LMFDB - Embedded newform 165.2.k.c.122.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(23,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("165.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.k (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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 19 x^{12} - 80 x^{11} + 168 x^{10} + 28 x^{9} + 119 x^{8} - 432 x^{7} + \cdots + 16 $ x^16 - 4x^15 + 8x^14 + 19x^12 - 80x^11 + 168x^10 + 28x^9 + 119x^8 - 432x^7 + 784x^6 + 84x^5 + 169x^4 - 420x^3 + 392x^2 - 112x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			122.2
Root			$1.63522 + 1.63522i$ of defining polynomial
Character	$\chi$	$=$	165.122
Dual form			165.2.k.c.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63522 + 1.63522i) q^{2} +(-1.37033 - 1.05933i) q^{3} -3.34791i q^{4} +(1.69456 + 1.45893i) q^{5} +(3.97305 - 0.508557i) q^{6} +(0.491443 + 0.491443i) q^{7} +(2.20413 + 2.20413i) q^{8} +(0.755630 + 2.90328i) q^{9} +O(q^{10})$	\(q+(-1.63522 + 1.63522i) q^{2} +(-1.37033 - 1.05933i) q^{3} -3.34791i q^{4} +(1.69456 + 1.45893i) q^{5} +(3.97305 - 0.508557i) q^{6} +(0.491443 + 0.491443i) q^{7} +(2.20413 + 2.20413i) q^{8} +(0.755630 + 2.90328i) q^{9} +(-5.15665 + 0.385296i) q^{10} +1.00000i q^{11} +(-3.54655 + 4.58775i) q^{12} +(-4.03339 + 4.03339i) q^{13} -1.60724 q^{14} +(-0.776612 - 3.79432i) q^{15} -0.512664 q^{16} +(-1.93184 + 1.93184i) q^{17} +(-5.98313 - 3.51188i) q^{18} +1.61176i q^{19} +(4.88437 - 5.67321i) q^{20} +(-0.152840 - 1.19404i) q^{21} +(-1.63522 - 1.63522i) q^{22} +(3.14765 + 3.14765i) q^{23} +(-0.685487 - 5.35529i) q^{24} +(0.743034 + 4.94448i) q^{25} -13.1910i q^{26} +(2.04007 - 4.77892i) q^{27} +(1.64531 - 1.64531i) q^{28} +1.42120 q^{29} +(7.47449 + 4.93463i) q^{30} -4.25130 q^{31} +(-3.56993 + 3.56993i) q^{32} +(1.05933 - 1.37033i) q^{33} -6.31798i q^{34} +(0.115795 + 1.54976i) q^{35} +(9.71990 - 2.52978i) q^{36} +(4.17033 + 4.17033i) q^{37} +(-2.63558 - 2.63558i) q^{38} +(9.79980 - 1.25439i) q^{39} +(0.519343 + 6.95069i) q^{40} +10.7308i q^{41} +(2.20245 + 1.70260i) q^{42} +(7.58453 - 7.58453i) q^{43} +3.34791 q^{44} +(-2.95523 + 6.02218i) q^{45} -10.2942 q^{46} +(7.14711 - 7.14711i) q^{47} +(0.702521 + 0.543082i) q^{48} -6.51697i q^{49} +(-9.30035 - 6.87030i) q^{50} +(4.69373 - 0.600806i) q^{51} +(13.5034 + 13.5034i) q^{52} +(-7.01771 - 7.01771i) q^{53} +(4.47863 + 11.1506i) q^{54} +(-1.45893 + 1.69456i) q^{55} +2.16641i q^{56} +(1.70739 - 2.20864i) q^{57} +(-2.32398 + 2.32398i) q^{58} -7.03856 q^{59} +(-12.7030 + 2.60002i) q^{60} -2.26528 q^{61} +(6.95182 - 6.95182i) q^{62} +(-1.05545 + 1.79815i) q^{63} -12.7006i q^{64} +(-12.7193 + 0.950360i) q^{65} +(0.508557 + 3.97305i) q^{66} +(-1.60076 - 1.60076i) q^{67} +(6.46762 + 6.46762i) q^{68} +(-0.978923 - 7.64773i) q^{69} +(-2.72355 - 2.34485i) q^{70} +2.57260i q^{71} +(-4.73369 + 8.06470i) q^{72} +(5.90351 - 5.90351i) q^{73} -13.6388 q^{74} +(4.21965 - 7.56271i) q^{75} +5.39601 q^{76} +(-0.491443 + 0.491443i) q^{77} +(-13.9736 + 18.0761i) q^{78} -4.09127i q^{79} +(-0.868738 - 0.747943i) q^{80} +(-7.85805 + 4.38761i) q^{81} +(-17.5472 - 17.5472i) q^{82} +(-1.51580 - 1.51580i) q^{83} +(-3.99755 + 0.511693i) q^{84} +(-6.09204 + 0.455186i) q^{85} +24.8048i q^{86} +(-1.94752 - 1.50553i) q^{87} +(-2.20413 + 2.20413i) q^{88} +15.8719 q^{89} +(-5.01514 - 14.6801i) q^{90} -3.96437 q^{91} +(10.5380 - 10.5380i) q^{92} +(5.82570 + 4.50354i) q^{93} +23.3742i q^{94} +(-2.35144 + 2.73121i) q^{95} +(8.67375 - 1.11025i) q^{96} +(9.36942 + 9.36942i) q^{97} +(10.6567 + 10.6567i) q^{98} +(-2.90328 + 0.755630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 4 q^{6} + 8 q^{7} + 16 q^{8} + 6 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 4 * q^6 + 8 * q^7 + 16 * q^8 + 6 * q^9	$ 16 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 4 q^{6} + 8 q^{7} + 16 q^{8} + 6 q^{9} - 4 q^{10} - 4 q^{12} - 24 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} - 32 q^{18} - 20 q^{20} - 8 q^{21} - 4 q^{22} + 14 q^{23} + 12 q^{24} - 18 q^{25} - 20 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{30} + 8 q^{31} + 28 q^{32} + 4 q^{33} + 44 q^{36} - 6 q^{37} + 24 q^{38} + 24 q^{39} + 16 q^{40} - 60 q^{42} + 16 q^{43} + 12 q^{44} + 24 q^{45} - 32 q^{46} + 48 q^{47} - 48 q^{48} - 12 q^{50} - 8 q^{51} + 36 q^{52} - 4 q^{53} + 4 q^{54} + 2 q^{55} - 8 q^{57} - 12 q^{58} - 68 q^{59} - 28 q^{60} - 8 q^{61} + 48 q^{62} - 12 q^{63} - 48 q^{65} + 8 q^{66} + 6 q^{67} + 24 q^{68} + 12 q^{69} - 4 q^{70} - 8 q^{72} + 8 q^{74} + 8 q^{75} + 16 q^{76} - 8 q^{77} - 48 q^{78} - 24 q^{80} + 2 q^{81} + 12 q^{82} - 8 q^{83} + 52 q^{84} - 4 q^{85} - 36 q^{87} - 16 q^{88} + 32 q^{89} + 44 q^{90} - 56 q^{91} + 20 q^{92} + 28 q^{93} - 48 q^{95} + 80 q^{96} + 18 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 4 * q^6 + 8 * q^7 + 16 * q^8 + 6 * q^9 - 4 * q^10 - 4 * q^12 - 24 * q^14 + 8 * q^15 - 4 * q^16 + 8 * q^17 - 32 * q^18 - 20 * q^20 - 8 * q^21 - 4 * q^22 + 14 * q^23 + 12 * q^24 - 18 * q^25 - 20 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^30 + 8 * q^31 + 28 * q^32 + 4 * q^33 + 44 * q^36 - 6 * q^37 + 24 * q^38 + 24 * q^39 + 16 * q^40 - 60 * q^42 + 16 * q^43 + 12 * q^44 + 24 * q^45 - 32 * q^46 + 48 * q^47 - 48 * q^48 - 12 * q^50 - 8 * q^51 + 36 * q^52 - 4 * q^53 + 4 * q^54 + 2 * q^55 - 8 * q^57 - 12 * q^58 - 68 * q^59 - 28 * q^60 - 8 * q^61 + 48 * q^62 - 12 * q^63 - 48 * q^65 + 8 * q^66 + 6 * q^67 + 24 * q^68 + 12 * q^69 - 4 * q^70 - 8 * q^72 + 8 * q^74 + 8 * q^75 + 16 * q^76 - 8 * q^77 - 48 * q^78 - 24 * q^80 + 2 * q^81 + 12 * q^82 - 8 * q^83 + 52 * q^84 - 4 * q^85 - 36 * q^87 - 16 * q^88 + 32 * q^89 + 44 * q^90 - 56 * q^91 + 20 * q^92 + 28 * q^93 - 48 * q^95 + 80 * q^96 + 18 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.63522	+	1.63522i	−1.15628	+	1.15628i	−0.171007	+	0.985270i	$0.554702\pi$
$2$	−1.63522	+	1.63522i	−1.15628	+	1.15628i	−0.985270	+	0.171007i	$0.945298\pi$
$3$	−1.37033	−	1.05933i	−0.791163	−	0.611606i
$3$	−1.37033	−	1.05933i	−0.791163	−	0.611606i
$4$		−	3.34791i		−	1.67395i
$5$	1.69456	+	1.45893i	0.757828	+	0.652454i
$5$	1.69456	+	1.45893i	0.757828	+	0.652454i
$6$	3.97305	−	0.508557i	1.62199	−	0.207617i
$7$	0.491443	+	0.491443i	0.185748	+	0.185748i	0.793855	−	0.608107i	$-0.208071\pi$
$7$	0.491443	+	0.491443i	0.185748	+	0.185748i	−0.608107	+	0.793855i	$0.708071\pi$
$8$	2.20413	+	2.20413i	0.779277	+	0.779277i
$9$	0.755630	+	2.90328i	0.251877	+	0.967759i
$10$	−5.15665	+	0.385296i	−1.63068	+	0.121841i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−3.54655	+	4.58775i	−1.02380	+	1.32437i
$13$	−4.03339	+	4.03339i	−1.11866	+	1.11866i	−0.126724	+	0.991938i	$0.540446\pi$
$13$	−4.03339	+	4.03339i	−1.11866	+	1.11866i	−0.991938	+	0.126724i	$0.959554\pi$
$14$	−1.60724			−0.429553
$15$	−0.776612	−	3.79432i	−0.200520	−	0.979690i
$16$	−0.512664			−0.128166
$17$	−1.93184	+	1.93184i	−0.468540	+	0.468540i	−0.901441	−	0.432901i	$-0.857490\pi$
$17$	−1.93184	+	1.93184i	−0.468540	+	0.468540i	0.432901	+	0.901441i	$0.357490\pi$
$18$	−5.98313	−	3.51188i	−1.41024	−	0.827759i
$19$			1.61176i			0.369762i	0.982761	+	0.184881i	$0.0591900\pi$
$19$			1.61176i			0.369762i	−0.982761	+	0.184881i	$0.940810\pi$
$20$	4.88437	−	5.67321i	1.09218	−	1.26857i
$21$	−0.152840	−	1.19404i	−0.0333523	−	0.260562i
$22$	−1.63522	−	1.63522i	−0.348631	−	0.348631i
$23$	3.14765	+	3.14765i	0.656330	+	0.656330i	0.954510	−	0.298180i	$-0.0963795\pi$
$23$	3.14765	+	3.14765i	0.656330	+	0.656330i	−0.298180	+	0.954510i	$0.596379\pi$
$24$	−0.685487	−	5.35529i	−0.139924	−	1.09314i
$25$	0.743034	+	4.94448i	0.148607	+	0.988896i
$26$		−	13.1910i		−	2.58697i
$27$	2.04007	−	4.77892i	0.392612	−	0.919704i
$28$	1.64531	−	1.64531i	0.310934	−	0.310934i
$29$	1.42120			0.263911			0.131955	−	0.991256i	$-0.457874\pi$
$29$	1.42120			0.263911			0.131955	+	0.991256i	$0.457874\pi$
$30$	7.47449	+	4.93463i	1.36465	+	0.900935i
$31$	−4.25130			−0.763556			−0.381778	−	0.924254i	$-0.624688\pi$
$31$	−4.25130			−0.763556			−0.381778	+	0.924254i	$0.624688\pi$
$32$	−3.56993	+	3.56993i	−0.631081	+	0.631081i
$33$	1.05933	−	1.37033i	0.184406	−	0.238545i
$34$		−	6.31798i		−	1.08353i
$35$	0.115795	+	1.54976i	0.0195730	+	0.261957i
$36$	9.71990	−	2.52978i	1.61998	−	0.421630i
$37$	4.17033	+	4.17033i	0.685599	+	0.685599i	0.961256	−	0.275657i	$-0.0888955\pi$
$37$	4.17033	+	4.17033i	0.685599	+	0.685599i	−0.275657	+	0.961256i	$0.588895\pi$
$38$	−2.63558	−	2.63558i	−0.427548	−	0.427548i
$39$	9.79980	−	1.25439i	1.56922	−	0.200863i
$40$	0.519343	+	6.95069i	0.0821153	+	1.09900i
$41$			10.7308i			1.67586i	0.545776	+	0.837931i	$0.316235\pi$
$41$			10.7308i			1.67586i	−0.545776	+	0.837931i	$0.683765\pi$
$42$	2.20245	+	1.70260i	0.339846	+	0.262717i
$43$	7.58453	−	7.58453i	1.15663	−	1.15663i	0.171435	−	0.985195i	$-0.445160\pi$
$43$	7.58453	−	7.58453i	1.15663	−	1.15663i	0.985195	−	0.171435i	$-0.0548405\pi$
$44$	3.34791			0.504716
$45$	−2.95523	+	6.02218i	−0.440540	+	0.897733i
$46$	−10.2942			−1.51780
$47$	7.14711	−	7.14711i	1.04251	−	1.04251i	0.0434573	−	0.999055i	$-0.486163\pi$
$47$	7.14711	−	7.14711i	1.04251	−	1.04251i	0.999055	−	0.0434573i	$-0.0138372\pi$
$48$	0.702521	+	0.543082i	0.101400	+	0.0783871i
$49$		−	6.51697i		−	0.930995i
$50$	−9.30035	−	6.87030i	−1.31527	−	0.971608i
$51$	4.69373	−	0.600806i	0.657254	−	0.0841296i
$52$	13.5034	+	13.5034i	1.87259	+	1.87259i
$53$	−7.01771	−	7.01771i	−0.963957	−	0.963957i	0.0354157	−	0.999373i	$-0.488724\pi$
$53$	−7.01771	−	7.01771i	−0.963957	−	0.963957i	−0.999373	+	0.0354157i	$0.988724\pi$
$54$	4.47863	+	11.1506i	0.609465	+	1.51740i
$55$	−1.45893	+	1.69456i	−0.196722	+	0.228494i
$56$			2.16641i			0.289498i
$57$	1.70739	−	2.20864i	0.226149	−	0.292542i
$58$	−2.32398	+	2.32398i	−0.305154	+	0.305154i
$59$	−7.03856			−0.916342			−0.458171	−	0.888864i	$-0.651495\pi$
$59$	−7.03856			−0.916342			−0.458171	+	0.888864i	$0.651495\pi$
$60$	−12.7030	+	2.60002i	−1.63995	+	0.335662i
$61$	−2.26528			−0.290040			−0.145020	−	0.989429i	$-0.546325\pi$
$61$	−2.26528			−0.290040			−0.145020	+	0.989429i	$0.546325\pi$
$62$	6.95182	−	6.95182i	0.882883	−	0.882883i
$63$	−1.05545	+	1.79815i	−0.132974	+	0.226545i
$64$		−	12.7006i		−	1.58758i
$65$	−12.7193	+	0.950360i	−1.57763	+	0.117878i
$66$	0.508557	+	3.97305i	0.0625990	+	0.489048i
$67$	−1.60076	−	1.60076i	−0.195564	−	0.195564i	0.602531	−	0.798095i	$-0.294159\pi$
$67$	−1.60076	−	1.60076i	−0.195564	−	0.195564i	−0.798095	+	0.602531i	$0.794159\pi$
$68$	6.46762	+	6.46762i	0.784315	+	0.784315i
$69$	−0.978923	−	7.64773i	−0.117849	−	0.920679i
$70$	−2.72355	−	2.34485i	−0.325527	−	0.280263i
$71$			2.57260i			0.305312i	0.988279	+	0.152656i	$0.0487826\pi$
$71$			2.57260i			0.305312i	−0.988279	+	0.152656i	$0.951217\pi$
$72$	−4.73369	+	8.06470i	−0.557871	+	0.950434i
$73$	5.90351	−	5.90351i	0.690953	−	0.690953i	−0.271489	−	0.962442i	$-0.587516\pi$
$73$	5.90351	−	5.90351i	0.690953	−	0.690953i	0.962442	+	0.271489i	$0.0875159\pi$
$74$	−13.6388			−1.58548
$75$	4.21965	−	7.56271i	0.487243	−	0.873267i
$76$	5.39601			0.618965
$77$	−0.491443	+	0.491443i	−0.0560052	+	0.0560052i
$78$	−13.9736	+	18.0761i	−1.58220	+	2.04671i
$79$		−	4.09127i		−	0.460303i	−0.973155	−	0.230152i	$-0.926078\pi$
$79$		−	4.09127i		−	0.460303i	0.973155	−	0.230152i	$-0.0739222\pi$
$80$	−0.868738	−	0.747943i	−0.0971279	−	0.0836225i
$81$	−7.85805	+	4.38761i	−0.873116	+	0.487512i
$82$	−17.5472	−	17.5472i	−1.93776	−	1.93776i
$83$	−1.51580	−	1.51580i	−0.166381	−	0.166381i	0.619006	−	0.785386i	$-0.287536\pi$
$83$	−1.51580	−	1.51580i	−0.166381	−	0.166381i	−0.785386	+	0.619006i	$0.787536\pi$
$84$	−3.99755	+	0.511693i	−0.436168	+	0.0558302i
$85$	−6.09204	+	0.455186i	−0.660774	+	0.0493719i
$86$			24.8048i			2.67477i
$87$	−1.94752	−	1.50553i	−0.208796	−	0.161409i
$88$	−2.20413	+	2.20413i	−0.234961	+	0.234961i
$89$	15.8719			1.68242			0.841211	−	0.540707i	$-0.181843\pi$
$89$	15.8719			1.68242			0.841211	+	0.540707i	$0.181843\pi$
$90$	−5.01514	−	14.6801i	−0.528642	−	1.54741i
$91$	−3.96437			−0.415579
$92$	10.5380	−	10.5380i	1.09867	−	1.09867i
$93$	5.82570	+	4.50354i	0.604097	+	0.466995i
$94$			23.3742i			2.41087i
$95$	−2.35144	+	2.73121i	−0.241253	+	0.280216i
$96$	8.67375	−	1.11025i	0.885261	−	0.113315i
$97$	9.36942	+	9.36942i	0.951321	+	0.951321i	0.998869	−	0.0475481i	$-0.0151407\pi$
$97$	9.36942	+	9.36942i	0.951321	+	0.951321i	−0.0475481	+	0.998869i	$0.515141\pi$
$98$	10.6567	+	10.6567i	1.07649	+	1.07649i
$99$	−2.90328	+	0.755630i	−0.291790	+	0.0759436i
$100$	16.5537	−	2.48761i	1.65537	−	0.248761i
$101$			2.78367i			0.276986i	0.990363	+	0.138493i	$0.0442258\pi$
$101$			2.78367i			0.276986i	−0.990363	+	0.138493i	$0.955774\pi$
$102$	−6.69284	+	8.65775i	−0.662690	+	0.857244i
$103$	−9.25279	+	9.25279i	−0.911705	+	0.911705i	−0.996406	−	0.0847016i	$-0.973006\pi$
$103$	−9.25279	+	9.25279i	−0.911705	+	0.911705i	0.0847016	+	0.996406i	$0.473006\pi$
$104$	−17.7802			−1.74349
$105$	1.48303	−	2.24635i	0.144729	−	0.219222i
$106$	22.9510			2.22920
$107$	3.31844	−	3.31844i	0.320805	−	0.320805i	−0.528271	−	0.849076i	$-0.677159\pi$
$107$	3.31844	−	3.31844i	0.320805	−	0.320805i	0.849076	+	0.528271i	$0.177159\pi$
$108$	−15.9994	−	6.82997i	−1.53954	−	0.657214i
$109$		−	5.80567i		−	0.556082i	−0.960569	−	0.278041i	$-0.910315\pi$
$109$		−	5.80567i		−	0.556082i	0.960569	−	0.278041i	$-0.0896851\pi$
$110$	−0.385296	−	5.15665i	−0.0367365	−	0.491668i
$111$	−1.29698	−	10.1325i	−0.123104	−	0.961736i
$112$	−0.251946	−	0.251946i	−0.0238066	−	0.0238066i
$113$	−1.06453	−	1.06453i	−0.100143	−	0.100143i	0.655260	−	0.755403i	$-0.272559\pi$
$113$	−1.06453	−	1.06453i	−0.100143	−	0.100143i	−0.755403	+	0.655260i	$0.772559\pi$
$114$	0.819669	+	6.40358i	0.0767691	+	0.599750i
$115$	0.741658	+	9.92607i	0.0691600	+	0.925611i
$116$		−	4.75805i		−	0.441774i
$117$	−14.7578	−	8.66231i	−1.36436	−	0.800831i
$118$	11.5096	−	11.5096i	1.05955	−	1.05955i
$119$	−1.89878			−0.174061
$120$	6.65141	−	10.0749i	0.607188	−	0.919710i
$121$	−1.00000			−0.0909091
$122$	3.70424	−	3.70424i	0.335366	−	0.335366i
$123$	11.3674	−	14.7047i	1.02497	−	1.32588i
$124$			14.2330i			1.27816i
$125$	−5.95455	+	9.46273i	−0.532591	+	0.846373i
$126$	−1.21448	−	4.66626i	−0.108194	−	0.415704i
$127$	7.66754	+	7.66754i	0.680384	+	0.680384i	0.960087	−	0.279703i	$-0.0902359\pi$
$127$	7.66754	+	7.66754i	0.680384	+	0.680384i	−0.279703	+	0.960087i	$0.590236\pi$
$128$	13.6284	+	13.6284i	1.20460	+	1.20460i
$129$	−18.4279	+	2.35880i	−1.62249	+	0.207681i
$130$	19.2448	−	22.3529i	1.68788	−	1.96048i
$131$		−	13.3177i		−	1.16357i	−0.813341	−	0.581787i	$-0.802354\pi$
$131$		−	13.3177i		−	1.16357i	0.813341	−	0.581787i	$-0.197646\pi$
$132$	−4.58775	−	3.54655i	−0.399312	−	0.308687i
$133$	−0.792087	+	0.792087i	−0.0686826	+	0.0686826i
$134$	5.23519			0.452252
$135$	10.4291	−	5.12182i	0.897597	−	0.440816i
$136$	−8.51605			−0.730245
$137$	9.45440	−	9.45440i	0.807744	−	0.807744i	−0.176548	−	0.984292i	$-0.556493\pi$
$137$	9.45440	−	9.45440i	0.807744	−	0.807744i	0.984292	+	0.176548i	$0.0564931\pi$
$138$	14.1065	+	10.9050i	1.20083	+	0.928295i
$139$			10.5722i			0.896722i	0.893853	+	0.448361i	$0.147992\pi$
$139$			10.5722i			0.896722i	−0.893853	+	0.448361i	$0.852008\pi$
$140$	5.18845	−	0.387672i	0.438504	−	0.0327643i
$141$	−17.3651	+	2.22276i	−1.46240	+	0.187190i
$142$	−4.20678	−	4.20678i	−0.353025	−	0.353025i
$143$	−4.03339	−	4.03339i	−0.337289	−	0.337289i
$144$	−0.387384	−	1.48841i	−0.0322820	−	0.124034i
$145$	2.40831	+	2.07344i	0.199999	+	0.172190i
$146$			19.3071i			1.59787i
$147$	−6.90363	+	8.93042i	−0.569402	+	0.736569i
$148$	13.9619	−	13.9619i	1.14766	−	1.14766i
$149$	0.478984			0.0392399			0.0196199	−	0.999808i	$-0.493754\pi$
$149$	0.478984			0.0392399			0.0196199	+	0.999808i	$0.493754\pi$
$150$	5.46666	+	19.2668i	0.446351	+	1.57313i
$151$	−8.48385			−0.690406			−0.345203	−	0.938528i	$-0.612190\pi$
$151$	−8.48385			−0.690406			−0.345203	+	0.938528i	$0.612190\pi$
$152$	−3.55251	+	3.55251i	−0.288147	+	0.288147i
$153$	−7.06843	−	4.14892i	−0.571449	−	0.335420i
$154$		−	1.60724i		−	0.129515i
$155$	−7.20406	−	6.20236i	−0.578644	−	0.498186i
$156$	−4.19958	−	32.8088i	−0.336236	−	2.62681i
$157$	7.27564	+	7.27564i	0.580659	+	0.580659i	0.935084	−	0.354425i	$-0.115323\pi$
$157$	7.27564	+	7.27564i	0.580659	+	0.580659i	−0.354425	+	0.935084i	$0.615323\pi$
$158$	6.69013	+	6.69013i	0.532238	+	0.532238i
$159$	2.18252	+	17.0507i	0.173085	+	1.35221i
$160$	−11.2577	+	0.841158i	−0.890003	+	0.0664994i
$161$			3.09378i			0.243824i
$162$	5.67494	−	20.0244i	0.445866	−	1.57326i
$163$	−4.09957	+	4.09957i	−0.321103	+	0.321103i	−0.849190	−	0.528087i	$-0.822909\pi$
$163$	−4.09957	+	4.09957i	−0.321103	+	0.321103i	0.528087	+	0.849190i	$0.322909\pi$
$164$	35.9256			2.80531
$165$	3.79432	−	0.776612i	0.295388	−	0.0604592i
$166$	4.95734			0.384764
$167$	3.24917	−	3.24917i	0.251429	−	0.251429i	−0.570128	−	0.821556i	$-0.693106\pi$
$167$	3.24917	−	3.24917i	0.251429	−	0.251429i	0.821556	+	0.570128i	$0.193106\pi$
$168$	2.29495	−	2.96870i	0.177059	−	0.229040i
$169$		−	19.5365i		−	1.50281i
$170$	9.21751	−	10.7062i	0.706951	−	0.821126i
$171$	−4.67938	+	1.21789i	−0.357841	+	0.0931344i
$172$	−25.3923	−	25.3923i	−1.93615	−	1.93615i
$173$	−13.4186	−	13.4186i	−1.02020	−	1.02020i	−0.999792	−	0.0204047i	$-0.993505\pi$
$173$	−13.4186	−	13.4186i	−1.02020	−	1.02020i	−0.0204047	−	0.999792i	$-0.506495\pi$
$174$	5.64650	−	0.722762i	0.428060	−	0.0547924i
$175$	−2.06477	+	2.79509i	−0.156082	+	0.211289i
$176$		−	0.512664i		−	0.0386435i
$177$	9.64518	+	7.45617i	0.724976	+	0.560440i
$178$	−25.9542	+	25.9542i	−1.94535	+	1.94535i
$179$	7.91627			0.591690			0.295845	−	0.955236i	$-0.404399\pi$
$179$	7.91627			0.591690			0.295845	+	0.955236i	$0.404399\pi$
$180$	20.1617	+	9.89383i	1.50276	+	0.737443i
$181$	6.52252			0.484815			0.242408	−	0.970174i	$-0.422063\pi$
$181$	6.52252			0.484815			0.242408	+	0.970174i	$0.422063\pi$
$182$	6.48263	−	6.48263i	0.480524	−	0.480524i
$183$	3.10420	+	2.39969i	0.229469	+	0.177390i
$184$			13.8756i			1.02293i
$185$	0.982626	+	13.1511i	0.0722441	+	0.966888i
$186$	−16.8906	+	2.16203i	−1.23848	+	0.158528i
$187$	−1.93184	−	1.93184i	−0.141270	−	0.141270i
$188$	−23.9278	−	23.9278i	−1.74512	−	1.74512i
$189$	3.35115	−	1.34599i	0.243760	−	0.0979064i
$190$	−0.621003	−	8.31127i	−0.0450523	−	0.602963i
$191$		−	6.39291i		−	0.462575i	−0.972885	−	0.231288i	$-0.925706\pi$
$191$		−	6.39291i		−	0.462575i	0.972885	−	0.231288i	$-0.0742938\pi$
$192$	−13.4542	+	17.4041i	−0.970970	+	1.25603i
$193$	17.7016	−	17.7016i	1.27419	−	1.27419i	0.330320	−	0.943869i	$-0.392843\pi$
$193$	17.7016	−	17.7016i	1.27419	−	1.27419i	0.943869	−	0.330320i	$-0.107157\pi$
$194$	−30.6422			−2.19998
$195$	18.4364	+	12.1716i	1.32026	+	0.871627i
$196$	−21.8182			−1.55844
$197$	−14.8126	+	14.8126i	−1.05536	+	1.05536i	−0.0569814	+	0.998375i	$0.518148\pi$
$197$	−14.8126	+	14.8126i	−1.05536	+	1.05536i	−0.998375	+	0.0569814i	$0.981852\pi$
$198$	3.51188	−	5.98313i	0.249579	−	0.425202i
$199$		−	10.0017i		−	0.709004i	−0.935055	−	0.354502i	$-0.884650\pi$
$199$		−	10.0017i		−	0.709004i	0.935055	−	0.354502i	$-0.115350\pi$
$200$	−9.26053	+	12.5360i	−0.654818	+	0.886430i
$201$	0.497838	+	3.88931i	0.0351148	+	0.274331i
$202$	−4.55193	−	4.55193i	−0.320273	−	0.320273i
$203$	0.698441	+	0.698441i	0.0490209	+	0.0490209i
$204$	−2.01144	−	15.7142i	−0.140829	−	1.10021i
$205$	−15.6554	+	18.1839i	−1.09342	+	1.27002i
$206$		−	30.2608i		−	2.10837i
$207$	−6.76004	+	11.5170i	−0.469855	+	0.800484i
$208$	2.06778	−	2.06778i	0.143375	−	0.143375i
$209$	−1.61176			−0.111487
$210$	1.24820	+	6.09838i	0.0861340	+	0.420828i
$211$	−0.897130			−0.0617610			−0.0308805	−	0.999523i	$-0.509831\pi$
$211$	−0.897130			−0.0617610			−0.0308805	+	0.999523i	$0.509831\pi$
$212$	−23.4946	+	23.4946i	−1.61362	+	1.61362i
$213$	2.72524	−	3.52532i	0.186730	−	0.241551i
$214$			10.8528i			0.741880i
$215$	23.9177	−	1.78709i	1.63118	−	0.121879i
$216$	15.0299	−	6.03678i	1.02266	−	0.410751i
$217$	−2.08927	−	2.08927i	−0.141829	−	0.141829i
$218$	9.49356	+	9.49356i	0.642985	+	0.642985i
$219$	−14.3435	+	1.83600i	−0.969247	+	0.124065i
$220$	5.67321	+	4.88437i	0.382488	+	0.329304i
$221$		−	15.5838i		−	1.04828i
$222$	18.6898	+	14.4481i	1.25438	+	0.969691i
$223$	−4.67651	+	4.67651i	−0.313162	+	0.313162i	−0.846133	−	0.532971i	$-0.821075\pi$
$223$	−4.67651	+	4.67651i	−0.313162	+	0.313162i	0.532971	+	0.846133i	$0.321075\pi$
$224$	−3.50884			−0.234444
$225$	−13.7937	+	5.89343i	−0.919583	+	0.392895i
$226$	3.48149			0.231585
$227$	−4.09163	+	4.09163i	−0.271571	+	0.271571i	−0.829732	−	0.558161i	$-0.811507\pi$
$227$	−4.09163	+	4.09163i	−0.271571	+	0.271571i	0.558161	+	0.829732i	$0.311507\pi$
$228$	−7.39433	−	5.71617i	−0.489702	−	0.378562i
$229$			9.82921i			0.649533i	0.945794	+	0.324766i	$0.105286\pi$
$229$			9.82921i			0.649533i	−0.945794	+	0.324766i	$0.894714\pi$
$230$	−17.4441	−	15.0186i	−1.15023	−	0.990294i
$231$	1.19404	−	0.152840i	0.0785623	−	0.0100561i
$232$	3.13251	+	3.13251i	0.205659	+	0.205659i
$233$	1.95126	+	1.95126i	0.127831	+	0.127831i	0.768128	−	0.640297i	$-0.221189\pi$
$233$	1.95126	+	1.95126i	0.127831	+	0.127831i	−0.640297	+	0.768128i	$0.721189\pi$
$234$	38.2971	−	9.96751i	2.50356	−	0.651596i
$235$	22.5383	−	1.68402i	1.47024	−	0.109853i
$236$			23.5644i			1.53391i
$237$	−4.33401	+	5.60640i	−0.281524	+	0.364175i
$238$	3.10493	−	3.10493i	0.201263	−	0.201263i
$239$	17.7222			1.14635			0.573176	−	0.819432i	$-0.305711\pi$
$239$	17.7222			1.14635			0.573176	+	0.819432i	$0.305711\pi$
$240$	0.398141	+	1.94521i	0.0256999	+	0.125563i
$241$	22.6407			1.45841			0.729206	−	0.684294i	$-0.239889\pi$
$241$	22.6407			1.45841			0.729206	+	0.684294i	$0.239889\pi$
$242$	1.63522	−	1.63522i	0.105116	−	0.105116i
$243$	15.4161	+	2.31180i	0.988942	+	0.148302i
$244$			7.58396i			0.485513i
$245$	9.50781	−	11.0434i	0.607432	−	0.705534i
$246$	5.45720	+	42.6338i	0.347938	+	2.71823i
$247$	−6.50085	−	6.50085i	−0.413639	−	0.413639i
$248$	−9.37041	−	9.37041i	−0.595022	−	0.595022i
$249$	0.471416	+	3.68289i	0.0298748	+	0.233394i
$250$	−5.73666	−	25.2107i	−0.362818	−	1.59446i
$251$		−	12.3836i		−	0.781644i	−0.920466	−	0.390822i	$-0.872191\pi$
$251$		−	12.3836i		−	0.781644i	0.920466	−	0.390822i	$-0.127809\pi$
$252$	6.02002	+	3.53354i	0.379226	+	0.222592i
$253$	−3.14765	+	3.14765i	−0.197891	+	0.197891i
$254$	−25.0763			−1.57342
$255$	8.83032	+	5.82974i	0.552976	+	0.365072i
$256$	−19.1699			−1.19812
$257$	−2.90072	+	2.90072i	−0.180942	+	0.180942i	−0.791766	−	0.610824i	$-0.790838\pi$
$257$	−2.90072	+	2.90072i	−0.180942	+	0.180942i	0.610824	+	0.791766i	$0.290838\pi$
$258$	26.2765	−	33.9909i	1.63591	−	2.11618i
$259$			4.09897i			0.254697i
$260$	3.18172	+	42.5829i	0.197322	+	2.64088i
$261$	1.07390	+	4.12615i	0.0664729	+	0.255402i
$262$	21.7774	+	21.7774i	1.34541	+	1.34541i
$263$	6.54940	+	6.54940i	0.403853	+	0.403853i	0.879589	−	0.475735i	$-0.157818\pi$
$263$	6.54940	+	6.54940i	0.403853	+	0.403853i	−0.475735	+	0.879589i	$0.657818\pi$
$264$	5.35529	−	0.685487i	0.329596	−	0.0421888i
$265$	−1.65353	−	22.1303i	−0.101576	−	1.35945i
$266$		−	2.59048i		−	0.158832i
$267$	−21.7499	−	16.8137i	−1.33107	−	1.02898i
$268$	−5.35919	+	5.35919i	−0.327364	+	0.327364i
$269$	3.64604			0.222303			0.111151	−	0.993803i	$-0.464546\pi$
$269$	3.64604			0.222303			0.111151	+	0.993803i	$0.464546\pi$
$270$	−8.67864	+	25.4293i	−0.528165	+	1.54758i
$271$	−0.267292			−0.0162368			−0.00811842	−	0.999967i	$-0.502584\pi$
$271$	−0.267292			−0.0162368			−0.00811842	+	0.999967i	$0.502584\pi$
$272$	0.990386	−	0.990386i	0.0600510	−	0.0600510i
$273$	5.43251	+	4.19958i	0.328790	+	0.254170i
$274$			30.9201i			1.86795i
$275$	−4.94448	+	0.743034i	−0.298163	+	0.0448066i
$276$	−25.6039	+	3.27734i	−1.54117	+	0.197273i
$277$	−5.69620	−	5.69620i	−0.342251	−	0.342251i	0.514962	−	0.857213i	$-0.327806\pi$
$277$	−5.69620	−	5.69620i	−0.342251	−	0.342251i	−0.857213	+	0.514962i	$0.827806\pi$
$278$	−17.2879	−	17.2879i	−1.03686	−	1.03686i
$279$	−3.21241	−	12.3427i	−0.192322	−	0.738939i
$280$	−3.16064	+	3.67110i	−0.188884	+	0.219390i
$281$			1.61792i			0.0965167i	0.998835	+	0.0482584i	$0.0153671\pi$
$281$			1.61792i			0.0965167i	−0.998835	+	0.0482584i	$0.984633\pi$
$282$	24.7611	−	32.0305i	1.47450	−	1.90739i
$283$	−11.3297	+	11.3297i	−0.673483	+	0.673483i	−0.958517	−	0.285034i	$-0.907995\pi$
$283$	−11.3297	+	11.3297i	−0.673483	+	0.673483i	0.285034	+	0.958517i	$0.407995\pi$
$284$	8.61283			0.511077
$285$	6.11552	−	1.25171i	0.362252	−	0.0741448i
$286$	13.1910			0.780000
$287$	−5.27356	+	5.27356i	−0.311288	+	0.311288i
$288$	−13.0621	−	7.66696i	−0.769689	−	0.451780i
$289$			9.53598i			0.560940i
$290$	−7.32865	+	0.547583i	−0.430353	+	0.0321552i
$291$	−2.91390	−	22.7646i	−0.170816	−	1.33448i
$292$	−19.7644	−	19.7644i	−1.15662	−	1.15662i
$293$	6.82264	+	6.82264i	0.398583	+	0.398583i	0.877733	−	0.479150i	$-0.159055\pi$
$293$	6.82264	+	6.82264i	0.398583	+	0.398583i	−0.479150	+	0.877733i	$0.659055\pi$
$294$	−3.31425	−	25.8922i	−0.193291	−	1.51006i
$295$	−11.9272	−	10.2688i	−0.694430	−	0.597872i
$296$			18.3839i			1.06854i
$297$	4.77892	+	2.04007i	0.277301	+	0.118377i
$298$	−0.783245	+	0.783245i	−0.0453722	+	0.0453722i
$299$	−25.3914			−1.46842
$300$	−25.3192	−	14.1270i	−1.46181	−	0.815621i
$301$	7.45474			0.429684
$302$	13.8730	−	13.8730i	0.798301	−	0.798301i
$303$	2.94884	−	3.81456i	0.169406	−	0.219141i
$304$		−	0.826290i		−	0.0473910i
$305$	−3.83865	−	3.30490i	−0.219800	−	0.189238i
$306$	18.3429	−	4.77406i	1.04859	−	0.272915i
$307$	−21.3329	−	21.3329i	−1.21753	−	1.21753i	−0.968494	−	0.249038i	$-0.919886\pi$
$307$	−21.3329	−	21.3329i	−1.21753	−	1.21753i	−0.249038	−	0.968494i	$-0.580114\pi$
$308$	1.64531	+	1.64531i	0.0937500	+	0.0937500i
$309$	22.4812	−	2.87763i	1.27891	−	0.163703i
$310$	21.9225	−	1.63801i	1.24511	−	0.0930327i
$311$			23.1687i			1.31378i	0.753987	+	0.656889i	$0.228128\pi$
$311$			23.1687i			1.31378i	−0.753987	+	0.656889i	$0.771872\pi$
$312$	24.3648	+	18.8352i	1.37939	+	1.06633i
$313$	−17.3945	+	17.3945i	−0.983195	+	0.983195i	−0.999861	−	0.0166665i	$-0.994695\pi$
$313$	−17.3945	+	17.3945i	−0.983195	+	0.983195i	0.0166665	+	0.999861i	$0.494695\pi$
$314$	−23.7946			−1.34281
$315$	−4.41189	+	1.50723i	−0.248582	+	0.0849228i
$316$	−13.6972			−0.770526
$317$	4.62870	−	4.62870i	0.259974	−	0.259974i	−0.565069	−	0.825043i	$-0.691151\pi$
$317$	4.62870	−	4.62870i	0.259974	−	0.259974i	0.825043	+	0.565069i	$0.191151\pi$
$318$	−31.4506	−	24.3128i	−1.76366	−	1.36339i
$319$			1.42120i			0.0795721i
$320$	18.5293	−	21.5219i	1.03582	−	1.20311i
$321$	−8.06269	+	1.03204i	−0.450016	+	0.0576028i
$322$	−5.05902	−	5.05902i	−0.281928	−	0.281928i
$323$	−3.11366	−	3.11366i	−0.173249	−	0.173249i
$324$	14.6893	+	26.3080i	0.816072	+	1.46156i
$325$	−22.9400	−	16.9461i	−1.27248	−	0.940000i
$326$		−	13.4074i		−	0.742568i
$327$	−6.15013	+	7.95570i	−0.340103	+	0.439951i
$328$	−23.6519	+	23.6519i	−1.30596	+	1.30596i
$329$	7.02480			0.387290
$330$	−4.93463	+	7.47449i	−0.271642	+	0.411457i
$331$	−9.51523			−0.523004			−0.261502	−	0.965203i	$-0.584218\pi$
$331$	−9.51523			−0.523004			−0.261502	+	0.965203i	$0.584218\pi$
$332$	−5.07476	+	5.07476i	−0.278514	+	0.278514i
$333$	−8.95641	+	15.2589i	−0.490808	+	0.836181i
$334$			10.6262i			0.581442i
$335$	−0.377175	−	5.04797i	−0.0206073	−	0.275800i
$336$	0.0783554	+	0.612143i	0.00427464	+	0.0333952i
$337$	2.15236	+	2.15236i	0.117247	+	0.117247i	0.763296	−	0.646049i	$-0.223580\pi$
$337$	2.15236	+	2.15236i	0.117247	+	0.117247i	−0.646049	+	0.763296i	$0.723580\pi$
$338$	31.9466	+	31.9466i	1.73766	+	1.73766i
$339$	0.331071	+	2.58646i	0.0179813	+	0.140477i
$340$	1.52392	+	20.3956i	0.0826462	+	1.10611i
$341$		−	4.25130i		−	0.230221i
$342$	5.66030	−	9.64334i	0.306074	−	0.521452i
$343$	6.64282	−	6.64282i	0.358679	−	0.358679i
$344$	33.4346			1.80267
$345$	9.49869	−	14.3877i	0.511392	−	0.774607i
$346$	43.8848			2.35926
$347$	21.5105	−	21.5105i	1.15474	−	1.15474i	0.169152	−	0.985590i	$-0.445897\pi$
$347$	21.5105	−	21.5105i	1.15474	−	1.15474i	0.985590	−	0.169152i	$-0.0541029\pi$
$348$	−5.04036	+	6.52012i	−0.270192	+	0.349515i
$349$		−	17.5966i		−	0.941923i	−0.882154	−	0.470961i	$-0.843907\pi$
$349$		−	17.5966i		−	0.941923i	0.882154	−	0.470961i	$-0.156093\pi$
$350$	−1.19423	−	7.94696i	−0.0638344	−	0.424783i
$351$	11.0469	+	27.5037i	0.589638	+	1.46804i
$352$	−3.56993	−	3.56993i	−0.190278	−	0.190278i
$353$	5.08168	+	5.08168i	0.270471	+	0.270471i	0.829290	−	0.558819i	$-0.188745\pi$
$353$	5.08168	+	5.08168i	0.270471	+	0.270471i	−0.558819	+	0.829290i	$0.688745\pi$
$354$	−27.9645	+	3.57951i	−1.48630	+	0.190249i
$355$	−3.75325	+	4.35942i	−0.199202	+	0.231374i
$356$		−	53.1378i		−	2.81630i
$357$	2.60196	+	2.01144i	0.137711	+	0.106457i
$358$	−12.9449	+	12.9449i	−0.684158	+	0.684158i
$359$	2.31264			0.122057			0.0610283	−	0.998136i	$-0.480562\pi$
$359$	2.31264			0.122057			0.0610283	+	0.998136i	$0.480562\pi$
$360$	−19.7873	+	6.75994i	−1.04288	+	0.356280i
$361$	16.4022			0.863276
$362$	−10.6658	+	10.6658i	−0.560581	+	0.560581i
$363$	1.37033	+	1.05933i	0.0719239	+	0.0556005i
$364$			13.2723i			0.695659i
$365$	18.6166	−	1.39100i	0.974439	−	0.0728083i
$366$	−9.00008	+	1.15203i	−0.470442	+	0.0602173i
$367$	13.8116	+	13.8116i	0.720961	+	0.720961i	0.968801	−	0.247840i	$-0.0797206\pi$
$367$	13.8116	+	13.8116i	0.720961	+	0.720961i	−0.247840	+	0.968801i	$0.579721\pi$
$368$	−1.61369	−	1.61369i	−0.0841193	−	0.0841193i
$369$	−31.1544	+	8.10848i	−1.62183	+	0.422110i
$370$	−23.1118	−	19.8982i	−1.20152	−	1.03446i
$371$		−	6.89762i		−	0.358106i
$372$	15.0774	−	19.5039i	0.781729	−	1.01123i
$373$	11.5258	−	11.5258i	0.596783	−	0.596783i	−0.342672	−	0.939455i	$-0.611332\pi$
$373$	11.5258	−	11.5258i	0.596783	−	0.596783i	0.939455	+	0.342672i	$0.111332\pi$
$374$	6.31798			0.326695
$375$	18.1839	−	6.65925i	0.939013	−	0.343882i
$376$	31.5063			1.62481
$377$	−5.73227	+	5.73227i	−0.295227	+	0.295227i
$378$	−3.27888	+	7.68087i	−0.168647	+	0.395061i
$379$		−	10.2418i		−	0.526086i	−0.964784	−	0.263043i	$-0.915274\pi$
$379$		−	10.2418i		−	0.526086i	0.964784	−	0.263043i	$-0.0847261\pi$
$380$	9.14383	+	7.87241i	0.469069	+	0.403846i
$381$	−2.38462	−	18.6296i	−0.122168	−	0.954421i
$382$	10.4538	+	10.4538i	0.534865	+	0.534865i
$383$	25.1128	+	25.1128i	1.28320	+	1.28320i	0.938834	+	0.344370i	$0.111908\pi$
$383$	25.1128	+	25.1128i	1.28320	+	1.28320i	0.344370	+	0.938834i	$0.388092\pi$
$384$	−4.23847	−	33.1126i	−0.216293	−	1.68977i
$385$	−1.54976	+	0.115795i	−0.0789831	+	0.00590148i
$386$			57.8921i			2.94663i
$387$	27.7511	+	16.2889i	1.41067	+	0.828012i
$388$	31.3680	−	31.3680i	1.59247	−	1.59247i
$389$	−2.67379			−0.135567			−0.0677833	−	0.997700i	$-0.521593\pi$
$389$	−2.67379			−0.135567			−0.0677833	+	0.997700i	$0.521593\pi$
$390$	−50.0509	+	10.2443i	−2.53442	+	0.518739i
$391$	−12.1615			−0.615034
$392$	14.3642	−	14.3642i	0.725503	−	0.725503i
$393$	−14.1079	+	18.2497i	−0.711648	+	0.920576i
$394$		−	48.4439i		−	2.44057i
$395$	5.96888	−	6.93288i	0.300327	−	0.348831i
$396$	2.52978	+	9.71990i	0.127126	+	0.488444i
$397$	6.20435	+	6.20435i	0.311387	+	0.311387i	0.845447	−	0.534060i	$-0.179334\pi$
$397$	6.20435	+	6.20435i	0.311387	+	0.311387i	−0.534060	+	0.845447i	$0.679334\pi$
$398$	16.3551	+	16.3551i	0.819805	+	0.819805i
$399$	1.92451	−	0.246340i	0.0963458	−	0.0123324i
$400$	−0.380927	−	2.53486i	−0.0190463	−	0.126743i
$401$			15.9779i			0.797898i	0.916973	+	0.398949i	$0.130625\pi$
$401$			15.9779i			0.797898i	−0.916973	+	0.398949i	$0.869375\pi$
$402$	−7.17396	−	5.54581i	−0.357804	−	0.276600i
$403$	17.1472	−	17.1472i	0.854161	−	0.854161i
$404$	9.31948			0.463662
$405$	−19.7171	−	4.02932i	−0.979751	−	0.200218i
$406$	−2.28421			−0.113364
$407$	−4.17033	+	4.17033i	−0.206716	+	0.206716i
$408$	11.6698	+	9.02133i	0.577743	+	0.446622i
$409$		−	30.7605i		−	1.52101i	−0.649333	−	0.760504i	$-0.724952\pi$
$409$		−	30.7605i		−	1.52101i	0.649333	−	0.760504i	$-0.275048\pi$
$410$	−4.13452	−	55.3348i	−0.204189	−	2.73279i
$411$	−22.9710	+	2.94033i	−1.13308	+	0.145036i
$412$	30.9775	+	30.9775i	1.52615	+	1.52615i
$413$	−3.45905	−	3.45905i	−0.170209	−	0.170209i
$414$	−7.77861	−	29.8870i	−0.382298	−	1.46886i
$415$	−0.357157	−	4.78006i	−0.0175322	−	0.234644i
$416$		−	28.7979i		−	1.41193i
$417$	11.1995	−	14.4874i	0.548440	−	0.709453i
$418$	2.63558	−	2.63558i	0.128910	−	0.128910i
$419$	−19.4061			−0.948048			−0.474024	−	0.880512i	$-0.657199\pi$
$419$	−19.4061			−0.948048			−0.474024	+	0.880512i	$0.657199\pi$
$420$	−7.52059	−	4.96506i	−0.366967	−	0.242270i
$421$	28.2534			1.37699			0.688493	−	0.725243i	$-0.258272\pi$
$421$	28.2534			1.37699			0.688493	+	0.725243i	$0.258272\pi$
$422$	1.46701	−	1.46701i	0.0714128	−	0.0714128i
$423$	26.1506	+	15.3495i	1.27149	+	0.746317i
$424$		−	30.9359i		−	1.50238i
$425$	−10.9874	−	8.11653i	−0.532966	−	0.393710i
$426$	1.30831	+	10.2211i	0.0633880	+	0.495212i
$427$	−1.11326	−	1.11326i	−0.0538744	−	0.0538744i
$428$	−11.1098	−	11.1098i	−0.537013	−	0.537013i
$429$	1.25439	+	9.79980i	0.0605626	+	0.473139i
$430$	−36.1885	+	42.0331i	−1.74517	+	2.02702i
$431$			27.1552i			1.30802i	0.756486	+	0.654010i	$0.226914\pi$
$431$			27.1552i			1.30802i	−0.756486	+	0.654010i	$0.773086\pi$
$432$	−1.04587	+	2.44998i	−0.0503195	+	0.117875i
$433$	−13.9565	+	13.9565i	−0.670709	+	0.670709i	−0.957879	−	0.287171i	$-0.907285\pi$
$433$	−13.9565	+	13.9565i	−0.670709	+	0.670709i	0.287171	+	0.957879i	$0.407285\pi$
$434$	6.83286			0.327988
$435$	−1.10372	−	5.39250i	−0.0529195	−	0.258551i
$436$	−19.4368			−0.930855
$437$	−5.07324	+	5.07324i	−0.242686	+	0.242686i
$438$	20.4526	−	26.4572i	0.977264	−	1.26417i
$439$		−	9.86280i		−	0.470726i	−0.971908	−	0.235363i	$-0.924372\pi$
$439$		−	9.86280i		−	0.470726i	0.971908	−	0.235363i	$-0.0756279\pi$
$440$	−6.95069	+	0.519343i	−0.331361	+	0.0247587i
$441$	18.9206	−	4.92441i	0.900979	−	0.234496i
$442$	25.4829	+	25.4829i	1.21210	+	1.21210i
$443$	−8.97581	−	8.97581i	−0.426454	−	0.426454i	0.460965	−	0.887418i	$-0.347503\pi$
$443$	−8.97581	−	8.97581i	−0.426454	−	0.426454i	−0.887418	+	0.460965i	$0.847503\pi$
$444$	−33.9227	+	4.34217i	−1.60990	+	0.206070i
$445$	26.8959	+	23.1561i	1.27499	+	1.09770i
$446$		−	15.2943i		−	0.724204i
$447$	−0.656368	−	0.507403i	−0.0310451	−	0.0239993i
$448$	6.24163	−	6.24163i	0.294889	−	0.294889i
$449$	0.995460			0.0469786			0.0234893	−	0.999724i	$-0.492522\pi$
$449$	0.995460			0.0469786			0.0234893	+	0.999724i	$0.492522\pi$
$450$	12.9188	−	32.1929i	0.608997	−	1.51759i
$451$	−10.7308			−0.505291
$452$	−3.56395	+	3.56395i	−0.167634	+	0.167634i
$453$	11.6257	+	8.98722i	0.546223	+	0.422256i
$454$		−	13.3815i		−	0.628023i
$455$	−6.71784	−	5.78374i	−0.314937	−	0.271146i
$456$	8.63143	−	1.10484i	0.404204	−	0.0517387i
$457$	22.8526	+	22.8526i	1.06900	+	1.06900i	0.997436	+	0.0715636i	$0.0227989\pi$
$457$	22.8526	+	22.8526i	1.06900	+	1.06900i	0.0715636	+	0.997436i	$0.477201\pi$
$458$	−16.0730	−	16.0730i	−0.751040	−	0.751040i
$459$	5.29103	+	13.1732i	0.246964	+	0.614873i
$460$	33.2315	−	2.48300i	1.54943	−	0.115771i
$461$			23.3031i			1.08533i	0.839948	+	0.542666i	$0.182585\pi$
$461$			23.3031i			1.08533i	−0.839948	+	0.542666i	$0.817415\pi$
$462$	−1.70260	+	2.20245i	−0.0792121	+	0.102467i
$463$	−10.5585	+	10.5585i	−0.490693	+	0.490693i	−0.908525	−	0.417831i	$-0.862790\pi$
$463$	−10.5585	+	10.5585i	−0.490693	+	0.490693i	0.417831	+	0.908525i	$0.362790\pi$
$464$	−0.728600			−0.0338244
$465$	3.30161	+	16.1308i	0.153109	+	0.748048i
$466$	−6.38148			−0.295616
$467$	−22.3950	+	22.3950i	−1.03632	+	1.03632i	−0.0370024	+	0.999315i	$0.511781\pi$
$467$	−22.3950	+	22.3950i	−1.03632	+	1.03632i	−0.999315	+	0.0370024i	$0.988219\pi$
$468$	−29.0006	+	49.4078i	−1.34055	+	2.28388i
$469$		−	1.57336i		−	0.0726512i
$470$	−34.1014	+	39.6089i	−1.57298	+	1.82702i
$471$	−2.26273	−	17.6774i	−0.104261	−	0.814530i
$472$	−15.5139	−	15.5139i	−0.714084	−	0.714084i
$473$	7.58453	+	7.58453i	0.348737	+	0.348737i
$474$	−2.08064	−	16.2548i	−0.0955670	−	0.746607i
$475$	−7.96930	+	1.19759i	−0.365656	+	0.0549492i
$476$			6.35694i			0.291370i
$477$	15.0716	−	25.6772i	0.690080	−	1.17568i
$478$	−28.9797	+	28.9797i	−1.32550	+	1.32550i
$479$	−4.78703			−0.218725			−0.109363	−	0.994002i	$-0.534881\pi$
$479$	−4.78703			−0.218725			−0.109363	+	0.994002i	$0.534881\pi$
$480$	16.3179	+	10.7730i	0.744808	+	0.491719i
$481$	−33.6412			−1.53391
$482$	−37.0225	+	37.0225i	−1.68633	+	1.68633i
$483$	3.27734	−	4.23951i	0.149124	−	0.192905i
$484$			3.34791i			0.152178i
$485$	2.20765	+	29.5464i	0.100244	+	1.34163i
$486$	−28.9890	+	21.4284i	−1.31497	+	0.972013i
$487$	−12.0835	−	12.0835i	−0.547558	−	0.547558i	0.378176	−	0.925734i	$-0.376551\pi$
$487$	−12.0835	−	12.0835i	−0.547558	−	0.547558i	−0.925734	+	0.378176i	$0.876551\pi$
$488$	−4.99297	−	4.99297i	−0.226021	−	0.226021i
$489$	9.96058	−	1.27497i	0.450433	−	0.0576562i
$490$	2.51096	+	33.6057i	0.113434	+	1.51815i
$491$		−	16.3631i		−	0.738455i	−0.929339	−	0.369227i	$-0.879622\pi$
$491$		−	16.3631i		−	0.738455i	0.929339	−	0.369227i	$-0.120378\pi$
$492$	−49.2300	−	38.0571i	−2.21946	−	1.71575i
$493$	−2.74554	+	2.74554i	−0.123653	+	0.123653i
$494$	21.2607			0.956562
$495$	−6.02218	−	2.95523i	−0.270677	−	0.132828i
$496$	2.17949			0.0978620
$497$	−1.26429	+	1.26429i	−0.0567111	+	0.0567111i
$498$	−6.79321	−	5.25147i	−0.304411	−	0.235324i
$499$			18.3147i			0.819880i	0.912113	+	0.409940i	$0.134450\pi$
$499$			18.3147i			0.819880i	−0.912113	+	0.409940i	$0.865550\pi$
$500$	31.6803	+	19.9353i	1.41679	+	0.891533i
$501$	−7.89441	+	1.01050i	−0.352696	+	0.0451457i
$502$	20.2499	+	20.2499i	0.903797	+	0.903797i
$503$	15.2637	+	15.2637i	0.680573	+	0.680573i	0.960129	−	0.279556i	$-0.0901873\pi$
$503$	15.2637	+	15.2637i	0.680573	+	0.680573i	−0.279556	+	0.960129i	$0.590187\pi$
$504$	−6.28968	+	1.63700i	−0.280165	+	0.0729179i
$505$	−4.06119	+	4.71709i	−0.180721	+	0.209908i
$506$		−	10.2942i		−	0.457634i
$507$	−20.6957	+	26.7716i	−0.919127	+	1.18897i
$508$	25.6702	−	25.6702i	1.13893	−	1.13893i
$509$	6.56781			0.291113			0.145556	−	0.989350i	$-0.453503\pi$
$509$	6.56781			0.291113			0.145556	+	0.989350i	$0.453503\pi$
$510$	−23.9725	+	4.90662i	−1.06152	+	0.217269i
$511$	5.80248			0.256686
$512$	4.09013	−	4.09013i	0.180760	−	0.180760i
$513$	7.70246	+	3.28810i	0.340072	+	0.145173i
$514$		−	9.48664i		−	0.418438i
$515$	−29.1786	+	2.18017i	−1.28576	+	0.0960698i
$516$	7.89705	+	61.6948i	0.347648	+	2.71596i
$517$	7.14711	+	7.14711i	0.314329	+	0.314329i
$518$	−6.70272	−	6.70272i	−0.294501	−	0.294501i
$519$	4.17320	+	32.6027i	0.183183	+	1.43110i
$520$	−30.1296	−	25.9401i	−1.32127	−	1.13755i
$521$		−	34.7218i		−	1.52119i	−0.649226	−	0.760596i	$-0.724907\pi$
$521$		−	34.7218i		−	1.52119i	0.649226	−	0.760596i	$-0.275093\pi$
$522$	−8.50324	−	4.99110i	−0.372177	−	0.218454i
$523$	14.5590	−	14.5590i	0.636620	−	0.636620i	−0.313100	−	0.949720i	$-0.601368\pi$
$523$	14.5590	−	14.5590i	0.636620	−	0.636620i	0.949720	+	0.313100i	$0.101368\pi$
$524$	−44.5864			−1.94777
$525$	5.79036	−	1.64293i	0.252712	−	0.0717032i
$526$	−21.4195			−0.933933
$527$	8.21284	−	8.21284i	0.357757	−	0.357757i
$528$	−0.543082	+	0.702521i	−0.0236346	+	0.0305733i
$529$		−	3.18462i		−	0.138462i
$530$	38.8918	+	33.4840i	1.68935	+	1.45445i
$531$	−5.31855	−	20.4349i	−0.230805	−	0.886799i
$532$	2.65183	+	2.65183i	0.114972	+	0.114972i
$533$	−43.2813	−	43.2813i	−1.87472	−	1.87472i
$534$	63.0599	−	8.07178i	2.72887	−	0.349300i
$535$	10.4646	−	0.781900i	0.452426	−	0.0338045i
$536$		−	7.05655i		−	0.304796i
$537$	−10.8479	−	8.38597i	−0.468123	−	0.361881i
$538$	−5.96208	+	5.96208i	−0.257044	+	0.257044i
$539$	6.51697			0.280706
$540$	−17.1474	−	34.9158i	−0.737906	−	1.50254i
$541$	31.8748			1.37040			0.685202	−	0.728353i	$-0.259714\pi$
$541$	31.8748			1.37040			0.685202	+	0.728353i	$0.259714\pi$
$542$	0.437082	−	0.437082i	0.0187743	−	0.0187743i
$543$	−8.93804	−	6.90952i	−0.383568	−	0.296516i
$544$		−	13.7931i		−	0.591374i
$545$	8.47007	−	9.83802i	0.362818	−	0.421415i
$546$	−15.7506	+	2.01611i	−0.674064	+	0.0862814i
$547$	−9.90141	−	9.90141i	−0.423354	−	0.423354i	0.463003	−	0.886357i	$-0.346772\pi$
$547$	−9.90141	−	9.90141i	−0.423354	−	0.423354i	−0.886357	+	0.463003i	$0.846772\pi$
$548$	−31.6525	−	31.6525i	−1.35213	−	1.35213i
$549$	−1.71172	−	6.57675i	−0.0730543	−	0.280689i
$550$	6.87030	−	9.30035i	0.292951	−	0.396568i
$551$			2.29063i			0.0975842i
$552$	14.6989	−	19.0143i	0.625627	−	0.809300i
$553$	2.01063	−	2.01063i	0.0855005	−	0.0855005i
$554$	18.6291			0.791475
$555$	12.5849	−	19.0623i	0.534197	−	0.809150i
$556$	35.3947			1.50107
$557$	18.9330	−	18.9330i	0.802218	−	0.802218i	−0.181224	−	0.983442i	$-0.558006\pi$
$557$	18.9330	−	18.9330i	0.802218	−	0.802218i	0.983442	+	0.181224i	$0.0580059\pi$
$558$	25.4361	+	14.9301i	1.07680	+	0.632040i
$559$			61.1828i			2.58776i
$560$	−0.0593641	−	0.794507i	−0.00250859	−	0.0335740i
$561$	0.600806	+	4.69373i	0.0253660	+	0.198169i
$562$	−2.64565	−	2.64565i	−0.111600	−	0.111600i
$563$	−29.6786	−	29.6786i	−1.25080	−	1.25080i	−0.955361	−	0.295442i	$-0.904533\pi$
$563$	−29.6786	−	29.6786i	−1.25080	−	1.25080i	−0.295442	−	0.955361i	$-0.595467\pi$
$564$	7.44159	+	58.1367i	0.313348	+	2.44800i
$565$	−0.250828	−	3.35699i	−0.0105524	−	0.141230i
$566$		−	37.0533i		−	1.55747i
$567$	−6.01805	−	1.70553i	−0.252734	−	0.0716253i
$568$	−5.67034	+	5.67034i	−0.237922	+	0.237922i
$569$	−5.92967			−0.248585			−0.124292	−	0.992246i	$-0.539666\pi$
$569$	−5.92967			−0.248585			−0.124292	+	0.992246i	$0.539666\pi$
$570$	−7.95341	+	12.0471i	−0.333132	+	0.504596i
$571$	−33.0849			−1.38456			−0.692280	−	0.721629i	$-0.743394\pi$
$571$	−33.0849			−1.38456			−0.692280	+	0.721629i	$0.743394\pi$
$572$	−13.5034	+	13.5034i	−0.564606	+	0.564606i
$573$	−6.77222	+	8.76043i	−0.282914	+	0.365972i
$574$		−	17.2469i		−	0.719871i
$575$	−13.2247	+	17.9023i	−0.551507	+	0.746577i
$576$	36.8734	−	9.59695i	1.53639	−	0.399873i
$577$	−20.3628	−	20.3628i	−0.847713	−	0.847713i	0.142134	−	0.989847i	$-0.454604\pi$
$577$	−20.3628	−	20.3628i	−0.847713	−	0.847713i	−0.989847	+	0.142134i	$0.954604\pi$
$578$	−15.5934	−	15.5934i	−0.648602	−	0.648602i
$579$	−43.0090	+	5.50522i	−1.78739	+	0.228789i
$580$	6.94168	−	8.06278i	0.288237	−	0.334789i
$581$		−	1.48986i		−	0.0618098i
$582$	41.9900	+	32.4603i	1.74054	+	1.34552i
$583$	7.01771	−	7.01771i	0.290644	−	0.290644i
$584$	26.0242			1.07689
$585$	−12.3702	−	36.2094i	−0.511445	−	1.49707i
$586$	−22.3131			−0.921744
$587$	−7.61833	+	7.61833i	−0.314442	+	0.314442i	−0.846628	−	0.532186i	$-0.821371\pi$
$587$	−7.61833	+	7.61833i	−0.314442	+	0.314442i	0.532186	+	0.846628i	$0.321371\pi$
$588$	29.8982	+	23.1127i	1.23298	+	0.953153i
$589$		−	6.85206i		−	0.282334i
$590$	36.2954	−	2.71193i	1.49426	−	0.111648i
$591$	35.9898	−	4.60675i	1.48042	−	0.189496i
$592$	−2.13798	−	2.13798i	−0.0878705	−	0.0878705i
$593$	−3.19158	−	3.19158i	−0.131062	−	0.131062i	0.638533	−	0.769595i	$-0.279542\pi$
$593$	−3.19158	−	3.19158i	−0.131062	−	0.131062i	−0.769595	+	0.638533i	$0.779542\pi$
$594$	−11.1506	+	4.47863i	−0.457514	+	0.183761i
$595$	−3.21759	−	2.77019i	−0.131908	−	0.113567i
$596$		−	1.60359i		−	0.0656857i
$597$	−10.5952	+	13.7057i	−0.433631	+	0.560937i
$598$	41.5206	−	41.5206i	1.69790	−	1.69790i
$599$	−20.5771			−0.840756			−0.420378	−	0.907349i	$-0.638103\pi$
$599$	−20.5771			−0.840756			−0.420378	+	0.907349i	$0.638103\pi$
$600$	25.9698	−	7.36854i	1.06021	−	0.300819i
$601$	18.0422			0.735955			0.367977	−	0.929835i	$-0.380050\pi$
$601$	18.0422			0.735955			0.367977	+	0.929835i	$0.380050\pi$
$602$	−12.1902	+	12.1902i	−0.496834	+	0.496834i
$603$	3.43786	−	5.85702i	0.140001	−	0.238516i
$604$			28.4031i			1.15571i
$605$	−1.69456	−	1.45893i	−0.0688935	−	0.0593140i
$606$	1.41566	+	11.0597i	0.0575071	+	0.449268i
$607$	−19.6944	−	19.6944i	−0.799369	−	0.799369i	0.183627	−	0.982996i	$-0.441216\pi$
$607$	−19.6944	−	19.6944i	−0.799369	−	0.799369i	−0.982996	+	0.183627i	$0.941216\pi$
$608$	−5.75386	−	5.75386i	−0.233350	−	0.233350i
$609$	−0.217216	−	1.69698i	−0.00880204	−	0.0687650i
$610$	11.6813	−	0.872805i	0.472961	−	0.0353388i
$611$			57.6542i			2.33244i
$612$	−13.8902	+	23.6644i	−0.561477	+	0.956578i
$613$	−2.97610	+	2.97610i	−0.120204	+	0.120204i	−0.764650	−	0.644446i	$-0.777088\pi$
$613$	−2.97610	+	2.97610i	−0.120204	+	0.120204i	0.644446	+	0.764650i	$0.277088\pi$
$614$	69.7680			2.81561
$615$	40.7159	−	8.33363i	1.64182	−	0.336045i
$616$	−2.16641			−0.0872870
$617$	18.5684	−	18.5684i	0.747536	−	0.747536i	−0.226480	−	0.974016i	$-0.572722\pi$
$617$	18.5684	−	18.5684i	0.747536	−	0.747536i	0.974016	+	0.226480i	$0.0727217\pi$
$618$	−32.0562	+	41.4673i	−1.28949	+	1.66806i
$619$		−	42.1620i		−	1.69463i	−0.531088	−	0.847317i	$-0.678217\pi$
$619$		−	42.1620i		−	1.69463i	0.531088	−	0.847317i	$-0.321783\pi$
$620$	−20.7649	+	24.1185i	−0.833939	+	0.968624i
$621$	21.4638	−	8.62094i	0.861313	−	0.345946i
$622$	−37.8860	−	37.8860i	−1.51909	−	1.51909i
$623$	7.80016	+	7.80016i	0.312507	+	0.312507i
$624$	−5.02401	+	0.643082i	−0.201121	+	0.0257439i
$625$	−23.8958	+	7.34783i	−0.955832	+	0.293913i
$626$		−	56.8877i		−	2.27369i
$627$	2.20864	+	1.70739i	0.0882047	+	0.0681864i
$628$	24.3582	−	24.3582i	0.971996	−	0.971996i
$629$	−16.1128			−0.642461
$630$	4.74976	−	9.67908i	0.189235	−	0.385624i
$631$	37.6469			1.49870			0.749350	−	0.662175i	$-0.230366\pi$
$631$	37.6469			1.49870			0.749350	+	0.662175i	$0.230366\pi$
$632$	9.01767	−	9.01767i	0.358704	−	0.358704i
$633$	1.22937	+	0.950359i	0.0488630	+	0.0377734i
$634$			15.1379i			0.601204i
$635$	1.80665	+	24.1795i	0.0716946	+	0.959533i
$636$	57.0841	−	7.30687i	2.26353	−	0.289736i
$637$	26.2855	+	26.2855i	1.04147	+	1.04147i
$638$	−2.32398	−	2.32398i	−0.0920073	−	0.0920073i
$639$	−7.46898	+	1.94393i	−0.295468	+	0.0769009i
$640$	3.21117	+	42.9771i	0.126933	+	1.69882i
$641$		−	5.14588i		−	0.203250i	−0.994823	−	0.101625i	$-0.967596\pi$
$641$		−	5.14588i		−	0.203250i	0.994823	−	0.101625i	$-0.0324042\pi$
$642$	11.4967	−	14.8719i	0.453738	−	0.586948i
$643$	−18.2879	+	18.2879i	−0.721205	+	0.721205i	−0.968851	−	0.247645i	$-0.920343\pi$
$643$	−18.2879	+	18.2879i	−0.721205	+	0.721205i	0.247645	+	0.968851i	$0.420343\pi$
$644$	10.3577			0.408150
$645$	−34.6684	−	22.8879i	−1.36507	−	0.901211i
$646$	10.1830			0.400647
$647$	2.03209	−	2.03209i	0.0798896	−	0.0798896i	−0.666033	−	0.745922i	$-0.732009\pi$
$647$	2.03209	−	2.03209i	0.0798896	−	0.0798896i	0.745922	+	0.666033i	$0.232009\pi$
$648$	−26.9910	−	7.64929i	−1.06031	−	0.300493i
$649$		−	7.03856i		−	0.276288i
$650$	65.2226	−	9.80135i	2.55824	−	0.384441i
$651$	0.649767	+	5.07624i	0.0254664	+	0.198953i
$652$	13.7250	+	13.7250i	0.537511	+	0.537511i
$653$	11.3539	+	11.3539i	0.444314	+	0.444314i	0.893459	−	0.449145i	$-0.148271\pi$
$653$	11.3539	+	11.3539i	0.444314	+	0.444314i	−0.449145	+	0.893459i	$0.648271\pi$
$654$	−2.95251	−	23.0662i	−0.115452	−	0.901959i
$655$	19.4296	−	22.5676i	0.759179	−	0.881789i
$656$		−	5.50128i		−	0.214789i
$657$	21.6004	+	12.6787i	0.842711	+	0.494641i
$658$	−11.4871	+	11.4871i	−0.447814	+	0.447814i
$659$	20.8399			0.811807			0.405904	−	0.913916i	$-0.366957\pi$
$659$	20.8399			0.811807			0.405904	+	0.913916i	$0.366957\pi$
$660$	−2.60002	−	12.7030i	−0.101206	−	0.494465i
$661$	−18.3117			−0.712243			−0.356121	−	0.934440i	$-0.615901\pi$
$661$	−18.3117			−0.712243			−0.356121	+	0.934440i	$0.615901\pi$
$662$	15.5595	−	15.5595i	0.604738	−	0.604738i
$663$	−16.5084	+	21.3549i	−0.641132	+	0.829357i
$664$		−	6.68203i		−	0.259313i
$665$	−2.49784	+	0.186634i	−0.0968619	+	0.00723735i
$666$	−10.3059	−	39.5974i	−0.399346	−	1.53437i
$667$	4.47345	+	4.47345i	0.173213	+	0.173213i
$668$	−10.8779	−	10.8779i	−0.420880	−	0.420880i
$669$	11.3624	−	1.45440i	0.439294	−	0.0562304i
$670$	8.87132	+	7.63779i	0.342729	+	0.295073i
$671$		−	2.26528i		−	0.0874503i
$672$	4.80828	+	3.71703i	0.185484	+	0.143387i
$673$	4.93683	−	4.93683i	0.190301	−	0.190301i	−0.605525	−	0.795826i	$-0.707037\pi$
$673$	4.93683	−	4.93683i	0.190301	−	0.190301i	0.795826	+	0.605525i	$0.207037\pi$
$674$	−7.03919			−0.271139
$675$	25.1451	+	6.53620i	0.967837	+	0.251578i
$676$	−65.4064			−2.51563
$677$	−13.0644	+	13.0644i	−0.502106	+	0.502106i	−0.912092	−	0.409986i	$-0.865534\pi$
$677$	−13.0644	+	13.0644i	−0.502106	+	0.502106i	0.409986	+	0.912092i	$0.365534\pi$
$678$	−4.77081	−	3.68806i	−0.183222	−	0.141639i
$679$			9.20908i			0.353412i
$680$	−14.4309	−	12.4243i	−0.553400	−	0.476452i
$681$	9.94130	−	1.27250i	0.380951	−	0.0487624i
$682$	6.95182	+	6.95182i	0.266199	+	0.266199i
$683$	−5.18414	−	5.18414i	−0.198366	−	0.198366i	0.600933	−	0.799299i	$-0.294796\pi$
$683$	−5.18414	−	5.18414i	−0.198366	−	0.198366i	−0.799299	+	0.600933i	$0.794796\pi$
$684$	4.07738	+	15.6661i	0.155903	+	0.599009i
$685$	29.8143	−	2.22767i	1.13915	−	0.0851150i
$686$			21.7250i			0.829464i
$687$	10.4124	−	13.4693i	0.397258	−	0.513886i
$688$	−3.88832	+	3.88832i	−0.148241	+	0.148241i
$689$	56.6104			2.15668
$690$	7.99461	+	39.0595i	0.304350	+	1.48697i
$691$	−38.4850			−1.46404			−0.732019	−	0.681284i	$-0.761422\pi$
$691$	−38.4850			−1.46404			−0.732019	+	0.681284i	$0.761422\pi$
$692$	−44.9242	+	44.9242i	−1.70776	+	1.70776i
$693$	−1.79815	−	1.05545i	−0.0683059	−	0.0400931i
$694$			70.3488i			2.67040i
$695$	−15.4241	+	17.9152i	−0.585070	+	0.679561i
$696$	−0.974215	−	7.61096i	−0.0369275	−	0.288493i
$697$	−20.7301	−	20.7301i	−0.785209	−	0.785209i
$698$	28.7743	+	28.7743i	1.08912	+	1.08912i
$699$	−0.606844	−	4.74090i	−0.0229529	−	0.179317i
$700$	9.35771	+	6.91267i	0.353688	+	0.261274i
$701$		−	46.7507i		−	1.76575i	−0.469608	−	0.882875i	$-0.655605\pi$
$701$		−	46.7507i		−	1.76575i	0.469608	−	0.882875i	$-0.344395\pi$
$702$	−63.0387	−	26.9106i	−2.37924	−	1.01567i
$703$	−6.72156	+	6.72156i	−0.253508	+	0.253508i
$704$	12.7006			0.478672
$705$	−32.6689	−	21.5679i	−1.23038	−	0.812294i
$706$	−16.6194			−0.625478
$707$	−1.36802	+	1.36802i	−0.0514496	+	0.0514496i
$708$	24.9626	−	32.2911i	0.938151	−	1.21358i
$709$		−	28.1042i		−	1.05547i	−0.849408	−	0.527737i	$-0.823041\pi$
$709$		−	28.1042i		−	1.05547i	0.849408	−	0.527737i	$-0.176959\pi$
$710$	−0.991213	−	13.2660i	−0.0371996	−	0.497865i
$711$	11.8781	−	3.09148i	0.445463	−	0.115940i
$712$	34.9838	+	34.9838i	1.31107	+	1.31107i
$713$	−13.3816	−	13.3816i	−0.501145	−	0.501145i
$714$	−7.54394	+	0.965638i	−0.282325	+	0.0361381i
$715$	−0.950360	−	12.7193i	−0.0355414	−	0.475673i
$716$		−	26.5029i		−	0.990461i
$717$	−24.2853	−	18.7737i	−0.906951	−	0.701116i
$718$	−3.78169	+	3.78169i	−0.141131	+	0.141131i
$719$	31.9706			1.19230			0.596151	−	0.802873i	$-0.296696\pi$
$719$	31.9706			1.19230			0.596151	+	0.802873i	$0.296696\pi$
$720$	1.51504	−	3.08736i	0.0564622	−	0.115059i
$721$	−9.09445			−0.338695
$722$	−26.8213	+	26.8213i	−0.998186	+	0.998186i
$723$	−31.0253	−	23.9840i	−1.15384	−	0.891974i
$724$		−	21.8368i		−	0.811558i
$725$	1.05600	+	7.02711i	0.0392189	+	0.260980i
$726$	−3.97305	+	0.508557i	−0.147454	+	0.0188743i
$727$	−28.7104	−	28.7104i	−1.06481	−	1.06481i	−0.997749	−	0.0670618i	$-0.978638\pi$
$727$	−28.7104	−	28.7104i	−1.06481	−	1.06481i	−0.0670618	−	0.997749i	$-0.521362\pi$
$728$	−8.73797	−	8.73797i	−0.323851	−	0.323851i
$729$	−18.6762	−	19.4987i	−0.691712	−	0.722174i
$730$	−28.1677	+	32.7169i	−1.04253	+	1.21091i
$731$			29.3042i			1.08386i
$732$	8.03393	−	10.3926i	0.296943	−	0.384120i
$733$	−4.30731	+	4.30731i	−0.159094	+	0.159094i	−0.782165	−	0.623071i	$-0.785885\pi$
$733$	−4.30731	+	4.30731i	−0.159094	+	0.159094i	0.623071	+	0.782165i	$0.285885\pi$
$734$	−45.1702			−1.66726
$735$	−24.7275	+	5.06115i	−0.912086	+	0.186684i
$736$	−22.4738			−0.828395
$737$	1.60076	−	1.60076i	0.0589647	−	0.0589647i
$738$	37.6852	−	64.2035i	1.38721	−	2.36336i
$739$			26.2315i			0.964942i	0.875912	+	0.482471i	$0.160261\pi$
$739$			26.2315i			0.964942i	−0.875912	+	0.482471i	$0.839739\pi$
$740$	44.0286	−	3.28974i	1.61852	−	0.120933i
$741$	2.02177	+	15.7949i	0.0742717	+	0.580240i
$742$	11.2791	+	11.2791i	0.414070	+	0.414070i
$743$	−27.2032	−	27.2032i	−0.997989	−	0.997989i	0.00200891	−	0.999998i	$-0.499361\pi$
$743$	−27.2032	−	27.2032i	−0.997989	−	0.997989i	−0.999998	+	0.00200891i	$0.999361\pi$
$744$	2.91421	+	22.7670i	0.106840	+	0.834677i
$745$	0.811665	+	0.698805i	0.0297371	+	0.0256022i
$746$			37.6945i			1.38009i
$747$	3.25541	−	5.54617i	0.119109	−	0.202924i
$748$	−6.46762	+	6.46762i	−0.236480	+	0.236480i
$749$	3.26165			0.119178
$750$	−18.8454	+	40.6241i	−0.688136	+	1.48338i
$751$	−17.1517			−0.625875			−0.312938	−	0.949774i	$-0.601313\pi$
$751$	−17.1517			−0.625875			−0.312938	+	0.949774i	$0.601313\pi$
$752$	−3.66407	+	3.66407i	−0.133615	+	0.133615i
$753$	−13.1183	+	16.9696i	−0.478058	+	0.618407i
$754$		−	18.7471i		−	0.682728i
$755$	−14.3764	−	12.3774i	−0.523209	−	0.450458i
$756$	−4.50625	−	11.2193i	−0.163891	−	0.408043i
$757$	21.0104	+	21.0104i	0.763634	+	0.763634i	0.976977	−	0.213343i	$-0.0684352\pi$
$757$	21.0104	+	21.0104i	0.763634	+	0.763634i	−0.213343	+	0.976977i	$0.568435\pi$
$758$	16.7476	+	16.7476i	0.608301	+	0.608301i
$759$	7.64773	−	0.978923i	0.277595	−	0.0355327i
$760$	−11.2028	+	0.837054i	−0.406369	+	0.0303631i
$761$		−	19.7236i		−	0.714980i	−0.933917	−	0.357490i	$-0.883633\pi$
$761$		−	19.7236i		−	0.714980i	0.933917	−	0.357490i	$-0.116367\pi$
$762$	34.3628	+	26.5641i	1.24483	+	0.962316i
$763$	2.85316	−	2.85316i	0.103291	−	0.103291i
$764$	−21.4029			−0.774329
$765$	−5.92486	−	17.3429i	−0.214214	−	0.627035i
$766$	−82.1300			−2.96748
$767$	28.3893	−	28.3893i	1.02508	−	1.02508i
$768$	26.2691	+	20.3073i	0.947906	+	0.732776i
$769$			15.6320i			0.563706i	0.959458	+	0.281853i	$0.0909490\pi$
$769$			15.6320i			0.563706i	−0.959458	+	0.281853i	$0.909051\pi$
$770$	2.34485	−	2.72355i	0.0845026	−	0.0981501i
$771$	7.04777	−	0.902127i	0.253819	−	0.0324893i
$772$	−59.2633	−	59.2633i	−2.13293	−	2.13293i
$773$	6.65390	+	6.65390i	0.239324	+	0.239324i	0.816570	−	0.577246i	$-0.195873\pi$
$773$	6.65390	+	6.65390i	0.239324	+	0.239324i	−0.577246	+	0.816570i	$0.695873\pi$
$774$	−72.0153	+	18.7432i	−2.58853	+	0.673712i
$775$	−3.15886	−	21.0205i	−0.113470	−	0.755078i
$776$			41.3028i			1.48268i
$777$	4.34217	−	5.61695i	0.155774	−	0.201507i
$778$	4.37225	−	4.37225i	0.156753	−	0.156753i
$779$	−17.2954			−0.619670
$780$	40.7494	−	61.7232i	1.45906	−	2.21005i
$781$	−2.57260			−0.0920549
$782$	19.8868	−	19.8868i	0.711150	−	0.711150i
$783$	2.89935	−	6.79182i	0.103614	−	0.242720i
$784$			3.34102i			0.119322i
$785$	1.71431	+	22.9436i	0.0611862	+	0.818893i
$786$	−6.77281	−	52.9119i	−0.241578	−	1.88730i
$787$	4.27423	+	4.27423i	0.152360	+	0.152360i	0.779171	−	0.626811i	$-0.215640\pi$
$787$	4.27423	+	4.27423i	0.152360	+	0.152360i	−0.626811	+	0.779171i	$0.715640\pi$
$788$	49.5913	+	49.5913i	1.76662	+	1.76662i
$789$	−2.03687	−	15.9129i	−0.0725146	−	0.566513i
$790$	1.57635	+	21.0972i	0.0560839	+	0.750606i
$791$		−	1.04631i		−	0.0372026i
$792$	−8.06470	−	4.73369i	−0.286567	−	0.168204i
$793$	9.13678	−	9.13678i	0.324457	−	0.324457i
$794$	−20.2910			−0.720100
$795$	−21.1774	+	32.0775i	−0.751086	+	1.13767i
$796$	−33.4849			−1.18684
$797$	−19.2019	+	19.2019i	−0.680168	+	0.680168i	−0.960038	−	0.279870i	$-0.909709\pi$
$797$	−19.2019	+	19.2019i	−0.680168	+	0.680168i	0.279870	+	0.960038i	$0.409709\pi$
$798$	−2.74418	+	3.54982i	−0.0971428	+	0.125662i
$799$			27.6142i			0.976919i
$800$	−20.3041	−	14.9989i	−0.717857	−	0.530291i
$801$	11.9933	+	46.0806i	0.423763	+	1.62818i
$802$	−26.1274	−	26.1274i	−0.922591	−	0.922591i
$803$	5.90351	+	5.90351i	0.208330	+	0.208330i
$804$	13.0210	−	1.66671i	0.459216	−	0.0587805i
$805$	−4.51362	+	5.24258i	−0.159084	+	0.184777i
$806$			56.0789i			1.97529i
$807$	−4.99629	−	3.86236i	−0.175878	−	0.135962i
$808$	−6.13557	+	6.13557i	−0.215849	+	0.215849i
$809$	−18.7702			−0.659926			−0.329963	−	0.943994i	$-0.607036\pi$
$809$	−18.7702			−0.659926			−0.329963	+	0.943994i	$0.607036\pi$
$810$	38.8307	−	25.6530i	1.36437	−	0.901356i
$811$	45.4259			1.59512			0.797559	−	0.603241i	$-0.206124\pi$
$811$	45.4259			1.59512			0.797559	+	0.603241i	$0.206124\pi$
$812$	2.33831	−	2.33831i	0.0820587	−	0.0820587i
$813$	0.366279	+	0.283151i	0.0128460	+	0.00993055i
$814$		−	13.6388i		−	0.478041i
$815$	−12.9279	+	0.965952i	−0.452846	+	0.0338358i
$816$	−2.40631	+	0.308012i	−0.0842376	+	0.0107826i
$817$	12.2244	+	12.2244i	0.427678	+	0.427678i
$818$	50.3003	+	50.3003i	1.75871	+	1.75871i
$819$	−2.99559	−	11.5097i	−0.104675	−	0.402180i
$820$	60.8778	+	52.4130i	2.12595	+	1.83034i
$821$		−	7.17085i		−	0.250264i	−0.992140	−	0.125132i	$-0.960065\pi$
$821$		−	7.17085i		−	0.250264i	0.992140	−	0.125132i	$-0.0399355\pi$
$822$	32.7547	−	42.3709i	1.14245	−	1.47785i
$823$	31.3880	−	31.3880i	1.09412	−	1.09412i	0.0990308	−	0.995084i	$-0.468426\pi$
$823$	31.3880	−	31.3880i	1.09412	−	1.09412i	0.995084	−	0.0990308i	$-0.0315742\pi$
$824$	−40.7887			−1.42094
$825$	7.56271	+	4.21965i	0.263300	+	0.146909i
$826$	11.3126			0.393617
$827$	30.2808	−	30.2808i	1.05297	−	1.05297i	0.0544494	−	0.998517i	$-0.482660\pi$
$827$	30.2808	−	30.2808i	1.05297	−	1.05297i	0.998517	−	0.0544494i	$-0.0173403\pi$
$828$	38.5577	+	22.6320i	1.33997	+	0.786516i
$829$			0.110862i			0.00385040i	0.999998	+	0.00192520i	$0.000612811\pi$
$829$			0.110862i			0.00385040i	−0.999998	+	0.00192520i	$0.999387\pi$
$830$	8.40049	+	7.23243i	0.291585	+	0.251041i
$831$	1.77153	+	13.8399i	0.0614536	+	0.480100i
$832$	51.2265	+	51.2265i	1.77596	+	1.77596i
$833$	12.5897	+	12.5897i	0.436209	+	0.436209i
$834$	5.37656	+	42.0038i	0.186175	+	1.45447i
$835$	10.2462	−	0.765579i	0.354585	−	0.0264940i
$836$			5.39601i			0.186625i
$837$	−8.67296	+	20.3166i	−0.299781	+	0.702246i
$838$	31.7332	−	31.7332i	1.09621	−	1.09621i
$839$	8.28380			0.285989			0.142994	−	0.989724i	$-0.454327\pi$
$839$	8.28380			0.285989			0.142994	+	0.989724i	$0.454327\pi$
$840$	8.22005	−	1.68246i	0.283619	−	0.0580503i
$841$	−26.9802			−0.930351
$842$	−46.2006	+	46.2006i	−1.59218	+	1.59218i
$843$	1.71391	−	2.21708i	0.0590302	−	0.0763604i
$844$			3.00351i			0.103385i
$845$	28.5025	−	33.1057i	0.980514	−	1.13887i
$846$	−67.8619	+	17.6623i	−2.33314	+	0.607241i
$847$	−0.491443	−	0.491443i	−0.0168862	−	0.0168862i
$848$	3.59773	+	3.59773i	0.123547	+	0.123547i
$849$	27.5275	−	3.52356i	0.944741	−	0.120928i
$850$	31.2391	−	4.69447i	1.07149	−	0.161019i
$851$			26.2535i			0.899958i
$852$	−11.8025	−	9.12385i	−0.404345	−	0.312578i
$853$	1.56944	−	1.56944i	0.0537366	−	0.0537366i	−0.679728	−	0.733464i	$-0.737902\pi$
$853$	1.56944	−	1.56944i	0.0537366	−	0.0537366i	0.733464	+	0.679728i	$0.237902\pi$
$854$	3.64085			0.124587
$855$	−9.70628	−	4.76311i	−0.331948	−	0.162895i
$856$	14.6285			0.499992
$857$	17.1935	−	17.1935i	0.587318	−	0.587318i	−0.349586	−	0.936904i	$-0.613678\pi$
$857$	17.1935	−	17.1935i	0.587318	−	0.587318i	0.936904	+	0.349586i	$0.113678\pi$
$858$	−18.0761	−	13.9736i	−0.617107	−	0.477052i
$859$			13.6126i			0.464456i	0.972661	+	0.232228i	$0.0746015\pi$
$859$			13.6126i			0.464456i	−0.972661	+	0.232228i	$0.925398\pi$
$860$	−5.98301	−	80.0743i	−0.204019	−	2.73051i
$861$	12.8130	−	1.64008i	0.436665	−	0.0558939i
$862$	−44.4048	−	44.4048i	−1.51243	−	1.51243i
$863$	−14.1694	−	14.1694i	−0.482333	−	0.482333i	0.423543	−	0.905876i	$-0.360786\pi$
$863$	−14.1694	−	14.1694i	−0.482333	−	0.482333i	−0.905876	+	0.423543i	$0.860786\pi$
$864$	9.77752	+	24.3434i	0.332638	+	0.828178i
$865$	−3.16173	−	42.3154i	−0.107502	−	1.43877i
$866$		−	45.6441i		−	1.55105i
$867$	10.1018	−	13.0675i	0.343074	−	0.443795i
$868$	−6.99469	+	6.99469i	−0.237415	+	0.237415i
$869$	4.09127			0.138787
$870$	10.6228	+	7.01310i	0.360146	+	0.237766i
$871$	12.9130			0.437539
$872$	12.7964	−	12.7964i	0.433342	−	0.433342i
$873$	−20.1222	+	34.2819i	−0.681034	+	1.16027i
$874$		−	16.5918i		−	0.561225i
$875$	−7.57672	+	1.72407i	−0.256140	+	0.0582843i
$876$	6.14675	+	48.0209i	0.207680	+	1.62247i
$877$	−25.8261	−	25.8261i	−0.872087	−	0.872087i	0.120613	−	0.992700i	$-0.461514\pi$
$877$	−25.8261	−	25.8261i	−0.872087	−	0.872087i	−0.992700	+	0.120613i	$0.961514\pi$
$878$	16.1279	+	16.1279i	0.544289	+	0.544289i
$879$	−2.12185	−	16.5767i	−0.0715682	−	0.559119i
$880$	0.747943	−	0.868738i	0.0252131	−	0.0292852i
$881$		−	9.21038i		−	0.310306i	−0.987890	−	0.155153i	$-0.950413\pi$
$881$		−	9.21038i		−	0.310306i	0.987890	−	0.155153i	$-0.0495870\pi$
$882$	−22.8868	+	38.9919i	−0.770640	+	1.31292i
$883$	−15.5404	+	15.5404i	−0.522975	+	0.522975i	−0.918469	−	0.395494i	$-0.870574\pi$
$883$	−15.5404	+	15.5404i	−0.522975	+	0.522975i	0.395494	+	0.918469i	$0.370574\pi$
$884$	−52.1729			−1.75477
$885$	5.46623	+	26.7066i	0.183745	+	0.897731i
$886$	29.3549			0.986197
$887$	−21.2924	+	21.2924i	−0.714928	+	0.714928i	−0.967562	−	0.252634i	$-0.918703\pi$
$887$	−21.2924	+	21.2924i	−0.714928	+	0.714928i	0.252634	+	0.967562i	$0.418703\pi$
$888$	19.4747	−	25.1921i	0.653527	−	0.845391i
$889$			7.53632i			0.252760i
$890$	−81.8461	+	6.11539i	−2.74349	+	0.204988i
$891$	−4.38761	−	7.85805i	−0.146990	−	0.263254i
$892$	15.6565	+	15.6565i	0.524219	+	0.524219i
$893$	11.5194	+	11.5194i	0.385482	+	0.385482i
$894$	1.90302	−	0.243590i	0.0636467	−	0.00814688i
$895$	13.4146	+	11.5493i	0.448399	+	0.386051i
$896$			13.3952i			0.447503i
$897$	34.7947	+	26.8979i	1.16176	+	0.898096i
$898$	−1.62780	+	1.62780i	−0.0543203	+	0.0543203i
$899$	−6.04196			−0.201511
$900$	19.7307	+	46.1802i	0.657689	+	1.53934i
$901$	27.1142			0.903306
$902$	17.5472	−	17.5472i	0.584257	−	0.584257i
$903$	−10.2155	−	7.89705i	−0.339950	−	0.262797i
$904$		−	4.69273i		−	0.156078i
$905$	11.0528	+	9.51592i	0.367407	+	0.316320i
$906$	−33.7067	+	4.31452i	−1.11983	+	0.143340i
$907$	37.1894	+	37.1894i	1.23485	+	1.23485i	0.962077	+	0.272777i	$0.0879420\pi$
$907$	37.1894	+	37.1894i	1.23485	+	1.23485i	0.272777	+	0.962077i	$0.412058\pi$
$908$	13.6984	+	13.6984i	0.454597	+	0.454597i
$909$	−8.08178	+	2.10343i	−0.268056	+	0.0697663i
$910$	20.4429	−	1.52745i	0.677675	−	0.0506346i
$911$			16.9661i			0.562112i	0.959691	+	0.281056i	$0.0906847\pi$
$911$			16.9661i			0.562112i	−0.959691	+	0.281056i	$0.909315\pi$
$912$	−0.875316	+	1.13229i	−0.0289846	+	0.0374940i
$913$	1.51580	−	1.51580i	0.0501657	−	0.0501657i
$914$	−74.7382			−2.47212
$915$	1.75925	+	8.59522i	0.0581589	+	0.284149i
$916$	32.9073			1.08729
$917$	6.54490	−	6.54490i	0.216132	−	0.216132i
$918$	−30.1932	−	12.8891i	−0.996523	−	0.425405i
$919$			55.6816i			1.83677i	0.395693	+	0.918383i	$0.370504\pi$
$919$			55.6816i			1.83677i	−0.395693	+	0.918383i	$0.629496\pi$
$920$	−20.2436	+	23.5130i	−0.667412	+	0.775202i
$921$	6.63456	+	51.8318i	0.218616	+	1.70792i
$922$	−38.1057	−	38.1057i	−1.25495	−	1.25495i
$923$	−10.3763	−	10.3763i	−0.341541	−	0.341541i
$924$	−0.511693	−	3.99755i	−0.0168335	−	0.131510i
$925$	−17.5214	+	23.7188i	−0.576101	+	0.779871i
$926$		−	34.5309i		−	1.13475i
$927$	−33.8551	−	19.8717i	−1.11195	−	0.652674i
$928$	−5.07360	+	5.07360i	−0.166549	+	0.166549i
$929$	−39.3158			−1.28991			−0.644955	−	0.764221i	$-0.723124\pi$
$929$	−39.3158			−1.28991			−0.644955	+	0.764221i	$0.723124\pi$
$930$	−31.7763	−	20.9786i	−1.04199	−	0.687915i
$931$	10.5038			0.344247
$932$	6.53263	−	6.53263i	0.213983	−	0.213983i
$933$	24.5434	−	31.7489i	0.803514	−	1.03941i
$934$		−	73.2417i		−	2.39654i
$935$	−0.455186	−	6.09204i	−0.0148862	−	0.199231i
$936$	−13.4353	−	51.6209i	−0.439145	−	1.68728i
$937$	−16.1616	−	16.1616i	−0.527978	−	0.527978i	0.391991	−	0.919969i	$-0.371786\pi$
$937$	−16.1616	−	16.1616i	−0.527978	−	0.527978i	−0.919969	+	0.391991i	$0.871786\pi$
$938$	2.57280	+	2.57280i	0.0840049	+	0.0840049i
$939$	42.2628	−	5.40971i	1.37919	−	0.176539i
$940$	−5.63795	−	75.4561i	−0.183890	−	2.46111i
$941$			0.931023i			0.0303505i	0.999885	+	0.0151752i	$0.00483061\pi$
$941$			0.931023i			0.0303505i	−0.999885	+	0.0151752i	$0.995169\pi$
$942$	32.6065	+	25.2064i	1.06238	+	0.821268i
$943$	−33.7766	+	33.7766i	−1.09992	+	1.09992i
$944$	3.60842			0.117444
$945$	7.64242	+	2.60825i	0.248608	+	0.0848462i
$946$	−24.8048			−0.806474
$947$	0.798190	−	0.798190i	0.0259377	−	0.0259377i	−0.694019	−	0.719957i	$-0.744162\pi$
$947$	0.798190	−	0.798190i	0.0259377	−	0.0259377i	0.719957	+	0.694019i	$0.244162\pi$
$948$	18.7697	+	14.5099i	0.609612	+	0.471258i
$949$			47.6223i			1.54589i
$950$	11.0733	−	14.9899i	0.359264	−	0.486337i
$951$	−11.2462	+	1.43953i	−0.364683	+	0.0466801i
$952$	−4.18516	−	4.18516i	−0.135642	−	0.135642i
$953$	−7.37483	−	7.37483i	−0.238894	−	0.238894i	0.577498	−	0.816392i	$-0.304029\pi$
$953$	−7.37483	−	7.37483i	−0.238894	−	0.238894i	−0.816392	+	0.577498i	$0.804029\pi$
$954$	17.3425	+	66.6333i	0.561484	+	2.15733i
$955$	9.32683	−	10.8331i	0.301809	−	0.350552i
$956$		−	59.3322i		−	1.91894i
$957$	1.50553	−	1.94752i	0.0486667	−	0.0629544i
$958$	7.82787	−	7.82787i	0.252907	−	0.252907i
$959$	9.29261			0.300074
$960$	−48.1902	+	9.86344i	−1.55533	+	0.318341i
$961$	−12.9264			−0.416982
$962$	55.0108	−	55.0108i	1.77362	−	1.77362i
$963$	12.1419	+	7.12683i	0.391266	+	0.229659i
$964$		−	75.7988i		−	2.44131i
$965$	55.8218	−	4.17090i	1.79697	−	0.134266i
$966$	1.57336	+	12.2917i	0.0506221	+	0.395480i
$967$	−13.2645	−	13.2645i	−0.426559	−	0.426559i	0.460896	−	0.887454i	$-0.347528\pi$
$967$	−13.2645	−	13.2645i	−0.426559	−	0.426559i	−0.887454	+	0.460896i	$0.847528\pi$
$968$	−2.20413	−	2.20413i	−0.0708433	−	0.0708433i
$969$	0.968352	+	7.56515i	0.0311079	+	0.243028i
$970$	−51.9249	−	44.7049i	−1.66721	−	1.43539i
$971$		−	28.0856i		−	0.901310i	−0.892698	−	0.450655i	$-0.851191\pi$
$971$		−	28.0856i		−	0.901310i	0.892698	−	0.450655i	$-0.148809\pi$
$972$	7.73968	−	51.6116i	0.248250	−	1.65544i
$973$	−5.19564	+	5.19564i	−0.166564	+	0.166564i
$974$	39.5186			1.26626
$975$	13.4839	+	47.5229i	0.431830	+	1.52195i
$976$	1.16133			0.0371733
$977$	−3.91150	+	3.91150i	−0.125140	+	0.125140i	−0.766903	−	0.641763i	$-0.778203\pi$
$977$	−3.91150	+	3.91150i	−0.125140	+	0.125140i	0.641763	+	0.766903i	$0.278203\pi$
$978$	−14.2029	+	18.3726i	−0.454159	+	0.587492i
$979$			15.8719i			0.507269i
$980$	−36.9721	−	31.8313i	−1.18103	−	1.01681i
$981$	16.8555	−	4.38693i	0.538154	−	0.140064i
$982$	26.7572	+	26.7572i	0.853858	+	0.853858i
$983$	1.07974	+	1.07974i	0.0344383	+	0.0344383i	0.724116	−	0.689678i	$-0.242248\pi$
$983$	1.07974	+	1.07974i	0.0344383	+	0.0344383i	−0.689678	+	0.724116i	$0.742248\pi$
$984$	57.4663	−	7.35579i	1.83196	−	0.234494i
$985$	−46.7115	+	3.49020i	−1.48835	+	0.111207i
$986$		−	8.97913i		−	0.285954i
$987$	−9.62632	−	7.44159i	−0.306409	−	0.236869i
$988$	−21.7642	+	21.7642i	−0.692412	+	0.692412i
$989$	47.7469			1.51826
$990$	14.6801	−	5.01514i	0.466563	−	0.159392i
$991$	35.7855			1.13676			0.568381	−	0.822765i	$-0.307570\pi$
$991$	35.7855			1.13676			0.568381	+	0.822765i	$0.307570\pi$
$992$	15.1769	−	15.1769i	0.481866	−	0.481866i
$993$	13.0390	+	10.0798i	0.413781	+	0.319873i
$994$		−	4.13479i		−	0.131147i
$995$	14.5918	−	16.9485i	0.462593	−	0.537303i
$996$	12.3300	−	1.57826i	0.390690	−	0.0500090i
$997$	12.2473	+	12.2473i	0.387875	+	0.387875i	0.873929	−	0.486054i	$-0.161564\pi$
$997$	12.2473	+	12.2473i	0.387875	+	0.387875i	−0.486054	+	0.873929i	$0.661564\pi$
$998$	−29.9487	−	29.9487i	−0.948008	−	0.948008i
$999$	28.4375	−	11.4219i	0.899722	−	0.361374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.k.c.122.2	yes	16
3.2	odd	2		165.2.k.d.122.7	yes	16
5.2	odd	4		825.2.k.i.518.2		16
5.3	odd	4		165.2.k.d.23.7	yes	16
5.4	even	2		825.2.k.j.782.7		16
15.2	even	4		825.2.k.j.518.7		16
15.8	even	4	inner	165.2.k.c.23.2	✓	16
15.14	odd	2		825.2.k.i.782.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.k.c.23.2	✓	16	15.8	even	4	inner
165.2.k.c.122.2	yes	16	1.1	even	1	trivial
165.2.k.d.23.7	yes	16	5.3	odd	4
165.2.k.d.122.7	yes	16	3.2	odd	2
825.2.k.i.518.2		16	5.2	odd	4
825.2.k.i.782.2		16	15.14	odd	2
825.2.k.j.518.7		16	15.2	even	4
825.2.k.j.782.7		16	5.4	even	2

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63522 + 1.63522i) q^{2} +(-1.37033 - 1.05933i) q^{3} -3.34791i q^{4} +(1.69456 + 1.45893i) q^{5} +(3.97305 - 0.508557i) q^{6} +(0.491443 + 0.491443i) q^{7} +(2.20413 + 2.20413i) q^{8} +(0.755630 + 2.90328i) q^{9} +O(q^{10})\)	\(q+(-1.63522 + 1.63522i) q^{2} +(-1.37033 - 1.05933i) q^{3} -3.34791i q^{4} +(1.69456 + 1.45893i) q^{5} +(3.97305 - 0.508557i) q^{6} +(0.491443 + 0.491443i) q^{7} +(2.20413 + 2.20413i) q^{8} +(0.755630 + 2.90328i) q^{9} +(-5.15665 + 0.385296i) q^{10} +1.00000i q^{11} +(-3.54655 + 4.58775i) q^{12} +(-4.03339 + 4.03339i) q^{13} -1.60724 q^{14} +(-0.776612 - 3.79432i) q^{15} -0.512664 q^{16} +(-1.93184 + 1.93184i) q^{17} +(-5.98313 - 3.51188i) q^{18} +1.61176i q^{19} +(4.88437 - 5.67321i) q^{20} +(-0.152840 - 1.19404i) q^{21} +(-1.63522 - 1.63522i) q^{22} +(3.14765 + 3.14765i) q^{23} +(-0.685487 - 5.35529i) q^{24} +(0.743034 + 4.94448i) q^{25} -13.1910i q^{26} +(2.04007 - 4.77892i) q^{27} +(1.64531 - 1.64531i) q^{28} +1.42120 q^{29} +(7.47449 + 4.93463i) q^{30} -4.25130 q^{31} +(-3.56993 + 3.56993i) q^{32} +(1.05933 - 1.37033i) q^{33} -6.31798i q^{34} +(0.115795 + 1.54976i) q^{35} +(9.71990 - 2.52978i) q^{36} +(4.17033 + 4.17033i) q^{37} +(-2.63558 - 2.63558i) q^{38} +(9.79980 - 1.25439i) q^{39} +(0.519343 + 6.95069i) q^{40} +10.7308i q^{41} +(2.20245 + 1.70260i) q^{42} +(7.58453 - 7.58453i) q^{43} +3.34791 q^{44} +(-2.95523 + 6.02218i) q^{45} -10.2942 q^{46} +(7.14711 - 7.14711i) q^{47} +(0.702521 + 0.543082i) q^{48} -6.51697i q^{49} +(-9.30035 - 6.87030i) q^{50} +(4.69373 - 0.600806i) q^{51} +(13.5034 + 13.5034i) q^{52} +(-7.01771 - 7.01771i) q^{53} +(4.47863 + 11.1506i) q^{54} +(-1.45893 + 1.69456i) q^{55} +2.16641i q^{56} +(1.70739 - 2.20864i) q^{57} +(-2.32398 + 2.32398i) q^{58} -7.03856 q^{59} +(-12.7030 + 2.60002i) q^{60} -2.26528 q^{61} +(6.95182 - 6.95182i) q^{62} +(-1.05545 + 1.79815i) q^{63} -12.7006i q^{64} +(-12.7193 + 0.950360i) q^{65} +(0.508557 + 3.97305i) q^{66} +(-1.60076 - 1.60076i) q^{67} +(6.46762 + 6.46762i) q^{68} +(-0.978923 - 7.64773i) q^{69} +(-2.72355 - 2.34485i) q^{70} +2.57260i q^{71} +(-4.73369 + 8.06470i) q^{72} +(5.90351 - 5.90351i) q^{73} -13.6388 q^{74} +(4.21965 - 7.56271i) q^{75} +5.39601 q^{76} +(-0.491443 + 0.491443i) q^{77} +(-13.9736 + 18.0761i) q^{78} -4.09127i q^{79} +(-0.868738 - 0.747943i) q^{80} +(-7.85805 + 4.38761i) q^{81} +(-17.5472 - 17.5472i) q^{82} +(-1.51580 - 1.51580i) q^{83} +(-3.99755 + 0.511693i) q^{84} +(-6.09204 + 0.455186i) q^{85} +24.8048i q^{86} +(-1.94752 - 1.50553i) q^{87} +(-2.20413 + 2.20413i) q^{88} +15.8719 q^{89} +(-5.01514 - 14.6801i) q^{90} -3.96437 q^{91} +(10.5380 - 10.5380i) q^{92} +(5.82570 + 4.50354i) q^{93} +23.3742i q^{94} +(-2.35144 + 2.73121i) q^{95} +(8.67375 - 1.11025i) q^{96} +(9.36942 + 9.36942i) q^{97} +(10.6567 + 10.6567i) q^{98} +(-2.90328 + 0.755630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 4 q^{6} + 8 q^{7} + 16 q^{8} + 6 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 4 * q^6 + 8 * q^7 + 16 * q^8 + 6 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 4 q^{6} + 8 q^{7} + 16 q^{8} + 6 q^{9} - 4 q^{10} - 4 q^{12} - 24 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} - 32 q^{18} - 20 q^{20} - 8 q^{21} - 4 q^{22} + 14 q^{23} + 12 q^{24} - 18 q^{25} - 20 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{30} + 8 q^{31} + 28 q^{32} + 4 q^{33} + 44 q^{36} - 6 q^{37} + 24 q^{38} + 24 q^{39} + 16 q^{40} - 60 q^{42} + 16 q^{43} + 12 q^{44} + 24 q^{45} - 32 q^{46} + 48 q^{47} - 48 q^{48} - 12 q^{50} - 8 q^{51} + 36 q^{52} - 4 q^{53} + 4 q^{54} + 2 q^{55} - 8 q^{57} - 12 q^{58} - 68 q^{59} - 28 q^{60} - 8 q^{61} + 48 q^{62} - 12 q^{63} - 48 q^{65} + 8 q^{66} + 6 q^{67} + 24 q^{68} + 12 q^{69} - 4 q^{70} - 8 q^{72} + 8 q^{74} + 8 q^{75} + 16 q^{76} - 8 q^{77} - 48 q^{78} - 24 q^{80} + 2 q^{81} + 12 q^{82} - 8 q^{83} + 52 q^{84} - 4 q^{85} - 36 q^{87} - 16 q^{88} + 32 q^{89} + 44 q^{90} - 56 q^{91} + 20 q^{92} + 28 q^{93} - 48 q^{95} + 80 q^{96} + 18 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 4 * q^6 + 8 * q^7 + 16 * q^8 + 6 * q^9 - 4 * q^10 - 4 * q^12 - 24 * q^14 + 8 * q^15 - 4 * q^16 + 8 * q^17 - 32 * q^18 - 20 * q^20 - 8 * q^21 - 4 * q^22 + 14 * q^23 + 12 * q^24 - 18 * q^25 - 20 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^30 + 8 * q^31 + 28 * q^32 + 4 * q^33 + 44 * q^36 - 6 * q^37 + 24 * q^38 + 24 * q^39 + 16 * q^40 - 60 * q^42 + 16 * q^43 + 12 * q^44 + 24 * q^45 - 32 * q^46 + 48 * q^47 - 48 * q^48 - 12 * q^50 - 8 * q^51 + 36 * q^52 - 4 * q^53 + 4 * q^54 + 2 * q^55 - 8 * q^57 - 12 * q^58 - 68 * q^59 - 28 * q^60 - 8 * q^61 + 48 * q^62 - 12 * q^63 - 48 * q^65 + 8 * q^66 + 6 * q^67 + 24 * q^68 + 12 * q^69 - 4 * q^70 - 8 * q^72 + 8 * q^74 + 8 * q^75 + 16 * q^76 - 8 * q^77 - 48 * q^78 - 24 * q^80 + 2 * q^81 + 12 * q^82 - 8 * q^83 + 52 * q^84 - 4 * q^85 - 36 * q^87 - 16 * q^88 + 32 * q^89 + 44 * q^90 - 56 * q^91 + 20 * q^92 + 28 * q^93 - 48 * q^95 + 80 * q^96 + 18 * q^97 + 16 * q^98 - 4 * q^99

Introduction

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