LMFDB - Embedded newform 138.3.c.a.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,3,Mod(47,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("138.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	138.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.76022764817$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} + 8 x^{13} - 119 x^{12} + 416 x^{11} - 774 x^{10} - 1284 x^{9} + \cdots + 43046721 $ x^16 - 4x^15 + 10x^14 + 8x^13 - 119x^12 + 416x^11 - 774x^10 - 1284x^9 + 7956x^8 - 11556x^7 - 62694x^6 + 303264x^5 - 780759x^4 + 472392x^3 + 5314410x^2 - 19131876*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.3
Root			$-0.752365 - 2.90413i$ of defining polynomial
Character	$\chi$	$=$	138.47
Dual form			138.3.c.a.47.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-0.752365 - 2.90413i) q^{3} -2.00000 q^{4} +9.12709i q^{5} +(-4.10705 + 1.06400i) q^{6} -11.5474 q^{7} +2.82843i q^{8} +(-7.86789 + 4.36992i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-0.752365 - 2.90413i) q^{3} -2.00000 q^{4} +9.12709i q^{5} +(-4.10705 + 1.06400i) q^{6} -11.5474 q^{7} +2.82843i q^{8} +(-7.86789 + 4.36992i) q^{9} +12.9076 q^{10} -3.58264i q^{11} +(1.50473 + 5.80825i) q^{12} -14.9991 q^{13} +16.3304i q^{14} +(26.5062 - 6.86690i) q^{15} +4.00000 q^{16} -0.210098i q^{17} +(6.18001 + 11.1269i) q^{18} +22.3543 q^{19} -18.2542i q^{20} +(8.68783 + 33.5350i) q^{21} -5.06663 q^{22} -4.79583i q^{23} +(8.21411 - 2.12801i) q^{24} -58.3037 q^{25} +21.2119i q^{26} +(18.6103 + 19.5616i) q^{27} +23.0947 q^{28} -23.9401i q^{29} +(-9.71126 - 37.4854i) q^{30} -40.1198 q^{31} -5.65685i q^{32} +(-10.4045 + 2.69546i) q^{33} -0.297123 q^{34} -105.394i q^{35} +(15.7358 - 8.73985i) q^{36} -14.3518 q^{37} -31.6138i q^{38} +(11.2848 + 43.5592i) q^{39} -25.8153 q^{40} +41.9190i q^{41} +(47.4257 - 12.2865i) q^{42} -18.5236 q^{43} +7.16529i q^{44} +(-39.8847 - 71.8110i) q^{45} -6.78233 q^{46} +21.5610i q^{47} +(-3.00946 - 11.6165i) q^{48} +84.3418 q^{49} +82.4539i q^{50} +(-0.610151 + 0.158070i) q^{51} +29.9982 q^{52} +72.8659i q^{53} +(27.6643 - 26.3190i) q^{54} +32.6991 q^{55} -32.6609i q^{56} +(-16.8186 - 64.9198i) q^{57} -33.8565 q^{58} -55.5555i q^{59} +(-53.0124 + 13.7338i) q^{60} +74.4322 q^{61} +56.7380i q^{62} +(90.8535 - 50.4611i) q^{63} -8.00000 q^{64} -136.898i q^{65} +(3.81195 + 14.7141i) q^{66} -94.2027 q^{67} +0.420196i q^{68} +(-13.9277 + 3.60821i) q^{69} -149.049 q^{70} +62.3455i q^{71} +(-12.3600 - 22.2538i) q^{72} -60.5338 q^{73} +20.2966i q^{74} +(43.8656 + 169.321i) q^{75} -44.7087 q^{76} +41.3701i q^{77} +(61.6020 - 15.9591i) q^{78} +51.1651 q^{79} +36.5083i q^{80} +(42.8075 - 68.7642i) q^{81} +59.2824 q^{82} +5.69524i q^{83} +(-17.3757 - 67.0700i) q^{84} +1.91758 q^{85} +26.1963i q^{86} +(-69.5252 + 18.0117i) q^{87} +10.1333 q^{88} -41.8683i q^{89} +(-101.556 + 56.4054i) q^{90} +173.200 q^{91} +9.59166i q^{92} +(30.1847 + 116.513i) q^{93} +30.4918 q^{94} +204.030i q^{95} +(-16.4282 + 4.25602i) q^{96} -61.6132 q^{97} -119.277i q^{98} +(15.6559 + 28.1879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9	$ 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9} - 8 q^{12} - 8 q^{13} + 28 q^{15} + 64 q^{16} + 16 q^{18} + 40 q^{19} + 4 q^{21} + 16 q^{22} + 16 q^{24} - 192 q^{25} - 80 q^{27} - 24 q^{30} + 136 q^{31} - 84 q^{33} - 16 q^{34} + 8 q^{36} - 136 q^{37} + 156 q^{39} + 128 q^{42} + 72 q^{43} + 4 q^{45} + 16 q^{48} + 224 q^{49} - 4 q^{51} + 16 q^{52} - 176 q^{54} - 96 q^{55} - 160 q^{57} - 56 q^{60} + 48 q^{61} + 204 q^{63} - 128 q^{64} - 144 q^{66} - 304 q^{67} - 176 q^{70} - 32 q^{72} + 408 q^{73} + 68 q^{75} - 80 q^{76} + 328 q^{78} + 312 q^{79} + 164 q^{81} + 160 q^{82} - 8 q^{84} - 464 q^{85} - 268 q^{87} - 32 q^{88} + 32 q^{90} - 72 q^{91} - 108 q^{93} - 32 q^{96} + 168 q^{97} - 60 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9 - 8 * q^12 - 8 * q^13 + 28 * q^15 + 64 * q^16 + 16 * q^18 + 40 * q^19 + 4 * q^21 + 16 * q^22 + 16 * q^24 - 192 * q^25 - 80 * q^27 - 24 * q^30 + 136 * q^31 - 84 * q^33 - 16 * q^34 + 8 * q^36 - 136 * q^37 + 156 * q^39 + 128 * q^42 + 72 * q^43 + 4 * q^45 + 16 * q^48 + 224 * q^49 - 4 * q^51 + 16 * q^52 - 176 * q^54 - 96 * q^55 - 160 * q^57 - 56 * q^60 + 48 * q^61 + 204 * q^63 - 128 * q^64 - 144 * q^66 - 304 * q^67 - 176 * q^70 - 32 * q^72 + 408 * q^73 + 68 * q^75 - 80 * q^76 + 328 * q^78 + 312 * q^79 + 164 * q^81 + 160 * q^82 - 8 * q^84 - 464 * q^85 - 268 * q^87 - 32 * q^88 + 32 * q^90 - 72 * q^91 - 108 * q^93 - 32 * q^96 + 168 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−0.752365	−	2.90413i	−0.250788	−	0.968042i
$3$	−0.752365	−	2.90413i	−0.250788	−	0.968042i
$4$	−2.00000			−0.500000
$5$			9.12709i			1.82542i	0.408611	+	0.912709i	$0.366013\pi$
$5$			9.12709i			1.82542i	−0.408611	+	0.912709i	$0.633987\pi$
$6$	−4.10705	+	1.06400i	−0.684509	+	0.177334i
$7$	−11.5474			−1.64962			−0.824812	−	0.565407i	$-0.808719\pi$
$7$	−11.5474			−1.64962			−0.824812	+	0.565407i	$0.808719\pi$
$8$			2.82843i			0.353553i
$9$	−7.86789	+	4.36992i	−0.874211	+	0.485547i
$10$	12.9076			1.29076
$11$		−	3.58264i		−	0.325695i	−0.986651	−	0.162847i	$-0.947932\pi$
$11$		−	3.58264i		−	0.325695i	0.986651	−	0.162847i	$-0.0520679\pi$
$12$	1.50473	+	5.80825i	0.125394	+	0.484021i
$13$	−14.9991			−1.15378			−0.576888	−	0.816823i	$-0.695733\pi$
$13$	−14.9991			−1.15378			−0.576888	+	0.816823i	$0.695733\pi$
$14$			16.3304i			1.16646i
$15$	26.5062	−	6.86690i	1.76708	−	0.457793i
$16$	4.00000			0.250000
$17$		−	0.210098i		−	0.0123587i	−0.999981	−	0.00617935i	$-0.998033\pi$
$17$		−	0.210098i		−	0.0123587i	0.999981	−	0.00617935i	$-0.00196696\pi$
$18$	6.18001	+	11.1269i	0.343334	+	0.618160i
$19$	22.3543			1.17654			0.588272	−	0.808663i	$-0.299809\pi$
$19$	22.3543			1.17654			0.588272	+	0.808663i	$0.299809\pi$
$20$		−	18.2542i		−	0.912709i
$21$	8.68783	+	33.5350i	0.413706	+	1.59691i
$22$	−5.06663			−0.230301
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	8.21411	−	2.12801i	0.342255	−	0.0886670i
$25$	−58.3037			−2.33215
$26$			21.2119i			0.815842i
$27$	18.6103	+	19.5616i	0.689272	+	0.724503i
$28$	23.0947			0.824812
$29$		−	23.9401i		−	0.825522i	−0.910839	−	0.412761i	$-0.864564\pi$
$29$		−	23.9401i		−	0.825522i	0.910839	−	0.412761i	$-0.135436\pi$
$30$	−9.71126	−	37.4854i	−0.323709	−	1.24951i
$31$	−40.1198			−1.29419			−0.647094	−	0.762411i	$-0.724016\pi$
$31$	−40.1198			−1.29419			−0.647094	+	0.762411i	$0.724016\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−10.4045	+	2.69546i	−0.315286	+	0.0816805i
$34$	−0.297123			−0.00873892
$35$		−	105.394i		−	3.01125i
$36$	15.7358	−	8.73985i	0.437105	−	0.242774i
$37$	−14.3518			−0.387888			−0.193944	−	0.981013i	$-0.562128\pi$
$37$	−14.3518			−0.387888			−0.193944	+	0.981013i	$0.562128\pi$
$38$		−	31.6138i		−	0.831942i
$39$	11.2848	+	43.5592i	0.289353	+	1.11690i
$40$	−25.8153			−0.645382
$41$			41.9190i			1.02241i	0.859457	+	0.511207i	$0.170802\pi$
$41$			41.9190i			1.02241i	−0.859457	+	0.511207i	$0.829198\pi$
$42$	47.4257	−	12.2865i	1.12918	−	0.292535i
$43$	−18.5236			−0.430782			−0.215391	−	0.976528i	$-0.569103\pi$
$43$	−18.5236			−0.430782			−0.215391	+	0.976528i	$0.569103\pi$
$44$			7.16529i			0.162847i
$45$	−39.8847	−	71.8110i	−0.886326	−	1.59580i
$46$	−6.78233			−0.147442
$47$			21.5610i			0.458744i	0.973339	+	0.229372i	$0.0736672\pi$
$47$			21.5610i			0.458744i	−0.973339	+	0.229372i	$0.926333\pi$
$48$	−3.00946	−	11.6165i	−0.0626971	−	0.242010i
$49$	84.3418			1.72126
$50$			82.4539i			1.64908i
$51$	−0.610151	+	0.158070i	−0.0119637	+	0.00309942i
$52$	29.9982			0.576888
$53$			72.8659i			1.37483i	0.726265	+	0.687414i	$0.241254\pi$
$53$			72.8659i			1.37483i	−0.726265	+	0.687414i	$0.758746\pi$
$54$	27.6643	−	26.3190i	0.512301	−	0.487389i
$55$	32.6991			0.594529
$56$		−	32.6609i		−	0.583230i
$57$	−16.8186	−	64.9198i	−0.295063	−	1.13894i
$58$	−33.8565			−0.583732
$59$		−	55.5555i		−	0.941618i	−0.882235	−	0.470809i	$-0.843962\pi$
$59$		−	55.5555i		−	0.941618i	0.882235	−	0.470809i	$-0.156038\pi$
$60$	−53.0124	+	13.7338i	−0.883540	+	0.228897i
$61$	74.4322			1.22020			0.610100	−	0.792325i	$-0.291129\pi$
$61$	74.4322			1.22020			0.610100	+	0.792325i	$0.291129\pi$
$62$			56.7380i			0.915128i
$63$	90.8535	−	50.4611i	1.44212	−	0.800970i
$64$	−8.00000			−0.125000
$65$		−	136.898i		−	2.10612i
$66$	3.81195	+	14.7141i	0.0577568	+	0.222941i
$67$	−94.2027			−1.40601			−0.703005	−	0.711185i	$-0.748159\pi$
$67$	−94.2027			−1.40601			−0.703005	+	0.711185i	$0.748159\pi$
$68$			0.420196i			0.00617935i
$69$	−13.9277	+	3.60821i	−0.201851	+	0.0522930i
$70$	−149.049			−2.12928
$71$			62.3455i			0.878106i	0.898461	+	0.439053i	$0.144686\pi$
$71$			62.3455i			0.878106i	−0.898461	+	0.439053i	$0.855314\pi$
$72$	−12.3600	−	22.2538i	−0.171667	−	0.309080i
$73$	−60.5338			−0.829230			−0.414615	−	0.909997i	$-0.636084\pi$
$73$	−60.5338			−0.829230			−0.414615	+	0.909997i	$0.636084\pi$
$74$			20.2966i			0.274278i
$75$	43.8656	+	169.321i	0.584875	+	2.25762i
$76$	−44.7087			−0.588272
$77$			41.3701i			0.537274i
$78$	61.6020	−	15.9591i	0.789770	−	0.204604i
$79$	51.1651			0.647659			0.323830	−	0.946115i	$-0.395030\pi$
$79$	51.1651			0.647659			0.323830	+	0.946115i	$0.395030\pi$
$80$			36.5083i			0.456354i
$81$	42.8075	−	68.7642i	0.528488	−	0.848941i
$82$	59.2824			0.722956
$83$			5.69524i			0.0686173i	0.999411	+	0.0343087i	$0.0109229\pi$
$83$			5.69524i			0.0686173i	−0.999411	+	0.0343087i	$0.989077\pi$
$84$	−17.3757	−	67.0700i	−0.206853	−	0.798453i
$85$	1.91758			0.0225598
$86$			26.1963i			0.304609i
$87$	−69.5252	+	18.0117i	−0.799140	+	0.207031i
$88$	10.1333			0.115151
$89$		−	41.8683i		−	0.470430i	−0.971943	−	0.235215i	$-0.924421\pi$
$89$		−	41.8683i		−	0.470430i	0.971943	−	0.235215i	$-0.0755794\pi$
$90$	−101.556	+	56.4054i	−1.12840	+	0.626727i
$91$	173.200			1.90330
$92$			9.59166i			0.104257i
$93$	30.1847	+	116.513i	0.324567	+	1.25283i
$94$	30.4918			0.324381
$95$			204.030i			2.14768i
$96$	−16.4282	+	4.25602i	−0.171127	+	0.0443335i
$97$	−61.6132			−0.635188			−0.317594	−	0.948227i	$-0.602875\pi$
$97$	−61.6132			−0.635188			−0.317594	+	0.948227i	$0.602875\pi$
$98$		−	119.277i		−	1.21711i
$99$	15.6559	+	28.1879i	0.158140	+	0.284726i
$100$	116.607			1.16607
$101$			146.746i			1.45293i	0.687202	+	0.726467i	$0.258839\pi$
$101$			146.746i			1.45293i	−0.687202	+	0.726467i	$0.741161\pi$
$102$	0.223545	+	0.862883i	0.00219162	+	0.00845964i
$103$	75.8078			0.735998			0.367999	−	0.929826i	$-0.380043\pi$
$103$	75.8078			0.735998			0.367999	+	0.929826i	$0.380043\pi$
$104$		−	42.4238i		−	0.407921i
$105$	−306.077	+	79.2946i	−2.91502	+	0.755187i
$106$	103.048			0.972151
$107$		−	68.4654i		−	0.639863i	−0.947441	−	0.319932i	$-0.896340\pi$
$107$		−	68.4654i		−	0.639863i	0.947441	−	0.319932i	$-0.103660\pi$
$108$	−37.2207	−	39.1232i	−0.344636	−	0.362252i
$109$	−100.417			−0.921255			−0.460627	−	0.887594i	$-0.652376\pi$
$109$	−100.417			−0.921255			−0.460627	+	0.887594i	$0.652376\pi$
$110$		−	46.2435i		−	0.420396i
$111$	10.7978	+	41.6796i	0.0972777	+	0.375492i
$112$	−46.1895			−0.412406
$113$		−	4.76149i		−	0.0421371i	−0.999778	−	0.0210685i	$-0.993293\pi$
$113$		−	4.76149i		−	0.0421371i	0.999778	−	0.0210685i	$-0.00670682\pi$
$114$	−91.8104	+	23.7851i	−0.805355	+	0.208641i
$115$	43.7720			0.380626
$116$			47.8803i			0.412761i
$117$	118.011	−	65.5448i	1.00864	−	0.560212i
$118$	−78.5673			−0.665824
$119$			2.42608i			0.0203872i
$120$	19.4225	+	74.9709i	0.161854	+	0.624757i
$121$	108.165			0.893923
$122$		−	105.263i		−	0.862811i
$123$	121.738	−	31.5384i	0.989740	−	0.256410i
$124$	80.2396			0.647094
$125$		−	303.966i		−	2.43173i
$126$	−71.3628	−	128.486i	−0.566371	−	1.01973i
$127$	−22.2552			−0.175238			−0.0876189	−	0.996154i	$-0.527926\pi$
$127$	−22.2552			−0.175238			−0.0876189	+	0.996154i	$0.527926\pi$
$128$			11.3137i			0.0883883i
$129$	13.9365	+	53.7949i	0.108035	+	0.417015i
$130$	−193.603			−1.48925
$131$			37.5709i			0.286801i	0.989665	+	0.143400i	$0.0458036\pi$
$131$			37.5709i			0.286801i	−0.989665	+	0.143400i	$0.954196\pi$
$132$	20.8089	−	5.39091i	0.157643	−	0.0408402i
$133$	−258.134			−1.94085
$134$			133.223i			0.994199i
$135$	−178.540	+	169.858i	−1.32252	+	1.25821i
$136$	0.594247			0.00436946
$137$		−	164.715i		−	1.20230i	−0.799136	−	0.601150i	$-0.794709\pi$
$137$		−	164.715i		−	1.20230i	0.799136	−	0.601150i	$-0.205291\pi$
$138$	5.10279	+	19.6967i	0.0369767	+	0.142730i
$139$	121.221			0.872093			0.436047	−	0.899924i	$-0.356378\pi$
$139$	121.221			0.872093			0.436047	+	0.899924i	$0.356378\pi$
$140$			210.788i			1.50563i
$141$	62.6157	−	16.2217i	0.444083	−	0.115048i
$142$	88.1699			0.620915
$143$			53.7364i			0.375779i
$144$	−31.4716	+	17.4797i	−0.218553	+	0.121387i
$145$	218.504			1.50692
$146$			85.6077i			0.586354i
$147$	−63.4558	−	244.939i	−0.431672	−	1.66625i
$148$	28.7037			0.193944
$149$			61.6498i			0.413757i	0.978367	+	0.206878i	$0.0663305\pi$
$149$			61.6498i			0.413757i	−0.978367	+	0.206878i	$0.933670\pi$
$150$	239.456	−	62.0354i	1.59638	−	0.413569i
$151$	−131.002			−0.867565			−0.433782	−	0.901018i	$-0.642821\pi$
$151$	−131.002			−0.867565			−0.433782	+	0.901018i	$0.642821\pi$
$152$			63.2276i			0.415971i
$153$	0.918112	+	1.65303i	0.00600073	+	0.0108041i
$154$	58.5062			0.379910
$155$		−	366.177i		−	2.36243i
$156$	−22.5696	−	87.1184i	−0.144677	−	0.558452i
$157$	31.7494			0.202226			0.101113	−	0.994875i	$-0.467760\pi$
$157$	31.7494			0.202226			0.101113	+	0.994875i	$0.467760\pi$
$158$		−	72.3584i		−	0.457964i
$159$	211.612	−	54.8218i	1.33089	−	0.344791i
$160$	51.6306			0.322691
$161$			55.3792i			0.343970i
$162$	−97.2473	−	60.5390i	−0.600292	−	0.373698i
$163$	−297.055			−1.82242			−0.911211	−	0.411940i	$-0.864851\pi$
$163$	−297.055			−1.82242			−0.911211	+	0.411940i	$0.864851\pi$
$164$		−	83.8380i		−	0.511207i
$165$	−24.6017	−	94.9623i	−0.149101	−	0.575529i
$166$	8.05428			0.0485198
$167$		−	211.344i		−	1.26553i	−0.774343	−	0.632766i	$-0.781920\pi$
$167$		−	211.344i		−	1.26553i	0.774343	−	0.632766i	$-0.218080\pi$
$168$	−94.8514	+	24.5729i	−0.564591	+	0.146267i
$169$	55.9724			0.331198
$170$		−	2.71187i		−	0.0159522i
$171$	−175.882	+	97.6867i	−1.02855	+	0.571267i
$172$	37.0472			0.215391
$173$			337.342i			1.94996i	0.222302	+	0.974978i	$0.428643\pi$
$173$			337.342i			1.94996i	−0.222302	+	0.974978i	$0.571357\pi$
$174$	25.4724	+	98.3235i	0.146393	+	0.565078i
$175$	673.254			3.84717
$176$		−	14.3306i		−	0.0814237i
$177$	−161.340	+	41.7980i	−0.911526	+	0.236147i
$178$	−59.2107			−0.332644
$179$		−	136.725i		−	0.763826i	−0.924198	−	0.381913i	$-0.875265\pi$
$179$		−	136.725i		−	0.763826i	0.924198	−	0.381913i	$-0.124735\pi$
$180$	79.7693	+	143.622i	0.443163	+	0.797900i
$181$	−164.599			−0.909385			−0.454692	−	0.890649i	$-0.650251\pi$
$181$	−164.599			−0.909385			−0.454692	+	0.890649i	$0.650251\pi$
$182$		−	244.942i		−	1.34583i
$183$	−56.0001	−	216.160i	−0.306012	−	1.18120i
$184$	13.5647			0.0737210
$185$		−	130.991i		−	0.708057i
$186$	164.774	−	42.6876i	0.885883	−	0.229503i
$187$	−0.752706			−0.00402517
$188$		−	43.1219i		−	0.229372i
$189$	−214.900	−	225.885i	−1.13704	−	1.19516i
$190$	288.542			1.51864
$191$			172.354i			0.902375i	0.892429	+	0.451188i	$0.148999\pi$
$191$			172.354i			0.902375i	−0.892429	+	0.451188i	$0.851001\pi$
$192$	6.01892	+	23.2330i	0.0313485	+	0.121005i
$193$	132.153			0.684732			0.342366	−	0.939567i	$-0.388772\pi$
$193$	132.153			0.684732			0.342366	+	0.939567i	$0.388772\pi$
$194$			87.1342i			0.449146i
$195$	−397.569	+	102.997i	−2.03881	+	0.528190i
$196$	−168.684			−0.860630
$197$			142.875i			0.725256i	0.931934	+	0.362628i	$0.118120\pi$
$197$			142.875i			0.725256i	−0.931934	+	0.362628i	$0.881880\pi$
$198$	39.8637	−	22.1408i	0.201332	−	0.111822i
$199$	211.240			1.06151			0.530754	−	0.847526i	$-0.321909\pi$
$199$	211.240			1.06151			0.530754	+	0.847526i	$0.321909\pi$
$200$		−	164.908i		−	0.824539i
$201$	70.8748	+	273.576i	0.352611	+	1.36108i
$202$	207.531			1.02738
$203$			276.446i			1.36180i
$204$	1.22030	−	0.316140i	0.00598187	−	0.00154971i
$205$	−382.598			−1.86633
$206$		−	107.208i		−	0.520430i
$207$	20.9574	+	37.7331i	0.101244	+	0.182285i
$208$	−59.9963			−0.288444
$209$		−	80.0876i		−	0.383194i
$210$	112.140	+	432.858i	0.533998	+	2.06123i
$211$	−243.763			−1.15528			−0.577638	−	0.816293i	$-0.696026\pi$
$211$	−243.763			−1.15528			−0.577638	+	0.816293i	$0.696026\pi$
$212$		−	145.732i		−	0.687414i
$213$	181.059	−	46.9066i	0.850043	−	0.220219i
$214$	−96.8246			−0.452452
$215$		−	169.067i		−	0.786356i
$216$	−55.3285	+	52.6380i	−0.256150	+	0.243694i
$217$	463.278			2.13492
$218$			142.011i			0.651425i
$219$	45.5435	+	175.798i	0.207961	+	0.802729i
$220$	−65.3982			−0.297265
$221$			3.15128i			0.0142592i
$222$	58.9438	−	15.2704i	0.265513	−	0.0687857i
$223$	−144.094			−0.646163			−0.323081	−	0.946371i	$-0.604719\pi$
$223$	−144.094			−0.646163			−0.323081	+	0.946371i	$0.604719\pi$
$224$			65.3218i			0.291615i
$225$	458.727	−	254.783i	2.03879	−	1.13237i
$226$	−6.73376			−0.0297954
$227$			137.319i			0.604932i	0.953160	+	0.302466i	$0.0978098\pi$
$227$			137.319i			0.604932i	−0.953160	+	0.302466i	$0.902190\pi$
$228$	33.6372	+	129.840i	0.147532	+	0.569472i
$229$	−315.550			−1.37795			−0.688974	−	0.724786i	$-0.741939\pi$
$229$	−315.550			−1.37795			−0.688974	+	0.724786i	$0.741939\pi$
$230$		−	61.9029i		−	0.269143i
$231$	120.144	−	31.1254i	0.520104	−	0.134742i
$232$	67.7130			0.291866
$233$			108.984i			0.467743i	0.972268	+	0.233871i	$0.0751395\pi$
$233$			108.984i			0.467743i	−0.972268	+	0.233871i	$0.924861\pi$
$234$	−92.6944	−	166.893i	−0.396130	−	0.713218i
$235$	−196.789			−0.837399
$236$			111.111i			0.470809i
$237$	−38.4948	−	148.590i	−0.162425	−	0.626961i
$238$	3.43099			0.0144159
$239$			56.0773i			0.234633i	0.993095	+	0.117317i	$0.0374292\pi$
$239$			56.0773i			0.234633i	−0.993095	+	0.117317i	$0.962571\pi$
$240$	106.025	−	27.4676i	0.441770	−	0.114448i
$241$	−97.3916			−0.404115			−0.202057	−	0.979374i	$-0.564763\pi$
$241$	−97.3916			−0.404115			−0.202057	+	0.979374i	$0.564763\pi$
$242$		−	152.968i		−	0.632099i
$243$	−231.907	−	72.5827i	−0.954349	−	0.298694i
$244$	−148.864			−0.610100
$245$			769.794i			3.14202i
$246$	−44.6020	−	172.164i	−0.181309	−	0.699852i
$247$	−335.294			−1.35747
$248$		−	113.476i		−	0.457564i
$249$	16.5397	−	4.28489i	0.0664244	−	0.0172084i
$250$	−429.873			−1.71949
$251$		−	106.355i		−	0.423723i	−0.977300	−	0.211862i	$-0.932047\pi$
$251$		−	106.355i		−	0.423723i	0.977300	−	0.211862i	$-0.0679527\pi$
$252$	−181.707	+	100.922i	−0.721059	+	0.400485i
$253$	−17.1818			−0.0679121
$254$			31.4736i			0.123912i
$255$	−1.44272	−	5.56890i	−0.00565773	−	0.0218388i
$256$	16.0000			0.0625000
$257$			31.7206i			0.123426i	0.998094	+	0.0617132i	$0.0196564\pi$
$257$			31.7206i			0.123426i	−0.998094	+	0.0617132i	$0.980344\pi$
$258$	76.0775	−	19.7092i	0.294874	−	0.0763923i
$259$	165.726			0.639869
$260$			273.796i			1.05306i
$261$	104.617	+	188.359i	0.400830	+	0.721680i
$262$	53.1333			0.202799
$263$			195.037i			0.741587i	0.928715	+	0.370793i	$0.120914\pi$
$263$			195.037i			0.741587i	−0.928715	+	0.370793i	$0.879086\pi$
$264$	−7.62390	−	29.4282i	−0.0288784	−	0.111471i
$265$	−665.054			−2.50964
$266$			365.056i			1.37239i
$267$	−121.591	+	31.5002i	−0.455396	+	0.117978i
$268$	188.405			0.703005
$269$		−	333.002i		−	1.23792i	−0.785421	−	0.618962i	$-0.787553\pi$
$269$		−	333.002i		−	1.23792i	0.785421	−	0.618962i	$-0.212447\pi$
$270$	240.216	+	252.494i	0.889688	+	0.935163i
$271$	63.3042			0.233595			0.116797	−	0.993156i	$-0.462737\pi$
$271$	63.3042			0.233595			0.116797	+	0.993156i	$0.462737\pi$
$272$		−	0.840392i		−	0.00308967i
$273$	−130.310	−	502.994i	−0.477324	−	1.84247i
$274$	−232.942			−0.850155
$275$			208.881i			0.759569i
$276$	27.8554	−	7.21643i	0.100925	−	0.0261465i
$277$	−262.378			−0.947214			−0.473607	−	0.880736i	$-0.657048\pi$
$277$	−262.378			−0.947214			−0.473607	+	0.880736i	$0.657048\pi$
$278$		−	171.432i		−	0.616663i
$279$	315.658	−	175.320i	1.13139	−	0.628389i
$280$	298.099			1.06464
$281$			544.972i			1.93940i	0.244296	+	0.969701i	$0.421443\pi$
$281$			544.972i			1.93940i	−0.244296	+	0.969701i	$0.578557\pi$
$282$	−22.9410	−	88.5520i	−0.0813509	−	0.314014i
$283$	−499.928			−1.76653			−0.883266	−	0.468872i	$-0.844660\pi$
$283$	−499.928			−1.76653			−0.883266	+	0.468872i	$0.844660\pi$
$284$		−	124.691i		−	0.439053i
$285$	592.528	−	153.505i	2.07905	−	0.538614i
$286$	75.9947			0.265716
$287$		−	484.054i		−	1.68660i
$288$	24.7200	+	44.5075i	0.0858334	+	0.154540i
$289$	288.956			0.999847
$290$		−	309.011i		−	1.06556i
$291$	46.3556	+	178.933i	0.159298	+	0.614888i
$292$	121.068			0.414615
$293$		−	516.131i		−	1.76154i	−0.473546	−	0.880769i	$-0.657026\pi$
$293$		−	516.131i		−	1.76154i	0.473546	−	0.880769i	$-0.342974\pi$
$294$	−346.396	+	89.7400i	−1.17822	+	0.305238i
$295$	507.059			1.71885
$296$		−	40.5932i		−	0.137139i
$297$	70.0822	−	66.6742i	0.235967	−	0.224492i
$298$	87.1859			0.292570
$299$			71.9331i			0.240579i
$300$	−87.7313	−	338.643i	−0.292438	−	1.12881i
$301$	213.899			0.710628
$302$			185.265i			0.613461i
$303$	426.170	−	110.407i	1.40650	−	0.364379i
$304$	89.4173			0.294136
$305$			679.349i			2.22737i
$306$	2.33773	−	1.29841i	0.00763966	−	0.00424316i
$307$	586.720			1.91114			0.955570	−	0.294764i	$-0.0952410\pi$
$307$	586.720			1.91114			0.955570	+	0.294764i	$0.0952410\pi$
$308$		−	82.7403i		−	0.268637i
$309$	−57.0351	−	220.156i	−0.184580	−	0.712477i
$310$	−517.852			−1.67049
$311$			272.742i			0.876983i	0.898735	+	0.438492i	$0.144487\pi$
$311$			272.742i			0.876983i	−0.898735	+	0.438492i	$0.855513\pi$
$312$	−123.204	+	31.9182i	−0.394885	+	0.102302i
$313$	81.8183			0.261400			0.130700	−	0.991422i	$-0.458277\pi$
$313$	81.8183			0.261400			0.130700	+	0.991422i	$0.458277\pi$
$314$		−	44.9004i		−	0.142995i
$315$	460.563	+	829.228i	1.46210	+	2.63247i
$316$	−102.330			−0.323830
$317$			200.265i			0.631750i	0.948801	+	0.315875i	$0.102298\pi$
$317$			200.265i			0.631750i	−0.948801	+	0.315875i	$0.897702\pi$
$318$	−77.5297	−	299.264i	−0.243804	−	0.941083i
$319$	−85.7691			−0.268868
$320$		−	73.0167i		−	0.228177i
$321$	−198.832	+	51.5109i	−0.619414	+	0.160470i
$322$	78.3181			0.243224
$323$		−	4.69660i		−	0.0145405i
$324$	−85.6151	+	137.528i	−0.264244	+	0.424470i
$325$	874.502			2.69078
$326$			420.099i			1.28865i
$327$	75.5500	+	291.623i	0.231040	+	0.891813i
$328$	−118.565			−0.361478
$329$		−	248.972i		−	0.756755i
$330$	−134.297	+	34.7920i	−0.406961	+	0.105430i
$331$	−440.754			−1.33158			−0.665791	−	0.746138i	$-0.731906\pi$
$331$	−440.754			−1.33158			−0.665791	+	0.746138i	$0.731906\pi$
$332$		−	11.3905i		−	0.0343087i
$333$	112.919	−	62.7165i	0.339096	−	0.188338i
$334$	−298.885			−0.894866
$335$		−	859.796i		−	2.56655i
$336$	34.7513	+	134.140i	0.103427	+	0.399226i
$337$	228.802			0.678937			0.339468	−	0.940618i	$-0.389753\pi$
$337$	228.802			0.678937			0.339468	+	0.940618i	$0.389753\pi$
$338$		−	79.1569i		−	0.234192i
$339$	−13.8280	+	3.58238i	−0.0407905	+	0.0105675i
$340$	−3.83516			−0.0112799
$341$			143.735i			0.421510i
$342$	138.150	+	248.734i	0.403947	+	0.727292i
$343$	−408.104			−1.18981
$344$		−	52.3927i		−	0.152304i
$345$	−32.9325	−	127.119i	−0.0954565	−	0.368462i
$346$	477.074			1.37883
$347$		−	366.863i		−	1.05724i	−0.848858	−	0.528620i	$-0.822710\pi$
$347$		−	366.863i		−	1.05724i	0.848858	−	0.528620i	$-0.177290\pi$
$348$	139.050	−	36.0234i	0.399570	−	0.103516i
$349$	−242.235			−0.694082			−0.347041	−	0.937850i	$-0.612814\pi$
$349$	−242.235			−0.694082			−0.347041	+	0.937850i	$0.612814\pi$
$350$		−	952.126i		−	2.72036i
$351$	−279.138	−	293.406i	−0.795265	−	0.835914i
$352$	−20.2665			−0.0575753
$353$		−	127.231i		−	0.360429i	−0.983627	−	0.180214i	$-0.942321\pi$
$353$		−	127.231i		−	0.360429i	0.983627	−	0.180214i	$-0.0576791\pi$
$354$	59.1112	+	228.169i	0.166981	+	0.644546i
$355$	−569.033			−1.60291
$356$			83.7365i			0.235215i
$357$	7.04564	−	1.82530i	0.0197357	−	0.00511287i
$358$	−193.358			−0.540106
$359$		−	175.718i		−	0.489464i	−0.969591	−	0.244732i	$-0.921300\pi$
$359$		−	175.718i		−	0.489464i	0.969591	−	0.244732i	$-0.0787000\pi$
$360$	203.112	−	112.811i	0.564200	−	0.313364i
$361$	138.716			0.384255
$362$			232.778i			0.643032i
$363$	−81.3793	−	314.124i	−0.224185	−	0.865355i
$364$	−346.400			−0.951648
$365$		−	552.497i		−	1.51369i
$366$	−305.697	+	79.1962i	−0.835238	+	0.216383i
$367$	232.660			0.633950			0.316975	−	0.948434i	$-0.397333\pi$
$367$	232.660			0.633950			0.316975	+	0.948434i	$0.397333\pi$
$368$		−	19.1833i		−	0.0521286i
$369$	−183.183	−	329.814i	−0.496430	−	0.893806i
$370$	−185.249			−0.500672
$371$		−	841.410i		−	2.26795i
$372$	−60.3694	−	233.026i	−0.162283	−	0.626414i
$373$	352.892			0.946091			0.473046	−	0.881038i	$-0.343155\pi$
$373$	352.892			0.946091			0.473046	+	0.881038i	$0.343155\pi$
$374$			1.06449i			0.00284622i
$375$	−882.755	+	228.693i	−2.35401	+	0.609848i
$376$	−60.9836			−0.162190
$377$			359.080i			0.952467i
$378$	−319.449	+	303.915i	−0.845104	+	0.804008i
$379$	−194.889			−0.514219			−0.257109	−	0.966382i	$-0.582770\pi$
$379$	−194.889			−0.514219			−0.257109	+	0.966382i	$0.582770\pi$
$380$		−	408.060i		−	1.07384i
$381$	16.7440	+	64.6319i	0.0439476	+	0.169637i
$382$	243.745			0.638076
$383$		−	727.698i		−	1.89999i	−0.312258	−	0.949997i	$-0.601085\pi$
$383$		−	727.698i		−	1.89999i	0.312258	−	0.949997i	$-0.398915\pi$
$384$	32.8564	−	8.51203i	0.0855636	−	0.0221668i
$385$	−377.589			−0.980750
$386$		−	186.893i		−	0.484178i
$387$	145.742	−	80.9468i	0.376594	−	0.209165i
$388$	123.226			0.317594
$389$			554.479i			1.42540i	0.701471	+	0.712698i	$0.252527\pi$
$389$			554.479i			1.42540i	−0.701471	+	0.712698i	$0.747473\pi$
$390$	145.660	+	562.247i	0.373487	+	1.44166i
$391$	−1.00759			−0.00257697
$392$			238.555i			0.608557i
$393$	109.111	−	28.2670i	0.277635	−	0.0719262i
$394$	202.056			0.512833
$395$			466.988i			1.18225i
$396$	−31.3118	−	56.3757i	−0.0790701	−	0.142363i
$397$	33.5516			0.0845129			0.0422564	−	0.999107i	$-0.486545\pi$
$397$	33.5516			0.0845129			0.0422564	+	0.999107i	$0.486545\pi$
$398$		−	298.739i		−	0.750600i
$399$	194.211	+	749.653i	0.486744	+	1.87883i
$400$	−233.215			−0.583037
$401$			210.249i			0.524311i	0.965026	+	0.262155i	$0.0844333\pi$
$401$			210.249i			0.524311i	−0.965026	+	0.262155i	$0.915567\pi$
$402$	386.895	−	100.232i	0.962427	−	0.249333i
$403$	601.760			1.49320
$404$		−	293.493i		−	0.726467i
$405$	627.617	+	390.708i	1.54967	+	0.964711i
$406$	390.953			0.962939
$407$			51.4176i			0.126333i
$408$	−0.447090	−	1.72577i	−0.00109581	−	0.00422982i
$409$	−94.2476			−0.230434			−0.115217	−	0.993340i	$-0.536756\pi$
$409$	−94.2476			−0.230434			−0.115217	+	0.993340i	$0.536756\pi$
$410$			541.076i			1.31970i
$411$	−478.354	+	123.926i	−1.16388	+	0.301523i
$412$	−151.616			−0.367999
$413$			641.519i			1.55332i
$414$	53.3627	−	29.6383i	0.128895	−	0.0715900i
$415$	−51.9809			−0.125255
$416$			84.8476i			0.203961i
$417$	−91.2024	−	352.041i	−0.218711	−	0.844223i
$418$	−113.261			−0.270959
$419$		−	248.460i		−	0.592982i	−0.955036	−	0.296491i	$-0.904183\pi$
$419$		−	248.460i		−	0.592982i	0.955036	−	0.296491i	$-0.0958166\pi$
$420$	612.154	−	158.589i	1.45751	−	0.377593i
$421$	131.852			0.313188			0.156594	−	0.987663i	$-0.449949\pi$
$421$	131.852			0.313188			0.156594	+	0.987663i	$0.449949\pi$
$422$			344.734i			0.816904i
$423$	−94.2197	−	169.639i	−0.222742	−	0.401039i
$424$	−206.096			−0.486075
$425$			12.2495i			0.0288223i
$426$	−66.3359	−	256.056i	−0.155718	−	0.601071i
$427$	−859.496			−2.01287
$428$			136.931i			0.319932i
$429$	156.057	−	40.4294i	0.363770	−	0.0942409i
$430$	−239.096			−0.556038
$431$			336.914i			0.781704i	0.920454	+	0.390852i	$0.127820\pi$
$431$			336.914i			0.781704i	−0.920454	+	0.390852i	$0.872180\pi$
$432$	74.4413	+	78.2463i	0.172318	+	0.181126i
$433$	621.856			1.43616			0.718079	−	0.695962i	$-0.245022\pi$
$433$	621.856			1.43616			0.718079	+	0.695962i	$0.245022\pi$
$434$		−	655.174i		−	1.50962i
$435$	−164.395	−	634.563i	−0.377918	−	1.45876i
$436$	200.834			0.460627
$437$		−	107.208i		−	0.245326i
$438$	248.615	−	64.4082i	0.567615	−	0.147051i
$439$	195.968			0.446395			0.223198	−	0.974773i	$-0.428350\pi$
$439$	195.968			0.446395			0.223198	+	0.974773i	$0.428350\pi$
$440$			92.4870i			0.210198i
$441$	−663.592	+	368.567i	−1.50474	+	0.835753i
$442$	4.45658			0.0100828
$443$			577.414i			1.30342i	0.758469	+	0.651709i	$0.225948\pi$
$443$			577.414i			1.30342i	−0.758469	+	0.651709i	$0.774052\pi$
$444$	−21.5956	−	83.3591i	−0.0486388	−	0.187746i
$445$	382.135			0.858731
$446$			203.780i			0.456906i
$447$	179.039	−	46.3831i	0.400534	−	0.103765i
$448$	92.3790			0.206203
$449$			109.519i			0.243918i	0.992535	+	0.121959i	$0.0389177\pi$
$449$			109.519i			0.243918i	−0.992535	+	0.121959i	$0.961082\pi$
$450$	−360.317	−	648.739i	−0.800705	−	1.44164i
$451$	150.181			0.332995
$452$			9.52298i			0.0210685i
$453$	98.5615	+	380.447i	0.217575	+	0.839839i
$454$	194.199			0.427751
$455$			1580.81i			3.47431i
$456$	183.621	−	47.5702i	0.402677	−	0.104321i
$457$	710.438			1.55457			0.777284	−	0.629150i	$-0.216597\pi$
$457$	710.438			1.55457			0.777284	+	0.629150i	$0.216597\pi$
$458$			446.255i			0.974357i
$459$	4.10985	−	3.90999i	0.00895391	−	0.00851850i
$460$	−87.5439			−0.190313
$461$			25.7896i			0.0559428i	0.999609	+	0.0279714i	$0.00890474\pi$
$461$			25.7896i			0.0559428i	−0.999609	+	0.0279714i	$0.991095\pi$
$462$	−44.0180	−	169.909i	−0.0952770	−	0.367769i
$463$	−283.020			−0.611275			−0.305637	−	0.952148i	$-0.598870\pi$
$463$	−283.020			−0.611275			−0.305637	+	0.952148i	$0.598870\pi$
$464$		−	95.7606i		−	0.206381i
$465$	−1063.42	+	275.499i	−2.28693	+	0.592470i
$466$	154.127			0.330744
$467$		−	198.693i		−	0.425466i	−0.977110	−	0.212733i	$-0.931764\pi$
$467$		−	198.693i		−	0.425466i	0.977110	−	0.212733i	$-0.0682365\pi$
$468$	−236.022	+	131.090i	−0.504321	+	0.280106i
$469$	1087.79			2.31939
$470$			278.301i			0.592130i
$471$	−23.8871	−	92.2043i	−0.0507158	−	0.195763i
$472$	157.135			0.332912
$473$			66.3635i			0.140303i
$474$	−210.138	+	54.4399i	−0.443329	+	0.114852i
$475$	−1303.34			−2.74387
$476$		−	4.85216i		−	0.0101936i
$477$	−318.419	−	573.302i	−0.667544	−	1.20189i
$478$	79.3053			0.165911
$479$		−	214.270i		−	0.447328i	−0.974666	−	0.223664i	$-0.928198\pi$
$479$		−	214.270i		−	0.447328i	0.974666	−	0.223664i	$-0.0718019\pi$
$480$	−38.8450	−	149.942i	−0.0809272	−	0.312379i
$481$	215.264			0.447535
$482$			137.733i			0.285752i
$483$	160.828	−	41.6654i	0.332978	−	0.0862637i
$484$	−216.329			−0.446961
$485$		−	562.349i		−	1.15948i
$486$	−102.647	+	327.966i	−0.211209	+	0.674827i
$487$	132.640			0.272362			0.136181	−	0.990684i	$-0.456517\pi$
$487$	132.640			0.272362			0.136181	+	0.990684i	$0.456517\pi$
$488$			210.526i			0.431406i
$489$	223.494	+	862.684i	0.457042	+	1.76418i
$490$	1088.65			2.22174
$491$		−	267.430i		−	0.544663i	−0.962203	−	0.272332i	$-0.912205\pi$
$491$		−	267.430i		−	0.544663i	0.962203	−	0.272332i	$-0.0877947\pi$
$492$	−243.476	+	63.0767i	−0.494870	+	0.128205i
$493$	−5.02977			−0.0102024
$494$			474.178i			0.959874i
$495$	−257.273	+	142.893i	−0.519744	+	0.288672i
$496$	−160.479			−0.323547
$497$		−	719.927i		−	1.44854i
$498$	−6.05976	−	23.3906i	−0.0121682	−	0.0469692i
$499$	−804.117			−1.61146			−0.805728	−	0.592285i	$-0.798226\pi$
$499$	−804.117			−1.61146			−0.805728	+	0.592285i	$0.798226\pi$
$500$			607.932i			1.21586i
$501$	−613.769	+	159.008i	−1.22509	+	0.317380i
$502$	−150.408			−0.299618
$503$			126.819i			0.252125i	0.992022	+	0.126062i	$0.0402340\pi$
$503$			126.819i			0.252125i	−0.992022	+	0.126062i	$0.959766\pi$
$504$	142.726	+	256.972i	0.283186	+	0.509866i
$505$	−1339.37			−2.65221
$506$			24.2987i			0.0480211i
$507$	−42.1117	−	162.551i	−0.0830605	−	0.320613i
$508$	44.5104			0.0876189
$509$		−	254.181i		−	0.499373i	−0.968327	−	0.249687i	$-0.919672\pi$
$509$		−	254.181i		−	0.499373i	0.968327	−	0.249687i	$-0.0803276\pi$
$510$	−7.87561	+	2.04032i	−0.0154424	+	0.00400062i
$511$	699.006			1.36792
$512$		−	22.6274i		−	0.0441942i
$513$	416.022	+	437.286i	0.810958	+	0.852409i
$514$	44.8597			0.0872757
$515$			691.905i			1.34350i
$516$	−27.8730	−	107.590i	−0.0540175	−	0.208507i
$517$	77.2453			0.149411
$518$		−	234.372i		−	0.452456i
$519$	979.685	−	253.804i	1.88764	−	0.489026i
$520$	387.206			0.744626
$521$		−	368.300i		−	0.706910i	−0.935452	−	0.353455i	$-0.885007\pi$
$521$		−	368.300i		−	0.706910i	0.935452	−	0.353455i	$-0.114993\pi$
$522$	266.379	−	147.950i	0.510305	−	0.283430i
$523$	650.275			1.24336			0.621678	−	0.783273i	$-0.286451\pi$
$523$	650.275			1.24336			0.621678	+	0.783273i	$0.286451\pi$
$524$		−	75.1418i		−	0.143400i
$525$	−506.533	−	1955.22i	−0.964825	−	3.72422i
$526$	275.824			0.524381
$527$			8.42909i			0.0159945i
$528$	−41.6178	+	10.7818i	−0.0788216	+	0.0204201i
$529$	−23.0000			−0.0434783
$530$			940.528i			1.77458i
$531$	242.773	+	437.105i	0.457200	+	0.823172i
$532$	516.267			0.970427
$533$		−	628.746i		−	1.17964i
$534$	44.5480	+	171.955i	0.0834233	+	0.322014i
$535$	624.889			1.16802
$536$		−	266.445i		−	0.497100i
$537$	−397.066	+	102.867i	−0.739415	+	0.191559i
$538$	−470.936			−0.875345
$539$		−	302.167i		−	0.560606i
$540$	357.080	−	339.716i	0.661260	−	0.629104i
$541$	−454.716			−0.840510			−0.420255	−	0.907406i	$-0.638059\pi$
$541$	−454.716			−0.840510			−0.420255	+	0.907406i	$0.638059\pi$
$542$		−	89.5256i		−	0.165176i
$543$	123.838	+	478.015i	0.228063	+	0.880323i
$544$	−1.18849			−0.00218473
$545$		−	916.512i		−	1.68167i
$546$	−711.342	+	184.285i	−1.30282	+	0.337519i
$547$	−594.830			−1.08744			−0.543720	−	0.839266i	$-0.682985\pi$
$547$	−594.830			−1.08744			−0.543720	+	0.839266i	$0.682985\pi$
$548$			329.430i			0.601150i
$549$	−585.625	+	325.263i	−1.06671	+	0.592464i
$550$	295.403			0.537096
$551$		−	535.166i		−	0.971263i
$552$	−10.2056	−	39.3935i	−0.0184884	−	0.0713650i
$553$	−590.822			−1.06839
$554$			371.059i			0.669782i
$555$	−380.413	+	98.5527i	−0.685429	+	0.177572i
$556$	−242.442			−0.436047
$557$		−	178.943i		−	0.321262i	−0.987015	−	0.160631i	$-0.948647\pi$
$557$		−	178.943i		−	0.321262i	0.987015	−	0.160631i	$-0.0513530\pi$
$558$	−247.941	−	446.408i	−0.444338	−	0.800015i
$559$	277.837			0.497025
$560$		−	421.575i		−	0.752813i
$561$	0.566309	+	2.18595i	0.00100946	+	0.00389653i
$562$	770.706			1.37136
$563$			323.423i			0.574464i	0.957861	+	0.287232i	$0.0927351\pi$
$563$			323.423i			0.574464i	−0.957861	+	0.287232i	$0.907265\pi$
$564$	−125.231	+	32.4434i	−0.222042	+	0.0575238i
$565$	43.4585			0.0769178
$566$			707.006i			1.24913i
$567$	−494.314	+	794.046i	−0.871807	+	1.40043i
$568$	−176.340			−0.310457
$569$		−	292.517i		−	0.514090i	−0.966399	−	0.257045i	$-0.917251\pi$
$569$		−	292.517i		−	0.514090i	0.966399	−	0.257045i	$-0.0827489\pi$
$570$	−217.089	−	837.962i	−0.380857	−	1.47011i
$571$	732.290			1.28247			0.641235	−	0.767345i	$-0.278422\pi$
$571$	732.290			1.28247			0.641235	+	0.767345i	$0.278422\pi$
$572$		−	107.473i		−	0.187889i
$573$	500.537	−	129.673i	0.873537	−	0.226305i
$574$	−684.556			−1.19261
$575$			279.615i			0.486287i
$576$	62.9432	−	34.9594i	0.109276	−	0.0606934i
$577$	48.4191			0.0839153			0.0419576	−	0.999119i	$-0.486641\pi$
$577$	48.4191			0.0839153			0.0419576	+	0.999119i	$0.486641\pi$
$578$		−	408.645i		−	0.706999i
$579$	−99.4274	−	383.790i	−0.171723	−	0.662849i
$580$	−437.008			−0.753461
$581$		−	65.7650i		−	0.113193i
$582$	253.049	−	65.5567i	0.434792	−	0.112640i
$583$	261.053			0.447775
$584$		−	171.215i		−	0.293177i
$585$	598.233	+	1077.10i	1.02262	+	1.84119i
$586$	−729.919			−1.24560
$587$		−	958.440i		−	1.63278i	−0.577503	−	0.816389i	$-0.695973\pi$
$587$		−	958.440i		−	1.63278i	0.577503	−	0.816389i	$-0.304027\pi$
$588$	126.912	+	489.878i	0.215836	+	0.833126i
$589$	−896.851			−1.52267
$590$		−	717.090i		−	1.21541i
$591$	414.928	−	107.494i	0.702078	−	0.181886i
$592$	−57.4074			−0.0969719
$593$			545.136i			0.919285i	0.888104	+	0.459642i	$0.152022\pi$
$593$			545.136i			0.919285i	−0.888104	+	0.459642i	$0.847978\pi$
$594$	−94.2916	−	99.1112i	−0.158740	−	0.166854i
$595$	−22.1430			−0.0372152
$596$		−	123.300i		−	0.206878i
$597$	−158.930	−	613.468i	−0.266214	−	1.02758i
$598$	101.729			0.170115
$599$		−	513.060i		−	0.856528i	−0.903654	−	0.428264i	$-0.859125\pi$
$599$		−	513.060i		−	0.856528i	0.903654	−	0.428264i	$-0.140875\pi$
$600$	−478.913	+	124.071i	−0.798188	+	0.206785i
$601$	−310.550			−0.516722			−0.258361	−	0.966048i	$-0.583182\pi$
$601$	−310.550			−0.516722			−0.258361	+	0.966048i	$0.583182\pi$
$602$		−	302.499i		−	0.502490i
$603$	741.177	−	411.658i	1.22915	−	0.682684i
$604$	262.005			0.433782
$605$			987.228i			1.63178i
$606$	−156.139	−	602.695i	−0.257655	−	0.994546i
$607$	−658.943			−1.08557			−0.542787	−	0.839870i	$-0.682631\pi$
$607$	−658.943			−1.08557			−0.542787	+	0.839870i	$0.682631\pi$
$608$		−	126.455i		−	0.207985i
$609$	802.833	−	207.988i	1.31828	−	0.341524i
$610$	960.744			1.57499
$611$		−	323.395i		−	0.529287i
$612$	−1.83622	−	3.30606i	−0.00300036	−	0.00540205i
$613$	301.956			0.492588			0.246294	−	0.969195i	$-0.420787\pi$
$613$	301.956			0.492588			0.246294	+	0.969195i	$0.420787\pi$
$614$		−	829.747i		−	1.35138i
$615$	287.853	+	1111.11i	0.468054	+	1.80669i
$616$	−117.012			−0.189955
$617$			919.808i			1.49077i	0.666632	+	0.745387i	$0.267735\pi$
$617$			919.808i			1.49077i	−0.666632	+	0.745387i	$0.732265\pi$
$618$	−311.347	+	80.6599i	−0.503798	+	0.130518i
$619$	152.731			0.246739			0.123369	−	0.992361i	$-0.460630\pi$
$619$	152.731			0.246739			0.123369	+	0.992361i	$0.460630\pi$
$620$			732.354i			1.18122i
$621$	93.8140	−	89.2520i	0.151069	−	0.143723i
$622$	385.715			0.620121
$623$			483.468i			0.776033i
$624$	45.1391	+	174.237i	0.0723383	+	0.279226i
$625$	1316.73			2.10677
$626$		−	115.709i		−	0.184838i
$627$	−232.585	+	60.2551i	−0.370948	+	0.0961006i
$628$	−63.4988			−0.101113
$629$			3.01529i			0.00479379i
$630$	1172.71	−	651.334i	1.86144	−	1.03386i
$631$	−23.4846			−0.0372181			−0.0186091	−	0.999827i	$-0.505924\pi$
$631$	−23.4846			−0.0372181			−0.0186091	+	0.999827i	$0.505924\pi$
$632$			144.717i			0.228982i
$633$	183.399	+	707.920i	0.289730	+	1.11836i
$634$	283.217			0.446714
$635$		−	203.125i		−	0.319882i
$636$	−423.224	+	109.644i	−0.665446	+	0.172395i
$637$	−1265.05			−1.98595
$638$			121.296i			0.190119i
$639$	−272.445	−	490.528i	−0.426362	−	0.767649i
$640$	−103.261			−0.161346
$641$			344.344i			0.537198i	0.963252	+	0.268599i	$0.0865606\pi$
$641$			344.344i			0.537198i	−0.963252	+	0.268599i	$0.913439\pi$
$642$	72.8474	+	281.191i	0.113470	+	0.437992i
$643$	934.005			1.45257			0.726287	−	0.687392i	$-0.241244\pi$
$643$	934.005			1.45257			0.726287	+	0.687392i	$0.241244\pi$
$644$		−	110.758i		−	0.171985i
$645$	−490.991	+	127.200i	−0.761226	+	0.197209i
$646$	−6.64199			−0.0102817
$647$			38.0183i			0.0587610i	0.999568	+	0.0293805i	$0.00935344\pi$
$647$			38.0183i			0.0587610i	−0.999568	+	0.0293805i	$0.990647\pi$
$648$	194.495	+	121.078i	0.300146	+	0.186849i
$649$	−199.035			−0.306680
$650$		−	1236.73i		−	1.90267i
$651$	−348.554	−	1345.42i	−0.535413	−	2.06669i
$652$	594.110			0.911211
$653$		−	107.824i		−	0.165120i	−0.996586	−	0.0825601i	$-0.973690\pi$
$653$		−	107.824i		−	0.165120i	0.996586	−	0.0825601i	$-0.0263097\pi$
$654$	412.417	−	106.844i	0.630607	−	0.163370i
$655$	−342.913			−0.523531
$656$			167.676i			0.255604i
$657$	476.273	−	264.528i	0.724921	−	0.402630i
$658$	−352.100			−0.535107
$659$			553.617i			0.840086i	0.907504	+	0.420043i	$0.137985\pi$
$659$			553.617i			0.840086i	−0.907504	+	0.420043i	$0.862015\pi$
$660$	49.2033	+	189.925i	0.0745505	+	0.287765i
$661$	1212.26			1.83397			0.916987	−	0.398916i	$-0.130614\pi$
$661$	1212.26			1.83397			0.916987	+	0.398916i	$0.130614\pi$
$662$			623.320i			0.941571i
$663$	9.15170	−	2.37091i	0.0138035	−	0.00357603i
$664$	−16.1086			−0.0242599
$665$		−	2356.01i		−	3.54287i
$666$	−88.6945	−	159.691i	−0.133175	−	0.239777i
$667$	−114.813			−0.172133
$668$			422.687i			0.632766i
$669$	108.411	+	418.468i	0.162050	+	0.625513i
$670$	−1215.93			−1.81483
$671$		−	266.664i		−	0.397413i
$672$	189.703	−	49.1458i	0.282296	−	0.0731336i
$673$	−723.025			−1.07433			−0.537166	−	0.843477i	$-0.680505\pi$
$673$	−723.025			−1.07433			−0.537166	+	0.843477i	$0.680505\pi$
$674$		−	323.574i		−	0.480081i
$675$	−1085.05	−	1140.51i	−1.60748	−	1.68965i
$676$	−111.945			−0.165599
$677$			644.772i			0.952396i	0.879338	+	0.476198i	$0.157985\pi$
$677$			644.772i			0.952396i	−0.879338	+	0.476198i	$0.842015\pi$
$678$	5.06625	+	19.5557i	0.00747234	+	0.0288432i
$679$	711.470			1.04782
$680$			5.42374i			0.00797609i
$681$	398.793	−	103.314i	0.585599	−	0.151710i
$682$	203.272			0.298053
$683$			499.981i			0.732037i	0.930608	+	0.366019i	$0.119279\pi$
$683$			499.981i			0.732037i	−0.930608	+	0.366019i	$0.880721\pi$
$684$	351.763	−	195.373i	0.514273	−	0.285634i
$685$	1503.37			2.19470
$686$			577.147i			0.841322i
$687$	237.409	+	916.398i	0.345573	+	1.33391i
$688$	−74.0944			−0.107695
$689$		−	1092.92i		−	1.58624i
$690$	−179.774	+	46.5736i	−0.260542	+	0.0674979i
$691$	672.996			0.973946			0.486973	−	0.873417i	$-0.338101\pi$
$691$	672.996			0.973946			0.486973	+	0.873417i	$0.338101\pi$
$692$		−	674.685i		−	0.974978i
$693$	−180.784	−	325.496i	−0.260872	−	0.469691i
$694$	−518.822			−0.747582
$695$			1106.39i			1.59193i
$696$	−50.9448	−	196.647i	−0.0731966	−	0.282539i
$697$	8.80709			0.0126357
$698$			342.572i			0.490790i
$699$	316.503	−	81.9958i	0.452795	−	0.117304i
$700$	−1346.51			−1.92358
$701$			697.370i			0.994821i	0.867515	+	0.497411i	$0.165716\pi$
$701$			697.370i			0.994821i	−0.867515	+	0.497411i	$0.834284\pi$
$702$	−414.938	+	394.761i	−0.591080	+	0.562337i
$703$	−320.826			−0.456367
$704$			28.6612i			0.0407119i
$705$	148.057	+	571.499i	0.210010	+	0.810637i
$706$	−179.932			−0.254862
$707$		−	1694.53i		−	2.39679i
$708$	322.680	−	83.5959i	0.455763	−	0.118073i
$709$	−1238.36			−1.74663			−0.873313	−	0.487159i	$-0.838033\pi$
$709$	−1238.36			−1.74663			−0.873313	+	0.487159i	$0.838033\pi$
$710$			804.734i			1.13343i
$711$	−402.561	+	223.587i	−0.566191	+	0.314469i
$712$	118.421			0.166322
$713$			192.408i			0.269857i
$714$	−2.58136	−	9.96403i	−0.00361535	−	0.0139552i
$715$	−490.457			−0.685953
$716$			273.450i			0.381913i
$717$	162.856	−	42.1906i	0.227135	−	0.0588432i
$718$	−248.502			−0.346103
$719$			359.695i			0.500272i	0.968211	+	0.250136i	$0.0804753\pi$
$719$			359.695i			0.500272i	−0.968211	+	0.250136i	$0.919525\pi$
$720$	−159.539	−	287.244i	−0.221581	−	0.398950i
$721$	−875.381			−1.21412
$722$		−	196.174i		−	0.271709i
$723$	73.2740	+	282.838i	0.101347	+	0.391200i
$724$	329.197			0.454692
$725$			1395.80i			1.92524i
$726$	−444.238	+	115.088i	−0.611898	+	0.158523i
$727$	166.247			0.228676			0.114338	−	0.993442i	$-0.463525\pi$
$727$	166.247			0.228676			0.114338	+	0.993442i	$0.463525\pi$
$728$			489.883i			0.672917i
$729$	−36.3109	+	728.095i	−0.0498092	+	0.998759i
$730$	−781.349			−1.07034
$731$			3.89177i			0.00532390i
$732$	112.000	+	432.321i	0.153006	+	0.590602i
$733$	−1058.02			−1.44341			−0.721706	−	0.692199i	$-0.756642\pi$
$733$	−1058.02			−1.44341			−0.721706	+	0.692199i	$0.756642\pi$
$734$		−	329.030i		−	0.448270i
$735$	2235.58	−	579.166i	3.04161	−	0.787981i
$736$	−27.1293			−0.0368605
$737$			337.495i			0.457930i
$738$	−466.428	+	259.060i	−0.632016	+	0.351029i
$739$	783.694			1.06048			0.530240	−	0.847848i	$-0.322102\pi$
$739$	783.694			1.06048			0.530240	+	0.847848i	$0.322102\pi$
$740$			261.981i			0.354028i
$741$	252.264	+	973.737i	0.340437	+	1.31409i
$742$	−1189.93			−1.60368
$743$		−	841.995i		−	1.13324i	−0.823980	−	0.566619i	$-0.808251\pi$
$743$		−	841.995i		−	1.13324i	0.823980	−	0.566619i	$-0.191749\pi$
$744$	−329.548	+	85.3753i	−0.442941	+	0.114752i
$745$	−562.683			−0.755279
$746$		−	499.065i		−	0.668987i
$747$	−24.8877	−	44.8095i	−0.0333169	−	0.0599860i
$748$	1.50541			0.00201258
$749$			790.595i			1.05553i
$750$	323.421	+	1248.40i	0.431228	+	1.66454i
$751$	−778.256			−1.03629			−0.518146	−	0.855292i	$-0.673378\pi$
$751$	−778.256			−1.03629			−0.518146	+	0.855292i	$0.673378\pi$
$752$			86.2438i			0.114686i
$753$	−308.867	+	80.0174i	−0.410182	+	0.106265i
$754$	507.816			0.673496
$755$		−	1195.67i		−	1.58367i
$756$	429.801	+	451.770i	0.568520	+	0.597579i
$757$	−1075.73			−1.42104			−0.710521	−	0.703676i	$-0.751541\pi$
$757$	−1075.73			−1.42104			−0.710521	+	0.703676i	$0.751541\pi$
$758$			275.615i			0.363608i
$759$	12.9270	+	49.8980i	0.0170316	+	0.0657418i
$760$	−577.084			−0.759321
$761$			597.877i			0.785646i	0.919614	+	0.392823i	$0.128502\pi$
$761$			597.877i			0.785646i	−0.919614	+	0.392823i	$0.871498\pi$
$762$	91.4033	−	23.6796i	0.119952	−	0.0310756i
$763$	1159.55			1.51972
$764$		−	344.707i		−	0.451188i
$765$	−15.0873	+	8.37968i	−0.0197220	+	0.0109538i
$766$	−1029.12			−1.34350
$767$			833.281i			1.08642i
$768$	−12.0378	−	46.4660i	−0.0156743	−	0.0605026i
$769$	615.416			0.800281			0.400140	−	0.916454i	$-0.368961\pi$
$769$	615.416			0.800281			0.400140	+	0.916454i	$0.368961\pi$
$770$			533.991i			0.693495i
$771$	92.1206	−	23.8655i	0.119482	−	0.0309539i
$772$	−264.306			−0.342366
$773$		−	1277.04i		−	1.65206i	−0.563627	−	0.826030i	$-0.690594\pi$
$773$		−	1277.04i		−	1.65206i	0.563627	−	0.826030i	$-0.309406\pi$
$774$	−114.476	−	206.110i	−0.147902	−	0.266292i
$775$	2339.13			3.01824
$776$		−	174.268i		−	0.224573i
$777$	−124.686	−	481.289i	−0.160472	−	0.619420i
$778$	784.151			1.00791
$779$			937.071i			1.20292i
$780$	795.137	−	205.994i	1.01941	−	0.264095i
$781$	223.362			0.285995
$782$			1.42495i			0.00182219i
$783$	468.307	−	445.534i	0.598093	−	0.569009i
$784$	337.367			0.430315
$785$			289.780i			0.369146i
$786$	−39.9756	−	154.306i	−0.0508595	−	0.196318i
$787$	−169.531			−0.215414			−0.107707	−	0.994183i	$-0.534351\pi$
$787$	−169.531			−0.215414			−0.107707	+	0.994183i	$0.534351\pi$
$788$		−	285.751i		−	0.362628i
$789$	566.413	−	146.739i	0.717887	−	0.185981i
$790$	660.421			0.835976
$791$			54.9827i			0.0695104i
$792$	−79.7273	+	44.2815i	−0.100666	+	0.0559110i
$793$	−1116.41			−1.40784
$794$		−	47.4491i		−	0.0597596i
$795$	500.363	+	1931.40i	0.629387	+	2.42943i
$796$	−422.480			−0.530754
$797$			536.034i			0.672565i	0.941761	+	0.336282i	$0.109170\pi$
$797$			536.034i			0.672565i	−0.941761	+	0.336282i	$0.890830\pi$
$798$	1060.17	−	274.655i	1.32853	−	0.344180i
$799$	4.52991			0.00566948
$800$			329.816i			0.412269i
$801$	182.961	+	329.415i	0.228416	+	0.411255i
$802$	297.336			0.370744
$803$			216.871i			0.270076i
$804$	−141.750	−	547.153i	−0.176305	−	0.680538i
$805$	−505.451			−0.627890
$806$		−	851.017i		−	1.05585i
$807$	−967.079	+	250.539i	−1.19836	+	0.310457i
$808$	−415.061			−0.513689
$809$		−	698.560i		−	0.863486i	−0.901997	−	0.431743i	$-0.857899\pi$
$809$		−	698.560i		−	0.863486i	0.901997	−	0.431743i	$-0.142101\pi$
$810$	552.545	−	887.584i	0.682154	−	1.09578i
$811$	−1371.25			−1.69081			−0.845405	−	0.534125i	$-0.820641\pi$
$811$	−1371.25			−1.69081			−0.845405	+	0.534125i	$0.820641\pi$
$812$		−	552.892i		−	0.680901i
$813$	−47.6278	−	183.843i	−0.0585828	−	0.226129i
$814$	72.7154			0.0893310
$815$		−	2711.24i		−	3.32668i
$816$	−2.44060	+	0.632281i	−0.00299093	+	0.000774854i
$817$	−414.083			−0.506833
$818$			133.286i			0.162942i
$819$	−1362.72	+	756.870i	−1.66388	+	0.924140i
$820$	765.197			0.933167
$821$		−	609.271i		−	0.742108i	−0.928611	−	0.371054i	$-0.878996\pi$
$821$		−	609.271i		−	0.742108i	0.928611	−	0.371054i	$-0.121004\pi$
$822$	175.258	+	676.494i	0.213209	+	0.822986i
$823$	−1511.73			−1.83685			−0.918426	−	0.395592i	$-0.870539\pi$
$823$	−1511.73			−1.83685			−0.918426	+	0.395592i	$0.870539\pi$
$824$			214.417i			0.260215i
$825$	606.618	−	157.155i	0.735295	−	0.190491i
$826$	907.246			1.09836
$827$			802.996i			0.970975i	0.874244	+	0.485487i	$0.161358\pi$
$827$			802.996i			0.970975i	−0.874244	+	0.485487i	$0.838642\pi$
$828$	−41.9148	−	75.4662i	−0.0506218	−	0.0911427i
$829$	1072.65			1.29391			0.646955	−	0.762528i	$-0.276042\pi$
$829$	1072.65			1.29391			0.646955	+	0.762528i	$0.276042\pi$
$830$			73.5121i			0.0885688i
$831$	197.404	+	761.980i	0.237550	+	0.916943i
$832$	119.993			0.144222
$833$		−	17.7200i		−	0.0212725i
$834$	−497.861	+	128.980i	−0.596956	+	0.154652i
$835$	1928.95			2.31012
$836$			160.175i			0.191597i
$837$	−746.643	−	784.807i	−0.892046	−	0.937642i
$838$	−351.375			−0.419302
$839$			706.968i			0.842631i	0.906914	+	0.421316i	$0.138432\pi$
$839$			706.968i			0.842631i	−0.906914	+	0.421316i	$0.861568\pi$
$840$	−224.279	−	865.716i	−0.266999	−	1.03061i
$841$	267.869			0.318513
$842$		−	186.467i		−	0.221457i
$843$	1582.67	−	410.018i	1.87742	−	0.486379i
$844$	487.527			0.577638
$845$			510.865i			0.604574i
$846$	−239.906	+	133.247i	−0.283577	+	0.157502i
$847$	−1249.02			−1.47464
$848$			291.464i			0.343707i
$849$	376.129	+	1451.86i	0.443025	+	1.71008i
$850$	17.3234			0.0203805
$851$			68.8290i			0.0808802i
$852$	−362.119	+	93.8131i	−0.425022	+	0.110109i
$853$	−374.731			−0.439310			−0.219655	−	0.975578i	$-0.570493\pi$
$853$	−374.731			−0.439310			−0.219655	+	0.975578i	$0.570493\pi$
$854$			1215.51i			1.42331i
$855$	−891.595	−	1605.29i	−1.04280	−	1.87753i
$856$	193.649			0.226226
$857$		−	1441.06i		−	1.68151i	−0.541415	−	0.840756i	$-0.682111\pi$
$857$		−	1441.06i		−	1.68151i	0.541415	−	0.840756i	$-0.317889\pi$
$858$	−57.1757	−	220.698i	−0.0666384	−	0.257224i
$859$	77.0440			0.0896904			0.0448452	−	0.998994i	$-0.485721\pi$
$859$	77.0440			0.0896904			0.0448452	+	0.998994i	$0.485721\pi$
$860$			338.133i			0.393178i
$861$	−1405.75	+	364.185i	−1.63270	+	0.422979i
$862$	476.469			0.552748
$863$			279.495i			0.323864i	0.986802	+	0.161932i	$0.0517725\pi$
$863$			279.495i			0.323864i	−0.986802	+	0.161932i	$0.948227\pi$
$864$	110.657	−	105.276i	0.128075	−	0.121847i
$865$	−3078.95			−3.55948
$866$		−	879.438i		−	1.01552i
$867$	−217.400	−	839.164i	−0.250750	−	0.967894i
$868$	−926.556			−1.06746
$869$		−	183.306i		−	0.210939i
$870$	−897.407	+	232.489i	−1.03150	+	0.267229i
$871$	1412.95			1.62222
$872$		−	284.021i		−	0.325713i
$873$	484.766	−	269.245i	0.555288	−	0.308414i
$874$	−151.614			−0.173472
$875$			3510.01i			4.01143i
$876$	−91.0869	−	351.595i	−0.103981	−	0.401365i
$877$	−41.7588			−0.0476155			−0.0238078	−	0.999717i	$-0.507579\pi$
$877$	−41.7588			−0.0476155			−0.0238078	+	0.999717i	$0.507579\pi$
$878$		−	277.140i		−	0.315649i
$879$	−1498.91	+	388.318i	−1.70524	+	0.441773i
$880$	130.796			0.148632
$881$			741.612i			0.841784i	0.907111	+	0.420892i	$0.138283\pi$
$881$			741.612i			0.841784i	−0.907111	+	0.420892i	$0.861717\pi$
$882$	521.232	+	938.461i	0.590967	+	1.06401i
$883$	−591.146			−0.669474			−0.334737	−	0.942312i	$-0.608648\pi$
$883$	−591.146			−0.669474			−0.334737	+	0.942312i	$0.608648\pi$
$884$		−	6.30255i		−	0.00712958i
$885$	−381.494	−	1472.56i	−0.431066	−	1.66391i
$886$	816.587			0.921656
$887$			134.748i			0.151914i	0.997111	+	0.0759570i	$0.0242012\pi$
$887$			134.748i			0.151914i	−0.997111	+	0.0759570i	$0.975799\pi$
$888$	−117.888	+	30.5409i	−0.132756	+	0.0343929i
$889$	256.989			0.289076
$890$		−	540.421i		−	0.607215i
$891$	−246.358	−	153.364i	−0.276496	−	0.172126i
$892$	288.189			0.323081
$893$			481.981i			0.539732i
$894$	−65.5956	−	253.199i	−0.0733732	−	0.283220i
$895$	1247.90			1.39430
$896$		−	130.644i		−	0.145808i
$897$	208.903	−	54.1199i	0.232890	−	0.0603343i
$898$	154.884			0.172476
$899$			960.474i			1.06838i
$900$	−917.455	+	509.565i	−1.01939	+	0.566184i
$901$	15.3090			0.0169911
$902$		−	212.388i		−	0.235463i
$903$	−160.930	−	621.190i	−0.178217	−	0.687918i
$904$	13.4675			0.0148977
$905$		−	1502.31i		−	1.66001i
$906$	538.033	−	139.387i	0.593856	−	0.153849i
$907$	−36.6352			−0.0403916			−0.0201958	−	0.999796i	$-0.506429\pi$
$907$	−36.6352			−0.0403916			−0.0201958	+	0.999796i	$0.506429\pi$
$908$		−	274.639i		−	0.302466i
$909$	−641.270	−	1154.58i	−0.705467	−	1.27017i
$910$	2235.60			2.45671
$911$		−	1666.48i		−	1.82928i	−0.404265	−	0.914642i	$-0.632473\pi$
$911$		−	1666.48i		−	1.82928i	0.404265	−	0.914642i	$-0.367527\pi$
$912$	−67.2744	−	259.679i	−0.0737658	−	0.284736i
$913$	20.4040			0.0223483
$914$		−	1004.71i		−	1.09925i
$915$	1972.91	−	511.118i	2.15619	−	0.558599i
$916$	631.100			0.688974
$917$		−	433.845i		−	0.473113i
$918$	−5.52956	−	5.81220i	−0.00602349	−	0.00633137i
$919$	−193.580			−0.210642			−0.105321	−	0.994438i	$-0.533587\pi$
$919$	−193.580			−0.210642			−0.105321	+	0.994438i	$0.533587\pi$
$920$			123.806i			0.134572i
$921$	−441.427	−	1703.91i	−0.479291	−	1.85006i
$922$	36.4721			0.0395575
$923$		−	935.126i		−	1.01314i
$924$	−240.288	+	62.2508i	−0.260052	+	0.0673710i
$925$	836.766			0.904612
$926$			400.251i			0.432237i
$927$	−596.448	+	331.274i	−0.643418	+	0.357362i
$928$	−135.426			−0.145933
$929$			990.762i			1.06648i	0.845963	+	0.533241i	$0.179026\pi$
$929$			990.762i			1.06648i	−0.845963	+	0.533241i	$0.820974\pi$
$930$	389.614	+	1503.91i	0.418940	+	1.61711i
$931$	1885.40			2.02514
$932$		−	217.968i		−	0.233871i
$933$	792.077	−	205.201i	0.848957	−	0.219937i
$934$	−280.994			−0.300850
$935$		−	6.87001i		−	0.00734761i
$936$	185.389	+	333.786i	0.198065	+	0.356609i
$937$	1255.18			1.33957			0.669785	−	0.742555i	$-0.266386\pi$
$937$	1255.18			1.33957			0.669785	+	0.742555i	$0.266386\pi$
$938$		−	1538.37i		−	1.64006i
$939$	−61.5572	−	237.611i	−0.0655561	−	0.253047i
$940$	393.577			0.418699
$941$		−	687.884i		−	0.731014i	−0.930809	−	0.365507i	$-0.880896\pi$
$941$		−	687.884i		−	0.731014i	0.930809	−	0.365507i	$-0.119104\pi$
$942$	−130.397	+	33.7815i	−0.138425	+	0.0358615i
$943$	201.036			0.213188
$944$		−	222.222i		−	0.235404i
$945$	2061.67	−	1961.41i	2.18166	−	2.07557i
$946$	93.8522			0.0992095
$947$			1469.96i			1.55223i	0.630594	+	0.776113i	$0.282811\pi$
$947$			1469.96i			1.55223i	−0.630594	+	0.776113i	$0.717189\pi$
$948$	76.9896	+	297.180i	0.0812127	+	0.313481i
$949$	907.951			0.956745
$950$			1843.20i			1.94021i
$951$	581.594	−	150.672i	0.611560	−	0.158435i
$952$	−6.86198			−0.00720797
$953$		−	1446.50i		−	1.51783i	−0.651187	−	0.758917i	$-0.725729\pi$
$953$		−	1446.50i		−	1.51783i	0.651187	−	0.758917i	$-0.274271\pi$
$954$	−810.771	+	450.312i	−0.849865	+	0.472025i
$955$	−1573.09			−1.64721
$956$		−	112.155i		−	0.117317i
$957$	64.5296	+	249.084i	0.0674291	+	0.260276i
$958$	−303.024			−0.316309
$959$			1902.03i			1.98334i
$960$	−212.050	+	54.9352i	−0.220885	+	0.0572241i
$961$	648.598			0.674920
$962$		−	304.430i		−	0.316455i
$963$	299.188	+	538.678i	0.310684	+	0.559375i
$964$	194.783			0.202057
$965$			1206.17i			1.24992i
$966$	−58.9238	−	227.446i	−0.0609977	−	0.235451i
$967$	−113.524			−0.117398			−0.0586991	−	0.998276i	$-0.518695\pi$
$967$	−113.524			−0.117398			−0.0586991	+	0.998276i	$0.518695\pi$
$968$			305.936i			0.316049i
$969$	−13.6395	+	3.53355i	−0.0140759	+	0.00364660i
$970$	−795.282			−0.819878
$971$		−	149.421i		−	0.153884i	−0.997036	−	0.0769419i	$-0.975484\pi$
$971$		−	149.421i		−	0.153884i	0.997036	−	0.0769419i	$-0.0245156\pi$
$972$	463.814	+	145.165i	0.477174	+	0.149347i
$973$	−1399.78			−1.43863
$974$		−	187.582i		−	0.192589i
$975$	−657.944	−	2539.66i	−0.674815	−	2.60478i
$976$	297.729			0.305050
$977$			581.460i			0.595148i	0.954699	+	0.297574i	$0.0961775\pi$
$977$			581.460i			0.595148i	−0.954699	+	0.297574i	$0.903822\pi$
$978$	1220.02	−	316.068i	1.24746	−	0.323177i
$979$	−149.999			−0.153217
$980$		−	1539.59i		−	1.57101i
$981$	790.068	−	438.814i	0.805370	−	0.447312i
$982$	−378.202			−0.385135
$983$		−	87.9396i		−	0.0894605i	−0.998999	−	0.0447302i	$-0.985757\pi$
$983$		−	87.9396i		−	0.0894605i	0.998999	−	0.0447302i	$-0.0142428\pi$
$984$	89.2040	+	344.327i	0.0906545	+	0.349926i
$985$	−1304.04			−1.32389
$986$			7.11318i			0.00721417i
$987$	−723.047	+	187.318i	−0.732571	+	0.189785i
$988$	670.589			0.678734
$989$			88.8361i			0.0898242i
$990$	202.081	+	363.839i	0.204122	+	0.367514i
$991$	−651.226			−0.657140			−0.328570	−	0.944480i	$-0.606567\pi$
$991$	−651.226			−0.657140			−0.328570	+	0.944480i	$0.606567\pi$
$992$			226.952i			0.228782i
$993$	331.608	+	1280.00i	0.333945	+	1.28903i
$994$	−1018.13			−1.02428
$995$			1928.01i			1.93770i
$996$	−33.0794	+	8.56979i	−0.0332122	+	0.00860421i
$997$	−1481.53			−1.48599			−0.742995	−	0.669298i	$-0.766595\pi$
$997$	−1481.53			−1.48599			−0.742995	+	0.669298i	$0.766595\pi$
$998$			1137.19i			1.13947i
$999$	−267.093	−	280.745i	−0.267360	−	0.281026i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.3.c.a.47.3	✓	16
3.2	odd	2	inner	138.3.c.a.47.11	yes	16
4.3	odd	2		1104.3.g.c.737.12		16
12.11	even	2		1104.3.g.c.737.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.3.c.a.47.3	✓	16	1.1	even	1	trivial
138.3.c.a.47.11	yes	16	3.2	odd	2	inner
1104.3.g.c.737.11		16	12.11	even	2
1104.3.g.c.737.12		16	4.3	odd	2

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	138.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-0.752365 - 2.90413i) q^{3} -2.00000 q^{4} +9.12709i q^{5} +(-4.10705 + 1.06400i) q^{6} -11.5474 q^{7} +2.82843i q^{8} +(-7.86789 + 4.36992i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-0.752365 - 2.90413i) q^{3} -2.00000 q^{4} +9.12709i q^{5} +(-4.10705 + 1.06400i) q^{6} -11.5474 q^{7} +2.82843i q^{8} +(-7.86789 + 4.36992i) q^{9} +12.9076 q^{10} -3.58264i q^{11} +(1.50473 + 5.80825i) q^{12} -14.9991 q^{13} +16.3304i q^{14} +(26.5062 - 6.86690i) q^{15} +4.00000 q^{16} -0.210098i q^{17} +(6.18001 + 11.1269i) q^{18} +22.3543 q^{19} -18.2542i q^{20} +(8.68783 + 33.5350i) q^{21} -5.06663 q^{22} -4.79583i q^{23} +(8.21411 - 2.12801i) q^{24} -58.3037 q^{25} +21.2119i q^{26} +(18.6103 + 19.5616i) q^{27} +23.0947 q^{28} -23.9401i q^{29} +(-9.71126 - 37.4854i) q^{30} -40.1198 q^{31} -5.65685i q^{32} +(-10.4045 + 2.69546i) q^{33} -0.297123 q^{34} -105.394i q^{35} +(15.7358 - 8.73985i) q^{36} -14.3518 q^{37} -31.6138i q^{38} +(11.2848 + 43.5592i) q^{39} -25.8153 q^{40} +41.9190i q^{41} +(47.4257 - 12.2865i) q^{42} -18.5236 q^{43} +7.16529i q^{44} +(-39.8847 - 71.8110i) q^{45} -6.78233 q^{46} +21.5610i q^{47} +(-3.00946 - 11.6165i) q^{48} +84.3418 q^{49} +82.4539i q^{50} +(-0.610151 + 0.158070i) q^{51} +29.9982 q^{52} +72.8659i q^{53} +(27.6643 - 26.3190i) q^{54} +32.6991 q^{55} -32.6609i q^{56} +(-16.8186 - 64.9198i) q^{57} -33.8565 q^{58} -55.5555i q^{59} +(-53.0124 + 13.7338i) q^{60} +74.4322 q^{61} +56.7380i q^{62} +(90.8535 - 50.4611i) q^{63} -8.00000 q^{64} -136.898i q^{65} +(3.81195 + 14.7141i) q^{66} -94.2027 q^{67} +0.420196i q^{68} +(-13.9277 + 3.60821i) q^{69} -149.049 q^{70} +62.3455i q^{71} +(-12.3600 - 22.2538i) q^{72} -60.5338 q^{73} +20.2966i q^{74} +(43.8656 + 169.321i) q^{75} -44.7087 q^{76} +41.3701i q^{77} +(61.6020 - 15.9591i) q^{78} +51.1651 q^{79} +36.5083i q^{80} +(42.8075 - 68.7642i) q^{81} +59.2824 q^{82} +5.69524i q^{83} +(-17.3757 - 67.0700i) q^{84} +1.91758 q^{85} +26.1963i q^{86} +(-69.5252 + 18.0117i) q^{87} +10.1333 q^{88} -41.8683i q^{89} +(-101.556 + 56.4054i) q^{90} +173.200 q^{91} +9.59166i q^{92} +(30.1847 + 116.513i) q^{93} +30.4918 q^{94} +204.030i q^{95} +(-16.4282 + 4.25602i) q^{96} -61.6132 q^{97} -119.277i q^{98} +(15.6559 + 28.1879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9	\( 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9} - 8 q^{12} - 8 q^{13} + 28 q^{15} + 64 q^{16} + 16 q^{18} + 40 q^{19} + 4 q^{21} + 16 q^{22} + 16 q^{24} - 192 q^{25} - 80 q^{27} - 24 q^{30} + 136 q^{31} - 84 q^{33} - 16 q^{34} + 8 q^{36} - 136 q^{37} + 156 q^{39} + 128 q^{42} + 72 q^{43} + 4 q^{45} + 16 q^{48} + 224 q^{49} - 4 q^{51} + 16 q^{52} - 176 q^{54} - 96 q^{55} - 160 q^{57} - 56 q^{60} + 48 q^{61} + 204 q^{63} - 128 q^{64} - 144 q^{66} - 304 q^{67} - 176 q^{70} - 32 q^{72} + 408 q^{73} + 68 q^{75} - 80 q^{76} + 328 q^{78} + 312 q^{79} + 164 q^{81} + 160 q^{82} - 8 q^{84} - 464 q^{85} - 268 q^{87} - 32 q^{88} + 32 q^{90} - 72 q^{91} - 108 q^{93} - 32 q^{96} + 168 q^{97} - 60 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9 - 8 * q^12 - 8 * q^13 + 28 * q^15 + 64 * q^16 + 16 * q^18 + 40 * q^19 + 4 * q^21 + 16 * q^22 + 16 * q^24 - 192 * q^25 - 80 * q^27 - 24 * q^30 + 136 * q^31 - 84 * q^33 - 16 * q^34 + 8 * q^36 - 136 * q^37 + 156 * q^39 + 128 * q^42 + 72 * q^43 + 4 * q^45 + 16 * q^48 + 224 * q^49 - 4 * q^51 + 16 * q^52 - 176 * q^54 - 96 * q^55 - 160 * q^57 - 56 * q^60 + 48 * q^61 + 204 * q^63 - 128 * q^64 - 144 * q^66 - 304 * q^67 - 176 * q^70 - 32 * q^72 + 408 * q^73 + 68 * q^75 - 80 * q^76 + 328 * q^78 + 312 * q^79 + 164 * q^81 + 160 * q^82 - 8 * q^84 - 464 * q^85 - 268 * q^87 - 32 * q^88 + 32 * q^90 - 72 * q^91 - 108 * q^93 - 32 * q^96 + 168 * q^97 - 60 * q^99

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