LMFDB - Embedded newform 175.2.o.a.157.1

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			157.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	175.157
Dual form			175.2.o.a.68.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	1.86603i	−0.353553	+	1.31948i	0.528742	+	0.848783i	$0.322664\pi$
$2$	−0.500000	+	1.86603i	−0.353553	+	1.31948i	−0.882295	+	0.470696i	$0.844003\pi$
$3$	1.86603	−	0.500000i	1.07735	−	0.288675i	0.323840	−	0.946112i	$-0.395026\pi$
$3$	1.86603	−	0.500000i	1.07735	−	0.288675i	0.753510	+	0.657437i	$0.228359\pi$
$4$	−1.50000	−	0.866025i	−0.750000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			3.73205i			1.52360i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$	−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	$0.201867\pi$
$12$	−3.23205	−	0.866025i	−0.933013	−	0.250000i
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	0.927794	−	0.373094i	$-0.121703\pi$
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	−0.373094	+	0.927794i	$0.621703\pi$
$14$	0.366025	+	5.09808i	0.0978244	+	1.36252i
$15$		0			0
$16$	−2.23205	−	3.86603i	−0.558013	−	0.966506i
$17$	−0.267949	−	1.00000i	−0.0649872	−	0.242536i	0.925790	−	0.378039i	$-0.123401\pi$
$17$	−0.267949	−	1.00000i	−0.0649872	−	0.242536i	−0.990777	+	0.135503i	$0.956735\pi$
$18$	0.366025	+	1.36603i	0.0862730	+	0.321975i
$19$	−1.36603	−	2.36603i	−0.313388	−	0.542803i	0.665706	−	0.746214i	$-0.268131\pi$
$19$	−1.36603	−	2.36603i	−0.313388	−	0.542803i	−0.979093	+	0.203411i	$0.934797\pi$
$20$		0			0
$21$	4.23205	−	2.86603i	0.923509	−	0.625418i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	−6.96410	−	1.86603i	−1.45212	−	0.389093i	−0.555357	−	0.831612i	$-0.687418\pi$
$23$	−6.96410	−	1.86603i	−1.45212	−	0.389093i	−0.896759	+	0.442519i	$0.854085\pi$
$24$	−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
$28$	−4.50000	−	0.866025i	−0.850420	−	0.163663i
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$		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	$0.651342\pi$
$32$	7.33013	−	1.96410i	1.29580	−	0.347207i
$33$	−0.366025	+	1.36603i	−0.0637168	+	0.237795i
$34$	2.00000			0.342997
$35$		0			0
$36$	−1.26795			−0.211325
$37$	1.26795	−	4.73205i	0.208450	−	0.777944i	−0.779921	−	0.625878i	$-0.784741\pi$
$37$	1.26795	−	4.73205i	0.208450	−	0.777944i	0.988370	−	0.152066i	$-0.0485927\pi$
$38$	5.09808	−	1.36603i	0.827017	−	0.221599i
$39$	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	$0.988462\pi$
$42$	3.23205	+	9.33013i	0.498716	+	1.43967i
$43$	5.83013	−	5.83013i	0.889086	−	0.889086i	−0.105349	−	0.994435i	$-0.533596\pi$
$43$	5.83013	−	5.83013i	0.889086	−	0.889086i	0.994435	+	0.105349i	$0.0335960\pi$
$44$	1.09808	−	0.633975i	0.165541	−	0.0955753i
$45$		0			0
$46$	6.96410	−	12.0622i	1.02680	−	1.77847i
$47$	−0.633975	−	0.169873i	−0.0924747	−	0.0247785i	0.212285	−	0.977208i	$-0.431909\pi$
$47$	−0.633975	−	0.169873i	−0.0924747	−	0.0247785i	−0.304760	+	0.952429i	$0.598576\pi$
$48$	−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
$52$	−1.26795	−	4.73205i	−0.175833	−	0.656217i
$53$	1.83013	+	6.83013i	0.251387	+	0.938190i	0.970065	+	0.242846i	$0.0780811\pi$
$53$	1.83013	+	6.83013i	0.251387	+	0.938190i	−0.718677	+	0.695344i	$0.755252\pi$
$54$	−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
$58$	5.59808	+	1.50000i	0.735063	+	0.196960i
$59$	1.09808	−	1.90192i	0.142957	−	0.247609i	−0.785652	−	0.618669i	$-0.787672\pi$
$59$	1.09808	−	1.90192i	0.142957	−	0.247609i	0.928609	+	0.371060i	$0.121005\pi$
$60$		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
$63$	1.26795	−	1.46410i	0.159747	−	0.184459i
$64$			5.73205i			0.716506i
$65$		0			0
$66$	−2.36603	−	1.36603i	−0.291238	−	0.168146i
$67$	−1.13397	+	0.303848i	−0.138537	+	0.0371209i	−0.327421	−	0.944878i	$-0.606180\pi$
$67$	−1.13397	+	0.303848i	−0.138537	+	0.0371209i	0.188884	+	0.981999i	$0.439513\pi$
$68$	−0.464102	+	1.73205i	−0.0562806	+	0.210042i
$69$	−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	$0.409402\pi$
$72$	−0.0980762	+	0.366025i	−0.0115584	+	0.0431365i
$73$	−3.46410	+	0.928203i	−0.405442	+	0.108638i	−0.455776	−	0.890094i	$-0.650638\pi$
$73$	−3.46410	+	0.928203i	−0.405442	+	0.108638i	0.0503336	+	0.998732i	$0.483972\pi$
$74$	8.19615	+	4.73205i	0.952783	+	0.550090i
$75$		0			0
$76$			4.73205i			0.542803i
$77$	−0.366025	+	1.90192i	−0.0417125	+	0.216744i
$78$	−7.46410	+	7.46410i	−0.845143	+	0.845143i
$79$	−5.83013	+	3.36603i	−0.655941	+	0.378707i	−0.790728	−	0.612167i	$-0.790298\pi$
$79$	−5.83013	+	3.36603i	−0.655941	+	0.378707i	0.134788	+	0.990874i	$0.456965\pi$
$80$		0			0
$81$	−5.33013	+	9.23205i	−0.592236	+	1.02578i
$82$	−0.866025	−	0.232051i	−0.0956365	−	0.0256257i
$83$	−3.09808	−	3.09808i	−0.340058	−	0.340058i	0.516331	−	0.856389i	$-0.327297\pi$
$83$	−3.09808	−	3.09808i	−0.340058	−	0.340058i	−0.856389	+	0.516331i	$0.827297\pi$
$84$	−8.83013	+	0.633975i	−0.963446	+	0.0691723i
$85$		0			0
$86$	7.96410	+	13.7942i	0.858791	+	1.48747i
$87$	−1.50000	−	5.59808i	−0.160817	−	0.600177i
$88$	−0.0980762	−	0.366025i	−0.0104550	−	0.0390184i
$89$	8.33013	+	14.4282i	0.882992	+	1.52939i	0.847998	+	0.529999i	$0.177808\pi$
$89$	8.33013	+	14.4282i	0.882992	+	1.52939i	0.0349934	+	0.999388i	$0.488859\pi$
$90$		0			0
$91$	6.73205	+	3.26795i	0.705711	+	0.342574i
$92$	8.83013	+	8.83013i	0.920604	+	0.920604i
$93$	1.00000	+	0.267949i	0.103695	+	0.0277850i
$94$	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	$-0.942752\pi$
$97$	−7.92820	+	7.92820i	−0.804987	+	0.804987i	0.178883	+	0.983870i	$0.442752\pi$
$98$	5.33013	+	12.4282i	0.538424	+	1.25544i
$99$			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	$0.865059\pi$
$102$	3.73205	−	1.00000i	0.369528	−	0.0990148i
$103$	0.598076	−	2.23205i	0.0589302	−	0.219931i	−0.930181	−	0.367102i	$-0.880350\pi$
$103$	0.598076	−	2.23205i	0.0589302	−	0.219931i	0.989111	+	0.147171i	$0.0470168\pi$
$104$	−1.46410			−0.143567
$105$		0			0
$106$	−13.6603			−1.32680
$107$	−2.30385	+	8.59808i	−0.222721	+	0.831207i	0.760583	+	0.649240i	$0.224913\pi$
$107$	−2.30385	+	8.59808i	−0.222721	+	0.831207i	−0.983305	+	0.181967i	$0.941754\pi$
$108$	7.33013	−	1.96410i	0.705342	−	0.188996i
$109$	−12.2321	−	7.06218i	−1.17162	−	0.676434i	−0.217557	−	0.976048i	$-0.569809\pi$
$109$	−12.2321	−	7.06218i	−1.17162	−	0.676434i	−0.954061	+	0.299614i	$0.903142\pi$
$110$		0			0
$111$		−	9.46410i		−	0.898293i
$112$	−8.92820	−	7.73205i	−0.843636	−	0.730610i
$113$	4.26795	−	4.26795i	0.401495	−	0.401495i	−0.477265	−	0.878760i	$-0.658372\pi$
$113$	4.26795	−	4.26795i	0.401495	−	0.401495i	0.878760	+	0.477265i	$0.158372\pi$
$114$	8.83013	−	5.09808i	0.827017	−	0.477479i
$115$		0			0
$116$	−2.59808	+	4.50000i	−0.241225	+	0.417815i
$117$	2.00000	+	0.535898i	0.184900	+	0.0495438i
$118$	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
$122$	−4.23205	−	15.7942i	−0.383152	−	1.42994i
$123$	0.232051	+	0.866025i	0.0209233	+	0.0780869i
$124$	−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	0.933132	−	0.359535i	$-0.117065\pi$
$127$	6.46410	+	6.46410i	0.573596	+	0.573596i	−0.359535	+	0.933132i	$0.617065\pi$
$128$	3.96410	+	1.06218i	0.350380	+	0.0938841i
$129$	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
$133$	−5.46410	−	4.73205i	−0.473798	−	0.410321i
$134$		−	2.26795i		−	0.195921i
$135$		0			0
$136$	0.464102	+	0.267949i	0.0397964	+	0.0229765i
$137$	10.4641	−	2.80385i	0.894009	−	0.239549i	0.217567	−	0.976045i	$-0.430188\pi$
$137$	10.4641	−	2.80385i	0.894009	−	0.239549i	0.676441	+	0.736496i	$0.263521\pi$
$138$	6.96410	−	25.9904i	0.592824	−	2.21245i
$139$	11.6603			0.989010			0.494505	−	0.869175i	$-0.335349\pi$
$139$	11.6603			0.989010			0.494505	+	0.869175i	$0.335349\pi$
$140$		0			0
$141$	−1.26795			−0.106781
$142$	−2.36603	+	8.83013i	−0.198552	+	0.741008i
$143$	−2.00000	+	0.535898i	−0.167248	+	0.0448141i
$144$	−2.83013	−	1.63397i	−0.235844	−	0.136165i
$145$		0			0
$146$		−	6.92820i		−	0.573382i
$147$	8.09808	−	10.8301i	0.667918	−	0.893254i
$148$	−6.00000	+	6.00000i	−0.493197	+	0.493197i
$149$	−9.69615	+	5.59808i	−0.794340	+	0.458612i	−0.841488	−	0.540276i	$-0.818320\pi$
$149$	−9.69615	+	5.59808i	−0.794340	+	0.458612i	0.0471484	+	0.998888i	$0.484987\pi$
$150$		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	$-0.0239980\pi$
$152$	1.36603	+	0.366025i	0.110799	+	0.0296886i
$153$	−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
$157$	6.36603	+	23.7583i	0.508064	+	1.89612i	0.438948	+	0.898513i	$0.355351\pi$
$157$	6.36603	+	23.7583i	0.508064	+	1.89612i	0.0691164	+	0.997609i	$0.477982\pi$
$158$	−3.36603	−	12.5622i	−0.267787	−	0.999393i
$159$	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
$163$	5.36603	+	1.43782i	0.420300	+	0.112619i	0.462769	−	0.886479i	$-0.346856\pi$
$163$	5.36603	+	1.43782i	0.420300	+	0.112619i	−0.0424696	+	0.999098i	$0.513523\pi$
$164$	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	$-0.549652\pi$
$167$	10.7583	−	10.7583i	0.832505	−	0.832505i	0.987859	+	0.155354i	$0.0496519\pi$
$168$	−0.500000	+	2.59808i	−0.0385758	+	0.200446i
$169$		−	5.00000i		−	0.384615i
$170$		0			0
$171$	−1.73205	−	1.00000i	−0.132453	−	0.0764719i
$172$	−13.7942	+	3.69615i	−1.05180	+	0.281829i
$173$	−6.07180	+	22.6603i	−0.461630	+	1.72283i	0.206197	+	0.978511i	$0.433891\pi$
$173$	−6.07180	+	22.6603i	−0.461630	+	1.72283i	−0.667827	+	0.744317i	$0.732775\pi$
$174$	11.1962			0.848778
$175$		0			0
$176$	3.26795			0.246331
$177$	1.09808	−	4.09808i	0.0825365	−	0.308030i
$178$	−31.0885	+	8.33013i	−2.33018	+	0.624369i
$179$	17.1962	+	9.92820i	1.28530	+	0.742069i	0.977812	−	0.209483i	$-0.0671781\pi$
$179$	17.1962	+	9.92820i	1.28530	+	0.742069i	0.307488	+	0.951552i	$0.400511\pi$
$180$		0			0
$181$			9.19615i			0.683545i	0.939783	+	0.341772i	$0.111027\pi$
$181$			9.19615i			0.683545i	−0.939783	+	0.341772i	$0.888973\pi$
$182$	−9.46410	+	10.9282i	−0.701526	+	0.810052i
$183$	−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
$187$	0.732051	+	0.196152i	0.0535329	+	0.0143441i
$188$	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	$-0.373631\pi$
$192$	2.86603	+	10.6962i	0.206838	+	0.771928i
$193$	−0.830127	−	3.09808i	−0.0597539	−	0.223004i	0.929592	−	0.368591i	$-0.120160\pi$
$193$	−0.830127	−	3.09808i	−0.0597539	−	0.223004i	−0.989346	+	0.145587i	$0.953493\pi$
$194$	−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	−0.999980	−	0.00633876i	$-0.997982\pi$
$197$	−14.1244	−	14.1244i	−1.00632	−	1.00632i	−0.00633876	−	0.999980i	$-0.502018\pi$
$198$	−1.00000	−	0.267949i	−0.0710669	−	0.0190423i
$199$	−12.4641	+	21.5885i	−0.883557	+	1.53037i	−0.0361978	+	0.999345i	$0.511525\pi$
$199$	−12.4641	+	21.5885i	−0.883557	+	1.53037i	−0.847359	+	0.531021i	$0.821809\pi$
$200$		0			0
$201$	−1.96410	+	1.13397i	−0.138537	+	0.0799844i
$202$	16.0263	−	16.0263i	1.12761	−	1.12761i
$203$	−2.59808	−	7.50000i	−0.182349	−	0.526397i
$204$			3.46410i			0.242536i
$205$		0			0
$206$	3.86603	+	2.23205i	0.269359	+	0.155514i
$207$	−5.09808	+	1.36603i	−0.354341	+	0.0949453i
$208$	3.26795	−	12.1962i	0.226592	−	0.845651i
$209$	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	$0.385853\pi$
$212$	3.16987	−	11.8301i	0.217708	−	0.812496i
$213$	8.83013	−	2.36603i	0.605030	−	0.162117i
$214$	−14.8923	−	8.59808i	−1.01802	−	0.587752i
$215$		0			0
$216$		−	2.26795i		−	0.154314i
$217$	1.39230	+	0.267949i	0.0945158	+	0.0181896i
$218$	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
$222$	17.6603	+	4.73205i	1.18528	+	0.317594i
$223$	6.12436	+	6.12436i	0.410117	+	0.410117i	0.881779	−	0.471662i	$-0.156346\pi$
$223$	6.12436	+	6.12436i	0.410117	+	0.410117i	−0.471662	+	0.881779i	$0.656346\pi$
$224$	16.6244	−	11.2583i	1.11076	−	0.752229i
$225$		0			0
$226$	5.83013	+	10.0981i	0.387814	+	0.671714i
$227$	−0.0262794	−	0.0980762i	−0.00174423	−	0.00650955i	0.965048	−	0.262072i	$-0.0844059\pi$
$227$	−0.0262794	−	0.0980762i	−0.00174423	−	0.00650955i	−0.966792	+	0.255563i	$0.917739\pi$
$228$	2.36603	+	8.83013i	0.156694	+	0.584789i
$229$	1.19615	+	2.07180i	0.0790440	+	0.136908i	0.902838	−	0.429981i	$-0.141480\pi$
$229$	1.19615	+	2.07180i	0.0790440	+	0.136908i	−0.823794	+	0.566890i	$0.808147\pi$
$230$		0			0
$231$	0.267949	+	3.73205i	0.0176298	+	0.245551i
$232$	1.09808	+	1.09808i	0.0720922	+	0.0720922i
$233$	−1.73205	−	0.464102i	−0.113470	−	0.0304043i	0.201637	−	0.979460i	$-0.435374\pi$
$233$	−1.73205	−	0.464102i	−0.113470	−	0.0304043i	−0.315107	+	0.949056i	$0.602041\pi$
$234$	−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
$238$	5.00000	−	1.73205i	0.324102	−	0.112272i
$239$		−	18.3923i		−	1.18970i	−0.803837	−	0.594850i	$-0.797212\pi$
$239$		−	18.3923i		−	1.18970i	0.803837	−	0.594850i	$-0.202788\pi$
$240$		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	$0.484865\pi$
$242$	−19.5263	+	5.23205i	−1.25520	+	0.336329i
$243$	−1.92820	+	7.19615i	−0.123694	+	0.461633i
$244$	14.6603			0.938527
$245$		0			0
$246$	−1.73205			−0.110432
$247$	2.00000	−	7.46410i	0.127257	−	0.474929i
$248$	−0.267949	+	0.0717968i	−0.0170148	+	0.00455910i
$249$	−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	$-0.0591723\pi$
$252$	−3.16987	+	1.09808i	−0.199683	+	0.0691723i
$253$	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
$257$	−2.73205	−	0.732051i	−0.170421	−	0.0456641i	0.172600	−	0.984992i	$-0.444783\pi$
$257$	−2.73205	−	0.732051i	−0.170421	−	0.0456641i	−0.343020	+	0.939328i	$0.611450\pi$
$258$	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
$262$	4.26795	+	15.9282i	0.263675	+	0.984048i
$263$	−2.16025	−	8.06218i	−0.133207	−	0.497135i	0.866792	−	0.498670i	$-0.166178\pi$
$263$	−2.16025	−	8.06218i	−0.133207	−	0.497135i	−0.999999	+	0.00153494i	$0.999511\pi$
$264$	−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
$268$	1.96410	+	0.526279i	0.119977	+	0.0321476i
$269$	−2.42820	+	4.20577i	−0.148050	+	0.256430i	−0.930507	−	0.366275i	$-0.880633\pi$
$269$	−2.42820	+	4.20577i	−0.148050	+	0.256430i	0.782457	+	0.622705i	$0.213966\pi$
$270$		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
$273$	14.1962	+	2.73205i	0.859190	+	0.165351i
$274$			20.9282i			1.26432i
$275$		0			0
$276$	20.8923	+	12.0622i	1.25757	+	0.726058i
$277$	−19.3923	+	5.19615i	−1.16517	+	0.312207i	−0.789029	−	0.614356i	$-0.789416\pi$
$277$	−19.3923	+	5.19615i	−1.16517	+	0.312207i	−0.376141	+	0.926562i	$0.622749\pi$
$278$	−5.83013	+	21.7583i	−0.349668	+	1.30498i
$279$	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	$0.373989\pi$
$282$	0.633975	−	2.36603i	0.0377526	−	0.140895i
$283$	26.4904	−	7.09808i	1.57469	−	0.421937i	0.637413	−	0.770523i	$-0.280005\pi$
$283$	26.4904	−	7.09808i	1.57469	−	0.421937i	0.937277	+	0.348586i	$0.113338\pi$
$284$	−7.09808	−	4.09808i	−0.421193	−	0.243176i
$285$		0			0
$286$		−	4.00000i		−	0.236525i
$287$	0.401924	+	1.16025i	0.0237248	+	0.0684876i
$288$	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
$292$	6.00000	+	1.60770i	0.351123	+	0.0940832i
$293$	−18.3923	−	18.3923i	−1.07449	−	1.07449i	−0.996993	−	0.0774974i	$-0.975307\pi$
$293$	−18.3923	−	18.3923i	−1.07449	−	1.07449i	−0.0774974	−	0.996993i	$-0.524693\pi$
$294$	16.1603	+	20.5263i	0.942485	+	1.19712i
$295$		0			0
$296$	1.26795	+	2.19615i	0.0736980	+	0.127649i
$297$	−0.830127	−	3.09808i	−0.0481689	−	0.179769i
$298$	−5.59808	−	20.8923i	−0.324288	−	1.21026i
$299$	−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
$303$	−21.8923	−	5.86603i	−1.25768	−	0.336994i
$304$	−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	$-0.627614\pi$
$307$	9.29423	−	9.29423i	0.530450	−	0.530450i	0.920706	+	0.390257i	$0.127614\pi$
$308$	2.19615	−	2.53590i	0.125137	−	0.144496i
$309$		−	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	$0.488446\pi$
$312$	−2.73205	+	0.732051i	−0.154672	+	0.0414442i
$313$	−5.19615	+	19.3923i	−0.293704	+	1.09612i	0.648537	+	0.761183i	$0.275381\pi$
$313$	−5.19615	+	19.3923i	−0.293704	+	1.09612i	−0.942241	+	0.334935i	$0.891286\pi$
$314$	−47.5167			−2.68152
$315$		0			0
$316$	11.6603			0.655941
$317$	1.19615	−	4.46410i	0.0671826	−	0.250729i	−0.924165	−	0.381994i	$-0.875237\pi$
$317$	1.19615	−	4.46410i	0.0671826	−	0.250729i	0.991347	+	0.131265i	$0.0419040\pi$
$318$	−25.4904	+	6.83013i	−1.42943	+	0.383015i
$319$	1.90192	+	1.09808i	0.106487	+	0.0614805i
$320$		0			0
$321$			17.1962i			0.959796i
$322$	6.96410	−	36.1865i	0.388094	−	2.01660i
$323$	−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
$327$	−26.3564	−	7.06218i	−1.45751	−	0.390539i
$328$	−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	$-0.418242\pi$
$332$	1.96410	+	7.33013i	0.107794	+	0.402293i
$333$	−0.928203	−	3.46410i	−0.0508652	−	0.189832i
$334$	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	0.0983001	−	0.995157i	$-0.468660\pi$
$337$	−16.4641	−	16.4641i	−0.896857	−	0.896857i	−0.995157	+	0.0983001i	$0.968660\pi$
$338$	9.33013	+	2.50000i	0.507492	+	0.135982i
$339$	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
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$			4.26795i			0.230112i
$345$		0			0
$346$	−39.2487	−	22.6603i	−2.11002	−	1.21822i
$347$	−7.79423	+	2.08846i	−0.418416	+	0.112114i	−0.461884	−	0.886941i	$-0.652826\pi$
$347$	−7.79423	+	2.08846i	−0.418416	+	0.112114i	0.0434674	+	0.999055i	$0.486160\pi$
$348$	−2.59808	+	9.69615i	−0.139272	+	0.519768i
$349$	9.73205			0.520945			0.260472	−	0.965481i	$-0.416122\pi$
$349$	9.73205			0.520945			0.260472	+	0.965481i	$0.416122\pi$
$350$		0			0
$351$	−12.3923			−0.661452
$352$	−1.43782	+	5.36603i	−0.0766362	+	0.286010i
$353$	−5.36603	+	1.43782i	−0.285605	+	0.0765276i	−0.398777	−	0.917048i	$-0.630565\pi$
$353$	−5.36603	+	1.43782i	−0.285605	+	0.0765276i	0.113173	+	0.993575i	$0.463899\pi$
$354$	7.09808	+	4.09808i	0.377258	+	0.217810i
$355$		0			0
$356$		−	28.8564i		−	1.52939i
$357$	−4.00000	−	3.46410i	−0.211702	−	0.183340i
$358$	−27.1244	+	27.1244i	−1.43357	+	1.43357i
$359$	12.3397	−	7.12436i	0.651267	−	0.376009i	−0.137675	−	0.990478i	$-0.543963\pi$
$359$	12.3397	−	7.12436i	0.651267	−	0.376009i	0.788941	+	0.614468i	$0.210629\pi$
$360$		0			0
$361$	5.76795	−	9.99038i	0.303576	−	0.525810i
$362$	−17.1603	−	4.59808i	−0.901923	−	0.241670i
$363$	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
$367$	−0.500000	−	1.86603i	−0.0260998	−	0.0974057i	0.951647	−	0.307193i	$-0.0993896\pi$
$367$	−0.500000	−	1.86603i	−0.0260998	−	0.0974057i	−0.977747	+	0.209787i	$0.932723\pi$
$368$	8.33013	+	31.0885i	0.434238	+	1.62060i
$369$	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
$373$	−15.9282	−	4.26795i	−0.824731	−	0.220986i	−0.178317	−	0.983973i	$-0.557065\pi$
$373$	−15.9282	−	4.26795i	−0.824731	−	0.220986i	−0.646414	+	0.762987i	$0.723732\pi$
$374$	−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
$378$	−16.9282	−	14.6603i	−0.870693	−	0.754042i
$379$			19.6603i			1.00988i	0.863155	+	0.504940i	$0.168485\pi$
$379$			19.6603i			1.00988i	−0.863155	+	0.504940i	$0.831515\pi$
$380$		0			0
$381$	15.2942	+	8.83013i	0.783547	+	0.452381i
$382$	31.2224	−	8.36603i	1.59748	−	0.428043i
$383$	7.55256	−	28.1865i	0.385918	−	1.44026i	−0.450797	−	0.892626i	$-0.648860\pi$
$383$	7.55256	−	28.1865i	0.385918	−	1.44026i	0.836715	−	0.547638i	$-0.184473\pi$
$384$	7.92820			0.404584
$385$		0			0
$386$	6.19615			0.315376
$387$	1.56218	−	5.83013i	0.0794100	−	0.296362i
$388$	18.7583	−	5.02628i	0.952310	−	0.255171i
$389$	−7.73205	−	4.46410i	−0.392031	−	0.226339i	0.291009	−	0.956720i	$-0.406009\pi$
$389$	−7.73205	−	4.46410i	−0.392031	−	0.226339i	−0.683040	+	0.730381i	$0.739342\pi$
$390$		0			0
$391$			7.46410i			0.377476i
$392$	−0.428203	+	3.59808i	−0.0216275	+	0.181730i
$393$	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
$397$	20.0263	+	5.36603i	1.00509	+	0.269313i	0.723577	−	0.690244i	$-0.242497\pi$
$397$	20.0263	+	5.36603i	1.00509	+	0.269313i	0.281514	+	0.959557i	$0.409164\pi$
$398$	−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	$0.921898\pi$
$402$	−1.13397	−	4.23205i	−0.0565575	−	0.211076i
$403$	0.392305	+	1.46410i	0.0195421	+	0.0729321i
$404$	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
$408$	1.00000	+	0.267949i	0.0495074	+	0.0132655i
$409$	3.42820	−	5.93782i	0.169514	−	0.293606i	−0.768735	−	0.639567i	$-0.779114\pi$
$409$	3.42820	−	5.93782i	0.169514	−	0.293606i	0.938249	+	0.345961i	$0.112447\pi$
$410$		0			0
$411$	18.1244	−	10.4641i	0.894009	−	0.516156i
$412$	−2.83013	+	2.83013i	−0.139430	+	0.139430i
$413$	1.09808	−	5.70577i	0.0540328	−	0.280763i
$414$		−	10.1962i		−	0.501114i
$415$		0			0
$416$	18.5885	+	10.7321i	0.911374	+	0.526182i
$417$	21.7583	−	5.83013i	1.06551	−	0.285503i
$418$	−1.00000	+	3.73205i	−0.0489116	+	0.182541i
$419$	−3.85641			−0.188398			−0.0941989	−	0.995553i	$-0.530029\pi$
$419$	−3.85641			−0.188398			−0.0941989	+	0.995553i	$0.530029\pi$
$420$		0			0
$421$	−34.6603			−1.68924			−0.844619	−	0.535368i	$-0.820173\pi$
$421$	−34.6603			−1.68924			−0.844619	+	0.535368i	$0.820173\pi$
$422$	−5.09808	+	19.0263i	−0.248170	+	0.926185i
$423$	−0.464102	+	0.124356i	−0.0225654	+	0.00604638i
$424$	−3.16987	−	1.83013i	−0.153943	−	0.0888788i
$425$		0			0
$426$			17.6603i			0.855642i
$427$	−14.6603	+	16.9282i	−0.709459	+	0.819213i
$428$	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	$0.134443\pi$
$432$	18.8923	+	5.06218i	0.908956	+	0.243554i
$433$	24.4641	+	24.4641i	1.17567	+	1.17567i	0.980836	+	0.194833i	$0.0624166\pi$
$433$	24.4641	+	24.4641i	1.17567	+	1.17567i	0.194833	+	0.980836i	$0.437583\pi$
$434$	−1.19615	+	2.46410i	−0.0574172	+	0.118281i
$435$		0			0
$436$	12.2321	+	21.1865i	0.585809	+	1.01465i
$437$	5.09808	+	19.0263i	0.243874	+	0.910150i
$438$	−3.46410	−	12.9282i	−0.165521	−	0.617733i
$439$	−15.6603	−	27.1244i	−0.747423	−	1.29457i	−0.949054	−	0.315113i	$-0.897957\pi$
$439$	−15.6603	−	27.1244i	−0.747423	−	1.29457i	0.201631	−	0.979462i	$-0.435376\pi$
$440$		0			0
$441$	1.90192	−	4.75833i	0.0905678	−	0.226587i
$442$	4.00000	+	4.00000i	0.190261	+	0.190261i
$443$	3.50000	+	0.937822i	0.166290	+	0.0445573i	0.341003	−	0.940062i	$-0.389233\pi$
$443$	3.50000	+	0.937822i	0.166290	+	0.0445573i	−0.174713	+	0.984619i	$0.555900\pi$
$444$	−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
$448$	4.96410	+	14.3301i	0.234532	+	0.677035i
$449$			5.05256i			0.238445i	0.992868	+	0.119222i	$0.0380402\pi$
$449$			5.05256i			0.238445i	−0.992868	+	0.119222i	$0.961960\pi$
$450$		0			0
$451$	−0.294229	−	0.169873i	−0.0138547	−	0.00799901i
$452$	−10.0981	+	2.70577i	−0.474974	+	0.127269i
$453$	6.92820	−	25.8564i	0.325515	−	1.21484i
$454$	0.196152			0.00920589
$455$		0			0
$456$	2.73205			0.127940
$457$	8.26795	−	30.8564i	0.386758	−	1.44340i	−0.448618	−	0.893724i	$-0.648084\pi$
$457$	8.26795	−	30.8564i	0.386758	−	1.44340i	0.835376	−	0.549678i	$-0.185250\pi$
$458$	−4.46410	+	1.19615i	−0.208594	+	0.0558925i
$459$	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	$-0.210685\pi$
$462$	−7.09808	−	1.36603i	−0.330232	−	0.0635533i
$463$	−17.7583	+	17.7583i	−0.825300	+	0.825300i	−0.986862	−	0.161563i	$-0.948347\pi$
$463$	−17.7583	+	17.7583i	−0.825300	+	0.825300i	0.161563	+	0.986862i	$0.448347\pi$
$464$	−11.5981	+	6.69615i	−0.538427	+	0.310861i
$465$		0			0
$466$	1.73205	−	3.00000i	0.0802357	−	0.138972i
$467$	−31.3564	−	8.40192i	−1.45100	−	0.388795i	−0.554629	−	0.832097i	$-0.687140\pi$
$467$	−31.3564	−	8.40192i	−1.45100	−	0.388795i	−0.896372	+	0.443303i	$0.853807\pi$
$468$	−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
$472$	0.294229	+	1.09808i	0.0135430	+	0.0505431i
$473$	1.56218	+	5.83013i	0.0718290	+	0.268070i
$474$	−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
$478$	34.3205	+	9.19615i	1.56978	+	0.420622i
$479$	13.4641	−	23.3205i	0.615191	−	1.06554i	−0.375161	−	0.926960i	$-0.622412\pi$
$479$	13.4641	−	23.3205i	0.615191	−	1.06554i	0.990351	−	0.138581i	$-0.0442542\pi$
$480$		0			0
$481$	12.0000	−	6.92820i	0.547153	−	0.315899i
$482$	−22.9282	+	22.9282i	−1.04435	+	1.04435i
$483$	−34.8205	+	12.0622i	−1.58439	+	0.548848i
$484$		−	18.1244i		−	0.823834i
$485$		0			0
$486$	−12.4641	−	7.19615i	−0.565383	−	0.326424i
$487$	8.29423	−	2.22243i	0.375847	−	0.100708i	−0.0659498	−	0.997823i	$-0.521008\pi$
$487$	8.29423	−	2.22243i	0.375847	−	0.100708i	0.441797	+	0.897115i	$0.354341\pi$
$488$	1.13397	−	4.23205i	0.0513326	−	0.191576i
$489$	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	$0.630880\pi$
$492$	0.401924	−	1.50000i	0.0181201	−	0.0676252i
$493$	−3.00000	+	0.803848i	−0.135113	+	0.0362035i
$494$	12.9282	+	7.46410i	0.581667	+	0.335826i
$495$		0			0
$496$		−	2.39230i		−	0.107418i
$497$	11.8301	−	4.09808i	0.530654	−	0.183824i
$498$	11.5622	−	11.5622i	0.518114	−	0.518114i
$499$	−29.0263	+	16.7583i	−1.29939	+	0.750206i	−0.980300	−	0.197517i	$-0.936712\pi$
$499$	−29.0263	+	16.7583i	−1.29939	+	0.750206i	−0.319095	+	0.947723i	$0.603379\pi$
$500$		0			0
$501$	14.6962	−	25.4545i	0.656576	−	1.13722i
$502$	10.9282	+	2.92820i	0.487750	+	0.130692i
$503$	19.3660	+	19.3660i	0.863488	+	0.863488i	0.991741	−	0.128253i	$-0.0409370\pi$
$503$	19.3660	+	19.3660i	0.863488	+	0.863488i	−0.128253	+	0.991741i	$0.540937\pi$
$504$	0.0717968	+	1.00000i	0.00319808	+	0.0445435i
$505$		0			0
$506$	5.09808	+	8.83013i	0.226637	+	0.392547i
$507$	−2.50000	−	9.33013i	−0.111029	−	0.414365i
$508$	−4.09808	−	15.2942i	−0.181823	−	0.678572i
$509$	13.4545	+	23.3038i	0.596359	+	1.03292i	0.993353	+	0.115104i	$0.0367200\pi$
$509$	13.4545	+	23.3038i	0.596359	+	1.03292i	−0.396994	+	0.917821i	$0.629947\pi$
$510$		0			0
$511$	−7.85641	+	5.32051i	−0.347547	+	0.235365i
$512$	−20.6865	−	20.6865i	−0.914224	−	0.914224i
$513$	11.5622	+	3.09808i	0.510483	+	0.136783i
$514$	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
$518$	24.5885	+	4.73205i	1.08035	+	0.207914i
$519$			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	$0.693588\pi$
$522$	4.09808	−	1.09808i	0.179368	−	0.0480615i
$523$	−3.88269	+	14.4904i	−0.169778	+	0.633620i	0.827604	+	0.561312i	$0.189703\pi$
$523$	−3.88269	+	14.4904i	−0.169778	+	0.633620i	−0.997382	+	0.0723082i	$0.976963\pi$
$524$	−14.7846			−0.645869
$525$		0			0
$526$	16.1244			0.703055
$527$	0.143594	−	0.535898i	0.00625503	−	0.0233441i
$528$	6.09808	−	1.63397i	0.265385	−	0.0711096i
$529$	25.0981	+	14.4904i	1.09122	+	0.630017i
$530$		0			0
$531$		−	1.60770i		−	0.0697680i
$532$	4.09808	+	11.8301i	0.177674	+	0.512901i
$533$	−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
$537$	37.0526	+	9.92820i	1.59894	+	0.428434i
$538$	−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	$0.701557\pi$
$542$	−12.3660	−	46.1506i	−0.531166	−	1.98234i
$543$	4.59808	+	17.1603i	0.197322	+	0.736417i
$544$	−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	0.573204	−	0.819413i	$-0.305700\pi$
$547$	−5.75833	−	5.75833i	−0.246208	−	0.246208i	−0.819413	+	0.573204i	$0.805700\pi$
$548$	−18.1244	−	4.85641i	−0.774234	−	0.207455i
$549$	−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
$553$	−11.6603	+	13.4641i	−0.495844	+	0.572552i
$554$		−	38.7846i		−	1.64780i
$555$		0			0
$556$	−17.4904	−	10.0981i	−0.741757	−	0.428254i
$557$	−6.63397	+	1.77757i	−0.281091	+	0.0753180i	−0.396610	−	0.917987i	$-0.629813\pi$
$557$	−6.63397	+	1.77757i	−0.281091	+	0.0753180i	0.115519	+	0.993305i	$0.463147\pi$
$558$	−0.196152	+	0.732051i	−0.00830379	+	0.0309902i
$559$	23.3205			0.986352
$560$		0			0
$561$	1.46410			0.0618144
$562$	−6.46410	+	24.1244i	−0.272672	+	1.01762i
$563$	−21.3564	+	5.72243i	−0.900065	+	0.241172i	−0.679044	−	0.734097i	$-0.737606\pi$
$563$	−21.3564	+	5.72243i	−0.900065	+	0.241172i	−0.221021	+	0.975269i	$0.570939\pi$
$564$	1.90192	+	1.09808i	0.0800854	+	0.0462373i
$565$		0			0
$566$			52.9808i			2.22695i
$567$	−5.33013	+	27.6962i	−0.223844	+	1.16313i
$568$	−1.73205	+	1.73205i	−0.0726752	+	0.0726752i
$569$	13.0526	−	7.53590i	0.547192	−	0.315921i	−0.200797	−	0.979633i	$-0.564353\pi$
$569$	13.0526	−	7.53590i	0.547192	−	0.315921i	0.747989	+	0.663712i	$0.231020\pi$
$570$		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	$0.304492\pi$
$572$	3.46410	+	0.928203i	0.144841	+	0.0388101i
$573$	−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
$577$	−7.36603	−	27.4904i	−0.306652	−	1.14444i	−0.931514	−	0.363705i	$-0.881512\pi$
$577$	−7.36603	−	27.4904i	−0.306652	−	1.14444i	0.624863	−	0.780735i	$-0.285155\pi$
$578$	7.96410	+	29.7224i	0.331263	+	1.23629i
$579$	−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
$583$	−5.00000	−	1.33975i	−0.207079	−	0.0554866i
$584$	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	0.0664553	−	0.997789i	$-0.478831\pi$
$587$	25.7846	−	25.7846i	1.06424	−	1.06424i	0.997789	−	0.0664553i	$-0.0211690\pi$
$588$	−21.5263	+	9.23205i	−0.887729	+	0.380723i
$589$		−	1.46410i		−	0.0603273i
$590$		0			0
$591$	−33.4186	−	19.2942i	−1.37466	−	0.793659i
$592$	−21.1244	+	5.66025i	−0.868206	+	0.232635i
$593$	1.75833	−	6.56218i	0.0722060	−	0.269476i	−0.920379	−	0.391027i	$-0.872120\pi$
$593$	1.75833	−	6.56218i	0.0722060	−	0.269476i	0.992585	+	0.121550i	$0.0387866\pi$
$594$	6.19615			0.254231
$595$		0			0
$596$	19.3923			0.794340
$597$	−12.4641	+	46.5167i	−0.510122	+	1.90380i
$598$	38.0526	−	10.1962i	1.55608	−	0.416952i
$599$	−32.6603	−	18.8564i	−1.33446	−	0.770452i	−0.348482	−	0.937316i	$-0.613303\pi$
$599$	−32.6603	−	18.8564i	−1.33446	−	0.770452i	−0.985980	+	0.166864i	$0.946636\pi$
$600$		0			0
$601$			21.1769i			0.863824i	0.901916	+	0.431912i	$0.142161\pi$
$601$			21.1769i			0.863824i	−0.901916	+	0.431912i	$0.857839\pi$
$602$	31.8564	+	27.5885i	1.29837	+	1.12442i
$603$	−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
$607$	−8.59808	−	2.30385i	−0.348985	−	0.0935103i	0.0800683	−	0.996789i	$-0.474486\pi$
$607$	−8.59808	−	2.30385i	−0.348985	−	0.0935103i	−0.429053	+	0.903279i	$0.641153\pi$
$608$	−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
$612$	0.339746	+	1.26795i	0.0137334	+	0.0512538i
$613$	−3.60770	−	13.4641i	−0.145713	−	0.543810i	−0.999723	−	0.0235520i	$-0.992502\pi$
$613$	−3.60770	−	13.4641i	−0.145713	−	0.543810i	0.854009	−	0.520258i	$-0.174164\pi$
$614$	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	0.938017	+	0.346590i	$0.112660\pi$
$617$	31.9090	+	31.9090i	1.28461	+	1.28461i	0.346590	+	0.938017i	$0.387340\pi$
$618$	8.33013	+	2.23205i	0.335087	+	0.0897863i
$619$	−0.0980762	+	0.169873i	−0.00394202	+	0.00682777i	−0.867990	−	0.496582i	$-0.834588\pi$
$619$	−0.0980762	+	0.169873i	−0.00394202	+	0.00682777i	0.864048	+	0.503410i	$0.167921\pi$
$620$		0			0
$621$	27.3564	−	15.7942i	1.09777	−	0.633801i
$622$	−25.5885	+	25.5885i	−1.02600	+	1.02600i
$623$	33.3205	+	28.8564i	1.33496	+	1.15611i
$624$		−	24.3923i		−	0.976474i
$625$		0			0
$626$	−33.5885	−	19.3923i	−1.34246	−	0.775072i
$627$	3.73205	−	1.00000i	0.149044	−	0.0399362i
$628$	11.0263	−	41.1506i	0.439996	−	1.64209i
$629$	−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	$0.322479\pi$
$632$	0.901924	−	3.36603i	0.0358766	−	0.133893i
$633$	19.0263	−	5.09808i	0.756227	−	0.202630i
$634$	7.73205	+	4.46410i	0.307079	+	0.177292i
$635$		0			0
$636$		−	23.6603i		−	0.938190i
$637$	19.6603	+	2.33975i	0.778968	+	0.0927041i
$638$	−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	$0.124677\pi$
$642$	−32.0885	−	8.59808i	−1.26643	−	0.339339i
$643$	−24.4641	−	24.4641i	−0.964770	−	0.964770i	0.0346302	−	0.999400i	$-0.488975\pi$
$643$	−24.4641	−	24.4641i	−0.964770	−	0.964770i	−0.999400	+	0.0346302i	$0.988975\pi$
$644$	29.7224	+	14.4282i	1.17123	+	0.568551i
$645$		0			0
$646$	−2.73205	−	4.73205i	−0.107491	−	0.186180i
$647$	−1.44744	−	5.40192i	−0.0569048	−	0.212372i	0.931619	−	0.363436i	$-0.118397\pi$
$647$	−1.44744	−	5.40192i	−0.0569048	−	0.212372i	−0.988524	+	0.151065i	$0.951730\pi$
$648$	−1.42820	−	5.33013i	−0.0561051	−	0.209387i
$649$	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
$653$	8.73205	+	2.33975i	0.341712	+	0.0915613i	0.425594	−	0.904914i	$-0.360065\pi$
$653$	8.73205	+	2.33975i	0.341712	+	0.0915613i	−0.0838822	+	0.996476i	$0.526732\pi$
$654$	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
$658$	0.633975	−	3.29423i	0.0247149	−	0.128422i
$659$		−	10.3397i		−	0.402779i	−0.979511	−	0.201390i	$-0.935454\pi$
$659$		−	10.3397i		−	0.402779i	0.979511	−	0.201390i	$-0.0645457\pi$
$660$		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	$0.755579\pi$
$662$	48.2487	−	12.9282i	1.87524	−	0.502469i
$663$	1.46410	−	5.46410i	0.0568610	−	0.212208i
$664$	2.26795			0.0880135
$665$		0			0
$666$	6.92820			0.268462
$667$	−5.59808	+	20.8923i	−0.216758	+	0.808953i
$668$	−25.4545	+	6.82051i	−0.984864	+	0.263893i
$669$	14.4904	+	8.36603i	0.560230	+	0.323449i
$670$		0			0
$671$		−	6.19615i		−	0.239200i
$672$	25.3923	−	29.3205i	0.979529	−	1.13106i
$673$	16.3923	−	16.3923i	0.631877	−	0.631877i	−0.316662	−	0.948539i	$-0.602562\pi$
$673$	16.3923	−	16.3923i	0.631877	−	0.631877i	0.948539	+	0.316662i	$0.102562\pi$
$674$	38.9545	−	22.4904i	1.50047	−	0.866297i
$675$		0			0
$676$	−4.33013	+	7.50000i	−0.166543	+	0.288462i
$677$	−6.92820	−	1.85641i	−0.266272	−	0.0713475i	0.123213	−	0.992380i	$-0.460680\pi$
$677$	−6.92820	−	1.85641i	−0.266272	−	0.0713475i	−0.389485	+	0.921033i	$0.627347\pi$
$678$	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
$682$	−0.196152	−	0.732051i	−0.00751106	−	0.0280317i
$683$	−4.93782	−	18.4282i	−0.188941	−	0.705136i	−0.993753	−	0.111606i	$-0.964401\pi$
$683$	−4.93782	−	18.4282i	−0.188941	−	0.705136i	0.804812	−	0.593530i	$-0.202266\pi$
$684$	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
$688$	−35.5526	−	9.52628i	−1.35543	−	0.363186i
$689$	−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
$693$	0.464102	+	1.33975i	0.0176298	+	0.0508927i
$694$		−	15.5885i		−	0.591730i
$695$		0			0
$696$	2.59808	+	1.50000i	0.0984798	+	0.0568574i
$697$	0.464102	−	0.124356i	0.0175791	−	0.00471031i
$698$	−4.86603	+	18.1603i	−0.184182	+	0.687376i
$699$	−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	$0.647925\pi$
$702$	6.19615	−	23.1244i	0.233859	−	0.872773i
$703$	−12.9282	+	3.46410i	−0.487596	+	0.130651i
$704$	−3.63397	−	2.09808i	−0.136961	−	0.0790742i
$705$		0			0
$706$		−	10.7321i		−	0.403906i
$707$	−30.4808	−	5.86603i	−1.14635	−	0.220615i
$708$	−5.19615	+	5.19615i	−0.195283	+	0.195283i
$709$	−6.99038	+	4.03590i	−0.262529	+	0.151571i	−0.625488	−	0.780234i	$-0.715100\pi$
$709$	−6.99038	+	4.03590i	−0.262529	+	0.151571i	0.362959	+	0.931805i	$0.381767\pi$
$710$		0			0
$711$	−2.46410	+	4.26795i	−0.0924110	+	0.160061i
$712$	−8.33013	−	2.23205i	−0.312185	−	0.0836496i
$713$	−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
$717$	−9.19615	−	34.3205i	−0.343437	−	1.28172i
$718$	7.12436	+	26.5885i	0.265879	+	0.992272i
$719$	3.70577	+	6.41858i	0.138202	+	0.239373i	0.926816	−	0.375516i	$-0.122534\pi$
$719$	3.70577	+	6.41858i	0.138202	+	0.239373i	−0.788614	+	0.614888i	$0.789201\pi$
$720$		0			0
$721$	−0.437822	−	6.09808i	−0.0163053	−	0.227104i
$722$	15.7583	+	15.7583i	0.586464	+	0.586464i
$723$	31.3205	+	8.39230i	1.16482	+	0.312113i
$724$	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	$-0.708967\pi$
$727$	4.90192	−	4.90192i	0.181802	−	0.181802i	0.792141	+	0.610338i	$0.208967\pi$
$728$	−3.66025	+	1.26795i	−0.135658	+	0.0469933i
$729$		−	17.5885i		−	0.651424i
$730$		0			0
$731$	−7.39230	−	4.26795i	−0.273414	−	0.157856i
$732$	27.3564	−	7.33013i	1.01112	−	0.270929i
$733$	2.63397	−	9.83013i	0.0972881	−	0.363084i	−0.900068	−	0.435749i	$-0.856484\pi$
$733$	2.63397	−	9.83013i	0.0972881	−	0.363084i	0.997356	+	0.0726647i	$0.0231503\pi$
$734$	3.73205			0.137753
$735$		0			0
$736$	−54.7128			−2.01674
$737$	0.222432	−	0.830127i	0.00819338	−	0.0305781i
$738$	−0.633975	+	0.169873i	−0.0233369	+	0.00625311i
$739$	−7.43782	−	4.29423i	−0.273605	−	0.157966i	0.356920	−	0.934135i	$-0.383827\pi$
$739$	−7.43782	−	4.29423i	−0.273605	−	0.157966i	−0.630525	+	0.776169i	$0.717160\pi$
$740$		0			0
$741$		−	14.9282i		−	0.548401i
$742$	−34.1506	+	11.8301i	−1.25371	+	0.434298i
$743$	14.8301	−	14.8301i	0.544065	−	0.544065i	−0.380653	−	0.924718i	$-0.624301\pi$
$743$	14.8301	−	14.8301i	0.544065	−	0.544065i	0.924718	+	0.380653i	$0.124301\pi$
$744$	−0.464102	+	0.267949i	−0.0170148	+	0.00982349i
$745$		0			0
$746$	15.9282	−	27.5885i	0.583173	−	1.01009i
$747$	−3.09808	−	0.830127i	−0.113353	−	0.0303728i
$748$	−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	$0.917910\pi$
$752$	0.758330	+	2.83013i	0.0276535	+	0.103204i
$753$	−2.92820	−	10.9282i	−0.106710	−	0.398246i
$754$	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	0.518331	−	0.855180i	$-0.326554\pi$
$757$	−9.26795	−	9.26795i	−0.336849	−	0.336849i	−0.855180	+	0.518331i	$0.826554\pi$
$758$	−36.6865	−	9.83013i	−1.33251	−	0.357046i
$759$	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
$763$	−36.6962	−	7.06218i	−1.32849	−	0.255668i
$764$			28.9808i			1.04849i
$765$		0			0
$766$	48.8205	+	28.1865i	1.76396	+	1.01842i
$767$	6.00000	−	1.60770i	0.216647	−	0.0580505i
$768$	−9.69615	+	36.1865i	−0.349880	+	1.30577i
$769$	−47.1769			−1.70124			−0.850622	−	0.525778i	$-0.823774\pi$
$769$	−47.1769			−1.70124			−0.850622	+	0.525778i	$0.823774\pi$
$770$		0			0
$771$	−5.46410			−0.196785
$772$	−1.43782	+	5.36603i	−0.0517484	+	0.193127i
$773$	−17.9282	+	4.80385i	−0.644833	+	0.172782i	−0.566391	−	0.824136i	$-0.691661\pi$
$773$	−17.9282	+	4.80385i	−0.644833	+	0.172782i	−0.0784412	+	0.996919i	$0.524994\pi$
$774$	10.0981	+	5.83013i	0.362968	+	0.209560i
$775$		0			0
$776$		−	5.80385i		−	0.208346i
$777$	−8.19615	−	23.6603i	−0.294035	−	0.848807i
$778$	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
$782$	−13.9282	−	3.73205i	−0.498072	−	0.133458i
$783$	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
$787$	5.18653	+	19.3564i	0.184880	+	0.689981i	0.994656	+	0.103243i	$0.0329218\pi$
$787$	5.18653	+	19.3564i	0.184880	+	0.689981i	−0.809776	+	0.586739i	$0.800412\pi$
$788$	8.95448	+	33.4186i	0.318990	+	1.19049i
$789$	−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
$793$	−23.1244	−	6.19615i	−0.821170	−	0.220032i
$794$	−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	−0.0446702	+	0.999002i	$0.514224\pi$
$797$	−29.4641	+	29.4641i	−1.04367	+	1.04367i	−0.999002	+	0.0446702i	$0.985776\pi$
$798$	17.6603	−	20.3923i	0.625166	−	0.721880i
$799$			0.679492i			0.0240387i
$800$		0			0
$801$	10.5622	+	6.09808i	0.373196	+	0.215465i
$802$	20.5263	−	5.50000i	0.724808	−	0.194212i
$803$	0.679492	−	2.53590i	0.0239787	−	0.0894899i
$804$	3.92820			0.138537
$805$		0			0
$806$	−2.92820			−0.103142
$807$	−2.42820	+	9.06218i	−0.0854768	+	0.319004i
$808$	5.86603	−	1.57180i	0.206366	−	0.0552956i
$809$	21.9904	+	12.6962i	0.773141	+	0.446373i	0.833994	−	0.551774i	$-0.186049\pi$
$809$	21.9904	+	12.6962i	0.773141	+	0.446373i	−0.0608532	+	0.998147i	$0.519382\pi$
$810$		0			0
$811$			29.0718i			1.02085i	0.859923	+	0.510424i	$0.170512\pi$
$811$			29.0718i			1.02085i	−0.859923	+	0.510424i	$0.829488\pi$
$812$	−2.59808	+	13.5000i	−0.0911746	+	0.473757i
$813$	−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
$817$	−21.7583	−	5.83013i	−0.761228	−	0.203970i
$818$	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	$0.750876\pi$
$822$	10.4641	+	39.0526i	0.364977	+	1.36211i
$823$	6.61731	+	24.6962i	0.230665	+	0.860854i	0.980055	+	0.198725i	$0.0636801\pi$
$823$	6.61731	+	24.6962i	0.230665	+	0.860854i	−0.749390	+	0.662129i	$0.769653\pi$
$824$	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	0.769729	−	0.638370i	$-0.220391\pi$
$827$	3.77757	+	3.77757i	0.131359	+	0.131359i	−0.638370	+	0.769729i	$0.720391\pi$
$828$	8.83013	+	2.36603i	0.306868	+	0.0822251i
$829$	−10.7321	+	18.5885i	−0.372740	+	0.645604i	−0.989986	−	0.141166i	$-0.954915\pi$
$829$	−10.7321	+	18.5885i	−0.372740	+	0.645604i	0.617246	+	0.786770i	$0.288248\pi$
$830$		0			0
$831$	−33.5885	+	19.3923i	−1.16517	+	0.672712i
$832$	−11.4641	+	11.4641i	−0.397446	+	0.397446i
$833$	−5.80385	−	4.33975i	−0.201091	−	0.150363i
$834$			43.5167i			1.50686i
$835$		0			0
$836$	−3.00000	−	1.73205i	−0.103757	−	0.0599042i
$837$	−2.26795	+	0.607695i	−0.0783918	+	0.0210050i
$838$	1.92820	−	7.19615i	0.0666087	−	0.248587i
$839$	31.1244			1.07453			0.537266	−	0.843413i	$-0.319457\pi$
$839$	31.1244			1.07453			0.537266	+	0.843413i	$0.319457\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	17.3301	−	64.6769i	0.597236	−	2.22891i
$843$	24.1244	−	6.46410i	0.830887	−	0.222635i
$844$	−15.2942	−	8.83013i	−0.526449	−	0.303946i
$845$		0			0
$846$		−	0.928203i		−	0.0319123i
$847$	20.9282	+	18.1244i	0.719102	+	0.622760i
$848$	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
$852$	−15.2942	−	4.09808i	−0.523972	−	0.140398i
$853$	−6.12436	−	6.12436i	−0.209694	−	0.209694i	0.594443	−	0.804137i	$-0.297372\pi$
$853$	−6.12436	−	6.12436i	−0.209694	−	0.209694i	−0.804137	+	0.594443i	$0.797372\pi$
$854$	−24.2583	−	35.8205i	−0.830103	−	1.22575i
$855$		0			0
$856$	−2.30385	−	3.99038i	−0.0787439	−	0.136388i
$857$	5.90192	+	22.0263i	0.201606	+	0.752403i	0.990457	+	0.137820i	$0.0440094\pi$
$857$	5.90192	+	22.0263i	0.201606	+	0.752403i	−0.788851	+	0.614584i	$0.789324\pi$
$858$	−2.00000	−	7.46410i	−0.0682789	−	0.254820i
$859$	−10.5359	−	18.2487i	−0.359480	−	0.622638i	0.628394	−	0.777895i	$-0.283713\pi$
$859$	−10.5359	−	18.2487i	−0.359480	−	0.622638i	−0.987874	+	0.155257i	$0.950379\pi$
$860$		0			0
$861$	1.33013	+	1.96410i	0.0453306	+	0.0669364i
$862$	5.73205	+	5.73205i	0.195234	+	0.195234i
$863$	33.3827	+	8.94486i	1.13636	+	0.304487i	0.777487	−	0.628900i	$-0.216494\pi$
$863$	33.3827	+	8.94486i	1.13636	+	0.304487i	0.358873	+	0.933386i	$0.383161\pi$
$864$	−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
$868$	−1.85641	−	1.60770i	−0.0630105	−	0.0545687i
$869$		−	4.92820i		−	0.167178i
$870$		0			0
$871$	−2.87564	−	1.66025i	−0.0974375	−	0.0562556i
$872$	7.06218	−	1.89230i	0.239156	−	0.0640815i
$873$	−2.12436	+	7.92820i	−0.0718985	+	0.268329i
$874$	−38.0526			−1.28715
$875$		0			0
$876$	12.0000			0.405442
$877$	−4.15064	+	15.4904i	−0.140157	+	0.523073i	0.859766	+	0.510688i	$0.170609\pi$
$877$	−4.15064	+	15.4904i	−0.140157	+	0.523073i	−0.999923	+	0.0123853i	$0.996058\pi$
$878$	58.4449	−	15.6603i	1.97242	−	0.528508i
$879$	−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	$0.650433\pi$
$882$	7.92820	+	5.92820i	0.266956	+	0.199613i
$883$	−21.9282	+	21.9282i	−0.737943	+	0.737943i	−0.972180	−	0.234237i	$-0.924741\pi$
$883$	−21.9282	+	21.9282i	−0.737943	+	0.737943i	0.234237	+	0.972180i	$0.424741\pi$
$884$	−4.39230	+	2.53590i	−0.147729	+	0.0852915i
$885$		0			0
$886$	−3.50000	+	6.06218i	−0.117585	+	0.203663i
$887$	36.9186	+	9.89230i	1.23960	+	0.332151i	0.818312	−	0.574774i	$-0.194910\pi$
$887$	36.9186	+	9.89230i	1.23960	+	0.332151i	0.421292	+	0.906925i	$0.361577\pi$
$888$	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
$892$	−3.88269	−	14.4904i	−0.130002	−	0.485174i
$893$	0.464102	+	1.73205i	0.0155306	+	0.0579609i
$894$	−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
$898$	−9.42820	−	2.52628i	−0.314623	−	0.0843030i
$899$	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
$903$	7.96410	−	41.3827i	0.265029	−	1.37713i
$904$			3.12436i			0.103915i
$905$		0			0
$906$	44.7846	+	25.8564i	1.48787	+	0.859022i
$907$	−1.69615	+	0.454483i	−0.0563198	+	0.0150908i	−0.286869	−	0.957970i	$-0.592614\pi$
$907$	−1.69615	+	0.454483i	−0.0563198	+	0.0150908i	0.230549	+	0.973061i	$0.425948\pi$
$908$	−0.0455173	+	0.169873i	−0.00151055	+	0.00563743i
$909$	−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	$0.286527\pi$
$912$	−6.09808	+	22.7583i	−0.201927	+	0.753604i
$913$	3.09808	−	0.830127i	0.102531	−	0.0274732i
$914$	53.4449	+	30.8564i	1.76780	+	1.02064i
$915$		0			0
$916$		−	4.14359i		−	0.136908i
$917$	14.7846	−	17.0718i	0.488231	−	0.563760i
$918$	−6.19615	+	6.19615i	−0.204504	+	0.204504i
$919$	39.6673	−	22.9019i	1.30850	−	0.755465i	0.326657	−	0.945143i	$-0.394078\pi$
$919$	39.6673	−	22.9019i	1.30850	−	0.755465i	0.981846	+	0.189678i	$0.0607445\pi$
$920$		0			0
$921$	12.6962	−	21.9904i	0.418352	−	0.724608i
$922$	49.2487	+	13.1962i	1.62192	+	0.434592i
$923$	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
$927$	−0.437822	−	1.63397i	−0.0143800	−	0.0536668i
$928$	−5.89230	−	21.9904i	−0.193424	−	0.721870i
$929$	−0.839746	−	1.45448i	−0.0275512	−	0.0477200i	0.851921	−	0.523670i	$-0.175438\pi$
$929$	−0.839746	−	1.45448i	−0.0275512	−	0.0477200i	−0.879472	+	0.475950i	$0.842104\pi$
$930$		0			0
$931$	−17.7583	−	7.09808i	−0.582006	−	0.232630i
$932$	2.19615	+	2.19615i	0.0719374	+	0.0719374i
$933$	34.9545	+	9.36603i	1.14436	+	0.306630i
$934$	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	−0.0104348	+	0.999946i	$0.503322\pi$
$937$	−30.9282	+	30.9282i	−1.01038	+	1.01038i	−0.999946	+	0.0104348i	$0.996678\pi$
$938$	−1.96410	−	5.66987i	−0.0641302	−	0.185128i
$939$			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	$0.512061\pi$
$942$	−88.6673	+	23.7583i	−2.88894	+	0.774088i
$943$	0.866025	−	3.23205i	0.0282017	−	0.105250i
$944$	−9.80385			−0.319088
$945$		0			0
$946$	−11.6603			−0.379108
$947$	11.6962	−	43.6506i	0.380074	−	1.41846i	−0.465714	−	0.884935i	$-0.654202\pi$
$947$	11.6962	−	43.6506i	0.380074	−	1.41846i	0.845788	−	0.533520i	$-0.179131\pi$
$948$	21.7583	−	5.83013i	0.706678	−	0.189354i
$949$	−8.78461	−	5.07180i	−0.285160	−	0.164637i
$950$		0			0
$951$		−	8.92820i		−	0.289517i
$952$	1.39230	+	0.267949i	0.0451249	+	0.00868428i
$953$	10.1436	−	10.1436i	0.328583	−	0.328583i	−0.523464	−	0.852048i	$-0.675361\pi$
$953$	10.1436	−	10.1436i	0.328583	−	0.328583i	0.852048	+	0.523464i	$0.175361\pi$
$954$	−8.66025	+	5.00000i	−0.280386	+	0.161881i
$955$		0			0
$956$	−15.9282	+	27.5885i	−0.515155	+	0.892274i
$957$	4.09808	+	1.09808i	0.132472	+	0.0354958i
$958$	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
$962$	6.92820	+	25.8564i	0.223374	+	0.833644i
$963$	1.68653	+	6.29423i	0.0543478	+	0.202829i
$964$	−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	0.729847	−	0.683610i	$-0.239591\pi$
$967$	1.43782	+	1.43782i	0.0462372	+	0.0462372i	−0.683610	+	0.729847i	$0.739591\pi$
$968$	−5.23205	−	1.40192i	−0.168164	−	0.0450595i
$969$	−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
$973$	29.1506	−	10.0981i	0.934526	−	0.323729i
$974$			16.5885i			0.531528i
$975$		0			0
$976$	32.7224	+	18.8923i	1.04742	+	0.604728i
$977$	−43.1506	+	11.5622i	−1.38051	+	0.369907i	−0.871307	−	0.490739i	$-0.836727\pi$
$977$	−43.1506	+	11.5622i	−1.38051	+	0.369907i	−0.509204	+	0.860646i	$0.670060\pi$
$978$	−5.36603	+	20.0263i	−0.171587	+	0.640370i
$979$	−12.1962			−0.389791
$980$		0			0
$981$	−10.3397			−0.330123
$982$	8.85641	−	33.0526i	0.282619	−	1.05475i
$983$	−14.5000	+	3.88526i	−0.462478	+	0.123921i	−0.482532	−	0.875878i	$-0.660283\pi$
$983$	−14.5000	+	3.88526i	−0.462478	+	0.123921i	0.0200540	+	0.999799i	$0.493616\pi$
$984$	−0.401924	−	0.232051i	−0.0128129	−	0.00739751i
$985$		0			0
$986$		−	6.00000i		−	0.191079i
$987$	−3.16987	+	1.09808i	−0.100898	+	0.0349522i
$988$	−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	$0.0437491\pi$
$992$	3.92820	+	1.05256i	0.124721	+	0.0334188i
$993$	−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
$997$	−6.88269	−	25.6865i	−0.217977	−	0.813501i	−0.985097	−	0.171998i	$-0.944978\pi$
$997$	−6.88269	−	25.6865i	−0.217977	−	0.813501i	0.767121	−	0.641503i	$-0.221689\pi$
$998$	−16.7583	−	62.5429i	−0.530476	−	1.97976i
$999$	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.a.157.1		4
5.2	odd	4		35.2.k.a.3.1	✓	4
5.3	odd	4		175.2.o.b.143.1		4
5.4	even	2		35.2.k.b.17.1	yes	4
7.5	odd	6		175.2.o.b.82.1		4
15.2	even	4		315.2.bz.b.73.1		4
15.14	odd	2		315.2.bz.a.262.1		4
20.7	even	4		560.2.ci.a.353.1		4
20.19	odd	2		560.2.ci.b.17.1		4
35.2	odd	12		245.2.l.b.68.1		4
35.4	even	6		245.2.f.b.97.2		4
35.9	even	6		245.2.l.a.117.1		4
35.12	even	12		35.2.k.b.33.1	yes	4
35.17	even	12		245.2.f.b.48.2		4
35.19	odd	6		35.2.k.a.12.1	yes	4
35.24	odd	6		245.2.f.a.97.2		4
35.27	even	4		245.2.l.a.178.1		4
35.32	odd	12		245.2.f.a.48.2		4
35.33	even	12	inner	175.2.o.a.68.1		4
35.34	odd	2		245.2.l.b.227.1		4
105.47	odd	12		315.2.bz.a.208.1		4
105.89	even	6		315.2.bz.b.82.1		4
140.19	even	6		560.2.ci.a.257.1		4
140.47	odd	12		560.2.ci.b.33.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.3.1	✓	4	5.2	odd	4
35.2.k.a.12.1	yes	4	35.19	odd	6
35.2.k.b.17.1	yes	4	5.4	even	2
35.2.k.b.33.1	yes	4	35.12	even	12
175.2.o.a.68.1		4	35.33	even	12	inner
175.2.o.a.157.1		4	1.1	even	1	trivial
175.2.o.b.82.1		4	7.5	odd	6
175.2.o.b.143.1		4	5.3	odd	4
245.2.f.a.48.2		4	35.32	odd	12
245.2.f.a.97.2		4	35.24	odd	6
245.2.f.b.48.2		4	35.17	even	12
245.2.f.b.97.2		4	35.4	even	6
245.2.l.a.117.1		4	35.9	even	6
245.2.l.a.178.1		4	35.27	even	4
245.2.l.b.68.1		4	35.2	odd	12
245.2.l.b.227.1		4	35.34	odd	2
315.2.bz.a.208.1		4	105.47	odd	12
315.2.bz.a.262.1		4	15.14	odd	2
315.2.bz.b.73.1		4	15.2	even	4
315.2.bz.b.82.1		4	105.89	even	6
560.2.ci.a.257.1		4	140.19	even	6
560.2.ci.a.353.1		4	20.7	even	4
560.2.ci.b.17.1		4	20.19	odd	2
560.2.ci.b.33.1		4	140.47	odd	12

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)

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

Introduction

L-functions

Modular forms

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