LMFDB - Embedded newform 26.3.f.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,3,Mod(7,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("26.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	26.f (of order $12$, degree $4$, 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:	$0.708448687337$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.2
Root			$-4.71318 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	26.7
Dual form			26.3.f.b.15.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(1.92358 - 3.33174i) q^{3} +(1.73205 - 1.00000i) q^{4} +(3.77418 + 3.77418i) q^{5} +(-1.40816 + 5.25532i) q^{6} +(-9.91095 - 2.65563i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.90031 - 5.02349i) q^{9} +O(q^{10})$	\(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} +(-8.18513 + 10.0997i) q^{13} +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} +(7.48435 - 16.7924i) q^{26} +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} +(17.9048 + 46.6982i) q^{39} -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} +(-4.07737 + 25.6783i) q^{52} +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} +(-69.0102 + 7.22589i) q^{65} -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} +(-41.5511 - 57.2374i) q^{78} +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} +(107.943 - 78.3608i) q^{91} -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}+O(q^{10}) $ 8 * q - 4 * q^2 + 6 * q^5 + 6 * q^6 - 2 * q^7 - 16 * q^8 - 42 * q^9	\( 8 q - 4 q^{2} + 6 q^{5} + 6 q^{6} - 2 q^{7} - 16 q^{8} - 42 q^{9} - 18 q^{10} - 18 q^{11} + 36 q^{13} + 20 q^{14} + 66 q^{15} + 16 q^{16} - 42 q^{17} + 84 q^{18} + 46 q^{19} + 24 q^{20} - 102 q^{21} - 42 q^{22} - 36 q^{23} - 12 q^{24} + 40 q^{26} + 72 q^{27} - 4 q^{28} - 6 q^{29} - 192 q^{30} + 32 q^{31} + 16 q^{32} + 42 q^{33} - 60 q^{34} - 78 q^{35} - 48 q^{36} - 106 q^{37} + 12 q^{39} - 24 q^{40} + 132 q^{41} + 102 q^{42} - 108 q^{43} + 84 q^{44} + 240 q^{45} + 90 q^{46} + 60 q^{47} + 258 q^{49} + 194 q^{50} + 32 q^{52} - 132 q^{53} - 270 q^{54} - 162 q^{55} - 12 q^{56} - 294 q^{57} - 24 q^{58} + 18 q^{59} - 120 q^{60} + 36 q^{61} - 12 q^{62} - 72 q^{63} - 300 q^{65} + 108 q^{66} - 74 q^{67} + 60 q^{68} + 258 q^{69} + 156 q^{70} - 174 q^{71} + 132 q^{72} + 166 q^{73} - 32 q^{74} + 6 q^{75} - 92 q^{76} + 126 q^{78} - 96 q^{79} + 48 q^{80} - 12 q^{81} - 252 q^{82} - 240 q^{83} - 132 q^{84} - 24 q^{85} + 132 q^{86} + 360 q^{87} - 12 q^{88} + 294 q^{89} + 298 q^{91} - 216 q^{92} + 270 q^{93} - 60 q^{94} + 714 q^{95} - 58 q^{97} - 250 q^{98} + 252 q^{99}+O(q^{100}) \) 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 + 36 * q^13 + 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 + 40 * q^26 + 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 + 12 * q^39 - 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 + 32 * q^52 - 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 - 300 * q^65 + 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 + 126 * q^78 - 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 + 298 * q^91 - 216 * q^92 + 270 * q^93 - 60 * q^94 + 714 * q^95 - 58 * q^97 - 250 * q^98 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

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	−0.343974	−	0.938979i	$-0.611773\pi$
$3$	1.92358	−	3.33174i	0.641193	−	1.11058i	0.985167	−	0.171600i	$-0.0548936\pi$
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	3.77418	+	3.77418i	0.754837	+	0.754837i	0.975378	−	0.220541i	$-0.0707823\pi$
$5$	3.77418	+	3.77418i	0.754837	+	0.754837i	−0.220541	+	0.975378i	$0.570782\pi$
$6$	−1.40816	+	5.25532i	−0.234693	+	0.875886i
$7$	−9.91095	−	2.65563i	−1.41585	−	0.379376i	−0.531840	−	0.846845i	$-0.678499\pi$
$7$	−9.91095	−	2.65563i	−1.41585	−	0.379376i	−0.884009	+	0.467469i	$0.845166\pi$
$8$	−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	0.972620	+	0.232401i	$0.0746581\pi$
$11$	2.71157	+	10.1197i	0.246507	+	0.919976i	−0.726113	+	0.687575i	$0.758675\pi$
$12$		−	7.69432i		−	0.641193i
$13$	−8.18513	+	10.0997i	−0.629625	+	0.776899i
$13$	−8.18513	+	10.0997i	−0.629625	+	0.776899i
$14$	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	−0.370299	−	0.928913i	$-0.620745\pi$
$17$	4.23323	−	2.44406i	0.249013	−	0.143768i	0.619312	+	0.785145i	$0.287411\pi$
$18$	5.80063	+	5.80063i	0.322257	+	0.322257i
$19$	6.83679	−	25.5153i	0.359831	−	1.34291i	−0.514463	−	0.857512i	$-0.672009\pi$
$19$	6.83679	−	25.5153i	0.359831	−	1.34291i	0.874295	−	0.485396i	$-0.161325\pi$
$20$	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	0.0747206	−	0.997205i	$-0.476194\pi$
$23$	−17.2850	−	9.97952i	−0.751524	−	0.433892i	−0.826244	+	0.563312i	$0.809527\pi$
$24$	2.81632	+	10.5106i	0.117346	+	0.437943i
$25$			3.48892i			0.139557i
$26$	7.48435	−	16.7924i	0.287860	−	0.645861i
$27$	12.3085			0.455870
$28$	−19.8219	+	5.31126i	−0.707925	+	0.189688i
$29$	−7.15218	+	12.3879i	−0.246627	+	0.427171i	−0.962588	−	0.270970i	$-0.912656\pi$
$29$	−7.15218	+	12.3879i	−0.246627	+	0.427171i	0.715961	+	0.698141i	$0.245989\pi$
$30$	−25.1492	+	14.5199i	−0.838306	+	0.483996i
$31$	19.0056	+	19.0056i	0.613083	+	0.613083i	0.943748	−	0.330665i	$-0.107273\pi$
$31$	19.0056	+	19.0056i	0.613083	+	0.613083i	−0.330665	+	0.943748i	$0.607273\pi$
$32$	−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	−0.765094	−	0.643919i	$-0.777307\pi$
$37$	−15.7051	−	58.6123i	−0.424463	−	1.58412i	0.340631	−	0.940197i	$-0.389359\pi$
$38$			37.3569i			0.983077i
$39$	17.9048	+	46.6982i	0.459096	+	1.19739i
$40$	−15.0967			−0.377418
$41$	−4.83709	+	1.29609i	−0.117978	+	0.0316120i	−0.317325	−	0.948317i	$-0.602785\pi$
$41$	−4.83709	+	1.29609i	−0.117978	+	0.0316120i	0.199347	+	0.979929i	$0.436118\pi$
$42$	27.9124	−	48.3456i	0.664580	−	1.15109i
$43$	−10.3688	+	5.98641i	−0.241134	+	0.139219i	−0.615698	−	0.787982i	$-0.711126\pi$
$43$	−10.3688	+	5.98641i	−0.241134	+	0.139219i	0.374564	+	0.927201i	$0.377793\pi$
$44$	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	$-0.786435\pi$
$47$	−7.59168	+	7.59168i	−0.161525	+	0.161525i	0.621717	+	0.783242i	$0.286435\pi$
$48$	−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
$52$	−4.07737	+	25.6783i	−0.0784110	+	0.493813i
$53$	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	$-0.595643\pi$
$59$	−60.7634	−	16.2815i	−1.02989	−	0.275957i	−0.733917	+	0.679240i	$0.762310\pi$
$60$	29.0398	−	29.0398i	0.483996	−	0.483996i
$61$	28.1382	+	48.7368i	0.461282	+	0.798964i	0.999025	−	0.0441448i	$-0.0140563\pi$
$61$	28.1382	+	48.7368i	0.461282	+	0.798964i	−0.537743	+	0.843109i	$0.680723\pi$
$62$	−32.9186	−	19.0056i	−0.530946	−	0.306542i
$63$	15.4043	+	57.4897i	0.244513	+	0.912535i
$64$		−	8.00000i		−	0.125000i
$65$	−69.0102	+	7.22589i	−1.06170	+	0.111168i
$66$	−57.0007			−0.863647
$67$	5.90406	−	1.58199i	0.0881202	−	0.0236117i	−0.214490	−	0.976726i	$-0.568809\pi$
$67$	5.90406	−	1.58199i	0.0881202	−	0.0236117i	0.302610	+	0.953115i	$0.402142\pi$
$68$	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	0.779955	+	0.625836i	$0.215242\pi$
$71$	−14.7981	+	55.2272i	−0.208424	+	0.777847i	−0.988379	+	0.152012i	$0.951425\pi$
$72$	15.8476	+	4.24635i	0.220106	+	0.0589771i
$73$	12.7990	−	12.7990i	0.175329	−	0.175329i	−0.613987	−	0.789316i	$-0.710435\pi$
$73$	12.7990	−	12.7990i	0.175329	−	0.175329i	0.789316	+	0.613987i	$0.210435\pi$
$74$	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
$78$	−41.5511	−	57.2374i	−0.532706	−	0.733813i
$79$	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	$-0.348752\pi$
$83$	−35.8343	−	35.8343i	−0.431738	−	0.431738i	−0.889219	+	0.457481i	$0.848752\pi$
$84$	−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	0.977877	+	0.209178i	$0.0670790\pi$
$89$	20.9684	+	78.2551i	0.235600	+	0.879271i	−0.742277	+	0.670093i	$0.766254\pi$
$90$			43.7853i			0.486503i
$91$	107.943	−	78.3608i	1.18619	−	0.861107i
$92$	−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	0.853307	+	0.521409i	$0.174593\pi$
$97$	−14.1991	+	52.9919i	−0.146383	+	0.546309i	−0.999690	+	0.0248998i	$0.992073\pi$
$98$	−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	0.559081	−	0.829113i	$-0.311154\pi$
$101$	12.1793	+	7.03175i	0.120588	+	0.0696212i	−0.438493	+	0.898735i	$0.644488\pi$
$102$	6.88323	+	25.6886i	0.0674827	+	0.251849i
$103$			80.8399i			0.784853i	0.919783	+	0.392426i	$0.128364\pi$
$103$			80.8399i			0.784853i	−0.919783	+	0.392426i	$0.871636\pi$
$104$	−3.82911	−	36.5696i	−0.0368184	−	0.351631i
$105$	−210.693			−2.00660
$106$	−105.245	+	28.2004i	−0.992881	+	0.266042i
$107$	−81.3525	+	140.907i	−0.760304	+	1.31688i	0.182390	+	0.983226i	$0.441617\pi$
$107$	−81.3525	+	140.907i	−0.760304	+	1.31688i	−0.942694	+	0.333659i	$0.891717\pi$
$108$	21.3189	−	12.3085i	0.197398	−	0.113968i
$109$	−62.6738	−	62.6738i	−0.574989	−	0.574989i	0.358530	−	0.933518i	$-0.383278\pi$
$109$	−62.6738	−	62.6738i	−0.574989	−	0.574989i	−0.933518	+	0.358530i	$0.883278\pi$
$110$	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	0.978189	−	0.207716i	$-0.0666029\pi$
$113$	34.9405	+	60.5187i	0.309208	+	0.535563i	−0.668982	+	0.743279i	$0.733270\pi$
$114$	124.463	+	71.8590i	1.09178	+	0.630342i
$115$	−27.5724	−	102.901i	−0.239760	−	0.894795i
$116$			28.6087i			0.246627i
$117$	74.4751	+	11.8257i	0.636540	+	0.101074i
$118$	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	0.754973	−	0.655756i	$-0.227650\pi$
$127$	71.6989	+	41.3954i	0.564558	+	0.325948i	−0.190415	+	0.981704i	$0.560983\pi$
$128$	2.92820	+	10.9282i	0.0228766	+	0.0853766i
$129$			46.0614i			0.357065i
$130$	91.6249	−	35.1302i	0.704807	−	0.270233i
$131$	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	$-0.168793\pi$
$137$	185.891	+	49.8094i	1.35687	+	0.363572i	0.494204	+	0.869346i	$0.335459\pi$
$138$	76.7856	−	76.7856i	0.556417	−	0.556417i
$139$	−96.5464	−	167.223i	−0.694578	−	1.20305i	−0.970323	−	0.241814i	$-0.922258\pi$
$139$	−96.5464	−	167.223i	−0.694578	−	1.20305i	0.275744	−	0.961231i	$-0.411076\pi$
$140$	−94.8571	−	54.7658i	−0.677551	−	0.391184i
$141$	10.6903	+	39.8967i	0.0758176	+	0.282955i
$142$		−	80.8582i		−	0.569424i
$143$	−124.401	−	55.4453i	−0.869935	−	0.387729i
$144$	−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	−0.745197	−	0.666844i	$-0.767645\pi$
$149$	34.8041	−	129.891i	0.233585	−	0.871750i	0.978782	−	0.204905i	$-0.0656887\pi$
$150$	−18.3354	−	4.91294i	−0.122236	−	0.0327530i
$151$	26.5821	−	26.5821i	0.176041	−	0.176041i	−0.613587	−	0.789627i	$-0.710274\pi$
$151$	26.5821	−	26.5821i	0.176041	−	0.176041i	0.789627	+	0.613587i	$0.210274\pi$
$152$	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
$156$	77.7102	+	62.9790i	0.498142	+	0.403711i
$157$	−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	$-0.295015\pi$
$163$	117.437	+	31.4672i	0.720474	+	0.193050i	0.120091	+	0.992763i	$0.461681\pi$
$164$	−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	$-0.142670\pi$
$167$	−16.0213	−	59.7923i	−0.0959359	−	0.358038i	−0.997160	+	0.0753164i	$0.976003\pi$
$168$		−	111.649i		−	0.664580i
$169$	−35.0073	−	165.334i	−0.207144	−	0.978310i
$170$	−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	−0.558387	+	0.829580i	$0.688580\pi$
$173$	−269.191	+	155.418i	−1.55602	+	0.898368i	−0.997631	+	0.0687875i	$0.978087\pi$
$174$	−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	0.338888	−	0.940827i	$-0.389949\pi$
$179$	−54.8543	−	31.6701i	−0.306449	−	0.176928i	−0.645336	+	0.763899i	$0.723283\pi$
$180$	−16.0265	−	59.8118i	−0.0890362	−	0.332288i
$181$		−	186.504i		−	1.03041i	−0.857067	−	0.515205i	$-0.827716\pi$
$181$		−	186.504i		−	1.03041i	0.857067	−	0.515205i	$-0.172284\pi$
$182$	−118.771	+	146.553i	−0.652590	+	0.805235i
$183$	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	0.999689	−	0.0249353i	$-0.00793798\pi$
$191$	91.3457	+	158.215i	0.478250	+	0.828353i	−0.521439	+	0.853288i	$0.674605\pi$
$192$	−26.6539	−	15.3886i	−0.138822	−	0.0801491i
$193$	−23.5921	−	88.0470i	−0.122239	−	0.456202i	0.877487	−	0.479600i	$-0.159218\pi$
$193$	−23.5921	−	88.0470i	−0.122239	−	0.456202i	−0.999726	+	0.0233980i	$0.992552\pi$
$194$		−	77.5856i		−	0.399926i
$195$	−108.672	+	243.824i	−0.557292	+	1.25038i
$196$	112.558			0.574278
$197$	208.450	−	55.8541i	1.05812	−	0.283523i	0.312519	−	0.949912i	$-0.398827\pi$
$197$	208.450	−	55.8541i	1.05812	−	0.283523i	0.745605	+	0.666388i	$0.232161\pi$
$198$	−42.9720	+	74.4296i	−0.217030	+	0.375907i
$199$	−67.9737	+	39.2446i	−0.341576	+	0.197209i	−0.660969	−	0.750413i	$-0.729854\pi$
$199$	−67.9737	+	39.2446i	−0.341576	+	0.197209i	0.319393	+	0.947623i	$0.396521\pi$
$200$	−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
$208$	18.6161	+	48.5535i	0.0895004	+	0.233430i
$209$	276.746			1.32414
$210$	287.812	−	77.1189i	1.37053	−	0.367233i
$211$	66.1990	−	114.660i	0.313739	−	0.543412i	−0.665429	−	0.746461i	$-0.731752\pi$
$211$	66.1990	−	114.660i	0.313739	−	0.543412i	0.979169	+	0.203048i	$0.0650849\pi$
$212$	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
$221$	−9.96533	+	62.7592i	−0.0450920	+	0.283978i
$222$	330.141			1.48712
$223$	−115.427	+	30.9286i	−0.517610	+	0.138693i	−0.508161	−	0.861262i	$-0.669675\pi$
$223$	−115.427	+	30.9286i	−0.517610	+	0.138693i	−0.00944934	+	0.999955i	$0.503008\pi$
$224$	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	0.102464	+	0.994737i	$0.467327\pi$
$227$	−109.786	+	409.729i	−0.483641	+	1.80497i	−0.586105	+	0.810235i	$0.699339\pi$
$228$	−196.322	−	52.6044i	−0.861063	−	0.230721i
$229$	−158.206	+	158.206i	−0.690856	+	0.690856i	−0.962420	−	0.271564i	$-0.912459\pi$
$229$	−158.206	+	158.206i	−0.690856	+	0.690856i	0.271564	+	0.962420i	$0.412459\pi$
$230$	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	$-0.886232\pi$
$233$		−	163.030i		−	0.699701i	0.936806	−	0.349850i	$-0.113768\pi$
$234$	−106.063	+	11.1056i	−0.453262	+	0.0474600i
$235$	−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	$-0.434873\pi$
$239$	−185.455	−	185.455i	−0.775962	−	0.775962i	−0.979142	+	0.203179i	$0.934873\pi$
$240$	21.2586	−	79.3381i	0.0885774	−	0.330575i
$241$	438.820	+	117.581i	1.82083	+	0.487890i	0.996891	−	0.0787895i	$-0.0251055\pi$
$241$	438.820	+	117.581i	1.82083	+	0.487890i	0.823938	+	0.566679i	$0.191772\pi$
$242$	−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
$247$	201.736	+	277.895i	0.816745	+	1.12508i
$248$	−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	−0.514817	+	0.857300i	$0.672140\pi$
$251$	−380.182	+	219.498i	−1.51467	+	0.874495i	−0.999852	+	0.0171951i	$0.994526\pi$
$252$	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	−0.473733	−	0.880669i	$-0.657094\pi$
$257$	−378.633	−	218.604i	−1.47328	−	0.850599i	−0.999548	+	0.0300694i	$0.990427\pi$
$258$	−16.8596	−	62.9210i	−0.0653474	−	0.243880i
$259$			622.610i			2.40390i
$260$	−112.303	+	81.5258i	−0.431936	+	0.313561i
$261$	82.9743			0.317909
$262$	−65.3652	+	17.5145i	−0.249485	+	0.0668494i
$263$	143.980	−	249.380i	0.547451	−	0.948213i	−0.450997	−	0.892525i	$-0.648931\pi$
$263$	143.980	−	249.380i	0.547451	−	0.948213i	0.998448	−	0.0556879i	$-0.0177352\pi$
$264$	−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	−0.985808	−	0.167878i	$-0.946309\pi$
$269$	−171.700	−	297.393i	−0.638290	−	1.10555i	0.347518	−	0.937673i	$-0.387025\pi$
$270$	−80.4616	−	46.4545i	−0.298006	−	0.172054i
$271$	2.15014	+	8.02443i	0.00793410	+	0.0296105i	0.969779	−	0.243983i	$-0.0784542\pi$
$271$	2.15014	+	8.02443i	0.00793410	+	0.0296105i	−0.961845	+	0.273594i	$0.911788\pi$
$272$		−	19.5524i		−	0.0718840i
$273$	−53.4398	−	510.372i	−0.195750	−	1.86950i
$274$	−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	0.395722	−	0.918370i	$-0.370494\pi$
$277$	384.730	−	222.124i	1.38892	−	0.801891i	0.993193	+	0.116480i	$0.0371610\pi$
$278$	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	$-0.885128\pi$
$281$	−163.678	+	163.678i	−0.582486	+	0.582486i	0.353100	+	0.935586i	$0.385128\pi$
$282$	−29.2064	−	50.5869i	−0.103569	−	0.179386i
$283$	401.956	+	232.070i	1.42034	+	0.820034i	0.996328	−	0.0856229i	$-0.0272880\pi$
$283$	401.956	+	232.070i	1.42034	+	0.820034i	0.424012	+	0.905656i	$0.360621\pi$
$284$	29.5961	+	110.454i	0.104212	+	0.388924i
$285$		−	542.418i		−	1.90322i
$286$	190.229	+	30.2058i	0.665136	+	0.105615i
$287$	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	$-0.451263\pi$
$293$	−61.3995	−	16.4519i	−0.209555	−	0.0561500i	−0.362069	+	0.932151i	$0.617930\pi$
$294$	−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
$299$	242.270	−	92.8898i	0.810269	−	0.310668i
$300$	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	$-0.700578\pi$
$307$	67.1395	−	67.1395i	0.218695	−	0.218695i	0.807948	+	0.589253i	$0.200578\pi$
$308$	−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	$-0.821297\pi$
$311$		−	331.141i		−	1.06476i	0.846505	−	0.532381i	$-0.178703\pi$
$312$	−129.206	−	57.5870i	−0.414122	−	0.184574i
$313$	−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	−0.999820	−	0.0189927i	$-0.993954\pi$
$317$	−322.964	−	322.964i	−1.01881	−	1.01881i	−0.0189927	−	0.999820i	$-0.506046\pi$
$318$	−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
$325$	−35.2370	−	28.5572i	−0.108421	−	0.0878684i
$326$	−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	−0.457826	−	0.889042i	$-0.651372\pi$
$331$	126.834	−	473.350i	0.383184	−	1.43006i	0.841010	−	0.541020i	$-0.181962\pi$
$332$	−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	$0.264992\pi$
$337$			498.500i			1.47923i	−0.673031	+	0.739614i	$0.735008\pi$
$338$	108.338	+	213.038i	0.320525	+	0.630289i
$339$	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	0.984071	−	0.177777i	$-0.0568905\pi$
$347$	117.312	+	203.191i	0.338076	+	0.585565i	−0.645995	+	0.763342i	$0.723557\pi$
$348$	95.3168	+	55.0312i	0.273899	+	0.158136i
$349$	45.7756	+	170.837i	0.131162	+	0.489504i	0.999984	−	0.00562078i	$-0.00178916\pi$
$349$	45.7756	+	170.837i	0.131162	+	0.489504i	−0.868822	+	0.495124i	$0.835122\pi$
$350$			50.6264i			0.144647i
$351$	−100.747	+	124.312i	−0.287027	+	0.354165i
$352$	−59.2653			−0.168367
$353$	217.243	−	58.2100i	0.615418	−	0.164901i	0.0623743	−	0.998053i	$-0.480133\pi$
$353$	217.243	−	58.2100i	0.615418	−	0.164901i	0.553044	+	0.833152i	$0.313466\pi$
$354$	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	$-0.556265\pi$
$359$	290.278	−	290.278i	0.808574	−	0.808574i	0.984418	+	0.175844i	$0.0562653\pi$
$360$	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
$364$	108.603	−	243.668i	0.298359	−	0.669418i
$365$	96.6115			0.264689
$366$	−295.750	+	79.2461i	−0.808061	+	0.216519i
$367$	110.372	−	191.170i	0.300741	−	0.520898i	−0.675563	−	0.737302i	$-0.736099\pi$
$367$	110.372	−	191.170i	0.300741	−	0.520898i	0.976304	+	0.216404i	$0.0694328\pi$
$368$	−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	0.904676	−	0.426101i	$-0.140113\pi$
$373$	31.0796	+	53.8315i	0.0833235	+	0.144320i	−0.821352	+	0.570422i	$0.806780\pi$
$374$	−62.7209	−	36.2119i	−0.167703	−	0.0968233i
$375$	−114.324	−	426.662i	−0.304863	−	1.13777i
$376$		−	30.3667i		−	0.0807625i
$377$	−66.5728	−	173.632i	−0.176586	−	0.460562i
$378$	178.604			0.472497
$379$	140.323	−	37.5994i	0.370245	−	0.0992069i	−0.0688986	−	0.997624i	$-0.521949\pi$
$379$	140.323	−	37.5994i	0.370245	−	0.0992069i	0.439144	+	0.898417i	$0.355282\pi$
$380$	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	0.558837	+	0.829277i	$0.311248\pi$
$383$	−130.131	+	485.657i	−0.339769	+	1.26803i	−0.898606	+	0.438756i	$0.855419\pi$
$384$	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	$0.119372\pi$
$389$			284.973i			0.732579i	−0.930501	+	0.366289i	$0.880628\pi$
$390$	59.2030	−	372.846i	0.151803	−	0.956015i
$391$	−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	$-0.295046\pi$
$397$	285.958	+	76.6221i	0.720296	+	0.193003i	0.119992	+	0.992775i	$0.461713\pi$
$398$	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	0.999008	+	0.0445319i	$0.0141796\pi$
$401$	62.5992	+	233.623i	0.156108	+	0.582602i	−0.842900	+	0.538070i	$0.819154\pi$
$402$			33.2554i			0.0827248i
$403$	−347.513	+	36.3873i	−0.862316	+	0.0902910i
$404$	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	$-0.839995\pi$
$409$	50.5043	−	188.485i	0.123483	−	0.460843i	0.999781	+	0.0209255i	$0.00666128\pi$
$410$	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
$416$	−43.2019	−	59.5113i	−0.103851	−	0.143056i
$417$	−742.859			−1.78144
$418$	−378.042	+	101.296i	−0.904407	+	0.242335i
$419$	−23.9555	+	41.4921i	−0.0571730	+	0.0990265i	−0.893195	−	0.449669i	$-0.851542\pi$
$419$	−23.9555	+	41.4921i	−0.0571730	+	0.0990265i	0.836022	+	0.548695i	$0.184875\pi$
$420$	−364.930	+	210.693i	−0.868882	+	0.501649i
$421$	−477.018	−	477.018i	−1.13306	−	1.13306i	−0.989666	−	0.143394i	$-0.954198\pi$
$421$	−477.018	−	477.018i	−1.13306	−	1.13306i	−0.143394	−	0.989666i	$-0.545802\pi$
$422$	−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
$429$	−424.024	+	307.817i	−0.988400	+	0.717522i
$430$	90.3753			0.210175
$431$	−75.2127	+	20.1532i	−0.174507	+	0.0467591i	−0.345015	−	0.938597i	$-0.612126\pi$
$431$	−75.2127	+	20.1532i	−0.174507	+	0.0467591i	0.170507	+	0.985356i	$0.445459\pi$
$432$	24.6170	−	42.6379i	0.0569838	−	0.0986988i
$433$	−430.937	+	248.802i	−0.995235	+	0.574599i	−0.906835	−	0.421486i	$-0.861509\pi$
$433$	−430.937	+	248.802i	−0.995235	+	0.574599i	−0.0884003	+	0.996085i	$0.528175\pi$
$434$	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	0.656042	−	0.754725i	$-0.272230\pi$
$439$	145.068	+	83.7551i	0.330451	+	0.190786i	−0.325590	+	0.945511i	$0.605563\pi$
$440$	−40.9359	−	152.775i	−0.0930361	−	0.347216i
$441$		−	326.455i		−	0.740260i
$442$	−9.35857	−	89.3782i	−0.0211732	−	0.202213i
$443$	−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	$-0.324351\pi$
$449$	248.050	+	66.4648i	0.552450	+	0.148029i	0.0282145	+	0.999602i	$0.491018\pi$
$450$	−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
$455$	703.146	+	111.650i	1.54538	+	0.245385i
$456$	287.436			0.630342
$457$	−84.1413	+	22.5456i	−0.184117	+	0.0493339i	−0.349699	−	0.936862i	$-0.613716\pi$
$457$	−84.1413	+	22.5456i	−0.184117	+	0.0493339i	0.165583	+	0.986196i	$0.447050\pi$
$458$	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	−0.676122	−	0.736790i	$-0.736341\pi$
$461$	128.071	−	477.968i	0.277812	−	1.03681i	0.953934	−	0.300018i	$-0.0969925\pi$
$462$	564.931	+	151.373i	1.22279	+	0.327647i
$463$	−399.472	+	399.472i	−0.862789	+	0.862789i	−0.991661	−	0.128872i	$-0.958864\pi$
$463$	−399.472	+	399.472i	−0.862789	+	0.862789i	0.128872	+	0.991661i	$0.458864\pi$
$464$	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	$-0.855413\pi$
$467$		−	409.816i		−	0.877550i	0.898597	−	0.438775i	$-0.144587\pi$
$468$	140.820	−	53.9925i	0.300898	−	0.115369i
$469$	−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	0.946805	+	0.321809i	$0.104291\pi$
$479$	137.833	+	514.401i	0.287752	+	1.07391i	−0.659053	+	0.752097i	$0.729043\pi$
$480$			116.159i			0.241998i
$481$	720.514	+	321.132i	1.49795	+	0.667635i
$482$	−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	−0.519137	−	0.854691i	$-0.673747\pi$
$487$	174.246	−	650.294i	0.357794	−	1.33531i	0.876932	−	0.480615i	$-0.159587\pi$
$488$	−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	0.599995	−	0.800003i	$-0.295169\pi$
$491$	101.720	+	58.7282i	0.207170	+	0.119609i	−0.392826	+	0.919613i	$0.628502\pi$
$492$	9.97256	+	37.2181i	0.0202694	+	0.0756465i
$493$			69.9214i			0.141828i
$494$	−377.293	−	305.771i	−0.763752	−	0.618970i
$495$	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	$-0.179332\pi$
$499$	155.387	+	155.387i	0.311396	+	0.311396i	−0.534054	+	0.845450i	$0.679332\pi$
$500$	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	0.658028	−	0.752994i	$-0.271391\pi$
$503$	−162.518	−	281.490i	−0.323098	−	0.559622i	−0.981126	+	0.193372i	$0.938058\pi$
$504$	−145.788	−	84.1708i	−0.289262	−	0.167006i
$505$	19.4280	+	72.5062i	0.0384712	+	0.143577i
$506$			295.720i			0.584426i
$507$	−618.190	−	201.399i	−1.21931	−	0.397236i
$508$	165.582			0.325948
$509$	−561.220	+	150.378i	−1.10259	+	0.295439i	−0.763820	−	0.645429i	$-0.776679\pi$
$509$	−561.220	+	150.378i	−1.10259	+	0.295439i	−0.338773	+	0.940868i	$0.610012\pi$
$510$	−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
$520$	123.569	−	152.472i	0.237632	−	0.293216i
$521$	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	−0.998260	−	0.0589705i	$-0.981218\pi$
$523$	−234.335	+	405.881i	−0.448060	+	0.776063i	0.550200	+	0.835033i	$0.314552\pi$
$524$	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
$533$	26.5020	−	59.4618i	0.0497224	−	0.111561i
$534$	−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	$-0.684809\pi$
$541$	155.599	−	155.599i	0.287614	−	0.287614i	0.836136	+	0.548522i	$0.184809\pi$
$542$	−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
$546$	259.809	+	677.621i	0.475841	+	1.24106i
$547$	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	−0.971978	−	0.235071i	$-0.924468\pi$
$557$	−138.000	−	515.023i	−0.247756	−	0.924637i	0.724223	−	0.689566i	$-0.242199\pi$
$558$			220.489i			0.395141i
$559$	24.4088	−	153.721i	0.0436652	−	0.274993i
$560$	−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	−0.126975	−	0.991906i	$-0.540527\pi$
$563$	376.396	−	217.312i	0.668554	−	0.385990i	0.795528	+	0.605916i	$0.207193\pi$
$564$	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	0.225353	−	0.974277i	$-0.427647\pi$
$569$	−287.755	−	166.135i	−0.505720	−	0.291978i	−0.731073	+	0.682300i	$0.760980\pi$
$570$	198.539	+	740.957i	0.348314	+	1.29992i
$571$		−	555.806i		−	0.973391i	−0.873572	−	0.486696i	$-0.838202\pi$
$571$		−	555.806i		−	0.973391i	0.873572	−	0.486696i	$-0.161798\pi$
$572$	−270.914	+	28.3667i	−0.473625	+	0.0495921i
$573$	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	$-0.135285\pi$
$577$	287.753	+	287.753i	0.498705	+	0.498705i	−0.412330	+	0.911035i	$0.635285\pi$
$578$	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
$585$	236.451	+	325.715i	0.404189	+	0.556778i
$586$	89.8951			0.153405
$587$	647.190	−	173.414i	1.10254	−	0.295424i	0.338741	−	0.940880i	$-0.389999\pi$
$587$	647.190	−	173.414i	1.10254	−	0.295424i	0.763798	+	0.645455i	$0.223332\pi$
$588$	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	$-0.776241\pi$
$593$	−69.0570	+	69.0570i	−0.116454	+	0.116454i	0.646479	+	0.762932i	$0.276241\pi$
$594$	−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
$598$	−296.947	+	215.567i	−0.496568	+	0.360480i
$599$	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	−0.929953	−	0.367678i	$-0.880153\pi$
$601$	−88.0811	+	152.561i	−0.146558	+	0.253845i	0.783395	+	0.621524i	$0.213486\pi$
$602$	−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	0.966192	−	0.257824i	$-0.0830054\pi$
$607$	157.707	+	273.157i	0.259814	+	0.450011i	−0.706378	+	0.707835i	$0.749672\pi$
$608$	129.408	+	74.7139i	0.212842	+	0.122885i
$609$	−146.142	−	545.411i	−0.239971	−	0.895585i
$610$		−	424.795i		−	0.696385i
$611$	−14.5347	−	138.812i	−0.0237884	−	0.227189i
$612$	−56.7082			−0.0926605
$613$	872.008	−	233.654i	1.42253	−	0.381165i	0.536147	−	0.844125i	$-0.319879\pi$
$613$	872.008	−	233.654i	1.42253	−	0.381165i	0.886379	+	0.462960i	$0.153213\pi$
$614$	−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	0.661162	+	0.750243i	$0.270064\pi$
$617$	−176.797	+	659.815i	−0.286543	+	1.06939i	−0.947705	+	0.319149i	$0.896603\pi$
$618$	−424.839	−	113.835i	−0.687442	−	0.184199i
$619$	−413.378	+	413.378i	−0.667816	+	0.667816i	−0.957210	−	0.289394i	$-0.906546\pi$
$619$	−413.378	+	413.378i	−0.667816	+	0.667816i	0.289394	+	0.957210i	$0.406546\pi$
$620$	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
$624$	197.577	+	31.3726i	0.316630	+	0.0502766i
$625$	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	$-0.417090\pi$
$631$	−1.62079	−	0.434289i	−0.00256861	−	0.000688256i	−0.260103	+	0.965581i	$0.583757\pi$
$632$	−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
$637$	−683.138	+	261.925i	−1.07243	+	0.411185i
$638$	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	−0.685024	+	0.728521i	$0.740208\pi$
$641$	−1063.07	+	613.763i	−1.65845	+	0.957508i	−0.973429	+	0.228988i	$0.926458\pi$
$642$	−625.952	−	625.952i	−0.975003	−	0.975003i
$643$	−156.134	+	582.701i	−0.242822	+	0.906223i	0.731644	+	0.681687i	$0.238753\pi$
$643$	−156.134	+	582.701i	−0.242822	+	0.906223i	−0.974466	+	0.224536i	$0.927913\pi$
$644$	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	0.954529	−	0.298119i	$-0.0963592\pi$
$647$	759.328	+	438.399i	1.17361	+	0.677587i	0.219086	+	0.975706i	$0.429693\pi$
$648$	72.8818	+	271.999i	0.112472	+	0.419751i
$649$		−	659.057i		−	1.01550i
$650$	58.5873	+	26.1123i	0.0901342	+	0.0401727i
$651$	−1060.98			−1.62977
$652$	234.875	−	62.9345i	0.360237	−	0.0965252i
$653$	−75.1803	+	130.216i	−0.115131	+	0.199412i	−0.917832	−	0.396969i	$-0.870062\pi$
$653$	−75.1803	+	130.216i	−0.115131	+	0.199412i	0.802701	+	0.596381i	$0.203395\pi$
$654$	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	−0.979883	−	0.199574i	$-0.936044\pi$
$659$	−436.771	−	756.509i	−0.662778	−	1.14796i	0.317105	−	0.948390i	$-0.397289\pi$
$660$	372.618	+	215.131i	0.564573	+	0.325956i
$661$	−123.160	−	459.641i	−0.186324	−	0.695372i	−0.994343	−	0.106216i	$-0.966127\pi$
$661$	−123.160	−	459.641i	−0.186324	−	0.695372i	0.808019	−	0.589157i	$-0.200540\pi$
$662$			693.033i			1.04688i
$663$	189.928	+	153.924i	0.286468	+	0.232163i
$664$	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	−0.426355	−	0.904556i	$-0.640203\pi$
$673$	−957.612	−	552.878i	−1.42290	−	0.821512i	−0.996546	+	0.0830435i	$0.973536\pi$
$674$	−182.464	−	680.964i	−0.270718	−	1.01033i
$675$			42.9433i			0.0636197i
$676$	−225.969	−	251.360i	−0.334274	−	0.371835i
$677$	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	$-0.138127\pi$
$683$	1012.79	+	271.376i	1.48285	+	0.397329i	0.575535	+	0.817777i	$0.304794\pi$
$684$	−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
$689$	−630.623	+	778.130i	−0.915273	+	1.12936i
$690$	579.606			0.840009
$691$	391.766	−	104.973i	0.566956	−	0.151915i	0.0360556	−	0.999350i	$-0.488521\pi$
$691$	391.766	−	104.973i	0.566956	−	0.151915i	0.530900	+	0.847434i	$0.321854\pi$
$692$	−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	$0.0739378\pi$
$701$			322.739i			0.460398i	−0.973144	+	0.230199i	$0.926062\pi$
$702$	92.1211	−	206.689i	0.131227	−	0.294429i
$703$	−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	$-0.438559\pi$
$709$	−94.1274	−	25.2214i	−0.132761	−	0.0355732i	−0.324588	+	0.945856i	$0.605226\pi$
$710$	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
$715$	−260.250	−	678.772i	−0.363987	−	0.949331i
$716$	−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	0.145419	−	0.989370i	$-0.453547\pi$
$719$	772.888	−	446.227i	1.07495	−	0.620622i	0.929529	+	0.368748i	$0.120214\pi$
$720$	−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	$0.270995\pi$
$727$			1093.66i			1.50435i	−0.658964	+	0.752175i	$0.729005\pi$
$728$	−59.1653	+	372.608i	−0.0812710	+	0.511825i
$729$	−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	$-0.207869\pi$
$733$	136.804	+	136.804i	0.186636	+	0.186636i	−0.607604	+	0.794240i	$0.707869\pi$
$734$	−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	−0.951469	−	0.307745i	$-0.900426\pi$
$739$	−207.914	−	775.945i	−0.281345	−	1.04999i	0.670124	−	0.742249i	$-0.266241\pi$
$740$		−	647.758i		−	0.875349i
$741$	1313.93	−	137.578i	1.77318	−	0.185666i
$742$	1117.97			1.50670
$743$	−690.270	+	184.957i	−0.929031	+	0.248933i	−0.691441	−	0.722432i	$-0.743024\pi$
$743$	−690.270	+	184.957i	−0.929031	+	0.248933i	−0.237590	+	0.971366i	$0.576357\pi$
$744$	−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	0.485869	−	0.874032i	$-0.338503\pi$
$751$	−21.1260	−	12.1971i	−0.0281305	−	0.0162412i	−0.513999	+	0.857791i	$0.671837\pi$
$752$	11.1150	+	41.4817i	0.0147806	+	0.0551618i
$753$			1688.89i			2.24288i
$754$	154.494	+	212.818i	0.204899	+	0.282252i
$755$	200.652			0.265764
$756$	−243.978	+	65.3736i	−0.322722	+	0.0864730i
$757$	512.612	−	887.871i	0.677163	−	1.17288i	−0.298669	−	0.954357i	$-0.596543\pi$
$757$	512.612	−	887.871i	0.677163	−	1.17288i	0.975832	−	0.218524i	$-0.0701241\pi$
$758$	−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	$-0.335138\pi$
$761$	372.443	+	99.7959i	0.489413	+	0.131138i	−0.00566927	+	0.999984i	$0.501805\pi$
$762$	−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

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	26.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.92358 - 3.33174i) q^{3} +(1.73205 - 1.00000i) q^{4} +(3.77418 + 3.77418i) q^{5} +(-1.40816 + 5.25532i) q^{6} +(-9.91095 - 2.65563i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.90031 - 5.02349i) q^{9} +O(q^{10})\)	\(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} +(-8.18513 + 10.0997i) q^{13} +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} +(7.48435 - 16.7924i) q^{26} +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} +(17.9048 + 46.6982i) q^{39} -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} +(-4.07737 + 25.6783i) q^{52} +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} +(-69.0102 + 7.22589i) q^{65} -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} +(-41.5511 - 57.2374i) q^{78} +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} +(107.943 - 78.3608i) q^{91} -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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 6 q^{5} + 6 q^{6} - 2 q^{7} - 16 q^{8} - 42 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 6 * q^5 + 6 * q^6 - 2 * q^7 - 16 * q^8 - 42 * q^9	\( 8 q - 4 q^{2} + 6 q^{5} + 6 q^{6} - 2 q^{7} - 16 q^{8} - 42 q^{9} - 18 q^{10} - 18 q^{11} + 36 q^{13} + 20 q^{14} + 66 q^{15} + 16 q^{16} - 42 q^{17} + 84 q^{18} + 46 q^{19} + 24 q^{20} - 102 q^{21} - 42 q^{22} - 36 q^{23} - 12 q^{24} + 40 q^{26} + 72 q^{27} - 4 q^{28} - 6 q^{29} - 192 q^{30} + 32 q^{31} + 16 q^{32} + 42 q^{33} - 60 q^{34} - 78 q^{35} - 48 q^{36} - 106 q^{37} + 12 q^{39} - 24 q^{40} + 132 q^{41} + 102 q^{42} - 108 q^{43} + 84 q^{44} + 240 q^{45} + 90 q^{46} + 60 q^{47} + 258 q^{49} + 194 q^{50} + 32 q^{52} - 132 q^{53} - 270 q^{54} - 162 q^{55} - 12 q^{56} - 294 q^{57} - 24 q^{58} + 18 q^{59} - 120 q^{60} + 36 q^{61} - 12 q^{62} - 72 q^{63} - 300 q^{65} + 108 q^{66} - 74 q^{67} + 60 q^{68} + 258 q^{69} + 156 q^{70} - 174 q^{71} + 132 q^{72} + 166 q^{73} - 32 q^{74} + 6 q^{75} - 92 q^{76} + 126 q^{78} - 96 q^{79} + 48 q^{80} - 12 q^{81} - 252 q^{82} - 240 q^{83} - 132 q^{84} - 24 q^{85} + 132 q^{86} + 360 q^{87} - 12 q^{88} + 294 q^{89} + 298 q^{91} - 216 q^{92} + 270 q^{93} - 60 q^{94} + 714 q^{95} - 58 q^{97} - 250 q^{98} + 252 q^{99}+O(q^{100}) \) 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 + 36 * q^13 + 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 + 40 * q^26 + 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 + 12 * q^39 - 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 + 32 * q^52 - 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 - 300 * q^65 + 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 + 126 * q^78 - 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 + 298 * q^91 - 216 * q^92 + 270 * q^93 - 60 * q^94 + 714 * q^95 - 58 * q^97 - 250 * q^98 + 252 * q^99

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