	−4.93932	+	10.4966i	−0.181696	+	0.386123i	−0.974838	−	0.222913i	$-0.928444\pi$
$739$	−4.93932	+	10.4966i	−0.181696	+	0.386123i	0.793143	+	0.609036i	$0.208444\pi$
$740$	−2.04918	+	8.98647i	−0.0753295	+	0.330349i
$741$	−26.0734	+	3.29384i	−0.957832	+	0.121002i
$742$	−3.04868	−	11.8738i	−0.111921	−	0.435902i
$743$	−12.0332	+	3.90981i	−0.441454	+	0.143437i	−0.521306	−	0.853370i	$-0.674555\pi$
$743$	−12.0332	+	3.90981i	−0.441454	+	0.143437i	0.0798525	+	0.996807i	$0.474555\pi$
$744$	33.2912	+	13.1809i	1.22052	+	0.483236i
$745$	8.44595	−	19.2902i	0.309436	−	0.706740i
$746$	−9.25727	−	11.1901i	−0.338933	−	0.409699i
$747$	1.02639	−	0.0645749i	0.0375536	−	0.00236267i
$748$	−6.55654	−	3.08527i	−0.239731	−	0.112809i
$749$	−42.3504			−1.54745
$750$	−16.7878	+	11.0962i	−0.613004	+	0.405177i
$751$	−9.03639			−0.329742			−0.164871	−	0.986315i	$-0.552721\pi$
$751$	−9.03639			−0.329742			−0.164871	+	0.986315i	$0.552721\pi$
$752$	6.26413	+	2.94767i	0.228429	+	0.107491i
$753$	19.6906	−	1.23883i	0.717565	−	0.0451454i
$754$	1.56966	+	1.89739i	0.0571635	+	0.0690988i
$755$	0.903670	−	0.529215i	0.0328879	−	0.0192601i
$756$	16.1017	+	6.37513i	0.585614	+	0.231861i
$757$	29.2367	−	9.49958i	1.06263	−	0.345268i	0.275015	−	0.961440i	$-0.411317\pi$
$757$	29.2367	−	9.49958i	1.06263	−	0.345268i	0.787612	+	0.616172i	$0.211317\pi$
$758$	5.04268	+	19.6399i	0.183158	+	0.713355i
$759$	−24.0024	+	3.03221i	−0.871233	+	0.110062i
$760$	13.3662	+	7.98224i	0.484842	+	0.289546i
$761$	10.0402	−	21.3366i	0.363958	−	0.773449i	−0.636041	−	0.771656i	$-0.719429\pi$
$761$	10.0402	−	21.3366i	0.363958	−	0.773449i	0.999998	−	0.00179394i	$-0.000571030\pi$
$762$	−5.06769	−	5.39654i	−0.183583	−	0.195496i
$763$	−2.01100	−	15.9187i	−0.0728030	−	0.576295i
$764$	14.4140	+	1.82092i	0.521482	+	0.0658784i
$765$	−0.241399	−	0.844389i	−0.00872779	−	0.0305289i
$766$	6.02832	−	31.6016i	0.217812	−	1.14181i
$767$	2.73859	+	2.26556i	0.0988848	+	0.0818046i
$768$	−28.1799	−	9.15621i	−1.01686	−	0.330396i
$769$	1.57744	−	25.0727i	0.0568840	−	0.904145i	−0.861326	−	0.508052i	$-0.830366\pi$
$769$	1.57744	−	25.0727i	0.0568840	−	0.904145i	0.918210	−	0.396093i	$-0.129634\pi$
$770$	−13.9407	+	3.98545i	−0.502388	+	0.143626i
$771$	22.9339	−	9.08017i	0.825944	−	0.327014i
$772$	9.50192	−	7.86067i	0.341982	−	0.282912i
$773$	10.5871	+	19.2579i	0.380792	+	0.692659i	0.995362	−	0.0962040i	$-0.0306701\pi$
$773$	10.5871	+	19.2579i	0.380792	+	0.692659i	−0.614569	+	0.788863i	$0.710670\pi$
$774$	−0.144137	−	0.443608i	−0.00518090	−	0.0159452i
$775$	−28.2911	−	18.2960i	−1.01625	−	0.657213i
$776$	−5.83993	+	17.9735i	−0.209641	+	0.645210i
$777$	−26.5927	+	5.07284i	−0.954009	+	0.181987i
$778$	5.13494	+	3.25873i	0.184096	+	0.116831i
$779$	8.55475	−	13.4801i	0.306506	−	0.482975i
$780$	−24.0048	+	3.69662i	−0.859510	+	0.132360i
$781$	−2.85791	+	3.45462i	−0.102264	+	0.123616i
$782$	19.8577	−	27.3317i	0.710109	−	0.977381i
$783$	−0.698081	+	1.76315i	−0.0249474	+	0.0630099i
$784$	−2.85966	−	6.07708i	−0.102131	−	0.217039i
$785$	−33.6073	+	7.36106i	−1.19950	+	0.262727i
$786$	−2.84371	−	2.67042i	−0.101432	−	0.0952507i
$787$	29.8012	+	5.68488i	1.06230	+	0.202644i	0.688773	−	0.724977i	$-0.258150\pi$
$787$	29.8012	+	5.68488i	1.06230	+	0.202644i	0.373524	+	0.927621i	$0.378150\pi$
$788$	5.67452	−	10.3219i	0.202147	−	0.367703i
$789$	−4.12265	−	21.6117i	−0.146770	−	0.769397i
$790$	28.4977	−	14.3668i	1.01390	−	0.511148i
$791$	35.7423	+	19.6495i	1.27085	+	0.698656i
$792$	−0.493795	−	0.0310670i	−0.0175463	−	0.00110392i
$793$	−11.8629	−	16.3279i	−0.421265	−	0.579821i
$794$	−10.9685	+	2.81623i	−0.389258	+	0.0999444i
$795$	−3.74824	+	12.6982i	−0.132936	+	0.450358i
$796$	−0.431076	−	6.85176i	−0.0152791	−	0.242854i
$797$	−3.64264	+	14.1871i	−0.129029	+	0.502534i	0.870910	+	0.491443i	$0.163530\pi$
$797$	−3.64264	+	14.1871i	−0.129029	+	0.502534i	−0.999938	+	0.0110909i	$0.996470\pi$
$798$	−1.84852	+	14.6325i	−0.0654368	+	0.517985i
$799$	20.1287	−	14.6243i	0.712101	−	0.517372i
$800$	21.0490	+	11.8078i	0.744195	+	0.417470i
$801$	0.222102	+	0.161367i	0.00784760	+	0.00570161i
$802$	−4.81347	+	5.12582i	−0.169969	+	0.180999i
$803$	9.38090	+	23.6934i	0.331045	+	0.836123i
$804$	−9.58250	−	2.46037i	−0.337949	−	0.0867705i
$805$	5.51936	+	61.1861i	0.194532	+	2.15653i
$806$	23.9752	+	37.7789i	0.844492	+	1.33071i
$807$			8.75477i			0.308183i
$808$	18.2133	−	11.5585i	0.640741	−	0.406627i
$809$	−1.45269	+	1.36417i	−0.0510740	+	0.0479617i	−0.709664	−	0.704540i	$-0.751153\pi$
$809$	−1.45269	+	1.36417i	−0.0510740	+	0.0479617i	0.658590	+	0.752502i	$0.271153\pi$
$810$	12.9288	+	16.8160i	0.454273	+	0.590855i
$811$	24.6610	−	13.5575i	0.865966	−	0.476069i	0.0141439	−	0.999900i	$-0.495498\pi$
$811$	24.6610	−	13.5575i	0.865966	−	0.476069i	0.851822	+	0.523831i	$0.175498\pi$
$812$	−1.13640	+	0.534748i	−0.0398797	+	0.0187660i
$813$	28.8132	−	13.5584i	1.01052	−	0.475515i
$814$	−6.91596	+	3.80208i	−0.242404	+	0.133263i
$815$	−39.9409	+	14.1866i	−1.39907	+	0.496934i
$816$	6.51071	−	6.11396i	0.227920	−	0.214032i
$817$	9.64290	−	6.11957i	0.337362	−	0.214097i
$818$			40.3417i			1.41051i
$819$	−1.13644	−	1.79074i	−0.0397103	−	0.0625734i
$820$	7.56517	−	12.6678i	0.264187	−	0.442379i
$821$	20.5115	+	5.26645i	0.715855	+	0.183800i	0.589014	−	0.808123i	$-0.299516\pi$
$821$	20.5115	+	5.26645i	0.715855	+	0.183800i	0.126841	+	0.991923i	$0.459516\pi$
$822$	10.0550	+	25.3960i	0.350708	+	0.885786i
$823$	−13.6013	+	14.4840i	−0.474113	+	0.504879i	−0.920920	−	0.389751i	$-0.872561\pi$
$823$	−13.6013	+	14.4840i	−0.474113	+	0.504879i	0.446807	+	0.894630i	$0.352561\pi$
$824$	−2.10629	−	1.53031i	−0.0733759	−	0.0533107i
$825$	15.1334	+	4.02415i	0.526877	+	0.140103i
$826$	1.61371	−	1.17243i	0.0561482	−	0.0407940i
$827$	5.27524	−	41.7578i	0.183438	−	1.45206i	−0.584426	−	0.811447i	$-0.698680\pi$
$827$	5.27524	−	41.7578i	0.183438	−	1.45206i	0.767863	−	0.640614i	$-0.221320\pi$
$828$	−0.168159	+	0.654936i	−0.00584393	+	0.0227606i
$829$	−0.434588	−	6.90758i	−0.0150939	−	0.239910i	−0.998339	−	0.0576198i	$-0.981649\pi$
$829$	−0.434588	−	6.90758i	−0.0150939	−	0.239910i	0.983245	−	0.182290i	$-0.0583511\pi$
$830$	−8.57069	−	24.1299i	−0.297493	−	0.837563i
$831$	31.9285	−	8.19784i	1.10759	−	0.284380i
$832$	−27.9059	−	38.4092i	−0.967464	−	1.33160i
$833$	−24.0899	−	1.51561i	−0.834664	−	0.0525126i
$834$	−15.3265	−	8.42581i	−0.530713	−	0.291762i
$835$	−0.393331	−	0.396717i	−0.0136118	−	0.0137289i
$836$	−0.732189	−	3.83827i	−0.0253233	−	0.132749i
$837$	−16.5996	+	30.1946i	−0.573767	+	1.04368i
$838$	−35.3587	−	6.74502i	−1.22144	−	0.233003i
$839$	−25.9781	−	24.3950i	−0.896863	−	0.842211i	0.0912675	−	0.995826i	$-0.470908\pi$
$839$	−25.9781	−	24.3950i	−0.896863	−	0.842211i	−0.988131	+	0.153616i	$0.950908\pi$
$840$	−4.15717	+	42.0541i	−0.143436	+	1.45100i
$841$	12.2890	+	26.1155i	0.423760	+	0.900536i
$842$	10.7170	−	27.0681i	0.369333	−	0.932828i
$843$	−11.3367	+	15.6036i	−0.390457	+	0.537417i
$844$	−0.636300	+	0.769154i	−0.0219023	+	0.0264754i
$845$	−57.8154	−	29.7712i	−1.98891	−	1.02416i
$846$	0.293607	−	0.462650i	0.0100944	−	0.0159063i
$847$	−23.5061	−	14.9174i	−0.807680	−	0.512569i
$848$	−3.93226	+	0.750119i	−0.135034	+	0.0257592i
$849$	−11.7772	+	36.2465i	−0.404193	+	1.24398i
$850$	−18.5626	+	11.5583i	−0.636693	+	0.396445i
$851$	10.3335	+	31.8032i	0.354228	+	1.09020i
$852$	2.03053	+	3.69352i	0.0695648	+	0.126538i
$853$	28.1119	−	23.2562i	0.962533	−	0.796277i	−0.0165236	−	0.999863i	$-0.505260\pi$
$853$	28.1119	−	23.2562i	0.962533	−	0.796277i	0.979057	+	0.203587i	$0.0652599\pi$
$854$	−10.5311	+	4.16954i	−0.360365	+	0.142679i
$855$	0.291859	−	0.372951i	0.00998136	−	0.0127547i
$856$	−2.25943	+	35.9126i	−0.0772258	+	1.22747i
$857$	37.1537	+	12.0720i	1.26915	+	0.412370i	0.864745	−	0.502212i	$-0.167480\pi$
$857$	37.1537	+	12.0720i	1.26915	+	0.412370i	0.404401	+	0.914582i	$0.367480\pi$
$858$	−16.0239	−	13.2561i	−0.547046	−	0.452556i
$859$	−0.931033	+	4.88065i	−0.0317664	+	0.166525i	−0.994635	−	0.103444i	$-0.967014\pi$
$859$	−0.931033	+	4.88065i	−0.0317664	+	0.166525i	0.962869	+	0.269970i	$0.0870137\pi$
$860$	8.75496	−	5.89518i	0.298542	−	0.201024i
$861$	42.9956	+	5.43161i	1.46529	+	0.185109i
$862$	−0.210712	−	1.66795i	−0.00717687	−	0.0568108i
$863$	−38.2649	−	40.7480i	−1.30255	−	1.38708i	−0.875773	−	0.482724i	$-0.839647\pi$
$863$	−38.2649	−	40.7480i	−1.30255	−	1.38708i	−0.426781	−	0.904355i	$-0.640353\pi$
$864$	10.5094	−	22.3336i	0.357536	−	0.759804i
$865$	23.9834	−	20.9623i	0.815461	−	0.712739i
$866$	−25.6394	+	3.23901i	−0.871263	+	0.110066i
$867$	−0.548539	−	2.13642i	−0.0186294	−	0.0725566i
$868$	−21.7037	+	7.05195i	−0.736671	+	0.239359i
$869$	−23.0904	−	9.14215i	−0.783289	−	0.310126i
$870$	−1.48530	−	0.146826i	−0.0503563	−	0.00497787i
$871$	−24.4326	−	29.5339i	−0.827866	−	1.00072i
$872$	−13.6061	+	0.856026i	−0.460762	+	0.0289887i
$873$	0.520164	+	0.244771i	0.0176049	+	0.00828424i
$874$	18.2179			0.616228
$875$	11.5838	−	38.0395i	0.391603	−	1.28597i
$876$	23.9560			0.809398
$877$	20.4459	+	9.62112i	0.690410	+	0.324882i	0.738779	−	0.673947i	$-0.235403\pi$
$877$	20.4459	+	9.62112i	0.690410	+	0.324882i	−0.0483697	+	0.998829i	$0.515403\pi$
$878$	1.63225	−	0.102692i	0.0550857	−	0.00346570i
$879$	−1.64520	−	1.98871i	−0.0554913	−	0.0670775i
$880$	1.01304	+	4.62507i	0.0341495	+	0.155911i
$881$	−27.6188	−	10.9350i	−0.930500	−	0.368411i	−0.146527	−	0.989207i	$-0.546810\pi$
$881$	−27.6188	−	10.9350i	−0.930500	−	0.368411i	−0.783972	+	0.620796i	$0.786810\pi$
$882$	−0.505572	+	0.164270i	−0.0170235	+	0.00553127i
$883$	−6.01784	−	23.4379i	−0.202516	−	0.788749i	−0.985917	−	0.167233i	$-0.946517\pi$
$883$	−6.01784	−	23.4379i	−0.202516	−	0.788749i	0.783401	−	0.621516i	$-0.213483\pi$
$884$	−26.1839	+	3.30779i	−0.880659	+	0.111253i
$885$	−2.14554	+	0.193541i	−0.0721215	+	0.00650581i
$886$	−5.92647	+	12.5944i	−0.199104	+	0.423117i
$887$	−24.2563	−	25.8304i	−0.814448	−	0.867300i	0.178731	−	0.983898i	$-0.442801\pi$
$887$	−24.2563	−	25.8304i	−0.814448	−	0.867300i	−0.993179	+	0.116599i	$0.962801\pi$
$888$	2.88296	+	22.8210i	0.0967457	+	0.765821i
$889$	14.5129	+	1.83341i	0.486749	+	0.0614907i
$890$	2.34304	−	6.42158i	0.0785390	−	0.215252i
$891$	3.09292	−	16.2136i	0.103617	−	0.543177i
$892$	−1.08843	−	0.900431i	−0.0364435	−	0.0301487i
$893$	12.7600	+	4.14598i	0.426998	+	0.138740i
$894$	1.06434	−	16.9172i	0.0355968	−	0.565795i
$895$	15.6841	+	23.2925i	0.524260	+	0.778581i
$896$	7.15111	−	2.83132i	0.238902	−	0.0945879i
$897$	−67.8947	+	56.1674i	−2.26694	+	1.87538i
$898$	18.5052	+	33.6609i	0.617527	+	1.12328i
$899$	−0.772194	−	2.37657i	−0.0257541	−	0.0792630i
$900$	0.260278	−	0.351860i	0.00867592	−	0.0117287i
$901$	−4.44579	+	13.6827i	−0.148111	+	0.455838i
$902$	12.4100	−	2.36734i	0.413208	−	0.0788237i
$903$	26.1750	+	16.6112i	0.871050	+	0.552785i
$904$	18.5694	−	29.2607i	0.617610	−	0.973197i
$905$	3.30841	−	20.3244i	0.109975	−	0.675607i
$906$	0.537322	−	0.649510i	0.0178513	−	0.0215785i
$907$	−6.14217	+	8.45398i	−0.203948	+	0.280710i	−0.898723	−	0.438517i	$-0.855504\pi$
$907$	−6.14217	+	8.45398i	−0.203948	+	0.280710i	0.694775	+	0.719227i	$0.255504\pi$
$908$	−1.30127	+	3.28662i	−0.0431840	+	0.109070i
$909$	−0.279390	−	0.593735i	−0.00926679	−	0.0196929i
$910$	−35.0925	+	39.4625i	−1.16331	+	1.30817i
$911$	0.463626	+	0.435374i	0.0153606	+	0.0144246i	0.692189	−	0.721716i	$-0.256646\pi$
$911$	0.463626	+	0.435374i	0.0153606	+	0.0144246i	−0.676829	+	0.736140i	$0.736646\pi$
$912$	4.73092	+	0.902471i	0.156656	+	0.0298838i
$913$	−9.59951	+	17.4614i	−0.317697	+	0.577889i
$914$	−5.46680	−	28.6580i	−0.180826	−	0.947922i
$915$	12.0738	+	1.96537i	0.399147	+	0.0649731i
$916$	−17.3410	−	9.53331i	−0.572964	−	0.314989i
$917$	7.69317	+	0.484013i	0.254051	+	0.0159835i
$918$	13.1449	+	18.0924i	0.433846	+	0.597138i
$919$	13.2871	−	3.41155i	0.438301	−	0.112537i	−0.0230903	−	0.999733i	$-0.507351\pi$
$919$	13.2871	−	3.41155i	0.438301	−	0.112537i	0.461391	+	0.887197i	$0.347351\pi$
$920$	52.1795	−	1.41602i	1.72031	−	0.0466849i
$921$	3.53163	+	56.1337i	0.116371	+	1.84967i
$922$	2.81528	−	10.9648i	0.0927163	−	0.361106i
$923$	−2.04668	+	16.2011i	−0.0673671	+	0.533266i
$924$	8.58092	−	6.23440i	0.282292	−	0.205097i
$925$	1.54413	−	21.5892i	0.0507708	−	0.709847i
$926$	−7.16105	−	5.20280i	−0.235327	−	0.170975i
$927$	−0.0542141	+	0.0577322i	−0.00178063	+	0.00189617i
$928$	0.658959	+	1.66434i	0.0216314	+	0.0546346i
$929$	42.6979	+	10.9630i	1.40087	+	0.359683i	0.872202	−	0.489145i	$-0.162691\pi$
$929$	42.6979	+	10.9630i	1.40087	+	0.359683i	0.528669	+	0.848828i	$0.322691\pi$
$930$	−26.4411	−	6.02937i	−0.867039	−	0.197711i
$931$	−6.97436	−	10.9898i	−0.228575	−	0.360177i
$932$			18.2151i			0.596655i
$933$	−9.19959	+	5.83824i	−0.301181	+	0.191135i
$934$	17.8530	−	16.7651i	0.584168	−	0.548570i
$935$	16.3198	+	4.81728i	0.533715	+	0.157542i
$936$	−1.57915	+	0.868146i	−0.0516162	+	0.0283762i
$937$	37.3656	−	17.5829i	1.22068	−	0.574409i	0.296013	−	0.955184i	$-0.404343\pi$
$937$	37.3656	−	17.5829i	1.22068	−	0.574409i	0.924668	+	0.380775i	$0.124343\pi$
$938$	−19.4638	+	9.15895i	−0.635514	+	0.299050i
$939$	7.32534	−	4.02714i	0.239053	−	0.131421i
$940$	11.8920	+	3.51028i	0.387875	+	0.114493i
$941$	27.5484	−	25.8697i	0.898054	−	0.843329i	−0.0902355	−	0.995920i	$-0.528762\pi$
$941$	27.5484	−	25.8697i	0.898054	−	0.843329i	0.988289	+	0.152592i	$0.0487620\pi$
$942$	−23.3822	+	14.8388i	−0.761832	+	0.483473i
$943$		−	53.5306i		−	1.74320i
$944$	−0.349014	−	0.549957i	−0.0113594	−	0.0178996i
$945$	−39.6492	−	9.04120i	−1.28979	−	0.294110i
$946$	8.75356	+	2.24753i	0.284603	+	0.0730735i
$947$	−16.3636	−	41.3298i	−0.531746	−	1.34304i	−0.908949	−	0.416907i	$-0.863114\pi$
$947$	−16.3636	−	41.3298i	−0.531746	−	1.34304i	0.377203	−	0.926131i	$-0.376886\pi$
$948$	−15.9816	+	17.0187i	−0.519059	+	0.552742i
$949$	75.0879	+	54.5546i	2.43746	+	1.77092i
$950$	−10.9260	−	4.43461i	−0.354487	−	0.143878i
$951$	−6.67666	+	4.85087i	−0.216505	+	0.157300i
$952$	−5.75533	+	45.5581i	−0.186531	+	1.47655i
$953$	−13.6304	+	53.0870i	−0.441533	+	1.71966i	0.225156	+	0.974323i	$0.427711\pi$
$953$	−13.6304	+	53.0870i	−0.441533	+	1.71966i	−0.666690	+	0.745336i	$0.732289\pi$
$954$	0.0198950	+	0.316223i	0.000644126	+	0.0102381i
$955$	−34.1045	+	0.925511i	−1.10359	+	0.0299488i
$956$	−5.79832	+	1.48876i	−0.187531	+	0.0481498i
$957$	0.682671	+	0.939617i	0.0220676	+	0.0303735i
$958$	−10.0422	−	0.631799i	−0.324447	−	0.0204125i
$959$	−47.2966	−	26.0015i	−1.52729	−	0.839632i
$960$	28.4019	+	4.62326i	0.916668	+	0.149215i
$961$	−2.69928	−	14.1501i	−0.0870734	−	0.456455i
$962$	−13.8479	+	25.1893i	−0.446475	+	0.812134i
$963$	1.07521	+	0.205107i	0.0346481	+	0.00660949i
$964$	−3.65987	−	3.43684i	−0.117876	−	0.110693i
$965$	−19.2436	+	21.6400i	−0.619474	+	0.696615i
$966$	21.0553	+	44.7448i	0.677443	+	1.43964i
$967$	−11.0737	+	27.9691i	−0.356107	+	0.899425i	0.635729	+	0.771912i	$0.280699\pi$
$967$	−11.0737	+	27.9691i	−0.356107	+	0.899425i	−0.991837	+	0.127513i	$0.959301\pi$
$968$	−13.9039	+	19.1371i	−0.446888	+	0.615088i
$969$	11.0331	−	13.3367i	0.354435	−	0.428438i
$970$	2.29977	−	14.1281i	0.0738411	−	0.453625i
$971$	−8.80293	+	13.8712i	−0.282499	+	0.445148i	−0.955713	−	0.294300i	$-0.904913\pi$
$971$	−8.80293	+	13.8712i	−0.282499	+	0.445148i	0.673214	+	0.739448i	$0.264913\pi$
$972$	−0.767790	−	0.487254i	−0.0246269	−	0.0156287i
$973$	33.9478	−	6.47589i	1.08832	−	0.207608i
$974$	−5.67887	+	17.4778i	−0.181963	+	0.560024i
$975$	54.3918	−	17.1590i	1.74193	−	0.549528i
$976$	1.14295	+	3.51763i	0.0365848	+	0.112597i
$977$	−6.40418	−	11.6492i	−0.204888	−	0.372690i	0.753821	−	0.657080i	$-0.228209\pi$
$977$	−6.40418	−	11.6492i	−0.204888	−	0.372690i	−0.958708	+	0.284391i	$0.908209\pi$
$978$	−26.2883	+	21.7476i	−0.840607	+	0.695410i
$979$	−4.94571	+	1.95814i	−0.158065	+	0.0625825i
$980$	−6.71863	−	9.97787i	−0.214619	−	0.318731i
$981$	−0.0260397	+	0.413890i	−0.000831384	+	0.0132145i
$982$	−21.3574	−	6.93945i	−0.681543	−	0.221447i
$983$	−3.37425	−	2.79142i	−0.107622	−	0.0890326i	0.582057	−	0.813148i	$-0.302248\pi$
$983$	−3.37425	−	2.79142i	−0.107622	−	0.0890326i	−0.689679	+	0.724116i	$0.742248\pi$
$984$	6.89979	−	36.1700i	0.219957	−	1.15306i
$985$	−9.48091	+	25.9844i	−0.302087	+	0.827930i
$986$	−1.60906	−	0.203271i	−0.0512428	−	0.00647347i
$987$	4.56447	+	36.1315i	0.145289	+	1.15008i
$988$	−9.74233	−	10.3745i	−0.309945	−	0.330058i
$989$	16.3042	−	34.6483i	0.518445	−	1.10175i
$990$	0.373234	−	0.0336680i	0.0118622	−	0.00107004i
$991$	16.4930	−	2.08355i	0.523916	−	0.0661860i	0.141073	−	0.989999i	$-0.454945\pi$
$991$	16.4930	−	2.08355i	0.523916	−	0.0661860i	0.382843	+	0.923813i	$0.374945\pi$
$992$	8.08879	+	31.5038i	0.256819	+	1.00025i
$993$	−41.2229	+	13.3941i	−1.30817	+	0.425050i
$994$	8.52083	+	3.37364i	0.270264	+	0.107005i
$995$	3.44936	+	15.7482i	0.109352	+	0.499253i
$996$	11.9403	+	14.4334i	0.378344	+	0.457340i
$997$	−7.51887	+	0.473047i	−0.238125	+	0.0149815i	−0.181405	−	0.983409i	$-0.558064\pi$
$997$	−7.51887	+	0.473047i	−0.238125	+	0.0149815i	−0.0567203	+	0.998390i	$0.518064\pi$
$998$	17.9743	+	8.45808i	0.568968	+	0.267736i
$999$	−22.1357			−0.700344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.9.5	✓	240
5.2	odd	4		625.2.g.b.326.17		480
5.3	odd	4		625.2.g.b.326.8		480
5.4	even	2		625.2.h.a.299.8		240
125.14	even	50	inner	125.2.h.a.14.5	yes	240
125.48	odd	100		625.2.g.b.301.8		480
125.77	odd	100		625.2.g.b.301.17		480
125.111	even	25		625.2.h.a.324.8		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.9.5	✓	240	1.1	even	1	trivial
125.2.h.a.14.5	yes	240	125.14	even	50	inner
625.2.g.b.301.8		480	125.48	odd	100
625.2.g.b.301.17		480	125.77	odd	100
625.2.g.b.326.8		480	5.3	odd	4
625.2.g.b.326.17		480	5.2	odd	4
625.2.h.a.299.8		240	5.4	even	2
625.2.h.a.324.8		240	125.111	even	25

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.926191 - 0.435832i) q^{2} +(-1.75492 + 0.110410i) q^{3} +(-0.606968 - 0.733699i) q^{4} +(1.67095 + 1.48591i) q^{5} +(1.67351 + 0.662589i) q^{6} +(-3.38254 + 1.09905i) q^{7} +(0.751522 + 2.92699i) q^{8} +(0.0912001 - 0.0115212i) q^{9} +O(q^{10})\)	\(q+(-0.926191 - 0.435832i) q^{2} +(-1.75492 + 0.110410i) q^{3} +(-0.606968 - 0.733699i) q^{4} +(1.67095 + 1.48591i) q^{5} +(1.67351 + 0.662589i) q^{6} +(-3.38254 + 1.09905i) q^{7} +(0.751522 + 2.92699i) q^{8} +(0.0912001 - 0.0115212i) q^{9} +(-0.900008 - 2.10449i) q^{10} +(-0.758354 + 1.61159i) q^{11} +(1.14619 + 1.22057i) q^{12} +(0.813049 + 6.43595i) q^{13} +(3.61188 + 0.456286i) q^{14} +(-3.09643 - 2.42316i) q^{15} +(0.222765 - 1.16778i) q^{16} +(-3.29203 - 2.72340i) q^{17} +(-0.0894900 - 0.0290771i) q^{18} +(0.144666 - 2.29939i) q^{19} +(0.0759995 - 2.12787i) q^{20} +(5.81473 - 2.30221i) q^{21} +(1.40476 - 1.16212i) q^{22} +(-3.72148 - 6.76935i) q^{23} +(-1.64203 - 5.05364i) q^{24} +(0.584131 + 4.96576i) q^{25} +(2.05196 - 6.31527i) q^{26} +(5.02295 - 0.958178i) q^{27} +(2.85947 + 1.81467i) q^{28} +(-0.198708 + 0.313114i) q^{29} +(1.81180 + 3.59384i) q^{30} +(-4.29518 + 5.19198i) q^{31} +(2.83721 - 3.90508i) q^{32} +(1.15291 - 2.91193i) q^{33} +(1.86210 + 3.95717i) q^{34} +(-7.28514 - 3.18969i) q^{35} +(-0.0638087 - 0.0599203i) q^{36} +(-4.25219 - 0.811148i) q^{37} +(-1.13614 + 2.06663i) q^{38} +(-2.13743 - 11.2048i) q^{39} +(-3.09349 + 6.00754i) q^{40} +(6.07250 + 3.33838i) q^{41} +(-6.38893 - 0.401957i) q^{42} +(2.91369 + 4.01035i) q^{43} +(1.64272 - 0.421778i) q^{44} +(0.169510 + 0.116264i) q^{45} +(0.496501 + 7.89165i) q^{46} +(-1.44821 + 5.64041i) q^{47} +(-0.262000 + 2.07395i) q^{48} +(4.57052 - 3.32068i) q^{49} +(1.62322 - 4.85383i) q^{50} +(6.07793 + 4.41588i) q^{51} +(4.22855 - 4.50295i) q^{52} +(-1.23959 - 3.13084i) q^{53} +(-5.06981 - 1.30171i) q^{54} +(-3.66184 + 1.56603i) q^{55} +(-5.75897 - 9.07468i) q^{56} +4.05122i q^{57} +(0.320507 - 0.203400i) q^{58} +(0.399398 - 0.375059i) q^{59} +(0.101566 + 3.74263i) q^{60} +(-2.72633 + 1.49881i) q^{61} +(6.24099 - 2.93679i) q^{62} +(-0.295825 + 0.139205i) q^{63} +(-6.41332 + 3.52575i) q^{64} +(-8.20469 + 11.9622i) q^{65} +(-2.33693 + 2.19452i) q^{66} +(-4.98886 + 3.16603i) q^{67} +4.06838i q^{68} +(7.27830 + 11.4688i) q^{69} +(5.35726 + 6.12936i) q^{70} +(2.43820 + 0.626023i) q^{71} +(0.102261 + 0.258283i) q^{72} +(9.79412 - 10.4297i) q^{73} +(3.58481 + 2.60452i) q^{74} +(-1.57337 - 8.65001i) q^{75} +(-1.77487 + 1.28952i) q^{76} +(0.793945 - 6.28472i) q^{77} +(-2.90374 + 11.3093i) q^{78} +(0.875507 + 13.9158i) q^{79} +(2.10744 - 1.62028i) q^{80} +(-8.97617 + 2.30469i) q^{81} +(-4.16932 - 5.73857i) q^{82} +(11.1655 + 0.702474i) q^{83} +(-5.21849 - 2.86889i) q^{84} +(-1.45407 - 9.44233i) q^{85} +(-0.950793 - 4.98423i) q^{86} +(0.314145 - 0.571428i) q^{87} +(-5.28701 - 1.00855i) q^{88} +(2.17706 + 2.04440i) q^{89} +(-0.106327 - 0.181561i) q^{90} +(-9.82362 - 20.8763i) q^{91} +(-2.70784 + 6.83923i) q^{92} +(6.96444 - 9.58573i) q^{93} +(3.79959 - 4.59292i) q^{94} +(3.65843 - 3.62721i) q^{95} +(-4.54791 + 7.16635i) q^{96} +(5.28023 + 3.35094i) q^{97} +(-5.68044 + 1.08360i) q^{98} +(-0.0505945 + 0.155714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

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