LMFDB - Embedded newform 783.2.bf.a.196.18

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			196.18
Character	$\chi$	$=$	783.196
Dual form			783.2.bf.a.4.18

$q$-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 $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{8}{9}\right)$

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	−0.964443	−	0.264292i	$-0.914862\pi$
$2$	−1.58421	+	1.02319i	−1.12020	+	0.723503i	−0.155760	+	0.987795i	$0.549782\pi$
$3$	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	0.270889	−	0.962611i	$-0.412682\pi$
$5$	2.56954	−	1.08315i	1.14913	−	0.484401i	0.878246	+	0.478210i	$0.158714\pi$
$6$	−1.74280	+	2.76270i	−0.711495	+	1.12787i
$7$	−1.47186	−	3.26199i	−0.556312	−	1.23291i	−0.949590	−	0.313495i	$-0.898500\pi$
$7$	−1.47186	−	3.26199i	−0.556312	−	1.23291i	0.393277	−	0.919420i	$-0.371341\pi$
$8$	−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	−0.858656	−	0.512553i	$-0.828700\pi$
$11$	−1.51520	+	1.33717i	−0.456849	+	0.403172i	0.401806	+	0.915725i	$0.368383\pi$
$12$	−0.0288017	−	2.69599i	−0.00831433	−	0.778266i
$13$	−3.74342	+	2.28755i	−1.03824	+	0.634453i	−0.932956	−	0.359989i	$-0.882780\pi$
$13$	−3.74342	+	2.28755i	−1.03824	+	0.634453i	−0.105280	+	0.994443i	$0.533574\pi$
$14$	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	−0.111070	−	0.993813i	$-0.535428\pi$
$17$	2.86169	−	1.65220i	0.694062	−	0.400717i	0.805132	+	0.593096i	$0.202094\pi$
$18$	−0.723524	+	5.61125i	−0.170536	+	1.32258i
$19$	6.04936	+	0.453337i	1.38782	+	0.104003i	0.747579	−	0.664173i	$-0.231216\pi$
$19$	6.04936	+	0.453337i	1.38782	+	0.104003i	0.640239	+	0.768176i	$0.278835\pi$
$20$	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	−0.776453	−	0.630176i	$-0.782983\pi$
$23$	−4.00388	−	7.80986i	−0.834867	−	1.62847i	−0.0584141	−	0.998292i	$-0.518604\pi$
$24$	−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	−0.373961	−	0.927445i	$-0.622000\pi$
$31$	3.45259	−	4.55805i	0.620104	−	0.818651i	0.994064	+	0.108794i	$0.0346989\pi$
$32$	−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	0.539741	−	0.841831i	$-0.318522\pi$
$37$	2.20687	+	0.866134i	0.362808	+	0.142392i	−0.176933	+	0.984223i	$0.556618\pi$
$38$	−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	0.710758	+	0.703437i	$0.248352\pi$
$41$	−1.83049	+	5.02923i	−0.285875	+	0.785434i	−0.996633	+	0.0819973i	$0.973870\pi$
$42$	11.5771	+	1.61867i	1.78638	+	0.249767i
$43$	−1.85940	+	4.41103i	−0.283557	+	0.672676i	−0.999680	−	0.0252981i	$-0.991947\pi$
$43$	−1.85940	+	4.41103i	−0.283557	+	0.672676i	0.716123	+	0.697974i	$0.245915\pi$
$44$	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	−0.762028	−	0.647544i	$-0.775796\pi$
$47$	−2.13462	−	10.5593i	−0.311366	−	1.54024i	0.450662	−	0.892695i	$-0.351188\pi$
$48$	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	−0.700587	−	0.713567i	$-0.747079\pi$
$53$	−2.75905	−	12.0882i	−0.378985	−	1.66044i	0.321603	−	0.946875i	$-0.395779\pi$
$54$	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	0.990120	−	0.140220i	$-0.0447808\pi$
$59$	0.0902815	+	0.512012i	0.0117536	+	0.0666582i	−0.978367	+	0.206878i	$0.933670\pi$
$60$	−2.99418	−	6.89627i	−0.386547	−	0.890305i
$61$	3.34375	−	1.50876i	0.428124	−	0.193177i	−0.185723	−	0.982602i	$-0.559463\pi$
$61$	3.34375	−	1.50876i	0.428124	−	0.193177i	0.613846	+	0.789425i	$0.289621\pi$
$62$	−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	0.995613	−	0.0935692i	$-0.0298276\pi$
$67$	1.19080	+	3.54425i	0.145480	+	0.432999i	−0.850133	+	0.526568i	$0.823478\pi$
$68$	−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	0.432351	−	0.901706i	$-0.357684\pi$
$71$	4.88473	+	0.736254i	0.579711	+	0.0873773i	0.147360	+	0.989083i	$0.452922\pi$
$72$	−2.13581	−	1.31565i	−0.251707	−	0.155051i
$73$	0.849667	−	0.915723i	0.0994460	−	0.107177i	−0.681367	−	0.731941i	$-0.738614\pi$
$73$	0.849667	−	0.915723i	0.0994460	−	0.107177i	0.780813	+	0.624764i	$0.214805\pi$
$74$	−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	−0.742062	−	0.670331i	$-0.766152\pi$
$79$	1.71527	−	2.80692i	0.192983	−	0.315803i	0.935045	+	0.354528i	$0.115359\pi$
$80$	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	−0.547982	−	0.836490i	$-0.684604\pi$
$83$	2.75052	−	2.81997i	0.301909	−	0.309532i	0.849892	+	0.526958i	$0.176667\pi$
$84$	−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	−0.684192	−	0.729302i	$-0.739845\pi$
$89$	2.75420	−	8.92890i	0.291945	−	0.946461i	0.976136	−	0.217159i	$-0.0696790\pi$
$90$	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	−0.960734	−	0.277472i	$-0.910503\pi$
$97$	−16.1111	+	4.53296i	−1.63584	+	0.460253i	−0.675102	+	0.737725i	$0.735900\pi$
$98$	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	0.975145	−	0.221566i	$-0.0711168\pi$
$101$	5.00234	+	6.60401i	0.497752	+	0.657124i	−0.477394	+	0.878690i	$0.658418\pi$
$102$	−0.422831	+	10.7854i	−0.0418665	+	1.06792i
$103$	14.8891	+	8.10819i	1.46707	+	0.798924i	0.996512	−	0.0834457i	$-0.0265925\pi$
$103$	14.8891	+	8.10819i	1.46707	+	0.798924i	0.470558	+	0.882369i	$0.344053\pi$
$104$	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	0.998382	−	0.0568624i	$-0.0181096\pi$
$107$	7.45585	+	9.34934i	0.720784	+	0.903835i	−0.277598	+	0.960697i	$0.589538\pi$
$108$	−6.23294	−	5.15493i	−0.599765	−	0.496034i
$109$	7.67560	+	3.69638i	0.735189	+	0.354049i	0.763723	−	0.645544i	$-0.223369\pi$
$109$	7.67560	+	3.69638i	0.735189	+	0.354049i	−0.0285334	+	0.999593i	$0.509084\pi$
$110$	−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	0.252702	−	0.967544i	$-0.418681\pi$
$113$	−0.384621	−	0.108216i	−0.0361821	−	0.0101801i	−0.288884	+	0.957364i	$0.593284\pi$
$114$	−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	−0.375367	−	0.926876i	$-0.622483\pi$
$127$	−0.226450	+	0.0888750i	−0.0200942	+	0.00788638i	0.355273	+	0.934763i	$0.384388\pi$
$128$	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	0.225493	−	0.974245i	$-0.427601\pi$
$131$	13.1412	−	6.73708i	1.14815	−	0.588622i	0.922656	+	0.385623i	$0.126014\pi$
$132$	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	0.260422	+	0.965495i	$0.416138\pi$
$137$	−8.39873	+	13.7439i	−0.717552	+	1.17422i	−0.977974	+	0.208726i	$0.933068\pi$
$138$	28.5543	+	2.54951i	2.43070	+	0.217029i
$139$	8.20320	+	16.0009i	0.695786	+	1.35718i	0.923555	+	0.383466i	$0.125270\pi$
$139$	8.20320	+	16.0009i	0.695786	+	1.35718i	−0.227769	+	0.973715i	$0.573143\pi$
$140$	−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	−0.0971930	−	0.995266i	$-0.530986\pi$
$149$	0.0579713	−	0.00580091i	0.00474920	−	0.000475229i	0.101942	+	0.994790i	$0.467494\pi$
$150$	2.11191	+	8.81761i	0.172437	+	0.719955i
$151$	4.07687	+	1.71855i	0.331771	+	0.139853i	0.547974	−	0.836495i	$-0.315399\pi$
$151$	4.07687	+	1.71855i	0.331771	+	0.139853i	−0.216203	+	0.976348i	$0.569367\pi$
$152$	−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	0.0796187	−	0.996825i	$-0.474630\pi$
$157$	6.20697	−	1.09446i	0.495370	−	0.0873471i	0.415751	+	0.909478i	$0.363519\pi$
$158$	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	0.999975	+	0.00701244i	$0.00223215\pi$
$163$	15.6950	+	12.5163i	1.22933	+	0.980356i	0.229352	+	0.973344i	$0.426339\pi$
$164$	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	0.421674	+	0.906748i	$0.361443\pi$
$167$	−5.31060	+	18.8750i	−0.410947	+	1.46059i	−0.832620	+	0.553844i	$0.813160\pi$
$168$	−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	−0.999329	−	0.0366398i	$-0.988335\pi$
$173$	−0.627860	+	3.56077i	−0.0477353	+	0.270721i	0.951593	+	0.307360i	$0.0994457\pi$
$174$	−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	−0.990614	−	0.136686i	$-0.956355\pi$
$179$	−12.4203	+	11.5244i	−0.928339	+	0.861373i	0.0622753	+	0.998059i	$0.480164\pi$
$180$	−9.73281	−	8.65122i	−0.725441	−	0.644824i
$181$	10.0115	−	6.82572i	0.744148	−	0.507352i	−0.130895	−	0.991396i	$-0.541785\pi$
$181$	10.0115	−	6.82572i	0.744148	−	0.507352i	0.875043	+	0.484045i	$0.160833\pi$
$182$	−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	−0.984235	−	0.176867i	$-0.943404\pi$
$191$	−4.75355	−	13.0603i	−0.343955	−	0.945008i	0.640280	−	0.768142i	$-0.278818\pi$
$192$	5.33441	−	4.80998i	0.384978	−	0.347130i
$193$	−9.61164	−	4.33694i	−0.691861	−	0.312180i	0.0345862	−	0.999402i	$-0.488989\pi$
$193$	−9.61164	−	4.33694i	−0.691861	−	0.312180i	−0.726447	+	0.687222i	$0.758830\pi$
$194$	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	0.677888	−	0.735166i	$-0.262896\pi$
$197$	−0.0640563	−	0.0594356i	−0.00456382	−	0.00423461i	−0.682451	+	0.730931i	$0.739086\pi$
$198$	−6.40691	−	9.46963i	−0.455319	−	0.672977i
$199$	−13.6251	−	9.28944i	−0.965858	−	0.658511i	−0.0258509	−	0.999666i	$-0.508230\pi$
$199$	−13.6251	−	9.28944i	−0.965858	−	0.658511i	−0.940007	+	0.341155i	$0.889182\pi$
$200$	−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	0.0410845	−	0.999156i	$-0.486919\pi$
$211$	−13.7299	−	12.1167i	−0.945208	−	0.834151i	−0.986293	+	0.165004i	$0.947236\pi$
$212$	−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	0.269518	+	0.962995i	$0.413136\pi$
$223$	−0.711810	+	28.5427i	−0.0476663	+	1.91136i	−0.317185	+	0.948364i	$0.602737\pi$
$224$	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	0.974882	−	0.222722i	$-0.0714942\pi$
$227$	29.6373	−	1.47914i	1.96710	−	0.0981737i	0.992214	+	0.124548i	$0.0397482\pi$
$228$	1.04796	−	16.3221i	0.0694029	−	1.08096i
$229$	5.92145	−	5.77562i	0.391300	−	0.381664i	−0.476003	−	0.879444i	$-0.657915\pi$
$229$	5.92145	−	5.77562i	0.391300	−	0.381664i	0.867303	+	0.497780i	$0.165851\pi$
$230$	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	0.632641	−	0.774445i	$-0.281971\pi$
$233$	−5.40920	−	9.36900i	−0.354368	−	0.613784i	−0.987010	+	0.160661i	$0.948637\pi$
$234$	−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	0.0781497	−	0.996942i	$-0.475099\pi$
$239$	9.64022	−	2.45470i	0.623574	−	0.158781i	0.545424	+	0.838160i	$0.316369\pi$
$240$	22.6505	+	0.322803i	1.46208	+	0.0208368i
$241$	5.84144	+	3.56963i	0.376280	+	0.229940i	0.696743	−	0.717321i	$-0.254632\pi$
$241$	5.84144	+	3.56963i	0.376280	+	0.229940i	−0.320463	+	0.947261i	$0.603838\pi$
$242$	−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	0.375914	−	0.926655i	$-0.377329\pi$
$251$	9.65659	+	0.723661i	0.609518	+	0.0456771i	0.233605	+	0.972332i	$0.424948\pi$
$252$	−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	0.584011	−	0.811745i	$-0.301482\pi$
$257$	21.1177	−	2.11315i	1.31729	−	0.131815i	0.733276	+	0.679931i	$0.237990\pi$
$258$	−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	−0.0193969	−	0.999812i	$-0.506175\pi$
$263$	−13.6631	−	7.00468i	−0.842505	−	0.431927i	−0.823108	+	0.567885i	$0.807762\pi$
$264$	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	−0.691806	−	0.722083i	$-0.743185\pi$
$269$	−2.32518	+	1.85427i	−0.141769	+	0.113057i	0.550038	+	0.835140i	$0.314613\pi$
$270$	17.7132	+	20.8073i	1.07799	+	1.26629i
$271$	2.34644	+	4.87243i	0.142536	+	0.295979i	0.960000	−	0.280001i	$-0.0903349\pi$
$271$	2.34644	+	4.87243i	0.142536	+	0.295979i	−0.817464	+	0.575980i	$0.804621\pi$
$272$	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	−0.342077	−	0.939672i	$-0.611130\pi$
$277$	−4.86471	+	0.983422i	−0.292292	+	0.0590881i	0.0497853	+	0.998760i	$0.484146\pi$
$278$	−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	−0.496238	−	0.868186i	$-0.665286\pi$
$281$	−0.606347	+	0.330199i	−0.0361716	+	0.0196980i	0.460067	+	0.887884i	$0.347825\pi$
$282$	32.8925	+	12.5055i	1.95872	+	0.744693i
$283$	−6.96227	−	7.13806i	−0.413864	−	0.424314i	0.476775	−	0.879026i	$-0.341806\pi$
$283$	−6.96227	−	7.13806i	−0.413864	−	0.424314i	−0.890639	+	0.454712i	$0.849742\pi$
$284$	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	0.957772	−	0.287527i	$-0.0928332\pi$
$293$	−0.357324	−	1.40330i	−0.0208751	−	0.0819816i	−0.978648	+	0.205546i	$0.934103\pi$
$294$	−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	−0.00790434	−	0.999969i	$-0.502516\pi$
$307$	14.9658	−	8.64049i	0.854142	−	0.493139i	0.862046	+	0.506830i	$0.169183\pi$
$308$	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	0.255143	−	0.966903i	$-0.417877\pi$
$311$	18.3820	−	6.17602i	1.04235	−	0.350210i	0.787203	+	0.616693i	$0.211528\pi$
$312$	5.75359	+	2.69545i	0.325733	+	0.152600i
$313$	−21.2653	−	8.96408i	−1.20199	−	0.506680i	−0.306544	−	0.951856i	$-0.599173\pi$
$313$	−21.2653	−	8.96408i	−1.20199	−	0.506680i	−0.895443	+	0.445177i	$0.853141\pi$
$314$	−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	0.746361	−	0.665541i	$-0.231799\pi$
$317$	11.4245	+	5.85702i	0.641666	+	0.328963i	−0.104695	+	0.994504i	$0.533387\pi$
$318$	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	−0.918667	−	0.395033i	$-0.870733\pi$
$331$	−6.73358	+	8.02477i	−0.370111	+	0.441081i	0.548556	+	0.836114i	$0.315178\pi$
$332$	−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	0.944393	−	0.328818i	$-0.106650\pi$
$337$	4.05602	+	6.63739i	0.220946	+	0.361562i	−0.723448	+	0.690379i	$0.757444\pi$
$338$	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	−0.999848	−	0.0174355i	$-0.994450\pi$
$347$	−21.5395	+	18.0738i	−1.15630	+	0.970250i	−0.156451	+	0.987686i	$0.550005\pi$
$348$	8.87510	+	11.4908i	0.475756	+	0.615974i
$349$	20.4499	−	7.44317i	1.09466	−	0.398424i	0.269315	−	0.963052i	$-0.413203\pi$
$349$	20.4499	−	7.44317i	1.09466	−	0.398424i	0.825345	+	0.564629i	$0.190981\pi$
$350$	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	0.849760	−	0.527169i	$-0.176747\pi$
$353$	0.371010	+	0.574436i	0.0197469	+	0.0305741i	−0.830013	+	0.557743i	$0.811667\pi$
$354$	−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	−0.925272	−	0.379304i	$-0.876164\pi$
$359$	−25.4946	+	10.0059i	−1.34555	+	0.528091i	−0.420281	+	0.907394i	$0.638068\pi$
$360$	−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	0.0788320	−	0.996888i	$-0.474881\pi$
$367$	12.7570	−	3.58927i	0.665911	−	0.187358i	0.587079	+	0.809530i	$0.300278\pi$
$368$	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	0.898855	−	0.438246i	$-0.144400\pi$
$373$	3.80773	+	5.29623i	0.197157	+	0.274228i	−0.701698	+	0.712474i	$0.747575\pi$
$374$	−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	−0.233598	−	0.972333i	$-0.575050\pi$
$379$	−0.431865	+	0.0985705i	−0.0221834	+	0.00506322i	0.211415	+	0.977396i	$0.432193\pi$
$380$	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	0.330209	−	0.943908i	$-0.392881\pi$
$383$	11.0532	+	0.551644i	0.564793	+	0.0281877i	0.234585	+	0.972096i	$0.424627\pi$
$384$	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	0.208332	−	0.978058i	$-0.433197\pi$
$389$	1.37241	+	0.241993i	0.0695840	+	0.0122695i	−0.138748	+	0.990328i	$0.544308\pi$
$390$	−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	−0.848530	−	0.529148i	$-0.822512\pi$
$397$	−29.9549	+	4.51497i	−1.50339	+	0.226600i	−0.654863	+	0.755748i	$0.727274\pi$
$398$	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	0.171589	−	0.985169i	$-0.445110\pi$
$401$	−14.6239	−	11.0772i	−0.730285	−	0.553169i	−0.901874	+	0.431999i	$0.857808\pi$
$402$	−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	0.959969	−	0.280108i	$-0.0903702\pi$
$409$	−0.345000	−	1.35490i	−0.0170592	−	0.0669956i	−0.977028	+	0.213112i	$0.931640\pi$
$410$	−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	0.0716465	−	0.997430i	$-0.477175\pi$
$419$	20.3040	−	12.4075i	0.991917	−	0.606148i	0.920271	+	0.391282i	$0.127968\pi$
$420$	−18.0885	+	19.9174i	−0.882629	+	0.971867i
$421$	−9.27647	+	22.0064i	−0.452107	+	1.07253i	0.523306	+	0.852145i	$0.324698\pi$
$421$	−9.27647	+	22.0064i	−0.452107	+	1.07253i	−0.975414	+	0.220381i	$0.929270\pi$
$422$	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	−0.996925	−	0.0783647i	$-0.975030\pi$
$431$	−32.3289	+	15.5688i	−1.55723	+	0.749922i	−0.560304	+	0.828287i	$0.689316\pi$
$432$	21.8816	−	10.7301i	1.05278	−	0.516251i
$433$	27.9714	−	6.38428i	1.34422	−	0.306809i	0.510918	−	0.859630i	$-0.329306\pi$
$433$	27.9714	−	6.38428i	1.34422	−	0.306809i	0.833300	+	0.552821i	$0.186448\pi$
$434$	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	0.860120	−	0.510091i	$-0.170388\pi$
$439$	28.7370	+	7.31735i	1.37154	+	0.349238i	0.511423	+	0.859329i	$0.329118\pi$
$440$	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	−0.972101	−	0.234562i	$-0.924634\pi$
$443$	−13.5068	−	24.8027i	−0.641729	−	1.17841i	0.330372	−	0.943851i	$-0.392826\pi$
$444$	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	0.999990	+	0.00445024i	$0.00141656\pi$
$449$	3.73502	+	12.1086i	0.176266	+	0.571442i	−0.823724	+	0.566991i	$0.808107\pi$
$450$	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	0.470283	−	0.882516i	$-0.344152\pi$
$457$	16.1694	+	1.61800i	0.756374	+	0.0756866i	0.286091	+	0.958202i	$0.407644\pi$
$458$	−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	0.934703	+	0.355430i	$0.115666\pi$
$461$	−1.11422	+	11.1349i	−0.0518943	+	0.518605i	−0.986597	+	0.163175i	$0.947826\pi$
$462$	−19.7060	+	13.0279i	−0.916805	+	0.606112i
$463$	27.3606	−	22.9583i	1.27156	−	1.06696i	0.277207	−	0.960810i	$-0.410591\pi$
$463$	27.3606	−	22.9583i	1.27156	−	1.06696i	0.994350	−	0.106153i	$-0.0338533\pi$
$464$	−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	0.899578	+	0.436761i	$0.143875\pi$
$467$	21.1238	+	30.9830i	0.977494	+	1.43372i	0.0779169	+	0.996960i	$0.475173\pi$
$468$	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	0.503694	−	0.863882i	$-0.331974\pi$
$479$	−10.1621	−	13.4159i	−0.464320	−	0.612988i	−0.968015	+	0.250894i	$0.919275\pi$
$480$	−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	−0.952788	−	0.303635i	$-0.901800\pi$
$487$	0.825049	−	3.61477i	0.0373865	−	0.163801i	0.990175	+	0.139834i	$0.0446568\pi$
$488$	−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	−0.996838	−	0.0794626i	$-0.974680\pi$
$491$	−7.92596	−	18.8026i	−0.357694	−	0.848549i	0.639144	−	0.769087i	$-0.279289\pi$
$492$	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	−0.537233	−	0.843434i	$-0.680531\pi$
$499$	10.1085	−	15.6510i	0.452518	−	0.700636i	0.989752	+	0.142798i	$0.0456099\pi$
$500$	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	−0.628728	−	0.777626i	$-0.716424\pi$
$503$	7.28548	−	10.6858i	0.324844	−	0.476458i	0.953571	+	0.301167i	$0.0973763\pi$
$504$	−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	0.328233	+	0.944597i	$0.393547\pi$
$509$	1.07147	+	42.9648i	0.0474923	+	1.90438i	−0.280741	+	0.959784i	$0.590580\pi$
$510$	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	−0.877229	−	0.480073i	$-0.840610\pi$
$521$	−0.521763	+	0.903720i	−0.0228589	+	0.0395927i	0.854370	+	0.519666i	$0.173944\pi$
$522$	−15.1055	−	26.4594i	−0.661152	−	1.15810i
$523$	−10.6428	−	18.4340i	−0.465379	−	0.806060i	0.533839	−	0.845586i	$-0.320749\pi$
$523$	−10.6428	−	18.4340i	−0.465379	−	0.806060i	−0.999219	+	0.0395255i	$0.987415\pi$
$524$	−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	0.897761	−	0.440484i	$-0.145193\pi$
$541$	−0.148120	−	0.307573i	−0.00636816	−	0.0132236i	−0.904129	+	0.427260i	$0.859479\pi$
$542$	−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	0.193945	−	0.981012i	$-0.437872\pi$
$547$	−2.45342	−	0.624717i	−0.104901	−	0.0267110i	−0.298846	+	0.954301i	$0.596602\pi$
$548$	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	−0.864263	−	0.503040i	$-0.832215\pi$
$557$	−30.5626	+	9.42731i	−1.29498	+	0.399448i	−0.430716	+	0.902488i	$0.641739\pi$
$558$	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	−0.998795	−	0.0490836i	$-0.984370\pi$
$563$	−20.7307	−	24.7059i	−0.873694	−	1.04123i	0.125101	−	0.992144i	$-0.460075\pi$
$564$	−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	−0.395899	−	0.918294i	$-0.629567\pi$
$569$	−30.1977	−	10.1459i	−1.26595	−	0.425338i	−0.870054	+	0.492957i	$0.835916\pi$
$570$	−13.0619	+	53.6896i	−0.547105	+	2.24881i
$571$	−32.5872	−	6.58765i	−1.36373	−	0.275684i	−0.539524	−	0.841970i	$-0.681396\pi$
$571$	−32.5872	−	6.58765i	−1.36373	−	0.275684i	−0.824209	+	0.566286i	$0.808380\pi$
$572$	−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	0.205178	−	0.978725i	$-0.434223\pi$
$577$	13.3060	−	0.997147i	0.553936	−	0.0415118i	0.348758	+	0.937213i	$0.386604\pi$
$578$	−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	0.904067	−	0.427391i	$-0.140567\pi$
$587$	−0.353516	−	0.783471i	−0.0145912	−	0.0323373i	−0.918658	+	0.395054i	$0.870726\pi$
$588$	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	−0.481217	−	0.876602i	$-0.659805\pi$
$593$	11.7006	−	14.6721i	0.480487	−	0.602512i	0.961704	+	0.274090i	$0.0883765\pi$
$594$	−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	−0.411488	−	0.911415i	$-0.634991\pi$
$599$	7.86642	−	5.65557i	0.321413	−	0.231080i	0.732902	+	0.680335i	$0.238166\pi$
$600$	−3.94869	−	0.754432i	−0.161205	−	0.0307995i
$601$	−17.9951	−	0.448771i	−0.734037	−	0.0183057i	−0.343829	−	0.939032i	$-0.611724\pi$
$601$	−17.9951	−	0.448771i	−0.734037	−	0.0183057i	−0.390208	+	0.920727i	$0.627597\pi$
$602$	−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	0.671204	−	0.741273i	$-0.265778\pi$
$607$	28.0555	+	3.51581i	1.13874	+	0.142702i	0.467534	+	0.883975i	$0.345143\pi$
$608$	−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	−0.883705	−	0.468045i	$-0.844959\pi$
$613$	1.48276	−	19.7861i	0.0598882	−	0.799153i	0.943593	−	0.331108i	$-0.107422\pi$
$614$	−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	0.750245	+	0.661160i	$0.229935\pi$
$617$	−4.91586	+	24.3174i	−0.197905	+	0.978981i	−0.948151	+	0.317821i	$0.897049\pi$
$618$	−48.3493	+	27.0032i	−1.94489	+	1.08623i
$619$	19.2330	+	18.7593i	0.773040	+	0.754002i	0.974232	−	0.225550i	$-0.0724180\pi$
$619$	19.2330	+	18.7593i	0.773040	+	0.754002i	−0.201192	+	0.979552i	$0.564482\pi$
$620$	−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	−0.865827	−	0.500344i	$-0.833207\pi$
$631$	−2.11616	−	28.2382i	−0.0842430	−	1.12414i	0.781584	−	0.623800i	$-0.214412\pi$
$632$	−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	0.713828	−	0.700321i	$-0.246960\pi$
$641$	43.3253	−	19.5491i	1.71125	−	0.772144i	0.997417	−	0.0718230i	$-0.0228817\pi$
$642$	−38.8235	+	4.30423i	−1.53224	+	0.169875i
$643$	−26.7256	+	11.2658i	−1.05395	+	0.444279i	−0.845623	−	0.533780i	$-0.820771\pi$
$643$	−26.7256	+	11.2658i	−1.05395	+	0.444279i	−0.208330	+	0.978059i	$0.566803\pi$
$644$	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	0.996639	+	0.0819224i	$0.0261060\pi$
$647$	21.7412	+	27.2626i	0.854734	+	1.07180i	−0.141905	+	0.989880i	$0.545323\pi$
$648$	−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	−0.983758	−	0.179497i	$-0.942553\pi$
$653$	0.331782	−	6.64788i	0.0129836	−	0.260152i	0.996742	−	0.0806546i	$-0.0257011\pi$
$654$	−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	−0.980156	−	0.198227i	$-0.936482\pi$
$659$	−15.7849	−	28.9859i	−0.614892	−	1.12913i	0.365264	−	0.930904i	$-0.380979\pi$
$660$	13.7583	+	6.44549i	0.535540	+	0.250890i
$661$	−22.1351	+	34.2718i	−0.860955	+	1.33302i	0.0808039	+	0.996730i	$0.474251\pi$
$661$	−22.1351	+	34.2718i	−0.860955	+	1.33302i	−0.941759	+	0.336289i	$0.890828\pi$
$662$	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	−0.998133	−	0.0610839i	$-0.980544\pi$
$673$	−1.19173	−	9.50979i	−0.0459379	−	0.366575i	0.952195	−	0.305492i	$-0.0988208\pi$
$674$	−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	0.990983	−	0.133990i	$-0.0427789\pi$
$677$	22.9422	+	22.3772i	0.881740	+	0.860025i	−0.109242	+	0.994015i	$0.534842\pi$
$678$	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	0.989803	−	0.142443i	$-0.0454956\pi$
$683$	4.37332	+	11.1430i	0.167340	+	0.426377i	−0.822463	+	0.568819i	$0.807400\pi$
$684$	−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	0.472292	−	0.881442i	$-0.343427\pi$
$691$	27.0755	−	1.35128i	1.03000	−	0.0514052i	0.557708	+	0.830037i	$0.311681\pi$
$692$	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	0.989939	−	0.141495i	$-0.0451908\pi$
$701$	0.970163	+	4.25056i	0.0366425	+	0.160541i	−0.953296	+	0.302036i	$0.902334\pi$
$702$	−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	−0.355248	−	0.934772i	$-0.615603\pi$
$709$	−8.50739	+	1.71981i	−0.319502	+	0.0645887i	0.0357458	+	0.999361i	$0.488619\pi$
$710$	−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	−0.718960	−	0.695052i	$-0.755381\pi$
$719$	−24.7081	+	7.62143i	−0.921455	+	0.284231i	−0.202496	+	0.979283i	$0.564905\pi$
$720$	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	−0.0881331	−	0.996109i	$-0.528090\pi$
$727$	21.1276	−	13.6456i	0.783578	−	0.506088i	0.871711	+	0.490021i	$0.163011\pi$
$728$	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	0.810669	+	0.585505i	$0.199104\pi$
$733$	−4.43401	+	21.9338i	−0.163774	+	0.810143i	−0.974442	+	0.224637i	$0.927880\pi$
$734$	−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	0.999297	−	0.0374916i	$-0.0119367\pi$
$739$	4.14617	+	13.4416i	0.152519	+	0.494455i	−0.846778	+	0.531947i	$0.821461\pi$
$740$	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	0.937083	−	0.349108i	$-0.113515\pi$
$743$	5.42201	+	8.87273i	0.198914	+	0.325509i	−0.738168	+	0.674617i	$0.764309\pi$
$744$	−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	0.514710	−	0.857365i	$-0.327900\pi$
$751$	13.8898	+	3.90799i	0.506847	+	0.142604i	−0.00786307	+	0.999969i	$0.502503\pi$
$752$	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	−0.907146	−	0.420817i	$-0.861744\pi$
$757$	−0.345075	+	0.716555i	−0.0125420	+	0.0260436i	0.894604	+	0.446860i	$0.147458\pi$
$758$	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	0.770690	+	0.637210i	$0.219912\pi$
$761$	−6.04681	+	21.4916i	−0.219197	+	0.779071i	−0.989887	+	0.141861i	$0.954691\pi$
$762$	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	0.0178444	−	0.999841i	$-0.494320\pi$
$769$	−24.5744	−	15.8719i	−0.886177	−	0.572354i	−0.904022	+	0.427487i	$0.859399\pi$
$770$	−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	−0.469015	−	0.883190i	$-0.655391\pi$
$773$	14.5819	−	21.3877i	0.524474	−	0.769262i	0.993489	+	0.113928i	$0.0363433\pi$
$774$	−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	−0.911748	−	0.410750i	$-0.865267\pi$
$787$	−0.0136021	+	0.0301453i	−0.000484862	+	0.00107457i	0.911263	+	0.411824i	$0.135108\pi$
$788$	−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	0.629144	−	0.777289i	$-0.283406\pi$
$797$	5.06463	+	3.27109i	0.179399	+	0.115868i	−0.449745	+	0.893157i	$0.648485\pi$
$798$	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	−0.264565	−	0.964368i	$-0.585228\pi$
$809$	18.6120	−	38.6481i	0.654362	−	1.35880i	0.918927	−	0.394428i	$-0.129057\pi$
$810$	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	−0.994664	−	0.103170i	$-0.967102\pi$
$821$	−41.4796	+	22.5886i	−1.44765	+	0.788348i	−0.452986	+	0.891518i	$0.649641\pi$
$822$	−23.3330	−	47.1560i	−0.813831	−	1.64476i
$823$	−25.8145	−	42.2436i	−0.899838	−	1.47252i	−0.881228	−	0.472692i	$-0.843282\pi$
$823$	−25.8145	−	42.2436i	−0.899838	−	1.47252i	−0.0186101	−	0.999827i	$-0.505924\pi$
$824$	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	0.849326	−	0.527869i	$-0.177009\pi$
$827$	−4.30729	−	13.9639i	−0.149779	−	0.485573i	−0.999105	+	0.0422964i	$0.986533\pi$
$828$	−24.8630	+	32.5816i	−0.864050	+	1.13229i
$829$	−5.27986	−	3.04833i	−0.183377	−	0.105873i	0.405501	−	0.914094i	$-0.367097\pi$
$829$	−5.27986	−	3.04833i	−0.183377	−	0.105873i	−0.588878	+	0.808222i	$0.700430\pi$
$830$	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	−0.740610	−	0.671935i	$-0.765463\pi$
$839$	−12.5345	+	8.09565i	−0.432740	+	0.279493i	0.307870	+	0.951428i	$0.400384\pi$
$840$	−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	0.608466	−	0.793580i	$-0.291785\pi$
$853$	26.5431	+	4.68026i	0.908817	+	0.160249i	0.300351	+	0.953829i	$0.402896\pi$
$854$	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	−0.474388	−	0.880316i	$-0.657330\pi$
$857$	−16.6742	+	3.37076i	−0.569579	+	0.115143i	−0.0951914	+	0.995459i	$0.530346\pi$
$858$	18.8505	+	21.9839i	0.643545	+	0.750516i
$859$	13.1734	−	24.1905i	0.449472	−	0.825368i	−0.550483	−	0.834846i	$-0.685557\pi$
$859$	13.1734	−	24.1905i	0.449472	−	0.825368i	0.999955	+	0.00947777i	$0.00301691\pi$
$860$	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	0.229867	−	0.973222i	$-0.426171\pi$
$863$	−11.3897	−	5.48499i	−0.387710	−	0.186711i	−0.617576	+	0.786511i	$0.711885\pi$
$864$	−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	0.716928	−	0.697147i	$-0.245547\pi$
$877$	0.0629153	+	0.0645039i	0.00212450	+	0.00217814i	−0.714804	+	0.699325i	$0.753484\pi$
$878$	−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	0.769942	+	0.638114i	$0.220285\pi$
$881$	−4.56744	+	30.3030i	−0.153881	+	1.02093i	−0.923823	+	0.382820i	$0.874953\pi$
$882$	−21.6510	−	24.7107i	−0.729026	−	0.832051i
$883$	5.06272	+	12.8996i	0.170374	+	0.434106i	0.990402	−	0.138218i	$-0.0441374\pi$
$883$	5.06272	+	12.8996i	0.170374	+	0.434106i	−0.820028	+	0.572324i	$0.806042\pi$
$884$	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	0.741081	−	0.671415i	$-0.234313\pi$
$887$	−1.45401	−	1.73283i	−0.0488210	−	0.0581826i	−0.789902	+	0.613233i	$0.789869\pi$
$888$	−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	0.594076	−	0.804409i	$-0.297518\pi$
$907$	−12.1659	−	22.3403i	−0.403962	−	0.741798i	−0.998038	+	0.0626105i	$0.980057\pi$
$908$	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	−0.626663	−	0.779290i	$-0.715580\pi$
$911$	7.53384	−	8.97848i	0.249607	−	0.297470i	0.876270	+	0.481820i	$0.160024\pi$
$912$	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	−0.999550	−	0.0299900i	$-0.990452\pi$
$919$	−24.4450	−	30.6531i	−0.806367	−	1.01115i	0.193183	−	0.981163i	$-0.438119\pi$
$920$	−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	−0.729810	−	0.683650i	$-0.760391\pi$
$929$	5.78529	−	32.8100i	0.189809	−	1.07646i	0.919619	−	0.392812i	$-0.128498\pi$
$930$	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	−0.616051	−	0.787706i	$-0.711269\pi$
$937$	−29.7703	+	4.48715i	−0.972553	+	0.146589i	−0.356501	+	0.934295i	$0.616030\pi$
$938$	−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	0.999068	−	0.0431589i	$-0.0137422\pi$
$941$	−0.0278957	−	1.11858i	−0.000909374	−	0.0364648i	−0.999978	+	0.00669417i	$0.997869\pi$
$942$	−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	0.852502	−	0.522724i	$-0.175084\pi$
$947$	10.8074	+	10.5413i	0.351194	+	0.342545i	−0.501308	+	0.865269i	$0.667148\pi$
$948$	−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	−0.837017	−	0.547176i	$-0.815703\pi$
$953$	2.22898	−	29.7436i	0.0722036	−	0.963490i	0.909221	−	0.416314i	$-0.136678\pi$
$954$	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	−0.509932	+	0.860215i	$0.670329\pi$
$967$	−46.2643	+	33.2618i	−1.48776	+	1.06963i	−0.977828	+	0.209412i	$0.932845\pi$
$968$	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	0.417767	−	0.908554i	$-0.362813\pi$
$971$	12.4630	+	2.84459i	0.399955	+	0.0912872i	−0.0178118	+	0.999841i	$0.505670\pi$
$972$	−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	−0.0539541	+	0.998543i	$0.517182\pi$
$977$	−32.4460	+	36.7658i	−1.03804	+	1.17624i	−0.984085	+	0.177698i	$0.943135\pi$
$978$	−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	−0.221773	−	0.975098i	$-0.571184\pi$
$983$	−38.1478	−	27.4264i	−1.21673	−	0.874767i	−0.994954	+	0.100331i	$0.968010\pi$
$984$	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	0.990640	−	0.136498i	$-0.0435848\pi$
$991$	54.5316	+	16.8208i	1.73225	+	0.534329i	0.741613	+	0.670828i	$0.234061\pi$
$992$	−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	−0.108318	−	0.994116i	$-0.534546\pi$
$997$	−25.0996	−	8.43303i	−0.794914	−	0.267077i	−0.686596	+	0.727039i	$0.740896\pi$
$998$			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.196.18	yes	3168
27.4	even	9	inner	783.2.bf.a.544.18	yes	3168
29.4	even	14	inner	783.2.bf.a.439.18	yes	3168
783.4	even	126	inner	783.2.bf.a.4.18	✓	3168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.bf.a.4.18	✓	3168	783.4	even	126	inner
783.2.bf.a.196.18	yes	3168	1.1	even	1	trivial
783.2.bf.a.439.18	yes	3168	29.4	even	14	inner
783.2.bf.a.544.18	yes	3168	27.4	even	9	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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