LMFDB - Embedded newform 415.2.l.a.102.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [415,2,Mod(2,415)] 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("415.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(415, base_ring=CyclotomicField(164)) chi = DirichletCharacter(H, H._module([41, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 415 = 5 \cdot 83 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	415.l (of order $164$, degree $80$, 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:	$3.31379168388$
Analytic rank:	$0$
Dimension:	$3200$
Relative dimension:	$40$ over $\Q(\zeta_{164})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{164}]$

Embedding invariants

Embedding label			102.4
Character	$\chi$	$=$	415.102
Dual form			415.2.l.a.118.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96491 + 1.21968i) q^{2} +(2.61910 + 0.150681i) q^{3} +(1.48579 - 3.00080i) q^{4} +(-1.65344 + 1.50537i) q^{5} +(-5.33006 + 2.89839i) q^{6} +(2.73458 - 1.55561i) q^{7} +(0.298245 + 3.10431i) q^{8} +(3.85675 + 0.445243i) q^{9} +(1.41279 - 4.97458i) q^{10} +(1.73500 - 1.66977i) q^{11} +(4.34358 - 7.63549i) q^{12} +(1.84795 - 0.703950i) q^{13} +(-3.47584 + 6.39196i) q^{14} +(-4.55735 + 3.69356i) q^{15} +(-0.312432 - 0.409872i) q^{16} +(-0.0121305 - 0.0233632i) q^{17} +(-8.12121 + 3.82915i) q^{18} +(0.649757 + 3.35032i) q^{19} +(2.06063 + 7.19830i) q^{20} +(7.39653 - 3.66225i) q^{21} +(-1.37252 + 5.39708i) q^{22} +(-0.390432 - 0.184089i) q^{23} +(0.313371 + 8.17544i) q^{24} +(0.467742 - 4.97807i) q^{25} +(-2.77244 + 3.63710i) q^{26} +(2.28051 + 0.397112i) q^{27} +(-0.605072 - 10.5172i) q^{28} +(2.15492 + 5.34673i) q^{29} +(4.44980 - 12.8160i) q^{30} +(7.46370 - 6.15526i) q^{31} +(-4.71482 - 1.79605i) q^{32} +(4.79572 - 4.11185i) q^{33} +(0.0523311 + 0.0311111i) q^{34} +(-2.17970 + 6.68866i) q^{35} +(7.06640 - 10.9118i) q^{36} +(-3.38676 + 4.27079i) q^{37} +(-5.36304 - 5.79057i) q^{38} +(4.94602 - 1.56526i) q^{39} +(-5.16626 - 4.68384i) q^{40} +(-2.86425 + 0.670260i) q^{41} +(-10.0667 + 16.2174i) q^{42} +(0.140689 + 0.807939i) q^{43} +(-2.43279 - 7.68729i) q^{44} +(-7.04717 + 5.06964i) q^{45} +(0.991693 - 0.114486i) q^{46} +(-0.516341 - 2.41403i) q^{47} +(-0.756529 - 1.12057i) q^{48} +(1.48086 - 2.49092i) q^{49} +(5.15260 + 10.3519i) q^{50} +(-0.0282507 - 0.0630183i) q^{51} +(0.633247 - 6.59123i) q^{52} +(-2.81090 + 13.1417i) q^{53} +(-4.96533 + 2.00121i) q^{54} +(-0.355105 + 5.37267i) q^{55} +(5.64469 + 8.02504i) q^{56} +(1.19695 + 8.87272i) q^{57} +(-10.7555 - 7.87749i) q^{58} +(4.25480 - 0.163090i) q^{59} +(4.31235 + 19.1635i) q^{60} +(-12.8846 + 7.65999i) q^{61} +(-7.15799 + 21.1979i) q^{62} +(11.2392 - 4.78206i) q^{63} +(12.4667 - 2.41777i) q^{64} +(-1.99577 + 3.94578i) q^{65} +(-4.40799 + 13.9287i) q^{66} +(-7.52316 - 1.01489i) q^{67} +(-0.0881316 + 0.00168846i) q^{68} +(-0.994841 - 0.540977i) q^{69} +(-3.87515 - 15.8011i) q^{70} +(15.1346 - 4.15906i) q^{71} +(-0.231919 + 12.1054i) q^{72} +(-9.15039 - 12.4935i) q^{73} +(1.44566 - 12.5225i) q^{74} +(1.97516 - 12.9676i) q^{75} +(11.0190 + 3.02808i) q^{76} +(2.14698 - 7.26510i) q^{77} +(-7.80933 + 9.10817i) q^{78} +(12.6641 + 6.27039i) q^{79} +(1.13360 + 0.207375i) q^{80} +(-5.42770 - 1.27013i) q^{81} +(4.81047 - 4.81047i) q^{82} +(-5.79396 - 7.03065i) q^{83} -27.6368i q^{84} +(0.0552273 + 0.0203688i) q^{85} +(-1.26187 - 1.41593i) q^{86} +(4.83830 + 14.3283i) q^{87} +(5.70094 + 4.88798i) q^{88} +(-5.40459 - 9.93887i) q^{89} +(7.66367 - 18.5567i) q^{90} +(3.95828 - 4.79970i) q^{91} +(-1.13251 + 0.898090i) q^{92} +(20.4756 - 14.9966i) q^{93} +(3.95891 + 4.11357i) q^{94} +(-6.11780 - 4.56144i) q^{95} +(-12.0779 - 5.41445i) q^{96} +(3.47592 + 11.7621i) q^{97} +(0.128373 + 6.70060i) q^{98} +(7.43490 - 5.66738i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3200 q - 82 q^{2} - 78 q^{3} - 82 q^{5} - 164 q^{6} - 74 q^{7} - 82 q^{8} - 102 q^{10} - 164 q^{11} - 114 q^{12} - 82 q^{13} - 82 q^{15} - 96 q^{16} - 82 q^{17} - 82 q^{18} - 82 q^{20} - 148 q^{21} - 82 q^{22}+ \cdots + 246 q^{98}+O(q^{100}) $ 3200 * q - 82 * q^2 - 78 * q^3 - 82 * q^5 - 164 * q^6 - 74 * q^7 - 82 * q^8 - 102 * q^10 - 164 * q^11 - 114 * q^12 - 82 * q^13 - 82 * q^15 - 96 * q^16 - 82 * q^17 - 82 * q^18 - 82 * q^20 - 148 * q^21 - 82 * q^22 - 86 * q^23 - 74 * q^25 - 140 * q^26 - 90 * q^27 - 78 * q^28 - 114 * q^30 - 148 * q^31 - 82 * q^32 - 42 * q^33 - 82 * q^35 - 104 * q^36 - 66 * q^37 - 26 * q^38 - 130 * q^40 - 156 * q^41 - 82 * q^42 - 82 * q^43 - 82 * q^45 - 164 * q^46 - 82 * q^47 - 102 * q^48 - 82 * q^50 - 164 * q^51 - 82 * q^52 - 82 * q^53 - 82 * q^55 - 164 * q^56 - 82 * q^57 - 82 * q^58 - 82 * q^60 - 100 * q^61 - 82 * q^62 - 38 * q^63 - 134 * q^65 - 164 * q^66 - 82 * q^67 + 182 * q^68 - 138 * q^70 - 164 * q^71 - 82 * q^72 + 164 * q^73 - 138 * q^75 - 164 * q^76 - 106 * q^77 + 606 * q^78 - 82 * q^80 - 188 * q^81 + 192 * q^83 - 82 * q^85 - 84 * q^86 - 54 * q^87 + 738 * q^88 - 198 * q^90 - 164 * q^91 - 82 * q^92 + 576 * q^93 - 50 * q^95 - 164 * q^96 - 82 * q^97 + 246 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/415\mathbb{Z}\right)^\times$.

$n$	$167$	$251$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{47}{82}\right)$

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 $

$2$	−1.96491	+	1.21968i	−1.38940	+	0.862446i	−0.998322	−	0.0579117i	$-0.981556\pi$
$2$	−1.96491	+	1.21968i	−1.38940	+	0.862446i	−0.391077	+	0.920358i	$0.627897\pi$
$3$	2.61910	+	0.150681i	1.51214	+	0.0869954i	0.793576	−	0.608471i	$-0.208217\pi$
$3$	2.61910	+	0.150681i	1.51214	+	0.0869954i	0.718559	+	0.695466i	$0.244802\pi$
$4$	1.48579	−	3.00080i	0.742894	−	1.50040i
$5$	−1.65344	+	1.50537i	−0.739442	+	0.673220i
$5$	−1.65344	+	1.50537i	−0.739442	+	0.673220i
$6$	−5.33006	+	2.89839i	−2.17599	+	1.18326i
$7$	2.73458	−	1.55561i	1.03357	−	0.587967i	0.119214	−	0.992869i	$-0.461963\pi$
$7$	2.73458	−	1.55561i	1.03357	−	0.587967i	0.914360	+	0.404902i	$0.132694\pi$
$8$	0.298245	+	3.10431i	0.105445	+	1.09754i
$9$	3.85675	+	0.445243i	1.28558	+	0.148414i
$10$	1.41279	−	4.97458i	0.446763	−	1.57310i
$11$	1.73500	−	1.66977i	0.523121	−	0.503454i	−0.384568	−	0.923097i	$-0.625650\pi$
$11$	1.73500	−	1.66977i	0.523121	−	0.503454i	0.907689	+	0.419643i	$0.137845\pi$
$12$	4.34358	−	7.63549i	1.25388	−	2.20418i
$13$	1.84795	−	0.703950i	0.512528	−	0.195240i	−0.0860717	−	0.996289i	$-0.527431\pi$
$13$	1.84795	−	0.703950i	0.512528	−	0.195240i	0.598600	+	0.801048i	$0.295724\pi$
$14$	−3.47584	+	6.39196i	−0.928956	+	1.70832i
$15$	−4.55735	+	3.69356i	−1.17670	+	0.953673i
$16$	−0.312432	−	0.409872i	−0.0781080	−	0.102468i
$17$	−0.0121305	−	0.0233632i	−0.00294209	−	0.00566641i	0.886026	−	0.463635i	$-0.153455\pi$
$17$	−0.0121305	−	0.0233632i	−0.00294209	−	0.00566641i	−0.888968	+	0.457969i	$0.848577\pi$
$18$	−8.12121	+	3.82915i	−1.91419	+	0.902540i
$19$	0.649757	+	3.35032i	0.149064	+	0.768617i	0.977892	+	0.209112i	$0.0670573\pi$
$19$	0.649757	+	3.35032i	0.149064	+	0.768617i	−0.828827	+	0.559505i	$0.810991\pi$
$20$	2.06063	+	7.19830i	0.460771	+	1.60959i
$21$	7.39653	−	3.66225i	1.61405	−	0.799169i
$22$	−1.37252	+	5.39708i	−0.292622	+	1.15066i
$23$	−0.390432	−	0.184089i	−0.0814108	−	0.0383852i	0.385335	−	0.922777i	$-0.374086\pi$
$23$	−0.390432	−	0.184089i	−0.0814108	−	0.0383852i	−0.466746	+	0.884392i	$0.654574\pi$
$24$	0.313371	+	8.17544i	0.0639667	+	1.66880i
$25$	0.467742	−	4.97807i	0.0935484	−	0.995615i
$26$	−2.77244	+	3.63710i	−0.543721	+	0.713295i
$27$	2.28051	+	0.397112i	0.438884	+	0.0764242i
$28$	−0.605072	−	10.5172i	−0.114348	−	1.98757i
$29$	2.15492	+	5.34673i	0.400159	+	0.992862i	0.983544	+	0.180666i	$0.0578254\pi$
$29$	2.15492	+	5.34673i	0.400159	+	0.992862i	−0.583385	+	0.812196i	$0.698272\pi$
$30$	4.44980	−	12.8160i	0.812418	−	2.33987i
$31$	7.46370	−	6.15526i	1.34052	−	1.10552i	0.355201	−	0.934790i	$-0.384412\pi$
$31$	7.46370	−	6.15526i	1.34052	−	1.10552i	0.985318	−	0.170728i	$-0.0546120\pi$
$32$	−4.71482	−	1.79605i	−0.833470	−	0.317499i
$33$	4.79572	−	4.11185i	0.834829	−	0.715781i
$34$	0.0523311	+	0.0311111i	0.00897471	+	0.00533551i
$35$	−2.17970	+	6.68866i	−0.368437	+	1.13059i
$36$	7.06640	−	10.9118i	1.17773	−	1.81863i
$37$	−3.38676	+	4.27079i	−0.556780	+	0.702113i	−0.978880	−	0.204436i	$-0.934464\pi$
$37$	−3.38676	+	4.27079i	−0.556780	+	0.702113i	0.422100	+	0.906549i	$0.361293\pi$
$38$	−5.36304	−	5.79057i	−0.870000	−	0.939355i
$39$	4.94602	−	1.56526i	0.791997	−	0.250643i
$40$	−5.16626	−	4.68384i	−0.816858	−	0.740580i
$41$	−2.86425	+	0.670260i	−0.447320	+	0.104677i	−0.445421	−	0.895321i	$-0.646946\pi$
$41$	−2.86425	+	0.670260i	−0.447320	+	0.104677i	−0.00189927	+	0.999998i	$0.500605\pi$
$42$	−10.0667	+	16.2174i	−1.55332	+	2.50240i
$43$	0.140689	+	0.807939i	0.0214549	+	0.123210i	0.993975	−	0.109611i	$-0.0349606\pi$
$43$	0.140689	+	0.807939i	0.0214549	+	0.123210i	−0.972520	+	0.232821i	$0.925204\pi$
$44$	−2.43279	−	7.68729i	−0.366757	−	1.15890i
$45$	−7.04717	+	5.06964i	−1.05053	+	0.755737i
$46$	0.991693	−	0.114486i	0.146217	−	0.0168801i
$47$	−0.516341	−	2.41403i	−0.0753160	−	0.352122i	0.924243	−	0.381804i	$-0.124697\pi$
$47$	−0.516341	−	2.41403i	−0.0753160	−	0.352122i	−0.999559	+	0.0296816i	$0.990551\pi$
$48$	−0.756529	−	1.12057i	−0.109196	−	0.161741i
$49$	1.48086	−	2.49092i	0.211552	−	0.355845i
$50$	5.15260	+	10.3519i	0.728688	+	1.46399i
$51$	−0.0282507	−	0.0630183i	−0.00395588	−	0.00882433i
$52$	0.633247	−	6.59123i	0.0878155	−	0.914038i
$53$	−2.81090	+	13.1417i	−0.386107	+	1.80515i	0.183256	+	0.983065i	$0.441336\pi$
$53$	−2.81090	+	13.1417i	−0.386107	+	1.80515i	−0.569363	+	0.822086i	$0.692810\pi$
$54$	−4.96533	+	2.00121i	−0.675696	+	0.272330i
$55$	−0.355105	+	5.37267i	−0.0478824	+	0.724451i
$56$	5.64469	+	8.02504i	0.754303	+	1.07239i
$57$	1.19695	+	8.87272i	0.158539	+	1.17522i
$58$	−10.7555	−	7.87749i	−1.41227	−	1.03436i
$59$	4.25480	−	0.163090i	0.553928	−	0.0212325i	0.240162	−	0.970733i	$-0.422800\pi$
$59$	4.25480	−	0.163090i	0.553928	−	0.0212325i	0.313766	+	0.949500i	$0.398409\pi$
$60$	4.31235	+	19.1635i	0.556722	+	2.47400i
$61$	−12.8846	+	7.65999i	−1.64971	+	0.980761i	−0.681095	+	0.732195i	$0.738496\pi$
$61$	−12.8846	+	7.65999i	−1.64971	+	0.980761i	−0.968615	+	0.248566i	$0.920041\pi$
$62$	−7.15799	+	21.1979i	−0.909065	+	2.69213i
$63$	11.2392	−	4.78206i	1.41601	−	0.602483i
$64$	12.4667	−	2.41777i	1.55833	−	0.302221i
$65$	−1.99577	+	3.94578i	−0.247545	+	0.489413i
$66$	−4.40799	+	13.9287i	−0.542586	+	1.71450i
$67$	−7.52316	−	1.01489i	−0.919100	−	0.123988i	−0.341102	−	0.940026i	$-0.610800\pi$
$67$	−7.52316	−	1.01489i	−0.919100	−	0.123988i	−0.577998	+	0.816038i	$0.696166\pi$
$68$	−0.0881316	+	0.00168846i	−0.0106875	+	0.000204756i
$69$	−0.994841	−	0.540977i	−0.119765	−	0.0651260i
$70$	−3.87515	−	15.8011i	−0.463169	−	1.88860i
$71$	15.1346	−	4.15906i	1.79615	−	0.493590i	0.801598	−	0.597863i	$-0.203983\pi$
$71$	15.1346	−	4.15906i	1.79615	−	0.493590i	0.994549	+	0.104274i	$0.0332518\pi$
$72$	−0.231919	+	12.1054i	−0.0273319	+	1.42663i
$73$	−9.15039	−	12.4935i	−1.07097	−	1.46225i	−0.876535	−	0.481338i	$-0.840151\pi$
$73$	−9.15039	−	12.4935i	−1.07097	−	1.46225i	−0.194437	−	0.980915i	$-0.562288\pi$
$74$	1.44566	−	12.5225i	0.168054	−	1.45571i
$75$	1.97516	−	12.9676i	0.228072	−	1.49737i
$76$	11.0190	+	3.02808i	1.26397	+	0.347345i
$77$	2.14698	−	7.26510i	0.244671	−	0.827935i
$78$	−7.80933	+	9.10817i	−0.884233	+	1.03130i
$79$	12.6641	+	6.27039i	1.42482	+	0.705474i	0.981602	−	0.190939i	$-0.0611533\pi$
$79$	12.6641	+	6.27039i	1.42482	+	0.705474i	0.443220	+	0.896413i	$0.353836\pi$
$80$	1.13360	+	0.207375i	0.126740	+	0.0231852i
$81$	−5.42770	−	1.27013i	−0.603078	−	0.141126i
$82$	4.81047	−	4.81047i	0.531228	−	0.531228i
$83$	−5.79396	−	7.03065i	−0.635970	−	0.771714i
$83$	−5.79396	−	7.03065i	−0.635970	−	0.771714i
$84$		−	27.6368i		−	3.01542i
$85$	0.0552273	+	0.0203688i	0.00599025	+	0.00220931i
$86$	−1.26187	−	1.41593i	−0.136071	−	0.152683i
$87$	4.83830	+	14.3283i	0.518721	+	1.53615i
$88$	5.70094	+	4.88798i	0.607722	+	0.521060i
$89$	−5.40459	−	9.93887i	−0.572885	−	1.05352i	−0.989513	−	0.144441i	$-0.953862\pi$
$89$	−5.40459	−	9.93887i	−0.572885	−	1.05352i	0.416628	−	0.909077i	$-0.363212\pi$
$90$	7.66367	−	18.5567i	0.807821	−	1.95605i
$91$	3.95828	−	4.79970i	0.414941	−	0.503145i
$92$	−1.13251	+	0.898090i	−0.118073	+	0.0936324i
$93$	20.4756	−	14.9966i	2.12322	−	1.55507i
$94$	3.95891	+	4.11357i	0.408331	+	0.424282i
$95$	−6.11780	−	4.56144i	−0.627673	−	0.467994i
$96$	−12.0779	−	5.41445i	−1.23270	−	0.552610i
$97$	3.47592	+	11.7621i	0.352926	+	1.19426i	0.926876	+	0.375367i	$0.122483\pi$
$97$	3.47592	+	11.7621i	0.352926	+	1.19426i	−0.573950	+	0.818890i	$0.694590\pi$
$98$	0.128373	+	6.70060i	0.0129676	+	0.676863i
$99$	7.43490	−	5.66738i	0.747236	−	0.569593i
$100$	−14.2432	−	8.79996i	−1.42432	−	0.879996i
$101$	−4.13209	−	1.48407i	−0.411158	−	0.147670i	0.124275	−	0.992248i	$-0.460339\pi$
$101$	−4.13209	−	1.48407i	−0.411158	−	0.147670i	−0.535433	+	0.844577i	$0.679852\pi$
$102$	0.132372	+	0.0893682i	0.0131068	+	0.00884877i
$103$	−3.58850	−	8.43400i	−0.353585	−	0.831027i	−0.997807	−	0.0661881i	$-0.978916\pi$
$103$	−3.58850	−	8.43400i	−0.353585	−	0.831027i	0.644222	−	0.764839i	$-0.277181\pi$
$104$	2.73642	+	5.52665i	0.268328	+	0.541933i
$105$	−6.71670	+	17.1898i	−0.655482	+	1.67755i
$106$	−10.5056	−	29.2506i	−1.02039	−	2.84107i
$107$	−9.09685	−	8.42522i	−0.879426	−	0.814497i	0.104230	−	0.994553i	$-0.466762\pi$
$107$	−9.09685	−	8.42522i	−0.879426	−	0.814497i	−0.983656	+	0.180057i	$0.942372\pi$
$108$	4.58000	−	6.25331i	0.440711	−	0.601725i
$109$	−5.27581	−	4.02158i	−0.505331	−	0.385197i	0.322152	−	0.946688i	$-0.395594\pi$
$109$	−5.27581	−	4.02158i	−0.505331	−	0.385197i	−0.827483	+	0.561491i	$0.810228\pi$
$110$	−5.85521	−	10.9899i	−0.558272	−	1.04785i
$111$	−9.51377	+	10.6753i	−0.903007	+	1.01325i
$112$	−1.49197	−	0.634805i	−0.140978	−	0.0599834i
$113$	5.28065	+	1.12949i	0.496762	+	0.106253i	0.450682	−	0.892684i	$-0.351181\pi$
$113$	5.28065	+	1.12949i	0.496762	+	0.106253i	0.0460800	+	0.998938i	$0.485327\pi$
$114$	−13.1738	−	15.9742i	−1.23384	−	1.49612i
$115$	0.922679	−	0.283363i	0.0860402	−	0.0264238i
$116$	19.2462	+	1.47762i	1.78696	+	0.137193i
$117$	7.44049	−	1.89217i	0.687874	−	0.174932i
$118$	−8.16136	+	5.50996i	−0.751314	+	0.507233i
$119$	−0.0695161	−	0.0450182i	−0.00637253	−	0.00412681i
$120$	−12.8252	−	13.0459i	−1.17077	−	1.19092i
$121$	−0.199238	+	5.19784i	−0.0181125	+	0.472531i
$122$	15.9744	−	30.7663i	1.44625	−	2.78545i
$123$	−7.60273	+	1.32389i	−0.685515	+	0.119371i
$124$	−7.38122	−	31.5424i	−0.662853	−	2.83259i
$125$	6.72044	+	8.93508i	0.601095	+	0.799178i
$126$	−16.2514	+	23.1046i	−1.44779	+	2.05832i
$127$	3.87894	+	2.01401i	0.344201	+	0.178714i	0.624158	−	0.781298i	$-0.285442\pi$
$127$	3.87894	+	2.01401i	0.344201	+	0.178714i	−0.279957	+	0.960012i	$0.590320\pi$
$128$	−14.1437	+	13.0995i	−1.25014	+	1.15784i
$129$	0.246737	+	2.13727i	0.0217240	+	0.188176i
$130$	−0.891099	−	10.1873i	−0.0781546	−	0.893484i
$131$	3.59675	−	18.5458i	0.314250	−	1.62036i	−0.397277	−	0.917699i	$-0.630045\pi$
$131$	3.59675	−	18.5458i	0.314250	−	1.62036i	0.711527	−	0.702659i	$-0.248004\pi$
$132$	−5.21339	−	20.5003i	−0.453767	−	1.78432i
$133$	6.98862	+	8.15095i	0.605990	+	0.706777i
$134$	16.0201	−	7.18171i	1.38393	−	0.620405i
$135$	−4.36848	+	2.77640i	−0.375979	+	0.238954i
$136$	0.0689089	−	0.0446249i	0.00590889	−	0.00382656i
$137$	3.47722	−	8.17245i	0.297079	−	0.698220i	−0.702835	−	0.711353i	$-0.748083\pi$
$137$	3.47722	−	8.17245i	0.297079	−	0.698220i	0.999914	+	0.0131328i	$0.00418043\pi$
$138$	2.61459	−	0.150421i	0.222569	−	0.0128047i
$139$	1.55912	−	1.09666i	0.132243	−	0.0930178i	−0.507314	−	0.861761i	$-0.669362\pi$
$139$	1.55912	−	1.09666i	0.132243	−	0.0930178i	0.639557	+	0.768743i	$0.279118\pi$
$140$	16.8327	+	16.4788i	1.42263	+	1.39271i
$141$	−0.988599	−	6.40037i	−0.0832550	−	0.539009i
$142$	−24.6653	+	26.6316i	−2.06987	+	2.23487i
$143$	2.03075	−	4.30699i	0.169820	−	0.360169i
$144$	−1.02248	−	1.71988i	−0.0852066	−	0.143324i
$145$	−11.6118	−	5.59655i	−0.964310	−	0.464768i
$146$	33.2178	+	13.3880i	2.74912	+	1.10800i
$147$	4.25386	−	6.30081i	0.350852	−	0.519682i
$148$	7.78374	+	16.5085i	0.639820	+	1.35699i
$149$	6.37652	+	2.01797i	0.522385	+	0.165319i	0.551369	−	0.834261i	$-0.314105\pi$
$149$	6.37652	+	2.01797i	0.522385	+	0.165319i	−0.0289848	+	0.999580i	$0.509227\pi$
$150$	11.9353	+	27.8891i	0.974515	+	2.27714i
$151$	−7.16751	−	6.89803i	−0.583283	−	0.561354i	0.342447	−	0.939537i	$-0.388744\pi$
$151$	−7.16751	−	6.89803i	−0.583283	−	0.561354i	−0.925731	+	0.378183i	$0.876549\pi$
$152$	−10.2067	+	3.01626i	−0.827870	+	0.244651i
$153$	−0.0363821	−	0.0955071i	−0.00294132	−	0.00772129i
$154$	4.64252	+	16.8939i	0.374105	+	1.36135i
$155$	−3.07486	+	21.4130i	−0.246979	+	1.71993i
$156$	2.65170	−	17.1676i	0.212306	−	1.37451i
$157$	−6.01969	−	7.59097i	−0.480423	−	0.605825i	0.482402	−	0.875950i	$-0.339764\pi$
$157$	−6.01969	−	7.59097i	−0.480423	−	0.605825i	−0.962825	+	0.270125i	$0.912935\pi$
$158$	−32.5316	+	3.12545i	−2.58808	+	0.248648i
$159$	−9.34222	+	33.9958i	−0.740886	+	2.69604i
$160$	10.4994	−	4.12787i	0.830050	−	0.326337i
$161$	−1.35404	+	0.103956i	−0.106713	+	0.00819286i
$162$	12.2141	−	4.12439i	0.959629	−	0.324043i
$163$	0.923826	−	16.0577i	0.0723596	−	1.25774i	−0.739207	−	0.673479i	$-0.764799\pi$
$163$	0.923826	−	16.0577i	0.0723596	−	1.25774i	0.811566	−	0.584260i	$-0.198615\pi$
$164$	−2.24435	+	9.59089i	−0.175255	+	0.748922i
$165$	−1.73961	+	14.0180i	−0.135429	+	1.09130i
$166$	19.9598	+	6.74777i	1.54918	+	0.523729i
$167$	−3.28719	−	3.28719i	−0.254371	−	0.254371i	0.568389	−	0.822760i	$-0.307567\pi$
$167$	−3.28719	−	3.28719i	−0.254371	−	0.254371i	−0.822760	+	0.568389i	$0.807567\pi$
$168$	13.5748	+	21.8689i	1.04732	+	1.68722i
$169$	−6.78584	+	6.04751i	−0.521987	+	0.465193i
$170$	−0.133360	+	0.0273371i	−0.0102282	+	0.00209666i
$171$	1.01424	+	13.2107i	0.0775610	+	1.01024i
$172$	2.63349	+	0.778247i	0.200802	+	0.0593408i
$173$	−1.96501	−	3.45425i	−0.149397	−	0.262622i	0.784526	−	0.620096i	$-0.212906\pi$
$173$	−1.96501	−	3.45425i	−0.149397	−	0.262622i	−0.933923	+	0.357474i	$0.883638\pi$
$174$	−26.9828	−	22.2525i	−2.04556	−	1.68696i
$175$	−6.46488	−	14.3406i	−0.488699	−	1.08405i
$176$	−1.22646	−	0.189438i	−0.0924479	−	0.0142794i
$177$	11.1683	+	0.213967i	0.839461	+	0.0160827i
$178$	22.7418	+	12.9371i	1.70457	+	0.969674i
$179$	−5.38506	+	12.0124i	−0.402499	+	0.897848i	0.593188	+	0.805064i	$0.297869\pi$
$179$	−5.38506	+	12.0124i	−0.402499	+	0.897848i	−0.995686	+	0.0927838i	$0.970423\pi$
$180$	4.74235	+	28.6795i	0.353474	+	2.13765i
$181$	4.47824	−	4.65318i	0.332865	−	0.345868i	−0.533028	−	0.846097i	$-0.678946\pi$
$181$	4.47824	−	4.65318i	0.332865	−	0.345868i	0.865893	+	0.500229i	$0.166751\pi$
$182$	−1.92354	+	14.2588i	−0.142582	+	1.05693i
$183$	−34.9003	+	18.1208i	−2.57991	+	1.33953i
$184$	0.455026	−	1.26693i	0.0335450	−	0.0933992i
$185$	−0.829288	−	12.1598i	−0.0609705	−	0.894007i
$186$	−21.9416	+	54.4407i	−1.60883	+	3.99178i
$187$	−0.0600576	−	0.0202799i	−0.00439185	−	0.00148302i
$188$	−8.01118	−	2.03730i	−0.584275	−	0.148586i
$189$	6.85398	−	2.46165i	0.498554	−	0.179059i
$190$	17.5844	+	1.50103i	1.27571	+	0.108896i
$191$	3.74898	−	0.579066i	0.271267	−	0.0418997i	−0.0155714	−	0.999879i	$-0.504957\pi$
$191$	3.74898	−	0.579066i	0.271267	−	0.0418997i	0.286838	+	0.957979i	$0.407396\pi$
$192$	33.0157	−	4.45388i	2.38270	−	0.321431i
$193$	−1.33046	+	7.64050i	−0.0957690	+	0.549975i	0.898134	+	0.439721i	$0.144923\pi$
$193$	−1.33046	+	7.64050i	−0.0957690	+	0.549975i	−0.993903	+	0.110254i	$0.964833\pi$
$194$	−21.1758	−	18.8718i	−1.52034	−	1.35492i
$195$	−5.82166	+	10.0336i	−0.416898	+	0.718524i
$196$	−5.27448	−	8.14475i	−0.376749	−	0.581768i
$197$	−24.4030	−	2.34450i	−1.73864	−	0.167038i	−0.822732	−	0.568429i	$-0.807551\pi$
$197$	−24.4030	−	2.34450i	−1.73864	−	0.167038i	−0.915907	+	0.401390i	$0.868527\pi$
$198$	−7.69648	+	20.2041i	−0.546965	+	1.43584i
$199$	−1.10635	+	14.4104i	−0.0784273	+	1.02153i	0.817093	+	0.576506i	$0.195584\pi$
$199$	−1.10635	+	14.4104i	−0.0784273	+	1.02153i	−0.895520	+	0.445021i	$0.853196\pi$
$200$	15.5930	−	0.0326656i	1.10259	−	0.00230981i
$201$	−19.5509	−	3.79168i	−1.37902	−	0.267445i
$202$	9.92926	−	2.12379i	0.698620	−	0.149429i
$203$	14.2103	+	11.2688i	0.997364	+	0.790916i
$204$	−0.231080	−	0.00885748i	−0.0161788	−	0.000620148i
$205$	3.72688	−	5.41998i	0.260297	−	0.378548i
$206$	17.3379	+	12.1952i	1.20799	+	0.849679i
$207$	−1.42384	−	0.883823i	−0.0989634	−	0.0614299i
$208$	−0.865886	−	0.537485i	−0.0600384	−	0.0372679i
$209$	6.72158	+	4.72786i	0.464942	+	0.327033i
$210$	−7.76845	−	41.9686i	−0.536074	−	2.89611i
$211$	−20.9353	−	0.802466i	−1.44124	−	0.0552441i	−0.694086	−	0.719892i	$-0.744191\pi$
$211$	−20.9353	−	0.802466i	−1.44124	−	0.0552441i	−0.747156	+	0.664648i	$0.768581\pi$
$212$	35.2592	+	27.9607i	2.42161	+	1.92035i
$213$	40.2657	−	8.61249i	2.75896	−	0.590118i
$214$	28.1506	+	5.45948i	1.92433	+	0.373202i
$215$	−1.44887	−	1.12409i	−0.0988118	−	0.0766624i
$216$	−0.552611	+	7.19784i	−0.0376004	+	0.489751i
$217$	10.8349	−	28.4427i	0.735518	−	1.93082i
$218$	15.2715	+	1.46720i	1.03432	+	0.0993713i
$219$	−22.0832	−	34.1004i	−1.49225	−	2.30429i
$220$	15.5947	+	9.04825i	1.05139	+	0.610033i
$221$	−0.0388631	−	0.0346347i	−0.00261421	−	0.00232978i
$222$	5.67321	−	32.5797i	0.380761	−	2.18661i
$223$	−4.85992	+	0.655612i	−0.325444	+	0.0439030i	−0.294598	−	0.955621i	$-0.595186\pi$
$223$	−4.85992	+	0.655612i	−0.325444	+	0.0439030i	−0.0308457	+	0.999524i	$0.509820\pi$
$224$	−15.6870	+	2.42301i	−1.04813	+	0.161894i
$225$	4.02042	−	18.9909i	0.268028	−	1.26606i
$226$	−11.7536	+	4.22139i	−0.781838	+	0.280803i
$227$	7.96206	+	2.02481i	0.528460	+	0.134391i	0.501356	−	0.865241i	$-0.332835\pi$
$227$	7.96206	+	2.02481i	0.528460	+	0.134391i	0.0271044	+	0.999633i	$0.491371\pi$
$228$	28.4036	+	9.59119i	1.88108	+	0.635192i
$229$	−5.77005	+	14.3164i	−0.381295	+	0.946058i	0.607165	+	0.794576i	$0.292307\pi$
$229$	−5.77005	+	14.3164i	−0.381295	+	0.946058i	−0.988460	+	0.151482i	$0.951596\pi$
$230$	−1.46736	+	1.68216i	−0.0967551	+	0.110918i
$231$	6.71784	−	18.7045i	0.442002	−	1.23066i
$232$	−15.9552	+	8.28419i	−1.04751	+	0.543884i
$233$	2.49848	−	18.5207i	0.163681	−	1.21333i	−0.701794	−	0.712380i	$-0.747617\pi$
$233$	2.49848	−	18.5207i	0.163681	−	1.21333i	0.865475	−	0.500952i	$-0.167017\pi$
$234$	−12.3120	+	12.7930i	−0.804862	+	0.836304i
$235$	4.48774	+	3.21417i	0.292748	+	0.209670i
$236$	5.83233	−	13.0101i	0.379652	−	0.846885i
$237$	32.2236	+	18.3310i	2.09315	+	1.19073i
$238$	0.191500	+	0.00366884i	0.0124131	+	0.000237816i
$239$	−3.37828	−	0.521807i	−0.218522	−	0.0337529i	0.0424523	−	0.999098i	$-0.486483\pi$
$239$	−3.37828	−	0.521807i	−0.218522	−	0.0337529i	−0.260975	+	0.965346i	$0.584044\pi$
$240$	2.93775	+	0.713946i	0.189631	+	0.0460850i
$241$	−0.000427251	0	0.000352352i	−2.75217e−5	0	2.26970e-5i	0.636229	−	0.771501i	$-0.280493\pi$
$241$	−0.000427251	0	0.000352352i	−2.75217e−5	0	2.26970e-5i	−0.636256	+	0.771478i	$0.719518\pi$
$242$	−5.94824	−	10.4563i	−0.382367	−	0.672155i
$243$	−20.6840	−	6.11253i	−1.32688	−	0.392119i
$244$	3.84220	+	50.0453i	0.245972	+	3.20382i
$245$	1.30122	+	6.34783i	0.0831320	+	0.405548i
$246$	13.3239	−	11.8742i	0.849503	−	0.757074i
$247$	3.55917	+	5.73382i	0.226465	+	0.364834i
$248$	21.3339	+	21.3339i	1.35470	+	1.35470i
$249$	−14.1155	−	19.2870i	−0.894537	−	1.22226i
$250$	−24.1030	−	9.35978i	−1.52441	−	0.591965i
$251$	−4.45434	+	19.0349i	−0.281156	+	1.20147i	0.625711	+	0.780055i	$0.284809\pi$
$251$	−4.45434	+	19.0349i	−0.281156	+	1.20147i	−0.906866	+	0.421418i	$0.861532\pi$
$252$	2.34911	−	40.8317i	0.147980	−	2.57216i
$253$	−0.984785	+	0.332537i	−0.0619129	+	0.0209064i
$254$	−10.0782	+	0.773750i	−0.632363	+	0.0485494i
$255$	0.141577	+	0.0616696i	0.00886587	+	0.00386190i
$256$	5.08389	−	18.5000i	0.317743	−	1.15625i
$257$	−8.77734	+	0.843276i	−0.547516	+	0.0526021i	−0.365704	−	0.930731i	$-0.619172\pi$
$257$	−8.77734	+	0.843276i	−0.547516	+	0.0526021i	−0.181812	+	0.983333i	$0.558196\pi$
$258$	−3.09161	−	3.89859i	−0.192475	−	0.242716i
$259$	−2.61767	+	16.9473i	−0.162654	+	1.05305i
$260$	8.87517	+	11.8515i	0.550415	+	0.734998i
$261$	5.93041	+	21.5805i	0.367083	+	1.33580i
$262$	15.5528	+	40.8277i	0.960853	+	2.52235i
$263$	−7.93593	+	2.34522i	−0.489350	+	0.144612i	−0.518699	−	0.854957i	$-0.673583\pi$
$263$	−7.93593	+	2.34522i	−0.489350	+	0.144612i	0.0293488	+	0.999569i	$0.490657\pi$
$264$	14.1948	+	13.6611i	0.873628	+	0.840783i
$265$	−15.1354	−	25.9605i	−0.929761	−	1.59474i
$266$	−23.6736	−	7.49195i	−1.45152	−	0.459361i
$267$	−12.6575	−	26.8452i	−0.774629	−	1.64290i
$268$	−14.2233	+	21.0675i	−0.868826	+	1.28690i
$269$	21.5539	+	8.68702i	1.31417	+	0.529657i	0.920911	−	0.389773i	$-0.127446\pi$
$269$	21.5539	+	8.68702i	1.31417	+	0.529657i	0.393255	+	0.919429i	$0.371349\pi$
$270$	5.19734	−	10.7835i	0.316300	−	0.656265i
$271$	4.58557	+	7.71326i	0.278554	+	0.468547i	0.966305	−	0.257399i	$-0.0828656\pi$
$271$	4.58557	+	7.71326i	0.278554	+	0.468547i	−0.687752	+	0.725946i	$0.741402\pi$
$272$	−0.00578596	+	0.0122714i	−0.000350826	+	0.000744062i
$273$	11.0903	−	11.9744i	0.671218	−	0.724725i
$274$	3.13540	+	20.2992i	0.189417	+	1.22632i
$275$	−7.50069	−	9.41796i	−0.452309	−	0.567925i
$276$	−3.10149	+	2.18154i	−0.186687	+	0.131313i
$277$	−11.3971	+	0.655693i	−0.684786	+	0.0393968i	−0.396346	−	0.918101i	$-0.629722\pi$
$277$	−11.3971	+	0.655693i	−0.684786	+	0.0393968i	−0.288440	+	0.957498i	$0.593137\pi$
$278$	−1.72595	+	4.05648i	−0.103516	+	0.243291i
$279$	31.5262	−	20.4162i	1.88742	−	1.22228i
$280$	−21.4138	−	4.77162i	−1.27972	−	0.285159i
$281$	−6.27576	+	2.81338i	−0.374380	+	0.167832i	−0.587559	−	0.809181i	$-0.699911\pi$
$281$	−6.27576	+	2.81338i	−0.374380	+	0.167832i	0.213179	+	0.977013i	$0.431618\pi$
$282$	9.74893	+	11.3704i	0.580541	+	0.677095i
$283$	2.75262	+	10.8240i	0.163626	+	0.643418i	0.996012	+	0.0892215i	$0.0284379\pi$
$283$	2.75262	+	10.8240i	0.163626	+	0.643418i	−0.832386	+	0.554197i	$0.813025\pi$
$284$	10.0063	−	51.5953i	0.593766	−	3.06162i
$285$	−15.3358	−	12.8687i	−0.908413	−	0.762275i
$286$	1.26293	+	10.9397i	0.0746789	+	0.646878i
$287$	−6.78985	+	6.28854i	−0.400792	+	0.371201i
$288$	−17.3842	−	9.02614i	−1.02437	−	0.531871i
$289$	9.78002	−	13.9042i	0.575295	−	0.817896i
$290$	29.6422	−	3.16605i	1.74065	−	0.185917i
$291$	7.33144	+	31.3297i	0.429777	+	1.83658i
$292$	−51.0860	+	8.89576i	−2.98958	+	0.520585i
$293$	−9.10262	+	17.5315i	−0.531781	+	1.02420i	0.458963	+	0.888455i	$0.348221\pi$
$293$	−9.10262	+	17.5315i	−0.531781	+	1.02420i	−0.990744	+	0.135745i	$0.956657\pi$
$294$	−0.673430	+	17.5689i	−0.0392752	+	1.02464i
$295$	−6.78955	+	6.67469i	−0.395303	+	0.388616i
$296$	−14.2679	−	9.23983i	−0.829307	−	0.537054i
$297$	4.61976	−	3.11893i	0.268065	−	0.180979i
$298$	−14.9905	+	3.81221i	−0.868379	+	0.220835i
$299$	−0.851087	−	0.0653418i	−0.0492196	−	0.00377881i
$300$	−35.9784	−	25.1941i	−2.07721	−	1.45458i
$301$	1.64157	+	1.99052i	0.0946183	+	0.114731i
$302$	22.4969	+	4.81190i	1.29455	+	0.276894i
$303$	−10.5987	−	4.50954i	−0.608881	−	0.259066i
$304$	1.17020	−	1.31306i	0.0671155	−	0.0753094i
$305$	9.77292	−	32.0615i	0.559596	−	1.83583i
$306$	0.187976	+	0.143288i	0.0107459	+	0.00819122i
$307$	18.9415	−	25.8618i	1.08105	−	1.47601i	0.214632	−	0.976695i	$-0.431145\pi$
$307$	18.9415	−	25.8618i	1.08105	−	1.47601i	0.866419	−	0.499318i	$-0.166416\pi$
$308$	−18.6111	−	17.2370i	−1.06047	−	0.982171i
$309$	−8.12778	−	22.6302i	−0.462373	−	1.28739i
$310$	−20.0752	−	45.8248i	−1.14020	−	2.60268i
$311$	10.4152	+	21.0352i	0.590591	+	1.19280i	0.964191	+	0.265207i	$0.0854404\pi$
$311$	10.4152	+	21.0352i	0.590591	+	1.19280i	−0.373600	+	0.927590i	$0.621877\pi$
$312$	6.33419	+	14.8872i	0.358603	+	0.842819i
$313$	21.4093	+	14.4540i	1.21013	+	0.816990i	0.987455	−	0.157904i	$-0.0504735\pi$
$313$	21.4093	+	14.4540i	1.21013	+	0.816990i	0.222671	+	0.974894i	$0.428522\pi$
$314$	21.0867	+	7.57343i	1.18999	+	0.427393i
$315$	−11.3846	+	24.8260i	−0.641452	+	1.39879i
$316$	37.6323	−	28.6859i	2.11698	−	1.61371i
$317$	0.274316	+	14.3183i	0.0154071	+	0.804198i	0.923099	+	0.384561i	$0.125647\pi$
$317$	0.274316	+	14.3183i	0.0154071	+	0.804198i	−0.907692	+	0.419636i	$0.862158\pi$
$318$	−23.1076	−	78.1931i	−1.29581	−	4.38485i
$319$	12.6666	+	5.67833i	0.709192	+	0.317926i
$320$	−16.9733	+	22.7646i	−0.948836	+	1.27258i
$321$	−22.5560	−	23.4372i	−1.25895	−	1.30814i
$322$	2.53377	−	1.85576i	0.141201	−	0.103418i
$323$	0.0703924	−	0.0558216i	0.00391674	−	0.00310600i
$324$	−11.8758	+	14.4003i	−0.659768	+	0.800015i
$325$	−2.63995	−	9.52847i	−0.146438	−	0.528545i
$326$	17.7701	+	32.6787i	0.984196	+	1.80991i
$327$	−13.2119	−	11.3279i	−0.730619	−	0.626432i
$328$	−2.93494	−	8.69162i	−0.162055	−	0.479915i
$329$	−5.16727	−	5.79813i	−0.284881	−	0.319661i
$330$	−13.6794	−	29.6659i	−0.753025	−	1.63305i
$331$			7.23331i			0.397579i	0.980042	+	0.198789i	$0.0637010\pi$
$331$			7.23331i			0.397579i	−0.980042	+	0.198789i	$0.936299\pi$
$332$	−29.7061	+	6.94042i	−1.63034	+	0.380905i
$333$	−14.9634	+	14.9634i	−0.819991	+	0.819991i
$334$	10.4684	+	2.44969i	0.572803	+	0.134041i
$335$	13.9669	−	9.64705i	0.763092	−	0.527075i
$336$	−3.81197	−	1.88743i	−0.207960	−	0.102967i
$337$	−11.6890	+	13.6331i	−0.636743	+	0.742644i	−0.980523	−	0.196406i	$-0.937073\pi$
$337$	−11.6890	+	13.6331i	−0.636743	+	0.742644i	0.343780	+	0.939050i	$0.388293\pi$
$338$	5.95748	−	20.1594i	0.324044	−	1.09652i
$339$	13.6603	+	3.75393i	0.741928	+	0.203885i
$340$	0.143179	−	0.135462i	0.00776496	−	0.00734647i
$341$	2.67163	−	23.1420i	0.144677	−	1.25321i
$342$	−18.1057	−	24.7206i	−0.979045	−	1.33674i
$343$	−0.247207	+	12.9033i	−0.0133479	+	0.696713i
$344$	−2.46614	+	0.677706i	−0.132965	+	0.0365395i
$345$	2.45928	−	0.603126i	0.132403	−	0.0324712i
$346$	8.07416	+	4.39059i	0.434069	+	0.236039i
$347$	−21.8993	+	0.419555i	−1.17561	+	0.0225229i	−0.603302	−	0.797513i	$-0.706149\pi$
$347$	−21.8993	+	0.419555i	−1.17561	+	0.0225229i	−0.572312	+	0.820036i	$0.693953\pi$
$348$	50.1850	+	6.77005i	2.69020	+	0.362913i
$349$	−7.91881	+	25.0224i	−0.423884	+	1.33942i	0.466627	+	0.884454i	$0.345469\pi$
$349$	−7.91881	+	25.0224i	−0.423884	+	1.33942i	−0.890511	+	0.454962i	$0.849653\pi$
$350$	30.1938	+	20.2928i	1.61393	+	1.08469i
$351$	4.49380	−	0.871521i	0.239861	−	0.0465183i
$352$	−11.1792	+	4.75652i	−0.595852	+	0.253523i
$353$	2.72519	−	8.07045i	0.145047	−	0.429547i	−0.850254	−	0.526372i	$-0.823552\pi$
$353$	2.72519	−	8.07045i	0.145047	−	0.429547i	0.995301	+	0.0968255i	$0.0308689\pi$
$354$	−22.2056	+	13.2014i	−1.18022	+	0.701645i
$355$	−18.7633	+	29.6599i	−0.995851	+	1.57418i
$356$	−37.8546	+	1.45100i	−2.00629	+	0.0769028i
$357$	−0.175286	−	0.128382i	−0.00927711	−	0.00679467i
$358$	−4.07016	−	30.1713i	−0.215115	−	1.59460i
$359$	−8.42574	−	11.9789i	−0.444694	−	0.632220i	0.532029	−	0.846726i	$-0.321430\pi$
$359$	−8.42574	−	11.9789i	−0.444694	−	0.632220i	−0.976723	+	0.214506i	$0.931186\pi$
$360$	−17.8395	−	20.3646i	−0.940226	−	1.07331i
$361$	6.82007	−	2.74874i	0.358951	−	0.144670i
$362$	−3.12391	+	14.6051i	−0.164189	+	0.767626i
$363$	−1.30504	+	13.5836i	−0.0684967	+	0.712956i
$364$	−8.52174	−	19.0093i	−0.446661	−	0.996359i
$365$	33.9369	+	6.88258i	1.77634	+	0.360250i
$366$	46.4742	−	78.1730i	2.42925	−	4.08617i
$367$	11.1310	+	16.4872i	0.581032	+	0.860625i	0.998852	−	0.0479052i	$-0.0152545\pi$
$367$	11.1310	+	16.4872i	0.581032	+	0.860625i	−0.417820	+	0.908530i	$0.637206\pi$
$368$	0.0465305	+	0.217543i	0.00242557	+	0.0113402i
$369$	−11.3451	+	1.30974i	−0.590603	+	0.0681823i
$370$	16.4606	+	22.8814i	0.855745	+	1.18955i
$371$	12.7568	+	40.3097i	0.662299	+	2.09278i
$372$	−14.5793	−	83.7249i	−0.755900	−	4.34093i
$373$	2.56447	−	4.13135i	0.132783	−	0.213913i	−0.776473	−	0.630151i	$-0.782993\pi$
$373$	2.56447	−	4.13135i	0.132783	−	0.213913i	0.909256	+	0.416238i	$0.136652\pi$
$374$	0.142743	−	0.0334031i	0.00738104	−	0.00172723i
$375$	16.2551	+	24.4145i	0.839412	+	1.26076i
$376$	7.33991	−	2.32285i	0.378527	−	0.119792i
$377$	7.74601	+	8.36350i	0.398940	+	0.430742i
$378$	−10.4650	+	13.1966i	−0.538261	+	0.678760i
$379$	17.2800	−	26.6834i	0.887615	−	1.37064i	−0.0408296	−	0.999166i	$-0.513000\pi$
$379$	17.2800	−	26.6834i	0.887615	−	1.37064i	0.928445	−	0.371470i	$-0.121146\pi$
$380$	−22.7777	+	11.5809i	−1.16847	+	0.594089i
$381$	9.85585	+	5.85936i	0.504931	+	0.300184i
$382$	−6.66012	+	5.71038i	−0.340761	+	0.292168i
$383$	5.43713	+	2.07120i	0.277825	+	0.105833i	0.490940	−	0.871194i	$-0.336654\pi$
$383$	5.43713	+	2.07120i	0.277825	+	0.105833i	−0.213115	+	0.977027i	$0.568361\pi$
$384$	−39.0175	+	32.1775i	−1.99111	+	1.64205i
$385$	7.38674	+	15.2444i	0.376463	+	0.776927i
$386$	−6.70475	−	16.6356i	−0.341263	−	0.846730i
$387$	0.182873	+	3.17866i	0.00929596	+	0.161580i
$388$	40.4600	+	7.04543i	2.05405	+	0.357678i
$389$	−0.943374	+	1.23759i	−0.0478309	+	0.0627483i	−0.818589	−	0.574379i	$-0.805243\pi$
$389$	−0.943374	+	1.23759i	−0.0478309	+	0.0627483i	0.770758	+	0.637128i	$0.219878\pi$
$390$	−0.798850	−	26.8157i	−0.0404513	−	1.35787i
$391$	0.000435241		0.0113549i	2.20111e−5		0.000574240i
$392$	8.17425	+	3.85416i	0.412862	+	0.194665i
$393$	12.2147	−	48.0314i	0.616152	−	2.42286i
$394$	50.8091	−	25.1572i	2.55972	−	1.26740i
$395$	−30.3786	+	8.69637i	−1.52851	+	0.437562i
$396$	−5.95996	−	30.7312i	−0.299499	−	1.54430i
$397$	29.6319	−	13.9715i	1.48718	−	0.701208i	0.500785	−	0.865572i	$-0.333045\pi$
$397$	29.6319	−	13.9715i	1.48718	−	0.701208i	0.986400	+	0.164363i	$0.0525569\pi$
$398$	−15.4023	−	29.6645i	−0.772046	−	1.48695i
$399$	17.0757	+	22.4012i	0.854853	+	1.12146i
$400$	−2.18651	+	1.36359i	−0.109326	+	0.0681797i
$401$	0.636117	−	1.16980i	0.0317662	−	0.0584170i	−0.862143	−	0.506664i	$-0.830878\pi$
$401$	0.636117	−	1.16980i	0.0317662	−	0.0584170i	0.893910	+	0.448247i	$0.147952\pi$
$402$	43.0404	−	16.3957i	2.14666	−	0.817741i
$403$	9.45950	−	16.6287i	0.471211	−	0.828332i
$404$	−10.5928	+	10.1945i	−0.527011	+	0.507198i
$405$	10.8864	−	6.07059i	0.540950	−	0.301650i
$406$	−41.6662	−	4.81016i	−2.06786	−	0.238724i
$407$	1.25520	+	13.0649i	0.0622180	+	0.647603i
$408$	0.187203	−	0.106494i	0.00926793	−	0.00527223i
$409$	−5.89821	+	3.20735i	−0.291648	+	0.158593i	−0.616917	−	0.787029i	$-0.711618\pi$
$409$	−5.89821	+	3.20735i	−0.291648	+	0.158593i	0.325269	+	0.945622i	$0.394545\pi$
$410$	−0.712313	+	15.1954i	−0.0351786	+	0.750446i
$411$	10.3386	−	20.8805i	0.509965	−	1.02996i
$412$	−30.6405	−	1.76279i	−1.50955	−	0.0868465i
$413$	11.3814	−	7.06481i	0.560041	−	0.347637i
$414$	3.87569			0.190480
$415$	20.1637	+	2.90274i	0.989796	+	0.142490i
$416$	−9.97705			−0.489165
$417$	4.24874	−	2.63734i	0.208062	−	0.129151i
$418$	−18.9738	−	1.09159i	−0.928037	−	0.0533914i
$419$	7.17367	−	14.4884i	0.350456	−	0.707805i	−0.648098	−	0.761557i	$-0.724435\pi$
$419$	7.17367	−	14.4884i	0.350456	−	0.707805i	0.998554	+	0.0537523i	$0.0171181\pi$
$420$	41.6035	+	45.6959i	2.03004	+	2.22973i
$421$	−16.2456	+	8.83406i	−0.791760	+	0.430546i	−0.822347	−	0.568987i	$-0.807336\pi$
$421$	−16.2456	+	8.83406i	−0.791760	+	0.430546i	0.0305866	+	0.999532i	$0.490262\pi$
$422$	42.1146	−	23.9576i	2.05010	−	1.16624i
$423$	−0.916568	−	9.54020i	−0.0445651	−	0.463861i
$424$	−41.6343	−	4.80648i	−2.02194	−	0.233423i
$425$	−0.121978	+	0.0494587i	−0.00591679	+	0.00239910i
$426$	−68.6137	+	66.0341i	−3.32435	+	3.19936i
$427$	−23.3181	+	40.9904i	−1.12844	+	1.98366i
$428$	−38.7984	+	14.7797i	−1.87539	+	0.714404i
$429$	5.96770	−	10.9744i	0.288123	−	0.529850i
$430$	4.21792	+	0.441578i	0.203406	+	0.0212948i
$431$	−20.9916	−	27.5384i	−1.01113	−	1.32648i	−0.944432	−	0.328706i	$-0.893387\pi$
$431$	−20.9916	−	27.5384i	−1.01113	−	1.32648i	−0.0666993	−	0.997773i	$-0.521247\pi$
$432$	−0.549738	−	1.05879i	−0.0264493	−	0.0509409i
$433$	−12.0804	+	5.69590i	−0.580545	+	0.273727i	−0.694187	−	0.719794i	$-0.744236\pi$
$433$	−12.0804	+	5.69590i	−0.580545	+	0.273727i	0.113642	+	0.993522i	$0.463748\pi$
$434$	13.4016	+	69.1023i	0.643298	+	3.31702i
$435$	−29.5692	−	16.4076i	−1.41773	−	0.786683i
$436$	−19.9067	+	9.85642i	−0.953357	+	0.472037i
$437$	0.363072	−	1.42769i	0.0173681	−	0.0682955i
$438$	84.9832	+	40.0696i	4.06065	+	1.91460i
$439$	0.563776	+	14.7082i	0.0269076	+	0.701982i	0.949049	+	0.315129i	$0.102048\pi$
$439$	0.563776	+	14.7082i	0.0269076	+	0.701982i	−0.922141	+	0.386853i	$0.873562\pi$
$440$	−16.7844	+	0.500012i	−0.800163	+	0.0238371i
$441$	6.82039	−	8.94751i	0.324780	−	0.426072i
$442$	0.118606	+	0.0206532i	0.00564149	+	0.000982371i
$443$	2.15525	+	37.4621i	0.102399	+	1.77988i	0.503648	+	0.863909i	$0.331991\pi$
$443$	2.15525	+	37.4621i	0.102399	+	1.77988i	−0.401249	+	0.915969i	$0.631424\pi$
$444$	17.8989	+	44.4101i	0.849443	+	2.10761i
$445$	23.8978	+	8.29746i	1.13287	+	0.393337i
$446$	8.74964	−	7.21578i	0.414308	−	0.341677i
$447$	16.3966	+	6.24608i	0.775534	+	0.295429i
$448$	30.3300	−	26.0049i	1.43296	−	1.22862i
$449$	−1.30410	−	0.775293i	−0.0615442	−	0.0365883i	0.479919	−	0.877313i	$-0.340666\pi$
$449$	−1.30410	−	0.775293i	−0.0615442	−	0.0365883i	−0.541463	+	0.840724i	$0.682129\pi$
$450$	15.2632	+	42.2190i	0.719513	+	1.99022i
$451$	−3.85028	+	5.94553i	−0.181303	+	0.279964i
$452$	11.2353	−	14.1680i	0.528464	−	0.666406i
$453$	−17.7330	−	19.1466i	−0.833168	−	0.899586i
$454$	−18.1143	+	5.73262i	−0.850147	+	0.269045i
$455$	0.680516	+	13.8947i	0.0319031	+	0.651393i
$456$	−27.1867	+	6.36194i	−1.27314	+	0.297925i
$457$	−14.7438	+	23.7521i	−0.689684	+	1.11108i	0.297993	+	0.954568i	$0.403683\pi$
$457$	−14.7438	+	23.7521i	−0.689684	+	1.11108i	−0.987676	+	0.156510i	$0.949976\pi$
$458$	−6.12393	−	35.1681i	−0.286153	−	1.64330i
$459$	−0.0183860	−	0.0580971i	−0.000858183	−	0.00271174i
$460$	0.520590	−	3.18979i	0.0242726	−	0.148725i
$461$	11.2440	−	1.29807i	0.523687	−	0.0604572i	0.151216	−	0.988501i	$-0.451681\pi$
$461$	11.2440	−	1.29807i	0.523687	−	0.0604572i	0.372472	+	0.928044i	$0.378510\pi$
$462$	9.61362	+	44.9462i	0.447266	+	2.09109i
$463$	−6.76658	−	10.0227i	−0.314469	−	0.465792i	0.638169	−	0.769896i	$-0.279692\pi$
$463$	−6.76658	−	10.0227i	−0.314469	−	0.465792i	−0.952639	+	0.304104i	$0.901643\pi$
$464$	1.51821	−	2.55373i	0.0704810	−	0.118554i
$465$	−11.2799	+	55.6193i	−0.523091	+	2.57928i
$466$	17.6801	+	39.4388i	0.819016	+	1.82697i
$467$	0.971923	−	10.1164i	0.0449752	−	0.468130i	−0.945018	−	0.327017i	$-0.893956\pi$
$467$	0.971923	−	10.1164i	0.0449752	−	0.468130i	0.989994	−	0.141113i	$-0.0450680\pi$
$468$	5.37697	−	25.1388i	0.248551	−	1.16204i
$469$	−22.1514	+	8.92784i	−1.02286	+	0.412249i
$470$	−12.7383	−	0.841932i	−0.587572	−	0.0388354i
$471$	−14.6223	−	20.7885i	−0.673761	−	0.957885i
$472$	1.77525	+	13.1596i	0.0817127	+	0.605719i
$473$	1.59316	+	1.16685i	0.0732538	+	0.0536520i
$474$	−85.6744	+	3.28397i	−3.93516	+	0.150838i
$475$	16.9821	−	1.66745i	0.779191	−	0.0765079i
$476$	−0.238376	+	0.141716i	−0.0109260	+	0.00649554i
$477$	−16.6922	+	49.4327i	−0.764283	+	2.26337i
$478$	7.27443	−	3.09513i	0.332725	−	0.141568i
$479$	−6.34526	+	1.23059i	−0.289922	+	0.0562271i	−0.333265	−	0.942833i	$-0.608150\pi$
$479$	−6.34526	+	1.23059i	−0.289922	+	0.0562271i	0.0433428	+	0.999060i	$0.486199\pi$
$480$	28.1209	−	9.22924i	1.28354	−	0.421255i
$481$	−3.25213	+	10.2763i	−0.148284	+	0.468558i
$482$	0.00126927		0.000171226i	5.78135e−5		7.79915e-6i
$483$	−3.56202	+	0.0682427i	−0.162078	+	0.00310515i
$484$	15.3016	+	8.32077i	0.695529	+	0.378217i
$485$	−23.4535	−	14.2154i	−1.06497	−	0.645487i
$486$	48.0975	−	13.2174i	2.18175	−	0.599555i
$487$	−0.142446	+	7.43516i	−0.00645483	+	0.336919i	0.982295	+	0.187341i	$0.0599868\pi$
$487$	−0.142446	+	7.43516i	−0.00645483	+	0.336919i	−0.988750	+	0.149579i	$0.952208\pi$
$488$	−27.6218	−	37.7134i	−1.25038	−	1.70721i
$489$	4.83918	−	41.9175i	0.218835	−	1.89558i
$490$	−10.2991	−	10.8858i	−0.465267	−	0.491771i
$491$	−19.0731	−	5.24139i	−0.860759	−	0.236541i	−0.193256	−	0.981148i	$-0.561905\pi$
$491$	−19.0731	−	5.24139i	−0.860759	−	0.236541i	−0.667502	+	0.744608i	$0.732637\pi$
$492$	−7.32334	+	24.7813i	−0.330161	+	1.11723i
$493$	0.0987763	−	0.115205i	0.00444866	−	0.00518855i
$494$	−13.9869	−	6.92535i	−0.629299	−	0.311586i
$495$	−3.76170	+	20.5629i	−0.169076	+	0.924236i
$496$	−4.85477	−	1.13606i	−0.217985	−	0.0510106i
$497$	34.9169	−	34.9169i	1.56624	−	1.56624i
$498$	51.2597	+	20.6806i	2.29700	+	0.926720i
$499$		−	2.16719i		−	0.0970167i	−0.998823	−	0.0485084i	$-0.984553\pi$
$499$		−	2.16719i		−	0.0970167i	0.998823	−	0.0485084i	$-0.0154468\pi$
$500$	36.7975	−	6.89103i	1.64563	−	0.308176i
$501$	−8.11416	−	9.10479i	−0.362514	−	0.406772i
$502$	−14.4642	−	42.8347i	−0.645569	−	1.91181i
$503$	3.10195	+	2.65961i	0.138309	+	0.118586i	0.717352	−	0.696711i	$-0.245354\pi$
$503$	3.10195	+	2.65961i	0.138309	+	0.118586i	−0.579043	+	0.815297i	$0.696574\pi$
$504$	18.1971	+	33.4639i	0.810562	+	1.49060i
$505$	9.06624	−	3.76649i	0.403442	−	0.167607i
$506$	1.52942	−	1.85453i	0.0679910	−	0.0824439i
$507$	−18.6840	+	14.8165i	−0.829785	+	0.658025i
$508$	11.8069	−	8.64753i	0.523847	−	0.383672i
$509$	−15.9841	−	16.6085i	−0.708483	−	0.736160i	0.265168	−	0.964202i	$-0.414572\pi$
$509$	−15.9841	−	16.6085i	−0.708483	−	0.736160i	−0.973651	+	0.228042i	$0.926768\pi$
$510$	−0.353402	+	0.0515036i	−0.0156489	+	0.00228062i
$511$	−44.4575	−	19.9300i	−1.96669	−	0.881651i
$512$	1.64791	+	5.57631i	0.0728279	+	0.246441i
$513$	0.151322	+	7.89846i	0.00668102	+	0.348725i
$514$	16.2181	−	12.3625i	0.715351	−	0.545288i
$515$	18.6296	+	8.54312i	0.820920	+	0.376455i
$516$	6.78010	+	2.43512i	0.298477	+	0.107200i
$517$	−4.92672	−	3.32616i	−0.216677	−	0.146285i
$518$	−15.5269	−	36.4926i	−0.682211	−	1.60339i
$519$	−4.62607	−	9.34310i	−0.203062	−	0.410117i
$520$	−12.8442	−	5.01869i	−0.563253	−	0.220084i
$521$	−9.51926	−	26.5045i	−0.417046	−	1.16118i	−0.949238	−	0.314558i	$-0.898144\pi$
$521$	−9.51926	−	26.5045i	−0.417046	−	1.16118i	0.532192	−	0.846624i	$-0.321368\pi$
$522$	−37.9740	−	35.1703i	−1.66208	−	1.53936i
$523$	−6.76204	+	9.23256i	−0.295683	+	0.403712i	−0.928940	−	0.370230i	$-0.879279\pi$
$523$	−6.76204	+	9.23256i	−0.295683	+	0.403712i	0.633257	+	0.773942i	$0.281718\pi$
$524$	−50.3083	−	38.3483i	−2.19773	−	1.67525i
$525$	−14.7713	−	38.5335i	−0.644673	−	1.68174i
$526$	12.7329	−	14.2874i	0.555182	−	0.622962i
$527$	−0.234345	−	0.0997093i	−0.0102082	−	0.00434340i
$528$	−3.18367	−	0.680961i	−0.138551	−	0.0296350i
$529$	−14.5150	−	17.6005i	−0.631088	−	0.765239i
$530$	61.4032	+	32.5495i	2.66719	+	1.41386i
$531$	16.4823	+	1.26542i	0.715271	+	0.0549146i
$532$	34.8430	−	8.86083i	1.51063	−	0.384166i
$533$	−4.82114	+	3.25489i	−0.208827	+	0.140985i
$534$	57.6135	+	37.3101i	2.49318	+	1.61457i
$535$	27.7242	+	0.236509i	1.19862	+	0.0102252i
$536$	0.906790	−	23.6569i	0.0391674	−	1.02182i
$537$	−15.9140	+	30.6502i	−0.686741	+	1.32265i
$538$	−52.9469	+	9.21980i	−2.28270	+	0.397494i
$539$	−1.58996	−	6.79443i	−0.0684844	−	0.292657i
$540$	1.84076	+	17.2341i	0.0792135	+	0.741636i
$541$	1.77021	−	2.51671i	0.0761074	−	0.108202i	−0.778084	−	0.628160i	$-0.783808\pi$
$541$	1.77021	−	2.51671i	0.0761074	−	0.108202i	0.854192	+	0.519958i	$0.174052\pi$
$542$	−18.4179	−	9.56288i	−0.791119	−	0.410761i
$543$	12.4301	−	11.5123i	0.533425	−	0.494042i
$544$	0.0152319	+	0.131940i	0.000653061	+	0.00565690i
$545$	14.7772	−	1.29259i	0.632986	−	0.0553684i
$546$	−7.18646	+	37.0553i	−0.307552	+	1.58582i
$547$	−6.17304	−	24.2739i	−0.263940	−	1.03788i	−0.950480	−	0.310786i	$-0.899408\pi$
$547$	−6.17304	−	24.2739i	−0.263940	−	1.03788i	0.686540	−	0.727092i	$-0.259129\pi$
$548$	−19.3575	−	22.5769i	−0.826909	−	0.964439i
$549$	−53.1034	+	23.8059i	−2.26640	+	1.01601i
$550$	26.2251	+	9.35694i	1.11824	+	0.398981i
$551$	−16.5131	+	10.6938i	−0.703481	+	0.455569i
$552$	1.38266	−	3.24964i	0.0588498	−	0.138314i
$553$	44.3853	−	2.55355i	1.88745	−	0.108588i
$554$	21.5945	−	15.1892i	0.917462	−	0.645329i
$555$	−0.339737	−	31.9727i	−0.0144210	−	1.35716i
$556$	−0.974334	−	6.30802i	−0.0413210	−	0.267520i
$557$	27.4206	−	29.6064i	1.16185	−	1.25447i	0.200326	−	0.979729i	$-0.435800\pi$
$557$	27.4206	−	29.6064i	1.16185	−	1.25447i	0.961520	−	0.274736i	$-0.0885905\pi$
$558$	−37.0448	+	78.5678i	−1.56823	+	3.32604i
$559$	0.828734	+	1.39399i	0.0350517	+	0.0589594i
$560$	3.42250	−	1.19635i	0.144627	−	0.0505552i
$561$	−0.154241	−	0.0621646i	−0.00651205	−	0.00262459i
$562$	8.89985	−	13.1825i	0.375417	−	0.556068i
$563$	15.6529	+	33.1980i	0.659689	+	1.39913i	0.903196	+	0.429228i	$0.141214\pi$
$563$	15.6529	+	33.1980i	0.659689	+	1.39913i	−0.243507	+	0.969899i	$0.578298\pi$
$564$	−20.6751	−	6.54302i	−0.870577	−	0.275511i
$565$	−10.4316	+	6.08178i	−0.438859	+	0.255862i
$566$	−18.6105	−	17.9108i	−0.782256	−	0.752846i
$567$	−16.8183	+	4.97013i	−0.706303	+	0.208726i
$568$	17.4248	+	45.7421i	0.731130	+	1.91930i
$569$	−2.02496	−	7.36871i	−0.0848907	−	0.308913i	0.909357	−	0.416016i	$-0.136574\pi$
$569$	−2.02496	−	7.36871i	−0.0848907	−	0.308913i	−0.994248	+	0.107104i	$0.965842\pi$
$570$	45.8291	+	6.58096i	1.91957	+	0.275646i
$571$	−0.726673	+	4.70462i	−0.0304103	+	0.196882i	−0.998571	−	0.0534490i	$-0.982979\pi$
$571$	−0.726673	+	4.70462i	−0.0304103	+	0.196882i	0.968160	+	0.250331i	$0.0805395\pi$
$572$	−9.90713	−	12.4931i	−0.414238	−	0.522364i
$573$	9.90620	−	0.951730i	0.413837	−	0.0397591i
$574$	5.67138	−	20.6379i	0.236719	−	0.861408i
$575$	−1.09903	+	1.85749i	−0.0458327	+	0.0774629i
$576$	49.1574	−	3.77403i	2.04822	−	0.157251i
$577$	10.7519	−	3.63065i	0.447608	−	0.151146i	−0.0870694	−	0.996202i	$-0.527750\pi$
$577$	10.7519	−	3.63065i	0.447608	−	0.151146i	0.534677	+	0.845056i	$0.320433\pi$
$578$	−2.25806	+	39.2490i	−0.0939228	+	1.63254i
$579$	−4.63589	+	19.8107i	−0.192661	+	0.823306i
$580$	−34.0468	+	26.5294i	−1.41372	+	1.10157i
$581$	−26.7810	−	10.2127i	−1.11106	−	0.423695i
$582$	−52.6180	−	52.6180i	−2.18108	−	2.18108i
$583$	17.0667	+	27.4944i	0.706830	+	1.13870i
$584$	36.0547	−	32.1318i	1.49195	−	1.32962i
$585$	−9.45401	+	14.3293i	−0.390875	+	0.592442i
$586$	−3.49708	−	45.5500i	−0.144463	−	1.88166i
$587$	−21.0663	−	6.22550i	−0.869501	−	0.256954i	−0.182142	−	0.983272i	$-0.558303\pi$
$587$	−21.0663	−	6.22550i	−0.869501	−	0.256954i	−0.687359	+	0.726318i	$0.741230\pi$
$588$	−12.5871	−	22.1266i	−0.519084	−	0.912487i
$589$	25.4717	+	21.0064i	1.04954	+	0.865552i
$590$	5.19982	−	21.3962i	0.214073	−	0.880870i
$591$	−63.5604	−	9.81751i	−2.61453	−	0.403838i
$592$	2.80861	+	0.0538084i	0.115433	+	0.00221151i
$593$	24.3762	+	13.8668i	1.00101	+	0.569442i	0.904763	−	0.425915i	$-0.140048\pi$
$593$	24.3762	+	13.8668i	1.00101	+	0.569442i	0.0962469	+	0.995357i	$0.469316\pi$
$594$	−5.27328	+	11.7630i	−0.216365	+	0.482643i
$595$	0.182710	−	0.0302123i	0.00749037	−	0.00123858i
$596$	15.5297	−	16.1363i	0.636120	−	0.660970i
$597$	−5.06901	+	37.5755i	−0.207461	+	1.53786i
$598$	1.75200	−	0.909666i	0.0716447	−	0.0371990i
$599$	10.1339	−	28.2158i	0.414060	−	1.15287i	−0.536925	−	0.843630i	$-0.680414\pi$
$599$	10.1339	−	28.2158i	0.414060	−	1.15287i	0.950985	−	0.309237i	$-0.100073\pi$
$600$	40.8445	+	2.26401i	1.66747	+	0.0924277i
$601$	12.3499	−	30.6421i	0.503761	−	1.24992i	−0.433458	−	0.901174i	$-0.642707\pi$
$601$	12.3499	−	30.6421i	0.503761	−	1.24992i	0.937219	−	0.348742i	$-0.113391\pi$
$602$	−5.65332	−	1.90899i	−0.230412	−	0.0778044i
$603$	−28.5631	−	7.26380i	−1.16318	−	0.295805i
$604$	−31.3490	+	11.2592i	−1.27557	+	0.458130i
$605$	−7.49523	−	8.89426i	−0.304725	−	0.361603i
$606$	26.3257	−	4.06625i	1.06941	−	0.165180i
$607$	6.05177	−	0.816395i	0.245634	−	0.0331364i	−0.00984342	−	0.999952i	$-0.503133\pi$
$607$	6.05177	−	0.816395i	0.245634	−	0.0331364i	0.255477	+	0.966815i	$0.417767\pi$
$608$	2.95385	−	16.9632i	0.119794	−	0.687947i
$609$	35.5200	+	31.6553i	1.43934	+	1.28274i
$610$	19.9020	+	74.9176i	0.805807	+	3.03333i
$611$	−2.65352	−	4.09752i	−0.107350	−	0.165768i
$612$	−0.340654	−	0.0327280i	−0.0137701	−	0.00132295i
$613$	5.89289	−	15.4695i	0.238011	−	0.624806i	−0.761722	−	0.647904i	$-0.775646\pi$
$613$	5.89289	−	15.4695i	0.238011	−	0.624806i	0.999733	+	0.0230980i	$0.00735298\pi$
$614$	−5.67508	+	73.9188i	−0.229027	+	2.98312i
$615$	10.5777	−	13.6339i	0.426536	−	0.549771i
$616$	23.1935	+	4.49811i	0.934492	+	0.181234i
$617$	−28.7497	+	6.14931i	−1.15742	+	0.247562i	−0.747310	−	0.664475i	$-0.768655\pi$
$617$	−28.7497	+	6.14931i	−1.15742	+	0.247562i	−0.410107	+	0.912037i	$0.634509\pi$
$618$	43.5720	+	34.5528i	1.75272	+	1.38992i
$619$	−1.50029	−	0.0575074i	−0.0603018	−	0.00231142i	0.00813440	−	0.999967i	$-0.497411\pi$
$619$	−1.50029	−	0.0575074i	−0.0603018	−	0.00231142i	−0.0684362	+	0.997655i	$0.521801\pi$
$620$	59.6874	+	41.0422i	2.39710	+	1.64829i
$621$	−0.817279	−	0.574861i	−0.0327963	−	0.0230684i
$622$	−46.1212	−	28.6290i	−1.84929	−	1.14792i
$623$	−30.2403	−	18.7712i	−1.21155	−	0.752052i
$624$	−2.18685	−	1.53820i	−0.0875441	−	0.0615771i
$625$	−24.5624	−	4.65691i	−0.982497	−	0.186276i
$626$	−59.6966	−	2.28822i	−2.38596	−	0.0914558i
$627$	16.8921	+	13.3955i	0.674605	+	0.534966i
$628$	−31.7229	+	6.78527i	−1.26588	+	0.270762i
$629$	0.140862	+	0.0273187i	0.00561656	+	0.00108927i
$630$	−7.91012	−	62.6665i	−0.315147	−	2.49669i
$631$	−0.706995	+	9.20872i	−0.0281450	+	0.366593i	0.966000	+	0.258541i	$0.0832418\pi$
$631$	−0.706995	+	9.20872i	−0.0281450	+	0.366593i	−0.994145	+	0.108052i	$0.965539\pi$
$632$	−15.6883	+	41.1834i	−0.624046	+	1.63819i
$633$	−54.7105	−	5.25627i	−2.17455	−	0.208918i
$634$	−18.0028	−	27.7996i	−0.714984	−	1.10406i
$635$	−9.44543	+	2.50919i	−0.374830	+	0.0995742i
$636$	88.1340	+	78.5447i	3.49474	+	3.11450i
$637$	0.983075	−	5.64553i	0.0389508	−	0.223684i
$638$	−31.8144	+	4.29182i	−1.25954	+	0.169915i
$639$	60.2222	−	9.30189i	2.38235	−	0.367977i
$640$	3.66632	−	42.9506i	0.144924	−	1.69777i
$641$	−5.01094	+	1.79971i	−0.197920	+	0.0710844i	−0.435103	−	0.900381i	$-0.643288\pi$
$641$	−5.01094	+	1.79971i	−0.197920	+	0.0710844i	0.237183	+	0.971465i	$0.423776\pi$
$642$	72.9064	+	18.5406i	2.87739	+	0.731741i
$643$	1.96077	+	0.662102i	0.0773251	+	0.0261108i	0.358324	−	0.933597i	$-0.383348\pi$
$643$	1.96077	+	0.662102i	0.0773251	+	0.0261108i	−0.280998	+	0.959708i	$0.590666\pi$
$644$	−1.69987	+	4.21765i	−0.0669841	+	0.166199i
$645$	−3.62534	−	3.16242i	−0.142748	−	0.124520i
$646$	−0.0702298	+	0.195541i	−0.00276315	+	0.00769344i
$647$	25.6865	−	13.3368i	1.00984	−	0.524324i	0.125959	−	0.992035i	$-0.459799\pi$
$647$	25.6865	−	13.3368i	1.00984	−	0.524324i	0.883881	+	0.467711i	$0.154921\pi$
$648$	2.32410	−	17.2281i	0.0912994	−	0.676784i
$649$	7.10974	−	7.38748i	0.279082	−	0.289984i
$650$	16.8090	+	15.5027i	0.659302	+	0.608064i
$651$	32.6633	−	72.8615i	1.28018	−	2.85567i
$652$	−46.8134	−	26.6306i	−1.83335	−	1.04294i
$653$	47.8271	+	0.916290i	1.87162	+	0.0358572i	0.942553	−	0.334058i	$-0.108418\pi$
$653$	47.8271	+	0.916290i	1.87162	+	0.0358572i	0.929066	+	0.369915i	$0.120613\pi$
$654$	39.7765	+	6.14386i	1.55538	+	0.240244i
$655$	21.9713	+	36.0789i	0.858488	+	1.40972i
$656$	1.16960	+	0.964565i	0.0456653	+	0.0376599i
$657$	−29.7281	−	52.2584i	−1.15981	−	2.03880i
$658$	17.2251	+	5.09034i	0.671504	+	0.198442i
$659$	0.405127	+	5.27684i	0.0157815	+	0.205556i	0.999645	+	0.0266367i	$0.00847974\pi$
$659$	0.405127	+	5.27684i	0.0157815	+	0.205556i	−0.983864	+	0.178920i	$0.942740\pi$
$660$	39.4805	+	26.0480i	1.53678	+	1.01392i
$661$	27.3444	−	24.3693i	1.06358	−	0.947854i	0.0648279	−	0.997896i	$-0.479350\pi$
$661$	27.3444	−	24.3693i	1.06358	−	0.947854i	0.998747	+	0.0500420i	$0.0159355\pi$
$662$	−8.82235	−	14.2128i	−0.342890	−	0.552395i
$663$	−0.0965674	−	0.0965674i	−0.00375037	−	0.00375037i
$664$	20.0973	−	20.0831i	0.779928	−	0.779376i
$665$	−23.8255	−	2.95669i	−0.923912	−	0.114656i
$666$	11.1511	−	47.6524i	0.432096	−	1.84649i
$667$	0.142922	−	2.48423i	0.00553395	−	0.0961898i
$668$	−14.7483	+	4.98012i	−0.570628	+	0.192687i
$669$	−12.8274	+	0.984816i	−0.495935	+	0.0380752i
$670$	−15.6773	+	35.9907i	−0.605665	+	1.39044i
$671$	−9.56442	+	34.8044i	−0.369230	+	1.34361i
$672$	−41.4509	+	3.98236i	−1.59900	+	0.153623i
$673$	19.6294	+	24.7532i	0.756659	+	0.954166i	0.999875	−	0.0158065i	$-0.00503157\pi$
$673$	19.6294	+	24.7532i	0.756659	+	0.954166i	−0.243216	+	0.969972i	$0.578202\pi$
$674$	6.33975	−	41.0448i	0.244198	−	1.58099i
$675$	3.04354	−	11.1668i	0.117146	−	0.429810i
$676$	8.06503	+	29.3482i	0.310194	+	1.12878i
$677$	−6.18594	−	16.2388i	−0.237745	−	0.624107i	0.761979	−	0.647602i	$-0.224228\pi$
$677$	−6.18594	−	16.2388i	−0.237745	−	0.624107i	−0.999724	+	0.0234949i	$0.992521\pi$
$678$	−31.4199	+	9.28518i	−1.20667	+	0.356595i
$679$	27.8024	+	26.7571i	1.06696	+	1.02684i
$680$	−0.0467600	+	0.177518i	−0.00179316	+	0.00680750i
$681$	20.5483	+	6.50290i	0.787412	+	0.249192i
$682$	22.9764	+	48.7304i	0.879812	+	1.86598i
$683$	−12.4496	+	18.4403i	−0.476369	+	0.705598i	−0.988145	−	0.153521i	$-0.950939\pi$
$683$	−12.4496	+	18.4403i	−0.476369	+	0.705598i	0.511777	+	0.859119i	$0.328988\pi$
$684$	41.1494	+	16.5847i	1.57339	+	0.634132i
$685$	6.55317	+	18.7472i	0.250384	+	0.716292i
$686$	−15.2522	−	25.6553i	−0.582332	−	0.979524i
$687$	−17.2695	+	36.6267i	−0.658873	+	1.39740i
$688$	0.287196	−	0.310090i	0.0109492	−	0.0118221i
$689$	4.05671	+	26.2639i	0.154548	+	1.00057i
$690$	−4.09663	+	4.18463i	−0.155956	+	0.159306i
$691$	25.6188	−	18.0198i	0.974584	−	0.685507i	0.0252187	−	0.999682i	$-0.491972\pi$
$691$	25.6188	−	18.0198i	0.974584	−	0.685507i	0.949365	+	0.314175i	$0.101728\pi$
$692$	−13.2851	+	0.764311i	−0.505023	+	0.0290548i
$693$	11.5151	−	27.0638i	0.437422	−	1.02807i
$694$	42.5183	−	27.5345i	1.61397	−	1.04520i
$695$	−0.927041	+	4.16032i	−0.0351647	+	0.157810i
$696$	−43.0365	+	19.2930i	−1.63129	+	0.731297i
$697$	0.0504043	+	0.0587874i	0.00190920	+	0.00222673i
$698$	−14.9597	−	58.8250i	−0.566231	−	2.22656i
$699$	9.33446	−	48.1310i	0.353062	−	1.82048i
$700$	−52.6386	−	1.90726i	−1.98955	−	0.0720875i
$701$	1.57014	+	13.6007i	0.0593032	+	0.513692i	0.989275	+	0.146062i	$0.0466599\pi$
$701$	1.57014	+	13.6007i	0.0593032	+	0.513692i	−0.929972	+	0.367630i	$0.880169\pi$
$702$	−7.76691	+	7.19347i	−0.293143	+	0.271500i
$703$	−16.5091	−	8.57176i	−0.622652	−	0.323290i
$704$	17.5925	−	25.0113i	0.663044	−	0.942648i
$705$	11.2695	+	9.09445i	0.424434	+	0.342517i
$706$	4.48865	+	19.1815i	0.168933	+	0.721907i
$707$	−13.6082	+	2.36963i	−0.511788	+	0.0891193i
$708$	17.2358	−	33.1959i	0.647761	−	1.24758i
$709$	−1.48547	+	38.7539i	−0.0557880	+	1.45543i	0.656914	+	0.753966i	$0.271862\pi$
$709$	−1.48547	+	38.7539i	−0.0557880	+	1.45543i	−0.712702	+	0.701467i	$0.752529\pi$
$710$	0.692394	−	81.1642i	0.0259851	−	3.04604i
$711$	46.0504	+	29.8219i	1.72702	+	1.11841i
$712$	29.2415	−	19.7417i	1.09587	−	0.739853i
$713$	−4.04718	+	1.02923i	−0.151568	+	0.0385449i
$714$	0.501005	+	0.0384644i	0.0187496	+	0.00143950i
$715$	3.12587	+	10.1784i	0.116901	+	0.380650i
$716$	28.0456	+	34.0073i	1.04812	+	1.27091i
$717$	−8.76940	−	1.87570i	−0.327499	−	0.0700494i
$718$	31.1662	+	13.2606i	1.16311	+	0.494881i
$719$	21.8015	−	24.4631i	0.813058	−	0.912321i	−0.184453	−	0.982841i	$-0.559051\pi$
$719$	21.8015	−	24.4631i	0.813058	−	0.912321i	0.997510	+	0.0705199i	$0.0224658\pi$
$720$	4.27966	+	1.30452i	0.159494	+	0.0486166i
$721$	−22.9331	−	17.4811i	−0.854073	−	0.651031i
$722$	−10.0482	+	13.7193i	−0.373956	+	0.510581i
$723$	−0.00106592		0.000987221i	−3.96420e−5		3.67152e-5i
$724$	−7.30953	−	20.3519i	−0.271656	−	0.756373i
$725$	27.6243	−	8.22648i	1.02594	−	0.305524i
$726$	−14.0035	−	28.2823i	−0.519717	−	1.04965i
$727$	3.24752	+	7.63262i	0.120444	+	0.283078i	0.969443	−	0.245316i	$-0.0788918\pi$
$727$	3.24752	+	7.63262i	0.120444	+	0.283078i	−0.848999	+	0.528394i	$0.822794\pi$
$728$	16.0803	+	10.8563i	0.595976	+	0.402360i
$729$	−37.5137	−	13.4733i	−1.38940	−	0.499012i
$730$	−75.0774	+	27.8687i	−2.77874	+	1.03147i
$731$	0.0171694	−	0.0130877i	0.000635034	−	0.000484065i
$732$	2.52225	+	131.652i	0.0932250	+	4.86601i
$733$	−3.86432	−	13.0764i	−0.142732	−	0.482987i	0.856731	−	0.515764i	$-0.172492\pi$
$733$	−3.86432	−	13.0764i	−0.142732	−	0.482987i	−0.999463	+	0.0327769i	$0.989565\pi$
$734$	−41.9805	−	18.8195i	−1.54953	−	0.694642i
$735$	2.45153	+	16.8216i	0.0904261	+	0.620476i
$736$	1.51019	+	1.56918i	0.0556662	+	0.0578408i
$737$	−14.7473	+	10.8011i	−0.543223	+	0.397863i
$738$	20.6946	−	16.4110i	0.761780	−	0.604096i
$739$	−8.55957	+	10.3791i	−0.314869	+	0.381801i	−0.904932	−	0.425556i	$-0.860078\pi$
$739$	−8.55957	+	10.3791i	−0.314869	+	0.381801i	0.590063	+	0.807357i	$0.299103\pi$
$740$	−37.7213	−	15.5784i	−1.38666	−	0.572673i
$741$	8.45784	+	15.5537i	0.310706	+	0.571380i
$742$	−74.2310	−	63.6456i	−2.72510	−	2.33650i
$743$	−2.46798	−	7.30875i	−0.0905415	−	0.268132i	0.892638	−	0.450774i	$-0.148852\pi$
$743$	−2.46798	−	7.30875i	−0.0905415	−	0.268132i	−0.983179	+	0.182642i	$0.941535\pi$
$744$	52.6609	+	59.0901i	1.93064	+	2.16635i
$745$	−13.5810	+	6.26240i	−0.497569	+	0.229436i
$746$			11.2455i			0.411729i
$747$	−19.2155	−	29.6952i	−0.703059	−	1.08649i
$748$	−0.150089	+	0.150089i	−0.00548779	+	0.00548779i
$749$	−37.9825	−	8.88824i	−1.38785	−	0.324769i
$750$	−61.7177	−	28.1460i	−2.25361	−	1.02775i
$751$	29.0543	+	14.3857i	1.06021	+	0.524942i	0.887869	−	0.460096i	$-0.152185\pi$
$751$	29.0543	+	14.3857i	1.06021	+	0.524942i	0.172338	+	0.985038i	$0.444868\pi$
$752$	−0.828122	+	0.965853i	−0.0301985	+	0.0352210i
$753$	−14.5345	+	49.1831i	−0.529668	+	1.79233i
$754$	−25.4210	−	6.98581i	−0.925778	−	0.254408i
$755$	22.2351	+	0.615773i	0.809219	+	0.0224103i
$756$	2.79665	−	24.2249i	0.101713	−	0.881051i
$757$	25.7968	+	35.2216i	0.937599	+	1.28015i	0.959883	+	0.280400i	$0.0904671\pi$
$757$	25.7968	+	35.2216i	0.937599	+	1.28015i	−0.0222841	+	0.999752i	$0.507094\pi$
$758$	−1.40827	+	73.5066i	−0.0511506	+	2.66988i
$759$	−2.62935	+	0.722559i	−0.0954394	+	0.0262272i
$760$	12.3355	−	20.3520i	0.447457	−	0.738244i
$761$	40.8178	+	22.1960i	1.47964	+	0.804604i	0.997444	−	0.0714578i	$-0.0227651\pi$
$761$	40.8178	+	22.1960i	1.47964	+	0.804604i	0.482199	+	0.876062i	$0.339838\pi$
$762$	−26.5124	+	0.507935i	−0.960442	+	0.0184005i
$763$	−20.6832	−	2.79020i	−0.748781	−	0.101012i
$764$	3.83254	−	12.1103i	0.138656	−	0.438135i
$765$	0.203929	+	0.103147i	0.00737307	+	0.00372929i
$766$	−13.2097	+	2.56186i	−0.477285	+	0.0925639i
$767$	7.74783	−	3.29655i	0.279758	−	0.119031i
$768$	16.1028	−	47.6872i	0.581059	−	1.72076i
$769$	17.7973	−	10.5806i	0.641786	−	0.381545i	−0.153181	−	0.988198i	$-0.548952\pi$
$769$	17.7973	−	10.5806i	0.641786	−	0.381545i	0.794967	+	0.606653i	$0.207488\pi$
$770$	−33.1076	−	20.9443i	−1.19312	−	0.754782i
$771$	−23.1158	+	0.886047i	−0.832494	+	0.0319102i
$772$	20.9508	+	15.3446i	0.754035	+	0.552265i
$773$	0.749810	+	5.55819i	0.0269688	+	0.199914i	0.999454	−	0.0330520i	$-0.0105227\pi$
$773$	0.749810	+	5.55819i	0.0269688	+	0.199914i	−0.972485	+	0.232966i	$0.925157\pi$
$774$	−4.23629	−	6.02272i	−0.152270	−	0.216482i
$775$	−27.1503	−	40.0339i	−0.975267	−	1.43806i
$776$	−35.4765	+	14.2983i	−1.27353	+	0.513279i
$777$	−9.40956	+	43.9922i	−0.337566	+	1.57821i
$778$	0.344173	−	3.58236i	0.0123392	−	0.128434i
$779$	−4.10665	−	9.16065i	−0.147136	−	0.328214i
$780$	21.4591	+	32.3775i	0.768361	+	1.15930i
$781$	19.3138	−	32.4872i	0.691103	−	1.16248i
$782$	−0.0147045	−	0.0217804i	−0.000525833	−	0.000778864i
$783$	2.79107	+	13.0490i	0.0997447	+	0.466333i
$784$	−1.48363	+	0.171277i	−0.0529867	+	0.00611705i
$785$	21.3804	+	3.48939i	0.763099	+	0.124542i
$786$	34.5822	+	109.275i	1.23351	+	3.89772i
$787$	−0.564154	−	3.23979i	−0.0201099	−	0.115486i	0.973426	−	0.229000i	$-0.0735455\pi$
$787$	−0.564154	−	3.23979i	−0.0201099	−	0.115486i	−0.993536	+	0.113514i	$0.963789\pi$
$788$	−43.2930	+	69.7449i	−1.54225	+	2.48456i
$789$	−21.1383	+	4.94656i	−0.752544	+	0.176102i
$790$	49.0842	−	54.1398i	1.74634	−	1.92621i
$791$	16.1974	−	5.12599i	0.575914	−	0.182259i
$792$	19.8108	+	21.3900i	0.703944	+	0.760061i
$793$	−18.4179	+	23.2254i	−0.654038	+	0.824757i
$794$	−41.1832	+	63.5942i	−1.46154	+	2.25688i
$795$	−35.7294	−	70.2736i	−1.26719	−	2.49235i
$796$	41.5989	+	24.7308i	1.47443	+	0.876559i
$797$	32.4753	−	27.8443i	1.15033	−	0.986296i	0.150337	−	0.988635i	$-0.451964\pi$
$797$	32.4753	−	27.8443i	1.15033	−	0.986296i	0.999997	+	0.00233923i	$0.000744601\pi$
$798$	−60.8744	−	23.1893i	−2.15493	−	0.820892i
$799$	−0.0501360	+	0.0413468i	−0.00177368	+	0.00146275i
$800$	−11.1462	+	22.6306i	−0.394077	+	0.800114i
$801$	−16.4189	−	40.7381i	−0.580134	−	1.43941i
$802$	0.176875	+	3.07441i	0.00624569	+	0.108561i
$803$	−36.7371	−	6.39715i	−1.29643	−	0.225751i
$804$	−40.4266	+	53.0347i	−1.42574	+	1.87039i
$805$	2.08234	−	2.21021i	0.0733927	−	0.0778997i
$806$	1.69466	+	44.2113i	0.0596918	+	1.55728i
$807$	55.1428	+	25.9999i	1.94112	+	0.915239i
$808$	3.37464	−	13.2699i	0.118719	−	0.466834i
$809$	20.8118	−	10.3046i	0.731703	−	0.362289i	−0.0392092	−	0.999231i	$-0.512484\pi$
$809$	20.8118	−	10.3046i	0.731703	−	0.362289i	0.770912	+	0.636942i	$0.219801\pi$
$810$	−13.9866	+	25.2061i	−0.491437	+	0.885652i
$811$	2.25695	+	11.6374i	0.0792522	+	0.408646i	0.999836	+	0.0181011i	$0.00576209\pi$
$811$	2.25695	+	11.6374i	0.0792522	+	0.408646i	−0.920584	+	0.390545i	$0.872287\pi$
$812$	54.9289	−	25.8990i	1.92762	−	0.908876i
$813$	10.8478	+	20.8927i	0.380449	+	0.732739i
$814$	−18.4014	−	24.1404i	−0.644969	−	0.846119i
$815$	22.6453	+	27.9412i	0.793230	+	0.978739i
$816$	−0.0170030	+	0.0312681i	−0.000595226	+	0.00109460i
$817$	−2.61544	+	0.996317i	−0.0915027	+	0.0348567i
$818$	7.67749	−	13.4961i	0.268437	−	0.471880i
$819$	17.4031	−	16.7488i	0.608115	−	0.585252i
$820$	−10.7269	−	19.2365i	−0.374599	−	0.671769i
$821$	2.64254	+	0.305069i	0.0922254	+	0.0106470i	0.160672	−	0.987008i	$-0.448634\pi$
$821$	2.64254	+	0.305069i	0.0922254	+	0.0106470i	−0.0684471	+	0.997655i	$0.521804\pi$
$822$	5.15323	+	53.6380i	0.179740	+	1.87084i
$823$	−33.7396	+	19.1934i	−1.17609	+	0.669039i	−0.952170	−	0.305569i	$-0.901153\pi$
$823$	−33.7396	+	19.1934i	−1.17609	+	0.669039i	−0.223919	+	0.974608i	$0.571885\pi$
$824$	25.1115	−	13.6552i	0.874802	−	0.475702i
$825$	−18.2259	−	25.7968i	−0.634545	−	0.898128i
$826$	−13.7465	+	27.7634i	−0.478303	+	0.966011i
$827$	14.9412	+	0.859592i	0.519558	+	0.0298910i	0.315237	−	0.949013i	$-0.397916\pi$
$827$	14.9412	+	0.859592i	0.519558	+	0.0298910i	0.204321	+	0.978904i	$0.434501\pi$
$828$	−4.76769	+	2.95947i	−0.165689	+	0.102849i
$829$	−34.1478			−1.18600			−0.593002	−	0.805201i	$-0.702057\pi$
$829$	−34.1478			−1.18600			−0.593002	+	0.805201i	$0.702057\pi$
$830$	−43.1602	+	18.8897i	−1.49811	+	0.655671i
$831$	−29.9489			−1.03892
$832$	21.3357	−	13.2438i	0.739684	−	0.459147i
$833$	−0.0761595	−	0.00438157i	−0.00263877	−	0.000151812i
$834$	−5.13166	+	10.3642i	−0.177695	+	0.358884i
$835$	10.3836	+	0.486753i	0.359340	+	0.0168448i
$836$	24.1742	−	13.1455i	0.836082	−	0.454647i
$837$	19.4653	−	11.0732i	0.672820	−	0.382746i
$838$	3.57569	+	37.2179i	0.123520	+	1.28567i
$839$	41.6934	+	4.81330i	1.43942	+	0.166174i	0.798758	−	0.601653i	$-0.205491\pi$
$839$	41.6934	+	4.81330i	1.43942	+	0.166174i	0.640658	+	0.767826i	$0.278662\pi$
$840$	−55.3658	−	15.7240i	−1.91030	−	0.542528i
$841$	−3.04865	+	2.93403i	−0.105126	+	0.101173i
$842$	21.1463	−	37.1725i	0.728748	−	1.28105i
$843$	−16.8607	+	6.42287i	−0.580715	+	0.221215i
$844$	−33.5134	+	61.6301i	−1.15358	+	2.12140i
$845$	2.11626	−	20.2144i	0.0728016	−	0.695396i
$846$	13.4370	+	17.6277i	0.461974	+	0.606052i
$847$	7.54101	+	14.5239i	0.259112	+	0.499046i
$848$	6.26463	−	2.95378i	0.215128	−	0.101433i
$849$	5.57841	+	28.7638i	0.191450	+	0.987170i
$850$	0.179351	−	0.245956i	0.00615168	−	0.00843622i
$851$	2.10851	−	1.04399i	0.0722786	−	0.0357874i
$852$	33.9819	−	133.625i	1.16420	−	4.57793i
$853$	8.06411	+	3.80223i	0.276110	+	0.130186i	0.559531	−	0.828810i	$-0.310981\pi$
$853$	8.06411	+	3.80223i	0.276110	+	0.130186i	−0.283421	+	0.958996i	$0.591469\pi$
$854$	−4.17741	−	108.983i	−0.142948	−	3.72932i
$855$	−21.5639	−	20.3163i	−0.737469	−	0.694801i
$856$	23.4414	−	30.7523i	0.801212	−	1.05109i
$857$	−1.92707	−	0.335567i	−0.0658275	−	0.0114627i	0.138542	−	0.990357i	$-0.455758\pi$
$857$	−1.92707	−	0.335567i	−0.0658275	−	0.0114627i	−0.204370	+	0.978894i	$0.565514\pi$
$858$	1.65935	+	28.8424i	0.0566492	+	0.984664i
$859$	−17.2285	−	42.7469i	−0.587830	−	1.45850i	−0.867022	−	0.498269i	$-0.833969\pi$
$859$	−17.2285	−	42.7469i	−0.587830	−	1.45850i	0.279192	−	0.960235i	$-0.409933\pi$
$860$	−5.52588	+	2.67759i	−0.188431	+	0.0913049i
$861$	−18.7308	+	15.4472i	−0.638345	+	0.526439i
$862$	74.8348	+	28.5073i	2.54888	+	0.970962i
$863$	27.2768	−	23.3871i	0.928513	−	0.796106i	−0.0507473	−	0.998712i	$-0.516160\pi$
$863$	27.2768	−	23.3871i	0.928513	−	0.796106i	0.979261	+	0.202605i	$0.0649408\pi$
$864$	−10.0389	−	5.96821i	−0.341532	−	0.203042i
$865$	8.44895	+	2.75334i	0.287273	+	0.0936164i
$866$	16.7896	−	25.9261i	0.570533	−	0.881005i
$867$	27.7099	−	34.9429i	0.941078	−	1.18672i
$868$	−69.2524	−	74.7730i	−2.35058	−	2.53796i
$869$	32.4423	−	10.2670i	1.10053	−	0.348283i
$870$	78.1127	−	3.82570i	2.64827	−	0.129703i
$871$	−14.6168	+	3.42047i	−0.495272	+	0.115898i
$872$	10.9108	−	17.5772i	0.369485	−	0.595239i
$873$	8.16876	+	46.9110i	0.276471	+	1.58770i
$874$	1.02792	+	3.24810i	0.0347701	+	0.109869i
$875$	32.2771	+	13.9793i	1.09117	+	0.472586i
$876$	−135.139	+	15.6012i	−4.56594	+	0.527115i
$877$	4.37442	+	20.4516i	0.147714	+	0.690600i	0.988745	+	0.149613i	$0.0478028\pi$
$877$	4.37442	+	20.4516i	0.147714	+	0.690600i	−0.841031	+	0.540987i	$0.818051\pi$
$878$	−19.0471	−	28.2125i	−0.642807	−	0.952126i
$879$	−26.4823	+	44.5451i	−0.893225	+	1.50247i
$880$	2.31305	−	1.53305i	0.0779730	−	0.0516790i
$881$	−0.0102678	−	0.0229042i	−0.000345930	−	0.000771662i	0.912331	−	0.409454i	$-0.134281\pi$
$881$	−0.0102678	−	0.0229042i	−0.000345930	−	0.000771662i	−0.912677	+	0.408683i	$0.865988\pi$
$882$	−2.48830	+	25.8997i	−0.0837853	+	0.872089i
$883$	−2.05024	+	9.58539i	−0.0689959	+	0.322574i	−0.998987	−	0.0450090i	$-0.985668\pi$
$883$	−2.05024	+	9.58539i	−0.0689959	+	0.322574i	0.929991	+	0.367583i	$0.119815\pi$
$884$	−0.161674	+	0.0651604i	−0.00543768	+	0.00219158i
$885$	−18.7882	+	16.4586i	−0.631560	+	0.553250i
$886$	−49.9268	−	70.9808i	−1.67732	−	2.38465i
$887$	7.09545	+	52.5972i	0.238242	+	1.76604i	0.569013	+	0.822328i	$0.307325\pi$
$887$	7.09545	+	52.5972i	0.238242	+	1.76604i	−0.330771	+	0.943711i	$0.607309\pi$
$888$	−35.9768	−	26.3499i	−1.20730	−	0.884244i
$889$	13.7403	−	0.526678i	0.460835	−	0.0176642i
$890$	−57.0772	+	12.8440i	−1.91323	+	0.430533i
$891$	−11.5379	+	6.85932i	−0.386533	+	0.229796i
$892$	−5.25345	+	15.5577i	−0.175899	+	0.520911i
$893$	7.75228	−	3.29844i	0.259420	−	0.110378i
$894$	−39.8361	+	7.72575i	−1.33232	+	0.258388i
$895$	−9.17916	−	27.9683i	−0.306825	−	0.934877i
$896$	−18.2994	+	57.8237i	−0.611340	+	1.93175i
$897$	−2.21923	−	0.299379i	−0.0740980	−	0.00999596i
$898$	3.50804	−	0.0672084i	0.117065	−	0.00224277i
$899$	48.9942	+	26.6422i	1.63405	+	0.888567i
$900$	−51.0144	−	40.2810i	−1.70048	−	1.34270i
$901$	0.341130	−	0.0937442i	0.0113647	−	0.00312307i
$902$	0.313786	−	16.3785i	0.0104479	−	0.545345i
$903$	3.99949	+	5.46070i	0.133095	+	0.181721i
$904$	−1.93136	+	16.7297i	−0.0642361	+	0.556421i
$905$	−0.399763	+	14.4352i	−0.0132886	+	0.479841i
$906$	58.1965	+	15.9927i	1.93345	+	0.531321i
$907$	14.3019	−	48.3959i	0.474887	−	1.60696i	−0.286106	−	0.958198i	$-0.592361\pi$
$907$	14.3019	−	48.3959i	0.474887	−	1.60696i	0.760993	−	0.648760i	$-0.224712\pi$
$908$	17.9060	−	20.8841i	0.594231	−	0.693062i
$909$	−15.2757	−	7.56347i	−0.506662	−	0.250864i
$910$	−18.2843	−	26.4717i	−0.606118	−	0.877530i
$911$	17.3063	+	4.04983i	0.573383	+	0.134177i	0.504444	−	0.863444i	$-0.331697\pi$
$911$	17.3063	+	4.04983i	0.573383	+	0.134177i	0.0689384	+	0.997621i	$0.478039\pi$
$912$	3.26272	−	3.26272i	0.108039	−	0.108039i
$913$	−21.7921	−	2.52360i	−0.721212	−	0.0835189i
$914$		−	64.6534i		−	2.13855i
$915$	30.4273	−	82.4995i	1.00589	−	2.72735i
$916$	34.3877	+	38.5859i	1.13620	+	1.27492i
$917$	−19.0146	−	56.3103i	−0.627916	−	1.85953i
$918$	0.106987	+	0.0917304i	0.00353109	+	0.00302755i
$919$	−9.92629	−	18.2541i	−0.327438	−	0.602149i	0.661592	−	0.749864i	$-0.269881\pi$
$919$	−9.92629	−	18.2541i	−0.327438	−	0.602149i	−0.989030	+	0.147715i	$0.952808\pi$
$920$	1.15483	+	2.77977i	0.0380737	+	0.0916464i
$921$	53.5066	−	64.8805i	1.76310	−	2.13789i
$922$	−20.5103	+	16.2648i	−0.675469	+	0.535651i
$923$	25.0401	−	18.3397i	0.824206	−	0.603659i
$924$	−46.1470	−	47.9498i	−1.51813	−	1.57743i
$925$	19.6762	+	18.8572i	0.646948	+	0.620020i
$926$	25.5202	+	11.4405i	0.838644	+	0.375958i
$927$	−10.0848	−	34.1256i	−0.331227	−	1.12083i
$928$	−0.557111	−	29.0792i	−0.0182881	−	0.954571i
$929$	−30.8607	+	23.5241i	−1.01251	+	0.771801i	−0.973790	−	0.227449i	$-0.926962\pi$
$929$	−30.8607	+	23.5241i	−1.01251	+	0.771801i	−0.0387181	+	0.999250i	$0.512327\pi$
$930$	−45.6741	−	123.045i	−1.49771	−	4.03479i
$931$	9.30758	+	3.34288i	0.305044	+	0.109558i
$932$	−51.8646	−	35.0153i	−1.69888	−	1.14696i
$933$	24.1088	+	56.6626i	0.789286	+	1.85505i
$934$	10.4290	+	21.0632i	0.341249	+	0.689208i
$935$	0.129830	−	0.0568770i	0.00424591	−	0.00186008i
$936$	8.09299	+	22.5333i	0.264528	+	0.736524i
$937$	17.9103	+	16.5880i	0.585105	+	0.541906i	0.915698	−	0.401868i	$-0.131639\pi$
$937$	17.9103	+	16.5880i	0.585105	+	0.541906i	−0.330592	+	0.943774i	$0.607249\pi$
$938$	32.6364	−	44.5601i	1.06562	−	1.45494i
$939$	53.8951	+	41.0824i	1.75880	+	1.34067i
$940$	16.3129	−	8.69120i	0.532068	−	0.283476i
$941$	14.2563	−	15.9968i	0.464741	−	0.521480i	−0.467170	−	0.884168i	$-0.654726\pi$
$941$	14.2563	−	15.9968i	0.464741	−	0.521480i	0.931911	+	0.362688i	$0.118141\pi$
$942$	54.0869	+	23.0129i	1.76225	+	0.749801i
$943$	1.24168	+	0.265586i	0.0404347	+	0.00864866i
$944$	−1.39618	−	1.69297i	−0.0454418	−	0.0551014i
$945$	−7.62697	+	14.3880i	−0.248105	+	0.468040i
$946$	−4.55361	−	0.349601i	−0.148051	−	0.0113665i
$947$	−30.3996	+	7.73084i	−0.987854	+	0.251219i	−0.705979	−	0.708233i	$-0.749493\pi$
$947$	−30.3996	+	7.73084i	−0.987854	+	0.251219i	−0.281875	+	0.959451i	$0.590956\pi$
$948$	102.885	−	69.4606i	3.34155	−	2.25597i
$949$	−25.7042	−	16.6459i	−0.834394	−	0.540348i
$950$	−31.3344	+	23.9891i	−1.01662	+	0.778310i
$951$	−1.43903	+	37.5424i	−0.0466639	+	1.21740i
$952$	0.119018	−	0.229226i	0.00385739	−	0.00742926i
$953$	−24.4773	+	4.26231i	−0.792897	+	0.138070i	−0.553497	−	0.832851i	$-0.686707\pi$
$953$	−24.4773	+	4.26231i	−0.792897	+	0.138070i	−0.239400	+	0.970921i	$0.576951\pi$
$954$	−27.4937	−	117.490i	−0.890141	−	3.80388i
$955$	−5.32702	+	6.60104i	−0.172378	+	0.213605i
$956$	−6.58524	+	9.36222i	−0.212982	+	0.302796i
$957$	32.3194	+	16.7807i	1.04474	+	0.542443i
$958$	10.9669	−	10.1572i	0.354325	−	0.328164i
$959$	−3.20446	−	27.7574i	−0.103477	−	0.896335i
$960$	−47.8849	+	57.0650i	−1.54548	+	1.84177i
$961$	11.9173	−	61.4491i	0.384430	−	1.98223i
$962$	−6.14369	−	24.1585i	−0.198080	−	0.778901i
$963$	−31.3330	−	36.5443i	−1.00969	−	1.17762i
$964$	−0.00169214		0.000758574i	−5.45002e−5		2.44320e-5i
$965$	−9.30191	−	14.6360i	−0.299439	−	0.471148i
$966$	6.91581	−	4.47863i	0.222513	−	0.144098i
$967$	−1.43738	+	3.37825i	−0.0462230	+	0.108637i	−0.941679	−	0.336513i	$-0.890752\pi$
$967$	−1.43738	+	3.37825i	−0.0462230	+	0.108637i	0.895456	+	0.445151i	$0.146850\pi$
$968$	−16.1952	+	0.931732i	−0.520532	+	0.0299470i
$969$	0.192776	−	0.135595i	0.00619285	−	0.00435595i
$970$	63.4221	−	0.673915i	2.03636	−	0.0216381i
$971$	5.10916	+	33.0777i	0.163961	+	1.06151i	0.915645	+	0.401989i	$0.131681\pi$
$971$	5.10916	+	33.0777i	0.163961	+	1.06151i	−0.751684	+	0.659524i	$0.770758\pi$
$972$	−49.0745	+	52.9866i	−1.57407	+	1.69955i
$973$	2.55757	−	5.42431i	0.0819918	−	0.173895i
$974$	−8.78865	−	14.7831i	−0.281607	−	0.473682i
$975$	−5.47853	−	25.3538i	−0.175453	−	0.811971i
$976$	7.16519	+	2.88783i	0.229352	+	0.0924372i
$977$	0.811531	−	1.20204i	0.0259632	−	0.0384566i	−0.815595	−	0.578623i	$-0.803590\pi$
$977$	0.811531	−	1.20204i	0.0259632	−	0.0384566i	0.841558	+	0.540167i	$0.181639\pi$
$978$	41.6176	+	88.2663i	1.33078	+	2.82244i
$979$	−25.9725	−	8.21951i	−0.830086	−	0.262697i
$980$	20.9819	+	5.52683i	0.670242	+	0.176548i
$981$	−18.5569	−	17.8592i	−0.592477	−	0.570202i
$982$	43.8698	−	12.9643i	1.39994	−	0.413709i
$983$	8.98713	+	23.5922i	0.286645	+	0.752475i	0.998730	+	0.0503814i	$0.0160437\pi$
$983$	8.98713	+	23.5922i	0.286645	+	0.752475i	−0.712085	+	0.702093i	$0.752249\pi$
$984$	−6.37724	−	23.2064i	−0.203299	−	0.739794i
$985$	43.8782	−	32.8589i	1.39808	−	1.04697i
$986$	−0.0535730	+	0.346842i	−0.00170611	+	0.0110457i
$987$	−12.6599	−	15.9645i	−0.402970	−	0.508154i
$988$	22.4942	−	2.16111i	0.715635	−	0.0687541i
$989$	0.0938032	−	0.341345i	0.00298277	−	0.0108541i
$990$	−17.6889	−	44.9923i	−0.562190	−	1.42995i
$991$	5.78851	−	0.444410i	0.183878	−	0.0141172i	0.0157160	−	0.999876i	$-0.494997\pi$
$991$	5.78851	−	0.444410i	0.183878	−	0.0141172i	0.168162	+	0.985759i	$0.446217\pi$
$992$	−46.2451	+	15.6158i	−1.46828	+	0.495803i
$993$	−1.08992	+	18.9447i	−0.0345875	+	0.601193i
$994$	−26.0209	+	111.196i	−0.825331	+	3.52692i
$995$	−19.8637	−	25.4922i	−0.629721	−	0.808159i
$996$	−78.8490	+	13.7015i	−2.49843	+	0.434148i
$997$	−13.3475	−	13.3475i	−0.422721	−	0.422721i	0.463419	−	0.886139i	$-0.346623\pi$
$997$	−13.3475	−	13.3475i	−0.422721	−	0.422721i	−0.886139	+	0.463419i	$0.846623\pi$
$998$	2.64329	+	4.25832i	0.0836717	+	0.134795i
$999$	−9.41951	+	8.39463i	−0.298020	+	0.265594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	415.2.l.a.102.4	✓	3200
5.3	odd	4	inner	415.2.l.a.268.37	yes	3200
83.35	odd	82	inner	415.2.l.a.367.37	yes	3200
415.118	even	164	inner	415.2.l.a.118.4	yes	3200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
415.2.l.a.102.4	✓	3200	1.1	even	1	trivial
415.2.l.a.118.4	yes	3200	415.118	even	164	inner
415.2.l.a.268.37	yes	3200	5.3	odd	4	inner
415.2.l.a.367.37	yes	3200	83.35	odd	82	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:	\( N \)	\(=\)	\( 415 = 5 \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	415.l (of order \(164\), degree \(80\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96491 + 1.21968i) q^{2} +(2.61910 + 0.150681i) q^{3} +(1.48579 - 3.00080i) q^{4} +(-1.65344 + 1.50537i) q^{5} +(-5.33006 + 2.89839i) q^{6} +(2.73458 - 1.55561i) q^{7} +(0.298245 + 3.10431i) q^{8} +(3.85675 + 0.445243i) q^{9} +(1.41279 - 4.97458i) q^{10} +(1.73500 - 1.66977i) q^{11} +(4.34358 - 7.63549i) q^{12} +(1.84795 - 0.703950i) q^{13} +(-3.47584 + 6.39196i) q^{14} +(-4.55735 + 3.69356i) q^{15} +(-0.312432 - 0.409872i) q^{16} +(-0.0121305 - 0.0233632i) q^{17} +(-8.12121 + 3.82915i) q^{18} +(0.649757 + 3.35032i) q^{19} +(2.06063 + 7.19830i) q^{20} +(7.39653 - 3.66225i) q^{21} +(-1.37252 + 5.39708i) q^{22} +(-0.390432 - 0.184089i) q^{23} +(0.313371 + 8.17544i) q^{24} +(0.467742 - 4.97807i) q^{25} +(-2.77244 + 3.63710i) q^{26} +(2.28051 + 0.397112i) q^{27} +(-0.605072 - 10.5172i) q^{28} +(2.15492 + 5.34673i) q^{29} +(4.44980 - 12.8160i) q^{30} +(7.46370 - 6.15526i) q^{31} +(-4.71482 - 1.79605i) q^{32} +(4.79572 - 4.11185i) q^{33} +(0.0523311 + 0.0311111i) q^{34} +(-2.17970 + 6.68866i) q^{35} +(7.06640 - 10.9118i) q^{36} +(-3.38676 + 4.27079i) q^{37} +(-5.36304 - 5.79057i) q^{38} +(4.94602 - 1.56526i) q^{39} +(-5.16626 - 4.68384i) q^{40} +(-2.86425 + 0.670260i) q^{41} +(-10.0667 + 16.2174i) q^{42} +(0.140689 + 0.807939i) q^{43} +(-2.43279 - 7.68729i) q^{44} +(-7.04717 + 5.06964i) q^{45} +(0.991693 - 0.114486i) q^{46} +(-0.516341 - 2.41403i) q^{47} +(-0.756529 - 1.12057i) q^{48} +(1.48086 - 2.49092i) q^{49} +(5.15260 + 10.3519i) q^{50} +(-0.0282507 - 0.0630183i) q^{51} +(0.633247 - 6.59123i) q^{52} +(-2.81090 + 13.1417i) q^{53} +(-4.96533 + 2.00121i) q^{54} +(-0.355105 + 5.37267i) q^{55} +(5.64469 + 8.02504i) q^{56} +(1.19695 + 8.87272i) q^{57} +(-10.7555 - 7.87749i) q^{58} +(4.25480 - 0.163090i) q^{59} +(4.31235 + 19.1635i) q^{60} +(-12.8846 + 7.65999i) q^{61} +(-7.15799 + 21.1979i) q^{62} +(11.2392 - 4.78206i) q^{63} +(12.4667 - 2.41777i) q^{64} +(-1.99577 + 3.94578i) q^{65} +(-4.40799 + 13.9287i) q^{66} +(-7.52316 - 1.01489i) q^{67} +(-0.0881316 + 0.00168846i) q^{68} +(-0.994841 - 0.540977i) q^{69} +(-3.87515 - 15.8011i) q^{70} +(15.1346 - 4.15906i) q^{71} +(-0.231919 + 12.1054i) q^{72} +(-9.15039 - 12.4935i) q^{73} +(1.44566 - 12.5225i) q^{74} +(1.97516 - 12.9676i) q^{75} +(11.0190 + 3.02808i) q^{76} +(2.14698 - 7.26510i) q^{77} +(-7.80933 + 9.10817i) q^{78} +(12.6641 + 6.27039i) q^{79} +(1.13360 + 0.207375i) q^{80} +(-5.42770 - 1.27013i) q^{81} +(4.81047 - 4.81047i) q^{82} +(-5.79396 - 7.03065i) q^{83} -27.6368i q^{84} +(0.0552273 + 0.0203688i) q^{85} +(-1.26187 - 1.41593i) q^{86} +(4.83830 + 14.3283i) q^{87} +(5.70094 + 4.88798i) q^{88} +(-5.40459 - 9.93887i) q^{89} +(7.66367 - 18.5567i) q^{90} +(3.95828 - 4.79970i) q^{91} +(-1.13251 + 0.898090i) q^{92} +(20.4756 - 14.9966i) q^{93} +(3.95891 + 4.11357i) q^{94} +(-6.11780 - 4.56144i) q^{95} +(-12.0779 - 5.41445i) q^{96} +(3.47592 + 11.7621i) q^{97} +(0.128373 + 6.70060i) q^{98} +(7.43490 - 5.66738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3200 q - 82 q^{2} - 78 q^{3} - 82 q^{5} - 164 q^{6} - 74 q^{7} - 82 q^{8} - 102 q^{10} - 164 q^{11} - 114 q^{12} - 82 q^{13} - 82 q^{15} - 96 q^{16} - 82 q^{17} - 82 q^{18} - 82 q^{20} - 148 q^{21} - 82 q^{22}+ \cdots + 246 q^{98}+O(q^{100}) \) 3200 * q - 82 * q^2 - 78 * q^3 - 82 * q^5 - 164 * q^6 - 74 * q^7 - 82 * q^8 - 102 * q^10 - 164 * q^11 - 114 * q^12 - 82 * q^13 - 82 * q^15 - 96 * q^16 - 82 * q^17 - 82 * q^18 - 82 * q^20 - 148 * q^21 - 82 * q^22 - 86 * q^23 - 74 * q^25 - 140 * q^26 - 90 * q^27 - 78 * q^28 - 114 * q^30 - 148 * q^31 - 82 * q^32 - 42 * q^33 - 82 * q^35 - 104 * q^36 - 66 * q^37 - 26 * q^38 - 130 * q^40 - 156 * q^41 - 82 * q^42 - 82 * q^43 - 82 * q^45 - 164 * q^46 - 82 * q^47 - 102 * q^48 - 82 * q^50 - 164 * q^51 - 82 * q^52 - 82 * q^53 - 82 * q^55 - 164 * q^56 - 82 * q^57 - 82 * q^58 - 82 * q^60 - 100 * q^61 - 82 * q^62 - 38 * q^63 - 134 * q^65 - 164 * q^66 - 82 * q^67 + 182 * q^68 - 138 * q^70 - 164 * q^71 - 82 * q^72 + 164 * q^73 - 138 * q^75 - 164 * q^76 - 106 * q^77 + 606 * q^78 - 82 * q^80 - 188 * q^81 + 192 * q^83 - 82 * q^85 - 84 * q^86 - 54 * q^87 + 738 * q^88 - 198 * q^90 - 164 * q^91 - 82 * q^92 + 576 * q^93 - 50 * q^95 - 164 * q^96 - 82 * q^97 + 246 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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