LMFDB - Embedded newform 117.3.k.a.29.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(29,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.k (of order $6$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.6
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.57904i q^{2} +(2.93962 + 0.598857i) q^{3} -2.65146 q^{4} +(-0.817198 + 0.471810i) q^{5} +(1.54448 - 7.58141i) q^{6} +(-2.52350 - 4.37084i) q^{7} -3.47795i q^{8} +(8.28274 + 3.52082i) q^{9} +(1.21682 + 2.10759i) q^{10} -15.9839i q^{11} +(-7.79428 - 1.58784i) q^{12} +(11.8077 + 5.43860i) q^{13} +(-11.2726 + 6.50822i) q^{14} +(-2.68480 + 0.897556i) q^{15} -19.5756 q^{16} +(21.5804 + 12.4595i) q^{17} +(9.08035 - 21.3615i) q^{18} +(-17.4215 + 30.1749i) q^{19} +(2.16677 - 1.25098i) q^{20} +(-4.80064 - 14.3598i) q^{21} -41.2231 q^{22} +(-17.7825 - 10.2667i) q^{23} +(2.08279 - 10.2238i) q^{24} +(-12.0548 + 20.8795i) q^{25} +(14.0264 - 30.4525i) q^{26} +(22.2396 + 15.3101i) q^{27} +(6.69097 + 11.5891i) q^{28} +17.8550i q^{29} +(2.31484 + 6.92421i) q^{30} +(10.2399 + 17.7361i) q^{31} +36.5745i q^{32} +(9.57206 - 46.9866i) q^{33} +(32.1335 - 55.6568i) q^{34} +(4.12441 + 2.38123i) q^{35} +(-21.9613 - 9.33532i) q^{36} +(1.09928 + 1.90401i) q^{37} +(77.8224 + 44.9308i) q^{38} +(31.4532 + 23.0585i) q^{39} +(1.64093 + 2.84217i) q^{40} +(5.08651 + 2.93670i) q^{41} +(-37.0346 + 12.3811i) q^{42} +(-0.939802 - 1.62778i) q^{43} +42.3806i q^{44} +(-8.42980 + 1.03067i) q^{45} +(-26.4783 + 45.8617i) q^{46} +(-6.18058 - 3.56836i) q^{47} +(-57.5448 - 11.7230i) q^{48} +(11.7638 - 20.3756i) q^{49} +(53.8491 + 31.0898i) q^{50} +(55.9768 + 49.5497i) q^{51} +(-31.3076 - 14.4202i) q^{52} -34.1353i q^{53} +(39.4853 - 57.3570i) q^{54} +(7.54135 + 13.0620i) q^{55} +(-15.2015 + 8.77662i) q^{56} +(-69.2831 + 78.2699i) q^{57} +46.0487 q^{58} +32.6220i q^{59} +(7.11863 - 2.37983i) q^{60} +(-6.68183 - 11.5733i) q^{61} +(45.7421 - 26.4092i) q^{62} +(-5.51258 - 45.0873i) q^{63} +16.0248 q^{64} +(-12.2152 + 1.12657i) q^{65} +(-121.180 - 24.6867i) q^{66} +(39.2885 - 68.0497i) q^{67} +(-57.2196 - 33.0357i) q^{68} +(-46.1254 - 40.8294i) q^{69} +(6.14128 - 10.6370i) q^{70} +(-121.405 - 70.0932i) q^{71} +(12.2452 - 28.8069i) q^{72} -89.5686 q^{73} +(4.91052 - 2.83509i) q^{74} +(-47.9404 + 54.1588i) q^{75} +(46.1924 - 80.0076i) q^{76} +(-69.8630 + 40.3354i) q^{77} +(59.4689 - 81.1191i) q^{78} +(28.9076 - 50.0695i) q^{79} +(15.9971 - 9.23596i) q^{80} +(56.2076 + 58.3242i) q^{81} +(7.57387 - 13.1183i) q^{82} +(38.2595 + 22.0891i) q^{83} +(12.7287 + 38.0745i) q^{84} -23.5140 q^{85} +(-4.19812 + 2.42379i) q^{86} +(-10.6926 + 52.4868i) q^{87} -55.5911 q^{88} +(48.6143 - 28.0675i) q^{89} +(2.65813 + 21.7408i) q^{90} +(-6.02555 - 65.3338i) q^{91} +(47.1494 + 27.2217i) q^{92} +(19.4802 + 58.2697i) q^{93} +(-9.20294 + 15.9400i) q^{94} -32.8785i q^{95} +(-21.9029 + 107.515i) q^{96} +(78.3791 + 135.757i) q^{97} +(-52.5495 - 30.3395i) q^{98} +(56.2764 - 132.390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	2.57904i		−	1.28952i	−0.764385	−	0.644761i	$-0.776957\pi$
$2$		−	2.57904i		−	1.28952i	0.764385	−	0.644761i	$-0.223043\pi$
$3$	2.93962	+	0.598857i	0.979874	+	0.199619i
$3$	2.93962	+	0.598857i	0.979874	+	0.199619i
$4$	−2.65146			−0.662864
$5$	−0.817198	+	0.471810i	−0.163440	+	0.0943619i	−0.579489	−	0.814980i	$-0.696748\pi$
$5$	−0.817198	+	0.471810i	−0.163440	+	0.0943619i	0.416049	+	0.909342i	$0.363414\pi$
$6$	1.54448	−	7.58141i	0.257413	−	1.26357i
$7$	−2.52350	−	4.37084i	−0.360501	−	0.624405i	0.627543	−	0.778582i	$-0.284061\pi$
$7$	−2.52350	−	4.37084i	−0.360501	−	0.624405i	−0.988043	+	0.154177i	$0.950727\pi$
$8$		−	3.47795i		−	0.434743i
$9$	8.28274	+	3.52082i	0.920305	+	0.391203i
$10$	1.21682	+	2.10759i	0.121682	+	0.210759i
$11$		−	15.9839i		−	1.45308i	−0.687124	−	0.726540i	$-0.741127\pi$
$11$		−	15.9839i		−	1.45308i	0.687124	−	0.726540i	$-0.258873\pi$
$12$	−7.79428	−	1.58784i	−0.649523	−	0.132320i
$13$	11.8077	+	5.43860i	0.908284	+	0.418354i
$13$	11.8077	+	5.43860i	0.908284	+	0.418354i
$14$	−11.2726	+	6.50822i	−0.805184	+	0.464873i
$15$	−2.68480	+	0.897556i	−0.178987	+	0.0598371i
$16$	−19.5756			−1.22348
$17$	21.5804	+	12.4595i	1.26944	+	0.732909i	0.974881	−	0.222725i	$-0.0714952\pi$
$17$	21.5804	+	12.4595i	1.26944	+	0.732909i	0.294555	+	0.955635i	$0.404829\pi$
$18$	9.08035	−	21.3615i	0.504464	−	1.18675i
$19$	−17.4215	+	30.1749i	−0.916921	+	1.58815i	−0.112858	+	0.993611i	$0.536000\pi$
$19$	−17.4215	+	30.1749i	−0.916921	+	1.58815i	−0.804064	+	0.594543i	$0.797333\pi$
$20$	2.16677	−	1.25098i	0.108338	−	0.0625491i
$21$	−4.80064	−	14.3598i	−0.228602	−	0.683801i
$22$	−41.2231			−1.87378
$23$	−17.7825	−	10.2667i	−0.773150	−	0.446379i	0.0608469	−	0.998147i	$-0.480620\pi$
$23$	−17.7825	−	10.2667i	−0.773150	−	0.446379i	−0.833997	+	0.551769i	$0.813953\pi$
$24$	2.08279	−	10.2238i	0.0867830	−	0.425994i
$25$	−12.0548	+	20.8795i	−0.482192	+	0.835180i
$26$	14.0264	−	30.4525i	0.539476	−	1.17125i
$27$	22.2396	+	15.3101i	0.823691	+	0.567039i
$28$	6.69097	+	11.5891i	0.238963	+	0.413896i
$29$			17.8550i			0.615688i	0.951437	+	0.307844i	$0.0996075\pi$
$29$			17.8550i			0.615688i	−0.951437	+	0.307844i	$0.900393\pi$
$30$	2.31484	+	6.92421i	0.0771612	+	0.230807i
$31$	10.2399	+	17.7361i	0.330321	+	0.572132i	0.982575	−	0.185868i	$-0.0595098\pi$
$31$	10.2399	+	17.7361i	0.330321	+	0.572132i	−0.652254	+	0.758001i	$0.726176\pi$
$32$			36.5745i			1.14295i
$33$	9.57206	−	46.9866i	0.290062	−	1.42384i
$34$	32.1335	−	55.6568i	0.945102	−	1.63696i
$35$	4.12441	+	2.38123i	0.117840	+	0.0680351i
$36$	−21.9613	−	9.33532i	−0.610037	−	0.259314i
$37$	1.09928	+	1.90401i	0.0297103	+	0.0514597i	0.880498	−	0.474049i	$-0.157208\pi$
$37$	1.09928	+	1.90401i	0.0297103	+	0.0514597i	−0.850788	+	0.525509i	$0.823875\pi$
$38$	77.8224	+	44.9308i	2.04796	+	1.18239i
$39$	31.4532	+	23.0585i	0.806492	+	0.591244i
$40$	1.64093	+	2.84217i	0.0410232	+	0.0710543i
$41$	5.08651	+	2.93670i	0.124061	+	0.0716268i	0.560746	−	0.827988i	$-0.310514\pi$
$41$	5.08651	+	2.93670i	0.124061	+	0.0716268i	−0.436685	+	0.899614i	$0.643848\pi$
$42$	−37.0346	+	12.3811i	−0.881776	+	0.294787i
$43$	−0.939802	−	1.62778i	−0.0218559	−	0.0378555i	0.854891	−	0.518808i	$-0.173624\pi$
$43$	−0.939802	−	1.62778i	−0.0218559	−	0.0378555i	−0.876746	+	0.480953i	$0.840291\pi$
$44$			42.3806i			0.963195i
$45$	−8.42980	+	1.03067i	−0.187329	+	0.0229037i
$46$	−26.4783	+	45.8617i	−0.575615	+	0.996994i
$47$	−6.18058	−	3.56836i	−0.131502	−	0.0759225i	0.432806	−	0.901487i	$-0.357523\pi$
$47$	−6.18058	−	3.56836i	−0.131502	−	0.0759225i	−0.564308	+	0.825565i	$0.690857\pi$
$48$	−57.5448	−	11.7230i	−1.19885	−	0.244229i
$49$	11.7638	−	20.3756i	0.240079	−	0.415828i
$50$	53.8491	+	31.0898i	1.07698	+	0.621796i
$51$	55.9768	+	49.5497i	1.09758	+	0.971562i
$52$	−31.3076	−	14.4202i	−0.602069	−	0.277312i
$53$		−	34.1353i		−	0.644062i	−0.946729	−	0.322031i	$-0.895634\pi$
$53$		−	34.1353i		−	0.644062i	0.946729	−	0.322031i	$-0.104366\pi$
$54$	39.4853	−	57.3570i	0.731209	−	1.06217i
$55$	7.54135	+	13.0620i	0.137115	+	0.237491i
$56$	−15.2015	+	8.77662i	−0.271456	+	0.156725i
$57$	−69.2831	+	78.2699i	−1.21549	+	1.37316i
$58$	46.0487			0.793943
$59$			32.6220i			0.552916i	0.961026	+	0.276458i	$0.0891606\pi$
$59$			32.6220i			0.552916i	−0.961026	+	0.276458i	$0.910839\pi$
$60$	7.11863	−	2.37983i	0.118644	−	0.0396639i
$61$	−6.68183	−	11.5733i	−0.109538	−	0.189726i	0.806045	−	0.591854i	$-0.201604\pi$
$61$	−6.68183	−	11.5733i	−0.109538	−	0.189726i	−0.915583	+	0.402128i	$0.868271\pi$
$62$	45.7421	−	26.4092i	0.737777	−	0.425956i
$63$	−5.51258	−	45.0873i	−0.0875013	−	0.715672i
$64$	16.0248			0.250387
$65$	−12.2152	+	1.12657i	−0.187926	+	0.0173319i
$66$	−121.180	−	24.6867i	−1.83607	−	0.374042i
$67$	39.2885	−	68.0497i	0.586396	−	1.01567i	−0.408304	−	0.912846i	$-0.633880\pi$
$67$	39.2885	−	68.0497i	0.586396	−	1.01567i	0.994700	−	0.102821i	$-0.0327870\pi$
$68$	−57.2196	−	33.0357i	−0.841464	−	0.485820i
$69$	−46.1254	−	40.8294i	−0.668484	−	0.591730i
$70$	6.14128	−	10.6370i	0.0877326	−	0.151957i
$71$	−121.405	−	70.0932i	−1.70993	−	0.987228i	−0.934622	−	0.355643i	$-0.884262\pi$
$71$	−121.405	−	70.0932i	−1.70993	−	0.987228i	−0.775307	−	0.631585i	$-0.782405\pi$
$72$	12.2452	−	28.8069i	0.170073	−	0.400096i
$73$	−89.5686			−1.22697			−0.613483	−	0.789708i	$-0.710232\pi$
$73$	−89.5686			−1.22697			−0.613483	+	0.789708i	$0.710232\pi$
$74$	4.91052	−	2.83509i	0.0663584	−	0.0383120i
$75$	−47.9404	+	54.1588i	−0.639205	+	0.722117i
$76$	46.1924	−	80.0076i	0.607795	−	1.05273i
$77$	−69.8630	+	40.3354i	−0.907311	+	0.523836i
$78$	59.4689	−	81.1191i	0.762422	−	1.03999i
$79$	28.9076	−	50.0695i	0.365920	−	0.633791i	−0.623004	−	0.782219i	$-0.714088\pi$
$79$	28.9076	−	50.0695i	0.365920	−	0.633791i	0.988923	+	0.148428i	$0.0474212\pi$
$80$	15.9971	−	9.23596i	0.199964	−	0.115449i
$81$	56.2076	+	58.3242i	0.693921	+	0.720051i
$82$	7.57387	−	13.1183i	0.0923643	−	0.159980i
$83$	38.2595	+	22.0891i	0.460958	+	0.266134i	0.712447	−	0.701726i	$-0.247587\pi$
$83$	38.2595	+	22.0891i	0.460958	+	0.266134i	−0.251489	+	0.967860i	$0.580920\pi$
$84$	12.7287	+	38.0745i	0.151532	+	0.453267i
$85$	−23.5140			−0.276635
$86$	−4.19812	+	2.42379i	−0.0488154	+	0.0281836i
$87$	−10.6926	+	52.4868i	−0.122903	+	0.603296i
$88$	−55.5911			−0.631717
$89$	48.6143	−	28.0675i	0.546228	−	0.315365i	−0.201371	−	0.979515i	$-0.564540\pi$
$89$	48.6143	−	28.0675i	0.546228	−	0.315365i	0.747599	+	0.664150i	$0.231206\pi$
$90$	2.65813	+	21.7408i	0.0295348	+	0.241564i
$91$	−6.02555	−	65.3338i	−0.0662148	−	0.717954i
$92$	47.1494	+	27.2217i	0.512494	+	0.295888i
$93$	19.4802	+	58.2697i	0.209464	+	0.626556i
$94$	−9.20294	+	15.9400i	−0.0979037	+	0.169574i
$95$		−	32.8785i		−	0.346090i
$96$	−21.9029	+	107.515i	−0.228155	+	1.11995i
$97$	78.3791	+	135.757i	0.808032	+	1.39955i	0.914225	+	0.405206i	$0.132800\pi$
$97$	78.3791	+	135.757i	0.808032	+	1.39955i	−0.106194	+	0.994345i	$0.533866\pi$
$98$	−52.5495	−	30.3395i	−0.536219	−	0.309586i
$99$	56.2764	−	132.390i	0.568449	−	1.33728i
$100$	31.9628	−	55.3611i	0.319628	−	0.553611i
$101$		−	111.828i		−	1.10721i	−0.832779	−	0.553606i	$-0.813251\pi$
$101$		−	111.828i		−	1.10721i	0.832779	−	0.553606i	$-0.186749\pi$
$102$	127.791	−	144.367i	1.25285	−	1.41536i
$103$	79.5352	+	137.759i	0.772187	+	1.33747i	0.936362	+	0.351035i	$0.114170\pi$
$103$	79.5352	+	137.759i	0.772187	+	1.33747i	−0.164176	+	0.986431i	$0.552496\pi$
$104$	18.9152	−	41.0665i	0.181876	−	0.394871i
$105$	10.6982	+	9.46983i	0.101887	+	0.0901889i
$106$	−88.0364			−0.830532
$107$	−172.079	+	99.3501i	−1.60822	+	0.928505i	−0.618450	+	0.785824i	$0.712239\pi$
$107$	−172.079	+	99.3501i	−1.60822	+	0.928505i	−0.989769	+	0.142681i	$0.954428\pi$
$108$	−58.9675	−	40.5940i	−0.545995	−	0.375870i
$109$	99.6164			0.913912			0.456956	−	0.889489i	$-0.348940\pi$
$109$	99.6164			0.913912			0.456956	+	0.889489i	$0.348940\pi$
$110$	33.6874	−	19.4495i	0.306249	−	0.176813i
$111$	2.09124	+	6.25538i	0.0188400	+	0.0563547i
$112$	49.3991	+	85.5618i	0.441064	+	0.763945i
$113$		−	22.5030i		−	0.199142i	−0.995030	−	0.0995708i	$-0.968253\pi$
$113$		−	22.5030i		−	0.199142i	0.995030	−	0.0995708i	$-0.0317470\pi$
$114$	201.861	+	178.684i	1.77071	+	1.56740i
$115$	19.3757			0.168485
$116$		−	47.3417i		−	0.408118i
$117$	78.6517	+	86.6193i	0.672237	+	0.740336i
$118$	84.1336			0.712996
$119$		−	125.766i		−	1.05686i
$120$	3.12165	+	9.33759i	0.0260138	+	0.0778132i
$121$	−134.485			−1.11144
$122$	−29.8480	+	17.2327i	−0.244655	+	0.141252i
$123$	13.1938	+	11.6789i	0.107266	+	0.0949502i
$124$	−27.1508	−	47.0265i	−0.218958	−	0.379246i
$125$		−	46.3407i		−	0.370726i
$126$	−116.282	+	14.2172i	−0.922874	+	0.112835i
$127$	−58.8631	−	101.954i	−0.463489	−	0.802786i	0.535643	−	0.844444i	$-0.320069\pi$
$127$	−58.8631	−	101.954i	−0.463489	−	0.802786i	−0.999132	+	0.0416583i	$0.986736\pi$
$128$			104.969i			0.820074i
$129$	−1.78785	−	5.34788i	−0.0138593	−	0.0414564i
$130$	2.90548	+	31.5035i	0.0223498	+	0.242335i
$131$	−77.7495	+	44.8887i	−0.593507	+	0.342662i	−0.766483	−	0.642264i	$-0.777995\pi$
$131$	−77.7495	+	44.8887i	−0.593507	+	0.342662i	0.172976	+	0.984926i	$0.444662\pi$
$132$	−25.3799	+	124.583i	−0.192272	+	0.943810i
$133$	175.853			1.32220
$134$	−175.503	−	101.327i	−1.30972	−	0.756170i
$135$	−25.3976	−	2.01848i	−0.188131	−	0.0149517i
$136$	43.3333	−	75.0556i	0.318628	−	0.551879i
$137$	7.91314	−	4.56866i	0.0577602	−	0.0333478i	−0.470842	−	0.882218i	$-0.656050\pi$
$137$	7.91314	−	4.56866i	0.0577602	−	0.0333478i	0.528602	+	0.848870i	$0.322716\pi$
$138$	−105.301	+	118.959i	−0.763048	+	0.862024i
$139$	−148.704			−1.06982			−0.534908	−	0.844910i	$-0.679654\pi$
$139$	−148.704			−1.06982			−0.534908	+	0.844910i	$0.679654\pi$
$140$	−10.9357	−	6.31372i	−0.0781121	−	0.0450980i
$141$	−16.0316	−	14.1909i	−0.113699	−	0.100645i
$142$	−180.773	+	313.108i	−1.27305	+	2.20499i
$143$	86.9299	−	188.733i	0.607901	−	1.31981i
$144$	−162.140	−	68.9223i	−1.12597	−	0.478627i
$145$	−8.42414	−	14.5910i	−0.0580975	−	0.100628i
$146$			231.001i			1.58220i
$147$	46.7833	−	52.8516i	0.318254	−	0.359535i
$148$	−2.91469	−	5.04840i	−0.0196939	−	0.0341108i
$149$		−	32.9169i		−	0.220919i	−0.993881	−	0.110459i	$-0.964768\pi$
$149$		−	32.9169i		−	0.220919i	0.993881	−	0.110459i	$-0.0352322\pi$
$150$	139.678	+	123.640i	0.931185	+	0.824268i
$151$	53.6782	−	92.9733i	0.355485	−	0.615717i	−0.631716	−	0.775200i	$-0.717649\pi$
$151$	53.6782	−	92.9733i	0.355485	−	0.615717i	0.987201	+	0.159482i	$0.0509825\pi$
$152$	104.947	+	60.5911i	0.690440	+	0.398626i
$153$	134.877	+	179.179i	0.881552	+	1.17111i
$154$	104.027	+	180.180i	0.675498	+	1.17000i
$155$	−16.7361	−	9.66260i	−0.107975	−	0.0623394i
$156$	−83.3968	−	61.1387i	−0.534595	−	0.391915i
$157$	−2.21063	−	3.82892i	−0.0140804	−	0.0243880i	0.858899	−	0.512144i	$-0.171149\pi$
$157$	−2.21063	−	3.82892i	−0.0140804	−	0.0243880i	−0.872980	+	0.487756i	$0.837815\pi$
$158$	−129.131	−	74.5540i	−0.817287	−	0.471861i
$159$	20.4422	−	100.345i	0.128567	−	0.631100i
$160$	−17.2562	−	29.8886i	−0.107851	−	0.186804i
$161$			103.632i			0.643679i
$162$	150.420	−	144.962i	0.928521	−	0.894826i
$163$	47.2209	−	81.7891i	0.289699	−	0.501774i	−0.684039	−	0.729446i	$-0.739778\pi$
$163$	47.2209	−	81.7891i	0.289699	−	0.501774i	0.973738	+	0.227672i	$0.0731114\pi$
$164$	−13.4867	−	7.78654i	−0.0822358	−	0.0474789i
$165$	14.3464	+	42.9135i	0.0869481	+	0.260082i
$166$	56.9688	−	98.6729i	0.343186	−	0.594415i
$167$	−142.317	−	82.1665i	−0.852195	−	0.492015i	0.00919597	−	0.999958i	$-0.497073\pi$
$167$	−142.317	−	82.1665i	−0.852195	−	0.492015i	−0.861391	+	0.507943i	$0.830406\pi$
$168$	−49.9427	+	16.6964i	−0.297278	+	0.0993832i
$169$	109.843	+	128.435i	0.649961	+	0.759968i
$170$			60.6435i			0.356727i
$171$	−250.538	+	188.593i	−1.46514	+	1.10288i
$172$	2.49184	+	4.31600i	0.0144875	+	0.0250930i
$173$	−87.6553	+	50.6078i	−0.506678	+	0.292531i	−0.731467	−	0.681877i	$-0.761164\pi$
$173$	−87.6553	+	50.6078i	−0.506678	+	0.292531i	0.224789	+	0.974407i	$0.427831\pi$
$174$	135.366	+	27.5766i	0.777963	+	0.158486i
$175$	121.681			0.695322
$176$			312.894i			1.77781i
$177$	−19.5359	+	95.8964i	−0.110372	+	0.541788i
$178$	−72.3872	−	125.378i	−0.406670	−	0.704372i
$179$	176.959	−	102.167i	0.988595	−	0.570766i	0.0837411	−	0.996488i	$-0.473313\pi$
$179$	176.959	−	102.167i	0.988595	−	0.570766i	0.904854	+	0.425722i	$0.139980\pi$
$180$	22.3513	−	2.73277i	0.124174	−	0.0151820i
$181$	−121.248			−0.669879			−0.334939	−	0.942240i	$-0.608716\pi$
$181$	−121.248			−0.669879			−0.334939	+	0.942240i	$0.608716\pi$
$182$	−168.499	+	15.5401i	−0.925817	+	0.0853854i
$183$	−12.7113	−	38.0225i	−0.0694608	−	0.207773i
$184$	−35.7071	+	61.8465i	−0.194060	+	0.336122i
$185$	−1.79666	−	1.03730i	−0.00971167	−	0.00560704i
$186$	150.280	−	50.2402i	0.807957	−	0.270108i
$187$	199.151	−	344.939i	1.06498	−	1.84459i
$188$	16.3875	+	9.46135i	0.0871677	+	0.0503263i
$189$	10.7960	−	135.841i	0.0571215	−	0.718735i
$190$	−84.7951			−0.446290
$191$	157.021	−	90.6562i	0.822100	−	0.474640i	−0.0290401	−	0.999578i	$-0.509245\pi$
$191$	157.021	−	90.6562i	0.822100	−	0.474640i	0.851140	+	0.524939i	$0.175912\pi$
$192$	47.1068	+	9.59656i	0.245348	+	0.0499821i
$193$	1.22711	−	2.12542i	0.00635808	−	0.0110125i	−0.862829	−	0.505496i	$-0.831309\pi$
$193$	1.22711	−	2.12542i	0.00635808	−	0.0110125i	0.869187	+	0.494484i	$0.164643\pi$
$194$	350.122	−	202.143i	1.80475	−	1.04197i
$195$	−36.5827	−	4.00346i	−0.187604	−	0.0205306i
$196$	−31.1913	+	54.0250i	−0.159140	+	0.275638i
$197$	−300.863	+	173.703i	−1.52722	+	0.881743i	−0.527748	+	0.849401i	$0.676963\pi$
$197$	−300.863	+	173.703i	−1.52722	+	0.881743i	−0.999477	+	0.0323423i	$0.989703\pi$
$198$	−341.440	−	145.139i	−1.72445	−	0.733027i
$199$	88.3111	−	152.959i	0.443774	−	0.768640i	−0.554192	−	0.832389i	$-0.686973\pi$
$199$	88.3111	−	152.959i	0.443774	−	0.768640i	0.997966	+	0.0637495i	$0.0203059\pi$
$200$	72.6178	+	41.9259i	0.363089	+	0.209630i
$201$	156.245	−	176.512i	0.777340	−	0.878170i
$202$	−288.410			−1.42777
$203$	78.0411	−	45.0571i	0.384439	−	0.221956i
$204$	−148.420	−	131.379i	−0.727550	−	0.644014i
$205$	−5.54225			−0.0270354
$206$	355.286	−	205.125i	1.72469	−	0.995751i
$207$	−111.140	−	147.645i	−0.536909	−	0.713263i
$208$	−231.143	−	106.464i	−1.11126	−	0.511845i
$209$	482.313	+	278.463i	2.30772	+	1.33236i
$210$	24.4231	−	27.5910i	0.116300	−	0.131386i
$211$	136.380	−	236.218i	0.646352	−	1.11952i	−0.337635	−	0.941277i	$-0.609627\pi$
$211$	136.380	−	236.218i	0.646352	−	1.11952i	0.983987	−	0.178238i	$-0.0570397\pi$
$212$			90.5083i			0.426926i
$213$	−314.909	−	278.752i	−1.47844	−	1.30869i
$214$	256.228	+	443.800i	1.19733	+	2.07383i
$215$	1.53601	+	0.886815i	0.00714423	+	0.00412472i
$216$	53.2476	−	77.3483i	0.246517	−	0.358094i
$217$	51.6811	−	89.5143i	0.238162	−	0.412508i
$218$		−	256.915i		−	1.17851i
$219$	−263.298	−	53.6388i	−1.20227	−	0.244926i
$220$	−19.9956	−	34.6333i	−0.0908889	−	0.157424i
$221$	187.053	+	264.485i	0.846394	+	1.19676i
$222$	16.1329	−	5.39339i	0.0726706	−	0.0242946i
$223$	−37.3803			−0.167625			−0.0838124	−	0.996482i	$-0.526710\pi$
$223$	−37.3803			−0.167625			−0.0838124	+	0.996482i	$0.526710\pi$
$224$	159.861	−	92.2960i	0.713666	−	0.412036i
$225$	−173.360	+	130.497i	−0.770488	+	0.579986i
$226$	−58.0362			−0.256797
$227$	−172.213	+	99.4272i	−0.758648	+	0.438005i	−0.828810	−	0.559530i	$-0.810982\pi$
$227$	−172.213	+	99.4272i	−0.758648	+	0.438005i	0.0701623	+	0.997536i	$0.477648\pi$
$228$	183.701	−	207.529i	0.805707	−	0.910216i
$229$	−138.042	−	239.095i	−0.602802	−	1.04408i	−0.992395	−	0.123096i	$-0.960718\pi$
$229$	−138.042	−	239.095i	−0.602802	−	1.04408i	0.389593	−	0.920987i	$-0.372616\pi$
$230$		−	49.9708i		−	0.217264i
$231$	−229.526	+	76.7329i	−0.993618	+	0.332177i
$232$	62.0986			0.267666
$233$			106.047i			0.455137i	0.973762	+	0.227568i	$0.0730775\pi$
$233$			106.047i			0.455137i	−0.973762	+	0.227568i	$0.926922\pi$
$234$	223.395	−	202.846i	0.954679	−	0.866864i
$235$	6.73434			0.0286568
$236$		−	86.4959i		−	0.366508i
$237$	114.962	−	129.874i	0.485072	−	0.547991i
$238$	−324.356			−1.36284
$239$	−331.745	+	191.533i	−1.38805	+	0.801393i	−0.993096	−	0.117307i	$-0.962574\pi$
$239$	−331.745	+	191.533i	−1.38805	+	0.801393i	−0.394957	+	0.918700i	$0.629241\pi$
$240$	52.5566	−	17.5702i	0.218986	−	0.0732092i
$241$	23.4930	+	40.6911i	0.0974813	+	0.168843i	0.910641	−	0.413197i	$-0.135588\pi$
$241$	23.4930	+	40.6911i	0.0974813	+	0.168843i	−0.813160	+	0.582040i	$0.802255\pi$
$242$			346.841i			1.43323i
$243$	130.301	+	205.111i	0.536219	+	0.844079i
$244$	17.7166	+	30.6860i	0.0726090	+	0.125762i
$245$			22.2012i			0.0906171i
$246$	30.1203	−	34.0273i	0.122440	−	0.138322i
$247$	−369.817	+	261.548i	−1.49724	+	1.05890i
$248$	61.6852	−	35.6140i	0.248731	−	0.143605i
$249$	99.2402	+	87.8456i	0.398555	+	0.352794i
$250$	−119.515			−0.478059
$251$	40.4117	+	23.3317i	0.161003	+	0.0929549i	0.578336	−	0.815798i	$-0.303702\pi$
$251$	40.4117	+	23.3317i	0.161003	+	0.0929549i	−0.417334	+	0.908753i	$0.637035\pi$
$252$	14.6164	+	119.547i	0.0580015	+	0.474394i
$253$	−164.102	+	284.233i	−0.648624	+	1.12345i
$254$	−262.943	+	151.810i	−1.03521	+	0.597679i
$255$	−69.1221	−	14.0815i	−0.271067	−	0.0552216i
$256$	334.820			1.30789
$257$	−103.885	−	59.9783i	−0.404224	−	0.233379i	0.284081	−	0.958800i	$-0.408312\pi$
$257$	−103.885	−	59.9783i	−0.404224	−	0.233379i	−0.688305	+	0.725422i	$0.741645\pi$
$258$	−13.7924	+	4.61094i	−0.0534589	+	0.0178719i
$259$	5.54808	−	9.60955i	0.0214211	−	0.0371025i
$260$	32.3881	−	2.98706i	0.124570	−	0.0114887i
$261$	−62.8642	+	147.888i	−0.240859	+	0.566621i
$262$	115.770	+	200.519i	0.441869	+	0.765340i
$263$		−	338.862i		−	1.28845i	−0.764836	−	0.644225i	$-0.777180\pi$
$263$		−	338.862i		−	1.28845i	0.764836	−	0.644225i	$-0.222820\pi$
$264$	−163.417	−	33.2911i	−0.619003	−	0.126103i
$265$	16.1054	+	27.8953i	0.0607749	+	0.105265i
$266$		−	453.532i		−	1.70501i
$267$	159.716	−	53.3947i	0.598187	−	0.199980i
$268$	−104.172	+	180.431i	−0.388701	+	0.673250i
$269$	194.820	+	112.479i	0.724236	+	0.418138i	0.816310	−	0.577614i	$-0.196016\pi$
$269$	194.820	+	112.479i	0.724236	+	0.418138i	−0.0920735	+	0.995752i	$0.529349\pi$
$270$	−5.20574	+	65.5016i	−0.0192805	+	0.242598i
$271$	2.75897	+	4.77868i	0.0101807	+	0.0176335i	0.871071	−	0.491157i	$-0.163426\pi$
$271$	2.75897	+	4.77868i	0.0101807	+	0.0176335i	−0.860890	+	0.508791i	$0.830093\pi$
$272$	−422.450	−	243.901i	−1.55312	−	0.896696i
$273$	21.4128	−	195.665i	0.0784351	−	0.716722i
$274$	−11.7828	−	20.4083i	−0.0430027	−	0.0744829i
$275$	333.736	+	192.682i	1.21358	+	0.700663i
$276$	122.300	+	108.257i	0.443114	+	0.392237i
$277$	−116.170	−	201.213i	−0.419387	−	0.726400i	0.576491	−	0.817104i	$-0.304422\pi$
$277$	−116.170	−	201.213i	−0.419387	−	0.726400i	−0.995878	+	0.0907036i	$0.971088\pi$
$278$			383.515i			1.37955i
$279$	22.3691	+	182.957i	0.0801760	+	0.655758i
$280$	8.28178	−	14.3445i	0.0295778	−	0.0512302i
$281$	108.117	+	62.4211i	0.384757	+	0.222139i	0.679886	−	0.733318i	$-0.262029\pi$
$281$	108.117	+	62.4211i	0.384757	+	0.222139i	−0.295129	+	0.955457i	$0.595363\pi$
$282$	−36.5989	+	41.3462i	−0.129783	+	0.146618i
$283$	−214.400	+	371.352i	−0.757597	+	1.31220i	0.186476	+	0.982460i	$0.440293\pi$
$283$	−214.400	+	371.352i	−0.757597	+	1.31220i	−0.944073	+	0.329737i	$0.893040\pi$
$284$	321.900	+	185.849i	1.13345	+	0.654398i
$285$	19.6895	−	96.6504i	0.0690861	−	0.339124i
$286$	−486.750	−	224.196i	−1.70192	−	0.783902i
$287$		−	29.6431i		−	0.103286i
$288$	−128.772	+	302.937i	−0.447127	+	1.05187i
$289$	165.976	+	287.479i	0.574312	+	0.994738i
$290$	−37.6309	+	21.7262i	−0.129762	+	0.0749179i
$291$	149.106	+	446.011i	0.512392	+	1.53268i
$292$	237.487			0.813313
$293$			152.486i			0.520431i	0.965551	+	0.260215i	$0.0837936\pi$
$293$			152.486i			0.520431i	−0.965551	+	0.260215i	$0.916206\pi$
$294$	−136.307	−	120.656i	−0.463628	−	0.410395i
$295$	−15.3914	−	26.6587i	−0.0521742	−	0.0903683i
$296$	6.62204	−	3.82324i	0.0223718	−	0.0129163i
$297$	244.714	−	355.476i	0.823954	−	1.19689i
$298$	−84.8940			−0.284879
$299$	−154.133	−	217.938i	−0.515496	−	0.728889i
$300$	127.112	−	143.600i	0.423706	−	0.478665i
$301$	−4.74319	+	8.21544i	−0.0157581	+	0.0272938i
$302$	−239.782	−	138.438i	−0.793980	−	0.458405i
$303$	66.9692	−	328.733i	0.221020	−	1.08493i
$304$	341.036	−	590.692i	1.12183	−	1.94307i
$305$	10.9208	+	6.30510i	0.0358058	+	0.0206725i
$306$	462.111	−	347.855i	1.51017	−	1.13678i
$307$	559.739			1.82325			0.911627	−	0.411019i	$-0.134827\pi$
$307$	559.739			1.82325			0.911627	+	0.411019i	$0.134827\pi$
$308$	185.239	−	106.948i	0.601424	−	0.347233i
$309$	151.305	+	452.590i	0.489662	+	1.46469i
$310$	−24.9203	+	43.1632i	−0.0803879	+	0.139236i
$311$	278.602	−	160.851i	0.895827	−	0.517206i	0.0199832	−	0.999800i	$-0.493639\pi$
$311$	278.602	−	160.851i	0.895827	−	0.517206i	0.875844	+	0.482594i	$0.160305\pi$
$312$	80.1964	−	109.393i	0.257040	−	0.350617i
$313$	−174.107	+	301.562i	−0.556252	+	0.963456i	0.441553	+	0.897235i	$0.354428\pi$
$313$	−174.107	+	301.562i	−0.556252	+	0.963456i	−0.997805	+	0.0662213i	$0.978906\pi$
$314$	−9.87494	+	5.70130i	−0.0314488	+	0.0181570i
$315$	25.7775	+	34.2444i	0.0818333	+	0.108712i
$316$	−76.6474	+	132.757i	−0.242555	+	0.420118i
$317$	−74.3159	−	42.9063i	−0.234435	−	0.135351i	0.378181	−	0.925732i	$-0.376550\pi$
$317$	−74.3159	−	42.9063i	−0.234435	−	0.135351i	−0.612616	+	0.790380i	$0.709883\pi$
$318$	−258.794	−	52.7212i	−0.813816	−	0.165790i
$319$	285.392			0.894644
$320$	−13.0954	+	7.56065i	−0.0409232	+	0.0236270i
$321$	−565.345	+	189.001i	−1.76120	+	0.588787i
$322$	267.272			0.830038
$323$	−751.927	+	434.125i	−2.32795	+	1.34404i
$324$	−149.032	−	154.644i	−0.459975	−	0.477296i
$325$	−255.895	+	180.978i	−0.787368	+	0.556855i
$326$	−210.937	−	121.785i	−0.647047	−	0.373573i
$327$	292.834	+	59.6559i	0.895518	+	0.182434i
$328$	10.2137	−	17.6906i	0.0311393	−	0.0539348i
$329$			36.0191i			0.109480i
$330$	110.676	−	37.0001i	0.335381	−	0.112121i
$331$	−3.02205	−	5.23434i	−0.00913006	−	0.0158137i	0.861424	−	0.507886i	$-0.169573\pi$
$331$	−3.02205	−	5.23434i	−0.00913006	−	0.0158137i	−0.870554	+	0.492072i	$0.836240\pi$
$332$	−101.443	−	58.5684i	−0.305553	−	0.176411i
$333$	2.40137	+	19.6408i	0.00721132	+	0.0589813i
$334$	−211.911	+	367.040i	−0.634464	+	1.09892i
$335$			74.1468i			0.221334i
$336$	93.9754	+	281.102i	0.279689	+	0.836614i
$337$	201.907	+	349.714i	0.599132	+	1.03773i	0.992950	+	0.118538i	$0.0378208\pi$
$337$	201.907	+	349.714i	0.599132	+	1.03773i	−0.393818	+	0.919189i	$0.628846\pi$
$338$	331.238	−	283.291i	0.979995	−	0.838138i
$339$	13.4761	−	66.1503i	0.0397524	−	0.195134i
$340$	62.3463			0.183371
$341$	283.492	−	163.674i	0.831354	−	0.479983i
$342$	486.389	+	646.149i	1.42219	+	1.88933i
$343$	−366.048			−1.06720
$344$	−5.66135	+	3.26858i	−0.0164574	+	0.00950169i
$345$	56.9573	+	11.6033i	0.165094	+	0.0336327i
$346$	130.520	+	226.067i	0.377225	+	0.653372i
$347$		−	294.439i		−	0.848528i	−0.905538	−	0.424264i	$-0.860533\pi$
$347$		−	294.439i		−	0.848528i	0.905538	−	0.424264i	$-0.139467\pi$
$348$	28.3509	−	139.167i	0.0814680	−	0.399904i
$349$	−510.269			−1.46209			−0.731045	−	0.682330i	$-0.760967\pi$
$349$	−510.269			−1.46209			−0.731045	+	0.682330i	$0.760967\pi$
$350$		−	313.821i		−	0.896632i
$351$	179.334	+	301.729i	0.510922	+	0.859627i
$352$	584.603			1.66080
$353$		−	502.273i		−	1.42287i	−0.702752	−	0.711435i	$-0.748046\pi$
$353$		−	502.273i		−	1.42287i	0.702752	−	0.711435i	$-0.251954\pi$
$354$	247.321	+	50.3840i	0.698646	+	0.142328i
$355$	132.283			0.372627
$356$	−128.899	+	74.4197i	−0.362075	+	0.209044i
$357$	75.3158	−	369.704i	0.210969	−	1.03559i
$358$	−263.493	−	456.383i	−0.736014	−	1.27481i
$359$		−	258.046i		−	0.718791i	−0.933185	−	0.359395i	$-0.882983\pi$
$359$		−	258.046i		−	0.718791i	0.933185	−	0.359395i	$-0.117017\pi$
$360$	3.58460	+	29.3184i	0.00995722	+	0.0814400i
$361$	−426.518	−	738.750i	−1.18149	−	2.04640i
$362$			312.704i			0.863822i
$363$	−395.334	−	80.5370i	−1.08907	−	0.221865i
$364$	15.9765	+	173.230i	0.0438915	+	0.475906i
$365$	73.1953	−	42.2593i	0.200535	−	0.115779i
$366$	−98.0616	+	32.7830i	−0.267928	+	0.0895711i
$367$	−117.287			−0.319584			−0.159792	−	0.987151i	$-0.551082\pi$
$367$	−117.287			−0.319584			−0.159792	+	0.987151i	$0.551082\pi$
$368$	348.102	+	200.977i	0.945930	+	0.546133i
$369$	31.7907	+	42.2327i	0.0861536	+	0.114452i
$370$	−2.67524	+	4.63366i	−0.00723039	+	0.0125234i
$371$	−149.200	+	86.1406i	−0.402156	+	0.232185i
$372$	−51.6508	−	154.500i	−0.138846	−	0.415321i
$373$	703.087			1.88495			0.942476	−	0.334273i	$-0.108491\pi$
$373$	703.087			1.88495			0.942476	+	0.334273i	$0.108491\pi$
$374$	−889.612	−	513.618i	−2.37864	−	1.37331i
$375$	27.7515	−	136.224i	0.0740039	−	0.363265i
$376$	−12.4106	+	21.4957i	−0.0330068	+	0.0571695i
$377$	−97.1059	+	210.826i	−0.257575	+	0.559220i
$378$	−350.339	−	27.8432i	−0.926824	−	0.0736594i
$379$	166.355	+	288.136i	0.438932	+	0.760252i	0.997607	−	0.0691341i	$-0.0220236\pi$
$379$	166.355	+	288.136i	0.438932	+	0.760252i	−0.558676	+	0.829386i	$0.688690\pi$
$380$			87.1760i			0.229411i
$381$	−111.979	−	334.956i	−0.293909	−	0.879150i
$382$	−233.806	−	404.964i	−0.612058	−	1.06012i
$383$			333.347i			0.870357i	0.900344	+	0.435179i	$0.143315\pi$
$383$			333.347i			0.870357i	−0.900344	+	0.435179i	$0.856685\pi$
$384$	−62.8617	+	308.570i	−0.163702	+	0.803569i
$385$	38.0613	−	65.9240i	0.0988604	−	0.171231i
$386$	−5.48154	−	3.16477i	−0.0142009	−	0.00819888i
$387$	−2.05299	−	16.7914i	−0.00530489	−	0.0433886i
$388$	−207.819	−	359.953i	−0.535615	−	0.927713i
$389$	505.351	+	291.765i	1.29910	+	0.750038i	0.980249	−	0.197766i	$-0.0633685\pi$
$389$	505.351	+	291.765i	1.29910	+	0.750038i	0.318855	+	0.947804i	$0.396702\pi$
$390$	−10.3251	+	94.3484i	−0.0264746	+	0.241919i
$391$	−255.835	−	443.120i	−0.654310	−	1.13330i
$392$	−70.8652	−	40.9140i	−0.180779	−	0.104373i
$393$	−255.436	+	85.3949i	−0.649964	+	0.217290i
$394$	447.989	+	775.939i	1.13703	+	1.96939i
$395$			54.5556i			0.138115i
$396$	−149.215	+	351.027i	−0.376805	+	0.886433i
$397$	−107.622	+	186.406i	−0.271088	+	0.469538i	−0.969141	−	0.246508i	$-0.920717\pi$
$397$	−107.622	+	186.406i	−0.271088	+	0.469538i	0.698053	+	0.716046i	$0.254050\pi$
$398$	−394.488	−	227.758i	−0.991177	−	0.572256i
$399$	516.941	+	105.311i	1.29559	+	0.263937i
$400$	235.980	−	408.729i	0.589950	−	1.02182i
$401$	−114.212	−	65.9404i	−0.284818	−	0.164440i	0.350784	−	0.936456i	$-0.385915\pi$
$401$	−114.212	−	65.9404i	−0.284818	−	0.164440i	−0.635603	+	0.772016i	$0.719248\pi$
$402$	−455.232	−	402.963i	−1.13242	−	1.00240i
$403$	24.4506	+	265.113i	0.0606715	+	0.657850i
$404$			296.508i			0.733931i
$405$	−73.4506	−	21.1431i	−0.181360	−	0.0522052i
$406$	−116.204	−	201.271i	−0.286217	−	0.495742i
$407$	30.4335	−	17.5708i	0.0747751	−	0.0431714i
$408$	172.331	−	194.684i	0.422380	−	0.477168i
$409$	−59.9512			−0.146580			−0.0732899	−	0.997311i	$-0.523350\pi$
$409$	−59.9512			−0.146580			−0.0732899	+	0.997311i	$0.523350\pi$
$410$			14.2937i			0.0348627i
$411$	25.9976	−	8.69127i	0.0632545	−	0.0211467i
$412$	−210.884	−	365.262i	−0.511855	−	0.886559i
$413$	142.586	−	82.3218i	0.345244	−	0.199326i
$414$	−380.784	+	286.635i	−0.919767	+	0.692356i
$415$	−41.6875			−0.100452
$416$	−198.914	+	431.861i	−0.478159	+	1.03813i
$417$	−437.135	−	89.0527i	−1.04828	−	0.213556i
$418$	718.169	−	1243.90i	1.71811	−	2.97585i
$419$	360.213	+	207.969i	0.859696	+	0.496346i	0.863910	−	0.503645i	$-0.168008\pi$
$419$	360.213	+	207.969i	0.859696	+	0.496346i	−0.00421444	+	0.999991i	$0.501342\pi$
$420$	−28.3658	−	25.1089i	−0.0675375	−	0.0597830i
$421$	−3.52056	+	6.09779i	−0.00836237	+	0.0144841i	−0.870176	−	0.492740i	$-0.835995\pi$
$421$	−3.52056	+	6.09779i	−0.00836237	+	0.0144841i	0.861814	+	0.507225i	$0.169329\pi$
$422$	−609.215	−	351.731i	−1.44364	−	0.833485i
$423$	−38.6286	−	51.3165i	−0.0913205	−	0.121316i
$424$	−118.721			−0.280002
$425$	−520.295	+	300.392i	−1.22422	+	0.706806i
$426$	−718.912	+	812.163i	−1.68759	+	1.90649i
$427$	−33.7233	+	58.4104i	−0.0789772	+	0.136793i
$428$	456.261	−	263.423i	1.06603	−	0.615473i
$429$	368.565	−	502.744i	0.859126	−	1.17190i
$430$	2.28713	−	3.96143i	0.00531891	−	0.00921263i
$431$	−28.5577	+	16.4878i	−0.0662592	+	0.0382548i	−0.532764	−	0.846264i	$-0.678847\pi$
$431$	−28.5577	+	16.4878i	−0.0662592	+	0.0382548i	0.466504	+	0.884519i	$0.345513\pi$
$432$	−435.355	−	299.704i	−1.00777	−	0.693759i
$433$	169.487	−	293.559i	0.391424	−	0.677966i	−0.601214	−	0.799088i	$-0.705316\pi$
$433$	169.487	−	293.559i	0.391424	−	0.677966i	0.992638	+	0.121122i	$0.0386492\pi$
$434$	−230.861	−	133.288i	−0.531938	−	0.307114i
$435$	−16.0258	−	47.9370i	−0.0368410	−	0.110200i
$436$	−264.129			−0.605799
$437$	619.594	−	357.723i	1.41784	−	0.818588i
$438$	−138.337	+	679.056i	−0.315837	+	1.55036i
$439$	490.839			1.11808			0.559042	−	0.829139i	$-0.311169\pi$
$439$	490.839			1.11808			0.559042	+	0.829139i	$0.311169\pi$
$440$	45.4289	−	26.2284i	0.103248	−	0.0596100i
$441$	169.176	−	127.347i	0.383619	−	0.288769i
$442$	682.117	−	482.418i	1.54325	−	1.09144i
$443$	−182.064	−	105.115i	−0.410980	−	0.237279i	0.280231	−	0.959933i	$-0.409589\pi$
$443$	−182.064	−	105.115i	−0.410980	−	0.237279i	−0.691211	+	0.722653i	$0.742922\pi$
$444$	−5.54483	−	16.5859i	−0.0124884	−	0.0373556i
$445$	−26.4850	+	45.8734i	−0.0595169	+	0.103086i
$446$			96.4054i			0.216156i
$447$	19.7125	−	96.7631i	0.0440995	−	0.216472i
$448$	−40.4386	−	70.0418i	−0.0902648	−	0.156343i
$449$	70.3212	+	40.6000i	0.156617	+	0.0904231i	0.576260	−	0.817266i	$-0.304511\pi$
$449$	70.3212	+	40.6000i	0.156617	+	0.0904231i	−0.419643	+	0.907689i	$0.637845\pi$
$450$	336.557	+	447.102i	0.747904	+	0.993560i
$451$	46.9399	−	81.3023i	0.104080	−	0.180271i
$452$			59.6657i			0.132004i
$453$	213.471	−	241.161i	0.471239	−	0.532364i
$454$	256.427	+	444.145i	0.564817	+	0.978292i
$455$	35.7492	+	50.5478i	0.0785697	+	0.111094i
$456$	272.218	+	240.963i	0.596970	+	0.528427i
$457$	21.8247			0.0477565			0.0238782	−	0.999715i	$-0.492399\pi$
$457$	21.8247			0.0477565			0.0238782	+	0.999715i	$0.492399\pi$
$458$	−616.636	+	356.015i	−1.34637	+	0.777326i
$459$	289.186	+	607.492i	0.630034	+	1.32351i
$460$	−51.3739			−0.111682
$461$	403.982	−	233.239i	0.876318	−	0.505942i	0.00687516	−	0.999976i	$-0.497812\pi$
$461$	403.982	−	233.239i	0.876318	−	0.505942i	0.869443	+	0.494034i	$0.164478\pi$
$462$	197.897	+	591.957i	0.428349	+	1.28129i
$463$	132.919	+	230.222i	0.287081	+	0.497239i	0.973112	−	0.230333i	$-0.0739817\pi$
$463$	132.919	+	230.222i	0.287081	+	0.497239i	−0.686031	+	0.727573i	$0.740648\pi$
$464$		−	349.521i		−	0.753279i
$465$	−43.4113	−	38.4269i	−0.0933577	−	0.0826386i
$466$	273.499			0.586908
$467$		−	534.686i		−	1.14494i	−0.819926	−	0.572469i	$-0.805986\pi$
$467$		−	534.686i		−	1.14494i	0.819926	−	0.572469i	$-0.194014\pi$
$468$	−208.542	−	229.667i	−0.445602	−	0.490742i
$469$	−396.579			−0.845584
$470$		−	17.3681i		−	0.0369535i
$471$	−4.20543	−	12.5794i	−0.00892872	−	0.0267079i
$472$	113.458			0.240376
$473$	−26.0183	+	15.0217i	−0.0550070	+	0.0317583i
$474$	−334.950	−	296.492i	−0.706646	−	0.625510i
$475$	−420.025	−	727.505i	−0.884264	−	1.53159i
$476$			333.463i			0.700553i
$477$	120.184	−	282.734i	0.251959	−	0.592733i
$478$	493.971	+	855.583i	1.03341	+	1.78992i
$479$			158.438i			0.330769i	0.986229	+	0.165384i	$0.0528864\pi$
$479$			158.438i			0.330769i	−0.986229	+	0.165384i	$0.947114\pi$
$480$	−32.8277	−	98.1952i	−0.0683910	−	0.204573i
$481$	2.62483	+	28.4605i	0.00545702	+	0.0591694i
$482$	104.944	−	60.5894i	0.217726	−	0.125704i
$483$	−62.0609	+	304.640i	−0.128491	+	0.630724i
$484$	356.580			0.736736
$485$	−128.102	−	73.9600i	−0.264129	−	0.152495i
$486$	528.990	−	336.052i	1.08846	−	0.691466i
$487$	280.748	−	486.271i	0.576486	−	0.998502i	−0.419393	−	0.907805i	$-0.637757\pi$
$487$	280.748	−	486.271i	0.576486	−	0.998502i	0.995878	−	0.0906974i	$-0.0289096\pi$
$488$	−40.2512	+	23.2391i	−0.0824820	+	0.0476210i
$489$	187.792	−	212.150i	0.384032	−	0.433845i
$490$	57.2578			0.116853
$491$	400.940	+	231.483i	0.816579	+	0.471452i	0.849235	−	0.528015i	$-0.177063\pi$
$491$	400.940	+	231.483i	0.816579	+	0.471452i	−0.0326565	+	0.999467i	$0.510397\pi$
$492$	−34.9827	−	30.9661i	−0.0711030	−	0.0629391i
$493$	−222.463	+	385.317i	−0.451244	+	0.781577i
$494$	674.543	+	953.774i	1.36547	+	1.93072i
$495$	16.4740	+	134.741i	0.0332809	+	0.272204i
$496$	−200.453	−	347.195i	−0.404139	−	0.699990i
$497$			707.522i			1.42359i
$498$	226.558	−	255.945i	0.454935	−	0.513945i
$499$	161.354	+	279.473i	0.323354	+	0.560065i	0.981178	−	0.193106i	$-0.0618563\pi$
$499$	161.354	+	279.473i	0.323354	+	0.560065i	−0.657824	+	0.753172i	$0.728523\pi$
$500$			122.871i			0.245741i
$501$	−369.151	−	326.766i	−0.736828	−	0.652227i
$502$	60.1734	−	104.223i	0.119867	−	0.207616i
$503$	−278.116	−	160.570i	−0.552915	−	0.319225i	0.197382	−	0.980327i	$-0.436756\pi$
$503$	−278.116	−	160.570i	−0.552915	−	0.319225i	−0.750297	+	0.661101i	$0.770089\pi$
$504$	−156.811	+	19.1725i	−0.311134	+	0.0380406i
$505$	52.7617	+	91.3859i	0.104479	+	0.180962i
$506$	733.048	+	423.226i	1.44871	+	0.836414i
$507$	245.984	+	443.329i	0.485175	+	0.874417i
$508$	156.073	+	270.326i	0.307230	+	0.532138i
$509$	−630.554	−	364.050i	−1.23881	−	0.715226i	−0.269958	−	0.962872i	$-0.587010\pi$
$509$	−630.554	−	364.050i	−1.23881	−	0.715226i	−0.968851	+	0.247646i	$0.920343\pi$
$510$	−36.3168	+	178.269i	−0.0712094	+	0.349547i
$511$	226.027	+	391.490i	0.442322	+	0.766125i
$512$		−	443.636i		−	0.866477i
$513$	−849.428	+	404.355i	−1.65581	+	0.788217i
$514$	−154.687	+	267.925i	−0.300947	+	0.521255i
$515$	−129.992	−	75.0509i	−0.252412	−	0.145730i
$516$	4.74041	+	14.1797i	0.00918684	+	0.0274800i
$517$	−57.0362	+	98.7896i	−0.110321	+	0.191082i
$518$	−24.7834	−	14.3087i	−0.0478445	−	0.0276230i
$519$	−287.980	+	96.2748i	−0.554875	+	0.185501i
$520$	3.91816	+	42.4838i	0.00753492	+	0.0816997i
$521$		−	819.761i		−	1.57344i	−0.617311	−	0.786719i	$-0.711778\pi$
$521$		−	819.761i		−	1.57344i	0.617311	−	0.786719i	$-0.288222\pi$
$522$	381.409	+	162.129i	0.730669	+	0.310593i
$523$	485.658	+	841.184i	0.928601	+	1.60838i	0.785666	+	0.618651i	$0.212321\pi$
$523$	485.658	+	841.184i	0.928601	+	1.60838i	0.142935	+	0.989732i	$0.454346\pi$
$524$	206.149	−	119.020i	0.393415	−	0.227138i
$525$	357.697	+	72.8697i	0.681327	+	0.138799i
$526$	−873.940			−1.66148
$527$			510.337i			0.968381i
$528$	−187.379	+	919.790i	−0.354884	+	1.74203i
$529$	−53.6894	−	92.9928i	−0.101492	−	0.175790i
$530$	71.9432	−	41.5364i	0.135742	−	0.0783706i
$531$	−114.856	+	270.200i	−0.216302	+	0.508851i
$532$	−466.267			−0.876441
$533$	44.0885	+	62.3392i	0.0827176	+	0.116959i
$534$	−137.707	−	411.914i	−0.257879	−	0.771375i
$535$	93.7486	−	162.377i	0.175231	−	0.303509i
$536$	−236.673	−	136.643i	−0.441555	−	0.254932i
$537$	581.374	−	194.360i	1.08263	−	0.361936i
$538$	290.088	−	502.448i	0.539198	−	0.933918i
$539$	−325.681	−	188.032i	−0.604232	−	0.348853i
$540$	67.3407	+	5.35191i	0.124705	+	0.00991094i
$541$	−850.073			−1.57130			−0.785650	−	0.618672i	$-0.787671\pi$
$541$	−850.073			−1.57130			−0.785650	+	0.618672i	$0.787671\pi$
$542$	12.3244	−	7.11551i	0.0227388	−	0.0131282i
$543$	−356.423	−	72.6102i	−0.656396	−	0.133720i
$544$	−455.699	+	789.293i	−0.837681	+	1.45091i
$545$	−81.4063	+	46.9999i	−0.149369	+	0.0862384i
$546$	−504.629	−	55.2245i	−0.924228	−	0.101144i
$547$	−290.185	+	502.616i	−0.530503	+	0.918859i	0.468863	+	0.883271i	$0.344664\pi$
$547$	−290.185	+	502.616i	−0.530503	+	0.918859i	−0.999367	+	0.0355881i	$0.988670\pi$
$548$	−20.9814	+	12.1136i	−0.0382872	+	0.0221051i
$549$	−14.5964	−	119.384i	−0.0265873	−	0.217457i
$550$	496.936	−	860.718i	0.903520	−	1.56494i
$551$	−538.772	−	311.060i	−0.977808	−	0.564538i
$552$	−142.002	+	160.422i	−0.257251	+	0.290619i
$553$	−291.794			−0.527657
$554$	−518.936	+	299.608i	−0.936708	+	0.540809i
$555$	−4.66030	−	4.12522i	−0.00839694	−	0.00743282i
$556$	394.284			0.709143
$557$	76.5165	−	44.1768i	0.137373	−	0.0793121i	−0.429739	−	0.902953i	$-0.641394\pi$
$557$	76.5165	−	44.1768i	0.137373	−	0.0793121i	0.567111	+	0.823641i	$0.308061\pi$
$558$	471.853	−	57.6908i	0.845614	−	0.103389i
$559$	−2.24403	−	24.3316i	−0.00401437	−	0.0435270i
$560$	−80.7377	−	46.6140i	−0.144175	−	0.0832392i
$561$	791.996	−	894.727i	1.41176	−	1.59488i
$562$	160.987	−	278.837i	0.286453	−	0.496152i
$563$			849.876i			1.50955i	0.655984	+	0.754774i	$0.272254\pi$
$563$			849.876i			1.50955i	−0.655984	+	0.754774i	$0.727746\pi$
$564$	42.5071	+	37.6266i	0.0753673	+	0.0667138i
$565$	10.6171	+	18.3894i	0.0187914	+	0.0325476i
$566$	957.732	+	552.947i	1.69211	+	0.976937i
$567$	113.085	−	392.856i	0.199445	−	0.692867i
$568$	−243.780	+	422.240i	−0.429191	+	0.743380i
$569$			305.664i			0.537196i	0.963252	+	0.268598i	$0.0865602\pi$
$569$			305.664i			0.537196i	−0.963252	+	0.268598i	$0.913440\pi$
$570$	−249.265	−	50.7801i	−0.437308	−	0.0890879i
$571$	−76.3088	−	132.171i	−0.133641	−	0.231472i	0.791437	−	0.611251i	$-0.209333\pi$
$571$	−76.3088	−	132.171i	−0.133641	−	0.231472i	−0.925077	+	0.379779i	$0.876000\pi$
$572$	−230.491	+	500.417i	−0.402956	+	0.874855i
$573$	515.873	−	172.462i	0.900301	−	0.300980i
$574$	−76.4508			−0.133190
$575$	428.728	−	247.526i	0.745613	−	0.430480i
$576$	132.729	+	56.4205i	0.230433	+	0.0979522i
$577$	−357.654			−0.619851			−0.309926	−	0.950761i	$-0.600304\pi$
$577$	−357.654			−0.619851			−0.309926	+	0.950761i	$0.600304\pi$
$578$	741.421	−	428.060i	1.28274	−	0.740588i
$579$	4.88006	−	5.51305i	0.00842842	−	0.00952168i
$580$	22.3362	+	38.6875i	0.0385108	+	0.0667026i
$581$		−	222.968i		−	0.383766i
$582$	1150.28	−	384.551i	1.97643	−	0.660740i
$583$	−545.615			−0.935874
$584$			311.515i			0.533416i
$585$	−105.142	−	33.6765i	−0.179730	−	0.0575666i
$586$	393.268			0.671106
$587$		−	807.369i		−	1.37542i	−0.725987	−	0.687708i	$-0.758617\pi$
$587$		−	807.369i		−	1.37542i	0.725987	−	0.687708i	$-0.241383\pi$
$588$	−124.044	+	140.134i	−0.210959	+	0.238323i
$589$	−713.581			−1.21151
$590$	−68.7538	+	39.6950i	−0.116532	+	0.0672797i
$591$	−988.447	+	330.448i	−1.67250	+	0.559134i
$592$	−21.5191	−	37.2721i	−0.0363498	−	0.0629597i
$593$			246.824i			0.416230i	0.978104	+	0.208115i	$0.0667328\pi$
$593$			246.824i			0.416230i	−0.978104	+	0.208115i	$0.933267\pi$
$594$	−916.787	−	631.128i	−1.54341	−	1.06251i
$595$	59.3376	+	102.776i	0.0997271	+	0.172732i
$596$			87.2777i			0.146439i
$597$	351.202	−	396.757i	0.588278	−	0.664584i
$598$	−562.071	+	397.516i	−0.939918	+	0.664743i
$599$	120.864	−	69.7811i	0.201777	−	0.116496i	−0.395707	−	0.918377i	$-0.629500\pi$
$599$	120.864	−	69.7811i	0.201777	−	0.116496i	0.597484	+	0.801881i	$0.296167\pi$
$600$	188.361	+	166.734i	0.313935	+	0.277890i
$601$	−969.145			−1.61255			−0.806277	−	0.591538i	$-0.798521\pi$
$601$	−969.145			−1.61255			−0.806277	+	0.591538i	$0.798521\pi$
$602$	21.1880	+	12.2329i	0.0351960	+	0.0203204i
$603$	565.008	−	425.310i	0.936994	−	0.705324i
$604$	−142.325	+	246.515i	−0.235638	+	0.408137i
$605$	109.900	−	63.4511i	0.181654	−	0.104878i
$606$	−847.816	−	172.716i	−1.39904	−	0.285010i
$607$	−603.040			−0.993476			−0.496738	−	0.867900i	$-0.665469\pi$
$607$	−603.040			−0.993476			−0.496738	+	0.867900i	$0.665469\pi$
$608$	−1103.63	−	637.183i	−1.81519	−	1.04800i
$609$	256.394	−	85.7152i	0.421008	−	0.140747i
$610$	16.2611	−	28.1651i	0.0266576	−	0.0461723i
$611$	−53.5715	−	75.7477i	−0.0876784	−	0.123973i
$612$	−357.622	−	475.086i	−0.584349	−	0.776285i
$613$	520.011	+	900.685i	0.848305	+	1.46931i	0.882720	+	0.469900i	$0.155710\pi$
$613$	520.011	+	900.685i	0.848305	+	1.46931i	−0.0344149	+	0.999408i	$0.510957\pi$
$614$		−	1443.59i		−	2.35112i
$615$	−16.2921	−	3.31902i	−0.0264913	−	0.00539677i
$616$	140.284	+	242.980i	0.227734	+	0.394448i
$617$		−	189.448i		−	0.307047i	−0.988145	−	0.153523i	$-0.950938\pi$
$617$		−	189.448i		−	0.307047i	0.988145	−	0.153523i	$-0.0490620\pi$
$618$	1167.25	−	390.223i	1.88875	−	0.631429i
$619$	−378.224	+	655.103i	−0.611024	+	1.05832i	0.380044	+	0.924968i	$0.375909\pi$
$619$	−378.224	+	655.103i	−0.611024	+	1.05832i	−0.991068	+	0.133356i	$0.957425\pi$
$620$	44.3751	+	25.6200i	0.0715728	+	0.0413226i
$621$	−238.292	−	500.579i	−0.383722	−	0.806085i
$622$	−414.842	−	718.527i	−0.666948	−	1.15519i
$623$	−245.357	−	141.657i	−0.393831	−	0.227378i
$624$	−615.715	−	451.385i	−0.986724	−	0.723373i
$625$	−279.506	−	484.118i	−0.447209	−	0.774589i
$626$	777.741	+	449.029i	1.24240	+	0.717298i
$627$	1251.06	+	1107.41i	1.99531	+	1.76621i
$628$	5.86138	+	10.1522i	0.00933341	+	0.0161659i
$629$			54.7857i			0.0870998i
$630$	88.3177	−	66.4813i	0.140187	−	0.105526i
$631$	363.821	−	630.156i	0.576578	−	0.998662i	−0.419290	−	0.907852i	$-0.637721\pi$
$631$	363.821	−	630.156i	0.576578	−	0.998662i	0.995868	−	0.0908100i	$-0.0289456\pi$
$632$	−174.139	−	100.539i	−0.275537	−	0.159081i
$633$	542.367	−	612.718i	0.856820	−	0.967959i
$634$	−110.657	+	191.664i	−0.174538	+	0.302309i
$635$	96.2056	+	55.5443i	0.151505	+	0.0874714i
$636$	−54.2015	+	266.060i	−0.0852225	+	0.418333i
$637$	249.719	−	176.610i	0.392023	−	0.277253i
$638$		−	736.037i		−	1.15366i
$639$	−758.780	−	1008.01i	−1.18745	−	1.57748i
$640$	−49.5256	−	85.7808i	−0.0773837	−	0.134033i
$641$	759.962	−	438.764i	1.18559	−	0.684499i	0.228287	−	0.973594i	$-0.426688\pi$
$641$	759.962	−	438.764i	1.18559	−	0.684499i	0.957301	+	0.289095i	$0.0933542\pi$
$642$	487.441	+	1458.05i	0.759253	+	2.27110i
$643$	−415.517			−0.646217			−0.323108	−	0.946362i	$-0.604728\pi$
$643$	−415.517			−0.646217			−0.323108	+	0.946362i	$0.604728\pi$
$644$		−	274.777i		−	0.426672i
$645$	3.98421	+	3.52675i	0.00617707	+	0.00546783i
$646$	1119.63	+	1939.25i	1.73317	+	3.00194i
$647$	−327.840	+	189.279i	−0.506708	+	0.292548i	−0.731479	−	0.681864i	$-0.761170\pi$
$647$	−327.840	+	189.279i	−0.506708	+	0.292548i	0.224772	+	0.974411i	$0.427836\pi$
$648$	202.848	−	195.487i	0.313038	−	0.301678i
$649$	521.427			0.803431
$650$	466.749	+	659.963i	0.718076	+	1.01533i
$651$	205.529	−	232.188i	0.315713	−	0.356664i
$652$	−125.204	+	216.860i	−0.192031	+	0.332608i
$653$	261.706	+	151.096i	0.400775	+	0.231387i	0.686818	−	0.726829i	$-0.259007\pi$
$653$	261.706	+	151.096i	0.400775	+	0.231387i	−0.286043	+	0.958217i	$0.592340\pi$
$654$	153.855	−	755.232i	0.235253	−	1.15479i
$655$	42.3578	−	73.3659i	0.0646684	−	0.112009i
$656$	−99.5716	−	57.4877i	−0.151786	−	0.0876337i
$657$	−741.873	−	315.355i	−1.12918	−	0.479993i
$658$	92.8947			0.141177
$659$	−6.36168	+	3.67292i	−0.00965354	+	0.00557347i	−0.504819	−	0.863225i	$-0.668441\pi$
$659$	−6.36168	+	3.67292i	−0.00965354	+	0.00557347i	0.495165	+	0.868799i	$0.335107\pi$
$660$	−38.0390	−	113.783i	−0.0576348	−	0.172399i
$661$	−315.997	+	547.323i	−0.478059	+	0.828022i	−0.999684	−	0.0251527i	$-0.991993\pi$
$661$	−315.997	+	547.323i	−0.478059	+	0.828022i	0.521625	+	0.853175i	$0.325326\pi$
$662$	−13.4996	+	7.79399i	−0.0203921	+	0.0117734i
$663$	391.476	+	889.503i	0.590462	+	1.34163i
$664$	76.8248	−	133.065i	0.115700	−	0.200398i
$665$	−143.707	+	82.9691i	−0.216100	+	0.124766i
$666$	50.6544	−	6.19324i	0.0760577	−	0.00929915i
$667$	183.312	−	317.505i	0.274830	−	0.476019i
$668$	377.346	+	217.861i	0.564890	+	0.326139i
$669$	−109.884	−	22.3855i	−0.164251	−	0.0334611i
$670$	191.228			0.285414
$671$	−184.986	+	106.802i	−0.275687	+	0.159168i
$672$	525.204	−	175.581i	0.781553	−	0.261281i
$673$	1010.99			1.50221			0.751105	−	0.660183i	$-0.229521\pi$
$673$	1010.99			1.50221			0.751105	+	0.660183i	$0.229521\pi$
$674$	901.927	−	520.728i	1.33817	−	0.772593i
$675$	−587.761	+	279.793i	−0.870757	+	0.414509i
$676$	−291.245	−	340.539i	−0.430836	−	0.503756i
$677$	453.715	+	261.952i	0.670185	+	0.386931i	0.796147	−	0.605104i	$-0.206868\pi$
$677$	453.715	+	261.952i	0.670185	+	0.386931i	−0.125962	+	0.992035i	$0.540202\pi$
$678$	−170.604	−	34.7554i	−0.251629	−	0.0512616i
$679$	395.580	−	685.164i	0.582592	−	1.00908i
$680$			81.7803i			0.120265i
$681$	−565.784	+	189.147i	−0.830813	+	0.277750i
$682$	−422.122	−	731.137i	−0.618948	−	1.07205i
$683$	733.152	+	423.286i	1.07343	+	0.619745i	0.929116	−	0.369787i	$-0.120569\pi$
$683$	733.152	+	423.286i	1.07343	+	0.619745i	0.144313	+	0.989532i	$0.453903\pi$
$684$	664.292	−	500.047i	0.971187	−	0.731062i
$685$	−4.31107	+	7.46699i	−0.00629353	+	0.0109007i
$686$			944.053i			1.37617i
$687$	−262.606	−	785.516i	−0.382251	−	1.14340i
$688$	18.3972	+	31.8649i	0.0267401	+	0.0463152i
$689$	185.648	−	403.059i	0.269446	−	0.584992i
$690$	29.9254	−	146.895i	0.0433701	−	0.212892i
$691$	681.316			0.985985			0.492993	−	0.870034i	$-0.335903\pi$
$691$	681.316			0.985985			0.492993	+	0.870034i	$0.335903\pi$
$692$	232.414	−	134.185i	0.335859	−	0.193908i
$693$	−720.671	+	88.1125i	−1.03993	+	0.127146i
$694$	−759.371			−1.09419
$695$	121.521	−	70.1602i	0.174850	−	0.100950i
$696$	182.546	+	37.1882i	0.262279	+	0.0534313i
$697$	73.1794	+	126.750i	0.104992	+	0.181851i
$698$			1316.01i			1.88539i
$699$	−63.5069	+	311.738i	−0.0908539	+	0.445976i
$700$	−322.633			−0.460904
$701$			253.593i			0.361759i	0.983505	+	0.180880i	$0.0578945\pi$
$701$			253.593i			0.361759i	−0.983505	+	0.180880i	$0.942106\pi$
$702$	778.172	−	462.509i	1.10851	−	0.658845i
$703$	−76.6045			−0.108968
$704$		−	256.138i		−	0.363833i
$705$	19.7964	+	4.03291i	0.0280800	+	0.00572043i
$706$	−1295.38			−1.83482
$707$	−488.784	+	282.199i	−0.691349	+	0.399150i
$708$	51.7987	−	254.265i	0.0731620	−	0.359132i
$709$	−127.391	−	220.647i	−0.179677	−	0.311209i	0.762093	−	0.647468i	$-0.224172\pi$
$709$	−127.391	−	220.647i	−0.179677	−	0.311209i	−0.941770	+	0.336258i	$0.890839\pi$
$710$		−	341.162i		−	0.480510i
$711$	415.720	−	312.934i	0.584698	−	0.440132i
$712$	−97.6172	−	169.078i	−0.137103	−	0.237469i
$713$		−	420.522i		−	0.589792i
$714$	−953.483	−	194.243i	−1.33541	−	0.272049i
$715$	18.0070	+	195.246i	0.0251846	+	0.273072i
$716$	−469.198	+	270.892i	−0.655305	+	0.378340i
$717$	−1089.90	+	364.366i	−1.52009	+	0.508182i
$718$	−665.511			−0.926896
$719$	−129.197	−	74.5922i	−0.179690	−	0.103744i	0.407457	−	0.913224i	$-0.366416\pi$
$719$	−129.197	−	74.5922i	−0.179690	−	0.103744i	−0.587147	+	0.809480i	$0.699749\pi$
$720$	165.018	−	20.1759i	0.229192	−	0.0280221i
$721$	401.415	−	695.271i	0.556748	−	0.964315i
$722$	−1905.27	+	1100.01i	−2.63888	+	1.52356i
$723$	44.6924	+	133.685i	0.0618152	+	0.184904i
$724$	321.484			0.444039
$725$	−372.803	−	215.238i	−0.514211	−	0.296880i
$726$	−207.708	+	1019.58i	−0.286100	+	1.40438i
$727$	495.936	−	858.987i	0.682168	−	1.18155i	−0.292149	−	0.956373i	$-0.594370\pi$
$727$	495.936	−	858.987i	0.682168	−	1.18155i	0.974318	−	0.225178i	$-0.0722962\pi$
$728$	−227.228	+	20.9565i	−0.312126	+	0.0287865i
$729$	260.204	+	680.981i	0.356933	+	0.934130i
$730$	−108.989	−	188.774i	−0.149299	−	0.258594i
$731$		−	46.8377i		−	0.0640735i
$732$	33.7035	+	100.815i	0.0460431	+	0.137725i
$733$	−48.4482	−	83.9147i	−0.0660958	−	0.114481i	0.831084	−	0.556147i	$-0.187721\pi$
$733$	−48.4482	−	83.9147i	−0.0660958	−	0.114481i	−0.897180	+	0.441666i	$0.854388\pi$
$734$			302.489i			0.412110i
$735$	−13.2953	+	65.2631i	−0.0180889	+	0.0887933i
$736$	375.500	−	650.385i	0.510190	−	0.883675i
$737$	−1087.70	−	627.983i	−1.47585	−	0.852080i
$738$	108.920	−	81.9895i	0.147588	−	0.111097i
$739$	508.944	+	881.516i	0.688692	+	1.19285i	0.972261	+	0.233898i	$0.0751483\pi$
$739$	508.944	+	881.516i	0.688692	+	1.19285i	−0.283569	+	0.958952i	$0.591518\pi$
$740$	4.76377	+	2.75036i	0.00643752	+	0.00371670i
$741$	−1243.75	+	547.384i	−1.67848	+	0.738710i
$742$	222.160	+	384.793i	0.299407	+	0.518589i
$743$	−1.46824	−	0.847690i	−0.00197610	−	0.00114090i	0.499012	−	0.866595i	$-0.333696\pi$
$743$	−1.46824	−	0.847690i	−0.00197610	−	0.00114090i	−0.500988	+	0.865454i	$0.667030\pi$
$744$	202.659	−	67.7510i	0.272391	−	0.0910631i
$745$	15.5305	+	26.8996i	0.0208463	+	0.0361068i
$746$		−	1813.29i		−	2.43069i
$747$	239.122	+	317.664i	0.320109	+	0.425252i
$748$	−528.039	+	914.591i	−0.705935	+	1.22271i
$749$	868.486	+	501.421i	1.15953	+	0.669454i
$750$	−351.328	−	71.5722i	−0.468437	−	0.0954296i
$751$	696.728	−	1206.77i	0.927734	−	1.60688i	0.140630	−	0.990062i	$-0.455087\pi$
$751$	696.728	−	1206.77i	0.927734	−	1.60688i	0.787104	−	0.616820i	$-0.211579\pi$
$752$	120.989	+	69.8527i	0.160889	+	0.0928893i
$753$	104.823	+	92.7871i	0.139207	+	0.123223i
$754$	543.729	+	250.440i	0.721126	+	0.332149i
$755$			101.303i			0.134177i
$756$	−28.6250	+	360.176i	−0.0378638	+	0.476424i
$757$	−89.1160	−	154.353i	−0.117723	−	0.203901i	0.801142	−	0.598474i	$-0.204226\pi$
$757$	−89.1160	−	154.353i	−0.117723	−	0.203901i	−0.918865	+	0.394573i	$0.870893\pi$
$758$	743.114	−	429.037i	0.980361	−	0.566012i
$759$	−652.612	+	737.263i	−0.859831	+	0.971361i
$760$	−114.350			−0.150460
$761$			82.8037i			0.108809i	0.998519	+	0.0544046i	$0.0173261\pi$
$761$			82.8037i			0.108809i	−0.998519	+	0.0544046i	$0.982674\pi$
$762$	−863.866	+	288.799i	−1.13368	+	0.379002i
$763$	−251.382	−	435.407i	−0.329466	−	0.570651i
$764$	−416.335	+	240.371i	−0.544941	+	0.314622i
$765$	−194.760	−	82.7885i	−0.254588	−	0.108220i
$766$	859.715			1.12234
$767$	−177.418	+	385.191i	−0.231314	+	0.502205i
$768$	984.243	+	200.509i	1.28157	+	0.261080i
$769$	292.701	−	506.973i	0.380625	−	0.659263i	−0.610526	−	0.791996i	$-0.709042\pi$
$769$	292.701	−	506.973i	0.380625	−	0.659263i	0.991152	+	0.132733i	$0.0423754\pi$

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.57904i q^{2} +(2.93962 + 0.598857i) q^{3} -2.65146 q^{4} +(-0.817198 + 0.471810i) q^{5} +(1.54448 - 7.58141i) q^{6} +(-2.52350 - 4.37084i) q^{7} -3.47795i q^{8} +(8.28274 + 3.52082i) q^{9} +(1.21682 + 2.10759i) q^{10} -15.9839i q^{11} +(-7.79428 - 1.58784i) q^{12} +(11.8077 + 5.43860i) q^{13} +(-11.2726 + 6.50822i) q^{14} +(-2.68480 + 0.897556i) q^{15} -19.5756 q^{16} +(21.5804 + 12.4595i) q^{17} +(9.08035 - 21.3615i) q^{18} +(-17.4215 + 30.1749i) q^{19} +(2.16677 - 1.25098i) q^{20} +(-4.80064 - 14.3598i) q^{21} -41.2231 q^{22} +(-17.7825 - 10.2667i) q^{23} +(2.08279 - 10.2238i) q^{24} +(-12.0548 + 20.8795i) q^{25} +(14.0264 - 30.4525i) q^{26} +(22.2396 + 15.3101i) q^{27} +(6.69097 + 11.5891i) q^{28} +17.8550i q^{29} +(2.31484 + 6.92421i) q^{30} +(10.2399 + 17.7361i) q^{31} +36.5745i q^{32} +(9.57206 - 46.9866i) q^{33} +(32.1335 - 55.6568i) q^{34} +(4.12441 + 2.38123i) q^{35} +(-21.9613 - 9.33532i) q^{36} +(1.09928 + 1.90401i) q^{37} +(77.8224 + 44.9308i) q^{38} +(31.4532 + 23.0585i) q^{39} +(1.64093 + 2.84217i) q^{40} +(5.08651 + 2.93670i) q^{41} +(-37.0346 + 12.3811i) q^{42} +(-0.939802 - 1.62778i) q^{43} +42.3806i q^{44} +(-8.42980 + 1.03067i) q^{45} +(-26.4783 + 45.8617i) q^{46} +(-6.18058 - 3.56836i) q^{47} +(-57.5448 - 11.7230i) q^{48} +(11.7638 - 20.3756i) q^{49} +(53.8491 + 31.0898i) q^{50} +(55.9768 + 49.5497i) q^{51} +(-31.3076 - 14.4202i) q^{52} -34.1353i q^{53} +(39.4853 - 57.3570i) q^{54} +(7.54135 + 13.0620i) q^{55} +(-15.2015 + 8.77662i) q^{56} +(-69.2831 + 78.2699i) q^{57} +46.0487 q^{58} +32.6220i q^{59} +(7.11863 - 2.37983i) q^{60} +(-6.68183 - 11.5733i) q^{61} +(45.7421 - 26.4092i) q^{62} +(-5.51258 - 45.0873i) q^{63} +16.0248 q^{64} +(-12.2152 + 1.12657i) q^{65} +(-121.180 - 24.6867i) q^{66} +(39.2885 - 68.0497i) q^{67} +(-57.2196 - 33.0357i) q^{68} +(-46.1254 - 40.8294i) q^{69} +(6.14128 - 10.6370i) q^{70} +(-121.405 - 70.0932i) q^{71} +(12.2452 - 28.8069i) q^{72} -89.5686 q^{73} +(4.91052 - 2.83509i) q^{74} +(-47.9404 + 54.1588i) q^{75} +(46.1924 - 80.0076i) q^{76} +(-69.8630 + 40.3354i) q^{77} +(59.4689 - 81.1191i) q^{78} +(28.9076 - 50.0695i) q^{79} +(15.9971 - 9.23596i) q^{80} +(56.2076 + 58.3242i) q^{81} +(7.57387 - 13.1183i) q^{82} +(38.2595 + 22.0891i) q^{83} +(12.7287 + 38.0745i) q^{84} -23.5140 q^{85} +(-4.19812 + 2.42379i) q^{86} +(-10.6926 + 52.4868i) q^{87} -55.5911 q^{88} +(48.6143 - 28.0675i) q^{89} +(2.65813 + 21.7408i) q^{90} +(-6.02555 - 65.3338i) q^{91} +(47.1494 + 27.2217i) q^{92} +(19.4802 + 58.2697i) q^{93} +(-9.20294 + 15.9400i) q^{94} -32.8785i q^{95} +(-21.9029 + 107.515i) q^{96} +(78.3791 + 135.757i) q^{97} +(-52.5495 - 30.3395i) q^{98} +(56.2764 - 132.390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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