LMFDB - Embedded newform 783.2.bf.a.4.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(4,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(126)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.bf (of order $126$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$3168$
Relative dimension:	$88$ over $\Q(\zeta_{126})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{126}]$

Embedding invariants

Embedding label			4.18
Character	$\chi$	$=$	783.4
Dual form			783.2.bf.a.196.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.58421 - 1.02319i) q^{2} +(1.57107 + 0.729195i) q^{3} +(0.640218 + 1.41887i) q^{4} +(2.56954 + 1.08315i) q^{5} +(-1.74280 - 2.76270i) q^{6} +(-1.47186 + 3.26199i) q^{7} +(-0.124625 + 0.826830i) q^{8} +(1.93655 + 2.29124i) q^{9} +(-2.96241 - 4.34506i) q^{10} +(-1.51520 - 1.33717i) q^{11} +(-0.0288017 + 2.69599i) q^{12} +(-3.74342 - 2.28755i) q^{13} +(5.66936 - 3.66166i) q^{14} +(3.24711 + 3.57541i) q^{15} +(3.10342 - 3.51660i) q^{16} +(2.86169 + 1.65220i) q^{17} +(-0.723524 - 5.61125i) q^{18} +(6.04936 - 0.453337i) q^{19} +(0.108215 + 4.33930i) q^{20} +(-4.69103 + 4.05155i) q^{21} +(1.03221 + 3.66869i) q^{22} +(-4.00388 + 7.80986i) q^{23} +(-0.798714 + 1.20814i) q^{24} +(1.93815 + 1.98708i) q^{25} +(3.58974 + 7.45417i) q^{26} +(1.37170 + 5.01183i) q^{27} -5.57065 q^{28} +(-4.29687 - 3.24606i) q^{29} +(-1.48578 - 8.98660i) q^{30} +(3.45259 + 4.55805i) q^{31} +(-6.90477 + 1.94270i) q^{32} +(-1.40543 - 3.20567i) q^{33} +(-2.84300 - 5.54547i) q^{34} +(-7.31525 + 6.78756i) q^{35} +(-2.01115 + 4.21460i) q^{36} +(2.20687 - 0.866134i) q^{37} +(-10.0473 - 5.47145i) q^{38} +(-4.21311 - 6.32360i) q^{39} +(-1.21581 + 1.98959i) q^{40} +(-1.83049 - 5.02923i) q^{41} +(11.5771 - 1.61867i) q^{42} +(-1.85940 - 4.41103i) q^{43} +(0.927212 - 3.00595i) q^{44} +(2.49429 + 7.98502i) q^{45} +(14.3339 - 8.27570i) q^{46} +(-2.13462 + 10.5593i) q^{47} +(7.43999 - 3.26185i) q^{48} +(-3.84237 - 4.35393i) q^{49} +(-1.03726 - 5.13104i) q^{50} +(3.29116 + 4.68246i) q^{51} +(0.849137 - 6.77595i) q^{52} +(-2.75905 + 12.0882i) q^{53} +(2.95498 - 9.34328i) q^{54} +(-2.44501 - 5.07711i) q^{55} +(-2.51368 - 1.62350i) q^{56} +(9.83456 + 3.69893i) q^{57} +(3.48580 + 9.53893i) q^{58} +(0.0902815 - 0.512012i) q^{59} +(-2.99418 + 6.89627i) q^{60} +(3.34375 + 1.50876i) q^{61} +(-0.805867 - 10.7535i) q^{62} +(-10.3243 + 2.94461i) q^{63} +(3.96272 + 1.22234i) q^{64} +(-7.14110 - 9.93266i) q^{65} +(-1.05351 + 6.51646i) q^{66} +(1.19080 - 3.54425i) q^{67} +(-0.512147 + 5.11813i) q^{68} +(-11.9853 + 9.35026i) q^{69} +(18.5338 - 3.26801i) q^{70} +(4.88473 - 0.736254i) q^{71} +(-2.13581 + 1.31565i) q^{72} +(0.849667 + 0.915723i) q^{73} +(-4.38236 - 0.885913i) q^{74} +(1.59600 + 4.53514i) q^{75} +(4.51613 + 8.29301i) q^{76} +(6.59200 - 2.97442i) q^{77} +(0.204205 + 14.3287i) q^{78} +(1.71527 + 2.80692i) q^{79} +(11.7834 - 5.67458i) q^{80} +(-1.49955 + 8.87420i) q^{81} +(-2.24598 + 9.84027i) q^{82} +(2.75052 + 2.81997i) q^{83} +(-8.75190 - 4.06209i) q^{84} +(5.56366 + 7.34505i) q^{85} +(-1.56763 + 8.89050i) q^{86} +(-4.38370 - 8.23306i) q^{87} +(1.29444 - 1.08617i) q^{88} +(2.75420 + 8.92890i) q^{89} +(4.21872 - 15.2020i) q^{90} +(12.9718 - 8.84400i) q^{91} +(-13.6445 - 0.680970i) q^{92} +(2.10057 + 9.67865i) q^{93} +(14.1859 - 14.5441i) q^{94} +(16.0351 + 5.38751i) q^{95} +(-12.2645 - 1.98279i) q^{96} +(-16.1111 - 4.53296i) q^{97} +(1.63221 + 10.8290i) q^{98} +(0.129520 - 6.06118i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3168 q - 42 q^{2} - 42 q^{3} - 30 q^{4} - 30 q^{5} - 60 q^{6} - 30 q^{7} - 21 q^{8} - 42 q^{9} - 21 q^{10} - 42 q^{11} - 30 q^{13} - 42 q^{14} - 42 q^{15} - 18 q^{16} - 189 q^{18} - 21 q^{19} + 24 q^{20}+ \cdots - 21 q^{98}+O(q^{100}) $ 3168 * q - 42 * q^2 - 42 * q^3 - 30 * q^4 - 30 * q^5 - 60 * q^6 - 30 * q^7 - 21 * q^8 - 42 * q^9 - 21 * q^10 - 42 * q^11 - 30 * q^13 - 42 * q^14 - 42 * q^15 - 18 * q^16 - 189 * q^18 - 21 * q^19 + 24 * q^20 - 42 * q^21 - 30 * q^22 + 60 * q^23 + 60 * q^24 - 30 * q^25 - 84 * q^26 - 168 * q^27 - 144 * q^28 - 72 * q^29 - 54 * q^30 - 42 * q^31 - 42 * q^32 + 60 * q^33 - 60 * q^34 - 45 * q^35 + 60 * q^36 - 21 * q^37 - 42 * q^39 - 42 * q^40 - 30 * q^42 - 42 * q^43 - 21 * q^44 + 12 * q^45 - 42 * q^47 - 105 * q^48 - 120 * q^49 - 42 * q^50 - 57 * q^51 - 132 * q^53 - 12 * q^54 - 84 * q^55 - 126 * q^56 - 36 * q^57 - 63 * q^58 - 66 * q^59 - 42 * q^60 - 42 * q^61 + 3 * q^62 + 150 * q^63 - 237 * q^64 + 66 * q^65 - 42 * q^66 - 30 * q^67 - 126 * q^68 - 42 * q^69 - 111 * q^71 - 42 * q^72 - 21 * q^73 + 270 * q^74 - 42 * q^76 - 42 * q^77 - 66 * q^78 - 42 * q^79 - 246 * q^80 - 42 * q^81 - 60 * q^82 - 228 * q^83 - 168 * q^84 - 147 * q^85 + 36 * q^86 + 39 * q^87 - 12 * q^88 - 21 * q^89 - 42 * q^90 - 15 * q^91 + 120 * q^92 - 24 * q^93 + 96 * q^94 - 210 * q^95 - 258 * q^96 - 42 * q^97 - 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−1.58421	−	1.02319i	−1.12020	−	0.723503i	−0.155760	−	0.987795i	$-0.549782\pi$
$2$	−1.58421	−	1.02319i	−1.12020	−	0.723503i	−0.964443	+	0.264292i	$0.914862\pi$
$3$	1.57107	+	0.729195i	0.907060	+	0.421001i
$3$	1.57107	+	0.729195i	0.907060	+	0.421001i
$4$	0.640218	+	1.41887i	0.320109	+	0.709435i
$5$	2.56954	+	1.08315i	1.14913	+	0.484401i	0.878246	−	0.478210i	$-0.158714\pi$
$5$	2.56954	+	1.08315i	1.14913	+	0.484401i	0.270889	+	0.962611i	$0.412682\pi$
$6$	−1.74280	−	2.76270i	−0.711495	−	1.12787i
$7$	−1.47186	+	3.26199i	−0.556312	+	1.23291i	0.393277	+	0.919420i	$0.371341\pi$
$7$	−1.47186	+	3.26199i	−0.556312	+	1.23291i	−0.949590	+	0.313495i	$0.898500\pi$
$8$	−0.124625	+	0.826830i	−0.0440614	+	0.292328i
$9$	1.93655	+	2.29124i	0.645517	+	0.763746i
$10$	−2.96241	−	4.34506i	−0.936798	−	1.37403i
$11$	−1.51520	−	1.33717i	−0.456849	−	0.403172i	0.401806	−	0.915725i	$-0.368383\pi$
$11$	−1.51520	−	1.33717i	−0.456849	−	0.403172i	−0.858656	+	0.512553i	$0.828700\pi$
$12$	−0.0288017	+	2.69599i	−0.00831433	+	0.778266i
$13$	−3.74342	−	2.28755i	−1.03824	−	0.634453i	−0.105280	−	0.994443i	$-0.533574\pi$
$13$	−3.74342	−	2.28755i	−1.03824	−	0.634453i	−0.932956	+	0.359989i	$0.882780\pi$
$14$	5.66936	−	3.66166i	1.51520	−	0.978620i
$15$	3.24711	+	3.57541i	0.838401	+	0.923167i
$16$	3.10342	−	3.51660i	0.775855	−	0.879151i
$17$	2.86169	+	1.65220i	0.694062	+	0.400717i	0.805132	−	0.593096i	$-0.202094\pi$
$17$	2.86169	+	1.65220i	0.694062	+	0.400717i	−0.111070	+	0.993813i	$0.535428\pi$
$18$	−0.723524	−	5.61125i	−0.170536	−	1.32258i
$19$	6.04936	−	0.453337i	1.38782	−	0.104003i	0.640239	−	0.768176i	$-0.278835\pi$
$19$	6.04936	−	0.453337i	1.38782	−	0.104003i	0.747579	+	0.664173i	$0.231216\pi$
$20$	0.108215	+	4.33930i	0.0241977	+	0.970297i
$21$	−4.69103	+	4.05155i	−1.02367	+	0.884120i
$22$	1.03221	+	3.66869i	0.220068	+	0.782166i
$23$	−4.00388	+	7.80986i	−0.834867	+	1.62847i	−0.0584141	+	0.998292i	$0.518604\pi$
$23$	−4.00388	+	7.80986i	−0.834867	+	1.62847i	−0.776453	+	0.630176i	$0.782983\pi$
$24$	−0.798714	+	1.20814i	−0.163037	+	0.246610i
$25$	1.93815	+	1.98708i	0.387629	+	0.397417i
$26$	3.58974	+	7.45417i	0.704006	+	1.46188i
$27$	1.37170	+	5.01183i	0.263985	+	0.964527i
$28$	−5.57065			−1.05275
$29$	−4.29687	−	3.24606i	−0.797909	−	0.602778i
$29$	−4.29687	−	3.24606i	−0.797909	−	0.602778i
$30$	−1.48578	−	8.98660i	−0.271264	−	1.64072i
$31$	3.45259	+	4.55805i	0.620104	+	0.818651i	0.994064	−	0.108794i	$-0.0346989\pi$
$31$	3.45259	+	4.55805i	0.620104	+	0.818651i	−0.373961	+	0.927445i	$0.622000\pi$
$32$	−6.90477	+	1.94270i	−1.22060	+	0.343424i
$33$	−1.40543	−	3.20567i	−0.244654	−	0.558035i
$34$	−2.84300	−	5.54547i	−0.487570	−	0.951041i
$35$	−7.31525	+	6.78756i	−1.23650	+	1.14731i
$36$	−2.01115	+	4.21460i	−0.335192	+	0.702434i
$37$	2.20687	−	0.866134i	0.362808	−	0.142392i	−0.176933	−	0.984223i	$-0.556618\pi$
$37$	2.20687	−	0.866134i	0.362808	−	0.142392i	0.539741	+	0.841831i	$0.318522\pi$
$38$	−10.0473	−	5.47145i	−1.62988	−	0.887587i
$39$	−4.21311	−	6.32360i	−0.674638	−	1.01259i
$40$	−1.21581	+	1.98959i	−0.192237	+	0.314581i
$41$	−1.83049	−	5.02923i	−0.285875	−	0.785434i	−0.996633	−	0.0819973i	$-0.973870\pi$
$41$	−1.83049	−	5.02923i	−0.285875	−	0.785434i	0.710758	−	0.703437i	$-0.248352\pi$
$42$	11.5771	−	1.61867i	1.78638	−	0.249767i
$43$	−1.85940	−	4.41103i	−0.283557	−	0.672676i	0.716123	−	0.697974i	$-0.245915\pi$
$43$	−1.85940	−	4.41103i	−0.283557	−	0.672676i	−0.999680	+	0.0252981i	$0.991947\pi$
$44$	0.927212	−	3.00595i	0.139783	−	0.453164i
$45$	2.49429	+	7.98502i	0.371826	+	1.19034i
$46$	14.3339	−	8.27570i	2.11342	−	1.22018i
$47$	−2.13462	+	10.5593i	−0.311366	+	1.54024i	0.450662	+	0.892695i	$0.351188\pi$
$47$	−2.13462	+	10.5593i	−0.311366	+	1.54024i	−0.762028	+	0.647544i	$0.775796\pi$
$48$	7.43999	−	3.26185i	1.07387	−	0.470807i
$49$	−3.84237	−	4.35393i	−0.548910	−	0.621991i
$50$	−1.03726	−	5.13104i	−0.146691	−	0.725639i
$51$	3.29116	+	4.68246i	0.460854	+	0.655675i
$52$	0.849137	−	6.77595i	0.117754	−	0.939655i
$53$	−2.75905	+	12.0882i	−0.378985	+	1.66044i	0.321603	+	0.946875i	$0.395779\pi$
$53$	−2.75905	+	12.0882i	−0.378985	+	1.66044i	−0.700587	+	0.713567i	$0.747079\pi$
$54$	2.95498	−	9.34328i	0.402122	−	1.27146i
$55$	−2.44501	−	5.07711i	−0.329685	−	0.684597i
$56$	−2.51368	−	1.62350i	−0.335904	−	0.216950i
$57$	9.83456	+	3.69893i	1.30262	+	0.489936i
$58$	3.48580	+	9.53893i	0.457708	+	1.25252i
$59$	0.0902815	−	0.512012i	0.0117536	−	0.0666582i	−0.978367	−	0.206878i	$-0.933670\pi$
$59$	0.0902815	−	0.512012i	0.0117536	−	0.0666582i	0.990120	+	0.140220i	$0.0447808\pi$
$60$	−2.99418	+	6.89627i	−0.386547	+	0.890305i
$61$	3.34375	+	1.50876i	0.428124	+	0.193177i	0.613846	−	0.789425i	$-0.289621\pi$
$61$	3.34375	+	1.50876i	0.428124	+	0.193177i	−0.185723	+	0.982602i	$0.559463\pi$
$62$	−0.805867	−	10.7535i	−0.102345	−	1.36570i
$63$	−10.3243	+	2.94461i	−1.30074	+	0.370986i
$64$	3.96272	+	1.22234i	0.495340	+	0.152792i
$65$	−7.14110	−	9.93266i	−0.885744	−	1.23200i
$66$	−1.05351	+	6.51646i	−0.129678	+	0.802121i
$67$	1.19080	−	3.54425i	0.145480	−	0.432999i	−0.850133	−	0.526568i	$-0.823478\pi$
$67$	1.19080	−	3.54425i	0.145480	−	0.432999i	0.995613	+	0.0935692i	$0.0298276\pi$
$68$	−0.512147	+	5.11813i	−0.0621069	+	0.620665i
$69$	−11.9853	+	9.35026i	−1.44286	+	1.12564i
$70$	18.5338	−	3.26801i	2.21521	−	0.390602i
$71$	4.88473	−	0.736254i	0.579711	−	0.0873773i	0.147360	−	0.989083i	$-0.452922\pi$
$71$	4.88473	−	0.736254i	0.579711	−	0.0873773i	0.432351	+	0.901706i	$0.357684\pi$
$72$	−2.13581	+	1.31565i	−0.251707	+	0.155051i
$73$	0.849667	+	0.915723i	0.0994460	+	0.107177i	0.780813	−	0.624764i	$-0.214805\pi$
$73$	0.849667	+	0.915723i	0.0994460	+	0.107177i	−0.681367	+	0.731941i	$0.738614\pi$
$74$	−4.38236	−	0.885913i	−0.509439	−	0.102985i
$75$	1.59600	+	4.53514i	0.184290	+	0.523673i
$76$	4.51613	+	8.29301i	0.518036	+	0.951274i
$77$	6.59200	−	2.97442i	0.751228	−	0.338967i
$78$	0.204205	+	14.3287i	0.0231217	+	1.62240i
$79$	1.71527	+	2.80692i	0.192983	+	0.315803i	0.935045	−	0.354528i	$-0.115359\pi$
$79$	1.71527	+	2.80692i	0.192983	+	0.315803i	−0.742062	+	0.670331i	$0.766152\pi$
$80$	11.7834	−	5.67458i	1.31742	−	0.634438i
$81$	−1.49955	+	8.87420i	−0.166617	+	0.986022i
$82$	−2.24598	+	9.84027i	−0.248027	+	1.08668i
$83$	2.75052	+	2.81997i	0.301909	+	0.309532i	0.849892	−	0.526958i	$-0.176667\pi$
$83$	2.75052	+	2.81997i	0.301909	+	0.309532i	−0.547982	+	0.836490i	$0.684604\pi$
$84$	−8.75190	−	4.06209i	−0.954910	−	0.443210i
$85$	5.56366	+	7.34505i	0.603463	+	0.796682i
$86$	−1.56763	+	8.89050i	−0.169042	+	0.958687i
$87$	−4.38370	−	8.23306i	−0.469982	−	0.882676i
$88$	1.29444	−	1.08617i	0.137988	−	0.115786i
$89$	2.75420	+	8.92890i	0.291945	+	0.946461i	0.976136	+	0.217159i	$0.0696790\pi$
$89$	2.75420	+	8.92890i	0.291945	+	0.946461i	−0.684192	+	0.729302i	$0.739845\pi$
$90$	4.21872	−	15.2020i	0.444692	−	1.60243i
$91$	12.9718	−	8.84400i	1.35981	−	0.927103i
$92$	−13.6445	−	0.680970i	−1.42254	−	0.0709960i
$93$	2.10057	+	9.67865i	0.217819	+	1.00363i
$94$	14.1859	−	14.5441i	1.46316	−	1.50010i
$95$	16.0351	+	5.38751i	1.64517	+	0.552747i
$96$	−12.2645	−	1.98279i	−1.25174	−	0.202368i
$97$	−16.1111	−	4.53296i	−1.63584	−	0.460253i	−0.675102	−	0.737725i	$-0.735900\pi$
$97$	−16.1111	−	4.53296i	−1.63584	−	0.460253i	−0.960734	+	0.277472i	$0.910503\pi$
$98$	1.63221	+	10.8290i	0.164878	+	1.09389i
$99$	0.129520	−	6.06118i	0.0130172	−	0.609171i
$100$	−1.57858	+	4.02214i	−0.157858	+	0.402214i
$101$	5.00234	−	6.60401i	0.497752	−	0.657124i	−0.477394	−	0.878690i	$-0.658418\pi$
$101$	5.00234	−	6.60401i	0.497752	−	0.657124i	0.975145	+	0.221566i	$0.0711168\pi$
$102$	−0.422831	−	10.7854i	−0.0418665	−	1.06792i
$103$	14.8891	−	8.10819i	1.46707	−	0.798924i	0.470558	−	0.882369i	$-0.344053\pi$
$103$	14.8891	−	8.10819i	1.46707	−	0.798924i	0.996512	+	0.0834457i	$0.0265925\pi$
$104$	2.35794	−	2.81008i	0.231215	−	0.275551i
$105$	−16.4423	+	5.32952i	−1.60460	+	0.520108i
$106$	16.7394	−	16.3272i	1.62587	−	1.58583i
$107$	7.45585	−	9.34934i	0.720784	−	0.903835i	−0.277598	−	0.960697i	$-0.589538\pi$
$107$	7.45585	−	9.34934i	0.720784	−	0.903835i	0.998382	+	0.0568624i	$0.0181096\pi$
$108$	−6.23294	+	5.15493i	−0.599765	+	0.496034i
$109$	7.67560	−	3.69638i	0.735189	−	0.354049i	−0.0285334	−	0.999593i	$-0.509084\pi$
$109$	7.67560	−	3.69638i	0.735189	−	0.354049i	0.763723	+	0.645544i	$0.223369\pi$
$110$	−1.32145	+	10.5449i	−0.125995	+	1.00542i
$111$	4.09874	+	0.248480i	0.389036	+	0.0235847i
$112$	6.90330	+	15.2993i	0.652300	+	1.44565i
$113$	−0.384621	+	0.108216i	−0.0361821	+	0.0101801i	−0.288884	−	0.957364i	$-0.593284\pi$
$113$	−0.384621	+	0.108216i	−0.0361821	+	0.0101801i	0.252702	+	0.967544i	$0.418681\pi$
$114$	−11.7953	−	15.9225i	−1.10473	−	1.49128i
$115$	−18.7474	+	15.7310i	−1.74821	+	1.46692i
$116$	1.85480	−	8.17488i	0.172213	−	0.759019i
$117$	−2.00798	−	13.0070i	−0.185638	−	1.20250i
$118$	−0.666909	+	0.718757i	−0.0613939	+	0.0661669i
$119$	−9.60147	+	6.90299i	−0.880166	+	0.632796i
$120$	−3.36093	+	2.23923i	−0.306809	+	0.204412i
$121$	−0.859980	−	6.86247i	−0.0781800	−	0.623861i
$122$	−3.75345	−	5.81147i	−0.339821	−	0.526146i
$123$	0.791453	−	9.23608i	0.0713629	−	0.832789i
$124$	−4.25687	+	7.81692i	−0.382278	+	0.701981i
$125$	−2.26594	−	5.77353i	−0.202672	−	0.516400i
$126$	19.3687	+	5.89887i	1.72550	+	0.525513i
$127$	−0.226450	−	0.0888750i	−0.0200942	−	0.00788638i	0.355273	−	0.934763i	$-0.384388\pi$
$127$	−0.226450	−	0.0888750i	−0.0200942	−	0.00788638i	−0.375367	+	0.926876i	$0.622483\pi$
$128$	4.19417	+	4.99842i	0.370716	+	0.441802i
$129$	0.295236	−	8.28592i	0.0259941	−	0.729535i
$130$	1.14998	+	23.0421i	0.100860	+	2.02092i
$131$	13.1412	+	6.73708i	1.14815	+	0.588622i	0.922656	−	0.385623i	$-0.126014\pi$
$131$	13.1412	+	6.73708i	1.14815	+	0.588622i	0.225493	+	0.974245i	$0.427601\pi$
$132$	3.64864	−	4.04645i	0.317574	−	0.352198i
$133$	−7.42506	+	20.4002i	−0.643834	+	1.76892i
$134$	−5.51291	+	4.39640i	−0.476243	+	0.379791i
$135$	−1.90392	+	14.3639i	−0.163864	+	1.23625i
$136$	−1.72272	+	2.16023i	−0.147722	+	0.185238i
$137$	−8.39873	−	13.7439i	−0.717552	−	1.17422i	−0.977974	−	0.208726i	$-0.933068\pi$
$137$	−8.39873	−	13.7439i	−0.717552	−	1.17422i	0.260422	−	0.965495i	$-0.416138\pi$
$138$	28.5543	−	2.54951i	2.43070	−	0.217029i
$139$	8.20320	−	16.0009i	0.695786	−	1.35718i	−0.227769	−	0.973715i	$-0.573143\pi$
$139$	8.20320	−	16.0009i	0.695786	−	1.35718i	0.923555	−	0.383466i	$-0.125270\pi$
$140$	−14.3140	−	6.03386i	−1.20976	−	0.509955i
$141$	−11.0535	+	15.0330i	−0.930870	+	1.26600i
$142$	−8.49174	−	3.83162i	−0.712611	−	0.321542i
$143$	2.61317	+	8.47168i	0.218524	+	0.708438i
$144$	14.0673	+	0.300601i	1.17228	+	0.0250501i
$145$	−7.52502	−	12.9951i	−0.624919	−	1.07918i
$146$	−0.409090	−	2.32006i	−0.0338565	−	0.192010i
$147$	−2.86178	−	9.64219i	−0.236036	−	0.795275i
$148$	2.64181	+	2.57675i	0.217156	+	0.211808i
$149$	0.0579713	+	0.00580091i	0.00474920	+	0.000475229i	0.101942	−	0.994790i	$-0.467494\pi$
$149$	0.0579713	+	0.00580091i	0.00474920	+	0.000475229i	−0.0971930	+	0.995266i	$0.530986\pi$
$150$	2.11191	−	8.81761i	0.172437	−	0.719955i
$151$	4.07687	−	1.71855i	0.331771	−	0.139853i	−0.216203	−	0.976348i	$-0.569367\pi$
$151$	4.07687	−	1.71855i	0.331771	−	0.139853i	0.547974	+	0.836495i	$0.315399\pi$
$152$	−0.379066	+	5.05828i	−0.0307463	+	0.410281i
$153$	1.75623	+	9.75639i	0.141983	+	0.788757i
$154$	−13.4865	−	2.03276i	−1.08677	−	0.163804i
$155$	3.93451	+	15.4518i	0.316028	+	1.24112i
$156$	6.27504	−	10.0263i	0.502406	−	0.802749i
$157$	6.20697	+	1.09446i	0.495370	+	0.0873471i	0.415751	−	0.909478i	$-0.363519\pi$
$157$	6.20697	+	1.09446i	0.495370	+	0.0873471i	0.0796187	+	0.996825i	$0.474630\pi$
$158$	0.154663	−	6.20178i	0.0123043	−	0.493387i
$159$	−13.1493	+	16.9796i	−1.04281	+	1.34657i
$160$	−19.8464	−	2.48707i	−1.56899	−	0.196620i
$161$	−19.5825	−	24.5557i	−1.54332	−	1.93526i
$162$	11.4556	−	12.5242i	0.900034	−	0.983996i
$163$	15.6950	−	12.5163i	1.22933	−	0.980356i	0.229352	−	0.973344i	$-0.426339\pi$
$163$	15.6950	−	12.5163i	1.22933	−	0.980356i	0.999975	−	0.00701244i	$-0.00223215\pi$
$164$	5.96391	−	5.81703i	0.465703	−	0.454234i
$165$	−0.139086	−	9.75940i	−0.0108278	−	0.759769i
$166$	−1.47203	−	7.28172i	−0.114252	−	0.565171i
$167$	−5.31060	−	18.8750i	−0.410947	−	1.46059i	−0.832620	−	0.553844i	$-0.813160\pi$
$167$	−5.31060	−	18.8750i	−0.410947	−	1.46059i	0.421674	−	0.906748i	$-0.361443\pi$
$168$	−2.76532	−	4.38361i	−0.213349	−	0.338203i
$169$	2.84952	+	5.55820i	0.219194	+	0.427553i
$170$	−1.29861	−	17.3287i	−0.0995988	−	1.32905i
$171$	12.7536	+	12.9826i	0.975291	+	0.992805i
$172$	5.06825	−	5.46227i	0.386450	−	0.416494i
$173$	−0.627860	−	3.56077i	−0.0477353	−	0.270721i	0.951593	−	0.307360i	$-0.0994457\pi$
$173$	−0.627860	−	3.56077i	−0.0477353	−	0.270721i	−0.999329	+	0.0366398i	$0.988335\pi$
$174$	−1.47929	+	17.5282i	−0.112145	+	1.32881i
$175$	−9.33453	+	3.39749i	−0.705624	+	0.256826i
$176$	−9.40460	+	1.17855i	−0.708898	+	0.0888365i
$177$	0.515195	−	0.738576i	0.0387244	−	0.0555147i
$178$	4.77272	−	16.9633i	0.357731	−	1.27145i
$179$	−12.4203	−	11.5244i	−0.928339	−	0.861373i	0.0622753	−	0.998059i	$-0.480164\pi$
$179$	−12.4203	−	11.5244i	−0.928339	−	0.861373i	−0.990614	+	0.136686i	$0.956355\pi$
$180$	−9.73281	+	8.65122i	−0.725441	+	0.644824i
$181$	10.0115	+	6.82572i	0.744148	+	0.507352i	0.875043	−	0.484045i	$-0.160833\pi$
$181$	10.0115	+	6.82572i	0.744148	+	0.507352i	−0.130895	+	0.991396i	$0.541785\pi$
$182$	−29.5990	+	0.738154i	−2.19403	+	0.0547156i
$183$	4.15310	+	4.80862i	0.307006	+	0.355463i
$184$	−5.95844	−	4.28383i	−0.439262	−	0.315808i
$185$	6.60881	+	0.164814i	0.485890	+	0.0121173i
$186$	6.57535	−	17.4823i	0.482128	−	1.28186i
$187$	−2.12676	−	6.32998i	−0.155524	−	0.462894i
$188$	−16.3489	+	3.73154i	−1.19237	+	0.272151i
$189$	−18.3675	−	2.90225i	−1.33604	−	0.211108i
$190$	−19.8905	−	24.9419i	−1.44301	−	1.80947i
$191$	−4.75355	+	13.0603i	−0.343955	+	0.945008i	0.640280	+	0.768142i	$0.278818\pi$
$191$	−4.75355	+	13.0603i	−0.343955	+	0.945008i	−0.984235	+	0.176867i	$0.943404\pi$
$192$	5.33441	+	4.80998i	0.384978	+	0.347130i
$193$	−9.61164	+	4.33694i	−0.691861	+	0.312180i	−0.726447	−	0.687222i	$-0.758830\pi$
$193$	−9.61164	+	4.33694i	−0.691861	+	0.312180i	0.0345862	+	0.999402i	$0.488989\pi$
$194$	20.8852	+	23.6658i	1.49947	+	1.69911i
$195$	−3.97635	−	20.8122i	−0.284752	−	1.49039i
$196$	3.71771	−	8.23929i	0.265551	−	0.588521i
$197$	−0.0640563	+	0.0594356i	−0.00456382	+	0.00423461i	−0.682451	−	0.730931i	$-0.739086\pi$
$197$	−0.0640563	+	0.0594356i	−0.00456382	+	0.00423461i	0.677888	+	0.735166i	$0.262896\pi$
$198$	−6.40691	+	9.46963i	−0.455319	+	0.672977i
$199$	−13.6251	+	9.28944i	−0.965858	+	0.658511i	−0.940007	−	0.341155i	$-0.889182\pi$
$199$	−13.6251	+	9.28944i	−0.965858	+	0.658511i	−0.0258509	+	0.999666i	$0.508230\pi$
$200$	−1.88452	+	1.35488i	−0.133256	+	0.0958044i
$201$	4.45529	−	4.69995i	0.314252	−	0.331509i
$202$	−14.6819	+	5.34377i	−1.03301	+	0.375986i
$203$	16.9130	−	9.23858i	1.18706	−	0.648421i
$204$	−4.53674	+	7.66752i	−0.317635	+	0.536833i
$205$	0.743904	−	14.9055i	0.0519565	−	1.04105i
$206$	−31.8836	−	2.38935i	−2.22144	−	0.166474i
$207$	−25.6480	+	5.95033i	−1.78266	+	0.413577i
$208$	−19.6618	+	6.06487i	−1.36330	+	0.420523i
$209$	−9.77217	−	7.40213i	−0.675955	−	0.512016i
$210$	31.5010	+	8.38047i	2.17378	+	0.578307i
$211$	−13.7299	+	12.1167i	−0.945208	+	0.834151i	−0.986293	−	0.165004i	$-0.947236\pi$
$211$	−13.7299	+	12.1167i	−0.945208	+	0.834151i	0.0410845	+	0.999156i	$0.486919\pi$
$212$	−18.9180	+	3.82435i	−1.29929	+	0.262657i
$213$	8.21114	+	2.40521i	0.562618	+	0.164802i
$214$	−21.3777	+	7.18254i	−1.46135	+	0.490988i
$215$		−	13.3483i		−	0.910350i
$216$	−4.31488	+	0.509569i	−0.293590	+	0.0346718i
$217$	−19.9501	+	4.55347i	−1.35430	+	0.309110i
$218$	−15.9418	−	1.99777i	−1.07972	−	0.135306i
$219$	0.667149	+	2.05824i	0.0450818	+	0.139083i
$220$	5.63842	−	6.71960i	0.380142	−	0.453036i
$221$	−6.93301	−	12.7311i	−0.466365	−	0.856389i
$222$	−6.23901	−	4.58743i	−0.418735	−	0.307888i
$223$	−0.711810	−	28.5427i	−0.0476663	−	1.91136i	−0.317185	−	0.948364i	$-0.602737\pi$
$223$	−0.711810	−	28.5427i	−0.0476663	−	1.91136i	0.269518	−	0.962995i	$-0.413136\pi$
$224$	3.82582	−	25.3827i	0.255623	−	1.69595i
$225$	−0.799566	+	8.28885i	−0.0533044	+	0.552590i
$226$	0.720043	+	0.222104i	0.0478966	+	0.0147741i
$227$	29.6373	+	1.47914i	1.96710	+	0.0981737i	0.992214	−	0.124548i	$-0.0397482\pi$
$227$	29.6373	+	1.47914i	1.96710	+	0.0981737i	0.974882	+	0.222722i	$0.0714942\pi$
$228$	1.04796	+	16.3221i	0.0694029	+	1.08096i
$229$	5.92145	+	5.77562i	0.391300	+	0.381664i	0.867303	−	0.497780i	$-0.165851\pi$
$229$	5.92145	+	5.77562i	0.391300	+	0.381664i	−0.476003	+	0.879444i	$0.657915\pi$
$230$	45.7955	−	5.73892i	3.01966	−	0.378413i
$231$	12.5255	+	0.133811i	0.824114	+	0.00880414i
$232$	3.21943	−	3.14824i	0.211366	−	0.206692i
$233$	−5.40920	+	9.36900i	−0.354368	+	0.613784i	−0.987010	−	0.160661i	$-0.948637\pi$
$233$	−5.40920	+	9.36900i	−0.354368	+	0.613784i	0.632641	+	0.774445i	$0.281971\pi$
$234$	−10.1276	+	22.6603i	−0.662061	+	1.48135i
$235$	−16.9224	+	24.8206i	−1.10389	+	1.61912i
$236$	0.784277	−	0.199702i	0.0510521	−	0.0129995i
$237$	0.648029	+	5.66064i	0.0420940	+	0.367698i
$238$	22.2738	−	1.11164i	1.44379	−	0.0720567i
$239$	9.64022	+	2.45470i	0.623574	+	0.158781i	0.545424	−	0.838160i	$-0.316369\pi$
$239$	9.64022	+	2.45470i	0.623574	+	0.158781i	0.0781497	+	0.996942i	$0.475099\pi$
$240$	22.6505	−	0.322803i	1.46208	−	0.0208368i
$241$	5.84144	−	3.56963i	0.376280	−	0.229940i	−0.320463	−	0.947261i	$-0.603838\pi$
$241$	5.84144	−	3.56963i	0.376280	−	0.229940i	0.696743	+	0.717321i	$0.254632\pi$
$242$	−5.65922	+	11.7515i	−0.363788	+	0.755414i
$243$	−8.82692	+	12.8486i	−0.566247	+	0.824235i
$244$			5.71028i			0.365563i
$245$	−5.15716	−	15.3495i	−0.329479	−	0.980643i
$246$	−10.7041	+	13.8220i	−0.682467	+	0.881261i
$247$	−23.6823	−	12.1412i	−1.50687	−	0.772526i
$248$	−4.19901	+	2.28666i	−0.266637	+	0.145203i
$249$	2.26497	+	6.43606i	0.143537	+	0.407868i
$250$	−2.31769	+	11.4649i	−0.146584	+	0.725107i
$251$	9.65659	−	0.723661i	0.609518	−	0.0456771i	0.233605	−	0.972332i	$-0.424948\pi$
$251$	9.65659	−	0.723661i	0.609518	−	0.0456771i	0.375914	+	0.926655i	$0.377329\pi$
$252$	−10.7878	−	12.7637i	−0.679570	−	0.804036i
$253$	16.5098	−	6.47961i	1.03796	−	0.407370i
$254$	0.267807	+	0.372497i	0.0168037	+	0.0233726i
$255$	3.38495	+	15.5966i	0.211974	+	0.976697i
$256$	−2.56140	−	20.4395i	−0.160088	−	1.27747i
$257$	21.1177	+	2.11315i	1.31729	+	0.131815i	0.733276	−	0.679931i	$-0.237990\pi$
$257$	21.1177	+	2.11315i	1.31729	+	0.131815i	0.584011	+	0.811745i	$0.301482\pi$
$258$	−8.94577	+	12.8245i	−0.556940	+	0.798420i
$259$	−0.422901	+	8.47363i	−0.0262778	+	0.526525i
$260$	9.52129	−	16.4914i	0.590485	−	1.02275i
$261$	−0.883614	−	16.1313i	−0.0546943	−	0.998503i
$262$	−13.9250	−	24.1188i	−0.860289	−	1.49006i
$263$	−13.6631	+	7.00468i	−0.842505	+	0.431927i	−0.823108	−	0.567885i	$-0.807762\pi$
$263$	−13.6631	+	7.00468i	−0.842505	+	0.431927i	−0.0193969	+	0.999812i	$0.506175\pi$
$264$	2.82569	−	0.762547i	0.173909	−	0.0469316i
$265$	−20.1829	+	28.0727i	−1.23982	+	1.72449i
$266$	32.6360	−	24.7208i	2.00104	−	1.51573i
$267$	−2.18385	+	16.0363i	−0.133650	+	0.981406i
$268$	5.79120	−	0.579497i	0.353754	−	0.0353984i
$269$	−2.32518	−	1.85427i	−0.141769	−	0.113057i	0.550038	−	0.835140i	$-0.314613\pi$
$269$	−2.32518	−	1.85427i	−0.141769	−	0.113057i	−0.691806	+	0.722083i	$0.743185\pi$
$270$	17.7132	−	20.8073i	1.07799	−	1.26629i
$271$	2.34644	−	4.87243i	0.142536	−	0.295979i	−0.817464	−	0.575980i	$-0.804621\pi$
$271$	2.34644	−	4.87243i	0.142536	−	0.295979i	0.960000	+	0.280001i	$0.0903349\pi$
$272$	14.6912	−	4.93597i	0.890783	−	0.299287i
$273$	26.8286	−	4.43564i	1.62374	−	0.268457i
$274$	−0.757297	+	30.3666i	−0.0457500	+	1.83452i
$275$	−0.279607	−	5.60246i	−0.0168609	−	0.337841i
$276$	−20.9400	−	11.0194i	−1.26044	−	0.663288i
$277$	−4.86471	−	0.983422i	−0.292292	−	0.0590881i	0.0497853	−	0.998760i	$-0.484146\pi$
$277$	−4.86471	−	0.983422i	−0.292292	−	0.0590881i	−0.342077	+	0.939672i	$0.611130\pi$
$278$	−29.3675	+	16.9553i	−1.76135	+	1.01691i
$279$	−3.75747	+	16.7376i	−0.224954	+	1.00205i
$280$	−4.70050	−	6.89436i	−0.280908	−	0.412017i
$281$	−0.606347	−	0.330199i	−0.0361716	−	0.0196980i	0.460067	−	0.887884i	$-0.347825\pi$
$281$	−0.606347	−	0.330199i	−0.0361716	−	0.0196980i	−0.496238	+	0.868186i	$0.665286\pi$
$282$	32.8925	−	12.5055i	1.95872	−	0.744693i
$283$	−6.96227	+	7.13806i	−0.413864	+	0.424314i	−0.890639	−	0.454712i	$-0.849742\pi$
$283$	−6.96227	+	7.13806i	−0.413864	+	0.424314i	0.476775	+	0.879026i	$0.341806\pi$
$284$	4.17194	+	6.45943i	0.247559	+	0.383296i
$285$	21.2638	+	20.1569i	1.25956	+	1.19399i
$286$	4.52833	−	16.0946i	0.267766	−	0.951696i
$287$	19.0995	+	1.43131i	1.12741	+	0.0844876i
$288$	−17.8226	−	12.0583i	−1.05021	−	0.710545i
$289$	−3.04048	−	5.26626i	−0.178852	−	0.309780i
$290$	−1.37521	+	28.2864i	−0.0807552	+	1.66103i
$291$	−22.0063	−	18.8698i	−1.29003	−	1.10617i
$292$	−0.755319	+	1.79183i	−0.0442017	+	0.104859i
$293$	−0.357324	+	1.40330i	−0.0208751	+	0.0819816i	−0.978648	−	0.205546i	$-0.934103\pi$
$293$	−0.357324	+	1.40330i	−0.0208751	+	0.0819816i	0.957772	+	0.287527i	$0.0928332\pi$
$294$	−5.33213	+	18.2034i	−0.310976	+	1.06164i
$295$	0.786569	−	1.21785i	0.0457958	−	0.0709058i
$296$	0.441115	+	1.93265i	0.0256393	+	0.112333i
$297$	4.62327	−	9.42812i	0.268269	−	0.547075i
$298$	−0.0859031	−	0.0685054i	−0.00497623	−	0.00396841i
$299$	32.8537	−	20.0765i	1.89998	−	1.16105i
$300$	−5.41299	+	5.16800i	−0.312519	+	0.298375i
$301$	17.1255	+	0.427083i	0.987098	+	0.0246167i
$302$	−8.21700	−	1.44888i	−0.472835	−	0.0833736i
$303$	12.6747	−	6.72771i	0.728141	−	0.386497i
$304$	17.1795	−	22.6801i	0.985312	−	1.30079i
$305$	6.95770	+	7.49862i	0.398397	+	0.429370i
$306$	7.20039	−	17.2531i	0.411619	−	0.986292i
$307$	14.9658	+	8.64049i	0.854142	+	0.493139i	0.862046	−	0.506830i	$-0.169183\pi$
$307$	14.9658	+	8.64049i	0.854142	+	0.493139i	−0.00790434	+	0.999969i	$0.502516\pi$
$308$	8.44063	+	7.44890i	0.480950	+	0.424441i
$309$	29.3044	−	1.88149i	1.66707	−	0.107034i
$310$	9.57703	−	28.5046i	0.543939	−	1.61895i
$311$	18.3820	+	6.17602i	1.04235	+	0.350210i	0.787203	−	0.616693i	$-0.211528\pi$
$311$	18.3820	+	6.17602i	1.04235	+	0.350210i	0.255143	+	0.966903i	$0.417877\pi$
$312$	5.75359	−	2.69545i	0.325733	−	0.152600i
$313$	−21.2653	+	8.96408i	−1.20199	+	0.506680i	−0.895443	−	0.445177i	$-0.853141\pi$
$313$	−21.2653	+	8.96408i	−1.20199	+	0.506680i	−0.306544	+	0.951856i	$0.599173\pi$
$314$	−8.71328	−	8.08474i	−0.491719	−	0.456248i
$315$	−29.7183	−	3.61654i	−1.67443	−	0.203769i
$316$	−2.88450	+	4.23078i	−0.162266	+	0.238000i
$317$	11.4245	−	5.85702i	0.641666	−	0.328963i	−0.104695	−	0.994504i	$-0.533387\pi$
$317$	11.4245	−	5.85702i	0.641666	−	0.328963i	0.746361	+	0.665541i	$0.231799\pi$
$318$	38.2045	−	13.4449i	2.14240	−	0.753952i
$319$	2.17008	+	10.6641i	0.121501	+	0.597073i
$320$	8.85840	+	7.43308i	0.495200	+	0.415522i
$321$	18.5312	−	9.25174i	1.03431	−	0.516382i
$322$	5.89761	+	58.9378i	0.328661	+	3.28447i
$323$	18.0604	+	8.69743i	1.00491	+	0.483938i
$324$	−13.5514	+	3.55376i	−0.752853	+	0.197431i
$325$	−2.70973	−	11.8721i	−0.150309	−	0.658546i
$326$	−37.6707	+	3.76952i	−2.08639	+	0.208774i
$327$	14.7543	−	0.210271i	0.815916	−	0.0116280i
$328$	4.38644	−	0.886738i	0.242201	−	0.0489619i
$329$	−31.3026	−	22.5050i	−1.72577	−	1.24074i
$330$	−9.76537	+	15.6032i	−0.537566	+	0.858928i
$331$	−6.73358	−	8.02477i	−0.370111	−	0.441081i	0.548556	−	0.836114i	$-0.315178\pi$
$331$	−6.73358	−	8.02477i	−0.370111	−	0.441081i	−0.918667	+	0.395033i	$0.870733\pi$
$332$	−2.24024	+	5.70803i	−0.122949	+	0.313269i
$333$	6.25824	+	3.37916i	0.342950	+	0.185177i
$334$	−10.8996	+	35.3356i	−0.596399	+	1.93348i
$335$	6.89879	−	7.81728i	0.376921	−	0.427104i
$336$	−0.310561	+	29.0702i	−0.0169425	+	1.58591i
$337$	4.05602	−	6.63739i	0.220946	−	0.361562i	−0.723448	−	0.690379i	$-0.757444\pi$
$337$	4.05602	−	6.63739i	0.220946	−	0.361562i	0.944393	+	0.328818i	$0.106650\pi$
$338$	1.17285	−	11.7209i	0.0637949	−	0.637534i
$339$	−0.683178	−	0.110449i	−0.0371051	−	0.00599876i
$340$	−6.85971	+	12.5965i	−0.372020	+	0.683143i
$341$	0.863534	−	11.5231i	0.0467630	−	0.624009i
$342$	−6.92064	−	33.6164i	−0.374225	−	1.81777i
$343$	−4.07989	+	1.25848i	−0.220294	+	0.0679516i
$344$	3.87890	−	0.987688i	0.209136	−	0.0532526i
$345$	−40.9245	+	11.0440i	−2.20330	+	0.594588i
$346$	−2.64868	+	6.28342i	−0.142394	+	0.337799i
$347$	−21.5395	−	18.0738i	−1.15630	−	0.970250i	−0.156451	−	0.987686i	$-0.550005\pi$
$347$	−21.5395	−	18.0738i	−1.15630	−	0.970250i	−0.999848	+	0.0174355i	$0.994450\pi$
$348$	8.87510	−	11.4908i	0.475756	−	0.615974i
$349$	20.4499	+	7.44317i	1.09466	+	0.398424i	0.825345	−	0.564629i	$-0.190981\pi$
$349$	20.4499	+	7.44317i	1.09466	+	0.398424i	0.269315	+	0.963052i	$0.413203\pi$
$350$	18.2641	+	4.16866i	0.976257	+	0.222824i
$351$	6.32997	−	21.8992i	0.337869	−	1.16889i
$352$	13.0598	+	6.28928i	0.696091	+	0.335220i
$353$	0.371010	−	0.574436i	0.0197469	−	0.0305741i	−0.830013	−	0.557743i	$-0.811667\pi$
$353$	0.371010	−	0.574436i	0.0197469	−	0.0305741i	0.849760	+	0.527169i	$0.176747\pi$
$354$	−1.57188	+	0.642914i	−0.0835443	+	0.0341705i
$355$	13.3490	+	3.39907i	0.708491	+	0.180404i
$356$	−10.9056	+	9.62429i	−0.577998	+	0.510086i
$357$	−20.1183	+	3.84376i	−1.06477	+	0.203434i
$358$	7.88474	+	30.9653i	0.416721	+	1.63657i
$359$	−25.4946	−	10.0059i	−1.34555	−	0.528091i	−0.420281	−	0.907394i	$-0.638068\pi$
$359$	−25.4946	−	10.0059i	−1.34555	−	0.528091i	−0.925272	+	0.379304i	$0.876164\pi$
$360$	−6.91310	+	1.06722i	−0.364352	+	0.0562474i
$361$	17.6014	−	2.65299i	0.926391	−	0.139631i
$362$	−8.87626	−	21.0570i	−0.466526	−	1.10673i
$363$	3.65299	−	11.4086i	0.191732	−	0.598794i
$364$	20.8532	+	12.7432i	1.09301	+	0.667923i
$365$	1.19139	+	3.27331i	0.0623601	+	0.171333i
$366$	−1.65925	−	11.8672i	−0.0867303	−	0.620311i
$367$	12.7570	+	3.58927i	0.665911	+	0.187358i	0.587079	−	0.809530i	$-0.300278\pi$
$367$	12.7570	+	3.58927i	0.665911	+	0.187358i	0.0788320	+	0.996888i	$0.474881\pi$
$368$	15.0384	+	38.3173i	0.783933	+	1.99743i
$369$	7.97833	−	13.9334i	0.415335	−	0.725346i
$370$	−10.3011	−	7.02316i	−0.535528	−	0.365117i
$371$	−35.3706	−	26.7922i	−1.83635	−	1.39098i
$372$	−12.3879	+	9.17688i	−0.642284	+	0.475799i
$373$	3.80773	−	5.29623i	0.197157	−	0.274228i	−0.701698	−	0.712474i	$-0.747575\pi$
$373$	3.80773	−	5.29623i	0.197157	−	0.274228i	0.898855	+	0.438246i	$0.144400\pi$
$374$	−3.10754	+	12.2041i	−0.160687	+	0.631057i
$375$	0.650062	−	10.7230i	0.0335691	−	0.553731i
$376$	−8.46475	−	3.08092i	−0.436536	−	0.158886i
$377$	8.65945	+	21.9807i	0.445984	+	1.13206i
$378$	26.1283	+	23.3912i	1.34390	+	1.20311i
$379$	−0.431865	−	0.0985705i	−0.0221834	−	0.00506322i	0.211415	−	0.977396i	$-0.432193\pi$
$379$	−0.431865	−	0.0985705i	−0.0221834	−	0.00506322i	−0.233598	+	0.972333i	$0.575050\pi$
$380$	2.62180	+	26.2009i	0.134495	+	1.34408i
$381$	−0.290962	−	0.304755i	−0.0149065	−	0.0156131i
$382$	20.8937	−	15.8264i	1.06902	−	0.809748i
$383$	11.0532	−	0.551644i	0.564793	−	0.0281877i	0.234585	−	0.972096i	$-0.424627\pi$
$383$	11.0532	−	0.551644i	0.564793	−	0.0281877i	0.330209	+	0.943908i	$0.392881\pi$
$384$	2.94453	+	10.9113i	0.150263	+	0.556813i
$385$	20.1602	−	0.502764i	1.02746	−	0.0256232i
$386$	19.6643	+	2.96392i	1.00089	+	0.150860i
$387$	6.50589	−	12.8025i	0.330713	−	0.650788i
$388$	−3.88294	−	25.7616i	−0.197127	−	1.30785i
$389$	1.37241	−	0.241993i	0.0695840	−	0.0122695i	−0.138748	−	0.990328i	$-0.544308\pi$
$389$	1.37241	−	0.241993i	0.0695840	−	0.0122695i	0.208332	+	0.978058i	$0.433197\pi$
$390$	−14.9954	+	37.0394i	−0.759324	+	1.87556i
$391$	−24.3613	+	15.7342i	−1.23200	+	0.795713i
$392$	4.07882	−	2.63438i	0.206011	−	0.133056i
$393$	15.7331	+	20.1669i	0.793630	+	1.01729i
$394$	0.162292	−	0.0286165i	0.00817616	−	0.00144168i
$395$	1.36714	+	9.07039i	0.0687884	+	0.456381i
$396$	8.68294	−	3.69670i	0.436334	−	0.185766i
$397$	−29.9549	−	4.51497i	−1.50339	−	0.226600i	−0.654863	−	0.755748i	$-0.727274\pi$
$397$	−29.9549	−	4.51497i	−1.50339	−	0.226600i	−0.848530	+	0.529148i	$0.822512\pi$
$398$	31.0898	−	0.775331i	1.55839	−	0.0388639i
$399$	−26.5410	+	26.6359i	−1.32871	+	1.33346i
$400$	13.0027	−	0.648937i	0.650134	−	0.0324468i
$401$	−14.6239	+	11.0772i	−0.730285	+	0.553169i	−0.901874	−	0.431999i	$-0.857808\pi$
$401$	−14.6239	+	11.0772i	−0.730285	+	0.553169i	0.171589	+	0.985169i	$0.445110\pi$
$402$	−11.8670	+	2.88709i	−0.591874	+	0.143995i
$403$	−2.49769	−	24.9607i	−0.124419	−	1.24338i
$404$	12.5728	+	2.86966i	0.625521	+	0.142771i
$405$	−13.4653	+	21.1784i	−0.669095	+	1.05236i
$406$	−36.2465	−	2.66938i	−1.79888	−	0.132479i
$407$	−4.50202	−	1.63860i	−0.223157	−	0.0812225i
$408$	−4.28175	+	2.13768i	−0.211978	+	0.105831i
$409$	−0.345000	+	1.35490i	−0.0170592	+	0.0669956i	−0.977028	−	0.213112i	$-0.931640\pi$
$409$	−0.345000	+	1.35490i	−0.0170592	+	0.0669956i	0.959969	+	0.280108i	$0.0903702\pi$
$410$	−16.4297	+	22.8523i	−0.811403	+	1.12859i
$411$	−3.17304	−	27.7170i	−0.156514	−	1.36718i
$412$	21.0368	+	15.9347i	1.03641	+	0.785047i
$413$	1.53729	+	1.04811i	0.0756452	+	0.0515741i
$414$	46.7200	+	16.8161i	2.29616	+	0.826469i
$415$	4.01313	+	10.2253i	0.196997	+	0.501939i
$416$	30.2915	+	8.52270i	1.48516	+	0.417860i
$417$	24.5556	−	19.1569i	1.20249	−	0.938119i
$418$	7.90735	+	21.7253i	0.386761	+	1.06262i
$419$	20.3040	+	12.4075i	0.991917	+	0.606148i	0.920271	−	0.391282i	$-0.127968\pi$
$419$	20.3040	+	12.4075i	0.991917	+	0.606148i	0.0716465	+	0.997430i	$0.477175\pi$
$420$	−18.0885	−	19.9174i	−0.882629	−	0.971867i
$421$	−9.27647	−	22.0064i	−0.452107	−	1.07253i	−0.975414	−	0.220381i	$-0.929270\pi$
$421$	−9.27647	−	22.0064i	−0.452107	−	1.07253i	0.523306	−	0.852145i	$-0.324698\pi$
$422$	34.1488	−	5.14710i	1.66234	−	0.250557i
$423$	−28.3278	+	15.5578i	−1.37734	+	0.756445i
$424$	−9.65103	−	3.78775i	−0.468696	−	0.183949i
$425$	2.26332	+	8.88863i	0.109787	+	0.431162i
$426$	−10.5472	−	12.2119i	−0.511012	−	0.591668i
$427$	−9.84310	+	8.68659i	−0.476341	+	0.420373i
$428$	18.0389	+	4.59326i	0.871941	+	0.222024i
$429$	−2.07203	+	15.2152i	−0.100038	+	0.734595i
$430$	−13.6579	+	21.1465i	−0.658641	+	1.01978i
$431$	−32.3289	−	15.5688i	−1.55723	−	0.749922i	−0.560304	−	0.828287i	$-0.689316\pi$
$431$	−32.3289	−	15.5688i	−1.55723	−	0.749922i	−0.996925	+	0.0783647i	$0.975030\pi$
$432$	21.8816	+	10.7301i	1.05278	+	0.516251i
$433$	27.9714	+	6.38428i	1.34422	+	0.306809i	0.833300	−	0.552821i	$-0.186448\pi$
$433$	27.9714	+	6.38428i	1.34422	+	0.306809i	0.510918	+	0.859630i	$0.329306\pi$
$434$	36.2640	+	13.1990i	1.74073	+	0.633574i
$435$	−2.34644	−	25.9034i	−0.112503	−	1.24197i
$436$	10.1587	+	8.52419i	0.486515	+	0.408235i
$437$	−20.6804	+	49.0597i	−0.989278	+	2.34685i
$438$	1.04907	−	3.94330i	0.0501264	−	0.188418i
$439$	28.7370	−	7.31735i	1.37154	−	0.349238i	0.511423	−	0.859329i	$-0.329118\pi$
$439$	28.7370	−	7.31735i	1.37154	−	0.349238i	0.860120	+	0.510091i	$0.170388\pi$
$440$	4.50261	−	1.38887i	0.214654	−	0.0662119i
$441$	2.53496	−	17.2354i	0.120712	−	0.820733i
$442$	−2.04304	+	27.2625i	−0.0971777	+	1.29675i
$443$	−13.5068	+	24.8027i	−0.641729	+	1.17841i	0.330372	+	0.943851i	$0.392826\pi$
$443$	−13.5068	+	24.8027i	−0.641729	+	1.17841i	−0.972101	+	0.234562i	$0.924634\pi$
$444$	2.27153	+	5.97466i	0.107802	+	0.283545i
$445$	−2.59433	+	25.9264i	−0.122983	+	1.22903i
$446$	−28.0769	+	45.9458i	−1.32948	+	2.17560i
$447$	0.0868473	+	0.0513860i	0.00410774	+	0.00243048i
$448$	−9.81984	+	11.1272i	−0.463944	+	0.525712i
$449$	3.73502	−	12.1086i	0.176266	−	0.571442i	−0.823724	−	0.566991i	$-0.808107\pi$
$449$	3.73502	−	12.1086i	0.176266	−	0.571442i	0.999990	−	0.00445024i	$-0.00141656\pi$
$450$	9.74773	−	12.3131i	0.459512	−	0.580446i
$451$	−3.95138	+	10.0680i	−0.186063	+	0.474082i
$452$	−0.399785	−	0.476445i	−0.0188043	−	0.0224101i
$453$	7.65822	+	0.272871i	0.359815	+	0.0128206i
$454$	−45.4381	−	32.6678i	−2.13252	−	1.53317i
$455$	42.9109	−	8.67463i	2.01170	−	0.406673i
$456$	−4.28402	+	7.67053i	−0.200617	+	0.359205i
$457$	16.1694	−	1.61800i	0.756374	−	0.0756866i	0.286091	−	0.958202i	$-0.407644\pi$
$457$	16.1694	−	1.61800i	0.756374	−	0.0756866i	0.470283	+	0.882516i	$0.344152\pi$
$458$	−3.47125	−	15.2085i	−0.162201	−	0.710648i
$459$	−4.35514	+	16.6086i	−0.203281	+	0.775225i
$460$	−34.3226	−	16.5289i	−1.60030	−	0.770664i
$461$	−1.11422	−	11.1349i	−0.0518943	−	0.518605i	−0.986597	−	0.163175i	$-0.947826\pi$
$461$	−1.11422	−	11.1349i	−0.0518943	−	0.518605i	0.934703	−	0.355430i	$-0.115666\pi$
$462$	−19.7060	−	13.0279i	−0.916805	−	0.606112i
$463$	27.3606	+	22.9583i	1.27156	+	1.06696i	0.994350	+	0.106153i	$0.0338533\pi$
$463$	27.3606	+	22.9583i	1.27156	+	1.06696i	0.277207	+	0.960810i	$0.410591\pi$
$464$	−24.7501	+	5.03651i	−1.14899	+	0.233814i
$465$	−5.08596	+	27.1450i	−0.235856	+	1.25882i
$466$	18.1555	−	9.30780i	0.841039	−	0.431175i
$467$	21.1238	−	30.9830i	0.977494	−	1.43372i	0.0779169	−	0.996960i	$-0.475173\pi$
$467$	21.1238	−	30.9830i	0.977494	−	1.43372i	0.899578	−	0.436761i	$-0.143875\pi$
$468$	17.1697	−	11.1764i	0.793670	−	0.516629i
$469$	9.80859	+	9.10104i	0.452919	+	0.420247i
$470$	52.2047	−	22.0061i	2.40802	−	1.01507i
$471$	8.95354	+	6.24556i	0.412557	+	0.287780i
$472$	0.412095	+	0.138457i	0.0189682	+	0.00637298i
$473$	−3.08093	+	9.16992i	−0.141661	+	0.421634i
$474$	4.76529	−	9.63067i	0.218877	−	0.442351i
$475$	12.6254	+	11.1420i	0.579292	+	0.511228i
$476$	−15.9415	−	9.20381i	−0.730676	−	0.421856i
$477$	−33.0400	+	17.0877i	−1.51280	+	0.782394i
$478$	−12.7605	−	13.7525i	−0.583650	−	0.629025i
$479$	−10.1621	+	13.4159i	−0.464320	+	0.612988i	−0.968015	−	0.250894i	$-0.919275\pi$
$479$	−10.1621	+	13.4159i	−0.464320	+	0.612988i	0.503694	+	0.863882i	$0.331974\pi$
$480$	−29.3665	−	18.3792i	−1.34039	−	0.838893i
$481$	−10.2426	−	1.80604i	−0.467021	−	0.0823484i
$482$	−12.9064	−	0.321866i	−0.587872	−	0.0146606i
$483$	−12.8597	−	52.8582i	−0.585136	−	2.40513i
$484$	9.18638	−	5.61368i	0.417563	−	0.255167i
$485$	−36.4883	−	29.0985i	−1.65685	−	1.32129i
$486$	27.1302	−	11.3232i	1.23065	−	0.513629i
$487$	0.825049	+	3.61477i	0.0373865	+	0.163801i	0.990175	−	0.139834i	$-0.0446568\pi$
$487$	0.825049	+	3.61477i	0.0373865	+	0.163801i	−0.952788	+	0.303635i	$0.901800\pi$
$488$	−1.66420	+	2.57668i	−0.0753348	+	0.116641i
$489$	33.7849	−	8.21940i	1.52780	−	0.371694i
$490$	−7.53543	+	29.5935i	−0.340416	+	1.33690i
$491$	−7.92596	+	18.8026i	−0.357694	+	0.848549i	0.639144	+	0.769087i	$0.279289\pi$
$491$	−7.92596	+	18.8026i	−0.357694	+	0.848549i	−0.996838	+	0.0794626i	$0.974680\pi$
$492$	13.6115	−	4.79014i	0.613653	−	0.215956i
$493$	−6.93319	−	16.3885i	−0.312255	−	0.738101i
$494$	25.0949	+	43.4656i	1.12907	+	1.95561i
$495$	6.89799	−	15.4342i	0.310042	−	0.693714i
$496$	26.7437	+	2.00416i	1.20083	+	0.0899896i
$497$	−4.78801	+	17.0176i	−0.214771	+	0.763343i
$498$	2.99712	−	12.5135i	0.134304	−	0.560744i
$499$	10.1085	+	15.6510i	0.452518	+	0.700636i	0.989752	−	0.142798i	$-0.0456099\pi$
$499$	10.1085	+	15.6510i	0.452518	+	0.700636i	−0.537233	+	0.843434i	$0.680531\pi$
$500$	6.74119	−	6.91140i	0.301475	−	0.309087i
$501$	5.42020	−	33.5265i	0.242157	−	1.49785i
$502$	−16.0385	−	8.73408i	−0.715832	−	0.389821i
$503$	7.28548	+	10.6858i	0.324844	+	0.476458i	0.953571	−	0.301167i	$-0.0973763\pi$
$503$	7.28548	+	10.6858i	0.324844	+	0.476458i	−0.628728	+	0.777626i	$0.716424\pi$
$504$	−1.14802	−	8.90343i	−0.0511370	−	0.396590i
$505$	20.0069	−	11.5510i	0.890295	−	0.514012i
$506$	−32.7848	−	6.62758i	−1.45746	−	0.294632i
$507$	0.423801	+	10.8102i	0.0188217	+	0.480098i
$508$	−0.0188753	−	0.378202i	−0.000837455	−	0.0167800i
$509$	1.07147	−	42.9648i	0.0474923	−	1.90438i	−0.280741	−	0.959784i	$-0.590580\pi$
$509$	1.07147	−	42.9648i	0.0474923	−	1.90438i	0.328233	−	0.944597i	$-0.393547\pi$
$510$	10.5958	−	28.1717i	0.469190	−	1.24746i
$511$	−4.23767	+	1.42378i	−0.187464	+	0.0629844i
$512$	−11.1935	+	23.2436i	−0.494688	+	1.02723i
$513$	10.5700	+	29.6965i	0.466676	+	1.31113i
$514$	−31.2927	−	24.9551i	−1.38026	−	1.10072i
$515$	47.0407	−	4.70713i	2.07286	−	0.207421i
$516$	11.9457	−	4.88590i	0.525878	−	0.215090i
$517$	17.3540	−	13.1452i	0.763229	−	0.578123i
$518$	9.34008	−	12.9913i	0.410379	−	0.570803i
$519$	1.61008	−	6.05207i	0.0706748	−	0.265656i
$520$	9.10257	−	4.66662i	0.399174	−	0.204645i
$521$	−0.521763	−	0.903720i	−0.0228589	−	0.0395927i	0.854370	−	0.519666i	$-0.173944\pi$
$521$	−0.521763	−	0.903720i	−0.0228589	−	0.0395927i	−0.877229	+	0.480073i	$0.840610\pi$
$522$	−15.1055	+	26.4594i	−0.661152	+	1.15810i
$523$	−10.6428	+	18.4340i	−0.465379	+	0.806060i	−0.999219	−	0.0395255i	$-0.987415\pi$
$523$	−10.6428	+	18.4340i	−0.465379	+	0.806060i	0.533839	+	0.845586i	$0.320749\pi$
$524$	−1.14583	+	22.9588i	−0.0500556	+	1.00296i
$525$	−17.1427	−	1.46898i	−0.748168	−	0.0641115i
$526$	28.8123	+	2.88311i	1.25628	+	0.125709i
$527$	2.34944	+	18.7481i	0.102343	+	0.816681i
$528$	−15.6347	−	5.00620i	−0.680414	−	0.217867i
$529$	−31.5367	−	43.8649i	−1.37116	−	1.90717i
$530$	60.6974	−	23.8220i	2.63653	−	1.03476i
$531$	1.34798	−	0.784680i	0.0584972	−	0.0340522i
$532$	−33.6988	+	2.52538i	−1.46103	+	0.109489i
$533$	−4.65235	+	23.0138i	−0.201516	+	0.996840i
$534$	19.8678	−	23.1703i	0.859765	−	1.00268i
$535$	29.2849	−	15.9477i	1.26610	−	0.689480i
$536$	2.78209	+	1.42629i	0.120168	+	0.0616065i
$537$	−11.1097	−	27.1625i	−0.479421	−	1.17215i
$538$	1.78629	+	5.31663i	0.0770126	+	0.229216i
$539$			11.7350i			0.505461i
$540$	−21.5994	+	6.49459i	−0.929490	+	0.279483i
$541$	−0.148120	+	0.307573i	−0.00636816	+	0.0132236i	−0.904129	−	0.427260i	$-0.859479\pi$
$541$	−0.148120	+	0.307573i	−0.00636816	+	0.0132236i	0.897761	+	0.440484i	$0.145193\pi$
$542$	−8.70265	+	5.31808i	−0.373811	+	0.228431i
$543$	10.7515	+	18.0240i	0.461392	+	0.773486i
$544$	−22.9691	−	5.84864i	−0.984790	−	0.250758i
$545$	23.7265	−	1.18414i	1.01633	−	0.0507231i
$546$	−47.0405	−	20.4238i	−2.01315	−	0.874056i
$547$	−2.45342	+	0.624717i	−0.104901	+	0.0267110i	−0.298846	−	0.954301i	$-0.596602\pi$
$547$	−2.45342	+	0.624717i	−0.104901	+	0.0267110i	0.193945	+	0.981012i	$0.437872\pi$
$548$	14.1238	−	20.7158i	0.603338	−	0.884935i
$549$	3.01842	+	10.5831i	0.128823	+	0.451677i
$550$	−5.28942	+	9.16154i	−0.225542	+	0.390649i
$551$	−27.4649	−	17.6886i	−1.17004	−	0.753561i
$552$	−6.23741	−	11.0751i	−0.265482	−	0.471386i
$553$	−11.6808	+	1.46379i	−0.496717	+	0.0622467i
$554$	6.70047	+	6.53545i	0.284676	+	0.277665i
$555$	10.2628	+	5.07805i	0.435630	+	0.215551i
$556$	27.9551	+	1.39518i	1.18556	+	0.0591688i
$557$	−30.5626	−	9.42731i	−1.29498	−	0.399448i	−0.430716	−	0.902488i	$-0.641739\pi$
$557$	−30.5626	−	9.42731i	−1.29498	−	0.399448i	−0.864263	+	0.503040i	$0.832215\pi$
$558$	23.0783	−	22.6712i	0.976984	−	0.959749i
$559$	−3.12994	+	20.7658i	−0.132382	+	0.878300i
$560$	1.16686	+	46.7895i	0.0493087	+	1.97722i
$561$	1.27449	−	11.4957i	0.0538090	−	0.485348i
$562$	0.622722	+	1.14351i	0.0262680	+	0.0482361i
$563$	−20.7307	+	24.7059i	−0.873694	+	1.04123i	0.125101	+	0.992144i	$0.460075\pi$
$563$	−20.7307	+	24.7059i	−0.873694	+	1.04123i	−0.998795	+	0.0490836i	$0.984370\pi$
$564$	−28.4064	−	6.05904i	−1.19613	−	0.255132i
$565$	−1.10551	−	0.138539i	−0.0465093	−	0.00582837i
$566$	18.3332	−	4.18444i	0.770604	−	0.175885i
$567$	−26.7404	−	17.9531i	−1.12299	−	0.753960i
$568$			4.13059i			0.173316i
$569$	−30.1977	+	10.1459i	−1.26595	+	0.425338i	−0.870054	−	0.492957i	$-0.835916\pi$
$569$	−30.1977	+	10.1459i	−1.26595	+	0.425338i	−0.395899	+	0.918294i	$0.629567\pi$
$570$	−13.0619	−	53.6896i	−0.547105	−	2.24881i
$571$	−32.5872	+	6.58765i	−1.36373	+	0.275684i	−0.824209	−	0.566286i	$-0.808380\pi$
$571$	−32.5872	+	6.58765i	−1.36373	+	0.275684i	−0.539524	+	0.841970i	$0.681396\pi$
$572$	−10.3472	+	9.13147i	−0.432639	+	0.381806i
$573$	−16.9917	+	17.0524i	−0.709837	+	0.712374i
$574$	−28.7931	−	21.8099i	−1.20180	−	0.910327i
$575$	−23.2790	+	7.18061i	−0.970800	+	0.299452i
$576$	4.87334	+	11.4467i	0.203056	+	0.476944i
$577$	13.3060	+	0.997147i	0.553936	+	0.0415118i	0.348758	−	0.937213i	$-0.386604\pi$
$577$	13.3060	+	0.997147i	0.553936	+	0.0415118i	0.205178	+	0.978725i	$0.434223\pi$
$578$	−0.571637	+	11.4538i	−0.0237769	+	0.476416i
$579$	−18.2631	−	0.195107i	−0.758988	−	0.00810838i
$580$	13.6206	−	18.9967i	0.565566	−	0.788795i
$581$	−13.2471	+	4.82155i	−0.549583	+	0.200032i
$582$	15.5552	+	52.4102i	0.644786	+	2.17247i
$583$	20.3445	−	14.6267i	0.842583	−	0.605776i
$584$	−0.863036	+	0.588408i	−0.0357127	+	0.0243485i
$585$	8.92901	−	35.5971i	0.369169	−	1.47176i
$586$	2.00191	−	1.85750i	0.0826983	−	0.0767328i
$587$	−0.353516	+	0.783471i	−0.0145912	+	0.0323373i	−0.918658	−	0.395054i	$-0.870726\pi$
$587$	−0.353516	+	0.783471i	−0.0145912	+	0.0323373i	0.904067	+	0.427391i	$0.140567\pi$
$588$	11.8488	−	10.2336i	0.488638	−	0.422027i
$589$	22.9523	+	26.0081i	0.945733	+	1.07165i
$590$	−2.49217	+	1.12451i	−0.102601	+	0.0462954i
$591$	−0.143977	+	0.0466682i	−0.00592244	+	0.00191967i
$592$	3.80301	−	10.4487i	0.156303	−	0.429438i
$593$	11.7006	+	14.6721i	0.480487	+	0.602512i	0.961704	−	0.274090i	$-0.0883765\pi$
$593$	11.7006	+	14.6721i	0.480487	+	0.602512i	−0.481217	+	0.876602i	$0.659805\pi$
$594$	−16.9709	+	10.2056i	−0.696326	+	0.418741i
$595$	−32.1484	+	7.33766i	−1.31796	+	0.300815i
$596$	0.0288836	+	0.0859676i	0.00118312	+	0.00352137i
$597$	−28.1799	+	4.65904i	−1.15333	+	0.190682i
$598$	−72.5889	−	1.81025i	−2.96838	−	0.0740268i
$599$	7.86642	+	5.65557i	0.321413	+	0.231080i	0.732902	−	0.680335i	$-0.238166\pi$
$599$	7.86642	+	5.65557i	0.321413	+	0.231080i	−0.411488	+	0.911415i	$0.634991\pi$
$600$	−3.94869	+	0.754432i	−0.161205	+	0.0307995i
$601$	−17.9951	+	0.448771i	−0.734037	+	0.0183057i	−0.390208	−	0.920727i	$-0.627597\pi$
$601$	−17.9951	+	0.448771i	−0.734037	+	0.0183057i	−0.343829	+	0.939032i	$0.611724\pi$
$602$	−26.6933	−	18.1992i	−1.08794	−	0.741744i
$603$	10.4268	−	4.13520i	0.424611	−	0.168398i
$604$	5.04848	+	4.68430i	0.205420	+	0.190602i
$605$	5.22336	−	18.5649i	0.212360	−	0.754771i
$606$	−26.9630	−	2.31050i	−1.09530	−	0.0938575i
$607$	28.0555	−	3.51581i	1.13874	−	0.142702i	0.467534	−	0.883975i	$-0.345143\pi$
$607$	28.0555	−	3.51581i	1.13874	−	0.142702i	0.671204	+	0.741273i	$0.265778\pi$
$608$	−40.8887	+	14.8823i	−1.65826	+	0.603556i
$609$	33.3083	−	2.18162i	1.34972	−	0.0884038i
$610$	−3.34993	−	18.9984i	−0.135635	−	0.769222i
$611$	32.1458	−	34.6450i	1.30048	−	1.40159i
$612$	−12.7187	+	8.73807i	−0.514122	+	0.353216i
$613$	1.48276	+	19.7861i	0.0598882	+	0.799153i	0.943593	+	0.331108i	$0.107422\pi$
$613$	1.48276	+	19.7861i	0.0598882	+	0.799153i	−0.883705	+	0.468045i	$0.844959\pi$
$614$	−14.8680	−	29.0011i	−0.600024	−	1.17039i
$615$	12.0378	−	22.8752i	0.485409	−	0.922419i
$616$	1.63782	+	5.82115i	0.0659895	+	0.234541i
$617$	−4.91586	−	24.3174i	−0.197905	−	0.978981i	−0.948151	−	0.317821i	$-0.897049\pi$
$617$	−4.91586	−	24.3174i	−0.197905	−	0.978981i	0.750245	−	0.661160i	$-0.229935\pi$
$618$	−48.3493	−	27.0032i	−1.94489	−	1.08623i
$619$	19.2330	−	18.7593i	0.773040	−	0.754002i	−0.201192	−	0.979552i	$-0.564482\pi$
$619$	19.2330	−	18.7593i	0.773040	−	0.754002i	0.974232	+	0.225550i	$0.0724180\pi$
$620$	−19.4051	+	15.4751i	−0.779329	+	0.621494i
$621$	−44.6338	−	9.35395i	−1.79109	−	0.375361i
$622$	−22.8016	−	28.5923i	−0.914261	−	1.14645i
$623$	−33.1797	−	4.15796i	−1.32932	−	0.166585i
$624$	−35.3126	−	4.80894i	−1.41364	−	0.192512i
$625$	0.777188	−	31.1643i	0.0310875	−	1.24657i
$626$	42.8606	+	7.55748i	1.71305	+	0.302057i
$627$	−9.95521	−	18.7551i	−0.397573	−	0.749007i
$628$	2.42092	+	9.50757i	0.0966054	+	0.379393i
$629$	7.74642	+	1.16759i	0.308870	+	0.0465547i
$630$	43.3794	+	36.1367i	1.72828	+	1.43972i
$631$	−2.11616	+	28.2382i	−0.0842430	+	1.12414i	0.781584	+	0.623800i	$0.214412\pi$
$631$	−2.11616	+	28.2382i	−0.0842430	+	1.12414i	−0.865827	+	0.500344i	$0.833207\pi$
$632$	−2.53461	+	1.06843i	−0.100821	+	0.0424997i
$633$	−30.4062	+	9.02451i	−1.20854	+	0.358692i
$634$	−24.0917	−	2.41073i	−0.956802	−	0.0957425i
$635$	−0.485608	−	0.473648i	−0.0192707	−	0.0187962i
$636$	−32.5102	−	7.78654i	−1.28911	−	0.308757i
$637$	4.42373	+	25.0882i	0.175275	+	0.994031i
$638$	7.47350	−	19.1145i	0.295879	−	0.756750i
$639$	11.1465	+	9.76629i	0.440947	+	0.386348i
$640$	5.36305	+	17.3866i	0.211993	+	0.687265i
$641$	43.3253	+	19.5491i	1.71125	+	0.772144i	0.997417	+	0.0718230i	$0.0228817\pi$
$641$	43.3253	+	19.5491i	1.71125	+	0.772144i	0.713828	+	0.700321i	$0.246960\pi$
$642$	−38.8235	−	4.30423i	−1.53224	−	0.169875i
$643$	−26.7256	−	11.2658i	−1.05395	−	0.444279i	−0.208330	−	0.978059i	$-0.566803\pi$
$643$	−26.7256	−	11.2658i	−1.05395	−	0.444279i	−0.845623	+	0.533780i	$0.820771\pi$
$644$	22.3042	−	43.5060i	0.878909	−	1.71437i
$645$	9.73355	−	20.9713i	0.383258	−	0.825742i
$646$	−19.7123	−	32.2577i	−0.775569	−	1.26916i
$647$	21.7412	−	27.2626i	0.854734	−	1.07180i	−0.141905	−	0.989880i	$-0.545323\pi$
$647$	21.7412	−	27.2626i	0.854734	−	1.07180i	0.996639	−	0.0819224i	$-0.0261060\pi$
$648$	−7.15057	−	2.34581i	−0.280901	−	0.0921523i
$649$	−0.821441	+	0.655077i	−0.0322444	+	0.0257140i
$650$	−7.85463	+	21.5804i	−0.308084	+	0.846453i
$651$	−34.6634	−	7.39364i	−1.35857	−	0.289779i
$652$	27.8073	+	14.2560i	1.08902	+	0.558307i
$653$	0.331782	+	6.64788i	0.0129836	+	0.260152i	0.996742	+	0.0806546i	$0.0257011\pi$
$653$	0.331782	+	6.64788i	0.0129836	+	0.260152i	−0.983758	+	0.179497i	$0.942553\pi$
$654$	−23.5890	−	14.7633i	−0.922404	−	0.577292i
$655$	26.4695	+	31.5451i	1.03425	+	1.23257i
$656$	−23.3666	−	9.17071i	−0.912312	−	0.358056i
$657$	−0.452718	+	3.72013i	−0.0176622	+	0.145136i
$658$	26.5628	+	67.6810i	1.03553	+	2.63848i
$659$	−15.7849	+	28.9859i	−0.614892	+	1.12913i	0.365264	+	0.930904i	$0.380979\pi$
$659$	−15.7849	+	28.9859i	−0.614892	+	1.12913i	−0.980156	+	0.198227i	$0.936482\pi$
$660$	13.7583	−	6.44549i	0.535540	−	0.250890i
$661$	−22.1351	−	34.2718i	−0.860955	−	1.33302i	−0.941759	−	0.336289i	$-0.890828\pi$
$661$	−22.1351	−	34.2718i	−0.860955	−	1.33302i	0.0808039	−	0.996730i	$-0.474251\pi$
$662$	2.45653	+	19.6026i	0.0954756	+	0.761877i
$663$	−1.60879	−	25.0571i	−0.0624803	−	0.973137i
$664$	−2.67442	+	1.92278i	−0.103788	+	0.0746182i
$665$	−41.1755	+	44.3767i	−1.59672	+	1.72085i
$666$	−6.45682	−	11.7566i	−0.250197	−	0.455561i
$667$	42.5554	−	20.5611i	1.64775	−	0.796130i
$668$	23.3812	−	19.6192i	0.904646	−	0.759088i
$669$	19.6949	−	45.3617i	0.761448	−	1.75379i
$670$	−18.9276	+	5.32541i	−0.731239	+	0.205739i
$671$	−3.04898	−	6.75723i	−0.117705	−	0.260860i
$672$	24.5196	−	37.0883i	0.945862	−	1.43071i
$673$	−1.19173	+	9.50979i	−0.0459379	+	0.366575i	0.952195	+	0.305492i	$0.0988208\pi$
$673$	−1.19173	+	9.50979i	−0.0459379	+	0.366575i	−0.998133	+	0.0610839i	$0.980544\pi$
$674$	−13.2169	+	6.36491i	−0.509095	+	0.245167i
$675$	−7.30036	+	12.4394i	−0.280991	+	0.478791i
$676$	−6.06204	+	7.60155i	−0.233155	+	0.292367i
$677$	22.9422	−	22.3772i	0.881740	−	0.860025i	−0.109242	−	0.994015i	$-0.534842\pi$
$677$	22.9422	−	22.3772i	0.881740	−	0.860025i	0.990983	+	0.133990i	$0.0427789\pi$
$678$	0.969285	+	0.873994i	0.0372252	+	0.0335655i
$679$	38.4998	−	45.8823i	1.47749	−	1.76080i
$680$	−6.76647	+	3.68482i	−0.259482	+	0.141307i
$681$	45.4838	+	23.9352i	1.74294	+	0.917198i
$682$	−13.1583	+	17.3713i	−0.503856	+	0.665183i
$683$	4.37332	−	11.1430i	0.167340	−	0.426377i	−0.822463	−	0.568819i	$-0.807400\pi$
$683$	4.37332	−	11.1430i	0.167340	−	0.426377i	0.989803	+	0.142443i	$0.0454956\pi$
$684$	−10.2556	+	26.4074i	−0.392131	+	1.00971i
$685$	−6.69413	−	44.4127i	−0.255770	−	1.69692i
$686$	7.75105	+	2.18081i	0.295937	+	0.0832636i
$687$	5.09149	+	13.3918i	0.194252	+	0.510930i
$688$	−21.2824	−	7.15049i	−0.811382	−	0.272610i
$689$	37.9807	−	38.9397i	1.44695	−	1.48348i
$690$	76.1329	+	24.3776i	2.89833	+	0.928038i
$691$	27.0755	+	1.35128i	1.03000	+	0.0514052i	0.557708	−	0.830037i	$-0.311681\pi$
$691$	27.0755	+	1.35128i	1.03000	+	0.0514052i	0.472292	+	0.881442i	$0.343427\pi$
$692$	4.65030	−	3.17052i	0.176778	−	0.120525i
$693$	19.5808	+	9.34372i	0.743815	+	0.354939i
$694$	15.6301	+	50.6715i	0.593310	+	1.92346i
$695$	38.4099	−	32.2298i	1.45697	−	1.22254i
$696$	7.35365	−	2.59853i	0.278739	−	0.0984970i
$697$	3.07099	−	17.4164i	0.116322	−	0.659695i
$698$	−24.7811	−	32.7156i	−0.937979	−	1.23830i
$699$	−15.3301	+	10.7750i	−0.579837	+	0.407549i
$700$	−10.7967	−	11.0693i	−0.408078	−	0.418382i
$701$	0.970163	−	4.25056i	0.0366425	−	0.160541i	−0.953296	−	0.302036i	$-0.902334\pi$
$701$	0.970163	−	4.25056i	0.0366425	−	0.160541i	0.989939	+	0.141495i	$0.0451908\pi$
$702$	−32.4350	+	28.2161i	−1.22418	+	1.06495i
$703$	12.9575	−	6.24001i	0.488702	−	0.235347i
$704$	−4.36983	−	7.15092i	−0.164694	−	0.269510i
$705$	−44.6854	+	26.6553i	−1.68295	+	1.00390i
$706$	−1.17551	+	0.530411i	−0.0442410	+	0.0199623i
$707$	14.1794	+	26.0378i	0.533272	+	0.979252i
$708$	1.37778	+	0.258145i	0.0517801	+	0.00970168i
$709$	−8.50739	−	1.71981i	−0.319502	−	0.0645887i	0.0357458	−	0.999361i	$-0.488619\pi$
$709$	−8.50739	−	1.71981i	−0.319502	−	0.0645887i	−0.355248	+	0.934772i	$0.615603\pi$
$710$	−17.6697	−	19.0434i	−0.663131	−	0.714685i
$711$	−3.10961	+	9.36583i	−0.116619	+	0.351246i
$712$	−7.72592	+	1.16449i	−0.289541	+	0.0436413i
$713$	−49.4215	+	8.71435i	−1.85085	+	0.326355i
$714$	35.8043	+	14.4954i	1.33994	+	0.542478i
$715$	−2.46148	+	24.5988i	−0.0920542	+	0.919944i
$716$	8.39987	−	25.0009i	0.313918	−	0.934329i
$717$	13.3555	+	10.8861i	0.498772	+	0.406549i
$718$	30.1508	+	41.9371i	1.12522	+	1.56508i
$719$	−24.7081	−	7.62143i	−0.921455	−	0.284231i	−0.202496	−	0.979283i	$-0.564905\pi$
$719$	−24.7081	−	7.62143i	−0.921455	−	0.284231i	−0.718960	+	0.695052i	$0.755381\pi$
$720$	35.8210	+	16.0095i	1.33497	+	0.596637i
$721$	4.53402	+	60.5023i	0.168856	+	2.25322i
$722$	−30.5988	−	13.8067i	−1.13877	−	0.513832i
$723$	11.7803	−	1.34861i	0.438114	−	0.0501552i
$724$	−3.27526	+	18.5749i	−0.121724	+	0.690332i
$725$	−1.87778	−	14.8296i	−0.0697390	−	0.550757i
$726$	−17.4602	+	14.3358i	−0.648008	+	0.532051i
$727$	21.1276	+	13.6456i	0.783578	+	0.506088i	0.871711	−	0.490021i	$-0.163011\pi$
$727$	21.1276	+	13.6456i	0.783578	+	0.506088i	−0.0881331	+	0.996109i	$0.528090\pi$
$728$	5.69588	+	11.8276i	0.211103	+	0.438361i
$729$	−23.2369	+	13.7495i	−0.860624	+	0.509241i
$730$	1.46181	−	6.40461i	0.0541040	−	0.237045i
$731$	1.96685	−	15.6951i	0.0727467	−	0.580505i
$732$	−4.16391	+	8.97128i	−0.153902	+	0.331588i
$733$	−4.43401	−	21.9338i	−0.163774	−	0.810143i	−0.974442	−	0.224637i	$-0.927880\pi$
$733$	−4.43401	−	21.9338i	−0.163774	−	0.810143i	0.810669	−	0.585505i	$-0.199104\pi$
$734$	−16.5372	−	18.7390i	−0.610401	−	0.691668i
$735$	3.09050	−	27.8758i	0.113995	−	1.02821i
$736$	12.4737	−	61.7036i	0.459785	−	2.27443i
$737$	−6.54357	+	3.77793i	−0.241036	+	0.139162i
$738$	−26.8959	+	13.9101i	−0.990050	+	0.512038i
$739$	4.14617	−	13.4416i	0.152519	−	0.494455i	−0.846778	−	0.531947i	$-0.821461\pi$
$739$	4.14617	−	13.4416i	0.152519	−	0.494455i	0.999297	+	0.0374916i	$0.0119367\pi$
$740$	3.99723	+	9.48256i	0.146941	+	0.348586i
$741$	−28.3533	−	36.3437i	−1.04159	−	1.33512i
$742$	28.6208	+	78.6351i	1.05070	+	2.88678i
$743$	5.42201	−	8.87273i	0.198914	−	0.325509i	−0.738168	−	0.674617i	$-0.764309\pi$
$743$	5.42201	−	8.87273i	0.198914	−	0.325509i	0.937083	+	0.349108i	$0.113515\pi$
$744$	−8.26438	+	0.530615i	−0.302987	+	0.0194533i
$745$	0.142677	+	0.0776975i	0.00522726	+	0.00284662i
$746$	−11.4513	+	4.49429i	−0.419261	+	0.164548i
$747$	−1.13470	+	11.7631i	−0.0415167	+	0.430390i
$748$	7.61982	−	7.07016i	0.278608	−	0.258511i
$749$	19.5234	+	38.0819i	0.713370	+	1.39148i
$750$	−12.0014	+	16.3222i	−0.438231	+	0.596004i
$751$	13.8898	−	3.90799i	0.506847	−	0.142604i	−0.00786307	−	0.999969i	$-0.502503\pi$
$751$	13.8898	−	3.90799i	0.506847	−	0.142604i	0.514710	+	0.857365i	$0.327900\pi$
$752$	30.5084	+	40.2767i	1.11253	+	1.46874i
$753$	15.6989	+	5.90461i	0.572100	+	0.215176i
$754$	8.77202	−	43.6821i	0.319458	−	1.59081i
$755$	12.3371			0.448995
$756$	−7.64128	−	27.9191i	−0.277911	−	1.01541i
$757$	−0.345075	−	0.716555i	−0.0125420	−	0.0260436i	0.894604	−	0.446860i	$-0.147458\pi$
$757$	−0.345075	−	0.716555i	−0.0125420	−	0.0260436i	−0.907146	+	0.420817i	$0.861744\pi$
$758$	0.583307	+	0.598035i	0.0211867	+	0.0217216i
$759$	30.6630	+	1.85890i	1.11300	+	0.0674736i
$760$	−6.45292	+	12.5869i	−0.234072	+	0.456575i
$761$	−6.04681	−	21.4916i	−0.219197	−	0.779071i	−0.989887	−	0.141861i	$-0.954691\pi$
$761$	−6.04681	−	21.4916i	−0.219197	−	0.779071i	0.770690	−	0.637210i	$-0.219912\pi$
$762$	0.149122	+	0.780505i	0.00540212	+	0.0282747i
$763$	0.760081	+	30.4783i	0.0275168	+	1.10339i
$764$	−21.5741	+	1.61676i	−0.780524	+	0.0584922i
$765$	−6.05496	+	26.9717i	−0.218917	+	0.975165i
$766$	−18.0750	−	10.4356i	−0.653077	−	0.377054i
$767$	−1.50922	+	1.71015i	−0.0544946	+	0.0617499i
$768$	10.8802	−	33.9797i	0.392606	−	1.22614i
$769$	−24.5744	+	15.8719i	−0.886177	+	0.572354i	−0.904022	−	0.427487i	$-0.859399\pi$
$769$	−24.5744	+	15.8719i	−0.886177	+	0.572354i	0.0178444	+	0.999841i	$0.494320\pi$
$770$	−32.4523	−	19.8312i	−1.16950	−	0.714666i
$771$	31.6366	+	18.7188i	1.13937	+	0.674143i
$772$	−12.3071	−	10.8611i	−0.442942	−	0.390899i
$773$	14.5819	+	21.3877i	0.524474	+	0.769262i	0.993489	−	0.113928i	$-0.0363433\pi$
$773$	14.5819	+	21.3877i	0.524474	+	0.769262i	−0.469015	+	0.883190i	$0.655391\pi$
$774$	−23.4061	+	13.6251i	−0.841313	+	0.489743i
$775$	−2.36561	+	15.6948i	−0.0849751	+	0.563773i
$776$	5.75583	−	12.7562i	0.206622	−	0.457922i
$777$	−6.84333	+	13.0043i	−0.245503	+	0.466527i
$778$	−2.42179	−	1.02087i	−0.0868252	−	0.0365999i
$779$	−13.3532	−	29.5938i	−0.478429	−	1.06031i
$780$	26.9841	−	18.9663i	0.966184	−	0.679101i
$781$	−8.38583	−	5.41614i	−0.300069	−	0.193805i
$782$	54.6924			1.95580
$783$	10.3746	−	25.9878i	0.370760	−	0.928729i
$784$	−27.2356			−0.972698
$785$	14.7636	+	9.53535i	0.526936	+	0.340331i
$786$	−4.28990	−	48.0465i	−0.153016	−	1.71376i
$787$	−0.0136021	−	0.0301453i	−0.000484862	−	0.00107457i	0.911263	−	0.411824i	$-0.135108\pi$
$787$	−0.0136021	−	0.0301453i	−0.000484862	−	0.00107457i	−0.911748	+	0.410750i	$0.865267\pi$
$788$	−0.125341	−	0.0528358i	−0.00446510	−	0.00188220i
$789$	−26.5736	+	1.04179i	−0.946044	+	0.0370886i
$790$	7.11489	−	15.7682i	0.253136	−	0.561008i
$791$	0.213112	−	1.41391i	0.00757740	−	0.0502727i
$792$	4.99542	+	0.862462i	0.177505	+	0.0306463i
$793$	−9.06569	−	13.2969i	−0.321932	−	0.472188i
$794$	42.8350	+	37.8021i	1.52016	+	1.34155i
$795$	−52.1792	+	29.3870i	−1.85061	+	1.04225i
$796$	−21.9035	−	13.3850i	−0.776350	−	0.474418i
$797$	5.06463	−	3.27109i	0.179399	−	0.115868i	−0.449745	−	0.893157i	$-0.648485\pi$
$797$	5.06463	−	3.27109i	0.179399	−	0.115868i	0.629144	+	0.777289i	$0.283406\pi$
$798$	69.2999	−	15.0402i	2.45319	−	0.532419i
$799$	−23.5548	+	26.6908i	−0.833307	+	0.944252i
$800$	−17.2428	−	9.95512i	−0.609624	−	0.351967i
$801$	−15.1246	+	23.6018i	−0.534401	+	0.833928i
$802$	34.5014	−	2.58552i	1.21829	−	0.0912980i
$803$	−0.0629359	−	2.52365i	−0.00222096	−	0.0890577i
$804$	9.52097	+	3.31248i	0.335779	+	0.116822i
$805$	−23.7205	−	84.3076i	−0.836038	−	2.97145i
$806$	−21.5826	+	42.0985i	−0.760215	+	1.48285i
$807$	−2.30090	−	4.60870i	−0.0809957	−	0.162234i
$808$	4.83698	+	4.95911i	0.170164	+	0.174461i
$809$	18.6120	+	38.6481i	0.654362	+	1.35880i	0.918927	+	0.394428i	$0.129057\pi$
$809$	18.6120	+	38.6481i	0.654362	+	1.35880i	−0.264565	+	0.964368i	$0.585228\pi$
$810$	43.0012	−	19.7734i	1.51091	−	0.694767i
$811$	34.0732			1.19647			0.598236	−	0.801320i	$-0.295868\pi$
$811$	34.0732			1.19647			0.598236	+	0.801320i	$0.295868\pi$
$812$	23.9364	+	18.0826i	0.840001	+	0.634576i
$813$	7.23937	−	5.94393i	0.253896	−	0.208463i
$814$	5.45553	+	7.20230i	0.191216	+	0.252440i
$815$	53.8861	−	15.1612i	1.88755	−	0.531074i
$816$	26.6802	+	2.95795i	0.933994	+	0.103549i
$817$	−13.2479	−	25.8410i	−0.463485	−	0.904061i
$818$	1.93287	−	1.79344i	0.0675812	−	0.0627062i
$819$	45.3842	+	12.5946i	1.58585	+	0.440090i
$820$	21.6253	−	8.48729i	0.755187	−	0.296389i
$821$	−41.4796	−	22.5886i	−1.44765	−	0.788348i	−0.452986	−	0.891518i	$-0.649641\pi$
$821$	−41.4796	−	22.5886i	−1.44765	−	0.788348i	−0.994664	+	0.103170i	$0.967102\pi$
$822$	−23.3330	+	47.1560i	−0.813831	+	1.64476i
$823$	−25.8145	+	42.2436i	−0.899838	+	1.47252i	−0.0186101	+	0.999827i	$0.505924\pi$
$823$	−25.8145	+	42.2436i	−0.899838	+	1.47252i	−0.881228	+	0.472692i	$0.843282\pi$
$824$	4.84854	+	13.3213i	0.168907	+	0.464068i
$825$	3.64600	−	9.00577i	0.126937	−	0.313541i
$826$	−1.36298	−	3.23336i	−0.0474240	−	0.112503i
$827$	−4.30729	+	13.9639i	−0.149779	+	0.485573i	−0.999105	−	0.0422964i	$-0.986533\pi$
$827$	−4.30729	+	13.9639i	−0.149779	+	0.485573i	0.849326	+	0.527869i	$0.177009\pi$
$828$	−24.8630	−	32.5816i	−0.864050	−	1.13229i
$829$	−5.27986	+	3.04833i	−0.183377	+	0.105873i	−0.588878	−	0.808222i	$-0.700430\pi$
$829$	−5.27986	+	3.04833i	−0.183377	+	0.105873i	0.405501	+	0.914094i	$0.367097\pi$
$830$	4.10477	−	20.3051i	0.142479	−	0.704801i
$831$	−6.92571	−	5.09235i	−0.240250	−	0.176652i
$832$	−12.0379	−	13.6407i	−0.417341	−	0.472905i
$833$	−3.80211	−	18.8080i	−0.131735	−	0.651658i
$834$	−58.5023	+	5.22347i	−2.02577	+	0.180874i
$835$	6.79870	−	54.2523i	0.235279	−	1.87748i
$836$	4.24633	−	18.6044i	0.146862	−	0.643447i
$837$	−18.1083	+	23.5561i	−0.625913	+	0.814218i
$838$	−19.4705	−	40.4310i	−0.672598	−	1.39666i
$839$	−12.5345	−	8.09565i	−0.432740	−	0.279493i	0.307870	−	0.951428i	$-0.400384\pi$
$839$	−12.5345	−	8.09565i	−0.432740	−	0.279493i	−0.740610	+	0.671935i	$0.765463\pi$
$840$	−2.35750	−	14.2591i	−0.0813414	−	0.491987i
$841$	7.92622	+	27.8958i	0.273318	+	0.961924i
$842$	−7.82084	+	44.3542i	−0.269524	+	1.52855i
$843$	−0.711837	−	0.960912i	−0.0245170	−	0.0330956i
$844$	−25.9822	−	11.7236i	−0.894345	−	0.403544i
$845$	1.30159	+	17.3685i	0.0447760	+	0.597494i
$846$	60.7956	+	4.33793i	2.09019	+	0.149141i
$847$	23.6511	+	7.29539i	0.812660	+	0.250673i
$848$	33.9469	+	47.2173i	1.16574	+	1.62145i
$849$	−16.1433	+	6.13758i	−0.554036	+	0.210641i
$850$	5.50917	−	16.3972i	0.188963	−	0.562420i
$851$	−2.07167	+	20.7033i	−0.0710161	+	0.709699i
$852$	1.84425	+	13.1904i	0.0631829	+	0.451896i
$853$	26.5431	−	4.68026i	0.908817	−	0.160249i	0.300351	−	0.953829i	$-0.402896\pi$
$853$	26.5431	−	4.68026i	0.908817	−	0.160249i	0.608466	+	0.793580i	$0.291785\pi$
$854$	24.4815	−	3.68999i	0.837740	−	0.126269i
$855$	18.7087	+	47.1735i	0.639825	+	1.61330i
$856$	6.80113	+	7.32988i	0.232458	+	0.250530i
$857$	−16.6742	−	3.37076i	−0.569579	−	0.115143i	−0.0951914	−	0.995459i	$-0.530346\pi$
$857$	−16.6742	−	3.37076i	−0.569579	−	0.115143i	−0.474388	+	0.880316i	$0.657330\pi$
$858$	18.8505	−	21.9839i	0.643545	−	0.750516i
$859$	13.1734	+	24.1905i	0.449472	+	0.825368i	0.999955	−	0.00947777i	$-0.00301691\pi$
$859$	13.1734	+	24.1905i	0.449472	+	0.825368i	−0.550483	+	0.834846i	$0.685557\pi$
$860$	18.9396	−	8.54586i	0.645834	−	0.291411i
$861$	28.9631	+	16.1760i	0.987058	+	0.551275i
$862$	35.2858	+	57.7427i	1.20184	+	1.96673i
$863$	−11.3897	+	5.48499i	−0.387710	+	0.186711i	−0.617576	−	0.786511i	$-0.711885\pi$
$863$	−11.3897	+	5.48499i	−0.387710	+	0.186711i	0.229867	+	0.973222i	$0.426171\pi$
$864$	−19.2078	−	31.9407i	−0.653462	−	1.08665i
$865$	2.24355	−	9.82963i	0.0762830	−	0.334217i
$866$	−37.7801	−	38.7340i	−1.28382	−	1.31623i
$867$	−0.936686	−	10.4908i	−0.0318115	−	0.356286i
$868$	−19.2332	−	25.3913i	−0.652816	−	0.861837i
$869$	1.15435	−	6.54664i	0.0391586	−	0.222080i
$870$	−22.7868	+	43.4372i	−0.772546	+	1.47266i
$871$	−12.5653	+	10.5436i	−0.425760	+	0.357255i
$872$	2.09970	+	6.80707i	0.0711050	+	0.230517i
$873$	−20.8139	−	45.6927i	−0.704443	−	1.54646i
$874$	82.9594	−	56.5607i	2.80614	−	1.91320i
$875$	22.1683	+	1.10638i	0.749427	+	0.0374023i
$876$	−2.49325	+	2.26432i	−0.0842393	+	0.0765043i
$877$	0.0629153	−	0.0645039i	0.00212450	−	0.00217814i	−0.714804	−	0.699325i	$-0.753484\pi$
$877$	0.0629153	−	0.0645039i	0.00212450	−	0.00217814i	0.716928	+	0.697147i	$0.245547\pi$
$878$	−53.0124	−	17.8112i	−1.78908	−	0.601099i
$879$	−1.58466	+	1.94413i	−0.0534493	+	0.0655738i
$880$	−25.4421	−	7.15829i	−0.857652	−	0.241306i
$881$	−4.56744	−	30.3030i	−0.153881	−	1.02093i	−0.923823	−	0.382820i	$-0.874953\pi$
$881$	−4.56744	−	30.3030i	−0.153881	−	1.02093i	0.769942	−	0.638114i	$-0.220285\pi$
$882$	−21.6510	+	24.7107i	−0.729026	+	0.832051i
$883$	5.06272	−	12.8996i	0.170374	−	0.434106i	−0.820028	−	0.572324i	$-0.806042\pi$
$883$	5.06272	−	12.8996i	0.170374	−	0.434106i	0.990402	+	0.138218i	$0.0441374\pi$
$884$	13.6252	−	17.9877i	0.458265	−	0.604993i
$885$	2.12381	−	1.33977i	0.0713910	−	0.0450358i
$886$	46.7755	−	25.4726i	1.57145	−	0.855767i
$887$	−1.45401	+	1.73283i	−0.0488210	+	0.0581826i	−0.789902	−	0.613233i	$-0.789869\pi$
$887$	−1.45401	+	1.73283i	−0.0488210	+	0.0581826i	0.741081	+	0.671415i	$0.234313\pi$
$888$	−0.716254	+	3.35800i	−0.0240359	+	0.112687i
$889$	0.623213	−	0.607865i	0.0209019	−	0.0203871i
$890$	30.6375	−	38.4183i	1.02697	−	1.28778i
$891$	14.1384	−	11.4410i	0.473655	−	0.383288i
$892$	40.0426	−	19.2835i	1.34073	−	0.645659i
$893$	−8.12613	+	64.8450i	−0.271930	+	2.16995i
$894$	−0.0850063	−	0.170267i	−0.00284304	−	0.00569459i
$895$	−19.4319	−	43.0655i	−0.649537	−	1.43952i
$896$	−22.4780	+	6.32434i	−0.750938	+	0.211281i
$897$	66.2552	−	7.58488i	2.21220	−	0.253252i
$898$	−18.3064	+	15.3609i	−0.610894	+	0.512601i
$899$	−0.0396395	−	30.7927i	−0.00132205	−	1.02699i
$900$	−12.2727	+	4.17219i	−0.409089	+	0.139073i
$901$	−27.8677	+	30.0342i	−0.928406	+	1.00058i
$902$	16.5612	−	11.9067i	0.551428	−	0.396450i
$903$	26.5940	+	13.1588i	0.884994	+	0.437898i
$904$	−0.0415426	−	0.331502i	−0.00138169	−	0.0110256i
$905$	18.3317	+	28.3830i	0.609365	+	0.943482i
$906$	−11.8530	−	8.26809i	−0.393790	−	0.274689i
$907$	−12.1659	+	22.3403i	−0.403962	+	0.741798i	−0.998038	−	0.0626105i	$-0.980057\pi$
$907$	−12.1659	+	22.3403i	−0.403962	+	0.741798i	0.594076	+	0.804409i	$0.297518\pi$
$908$	16.8756	+	42.9984i	0.560037	+	1.42695i
$909$	24.8187	−	1.32743i	0.823183	−	0.0440281i
$910$	−76.8555	−	30.1636i	−2.54774	−	0.999912i
$911$	7.53384	+	8.97848i	0.249607	+	0.297470i	0.876270	−	0.481820i	$-0.160024\pi$
$911$	7.53384	+	8.97848i	0.249607	+	0.297470i	−0.626663	+	0.779290i	$0.715580\pi$
$912$	43.5285	−	23.1049i	1.44137	−	0.765080i
$913$	−0.396805	−	7.95074i	−0.0131323	−	0.263131i
$914$	−27.2712	−	13.9811i	−0.902051	−	0.462455i
$915$	5.46311	+	16.8544i	0.180605	+	0.557189i
$916$	−4.40383	+	12.0994i	−0.145507	+	0.399776i
$917$	−41.3183	+	32.9502i	−1.36445	+	1.08811i
$918$	23.8932	−	21.8554i	0.788593	−	0.721335i
$919$	−24.4450	+	30.6531i	−0.806367	+	1.01115i	0.193183	+	0.981163i	$0.438119\pi$
$919$	−24.4450	+	30.6531i	−0.806367	+	1.01115i	−0.999550	+	0.0299900i	$0.990452\pi$
$920$	−10.6704	−	17.4614i	−0.351794	−	0.575685i
$921$	17.2117	+	24.4878i	0.567146	+	0.806901i
$922$	−9.62797	+	18.7801i	−0.317080	+	0.618488i
$923$	−19.9698	−	8.41797i	−0.657314	−	0.277081i
$924$	7.82916	+	17.8576i	0.257561	+	0.587473i
$925$	5.99833	+	2.70655i	0.197224	+	0.0889908i
$926$	−19.8542	−	64.3658i	−0.652450	−	2.11519i
$927$	47.4113	+	18.4126i	1.55719	+	0.604751i
$928$	35.9750	+	14.0657i	1.18094	+	0.461731i
$929$	5.78529	+	32.8100i	0.189809	+	1.07646i	0.919619	+	0.392812i	$0.128498\pi$
$929$	5.78529	+	32.8100i	0.189809	+	1.07646i	−0.729810	+	0.683650i	$0.760391\pi$
$930$	35.8316	−	37.7993i	1.17496	−	1.23949i
$931$	−25.2177	−	24.5966i	−0.826476	−	0.806122i
$932$	−16.7565	−	1.67674i	−0.548876	−	0.0549233i
$933$	24.3759	+	23.1070i	0.798033	+	0.756490i
$934$	−65.1659	+	27.4697i	−2.13229	+	0.898837i
$935$	1.39154	−	18.5688i	0.0455081	−	0.607263i
$936$	11.0048	−	0.0392631i	0.359704	−	0.00128335i
$937$	−29.7703	−	4.48715i	−0.972553	−	0.146589i	−0.356501	−	0.934295i	$-0.616030\pi$
$937$	−29.7703	−	4.48715i	−0.972553	−	0.146589i	−0.616051	+	0.787706i	$0.711269\pi$
$938$	−6.22674	−	24.4540i	−0.203310	−	0.798450i
$939$	−39.9460	−	1.42332i	−1.30359	−	0.0464482i
$940$	−46.0512	−	8.12006i	−1.50202	−	0.264847i
$941$	−0.0278957	+	1.11858i	−0.000909374	+	0.0364648i	−0.999978	−	0.00669417i	$-0.997869\pi$
$941$	−0.0278957	+	1.11858i	−0.000909374	+	0.0364648i	0.999068	+	0.0431589i	$0.0137422\pi$
$942$	−7.79386	−	19.0554i	−0.253938	−	0.620859i
$943$	46.6066	+	5.84057i	1.51772	+	0.190195i
$944$	−1.52036	−	1.90647i	−0.0494835	−	0.0620504i
$945$	−44.0525	−	27.3523i	−1.43303	−	0.889769i
$946$	14.2634	−	11.3747i	0.463743	−	0.369822i
$947$	10.8074	−	10.5413i	0.351194	−	0.342545i	−0.501308	−	0.865269i	$-0.667148\pi$
$947$	10.8074	−	10.5413i	0.351194	−	0.342545i	0.852502	+	0.522724i	$0.175084\pi$
$948$	−7.61683	+	4.54351i	−0.247383	+	0.147566i
$949$	−1.08589	−	5.37159i	−0.0352495	−	0.174369i
$950$	−8.60086	−	30.5693i	−0.279049	−	0.991798i
$951$	22.2197	−	0.871099i	0.720524	−	0.0282473i
$952$	−4.51102	−	8.79906i	−0.146203	−	0.285179i
$953$	2.22898	+	29.7436i	0.0722036	+	0.963490i	0.909221	+	0.416314i	$0.136678\pi$
$953$	2.22898	+	29.7436i	0.0722036	+	0.963490i	−0.837017	+	0.547176i	$0.815703\pi$
$954$	69.8261	+	6.73562i	2.26070	+	0.218074i
$955$	−26.3607	+	28.4101i	−0.853013	+	0.919330i
$956$	2.68894	+	15.2497i	0.0869666	+	0.493212i
$957$	−4.36683	+	18.3365i	−0.141159	+	0.592734i
$958$	29.8259	−	10.8557i	0.963632	−	0.350733i
$959$	57.1942	−	7.16737i	1.84690	−	0.231446i
$960$	8.49705	+	18.1374i	0.274241	+	0.585383i
$961$	−0.459412	+	1.63285i	−0.0148197	+	0.0526725i
$962$	14.3784	+	13.3412i	0.463579	+	0.430138i
$963$	35.8602	−	1.02233i	1.15558	−	0.0329441i
$964$	8.80463	+	6.00289i	0.283578	+	0.193340i
$965$	−29.3951	+	0.733068i	−0.946262	+	0.0235983i
$966$	−33.7115	+	96.8961i	−1.08465	+	3.11758i
$967$	−46.2643	−	33.2618i	−1.48776	−	1.06963i	−0.977828	−	0.209412i	$-0.932845\pi$
$967$	−46.2643	−	33.2618i	−1.48776	−	1.06963i	−0.509932	−	0.860215i	$-0.670329\pi$
$968$	5.78127	+	0.144176i	0.185817	+	0.00463399i
$969$	22.0321	+	26.8339i	0.707774	+	0.862028i
$970$	28.0318	+	83.4323i	0.900046	+	2.67885i
$971$	12.4630	−	2.84459i	0.399955	−	0.0912872i	−0.0178118	−	0.999841i	$-0.505670\pi$
$971$	12.4630	−	2.84459i	0.399955	−	0.0912872i	0.417767	+	0.908554i	$0.362813\pi$
$972$	−23.8816	−	4.29837i	−0.766002	−	0.137870i
$973$	40.1208	+	50.3099i	1.28621	+	1.61286i
$974$	2.39155	−	6.57073i	0.0766302	−	0.210540i
$975$	4.39989	−	20.6279i	0.140909	−	0.660621i
$976$	15.6828	−	7.07634i	0.501993	−	0.226508i
$977$	−32.4460	−	36.7658i	−1.03804	−	1.17624i	−0.984085	−	0.177698i	$-0.943135\pi$
$977$	−32.4460	−	36.7658i	−1.03804	−	1.17624i	−0.0539541	−	0.998543i	$-0.517182\pi$
$978$	−61.9322	−	21.5471i	−1.98037	−	0.688999i
$979$	7.76630	−	17.2119i	0.248212	−	0.550094i
$980$	18.4772	−	17.1444i	0.590233	−	0.547656i
$981$	23.3335	+	10.4284i	0.744980	+	0.332954i
$982$	31.7950	−	21.6774i	1.01462	−	0.691755i
$983$	−38.1478	+	27.4264i	−1.21673	+	0.874767i	−0.994954	−	0.100331i	$-0.968010\pi$
$983$	−38.1478	+	27.4264i	−1.21673	+	0.874767i	−0.221773	+	0.975098i	$0.571184\pi$
$984$	7.53803	+	1.80544i	0.240304	+	0.0575553i
$985$	−0.228973	+	0.0833395i	−0.00729569	+	0.00265542i
$986$	−5.78492	+	33.0567i	−0.184230	+	1.05274i
$987$	−32.7681	−	58.1827i	−1.04302	−	1.85198i
$988$	2.06494	−	41.3751i	0.0656947	−	1.31632i
$989$	41.8943	+	3.13955i	1.33216	+	0.0998318i
$990$	−26.7199	+	17.3930i	−0.849214	+	0.552784i
$991$	54.5316	−	16.8208i	1.73225	−	0.534329i	0.741613	−	0.670828i	$-0.234061\pi$
$991$	54.5316	−	16.8208i	1.73225	−	0.534329i	0.990640	+	0.136498i	$0.0435848\pi$
$992$	−32.6943	−	24.7650i	−1.03804	−	0.786288i
$993$	−4.72734	−	17.5176i	−0.150018	−	0.555904i
$994$	24.9974	−	22.0603i	0.792869	−	0.699711i
$995$	−45.0722	+	9.11154i	−1.42888	+	0.288855i
$996$	−7.68185	+	7.33417i	−0.243409	+	0.232392i
$997$	−25.0996	+	8.43303i	−0.794914	+	0.267077i	−0.686596	−	0.727039i	$-0.740896\pi$
$997$	−25.0996	+	8.43303i	−0.794914	+	0.267077i	−0.108318	+	0.994116i	$0.534546\pi$
$998$		−	35.1373i		−	1.11225i
$999$	7.36810	+	9.87239i	0.233116	+	0.312349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.bf.a.4.18	✓	3168
27.7	even	9	inner	783.2.bf.a.439.18	yes	3168
29.22	even	14	inner	783.2.bf.a.544.18	yes	3168
783.196	even	126	inner	783.2.bf.a.196.18	yes	3168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.bf.a.4.18	✓	3168	1.1	even	1	trivial
783.2.bf.a.196.18	yes	3168	783.196	even	126	inner
783.2.bf.a.439.18	yes	3168	27.7	even	9	inner
783.2.bf.a.544.18	yes	3168	29.22	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.bf (of order \(126\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58421 - 1.02319i) q^{2} +(1.57107 + 0.729195i) q^{3} +(0.640218 + 1.41887i) q^{4} +(2.56954 + 1.08315i) q^{5} +(-1.74280 - 2.76270i) q^{6} +(-1.47186 + 3.26199i) q^{7} +(-0.124625 + 0.826830i) q^{8} +(1.93655 + 2.29124i) q^{9} +(-2.96241 - 4.34506i) q^{10} +(-1.51520 - 1.33717i) q^{11} +(-0.0288017 + 2.69599i) q^{12} +(-3.74342 - 2.28755i) q^{13} +(5.66936 - 3.66166i) q^{14} +(3.24711 + 3.57541i) q^{15} +(3.10342 - 3.51660i) q^{16} +(2.86169 + 1.65220i) q^{17} +(-0.723524 - 5.61125i) q^{18} +(6.04936 - 0.453337i) q^{19} +(0.108215 + 4.33930i) q^{20} +(-4.69103 + 4.05155i) q^{21} +(1.03221 + 3.66869i) q^{22} +(-4.00388 + 7.80986i) q^{23} +(-0.798714 + 1.20814i) q^{24} +(1.93815 + 1.98708i) q^{25} +(3.58974 + 7.45417i) q^{26} +(1.37170 + 5.01183i) q^{27} -5.57065 q^{28} +(-4.29687 - 3.24606i) q^{29} +(-1.48578 - 8.98660i) q^{30} +(3.45259 + 4.55805i) q^{31} +(-6.90477 + 1.94270i) q^{32} +(-1.40543 - 3.20567i) q^{33} +(-2.84300 - 5.54547i) q^{34} +(-7.31525 + 6.78756i) q^{35} +(-2.01115 + 4.21460i) q^{36} +(2.20687 - 0.866134i) q^{37} +(-10.0473 - 5.47145i) q^{38} +(-4.21311 - 6.32360i) q^{39} +(-1.21581 + 1.98959i) q^{40} +(-1.83049 - 5.02923i) q^{41} +(11.5771 - 1.61867i) q^{42} +(-1.85940 - 4.41103i) q^{43} +(0.927212 - 3.00595i) q^{44} +(2.49429 + 7.98502i) q^{45} +(14.3339 - 8.27570i) q^{46} +(-2.13462 + 10.5593i) q^{47} +(7.43999 - 3.26185i) q^{48} +(-3.84237 - 4.35393i) q^{49} +(-1.03726 - 5.13104i) q^{50} +(3.29116 + 4.68246i) q^{51} +(0.849137 - 6.77595i) q^{52} +(-2.75905 + 12.0882i) q^{53} +(2.95498 - 9.34328i) q^{54} +(-2.44501 - 5.07711i) q^{55} +(-2.51368 - 1.62350i) q^{56} +(9.83456 + 3.69893i) q^{57} +(3.48580 + 9.53893i) q^{58} +(0.0902815 - 0.512012i) q^{59} +(-2.99418 + 6.89627i) q^{60} +(3.34375 + 1.50876i) q^{61} +(-0.805867 - 10.7535i) q^{62} +(-10.3243 + 2.94461i) q^{63} +(3.96272 + 1.22234i) q^{64} +(-7.14110 - 9.93266i) q^{65} +(-1.05351 + 6.51646i) q^{66} +(1.19080 - 3.54425i) q^{67} +(-0.512147 + 5.11813i) q^{68} +(-11.9853 + 9.35026i) q^{69} +(18.5338 - 3.26801i) q^{70} +(4.88473 - 0.736254i) q^{71} +(-2.13581 + 1.31565i) q^{72} +(0.849667 + 0.915723i) q^{73} +(-4.38236 - 0.885913i) q^{74} +(1.59600 + 4.53514i) q^{75} +(4.51613 + 8.29301i) q^{76} +(6.59200 - 2.97442i) q^{77} +(0.204205 + 14.3287i) q^{78} +(1.71527 + 2.80692i) q^{79} +(11.7834 - 5.67458i) q^{80} +(-1.49955 + 8.87420i) q^{81} +(-2.24598 + 9.84027i) q^{82} +(2.75052 + 2.81997i) q^{83} +(-8.75190 - 4.06209i) q^{84} +(5.56366 + 7.34505i) q^{85} +(-1.56763 + 8.89050i) q^{86} +(-4.38370 - 8.23306i) q^{87} +(1.29444 - 1.08617i) q^{88} +(2.75420 + 8.92890i) q^{89} +(4.21872 - 15.2020i) q^{90} +(12.9718 - 8.84400i) q^{91} +(-13.6445 - 0.680970i) q^{92} +(2.10057 + 9.67865i) q^{93} +(14.1859 - 14.5441i) q^{94} +(16.0351 + 5.38751i) q^{95} +(-12.2645 - 1.98279i) q^{96} +(-16.1111 - 4.53296i) q^{97} +(1.63221 + 10.8290i) q^{98} +(0.129520 - 6.06118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 42 q^{2} - 42 q^{3} - 30 q^{4} - 30 q^{5} - 60 q^{6} - 30 q^{7} - 21 q^{8} - 42 q^{9} - 21 q^{10} - 42 q^{11} - 30 q^{13} - 42 q^{14} - 42 q^{15} - 18 q^{16} - 189 q^{18} - 21 q^{19} + 24 q^{20}+ \cdots - 21 q^{98}+O(q^{100}) \) 3168 * q - 42 * q^2 - 42 * q^3 - 30 * q^4 - 30 * q^5 - 60 * q^6 - 30 * q^7 - 21 * q^8 - 42 * q^9 - 21 * q^10 - 42 * q^11 - 30 * q^13 - 42 * q^14 - 42 * q^15 - 18 * q^16 - 189 * q^18 - 21 * q^19 + 24 * q^20 - 42 * q^21 - 30 * q^22 + 60 * q^23 + 60 * q^24 - 30 * q^25 - 84 * q^26 - 168 * q^27 - 144 * q^28 - 72 * q^29 - 54 * q^30 - 42 * q^31 - 42 * q^32 + 60 * q^33 - 60 * q^34 - 45 * q^35 + 60 * q^36 - 21 * q^37 - 42 * q^39 - 42 * q^40 - 30 * q^42 - 42 * q^43 - 21 * q^44 + 12 * q^45 - 42 * q^47 - 105 * q^48 - 120 * q^49 - 42 * q^50 - 57 * q^51 - 132 * q^53 - 12 * q^54 - 84 * q^55 - 126 * q^56 - 36 * q^57 - 63 * q^58 - 66 * q^59 - 42 * q^60 - 42 * q^61 + 3 * q^62 + 150 * q^63 - 237 * q^64 + 66 * q^65 - 42 * q^66 - 30 * q^67 - 126 * q^68 - 42 * q^69 - 111 * q^71 - 42 * q^72 - 21 * q^73 + 270 * q^74 - 42 * q^76 - 42 * q^77 - 66 * q^78 - 42 * q^79 - 246 * q^80 - 42 * q^81 - 60 * q^82 - 228 * q^83 - 168 * q^84 - 147 * q^85 + 36 * q^86 + 39 * q^87 - 12 * q^88 - 21 * q^89 - 42 * q^90 - 15 * q^91 + 120 * q^92 - 24 * q^93 + 96 * q^94 - 210 * q^95 - 258 * q^96 - 42 * q^97 - 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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