LMFDB - Embedded newform 338.3.f.i.249.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,3,Mod(19,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	338.f (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,0,0,-6,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.20983293538$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.612074651904.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 74x^{6} + 2067x^{4} - 25778x^{2} + 121801 $ x^8 - 74x^6 + 2067x^4 - 25778*x^2 + 121801
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			249.2
Root			$4.71318 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.249
Dual form			338.3.f.i.319.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 + 0.366025i) q^{2} +(1.92358 + 3.33174i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-3.77418 + 3.77418i) q^{5} +(1.40816 + 5.25532i) q^{6} +(9.91095 - 2.65563i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-2.90031 + 5.02349i) q^{9} +(-6.53708 + 3.77418i) q^{10} +(-2.71157 + 10.1197i) q^{11} +7.69432i q^{12} +14.5106 q^{14} +(-19.8345 - 5.31465i) q^{15} +(2.00000 + 3.46410i) q^{16} +(4.23323 + 2.44406i) q^{17} +(-5.80063 + 5.80063i) q^{18} +(-6.83679 - 25.5153i) q^{19} +(-10.3113 + 2.76289i) q^{20} +(27.9124 + 27.9124i) q^{21} +(-7.40816 + 12.8313i) q^{22} +(-17.2850 + 9.97952i) q^{23} +(-2.81632 + 10.5106i) q^{24} -3.48892i q^{25} +12.3085 q^{27} +(19.8219 + 5.31126i) q^{28} +(-7.15218 - 12.3879i) q^{29} +(-25.1492 - 14.5199i) q^{30} +(-19.0056 + 19.0056i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-38.9322 + 10.4319i) q^{33} +(4.88811 + 4.88811i) q^{34} +(-27.3829 + 47.4286i) q^{35} +(-10.0470 + 5.80063i) q^{36} +(15.7051 - 58.6123i) q^{37} -37.3569i q^{38} -15.0967 q^{40} +(4.83709 + 1.29609i) q^{41} +(27.9124 + 48.3456i) q^{42} +(-10.3688 - 5.98641i) q^{43} +(-14.8163 + 14.8163i) q^{44} +(-8.01326 - 29.9059i) q^{45} +(-27.2646 + 7.30552i) q^{46} +(7.59168 + 7.59168i) q^{47} +(-7.69432 + 13.3269i) q^{48} +(48.7392 - 28.1396i) q^{49} +(1.27703 - 4.76595i) q^{50} +18.8053i q^{51} +77.0450 q^{53} +(16.8137 + 4.50522i) q^{54} +(-27.9597 - 48.4277i) q^{55} +(25.1332 + 14.5106i) q^{56} +(71.8590 - 71.8590i) q^{57} +(-5.23576 - 19.5401i) q^{58} +(60.7634 - 16.2815i) q^{59} +(-29.0398 - 29.0398i) q^{60} +(28.1382 - 48.7368i) q^{61} +(-32.9186 + 19.0056i) q^{62} +(-15.4043 + 57.4897i) q^{63} +8.00000i q^{64} -57.0007 q^{66} +(-5.90406 - 1.58199i) q^{67} +(4.88811 + 8.46646i) q^{68} +(-66.4983 - 38.3928i) q^{69} +(-54.7658 + 54.7658i) q^{70} +(14.7981 + 55.2272i) q^{71} +(-15.8476 + 4.24635i) q^{72} +(-12.7990 - 12.7990i) q^{73} +(42.9072 - 74.3174i) q^{74} +(11.6242 - 6.71121i) q^{75} +(13.6736 - 51.0305i) q^{76} +107.497i q^{77} +7.98532 q^{79} +(-20.6225 - 5.52579i) q^{80} +(49.7792 + 86.2201i) q^{81} +(6.13318 + 3.54099i) q^{82} +(35.8343 - 35.8343i) q^{83} +(20.4333 + 76.2580i) q^{84} +(-25.2013 + 6.75267i) q^{85} +(-11.9728 - 11.9728i) q^{86} +(27.5156 - 47.6584i) q^{87} +(-25.6626 + 14.8163i) q^{88} +(-20.9684 + 78.2551i) q^{89} -43.7853i q^{90} -39.9181 q^{92} +(-99.8803 - 26.7628i) q^{93} +(7.59168 + 13.1492i) q^{94} +(122.103 + 70.4959i) q^{95} +(-15.3886 + 15.3886i) q^{96} +(14.1991 + 52.9919i) q^{97} +(76.8788 - 20.5996i) q^{98} +(-42.9720 - 42.9720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{8} - 42 q^{9} - 18 q^{10} + 18 q^{11} + 20 q^{14} - 66 q^{15} + 16 q^{16} - 42 q^{17} - 84 q^{18} - 46 q^{19} - 24 q^{20} + 102 q^{21} - 42 q^{22} - 36 q^{23}+ \cdots - 252 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^8 - 42 * q^9 - 18 * q^10 + 18 * q^11 + 20 * q^14 - 66 * q^15 + 16 * q^16 - 42 * q^17 - 84 * q^18 - 46 * q^19 - 24 * q^20 + 102 * q^21 - 42 * q^22 - 36 * q^23 + 12 * q^24 + 72 * q^27 + 4 * q^28 - 6 * q^29 - 192 * q^30 - 32 * q^31 - 16 * q^32 - 42 * q^33 + 60 * q^34 - 78 * q^35 - 48 * q^36 + 106 * q^37 - 24 * q^40 - 132 * q^41 + 102 * q^42 - 108 * q^43 - 84 * q^44 - 240 * q^45 - 90 * q^46 - 60 * q^47 + 258 * q^49 - 194 * q^50 - 132 * q^53 + 270 * q^54 - 162 * q^55 - 12 * q^56 + 294 * q^57 + 24 * q^58 - 18 * q^59 + 120 * q^60 + 36 * q^61 - 12 * q^62 + 72 * q^63 + 108 * q^66 + 74 * q^67 + 60 * q^68 + 258 * q^69 - 156 * q^70 + 174 * q^71 - 132 * q^72 - 166 * q^73 - 32 * q^74 + 6 * q^75 + 92 * q^76 - 96 * q^79 - 48 * q^80 - 12 * q^81 - 252 * q^82 + 240 * q^83 + 132 * q^84 + 24 * q^85 - 132 * q^86 + 360 * q^87 - 12 * q^88 - 294 * q^89 - 216 * q^92 - 270 * q^93 - 60 * q^94 + 714 * q^95 + 58 * q^97 + 250 * q^98 - 252 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$	1.92358	+	3.33174i	0.641193	+	1.11058i	0.985167	+	0.171600i	$0.0548936\pi$
$3$	1.92358	+	3.33174i	0.641193	+	1.11058i	−0.343974	+	0.938979i	$0.611773\pi$
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	−3.77418	+	3.77418i	−0.754837	+	0.754837i	−0.975378	−	0.220541i	$-0.929218\pi$
$5$	−3.77418	+	3.77418i	−0.754837	+	0.754837i	0.220541	+	0.975378i	$0.429218\pi$
$6$	1.40816	+	5.25532i	0.234693	+	0.875886i
$7$	9.91095	−	2.65563i	1.41585	−	0.379376i	0.531840	−	0.846845i	$-0.321501\pi$
$7$	9.91095	−	2.65563i	1.41585	−	0.379376i	0.884009	+	0.467469i	$0.154834\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	−2.90031	+	5.02349i	−0.322257	+	0.558166i
$10$	−6.53708	+	3.77418i	−0.653708	+	0.377418i
$11$	−2.71157	+	10.1197i	−0.246507	+	0.919976i	0.726113	+	0.687575i	$0.241325\pi$
$11$	−2.71157	+	10.1197i	−0.246507	+	0.919976i	−0.972620	+	0.232401i	$0.925342\pi$
$12$			7.69432i			0.641193i
$13$		0			0
$13$		0			0
$14$	14.5106			1.03647
$15$	−19.8345	−	5.31465i	−1.32230	−	0.354310i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	4.23323	+	2.44406i	0.249013	+	0.143768i	0.619312	−	0.785145i	$-0.287411\pi$
$17$	4.23323	+	2.44406i	0.249013	+	0.143768i	−0.370299	+	0.928913i	$0.620745\pi$
$18$	−5.80063	+	5.80063i	−0.322257	+	0.322257i
$19$	−6.83679	−	25.5153i	−0.359831	−	1.34291i	−0.874295	−	0.485396i	$-0.838675\pi$
$19$	−6.83679	−	25.5153i	−0.359831	−	1.34291i	0.514463	−	0.857512i	$-0.327991\pi$
$20$	−10.3113	+	2.76289i	−0.515563	+	0.138145i
$21$	27.9124	+	27.9124i	1.32916	+	1.32916i
$22$	−7.40816	+	12.8313i	−0.336734	+	0.583241i
$23$	−17.2850	+	9.97952i	−0.751524	+	0.433892i	−0.826244	−	0.563312i	$-0.809527\pi$
$23$	−17.2850	+	9.97952i	−0.751524	+	0.433892i	0.0747206	+	0.997205i	$0.476194\pi$
$24$	−2.81632	+	10.5106i	−0.117346	+	0.437943i
$25$		−	3.48892i		−	0.139557i
$26$		0			0
$27$	12.3085			0.455870
$28$	19.8219	+	5.31126i	0.707925	+	0.189688i
$29$	−7.15218	−	12.3879i	−0.246627	−	0.427171i	0.715961	−	0.698141i	$-0.245989\pi$
$29$	−7.15218	−	12.3879i	−0.246627	−	0.427171i	−0.962588	+	0.270970i	$0.912656\pi$
$30$	−25.1492	−	14.5199i	−0.838306	−	0.483996i
$31$	−19.0056	+	19.0056i	−0.613083	+	0.613083i	−0.943748	−	0.330665i	$-0.892727\pi$
$31$	−19.0056	+	19.0056i	−0.613083	+	0.613083i	0.330665	+	0.943748i	$0.392727\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	−38.9322	+	10.4319i	−1.17976	+	0.316117i
$34$	4.88811	+	4.88811i	0.143768	+	0.143768i
$35$	−27.3829	+	47.4286i	−0.782368	+	1.35510i
$36$	−10.0470	+	5.80063i	−0.279083	+	0.161129i
$37$	15.7051	−	58.6123i	0.424463	−	1.58412i	−0.340631	−	0.940197i	$-0.610641\pi$
$37$	15.7051	−	58.6123i	0.424463	−	1.58412i	0.765094	−	0.643919i	$-0.222693\pi$
$38$		−	37.3569i		−	0.983077i
$39$		0			0
$40$	−15.0967			−0.377418
$41$	4.83709	+	1.29609i	0.117978	+	0.0316120i	0.317325	−	0.948317i	$-0.397215\pi$
$41$	4.83709	+	1.29609i	0.117978	+	0.0316120i	−0.199347	+	0.979929i	$0.563882\pi$
$42$	27.9124	+	48.3456i	0.664580	+	1.15109i
$43$	−10.3688	−	5.98641i	−0.241134	−	0.139219i	0.374564	−	0.927201i	$-0.377793\pi$
$43$	−10.3688	−	5.98641i	−0.241134	−	0.139219i	−0.615698	+	0.787982i	$0.711126\pi$
$44$	−14.8163	+	14.8163i	−0.336734	+	0.336734i
$45$	−8.01326	−	29.9059i	−0.178072	−	0.664575i
$46$	−27.2646	+	7.30552i	−0.592708	+	0.158816i
$47$	7.59168	+	7.59168i	0.161525	+	0.161525i	0.783242	−	0.621717i	$-0.213565\pi$
$47$	7.59168	+	7.59168i	0.161525	+	0.161525i	−0.621717	+	0.783242i	$0.713565\pi$
$48$	−7.69432	+	13.3269i	−0.160298	+	0.277645i
$49$	48.7392	−	28.1396i	0.994678	−	0.574278i
$50$	1.27703	−	4.76595i	0.0255406	−	0.0953190i
$51$			18.8053i			0.368732i
$52$		0			0
$53$	77.0450			1.45368			0.726840	−	0.686807i	$-0.240988\pi$
$53$	77.0450			1.45368			0.726840	+	0.686807i	$0.240988\pi$
$54$	16.8137	+	4.50522i	0.311365	+	0.0834300i
$55$	−27.9597	−	48.4277i	−0.508359	−	0.880504i
$56$	25.1332	+	14.5106i	0.448806	+	0.259118i
$57$	71.8590	−	71.8590i	1.26068	−	1.26068i
$58$	−5.23576	−	19.5401i	−0.0902718	−	0.336899i
$59$	60.7634	−	16.2815i	1.02989	−	0.275957i	0.295971	−	0.955197i	$-0.404357\pi$
$59$	60.7634	−	16.2815i	1.02989	−	0.275957i	0.733917	+	0.679240i	$0.237690\pi$
$60$	−29.0398	−	29.0398i	−0.483996	−	0.483996i
$61$	28.1382	−	48.7368i	0.461282	−	0.798964i	−0.537743	−	0.843109i	$-0.680723\pi$
$61$	28.1382	−	48.7368i	0.461282	−	0.798964i	0.999025	+	0.0441448i	$0.0140563\pi$
$62$	−32.9186	+	19.0056i	−0.530946	+	0.306542i
$63$	−15.4043	+	57.4897i	−0.244513	+	0.912535i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−57.0007			−0.863647
$67$	−5.90406	−	1.58199i	−0.0881202	−	0.0236117i	0.214490	−	0.976726i	$-0.431191\pi$
$67$	−5.90406	−	1.58199i	−0.0881202	−	0.0236117i	−0.302610	+	0.953115i	$0.597858\pi$
$68$	4.88811	+	8.46646i	0.0718840	+	0.124507i
$69$	−66.4983	−	38.3928i	−0.963743	−	0.556417i
$70$	−54.7658	+	54.7658i	−0.782368	+	0.782368i
$71$	14.7981	+	55.2272i	0.208424	+	0.777847i	0.988379	+	0.152012i	$0.0485752\pi$
$71$	14.7981	+	55.2272i	0.208424	+	0.777847i	−0.779955	+	0.625836i	$0.784758\pi$
$72$	−15.8476	+	4.24635i	−0.220106	+	0.0589771i
$73$	−12.7990	−	12.7990i	−0.175329	−	0.175329i	0.613987	−	0.789316i	$-0.289565\pi$
$73$	−12.7990	−	12.7990i	−0.175329	−	0.175329i	−0.789316	+	0.613987i	$0.789565\pi$
$74$	42.9072	−	74.3174i	0.579827	−	1.00429i
$75$	11.6242	−	6.71121i	0.154989	−	0.0894828i
$76$	13.6736	−	51.0305i	0.179916	−	0.671454i
$77$			107.497i			1.39607i
$78$		0			0
$79$	7.98532			0.101080			0.0505400	−	0.998722i	$-0.483906\pi$
$79$	7.98532			0.101080			0.0505400	+	0.998722i	$0.483906\pi$
$80$	−20.6225	−	5.52579i	−0.257782	−	0.0690723i
$81$	49.7792	+	86.2201i	0.614558	+	1.06445i
$82$	6.13318	+	3.54099i	0.0747949	+	0.0431829i
$83$	35.8343	−	35.8343i	0.431738	−	0.431738i	−0.457481	−	0.889219i	$-0.651248\pi$
$83$	35.8343	−	35.8343i	0.431738	−	0.431738i	0.889219	+	0.457481i	$0.151248\pi$
$84$	20.4333	+	76.2580i	0.243253	+	0.907833i
$85$	−25.2013	+	6.75267i	−0.296486	+	0.0794431i
$86$	−11.9728	−	11.9728i	−0.139219	−	0.139219i
$87$	27.5156	−	47.6584i	0.316271	−	0.547798i
$88$	−25.6626	+	14.8163i	−0.291621	+	0.168367i
$89$	−20.9684	+	78.2551i	−0.235600	+	0.879271i	0.742277	+	0.670093i	$0.233746\pi$
$89$	−20.9684	+	78.2551i	−0.235600	+	0.879271i	−0.977877	+	0.209178i	$0.932921\pi$
$90$		−	43.7853i		−	0.486503i
$91$		0			0
$92$	−39.9181			−0.433892
$93$	−99.8803	−	26.7628i	−1.07398	−	0.287773i
$94$	7.59168	+	13.1492i	0.0807625	+	0.139885i
$95$	122.103	+	70.4959i	1.28529	+	0.742063i
$96$	−15.3886	+	15.3886i	−0.160298	+	0.160298i
$97$	14.1991	+	52.9919i	0.146383	+	0.546309i	0.999690	+	0.0248998i	$0.00792667\pi$
$97$	14.1991	+	52.9919i	0.146383	+	0.546309i	−0.853307	+	0.521409i	$0.825407\pi$
$98$	76.8788	−	20.5996i	0.784478	−	0.210200i
$99$	−42.9720	−	42.9720i	−0.434060	−	0.434060i
$100$	3.48892	−	6.04298i	0.0348892	−	0.0604298i
$101$	12.1793	−	7.03175i	0.120588	−	0.0696212i	−0.438493	−	0.898735i	$-0.644488\pi$
$101$	12.1793	−	7.03175i	0.120588	−	0.0696212i	0.559081	+	0.829113i	$0.311154\pi$
$102$	−6.88323	+	25.6886i	−0.0674827	+	0.251849i
$103$		−	80.8399i		−	0.784853i	−0.919783	−	0.392426i	$-0.871636\pi$
$103$		−	80.8399i		−	0.784853i	0.919783	−	0.392426i	$-0.128364\pi$
$104$		0			0
$105$	−210.693			−2.00660
$106$	105.245	+	28.2004i	0.992881	+	0.266042i
$107$	−81.3525	−	140.907i	−0.760304	−	1.31688i	−0.942694	−	0.333659i	$-0.891717\pi$
$107$	−81.3525	−	140.907i	−0.760304	−	1.31688i	0.182390	−	0.983226i	$-0.441617\pi$
$108$	21.3189	+	12.3085i	0.197398	+	0.113968i
$109$	62.6738	−	62.6738i	0.574989	−	0.574989i	−0.358530	−	0.933518i	$-0.616722\pi$
$109$	62.6738	−	62.6738i	0.574989	−	0.574989i	0.933518	+	0.358530i	$0.116722\pi$
$110$	−20.4680	−	76.3874i	−0.186072	−	0.694431i
$111$	225.491	−	60.4201i	2.03145	−	0.544325i
$112$	29.0213	+	29.0213i	0.259118	+	0.259118i
$113$	34.9405	−	60.5187i	0.309208	−	0.535563i	−0.668982	−	0.743279i	$-0.733270\pi$
$113$	34.9405	−	60.5187i	0.309208	−	0.535563i	0.978189	+	0.207716i	$0.0666029\pi$
$114$	124.463	−	71.8590i	1.09178	−	0.630342i
$115$	27.5724	−	102.901i	0.239760	−	0.894795i
$116$		−	28.6087i		−	0.246627i
$117$		0			0
$118$	88.9637			0.753930
$119$	48.4458	+	12.9810i	0.407108	+	0.109084i
$120$	−29.0398	−	50.2983i	−0.241998	−	0.419153i
$121$	9.73274	+	5.61920i	0.0804359	+	0.0464397i
$122$	56.2764	−	56.2764i	0.461282	−	0.461282i
$123$	4.98628	+	18.6090i	0.0405388	+	0.151293i
$124$	−51.9242	+	13.9130i	−0.418744	+	0.112202i
$125$	−81.1868	−	81.1868i	−0.649494	−	0.649494i
$126$	−42.0854	+	72.8940i	−0.334011	+	0.578524i
$127$	71.6989	−	41.3954i	0.564558	−	0.325948i	−0.190415	−	0.981704i	$-0.560983\pi$
$127$	71.6989	−	41.3954i	0.564558	−	0.325948i	0.754973	+	0.655756i	$0.227650\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$		−	46.0614i		−	0.357065i
$130$		0			0
$131$	47.8506			0.365272			0.182636	−	0.983181i	$-0.441537\pi$
$131$	47.8506			0.365272			0.182636	+	0.983181i	$0.441537\pi$
$132$	−77.8644	−	20.8637i	−0.589882	−	0.158058i
$133$	−135.518	−	234.724i	−1.01893	−	1.76484i
$134$	−7.48604	−	4.32207i	−0.0558660	−	0.0322542i
$135$	−46.4545	+	46.4545i	−0.344107	+	0.344107i
$136$	3.57835	+	13.3546i	0.0263114	+	0.0981954i
$137$	−185.891	+	49.8094i	−1.35687	+	0.363572i	−0.862666	−	0.505773i	$-0.831207\pi$
$137$	−185.891	+	49.8094i	−1.35687	+	0.363572i	−0.494204	+	0.869346i	$0.664541\pi$
$138$	−76.7856	−	76.7856i	−0.556417	−	0.556417i
$139$	−96.5464	+	167.223i	−0.694578	+	1.20305i	0.275744	+	0.961231i	$0.411076\pi$
$139$	−96.5464	+	167.223i	−0.694578	+	1.20305i	−0.970323	+	0.241814i	$0.922258\pi$
$140$	−94.8571	+	54.7658i	−0.677551	+	0.391184i
$141$	−10.6903	+	39.8967i	−0.0758176	+	0.282955i
$142$			80.8582i			0.569424i
$143$		0			0
$144$	−23.2025			−0.161129
$145$	73.7480	+	19.7607i	0.508607	+	0.136281i
$146$	−12.7990	−	22.1685i	−0.0876644	−	0.151839i
$147$	187.508	+	108.258i	1.27556	+	0.736446i
$148$	85.8143	−	85.8143i	0.579827	−	0.579827i
$149$	−34.8041	−	129.891i	−0.233585	−	0.871750i	−0.978782	−	0.204905i	$-0.934311\pi$
$149$	−34.8041	−	129.891i	−0.233585	−	0.871750i	0.745197	−	0.666844i	$-0.232355\pi$
$150$	18.3354	−	4.91294i	0.122236	−	0.0327530i
$151$	−26.5821	−	26.5821i	−0.176041	−	0.176041i	0.613587	−	0.789627i	$-0.289726\pi$
$151$	−26.5821	−	26.5821i	−0.176041	−	0.176041i	−0.789627	+	0.613587i	$0.789726\pi$
$152$	37.3569	−	64.7041i	0.245769	−	0.425685i
$153$	−24.5554	+	14.1771i	−0.160493	+	0.0926605i
$154$	−39.3467	+	146.844i	−0.255498	+	0.953531i
$155$		−	143.461i		−	0.925555i
$156$		0			0
$157$	−251.005			−1.59876			−0.799380	−	0.600826i	$-0.794838\pi$
$157$	−251.005			−1.59876			−0.799380	+	0.600826i	$0.794838\pi$
$158$	10.9081	+	2.92283i	0.0690389	+	0.0184989i
$159$	148.202	+	256.694i	0.932089	+	1.61443i
$160$	−26.1483	−	15.0967i	−0.163427	−	0.0943546i
$161$	−144.809	+	144.809i	−0.899436	+	0.899436i
$162$	36.4409	+	135.999i	0.224944	+	0.839502i
$163$	−117.437	+	31.4672i	−0.720474	+	0.193050i	−0.600383	−	0.799712i	$-0.704985\pi$
$163$	−117.437	+	31.4672i	−0.720474	+	0.193050i	−0.120091	+	0.992763i	$0.538319\pi$
$164$	7.08199	+	7.08199i	0.0431829	+	0.0431829i
$165$	107.566	−	186.309i	0.651913	−	1.12915i
$166$	62.0668	−	35.8343i	0.373896	−	0.215869i
$167$	16.0213	−	59.7923i	0.0959359	−	0.358038i	−0.901224	−	0.433354i	$-0.857330\pi$
$167$	16.0213	−	59.7923i	0.0959359	−	0.358038i	0.997160	+	0.0753164i	$0.0239967\pi$
$168$			111.649i			0.664580i
$169$		0			0
$170$	−36.8973			−0.217043
$171$	148.005	+	39.6577i	0.865523	+	0.231916i
$172$	−11.9728	−	20.7375i	−0.0696095	−	0.120567i
$173$	−269.191	−	155.418i	−1.55602	−	0.898368i	−0.997631	−	0.0687875i	$-0.978087\pi$
$173$	−269.191	−	155.418i	−1.55602	−	0.898368i	−0.558387	−	0.829580i	$-0.688580\pi$
$174$	55.0312	−	55.0312i	0.316271	−	0.316271i
$175$	−9.26527	−	34.5785i	−0.0529444	−	0.197591i
$176$	−40.4789	+	10.8463i	−0.229994	+	0.0616267i
$177$	171.129	+	171.129i	0.966829	+	0.966829i
$178$	−57.2867	+	99.2235i	−0.321836	+	0.557436i
$179$	−54.8543	+	31.6701i	−0.306449	+	0.176928i	−0.645336	−	0.763899i	$-0.723283\pi$
$179$	−54.8543	+	31.6701i	−0.306449	+	0.176928i	0.338888	+	0.940827i	$0.389949\pi$
$180$	16.0265	−	59.8118i	0.0890362	−	0.332288i
$181$			186.504i			1.03041i	0.857067	+	0.515205i	$0.172284\pi$
$181$			186.504i			1.03041i	−0.857067	+	0.515205i	$0.827716\pi$
$182$		0			0
$183$	216.504			1.18308
$184$	−54.5291	−	14.6110i	−0.296354	−	0.0794078i
$185$	161.940	+	280.487i	0.875349	+	1.51615i
$186$	−126.643	−	73.1175i	−0.680877	−	0.393105i
$187$	−36.2119	+	36.2119i	−0.193647	+	0.193647i
$188$	5.55749	+	20.7408i	0.0295611	+	0.110324i
$189$	121.989	−	32.6868i	0.645443	−	0.172946i
$190$	140.992	+	140.992i	0.742063	+	0.742063i
$191$	91.3457	−	158.215i	0.478250	−	0.828353i	−0.521439	−	0.853288i	$-0.674605\pi$
$191$	91.3457	−	158.215i	0.478250	−	0.828353i	0.999689	+	0.0249353i	$0.00793798\pi$
$192$	−26.6539	+	15.3886i	−0.138822	+	0.0801491i
$193$	23.5921	−	88.0470i	0.122239	−	0.456202i	−0.877487	−	0.479600i	$-0.840782\pi$
$193$	23.5921	−	88.0470i	0.122239	−	0.456202i	0.999726	+	0.0233980i	$0.00744850\pi$
$194$			77.5856i			0.399926i
$195$		0			0
$196$	112.558			0.574278
$197$	−208.450	−	55.8541i	−1.05812	−	0.283523i	−0.312519	−	0.949912i	$-0.601173\pi$
$197$	−208.450	−	55.8541i	−1.05812	−	0.283523i	−0.745605	+	0.666388i	$0.767839\pi$
$198$	−42.9720	−	74.4296i	−0.217030	−	0.375907i
$199$	−67.9737	−	39.2446i	−0.341576	−	0.197209i	0.319393	−	0.947623i	$-0.396521\pi$
$199$	−67.9737	−	39.2446i	−0.341576	−	0.197209i	−0.660969	+	0.750413i	$0.729854\pi$
$200$	6.97783	−	6.97783i	0.0348892	−	0.0348892i
$201$	−6.08615	−	22.7138i	−0.0302794	−	0.113004i
$202$	19.2111	−	5.14760i	0.0951044	−	0.0254831i
$203$	−103.783	−	103.783i	−0.511245	−	0.511245i
$204$	−18.8053	+	32.5718i	−0.0921830	+	0.159666i
$205$	−23.1478	+	13.3644i	−0.112916	+	0.0651920i
$206$	29.5894	−	110.429i	0.143638	−	0.536065i
$207$		−	115.775i		−	0.559300i
$208$		0			0
$209$	276.746			1.32414
$210$	−287.812	−	77.1189i	−1.37053	−	0.367233i
$211$	66.1990	+	114.660i	0.313739	+	0.543412i	0.979169	−	0.203048i	$-0.0650849\pi$
$211$	66.1990	+	114.660i	0.313739	+	0.543412i	−0.665429	+	0.746461i	$0.731752\pi$
$212$	133.446	+	77.0450i	0.629462	+	0.363420i
$213$	−155.537	+	155.537i	−0.730221	+	0.730221i
$214$	−59.5542	−	222.259i	−0.278291	−	1.03859i
$215$	61.7275	−	16.5398i	0.287105	−	0.0769294i
$216$	24.6170	+	24.6170i	0.113968	+	0.113968i
$217$	−137.891	+	238.835i	−0.635445	+	1.10062i
$218$	108.554	−	62.6738i	0.497955	−	0.287494i
$219$	18.0230	−	67.2628i	0.0822968	−	0.307136i
$220$		−	111.839i		−	0.508359i
$221$		0			0
$222$	330.141			1.48712
$223$	115.427	+	30.9286i	0.517610	+	0.138693i	0.508161	−	0.861262i	$-0.330325\pi$
$223$	115.427	+	30.9286i	0.517610	+	0.138693i	0.00944934	+	0.999955i	$0.496992\pi$
$224$	29.0213	+	50.2663i	0.129559	+	0.224403i
$225$	17.5265	+	10.1190i	0.0778957	+	0.0449731i
$226$	69.8809	−	69.8809i	0.309208	−	0.309208i
$227$	109.786	+	409.729i	0.483641	+	1.80497i	0.586105	+	0.810235i	$0.300661\pi$
$227$	109.786	+	409.729i	0.483641	+	1.80497i	−0.102464	+	0.994737i	$0.532673\pi$
$228$	196.322	−	52.6044i	0.861063	−	0.230721i
$229$	158.206	+	158.206i	0.690856	+	0.690856i	0.962420	−	0.271564i	$-0.0875409\pi$
$229$	158.206	+	158.206i	0.690856	+	0.690856i	−0.271564	+	0.962420i	$0.587541\pi$
$230$	75.3291	−	130.474i	0.327518	−	0.567277i
$231$	−358.152	+	206.779i	−1.55044	+	0.895148i
$232$	10.4715	−	39.0803i	0.0451359	−	0.168449i
$233$			163.030i			0.699701i	0.936806	+	0.349850i	$0.113768\pi$
$233$			163.030i			0.699701i	−0.936806	+	0.349850i	$0.886232\pi$
$234$		0			0
$235$	−57.3048			−0.243850
$236$	121.527	+	32.5630i	0.514944	+	0.137979i
$237$	15.3604	+	26.6050i	0.0648118	+	0.112257i
$238$	61.4268	+	35.4648i	0.258096	+	0.149012i
$239$	185.455	−	185.455i	0.775962	−	0.775962i	−0.203179	−	0.979142i	$-0.565127\pi$
$239$	185.455	−	185.455i	0.775962	−	0.775962i	0.979142	+	0.203179i	$0.0651275\pi$
$240$	−21.2586	−	79.3381i	−0.0885774	−	0.330575i
$241$	−438.820	+	117.581i	−1.82083	+	0.487890i	−0.996891	−	0.0787895i	$-0.974894\pi$
$241$	−438.820	+	117.581i	−1.82083	+	0.487890i	−0.823938	+	0.566679i	$0.808228\pi$
$242$	11.2384	+	11.2384i	0.0464397	+	0.0464397i
$243$	−136.120	+	235.767i	−0.560165	+	0.970235i
$244$	97.4736	−	56.2764i	0.399482	−	0.230641i
$245$	−77.7468	+	290.155i	−0.317334	+	1.18431i
$246$			27.2455i			0.110754i
$247$		0			0
$248$	−76.0223			−0.306542
$249$	188.320	+	50.4603i	0.756307	+	0.202652i
$250$	−81.1868	−	140.620i	−0.324747	−	0.562478i
$251$	−380.182	−	219.498i	−1.51467	−	0.874495i	−0.999852	−	0.0171951i	$-0.994526\pi$
$251$	−380.182	−	219.498i	−1.51467	−	0.874495i	−0.514817	−	0.857300i	$-0.672140\pi$
$252$	−84.1708	+	84.1708i	−0.334011	+	0.334011i
$253$	−54.1204	−	201.980i	−0.213915	−	0.798341i
$254$	113.094	−	30.3035i	0.445253	−	0.119305i
$255$	−70.9748	−	70.9748i	−0.278333	−	0.278333i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−378.633	+	218.604i	−1.47328	+	0.850599i	−0.999548	−	0.0300694i	$-0.990427\pi$
$257$	−378.633	+	218.604i	−1.47328	+	0.850599i	−0.473733	+	0.880669i	$0.657094\pi$
$258$	16.8596	−	62.9210i	0.0653474	−	0.243880i
$259$		−	622.610i		−	2.40390i
$260$		0			0
$261$	82.9743			0.317909
$262$	65.3652	+	17.5145i	0.249485	+	0.0668494i
$263$	143.980	+	249.380i	0.547451	+	0.948213i	0.998448	+	0.0556879i	$0.0177352\pi$
$263$	143.980	+	249.380i	0.547451	+	0.948213i	−0.450997	+	0.892525i	$0.648931\pi$
$264$	−98.7281	−	57.0007i	−0.373970	−	0.215912i
$265$	−290.782	+	290.782i	−1.09729	+	1.09729i
$266$	−99.2062	−	370.242i	−0.372956	−	1.39189i
$267$	−301.060	+	80.6688i	−1.12757	+	0.302130i
$268$	−8.64414	−	8.64414i	−0.0322542	−	0.0322542i
$269$	−171.700	+	297.393i	−0.638290	+	1.10555i	0.347518	+	0.937673i	$0.387025\pi$
$269$	−171.700	+	297.393i	−0.638290	+	1.10555i	−0.985808	+	0.167878i	$0.946309\pi$
$270$	−80.4616	+	46.4545i	−0.298006	+	0.172054i
$271$	−2.15014	+	8.02443i	−0.00793410	+	0.0296105i	−0.969779	−	0.243983i	$-0.921546\pi$
$271$	−2.15014	+	8.02443i	−0.00793410	+	0.0296105i	0.961845	+	0.273594i	$0.0882124\pi$
$272$			19.5524i			0.0718840i
$273$		0			0
$274$	−272.164			−0.993298
$275$	35.3069	+	9.46045i	0.128389	+	0.0344017i
$276$	−76.7856	−	132.997i	−0.278209	−	0.481872i
$277$	384.730	+	222.124i	1.38892	+	0.801891i	0.993193	−	0.116480i	$-0.0371610\pi$
$277$	384.730	+	222.124i	1.38892	+	0.801891i	0.395722	+	0.918370i	$0.370494\pi$
$278$	−193.093	+	193.093i	−0.694578	+	0.694578i
$279$	−40.3522	−	150.596i	−0.144632	−	0.539772i
$280$	−149.623	+	40.0913i	−0.534368	+	0.143183i
$281$	163.678	+	163.678i	0.582486	+	0.582486i	0.935586	−	0.353100i	$-0.114872\pi$
$281$	163.678	+	163.678i	0.582486	+	0.582486i	−0.353100	+	0.935586i	$0.614872\pi$
$282$	−29.2064	+	50.5869i	−0.103569	+	0.179386i
$283$	401.956	−	232.070i	1.42034	−	0.820034i	0.424012	−	0.905656i	$-0.360621\pi$
$283$	401.956	−	232.070i	1.42034	−	0.820034i	0.996328	+	0.0856229i	$0.0272880\pi$
$284$	−29.5961	+	110.454i	−0.104212	+	0.388924i
$285$			542.418i			1.90322i
$286$		0			0
$287$	51.3821			0.179032
$288$	−31.6952	−	8.49271i	−0.110053	−	0.0294886i
$289$	−132.553	−	229.589i	−0.458662	−	0.794425i
$290$	93.5088	+	53.9873i	0.322444	+	0.186163i
$291$	−149.242	+	149.242i	−0.512859	+	0.512859i
$292$	−9.36952	−	34.9675i	−0.0320874	−	0.119752i
$293$	61.3995	−	16.4519i	0.209555	−	0.0561500i	−0.152515	−	0.988301i	$-0.548737\pi$
$293$	61.3995	−	16.4519i	0.209555	−	0.0561500i	0.362069	+	0.932151i	$0.382070\pi$
$294$	216.515	+	216.515i	0.736446	+	0.736446i
$295$	−167.883	+	290.781i	−0.569094	+	0.985699i
$296$	148.635	−	85.8143i	0.502145	−	0.289913i
$297$	−33.3754	+	124.559i	−0.112375	+	0.419389i
$298$		−	190.173i		−	0.638165i
$299$		0			0
$300$	26.8448			0.0894828
$301$	−118.662	−	31.7954i	−0.394226	−	0.105633i
$302$	−26.5821	−	46.0416i	−0.0880203	−	0.152456i
$303$	46.8559	+	27.0522i	0.154640	+	0.0892813i
$304$	74.7139	−	74.7139i	0.245769	−	0.245769i
$305$	77.7429	+	290.140i	0.254895	+	0.951280i
$306$	−38.7324	+	10.3783i	−0.126577	+	0.0339161i
$307$	−67.1395	−	67.1395i	−0.218695	−	0.218695i	0.589253	−	0.807948i	$-0.299422\pi$
$307$	−67.1395	−	67.1395i	−0.218695	−	0.218695i	−0.807948	+	0.589253i	$0.799422\pi$
$308$	−107.497	+	186.190i	−0.349016	+	0.604514i
$309$	269.337	−	155.502i	0.871641	−	0.503242i
$310$	52.5104	−	195.971i	0.169388	−	0.632166i
$311$			331.141i			1.06476i	0.846505	+	0.532381i	$0.178703\pi$
$311$			331.141i			1.06476i	−0.846505	+	0.532381i	$0.821297\pi$
$312$		0			0
$313$	−391.075			−1.24944			−0.624721	−	0.780848i	$-0.714787\pi$
$313$	−391.075			−1.24944			−0.624721	+	0.780848i	$0.714787\pi$
$314$	−342.879	−	91.8743i	−1.09197	−	0.292593i
$315$	−158.838	−	275.115i	−0.504247	−	0.873382i
$316$	13.8310	+	7.98532i	0.0437689	+	0.0252700i
$317$	322.964	−	322.964i	1.01881	−	1.01881i	0.0189927	−	0.999820i	$-0.493954\pi$
$317$	322.964	−	322.964i	1.01881	−	1.01881i	0.999820	−	0.0189927i	$-0.00604594\pi$
$318$	108.492	+	404.896i	0.341168	+	1.27326i
$319$	144.756	−	38.7874i	0.453782	−	0.121590i
$320$	−30.1935	−	30.1935i	−0.0943546	−	0.0943546i
$321$	312.976	−	542.090i	0.975003	−	1.68875i
$322$	−250.817	+	144.809i	−0.778934	+	0.449718i
$323$	33.4190	−	124.721i	0.103464	−	0.386134i
$324$			199.117i			0.614558i
$325$		0			0
$326$	−171.940			−0.527424
$327$	329.370	+	88.2545i	1.00725	+	0.269892i
$328$	7.08199	+	12.2664i	0.0215914	+	0.0373975i
$329$	95.4014	+	55.0800i	0.289974	+	0.167416i
$330$	215.131	−	215.131i	0.651913	−	0.651913i
$331$	−126.834	−	473.350i	−0.383184	−	1.43006i	−0.841010	−	0.541020i	$-0.818038\pi$
$331$	−126.834	−	473.350i	−0.383184	−	1.43006i	0.457826	−	0.889042i	$-0.348628\pi$
$332$	97.9011	−	26.2325i	0.294883	−	0.0790136i
$333$	248.889	+	248.889i	0.747413	+	0.747413i
$334$	43.7710	−	75.8136i	0.131051	−	0.226987i
$335$	28.2537	−	16.3123i	0.0843394	−	0.0486934i
$336$	−40.8665	+	152.516i	−0.121627	+	0.453916i
$337$		−	498.500i		−	1.47923i	−0.673031	−	0.739614i	$-0.735008\pi$
$337$		−	498.500i		−	1.47923i	0.673031	−	0.739614i	$-0.264992\pi$
$338$		0			0
$339$	268.843			0.793047
$340$	−50.4026	−	13.5053i	−0.148243	−	0.0397216i
$341$	−140.796	−	243.866i	−0.412892	−	0.715151i
$342$	187.662	+	108.347i	0.548720	+	0.316804i
$343$	52.8131	−	52.8131i	0.153974	−	0.153974i
$344$	−8.76472	−	32.7104i	−0.0254788	−	0.0950883i
$345$	395.878	−	106.075i	1.14747	−	0.307464i
$346$	−310.835	−	310.835i	−0.898368	−	0.898368i
$347$	117.312	−	203.191i	0.338076	−	0.585565i	−0.645995	−	0.763342i	$-0.723557\pi$
$347$	117.312	−	203.191i	0.338076	−	0.585565i	0.984071	+	0.177777i	$0.0568905\pi$
$348$	95.3168	−	55.0312i	0.273899	−	0.158136i
$349$	−45.7756	+	170.837i	−0.131162	+	0.489504i	−0.999984	−	0.00562078i	$-0.998211\pi$
$349$	−45.7756	+	170.837i	−0.131162	+	0.489504i	0.868822	+	0.495124i	$0.164878\pi$
$350$		−	50.6264i		−	0.144647i
$351$		0			0
$352$	−59.2653			−0.168367
$353$	−217.243	−	58.2100i	−0.615418	−	0.164901i	−0.0623743	−	0.998053i	$-0.519867\pi$
$353$	−217.243	−	58.2100i	−0.615418	−	0.164901i	−0.553044	+	0.833152i	$0.686534\pi$
$354$	171.129	+	296.404i	0.483415	+	0.837299i
$355$	−264.288	−	152.587i	−0.744473	−	0.429822i
$356$	−114.573	+	114.573i	−0.321836	+	0.321836i
$357$	49.9400	+	186.379i	0.139888	+	0.522069i
$358$	−86.5245	+	23.1842i	−0.241688	+	0.0647602i
$359$	−290.278	−	290.278i	−0.808574	−	0.808574i	0.175844	−	0.984418i	$-0.443735\pi$
$359$	−290.278	−	290.278i	−0.808574	−	0.808574i	−0.984418	+	0.175844i	$0.943735\pi$
$360$	43.7853	−	75.8383i	0.121626	−	0.210662i
$361$	−291.651	+	168.385i	−0.807899	+	0.466440i
$362$	−68.2652	+	254.769i	−0.188578	+	0.703783i
$363$			43.2359i			0.119107i
$364$		0			0
$365$	96.6115			0.264689
$366$	295.750	+	79.2461i	0.808061	+	0.216519i
$367$	110.372	+	191.170i	0.300741	+	0.520898i	0.976304	−	0.216404i	$-0.0694328\pi$
$367$	110.372	+	191.170i	0.300741	+	0.520898i	−0.675563	+	0.737302i	$0.736099\pi$
$368$	−69.1402	−	39.9181i	−0.187881	−	0.108473i
$369$	−20.5400	+	20.5400i	−0.0556639	+	0.0556639i
$370$	118.548	+	442.427i	0.320400	+	1.19575i
$371$	763.589	−	204.603i	2.05819	−	0.551491i
$372$	−146.235	−	146.235i	−0.393105	−	0.393105i
$373$	31.0796	−	53.8315i	0.0833235	−	0.144320i	−0.821352	−	0.570422i	$-0.806780\pi$
$373$	31.0796	−	53.8315i	0.0833235	−	0.144320i	0.904676	+	0.426101i	$0.140113\pi$
$374$	−62.7209	+	36.2119i	−0.167703	+	0.0968233i
$375$	114.324	−	426.662i	0.304863	−	1.13777i
$376$			30.3667i			0.0807625i
$377$		0			0
$378$	178.604			0.472497
$379$	−140.323	−	37.5994i	−0.370245	−	0.0992069i	0.0688986	−	0.997624i	$-0.478051\pi$
$379$	−140.323	−	37.5994i	−0.370245	−	0.0992069i	−0.439144	+	0.898417i	$0.644718\pi$
$380$	140.992	+	244.205i	0.371031	+	0.642645i
$381$	275.837	+	159.255i	0.723982	+	0.417991i
$382$	182.691	−	182.691i	0.478250	−	0.478250i
$383$	130.131	+	485.657i	0.339769	+	1.26803i	0.898606	+	0.438756i	$0.144581\pi$
$383$	130.131	+	485.657i	0.339769	+	1.26803i	−0.558837	+	0.829277i	$0.688752\pi$
$384$	−42.0425	+	11.2653i	−0.109486	+	0.0293366i
$385$	−405.714	−	405.714i	−1.05380	−	1.05380i
$386$	64.4548	−	111.639i	0.166981	−	0.289220i
$387$	60.1454	−	34.7250i	0.155414	−	0.0897286i
$388$	−28.3983	+	105.984i	−0.0731915	+	0.273154i
$389$		−	284.973i		−	0.732579i	−0.930501	−	0.366289i	$-0.880628\pi$
$389$		−	284.973i		−	0.732579i	0.930501	−	0.366289i	$-0.119372\pi$
$390$		0			0
$391$	−97.5621			−0.249519
$392$	153.758	+	41.1993i	0.392239	+	0.105100i
$393$	92.0445	+	159.426i	0.234210	+	0.405663i
$394$	−264.304	−	152.596i	−0.670824	−	0.387300i
$395$	−30.1380	+	30.1380i	−0.0762988	+	0.0762988i
$396$	−31.4577	−	117.402i	−0.0794385	−	0.296469i
$397$	−285.958	+	76.6221i	−0.720296	+	0.193003i	−0.600304	−	0.799772i	$-0.704954\pi$
$397$	−285.958	+	76.6221i	−0.720296	+	0.193003i	−0.119992	+	0.992775i	$0.538287\pi$
$398$	−78.4893	−	78.4893i	−0.197209	−	0.197209i
$399$	521.360	−	903.022i	1.30667	−	2.26321i
$400$	12.0860	−	6.97783i	0.0302149	−	0.0174446i
$401$	−62.5992	+	233.623i	−0.156108	+	0.582602i	0.842900	+	0.538070i	$0.180846\pi$
$401$	−62.5992	+	233.623i	−0.156108	+	0.582602i	−0.999008	+	0.0445319i	$0.985820\pi$
$402$		−	33.2554i		−	0.0827248i
$403$		0			0
$404$	28.1270			0.0696212
$405$	−513.286	−	137.535i	−1.26737	−	0.339592i
$406$	−103.783	−	179.757i	−0.255622	−	0.442751i
$407$	550.555	+	317.863i	1.35272	+	0.780990i
$408$	−37.6107	+	37.6107i	−0.0921830	+	0.0921830i
$409$	−50.5043	−	188.485i	−0.123483	−	0.460843i	0.876299	−	0.481769i	$-0.160005\pi$
$409$	−50.5043	−	188.485i	−0.123483	−	0.460843i	−0.999781	+	0.0209255i	$0.993339\pi$
$410$	−36.5121	+	9.78339i	−0.0890539	+	0.0238619i
$411$	−523.529	−	523.529i	−1.27379	−	1.27379i
$412$	80.8399	−	140.019i	0.196213	−	0.339851i
$413$	558.985	−	322.730i	1.35347	−	0.781428i
$414$	42.3766	−	158.152i	0.102359	−	0.382009i
$415$			270.490i			0.651784i
$416$		0			0
$417$	−742.859			−1.78144
$418$	378.042	+	101.296i	0.904407	+	0.242335i
$419$	−23.9555	−	41.4921i	−0.0571730	−	0.0990265i	0.836022	−	0.548695i	$-0.184875\pi$
$419$	−23.9555	−	41.4921i	−0.0571730	−	0.0990265i	−0.893195	+	0.449669i	$0.851542\pi$
$420$	−364.930	−	210.693i	−0.868882	−	0.501649i
$421$	477.018	−	477.018i	1.13306	−	1.13306i	0.143394	−	0.989666i	$-0.454198\pi$
$421$	477.018	−	477.018i	1.13306	−	1.13306i	0.989666	−	0.143394i	$-0.0458016\pi$
$422$	48.4610	+	180.859i	0.114837	+	0.428576i
$423$	−60.1550	+	16.1185i	−0.142210	+	0.0381051i
$424$	154.090	+	154.090i	0.363420	+	0.363420i
$425$	8.52711	−	14.7694i	0.0200638	−	0.0347515i
$426$	−269.398	+	155.537i	−0.632390	+	0.365111i
$427$	149.449	−	557.753i	0.349998	−	1.30621i
$428$		−	325.410i		−	0.760304i
$429$		0			0
$430$	90.3753			0.210175
$431$	75.2127	+	20.1532i	0.174507	+	0.0467591i	0.345015	−	0.938597i	$-0.387874\pi$
$431$	75.2127	+	20.1532i	0.174507	+	0.0467591i	−0.170507	+	0.985356i	$0.554541\pi$
$432$	24.6170	+	42.6379i	0.0569838	+	0.0986988i
$433$	−430.937	−	248.802i	−0.995235	−	0.574599i	−0.0884003	−	0.996085i	$-0.528175\pi$
$433$	−430.937	−	248.802i	−0.995235	−	0.574599i	−0.906835	+	0.421486i	$0.861509\pi$
$434$	−275.783	+	275.783i	−0.635445	+	0.635445i
$435$	76.0226	+	283.720i	0.174765	+	0.652231i
$436$	171.228	−	45.8804i	0.392725	−	0.105230i
$437$	372.804	+	372.804i	0.853099	+	0.853099i
$438$	49.2398	−	85.2858i	0.112420	−	0.194716i
$439$	145.068	−	83.7551i	0.330451	−	0.190786i	−0.325590	−	0.945511i	$-0.605563\pi$
$439$	145.068	−	83.7551i	0.330451	−	0.190786i	0.656042	+	0.754725i	$0.272230\pi$
$440$	40.9359	−	152.775i	0.0930361	−	0.347216i
$441$			326.455i			0.740260i
$442$		0			0
$443$	−443.835			−1.00188			−0.500942	−	0.865481i	$-0.667013\pi$
$443$	−443.835			−1.00188			−0.500942	+	0.865481i	$0.667013\pi$
$444$	450.981	+	120.840i	1.01572	+	0.272162i
$445$	−216.211	−	374.488i	−0.485867	−	0.841546i
$446$	146.356	+	84.4985i	0.328152	+	0.189459i
$447$	365.813	−	365.813i	0.818374	−	0.818374i
$448$	21.2450	+	79.2876i	0.0474220	+	0.176981i
$449$	−248.050	+	66.4648i	−0.552450	+	0.148029i	−0.524235	−	0.851573i	$-0.675649\pi$
$449$	−248.050	+	66.4648i	−0.552450	+	0.148029i	−0.0282145	+	0.999602i	$0.508982\pi$
$450$	20.2379	+	20.2379i	0.0449731	+	0.0449731i
$451$	−26.2322	+	45.4356i	−0.0581646	+	0.100744i
$452$	121.037	−	69.8809i	0.267782	−	0.154604i
$453$	37.4318	−	139.698i	0.0826310	−	0.308383i
$454$			599.884i			1.32133i
$455$		0			0
$456$	287.436			0.630342
$457$	84.1413	+	22.5456i	0.184117	+	0.0493339i	0.349699	−	0.936862i	$-0.386284\pi$
$457$	84.1413	+	22.5456i	0.184117	+	0.0493339i	−0.165583	+	0.986196i	$0.552950\pi$
$458$	158.206	+	274.021i	0.345428	+	0.598299i
$459$	52.1047	+	30.0826i	0.113518	+	0.0655395i
$460$	150.658	−	150.658i	0.327518	−	0.327518i
$461$	−128.071	−	477.968i	−0.277812	−	1.03681i	−0.953934	−	0.300018i	$-0.903007\pi$
$461$	−128.071	−	477.968i	−0.277812	−	1.03681i	0.676122	−	0.736790i	$-0.263659\pi$
$462$	−564.931	+	151.373i	−1.22279	+	0.327647i
$463$	399.472	+	399.472i	0.862789	+	0.862789i	0.991661	−	0.128872i	$-0.0411356\pi$
$463$	399.472	+	399.472i	0.862789	+	0.862789i	−0.128872	+	0.991661i	$0.541136\pi$
$464$	28.6087	−	49.5518i	0.0616568	−	0.106793i
$465$	477.974	−	275.959i	1.02790	−	0.593460i
$466$	−59.6732	+	222.704i	−0.128054	+	0.477905i
$467$			409.816i			0.877550i	0.898597	+	0.438775i	$0.144587\pi$
$467$			409.816i			0.877550i	−0.898597	+	0.438775i	$0.855413\pi$
$468$		0			0
$469$	−62.7159			−0.133723
$470$	−78.2798	−	20.9750i	−0.166553	−	0.0446277i
$471$	−482.828	−	836.283i	−1.02511	−	1.77555i
$472$	154.090	+	88.9637i	0.326461	+	0.188482i
$473$	88.6966	−	88.6966i	0.187519	−	0.187519i
$474$	11.2446	+	41.9654i	0.0237227	+	0.0885345i
$475$	−89.0206	+	23.8530i	−0.187412	+	0.0502168i
$476$	70.9296	+	70.9296i	0.149012	+	0.149012i
$477$	−223.455	+	387.035i	−0.468458	+	0.811394i
$478$	321.217	−	185.455i	0.672003	−	0.387981i
$479$	−137.833	+	514.401i	−0.287752	+	1.07391i	0.659053	+	0.752097i	$0.270957\pi$
$479$	−137.833	+	514.401i	−0.287752	+	1.07391i	−0.946805	+	0.321809i	$0.895709\pi$
$480$		−	116.159i		−	0.241998i
$481$		0			0
$482$	−642.477			−1.33294
$483$	−761.018	−	203.914i	−1.57561	−	0.422183i
$484$	11.2384	+	19.4655i	0.0232198	+	0.0402179i
$485$	−253.591	−	146.411i	−0.522869	−	0.301879i
$486$	−272.240	+	272.240i	−0.560165	+	0.560165i
$487$	−174.246	−	650.294i	−0.357794	−	1.33531i	−0.876932	−	0.480615i	$-0.840413\pi$
$487$	−174.246	−	650.294i	−0.357794	−	1.33531i	0.519137	−	0.854691i	$-0.326253\pi$
$488$	153.750	−	41.1972i	0.315062	−	0.0844205i
$489$	−330.740	−	330.740i	−0.676361	−	0.676361i
$490$	−212.408	+	367.902i	−0.433486	+	0.750820i
$491$	101.720	−	58.7282i	0.207170	−	0.119609i	−0.392826	−	0.919613i	$-0.628502\pi$
$491$	101.720	−	58.7282i	0.207170	−	0.119609i	0.599995	+	0.800003i	$0.295169\pi$
$492$	−9.97256	+	37.2181i	−0.0202694	+	0.0756465i
$493$		−	69.9214i		−	0.141828i
$494$		0			0
$495$	324.368			0.655289
$496$	−103.848	−	27.8261i	−0.209372	−	0.0561010i
$497$	293.326	+	508.055i	0.590193	+	1.02224i
$498$	238.781	+	137.860i	0.479479	+	0.276828i
$499$	−155.387	+	155.387i	−0.311396	+	0.311396i	−0.845450	−	0.534054i	$-0.820668\pi$
$499$	−155.387	+	155.387i	−0.311396	+	0.311396i	0.534054	+	0.845450i	$0.320668\pi$
$500$	−59.4328	−	221.806i	−0.118866	−	0.443613i
$501$	230.030	−	61.6364i	0.459142	−	0.123027i
$502$	−438.996	−	438.996i	−0.874495	−	0.874495i
$503$	−162.518	+	281.490i	−0.323098	+	0.559622i	−0.981126	−	0.193372i	$-0.938058\pi$
$503$	−162.518	+	281.490i	−0.323098	+	0.559622i	0.658028	+	0.752994i	$0.271391\pi$
$504$	−145.788	+	84.1708i	−0.289262	+	0.167006i
$505$	−19.4280	+	72.5062i	−0.0384712	+	0.143577i
$506$		−	295.720i		−	0.584426i
$507$		0			0
$508$	165.582			0.325948
$509$	561.220	+	150.378i	1.10259	+	0.295439i	0.763820	−	0.645429i	$-0.223321\pi$
$509$	561.220	+	150.378i	1.10259	+	0.295439i	0.338773	+	0.940868i	$0.389988\pi$
$510$	−70.9748	−	122.932i	−0.139166	−	0.241043i
$511$	−160.840	−	92.8608i	−0.314755	−	0.181724i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−84.1506	−	314.054i	−0.164036	−	0.612192i
$514$	−597.237	+	160.029i	−1.16194	+	0.311341i
$515$	305.104	+	305.104i	0.592436	+	0.592436i
$516$	46.0614	−	79.7806i	0.0892662	−	0.154614i
$517$	−97.4111	+	56.2403i	−0.188416	+	0.108782i
$518$	227.891	−	850.501i	0.439944	−	1.64189i
$519$		−	1195.83i		−	2.30411i
$520$		0			0
$521$	400.067			0.767883			0.383942	−	0.923357i	$-0.374566\pi$
$521$	400.067			0.767883			0.383942	+	0.923357i	$0.374566\pi$
$522$	113.345	+	30.3707i	0.217136	+	0.0581814i
$523$	−234.335	−	405.881i	−0.448060	−	0.776063i	0.550200	−	0.835033i	$-0.314552\pi$
$523$	−234.335	−	405.881i	−0.448060	−	0.776063i	−0.998260	+	0.0589705i	$0.981218\pi$
$524$	82.8797	+	47.8506i	0.158167	+	0.0913180i
$525$	97.3839	−	97.3839i	0.185493	−	0.185493i
$526$	105.400	+	393.360i	0.200381	+	0.747832i
$527$	−126.906	+	34.0043i	−0.240808	+	0.0645242i
$528$	−114.001	−	114.001i	−0.215912	−	0.215912i
$529$	−65.3182	+	113.135i	−0.123475	+	0.213865i
$530$	−503.649	+	290.782i	−0.950281	+	0.548645i
$531$	−94.4429	+	352.466i	−0.177859	+	0.663777i
$532$		−	542.073i		−	1.01893i
$533$		0			0
$534$	−440.782			−0.825435
$535$	838.847	+	224.768i	1.56794	+	0.420128i
$536$	−8.64414	−	14.9721i	−0.0161271	−	0.0279330i
$537$	−211.033	−	121.840i	−0.392985	−	0.226890i
$538$	−343.400	+	343.400i	−0.638290	+	0.638290i
$539$	152.605	+	569.531i	0.283127	+	1.05664i
$540$	−126.916	+	34.0071i	−0.235030	+	0.0629760i
$541$	−155.599	−	155.599i	−0.287614	−	0.287614i	0.548522	−	0.836136i	$-0.315191\pi$
$541$	−155.599	−	155.599i	−0.287614	−	0.287614i	−0.836136	+	0.548522i	$0.815191\pi$
$542$	−5.87429	+	10.1746i	−0.0108382	+	0.0187723i
$543$	−621.383	+	358.755i	−1.14435	+	0.660691i
$544$	−7.15669	+	26.7091i	−0.0131557	+	0.0490977i
$545$			473.085i			0.868045i
$546$		0			0
$547$	858.888			1.57018			0.785090	−	0.619382i	$-0.212617\pi$
$547$	858.888			1.57018			0.785090	+	0.619382i	$0.212617\pi$
$548$	−371.783	−	99.6188i	−0.678435	−	0.181786i
$549$	163.219	+	282.704i	0.297303	+	0.514944i
$550$	44.7674	+	25.8464i	0.0813952	+	0.0469935i
$551$	−267.184	+	267.184i	−0.484907	+	0.484907i
$552$	−56.2110	−	209.782i	−0.101831	−	0.380040i
$553$	79.1420	−	21.2060i	0.143114	−	0.0383473i
$554$	444.247	+	444.247i	0.801891	+	0.801891i
$555$	−623.007	+	1079.08i	−1.12254	+	1.94429i
$556$	−334.447	+	193.093i	−0.601523	+	0.347289i
$557$	138.000	−	515.023i	0.247756	−	0.924637i	−0.724223	−	0.689566i	$-0.757801\pi$
$557$	138.000	−	515.023i	0.247756	−	0.924637i	0.971978	−	0.235071i	$-0.0755321\pi$
$558$		−	220.489i		−	0.395141i
$559$		0			0
$560$	−219.063			−0.391184
$561$	−190.305	−	50.9921i	−0.339225	−	0.0908950i
$562$	163.678	+	283.499i	0.291243	+	0.504447i
$563$	376.396	+	217.312i	0.668554	+	0.385990i	0.795528	−	0.605916i	$-0.207193\pi$
$563$	376.396	+	217.312i	0.668554	+	0.385990i	−0.126975	+	0.991906i	$0.540527\pi$
$564$	−58.4128	+	58.4128i	−0.103569	+	0.103569i
$565$	96.5368	+	360.280i	0.170862	+	0.637664i
$566$	634.026	−	169.887i	1.12019	−	0.300153i
$567$	722.327	+	722.327i	1.27395	+	1.27395i
$568$	−80.8582	+	140.050i	−0.142356	+	0.246568i
$569$	−287.755	+	166.135i	−0.505720	+	0.291978i	−0.731073	−	0.682300i	$-0.760980\pi$
$569$	−287.755	+	166.135i	−0.505720	+	0.291978i	0.225353	+	0.974277i	$0.427647\pi$
$570$	−198.539	+	740.957i	−0.348314	+	1.29992i
$571$			555.806i			0.973391i	0.873572	+	0.486696i	$0.161798\pi$
$571$			555.806i			0.973391i	−0.873572	+	0.486696i	$0.838202\pi$
$572$		0			0
$573$	702.843			1.22660
$574$	70.1892	+	18.8071i	0.122281	+	0.0327651i
$575$	34.8177	+	60.3061i	0.0605526	+	0.104880i
$576$	−40.1879	−	23.2025i	−0.0697707	−	0.0402821i
$577$	−287.753	+	287.753i	−0.498705	+	0.498705i	−0.911035	−	0.412330i	$-0.864715\pi$
$577$	−287.753	+	287.753i	−0.498705	+	0.498705i	0.412330	+	0.911035i	$0.364715\pi$
$578$	−97.0357	−	362.142i	−0.167882	−	0.626543i
$579$	338.731	−	90.7626i	0.585027	−	0.156757i
$580$	107.975	+	107.975i	0.186163	+	0.186163i
$581$	259.989	−	450.314i	0.447485	−	0.775067i
$582$	−258.495	+	149.242i	−0.444149	+	0.256430i
$583$	−208.913	+	779.675i	−0.358342	+	1.33735i
$584$		−	51.1960i		−	0.0876644i
$585$		0			0
$586$	89.8951			0.153405
$587$	−647.190	−	173.414i	−1.10254	−	0.295424i	−0.338741	−	0.940880i	$-0.610001\pi$
$587$	−647.190	−	173.414i	−1.10254	−	0.295424i	−0.763798	+	0.645455i	$0.776668\pi$
$588$	216.515	+	375.015i	0.368223	+	0.637781i
$589$	614.869	+	354.995i	1.04392	+	0.602708i
$590$	−335.765	+	335.765i	−0.569094	+	0.569094i
$591$	−214.880	−	801.942i	−0.363586	−	1.35692i
$592$	234.449	−	62.8205i	0.396029	−	0.106116i
$593$	69.0570	+	69.0570i	0.116454	+	0.116454i	0.762932	−	0.646479i	$-0.223759\pi$
$593$	69.0570	+	69.0570i	0.116454	+	0.116454i	−0.646479	+	0.762932i	$0.723759\pi$
$594$	−91.1832	+	157.934i	−0.153507	+	0.265882i
$595$	−231.836	+	133.851i	−0.389641	+	0.224959i
$596$	69.6082	−	259.781i	0.116792	−	0.435875i
$597$		−	301.961i		−	0.505797i
$598$		0			0
$599$	461.140			0.769850			0.384925	−	0.922948i	$-0.374227\pi$
$599$	461.140			0.769850			0.384925	+	0.922948i	$0.374227\pi$
$600$	36.6707	+	9.82589i	0.0611179	+	0.0163765i
$601$	−88.0811	−	152.561i	−0.146558	−	0.253845i	0.783395	−	0.621524i	$-0.213486\pi$
$601$	−88.0811	−	152.561i	−0.146558	−	0.253845i	−0.929953	+	0.367678i	$0.880153\pi$
$602$	−150.457	−	86.8667i	−0.249929	−	0.144297i
$603$	25.0707	−	25.0707i	0.0415766	−	0.0415766i
$604$	−19.4595	−	72.6238i	−0.0322177	−	0.120238i
$605$	−57.9410	+	15.5253i	−0.0957703	+	0.0256616i
$606$	54.1045	+	54.1045i	0.0892813	+	0.0892813i
$607$	157.707	−	273.157i	0.259814	−	0.450011i	−0.706378	−	0.707835i	$-0.749672\pi$
$607$	157.707	−	273.157i	0.259814	−	0.450011i	0.966192	+	0.257824i	$0.0830054\pi$
$608$	129.408	−	74.7139i	0.212842	−	0.122885i
$609$	146.142	−	545.411i	0.239971	−	0.895585i
$610$			424.795i			0.696385i
$611$		0			0
$612$	−56.7082			−0.0926605
$613$	−872.008	−	233.654i	−1.42253	−	0.381165i	−0.536147	−	0.844125i	$-0.680121\pi$
$613$	−872.008	−	233.654i	−1.42253	−	0.381165i	−0.886379	+	0.462960i	$0.846787\pi$
$614$	−67.1395	−	116.289i	−0.109348	−	0.189396i
$615$	−89.0531	−	51.4148i	−0.144802	−	0.0836013i
$616$	−214.994	+	214.994i	−0.349016	+	0.349016i
$617$	176.797	+	659.815i	0.286543	+	1.06939i	0.947705	+	0.319149i	$0.103397\pi$
$617$	176.797	+	659.815i	0.286543	+	1.06939i	−0.661162	+	0.750243i	$0.729936\pi$
$618$	424.839	−	113.835i	0.687442	−	0.184199i
$619$	413.378	+	413.378i	0.667816	+	0.667816i	0.957210	−	0.289394i	$-0.0934538\pi$
$619$	413.378	+	413.378i	0.667816	+	0.667816i	−0.289394	+	0.957210i	$0.593454\pi$
$620$	143.461	−	248.482i	0.231389	−	0.400777i
$621$	−212.753	+	122.833i	−0.342597	+	0.197799i
$622$	−121.206	+	452.347i	−0.194865	+	0.727246i
$623$			831.267i			1.33430i
$624$		0			0
$625$	700.050			1.12008
$626$	−534.219	−	143.143i	−0.853384	−	0.228664i
$627$	532.343	+	922.045i	0.849032	+	1.47057i
$628$	−434.754	−	251.005i	−0.692283	−	0.399690i
$629$	209.735	−	209.735i	0.333442	−	0.333442i
$630$	−116.277	−	433.953i	−0.184567	−	0.688815i
$631$	1.62079	−	0.434289i	0.00256861	−	0.000688256i	−0.257535	−	0.966269i	$-0.582910\pi$
$631$	1.62079	−	0.434289i	0.00256861	−	0.000688256i	0.260103	+	0.965581i	$0.416243\pi$
$632$	15.9706	+	15.9706i	0.0252700	+	0.0252700i
$633$	−254.678	+	441.115i	−0.402335	+	0.696864i
$634$	559.389	−	322.964i	0.882317	−	0.509406i
$635$	−114.371	+	426.839i	−0.180112	+	0.672187i
$636$			592.809i			0.932089i
$637$		0			0
$638$	211.938			0.332191
$639$	−320.352	−	85.8381i	−0.501334	−	0.134332i
$640$	−30.1935	−	52.2966i	−0.0471773	−	0.0817135i
$641$	−1063.07	−	613.763i	−1.65845	−	0.957508i	−0.973429	−	0.228988i	$-0.926458\pi$
$641$	−1063.07	−	613.763i	−1.65845	−	0.957508i	−0.685024	−	0.728521i	$-0.740208\pi$
$642$	625.952	−	625.952i	0.975003	−	0.975003i
$643$	156.134	+	582.701i	0.242822	+	0.906223i	0.974466	+	0.224536i	$0.0720866\pi$
$643$	156.134	+	582.701i	0.242822	+	0.906223i	−0.731644	+	0.681687i	$0.761247\pi$
$644$	−395.626	+	106.008i	−0.614326	+	0.164608i
$645$	173.844	+	173.844i	0.269526	+	0.269526i
$646$	91.3024	−	158.140i	0.141335	−	0.244799i
$647$	759.328	−	438.399i	1.17361	−	0.677587i	0.219086	−	0.975706i	$-0.429693\pi$
$647$	759.328	−	438.399i	1.17361	−	0.677587i	0.954529	+	0.298119i	$0.0963592\pi$
$648$	−72.8818	+	271.999i	−0.112472	+	0.419751i
$649$			659.057i			1.01550i
$650$		0			0
$651$	−1060.98			−1.62977
$652$	−234.875	−	62.9345i	−0.360237	−	0.0965252i
$653$	−75.1803	−	130.216i	−0.115131	−	0.199412i	0.802701	−	0.596381i	$-0.203395\pi$
$653$	−75.1803	−	130.216i	−0.115131	−	0.199412i	−0.917832	+	0.396969i	$0.870062\pi$
$654$	417.625	+	241.116i	0.638570	+	0.368679i
$655$	−180.597	+	180.597i	−0.275721	+	0.275721i
$656$	5.18438	+	19.3484i	0.00790301	+	0.0294944i
$657$	101.417	−	27.1745i	0.154363	−	0.0413616i
$658$	110.160	+	110.160i	0.167416	+	0.167416i
$659$	−436.771	+	756.509i	−0.662778	+	1.14796i	0.317105	+	0.948390i	$0.397289\pi$
$659$	−436.771	+	756.509i	−0.662778	+	1.14796i	−0.979883	+	0.199574i	$0.936044\pi$
$660$	372.618	−	215.131i	0.564573	−	0.325956i
$661$	123.160	−	459.641i	0.186324	−	0.695372i	−0.808019	−	0.589157i	$-0.799460\pi$
$661$	123.160	−	459.641i	0.186324	−	0.695372i	0.994343	−	0.106216i	$-0.0338733\pi$
$662$		−	693.033i		−	1.04688i
$663$		0			0
$664$	143.337			0.215869
$665$	1397.36	+	374.422i	2.10130	+	0.563041i
$666$	248.889	+	431.088i	0.373706	+	0.647279i
$667$	247.252	+	142.751i	0.370692	+	0.214019i
$668$	87.5419	−	87.5419i	0.131051	−	0.131051i
$669$	118.987	+	444.066i	0.177858	+	0.663776i
$670$	44.5660	−	11.9414i	0.0665164	−	0.0178230i
$671$	416.905	+	416.905i	0.621318	+	0.621318i
$672$	−111.649	+	193.382i	−0.166145	+	0.287771i
$673$	−957.612	+	552.878i	−1.42290	+	0.821512i	−0.996546	−	0.0830435i	$-0.973536\pi$
$673$	−957.612	+	552.878i	−1.42290	+	0.821512i	−0.426355	+	0.904556i	$0.640203\pi$
$674$	182.464	−	680.964i	0.270718	−	1.01033i
$675$		−	42.9433i		−	0.0636197i
$676$		0			0
$677$	474.341			0.700651			0.350326	−	0.936628i	$-0.386071\pi$
$677$	474.341			0.700651			0.350326	+	0.936628i	$0.386071\pi$
$678$	367.246	+	98.4034i	0.541661	+	0.145138i
$679$	281.454	+	487.493i	0.414512	+	0.717957i
$680$	−63.9079	−	36.8973i	−0.0939823	−	0.0542607i
$681$	−1153.93	+	1153.93i	−1.69446	+	1.69446i
$682$	−103.070	−	384.663i	−0.151129	−	0.564022i
$683$	−1012.79	+	271.376i	−1.48285	+	0.397329i	−0.907317	−	0.420448i	$-0.861873\pi$
$683$	−1012.79	+	271.376i	−1.48285	+	0.397329i	−0.575535	+	0.817777i	$0.695206\pi$
$684$	216.694	+	216.694i	0.316804	+	0.316804i
$685$	513.598	−	889.578i	0.749778	−	1.29865i
$686$	91.4749	−	52.8131i	0.133345	−	0.0769870i
$687$	−222.779	+	831.423i	−0.324278	+	1.21022i
$688$		−	47.8913i		−	0.0696095i
$689$		0			0
$690$	579.606			0.840009
$691$	−391.766	−	104.973i	−0.566956	−	0.151915i	−0.0360556	−	0.999350i	$-0.511479\pi$
$691$	−391.766	−	104.973i	−0.566956	−	0.151915i	−0.530900	+	0.847434i	$0.678146\pi$
$692$	−310.835	−	538.382i	−0.449184	−	0.778009i
$693$	−540.010	−	311.775i	−0.779236	−	0.449892i
$694$	234.625	−	234.625i	0.338076	−	0.338076i
$695$	−266.747	−	995.515i	−0.383809	−	1.43240i
$696$	150.348	−	40.2856i	0.216017	−	0.0578816i
$697$	17.3088	+	17.3088i	0.0248333	+	0.0248333i
$698$	−125.061	+	216.612i	−0.179171	+	0.310333i
$699$	−543.174	+	313.602i	−0.777073	+	0.448643i
$700$	18.5305	−	69.1569i	0.0264722	−	0.0987956i
$701$		−	322.739i		−	0.460398i	−0.973144	−	0.230199i	$-0.926062\pi$
$701$		−	322.739i		−	0.460398i	0.973144	−	0.230199i	$-0.0739378\pi$
$702$		0			0
$703$	−1602.88			−2.28006
$704$	−80.9579	−	21.6926i	−0.114997	−	0.0308133i
$705$	−110.230	−	190.924i	−0.156355	−	0.270815i
$706$	−275.453	−	159.033i	−0.390160	−	0.225259i
$707$	102.035	−	102.035i	0.144321	−	0.144321i
$708$	125.275	+	467.532i	0.176942	+	0.660357i
$709$	94.1274	−	25.2214i	0.132761	−	0.0355732i	−0.191827	−	0.981429i	$-0.561441\pi$
$709$	94.1274	−	25.2214i	0.132761	−	0.0355732i	0.324588	+	0.945856i	$0.394774\pi$
$710$	−305.174	−	305.174i	−0.429822	−	0.429822i
$711$	−23.1599	+	40.1142i	−0.0325737	+	0.0564194i
$712$	−198.447	+	114.573i	−0.278718	+	0.160918i
$713$	138.846	−	518.179i	0.194734	−	0.726758i
$714$			272.877i			0.382181i
$715$		0			0
$716$	−126.681			−0.176928
$717$	974.624	+	261.150i	1.35931	+	0.364226i
$718$	−290.278	−	502.777i	−0.404287	−	0.700246i
$719$	772.888	+	446.227i	1.07495	+	0.620622i	0.929529	−	0.368748i	$-0.120214\pi$
$719$	772.888	+	446.227i	1.07495	+	0.620622i	0.145419	+	0.989370i	$0.453547\pi$
$720$	87.5705	−	87.5705i	0.121626	−	0.121626i
$721$	−214.681	−	801.199i	−0.297754	−	1.11123i
$722$	−460.036	+	123.266i	−0.637170	+	0.170729i
$723$	−1235.86	−	1235.86i	−1.70934	−	1.70934i
$724$	−186.504	+	323.035i	−0.257602	+	0.446180i
$725$	−43.2205	+	24.9534i	−0.0596145	+	0.0344184i
$726$	−15.8254	+	59.0613i	−0.0217981	+	0.0813517i
$727$		−	1093.66i		−	1.50435i	−0.658964	−	0.752175i	$-0.729005\pi$
$727$		−	1093.66i		−	1.50435i	0.658964	−	0.752175i	$-0.270995\pi$
$728$		0			0
$729$	−151.327			−0.207581
$730$	131.974	+	35.3623i	0.180786	+	0.0484415i
$731$	−29.2623	−	50.6837i	−0.0400305	−	0.0693348i
$732$	374.996	+	216.504i	0.512290	+	0.295771i
$733$	−136.804	+	136.804i	−0.186636	+	0.186636i	−0.794240	−	0.607604i	$-0.792131\pi$
$733$	−136.804	+	136.804i	−0.186636	+	0.186636i	0.607604	+	0.794240i	$0.292131\pi$
$734$	80.7978	+	301.541i	0.110079	+	0.410819i
$735$	−1116.27	+	299.104i	−1.51874	+	0.406944i
$736$	−79.8362	−	79.8362i	−0.108473	−	0.108473i
$737$	32.0186	−	55.4578i	0.0434445	−	0.0752480i
$738$	−35.5763	+	20.5400i	−0.0482064	+	0.0278320i
$739$	207.914	−	775.945i	0.281345	−	1.04999i	−0.670124	−	0.742249i	$-0.733759\pi$
$739$	207.914	−	775.945i	0.281345	−	1.04999i	0.951469	−	0.307745i	$-0.0995743\pi$
$740$			647.758i			0.875349i
$741$		0			0
$742$	1117.97			1.50670
$743$	690.270	+	184.957i	0.929031	+	0.248933i	0.691441	−	0.722432i	$-0.256976\pi$
$743$	690.270	+	184.957i	0.929031	+	0.248933i	0.237590	+	0.971366i	$0.423643\pi$
$744$	−146.235	−	253.286i	−0.196552	−	0.340439i
$745$	621.588	+	358.874i	0.834347	+	0.481710i
$746$	62.1593	−	62.1593i	0.0833235	−	0.0833235i
$747$	76.0825	+	283.944i	0.101851	+	0.380112i
$748$	−98.9328	+	26.5090i	−0.132263	+	0.0354398i
$749$	−1180.48	−	1180.48i	−1.57607	−	1.57607i
$750$	312.338	−	540.986i	0.416451	−	0.721315i
$751$	−21.1260	+	12.1971i	−0.0281305	+	0.0162412i	−0.513999	−	0.857791i	$-0.671837\pi$
$751$	−21.1260	+	12.1971i	−0.0281305	+	0.0162412i	0.485869	+	0.874032i	$0.338503\pi$
$752$	−11.1150	+	41.4817i	−0.0147806	+	0.0551618i
$753$		−	1688.89i		−	2.24288i
$754$		0			0
$755$	200.652			0.265764
$756$	243.978	+	65.3736i	0.322722	+	0.0864730i
$757$	512.612	+	887.871i	0.677163	+	1.17288i	0.975832	+	0.218524i	$0.0701241\pi$
$757$	512.612	+	887.871i	0.677163	+	1.17288i	−0.298669	+	0.954357i	$0.596543\pi$
$758$	−177.922	−	102.724i	−0.234726	−	0.135519i
$759$	568.840	−	568.840i	0.749460	−	0.749460i
$760$	103.213	+	385.197i	0.135807	+	0.506838i
$761$	−372.443	+	99.7959i	−0.489413	+	0.131138i	−0.495082	−	0.868846i	$-0.664862\pi$
$761$	−372.443	+	99.7959i	−0.489413	+	0.131138i	0.00566927	+	0.999984i	$0.498195\pi$
$762$	318.509	+	318.509i	0.417991	+	0.417991i
$763$	454.718	−	787.595i	0.595961	−	1.03223i
$764$	316.431	−	182.691i	0.414177	−	0.239125i
$765$	39.1697	−	146.183i	0.0512022	−	0.191089i
$766$			711.051i			0.928265i
$767$		0			0
$768$	−61.5545			−0.0801491
$769$	234.432	+	62.8158i	0.304853	+	0.0816850i	0.408003	−	0.912981i	$-0.366225\pi$
$769$	234.432	+	62.8158i	0.304853	+	0.0816850i	−0.103150	+	0.994666i	$0.532892\pi$
$770$	−405.714	−	702.716i	−0.526901	−	0.912619i
$771$	−1456.66	−	841.004i	−1.88931	−	1.09080i
$772$	128.910	−	128.910i	0.166981	−	0.166981i
$773$	−134.645	−	502.503i	−0.174185	−	0.650068i	−0.996689	−	0.0813084i	$-0.974090\pi$
$773$	−134.645	−	502.503i	−0.174185	−	0.650068i	0.822504	−	0.568760i	$-0.192577\pi$
$774$	94.8704	−	25.4204i	0.122572	−	0.0328429i
$775$	66.3089	+	66.3089i	0.0855598	+	0.0855598i
$776$	−77.5856	+	134.382i	−0.0999814	+	0.173173i
$777$	2074.37	−	1197.64i	2.66972	−	1.54136i
$778$	104.307	−	389.281i	0.134071	−	0.500361i
$779$		−	132.281i		−	0.169808i
$780$		0			0
$781$	−599.010			−0.766978
$782$	−133.272	−	35.7102i	−0.170425	−	0.0456652i
$783$	−88.0326	−	152.477i	−0.112430	−	0.194734i
$784$	194.957	+	112.558i	0.248670	+	0.143569i
$785$	947.340	−	947.340i	1.20680	−	1.20680i
$786$	67.3812	+	251.470i	0.0857268	+	0.319937i
$787$	1404.51	−	376.336i	1.78463	−	0.478191i	0.793218	−	0.608938i	$-0.208404\pi$
$787$	1404.51	−	376.336i	1.78463	−	0.478191i	0.991416	+	0.130746i	$0.0417374\pi$
$788$	−305.193	−	305.193i	−0.387300	−	0.387300i
$789$	−553.913	+	959.405i	−0.702044	+	1.21598i
$790$	−52.2006	+	30.1380i	−0.0660767	+	0.0381494i
$791$	185.578	−	692.586i	0.234612	−	0.875583i
$792$		−	171.888i		−	0.217030i
$793$		0			0
$794$	−418.671			−0.527294
$795$	−1528.15	−	409.467i	−1.92220	−	0.515053i
$796$	−78.4893	−	135.947i	−0.0986046	−	0.170788i
$797$	−408.951	−	236.108i	−0.513113	−	0.296246i	0.221000	−	0.975274i	$-0.429068\pi$
$797$	−408.951	−	236.108i	−0.513113	−	0.296246i	−0.734112	+	0.679028i	$0.762401\pi$
$798$	1042.72	−	1042.72i	1.30667	−	1.30667i
$799$	13.5828	+	50.6918i	0.0169998	+	0.0634440i
$800$	19.0638	−	5.10813i	0.0238297	−	0.00638516i
$801$	−332.299	−	332.299i	−0.414855	−	0.414855i
$802$	−171.024	+	296.222i	−0.213247	+	0.369355i
$803$	164.228	−	94.8170i	0.204518	−	0.118078i
$804$	12.1723	−	45.4277i	0.0151397	−	0.0565021i
$805$		−	1093.07i		−	1.35785i
$806$		0			0
$807$	−1321.11			−1.63707
$808$	38.4222	+	10.2952i	0.0475522	+	0.0127416i
$809$	−477.215	−	826.561i	−0.589883	−	1.02171i	−0.994247	−	0.107109i	$-0.965840\pi$
$809$	−477.215	−	826.561i	−0.589883	−	1.02171i	0.404364	−	0.914598i	$-0.367493\pi$
$810$	−650.821	−	375.752i	−0.803482	−	0.463891i
$811$	−643.215	+	643.215i	−0.793114	+	0.793114i	−0.981999	−	0.188885i	$-0.939513\pi$
$811$	−643.215	+	643.215i	−0.793114	+	0.793114i	0.188885	+	0.981999i	$0.439513\pi$
$812$	−75.9742	−	283.540i	−0.0935643	−	0.349187i
$813$	−30.8713	+	8.27193i	−0.0379720	+	0.0101746i
$814$	635.726	+	635.726i	0.780990	+	0.780990i
$815$	324.467	−	561.993i	0.398119	−	0.689562i
$816$	−65.1436	+	37.6107i	−0.0798329	+	0.0460915i
$817$	−81.8557	+	305.490i	−0.100191	+	0.373917i
$818$		−	275.961i		−	0.337361i
$819$		0			0
$820$	−53.4574			−0.0651920
$821$	832.236	+	222.997i	1.01369	+	0.271616i	0.727169	−	0.686459i	$-0.240836\pi$
$821$	832.236	+	222.997i	1.01369	+	0.271616i	0.286517	+	0.958075i	$0.407503\pi$
$822$	−523.529	−	906.778i	−0.636896	−	1.10314i
$823$	646.953	+	373.519i	0.786092	+	0.453850i	0.838585	−	0.544771i	$-0.183383\pi$
$823$	646.953	+	373.519i	0.786092	+	0.453850i	−0.0524933	+	0.998621i	$0.516717\pi$
$824$	161.680	−	161.680i	0.196213	−	0.196213i
$825$	36.3959	+	135.831i	0.0441162	+	0.164644i
$826$	881.715	−	236.255i	1.06745	−	0.286023i
$827$	1064.80	+	1064.80i	1.28755	+	1.28755i	0.936273	+	0.351272i	$0.114251\pi$
$827$	1064.80	+	1064.80i	1.28755	+	1.28755i	0.351272	+	0.936273i	$0.385749\pi$
$828$	115.775	−	200.528i	0.139825	−	0.242184i
$829$	−110.480	+	63.7857i	−0.133269	+	0.0769429i	−0.565152	−	0.824987i	$-0.691183\pi$
$829$	−110.480	+	63.7857i	−0.133269	+	0.0769429i	0.431883	+	0.901930i	$0.357849\pi$
$830$	−99.0063	+	369.497i	−0.119285	+	0.445177i
$831$			1709.09i			2.05667i
$832$		0			0
$833$	275.099			0.330251
$834$	−1014.76	−	271.905i	−1.21674	−	0.326025i
$835$	165.200	+	286.134i	0.197844	+	0.342676i
$836$	479.338	+	276.746i	0.573371	+	0.331036i
$837$	−233.930	+	233.930i	−0.279486	+	0.279486i
$838$	−17.5366	−	65.4476i	−0.0209268	−	0.0780998i
$839$	−458.520	+	122.860i	−0.546507	+	0.146436i	−0.521500	−	0.853251i	$-0.674627\pi$
$839$	−458.520	+	122.860i	−0.546507	+	0.146436i	−0.0250069	+	0.999687i	$0.507961\pi$
$840$	−421.385	−	421.385i	−0.501649	−	0.501649i
$841$	318.193	−	551.126i	0.378350	−	0.655322i
$842$	826.220	−	477.018i	0.981259	−	0.566530i
$843$	−230.485	+	860.182i	−0.273411	+	1.02038i
$844$			264.796i			0.313739i
$845$		0			0
$846$	−88.0730			−0.104105
$847$	111.383	+	29.8450i	0.131503	+	0.0352362i
$848$	154.090	+	266.892i	0.181710	+	0.314731i
$849$	1546.39	+	892.808i	1.82142	+	1.05160i
$850$	17.0542	−	17.0542i	0.0200638	−	0.0200638i
$851$	313.459	+	1169.85i	0.368342	+	1.37467i
$852$	−424.935	+	113.861i	−0.498750	+	0.133640i
$853$	−425.319	−	425.319i	−0.498616	−	0.498616i	0.412391	−	0.911007i	$-0.364694\pi$
$853$	−425.319	−	425.319i	−0.498616	−	0.498616i	−0.911007	+	0.412391i	$0.864694\pi$
$854$	408.303	−	707.202i	0.478107	−	0.828105i
$855$	−708.271	+	408.921i	−0.828388	+	0.478270i
$856$	119.108	−	444.518i	0.139145	−	0.519297i
$857$		−	48.5237i		−	0.0566204i	−0.999599	−	0.0283102i	$-0.990987\pi$
$857$		−	48.5237i		−	0.0566204i	0.999599	−	0.0283102i	$-0.00901262\pi$
$858$		0			0
$859$	165.922			0.193157			0.0965787	−	0.995325i	$-0.469210\pi$
$859$	165.922			0.193157			0.0965787	+	0.995325i	$0.469210\pi$
$860$	123.455	+	33.0797i	0.143552	+	0.0384647i
$861$	98.8375	+	171.192i	0.114794	+	0.198829i
$862$	95.3659	+	55.0595i	0.110633	+	0.0638741i
$863$	−376.277	+	376.277i	−0.436010	+	0.436010i	−0.890667	−	0.454657i	$-0.849762\pi$
$863$	−376.277	+	376.277i	−0.436010	+	0.436010i	0.454657	+	0.890667i	$0.349762\pi$
$864$	18.0209	+	67.2548i	0.0208575	+	0.0778413i
$865$	1602.55	−	429.402i	1.85266	−	0.496419i
$866$	−497.603	−	497.603i	−0.574599	−	0.574599i
$867$	509.953	−	883.265i	0.588181	−	1.01876i
$868$	−477.670	+	275.783i	−0.550311	+	0.317722i
$869$	−21.6528	+	80.8092i	−0.0249169	+	0.0929911i
$870$			415.395i			0.477466i
$871$		0			0
$872$	250.695			0.287494
$873$	−307.386	−	82.3640i	−0.352104	−	0.0943459i
$874$	372.804	+	645.716i	0.426550	+	0.738806i
$875$	−1020.24	−	589.036i	−1.16599	−	0.673184i
$876$	98.4795	−	98.4795i	0.112420	−	0.112420i
$877$	330.834	+	1234.69i	0.377234	+	1.40786i	0.850053	+	0.526698i	$0.176570\pi$
$877$	330.834	+	1234.69i	0.377234	+	1.40786i	−0.472818	+	0.881160i	$0.656763\pi$
$878$	228.823	−	61.3130i	0.260619	−	0.0698326i
$879$	172.920	+	172.920i	0.196724	+	0.196724i
$880$	111.839	−	193.711i	0.127090	−	0.220126i
$881$	−1081.10	+	624.174i	−1.22713	+	0.708484i	−0.966429	−	0.256936i	$-0.917287\pi$
$881$	−1081.10	+	624.174i	−1.22713	+	0.708484i	−0.260702	+	0.965419i	$0.583954\pi$
$882$	−119.491	+	445.946i	−0.135477	+	0.505607i
$883$			1217.43i			1.37874i	0.724408	+	0.689371i	$0.242113\pi$
$883$			1217.43i			1.37874i	−0.724408	+	0.689371i	$0.757887\pi$
$884$		0			0
$885$	−1291.74			−1.45960
$886$	−606.290	−	162.455i	−0.684300	−	0.183358i
$887$	15.5485	+	26.9308i	0.0175293	+	0.0303617i	0.874657	−	0.484742i	$-0.161087\pi$
$887$	15.5485	+	26.9308i	0.0175293	+	0.0303617i	−0.857128	+	0.515104i	$0.827753\pi$
$888$	571.822	+	330.141i	0.643943	+	0.371781i
$889$	600.673	−	600.673i	0.675673	−	0.675673i
$890$	−158.277	−	590.698i	−0.177840	−	0.663706i
$891$	−1007.50	+	269.960i	−1.13076	+	0.302985i
$892$	168.997	+	168.997i	0.189459	+	0.189459i
$893$	141.801	−	245.606i	0.158792	−	0.275035i
$894$	633.607	−	365.813i	0.708733	−	0.409187i
$895$	87.5013	−	326.559i	0.0977668	−	0.364871i
$896$			116.085i			0.129559i
$897$		0			0
$898$	−363.170			−0.404421
$899$	371.371	+	99.5087i	0.413094	+	0.110688i
$900$	20.2379	+	35.0531i	0.0224866	+	0.0389479i
$901$	326.149	+	188.302i	0.361986	+	0.208993i
$902$	−52.4645	+	52.4645i	−0.0581646	+	0.0581646i
$903$	−122.322	−	456.512i	−0.135462	−	0.505550i
$904$	190.918	−	51.1564i	0.211193	−	0.0565889i
$905$	−703.901	−	703.901i	−0.777791	−	0.777791i
$906$	102.266	−	177.129i	0.112876	−	0.195507i
$907$	1333.19	−	769.718i	1.46989	−	0.848642i	0.470461	−	0.882421i	$-0.344088\pi$
$907$	1333.19	−	769.718i	1.46989	−	0.848642i	0.999429	+	0.0337789i	$0.0107542\pi$
$908$	−219.573	+	819.457i	−0.241820	+	0.902486i
$909$			81.5771i			0.0897438i
$910$		0			0
$911$	−148.518			−0.163027			−0.0815136	−	0.996672i	$-0.525975\pi$
$911$	−148.518			−0.163027			−0.0815136	+	0.996672i	$0.525975\pi$
$912$	392.645	+	105.209i	0.430532	+	0.115361i
$913$	265.466	+	459.801i	0.290762	+	0.503615i
$914$	106.687	+	61.5957i	0.116725	+	0.0673913i
$915$	−817.127	+	817.127i	−0.893035	+	0.893035i
$916$	115.815	+	432.227i	0.126435	+	0.471864i
$917$	474.245	−	127.074i	0.517170	−	0.138575i
$918$	60.1653	+	60.1653i	0.0655395	+	0.0655395i
$919$	875.083	−	1515.69i	0.952212	−	1.64928i	0.211589	−	0.977359i	$-0.432136\pi$
$919$	875.083	−	1515.69i	0.952212	−	1.64928i	0.740623	−	0.671921i	$-0.234531\pi$
$920$	260.948	−	150.658i	0.283639	−	0.163759i
$921$	94.5430	−	352.839i	0.102653	−	0.383104i
$922$		−	699.794i		−	0.758996i
$923$		0			0
$924$	−827.116			−0.895148
$925$	−204.493	−	54.7938i	−0.221074	−	0.0592366i
$926$	399.472	+	691.905i	0.431395	+	0.747198i
$927$	406.098	+	234.461i	0.438078	+	0.252924i
$928$	57.2175	−	57.2175i	0.0616568	−	0.0616568i
$929$	254.851	+	951.116i	0.274328	+	1.02381i	0.956290	+	0.292419i	$0.0944601\pi$
$929$	254.851	+	951.116i	0.274328	+	1.02381i	−0.681962	+	0.731387i	$0.738873\pi$
$930$	753.933	−	202.016i	0.810681	−	0.217221i
$931$	−1051.21	−	1051.21i	−1.12912	−	1.12912i
$932$	−163.030	+	282.377i	−0.174925	+	0.302979i
$933$	−1103.27	+	636.976i	−1.18250	+	0.682718i
$934$	−150.003	+	559.819i	−0.160603	+	0.599378i
$935$		−	273.341i		−	0.292343i
$936$		0			0
$937$	835.853			0.892052			0.446026	−	0.895020i	$-0.352839\pi$
$937$	835.853			0.892052			0.446026	+	0.895020i	$0.352839\pi$
$938$	−85.6716	−	22.9556i	−0.0913343	−	0.0244730i
$939$	−752.264	−	1302.96i	−0.801133	−	1.38760i
$940$	−99.2548	−	57.3048i	−0.105590	−	0.0609625i
$941$	−759.883	+	759.883i	−0.807527	+	0.807527i	−0.984259	−	0.176732i	$-0.943447\pi$
$941$	−759.883	+	759.883i	−0.807527	+	0.807527i	0.176732	+	0.984259i	$0.443447\pi$
$942$	−353.455	−	1319.11i	−0.375218	−	1.40033i
$943$	−96.5437	+	25.8688i	−0.102379	+	0.0274324i
$944$	177.927	+	177.927i	0.188482	+	0.188482i
$945$	−337.042	+	583.774i	−0.356658	+	0.617750i
$946$	153.627	−	88.6966i	0.162396	−	0.0937596i
$947$	−298.691	+	1114.73i	−0.315407	+	1.17712i	0.608202	+	0.793782i	$0.291891\pi$
$947$	−298.691	+	1114.73i	−0.315407	+	1.17712i	−0.923610	+	0.383335i	$0.874776\pi$
$948$			61.4415i			0.0648118i
$949$		0			0
$950$	−130.335			−0.137195
$951$	1697.28	+	454.784i	1.78473	+	0.478216i
$952$	70.9296	+	122.854i	0.0745059	+	0.129048i
$953$	1410.01	+	814.070i	1.47955	+	0.854219i	0.999732	−	0.0231495i	$-0.00736938\pi$
$953$	1410.01	+	814.070i	1.47955	+	0.854219i	0.479818	+	0.877368i	$0.340703\pi$
$954$	−446.909	+	446.909i	−0.468458	+	0.468458i
$955$	252.379	+	941.890i	0.264271	+	0.986272i
$956$	506.672	−	135.762i	0.529992	−	0.142011i
$957$	407.680	+	407.680i	0.425998	+	0.425998i
$958$	−376.568	+	652.234i	−0.393077	+	0.680829i
$959$	−1710.08	+	987.317i	−1.78319	+	1.02953i
$960$	42.5172	−	158.676i	0.0442887	−	0.165288i
$961$			238.576i			0.248258i
$962$		0			0
$963$	943.791			0.980053
$964$	−877.640	−	235.163i	−0.910415	−	0.243945i
$965$	243.264	+	421.346i	0.252087	+	0.436628i
$966$	−964.932	−	557.104i	−0.998895	−	0.576712i
$967$	1097.29	−	1097.29i	1.13473	−	1.13473i	0.145354	−	0.989380i	$-0.453568\pi$
$967$	1097.29	−	1097.29i	1.13473	−	1.13473i	0.989380	−	0.145354i	$-0.0464320\pi$
$968$	8.22708	+	30.7039i	0.00849905	+	0.0317189i
$969$	479.823	−	128.568i	0.495173	−	0.132681i
$970$	−292.822	−	292.822i	−0.301879	−	0.301879i
$971$	−644.897	+	1116.99i	−0.664157	+	1.15035i	0.315356	+	0.948974i	$0.397876\pi$
$971$	−644.897	+	1116.99i	−0.664157	+	1.15035i	−0.979513	+	0.201381i	$0.935457\pi$
$972$	−471.534	+	272.240i	−0.485117	+	0.280083i
$973$	−512.783	+	1913.73i	−0.527012	+	1.96684i
$974$		−	952.097i		−	0.977512i
$975$		0			0
$976$	225.106			0.230641
$977$	−1509.47	−	404.461i	−1.54500	−	0.413982i	−0.617124	−	0.786866i	$-0.711702\pi$
$977$	−1509.47	−	404.461i	−1.54500	−	0.413982i	−0.927878	+	0.372884i	$0.878369\pi$
$978$	−330.740	−	572.859i	−0.338180	−	0.585746i
$979$	−735.064	−	424.389i	−0.750831	−	0.433492i
$980$	−424.816	+	424.816i	−0.433486	+	0.433486i
$981$	133.068	+	496.615i	0.135645	+	0.506233i
$982$	160.449	−	42.9921i	0.163390	−	0.0437801i
$983$	−79.2765	−	79.2765i	−0.0806475	−	0.0806475i	0.665632	−	0.746280i	$-0.268162\pi$
$983$	−79.2765	−	79.2765i	−0.0806475	−	0.0806475i	−0.746280	+	0.665632i	$0.768162\pi$
$984$	−27.2455	+	47.1906i	−0.0276885	+	0.0479580i
$985$	997.533	−	575.926i	1.01272	−	0.584697i
$986$	25.5930	−	95.5144i	0.0259564	−	0.0968705i
$987$			423.803i			0.429385i
$988$		0			0
$989$	238.966			0.241624
$990$	443.095	+	118.727i	0.447571	+	0.119926i
$991$	101.592	+	175.963i	0.102515	+	0.177561i	0.912720	−	0.408585i	$-0.133978\pi$
$991$	101.592	+	175.963i	0.102515	+	0.177561i	−0.810205	+	0.586146i	$0.800644\pi$
$992$	−131.674	−	76.0223i	−0.132736	−	0.0766354i
$993$	1333.10	−	1333.10i	1.34250	−	1.34250i
$994$	214.729	+	801.381i	0.216026	+	0.806218i
$995$	404.662	−	108.429i	0.406695	−	0.108974i
$996$	275.720	+	275.720i	0.276828	+	0.276828i
$997$	−986.022	+	1707.84i	−0.988989	+	1.71298i	−0.366335	+	0.930483i	$0.619387\pi$
$997$	−986.022	+	1707.84i	−0.988989	+	1.71298i	−0.622655	+	0.782497i	$0.713946\pi$
$998$	−269.138	+	155.387i	−0.269677	+	0.155698i
$999$	193.306	−	721.429i	0.193500	−	0.722151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.3.f.i.249.2		8
13.2	odd	12		338.3.d.g.99.2		8
13.3	even	3		338.3.d.f.239.2		8
13.4	even	6		338.3.f.h.19.2		8
13.5	odd	4		338.3.f.h.89.2		8
13.6	odd	12		26.3.f.b.7.2	✓	8
13.7	odd	12	inner	338.3.f.i.319.2		8
13.8	odd	4		338.3.f.j.89.2		8
13.9	even	3		338.3.f.j.19.2		8
13.10	even	6		338.3.d.g.239.2		8
13.11	odd	12		338.3.d.f.99.2		8
13.12	even	2		26.3.f.b.15.2	yes	8
39.32	even	12		234.3.bb.f.163.1		8
39.38	odd	2		234.3.bb.f.145.1		8
52.19	even	12		208.3.bd.f.33.1		8
52.51	odd	2		208.3.bd.f.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.b.7.2	✓	8	13.6	odd	12
26.3.f.b.15.2	yes	8	13.12	even	2
208.3.bd.f.33.1		8	52.19	even	12
208.3.bd.f.145.1		8	52.51	odd	2
234.3.bb.f.145.1		8	39.38	odd	2
234.3.bb.f.163.1		8	39.32	even	12
338.3.d.f.99.2		8	13.11	odd	12
338.3.d.f.239.2		8	13.3	even	3
338.3.d.g.99.2		8	13.2	odd	12
338.3.d.g.239.2		8	13.10	even	6
338.3.f.h.19.2		8	13.4	even	6
338.3.f.h.89.2		8	13.5	odd	4
338.3.f.i.249.2		8	1.1	even	1	trivial
338.3.f.i.319.2		8	13.7	odd	12	inner
338.3.f.j.19.2		8	13.9	even	3
338.3.f.j.89.2		8	13.8	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	338.f (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.92358 + 3.33174i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-3.77418 + 3.77418i) q^{5} +(1.40816 + 5.25532i) q^{6} +(9.91095 - 2.65563i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-2.90031 + 5.02349i) q^{9} +(-6.53708 + 3.77418i) q^{10} +(-2.71157 + 10.1197i) q^{11} +7.69432i q^{12} +14.5106 q^{14} +(-19.8345 - 5.31465i) q^{15} +(2.00000 + 3.46410i) q^{16} +(4.23323 + 2.44406i) q^{17} +(-5.80063 + 5.80063i) q^{18} +(-6.83679 - 25.5153i) q^{19} +(-10.3113 + 2.76289i) q^{20} +(27.9124 + 27.9124i) q^{21} +(-7.40816 + 12.8313i) q^{22} +(-17.2850 + 9.97952i) q^{23} +(-2.81632 + 10.5106i) q^{24} -3.48892i q^{25} +12.3085 q^{27} +(19.8219 + 5.31126i) q^{28} +(-7.15218 - 12.3879i) q^{29} +(-25.1492 - 14.5199i) q^{30} +(-19.0056 + 19.0056i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-38.9322 + 10.4319i) q^{33} +(4.88811 + 4.88811i) q^{34} +(-27.3829 + 47.4286i) q^{35} +(-10.0470 + 5.80063i) q^{36} +(15.7051 - 58.6123i) q^{37} -37.3569i q^{38} -15.0967 q^{40} +(4.83709 + 1.29609i) q^{41} +(27.9124 + 48.3456i) q^{42} +(-10.3688 - 5.98641i) q^{43} +(-14.8163 + 14.8163i) q^{44} +(-8.01326 - 29.9059i) q^{45} +(-27.2646 + 7.30552i) q^{46} +(7.59168 + 7.59168i) q^{47} +(-7.69432 + 13.3269i) q^{48} +(48.7392 - 28.1396i) q^{49} +(1.27703 - 4.76595i) q^{50} +18.8053i q^{51} +77.0450 q^{53} +(16.8137 + 4.50522i) q^{54} +(-27.9597 - 48.4277i) q^{55} +(25.1332 + 14.5106i) q^{56} +(71.8590 - 71.8590i) q^{57} +(-5.23576 - 19.5401i) q^{58} +(60.7634 - 16.2815i) q^{59} +(-29.0398 - 29.0398i) q^{60} +(28.1382 - 48.7368i) q^{61} +(-32.9186 + 19.0056i) q^{62} +(-15.4043 + 57.4897i) q^{63} +8.00000i q^{64} -57.0007 q^{66} +(-5.90406 - 1.58199i) q^{67} +(4.88811 + 8.46646i) q^{68} +(-66.4983 - 38.3928i) q^{69} +(-54.7658 + 54.7658i) q^{70} +(14.7981 + 55.2272i) q^{71} +(-15.8476 + 4.24635i) q^{72} +(-12.7990 - 12.7990i) q^{73} +(42.9072 - 74.3174i) q^{74} +(11.6242 - 6.71121i) q^{75} +(13.6736 - 51.0305i) q^{76} +107.497i q^{77} +7.98532 q^{79} +(-20.6225 - 5.52579i) q^{80} +(49.7792 + 86.2201i) q^{81} +(6.13318 + 3.54099i) q^{82} +(35.8343 - 35.8343i) q^{83} +(20.4333 + 76.2580i) q^{84} +(-25.2013 + 6.75267i) q^{85} +(-11.9728 - 11.9728i) q^{86} +(27.5156 - 47.6584i) q^{87} +(-25.6626 + 14.8163i) q^{88} +(-20.9684 + 78.2551i) q^{89} -43.7853i q^{90} -39.9181 q^{92} +(-99.8803 - 26.7628i) q^{93} +(7.59168 + 13.1492i) q^{94} +(122.103 + 70.4959i) q^{95} +(-15.3886 + 15.3886i) q^{96} +(14.1991 + 52.9919i) q^{97} +(76.8788 - 20.5996i) q^{98} +(-42.9720 - 42.9720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{8} - 42 q^{9} - 18 q^{10} + 18 q^{11} + 20 q^{14} - 66 q^{15} + 16 q^{16} - 42 q^{17} - 84 q^{18} - 46 q^{19} - 24 q^{20} + 102 q^{21} - 42 q^{22} - 36 q^{23}+ \cdots - 252 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^8 - 42 * q^9 - 18 * q^10 + 18 * q^11 + 20 * q^14 - 66 * q^15 + 16 * q^16 - 42 * q^17 - 84 * q^18 - 46 * q^19 - 24 * q^20 + 102 * q^21 - 42 * q^22 - 36 * q^23 + 12 * q^24 + 72 * q^27 + 4 * q^28 - 6 * q^29 - 192 * q^30 - 32 * q^31 - 16 * q^32 - 42 * q^33 + 60 * q^34 - 78 * q^35 - 48 * q^36 + 106 * q^37 - 24 * q^40 - 132 * q^41 + 102 * q^42 - 108 * q^43 - 84 * q^44 - 240 * q^45 - 90 * q^46 - 60 * q^47 + 258 * q^49 - 194 * q^50 - 132 * q^53 + 270 * q^54 - 162 * q^55 - 12 * q^56 + 294 * q^57 + 24 * q^58 - 18 * q^59 + 120 * q^60 + 36 * q^61 - 12 * q^62 + 72 * q^63 + 108 * q^66 + 74 * q^67 + 60 * q^68 + 258 * q^69 - 156 * q^70 + 174 * q^71 - 132 * q^72 - 166 * q^73 - 32 * q^74 + 6 * q^75 + 92 * q^76 - 96 * q^79 - 48 * q^80 - 12 * q^81 - 252 * q^82 + 240 * q^83 + 132 * q^84 + 24 * q^85 - 132 * q^86 + 360 * q^87 - 12 * q^88 - 294 * q^89 - 216 * q^92 - 270 * q^93 - 60 * q^94 + 714 * q^95 + 58 * q^97 + 250 * q^98 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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