LMFDB - Embedded newform 1183.2.e.l.508.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.2
Character	$\chi$	$=$	1183.508
Dual form			1183.2.e.l.170.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21736 - 2.10853i) q^{2} +(-0.979025 + 1.69572i) q^{3} +(-1.96394 + 3.40165i) q^{4} +(-2.07488 - 3.59380i) q^{5} +4.76731 q^{6} +(-2.28564 + 1.33262i) q^{7} +4.69388 q^{8} +(-0.416980 - 0.722230i) q^{9} +O(q^{10})$	\(q+(-1.21736 - 2.10853i) q^{2} +(-0.979025 + 1.69572i) q^{3} +(-1.96394 + 3.40165i) q^{4} +(-2.07488 - 3.59380i) q^{5} +4.76731 q^{6} +(-2.28564 + 1.33262i) q^{7} +4.69388 q^{8} +(-0.416980 - 0.722230i) q^{9} +(-5.05176 + 8.74991i) q^{10} +(-0.336584 + 0.582980i) q^{11} +(-3.84550 - 6.66060i) q^{12} +(5.59232 + 3.19706i) q^{14} +8.12544 q^{15} +(-1.78626 - 3.09390i) q^{16} +(0.0504652 - 0.0874083i) q^{17} +(-1.01523 + 1.75843i) q^{18} +(2.72197 + 4.71460i) q^{19} +16.2998 q^{20} +(-0.0220519 - 5.18047i) q^{21} +1.63898 q^{22} +(-0.231150 - 0.400364i) q^{23} +(-4.59542 + 7.95950i) q^{24} +(-6.11026 + 10.5833i) q^{25} -4.24122 q^{27} +(-0.0442366 - 10.3921i) q^{28} +1.30939 q^{29} +(-9.89161 - 17.1328i) q^{30} +(-3.61546 + 6.26215i) q^{31} +(0.344818 - 0.597242i) q^{32} +(-0.659048 - 1.14150i) q^{33} -0.245738 q^{34} +(9.53158 + 5.44909i) q^{35} +3.27570 q^{36} +(-2.62259 - 4.54246i) q^{37} +(6.62726 - 11.4787i) q^{38} +(-9.73923 - 16.8688i) q^{40} -4.44603 q^{41} +(-10.8963 + 6.35300i) q^{42} +4.83284 q^{43} +(-1.32206 - 2.28988i) q^{44} +(-1.73037 + 2.99708i) q^{45} +(-0.562787 + 0.974776i) q^{46} +(1.41690 + 2.45415i) q^{47} +6.99518 q^{48} +(3.44826 - 6.09175i) q^{49} +29.7536 q^{50} +(0.0988133 + 0.171150i) q^{51} +(7.17169 - 12.4217i) q^{53} +(5.16310 + 8.94275i) q^{54} +2.79348 q^{55} +(-10.7285 + 6.25514i) q^{56} -10.6595 q^{57} +(-1.59400 - 2.76088i) q^{58} +(-0.208629 + 0.361356i) q^{59} +(-15.9579 + 27.6399i) q^{60} +(-0.768086 - 1.33036i) q^{61} +17.6053 q^{62} +(1.91552 + 1.09508i) q^{63} -8.82412 q^{64} +(-1.60460 + 2.77925i) q^{66} +(2.94263 - 5.09679i) q^{67} +(0.198222 + 0.343330i) q^{68} +0.905207 q^{69} +(-0.113788 - 26.7312i) q^{70} -10.0629 q^{71} +(-1.95725 - 3.39006i) q^{72} +(3.19860 - 5.54014i) q^{73} +(-6.38529 + 11.0597i) q^{74} +(-11.9642 - 20.7226i) q^{75} -21.3832 q^{76} +(-0.00758135 - 1.78102i) q^{77} +(-0.143925 - 0.249286i) q^{79} +(-7.41256 + 12.8389i) q^{80} +(5.40319 - 9.35861i) q^{81} +(5.41243 + 9.37461i) q^{82} +9.43279 q^{83} +(17.6654 + 10.0991i) q^{84} -0.418837 q^{85} +(-5.88332 - 10.1902i) q^{86} +(-1.28192 + 2.22035i) q^{87} +(-1.57988 + 2.73644i) q^{88} +(-5.02856 - 8.70972i) q^{89} +8.42593 q^{90} +1.81586 q^{92} +(-7.07924 - 12.2616i) q^{93} +(3.44977 - 5.97518i) q^{94} +(11.2955 - 19.5645i) q^{95} +(0.675170 + 1.16943i) q^{96} -3.84295 q^{97} +(-17.0425 + 0.145094i) q^{98} +0.561394 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) $ 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.21736	−	2.10853i	−0.860805	−	1.49096i	−0.871153	−	0.491012i	$-0.836627\pi$
$2$	−1.21736	−	2.10853i	−0.860805	−	1.49096i	0.0103473	−	0.999946i	$-0.496706\pi$
$3$	−0.979025	+	1.69572i	−0.565240	+	0.979025i	0.431787	+	0.901976i	$0.357883\pi$
$3$	−0.979025	+	1.69572i	−0.565240	+	0.979025i	−0.997027	+	0.0770493i	$0.975450\pi$
$4$	−1.96394	+	3.40165i	−0.981972	+	1.70083i
$5$	−2.07488	−	3.59380i	−0.927915	−	1.60720i	−0.786805	−	0.617202i	$-0.788266\pi$
$5$	−2.07488	−	3.59380i	−0.927915	−	1.60720i	−0.141110	−	0.989994i	$-0.545067\pi$
$6$	4.76731			1.94625
$7$	−2.28564	+	1.33262i	−0.863889	+	0.503682i
$7$	−2.28564	+	1.33262i	−0.863889	+	0.503682i
$8$	4.69388			1.65954
$9$	−0.416980	−	0.722230i	−0.138993	−	0.240743i
$10$	−5.05176	+	8.74991i	−1.59751	+	2.76697i
$11$	−0.336584	+	0.582980i	−0.101484	+	0.175775i	−0.912296	−	0.409531i	$-0.865692\pi$
$11$	−0.336584	+	0.582980i	−0.101484	+	0.175775i	0.810812	+	0.585306i	$0.199026\pi$
$12$	−3.84550	−	6.66060i	−1.11010	−	1.92275i
$13$		0			0
$13$		0			0
$14$	5.59232	+	3.19706i	1.49461	+	0.854451i
$15$	8.12544			2.09798
$16$	−1.78626	−	3.09390i	−0.446566	−	0.773474i
$17$	0.0504652	−	0.0874083i	0.0122396	−	0.0211996i	−0.859841	−	0.510562i	$-0.829437\pi$
$17$	0.0504652	−	0.0874083i	0.0122396	−	0.0211996i	0.872080	+	0.489363i	$0.162771\pi$
$18$	−1.01523	+	1.75843i	−0.239292	+	0.414466i
$19$	2.72197	+	4.71460i	0.624464	+	1.08160i	0.988644	+	0.150274i	$0.0480157\pi$
$19$	2.72197	+	4.71460i	0.624464	+	1.08160i	−0.364181	+	0.931328i	$0.618651\pi$
$20$	16.2998			3.64475
$21$	−0.0220519	−	5.18047i	−0.00481213	−	1.13047i
$22$	1.63898			0.349431
$23$	−0.231150	−	0.400364i	−0.0481981	−	0.0834816i	0.840920	−	0.541160i	$-0.182015\pi$
$23$	−0.231150	−	0.400364i	−0.0481981	−	0.0834816i	−0.889118	+	0.457678i	$0.848681\pi$
$24$	−4.59542	+	7.95950i	−0.938037	+	1.62473i
$25$	−6.11026	+	10.5833i	−1.22205	+	2.11666i
$26$		0			0
$27$	−4.24122			−0.816222
$28$	−0.0442366	−	10.3921i	−0.00835994	−	1.96393i
$29$	1.30939			0.243147			0.121573	−	0.992582i	$-0.461206\pi$
$29$	1.30939			0.243147			0.121573	+	0.992582i	$0.461206\pi$
$30$	−9.89161	−	17.1328i	−1.80595	−	3.12800i
$31$	−3.61546	+	6.26215i	−0.649355	+	1.12472i	0.333922	+	0.942601i	$0.391628\pi$
$31$	−3.61546	+	6.26215i	−0.649355	+	1.12472i	−0.983277	+	0.182115i	$0.941706\pi$
$32$	0.344818	−	0.597242i	0.0609557	−	0.105578i
$33$	−0.659048	−	1.14150i	−0.114726	−	0.198710i
$34$	−0.245738			−0.0421437
$35$	9.53158	+	5.44909i	1.61113	+	0.921065i
$36$	3.27570			0.545950
$37$	−2.62259	−	4.54246i	−0.431152	−	0.746776i	0.565821	−	0.824528i	$-0.308559\pi$
$37$	−2.62259	−	4.54246i	−0.431152	−	0.746776i	−0.996973	+	0.0777516i	$0.975226\pi$
$38$	6.62726	−	11.4787i	1.07508	−	1.86210i
$39$		0			0
$40$	−9.73923	−	16.8688i	−1.53991	−	2.66720i
$41$	−4.44603			−0.694353			−0.347177	−	0.937800i	$-0.612860\pi$
$41$	−4.44603			−0.694353			−0.347177	+	0.937800i	$0.612860\pi$
$42$	−10.8963	+	6.35300i	−1.68134	+	0.980290i
$43$	4.83284			0.737002			0.368501	−	0.929627i	$-0.379871\pi$
$43$	4.83284			0.737002			0.368501	+	0.929627i	$0.379871\pi$
$44$	−1.32206	−	2.28988i	−0.199309	−	0.345213i
$45$	−1.73037	+	2.99708i	−0.257948	+	0.446779i
$46$	−0.562787	+	0.974776i	−0.0829784	+	0.143723i
$47$	1.41690	+	2.45415i	0.206677	+	0.357974i	0.950666	−	0.310218i	$-0.100402\pi$
$47$	1.41690	+	2.45415i	0.206677	+	0.357974i	−0.743989	+	0.668192i	$0.767069\pi$
$48$	6.99518			1.00967
$49$	3.44826	−	6.09175i	0.492609	−	0.870251i
$50$	29.7536			4.20780
$51$	0.0988133	+	0.171150i	0.0138366	+	0.0239658i
$52$		0			0
$53$	7.17169	−	12.4217i	0.985108	−	1.70626i	0.343652	−	0.939097i	$-0.388336\pi$
$53$	7.17169	−	12.4217i	0.985108	−	1.70626i	0.641456	−	0.767160i	$-0.278331\pi$
$54$	5.16310	+	8.94275i	0.702609	+	1.21695i
$55$	2.79348			0.376673
$56$	−10.7285	+	6.25514i	−1.43366	+	0.835878i
$57$	−10.6595			−1.41189
$58$	−1.59400	−	2.76088i	−0.209302	−	0.362522i
$59$	−0.208629	+	0.361356i	−0.0271612	+	0.0470446i	−0.879286	−	0.476293i	$-0.841980\pi$
$59$	−0.208629	+	0.361356i	−0.0271612	+	0.0470446i	0.852125	+	0.523338i	$0.175313\pi$
$60$	−15.9579	+	27.6399i	−2.06016	+	3.56830i
$61$	−0.768086	−	1.33036i	−0.0983433	−	0.170336i	0.812656	−	0.582744i	$-0.198021\pi$
$61$	−0.768086	−	1.33036i	−0.0983433	−	0.170336i	−0.910999	+	0.412408i	$0.864688\pi$
$62$	17.6053			2.23587
$63$	1.91552	+	1.09508i	0.241333	+	0.137967i
$64$	−8.82412			−1.10302
$65$		0			0
$66$	−1.60460	+	2.77925i	−0.197513	+	0.342102i
$67$	2.94263	−	5.09679i	0.359500	−	0.622672i	−0.628377	−	0.777909i	$-0.716281\pi$
$67$	2.94263	−	5.09679i	0.359500	−	0.622672i	0.987877	+	0.155236i	$0.0496139\pi$
$68$	0.198222	+	0.343330i	0.0240379	+	0.0416349i
$69$	0.905207			0.108974
$70$	−0.113788	−	26.7312i	−0.0136003	−	3.19499i
$71$	−10.0629			−1.19425			−0.597123	−	0.802150i	$-0.703690\pi$
$71$	−10.0629			−1.19425			−0.597123	+	0.802150i	$0.703690\pi$
$72$	−1.95725	−	3.39006i	−0.230664	−	0.399522i
$73$	3.19860	−	5.54014i	0.374368	−	0.648424i	−0.615865	−	0.787852i	$-0.711193\pi$
$73$	3.19860	−	5.54014i	0.374368	−	0.648424i	0.990232	+	0.139428i	$0.0445265\pi$
$74$	−6.38529	+	11.0597i	−0.742275	+	1.28566i
$75$	−11.9642	−	20.7226i	−1.38151	−	2.39284i
$76$	−21.3832			−2.45282
$77$	−0.00758135	−	1.78102i	−0.000863975	−	0.202966i
$78$		0			0
$79$	−0.143925	−	0.249286i	−0.0161928	−	0.0280468i	0.857815	−	0.513958i	$-0.171821\pi$
$79$	−0.143925	−	0.249286i	−0.0161928	−	0.0280468i	−0.874008	+	0.485911i	$0.838488\pi$
$80$	−7.41256	+	12.8389i	−0.828750	+	1.43544i
$81$	5.40319	−	9.35861i	0.600355	−	1.03985i
$82$	5.41243	+	9.37461i	0.597703	+	1.03525i
$83$	9.43279			1.03538			0.517692	−	0.855567i	$-0.326791\pi$
$83$	9.43279			1.03538			0.517692	+	0.855567i	$0.326791\pi$
$84$	17.6654	+	10.0991i	1.92746	+	1.10191i
$85$	−0.418837			−0.0454292
$86$	−5.88332	−	10.1902i	−0.634415	−	1.09884i
$87$	−1.28192	+	2.22035i	−0.137436	+	0.238047i
$88$	−1.57988	+	2.73644i	−0.168416	+	0.291705i
$89$	−5.02856	−	8.70972i	−0.533026	−	0.923228i	−0.999256	−	0.0385648i	$-0.987721\pi$
$89$	−5.02856	−	8.70972i	−0.533026	−	0.923228i	0.466230	−	0.884664i	$-0.345612\pi$
$90$	8.42593			0.888171
$91$		0			0
$92$	1.81586			0.189317
$93$	−7.07924	−	12.2616i	−0.734083	−	1.27147i
$94$	3.44977	−	5.97518i	0.355816	−	0.616292i
$95$	11.2955	−	19.5645i	1.15890	−	2.00727i
$96$	0.675170	+	1.16943i	0.0689093	+	0.119354i
$97$	−3.84295			−0.390192			−0.195096	−	0.980784i	$-0.562502\pi$
$97$	−3.84295			−0.390192			−0.195096	+	0.980784i	$0.562502\pi$
$98$	−17.0425	+	0.145094i	−1.72155	+	0.0146567i
$99$	0.561394			0.0564223
$100$	−24.0004	−	41.5699i	−2.40004	−	4.15699i
$101$	0.0426833	−	0.0739297i	0.00424715	−	0.00735628i	−0.863894	−	0.503674i	$-0.831981\pi$
$101$	0.0426833	−	0.0739297i	0.00424715	−	0.00735628i	0.868141	+	0.496317i	$0.165315\pi$
$102$	0.240583	−	0.416703i	0.0238213	−	0.0412597i
$103$	−5.78852	−	10.0260i	−0.570360	−	0.987893i	−0.996529	−	0.0832490i	$-0.973470\pi$
$103$	−5.78852	−	10.0260i	−0.570360	−	0.987893i	0.426169	−	0.904644i	$-0.359863\pi$
$104$		0			0
$105$	−18.5718	+	10.8281i	−1.81242	+	1.05671i
$106$	−34.9222			−3.39195
$107$	−2.17303	−	3.76379i	−0.210075	−	0.363860i	0.741663	−	0.670773i	$-0.234037\pi$
$107$	−2.17303	−	3.76379i	−0.210075	−	0.363860i	−0.951738	+	0.306913i	$0.900704\pi$
$108$	8.32951	−	14.4271i	0.801507	−	1.38825i
$109$	3.92756	−	6.80274i	0.376192	−	0.651584i	−0.614312	−	0.789063i	$-0.710566\pi$
$109$	3.92756	−	6.80274i	0.376192	−	0.651584i	0.990505	+	0.137479i	$0.0438998\pi$
$110$	−3.40068	−	5.89016i	−0.324243	−	0.561605i
$111$	10.2703			0.974817
$112$	8.20573	+	4.69112i	0.775368	+	0.443269i
$113$	−0.189171			−0.0177957			−0.00889785	−	0.999960i	$-0.502832\pi$
$113$	−0.189171			−0.0177957			−0.00889785	+	0.999960i	$0.502832\pi$
$114$	12.9765	+	22.4760i	1.21536	+	2.10507i
$115$	−0.959218	+	1.66141i	−0.0894475	+	0.154928i
$116$	−2.57156	+	4.45407i	−0.238763	+	0.413550i
$117$		0			0
$118$	1.01591			0.0935220
$119$	0.00113670	+	0.267034i	0.000104201	+	0.0244790i
$120$	38.1398			3.48167
$121$	5.27342	+	9.13384i	0.479402	+	0.830349i
$122$	−1.87008	+	3.23907i	−0.169309	+	0.293252i
$123$	4.35277	−	7.53923i	0.392476	−	0.679789i
$124$	−14.2011	−	24.5970i	−1.27530	−	2.20888i
$125$	29.9634			2.68001
$126$	−0.0228675	−	5.37205i	−0.00203720	−	0.478580i
$127$	15.8811			1.40922			0.704609	−	0.709595i	$-0.251122\pi$
$127$	15.8811			1.40922			0.704609	+	0.709595i	$0.251122\pi$
$128$	10.0525	+	17.4115i	0.888526	+	1.53897i
$129$	−4.73147	+	8.19515i	−0.416583	+	0.721543i
$130$		0			0
$131$	−1.12327	−	1.94556i	−0.0981406	−	0.169984i	0.812774	−	0.582579i	$-0.197956\pi$
$131$	−1.12327	−	1.94556i	−0.0981406	−	0.169984i	−0.910915	+	0.412594i	$0.864623\pi$
$132$	5.17733			0.450629
$133$	−12.5042	−	7.14850i	−1.08425	−	0.619854i
$134$	−14.3290			−1.23784
$135$	8.80002	+	15.2421i	0.757385	+	1.31183i
$136$	0.236877	−	0.410284i	0.0203121	−	0.0351815i
$137$	−6.18122	+	10.7062i	−0.528097	+	0.914692i	0.471366	+	0.881938i	$0.343761\pi$
$137$	−6.18122	+	10.7062i	−0.528097	+	0.914692i	−0.999463	+	0.0327539i	$0.989572\pi$
$138$	−1.10196	−	1.90866i	−0.0938055	−	0.162476i
$139$	−13.6036			−1.15385			−0.576923	−	0.816798i	$-0.695747\pi$
$139$	−13.6036			−1.15385			−0.576923	+	0.816798i	$0.695747\pi$
$140$	−37.2554	+	21.7214i	−3.14866	+	1.83579i
$141$	−5.54873			−0.467288
$142$	12.2502	+	21.2180i	1.02801	+	1.78057i
$143$		0			0
$144$	−1.48967	+	2.58019i	−0.124139	+	0.215015i
$145$	−2.71682	−	4.70567i	−0.225620	−	0.390784i
$146$	−15.5754			−1.28903
$147$	6.95398	+	11.8113i	0.573555	+	0.974177i
$148$	20.6025			1.69351
$149$	5.87086	+	10.1686i	0.480960	+	0.833047i	0.999761	−	0.0218480i	$-0.00695498\pi$
$149$	5.87086	+	10.1686i	0.480960	+	0.833047i	−0.518802	+	0.854895i	$0.673622\pi$
$150$	−29.1295	+	50.4538i	−2.37842	+	4.11954i
$151$	5.81613	−	10.0738i	0.473310	−	0.819797i	−0.526223	−	0.850347i	$-0.676392\pi$
$151$	5.81613	−	10.0738i	0.473310	−	0.819797i	0.999533	+	0.0305493i	$0.00972564\pi$
$152$	12.7766	+	22.1297i	1.03632	+	1.79496i
$153$	−0.0841718			−0.00680489
$154$	−3.74611	+	2.18413i	−0.301870	+	0.176002i
$155$	30.0066			2.41018
$156$		0			0
$157$	−9.06738	+	15.7052i	−0.723656	+	1.25341i	0.235870	+	0.971785i	$0.424206\pi$
$157$	−9.06738	+	15.7052i	−0.723656	+	1.25341i	−0.959525	+	0.281623i	$0.909127\pi$
$158$	−0.350418	+	0.606942i	−0.0278778	+	0.0482857i
$159$	14.0425	+	24.3224i	1.11365	+	1.92889i
$160$	−2.86182			−0.226247
$161$	1.06186	+	0.607051i	0.0836860	+	0.0478423i
$162$	−26.3106			−2.06716
$163$	4.31886	+	7.48048i	0.338279	+	0.585916i	0.984109	−	0.177565i	$-0.0568220\pi$
$163$	4.31886	+	7.48048i	0.338279	+	0.585916i	−0.645830	+	0.763481i	$0.723489\pi$
$164$	8.73175	−	15.1238i	0.681835	−	1.18097i
$165$	−2.73489	+	4.73697i	−0.212911	+	0.368773i
$166$	−11.4831	−	19.8894i	−0.891263	−	1.54371i
$167$	5.12092			0.396269			0.198134	−	0.980175i	$-0.436512\pi$
$167$	5.12092			0.396269			0.198134	+	0.980175i	$0.436512\pi$
$168$	−0.103509	−	24.3165i	−0.00798590	−	1.87606i
$169$		0			0
$170$	0.509876	+	0.883132i	0.0391057	+	0.0677331i
$171$	2.27002	−	3.93178i	0.173592	−	0.300671i
$172$	−9.49143	+	16.4396i	−0.723715	+	1.25351i
$173$	−7.70252	−	13.3412i	−0.585612	−	1.01431i	−0.994799	−	0.101859i	$-0.967521\pi$
$173$	−7.70252	−	13.3412i	−0.585612	−	1.01431i	0.409187	−	0.912450i	$-0.365812\pi$
$174$	6.24225			0.473224
$175$	−0.137630	−	32.3322i	−0.0104038	−	2.44408i
$176$	2.40491			0.181277
$177$	−0.408506	−	0.707553i	−0.0307052	−	0.0531830i
$178$	−12.2432	+	21.2058i	−0.917664	+	1.58944i
$179$	−1.72550	+	2.98866i	−0.128970	+	0.223383i	−0.923278	−	0.384133i	$-0.874500\pi$
$179$	−1.72550	+	2.98866i	−0.128970	+	0.223383i	0.794308	+	0.607516i	$0.207834\pi$
$180$	−6.79668	−	11.7722i	−0.506595	−	0.877448i
$181$	−6.36457			−0.473074			−0.236537	−	0.971622i	$-0.576013\pi$
$181$	−6.36457			−0.473074			−0.236537	+	0.971622i	$0.576013\pi$
$182$		0			0
$183$	3.00790			0.222350
$184$	−1.08499	−	1.87926i	−0.0799865	−	0.138541i
$185$	−10.8831	+	18.8501i	−0.800144	+	1.38589i
$186$	−17.2360	+	29.8537i	−1.26381	+	2.18898i
$187$	0.0339715	+	0.0588404i	0.00248424	+	0.00430284i
$188$	−11.1309			−0.811802
$189$	9.69387	−	5.65192i	0.705126	−	0.411116i
$190$	−55.0031			−3.99034
$191$	11.3562	+	19.6694i	0.821702	+	1.42323i	0.904414	+	0.426656i	$0.140309\pi$
$191$	11.3562	+	19.6694i	0.821702	+	1.42323i	−0.0827115	+	0.996574i	$0.526358\pi$
$192$	8.63904	−	14.9633i	0.623469	−	1.07988i
$193$	12.4862	−	21.6268i	0.898778	−	1.55673i	0.0697197	−	0.997567i	$-0.477790\pi$
$193$	12.4862	−	21.6268i	0.898778	−	1.55673i	0.829058	−	0.559162i	$-0.188877\pi$
$194$	4.67826	+	8.10299i	0.335880	+	0.581760i
$195$		0			0
$196$	13.9498	+	23.6937i	0.996416	+	1.69240i
$197$	11.4085			0.812818			0.406409	−	0.913691i	$-0.366781\pi$
$197$	11.4085			0.812818			0.406409	+	0.913691i	$0.366781\pi$
$198$	−0.683421	−	1.18372i	−0.0485686	−	0.0841233i
$199$	10.6843	−	18.5058i	0.757390	−	1.31184i	−0.186787	−	0.982400i	$-0.559807\pi$
$199$	10.6843	−	18.5058i	0.757390	−	1.31184i	0.944177	−	0.329438i	$-0.106859\pi$
$200$	−28.6808	+	49.6766i	−2.02804	+	3.51267i
$201$	5.76182	+	9.97977i	0.406408	+	0.703919i
$202$	−0.207844			−0.0146239
$203$	−2.99278	+	1.74491i	−0.210052	+	0.122469i
$204$	−0.776255			−0.0543487
$205$	9.22498	+	15.9781i	0.644301	+	1.11596i
$206$	−14.0935	+	24.4106i	−0.981938	+	1.70077i
$207$	−0.192770	+	0.333887i	−0.0133984	+	0.0232068i
$208$		0			0
$209$	−3.66469			−0.253492
$210$	45.4400	+	25.9775i	3.13566	+	1.79262i
$211$	20.2000			1.39062			0.695312	−	0.718708i	$-0.255266\pi$
$211$	20.2000			1.39062			0.695312	+	0.718708i	$0.255266\pi$
$212$	28.1696	+	48.7912i	1.93470	+	3.35099i
$213$	9.85183	−	17.0639i	0.675036	−	1.16920i
$214$	−5.29073	+	9.16381i	−0.361667	+	0.626425i
$215$	−10.0276	−	17.3683i	−0.683875	−	1.18451i
$216$	−19.9077			−1.35455
$217$	−0.0814360	−	19.1310i	−0.00552823	−	1.29870i
$218$	−19.1251			−1.29531
$219$	6.26302	+	10.8479i	0.423215	+	0.733031i
$220$	−5.48625	+	9.50246i	−0.369883	+	0.640656i
$221$		0			0
$222$	−12.5027	−	21.6553i	−0.839128	−	1.45341i
$223$	11.2430			0.752884			0.376442	−	0.926440i	$-0.377147\pi$
$223$	11.2430			0.752884			0.376442	+	0.926440i	$0.377147\pi$
$224$	0.00776681	+	1.82459i	0.000518942	+	0.121910i
$225$	10.1914			0.679428
$226$	0.230290	+	0.398873i	0.0153186	+	0.0265327i
$227$	−5.31446	+	9.20491i	−0.352733	+	0.610951i	−0.986727	−	0.162386i	$-0.948081\pi$
$227$	−5.31446	+	9.20491i	−0.352733	+	0.610951i	0.633994	+	0.773338i	$0.281414\pi$
$228$	20.9347	−	36.2600i	1.38643	−	2.40138i
$229$	5.40693	+	9.36507i	0.357300	+	0.618861i	0.987509	−	0.157564i	$-0.0503641\pi$
$229$	5.40693	+	9.36507i	0.357300	+	0.618861i	−0.630209	+	0.776426i	$0.717031\pi$
$230$	4.67086			0.307988
$231$	3.02753	+	1.73081i	0.199197	+	0.113879i
$232$	6.14609			0.403511
$233$	−12.0362	−	20.8473i	−0.788519	−	1.36576i	−0.926874	−	0.375372i	$-0.877515\pi$
$233$	−12.0362	−	20.8473i	−0.788519	−	1.36576i	0.138355	−	0.990383i	$-0.455819\pi$
$234$		0			0
$235$	5.87981	−	10.1841i	0.383556	−	0.664339i
$236$	−0.819472	−	1.41937i	−0.0533431	−	0.0923929i
$237$	0.563625			0.0366114
$238$	0.561667	−	0.327474i	0.0364075	−	0.0212270i
$239$	8.54995			0.553050			0.276525	−	0.961007i	$-0.410817\pi$
$239$	8.54995			0.553050			0.276525	+	0.961007i	$0.410817\pi$
$240$	−14.5142	−	25.1393i	−0.936886	−	1.62273i
$241$	7.13666	−	12.3611i	0.459713	−	0.796246i	−0.539233	−	0.842157i	$-0.681286\pi$
$241$	7.13666	−	12.3611i	0.459713	−	0.796246i	0.998946	+	0.0459109i	$0.0146190\pi$
$242$	12.8393	−	22.2384i	0.825344	−	1.42954i
$243$	4.21790	+	7.30562i	0.270579	+	0.468656i
$244$	6.03391			0.386282
$245$	−29.0473	+	0.247298i	−1.85576	+	0.0157993i
$246$	−21.1956			−1.35138
$247$		0			0
$248$	−16.9705	+	29.3938i	−1.07763	+	1.86651i
$249$	−9.23494	+	15.9954i	−0.585240	+	1.01367i
$250$	−36.4764	−	63.1789i	−2.30697	−	3.99579i
$251$	−13.0948			−0.826537			−0.413269	−	0.910609i	$-0.635613\pi$
$251$	−13.0948			−0.826537			−0.413269	+	0.910609i	$0.635613\pi$
$252$	−7.48706	+	4.36525i	−0.471640	+	0.274985i
$253$	0.311205			0.0195653
$254$	−19.3330	−	33.4858i	−1.21306	−	2.10109i
$255$	0.410052	−	0.710231i	0.0256784	−	0.0444764i
$256$	15.6510	−	27.1083i	0.978188	−	1.69427i
$257$	−0.782994	−	1.35619i	−0.0488418	−	0.0845965i	0.840571	−	0.541702i	$-0.182220\pi$
$257$	−0.782994	−	1.35619i	−0.0488418	−	0.0845965i	−0.889413	+	0.457105i	$0.848886\pi$
$258$	23.0397			1.43439
$259$	12.0477	+	6.88751i	0.748605	+	0.427969i
$260$		0			0
$261$	−0.545987	−	0.945678i	−0.0337958	−	0.0585360i
$262$	−2.73485	+	4.73691i	−0.168960	+	0.292647i
$263$	10.7552	−	18.6286i	0.663194	−	1.14869i	−0.316577	−	0.948567i	$-0.602534\pi$
$263$	10.7552	−	18.6286i	0.663194	−	1.14869i	0.979772	−	0.200119i	$-0.0641330\pi$
$264$	−3.09349	−	5.35808i	−0.190391	−	0.329767i
$265$	−59.5216			−3.65639
$266$	0.149275	+	35.0678i	0.00915264	+	2.15015i
$267$	19.6923			1.20515
$268$	11.5583	+	20.0196i	0.706038	+	1.22289i
$269$	5.34864	−	9.26412i	0.326113	−	0.564843i	−0.655624	−	0.755087i	$-0.727595\pi$
$269$	5.34864	−	9.26412i	0.326113	−	0.564843i	0.981737	+	0.190244i	$0.0609278\pi$
$270$	21.4256	−	37.1103i	1.30392	−	2.25846i
$271$	−7.29005	−	12.6267i	−0.442839	−	0.767020i	0.555060	−	0.831810i	$-0.312695\pi$
$271$	−7.29005	−	12.6267i	−0.442839	−	0.767020i	−0.997899	+	0.0647907i	$0.979362\pi$
$272$	−0.360576			−0.0218631
$273$		0			0
$274$	30.0992			1.81836
$275$	−4.11323	−	7.12432i	−0.248037	−	0.429613i
$276$	−1.77778	+	3.07920i	−0.107009	+	0.185346i
$277$	7.56348	−	13.1003i	0.454445	−	0.787123i	−0.544211	−	0.838949i	$-0.683171\pi$
$277$	7.56348	−	13.1003i	0.454445	−	0.787123i	0.998656	+	0.0518260i	$0.0165041\pi$
$278$	16.5606	+	28.6837i	0.993237	+	1.72034i
$279$	6.03029			0.361024
$280$	44.7401	+	25.5774i	2.67373	+	1.52854i
$281$	−15.4331			−0.920660			−0.460330	−	0.887748i	$-0.652269\pi$
$281$	−15.4331			−0.920660			−0.460330	+	0.887748i	$0.652269\pi$
$282$	6.75482	+	11.6997i	0.402244	+	0.696706i
$283$	−8.94260	+	15.4890i	−0.531582	+	0.920727i	0.467738	+	0.883867i	$0.345069\pi$
$283$	−8.94260	+	15.4890i	−0.531582	+	0.920727i	−0.999320	+	0.0368603i	$0.988264\pi$
$284$	19.7630	−	34.2305i	1.17272	−	2.03120i
$285$	22.1172	+	38.3082i	1.31011	+	2.26918i
$286$		0			0
$287$	10.1620	−	5.92486i	0.599844	−	0.349733i
$288$	−0.575128			−0.0338897
$289$	8.49491	+	14.7136i	0.499700	+	0.865506i
$290$	−6.61471	+	11.4570i	−0.388429	+	0.672779i
$291$	3.76234	−	6.51657i	0.220552	−	0.382008i
$292$	12.5637	+	21.7610i	0.735237	+	1.27347i
$293$	33.9848			1.98541			0.992707	−	0.120549i	$-0.0384654\pi$
$293$	33.9848			1.98541			0.992707	+	0.120549i	$0.0384654\pi$
$294$	16.4390	−	29.0413i	0.958739	−	1.69372i
$295$	1.73152			0.100813
$296$	−12.3101	−	21.3218i	−0.715512	−	1.23930i
$297$	1.42752	−	2.47254i	0.0828334	−	0.143472i
$298$	14.2939	−	24.7578i	0.828026	−	1.43418i
$299$		0			0
$300$	93.9880			5.42640
$301$	−11.0461	+	6.44033i	−0.636688	+	0.371214i
$302$	−28.3214			−1.62971
$303$	0.0835761	+	0.144758i	0.00480132	+	0.00831614i
$304$	9.72432	−	16.8430i	0.557728	−	0.966013i
$305$	−3.18737	+	5.52069i	−0.182508	+	0.316114i
$306$	0.102468	+	0.177479i	0.00585768	+	0.0101458i
$307$	−7.14276			−0.407659			−0.203829	−	0.979006i	$-0.565339\pi$
$307$	−7.14276			−0.407659			−0.203829	+	0.979006i	$0.565339\pi$
$308$	6.07329	+	3.47203i	0.346058	+	0.197837i
$309$	22.6684			1.28956
$310$	−36.5289	−	63.2699i	−2.07470	−	3.59349i
$311$	7.40837	−	12.8317i	0.420090	−	0.727617i	−0.575858	−	0.817550i	$-0.695332\pi$
$311$	7.40837	−	12.8317i	0.420090	−	0.727617i	0.995948	+	0.0899328i	$0.0286652\pi$
$312$		0			0
$313$	16.7457	+	29.0044i	0.946523	+	1.63943i	0.752673	+	0.658394i	$0.228764\pi$
$313$	16.7457	+	29.0044i	0.946523	+	1.63943i	0.193849	+	0.981031i	$0.437903\pi$
$314$	44.1531			2.49171
$315$	−0.0389755	−	9.15615i	−0.00219602	−	0.515891i
$316$	1.13064			0.0636037
$317$	−4.38936	−	7.60260i	−0.246531	−	0.427004i	0.716030	−	0.698070i	$-0.245957\pi$
$317$	−4.38936	−	7.60260i	−0.246531	−	0.427004i	−0.962561	+	0.271065i	$0.912624\pi$
$318$	34.1897	−	59.2183i	1.91726	−	3.32080i
$319$	−0.440718	+	0.763346i	−0.0246755	+	0.0427392i
$320$	18.3090	+	31.7121i	1.02350	+	1.77276i
$321$	8.50979			0.474970
$322$	−0.0126764	−	2.97796i	−0.000706430	−	0.165955i
$323$	0.549460			0.0305728
$324$	21.2231	+	36.7596i	1.17906	+	2.04220i
$325$		0			0
$326$	10.5152	−	18.2129i	0.582385	−	1.00872i
$327$	7.69037	+	13.3201i	0.425278	+	0.736604i
$328$	−20.8691			−1.15230
$329$	−6.50896	−	3.72110i	−0.358851	−	0.205151i
$330$	13.3174			0.733100
$331$	−3.24426	−	5.61922i	−0.178320	−	0.308860i	0.762985	−	0.646416i	$-0.223733\pi$
$331$	−3.24426	−	5.61922i	−0.178320	−	0.308860i	−0.941305	+	0.337556i	$0.890400\pi$
$332$	−18.5255	+	32.0871i	−1.01672	+	1.76101i
$333$	−2.18714	+	3.78823i	−0.119854	+	0.207594i
$334$	−6.23402	−	10.7976i	−0.341110	−	0.590820i
$335$	−24.4225			−1.33434
$336$	−15.9884	+	9.32190i	−0.872241	+	0.508551i
$337$	−25.4871			−1.38837			−0.694187	−	0.719795i	$-0.744236\pi$
$337$	−25.4871			−1.38837			−0.694187	+	0.719795i	$0.744236\pi$
$338$		0			0
$339$	0.185203	−	0.320781i	0.0100589	−	0.0174224i
$340$	0.822572	−	1.42474i	0.0446102	−	0.0772672i
$341$	−2.43381	−	4.21548i	−0.131798	−	0.228281i
$342$	−11.0537			−0.597717
$343$	0.236500	+	18.5187i	0.0127698	+	0.999918i
$344$	22.6848			1.22308
$345$	−1.87820	−	3.25313i	−0.101119	−	0.175143i
$346$	−18.7535	+	32.4820i	−1.00820	+	1.74625i
$347$	7.10172	−	12.3005i	0.381240	−	0.660327i	−0.610000	−	0.792402i	$-0.708830\pi$
$347$	7.10172	−	12.3005i	0.381240	−	0.660327i	0.991240	+	0.132074i	$0.0421638\pi$
$348$	−5.03524	−	8.72129i	−0.269917	−	0.467510i
$349$	25.7839			1.38018			0.690089	−	0.723725i	$-0.257571\pi$
$349$	25.7839			1.38018			0.690089	+	0.723725i	$0.257571\pi$
$350$	−68.0059	+	39.6502i	−3.63507	+	2.11939i
$351$		0			0
$352$	0.232120	+	0.402044i	0.0123720	+	0.0214290i
$353$	−7.44269	+	12.8911i	−0.396134	+	0.686125i	−0.993245	−	0.116034i	$-0.962982\pi$
$353$	−7.44269	+	12.8911i	−0.396134	+	0.686125i	0.597111	+	0.802159i	$0.296315\pi$
$354$	−0.994600	+	1.72270i	−0.0528624	+	0.0915604i
$355$	20.8793	+	36.1640i	1.10816	+	1.91939i
$356$	39.5032			2.09367
$357$	−0.453928	−	0.259506i	−0.0240244	−	0.0137345i
$358$	8.40225			0.444073
$359$	−1.21600	−	2.10617i	−0.0641780	−	0.111160i	0.832151	−	0.554549i	$-0.187109\pi$
$359$	−1.21600	−	2.10617i	−0.0641780	−	0.111160i	−0.896329	+	0.443389i	$0.853776\pi$
$360$	−8.12213	+	14.0679i	−0.428074	+	0.741445i
$361$	−5.31829	+	9.21154i	−0.279910	+	0.484818i
$362$	7.74799	+	13.4199i	0.407225	+	0.705334i
$363$	−20.6512			−1.08391
$364$		0			0
$365$	−26.5468			−1.38953
$366$	−3.66171	−	6.34226i	−0.191400	−	0.331515i
$367$	7.99441	−	13.8467i	0.417305	−	0.722793i	−0.578363	−	0.815780i	$-0.696308\pi$
$367$	7.99441	−	13.8467i	0.417305	−	0.722793i	0.995667	+	0.0929867i	$0.0296414\pi$
$368$	−0.825789	+	1.43031i	−0.0430472	+	0.0745600i
$369$	1.85390	+	3.21106i	0.0965104	+	0.167161i
$370$	52.9949			2.75507
$371$	0.161538	+	37.9487i	0.00838664	+	1.97020i
$372$	55.6129			2.88340
$373$	3.51708	+	6.09176i	0.182107	+	0.315419i	0.942598	−	0.333930i	$-0.108375\pi$
$373$	3.51708	+	6.09176i	0.182107	+	0.315419i	−0.760491	+	0.649349i	$0.775041\pi$
$374$	0.0827113	−	0.143260i	0.00427690	−	0.00740781i
$375$	−29.3350	+	50.8096i	−1.51485	+	2.62380i
$376$	6.65077	+	11.5195i	0.342987	+	0.594071i
$377$		0			0
$378$	−23.7182	−	13.5594i	−1.21993	−	0.697422i
$379$	23.4139			1.20269			0.601346	−	0.798988i	$-0.294631\pi$
$379$	23.4139			1.20269			0.601346	+	0.798988i	$0.294631\pi$
$380$	44.3676	+	76.8470i	2.27601	+	3.94217i
$381$	−15.5480	+	26.9299i	−0.796547	+	1.37966i
$382$	27.6491	−	47.8897i	1.41465	−	2.45025i
$383$	−17.9715	−	31.1275i	−0.918299	−	1.59054i	−0.801998	−	0.597326i	$-0.796230\pi$
$383$	−17.9715	−	31.1275i	−0.918299	−	1.59054i	−0.116301	−	0.993214i	$-0.537104\pi$
$384$	−39.3667			−2.00892
$385$	−6.38489	+	3.72265i	−0.325404	+	0.189724i
$386$	−60.8010			−3.09469
$387$	−2.01520	−	3.49042i	−0.102438	−	0.177428i
$388$	7.54733	−	13.0724i	0.383158	−	0.663649i
$389$	7.02802	−	12.1729i	0.356335	−	0.617190i	−0.631011	−	0.775774i	$-0.717360\pi$
$389$	7.02802	−	12.1729i	0.356335	−	0.617190i	0.987345	+	0.158584i	$0.0506929\pi$
$390$		0			0
$391$	−0.0466601			−0.00235970
$392$	16.1857	−	28.5939i	0.817503	−	1.44421i
$393$	4.39884			0.221892
$394$	−13.8882	−	24.0551i	−0.699679	−	1.21188i
$395$	−0.597255	+	1.03448i	−0.0300512	+	0.0520501i
$396$	−1.10255	+	1.90967i	−0.0554051	+	0.0959644i
$397$	−1.58944	−	2.75299i	−0.0797716	−	0.138168i	0.823380	−	0.567491i	$-0.192086\pi$
$397$	−1.58944	−	2.75299i	−0.0797716	−	0.138168i	−0.903151	+	0.429322i	$0.858752\pi$
$398$	−52.0267			−2.60786
$399$	24.3638	−	14.2051i	1.21971	−	0.711143i
$400$	43.6581			2.18291
$401$	10.8446	+	18.7834i	0.541553	+	0.937997i	0.998815	+	0.0486649i	$0.0154966\pi$
$401$	10.8446	+	18.7834i	0.541553	+	0.937997i	−0.457263	+	0.889332i	$0.651170\pi$
$402$	14.0285	−	24.2980i	0.699676	−	1.21187i
$403$		0			0
$404$	0.167655	+	0.290388i	0.00834117	+	0.0144473i
$405$	−44.8439			−2.22831
$406$	7.32250	+	4.18619i	0.363409	+	0.207757i
$407$	3.53089			0.175020
$408$	0.463818	+	0.803356i	0.0229624	+	0.0397720i
$409$	−12.7321	+	22.0526i	−0.629562	+	1.09043i	0.358078	+	0.933692i	$0.383432\pi$
$409$	−12.7321	+	22.0526i	−0.629562	+	1.09043i	−0.987640	+	0.156741i	$0.949901\pi$
$410$	22.4603	−	38.9024i	1.10924	−	1.92125i
$411$	−12.1031	−	20.9633i	−0.597004	−	1.03404i
$412$	45.4733			2.24031
$413$	−0.00469924	−	1.10395i	−0.000231235	−	0.0543219i
$414$	0.938683			0.0461337
$415$	−19.5719	−	33.8996i	−0.960748	−	1.66406i
$416$		0			0
$417$	13.3183	−	23.0680i	0.652200	−	1.12964i
$418$	4.46126	+	7.72712i	0.218207	+	0.377946i
$419$	7.01689			0.342798			0.171399	−	0.985202i	$-0.445171\pi$
$419$	7.01689			0.342798			0.171399	+	0.985202i	$0.445171\pi$
$420$	−0.359442	−	84.4405i	−0.0175390	−	4.12028i
$421$	1.00282			0.0488744			0.0244372	−	0.999701i	$-0.492221\pi$
$421$	1.00282			0.0488744			0.0244372	+	0.999701i	$0.492221\pi$
$422$	−24.5907	−	42.5923i	−1.19706	−	2.07336i
$423$	1.18164	−	2.04666i	0.0574533	−	0.0995120i
$424$	33.6630	−	58.3061i	1.63482	−	2.83159i
$425$	0.616711	+	1.06817i	0.0299149	+	0.0518141i
$426$	−47.9730			−2.32430
$427$	3.52843	+	2.01716i	0.170753	+	0.0976174i
$428$	17.0708			0.825149
$429$		0			0
$430$	−24.4144	+	42.2870i	−1.17737	+	2.03926i
$431$	13.1141	−	22.7142i	0.631682	−	1.09411i	−0.355526	−	0.934666i	$-0.615698\pi$
$431$	13.1141	−	22.7142i	0.631682	−	1.09411i	0.987208	−	0.159439i	$-0.0509685\pi$
$432$	7.57592	+	13.1219i	0.364497	+	0.631327i
$433$	14.8546			0.713864			0.356932	−	0.934130i	$-0.383823\pi$
$433$	14.8546			0.713864			0.356932	+	0.934130i	$0.383823\pi$
$434$	−40.2393	+	23.4611i	−1.93155	+	1.12617i
$435$	10.6393			0.510117
$436$	15.4270	+	26.7204i	0.738821	+	1.27968i
$437$	1.25837	−	2.17956i	0.0601960	−	0.104262i
$438$	15.2487	−	26.4116i	0.728612	−	1.26199i
$439$	−7.33704	−	12.7081i	−0.350178	−	0.606525i	0.636103	−	0.771604i	$-0.280545\pi$
$439$	−7.33704	−	12.7081i	−0.350178	−	0.606525i	−0.986280	+	0.165079i	$0.947212\pi$
$440$	13.1123			0.625103
$441$	−5.83750	+	0.0496985i	−0.277976	+	0.00236659i
$442$		0			0
$443$	2.78344	+	4.82106i	0.132245	+	0.229056i	0.924542	−	0.381081i	$-0.124448\pi$
$443$	2.78344	+	4.82106i	0.132245	+	0.229056i	−0.792296	+	0.610136i	$0.791115\pi$
$444$	−20.1704	+	34.9361i	−0.957243	+	1.65799i
$445$	−20.8673	+	36.1433i	−0.989206	+	1.71335i
$446$	−13.6868	−	23.7062i	−0.648087	−	1.12252i
$447$	−22.9909			−1.08743
$448$	20.1687	−	11.7592i	0.952883	−	0.555569i
$449$	−5.99261			−0.282809			−0.141404	−	0.989952i	$-0.545162\pi$
$449$	−5.99261			−0.282809			−0.141404	+	0.989952i	$0.545162\pi$
$450$	−12.4067	−	21.4890i	−0.584855	−	1.01300i
$451$	1.49646	−	2.59195i	0.0704656	−	0.122050i
$452$	0.371521	−	0.643493i	0.0174749	−	0.0302674i
$453$	11.3883	+	19.7251i	0.535068	+	0.926765i
$454$	25.8785			1.21454
$455$		0			0
$456$	−50.0345			−2.34308
$457$	−9.09992	−	15.7615i	−0.425676	−	0.737293i	0.570807	−	0.821084i	$-0.306630\pi$
$457$	−9.09992	−	15.7615i	−0.425676	−	0.737293i	−0.996483	+	0.0837914i	$0.973297\pi$
$458$	13.1644	−	22.8014i	0.615131	−	1.06544i
$459$	−0.214034	+	0.370717i	−0.00999024	+	0.0173036i
$460$	−3.76770	−	6.52585i	−0.175670	−	0.304269i
$461$	−6.54384			−0.304777			−0.152389	−	0.988321i	$-0.548697\pi$
$461$	−6.54384			−0.304777			−0.152389	+	0.988321i	$0.548697\pi$
$462$	−0.0361427	−	8.49067i	−0.00168151	−	0.395022i
$463$	35.9986			1.67300			0.836499	−	0.547968i	$-0.184599\pi$
$463$	35.9986			1.67300			0.836499	+	0.547968i	$0.184599\pi$
$464$	−2.33891	−	4.05110i	−0.108581	−	0.188068i
$465$	−29.3772	+	50.8828i	−1.36233	+	2.35963i
$466$	−29.3049	+	50.7576i	−1.35752	+	2.35130i
$467$	−3.29684	−	5.71030i	−0.152560	−	0.264241i	0.779608	−	0.626268i	$-0.215418\pi$
$467$	−3.29684	−	5.71030i	−0.152560	−	0.264241i	−0.932168	+	0.362027i	$0.882085\pi$
$468$		0			0
$469$	0.0662811	+	15.5708i	0.00306057	+	0.718993i
$470$	−28.6314			−1.32067
$471$	−17.7544	−	30.7515i	−0.818079	−	1.41695i
$472$	−0.979279	+	1.69616i	−0.0450750	+	0.0780721i
$473$	−1.62666	+	2.81745i	−0.0747937	+	0.129547i
$474$	−0.686136	−	1.18842i	−0.0315153	−	0.0545861i
$475$	−66.5279			−3.05251
$476$	−0.910589	−	0.520574i	−0.0417368	−	0.0238604i
$477$	−11.9618			−0.547693
$478$	−10.4084	−	18.0279i	−0.476069	−	0.824575i
$479$	−13.9620	+	24.1828i	−0.637939	+	1.10494i	0.347945	+	0.937515i	$0.386879\pi$
$479$	−13.9620	+	24.1828i	−0.637939	+	1.10494i	−0.985884	+	0.167428i	$0.946454\pi$
$480$	2.80180	−	4.85285i	0.127884	−	0.221501i
$481$		0			0
$482$	−34.7516			−1.58289
$483$	−2.06897	+	1.20629i	−0.0941415	+	0.0548883i
$484$	−41.4268			−1.88304
$485$	7.97366	+	13.8108i	0.362065	+	0.627115i
$486$	10.2694	−	17.7872i	0.465831	−	0.806843i
$487$	−8.32640	+	14.4218i	−0.377305	+	0.653512i	−0.990669	−	0.136289i	$-0.956483\pi$
$487$	−8.32640	+	14.4218i	−0.377305	+	0.653512i	0.613364	+	0.789800i	$0.289816\pi$
$488$	−3.60530	−	6.24456i	−0.163204	−	0.282678i
$489$	−16.9131			−0.764835
$490$	35.8825	+	60.9461i	1.62101	+	2.75327i
$491$	22.2229			1.00291			0.501454	−	0.865184i	$-0.332799\pi$
$491$	22.2229			1.00291			0.501454	+	0.865184i	$0.332799\pi$
$492$	17.0972	+	29.6132i	0.770802	+	1.33507i
$493$	0.0660784	−	0.114451i	0.00297602	−	0.00515462i
$494$		0			0
$495$	−1.16483	−	2.01754i	−0.0523551	−	0.0906816i
$496$	25.8326			1.15992
$497$	23.0001	−	13.4100i	1.03170	−	0.601520i
$498$	44.9691			2.01511
$499$	−11.9578	−	20.7115i	−0.535303	−	0.927172i	−0.999149	−	0.0412563i	$-0.986864\pi$
$499$	−11.9578	−	20.7115i	−0.535303	−	0.927172i	0.463845	−	0.885916i	$-0.346469\pi$
$500$	−58.8465	+	101.925i	−2.63170	+	4.55823i
$501$	−5.01351	+	8.68365i	−0.223987	+	0.387957i
$502$	15.9411	+	27.6109i	0.711488	+	1.23233i
$503$	−17.5269			−0.781487			−0.390744	−	0.920500i	$-0.627782\pi$
$503$	−17.5269			−0.781487			−0.390744	+	0.920500i	$0.627782\pi$
$504$	8.99121	+	5.14017i	0.400500	+	0.228962i
$505$	−0.354251			−0.0157640
$506$	−0.378850	−	0.656187i	−0.0168419	−	0.0291711i
$507$		0			0
$508$	−31.1896	+	54.0219i	−1.38381	+	2.39683i
$509$	10.2866	+	17.8169i	0.455944	+	0.789719i	0.998742	−	0.0501449i	$-0.0159683\pi$
$509$	10.2866	+	17.8169i	0.455944	+	0.789719i	−0.542798	+	0.839863i	$0.682635\pi$
$510$	−1.99673			−0.0884166
$511$	0.0720465	+	16.9252i	0.00318715	+	0.748728i
$512$	−36.0017			−1.59107
$513$	−11.5445	−	19.9956i	−0.509701	−	0.882828i
$514$	−1.90638	+	3.30194i	−0.0840866	+	0.145642i
$515$	−24.0210	+	41.6056i	−1.05849	+	1.83336i
$516$	−18.5847	−	32.1896i	−0.818146	−	1.41707i
$517$	−1.90763			−0.0838973
$518$	−0.143825	−	33.7875i	−0.00631930	−	1.48454i
$519$	30.1638			1.32404
$520$		0			0
$521$	19.3686	−	33.5474i	0.848555	−	1.46974i	−0.0339436	−	0.999424i	$-0.510807\pi$
$521$	19.3686	−	33.5474i	0.848555	−	1.46974i	0.882498	−	0.470316i	$-0.155860\pi$
$522$	−1.32933	+	2.30247i	−0.0581831	+	0.100776i
$523$	−7.79404	−	13.4997i	−0.340810	−	0.590300i	0.643774	−	0.765216i	$-0.277368\pi$
$523$	−7.79404	−	13.4997i	−0.340810	−	0.590300i	−0.984583	+	0.174916i	$0.944034\pi$
$524$	8.82416			0.385485
$525$	54.9611	+	31.4206i	2.39870	+	1.37131i
$526$	−52.3719			−2.28352
$527$	0.364909	+	0.632041i	0.0158957	+	0.0275322i
$528$	−2.35447	+	4.07805i	−0.102465	+	0.177474i
$529$	11.3931	−	19.7335i	0.495354	−	0.857978i
$530$	72.4594	+	125.503i	3.14744	+	5.45152i
$531$	0.347976			0.0151009
$532$	48.8742	−	28.4956i	2.11897	−	1.23544i
$533$		0			0
$534$	−23.9727	−	41.5220i	−1.03740	−	1.79683i
$535$	−9.01755	+	15.6189i	−0.389863	+	0.675262i
$536$	13.8124	−	23.9237i	0.596603	−	1.03335i
$537$	−3.37862	−	5.85194i	−0.145798	−	0.252530i
$538$	−26.0450			−1.12288
$539$	2.39074	+	4.06066i	0.102977	+	0.174905i
$540$	−69.1309			−2.97492
$541$	3.65880	+	6.33722i	0.157304	+	0.272459i	0.933896	−	0.357546i	$-0.116386\pi$
$541$	3.65880	+	6.33722i	0.157304	+	0.272459i	−0.776592	+	0.630004i	$0.783053\pi$
$542$	−17.7493	+	30.7426i	−0.762396	+	1.32051i
$543$	6.23107	−	10.7925i	0.267401	−	0.463152i
$544$	−0.0348026	−	0.0602798i	−0.00149215	−	0.00258448i
$545$	−32.5969			−1.39630
$546$		0			0
$547$	35.8280			1.53189			0.765946	−	0.642904i	$-0.222271\pi$
$547$	35.8280			1.53189			0.765946	+	0.642904i	$0.222271\pi$
$548$	−24.2791	−	42.0527i	−1.03715	−	1.79640i
$549$	−0.640553	+	1.10947i	−0.0273381	+	0.0473510i
$550$	−10.0146	+	17.3458i	−0.427023	+	0.739626i
$551$	3.56411	+	6.17323i	0.151836	+	0.262988i
$552$	4.24893			0.180846
$553$	0.661163	+	0.377979i	0.0281155	+	0.0160733i
$554$	−36.8300			−1.56476
$555$	−21.3097	−	36.9095i	−0.904547	−	1.56672i
$556$	26.7168	−	46.2748i	1.13304	−	1.96249i
$557$	12.5345	−	21.7104i	0.531105	−	0.919901i	−0.468236	−	0.883604i	$-0.655110\pi$
$557$	12.5345	−	21.7104i	0.531105	−	0.919901i	0.999341	−	0.0362976i	$-0.0115564\pi$
$558$	−7.34105	−	12.7151i	−0.310771	−	0.538272i
$559$		0			0
$560$	−0.166964	−	39.2232i	−0.00705550	−	1.65748i
$561$	−0.133036			−0.00561678
$562$	18.7877	+	32.5412i	0.792509	+	1.37267i
$563$	−16.9858	+	29.4203i	−0.715866	+	1.23992i	0.246758	+	0.969077i	$0.420635\pi$
$563$	−16.9858	+	29.4203i	−0.715866	+	1.23992i	−0.962624	+	0.270840i	$0.912699\pi$
$564$	10.8974	−	18.8748i	0.458863	−	0.794774i
$565$	0.392507	+	0.679842i	0.0165129	+	0.0286012i
$566$	43.5455			1.83036
$567$	0.121704	+	28.5908i	0.00511108	+	1.20070i
$568$	−47.2340			−1.98189
$569$	−4.87346	−	8.44108i	−0.204306	−	0.353869i	0.745605	−	0.666388i	$-0.232160\pi$
$569$	−4.87346	−	8.44108i	−0.204306	−	0.353869i	−0.949911	+	0.312519i	$0.898827\pi$
$570$	53.8494	−	93.2699i	2.25550	−	3.90665i
$571$	−8.54868	+	14.8068i	−0.357751	+	0.619643i	−0.987585	−	0.157087i	$-0.949790\pi$
$571$	−8.54868	+	14.8068i	−0.357751	+	0.619643i	0.629834	+	0.776730i	$0.283123\pi$
$572$		0			0
$573$	−44.4718			−1.85784
$574$	−24.8636	−	14.2142i	−1.03779	−	0.593291i
$575$	5.64955			0.235602
$576$	3.67948	+	6.37305i	0.153312	+	0.265544i
$577$	11.9253	−	20.6553i	0.496458	−	0.859890i	−0.503534	−	0.863976i	$-0.667967\pi$
$577$	11.9253	−	20.6553i	0.496458	−	0.859890i	0.999992	+	0.00408534i	$0.00130041\pi$
$578$	20.6828	−	35.8236i	0.860290	−	1.49007i
$579$	24.4486	+	42.3463i	1.01605	+	1.75985i
$580$	21.3427			0.886208
$581$	−21.5599	+	12.5703i	−0.894456	+	0.521504i
$582$	−18.3205			−0.759411
$583$	4.82775	+	8.36191i	0.199945	+	0.346315i
$584$	15.0138	−	26.0047i	0.621277	−	1.07608i
$585$		0			0
$586$	−41.3719	−	71.6582i	−1.70906	−	2.96017i
$587$	−32.5384			−1.34300			−0.671502	−	0.741003i	$-0.734350\pi$
$587$	−32.5384			−1.34300			−0.671502	+	0.741003i	$0.734350\pi$
$588$	−53.8350	+	0.458333i	−2.22012	+	0.0189013i
$589$	−39.3647			−1.62199
$590$	−2.10789	−	3.65097i	−0.0867805	−	0.150308i
$591$	−11.1692	+	19.3455i	−0.459438	+	0.795770i
$592$	−9.36928	+	16.2281i	−0.385075	+	0.666969i
$593$	−15.7190	−	27.2261i	−0.645501	−	1.11804i	−0.984186	−	0.177140i	$-0.943315\pi$
$593$	−15.7190	−	27.2261i	−0.645501	−	1.11804i	0.338685	−	0.940900i	$-0.390018\pi$
$594$	−6.95126			−0.285214
$595$	0.957309	−	0.558149i	0.0392458	−	0.0228819i
$596$	−46.1202			−1.88916
$597$	20.9204	+	36.2352i	0.856215	+	1.48301i
$598$		0			0
$599$	−17.3430	+	30.0389i	−0.708615	+	1.22736i	0.256756	+	0.966476i	$0.417346\pi$
$599$	−17.3430	+	30.0389i	−0.708615	+	1.22736i	−0.965371	+	0.260881i	$0.915987\pi$
$600$	−56.1584	−	97.2693i	−2.29266	−	3.97100i
$601$	10.4187			0.424986			0.212493	−	0.977163i	$-0.431842\pi$
$601$	10.4187			0.424986			0.212493	+	0.977163i	$0.431842\pi$
$602$	27.0268	+	15.4509i	1.10153	+	0.629732i
$603$	−4.90808			−0.199872
$604$	22.8451	+	39.5689i	0.929555	+	1.61004i
$605$	21.8834	−	37.9032i	0.889689	−	1.54099i
$606$	0.203485	−	0.352446i	0.00826601	−	0.0143171i
$607$	−7.18978	−	12.4531i	−0.291824	−	0.505454i	0.682417	−	0.730963i	$-0.260929\pi$
$607$	−7.18978	−	12.4531i	−0.291824	−	0.505454i	−0.974241	+	0.225509i	$0.927596\pi$
$608$	3.75434			0.152259
$609$	−0.0288745	−	6.78323i	−0.00117005	−	0.274870i
$610$	15.5208			0.628417
$611$		0			0
$612$	0.165309	−	0.286323i	0.00668221	−	0.0115739i
$613$	−11.6671	+	20.2080i	−0.471228	+	0.816192i	−0.999458	−	0.0329099i	$-0.989523\pi$
$613$	−11.6671	+	20.2080i	−0.471228	+	0.816192i	0.528230	+	0.849101i	$0.322856\pi$
$614$	8.69533	+	15.0608i	0.350915	+	0.607802i
$615$	−36.1260			−1.45674
$616$	−0.0355859	−	8.35988i	−0.00143380	−	0.336829i
$617$	28.2233			1.13623			0.568115	−	0.822949i	$-0.307673\pi$
$617$	28.2233			1.13623			0.568115	+	0.822949i	$0.307673\pi$
$618$	−27.5957	−	47.7972i	−1.11006	−	1.92268i
$619$	−15.1449	+	26.2317i	−0.608725	+	1.05434i	0.382726	+	0.923862i	$0.374985\pi$
$619$	−15.1449	+	26.2317i	−0.608725	+	1.05434i	−0.991451	+	0.130480i	$0.958348\pi$
$620$	−58.9312	+	102.072i	−2.36673	+	4.09930i
$621$	0.980357	+	1.69803i	0.0393404	+	0.0681395i
$622$	−36.0747			−1.44646
$623$	23.1002	+	13.2061i	0.925489	+	0.529091i
$624$		0			0
$625$	−31.6193	−	54.7662i	−1.26477	−	2.19065i
$626$	40.7712	−	70.6177i	1.62954	−	2.82245i
$627$	3.58782	−	6.21429i	0.143284	−	0.248175i
$628$	−35.6156	−	61.6881i	−1.42122	−	2.46162i
$629$	−0.529398			−0.0211085
$630$	−19.2586	+	11.2285i	−0.767282	+	0.447356i
$631$	−25.3506			−1.00919			−0.504596	−	0.863355i	$-0.668359\pi$
$631$	−25.3506			−1.00919			−0.504596	+	0.863355i	$0.668359\pi$
$632$	−0.675567	−	1.17012i	−0.0268726	−	0.0465447i
$633$	−19.7763	+	34.2535i	−0.786036	+	1.36145i
$634$	−10.6869	+	18.5102i	−0.424431	+	0.735135i
$635$	−32.9514	−	57.0734i	−1.30764	−	2.26489i
$636$	−110.315			−4.37427
$637$		0			0
$638$	2.14605			0.0849631
$639$	4.19602	+	7.26773i	0.165992	+	0.287507i
$640$	41.7156	−	72.2535i	1.64895	−	2.85607i
$641$	5.13404	−	8.89242i	0.202782	−	0.351229i	−0.746642	−	0.665227i	$-0.768335\pi$
$641$	5.13404	−	8.89242i	0.202782	−	0.351229i	0.949424	+	0.313997i	$0.101668\pi$
$642$	−10.3595	−	17.9432i	−0.408857	−	0.708161i
$643$	−3.80764			−0.150159			−0.0750793	−	0.997178i	$-0.523921\pi$
$643$	−3.80764			−0.150159			−0.0750793	+	0.997178i	$0.523921\pi$
$644$	−4.15040	+	2.41985i	−0.163549	+	0.0953554i
$645$	39.2690			1.54621
$646$	−0.668892	−	1.15855i	−0.0263172	−	0.0455827i
$647$	13.8932	−	24.0637i	0.546198	−	0.946042i	−0.452333	−	0.891849i	$-0.649408\pi$
$647$	13.8932	−	24.0637i	0.546198	−	0.946042i	0.998530	−	0.0541928i	$-0.0172586\pi$
$648$	25.3619	−	43.9282i	0.996311	−	1.72566i
$649$	−0.140442	−	0.243253i	−0.00551284	−	0.00954853i
$650$		0			0
$651$	32.5206	+	18.5917i	1.27458	+	0.728664i
$652$	−33.9280			−1.32872
$653$	2.00163	+	3.46692i	0.0783297	+	0.135671i	0.902529	−	0.430628i	$-0.141708\pi$
$653$	2.00163	+	3.46692i	0.0783297	+	0.135671i	−0.824200	+	0.566299i	$0.808375\pi$
$654$	18.7239	−	32.4308i	0.732164	−	1.26814i
$655$	−4.66130	+	8.07361i	−0.182132	+	0.315462i
$656$	7.94178	+	13.7556i	0.310074	+	0.537064i
$657$	−5.33500			−0.208138
$658$	0.0777040	+	18.2543i	0.00302922	+	0.711627i
$659$	−0.740310			−0.0288384			−0.0144192	−	0.999896i	$-0.504590\pi$
$659$	−0.740310			−0.0288384			−0.0144192	+	0.999896i	$0.504590\pi$
$660$	−10.7423	−	18.6063i	−0.418145	−	0.724249i
$661$	−14.1947	+	24.5860i	−0.552110	+	0.956283i	0.446012	+	0.895027i	$0.352844\pi$
$661$	−14.1947	+	24.5860i	−0.552110	+	0.956283i	−0.998122	+	0.0612560i	$0.980489\pi$
$662$	−7.89887	+	13.6813i	−0.306998	+	0.531737i
$663$		0			0
$664$	44.2764			1.71826
$665$	0.254425	+	59.7699i	0.00986619	+	2.31778i
$666$	10.6501			0.412685
$667$	−0.302665	−	0.524230i	−0.0117192	−	0.0202983i
$668$	−10.0572	+	17.4196i	−0.389125	+	0.673984i
$669$	−11.0071	+	19.0649i	−0.425561	+	0.737093i
$670$	29.7310	+	51.4956i	1.14861	+	1.98945i
$671$	1.03410			0.0399210
$672$	−3.10160	−	1.77315i	−0.119647	−	0.0684006i
$673$	−39.3719			−1.51768			−0.758838	−	0.651279i	$-0.774233\pi$
$673$	−39.3719			−1.51768			−0.758838	+	0.651279i	$0.774233\pi$
$674$	31.0271	+	53.7405i	1.19512	+	2.07001i
$675$	25.9149	−	44.8860i	0.997466	−	1.72766i
$676$		0			0
$677$	13.0844	+	22.6628i	0.502874	+	0.871004i	0.999994	+	0.00332225i	$0.00105751\pi$
$677$	13.0844	+	22.6628i	0.502874	+	0.871004i	−0.497120	+	0.867682i	$0.665609\pi$
$678$	−0.901837			−0.0346349
$679$	8.78358	−	5.12118i	0.337083	−	0.196533i
$680$	−1.96597			−0.0753915
$681$	−10.4060	−	18.0237i	−0.398758	−	0.690668i
$682$	−5.92565	+	10.2635i	−0.226905	+	0.393011i
$683$	20.8334	−	36.0846i	0.797170	−	1.38074i	−0.124283	−	0.992247i	$-0.539663\pi$
$683$	20.8334	−	36.0846i	0.797170	−	1.38074i	0.921452	−	0.388491i	$-0.127004\pi$
$684$	8.91637	+	15.4436i	0.340926	+	0.590501i
$685$	51.3012			1.96012
$686$	38.7595	−	23.0427i	1.47984	−	0.879774i
$687$	−21.1741			−0.807841
$688$	−8.63273	−	14.9523i	−0.329120	−	0.570052i
$689$		0			0
$690$	−4.57289	+	7.92048i	−0.174087	+	0.301528i
$691$	0.946188	+	1.63885i	0.0359947	+	0.0623446i	0.883462	−	0.468504i	$-0.155207\pi$
$691$	0.946188	+	1.63885i	0.0359947	+	0.0623446i	−0.847467	+	0.530848i	$0.821873\pi$
$692$	60.5092			2.30022
$693$	−1.28314	+	0.748124i	−0.0487426	+	0.0284189i
$694$	−34.5815			−1.31269
$695$	28.2259	+	48.8888i	1.07067	+	1.85446i
$696$	−6.01718	+	10.4221i	−0.228081	+	0.395047i
$697$	−0.224370	+	0.388620i	−0.00849861	+	0.0147200i
$698$	−31.3883	−	54.3661i	−1.18806	−	2.05779i
$699$	47.1350			1.78281
$700$	110.253	+	63.0304i	4.16717	+	2.38232i
$701$	28.5701			1.07908			0.539539	−	0.841961i	$-0.318599\pi$
$701$	28.5701			1.07908			0.539539	+	0.841961i	$0.318599\pi$
$702$		0			0
$703$	14.2773	−	24.7289i	0.538477	−	0.932670i
$704$	2.97006	−	5.14429i	0.111938	−	0.193883i
$705$	11.5130	+	19.9410i	0.433603	+	0.751023i
$706$	36.2418			1.36398
$707$	0.000961417		0.225857i	3.61578e−5		0.00849423i
$708$	3.20913			0.120607
$709$	−18.6010	−	32.2178i	−0.698574	−	1.20997i	−0.968961	−	0.247213i	$-0.920485\pi$
$709$	−18.6010	−	32.2178i	−0.698574	−	1.20997i	0.270387	−	0.962752i	$-0.412848\pi$
$710$	50.8354	−	88.0495i	1.90782	−	3.30444i
$711$	−0.120028	+	0.207894i	−0.00450139	+	0.00779664i
$712$	−23.6034	−	40.8823i	−0.884576	−	1.53213i
$713$	3.34285			0.125191
$714$	0.00541899	+	1.27304i	0.000202801	+	0.0476422i
$715$		0			0
$716$	−6.77758	−	11.7391i	−0.253290	−	0.438711i
$717$	−8.37061	+	14.4983i	−0.312606	+	0.541450i
$718$	−2.96063	+	5.12795i	−0.110490	+	0.191374i
$719$	2.85853	+	4.95112i	0.106605	+	0.184646i	0.914393	−	0.404828i	$-0.132669\pi$
$719$	2.85853	+	4.95112i	0.106605	+	0.184646i	−0.807788	+	0.589473i	$0.799335\pi$
$720$	12.3636			0.460762
$721$	26.5913	+	15.2019i	0.990312	+	0.566150i
$722$	25.8971			0.963791
$723$	13.9739	+	24.2036i	0.519696	+	0.900141i
$724$	12.4996	−	21.6500i	0.464546	−	0.804617i
$725$	−8.00069	+	13.8576i	−0.297138	+	0.514658i
$726$	25.1401	+	43.5439i	0.933035	+	1.61606i
$727$	−1.37012			−0.0508149			−0.0254074	−	0.999677i	$-0.508088\pi$
$727$	−1.37012			−0.0508149			−0.0254074	+	0.999677i	$0.508088\pi$
$728$		0			0
$729$	15.9014			0.588942
$730$	32.3171	+	55.9749i	1.19611	+	2.07172i
$731$	0.243890	−	0.422430i	0.00902061	−	0.0156241i
$732$	−5.90735	+	10.2318i	−0.218342	+	0.378179i
$733$	−1.65651	−	2.86916i	−0.0611846	−	0.105975i	0.833811	−	0.552051i	$-0.186154\pi$
$733$	−1.65651	−	2.86916i	−0.0611846	−	0.105975i	−0.894995	+	0.446076i	$0.852821\pi$
$734$	−38.9284			−1.43687
$735$	28.0187	−	49.4982i	1.03348	−	1.82577i
$736$	−0.318819			−0.0117518
$737$	1.98089	+	3.43100i	0.0729669	+	0.126382i
$738$	4.51375	−	7.81804i	0.166153	−	0.287786i
$739$	2.36297	−	4.09278i	0.0869231	−	0.150555i	−0.819286	−	0.573385i	$-0.805630\pi$
$739$	2.36297	−	4.09278i	0.0869231	−	0.150555i	0.906209	+	0.422830i	$0.138963\pi$
$740$	−42.7477	−	74.0412i	−1.57144	−	2.72181i
$741$		0			0
$742$	79.8195	−	46.5379i	2.93026	−	1.70846i
$743$	−27.9917			−1.02692			−0.513458	−	0.858115i	$-0.671636\pi$
$743$	−27.9917			−1.02692			−0.513458	+	0.858115i	$0.671636\pi$
$744$	−33.2291	−	57.5545i	−1.21824	−	2.11005i
$745$	24.3627	−	42.1974i	0.892579	−	1.54599i
$746$	8.56312	−	14.8318i	0.313518	−	0.543029i
$747$	−3.93328	−	6.81264i	−0.143911	−	0.249262i
$748$	−0.266873			−0.00975783
$749$	9.98245	+	5.70685i	0.364751	+	0.208524i
$750$	142.845			5.21597
$751$	9.07867	+	15.7247i	0.331285	+	0.573803i	0.982764	−	0.184864i	$-0.0591843\pi$
$751$	9.07867	+	15.7247i	0.331285	+	0.573803i	−0.651479	+	0.758667i	$0.725851\pi$
$752$	5.06192	−	8.76750i	0.184589	−	0.319718i
$753$	12.8201	−	22.2051i	0.467192	−	0.809201i
$754$		0			0
$755$	−48.2711			−1.75677
$756$	0.187617	+	44.0752i	0.00682357	+	1.60300i
$757$	−25.1014			−0.912327			−0.456164	−	0.889896i	$-0.650777\pi$
$757$	−25.1014			−0.912327			−0.456164	+	0.889896i	$0.650777\pi$
$758$	−28.5032	−	49.3691i	−1.03528	−	1.79317i
$759$	−0.304678	+	0.527718i	−0.0110591	+	0.0191549i
$760$	53.0199	−	91.8331i	1.92323	−	3.33114i
$761$	−17.4845	−	30.2841i	−0.633814	−	1.09780i	−0.986765	−	0.162156i	$-0.948155\pi$
$761$	−17.4845	−	30.2841i	−0.633814	−	1.09780i	0.352952	−	0.935642i	$-0.385178\pi$
$762$	75.7101			2.74269
$763$	0.0884660	+	20.7825i	0.00320268	+	0.752378i
$764$	−89.2114			−3.22755
$765$	0.174646	+	0.302497i	0.00631436	+	0.0109368i
$766$	−43.7556	+	75.7869i	−1.58095	+	2.73829i
$767$		0			0
$768$	30.6455	+	53.0795i	1.10582	+	1.91534i
$769$	37.5705			1.35483			0.677413	−	0.735603i	$-0.263101\pi$
$769$	37.5705			1.35483			0.677413	+	0.735603i	$0.263101\pi$
$770$	15.6221	+	8.93095i	0.562980	+	0.321849i
$771$	3.06628			0.110430
$772$	49.0445	+	84.9475i	1.76515	+	3.05733i
$773$	20.9794	−	36.3374i	0.754578	−	1.30697i	−0.191007	−	0.981589i	$-0.561175\pi$
$773$	20.9794	−	36.3374i	0.754578	−	1.30697i	0.945584	−	0.325378i	$-0.105491\pi$
$774$	−4.90645	+	8.49822i	−0.176359	+	0.305462i
$775$	−44.1828	−	76.5268i	−1.58709	−	2.74892i
$776$	−18.0383			−0.647538
$777$	−23.4742	+	13.6864i	−0.842134	+	0.490998i
$778$	−34.2226			−1.22694
$779$	−12.1020	−	20.9612i	−0.433598	−	0.751014i
$780$		0			0
$781$	3.38701	−	5.86647i	0.121197	−	0.209919i
$782$	0.0568023	+	0.0983844i	0.00203125	+	0.00351822i
$783$	−5.55339			−0.198462
$784$	−25.0068	+	0.212899i	−0.893099	+	0.00760353i
$785$	75.2549			2.68596
$786$	−5.35498	−	9.27510i	−0.191006	−	0.330832i
$787$	−16.9480	+	29.3548i	−0.604131	+	1.04639i	0.388057	+	0.921635i	$0.373146\pi$
$787$	−16.9480	+	29.3548i	−0.604131	+	1.04639i	−0.992188	+	0.124751i	$0.960187\pi$
$788$	−22.4056	+	38.8076i	−0.798165	+	1.38246i
$789$	21.0592	+	36.4756i	0.749728	+	1.29857i
$790$	2.90830			0.103473
$791$	0.432376	−	0.252092i	0.0153735	−	0.00896337i
$792$	2.63512			0.0936348
$793$		0			0
$794$	−3.86985	+	6.70277i	−0.137336	+	0.237872i
$795$	58.2732	−	100.932i	2.06674	−	3.57969i
$796$	41.9667	+	72.6885i	1.48747	+	2.57638i
$797$	−34.4758			−1.22119			−0.610597	−	0.791941i	$-0.709071\pi$
$797$	−34.4758			−1.22119			−0.610597	+	0.791941i	$0.709071\pi$
$798$	−59.6114	−	34.0792i	−2.11022	−	1.20639i
$799$	0.286017			0.0101186
$800$	4.21385	+	7.29861i	0.148982	+	0.258045i
$801$	−4.19361	+	7.26355i	−0.148174	+	0.256645i
$802$	26.4036	−	45.7323i	0.932343	−	1.61487i
$803$	2.15319	+	3.72944i	0.0759845	+	0.131609i
$804$	−45.2636			−1.59632
$805$	−0.0216058	−	5.07566i	−0.000761504	−	0.178893i
$806$		0			0
$807$	10.4729	+	18.1396i	0.368664	+	0.638545i
$808$	0.200350	−	0.347017i	0.00704830	−	0.0122080i
$809$	−19.7432	+	34.1963i	−0.694135	+	1.20228i	0.276336	+	0.961061i	$0.410880\pi$
$809$	−19.7432	+	34.1963i	−0.694135	+	1.20228i	−0.970471	+	0.241216i	$0.922454\pi$
$810$	54.5913	+	94.5550i	1.91814	+	3.32232i
$811$	18.5399			0.651023			0.325512	−	0.945538i	$-0.394463\pi$
$811$	18.5399			0.651023			0.325512	+	0.945538i	$0.394463\pi$
$812$	−0.0579228	−	13.6073i	−0.00203269	−	0.477522i
$813$	28.5486			1.00124
$814$	−4.29837	−	7.44500i	−0.150658	−	0.260947i
$815$	17.9222	−	31.0422i	0.627788	−	1.08736i
$816$	0.353013	−	0.611437i	0.0123579	−	0.0214046i
$817$	13.1549	+	22.7849i	0.460231	+	0.797143i
$818$	61.9983			2.16772
$819$		0			0
$820$	−72.4694			−2.53074
$821$	22.3619	+	38.7320i	0.780437	+	1.35176i	0.931687	+	0.363261i	$0.118337\pi$
$821$	22.3619	+	38.7320i	0.780437	+	1.35176i	−0.151250	+	0.988496i	$0.548330\pi$
$822$	−29.4678	+	51.0398i	−1.02781	+	1.78022i
$823$	12.7371	−	22.0613i	0.443988	−	0.769010i	−0.553993	−	0.832521i	$-0.686897\pi$
$823$	12.7371	−	22.0613i	0.443988	−	0.769010i	0.997981	+	0.0635112i	$0.0202299\pi$
$824$	−27.1706	−	47.0609i	−0.946533	−	1.63944i
$825$	16.1078			0.560802
$826$	−2.32200	+	1.35382i	−0.0807926	+	0.0471053i
$827$	14.1027			0.490399			0.245200	−	0.969473i	$-0.421147\pi$
$827$	14.1027			0.490399			0.245200	+	0.969473i	$0.421147\pi$
$828$	−0.757178	−	1.31147i	−0.0263138	−	0.0455768i
$829$	17.4025	−	30.1421i	0.604415	−	1.04688i	−0.387729	−	0.921773i	$-0.626740\pi$
$829$	17.4025	−	30.1421i	0.604415	−	1.04688i	0.992144	−	0.125103i	$-0.0399263\pi$
$830$	−47.6522	+	82.5361i	−1.65403	+	2.86487i
$831$	14.8097	+	25.6511i	0.513742	+	0.889827i
$832$		0			0
$833$	−0.358452	−	0.608828i	−0.0124196	−	0.0210946i
$834$	−64.8528			−2.24567
$835$	−10.6253	−	18.4036i	−0.367704	−	0.636882i
$836$	7.19724	−	12.4660i	0.248922	−	0.431145i
$837$	15.3339	−	26.5591i	0.530018	−	0.918018i
$838$	−8.54210	−	14.7954i	−0.295082	−	0.511097i
$839$	32.3178			1.11573			0.557867	−	0.829931i	$-0.311620\pi$
$839$	32.3178			1.11573			0.557867	+	0.829931i	$0.311620\pi$
$840$	−87.1737	+	50.8258i	−3.00778	+	1.75366i
$841$	−27.2855			−0.940880
$842$	−1.22079	−	2.11448i	−0.0420713	−	0.0728697i
$843$	15.1094	−	26.1702i	0.520394	−	0.901350i
$844$	−39.6716	+	68.7132i	−1.36555	+	2.36521i
$845$		0			0
$846$	−5.75393			−0.197824
$847$	−24.2250	−	13.8492i	−0.832382	−	0.475863i
$848$	−51.2421			−1.75966
$849$	−17.5100	−	30.3283i	−0.600943	−	1.04086i
$850$	1.50152	−	2.60071i	0.0515018	−	0.0892037i
$851$	−1.21242	+	2.09998i	−0.0415614	+	0.0719864i
$852$	38.6969	+	67.0249i	1.32573	+	2.29624i
$853$	−5.51656			−0.188883			−0.0944417	−	0.995530i	$-0.530107\pi$
$853$	−5.51656			−0.188883			−0.0944417	+	0.995530i	$0.530107\pi$
$854$	−0.0421224	−	9.89544i	−0.00144140	−	0.338615i
$855$	−18.8400			−0.644316
$856$	−10.1999	−	17.6668i	−0.348626	−	0.603838i
$857$	−20.5763	+	35.6391i	−0.702871	+	1.21741i	0.264583	+	0.964363i	$0.414766\pi$
$857$	−20.5763	+	35.6391i	−0.702871	+	1.21741i	−0.967454	+	0.253046i	$0.918568\pi$
$858$		0			0
$859$	−3.96468	−	6.86703i	−0.135273	−	0.234300i	0.790429	−	0.612554i	$-0.209858\pi$
$859$	−3.96468	−	6.86703i	−0.135273	−	0.234300i	−0.925702	+	0.378254i	$0.876525\pi$
$860$	78.7743			2.68618
$861$	0.0980436	+	23.0325i	0.00334132	+	0.784946i
$862$	−63.8583			−2.17502
$863$	3.63556	+	6.29698i	0.123756	+	0.214352i	0.921246	−	0.388980i	$-0.127173\pi$
$863$	3.63556	+	6.29698i	0.123756	+	0.214352i	−0.797490	+	0.603332i	$0.793839\pi$
$864$	−1.46245	+	2.53303i	−0.0497534	+	0.0861755i
$865$	−31.9636	+	55.3626i	−1.08680	+	1.88238i
$866$	−18.0834	−	31.3213i	−0.614498	−	1.06434i
$867$	−33.2669			−1.12980
$868$	65.2370	+	37.2952i	2.21429	+	1.26588i
$869$	0.193772			0.00657325
$870$	−12.9519	−	22.4334i	−0.439111	−	0.760563i
$871$		0			0
$872$	18.4355	−	31.9312i	0.624305	−	1.08133i
$873$	1.60243	+	2.77549i	0.0542341	+	0.0939362i
$874$	−6.12757			−0.207268
$875$	−68.4855	+	39.9298i	−2.31523	+	1.34987i
$876$	−49.2008			−1.66234
$877$	−6.05364	−	10.4852i	−0.204417	−	0.354060i	0.745530	−	0.666472i	$-0.232196\pi$
$877$	−6.05364	−	10.4852i	−0.204417	−	0.354060i	−0.949947	+	0.312412i	$0.898863\pi$
$878$	−17.8637	+	30.9408i	−0.602870	+	1.04420i
$879$	−33.2720	+	57.6288i	−1.12224	+	1.94377i
$880$	−4.98990	−	8.64276i	−0.168209	−	0.291347i
$881$	3.32436			0.112001			0.0560003	−	0.998431i	$-0.482165\pi$
$881$	3.32436			0.112001			0.0560003	+	0.998431i	$0.482165\pi$
$882$	7.21115	+	12.2481i	0.242812	+	0.412414i
$883$	−21.1635			−0.712208			−0.356104	−	0.934446i	$-0.615895\pi$
$883$	−21.1635			−0.712208			−0.356104	+	0.934446i	$0.615895\pi$
$884$		0			0
$885$	−1.69520	+	2.93618i	−0.0569836	+	0.0986985i
$886$	6.77692	−	11.7380i	0.227675	−	0.394345i
$887$	−13.3758	−	23.1675i	−0.449115	−	0.777889i	0.549214	−	0.835682i	$-0.314927\pi$
$887$	−13.3758	−	23.1675i	−0.449115	−	0.777889i	−0.998329	+	0.0577923i	$0.981594\pi$
$888$	48.2077			1.61774
$889$	−36.2984	+	21.1634i	−1.21741	+	0.709798i
$890$	101.612			3.40605
$891$	3.63726	+	6.29991i	0.121853	+	0.211055i
$892$	−22.0805	+	38.2446i	−0.739311	+	1.28052i
$893$	−7.71354	+	13.3603i	−0.258124	+	0.447084i
$894$	27.9882	+	48.4771i	0.936067	+	1.62132i
$895$	14.3209			0.478693
$896$	−46.1792	−	26.4001i	−1.54274	−	0.881967i
$897$		0			0
$898$	7.29519	+	12.6356i	0.243443	+	0.421656i
$899$	−4.73403	+	8.19957i	−0.157889	+	0.273471i
$900$	−20.0154	+	34.6676i	−0.667179	+	1.15559i
$901$	−0.723842	−	1.25373i	−0.0241147	−	0.0417678i
$902$	−7.28695			−0.242629
$903$	−0.106574	−	25.0364i	−0.00354655	−	0.833158i
$904$	−0.887945			−0.0295326
$905$	13.2057	+	22.8730i	0.438973	+	0.760323i
$906$	27.7273	−	48.0251i	0.921179	−	1.59553i
$907$	−21.1288	+	36.5961i	−0.701570	+	1.21515i	0.266345	+	0.963878i	$0.414184\pi$
$907$	−21.1288	+	36.5961i	−0.701570	+	1.21515i	−0.967915	+	0.251277i	$0.919149\pi$
$908$	−20.8746	−	36.1558i	−0.692747	−	1.19987i
$909$	−0.0711924			−0.00236130
$910$		0			0
$911$	−27.4466			−0.909347			−0.454673	−	0.890658i	$-0.650244\pi$
$911$	−27.4466			−0.909347			−0.454673	+	0.890658i	$0.650244\pi$
$912$	19.0407	+	32.9795i	0.630501	+	1.09206i
$913$	−3.17492	+	5.49913i	−0.105075	+	0.181995i
$914$	−22.1558	+	38.3750i	−0.732849	+	1.26933i
$915$	−6.24104	−	10.8098i	−0.206322	−	0.357361i
$916$	−42.4756			−1.40343
$917$	5.16007	+	2.94996i	0.170401	+	0.0974161i
$918$	1.04223			0.0343986
$919$	−0.459370	−	0.795652i	−0.0151532	−	0.0262461i	0.858349	−	0.513066i	$-0.171490\pi$
$919$	−0.459370	−	0.795652i	−0.0151532	−	0.0262461i	−0.873503	+	0.486820i	$0.838157\pi$
$920$	−4.50245	+	7.79847i	−0.148441	+	0.257108i
$921$	6.99294	−	12.1121i	0.230425	−	0.399108i
$922$	7.96623	+	13.7979i	0.262354	+	0.454410i
$923$		0			0
$924$	−11.8335	+	6.89940i	−0.389293	+	0.226974i
$925$	64.0989			2.10756
$926$	−43.8234	−	75.9043i	−1.44013	−	2.49437i
$927$	−4.82739	+	8.36129i	−0.158552	+	0.274621i
$928$	0.451499	−	0.782020i	0.0148212	−	0.0256711i
$929$	−23.6248	−	40.9193i	−0.775104	−	1.34252i	−0.934736	−	0.355343i	$-0.884364\pi$
$929$	−23.6248	−	40.9193i	−0.775104	−	1.34252i	0.159632	−	0.987177i	$-0.448969\pi$
$930$	143.051			4.69082
$931$	38.1063	−	0.324423i	1.24888	−	0.0106325i
$932$	94.5539			3.09721
$933$	14.5059	+	25.1250i	0.474903	+	0.822557i
$934$	−8.02690	+	13.9030i	−0.262648	+	0.454920i
$935$	0.140974	−	0.244174i	0.00461033	−	0.00798533i
$936$		0			0
$937$	11.3635			0.371230			0.185615	−	0.982623i	$-0.440572\pi$
$937$	11.3635			0.371230			0.185615	+	0.982623i	$0.440572\pi$
$938$	32.7509	−	19.0951i	1.06936	−	0.623477i
$939$	−65.5778			−2.14005
$940$	23.0952	+	40.0021i	0.753283	+	1.30472i
$941$	−10.1916	+	17.6524i	−0.332237	+	0.575451i	−0.982950	−	0.183872i	$-0.941137\pi$
$941$	−10.1916	+	17.6524i	−0.332237	+	0.575451i	0.650713	+	0.759324i	$0.274470\pi$
$942$	−43.2270	+	74.8714i	−1.40841	+	2.43944i
$943$	1.02770	+	1.78003i	0.0334665	+	0.0579657i
$944$	1.49067			0.0485170
$945$	−40.4255	−	23.1108i	−1.31504	−	0.751794i
$946$	7.92092			0.257531
$947$	−24.1089	−	41.7579i	−0.783435	−	1.35695i	−0.929929	−	0.367738i	$-0.880132\pi$
$947$	−24.1089	−	41.7579i	−0.783435	−	1.35695i	0.146494	−	0.989212i	$-0.453201\pi$
$948$	−1.10693	+	1.91726i	−0.0359514	+	0.0622696i
$949$		0			0
$950$	80.9886	+	140.276i	2.62762	+	4.55116i
$951$	17.1892			0.557397
$952$	0.00533552	+	1.25343i	0.000172925	+	0.0406238i
$953$	55.8697			1.80980			0.904899	−	0.425627i	$-0.139946\pi$
$953$	55.8697			1.80980			0.904899	+	0.425627i	$0.139946\pi$
$954$	14.5619	+	25.2219i	0.471457	+	0.816588i
$955$	47.1253	−	81.6234i	1.52494	−	2.64127i
$956$	−16.7916	+	29.0839i	−0.543080	+	0.940642i
$957$	−0.862948	−	1.49467i	−0.0278951	−	0.0483158i
$958$	67.9871			2.19657
$959$	−0.139228	−	32.7077i	−0.00449592	−	1.05619i
$960$	−71.6999			−2.31410
$961$	−10.6430	−	18.4343i	−0.343324	−	0.594655i
$962$		0			0
$963$	−1.81222	+	3.13885i	−0.0583979	+	0.101148i
$964$	28.0320	+	48.5529i	0.902850	+	1.56378i
$965$	−103.630			−3.33596
$966$	5.06220	+	2.89400i	0.162874	+	0.0931130i
$967$	−32.7379			−1.05278			−0.526391	−	0.850243i	$-0.676455\pi$
$967$	−32.7379			−1.05278			−0.526391	+	0.850243i	$0.676455\pi$
$968$	24.7528	+	42.8731i	0.795585	+	1.37799i
$969$	−0.537935	+	0.931730i	−0.0172810	+	0.0299315i
$970$	19.4137	−	33.6255i	0.623335	−	1.07965i
$971$	1.65284	+	2.86280i	0.0530422	+	0.0918717i	0.891327	−	0.453360i	$-0.149775\pi$
$971$	1.65284	+	2.86280i	0.0530422	+	0.0918717i	−0.838285	+	0.545232i	$0.816442\pi$
$972$	−33.1349			−1.06280
$973$	31.0930	−	18.1284i	0.996795	−	0.581171i
$974$	40.5450			1.29915
$975$		0			0
$976$	−2.74401	+	4.75276i	−0.0878335	+	0.152132i
$977$	1.64212	−	2.84423i	0.0525360	−	0.0909950i	−0.838561	−	0.544807i	$-0.816603\pi$
$977$	1.64212	−	2.84423i	0.0525360	−	0.0909950i	0.891097	+	0.453812i	$0.149936\pi$
$978$	20.5893	+	35.6618i	0.658374	+	1.14034i
$979$	6.77013			0.216374
$980$	56.2060	−	99.2944i	1.79543	−	3.17184i
$981$	−6.55086			−0.209153
$982$	−27.0534	−	46.8578i	−0.863308	−	1.49529i
$983$	17.1120	−	29.6388i	0.545787	−	0.945331i	−0.452770	−	0.891628i	$-0.649564\pi$
$983$	17.1120	−	29.6388i	0.545787	−	0.945331i	0.998557	−	0.0537039i	$-0.0171027\pi$
$984$	20.4314	−	35.3882i	0.651329	−	1.12813i
$985$	−23.6712	−	40.9997i	−0.754226	−	1.30636i
$986$	−0.321765			−0.0102471
$987$	12.6824	−	7.39434i	0.403685	−	0.235364i
$988$		0			0
$989$	−1.11711	−	1.93489i	−0.0355221	−	0.0615261i
$990$	−2.83603	+	4.91215i	−0.0901350	+	0.156118i
$991$	22.3676	−	38.7419i	0.710531	−	1.23068i	−0.254127	−	0.967171i	$-0.581788\pi$
$991$	22.3676	−	38.7419i	0.710531	−	1.23068i	0.964658	−	0.263505i	$-0.0848785\pi$
$992$	2.49335	+	4.31860i	0.0791638	+	0.137116i
$993$	12.7048			0.403176
$994$	−56.2749	−	32.1717i	−1.78493	−	1.02042i
$995$	−88.6746			−2.81117
$996$	−36.2738	−	62.8281i	−1.14938	−	1.99078i
$997$	4.73539	−	8.20193i	0.149971	−	0.259758i	−0.781245	−	0.624224i	$-0.785415\pi$
$997$	4.73539	−	8.20193i	0.149971	−	0.259758i	0.931217	+	0.364466i	$0.118749\pi$
$998$	−29.1139	+	50.4267i	−0.921584	+	1.59623i
$999$	11.1230	+	19.2656i	0.351916	+	0.609536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.l.508.2	yes	48
7.2	even	3	inner	1183.2.e.l.170.2	yes	48
7.3	odd	6		8281.2.a.ct.1.23		24
7.4	even	3		8281.2.a.cu.1.23		24
13.12	even	2		1183.2.e.k.508.23	yes	48
91.25	even	6		8281.2.a.cv.1.2		24
91.38	odd	6		8281.2.a.cw.1.2		24
91.51	even	6		1183.2.e.k.170.23	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.23	✓	48	91.51	even	6
1183.2.e.k.508.23	yes	48	13.12	even	2
1183.2.e.l.170.2	yes	48	7.2	even	3	inner
1183.2.e.l.508.2	yes	48	1.1	even	1	trivial
8281.2.a.ct.1.23		24	7.3	odd	6
8281.2.a.cu.1.23		24	7.4	even	3
8281.2.a.cv.1.2		24	91.25	even	6
8281.2.a.cw.1.2		24	91.38	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21736 - 2.10853i) q^{2} +(-0.979025 + 1.69572i) q^{3} +(-1.96394 + 3.40165i) q^{4} +(-2.07488 - 3.59380i) q^{5} +4.76731 q^{6} +(-2.28564 + 1.33262i) q^{7} +4.69388 q^{8} +(-0.416980 - 0.722230i) q^{9} +O(q^{10})\)	\(q+(-1.21736 - 2.10853i) q^{2} +(-0.979025 + 1.69572i) q^{3} +(-1.96394 + 3.40165i) q^{4} +(-2.07488 - 3.59380i) q^{5} +4.76731 q^{6} +(-2.28564 + 1.33262i) q^{7} +4.69388 q^{8} +(-0.416980 - 0.722230i) q^{9} +(-5.05176 + 8.74991i) q^{10} +(-0.336584 + 0.582980i) q^{11} +(-3.84550 - 6.66060i) q^{12} +(5.59232 + 3.19706i) q^{14} +8.12544 q^{15} +(-1.78626 - 3.09390i) q^{16} +(0.0504652 - 0.0874083i) q^{17} +(-1.01523 + 1.75843i) q^{18} +(2.72197 + 4.71460i) q^{19} +16.2998 q^{20} +(-0.0220519 - 5.18047i) q^{21} +1.63898 q^{22} +(-0.231150 - 0.400364i) q^{23} +(-4.59542 + 7.95950i) q^{24} +(-6.11026 + 10.5833i) q^{25} -4.24122 q^{27} +(-0.0442366 - 10.3921i) q^{28} +1.30939 q^{29} +(-9.89161 - 17.1328i) q^{30} +(-3.61546 + 6.26215i) q^{31} +(0.344818 - 0.597242i) q^{32} +(-0.659048 - 1.14150i) q^{33} -0.245738 q^{34} +(9.53158 + 5.44909i) q^{35} +3.27570 q^{36} +(-2.62259 - 4.54246i) q^{37} +(6.62726 - 11.4787i) q^{38} +(-9.73923 - 16.8688i) q^{40} -4.44603 q^{41} +(-10.8963 + 6.35300i) q^{42} +4.83284 q^{43} +(-1.32206 - 2.28988i) q^{44} +(-1.73037 + 2.99708i) q^{45} +(-0.562787 + 0.974776i) q^{46} +(1.41690 + 2.45415i) q^{47} +6.99518 q^{48} +(3.44826 - 6.09175i) q^{49} +29.7536 q^{50} +(0.0988133 + 0.171150i) q^{51} +(7.17169 - 12.4217i) q^{53} +(5.16310 + 8.94275i) q^{54} +2.79348 q^{55} +(-10.7285 + 6.25514i) q^{56} -10.6595 q^{57} +(-1.59400 - 2.76088i) q^{58} +(-0.208629 + 0.361356i) q^{59} +(-15.9579 + 27.6399i) q^{60} +(-0.768086 - 1.33036i) q^{61} +17.6053 q^{62} +(1.91552 + 1.09508i) q^{63} -8.82412 q^{64} +(-1.60460 + 2.77925i) q^{66} +(2.94263 - 5.09679i) q^{67} +(0.198222 + 0.343330i) q^{68} +0.905207 q^{69} +(-0.113788 - 26.7312i) q^{70} -10.0629 q^{71} +(-1.95725 - 3.39006i) q^{72} +(3.19860 - 5.54014i) q^{73} +(-6.38529 + 11.0597i) q^{74} +(-11.9642 - 20.7226i) q^{75} -21.3832 q^{76} +(-0.00758135 - 1.78102i) q^{77} +(-0.143925 - 0.249286i) q^{79} +(-7.41256 + 12.8389i) q^{80} +(5.40319 - 9.35861i) q^{81} +(5.41243 + 9.37461i) q^{82} +9.43279 q^{83} +(17.6654 + 10.0991i) q^{84} -0.418837 q^{85} +(-5.88332 - 10.1902i) q^{86} +(-1.28192 + 2.22035i) q^{87} +(-1.57988 + 2.73644i) q^{88} +(-5.02856 - 8.70972i) q^{89} +8.42593 q^{90} +1.81586 q^{92} +(-7.07924 - 12.2616i) q^{93} +(3.44977 - 5.97518i) q^{94} +(11.2955 - 19.5645i) q^{95} +(0.675170 + 1.16943i) q^{96} -3.84295 q^{97} +(-17.0425 + 0.145094i) q^{98} +0.561394 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Introduction

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