LMFDB - Embedded newform 175.2.o.b.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(68,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("175.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.o (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			143.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	175.143
Dual form			175.2.o.b.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86603 + 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(1.50000 + 0.866025i) q^{4} +3.73205i q^{6} +(-0.866025 - 2.50000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(-0.633975 + 0.366025i) q^{9} +O(q^{10})$	\(q+(1.86603 + 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(1.50000 + 0.866025i) q^{4} +3.73205i q^{6} +(-0.866025 - 2.50000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(-0.633975 + 0.366025i) q^{9} +(-0.366025 + 0.633975i) q^{11} +(-0.866025 + 3.23205i) q^{12} +(-2.00000 + 2.00000i) q^{13} +(-0.366025 - 5.09808i) q^{14} +(-2.23205 - 3.86603i) q^{16} +(-1.00000 + 0.267949i) q^{17} +(-1.36603 + 0.366025i) q^{18} +(1.36603 + 2.36603i) q^{19} +(4.23205 - 2.86603i) q^{21} +(-1.00000 + 1.00000i) q^{22} +(1.86603 - 6.96410i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.73205 + 2.73205i) q^{26} +(3.09808 + 3.09808i) q^{27} +(0.866025 - 4.50000i) q^{28} +3.00000i q^{29} +(0.464102 + 0.267949i) q^{31} +(-1.96410 - 7.33013i) q^{32} +(-1.36603 - 0.366025i) q^{33} -2.00000 q^{34} -1.26795 q^{36} +(-4.73205 - 1.26795i) q^{37} +(1.36603 + 5.09808i) q^{38} +(-4.73205 - 2.73205i) q^{39} +0.464102i q^{41} +(9.33013 - 3.23205i) q^{42} +(5.83013 + 5.83013i) q^{43} +(-1.09808 + 0.633975i) q^{44} +(6.96410 - 12.0622i) q^{46} +(-0.169873 + 0.633975i) q^{47} +(6.09808 - 6.09808i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(-4.73205 + 1.26795i) q^{52} +(-6.83013 + 1.83013i) q^{53} +(4.23205 + 7.33013i) q^{54} +(-0.598076 + 1.23205i) q^{56} +(-3.73205 + 3.73205i) q^{57} +(-1.50000 + 5.59808i) q^{58} +(-1.09808 + 1.90192i) q^{59} +(-7.33013 + 4.23205i) q^{61} +(0.732051 + 0.732051i) q^{62} +(1.46410 + 1.26795i) q^{63} -5.73205i q^{64} +(-2.36603 - 1.36603i) q^{66} +(0.303848 + 1.13397i) q^{67} +(-1.73205 - 0.464102i) q^{68} +13.9282 q^{69} +4.73205 q^{71} +(0.366025 + 0.0980762i) q^{72} +(-0.928203 - 3.46410i) q^{73} +(-8.19615 - 4.73205i) q^{74} +4.73205i q^{76} +(1.90192 + 0.366025i) q^{77} +(-7.46410 - 7.46410i) q^{78} +(5.83013 - 3.36603i) q^{79} +(-5.33013 + 9.23205i) q^{81} +(-0.232051 + 0.866025i) q^{82} +(3.09808 - 3.09808i) q^{83} +(8.83013 - 0.633975i) q^{84} +(7.96410 + 13.7942i) q^{86} +(-5.59808 + 1.50000i) q^{87} +(0.366025 - 0.0980762i) q^{88} +(-8.33013 - 14.4282i) q^{89} +(6.73205 + 3.26795i) q^{91} +(8.83013 - 8.83013i) q^{92} +(-0.267949 + 1.00000i) q^{93} +(-0.633975 + 1.09808i) q^{94} +(12.6962 - 7.33013i) q^{96} +(7.92820 + 7.92820i) q^{97} +(-12.4282 + 5.33013i) q^{98} -0.535898i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^8 - 6 * q^9	$ 4 q + 4 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{8} - 6 q^{9} + 2 q^{11} - 8 q^{13} + 2 q^{14} - 2 q^{16} - 4 q^{17} - 2 q^{18} + 2 q^{19} + 10 q^{21} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 12 q^{26} + 2 q^{27} - 12 q^{31} + 6 q^{32} - 2 q^{33} - 8 q^{34} - 12 q^{36} - 12 q^{37} + 2 q^{38} - 12 q^{39} + 20 q^{42} + 6 q^{43} + 6 q^{44} + 14 q^{46} - 18 q^{47} + 14 q^{48} - 22 q^{49} - 4 q^{51} - 12 q^{52} - 10 q^{53} + 10 q^{54} + 8 q^{56} - 8 q^{57} - 6 q^{58} + 6 q^{59} - 12 q^{61} - 4 q^{62} - 8 q^{63} - 6 q^{66} + 22 q^{67} + 28 q^{69} + 12 q^{71} - 2 q^{72} + 24 q^{73} - 12 q^{74} + 18 q^{77} - 16 q^{78} + 6 q^{79} - 4 q^{81} + 6 q^{82} + 2 q^{83} + 18 q^{84} + 18 q^{86} - 12 q^{87} - 2 q^{88} - 16 q^{89} + 20 q^{91} + 18 q^{92} - 8 q^{93} - 6 q^{94} + 30 q^{96} + 4 q^{97} - 22 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^8 - 6 * q^9 + 2 * q^11 - 8 * q^13 + 2 * q^14 - 2 * q^16 - 4 * q^17 - 2 * q^18 + 2 * q^19 + 10 * q^21 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 12 * q^26 + 2 * q^27 - 12 * q^31 + 6 * q^32 - 2 * q^33 - 8 * q^34 - 12 * q^36 - 12 * q^37 + 2 * q^38 - 12 * q^39 + 20 * q^42 + 6 * q^43 + 6 * q^44 + 14 * q^46 - 18 * q^47 + 14 * q^48 - 22 * q^49 - 4 * q^51 - 12 * q^52 - 10 * q^53 + 10 * q^54 + 8 * q^56 - 8 * q^57 - 6 * q^58 + 6 * q^59 - 12 * q^61 - 4 * q^62 - 8 * q^63 - 6 * q^66 + 22 * q^67 + 28 * q^69 + 12 * q^71 - 2 * q^72 + 24 * q^73 - 12 * q^74 + 18 * q^77 - 16 * q^78 + 6 * q^79 - 4 * q^81 + 6 * q^82 + 2 * q^83 + 18 * q^84 + 18 * q^86 - 12 * q^87 - 2 * q^88 - 16 * q^89 + 20 * q^91 + 18 * q^92 - 8 * q^93 - 6 * q^94 + 30 * q^96 + 4 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.86603	+	0.500000i	1.31948	+	0.353553i	0.848783	−	0.528742i	$-0.177336\pi$
$2$	1.86603	+	0.500000i	1.31948	+	0.353553i	0.470696	+	0.882295i	$0.344003\pi$
$3$	0.500000	+	1.86603i	0.288675	+	1.07735i	0.946112	+	0.323840i	$0.104974\pi$
$3$	0.500000	+	1.86603i	0.288675	+	1.07735i	−0.657437	+	0.753510i	$0.728359\pi$
$4$	1.50000	+	0.866025i	0.750000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			3.73205i			1.52360i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$	−0.366025	−	0.366025i	−0.129410	−	0.129410i
$9$	−0.633975	+	0.366025i	−0.211325	+	0.122008i
$10$		0			0
$11$	−0.366025	+	0.633975i	−0.110361	+	0.191151i	−0.915916	−	0.401371i	$-0.868534\pi$
$11$	−0.366025	+	0.633975i	−0.110361	+	0.191151i	0.805555	+	0.592521i	$0.201867\pi$
$12$	−0.866025	+	3.23205i	−0.250000	+	0.933013i
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	−0.927794	−	0.373094i	$-0.878297\pi$
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	0.373094	+	0.927794i	$0.378297\pi$
$14$	−0.366025	−	5.09808i	−0.0978244	−	1.36252i
$15$		0			0
$16$	−2.23205	−	3.86603i	−0.558013	−	0.966506i
$17$	−1.00000	+	0.267949i	−0.242536	+	0.0649872i	−0.378039	−	0.925790i	$-0.623401\pi$
$17$	−1.00000	+	0.267949i	−0.242536	+	0.0649872i	0.135503	+	0.990777i	$0.456735\pi$
$18$	−1.36603	+	0.366025i	−0.321975	+	0.0862730i
$19$	1.36603	+	2.36603i	0.313388	+	0.542803i	0.979093	−	0.203411i	$-0.0652027\pi$
$19$	1.36603	+	2.36603i	0.313388	+	0.542803i	−0.665706	+	0.746214i	$0.731869\pi$
$20$		0			0
$21$	4.23205	−	2.86603i	0.923509	−	0.625418i
$22$	−1.00000	+	1.00000i	−0.213201	+	0.213201i
$23$	1.86603	−	6.96410i	0.389093	−	1.45212i	−0.442519	−	0.896759i	$-0.645915\pi$
$23$	1.86603	−	6.96410i	0.389093	−	1.45212i	0.831612	−	0.555357i	$-0.187418\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	−4.73205	+	2.73205i	−0.928032	+	0.535799i
$27$	3.09808	+	3.09808i	0.596225	+	0.596225i
$28$	0.866025	−	4.50000i	0.163663	−	0.850420i
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$		0			0
$31$	0.464102	+	0.267949i	0.0833551	+	0.0481251i	0.541098	−	0.840959i	$-0.318009\pi$
$31$	0.464102	+	0.267949i	0.0833551	+	0.0481251i	−0.457743	+	0.889085i	$0.651342\pi$
$32$	−1.96410	−	7.33013i	−0.347207	−	1.29580i
$33$	−1.36603	−	0.366025i	−0.237795	−	0.0637168i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	−1.26795			−0.211325
$37$	−4.73205	−	1.26795i	−0.777944	−	0.208450i	−0.152066	−	0.988370i	$-0.548593\pi$
$37$	−4.73205	−	1.26795i	−0.777944	−	0.208450i	−0.625878	+	0.779921i	$0.715259\pi$
$38$	1.36603	+	5.09808i	0.221599	+	0.827017i
$39$	−4.73205	−	2.73205i	−0.757735	−	0.437478i
$40$		0			0
$41$			0.464102i			0.0724805i	0.999343	+	0.0362402i	$0.0115382\pi$
$41$			0.464102i			0.0724805i	−0.999343	+	0.0362402i	$0.988462\pi$
$42$	9.33013	−	3.23205i	1.43967	−	0.498716i
$43$	5.83013	+	5.83013i	0.889086	+	0.889086i	0.994435	−	0.105349i	$-0.0335960\pi$
$43$	5.83013	+	5.83013i	0.889086	+	0.889086i	−0.105349	+	0.994435i	$0.533596\pi$
$44$	−1.09808	+	0.633975i	−0.165541	+	0.0955753i
$45$		0			0
$46$	6.96410	−	12.0622i	1.02680	−	1.77847i
$47$	−0.169873	+	0.633975i	−0.0247785	+	0.0924747i	−0.977208	−	0.212285i	$-0.931909\pi$
$47$	−0.169873	+	0.633975i	−0.0247785	+	0.0924747i	0.952429	+	0.304760i	$0.0985762\pi$
$48$	6.09808	−	6.09808i	0.880181	−	0.880181i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	−4.73205	+	1.26795i	−0.656217	+	0.175833i
$53$	−6.83013	+	1.83013i	−0.938190	+	0.251387i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	−6.83013	+	1.83013i	−0.938190	+	0.251387i	−0.242846	+	0.970065i	$0.578081\pi$
$54$	4.23205	+	7.33013i	0.575909	+	0.997504i
$55$		0			0
$56$	−0.598076	+	1.23205i	−0.0799213	+	0.164640i
$57$	−3.73205	+	3.73205i	−0.494322	+	0.494322i
$58$	−1.50000	+	5.59808i	−0.196960	+	0.735063i
$59$	−1.09808	+	1.90192i	−0.142957	+	0.247609i	−0.928609	−	0.371060i	$-0.878995\pi$
$59$	−1.09808	+	1.90192i	−0.142957	+	0.247609i	0.785652	+	0.618669i	$0.212328\pi$
$60$		0			0
$61$	−7.33013	+	4.23205i	−0.938527	+	0.541859i	−0.889498	−	0.456939i	$-0.848946\pi$
$61$	−7.33013	+	4.23205i	−0.938527	+	0.541859i	−0.0490285	+	0.998797i	$0.515613\pi$
$62$	0.732051	+	0.732051i	0.0929705	+	0.0929705i
$63$	1.46410	+	1.26795i	0.184459	+	0.159747i
$64$		−	5.73205i		−	0.716506i
$65$		0			0
$66$	−2.36603	−	1.36603i	−0.291238	−	0.168146i
$67$	0.303848	+	1.13397i	0.0371209	+	0.138537i	0.981999	−	0.188884i	$-0.0604871\pi$
$67$	0.303848	+	1.13397i	0.0371209	+	0.138537i	−0.944878	+	0.327421i	$0.893820\pi$
$68$	−1.73205	−	0.464102i	−0.210042	−	0.0562806i
$69$	13.9282			1.67676
$70$		0			0
$71$	4.73205			0.561591			0.280796	−	0.959768i	$-0.409402\pi$
$71$	4.73205			0.561591			0.280796	+	0.959768i	$0.409402\pi$
$72$	0.366025	+	0.0980762i	0.0431365	+	0.0115584i
$73$	−0.928203	−	3.46410i	−0.108638	−	0.405442i	0.890094	−	0.455776i	$-0.150638\pi$
$73$	−0.928203	−	3.46410i	−0.108638	−	0.405442i	−0.998732	+	0.0503336i	$0.983972\pi$
$74$	−8.19615	−	4.73205i	−0.952783	−	0.550090i
$75$		0			0
$76$			4.73205i			0.542803i
$77$	1.90192	+	0.366025i	0.216744	+	0.0417125i
$78$	−7.46410	−	7.46410i	−0.845143	−	0.845143i
$79$	5.83013	−	3.36603i	0.655941	−	0.378707i	−0.134788	−	0.990874i	$-0.543035\pi$
$79$	5.83013	−	3.36603i	0.655941	−	0.378707i	0.790728	+	0.612167i	$0.209702\pi$
$80$		0			0
$81$	−5.33013	+	9.23205i	−0.592236	+	1.02578i
$82$	−0.232051	+	0.866025i	−0.0256257	+	0.0956365i
$83$	3.09808	−	3.09808i	0.340058	−	0.340058i	−0.516331	−	0.856389i	$-0.672703\pi$
$83$	3.09808	−	3.09808i	0.340058	−	0.340058i	0.856389	+	0.516331i	$0.172703\pi$
$84$	8.83013	−	0.633975i	0.963446	−	0.0691723i
$85$		0			0
$86$	7.96410	+	13.7942i	0.858791	+	1.48747i
$87$	−5.59808	+	1.50000i	−0.600177	+	0.160817i
$88$	0.366025	−	0.0980762i	0.0390184	−	0.0104550i
$89$	−8.33013	−	14.4282i	−0.882992	−	1.52939i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	−8.33013	−	14.4282i	−0.882992	−	1.52939i	−0.0349934	−	0.999388i	$-0.511141\pi$
$90$		0			0
$91$	6.73205	+	3.26795i	0.705711	+	0.342574i
$92$	8.83013	−	8.83013i	0.920604	−	0.920604i
$93$	−0.267949	+	1.00000i	−0.0277850	+	0.103695i
$94$	−0.633975	+	1.09808i	−0.0653895	+	0.113258i
$95$		0			0
$96$	12.6962	−	7.33013i	1.29580	−	0.748128i
$97$	7.92820	+	7.92820i	0.804987	+	0.804987i	0.983870	−	0.178883i	$-0.0572484\pi$
$97$	7.92820	+	7.92820i	0.804987	+	0.804987i	−0.178883	+	0.983870i	$0.557248\pi$
$98$	−12.4282	+	5.33013i	−1.25544	+	0.538424i
$99$		−	0.535898i		−	0.0538598i
$100$		0			0
$101$	−10.1603	−	5.86603i	−1.01098	−	0.583691i	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−10.1603	−	5.86603i	−1.01098	−	0.583691i	−0.911479	+	0.411346i	$0.865059\pi$
$102$	−1.00000	−	3.73205i	−0.0990148	−	0.369528i
$103$	2.23205	+	0.598076i	0.219931	+	0.0589302i	0.367102	−	0.930181i	$-0.380350\pi$
$103$	2.23205	+	0.598076i	0.219931	+	0.0589302i	−0.147171	+	0.989111i	$0.547017\pi$
$104$	1.46410			0.143567
$105$		0			0
$106$	−13.6603			−1.32680
$107$	8.59808	+	2.30385i	0.831207	+	0.222721i	0.649240	−	0.760583i	$-0.275087\pi$
$107$	8.59808	+	2.30385i	0.831207	+	0.222721i	0.181967	+	0.983305i	$0.441754\pi$
$108$	1.96410	+	7.33013i	0.188996	+	0.705342i
$109$	12.2321	+	7.06218i	1.17162	+	0.676434i	0.954061	−	0.299614i	$-0.0968578\pi$
$109$	12.2321	+	7.06218i	1.17162	+	0.676434i	0.217557	+	0.976048i	$0.430191\pi$
$110$		0			0
$111$		−	9.46410i		−	0.898293i
$112$	−7.73205	+	8.92820i	−0.730610	+	0.843636i
$113$	4.26795	+	4.26795i	0.401495	+	0.401495i	0.878760	−	0.477265i	$-0.158372\pi$
$113$	4.26795	+	4.26795i	0.401495	+	0.401495i	−0.477265	+	0.878760i	$0.658372\pi$
$114$	−8.83013	+	5.09808i	−0.827017	+	0.477479i
$115$		0			0
$116$	−2.59808	+	4.50000i	−0.241225	+	0.417815i
$117$	0.535898	−	2.00000i	0.0495438	−	0.184900i
$118$	−3.00000	+	3.00000i	−0.276172	+	0.276172i
$119$	1.53590	+	2.26795i	0.140796	+	0.207903i
$120$		0			0
$121$	5.23205	+	9.06218i	0.475641	+	0.823834i
$122$	−15.7942	+	4.23205i	−1.42994	+	0.383152i
$123$	−0.866025	+	0.232051i	−0.0780869	+	0.0209233i
$124$	0.464102	+	0.803848i	0.0416776	+	0.0721876i
$125$		0			0
$126$	2.09808	+	3.09808i	0.186911	+	0.275999i
$127$	6.46410	−	6.46410i	0.573596	−	0.573596i	−0.359535	−	0.933132i	$-0.617065\pi$
$127$	6.46410	−	6.46410i	0.573596	−	0.573596i	0.933132	+	0.359535i	$0.117065\pi$
$128$	−1.06218	+	3.96410i	−0.0938841	+	0.350380i
$129$	−7.96410	+	13.7942i	−0.701200	+	1.21451i
$130$		0			0
$131$	7.39230	−	4.26795i	0.645869	−	0.372892i	−0.141003	−	0.990009i	$-0.545033\pi$
$131$	7.39230	−	4.26795i	0.645869	−	0.372892i	0.786872	+	0.617117i	$0.211699\pi$
$132$	−1.73205	−	1.73205i	−0.150756	−	0.150756i
$133$	4.73205	−	5.46410i	0.410321	−	0.473798i
$134$			2.26795i			0.195921i
$135$		0			0
$136$	0.464102	+	0.267949i	0.0397964	+	0.0229765i
$137$	−2.80385	−	10.4641i	−0.239549	−	0.894009i	−0.976045	−	0.217567i	$-0.930188\pi$
$137$	−2.80385	−	10.4641i	−0.239549	−	0.894009i	0.736496	−	0.676441i	$-0.236479\pi$
$138$	25.9904	+	6.96410i	2.21245	+	0.592824i
$139$	−11.6603			−0.989010			−0.494505	−	0.869175i	$-0.664651\pi$
$139$	−11.6603			−0.989010			−0.494505	+	0.869175i	$0.664651\pi$
$140$		0			0
$141$	−1.26795			−0.106781
$142$	8.83013	+	2.36603i	0.741008	+	0.198552i
$143$	−0.535898	−	2.00000i	−0.0448141	−	0.167248i
$144$	2.83013	+	1.63397i	0.235844	+	0.136165i
$145$		0			0
$146$		−	6.92820i		−	0.573382i
$147$	−10.8301	−	8.09808i	−0.893254	−	0.667918i
$148$	−6.00000	−	6.00000i	−0.493197	−	0.493197i
$149$	9.69615	−	5.59808i	0.794340	−	0.458612i	−0.0471484	−	0.998888i	$-0.515013\pi$
$149$	9.69615	−	5.59808i	0.794340	−	0.458612i	0.841488	+	0.540276i	$0.181680\pi$
$150$		0			0
$151$	6.92820	−	12.0000i	0.563809	−	0.976546i	−0.433350	−	0.901226i	$-0.642669\pi$
$151$	6.92820	−	12.0000i	0.563809	−	0.976546i	0.997159	−	0.0753205i	$-0.0239980\pi$
$152$	0.366025	−	1.36603i	0.0296886	−	0.110799i
$153$	0.535898	−	0.535898i	0.0433248	−	0.0433248i
$154$	3.36603	+	1.63397i	0.271242	+	0.131669i
$155$		0			0
$156$	−4.73205	−	8.19615i	−0.378867	−	0.656217i
$157$	23.7583	−	6.36603i	1.89612	−	0.508064i	0.898513	−	0.438948i	$-0.144649\pi$
$157$	23.7583	−	6.36603i	1.89612	−	0.508064i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$	12.5622	−	3.36603i	0.999393	−	0.267787i
$159$	−6.83013	−	11.8301i	−0.541664	−	0.938190i
$160$		0			0
$161$	−19.0263	+	1.36603i	−1.49948	+	0.107658i
$162$	−14.5622	+	14.5622i	−1.14411	+	1.14411i
$163$	−1.43782	+	5.36603i	−0.112619	+	0.420300i	−0.999098	−	0.0424696i	$-0.986477\pi$
$163$	−1.43782	+	5.36603i	−0.112619	+	0.420300i	0.886479	+	0.462769i	$0.153144\pi$
$164$	−0.401924	+	0.696152i	−0.0313850	+	0.0543604i
$165$		0			0
$166$	7.33013	−	4.23205i	0.568928	−	0.328471i
$167$	−10.7583	−	10.7583i	−0.832505	−	0.832505i	0.155354	−	0.987859i	$-0.450348\pi$
$167$	−10.7583	−	10.7583i	−0.832505	−	0.832505i	−0.987859	+	0.155354i	$0.950348\pi$
$168$	−2.59808	−	0.500000i	−0.200446	−	0.0385758i
$169$			5.00000i			0.384615i
$170$		0			0
$171$	−1.73205	−	1.00000i	−0.132453	−	0.0764719i
$172$	3.69615	+	13.7942i	0.281829	+	1.05180i
$173$	−22.6603	−	6.07180i	−1.72283	−	0.461630i	−0.744317	−	0.667827i	$-0.767225\pi$
$173$	−22.6603	−	6.07180i	−1.72283	−	0.461630i	−0.978511	+	0.206197i	$0.933891\pi$
$174$	−11.1962			−0.848778
$175$		0			0
$176$	3.26795			0.246331
$177$	−4.09808	−	1.09808i	−0.308030	−	0.0825365i
$178$	−8.33013	−	31.0885i	−0.624369	−	2.33018i
$179$	−17.1962	−	9.92820i	−1.28530	−	0.742069i	−0.307488	−	0.951552i	$-0.599489\pi$
$179$	−17.1962	−	9.92820i	−1.28530	−	0.742069i	−0.977812	+	0.209483i	$0.932822\pi$
$180$		0			0
$181$			9.19615i			0.683545i	0.939783	+	0.341772i	$0.111027\pi$
$181$			9.19615i			0.683545i	−0.939783	+	0.341772i	$0.888973\pi$
$182$	10.9282	+	9.46410i	0.810052	+	0.701526i
$183$	−11.5622	−	11.5622i	−0.854701	−	0.854701i
$184$	−3.23205	+	1.86603i	−0.238270	+	0.137565i
$185$		0			0
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	0.196152	−	0.732051i	0.0143441	−	0.0535329i
$188$	−0.803848	+	0.803848i	−0.0586266	+	0.0586266i
$189$	5.06218	−	10.4282i	0.368219	−	0.758540i
$190$		0			0
$191$	−8.36603	−	14.4904i	−0.605344	−	1.04849i	−0.991997	−	0.126262i	$-0.959702\pi$
$191$	−8.36603	−	14.4904i	−0.605344	−	1.04849i	0.386653	−	0.922225i	$-0.373631\pi$
$192$	10.6962	−	2.86603i	0.771928	−	0.206838i
$193$	3.09808	−	0.830127i	0.223004	−	0.0597539i	−0.145587	−	0.989346i	$-0.546507\pi$
$193$	3.09808	−	0.830127i	0.223004	−	0.0597539i	0.368591	+	0.929592i	$0.379840\pi$
$194$	10.8301	+	18.7583i	0.777558	+	1.34677i
$195$		0			0
$196$	−12.0000	+	1.73205i	−0.857143	+	0.123718i
$197$	−14.1244	+	14.1244i	−1.00632	+	1.00632i	−0.00633876	+	0.999980i	$0.502018\pi$
$197$	−14.1244	+	14.1244i	−1.00632	+	1.00632i	−0.999980	+	0.00633876i	$0.997982\pi$
$198$	0.267949	−	1.00000i	0.0190423	−	0.0710669i
$199$	12.4641	−	21.5885i	0.883557	−	1.53037i	0.0361978	−	0.999345i	$-0.488475\pi$
$199$	12.4641	−	21.5885i	0.883557	−	1.53037i	0.847359	−	0.531021i	$-0.178191\pi$
$200$		0			0
$201$	−1.96410	+	1.13397i	−0.138537	+	0.0799844i
$202$	−16.0263	−	16.0263i	−1.12761	−	1.12761i
$203$	7.50000	−	2.59808i	0.526397	−	0.182349i
$204$		−	3.46410i		−	0.242536i
$205$		0			0
$206$	3.86603	+	2.23205i	0.269359	+	0.155514i
$207$	1.36603	+	5.09808i	0.0949453	+	0.354341i
$208$	12.1962	+	3.26795i	0.845651	+	0.226592i
$209$	−2.00000			−0.138343
$210$		0			0
$211$	10.1962			0.701932			0.350966	−	0.936388i	$-0.385853\pi$
$211$	10.1962			0.701932			0.350966	+	0.936388i	$0.385853\pi$
$212$	−11.8301	−	3.16987i	−0.812496	−	0.217708i
$213$	2.36603	+	8.83013i	0.162117	+	0.605030i
$214$	14.8923	+	8.59808i	1.01802	+	0.587752i
$215$		0			0
$216$		−	2.26795i		−	0.154314i
$217$	0.267949	−	1.39230i	0.0181896	−	0.0945158i
$218$	19.2942	+	19.2942i	1.30677	+	1.30677i
$219$	6.00000	−	3.46410i	0.405442	−	0.234082i
$220$		0			0
$221$	1.46410	−	2.53590i	0.0984861	−	0.170583i
$222$	4.73205	−	17.6603i	0.317594	−	1.18528i
$223$	−6.12436	+	6.12436i	−0.410117	+	0.410117i	−0.881779	−	0.471662i	$-0.843654\pi$
$223$	−6.12436	+	6.12436i	−0.410117	+	0.410117i	0.471662	+	0.881779i	$0.343654\pi$
$224$	−16.6244	+	11.2583i	−1.11076	+	0.752229i
$225$		0			0
$226$	5.83013	+	10.0981i	0.387814	+	0.671714i
$227$	−0.0980762	+	0.0262794i	−0.00650955	+	0.00174423i	−0.262072	−	0.965048i	$-0.584406\pi$
$227$	−0.0980762	+	0.0262794i	−0.00650955	+	0.00174423i	0.255563	+	0.966792i	$0.417739\pi$
$228$	−8.83013	+	2.36603i	−0.584789	+	0.156694i
$229$	−1.19615	−	2.07180i	−0.0790440	−	0.136908i	0.823794	−	0.566890i	$-0.191853\pi$
$229$	−1.19615	−	2.07180i	−0.0790440	−	0.136908i	−0.902838	+	0.429981i	$0.858520\pi$
$230$		0			0
$231$	0.267949	+	3.73205i	0.0176298	+	0.245551i
$232$	1.09808	−	1.09808i	0.0720922	−	0.0720922i
$233$	0.464102	−	1.73205i	0.0304043	−	0.113470i	−0.949056	−	0.315107i	$-0.897959\pi$
$233$	0.464102	−	1.73205i	0.0304043	−	0.113470i	0.979460	+	0.201637i	$0.0646261\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$		0			0
$236$	−3.29423	+	1.90192i	−0.214436	+	0.123805i
$237$	9.19615	+	9.19615i	0.597354	+	0.597354i
$238$	1.73205	+	5.00000i	0.112272	+	0.324102i
$239$			18.3923i			1.18970i	0.803837	+	0.594850i	$0.202788\pi$
$239$			18.3923i			1.18970i	−0.803837	+	0.594850i	$0.797212\pi$
$240$		0			0
$241$	14.5359	+	8.39230i	0.936340	+	0.540596i	0.888811	−	0.458274i	$-0.151532\pi$
$241$	14.5359	+	8.39230i	0.936340	+	0.540596i	0.0475286	+	0.998870i	$0.484865\pi$
$242$	5.23205	+	19.5263i	0.336329	+	1.25520i
$243$	−7.19615	−	1.92820i	−0.461633	−	0.123694i
$244$	−14.6603			−0.938527
$245$		0			0
$246$	−1.73205			−0.110432
$247$	−7.46410	−	2.00000i	−0.474929	−	0.127257i
$248$	−0.0717968	−	0.267949i	−0.00455910	−	0.0170148i
$249$	7.33013	+	4.23205i	0.464528	+	0.268195i
$250$		0			0
$251$		−	5.85641i		−	0.369653i	−0.982771	−	0.184827i	$-0.940828\pi$
$251$		−	5.85641i		−	0.369653i	0.982771	−	0.184827i	$-0.0591723\pi$
$252$	1.09808	+	3.16987i	0.0691723	+	0.199683i
$253$	3.73205	+	3.73205i	0.234632	+	0.234632i
$254$	15.2942	−	8.83013i	0.959645	−	0.554051i
$255$		0			0
$256$	−9.69615	+	16.7942i	−0.606010	+	1.04964i
$257$	−0.732051	+	2.73205i	−0.0456641	+	0.170421i	−0.984992	−	0.172600i	$-0.944783\pi$
$257$	−0.732051	+	2.73205i	−0.0456641	+	0.170421i	0.939328	+	0.343020i	$0.111450\pi$
$258$	−21.7583	+	21.7583i	−1.35461	+	1.35461i
$259$	0.928203	+	12.9282i	0.0576757	+	0.803319i
$260$		0			0
$261$	−1.09808	−	1.90192i	−0.0679692	−	0.117726i
$262$	15.9282	−	4.26795i	0.984048	−	0.263675i
$263$	8.06218	−	2.16025i	0.497135	−	0.133207i	−0.00153494	−	0.999999i	$-0.500489\pi$
$263$	8.06218	−	2.16025i	0.497135	−	0.133207i	0.498670	+	0.866792i	$0.333822\pi$
$264$	0.366025	+	0.633975i	0.0225273	+	0.0390184i
$265$		0			0
$266$	11.5622	−	7.83013i	0.708923	−	0.480096i
$267$	22.7583	−	22.7583i	1.39279	−	1.39279i
$268$	−0.526279	+	1.96410i	−0.0321476	+	0.119977i
$269$	2.42820	−	4.20577i	0.148050	−	0.256430i	−0.782457	−	0.622705i	$-0.786034\pi$
$269$	2.42820	−	4.20577i	0.148050	−	0.256430i	0.930507	+	0.366275i	$0.119367\pi$
$270$		0			0
$271$	−21.4186	+	12.3660i	−1.30109	+	0.751183i	−0.980590	−	0.196067i	$-0.937183\pi$
$271$	−21.4186	+	12.3660i	−1.30109	+	0.751183i	−0.320496	+	0.947250i	$0.603850\pi$
$272$	3.26795	+	3.26795i	0.198149	+	0.198149i
$273$	−2.73205	+	14.1962i	−0.165351	+	0.859190i
$274$		−	20.9282i		−	1.26432i
$275$		0			0
$276$	20.8923	+	12.0622i	1.25757	+	0.726058i
$277$	5.19615	+	19.3923i	0.312207	+	1.16517i	0.926562	+	0.376141i	$0.122749\pi$
$277$	5.19615	+	19.3923i	0.312207	+	1.16517i	−0.614356	+	0.789029i	$0.710584\pi$
$278$	−21.7583	−	5.83013i	−1.30498	−	0.349668i
$279$	−0.392305			−0.0234867
$280$		0			0
$281$	12.9282			0.771232			0.385616	−	0.922659i	$-0.373989\pi$
$281$	12.9282			0.771232			0.385616	+	0.922659i	$0.373989\pi$
$282$	−2.36603	−	0.633975i	−0.140895	−	0.0377526i
$283$	7.09808	+	26.4904i	0.421937	+	1.57469i	0.770523	+	0.637413i	$0.219995\pi$
$283$	7.09808	+	26.4904i	0.421937	+	1.57469i	−0.348586	+	0.937277i	$0.613338\pi$
$284$	7.09808	+	4.09808i	0.421193	+	0.243176i
$285$		0			0
$286$		−	4.00000i		−	0.236525i
$287$	1.16025	−	0.401924i	0.0684876	−	0.0237248i
$288$	3.92820	+	3.92820i	0.231472	+	0.231472i
$289$	−13.7942	+	7.96410i	−0.811425	+	0.468477i
$290$		0			0
$291$	−10.8301	+	18.7583i	−0.634873	+	1.09963i
$292$	1.60770	−	6.00000i	0.0940832	−	0.351123i
$293$	18.3923	−	18.3923i	1.07449	−	1.07449i	0.0774974	−	0.996993i	$-0.475307\pi$
$293$	18.3923	−	18.3923i	1.07449	−	1.07449i	0.996993	−	0.0774974i	$-0.0246929\pi$
$294$	−16.1603	−	20.5263i	−0.942485	−	1.19712i
$295$		0			0
$296$	1.26795	+	2.19615i	0.0736980	+	0.127649i
$297$	−3.09808	+	0.830127i	−0.179769	+	0.0481689i
$298$	20.8923	−	5.59808i	1.21026	−	0.324288i
$299$	10.1962	+	17.6603i	0.589659	+	1.02132i
$300$		0			0
$301$	9.52628	−	19.6244i	0.549086	−	1.13113i
$302$	18.9282	−	18.9282i	1.08920	−	1.08920i
$303$	5.86603	−	21.8923i	0.336994	−	1.25768i
$304$	6.09808	−	10.5622i	0.349749	−	0.605782i
$305$		0			0
$306$	1.26795	−	0.732051i	0.0724838	−	0.0418486i
$307$	−9.29423	−	9.29423i	−0.530450	−	0.530450i	0.390257	−	0.920706i	$-0.372386\pi$
$307$	−9.29423	−	9.29423i	−0.530450	−	0.530450i	−0.920706	+	0.390257i	$0.872386\pi$
$308$	2.53590	+	2.19615i	0.144496	+	0.125137i
$309$			4.46410i			0.253954i
$310$		0			0
$311$	16.2224	+	9.36603i	0.919890	+	0.531099i	0.883600	−	0.468243i	$-0.155113\pi$
$311$	16.2224	+	9.36603i	0.919890	+	0.531099i	0.0362898	+	0.999341i	$0.488446\pi$
$312$	0.732051	+	2.73205i	0.0414442	+	0.154672i
$313$	−19.3923	−	5.19615i	−1.09612	−	0.293704i	−0.334935	−	0.942241i	$-0.608714\pi$
$313$	−19.3923	−	5.19615i	−1.09612	−	0.293704i	−0.761183	+	0.648537i	$0.775381\pi$
$314$	47.5167			2.68152
$315$		0			0
$316$	11.6603			0.655941
$317$	−4.46410	−	1.19615i	−0.250729	−	0.0671826i	0.131265	−	0.991347i	$-0.458096\pi$
$317$	−4.46410	−	1.19615i	−0.250729	−	0.0671826i	−0.381994	+	0.924165i	$0.624763\pi$
$318$	−6.83013	−	25.4904i	−0.383015	−	1.42943i
$319$	−1.90192	−	1.09808i	−0.106487	−	0.0614805i
$320$		0			0
$321$			17.1962i			0.959796i
$322$	−36.1865	−	6.96410i	−2.01660	−	0.388094i
$323$	−2.00000	−	2.00000i	−0.111283	−	0.111283i
$324$	−15.9904	+	9.23205i	−0.888355	+	0.512892i
$325$		0			0
$326$	−5.36603	+	9.29423i	−0.297197	+	0.514760i
$327$	−7.06218	+	26.3564i	−0.390539	+	1.45751i
$328$	0.169873	−	0.169873i	0.00937967	−	0.00937967i
$329$	1.73205	−	0.124356i	0.0954911	−	0.00685595i
$330$		0			0
$331$	−12.9282	−	22.3923i	−0.710598	−	1.23079i	−0.964633	−	0.263597i	$-0.915091\pi$
$331$	−12.9282	−	22.3923i	−0.710598	−	1.23079i	0.254035	−	0.967195i	$-0.418242\pi$
$332$	7.33013	−	1.96410i	0.402293	−	0.107794i
$333$	3.46410	−	0.928203i	0.189832	−	0.0508652i
$334$	−14.6962	−	25.4545i	−0.804138	−	1.39281i
$335$		0			0
$336$	−20.5263	−	9.96410i	−1.11980	−	0.543586i
$337$	−16.4641	+	16.4641i	−0.896857	+	0.896857i	−0.995157	−	0.0983001i	$-0.968660\pi$
$337$	−16.4641	+	16.4641i	−0.896857	+	0.896857i	0.0983001	+	0.995157i	$0.468660\pi$
$338$	−2.50000	+	9.33013i	−0.135982	+	0.507492i
$339$	−5.83013	+	10.0981i	−0.316649	+	0.548452i
$340$		0			0
$341$	−0.339746	+	0.196152i	−0.0183983	+	0.0106222i
$342$	−2.73205	−	2.73205i	−0.147732	−	0.147732i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		−	4.26795i		−	0.230112i
$345$		0			0
$346$	−39.2487	−	22.6603i	−2.11002	−	1.21822i
$347$	2.08846	+	7.79423i	0.112114	+	0.418416i	0.999055	−	0.0434674i	$-0.0138405\pi$
$347$	2.08846	+	7.79423i	0.112114	+	0.418416i	−0.886941	+	0.461884i	$0.847174\pi$
$348$	−9.69615	−	2.59808i	−0.519768	−	0.139272i
$349$	−9.73205			−0.520945			−0.260472	−	0.965481i	$-0.583878\pi$
$349$	−9.73205			−0.520945			−0.260472	+	0.965481i	$0.583878\pi$
$350$		0			0
$351$	−12.3923			−0.661452
$352$	5.36603	+	1.43782i	0.286010	+	0.0766362i
$353$	−1.43782	−	5.36603i	−0.0765276	−	0.285605i	0.917048	−	0.398777i	$-0.130565\pi$
$353$	−1.43782	−	5.36603i	−0.0765276	−	0.285605i	−0.993575	+	0.113173i	$0.963899\pi$
$354$	−7.09808	−	4.09808i	−0.377258	−	0.217810i
$355$		0			0
$356$		−	28.8564i		−	1.52939i
$357$	−3.46410	+	4.00000i	−0.183340	+	0.211702i
$358$	−27.1244	−	27.1244i	−1.43357	−	1.43357i
$359$	−12.3397	+	7.12436i	−0.651267	+	0.376009i	−0.788941	−	0.614468i	$-0.789371\pi$
$359$	−12.3397	+	7.12436i	−0.651267	+	0.376009i	0.137675	+	0.990478i	$0.456037\pi$
$360$		0			0
$361$	5.76795	−	9.99038i	0.303576	−	0.525810i
$362$	−4.59808	+	17.1603i	−0.241670	+	0.901923i
$363$	−14.2942	+	14.2942i	−0.750252	+	0.750252i
$364$	7.26795	+	10.7321i	0.380944	+	0.562512i
$365$		0			0
$366$	−15.7942	−	27.3564i	−0.825578	−	1.42994i
$367$	−1.86603	+	0.500000i	−0.0974057	+	0.0260998i	−0.307193	−	0.951647i	$-0.599390\pi$
$367$	−1.86603	+	0.500000i	−0.0974057	+	0.0260998i	0.209787	+	0.977747i	$0.432723\pi$
$368$	−31.0885	+	8.33013i	−1.62060	+	0.434238i
$369$	−0.169873	−	0.294229i	−0.00884323	−	0.0153169i
$370$		0			0
$371$	10.4904	+	15.4904i	0.544633	+	0.804221i
$372$	−1.26795	+	1.26795i	−0.0657401	+	0.0657401i
$373$	4.26795	−	15.9282i	0.220986	−	0.824731i	−0.762987	−	0.646414i	$-0.776268\pi$
$373$	4.26795	−	15.9282i	0.220986	−	0.824731i	0.983973	−	0.178317i	$-0.0570653\pi$
$374$	0.732051	−	1.26795i	0.0378534	−	0.0655641i
$375$		0			0
$376$	0.294229	−	0.169873i	0.0151737	−	0.00876053i
$377$	−6.00000	−	6.00000i	−0.309016	−	0.309016i
$378$	14.6603	−	16.9282i	0.754042	−	0.870693i
$379$		−	19.6603i		−	1.00988i	−0.863155	−	0.504940i	$-0.831515\pi$
$379$		−	19.6603i		−	1.00988i	0.863155	−	0.504940i	$-0.168485\pi$
$380$		0			0
$381$	15.2942	+	8.83013i	0.783547	+	0.452381i
$382$	−8.36603	−	31.2224i	−0.428043	−	1.59748i
$383$	28.1865	+	7.55256i	1.44026	+	0.385918i	0.892626	−	0.450797i	$-0.148860\pi$
$383$	28.1865	+	7.55256i	1.44026	+	0.385918i	0.547638	+	0.836715i	$0.315527\pi$
$384$	−7.92820			−0.404584
$385$		0			0
$386$	6.19615			0.315376
$387$	−5.83013	−	1.56218i	−0.296362	−	0.0794100i
$388$	5.02628	+	18.7583i	0.255171	+	0.952310i
$389$	7.73205	+	4.46410i	0.392031	+	0.226339i	0.683040	−	0.730381i	$-0.260658\pi$
$389$	7.73205	+	4.46410i	0.392031	+	0.226339i	−0.291009	+	0.956720i	$0.593991\pi$
$390$		0			0
$391$			7.46410i			0.377476i
$392$	3.59808	+	0.428203i	0.181730	+	0.0216275i
$393$	11.6603	+	11.6603i	0.588182	+	0.588182i
$394$	−33.4186	+	19.2942i	−1.68360	+	0.972029i
$395$		0			0
$396$	0.464102	−	0.803848i	0.0233220	−	0.0403949i
$397$	5.36603	−	20.0263i	0.269313	−	1.00509i	−0.690244	−	0.723577i	$-0.742497\pi$
$397$	5.36603	−	20.0263i	0.269313	−	1.00509i	0.959557	−	0.281514i	$-0.0908365\pi$
$398$	34.0526	−	34.0526i	1.70690	−	1.70690i
$399$	12.5622	+	6.09808i	0.628896	+	0.305286i
$400$		0			0
$401$	−5.50000	−	9.52628i	−0.274657	−	0.475720i	0.695392	−	0.718631i	$-0.255231\pi$
$401$	−5.50000	−	9.52628i	−0.274657	−	0.475720i	−0.970049	+	0.242911i	$0.921898\pi$
$402$	−4.23205	+	1.13397i	−0.211076	+	0.0565575i
$403$	−1.46410	+	0.392305i	−0.0729321	+	0.0195421i
$404$	−10.1603	−	17.5981i	−0.505492	−	0.875537i
$405$		0			0
$406$	15.2942	−	1.09808i	0.759040	−	0.0544966i
$407$	2.53590	−	2.53590i	0.125700	−	0.125700i
$408$	−0.267949	+	1.00000i	−0.0132655	+	0.0495074i
$409$	−3.42820	+	5.93782i	−0.169514	+	0.293606i	−0.938249	−	0.345961i	$-0.887553\pi$
$409$	−3.42820	+	5.93782i	−0.169514	+	0.293606i	0.768735	+	0.639567i	$0.220886\pi$
$410$		0			0
$411$	18.1244	−	10.4641i	0.894009	−	0.516156i
$412$	2.83013	+	2.83013i	0.139430	+	0.139430i
$413$	5.70577	+	1.09808i	0.280763	+	0.0540328i
$414$			10.1962i			0.501114i
$415$		0			0
$416$	18.5885	+	10.7321i	0.911374	+	0.526182i
$417$	−5.83013	−	21.7583i	−0.285503	−	1.06551i
$418$	−3.73205	−	1.00000i	−0.182541	−	0.0489116i
$419$	3.85641			0.188398			0.0941989	−	0.995553i	$-0.469971\pi$
$419$	3.85641			0.188398			0.0941989	+	0.995553i	$0.469971\pi$
$420$		0			0
$421$	−34.6603			−1.68924			−0.844619	−	0.535368i	$-0.820173\pi$
$421$	−34.6603			−1.68924			−0.844619	+	0.535368i	$0.820173\pi$
$422$	19.0263	+	5.09808i	0.926185	+	0.248170i
$423$	−0.124356	−	0.464102i	−0.00604638	−	0.0225654i
$424$	3.16987	+	1.83013i	0.153943	+	0.0888788i
$425$		0			0
$426$			17.6603i			0.855642i
$427$	16.9282	+	14.6603i	0.819213	+	0.709459i
$428$	10.9019	+	10.9019i	0.526964	+	0.526964i
$429$	3.46410	−	2.00000i	0.167248	−	0.0965609i
$430$		0			0
$431$	2.09808	−	3.63397i	0.101061	−	0.175042i	−0.811061	−	0.584961i	$-0.801110\pi$
$431$	2.09808	−	3.63397i	0.101061	−	0.175042i	0.912122	+	0.409919i	$0.134443\pi$
$432$	5.06218	−	18.8923i	0.243554	−	0.908956i
$433$	−24.4641	+	24.4641i	−1.17567	+	1.17567i	−0.194833	+	0.980836i	$0.562417\pi$
$433$	−24.4641	+	24.4641i	−1.17567	+	1.17567i	−0.980836	+	0.194833i	$0.937583\pi$
$434$	1.19615	−	2.46410i	0.0574172	−	0.118281i
$435$		0			0
$436$	12.2321	+	21.1865i	0.585809	+	1.01465i
$437$	19.0263	−	5.09808i	0.910150	−	0.243874i
$438$	12.9282	−	3.46410i	0.617733	−	0.165521i
$439$	15.6603	+	27.1244i	0.747423	+	1.29457i	0.949054	+	0.315113i	$0.102043\pi$
$439$	15.6603	+	27.1244i	0.747423	+	1.29457i	−0.201631	+	0.979462i	$0.564624\pi$
$440$		0			0
$441$	1.90192	−	4.75833i	0.0905678	−	0.226587i
$442$	4.00000	−	4.00000i	0.190261	−	0.190261i
$443$	−0.937822	+	3.50000i	−0.0445573	+	0.166290i	−0.984619	−	0.174713i	$-0.944100\pi$
$443$	−0.937822	+	3.50000i	−0.0445573	+	0.166290i	0.940062	+	0.341003i	$0.110767\pi$
$444$	8.19615	−	14.1962i	0.388972	−	0.673720i
$445$		0			0
$446$	−14.4904	+	8.36603i	−0.686139	+	0.396143i
$447$	15.2942	+	15.2942i	0.723392	+	0.723392i
$448$	−14.3301	+	4.96410i	−0.677035	+	0.234532i
$449$		−	5.05256i		−	0.238445i	−0.992868	−	0.119222i	$-0.961960\pi$
$449$		−	5.05256i		−	0.238445i	0.992868	−	0.119222i	$-0.0380402\pi$
$450$		0			0
$451$	−0.294229	−	0.169873i	−0.0138547	−	0.00799901i
$452$	2.70577	+	10.0981i	0.127269	+	0.474974i
$453$	25.8564	+	6.92820i	1.21484	+	0.325515i
$454$	−0.196152			−0.00920589
$455$		0			0
$456$	2.73205			0.127940
$457$	−30.8564	−	8.26795i	−1.44340	−	0.386758i	−0.549678	−	0.835376i	$-0.685250\pi$
$457$	−30.8564	−	8.26795i	−1.44340	−	0.386758i	−0.893724	+	0.448618i	$0.851916\pi$
$458$	−1.19615	−	4.46410i	−0.0558925	−	0.208594i
$459$	−3.92820	−	2.26795i	−0.183353	−	0.105859i
$460$		0			0
$461$		−	26.3923i		−	1.22921i	−0.788834	−	0.614606i	$-0.789315\pi$
$461$		−	26.3923i		−	1.22921i	0.788834	−	0.614606i	$-0.210685\pi$
$462$	−1.36603	+	7.09808i	−0.0635533	+	0.330232i
$463$	−17.7583	−	17.7583i	−0.825300	−	0.825300i	0.161563	−	0.986862i	$-0.448347\pi$
$463$	−17.7583	−	17.7583i	−0.825300	−	0.825300i	−0.986862	+	0.161563i	$0.948347\pi$
$464$	11.5981	−	6.69615i	0.538427	−	0.310861i
$465$		0			0
$466$	1.73205	−	3.00000i	0.0802357	−	0.138972i
$467$	−8.40192	+	31.3564i	−0.388795	+	1.45100i	0.443303	+	0.896372i	$0.353807\pi$
$467$	−8.40192	+	31.3564i	−0.388795	+	1.45100i	−0.832097	+	0.554629i	$0.812860\pi$
$468$	2.53590	−	2.53590i	0.117222	−	0.117222i
$469$	2.57180	−	1.74167i	0.118755	−	0.0804228i
$470$		0			0
$471$	23.7583	+	41.1506i	1.09473	+	1.89612i
$472$	1.09808	−	0.294229i	0.0505431	−	0.0135430i
$473$	−5.83013	+	1.56218i	−0.268070	+	0.0718290i
$474$	12.5622	+	21.7583i	0.577000	+	0.999393i
$475$		0			0
$476$	0.339746	+	4.73205i	0.0155722	+	0.216893i
$477$	3.66025	−	3.66025i	0.167592	−	0.167592i
$478$	−9.19615	+	34.3205i	−0.420622	+	1.56978i
$479$	−13.4641	+	23.3205i	−0.615191	+	1.06554i	0.375161	+	0.926960i	$0.377588\pi$
$479$	−13.4641	+	23.3205i	−0.615191	+	1.06554i	−0.990351	+	0.138581i	$0.955746\pi$
$480$		0			0
$481$	12.0000	−	6.92820i	0.547153	−	0.315899i
$482$	22.9282	+	22.9282i	1.04435	+	1.04435i
$483$	−12.0622	−	34.8205i	−0.548848	−	1.58439i
$484$			18.1244i			0.823834i
$485$		0			0
$486$	−12.4641	−	7.19615i	−0.565383	−	0.326424i
$487$	−2.22243	−	8.29423i	−0.100708	−	0.375847i	0.897115	−	0.441797i	$-0.145659\pi$
$487$	−2.22243	−	8.29423i	−0.100708	−	0.375847i	−0.997823	+	0.0659498i	$0.978992\pi$
$488$	4.23205	+	1.13397i	0.191576	+	0.0513326i
$489$	−10.7321			−0.485320
$490$		0			0
$491$	−17.7128			−0.799368			−0.399684	−	0.916653i	$-0.630880\pi$
$491$	−17.7128			−0.799368			−0.399684	+	0.916653i	$0.630880\pi$
$492$	−1.50000	−	0.401924i	−0.0676252	−	0.0181201i
$493$	−0.803848	−	3.00000i	−0.0362035	−	0.135113i
$494$	−12.9282	−	7.46410i	−0.581667	−	0.335826i
$495$		0			0
$496$		−	2.39230i		−	0.107418i
$497$	−4.09808	−	11.8301i	−0.183824	−	0.530654i
$498$	11.5622	+	11.5622i	0.518114	+	0.518114i
$499$	29.0263	−	16.7583i	1.29939	−	0.750206i	0.319095	−	0.947723i	$-0.396621\pi$
$499$	29.0263	−	16.7583i	1.29939	−	0.750206i	0.980300	+	0.197517i	$0.0632877\pi$
$500$		0			0
$501$	14.6962	−	25.4545i	0.656576	−	1.13722i
$502$	2.92820	−	10.9282i	0.130692	−	0.487750i
$503$	−19.3660	+	19.3660i	−0.863488	+	0.863488i	−0.991741	−	0.128253i	$-0.959063\pi$
$503$	−19.3660	+	19.3660i	−0.863488	+	0.863488i	0.128253	+	0.991741i	$0.459063\pi$
$504$	−0.0717968	−	1.00000i	−0.00319808	−	0.0445435i
$505$		0			0
$506$	5.09808	+	8.83013i	0.226637	+	0.392547i
$507$	−9.33013	+	2.50000i	−0.414365	+	0.111029i
$508$	15.2942	−	4.09808i	0.678572	−	0.181823i
$509$	−13.4545	−	23.3038i	−0.596359	−	1.03292i	−0.993353	−	0.115104i	$-0.963280\pi$
$509$	−13.4545	−	23.3038i	−0.596359	−	1.03292i	0.396994	−	0.917821i	$-0.370053\pi$
$510$		0			0
$511$	−7.85641	+	5.32051i	−0.347547	+	0.235365i
$512$	−20.6865	+	20.6865i	−0.914224	+	0.914224i
$513$	−3.09808	+	11.5622i	−0.136783	+	0.510483i
$514$	−2.73205	+	4.73205i	−0.120506	+	0.208722i
$515$		0			0
$516$	−23.8923	+	13.7942i	−1.05180	+	0.607257i
$517$	−0.339746	−	0.339746i	−0.0149420	−	0.0149420i
$518$	−4.73205	+	24.5885i	−0.207914	+	1.08035i
$519$		−	45.3205i		−	1.98935i
$520$		0			0
$521$	−3.33975	−	1.92820i	−0.146317	−	0.0844761i	0.425054	−	0.905168i	$-0.360255\pi$
$521$	−3.33975	−	1.92820i	−0.146317	−	0.0844761i	−0.571371	+	0.820692i	$0.693588\pi$
$522$	−1.09808	−	4.09808i	−0.0480615	−	0.179368i
$523$	−14.4904	−	3.88269i	−0.633620	−	0.169778i	−0.0723082	−	0.997382i	$-0.523037\pi$
$523$	−14.4904	−	3.88269i	−0.633620	−	0.169778i	−0.561312	+	0.827604i	$0.689703\pi$
$524$	14.7846			0.645869
$525$		0			0
$526$	16.1244			0.703055
$527$	−0.535898	−	0.143594i	−0.0233441	−	0.00625503i
$528$	1.63397	+	6.09808i	0.0711096	+	0.265385i
$529$	−25.0981	−	14.4904i	−1.09122	−	0.630017i
$530$		0			0
$531$		−	1.60770i		−	0.0697680i
$532$	11.8301	−	4.09808i	0.512901	−	0.177674i
$533$	−0.928203	−	0.928203i	−0.0402049	−	0.0402049i
$534$	53.8468	−	31.0885i	2.33018	−	1.34533i
$535$		0			0
$536$	0.303848	−	0.526279i	0.0131242	−	0.0227318i
$537$	9.92820	−	37.0526i	0.428434	−	1.59894i
$538$	6.63397	−	6.63397i	0.286011	−	0.286011i
$539$	−0.732051	−	5.07180i	−0.0315317	−	0.218458i
$540$		0			0
$541$	9.35641	+	16.2058i	0.402263	+	0.696741i	0.993999	−	0.109392i	$-0.0348903\pi$
$541$	9.35641	+	16.2058i	0.402263	+	0.696741i	−0.591735	+	0.806132i	$0.701557\pi$
$542$	−46.1506	+	12.3660i	−1.98234	+	0.531166i
$543$	−17.1603	+	4.59808i	−0.736417	+	0.197322i
$544$	3.92820	+	6.80385i	0.168420	+	0.291713i
$545$		0			0
$546$	−12.1962	+	25.1244i	−0.521947	+	1.07522i
$547$	−5.75833	+	5.75833i	−0.246208	+	0.246208i	−0.819413	−	0.573204i	$-0.805700\pi$
$547$	−5.75833	+	5.75833i	−0.246208	+	0.246208i	0.573204	+	0.819413i	$0.305700\pi$
$548$	4.85641	−	18.1244i	0.207455	−	0.774234i
$549$	3.09808	−	5.36603i	0.132223	−	0.229016i
$550$		0			0
$551$	−7.09808	+	4.09808i	−0.302388	+	0.174584i
$552$	−5.09808	−	5.09808i	−0.216989	−	0.216989i
$553$	−13.4641	−	11.6603i	−0.572552	−	0.495844i
$554$			38.7846i			1.64780i
$555$		0			0
$556$	−17.4904	−	10.0981i	−0.741757	−	0.428254i
$557$	1.77757	+	6.63397i	0.0753180	+	0.281091i	0.993305	−	0.115519i	$-0.0368532\pi$
$557$	1.77757	+	6.63397i	0.0753180	+	0.281091i	−0.917987	+	0.396610i	$0.870187\pi$
$558$	−0.732051	−	0.196152i	−0.0309902	−	0.00830379i
$559$	−23.3205			−0.986352
$560$		0			0
$561$	1.46410			0.0618144
$562$	24.1244	+	6.46410i	1.01762	+	0.272672i
$563$	−5.72243	−	21.3564i	−0.241172	−	0.900065i	−0.975269	−	0.221021i	$-0.929061\pi$
$563$	−5.72243	−	21.3564i	−0.241172	−	0.900065i	0.734097	−	0.679044i	$-0.237606\pi$
$564$	−1.90192	−	1.09808i	−0.0800854	−	0.0462373i
$565$		0			0
$566$			52.9808i			2.22695i
$567$	27.6962	+	5.33013i	1.16313	+	0.223844i
$568$	−1.73205	−	1.73205i	−0.0726752	−	0.0726752i
$569$	−13.0526	+	7.53590i	−0.547192	+	0.315921i	−0.747989	−	0.663712i	$-0.768980\pi$
$569$	−13.0526	+	7.53590i	−0.547192	+	0.315921i	0.200797	+	0.979633i	$0.435647\pi$
$570$		0			0
$571$	−10.0263	+	17.3660i	−0.419587	+	0.726746i	−0.995898	−	0.0904849i	$-0.971158\pi$
$571$	−10.0263	+	17.3660i	−0.419587	+	0.726746i	0.576311	+	0.817230i	$0.304492\pi$
$572$	0.928203	−	3.46410i	0.0388101	−	0.144841i
$573$	22.8564	−	22.8564i	0.954840	−	0.954840i
$574$	2.36603	−	0.169873i	0.0987560	−	0.00709036i
$575$		0			0
$576$	2.09808	+	3.63397i	0.0874198	+	0.151416i
$577$	−27.4904	+	7.36603i	−1.14444	+	0.306652i	−0.780735	−	0.624863i	$-0.785155\pi$
$577$	−27.4904	+	7.36603i	−1.14444	+	0.306652i	−0.363705	+	0.931514i	$0.618488\pi$
$578$	−29.7224	+	7.96410i	−1.23629	+	0.331263i
$579$	3.09808	+	5.36603i	0.128752	+	0.223004i
$580$		0			0
$581$	−10.4282	−	5.06218i	−0.432635	−	0.210015i
$582$	−29.5885	+	29.5885i	−1.22648	+	1.22648i
$583$	1.33975	−	5.00000i	0.0554866	−	0.207079i
$584$	−0.928203	+	1.60770i	−0.0384093	+	0.0665269i
$585$		0			0
$586$	43.5167	−	25.1244i	1.79766	−	1.03788i
$587$	−25.7846	−	25.7846i	−1.06424	−	1.06424i	−0.997789	−	0.0664553i	$-0.978831\pi$
$587$	−25.7846	−	25.7846i	−1.06424	−	1.06424i	−0.0664553	−	0.997789i	$-0.521169\pi$
$588$	−9.23205	−	21.5263i	−0.380723	−	0.887729i
$589$			1.46410i			0.0603273i
$590$		0			0
$591$	−33.4186	−	19.2942i	−1.37466	−	0.793659i
$592$	5.66025	+	21.1244i	0.232635	+	0.868206i
$593$	6.56218	+	1.75833i	0.269476	+	0.0722060i	0.391027	−	0.920379i	$-0.372120\pi$
$593$	6.56218	+	1.75833i	0.269476	+	0.0722060i	−0.121550	+	0.992585i	$0.538787\pi$
$594$	−6.19615			−0.254231
$595$		0			0
$596$	19.3923			0.794340
$597$	46.5167	+	12.4641i	1.90380	+	0.510122i
$598$	10.1962	+	38.0526i	0.416952	+	1.55608i
$599$	32.6603	+	18.8564i	1.33446	+	0.770452i	0.985980	−	0.166864i	$-0.0533640\pi$
$599$	32.6603	+	18.8564i	1.33446	+	0.770452i	0.348482	+	0.937316i	$0.386697\pi$
$600$		0			0
$601$			21.1769i			0.863824i	0.901916	+	0.431912i	$0.142161\pi$
$601$			21.1769i			0.863824i	−0.901916	+	0.431912i	$0.857839\pi$
$602$	27.5885	−	31.8564i	1.12442	−	1.29837i
$603$	−0.607695	−	0.607695i	−0.0247473	−	0.0247473i
$604$	20.7846	−	12.0000i	0.845714	−	0.488273i
$605$		0			0
$606$	21.8923	−	37.9186i	0.889314	−	1.54034i
$607$	−2.30385	+	8.59808i	−0.0935103	+	0.348985i	−0.996789	−	0.0800683i	$-0.974486\pi$
$607$	−2.30385	+	8.59808i	−0.0935103	+	0.348985i	0.903279	+	0.429053i	$0.141153\pi$
$608$	14.6603	−	14.6603i	0.594552	−	0.594552i
$609$	8.59808	+	12.6962i	0.348412	+	0.514474i
$610$		0			0
$611$	−0.928203	−	1.60770i	−0.0375511	−	0.0650404i
$612$	1.26795	−	0.339746i	0.0512538	−	0.0137334i
$613$	13.4641	−	3.60770i	0.543810	−	0.145713i	0.0235520	−	0.999723i	$-0.492502\pi$
$613$	13.4641	−	3.60770i	0.543810	−	0.145713i	0.520258	+	0.854009i	$0.325836\pi$
$614$	−12.6962	−	21.9904i	−0.512375	−	0.887460i
$615$		0			0
$616$	−0.562178	−	0.830127i	−0.0226508	−	0.0334468i
$617$	31.9090	−	31.9090i	1.28461	−	1.28461i	0.346590	−	0.938017i	$-0.387340\pi$
$617$	31.9090	−	31.9090i	1.28461	−	1.28461i	0.938017	−	0.346590i	$-0.112660\pi$
$618$	−2.23205	+	8.33013i	−0.0897863	+	0.335087i
$619$	0.0980762	−	0.169873i	0.00394202	−	0.00682777i	−0.864048	−	0.503410i	$-0.832079\pi$
$619$	0.0980762	−	0.169873i	0.00394202	−	0.00682777i	0.867990	+	0.496582i	$0.165412\pi$
$620$		0			0
$621$	27.3564	−	15.7942i	1.09777	−	0.633801i
$622$	25.5885	+	25.5885i	1.02600	+	1.02600i
$623$	−28.8564	+	33.3205i	−1.15611	+	1.33496i
$624$			24.3923i			0.976474i
$625$		0			0
$626$	−33.5885	−	19.3923i	−1.34246	−	0.775072i
$627$	−1.00000	−	3.73205i	−0.0399362	−	0.149044i
$628$	41.1506	+	11.0263i	1.64209	+	0.439996i
$629$	5.07180			0.202226
$630$		0			0
$631$	26.5885			1.05847			0.529235	−	0.848475i	$-0.322479\pi$
$631$	26.5885			1.05847			0.529235	+	0.848475i	$0.322479\pi$
$632$	−3.36603	−	0.901924i	−0.133893	−	0.0358766i
$633$	5.09808	+	19.0263i	0.202630	+	0.756227i
$634$	−7.73205	−	4.46410i	−0.307079	−	0.177292i
$635$		0			0
$636$		−	23.6603i		−	0.938190i
$637$	2.33975	−	19.6603i	0.0927041	−	0.778968i
$638$	−3.00000	−	3.00000i	−0.118771	−	0.118771i
$639$	−3.00000	+	1.73205i	−0.118678	+	0.0685189i
$640$		0			0
$641$	3.33013	−	5.76795i	0.131532	−	0.227820i	−0.792735	−	0.609566i	$-0.791344\pi$
$641$	3.33013	−	5.76795i	0.131532	−	0.227820i	0.924267	+	0.381746i	$0.124677\pi$
$642$	−8.59808	+	32.0885i	−0.339339	+	1.26643i
$643$	24.4641	−	24.4641i	0.964770	−	0.964770i	−0.0346302	−	0.999400i	$-0.511025\pi$
$643$	24.4641	−	24.4641i	0.964770	−	0.964770i	0.999400	+	0.0346302i	$0.0110253\pi$
$644$	−29.7224	−	14.4282i	−1.17123	−	0.568551i
$645$		0			0
$646$	−2.73205	−	4.73205i	−0.107491	−	0.186180i
$647$	−5.40192	+	1.44744i	−0.212372	+	0.0569048i	−0.363436	−	0.931619i	$-0.618397\pi$
$647$	−5.40192	+	1.44744i	−0.212372	+	0.0569048i	0.151065	+	0.988524i	$0.451730\pi$
$648$	5.33013	−	1.42820i	0.209387	−	0.0561051i
$649$	−0.803848	−	1.39230i	−0.0315538	−	0.0546527i
$650$		0			0
$651$	2.73205	−	0.196152i	0.107078	−	0.00768782i
$652$	−6.80385	+	6.80385i	−0.266459	+	0.266459i
$653$	−2.33975	+	8.73205i	−0.0915613	+	0.341712i	−0.996476	−	0.0838822i	$-0.973268\pi$
$653$	−2.33975	+	8.73205i	−0.0915613	+	0.341712i	0.904914	+	0.425594i	$0.139935\pi$
$654$	−26.3564	+	45.6506i	−1.03062	+	1.78508i
$655$		0			0
$656$	1.79423	−	1.03590i	0.0700529	−	0.0404450i
$657$	1.85641	+	1.85641i	0.0724253	+	0.0724253i
$658$	3.29423	+	0.633975i	0.128422	+	0.0247149i
$659$			10.3397i			0.402779i	0.979511	+	0.201390i	$0.0645457\pi$
$659$			10.3397i			0.402779i	−0.979511	+	0.201390i	$0.935454\pi$
$660$		0			0
$661$	−12.2776	−	7.08846i	−0.477542	−	0.275709i	0.241850	−	0.970314i	$-0.422246\pi$
$661$	−12.2776	−	7.08846i	−0.477542	−	0.275709i	−0.719392	+	0.694605i	$0.755579\pi$
$662$	−12.9282	−	48.2487i	−0.502469	−	1.87524i
$663$	5.46410	+	1.46410i	0.212208	+	0.0568610i
$664$	−2.26795			−0.0880135
$665$		0			0
$666$	6.92820			0.268462
$667$	20.8923	+	5.59808i	0.808953	+	0.216758i
$668$	−6.82051	−	25.4545i	−0.263893	−	0.984864i
$669$	−14.4904	−	8.36603i	−0.560230	−	0.323449i
$670$		0			0
$671$		−	6.19615i		−	0.239200i
$672$	−29.3205	−	25.3923i	−1.13106	−	0.979529i
$673$	16.3923	+	16.3923i	0.631877	+	0.631877i	0.948539	−	0.316662i	$-0.102562\pi$
$673$	16.3923	+	16.3923i	0.631877	+	0.631877i	−0.316662	+	0.948539i	$0.602562\pi$
$674$	−38.9545	+	22.4904i	−1.50047	+	0.866297i
$675$		0			0
$676$	−4.33013	+	7.50000i	−0.166543	+	0.288462i
$677$	−1.85641	+	6.92820i	−0.0713475	+	0.266272i	−0.992380	−	0.123213i	$-0.960680\pi$
$677$	−1.85641	+	6.92820i	−0.0713475	+	0.266272i	0.921033	+	0.389485i	$0.127347\pi$
$678$	−15.9282	+	15.9282i	−0.611719	+	0.611719i
$679$	12.9545	−	26.6865i	0.497147	−	1.02414i
$680$		0			0
$681$	−0.0980762	−	0.169873i	−0.00375829	−	0.00650955i
$682$	−0.732051	+	0.196152i	−0.0280317	+	0.00751106i
$683$	18.4282	−	4.93782i	0.705136	−	0.188941i	0.111606	−	0.993753i	$-0.464401\pi$
$683$	18.4282	−	4.93782i	0.705136	−	0.188941i	0.593530	+	0.804812i	$0.297734\pi$
$684$	−1.73205	−	3.00000i	−0.0662266	−	0.114708i
$685$		0			0
$686$	24.0885	+	26.4545i	0.919702	+	1.01004i
$687$	3.26795	−	3.26795i	0.124680	−	0.124680i
$688$	9.52628	−	35.5526i	0.363186	−	1.35543i
$689$	10.0000	−	17.3205i	0.380970	−	0.659859i
$690$		0			0
$691$	−24.9737	+	14.4186i	−0.950045	+	0.548509i	−0.893095	−	0.449868i	$-0.851471\pi$
$691$	−24.9737	+	14.4186i	−0.950045	+	0.548509i	−0.0569502	+	0.998377i	$0.518138\pi$
$692$	−28.7321	−	28.7321i	−1.09223	−	1.09223i
$693$	−1.33975	+	0.464102i	−0.0508927	+	0.0176298i
$694$			15.5885i			0.591730i
$695$		0			0
$696$	2.59808	+	1.50000i	0.0984798	+	0.0568574i
$697$	−0.124356	−	0.464102i	−0.00471031	−	0.0175791i
$698$	−18.1603	−	4.86603i	−0.687376	−	0.184182i
$699$	3.46410			0.131024
$700$		0			0
$701$	−23.7321			−0.896347			−0.448174	−	0.893947i	$-0.647925\pi$
$701$	−23.7321			−0.896347			−0.448174	+	0.893947i	$0.647925\pi$
$702$	−23.1244	−	6.19615i	−0.872773	−	0.233859i
$703$	−3.46410	−	12.9282i	−0.130651	−	0.487596i
$704$	3.63397	+	2.09808i	0.136961	+	0.0790742i
$705$		0			0
$706$		−	10.7321i		−	0.403906i
$707$	−5.86603	+	30.4808i	−0.220615	+	1.14635i
$708$	−5.19615	−	5.19615i	−0.195283	−	0.195283i
$709$	6.99038	−	4.03590i	0.262529	−	0.151571i	−0.362959	−	0.931805i	$-0.618233\pi$
$709$	6.99038	−	4.03590i	0.262529	−	0.151571i	0.625488	+	0.780234i	$0.284900\pi$
$710$		0			0
$711$	−2.46410	+	4.26795i	−0.0924110	+	0.160061i
$712$	−2.23205	+	8.33013i	−0.0836496	+	0.312185i
$713$	2.73205	−	2.73205i	0.102316	−	0.102316i
$714$	−8.46410	+	5.73205i	−0.316761	+	0.214517i
$715$		0			0
$716$	−17.1962	−	29.7846i	−0.642650	−	1.11310i
$717$	−34.3205	+	9.19615i	−1.28172	+	0.343437i
$718$	−26.5885	+	7.12436i	−0.992272	+	0.265879i
$719$	−3.70577	−	6.41858i	−0.138202	−	0.239373i	0.788614	−	0.614888i	$-0.210799\pi$
$719$	−3.70577	−	6.41858i	−0.138202	−	0.239373i	−0.926816	+	0.375516i	$0.877466\pi$
$720$		0			0
$721$	−0.437822	−	6.09808i	−0.0163053	−	0.227104i
$722$	15.7583	−	15.7583i	0.586464	−	0.586464i
$723$	−8.39230	+	31.3205i	−0.312113	+	1.16482i
$724$	−7.96410	+	13.7942i	−0.295984	+	0.512658i
$725$		0			0
$726$	−33.8205	+	19.5263i	−1.25520	+	0.724688i
$727$	−4.90192	−	4.90192i	−0.181802	−	0.181802i	0.610338	−	0.792141i	$-0.291033\pi$
$727$	−4.90192	−	4.90192i	−0.181802	−	0.181802i	−0.792141	+	0.610338i	$0.791033\pi$
$728$	−1.26795	−	3.66025i	−0.0469933	−	0.135658i
$729$			17.5885i			0.651424i
$730$		0			0
$731$	−7.39230	−	4.26795i	−0.273414	−	0.157856i
$732$	−7.33013	−	27.3564i	−0.270929	−	1.01112i
$733$	9.83013	+	2.63397i	0.363084	+	0.0972881i	0.435749	−	0.900068i	$-0.356484\pi$
$733$	9.83013	+	2.63397i	0.363084	+	0.0972881i	−0.0726647	+	0.997356i	$0.523150\pi$
$734$	−3.73205			−0.137753
$735$		0			0
$736$	−54.7128			−2.01674
$737$	−0.830127	−	0.222432i	−0.0305781	−	0.00819338i
$738$	−0.169873	−	0.633975i	−0.00625311	−	0.0233369i
$739$	7.43782	+	4.29423i	0.273605	+	0.157966i	0.630525	−	0.776169i	$-0.282840\pi$
$739$	7.43782	+	4.29423i	0.273605	+	0.157966i	−0.356920	+	0.934135i	$0.616173\pi$
$740$		0			0
$741$		−	14.9282i		−	0.548401i
$742$	11.8301	+	34.1506i	0.434298	+	1.25371i
$743$	14.8301	+	14.8301i	0.544065	+	0.544065i	0.924718	−	0.380653i	$-0.124301\pi$
$743$	14.8301	+	14.8301i	0.544065	+	0.544065i	−0.380653	+	0.924718i	$0.624301\pi$
$744$	0.464102	−	0.267949i	0.0170148	−	0.00982349i
$745$		0			0
$746$	15.9282	−	27.5885i	0.583173	−	1.01009i
$747$	−0.830127	+	3.09808i	−0.0303728	+	0.113353i
$748$	0.928203	−	0.928203i	0.0339385	−	0.0339385i
$749$	−1.68653	−	23.4904i	−0.0616246	−	0.858320i
$750$		0			0
$751$	−7.19615	−	12.4641i	−0.262591	−	0.454822i	0.704338	−	0.709864i	$-0.251244\pi$
$751$	−7.19615	−	12.4641i	−0.262591	−	0.454822i	−0.966930	+	0.255043i	$0.917910\pi$
$752$	2.83013	−	0.758330i	0.103204	−	0.0276535i
$753$	10.9282	−	2.92820i	0.398246	−	0.106710i
$754$	−8.19615	−	14.1962i	−0.298486	−	0.516993i
$755$		0			0
$756$	16.6244	−	11.2583i	0.604622	−	0.409462i
$757$	−9.26795	+	9.26795i	−0.336849	+	0.336849i	−0.855180	−	0.518331i	$-0.826554\pi$
$757$	−9.26795	+	9.26795i	−0.336849	+	0.336849i	0.518331	+	0.855180i	$0.326554\pi$
$758$	9.83013	−	36.6865i	0.357046	−	1.33251i
$759$	−5.09808	+	8.83013i	−0.185048	+	0.320513i
$760$		0			0
$761$	11.0718	−	6.39230i	0.401352	−	0.231721i	−0.285715	−	0.958315i	$-0.592231\pi$
$761$	11.0718	−	6.39230i	0.401352	−	0.231721i	0.687067	+	0.726594i	$0.258898\pi$
$762$	24.1244	+	24.1244i	0.873933	+	0.873933i
$763$	7.06218	−	36.6962i	0.255668	−	1.32849i
$764$		−	28.9808i		−	1.04849i
$765$		0			0
$766$	48.8205	+	28.1865i	1.76396	+	1.01842i
$767$	−1.60770	−	6.00000i	−0.0580505	−	0.216647i
$768$	−36.1865	−	9.69615i	−1.30577	−	0.349880i
$769$	47.1769			1.70124			0.850622	−	0.525778i	$-0.176226\pi$
$769$	47.1769			1.70124			0.850622	+	0.525778i	$0.176226\pi$
$770$		0			0
$771$	−5.46410			−0.196785
$772$	5.36603	+	1.43782i	0.193127	+	0.0517484i
$773$	−4.80385	−	17.9282i	−0.172782	−	0.644833i	−0.996919	−	0.0784412i	$-0.975006\pi$
$773$	−4.80385	−	17.9282i	−0.172782	−	0.644833i	0.824136	−	0.566391i	$-0.191661\pi$
$774$	−10.0981	−	5.83013i	−0.362968	−	0.209560i
$775$		0			0
$776$		−	5.80385i		−	0.208346i
$777$	−23.6603	+	8.19615i	−0.848807	+	0.294035i
$778$	12.1962	+	12.1962i	0.437253	+	0.437253i
$779$	−1.09808	+	0.633975i	−0.0393427	+	0.0227145i
$780$		0			0
$781$	−1.73205	+	3.00000i	−0.0619777	+	0.107348i
$782$	−3.73205	+	13.9282i	−0.133458	+	0.498072i
$783$	−9.29423	+	9.29423i	−0.332149	+	0.332149i
$784$	29.0167	+	11.5981i	1.03631	+	0.414217i
$785$		0			0
$786$	15.9282	+	27.5885i	0.568140	+	0.984048i
$787$	19.3564	−	5.18653i	0.689981	−	0.184880i	0.103243	−	0.994656i	$-0.467078\pi$
$787$	19.3564	−	5.18653i	0.689981	−	0.184880i	0.586739	+	0.809776i	$0.300412\pi$
$788$	−33.4186	+	8.95448i	−1.19049	+	0.318990i
$789$	8.06218	+	13.9641i	0.287021	+	0.497135i
$790$		0			0
$791$	6.97372	−	14.3660i	0.247957	−	0.510797i
$792$	−0.196152	+	0.196152i	−0.00696997	+	0.00696997i
$793$	6.19615	−	23.1244i	0.220032	−	0.821170i
$794$	20.0263	−	34.6865i	0.710706	−	1.23098i
$795$		0			0
$796$	37.3923	−	21.5885i	1.32534	−	0.765183i
$797$	29.4641	+	29.4641i	1.04367	+	1.04367i	0.999002	+	0.0446702i	$0.0142237\pi$
$797$	29.4641	+	29.4641i	1.04367	+	1.04367i	0.0446702	+	0.999002i	$0.485776\pi$
$798$	20.3923	+	17.6603i	0.721880	+	0.625166i
$799$		−	0.679492i		−	0.0240387i
$800$		0			0
$801$	10.5622	+	6.09808i	0.373196	+	0.215465i
$802$	−5.50000	−	20.5263i	−0.194212	−	0.724808i
$803$	2.53590	+	0.679492i	0.0894899	+	0.0239787i
$804$	−3.92820			−0.138537
$805$		0			0
$806$	−2.92820			−0.103142
$807$	9.06218	+	2.42820i	0.319004	+	0.0854768i
$808$	1.57180	+	5.86603i	0.0552956	+	0.206366i
$809$	−21.9904	−	12.6962i	−0.773141	−	0.446373i	0.0608532	−	0.998147i	$-0.480618\pi$
$809$	−21.9904	−	12.6962i	−0.773141	−	0.446373i	−0.833994	+	0.551774i	$0.813951\pi$
$810$		0			0
$811$			29.0718i			1.02085i	0.859923	+	0.510424i	$0.170512\pi$
$811$			29.0718i			1.02085i	−0.859923	+	0.510424i	$0.829488\pi$
$812$	13.5000	+	2.59808i	0.473757	+	0.0911746i
$813$	−33.7846	−	33.7846i	−1.18488	−	1.18488i
$814$	6.00000	−	3.46410i	0.210300	−	0.121417i
$815$		0			0
$816$	−4.46410	+	7.73205i	−0.156275	+	0.270676i
$817$	−5.83013	+	21.7583i	−0.203970	+	0.761228i
$818$	−9.36603	+	9.36603i	−0.327475	+	0.327475i
$819$	−5.46410	+	0.392305i	−0.190931	+	0.0137082i
$820$		0			0
$821$	7.33975	+	12.7128i	0.256159	+	0.443680i	0.965210	−	0.261477i	$-0.0842096\pi$
$821$	7.33975	+	12.7128i	0.256159	+	0.443680i	−0.709051	+	0.705157i	$0.750876\pi$
$822$	39.0526	−	10.4641i	1.36211	−	0.364977i
$823$	−24.6962	+	6.61731i	−0.860854	+	0.230665i	−0.662129	−	0.749390i	$-0.730347\pi$
$823$	−24.6962	+	6.61731i	−0.860854	+	0.230665i	−0.198725	+	0.980055i	$0.563680\pi$
$824$	−0.598076	−	1.03590i	−0.0208350	−	0.0360872i
$825$		0			0
$826$	10.0981	+	4.90192i	0.351357	+	0.170560i
$827$	3.77757	−	3.77757i	0.131359	−	0.131359i	−0.638370	−	0.769729i	$-0.720391\pi$
$827$	3.77757	−	3.77757i	0.131359	−	0.131359i	0.769729	+	0.638370i	$0.220391\pi$
$828$	−2.36603	+	8.83013i	−0.0822251	+	0.306868i
$829$	10.7321	−	18.5885i	0.372740	−	0.645604i	−0.617246	−	0.786770i	$-0.711752\pi$
$829$	10.7321	−	18.5885i	0.372740	−	0.645604i	0.989986	+	0.141166i	$0.0450852\pi$
$830$		0			0
$831$	−33.5885	+	19.3923i	−1.16517	+	0.672712i
$832$	11.4641	+	11.4641i	0.397446	+	0.397446i
$833$	4.33975	−	5.80385i	0.150363	−	0.201091i
$834$		−	43.5167i		−	1.50686i
$835$		0			0
$836$	−3.00000	−	1.73205i	−0.103757	−	0.0599042i
$837$	0.607695	+	2.26795i	0.0210050	+	0.0783918i
$838$	7.19615	+	1.92820i	0.248587	+	0.0666087i
$839$	−31.1244			−1.07453			−0.537266	−	0.843413i	$-0.680543\pi$
$839$	−31.1244			−1.07453			−0.537266	+	0.843413i	$0.680543\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	−64.6769	−	17.3301i	−2.22891	−	0.597236i
$843$	6.46410	+	24.1244i	0.222635	+	0.830887i
$844$	15.2942	+	8.83013i	0.526449	+	0.303946i
$845$		0			0
$846$		−	0.928203i		−	0.0319123i
$847$	18.1244	−	20.9282i	0.622760	−	0.719102i
$848$	22.3205	+	22.3205i	0.766489	+	0.766489i
$849$	−45.8827	+	26.4904i	−1.57469	+	0.909148i
$850$		0			0
$851$	−17.6603	+	30.5885i	−0.605386	+	1.04856i
$852$	−4.09808	+	15.2942i	−0.140398	+	0.523972i
$853$	6.12436	−	6.12436i	0.209694	−	0.209694i	−0.594443	−	0.804137i	$-0.702628\pi$
$853$	6.12436	−	6.12436i	0.209694	−	0.209694i	0.804137	+	0.594443i	$0.202628\pi$
$854$	24.2583	+	35.8205i	0.830103	+	1.22575i
$855$		0			0
$856$	−2.30385	−	3.99038i	−0.0787439	−	0.136388i
$857$	22.0263	−	5.90192i	0.752403	−	0.201606i	0.137820	−	0.990457i	$-0.455991\pi$
$857$	22.0263	−	5.90192i	0.752403	−	0.201606i	0.614584	+	0.788851i	$0.289324\pi$
$858$	7.46410	−	2.00000i	0.254820	−	0.0682789i
$859$	10.5359	+	18.2487i	0.359480	+	0.622638i	0.987874	−	0.155257i	$-0.0496207\pi$
$859$	10.5359	+	18.2487i	0.359480	+	0.622638i	−0.628394	+	0.777895i	$0.716287\pi$
$860$		0			0
$861$	1.33013	+	1.96410i	0.0453306	+	0.0669364i
$862$	5.73205	−	5.73205i	0.195234	−	0.195234i
$863$	−8.94486	+	33.3827i	−0.304487	+	1.13636i	0.628900	+	0.777487i	$0.283506\pi$
$863$	−8.94486	+	33.3827i	−0.304487	+	1.13636i	−0.933386	+	0.358873i	$0.883161\pi$
$864$	16.6244	−	28.7942i	0.565572	−	0.979600i
$865$		0			0
$866$	−57.8827	+	33.4186i	−1.96693	+	1.13561i
$867$	−21.7583	−	21.7583i	−0.738952	−	0.738952i
$868$	1.60770	−	1.85641i	0.0545687	−	0.0630105i
$869$			4.92820i			0.167178i
$870$		0			0
$871$	−2.87564	−	1.66025i	−0.0974375	−	0.0562556i
$872$	−1.89230	−	7.06218i	−0.0640815	−	0.239156i
$873$	−7.92820	−	2.12436i	−0.268329	−	0.0718985i
$874$	38.0526			1.28715
$875$		0			0
$876$	12.0000			0.405442
$877$	15.4904	+	4.15064i	0.523073	+	0.140157i	0.510688	−	0.859766i	$-0.329391\pi$
$877$	15.4904	+	4.15064i	0.523073	+	0.140157i	0.0123853	+	0.999923i	$0.496058\pi$
$878$	15.6603	+	58.4449i	0.528508	+	1.97242i
$879$	43.5167	+	25.1244i	1.46778	+	0.847423i
$880$		0			0
$881$			52.8564i			1.78078i	0.455201	+	0.890389i	$0.349567\pi$
$881$			52.8564i			1.78078i	−0.455201	+	0.890389i	$0.650433\pi$
$882$	5.92820	−	7.92820i	0.199613	−	0.266956i
$883$	−21.9282	−	21.9282i	−0.737943	−	0.737943i	0.234237	−	0.972180i	$-0.424741\pi$
$883$	−21.9282	−	21.9282i	−0.737943	−	0.737943i	−0.972180	+	0.234237i	$0.924741\pi$
$884$	4.39230	−	2.53590i	0.147729	−	0.0852915i
$885$		0			0
$886$	−3.50000	+	6.06218i	−0.117585	+	0.203663i
$887$	9.89230	−	36.9186i	0.332151	−	1.23960i	−0.574774	−	0.818312i	$-0.694910\pi$
$887$	9.89230	−	36.9186i	0.332151	−	1.23960i	0.906925	−	0.421292i	$-0.138423\pi$
$888$	−3.46410	+	3.46410i	−0.116248	+	0.116248i
$889$	−21.7583	−	10.5622i	−0.729751	−	0.354244i
$890$		0			0
$891$	−3.90192	−	6.75833i	−0.130719	−	0.226413i
$892$	−14.4904	+	3.88269i	−0.485174	+	0.130002i
$893$	−1.73205	+	0.464102i	−0.0579609	+	0.0155306i
$894$	20.8923	+	36.1865i	0.698743	+	1.21026i
$895$		0			0
$896$	10.8301	−	0.777568i	0.361809	−	0.0259767i
$897$	−27.8564	+	27.8564i	−0.930098	+	0.930098i
$898$	2.52628	−	9.42820i	0.0843030	−	0.314623i
$899$	−0.803848	+	1.39230i	−0.0268098	+	0.0464360i
$900$		0			0
$901$	6.33975	−	3.66025i	0.211208	−	0.121941i
$902$	−0.464102	−	0.464102i	−0.0154529	−	0.0154529i
$903$	41.3827	+	7.96410i	1.37713	+	0.265029i
$904$		−	3.12436i		−	0.103915i
$905$		0			0
$906$	44.7846	+	25.8564i	1.48787	+	0.859022i
$907$	0.454483	+	1.69615i	0.0150908	+	0.0563198i	0.973061	−	0.230549i	$-0.0740522\pi$
$907$	0.454483	+	1.69615i	0.0150908	+	0.0563198i	−0.957970	+	0.286869i	$0.907386\pi$
$908$	−0.169873	−	0.0455173i	−0.00563743	−	0.00151055i
$909$	8.58846			0.284861
$910$		0			0
$911$	37.5167			1.24298			0.621491	−	0.783421i	$-0.286527\pi$
$911$	37.5167			1.24298			0.621491	+	0.783421i	$0.286527\pi$
$912$	22.7583	+	6.09808i	0.753604	+	0.201927i
$913$	0.830127	+	3.09808i	0.0274732	+	0.102531i
$914$	−53.4449	−	30.8564i	−1.76780	−	1.02064i
$915$		0			0
$916$		−	4.14359i		−	0.136908i
$917$	−17.0718	−	14.7846i	−0.563760	−	0.488231i
$918$	−6.19615	−	6.19615i	−0.204504	−	0.204504i
$919$	−39.6673	+	22.9019i	−1.30850	+	0.755465i	−0.981846	−	0.189678i	$-0.939256\pi$
$919$	−39.6673	+	22.9019i	−1.30850	+	0.755465i	−0.326657	+	0.945143i	$0.605922\pi$
$920$		0			0
$921$	12.6962	−	21.9904i	0.418352	−	0.724608i
$922$	13.1962	−	49.2487i	0.434592	−	1.62192i
$923$	−9.46410	+	9.46410i	−0.311515	+	0.311515i
$924$	−2.83013	+	5.83013i	−0.0931043	+	0.191797i
$925$		0			0
$926$	−24.2583	−	42.0167i	−0.797178	−	1.38075i
$927$	−1.63397	+	0.437822i	−0.0536668	+	0.0143800i
$928$	21.9904	−	5.89230i	0.721870	−	0.193424i
$929$	0.839746	+	1.45448i	0.0275512	+	0.0477200i	0.879472	−	0.475950i	$-0.157896\pi$
$929$	0.839746	+	1.45448i	0.0275512	+	0.0477200i	−0.851921	+	0.523670i	$0.824562\pi$
$930$		0			0
$931$	−17.7583	−	7.09808i	−0.582006	−	0.232630i
$932$	2.19615	−	2.19615i	0.0719374	−	0.0719374i
$933$	−9.36603	+	34.9545i	−0.306630	+	1.14436i
$934$	−31.3564	+	54.3109i	−1.02601	+	1.77711i
$935$		0			0
$936$	−0.928203	+	0.535898i	−0.0303393	+	0.0175164i
$937$	30.9282	+	30.9282i	1.01038	+	1.01038i	0.999946	+	0.0104348i	$0.00332156\pi$
$937$	30.9282	+	30.9282i	1.01038	+	1.01038i	0.0104348	+	0.999946i	$0.496678\pi$
$938$	5.66987	−	1.96410i	0.185128	−	0.0641302i
$939$		−	38.7846i		−	1.26569i
$940$		0			0
$941$	24.8038	+	14.3205i	0.808582	+	0.466835i	0.846463	−	0.532447i	$-0.178727\pi$
$941$	24.8038	+	14.3205i	0.808582	+	0.466835i	−0.0378810	+	0.999282i	$0.512061\pi$
$942$	23.7583	+	88.6673i	0.774088	+	2.88894i
$943$	3.23205	+	0.866025i	0.105250	+	0.0282017i
$944$	9.80385			0.319088
$945$		0			0
$946$	−11.6603			−0.379108
$947$	−43.6506	−	11.6962i	−1.41846	−	0.380074i	−0.533520	−	0.845788i	$-0.679131\pi$
$947$	−43.6506	−	11.6962i	−1.41846	−	0.380074i	−0.884935	+	0.465714i	$0.845798\pi$
$948$	5.83013	+	21.7583i	0.189354	+	0.706678i
$949$	8.78461	+	5.07180i	0.285160	+	0.164637i
$950$		0			0
$951$		−	8.92820i		−	0.289517i
$952$	0.267949	−	1.39230i	0.00868428	−	0.0451249i
$953$	10.1436	+	10.1436i	0.328583	+	0.328583i	0.852048	−	0.523464i	$-0.175361\pi$
$953$	10.1436	+	10.1436i	0.328583	+	0.328583i	−0.523464	+	0.852048i	$0.675361\pi$
$954$	8.66025	−	5.00000i	0.280386	−	0.161881i
$955$		0			0
$956$	−15.9282	+	27.5885i	−0.515155	+	0.892274i
$957$	1.09808	−	4.09808i	0.0354958	−	0.132472i
$958$	−36.7846	+	36.7846i	−1.18846	+	1.18846i
$959$	−23.7321	+	16.0718i	−0.766348	+	0.518985i
$960$		0			0
$961$	−15.3564	−	26.5981i	−0.495368	−	0.858002i
$962$	25.8564	−	6.92820i	0.833644	−	0.223374i
$963$	−6.29423	+	1.68653i	−0.202829	+	0.0543478i
$964$	14.5359	+	25.1769i	0.468170	+	0.810894i
$965$		0			0
$966$	−5.09808	−	71.0070i	−0.164028	−	2.28461i
$967$	1.43782	−	1.43782i	0.0462372	−	0.0462372i	−0.683610	−	0.729847i	$-0.739591\pi$
$967$	1.43782	−	1.43782i	0.0462372	−	0.0462372i	0.729847	+	0.683610i	$0.239591\pi$
$968$	1.40192	−	5.23205i	0.0450595	−	0.168164i
$969$	2.73205	−	4.73205i	0.0877661	−	0.152015i
$970$		0			0
$971$	42.9282	−	24.7846i	1.37763	−	0.795376i	0.385758	−	0.922600i	$-0.373940\pi$
$971$	42.9282	−	24.7846i	1.37763	−	0.795376i	0.991874	+	0.127224i	$0.0406068\pi$
$972$	−9.12436	−	9.12436i	−0.292664	−	0.292664i
$973$	10.0981	+	29.1506i	0.323729	+	0.934526i
$974$		−	16.5885i		−	0.531528i
$975$		0			0
$976$	32.7224	+	18.8923i	1.04742	+	0.604728i
$977$	11.5622	+	43.1506i	0.369907	+	1.38051i	0.860646	+	0.509204i	$0.170060\pi$
$977$	11.5622	+	43.1506i	0.369907	+	1.38051i	−0.490739	+	0.871307i	$0.663273\pi$
$978$	−20.0263	−	5.36603i	−0.640370	−	0.171587i
$979$	12.1962			0.389791
$980$		0			0
$981$	−10.3397			−0.330123
$982$	−33.0526	−	8.85641i	−1.05475	−	0.282619i
$983$	−3.88526	−	14.5000i	−0.123921	−	0.462478i	0.875878	−	0.482532i	$-0.160283\pi$
$983$	−3.88526	−	14.5000i	−0.123921	−	0.462478i	−0.999799	+	0.0200540i	$0.993616\pi$
$984$	0.401924	+	0.232051i	0.0128129	+	0.00739751i
$985$		0			0
$986$		−	6.00000i		−	0.191079i
$987$	1.09808	+	3.16987i	0.0349522	+	0.100898i
$988$	−9.46410	−	9.46410i	−0.301093	−	0.301093i
$989$	51.4808	−	29.7224i	1.63699	−	0.945118i
$990$		0			0
$991$	11.8564	−	20.5359i	0.376631	−	0.652344i	−0.613939	−	0.789354i	$-0.710416\pi$
$991$	11.8564	−	20.5359i	0.376631	−	0.652344i	0.990570	+	0.137009i	$0.0437491\pi$
$992$	1.05256	−	3.92820i	0.0334188	−	0.124721i
$993$	35.3205	−	35.3205i	1.12086	−	1.12086i
$994$	−1.73205	−	24.1244i	−0.0549373	−	0.765178i
$995$		0			0
$996$	7.33013	+	12.6962i	0.232264	+	0.402293i
$997$	−25.6865	+	6.88269i	−0.813501	+	0.217977i	−0.641503	−	0.767121i	$-0.721689\pi$
$997$	−25.6865	+	6.88269i	−0.813501	+	0.217977i	−0.171998	+	0.985097i	$0.555022\pi$
$998$	62.5429	−	16.7583i	1.97976	−	0.530476i
$999$	−10.7321	−	18.5885i	−0.339547	−	0.588113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.o.b.143.1		4
5.2	odd	4		175.2.o.a.157.1		4
5.3	odd	4		35.2.k.b.17.1	yes	4
5.4	even	2		35.2.k.a.3.1	✓	4
7.5	odd	6		175.2.o.a.68.1		4
15.8	even	4		315.2.bz.a.262.1		4
15.14	odd	2		315.2.bz.b.73.1		4
20.3	even	4		560.2.ci.b.17.1		4
20.19	odd	2		560.2.ci.a.353.1		4
35.3	even	12		245.2.f.a.97.2		4
35.4	even	6		245.2.f.a.48.2		4
35.9	even	6		245.2.l.b.68.1		4
35.12	even	12	inner	175.2.o.b.82.1		4
35.13	even	4		245.2.l.b.227.1		4
35.18	odd	12		245.2.f.b.97.2		4
35.19	odd	6		35.2.k.b.33.1	yes	4
35.23	odd	12		245.2.l.a.117.1		4
35.24	odd	6		245.2.f.b.48.2		4
35.33	even	12		35.2.k.a.12.1	yes	4
35.34	odd	2		245.2.l.a.178.1		4
105.68	odd	12		315.2.bz.b.82.1		4
105.89	even	6		315.2.bz.a.208.1		4
140.19	even	6		560.2.ci.b.33.1		4
140.103	odd	12		560.2.ci.a.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.3.1	✓	4	5.4	even	2
35.2.k.a.12.1	yes	4	35.33	even	12
35.2.k.b.17.1	yes	4	5.3	odd	4
35.2.k.b.33.1	yes	4	35.19	odd	6
175.2.o.a.68.1		4	7.5	odd	6
175.2.o.a.157.1		4	5.2	odd	4
175.2.o.b.82.1		4	35.12	even	12	inner
175.2.o.b.143.1		4	1.1	even	1	trivial
245.2.f.a.48.2		4	35.4	even	6
245.2.f.a.97.2		4	35.3	even	12
245.2.f.b.48.2		4	35.24	odd	6
245.2.f.b.97.2		4	35.18	odd	12
245.2.l.a.117.1		4	35.23	odd	12
245.2.l.a.178.1		4	35.34	odd	2
245.2.l.b.68.1		4	35.9	even	6
245.2.l.b.227.1		4	35.13	even	4
315.2.bz.a.208.1		4	105.89	even	6
315.2.bz.a.262.1		4	15.8	even	4
315.2.bz.b.73.1		4	15.14	odd	2
315.2.bz.b.82.1		4	105.68	odd	12
560.2.ci.a.257.1		4	140.103	odd	12
560.2.ci.a.353.1		4	20.19	odd	2
560.2.ci.b.17.1		4	20.3	even	4
560.2.ci.b.33.1		4	140.19	even	6

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86603 + 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(1.50000 + 0.866025i) q^{4} +3.73205i q^{6} +(-0.866025 - 2.50000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(-0.633975 + 0.366025i) q^{9} +O(q^{10})\)	\(q+(1.86603 + 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(1.50000 + 0.866025i) q^{4} +3.73205i q^{6} +(-0.866025 - 2.50000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(-0.633975 + 0.366025i) q^{9} +(-0.366025 + 0.633975i) q^{11} +(-0.866025 + 3.23205i) q^{12} +(-2.00000 + 2.00000i) q^{13} +(-0.366025 - 5.09808i) q^{14} +(-2.23205 - 3.86603i) q^{16} +(-1.00000 + 0.267949i) q^{17} +(-1.36603 + 0.366025i) q^{18} +(1.36603 + 2.36603i) q^{19} +(4.23205 - 2.86603i) q^{21} +(-1.00000 + 1.00000i) q^{22} +(1.86603 - 6.96410i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.73205 + 2.73205i) q^{26} +(3.09808 + 3.09808i) q^{27} +(0.866025 - 4.50000i) q^{28} +3.00000i q^{29} +(0.464102 + 0.267949i) q^{31} +(-1.96410 - 7.33013i) q^{32} +(-1.36603 - 0.366025i) q^{33} -2.00000 q^{34} -1.26795 q^{36} +(-4.73205 - 1.26795i) q^{37} +(1.36603 + 5.09808i) q^{38} +(-4.73205 - 2.73205i) q^{39} +0.464102i q^{41} +(9.33013 - 3.23205i) q^{42} +(5.83013 + 5.83013i) q^{43} +(-1.09808 + 0.633975i) q^{44} +(6.96410 - 12.0622i) q^{46} +(-0.169873 + 0.633975i) q^{47} +(6.09808 - 6.09808i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(-4.73205 + 1.26795i) q^{52} +(-6.83013 + 1.83013i) q^{53} +(4.23205 + 7.33013i) q^{54} +(-0.598076 + 1.23205i) q^{56} +(-3.73205 + 3.73205i) q^{57} +(-1.50000 + 5.59808i) q^{58} +(-1.09808 + 1.90192i) q^{59} +(-7.33013 + 4.23205i) q^{61} +(0.732051 + 0.732051i) q^{62} +(1.46410 + 1.26795i) q^{63} -5.73205i q^{64} +(-2.36603 - 1.36603i) q^{66} +(0.303848 + 1.13397i) q^{67} +(-1.73205 - 0.464102i) q^{68} +13.9282 q^{69} +4.73205 q^{71} +(0.366025 + 0.0980762i) q^{72} +(-0.928203 - 3.46410i) q^{73} +(-8.19615 - 4.73205i) q^{74} +4.73205i q^{76} +(1.90192 + 0.366025i) q^{77} +(-7.46410 - 7.46410i) q^{78} +(5.83013 - 3.36603i) q^{79} +(-5.33013 + 9.23205i) q^{81} +(-0.232051 + 0.866025i) q^{82} +(3.09808 - 3.09808i) q^{83} +(8.83013 - 0.633975i) q^{84} +(7.96410 + 13.7942i) q^{86} +(-5.59808 + 1.50000i) q^{87} +(0.366025 - 0.0980762i) q^{88} +(-8.33013 - 14.4282i) q^{89} +(6.73205 + 3.26795i) q^{91} +(8.83013 - 8.83013i) q^{92} +(-0.267949 + 1.00000i) q^{93} +(-0.633975 + 1.09808i) q^{94} +(12.6962 - 7.33013i) q^{96} +(7.92820 + 7.92820i) q^{97} +(-12.4282 + 5.33013i) q^{98} -0.535898i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^8 - 6 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{8} - 6 q^{9} + 2 q^{11} - 8 q^{13} + 2 q^{14} - 2 q^{16} - 4 q^{17} - 2 q^{18} + 2 q^{19} + 10 q^{21} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 12 q^{26} + 2 q^{27} - 12 q^{31} + 6 q^{32} - 2 q^{33} - 8 q^{34} - 12 q^{36} - 12 q^{37} + 2 q^{38} - 12 q^{39} + 20 q^{42} + 6 q^{43} + 6 q^{44} + 14 q^{46} - 18 q^{47} + 14 q^{48} - 22 q^{49} - 4 q^{51} - 12 q^{52} - 10 q^{53} + 10 q^{54} + 8 q^{56} - 8 q^{57} - 6 q^{58} + 6 q^{59} - 12 q^{61} - 4 q^{62} - 8 q^{63} - 6 q^{66} + 22 q^{67} + 28 q^{69} + 12 q^{71} - 2 q^{72} + 24 q^{73} - 12 q^{74} + 18 q^{77} - 16 q^{78} + 6 q^{79} - 4 q^{81} + 6 q^{82} + 2 q^{83} + 18 q^{84} + 18 q^{86} - 12 q^{87} - 2 q^{88} - 16 q^{89} + 20 q^{91} + 18 q^{92} - 8 q^{93} - 6 q^{94} + 30 q^{96} + 4 q^{97} - 22 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^8 - 6 * q^9 + 2 * q^11 - 8 * q^13 + 2 * q^14 - 2 * q^16 - 4 * q^17 - 2 * q^18 + 2 * q^19 + 10 * q^21 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 12 * q^26 + 2 * q^27 - 12 * q^31 + 6 * q^32 - 2 * q^33 - 8 * q^34 - 12 * q^36 - 12 * q^37 + 2 * q^38 - 12 * q^39 + 20 * q^42 + 6 * q^43 + 6 * q^44 + 14 * q^46 - 18 * q^47 + 14 * q^48 - 22 * q^49 - 4 * q^51 - 12 * q^52 - 10 * q^53 + 10 * q^54 + 8 * q^56 - 8 * q^57 - 6 * q^58 + 6 * q^59 - 12 * q^61 - 4 * q^62 - 8 * q^63 - 6 * q^66 + 22 * q^67 + 28 * q^69 + 12 * q^71 - 2 * q^72 + 24 * q^73 - 12 * q^74 + 18 * q^77 - 16 * q^78 + 6 * q^79 - 4 * q^81 + 6 * q^82 + 2 * q^83 + 18 * q^84 + 18 * q^86 - 12 * q^87 - 2 * q^88 - 16 * q^89 + 20 * q^91 + 18 * q^92 - 8 * q^93 - 6 * q^94 + 30 * q^96 + 4 * q^97 - 22 * q^98

Introduction

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