LMFDB - Embedded newform 1000.2.t.b.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(101,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("1000.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.t (of order $10$, degree $4$, not 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.8
Character	$\chi$	$=$	1000.101
Dual form			1000.2.t.b.901.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30028 - 0.556118i) q^{2} +(-0.0718391 + 0.0988780i) q^{3} +(1.38147 + 1.44622i) q^{4} +(0.148399 - 0.0886183i) q^{6} +4.12326 q^{7} +(-0.992028 - 2.64875i) q^{8} +(0.922435 + 2.83896i) q^{9} +O(q^{10})$	\(q+(-1.30028 - 0.556118i) q^{2} +(-0.0718391 + 0.0988780i) q^{3} +(1.38147 + 1.44622i) q^{4} +(0.148399 - 0.0886183i) q^{6} +4.12326 q^{7} +(-0.992028 - 2.64875i) q^{8} +(0.922435 + 2.83896i) q^{9} +(-0.296291 - 0.0962708i) q^{11} +(-0.242243 + 0.0327016i) q^{12} +(4.08381 - 1.32691i) q^{13} +(-5.36140 - 2.29302i) q^{14} +(-0.183100 + 3.99581i) q^{16} +(-2.03874 + 1.48123i) q^{17} +(0.379371 - 4.20443i) q^{18} +(2.96240 + 4.07740i) q^{19} +(-0.296211 + 0.407699i) q^{21} +(0.331724 + 0.289952i) q^{22} +(1.97104 - 6.06625i) q^{23} +(0.333170 + 0.0921940i) q^{24} +(-6.04802 - 0.545721i) q^{26} +(-0.695692 - 0.226044i) q^{27} +(5.69614 + 5.96313i) q^{28} +(0.365173 - 0.502617i) q^{29} +(-5.55444 + 4.03554i) q^{31} +(2.46022 - 5.09385i) q^{32} +(0.0308043 - 0.0223807i) q^{33} +(3.47468 - 0.792241i) q^{34} +(-2.83145 + 5.25598i) q^{36} +(-8.16992 + 2.65457i) q^{37} +(-1.58445 - 6.94921i) q^{38} +(-0.162175 + 0.499123i) q^{39} +(-1.64354 - 5.05830i) q^{41} +(0.611887 - 0.365396i) q^{42} +2.23204i q^{43} +(-0.270087 - 0.561497i) q^{44} +(-5.93646 + 6.79170i) q^{46} +(5.15860 + 3.74794i) q^{47} +(-0.381944 - 0.305160i) q^{48} +10.0013 q^{49} -0.307997i q^{51} +(7.56065 + 4.07300i) q^{52} +(-2.76989 + 3.81243i) q^{53} +(0.778889 + 0.680807i) q^{54} +(-4.09039 - 10.9215i) q^{56} -0.615981 q^{57} +(-0.754342 + 0.450465i) q^{58} +(2.59396 - 0.842829i) q^{59} +(12.9582 + 4.21037i) q^{61} +(9.46657 - 2.15841i) q^{62} +(3.80344 + 11.7058i) q^{63} +(-6.03176 + 5.25527i) q^{64} +(-0.0525006 + 0.0119703i) q^{66} +(-5.75286 - 7.91813i) q^{67} +(-4.95865 - 0.902195i) q^{68} +(0.458220 + 0.630686i) q^{69} +(6.63373 + 4.81969i) q^{71} +(6.60462 - 5.25963i) q^{72} +(2.33319 - 7.18083i) q^{73} +(12.0994 + 1.09175i) q^{74} +(-1.80435 + 9.91707i) q^{76} +(-1.22168 - 0.396949i) q^{77} +(0.488444 - 0.558812i) q^{78} +(-3.65256 - 2.65374i) q^{79} +(-7.17257 + 5.21118i) q^{81} +(-0.675942 + 7.49122i) q^{82} +(4.15816 + 5.72321i) q^{83} +(-0.998828 + 0.134837i) q^{84} +(1.24127 - 2.90228i) q^{86} +(0.0234641 + 0.0722151i) q^{87} +(0.0389318 + 0.880304i) q^{88} +(2.63206 - 8.10065i) q^{89} +(16.8386 - 5.47119i) q^{91} +(11.4961 - 5.52976i) q^{92} -0.839121i q^{93} +(-4.62334 - 7.74217i) q^{94} +(0.326930 + 0.609199i) q^{96} +(-0.640392 - 0.465272i) q^{97} +(-13.0044 - 5.56187i) q^{98} -0.929963i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.30028	−	0.556118i	−0.919438	−	0.393234i
$2$	−1.30028	−	0.556118i	−0.919438	−	0.393234i
$3$	−0.0718391	+	0.0988780i	−0.0414763	+	0.0570872i	−0.829251	−	0.558876i	$-0.811233\pi$
$3$	−0.0718391	+	0.0988780i	−0.0414763	+	0.0570872i	0.787775	+	0.615963i	$0.211233\pi$
$4$	1.38147	+	1.44622i	0.690733	+	0.723110i
$5$		0			0
$5$		0			0
$6$	0.148399	−	0.0886183i	0.0605836	−	0.0361783i
$7$	4.12326			1.55844			0.779222	−	0.626748i	$-0.215614\pi$
$7$	4.12326			1.55844			0.779222	+	0.626748i	$0.215614\pi$
$8$	−0.992028	−	2.64875i	−0.350735	−	0.936475i
$9$	0.922435	+	2.83896i	0.307478	+	0.946321i
$10$		0			0
$11$	−0.296291	−	0.0962708i	−0.0893351	−	0.0290267i	0.264008	−	0.964520i	$-0.414955\pi$
$11$	−0.296291	−	0.0962708i	−0.0893351	−	0.0290267i	−0.353344	+	0.935494i	$0.614955\pi$
$12$	−0.242243	+	0.0327016i	−0.0699294	+	0.00944014i
$13$	4.08381	−	1.32691i	1.13264	−	0.368019i	0.318064	−	0.948069i	$-0.396967\pi$
$13$	4.08381	−	1.32691i	1.13264	−	0.368019i	0.814581	+	0.580050i	$0.196967\pi$
$14$	−5.36140	−	2.29302i	−1.43289	−	0.612834i
$15$		0			0
$16$	−0.183100	+	3.99581i	−0.0457750	+	0.998952i
$17$	−2.03874	+	1.48123i	−0.494468	+	0.359252i	−0.806900	−	0.590688i	$-0.798856\pi$
$17$	−2.03874	+	1.48123i	−0.494468	+	0.359252i	0.312432	+	0.949940i	$0.398856\pi$
$18$	0.379371	−	4.20443i	0.0894187	−	0.990995i
$19$	2.96240	+	4.07740i	0.679622	+	0.935419i	0.999929	−	0.0118946i	$-0.00378626\pi$
$19$	2.96240	+	4.07740i	0.679622	+	0.935419i	−0.320308	+	0.947314i	$0.603786\pi$
$20$		0			0
$21$	−0.296211	+	0.407699i	−0.0646385	+	0.0889673i
$22$	0.331724	+	0.289952i	0.0707238	+	0.0618179i
$23$	1.97104	−	6.06625i	0.410991	−	1.26490i	−0.504797	−	0.863238i	$-0.668433\pi$
$23$	1.97104	−	6.06625i	0.410991	−	1.26490i	0.915788	−	0.401662i	$-0.131567\pi$
$24$	0.333170	+	0.0921940i	0.0680079	+	0.0188190i
$25$		0			0
$26$	−6.04802	−	0.545721i	−1.18611	−	0.107025i
$27$	−0.695692	−	0.226044i	−0.133886	−	0.0435022i
$28$	5.69614	+	5.96313i	1.07647	+	1.12693i
$29$	0.365173	−	0.502617i	0.0678109	−	0.0933337i	−0.773764	−	0.633473i	$-0.781629\pi$
$29$	0.365173	−	0.502617i	0.0678109	−	0.0933337i	0.841575	+	0.540140i	$0.181629\pi$
$30$		0			0
$31$	−5.55444	+	4.03554i	−0.997607	+	0.724804i	−0.961574	−	0.274547i	$-0.911472\pi$
$31$	−5.55444	+	4.03554i	−0.997607	+	0.724804i	−0.0360329	+	0.999351i	$0.511472\pi$
$32$	2.46022	−	5.09385i	0.434910	−	0.900474i
$33$	0.0308043	−	0.0223807i	0.00536235	−	0.00389597i
$34$	3.47468	−	0.792241i	0.595903	−	0.135868i
$35$		0			0
$36$	−2.83145	+	5.25598i	−0.471908	+	0.875996i
$37$	−8.16992	+	2.65457i	−1.34313	+	0.436408i	−0.890374	−	0.455229i	$-0.849557\pi$
$37$	−8.16992	+	2.65457i	−1.34313	+	0.436408i	−0.452751	+	0.891637i	$0.649557\pi$
$38$	−1.58445	−	6.94921i	−0.257031	−	1.12731i
$39$	−0.162175	+	0.499123i	−0.0259688	+	0.0799236i
$40$		0			0
$41$	−1.64354	−	5.05830i	−0.256678	−	0.789974i	−0.993494	−	0.113881i	$-0.963672\pi$
$41$	−1.64354	−	5.05830i	−0.256678	−	0.789974i	0.736816	−	0.676093i	$-0.236328\pi$
$42$	0.611887	−	0.365396i	0.0944161	−	0.0563818i
$43$			2.23204i			0.340382i	0.985411	+	0.170191i	$0.0544385\pi$
$43$			2.23204i			0.340382i	−0.985411	+	0.170191i	$0.945561\pi$
$44$	−0.270087	−	0.561497i	−0.0407172	−	0.0846488i
$45$		0			0
$46$	−5.93646	+	6.79170i	−0.875283	+	1.00138i
$47$	5.15860	+	3.74794i	0.752459	+	0.546693i	0.896588	−	0.442866i	$-0.146038\pi$
$47$	5.15860	+	3.74794i	0.752459	+	0.546693i	−0.144129	+	0.989559i	$0.546038\pi$
$48$	−0.381944	−	0.305160i	−0.0551288	−	0.0440460i
$49$	10.0013			1.42875
$50$		0			0
$51$		−	0.307997i		−	0.0431283i
$52$	7.56065	+	4.07300i	1.04847	+	0.564824i
$53$	−2.76989	+	3.81243i	−0.380474	+	0.523678i	−0.955710	−	0.294310i	$-0.904910\pi$
$53$	−2.76989	+	3.81243i	−0.380474	+	0.523678i	0.575236	+	0.817988i	$0.304910\pi$
$54$	0.778889	+	0.680807i	0.105993	+	0.0926462i
$55$		0			0
$56$	−4.09039	−	10.9215i	−0.546601	−	1.45944i
$57$	−0.615981			−0.0815887
$58$	−0.754342	+	0.450465i	−0.0990500	+	0.0591490i
$59$	2.59396	−	0.842829i	0.337705	−	0.109727i	−0.135255	−	0.990811i	$-0.543185\pi$
$59$	2.59396	−	0.842829i	0.337705	−	0.109727i	0.472960	+	0.881084i	$0.343185\pi$
$60$		0			0
$61$	12.9582	+	4.21037i	1.65913	+	0.539082i	0.980688	−	0.195576i	$-0.0626577\pi$
$61$	12.9582	+	4.21037i	1.65913	+	0.539082i	0.678437	+	0.734659i	$0.262658\pi$
$62$	9.46657	−	2.15841i	1.20226	−	0.274119i
$63$	3.80344	+	11.7058i	0.479188	+	1.47479i
$64$	−6.03176	+	5.25527i	−0.753970	+	0.656909i
$65$		0			0
$66$	−0.0525006	+	0.0119703i	−0.00646238	+	0.00147345i
$67$	−5.75286	−	7.91813i	−0.702824	−	0.967354i	−0.999922	−	0.0125070i	$-0.996019\pi$
$67$	−5.75286	−	7.91813i	−0.702824	−	0.967354i	0.297098	−	0.954847i	$-0.403981\pi$
$68$	−4.95865	−	0.902195i	−0.601324	−	0.109407i
$69$	0.458220	+	0.630686i	0.0551633	+	0.0759257i
$70$		0			0
$71$	6.63373	+	4.81969i	0.787279	+	0.571992i	0.907155	−	0.420797i	$-0.138250\pi$
$71$	6.63373	+	4.81969i	0.787279	+	0.571992i	−0.119876	+	0.992789i	$0.538250\pi$
$72$	6.60462	−	5.25963i	0.778362	−	0.619854i
$73$	2.33319	−	7.18083i	0.273079	−	0.840452i	−0.716642	−	0.697441i	$-0.754322\pi$
$73$	2.33319	−	7.18083i	0.273079	−	0.840452i	0.989721	−	0.143011i	$-0.0456783\pi$
$74$	12.0994	+	1.09175i	1.40653	+	0.126913i
$75$		0			0
$76$	−1.80435	+	9.91707i	−0.206973	+	1.13757i
$77$	−1.22168	−	0.396949i	−0.139224	−	0.0452366i
$78$	0.488444	−	0.558812i	0.0553054	−	0.0632730i
$79$	−3.65256	−	2.65374i	−0.410945	−	0.298569i	0.363040	−	0.931774i	$-0.381739\pi$
$79$	−3.65256	−	2.65374i	−0.410945	−	0.298569i	−0.773984	+	0.633205i	$0.781739\pi$
$80$		0			0
$81$	−7.17257	+	5.21118i	−0.796952	+	0.579020i
$82$	−0.675942	+	7.49122i	−0.0746453	+	0.827267i
$83$	4.15816	+	5.72321i	0.456417	+	0.628204i	0.973761	−	0.227573i	$-0.0730792\pi$
$83$	4.15816	+	5.72321i	0.456417	+	0.628204i	−0.517344	+	0.855778i	$0.673079\pi$
$84$	−0.998828	+	0.134837i	−0.108981	+	0.0147119i
$85$		0			0
$86$	1.24127	−	2.90228i	0.133850	−	0.312960i
$87$	0.0234641	+	0.0722151i	0.00251562	+	0.00774227i
$88$	0.0389318	+	0.880304i	0.00415014	+	0.0938408i
$89$	2.63206	−	8.10065i	0.278998	−	0.858667i	−0.709136	−	0.705072i	$-0.750915\pi$
$89$	2.63206	−	8.10065i	0.278998	−	0.858667i	0.988134	−	0.153595i	$-0.0490852\pi$
$90$		0			0
$91$	16.8386	−	5.47119i	1.76516	−	0.573537i
$92$	11.4961	−	5.52976i	1.19855	−	0.576517i
$93$		−	0.839121i		−	0.0870128i
$94$	−4.62334	−	7.74217i	−0.476861	−	0.798543i
$95$		0			0
$96$	0.326930	+	0.609199i	0.0333671	+	0.0621761i
$97$	−0.640392	−	0.465272i	−0.0650220	−	0.0472412i	0.554799	−	0.831984i	$-0.312795\pi$
$97$	−0.640392	−	0.465272i	−0.0650220	−	0.0472412i	−0.619821	+	0.784743i	$0.712795\pi$
$98$	−13.0044	−	5.56187i	−1.31365	−	0.561834i
$99$		−	0.929963i		−	0.0934648i
$100$		0			0
$101$		−	3.69351i		−	0.367518i	−0.982971	−	0.183759i	$-0.941173\pi$
$101$		−	3.69351i		−	0.367518i	0.982971	−	0.183759i	$-0.0588267\pi$
$102$	−0.171283	+	0.400484i	−0.0169595	+	0.0396538i
$103$	11.7798	+	8.55853i	1.16070	+	0.843297i	0.989866	−	0.142003i	$-0.0453542\pi$
$103$	11.7798	+	8.55853i	1.16070	+	0.843297i	0.170833	+	0.985300i	$0.445354\pi$
$104$	−7.56591	−	9.50066i	−0.741898	−	0.931616i
$105$		0			0
$106$	5.72180	−	3.41685i	0.555751	−	0.331874i
$107$			16.7052i			1.61496i	0.589897	+	0.807478i	$0.299168\pi$
$107$			16.7052i			1.61496i	−0.589897	+	0.807478i	$0.700832\pi$
$108$	−0.634166	−	1.31840i	−0.0610227	−	0.126863i
$109$	13.9033	−	4.51745i	1.33169	−	0.432693i	0.445198	−	0.895432i	$-0.353133\pi$
$109$	13.9033	−	4.51745i	1.33169	−	0.432693i	0.886494	+	0.462739i	$0.153133\pi$
$110$		0			0
$111$	0.324441	−	0.998526i	0.0307946	−	0.0947759i
$112$	−0.754969	+	16.4757i	−0.0713378	+	1.55681i
$113$	−3.33141	−	10.2530i	−0.313393	−	0.964523i	−0.976411	−	0.215920i	$-0.930725\pi$
$113$	−3.33141	−	10.2530i	−0.313393	−	0.964523i	0.663018	−	0.748603i	$-0.269275\pi$
$114$	0.800949	+	0.342558i	0.0750157	+	0.0320835i
$115$		0			0
$116$	1.23137	−	0.166229i	0.114330	−	0.0154340i
$117$	7.53410	+	10.3698i	0.696528	+	0.958688i
$118$	−3.84159	−	0.346632i	−0.353647	−	0.0319100i
$119$	−8.40627	+	6.10751i	−0.770601	+	0.559875i
$120$		0			0
$121$	−8.82067	−	6.40859i	−0.801879	−	0.582599i
$122$	−14.5078	−	12.6809i	−1.31348	−	1.14808i
$123$	0.618225	+	0.200874i	0.0557435	+	0.0181122i
$124$	−13.5095	−	2.45798i	−1.21319	−	0.220733i
$125$		0			0
$126$	1.56425	−	17.3360i	0.139354	−	1.54441i
$127$	0.691823	−	2.12921i	0.0613894	−	0.188937i	−0.915658	−	0.401957i	$-0.868330\pi$
$127$	0.691823	−	2.12921i	0.0613894	−	0.188937i	0.977048	+	0.213020i	$0.0683300\pi$
$128$	10.7655	−	3.47897i	0.951548	−	0.307500i
$129$	−0.220699	−	0.160347i	−0.0194315	−	0.0141178i
$130$		0			0
$131$	2.08338	+	2.86752i	0.182026	+	0.250537i	0.890273	−	0.455428i	$-0.150514\pi$
$131$	2.08338	+	2.86752i	0.182026	+	0.250537i	−0.708247	+	0.705965i	$0.750514\pi$
$132$	0.0749225	+	0.0136317i	0.00652117	+	0.00118649i
$133$	12.2147	+	16.8122i	1.05915	+	1.45780i
$134$	3.07693	+	13.4951i	0.265806	+	1.16580i
$135$		0			0
$136$	5.94591	+	3.93070i	0.509858	+	0.337055i
$137$	−4.16928	−	12.8317i	−0.356205	−	1.09629i	−0.955307	−	0.295614i	$-0.904476\pi$
$137$	−4.16928	−	12.8317i	−0.356205	−	1.09629i	0.599102	−	0.800673i	$-0.295524\pi$
$138$	−0.245080	−	1.07489i	−0.0208626	−	0.0915011i
$139$	9.64111	+	3.13259i	0.817749	+	0.265703i	0.687876	−	0.725828i	$-0.258543\pi$
$139$	9.64111	+	3.13259i	0.817749	+	0.265703i	0.129872	+	0.991531i	$0.458543\pi$
$140$		0			0
$141$	−0.741178	+	0.240823i	−0.0624184	+	0.0202810i
$142$	−5.94541	−	9.95608i	−0.498927	−	0.835496i
$143$	−1.33774			−0.111867
$144$	−11.5128	+	3.16606i	−0.959404	+	0.263838i
$145$		0			0
$146$	−7.02719	+	8.03957i	−0.581574	+	0.665359i
$147$	−0.718481	+	0.988904i	−0.0592593	+	0.0815634i
$148$	−15.1256	−	8.14829i	−1.24331	−	0.669786i
$149$			14.3531i			1.17585i	0.808916	+	0.587925i	$0.200055\pi$
$149$			14.3531i			1.17585i	−0.808916	+	0.587925i	$0.799945\pi$
$150$		0			0
$151$	14.4342			1.17464			0.587321	−	0.809354i	$-0.300183\pi$
$151$	14.4342			1.17464			0.587321	+	0.809354i	$0.300183\pi$
$152$	7.86122	−	11.8916i	0.637629	−	0.964533i
$153$	−6.08578	−	4.42158i	−0.492006	−	0.357463i
$154$	1.36778	+	1.19555i	0.110219	+	0.0963398i
$155$		0			0
$156$	−0.945880	+	0.454981i	−0.0757310	+	0.0364276i
$157$		−	19.2873i		−	1.53930i	−0.638469	−	0.769648i	$-0.720432\pi$
$157$		−	19.2873i		−	1.53930i	0.638469	−	0.769648i	$-0.279568\pi$
$158$	3.27356	+	5.48186i	0.260431	+	0.436113i
$159$	−0.177979	−	0.547763i	−0.0141147	−	0.0434404i
$160$		0			0
$161$	8.12712	−	25.0127i	0.640507	−	1.97128i
$162$	12.2244	−	2.78721i	0.960439	−	0.218984i
$163$	8.73364	−	2.83773i	0.684072	−	0.222268i	0.0536946	−	0.998557i	$-0.482900\pi$
$163$	8.73364	−	2.83773i	0.684072	−	0.222268i	0.630377	+	0.776289i	$0.282900\pi$
$164$	5.04492	−	9.36480i	0.393942	−	0.731268i
$165$		0			0
$166$	−2.22400	−	9.75421i	−0.172616	−	0.757074i
$167$	−7.15453	+	5.19807i	−0.553634	+	0.402239i	−0.829124	−	0.559065i	$-0.811160\pi$
$167$	−7.15453	+	5.19807i	−0.553634	+	0.402239i	0.275489	+	0.961304i	$0.411160\pi$
$168$	1.37374	+	0.380140i	0.105987	+	0.0293284i
$169$	4.39959	−	3.19649i	0.338430	−	0.245884i
$170$		0			0
$171$	−8.84296	+	12.1713i	−0.676238	+	0.930761i
$172$	−3.22801	+	3.08348i	−0.246134	+	0.235113i
$173$	−12.4913	−	4.05868i	−0.949698	−	0.308576i	−0.207105	−	0.978319i	$-0.566404\pi$
$173$	−12.4913	−	4.05868i	−0.949698	−	0.308576i	−0.742593	+	0.669743i	$0.766404\pi$
$174$	0.00965013	−	0.106949i	0.000731574	−	0.00810777i
$175$		0			0
$176$	0.438930	−	1.16629i	0.0330856	−	0.0879128i
$177$	−0.103011	+	0.317034i	−0.00774274	+	0.0238297i
$178$	−7.92733	+	9.06939i	−0.594179	+	0.679780i
$179$	−0.375298	+	0.516553i	−0.0280511	+	0.0386090i	−0.822812	−	0.568313i	$-0.807596\pi$
$179$	−0.375298	+	0.516553i	−0.0280511	+	0.0386090i	0.794761	+	0.606922i	$0.207596\pi$
$180$		0			0
$181$	−11.7000	−	16.1037i	−0.869656	−	1.19698i	−0.979180	−	0.202995i	$-0.934932\pi$
$181$	−11.7000	−	16.1037i	−0.869656	−	1.19698i	0.109523	−	0.993984i	$-0.465068\pi$
$182$	−24.9376	−	2.25015i	−1.84849	−	0.166792i
$183$	−1.34722	+	0.978810i	−0.0995891	+	0.0723557i
$184$	−18.0233	+	0.797087i	−1.32870	+	0.0587620i
$185$		0			0
$186$	−0.466650	+	1.09109i	−0.0342164	+	0.0800029i
$187$	0.746661	−	0.242605i	0.0546013	−	0.0177410i
$188$	1.70609	+	12.6381i	0.124429	+	0.921729i
$189$	−2.86852	−	0.932038i	−0.208654	−	0.0677958i
$190$		0			0
$191$	5.61154	+	17.2706i	0.406037	+	1.24965i	0.920026	+	0.391857i	$0.128167\pi$
$191$	5.61154	+	17.2706i	0.406037	+	1.24965i	−0.513989	+	0.857797i	$0.671833\pi$
$192$	−0.0863147	−	0.973942i	−0.00622923	−	0.0702882i
$193$	−16.2523			−1.16986			−0.584932	−	0.811083i	$-0.698879\pi$
$193$	−16.2523			−1.16986			−0.584932	+	0.811083i	$0.698879\pi$
$194$	0.573945	+	0.961119i	0.0412068	+	0.0690043i
$195$		0			0
$196$	13.8164	+	14.4640i	0.986885	+	1.03314i
$197$	−6.77613	+	9.32654i	−0.482779	+	0.664488i	−0.979036	−	0.203687i	$-0.934707\pi$
$197$	−6.77613	+	9.32654i	−0.482779	+	0.664488i	0.496257	+	0.868176i	$0.334707\pi$
$198$	−0.517169	+	1.20921i	−0.0367536	+	0.0859351i
$199$	−14.9527			−1.05997			−0.529983	−	0.848008i	$-0.677802\pi$
$199$	−14.9527			−1.05997			−0.529983	+	0.848008i	$0.677802\pi$
$200$		0			0
$201$	1.19621			0.0843741
$202$	−2.05403	+	4.80261i	−0.144521	+	0.337911i
$203$	1.50570	−	2.07242i	0.105680	−	0.145455i
$204$	0.445432	−	0.425488i	0.0311865	−	0.0297901i
$205$		0			0
$206$	−10.5575	−	17.6795i	−0.735578	−	1.23179i
$207$	19.0400			1.32337
$208$	4.55433	+	16.5611i	0.315786	+	1.14830i
$209$	−0.485199	−	1.49329i	−0.0335619	−	0.103293i
$210$		0			0
$211$	2.07919	+	0.675570i	0.143137	+	0.0465082i	0.379710	−	0.925106i	$-0.376024\pi$
$211$	2.07919	+	0.675570i	0.143137	+	0.0465082i	−0.236572	+	0.971614i	$0.576024\pi$
$212$	−9.34013	+	1.26087i	−0.641483	+	0.0865972i
$213$	−0.953122	+	0.309688i	−0.0653068	+	0.0212195i
$214$	9.29008	−	21.7215i	0.635057	−	1.48485i
$215$		0			0
$216$	0.0914119	+	2.06696i	0.00621979	+	0.140639i
$217$	−22.9024	+	16.6396i	−1.55471	+	1.12957i
$218$	−20.5904	−	1.85790i	−1.39456	−	0.125833i
$219$	0.542411	+	0.746565i	0.0366528	+	0.0504482i
$220$		0			0
$221$	−6.36038	+	8.75431i	−0.427845	+	0.588879i
$222$	−0.977163	+	1.11794i	−0.0655829	+	0.0750311i
$223$	−6.16124	+	18.9624i	−0.412587	+	1.26981i	0.501804	+	0.864981i	$0.332670\pi$
$223$	−6.16124	+	18.9624i	−0.412587	+	1.26981i	−0.914391	+	0.404832i	$0.867330\pi$
$224$	10.1441	−	21.0033i	0.677783	−	1.40334i
$225$		0			0
$226$	−1.37011	+	15.1845i	−0.0911386	+	1.01006i
$227$	−10.6573	−	3.46276i	−0.707349	−	0.229832i	−0.0668195	−	0.997765i	$-0.521285\pi$
$227$	−10.6573	−	3.46276i	−0.707349	−	0.229832i	−0.640530	+	0.767933i	$0.721285\pi$
$228$	−0.850957	−	0.890844i	−0.0563560	−	0.0589976i
$229$	−4.28891	+	5.90318i	−0.283419	+	0.390093i	−0.926863	−	0.375401i	$-0.877505\pi$
$229$	−4.28891	+	5.90318i	−0.283419	+	0.390093i	0.643444	+	0.765494i	$0.277505\pi$
$230$		0			0
$231$	0.127014	−	0.0922812i	0.00835692	−	0.00607166i
$232$	−1.69357	−	0.468641i	−0.111188	−	0.0307678i
$233$	−9.35234	+	6.79487i	−0.612692	+	0.445147i	−0.850361	−	0.526199i	$-0.823617\pi$
$233$	−9.35234	+	6.79487i	−0.612692	+	0.445147i	0.237669	+	0.971346i	$0.423617\pi$
$234$	−4.02963	−	17.6735i	−0.263425	−	1.15535i
$235$		0			0
$236$	4.80239	+	2.58710i	0.312609	+	0.168406i
$237$	0.524792	−	0.170515i	0.0340889	−	0.0110762i
$238$	14.3270	−	3.26661i	0.928682	−	0.211743i
$239$	0.177923	−	0.547590i	0.0115089	−	0.0354207i	−0.945137	−	0.326674i	$-0.894072\pi$
$239$	0.177923	−	0.547590i	0.0115089	−	0.0354207i	0.956646	+	0.291253i	$0.0940722\pi$
$240$		0			0
$241$	0.273524	+	0.841820i	0.0176192	+	0.0542264i	0.959480	−	0.281778i	$-0.0909242\pi$
$241$	0.273524	+	0.841820i	0.0176192	+	0.0542264i	−0.941860	+	0.336005i	$0.890924\pi$
$242$	7.90543	+	13.2383i	0.508180	+	0.850990i
$243$		−	3.27806i		−	0.210287i
$244$	11.8122	+	24.5569i	0.756197	+	1.57209i
$245$		0			0
$246$	−0.692158	−	0.604998i	−0.0441304	−	0.0385733i
$247$	17.5082	+	12.7205i	1.11402	+	0.809384i
$248$	16.1993	+	10.7090i	1.02866	+	0.680019i
$249$	−0.864618			−0.0547929
$250$		0			0
$251$		−	10.4673i		−	0.660692i	−0.943860	−	0.330346i	$-0.892835\pi$
$251$		−	10.4673i		−	0.660692i	0.943860	−	0.330346i	$-0.107165\pi$
$252$	−11.6748	+	21.6717i	−0.735443	+	1.36519i
$253$	−1.16800	+	1.60762i	−0.0734318	+	0.101070i
$254$	−2.08366	+	2.38384i	−0.130740	+	0.149576i
$255$		0			0
$256$	−15.9329	−	1.46327i	−0.995809	−	0.0914541i
$257$	−17.6103			−1.09850			−0.549250	−	0.835658i	$-0.685086\pi$
$257$	−17.6103			−1.09850			−0.549250	+	0.835658i	$0.685086\pi$
$258$	0.197799	+	0.331231i	0.0123144	+	0.0206216i
$259$	−33.6867	+	10.9455i	−2.09319	+	0.680118i
$260$		0			0
$261$	1.76376	+	0.573081i	0.109174	+	0.0354728i
$262$	−1.11430	−	4.88719i	−0.0688416	−	0.301932i
$263$	−6.72853	−	20.7083i	−0.414899	−	1.27693i	−0.912341	−	0.409430i	$-0.865727\pi$
$263$	−6.72853	−	20.7083i	−0.414899	−	1.27693i	0.497442	−	0.867497i	$-0.334273\pi$
$264$	−0.0898395	−	0.0593907i	−0.00552924	−	0.00365525i
$265$		0			0
$266$	−6.53308	−	28.6534i	−0.400569	−	1.75685i
$267$	0.611891	+	0.842196i	0.0374471	+	0.0515416i
$268$	3.50397	−	19.2585i	0.214039	−	1.17640i
$269$	−7.13157	−	9.81576i	−0.434819	−	0.598477i	0.534232	−	0.845338i	$-0.320601\pi$
$269$	−7.13157	−	9.81576i	−0.434819	−	0.598477i	−0.969051	+	0.246861i	$0.920601\pi$
$270$		0			0
$271$	−12.7055	−	9.23111i	−0.771806	−	0.560750i	0.130702	−	0.991422i	$-0.458277\pi$
$271$	−12.7055	−	9.23111i	−0.771806	−	0.560750i	−0.902509	+	0.430672i	$0.858277\pi$
$272$	−5.54543	−	8.41764i	−0.336241	−	0.510395i
$273$	−0.668689	+	2.05801i	−0.0404709	+	0.124557i
$274$	−1.71471	+	19.0034i	−0.103589	+	1.14804i
$275$		0			0
$276$	−0.279094	+	1.53396i	−0.0167995	+	0.0923335i
$277$	−2.21665	−	0.720234i	−0.133186	−	0.0432747i	0.241666	−	0.970360i	$-0.422306\pi$
$277$	−2.21665	−	0.720234i	−0.133186	−	0.0432747i	−0.374851	+	0.927085i	$0.622306\pi$
$278$	−10.7941	−	9.43484i	−0.647386	−	0.565864i
$279$	−16.5803	−	12.0463i	−0.992639	−	0.721195i
$280$		0			0
$281$	11.0233	−	8.00887i	0.657592	−	0.477769i	−0.208257	−	0.978074i	$-0.566779\pi$
$281$	11.0233	−	8.00887i	0.657592	−	0.477769i	0.865849	+	0.500305i	$0.166779\pi$
$282$	1.09767	+	0.0990438i	0.0653650	+	0.00589797i
$283$	−2.34292	−	3.22475i	−0.139272	−	0.191691i	0.733683	−	0.679491i	$-0.237800\pi$
$283$	−2.34292	−	3.22475i	−0.139272	−	0.191691i	−0.872955	+	0.487800i	$0.837800\pi$
$284$	2.19395	+	16.2521i	0.130187	+	0.964382i
$285$		0			0
$286$	1.73944	+	0.743940i	0.102855	+	0.0439901i
$287$	−6.77675	−	20.8567i	−0.400019	−	1.23113i
$288$	16.7306	+	2.28573i	0.985863	+	0.134688i
$289$	−3.29087	+	10.1282i	−0.193580	+	0.595779i
$290$		0			0
$291$	0.0920104	−	0.0298960i	0.00539374	−	0.00175253i
$292$	13.6083	−	6.54576i	0.796364	−	0.383062i
$293$		−	9.63185i		−	0.562699i	−0.959605	−	0.281349i	$-0.909218\pi$
$293$		−	9.63185i		−	0.562699i	0.959605	−	0.281349i	$-0.0907820\pi$
$294$	1.48417	−	0.886294i	0.0865588	−	0.0516897i
$295$		0			0
$296$	15.1361	+	19.0067i	0.879766	+	1.10474i
$297$	0.184366	+	0.133950i	0.0106980	+	0.00777255i
$298$	7.98199	−	18.6630i	0.462384	−	1.08112i
$299$		−	27.3888i		−	1.58393i
$300$		0			0
$301$			9.20326i			0.530467i
$302$	−18.7686	−	8.02713i	−1.08001	−	0.461909i
$303$	0.365207	+	0.265339i	0.0209806	+	0.0152433i
$304$	−16.8349	+	11.0906i	−0.965548	+	0.636090i
$305$		0			0
$306$	5.45431	+	9.13371i	0.311802	+	0.522139i
$307$		−	8.12625i		−	0.463790i	−0.972741	−	0.231895i	$-0.925507\pi$
$307$		−	8.12625i		−	0.463790i	0.972741	−	0.231895i	$-0.0744925\pi$
$308$	−1.11364	−	2.31520i	−0.0634555	−	0.131920i
$309$	−1.69250	+	0.549927i	−0.0962830	+	0.0312842i
$310$		0			0
$311$	−1.39243	+	4.28546i	−0.0789575	+	0.243006i	−0.982742	−	0.184982i	$-0.940777\pi$
$311$	−1.39243	+	4.28546i	−0.0789575	+	0.243006i	0.903784	+	0.427988i	$0.140777\pi$
$312$	1.48293	−	0.0655833i	0.0839546	−	0.00371292i
$313$	−0.613980	−	1.88964i	−0.0347042	−	0.106809i	0.932204	−	0.361934i	$-0.117883\pi$
$313$	−0.613980	−	1.88964i	−0.0347042	−	0.106809i	−0.966908	+	0.255125i	$0.917883\pi$
$314$	−10.7260	+	25.0789i	−0.605304	+	1.41529i
$315$		0			0
$316$	−1.20800	−	8.94844i	−0.0679552	−	0.503389i
$317$	7.24561	+	9.97273i	0.406954	+	0.560124i	0.962472	−	0.271380i	$-0.0874800\pi$
$317$	7.24561	+	9.97273i	0.406954	+	0.560124i	−0.555518	+	0.831504i	$0.687480\pi$
$318$	−0.0731978	+	0.811224i	−0.00410473	+	0.0454912i
$319$	−0.156585	+	0.113766i	−0.00876707	+	0.00636965i
$320$		0			0
$321$	−1.65178	−	1.20009i	−0.0921934	−	0.0669824i
$322$	−24.4775	+	28.0039i	−1.36408	+	1.56060i
$323$	−12.0792	−	3.92476i	−0.672103	−	0.218379i
$324$	−17.4452	−	3.17404i	−0.969176	−	0.176336i
$325$		0			0
$326$	−12.9343	−	1.16708i	−0.716365	−	0.0646385i
$327$	−0.552122	+	1.69926i	−0.0305324	+	0.0939691i
$328$	−11.7677	+	9.37131i	−0.649765	+	0.517444i
$329$	21.2702	+	15.4537i	1.17267	+	0.851991i
$330$		0			0
$331$	−15.4091	−	21.2088i	−0.846960	−	1.16574i	−0.984524	−	0.175247i	$-0.943928\pi$
$331$	−15.4091	−	21.2088i	−0.846960	−	1.16574i	0.137565	−	0.990493i	$-0.456072\pi$
$332$	−2.53266	+	13.9200i	−0.138998	+	0.763961i
$333$	−15.0724	−	20.7454i	−0.825964	−	1.13684i
$334$	12.1936	−	2.78020i	0.667206	−	0.152126i
$335$		0			0
$336$	−1.57485	−	1.25825i	−0.0859152	−	0.0686433i
$337$	−7.86898	−	24.2182i	−0.428651	−	1.31925i	−0.899455	−	0.437013i	$-0.856036\pi$
$337$	−7.86898	−	24.2182i	−0.428651	−	1.31925i	0.470805	−	0.882238i	$-0.343964\pi$
$338$	−7.49833	+	1.70965i	−0.407855	+	0.0929926i
$339$	1.25312	+	0.407164i	0.0680603	+	0.0221141i
$340$		0			0
$341$	2.03423	−	0.660963i	0.110160	−	0.0357931i
$342$	18.2670	−	10.9084i	0.987766	−	0.589858i
$343$	12.3749			0.668184
$344$	5.91211	−	2.21424i	0.318759	−	0.119384i
$345$		0			0
$346$	13.9851	+	12.2241i	0.751846	+	0.657170i
$347$	15.7492	−	21.6770i	0.845463	−	1.16368i	−0.139381	−	0.990239i	$-0.544511\pi$
$347$	15.7492	−	21.6770i	0.845463	−	1.16368i	0.984844	−	0.173442i	$-0.0554888\pi$
$348$	−0.0720240	+	0.133697i	−0.00386089	+	0.00716691i
$349$		−	9.22396i		−	0.493747i	−0.969048	−	0.246874i	$-0.920597\pi$
$349$		−	9.22396i		−	0.493747i	0.969048	−	0.246874i	$-0.0794032\pi$
$350$		0			0
$351$	−3.14101			−0.167655
$352$	−1.21933	+	1.27241i	−0.0649905	+	0.0678199i
$353$	11.6931	+	8.49553i	0.622361	+	0.452172i	0.853745	−	0.520691i	$-0.174326\pi$
$353$	11.6931	+	8.49553i	0.622361	+	0.452172i	−0.231384	+	0.972862i	$0.574326\pi$
$354$	0.310251	−	0.354947i	0.0164896	−	0.0188652i
$355$		0			0
$356$	15.3514	−	7.38424i	0.813624	−	0.391364i
$357$		−	1.26995i		−	0.0672130i
$358$	0.775257	−	0.462955i	0.0409736	−	0.0244679i
$359$	0.995352	+	3.06338i	0.0525327	+	0.161679i	0.973881	−	0.227059i	$-0.0729111\pi$
$359$	0.995352	+	3.06338i	0.0525327	+	0.161679i	−0.921348	+	0.388738i	$0.872911\pi$
$360$		0			0
$361$	−1.97802	+	6.08771i	−0.104106	+	0.320406i
$362$	6.25778	+	27.4460i	0.328902	+	1.44253i
$363$	1.26734	−	0.411783i	0.0665179	−	0.0216130i
$364$	31.1745	+	16.7940i	1.63399	+	0.880247i
$365$		0			0
$366$	2.29609	−	0.523518i	0.120019	−	0.0273647i
$367$	−7.29490	+	5.30006i	−0.380791	+	0.276661i	−0.761671	−	0.647964i	$-0.775621\pi$
$367$	−7.29490	+	5.30006i	−0.380791	+	0.276661i	0.380881	+	0.924624i	$0.375621\pi$
$368$	23.8787	+	8.98664i	1.24476	+	0.468461i
$369$	12.8443	−	9.33191i	0.668646	−	0.485800i
$370$		0			0
$371$	−11.4210	+	15.7196i	−0.592948	+	0.816123i
$372$	1.21355	−	1.15922i	0.0629198	−	0.0601026i
$373$	9.13862	+	2.96932i	0.473180	+	0.153746i	0.535893	−	0.844286i	$-0.319975\pi$
$373$	9.13862	+	2.96932i	0.473180	+	0.153746i	−0.0627126	+	0.998032i	$0.519975\pi$
$374$	−1.10579	−	0.0997766i	−0.0571789	−	0.00515932i
$375$		0			0
$376$	4.80988	−	17.3819i	0.248051	−	0.896403i
$377$	0.824369	−	2.53715i	0.0424571	−	0.130670i
$378$	3.21156	+	2.80714i	0.165185	+	0.144384i
$379$	0.875430	−	1.20493i	0.0449678	−	0.0618929i	−0.785941	−	0.618302i	$-0.787821\pi$
$379$	0.875430	−	1.20493i	0.0449678	−	0.0618929i	0.830909	+	0.556409i	$0.187821\pi$
$380$		0			0
$381$	0.160832	+	0.221367i	0.00823969	+	0.0113410i
$382$	2.30787	−	25.5773i	0.118081	−	1.30865i
$383$	9.99860	−	7.26441i	0.510905	−	0.371194i	−0.302262	−	0.953225i	$-0.597742\pi$
$383$	9.99860	−	7.26441i	0.510905	−	0.371194i	0.813167	+	0.582031i	$0.197742\pi$
$384$	−0.429393	+	1.31440i	−0.0219124	+	0.0670752i
$385$		0			0
$386$	21.1325	+	9.03817i	1.07562	+	0.460031i
$387$	−6.33667	+	2.05891i	−0.322111	+	0.104660i
$388$	−0.211795	−	1.56891i	−0.0107523	−	0.0796491i
$389$	−11.0661	−	3.59560i	−0.561074	−	0.182304i	0.0147301	−	0.999892i	$-0.495311\pi$
$389$	−11.0661	−	3.59560i	−0.561074	−	0.182304i	−0.575805	+	0.817587i	$0.695311\pi$
$390$		0			0
$391$	4.96708	+	15.2871i	0.251196	+	0.773102i
$392$	−9.92153	−	26.4908i	−0.501113	−	1.33799i
$393$	−0.433203			−0.0218522
$394$	13.9975	−	8.35881i	0.705185	−	0.421111i
$395$		0			0
$396$	1.34493	−	1.28471i	0.0675853	−	0.0645592i
$397$	1.99057	−	2.73979i	0.0999040	−	0.137506i	−0.756138	−	0.654412i	$-0.772916\pi$
$397$	1.99057	−	2.73979i	0.0999040	−	0.137506i	0.856042	+	0.516906i	$0.172916\pi$
$398$	19.4427	+	8.31543i	0.974573	+	0.416815i
$399$	−2.53985			−0.127151
$400$		0			0
$401$	3.08560			0.154088			0.0770439	−	0.997028i	$-0.475452\pi$
$401$	3.08560			0.154088			0.0770439	+	0.997028i	$0.475452\pi$
$402$	−1.55541	−	0.665233i	−0.0775768	−	0.0331788i
$403$	−17.3285	+	23.8506i	−0.863193	+	1.18808i
$404$	5.34163	−	5.10247i	0.265756	−	0.253857i
$405$		0			0
$406$	−3.11035	+	1.85738i	−0.154364	+	0.0921804i
$407$	2.67623			0.132656
$408$	−0.815809	+	0.305542i	−0.0403885	+	0.0151266i
$409$	−3.02158	−	9.29945i	−0.149407	−	0.459828i	0.848144	−	0.529766i	$-0.177720\pi$
$409$	−3.02158	−	9.29945i	−0.149407	−	0.459828i	−0.997551	+	0.0699372i	$0.977720\pi$
$410$		0			0
$411$	1.56829	+	0.509568i	0.0773581	+	0.0251352i
$412$	3.89590	+	28.8595i	0.191937	+	1.42181i
$413$	10.6956	−	3.47520i	0.526295	−	0.171003i
$414$	−24.7574	−	10.5885i	−1.21676	−	0.520396i
$415$		0			0
$416$	3.28799	−	24.0668i	0.161207	−	1.17997i
$417$	−1.00235	+	0.728252i	−0.0490854	+	0.0356626i
$418$	−0.199549	+	2.21152i	−0.00976024	+	0.108169i
$419$	22.2630	+	30.6425i	1.08762	+	1.49698i	0.850844	+	0.525418i	$0.176091\pi$
$419$	22.2630	+	30.6425i	1.08762	+	1.49698i	0.236776	+	0.971564i	$0.423909\pi$
$420$		0			0
$421$	−8.76743	+	12.0673i	−0.427298	+	0.588126i	−0.967331	−	0.253519i	$-0.918412\pi$
$421$	−8.76743	+	12.0673i	−0.427298	+	0.588126i	0.540032	+	0.841644i	$0.318412\pi$
$422$	−2.32784	−	2.03471i	−0.113317	−	0.0990480i
$423$	−5.88179	+	18.1023i	−0.285983	+	0.880164i
$424$	12.8460	+	3.55472i	0.623857	+	0.172632i
$425$		0			0
$426$	1.41155	+	0.127366i	0.0683898	+	0.00617090i
$427$	53.4299	+	17.3604i	2.58566	+	0.840130i
$428$	−24.1594	+	23.0777i	−1.16779	+	1.11550i
$429$	0.0961019	−	0.132273i	0.00463984	−	0.00638620i
$430$		0			0
$431$	−7.25169	+	5.26866i	−0.349302	+	0.253782i	−0.748576	−	0.663049i	$-0.769262\pi$
$431$	−7.25169	+	5.26866i	−0.349302	+	0.253782i	0.399274	+	0.916831i	$0.369262\pi$
$432$	1.03061	−	2.73846i	0.0495852	−	0.131754i
$433$	22.7455	−	16.5255i	1.09308	−	0.794167i	0.113161	−	0.993577i	$-0.463903\pi$
$433$	22.7455	−	16.5255i	1.09308	−	0.794167i	0.979916	+	0.199410i	$0.0639026\pi$
$434$	39.0331	−	8.89970i	1.87365	−	0.427199i
$435$		0			0
$436$	25.7401	+	13.8665i	1.23273	+	0.664084i
$437$	30.5735	−	9.93394i	1.46253	−	0.475205i
$438$	−0.290110	−	1.27239i	−0.0138620	−	0.0607971i
$439$	1.43731	−	4.42358i	0.0685991	−	0.211126i	−0.910880	−	0.412671i	$-0.864596\pi$
$439$	1.43731	−	4.42358i	0.0685991	−	0.211126i	0.979479	+	0.201544i	$0.0645961\pi$
$440$		0			0
$441$	9.22550	+	28.3932i	0.439310	+	1.35206i
$442$	13.1387	−	7.84596i	0.624945	−	0.373194i
$443$		−	33.9122i		−	1.61122i	−0.592448	−	0.805609i	$-0.701838\pi$
$443$		−	33.9122i		−	1.61122i	0.592448	−	0.805609i	$-0.298162\pi$
$444$	1.89229	−	0.910218i	0.0898042	−	0.0431970i
$445$		0			0
$446$	18.5566	−	21.2300i	0.878683	−	1.00527i
$447$	−1.41920	−	1.03111i	−0.0671260	−	0.0487699i
$448$	−24.8705	+	21.6688i	−1.17502	+	1.02376i
$449$	−6.81383			−0.321565			−0.160782	−	0.986990i	$-0.551402\pi$
$449$	−6.81383			−0.321565			−0.160782	+	0.986990i	$0.551402\pi$
$450$		0			0
$451$			1.65695i			0.0780229i
$452$	10.2259	−	18.9822i	0.480985	−	0.892845i
$453$	−1.03694	+	1.42723i	−0.0487198	+	0.0670570i
$454$	11.9318	+	10.4293i	0.559986	+	0.489470i
$455$		0			0
$456$	0.611071	+	1.63158i	0.0286160	+	0.0764057i
$457$	41.0652			1.92095			0.960475	−	0.278365i	$-0.0897925\pi$
$457$	41.0652			1.92095			0.960475	+	0.278365i	$0.0897925\pi$
$458$	8.85965	−	5.29066i	0.413984	−	0.247216i
$459$	1.75316	−	0.569637i	0.0818306	−	0.0265884i
$460$		0			0
$461$	−23.5979	−	7.66744i	−1.09907	−	0.357108i	−0.297323	−	0.954777i	$-0.596094\pi$
$461$	−23.5979	−	7.66744i	−1.09907	−	0.357108i	−0.801743	+	0.597669i	$0.796094\pi$
$462$	−0.216473	+	0.0493568i	−0.0100713	+	0.00229629i
$463$	5.99593	+	18.4536i	0.278654	+	0.857610i	0.988229	+	0.152980i	$0.0488870\pi$
$463$	5.99593	+	18.4536i	0.278654	+	0.857610i	−0.709575	+	0.704630i	$0.751113\pi$
$464$	1.94150	+	1.55119i	0.0901318	+	0.0720122i
$465$		0			0
$466$	15.9394	−	3.63425i	0.738380	−	0.168353i
$467$	0.0396935	+	0.0546334i	0.00183679	+	0.00252813i	0.809934	−	0.586520i	$-0.199503\pi$
$467$	0.0396935	+	0.0546334i	0.00183679	+	0.00252813i	−0.808098	+	0.589049i	$0.799503\pi$
$468$	−4.58889	+	25.2215i	−0.212122	+	1.16586i
$469$	−23.7205	−	32.6485i	−1.09531	−	1.50757i
$470$		0			0
$471$	1.90709	+	1.38558i	0.0878741	+	0.0638443i
$472$	−4.80573	−	6.03465i	−0.221202	−	0.277767i
$473$	0.214880	−	0.661332i	0.00988019	−	0.0304081i
$474$	−0.777205	−	0.0701281i	−0.0356982	−	0.00322109i
$475$		0			0
$476$	−20.4458	−	3.71998i	−0.937131	−	0.170505i
$477$	−13.3784	−	4.34691i	−0.612555	−	0.199031i
$478$	−0.535875	+	0.613076i	−0.0245103	+	0.0280414i
$479$	29.8640	+	21.6974i	1.36452	+	0.991381i	0.998143	+	0.0609142i	$0.0194016\pi$
$479$	29.8640	+	21.6974i	1.36452	+	0.991381i	0.366376	+	0.930467i	$0.380598\pi$
$480$		0			0
$481$	−29.8420	+	21.6815i	−1.36068	+	0.988591i
$482$	0.112493	−	1.24672i	0.00512390	−	0.0567863i
$483$	1.88936	+	2.60048i	0.0859689	+	0.118326i
$484$	−2.91723	−	21.6099i	−0.132601	−	0.982267i
$485$		0			0
$486$	−1.82298	+	4.26240i	−0.0826923	+	0.193346i
$487$	−1.82721	−	5.62357i	−0.0827987	−	0.254828i	0.901084	−	0.433645i	$-0.142773\pi$
$487$	−1.82721	−	5.62357i	−0.0827987	−	0.254828i	−0.983882	+	0.178817i	$0.942773\pi$
$488$	−1.70267	−	38.4998i	−0.0770761	−	1.74280i
$489$	−0.346827	+	1.06743i	−0.0156841	+	0.0482706i
$490$		0			0
$491$	−33.7674	+	10.9717i	−1.52390	+	0.495146i	−0.946881	−	0.321584i	$-0.895785\pi$
$491$	−33.7674	+	10.9717i	−1.52390	+	0.495146i	−0.577020	+	0.816730i	$0.695785\pi$
$492$	0.563550	+	1.17159i	0.0254068	+	0.0528193i
$493$			1.56562i			0.0705118i
$494$	−15.6916	−	26.2768i	−0.705996	−	1.18225i
$495$		0			0
$496$	−15.1082	−	22.9334i	−0.678378	−	1.02974i
$497$	27.3526	+	19.8728i	1.22693	+	0.891417i
$498$	1.12425	+	0.480829i	0.0503787	+	0.0215465i
$499$		−	24.7413i		−	1.10757i	−0.832658	−	0.553787i	$-0.813182\pi$
$499$		−	24.7413i		−	1.10757i	0.832658	−	0.553787i	$-0.186818\pi$
$500$		0			0
$501$		−	1.08085i		−	0.0482888i
$502$	−5.82107	+	13.6105i	−0.259807	+	0.607466i
$503$	−10.0428	−	7.29652i	−0.447786	−	0.325336i	0.340935	−	0.940087i	$-0.389256\pi$
$503$	−10.0428	−	7.29652i	−0.447786	−	0.325336i	−0.788721	+	0.614751i	$0.789256\pi$
$504$	27.2326	−	21.6868i	1.21303	−	0.966008i
$505$		0			0
$506$	2.41276	−	1.44081i	0.107260	−	0.0640519i
$507$			0.664655i			0.0295184i
$508$	4.03504	−	1.94091i	0.179026	−	0.0861139i
$509$	20.9803	−	6.81693i	0.929937	−	0.302155i	0.195400	−	0.980724i	$-0.437399\pi$
$509$	20.9803	−	6.81693i	0.929937	−	0.302155i	0.734537	+	0.678569i	$0.237399\pi$
$510$		0			0
$511$	9.62035	−	29.6084i	0.425579	−	1.30980i
$512$	19.9036	+	10.7632i	0.879622	+	0.475673i
$513$	−1.13925	−	3.50625i	−0.0502990	−	0.154805i
$514$	22.8983	+	9.79339i	1.01000	+	0.431968i
$515$		0			0
$516$	−0.0729911	−	0.540694i	−0.00321326	−	0.0238027i
$517$	−1.16763	−	1.60710i	−0.0513523	−	0.0706803i
$518$	49.8891	+	4.50156i	2.19200	+	0.197787i
$519$	1.29868	−	0.943546i	0.0570057	−	0.0414171i
$520$		0			0
$521$	−30.0779	−	21.8528i	−1.31773	−	0.957390i	−0.999957	−	0.00922497i	$-0.997064\pi$
$521$	−30.0779	−	21.8528i	−1.31773	−	0.957390i	−0.317777	−	0.948165i	$-0.602936\pi$
$522$	−1.97469	−	1.72602i	−0.0864297	−	0.0755460i
$523$	−5.33924	−	1.73482i	−0.233469	−	0.0758585i	0.189946	−	0.981795i	$-0.439169\pi$
$523$	−5.33924	−	1.73482i	−0.233469	−	0.0758585i	−0.423415	+	0.905936i	$0.639169\pi$
$524$	−1.26895	+	6.97441i	−0.0554344	+	0.304678i
$525$		0			0
$526$	−2.76725	+	30.6685i	−0.120658	+	1.33721i
$527$	5.34651	−	16.4549i	0.232897	−	0.716785i
$528$	0.0837885	+	0.127186i	0.00364643	+	0.00553506i
$529$	−14.3070	−	10.3946i	−0.622041	−	0.451940i
$530$		0			0
$531$	4.78552	+	6.58671i	0.207674	+	0.285839i
$532$	−7.43980	+	40.8906i	−0.322556	+	1.77283i
$533$	−13.4238	−	18.4763i	−0.581450	−	0.800298i
$534$	−0.327271	−	1.43538i	−0.0141624	−	0.0621148i
$535$		0			0
$536$	−15.2662	+	23.0929i	−0.659398	+	0.997462i
$537$	−0.0241147	−	0.0742173i	−0.00104063	−	0.00320271i
$538$	3.81433	+	16.7292i	0.164448	+	0.721249i
$539$	−2.96328	−	0.962828i	−0.127638	−	0.0414720i
$540$		0			0
$541$	24.9767	−	8.11542i	1.07383	−	0.348909i	0.281853	−	0.959458i	$-0.409051\pi$
$541$	24.9767	−	8.11542i	1.07383	−	0.348909i	0.791979	+	0.610549i	$0.209051\pi$
$542$	11.3872	+	19.0688i	0.489122	+	0.819076i
$543$	2.43282			0.104402
$544$	2.52943	+	14.0292i	0.108448	+	0.601498i
$545$		0			0
$546$	2.01398	−	2.30413i	0.0861904	−	0.0986075i
$547$	18.8818	−	25.9886i	0.807327	−	1.11119i	−0.184403	−	0.982851i	$-0.559035\pi$
$547$	18.8818	−	25.9886i	0.807327	−	1.11119i	0.991730	−	0.128340i	$-0.0409648\pi$
$548$	12.7978	−	23.7563i	0.546693	−	1.01482i
$549$			40.6716i			1.73582i
$550$		0			0
$551$	3.13116			0.133392
$552$	1.21596	−	1.83937i	0.0517548	−	0.0782888i
$553$	−15.0604	−	10.9420i	−0.640434	−	0.465303i
$554$	2.48174	+	2.16923i	0.105439	+	0.0921616i
$555$		0			0
$556$	8.78847	+	18.2707i	0.372714	+	0.774851i
$557$			10.0696i			0.426664i	0.976980	+	0.213332i	$0.0684316\pi$
$557$			10.0696i			0.426664i	−0.976980	+	0.213332i	$0.931568\pi$
$558$	14.8600	+	24.8842i	0.629072	+	1.05343i
$559$	2.96171	+	9.11521i	0.125267	+	0.385532i
$560$		0			0
$561$	−0.0296512	+	0.0912569i	−0.00125187	+	0.00385287i
$562$	−18.7872	+	4.28356i	−0.792491	+	0.180691i
$563$	−27.0978	+	8.80460i	−1.14203	+	0.371069i	−0.818137	−	0.575023i	$-0.804993\pi$
$563$	−27.0978	+	8.80460i	−1.14203	+	0.371069i	−0.323897	+	0.946092i	$0.604993\pi$
$564$	−1.37220	−	0.739216i	−0.0577798	−	0.0311266i
$565$		0			0
$566$	1.25311	+	5.49602i	0.0526723	+	0.231015i
$567$	−29.5744	+	21.4870i	−1.24201	+	0.902370i
$568$	6.18530	−	22.3524i	0.259529	−	0.937884i
$569$	−21.6286	+	15.7141i	−0.906718	+	0.658769i	−0.940183	−	0.340671i	$-0.889346\pi$
$569$	−21.6286	+	15.7141i	−0.906718	+	0.658769i	0.0334647	+	0.999440i	$0.489346\pi$
$570$		0			0
$571$	16.2766	−	22.4028i	0.681155	−	0.937529i	−0.318792	−	0.947825i	$-0.603277\pi$
$571$	16.2766	−	22.4028i	0.681155	−	0.937529i	0.999947	+	0.0102955i	$0.00327723\pi$
$572$	−1.84804	−	1.93466i	−0.0772705	−	0.0808923i
$573$	−2.11081	−	0.685842i	−0.0881802	−	0.0286515i
$574$	−2.78708	+	30.8882i	−0.116331	+	1.28925i
$575$		0			0
$576$	−20.4834	−	12.2763i	−0.853476	−	0.511512i
$577$	1.09689	−	3.37588i	0.0456641	−	0.140540i	−0.925625	−	0.378442i	$-0.876460\pi$
$577$	1.09689	−	3.37588i	0.0456641	−	0.140540i	0.971289	+	0.237902i	$0.0764599\pi$
$578$	9.91155	−	11.3395i	0.412266	−	0.471659i
$579$	1.16755	−	1.60699i	0.0485216	−	0.0667843i
$580$		0			0
$581$	17.1452	+	23.5983i	0.711301	+	0.979022i
$582$	−0.136265	−	0.0122954i	−0.00564837	−	0.000509660i
$583$	1.18772	−	0.862930i	0.0491904	−	0.0357389i
$584$	−21.3348	+	0.943539i	−0.882841	+	0.0390439i
$585$		0			0
$586$	−5.35644	+	12.5241i	−0.221273	+	0.517367i
$587$	−44.5624	+	14.4792i	−1.83929	+	0.597620i	−0.840878	+	0.541224i	$0.817961\pi$
$587$	−44.5624	+	14.4792i	−1.83929	+	0.597620i	−0.998408	+	0.0563961i	$0.982039\pi$
$588$	−2.42273	+	0.327057i	−0.0999116	+	0.0134876i
$589$	−32.9090	−	10.6928i	−1.35599	−	0.440588i
$590$		0			0
$591$	−0.435399	−	1.34002i	−0.0179099	−	0.0551210i
$592$	−9.11122	−	33.1315i	−0.374469	−	1.36169i
$593$	9.84501			0.404286			0.202143	−	0.979356i	$-0.435209\pi$
$593$	9.84501			0.404286			0.202143	+	0.979356i	$0.435209\pi$
$594$	−0.165236	−	0.276701i	−0.00677971	−	0.0113532i
$595$		0			0
$596$	−20.7577	+	19.8283i	−0.850268	+	0.812198i
$597$	1.07418	−	1.47849i	0.0439635	−	0.0605105i
$598$	−15.2314	+	35.6132i	−0.622858	+	1.45633i
$599$	30.6535			1.25247			0.626235	−	0.779634i	$-0.284595\pi$
$599$	30.6535			1.25247			0.626235	+	0.779634i	$0.284595\pi$
$600$		0			0
$601$	19.2818			0.786520			0.393260	−	0.919427i	$-0.371347\pi$
$601$	19.2818			0.786520			0.393260	+	0.919427i	$0.371347\pi$
$602$	5.11809	−	11.9668i	0.208598	−	0.487732i
$603$	17.1726	−	23.6361i	0.699324	−	0.962537i
$604$	19.9404	+	20.8751i	0.811364	+	0.849394i
$605$		0			0
$606$	−0.327313	−	0.548113i	−0.0132962	−	0.0222656i
$607$	−7.58873			−0.308017			−0.154009	−	0.988070i	$-0.549218\pi$
$607$	−7.58873			−0.308017			−0.154009	+	0.988070i	$0.549218\pi$
$608$	28.0578	−	5.05874i	1.13789	−	0.205159i
$609$	0.0967486	+	0.297762i	0.00392045	+	0.0120659i
$610$		0			0
$611$	26.0399	+	8.46088i	1.05346	+	0.342291i
$612$	−2.01273	−	14.9096i	−0.0813598	−	0.602686i
$613$	−28.0241	+	9.10557i	−1.13188	+	0.367771i	−0.814291	−	0.580457i	$-0.802874\pi$
$613$	−28.0241	+	9.10557i	−1.13188	+	0.367771i	−0.317591	+	0.948228i	$0.602874\pi$
$614$	−4.51915	+	10.5664i	−0.182378	+	0.426426i
$615$		0			0
$616$	0.160526	+	3.62972i	0.00646777	+	0.146246i
$617$	−5.22886	+	3.79899i	−0.210506	+	0.152942i	−0.688043	−	0.725670i	$-0.741530\pi$
$617$	−5.22886	+	3.79899i	−0.210506	+	0.152942i	0.477537	+	0.878612i	$0.341530\pi$
$618$	2.50655	+	0.226169i	0.100828	+	0.00909787i
$619$	−25.9223	−	35.6790i	−1.04191	−	1.43406i	−0.895621	−	0.444819i	$-0.853268\pi$
$619$	−25.9223	−	35.6790i	−1.04191	−	1.43406i	−0.146286	−	0.989242i	$-0.546732\pi$
$620$		0			0
$621$	−2.74248	+	3.77470i	−0.110052	+	0.151473i
$622$	4.19377	−	4.79795i	0.168155	−	0.192380i
$623$	10.8527	−	33.4011i	0.434803	−	1.33819i
$624$	−1.96470	−	0.739409i	−0.0786511	−	0.0296000i
$625$		0			0
$626$	−0.252513	+	2.79850i	−0.0100924	+	0.111851i
$627$	0.182510	+	0.0593010i	0.00728873	+	0.00236825i
$628$	27.8937	−	26.6448i	1.11308	−	1.06324i
$629$	12.7243	−	17.5135i	0.507352	−	0.698311i
$630$		0			0
$631$	−25.4366	+	18.4808i	−1.01262	+	0.735708i	−0.964756	−	0.263146i	$-0.915240\pi$
$631$	−25.4366	+	18.4808i	−1.01262	+	0.735708i	−0.0478593	+	0.998854i	$0.515240\pi$
$632$	−3.40565	+	12.3073i	−0.135469	+	0.489558i
$633$	−0.216166	+	0.157054i	−0.00859183	+	0.00624233i
$634$	−3.87533	−	16.9968i	−0.153909	−	0.675028i
$635$		0			0
$636$	0.546314	−	1.01411i	0.0216627	−	0.0402122i
$637$	40.8432	−	13.2708i	1.61827	−	0.525807i
$638$	0.266871	−	0.0608477i	0.0105655	−	0.00240898i
$639$	−7.56373	+	23.2788i	−0.299216	+	0.920893i
$640$		0			0
$641$	−4.73875	−	14.5844i	−0.187169	−	0.576048i	0.812810	−	0.582529i	$-0.197937\pi$
$641$	−4.73875	−	14.5844i	−0.187169	−	0.576048i	−0.999979	+	0.00648140i	$0.997937\pi$
$642$	1.48039	+	2.47904i	0.0584263	+	0.0978398i
$643$			23.5431i			0.928448i	0.885718	+	0.464224i	$0.153667\pi$
$643$			23.5431i			0.928448i	−0.885718	+	0.464224i	$0.846333\pi$
$644$	47.4012	−	22.8006i	1.86787	−	0.898470i
$645$		0			0
$646$	13.5237	+	11.8207i	0.532083	+	0.465080i
$647$	10.0798	+	7.32343i	0.396280	+	0.287914i	0.768024	−	0.640421i	$-0.221240\pi$
$647$	10.0798	+	7.32343i	0.396280	+	0.287914i	−0.371744	+	0.928335i	$0.621240\pi$
$648$	20.9185	+	13.8287i	0.821756	+	0.543243i
$649$	−0.849707			−0.0333539
$650$		0			0
$651$		−	3.45991i		−	0.135605i
$652$	16.1692	+	8.71053i	0.633236	+	0.341131i
$653$	4.72734	−	6.50662i	0.184995	−	0.254624i	−0.706439	−	0.707773i	$-0.749700\pi$
$653$	4.72734	−	6.50662i	0.184995	−	0.254624i	0.891434	+	0.453150i	$0.149700\pi$
$654$	1.66290	−	1.90247i	0.0650246	−	0.0743924i
$655$		0			0
$656$	20.5129	−	5.64110i	0.800895	−	0.220248i
$657$	22.5383			0.879303
$658$	−19.0632	−	31.9229i	−0.743161	−	1.24449i
$659$	−43.9188	+	14.2701i	−1.71083	+	0.555883i	−0.990472	−	0.137716i	$-0.956024\pi$
$659$	−43.9188	+	14.2701i	−1.71083	+	0.555883i	−0.720361	+	0.693599i	$0.756024\pi$
$660$		0			0
$661$	−31.8290	−	10.3419i	−1.23800	−	0.402252i	−0.384396	−	0.923168i	$-0.625590\pi$
$661$	−31.8290	−	10.3419i	−1.23800	−	0.402252i	−0.853607	+	0.520917i	$0.825590\pi$
$662$	8.24158	+	36.1467i	0.320318	+	1.40488i
$663$	−0.408685	−	1.25780i	−0.0158720	−	0.0488490i
$664$	11.0344	−	16.6915i	0.428216	−	0.647756i
$665$		0			0
$666$	8.06152	+	35.3569i	0.312378	+	1.37005i
$667$	−2.32923	−	3.20591i	−0.0901881	−	0.124133i
$668$	−17.4013	−	3.16606i	−0.673276	−	0.122498i
$669$	−1.43234	−	1.97145i	−0.0553775	−	0.0762206i
$670$		0			0
$671$	−3.43406	−	2.49499i	−0.132570	−	0.0963180i
$672$	1.34802	+	2.51188i	0.0520008	+	0.0968981i
$673$	−9.78082	+	30.1023i	−0.377023	+	1.16036i	0.565081	+	0.825035i	$0.308845\pi$
$673$	−9.78082	+	30.1023i	−0.377023	+	1.16036i	−0.942104	+	0.335321i	$0.891155\pi$
$674$	−3.23629	+	35.8666i	−0.124657	+	1.38153i
$675$		0			0
$676$	10.7007	+	1.94693i	0.411566	+	0.0748818i
$677$	−33.1919	−	10.7847i	−1.27567	−	0.414489i	−0.408615	−	0.912707i	$-0.633988\pi$
$677$	−33.1919	−	10.7847i	−1.27567	−	0.414489i	−0.867052	+	0.498217i	$0.833988\pi$
$678$	−1.40298	−	1.22631i	−0.0538812	−	0.0470963i
$679$	−2.64050	−	1.91844i	−0.101333	−	0.0736229i
$680$		0			0
$681$	1.10800	−	0.805010i	0.0424587	−	0.0308480i
$682$	−3.01265	−	0.271835i	−0.115360	−	0.0104091i
$683$	−4.11817	−	5.66818i	−0.157578	−	0.216887i	0.722927	−	0.690924i	$-0.242796\pi$
$683$	−4.11817	−	5.66818i	−0.157578	−	0.216887i	−0.880505	+	0.474037i	$0.842796\pi$
$684$	−29.8186	+	4.02537i	−1.14014	+	0.153914i
$685$		0			0
$686$	−16.0909	−	6.88192i	−0.614354	−	0.262753i
$687$	−0.275583	−	0.848157i	−0.0105141	−	0.0323592i
$688$	−8.91878	−	0.408686i	−0.340025	−	0.0155810i
$689$	−6.25297	+	19.2447i	−0.238219	+	0.733163i
$690$		0			0
$691$	−7.77133	+	2.52506i	−0.295635	+	0.0960578i	−0.453079	−	0.891470i	$-0.649675\pi$
$691$	−7.77133	+	2.52506i	−0.295635	+	0.0960578i	0.157444	+	0.987528i	$0.449675\pi$
$692$	−11.3866	−	23.6721i	−0.432854	−	0.899879i
$693$		−	3.83448i		−	0.145660i
$694$	−32.5334	+	19.4277i	−1.23495	+	0.737467i
$695$		0			0
$696$	0.168003	−	0.133790i	0.00636813	−	0.00507130i
$697$	10.8433	+	7.87811i	0.410719	+	0.298405i
$698$	−5.12960	+	11.9937i	−0.194158	+	0.453970i
$699$		−	1.41288i		−	0.0534400i
$700$		0			0
$701$		−	20.0038i		−	0.755534i	−0.925901	−	0.377767i	$-0.876692\pi$
$701$		−	20.0038i		−	0.755534i	0.925901	−	0.377767i	$-0.123308\pi$
$702$	4.08420	+	1.74677i	0.154148	+	0.0659277i
$703$	−35.0263	−	25.4481i	−1.32104	−	0.959793i
$704$	2.29309	−	0.976407i	0.0864239	−	0.0367997i
$705$		0			0
$706$	−10.4798	−	17.5493i	−0.394413	−	0.660478i
$707$		−	15.2293i		−	0.572757i
$708$	−0.600806	+	0.288996i	−0.0225797	+	0.0108611i
$709$	46.7136	−	15.1782i	1.75437	−	0.570029i	0.757775	−	0.652516i	$-0.226286\pi$
$709$	46.7136	−	15.1782i	1.75437	−	0.570029i	0.996592	+	0.0824870i	$0.0262863\pi$
$710$		0			0
$711$	4.16462	−	12.8174i	0.156185	−	0.480689i
$712$	−24.0677	+	1.06440i	−0.901974	+	0.0398901i
$713$	13.5325	+	41.6488i	0.506797	+	1.55976i
$714$	−0.706243	+	1.65130i	−0.0264305	+	0.0617982i
$715$		0			0
$716$	−1.26551	+	0.170838i	−0.0472943	+	0.00638451i
$717$	0.0413628	+	0.0569310i	0.00154472	+	0.00212613i
$718$	0.409360	−	4.53679i	0.0152772	−	0.169311i
$719$	38.2305	−	27.7761i	1.42576	−	1.03587i	0.434971	−	0.900444i	$-0.356758\pi$
$719$	38.2305	−	27.7761i	1.42576	−	1.03587i	0.990787	−	0.135430i	$-0.0432415\pi$
$720$		0			0
$721$	48.5712	+	35.2890i	1.80889	+	1.31423i
$722$	5.95746	−	6.81573i	0.221714	−	0.253655i
$723$	−0.102887	−	0.0334301i	−0.00382642	−	0.00124328i
$724$	7.12629	−	39.1676i	0.264847	−	1.45565i
$725$		0			0
$726$	−1.87689	−	0.169355i	−0.0696581	−	0.00628534i
$727$	0.443325	−	1.36442i	0.0164420	−	0.0506034i	−0.942499	−	0.334209i	$-0.891531\pi$
$727$	0.443325	−	1.36442i	0.0164420	−	0.0506034i	0.958941	+	0.283606i	$0.0915308\pi$
$728$	−31.1962	−	39.1737i	−1.15621	−	1.45187i
$729$	−21.1936	−	15.3980i	−0.784947	−	0.570298i
$730$		0			0
$731$	−3.30617	−	4.55055i	−0.122283	−	0.168308i
$732$	−3.27671	−	0.596177i	−0.121111	−	0.0220353i
$733$	22.3782	+	30.8009i	0.826556	+	1.13766i	0.988554	+	0.150866i	$0.0482062\pi$
$733$	22.3782	+	30.8009i	0.826556	+	1.13766i	−0.161998	+	0.986791i	$0.551794\pi$
$734$	12.4329	−	2.83475i	0.458906	−	0.104632i
$735$		0			0
$736$	−26.0514	−	24.9645i	−0.960266	−	0.920204i
$737$	0.942236	+	2.89990i	0.0347077	+	0.106819i
$738$	−21.8908	+	4.99119i	−0.805812	+	0.183728i
$739$	30.0806	+	9.77378i	1.10653	+	0.359534i	0.804613	−	0.593799i	$-0.202373\pi$
$739$	30.0806	+	9.77378i	1.10653	+	0.359534i	0.301920	+	0.953333i	$0.402373\pi$
$740$		0			0
$741$	−2.51555	+	0.817351i	−0.0924110	+	0.0300262i
$742$	23.5925	−	14.0886i	0.866107	−	0.517207i
$743$	−13.6505			−0.500790			−0.250395	−	0.968144i	$-0.580560\pi$
$743$	−13.6505			−0.500790			−0.250395	+	0.968144i	$0.580560\pi$
$744$	−2.22262	+	0.832432i	−0.0814853	+	0.0305184i
$745$		0			0
$746$	−10.2315	−	8.94310i	−0.374602	−	0.327430i
$747$	−12.4124	+	17.0841i	−0.454144	+	0.625076i
$748$	1.38235	+	0.744685i	0.0505436	+	0.0272284i
$749$			68.8800i			2.51682i
$750$		0			0
$751$	13.2979			0.485247			0.242623	−	0.970121i	$-0.421992\pi$
$751$	13.2979			0.485247			0.242623	+	0.970121i	$0.421992\pi$
$752$	−15.9206	+	19.9265i	−0.580564	+	0.726645i
$753$	1.03499	+	0.751964i	0.0377171	+	0.0274031i
$754$	−2.48286	+	2.84056i	−0.0904205	+	0.103447i
$755$		0			0
$756$	−2.61483	−	5.43608i	−0.0951004	−	0.197708i
$757$		−	15.4070i		−	0.559979i	−0.960003	−	0.279989i	$-0.909669\pi$
$757$		−	15.4070i		−	0.559979i	0.960003	−	0.279989i	$-0.0903309\pi$
$758$	−1.80839	+	1.07990i	−0.0656836	+	0.0392238i
$759$	−0.0750499	−	0.230980i	−0.00272414	−	0.00838404i
$760$		0			0
$761$	−6.51536	+	20.0522i	−0.236182	+	0.726893i	0.760781	+	0.649009i	$0.224816\pi$
$761$	−6.51536	+	20.0522i	−0.236182	+	0.726893i	−0.996962	+	0.0778836i	$0.975184\pi$
$762$	−0.0860215	−	0.377281i	−0.00311623	−	0.0136674i
$763$	57.3268	−	18.6266i	2.07537	−	0.674328i
$764$	−17.2248	+	31.9742i	−0.623173	+	1.15679i
$765$		0			0
$766$	−17.0409	+	3.88538i	−0.615711	+	0.140385i
$767$	9.47489	−	6.88391i	0.342118	−	0.248563i
$768$	1.28929	−	1.47030i	0.0465233	−	0.0530548i
$769$	−12.8730	+	9.35276i	−0.464211	+	0.337269i	−0.795181	−	0.606372i	$-0.792624\pi$
$769$	−12.8730	+	9.35276i	−0.464211	+	0.337269i	0.330970	+	0.943641i	$0.392624\pi$
$770$		0			0
$771$	1.26511	−	1.74127i	0.0455617	−	0.0627103i
$772$	−22.4520	−	23.5043i	−0.808063	−	0.845939i
$773$	−2.21091	−	0.718367i	−0.0795208	−	0.0258379i	0.268986	−	0.963144i	$-0.413311\pi$
$773$	−2.21091	−	0.718367i	−0.0795208	−	0.0258379i	−0.348507	+	0.937306i	$0.613311\pi$
$774$	9.38445	+	0.846771i	0.337317	+	0.0304365i
$775$		0			0
$776$	−0.597103	+	2.15780i	−0.0214347	+	0.0774606i
$777$	1.33775	−	4.11718i	0.0479916	−	0.147703i
$778$	12.3895	+	10.8294i	0.444185	+	0.388251i
$779$	15.7559	−	21.6861i	0.564513	−	0.776985i
$780$		0			0
$781$	−1.50152	−	2.06666i	−0.0537286	−	0.0739511i
$782$	2.04282	−	22.6398i	0.0730511	−	0.809599i
$783$	−0.367662	+	0.267122i	−0.0131392	+	0.00954615i
$784$	−1.83123	+	39.9631i	−0.0654011	+	1.42725i
$785$		0			0
$786$	0.563286	+	0.240912i	0.0200917	+	0.00859304i
$787$	−35.5471	+	11.5499i	−1.26712	+	0.411711i	−0.864025	−	0.503449i	$-0.832064\pi$
$787$	−35.5471	+	11.5499i	−1.26712	+	0.411711i	−0.403091	+	0.915160i	$0.632064\pi$
$788$	−22.8492	+	3.08454i	−0.813969	+	0.109882i
$789$	2.53096	+	0.822360i	0.0901047	+	0.0292768i
$790$		0			0
$791$	−13.7363	−	42.2758i	−0.488405	−	1.50316i
$792$	−2.46324	+	0.922549i	−0.0875274	+	0.0327814i
$793$	58.5055			2.07759
$794$	−4.11195	+	2.45551i	−0.145928	+	0.0871426i
$795$		0			0
$796$	−20.6566	−	21.6248i	−0.732153	−	0.766471i
$797$	−20.0559	+	27.6045i	−0.710415	+	0.977802i	0.289373	+	0.957216i	$0.406553\pi$
$797$	−20.0559	+	27.6045i	−0.710415	+	0.977802i	−0.999788	+	0.0205856i	$0.993447\pi$
$798$	3.30252	+	1.41245i	0.116908	+	0.0500003i
$799$	−16.0686			−0.568468
$800$		0			0
$801$	25.4253			0.898361
$802$	−4.01216	−	1.71596i	−0.141674	−	0.0605926i
$803$	−1.38261	+	1.90300i	−0.0487912	+	0.0671553i
$804$	1.65252	+	1.72998i	0.0582800	+	0.0610117i
$805$		0			0
$806$	35.7956	−	21.3758i	1.26085	−	0.752932i
$807$	1.48289			0.0522001
$808$	−9.78320	+	3.66407i	−0.344172	+	0.128902i
$809$	−0.931838	−	2.86790i	−0.0327617	−	0.100830i	0.933338	−	0.358998i	$-0.116881\pi$
$809$	−0.931838	−	2.86790i	−0.0327617	−	0.100830i	−0.966100	+	0.258167i	$0.916881\pi$
$810$		0			0
$811$	−27.5066	−	8.93745i	−0.965889	−	0.313836i	−0.216734	−	0.976231i	$-0.569540\pi$
$811$	−27.5066	−	8.93745i	−0.965889	−	0.313836i	−0.749155	+	0.662394i	$0.769540\pi$
$812$	5.07725	−	0.685405i	0.178177	−	0.0240530i
$813$	1.82551	−	0.593143i	0.0640233	−	0.0208024i
$814$	−3.47985	−	1.48830i	−0.121969	−	0.0521648i
$815$		0			0
$816$	1.23070	+	0.0563944i	0.0430831	+	0.00197420i
$817$	−9.10090	+	6.61219i	−0.318400	+	0.231331i
$818$	−1.24269	+	13.7723i	−0.0434496	+	0.481536i
$819$	31.0650	+	42.7573i	1.08550	+	1.49406i
$820$		0			0
$821$	12.8958	−	17.7496i	0.450067	−	0.619464i	−0.522345	−	0.852734i	$-0.674943\pi$
$821$	12.8958	−	17.7496i	0.450067	−	0.619464i	0.972412	+	0.233270i	$0.0749427\pi$
$822$	−1.75584	−	1.53474i	−0.0612419	−	0.0535301i
$823$	6.18129	−	19.0241i	0.215466	−	0.663137i	−0.783654	−	0.621198i	$-0.786646\pi$
$823$	6.18129	−	19.0241i	0.215466	−	0.663137i	0.999120	−	0.0419394i	$-0.0133537\pi$
$824$	10.9835	−	39.6921i	0.382629	−	1.38274i
$825$		0			0
$826$	−15.8399	−	1.42925i	−0.551140	−	0.0497300i
$827$	16.2686	+	5.28600i	0.565716	+	0.183812i	0.577891	−	0.816114i	$-0.303876\pi$
$827$	16.2686	+	5.28600i	0.565716	+	0.183812i	−0.0121758	+	0.999926i	$0.503876\pi$
$828$	26.3031	+	27.5360i	0.914097	+	0.956943i
$829$	−21.2432	+	29.2388i	−0.737807	+	1.01550i	0.260935	+	0.965356i	$0.415969\pi$
$829$	−21.2432	+	29.2388i	−0.737807	+	1.01550i	−0.998742	+	0.0501475i	$0.984031\pi$
$830$		0			0
$831$	0.230458	−	0.167437i	0.00799448	−	0.00580833i
$832$	−17.6593	+	29.4651i	−0.612226	+	1.02152i
$833$	−20.3900	+	14.8142i	−0.706472	+	0.513282i
$834$	1.70833	−	0.389507i	0.0591548	−	0.0134875i
$835$		0			0
$836$	1.48934	−	2.76463i	0.0515098	−	0.0956168i
$837$	4.77639	−	1.55194i	0.165096	−	0.0536430i
$838$	−11.9074	−	52.2247i	−0.411335	−	1.80407i
$839$	9.69350	−	29.8335i	0.334657	−	1.02997i	−0.632234	−	0.774777i	$-0.717862\pi$
$839$	9.69350	−	29.8335i	0.334657	−	1.02997i	0.966891	−	0.255190i	$-0.0821381\pi$
$840$		0			0
$841$	8.84222	+	27.2136i	0.304904	+	0.938398i
$842$	18.1110	−	10.8152i	0.624146	−	0.372717i
$843$			1.66531i			0.0573562i
$844$	1.89531	+	3.94024i	0.0652393	+	0.135629i
$845$		0			0
$846$	17.7150	−	20.2671i	0.609054	−	0.696798i
$847$	−36.3699	−	26.4243i	−1.24968	−	0.907948i
$848$	−14.7266	−	11.7660i	−0.505713	−	0.404047i
$849$	0.487170			0.0167196
$850$		0			0
$851$			54.7930i			1.87828i
$852$	−1.76458	−	0.950599i	−0.0604536	−	0.0325670i
$853$	14.8302	−	20.4120i	0.507776	−	0.698894i	−0.475766	−	0.879572i	$-0.657829\pi$
$853$	14.8302	−	20.4120i	0.507776	−	0.698894i	0.983542	+	0.180678i	$0.0578292\pi$
$854$	−59.8195	−	52.2868i	−2.04698	−	1.78922i
$855$		0			0
$856$	44.2480	−	16.5721i	1.51237	−	0.566422i
$857$	−40.0337			−1.36753			−0.683763	−	0.729704i	$-0.739658\pi$
$857$	−40.0337			−1.36753			−0.683763	+	0.729704i	$0.739658\pi$
$858$	−0.198519	+	0.118548i	−0.00677732	+	0.00404717i
$859$	−18.4443	+	5.99291i	−0.629311	+	0.204475i	−0.606270	−	0.795259i	$-0.707335\pi$
$859$	−18.4443	+	5.99291i	−0.629311	+	0.204475i	−0.0230409	+	0.999735i	$0.507335\pi$
$860$		0			0
$861$	2.54910	+	0.828253i	0.0868732	+	0.0282268i
$862$	12.3592	−	2.81795i	0.420957	−	0.0959798i
$863$	−4.97690	−	15.3173i	−0.169416	−	0.521408i	0.829919	−	0.557884i	$-0.188387\pi$
$863$	−4.97690	−	15.3173i	−0.169416	−	0.521408i	−0.999335	+	0.0364763i	$0.988387\pi$
$864$	−2.86299	+	2.98763i	−0.0974009	+	0.101641i
$865$		0			0
$866$	−38.7656	+	8.83872i	−1.31731	+	0.300352i
$867$	−0.765048	−	1.05300i	−0.0259824	−	0.0357617i
$868$	−55.7033	−	10.1349i	−1.89069	−	0.344000i
$869$	0.826742	+	1.13791i	0.0280453	+	0.0386010i
$870$		0			0
$871$	−34.0002	−	24.7026i	−1.15205	−	0.837016i
$872$	−25.7580	−	32.3449i	−0.872277	−	1.09534i
$873$	0.730170	−	2.24723i	0.0247125	−	0.0760573i
$874$	−45.2786	−	4.08555i	−1.53157	−	0.138196i
$875$		0			0
$876$	−0.330374	+	1.81580i	−0.0111623	+	0.0613502i
$877$	−11.6300	−	3.77880i	−0.392716	−	0.127601i	0.106001	−	0.994366i	$-0.466195\pi$
$877$	−11.6300	−	3.77880i	−0.392716	−	0.127601i	−0.498717	+	0.866765i	$0.666195\pi$
$878$	−4.32894	+	4.95259i	−0.146095	+	0.167142i
$879$	0.952378	+	0.691943i	0.0321229	+	0.0233387i
$880$		0			0
$881$	−14.6870	+	10.6707i	−0.494818	+	0.359506i	−0.807034	−	0.590505i	$-0.798929\pi$
$881$	−14.6870	+	10.6707i	−0.494818	+	0.359506i	0.312216	+	0.950011i	$0.398929\pi$
$882$	3.79419	−	42.0496i	0.127757	−	1.41588i
$883$	−4.90179	−	6.74673i	−0.164958	−	0.227046i	0.718533	−	0.695492i	$-0.244814\pi$
$883$	−4.90179	−	6.74673i	−0.164958	−	0.227046i	−0.883492	+	0.468447i	$0.844814\pi$
$884$	−21.4473	+	2.89529i	−0.721351	+	0.0973790i
$885$		0			0
$886$	−18.8592	+	44.0954i	−0.633586	+	1.48142i
$887$	−15.5471	−	47.8491i	−0.522021	−	1.60662i	−0.770132	−	0.637885i	$-0.779810\pi$
$887$	−15.5471	−	47.8491i	−0.522021	−	1.60662i	0.248110	−	0.968732i	$-0.420190\pi$
$888$	−2.96670	+	0.131203i	−0.0995560	+	0.00440290i
$889$	2.85256	−	8.77929i	0.0956720	−	0.294448i
$890$		0			0
$891$	2.62685	−	0.853516i	0.0880029	−	0.0285939i
$892$	−35.9353	+	17.2854i	−1.20320	+	0.578756i
$893$			32.1366i			1.07541i
$894$	1.27194	+	2.12998i	0.0425402	+	0.0712371i
$895$		0			0
$896$	44.3891	−	14.3447i	1.48294	−	0.479222i
$897$	2.70815	+	1.96759i	0.0904225	+	0.0656958i
$898$	8.85991	+	3.78929i	0.295659	+	0.126450i
$899$			4.26543i			0.142260i
$900$		0			0
$901$		−	11.8754i		−	0.395628i
$902$	0.921461	−	2.15451i	0.0306813	−	0.0717373i
$903$	−0.910000	−	0.661153i	−0.0302829	−	0.0220018i
$904$	−23.8528	+	18.9954i	−0.793334	+	0.631776i
$905$		0			0
$906$	2.14202	−	1.27914i	0.0711639	−	0.0424965i
$907$			40.7553i			1.35326i	0.736324	+	0.676629i	$0.236560\pi$
$907$			40.7553i			1.35326i	−0.736324	+	0.676629i	$0.763440\pi$
$908$	−9.71478	−	20.1965i	−0.322396	−	0.670243i
$909$	10.4858	−	3.40703i	0.347790	−	0.113004i
$910$		0			0
$911$	0.0419150	−	0.129001i	0.00138871	−	0.00427400i	−0.950360	−	0.311153i	$-0.899285\pi$
$911$	0.0419150	−	0.129001i	0.00138871	−	0.00427400i	0.951748	+	0.306879i	$0.0992848\pi$
$912$	0.112786	−	2.46134i	0.00373472	−	0.0815032i
$913$	−0.681046	−	2.09605i	−0.0225393	−	0.0693690i
$914$	−53.3964	−	22.8371i	−1.76620	−	0.755384i
$915$		0			0
$916$	−14.4623	+	1.95234i	−0.477847	+	0.0645071i
$917$	8.59030	+	11.8235i	0.283677	+	0.390448i
$918$	−2.59639	−	0.234276i	−0.0856937	−	0.00773225i
$919$	−8.15739	+	5.92669i	−0.269087	+	0.195503i	−0.714144	−	0.699999i	$-0.753184\pi$
$919$	−8.15739	+	5.92669i	−0.269087	+	0.195503i	0.445056	+	0.895503i	$0.353184\pi$
$920$		0			0
$921$	0.803507	+	0.583782i	0.0264765	+	0.0192363i
$922$	26.4200	+	23.0931i	0.870096	+	0.760530i
$923$	33.4862	+	10.8803i	1.10221	+	0.358130i
$924$	0.308925	+	0.0562069i	0.0101629	+	0.00184907i
$925$		0			0
$926$	2.46596	−	27.3293i	0.0810363	−	0.898096i
$927$	−13.4312	+	41.3371i	−0.441140	+	1.35769i
$928$	−1.66185	−	3.09669i	−0.0545530	−	0.101654i
$929$	6.77547	+	4.92267i	0.222296	+	0.161508i	0.693360	−	0.720592i	$-0.256130\pi$
$929$	6.77547	+	4.92267i	0.222296	+	0.161508i	−0.471064	+	0.882099i	$0.656130\pi$
$930$		0			0
$931$	29.6277	+	40.7791i	0.971010	+	1.33648i
$932$	−22.7468	−	4.13865i	−0.745097	−	0.135566i
$933$	−0.323707	−	0.445544i	−0.0105977	−	0.0145865i
$934$	−0.0212301	−	0.0931130i	−0.000694671	−	0.00304675i
$935$		0			0
$936$	19.9930	−	30.2431i	0.653490	−	0.988526i
$937$	−4.94826	−	15.2292i	−0.161653	−	0.497516i	0.837121	−	0.547017i	$-0.184237\pi$
$937$	−4.94826	−	15.2292i	−0.161653	−	0.497516i	−0.998774	+	0.0495015i	$0.984237\pi$
$938$	12.6870	+	55.6437i	0.414244	+	1.81683i
$939$	0.230951	+	0.0750406i	0.00753681	+	0.00244886i
$940$		0			0
$941$	−33.5449	+	10.8994i	−1.09353	+	0.355311i	−0.799611	−	0.600519i	$-0.794961\pi$
$941$	−33.5449	+	10.8994i	−1.09353	+	0.355311i	−0.293923	+	0.955829i	$0.594961\pi$
$942$	−1.70921	−	2.86221i	−0.0556890	−	0.0932560i
$943$	−33.9244			−1.10473
$944$	2.89283	+	10.5193i	0.0941535	+	0.342374i
$945$		0			0
$946$	−0.647183	+	0.740420i	−0.0210417	+	0.0240731i
$947$	−9.59818	+	13.2108i	−0.311899	+	0.429292i	−0.935972	−	0.352074i	$-0.885477\pi$
$947$	−9.59818	+	13.2108i	−0.311899	+	0.429292i	0.624073	+	0.781366i	$0.285477\pi$
$948$	0.971586	+	0.523403i	0.0315556	+	0.0169994i
$949$		−	32.4211i		−	1.05243i
$950$		0			0
$951$	−1.50660			−0.0488549
$952$	24.5165	+	16.2073i	0.794585	+	0.525281i
$953$	12.9397	+	9.40127i	0.419159	+	0.304537i	0.777299	−	0.629131i	$-0.216589\pi$
$953$	12.9397	+	9.40127i	0.419159	+	0.304537i	−0.358140	+	0.933668i	$0.616589\pi$
$954$	14.9783	+	13.0922i	0.484941	+	0.423875i
$955$		0			0
$956$	1.03773	−	0.499162i	0.0335626	−	0.0161441i
$957$		−	0.0236556i		−	0.000764677i
$958$	−26.7652	−	44.8207i	−0.864746	−	1.44809i
$959$	−17.1910	−	52.9084i	−0.555126	−	1.70850i
$960$		0			0
$961$	4.98671	−	15.3475i	0.160862	−	0.495081i
$962$	50.8605	−	11.5964i	1.63981	−	0.373882i
$963$	−47.4256	+	15.4095i	−1.52827	+	0.496564i
$964$	−0.839593	+	1.55852i	−0.0270415	+	0.0501966i
$965$		0			0
$966$	−1.01053	−	4.43207i	−0.0325132	−	0.142599i
$967$	−38.4407	+	27.9288i	−1.23617	+	0.898129i	−0.997337	−	0.0729314i	$-0.976765\pi$
$967$	−38.4407	+	27.9288i	−1.23617	+	0.898129i	−0.238832	+	0.971061i	$0.576765\pi$
$968$	−8.22440	+	29.7212i	−0.264342	+	0.955277i
$969$	1.25583	−	0.912412i	0.0403430	−	0.0293109i
$970$		0			0
$971$	27.8358	−	38.3127i	0.893294	−	1.22951i	−0.0792647	−	0.996854i	$-0.525257\pi$
$971$	27.8358	−	38.3127i	0.893294	−	1.22951i	0.972558	−	0.232660i	$-0.0747428\pi$
$972$	4.74079	−	4.52853i	0.152061	−	0.145253i
$973$	39.7528	+	12.9165i	1.27442	+	0.414083i
$974$	−0.751479	+	8.32837i	−0.0240789	+	0.266858i
$975$		0			0
$976$	−19.1965	+	51.0075i	−0.614464	+	1.63271i
$977$	−6.87286	+	21.1525i	−0.219882	+	0.676728i	0.778889	+	0.627162i	$0.215784\pi$
$977$	−6.87286	+	21.1525i	−0.219882	+	0.676728i	−0.998771	+	0.0495655i	$0.984216\pi$
$978$	1.04459	−	1.19508i	0.0334022	−	0.0382143i
$979$	−1.55971	+	2.14676i	−0.0498486	+	0.0686107i
$980$		0			0
$981$	25.6497	+	35.3038i	0.818933	+	1.12716i
$982$	50.0087	+	4.51235i	1.59584	+	0.143995i
$983$	−37.2035	+	27.0299i	−1.18661	+	0.862121i	−0.992902	−	0.118938i	$-0.962051\pi$
$983$	−37.2035	+	27.0299i	−1.18661	+	0.862121i	−0.193707	+	0.981060i	$0.562051\pi$
$984$	−0.0812330	−	1.83680i	−0.00258961	−	0.0585549i
$985$		0			0
$986$	0.870666	−	2.03574i	0.0277277	−	0.0648312i
$987$	−3.05607	+	0.992976i	−0.0972756	+	0.0316068i
$988$	5.79044	+	42.8936i	0.184218	+	1.36463i
$989$	13.5401	+	4.39944i	0.430550	+	0.139894i
$990$		0			0
$991$	−4.44841	−	13.6908i	−0.141308	−	0.434902i	0.855209	−	0.518283i	$-0.173428\pi$
$991$	−4.44841	−	13.6908i	−0.141308	−	0.434902i	−0.996518	+	0.0833801i	$0.973428\pi$
$992$	6.89128	+	38.2218i	0.218798	+	1.21354i
$993$	3.20406			0.101678
$994$	−24.5144	−	41.0515i	−0.777551	−	1.30207i
$995$		0			0
$996$	−1.19444	−	1.25043i	−0.0378473	−	0.0396213i
$997$	−0.492360	+	0.677675i	−0.0155932	+	0.0214622i	−0.816742	−	0.577002i	$-0.804222\pi$
$997$	−0.492360	+	0.677675i	−0.0155932	+	0.0214622i	0.801149	+	0.598465i	$0.204222\pi$
$998$	−13.7591	+	32.1707i	−0.435537	+	1.01835i
$999$	6.28379			0.198810

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.t.b.101.8		224
5.2	odd	4		1000.2.o.a.149.18		112
5.3	odd	4		200.2.o.a.29.11	✓	112
5.4	even	2	inner	1000.2.t.b.101.49		224
8.5	even	2	inner	1000.2.t.b.101.52		224
20.3	even	4		800.2.be.a.529.15		112
25.6	even	5	inner	1000.2.t.b.901.52		224
25.8	odd	20		1000.2.o.a.349.11		112
25.17	odd	20		200.2.o.a.69.18	yes	112
25.19	even	10	inner	1000.2.t.b.901.5		224
40.3	even	4		800.2.be.a.529.14		112
40.13	odd	4		200.2.o.a.29.18	yes	112
40.29	even	2	inner	1000.2.t.b.101.5		224
40.37	odd	4		1000.2.o.a.149.11		112
100.67	even	20		800.2.be.a.369.14		112
200.67	even	20		800.2.be.a.369.15		112
200.69	even	10	inner	1000.2.t.b.901.49		224
200.117	odd	20		200.2.o.a.69.11	yes	112
200.133	odd	20		1000.2.o.a.349.18		112
200.181	even	10	inner	1000.2.t.b.901.8		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.11	✓	112	5.3	odd	4
200.2.o.a.29.18	yes	112	40.13	odd	4
200.2.o.a.69.11	yes	112	200.117	odd	20
200.2.o.a.69.18	yes	112	25.17	odd	20
800.2.be.a.369.14		112	100.67	even	20
800.2.be.a.369.15		112	200.67	even	20
800.2.be.a.529.14		112	40.3	even	4
800.2.be.a.529.15		112	20.3	even	4
1000.2.o.a.149.11		112	40.37	odd	4
1000.2.o.a.149.18		112	5.2	odd	4
1000.2.o.a.349.11		112	25.8	odd	20
1000.2.o.a.349.18		112	200.133	odd	20
1000.2.t.b.101.5		224	40.29	even	2	inner
1000.2.t.b.101.8		224	1.1	even	1	trivial
1000.2.t.b.101.49		224	5.4	even	2	inner
1000.2.t.b.101.52		224	8.5	even	2	inner
1000.2.t.b.901.5		224	25.19	even	10	inner
1000.2.t.b.901.8		224	200.181	even	10	inner
1000.2.t.b.901.49		224	200.69	even	10	inner
1000.2.t.b.901.52		224	25.6	even	5	inner

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.t (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30028 - 0.556118i) q^{2} +(-0.0718391 + 0.0988780i) q^{3} +(1.38147 + 1.44622i) q^{4} +(0.148399 - 0.0886183i) q^{6} +4.12326 q^{7} +(-0.992028 - 2.64875i) q^{8} +(0.922435 + 2.83896i) q^{9} +O(q^{10})\)	\(q+(-1.30028 - 0.556118i) q^{2} +(-0.0718391 + 0.0988780i) q^{3} +(1.38147 + 1.44622i) q^{4} +(0.148399 - 0.0886183i) q^{6} +4.12326 q^{7} +(-0.992028 - 2.64875i) q^{8} +(0.922435 + 2.83896i) q^{9} +(-0.296291 - 0.0962708i) q^{11} +(-0.242243 + 0.0327016i) q^{12} +(4.08381 - 1.32691i) q^{13} +(-5.36140 - 2.29302i) q^{14} +(-0.183100 + 3.99581i) q^{16} +(-2.03874 + 1.48123i) q^{17} +(0.379371 - 4.20443i) q^{18} +(2.96240 + 4.07740i) q^{19} +(-0.296211 + 0.407699i) q^{21} +(0.331724 + 0.289952i) q^{22} +(1.97104 - 6.06625i) q^{23} +(0.333170 + 0.0921940i) q^{24} +(-6.04802 - 0.545721i) q^{26} +(-0.695692 - 0.226044i) q^{27} +(5.69614 + 5.96313i) q^{28} +(0.365173 - 0.502617i) q^{29} +(-5.55444 + 4.03554i) q^{31} +(2.46022 - 5.09385i) q^{32} +(0.0308043 - 0.0223807i) q^{33} +(3.47468 - 0.792241i) q^{34} +(-2.83145 + 5.25598i) q^{36} +(-8.16992 + 2.65457i) q^{37} +(-1.58445 - 6.94921i) q^{38} +(-0.162175 + 0.499123i) q^{39} +(-1.64354 - 5.05830i) q^{41} +(0.611887 - 0.365396i) q^{42} +2.23204i q^{43} +(-0.270087 - 0.561497i) q^{44} +(-5.93646 + 6.79170i) q^{46} +(5.15860 + 3.74794i) q^{47} +(-0.381944 - 0.305160i) q^{48} +10.0013 q^{49} -0.307997i q^{51} +(7.56065 + 4.07300i) q^{52} +(-2.76989 + 3.81243i) q^{53} +(0.778889 + 0.680807i) q^{54} +(-4.09039 - 10.9215i) q^{56} -0.615981 q^{57} +(-0.754342 + 0.450465i) q^{58} +(2.59396 - 0.842829i) q^{59} +(12.9582 + 4.21037i) q^{61} +(9.46657 - 2.15841i) q^{62} +(3.80344 + 11.7058i) q^{63} +(-6.03176 + 5.25527i) q^{64} +(-0.0525006 + 0.0119703i) q^{66} +(-5.75286 - 7.91813i) q^{67} +(-4.95865 - 0.902195i) q^{68} +(0.458220 + 0.630686i) q^{69} +(6.63373 + 4.81969i) q^{71} +(6.60462 - 5.25963i) q^{72} +(2.33319 - 7.18083i) q^{73} +(12.0994 + 1.09175i) q^{74} +(-1.80435 + 9.91707i) q^{76} +(-1.22168 - 0.396949i) q^{77} +(0.488444 - 0.558812i) q^{78} +(-3.65256 - 2.65374i) q^{79} +(-7.17257 + 5.21118i) q^{81} +(-0.675942 + 7.49122i) q^{82} +(4.15816 + 5.72321i) q^{83} +(-0.998828 + 0.134837i) q^{84} +(1.24127 - 2.90228i) q^{86} +(0.0234641 + 0.0722151i) q^{87} +(0.0389318 + 0.880304i) q^{88} +(2.63206 - 8.10065i) q^{89} +(16.8386 - 5.47119i) q^{91} +(11.4961 - 5.52976i) q^{92} -0.839121i q^{93} +(-4.62334 - 7.74217i) q^{94} +(0.326930 + 0.609199i) q^{96} +(-0.640392 - 0.465272i) q^{97} +(-13.0044 - 5.56187i) q^{98} -0.929963i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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