LMFDB - Embedded newform 360.2.bo.a.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(43,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 8, 9]))

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

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

chi := DirichletCharacter("360.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bo (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.19
Character	$\chi$	$=$	360.43
Dual form			360.2.bo.a.67.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.871892 - 1.11347i) q^{2} +(1.72671 + 0.135893i) q^{3} +(-0.479609 + 1.94164i) q^{4} +(-0.893456 - 2.04981i) q^{5} +(-1.35419 - 2.04112i) q^{6} +(-0.371305 + 0.0994908i) q^{7} +(2.58012 - 1.15887i) q^{8} +(2.96307 + 0.469295i) q^{9} +O(q^{10})$	\(q+(-0.871892 - 1.11347i) q^{2} +(1.72671 + 0.135893i) q^{3} +(-0.479609 + 1.94164i) q^{4} +(-0.893456 - 2.04981i) q^{5} +(-1.35419 - 2.04112i) q^{6} +(-0.371305 + 0.0994908i) q^{7} +(2.58012 - 1.15887i) q^{8} +(2.96307 + 0.469295i) q^{9} +(-1.50340 + 2.78205i) q^{10} +(1.82960 - 3.16896i) q^{11} +(-1.09200 + 3.28748i) q^{12} +(-0.611267 - 0.163789i) q^{13} +(0.434517 + 0.326690i) q^{14} +(-1.26419 - 3.66085i) q^{15} +(-3.53995 - 1.86246i) q^{16} +(1.04920 - 1.04920i) q^{17} +(-2.06093 - 3.70845i) q^{18} -3.08348i q^{19} +(4.40851 - 0.751663i) q^{20} +(-0.654656 + 0.121334i) q^{21} +(-5.12375 + 0.725796i) q^{22} +(-0.326729 - 0.0875468i) q^{23} +(4.61260 - 1.65042i) q^{24} +(-3.40347 + 3.66284i) q^{25} +(0.350586 + 0.823431i) q^{26} +(5.05259 + 1.21300i) q^{27} +(-0.0150944 - 0.768657i) q^{28} +(2.03266 - 3.52066i) q^{29} +(-2.97400 + 4.59949i) q^{30} +(6.74573 - 3.89465i) q^{31} +(1.01267 + 5.56547i) q^{32} +(3.58983 - 5.22326i) q^{33} +(-2.08305 - 0.253460i) q^{34} +(0.535682 + 0.672215i) q^{35} +(-2.33232 + 5.52814i) q^{36} +(3.86294 + 3.86294i) q^{37} +(-3.43335 + 2.68846i) q^{38} +(-1.03322 - 0.365882i) q^{39} +(-4.68070 - 4.25336i) q^{40} +(0.556389 + 0.963693i) q^{41} +(0.705891 + 0.623146i) q^{42} +(-11.7624 + 3.15173i) q^{43} +(5.27550 + 5.07230i) q^{44} +(-1.68540 - 6.49303i) q^{45} +(0.187392 + 0.440133i) q^{46} +(-10.2314 + 2.74149i) q^{47} +(-5.85938 - 3.69698i) q^{48} +(-5.93421 + 3.42612i) q^{49} +(7.04590 + 0.596049i) q^{50} +(1.95425 - 1.66910i) q^{51} +(0.611188 - 1.10831i) q^{52} +(3.40965 - 3.40965i) q^{53} +(-3.05468 - 6.68348i) q^{54} +(-8.13046 - 0.919013i) q^{55} +(-0.842713 + 0.686993i) q^{56} +(0.419023 - 5.32429i) q^{57} +(-5.69239 + 0.806346i) q^{58} +(1.26667 - 0.731313i) q^{59} +(7.71438 - 0.698821i) q^{60} +(12.7371 + 7.35379i) q^{61} +(-10.2181 - 4.11542i) q^{62} +(-1.14689 + 0.120546i) q^{63} +(5.31402 - 5.98007i) q^{64} +(0.210405 + 1.39932i) q^{65} +(-8.94586 + 0.556961i) q^{66} +(3.22484 + 0.864093i) q^{67} +(1.53397 + 2.54039i) q^{68} +(-0.552270 - 0.195568i) q^{69} +(0.281431 - 1.18256i) q^{70} +8.89983i q^{71} +(8.18892 - 2.22299i) q^{72} +(0.582661 + 0.582661i) q^{73} +(0.933183 - 7.66932i) q^{74} +(-6.37457 + 5.86216i) q^{75} +(5.98702 + 1.47887i) q^{76} +(-0.364057 + 1.35868i) q^{77} +(0.493463 + 1.46947i) q^{78} +(-5.54816 + 9.60970i) q^{79} +(-0.654903 + 8.92026i) q^{80} +(8.55952 + 2.78110i) q^{81} +(0.587928 - 1.45976i) q^{82} +(2.43429 - 0.652265i) q^{83} +(0.0783911 - 1.32930i) q^{84} +(-3.08809 - 1.21326i) q^{85} +(13.7649 + 10.3491i) q^{86} +(3.98824 - 5.80295i) q^{87} +(1.04816 - 10.2966i) q^{88} +11.2263i q^{89} +(-5.76027 + 7.53786i) q^{90} +0.243262 q^{91} +(0.326687 - 0.592403i) q^{92} +(12.1772 - 5.80824i) q^{93} +(11.9732 + 9.00200i) q^{94} +(-6.32057 + 2.75496i) q^{95} +(0.992284 + 9.74758i) q^{96} +(4.84339 + 18.0758i) q^{97} +(8.98885 + 3.62033i) q^{98} +(6.90841 - 8.53123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.871892	−	1.11347i	−0.616521	−	0.787339i
$2$	−0.871892	−	1.11347i	−0.616521	−	0.787339i
$3$	1.72671	+	0.135893i	0.996917	+	0.0784576i
$3$	1.72671	+	0.135893i	0.996917	+	0.0784576i
$4$	−0.479609	+	1.94164i	−0.239805	+	0.970821i
$5$	−0.893456	−	2.04981i	−0.399566	−	0.916705i
$5$	−0.893456	−	2.04981i	−0.399566	−	0.916705i
$6$	−1.35419	−	2.04112i	−0.552847	−	0.833282i
$7$	−0.371305	+	0.0994908i	−0.140340	+	0.0376040i	−0.328305	−	0.944572i	$-0.606477\pi$
$7$	−0.371305	+	0.0994908i	−0.140340	+	0.0376040i	0.187965	+	0.982176i	$0.439811\pi$
$8$	2.58012	−	1.15887i	0.912210	−	0.409724i
$9$	2.96307	+	0.469295i	0.987689	+	0.156432i
$10$	−1.50340	+	2.78205i	−0.475416	+	0.879761i
$11$	1.82960	−	3.16896i	0.551646	−	0.955479i	−0.446510	−	0.894779i	$-0.647333\pi$
$11$	1.82960	−	3.16896i	0.551646	−	0.955479i	0.998156	−	0.0607002i	$-0.0193333\pi$
$12$	−1.09200	+	3.28748i	−0.315234	+	0.949014i
$13$	−0.611267	−	0.163789i	−0.169535	−	0.0454268i	0.173053	−	0.984913i	$-0.444637\pi$
$13$	−0.611267	−	0.163789i	−0.169535	−	0.0454268i	−0.342588	+	0.939486i	$0.611303\pi$
$14$	0.434517	+	0.326690i	0.116130	+	0.0873114i
$15$	−1.26419	−	3.66085i	−0.326412	−	0.945228i
$16$	−3.53995	−	1.86246i	−0.884988	−	0.465615i
$17$	1.04920	−	1.04920i	0.254470	−	0.254470i	−0.568331	−	0.822800i	$-0.692411\pi$
$17$	1.04920	−	1.04920i	0.254470	−	0.254470i	0.822800	+	0.568331i	$0.192411\pi$
$18$	−2.06093	−	3.70845i	−0.485766	−	0.874089i
$19$		−	3.08348i		−	0.707400i	−0.935359	−	0.353700i	$-0.884923\pi$
$19$		−	3.08348i		−	0.707400i	0.935359	−	0.353700i	$-0.115077\pi$
$20$	4.40851	−	0.751663i	0.985774	−	0.168077i
$21$	−0.654656	+	0.121334i	−0.142858	+	0.0264773i
$22$	−5.12375	+	0.725796i	−1.09239	+	0.154740i
$23$	−0.326729	−	0.0875468i	−0.0681278	−	0.0182548i	0.224594	−	0.974452i	$-0.427894\pi$
$23$	−0.326729	−	0.0875468i	−0.0681278	−	0.0182548i	−0.292722	+	0.956198i	$0.594561\pi$
$24$	4.61260	−	1.65042i	0.941544	−	0.336891i
$25$	−3.40347	+	3.66284i	−0.680694	+	0.732567i
$26$	0.350586	+	0.823431i	0.0687556	+	0.161488i
$27$	5.05259	+	1.21300i	0.972371	+	0.233441i
$28$	−0.0150944	−	0.768657i	−0.00285258	−	0.145263i
$29$	2.03266	−	3.52066i	0.377455	−	0.653771i	−0.613237	−	0.789899i	$-0.710133\pi$
$29$	2.03266	−	3.52066i	0.377455	−	0.653771i	0.990691	+	0.136129i	$0.0434661\pi$
$30$	−2.97400	+	4.59949i	−0.542975	+	0.839749i
$31$	6.74573	−	3.89465i	1.21157	−	0.699499i	0.248467	−	0.968640i	$-0.420073\pi$
$31$	6.74573	−	3.89465i	1.21157	−	0.699499i	0.963101	+	0.269141i	$0.0867398\pi$
$32$	1.01267	+	5.56547i	0.179017	+	0.983846i
$33$	3.58983	−	5.22326i	0.624910	−	0.909253i
$34$	−2.08305	−	0.253460i	−0.357239	−	0.0434680i
$35$	0.535682	+	0.672215i	0.0905468	+	0.113625i
$36$	−2.33232	+	5.52814i	−0.388719	+	0.921356i
$37$	3.86294	+	3.86294i	0.635064	+	0.635064i	0.949334	−	0.314270i	$-0.101760\pi$
$37$	3.86294	+	3.86294i	0.635064	+	0.635064i	−0.314270	+	0.949334i	$0.601760\pi$
$38$	−3.43335	+	2.68846i	−0.556963	+	0.436126i
$39$	−1.03322	−	0.365882i	−0.165448	−	0.0585881i
$40$	−4.68070	−	4.25336i	−0.740083	−	0.672515i
$41$	0.556389	+	0.963693i	0.0868933	+	0.150504i	0.906196	−	0.422857i	$-0.138973\pi$
$41$	0.556389	+	0.963693i	0.0868933	+	0.150504i	−0.819303	+	0.573361i	$0.805639\pi$
$42$	0.705891	+	0.623146i	0.108921	+	0.0961536i
$43$	−11.7624	+	3.15173i	−1.79375	+	0.480635i	−0.992975	−	0.118327i	$-0.962247\pi$
$43$	−11.7624	+	3.15173i	−1.79375	+	0.480635i	−0.800778	+	0.598961i	$0.795580\pi$
$44$	5.27550	+	5.07230i	0.795312	+	0.764678i
$45$	−1.68540	−	6.49303i	−0.251245	−	0.967924i
$46$	0.187392	+	0.440133i	0.0276295	+	0.0648941i
$47$	−10.2314	+	2.74149i	−1.49240	+	0.399887i	−0.910547	−	0.413406i	$-0.864339\pi$
$47$	−10.2314	+	2.74149i	−1.49240	+	0.399887i	−0.581854	+	0.813294i	$0.697672\pi$
$48$	−5.85938	−	3.69698i	−0.845729	−	0.533613i
$49$	−5.93421	+	3.42612i	−0.847744	+	0.489445i
$50$	7.04590	+	0.596049i	0.996441	+	0.0842941i
$51$	1.95425	−	1.66910i	0.273650	−	0.233720i
$52$	0.611188	−	1.10831i	0.0847566	−	0.153695i
$53$	3.40965	−	3.40965i	0.468352	−	0.468352i	−0.433029	−	0.901380i	$-0.642555\pi$
$53$	3.40965	−	3.40965i	0.468352	−	0.468352i	0.901380	+	0.433029i	$0.142555\pi$
$54$	−3.05468	−	6.68348i	−0.415690	−	0.909507i
$55$	−8.13046	−	0.919013i	−1.09631	−	0.123920i
$56$	−0.842713	+	0.686993i	−0.112612	+	0.0918033i
$57$	0.419023	−	5.32429i	0.0555009	−	0.705219i
$58$	−5.69239	+	0.806346i	−0.747447	+	0.105878i
$59$	1.26667	−	0.731313i	0.164906	−	0.0952088i	−0.415275	−	0.909696i	$-0.636315\pi$
$59$	1.26667	−	0.731313i	0.164906	−	0.0952088i	0.580182	+	0.814487i	$0.302981\pi$
$60$	7.71438	−	0.698821i	0.995922	−	0.0902174i
$61$	12.7371	+	7.35379i	1.63082	+	0.941557i	0.983839	+	0.179054i	$0.0573035\pi$
$61$	12.7371	+	7.35379i	1.63082	+	0.941557i	0.646985	+	0.762503i	$0.276030\pi$
$62$	−10.2181	−	4.11542i	−1.29770	−	0.522659i
$63$	−1.14689	+	0.120546i	−0.144495	+	0.0151874i
$64$	5.31402	−	5.98007i	0.664253	−	0.747508i
$65$	0.210405	+	1.39932i	0.0260975	+	0.173565i
$66$	−8.94586	+	0.556961i	−1.10116	+	0.0685571i
$67$	3.22484	+	0.864093i	0.393977	+	0.105566i	0.450368	−	0.892843i	$-0.351293\pi$
$67$	3.22484	+	0.864093i	0.393977	+	0.105566i	−0.0563913	+	0.998409i	$0.517959\pi$
$68$	1.53397	+	2.54039i	0.186021	+	0.308067i
$69$	−0.552270	−	0.195568i	−0.0664855	−	0.0235436i
$70$	0.281431	−	1.18256i	0.0336374	−	0.141343i
$71$			8.89983i			1.05622i	0.849177	+	0.528108i	$0.177098\pi$
$71$			8.89983i			1.05622i	−0.849177	+	0.528108i	$0.822902\pi$
$72$	8.18892	−	2.22299i	0.965073	−	0.261981i
$73$	0.582661	+	0.582661i	0.0681953	+	0.0681953i	0.740382	−	0.672187i	$-0.234645\pi$
$73$	0.582661	+	0.582661i	0.0681953	+	0.0681953i	−0.672187	+	0.740382i	$0.734645\pi$
$74$	0.933183	−	7.66932i	0.108480	−	0.891540i
$75$	−6.37457	+	5.86216i	−0.736072	+	0.676904i
$76$	5.98702	+	1.47887i	0.686758	+	0.169638i
$77$	−0.364057	+	1.35868i	−0.0414882	+	0.154836i
$78$	0.493463	+	1.46947i	0.0558737	+	0.166385i
$79$	−5.54816	+	9.60970i	−0.624217	+	1.08118i	0.364474	+	0.931213i	$0.381249\pi$
$79$	−5.54816	+	9.60970i	−0.624217	+	1.08118i	−0.988692	+	0.149963i	$0.952085\pi$
$80$	−0.654903	+	8.92026i	−0.0732204	+	0.997316i
$81$	8.55952	+	2.78110i	0.951058	+	0.309011i
$82$	0.587928	−	1.45976i	0.0649258	−	0.161203i
$83$	2.43429	−	0.652265i	0.267198	−	0.0715954i	−0.122733	−	0.992440i	$-0.539166\pi$
$83$	2.43429	−	0.652265i	0.267198	−	0.0715954i	0.389930	+	0.920844i	$0.372499\pi$
$84$	0.0783911	−	1.32930i	0.00855318	−	0.145039i
$85$	−3.08809	−	1.21326i	−0.334951	−	0.131596i
$86$	13.7649	+	10.3491i	1.48431	+	1.11597i
$87$	3.98824	−	5.80295i	0.427584	−	0.622141i
$88$	1.04816	−	10.2966i	0.111734	−	1.09762i
$89$			11.2263i			1.18999i	0.803730	+	0.594994i	$0.202846\pi$
$89$			11.2263i			1.18999i	−0.803730	+	0.594994i	$0.797154\pi$
$90$	−5.76027	+	7.53786i	−0.607186	+	0.794560i
$91$	0.243262			0.0255008
$92$	0.326687	−	0.592403i	0.0340595	−	0.0617623i
$93$	12.1772	−	5.80824i	1.26271	−	0.602286i
$94$	11.9732	+	9.00200i	1.23494	+	0.928486i
$95$	−6.32057	+	2.75496i	−0.648476	+	0.282653i
$96$	0.992284	+	9.74758i	0.101275	+	0.994859i
$97$	4.84339	+	18.0758i	0.491772	+	1.83532i	0.547408	+	0.836866i	$0.315615\pi$
$97$	4.84339	+	18.0758i	0.491772	+	1.83532i	−0.0556358	+	0.998451i	$0.517719\pi$
$98$	8.98885	+	3.62033i	0.908011	+	0.365709i
$99$	6.90841	−	8.53123i	0.694322	−	0.857421i
$100$	−5.47958	−	8.36506i	−0.547958	−	0.836506i
$101$	1.82703	+	1.05484i	0.181797	+	0.104960i	0.588137	−	0.808762i	$-0.299862\pi$
$101$	1.82703	+	1.05484i	0.181797	+	0.104960i	−0.406340	+	0.913722i	$0.633195\pi$
$102$	−3.56238	−	0.720723i	−0.352728	−	0.0713622i
$103$	−9.50380	−	2.54654i	−0.936437	−	0.250918i	−0.241840	−	0.970316i	$-0.577751\pi$
$103$	−9.50380	−	2.54654i	−0.936437	−	0.250918i	−0.694597	+	0.719399i	$0.744417\pi$
$104$	−1.76695	+	0.285788i	−0.173264	+	0.0280238i
$105$	0.833619	+	1.23352i	0.0813529	+	0.120379i
$106$	−6.76937	−	0.823680i	−0.657500	−	0.0800029i
$107$	−6.59047	+	6.59047i	−0.637125	+	0.637125i	−0.949845	−	0.312721i	$-0.898760\pi$
$107$	−6.59047	+	6.59047i	−0.637125	+	0.637125i	0.312721	+	0.949845i	$0.398760\pi$
$108$	−4.77847	+	9.22855i	−0.459809	+	0.888018i
$109$	17.6789			1.69333			0.846666	−	0.532124i	$-0.178606\pi$
$109$	17.6789			1.69333			0.846666	+	0.532124i	$0.178606\pi$
$110$	6.06559	+	9.85426i	0.578331	+	0.939567i
$111$	6.14524	+	7.19513i	0.583281	+	0.682932i
$112$	1.49970	+	0.339347i	0.141708	+	0.0320653i
$113$	2.65220	−	9.89816i	0.249498	−	0.931141i	−0.721570	−	0.692341i	$-0.756579\pi$
$113$	2.65220	−	9.89816i	0.249498	−	0.931141i	0.971069	−	0.238800i	$-0.0767539\pi$
$114$	−6.29375	+	4.17563i	−0.589464	+	0.391084i
$115$	0.112464	+	0.747953i	0.0104873	+	0.0697470i
$116$	5.86099	+	5.63523i	0.544179	+	0.523218i
$117$	−1.73436	−	0.772181i	−0.160342	−	0.0713882i
$118$	−1.91869	−	0.772768i	−0.176630	−	0.0711391i
$119$	−0.285188	+	0.493961i	−0.0261432	+	0.0452813i
$120$	−7.50422	−	7.98040i	−0.685038	−	0.728507i
$121$	−1.19489	−	2.06961i	−0.108626	−	0.188146i
$122$	−2.91722	−	20.5941i	−0.264113	−	1.86450i
$123$	0.829764	+	1.73963i	0.0748173	+	0.156857i
$124$	4.32670	+	14.9657i	0.388549	+	1.34396i
$125$	10.5490	+	3.70390i	0.943530	+	0.331287i
$126$	1.13419	+	1.17192i	0.101042	+	0.104403i
$127$	−9.90246	−	9.90246i	−0.878701	−	0.878701i	0.114699	−	0.993400i	$-0.463410\pi$
$127$	−9.90246	−	9.90246i	−0.878701	−	0.878701i	−0.993400	+	0.114699i	$0.963410\pi$
$128$	−11.2918	−	0.703007i	−0.998068	−	0.0621376i
$129$	−20.7386	+	3.84371i	−1.82593	+	0.338419i
$130$	1.37465	−	1.45434i	0.120564	−	0.127554i
$131$	−9.09590	−	15.7546i	−0.794713	−	1.37648i	−0.923021	−	0.384749i	$-0.874288\pi$
$131$	−9.09590	−	15.7546i	−0.794713	−	1.37648i	0.128309	−	0.991734i	$-0.459045\pi$
$132$	8.41998	+	9.47530i	0.732865	+	0.824719i
$133$	0.306778	+	1.14491i	0.0266010	+	0.0992764i
$134$	−1.84957	−	4.34414i	−0.159779	−	0.375277i
$135$	−2.02785	−	11.4406i	−0.174530	−	0.984652i
$136$	1.49118	−	3.92297i	0.127867	−	0.336392i
$137$	−0.129942	−	0.484951i	−0.0111017	−	0.0414321i	0.960153	−	0.279476i	$-0.0901606\pi$
$137$	−0.129942	−	0.484951i	−0.0111017	−	0.0414321i	−0.971255	+	0.238043i	$0.923494\pi$
$138$	0.263762	+	0.785448i	0.0224529	+	0.0668618i
$139$	10.1185	−	5.84192i	0.858240	−	0.495505i	−0.00518281	−	0.999987i	$-0.501650\pi$
$139$	10.1185	−	5.84192i	0.858240	−	0.495505i	0.863422	+	0.504482i	$0.168316\pi$
$140$	−1.56212	+	0.717702i	−0.132023	+	0.0606569i
$141$	−18.0392	+	3.34339i	−1.51917	+	0.281565i
$142$	9.90965	−	7.75969i	0.831599	−	0.651178i
$143$	−1.63742	+	1.63742i	−0.136928	+	0.136928i
$144$	−9.61507	−	7.17987i	−0.801255	−	0.598322i
$145$	−9.03279	−	1.02101i	−0.750132	−	0.0847900i
$146$	0.140755	−	1.15679i	0.0116490	−	0.0957366i
$147$	−10.7123	+	5.10950i	−0.883532	+	0.421425i
$148$	−9.35315	+	5.64775i	−0.768825	+	0.464242i
$149$	−9.04041	−	15.6584i	−0.740619	−	1.28279i	−0.952214	−	0.305432i	$-0.901199\pi$
$149$	−9.04041	−	15.6584i	−0.740619	−	1.28279i	0.211595	−	0.977357i	$-0.432134\pi$
$150$	12.0852	+	1.98669i	0.986756	+	0.162213i
$151$	9.47821	+	5.47225i	0.771326	+	0.445325i	0.833347	−	0.552750i	$-0.186421\pi$
$151$	9.47821	+	5.47225i	0.771326	+	0.445325i	−0.0620217	+	0.998075i	$0.519755\pi$
$152$	−3.57337	−	7.95575i	−0.289839	−	0.645297i
$153$	3.60125	−	2.61648i	0.291144	−	0.211530i
$154$	1.83026	−	0.779257i	0.147487	−	0.0627943i
$155$	−14.0103	−	10.3478i	−1.12534	−	0.831154i
$156$	1.20596	−	1.83067i	0.0965538	−	0.146571i
$157$	−3.43139	+	12.8061i	−0.273855	+	1.02204i	0.682750	+	0.730652i	$0.260784\pi$
$157$	−3.43139	+	12.8061i	−0.273855	+	1.02204i	−0.956605	+	0.291388i	$0.905883\pi$
$158$	15.5375	−	2.20093i	1.23609	−	0.175097i
$159$	6.35083	−	5.42414i	0.503654	−	0.430162i
$160$	10.5034	−	7.04829i	0.830367	−	0.557217i
$161$	0.130026			0.0102475
$162$	−4.36632	−	11.9556i	−0.343050	−	0.939317i
$163$	7.57483	+	7.57483i	0.593306	+	0.593306i	0.938523	−	0.345217i	$-0.112195\pi$
$163$	7.57483	+	7.57483i	0.593306	+	0.593306i	−0.345217	+	0.938523i	$0.612195\pi$
$164$	−2.13800	+	0.618112i	−0.166950	+	0.0482664i
$165$	−13.9141	−	2.69174i	−1.08321	−	0.209552i
$166$	−2.84871	−	2.14179i	−0.221103	−	0.166235i
$167$	−4.94596	+	18.4586i	−0.382730	+	1.42837i	0.458984	+	0.888444i	$0.348213\pi$
$167$	−4.94596	+	18.4586i	−0.382730	+	1.42837i	−0.841714	+	0.539923i	$0.818453\pi$
$168$	−1.54848	+	1.07172i	−0.119468	+	0.0826851i
$169$	−10.9115	−	6.29976i	−0.839347	−	0.484597i
$170$	1.34157	+	4.49631i	0.102893	+	0.344851i
$171$	1.44706	−	9.13657i	0.110660	−	0.698691i
$172$	−0.478171	−	24.3500i	−0.0364602	−	1.85667i
$173$	2.41645	+	9.01833i	0.183720	+	0.685651i	0.994901	+	0.100856i	$0.0321583\pi$
$173$	2.41645	+	9.01833i	0.183720	+	0.685651i	−0.811181	+	0.584795i	$0.801175\pi$
$174$	−9.93869	+	0.618773i	−0.753450	+	0.0469091i
$175$	0.899306	−	1.69864i	0.0679812	−	0.128405i
$176$	−12.3788	+	7.81042i	−0.933085	+	0.588732i
$177$	2.28656	−	1.09063i	0.171868	−	0.0819771i
$178$	12.5001	−	9.78815i	0.936924	−	0.733653i
$179$			0.413699i			0.0309213i	0.999880	+	0.0154607i	$0.00492148\pi$
$179$			0.413699i			0.0309213i	−0.999880	+	0.0154607i	$0.995079\pi$
$180$	13.4155	−	0.158335i	0.999930	−	0.0118016i
$181$			13.8870i			1.03221i	0.856525	+	0.516105i	$0.172619\pi$
$181$			13.8870i			1.03221i	−0.856525	+	0.516105i	$0.827381\pi$
$182$	−0.212098	−	0.270864i	−0.0157218	−	0.0200777i
$183$	20.9940	+	14.4288i	1.55192	+	1.06660i
$184$	−0.944456	+	0.152757i	−0.0696262	+	0.0112614i
$185$	4.46694	−	11.3697i	0.328416	−	0.835916i
$186$	−17.0845	−	8.49471i	−1.25269	−	0.622862i
$187$	−1.40527	−	5.24452i	−0.102763	−	0.383517i
$188$	−0.415930	−	21.1805i	−0.0303348	−	1.54475i
$189$	−1.99673	+	0.0522950i	−0.145241	+	0.00380390i
$190$	8.57840	+	4.63570i	0.622342	+	0.336309i
$191$	−17.6927	−	10.2149i	−1.28020	−	0.739124i	−0.303315	−	0.952890i	$-0.598093\pi$
$191$	−17.6927	−	10.2149i	−1.28020	−	0.739124i	−0.976885	+	0.213767i	$0.931427\pi$
$192$	9.98843	−	9.60371i	0.720853	−	0.693088i
$193$	3.82497	−	14.2750i	0.275328	−	1.02754i	−0.680294	−	0.732939i	$-0.738148\pi$
$193$	3.82497	−	14.2750i	0.275328	−	1.02754i	0.955622	−	0.294597i	$-0.0951854\pi$
$194$	15.9038	−	21.1531i	1.14183	−	1.51870i
$195$	0.173150	+	2.44482i	0.0123996	+	0.175077i
$196$	−3.80619	−	13.1653i	−0.271871	−	0.940379i
$197$	−15.0612	−	15.0612i	−1.07307	−	1.07307i	−0.997111	−	0.0759541i	$-0.975800\pi$
$197$	−15.0612	−	15.0612i	−1.07307	−	1.07307i	−0.0759541	−	0.997111i	$-0.524200\pi$
$198$	−15.5226	−	0.253966i	−1.10314	−	0.0180486i
$199$	18.2638			1.29469			0.647344	−	0.762198i	$-0.275880\pi$
$199$	18.2638			1.29469			0.647344	+	0.762198i	$0.275880\pi$
$200$	−4.53659	+	13.3947i	−0.320786	+	0.947152i
$201$	5.45094	+	1.93027i	0.384480	+	0.136151i
$202$	−0.418450	−	2.95404i	−0.0294421	−	0.207846i
$203$	−0.404461	+	1.50947i	−0.0283876	+	0.105944i
$204$	2.30351	+	4.59497i	0.161278	+	0.321713i
$205$	1.47828	−	2.00151i	0.103248	−	0.139792i
$206$	5.45081	+	12.8025i	0.379776	+	0.891989i
$207$	−0.927035	−	0.412739i	−0.0644334	−	0.0286874i
$208$	1.85881	+	1.71826i	0.128885	+	0.119140i
$209$	−9.77145	−	5.64155i	−0.675905	−	0.390234i
$210$	0.646651	−	2.00370i	0.0446232	−	0.138268i
$211$	−4.67589	−	8.09888i	−0.321901	−	0.557550i	0.658979	−	0.752161i	$-0.270989\pi$
$211$	−4.67589	−	8.09888i	−0.321901	−	0.557550i	−0.980880	+	0.194612i	$0.937655\pi$
$212$	4.98502	+	8.25562i	0.342373	+	0.566998i
$213$	−1.20942	+	15.3674i	−0.0828681	+	1.05296i
$214$	13.0844	+	1.59208i	0.894433	+	0.108832i
$215$	16.9697	+	21.2948i	1.15732	+	1.45230i
$216$	14.4420	−	2.72564i	0.982652	−	0.185456i
$217$	−2.11724	+	2.11724i	−0.143727	+	0.143727i
$218$	−15.4141	−	19.6848i	−1.04397	−	1.33323i
$219$	0.926908	+	1.08527i	0.0626346	+	0.0733355i
$220$	5.68384	−	15.3457i	0.383204	−	1.03460i
$221$	−0.813193	+	0.469497i	−0.0547013	+	0.0315818i
$222$	2.65354	−	13.1159i	0.178094	−	0.880281i
$223$	−1.91107	−	7.13223i	−0.127975	−	0.477609i	0.871953	−	0.489589i	$-0.162853\pi$
$223$	−1.91107	−	7.13223i	−0.127975	−	0.477609i	−0.999928	+	0.0119799i	$0.996187\pi$
$224$	−0.929723	−	1.96573i	−0.0621197	−	0.131341i
$225$	−11.8037	+	9.25600i	−0.786911	+	0.617067i
$226$	−13.3337	+	5.67699i	−0.886944	+	0.377628i
$227$	−0.848646	−	3.16719i	−0.0563266	−	0.210214i	0.932027	−	0.362389i	$-0.118039\pi$
$227$	−0.848646	−	3.16719i	−0.0563266	−	0.210214i	−0.988354	+	0.152175i	$0.951372\pi$
$228$	10.1369	+	3.36717i	0.671332	+	0.222996i
$229$	−4.14572	−	7.18059i	−0.273957	−	0.474507i	0.695915	−	0.718124i	$-0.254999\pi$
$229$	−4.14572	−	7.18059i	−0.273957	−	0.474507i	−0.969871	+	0.243618i	$0.921666\pi$
$230$	0.734764	−	0.777359i	0.0484489	−	0.0512575i
$231$	−0.813256	+	2.29658i	−0.0535083	+	0.151104i
$232$	1.16449	−	11.4393i	0.0764523	−	0.751028i
$233$	3.92237	+	3.92237i	0.256963	+	0.256963i	0.823818	−	0.566855i	$-0.191840\pi$
$233$	3.92237	+	3.92237i	0.256963	+	0.256963i	−0.566855	+	0.823818i	$0.691840\pi$
$234$	0.652378	+	2.60441i	0.0426473	+	0.170256i
$235$	14.7608	+	18.5230i	0.962891	+	1.20831i
$236$	0.812441	+	2.81017i	0.0528854	+	0.182926i
$237$	−10.8860	+	15.8392i	−0.707120	+	1.02887i
$238$	0.798662	−	0.113133i	0.0517695	−	0.00733333i
$239$	0.294424	+	0.509958i	0.0190447	+	0.0329864i	0.875391	−	0.483416i	$-0.160604\pi$
$239$	0.294424	+	0.509958i	0.0190447	+	0.0329864i	−0.856346	+	0.516403i	$0.827271\pi$
$240$	−2.34303	+	15.3137i	−0.151242	+	0.988497i
$241$	9.05572	−	15.6850i	0.583330	−	1.01036i	−0.411751	−	0.911296i	$-0.635083\pi$
$241$	9.05572	−	15.6850i	0.583330	−	1.01036i	0.995081	−	0.0990610i	$-0.0315839\pi$
$242$	−1.26262	+	3.13495i	−0.0811646	+	0.201522i
$243$	14.4019	+	5.96534i	0.923882	+	0.382677i
$244$	−20.3873	+	21.2040i	−1.30516	+	1.35745i
$245$	12.3249	+	9.10294i	0.787406	+	0.581565i
$246$	1.21355	−	2.44068i	0.0773733	−	0.155612i
$247$	−0.505039	+	1.88483i	−0.0321349	+	0.119929i
$248$	12.8914	−	17.8661i	0.818602	−	1.13450i
$249$	4.29195	−	0.795472i	0.271991	−	0.0504110i
$250$	−5.07341	−	14.9753i	−0.320871	−	0.947123i
$251$	−23.4558			−1.48052			−0.740258	−	0.672323i	$-0.765297\pi$
$251$	−23.4558			−1.48052			−0.740258	+	0.672323i	$0.765297\pi$
$252$	0.316001	−	2.28467i	0.0199062	−	0.143920i
$253$	−0.875217	+	0.875217i	−0.0550245	+	0.0550245i
$254$	−2.39217	+	19.6599i	−0.150098	+	1.23357i
$255$	−5.16737	−	2.51459i	−0.323593	−	0.157470i
$256$	9.06250	+	13.1860i	0.566406	+	0.824126i
$257$	9.22367	+	2.47147i	0.575357	+	0.154166i	0.534752	−	0.845009i	$-0.320405\pi$
$257$	9.22367	+	2.47147i	0.575357	+	0.154166i	0.0406044	+	0.999175i	$0.487072\pi$
$258$	22.3617	+	19.7404i	1.39218	+	1.22899i
$259$	−1.81866	−	1.05000i	−0.113006	−	0.0652439i
$260$	−2.81790	−	0.262597i	−0.174758	−	0.0162856i
$261$	7.67512	−	9.47804i	0.475078	−	0.586676i
$262$	−9.61152	+	23.8642i	−0.593801	+	1.47434i
$263$	−1.21850	−	4.54752i	−0.0751362	−	0.280412i	0.918128	−	0.396284i	$-0.129700\pi$
$263$	−1.21850	−	4.54752i	−0.0751362	−	0.280412i	−0.993264	+	0.115872i	$0.963034\pi$
$264$	3.20910	−	17.6368i	0.197506	−	1.08547i
$265$	−10.0355	−	3.94278i	−0.616477	−	0.242203i
$266$	1.00734	−	1.33983i	0.0617641	−	0.0821500i
$267$	−1.52558	+	19.3846i	−0.0933637	+	1.18632i
$268$	−3.22442	+	5.84706i	−0.196963	+	0.357166i
$269$	−24.2542			−1.47880			−0.739402	−	0.673264i	$-0.764892\pi$
$269$	−24.2542			−1.47880			−0.739402	+	0.673264i	$0.764892\pi$
$270$	−10.9707	+	12.2329i	−0.667654	+	0.744472i
$271$		−	23.6440i		−	1.43627i	−0.695903	−	0.718135i	$-0.744996\pi$
$271$		−	23.6440i		−	1.43627i	0.695903	−	0.718135i	$-0.255004\pi$
$272$	−5.66823	+	1.76003i	−0.343687	+	0.106718i
$273$	0.420043	+	0.0330575i	0.0254222	+	0.00200073i
$274$	−0.426680	+	0.567511i	−0.0257767	+	0.0342846i
$275$	5.38040	+	17.4870i	0.324450	+	1.05451i
$276$	0.644597	−	0.978515i	0.0388002	−	0.0588997i
$277$	−9.10684	+	2.44017i	−0.547177	+	0.146616i	−0.521809	−	0.853062i	$-0.674743\pi$
$277$	−9.10684	+	2.44017i	−0.547177	+	0.146616i	−0.0253684	+	0.999678i	$0.508076\pi$
$278$	−15.3270	−	6.17307i	−0.919253	−	0.370236i
$279$	21.8158	−	8.37436i	1.30608	−	0.501360i
$280$	2.16113	+	1.11361i	0.129153	+	0.0665506i
$281$	−4.56127	+	7.90036i	−0.272103	+	0.471296i	−0.969400	−	0.245486i	$-0.921052\pi$
$281$	−4.56127	+	7.90036i	−0.272103	+	0.471296i	0.697297	+	0.716782i	$0.254386\pi$
$282$	19.4510	+	17.1709i	1.15829	+	1.02251i
$283$	−1.43482	+	5.35483i	−0.0852914	+	0.318312i	−0.995369	−	0.0961257i	$-0.969355\pi$
$283$	−1.43482	+	5.35483i	−0.0852914	+	0.318312i	0.910078	+	0.414437i	$0.136022\pi$
$284$	−17.2803	−	4.26844i	−1.02540	−	0.253285i
$285$	−11.2882	+	3.89810i	−0.668654	+	0.230903i
$286$	3.25086	+	0.395556i	0.192227	+	0.0233897i
$287$	−0.302468	−	0.302468i	−0.0178541	−	0.0178541i
$288$	0.388764	+	16.9661i	0.0229081	+	0.999738i
$289$			14.7983i			0.870490i
$290$	6.73876	+	10.9479i	0.395714	+	0.642883i
$291$	5.90677	+	31.8698i	0.346261	+	1.86824i
$292$	−1.41077	+	0.851869i	−0.0825589	+	0.0498519i
$293$	−2.21540	−	0.593616i	−0.129425	−	0.0346794i	0.193525	−	0.981095i	$-0.438008\pi$
$293$	−2.21540	−	0.593616i	−0.129425	−	0.0346794i	−0.322950	+	0.946416i	$0.604675\pi$
$294$	15.0292	+	7.47279i	0.876519	+	0.435822i
$295$	−2.63077	−	1.94304i	−0.153169	−	0.113128i
$296$	14.4435	+	5.49018i	0.839512	+	0.319110i
$297$	13.0882	−	13.7922i	0.759452	−	0.800303i
$298$	−9.55287	+	23.7186i	−0.553383	+	1.37398i
$299$	0.185380	+	0.107029i	0.0107208	+	0.00618965i
$300$	−8.32491	−	15.1887i	−0.480639	−	0.876919i
$301$	4.05387	−	2.34050i	0.233661	−	0.134904i
$302$	−2.17082	−	15.3249i	−0.124917	−	0.881847i
$303$	3.01142	+	2.06968i	0.173001	+	0.118900i
$304$	−5.74286	+	10.9154i	−0.329376	+	0.626040i
$305$	3.69383	−	32.6791i	0.211508	−	1.87120i
$306$	−6.05326	−	1.72858i	−0.346042	−	0.0988164i
$307$	−2.62325	+	2.62325i	−0.149717	+	0.149717i	−0.777991	−	0.628275i	$-0.783761\pi$
$307$	−2.62325	+	2.62325i	−0.149717	+	0.149717i	0.628275	+	0.777991i	$0.283761\pi$
$308$	−2.46346	−	1.35850i	−0.140369	−	0.0774079i
$309$	−16.0643	−	5.68863i	−0.913864	−	0.323615i
$310$	0.693578	+	24.6221i	0.0393926	+	1.39844i
$311$	24.3724	−	14.0714i	1.38203	−	0.797918i	0.389634	−	0.920970i	$-0.372601\pi$
$311$	24.3724	−	14.0714i	1.38203	−	0.797918i	0.992400	+	0.123052i	$0.0392682\pi$
$312$	−3.08985	+	0.253358i	−0.174929	+	0.0143436i
$313$	−11.7758	+	3.15532i	−0.665608	+	0.178349i	−0.575775	−	0.817608i	$-0.695300\pi$
$313$	−11.7758	+	3.15532i	−0.665608	+	0.178349i	−0.0898322	+	0.995957i	$0.528633\pi$
$314$	17.2510	−	7.34483i	0.973530	−	0.414493i
$315$	1.27179	+	2.24321i	0.0716575	+	0.126391i
$316$	−15.9977	−	15.3815i	−0.899939	−	0.865274i
$317$	22.9439	−	6.14780i	1.28866	−	0.345295i	0.451507	−	0.892267i	$-0.350887\pi$
$317$	22.9439	−	6.14780i	1.28866	−	0.345295i	0.837150	+	0.546973i	$0.184220\pi$
$318$	−11.5768	−	2.34217i	−0.649196	−	0.131342i
$319$	−7.43790	−	12.8828i	−0.416443	−	0.721300i
$320$	−17.0059	−	5.54983i	−0.950657	−	0.310245i
$321$	−12.2754	+	10.4842i	−0.685148	+	0.585173i
$322$	−0.113369	−	0.144780i	−0.00631779	−	0.00806825i
$323$	−3.23521	−	3.23521i	−0.180012	−	0.180012i
$324$	−9.50513	+	15.2857i	−0.528063	+	0.849205i
$325$	2.68036	−	1.68152i	0.148680	−	0.0932741i
$326$	1.82988	−	15.0387i	0.101347	−	0.832918i
$327$	30.5264	+	2.40243i	1.68811	+	0.132855i
$328$	2.55235	+	1.84166i	0.140930	+	0.101689i
$329$	3.52621	−	2.03586i	0.194406	−	0.112240i
$330$	9.13440	+	17.8397i	0.502832	+	0.982045i
$331$	4.95679	−	8.58541i	0.272450	−	0.471897i	−0.697039	−	0.717033i	$-0.745499\pi$
$331$	4.95679	−	8.58541i	0.272450	−	0.471897i	0.969489	+	0.245137i	$0.0788328\pi$
$332$	0.0989596	+	5.03935i	0.00543112	+	0.276570i
$333$	9.63330	+	13.2590i	0.527901	+	0.726589i
$334$	24.8653	−	10.5867i	1.36057	−	0.579280i
$335$	−1.11002	−	7.38235i	−0.0606470	−	0.403341i
$336$	2.54343	+	0.789752i	0.138755	+	0.0430845i
$337$	26.1519	+	7.00738i	1.42459	+	0.381717i	0.887108	−	0.461562i	$-0.152711\pi$
$337$	26.1519	+	7.00738i	1.42459	+	0.381717i	0.537477	+	0.843278i	$0.319377\pi$
$338$	2.49909	+	17.6423i	0.135933	+	0.959614i
$339$	5.92468	−	16.7309i	0.321784	−	0.908695i
$340$	3.83679	−	5.41408i	0.208079	−	0.293620i
$341$		−	28.5026i		−	1.54350i
$342$	−11.4349	+	6.35484i	−0.618330	+	0.343631i
$343$	3.76523	−	3.76523i	0.203303	−	0.203303i
$344$	−26.6960	+	21.7630i	−1.43935	+	1.17338i
$345$	0.0925508	+	1.30678i	0.00498277	+	0.0703548i
$346$	7.93471	−	10.5536i	0.426573	−	0.567368i
$347$	26.6840	+	7.14995i	1.43247	+	0.383829i	0.889890	−	0.456175i	$-0.150781\pi$
$347$	26.6840	+	7.14995i	1.43247	+	0.383829i	0.542580	+	0.840004i	$0.317447\pi$
$348$	9.35445	+	10.5269i	0.501451	+	0.564300i
$349$	−3.90044	+	6.75575i	−0.208786	+	0.361627i	−0.951332	−	0.308167i	$-0.900284\pi$
$349$	−3.90044	+	6.75575i	−0.208786	+	0.361627i	0.742547	+	0.669794i	$0.233618\pi$
$350$	−2.67548	+	0.479686i	−0.143010	+	0.0256403i
$351$	−2.88981	−	1.56902i	−0.154247	−	0.0837481i
$352$	19.4896	+	6.97349i	1.03880	+	0.371688i
$353$	−4.71046	+	1.26216i	−0.250712	+	0.0671782i	−0.381986	−	0.924168i	$-0.624760\pi$
$353$	−4.71046	+	1.26216i	−0.250712	+	0.0671782i	0.131274	+	0.991346i	$0.458093\pi$
$354$	−3.20801	−	1.59508i	−0.170504	−	0.0847777i
$355$	18.2430	−	7.95160i	0.968237	−	0.422027i
$356$	−21.7975	−	5.38425i	−1.15527	−	0.285365i
$357$	−0.559564	+	0.814173i	−0.0296153	+	0.0430906i
$358$	0.460640	−	0.360701i	0.0243456	−	0.0190636i
$359$	−4.27825			−0.225797			−0.112899	−	0.993607i	$-0.536014\pi$
$359$	−4.27825			−0.225797			−0.112899	+	0.993607i	$0.536014\pi$
$360$	−11.8731	−	14.7996i	−0.625770	−	0.780008i
$361$	9.49213			0.499586
$362$	15.4626	−	12.1079i	0.812699	−	0.636379i
$363$	−1.78199	−	3.73600i	−0.0935300	−	0.196089i
$364$	−0.116671	+	0.472328i	−0.00611520	+	0.0247567i
$365$	0.673764	−	1.71493i	0.0352664	−	0.0897634i
$366$	−2.23861	−	35.9565i	−0.117014	−	1.87947i
$367$	−10.6770	+	2.86090i	−0.557337	+	0.149338i	−0.526483	−	0.850186i	$-0.676489\pi$
$367$	−10.6770	+	2.86090i	−0.557337	+	0.149338i	−0.0308543	+	0.999524i	$0.509823\pi$
$368$	0.993553	+	0.918431i	0.0517925	+	0.0478765i
$369$	1.19636	+	3.11660i	0.0622800	+	0.162244i
$370$	−16.5544	+	4.93935i	−0.860624	+	0.256785i
$371$	−0.926790	+	1.60525i	−0.0481165	+	0.0833403i
$372$	5.43723	+	26.4294i	0.281907	+	1.37030i
$373$	−26.9400	−	7.21855i	−1.39490	−	0.373762i	−0.518389	−	0.855145i	$-0.673468\pi$
$373$	−26.9400	−	7.21855i	−1.39490	−	0.373762i	−0.876511	+	0.481383i	$0.840135\pi$
$374$	−4.61435	+	6.13737i	−0.238602	+	0.317356i
$375$	17.7117	+	7.82910i	0.914630	+	0.404293i
$376$	−23.2211	+	18.9303i	−1.19754	+	0.976253i
$377$	−1.81914	+	1.81914i	−0.0936905	+	0.0936905i
$378$	1.79916	+	2.17769i	0.0925389	+	0.112009i
$379$		−	14.9920i		−	0.770088i	−0.922898	−	0.385044i	$-0.874186\pi$
$379$		−	14.9920i		−	0.770088i	0.922898	−	0.385044i	$-0.125814\pi$
$380$	−2.31774	−	13.5936i	−0.118898	−	0.697336i
$381$	−15.7530	−	18.4444i	−0.807052	−	0.944933i
$382$	4.05221	+	28.6065i	0.207329	+	1.46364i
$383$	17.4658	+	4.67995i	0.892460	+	0.239134i	0.675775	−	0.737108i	$-0.263809\pi$
$383$	17.4658	+	4.67995i	0.892460	+	0.239134i	0.216685	+	0.976242i	$0.430476\pi$
$384$	−19.4022	−	2.74837i	−0.990116	−	0.140252i
$385$	3.11031	−	0.467671i	0.158516	−	0.0238347i
$386$	−19.2297	+	8.18728i	−0.978764	+	0.416721i
$387$	−36.3319	+	3.81875i	−1.84686	+	0.194118i
$388$	−37.4196	+	0.734824i	−1.89969	+	0.0373050i
$389$	−9.08299	+	15.7322i	−0.460526	+	0.797655i	−0.998987	−	0.0449958i	$-0.985673\pi$
$389$	−9.08299	+	15.7322i	−0.460526	+	0.797655i	0.538461	+	0.842650i	$0.319006\pi$
$390$	2.57125	−	2.32441i	0.130200	−	0.117701i
$391$	−0.434660	+	0.250951i	−0.0219817	+	0.0126912i
$392$	−11.3405	+	15.7168i	−0.572783	+	0.793818i
$393$	−13.5651	−	28.4397i	−0.684267	−	1.43459i
$394$	−3.63838	+	29.9018i	−0.183299	+	1.50643i
$395$	24.6551	+	2.78686i	1.24053	+	0.140222i
$396$	13.2513	+	17.5053i	0.665901	+	0.879675i
$397$	−8.38080	−	8.38080i	−0.420620	−	0.420620i	0.464797	−	0.885417i	$-0.346127\pi$
$397$	−8.38080	−	8.38080i	−0.420620	−	0.420620i	−0.885417	+	0.464797i	$0.846127\pi$
$398$	−15.9241	−	20.3361i	−0.798202	−	1.01936i
$399$	0.374132	+	2.01862i	0.0187300	+	0.101057i
$400$	18.8700	−	6.62744i	0.943500	−	0.331372i
$401$	13.5793	+	23.5200i	0.678117	+	1.17453i	0.975547	+	0.219790i	$0.0705371\pi$
$401$	13.5793	+	23.5200i	0.678117	+	1.17453i	−0.297430	+	0.954744i	$0.596130\pi$
$402$	−2.60334	−	7.75242i	−0.129843	−	0.386656i
$403$	−4.76134	+	1.27580i	−0.237179	+	0.0635520i
$404$	−2.92438	+	3.04154i	−0.145493	+	0.151322i
$405$	−1.94682	−	20.0302i	−0.0967381	−	0.995310i
$406$	2.03339	−	0.865740i	0.100915	−	0.0429660i
$407$	19.3092	−	5.17388i	0.957120	−	0.256460i
$408$	3.10793	−	6.57120i	0.153866	−	0.325323i
$409$	2.83036	−	1.63411i	0.139952	−	0.0808015i	−0.428389	−	0.903594i	$-0.640919\pi$
$409$	2.83036	−	1.63411i	0.139952	−	0.0808015i	0.568341	+	0.822793i	$0.307585\pi$
$410$	−3.51752	+	0.0990845i	−0.173718	+	0.00489343i
$411$	−0.158471	−	0.855028i	−0.00781682	−	0.0421754i
$412$	9.50257	−	17.2316i	0.468158	−	0.848942i
$413$	−0.397562	+	0.397562i	−0.0195627	+	0.0195627i
$414$	0.348704	+	1.39209i	0.0171378	+	0.0684173i
$415$	−3.51195	−	4.40706i	−0.172395	−	0.216334i
$416$	0.292548	−	3.56786i	0.0143434	−	0.174929i
$417$	18.2656	−	8.71228i	0.894470	−	0.426642i
$418$	2.23798	+	15.7990i	0.109463	+	0.772754i
$419$	−9.39719	+	5.42547i	−0.459083	+	0.265052i	−0.711658	−	0.702526i	$-0.752056\pi$
$419$	−9.39719	+	5.42547i	−0.459083	+	0.265052i	0.252576	+	0.967577i	$0.418722\pi$
$420$	−2.79486	+	1.02698i	−0.136375	+	0.0501117i
$421$	8.23619	+	4.75517i	0.401407	+	0.231753i	0.687091	−	0.726571i	$-0.258887\pi$
$421$	8.23619	+	4.75517i	0.401407	+	0.231753i	−0.285684	+	0.958324i	$0.592221\pi$
$422$	−4.94095	+	12.2678i	−0.240522	+	0.597186i
$423$	−31.6028	+	3.32168i	−1.53658	+	0.161506i
$424$	4.84595	−	12.7487i	0.235340	−	0.619130i
$425$	0.272127	+	7.41401i	0.0132001	+	0.359632i
$426$	18.1656	−	12.0521i	0.880126	−	0.583926i
$427$	−5.46099	−	1.46327i	−0.264276	−	0.0708125i
$428$	−9.63548	−	15.9572i	−0.465749	−	0.771320i
$429$	−3.04986	+	2.60483i	−0.147249	+	0.125763i
$430$	8.91534	−	37.4619i	0.429936	−	1.80657i
$431$		−	1.84170i		−	0.0887117i	−0.999016	−	0.0443558i	$-0.985876\pi$
$431$		−	1.84170i		−	0.0887117i	0.999016	−	0.0443558i	$-0.0141235\pi$
$432$	−15.6268	−	13.7042i	−0.751843	−	0.659343i
$433$	17.7326	+	17.7326i	0.852173	+	0.852173i	0.990401	−	0.138227i	$-0.0441405\pi$
$433$	17.7326	+	17.7326i	0.852173	+	0.852173i	−0.138227	+	0.990401i	$0.544140\pi$
$434$	4.20347	+	0.511468i	0.201773	+	0.0245512i
$435$	−15.4583	−	2.99047i	−0.741168	−	0.143382i
$436$	−8.47896	+	34.3261i	−0.406069	+	1.64392i
$437$	−0.269949	+	1.00746i	−0.0129134	+	0.0481935i
$438$	0.400243	−	1.97831i	0.0191243	−	0.0945275i
$439$	−1.54015	+	2.66761i	−0.0735072	+	0.127318i	−0.900436	−	0.434988i	$-0.856753\pi$
$439$	−1.54015	+	2.66761i	−0.0735072	+	0.127318i	0.826929	+	0.562306i	$0.190086\pi$
$440$	−22.0426	+	7.05101i	−1.05084	+	0.336144i
$441$	−19.1913	+	7.36692i	−0.913872	+	0.350806i
$442$	1.23178	+	0.496111i	0.0585900	+	0.0235976i
$443$	33.9803	−	9.10499i	1.61445	−	0.432591i	0.665087	−	0.746766i	$-0.268395\pi$
$443$	33.9803	−	9.10499i	1.61445	−	0.432591i	0.949365	+	0.314175i	$0.101728\pi$
$444$	−16.9177	+	8.48101i	−0.802878	+	0.402491i
$445$	23.0119	−	10.0302i	1.09087	−	0.475479i
$446$	−6.27524	+	8.34645i	−0.297141	+	0.395216i
$447$	−13.4823	−	28.2661i	−0.637691	−	1.33694i
$448$	−1.37816	+	2.74912i	−0.0651119	+	0.129884i
$449$			17.1121i			0.807568i	0.914854	+	0.403784i	$0.132305\pi$
$449$			17.1121i			0.807568i	−0.914854	+	0.403784i	$0.867695\pi$
$450$	20.5978	+	5.07274i	0.970987	+	0.239131i
$451$	4.07188			0.191737
$452$	17.9467	+	9.89688i	0.844140	+	0.465510i
$453$	15.6225	+	10.7370i	0.734009	+	0.504469i
$454$	−2.78663	+	3.70638i	−0.130783	+	0.173949i
$455$	−0.217344	−	0.498641i	−0.0101892	−	0.0233767i
$456$	−5.08905	−	14.2229i	−0.238317	−	0.666048i
$457$	−0.818653	−	3.05526i	−0.0382950	−	0.142919i	0.944131	−	0.329569i	$-0.106904\pi$
$457$	−0.818653	−	3.05526i	−0.0382950	−	0.142919i	−0.982426	+	0.186650i	$0.940237\pi$
$458$	−4.38072	+	10.8768i	−0.204698	+	0.508240i
$459$	6.57388	−	4.02852i	0.306842	−	0.188035i
$460$	−1.50620	−	0.140361i	−0.0702268	−	0.00654438i
$461$	8.08204	+	4.66617i	0.376418	+	0.217325i	0.676259	−	0.736664i	$-0.263600\pi$
$461$	8.08204	+	4.66617i	0.376418	+	0.217325i	−0.299841	+	0.953989i	$0.596934\pi$
$462$	3.26623	−	1.09683i	0.151959	−	0.0510293i
$463$	−20.0360	−	5.36864i	−0.931154	−	0.249502i	−0.238807	−	0.971067i	$-0.576756\pi$
$463$	−20.0360	−	5.36864i	−0.931154	−	0.249502i	−0.692347	+	0.721565i	$0.743423\pi$
$464$	−13.7526	+	8.67723i	−0.638448	+	0.402830i
$465$	−22.7856	−	19.7715i	−1.05666	−	0.916883i
$466$	0.947539	−	7.78730i	0.0438939	−	0.360740i
$467$	4.06280	−	4.06280i	0.188004	−	0.188004i	−0.606829	−	0.794833i	$-0.707559\pi$
$467$	4.06280	−	4.06280i	0.188004	−	0.188004i	0.794833	+	0.606829i	$0.207559\pi$
$468$	2.33111	−	2.99716i	0.107756	−	0.138544i
$469$	−1.28337			−0.0592604
$470$	7.75489	−	32.5858i	0.357706	−	1.50307i
$471$	−7.66529	+	21.6462i	−0.353198	+	0.997404i
$472$	2.42066	−	3.35479i	0.111420	−	0.154417i
$473$	−11.5328	+	43.0411i	−0.530280	+	1.97903i
$474$	27.1278	−	1.68895i	1.24602	−	0.0775761i
$475$	11.2943	+	10.4945i	0.518218	+	0.481523i
$476$	−0.822316	−	0.790642i	−0.0376908	−	0.0362390i
$477$	11.7032	−	8.50289i	0.535851	−	0.389321i
$478$	0.311114	−	0.772459i	0.0142300	−	0.0353315i
$479$	−9.93903	+	17.2149i	−0.454126	+	0.786569i	−0.998637	−	0.0521843i	$-0.983382\pi$
$479$	−9.93903	+	17.2149i	−0.454126	+	0.786569i	0.544512	+	0.838753i	$0.316715\pi$
$480$	19.0942	−	10.7430i	0.871525	−	0.490350i
$481$	−1.72858	−	2.99400i	−0.0788167	−	0.136515i
$482$	−25.3603	+	3.59237i	−1.15513	+	0.163628i
$483$	0.224518	+	0.0176696i	0.0102159	+	0.000803995i
$484$	4.59152	−	1.32745i	0.208706	−	0.0603384i
$485$	32.7246	−	26.0780i	1.48595	−	1.18414i
$486$	−5.91470	−	21.2371i	−0.268296	−	0.963336i
$487$	7.30644	+	7.30644i	0.331086	+	0.331086i	0.852999	−	0.521913i	$-0.174781\pi$
$487$	7.30644	+	7.30644i	0.331086	+	0.331086i	−0.521913	+	0.852999i	$0.674781\pi$
$488$	41.3855	+	4.21291i	1.87343	+	0.190709i
$489$	12.0502	+	14.1089i	0.544928	+	0.638027i
$490$	−0.610140	−	21.6601i	−0.0275633	−	0.978503i
$491$	−6.64647	−	11.5120i	−0.299951	−	0.519531i	0.676173	−	0.736743i	$-0.263637\pi$
$491$	−6.64647	−	11.5120i	−0.299951	−	0.519531i	−0.976124	+	0.217212i	$0.930304\pi$
$492$	−3.77570	+	0.776763i	−0.170222	+	0.0350192i
$493$	−1.56122	−	5.82657i	−0.0703140	−	0.262415i
$494$	2.53904	−	1.08103i	0.114237	−	0.0486377i
$495$	−23.6598	−	6.53868i	−1.06343	−	0.293892i
$496$	−31.1332	+	1.22322i	−1.39792	+	0.0549242i
$497$	−0.885451	−	3.30455i	−0.0397179	−	0.148229i
$498$	−4.62785	−	4.08537i	−0.207379	−	0.183070i
$499$	−2.04939	+	1.18322i	−0.0917435	+	0.0529681i	−0.545170	−	0.838326i	$-0.683535\pi$
$499$	−2.04939	+	1.18322i	−0.0917435	+	0.0529681i	0.453426	+	0.891294i	$0.350202\pi$
$500$	−12.2510	+	18.7059i	−0.547883	+	0.836555i
$501$	−11.0486	+	31.2005i	−0.493617	+	1.39394i
$502$	20.4509	+	26.1172i	0.912769	+	1.16567i
$503$	−6.76536	+	6.76536i	−0.301653	+	0.301653i	−0.841660	−	0.540008i	$-0.818421\pi$
$503$	−6.76536	+	6.76536i	−0.301653	+	0.301653i	0.540008	+	0.841660i	$0.318421\pi$
$504$	−2.81942	+	1.64013i	−0.125587	+	0.0730570i
$505$	0.529848	−	4.68753i	0.0235779	−	0.208592i
$506$	1.73762	+	0.211429i	0.0772466	+	0.00939917i
$507$	−17.9849	−	12.3607i	−0.798739	−	0.548957i
$508$	23.9763	−	14.4777i	1.06378	−	0.642345i
$509$	7.72338	+	13.3773i	0.342333	+	0.592938i	0.984866	−	0.173320i	$-0.0554496\pi$
$509$	7.72338	+	13.3773i	0.342333	+	0.592938i	−0.642533	+	0.766258i	$0.722116\pi$
$510$	1.70548	+	7.94614i	0.0755199	+	0.351861i
$511$	−0.274314	−	0.158375i	−0.0121349	−	0.00700611i
$512$	6.78066	−	21.5876i	0.299666	−	0.954044i
$513$	3.74025	−	15.5796i	0.165136	−	0.687855i
$514$	−5.29014	−	12.4251i	−0.233338	−	0.548047i
$515$	3.27131	+	21.7562i	0.144151	+	0.958694i
$516$	2.48332	−	42.1104i	0.109322	−	1.85381i
$517$	−10.0317	+	37.4387i	−0.441193	+	1.64655i
$518$	0.416531	+	2.94050i	0.0183013	+	0.129198i
$519$	2.94700	+	15.9004i	0.129359	+	0.697952i
$520$	2.16451	+	3.36658i	0.0949199	+	0.147635i
$521$	20.2837			0.888643			0.444321	−	0.895867i	$-0.353445\pi$
$521$	20.2837			0.888643			0.444321	+	0.895867i	$0.353445\pi$
$522$	−17.2453	−	0.282152i	−0.754808	−	0.0123495i
$523$	−18.5283	−	18.5283i	−0.810188	−	0.810188i	0.174474	−	0.984662i	$-0.444177\pi$
$523$	−18.5283	−	18.5283i	−0.810188	−	0.810188i	−0.984662	+	0.174474i	$0.944177\pi$
$524$	34.9522	−	10.1050i	1.52689	−	0.441437i
$525$	1.78368	−	2.81086i	0.0778460	−	0.122676i
$526$	−4.00110	+	5.32171i	−0.174456	+	0.232037i
$527$	2.99137	−	11.1639i	0.130306	−	0.486308i
$528$	−22.4359	+	11.8042i	−0.976399	+	0.513710i
$529$	−19.8195	−	11.4428i	−0.861717	−	0.497513i
$530$	4.35975	+	14.6119i	0.189375	+	0.634699i
$531$	4.09643	−	1.57249i	0.177770	−	0.0682401i
$532$	−2.37014	+	0.0465434i	−0.102759	+	0.00201791i
$533$	−0.182260	−	0.680204i	−0.00789457	−	0.0294629i
$534$	22.9143	−	15.2026i	0.991597	−	0.657882i
$535$	19.3975	+	7.62094i	0.838628	+	0.329482i
$536$	9.32184	−	1.50772i	0.402642	−	0.0651236i
$537$	−0.0562187	+	0.714340i	−0.00242602	+	0.0308260i
$538$	21.1470	+	27.0062i	0.911713	+	1.16432i
$539$			25.0737i			1.08000i
$540$	23.1862	+	1.54967i	0.997774	+	0.0666870i
$541$		−	24.9614i		−	1.07317i	−0.843845	−	0.536587i	$-0.819713\pi$
$541$		−	24.9614i		−	1.07317i	0.843845	−	0.536587i	$-0.180287\pi$
$542$	−26.3268	+	20.6150i	−1.13083	+	0.885491i
$543$	−1.88714	+	23.9788i	−0.0809847	+	1.02903i
$544$	6.90182	+	4.77682i	0.295913	+	0.204805i
$545$	−15.7953	−	36.2385i	−0.676598	−	1.55229i
$546$	−0.329424	−	0.496526i	−0.0140980	−	0.0212493i
$547$	−9.33735	−	34.8475i	−0.399236	−	1.48997i	−0.814444	−	0.580243i	$-0.802958\pi$
$547$	−9.33735	−	34.8475i	−0.399236	−	1.48997i	0.415207	−	0.909727i	$-0.363709\pi$
$548$	1.00392	−	0.0197144i	0.0428854	−	0.000842158i
$549$	34.2899	+	27.7672i	1.46346	+	1.18508i
$550$	14.7801	−	21.2377i	0.630224	−	0.905578i
$551$	−10.8559	−	6.26766i	−0.462477	−	0.267011i
$552$	−1.65156	+	0.135423i	−0.0702951	+	0.00576397i
$553$	1.10398	−	4.12012i	0.0469461	−	0.175205i
$554$	10.6572	+	8.01259i	0.452782	+	0.340422i
$555$	9.25818	−	19.0251i	0.392988	−	0.807572i
$556$	6.48999	+	22.4483i	0.275237	+	0.952021i
$557$	−2.38296	−	2.38296i	−0.100969	−	0.100969i	0.654818	−	0.755787i	$-0.272745\pi$
$557$	−2.38296	−	2.38296i	−0.100969	−	0.100969i	−0.755787	+	0.654818i	$0.772745\pi$
$558$	−28.3456	−	16.9896i	−1.19996	−	0.719225i
$559$	7.70620			0.325938
$560$	−0.644315	−	3.37729i	−0.0272273	−	0.142717i
$561$	−1.71380	−	9.24674i	−0.0723565	−	0.390398i
$562$	12.7737	−	1.80944i	0.538826	−	0.0763266i
$563$	−5.96626	+	22.2664i	−0.251448	+	0.938416i	0.718584	+	0.695440i	$0.244790\pi$
$563$	−5.96626	+	22.2664i	−0.251448	+	0.938416i	−0.970032	+	0.242977i	$0.921876\pi$
$564$	2.16009	−	36.6292i	0.0909560	−	1.54237i
$565$	−22.6590	+	3.40705i	−0.953272	+	0.143336i
$566$	7.21343	−	3.07121i	0.303203	−	0.129093i
$567$	−3.45488	−	0.181043i	−0.145092	−	0.00760308i
$568$	10.3138	+	22.9626i	0.432757	+	0.963490i
$569$	23.3887	+	13.5035i	0.980507	+	0.566096i	0.902423	−	0.430851i	$-0.141786\pi$
$569$	23.3887	+	13.5035i	0.980507	+	0.566096i	0.0780839	+	0.996947i	$0.475120\pi$
$570$	14.1825	+	9.17027i	0.594038	+	0.384100i
$571$	−11.6708	−	20.2144i	−0.488406	−	0.845944i	0.511505	−	0.859280i	$-0.329088\pi$
$571$	−11.6708	−	20.2144i	−0.488406	−	0.845944i	−0.999911	+	0.0133360i	$0.995755\pi$
$572$	−2.39396	−	3.96460i	−0.100096	−	0.165768i
$573$	−29.1621	−	20.0425i	−1.21826	−	0.837287i
$574$	−0.0730682	+	0.600507i	−0.00304981	+	0.0250647i
$575$	1.43268	−	0.898793i	0.0597470	−	0.0374823i
$576$	18.5522	−	15.2255i	0.773009	−	0.634395i
$577$	−5.60482	+	5.60482i	−0.233332	+	0.233332i	−0.814082	−	0.580750i	$-0.802759\pi$
$577$	−5.60482	+	5.60482i	−0.233332	+	0.233332i	0.580750	+	0.814082i	$0.302759\pi$
$578$	16.4774	−	12.9026i	0.685371	−	0.536675i
$579$	8.54449	−	24.1290i	0.355097	−	1.00277i
$580$	6.31464	−	17.0488i	0.262201	−	0.707911i
$581$	−0.838968	+	0.484378i	−0.0348062	+	0.0200954i
$582$	30.3359	−	34.3640i	1.25746	−	1.42444i
$583$	−4.56676	−	17.0434i	−0.189136	−	0.705864i
$584$	2.17856	+	0.828103i	0.0901496	+	0.0342671i
$585$	−0.0332521	+	4.24503i	−0.00137480	+	0.175510i
$586$	1.27062	+	2.98434i	0.0524889	+	0.123282i
$587$	−3.19249	−	11.9145i	−0.131768	−	0.491765i	0.868222	−	0.496176i	$-0.165263\pi$
$587$	−3.19249	−	11.9145i	−0.131768	−	0.491765i	−0.999990	+	0.00441044i	$0.998596\pi$
$588$	−4.78313	−	23.2499i	−0.197253	−	0.958811i
$589$	−12.0091	−	20.8003i	−0.494825	−	0.857063i
$590$	0.130236	+	4.62339i	0.00536172	+	0.190342i
$591$	−23.9596	−	28.0530i	−0.985567	−	1.15395i
$592$	−6.48005	−	20.8692i	−0.266329	−	0.857719i
$593$	14.4169	+	14.4169i	0.592032	+	0.592032i	0.938180	−	0.346148i	$-0.112510\pi$
$593$	14.4169	+	14.4169i	0.592032	+	0.592032i	−0.346148	+	0.938180i	$0.612510\pi$
$594$	−26.7686	−	2.54794i	−1.09833	−	0.104543i
$595$	1.26733	+	0.143251i	0.0519555	+	0.00587271i
$596$	34.7390	−	10.0433i	1.42296	−	0.411390i
$597$	31.5363	+	2.48192i	1.29070	+	0.101578i
$598$	−0.0424580	−	0.299732i	−0.00173624	−	0.0122569i
$599$	−1.17864	−	2.04147i	−0.0481581	−	0.0834122i	0.840942	−	0.541126i	$-0.182002\pi$
$599$	−1.17864	−	2.04147i	−0.0481581	−	0.0834122i	−0.889100	+	0.457714i	$0.848668\pi$
$600$	−9.65364	+	22.5124i	−0.394108	+	0.919064i
$601$	19.8418	−	34.3670i	0.809364	−	1.40186i	−0.103942	−	0.994583i	$-0.533145\pi$
$601$	19.8418	−	34.3670i	0.809364	−	1.40186i	0.913305	−	0.407276i	$-0.133521\pi$
$602$	−6.14061	−	2.47318i	−0.250273	−	0.100799i
$603$	9.14990	+	4.07377i	0.372613	+	0.165897i
$604$	−15.1710	+	15.7788i	−0.617298	+	0.642028i
$605$	−3.17473	+	4.29841i	−0.129071	+	0.174755i
$606$	−0.321110	−	5.15765i	−0.0130442	−	0.209515i
$607$	−2.35731	+	8.79761i	−0.0956804	+	0.357084i	−0.997122	−	0.0758172i	$-0.975843\pi$
$607$	−2.35731	+	8.79761i	−0.0956804	+	0.357084i	0.901441	+	0.432901i	$0.142510\pi$
$608$	17.1610	−	3.12255i	0.695972	−	0.126636i
$609$	−0.903513	+	2.55145i	−0.0366122	+	0.103390i
$610$	−39.6076	+	24.3797i	−1.60367	+	0.987104i
$611$	6.70314			0.271180
$612$	3.35307	+	8.24723i	0.135540	+	0.333374i
$613$	7.65083	−	7.65083i	0.309014	−	0.309014i	−0.535513	−	0.844527i	$-0.679882\pi$
$613$	7.65083	−	7.65083i	0.309014	−	0.309014i	0.844527	+	0.535513i	$0.179882\pi$
$614$	5.20808	+	0.633706i	0.210181	+	0.0255743i
$615$	2.82456	−	3.25514i	0.113897	−	0.131260i
$616$	0.635228	+	3.92745i	0.0255941	+	0.158241i
$617$	−36.1615	−	9.68945i	−1.45581	−	0.390083i	−0.557769	−	0.829997i	$-0.688342\pi$
$617$	−36.1615	−	9.68945i	−1.45581	−	0.390083i	−0.898040	+	0.439914i	$0.855009\pi$
$618$	7.67221	+	22.8469i	0.308622	+	0.919036i
$619$	13.2437	+	7.64626i	0.532310	+	0.307329i	0.741957	−	0.670448i	$-0.233898\pi$
$619$	13.2437	+	7.64626i	0.532310	+	0.307329i	−0.209647	+	0.977777i	$0.567231\pi$
$620$	26.8112	−	22.2401i	1.07676	−	0.893185i
$621$	−1.54463	−	0.838659i	−0.0619840	−	0.0336542i
$622$	−36.9182	−	14.8691i	−1.48028	−	0.596196i
$623$	−1.11692	−	4.16839i	−0.0447483	−	0.167003i
$624$	2.97612	+	3.21954i	0.119140	+	0.128885i
$625$	−1.83275	−	24.9327i	−0.0733102	−	0.997309i
$626$	13.7806	+	10.3608i	0.550782	+	0.414103i
$627$	−16.1058	−	11.0692i	−0.643205	−	0.442061i
$628$	−23.2192	−	12.8045i	−0.926547	−	0.510954i
$629$	8.10604			0.323209
$630$	1.38887	−	3.37193i	0.0553338	−	0.134341i
$631$			24.3452i			0.969165i	0.874746	+	0.484583i	$0.161028\pi$
$631$			24.3452i			0.969165i	−0.874746	+	0.484583i	$0.838972\pi$
$632$	−3.17848	+	31.2238i	−0.126433	+	1.24202i
$633$	−6.97333	−	14.6198i	−0.277165	−	0.581087i
$634$	−26.8500	−	20.1870i	−1.06635	−	0.801729i
$635$	−11.4508	+	29.1456i	−0.454410	+	1.15661i
$636$	7.48582	+	14.9325i	0.296832	+	0.592112i
$637$	4.18855	−	1.12232i	0.165956	−	0.0444679i
$638$	−7.85953	+	19.5143i	−0.311162	+	0.772578i
$639$	−4.17664	+	26.3708i	−0.165225	+	1.04321i
$640$	8.64774	+	23.7743i	0.341832	+	0.939761i
$641$	−18.3130	+	31.7190i	−0.723318	+	1.25282i	0.236344	+	0.971669i	$0.424051\pi$
$641$	−18.3130	+	31.7190i	−0.723318	+	1.25282i	−0.959662	+	0.281155i	$0.909283\pi$
$642$	22.3767	+	4.52714i	0.883138	+	0.178672i
$643$	−8.25532	+	30.8093i	−0.325558	+	1.21500i	0.588192	+	0.808722i	$0.299840\pi$
$643$	−8.25532	+	30.8093i	−0.325558	+	1.21500i	−0.913750	+	0.406278i	$0.866827\pi$
$644$	−0.0623617	+	0.252464i	−0.00245740	+	0.00994849i
$645$	26.4079	+	39.0761i	1.03981	+	1.53862i
$646$	−0.781539	+	6.42304i	−0.0307492	+	0.252711i
$647$	10.0137	+	10.0137i	0.393680	+	0.393680i	0.875997	−	0.482317i	$-0.160205\pi$
$647$	10.0137	+	10.0137i	0.393680	+	0.393680i	−0.482317	+	0.875997i	$0.660205\pi$
$648$	25.3075	−	2.74384i	0.994174	−	0.107788i
$649$		−	5.35205i		−	0.210086i
$650$	−4.20930	−	1.51838i	−0.165102	−	0.0595559i
$651$	−3.94358	+	3.36814i	−0.154561	+	0.132008i
$652$	−18.3406	+	11.0746i	−0.718272	+	0.433717i
$653$	−42.4548	−	11.3757i	−1.66138	−	0.445166i	−0.698616	−	0.715497i	$-0.746200\pi$
$653$	−42.4548	−	11.3757i	−1.66138	−	0.445166i	−0.962767	+	0.270331i	$0.912867\pi$
$654$	−23.9407	−	36.0847i	−0.936154	−	1.41102i
$655$	−24.1671	+	32.7209i	−0.944288	+	1.27851i
$656$	−0.174749	−	4.44768i	−0.00682280	−	0.173653i
$657$	1.45302	+	1.99990i	0.0566878	+	0.0780236i
$658$	−5.34133	−	2.15126i	−0.208227	−	0.0838649i
$659$	2.49612	+	1.44114i	0.0972351	+	0.0561387i	0.547829	−	0.836590i	$-0.315454\pi$
$659$	2.49612	+	1.44114i	0.0972351	+	0.0561387i	−0.450594	+	0.892729i	$0.648788\pi$
$660$	11.8997	−	25.7252i	0.463196	−	1.00135i
$661$	−26.2757	+	15.1703i	−1.02201	+	0.590057i	−0.914685	−	0.404168i	$-0.867561\pi$
$661$	−26.2757	+	15.1703i	−1.02201	+	0.590057i	−0.107323	+	0.994224i	$0.534228\pi$
$662$	−13.8813	+	1.96634i	−0.539513	+	0.0764239i
$663$	−1.46795	+	0.700179i	−0.0570105	+	0.0271927i
$664$	5.52486	−	4.50395i	0.214406	−	0.174787i
$665$	2.07276	−	1.65177i	0.0803783	−	0.0640527i
$666$	6.36426	−	22.2868i	0.246610	−	0.863595i
$667$	−0.972351	+	0.972351i	−0.0376496	+	0.0376496i
$668$	−33.4678	−	18.4562i	−1.29491	−	0.714092i
$669$	−2.33066	−	12.5750i	−0.0901084	−	0.486178i
$670$	−7.25217	+	7.67258i	−0.280176	+	0.296418i
$671$	46.6078	−	26.9090i	1.79927	−	1.03881i
$672$	−1.33823	−	3.52060i	−0.0516235	−	0.135810i
$673$	−18.2192	+	4.88182i	−0.702299	+	0.188180i	−0.592260	−	0.805747i	$-0.701764\pi$
$673$	−18.2192	+	4.88182i	−0.702299	+	0.188180i	−0.110039	+	0.993927i	$0.535097\pi$
$674$	−14.9992	−	35.2289i	−0.577746	−	1.35697i
$675$	−21.6393	+	14.3784i	−0.832899	+	0.553425i
$676$	17.4651	−	18.1648i	0.671736	−	0.698647i
$677$	24.8383	−	6.65541i	0.954615	−	0.255788i	0.252296	−	0.967650i	$-0.418814\pi$
$677$	24.8383	−	6.65541i	0.954615	−	0.255788i	0.702319	+	0.711862i	$0.252148\pi$
$678$	−23.7949	+	7.99057i	−0.913838	+	0.306876i
$679$	−3.59675	−	6.22975i	−0.138030	−	0.239076i
$680$	−9.37366	+	0.448368i	−0.359463	+	0.0171941i
$681$	−1.03497	−	5.58415i	−0.0396601	−	0.213985i
$682$	−31.7367	+	24.8512i	−1.21526	+	0.951602i
$683$	−22.1581	−	22.1581i	−0.847856	−	0.847856i	0.142009	−	0.989865i	$-0.454644\pi$
$683$	−22.1581	−	22.1581i	−0.847856	−	0.847856i	−0.989865	+	0.142009i	$0.954644\pi$
$684$	17.0459	+	7.19166i	0.651767	+	0.274980i
$685$	−0.877961	+	0.699639i	−0.0335452	+	0.0267318i
$686$	−7.47532	−	0.909578i	−0.285409	−	0.0347279i
$687$	−6.18267	−	12.9622i	−0.235883	−	0.494538i
$688$	47.5084	+	10.7501i	1.81124	+	0.409842i
$689$	−2.64267	+	1.52575i	−0.100678	+	0.0581263i
$690$	1.37436	−	1.24243i	0.0523211	−	0.0472983i
$691$	−23.1568	+	40.1087i	−0.880926	+	1.52581i	−0.0306122	+	0.999531i	$0.509746\pi$
$691$	−23.1568	+	40.1087i	−0.880926	+	1.52581i	−0.850313	+	0.526277i	$0.823588\pi$
$692$	−18.6693	+	0.366617i	−0.709701	+	0.0139367i
$693$	−1.71635	+	3.85501i	−0.0651986	+	0.146440i
$694$	−15.3043	−	35.9456i	−0.580944	−	1.36448i
$695$	−21.0153	−	15.5215i	−0.797155	−	0.588765i
$696$	3.56525	−	19.5942i	0.135140	−	0.742715i
$697$	1.59488	+	0.427346i	0.0604103	+	0.0161869i
$698$	10.9231	−	1.54729i	0.413444	−	0.0585657i
$699$	6.23978	+	7.30582i	0.236010	+	0.276331i
$700$	2.86684	+	2.56082i	0.108356	+	0.0967897i
$701$			32.8572i			1.24100i	0.784207	+	0.620500i	$0.213070\pi$
$701$			32.8572i			1.24100i	−0.784207	+	0.620500i	$0.786930\pi$
$702$	0.772549	+	4.58572i	0.0291580	+	0.173077i
$703$	11.9113	−	11.9113i	0.449244	−	0.449244i
$704$	−9.22807	−	27.7811i	−0.347796	−	1.04704i
$705$	22.9706	+	33.9898i	0.865122	+	1.28013i
$706$	5.51239	+	4.14446i	0.207461	+	0.155979i
$707$	−0.783333	−	0.209893i	−0.0294603	−	0.00789386i
$708$	1.02097	+	4.96275i	0.0383704	+	0.186512i
$709$	11.8222	−	20.4767i	0.443993	−	0.769018i	−0.553989	−	0.832524i	$-0.686895\pi$
$709$	11.8222	−	20.4767i	0.443993	−	0.769018i	0.997981	+	0.0635062i	$0.0202283\pi$
$710$	−24.7597	−	13.3800i	−0.929217	−	0.502142i
$711$	−20.9494	+	25.8705i	−0.785663	+	0.970218i
$712$	13.0099	+	28.9653i	0.487567	+	1.08552i
$713$	−2.54499	+	0.681928i	−0.0953106	+	0.0255384i
$714$	1.39443	−	0.0868160i	0.0521853	−	0.00324901i
$715$	4.81936	+	1.89344i	0.180234	+	0.0708106i
$716$	−0.803256	−	0.198414i	−0.0300191	−	0.00741508i
$717$	0.439086	+	0.920560i	0.0163980	+	0.0343790i
$718$	3.73017	+	4.76368i	0.139209	+	0.177779i
$719$	−39.8652			−1.48672			−0.743361	−	0.668890i	$-0.766770\pi$
$719$	−39.8652			−1.48672			−0.743361	+	0.668890i	$0.766770\pi$
$720$	−6.12675	+	26.1240i	−0.228331	+	0.973584i
$721$	3.78216			0.140855
$722$	−8.27611	−	10.5692i	−0.308005	−	0.393343i
$723$	17.7681	−	25.8528i	0.660802	−	0.961476i
$724$	−26.9635	−	6.66031i	−1.00209	−	0.247529i
$725$	5.97753	+	19.4278i	0.222000	+	0.721529i
$726$	−2.60620	+	5.24157i	−0.0967253	+	0.194533i
$727$	41.7447	−	11.1854i	1.54822	−	0.414845i	0.619311	−	0.785145i	$-0.287412\pi$
$727$	41.7447	−	11.1854i	1.54822	−	0.414845i	0.928912	+	0.370300i	$0.120745\pi$
$728$	0.627644	−	0.281910i	0.0232620	−	0.0104483i
$729$	24.0573	+	12.2575i	0.891010	+	0.453983i
$730$	−2.49696	+	0.745019i	−0.0924167	+	0.0275744i
$731$	−9.03438	+	15.6480i	−0.334149	+	0.578762i
$732$	−38.0844	+	33.8428i	−1.40764	+	1.25086i
$733$	44.1582	+	11.8322i	1.63102	+	0.437031i	0.954213	−	0.299129i	$-0.0966962\pi$
$733$	44.1582	+	11.8322i	1.63102	+	0.437031i	0.676808	+	0.736160i	$0.263363\pi$
$734$	12.4947	+	9.39411i	0.461189	+	0.346743i
$735$	20.0445	+	17.3930i	0.739351	+	0.641551i
$736$	0.156370	−	1.90706i	0.00576389	−	0.0702951i
$737$	8.63845	−	8.63845i	0.318202	−	0.318202i
$738$	2.42713	−	4.04944i	0.0893437	−	0.149062i
$739$			3.14088i			0.115539i	0.998330	+	0.0577696i	$0.0183989\pi$
$739$			3.14088i			0.115539i	−0.998330	+	0.0577696i	$0.981601\pi$
$740$	19.9335	+	14.1262i	0.732769	+	0.519290i
$741$	−1.12819	+	3.18593i	−0.0414452	+	0.117038i
$742$	2.59545	−	0.367654i	0.0952819	−	0.0134970i
$743$	4.87942	+	1.30744i	0.179009	+	0.0479652i	0.347210	−	0.937787i	$-0.387129\pi$
$743$	4.87942	+	1.30744i	0.179009	+	0.0479652i	−0.168201	+	0.985753i	$0.553796\pi$
$744$	24.6875	−	29.0978i	0.905089	−	1.06678i
$745$	−24.0197	+	32.5213i	−0.880013	+	1.19149i
$746$	15.4512	+	36.2905i	0.565707	+	1.32869i
$747$	7.51906	−	0.790307i	0.275108	−	0.0289158i
$748$	10.8570	−	0.213202i	0.396970	−	0.00779545i
$749$	1.79138	−	3.10276i	0.0654556	−	0.113372i
$750$	−6.72529	−	26.5475i	−0.245573	−	0.969378i
$751$	−27.9780	+	16.1531i	−1.02093	+	0.589435i	−0.914374	−	0.404871i	$-0.867316\pi$
$751$	−27.9780	+	16.1531i	−1.02093	+	0.589435i	−0.106558	+	0.994306i	$0.533983\pi$
$752$	41.3245	+	9.35079i	1.50695	+	0.340988i
$753$	−40.5014	−	3.18747i	−1.47595	−	0.116158i
$754$	3.61164	+	0.439456i	0.131528	+	0.0160040i
$755$	2.74872	−	24.3178i	0.100036	−	0.885014i
$756$	0.856112	−	3.90202i	0.0311365	−	0.141915i
$757$	−5.72946	−	5.72946i	−0.208241	−	0.208241i	0.595279	−	0.803519i	$-0.297042\pi$
$757$	−5.72946	−	5.72946i	−0.208241	−	0.208241i	−0.803519	+	0.595279i	$0.797042\pi$
$758$	−16.6931	+	13.0714i	−0.606320	+	0.474775i
$759$	−1.63018	+	1.39231i	−0.0591719	+	0.0505377i
$760$	−13.1152	+	14.4329i	−0.475737	+	0.523535i
$761$	−16.1336	−	27.9442i	−0.584842	−	1.01298i	−0.994895	−	0.100914i	$-0.967823\pi$
$761$	−16.1336	−	27.9442i	−0.584842	−	1.01298i	0.410053	−	0.912061i	$-0.365510\pi$
$762$	−6.80222	+	33.6219i	−0.246419	+	1.21799i
$763$	−6.56426	+	1.75889i	−0.237642	+	0.0636760i
$764$	28.3193	−	29.4538i	1.02455	−	1.06560i
$765$	−8.58085	−	5.04418i	−0.310241	−	0.182373i
$766$	−10.0173	−	23.5280i	−0.361941	−	0.850100i
$767$	−0.894055	+	0.239561i	−0.0322825	+	0.00865006i
$768$	13.8564	+	24.0000i	0.500001	+	0.866025i
$769$	−14.8013	+	8.54553i	−0.533748	+	0.308160i	−0.742541	−	0.669800i	$-0.766380\pi$
$769$	−14.8013	+	8.54553i	−0.533748	+	0.308160i	0.208793	+	0.977960i	$0.433046\pi$
$770$	−3.23259	−	3.05546i	−0.116494	−	0.110111i
$771$	15.5908	+	5.52095i	0.561487	+	0.198832i
$772$	25.8824	+	14.2731i	0.931529	+	0.513702i
$773$	21.2144	−	21.2144i	0.763027	−	0.763027i	−0.213841	−	0.976868i	$-0.568597\pi$
$773$	21.2144	−	21.2144i	0.763027	−	0.763027i	0.976868	+	0.213841i	$0.0685975\pi$
$774$	35.9296	+	37.1248i	1.29146	+	1.33442i
$775$	−8.69343	+	37.9638i	−0.312277	+	1.36370i
$776$	33.4441	+	41.0248i	1.20057	+	1.47270i
$777$	−2.99761	−	2.06019i	−0.107539	−	0.0739089i
$778$	25.4367	−	3.60319i	0.911948	−	0.129181i
$779$	2.97153	−	1.71561i	0.106466	−	0.0614683i
$780$	−4.83001	−	0.836361i	−0.172942	−	0.0299465i
$781$	28.2032	+	16.2831i	1.00919	+	0.582657i
$782$	0.658403	+	0.265177i	0.0235444	+	0.00948270i
$783$	14.5407	−	15.3229i	0.519643	−	0.547594i
$784$	27.3878	−	1.07607i	0.978136	−	0.0384309i
$785$	29.3160	−	4.40800i	1.04633	−	0.157328i
$786$	−19.8393	+	39.9005i	−0.707644	+	1.42321i
$787$	−37.8597	−	10.1445i	−1.34955	−	0.361611i	−0.489582	−	0.871957i	$-0.662851\pi$
$787$	−37.8597	−	10.1445i	−1.34955	−	0.361611i	−0.859969	+	0.510346i	$0.829517\pi$
$788$	36.4669	−	22.0200i	1.29908	−	0.784429i
$789$	−1.48603	−	8.01784i	−0.0529041	−	0.285443i
$790$	−18.3936	−	29.8825i	−0.654413	−	1.06317i
$791$			3.93910i			0.140058i
$792$	7.93790	−	30.0176i	0.282061	−	1.06663i
$793$	−6.58133	−	6.58133i	−0.233710	−	0.233710i
$794$	−2.02458	+	16.6389i	−0.0718496	+	0.590492i
$795$	−16.7927	−	8.17179i	−0.595574	−	0.289823i
$796$	−8.75949	+	35.4618i	−0.310472	+	1.25691i
$797$	−11.3159	+	42.2314i	−0.400829	+	1.49591i	0.410792	+	0.911729i	$0.365252\pi$
$797$	−11.3159	+	42.2314i	−0.400829	+	1.49591i	−0.811621	+	0.584185i	$0.801414\pi$
$798$	1.92146	−	2.17660i	0.0680190	−	0.0770509i
$799$	−7.85843	+	13.6112i	−0.278011	+	0.481530i
$800$	−23.8320	−	15.2327i	−0.842589	−	0.538557i
$801$	−5.26846	+	33.2644i	−0.186152	+	1.17534i
$802$	14.3490	−	35.6270i	0.506682	−	1.25803i
$803$	2.91247	−	0.780393i	0.102779	−	0.0275395i
$804$	−6.36222	+	9.65801i	−0.224378	+	0.340612i
$805$	−0.116173	−	0.266529i	−0.00409455	−	0.00939393i
$806$	5.57193	+	4.18923i	0.196263	+	0.147559i
$807$	−41.8800	−	3.29597i	−1.47425	−	0.116024i
$808$	5.93639	+	0.604306i	0.208841	+	0.0212594i
$809$		−	12.8430i		−	0.451537i	−0.974181	−	0.225768i	$-0.927511\pi$
$809$		−	12.8430i		−	0.451537i	0.974181	−	0.225768i	$-0.0724893\pi$
$810$	−20.6055	+	19.6319i	−0.724005	+	0.689795i
$811$	22.9548			0.806053			0.403027	−	0.915188i	$-0.367958\pi$
$811$	22.9548			0.806053			0.403027	+	0.915188i	$0.367958\pi$
$812$	−2.73686	−	1.50927i	−0.0960451	−	0.0529651i
$813$	3.21305	−	40.8264i	0.112686	−	1.43184i
$814$	−22.5964	−	16.9890i	−0.792005	−	0.595465i
$815$	8.75921	−	22.2948i	0.306822	−	0.780951i
$816$	−10.0266	+	2.26880i	−0.351001	+	0.0794238i
$817$	9.71831	+	36.2692i	0.340001	+	1.26890i
$818$	−4.28729	−	1.72674i	−0.149902	−	0.0603741i
$819$	0.720801	+	0.114162i	0.0251868	+	0.00398913i
$820$	3.17722	+	3.83024i	0.110953	+	0.133758i
$821$	−22.1396	−	12.7823i	−0.772679	−	0.446106i	0.0611506	−	0.998129i	$-0.480523\pi$
$821$	−22.1396	−	12.7823i	−0.772679	−	0.446106i	−0.833829	+	0.552022i	$0.813856\pi$
$822$	−0.813874	+	0.921945i	−0.0283871	+	0.0321565i
$823$	29.3106	+	7.85376i	1.02170	+	0.273765i	0.730512	−	0.682900i	$-0.239281\pi$
$823$	29.3106	+	7.85376i	1.02170	+	0.273765i	0.291192	+	0.956665i	$0.405948\pi$
$824$	−27.4720	+	4.44335i	−0.957034	+	0.154791i
$825$	6.91404	+	30.9262i	0.240716	+	1.07671i
$826$	0.789302	+	0.0960403i	0.0274633	+	0.00334167i
$827$	29.1884	−	29.1884i	1.01498	−	1.01498i	0.0150926	−	0.999886i	$-0.495196\pi$
$827$	29.1884	−	29.1884i	1.01498	−	1.01498i	0.999886	−	0.0150926i	$-0.00480430\pi$
$828$	1.24601	−	1.60202i	0.0433017	−	0.0556739i
$829$	−11.3730			−0.395001			−0.197501	−	0.980303i	$-0.563282\pi$
$829$	−11.3730			−0.395001			−0.197501	+	0.980303i	$0.563282\pi$
$830$	−1.84507	+	7.75292i	−0.0640434	+	0.269108i
$831$	−16.0565	+	2.97592i	−0.556994	+	0.103233i
$832$	−4.22775	+	2.78504i	−0.146571	+	0.0965540i
$833$	−2.63150	+	9.82090i	−0.0911761	+	0.340274i
$834$	−25.6264	−	12.7419i	−0.887371	−	0.441217i
$835$	42.2557	−	6.35363i	1.46232	−	0.219877i
$836$	15.6403	−	16.2669i	0.540933	−	0.562603i
$837$	38.8076	−	11.4955i	1.34139	−	0.397343i
$838$	14.2344	+	5.73302i	0.491719	+	0.198044i
$839$	14.5635	−	25.2247i	0.502788	−	0.870854i	−0.497207	−	0.867632i	$-0.665641\pi$
$839$	14.5635	−	25.2247i	0.502788	−	0.870854i	0.999995	−	0.00322220i	$-0.00102566\pi$
$840$	3.58033	+	2.21656i	0.123533	+	0.0764785i
$841$	6.23662	+	10.8022i	0.215056	+	0.372488i
$842$	−1.88636	−	13.3167i	−0.0650081	−	0.458924i
$843$	−8.94961	+	13.0218i	−0.308241	+	0.448495i
$844$	17.9677	−	5.19461i	0.618474	−	0.178806i
$845$	−3.16438	+	27.9951i	−0.108858	+	0.963061i
$846$	31.2528	+	32.2925i	1.07449	+	1.11024i
$847$	0.649575	+	0.649575i	0.0223197	+	0.0223197i
$848$	−18.4203	+	5.71966i	−0.632557	+	0.196414i
$849$	−3.20521	+	9.05127i	−0.110002	+	0.310639i
$850$	8.01797	−	6.76722i	0.275014	−	0.232114i
$851$	−0.923948	−	1.60032i	−0.0316725	−	0.0548584i
$852$	−29.2580	−	9.71862i	−1.00236	−	0.332955i
$853$	−8.65141	−	32.2875i	−0.296219	−	1.10550i	−0.940245	−	0.340500i	$-0.889404\pi$
$853$	−8.65141	−	32.2875i	−0.296219	−	1.10550i	0.644026	−	0.765004i	$-0.277263\pi$
$854$	3.13210	+	7.35644i	0.107178	+	0.251732i
$855$	−20.0211	+	5.19691i	−0.684709	+	0.177731i
$856$	−9.36666	+	24.6417i	−0.320146	+	0.842236i
$857$	−6.34825	−	23.6920i	−0.216852	−	0.809304i	−0.985506	−	0.169639i	$-0.945740\pi$
$857$	−6.34825	−	23.6920i	−0.216852	−	0.809304i	0.768654	−	0.639665i	$-0.220927\pi$
$858$	5.55954	+	1.12478i	0.189800	+	0.0383993i
$859$	−23.6379	+	13.6474i	−0.806516	+	0.465642i	−0.845745	−	0.533588i	$-0.820843\pi$
$859$	−23.6379	+	13.6474i	−0.806516	+	0.465642i	0.0392283	+	0.999230i	$0.487510\pi$
$860$	−49.4858	+	22.7358i	−1.68745	+	0.775285i
$861$	−0.481172	−	0.563379i	−0.0163983	−	0.0191999i
$862$	−2.05067	+	1.60577i	−0.0698462	+	0.0546926i
$863$	−11.5562	+	11.5562i	−0.393378	+	0.393378i	−0.875890	−	0.482511i	$-0.839725\pi$
$863$	−11.5562	+	11.5562i	−0.393378	+	0.393378i	0.482511	+	0.875890i	$0.339725\pi$
$864$	−1.63429	+	29.3484i	−0.0555995	+	0.998453i
$865$	16.3269	−	13.0108i	0.555131	−	0.442379i
$866$	4.28372	−	35.2055i	0.145567	−	1.19633i
$867$	−2.01099	+	25.5525i	−0.0682966	+	0.867807i
$868$	−3.09547	−	5.12636i	−0.105067	−	0.174000i
$869$	20.3019	+	35.1639i	0.688694	+	1.19285i
$870$	10.1482	+	19.8196i	0.344055	+	0.671948i
$871$	−1.82971	−	1.05638i	−0.0619974	−	0.0357942i
$872$	45.6137	−	20.4876i	1.54467	−	0.693799i
$873$	5.86842	+	55.8327i	0.198616	+	1.88965i
$874$	1.35714	−	0.577821i	0.0459060	−	0.0195451i
$875$	−4.28539	−	0.325748i	−0.144873	−	0.0110123i
$876$	−2.55175	+	1.27922i	−0.0862157	+	0.0432208i
$877$	13.9928	−	52.2220i	0.472505	−	1.76341i	−0.158219	−	0.987404i	$-0.550575\pi$
$877$	13.9928	−	52.2220i	0.472505	−	1.76341i	0.630723	−	0.776008i	$-0.282758\pi$
$878$	4.31313	−	0.610970i	0.145561	−	0.0206192i
$879$	−3.74470	−	1.32606i	−0.126305	−	0.0447269i
$880$	27.0698	+	18.3959i	0.912522	+	0.620126i
$881$	−14.2941			−0.481581			−0.240790	−	0.970577i	$-0.577407\pi$
$881$	−14.2941			−0.481581			−0.240790	+	0.970577i	$0.577407\pi$
$882$	24.9356	+	14.9457i	0.839624	+	0.503248i
$883$	−17.2963	−	17.2963i	−0.582068	−	0.582068i	0.353403	−	0.935471i	$-0.385024\pi$
$883$	−17.2963	−	17.2963i	−0.582068	−	0.582068i	−0.935471	+	0.353403i	$0.885024\pi$
$884$	−0.521581	−	1.80410i	−0.0175427	−	0.0606786i
$885$	−4.27854	−	3.71258i	−0.143821	−	0.124797i
$886$	−39.7652	−	29.8973i	−1.33594	−	1.00442i
$887$	5.85339	−	21.8451i	0.196538	−	0.733488i	−0.795326	−	0.606182i	$-0.792700\pi$
$887$	5.85339	−	21.8451i	0.196538	−	0.733488i	0.991863	−	0.127306i	$-0.0406330\pi$
$888$	24.1937	+	11.4427i	0.811888	+	0.383993i
$889$	4.66203	+	2.69163i	0.156360	+	0.0902742i
$890$	−31.2322	−	16.8777i	−1.04691	−	0.565740i
$891$	24.4737	−	22.0365i	0.819901	−	0.738251i
$892$	14.7648	−	0.289942i	0.494362	−	0.00970799i
$893$	8.45334	+	31.5483i	0.282880	+	1.05572i
$894$	−19.7182	+	39.6571i	−0.659477	+	1.32633i
$895$	0.848007	−	0.369622i	0.0283457	−	0.0123551i
$896$	4.26266	−	0.862405i	0.142405	−	0.0288109i
$897$	0.305553	+	0.210000i	0.0102021	+	0.00701170i
$898$	19.0537	−	14.9199i	0.635830	−	0.497882i
$899$		−	31.6659i		−	1.05612i
$900$	−12.3107	−	27.3578i	−0.410356	−	0.911925i
$901$		−	7.15484i		−	0.238362i
$902$	−3.55024	−	4.53390i	−0.118210	−	0.150962i
$903$	7.31793	−	3.49049i	0.243525	−	0.116156i
$904$	−4.62772	−	28.6120i	−0.153916	−	0.951621i
$905$	28.4657	−	12.4074i	0.946231	−	0.412436i
$906$	−1.66584	−	26.7566i	−0.0553438	−	0.888929i
$907$	−5.48025	−	20.4526i	−0.181969	−	0.679116i	−0.995259	−	0.0972582i	$-0.968993\pi$
$907$	−5.48025	−	20.4526i	−0.181969	−	0.679116i	0.813291	−	0.581858i	$-0.197674\pi$
$908$	6.55657	−	0.128754i	0.217587	−	0.00427285i
$909$	4.91859	+	3.98298i	0.163139	+	0.132107i
$910$	−0.365720	+	0.676766i	−0.0121235	+	0.0224346i
$911$	−7.19351	−	4.15318i	−0.238332	−	0.137601i	0.376078	−	0.926588i	$-0.377272\pi$
$911$	−7.19351	−	4.15318i	−0.238332	−	0.137601i	−0.614410	+	0.788987i	$0.710606\pi$
$912$	−11.3996	+	18.0673i	−0.377478	+	0.598268i
$913$	2.38677	−	8.90756i	0.0789906	−	0.294797i
$914$	−2.68814	+	3.57539i	−0.0889159	+	0.118264i
$915$	10.8190	−	55.9253i	0.357666	−	1.84884i
$916$	15.9305	−	4.60562i	0.526357	−	0.152174i
$917$	4.94478	+	4.94478i	0.163291	+	0.163291i
$918$	−10.2173	−	3.80735i	−0.337222	−	0.125661i
$919$	−7.09800			−0.234141			−0.117071	−	0.993124i	$-0.537350\pi$
$919$	−7.09800			−0.234141			−0.117071	+	0.993124i	$0.537350\pi$
$920$	1.15695	+	1.79948i	0.0381436	+	0.0593270i
$921$	−4.88607	+	4.17311i	−0.161002	+	0.137509i
$922$	−1.85105	−	13.0675i	−0.0609611	−	0.430354i
$923$	1.45769	−	5.44017i	0.0479805	−	0.179066i
$924$	−4.06908	−	2.68051i	−0.133863	−	0.0881823i
$925$	−27.2967	+	1.00191i	−0.897511	+	0.0329427i
$926$	11.4915	+	26.9903i	0.377633	+	0.886957i
$927$	−26.9653	−	12.0056i	−0.885657	−	0.394317i
$928$	21.6526	+	7.74742i	0.710780	+	0.254321i
$929$	4.60812	+	2.66050i	0.151188	+	0.0872882i	0.573685	−	0.819076i	$-0.305513\pi$
$929$	4.60812	+	2.66050i	0.151188	+	0.0872882i	−0.422498	+	0.906364i	$0.638847\pi$
$930$	−2.14836	+	42.6096i	−0.0704474	+	1.39722i
$931$	10.5644	+	18.2980i	0.346233	+	0.599694i
$932$	−9.49704	+	5.73463i	−0.311086	+	0.187844i
$933$	43.9964	−	20.9853i	1.44038	−	0.687027i
$934$	−8.06610	−	0.981463i	−0.263931	−	0.0321145i
$935$	−9.49475	+	7.56628i	−0.310511	+	0.247444i
$936$	−5.36972	+	0.0175874i	−0.175515	+	0.000574862i
$937$	−11.5629	+	11.5629i	−0.377742	+	0.377742i	−0.870287	−	0.492545i	$-0.836067\pi$
$937$	−11.5629	+	11.5629i	−0.377742	+	0.377742i	0.492545	+	0.870287i	$0.336067\pi$
$938$	1.11896	+	1.42898i	0.0365352	+	0.0466580i
$939$	−20.7622	+	3.84808i	−0.677549	+	0.125577i
$940$	−43.0445	+	19.7765i	−1.40396	+	0.645037i
$941$	−37.2137	+	21.4853i	−1.21313	+	0.700401i	−0.963440	−	0.267924i	$-0.913662\pi$
$941$	−37.2137	+	21.4853i	−1.21313	+	0.700401i	−0.249691	+	0.968326i	$0.580329\pi$
$942$	30.7856	−	10.3381i	1.00305	−	0.336834i
$943$	−0.0974201	−	0.363577i	−0.00317244	−	0.0118397i
$944$	−5.84599	+	0.229689i	−0.190271	+	0.00747573i
$945$	1.89119	+	4.04620i	0.0615203	+	0.131623i
$946$	57.9802	−	24.6858i	1.88510	−	0.802604i
$947$	9.35913	+	34.9287i	0.304131	+	1.13503i	0.933691	+	0.358080i	$0.116568\pi$
$947$	9.35913	+	34.9287i	0.304131	+	1.13503i	−0.629560	+	0.776952i	$0.716765\pi$
$948$	−25.5331	−	28.7333i	−0.829277	−	0.933214i
$949$	−0.260728	−	0.451595i	−0.00846360	−	0.0146594i
$950$	1.83791	−	21.7259i	0.0596296	−	0.704882i
$951$	40.4529	−	7.49757i	1.31178	−	0.243125i
$952$	−0.163381	+	1.60497i	−0.00529522	+	0.0520175i
$953$	−17.7318	−	17.7318i	−0.574390	−	0.574390i	0.358962	−	0.933352i	$-0.383131\pi$
$953$	−17.7318	−	17.7318i	−0.574390	−	0.574390i	−0.933352	+	0.358962i	$0.883131\pi$
$954$	−19.6716	−	5.61745i	−0.636890	−	0.181872i
$955$	−5.13096	+	45.3933i	−0.166034	+	1.46889i
$956$	−1.13136	+	0.327086i	−0.0365909	+	0.0105787i
$957$	−11.0924	−	23.2557i	−0.358567	−	0.751749i
$958$	27.8340	−	3.94277i	0.899274	−	0.127385i
$959$	0.0964962	+	0.167136i	0.00311603	+	0.00539712i
$960$	−28.6100	−	11.8939i	−0.923385	−	0.383875i
$961$	14.8365	−	25.6976i	0.478598	−	0.828956i
$962$	−1.82657	+	4.53516i	−0.0588910	+	0.146219i
$963$	−22.6209	+	16.4351i	−0.728947	+	0.529614i
$964$	26.1114	+	25.1056i	0.840991	+	0.808597i
$965$	−32.6785	+	4.91360i	−1.05196	+	0.158174i
$966$	−0.176081	−	0.265399i	−0.00566530	−	0.00853906i
$967$	−0.144279	+	0.538456i	−0.00463969	+	0.0173156i	−0.968207	−	0.250151i	$-0.919520\pi$
$967$	−0.144279	+	0.538456i	−0.00463969	+	0.0173156i	0.963567	+	0.267466i	$0.0861864\pi$
$968$	−5.48138	−	3.95511i	−0.176178	−	0.127122i
$969$	−5.14663	−	6.02591i	−0.165333	−	0.193580i
$970$	−57.5692	−	13.7006i	−1.84844	−	0.439898i
$971$	−50.1602			−1.60972			−0.804859	−	0.593466i	$-0.797759\pi$
$971$	−50.1602			−1.60972			−0.804859	+	0.593466i	$0.797759\pi$
$972$	−18.4898	+	25.1023i	−0.593062	+	0.805157i
$973$	−3.17583	+	3.17583i	−0.101812	+	0.101812i
$974$	1.76504	−	14.5059i	0.0565555	−	0.464799i
$975$	4.85672	−	2.53926i	0.155540	−	0.0813215i
$976$	−31.3927	−	49.7545i	−1.00486	−	1.59260i
$977$	−49.4711	−	13.2557i	−1.58272	−	0.424089i	−0.642953	−	0.765905i	$-0.722291\pi$
$977$	−49.4711	−	13.2557i	−1.58272	−	0.424089i	−0.939767	+	0.341817i	$0.888958\pi$
$978$	5.20332	−	25.7189i	0.166384	−	0.822399i
$979$	35.5758	+	20.5397i	1.13701	+	0.656452i
$980$	−23.5858	+	19.5646i	−0.753420	+	0.624969i
$981$	52.3838	+	8.29662i	1.67249	+	0.264891i
$982$	−7.02324	+	17.4379i	−0.224121	+	0.556465i
$983$	6.46485	+	24.1272i	0.206197	+	0.769537i	0.989081	+	0.147370i	$0.0470808\pi$
$983$	6.46485	+	24.1272i	0.206197	+	0.769537i	−0.782885	+	0.622167i	$0.786253\pi$
$984$	4.15690	+	3.52686i	0.132517	+	0.112432i
$985$	−17.4161	+	44.3291i	−0.554924	+	1.41244i
$986$	−5.12646	+	6.81851i	−0.163260	+	0.217145i
$987$	6.36540	−	3.03615i	0.202613	−	0.0966418i
$988$	−3.41745	−	1.88459i	−0.108724	−	0.0599568i
$989$	4.11905			0.130978
$990$	13.3482	+	32.0454i	0.424233	+	1.01847i
$991$			25.7153i			0.816872i	0.912787	+	0.408436i	$0.133926\pi$
$991$			25.7153i			0.816872i	−0.912787	+	0.408436i	$0.866074\pi$
$992$	28.5068	+	33.5992i	0.905090	+	1.06677i
$993$	9.72564	−	14.1509i	0.308634	−	0.449066i
$994$	−2.90748	+	3.86713i	−0.0922197	+	0.122658i
$995$	−16.3179	−	37.4374i	−0.517313	−	1.18685i
$996$	−0.513935	+	8.71495i	−0.0162847	+	0.276144i
$997$	−24.6902	+	6.61572i	−0.781947	+	0.209522i	−0.627643	−	0.778501i	$-0.715980\pi$
$997$	−24.6902	+	6.61572i	−0.781947	+	0.209522i	−0.154304	+	0.988023i	$0.549314\pi$
$998$	3.10432	+	1.25029i	0.0982656	+	0.0395772i
$999$	14.8321	+	24.2036i	0.469268	+	0.765768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bo.a.43.19	✓	272
5.2	odd	4	inner	360.2.bo.a.187.55	yes	272
8.3	odd	2	inner	360.2.bo.a.43.38	yes	272
9.4	even	3	inner	360.2.bo.a.283.64	yes	272
40.27	even	4	inner	360.2.bo.a.187.64	yes	272
45.22	odd	12	inner	360.2.bo.a.67.38	yes	272
72.67	odd	6	inner	360.2.bo.a.283.55	yes	272
360.67	even	12	inner	360.2.bo.a.67.19	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bo.a.43.19	✓	272	1.1	even	1	trivial
360.2.bo.a.43.38	yes	272	8.3	odd	2	inner
360.2.bo.a.67.19	yes	272	360.67	even	12	inner
360.2.bo.a.67.38	yes	272	45.22	odd	12	inner
360.2.bo.a.187.55	yes	272	5.2	odd	4	inner
360.2.bo.a.187.64	yes	272	40.27	even	4	inner
360.2.bo.a.283.55	yes	272	72.67	odd	6	inner
360.2.bo.a.283.64	yes	272	9.4	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.871892 - 1.11347i) q^{2} +(1.72671 + 0.135893i) q^{3} +(-0.479609 + 1.94164i) q^{4} +(-0.893456 - 2.04981i) q^{5} +(-1.35419 - 2.04112i) q^{6} +(-0.371305 + 0.0994908i) q^{7} +(2.58012 - 1.15887i) q^{8} +(2.96307 + 0.469295i) q^{9} +O(q^{10})\)	\(q+(-0.871892 - 1.11347i) q^{2} +(1.72671 + 0.135893i) q^{3} +(-0.479609 + 1.94164i) q^{4} +(-0.893456 - 2.04981i) q^{5} +(-1.35419 - 2.04112i) q^{6} +(-0.371305 + 0.0994908i) q^{7} +(2.58012 - 1.15887i) q^{8} +(2.96307 + 0.469295i) q^{9} +(-1.50340 + 2.78205i) q^{10} +(1.82960 - 3.16896i) q^{11} +(-1.09200 + 3.28748i) q^{12} +(-0.611267 - 0.163789i) q^{13} +(0.434517 + 0.326690i) q^{14} +(-1.26419 - 3.66085i) q^{15} +(-3.53995 - 1.86246i) q^{16} +(1.04920 - 1.04920i) q^{17} +(-2.06093 - 3.70845i) q^{18} -3.08348i q^{19} +(4.40851 - 0.751663i) q^{20} +(-0.654656 + 0.121334i) q^{21} +(-5.12375 + 0.725796i) q^{22} +(-0.326729 - 0.0875468i) q^{23} +(4.61260 - 1.65042i) q^{24} +(-3.40347 + 3.66284i) q^{25} +(0.350586 + 0.823431i) q^{26} +(5.05259 + 1.21300i) q^{27} +(-0.0150944 - 0.768657i) q^{28} +(2.03266 - 3.52066i) q^{29} +(-2.97400 + 4.59949i) q^{30} +(6.74573 - 3.89465i) q^{31} +(1.01267 + 5.56547i) q^{32} +(3.58983 - 5.22326i) q^{33} +(-2.08305 - 0.253460i) q^{34} +(0.535682 + 0.672215i) q^{35} +(-2.33232 + 5.52814i) q^{36} +(3.86294 + 3.86294i) q^{37} +(-3.43335 + 2.68846i) q^{38} +(-1.03322 - 0.365882i) q^{39} +(-4.68070 - 4.25336i) q^{40} +(0.556389 + 0.963693i) q^{41} +(0.705891 + 0.623146i) q^{42} +(-11.7624 + 3.15173i) q^{43} +(5.27550 + 5.07230i) q^{44} +(-1.68540 - 6.49303i) q^{45} +(0.187392 + 0.440133i) q^{46} +(-10.2314 + 2.74149i) q^{47} +(-5.85938 - 3.69698i) q^{48} +(-5.93421 + 3.42612i) q^{49} +(7.04590 + 0.596049i) q^{50} +(1.95425 - 1.66910i) q^{51} +(0.611188 - 1.10831i) q^{52} +(3.40965 - 3.40965i) q^{53} +(-3.05468 - 6.68348i) q^{54} +(-8.13046 - 0.919013i) q^{55} +(-0.842713 + 0.686993i) q^{56} +(0.419023 - 5.32429i) q^{57} +(-5.69239 + 0.806346i) q^{58} +(1.26667 - 0.731313i) q^{59} +(7.71438 - 0.698821i) q^{60} +(12.7371 + 7.35379i) q^{61} +(-10.2181 - 4.11542i) q^{62} +(-1.14689 + 0.120546i) q^{63} +(5.31402 - 5.98007i) q^{64} +(0.210405 + 1.39932i) q^{65} +(-8.94586 + 0.556961i) q^{66} +(3.22484 + 0.864093i) q^{67} +(1.53397 + 2.54039i) q^{68} +(-0.552270 - 0.195568i) q^{69} +(0.281431 - 1.18256i) q^{70} +8.89983i q^{71} +(8.18892 - 2.22299i) q^{72} +(0.582661 + 0.582661i) q^{73} +(0.933183 - 7.66932i) q^{74} +(-6.37457 + 5.86216i) q^{75} +(5.98702 + 1.47887i) q^{76} +(-0.364057 + 1.35868i) q^{77} +(0.493463 + 1.46947i) q^{78} +(-5.54816 + 9.60970i) q^{79} +(-0.654903 + 8.92026i) q^{80} +(8.55952 + 2.78110i) q^{81} +(0.587928 - 1.45976i) q^{82} +(2.43429 - 0.652265i) q^{83} +(0.0783911 - 1.32930i) q^{84} +(-3.08809 - 1.21326i) q^{85} +(13.7649 + 10.3491i) q^{86} +(3.98824 - 5.80295i) q^{87} +(1.04816 - 10.2966i) q^{88} +11.2263i q^{89} +(-5.76027 + 7.53786i) q^{90} +0.243262 q^{91} +(0.326687 - 0.592403i) q^{92} +(12.1772 - 5.80824i) q^{93} +(11.9732 + 9.00200i) q^{94} +(-6.32057 + 2.75496i) q^{95} +(0.992284 + 9.74758i) q^{96} +(4.84339 + 18.0758i) q^{97} +(8.98885 + 3.62033i) q^{98} +(6.90841 - 8.53123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Introduction

L-functions

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