LMFDB - Embedded newform 14.3.d.a.3.1

Newspace parameters

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	14.d (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.381472370104$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	14.3
Dual form			14.3.d.a.5.1

$q$-expansion

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(0.621320 + 0.358719i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-5.74264 + 3.31552i) q^{5} -1.01461i q^{6} +(6.24264 - 3.16693i) q^{7} +2.82843 q^{8} +(-4.24264 - 7.34847i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(0.621320 + 0.358719i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-5.74264 + 3.31552i) q^{5} -1.01461i q^{6} +(6.24264 - 3.16693i) q^{7} +2.82843 q^{8} +(-4.24264 - 7.34847i) q^{9} +(8.12132 + 4.68885i) q^{10} +(2.37868 - 4.11999i) q^{11} +(-1.24264 + 0.717439i) q^{12} +15.2913i q^{13} +(-8.29289 - 5.40629i) q^{14} -4.75736 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-3.25736 - 1.88064i) q^{17} +(-6.00000 + 10.3923i) q^{18} +(3.62132 - 2.09077i) q^{19} -13.2621i q^{20} +(5.01472 + 0.271680i) q^{21} -6.72792 q^{22} +(13.8640 + 24.0131i) q^{23} +(1.75736 + 1.01461i) q^{24} +(9.48528 - 16.4290i) q^{25} +(18.7279 - 10.8126i) q^{26} -12.5446i q^{27} +(-0.757359 + 13.9795i) q^{28} +3.51472 q^{29} +(3.36396 + 5.82655i) q^{30} +(-42.3198 - 24.4334i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(2.95584 - 1.70656i) q^{33} +5.31925i q^{34} +(-25.3492 + 38.8841i) q^{35} +16.9706 q^{36} +(1.47056 + 2.54709i) q^{37} +(-5.12132 - 2.95680i) q^{38} +(-5.48528 + 9.50079i) q^{39} +(-16.2426 + 9.37769i) q^{40} -27.9590i q^{41} +(-3.21320 - 6.33386i) q^{42} -10.4853 q^{43} +(4.75736 + 8.23999i) q^{44} +(48.7279 + 28.1331i) q^{45} +(19.6066 - 33.9596i) q^{46} +(45.6213 - 26.3395i) q^{47} -2.86976i q^{48} +(28.9411 - 39.5400i) q^{49} -26.8284 q^{50} +(-1.34924 - 2.33696i) q^{51} +(-26.4853 - 15.2913i) q^{52} +(-27.9853 + 48.4719i) q^{53} +(-15.3640 + 8.87039i) q^{54} +31.5462i q^{55} +(17.6569 - 8.95743i) q^{56} +3.00000 q^{57} +(-2.48528 - 4.30463i) q^{58} +(33.5330 + 19.3603i) q^{59} +(4.75736 - 8.23999i) q^{60} +(-78.3823 + 45.2540i) q^{61} +69.1080i q^{62} +(-49.7574 - 32.4377i) q^{63} +8.00000 q^{64} +(-50.6985 - 87.8124i) q^{65} +(-4.18019 - 2.41344i) q^{66} +(17.3198 - 29.9988i) q^{67} +(6.51472 - 3.76127i) q^{68} +19.8931i q^{69} +(65.5477 + 3.55114i) q^{70} +36.4264 q^{71} +(-12.0000 - 20.7846i) q^{72} +(45.5589 + 26.3034i) q^{73} +(2.07969 - 3.60213i) q^{74} +(11.7868 - 6.80511i) q^{75} +8.36308i q^{76} +(1.80152 - 33.2528i) q^{77} +15.5147 q^{78} +(16.8934 + 29.2602i) q^{79} +(22.9706 + 13.2621i) q^{80} +(-33.6838 + 58.3420i) q^{81} +(-34.2426 + 19.7700i) q^{82} -127.577i q^{83} +(-5.48528 + 8.41407i) q^{84} +24.9411 q^{85} +(7.41421 + 12.8418i) q^{86} +(2.18377 + 1.26080i) q^{87} +(6.72792 - 11.6531i) q^{88} +(-43.5883 + 25.1657i) q^{89} -79.5724i q^{90} +(48.4264 + 95.4580i) q^{91} -55.4558 q^{92} +(-17.5294 - 30.3619i) q^{93} +(-64.5183 - 37.2497i) q^{94} +(-13.8640 + 24.0131i) q^{95} +(-3.51472 + 2.02922i) q^{96} +101.792i q^{97} +(-68.8909 - 7.48650i) q^{98} -40.3675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7}+O(q^{10}) $ 4 * q - 6 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^7	$ 4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7} + 24 q^{10} + 18 q^{11} + 12 q^{12} - 36 q^{14} - 36 q^{15} - 8 q^{16} - 30 q^{17} - 24 q^{18} + 6 q^{19} + 54 q^{21} + 24 q^{22} + 30 q^{23} + 24 q^{24} + 4 q^{25} + 24 q^{26} - 20 q^{28} + 48 q^{29} - 12 q^{30} - 42 q^{31} - 90 q^{33} - 42 q^{35} - 62 q^{37} - 12 q^{38} + 12 q^{39} - 48 q^{40} + 72 q^{42} - 8 q^{43} + 36 q^{44} + 144 q^{45} + 36 q^{46} + 174 q^{47} - 20 q^{49} - 96 q^{50} + 54 q^{51} - 72 q^{52} - 78 q^{53} - 36 q^{54} + 48 q^{56} + 12 q^{57} + 24 q^{58} - 78 q^{59} + 36 q^{60} - 42 q^{61} - 216 q^{63} + 32 q^{64} - 84 q^{65} - 144 q^{66} - 58 q^{67} + 60 q^{68} + 84 q^{70} - 24 q^{71} - 48 q^{72} + 318 q^{73} + 96 q^{74} + 132 q^{75} + 126 q^{77} + 96 q^{78} + 110 q^{79} + 24 q^{80} + 18 q^{81} - 120 q^{82} + 12 q^{84} - 36 q^{85} + 24 q^{86} - 144 q^{87} - 24 q^{88} - 378 q^{89} + 24 q^{91} - 120 q^{92} - 138 q^{93} - 12 q^{94} - 30 q^{95} - 48 q^{96} - 120 q^{98} + 144 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^7 + 24 * q^10 + 18 * q^11 + 12 * q^12 - 36 * q^14 - 36 * q^15 - 8 * q^16 - 30 * q^17 - 24 * q^18 + 6 * q^19 + 54 * q^21 + 24 * q^22 + 30 * q^23 + 24 * q^24 + 4 * q^25 + 24 * q^26 - 20 * q^28 + 48 * q^29 - 12 * q^30 - 42 * q^31 - 90 * q^33 - 42 * q^35 - 62 * q^37 - 12 * q^38 + 12 * q^39 - 48 * q^40 + 72 * q^42 - 8 * q^43 + 36 * q^44 + 144 * q^45 + 36 * q^46 + 174 * q^47 - 20 * q^49 - 96 * q^50 + 54 * q^51 - 72 * q^52 - 78 * q^53 - 36 * q^54 + 48 * q^56 + 12 * q^57 + 24 * q^58 - 78 * q^59 + 36 * q^60 - 42 * q^61 - 216 * q^63 + 32 * q^64 - 84 * q^65 - 144 * q^66 - 58 * q^67 + 60 * q^68 + 84 * q^70 - 24 * q^71 - 48 * q^72 + 318 * q^73 + 96 * q^74 + 132 * q^75 + 126 * q^77 + 96 * q^78 + 110 * q^79 + 24 * q^80 + 18 * q^81 - 120 * q^82 + 12 * q^84 - 36 * q^85 + 24 * q^86 - 144 * q^87 - 24 * q^88 - 378 * q^89 + 24 * q^91 - 120 * q^92 - 138 * q^93 - 12 * q^94 - 30 * q^95 - 48 * q^96 - 120 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$	0.621320	+	0.358719i	0.207107	+	0.119573i	0.599966	−	0.800025i	$-0.295181\pi$
$3$	0.621320	+	0.358719i	0.207107	+	0.119573i	−0.392859	+	0.919599i	$0.628514\pi$
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	−5.74264	+	3.31552i	−1.14853	+	0.663103i	−0.948528	−	0.316693i	$-0.897428\pi$
$5$	−5.74264	+	3.31552i	−1.14853	+	0.663103i	−0.200000	+	0.979796i	$0.564094\pi$
$6$		−	1.01461i		−	0.169102i
$7$	6.24264	−	3.16693i	0.891806	−	0.452418i
$7$	6.24264	−	3.16693i	0.891806	−	0.452418i
$8$	2.82843			0.353553
$9$	−4.24264	−	7.34847i	−0.471405	−	0.816497i
$10$	8.12132	+	4.68885i	0.812132	+	0.468885i
$11$	2.37868	−	4.11999i	0.216244	−	0.374545i	−0.737413	−	0.675442i	$-0.763953\pi$
$11$	2.37868	−	4.11999i	0.216244	−	0.374545i	0.953657	+	0.300897i	$0.0972861\pi$
$12$	−1.24264	+	0.717439i	−0.103553	+	0.0597866i
$13$			15.2913i			1.17625i	0.808769	+	0.588126i	$0.200134\pi$
$13$			15.2913i			1.17625i	−0.808769	+	0.588126i	$0.799866\pi$
$14$	−8.29289	−	5.40629i	−0.592350	−	0.386163i
$15$	−4.75736			−0.317157
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−3.25736	−	1.88064i	−0.191609	−	0.110626i	0.401126	−	0.916023i	$-0.368619\pi$
$17$	−3.25736	−	1.88064i	−0.191609	−	0.110626i	−0.592736	+	0.805397i	$0.701952\pi$
$18$	−6.00000	+	10.3923i	−0.333333	+	0.577350i
$19$	3.62132	−	2.09077i	0.190596	−	0.110041i	−0.401666	−	0.915786i	$-0.631569\pi$
$19$	3.62132	−	2.09077i	0.190596	−	0.110041i	0.592261	+	0.805746i	$0.298235\pi$
$20$		−	13.2621i		−	0.663103i
$21$	5.01472	+	0.271680i	0.238796	+	0.0129371i
$22$	−6.72792			−0.305815
$23$	13.8640	+	24.0131i	0.602781	+	1.04405i	0.992398	+	0.123070i	$0.0392740\pi$
$23$	13.8640	+	24.0131i	0.602781	+	1.04405i	−0.389617	+	0.920977i	$0.627393\pi$
$24$	1.75736	+	1.01461i	0.0732233	+	0.0422755i
$25$	9.48528	−	16.4290i	0.379411	−	0.657160i
$26$	18.7279	−	10.8126i	0.720305	−	0.415868i
$27$		−	12.5446i		−	0.464616i
$28$	−0.757359	+	13.9795i	−0.0270485	+	0.499268i
$29$	3.51472			0.121197			0.0605986	−	0.998162i	$-0.480699\pi$
$29$	3.51472			0.121197			0.0605986	+	0.998162i	$0.480699\pi$
$30$	3.36396	+	5.82655i	0.112132	+	0.194218i
$31$	−42.3198	−	24.4334i	−1.36516	−	0.788173i	−0.374850	−	0.927085i	$-0.622306\pi$
$31$	−42.3198	−	24.4334i	−1.36516	−	0.788173i	−0.990305	+	0.138913i	$0.955639\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$	2.95584	−	1.70656i	0.0895710	−	0.0517139i
$34$			5.31925i			0.156448i
$35$	−25.3492	+	38.8841i	−0.724264	+	1.11097i
$36$	16.9706			0.471405
$37$	1.47056	+	2.54709i	0.0397449	+	0.0688403i	0.885214	−	0.465185i	$-0.154012\pi$
$37$	1.47056	+	2.54709i	0.0397449	+	0.0688403i	−0.845469	+	0.534025i	$0.820679\pi$
$38$	−5.12132	−	2.95680i	−0.134772	−	0.0778104i
$39$	−5.48528	+	9.50079i	−0.140648	+	0.243610i
$40$	−16.2426	+	9.37769i	−0.406066	+	0.234442i
$41$		−	27.9590i		−	0.681927i	−0.940077	−	0.340963i	$-0.889247\pi$
$41$		−	27.9590i		−	0.681927i	0.940077	−	0.340963i	$-0.110753\pi$
$42$	−3.21320	−	6.33386i	−0.0765048	−	0.150806i
$43$	−10.4853			−0.243844			−0.121922	−	0.992540i	$-0.538906\pi$
$43$	−10.4853			−0.243844			−0.121922	+	0.992540i	$0.538906\pi$
$44$	4.75736	+	8.23999i	0.108122	+	0.187272i
$45$	48.7279	+	28.1331i	1.08284	+	0.625180i
$46$	19.6066	−	33.9596i	0.426230	−	0.738253i
$47$	45.6213	−	26.3395i	0.970666	−	0.560415i	0.0712271	−	0.997460i	$-0.477309\pi$
$47$	45.6213	−	26.3395i	0.970666	−	0.560415i	0.899439	+	0.437046i	$0.143975\pi$
$48$		−	2.86976i		−	0.0597866i
$49$	28.9411	−	39.5400i	0.590635	−	0.806939i
$50$	−26.8284			−0.536569
$51$	−1.34924	−	2.33696i	−0.0264557	−	0.0458227i
$52$	−26.4853	−	15.2913i	−0.509332	−	0.294063i
$53$	−27.9853	+	48.4719i	−0.528024	+	0.914565i	0.471442	+	0.881897i	$0.343734\pi$
$53$	−27.9853	+	48.4719i	−0.528024	+	0.914565i	−0.999466	+	0.0326677i	$0.989600\pi$
$54$	−15.3640	+	8.87039i	−0.284518	+	0.164266i
$55$			31.5462i			0.573567i
$56$	17.6569	−	8.95743i	0.315301	−	0.159954i
$57$	3.00000			0.0526316
$58$	−2.48528	−	4.30463i	−0.0428497	−	0.0742178i
$59$	33.5330	+	19.3603i	0.568356	+	0.328141i	0.756492	−	0.654002i	$-0.226911\pi$
$59$	33.5330	+	19.3603i	0.568356	+	0.328141i	−0.188136	+	0.982143i	$0.560245\pi$
$60$	4.75736	−	8.23999i	0.0792893	−	0.137333i
$61$	−78.3823	+	45.2540i	−1.28495	+	0.741869i	−0.977750	−	0.209774i	$-0.932727\pi$
$61$	−78.3823	+	45.2540i	−1.28495	+	0.741869i	−0.307205	+	0.951643i	$0.599394\pi$
$62$			69.1080i			1.11464i
$63$	−49.7574	−	32.4377i	−0.789799	−	0.514884i
$64$	8.00000			0.125000
$65$	−50.6985	−	87.8124i	−0.779977	−	1.35096i
$66$	−4.18019	−	2.41344i	−0.0633363	−	0.0365672i
$67$	17.3198	−	29.9988i	0.258505	−	0.447743i	−0.707337	−	0.706877i	$-0.750104\pi$
$67$	17.3198	−	29.9988i	0.258505	−	0.447743i	0.965842	+	0.259134i	$0.0834370\pi$
$68$	6.51472	−	3.76127i	0.0958047	−	0.0553129i
$69$			19.8931i			0.288306i
$70$	65.5477	+	3.55114i	0.936396	+	0.0507306i
$71$	36.4264			0.513048			0.256524	−	0.966538i	$-0.417423\pi$
$71$	36.4264			0.513048			0.256524	+	0.966538i	$0.417423\pi$
$72$	−12.0000	−	20.7846i	−0.166667	−	0.288675i
$73$	45.5589	+	26.3034i	0.624094	+	0.360321i	0.778461	−	0.627693i	$-0.216001\pi$
$73$	45.5589	+	26.3034i	0.624094	+	0.360321i	−0.154367	+	0.988014i	$0.549334\pi$
$74$	2.07969	−	3.60213i	0.0281039	−	0.0486774i
$75$	11.7868	−	6.80511i	0.157157	−	0.0907348i
$76$			8.36308i			0.110041i
$77$	1.80152	−	33.2528i	0.0233963	−	0.431854i
$78$	15.5147			0.198907
$79$	16.8934	+	29.2602i	0.213840	+	0.370383i	0.952913	−	0.303243i	$-0.0980694\pi$
$79$	16.8934	+	29.2602i	0.213840	+	0.370383i	−0.739073	+	0.673626i	$0.764736\pi$
$80$	22.9706	+	13.2621i	0.287132	+	0.165776i
$81$	−33.6838	+	58.3420i	−0.415849	+	0.720272i
$82$	−34.2426	+	19.7700i	−0.417593	+	0.241098i
$83$		−	127.577i		−	1.53708i	−0.639803	−	0.768539i	$-0.720984\pi$
$83$		−	127.577i		−	1.53708i	0.639803	−	0.768539i	$-0.279016\pi$
$84$	−5.48528	+	8.41407i	−0.0653010	+	0.100167i
$85$	24.9411			0.293425
$86$	7.41421	+	12.8418i	0.0862118	+	0.149323i
$87$	2.18377	+	1.26080i	0.0251008	+	0.0144919i
$88$	6.72792	−	11.6531i	0.0764537	−	0.132422i
$89$	−43.5883	+	25.1657i	−0.489756	+	0.282761i	−0.724473	−	0.689303i	$-0.757917\pi$
$89$	−43.5883	+	25.1657i	−0.489756	+	0.282761i	0.234717	+	0.972064i	$0.424584\pi$
$90$		−	79.5724i		−	0.884137i
$91$	48.4264	+	95.4580i	0.532158	+	1.04899i
$92$	−55.4558			−0.602781
$93$	−17.5294	−	30.3619i	−0.188489	−	0.326472i
$94$	−64.5183	−	37.2497i	−0.686365	−	0.396273i
$95$	−13.8640	+	24.0131i	−0.145936	+	0.252769i
$96$	−3.51472	+	2.02922i	−0.0366117	+	0.0211377i
$97$			101.792i			1.04940i	0.851287	+	0.524700i	$0.175823\pi$
$97$			101.792i			1.04940i	−0.851287	+	0.524700i	$0.824177\pi$
$98$	−68.8909	−	7.48650i	−0.702968	−	0.0763928i
$99$	−40.3675			−0.407753
$100$	18.9706	+	32.8580i	0.189706	+	0.328580i
$101$	−51.6838	−	29.8396i	−0.511720	−	0.295442i	0.221820	−	0.975088i	$-0.428800\pi$
$101$	−51.6838	−	29.8396i	−0.511720	−	0.295442i	−0.733541	+	0.679646i	$0.762134\pi$
$102$	−1.90812	+	3.30496i	−0.0187070	+	0.0324015i
$103$	104.077	−	60.0890i	1.01046	−	0.583388i	0.0991322	−	0.995074i	$-0.468393\pi$
$103$	104.077	−	60.0890i	1.01046	−	0.583388i	0.911326	+	0.411686i	$0.135060\pi$
$104$			43.2503i			0.415868i
$105$	−29.6985	+	15.0662i	−0.282843	+	0.143488i
$106$	79.1543			0.746739
$107$	56.8051	+	98.3893i	0.530889	+	0.919526i	0.999350	+	0.0360423i	$0.0114751\pi$
$107$	56.8051	+	98.3893i	0.530889	+	0.919526i	−0.468462	+	0.883484i	$0.655192\pi$
$108$	21.7279	+	12.5446i	0.201184	+	0.116154i
$109$	72.6543	−	125.841i	0.666553	−	1.15450i	−0.312308	−	0.949981i	$-0.601102\pi$
$109$	72.6543	−	125.841i	0.666553	−	1.15450i	0.978862	−	0.204524i	$-0.0655645\pi$
$110$	38.6360	−	22.3065i	0.351237	−	0.202787i
$111$			2.11008i			0.0190097i
$112$	−23.4558	−	15.2913i	−0.209427	−	0.136529i
$113$	34.5442			0.305700			0.152850	−	0.988249i	$-0.451155\pi$
$113$	34.5442			0.305700			0.152850	+	0.988249i	$0.451155\pi$
$114$	−2.12132	−	3.67423i	−0.0186081	−	0.0322301i
$115$	−159.231	−	91.9323i	−1.38462	−	0.799412i
$116$	−3.51472	+	6.08767i	−0.0302993	+	0.0524799i
$117$	112.368	−	64.8754i	0.960406	−	0.554491i
$118$		−	54.7592i		−	0.464061i
$119$	−26.2904	−	1.42432i	−0.220927	−	0.0119691i
$120$	−13.4558			−0.112132
$121$	49.1838	+	85.1888i	0.406477	+	0.704040i
$122$	110.849	+	63.9988i	0.908600	+	0.524581i
$123$	10.0294	−	17.3715i	0.0815401	−	0.141232i
$124$	84.6396	−	48.8667i	0.682578	−	0.394086i
$125$		−	39.9814i		−	0.319851i
$126$	−4.54416	+	83.8770i	−0.0360647	+	0.665690i
$127$	−247.338			−1.94754			−0.973772	−	0.227526i	$-0.926936\pi$
$127$	−247.338			−1.94754			−0.973772	+	0.227526i	$0.926936\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$	−6.51472	−	3.76127i	−0.0505017	−	0.0291572i
$130$	−71.6985	+	124.185i	−0.551527	+	0.955272i
$131$	−127.864	+	73.8223i	−0.976061	+	0.563529i	−0.901079	−	0.433656i	$-0.857223\pi$
$131$	−127.864	+	73.8223i	−0.976061	+	0.563529i	−0.0749822	+	0.997185i	$0.523890\pi$
$132$			6.82623i			0.0517139i
$133$	15.9853	−	24.5204i	0.120190	−	0.184364i
$134$	−48.9878			−0.365581
$135$	41.5919	+	72.0393i	0.308088	+	0.533624i
$136$	−9.21320	−	5.31925i	−0.0677441	−	0.0391121i
$137$	16.2868	−	28.2096i	0.118882	−	0.205909i	−0.800443	−	0.599409i	$-0.795402\pi$
$137$	16.2868	−	28.2096i	0.118882	−	0.205909i	0.919325	+	0.393500i	$0.128736\pi$
$138$	24.3640	−	14.0665i	0.176550	−	0.101931i
$139$			68.5857i			0.493422i	0.969089	+	0.246711i	$0.0793499\pi$
$139$			68.5857i			0.493422i	−0.969089	+	0.246711i	$0.920650\pi$
$140$	−42.0000	−	82.7903i	−0.300000	−	0.591359i
$141$	37.7939			0.268042
$142$	−25.7574	−	44.6131i	−0.181390	−	0.314176i
$143$	63.0000	+	36.3731i	0.440559	+	0.254357i
$144$	−16.9706	+	29.3939i	−0.117851	+	0.204124i
$145$	−20.1838	+	11.6531i	−0.139198	+	0.0803662i
$146$		−	74.3973i		−	0.509571i
$147$	32.1655	−	14.1853i	0.218813	−	0.0964984i
$148$	−5.88225			−0.0397449
$149$	−46.1985	−	80.0181i	−0.310057	−	0.537034i	0.668317	−	0.743876i	$-0.267015\pi$
$149$	−46.1985	−	80.0181i	−0.310057	−	0.537034i	−0.978374	+	0.206842i	$0.933681\pi$
$150$	−16.6690	−	9.62388i	−0.111127	−	0.0641592i
$151$	45.8934	−	79.4897i	0.303930	−	0.526422i	−0.673093	−	0.739558i	$-0.735035\pi$
$151$	45.8934	−	79.4897i	0.303930	−	0.526422i	0.977022	+	0.213136i	$0.0683678\pi$
$152$	10.2426	−	5.91359i	0.0673858	−	0.0389052i
$153$			31.9155i			0.208598i
$154$	−42.0000	+	21.3068i	−0.272727	+	0.138356i
$155$	324.037			2.09056
$156$	−10.9706	−	19.0016i	−0.0703241	−	0.121805i
$157$	7.32338	+	4.22815i	0.0466457	+	0.0269309i	0.523142	−	0.852246i	$-0.324760\pi$
$157$	7.32338	+	4.22815i	0.0466457	+	0.0269309i	−0.476496	+	0.879177i	$0.658093\pi$
$158$	23.8909	−	41.3802i	0.151208	−	0.261900i
$159$	−34.7756	+	20.0777i	−0.218715	+	0.126275i
$160$		−	37.5108i		−	0.234442i
$161$	162.595	+	105.999i	1.00991	+	0.658378i
$162$	95.2721			0.588099
$163$	−110.989	−	192.238i	−0.680913	−	1.17938i	−0.974703	−	0.223506i	$-0.928250\pi$
$163$	−110.989	−	192.238i	−0.680913	−	1.17938i	0.293789	−	0.955870i	$-0.405084\pi$
$164$	48.4264	+	27.9590i	0.295283	+	0.170482i
$165$	−11.3162	+	19.6003i	−0.0685832	+	0.118790i
$166$	−156.250	+	90.2109i	−0.941264	+	0.543439i
$167$			168.841i			1.01102i	0.862820	+	0.505511i	$0.168696\pi$
$167$			168.841i			1.01102i	−0.862820	+	0.505511i	$0.831304\pi$
$168$	14.1838	+	0.768426i	0.0844272	+	0.00457396i
$169$	−64.8234			−0.383570
$170$	−17.6360	−	30.5465i	−0.103741	−	0.179685i
$171$	−30.7279	−	17.7408i	−0.179695	−	0.103747i
$172$	10.4853	−	18.1610i	0.0609609	−	0.105587i
$173$	−142.323	+	82.1704i	−0.822678	+	0.474974i	−0.851339	−	0.524616i	$-0.824209\pi$
$173$	−142.323	+	82.1704i	−0.822678	+	0.474974i	0.0286608	+	0.999589i	$0.490876\pi$
$174$		−	3.56608i		−	0.0204947i
$175$	7.18377	−	132.599i	0.0410501	−	0.757711i
$176$	−19.0294			−0.108122
$177$	13.8898	+	24.0579i	0.0784736	+	0.135920i
$178$	61.6432	+	35.5897i	0.346310	+	0.199942i
$179$	−92.5919	+	160.374i	−0.517273	+	0.895943i	0.482526	+	0.875882i	$0.339720\pi$
$179$	−92.5919	+	160.374i	−0.517273	+	0.895943i	−0.999799	+	0.0200614i	$0.993614\pi$
$180$	−97.4558	+	56.2662i	−0.541421	+	0.312590i
$181$		−	155.086i		−	0.856830i	−0.903582	−	0.428415i	$-0.859072\pi$
$181$		−	155.086i		−	0.856830i	0.903582	−	0.428415i	$-0.140928\pi$
$182$	82.6690	−	126.809i	0.454226	−	0.696753i
$183$	−64.9340			−0.354831
$184$	39.2132	+	67.9193i	0.213115	+	0.369126i
$185$	−16.8898	−	9.75135i	−0.0912964	−	0.0527100i
$186$	−24.7904	+	42.9382i	−0.133282	+	0.230850i
$187$	−15.4964	+	8.94687i	−0.0828686	+	0.0478442i
$188$			105.358i			0.560415i
$189$	−39.7279	−	78.3116i	−0.210201	−	0.414347i
$190$	39.2132			0.206385
$191$	−124.048	−	214.857i	−0.649465	−	1.12491i	−0.983251	−	0.182257i	$-0.941660\pi$
$191$	−124.048	−	214.857i	−0.649465	−	1.12491i	0.333786	−	0.942649i	$-0.391674\pi$
$192$	4.97056	+	2.86976i	0.0258883	+	0.0149466i
$193$	−77.1690	+	133.661i	−0.399840	+	0.692543i	−0.993706	−	0.112021i	$-0.964268\pi$
$193$	−77.1690	+	133.661i	−0.399840	+	0.692543i	0.593866	+	0.804564i	$0.297601\pi$
$194$	124.669	−	71.9777i	0.642624	−	0.371019i
$195$		−	72.7461i		−	0.373057i
$196$	39.5442	+	89.6675i	0.201756	+	0.457487i
$197$	−181.103			−0.919303			−0.459651	−	0.888099i	$-0.652026\pi$
$197$	−181.103			−0.919303			−0.459651	+	0.888099i	$0.652026\pi$
$198$	28.5442	+	49.4399i	0.144162	+	0.249697i
$199$	301.989	+	174.353i	1.51753	+	0.876147i	0.999788	+	0.0206121i	$0.00656150\pi$
$199$	301.989	+	174.353i	1.51753	+	0.876147i	0.517744	+	0.855535i	$0.326772\pi$
$200$	26.8284	−	46.4682i	0.134142	−	0.232341i
$201$	21.5223	−	12.4259i	0.107076	−	0.0618204i
$202$			84.3992i			0.417818i
$203$	21.9411	−	11.1309i	0.108084	−	0.0548318i
$204$	5.39697			0.0264557
$205$	92.6985	+	160.558i	0.452188	+	0.783212i
$206$	−147.187	−	84.9786i	−0.714502	−	0.412518i
$207$	117.640	−	203.758i	0.568307	−	0.984337i
$208$	52.9706	−	30.5826i	0.254666	−	0.147032i
$209$		−	19.8931i		−	0.0951823i
$210$	39.4523	+	25.7196i	0.187868	+	0.122474i
$211$	364.073			1.72547			0.862733	−	0.505660i	$-0.168751\pi$
$211$	364.073			1.72547			0.862733	+	0.505660i	$0.168751\pi$
$212$	−55.9706	−	96.9439i	−0.264012	−	0.457282i
$213$	22.6325	+	13.0669i	0.106256	+	0.0613468i
$214$	80.3345	−	139.143i	0.375395	−	0.650203i
$215$	60.2132	−	34.7641i	0.280061	−	0.161694i
$216$		−	35.4815i		−	0.164266i
$217$	−341.566	−	18.5048i	−1.57404	−	0.0852757i
$218$	−205.497			−0.942649
$219$	18.8711	+	32.6857i	0.0861694	+	0.149250i
$220$	−54.6396	−	31.5462i	−0.248362	−	0.143392i
$221$	28.7574	−	49.8092i	0.130124	−	0.225381i
$222$	2.58431	−	1.49205i	0.0116410	−	0.00672095i
$223$			123.231i			0.552603i	0.961071	+	0.276302i	$0.0891089\pi$
$223$			123.231i			0.552603i	−0.961071	+	0.276302i	$0.910891\pi$
$224$	−2.14214	+	39.5400i	−0.00956311	+	0.176518i
$225$	−160.971			−0.715425
$226$	−24.4264	−	42.3078i	−0.108081	−	0.187203i
$227$	−66.1432	−	38.1878i	−0.291380	−	0.168228i	0.347184	−	0.937797i	$-0.387138\pi$
$227$	−66.1432	−	38.1878i	−0.291380	−	0.168228i	−0.638564	+	0.769569i	$0.720471\pi$
$228$	−3.00000	+	5.19615i	−0.0131579	+	0.0227901i
$229$	309.419	−	178.643i	1.35117	−	0.780101i	0.362760	−	0.931883i	$-0.381834\pi$
$229$	309.419	−	178.643i	1.35117	−	0.780101i	0.988414	+	0.151782i	$0.0485012\pi$
$230$			260.024i			1.13054i
$231$	13.0477	−	20.0144i	0.0564837	−	0.0866423i
$232$	9.94113			0.0428497
$233$	136.537	+	236.488i	0.585994	+	1.01497i	0.994751	+	0.102328i	$0.0326291\pi$
$233$	136.537	+	236.488i	0.585994	+	1.01497i	−0.408757	+	0.912643i	$0.634038\pi$
$234$	−158.912	−	91.7477i	−0.679110	−	0.392084i
$235$	−174.658	+	302.516i	−0.743225	+	1.28730i
$236$	−67.0660	+	38.7206i	−0.284178	+	0.164070i
$237$			24.2400i			0.102278i
$238$	16.8457	+	33.2061i	0.0707801	+	0.139522i
$239$	−265.103			−1.10922			−0.554608	−	0.832112i	$-0.687132\pi$
$239$	−265.103			−1.10922			−0.554608	+	0.832112i	$0.687132\pi$
$240$	9.51472	+	16.4800i	0.0396447	+	0.0686666i
$241$	−75.8970	−	43.8191i	−0.314925	−	0.181822i	0.334203	−	0.942501i	$-0.391533\pi$
$241$	−75.8970	−	43.8191i	−0.314925	−	0.181822i	−0.649128	+	0.760679i	$0.724866\pi$
$242$	69.5563	−	120.475i	0.287423	−	0.497831i
$243$	−139.632	+	80.6168i	−0.574619	+	0.331757i
$244$		−	181.016i		−	0.741869i
$245$	−35.1030	+	323.019i	−0.143278	+	1.31844i
$246$	−28.3675			−0.115315
$247$	31.9706	+	55.3746i	0.129435	+	0.224189i
$248$	−119.698	−	69.1080i	−0.482655	−	0.278661i
$249$	45.7645	−	79.2664i	0.183793	−	0.318339i
$250$	−48.9670	+	28.2711i	−0.195868	+	0.113084i
$251$		−	495.655i		−	1.97472i	−0.158491	−	0.987360i	$-0.550663\pi$
$251$		−	495.655i		−	1.97472i	0.158491	−	0.987360i	$-0.449337\pi$
$252$	105.941	−	53.7446i	0.420401	−	0.213272i
$253$	131.912			0.521390
$254$	174.894	+	302.926i	0.688561	+	1.19262i
$255$	15.4964	+	8.94687i	0.0607703	+	0.0350858i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	346.875	−	200.268i	1.34971	−	0.779254i	0.361499	−	0.932372i	$-0.382265\pi$
$257$	346.875	−	200.268i	1.34971	−	0.779254i	0.988208	+	0.153119i	$0.0489317\pi$
$258$			10.6385i			0.0412345i
$259$	17.2466	+	11.2434i	0.0665894	+	0.0434108i
$260$	202.794			0.779977
$261$	−14.9117	−	25.8278i	−0.0571329	−	0.0989571i
$262$	180.827	+	104.400i	0.690179	+	0.398475i
$263$	16.1726	−	28.0118i	0.0614928	−	0.106509i	−0.833640	−	0.552308i	$-0.813747\pi$
$263$	16.1726	−	28.0118i	0.0614928	−	0.106509i	0.895133	+	0.445799i	$0.147081\pi$
$264$	8.36039	−	4.82687i	0.0316681	−	0.0182836i
$265$		−	371.142i		−	1.40054i
$266$	−41.3345	−	2.23936i	−0.155393	−	0.00841863i
$267$	−36.1097			−0.135242
$268$	34.6396	+	59.9976i	0.129252	+	0.223872i
$269$	−265.838	−	153.482i	−0.988246	−	0.570564i	−0.0834963	−	0.996508i	$-0.526609\pi$
$269$	−265.838	−	153.482i	−0.988246	−	0.570564i	−0.904749	+	0.425944i	$0.859942\pi$
$270$	58.8198	−	101.879i	0.217851	−	0.377329i
$271$	−65.8051	+	37.9926i	−0.242823	+	0.140194i	−0.616474	−	0.787376i	$-0.711439\pi$
$271$	−65.8051	+	37.9926i	−0.242823	+	0.140194i	0.373650	+	0.927570i	$0.378106\pi$
$272$			15.0451i			0.0553129i
$273$	−4.15433	+	76.6815i	−0.0152173	+	0.280885i
$274$	−46.0660			−0.168124
$275$	−45.1249	−	78.1586i	−0.164091	−	0.284213i
$276$	−34.4558	−	19.8931i	−0.124840	−	0.0720764i
$277$	−139.206	+	241.111i	−0.502547	+	0.870438i	0.497448	+	0.867494i	$0.334270\pi$
$277$	−139.206	+	241.111i	−0.502547	+	0.870438i	−0.999996	+	0.00294398i	$0.999063\pi$
$278$	84.0000	−	48.4974i	0.302158	−	0.174451i
$279$			414.648i			1.48619i
$280$	−71.6985	+	109.981i	−0.256066	+	0.392789i
$281$	394.690			1.40459			0.702296	−	0.711885i	$-0.252158\pi$
$281$	394.690			1.40459			0.702296	+	0.711885i	$0.252158\pi$
$282$	−26.7244	−	46.2879i	−0.0947672	−	0.164142i
$283$	126.783	+	73.1981i	0.447996	+	0.258650i	0.706983	−	0.707230i	$-0.250056\pi$
$283$	126.783	+	73.1981i	0.447996	+	0.258650i	−0.258988	+	0.965881i	$0.583389\pi$
$284$	−36.4264	+	63.0924i	−0.128262	+	0.222156i
$285$	−17.2279	+	9.94655i	−0.0604488	+	0.0349002i
$286$		−	102.879i		−	0.359715i
$287$	−88.5442	−	174.538i	−0.308516	−	0.608146i
$288$	48.0000			0.166667
$289$	−137.426	−	238.030i	−0.475524	−	0.823632i
$290$	28.5442	+	16.4800i	0.0984281	+	0.0568275i
$291$	−36.5147	+	63.2453i	−0.125480	+	0.217338i
$292$	−91.1177	+	52.6069i	−0.312047	+	0.180160i
$293$			299.678i			1.02279i	0.859345	+	0.511396i	$0.170872\pi$
$293$			299.678i			1.02279i	−0.859345	+	0.511396i	$0.829128\pi$
$294$	−40.1177	−	29.3640i	−0.136455	−	0.0998776i
$295$	−256.757			−0.870364
$296$	4.15938	+	7.20426i	0.0140520	+	0.0243387i
$297$	−51.6838	−	29.8396i	−0.174019	−	0.100470i
$298$	−65.3345	+	113.163i	−0.219243	+	0.379741i
$299$	−367.191	+	211.998i	−1.22806	+	0.709023i
$300$			27.2204i			0.0907348i
$301$	−65.4558	+	33.2061i	−0.217461	+	0.110319i
$302$	−129.806			−0.429822
$303$	−21.4081	−	37.0799i	−0.0706539	−	0.122376i
$304$	−14.4853	−	8.36308i	−0.0476490	−	0.0275101i
$305$	300.081	−	519.755i	0.983871	−	1.70412i
$306$	39.0883	−	22.5676i	0.127740	−	0.0737505i
$307$		−	20.9886i		−	0.0683666i	−0.999416	−	0.0341833i	$-0.989117\pi$
$307$		−	20.9886i		−	0.0683666i	0.999416	−	0.0341833i	$-0.0108830\pi$
$308$	55.7939	+	36.3731i	0.181149	+	0.118094i
$309$	86.2203			0.279030
$310$	−229.128	−	396.862i	−0.739124	−	1.28020i
$311$	157.651	+	91.0197i	0.506916	+	0.292668i	0.731565	−	0.681772i	$-0.238790\pi$
$311$	157.651	+	91.0197i	0.506916	+	0.292668i	−0.224649	+	0.974440i	$0.572124\pi$
$312$	−15.5147	+	26.8723i	−0.0497267	+	0.0861291i
$313$	−84.8087	+	48.9643i	−0.270954	+	0.156435i	−0.629321	−	0.777145i	$-0.716667\pi$
$313$	−84.8087	+	48.9643i	−0.270954	+	0.156435i	0.358367	+	0.933581i	$0.383334\pi$
$314$		−	11.9590i		−	0.0380861i
$315$	393.286	+	21.3068i	1.24853	+	0.0676408i
$316$	−67.5736			−0.213840
$317$	240.985	+	417.399i	0.760206	+	1.31672i	0.942744	+	0.333517i	$0.108235\pi$
$317$	240.985	+	417.399i	0.760206	+	1.31672i	−0.182538	+	0.983199i	$0.558431\pi$
$318$	49.1802	+	28.3942i	0.154655	+	0.0892899i
$319$	8.36039	−	14.4806i	0.0262081	−	0.0453938i
$320$	−45.9411	+	26.5241i	−0.143566	+	0.0828879i
$321$			81.5084i			0.253920i
$322$	14.8492	−	274.090i	0.0461157	−	0.851213i
$323$	−15.7279			−0.0486933
$324$	−67.3675	−	116.684i	−0.207924	−	0.360136i
$325$	251.220	+	145.042i	0.772986	+	0.446283i
$326$	−156.962	+	271.866i	−0.481478	+	0.833945i
$327$	90.2832	−	52.1250i	0.276095	−	0.159404i
$328$		−	79.0800i		−	0.241098i
$329$	201.382	−	308.907i	0.612104	−	0.938928i
$330$	32.0071			0.0969913
$331$	−112.504	−	194.862i	−0.339890	−	0.588707i	0.644522	−	0.764586i	$-0.277056\pi$
$331$	−112.504	−	194.862i	−0.339890	−	0.588707i	−0.984412	+	0.175879i	$0.943723\pi$
$332$	220.971	+	127.577i	0.665574	+	0.384269i
$333$	12.4781	−	21.6128i	0.0374719	−	0.0649032i
$334$	206.787	−	119.388i	0.619122	−	0.357450i
$335$			229.696i			0.685661i
$336$	−9.08831	−	17.9149i	−0.0270485	−	0.0533180i
$337$	−264.368			−0.784473			−0.392237	−	0.919864i	$-0.628299\pi$
$337$	−264.368			−0.784473			−0.392237	+	0.919864i	$0.628299\pi$
$338$	45.8370	+	79.3921i	0.135613	+	0.234888i
$339$	21.4630	+	12.3917i	0.0633126	+	0.0365536i
$340$	−24.9411	+	43.1993i	−0.0733563	+	0.127057i
$341$	−201.331	+	116.238i	−0.590412	+	0.340875i
$342$			50.1785i			0.146721i
$343$	55.4487	−	338.488i	0.161658	−	0.986847i
$344$	−29.6569			−0.0862118
$345$	−65.9558	−	114.239i	−0.191176	−	0.331127i
$346$	201.276	+	116.207i	0.581722	+	0.335857i
$347$	95.6285	−	165.633i	0.275586	−	0.477330i	−0.694697	−	0.719303i	$-0.744461\pi$
$347$	95.6285	−	165.633i	0.275586	−	0.477330i	0.970283	+	0.241973i	$0.0777947\pi$
$348$	−4.36753	+	2.52160i	−0.0125504	+	0.00724597i
$349$			135.448i			0.388104i	0.980991	+	0.194052i	$0.0621630\pi$
$349$			135.448i			0.388104i	−0.980991	+	0.194052i	$0.937837\pi$
$350$	−167.480	+	84.9637i	−0.478515	+	0.242753i
$351$	191.823			0.546505
$352$	13.4558	+	23.3062i	0.0382268	+	0.0662108i
$353$	−301.802	−	174.245i	−0.854962	−	0.493612i	0.00736010	−	0.999973i	$-0.497657\pi$
$353$	−301.802	−	174.245i	−0.854962	−	0.493612i	−0.862322	+	0.506360i	$0.830991\pi$
$354$	19.6432	−	34.0230i	0.0554892	−	0.0961101i
$355$	−209.184	+	120.772i	−0.589250	+	0.340204i
$356$		−	100.663i		−	0.282761i
$357$	−15.8238	−	10.3158i	−0.0443244	−	0.0288959i
$358$	261.889			0.731535
$359$	−152.415	−	263.991i	−0.424555	−	0.735351i	0.571824	−	0.820377i	$-0.306236\pi$
$359$	−152.415	−	263.991i	−0.424555	−	0.735351i	−0.996379	+	0.0850256i	$0.972903\pi$
$360$	137.823	+	79.5724i	0.382843	+	0.221034i
$361$	−171.757	+	297.492i	−0.475782	+	0.824079i
$362$	−189.941	+	109.663i	−0.524699	+	0.302935i
$363$			70.5727i			0.194415i
$364$	−213.765	−	11.5810i	−0.587265	−	0.0318159i
$365$	−348.838			−0.955720
$366$	45.9153	+	79.5276i	0.125452	+	0.217288i
$367$	−82.2761	−	47.5021i	−0.224186	−	0.129434i	0.383701	−	0.923457i	$-0.374649\pi$
$367$	−82.2761	−	47.5021i	−0.224186	−	0.129434i	−0.607887	+	0.794024i	$0.707983\pi$
$368$	55.4558	−	96.0523i	0.150695	−	0.261012i
$369$	−205.456	+	118.620i	−0.556791	+	0.321463i
$370$			27.5810i			0.0745432i
$371$	−21.1949	+	391.220i	−0.0571291	+	1.05450i
$372$	70.1177			0.188489
$373$	−126.779	−	219.588i	−0.339891	−	0.588708i	0.644521	−	0.764586i	$-0.277057\pi$
$373$	−126.779	−	219.588i	−0.339891	−	0.588708i	−0.984412	+	0.175879i	$0.943723\pi$
$374$	21.9153	+	12.6528i	0.0585970	+	0.0338310i
$375$	14.3421	−	24.8412i	0.0382456	−	0.0662433i
$376$	129.037	−	74.4993i	0.343182	−	0.198136i
$377$			53.7446i			0.142559i
$378$	−67.8198	+	104.031i	−0.179417	+	0.275215i
$379$	508.250			1.34103			0.670514	−	0.741897i	$-0.266074\pi$
$379$	508.250			1.34103			0.670514	+	0.741897i	$0.266074\pi$
$380$	−27.7279	−	48.0262i	−0.0729682	−	0.126385i
$381$	−153.676	−	88.7250i	−0.403350	−	0.232874i
$382$	−175.430	+	303.854i	−0.459241	+	0.795428i
$383$	413.753	−	238.881i	1.08030	−	0.623709i	0.149320	−	0.988789i	$-0.452292\pi$
$383$	413.753	−	238.881i	1.08030	−	0.623709i	0.930976	+	0.365080i	$0.118958\pi$
$384$		−	8.11689i		−	0.0211377i
$385$	99.9045	+	196.932i	0.259492	+	0.511511i
$386$	218.267			0.565459
$387$	44.4853	+	77.0508i	0.114949	+	0.199098i
$388$	−176.309	−	101.792i	−0.454404	−	0.262350i
$389$	−85.1102	+	147.415i	−0.218792	+	0.378959i	−0.954439	−	0.298406i	$-0.903545\pi$
$389$	−85.1102	+	147.415i	−0.218792	+	0.378959i	0.735647	+	0.677365i	$0.236878\pi$
$390$	−89.0955	+	51.4393i	−0.228450	+	0.131896i
$391$		−	104.292i		−	0.266732i
$392$	81.8579	−	111.836i	0.208821	−	0.285296i
$393$	−105.926			−0.269532
$394$	128.059	+	221.804i	0.325023	+	0.562956i
$395$	−194.025	−	112.021i	−0.491204	−	0.283597i
$396$	40.3675	−	69.9186i	0.101938	−	0.176562i
$397$	211.786	−	122.275i	0.533467	−	0.307997i	−0.208960	−	0.977924i	$-0.567008\pi$
$397$	211.786	−	122.275i	0.533467	−	0.307997i	0.742427	+	0.669927i	$0.233675\pi$
$398$		−	493.146i		−	1.23906i
$399$	18.7279	−	9.50079i	0.0469371	−	0.0238115i
$400$	−75.8823			−0.189706
$401$	208.786	+	361.629i	0.520664	+	0.901817i	0.999711	+	0.0240277i	$0.00764899\pi$
$401$	208.786	+	361.629i	0.520664	+	0.901817i	−0.479047	+	0.877789i	$0.659018\pi$
$402$	−30.4371	−	17.5729i	−0.0757142	−	0.0437136i
$403$	373.617	−	647.124i	0.927090	−	1.60577i
$404$	103.368	−	59.6793i	0.255860	−	0.147721i
$405$		−	446.716i		−	1.10300i
$406$	−29.1472	−	19.0016i	−0.0717911	−	0.0468019i
$407$	13.9920			0.0343784
$408$	−3.81623	−	6.60991i	−0.00935351	−	0.0162008i
$409$	266.919	+	154.106i	0.652614	+	0.376787i	0.789457	−	0.613806i	$-0.210362\pi$
$409$	266.919	+	154.106i	0.652614	+	0.376787i	−0.136843	+	0.990593i	$0.543696\pi$
$410$	131.095	−	227.064i	0.319745	−	0.553815i
$411$	20.2386	−	11.6848i	0.0492424	−	0.0284301i
$412$			240.356i			0.583388i
$413$	270.647	+	14.6627i	0.655320	+	0.0355029i
$414$	−332.735			−0.803708
$415$	422.985	+	732.631i	1.01924	+	1.76538i
$416$	−74.9117	−	43.2503i	−0.180076	−	0.103967i
$417$	−24.6030	+	42.6137i	−0.0590001	+	0.102191i
$418$	−24.3640	+	14.0665i	−0.0582870	+	0.0336520i
$419$		−	103.142i		−	0.246163i	−0.992397	−	0.123081i	$-0.960722\pi$
$419$		−	103.142i		−	0.246163i	0.992397	−	0.123081i	$-0.0392776\pi$
$420$	3.60303	−	66.5055i	0.00857864	−	0.158346i
$421$	−165.220			−0.392447			−0.196224	−	0.980559i	$-0.562868\pi$
$421$	−165.220			−0.392447			−0.196224	+	0.980559i	$0.562868\pi$
$422$	−257.439	−	445.897i	−0.610044	−	1.05663i
$423$	−387.110	−	223.498i	−0.915153	−	0.528364i
$424$	−79.1543	+	137.099i	−0.186685	+	0.323347i
$425$	−61.7939	+	35.6767i	−0.145398	+	0.0839453i
$426$		−	36.9587i		−	0.0867574i
$427$	−345.996	+	530.736i	−0.810295	+	1.24294i
$428$	−227.220			−0.530889
$429$	26.0955	+	45.1987i	0.0608286	+	0.105358i
$430$	−85.1543	−	49.1639i	−0.198033	−	0.114335i
$431$	−297.268	+	514.883i	−0.689717	+	1.19463i	0.282212	+	0.959352i	$0.408932\pi$
$431$	−297.268	+	514.883i	−0.689717	+	1.19463i	−0.971929	+	0.235273i	$0.924402\pi$
$432$	−43.4558	+	25.0892i	−0.100592	+	0.0580770i
$433$		−	40.6267i		−	0.0938261i	−0.998899	−	0.0469131i	$-0.985062\pi$
$433$		−	40.6267i		−	0.0938261i	0.998899	−	0.0469131i	$-0.0149384\pi$
$434$	218.860	+	431.416i	0.504286	+	0.994046i
$435$	−16.7208			−0.0384386
$436$	145.309	+	251.682i	0.333277	+	0.577252i
$437$	100.412	+	57.9727i	0.229775	+	0.132661i
$438$	26.6878	−	46.2246i	0.0609310	−	0.105536i
$439$	126.959	−	73.3001i	0.289201	−	0.166971i	−0.348380	−	0.937353i	$-0.613268\pi$
$439$	126.959	−	73.3001i	0.289201	−	0.166971i	0.637582	+	0.770383i	$0.279935\pi$
$440$			89.2261i			0.202787i
$441$	−413.345	−	44.9190i	−0.937291	−	0.101857i
$442$	−81.3381			−0.184023
$443$	−53.6802	−	92.9768i	−0.121174	−	0.209880i	0.799057	−	0.601256i	$-0.205333\pi$
$443$	−53.6802	−	92.9768i	−0.121174	−	0.209880i	−0.920231	+	0.391376i	$0.871999\pi$
$444$	−3.65476	−	2.11008i	−0.00823145	−	0.00475243i
$445$	166.875	−	289.035i	0.374999	−	0.649518i
$446$	150.926	−	87.1372i	0.338399	−	0.195375i
$447$		−	66.2892i		−	0.148298i
$448$	49.9411	−	25.3354i	0.111476	−	0.0565523i
$449$	135.161			0.301028			0.150514	−	0.988608i	$-0.451907\pi$
$449$	135.161			0.301028			0.150514	+	0.988608i	$0.451907\pi$
$450$	113.823	+	197.148i	0.252941	+	0.438106i
$451$	−115.191	−	66.5055i	−0.255412	−	0.147462i
$452$	−34.5442	+	59.8322i	−0.0764251	+	0.132372i
$453$	57.0290	−	32.9257i	0.125892	−	0.0726837i
$454$			108.011i			0.237910i
$455$	−594.588	−	387.622i	−1.30679	−	0.851918i
$456$	8.48528			0.0186081
$457$	−79.8675	−	138.335i	−0.174765	−	0.302702i	0.765315	−	0.643656i	$-0.222583\pi$
$457$	−79.8675	−	138.335i	−0.174765	−	0.302702i	−0.940080	+	0.340954i	$0.889250\pi$
$458$	−437.584	−	252.639i	−0.955424	−	0.551614i
$459$	−23.5919	+	40.8623i	−0.0513984	+	0.0890247i
$460$	318.463	−	183.865i	0.692311	−	0.399706i
$461$			310.250i			0.672993i	0.941685	+	0.336497i	$0.109242\pi$
$461$			310.250i			0.672993i	−0.941685	+	0.336497i	$0.890758\pi$
$462$	−33.7386	−	1.82784i	−0.0730274	−	0.00395636i
$463$	−326.014			−0.704135			−0.352067	−	0.935975i	$-0.614521\pi$
$463$	−326.014			−0.704135			−0.352067	+	0.935975i	$0.614521\pi$
$464$	−7.02944	−	12.1753i	−0.0151496	−	0.0262400i
$465$	201.331	+	116.238i	0.432969	+	0.249975i
$466$	193.092	−	334.445i	0.414360	−	0.717693i
$467$	515.769	−	297.779i	1.10443	−	0.637643i	0.167048	−	0.985949i	$-0.446576\pi$
$467$	515.769	−	297.779i	1.10443	−	0.637643i	0.937381	+	0.348306i	$0.113243\pi$
$468$			259.502i			0.554491i
$469$	13.1173	−	242.122i	0.0279687	−	0.516252i
$470$	494.007			1.05108
$471$	3.03344	+	5.25408i	0.00644043	+	0.0111551i
$472$	94.8457	+	54.7592i	0.200944	+	0.116015i
$473$	−24.9411	+	43.1993i	−0.0527297	+	0.0913304i
$474$	29.6878	−	17.1402i	0.0626324	−	0.0361608i
$475$		−	79.3262i		−	0.167002i
$476$	28.7574	−	44.1119i	0.0604146	−	0.0926721i
$477$	474.926			0.995652
$478$	187.456	+	324.683i	0.392167	+	0.679253i
$479$	438.798	+	253.340i	0.916071	+	0.528894i	0.882379	−	0.470539i	$-0.155940\pi$
$479$	438.798	+	253.340i	0.916071	+	0.528894i	0.0336914	+	0.999432i	$0.489274\pi$
$480$	13.4558	−	23.3062i	0.0280330	−	0.0485546i
$481$	−38.9483	+	22.4868i	−0.0809735	+	0.0467501i
$482$			123.939i			0.257135i
$483$	63.0000	+	124.185i	0.130435	+	0.257113i
$484$	−196.735			−0.406477
$485$	−337.492	−	584.554i	−0.695861	−	1.20527i
$486$	197.470	+	114.009i	0.406317	+	0.234587i
$487$	−105.651	+	182.992i	−0.216942	+	0.375755i	−0.953872	−	0.300215i	$-0.902942\pi$
$487$	−105.651	+	182.992i	−0.216942	+	0.375755i	0.736930	+	0.675970i	$0.236275\pi$
$488$	−221.698	+	127.998i	−0.454300	+	0.262290i
$489$		−	159.255i		−	0.325676i
$490$	420.437	−	185.416i	0.858035	−	0.378401i
$491$	−784.161			−1.59707			−0.798534	−	0.601949i	$-0.794391\pi$
$491$	−784.161			−1.59707			−0.798534	+	0.601949i	$0.794391\pi$
$492$	20.0589	+	34.7430i	0.0407701	+	0.0706158i
$493$	−11.4487	−	6.60991i	−0.0232225	−	0.0134075i
$494$	45.2132	−	78.3116i	0.0915247	−	0.158525i
$495$	231.816	−	133.839i	0.468316	−	0.270382i
$496$			195.467i			0.394086i
$497$	227.397	−	115.360i	0.457539	−	0.232112i
$498$	−129.442			−0.259923
$499$	85.7462	+	148.517i	0.171836	+	0.297629i	0.939062	−	0.343748i	$-0.111697\pi$
$499$	85.7462	+	148.517i	0.171836	+	0.297629i	−0.767226	+	0.641377i	$0.778363\pi$
$500$	69.2498	+	39.9814i	0.138500	+	0.0799628i
$501$	−60.5665	+	104.904i	−0.120891	+	0.209390i
$502$	−607.051	+	350.481i	−1.20926	+	0.698169i
$503$		−	20.0883i		−	0.0399370i	−0.999801	−	0.0199685i	$-0.993643\pi$
$503$		−	20.0883i		−	0.0399370i	0.999801	−	0.0199685i	$-0.00635659\pi$
$504$	−140.735	−	91.7477i	−0.279236	−	0.182039i
$505$	395.735			0.783634
$506$	−93.2756	−	161.558i	−0.184339	−	0.319285i
$507$	−40.2761	−	23.2534i	−0.0794400	−	0.0458647i
$508$	247.338	−	428.402i	0.486886	−	0.843311i
$509$	−412.890	+	238.382i	−0.811178	+	0.468334i	−0.847365	−	0.531011i	$-0.821812\pi$
$509$	−412.890	+	238.382i	−0.811178	+	0.468334i	0.0361865	+	0.999345i	$0.488479\pi$
$510$		−	25.3056i		−	0.0496187i
$511$	367.709	+	19.9211i	0.719587	+	0.0389846i
$512$	22.6274			0.0441942
$513$	−26.2279	−	45.4281i	−0.0511266	−	0.0885538i
$514$	−490.555	−	283.222i	−0.954387	−	0.551016i
$515$	−398.452	+	690.139i	−0.773693	+	1.34008i
$516$	13.0294	−	7.52255i	0.0252508	−	0.0145786i
$517$		−	250.613i		−	0.484744i
$518$	1.57507	−	29.0730i	0.00304068	−	0.0561255i
$519$	−117.905			−0.227176
$520$	−143.397	−	248.371i	−0.275763	−	0.477636i
$521$	739.823	+	427.137i	1.42001	+	0.819841i	0.996299	−	0.0859587i	$-0.0273953\pi$
$521$	739.823	+	427.137i	1.42001	+	0.819841i	0.423707	+	0.905799i	$0.360729\pi$
$522$	−21.0883	+	36.5260i	−0.0403991	+	0.0699732i
$523$	−513.554	+	296.501i	−0.981940	+	0.566923i	−0.902855	−	0.429945i	$-0.858533\pi$
$523$	−513.554	+	296.501i	−0.981940	+	0.566923i	−0.0790845	+	0.996868i	$0.525200\pi$
$524$		−	295.289i		−	0.563529i
$525$	52.0294	−	79.8098i	0.0991037	−	0.152019i
$526$	−45.7431			−0.0869640
$527$	91.9005	+	159.176i	0.174384	+	0.302043i
$528$	−11.8234	−	6.82623i	−0.0223928	−	0.0129285i
$529$	−119.919	+	207.706i	−0.226690	+	0.392638i
$530$	−454.555	+	262.437i	−0.857651	+	0.495165i
$531$		−	328.555i		−	0.618748i
$532$	26.4853	+	52.2077i	0.0497844	+	0.0981348i
$533$	427.529			0.802118
$534$	25.5334	+	44.2252i	0.0478154	+	0.0828188i
$535$	−652.422	−	376.676i	−1.21948	−	0.704068i
$536$	48.9878	−	84.8494i	0.0913952	−	0.158301i
$537$	−115.058	+	66.4290i	−0.214262	+	0.123704i
$538$			434.112i			0.806899i
$539$	−94.0629	−	213.290i	−0.174514	−	0.395715i
$540$	−166.368			−0.308088
$541$	−427.595	−	740.617i	−0.790380	−	1.36898i	−0.925732	−	0.378180i	$-0.876550\pi$
$541$	−427.595	−	740.617i	−0.790380	−	1.36898i	0.135352	−	0.990798i	$-0.456783\pi$
$542$	93.0624	+	53.7296i	0.171702	+	0.0991322i
$543$	55.6325	−	96.3583i	0.102454	−	0.177455i
$544$	18.4264	−	10.6385i	0.0338721	−	0.0195560i
$545$			963.546i			1.76797i
$546$	96.8528	−	49.1340i	0.177386	−	0.0899890i
$547$	415.897			0.760323			0.380161	−	0.924920i	$-0.375868\pi$
$547$	415.897			0.760323			0.380161	+	0.924920i	$0.375868\pi$
$548$	32.5736	+	56.4191i	0.0594409	+	0.102955i
$549$	665.095	+	383.993i	1.21147	+	0.699441i
$550$	−63.8162	+	110.533i	−0.116030	+	0.200969i
$551$	12.7279	−	7.34847i	0.0230997	−	0.0133366i
$552$			56.2662i			0.101931i
$553$	198.124	+	129.161i	0.358272	+	0.233564i
$554$	393.733			0.710709
$555$	−6.99600	−	12.1174i	−0.0126054	−	0.0218332i
$556$	−118.794	−	68.5857i	−0.213658	−	0.123356i
$557$	292.110	−	505.950i	0.524435	−	0.908348i	−0.475160	−	0.879899i	$-0.657610\pi$
$557$	292.110	−	505.950i	0.524435	−	0.908348i	0.999595	−	0.0284485i	$-0.00905667\pi$
$558$	507.838	−	293.200i	0.910103	−	0.525448i
$559$		−	160.333i		−	0.286822i
$560$	185.397	+	10.0441i	0.331066	+	0.0179360i
$561$	−12.8377			−0.0228835
$562$	−279.088	−	483.395i	−0.496598	−	0.860134i
$563$	789.076	+	455.573i	1.40156	+	0.809189i	0.994552	−	0.104237i	$-0.0332402\pi$
$563$	789.076	+	455.573i	1.40156	+	0.809189i	0.407004	+	0.913426i	$0.366573\pi$
$564$	−37.7939	+	65.4610i	−0.0670105	+	0.116066i
$565$	−198.375	+	114.532i	−0.351106	+	0.202711i
$566$		−	207.035i		−	0.365787i
$567$	−25.5107	+	470.882i	−0.0449924	+	0.830480i
$568$	103.029			0.181390
$569$	−350.000	−	606.217i	−0.615113	−	1.06541i	−0.990365	−	0.138485i	$-0.955777\pi$
$569$	−350.000	−	606.217i	−0.615113	−	1.06541i	0.375251	−	0.926923i	$-0.377556\pi$
$570$	24.3640	+	14.0665i	0.0427438	+	0.0246781i
$571$	281.231	−	487.107i	0.492525	−	0.853077i	−0.507438	−	0.861688i	$-0.669408\pi$
$571$	281.231	−	487.107i	0.492525	−	0.853077i	0.999963	+	0.00861055i	$0.00274086\pi$
$572$	−126.000	+	72.7461i	−0.220280	+	0.127179i
$573$		−	177.993i		−	0.310634i
$574$	−151.154	+	231.861i	−0.263335	+	0.403939i
$575$	526.014			0.914807
$576$	−33.9411	−	58.7878i	−0.0589256	−	0.102062i
$577$	−573.014	−	330.830i	−0.993092	−	0.573362i	−0.0868946	−	0.996218i	$-0.527694\pi$
$577$	−573.014	−	330.830i	−0.993092	−	0.573362i	−0.906197	+	0.422856i	$0.861028\pi$
$578$	−194.350	+	336.625i	−0.336246	+	0.582395i
$579$	−95.8934	+	55.3641i	−0.165619	+	0.0956202i
$580$		−	46.6124i		−	0.0803662i
$581$	−404.029	−	796.420i	−0.695402	−	1.37077i
$582$	103.279			0.177456
$583$	133.136	+	230.598i	0.228364	+	0.395538i
$584$	128.860	+	74.3973i	0.220651	+	0.127393i
$585$	−430.191	+	745.113i	−0.735369	+	1.27370i
$586$	367.029	−	211.905i	0.626330	−	0.361612i
$587$		−	823.029i		−	1.40209i	−0.713116	−	0.701046i	$-0.752717\pi$
$587$		−	823.029i		−	1.40209i	0.713116	−	0.701046i	$-0.247283\pi$
$588$	−7.59589	+	69.8975i	−0.0129182	+	0.118873i
$589$	−204.338			−0.346924
$590$	181.555	+	314.462i	0.307720	+	0.532987i
$591$	−112.523	−	64.9650i	−0.190394	−	0.109924i
$592$	5.88225	−	10.1884i	0.00993623	−	0.0172101i
$593$	−538.890	+	311.128i	−0.908752	+	0.524668i	−0.880029	−	0.474919i	$-0.842477\pi$
$593$	−538.890	+	311.128i	−0.908752	+	0.524668i	−0.0287225	+	0.999587i	$0.509144\pi$
$594$			84.3992i			0.142086i
$595$	155.698	−	78.9868i	0.261678	−	0.132751i
$596$	184.794			0.310057
$597$	125.088	+	216.659i	0.209527	+	0.362912i
$598$	519.286	+	299.810i	0.868372	+	0.501355i
$599$	256.422	−	444.137i	0.428084	−	0.741463i	−0.568619	−	0.822601i	$-0.692522\pi$
$599$	256.422	−	444.137i	0.428084	−	0.741463i	0.996703	+	0.0811377i	$0.0258554\pi$
$600$	33.3381	−	19.2478i	0.0555635	−	0.0320796i
$601$			680.160i			1.13171i	0.824504	+	0.565857i	$0.191454\pi$
$601$			680.160i			1.13171i	−0.824504	+	0.565857i	$0.808546\pi$
$602$	86.9533	+	56.6864i	0.144441	+	0.0941635i
$603$	−293.927			−0.487441
$604$	91.7868	+	158.979i	0.151965	+	0.263211i
$605$	−564.889	−	326.139i	−0.933701	−	0.539073i
$606$	−30.2756	+	52.4390i	−0.0499598	+	0.0865329i
$607$	33.5482	−	19.3690i	0.0552688	−	0.0319095i	−0.472111	−	0.881539i	$-0.656508\pi$
$607$	33.5482	−	19.3690i	0.0552688	−	0.0319095i	0.527380	+	0.849630i	$0.323175\pi$
$608$			23.6544i			0.0389052i
$609$	17.6253	+	0.954877i	0.0289414	+	0.00156794i
$610$	−848.756			−1.39140
$611$	402.765	+	697.609i	0.659189	+	1.14175i
$612$	−55.2792	−	31.9155i	−0.0903255	−	0.0521495i
$613$	−200.552	+	347.366i	−0.327164	+	0.566665i	−0.981948	−	0.189151i	$-0.939426\pi$
$613$	−200.552	+	347.366i	−0.327164	+	0.566665i	0.654784	+	0.755816i	$0.272760\pi$
$614$	−25.7056	+	14.8412i	−0.0418658	+	0.0241713i
$615$			133.011i			0.216278i
$616$	5.09545	−	94.0530i	0.00827184	−	0.152683i
$617$	−959.044			−1.55437			−0.777183	−	0.629275i	$-0.783352\pi$
$617$	−959.044			−1.55437			−0.777183	+	0.629275i	$0.783352\pi$
$618$	−60.9670	−	105.598i	−0.0986521	−	0.170870i
$619$	−869.951	−	502.267i	−1.40541	−	0.811416i	−0.410473	−	0.911873i	$-0.634636\pi$
$619$	−869.951	−	502.267i	−1.40541	−	0.811416i	−0.994941	+	0.100457i	$0.967970\pi$
$620$	−324.037	+	561.248i	−0.522640	+	0.905238i
$621$	301.235	−	173.918i	0.485081	−	0.280061i
$622$		−	257.443i		−	0.413895i
$623$	−192.408	+	295.142i	−0.308841	+	0.473743i
$624$	43.8823			0.0703241
$625$	369.691	+	640.323i	0.591505	+	1.02452i
$626$	119.938	+	69.2460i	0.191594	+	0.110617i
$627$	7.13604	−	12.3600i	0.0113812	−	0.0197129i
$628$	−14.6468	+	8.45631i	−0.0233229	+	0.0134655i
$629$		−	11.0624i		−	0.0175873i
$630$	−252.000	−	496.742i	−0.400000	−	0.788479i
$631$	−386.514			−0.612542			−0.306271	−	0.951944i	$-0.599081\pi$
$631$	−386.514			−0.612542			−0.306271	+	0.951944i	$0.599081\pi$
$632$	47.7817	+	82.7604i	0.0756040	+	0.130950i
$633$	226.206	+	130.600i	0.357356	+	0.206319i
$634$	340.805	−	590.291i	0.537547	−	0.931058i
$635$	1420.37	−	820.053i	2.23681	−	1.29142i
$636$		−	80.3109i		−	0.126275i
$637$	604.617	+	442.547i	0.949164	+	0.694736i
$638$	−23.6468			−0.0370639
$639$	−154.544	−	267.678i	−0.241853	−	0.418902i
$640$	64.9706	+	37.5108i	0.101517	+	0.0586106i
$641$	496.074	−	859.225i	0.773906	−	1.34044i	−0.161502	−	0.986872i	$-0.551634\pi$
$641$	496.074	−	859.225i	0.773906	−	1.34044i	0.935407	−	0.353572i	$-0.115033\pi$
$642$	99.8269	−	57.6351i	0.155494	−	0.0897743i
$643$			944.986i			1.46965i	0.678256	+	0.734826i	$0.262736\pi$
$643$			944.986i			1.46965i	−0.678256	+	0.734826i	$0.737264\pi$
$644$	−346.191	+	175.625i	−0.537564	+	0.272709i
$645$	49.8823			0.0773368
$646$	11.1213	+	19.2627i	0.0172157	+	0.0298184i
$647$	2.50357	+	1.44544i	0.00386951	+	0.00223406i	0.501934	−	0.864906i	$-0.332622\pi$
$647$	2.50357	+	1.44544i	0.00386951	+	0.00223406i	−0.498064	+	0.867140i	$0.665956\pi$
$648$	−95.2721	+	165.016i	−0.147025	+	0.254654i
$649$	159.529	−	92.1039i	0.245807	−	0.141917i
$650$		−	410.241i		−	0.631140i
$651$	−205.584	−	134.024i	−0.315797	−	0.205874i
$652$	443.955			0.680913
$653$	161.529	+	279.777i	0.247365	+	0.428449i	0.962794	−	0.270237i	$-0.0871019\pi$
$653$	161.529	+	279.777i	0.247365	+	0.428449i	−0.715429	+	0.698686i	$0.753769\pi$
$654$	−127.680	−	73.7159i	−0.195229	−	0.112716i
$655$	489.518	−	847.870i	0.747356	−	1.29446i
$656$	−96.8528	+	55.9180i	−0.147641	+	0.0852409i
$657$		−	446.384i		−	0.679428i
$658$	−520.731	−	28.2114i	−0.791385	−	0.0428744i
$659$	295.955			0.449098			0.224549	−	0.974463i	$-0.427909\pi$
$659$	295.955			0.449098			0.224549	+	0.974463i	$0.427909\pi$
$660$	−22.6325	−	39.2006i	−0.0342916	−	0.0593948i
$661$	17.9710	+	10.3756i	0.0271876	+	0.0156968i	0.513532	−	0.858070i	$-0.328337\pi$
$661$	17.9710	+	10.3756i	0.0271876	+	0.0156968i	−0.486345	+	0.873767i	$0.661670\pi$
$662$	−159.104	+	275.576i	−0.240338	+	0.416278i
$663$	35.7351	−	20.6316i	0.0538990	−	0.0311186i
$664$		−	360.843i		−	0.543439i
$665$	−10.5000	+	193.811i	−0.0157895	+	0.291445i
$666$	−35.2935			−0.0529933
$667$	48.7279	+	84.3992i	0.0730554	+	0.126536i
$668$	−292.441	−	168.841i	−0.437785	−	0.252756i
$669$	−44.2052	+	76.5656i	−0.0660765	+	0.114448i
$670$	281.319	−	162.420i	0.419880	−	0.242418i
$671$			430.579i			0.641698i
$672$	−15.5147	+	23.7986i	−0.0230874	+	0.0354146i
$673$	627.044			0.931714			0.465857	−	0.884860i	$-0.345746\pi$
$673$	627.044			0.931714			0.465857	+	0.884860i	$0.345746\pi$
$674$	186.936	+	323.783i	0.277353	+	0.480390i
$675$	−206.095	−	118.989i	−0.305327	−	0.176280i
$676$	64.8234	−	112.277i	0.0958926	−	0.166091i
$677$	−94.6097	+	54.6230i	−0.139749	+	0.0806838i	−0.568244	−	0.822860i	$-0.692377\pi$
$677$	−94.6097	+	54.6230i	−0.139749	+	0.0806838i	0.428496	+	0.903544i	$0.359044\pi$
$678$		−	35.0489i		−	0.0516946i
$679$	322.368	+	635.450i	0.474768	+	0.935861i
$680$	70.5442			0.103741
$681$	−27.3974	−	47.4537i	−0.0402311	−	0.0696824i
$682$	284.724	+	164.386i	0.417484	+	0.241035i
$683$	−396.783	+	687.248i	−0.580941	+	1.00622i	0.414427	+	0.910083i	$0.363982\pi$
$683$	−396.783	+	687.248i	−0.580941	+	1.00622i	−0.995368	+	0.0961370i	$0.969351\pi$
$684$	61.4558	−	35.4815i	0.0898477	−	0.0518736i
$685$			215.996i			0.315323i
$686$	−453.770	+	171.437i	−0.661473	+	0.249908i
$687$	256.331			0.373116
$688$	20.9706	+	36.3221i	0.0304805	+	0.0527937i
$689$	−741.198	−	427.931i	−1.07576	−	0.621090i
$690$	−93.2756	+	161.558i	−0.135182	+	0.234142i
$691$	159.253	−	91.9447i	0.230467	−	0.133060i	−0.380320	−	0.924855i	$-0.624186\pi$
$691$	159.253	−	91.9447i	0.230467	−	0.133060i	0.610788	+	0.791794i	$0.290853\pi$
$692$		−	328.682i		−	0.474974i
$693$	−252.000	+	127.841i	−0.363636	+	0.184475i
$694$	−270.478			−0.389738
$695$	−227.397	−	393.863i	−0.327190	−	0.566710i
$696$	6.17662	+	3.56608i	0.00887446	+	0.00512367i
$697$	−52.5807	+	91.0725i	−0.0754386	+	0.130664i
$698$	165.889	−	95.7763i	0.237664	−	0.137215i
$699$			195.913i			0.280277i
$700$	222.485	+	145.042i	0.317836	+	0.207203i
$701$	−1043.82			−1.48905			−0.744525	−	0.667595i	$-0.767324\pi$
$701$	−1043.82			−1.48905			−0.744525	+	0.667595i	$0.767324\pi$
$702$	−135.640	−	234.935i	−0.193219	−	0.334665i
$703$	10.6508	+	6.14922i	0.0151504	+	0.00874711i
$704$	19.0294	−	32.9600i	0.0270305	−	0.0468181i
$705$	−217.037	+	125.306i	−0.307854	+	0.177740i
$706$			492.840i			0.698073i
$707$	−417.143	−	22.5993i	−0.590019	−	0.0319651i
$708$	−55.5593			−0.0784736
$709$	490.279	+	849.188i	0.691507	+	1.19773i	0.971344	+	0.237678i	$0.0763864\pi$
$709$	490.279	+	849.188i	0.691507	+	1.19773i	−0.279836	+	0.960048i	$0.590280\pi$
$710$	295.831	+	170.798i	0.416663	+	0.240560i
$711$	143.345	−	248.281i	0.201611	−	0.349200i
$712$	−123.286	+	71.1794i	−0.173155	+	0.0999711i
$713$		−	1354.97i		−	1.90038i
$714$	−1.44513	+	26.6745i	−0.00202399	+	0.0373593i
$715$	−482.382			−0.674660
$716$	−185.184	−	320.748i	−0.258637	−	0.447972i
$717$	−164.714	−	95.0975i	−0.229726	−	0.132632i
$718$	−215.548	+	373.340i	−0.300206	+	0.519972i
$719$	−674.187	+	389.242i	−0.937673	+	0.541366i	−0.889230	−	0.457460i	$-0.848759\pi$
$719$	−674.187	+	389.242i	−0.937673	+	0.541366i	−0.0484429	+	0.998826i	$0.515426\pi$
$720$		−	225.065i		−	0.312590i
$721$	459.419	−	704.719i	0.637197	−	0.977419i
$722$	485.803			0.672858
$723$	−31.4376	−	54.4514i	−0.0434821	−	0.0753132i
$724$	268.617	+	155.086i	0.371018	+	0.214208i
$725$	33.3381	−	57.7433i	0.0459836	−	0.0796459i
$726$	86.4335	−	49.9024i	0.119054	−	0.0687361i
$727$		−	735.255i		−	1.01135i	−0.862723	−	0.505677i	$-0.831243\pi$
$727$		−	735.255i		−	1.01135i	0.862723	−	0.505677i	$-0.168757\pi$
$728$	136.971	+	269.996i	0.188146	+	0.370874i
$729$	490.632			0.673021
$730$	246.665	+	427.237i	0.337898	+	0.585256i
$731$	34.1543	+	19.7190i	0.0467227	+	0.0269754i
$732$	64.9340	−	112.469i	0.0887076	−	0.153646i
$733$	−414.705	+	239.430i	−0.565764	+	0.326644i	−0.755456	−	0.655200i	$-0.772585\pi$
$733$	−414.705	+	239.430i	−0.565764	+	0.326644i	0.189692	+	0.981844i	$0.439251\pi$
$734$			134.356i			0.183047i
$735$	−137.683	+	188.106i	−0.187324	+	0.255926i
$736$	−156.853			−0.213115
$737$	−82.3965	−	142.715i	−0.111800	−	0.193643i
$738$	290.558	+	167.754i	0.393711	+	0.227309i
$739$	9.95227	−	17.2378i	0.0134672	−	0.0233259i	−0.859213	−	0.511618i	$-0.829046\pi$
$739$	9.95227	−	17.2378i	0.0134672	−	0.0233259i	0.872680	+	0.488292i	$0.162380\pi$
$740$	33.7797	−	19.5027i	0.0456482	−	0.0263550i
$741$			45.8739i			0.0619080i
$742$	494.132	−	250.676i	0.665946	−	0.337838i
$743$	43.3095			0.0582901			0.0291450	−	0.999575i	$-0.490722\pi$
$743$	43.3095			0.0582901			0.0291450	+	0.999575i	$0.490722\pi$
$744$	−49.5807	−	85.8764i	−0.0666408	−	0.115425i
$745$	530.603	+	306.344i	0.712218	+	0.411199i
$746$	−179.293	+	310.544i	−0.240339	+	0.416279i
$747$	−937.499	+	541.265i	−1.25502	+	0.724585i
$748$		−	35.7875i		−	0.0478442i
$749$	666.206	+	434.311i	0.889460	+	0.579855i
$750$	−40.5656			−0.0540874
$751$	−112.665	−	195.142i	−0.150020	−	0.259842i	0.781215	−	0.624263i	$-0.214600\pi$
$751$	−112.665	−	195.142i	−0.150020	−	0.259842i	−0.931235	+	0.364420i	$0.881267\pi$
$752$	−182.485	−	105.358i	−0.242667	−	0.140104i
$753$	177.801	−	307.961i	0.236124	−	0.408978i
$754$	65.8234	−	38.0031i	0.0872989	−	0.0504020i
$755$			608.641i			0.806147i
$756$	175.368	+	9.50079i	0.231968	+	0.0125672i
$757$	935.779			1.23617			0.618084	−	0.786112i	$-0.287909\pi$
$757$	935.779			1.23617			0.618084	+	0.786112i	$0.287909\pi$
$758$	−359.387	−	622.476i	−0.474125	−	0.821209i
$759$	81.9594	+	47.3193i	0.107983	+	0.0623443i
$760$	−39.2132	+	67.9193i	−0.0515963	+	0.0893674i
$761$	1214.79	−	701.357i	1.59630	−	0.921625i	0.604110	−	0.796901i	$-0.293529\pi$
$761$	1214.79	−	701.357i	1.59630	−	0.921625i	0.992191	−	0.124724i	$-0.0398046\pi$
$762$			250.952i			0.329334i
$763$	55.0254	−	1015.67i	0.0721172	−	1.33115i
$764$	496.191			0.649465
$765$	−105.816	−	183.279i	−0.138322	−	0.239581i
$766$	−585.136	−	337.828i	−0.763885	−	0.441029i
$767$	−296.044	+	512.763i	−0.385976	+	0.668530i
$768$	−9.94113	+	5.73951i	−0.0129442	+	0.00747332i
$769$			1.72330i			0.00224097i	0.999999	+	0.00112048i	$0.000356661\pi$
$769$			1.72330i			0.00224097i	−0.999999	+	0.00112048i	$0.999643\pi$
$770$	170.548	−	261.609i	0.221491	−	0.339752i
$771$

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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(0.621320 + 0.358719i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-5.74264 + 3.31552i) q^{5} -1.01461i q^{6} +(6.24264 - 3.16693i) q^{7} +2.82843 q^{8} +(-4.24264 - 7.34847i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(0.621320 + 0.358719i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-5.74264 + 3.31552i) q^{5} -1.01461i q^{6} +(6.24264 - 3.16693i) q^{7} +2.82843 q^{8} +(-4.24264 - 7.34847i) q^{9} +(8.12132 + 4.68885i) q^{10} +(2.37868 - 4.11999i) q^{11} +(-1.24264 + 0.717439i) q^{12} +15.2913i q^{13} +(-8.29289 - 5.40629i) q^{14} -4.75736 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-3.25736 - 1.88064i) q^{17} +(-6.00000 + 10.3923i) q^{18} +(3.62132 - 2.09077i) q^{19} -13.2621i q^{20} +(5.01472 + 0.271680i) q^{21} -6.72792 q^{22} +(13.8640 + 24.0131i) q^{23} +(1.75736 + 1.01461i) q^{24} +(9.48528 - 16.4290i) q^{25} +(18.7279 - 10.8126i) q^{26} -12.5446i q^{27} +(-0.757359 + 13.9795i) q^{28} +3.51472 q^{29} +(3.36396 + 5.82655i) q^{30} +(-42.3198 - 24.4334i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(2.95584 - 1.70656i) q^{33} +5.31925i q^{34} +(-25.3492 + 38.8841i) q^{35} +16.9706 q^{36} +(1.47056 + 2.54709i) q^{37} +(-5.12132 - 2.95680i) q^{38} +(-5.48528 + 9.50079i) q^{39} +(-16.2426 + 9.37769i) q^{40} -27.9590i q^{41} +(-3.21320 - 6.33386i) q^{42} -10.4853 q^{43} +(4.75736 + 8.23999i) q^{44} +(48.7279 + 28.1331i) q^{45} +(19.6066 - 33.9596i) q^{46} +(45.6213 - 26.3395i) q^{47} -2.86976i q^{48} +(28.9411 - 39.5400i) q^{49} -26.8284 q^{50} +(-1.34924 - 2.33696i) q^{51} +(-26.4853 - 15.2913i) q^{52} +(-27.9853 + 48.4719i) q^{53} +(-15.3640 + 8.87039i) q^{54} +31.5462i q^{55} +(17.6569 - 8.95743i) q^{56} +3.00000 q^{57} +(-2.48528 - 4.30463i) q^{58} +(33.5330 + 19.3603i) q^{59} +(4.75736 - 8.23999i) q^{60} +(-78.3823 + 45.2540i) q^{61} +69.1080i q^{62} +(-49.7574 - 32.4377i) q^{63} +8.00000 q^{64} +(-50.6985 - 87.8124i) q^{65} +(-4.18019 - 2.41344i) q^{66} +(17.3198 - 29.9988i) q^{67} +(6.51472 - 3.76127i) q^{68} +19.8931i q^{69} +(65.5477 + 3.55114i) q^{70} +36.4264 q^{71} +(-12.0000 - 20.7846i) q^{72} +(45.5589 + 26.3034i) q^{73} +(2.07969 - 3.60213i) q^{74} +(11.7868 - 6.80511i) q^{75} +8.36308i q^{76} +(1.80152 - 33.2528i) q^{77} +15.5147 q^{78} +(16.8934 + 29.2602i) q^{79} +(22.9706 + 13.2621i) q^{80} +(-33.6838 + 58.3420i) q^{81} +(-34.2426 + 19.7700i) q^{82} -127.577i q^{83} +(-5.48528 + 8.41407i) q^{84} +24.9411 q^{85} +(7.41421 + 12.8418i) q^{86} +(2.18377 + 1.26080i) q^{87} +(6.72792 - 11.6531i) q^{88} +(-43.5883 + 25.1657i) q^{89} -79.5724i q^{90} +(48.4264 + 95.4580i) q^{91} -55.4558 q^{92} +(-17.5294 - 30.3619i) q^{93} +(-64.5183 - 37.2497i) q^{94} +(-13.8640 + 24.0131i) q^{95} +(-3.51472 + 2.02922i) q^{96} +101.792i q^{97} +(-68.8909 - 7.48650i) q^{98} -40.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7}+O(q^{10}) \) 4 * q - 6 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^7	\( 4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7} + 24 q^{10} + 18 q^{11} + 12 q^{12} - 36 q^{14} - 36 q^{15} - 8 q^{16} - 30 q^{17} - 24 q^{18} + 6 q^{19} + 54 q^{21} + 24 q^{22} + 30 q^{23} + 24 q^{24} + 4 q^{25} + 24 q^{26} - 20 q^{28} + 48 q^{29} - 12 q^{30} - 42 q^{31} - 90 q^{33} - 42 q^{35} - 62 q^{37} - 12 q^{38} + 12 q^{39} - 48 q^{40} + 72 q^{42} - 8 q^{43} + 36 q^{44} + 144 q^{45} + 36 q^{46} + 174 q^{47} - 20 q^{49} - 96 q^{50} + 54 q^{51} - 72 q^{52} - 78 q^{53} - 36 q^{54} + 48 q^{56} + 12 q^{57} + 24 q^{58} - 78 q^{59} + 36 q^{60} - 42 q^{61} - 216 q^{63} + 32 q^{64} - 84 q^{65} - 144 q^{66} - 58 q^{67} + 60 q^{68} + 84 q^{70} - 24 q^{71} - 48 q^{72} + 318 q^{73} + 96 q^{74} + 132 q^{75} + 126 q^{77} + 96 q^{78} + 110 q^{79} + 24 q^{80} + 18 q^{81} - 120 q^{82} + 12 q^{84} - 36 q^{85} + 24 q^{86} - 144 q^{87} - 24 q^{88} - 378 q^{89} + 24 q^{91} - 120 q^{92} - 138 q^{93} - 12 q^{94} - 30 q^{95} - 48 q^{96} - 120 q^{98} + 144 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^7 + 24 * q^10 + 18 * q^11 + 12 * q^12 - 36 * q^14 - 36 * q^15 - 8 * q^16 - 30 * q^17 - 24 * q^18 + 6 * q^19 + 54 * q^21 + 24 * q^22 + 30 * q^23 + 24 * q^24 + 4 * q^25 + 24 * q^26 - 20 * q^28 + 48 * q^29 - 12 * q^30 - 42 * q^31 - 90 * q^33 - 42 * q^35 - 62 * q^37 - 12 * q^38 + 12 * q^39 - 48 * q^40 + 72 * q^42 - 8 * q^43 + 36 * q^44 + 144 * q^45 + 36 * q^46 + 174 * q^47 - 20 * q^49 - 96 * q^50 + 54 * q^51 - 72 * q^52 - 78 * q^53 - 36 * q^54 + 48 * q^56 + 12 * q^57 + 24 * q^58 - 78 * q^59 + 36 * q^60 - 42 * q^61 - 216 * q^63 + 32 * q^64 - 84 * q^65 - 144 * q^66 - 58 * q^67 + 60 * q^68 + 84 * q^70 - 24 * q^71 - 48 * q^72 + 318 * q^73 + 96 * q^74 + 132 * q^75 + 126 * q^77 + 96 * q^78 + 110 * q^79 + 24 * q^80 + 18 * q^81 - 120 * q^82 + 12 * q^84 - 36 * q^85 + 24 * q^86 - 144 * q^87 - 24 * q^88 - 378 * q^89 + 24 * q^91 - 120 * q^92 - 138 * q^93 - 12 * q^94 - 30 * q^95 - 48 * q^96 - 120 * q^98 + 144 * q^99

Introduction

L-functions

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Varieties

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