LMFDB - Embedded newform 1089.2.e.p.364.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, degree $2$, 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:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			364.10
Character	$\chi$	$=$	1089.364
Dual form			1089.2.e.p.727.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.245247 + 0.424780i) q^{2} +(-0.361332 - 1.69394i) q^{3} +(0.879708 - 1.52370i) q^{4} +(-0.854089 + 1.47932i) q^{5} +(0.630937 - 0.568921i) q^{6} +(-1.70526 - 2.95360i) q^{7} +1.84397 q^{8} +(-2.73888 + 1.22415i) q^{9} -0.837851 q^{10} +(-2.89892 - 0.939612i) q^{12} +(1.99896 - 3.46230i) q^{13} +(0.836420 - 1.44872i) q^{14} +(2.81450 + 0.912248i) q^{15} +(-1.30719 - 2.26411i) q^{16} -3.30458 q^{17} +(-1.19170 - 0.863202i) q^{18} -4.41765 q^{19} +(1.50270 + 2.60275i) q^{20} +(-4.38706 + 3.95584i) q^{21} +(-3.74601 + 6.48827i) q^{23} +(-0.666286 - 3.12358i) q^{24} +(1.04107 + 1.80318i) q^{25} +1.96096 q^{26} +(3.06329 + 4.19717i) q^{27} -6.00053 q^{28} +(-0.845644 - 1.46470i) q^{29} +(0.302743 + 1.41927i) q^{30} +(1.94926 - 3.37621i) q^{31} +(2.48514 - 4.30439i) q^{32} +(-0.810437 - 1.40372i) q^{34} +5.82578 q^{35} +(-0.544173 + 5.25012i) q^{36} +3.06553 q^{37} +(-1.08342 - 1.87653i) q^{38} +(-6.58723 - 2.13508i) q^{39} +(-1.57491 + 2.72783i) q^{40} +(-0.195437 + 0.338507i) q^{41} +(-2.75628 - 0.893377i) q^{42} +(-4.80634 - 8.32483i) q^{43} +(0.528325 - 5.09722i) q^{45} -3.67479 q^{46} +(0.540129 + 0.935531i) q^{47} +(-3.36295 + 3.03240i) q^{48} +(-2.31583 + 4.01114i) q^{49} +(-0.510636 + 0.884448i) q^{50} +(1.19405 + 5.59776i) q^{51} +(-3.51700 - 6.09163i) q^{52} -12.5638 q^{53} +(-1.03161 + 2.33057i) q^{54} +(-3.14445 - 5.44635i) q^{56} +(1.59624 + 7.48324i) q^{57} +(0.414783 - 0.718426i) q^{58} +(1.82827 - 3.16666i) q^{59} +(3.86593 - 3.48594i) q^{60} +(1.92659 + 3.33695i) q^{61} +1.91220 q^{62} +(8.28616 + 6.00205i) q^{63} -2.79086 q^{64} +(3.41458 + 5.91423i) q^{65} +(-1.55060 + 2.68572i) q^{67} +(-2.90706 + 5.03518i) q^{68} +(12.3443 + 4.00109i) q^{69} +(1.42875 + 2.47467i) q^{70} +7.01715 q^{71} +(-5.05041 + 2.25730i) q^{72} -15.0426 q^{73} +(0.751812 + 1.30218i) q^{74} +(2.67831 - 2.41505i) q^{75} +(-3.88624 + 6.73117i) q^{76} +(-0.708557 - 3.32175i) q^{78} +(1.99957 + 3.46335i) q^{79} +4.46581 q^{80} +(6.00290 - 6.70561i) q^{81} -0.191722 q^{82} +(0.0624829 + 0.108224i) q^{83} +(2.16818 + 10.1645i) q^{84} +(2.82240 - 4.88854i) q^{85} +(2.35748 - 4.08328i) q^{86} +(-2.17556 + 1.96172i) q^{87} -7.93327 q^{89} +(2.29477 - 1.02566i) q^{90} -13.6350 q^{91} +(6.59078 + 11.4156i) q^{92} +(-6.42344 - 2.08199i) q^{93} +(-0.264930 + 0.458872i) q^{94} +(3.77307 - 6.53514i) q^{95} +(-8.18934 - 2.65437i) q^{96} +(-0.171580 - 0.297185i) q^{97} -2.27180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} - 3 q^{13} - 5 q^{15} + 8 q^{16} - 40 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20} - 8 q^{21} + 10 q^{23}+ \cdots - 164 q^{98}+O(q^{100}) $ 36 * q + 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 - q^6 - q^7 - 12 * q^8 - q^9 - 4 * q^10 - 8 * q^12 - 3 * q^13 - 5 * q^15 + 8 * q^16 - 40 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 8 * q^21 + 10 * q^23 - 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 + 38 * q^28 + 21 * q^29 + 12 * q^30 - 6 * q^31 + 9 * q^32 + 4 * q^34 - 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 + 42 * q^39 + 20 * q^41 + 18 * q^42 - 4 * q^43 + 20 * q^45 + 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 + 25 * q^50 - 4 * q^51 + 19 * q^52 + 62 * q^53 + 17 * q^54 + 57 * q^56 - 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 + 16 * q^61 - 38 * q^62 + 5 * q^63 - 32 * q^64 + 42 * q^65 + 5 * q^67 + 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 + 51 * q^72 + 9 * q^74 - 16 * q^75 + 8 * q^76 - 32 * q^78 + 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 + 36 * q^83 + 60 * q^84 - 25 * q^85 - 26 * q^86 - 60 * q^87 - 28 * q^89 + 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 - 4 * q^94 + 64 * q^95 - 21 * q^96 + 16 * q^97 - 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.245247	+	0.424780i	0.173416	+	0.300365i	0.939612	−	0.342242i	$-0.111186\pi$
$2$	0.245247	+	0.424780i	0.173416	+	0.300365i	−0.766196	+	0.642607i	$0.777853\pi$
$3$	−0.361332	−	1.69394i	−0.208615	−	0.977998i
$3$	−0.361332	−	1.69394i	−0.208615	−	0.977998i
$4$	0.879708	−	1.52370i	0.439854	−	0.761849i
$5$	−0.854089	+	1.47932i	−0.381960	+	0.661574i	−0.991342	−	0.131302i	$-0.958084\pi$
$5$	−0.854089	+	1.47932i	−0.381960	+	0.661574i	0.609382	+	0.792876i	$0.291417\pi$
$6$	0.630937	−	0.568921i	0.257579	−	0.232261i
$7$	−1.70526	−	2.95360i	−0.644528	−	1.11636i	−0.984410	−	0.175888i	$-0.943720\pi$
$7$	−1.70526	−	2.95360i	−0.644528	−	1.11636i	0.339882	−	0.940468i	$-0.389613\pi$
$8$	1.84397			0.651942
$9$	−2.73888	+	1.22415i	−0.912959	+	0.408051i
$10$	−0.837851			−0.264952
$11$		0			0
$11$		0			0
$12$	−2.89892	−	0.939612i	−0.836847	−	0.271243i
$13$	1.99896	−	3.46230i	0.554412	−	0.960270i	−0.443537	−	0.896256i	$-0.646276\pi$
$13$	1.99896	−	3.46230i	0.554412	−	0.960270i	0.997949	−	0.0640140i	$-0.0203902\pi$
$14$	0.836420	−	1.44872i	0.223543	−	0.387187i
$15$	2.81450	+	0.912248i	0.726701	+	0.235541i
$16$	−1.30719	−	2.26411i	−0.326797	−	0.566029i
$17$	−3.30458			−0.801477			−0.400739	−	0.916192i	$-0.631246\pi$
$17$	−3.30458			−0.801477			−0.400739	+	0.916192i	$0.631246\pi$
$18$	−1.19170	−	0.863202i	−0.280886	−	0.203459i
$19$	−4.41765			−1.01348			−0.506739	−	0.862099i	$-0.669149\pi$
$19$	−4.41765			−1.01348			−0.506739	+	0.862099i	$0.669149\pi$
$20$	1.50270	+	2.60275i	0.336013	+	0.581992i
$21$	−4.38706	+	3.95584i	−0.957335	+	0.863236i
$22$		0			0
$23$	−3.74601	+	6.48827i	−0.781096	+	1.35290i	0.150208	+	0.988654i	$0.452006\pi$
$23$	−3.74601	+	6.48827i	−0.781096	+	1.35290i	−0.931304	+	0.364244i	$0.881328\pi$
$24$	−0.666286	−	3.12358i	−0.136005	−	0.637598i
$25$	1.04107	+	1.80318i	0.208213	+	0.360636i
$26$	1.96096			0.384575
$27$	3.06329	+	4.19717i	0.589530	+	0.807746i
$28$	−6.00053			−1.13399
$29$	−0.845644	−	1.46470i	−0.157032	−	0.271988i	0.776765	−	0.629791i	$-0.216859\pi$
$29$	−0.845644	−	1.46470i	−0.157032	−	0.271988i	−0.933797	+	0.357803i	$0.883526\pi$
$30$	0.302743	+	1.41927i	0.0552730	+	0.259122i
$31$	1.94926	−	3.37621i	0.350097	−	0.606386i	−0.636169	−	0.771550i	$-0.719482\pi$
$31$	1.94926	−	3.37621i	0.350097	−	0.606386i	0.986266	+	0.165164i	$0.0528153\pi$
$32$	2.48514	−	4.30439i	0.439315	−	0.760915i
$33$		0			0
$34$	−0.810437	−	1.40372i	−0.138989	−	0.240736i
$35$	5.82578			0.984736
$36$	−0.544173	+	5.25012i	−0.0906955	+	0.875020i
$37$	3.06553			0.503970			0.251985	−	0.967731i	$-0.418917\pi$
$37$	3.06553			0.503970			0.251985	+	0.967731i	$0.418917\pi$
$38$	−1.08342	−	1.87653i	−0.175753	−	0.304414i
$39$	−6.58723	−	2.13508i	−1.05480	−	0.341887i
$40$	−1.57491	+	2.72783i	−0.249016	+	0.431308i
$41$	−0.195437	+	0.338507i	−0.0305222	+	0.0528660i	−0.880883	−	0.473334i	$-0.843050\pi$
$41$	−0.195437	+	0.338507i	−0.0305222	+	0.0528660i	0.850361	+	0.526200i	$0.176384\pi$
$42$	−2.75628	−	0.893377i	−0.425303	−	0.137851i
$43$	−4.80634	−	8.32483i	−0.732960	−	1.26952i	−0.955613	−	0.294626i	$-0.904805\pi$
$43$	−4.80634	−	8.32483i	−0.732960	−	1.26952i	0.222652	−	0.974898i	$-0.428529\pi$
$44$		0			0
$45$	0.528325	−	5.09722i	0.0787581	−	0.759849i
$46$	−3.67479			−0.541818
$47$	0.540129	+	0.935531i	0.0787859	+	0.136461i	0.902726	−	0.430215i	$-0.141562\pi$
$47$	0.540129	+	0.935531i	0.0787859	+	0.136461i	−0.823940	+	0.566676i	$0.808229\pi$
$48$	−3.36295	+	3.03240i	−0.485400	+	0.437689i
$49$	−2.31583	+	4.01114i	−0.330833	+	0.573020i
$50$	−0.510636	+	0.884448i	−0.0722149	+	0.125080i
$51$	1.19405	+	5.59776i	0.167200	+	0.783843i
$52$	−3.51700	−	6.09163i	−0.487721	−	0.844757i
$53$	−12.5638			−1.72577			−0.862884	−	0.505402i	$-0.831344\pi$
$53$	−12.5638			−1.72577			−0.862884	+	0.505402i	$0.831344\pi$
$54$	−1.03161	+	2.33057i	−0.140385	+	0.317150i
$55$		0			0
$56$	−3.14445	−	5.44635i	−0.420195	−	0.727799i
$57$	1.59624	+	7.48324i	0.211427	+	0.991180i
$58$	0.414783	−	0.718426i	0.0544637	−	0.0943339i
$59$	1.82827	−	3.16666i	0.238021	−	0.412264i	−0.722126	−	0.691762i	$-0.756835\pi$
$59$	1.82827	−	3.16666i	0.238021	−	0.412264i	0.960146	+	0.279498i	$0.0901681\pi$
$60$	3.86593	−	3.48594i	0.499089	−	0.450033i
$61$	1.92659	+	3.33695i	0.246674	+	0.427252i	0.962601	−	0.270923i	$-0.0873289\pi$
$61$	1.92659	+	3.33695i	0.246674	+	0.427252i	−0.715927	+	0.698175i	$0.753996\pi$
$62$	1.91220			0.242849
$63$	8.28616	+	6.00205i	1.04396	+	0.756187i
$64$	−2.79086			−0.348857
$65$	3.41458	+	5.91423i	0.423527	+	0.733570i
$66$		0			0
$67$	−1.55060	+	2.68572i	−0.189436	+	0.328113i	−0.945062	−	0.326890i	$-0.893999\pi$
$67$	−1.55060	+	2.68572i	−0.189436	+	0.328113i	0.755626	+	0.655003i	$0.227333\pi$
$68$	−2.90706	+	5.03518i	−0.352533	+	0.610605i
$69$	12.3443	+	4.00109i	1.48608	+	0.481675i
$70$	1.42875	+	2.47467i	0.170769	+	0.295780i
$71$	7.01715			0.832783			0.416391	−	0.909186i	$-0.363295\pi$
$71$	7.01715			0.832783			0.416391	+	0.909186i	$0.363295\pi$
$72$	−5.05041	+	2.25730i	−0.595197	+	0.266025i
$73$	−15.0426			−1.76060			−0.880302	−	0.474413i	$-0.842660\pi$
$73$	−15.0426			−1.76060			−0.880302	+	0.474413i	$0.842660\pi$
$74$	0.751812	+	1.30218i	0.0873963	+	0.151375i
$75$	2.67831	−	2.41505i	0.309264	−	0.278866i
$76$	−3.88624	+	6.73117i	−0.445783	+	0.772118i
$77$		0			0
$78$	−0.708557	−	3.32175i	−0.0802283	−	0.376114i
$79$	1.99957	+	3.46335i	0.224969	+	0.389657i	0.956310	−	0.292354i	$-0.0944387\pi$
$79$	1.99957	+	3.46335i	0.224969	+	0.389657i	−0.731341	+	0.682012i	$0.761105\pi$
$80$	4.46581			0.499293
$81$	6.00290	−	6.70561i	0.666989	−	0.745067i
$82$	−0.191722			−0.0211721
$83$	0.0624829	+	0.108224i	0.00685839	+	0.0118791i	0.869434	−	0.494049i	$-0.164484\pi$
$83$	0.0624829	+	0.108224i	0.00685839	+	0.0118791i	−0.862576	+	0.505928i	$0.831150\pi$
$84$	2.16818	+	10.1645i	0.236568	+	1.10904i
$85$	2.82240	−	4.88854i	0.306132	−	0.530237i
$86$	2.35748	−	4.08328i	0.254214	−	0.440311i
$87$	−2.17556	+	1.96172i	−0.233244	+	0.210318i
$88$		0			0
$89$	−7.93327			−0.840925			−0.420462	−	0.907310i	$-0.638132\pi$
$89$	−7.93327			−0.840925			−0.420462	+	0.907310i	$0.638132\pi$
$90$	2.29477	−	1.02566i	0.241890	−	0.108114i
$91$	−13.6350			−1.42934
$92$	6.59078	+	11.4156i	0.687136	+	1.19016i
$93$	−6.42344	−	2.08199i	−0.666080	−	0.215893i
$94$	−0.264930	+	0.458872i	−0.0273255	+	0.0473291i
$95$	3.77307	−	6.53514i	0.387108	−	0.670491i
$96$	−8.18934	−	2.65437i	−0.835821	−	0.270910i
$97$	−0.171580	−	0.297185i	−0.0174213	−	0.0301746i	0.857183	−	0.515011i	$-0.172212\pi$
$97$	−0.171580	−	0.297185i	−0.0174213	−	0.0301746i	−0.874605	+	0.484837i	$0.838879\pi$
$98$	−2.27180			−0.229487
$99$		0			0
$100$	3.66333			0.366333
$101$	−3.55779	−	6.16228i	−0.354014	−	0.613169i	0.632935	−	0.774205i	$-0.281850\pi$
$101$	−3.55779	−	6.16228i	−0.354014	−	0.613169i	−0.986949	+	0.161035i	$0.948517\pi$
$102$	−2.08498	+	1.88004i	−0.206444	+	0.186152i
$103$	0.827144	−	1.43266i	0.0815009	−	0.141164i	−0.822394	−	0.568918i	$-0.807362\pi$
$103$	0.827144	−	1.43266i	0.0815009	−	0.141164i	0.903895	+	0.427755i	$0.140695\pi$
$104$	3.68603	−	6.38439i	0.361445	−	0.626041i
$105$	−2.10504	−	9.86853i	−0.205431	−	0.963070i
$106$	−3.08123	−	5.33685i	−0.299275	−	0.518360i
$107$	3.30683			0.319683			0.159842	−	0.987143i	$-0.448902\pi$
$107$	3.30683			0.319683			0.159842	+	0.987143i	$0.448902\pi$
$108$	9.09003	−	0.975241i	0.874688	−	0.0938426i
$109$	−5.50709			−0.527484			−0.263742	−	0.964593i	$-0.584957\pi$
$109$	−5.50709			−0.527484			−0.263742	+	0.964593i	$0.584957\pi$
$110$		0			0
$111$	−1.10767	−	5.19283i	−0.105136	−	0.492881i
$112$	−4.45819	+	7.72182i	−0.421260	+	0.729643i
$113$	8.20461	−	14.2108i	0.771825	−	1.33684i	−0.164737	−	0.986338i	$-0.552677\pi$
$113$	8.20461	−	14.2108i	0.771825	−	1.33684i	0.936562	−	0.350503i	$-0.113989\pi$
$114$	−2.78726	+	2.51329i	−0.261051	+	0.235392i
$115$	−6.39884	−	11.0831i	−0.596695	−	1.03351i
$116$	−2.97568			−0.276285
$117$	−1.23653	+	11.9299i	−0.114317	+	1.10292i
$118$	1.79351			0.165106
$119$	5.63516	+	9.76039i	0.516575	+	0.894734i
$120$	5.18986	+	1.68216i	0.473767	+	0.153559i
$121$		0			0
$122$	−0.944980	+	1.63675i	−0.0855545	+	0.148185i
$123$	0.644030	+	0.208746i	0.0580702	+	0.0188220i
$124$	−3.42956	−	5.94016i	−0.307983	−	0.533442i
$125$	−12.0975			−1.08204
$126$	−0.517396	+	4.99178i	−0.0460933	+	0.444703i
$127$	10.7949			0.957894			0.478947	−	0.877844i	$-0.341019\pi$
$127$	10.7949			0.957894			0.478947	+	0.877844i	$0.341019\pi$
$128$	−5.65473	−	9.79427i	−0.499812	−	0.865700i
$129$	−12.3651	+	11.1497i	−1.08869	+	0.981676i
$130$	−1.67483	+	2.90089i	−0.146892	+	0.254425i
$131$	10.5778	−	18.3213i	0.924189	−	1.60074i	0.131329	−	0.991339i	$-0.458075\pi$
$131$	10.5778	−	18.3213i	0.924189	−	1.60074i	0.792860	−	0.609404i	$-0.208591\pi$
$132$		0			0
$133$	7.53325	+	13.0480i	0.653216	+	1.13140i
$134$	−1.52112			−0.131405
$135$	−8.82530	+	0.946840i	−0.759561	+	0.0814910i
$136$	−6.09354			−0.522517
$137$	−1.60026	−	2.77173i	−0.136720	−	0.236805i	0.789533	−	0.613708i	$-0.210323\pi$
$137$	−1.60026	−	2.77173i	−0.136720	−	0.236805i	−0.926253	+	0.376902i	$0.876989\pi$
$138$	1.32782	+	6.22487i	0.113031	+	0.529896i
$139$	7.49682	−	12.9849i	0.635872	−	1.10136i	−0.350457	−	0.936579i	$-0.613974\pi$
$139$	7.49682	−	12.9849i	0.635872	−	1.10136i	0.986330	−	0.164784i	$-0.0526928\pi$
$140$	5.12498	−	8.87673i	0.433140	−	0.750220i
$141$	1.38957	−	1.25299i	0.117023	−	0.105520i
$142$	1.72094	+	2.98075i	0.144418	+	0.250139i
$143$		0			0
$144$	6.35185	+	4.60094i	0.529321	+	0.383411i
$145$	2.88902			0.239920
$146$	−3.68916	−	6.38980i	−0.305317	−	0.528824i
$147$	7.63142	+	2.47353i	0.629429	+	0.204013i
$148$	2.69677	−	4.67094i	0.221673	−	0.383949i
$149$	−2.02556	+	3.50838i	−0.165940	+	0.287417i	−0.936989	−	0.349359i	$-0.886399\pi$
$149$	−2.02556	+	3.50838i	−0.165940	+	0.287417i	0.771048	+	0.636777i	$0.219733\pi$
$150$	1.68271	+	0.545409i	0.137393	+	0.0445324i
$151$	3.89699	+	6.74979i	0.317133	+	0.549290i	0.979889	−	0.199546i	$-0.0639466\pi$
$151$	3.89699	+	6.74979i	0.317133	+	0.549290i	−0.662756	+	0.748836i	$0.730613\pi$
$152$	−8.14602			−0.660729
$153$	9.05083	−	4.04530i	0.731716	−	0.327043i
$154$		0			0
$155$	3.32968	+	5.76717i	0.267446	+	0.463230i
$156$	−9.04806	+	8.15870i	−0.724425	+	0.653219i
$157$	−0.154576	+	0.267734i	−0.0123365	+	0.0213675i	−0.872128	−	0.489278i	$-0.837260\pi$
$157$	−0.154576	+	0.267734i	−0.0123365	+	0.0213675i	0.859791	+	0.510646i	$0.170594\pi$
$158$	−0.980775	+	1.69875i	−0.0780262	+	0.135145i
$159$	4.53970	+	21.2823i	0.360022	+	1.68780i
$160$	4.24506	+	7.35265i	0.335601	+	0.581278i
$161$	25.5517			2.01375
$162$	4.32060	+	0.905385i	0.339459	+	0.0711337i
$163$	10.9941			0.861125			0.430563	−	0.902561i	$-0.358315\pi$
$163$	10.9941			0.861125			0.430563	+	0.902561i	$0.358315\pi$
$164$	0.343855	+	0.595575i	0.0268506	+	0.0465066i
$165$		0			0
$166$	−0.0306475	+	0.0530830i	−0.00237871	+	0.00412004i
$167$	8.78693	−	15.2194i	0.679953	−	1.17771i	−0.295041	−	0.955485i	$-0.595333\pi$
$167$	8.78693	−	15.2194i	0.679953	−	1.17771i	0.974994	−	0.222229i	$-0.0713333\pi$
$168$	−8.08961	+	7.29446i	−0.624127	+	0.562780i
$169$	−1.49170	−	2.58369i	−0.114746	−	0.198746i
$170$	2.76874			0.212353
$171$	12.0994	−	5.40788i	0.925265	−	0.413551i
$172$	−16.9127			−1.28958
$173$	−6.18287	−	10.7090i	−0.470075	−	0.814193i	0.529340	−	0.848410i	$-0.322440\pi$
$173$	−6.18287	−	10.7090i	−0.470075	−	0.814193i	−0.999414	+	0.0342165i	$0.989106\pi$
$174$	−1.36685	−	0.443028i	−0.103620	−	0.0335859i
$175$	3.55058	−	6.14978i	0.268398	−	0.464880i
$176$		0			0
$177$	−6.02475	−	1.95277i	−0.452848	−	0.146779i
$178$	−1.94561	−	3.36990i	−0.145830	−	0.252584i
$179$	21.8823			1.63556			0.817780	−	0.575531i	$-0.195205\pi$
$179$	21.8823			1.63556			0.817780	+	0.575531i	$0.195205\pi$
$180$	−7.30186	−	5.28908i	−0.544249	−	0.394224i
$181$	−4.38018			−0.325576			−0.162788	−	0.986661i	$-0.552049\pi$
$181$	−4.38018			−0.325576			−0.162788	+	0.986661i	$0.552049\pi$
$182$	−3.34394	−	5.79188i	−0.247870	−	0.429323i
$183$	4.95646	−	4.46928i	0.366392	−	0.330378i
$184$	−6.90752	+	11.9642i	−0.509229	+	0.882011i
$185$	−2.61823	+	4.53491i	−0.192496	+	0.333413i
$186$	−0.690939	−	3.23915i	−0.0506621	−	0.237506i
$187$		0			0
$188$	1.90062			0.138617
$189$	7.17306	−	16.2050i	0.521764	−	1.17874i
$190$	3.70133			0.268523
$191$	−6.25737	−	10.8381i	−0.452767	−	0.784216i	0.545790	−	0.837922i	$-0.316230\pi$
$191$	−6.25737	−	10.8381i	−0.452767	−	0.784216i	−0.998557	+	0.0537064i	$0.982896\pi$
$192$	1.00843	+	4.72755i	0.0727770	+	0.341182i
$193$	6.28286	−	10.8822i	0.452250	−	0.783320i	−0.546276	−	0.837606i	$-0.683955\pi$
$193$	6.28286	−	10.8822i	0.452250	−	0.783320i	0.998525	+	0.0542857i	$0.0172882\pi$
$194$	0.0841588	−	0.145767i	0.00604225	−	0.0104655i
$195$	8.78456	−	7.92110i	0.629075	−	0.567242i
$196$	4.07451	+	7.05726i	0.291037	+	0.504090i
$197$	−10.3453			−0.737075			−0.368538	−	0.929613i	$-0.620141\pi$
$197$	−10.3453			−0.737075			−0.368538	+	0.929613i	$0.620141\pi$
$198$		0			0
$199$	26.4773			1.87693			0.938464	−	0.345376i	$-0.112249\pi$
$199$	26.4773			1.87693			0.938464	+	0.345376i	$0.112249\pi$
$200$	1.91969	+	3.32501i	0.135743	+	0.235114i
$201$	5.10973	+	1.65619i	0.360413	+	0.116819i
$202$	1.74508	−	3.02256i	0.122783	−	0.212667i
$203$	−2.88409	+	4.99539i	−0.202423	+	0.350608i
$204$	9.57971	+	3.10502i	0.670714	+	0.217395i
$205$	−0.333842	−	0.578231i	−0.0233165	−	0.0403854i
$206$	0.811418			0.0565342
$207$	2.31722	−	22.3563i	0.161058	−	1.55387i
$208$	−10.4521			−0.724721
$209$		0			0
$210$	3.67570	−	3.31441i	0.253647	−	0.228716i
$211$	3.64195	−	6.30804i	0.250722	−	0.434264i	−0.713003	−	0.701161i	$-0.752665\pi$
$211$	3.64195	−	6.30804i	0.250722	−	0.434264i	0.963725	+	0.266898i	$0.0859986\pi$
$212$	−11.0525	+	19.1434i	−0.759086	+	1.31478i
$213$	−2.53552	−	11.8866i	−0.173731	−	0.814459i
$214$	0.810990	+	1.40468i	0.0554382	+	0.0960217i
$215$	16.4202			1.11985
$216$	5.64861	+	7.73947i	0.384339	+	0.526604i
$217$	−13.2960			−0.902590
$218$	−1.35060	−	2.33930i	−0.0914741	−	0.158438i
$219$	5.43538	+	25.4813i	0.367289	+	1.72187i
$220$		0			0
$221$	−6.60572	+	11.4414i	−0.444349	+	0.769635i
$222$	1.93416	−	1.74404i	0.129812	−	0.117053i
$223$	−11.7550	−	20.3603i	−0.787175	−	1.36343i	−0.927691	−	0.373349i	$-0.878209\pi$
$223$	−11.7550	−	20.3603i	−0.787175	−	1.36343i	0.140516	−	0.990078i	$-0.455124\pi$
$224$	−16.9512			−1.13260
$225$	−5.05872	−	3.66426i	−0.337248	−	0.244284i
$226$	8.04863			0.535387
$227$	5.96109	+	10.3249i	0.395652	+	0.685289i	0.993184	−	0.116556i	$-0.0371854\pi$
$227$	5.96109	+	10.3249i	0.395652	+	0.685289i	−0.597532	+	0.801845i	$0.703852\pi$
$228$	12.8064	+	4.15088i	0.848127	+	0.274899i
$229$	−1.52879	+	2.64793i	−0.101025	+	0.174980i	−0.912107	−	0.409952i	$-0.865546\pi$
$229$	−1.52879	+	2.64793i	−0.101025	+	0.174980i	0.811082	+	0.584932i	$0.198879\pi$
$230$	3.13859	−	5.43620i	0.206953	−	0.358453i
$231$		0			0
$232$	−1.55934	−	2.70086i	−0.102376	−	0.177320i
$233$	−24.5314			−1.60710			−0.803552	−	0.595235i	$-0.797059\pi$
$233$	−24.5314			−1.60710			−0.803552	+	0.595235i	$0.797059\pi$
$234$	−5.37082	+	2.40051i	−0.351102	+	0.156926i
$235$	−1.84527			−0.120372
$236$	−3.21669	−	5.57147i	−0.209389	−	0.362672i
$237$	5.14420	−	4.63857i	0.334152	−	0.301307i
$238$	−2.76401	+	4.78741i	−0.179164	+	0.310322i
$239$	3.47531	−	6.01942i	0.224799	−	0.389364i	−0.731460	−	0.681885i	$-0.761161\pi$
$239$	3.47531	−	6.01942i	0.224799	−	0.389364i	0.956259	+	0.292521i	$0.0944940\pi$
$240$	−1.61364	−	7.56483i	−0.104160	−	0.488308i
$241$	3.88529	+	6.72952i	0.250274	+	0.433487i	0.963601	−	0.267344i	$-0.0861461\pi$
$241$	3.88529	+	6.72952i	0.250274	+	0.433487i	−0.713327	+	0.700831i	$0.752813\pi$
$242$		0			0
$243$	−13.5280	−	7.74562i	−0.867818	−	0.496881i
$244$	6.77934			0.434003
$245$	−3.95585	−	6.85174i	−0.252730	−	0.437741i
$246$	0.0692753	+	0.324765i	0.00441683	+	0.0207063i
$247$	−8.83072	+	15.2952i	−0.561885	+	0.973213i
$248$	3.59438	−	6.22564i	0.228243	−	0.395329i
$249$	0.160747	−	0.144947i	0.0101870	−	0.00918565i
$250$	−2.96688	−	5.13879i	−0.187642	−	0.325006i
$251$	0.327168			0.0206506			0.0103253	−	0.999947i	$-0.496713\pi$
$251$	0.327168			0.0206506			0.0103253	+	0.999947i	$0.496713\pi$
$252$	16.4347	−	7.34556i	1.03529	−	0.462727i
$253$		0			0
$254$	2.64742	+	4.58547i	0.166114	+	0.287718i
$255$	−9.30073	−	3.01459i	−0.582434	−	0.188781i
$256$	−0.0172493	+	0.0298766i	−0.00107808	+	0.00186729i
$257$	6.86458	−	11.8898i	0.428201	−	0.741666i	−0.568512	−	0.822675i	$-0.692481\pi$
$257$	6.86458	−	11.8898i	0.428201	−	0.741666i	0.996713	+	0.0810088i	$0.0258142\pi$
$258$	−7.76867	−	2.51802i	−0.483656	−	0.156765i
$259$	−5.22753	−	9.05434i	−0.324823	−	0.562609i
$260$	12.0153			0.745159
$261$	4.10913	+	2.97643i	0.254349	+	0.184237i
$262$	10.3767			0.641076
$263$	8.42709	+	14.5961i	0.519637	+	0.900037i	0.999739	+	0.0228249i	$0.00726603\pi$
$263$	8.42709	+	14.5961i	0.519637	+	0.900037i	−0.480103	+	0.877212i	$0.659401\pi$
$264$		0			0
$265$	10.7306	−	18.5859i	0.659174	−	1.14172i
$266$	−3.69501	+	6.39995i	−0.226556	+	0.392406i
$267$	2.86655	+	13.4385i	0.175430	+	0.822422i
$268$	2.72815	+	4.72529i	0.166648	+	0.288643i
$269$	12.3974			0.755882			0.377941	−	0.925830i	$-0.376632\pi$
$269$	12.3974			0.755882			0.377941	+	0.925830i	$0.376632\pi$
$270$	−2.56658	−	3.51660i	−0.156197	−	0.214014i
$271$	19.2695			1.17054			0.585269	−	0.810839i	$-0.300989\pi$
$271$	19.2695			1.17054			0.585269	+	0.810839i	$0.300989\pi$
$272$	4.31970	+	7.48194i	0.261920	+	0.453659i
$273$	4.92677	+	23.0969i	0.298182	+	1.39789i
$274$	0.784919	−	1.35952i	0.0474187	−	0.0821316i
$275$		0			0
$276$	16.9558	−	15.2892i	1.02062	−	0.920302i
$277$	−5.17554	−	8.96430i	−0.310968	−	0.538613i	0.667604	−	0.744516i	$-0.267320\pi$
$277$	−5.17554	−	8.96430i	−0.310968	−	0.538613i	−0.978572	+	0.205904i	$0.933987\pi$
$278$	7.35429			0.441081
$279$	−1.20578	+	11.6332i	−0.0721882	+	0.696463i
$280$	10.7426			0.641991
$281$	8.21790	+	14.2338i	0.490239	+	0.849119i	0.999937	−	0.0112348i	$-0.00357623\pi$
$281$	8.21790	+	14.2338i	0.490239	+	0.849119i	−0.509698	+	0.860353i	$0.670243\pi$
$282$	0.873031	+	0.282971i	0.0519882	+	0.0168507i
$283$	0.632477	−	1.09548i	0.0375968	−	0.0651197i	−0.846615	−	0.532206i	$-0.821363\pi$
$283$	0.632477	−	1.09548i	0.0375968	−	0.0651197i	0.884212	+	0.467087i	$0.154696\pi$
$284$	6.17304	−	10.6920i	0.366303	−	0.634455i
$285$	−12.4335	−	4.02999i	−0.736496	−	0.238716i
$286$		0			0
$287$	1.33309			0.0786896
$288$	−1.53727	+	14.8314i	−0.0905843	+	0.873947i
$289$	−6.07978			−0.357634
$290$	0.708523	+	1.22720i	0.0416059	+	0.0720636i
$291$	−0.441417	+	0.398029i	−0.0258763	+	0.0233329i
$292$	−13.2331	+	22.9204i	−0.774409	+	1.34132i
$293$	12.0437	−	20.8603i	0.703601	−	1.21867i	−0.263593	−	0.964634i	$-0.584908\pi$
$293$	12.0437	−	20.8603i	0.703601	−	1.21867i	0.967194	−	0.254038i	$-0.0817589\pi$
$294$	0.820876	+	3.84830i	0.0478745	+	0.224438i
$295$	3.12301	+	5.40921i	0.181829	+	0.314937i
$296$	5.65274			0.328559
$297$		0			0
$298$	−1.98705			−0.115107
$299$	14.9762	+	25.9396i	0.866098	+	1.50013i
$300$	−1.32368	−	6.20548i	−0.0764228	−	0.358273i
$301$	−16.3921	+	28.3920i	−0.944827	+	1.63649i
$302$	−1.91145	+	3.31073i	−0.109992	+	0.190511i
$303$	−9.15299	+	8.25332i	−0.525826	+	0.474141i
$304$	5.77470	+	10.0021i	0.331202	+	0.573658i
$305$	−6.58191			−0.376879
$306$	3.93805	+	2.85251i	0.225124	+	0.163067i
$307$	16.2949			0.930001			0.465001	−	0.885310i	$-0.346054\pi$
$307$	16.2949			0.930001			0.465001	+	0.885310i	$0.346054\pi$
$308$		0			0
$309$	−2.72571	−	0.883469i	−0.155060	−	0.0502588i
$310$	−1.63319	+	2.82876i	−0.0927588	+	0.160663i
$311$	−10.6856	+	18.5080i	−0.605926	+	1.04950i	0.385978	+	0.922508i	$0.373864\pi$
$311$	−10.6856	+	18.5080i	−0.605926	+	1.04950i	−0.991904	+	0.126987i	$0.959469\pi$
$312$	−12.1467	−	3.93703i	−0.687669	−	0.222890i
$313$	−1.55806	−	2.69864i	−0.0880669	−	0.152536i	0.818627	−	0.574325i	$-0.194736\pi$
$313$	−1.55806	−	2.69864i	−0.0880669	−	0.152536i	−0.906694	+	0.421789i	$0.861402\pi$
$314$	−0.151637			−0.00855738
$315$	−15.9561	+	7.13164i	−0.899024	+	0.401822i
$316$	7.03613			0.395813
$317$	9.13242	+	15.8178i	0.512928	+	0.888417i	0.999888	+	0.0149929i	$0.00477258\pi$
$317$	9.13242	+	15.8178i	0.512928	+	0.888417i	−0.486960	+	0.873425i	$0.661894\pi$
$318$	−7.92696	+	7.14780i	−0.444522	+	0.400829i
$319$		0			0
$320$	2.38364	−	4.12859i	0.133250	−	0.230795i
$321$	−1.19487	−	5.60158i	−0.0666909	−	0.312650i
$322$	6.26647	+	10.8538i	0.349217	+	0.604861i
$323$	14.5985			0.812280
$324$	−4.93652	−	15.0456i	−0.274251	−	0.835866i
$325$	8.32420			0.461744
$326$	2.69627	+	4.67008i	0.149333	+	0.258652i
$327$	1.98989	+	9.32870i	0.110041	+	0.515878i
$328$	−0.360381	+	0.624198i	−0.0198987	+	0.0344656i
$329$	1.84212	−	3.19065i	0.101560	−	0.175906i
$330$		0			0
$331$	−1.88308	−	3.26159i	−0.103503	−	0.179273i	0.809622	−	0.586951i	$-0.199672\pi$
$331$	−1.88308	−	3.26159i	−0.103503	−	0.179273i	−0.913126	+	0.407678i	$0.866339\pi$
$332$	0.219867			0.0120668
$333$	−8.39611	+	3.75267i	−0.460104	+	0.205645i
$334$	8.61988			0.471659
$335$	−2.64870	−	4.58768i	−0.144714	−	0.250652i
$336$	14.6912	+	4.76178i	0.801470	+	0.259776i
$337$	−2.98309	+	5.16686i	−0.162499	+	0.281457i	−0.935764	−	0.352626i	$-0.885289\pi$
$337$	−2.98309	+	5.16686i	−0.162499	+	0.281457i	0.773265	+	0.634083i	$0.218622\pi$
$338$	0.731668	−	1.26729i	0.0397975	−	0.0689313i
$339$	−27.0369	−	8.76331i	−1.46844	−	0.475958i
$340$	−4.96577	−	8.60097i	−0.269307	−	0.466453i
$341$		0			0
$342$	5.26450	+	3.81332i	0.284672	+	0.206201i
$343$	−8.07726			−0.436131
$344$	−8.86275	−	15.3507i	−0.477848	−	0.827656i
$345$	−16.4620	+	14.8440i	−0.886287	+	0.799172i
$346$	3.03266	−	5.25272i	0.163037	−	0.282388i
$347$	−12.1747	+	21.0871i	−0.653570	+	1.13202i	0.328680	+	0.944441i	$0.393396\pi$
$347$	−12.1747	+	21.0871i	−0.653570	+	1.13202i	−0.982250	+	0.187575i	$0.939937\pi$
$348$	1.07521	+	5.04063i	0.0576373	+	0.270206i
$349$	−8.37089	−	14.4988i	−0.448083	−	0.776103i	0.550178	−	0.835047i	$-0.314560\pi$
$349$	−8.37089	−	14.4988i	−0.448083	−	0.776103i	−0.998261	+	0.0589445i	$0.981227\pi$
$350$	3.48307			0.186178
$351$	20.6553	−	2.21604i	1.10250	−	0.118284i
$352$		0			0
$353$	4.01566	+	6.95533i	0.213732	+	0.370195i	0.952880	−	0.303349i	$-0.0981047\pi$
$353$	4.01566	+	6.95533i	0.213732	+	0.370195i	−0.739148	+	0.673544i	$0.764771\pi$
$354$	−0.648054	−	3.03811i	−0.0344437	−	0.161473i
$355$	−5.99327	+	10.3806i	−0.318090	+	0.550947i
$356$	−6.97896	+	12.0879i	−0.369884	+	0.640658i
$357$	14.4974	−	13.0724i	0.767282	−	0.691864i
$358$	5.36657	+	9.29517i	0.283632	+	0.491265i
$359$	−28.8250			−1.52133			−0.760663	−	0.649147i	$-0.775126\pi$
$359$	−28.8250			−1.52133			−0.760663	+	0.649147i	$0.775126\pi$
$360$	0.974217	−	9.39913i	0.0513457	−	0.495378i
$361$	0.515640			0.0271390
$362$	−1.07422	−	1.86061i	−0.0564600	−	0.0977916i
$363$		0			0
$364$	−11.9948	+	20.7756i	−0.628700	+	1.08894i
$365$	12.8477	−	22.2529i	0.672481	−	1.16477i
$366$	3.11402	+	1.00933i	0.162772	+	0.0527585i
$367$	−11.1717	−	19.3499i	−0.583158	−	1.01006i	−0.995102	−	0.0988500i	$-0.968484\pi$
$367$	−11.1717	−	19.3499i	−0.583158	−	1.01006i	0.411945	−	0.911209i	$-0.364850\pi$
$368$	19.5869			1.02104
$369$	0.120894	−	1.16638i	0.00629351	−	0.0607191i
$370$	−2.56845			−0.133528
$371$	21.4245	+	37.1084i	1.11231	+	1.92657i
$372$	−8.82308	+	7.95584i	−0.457456	+	0.412491i
$373$	−3.53936	+	6.13036i	−0.183261	+	0.317418i	−0.942989	−	0.332823i	$-0.891999\pi$
$373$	−3.53936	+	6.13036i	−0.183261	+	0.317418i	0.759728	+	0.650241i	$0.225332\pi$
$374$		0			0
$375$	4.37123	+	20.4925i	0.225729	+	1.05823i
$376$	0.995982	+	1.72509i	0.0513639	+	0.0889648i
$377$	−6.76164			−0.348242
$378$	8.64274	−	0.927253i	0.444534	−	0.0476927i
$379$	−24.3461			−1.25057			−0.625287	−	0.780394i	$-0.715018\pi$
$379$	−24.3461			−1.25057			−0.625287	+	0.780394i	$0.715018\pi$
$380$	−6.63839	−	11.4980i	−0.340542	−	0.589836i
$381$	−3.90055	−	18.2860i	−0.199831	−	0.936818i
$382$	3.06920	−	5.31601i	0.157034	−	0.271991i
$383$	8.81894	−	15.2749i	0.450627	−	0.780509i	−0.547798	−	0.836611i	$-0.684534\pi$
$383$	8.81894	−	15.2749i	0.450627	−	0.780509i	0.998425	+	0.0561017i	$0.0178671\pi$
$384$	−14.5477	+	13.1178i	−0.742384	+	0.669413i
$385$		0			0
$386$	6.16341			0.313709
$387$	23.3548	+	16.9170i	1.18719	+	0.859939i
$388$	−0.603760			−0.0306513
$389$	8.94149	+	15.4871i	0.453352	+	0.785228i	0.998592	−	0.0530517i	$-0.0168948\pi$
$389$	8.94149	+	15.4871i	0.453352	+	0.785228i	−0.545240	+	0.838280i	$0.683561\pi$
$390$	5.51911	+	1.78888i	0.279471	+	0.0905835i
$391$	12.3790	−	21.4410i	0.626031	−	1.08432i
$392$	−4.27033	+	7.39642i	−0.215684	+	0.373576i
$393$	−34.8574	−	11.2981i	−1.75832	−	0.569915i
$394$	−2.53717	−	4.39450i	−0.127821	−	0.221392i
$395$	−6.83122			−0.343716
$396$		0			0
$397$	−21.9395			−1.10111			−0.550556	−	0.834798i	$-0.685584\pi$
$397$	−21.9395			−1.10111			−0.550556	+	0.834798i	$0.685584\pi$
$398$	6.49349	+	11.2471i	0.325489	+	0.563764i
$399$	19.3805	−	17.4755i	0.970238	−	0.874871i
$400$	2.72174	−	4.71418i	0.136087	−	0.235709i
$401$	−2.70378	+	4.68308i	−0.135020	+	0.233862i	−0.925605	−	0.378490i	$-0.876443\pi$
$401$	−2.70378	+	4.68308i	−0.135020	+	0.233862i	0.790585	+	0.612352i	$0.209777\pi$
$402$	0.549630	+	2.57669i	0.0274131	+	0.128514i
$403$	−7.79298	−	13.4978i	−0.388196	−	0.672376i
$404$	−12.5193			−0.622857
$405$	4.79276	+	14.6074i	0.238154	+	0.725849i
$406$	−2.82926			−0.140414
$407$		0			0
$408$	2.20179	+	10.3221i	0.109005	+	0.511020i
$409$	−11.8101	+	20.4556i	−0.583970	+	1.01147i	0.411033	+	0.911621i	$0.365168\pi$
$409$	−11.8101	+	20.4556i	−0.583970	+	1.01147i	−0.995003	+	0.0998457i	$0.968165\pi$
$410$	0.163747	−	0.283619i	0.00808690	−	0.0140069i
$411$	−4.11693	+	3.71227i	−0.203073	+	0.183113i
$412$	−1.45529	−	2.52064i	−0.0716970	−	0.124183i
$413$	−12.4707			−0.613644
$414$	10.0648	−	4.49850i	0.494657	−	0.221089i
$415$	−0.213464			−0.0104785
$416$	−9.93539	−	17.2086i	−0.487123	−	0.843721i
$417$	−24.7045	−	8.00733i	−1.20978	−	0.392120i
$418$		0			0
$419$	9.06566	−	15.7022i	0.442886	−	0.767102i	−0.555016	−	0.831840i	$-0.687288\pi$
$419$	9.06566	−	15.7022i	0.442886	−	0.767102i	0.997902	+	0.0647380i	$0.0206212\pi$
$420$	−16.8885	−	5.47397i	−0.824074	−	0.267102i
$421$	6.40610	+	11.0957i	0.312214	+	0.540771i	0.978841	−	0.204620i	$-0.0655960\pi$
$421$	6.40610	+	11.0957i	0.312214	+	0.540771i	−0.666627	+	0.745391i	$0.732263\pi$
$422$	3.57271			0.173917
$423$	−2.62458	−	1.90111i	−0.127611	−	0.0924349i
$424$	−23.1672			−1.12510
$425$	−3.44028	−	5.95874i	−0.166878	−	0.289041i
$426$	4.42738	−	3.99220i	0.214507	−	0.193423i
$427$	6.57067	−	11.3807i	0.317977	−	0.550753i
$428$	2.90904	−	5.03861i	0.140614	−	0.243551i
$429$		0			0
$430$	4.02700	+	6.97496i	0.194199	+	0.336362i
$431$	−6.57916			−0.316907			−0.158453	−	0.987366i	$-0.550651\pi$
$431$	−6.57916			−0.316907			−0.158453	+	0.987366i	$0.550651\pi$
$432$	5.49859	−	12.4221i	0.264551	−	0.597660i
$433$	13.9978			0.672690			0.336345	−	0.941739i	$-0.390809\pi$
$433$	13.9978			0.672690			0.336345	+	0.941739i	$0.390809\pi$
$434$	−3.26080	−	5.64787i	−0.156523	−	0.271106i
$435$	−1.04390	−	4.89383i	−0.0500510	−	0.234641i
$436$	−4.84463	+	8.39115i	−0.232016	+	0.401863i
$437$	16.5485	−	28.6629i	0.791624	−	1.37113i
$438$	−9.49095	+	8.55806i	−0.453495	+	0.408920i
$439$	−12.5891	−	21.8050i	−0.600846	−	1.04070i	−0.992693	−	0.120665i	$-0.961497\pi$
$439$	−12.5891	−	21.8050i	−0.600846	−	1.04070i	0.391848	−	0.920030i	$-0.371836\pi$
$440$		0			0
$441$	1.43254	−	13.8210i	0.0682160	−	0.658141i
$442$	−6.48013			−0.308228
$443$	−13.4112	−	23.2289i	−0.637187	−	1.10364i	−0.986047	−	0.166466i	$-0.946765\pi$
$443$	−13.4112	−	23.2289i	−0.637187	−	1.10364i	0.348860	−	0.937175i	$-0.386569\pi$
$444$	−8.88673	−	2.88041i	−0.421746	−	0.136698i
$445$	6.77571	−	11.7359i	0.321200	−	0.556334i
$446$	5.76577	−	9.98661i	0.273017	−	0.472880i
$447$	6.67488	+	2.16349i	0.315711	+	0.102330i
$448$	4.75914	+	8.24308i	0.224848	+	0.389449i
$449$	14.1758			0.668999			0.334499	−	0.942396i	$-0.391433\pi$
$449$	14.1758			0.668999			0.334499	+	0.942396i	$0.391433\pi$
$450$	0.315872	−	3.04749i	0.0148903	−	0.143660i
$451$		0			0
$452$	−14.4353	−	25.0027i	−0.678981	−	1.17603i
$453$	10.0256	−	9.04020i	0.471046	−	0.424745i
$454$	−2.92388	+	5.06431i	−0.137225	+	0.237680i
$455$	11.6455	−	20.1706i	0.545950	−	0.945613i
$456$	2.94342	+	13.7989i	0.137838	+	0.646192i
$457$	−12.3206	−	21.3400i	−0.576335	−	0.998242i	−0.995895	−	0.0905145i	$-0.971149\pi$
$457$	−12.3206	−	21.3400i	−0.576335	−	0.998242i	0.419560	−	0.907728i	$-0.362184\pi$
$458$	−1.49972			−0.0700773
$459$	−10.1229	−	13.8699i	−0.472495	−	0.647390i
$460$	−22.5164			−1.04983
$461$	13.1227	+	22.7292i	0.611185	+	1.05860i	0.991041	+	0.133558i	$0.0426401\pi$
$461$	13.1227	+	22.7292i	0.611185	+	1.05860i	−0.379856	+	0.925046i	$0.624027\pi$
$462$		0			0
$463$	−6.34609	+	10.9917i	−0.294928	+	0.510830i	−0.974968	−	0.222345i	$-0.928629\pi$
$463$	−6.34609	+	10.9917i	−0.294928	+	0.510830i	0.680040	+	0.733175i	$0.261962\pi$
$464$	−2.21083	+	3.82927i	−0.102635	+	0.177769i
$465$	8.56613	−	7.72415i	0.397245	−	0.358199i
$466$	−6.01624	−	10.4204i	−0.278697	−	0.482718i
$467$	−27.7040			−1.28199			−0.640994	−	0.767546i	$-0.721478\pi$
$467$	−27.7040			−1.28199			−0.640994	+	0.767546i	$0.721478\pi$
$468$	17.0897	+	12.3789i	0.789973	+	0.572214i
$469$	10.5767			0.488387
$470$	−0.452548	−	0.783835i	−0.0208745	−	0.0361556i
$471$	0.509378	+	0.165102i	0.0234709	+	0.00760750i
$472$	3.37128	−	5.83923i	0.155176	−	0.268772i
$473$		0			0
$474$	3.23197	+	1.04756i	0.148449	+	0.0481161i
$475$	−4.59906	−	7.96581i	−0.211020	−	0.365497i
$476$	19.8292			0.908870
$477$	34.4107	−	15.3800i	1.57556	−	0.704201i
$478$	3.40924			0.155935
$479$	7.81110	+	13.5292i	0.356898	+	0.618166i	0.987441	−	0.157989i	$-0.0505009\pi$
$479$	7.81110	+	13.5292i	0.356898	+	0.618166i	−0.630543	+	0.776155i	$0.717168\pi$
$480$	10.9211	−	9.84763i	0.498477	−	0.449481i
$481$	6.12787	−	10.6138i	0.279407	−	0.483947i
$482$	−1.90571	+	3.30079i	−0.0868028	+	0.150347i
$483$	−9.23265	−	43.2830i	−0.420100	−	1.96945i
$484$		0			0
$485$	0.586177			0.0266169
$486$	−0.0275048	−	7.64600i	−0.00124764	−	0.346829i
$487$	26.9270			1.22018			0.610090	−	0.792332i	$-0.291133\pi$
$487$	26.9270			1.22018			0.610090	+	0.792332i	$0.291133\pi$
$488$	3.55257	+	6.15324i	0.160817	+	0.278544i
$489$	−3.97253	−	18.6234i	−0.179644	−	0.842178i
$490$	1.94032	−	3.36074i	0.0876548	−	0.151823i
$491$	−19.4999	+	33.7748i	−0.880017	+	1.52423i	−0.0286964	+	0.999588i	$0.509136\pi$
$491$	−19.4999	+	33.7748i	−0.880017	+	1.52423i	−0.851321	+	0.524646i	$0.824198\pi$
$492$	0.884624	−	0.797672i	0.0398819	−	0.0359618i
$493$	2.79450	+	4.84021i	0.125858	+	0.217992i
$494$	−8.66283			−0.389759
$495$		0			0
$496$	−10.1922			−0.457642
$497$	−11.9661	−	20.7259i	−0.536752	−	0.929681i
$498$	0.100993	+	0.0327345i	0.00452563	+	0.00146687i
$499$	12.0176	−	20.8150i	0.537980	−	0.931809i	−0.461033	−	0.887383i	$-0.652521\pi$
$499$	12.0176	−	20.8150i	0.537980	−	0.931809i	0.999013	−	0.0444256i	$-0.0141457\pi$
$500$	−10.6423	+	18.4330i	−0.475938	+	0.824349i
$501$	−28.9558	−	9.38528i	−1.29365	−	0.419304i
$502$	0.0802369	+	0.138974i	0.00358115	+	0.00620273i
$503$	−23.9865			−1.06950			−0.534752	−	0.845009i	$-0.679595\pi$
$503$	−23.9865			−1.06950			−0.534752	+	0.845009i	$0.679595\pi$
$504$	15.2794	+	11.0676i	0.680600	+	0.492990i
$505$	12.1547			0.540876
$506$		0			0
$507$	−3.83763	+	3.46042i	−0.170435	+	0.153683i
$508$	9.49637	−	16.4482i	0.421333	−	0.729771i
$509$	−1.84943	+	3.20331i	−0.0819746	+	0.141984i	−0.904098	−	0.427325i	$-0.859456\pi$
$509$	−1.84943	+	3.20331i	−0.0819746	+	0.141984i	0.822123	+	0.569309i	$0.192789\pi$
$510$	−1.00044	−	4.69009i	−0.0443000	−	0.207680i
$511$	25.6516	+	44.4298i	1.13476	+	1.96546i
$512$	−22.6358			−1.00037
$513$	−13.5325	−	18.5416i	−0.597476	−	0.818634i
$514$	6.73407			0.297027
$515$	1.41291	+	2.44723i	0.0622602	+	0.107838i
$516$	6.11111	+	28.6491i	0.269027	+	1.26121i
$517$		0			0
$518$	2.56407	−	4.44110i	0.112659	−	0.195131i
$519$	−15.9064	+	14.3429i	−0.698215	+	0.629585i
$520$	6.29639	+	10.9057i	0.276115	+	0.478245i
$521$	−6.41318			−0.280966			−0.140483	−	0.990083i	$-0.544866\pi$
$521$	−6.41318			−0.280966			−0.140483	+	0.990083i	$0.544866\pi$
$522$	−0.256578	+	2.47544i	−0.0112301	+	0.108347i
$523$	−2.73856			−0.119749			−0.0598745	−	0.998206i	$-0.519070\pi$
$523$	−2.73856			−0.119749			−0.0598745	+	0.998206i	$0.519070\pi$
$524$	−18.6108	−	32.2348i	−0.813016	−	1.40819i
$525$	−11.7003	−	3.79236i	−0.510643	−	0.165512i
$526$	−4.13344	+	7.15932i	−0.180226	+	0.312161i
$527$	−6.44147	+	11.1570i	−0.280595	+	0.486005i
$528$		0			0
$529$	−16.5651	−	28.6916i	−0.720222	−	1.24746i
$530$	10.5266			0.457245
$531$	−1.13094	+	10.9112i	−0.0490786	+	0.473505i
$532$	26.5082			1.14928
$533$	0.781343	+	1.35333i	0.0338437	+	0.0586191i
$534$	−5.00539	+	4.51340i	−0.216605	+	0.195314i
$535$	−2.82433	+	4.89188i	−0.122106	+	0.211494i
$536$	−2.85926	+	4.95239i	−0.123501	+	0.213910i
$537$	−7.90678	−	37.0673i	−0.341203	−	1.59957i
$538$	3.04042	+	5.26617i	0.131082	+	0.227041i
$539$		0			0
$540$	−6.32099	+	14.2800i	−0.272012	+	0.614515i
$541$	20.9037			0.898719			0.449359	−	0.893351i	$-0.351652\pi$
$541$	20.9037			0.898719			0.449359	+	0.893351i	$0.351652\pi$
$542$	4.72579	+	8.18530i	0.202990	+	0.351589i
$543$	1.58270	+	7.41976i	0.0679201	+	0.318412i
$544$	−8.21233	+	14.2242i	−0.352101	+	0.609856i
$545$	4.70355	−	8.14678i	0.201478	−	0.348970i
$546$	−8.60284	+	7.75724i	−0.368167	+	0.331979i
$547$	20.9382	+	36.2660i	0.895252	+	1.55062i	0.833493	+	0.552531i	$0.186338\pi$
$547$	20.9382	+	36.2660i	0.895252	+	1.55062i	0.0617594	+	0.998091i	$0.480329\pi$
$548$	−5.63105			−0.240547
$549$	−9.36162	−	6.78106i	−0.399544	−	0.289408i
$550$		0			0
$551$	3.73576	+	6.47053i	0.159149	+	0.275654i
$552$	22.7625	+	7.37790i	0.968838	+	0.314024i
$553$	6.81956	−	11.8118i	0.289997	−	0.502290i
$554$	2.53857	−	4.39693i	0.107854	−	0.186808i
$555$	8.62793	+	2.79652i	0.366235	+	0.118706i
$556$	−13.1900	−	22.8458i	−0.559382	−	0.968878i
$557$	−12.5244			−0.530675			−0.265337	−	0.964156i	$-0.585483\pi$
$557$	−12.5244			−0.530675			−0.265337	+	0.964156i	$0.585483\pi$
$558$	−5.23728	+	2.34082i	−0.221712	+	0.0990949i
$559$	−38.4308			−1.62545
$560$	−7.61538	−	13.1902i	−0.321809	−	0.557389i
$561$		0			0
$562$	−4.03083	+	6.98160i	−0.170030	+	0.294501i
$563$	7.25437	−	12.5649i	0.305735	−	0.529549i	−0.671690	−	0.740833i	$-0.734431\pi$
$563$	7.25437	−	12.5649i	0.305735	−	0.529549i	0.977425	+	0.211284i	$0.0677644\pi$
$564$	−0.686757	−	3.21955i	−0.0289177	−	0.135567i
$565$	14.0149	+	24.2746i	0.589613	+	1.02124i
$566$	0.620452			0.0260796
$567$	−30.0422	−	6.29536i	−1.26165	−	0.264380i
$568$	12.9394			0.542926
$569$	13.9862	+	24.2248i	0.586332	+	1.01556i	0.994708	+	0.102743i	$0.0327621\pi$
$569$	13.9862	+	24.2248i	0.586332	+	1.01556i	−0.408375	+	0.912814i	$0.633905\pi$
$570$	−1.33741	−	6.26984i	−0.0560180	−	0.262615i
$571$	−4.52443	+	7.83654i	−0.189341	+	0.327949i	−0.945031	−	0.326981i	$-0.893969\pi$
$571$	−4.52443	+	7.83654i	−0.189341	+	0.327949i	0.755689	+	0.654930i	$0.227302\pi$
$572$		0			0
$573$	−16.0981	+	14.5158i	−0.672507	+	0.606405i
$574$	0.326936	+	0.566269i	0.0136460	+	0.0236356i
$575$	−15.5993			−0.650538
$576$	7.64382	−	3.41644i	0.318493	−	0.142351i
$577$	38.3471			1.59641			0.798204	−	0.602387i	$-0.205783\pi$
$577$	38.3471			1.59641			0.798204	+	0.602387i	$0.205783\pi$
$578$	−1.49105	−	2.58257i	−0.0620194	−	0.107421i
$579$	−20.7041	−	6.71069i	−0.860431	−	0.278887i
$580$	2.54149	−	4.40200i	0.105530	−	0.182783i
$581$	0.213099	−	0.369099i	0.00884085	−	0.0153128i
$582$	−0.277331	−	0.0898897i	−0.0114957	−	0.00372605i
$583$		0			0
$584$	−27.7381			−1.14781
$585$	−16.5920	−	12.0184i	−0.685996	−	0.496899i
$586$	11.8147			0.488062
$587$	0.361309	+	0.625805i	0.0149128	+	0.0258297i	0.873385	−	0.487030i	$-0.161920\pi$
$587$	0.361309	+	0.625805i	0.0149128	+	0.0258297i	−0.858473	+	0.512859i	$0.828586\pi$
$588$	10.4823	−	9.45200i	0.432284	−	0.389794i
$589$	−8.61114	+	14.9149i	−0.354816	+	0.614559i
$590$	−1.53182	+	2.65319i	−0.0630640	+	0.109230i
$591$	3.73811	+	17.5244i	0.153765	+	0.720858i
$592$	−4.00722	−	6.94071i	−0.164696	−	0.285261i
$593$	−39.6596			−1.62863			−0.814313	−	0.580426i	$-0.802886\pi$
$593$	−39.6596			−1.62863			−0.814313	+	0.580426i	$0.802886\pi$
$594$		0			0
$595$	−19.2517			−0.789244
$596$	3.56380	+	6.17269i	0.145979	+	0.252843i
$597$	−9.56712	−	44.8511i	−0.391556	−	1.83563i
$598$	−7.34576	+	12.7232i	−0.300390	+	0.520291i
$599$	10.1884	−	17.6468i	0.416287	−	0.721030i	−0.579276	−	0.815132i	$-0.696665\pi$
$599$	10.1884	−	17.6468i	0.416287	−	0.721030i	0.995563	+	0.0941018i	$0.0299979\pi$
$600$	4.93872	−	4.45328i	0.201623	−	0.181805i
$601$	24.1859	+	41.8911i	0.986562	+	1.70878i	0.634780	+	0.772693i	$0.281091\pi$
$601$	24.1859	+	41.8911i	0.986562	+	1.70878i	0.351782	+	0.936082i	$0.385576\pi$
$602$	−16.0805			−0.655392
$603$	0.959176	−	9.25402i	0.0390607	−	0.376853i
$604$	13.7129			0.557968
$605$		0			0
$606$	−5.75059	−	1.86391i	−0.233602	−	0.0757161i
$607$	9.85114	−	17.0627i	0.399845	−	0.692553i	−0.593861	−	0.804568i	$-0.702397\pi$
$607$	9.85114	−	17.0627i	0.399845	−	0.692553i	0.993707	+	0.112015i	$0.0357304\pi$
$608$	−10.9785	+	19.0153i	−0.445236	+	0.771171i
$609$	9.50401	+	3.08048i	0.385122	+	0.124827i
$610$	−1.61419	−	2.79586i	−0.0653568	−	0.113201i
$611$	4.31879			0.174720
$612$	1.79826	−	17.3494i	0.0726904	−	0.701309i
$613$	5.71781			0.230940			0.115470	−	0.993311i	$-0.463163\pi$
$613$	5.71781			0.230940			0.115470	+	0.993311i	$0.463163\pi$
$614$	3.99629	+	6.92177i	0.161277	+	0.279340i
$615$	−0.858861	+	0.774442i	−0.0346326	+	0.0312285i
$616$		0			0
$617$	−3.05346	+	5.28875i	−0.122928	+	0.212917i	−0.920921	−	0.389749i	$-0.872562\pi$
$617$	−3.05346	+	5.28875i	−0.122928	+	0.212917i	0.797993	+	0.602666i	$0.205895\pi$
$618$	−0.293192	−	1.37450i	−0.0117939	−	0.0552903i
$619$	0.889867	+	1.54129i	0.0357668	+	0.0619499i	0.883355	−	0.468705i	$-0.155279\pi$
$619$	0.889867	+	1.54129i	0.0357668	+	0.0619499i	−0.847588	+	0.530655i	$0.821946\pi$
$620$	11.7166			0.470549
$621$	−38.7075	+	4.15281i	−1.55328	+	0.166646i
$622$	−10.4825			−0.420309
$623$	13.5283	+	23.4317i	0.542000	+	0.938771i
$624$	3.77667	+	17.7052i	0.151188	+	0.708775i
$625$	5.12704	−	8.88029i	0.205081	−	0.355212i
$626$	0.764220	−	1.32367i	0.0305444	−	0.0529044i
$627$		0			0
$628$	0.271963	+	0.471055i	0.0108525	+	0.0187971i
$629$	−10.1303			−0.403920
$630$	−6.94256	−	5.02882i	−0.276598	−	0.200353i
$631$	−44.8407			−1.78508			−0.892541	−	0.450966i	$-0.851079\pi$
$631$	−44.8407			−1.78508			−0.892541	+	0.450966i	$0.851079\pi$
$632$	3.68714	+	6.38631i	0.146667	+	0.254034i
$633$	−12.0014	−	3.88995i	−0.477013	−	0.154612i
$634$	−4.47940	+	7.75855i	−0.177900	+	0.308131i
$635$	−9.21981	+	15.9692i	−0.365877	+	0.633718i
$636$	36.4214	+	11.8051i	1.44420	+	0.468102i
$637$	9.25852	+	16.0362i	0.366836	+	0.635379i
$638$		0			0
$639$	−19.2191	+	8.59006i	−0.760297	+	0.339818i
$640$	19.3185			0.763633
$641$	13.5048	+	23.3910i	0.533407	+	0.923888i	0.999239	+	0.0390143i	$0.0124218\pi$
$641$	13.5048	+	23.3910i	0.533407	+	0.923888i	−0.465832	+	0.884873i	$0.654245\pi$
$642$	2.08640	−	1.88133i	0.0823438	−	0.0742500i
$643$	16.2787	−	28.1955i	0.641969	−	1.11192i	−0.343024	−	0.939327i	$-0.611451\pi$
$643$	16.2787	−	28.1955i	0.641969	−	1.11192i	0.984993	−	0.172596i	$-0.0552155\pi$
$644$	22.4780	−	38.9330i	0.885758	−	1.53418i
$645$	−5.93314	−	27.8148i	−0.233617	−	1.09521i
$646$	3.58023	+	6.20114i	0.140862	+	0.243981i
$647$	−31.4833			−1.23774			−0.618868	−	0.785495i	$-0.712408\pi$
$647$	−31.4833			−1.23774			−0.618868	+	0.785495i	$0.712408\pi$
$648$	11.0692	−	12.3649i	0.434838	−	0.485741i
$649$		0			0
$650$	2.04149	+	3.53596i	0.0800736	+	0.138692i
$651$	4.80427	+	22.5226i	0.188294	+	0.882731i
$652$	9.67160	−	16.7517i	0.378769	−	0.656048i
$653$	2.32989	−	4.03548i	0.0911755	−	0.157921i	−0.816831	−	0.576878i	$-0.804271\pi$
$653$	2.32989	−	4.03548i	0.0911755	−	0.157921i	0.908006	+	0.418957i	$0.137604\pi$
$654$	−3.47463	+	3.13310i	−0.135869	+	0.122514i
$655$	18.0688	+	31.2961i	0.706007	+	1.22284i
$656$	1.02189			0.0398982
$657$	41.1999	−	18.4144i	1.60736	−	0.718416i
$658$	1.80710			0.0704481
$659$	16.0209	+	27.7490i	0.624086	+	1.08095i	0.988717	+	0.149797i	$0.0478619\pi$
$659$	16.0209	+	27.7490i	0.624086	+	1.08095i	−0.364631	+	0.931152i	$0.618805\pi$
$660$		0			0
$661$	20.3527	−	35.2519i	0.791627	−	1.37114i	−0.133331	−	0.991072i	$-0.542567\pi$
$661$	20.3527	−	35.2519i	0.791627	−	1.37114i	0.924959	−	0.380067i	$-0.124099\pi$
$662$	0.923639	−	1.59979i	0.0358982	−	0.0621776i
$663$	21.7680	+	7.05554i	0.845399	+	0.274015i
$664$	0.115217	+	0.199561i	0.00447127	+	0.00774448i
$665$	−25.7362			−0.998009
$666$	−3.65318	−	2.64617i	−0.141558	−	0.102537i
$667$	12.6712			0.490629
$668$	−15.4599	−	26.7773i	−0.598160	−	1.03604i
$669$	−30.2417	+	27.2692i	−1.16921	+	1.05429i
$670$	1.29917	−	2.25023i	0.0501914	−	0.0869340i
$671$		0			0
$672$	6.12503	+	28.7144i	0.236278	+	1.10768i
$673$	18.8818	+	32.7042i	0.727838	+	1.26065i	0.957795	+	0.287452i	$0.0928083\pi$
$673$	18.8818	+	32.7042i	0.727838	+	1.26065i	−0.229957	+	0.973201i	$0.573858\pi$
$674$	−2.92637			−0.112720
$675$	−4.37917	+	9.89319i	−0.168554	+	0.380789i
$676$	−5.24903			−0.201886
$677$	−9.45033	−	16.3685i	−0.363206	−	0.629091i	0.625281	−	0.780400i	$-0.284984\pi$
$677$	−9.45033	−	16.3685i	−0.363206	−	0.629091i	−0.988487	+	0.151309i	$0.951651\pi$
$678$	−2.90823	−	13.6339i	−0.111690	−	0.523607i
$679$	−0.585177	+	1.01356i	−0.0224570	+	0.0388967i
$680$	5.20442	−	9.01433i	0.199581	−	0.345684i
$681$	15.3359	−	13.8285i	0.587672	−	0.529908i
$682$		0			0
$683$	31.1053			1.19021			0.595105	−	0.803648i	$-0.297110\pi$
$683$	31.1053			1.19021			0.595105	+	0.803648i	$0.297110\pi$
$684$	2.40397	−	23.1932i	0.0919180	−	0.886814i
$685$	5.46706			0.208886
$686$	−1.98092	−	3.43106i	−0.0756320	−	0.130998i
$687$	5.03785	+	1.63289i	0.192206	+	0.0622986i
$688$	−12.5656	+	21.7642i	−0.479058	+	0.829753i
$689$	−25.1145	+	43.4996i	−0.956787	+	1.65720i
$690$	−10.3427	−	3.35232i	−0.393739	−	0.127621i
$691$	−11.1057	−	19.2356i	−0.422481	−	0.731758i	0.573701	−	0.819065i	$-0.305507\pi$
$691$	−11.1057	−	19.2356i	−0.422481	−	0.731758i	−0.996181	+	0.0873068i	$0.972174\pi$
$692$	−21.7565			−0.827057
$693$		0			0
$694$	−11.9432			−0.453358
$695$	12.8059	+	22.1805i	0.485756	+	0.841353i
$696$	−4.01166	+	3.61735i	−0.152062	+	0.137115i
$697$	0.645837	−	1.11862i	0.0244628	−	0.0423709i
$698$	4.10587	−	7.11157i	0.155409	−	0.269177i
$699$	8.86398	+	41.5547i	0.335266	+	1.57174i
$700$	−6.24694	−	10.8200i	−0.236112	−	0.408958i
$701$	−29.9457			−1.13103			−0.565517	−	0.824736i	$-0.691323\pi$
$701$	−29.9457			−1.13103			−0.565517	+	0.824736i	$0.691323\pi$
$702$	6.00698	+	8.23048i	0.226719	+	0.310639i
$703$	−13.5424			−0.510763
$704$		0			0
$705$	0.666757	+	3.12578i	0.0251115	+	0.117724i
$706$	−1.96966	+	3.41155i	−0.0741290	+	0.128395i
$707$	−12.1339	+	21.0166i	−0.456343	+	0.790410i
$708$	−8.27545	+	7.46204i	−0.311010	+	0.280441i
$709$	−8.60286	−	14.9006i	−0.323087	−	0.559604i	0.658036	−	0.752986i	$-0.271387\pi$
$709$	−8.60286	−	14.9006i	−0.323087	−	0.559604i	−0.981123	+	0.193383i	$0.938054\pi$
$710$	−5.87932			−0.220647
$711$	−9.71623	−	7.03792i	−0.364387	−	0.263942i
$712$	−14.6287			−0.548234
$713$	14.6039	+	25.2946i	0.546919	+	0.947291i
$714$	9.10833	+	2.95223i	0.340871	+	0.110485i
$715$		0			0
$716$	19.2500	−	33.3420i	0.719407	−	1.24605i
$717$	−11.4523	−	3.71197i	−0.427694	−	0.138626i
$718$	−7.06925	−	12.2443i	−0.263822	−	0.456953i
$719$	4.72508			0.176216			0.0881079	−	0.996111i	$-0.471918\pi$
$719$	4.72508			0.176216			0.0881079	+	0.996111i	$0.471918\pi$
$720$	−12.2313	+	5.46684i	−0.455834	+	0.203737i
$721$	−5.64199			−0.210119
$722$	0.126459	+	0.219034i	0.00470633	+	0.00815160i
$723$	9.99554	−	9.01306i	0.371738	−	0.335199i
$724$	−3.85327	+	6.67407i	−0.143206	+	0.248040i
$725$	1.76074	−	3.04969i	0.0653923	−	0.113263i
$726$		0			0
$727$	−2.60044	−	4.50410i	−0.0964450	−	0.167048i	0.813766	−	0.581193i	$-0.197414\pi$
$727$	−2.60044	−	4.50410i	−0.0964450	−	0.167048i	−0.910211	+	0.414145i	$0.864081\pi$
$728$	−25.1426			−0.931845
$729$	−8.23253	+	25.7143i	−0.304909	+	0.952382i
$730$	12.6035			0.466475
$731$	15.8829	+	27.5100i	0.587451	+	1.01749i
$732$	−2.44959	−	11.4838i	−0.0905396	−	0.424454i
$733$	24.5316	−	42.4900i	0.906095	−	1.56940i	0.0866539	−	0.996238i	$-0.472383\pi$
$733$	24.5316	−	42.4900i	0.906095	−	1.56940i	0.819441	−	0.573164i	$-0.194284\pi$
$734$	5.47965	−	9.49103i	0.202258	−	0.350320i
$735$	−10.1771	+	9.17674i	−0.375387	+	0.338489i
$736$	18.6187	+	32.2485i	0.686294	+	1.18870i
$737$		0			0
$738$	0.525102	−	0.234697i	0.0193293	−	0.00863930i
$739$	−15.5942			−0.573641			−0.286821	−	0.957984i	$-0.592598\pi$
$739$	−15.5942			−0.573641			−0.286821	+	0.957984i	$0.592598\pi$
$740$	4.60656	+	7.97879i	0.169340	+	0.293306i
$741$	29.1001	+	9.43205i	1.06902	+	0.346495i
$742$	−10.5086	+	18.2014i	−0.385783	+	0.668196i
$743$	−5.56722	+	9.64271i	−0.204242	+	0.353757i	−0.949891	−	0.312582i	$-0.898806\pi$
$743$	−5.56722	+	9.64271i	−0.204242	+	0.353757i	0.745649	+	0.666339i	$0.232139\pi$
$744$	−11.8446	−	3.83914i	−0.434245	−	0.140750i
$745$	−3.46002	−	5.99293i	−0.126765	−	0.219564i
$746$	−3.47207			−0.127122
$747$	−0.303615	−	0.219923i	−0.0111087	−	0.00804655i
$748$		0			0
$749$	−5.63901	−	9.76705i	−0.206045	−	0.356880i
$750$	−7.63279	+	6.88254i	−0.278710	+	0.251315i
$751$	4.04260	−	7.00199i	0.147517	−	0.255506i	−0.782792	−	0.622283i	$-0.786205\pi$
$751$	4.04260	−	7.00199i	0.147517	−	0.255506i	0.930309	+	0.366777i	$0.119539\pi$
$752$	1.41210	−	2.44583i	0.0514940	−	0.0891902i
$753$	−0.118216	−	0.554203i	−0.00430804	−	0.0201963i
$754$	−1.65827	−	2.87221i	−0.0603907	−	0.104600i
$755$	−13.3135			−0.484528
$756$	−18.3813	−	25.1853i	−0.668523	−	0.915979i
$757$	29.8616			1.08534			0.542669	−	0.839947i	$-0.317414\pi$
$757$	29.8616			1.08534			0.542669	+	0.839947i	$0.317414\pi$
$758$	−5.97081	−	10.3417i	−0.216869	−	0.375629i
$759$		0			0
$760$	6.95742	−	12.0506i	0.252372	−	0.437121i
$761$	−17.4463	+	30.2179i	−0.632428	+	1.09540i	0.354626	+	0.935008i	$0.384608\pi$
$761$	−17.4463	+	30.2179i	−0.632428	+	1.09540i	−0.987054	+	0.160389i	$0.948725\pi$
$762$	6.81091	−	6.14145i	0.246733	−	0.222481i
$763$	9.39103	+	16.2657i	0.339978	+	0.588860i
$764$	−22.0186			−0.796606
$765$	−1.74589	+	16.8442i	−0.0631228	+	0.609002i
$766$	8.65128			0.312583
$767$	−7.30929	−	12.6601i	−0.263923	−	0.457128i
$768$	0.0568420	+	0.0184239i	0.00205111	+	0.000664815i
$769$	2.80362	−	4.85600i	0.101101	−	0.175112i	−0.811038	−	0.584994i	$-0.801097\pi$
$769$	2.80362	−	4.85600i	0.101101	−	0.175112i	0.912139	+	0.409882i	$0.134430\pi$
$770$		0			0
$771$	−22.6210	−	7.33203i	−0.814677	−	0.264057i
$772$	−11.0542	−	19.1464i	−0.397848	−	0.689093i
$773$	−10.8401			−0.389893			−0.194946	−	0.980814i	$-0.562453\pi$
$773$	−10.8401			−0.389893			−0.194946	+	0.980814i	$0.562453\pi$
$774$	−1.45830	+	14.0695i	−0.0524175	+	0.505718i
$775$	8.11722			0.291579
$776$	−0.316388	−	0.548000i	−0.0113577	−	0.0196721i
$777$	−13.4487	+	12.1268i	−0.482468	+	0.435045i
$778$	−4.38575	+	7.59634i	−0.157237	+	0.272342i
$779$	0.863374	−	1.49541i	0.0309336	−	0.0535785i
$780$	−4.34153	−	20.3533i	−0.155452	−	0.728764i
$781$		0			0
$782$	12.1436			0.434255
$783$	3.55714	−	8.03611i	0.127122	−	0.287187i
$784$	12.1089			0.432461
$785$	−0.264043	−	0.457336i	−0.00942411	−	0.0163230i
$786$	−3.74945	−	17.5776i	−0.133738	−	0.626971i
$787$	1.23822	−	2.14465i	0.0441376	−	0.0764486i	−0.843113	−	0.537737i	$-0.819279\pi$
$787$	1.23822	−	2.14465i	0.0441376	−	0.0764486i	0.887250	+	0.461288i	$0.152613\pi$
$788$	−9.10088	+	15.7632i	−0.324206	+	0.561540i
$789$	21.6800	−	19.5491i	0.771830	−	0.695965i
$790$	−1.67534	−	2.90177i	−0.0596058	−	0.103240i
$791$	−55.9640			−1.98985
$792$		0			0
$793$	15.4047			0.547037
$794$	−5.38060	−	9.31947i	−0.190950	−	0.330735i
$795$	−35.3608	−	11.4613i	−1.25412	−	0.406490i
$796$	23.2923	−	40.3435i	0.825574	−	1.42994i
$797$	4.83984	−	8.38286i	0.171436	−	0.296936i	−0.767486	−	0.641066i	$-0.778493\pi$
$797$	4.83984	−	8.38286i	0.171436	−	0.296936i	0.938922	+	0.344130i	$0.111826\pi$
$798$	12.1763	+	3.94663i	0.431035	+	0.139709i
$799$	−1.78490	−	3.09153i	−0.0631451	−	0.109371i
$800$	10.3488			0.365884
$801$	21.7282	−	9.71153i	0.767730	−	0.343140i
$802$	−2.65237			−0.0936586
$803$		0			0
$804$	7.01861	−	6.32873i	0.247527	−	0.223197i
$805$	−21.8234	+	37.7992i	−0.769173	+	1.33225i
$806$	3.82241	−	6.62061i	0.134639	−	0.233201i
$807$	−4.47958	−	21.0005i	−0.157689	−	0.739251i
$808$	−6.56046	−	11.3631i	−0.230796	−	0.399751i
$809$	−7.86532			−0.276530			−0.138265	−	0.990395i	$-0.544153\pi$
$809$	−7.86532			−0.276530			−0.138265	+	0.990395i	$0.544153\pi$
$810$	−5.02954	+	5.61830i	−0.176720	+	0.197407i
$811$	39.5047			1.38720			0.693599	−	0.720361i	$-0.256024\pi$
$811$	39.5047			1.38720			0.693599	+	0.720361i	$0.256024\pi$
$812$	5.07431	+	8.78896i	0.178073	+	0.308432i
$813$	−6.96269	−	32.6414i	−0.244192	−	1.14478i
$814$		0			0
$815$	−9.38994	+	16.2639i	−0.328915	+	0.569698i
$816$	11.1131	−	10.0208i	0.389037	−	0.350798i
$817$	21.2327	+	36.7762i	0.742839	+	1.28664i
$818$	−11.5855			−0.405079
$819$	37.3446	−	16.6913i	1.30493	−	0.583242i
$820$	−1.17473			−0.0410234
$821$	1.67681	+	2.90432i	0.0585211	+	0.101361i	0.893802	−	0.448462i	$-0.148028\pi$
$821$	1.67681	+	2.90432i	0.0585211	+	0.101361i	−0.835281	+	0.549824i	$0.814695\pi$
$822$	−2.58656	−	0.838368i	−0.0902167	−	0.0292415i
$823$	−8.05091	+	13.9446i	−0.280637	+	0.486078i	−0.971542	−	0.236868i	$-0.923879\pi$
$823$	−8.05091	+	13.9446i	−0.280637	+	0.486078i	0.690905	+	0.722946i	$0.257212\pi$
$824$	1.52523	−	2.64177i	0.0531339	−	0.0920306i
$825$		0			0
$826$	−3.05841	−	5.29732i	−0.106416	−	0.184317i
$827$	15.2905			0.531702			0.265851	−	0.964014i	$-0.414347\pi$
$827$	15.2905			0.531702			0.265851	+	0.964014i	$0.414347\pi$
$828$	−32.0257	−	23.1977i	−1.11297	−	0.806177i
$829$	−42.1463			−1.46380			−0.731901	−	0.681411i	$-0.761367\pi$
$829$	−42.1463			−1.46380			−0.731901	+	0.681411i	$0.761367\pi$
$830$	−0.0523514	−	0.0906752i	−0.00181714	−	0.00314738i
$831$	−13.3149	+	12.0062i	−0.461889	+	0.416489i
$832$	−5.57882	+	9.66280i	−0.193411	+	0.334997i
$833$	7.65284	−	13.2551i	0.265155	−	0.459262i
$834$	−2.65734	−	12.4577i	−0.0920163	−	0.431376i
$835$	15.0096	+	25.9975i	0.519430	+	0.899679i
$836$		0			0
$837$	20.1417	−	2.16094i	0.696199	−	0.0746930i
$838$	8.89330			0.307214
$839$	−1.32370	−	2.29271i	−0.0456990	−	0.0791531i	0.842271	−	0.539054i	$-0.181218\pi$
$839$	−1.32370	−	2.29271i	−0.0456990	−	0.0791531i	−0.887970	+	0.459901i	$0.847885\pi$
$840$	−3.88164	−	18.1973i	−0.133929	−	0.627866i
$841$	13.0698	−	22.6375i	0.450682	−	0.780604i
$842$	−3.14215	+	5.44237i	−0.108286	+	0.187556i
$843$	21.1419	−	19.0638i	0.728165	−	0.656592i
$844$	−6.40771	−	11.0985i	−0.220562	−	0.382025i
$845$	5.09616			0.175313
$846$	0.163882	−	1.58111i	0.00563436	−	0.0543597i
$847$		0			0
$848$	16.4232	+	28.4458i	0.563976	+	0.976834i
$849$	−2.08422	−	0.675546i	−0.0715302	−	0.0231847i
$850$	1.68744	−	2.92273i	0.0578786	−	0.100249i
$851$	−11.4835	+	19.8900i	−0.393649	+	0.681820i
$852$	−20.3422	−	6.59340i	−0.696912	−	0.225886i
$853$	−4.63519	−	8.02838i	−0.158706	−	0.274886i	0.775696	−	0.631106i	$-0.217399\pi$
$853$	−4.63519	−	8.02838i	−0.158706	−	0.274886i	−0.934402	+	0.356220i	$0.884065\pi$
$854$	6.44575			0.220569
$855$	−2.33396	+	22.5178i	−0.0798197	+	0.770091i
$856$	6.09770			0.208415
$857$	10.2678	+	17.7844i	0.350742	+	0.607502i	0.986380	−	0.164485i	$-0.0525962\pi$
$857$	10.2678	+	17.7844i	0.350742	+	0.607502i	−0.635638	+	0.771987i	$0.719263\pi$
$858$		0			0
$859$	−18.0139	+	31.2010i	−0.614626	+	1.06456i	0.375824	+	0.926691i	$0.377360\pi$
$859$	−18.0139	+	31.2010i	−0.614626	+	1.06456i	−0.990450	+	0.137872i	$0.955974\pi$
$860$	14.4449	−	25.0194i	0.492569	−	0.853154i
$861$	−0.481688	−	2.25817i	−0.0164159	−	0.0769583i
$862$	−1.61352	−	2.79470i	−0.0549566	−	0.0951877i
$863$	4.31646			0.146934			0.0734670	−	0.997298i	$-0.476594\pi$
$863$	4.31646			0.146934			0.0734670	+	0.997298i	$0.476594\pi$
$864$	25.6789	−	2.75502i	0.873616	−	0.0937275i
$865$	21.1229			0.718199
$866$	3.43291	+	5.94598i	0.116655	+	0.202053i
$867$	2.19682	+	10.2988i	0.0746080	+	0.349765i
$868$	−11.6966	+	20.2591i	−0.397008	+	0.687637i
$869$		0			0
$870$	1.82279	−	1.64362i	0.0617984	−	0.0557241i
$871$	6.19918	+	10.7373i	0.210051	+	0.363819i
$872$	−10.1549			−0.343889
$873$	0.833736	+	0.603913i	0.0282177	+	0.0204394i
$874$	16.2339			0.549121
$875$	20.6295	+	35.7313i	0.697403	+	1.20794i
$876$	43.6074	+	14.1342i	1.47336	+	0.477551i
$877$	−15.5580	+	26.9473i	−0.525356	+	0.909944i	0.474207	+	0.880413i	$0.342735\pi$
$877$	−15.5580	+	26.9473i	−0.525356	+	0.909944i	−0.999564	+	0.0295309i	$0.990599\pi$
$878$	6.17488	−	10.6952i	0.208392	−	0.360946i
$879$	−39.6879	−	12.8638i	−1.33864	−	0.433886i
$880$		0			0
$881$	43.9267			1.47993			0.739964	−	0.672647i	$-0.234843\pi$
$881$	43.9267			1.47993			0.739964	+	0.672647i	$0.234843\pi$
$882$	6.22219	−	2.78103i	0.209512	−	0.0936423i
$883$	−5.87946			−0.197860			−0.0989298	−	0.995094i	$-0.531542\pi$
$883$	−5.87946			−0.197860			−0.0989298	+	0.995094i	$0.531542\pi$
$884$	11.6222	+	20.1303i	0.390897	+	0.677054i
$885$	8.03445	−	7.24472i	0.270075	−	0.243529i
$886$	6.57813	−	11.3937i	0.220997	−	0.382777i
$887$	3.84755	−	6.66416i	0.129188	−	0.223760i	−0.794174	−	0.607690i	$-0.792096\pi$
$887$	3.84755	−	6.66416i	0.129188	−	0.223760i	0.923362	+	0.383930i	$0.125430\pi$
$888$	−2.04252	−	9.57542i	−0.0685425	−	0.321330i
$889$	−18.4082	−	31.8839i	−0.617390	−	1.06935i
$890$	6.64689			0.222804
$891$		0			0
$892$	−41.3640			−1.38497
$893$	−2.38610	−	4.13285i	−0.0798479	−	0.138301i
$894$	0.717986	+	3.36595i	0.0240130	+	0.112574i
$895$	−18.6894	+	32.3710i	−0.624718	+	1.08204i
$896$	−19.2856	+	33.4036i	−0.644286	+	1.11594i
$897$	38.5288	−	34.7417i	1.28644	−	1.15999i
$898$	3.47658	+	6.02161i	0.116015	+	0.200944i
$899$	−6.59352			−0.219906
$900$	−10.0334	+	4.48448i	−0.334447	+	0.149483i
$901$	41.5180			1.38316
$902$		0			0
$903$	54.0174	+	17.5084i	1.79759	+	0.582642i
$904$	15.1291	−	26.2043i	0.503185	−	0.871542i
$905$	3.74106	−	6.47970i	0.124357	−	0.215393i
$906$	6.29886	+	2.04161i	0.209265	+	0.0678281i
$907$	9.49528	+	16.4463i	0.315285	+	0.546091i	0.979498	−	0.201453i	$-0.0645664\pi$
$907$	9.49528	+	16.4463i	0.315285	+	0.546091i	−0.664213	+	0.747544i	$0.731233\pi$
$908$	20.9761			0.696116
$909$	17.2879	+	12.5224i	0.573404	+	0.415343i
$910$	11.4241			0.378705
$911$	−25.0176	−	43.3318i	−0.828871	−	1.43565i	−0.898924	−	0.438104i	$-0.855650\pi$
$911$	−25.0176	−	43.3318i	−0.828871	−	1.43565i	0.0700530	−	0.997543i	$-0.477683\pi$
$912$	14.8563	−	13.3961i	0.491943	−	0.443588i
$913$		0			0
$914$	6.04320	−	10.4671i	0.199891	−	0.346222i
$915$	2.37826	+	11.1494i	0.0786227	+	0.368587i
$916$	2.68977	+	4.65882i	0.0888725	+	0.153932i
$917$	−72.1519			−2.38266
$918$	3.40905	−	7.70154i	0.112515	−	0.254189i
$919$	3.07419			0.101408			0.0507042	−	0.998714i	$-0.483853\pi$
$919$	3.07419			0.101408			0.0507042	+	0.998714i	$0.483853\pi$
$920$	−11.7993	−	20.4369i	−0.389011	−	0.673786i
$921$	−5.88789	−	27.6027i	−0.194013	−	0.909539i
$922$	−6.43660	+	11.1485i	−0.211978	+	0.367157i
$923$	14.0270	−	24.2955i	0.461705	−	0.799696i
$924$		0			0
$925$	3.19142	+	5.52769i	0.104933	+	0.181749i
$926$	−6.22544			−0.204581
$927$	−0.511658	+	4.93642i	−0.0168051	+	0.162133i
$928$	−8.40617			−0.275946
$929$	0.452787	+	0.784250i	0.0148555	+	0.0257304i	0.873358	−	0.487080i	$-0.161938\pi$
$929$	0.452787	+	0.784250i	0.0148555	+	0.0257304i	−0.858502	+	0.512810i	$0.828605\pi$
$930$	5.38188	+	1.74440i	0.176479	+	0.0572011i
$931$	10.2305	−	17.7198i	0.335292	−	0.580743i
$932$	−21.5804	+	37.3784i	−0.706891	+	1.22437i
$933$	35.2126	+	11.4133i	1.15281	+	0.373654i
$934$	−6.79433	−	11.7681i	−0.222317	−	0.385065i
$935$		0			0
$936$	−2.28012	+	21.9983i	−0.0745280	+	0.719037i
$937$	−22.0542			−0.720481			−0.360240	−	0.932860i	$-0.617305\pi$
$937$	−22.0542			−0.720481			−0.360240	+	0.932860i	$0.617305\pi$
$938$	2.59391	+	4.49278i	0.0846941	+	0.146694i
$939$	−4.00837	+	3.61437i	−0.130808	+	0.117951i
$940$	−1.62330	+	2.81164i	−0.0529462	+	0.0917056i
$941$	−2.73046	+	4.72930i	−0.0890105	+	0.154171i	−0.907093	−	0.420930i	$-0.861704\pi$
$941$	−2.73046	+	4.72930i	−0.0890105	+	0.154171i	0.818083	+	0.575101i	$0.195037\pi$
$942$	0.0547914	+	0.256865i	0.00178520	+	0.00836910i
$943$	−1.46422	−	2.53610i	−0.0476815	−	0.0825868i
$944$	−9.55957			−0.311138
$945$	17.8460	+	24.4518i	0.580531	+	0.795417i
$946$		0			0
$947$	−16.2203	−	28.0944i	−0.527089	−	0.912945i	−0.999502	−	0.0315677i	$-0.989950\pi$
$947$	−16.2203	−	28.0944i	−0.527089	−	0.912945i	0.472412	−	0.881378i	$-0.343383\pi$
$948$	−2.54238	−	11.9188i	−0.0825728	−	0.387105i
$949$	−30.0696	+	52.0821i	−0.976101	+	1.69066i
$950$	2.25581	−	3.90718i	0.0731883	−	0.126766i
$951$	23.4946	−	21.1853i	0.761866	−	0.686980i
$952$	10.3911	+	17.9979i	0.336777	+	0.583315i
$953$	−53.8088			−1.74304			−0.871518	−	0.490363i	$-0.836864\pi$
$953$	−53.8088			−1.74304			−0.871518	+	0.490363i	$0.836864\pi$
$954$	14.9722	+	10.8451i	0.484744	+	0.351122i
$955$	21.3774			0.691756
$956$	−6.11452	−	10.5907i	−0.197758	−	0.342527i
$957$		0			0
$958$	−3.83130	+	6.63600i	−0.123784	+	0.214400i
$959$	−5.45773	+	9.45306i	−0.176239	+	0.305255i
$960$	−7.85487	−	2.54596i	−0.253515	−	0.0821704i
$961$	7.90079	+	13.6846i	0.254864	+	0.441437i
$962$	6.01137			0.193814
$963$	−9.05701	+	4.04806i	−0.291858	+	0.130447i
$964$	13.6717			0.440335
$965$	10.7322	+	18.5888i	0.345483	+	0.598394i
$966$	16.1215	−	14.5369i	0.518701	−	0.467717i
$967$	14.4075	−	24.9546i	0.463315	−	0.802486i	−0.535809	−	0.844340i	$-0.679993\pi$
$967$	14.4075	−	24.9546i	0.463315	−	0.802486i	0.999124	+	0.0418540i	$0.0133264\pi$
$968$		0			0
$969$	−5.27490	−	24.7289i	−0.169454	−	0.794408i
$970$	0.143758	+	0.248997i	0.00461580	+	0.00799480i
$971$	5.39405			0.173103			0.0865517	−	0.996247i	$-0.472415\pi$
$971$	5.39405			0.173103			0.0865517	+	0.996247i	$0.472415\pi$
$972$	−23.7026	+	13.7986i	−0.760262	+	0.442592i
$973$	−51.1362			−1.63935
$974$	6.60377	+	11.4381i	0.211598	+	0.366499i
$975$	−3.00780	−	14.1007i	−0.0963268	−	0.451584i
$976$	5.03682	−	8.72403i	0.161225	−	0.279250i
$977$	1.65618	−	2.86859i	0.0529859	−	0.0917742i	−0.838316	−	0.545185i	$-0.816460\pi$
$977$	1.65618	−	2.86859i	0.0529859	−	0.0917742i	0.891302	+	0.453411i	$0.149793\pi$
$978$	6.93659	−	6.25478i	0.221808	−	0.200006i
$979$		0			0
$980$	−13.9200			−0.444657
$981$	15.0833	−	6.74152i	0.481571	−	0.215240i
$982$	−19.1291			−0.610435
$983$	−16.9361	−	29.3341i	−0.540176	−	0.935613i	−0.998893	−	0.0470306i	$-0.985024\pi$
$983$	−16.9361	−	29.3341i	−0.540176	−	0.935613i	0.458717	−	0.888582i	$-0.348309\pi$
$984$	1.18757	+	0.384921i	0.0378584	+	0.0122708i
$985$	8.83584	−	15.3041i	0.281533	−	0.487630i
$986$	−1.37068	+	2.37409i	−0.0436514	+	0.0756065i
$987$	−6.07039	−	1.96756i	−0.193223	−	0.0626282i
$988$	15.5369	+	26.9107i	0.494295	+	0.856143i
$989$	72.0183			2.29005
$990$		0			0
$991$	8.66640			0.275297			0.137649	−	0.990481i	$-0.456046\pi$
$991$	8.66640			0.275297			0.137649	+	0.990481i	$0.456046\pi$
$992$	−9.68835	−	16.7807i	−0.307605	−	0.532788i
$993$	−4.84452	+	4.36834i	−0.153736	+	0.138625i
$994$	5.86929	−	10.1659i	0.186163	−	0.322443i
$995$	−22.6140	+	39.1686i	−0.716912	+	1.24173i
$996$	−0.0794450	−	0.372442i	−0.00251731	−	0.0118013i
$997$	15.1327	+	26.2106i	0.479258	+	0.830098i	0.999717	−	0.0237880i	$-0.00757266\pi$
$997$	15.1327	+	26.2106i	0.479258	+	0.830098i	−0.520459	+	0.853886i	$0.674239\pi$
$998$	11.7891			0.373177
$999$	9.39060	+	12.8666i	0.297105	+	0.407080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.p.364.10		36
9.4	even	3		9801.2.a.cm.1.9		18
9.5	odd	6		9801.2.a.cp.1.10		18
9.7	even	3	inner	1089.2.e.p.727.10		36
11.5	even	5		99.2.m.b.58.5	yes	72
11.9	even	5		99.2.m.b.4.5	✓	72
11.10	odd	2		1089.2.e.o.364.9		36
33.5	odd	10		297.2.n.b.91.5		72
33.20	odd	10		297.2.n.b.37.5		72
99.5	odd	30		891.2.f.e.487.5		36
99.16	even	15		99.2.m.b.25.5	yes	72
99.20	odd	30		297.2.n.b.235.5		72
99.31	even	15		891.2.f.f.730.5		36
99.32	even	6		9801.2.a.cn.1.9		18
99.38	odd	30		297.2.n.b.289.5		72
99.43	odd	6		1089.2.e.o.727.9		36
99.49	even	15		891.2.f.f.487.5		36
99.76	odd	6		9801.2.a.co.1.10		18
99.86	odd	30		891.2.f.e.730.5		36
99.97	even	15		99.2.m.b.70.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.5	✓	72	11.9	even	5
99.2.m.b.25.5	yes	72	99.16	even	15
99.2.m.b.58.5	yes	72	11.5	even	5
99.2.m.b.70.5	yes	72	99.97	even	15
297.2.n.b.37.5		72	33.20	odd	10
297.2.n.b.91.5		72	33.5	odd	10
297.2.n.b.235.5		72	99.20	odd	30
297.2.n.b.289.5		72	99.38	odd	30
891.2.f.e.487.5		36	99.5	odd	30
891.2.f.e.730.5		36	99.86	odd	30
891.2.f.f.487.5		36	99.49	even	15
891.2.f.f.730.5		36	99.31	even	15
1089.2.e.o.364.9		36	11.10	odd	2
1089.2.e.o.727.9		36	99.43	odd	6
1089.2.e.p.364.10		36	1.1	even	1	trivial
1089.2.e.p.727.10		36	9.7	even	3	inner
9801.2.a.cm.1.9		18	9.4	even	3
9801.2.a.cn.1.9		18	99.32	even	6
9801.2.a.co.1.10		18	99.76	odd	6
9801.2.a.cp.1.10		18	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.245247 + 0.424780i) q^{2} +(-0.361332 - 1.69394i) q^{3} +(0.879708 - 1.52370i) q^{4} +(-0.854089 + 1.47932i) q^{5} +(0.630937 - 0.568921i) q^{6} +(-1.70526 - 2.95360i) q^{7} +1.84397 q^{8} +(-2.73888 + 1.22415i) q^{9} -0.837851 q^{10} +(-2.89892 - 0.939612i) q^{12} +(1.99896 - 3.46230i) q^{13} +(0.836420 - 1.44872i) q^{14} +(2.81450 + 0.912248i) q^{15} +(-1.30719 - 2.26411i) q^{16} -3.30458 q^{17} +(-1.19170 - 0.863202i) q^{18} -4.41765 q^{19} +(1.50270 + 2.60275i) q^{20} +(-4.38706 + 3.95584i) q^{21} +(-3.74601 + 6.48827i) q^{23} +(-0.666286 - 3.12358i) q^{24} +(1.04107 + 1.80318i) q^{25} +1.96096 q^{26} +(3.06329 + 4.19717i) q^{27} -6.00053 q^{28} +(-0.845644 - 1.46470i) q^{29} +(0.302743 + 1.41927i) q^{30} +(1.94926 - 3.37621i) q^{31} +(2.48514 - 4.30439i) q^{32} +(-0.810437 - 1.40372i) q^{34} +5.82578 q^{35} +(-0.544173 + 5.25012i) q^{36} +3.06553 q^{37} +(-1.08342 - 1.87653i) q^{38} +(-6.58723 - 2.13508i) q^{39} +(-1.57491 + 2.72783i) q^{40} +(-0.195437 + 0.338507i) q^{41} +(-2.75628 - 0.893377i) q^{42} +(-4.80634 - 8.32483i) q^{43} +(0.528325 - 5.09722i) q^{45} -3.67479 q^{46} +(0.540129 + 0.935531i) q^{47} +(-3.36295 + 3.03240i) q^{48} +(-2.31583 + 4.01114i) q^{49} +(-0.510636 + 0.884448i) q^{50} +(1.19405 + 5.59776i) q^{51} +(-3.51700 - 6.09163i) q^{52} -12.5638 q^{53} +(-1.03161 + 2.33057i) q^{54} +(-3.14445 - 5.44635i) q^{56} +(1.59624 + 7.48324i) q^{57} +(0.414783 - 0.718426i) q^{58} +(1.82827 - 3.16666i) q^{59} +(3.86593 - 3.48594i) q^{60} +(1.92659 + 3.33695i) q^{61} +1.91220 q^{62} +(8.28616 + 6.00205i) q^{63} -2.79086 q^{64} +(3.41458 + 5.91423i) q^{65} +(-1.55060 + 2.68572i) q^{67} +(-2.90706 + 5.03518i) q^{68} +(12.3443 + 4.00109i) q^{69} +(1.42875 + 2.47467i) q^{70} +7.01715 q^{71} +(-5.05041 + 2.25730i) q^{72} -15.0426 q^{73} +(0.751812 + 1.30218i) q^{74} +(2.67831 - 2.41505i) q^{75} +(-3.88624 + 6.73117i) q^{76} +(-0.708557 - 3.32175i) q^{78} +(1.99957 + 3.46335i) q^{79} +4.46581 q^{80} +(6.00290 - 6.70561i) q^{81} -0.191722 q^{82} +(0.0624829 + 0.108224i) q^{83} +(2.16818 + 10.1645i) q^{84} +(2.82240 - 4.88854i) q^{85} +(2.35748 - 4.08328i) q^{86} +(-2.17556 + 1.96172i) q^{87} -7.93327 q^{89} +(2.29477 - 1.02566i) q^{90} -13.6350 q^{91} +(6.59078 + 11.4156i) q^{92} +(-6.42344 - 2.08199i) q^{93} +(-0.264930 + 0.458872i) q^{94} +(3.77307 - 6.53514i) q^{95} +(-8.18934 - 2.65437i) q^{96} +(-0.171580 - 0.297185i) q^{97} -2.27180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} - 3 q^{13} - 5 q^{15} + 8 q^{16} - 40 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20} - 8 q^{21} + 10 q^{23}+ \cdots - 164 q^{98}+O(q^{100}) \) 36 * q + 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 - q^6 - q^7 - 12 * q^8 - q^9 - 4 * q^10 - 8 * q^12 - 3 * q^13 - 5 * q^15 + 8 * q^16 - 40 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 8 * q^21 + 10 * q^23 - 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 + 38 * q^28 + 21 * q^29 + 12 * q^30 - 6 * q^31 + 9 * q^32 + 4 * q^34 - 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 + 42 * q^39 + 20 * q^41 + 18 * q^42 - 4 * q^43 + 20 * q^45 + 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 + 25 * q^50 - 4 * q^51 + 19 * q^52 + 62 * q^53 + 17 * q^54 + 57 * q^56 - 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 + 16 * q^61 - 38 * q^62 + 5 * q^63 - 32 * q^64 + 42 * q^65 + 5 * q^67 + 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 + 51 * q^72 + 9 * q^74 - 16 * q^75 + 8 * q^76 - 32 * q^78 + 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 + 36 * q^83 + 60 * q^84 - 25 * q^85 - 26 * q^86 - 60 * q^87 - 28 * q^89 + 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 - 4 * q^94 + 64 * q^95 - 21 * q^96 + 16 * q^97 - 164 * q^98

Introduction

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