LMFDB - Embedded newform 1000.2.o.a.149.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(149,1000)]

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, 1]))

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

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

chi := DirichletCharacter("1000.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.o (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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			149.18
Character	$\chi$	$=$	1000.149
Dual form			1000.2.o.a.349.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.556118 - 1.30028i) q^{2} +(0.0988780 + 0.0718391i) q^{3} +(-1.38147 - 1.44622i) q^{4} +(0.148399 - 0.0886183i) q^{6} +4.12326i q^{7} +(-2.64875 + 0.992028i) q^{8} +(-0.922435 - 2.83896i) q^{9} +O(q^{10})$	\(q+(0.556118 - 1.30028i) q^{2} +(0.0988780 + 0.0718391i) q^{3} +(-1.38147 - 1.44622i) q^{4} +(0.148399 - 0.0886183i) q^{6} +4.12326i q^{7} +(-2.64875 + 0.992028i) q^{8} +(-0.922435 - 2.83896i) q^{9} +(-0.296291 - 0.0962708i) q^{11} +(-0.0327016 - 0.242243i) q^{12} +(-1.32691 - 4.08381i) q^{13} +(5.36140 + 2.29302i) q^{14} +(-0.183100 + 3.99581i) q^{16} +(-1.48123 - 2.03874i) q^{17} +(-4.20443 - 0.379371i) q^{18} +(-2.96240 - 4.07740i) q^{19} +(-0.296211 + 0.407699i) q^{21} +(-0.289952 + 0.331724i) q^{22} +(-6.06625 - 1.97104i) q^{23} +(-0.333170 - 0.0921940i) q^{24} +(-6.04802 - 0.545721i) q^{26} +(0.226044 - 0.695692i) q^{27} +(5.96313 - 5.69614i) q^{28} +(-0.365173 + 0.502617i) q^{29} +(-5.55444 + 4.03554i) q^{31} +(5.09385 + 2.46022i) q^{32} +(-0.0223807 - 0.0308043i) q^{33} +(-3.47468 + 0.792241i) q^{34} +(-2.83145 + 5.25598i) q^{36} +(-2.65457 - 8.16992i) q^{37} +(-6.94921 + 1.58445i) q^{38} +(0.162175 - 0.499123i) q^{39} +(-1.64354 - 5.05830i) q^{41} +(0.365396 + 0.611887i) q^{42} +2.23204 q^{43} +(0.270087 + 0.561497i) q^{44} +(-5.93646 + 6.79170i) q^{46} +(-3.74794 + 5.15860i) q^{47} +(-0.305160 + 0.381944i) q^{48} -10.0013 q^{49} -0.307997i q^{51} +(-4.07300 + 7.56065i) q^{52} +(3.81243 + 2.76989i) q^{53} +(-0.778889 - 0.680807i) q^{54} +(-4.09039 - 10.9215i) q^{56} -0.615981i q^{57} +(0.450465 + 0.754342i) q^{58} +(-2.59396 + 0.842829i) q^{59} +(12.9582 + 4.21037i) q^{61} +(2.15841 + 9.46657i) q^{62} +(11.7058 - 3.80344i) q^{63} +(6.03176 - 5.25527i) q^{64} +(-0.0525006 + 0.0119703i) q^{66} +(7.91813 - 5.75286i) q^{67} +(-0.902195 + 4.95865i) q^{68} +(-0.458220 - 0.630686i) q^{69} +(6.63373 + 4.81969i) q^{71} +(5.25963 + 6.60462i) q^{72} +(-7.18083 - 2.33319i) q^{73} +(-12.0994 - 1.09175i) q^{74} +(-1.80435 + 9.91707i) q^{76} +(0.396949 - 1.22168i) q^{77} +(-0.558812 - 0.488444i) q^{78} +(3.65256 + 2.65374i) q^{79} +(-7.17257 + 5.21118i) q^{81} +(-7.49122 - 0.675942i) q^{82} +(5.72321 - 4.15816i) q^{83} +(0.998828 - 0.134837i) q^{84} +(1.24127 - 2.90228i) q^{86} +(-0.0722151 + 0.0234641i) q^{87} +(0.880304 - 0.0389318i) q^{88} +(-2.63206 + 8.10065i) q^{89} +(16.8386 - 5.47119i) q^{91} +(5.52976 + 11.4961i) q^{92} -0.839121 q^{93} +(4.62334 + 7.74217i) q^{94} +(0.326930 + 0.609199i) q^{96} +(0.465272 - 0.640392i) q^{97} +(-5.56187 + 13.0044i) q^{98} +0.929963i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$1$

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 $

$2$	0.556118	−	1.30028i	0.393234	−	0.919438i
$2$	0.556118	−	1.30028i	0.393234	−	0.919438i
$3$	0.0988780	+	0.0718391i	0.0570872	+	0.0414763i	0.615963	−	0.787775i	$-0.288767\pi$
$3$	0.0988780	+	0.0718391i	0.0570872	+	0.0414763i	−0.558876	+	0.829251i	$0.688767\pi$
$4$	−1.38147	−	1.44622i	−0.690733	−	0.723110i
$5$		0			0
$5$		0			0
$6$	0.148399	−	0.0886183i	0.0605836	−	0.0361783i
$7$			4.12326i			1.55844i	0.626748	+	0.779222i	$0.284386\pi$
$7$			4.12326i			1.55844i	−0.626748	+	0.779222i	$0.715614\pi$
$8$	−2.64875	+	0.992028i	−0.936475	+	0.350735i
$9$	−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	$0.614955\pi$
$12$	−0.0327016	−	0.242243i	−0.00944014	−	0.0699294i
$13$	−1.32691	−	4.08381i	−0.368019	−	1.13264i	−0.948069	−	0.318064i	$-0.896967\pi$
$13$	−1.32691	−	4.08381i	−0.368019	−	1.13264i	0.580050	−	0.814581i	$-0.303033\pi$
$14$	5.36140	+	2.29302i	1.43289	+	0.612834i
$15$		0			0
$16$	−0.183100	+	3.99581i	−0.0457750	+	0.998952i
$17$	−1.48123	−	2.03874i	−0.359252	−	0.494468i	0.590688	−	0.806900i	$-0.298856\pi$
$17$	−1.48123	−	2.03874i	−0.359252	−	0.494468i	−0.949940	+	0.312432i	$0.898856\pi$
$18$	−4.20443	−	0.379371i	−0.990995	−	0.0894187i
$19$	−2.96240	−	4.07740i	−0.679622	−	0.935419i	0.320308	−	0.947314i	$-0.396214\pi$
$19$	−2.96240	−	4.07740i	−0.679622	−	0.935419i	−0.999929	+	0.0118946i	$0.996214\pi$
$20$		0			0
$21$	−0.296211	+	0.407699i	−0.0646385	+	0.0889673i
$22$	−0.289952	+	0.331724i	−0.0618179	+	0.0707238i
$23$	−6.06625	−	1.97104i	−1.26490	−	0.410991i	−0.401662	−	0.915788i	$-0.631567\pi$
$23$	−6.06625	−	1.97104i	−1.26490	−	0.410991i	−0.863238	+	0.504797i	$0.831567\pi$
$24$	−0.333170	−	0.0921940i	−0.0680079	−	0.0188190i
$25$		0			0
$26$	−6.04802	−	0.545721i	−1.18611	−	0.107025i
$27$	0.226044	−	0.695692i	0.0435022	−	0.133886i
$28$	5.96313	−	5.69614i	1.12693	−	1.07647i
$29$	−0.365173	+	0.502617i	−0.0678109	+	0.0933337i	−0.841575	−	0.540140i	$-0.818371\pi$
$29$	−0.365173	+	0.502617i	−0.0678109	+	0.0933337i	0.773764	+	0.633473i	$0.218371\pi$
$30$		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	$0.511472\pi$
$32$	5.09385	+	2.46022i	0.900474	+	0.434910i
$33$	−0.0223807	−	0.0308043i	−0.00389597	−	0.00536235i
$34$	−3.47468	+	0.792241i	−0.595903	+	0.135868i
$35$		0			0
$36$	−2.83145	+	5.25598i	−0.471908	+	0.875996i
$37$	−2.65457	−	8.16992i	−0.436408	−	1.34313i	−0.891637	−	0.452751i	$-0.850443\pi$
$37$	−2.65457	−	8.16992i	−0.436408	−	1.34313i	0.455229	−	0.890374i	$-0.349557\pi$
$38$	−6.94921	+	1.58445i	−1.12731	+	0.257031i
$39$	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	$-0.236328\pi$
$42$	0.365396	+	0.611887i	0.0563818	+	0.0944161i
$43$	2.23204			0.340382			0.170191	−	0.985411i	$-0.445561\pi$
$43$	2.23204			0.340382			0.170191	+	0.985411i	$0.445561\pi$
$44$	0.270087	+	0.561497i	0.0407172	+	0.0846488i
$45$		0			0
$46$	−5.93646	+	6.79170i	−0.875283	+	1.00138i
$47$	−3.74794	+	5.15860i	−0.546693	+	0.752459i	−0.989559	−	0.144129i	$-0.953962\pi$
$47$	−3.74794	+	5.15860i	−0.546693	+	0.752459i	0.442866	+	0.896588i	$0.353962\pi$
$48$	−0.305160	+	0.381944i	−0.0440460	+	0.0551288i
$49$	−10.0013			−1.42875
$50$		0			0
$51$		−	0.307997i		−	0.0431283i
$52$	−4.07300	+	7.56065i	−0.564824	+	1.04847i
$53$	3.81243	+	2.76989i	0.523678	+	0.380474i	0.817988	−	0.575236i	$-0.195090\pi$
$53$	3.81243	+	2.76989i	0.523678	+	0.380474i	−0.294310	+	0.955710i	$0.595090\pi$
$54$	−0.778889	−	0.680807i	−0.105993	−	0.0926462i
$55$		0			0
$56$	−4.09039	−	10.9215i	−0.546601	−	1.45944i
$57$		−	0.615981i		−	0.0815887i
$58$	0.450465	+	0.754342i	0.0591490	+	0.0990500i
$59$	−2.59396	+	0.842829i	−0.337705	+	0.109727i	−0.472960	−	0.881084i	$-0.656815\pi$
$59$	−2.59396	+	0.842829i	−0.337705	+	0.109727i	0.135255	+	0.990811i	$0.456815\pi$
$60$		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	$0.262658\pi$
$62$	2.15841	+	9.46657i	0.274119	+	1.20226i
$63$	11.7058	−	3.80344i	1.47479	−	0.479188i
$64$	6.03176	−	5.25527i	0.753970	−	0.656909i
$65$		0			0
$66$	−0.0525006	+	0.0119703i	−0.00646238	+	0.00147345i
$67$	7.91813	−	5.75286i	0.967354	−	0.702824i	0.0125070	−	0.999922i	$-0.496019\pi$
$67$	7.91813	−	5.75286i	0.967354	−	0.702824i	0.954847	+	0.297098i	$0.0960188\pi$
$68$	−0.902195	+	4.95865i	−0.109407	+	0.601324i
$69$	−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	$0.538250\pi$
$72$	5.25963	+	6.60462i	0.619854	+	0.778362i
$73$	−7.18083	−	2.33319i	−0.840452	−	0.273079i	−0.143011	−	0.989721i	$-0.545678\pi$
$73$	−7.18083	−	2.33319i	−0.840452	−	0.273079i	−0.697441	+	0.716642i	$0.745678\pi$
$74$	−12.0994	−	1.09175i	−1.40653	−	0.126913i
$75$		0			0
$76$	−1.80435	+	9.91707i	−0.206973	+	1.13757i
$77$	0.396949	−	1.22168i	0.0452366	−	0.139224i
$78$	−0.558812	−	0.488444i	−0.0632730	−	0.0553054i
$79$	3.65256	+	2.65374i	0.410945	+	0.298569i	0.773984	−	0.633205i	$-0.218261\pi$
$79$	3.65256	+	2.65374i	0.410945	+	0.298569i	−0.363040	+	0.931774i	$0.618261\pi$
$80$		0			0
$81$	−7.17257	+	5.21118i	−0.796952	+	0.579020i
$82$	−7.49122	−	0.675942i	−0.827267	−	0.0746453i
$83$	5.72321	−	4.15816i	0.628204	−	0.456417i	−0.227573	−	0.973761i	$-0.573079\pi$
$83$	5.72321	−	4.15816i	0.628204	−	0.456417i	0.855778	+	0.517344i	$0.173079\pi$
$84$	0.998828	−	0.134837i	0.108981	−	0.0147119i
$85$		0			0
$86$	1.24127	−	2.90228i	0.133850	−	0.312960i
$87$	−0.0722151	+	0.0234641i	−0.00774227	+	0.00251562i
$88$	0.880304	−	0.0389318i	0.0938408	−	0.00415014i
$89$	−2.63206	+	8.10065i	−0.278998	+	0.858667i	0.709136	+	0.705072i	$0.249085\pi$
$89$	−2.63206	+	8.10065i	−0.278998	+	0.858667i	−0.988134	+	0.153595i	$0.950915\pi$
$90$		0			0
$91$	16.8386	−	5.47119i	1.76516	−	0.573537i
$92$	5.52976	+	11.4961i	0.576517	+	1.19855i
$93$	−0.839121			−0.0870128
$94$	4.62334	+	7.74217i	0.476861	+	0.798543i
$95$		0			0
$96$	0.326930	+	0.609199i	0.0333671	+	0.0621761i
$97$	0.465272	−	0.640392i	0.0472412	−	0.0650220i	−0.784743	−	0.619821i	$-0.787205\pi$
$97$	0.465272	−	0.640392i	0.0472412	−	0.0650220i	0.831984	+	0.554799i	$0.187205\pi$
$98$	−5.56187	+	13.0044i	−0.561834	+	1.31365i
$99$			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	$-0.0588267\pi$
$102$	−0.400484	−	0.171283i	−0.0396538	−	0.0169595i
$103$	8.55853	−	11.7798i	0.843297	−	1.16070i	−0.142003	−	0.989866i	$-0.545354\pi$
$103$	8.55853	−	11.7798i	0.843297	−	1.16070i	0.985300	−	0.170833i	$-0.0546458\pi$
$104$	7.56591	+	9.50066i	0.741898	+	0.931616i
$105$		0			0
$106$	5.72180	−	3.41685i	0.555751	−	0.331874i
$107$	−16.7052			−1.61496			−0.807478	−	0.589897i	$-0.799168\pi$
$107$	−16.7052			−1.61496			−0.807478	+	0.589897i	$0.799168\pi$
$108$	−1.31840	+	0.634166i	−0.126863	+	0.0610227i
$109$	−13.9033	+	4.51745i	−1.33169	+	0.432693i	−0.886494	−	0.462739i	$-0.846867\pi$
$109$	−13.9033	+	4.51745i	−1.33169	+	0.432693i	−0.445198	+	0.895432i	$0.646867\pi$
$110$		0			0
$111$	0.324441	−	0.998526i	0.0307946	−	0.0947759i
$112$	−16.4757	−	0.754969i	−1.55681	−	0.0713378i
$113$	−10.2530	+	3.33141i	−0.964523	+	0.313393i	−0.748603	−	0.663018i	$-0.769275\pi$
$113$	−10.2530	+	3.33141i	−0.964523	+	0.313393i	−0.215920	+	0.976411i	$0.569275\pi$
$114$	−0.800949	−	0.342558i	−0.0750157	−	0.0320835i
$115$		0			0
$116$	1.23137	−	0.166229i	0.114330	−	0.0154340i
$117$	−10.3698	+	7.53410i	−0.958688	+	0.696528i
$118$	−0.346632	+	3.84159i	−0.0319100	+	0.353647i
$119$	8.40627	−	6.10751i	0.770601	−	0.559875i
$120$		0			0
$121$	−8.82067	−	6.40859i	−0.801879	−	0.582599i
$122$	12.6809	−	14.5078i	1.14808	−	1.31348i
$123$	0.200874	−	0.618225i	0.0181122	−	0.0557435i
$124$	13.5095	+	2.45798i	1.21319	+	0.220733i
$125$		0			0
$126$	1.56425	−	17.3360i	0.139354	−	1.54441i
$127$	2.12921	+	0.691823i	0.188937	+	0.0613894i	0.401957	−	0.915658i	$-0.368330\pi$
$127$	2.12921	+	0.691823i	0.188937	+	0.0613894i	−0.213020	+	0.977048i	$0.568330\pi$
$128$	−3.47897	−	10.7655i	−0.307500	−	0.951548i
$129$	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	$0.750514\pi$
$132$	−0.0136317	+	0.0749225i	−0.00118649	+	0.00652117i
$133$	16.8122	−	12.2147i	1.45780	−	1.05915i
$134$	−3.07693	−	13.4951i	−0.265806	−	1.16580i
$135$		0			0
$136$	5.94591	+	3.93070i	0.509858	+	0.337055i
$137$	12.8317	−	4.16928i	1.09629	−	0.356205i	0.295614	−	0.955307i	$-0.404476\pi$
$137$	12.8317	−	4.16928i	1.09629	−	0.356205i	0.800673	+	0.599102i	$0.204476\pi$
$138$	−1.07489	+	0.245080i	−0.0915011	+	0.0208626i
$139$	−9.64111	−	3.13259i	−0.817749	−	0.265703i	−0.129872	−	0.991531i	$-0.541457\pi$
$139$	−9.64111	−	3.13259i	−0.817749	−	0.265703i	−0.687876	+	0.725828i	$0.741457\pi$
$140$		0			0
$141$	−0.741178	+	0.240823i	−0.0624184	+	0.0202810i
$142$	9.95608	−	5.94541i	0.835496	−	0.498927i
$143$			1.33774i			0.111867i
$144$	11.5128	−	3.16606i	0.959404	−	0.263838i
$145$		0			0
$146$	−7.02719	+	8.03957i	−0.581574	+	0.665359i
$147$	−0.988904	−	0.718481i	−0.0815634	−	0.0592593i
$148$	−8.14829	+	15.1256i	−0.669786	+	1.24331i
$149$		−	14.3531i		−	1.17585i	−0.808916	−	0.587925i	$-0.799945\pi$
$149$		−	14.3531i		−	1.17585i	0.808916	−	0.587925i	$-0.200055\pi$
$150$		0			0
$151$	14.4342			1.17464			0.587321	−	0.809354i	$-0.300183\pi$
$151$	14.4342			1.17464			0.587321	+	0.809354i	$0.300183\pi$
$152$	11.8916	+	7.86122i	0.964533	+	0.637629i
$153$	−4.42158	+	6.08578i	−0.357463	+	0.492006i
$154$	−1.36778	−	1.19555i	−0.110219	−	0.0963398i
$155$		0			0
$156$	−0.945880	+	0.454981i	−0.0757310	+	0.0364276i
$157$	19.2873			1.53930			0.769648	−	0.638469i	$-0.220432\pi$
$157$	19.2873			1.53930			0.769648	+	0.638469i	$0.220432\pi$
$158$	5.48186	−	3.27356i	0.436113	−	0.260431i
$159$	0.177979	+	0.547763i	0.0141147	+	0.0434404i
$160$		0			0
$161$	8.12712	−	25.0127i	0.640507	−	1.97128i
$162$	2.78721	+	12.2244i	0.218984	+	0.960439i
$163$	−2.83773	−	8.73364i	−0.222268	−	0.684072i	−0.998557	−	0.0536946i	$-0.982900\pi$
$163$	−2.83773	−	8.73364i	−0.222268	−	0.684072i	0.776289	−	0.630377i	$-0.217100\pi$
$164$	−5.04492	+	9.36480i	−0.393942	+	0.731268i
$165$		0			0
$166$	−2.22400	−	9.75421i	−0.172616	−	0.757074i
$167$	−5.19807	−	7.15453i	−0.402239	−	0.553634i	0.559065	−	0.829124i	$-0.311160\pi$
$167$	−5.19807	−	7.15453i	−0.402239	−	0.553634i	−0.961304	+	0.275489i	$0.911160\pi$
$168$	0.380140	−	1.37374i	0.0293284	−	0.105987i
$169$	−4.39959	+	3.19649i	−0.338430	+	0.245884i
$170$		0			0
$171$	−8.84296	+	12.1713i	−0.676238	+	0.930761i
$172$	−3.08348	−	3.22801i	−0.235113	−	0.246134i
$173$	−4.05868	+	12.4913i	−0.308576	+	0.949698i	0.669743	+	0.742593i	$0.266404\pi$
$173$	−4.05868	+	12.4913i	−0.308576	+	0.949698i	−0.978319	+	0.207105i	$0.933596\pi$
$174$	−0.00965013	+	0.106949i	−0.000731574	+	0.00810777i
$175$		0			0
$176$	0.438930	−	1.16629i	0.0330856	−	0.0879128i
$177$	−0.317034	−	0.103011i	−0.0238297	−	0.00774274i
$178$	9.06939	+	7.92733i	0.679780	+	0.594179i
$179$	0.375298	−	0.516553i	0.0280511	−	0.0386090i	−0.794761	−	0.606922i	$-0.792404\pi$
$179$	0.375298	−	0.516553i	0.0280511	−	0.0386090i	0.822812	+	0.568313i	$0.192404\pi$
$180$		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	$-0.465068\pi$
$182$	2.25015	−	24.9376i	0.166792	−	1.84849i
$183$	0.978810	+	1.34722i	0.0723557	+	0.0995891i
$184$	18.0233	−	0.797087i	1.32870	−	0.0587620i
$185$		0			0
$186$	−0.466650	+	1.09109i	−0.0342164	+	0.0800029i
$187$	0.242605	+	0.746661i	0.0177410	+	0.0546013i
$188$	12.6381	−	1.70609i	0.921729	−	0.124429i
$189$	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	$0.671833\pi$
$192$	0.973942	−	0.0863147i	0.0702882	−	0.00622923i
$193$			16.2523i			1.16986i	0.811083	+	0.584932i	$0.198879\pi$
$193$			16.2523i			1.16986i	−0.811083	+	0.584932i	$0.801121\pi$
$194$	−0.573945	−	0.961119i	−0.0412068	−	0.0690043i
$195$		0			0
$196$	13.8164	+	14.4640i	0.986885	+	1.03314i
$197$	−9.32654	−	6.77613i	−0.664488	−	0.482779i	0.203687	−	0.979036i	$-0.434707\pi$
$197$	−9.32654	−	6.77613i	−0.664488	−	0.482779i	−0.868176	+	0.496257i	$0.834707\pi$
$198$	1.20921	+	0.517169i	0.0859351	+	0.0367536i
$199$	14.9527			1.05997			0.529983	−	0.848008i	$-0.322198\pi$
$199$	14.9527			1.05997			0.529983	+	0.848008i	$0.322198\pi$
$200$		0			0
$201$	1.19621			0.0843741
$202$	−4.80261	−	2.05403i	−0.337911	−	0.144521i
$203$	−2.07242	−	1.50570i	−0.145455	−	0.105680i
$204$	−0.445432	+	0.425488i	−0.0311865	+	0.0297901i
$205$		0			0
$206$	−10.5575	−	17.6795i	−0.735578	−	1.23179i
$207$			19.0400i			1.32337i
$208$	16.5611	−	4.55433i	1.14830	−	0.315786i
$209$	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	$0.576024\pi$
$212$	−1.26087	−	9.34013i	−0.0865972	−	0.641483i
$213$	0.309688	+	0.953122i	0.0212195	+	0.0653068i
$214$	−9.29008	+	21.7215i	−0.635057	+	1.48485i
$215$		0			0
$216$	0.0914119	+	2.06696i	0.00621979	+	0.140639i
$217$	−16.6396	−	22.9024i	−1.12957	−	1.55471i
$218$	−1.85790	+	20.5904i	−0.125833	+	1.39456i
$219$	−0.542411	−	0.746565i	−0.0366528	−	0.0504482i
$220$		0			0
$221$	−6.36038	+	8.75431i	−0.427845	+	0.588879i
$222$	−1.11794	−	0.977163i	−0.0750311	−	0.0655829i
$223$	18.9624	+	6.16124i	1.26981	+	0.412587i	0.864981	−	0.501804i	$-0.167330\pi$
$223$	18.9624	+	6.16124i	1.26981	+	0.412587i	0.404832	+	0.914391i	$0.367330\pi$
$224$	−10.1441	+	21.0033i	−0.677783	+	1.40334i
$225$		0			0
$226$	−1.37011	+	15.1845i	−0.0911386	+	1.01006i
$227$	3.46276	−	10.6573i	0.229832	−	0.707349i	−0.767933	−	0.640530i	$-0.778715\pi$
$227$	3.46276	−	10.6573i	0.229832	−	0.707349i	0.997765	−	0.0668195i	$-0.0212852\pi$
$228$	−0.890844	+	0.850957i	−0.0589976	+	0.0563560i
$229$	4.28891	−	5.90318i	0.283419	−	0.390093i	−0.643444	−	0.765494i	$-0.722495\pi$
$229$	4.28891	−	5.90318i	0.283419	−	0.390093i	0.926863	+	0.375401i	$0.122495\pi$
$230$		0			0
$231$	0.127014	−	0.0922812i	0.00835692	−	0.00607166i
$232$	0.468641	−	1.69357i	0.0307678	−	0.111188i
$233$	6.79487	+	9.35234i	0.445147	+	0.612692i	0.971346	−	0.237669i	$-0.0763834\pi$
$233$	6.79487	+	9.35234i	0.445147	+	0.612692i	−0.526199	+	0.850361i	$0.676383\pi$
$234$	4.02963	+	17.6735i	0.263425	+	1.15535i
$235$		0			0
$236$	4.80239	+	2.58710i	0.312609	+	0.168406i
$237$	0.170515	+	0.524792i	0.0110762	+	0.0340889i
$238$	−3.26661	−	14.3270i	−0.211743	−	0.928682i
$239$	−0.177923	+	0.547590i	−0.0115089	+	0.0354207i	−0.956646	−	0.291253i	$-0.905928\pi$
$239$	−0.177923	+	0.547590i	−0.0115089	+	0.0354207i	0.945137	+	0.326674i	$0.105928\pi$
$240$		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	$0.890924\pi$
$242$	−13.2383	+	7.90543i	−0.850990	+	0.508180i
$243$	−3.27806			−0.210287
$244$	−11.8122	−	24.5569i	−0.756197	−	1.57209i
$245$		0			0
$246$	−0.692158	−	0.604998i	−0.0441304	−	0.0385733i
$247$	−12.7205	+	17.5082i	−0.809384	+	1.11402i
$248$	10.7090	−	16.1993i	0.680019	−	1.02866i
$249$	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	$-0.107165\pi$
$252$	−21.6717	−	11.6748i	−1.36519	−	0.735443i
$253$	1.60762	+	1.16800i	0.101070	+	0.0734318i
$254$	2.08366	−	2.38384i	0.130740	−	0.149576i
$255$		0			0
$256$	−15.9329	−	1.46327i	−0.995809	−	0.0914541i
$257$		−	17.6103i		−	1.09850i	−0.835658	−	0.549250i	$-0.814914\pi$
$257$		−	17.6103i		−	1.09850i	0.835658	−	0.549250i	$-0.185086\pi$
$258$	0.331231	−	0.197799i	0.0206216	−	0.0123144i
$259$	33.6867	−	10.9455i	2.09319	−	0.680118i
$260$		0			0
$261$	1.76376	+	0.573081i	0.109174	+	0.0354728i
$262$	4.88719	−	1.11430i	0.301932	−	0.0688416i
$263$	−20.7083	+	6.72853i	−1.27693	+	0.414899i	−0.867497	−	0.497442i	$-0.834273\pi$
$263$	−20.7083	+	6.72853i	−1.27693	+	0.414899i	−0.409430	+	0.912341i	$0.634273\pi$
$264$	0.0898395	+	0.0593907i	0.00552924	+	0.00365525i
$265$		0			0
$266$	−6.53308	−	28.6534i	−0.400569	−	1.75685i
$267$	−0.842196	+	0.611891i	−0.0515416	+	0.0374471i
$268$	−19.2585	−	3.50397i	−1.17640	−	0.214039i
$269$	7.13157	+	9.81576i	0.434819	+	0.598477i	0.969051	−	0.246861i	$-0.0793990\pi$
$269$	7.13157	+	9.81576i	0.434819	+	0.598477i	−0.534232	+	0.845338i	$0.679399\pi$
$270$		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	$0.858277\pi$
$272$	8.41764	−	5.54543i	0.510395	−	0.336241i
$273$	2.05801	+	0.668689i	0.124557	+	0.0404709i
$274$	1.71471	−	19.0034i	0.103589	−	1.14804i
$275$		0			0
$276$	−0.279094	+	1.53396i	−0.0167995	+	0.0923335i
$277$	0.720234	−	2.21665i	0.0432747	−	0.133186i	−0.927085	−	0.374851i	$-0.877694\pi$
$277$	0.720234	−	2.21665i	0.0432747	−	0.133186i	0.970360	+	0.241666i	$0.0776937\pi$
$278$	−9.43484	+	10.7941i	−0.565864	+	0.647386i
$279$	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	$0.166779\pi$
$282$	−0.0990438	+	1.09767i	−0.00589797	+	0.0653650i
$283$	−3.22475	+	2.34292i	−0.191691	+	0.139272i	−0.679491	−	0.733683i	$-0.737800\pi$
$283$	−3.22475	+	2.34292i	−0.191691	+	0.139272i	0.487800	+	0.872955i	$0.337800\pi$
$284$	−2.19395	−	16.2521i	−0.130187	−	0.964382i
$285$		0			0
$286$	1.73944	+	0.743940i	0.102855	+	0.0439901i
$287$	20.8567	−	6.77675i	1.23113	−	0.400019i
$288$	2.28573	−	16.7306i	0.134688	−	0.985863i
$289$	3.29087	−	10.1282i	0.193580	−	0.595779i
$290$		0			0
$291$	0.0920104	−	0.0298960i	0.00539374	−	0.00175253i
$292$	6.54576	+	13.6083i	0.383062	+	0.796364i
$293$	−9.63185			−0.562699			−0.281349	−	0.959605i	$-0.590782\pi$
$293$	−9.63185			−0.562699			−0.281349	+	0.959605i	$0.590782\pi$
$294$	−1.48417	+	0.886294i	−0.0865588	+	0.0516897i
$295$		0			0
$296$	15.1361	+	19.0067i	0.879766	+	1.10474i
$297$	−0.133950	+	0.184366i	−0.00777255	+	0.0106980i
$298$	−18.6630	−	7.98199i	−1.08112	−	0.462384i
$299$			27.3888i			1.58393i
$300$		0			0
$301$			9.20326i			0.530467i
$302$	8.02713	−	18.7686i	0.461909	−	1.08001i
$303$	0.265339	−	0.365207i	0.0152433	−	0.0209806i
$304$	16.8349	−	11.0906i	0.965548	−	0.636090i
$305$		0			0
$306$	5.45431	+	9.13371i	0.311802	+	0.522139i
$307$	8.12625			0.463790			0.231895	−	0.972741i	$-0.425507\pi$
$307$	8.12625			0.463790			0.231895	+	0.972741i	$0.425507\pi$
$308$	−2.31520	+	1.11364i	−0.131920	+	0.0634555i
$309$	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	$0.140777\pi$
$312$	0.0655833	+	1.48293i	0.00371292	+	0.0839546i
$313$	−1.88964	+	0.613980i	−0.106809	+	0.0347042i	−0.361934	−	0.932204i	$-0.617883\pi$
$313$	−1.88964	+	0.613980i	−0.106809	+	0.0347042i	0.255125	+	0.966908i	$0.417883\pi$
$314$	10.7260	−	25.0789i	0.605304	−	1.41529i
$315$		0			0
$316$	−1.20800	−	8.94844i	−0.0679552	−	0.503389i
$317$	−9.97273	+	7.24561i	−0.560124	+	0.406954i	−0.831504	−	0.555518i	$-0.812520\pi$
$317$	−9.97273	+	7.24561i	−0.560124	+	0.406954i	0.271380	+	0.962472i	$0.412520\pi$
$318$	0.811224	+	0.0731978i	0.0454912	+	0.00410473i
$319$	0.156585	−	0.113766i	0.00876707	−	0.00636965i
$320$		0			0
$321$	−1.65178	−	1.20009i	−0.0921934	−	0.0669824i
$322$	−28.0039	−	24.4775i	−1.56060	−	1.36408i
$323$	−3.92476	+	12.0792i	−0.218379	+	0.672103i
$324$	17.4452	+	3.17404i	0.969176	+	0.176336i
$325$		0			0
$326$	−12.9343	−	1.16708i	−0.716365	−	0.0646385i
$327$	−1.69926	−	0.552122i	−0.0939691	−	0.0305324i
$328$	9.37131	+	11.7677i	0.517444	+	0.649765i
$329$	−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	$-0.456072\pi$
$332$	−13.9200	−	2.53266i	−0.763961	−	0.138998i
$333$	−20.7454	+	15.0724i	−1.13684	+	0.825964i
$334$	−12.1936	+	2.78020i	−0.667206	+	0.152126i
$335$		0			0
$336$	−1.57485	−	1.25825i	−0.0859152	−	0.0686433i
$337$	24.2182	−	7.86898i	1.31925	−	0.428651i	0.437013	−	0.899455i	$-0.356036\pi$
$337$	24.2182	−	7.86898i	1.31925	−	0.428651i	0.882238	+	0.470805i	$0.156036\pi$
$338$	1.70965	+	7.49833i	0.0929926	+	0.407855i
$339$	−1.25312	−	0.407164i	−0.0680603	−	0.0221141i
$340$		0			0
$341$	2.03423	−	0.660963i	0.110160	−	0.0357931i
$342$	10.9084	+	18.2670i	0.589858	+	0.987766i
$343$		−	12.3749i		−	0.668184i
$344$	−5.91211	+	2.21424i	−0.318759	+	0.119384i
$345$		0			0
$346$	13.9851	+	12.2241i	0.751846	+	0.657170i
$347$	21.6770	+	15.7492i	1.16368	+	0.845463i	0.990239	−	0.139381i	$-0.0445112\pi$
$347$	21.6770	+	15.7492i	1.16368	+	0.845463i	0.173442	+	0.984844i	$0.444511\pi$
$348$	0.133697	+	0.0720240i	0.00716691	+	0.00386089i
$349$			9.22396i			0.493747i	0.969048	+	0.246874i	$0.0794032\pi$
$349$			9.22396i			0.493747i	−0.969048	+	0.246874i	$0.920597\pi$
$350$		0			0
$351$	−3.14101			−0.167655
$352$	−1.27241	−	1.21933i	−0.0678199	−	0.0649905i
$353$	8.49553	−	11.6931i	0.452172	−	0.622361i	−0.520691	−	0.853745i	$-0.674326\pi$
$353$	8.49553	−	11.6931i	0.452172	−	0.622361i	0.972862	+	0.231384i	$0.0743255\pi$
$354$	−0.310251	+	0.354947i	−0.0164896	+	0.0188652i
$355$		0			0
$356$	15.3514	−	7.38424i	0.813624	−	0.391364i
$357$	1.26995			0.0672130
$358$	−0.462955	−	0.775257i	−0.0244679	−	0.0409736i
$359$	−0.995352	−	3.06338i	−0.0525327	−	0.161679i	0.921348	−	0.388738i	$-0.127089\pi$
$359$	−0.995352	−	3.06338i	−0.0525327	−	0.161679i	−0.973881	+	0.227059i	$0.927089\pi$
$360$		0			0
$361$	−1.97802	+	6.08771i	−0.104106	+	0.320406i
$362$	−27.4460	+	6.25778i	−1.44253	+	0.328902i
$363$	−0.411783	−	1.26734i	−0.0216130	−	0.0665179i
$364$	−31.1745	−	16.7940i	−1.63399	−	0.880247i
$365$		0			0
$366$	2.29609	−	0.523518i	0.120019	−	0.0273647i
$367$	−5.30006	−	7.29490i	−0.276661	−	0.380791i	0.647964	−	0.761671i	$-0.275621\pi$
$367$	−5.30006	−	7.29490i	−0.276661	−	0.380791i	−0.924624	+	0.380881i	$0.875621\pi$
$368$	8.98664	−	23.8787i	0.468461	−	1.24476i
$369$	−12.8443	+	9.33191i	−0.668646	+	0.485800i
$370$		0			0
$371$	−11.4210	+	15.7196i	−0.592948	+	0.816123i
$372$	1.15922	+	1.21355i	0.0601026	+	0.0629198i
$373$	2.96932	−	9.13862i	0.153746	−	0.473180i	−0.844286	−	0.535893i	$-0.819975\pi$
$373$	2.96932	−	9.13862i	0.153746	−	0.473180i	0.998032	+	0.0627126i	$0.0199752\pi$
$374$	1.10579	+	0.0997766i	0.0571789	+	0.00515932i
$375$		0			0
$376$	4.80988	−	17.3819i	0.248051	−	0.896403i
$377$	2.53715	+	0.824369i	0.130670	+	0.0424571i
$378$	2.80714	−	3.21156i	0.144384	−	0.165185i
$379$	−0.875430	+	1.20493i	−0.0449678	+	0.0618929i	−0.830909	−	0.556409i	$-0.812179\pi$
$379$	−0.875430	+	1.20493i	−0.0449678	+	0.0618929i	0.785941	+	0.618302i	$0.212179\pi$
$380$		0			0
$381$	0.160832	+	0.221367i	0.00823969	+	0.0113410i
$382$	25.5773	+	2.30787i	1.30865	+	0.118081i
$383$	−7.26441	−	9.99860i	−0.371194	−	0.510905i	0.582031	−	0.813167i	$-0.302258\pi$
$383$	−7.26441	−	9.99860i	−0.371194	−	0.510905i	−0.953225	+	0.302262i	$0.902258\pi$
$384$	0.429393	−	1.31440i	0.0219124	−	0.0670752i
$385$		0			0
$386$	21.1325	+	9.03817i	1.07562	+	0.460031i
$387$	−2.05891	−	6.33667i	−0.104660	−	0.322111i
$388$	−1.56891	+	0.211795i	−0.0796491	+	0.0107523i
$389$	11.0661	+	3.59560i	0.561074	+	0.182304i	0.575805	−	0.817587i	$-0.304689\pi$
$389$	11.0661	+	3.59560i	0.561074	+	0.182304i	−0.0147301	+	0.999892i	$0.504689\pi$
$390$		0			0
$391$	4.96708	+	15.2871i	0.251196	+	0.773102i
$392$	26.4908	−	9.92153i	1.33799	−	0.501113i
$393$			0.433203i			0.0218522i
$394$	−13.9975	+	8.35881i	−0.705185	+	0.421111i
$395$		0			0
$396$	1.34493	−	1.28471i	0.0675853	−	0.0645592i
$397$	2.73979	+	1.99057i	0.137506	+	0.0999040i	0.654412	−	0.756138i	$-0.272916\pi$
$397$	2.73979	+	1.99057i	0.137506	+	0.0999040i	−0.516906	+	0.856042i	$0.672916\pi$
$398$	8.31543	−	19.4427i	0.416815	−	0.974573i
$399$	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	$0.475452\pi$
$402$	0.665233	−	1.55541i	0.0331788	−	0.0775768i
$403$	23.8506	+	17.3285i	1.18808	+	0.863193i
$404$	−5.34163	+	5.10247i	−0.265756	+	0.253857i
$405$		0			0
$406$	−3.11035	+	1.85738i	−0.154364	+	0.0921804i
$407$			2.67623i			0.132656i
$408$	0.305542	+	0.815809i	0.0151266	+	0.0403885i
$409$	3.02158	+	9.29945i	0.149407	+	0.459828i	0.997551	−	0.0699372i	$-0.0222799\pi$
$409$	3.02158	+	9.29945i	0.149407	+	0.459828i	−0.848144	+	0.529766i	$0.822280\pi$
$410$		0			0
$411$	1.56829	+	0.509568i	0.0773581	+	0.0251352i
$412$	−28.8595	+	3.89590i	−1.42181	+	0.191937i
$413$	−3.47520	−	10.6956i	−0.171003	−	0.526295i
$414$	24.7574	+	10.5885i	1.21676	+	0.520396i
$415$		0			0
$416$	3.28799	−	24.0668i	0.161207	−	1.17997i
$417$	−0.728252	−	1.00235i	−0.0356626	−	0.0490854i
$418$	2.21152	+	0.199549i	0.108169	+	0.00976024i
$419$	−22.2630	−	30.6425i	−1.08762	−	1.49698i	−0.850844	−	0.525418i	$-0.823909\pi$
$419$	−22.2630	−	30.6425i	−1.08762	−	1.49698i	−0.236776	−	0.971564i	$-0.576091\pi$
$420$		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	$0.318412\pi$
$422$	2.03471	−	2.32784i	0.0990480	−	0.113317i
$423$	18.1023	+	5.88179i	0.880164	+	0.285983i
$424$	−12.8460	−	3.55472i	−0.623857	−	0.172632i
$425$		0			0
$426$	1.41155	+	0.127366i	0.0683898	+	0.00617090i
$427$	−17.3604	+	53.4299i	−0.840130	+	2.58566i
$428$	23.0777	+	24.1594i	1.11550	+	1.16779i
$429$	−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	$0.369262\pi$
$432$	2.73846	+	1.03061i	0.131754	+	0.0495852i
$433$	−16.5255	−	22.7455i	−0.794167	−	1.09308i	−0.993577	−	0.113161i	$-0.963903\pi$
$433$	−16.5255	−	22.7455i	−0.794167	−	1.09308i	0.199410	−	0.979916i	$-0.436097\pi$
$434$	−39.0331	+	8.89970i	−1.87365	+	0.427199i
$435$		0			0
$436$	25.7401	+	13.8665i	1.23273	+	0.664084i
$437$	9.93394	+	30.5735i	0.475205	+	1.46253i
$438$	−1.27239	+	0.290110i	−0.0607971	+	0.0138620i
$439$	−1.43731	+	4.42358i	−0.0685991	+	0.211126i	−0.979479	−	0.201544i	$-0.935404\pi$
$439$	−1.43731	+	4.42358i	−0.0685991	+	0.211126i	0.910880	+	0.412671i	$0.135404\pi$
$440$		0			0
$441$	9.22550	+	28.3932i	0.439310	+	1.35206i
$442$	7.84596	+	13.1387i	0.373194	+	0.624945i
$443$	−33.9122			−1.61122			−0.805609	−	0.592448i	$-0.798162\pi$
$443$	−33.9122			−1.61122			−0.805609	+	0.592448i	$0.798162\pi$
$444$	−1.89229	+	0.910218i	−0.0898042	+	0.0431970i
$445$		0			0
$446$	18.5566	−	21.2300i	0.878683	−	1.00527i
$447$	1.03111	−	1.41920i	0.0487699	−	0.0671260i
$448$	21.6688	+	24.8705i	1.02376	+	1.17502i
$449$	6.81383			0.321565			0.160782	−	0.986990i	$-0.448598\pi$
$449$	6.81383			0.321565			0.160782	+	0.986990i	$0.448598\pi$
$450$		0			0
$451$			1.65695i			0.0780229i
$452$	18.9822	+	10.2259i	0.892845	+	0.480985i
$453$	1.42723	+	1.03694i	0.0670570	+	0.0487198i
$454$	−11.9318	−	10.4293i	−0.559986	−	0.489470i
$455$		0			0
$456$	0.611071	+	1.63158i	0.0286160	+	0.0764057i
$457$			41.0652i			1.92095i	0.278365	+	0.960475i	$0.410208\pi$
$457$			41.0652i			1.92095i	−0.278365	+	0.960475i	$0.589792\pi$
$458$	−5.29066	−	8.85965i	−0.247216	−	0.413984i
$459$	−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	$0.796094\pi$
$462$	−0.0493568	−	0.216473i	−0.00229629	−	0.0100713i
$463$	18.4536	−	5.99593i	0.857610	−	0.278654i	0.152980	−	0.988229i	$-0.451113\pi$
$463$	18.4536	−	5.99593i	0.857610	−	0.278654i	0.704630	+	0.709575i	$0.251113\pi$
$464$	−1.94150	−	1.55119i	−0.0901318	−	0.0720122i
$465$		0			0
$466$	15.9394	−	3.63425i	0.738380	−	0.168353i
$467$	−0.0546334	+	0.0396935i	−0.00252813	+	0.00183679i	−0.589049	−	0.808098i	$-0.700497\pi$
$467$	−0.0546334	+	0.0396935i	−0.00252813	+	0.00183679i	0.586520	+	0.809934i	$0.300497\pi$
$468$	25.2215	+	4.58889i	1.16586	+	0.212122i
$469$	23.7205	+	32.6485i	1.09531	+	1.50757i
$470$		0			0
$471$	1.90709	+	1.38558i	0.0878741	+	0.0638443i
$472$	6.03465	−	4.80573i	0.277767	−	0.221202i
$473$	−0.661332	−	0.214880i	−0.0304081	−	0.00988019i
$474$	0.777205	+	0.0701281i	0.0356982	+	0.00322109i
$475$		0			0
$476$	−20.4458	−	3.71998i	−0.937131	−	0.170505i
$477$	4.34691	−	13.3784i	0.199031	−	0.612555i
$478$	0.613076	+	0.535875i	0.0280414	+	0.0245103i
$479$	−29.8640	−	21.6974i	−1.36452	−	0.991381i	−0.998143	−	0.0609142i	$-0.980598\pi$
$479$	−29.8640	−	21.6974i	−1.36452	−	0.991381i	−0.366376	−	0.930467i	$-0.619402\pi$
$480$		0			0
$481$	−29.8420	+	21.6815i	−1.36068	+	0.988591i
$482$	1.24672	+	0.112493i	0.0567863	+	0.00512390i
$483$	2.60048	−	1.88936i	0.118326	−	0.0859689i
$484$	2.91723	+	21.6099i	0.132601	+	0.982267i
$485$		0			0
$486$	−1.82298	+	4.26240i	−0.0826923	+	0.193346i
$487$	5.62357	−	1.82721i	0.254828	−	0.0827987i	−0.178817	−	0.983882i	$-0.557227\pi$
$487$	5.62357	−	1.82721i	0.254828	−	0.0827987i	0.433645	+	0.901084i	$0.357227\pi$
$488$	−38.4998	+	1.70267i	−1.74280	+	0.0770761i
$489$	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	$0.695785\pi$
$492$	−1.17159	+	0.563550i	−0.0528193	+	0.0254068i
$493$	1.56562			0.0705118
$494$	15.6916	+	26.2768i	0.705996	+	1.18225i
$495$		0			0
$496$	−15.1082	−	22.9334i	−0.678378	−	1.02974i
$497$	−19.8728	+	27.3526i	−0.891417	+	1.22693i
$498$	0.480829	−	1.12425i	0.0215465	−	0.0503787i
$499$			24.7413i			1.10757i	0.832658	+	0.553787i	$0.186818\pi$
$499$			24.7413i			1.10757i	−0.832658	+	0.553787i	$0.813182\pi$
$500$		0			0
$501$		−	1.08085i		−	0.0482888i
$502$	−13.6105	−	5.82107i	−0.607466	−	0.259807i
$503$	−7.29652	+	10.0428i	−0.325336	+	0.447786i	−0.940087	−	0.340935i	$-0.889256\pi$
$503$	−7.29652	+	10.0428i	−0.325336	+	0.447786i	0.614751	+	0.788721i	$0.289256\pi$
$504$	−27.2326	+	21.6868i	−1.21303	+	0.966008i
$505$		0			0
$506$	2.41276	−	1.44081i	0.107260	−	0.0640519i
$507$	−0.664655			−0.0295184
$508$	−1.94091	−	4.03504i	−0.0861139	−	0.179026i
$509$	−20.9803	+	6.81693i	−0.929937	+	0.302155i	−0.734537	−	0.678569i	$-0.762601\pi$
$509$	−20.9803	+	6.81693i	−0.929937	+	0.302155i	−0.195400	+	0.980724i	$0.562601\pi$
$510$		0			0
$511$	9.62035	−	29.6084i	0.425579	−	1.30980i
$512$	−10.7632	+	19.9036i	−0.475673	+	0.879622i
$513$	−3.50625	+	1.13925i	−0.154805	+	0.0502990i
$514$	−22.8983	−	9.79339i	−1.01000	−	0.431968i
$515$		0			0
$516$	−0.0729911	−	0.540694i	−0.00321326	−	0.0238027i
$517$	1.60710	−	1.16763i	0.0706803	−	0.0513523i
$518$	4.50156	−	49.8891i	0.197787	−	2.19200i
$519$	−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	$-0.602936\pi$
$522$	1.72602	−	1.97469i	0.0755460	−	0.0864297i
$523$	−1.73482	+	5.33924i	−0.0758585	+	0.233469i	−0.981795	−	0.189946i	$-0.939169\pi$
$523$	−1.73482	+	5.33924i	−0.0758585	+	0.233469i	0.905936	+	0.423415i	$0.139169\pi$
$524$	1.26895	−	6.97441i	0.0554344	−	0.304678i
$525$		0			0
$526$	−2.76725	+	30.6685i	−0.120658	+	1.33721i
$527$	16.4549	+	5.34651i	0.716785	+	0.232897i
$528$	0.127186	−	0.0837885i	0.00553506	−	0.00364643i
$529$	14.3070	+	10.3946i	0.622041	+	0.451940i
$530$		0			0
$531$	4.78552	+	6.58671i	0.207674	+	0.285839i
$532$	−40.8906	−	7.43980i	−1.77283	−	0.322556i
$533$	−18.4763	+	13.4238i	−0.800298	+	0.581450i
$534$	0.327271	+	1.43538i	0.0141624	+	0.0621148i
$535$		0			0
$536$	−15.2662	+	23.0929i	−0.659398	+	0.997462i
$537$	0.0742173	−	0.0241147i	0.00320271	−	0.00104063i
$538$	16.7292	−	3.81433i	0.721249	−	0.164448i
$539$	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	$0.209051\pi$
$542$	−19.0688	+	11.3872i	−0.819076	+	0.489122i
$543$		−	2.43282i		−	0.104402i
$544$	−2.52943	−	14.0292i	−0.108448	−	0.601498i
$545$		0			0
$546$	2.01398	−	2.30413i	0.0861904	−	0.0986075i
$547$	25.9886	+	18.8818i	1.11119	+	0.807327i	0.982851	−	0.184403i	$-0.0590352\pi$
$547$	25.9886	+	18.8818i	1.11119	+	0.807327i	0.128340	+	0.991730i	$0.459035\pi$
$548$	−23.7563	−	12.7978i	−1.01482	−	0.546693i
$549$		−	40.6716i		−	1.73582i
$550$		0			0
$551$	3.13116			0.133392
$552$	1.83937	+	1.21596i	0.0782888	+	0.0517548i
$553$	−10.9420	+	15.0604i	−0.465303	+	0.640434i
$554$	−2.48174	−	2.16923i	−0.105439	−	0.0921616i
$555$		0			0
$556$	8.78847	+	18.2707i	0.372714	+	0.774851i
$557$	−10.0696			−0.426664			−0.213332	−	0.976980i	$-0.568432\pi$
$557$	−10.0696			−0.426664			−0.213332	+	0.976980i	$0.568432\pi$
$558$	24.8842	−	14.8600i	1.05343	−	0.629072i
$559$	−2.96171	−	9.11521i	−0.125267	−	0.385532i
$560$		0			0
$561$	−0.0296512	+	0.0912569i	−0.00125187	+	0.00385287i
$562$	−4.28356	−	18.7872i	−0.180691	−	0.792491i
$563$	8.80460	+	27.0978i	0.371069	+	1.14203i	0.946092	+	0.323897i	$0.104993\pi$
$563$	8.80460	+	27.0978i	0.371069	+	1.14203i	−0.575023	+	0.818137i	$0.695007\pi$
$564$	1.37220	+	0.739216i	0.0577798	+	0.0311266i
$565$		0			0
$566$	1.25311	+	5.49602i	0.0526723	+	0.231015i
$567$	−21.4870	−	29.5744i	−0.902370	−	1.24201i
$568$	−22.3524	−	6.18530i	−0.937884	−	0.259529i
$569$	21.6286	−	15.7141i	0.906718	−	0.658769i	−0.0334647	−	0.999440i	$-0.510654\pi$
$569$	21.6286	−	15.7141i	0.906718	−	0.658769i	0.940183	+	0.340671i	$0.110654\pi$
$570$		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	$0.00327723\pi$
$572$	1.93466	−	1.84804i	0.0808923	−	0.0772705i
$573$	−0.685842	+	2.11081i	−0.0286515	+	0.0881802i
$574$	2.78708	−	30.8882i	0.116331	−	1.28925i
$575$		0			0
$576$	−20.4834	−	12.2763i	−0.853476	−	0.511512i
$577$	3.37588	+	1.09689i	0.140540	+	0.0456641i	0.378442	−	0.925625i	$-0.376460\pi$
$577$	3.37588	+	1.09689i	0.140540	+	0.0456641i	−0.237902	+	0.971289i	$0.576460\pi$
$578$	−11.3395	−	9.91155i	−0.471659	−	0.412266i
$579$	−1.16755	+	1.60699i	−0.0485216	+	0.0667843i
$580$		0			0
$581$	17.1452	+	23.5983i	0.711301	+	0.979022i
$582$	0.0122954	−	0.136265i	0.000509660	−	0.00564837i
$583$	−0.862930	−	1.18772i	−0.0357389	−	0.0491904i
$584$	21.3348	−	0.943539i	0.882841	−	0.0390439i
$585$		0			0
$586$	−5.35644	+	12.5241i	−0.221273	+	0.517367i
$587$	−14.4792	−	44.5624i	−0.597620	−	1.83929i	−0.541224	−	0.840878i	$-0.682039\pi$
$587$	−14.4792	−	44.5624i	−0.597620	−	1.83929i	−0.0563961	−	0.998408i	$-0.517961\pi$
$588$	0.327057	+	2.42273i	0.0134876	+	0.0999116i
$589$	32.9090	+	10.6928i	1.35599	+	0.440588i
$590$		0			0
$591$	−0.435399	−	1.34002i	−0.0179099	−	0.0551210i
$592$	33.1315	−	9.11122i	1.36169	−	0.374469i
$593$		−	9.84501i		−	0.404286i	−0.979356	−	0.202143i	$-0.935209\pi$
$593$		−	9.84501i		−	0.404286i	0.979356	−	0.202143i	$-0.0647906\pi$
$594$	0.165236	+	0.276701i	0.00677971	+	0.0113532i
$595$		0			0
$596$	−20.7577	+	19.8283i	−0.850268	+	0.812198i
$597$	1.47849	+	1.07418i	0.0605105	+	0.0439635i
$598$	35.6132	+	15.2314i	1.45633	+	0.622858i
$599$	−30.6535			−1.25247			−0.626235	−	0.779634i	$-0.715405\pi$
$599$	−30.6535			−1.25247			−0.626235	+	0.779634i	$0.715405\pi$
$600$		0			0
$601$	19.2818			0.786520			0.393260	−	0.919427i	$-0.371347\pi$
$601$	19.2818			0.786520			0.393260	+	0.919427i	$0.371347\pi$
$602$	11.9668	+	5.11809i	0.487732	+	0.208598i
$603$	−23.6361	−	17.1726i	−0.962537	−	0.699324i
$604$	−19.9404	−	20.8751i	−0.811364	−	0.849394i
$605$		0			0
$606$	−0.327313	−	0.548113i	−0.0132962	−	0.0222656i
$607$		−	7.58873i		−	0.308017i	−0.988070	−	0.154009i	$-0.950782\pi$
$607$		−	7.58873i		−	0.308017i	0.988070	−	0.154009i	$-0.0492183\pi$
$608$	−5.05874	−	28.0578i	−0.205159	−	1.13789i
$609$	−0.0967486	−	0.297762i	−0.00392045	−	0.0120659i
$610$		0			0
$611$	26.0399	+	8.46088i	1.05346	+	0.342291i
$612$	14.9096	−	2.01273i	0.602686	−	0.0813598i
$613$	9.10557	+	28.0241i	0.367771	+	1.13188i	0.948228	+	0.317591i	$0.102874\pi$
$613$	9.10557	+	28.0241i	0.367771	+	1.13188i	−0.580457	+	0.814291i	$0.697126\pi$
$614$	4.51915	−	10.5664i	0.182378	−	0.426426i
$615$		0			0
$616$	0.160526	+	3.62972i	0.00646777	+	0.146246i
$617$	−3.79899	−	5.22886i	−0.152942	−	0.210506i	0.725670	−	0.688043i	$-0.241530\pi$
$617$	−3.79899	−	5.22886i	−0.152942	−	0.210506i	−0.878612	+	0.477537i	$0.841530\pi$
$618$	0.226169	−	2.50655i	0.00909787	−	0.100828i
$619$	25.9223	+	35.6790i	1.04191	+	1.43406i	0.895621	+	0.444819i	$0.146732\pi$
$619$	25.9223	+	35.6790i	1.04191	+	1.43406i	0.146286	+	0.989242i	$0.453268\pi$
$620$		0			0
$621$	−2.74248	+	3.77470i	−0.110052	+	0.151473i
$622$	4.79795	+	4.19377i	0.192380	+	0.168155i
$623$	−33.4011	−	10.8527i	−1.33819	−	0.434803i
$624$	1.96470	+	0.739409i	0.0786511	+	0.0296000i
$625$		0			0
$626$	−0.252513	+	2.79850i	−0.0100924	+	0.111851i
$627$	−0.0593010	+	0.182510i	−0.00236825	+	0.00728873i
$628$	−26.6448	−	27.8937i	−1.06324	−	1.11308i
$629$	−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	$0.515240\pi$
$632$	−12.3073	−	3.40565i	−0.489558	−	0.135469i
$633$	0.157054	+	0.216166i	0.00624233	+	0.00859183i
$634$	3.87533	+	16.9968i	0.153909	+	0.675028i
$635$		0			0
$636$	0.546314	−	1.01411i	0.0216627	−	0.0402122i
$637$	13.2708	+	40.8432i	0.525807	+	1.61827i
$638$	−0.0608477	−	0.266871i	−0.00240898	−	0.0105655i
$639$	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	$0.997937\pi$
$642$	−2.47904	+	1.48039i	−0.0978398	+	0.0584263i
$643$	23.5431			0.928448			0.464224	−	0.885718i	$-0.346333\pi$
$643$	23.5431			0.928448			0.464224	+	0.885718i	$0.346333\pi$
$644$	−47.4012	+	22.8006i	−1.86787	+	0.898470i
$645$		0			0
$646$	13.5237	+	11.8207i	0.532083	+	0.465080i
$647$	−7.32343	+	10.0798i	−0.287914	+	0.396280i	−0.928335	−	0.371744i	$-0.878760\pi$
$647$	−7.32343	+	10.0798i	−0.287914	+	0.396280i	0.640421	+	0.768024i	$0.278760\pi$
$648$	13.8287	−	20.9185i	0.543243	−	0.821756i
$649$	0.849707			0.0333539
$650$		0			0
$651$		−	3.45991i		−	0.135605i
$652$	−8.71053	+	16.1692i	−0.341131	+	0.633236i
$653$	−6.50662	−	4.72734i	−0.254624	−	0.184995i	0.453150	−	0.891434i	$-0.350300\pi$
$653$	−6.50662	−	4.72734i	−0.254624	−	0.184995i	−0.707773	+	0.706439i	$0.750300\pi$
$654$	−1.66290	+	1.90247i	−0.0650246	+	0.0743924i
$655$		0			0
$656$	20.5129	−	5.64110i	0.800895	−	0.220248i
$657$			22.5383i			0.879303i
$658$	−31.9229	+	19.0632i	−1.24449	+	0.743161i
$659$	43.9188	−	14.2701i	1.71083	−	0.555883i	0.720361	−	0.693599i	$-0.243976\pi$
$659$	43.9188	−	14.2701i	1.71083	−	0.555883i	0.990472	+	0.137716i	$0.0439762\pi$
$660$		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	$0.825590\pi$
$662$	−36.1467	+	8.24158i	−1.40488	+	0.320318i
$663$	−1.25780	+	0.408685i	−0.0488490	+	0.0158720i
$664$	−11.0344	+	16.6915i	−0.428216	+	0.647756i
$665$		0			0
$666$	8.06152	+	35.3569i	0.312378	+	1.37005i
$667$	3.20591	−	2.32923i	0.124133	−	0.0901881i
$668$	−3.16606	+	17.4013i	−0.122498	+	0.673276i
$669$	1.43234	+	1.97145i	0.0553775	+	0.0762206i
$670$		0			0
$671$	−3.43406	−	2.49499i	−0.132570	−	0.0963180i
$672$	−2.51188	+	1.34802i	−0.0968981	+	0.0520008i
$673$	30.1023	+	9.78082i	1.16036	+	0.377023i	0.825035	−	0.565081i	$-0.191155\pi$
$673$	30.1023	+	9.78082i	1.16036	+	0.377023i	0.335321	+	0.942104i	$0.391155\pi$
$674$	3.23629	−	35.8666i	0.124657	−	1.38153i
$675$		0			0
$676$	10.7007	+	1.94693i	0.411566	+	0.0748818i
$677$	10.7847	−	33.1919i	0.414489	−	1.27567i	−0.498217	−	0.867052i	$-0.666012\pi$
$677$	10.7847	−	33.1919i	0.414489	−	1.27567i	0.912707	−	0.408615i	$-0.133988\pi$
$678$	−1.22631	+	1.40298i	−0.0470963	+	0.0538812i
$679$	2.64050	+	1.91844i	0.101333	+	0.0736229i
$680$		0			0
$681$	1.10800	−	0.805010i	0.0424587	−	0.0308480i
$682$	0.271835	−	3.01265i	0.0104091	−	0.115360i
$683$	−5.66818	+	4.11817i	−0.216887	+	0.157578i	−0.690924	−	0.722927i	$-0.742796\pi$
$683$	−5.66818	+	4.11817i	−0.216887	+	0.157578i	0.474037	+	0.880505i	$0.342796\pi$
$684$	29.8186	−	4.02537i	1.14014	−	0.153914i
$685$		0			0
$686$	−16.0909	−	6.88192i	−0.614354	−	0.262753i
$687$	0.848157	−	0.275583i	0.0323592	−	0.0105141i
$688$	−0.408686	+	8.91878i	−0.0155810	+	0.340025i
$689$	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	$0.449675\pi$
$692$	23.6721	−	11.3866i	0.899879	−	0.432854i
$693$	−3.83448			−0.145660
$694$	32.5334	−	19.4277i	1.23495	−	0.737467i
$695$		0			0
$696$	0.168003	−	0.133790i	0.00636813	−	0.00507130i
$697$	−7.87811	+	10.8433i	−0.298405	+	0.410719i
$698$	11.9937	+	5.12960i	0.453970	+	0.194158i
$699$			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	$-0.123308\pi$
$702$	−1.74677	+	4.08420i	−0.0659277	+	0.154148i
$703$	−25.4481	+	35.0263i	−0.959793	+	1.32104i
$704$	−2.29309	+	0.976407i	−0.0864239	+	0.0367997i
$705$		0			0
$706$	−10.4798	−	17.5493i	−0.394413	−	0.660478i
$707$	15.2293			0.572757
$708$	0.288996	+	0.600806i	0.0108611	+	0.0225797i
$709$	−46.7136	+	15.1782i	−1.75437	+	0.570029i	−0.996592	−	0.0824870i	$-0.973714\pi$
$709$	−46.7136	+	15.1782i	−1.75437	+	0.570029i	−0.757775	+	0.652516i	$0.773714\pi$
$710$		0			0
$711$	4.16462	−	12.8174i	0.156185	−	0.480689i
$712$	−1.06440	−	24.0677i	−0.0398901	−	0.901974i
$713$	41.6488	−	13.5325i	1.55976	−	0.506797i
$714$	0.706243	−	1.65130i	0.0264305	−	0.0617982i
$715$		0			0
$716$	−1.26551	+	0.170838i	−0.0472943	+	0.00638451i
$717$	−0.0569310	+	0.0413628i	−0.00212613	+	0.00154472i
$718$	−4.53679	−	0.409360i	−0.169311	−	0.0152772i
$719$	−38.2305	+	27.7761i	−1.42576	+	1.03587i	−0.434971	+	0.900444i	$0.643242\pi$
$719$	−38.2305	+	27.7761i	−1.42576	+	1.03587i	−0.990787	+	0.135430i	$0.956758\pi$
$720$		0			0
$721$	48.5712	+	35.2890i	1.80889	+	1.31423i
$722$	6.81573	+	5.95746i	0.253655	+	0.221714i
$723$	−0.0334301	+	0.102887i	−0.00124328	+	0.00382642i
$724$	−7.12629	+	39.1676i	−0.264847	+	1.45565i
$725$		0			0
$726$	−1.87689	−	0.169355i	−0.0696581	−	0.00628534i
$727$	1.36442	+	0.443325i	0.0506034	+	0.0164420i	0.334209	−	0.942499i	$-0.391531\pi$
$727$	1.36442	+	0.443325i	0.0506034	+	0.0164420i	−0.283606	+	0.958941i	$0.591531\pi$
$728$	−39.1737	+	31.1962i	−1.45187	+	1.15621i
$729$	21.1936	+	15.3980i	0.784947	+	0.570298i
$730$		0			0
$731$	−3.30617	−	4.55055i	−0.122283	−	0.168308i
$732$	0.596177	−	3.27671i	0.0220353	−	0.121111i
$733$	30.8009	−	22.3782i	1.13766	−	0.826556i	0.150866	−	0.988554i	$-0.451794\pi$
$733$	30.8009	−	22.3782i	1.13766	−	0.826556i	0.986791	+	0.161998i	$0.0517938\pi$
$734$	−12.4329	+	2.83475i	−0.458906	+	0.104632i
$735$		0			0
$736$	−26.0514	−	24.9645i	−0.960266	−	0.920204i
$737$	−2.89990	+	0.942236i	−0.106819	+	0.0347077i
$738$	4.99119	+	21.8908i	0.183728	+	0.805812i
$739$	−30.0806	−	9.77378i	−1.10653	−	0.359534i	−0.301920	−	0.953333i	$-0.597627\pi$
$739$	−30.0806	−	9.77378i	−1.10653	−	0.359534i	−0.804613	+	0.593799i	$0.797627\pi$
$740$		0			0
$741$	−2.51555	+	0.817351i	−0.0924110	+	0.0300262i
$742$	14.0886	+	23.5925i	0.517207	+	0.866107i
$743$			13.6505i			0.500790i	0.968144	+	0.250395i	$0.0805605\pi$
$743$			13.6505i			0.500790i	−0.968144	+	0.250395i	$0.919440\pi$
$744$	2.22262	−	0.832432i	0.0814853	−	0.0305184i
$745$		0			0
$746$	−10.2315	−	8.94310i	−0.374602	−	0.327430i
$747$	−17.0841	−	12.4124i	−0.625076	−	0.454144i
$748$	0.744685	−	1.38235i	0.0272284	−	0.0505436i
$749$		−	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	$0.421992\pi$
$752$	−19.9265	−	15.9206i	−0.726645	−	0.580564i
$753$	0.751964	−	1.03499i	0.0274031	−	0.0377171i
$754$	2.48286	−	2.84056i	0.0904205	−	0.103447i
$755$		0			0
$756$	−2.61483	−	5.43608i	−0.0951004	−	0.197708i
$757$	15.4070			0.559979			0.279989	−	0.960003i	$-0.409669\pi$
$757$	15.4070			0.559979			0.279989	+	0.960003i	$0.409669\pi$
$758$	1.07990	+	1.80839i	0.0392238	+	0.0656836i
$759$	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	$0.975184\pi$
$762$	0.377281	−	0.0860215i	0.0136674	−	0.00311623i
$763$	−18.6266	−	57.3268i	−0.674328	−	2.07537i
$764$	17.2248	−	31.9742i	0.623173	−	1.15679i
$765$		0			0
$766$	−17.0409	+	3.88538i	−0.615711	+	0.140385i
$767$	6.88391	+	9.47489i	0.248563	+	0.342118i
$768$	−1.47030	−	1.28929i	−0.0530548	−	0.0465233i
$769$	12.8730	−	9.35276i	0.464211	−	0.337269i	−0.330970	−	0.943641i	$-0.607376\pi$
$769$	12.8730	−	9.35276i	0.464211	−	0.337269i	0.795181	+	0.606372i	$0.207376\pi$
$770$		0			0
$771$	1.26511	−	1.74127i	0.0455617	−	0.0627103i
$772$	23.5043	−	22.4520i	0.845939	−	0.808063i
$773$	−0.718367	+	2.21091i	−0.0258379	+	0.0795208i	−0.963144	−	0.268986i	$-0.913311\pi$
$773$	−0.718367	+	2.21091i	−0.0258379	+	0.0795208i	0.937306	+	0.348507i	$0.113311\pi$
$774$	−9.38445	−	0.846771i	−0.337317	−	0.0304365i
$775$		0			0
$776$	−0.597103	+	2.15780i	−0.0214347	+	0.0774606i
$777$	4.11718	+	1.33775i	0.147703	+	0.0479916i
$778$	10.8294	−	12.3895i	0.388251	−	0.444185i
$779$	−15.7559	+	21.6861i	−0.564513	+	0.776985i
$780$		0			0
$781$	−1.50152	−	2.06666i	−0.0537286	−	0.0739511i
$782$	22.6398	+	2.04282i	0.809599	+	0.0730511i
$783$	0.267122	+	0.367662i	0.00954615	+	0.0131392i
$784$	1.83123	−	39.9631i	0.0654011	−	1.42725i
$785$		0			0
$786$	0.563286	+	0.240912i	0.0200917	+	0.00859304i
$787$	−11.5499	−	35.5471i	−0.411711	−	1.26712i	−0.915160	−	0.403091i	$-0.867936\pi$
$787$	−11.5499	−	35.5471i	−0.411711	−	1.26712i	0.503449	−	0.864025i	$-0.332064\pi$
$788$	3.08454	+	22.8492i	0.109882	+	0.813969i
$789$	−2.53096	−	0.822360i	−0.0901047	−	0.0292768i
$790$		0			0
$791$	−13.7363	−	42.2758i	−0.488405	−	1.50316i
$792$	−0.922549	−	2.46324i	−0.0327814	−	0.0875274i
$793$		−	58.5055i		−	2.07759i
$794$	4.11195	−	2.45551i	0.145928	−	0.0871426i
$795$		0			0
$796$	−20.6566	−	21.6248i	−0.732153	−	0.766471i
$797$	−27.6045	−	20.0559i	−0.977802	−	0.710415i	−0.0205856	−	0.999788i	$-0.506553\pi$
$797$	−27.6045	−	20.0559i	−0.977802	−	0.710415i	−0.957216	+	0.289373i	$0.906553\pi$
$798$	1.41245	−	3.30252i	0.0500003	−	0.116908i
$799$	16.0686			0.568468
$800$		0			0
$801$	25.4253			0.898361
$802$	1.71596	−	4.01216i	0.0605926	−	0.141674i
$803$	1.90300	+	1.38261i	0.0671553	+	0.0487912i
$804$	−1.65252	−	1.72998i	−0.0582800	−	0.0610117i
$805$		0			0
$806$	35.7956	−	21.3758i	1.26085	−	0.752932i
$807$			1.48289i			0.0522001i
$808$	3.66407	+	9.78320i	0.128902	+	0.344172i
$809$	0.931838	+	2.86790i	0.0327617	+	0.100830i	0.966100	−	0.258167i	$-0.0831186\pi$
$809$	0.931838	+	2.86790i	0.0327617	+	0.100830i	−0.933338	+	0.358998i	$0.883119\pi$
$810$		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	$0.769540\pi$
$812$	0.685405	+	5.07725i	0.0240530	+	0.178177i
$813$	−0.593143	−	1.82551i	−0.0208024	−	0.0640233i
$814$	3.47985	+	1.48830i	0.121969	+	0.0521648i
$815$		0			0
$816$	1.23070	+	0.0563944i	0.0430831	+	0.00197420i
$817$	−6.61219	−	9.10090i	−0.231331	−	0.318400i
$818$	13.7723	+	1.24269i	0.481536	+	0.0434496i
$819$	−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	$0.0749427\pi$
$822$	1.53474	−	1.75584i	0.0535301	−	0.0612419i
$823$	−19.0241	−	6.18129i	−0.663137	−	0.215466i	−0.0419394	−	0.999120i	$-0.513354\pi$
$823$	−19.0241	−	6.18129i	−0.663137	−	0.215466i	−0.621198	+	0.783654i	$0.713354\pi$
$824$	−10.9835	+	39.6921i	−0.382629	+	1.38274i
$825$		0			0
$826$	−15.8399	−	1.42925i	−0.551140	−	0.0497300i
$827$	−5.28600	+	16.2686i	−0.183812	+	0.565716i	−0.999926	−	0.0121758i	$-0.996124\pi$
$827$	−5.28600	+	16.2686i	−0.183812	+	0.565716i	0.816114	+	0.577891i	$0.196124\pi$
$828$	27.5360	−	26.3031i	0.956943	−	0.914097i
$829$	21.2432	−	29.2388i	0.737807	−	1.01550i	−0.260935	−	0.965356i	$-0.584031\pi$
$829$	21.2432	−	29.2388i	0.737807	−	1.01550i	0.998742	−	0.0501475i	$-0.0159692\pi$
$830$		0			0
$831$	0.230458	−	0.167437i	0.00799448	−	0.00580833i
$832$	−29.4651	−	17.6593i	−1.02152	−	0.612226i
$833$	14.8142	+	20.3900i	0.513282	+	0.706472i
$834$	−1.70833	+	0.389507i	−0.0591548	+	0.0134875i
$835$		0			0
$836$	1.48934	−	2.76463i	0.0515098	−	0.0956168i
$837$	1.55194	+	4.77639i	0.0536430	+	0.165096i
$838$	−52.2247	+	11.9074i	−1.80407	+	0.411335i
$839$	−9.69350	+	29.8335i	−0.334657	+	1.02997i	0.632234	+	0.774777i	$0.282138\pi$
$839$	−9.69350	+	29.8335i	−0.334657	+	1.02997i	−0.966891	+	0.255190i	$0.917862\pi$
$840$		0			0
$841$	8.84222	+	27.2136i	0.304904	+	0.938398i
$842$	10.8152	+	18.1110i	0.372717	+	0.624146i
$843$	1.66531			0.0573562
$844$	−1.89531	−	3.94024i	−0.0652393	−	0.135629i
$845$		0			0
$846$	17.7150	−	20.2671i	0.609054	−	0.696798i
$847$	26.4243	−	36.3699i	0.907948	−	1.24968i
$848$	−11.7660	+	14.7266i	−0.404047	+	0.505713i
$849$	−0.487170			−0.0167196
$850$		0			0
$851$			54.7930i			1.87828i
$852$	0.950599	−	1.76458i	0.0325670	−	0.0604536i
$853$	−20.4120	−	14.8302i	−0.698894	−	0.507776i	0.180678	−	0.983542i	$-0.442171\pi$
$853$	−20.4120	−	14.8302i	−0.698894	−	0.507776i	−0.879572	+	0.475766i	$0.842171\pi$
$854$	59.8195	+	52.2868i	2.04698	+	1.78922i
$855$		0			0
$856$	44.2480	−	16.5721i	1.51237	−	0.566422i
$857$		−	40.0337i		−	1.36753i	−0.729704	−	0.683763i	$-0.760342\pi$
$857$		−	40.0337i		−	1.36753i	0.729704	−	0.683763i	$-0.239658\pi$
$858$	0.118548	+	0.198519i	0.00404717	+	0.00677732i
$859$	18.4443	−	5.99291i	0.629311	−	0.204475i	0.0230409	−	0.999735i	$-0.492665\pi$
$859$	18.4443	−	5.99291i	0.629311	−	0.204475i	0.606270	+	0.795259i	$0.292665\pi$
$860$		0			0
$861$	2.54910	+	0.828253i	0.0868732	+	0.0282268i
$862$	2.81795	+	12.3592i	0.0959798	+	0.420957i
$863$	−15.3173	+	4.97690i	−0.521408	+	0.169416i	−0.557884	−	0.829919i	$-0.688387\pi$
$863$	−15.3173	+	4.97690i	−0.521408	+	0.169416i	0.0364763	+	0.999335i	$0.488387\pi$
$864$	2.86299	−	2.98763i	0.0974009	−	0.101641i
$865$		0			0
$866$	−38.7656	+	8.83872i	−1.31731	+	0.300352i
$867$	1.05300	−	0.765048i	0.0357617	−	0.0259824i
$868$	−10.1349	+	55.7033i	−0.344000	+	1.89069i
$869$	−0.826742	−	1.13791i	−0.0280453	−	0.0386010i
$870$		0			0
$871$	−34.0002	−	24.7026i	−1.15205	−	0.837016i
$872$	32.3449	−	25.7580i	1.09534	−	0.872277i
$873$	−2.24723	−	0.730170i	−0.0760573	−	0.0247125i
$874$	45.2786	+	4.08555i	1.53157	+	0.138196i
$875$		0			0
$876$	−0.330374	+	1.81580i	−0.0111623	+	0.0613502i
$877$	3.77880	−	11.6300i	0.127601	−	0.392716i	−0.866765	−	0.498717i	$-0.833805\pi$
$877$	3.77880	−	11.6300i	0.127601	−	0.392716i	0.994366	+	0.106001i	$0.0338048\pi$
$878$	4.95259	+	4.32894i	0.167142	+	0.146095i
$879$	−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	$0.398929\pi$
$882$	42.0496	+	3.79419i	1.41588	+	0.127757i
$883$	−6.74673	+	4.90179i	−0.227046	+	0.164958i	−0.695492	−	0.718533i	$-0.744814\pi$
$883$	−6.74673	+	4.90179i	−0.227046	+	0.164958i	0.468447	+	0.883492i	$0.344814\pi$
$884$	21.4473	−	2.89529i	0.721351	−	0.0973790i
$885$		0			0
$886$	−18.8592	+	44.0954i	−0.633586	+	1.48142i
$887$	47.8491	−	15.5471i	1.60662	−	0.522021i	0.637885	−	0.770132i	$-0.279810\pi$
$887$	47.8491	−	15.5471i	1.60662	−	0.522021i	0.968732	+	0.248110i	$0.0798096\pi$
$888$	0.131203	+	2.96670i	0.00440290	+	0.0995560i
$889$	−2.85256	+	8.77929i	−0.0956720	+	0.294448i
$890$		0			0
$891$	2.62685	−	0.853516i	0.0880029	−	0.0285939i
$892$	−17.2854	−	35.9353i	−0.578756	−	1.20320i
$893$	32.1366			1.07541
$894$	−1.27194	−	2.12998i	−0.0425402	−	0.0712371i
$895$		0			0
$896$	44.3891	−	14.3447i	1.48294	−	0.479222i
$897$	−1.96759	+	2.70815i	−0.0656958	+	0.0904225i
$898$	3.78929	−	8.85991i	0.126450	−	0.295659i
$899$		−	4.26543i		−	0.142260i
$900$		0			0
$901$		−	11.8754i		−	0.395628i
$902$	2.15451	+	0.921461i	0.0717373	+	0.0306813i
$903$	−0.661153	+	0.910000i	−0.0220018	+	0.0302829i
$904$	23.8528	−	18.9954i	0.793334	−	0.631776i
$905$		0			0
$906$	2.14202	−	1.27914i	0.0711639	−	0.0424965i
$907$	−40.7553			−1.35326			−0.676629	−	0.736324i	$-0.736560\pi$
$907$	−40.7553			−1.35326			−0.676629	+	0.736324i	$0.736560\pi$
$908$	−20.1965	+	9.71478i	−0.670243	+	0.322396i
$909$	−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	$0.0992848\pi$
$912$	2.46134	+	0.112786i	0.0815032	+	0.00373472i
$913$	−2.09605	+	0.681046i	−0.0693690	+	0.0225393i
$914$	53.3964	+	22.8371i	1.76620	+	0.755384i
$915$		0			0
$916$	−14.4623	+	1.95234i	−0.477847	+	0.0645071i
$917$	−11.8235	+	8.59030i	−0.390448	+	0.283677i
$918$	−0.234276	+	2.59639i	−0.00773225	+	0.0856937i
$919$	8.15739	−	5.92669i	0.269087	−	0.195503i	−0.445056	−	0.895503i	$-0.646816\pi$
$919$	8.15739	−	5.92669i	0.269087	−	0.195503i	0.714144	+	0.699999i	$0.246816\pi$
$920$		0			0
$921$	0.803507	+	0.583782i	0.0264765	+	0.0192363i
$922$	−23.0931	+	26.4200i	−0.760530	+	0.870096i
$923$	10.8803	−	33.4862i	0.358130	−	1.10221i
$924$	−0.308925	−	0.0562069i	−0.0101629	−	0.00184907i
$925$		0			0
$926$	2.46596	−	27.3293i	0.0810363	−	0.898096i
$927$	−41.3371	−	13.4312i	−1.35769	−	0.441140i
$928$	−3.09669	+	1.66185i	−0.101654	+	0.0545530i
$929$	−6.77547	−	4.92267i	−0.222296	−	0.161508i	0.471064	−	0.882099i	$-0.343870\pi$
$929$	−6.77547	−	4.92267i	−0.222296	−	0.161508i	−0.693360	+	0.720592i	$0.743870\pi$
$930$		0			0
$931$	29.6277	+	40.7791i	0.971010	+	1.33648i
$932$	4.13865	−	22.7468i	0.135566	−	0.745097i
$933$	−0.445544	+	0.323707i	−0.0145865	+	0.0105977i
$934$	0.0212301	+	0.0931130i	0.000694671	+	0.00304675i
$935$		0			0
$936$	19.9930	−	30.2431i	0.653490	−	0.988526i
$937$	15.2292	−	4.94826i	0.497516	−	0.161653i	−0.0495015	−	0.998774i	$-0.515763\pi$
$937$	15.2292	−	4.94826i	0.497516	−	0.161653i	0.547017	+	0.837121i	$0.315763\pi$
$938$	55.6437	−	12.6870i	1.81683	−	0.414244i
$939$	−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	$0.594961\pi$
$942$	2.86221	−	1.70921i	0.0932560	−	0.0556890i
$943$			33.9244i			1.10473i
$944$	−2.89283	−	10.5193i	−0.0941535	−	0.342374i
$945$		0			0
$946$	−0.647183	+	0.740420i	−0.0210417	+	0.0240731i
$947$	−13.2108	−	9.59818i	−0.429292	−	0.311899i	0.352074	−	0.935972i	$-0.385477\pi$
$947$	−13.2108	−	9.59818i	−0.429292	−	0.311899i	−0.781366	+	0.624073i	$0.785477\pi$
$948$	0.523403	−	0.971586i	0.0169994	−	0.0315556i
$949$			32.4211i			1.05243i
$950$		0			0
$951$	−1.50660			−0.0488549
$952$	−16.2073	+	24.5165i	−0.525281	+	0.794585i
$953$	9.40127	−	12.9397i	0.304537	−	0.419159i	−0.629131	−	0.777299i	$-0.716589\pi$
$953$	9.40127	−	12.9397i	0.304537	−	0.419159i	0.933668	+	0.358140i	$0.116589\pi$
$954$	−14.9783	−	13.0922i	−0.484941	−	0.423875i
$955$		0			0
$956$	1.03773	−	0.499162i	0.0335626	−	0.0161441i
$957$	0.0236556			0.000764677
$958$	−44.8207	+	26.7652i	−1.44809	+	0.864746i
$959$	17.1910	+	52.9084i	0.555126	+	1.70850i
$960$		0			0
$961$	4.98671	−	15.3475i	0.160862	−	0.495081i
$962$	11.5964	+	50.8605i	0.373882	+	1.63981i
$963$	15.4095	+	47.4256i	0.496564	+	1.52827i
$964$	0.839593	−	1.55852i	0.0270415	−	0.0501966i
$965$		0			0
$966$	−1.01053	−	4.43207i	−0.0325132	−	0.142599i
$967$	−27.9288	−	38.4407i	−0.898129	−	1.23617i	−0.971061	−	0.238832i	$-0.923235\pi$
$967$	−27.9288	−	38.4407i	−0.898129	−	1.23617i	0.0729314	−	0.997337i	$-0.476765\pi$
$968$	29.7212	+	8.22440i	0.955277	+	0.264342i
$969$	−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	$-0.0747428\pi$
$972$	4.52853	+	4.74079i	0.145253	+	0.152061i
$973$	12.9165	−	39.7528i	0.414083	−	1.27442i
$974$	0.751479	−	8.32837i	0.0240789	−	0.266858i
$975$		0			0
$976$	−19.1965	+	51.0075i	−0.614464	+	1.63271i
$977$	−21.1525	−	6.87286i	−0.676728	−	0.219882i	−0.0495655	−	0.998771i	$-0.515784\pi$
$977$	−21.1525	−	6.87286i	−0.676728	−	0.219882i	−0.627162	+	0.778889i	$0.715784\pi$
$978$	−1.19508	−	1.04459i	−0.0382143	−	0.0334022i
$979$	1.55971	−	2.14676i	0.0498486	−	0.0686107i
$980$		0			0
$981$	25.6497	+	35.3038i	0.818933	+	1.12716i
$982$	−4.51235	+	50.0087i	−0.143995	+	1.59584i
$983$	27.0299	+	37.2035i	0.862121	+	1.18661i	0.981060	+	0.193707i	$0.0620510\pi$
$983$	27.0299	+	37.2035i	0.862121	+	1.18661i	−0.118938	+	0.992902i	$0.537949\pi$
$984$	0.0812330	+	1.83680i	0.00258961	+	0.0585549i
$985$		0			0
$986$	0.870666	−	2.03574i	0.0277277	−	0.0648312i
$987$	−0.992976	−	3.05607i	−0.0316068	−	0.0972756i
$988$	42.8936	−	5.79044i	1.36463	−	0.184218i
$989$	−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	$0.973428\pi$
$992$	−38.2218	+	6.89128i	−1.21354	+	0.218798i
$993$		−	3.20406i		−	0.101678i
$994$	24.5144	+	41.0515i	0.777551	+	1.30207i
$995$		0			0
$996$	−1.19444	−	1.25043i	−0.0378473	−	0.0396213i
$997$	−0.677675	−	0.492360i	−0.0214622	−	0.0155932i	0.577002	−	0.816742i	$-0.304222\pi$
$997$	−0.677675	−	0.492360i	−0.0214622	−	0.0155932i	−0.598465	+	0.801149i	$0.704222\pi$
$998$	32.1707	+	13.7591i	1.01835	+	0.435537i
$999$	−6.28379			−0.198810

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.11	✓	112	5.4	even	2
200.2.o.a.29.18	yes	112	40.29	even	2
200.2.o.a.69.11	yes	112	200.181	even	10
200.2.o.a.69.18	yes	112	25.6	even	5
800.2.be.a.369.14		112	100.31	odd	10
800.2.be.a.369.15		112	200.131	odd	10
800.2.be.a.529.14		112	40.19	odd	2
800.2.be.a.529.15		112	20.19	odd	2
1000.2.o.a.149.11		112	8.5	even	2	inner
1000.2.o.a.149.18		112	1.1	even	1	trivial
1000.2.o.a.349.11		112	25.19	even	10	inner
1000.2.o.a.349.18		112	200.69	even	10	inner
1000.2.t.b.101.5		224	40.37	odd	4
1000.2.t.b.101.8		224	5.3	odd	4
1000.2.t.b.101.49		224	5.2	odd	4
1000.2.t.b.101.52		224	40.13	odd	4
1000.2.t.b.901.5		224	25.17	odd	20
1000.2.t.b.901.8		224	200.133	odd	20
1000.2.t.b.901.49		224	200.117	odd	20
1000.2.t.b.901.52		224	25.8	odd	20

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.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.556118 - 1.30028i) q^{2} +(0.0988780 + 0.0718391i) q^{3} +(-1.38147 - 1.44622i) q^{4} +(0.148399 - 0.0886183i) q^{6} +4.12326i q^{7} +(-2.64875 + 0.992028i) q^{8} +(-0.922435 - 2.83896i) q^{9} +O(q^{10})\)	\(q+(0.556118 - 1.30028i) q^{2} +(0.0988780 + 0.0718391i) q^{3} +(-1.38147 - 1.44622i) q^{4} +(0.148399 - 0.0886183i) q^{6} +4.12326i q^{7} +(-2.64875 + 0.992028i) q^{8} +(-0.922435 - 2.83896i) q^{9} +(-0.296291 - 0.0962708i) q^{11} +(-0.0327016 - 0.242243i) q^{12} +(-1.32691 - 4.08381i) q^{13} +(5.36140 + 2.29302i) q^{14} +(-0.183100 + 3.99581i) q^{16} +(-1.48123 - 2.03874i) q^{17} +(-4.20443 - 0.379371i) q^{18} +(-2.96240 - 4.07740i) q^{19} +(-0.296211 + 0.407699i) q^{21} +(-0.289952 + 0.331724i) q^{22} +(-6.06625 - 1.97104i) q^{23} +(-0.333170 - 0.0921940i) q^{24} +(-6.04802 - 0.545721i) q^{26} +(0.226044 - 0.695692i) q^{27} +(5.96313 - 5.69614i) q^{28} +(-0.365173 + 0.502617i) q^{29} +(-5.55444 + 4.03554i) q^{31} +(5.09385 + 2.46022i) q^{32} +(-0.0223807 - 0.0308043i) q^{33} +(-3.47468 + 0.792241i) q^{34} +(-2.83145 + 5.25598i) q^{36} +(-2.65457 - 8.16992i) q^{37} +(-6.94921 + 1.58445i) q^{38} +(0.162175 - 0.499123i) q^{39} +(-1.64354 - 5.05830i) q^{41} +(0.365396 + 0.611887i) q^{42} +2.23204 q^{43} +(0.270087 + 0.561497i) q^{44} +(-5.93646 + 6.79170i) q^{46} +(-3.74794 + 5.15860i) q^{47} +(-0.305160 + 0.381944i) q^{48} -10.0013 q^{49} -0.307997i q^{51} +(-4.07300 + 7.56065i) q^{52} +(3.81243 + 2.76989i) q^{53} +(-0.778889 - 0.680807i) q^{54} +(-4.09039 - 10.9215i) q^{56} -0.615981i q^{57} +(0.450465 + 0.754342i) q^{58} +(-2.59396 + 0.842829i) q^{59} +(12.9582 + 4.21037i) q^{61} +(2.15841 + 9.46657i) q^{62} +(11.7058 - 3.80344i) q^{63} +(6.03176 - 5.25527i) q^{64} +(-0.0525006 + 0.0119703i) q^{66} +(7.91813 - 5.75286i) q^{67} +(-0.902195 + 4.95865i) q^{68} +(-0.458220 - 0.630686i) q^{69} +(6.63373 + 4.81969i) q^{71} +(5.25963 + 6.60462i) q^{72} +(-7.18083 - 2.33319i) q^{73} +(-12.0994 - 1.09175i) q^{74} +(-1.80435 + 9.91707i) q^{76} +(0.396949 - 1.22168i) q^{77} +(-0.558812 - 0.488444i) q^{78} +(3.65256 + 2.65374i) q^{79} +(-7.17257 + 5.21118i) q^{81} +(-7.49122 - 0.675942i) q^{82} +(5.72321 - 4.15816i) q^{83} +(0.998828 - 0.134837i) q^{84} +(1.24127 - 2.90228i) q^{86} +(-0.0722151 + 0.0234641i) q^{87} +(0.880304 - 0.0389318i) q^{88} +(-2.63206 + 8.10065i) q^{89} +(16.8386 - 5.47119i) q^{91} +(5.52976 + 11.4961i) q^{92} -0.839121 q^{93} +(4.62334 + 7.74217i) q^{94} +(0.326930 + 0.609199i) q^{96} +(0.465272 - 0.640392i) q^{97} +(-5.56187 + 13.0044i) q^{98} +0.929963i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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