LMFDB - Embedded newform 170.2.k.b.111.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(111,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("170.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.k (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
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} + 28x^{14} + 286x^{12} + 1412x^{10} + 3709x^{8} + 5264x^{6} + 3780x^{4} + 1072x^{2} + 4 $ x^16 + 28x^14 + 286x^12 + 1412x^10 + 3709x^8 + 5264x^6 + 3780x^4 + 1072*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			111.1
Root			$-3.51034i$ of defining polynomial
Character	$\chi$	$=$	170.111
Dual form			170.2.k.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-2.31925 - 0.960664i) q^{3} -1.00000i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-2.31925 + 0.960664i) q^{6} +(-1.57873 - 3.81140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.33472 + 2.33472i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-2.31925 - 0.960664i) q^{3} -1.00000i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-2.31925 + 0.960664i) q^{6} +(-1.57873 - 3.81140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.33472 + 2.33472i) q^{9} +(0.382683 + 0.923880i) q^{10} +(-5.33544 + 2.21001i) q^{11} +(-0.960664 + 2.31925i) q^{12} -3.02629i q^{13} +(-3.81140 - 1.57873i) q^{14} +(1.77508 - 1.77508i) q^{15} -1.00000 q^{16} +(4.11166 + 0.306969i) q^{17} +3.30179 q^{18} +(2.86967 - 2.86967i) q^{19} +(0.923880 + 0.382683i) q^{20} +10.3562i q^{21} +(-2.21001 + 5.33544i) q^{22} +(3.21055 - 1.32985i) q^{23} +(0.960664 + 2.31925i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(-2.13991 - 2.13991i) q^{26} +(-0.289917 - 0.699921i) q^{27} +(-3.81140 + 1.57873i) q^{28} +(3.23832 - 7.81800i) q^{29} -2.51034i q^{30} +(2.24871 + 0.931446i) q^{31} +(-0.707107 + 0.707107i) q^{32} +14.4973 q^{33} +(3.12444 - 2.69032i) q^{34} +4.12543 q^{35} +(2.33472 - 2.33472i) q^{36} +(-5.93157 - 2.45694i) q^{37} -4.05833i q^{38} +(-2.90725 + 7.01873i) q^{39} +(0.923880 - 0.382683i) q^{40} +(1.30775 + 3.15720i) q^{41} +(7.32295 + 7.32295i) q^{42} +(-0.597665 - 0.597665i) q^{43} +(2.21001 + 5.33544i) q^{44} +(-3.05045 + 1.26354i) q^{45} +(1.32985 - 3.21055i) q^{46} -8.38873i q^{47} +(2.31925 + 0.960664i) q^{48} +(-7.08462 + 7.08462i) q^{49} -1.00000 q^{50} +(-9.24107 - 4.66186i) q^{51} -3.02629 q^{52} +(-7.99832 + 7.99832i) q^{53} +(-0.699921 - 0.289917i) q^{54} -5.77504i q^{55} +(-1.57873 + 3.81140i) q^{56} +(-9.41228 + 3.89869i) q^{57} +(-3.23832 - 7.81800i) q^{58} +(6.34782 + 6.34782i) q^{59} +(-1.77508 - 1.77508i) q^{60} +(0.527018 + 1.27233i) q^{61} +(2.24871 - 0.931446i) q^{62} +(5.21264 - 12.5844i) q^{63} +1.00000i q^{64} +(2.79593 + 1.15811i) q^{65} +(10.2511 - 10.2511i) q^{66} -6.72859 q^{67} +(0.306969 - 4.11166i) q^{68} -8.72361 q^{69} +(2.91712 - 2.91712i) q^{70} +(1.35298 + 0.560421i) q^{71} -3.30179i q^{72} +(-0.491913 + 1.18758i) q^{73} +(-5.93157 + 2.45694i) q^{74} +(0.960664 + 2.31925i) q^{75} +(-2.86967 - 2.86967i) q^{76} +(16.8465 + 16.8465i) q^{77} +(2.90725 + 7.01873i) q^{78} +(3.03348 - 1.25651i) q^{79} +(0.382683 - 0.923880i) q^{80} -8.00356i q^{81} +(3.15720 + 1.30775i) q^{82} +(-1.23021 + 1.23021i) q^{83} +10.3562 q^{84} +(-1.85707 + 3.68121i) q^{85} -0.845225 q^{86} +(-15.0209 + 15.0209i) q^{87} +(5.33544 + 2.21001i) q^{88} -8.72132i q^{89} +(-1.26354 + 3.05045i) q^{90} +(-11.5344 + 4.77771i) q^{91} +(-1.32985 - 3.21055i) q^{92} +(-4.32051 - 4.32051i) q^{93} +(-5.93173 - 5.93173i) q^{94} +(1.55306 + 3.74941i) q^{95} +(2.31925 - 0.960664i) q^{96} +(5.02436 - 12.1299i) q^{97} +10.0192i q^{98} +(-17.6165 - 7.29699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−2.31925	−	0.960664i	−1.33902	−	0.554640i	−0.405804	−	0.913960i	$-0.633009\pi$
$3$	−2.31925	−	0.960664i	−1.33902	−	0.554640i	−0.933214	+	0.359320i	$0.883009\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−0.382683	+	0.923880i	−0.171141	+	0.413171i
$5$	−0.382683	+	0.923880i	−0.171141	+	0.413171i
$6$	−2.31925	+	0.960664i	−0.946829	+	0.392189i
$7$	−1.57873	−	3.81140i	−0.596705	−	1.44057i	−0.876920	−	0.480636i	$-0.840406\pi$
$7$	−1.57873	−	3.81140i	−0.596705	−	1.44057i	0.280215	−	0.959937i	$-0.409594\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.33472	+	2.33472i	0.778239	+	0.778239i
$10$	0.382683	+	0.923880i	0.121015	+	0.292156i
$11$	−5.33544	+	2.21001i	−1.60870	+	0.666344i	−0.992611	−	0.121336i	$-0.961282\pi$
$11$	−5.33544	+	2.21001i	−1.60870	+	0.666344i	−0.616085	+	0.787680i	$0.711282\pi$
$12$	−0.960664	+	2.31925i	−0.277320	+	0.669509i
$13$		−	3.02629i		−	0.839343i	−0.907676	−	0.419671i	$-0.862145\pi$
$13$		−	3.02629i		−	0.839343i	0.907676	−	0.419671i	$-0.137855\pi$
$14$	−3.81140	−	1.57873i	−1.01864	−	0.421934i
$15$	1.77508	−	1.77508i	0.458323	−	0.458323i
$16$	−1.00000			−0.250000
$17$	4.11166	+	0.306969i	0.997225	+	0.0744510i
$17$	4.11166	+	0.306969i	0.997225	+	0.0744510i
$18$	3.30179			0.778239
$19$	2.86967	−	2.86967i	0.658348	−	0.658348i	−0.296641	−	0.954989i	$-0.595866\pi$
$19$	2.86967	−	2.86967i	0.658348	−	0.658348i	0.954989	+	0.296641i	$0.0958664\pi$
$20$	0.923880	+	0.382683i	0.206586	+	0.0855706i
$21$			10.3562i			2.25991i
$22$	−2.21001	+	5.33544i	−0.471176	+	1.13752i
$23$	3.21055	−	1.32985i	0.669446	−	0.277294i	−0.0219610	−	0.999759i	$-0.506991\pi$
$23$	3.21055	−	1.32985i	0.669446	−	0.277294i	0.691407	+	0.722465i	$0.256991\pi$
$24$	0.960664	+	2.31925i	0.196095	+	0.473415i
$25$	−0.707107	−	0.707107i	−0.141421	−	0.141421i
$26$	−2.13991	−	2.13991i	−0.419671	−	0.419671i
$27$	−0.289917	−	0.699921i	−0.0557945	−	0.134700i
$28$	−3.81140	+	1.57873i	−0.720287	+	0.298353i
$29$	3.23832	−	7.81800i	0.601341	−	1.45177i	−0.270861	−	0.962619i	$-0.587308\pi$
$29$	3.23832	−	7.81800i	0.601341	−	1.45177i	0.872201	−	0.489147i	$-0.162692\pi$
$30$		−	2.51034i		−	0.458323i
$31$	2.24871	+	0.931446i	0.403880	+	0.167293i	0.575370	−	0.817893i	$-0.304858\pi$
$31$	2.24871	+	0.931446i	0.403880	+	0.167293i	−0.171490	+	0.985186i	$0.554858\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	14.4973			2.52365
$34$	3.12444	−	2.69032i	0.535838	−	0.461387i
$35$	4.12543			0.697325
$36$	2.33472	−	2.33472i	0.389119	−	0.389119i
$37$	−5.93157	−	2.45694i	−0.975145	−	0.403918i	−0.162520	−	0.986705i	$-0.551962\pi$
$37$	−5.93157	−	2.45694i	−0.975145	−	0.403918i	−0.812625	+	0.582787i	$0.801962\pi$
$38$		−	4.05833i		−	0.658348i
$39$	−2.90725	+	7.01873i	−0.465533	+	1.12390i
$40$	0.923880	−	0.382683i	0.146078	−	0.0605076i
$41$	1.30775	+	3.15720i	0.204237	+	0.493072i	0.992497	−	0.122271i	$-0.0390177\pi$
$41$	1.30775	+	3.15720i	0.204237	+	0.493072i	−0.788260	+	0.615343i	$0.789018\pi$
$42$	7.32295	+	7.32295i	1.12996	+	1.12996i
$43$	−0.597665	−	0.597665i	−0.0911430	−	0.0911430i	0.660065	−	0.751208i	$-0.270529\pi$
$43$	−0.597665	−	0.597665i	−0.0911430	−	0.0911430i	−0.751208	+	0.660065i	$0.770529\pi$
$44$	2.21001	+	5.33544i	0.333172	+	0.804348i
$45$	−3.05045	+	1.26354i	−0.454735	+	0.188357i
$46$	1.32985	−	3.21055i	0.196076	−	0.473370i
$47$		−	8.38873i		−	1.22362i	−0.791004	−	0.611811i	$-0.790441\pi$
$47$		−	8.38873i		−	1.22362i	0.791004	−	0.611811i	$-0.209559\pi$
$48$	2.31925	+	0.960664i	0.334755	+	0.138660i
$49$	−7.08462	+	7.08462i	−1.01209	+	1.01209i
$50$	−1.00000			−0.141421
$51$	−9.24107	−	4.66186i	−1.29401	−	0.652792i
$52$	−3.02629			−0.419671
$53$	−7.99832	+	7.99832i	−1.09865	+	1.09865i	−0.104086	+	0.994568i	$0.533192\pi$
$53$	−7.99832	+	7.99832i	−1.09865	+	1.09865i	−0.994568	+	0.104086i	$0.966808\pi$
$54$	−0.699921	−	0.289917i	−0.0952472	−	0.0394527i
$55$		−	5.77504i		−	0.778706i
$56$	−1.57873	+	3.81140i	−0.210967	+	0.509320i
$57$	−9.41228	+	3.89869i	−1.24669	+	0.516395i
$58$	−3.23832	−	7.81800i	−0.425212	−	1.02655i
$59$	6.34782	+	6.34782i	0.826416	+	0.826416i	0.987019	−	0.160603i	$-0.0513439\pi$
$59$	6.34782	+	6.34782i	0.826416	+	0.826416i	−0.160603	+	0.987019i	$0.551344\pi$
$60$	−1.77508	−	1.77508i	−0.229161	−	0.229161i
$61$	0.527018	+	1.27233i	0.0674778	+	0.162906i	0.954021	−	0.299740i	$-0.0969001\pi$
$61$	0.527018	+	1.27233i	0.0674778	+	0.162906i	−0.886543	+	0.462646i	$0.846900\pi$
$62$	2.24871	−	0.931446i	0.285586	−	0.118294i
$63$	5.21264	−	12.5844i	0.656731	−	1.58549i
$64$			1.00000i			0.125000i
$65$	2.79593	+	1.15811i	0.346793	+	0.143646i
$66$	10.2511	−	10.2511i	1.26183	−	1.26183i
$67$	−6.72859			−0.822028			−0.411014	−	0.911629i	$-0.634825\pi$
$67$	−6.72859			−0.822028			−0.411014	+	0.911629i	$0.634825\pi$
$68$	0.306969	−	4.11166i	0.0372255	−	0.498612i
$69$	−8.72361			−1.05020
$70$	2.91712	−	2.91712i	0.348662	−	0.348662i
$71$	1.35298	+	0.560421i	0.160569	+	0.0665098i	0.461520	−	0.887130i	$-0.347304\pi$
$71$	1.35298	+	0.560421i	0.160569	+	0.0665098i	−0.300951	+	0.953639i	$0.597304\pi$
$72$		−	3.30179i		−	0.389119i
$73$	−0.491913	+	1.18758i	−0.0575741	+	0.138996i	−0.950049	−	0.312101i	$-0.898967\pi$
$73$	−0.491913	+	1.18758i	−0.0575741	+	0.138996i	0.892475	+	0.451097i	$0.148967\pi$
$74$	−5.93157	+	2.45694i	−0.689531	+	0.285613i
$75$	0.960664	+	2.31925i	0.110928	+	0.267804i
$76$	−2.86967	−	2.86967i	−0.329174	−	0.329174i
$77$	16.8465	+	16.8465i	1.91983	+	1.91983i
$78$	2.90725	+	7.01873i	0.329181	+	0.794714i
$79$	3.03348	−	1.25651i	0.341293	−	0.141368i	−0.205452	−	0.978667i	$-0.565867\pi$
$79$	3.03348	−	1.25651i	0.341293	−	0.141368i	0.546745	+	0.837299i	$0.315867\pi$
$80$	0.382683	−	0.923880i	0.0427853	−	0.103293i
$81$		−	8.00356i		−	0.889284i
$82$	3.15720	+	1.30775i	0.348654	+	0.144417i
$83$	−1.23021	+	1.23021i	−0.135033	+	0.135033i	−0.771393	−	0.636360i	$-0.780439\pi$
$83$	−1.23021	+	1.23021i	−0.135033	+	0.135033i	0.636360	+	0.771393i	$0.280439\pi$
$84$	10.3562			1.12996
$85$	−1.85707	+	3.68121i	−0.201427	+	0.399283i
$86$	−0.845225			−0.0911430
$87$	−15.0209	+	15.0209i	−1.61041	+	1.61041i
$88$	5.33544	+	2.21001i	0.568760	+	0.235588i
$89$		−	8.72132i		−	0.924458i	−0.886761	−	0.462229i	$-0.847050\pi$
$89$		−	8.72132i		−	0.924458i	0.886761	−	0.462229i	$-0.152950\pi$
$90$	−1.26354	+	3.05045i	−0.133189	+	0.321546i
$91$	−11.5344	+	4.77771i	−1.20914	+	0.500840i
$92$	−1.32985	−	3.21055i	−0.138647	−	0.334723i
$93$	−4.32051	−	4.32051i	−0.448016	−	0.448016i
$94$	−5.93173	−	5.93173i	−0.611811	−	0.611811i
$95$	1.55306	+	3.74941i	0.159340	+	0.384681i
$96$	2.31925	−	0.960664i	0.236707	−	0.0980474i
$97$	5.02436	−	12.1299i	0.510147	−	1.23160i	−0.433651	−	0.901081i	$-0.642775\pi$
$97$	5.02436	−	12.1299i	0.510147	−	1.23160i	0.943798	−	0.330523i	$-0.107225\pi$
$98$			10.0192i			1.01209i
$99$	−17.6165	−	7.29699i	−1.77052	−	0.733375i
$100$	−0.707107	+	0.707107i	−0.0707107	+	0.0707107i
$101$	10.1292			1.00790			0.503948	−	0.863734i	$-0.331880\pi$
$101$	10.1292			1.00790			0.503948	+	0.863734i	$0.331880\pi$
$102$	−9.83086	+	3.23799i	−0.973400	+	0.320609i
$103$	5.63917			0.555644			0.277822	−	0.960633i	$-0.410388\pi$
$103$	5.63917			0.555644			0.277822	+	0.960633i	$0.410388\pi$
$104$	−2.13991	+	2.13991i	−0.209836	+	0.209836i
$105$	−9.56789	−	3.96315i	−0.933731	−	0.386764i
$106$			11.3113i			1.09865i
$107$	4.99648	−	12.0626i	0.483028	−	1.16613i	−0.475136	−	0.879912i	$-0.657601\pi$
$107$	4.99648	−	12.0626i	0.483028	−	1.16613i	0.958164	−	0.286220i	$-0.0923988\pi$
$108$	−0.699921	+	0.289917i	−0.0673499	+	0.0278973i
$109$	−2.58341	−	6.23691i	−0.247446	−	0.597387i	0.750540	−	0.660825i	$-0.229794\pi$
$109$	−2.58341	−	6.23691i	−0.247446	−	0.597387i	−0.997986	+	0.0634378i	$0.979794\pi$
$110$	−4.08357	−	4.08357i	−0.389353	−	0.389353i
$111$	11.3965	+	11.3965i	1.08171	+	1.08171i
$112$	1.57873	+	3.81140i	0.149176	+	0.360143i
$113$	−11.7693	+	4.87502i	−1.10717	+	0.458603i	−0.859961	−	0.510360i	$-0.829512\pi$
$113$	−11.7693	+	4.87502i	−1.10717	+	0.458603i	−0.247205	+	0.968963i	$0.579512\pi$
$114$	−3.89869	+	9.41228i	−0.365146	+	0.881541i
$115$			3.47508i			0.324053i
$116$	−7.81800	−	3.23832i	−0.725883	−	0.300670i
$117$	7.06554	−	7.06554i	0.653209	−	0.653209i
$118$	8.97717			0.826416
$119$	−5.32124	−	16.1558i	−0.487797	−	1.48100i
$120$	−2.51034			−0.229161
$121$	15.8046	−	15.8046i	1.43678	−	1.43678i
$122$	1.27233	+	0.527018i	0.115192	+	0.0477140i
$123$		−	8.57864i		−	0.773510i
$124$	0.931446	−	2.24871i	0.0836463	−	0.201940i
$125$	0.923880	−	0.382683i	0.0826343	−	0.0342282i
$126$	−5.21264	−	12.5844i	−0.464379	−	1.12111i
$127$	3.47327	+	3.47327i	0.308203	+	0.308203i	0.844212	−	0.536009i	$-0.180069\pi$
$127$	3.47327	+	3.47327i	0.308203	+	0.308203i	−0.536009	+	0.844212i	$0.680069\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	0.811978	+	1.96029i	0.0714907	+	0.172594i
$130$	2.79593	−	1.15811i	0.245219	−	0.101573i
$131$	−4.45469	+	10.7546i	−0.389208	+	0.939632i	0.600900	+	0.799325i	$0.294809\pi$
$131$	−4.45469	+	10.7546i	−0.389208	+	0.939632i	−0.990108	+	0.140308i	$0.955191\pi$
$132$		−	14.4973i		−	1.26183i
$133$	−15.4679	−	6.40702i	−1.34124	−	0.555559i
$134$	−4.75783	+	4.75783i	−0.411014	+	0.411014i
$135$	0.757589			0.0652029
$136$	−2.69032	−	3.12444i	−0.230693	−	0.267919i
$137$	−1.68924			−0.144321			−0.0721606	−	0.997393i	$-0.522989\pi$
$137$	−1.68924			−0.144321			−0.0721606	+	0.997393i	$0.522989\pi$
$138$	−6.16852	+	6.16852i	−0.525100	+	0.525100i
$139$	3.14072	+	1.30093i	0.266393	+	0.110344i	0.511882	−	0.859056i	$-0.328949\pi$
$139$	3.14072	+	1.30093i	0.266393	+	0.110344i	−0.245489	+	0.969399i	$0.578949\pi$
$140$		−	4.12543i		−	0.348662i
$141$	−8.05875	+	19.4555i	−0.678669	+	1.63845i
$142$	1.35298	−	0.560421i	0.113539	−	0.0470295i
$143$	6.68815	+	16.1466i	0.559291	+	1.35025i
$144$	−2.33472	−	2.33472i	−0.194560	−	0.194560i
$145$	5.98363	+	5.98363i	0.496914	+	0.496914i
$146$	0.491913	+	1.18758i	0.0407110	+	0.0982851i
$147$	23.2369	−	9.62505i	1.91655	−	0.793861i
$148$	−2.45694	+	5.93157i	−0.201959	+	0.487572i
$149$			10.0110i			0.820132i	0.912056	+	0.410066i	$0.134494\pi$
$149$			10.0110i			0.820132i	−0.912056	+	0.410066i	$0.865506\pi$
$150$	2.31925	+	0.960664i	0.189366	+	0.0784379i
$151$	−11.5827	+	11.5827i	−0.942583	+	0.942583i	−0.998439	−	0.0558554i	$-0.982211\pi$
$151$	−11.5827	+	11.5827i	−0.942583	+	0.942583i	0.0558554	+	0.998439i	$0.482211\pi$
$152$	−4.05833			−0.329174
$153$	8.88288	+	10.3163i	0.718138	+	0.834020i
$154$	23.8245			1.91983
$155$	−1.72109	+	1.72109i	−0.138241	+	0.138241i
$156$	7.01873	+	2.90725i	0.561948	+	0.232766i
$157$		−	7.32071i		−	0.584256i	−0.956379	−	0.292128i	$-0.905637\pi$
$157$		−	7.32071i		−	0.584256i	0.956379	−	0.292128i	$-0.0943634\pi$
$158$	1.25651	−	3.03348i	0.0999625	−	0.241331i
$159$	26.2338	−	10.8664i	2.08048	−	0.861761i
$160$	−0.382683	−	0.923880i	−0.0302538	−	0.0730391i
$161$	−10.1372	−	10.1372i	−0.798924	−	0.798924i
$162$	−5.65937	−	5.65937i	−0.444642	−	0.444642i
$163$	−0.476889	−	1.15131i	−0.0373528	−	0.0901776i	0.904102	−	0.427316i	$-0.140541\pi$
$163$	−0.476889	−	1.15131i	−0.0373528	−	0.0901776i	−0.941455	+	0.337139i	$0.890541\pi$
$164$	3.15720	−	1.30775i	0.246536	−	0.102119i
$165$	−5.54787	+	13.3938i	−0.431901	+	1.04270i
$166$			1.73978i			0.135033i
$167$	16.3461	+	6.77077i	1.26490	+	0.523938i	0.911409	−	0.411501i	$-0.134995\pi$
$167$	16.3461	+	6.77077i	1.26490	+	0.523938i	0.353489	+	0.935439i	$0.384995\pi$
$168$	7.32295	−	7.32295i	0.564978	−	0.564978i
$169$	3.84154			0.295503
$170$	1.28986	+	3.91615i	0.0989279	+	0.300355i
$171$	13.3998			1.02470
$172$	−0.597665	+	0.597665i	−0.0455715	+	0.0455715i
$173$	12.1864	+	5.04779i	0.926519	+	0.383777i	0.794357	−	0.607452i	$-0.207808\pi$
$173$	12.1864	+	5.04779i	0.926519	+	0.383777i	0.132162	+	0.991228i	$0.457808\pi$
$174$			21.2428i			1.61041i
$175$	−1.57873	+	3.81140i	−0.119341	+	0.288115i
$176$	5.33544	−	2.21001i	0.402174	−	0.166586i
$177$	−8.62405	−	20.8203i	−0.648223	−	1.56495i
$178$	−6.16690	−	6.16690i	−0.462229	−	0.462229i
$179$	10.9537	+	10.9537i	0.818715	+	0.818715i	0.985922	−	0.167206i	$-0.0534747\pi$
$179$	10.9537	+	10.9537i	0.818715	+	0.818715i	−0.167206	+	0.985922i	$0.553475\pi$
$180$	1.26354	+	3.05045i	0.0941787	+	0.227367i
$181$	17.6931	−	7.32872i	1.31512	−	0.544740i	0.388745	−	0.921346i	$-0.372909\pi$
$181$	17.6931	−	7.32872i	1.31512	−	0.544740i	0.926374	+	0.376606i	$0.122909\pi$
$182$	−4.77771	+	11.5344i	−0.354148	+	0.854988i
$183$		−	3.45715i		−	0.255560i
$184$	−3.21055	−	1.32985i	−0.236685	−	0.0980382i
$185$	4.53983	−	4.53983i	0.333775	−	0.333775i
$186$	−6.11012			−0.448016
$187$	−22.6159	+	7.44901i	−1.65384	+	0.544725i
$188$	−8.38873			−0.611811
$189$	−2.20998	+	2.20998i	−0.160752	+	0.160752i
$190$	3.74941	+	1.55306i	0.272011	+	0.112671i
$191$		−	15.8675i		−	1.14813i	−0.818808	−	0.574067i	$-0.805365\pi$
$191$		−	15.8675i		−	1.14813i	0.818808	−	0.574067i	$-0.194635\pi$
$192$	0.960664	−	2.31925i	0.0693300	−	0.167377i
$193$	3.62514	−	1.50158i	0.260943	−	0.108086i	−0.248377	−	0.968664i	$-0.579897\pi$
$193$	3.62514	−	1.50158i	0.260943	−	0.108086i	0.509320	+	0.860577i	$0.329897\pi$
$194$	−5.02436	−	12.1299i	−0.360728	−	0.870875i
$195$	−5.37190	−	5.37190i	−0.384690	−	0.384690i
$196$	7.08462	+	7.08462i	0.506044	+	0.506044i
$197$	6.29410	+	15.1953i	0.448436	+	1.08262i	0.972908	+	0.231193i	$0.0742628\pi$
$197$	6.29410	+	15.1953i	0.448436	+	1.08262i	−0.524472	+	0.851428i	$0.675737\pi$
$198$	−17.6165	+	7.29699i	−1.25195	+	0.518575i
$199$	8.40336	−	20.2875i	0.595698	−	1.43814i	−0.282228	−	0.959347i	$-0.591073\pi$
$199$	8.40336	−	20.2875i	0.595698	−	1.43814i	0.877926	−	0.478796i	$-0.158927\pi$
$200$			1.00000i			0.0707107i
$201$	15.6053	+	6.46392i	1.10071	+	0.455930i
$202$	7.16244	−	7.16244i	0.503948	−	0.503948i
$203$	−34.9099			−2.45020
$204$	−4.66186	+	9.24107i	−0.326396	+	0.647004i
$205$	−3.41733			−0.238677
$206$	3.98749	−	3.98749i	0.277822	−	0.277822i
$207$	10.6006	+	4.39090i	0.736790	+	0.305188i
$208$			3.02629i			0.209836i
$209$	−8.96896	+	21.6530i	−0.620396	+	1.49777i
$210$	−9.56789	+	3.96315i	−0.660247	+	0.273483i
$211$	4.69962	+	11.3459i	0.323535	+	0.781083i	0.999043	+	0.0437308i	$0.0139244\pi$
$211$	4.69962	+	11.3459i	0.323535	+	0.781083i	−0.675508	+	0.737353i	$0.736076\pi$
$212$	7.99832	+	7.99832i	0.549327	+	0.549327i
$213$	−2.59951	−	2.59951i	−0.178116	−	0.178116i
$214$	−4.99648	−	12.0626i	−0.341552	−	0.824580i
$215$	0.780886	−	0.323454i	0.0532560	−	0.0220594i
$216$	−0.289917	+	0.699921i	−0.0197263	+	0.0476236i
$217$		−	10.0412i		−	0.681643i
$218$	−6.23691	−	2.58341i	−0.422417	−	0.174971i
$219$	2.28174	−	2.28174i	0.154186	−	0.154186i
$220$	−5.77504			−0.389353
$221$	0.928980	−	12.4431i	0.0624899	−	0.837014i
$222$	16.1171			1.08171
$223$	−14.1323	+	14.1323i	−0.946369	+	0.946369i	−0.998633	−	0.0522648i	$-0.983356\pi$
$223$	−14.1323	+	14.1323i	−0.946369	+	0.946369i	0.0522648	+	0.998633i	$0.483356\pi$
$224$	3.81140	+	1.57873i	0.254660	+	0.105484i
$225$		−	3.30179i		−	0.220119i
$226$	−4.87502	+	11.7693i	−0.324281	+	0.782884i
$227$	−12.2731	+	5.08367i	−0.814591	+	0.337415i	−0.750784	−	0.660547i	$-0.770324\pi$
$227$	−12.2731	+	5.08367i	−0.814591	+	0.337415i	−0.0638071	+	0.997962i	$0.520324\pi$
$228$	3.89869	+	9.41228i	0.258197	+	0.623343i
$229$	−4.92945	−	4.92945i	−0.325747	−	0.325747i	0.525219	−	0.850967i	$-0.323983\pi$
$229$	−4.92945	−	4.92945i	−0.325747	−	0.325747i	−0.850967	+	0.525219i	$0.823983\pi$
$230$	2.45725	+	2.45725i	0.162026	+	0.162026i
$231$	−22.8874	−	55.2550i	−1.50588	−	3.63551i
$232$	−7.81800	+	3.23832i	−0.513277	+	0.212606i
$233$	−1.95462	+	4.71887i	−0.128051	+	0.309144i	−0.974883	−	0.222718i	$-0.928507\pi$
$233$	−1.95462	+	4.71887i	−0.128051	+	0.309144i	0.846832	+	0.531861i	$0.178507\pi$
$234$		−	9.99218i		−	0.653209i
$235$	7.75017	+	3.21023i	0.505566	+	0.209412i
$236$	6.34782	−	6.34782i	0.413208	−	0.413208i
$237$	−8.24248			−0.535406
$238$	−15.1866	−	7.66120i	−0.984399	−	0.496602i
$239$	6.71027			0.434051			0.217026	−	0.976166i	$-0.430365\pi$
$239$	6.71027			0.434051			0.217026	+	0.976166i	$0.430365\pi$
$240$	−1.77508	+	1.77508i	−0.114581	+	0.114581i
$241$	−5.47933	−	2.26961i	−0.352955	−	0.146199i	0.199160	−	0.979967i	$-0.436179\pi$
$241$	−5.47933	−	2.26961i	−0.352955	−	0.146199i	−0.552114	+	0.833768i	$0.686179\pi$
$242$		−	22.3511i		−	1.43678i
$243$	−8.55848	+	20.6620i	−0.549027	+	1.32547i
$244$	1.27233	−	0.527018i	0.0814529	−	0.0337389i
$245$	−3.83417	−	9.25650i	−0.244956	−	0.591376i
$246$	−6.06602	−	6.06602i	−0.386755	−	0.386755i
$247$	−8.68448	−	8.68448i	−0.552580	−	0.552580i
$248$	−0.931446	−	2.24871i	−0.0591469	−	0.142793i
$249$	4.03498	−	1.67134i	0.255706	−	0.105917i
$250$	0.382683	−	0.923880i	0.0242030	−	0.0584313i
$251$		−	14.9891i		−	0.946105i	−0.881034	−	0.473053i	$-0.843152\pi$
$251$		−	14.9891i		−	0.946105i	0.881034	−	0.473053i	$-0.156848\pi$
$252$	−12.5844	−	5.21264i	−0.792745	−	0.328366i
$253$	−14.1907	+	14.1907i	−0.892163	+	0.892163i
$254$	4.91194			0.308203
$255$	7.84341	−	6.75362i	0.491173	−	0.422928i
$256$	1.00000			0.0625000
$257$	−7.18594	+	7.18594i	−0.448246	+	0.448246i	−0.894771	−	0.446525i	$-0.852661\pi$
$257$	−7.18594	+	7.18594i	−0.448246	+	0.448246i	0.446525	+	0.894771i	$0.352661\pi$
$258$	1.96029	+	0.811978i	0.122042	+	0.0505515i
$259$			26.4864i			1.64579i
$260$	1.15811	−	2.79593i	0.0718231	−	0.173396i
$261$	25.8134	−	10.6922i	1.59781	−	0.661833i
$262$	4.45469	+	10.7546i	0.275212	+	0.664420i
$263$	−0.975807	−	0.975807i	−0.0601708	−	0.0601708i	0.676381	−	0.736552i	$-0.263547\pi$
$263$	−0.975807	−	0.975807i	−0.0601708	−	0.0601708i	−0.736552	+	0.676381i	$0.763547\pi$
$264$	−10.2511	−	10.2511i	−0.630914	−	0.630914i
$265$	−4.32866	−	10.4503i	−0.265908	−	0.641958i
$266$	−15.4679	+	6.40702i	−0.948399	+	0.392840i
$267$	−8.37825	+	20.2269i	−0.512741	+	1.23787i
$268$			6.72859i			0.411014i
$269$	−22.1343	−	9.16834i	−1.34955	−	0.559004i	−0.413386	−	0.910556i	$-0.635654\pi$
$269$	−22.1343	−	9.16834i	−1.34955	−	0.559004i	−0.936168	+	0.351552i	$0.885654\pi$
$270$	0.535696	−	0.535696i	0.0326014	−	0.0326014i
$271$	12.7628			0.775286			0.387643	−	0.921809i	$-0.373289\pi$
$271$	12.7628			0.775286			0.387643	+	0.921809i	$0.373289\pi$
$272$	−4.11166	−	0.306969i	−0.249306	−	0.0186128i
$273$	31.3409			1.89684
$274$	−1.19447	+	1.19447i	−0.0721606	+	0.0721606i
$275$	5.33544	+	2.21001i	0.321739	+	0.133269i
$276$			8.72361i			0.525100i
$277$	1.16351	−	2.80897i	0.0699088	−	0.168775i	−0.885063	−	0.465471i	$-0.845885\pi$
$277$	1.16351	−	2.80897i	0.0699088	−	0.168775i	0.954972	+	0.296696i	$0.0958849\pi$
$278$	3.14072	−	1.30093i	0.188368	−	0.0780246i
$279$	3.07544	+	7.42476i	0.184122	+	0.444509i
$280$	−2.91712	−	2.91712i	−0.174331	−	0.174331i
$281$	−13.9583	−	13.9583i	−0.832684	−	0.832684i	0.155199	−	0.987883i	$-0.450398\pi$
$281$	−13.9583	−	13.9583i	−0.832684	−	0.832684i	−0.987883	+	0.155199i	$0.950398\pi$
$282$	8.05875	+	19.4555i	0.479892	+	1.15856i
$283$	26.0534	−	10.7917i	1.54871	−	0.641498i	0.565629	−	0.824660i	$-0.308633\pi$
$283$	26.0534	−	10.7917i	1.54871	−	0.641498i	0.983083	+	0.183162i	$0.0586333\pi$
$284$	0.560421	−	1.35298i	0.0332549	−	0.0802844i
$285$		−	10.1878i		−	0.603472i
$286$	16.1466	+	6.68815i	0.954769	+	0.395478i
$287$	9.96875	−	9.96875i	0.588437	−	0.588437i
$288$	−3.30179			−0.194560
$289$	16.8115	+	2.52431i	0.988914	+	0.148489i
$290$	8.46214			0.496914
$291$	−23.3055	+	23.3055i	−1.36619	+	1.36619i
$292$	1.18758	+	0.491913i	0.0694981	+	0.0287870i
$293$		−	17.5349i		−	1.02440i	−0.858866	−	0.512200i	$-0.828831\pi$
$293$		−	17.5349i		−	1.02440i	0.858866	−	0.512200i	$-0.171169\pi$
$294$	9.62505	−	23.2369i	0.561344	−	1.35521i
$295$	−8.29383	+	3.43542i	−0.482885	+	0.200018i
$296$	2.45694	+	5.93157i	0.142807	+	0.344766i
$297$	3.09367	+	3.09367i	0.179513	+	0.179513i
$298$	7.07884	+	7.07884i	0.410066	+	0.410066i
$299$	−4.02453	−	9.71608i	−0.232745	−	0.561895i
$300$	2.31925	−	0.960664i	0.133902	−	0.0554640i
$301$	−1.33439	+	3.22149i	−0.0769127	+	0.185684i
$302$			16.3804i			0.942583i
$303$	−23.4922	−	9.73078i	−1.34959	−	0.559019i
$304$	−2.86967	+	2.86967i	−0.164587	+	0.164587i
$305$	−1.37716			−0.0788562
$306$	13.5758	+	1.01355i	0.776079	+	0.0579407i
$307$	−29.9568			−1.70973			−0.854864	−	0.518853i	$-0.826359\pi$
$307$	−29.9568			−1.70973			−0.854864	+	0.518853i	$0.826359\pi$
$308$	16.8465	−	16.8465i	0.959917	−	0.959917i
$309$	−13.0786	−	5.41735i	−0.744017	−	0.308182i
$310$			2.43399i			0.138241i
$311$	−1.86611	+	4.50518i	−0.105817	+	0.255465i	−0.967916	−	0.251276i	$-0.919150\pi$
$311$	−1.86611	+	4.50518i	−0.105817	+	0.255465i	0.862098	+	0.506741i	$0.169150\pi$
$312$	7.01873	−	2.90725i	0.397357	−	0.164591i
$313$	6.30862	+	15.2304i	0.356585	+	0.860871i	0.995775	+	0.0918230i	$0.0292694\pi$
$313$	6.30862	+	15.2304i	0.356585	+	0.860871i	−0.639191	+	0.769048i	$0.720731\pi$
$314$	−5.17652	−	5.17652i	−0.292128	−	0.292128i
$315$	9.63171	+	9.63171i	0.542685	+	0.542685i
$316$	−1.25651	−	3.03348i	−0.0706841	−	0.170647i
$317$	29.1474	−	12.0733i	1.63708	−	0.678102i	0.641084	−	0.767471i	$-0.278485\pi$
$317$	29.1474	−	12.0733i	1.63708	−	0.678102i	0.995999	+	0.0893690i	$0.0284850\pi$
$318$	10.8664	−	26.2338i	0.609357	−	1.47112i
$319$			48.8692i			2.73615i
$320$	−0.923880	−	0.382683i	−0.0516464	−	0.0213927i
$321$	−23.1761	+	23.1761i	−1.29357	+	1.29357i
$322$	−14.3362			−0.798924
$323$	12.6800	−	10.9182i	0.705536	−	0.607507i
$324$	−8.00356			−0.444642
$325$	−2.13991	+	2.13991i	−0.118701	+	0.118701i
$326$	−1.15131	−	0.476889i	−0.0637652	−	0.0264124i
$327$			16.9467i			0.937156i
$328$	1.30775	−	3.15720i	0.0722087	−	0.174327i
$329$	−31.9728	+	13.2436i	−1.76272	+	0.730141i
$330$	5.54787	+	13.3938i	0.305400	+	0.737302i
$331$	−1.49593	−	1.49593i	−0.0822238	−	0.0822238i	0.664799	−	0.747023i	$-0.268517\pi$
$331$	−1.49593	−	1.49593i	−0.0822238	−	0.0822238i	−0.747023	+	0.664799i	$0.768517\pi$
$332$	1.23021	+	1.23021i	0.0675165	+	0.0675165i
$333$	−8.11229	−	19.5848i	−0.444551	−	1.07324i
$334$	16.3461	−	6.77077i	0.894418	−	0.370480i
$335$	2.57492	−	6.21641i	0.140683	−	0.339639i
$336$		−	10.3562i		−	0.564978i
$337$	−0.968569	−	0.401194i	−0.0527613	−	0.0218544i	0.356147	−	0.934430i	$-0.384090\pi$
$337$	−0.968569	−	0.401194i	−0.0527613	−	0.0218544i	−0.408908	+	0.912576i	$0.634090\pi$
$338$	2.71638	−	2.71638i	0.147752	−	0.147752i
$339$	31.9793			1.73687
$340$	3.68121	+	1.85707i	0.199642	+	0.100714i
$341$	−14.0564			−0.761195
$342$	9.47505	−	9.47505i	0.512352	−	0.512352i
$343$	11.5072	+	4.76646i	0.621333	+	0.257365i
$344$			0.845225i			0.0455715i
$345$	3.33838	−	8.05957i	0.179732	−	0.433912i
$346$	12.1864	−	5.04779i	0.655148	−	0.271371i
$347$	−4.84478	−	11.6963i	−0.260081	−	0.627892i	0.738862	−	0.673857i	$-0.235364\pi$
$347$	−4.84478	−	11.6963i	−0.260081	−	0.627892i	−0.998943	+	0.0459651i	$0.985364\pi$
$348$	15.0209	+	15.0209i	0.805207	+	0.805207i
$349$	−11.4535	−	11.4535i	−0.613091	−	0.613091i	0.330659	−	0.943750i	$-0.392729\pi$
$349$	−11.4535	−	11.4535i	−0.613091	−	0.613091i	−0.943750	+	0.330659i	$0.892729\pi$
$350$	1.57873	+	3.81140i	0.0843868	+	0.203728i
$351$	−2.11817	+	0.877374i	−0.113059	+	0.0468307i
$352$	2.21001	−	5.33544i	0.117794	−	0.284380i
$353$			12.4529i			0.662803i	0.943490	+	0.331401i	$0.107521\pi$
$353$			12.4529i			0.662803i	−0.943490	+	0.331401i	$0.892479\pi$
$354$	−20.8203	−	8.62405i	−1.10659	−	0.458363i
$355$	−1.03552	+	1.03552i	−0.0549599	+	0.0549599i
$356$	−8.72132			−0.462229
$357$	−3.17904	+	42.5813i	−0.168253	+	2.25364i
$358$	15.4908			0.818715
$359$	3.76309	−	3.76309i	0.198608	−	0.198608i	−0.600795	−	0.799403i	$-0.705149\pi$
$359$	3.76309	−	3.76309i	0.198608	−	0.198608i	0.799403	+	0.600795i	$0.205149\pi$
$360$	3.05045	+	1.26354i	0.160773	+	0.0665944i
$361$			2.52994i			0.133155i
$362$	7.32872	−	17.6931i	0.385189	−	0.929929i
$363$	−51.8377	+	21.4719i	−2.72077	+	1.12698i
$364$	4.77771	+	11.5344i	0.250420	+	0.604568i
$365$	−0.908937	−	0.908937i	−0.0475759	−	0.0475759i
$366$	−2.44457	−	2.44457i	−0.127780	−	0.127780i
$367$	8.35529	+	20.1714i	0.436142	+	1.05294i	0.977270	+	0.212000i	$0.0679978\pi$
$367$	8.35529	+	20.1714i	0.436142	+	1.05294i	−0.541127	+	0.840941i	$0.682002\pi$
$368$	−3.21055	+	1.32985i	−0.167362	+	0.0693235i
$369$	−4.31793	+	10.4244i	−0.224782	+	0.542673i
$370$		−	6.42029i		−	0.333775i
$371$	43.1120	+	17.8576i	2.23827	+	0.927120i
$372$	−4.32051	+	4.32051i	−0.224008	+	0.224008i
$373$	35.0830			1.81653			0.908264	−	0.418398i	$-0.137408\pi$
$373$	35.0830			1.81653			0.908264	+	0.418398i	$0.137408\pi$
$374$	−10.7246	+	21.2591i	−0.554558	+	1.09928i
$375$	−2.51034			−0.129633
$376$	−5.93173	+	5.93173i	−0.305905	+	0.305905i
$377$	−23.6596	−	9.80011i	−1.21853	−	0.504731i
$378$			3.12538i			0.160752i
$379$	12.3088	−	29.7161i	0.632261	−	1.52641i	−0.204513	−	0.978864i	$-0.565561\pi$
$379$	12.3088	−	29.7161i	0.632261	−	1.52641i	0.836774	−	0.547549i	$-0.184439\pi$
$380$	3.74941	−	1.55306i	0.192341	−	0.0796701i
$381$	−4.71873	−	11.3920i	−0.241748	−	0.583631i
$382$	−11.2200	−	11.2200i	−0.574067	−	0.574067i
$383$	−3.25667	−	3.25667i	−0.166408	−	0.166408i	0.618990	−	0.785399i	$-0.287542\pi$
$383$	−3.25667	−	3.25667i	−0.166408	−	0.166408i	−0.785399	+	0.618990i	$0.787542\pi$
$384$	−0.960664	−	2.31925i	−0.0490237	−	0.118354i
$385$	−22.0110	+	9.11725i	−1.12178	+	0.464658i
$386$	1.50158	−	3.62514i	0.0764285	−	0.184515i
$387$		−	2.79076i		−	0.141862i
$388$	−12.1299	−	5.02436i	−0.615802	−	0.255073i
$389$	3.94933	−	3.94933i	0.200239	−	0.200239i	−0.599863	−	0.800102i	$-0.704778\pi$
$389$	3.94933	−	3.94933i	0.200239	−	0.200239i	0.800102	+	0.599863i	$0.204778\pi$
$390$	−7.59702			−0.384690
$391$	13.6089	−	4.48237i	0.688233	−	0.226683i
$392$	10.0192			0.506044
$393$	20.6631	−	20.6631i	1.04231	−	1.04231i
$394$	15.1953	+	6.29410i	0.765528	+	0.317092i
$395$			3.28342i			0.165207i
$396$	−7.29699	+	17.6165i	−0.366688	+	0.885262i
$397$	12.1262	−	5.02285i	0.608598	−	0.252090i	−0.0570307	−	0.998372i	$-0.518163\pi$
$397$	12.1262	−	5.02285i	0.608598	−	0.252090i	0.665629	+	0.746283i	$0.268163\pi$
$398$	−8.40336	−	20.2875i	−0.421222	−	1.01692i
$399$	29.7190	+	29.7190i	1.48781	+	1.48781i
$400$	0.707107	+	0.707107i	0.0353553	+	0.0353553i
$401$	11.0566	+	26.6929i	0.552139	+	1.33298i	0.915869	+	0.401477i	$0.131503\pi$
$401$	11.0566	+	26.6929i	0.552139	+	1.33298i	−0.363730	+	0.931505i	$0.618497\pi$
$402$	15.6053	−	6.46392i	0.778320	−	0.322391i
$403$	2.81883	−	6.80526i	0.140416	−	0.338994i
$404$		−	10.1292i		−	0.503948i
$405$	7.39433	+	3.06283i	0.367427	+	0.152193i
$406$	−24.6851	+	24.6851i	−1.22510	+	1.22510i
$407$	37.0774			1.83786
$408$	3.23799	+	9.83086i	0.160304	+	0.486700i
$409$	−18.0445			−0.892241			−0.446121	−	0.894973i	$-0.647195\pi$
$409$	−18.0445			−0.892241			−0.446121	+	0.894973i	$0.647195\pi$
$410$	−2.41642	+	2.41642i	−0.119338	+	0.119338i
$411$	3.91776	+	1.62279i	0.193249	+	0.0800463i
$412$		−	5.63917i		−	0.277822i
$413$	14.1726	−	34.2156i	0.697386	−	1.68364i
$414$	10.6006	−	4.39090i	0.520989	−	0.215801i
$415$	−0.665784	−	1.60734i	−0.0326820	−	0.0789014i
$416$	2.13991	+	2.13991i	0.104918	+	0.104918i
$417$	−6.03436	−	6.03436i	−0.295504	−	0.295504i
$418$	8.96896	+	21.6530i	0.438686	+	1.05908i
$419$	−32.6815	+	13.5371i	−1.59660	+	0.661333i	−0.990929	−	0.134384i	$-0.957094\pi$
$419$	−32.6815	+	13.5371i	−1.59660	+	0.661333i	−0.605669	+	0.795717i	$0.707094\pi$
$420$	−3.96315	+	9.56789i	−0.193382	+	0.466865i
$421$		−	5.06487i		−	0.246847i	−0.992354	−	0.123423i	$-0.960613\pi$
$421$		−	5.06487i		−	0.246847i	0.992354	−	0.123423i	$-0.0393873\pi$
$422$	11.3459	+	4.69962i	0.552309	+	0.228774i
$423$	19.5853	−	19.5853i	0.952270	−	0.952270i
$424$	11.3113			0.549327
$425$	−2.69032	−	3.12444i	−0.130500	−	0.151558i
$426$	−3.67627			−0.178116
$427$	4.01735	−	4.01735i	0.194413	−	0.194413i
$428$	−12.0626	−	4.99648i	−0.583066	−	0.241514i
$429$		−	43.8731i		−	2.11821i
$430$	0.323454	−	0.780886i	0.0155983	−	0.0376577i
$431$	13.1215	−	5.43512i	0.632042	−	0.261800i	−0.0435785	−	0.999050i	$-0.513876\pi$
$431$	13.1215	−	5.43512i	0.632042	−	0.261800i	0.675620	+	0.737250i	$0.263876\pi$
$432$	0.289917	+	0.699921i	0.0139486	+	0.0336750i
$433$	2.94389	+	2.94389i	0.141475	+	0.141475i	0.774297	−	0.632822i	$-0.218104\pi$
$433$	2.94389	+	2.94389i	0.141475	+	0.141475i	−0.632822	+	0.774297i	$0.718104\pi$
$434$	−7.10022	−	7.10022i	−0.340822	−	0.340822i
$435$	−8.12927	−	19.6258i	−0.389769	−	0.940985i
$436$	−6.23691	+	2.58341i	−0.298694	+	0.123723i
$437$	5.39699	−	13.0295i	0.258173	−	0.623285i
$438$		−	3.22686i		−	0.154186i
$439$	−2.33988	−	0.969210i	−0.111676	−	0.0462578i	0.326146	−	0.945320i	$-0.394250\pi$
$439$	−2.33988	−	0.969210i	−0.111676	−	0.0462578i	−0.437822	+	0.899062i	$0.644250\pi$
$440$	−4.08357	+	4.08357i	−0.194677	+	0.194677i
$441$	−33.0812			−1.57529
$442$	−8.14171	−	9.45549i	−0.387262	−	0.449752i
$443$	−19.9362			−0.947198			−0.473599	−	0.880741i	$-0.657045\pi$
$443$	−19.9362			−0.947198			−0.473599	+	0.880741i	$0.657045\pi$
$444$	11.3965	−	11.3965i	0.540854	−	0.540854i
$445$	8.05744	+	3.33750i	0.381960	+	0.158213i
$446$			19.9861i			0.946369i
$447$	9.61720	−	23.2180i	0.454878	−	1.09817i
$448$	3.81140	−	1.57873i	0.180072	−	0.0745881i
$449$	−9.88812	−	23.8720i	−0.466649	−	1.12659i	−0.965617	−	0.259970i	$-0.916287\pi$
$449$	−9.88812	−	23.8720i	−0.466649	−	1.12659i	0.498967	−	0.866621i	$-0.333713\pi$
$450$	−2.33472	−	2.33472i	−0.110060	−	0.110060i
$451$	−13.9549	−	13.9549i	−0.657111	−	0.657111i
$452$	4.87502	+	11.7693i	0.229302	+	0.553583i
$453$	37.9901	−	15.7360i	1.78493	−	0.739343i
$454$	−5.08367	+	12.2731i	−0.238588	+	0.576003i
$455$		−	12.4848i		−	0.585295i
$456$	9.41228	+	3.89869i	0.440770	+	0.182573i
$457$	−13.4787	+	13.4787i	−0.630506	+	0.630506i	−0.948195	−	0.317689i	$-0.897093\pi$
$457$	−13.4787	+	13.4787i	−0.630506	+	0.630506i	0.317689	+	0.948195i	$0.397093\pi$
$458$	−6.97130			−0.325747
$459$	−0.977186	−	2.96684i	−0.0456111	−	0.138480i
$460$	3.47508			0.162026
$461$	8.25318	−	8.25318i	0.384389	−	0.384389i	−0.488292	−	0.872680i	$-0.662380\pi$
$461$	8.25318	−	8.25318i	0.384389	−	0.384389i	0.872680	+	0.488292i	$0.162380\pi$
$462$	−55.2550	−	22.8874i	−2.57069	−	1.06482i
$463$			30.3885i			1.41228i	0.708075	+	0.706138i	$0.249564\pi$
$463$			30.3885i			1.41228i	−0.708075	+	0.706138i	$0.750436\pi$
$464$	−3.23832	+	7.81800i	−0.150335	+	0.362941i
$465$	5.64502	−	2.33824i	0.261781	−	0.108433i
$466$	1.95462	+	4.71887i	0.0905460	+	0.218597i
$467$	12.8013	+	12.8013i	0.592375	+	0.592375i	0.938272	−	0.345898i	$-0.112426\pi$
$467$	12.8013	+	12.8013i	0.592375	+	0.592375i	−0.345898	+	0.938272i	$0.612426\pi$
$468$	−7.06554	−	7.06554i	−0.326605	−	0.326605i
$469$	10.6227	+	25.6454i	0.490509	+	1.18419i
$470$	7.75017	−	3.21023i	0.357489	−	0.148077i
$471$	−7.03274	+	16.9785i	−0.324052	+	0.782330i
$472$		−	8.97717i		−	0.413208i
$473$	4.50965	+	1.86796i	0.207354	+	0.0858888i
$474$	−5.82831	+	5.82831i	−0.267703	+	0.267703i
$475$	−4.05833			−0.186209
$476$	−16.1558	+	5.32124i	−0.740500	+	0.243898i
$477$	−37.3476			−1.71003
$478$	4.74487	−	4.74487i	0.217026	−	0.217026i
$479$	3.90824	+	1.61885i	0.178572	+	0.0739670i	0.470178	−	0.882571i	$-0.344190\pi$
$479$	3.90824	+	1.61885i	0.178572	+	0.0739670i	−0.291606	+	0.956539i	$0.594190\pi$
$480$			2.51034i			0.114581i
$481$	−7.43542	+	17.9507i	−0.339026	+	0.818481i
$482$	−5.47933	+	2.26961i	−0.249577	+	0.103378i
$483$	13.7723	+	33.2492i	0.626659	+	1.51289i
$484$	−15.8046	−	15.8046i	−0.718391	−	0.718391i
$485$	9.28381	+	9.28381i	0.421556	+	0.421556i
$486$	8.55848	+	20.6620i	0.388221	+	0.937248i
$487$	−26.7553	+	11.0824i	−1.21240	+	0.502191i	−0.894985	−	0.446097i	$-0.852814\pi$
$487$	−26.7553	+	11.0824i	−1.21240	+	0.502191i	−0.317412	+	0.948288i	$0.602814\pi$
$488$	0.527018	−	1.27233i	0.0238570	−	0.0575959i
$489$			3.12831i			0.141467i
$490$	−9.25650	−	3.83417i	−0.418166	−	0.173210i
$491$	−7.88129	+	7.88129i	−0.355678	+	0.355678i	−0.862217	−	0.506539i	$-0.830925\pi$
$491$	−7.88129	+	7.88129i	−0.355678	+	0.355678i	0.506539	+	0.862217i	$0.330925\pi$
$492$	−8.57864			−0.386755
$493$	15.7148	−	31.1509i	0.707757	−	1.40297i
$494$	−12.2817			−0.552580
$495$	13.4831	−	13.4831i	0.606019	−	0.606019i
$496$	−2.24871	−	0.931446i	−0.100970	−	0.0418232i
$497$		−	6.04149i		−	0.270998i
$498$	1.67134	−	4.03498i	0.0748946	−	0.180812i
$499$	−14.7318	+	6.10212i	−0.659487	+	0.273168i	−0.687223	−	0.726447i	$-0.741170\pi$
$499$	−14.7318	+	6.10212i	−0.659487	+	0.273168i	0.0277358	+	0.999615i	$0.491170\pi$
$500$	−0.382683	−	0.923880i	−0.0171141	−	0.0413171i
$501$	−31.4062	−	31.4062i	−1.40313	−	1.40313i
$502$	−10.5989	−	10.5989i	−0.473053	−	0.473053i
$503$	9.30310	+	22.4597i	0.414805	+	1.00143i	0.983830	+	0.179107i	$0.0573208\pi$
$503$	9.30310	+	22.4597i	0.414805	+	1.00143i	−0.569025	+	0.822320i	$0.692679\pi$
$504$	−12.5844	+	5.21264i	−0.560555	+	0.232190i
$505$	−3.87629	+	9.35818i	−0.172492	+	0.416434i
$506$			20.0687i			0.892163i
$507$	−8.90949	−	3.69043i	−0.395685	−	0.163898i
$508$	3.47327	−	3.47327i	0.154101	−	0.154101i
$509$	−4.75342			−0.210692			−0.105346	−	0.994436i	$-0.533595\pi$
$509$	−4.75342			−0.210692			−0.105346	+	0.994436i	$0.533595\pi$
$510$	0.770596	−	10.3217i	0.0341226	−	0.457051i
$511$	5.30296			0.234589
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−2.84051	−	1.17658i	−0.125412	−	0.0519472i
$514$			10.1625i			0.448246i
$515$	−2.15802	+	5.20991i	−0.0950935	+	0.229576i
$516$	1.96029	−	0.811978i	0.0862968	−	0.0357453i
$517$	18.5392	+	44.7576i	0.815353	+	1.96844i
$518$	18.7287	+	18.7287i	0.822894	+	0.822894i
$519$	−23.4142	−	23.4142i	−1.02777	−	1.02777i
$520$	−1.15811	−	2.79593i	−0.0507866	−	0.122610i
$521$	−38.9283	+	16.1246i	−1.70548	+	0.706432i	−0.999997	−	0.00229597i	$-0.999269\pi$
$521$	−38.9283	+	16.1246i	−1.70548	+	0.706432i	−0.705481	+	0.708728i	$0.749269\pi$
$522$	10.6922	−	25.8134i	0.467987	−	1.12982i
$523$		−	26.8790i		−	1.17534i	−0.809102	−	0.587668i	$-0.800046\pi$
$523$		−	26.8790i		−	1.17534i	0.809102	−	0.587668i	$-0.199954\pi$
$524$	10.7546	+	4.45469i	0.469816	+	0.194604i
$525$	7.32295	−	7.32295i	0.319600	−	0.319600i
$526$	−1.38000			−0.0601708
$527$	8.96001	+	4.52008i	0.390304	+	0.196898i
$528$	−14.4973			−0.630914
$529$	−7.72432	+	7.72432i	−0.335840	+	0.335840i
$530$	−10.4503	−	4.32866i	−0.453933	−	0.188025i
$531$			29.6407i			1.28630i
$532$	−6.40702	+	15.4679i	−0.277780	+	0.670620i
$533$	9.55461	−	3.95765i	0.413856	−	0.171425i
$534$	8.37825	+	20.2269i	0.362563	+	0.875303i
$535$	9.23229	+	9.23229i	0.399147	+	0.399147i
$536$	4.75783	+	4.75783i	0.205507	+	0.205507i
$537$	−14.8815	−	35.9271i	−0.642183	−	1.55037i
$538$	−22.1343	+	9.16834i	−0.954279	+	0.395275i
$539$	22.1425	−	53.4567i	0.953744	−	2.30254i
$540$		−	0.757589i		−	0.0326014i
$541$	−14.9962	−	6.21163i	−0.644737	−	0.267059i	0.0362631	−	0.999342i	$-0.488455\pi$
$541$	−14.9962	−	6.21163i	−0.644737	−	0.267059i	−0.681000	+	0.732284i	$0.738455\pi$
$542$	9.02468	−	9.02468i	0.387643	−	0.387643i
$543$	−48.0751			−2.06310
$544$	−3.12444	+	2.69032i	−0.133959	+	0.115347i
$545$	6.75078			0.289172
$546$	22.1614	−	22.1614i	0.948420	−	0.948420i
$547$	40.1908	+	16.6476i	1.71844	+	0.711800i	0.999866	+	0.0163446i	$0.00520289\pi$
$547$	40.1908	+	16.6476i	1.71844	+	0.711800i	0.718570	+	0.695455i	$0.244797\pi$
$548$			1.68924i			0.0721606i
$549$	−1.74010	+	4.20098i	−0.0742657	+	0.179293i
$550$	5.33544	−	2.21001i	0.227504	−	0.0942352i
$551$	−13.1422	−	31.7280i	−0.559876	−	1.35166i
$552$	6.16852	+	6.16852i	0.262550	+	0.262550i
$553$	−9.57811	−	9.57811i	−0.407303	−	0.407303i
$554$	−1.16351	−	2.80897i	−0.0494330	−	0.119342i
$555$	−14.8902	+	6.16774i	−0.632056	+	0.261806i
$556$	1.30093	−	3.14072i	0.0551718	−	0.133196i
$557$			29.0943i			1.23276i	0.787447	+	0.616382i	$0.211402\pi$
$557$			29.0943i			1.23276i	−0.787447	+	0.616382i	$0.788598\pi$
$558$	7.42476	+	3.07544i	0.314315	+	0.130194i
$559$	−1.80871	+	1.80871i	−0.0765002	+	0.0765002i
$560$	−4.12543			−0.174331
$561$	59.6080	+	4.45022i	2.51665	+	0.187889i
$562$	−19.7401			−0.832684
$563$	14.3820	−	14.3820i	0.606127	−	0.606127i	−0.335804	−	0.941932i	$-0.609008\pi$
$563$	14.3820	−	14.3820i	0.606127	−	0.606127i	0.941932	+	0.335804i	$0.109008\pi$
$564$	19.4555	+	8.05875i	0.819226	+	0.339335i
$565$		−	12.7390i		−	0.535935i
$566$	10.7917	−	26.0534i	0.453607	−	1.09510i
$567$	−30.5048	+	12.6355i	−1.28108	+	0.530641i
$568$	−0.560421	−	1.35298i	−0.0235148	−	0.0567697i
$569$	19.3280	+	19.3280i	0.810271	+	0.810271i	0.984674	−	0.174403i	$-0.0557996\pi$
$569$	19.3280	+	19.3280i	0.810271	+	0.810271i	−0.174403	+	0.984674i	$0.555800\pi$
$570$	−7.20385	−	7.20385i	−0.301736	−	0.301736i
$571$	−3.11982	−	7.53190i	−0.130560	−	0.315200i	0.845058	−	0.534675i	$-0.179566\pi$
$571$	−3.11982	−	7.53190i	−0.130560	−	0.315200i	−0.975618	+	0.219474i	$0.929566\pi$
$572$	16.1466	−	6.68815i	0.675124	−	0.279645i
$573$	−15.2434	+	36.8007i	−0.636801	+	1.53737i
$574$		−	14.0979i		−	0.588437i
$575$	−3.21055	−	1.32985i	−0.133889	−	0.0554588i
$576$	−2.33472	+	2.33472i	−0.0972799	+	0.0972799i
$577$	40.5087			1.68640			0.843199	−	0.537601i	$-0.180669\pi$
$577$	40.5087			1.68640			0.843199	+	0.537601i	$0.180669\pi$
$578$	13.6725	−	10.1026i	0.568701	−	0.420213i
$579$	−9.85011			−0.409357
$580$	5.98363	−	5.98363i	0.248457	−	0.248457i
$581$	6.63099	+	2.74664i	0.275100	+	0.113950i
$582$			32.9589i			1.36619i
$583$	24.9982	−	60.3510i	1.03532	−	2.49948i
$584$	1.18758	−	0.491913i	0.0491426	−	0.0203555i
$585$	3.82384	+	9.23157i	0.158096	+	0.381679i
$586$	−12.3991	−	12.3991i	−0.512200	−	0.512200i
$587$	−13.6625	−	13.6625i	−0.563910	−	0.563910i	0.366505	−	0.930416i	$-0.380554\pi$
$587$	−13.6625	−	13.6625i	−0.563910	−	0.563910i	−0.930416	+	0.366505i	$0.880554\pi$
$588$	−9.62505	−	23.2369i	−0.396930	−	0.958275i
$589$	9.12601	−	3.78012i	0.376031	−	0.155757i
$590$	−3.43542	+	8.29383i	−0.141434	+	0.341451i
$591$		−	41.2882i		−	1.69837i
$592$	5.93157	+	2.45694i	0.243786	+	0.100980i
$593$	−20.3984	+	20.3984i	−0.837661	+	0.837661i	−0.988551	−	0.150890i	$-0.951786\pi$
$593$	−20.3984	+	20.3984i	−0.837661	+	0.837661i	0.150890	+	0.988551i	$0.451786\pi$
$594$	4.37511			0.179513
$595$	16.9624	+	1.26638i	0.695389	+	0.0519165i
$596$	10.0110			0.410066
$597$	−38.9790	+	38.9790i	−1.59530	+	1.59530i
$598$	−9.71608	−	4.02453i	−0.397320	−	0.164575i
$599$			16.6297i			0.679471i	0.940521	+	0.339735i	$0.110338\pi$
$599$			16.6297i			0.679471i	−0.940521	+	0.339735i	$0.889662\pi$
$600$	0.960664	−	2.31925i	0.0392189	−	0.0946829i
$601$	24.5603	−	10.1732i	1.00184	−	0.414974i	0.179366	−	0.983782i	$-0.442595\pi$
$601$	24.5603	−	10.1732i	1.00184	−	0.414974i	0.822470	+	0.568808i	$0.192595\pi$
$602$	1.33439	+	3.22149i	0.0543855	+	0.131298i
$603$	−15.7094	−	15.7094i	−0.639735	−	0.639735i
$604$	11.5827	+	11.5827i	0.471292	+	0.471292i
$605$	8.55339	+	20.6497i	0.347745	+	0.839530i
$606$	−23.4922	+	9.73078i	−0.954305	+	0.395286i
$607$	−0.622163	+	1.50203i	−0.0252528	+	0.0609656i	−0.936003	−	0.351992i	$-0.885504\pi$
$607$	−0.622163	+	1.50203i	−0.0252528	+	0.0609656i	0.910750	+	0.412958i	$0.135504\pi$
$608$			4.05833i			0.164587i
$609$	80.9648	+	33.5367i	3.28086	+	1.35898i
$610$	−0.973802	+	0.973802i	−0.0394281	+	0.0394281i
$611$	−25.3868			−1.02704
$612$	10.3163	−	8.88288i	0.417010	−	0.359069i
$613$	3.37067			0.136140			0.0680699	−	0.997681i	$-0.478316\pi$
$613$	3.37067			0.136140			0.0680699	+	0.997681i	$0.478316\pi$
$614$	−21.1827	+	21.1827i	−0.854864	+	0.854864i
$615$	7.92563	+	3.28290i	0.319592	+	0.132379i
$616$		−	23.8245i		−	0.959917i
$617$	−7.54493	+	18.2151i	−0.303748	+	0.733312i	0.696134	+	0.717912i	$0.254902\pi$
$617$	−7.54493	+	18.2151i	−0.303748	+	0.733312i	−0.999881	+	0.0153996i	$0.995098\pi$
$618$	−13.0786	+	5.41735i	−0.526100	+	0.217918i
$619$	14.8997	+	35.9711i	0.598871	+	1.44580i	0.874733	+	0.484605i	$0.161037\pi$
$619$	14.8997	+	35.9711i	0.598871	+	1.44580i	−0.275862	+	0.961197i	$0.588963\pi$
$620$	1.72109	+	1.72109i	0.0691205	+	0.0691205i
$621$	−1.86159	−	1.86159i	−0.0747029	−	0.0747029i
$622$	1.86611	+	4.50518i	0.0748241	+	0.180641i
$623$	−33.2404	+	13.7686i	−1.33175	+	0.551629i
$624$	2.90725	−	7.01873i	0.116383	−	0.280974i
$625$			1.00000i			0.0400000i
$626$	15.2304	+	6.30862i	0.608728	+	0.252143i
$627$	41.6025	−	41.6025i	1.66144	−	1.66144i
$628$	−7.32071			−0.292128
$629$	−23.6344	−	11.9229i	−0.942366	−	0.475398i
$630$	13.6213			0.542685
$631$	27.8378	−	27.8378i	1.10821	−	1.10821i	0.114819	−	0.993386i	$-0.463371\pi$
$631$	27.8378	−	27.8378i	1.10821	−	1.10821i	0.993386	−	0.114819i	$-0.0366289\pi$
$632$	−3.03348	−	1.25651i	−0.120665	−	0.0499812i
$633$		−	30.8287i		−	1.22533i
$634$	12.0733	−	29.1474i	0.479490	−	1.15759i
$635$	−4.53804	+	1.87972i	−0.180087	+	0.0745944i
$636$	−10.8664	−	26.2338i	−0.430881	−	1.04024i
$637$	21.4401	+	21.4401i	0.849489	+	0.849489i
$638$	34.5557	+	34.5557i	1.36807	+	1.36807i
$639$	1.85039	+	4.46724i	0.0732004	+	0.176721i
$640$	−0.923880	+	0.382683i	−0.0365195	+	0.0151269i
$641$	−12.5354	+	30.2630i	−0.495117	+	1.19532i	0.456968	+	0.889483i	$0.348935\pi$
$641$	−12.5354	+	30.2630i	−0.495117	+	1.19532i	−0.952085	+	0.305834i	$0.901065\pi$
$642$			32.7760i			1.29357i
$643$	35.1881	+	14.5754i	1.38768	+	0.574797i	0.946524	−	0.322633i	$-0.104568\pi$
$643$	35.1881	+	14.5754i	1.38768	+	0.574797i	0.441158	+	0.897430i	$0.354568\pi$
$644$	−10.1372	+	10.1372i	−0.399462	+	0.399462i
$645$	−2.12180			−0.0835458
$646$	1.24578	−	16.6865i	0.0490147	−	0.656521i
$647$	−17.8409			−0.701398			−0.350699	−	0.936488i	$-0.614056\pi$
$647$	−17.8409			−0.701398			−0.350699	+	0.936488i	$0.614056\pi$
$648$	−5.65937	+	5.65937i	−0.222321	+	0.222321i
$649$	−47.8972	−	19.8397i	−1.88013	−	0.778775i
$650$			3.02629i			0.118701i
$651$	−9.64625	+	23.2881i	−0.378066	+	0.912733i
$652$	−1.15131	+	0.476889i	−0.0450888	+	0.0186764i
$653$	−0.494101	−	1.19287i	−0.0193357	−	0.0466805i	0.913917	−	0.405902i	$-0.133042\pi$
$653$	−0.494101	−	1.19287i	−0.0193357	−	0.0466805i	−0.933253	+	0.359221i	$0.883042\pi$
$654$	11.9831	+	11.9831i	0.468578	+	0.468578i
$655$	−8.23120	−	8.23120i	−0.321620	−	0.321620i
$656$	−1.30775	−	3.15720i	−0.0510593	−	0.123268i
$657$	−3.92115	+	1.62419i	−0.152979	+	0.0633658i
$658$	−13.2436	+	31.9728i	−0.516288	+	1.24643i
$659$		−	31.9465i		−	1.24446i	−0.782835	−	0.622230i	$-0.786227\pi$
$659$		−	31.9465i		−	1.24446i	0.782835	−	0.622230i	$-0.213773\pi$
$660$	13.3938	+	5.54787i	0.521351	+	0.215951i
$661$	21.4284	−	21.4284i	0.833468	−	0.833468i	−0.154522	−	0.987989i	$-0.549384\pi$
$661$	21.4284	−	21.4284i	0.833468	−	0.833468i	0.987989	+	0.154522i	$0.0493836\pi$
$662$	−2.11556			−0.0822238
$663$	−14.1082	+	27.9662i	−0.547916	+	1.08612i
$664$	1.73978			0.0675165
$665$	11.8386	−	11.8386i	0.459083	−	0.459083i
$666$	−19.5848	−	8.11229i	−0.758896	−	0.314345i
$667$		−	29.4066i		−	1.13863i
$668$	6.77077	−	16.3461i	0.261969	−	0.632449i
$669$	46.3527	−	19.1999i	1.79210	−	0.742312i
$670$	−2.57492	−	6.21641i	−0.0994779	−	0.240161i
$671$	−5.62375	−	5.62375i	−0.217102	−	0.217102i
$672$	−7.32295	−	7.32295i	−0.282489	−	0.282489i
$673$	−12.2884	−	29.6669i	−0.473684	−	1.14357i	−0.962523	−	0.271200i	$-0.912580\pi$
$673$	−12.2884	−	29.6669i	−0.473684	−	1.14357i	0.488839	−	0.872374i	$-0.337420\pi$
$674$	−0.968569	+	0.401194i	−0.0373079	+	0.0154534i
$675$	−0.289917	+	0.699921i	−0.0111589	+	0.0269400i
$676$		−	3.84154i		−	0.147752i
$677$	0.672592	+	0.278597i	0.0258498	+	0.0107073i	0.395571	−	0.918435i	$-0.370547\pi$
$677$	0.672592	+	0.278597i	0.0258498	+	0.0107073i	−0.369721	+	0.929143i	$0.620547\pi$
$678$	22.6127	−	22.6127i	0.868437	−	0.868437i
$679$	−54.1640			−2.07862
$680$	3.91615	−	1.28986i	0.150178	−	0.0494640i
$681$	33.3480			1.27790
$682$	−9.93935	+	9.93935i	−0.380597	+	0.380597i
$683$	−31.5385	−	13.0637i	−1.20679	−	0.499868i	−0.313602	−	0.949555i	$-0.601536\pi$
$683$	−31.5385	−	13.0637i	−1.20679	−	0.499868i	−0.893186	+	0.449687i	$0.851536\pi$
$684$		−	13.3998i		−	0.512352i
$685$	0.646443	−	1.56065i	0.0246993	−	0.0596294i
$686$	11.5072	−	4.76646i	0.439349	−	0.181984i
$687$	6.69708	+	16.1682i	0.255509	+	0.616854i
$688$	0.597665	+	0.597665i	0.0227858	+	0.0227858i
$689$	24.2053	+	24.2053i	0.922148	+	0.922148i
$690$	−3.33838	−	8.05957i	−0.127090	−	0.306822i
$691$	12.5547	−	5.20033i	0.477603	−	0.197830i	−0.130877	−	0.991399i	$-0.541779\pi$
$691$	12.5547	−	5.20033i	0.477603	−	0.197830i	0.608481	+	0.793569i	$0.291779\pi$
$692$	5.04779	−	12.1864i	0.191888	−	0.463259i
$693$			78.6635i			2.98818i
$694$	−11.6963	−	4.84478i	−0.443987	−	0.183905i
$695$	−2.40381	+	2.40381i	−0.0911816	+	0.0911816i
$696$	21.2428			0.805207
$697$	4.40788	+	13.3828i	0.166960	+	0.506909i
$698$	−16.1977			−0.613091
$699$	9.06650	−	9.06650i	0.342927	−	0.342927i
$700$	3.81140	+	1.57873i	0.144057	+	0.0596705i
$701$			25.8451i			0.976155i	0.872800	+	0.488077i	$0.162302\pi$
$701$			25.8451i			0.976155i	−0.872800	+	0.488077i	$0.837698\pi$
$702$	−0.877374	+	2.11817i	−0.0331143	+	0.0799451i
$703$	−24.0723	+	9.97107i	−0.907904	+	0.376066i
$704$	−2.21001	−	5.33544i	−0.0832930	−	0.201087i
$705$	−14.8906	−	14.8906i	−0.560813	−	0.560813i
$706$	8.80555	+	8.80555i	0.331401	+	0.331401i
$707$	−15.9913	−	38.6065i	−0.601416	−	1.45195i
$708$	−20.8203	+	8.62405i	−0.782475	+	0.324112i
$709$	−3.64337	+	8.79586i	−0.136829	+	0.330336i	−0.977410	−	0.211351i	$-0.932214\pi$
$709$	−3.64337	+	8.79586i	−0.136829	+	0.330336i	0.840581	+	0.541686i	$0.182214\pi$
$710$			1.46445i			0.0549599i
$711$	10.0159	+	4.14873i	0.375626	+	0.155589i
$712$	−6.16690	+	6.16690i	−0.231114	+	0.231114i
$713$	8.45829			0.316765
$714$	27.8616	+	32.3574i	1.04269	+	1.21095i
$715$	−17.4770			−0.653602
$716$	10.9537	−	10.9537i	0.409358	−	0.409358i
$717$	−15.5628	−	6.44631i	−0.581202	−	0.240742i
$718$		−	5.32181i		−	0.198608i
$719$	−9.55864	+	23.0766i	−0.356477	+	0.860612i	0.639313	+	0.768947i	$0.279219\pi$
$719$	−9.55864	+	23.0766i	−0.356477	+	0.860612i	−0.995790	+	0.0916649i	$0.970781\pi$
$720$	3.05045	−	1.26354i	0.113684	−	0.0470893i
$721$	−8.90274	−	21.4931i	−0.331555	−	0.800446i
$722$	1.78894	+	1.78894i	0.0665775	+	0.0665775i
$723$	10.5276	+	10.5276i	0.391525	+	0.391525i
$724$	−7.32872	−	17.6931i	−0.272370	−	0.657559i
$725$	−7.81800	+	3.23832i	−0.290353	+	0.120268i
$726$	−21.4719	+	51.8377i	−0.796896	+	1.92388i
$727$			6.84261i			0.253778i	0.991917	+	0.126889i	$0.0404993\pi$
$727$			6.84261i			0.253778i	−0.991917	+	0.126889i	$0.959501\pi$
$728$	11.5344	+	4.77771i	0.427494	+	0.177074i
$729$	22.7204	−	22.7204i	0.841496	−	0.841496i
$730$	−1.28543			−0.0475759
$731$	−2.27393	−	2.64086i	−0.0841044	−	0.0976757i
$732$	−3.45715			−0.127780
$733$	−14.6775	+	14.6775i	−0.542124	+	0.542124i	−0.924151	−	0.382027i	$-0.875226\pi$
$733$	−14.6775	+	14.6775i	−0.542124	+	0.542124i	0.382027	+	0.924151i	$0.375226\pi$
$734$	20.1714	+	8.35529i	0.744542	+	0.308399i
$735$			25.1515i			0.927726i
$736$	−1.32985	+	3.21055i	−0.0490191	+	0.118343i
$737$	35.9000	−	14.8703i	1.32239	−	0.547754i
$738$	4.31793	+	10.4244i	0.158945	+	0.383728i
$739$	−8.75551	−	8.75551i	−0.322077	−	0.322077i	0.527487	−	0.849563i	$-0.323134\pi$
$739$	−8.75551	−	8.75551i	−0.322077	−	0.322077i	−0.849563	+	0.527487i	$0.823134\pi$
$740$	−4.53983	−	4.53983i	−0.166887	−	0.166887i
$741$	11.7986	+	28.4843i	0.433432	+	1.04640i
$742$	43.1120	−	17.8576i	1.58269	−	0.655573i
$743$	−2.62681	+	6.34167i	−0.0963682	+	0.232653i	−0.964711	−	0.263311i	$-0.915185\pi$
$743$	−2.62681	+	6.34167i	−0.0963682	+	0.232653i	0.868343	+	0.495965i	$0.165185\pi$
$744$			6.11012i			0.224008i
$745$	−9.24895	−	3.83104i	−0.338855	−	0.140358i
$746$	24.8074	−	24.8074i	0.908264	−	0.908264i
$747$	−5.74438			−0.210176
$748$	7.44901	+	22.6159i	0.272363	+	0.826921i
$749$	−53.8634			−1.96812
$750$	−1.77508	+	1.77508i	−0.0648166	+	0.0648166i
$751$	−13.2259	−	5.47835i	−0.482620	−	0.199908i	0.128089	−	0.991763i	$-0.459116\pi$
$751$	−13.2259	−	5.47835i	−0.482620	−	0.199908i	−0.610709	+	0.791855i	$0.709116\pi$
$752$			8.38873i			0.305905i
$753$	−14.3995	+	34.7635i	−0.524747	+	1.26685i
$754$	−23.6596	+	9.80011i	−0.861630	+	0.356899i
$755$	−6.26849	−	15.1335i	−0.228134	−	0.550764i
$756$	2.20998	+	2.20998i	0.0803761	+	0.0803761i
$757$	−13.1995	−	13.1995i	−0.479744	−	0.479744i	0.425306	−	0.905050i	$-0.360167\pi$
$757$	−13.1995	−	13.1995i	−0.479744	−	0.479744i	−0.905050	+	0.425306i	$0.860167\pi$
$758$	−12.3088	−	29.7161i	−0.447076	−	1.07934i
$759$	46.5443	−	19.2793i	1.68945	−	0.699794i
$760$	1.55306	−	3.74941i	0.0563353	−	0.136005i
$761$			30.9748i			1.12283i	0.827533	+	0.561417i	$0.189744\pi$
$761$			30.9748i			1.12283i	−0.827533	+	0.561417i	$0.810256\pi$
$762$	−11.3920	−	4.71873i	−0.412689	−	0.170941i
$763$	−19.6928	+	19.6928i	−0.712928	+	0.712928i
$764$	−15.8675			−0.574067
$765$	−12.9303	+	4.25885i	−0.467496	+	0.153979i
$766$	−4.60563			−0.166408
$767$	19.2104	−	19.2104i	0.693646	−	0.693646i
$768$	−2.31925	−	0.960664i	−0.0836887	−	0.0346650i
$769$		−	9.80159i		−	0.353455i	−0.984260	−	0.176727i	$-0.943449\pi$
$769$		−	9.80159i		−	0.353455i	0.984260	−	0.176727i	$-0.0565511\pi$
$770$	−9.11725	+	22.0110i	−0.328563	+	0.793221i
$771$	23.5692	−	9.76270i	0.848826	−	0.351595i
$772$	−1.50158	−	3.62514i	−0.0540431	−	0.130472i
$773$	27.8560	+	27.8560i	1.00191	+	1.00191i	0.999998	+	0.00191158i	$0.000608476\pi$
$773$	27.8560	+	27.8560i	1.00191	+	1.00191i	0.00191158	+	0.999998i	$0.499392\pi$
$774$	−1.97336	−	1.97336i	−0.0709310	−	0.0709310i
$775$	−0.931446	−	2.24871i	−0.0334585	−	0.0807760i
$776$	−12.1299	+	5.02436i	−0.435438	+	0.180364i
$777$	25.4446	−	61.4287i	0.912819	−	2.20374i
$778$		−	5.58520i		−	0.200239i
$779$	12.8130	+	5.30730i	0.459072	+	0.190154i
$780$	−5.37190	+	5.37190i	−0.192345	+	0.192345i
$781$	−8.45727			−0.302625
$782$	6.45345	−	12.7925i	0.230775	−	0.457458i
$783$	−6.41082			−0.229104
$784$	7.08462	−	7.08462i	0.253022	−	0.253022i
$785$	6.76345	+	2.80151i	0.241398	+	0.0999903i
$786$		−	29.2220i		−	1.04231i
$787$	19.4400	−	46.9323i	0.692961	−	1.67296i	−0.0457676	−	0.998952i	$-0.514573\pi$
$787$	19.4400	−	46.9323i	0.692961	−	1.67296i	0.738728	−	0.674003i	$-0.235427\pi$
$788$	15.1953	−	6.29410i	0.541310	−	0.224218i
$789$	1.32572	+	3.20056i	0.0471967	+	0.113943i
$790$	2.32173	+	2.32173i	0.0826033	+	0.0826033i
$791$	37.1613	+	37.1613i	1.32130	+	1.32130i
$792$	7.29699	+	17.6165i	0.259287	+	0.625975i
$793$	3.85046	−	1.59491i	0.136734	−	0.0566370i
$794$	5.02285	−	12.1262i	0.178254	−	0.430344i
$795$			28.3953i			1.00708i
$796$	−20.2875	−	8.40336i	−0.719072	−	0.297849i
$797$	−18.5512	+	18.5512i	−0.657118	+	0.657118i	−0.954697	−	0.297579i	$-0.903821\pi$
$797$	−18.5512	+	18.5512i	−0.657118	+	0.657118i	0.297579	+	0.954697i	$0.403821\pi$
$798$	42.0290			1.48781
$799$	2.57508	−	34.4916i	0.0910999	−	1.22023i
$800$	1.00000			0.0353553
$801$	20.3618	−	20.3618i	0.719449	−	0.719449i
$802$	26.6929	+	11.0566i	0.942561	+	0.390421i
$803$		−	7.42342i		−	0.261967i
$804$	6.46392	−	15.6053i	0.227965	−	0.550356i
$805$	13.2449	−	5.48622i	0.466822	−	0.193364i
$806$	−2.81883	−	6.80526i	−0.0992890	−	0.239705i
$807$	42.5273	+	42.5273i	1.49703	+	1.49703i
$808$	−7.16244	−	7.16244i	−0.251974	−	0.251974i
$809$	8.03895	+	19.4078i	0.282635	+	0.682340i	0.999895	−	0.0144645i	$-0.00460437\pi$
$809$	8.03895	+	19.4078i	0.282635	+	0.682340i	−0.717261	+	0.696805i	$0.754604\pi$
$810$	7.39433	−	3.06283i	0.259810	−	0.107617i
$811$	−4.03622	+	9.74430i	−0.141731	+	0.342169i	−0.978766	−	0.204980i	$-0.934287\pi$
$811$	−4.03622	+	9.74430i	−0.141731	+	0.342169i	0.837035	+	0.547149i	$0.184287\pi$
$812$			34.9099i			1.22510i
$813$	−29.6002	−	12.2608i	−1.03812	−	0.430005i
$814$	26.2177	−	26.2177i	0.918930	−	0.918930i
$815$	1.24617			0.0436514
$816$	9.24107	+	4.66186i	0.323502	+	0.163198i
$817$	−3.43021			−0.120008
$818$	−12.7594	+	12.7594i	−0.446121	+	0.446121i
$819$	−38.0842	−	15.7750i	−1.33077	−	0.551223i
$820$			3.41733i			0.119338i
$821$	0.352384	−	0.850730i	0.0122983	−	0.0296907i	−0.917611	−	0.397479i	$-0.869885\pi$
$821$	0.352384	−	0.850730i	0.0122983	−	0.0296907i	0.929909	+	0.367789i	$0.119885\pi$
$822$	3.91776	−	1.62279i	0.136648	−	0.0566013i
$823$	−20.7838	−	50.1765i	−0.724477	−	1.74904i	−0.660174	−	0.751112i	$-0.729518\pi$
$823$	−20.7838	−	50.1765i	−0.724477	−	1.74904i	−0.0643028	−	0.997930i	$-0.520482\pi$
$824$	−3.98749	−	3.98749i	−0.138911	−	0.138911i
$825$	−10.2511	−	10.2511i	−0.356899	−	0.356899i
$826$	−14.1726	−	34.2156i	−0.493127	−	1.19051i
$827$	−20.3824	+	8.44266i	−0.708765	+	0.293580i	−0.707793	−	0.706420i	$-0.750309\pi$
$827$	−20.3824	+	8.44266i	−0.708765	+	0.293580i	−0.000971374		1.00000i	$0.500309\pi$
$828$	4.39090	−	10.6006i	0.152594	−	0.368395i
$829$			41.3826i			1.43728i	0.695383	+	0.718639i	$0.255235\pi$
$829$			41.3826i			1.43728i	−0.695383	+	0.718639i	$0.744765\pi$
$830$	−1.60734	−	0.665784i	−0.0557917	−	0.0231097i
$831$	−5.39696	+	5.39696i	−0.187218	+	0.187218i
$832$	3.02629			0.104918
$833$	−31.3043	+	26.9548i	−1.08463	+	0.933929i
$834$	−8.53388			−0.295504
$835$	−12.5108	+	12.5108i	−0.432953	+	0.432953i
$836$	21.6530	+	8.96896i	0.748884	+	0.310198i
$837$		−	1.84396i		−	0.0637366i
$838$	−13.5371	+	32.6815i	−0.467633	+	1.12897i
$839$	17.1430	−	7.10088i	0.591844	−	0.245150i	−0.0665999	−	0.997780i	$-0.521215\pi$
$839$	17.1430	−	7.10088i	0.591844	−	0.245150i	0.658444	+	0.752630i	$0.271215\pi$
$840$	3.96315	+	9.56789i	0.136742	+	0.330124i
$841$	−30.1282	−	30.1282i	−1.03891	−	1.03891i
$842$	−3.58140	−	3.58140i	−0.123423	−	0.123423i
$843$	18.9636	+	45.7821i	0.653140	+	1.57682i
$844$	11.3459	−	4.69962i	0.390542	−	0.161768i
$845$	−1.47010	+	3.54912i	−0.0505728	+	0.122094i
$846$		−	27.6978i		−	0.952270i
$847$	−85.1889	−	35.2864i	−2.92713	−	1.21246i
$848$	7.99832	−	7.99832i	0.274664	−	0.274664i
$849$	−70.7914			−2.42955
$850$	−4.11166	−	0.306969i	−0.141029	−	0.0105290i
$851$	−22.3110			−0.764811
$852$	−2.59951	+	2.59951i	−0.0890578	+	0.0890578i
$853$	−0.273483	−	0.113280i	−0.00936388	−	0.00387865i	0.377997	−	0.925807i	$-0.376613\pi$
$853$	−0.273483	−	0.113280i	−0.00936388	−	0.00387865i	−0.387360	+	0.921928i	$0.626613\pi$
$854$		−	5.68140i		−	0.194413i
$855$	−5.12786	+	12.3798i	−0.175369	+	0.423379i
$856$	−12.0626	+	4.99648i	−0.412290	+	0.170776i
$857$	−14.7613	−	35.6370i	−0.504238	−	1.21734i	−0.947155	−	0.320776i	$-0.896056\pi$
$857$	−14.7613	−	35.6370i	−0.504238	−	1.21734i	0.442917	−	0.896563i	$-0.353944\pi$
$858$	−31.0229	−	31.0229i	−1.05911	−	1.05911i
$859$	−4.41392	−	4.41392i	−0.150601	−	0.150601i	0.627785	−	0.778387i	$-0.283962\pi$
$859$	−4.41392	−	4.41392i	−0.150601	−	0.150601i	−0.778387	+	0.627785i	$0.783962\pi$
$860$	−0.323454	−	0.780886i	−0.0110297	−	0.0266280i
$861$	−32.6966	+	13.5434i	−1.11430	+	0.461558i
$862$	5.43512	−	13.1215i	0.185121	−	0.446921i
$863$		−	27.6848i		−	0.942402i	−0.882026	−	0.471201i	$-0.843821\pi$
$863$		−	27.6848i		−	0.942402i	0.882026	−	0.471201i	$-0.156179\pi$
$864$	0.699921	+	0.289917i	0.0238118	+	0.00986317i
$865$	−9.32710	+	9.32710i	−0.317131	+	0.317131i
$866$	4.16330			0.141475
$867$	−36.5651	−	22.0047i	−1.24182	−	0.747320i
$868$	−10.0412			−0.340822
$869$	−13.4081	+	13.4081i	−0.454837	+	0.454837i
$870$	−19.6258	−	8.12927i	−0.665377	−	0.275608i
$871$			20.3627i			0.689964i
$872$	−2.58341	+	6.23691i	−0.0874854	+	0.211208i
$873$	40.0503	−	16.5894i	1.35550	−	0.561465i
$874$	−5.39699	−	13.0295i	−0.182556	−	0.440729i
$875$	−2.91712	−	2.91712i	−0.0986166	−	0.0986166i
$876$	−2.28174	−	2.28174i	−0.0770928	−	0.0770928i
$877$	−13.0152	−	31.4214i	−0.439491	−	1.06103i	−0.976125	−	0.217211i	$-0.930304\pi$
$877$	−13.0152	−	31.4214i	−0.439491	−	1.06103i	0.536633	−	0.843816i	$-0.319696\pi$
$878$	−2.33988	+	0.969210i	−0.0789671	+	0.0327092i
$879$	−16.8452	+	40.6678i	−0.568173	+	1.37169i
$880$			5.77504i			0.194677i
$881$	12.1369	+	5.02727i	0.408903	+	0.169373i	0.577647	−	0.816287i	$-0.303971\pi$
$881$	12.1369	+	5.02727i	0.408903	+	0.169373i	−0.168744	+	0.985660i	$0.553971\pi$
$882$	−23.3919	+	23.3919i	−0.787647	+	0.787647i
$883$	17.1739			0.577948			0.288974	−	0.957337i	$-0.406686\pi$
$883$	17.1739			0.577948			0.288974	+	0.957337i	$0.406686\pi$
$884$	−12.4431	−	0.928980i	−0.418507	−	0.0312450i
$885$	22.5357			0.757530
$886$	−14.0970	+	14.0970i	−0.473599	+	0.473599i
$887$	−35.0657	−	14.5247i	−1.17739	−	0.487691i	−0.293762	−	0.955879i	$-0.594907\pi$
$887$	−35.0657	−	14.5247i	−1.17739	−	0.487691i	−0.883629	+	0.468187i	$0.844907\pi$
$888$		−	16.1171i		−	0.540854i
$889$	7.75465	−	18.7214i	0.260083	−	0.627895i
$890$	8.05744	−	3.33750i	0.270086	−	0.111873i
$891$	17.6880	+	42.7025i	0.592569	+	1.43059i
$892$	14.1323	+	14.1323i	0.473184	+	0.473184i
$893$	−24.0729	−	24.0729i	−0.805569	−	0.805569i
$894$	−9.61720	−	23.2180i	−0.321647	−	0.776525i
$895$	−14.3117	+	5.92808i	−0.478386	+	0.198154i
$896$	1.57873	−	3.81140i	0.0527418	−	0.127330i
$897$			26.4002i			0.881477i
$898$	−23.8720	−	9.88812i	−0.796620	−	0.329971i
$899$	14.5641	−	14.5641i	0.485739	−	0.485739i
$900$	−3.30179			−0.110060
$901$	−35.3417	+	30.4312i	−1.17740	+	1.01381i
$902$	−19.7352			−0.657111
$903$	6.18954	−	6.18954i	0.205975	−	0.205975i
$904$	11.7693	+	4.87502i	0.391442	+	0.162141i
$905$			19.1509i			0.636597i
$906$	15.7360	−	37.9901i	0.522794	−	1.26214i
$907$	13.7694	−	5.70349i	0.457207	−	0.189381i	−0.142180	−	0.989841i	$-0.545411\pi$
$907$	13.7694	−	5.70349i	0.457207	−	0.189381i	0.599387	+	0.800459i	$0.295411\pi$
$908$	5.08367	+	12.2731i	0.168707	+	0.407296i
$909$	23.6489	+	23.6489i	0.784383	+	0.784383i
$910$	−8.82806	−	8.82806i	−0.292647	−	0.292647i
$911$	−23.0743	−	55.7062i	−0.764485	−	1.84563i	−0.426579	−	0.904450i	$-0.640282\pi$
$911$	−23.0743	−	55.7062i	−0.764485	−	1.84563i	−0.337906	−	0.941180i	$-0.609718\pi$
$912$	9.41228	−	3.89869i	0.311672	−	0.129099i
$913$	3.84493	−	9.28248i	0.127249	−	0.307205i
$914$			19.0617i			0.630506i
$915$	3.19399	+	1.32299i	0.105590	+	0.0437368i
$916$	−4.92945	+	4.92945i	−0.162874	+	0.162874i
$917$	48.0228			1.58585
$918$	−2.78884	−	1.40689i	−0.0920456	−	0.0464344i
$919$	42.6847			1.40804			0.704019	−	0.710181i	$-0.251387\pi$
$919$	42.6847			1.40804			0.704019	+	0.710181i	$0.251387\pi$
$920$	2.45725	−	2.45725i	0.0810131	−	0.0810131i
$921$	69.4774	+	28.7785i	2.28936	+	0.948283i
$922$		−	11.6718i		−	0.384389i
$923$	1.69600	−	4.09451i	0.0558245	−	0.134772i
$924$	−55.2550	+	22.8874i	−1.81776	+	0.752939i
$925$	2.45694	+	5.93157i	0.0807836	+	0.195029i
$926$	21.4879	+	21.4879i	0.706138	+	0.706138i
$927$	13.1659	+	13.1659i	0.432424	+	0.432424i
$928$	3.23832	+	7.81800i	0.106303	+	0.256638i
$929$	34.9761	−	14.4876i	1.14753	−	0.475321i	0.273824	−	0.961780i	$-0.411712\pi$
$929$	34.9761	−	14.4876i	1.14753	−	0.475321i	0.873704	+	0.486459i	$0.161712\pi$
$930$	2.33824	−	5.64502i	0.0766740	−	0.185107i
$931$			40.6611i			1.33261i
$932$	4.71887	+	1.95462i	0.154572	+	0.0640257i
$933$	8.65593	−	8.65593i	0.283382	−	0.283382i
$934$	18.1038			0.592375
$935$	1.77276	−	23.7450i	0.0579755	−	0.776545i
$936$	−9.99218			−0.326605
$937$	25.0017	−	25.0017i	0.816769	−	0.816769i	−0.168869	−	0.985638i	$-0.554012\pi$
$937$	25.0017	−	25.0017i	0.816769	−	0.816769i	0.985638	+	0.168869i	$0.0540116\pi$
$938$	25.6454	+	10.6227i	0.837351	+	0.346842i
$939$		−	41.3835i		−	1.35050i
$940$	3.21023	−	7.75017i	0.104706	−	0.252783i
$941$	−29.3256	+	12.1471i	−0.955987	+	0.395983i	−0.805478	−	0.592626i	$-0.798091\pi$
$941$	−29.3256	+	12.1471i	−0.955987	+	0.395983i	−0.150509	+	0.988609i	$0.548091\pi$
$942$	7.03274	+	16.9785i	0.229139	+	0.553191i
$943$	8.39723	+	8.39723i	0.273451	+	0.273451i
$944$	−6.34782	−	6.34782i	−0.206604	−	0.206604i
$945$	−1.19603	−	2.88748i	−0.0389069	−	0.0939296i
$946$	4.50965	−	1.86796i	0.146621	−	0.0607326i
$947$	−1.92981	+	4.65897i	−0.0627103	+	0.151396i	−0.952128	−	0.305699i	$-0.901110\pi$
$947$	−1.92981	+	4.65897i	−0.0627103	+	0.151396i	0.889418	+	0.457095i	$0.151110\pi$
$948$			8.24248i			0.267703i
$949$	3.59398	+	1.48867i	0.116665	+	0.0483244i
$950$	−2.86967	+	2.86967i	−0.0931045	+	0.0931045i
$951$	−79.1985			−2.56819
$952$	−7.66120	+	15.1866i	−0.248301	+	0.492199i
$953$	−7.68650			−0.248990			−0.124495	−	0.992220i	$-0.539731\pi$
$953$	−7.68650			−0.248990			−0.124495	+	0.992220i	$0.539731\pi$
$954$	−26.4088	+	26.4088i	−0.855016	+	0.855016i
$955$	14.6597	+	6.07224i	0.474376	+	0.196493i
$956$		−	6.71027i		−	0.217026i
$957$	46.9469	−	113.340i	1.51758	−	3.66375i
$958$	3.90824	−	1.61885i	0.126270	−	0.0523026i
$959$	2.66686	+	6.43836i	0.0861172	+	0.207905i
$960$	1.77508	+	1.77508i	0.0572903	+	0.0572903i
$961$	−17.7312	−	17.7312i	−0.571974	−	0.571974i
$962$	7.43542	+	17.9507i	0.239728	+	0.578753i
$963$	39.8280	−	16.4973i	1.28344	−	0.531618i
$964$	−2.26961	+	5.47933i	−0.0730993	+	0.176477i
$965$			3.92382i			0.126312i
$966$	33.2492	+	13.7723i	1.06977	+	0.443115i
$967$	−24.7202	+	24.7202i	−0.794948	+	0.794948i	−0.982294	−	0.187346i	$-0.940011\pi$
$967$	−24.7202	+	24.7202i	−0.794948	+	0.794948i	0.187346	+	0.982294i	$0.440011\pi$
$968$	−22.3511			−0.718391
$969$	−39.8969	+	13.1408i	−1.28167	+	0.422144i
$970$	13.1293			0.421556
$971$	28.2666	−	28.2666i	0.907120	−	0.907120i	−0.0889192	−	0.996039i	$-0.528341\pi$
$971$	28.2666	−	28.2666i	0.907120	−	0.907120i	0.996039	+	0.0889192i	$0.0283413\pi$
$972$	20.6620	+	8.55848i	0.662734	+	0.274513i
$973$		−	14.0244i		−	0.449601i
$974$	−11.0824	+	26.7553i	−0.355103	+	0.857294i
$975$	7.01873	−	2.90725i	0.224779	−	0.0931066i
$976$	−0.527018	−	1.27233i	−0.0168694	−	0.0407264i
$977$	−27.4850	−	27.4850i	−0.879323	−	0.879323i	0.114141	−	0.993465i	$-0.463588\pi$
$977$	−27.4850	−	27.4850i	−0.879323	−	0.879323i	−0.993465	+	0.114141i	$0.963588\pi$
$978$	2.21205	+	2.21205i	0.0707334	+	0.0707334i
$979$	19.2742	+	46.5321i	0.616007	+	1.48717i
$980$	−9.25650	+	3.83417i	−0.295688	+	0.122478i
$981$	8.52988	−	20.5929i	0.272338	−	0.657482i
$982$			11.1458i			0.355678i
$983$	21.3399	+	8.83927i	0.680637	+	0.281929i	0.696093	−	0.717952i	$-0.254920\pi$
$983$	21.3399	+	8.83927i	0.680637	+	0.281929i	−0.0154564	+	0.999881i	$0.504920\pi$
$984$	−6.06602	+	6.06602i	−0.193378	+	0.193378i
$985$	−16.4473			−0.524054
$986$	−10.9150	−	33.1390i	−0.347604	−	1.05536i
$987$	86.8755			2.76528
$988$	−8.68448	+	8.68448i	−0.276290	+	0.276290i
$989$	−2.71364	−	1.12403i	−0.0862887	−	0.0357420i
$990$		−	19.0680i		−	0.606019i
$991$	0.162252	−	0.391710i	0.00515409	−	0.0124431i	−0.921282	−	0.388896i	$-0.872856\pi$
$991$	0.162252	−	0.391710i	0.00515409	−	0.0124431i	0.926436	+	0.376453i	$0.122856\pi$
$992$	−2.24871	+	0.931446i	−0.0713966	+	0.0295734i
$993$	2.03235	+	4.90652i	0.0644946	+	0.155704i
$994$	−4.27198	−	4.27198i	−0.135499	−	0.135499i
$995$	15.5274	+	15.5274i	0.492251	+	0.492251i
$996$	−1.67134	−	4.03498i	−0.0529585	−	0.127853i
$997$	−4.11223	+	1.70334i	−0.130236	+	0.0539453i	−0.446849	−	0.894609i	$-0.647454\pi$
$997$	−4.11223	+	1.70334i	−0.130236	+	0.0539453i	0.316614	+	0.948554i	$0.397454\pi$
$998$	−6.10212	+	14.7318i	−0.193159	+	0.466328i
$999$			4.86394i			0.153888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.k.b.111.1	✓	16
5.2	odd	4		850.2.o.j.349.1		16
5.3	odd	4		850.2.o.g.349.4		16
5.4	even	2		850.2.l.e.451.4		16
17.2	even	8	inner	170.2.k.b.121.1	yes	16
17.6	odd	16		2890.2.a.bj.1.1		8
17.7	odd	16		2890.2.b.r.2311.15		16
17.10	odd	16		2890.2.b.r.2311.2		16
17.11	odd	16		2890.2.a.bi.1.8		8
85.2	odd	8		850.2.o.g.699.4		16
85.19	even	8		850.2.l.e.801.4		16
85.53	odd	8		850.2.o.j.699.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.b.111.1	✓	16	1.1	even	1	trivial
170.2.k.b.121.1	yes	16	17.2	even	8	inner
850.2.l.e.451.4		16	5.4	even	2
850.2.l.e.801.4		16	85.19	even	8
850.2.o.g.349.4		16	5.3	odd	4
850.2.o.g.699.4		16	85.2	odd	8
850.2.o.j.349.1		16	5.2	odd	4
850.2.o.j.699.1		16	85.53	odd	8
2890.2.a.bi.1.8		8	17.11	odd	16
2890.2.a.bj.1.1		8	17.6	odd	16
2890.2.b.r.2311.2		16	17.10	odd	16
2890.2.b.r.2311.15		16	17.7	odd	16

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.k (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-2.31925 - 0.960664i) q^{3} -1.00000i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-2.31925 + 0.960664i) q^{6} +(-1.57873 - 3.81140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.33472 + 2.33472i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-2.31925 - 0.960664i) q^{3} -1.00000i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-2.31925 + 0.960664i) q^{6} +(-1.57873 - 3.81140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.33472 + 2.33472i) q^{9} +(0.382683 + 0.923880i) q^{10} +(-5.33544 + 2.21001i) q^{11} +(-0.960664 + 2.31925i) q^{12} -3.02629i q^{13} +(-3.81140 - 1.57873i) q^{14} +(1.77508 - 1.77508i) q^{15} -1.00000 q^{16} +(4.11166 + 0.306969i) q^{17} +3.30179 q^{18} +(2.86967 - 2.86967i) q^{19} +(0.923880 + 0.382683i) q^{20} +10.3562i q^{21} +(-2.21001 + 5.33544i) q^{22} +(3.21055 - 1.32985i) q^{23} +(0.960664 + 2.31925i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(-2.13991 - 2.13991i) q^{26} +(-0.289917 - 0.699921i) q^{27} +(-3.81140 + 1.57873i) q^{28} +(3.23832 - 7.81800i) q^{29} -2.51034i q^{30} +(2.24871 + 0.931446i) q^{31} +(-0.707107 + 0.707107i) q^{32} +14.4973 q^{33} +(3.12444 - 2.69032i) q^{34} +4.12543 q^{35} +(2.33472 - 2.33472i) q^{36} +(-5.93157 - 2.45694i) q^{37} -4.05833i q^{38} +(-2.90725 + 7.01873i) q^{39} +(0.923880 - 0.382683i) q^{40} +(1.30775 + 3.15720i) q^{41} +(7.32295 + 7.32295i) q^{42} +(-0.597665 - 0.597665i) q^{43} +(2.21001 + 5.33544i) q^{44} +(-3.05045 + 1.26354i) q^{45} +(1.32985 - 3.21055i) q^{46} -8.38873i q^{47} +(2.31925 + 0.960664i) q^{48} +(-7.08462 + 7.08462i) q^{49} -1.00000 q^{50} +(-9.24107 - 4.66186i) q^{51} -3.02629 q^{52} +(-7.99832 + 7.99832i) q^{53} +(-0.699921 - 0.289917i) q^{54} -5.77504i q^{55} +(-1.57873 + 3.81140i) q^{56} +(-9.41228 + 3.89869i) q^{57} +(-3.23832 - 7.81800i) q^{58} +(6.34782 + 6.34782i) q^{59} +(-1.77508 - 1.77508i) q^{60} +(0.527018 + 1.27233i) q^{61} +(2.24871 - 0.931446i) q^{62} +(5.21264 - 12.5844i) q^{63} +1.00000i q^{64} +(2.79593 + 1.15811i) q^{65} +(10.2511 - 10.2511i) q^{66} -6.72859 q^{67} +(0.306969 - 4.11166i) q^{68} -8.72361 q^{69} +(2.91712 - 2.91712i) q^{70} +(1.35298 + 0.560421i) q^{71} -3.30179i q^{72} +(-0.491913 + 1.18758i) q^{73} +(-5.93157 + 2.45694i) q^{74} +(0.960664 + 2.31925i) q^{75} +(-2.86967 - 2.86967i) q^{76} +(16.8465 + 16.8465i) q^{77} +(2.90725 + 7.01873i) q^{78} +(3.03348 - 1.25651i) q^{79} +(0.382683 - 0.923880i) q^{80} -8.00356i q^{81} +(3.15720 + 1.30775i) q^{82} +(-1.23021 + 1.23021i) q^{83} +10.3562 q^{84} +(-1.85707 + 3.68121i) q^{85} -0.845225 q^{86} +(-15.0209 + 15.0209i) q^{87} +(5.33544 + 2.21001i) q^{88} -8.72132i q^{89} +(-1.26354 + 3.05045i) q^{90} +(-11.5344 + 4.77771i) q^{91} +(-1.32985 - 3.21055i) q^{92} +(-4.32051 - 4.32051i) q^{93} +(-5.93173 - 5.93173i) q^{94} +(1.55306 + 3.74941i) q^{95} +(2.31925 - 0.960664i) q^{96} +(5.02436 - 12.1299i) q^{97} +10.0192i q^{98} +(-17.6165 - 7.29699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

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