LMFDB - Embedded newform 80.2.s.b.27.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(3,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 3]))

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

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

chi := DirichletCharacter("80.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.5
Root			$0.235136 + 1.39453i$ of defining polynomial
Character	$\chi$	$=$	80.27
Dual form			80.2.s.b.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.430311 - 1.34716i) q^{2} -2.96561 q^{3} +(-1.62967 - 1.15939i) q^{4} +(-0.177336 - 2.22902i) q^{5} +(-1.27613 + 3.99515i) q^{6} +(-0.115101 - 0.115101i) q^{7} +(-2.26315 + 1.69652i) q^{8} +5.79486 q^{9} +O(q^{10})$	\(q+(0.430311 - 1.34716i) q^{2} -2.96561 q^{3} +(-1.62967 - 1.15939i) q^{4} +(-0.177336 - 2.22902i) q^{5} +(-1.27613 + 3.99515i) q^{6} +(-0.115101 - 0.115101i) q^{7} +(-2.26315 + 1.69652i) q^{8} +5.79486 q^{9} +(-3.07916 - 0.720273i) q^{10} +(2.95966 - 2.95966i) q^{11} +(4.83296 + 3.43831i) q^{12} -1.55822i q^{13} +(-0.204588 + 0.105530i) q^{14} +(0.525911 + 6.61042i) q^{15} +(1.31162 + 3.77884i) q^{16} +(0.299668 + 0.299668i) q^{17} +(2.49359 - 7.80658i) q^{18} +(-2.26261 + 2.26261i) q^{19} +(-2.29532 + 3.83817i) q^{20} +(0.341344 + 0.341344i) q^{21} +(-2.71356 - 5.26071i) q^{22} +(4.14573 - 4.14573i) q^{23} +(6.71162 - 5.03121i) q^{24} +(-4.93710 + 0.790575i) q^{25} +(-2.09917 - 0.670518i) q^{26} -8.28846 q^{27} +(0.0541288 + 0.321023i) q^{28} +(0.289656 + 0.289656i) q^{29} +(9.13159 + 2.13605i) q^{30} -4.18508i q^{31} +(5.65510 - 0.140879i) q^{32} +(-8.77721 + 8.77721i) q^{33} +(0.532650 - 0.274749i) q^{34} +(-0.236151 + 0.276974i) q^{35} +(-9.44368 - 6.71851i) q^{36} +1.63643i q^{37} +(2.07447 + 4.02172i) q^{38} +4.62107i q^{39} +(4.18292 + 4.74376i) q^{40} +7.61648i q^{41} +(0.606729 - 0.312960i) q^{42} +6.72651i q^{43} +(-8.25467 + 1.39185i) q^{44} +(-1.02764 - 12.9169i) q^{45} +(-3.80100 - 7.36890i) q^{46} +(4.38366 - 4.38366i) q^{47} +(-3.88975 - 11.2066i) q^{48} -6.97350i q^{49} +(-1.05946 + 6.99125i) q^{50} +(-0.888698 - 0.888698i) q^{51} +(-1.80659 + 2.53938i) q^{52} +11.4324 q^{53} +(-3.56661 + 11.1659i) q^{54} +(-7.12202 - 6.07231i) q^{55} +(0.455760 + 0.0652196i) q^{56} +(6.71003 - 6.71003i) q^{57} +(0.514854 - 0.265570i) q^{58} +(1.63497 + 1.63497i) q^{59} +(6.80702 - 11.3825i) q^{60} +(-1.23034 + 1.23034i) q^{61} +(-5.63796 - 1.80089i) q^{62} +(-0.666993 - 0.666993i) q^{63} +(2.24366 - 7.67893i) q^{64} +(-3.47331 + 0.276329i) q^{65} +(8.04736 + 15.6012i) q^{66} +2.49337i q^{67} +(-0.140926 - 0.835791i) q^{68} +(-12.2946 + 12.2946i) q^{69} +(0.271509 + 0.437317i) q^{70} +8.00096 q^{71} +(-13.1146 + 9.83107i) q^{72} +(-1.12102 - 1.12102i) q^{73} +(2.20453 + 0.704173i) q^{74} +(14.6415 - 2.34454i) q^{75} +(6.31056 - 1.06405i) q^{76} -0.681319 q^{77} +(6.22531 + 1.98850i) q^{78} +3.62218 q^{79} +(8.19054 - 3.59376i) q^{80} +7.19579 q^{81} +(10.2606 + 3.27745i) q^{82} +1.62629 q^{83} +(-0.160525 - 0.952029i) q^{84} +(0.614825 - 0.721109i) q^{85} +(9.06167 + 2.89449i) q^{86} +(-0.859007 - 0.859007i) q^{87} +(-1.67703 + 11.7193i) q^{88} -15.7149 q^{89} +(-17.8433 - 4.17388i) q^{90} +(-0.179352 + 0.179352i) q^{91} +(-11.5627 + 1.94962i) q^{92} +12.4113i q^{93} +(-4.01915 - 7.79182i) q^{94} +(5.44467 + 4.64218i) q^{95} +(-16.7708 + 0.417792i) q^{96} +(9.69217 + 9.69217i) q^{97} +(-9.39441 - 3.00077i) q^{98} +(17.1508 - 17.1508i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} - 16 q^{26} - 24 q^{27} + 40 q^{28} + 14 q^{29} + 40 q^{30} + 20 q^{32} - 8 q^{33} + 28 q^{34} + 2 q^{35} - 4 q^{36} + 24 q^{38} + 44 q^{40} + 8 q^{42} - 44 q^{44} - 14 q^{45} + 12 q^{46} + 38 q^{47} + 4 q^{48} - 8 q^{50} + 8 q^{51} + 8 q^{52} + 12 q^{53} + 4 q^{54} - 6 q^{55} + 20 q^{56} - 24 q^{57} + 20 q^{58} + 10 q^{59} + 8 q^{60} + 14 q^{61} - 40 q^{62} - 6 q^{63} + 16 q^{64} + 4 q^{66} - 60 q^{68} - 32 q^{69} - 28 q^{70} + 24 q^{71} - 68 q^{72} - 14 q^{73} - 48 q^{74} + 16 q^{75} - 16 q^{76} - 44 q^{77} - 36 q^{78} - 16 q^{79} - 92 q^{80} + 2 q^{81} + 48 q^{82} + 40 q^{83} + 24 q^{84} + 14 q^{85} - 36 q^{86} + 24 q^{87} - 8 q^{88} + 12 q^{89} - 8 q^{90} - 8 q^{92} - 28 q^{94} + 34 q^{95} - 40 q^{96} + 18 q^{97} - 56 q^{98} + 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.430311	−	1.34716i	0.304276	−	0.952584i
$2$	0.430311	−	1.34716i	0.304276	−	0.952584i
$3$	−2.96561			−1.71220			−0.856099	−	0.516813i	$-0.827118\pi$
$3$	−2.96561			−1.71220			−0.856099	+	0.516813i	$0.827118\pi$
$4$	−1.62967	−	1.15939i	−0.814833	−	0.579696i
$5$	−0.177336	−	2.22902i	−0.0793073	−	0.996850i
$5$	−0.177336	−	2.22902i	−0.0793073	−	0.996850i
$6$	−1.27613	+	3.99515i	−0.520980	+	1.63101i
$7$	−0.115101	−	0.115101i	−0.0435040	−	0.0435040i	0.685020	−	0.728524i	$-0.259793\pi$
$7$	−0.115101	−	0.115101i	−0.0435040	−	0.0435040i	−0.728524	+	0.685020i	$0.759793\pi$
$8$	−2.26315	+	1.69652i	−0.800143	+	0.599809i
$9$	5.79486			1.93162
$10$	−3.07916	−	0.720273i	−0.973715	−	0.227770i
$11$	2.95966	−	2.95966i	0.892372	−	0.892372i	−0.102374	−	0.994746i	$-0.532644\pi$
$11$	2.95966	−	2.95966i	0.892372	−	0.892372i	0.994746	+	0.102374i	$0.0326439\pi$
$12$	4.83296	+	3.43831i	1.39515	+	0.992554i
$13$		−	1.55822i		−	0.432172i	−0.976374	−	0.216086i	$-0.930671\pi$
$13$		−	1.55822i		−	0.432172i	0.976374	−	0.216086i	$-0.0693292\pi$
$14$	−0.204588	+	0.105530i	−0.0546784	+	0.0282040i
$15$	0.525911	+	6.61042i	0.135790	+	1.70680i
$16$	1.31162	+	3.77884i	0.327905	+	0.944711i
$17$	0.299668	+	0.299668i	0.0726801	+	0.0726801i	0.742512	−	0.669832i	$-0.233634\pi$
$17$	0.299668	+	0.299668i	0.0726801	+	0.0726801i	−0.669832	+	0.742512i	$0.733634\pi$
$18$	2.49359	−	7.80658i	0.587745	−	1.84003i
$19$	−2.26261	+	2.26261i	−0.519079	+	0.519079i	−0.917293	−	0.398214i	$-0.869630\pi$
$19$	−2.26261	+	2.26261i	−0.519079	+	0.519079i	0.398214	+	0.917293i	$0.369630\pi$
$20$	−2.29532	+	3.83817i	−0.513248	+	0.858240i
$21$	0.341344	+	0.341344i	0.0744874	+	0.0744874i
$22$	−2.71356	−	5.26071i	−0.578532	−	1.12159i
$23$	4.14573	−	4.14573i	0.864444	−	0.864444i	−0.127406	−	0.991851i	$-0.540665\pi$
$23$	4.14573	−	4.14573i	0.864444	−	0.864444i	0.991851	+	0.127406i	$0.0406652\pi$
$24$	6.71162	−	5.03121i	1.37000	−	1.02699i
$25$	−4.93710	+	0.790575i	−0.987421	+	0.158115i
$26$	−2.09917	−	0.670518i	−0.411680	−	0.131499i
$27$	−8.28846			−1.59511
$28$	0.0541288	+	0.321023i	0.0102294	+	0.0606676i
$29$	0.289656	+	0.289656i	0.0537878	+	0.0537878i	0.733489	−	0.679701i	$-0.237891\pi$
$29$	0.289656	+	0.289656i	0.0537878	+	0.0537878i	−0.679701	+	0.733489i	$0.737891\pi$
$30$	9.13159	+	2.13605i	1.66719	+	0.389988i
$31$		−	4.18508i		−	0.751663i	−0.926688	−	0.375832i	$-0.877357\pi$
$31$		−	4.18508i		−	0.751663i	0.926688	−	0.375832i	$-0.122643\pi$
$32$	5.65510	−	0.140879i	0.999690	−	0.0249041i
$33$	−8.77721	+	8.77721i	−1.52792	+	1.52792i
$34$	0.532650	−	0.274749i	0.0913487	−	0.0471191i
$35$	−0.236151	+	0.276974i	−0.0399168	+	0.0468172i
$36$	−9.44368	−	6.71851i	−1.57395	−	1.11975i
$37$			1.63643i			0.269027i	0.990912	+	0.134514i	$0.0429472\pi$
$37$			1.63643i			0.269027i	−0.990912	+	0.134514i	$0.957053\pi$
$38$	2.07447	+	4.02172i	0.336523	+	0.652410i
$39$			4.62107i			0.739964i
$40$	4.18292	+	4.74376i	0.661377	+	0.750054i
$41$			7.61648i			1.18949i	0.803913	+	0.594747i	$0.202748\pi$
$41$			7.61648i			1.18949i	−0.803913	+	0.594747i	$0.797252\pi$
$42$	0.606729	−	0.312960i	0.0936203	−	0.0482908i
$43$			6.72651i			1.02578i	0.858453	+	0.512892i	$0.171426\pi$
$43$			6.72651i			1.02578i	−0.858453	+	0.512892i	$0.828574\pi$
$44$	−8.25467	+	1.39185i	−1.24444	+	0.209829i
$45$	−1.02764	−	12.9169i	−0.153191	−	1.92553i
$46$	−3.80100	−	7.36890i	−0.560427	−	1.08649i
$47$	4.38366	−	4.38366i	0.639423	−	0.639423i	−0.310990	−	0.950413i	$-0.600661\pi$
$47$	4.38366	−	4.38366i	0.639423	−	0.639423i	0.950413	+	0.310990i	$0.100661\pi$
$48$	−3.88975	−	11.2066i	−0.561437	−	1.61753i
$49$		−	6.97350i		−	0.996215i
$50$	−1.05946	+	6.99125i	−0.149830	+	0.988712i
$51$	−0.888698	−	0.888698i	−0.124443	−	0.124443i
$52$	−1.80659	+	2.53938i	−0.250529	+	0.352148i
$53$	11.4324			1.57036			0.785182	−	0.619265i	$-0.212569\pi$
$53$	11.4324			1.57036			0.785182	+	0.619265i	$0.212569\pi$
$54$	−3.56661	+	11.1659i	−0.485355	+	1.51948i
$55$	−7.12202	−	6.07231i	−0.960333	−	0.818790i
$56$	0.455760	+	0.0652196i	0.0609035	+	0.00871533i
$57$	6.71003	−	6.71003i	0.888766	−	0.888766i
$58$	0.514854	−	0.265570i	0.0676037	−	0.0348711i
$59$	1.63497	+	1.63497i	0.212855	+	0.212855i	0.805479	−	0.592624i	$-0.201908\pi$
$59$	1.63497	+	1.63497i	0.212855	+	0.212855i	−0.592624	+	0.805479i	$0.701908\pi$
$60$	6.80702	−	11.3825i	0.878782	−	1.46948i
$61$	−1.23034	+	1.23034i	−0.157528	+	0.157528i	−0.781471	−	0.623942i	$-0.785530\pi$
$61$	−1.23034	+	1.23034i	−0.157528	+	0.157528i	0.623942	+	0.781471i	$0.285530\pi$
$62$	−5.63796	−	1.80089i	−0.716022	−	0.228713i
$63$	−0.666993	−	0.666993i	−0.0840332	−	0.0840332i
$64$	2.24366	−	7.67893i	0.280458	−	0.959866i
$65$	−3.47331	+	0.276329i	−0.430811	+	0.0342744i
$66$	8.04736	+	15.6012i	0.990561	+	1.92038i
$67$			2.49337i			0.304614i	0.988333	+	0.152307i	$0.0486702\pi$
$67$			2.49337i			0.304614i	−0.988333	+	0.152307i	$0.951330\pi$
$68$	−0.140926	−	0.835791i	−0.0170897	−	0.101354i
$69$	−12.2946	+	12.2946i	−1.48010	+	1.48010i
$70$	0.271509	+	0.437317i	0.0324516	+	0.0522694i
$71$	8.00096			0.949540			0.474770	−	0.880110i	$-0.342531\pi$
$71$	8.00096			0.949540			0.474770	+	0.880110i	$0.342531\pi$
$72$	−13.1146	+	9.83107i	−1.54557	+	1.15860i
$73$	−1.12102	−	1.12102i	−0.131205	−	0.131205i	0.638454	−	0.769660i	$-0.279574\pi$
$73$	−1.12102	−	1.12102i	−0.131205	−	0.131205i	−0.769660	+	0.638454i	$0.779574\pi$
$74$	2.20453	+	0.704173i	0.256271	+	0.0818584i
$75$	14.6415	−	2.34454i	1.69066	−	0.270724i
$76$	6.31056	−	1.06405i	0.723871	−	0.122054i
$77$	−0.681319			−0.0776435
$78$	6.22531	+	1.98850i	0.704878	+	0.225153i
$79$	3.62218			0.407527			0.203763	−	0.979020i	$-0.434683\pi$
$79$	3.62218			0.407527			0.203763	+	0.979020i	$0.434683\pi$
$80$	8.19054	−	3.59376i	0.915730	−	0.401794i
$81$	7.19579			0.799532
$82$	10.2606	+	3.27745i	1.13309	+	0.361934i
$83$	1.62629			0.178509			0.0892545	−	0.996009i	$-0.471552\pi$
$83$	1.62629			0.178509			0.0892545	+	0.996009i	$0.471552\pi$
$84$	−0.160525	−	0.952029i	−0.0175147	−	0.103875i
$85$	0.614825	−	0.721109i	0.0666871	−	0.0782152i
$86$	9.06167	+	2.89449i	0.977145	+	0.312121i
$87$	−0.859007	−	0.859007i	−0.0920953	−	0.0920953i
$88$	−1.67703	+	11.7193i	−0.178772	+	1.24928i
$89$	−15.7149			−1.66577			−0.832887	−	0.553443i	$-0.813314\pi$
$89$	−15.7149			−1.66577			−0.832887	+	0.553443i	$0.813314\pi$
$90$	−17.8433	−	4.17388i	−1.88085	−	0.439966i
$91$	−0.179352	+	0.179352i	−0.0188012	+	0.0188012i
$92$	−11.5627	+	1.94962i	−1.20549	+	0.203262i
$93$			12.4113i			1.28700i
$94$	−4.01915	−	7.79182i	−0.414543	−	0.803665i
$95$	5.44467	+	4.64218i	0.558611	+	0.476277i
$96$	−16.7708	+	0.417792i	−1.71167	+	0.0426407i
$97$	9.69217	+	9.69217i	0.984091	+	0.984091i	0.999875	−	0.0157848i	$-0.00502467\pi$
$97$	9.69217	+	9.69217i	0.984091	+	0.984091i	−0.0157848	+	0.999875i	$0.505025\pi$
$98$	−9.39441	−	3.00077i	−0.948978	−	0.303124i
$99$	17.1508	−	17.1508i	1.72372	−	1.72372i
$100$	8.96241	+	4.43567i	0.896241	+	0.443567i
$101$	−12.8067	−	12.8067i	−1.27432	−	1.27432i	−0.943800	−	0.330516i	$-0.892777\pi$
$101$	−12.8067	−	12.8067i	−1.27432	−	1.27432i	−0.330516	−	0.943800i	$-0.607223\pi$
$102$	−1.57963	+	0.814800i	−0.156407	+	0.0806772i
$103$	−4.33738	+	4.33738i	−0.427375	+	0.427375i	−0.887733	−	0.460358i	$-0.847721\pi$
$103$	−4.33738	+	4.33738i	−0.427375	+	0.427375i	0.460358	+	0.887733i	$0.347721\pi$
$104$	2.64354	+	3.52648i	0.259221	+	0.345800i
$105$	0.700332	−	0.821398i	0.0683454	−	0.0801602i
$106$	4.91950	−	15.4013i	0.477824	−	1.49590i
$107$	−11.9807			−1.15822			−0.579108	−	0.815251i	$-0.696599\pi$
$107$	−11.9807			−1.15822			−0.579108	+	0.815251i	$0.696599\pi$
$108$	13.5074	+	9.60958i	1.29975	+	0.924682i
$109$	4.01503	+	4.01503i	0.384570	+	0.384570i	0.872746	−	0.488175i	$-0.162337\pi$
$109$	4.01503	+	4.01503i	0.384570	+	0.384570i	−0.488175	+	0.872746i	$0.662337\pi$
$110$	−11.2450	+	6.98150i	−1.07217	+	0.665660i
$111$		−	4.85301i		−	0.460628i
$112$	0.283980	−	0.585916i	0.0268336	−	0.0553639i
$113$	6.47754	−	6.47754i	0.609356	−	0.609356i	−0.333422	−	0.942778i	$-0.608203\pi$
$113$	6.47754	−	6.47754i	0.609356	−	0.609356i	0.942778	+	0.333422i	$0.108203\pi$
$114$	−6.15207	−	11.9269i	−0.576194	−	1.11705i
$115$	−9.97612	−	8.50575i	−0.930278	−	0.793165i
$116$	−0.136217	−	0.807867i	−0.0126475	−	0.0750086i
$117$		−	9.02966i		−	0.834792i
$118$	2.90611	−	1.49902i	0.267529	−	0.137996i
$119$		−	0.0689840i		−	0.00632375i
$120$	−12.4049	−	14.0681i	−1.13241	−	1.28424i
$121$		−	6.51921i		−	0.592655i
$122$	1.12803	+	2.18688i	0.102127	+	0.197991i
$123$		−	22.5875i		−	2.03665i
$124$	−4.85215	+	6.82028i	−0.435736	+	0.612480i
$125$	2.63774	+	10.8647i	0.235927	+	0.971771i
$126$	−1.18556	+	0.611530i	−0.105618	+	0.0544794i
$127$	−12.2756	+	12.2756i	−1.08928	+	1.08928i	−0.0936781	+	0.995603i	$0.529862\pi$
$127$	−12.2756	+	12.2756i	−1.08928	+	1.08928i	−0.995603	+	0.0936781i	$0.970138\pi$
$128$	−9.37925	−	6.32690i	−0.829017	−	0.559224i
$129$		−	19.9482i		−	1.75634i
$130$	−1.12234	+	4.79800i	−0.0984360	+	0.420813i
$131$	7.99562	+	7.99562i	0.698581	+	0.698581i	0.964104	−	0.265524i	$-0.0855448\pi$
$131$	7.99562	+	7.99562i	0.698581	+	0.698581i	−0.265524	+	0.964104i	$0.585545\pi$
$132$	24.4802	−	4.12768i	2.13072	−	0.359269i
$133$	0.520857			0.0451641
$134$	3.35896	+	1.07292i	0.290170	+	0.0926865i
$135$	1.46985	+	18.4752i	0.126504	+	1.59009i
$136$	−1.18658	−	0.169801i	−0.101749	−	0.0145603i
$137$	−3.08551	+	3.08551i	−0.263613	+	0.263613i	−0.826520	−	0.562907i	$-0.809683\pi$
$137$	−3.08551	+	3.08551i	−0.263613	+	0.263613i	0.562907	+	0.826520i	$0.309683\pi$
$138$	11.2723	+	21.8533i	0.959561	+	1.86028i
$139$	12.2206	+	12.2206i	1.03654	+	1.03654i	0.999307	+	0.0372284i	$0.0118529\pi$
$139$	12.2206	+	12.2206i	1.03654	+	1.03654i	0.0372284	+	0.999307i	$0.488147\pi$
$140$	0.705969	−	0.177583i	0.0596653	−	0.0150085i
$141$	−13.0002	+	13.0002i	−1.09482	+	1.09482i
$142$	3.44290	−	10.7786i	0.288922	−	0.904516i
$143$	−4.61180	−	4.61180i	−0.385658	−	0.385658i
$144$	7.60064	+	21.8979i	0.633386	+	1.82482i
$145$	0.594284	−	0.697017i	0.0493526	−	0.0578841i
$146$	−1.99258	+	1.02780i	−0.164907	+	0.0850616i
$147$			20.6807i			1.70572i
$148$	1.89726	−	2.66683i	0.155954	−	0.219212i
$149$	2.59172	−	2.59172i	0.212322	−	0.212322i	−0.592931	−	0.805253i	$-0.702029\pi$
$149$	2.59172	−	2.59172i	0.212322	−	0.212322i	0.805253	+	0.592931i	$0.202029\pi$
$150$	3.14195	−	20.7333i	0.256539	−	1.69287i
$151$	−16.9594			−1.38014			−0.690068	−	0.723745i	$-0.742419\pi$
$151$	−16.9594			−1.38014			−0.690068	+	0.723745i	$0.742419\pi$
$152$	1.28207	−	8.95919i	0.103989	−	0.726686i
$153$	1.73653	+	1.73653i	0.140390	+	0.140390i
$154$	−0.293179	+	0.917844i	−0.0236250	+	0.0739620i
$155$	−9.32865	+	0.742168i	−0.749296	+	0.0596124i
$156$	5.35764	−	7.53080i	0.428954	−	0.602947i
$157$	8.55235			0.682552			0.341276	−	0.939963i	$-0.389141\pi$
$157$	8.55235			0.682552			0.341276	+	0.939963i	$0.389141\pi$
$158$	1.55866	−	4.87964i	0.124000	−	0.388203i
$159$	−33.9041			−2.68877
$160$	−1.31688	−	12.5804i	−0.104108	−	0.994566i
$161$	−0.954354			−0.0752136
$162$	3.09643	−	9.69386i	0.243278	−	0.761622i
$163$	−3.57797			−0.280248			−0.140124	−	0.990134i	$-0.544750\pi$
$163$	−3.57797			−0.280248			−0.140124	+	0.990134i	$0.544750\pi$
$164$	8.83049	−	12.4123i	0.689545	−	0.969238i
$165$	21.1211	+	18.0081i	1.64428	+	1.40193i
$166$	0.699812	−	2.19087i	0.0543159	−	0.170045i
$167$	0.482874	+	0.482874i	0.0373659	+	0.0373659i	0.725543	−	0.688177i	$-0.241589\pi$
$167$	0.482874	+	0.482874i	0.0373659	+	0.0373659i	−0.688177	+	0.725543i	$0.741589\pi$
$168$	−1.35161	−	0.193416i	−0.104279	−	0.0149224i
$169$	10.5720			0.813227
$170$	−0.706881	−	1.13857i	−0.0542153	−	0.0873241i
$171$	−13.1115	+	13.1115i	−1.00266	+	1.00266i
$172$	7.79867	−	10.9620i	0.594643	−	0.835842i
$173$		−	11.8189i		−	0.898576i	−0.893387	−	0.449288i	$-0.851678\pi$
$173$		−	11.8189i		−	0.898576i	0.893387	−	0.449288i	$-0.148322\pi$
$174$	−1.52686	+	0.787578i	−0.115751	+	0.0597061i
$175$	0.659260	+	0.477269i	0.0498354	+	0.0360781i
$176$	15.0661	+	7.30216i	1.13565	+	0.550421i
$177$	−4.84870	−	4.84870i	−0.364451	−	0.364451i
$178$	−6.76228	+	21.1704i	−0.506855	+	1.58679i
$179$	−4.71524	+	4.71524i	−0.352433	+	0.352433i	−0.861014	−	0.508581i	$-0.830170\pi$
$179$	−4.71524	+	4.71524i	−0.352433	+	0.352433i	0.508581	+	0.861014i	$0.330170\pi$
$180$	−13.3010	+	22.2416i	−0.991400	+	1.65779i
$181$	13.1843	+	13.1843i	0.979983	+	0.979983i	0.999804	−	0.0198205i	$-0.00630948\pi$
$181$	13.1843	+	13.1843i	0.979983	+	0.979983i	−0.0198205	+	0.999804i	$0.506309\pi$
$182$	0.164439	+	0.318793i	0.0121890	+	0.0236305i
$183$	3.64870	−	3.64870i	0.269720	−	0.269720i
$184$	−2.34910	+	16.4157i	−0.173178	+	1.21018i
$185$	3.64764	−	0.290199i	0.268180	−	0.0213358i
$186$	16.7200	+	5.34073i	1.22597	+	0.391601i
$187$	1.77383			0.129715
$188$	−12.2263	+	2.06152i	−0.891694	+	0.150352i
$189$	0.954008	+	0.954008i	0.0693939	+	0.0693939i
$190$	8.59664	−	5.33724i	0.623666	−	0.387204i
$191$		−	13.9872i		−	1.01208i	−0.862510	−	0.506040i	$-0.831109\pi$
$191$		−	13.9872i		−	1.01208i	0.862510	−	0.506040i	$-0.168891\pi$
$192$	−6.65384	+	22.7727i	−0.480199	+	1.64348i
$193$	3.88875	−	3.88875i	0.279919	−	0.279919i	−0.553158	−	0.833076i	$-0.686577\pi$
$193$	3.88875	−	3.88875i	0.279919	−	0.279919i	0.833076	+	0.553158i	$0.186577\pi$
$194$	17.2275	−	8.88623i	1.23686	−	0.637994i
$195$	10.3005	−	0.819485i	0.737633	−	0.0586845i
$196$	−8.08503	+	11.3645i	−0.577502	+	0.811748i
$197$		−	22.3277i		−	1.59078i	−0.606097	−	0.795391i	$-0.707266\pi$
$197$		−	22.3277i		−	1.59078i	0.606097	−	0.795391i	$-0.292734\pi$
$198$	−15.7247	−	30.4850i	−1.11750	−	2.16648i
$199$		−	9.83847i		−	0.697431i	−0.937229	−	0.348715i	$-0.886618\pi$
$199$		−	9.83847i		−	0.697431i	0.937229	−	0.348715i	$-0.113382\pi$
$200$	9.83217	−	10.1651i	0.695239	−	0.718779i
$201$		−	7.39437i		−	0.521559i
$202$	−22.7635	+	11.7418i	−1.60164	+	0.826150i
$203$		−	0.0666793i		−	0.00467997i
$204$	0.417931	+	2.47863i	0.0292610	+	0.173539i
$205$	16.9773	−	1.35068i	1.18575	−	0.0943355i
$206$	3.97671	+	7.70955i	0.277071	+	0.537150i
$207$	24.0239	−	24.0239i	1.66978	−	1.66978i
$208$	5.88827	−	2.04379i	0.408278	−	0.141711i
$209$			13.3931i			0.926423i
$210$	−0.805192	−	1.29691i	−0.0555635	−	0.0894956i
$211$	11.0531	+	11.0531i	0.760925	+	0.760925i	0.976490	−	0.215565i	$-0.0691592\pi$
$211$	11.0531	+	11.0531i	0.760925	+	0.760925i	−0.215565	+	0.976490i	$0.569159\pi$
$212$	−18.6310	−	13.2547i	−1.27958	−	0.910334i
$213$	−23.7278			−1.62580
$214$	−5.15541	+	16.1398i	−0.352417	+	1.10330i
$215$	14.9936	−	1.19286i	1.02255	−	0.0813521i
$216$	18.7580	−	14.0615i	1.27632	−	0.956764i
$217$	−0.481706	+	0.481706i	−0.0327004	+	0.0327004i
$218$	7.13659	−	3.68117i	0.483351	−	0.249320i
$219$	3.32451	+	3.32451i	0.224650	+	0.224650i
$220$	4.56632	+	18.1530i	0.307861	+	1.22388i
$221$	0.466948	−	0.466948i	0.0314103	−	0.0314103i
$222$	−6.53777	−	2.08830i	−0.438787	−	0.140158i
$223$	5.93975	+	5.93975i	0.397755	+	0.397755i	0.877440	−	0.479686i	$-0.159249\pi$
$223$	5.93975	+	5.93975i	0.397755	+	0.397755i	−0.479686	+	0.877440i	$0.659249\pi$
$224$	−0.667122	−	0.634691i	−0.0445740	−	0.0424071i
$225$	−28.6098	+	4.58127i	−1.90732	+	0.305418i
$226$	−5.93891	−	11.5136i	−0.395051	−	0.765875i
$227$		−	23.2105i		−	1.54054i	−0.637720	−	0.770269i	$-0.720122\pi$
$227$		−	23.2105i		−	1.54054i	0.637720	−	0.770269i	$-0.279878\pi$
$228$	−18.7147	+	3.15555i	−1.23941	+	0.208981i
$229$	5.59944	−	5.59944i	0.370021	−	0.370021i	−0.497464	−	0.867485i	$-0.665735\pi$
$229$	5.59944	−	5.59944i	0.370021	−	0.370021i	0.867485	+	0.497464i	$0.165735\pi$
$230$	−15.7514	+	9.77929i	−1.03862	+	0.644828i
$231$	2.02053			0.132941
$232$	−1.14694	−	0.164128i	−0.0753003	−	0.0107755i
$233$	3.01998	+	3.01998i	0.197845	+	0.197845i	0.799076	−	0.601230i	$-0.205323\pi$
$233$	3.01998	+	3.01998i	0.197845	+	0.197845i	−0.601230	+	0.799076i	$0.705323\pi$
$234$	−12.1644	−	3.88556i	−0.795209	−	0.254007i
$235$	−10.5487	−	8.99391i	−0.688120	−	0.586698i
$236$	−0.768884	−	4.56004i	−0.0500501	−	0.296833i
$237$	−10.7420			−0.697766
$238$	−0.0929323	−	0.0296846i	−0.00602391	−	0.00192416i
$239$	−0.00138865			−8.98241e−5			−4.49120e−5	−	1.00000i	$-0.500014\pi$
$239$	−0.00138865			−8.98241e−5			−4.49120e−5		1.00000i	$0.500014\pi$
$240$	−24.2900	+	10.6577i	−1.56791	+	0.687951i
$241$	−12.8578			−0.828245			−0.414123	−	0.910221i	$-0.635912\pi$
$241$	−12.8578			−0.828245			−0.414123	+	0.910221i	$0.635912\pi$
$242$	−8.78240	−	2.80529i	−0.564554	−	0.180331i
$243$	3.52546			0.226158
$244$	3.43148	−	0.578593i	0.219678	−	0.0370407i
$245$	−15.5441	+	1.23666i	−0.993077	+	0.0790071i
$246$	−30.4289	−	9.71965i	−1.94008	−	0.619702i
$247$	3.52565	+	3.52565i	0.224332	+	0.224332i
$248$	7.10006	+	9.47146i	0.450854	+	0.601438i
$249$	−4.82296			−0.305643
$250$	15.7715	+	1.12176i	0.997480	+	0.0709463i
$251$	−9.14111	+	9.14111i	−0.576982	+	0.576982i	−0.934071	−	0.357089i	$-0.883769\pi$
$251$	−9.14111	+	9.14111i	−0.576982	+	0.576982i	0.357089	+	0.934071i	$0.383769\pi$
$252$	0.313668	+	1.86028i	0.0197593	+	0.117187i
$253$		−	24.5399i		−	1.54281i
$254$	11.2548	+	21.8194i	0.706190	+	1.36907i
$255$	−1.82333	+	2.13853i	−0.114181	+	0.133920i
$256$	−12.5593	+	9.91280i	−0.784957	+	0.619550i
$257$	21.2733	+	21.2733i	1.32699	+	1.32699i	0.907980	+	0.419013i	$0.137624\pi$
$257$	21.2733	+	21.2733i	1.32699	+	1.32699i	0.419013	+	0.907980i	$0.362376\pi$
$258$	−26.8734	−	8.58394i	−1.67306	−	0.534413i
$259$	0.188354	−	0.188354i	0.0117038	−	0.0117038i
$260$	5.98071	+	3.57660i	0.370908	+	0.221812i
$261$	1.67851	+	1.67851i	0.103897	+	0.103897i
$262$	14.2120	−	7.33076i	0.878018	−	0.452896i
$263$	−16.7214	+	16.7214i	−1.03108	+	1.03108i	−0.0315818	+	0.999501i	$0.510054\pi$
$263$	−16.7214	+	16.7214i	−1.03108	+	1.03108i	−0.999501	+	0.0315818i	$0.989946\pi$
$264$	4.97343	−	34.7548i	0.306094	−	2.13901i
$265$	−2.02739	−	25.4832i	−0.124541	−	1.56542i
$266$	0.224131	−	0.701677i	0.0137423	−	0.0430226i
$267$	46.6043			2.85213
$268$	2.89079	−	4.06336i	0.176583	−	0.248209i
$269$	15.9096	+	15.9096i	0.970026	+	0.970026i	0.999564	−	0.0295378i	$-0.00940355\pi$
$269$	15.9096	+	15.9096i	0.970026	+	0.970026i	−0.0295378	+	0.999564i	$0.509404\pi$
$270$	25.5215	+	5.96996i	1.55319	+	0.363320i
$271$			12.3601i			0.750824i	0.926858	+	0.375412i	$0.122499\pi$
$271$			12.3601i			0.750824i	−0.926858	+	0.375412i	$0.877501\pi$
$272$	−0.739348	+	1.52545i	−0.0448295	+	0.0924938i
$273$	0.531889	−	0.531889i	0.0321914	−	0.0321914i
$274$	2.82894	+	5.48440i	0.170902	+	0.331324i
$275$	−12.2723	+	16.9520i	−0.740049	+	1.02224i
$276$	34.2904	−	5.78183i	2.06404	−	0.348025i
$277$			21.0270i			1.26339i	0.775217	+	0.631695i	$0.217641\pi$
$277$			21.0270i			1.26339i	−0.775217	+	0.631695i	$0.782359\pi$
$278$	21.7217	−	11.2044i	1.30278	−	0.671994i
$279$		−	24.2520i		−	1.45193i
$280$	0.0645531	−	1.02747i	0.00385779	−	0.0614029i
$281$			10.6807i			0.637158i	0.947896	+	0.318579i	$0.103206\pi$
$281$			10.6807i			0.637158i	−0.947896	+	0.318579i	$0.896794\pi$
$282$	11.9192	+	23.1075i	0.709780	+	1.37603i
$283$		−	12.5946i		−	0.748673i	−0.927293	−	0.374336i	$-0.877871\pi$
$283$		−	12.5946i		−	0.748673i	0.927293	−	0.374336i	$-0.122129\pi$
$284$	−13.0389	−	9.27626i	−0.773716	−	0.550445i
$285$	−16.1468	−	13.7669i	−0.956452	−	0.815481i
$286$	−8.19733	+	4.22832i	−0.484718	+	0.250026i
$287$	0.876663	−	0.876663i	0.0517478	−	0.0517478i
$288$	32.7705	−	0.816372i	1.93102	−	0.0481052i
$289$		−	16.8204i		−	0.989435i
$290$	−0.683265	−	1.10053i	−0.0401227	−	0.0646252i
$291$	−28.7432	−	28.7432i	−1.68496	−	1.68496i
$292$	0.527185	+	3.12659i	0.0308512	+	0.182970i
$293$	3.43132			0.200460			0.100230	−	0.994964i	$-0.468042\pi$
$293$	3.43132			0.200460			0.100230	+	0.994964i	$0.468042\pi$
$294$	27.8602	+	8.89913i	1.62484	+	0.519008i
$295$	3.35446	−	3.93434i	0.195304	−	0.229066i
$296$	−2.77623	−	3.70348i	−0.161365	−	0.215260i
$297$	−24.5310	+	24.5310i	−1.42344	+	1.42344i
$298$	−2.37621	−	4.60670i	−0.137650	−	0.266859i
$299$	−6.45996	−	6.45996i	−0.373589	−	0.373589i
$300$	−26.5790	−	13.1545i	−1.53454	−	0.759474i
$301$	0.774227	−	0.774227i	0.0446257	−	0.0446257i
$302$	−7.29781	+	22.8470i	−0.419942	+	1.31470i
$303$	37.9798	+	37.9798i	2.18188	+	2.18188i
$304$	−11.5177	−	5.58238i	−0.660588	−	0.320171i
$305$	2.96063	+	2.52427i	0.169525	+	0.144539i
$306$	3.08663	−	1.59213i	0.176451	−	0.0910162i
$307$		−	11.8104i		−	0.674053i	−0.941495	−	0.337027i	$-0.890579\pi$
$307$		−	11.8104i		−	0.674053i	0.941495	−	0.337027i	$-0.109421\pi$
$308$	1.11032	+	0.789916i	0.0632665	+	0.0450097i
$309$	12.8630	−	12.8630i	0.731750	−	0.731750i
$310$	−3.01440	+	12.8865i	−0.171207	+	0.731906i
$311$	22.6262			1.28301			0.641506	−	0.767118i	$-0.278310\pi$
$311$	22.6262			1.28301			0.641506	+	0.767118i	$0.278310\pi$
$312$	−7.83973	−	10.4582i	−0.443837	−	0.592077i
$313$	7.08945	+	7.08945i	0.400719	+	0.400719i	0.878486	−	0.477767i	$-0.158554\pi$
$313$	7.08945	+	7.08945i	0.400719	+	0.400719i	−0.477767	+	0.878486i	$0.658554\pi$
$314$	3.68017	−	11.5214i	0.207684	−	0.650188i
$315$	−1.36846	+	1.60503i	−0.0771040	+	0.0904329i
$316$	−5.90294	−	4.19952i	−0.332066	−	0.236242i
$317$	−25.1265			−1.41124			−0.705621	−	0.708589i	$-0.749332\pi$
$317$	−25.1265			−1.41124			−0.705621	+	0.708589i	$0.749332\pi$
$318$	−14.5893	+	45.6742i	−0.818128	+	2.56128i
$319$	1.71457			0.0959974
$320$	−17.5144	−	3.63943i	−0.979085	−	0.203450i
$321$	35.5300			1.98309
$322$	−0.410669	+	1.28566i	−0.0228857	+	0.0716473i
$323$	−1.35606			−0.0754535
$324$	−11.7267	−	8.34274i	−0.651485	−	0.463486i
$325$	1.23189	+	7.69309i	0.0683329	+	0.426736i
$326$	−1.53964	+	4.82008i	−0.0852726	+	0.266960i
$327$	−11.9070	−	11.9070i	−0.658460	−	0.658460i
$328$	−12.9215	−	17.2372i	−0.713469	−	0.951765i
$329$	−1.00913			−0.0556349
$330$	33.3484	−	20.7044i	1.83577	−	1.13974i
$331$	5.80829	−	5.80829i	0.319253	−	0.319253i	−0.529227	−	0.848480i	$-0.677518\pi$
$331$	5.80829	−	5.80829i	0.319253	−	0.319253i	0.848480	+	0.529227i	$0.177518\pi$
$332$	−2.65032	−	1.88551i	−0.145455	−	0.103481i
$333$			9.48287i			0.519658i
$334$	0.858293	−	0.442721i	0.0469637	−	0.0242246i
$335$	5.55778	−	0.442166i	0.303654	−	0.0241581i
$336$	−0.842174	+	1.73760i	−0.0459443	+	0.0947939i
$337$	−7.41679	−	7.41679i	−0.404019	−	0.404019i	0.475628	−	0.879647i	$-0.342221\pi$
$337$	−7.41679	−	7.41679i	−0.404019	−	0.404019i	−0.879647	+	0.475628i	$0.842221\pi$
$338$	4.54923	−	14.2421i	0.247445	−	0.774667i
$339$	−19.2099	+	19.2099i	−1.04334	+	1.04334i
$340$	−1.83801	+	0.462343i	−0.0996799	+	0.0250741i
$341$	−12.3864	−	12.3864i	−0.670763	−	0.670763i
$342$	12.0213	+	23.3053i	0.650035	+	1.26021i
$343$	−1.60836	+	1.60836i	−0.0868434	+	0.0868434i
$344$	−11.4116	−	15.2231i	−0.615274	−	0.820774i
$345$	29.5853	+	25.2247i	1.59282	+	1.35805i
$346$	−15.9220	−	5.08581i	−0.855970	−	0.273415i
$347$	−18.2493			−0.979673			−0.489837	−	0.871814i	$-0.662944\pi$
$347$	−18.2493			−0.979673			−0.489837	+	0.871814i	$0.662944\pi$
$348$	0.403968	+	2.39582i	0.0216549	+	0.128430i
$349$	−19.4413	−	19.4413i	−1.04067	−	1.04067i	−0.999137	−	0.0415330i	$-0.986776\pi$
$349$	−19.4413	−	19.4413i	−1.04067	−	1.04067i	−0.0415330	−	0.999137i	$-0.513224\pi$
$350$	0.926643	−	0.682754i	0.0495312	−	0.0364947i
$351$			12.9152i			0.689364i
$352$	16.3202	−	17.1541i	0.869871	−	0.914319i
$353$	−1.13598	+	1.13598i	−0.0604622	+	0.0604622i	−0.736691	−	0.676229i	$-0.763613\pi$
$353$	−1.13598	+	1.13598i	−0.0604622	+	0.0604622i	0.676229	+	0.736691i	$0.263613\pi$
$354$	−8.61841	+	4.44551i	−0.458063	+	0.236276i
$355$	−1.41886	−	17.8343i	−0.0753054	−	0.946549i
$356$	25.6100	+	18.2197i	1.35733	+	0.965643i
$357$			0.204580i			0.0108275i
$358$	4.32315	+	8.38118i	0.228485	+	0.442959i
$359$			28.4140i			1.49963i	0.661645	+	0.749817i	$0.269859\pi$
$359$			28.4140i			1.49963i	−0.661645	+	0.749817i	$0.730141\pi$
$360$	24.2394	+	27.4894i	1.27753	+	1.44882i
$361$			8.76116i			0.461114i
$362$	23.4347	−	12.0880i	1.23170	−	0.635331i
$363$			19.3334i			1.01474i
$364$	0.500224	−	0.0843445i	0.0262189	−	0.00442085i
$365$	−2.29998	+	2.69758i	−0.120387	+	0.141198i
$366$	−3.34530	−	6.48545i	−0.174861	−	0.339000i
$367$	−2.29692	+	2.29692i	−0.119898	+	0.119898i	−0.764510	−	0.644612i	$-0.777019\pi$
$367$	−2.29692	+	2.29692i	−0.119898	+	0.119898i	0.644612	+	0.764510i	$0.277019\pi$
$368$	21.1037	+	10.2285i	1.10011	+	0.533195i
$369$			44.1364i			2.29765i
$370$	1.17868	−	5.03882i	0.0612764	−	0.261956i
$371$	−1.31588	−	1.31588i	−0.0683172	−	0.0683172i
$372$	14.3896	−	20.2263i	0.746066	−	1.04869i
$373$	−18.0787			−0.936081			−0.468040	−	0.883707i	$-0.655040\pi$
$373$	−18.0787			−0.936081			−0.468040	+	0.883707i	$0.655040\pi$
$374$	0.763298	−	2.38963i	0.0394692	−	0.123565i
$375$	−7.82251	−	32.2206i	−0.403953	−	1.66386i
$376$	−2.48392	+	17.3578i	−0.128098	+	0.895162i
$377$	0.451348	−	0.451348i	0.0232456	−	0.0232456i
$378$	1.69572	−	0.874679i	0.0872184	−	0.0449886i
$379$	−2.79031	−	2.79031i	−0.143328	−	0.143328i	0.631802	−	0.775130i	$-0.282316\pi$
$379$	−2.79031	−	2.79031i	−0.143328	−	0.143328i	−0.775130	+	0.631802i	$0.782316\pi$
$380$	−3.49088	−	13.8777i	−0.179078	−	0.711911i
$381$	36.4046	−	36.4046i	1.86506	−	1.86506i
$382$	−18.8430	−	6.01885i	−0.964090	−	0.307951i
$383$	−8.12206	−	8.12206i	−0.415018	−	0.415018i	0.468464	−	0.883482i	$-0.344807\pi$
$383$	−8.12206	−	8.12206i	−0.415018	−	0.415018i	−0.883482	+	0.468464i	$0.844807\pi$
$384$	27.8152	+	18.7631i	1.41944	+	0.957501i
$385$	0.120823	+	1.51868i	0.00615770	+	0.0773990i
$386$	−3.56539	−	6.91213i	−0.181474	−	0.351818i
$387$			38.9792i			1.98142i
$388$	−4.55796	−	27.0320i	−0.231396	−	1.37234i
$389$	−14.4341	+	14.4341i	−0.731839	+	0.731839i	−0.970984	−	0.239145i	$-0.923133\pi$
$389$	−14.4341	+	14.4341i	−0.731839	+	0.731839i	0.239145	+	0.970984i	$0.423133\pi$
$390$	3.32844	−	14.2290i	0.168542	−	0.720514i
$391$	2.48468			0.125656
$392$	11.8307	+	15.7821i	0.597539	+	0.797114i
$393$	−23.7119	−	23.7119i	−1.19611	−	1.19611i
$394$	−30.0789	−	9.60785i	−1.51535	−	0.484036i
$395$	−0.642344	−	8.07392i	−0.0323198	−	0.406243i
$396$	−47.8346	+	8.06556i	−2.40378	+	0.405310i
$397$	−35.1624			−1.76475			−0.882374	−	0.470549i	$-0.844056\pi$
$397$	−35.1624			−1.76475			−0.882374	+	0.470549i	$0.844056\pi$
$398$	−13.2540	−	4.23360i	−0.664362	−	0.212211i
$399$	−1.54466			−0.0773298
$400$	−9.46305	−	17.6196i	−0.473153	−	0.880980i
$401$	−23.5164			−1.17435			−0.587176	−	0.809459i	$-0.699760\pi$
$401$	−23.5164			−1.17435			−0.587176	+	0.809459i	$0.699760\pi$
$402$	−9.96138	−	3.18188i	−0.496828	−	0.158698i
$403$	−6.52128			−0.324848
$404$	6.02265	+	35.7187i	0.299638	+	1.77707i
$405$	−1.27608	−	16.0396i	−0.0634087	−	0.797014i
$406$	−0.0898275	−	0.0286928i	−0.00445806	−	0.00142400i
$407$	4.84328	+	4.84328i	0.240072	+	0.240072i
$408$	3.51895	+	0.503563i	0.174214	+	0.0249301i
$409$	23.2595			1.15011			0.575054	−	0.818115i	$-0.304981\pi$
$409$	23.2595			1.15011			0.575054	+	0.818115i	$0.304981\pi$
$410$	5.48594	−	23.4523i	0.270931	−	1.15823i
$411$	9.15043	−	9.15043i	0.451357	−	0.451357i
$412$	12.0972	−	2.03975i	0.595986	−	0.100491i
$413$		−	0.376374i		−	0.0185201i
$414$	−22.0262	−	42.7017i	−1.08253	−	2.09868i
$415$	−0.288401	−	3.62505i	−0.0141571	−	0.177947i
$416$	−0.219520	−	8.81188i	−0.0107628	−	0.432038i
$417$	−36.2415	−	36.2415i	−1.77475	−	1.77475i
$418$	18.0427	+	5.76322i	0.882496	+	0.281888i
$419$	6.63975	−	6.63975i	0.324373	−	0.324373i	−0.526069	−	0.850442i	$-0.676335\pi$
$419$	6.63975	−	6.63975i	0.324373	−	0.324373i	0.850442	+	0.526069i	$0.176335\pi$
$420$	−2.09363	+	0.526644i	−0.102159	+	0.0256976i
$421$	7.28216	+	7.28216i	0.354911	+	0.354911i	0.861933	−	0.507022i	$-0.169254\pi$
$421$	7.28216	+	7.28216i	0.354911	+	0.354911i	−0.507022	+	0.861933i	$0.669254\pi$
$422$	19.6465	−	10.1340i	0.956376	−	0.493314i
$423$	25.4027	−	25.4027i	1.23512	−	1.23512i
$424$	−25.8733	+	19.3953i	−1.25652	+	0.941919i
$425$	−1.71640	−	1.24258i	−0.0832576	−	0.0602740i
$426$	−10.2103	+	31.9650i	−0.494691	+	1.54871i
$427$	0.283225			0.0137062
$428$	19.5245	+	13.8903i	0.943751	+	0.671413i
$429$	13.6768	+	13.6768i	0.660323	+	0.660323i
$430$	4.84493	−	20.7120i	0.233643	−	0.998821i
$431$		−	11.7250i		−	0.564771i	−0.959301	−	0.282386i	$-0.908874\pi$
$431$		−	11.7250i		−	0.564771i	0.959301	−	0.282386i	$-0.0911258\pi$
$432$	−10.8713	−	31.3208i	−0.523045	−	1.50692i
$433$	−20.8827	+	20.8827i	−1.00356	+	1.00356i	−0.00356603	+	0.999994i	$0.501135\pi$
$433$	−20.8827	+	20.8827i	−1.00356	+	1.00356i	−0.999994	+	0.00356603i	$0.998865\pi$
$434$	0.441651	+	0.856218i	0.0211999	+	0.0410998i
$435$	−1.76242	+	2.06708i	−0.0845014	+	0.0991090i
$436$	−1.88816	−	11.1982i	−0.0904265	−	0.536294i
$437$			18.7604i			0.897430i
$438$	5.90921	−	3.04807i	0.282353	−	0.145642i
$439$		−	7.53661i		−	0.359703i	−0.983694	−	0.179851i	$-0.942438\pi$
$439$		−	7.53661i		−	0.359703i	0.983694	−	0.179851i	$-0.0575617\pi$
$440$	26.4199	+	1.65990i	1.25952	+	0.0791325i
$441$		−	40.4105i		−	1.92431i
$442$	−0.428120	−	0.829985i	−0.0203636	−	0.0394784i
$443$			25.7280i			1.22237i	0.791486	+	0.611187i	$0.209308\pi$
$443$			25.7280i			1.22237i	−0.791486	+	0.611187i	$0.790692\pi$
$444$	−5.62655	+	7.90879i	−0.267024	+	0.375334i
$445$	2.78682	+	35.0289i	0.132108	+	1.66053i
$446$	10.5577	−	5.44584i	0.499922	−	0.257868i
$447$	−7.68604	+	7.68604i	−0.363537	+	0.363537i
$448$	−1.14210	+	0.625604i	−0.0539591	+	0.0295570i
$449$			2.33824i			0.110348i	0.998477	+	0.0551741i	$0.0175714\pi$
$449$			2.33824i			0.110348i	−0.998477	+	0.0551741i	$0.982429\pi$
$450$	−6.13942	+	40.5133i	−0.289415	+	1.90981i
$451$	22.5422	+	22.5422i	1.06147	+	1.06147i
$452$	−18.0662	+	3.04621i	−0.849765	+	0.143282i
$453$	50.2950			2.36306
$454$	−31.2682	−	9.98774i	−1.46749	−	0.468748i
$455$	0.431586	+	0.367975i	0.0202331	+	0.0172509i
$456$	−3.80211	+	26.5695i	−0.178050	+	1.24423i
$457$	10.4561	−	10.4561i	0.489115	−	0.489115i	−0.418912	−	0.908027i	$-0.637588\pi$
$457$	10.4561	−	10.4561i	0.489115	−	0.489115i	0.908027	+	0.418912i	$0.137588\pi$
$458$	−5.13383	−	9.95282i	−0.239888	−	0.465065i
$459$	−2.48378	−	2.48378i	−0.115933	−	0.115933i
$460$	6.39625	+	25.4278i	0.298226	+	1.18558i
$461$	15.6903	−	15.6903i	0.730769	−	0.730769i	−0.240003	−	0.970772i	$-0.577148\pi$
$461$	15.6903	−	15.6903i	0.730769	−	0.730769i	0.970772	+	0.240003i	$0.0771484\pi$
$462$	0.869455	−	2.72197i	0.0404507	−	0.126637i
$463$	−19.6332	−	19.6332i	−0.912434	−	0.912434i	0.0840297	−	0.996463i	$-0.473221\pi$
$463$	−19.6332	−	19.6332i	−0.912434	−	0.912434i	−0.996463	+	0.0840297i	$0.973221\pi$
$464$	−0.714647	+	1.47448i	−0.0331766	+	0.0684511i
$465$	27.6652	−	2.20098i	1.28294	−	0.102068i
$466$	5.36791	−	2.76886i	0.248664	−	0.128265i
$467$		−	24.4862i		−	1.13309i	−0.824032	−	0.566543i	$-0.808281\pi$
$467$		−	24.4862i		−	1.13309i	0.824032	−	0.566543i	$-0.191719\pi$
$468$	−10.4689	+	14.7153i	−0.483926	+	0.680216i
$469$	0.286989	−	0.286989i	0.0132519	−	0.0132519i
$470$	−16.6554	+	10.3406i	−0.768257	+	0.476974i
$471$	−25.3630			−1.16866
$472$	−6.47395	−	0.926426i	−0.297987	−	0.0426422i
$473$	19.9082	+	19.9082i	0.915380	+	0.915380i
$474$	−4.62239	+	14.4711i	−0.212313	+	0.664681i
$475$	9.38199	−	12.9595i	0.430475	−	0.594624i
$476$	−0.0799795	+	0.112421i	−0.00366586	+	0.00515280i
$477$	66.2493			3.03335
$478$	−0.000597550		0.00187073i	−2.73313e−5		8.55650e-5i
$479$	37.0609			1.69335			0.846677	−	0.532108i	$-0.178600\pi$
$479$	37.0609			1.69335			0.846677	+	0.532108i	$0.178600\pi$
$480$	3.90535	+	37.3085i	0.178254	+	1.70289i
$481$	2.54991			0.116266
$482$	−5.53286	+	17.3215i	−0.252015	+	0.788973i
$483$	2.83024			0.128781
$484$	−7.55832	+	10.6241i	−0.343560	+	0.482915i
$485$	19.8853	−	23.3229i	0.902945	−	1.05904i
$486$	1.51704	−	4.74935i	0.0688145	−	0.215435i
$487$	20.1912	+	20.1912i	0.914950	+	0.914950i	0.996656	−	0.0817061i	$-0.0260369\pi$
$487$	20.1912	+	20.1912i	0.914950	+	0.914950i	−0.0817061	+	0.996656i	$0.526037\pi$
$488$	0.697145	−	4.87172i	0.0315583	−	0.220532i
$489$	10.6109			0.479840
$490$	−5.02283	+	21.4725i	−0.226908	+	0.970029i
$491$	−7.45822	+	7.45822i	−0.336585	+	0.336585i	−0.855080	−	0.518496i	$-0.826492\pi$
$491$	−7.45822	+	7.45822i	−0.336585	+	0.336585i	0.518496	+	0.855080i	$0.326492\pi$
$492$	−26.1878	+	36.8101i	−1.18064	+	1.65953i
$493$			0.173601i			0.00781860i
$494$	6.26673	−	3.23248i	0.281953	−	0.145436i
$495$	−41.2711	−	35.1881i	−1.85500	−	1.58159i
$496$	15.8148	−	5.48923i	0.710104	−	0.246474i
$497$	−0.920917	−	0.920917i	−0.0413088	−	0.0413088i
$498$	−2.07537	+	6.49728i	−0.0929996	+	0.291150i
$499$	8.17420	−	8.17420i	0.365927	−	0.365927i	−0.500062	−	0.865990i	$-0.666689\pi$
$499$	8.17420	−	8.17420i	0.365927	−	0.365927i	0.865990	+	0.500062i	$0.166689\pi$
$500$	8.29785	−	20.7640i	0.371091	−	0.928596i
$501$	−1.43202	−	1.43202i	−0.0639778	−	0.0639778i
$502$	8.38100	+	16.2480i	0.374062	+	0.725185i
$503$	−29.2327	+	29.2327i	−1.30342	+	1.30342i	−0.377348	+	0.926072i	$0.623164\pi$
$503$	−29.2327	+	29.2327i	−1.30342	+	1.30342i	−0.926072	+	0.377348i	$0.876836\pi$
$504$	2.64107	+	0.377938i	0.117642	+	0.0168347i
$505$	−26.2754	+	30.8176i	−1.16924	+	1.37136i
$506$	−33.0591	−	10.5598i	−1.46966	−	0.469440i
$507$	−31.3523			−1.39241
$508$	34.2373	−	5.77287i	1.51903	−	0.256130i
$509$	−20.0340	−	20.0340i	−0.887992	−	0.887992i	0.106338	−	0.994330i	$-0.466088\pi$
$509$	−20.0340	−	20.0340i	−0.887992	−	0.887992i	−0.994330	+	0.106338i	$0.966088\pi$
$510$	2.09634	+	3.37655i	0.0928273	+	0.149516i
$511$			0.258061i			0.0114159i
$512$	7.94969	+	21.1850i	0.351330	+	0.936252i
$513$	18.7536	−	18.7536i	0.827991	−	0.827991i
$514$	37.8126	−	19.5044i	1.66784	−	0.860301i
$515$	10.4373	+	8.89895i	0.459922	+	0.392135i
$516$	−23.1278	+	32.5089i	−1.01815	+	1.43113i
$517$		−	25.9483i		−	1.14121i
$518$	−0.172692	−	0.334794i	−0.00758765	−	0.0147100i
$519$			35.0504i			1.53854i
$520$	7.39181	−	6.51790i	0.324152	−	0.285829i
$521$		−	5.89264i		−	0.258161i	−0.991634	−	0.129081i	$-0.958797\pi$
$521$		−	5.89264i		−	0.258161i	0.991634	−	0.129081i	$-0.0412026\pi$
$522$	2.98351	−	1.53894i	0.130585	−	0.0673576i
$523$			24.6537i			1.07803i	0.842296	+	0.539015i	$0.181203\pi$
$523$			24.6537i			1.07803i	−0.842296	+	0.539015i	$0.818797\pi$
$524$	−3.76012	−	22.3003i	−0.164262	−	0.974191i
$525$	−1.95511	−	1.41539i	−0.0853280	−	0.0617729i
$526$	15.3309	+	29.7217i	0.668460	+	1.29593i
$527$	1.25413	−	1.25413i	0.0546309	−	0.0546309i
$528$	−44.6801	−	21.6554i	−1.94445	−	0.942429i
$529$		−	11.3742i		−	0.494528i
$530$	−35.2022	−	8.23447i	−1.52909	−	0.357683i
$531$	9.47444	+	9.47444i	0.411156	+	0.411156i
$532$	−0.848823	−	0.603878i	−0.0368012	−	0.0261814i
$533$	11.8681			0.514066
$534$	20.0543	−	62.7833i	0.867835	−	2.71690i
$535$	2.12461	+	26.7052i	0.0918549	+	1.15457i
$536$	−4.23004	−	5.64286i	−0.182710	−	0.243735i
$537$	13.9836	−	13.9836i	0.603435	−	0.603435i
$538$	28.2788	−	14.5867i	1.21919	−	0.628876i
$539$	−20.6392	−	20.6392i	−0.888994	−	0.888994i
$540$	19.0246	−	31.8125i	0.818690	−	1.36899i
$541$	−27.1762	+	27.1762i	−1.16840	+	1.16840i	−0.185812	+	0.982585i	$0.559492\pi$
$541$	−27.1762	+	27.1762i	−1.16840	+	1.16840i	−0.982585	+	0.185812i	$0.940508\pi$
$542$	16.6510	+	5.31869i	0.715223	+	0.228457i
$543$	−39.0996	−	39.0996i	−1.67792	−	1.67792i
$544$	1.73687	+	1.65243i	0.0744676	+	0.0708475i
$545$	8.23759	−	9.66162i	0.352860	−	0.413858i
$546$	−0.487661	−	0.945416i	−0.0208700	−	0.0404601i
$547$			3.69225i			0.157869i	0.996880	+	0.0789347i	$0.0251519\pi$
$547$			3.69225i			0.157869i	−0.996880	+	0.0789347i	$0.974848\pi$
$548$	8.60567	−	1.45103i	0.367616	−	0.0619850i
$549$	−7.12962	+	7.12962i	−0.304285	+	0.304285i
$550$	17.5561	+	23.8274i	0.748594	+	1.01600i
$551$	−1.31076			−0.0558402
$552$	6.96651	−	48.6826i	0.296514	−	2.07207i
$553$	−0.416915	−	0.416915i	−0.0177290	−	0.0177290i
$554$	28.3267	+	9.04815i	1.20349	+	0.384419i
$555$	−10.8175	+	0.860616i	−0.459177	+	0.0365311i
$556$	−5.74700	−	34.0839i	−0.243727	−	1.44548i
$557$	12.2117			0.517426			0.258713	−	0.965954i	$-0.416702\pi$
$557$	12.2117			0.517426			0.258713	+	0.965954i	$0.416702\pi$
$558$	−32.6712	−	10.4359i	−1.38308	−	0.441786i
$559$	10.4814			0.443315
$560$	−1.35638	−	0.529093i	−0.0573176	−	0.0223583i
$561$	−5.26049			−0.222098
$562$	14.3886	+	4.59603i	0.606947	+	0.193872i
$563$	−12.2211			−0.515057			−0.257528	−	0.966271i	$-0.582908\pi$
$563$	−12.2211			−0.515057			−0.257528	+	0.966271i	$0.582908\pi$
$564$	36.2584	−	6.11366i	1.52676	−	0.257432i
$565$	−15.5873	−	13.2899i	−0.655763	−	0.559110i
$566$	−16.9669	−	5.41960i	−0.713174	−	0.227803i
$567$	−0.828241	−	0.828241i	−0.0347829	−	0.0347829i
$568$	−18.1074	+	13.5738i	−0.759768	+	0.569543i
$569$	−30.9592			−1.29788			−0.648938	−	0.760841i	$-0.724787\pi$
$569$	−30.9592			−1.29788			−0.648938	+	0.760841i	$0.724787\pi$
$570$	−25.4943	+	15.8282i	−1.06784	+	0.662970i
$571$	30.1508	−	30.1508i	1.26177	−	1.26177i	0.311539	−	0.950233i	$-0.399156\pi$
$571$	30.1508	−	30.1508i	1.26177	−	1.26177i	0.950233	−	0.311539i	$-0.100844\pi$
$572$	2.16881	+	12.8626i	0.0906823	+	0.537812i
$573$			41.4806i			1.73288i
$574$	−0.803765	−	1.55824i	−0.0335485	−	0.0650397i
$575$	−17.1904	+	23.7454i	−0.716889	+	0.990252i
$576$	13.0017	−	44.4983i	0.541738	−	1.85410i
$577$	1.98215	+	1.98215i	0.0825181	+	0.0825181i	0.747161	−	0.664643i	$-0.231416\pi$
$577$	1.98215	+	1.98215i	0.0825181	+	0.0825181i	−0.664643	+	0.747161i	$0.731416\pi$
$578$	−22.6597	−	7.23800i	−0.942520	−	0.301061i
$579$	−11.5325	+	11.5325i	−0.479276	+	0.479276i
$580$	−1.77660	+	0.446896i	−0.0737693	+	0.0185564i
$581$	−0.187188	−	0.187188i	−0.00776586	−	0.00776586i
$582$	−51.0901	+	26.3531i	−2.11775	+	1.09237i
$583$	33.8361	−	33.8361i	1.40135	−	1.40135i
$584$	4.43886	+	0.635204i	0.183681	+	0.0262849i
$585$	−20.1273	+	1.60129i	−0.832163	+	0.0662051i
$586$	1.47653	−	4.62253i	0.0609951	−	0.190955i
$587$	26.9680			1.11309			0.556544	−	0.830818i	$-0.312127\pi$
$587$	26.9680			1.11309			0.556544	+	0.830818i	$0.312127\pi$
$588$	23.9771	−	33.7026i	0.988797	−	1.38987i
$589$	9.46923	+	9.46923i	0.390173	+	0.390173i
$590$	−3.85671	−	6.21197i	−0.158778	−	0.255743i
$591$			66.2153i			2.72373i
$592$	−6.18381	+	2.14637i	−0.254153	+	0.0882152i
$593$	16.6701	−	16.6701i	0.684560	−	0.684560i	−0.276464	−	0.961024i	$-0.589163\pi$
$593$	16.6701	−	16.6701i	0.684560	−	0.684560i	0.961024	+	0.276464i	$0.0891626\pi$
$594$	22.4912	+	43.6032i	0.922825	+	1.78906i
$595$	−0.153767	+	0.0122334i	−0.00630383	+	0.000501520i
$596$	−7.22846	+	1.21882i	−0.296089	+	0.0499247i
$597$			29.1771i			1.19414i
$598$	−11.4824	+	5.92279i	−0.469549	+	0.242201i
$599$		−	28.8376i		−	1.17827i	−0.808033	−	0.589137i	$-0.799468\pi$
$599$		−	28.8376i		−	1.17827i	0.808033	−	0.589137i	$-0.200532\pi$
$600$	−29.1584	+	30.1456i	−1.19039	+	1.23069i
$601$		−	1.91377i		−	0.0780642i	−0.999238	−	0.0390321i	$-0.987573\pi$
$601$		−	1.91377i		−	0.0780642i	0.999238	−	0.0390321i	$-0.0124275\pi$
$602$	−0.709847	−	1.37616i	−0.0289312	−	0.0560882i
$603$			14.4487i			0.588397i
$604$	27.6381	+	19.6626i	1.12458	+	0.800059i
$605$	−14.5315	+	1.15609i	−0.590789	+	0.0470019i
$606$	67.5078	−	34.8216i	2.74232	−	1.41453i
$607$	−7.89049	+	7.89049i	−0.320265	+	0.320265i	−0.848869	−	0.528604i	$-0.822716\pi$
$607$	−7.89049	+	7.89049i	−0.320265	+	0.320265i	0.528604	+	0.848869i	$0.322716\pi$
$608$	−12.4766	+	13.1141i	−0.505991	+	0.531845i
$609$			0.197745i			0.00801303i
$610$	4.67457	−	2.90222i	0.189268	−	0.117507i
$611$	−6.83071	−	6.83071i	−0.276341	−	0.276341i
$612$	−0.816643	−	4.84329i	−0.0330109	−	0.195778i
$613$	−40.1035			−1.61976			−0.809882	−	0.586592i	$-0.800469\pi$
$613$	−40.1035			−1.61976			−0.809882	+	0.586592i	$0.800469\pi$
$614$	−15.9104	−	5.08213i	−0.642092	−	0.205098i
$615$	−50.3481	+	4.00559i	−2.03023	+	0.161521i
$616$	1.54193	−	1.15587i	0.0621259	−	0.0465713i
$617$	14.5821	−	14.5821i	0.587052	−	0.587052i	−0.349780	−	0.936832i	$-0.613744\pi$
$617$	14.5821	−	14.5821i	0.587052	−	0.587052i	0.936832	+	0.349780i	$0.113744\pi$
$618$	−11.7934	−	22.8635i	−0.474399	−	0.919707i
$619$	−4.01752	−	4.01752i	−0.161478	−	0.161478i	0.621743	−	0.783221i	$-0.286425\pi$
$619$	−4.01752	−	4.01752i	−0.161478	−	0.161478i	−0.783221	+	0.621743i	$0.786425\pi$
$620$	16.0630	+	9.60609i	0.645108	+	0.385790i
$621$	−34.3617	+	34.3617i	−1.37889	+	1.37889i
$622$	9.73628	−	30.4810i	0.390389	−	1.22218i
$623$	1.80880	+	1.80880i	0.0724679	+	0.0724679i
$624$	−17.4623	+	6.06108i	−0.699052	+	0.242638i
$625$	23.7500	−	7.80630i	0.949999	−	0.312252i
$626$	12.6013	−	6.49993i	0.503648	−	0.259790i
$627$		−	39.7189i		−	1.58622i
$628$	−13.9375	−	9.91553i	−0.556166	−	0.395673i
$629$	−0.490385	+	0.490385i	−0.0195529	+	0.0195529i
$630$	1.57336	+	2.53419i	0.0626841	+	0.100965i
$631$	−26.9309			−1.07210			−0.536052	−	0.844185i	$-0.680085\pi$
$631$	−26.9309			−1.07210			−0.536052	+	0.844185i	$0.680085\pi$
$632$	−8.19752	+	6.14508i	−0.326080	+	0.244438i
$633$	−32.7791	−	32.7791i	−1.30285	−	1.30285i
$634$	−10.8122	+	33.8493i	−0.429407	+	1.34433i
$635$	29.5395	+	25.1856i	1.17224	+	0.999462i
$636$	55.2524	+	39.3082i	2.19090	+	1.55867i
$637$	−10.8662			−0.430536
$638$	0.737797	−	2.30979i	0.0292097	−	0.0914456i
$639$	46.3644			1.83415
$640$	−12.4395	+	22.0286i	−0.491715	+	0.870756i
$641$	18.6880			0.738131			0.369065	−	0.929403i	$-0.379678\pi$
$641$	18.6880			0.738131			0.369065	+	0.929403i	$0.379678\pi$
$642$	15.2890	−	47.8645i	0.603407	−	1.88906i
$643$	29.6249			1.16829			0.584146	−	0.811648i	$-0.301429\pi$
$643$	29.6249			1.16829			0.584146	+	0.811648i	$0.301429\pi$
$644$	1.55528	+	1.10647i	0.0612865	+	0.0436011i
$645$	−44.4651	+	3.53755i	−1.75081	+	0.139291i
$646$	−0.583529	+	1.82683i	−0.0229586	+	0.0718758i
$647$	−5.04426	−	5.04426i	−0.198310	−	0.198310i	0.600965	−	0.799275i	$-0.294783\pi$
$647$	−5.04426	−	5.04426i	−0.198310	−	0.198310i	−0.799275	+	0.600965i	$0.794783\pi$
$648$	−16.2851	+	12.2078i	−0.639740	+	0.479567i
$649$	9.67794			0.379893
$650$	10.8939	+	1.65087i	0.427294	+	0.0647525i
$651$	1.42855	−	1.42855i	0.0559895	−	0.0559895i
$652$	5.83089	+	4.14827i	0.228355	+	0.162459i
$653$		−	3.04934i		−	0.119330i	−0.998218	−	0.0596649i	$-0.980997\pi$
$653$		−	3.04934i		−	0.119330i	0.998218	−	0.0596649i	$-0.0190032\pi$
$654$	−21.1644	+	10.9169i	−0.827592	+	0.426885i
$655$	16.4045	−	19.2404i	0.640978	−	0.751783i
$656$	−28.7815	+	9.98991i	−1.12373	+	0.390040i
$657$	−6.49615	−	6.49615i	−0.253439	−	0.253439i
$658$	−0.434238	+	1.35945i	−0.0169284	+	0.0529970i
$659$	22.0441	−	22.0441i	0.858718	−	0.858718i	−0.132469	−	0.991187i	$-0.542291\pi$
$659$	22.0441	−	22.0441i	0.858718	−	0.858718i	0.991187	+	0.132469i	$0.0422906\pi$
$660$	−13.5419	−	53.8349i	−0.527119	−	2.09552i
$661$	8.09788	+	8.09788i	0.314971	+	0.314971i	0.846832	−	0.531861i	$-0.178507\pi$
$661$	8.09788	+	8.09788i	0.314971	+	0.314971i	−0.531861	+	0.846832i	$0.678507\pi$
$662$	−5.32531	−	10.3241i	−0.206974	−	0.401256i
$663$	−1.38479	+	1.38479i	−0.0537807	+	0.0537807i
$664$	−3.68054	+	2.75904i	−0.142833	+	0.107071i
$665$	−0.0923670	−	1.16100i	−0.00358184	−	0.0450218i
$666$	12.7749	+	4.08058i	0.495018	+	0.158119i
$667$	2.40167			0.0929931
$668$	−0.227083	−	1.34676i	−0.00878609	−	0.0521078i
$669$	−17.6150	−	17.6150i	−0.681035	−	0.681035i
$670$	1.79591	−	7.67748i	0.0693820	−	0.296607i
$671$			7.28276i			0.281148i
$672$	1.97842	+	1.88225i	0.0763194	+	0.0726093i
$673$	−27.1768	+	27.1768i	−1.04759	+	1.04759i	−0.0487786	+	0.998810i	$0.515533\pi$
$673$	−27.1768	+	27.1768i	−1.04759	+	1.04759i	−0.998810	+	0.0487786i	$0.984467\pi$
$674$	−13.1831	+	6.80006i	−0.507795	+	0.261929i
$675$	40.9210	−	6.55265i	1.57505	−	0.252212i
$676$	−17.2287	−	12.2570i	−0.662644	−	0.471425i
$677$			28.6501i			1.10111i	0.834798	+	0.550557i	$0.185585\pi$
$677$			28.6501i			1.10111i	−0.834798	+	0.550557i	$0.814415\pi$
$678$	17.6125	+	34.1450i	0.676405	+	1.31133i
$679$		−	2.23115i		−	0.0856238i
$680$	−0.168066	+	2.67504i	−0.00644502	+	0.102583i
$681$			68.8334i			2.63770i
$682$	−22.0165	+	11.3565i	−0.843055	+	0.434861i
$683$		−	30.8472i		−	1.18034i	−0.807281	−	0.590168i	$-0.799062\pi$
$683$		−	30.8472i		−	1.18034i	0.807281	−	0.590168i	$-0.200938\pi$
$684$	36.5688	−	6.16599i	1.39824	−	0.235763i
$685$	7.42485	+	6.33051i	0.283689	+	0.241876i
$686$	1.47462	+	2.85881i	0.0563013	+	0.109150i
$687$	−16.6058	+	16.6058i	−0.633549	+	0.633549i
$688$	−25.4184	+	8.82261i	−0.969069	+	0.336359i
$689$		−	17.8142i		−	0.678668i
$690$	46.7126	−	29.0016i	1.77832	−	1.10407i
$691$	0.253186	+	0.253186i	0.00963164	+	0.00963164i	0.711906	−	0.702275i	$-0.247832\pi$
$691$	0.253186	+	0.253186i	0.00963164	+	0.00963164i	−0.702275	+	0.711906i	$0.747832\pi$
$692$	−13.7028	+	19.2609i	−0.520901	+	0.732189i
$693$	−3.94815			−0.149978
$694$	−7.85286	+	24.5847i	−0.298091	+	0.933221i
$695$	25.0728	−	29.4071i	0.951066	−	1.11548i
$696$	3.40138	+	0.486740i	0.128929	+	0.0184498i
$697$	−2.28241	+	2.28241i	−0.0864525	+	0.0864525i
$698$	−34.5563	+	17.8247i	−1.30798	+	0.674675i
$699$	−8.95608	−	8.95608i	−0.338750	−	0.338750i
$700$	−0.521032	−	1.54213i	−0.0196932	−	0.0582870i
$701$	10.5238	−	10.5238i	0.397479	−	0.397479i	−0.479864	−	0.877343i	$-0.659314\pi$
$701$	10.5238	−	10.5238i	0.397479	−	0.397479i	0.877343	+	0.479864i	$0.159314\pi$
$702$	17.3989	+	5.55756i	0.656677	+	0.209757i
$703$	−3.70261	−	3.70261i	−0.139646	−	0.139646i
$704$	−16.0866	−	29.3675i	−0.606285	−	1.10683i
$705$	31.2833	+	26.6725i	1.17820	+	1.00454i
$706$	1.04152	+	2.01917i	0.0391982	+	0.0759925i
$707$			2.94813i			0.110876i
$708$	2.28021	+	13.5233i	0.0856956	+	0.508237i
$709$	1.58968	−	1.58968i	0.0597015	−	0.0597015i	−0.676626	−	0.736327i	$-0.736558\pi$
$709$	1.58968	−	1.58968i	0.0597015	−	0.0597015i	0.736327	+	0.676626i	$0.236558\pi$
$710$	−24.6362	−	5.76288i	−0.924581	−	0.216277i
$711$	20.9900			0.787186
$712$	35.5651	−	26.6606i	1.33286	−	0.999147i
$713$	−17.3502	−	17.3502i	−0.649771	−	0.649771i
$714$	0.275601	+	0.0880329i	0.0103141	+	0.00329455i
$715$	−9.46198	+	11.0977i	−0.353858	+	0.415029i
$716$	13.1511	−	2.21745i	0.491478	−	0.0828699i
$717$	0.00411819			0.000153797
$718$	38.2781	+	12.2269i	1.42853	+	0.456302i
$719$	−22.8919			−0.853722			−0.426861	−	0.904317i	$-0.640381\pi$
$719$	−22.8919			−0.853722			−0.426861	+	0.904317i	$0.640381\pi$
$720$	47.4630	−	20.8253i	1.76884	−	0.776113i
$721$	0.998472			0.0371850
$722$	11.8027	+	3.77002i	0.439249	+	0.140306i
$723$	38.1313			1.41812
$724$	−6.20023	−	36.7718i	−0.230430	−	1.36661i
$725$	−1.65906	−	1.20107i	−0.0616158	−	0.0446065i
$726$	26.0452	+	8.31939i	0.966628	+	0.308762i
$727$	20.1893	+	20.1893i	0.748780	+	0.748780i	0.974250	−	0.225470i	$-0.0723919\pi$
$727$	20.1893	+	20.1893i	0.748780	+	0.748780i	−0.225470	+	0.974250i	$0.572392\pi$
$728$	0.101626	−	0.710175i	0.00376653	−	0.0263208i
$729$	−32.0425			−1.18676
$730$	2.64436	+	4.25924i	0.0978720	+	0.157641i
$731$	−2.01572	+	2.01572i	−0.0745540	+	0.0745540i
$732$	−10.1764	+	1.71588i	−0.376132	+	0.0634209i
$733$			14.3253i			0.529118i	0.964370	+	0.264559i	$0.0852263\pi$
$733$			14.3253i			0.529118i	−0.964370	+	0.264559i	$0.914774\pi$
$734$	2.10592	+	4.08270i	0.0777311	+	0.150695i
$735$	46.0978	−	3.66744i	1.70034	−	0.135276i
$736$	22.8605	−	24.0286i	0.842648	−	0.885705i
$737$	7.37954	+	7.37954i	0.271829	+	0.271829i
$738$	59.4587	+	18.9924i	2.18870	+	0.699119i
$739$	−32.3401	+	32.3401i	−1.18965	+	1.18965i	−0.212487	+	0.977164i	$0.568156\pi$
$739$	−32.3401	+	32.3401i	−1.18965	+	1.18965i	−0.977164	+	0.212487i	$0.931844\pi$
$740$	−6.28089	−	3.75612i	−0.230890	−	0.138078i
$741$	−10.4557	−	10.4557i	−0.384100	−	0.384100i
$742$	−2.33894	+	1.20646i	−0.0858651	+	0.0442906i
$743$	−6.06842	+	6.06842i	−0.222629	+	0.222629i	−0.809605	−	0.586976i	$-0.800318\pi$
$743$	−6.06842	+	6.06842i	−0.222629	+	0.222629i	0.586976	+	0.809605i	$0.300318\pi$
$744$	−21.0560	−	28.0887i	−0.771952	−	1.02978i
$745$	−6.23662	−	5.31741i	−0.228492	−	0.194815i
$746$	−7.77947	+	24.3549i	−0.284827	+	0.891696i
$747$	9.42414			0.344811
$748$	−2.89075	−	2.05657i	−0.105696	−	0.0751955i
$749$	1.37898	+	1.37898i	0.0503870	+	0.0503870i
$750$	−46.7723	−	3.32670i	−1.70788	−	0.121474i
$751$		−	49.6431i		−	1.81150i	−0.423810	−	0.905751i	$-0.639308\pi$
$751$		−	49.6431i		−	1.81150i	0.423810	−	0.905751i	$-0.360692\pi$
$752$	22.3149	+	10.8155i	0.813740	+	0.394400i
$753$	27.1090	−	27.1090i	0.987907	−	0.987907i
$754$	−0.413816	−	0.802256i	−0.0150703	−	0.0292164i
$755$	3.00752	+	37.8029i	0.109455	+	1.37579i
$756$	−0.448644	−	2.66078i	−0.0163170	−	0.0967718i
$757$		−	9.18443i		−	0.333814i	−0.985973	−	0.166907i	$-0.946622\pi$
$757$		−	9.18443i		−	0.333814i	0.985973	−	0.166907i	$-0.0533779\pi$
$758$	−4.95968	+	2.55828i	−0.180144	+	0.0929211i
$759$			72.7759i			2.64160i
$760$	−20.1976	−	1.26896i	−0.732644	−	0.0460302i
$761$			4.75310i			0.172300i	0.996282	+	0.0861499i	$0.0274564\pi$
$761$			4.75310i			0.172300i	−0.996282	+	0.0861499i	$0.972544\pi$
$762$	−33.3774	−	64.7080i	−1.20914	−	2.34412i
$763$		−	0.924267i		−	0.0334607i
$764$	−16.2167	+	22.7945i	−0.586698	+	0.824675i
$765$	3.56282	−	4.17872i	0.128814	−	0.151082i
$766$	−14.4367	+	7.44668i	−0.521619	+	0.269060i
$767$	2.54765	−	2.54765i	0.0919902	−	0.0919902i
$768$	37.2461	−	29.3975i	1.34400	−	1.06079i
$769$			19.4153i			0.700135i	0.936724	+	0.350067i	$0.113841\pi$
$769$			19.4153i			0.700135i	−0.936724	+	0.350067i	$0.886159\pi$
$770$	2.09789	+	0.490736i	0.0756027	+	0.0176849i
$771$	−63.0884	−	63.0884i	−2.27207	−	2.27207i
$772$	−10.8460	+	1.82877i	−0.390355	+	0.0658190i
$773$	26.0890			0.938356			0.469178	−	0.883104i	$-0.344550\pi$
$773$	26.0890			0.938356			0.469178	+	0.883104i	$0.344550\pi$
$774$	52.5111	+	16.7732i	1.88747	+	0.602899i
$775$	3.30862	+	20.6622i	0.118849	+	0.742208i
$776$	−38.3777	−	5.49187i	−1.37768	−	0.197147i
$777$	−0.558586	+	0.558586i	−0.0200392	+	0.0200392i
$778$	13.2339	+	25.6562i	0.474458	+	0.919819i
$779$	−17.2331	−	17.2331i	−0.617442	−	0.617442i
$780$	−17.7365	−	10.6068i	−0.635067	−	0.379785i
$781$	23.6802	−	23.6802i	0.847343	−	0.847343i
$782$	1.06919	−	3.34726i	0.0382340	−	0.119698i
$783$	−2.40080	−	2.40080i	−0.0857977	−	0.0857977i
$784$	26.3518	−	9.14657i	0.941135	−	0.326663i
$785$	−1.51664	−	19.0634i	−0.0541313	−	0.680402i
$786$	−42.1472	+	21.7402i	−1.50334	+	0.775447i
$787$		−	14.2339i		−	0.507384i	−0.967285	−	0.253692i	$-0.918355\pi$
$787$		−	14.2339i		−	0.507384i	0.967285	−	0.253692i	$-0.0816449\pi$
$788$	−25.8866	+	36.3867i	−0.922170	+	1.29622i
$789$	49.5891	−	49.5891i	1.76542	−	1.76542i
$790$	−11.1532	−	2.60896i	−0.396815	−	0.0928225i
$791$	−1.49114			−0.0530189
$792$	−9.71817	+	67.9115i	−0.345320	+	2.41313i
$793$	1.91713	+	1.91713i	0.0680794	+	0.0680794i
$794$	−15.1307	+	47.3692i	−0.536970	+	1.68107i
$795$	6.01244	+	75.5732i	0.213239	+	2.68030i
$796$	−11.4067	+	16.0334i	−0.404298	+	0.568289i
$797$	19.8283			0.702353			0.351176	−	0.936309i	$-0.385782\pi$
$797$	19.8283			0.702353			0.351176	+	0.936309i	$0.385782\pi$
$798$	−0.664684	+	2.08090i	−0.0235296	+	0.0736631i
$799$	2.62729			0.0929467
$800$	−27.8084	+	5.16631i	−0.983177	+	0.182657i
$801$	−91.0655			−3.21764
$802$	−10.1194	+	31.6803i	−0.357327	+	1.11867i
$803$	−6.63568			−0.234168
$804$	−8.57298	+	12.0503i	−0.302346	+	0.424983i
$805$	0.169242	+	2.12728i	0.00596499	+	0.0749767i
$806$	−2.80618	+	8.78518i	−0.0988433	+	0.309445i
$807$	−47.1817	−	47.1817i	−1.66088	−	1.66088i
$808$	50.7103	+	7.25667i	1.78398	+	0.255289i
$809$	21.3864			0.751907			0.375954	−	0.926639i	$-0.377315\pi$
$809$	21.3864			0.751907			0.375954	+	0.926639i	$0.377315\pi$
$810$	−22.1570	−	5.18293i	−0.778516	−	0.182110i
$811$	−9.90624	+	9.90624i	−0.347855	+	0.347855i	−0.859310	−	0.511455i	$-0.829107\pi$
$811$	−9.90624	+	9.90624i	−0.347855	+	0.347855i	0.511455	+	0.859310i	$0.329107\pi$
$812$	−0.0773075	+	0.108665i	−0.00271296	+	0.00381339i
$813$		−	36.6553i		−	1.28556i
$814$	8.60877	−	4.44054i	0.301737	−	0.155641i
$815$	0.634504	+	7.97538i	0.0222257	+	0.279365i
$816$	2.19262	−	4.52388i	0.0767570	−	0.158368i
$817$	−15.2195	−	15.2195i	−0.532463	−	0.532463i
$818$	10.0088	−	31.3342i	0.349950	−	1.09557i
$819$	−1.03932	+	1.03932i	−0.0363168	+	0.0363168i
$820$	−29.2333	−	17.4822i	−1.02087	−	0.610506i
$821$	22.6209	+	22.6209i	0.789474	+	0.789474i	0.981408	−	0.191934i	$-0.0614759\pi$
$821$	22.6209	+	22.6209i	0.789474	+	0.789474i	−0.191934	+	0.981408i	$0.561476\pi$
$822$	−8.38954	−	16.2646i	−0.292619	−	0.567293i
$823$	4.89892	−	4.89892i	0.170766	−	0.170766i	−0.616550	−	0.787316i	$-0.711470\pi$
$823$	4.89892	−	4.89892i	0.170766	−	0.170766i	0.787316	+	0.616550i	$0.211470\pi$
$824$	2.45769	−	17.1746i	0.0856177	−	0.598304i
$825$	36.3950	−	50.2731i	1.26711	−	1.75028i
$826$	−0.507034	−	0.161958i	−0.0176420	−	0.00563523i
$827$	1.05434			0.0366630			0.0183315	−	0.999832i	$-0.494165\pi$
$827$	1.05434			0.0366630			0.0183315	+	0.999832i	$0.494165\pi$
$828$	−67.0041	+	11.2978i	−2.32855	+	0.392625i
$829$	11.7754	+	11.7754i	0.408978	+	0.408978i	0.881382	−	0.472404i	$-0.156614\pi$
$829$	11.7754	+	11.7754i	0.408978	+	0.408978i	−0.472404	+	0.881382i	$0.656614\pi$
$830$	−5.00762	−	1.17138i	−0.173817	−	0.0406591i
$831$		−	62.3580i		−	2.16317i
$832$	−11.9655	−	3.49612i	−0.414828	−	0.121206i
$833$	2.08973	−	2.08973i	0.0724050	−	0.0724050i
$834$	−64.4181	+	33.2279i	−2.23061	+	1.15059i
$835$	0.990707	−	1.16197i	0.0342848	−	0.0402116i
$836$	15.5279	−	21.8263i	0.537044	−	0.754880i
$837$			34.6879i			1.19899i
$838$	−6.08763	−	11.8019i	−0.210294	−	0.407691i
$839$		−	41.1678i		−	1.42127i	−0.703560	−	0.710636i	$-0.748407\pi$
$839$		−	41.1678i		−	1.42127i	0.703560	−	0.710636i	$-0.251593\pi$
$840$	−0.191440	+	3.04707i	−0.00660529	+	0.105134i
$841$		−	28.8322i		−	0.994214i
$842$	12.9438	−	6.67662i	0.446073	−	0.230092i
$843$		−	31.6749i		−	1.09094i
$844$	−5.19796	−	30.8277i	−0.178921	−	1.06113i
$845$	−1.87479	−	23.5651i	−0.0644948	−	0.810666i
$846$	−23.2904	−	45.1525i	−0.800740	−	1.55237i
$847$	−0.750366	+	0.750366i	−0.0257829	+	0.0257829i
$848$	14.9950	+	43.2013i	0.514930	+	1.48354i
$849$			37.3508i			1.28188i
$850$	−2.41254	+	1.77757i	−0.0827493	+	0.0609700i
$851$	6.78419	+	6.78419i	0.232559	+	0.232559i
$852$	38.6683	+	27.5098i	1.32475	+	0.942470i
$853$	11.7179			0.401212			0.200606	−	0.979672i	$-0.435709\pi$
$853$	11.7179			0.401212			0.200606	+	0.979672i	$0.435709\pi$
$854$	0.121875	−	0.381549i	0.00417047	−	0.0130563i
$855$	31.5511	+	26.9008i	1.07902	+	0.919986i
$856$	27.1140	−	20.3254i	0.926738	−	0.694708i
$857$	−12.2154	+	12.2154i	−0.417270	+	0.417270i	−0.884262	−	0.466992i	$-0.845338\pi$
$857$	−12.2154	+	12.2154i	−0.417270	+	0.417270i	0.466992	+	0.884262i	$0.345338\pi$
$858$	24.3101	−	12.5395i	0.829933	−	0.428093i
$859$	17.2170	+	17.2170i	0.587436	+	0.587436i	0.936936	−	0.349500i	$-0.113649\pi$
$859$	17.2170	+	17.2170i	0.587436	+	0.587436i	−0.349500	+	0.936936i	$0.613649\pi$
$860$	−25.8175	−	15.4395i	−0.880369	−	0.526482i
$861$	−2.59984	+	2.59984i	−0.0886024	+	0.0886024i
$862$	−15.7954	−	5.04537i	−0.537992	−	0.171846i
$863$	−11.1929	−	11.1929i	−0.381011	−	0.381011i	0.490455	−	0.871466i	$-0.336831\pi$
$863$	−11.1929	−	11.1929i	−0.381011	−	0.381011i	−0.871466	+	0.490455i	$0.836831\pi$
$864$	−46.8721	+	1.16767i	−1.59462	+	0.0397249i
$865$	−26.3447	+	2.09593i	−0.895746	+	0.0712637i
$866$	19.1463	+	37.1184i	0.650616	+	1.26133i
$867$			49.8828i			1.69411i
$868$	1.34351	−	0.226533i	0.0456016	−	0.00768905i
$869$	10.7204	−	10.7204i	0.363665	−	0.363665i
$870$	2.02630	+	3.26374i	0.0686980	+	0.110651i
$871$	3.88522			0.131646
$872$	−15.8982	−	2.27504i	−0.538380	−	0.0770425i
$873$	56.1647	+	56.1647i	1.90089	+	1.90089i
$874$	25.2732	+	8.07279i	0.854878	+	0.273066i
$875$	0.946933	−	1.55415i	0.0320122	−	0.0525397i
$876$	−1.56343	−	9.27225i	−0.0528233	−	0.313280i
$877$	43.1739			1.45788			0.728940	−	0.684578i	$-0.240013\pi$
$877$	43.1739			1.45788			0.728940	+	0.684578i	$0.240013\pi$
$878$	−10.1530	−	3.24308i	−0.342647	−	0.109449i
$879$	−10.1760			−0.343227
$880$	13.6049	−	34.8775i	0.458622	−	1.17572i
$881$	−33.4204			−1.12596			−0.562981	−	0.826470i	$-0.690346\pi$
$881$	−33.4204			−1.12596			−0.562981	+	0.826470i	$0.690346\pi$
$882$	−54.4392	−	17.3891i	−1.83306	−	0.585520i
$883$	2.00362			0.0674270			0.0337135	−	0.999432i	$-0.489267\pi$
$883$	2.00362			0.0674270			0.0337135	+	0.999432i	$0.489267\pi$
$884$	−1.30234	+	0.219593i	−0.0438026	+	0.00738571i
$885$	−9.94802	+	11.6677i	−0.334399	+	0.392206i
$886$	34.6597	+	11.0710i	1.16441	+	0.371939i
$887$	−16.1765	−	16.1765i	−0.543154	−	0.543154i	0.381298	−	0.924452i	$-0.375477\pi$
$887$	−16.1765	−	16.1765i	−0.543154	−	0.543154i	−0.924452	+	0.381298i	$0.875477\pi$
$888$	8.23322	+	10.9831i	0.276289	+	0.368568i
$889$	2.82586			0.0947762
$890$	48.3886	+	11.3190i	1.62199	+	0.379414i
$891$	21.2971	−	21.2971i	0.713480	−	0.713480i
$892$	−2.79330	−	16.5663i	−0.0935266	−	0.554681i
$893$			19.8371i			0.663822i
$894$	7.04692	+	13.6617i	0.235684	+	0.456915i
$895$	11.3466	+	9.67419i	0.379274	+	0.323373i
$896$	0.351329	+	1.80779i	0.0117371	+	0.0603940i
$897$	19.1577	+	19.1577i	0.639658	+	0.639658i
$898$	3.14997	+	1.00617i	0.105116	+	0.0335763i
$899$	1.21223	−	1.21223i	0.0404303	−	0.0404303i
$900$	51.9359	+	25.7041i	1.73120	+	0.856802i
$901$	3.42593	+	3.42593i	0.114134	+	0.114134i
$902$	40.0680	−	20.6677i	1.33412	−	0.688161i
$903$	−2.29606	+	2.29606i	−0.0764080	+	0.0764080i
$904$	−3.67037	+	25.6489i	−0.122075	+	0.853070i
$905$	27.0501	−	31.7262i	0.899176	−	1.05462i
$906$	21.6425	−	67.7552i	0.719023	−	2.25102i
$907$	−29.7116			−0.986559			−0.493279	−	0.869871i	$-0.664202\pi$
$907$	−29.7116			−0.986559			−0.493279	+	0.869871i	$0.664202\pi$
$908$	−26.9101	+	37.8254i	−0.893044	+	1.25528i
$909$	−74.2131	−	74.2131i	−2.46149	−	2.46149i
$910$	0.681436	−	0.423071i	0.0225894	−	0.0140247i
$911$			44.6931i			1.48075i	0.672195	+	0.740374i	$0.265352\pi$
$911$			44.6931i			1.48075i	−0.672195	+	0.740374i	$0.734648\pi$
$912$	34.1572	+	16.5552i	1.13106	+	0.548196i
$913$	4.81328	−	4.81328i	0.159296	−	0.159296i
$914$	−9.58663	−	18.5854i	−0.317097	−	0.614749i
$915$	−8.78009	−	7.48599i	−0.290261	−	0.247479i
$916$	−15.6172	+	2.63326i	−0.516005	+	0.0870055i
$917$		−	1.84061i		−	0.0607821i
$918$	−4.41485	+	2.27725i	−0.145712	+	0.0751604i
$919$		−	40.1278i		−	1.32369i	−0.749639	−	0.661847i	$-0.769773\pi$
$919$		−	40.1278i		−	1.32369i	0.749639	−	0.661847i	$-0.230227\pi$
$920$	37.0076	+	2.32509i	1.22010	+	0.0766560i
$921$			35.0250i			1.15411i
$922$	−14.3856	−	27.8890i	−0.473764	−	0.918474i
$923$		−	12.4673i		−	0.410365i
$924$	−3.29279	−	2.34259i	−0.108325	−	0.0770654i
$925$	−1.29372	−	8.07922i	−0.0425372	−	0.265643i
$926$	−34.8974	+	18.0007i	−1.14680	+	0.591538i
$927$	−25.1345	+	25.1345i	−0.825525	+	0.825525i
$928$	1.67884	+	1.59723i	0.0551106	+	0.0524316i
$929$			27.7519i			0.910512i	0.890361	+	0.455256i	$0.150452\pi$
$929$			27.7519i			0.910512i	−0.890361	+	0.455256i	$0.849548\pi$
$930$	8.93955	−	38.2164i	0.293139	−	1.25317i
$931$	15.7783	+	15.7783i	0.517114	+	0.517114i
$932$	−1.42021	−	8.42289i	−0.0465206	−	0.275901i
$933$	−67.1004			−2.19677
$934$	−32.9867	−	10.5367i	−1.07936	−	0.344770i
$935$	−0.314565	−	3.95391i	−0.0102874	−	0.129307i
$936$	15.3190	+	20.4354i	0.500716	+	0.667953i
$937$	−17.2805	+	17.2805i	−0.564531	+	0.564531i	−0.930591	−	0.366060i	$-0.880706\pi$
$937$	−17.2805	+	17.2805i	−0.564531	+	0.564531i	0.366060	+	0.930591i	$0.380706\pi$
$938$	−0.263125	−	0.510114i	−0.00859133	−	0.0166558i
$939$	−21.0245	−	21.0245i	−0.686110	−	0.686110i
$940$	6.76334	+	26.8871i	0.220596	+	0.876961i
$941$	−4.81532	+	4.81532i	−0.156975	+	0.156975i	−0.781225	−	0.624250i	$-0.785405\pi$
$941$	−4.81532	+	4.81532i	−0.156975	+	0.156975i	0.624250	+	0.781225i	$0.285405\pi$
$942$	−10.9140	+	34.1679i	−0.355596	+	1.11325i
$943$	31.5759	+	31.5759i	1.02825	+	1.02825i
$944$	−4.03385	+	8.32277i	−0.131291	+	0.270883i
$945$	1.95733	−	2.29569i	0.0636719	−	0.0746788i
$946$	35.3862	−	18.2528i	1.15050	−	0.593449i
$947$			3.37347i			0.109623i	0.998497	+	0.0548115i	$0.0174558\pi$
$947$			3.37347i			0.109623i	−0.998497	+	0.0548115i	$0.982544\pi$
$948$	17.5058	+	12.4542i	0.568563	+	0.404492i
$949$	−1.74680	+	1.74680i	−0.0567034	+	0.0567034i
$950$	−13.4213	−	18.2156i	−0.435446	−	0.590993i
$951$	74.5153			2.41632
$952$	0.117032	+	0.156121i	0.00379304	+	0.00505991i
$953$	14.3663	+	14.3663i	0.465369	+	0.465369i	0.900410	−	0.435041i	$-0.143266\pi$
$953$	14.3663	+	14.3663i	0.465369	+	0.465369i	−0.435041	+	0.900410i	$0.643266\pi$
$954$	28.5078	−	89.2482i	0.922973	−	2.88952i
$955$	−31.1778	+	2.48044i	−1.00889	+	0.0802652i
$956$	0.00226303	+	0.00160999i	7.31916e−5	+	5.20707e-5i
$957$	−5.08475			−0.164366
$958$	15.9477	−	49.9268i	0.515246	−	1.61306i
$959$	0.710289			0.0229364
$960$	51.9409	+	10.7931i	1.67639	+	0.348347i
$961$	13.4851			0.435003
$962$	1.09726	−	3.43514i	0.0353769	−	0.110753i
$963$	−69.4263			−2.23723
$964$	20.9539	+	14.9073i	0.674881	+	0.480131i
$965$	−9.35775	−	7.97851i	−0.301236	−	0.256837i
$966$	1.21788	−	3.81278i	0.0391848	−	0.122674i
$967$	−11.8576	−	11.8576i	−0.381315	−	0.381315i	0.490260	−	0.871576i	$-0.336902\pi$
$967$	−11.8576	−	11.8576i	−0.381315	−	0.381315i	−0.871576	+	0.490260i	$0.836902\pi$
$968$	11.0599	+	14.7539i	0.355480	+	0.474209i
$969$	4.02156			0.129191
$970$	−22.8627	−	36.8247i	−0.734077	−	1.18237i
$971$	−14.6082	+	14.6082i	−0.468799	+	0.468799i	−0.901525	−	0.432726i	$-0.857552\pi$
$971$	−14.6082	+	14.6082i	−0.468799	+	0.468799i	0.432726	+	0.901525i	$0.357552\pi$
$972$	−5.74532	−	4.08739i	−0.184281	−	0.131103i
$973$		−	2.81319i		−	0.0901869i
$974$	35.8892	−	18.5122i	1.14996	−	0.593170i
$975$	−3.65330	−	22.8147i	−0.116999	−	0.730656i
$976$	−6.26298	−	3.03552i	−0.200473	−	0.0971645i
$977$	12.9249	+	12.9249i	0.413504	+	0.413504i	0.882957	−	0.469454i	$-0.155549\pi$
$977$	12.9249	+	12.9249i	0.413504	+	0.413504i	−0.469454	+	0.882957i	$0.655549\pi$
$978$	4.56597	−	14.2945i	0.146004	−	0.457088i
$979$	−46.5108	+	46.5108i	−1.48649	+	1.48649i
$980$	26.7655	+	16.0064i	0.854992	+	0.511305i
$981$	23.2665	+	23.2665i	0.742843	+	0.742843i
$982$	6.83804	+	13.2567i	0.218211	+	0.423040i
$983$	−0.133323	+	0.133323i	−0.00425235	+	0.00425235i	−0.709230	−	0.704977i	$-0.750957\pi$
$983$	−0.133323	+	0.133323i	−0.00425235	+	0.00425235i	0.704977	+	0.709230i	$0.250957\pi$
$984$	38.3201	+	51.1189i	1.22160	+	1.62961i
$985$	−49.7690	+	3.95951i	−1.58577	+	0.126161i
$986$	0.233868	+	0.0747024i	0.00744787	+	0.00237901i
$987$	2.99268			0.0952580
$988$	−1.65802	−	9.83324i	−0.0527485	−	0.312837i
$989$	27.8863	+	27.8863i	0.886733	+	0.886733i
$990$	−65.1633	+	40.4568i	−2.07103	+	1.28580i
$991$			47.9032i			1.52170i	0.648930	+	0.760848i	$0.275217\pi$
$991$			47.9032i			1.52170i	−0.648930	+	0.760848i	$0.724783\pi$
$992$	−0.589589	−	23.6671i	−0.0187195	−	0.751430i
$993$	−17.2251	+	17.2251i	−0.546624	+	0.546624i
$994$	−1.63690	+	0.844340i	−0.0519194	+	0.0267808i
$995$	−21.9302	+	1.74472i	−0.695234	+	0.0553114i
$996$	7.85981	+	5.59170i	0.249048	+	0.177180i
$997$		−	54.9379i		−	1.73990i	−0.493138	−	0.869951i	$-0.664150\pi$
$997$		−	54.9379i		−	1.73990i	0.493138	−	0.869951i	$-0.335850\pi$
$998$	−7.49449	−	14.5294i	−0.237234	−	0.459919i
$999$		−	13.5635i		−	0.429129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.s.b.27.5	yes	18
3.2	odd	2		720.2.z.g.667.5		18
4.3	odd	2		320.2.s.b.207.9		18
5.2	odd	4		400.2.j.d.43.9		18
5.3	odd	4		80.2.j.b.43.1	✓	18
5.4	even	2		400.2.s.d.107.5		18
8.3	odd	2		640.2.s.c.287.1		18
8.5	even	2		640.2.s.d.287.9		18
15.8	even	4		720.2.bd.g.523.9		18
16.3	odd	4		80.2.j.b.67.1	yes	18
16.5	even	4		640.2.j.c.607.9		18
16.11	odd	4		640.2.j.d.607.1		18
16.13	even	4		320.2.j.b.47.1		18
20.3	even	4		320.2.j.b.143.9		18
20.7	even	4		1600.2.j.d.143.1		18
20.19	odd	2		1600.2.s.d.207.1		18
40.3	even	4		640.2.j.c.543.1		18
40.13	odd	4		640.2.j.d.543.9		18
48.35	even	4		720.2.bd.g.307.9		18
80.3	even	4	inner	80.2.s.b.3.5	yes	18
80.13	odd	4		320.2.s.b.303.9		18
80.19	odd	4		400.2.j.d.307.9		18
80.29	even	4		1600.2.j.d.1007.9		18
80.43	even	4		640.2.s.d.223.9		18
80.53	odd	4		640.2.s.c.223.1		18
80.67	even	4		400.2.s.d.243.5		18
80.77	odd	4		1600.2.s.d.943.1		18
240.83	odd	4		720.2.z.g.163.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.1	✓	18	5.3	odd	4
80.2.j.b.67.1	yes	18	16.3	odd	4
80.2.s.b.3.5	yes	18	80.3	even	4	inner
80.2.s.b.27.5	yes	18	1.1	even	1	trivial
320.2.j.b.47.1		18	16.13	even	4
320.2.j.b.143.9		18	20.3	even	4
320.2.s.b.207.9		18	4.3	odd	2
320.2.s.b.303.9		18	80.13	odd	4
400.2.j.d.43.9		18	5.2	odd	4
400.2.j.d.307.9		18	80.19	odd	4
400.2.s.d.107.5		18	5.4	even	2
400.2.s.d.243.5		18	80.67	even	4
640.2.j.c.543.1		18	40.3	even	4
640.2.j.c.607.9		18	16.5	even	4
640.2.j.d.543.9		18	40.13	odd	4
640.2.j.d.607.1		18	16.11	odd	4
640.2.s.c.223.1		18	80.53	odd	4
640.2.s.c.287.1		18	8.3	odd	2
640.2.s.d.223.9		18	80.43	even	4
640.2.s.d.287.9		18	8.5	even	2
720.2.z.g.163.5		18	240.83	odd	4
720.2.z.g.667.5		18	3.2	odd	2
720.2.bd.g.307.9		18	48.35	even	4
720.2.bd.g.523.9		18	15.8	even	4
1600.2.j.d.143.1		18	20.7	even	4
1600.2.j.d.1007.9		18	80.29	even	4
1600.2.s.d.207.1		18	20.19	odd	2
1600.2.s.d.943.1		18	80.77	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.430311 - 1.34716i) q^{2} -2.96561 q^{3} +(-1.62967 - 1.15939i) q^{4} +(-0.177336 - 2.22902i) q^{5} +(-1.27613 + 3.99515i) q^{6} +(-0.115101 - 0.115101i) q^{7} +(-2.26315 + 1.69652i) q^{8} +5.79486 q^{9} +O(q^{10})\)	\(q+(0.430311 - 1.34716i) q^{2} -2.96561 q^{3} +(-1.62967 - 1.15939i) q^{4} +(-0.177336 - 2.22902i) q^{5} +(-1.27613 + 3.99515i) q^{6} +(-0.115101 - 0.115101i) q^{7} +(-2.26315 + 1.69652i) q^{8} +5.79486 q^{9} +(-3.07916 - 0.720273i) q^{10} +(2.95966 - 2.95966i) q^{11} +(4.83296 + 3.43831i) q^{12} -1.55822i q^{13} +(-0.204588 + 0.105530i) q^{14} +(0.525911 + 6.61042i) q^{15} +(1.31162 + 3.77884i) q^{16} +(0.299668 + 0.299668i) q^{17} +(2.49359 - 7.80658i) q^{18} +(-2.26261 + 2.26261i) q^{19} +(-2.29532 + 3.83817i) q^{20} +(0.341344 + 0.341344i) q^{21} +(-2.71356 - 5.26071i) q^{22} +(4.14573 - 4.14573i) q^{23} +(6.71162 - 5.03121i) q^{24} +(-4.93710 + 0.790575i) q^{25} +(-2.09917 - 0.670518i) q^{26} -8.28846 q^{27} +(0.0541288 + 0.321023i) q^{28} +(0.289656 + 0.289656i) q^{29} +(9.13159 + 2.13605i) q^{30} -4.18508i q^{31} +(5.65510 - 0.140879i) q^{32} +(-8.77721 + 8.77721i) q^{33} +(0.532650 - 0.274749i) q^{34} +(-0.236151 + 0.276974i) q^{35} +(-9.44368 - 6.71851i) q^{36} +1.63643i q^{37} +(2.07447 + 4.02172i) q^{38} +4.62107i q^{39} +(4.18292 + 4.74376i) q^{40} +7.61648i q^{41} +(0.606729 - 0.312960i) q^{42} +6.72651i q^{43} +(-8.25467 + 1.39185i) q^{44} +(-1.02764 - 12.9169i) q^{45} +(-3.80100 - 7.36890i) q^{46} +(4.38366 - 4.38366i) q^{47} +(-3.88975 - 11.2066i) q^{48} -6.97350i q^{49} +(-1.05946 + 6.99125i) q^{50} +(-0.888698 - 0.888698i) q^{51} +(-1.80659 + 2.53938i) q^{52} +11.4324 q^{53} +(-3.56661 + 11.1659i) q^{54} +(-7.12202 - 6.07231i) q^{55} +(0.455760 + 0.0652196i) q^{56} +(6.71003 - 6.71003i) q^{57} +(0.514854 - 0.265570i) q^{58} +(1.63497 + 1.63497i) q^{59} +(6.80702 - 11.3825i) q^{60} +(-1.23034 + 1.23034i) q^{61} +(-5.63796 - 1.80089i) q^{62} +(-0.666993 - 0.666993i) q^{63} +(2.24366 - 7.67893i) q^{64} +(-3.47331 + 0.276329i) q^{65} +(8.04736 + 15.6012i) q^{66} +2.49337i q^{67} +(-0.140926 - 0.835791i) q^{68} +(-12.2946 + 12.2946i) q^{69} +(0.271509 + 0.437317i) q^{70} +8.00096 q^{71} +(-13.1146 + 9.83107i) q^{72} +(-1.12102 - 1.12102i) q^{73} +(2.20453 + 0.704173i) q^{74} +(14.6415 - 2.34454i) q^{75} +(6.31056 - 1.06405i) q^{76} -0.681319 q^{77} +(6.22531 + 1.98850i) q^{78} +3.62218 q^{79} +(8.19054 - 3.59376i) q^{80} +7.19579 q^{81} +(10.2606 + 3.27745i) q^{82} +1.62629 q^{83} +(-0.160525 - 0.952029i) q^{84} +(0.614825 - 0.721109i) q^{85} +(9.06167 + 2.89449i) q^{86} +(-0.859007 - 0.859007i) q^{87} +(-1.67703 + 11.7193i) q^{88} -15.7149 q^{89} +(-17.8433 - 4.17388i) q^{90} +(-0.179352 + 0.179352i) q^{91} +(-11.5627 + 1.94962i) q^{92} +12.4113i q^{93} +(-4.01915 - 7.79182i) q^{94} +(5.44467 + 4.64218i) q^{95} +(-16.7708 + 0.417792i) q^{96} +(9.69217 + 9.69217i) q^{97} +(-9.39441 - 3.00077i) q^{98} +(17.1508 - 17.1508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} - 16 q^{26} - 24 q^{27} + 40 q^{28} + 14 q^{29} + 40 q^{30} + 20 q^{32} - 8 q^{33} + 28 q^{34} + 2 q^{35} - 4 q^{36} + 24 q^{38} + 44 q^{40} + 8 q^{42} - 44 q^{44} - 14 q^{45} + 12 q^{46} + 38 q^{47} + 4 q^{48} - 8 q^{50} + 8 q^{51} + 8 q^{52} + 12 q^{53} + 4 q^{54} - 6 q^{55} + 20 q^{56} - 24 q^{57} + 20 q^{58} + 10 q^{59} + 8 q^{60} + 14 q^{61} - 40 q^{62} - 6 q^{63} + 16 q^{64} + 4 q^{66} - 60 q^{68} - 32 q^{69} - 28 q^{70} + 24 q^{71} - 68 q^{72} - 14 q^{73} - 48 q^{74} + 16 q^{75} - 16 q^{76} - 44 q^{77} - 36 q^{78} - 16 q^{79} - 92 q^{80} + 2 q^{81} + 48 q^{82} + 40 q^{83} + 24 q^{84} + 14 q^{85} - 36 q^{86} + 24 q^{87} - 8 q^{88} + 12 q^{89} - 8 q^{90} - 8 q^{92} - 28 q^{94} + 34 q^{95} - 40 q^{96} + 18 q^{97} - 56 q^{98} + 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

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