LMFDB - Embedded newform 169.3.f.c.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,3,Mod(19,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("169.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	169.f (of order $12$, degree $4$, not 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:	$4.60491646769$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	169.19
Dual form			169.3.f.c.89.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.133975 + 0.500000i) q^{2} +(0.366025 - 0.633975i) q^{3} +(3.23205 - 1.86603i) q^{4} +(-2.63397 + 2.63397i) q^{5} +(0.366025 + 0.0980762i) q^{6} +(-1.53590 + 5.73205i) q^{7} +(2.83013 + 2.83013i) q^{8} +(4.23205 + 7.33013i) q^{9} +(-1.66987 - 0.964102i) q^{10} +(15.6603 - 4.19615i) q^{11} -2.73205i q^{12} -3.07180 q^{14} +(0.705771 + 2.63397i) q^{15} +(6.42820 - 11.1340i) q^{16} +(15.9904 - 9.23205i) q^{17} +(-3.09808 + 3.09808i) q^{18} +(-6.09808 - 1.63397i) q^{19} +(-3.59808 + 13.4282i) q^{20} +(3.07180 + 3.07180i) q^{21} +(4.19615 + 7.26795i) q^{22} +(-17.4904 - 10.0981i) q^{23} +(2.83013 - 0.758330i) q^{24} +11.1244i q^{25} +12.7846 q^{27} +(5.73205 + 21.3923i) q^{28} +(-4.69615 + 8.13397i) q^{29} +(-1.22243 + 0.705771i) q^{30} +(-11.9282 + 11.9282i) q^{31} +(21.8923 + 5.86603i) q^{32} +(3.07180 - 11.4641i) q^{33} +(6.75833 + 6.75833i) q^{34} +(-11.0526 - 19.1436i) q^{35} +(27.3564 + 15.7942i) q^{36} +(-30.2846 + 8.11474i) q^{37} -3.26795i q^{38} -14.9090 q^{40} +(-12.0359 - 44.9186i) q^{41} +(-1.12436 + 1.94744i) q^{42} +(-45.0000 + 25.9808i) q^{43} +(42.7846 - 42.7846i) q^{44} +(-30.4545 - 8.16025i) q^{45} +(2.70577 - 10.0981i) q^{46} +(-34.3205 - 34.3205i) q^{47} +(-4.70577 - 8.15064i) q^{48} +(11.9378 + 6.89230i) q^{49} +(-5.56218 + 1.49038i) q^{50} -13.5167i q^{51} -14.7654 q^{53} +(1.71281 + 6.39230i) q^{54} +(-30.1962 + 52.3013i) q^{55} +(-20.5692 + 11.8756i) q^{56} +(-3.26795 + 3.26795i) q^{57} +(-4.69615 - 1.25833i) q^{58} +(24.9090 - 92.9615i) q^{59} +(7.19615 + 7.19615i) q^{60} +(-12.8135 - 22.1936i) q^{61} +(-7.56218 - 4.36603i) q^{62} +(-48.5167 + 13.0000i) q^{63} -39.6936i q^{64} +6.14359 q^{66} +(-10.4571 - 39.0263i) q^{67} +(34.4545 - 59.6769i) q^{68} +(-12.8038 + 7.39230i) q^{69} +(8.09103 - 8.09103i) q^{70} +(44.6865 + 11.9737i) q^{71} +(-8.76795 + 32.7224i) q^{72} +(-19.2750 - 19.2750i) q^{73} +(-8.11474 - 14.0551i) q^{74} +(7.05256 + 4.07180i) q^{75} +(-22.7583 + 6.09808i) q^{76} +96.2102i q^{77} +62.7461 q^{79} +(12.3949 + 46.2583i) q^{80} +(-33.4090 + 57.8660i) q^{81} +(20.8468 - 12.0359i) q^{82} +(-24.4833 + 24.4833i) q^{83} +(15.6603 + 4.19615i) q^{84} +(-17.8013 + 66.4352i) q^{85} +(-19.0192 - 19.0192i) q^{86} +(3.43782 + 5.95448i) q^{87} +(56.1962 + 32.4449i) q^{88} +(86.4711 - 23.1699i) q^{89} -16.3205i q^{90} -75.3731 q^{92} +(3.19615 + 11.9282i) q^{93} +(12.5622 - 21.7583i) q^{94} +(20.3660 - 11.7583i) q^{95} +(11.7321 - 11.7321i) q^{96} +(-52.9545 - 14.1891i) q^{97} +(-1.84679 + 6.89230i) q^{98} +(97.0333 + 97.0333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 2 q^{3} + 6 q^{4} - 14 q^{5} - 2 q^{6} - 20 q^{7} - 6 q^{8} + 10 q^{9} - 24 q^{10} + 28 q^{11} - 40 q^{14} + 34 q^{15} - 2 q^{16} + 12 q^{17} - 2 q^{18} - 14 q^{19} - 4 q^{20} + 40 q^{21}+ \cdots + 208 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 2 * q^3 + 6 * q^4 - 14 * q^5 - 2 * q^6 - 20 * q^7 - 6 * q^8 + 10 * q^9 - 24 * q^10 + 28 * q^11 - 40 * q^14 + 34 * q^15 - 2 * q^16 + 12 * q^17 - 2 * q^18 - 14 * q^19 - 4 * q^20 + 40 * q^21 - 4 * q^22 - 18 * q^23 - 6 * q^24 - 32 * q^27 + 16 * q^28 + 2 * q^29 + 54 * q^30 - 20 * q^31 + 46 * q^32 + 40 * q^33 - 18 * q^34 + 32 * q^35 + 54 * q^36 - 38 * q^37 + 72 * q^40 - 62 * q^41 + 44 * q^42 - 180 * q^43 + 88 * q^44 - 56 * q^45 + 42 * q^46 - 68 * q^47 - 50 * q^48 + 72 * q^49 + 2 * q^50 + 128 * q^53 - 104 * q^54 - 100 * q^55 + 84 * q^56 - 20 * q^57 + 2 * q^58 - 32 * q^59 + 8 * q^60 - 124 * q^61 - 6 * q^62 - 104 * q^63 + 80 * q^66 - 170 * q^67 + 72 * q^68 - 72 * q^69 + 164 * q^70 + 106 * q^71 - 42 * q^72 + 58 * q^73 + 68 * q^74 - 48 * q^75 - 46 * q^76 - 40 * q^79 + 202 * q^80 - 2 * q^81 - 24 * q^82 - 188 * q^83 + 28 * q^84 + 102 * q^85 - 180 * q^86 + 38 * q^87 + 204 * q^88 + 190 * q^89 - 156 * q^92 - 8 * q^93 + 26 * q^94 + 78 * q^95 + 40 * q^96 - 146 * q^97 + 100 * q^98 + 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.133975	+	0.500000i	0.0669873	+	0.250000i	0.991297	−	0.131643i	$-0.0420252\pi$
$2$	0.133975	+	0.500000i	0.0669873	+	0.250000i	−0.924310	+	0.381643i	$0.875358\pi$
$3$	0.366025	−	0.633975i	0.122008	−	0.211325i	−0.798551	−	0.601927i	$-0.794400\pi$
$3$	0.366025	−	0.633975i	0.122008	−	0.211325i	0.920560	+	0.390602i	$0.127733\pi$
$4$	3.23205	−	1.86603i	0.808013	−	0.466506i
$5$	−2.63397	+	2.63397i	−0.526795	+	0.526795i	−0.919615	−	0.392820i	$-0.871499\pi$
$5$	−2.63397	+	2.63397i	−0.526795	+	0.526795i	0.392820	+	0.919615i	$0.371499\pi$
$6$	0.366025	+	0.0980762i	0.0610042	+	0.0163460i
$7$	−1.53590	+	5.73205i	−0.219414	+	0.818864i	0.765152	+	0.643850i	$0.222664\pi$
$7$	−1.53590	+	5.73205i	−0.219414	+	0.818864i	−0.984566	+	0.175014i	$0.944003\pi$
$8$	2.83013	+	2.83013i	0.353766	+	0.353766i
$9$	4.23205	+	7.33013i	0.470228	+	0.814459i
$10$	−1.66987	−	0.964102i	−0.166987	−	0.0964102i
$11$	15.6603	−	4.19615i	1.42366	−	0.381468i	0.536879	−	0.843659i	$-0.319603\pi$
$11$	15.6603	−	4.19615i	1.42366	−	0.381468i	0.886780	+	0.462191i	$0.152937\pi$
$12$		−	2.73205i		−	0.227671i
$13$		0			0
$13$		0			0
$14$	−3.07180			−0.219414
$15$	0.705771	+	2.63397i	0.0470514	+	0.175598i
$16$	6.42820	−	11.1340i	0.401763	−	0.695873i
$17$	15.9904	−	9.23205i	0.940611	−	0.543062i	0.0504590	−	0.998726i	$-0.483932\pi$
$17$	15.9904	−	9.23205i	0.940611	−	0.543062i	0.890152	+	0.455664i	$0.150598\pi$
$18$	−3.09808	+	3.09808i	−0.172115	+	0.172115i
$19$	−6.09808	−	1.63397i	−0.320951	−	0.0859987i	0.0947465	−	0.995501i	$-0.469796\pi$
$19$	−6.09808	−	1.63397i	−0.320951	−	0.0859987i	−0.415698	+	0.909503i	$0.636463\pi$
$20$	−3.59808	+	13.4282i	−0.179904	+	0.671410i
$21$	3.07180	+	3.07180i	0.146276	+	0.146276i
$22$	4.19615	+	7.26795i	0.190734	+	0.330361i
$23$	−17.4904	−	10.0981i	−0.760451	−	0.439047i	0.0690064	−	0.997616i	$-0.478017\pi$
$23$	−17.4904	−	10.0981i	−0.760451	−	0.439047i	−0.829458	+	0.558569i	$0.811350\pi$
$24$	2.83013	−	0.758330i	0.117922	−	0.0315971i
$25$			11.1244i			0.444974i
$26$		0			0
$27$	12.7846			0.473504
$28$	5.73205	+	21.3923i	0.204716	+	0.764011i
$29$	−4.69615	+	8.13397i	−0.161936	+	0.280482i	−0.935563	−	0.353160i	$-0.885107\pi$
$29$	−4.69615	+	8.13397i	−0.161936	+	0.280482i	0.773627	+	0.633642i	$0.218441\pi$
$30$	−1.22243	+	0.705771i	−0.0407477	+	0.0235257i
$31$	−11.9282	+	11.9282i	−0.384781	+	0.384781i	−0.872821	−	0.488040i	$-0.837712\pi$
$31$	−11.9282	+	11.9282i	−0.384781	+	0.384781i	0.488040	+	0.872821i	$0.337712\pi$
$32$	21.8923	+	5.86603i	0.684135	+	0.183313i
$33$	3.07180	−	11.4641i	0.0930848	−	0.347397i
$34$	6.75833	+	6.75833i	0.198774	+	0.198774i
$35$	−11.0526	−	19.1436i	−0.315787	−	0.546960i
$36$	27.3564	+	15.7942i	0.759900	+	0.438729i
$37$	−30.2846	+	8.11474i	−0.818503	+	0.219317i	−0.643692	−	0.765285i	$-0.722598\pi$
$37$	−30.2846	+	8.11474i	−0.818503	+	0.219317i	−0.174811	+	0.984602i	$0.555931\pi$
$38$		−	3.26795i		−	0.0859987i
$39$		0			0
$40$	−14.9090			−0.372724
$41$	−12.0359	−	44.9186i	−0.293558	−	1.09558i	−0.942355	−	0.334614i	$-0.891394\pi$
$41$	−12.0359	−	44.9186i	−0.293558	−	1.09558i	0.648797	−	0.760962i	$-0.275272\pi$
$42$	−1.12436	+	1.94744i	−0.0267704	+	0.0463676i
$43$	−45.0000	+	25.9808i	−1.04651	+	0.604204i	−0.921671	−	0.387973i	$-0.873175\pi$
$43$	−45.0000	+	25.9808i	−1.04651	+	0.604204i	−0.124841	+	0.992177i	$0.539842\pi$
$44$	42.7846	−	42.7846i	0.972377	−	0.972377i
$45$	−30.4545	−	8.16025i	−0.676766	−	0.181339i
$46$	2.70577	−	10.0981i	0.0588211	−	0.219523i
$47$	−34.3205	−	34.3205i	−0.730224	−	0.730224i	0.240440	−	0.970664i	$-0.422708\pi$
$47$	−34.3205	−	34.3205i	−0.730224	−	0.730224i	−0.970664	+	0.240440i	$0.922708\pi$
$48$	−4.70577	−	8.15064i	−0.0980369	−	0.169805i
$49$	11.9378	+	6.89230i	0.243629	+	0.140659i
$50$	−5.56218	+	1.49038i	−0.111244	+	0.0298076i
$51$		−	13.5167i		−	0.265033i
$52$		0			0
$53$	−14.7654			−0.278592			−0.139296	−	0.990251i	$-0.544484\pi$
$53$	−14.7654			−0.278592			−0.139296	+	0.990251i	$0.544484\pi$
$54$	1.71281	+	6.39230i	0.0317188	+	0.118376i
$55$	−30.1962	+	52.3013i	−0.549021	+	0.950932i
$56$	−20.5692	+	11.8756i	−0.367307	+	0.212065i
$57$	−3.26795	+	3.26795i	−0.0573324	+	0.0573324i
$58$	−4.69615	−	1.25833i	−0.0809681	−	0.0216953i
$59$	24.9090	−	92.9615i	0.422186	−	1.57562i	−0.347807	−	0.937566i	$-0.613073\pi$
$59$	24.9090	−	92.9615i	0.422186	−	1.57562i	0.769993	−	0.638053i	$-0.220260\pi$
$60$	7.19615	+	7.19615i	0.119936	+	0.119936i
$61$	−12.8135	−	22.1936i	−0.210057	−	0.363829i	0.741675	−	0.670759i	$-0.234032\pi$
$61$	−12.8135	−	22.1936i	−0.210057	−	0.363829i	−0.951732	+	0.306930i	$0.900698\pi$
$62$	−7.56218	−	4.36603i	−0.121971	−	0.0704198i
$63$	−48.5167	+	13.0000i	−0.770106	+	0.206349i
$64$		−	39.6936i		−	0.620212i
$65$		0			0
$66$	6.14359			0.0930848
$67$	−10.4571	−	39.0263i	−0.156076	−	0.582482i	−0.999011	−	0.0444669i	$-0.985841\pi$
$67$	−10.4571	−	39.0263i	−0.156076	−	0.582482i	0.842935	−	0.538015i	$-0.180826\pi$
$68$	34.4545	−	59.6769i	0.506684	−	0.877602i
$69$	−12.8038	+	7.39230i	−0.185563	+	0.107135i
$70$	8.09103	−	8.09103i	0.115586	−	0.115586i
$71$	44.6865	+	11.9737i	0.629388	+	0.168644i	0.559392	−	0.828903i	$-0.311035\pi$
$71$	44.6865	+	11.9737i	0.629388	+	0.168644i	0.0699959	+	0.997547i	$0.477701\pi$
$72$	−8.76795	+	32.7224i	−0.121777	+	0.454478i
$73$	−19.2750	−	19.2750i	−0.264041	−	0.264041i	0.562653	−	0.826693i	$-0.309781\pi$
$73$	−19.2750	−	19.2750i	−0.264041	−	0.264041i	−0.826693	+	0.562653i	$0.809781\pi$
$74$	−8.11474	−	14.0551i	−0.109659	−	0.189934i
$75$	7.05256	+	4.07180i	0.0940341	+	0.0542906i
$76$	−22.7583	+	6.09808i	−0.299452	+	0.0802378i
$77$			96.2102i			1.24948i
$78$		0			0
$79$	62.7461			0.794255			0.397127	−	0.917763i	$-0.370007\pi$
$79$	62.7461			0.794255			0.397127	+	0.917763i	$0.370007\pi$
$80$	12.3949	+	46.2583i	0.154936	+	0.578229i
$81$	−33.4090	+	57.8660i	−0.412456	+	0.714395i
$82$	20.8468	−	12.0359i	0.254229	−	0.146779i
$83$	−24.4833	+	24.4833i	−0.294980	+	0.294980i	−0.839044	−	0.544064i	$-0.816885\pi$
$83$	−24.4833	+	24.4833i	−0.294980	+	0.294980i	0.544064	+	0.839044i	$0.316885\pi$
$84$	15.6603	+	4.19615i	0.186432	+	0.0499542i
$85$	−17.8013	+	66.4352i	−0.209427	+	0.781591i
$86$	−19.0192	−	19.0192i	−0.221154	−	0.221154i
$87$	3.43782	+	5.95448i	0.0395152	+	0.0684423i
$88$	56.1962	+	32.4449i	0.638593	+	0.368692i
$89$	86.4711	−	23.1699i	0.971586	−	0.260336i	0.262089	−	0.965044i	$-0.415589\pi$
$89$	86.4711	−	23.1699i	0.971586	−	0.260336i	0.709497	+	0.704708i	$0.248922\pi$
$90$		−	16.3205i		−	0.181339i
$91$		0			0
$92$	−75.3731			−0.819272
$93$	3.19615	+	11.9282i	0.0343672	+	0.128260i
$94$	12.5622	−	21.7583i	0.133640	−	0.231472i
$95$	20.3660	−	11.7583i	0.214379	−	0.123772i
$96$	11.7321	−	11.7321i	0.122209	−	0.122209i
$97$	−52.9545	−	14.1891i	−0.545923	−	0.146279i	−0.0246915	−	0.999695i	$-0.507860\pi$
$97$	−52.9545	−	14.1891i	−0.545923	−	0.146279i	−0.521231	+	0.853416i	$0.674527\pi$
$98$	−1.84679	+	6.89230i	−0.0188448	+	0.0703296i
$99$	97.0333	+	97.0333i	0.980135	+	0.980135i
$100$	20.7583	+	35.9545i	0.207583	+	0.359545i
$101$	−138.560	−	79.9974i	−1.37188	−	0.792054i	−0.380713	−	0.924693i	$-0.624321\pi$
$101$	−138.560	−	79.9974i	−1.37188	−	0.792054i	−0.991164	+	0.132640i	$0.957655\pi$
$102$	6.75833	−	1.81089i	0.0662581	−	0.0177538i
$103$		−	78.7705i		−	0.764762i	−0.924005	−	0.382381i	$-0.875104\pi$
$103$		−	78.7705i		−	0.764762i	0.924005	−	0.382381i	$-0.124896\pi$
$104$		0			0
$105$	−16.1821			−0.154115
$106$	−1.97818	−	7.38269i	−0.0186621	−	0.0696480i
$107$	47.6673	−	82.5622i	0.445489	−	0.771609i	−0.552597	−	0.833448i	$-0.686363\pi$
$107$	47.6673	−	82.5622i	0.445489	−	0.771609i	0.998086	+	0.0618392i	$0.0196966\pi$
$108$	41.3205	−	23.8564i	0.382597	−	0.220893i
$109$	−51.9808	+	51.9808i	−0.476888	+	0.476888i	−0.904135	−	0.427247i	$-0.859483\pi$
$109$	−51.9808	+	51.9808i	−0.476888	+	0.476888i	0.427247	+	0.904135i	$0.359483\pi$
$110$	−30.1962	−	8.09103i	−0.274510	−	0.0735549i
$111$	−5.94040	+	22.1699i	−0.0535171	+	0.199729i
$112$	53.9474	+	53.9474i	0.481674	+	0.481674i
$113$	71.9904	+	124.691i	0.637083	+	1.10346i	0.986070	+	0.166332i	$0.0531925\pi$
$113$	71.9904	+	124.691i	0.637083	+	1.10346i	−0.348987	+	0.937128i	$0.613474\pi$
$114$	−2.07180	−	1.19615i	−0.0181737	−	0.0104926i
$115$	72.6673	−	19.4711i	0.631890	−	0.169314i
$116$			35.0526i			0.302177i
$117$		0			0
$118$	49.8179			0.422186
$119$	28.3590	+	105.837i	0.238311	+	0.889388i
$120$	−5.45706	+	9.45191i	−0.0454755	+	0.0787659i
$121$	122.847	−	70.9256i	1.01526	−	0.586162i
$122$	9.38011	−	9.38011i	0.0768861	−	0.0768861i
$123$	−32.8827	−	8.81089i	−0.267339	−	0.0716332i
$124$	−16.2942	+	60.8109i	−0.131405	+	0.490410i
$125$	−95.1506	−	95.1506i	−0.761205	−	0.761205i
$126$	−13.0000	−	22.5167i	−0.103175	−	0.178704i
$127$	24.6673	+	14.2417i	0.194231	+	0.112139i	0.593962	−	0.804493i	$-0.297563\pi$
$127$	24.6673	+	14.2417i	0.194231	+	0.112139i	−0.399731	+	0.916633i	$0.630896\pi$
$128$	107.416	−	28.7820i	0.839188	−	0.224860i
$129$			38.0385i			0.294872i
$130$		0			0
$131$	−2.98076			−0.0227539			−0.0113770	−	0.999935i	$-0.503621\pi$
$131$	−2.98076			−0.0227539			−0.0113770	+	0.999935i	$0.503621\pi$
$132$	−11.4641	−	42.7846i	−0.0868493	−	0.324126i
$133$	18.7321	−	32.4449i	0.140842	−	0.243946i
$134$	18.1122	−	10.4571i	0.135165	−	0.0780378i
$135$	−33.6743	+	33.6743i	−0.249440	+	0.249440i
$136$	71.3827	+	19.1269i	0.524873	+	0.140639i
$137$	−25.3494	+	94.6051i	−0.185032	+	0.690548i	0.809592	+	0.586993i	$0.199688\pi$
$137$	−25.3494	+	94.6051i	−0.185032	+	0.690548i	−0.994624	+	0.103555i	$0.966978\pi$
$138$	−5.41154	−	5.41154i	−0.0392141	−	0.0392141i
$139$	−16.2154	−	28.0859i	−0.116657	−	0.202057i	0.801784	−	0.597614i	$-0.203885\pi$
$139$	−16.2154	−	28.0859i	−0.116657	−	0.202057i	−0.918441	+	0.395558i	$0.870551\pi$
$140$	−71.4449	−	41.2487i	−0.510320	−	0.294634i
$141$	−34.3205	+	9.19615i	−0.243408	+	0.0652209i
$142$			23.9474i			0.168644i
$143$		0			0
$144$	108.818			0.755680
$145$	−9.05514	−	33.7942i	−0.0624492	−	0.233064i
$146$	7.05514	−	12.2199i	0.0483229	−	0.0836976i
$147$	8.73909	−	5.04552i	0.0594496	−	0.0343232i
$148$	−82.7391	+	82.7391i	−0.559048	+	0.559048i
$149$	123.495	+	33.0903i	0.828824	+	0.222083i	0.648201	−	0.761469i	$-0.275522\pi$
$149$	123.495	+	33.0903i	0.828824	+	0.222083i	0.180624	+	0.983552i	$0.442188\pi$
$150$	−1.09103	+	4.07180i	−0.00727356	+	0.0271453i
$151$	127.995	+	127.995i	0.847648	+	0.847648i	0.989839	−	0.142191i	$-0.0454148\pi$
$151$	127.995	+	127.995i	0.847648	+	0.847648i	−0.142191	+	0.989839i	$0.545415\pi$
$152$	−12.6340	−	21.8827i	−0.0831183	−	0.143965i
$153$	135.344	+	78.1410i	0.884603	+	0.510726i
$154$	−48.1051	+	12.8897i	−0.312371	+	0.0836995i
$155$		−	62.8372i		−	0.405401i
$156$		0			0
$157$	−97.7461			−0.622587			−0.311293	−	0.950314i	$-0.600762\pi$
$157$	−97.7461			−0.622587			−0.311293	+	0.950314i	$0.600762\pi$
$158$	8.40639	+	31.3731i	0.0532050	+	0.198564i
$159$	−5.40450	+	9.36087i	−0.0339906	+	0.0588734i
$160$	−73.1147	+	42.2128i	−0.456967	+	0.263830i
$161$	84.7461	−	84.7461i	0.526374	−	0.526374i
$162$	−33.4090	−	8.95191i	−0.206228	−	0.0552587i
$163$	32.7654	−	122.282i	0.201015	−	0.750197i	−0.789613	−	0.613605i	$-0.789719\pi$
$163$	32.7654	−	122.282i	0.201015	−	0.750197i	0.990627	−	0.136591i	$-0.0436147\pi$
$164$	−122.720	−	122.720i	−0.748292	−	0.748292i
$165$	22.1051	+	38.2872i	0.133970	+	0.232044i
$166$	−15.5218	−	8.96152i	−0.0935049	−	0.0539851i
$167$	50.7321	−	13.5936i	0.303785	−	0.0813989i	−0.103707	−	0.994608i	$-0.533070\pi$
$167$	50.7321	−	13.5936i	0.303785	−	0.0813989i	0.407491	+	0.913209i	$0.366404\pi$
$168$			17.3872i			0.103495i
$169$		0			0
$170$	−35.6025			−0.209427
$171$	−13.8301	−	51.6147i	−0.0808779	−	0.301841i
$172$	−96.9615	+	167.942i	−0.563730	+	0.976409i
$173$	−118.865	+	68.6269i	−0.687083	+	0.396687i	−0.802518	−	0.596628i	$-0.796507\pi$
$173$	−118.865	+	68.6269i	−0.687083	+	0.396687i	0.115435	+	0.993315i	$0.463174\pi$
$174$	−2.51666	+	2.51666i	−0.0144636	+	0.0144636i
$175$	−63.7654	−	17.0859i	−0.364374	−	0.0976336i
$176$	53.9474	−	201.335i	0.306520	−	1.14395i
$177$	−49.8179	−	49.8179i	−0.281457	−	0.281457i
$178$	23.1699	+	40.1314i	0.130168	+	0.225457i
$179$	−0.903811	−	0.521815i	−0.00504922	−	0.00291517i	0.497473	−	0.867479i	$-0.334261\pi$
$179$	−0.903811	−	0.521815i	−0.00504922	−	0.00291517i	−0.502522	+	0.864564i	$0.667595\pi$
$180$	−113.658	+	30.4545i	−0.631432	+	0.169192i
$181$		−	23.0807i		−	0.127518i	−0.997965	−	0.0637589i	$-0.979691\pi$
$181$		−	23.0807i		−	0.127518i	0.997965	−	0.0637589i	$-0.0203089\pi$
$182$		0			0
$183$	−18.7602			−0.102515
$184$	−20.9212	−	78.0788i	−0.113702	−	0.424342i
$185$	58.3949	−	101.143i	0.315648	−	0.546718i
$186$	−5.53590	+	3.19615i	−0.0297629	+	0.0171836i
$187$	211.674	−	211.674i	1.13195	−	1.13195i
$188$	−174.969	−	46.8827i	−0.930684	−	0.249376i
$189$	−19.6359	+	73.2820i	−0.103893	+	0.387736i
$190$	8.60770	+	8.60770i	0.0453037	+	0.0453037i
$191$	−147.002	−	254.615i	−0.769643	−	1.33306i	−0.937756	−	0.347294i	$-0.887101\pi$
$191$	−147.002	−	254.615i	−0.769643	−	1.33306i	0.168113	−	0.985768i	$-0.446233\pi$
$192$	−25.1647	−	14.5289i	−0.131066	−	0.0756711i
$193$	−319.279	+	85.5507i	−1.65430	+	0.443268i	−0.960812	−	0.277202i	$-0.910593\pi$
$193$	−319.279	+	85.5507i	−1.65430	+	0.443268i	−0.693486	+	0.720470i	$0.743926\pi$
$194$		−	28.3782i		−	0.146279i
$195$		0			0
$196$	51.4449			0.262474
$197$	−22.8057	−	85.1122i	−0.115765	−	0.432041i	0.883578	−	0.468284i	$-0.155128\pi$
$197$	−22.8057	−	85.1122i	−0.115765	−	0.432041i	−0.999343	+	0.0362429i	$0.988461\pi$
$198$	−35.5167	+	61.5167i	−0.179377	+	0.310690i
$199$	−174.452	+	100.720i	−0.876643	+	0.506130i	−0.869550	−	0.493845i	$-0.835591\pi$
$199$	−174.452	+	100.720i	−0.876643	+	0.506130i	−0.00709275	+	0.999975i	$0.502258\pi$
$200$	−31.4833	+	31.4833i	−0.157417	+	0.157417i
$201$	−28.5692	−	7.65510i	−0.142135	−	0.0380851i
$202$	21.4352	−	79.9974i	0.106115	−	0.396027i
$203$	−39.4115	−	39.4115i	−0.194146	−	0.194146i
$204$	−25.2224	−	43.6865i	−0.123639	−	0.214150i
$205$	150.017	+	86.6122i	0.731789	+	0.422498i
$206$	39.3853	−	10.5532i	0.191191	−	0.0512294i
$207$		−	170.942i		−	0.825808i
$208$		0			0
$209$	−102.354			−0.489731
$210$	−2.16799	−	8.09103i	−0.0103237	−	0.0385287i
$211$	−36.6481	+	63.4763i	−0.173687	+	0.300836i	−0.939706	−	0.341983i	$-0.888902\pi$
$211$	−36.6481	+	63.4763i	−0.173687	+	0.300836i	0.766019	+	0.642818i	$0.222235\pi$
$212$	−47.7224	+	27.5526i	−0.225106	+	0.129965i
$213$	23.9474	−	23.9474i	0.112429	−	0.112429i
$214$	47.6673	+	12.7724i	0.222744	+	0.0596842i
$215$	50.0962	−	186.962i	0.233006	−	0.869588i
$216$	36.1821	+	36.1821i	0.167510	+	0.167510i
$217$	−50.0526	−	86.6936i	−0.230657	−	0.399510i
$218$	−32.9545	−	19.0263i	−0.151167	−	0.0872765i
$219$	−19.2750	+	5.16472i	−0.0880137	+	0.0235832i
$220$			225.387i			1.02449i
$221$		0			0
$222$	−11.8808			−0.0535171
$223$	98.4801	+	367.533i	0.441615	+	1.64813i	0.724723	+	0.689040i	$0.241968\pi$
$223$	98.4801	+	367.533i	0.441615	+	1.64813i	−0.283108	+	0.959088i	$0.591366\pi$
$224$	−67.2487	+	116.478i	−0.300217	+	0.519992i
$225$	−81.5429	+	47.0788i	−0.362413	+	0.209239i
$226$	−52.7006	+	52.7006i	−0.233189	+	0.233189i
$227$	404.107	+	108.280i	1.78021	+	0.477005i	0.990621	−	0.136635i	$-0.0436289\pi$
$227$	404.107	+	108.280i	1.78021	+	0.477005i	0.789586	+	0.613640i	$0.210296\pi$
$228$	−4.46410	+	16.6603i	−0.0195794	+	0.0730713i
$229$	−72.2679	−	72.2679i	−0.315581	−	0.315581i	0.531486	−	0.847067i	$-0.321634\pi$
$229$	−72.2679	−	72.2679i	−0.315581	−	0.315581i	−0.847067	+	0.531486i	$0.821634\pi$
$230$	19.4711	+	33.7250i	0.0846571	+	0.146630i
$231$	60.9948	+	35.2154i	0.264047	+	0.152448i
$232$	−36.3109	+	9.72947i	−0.156512	+	0.0419374i
$233$			256.592i			1.10125i	0.834751	+	0.550627i	$0.185611\pi$
$233$			256.592i			1.10125i	−0.834751	+	0.550627i	$0.814389\pi$
$234$		0			0
$235$	180.799			0.769356
$236$	−92.9615	−	346.937i	−0.393905	−	1.47007i
$237$	22.9667	−	39.7795i	0.0969058	−	0.167846i
$238$	−49.1192	+	28.3590i	−0.206383	+	0.119155i
$239$	39.3449	−	39.3449i	0.164623	−	0.164623i	−0.619988	−	0.784611i	$-0.712863\pi$
$239$	39.3449	−	39.3449i	0.164623	−	0.164623i	0.784611	+	0.619988i	$0.212863\pi$
$240$	33.8634	+	9.07368i	0.141098	+	0.0378070i
$241$	−62.5263	+	233.351i	−0.259445	+	0.968262i	0.706118	+	0.708094i	$0.250445\pi$
$241$	−62.5263	+	233.351i	−0.259445	+	0.968262i	−0.965563	+	0.260168i	$0.916222\pi$
$242$	51.9212	+	51.9212i	0.214550	+	0.214550i
$243$	81.9878	+	142.007i	0.337398	+	0.584391i
$244$	−82.8275	−	47.8205i	−0.339457	−	0.195986i
$245$	−49.5981	+	13.2898i	−0.202441	+	0.0542439i
$246$		−	17.6218i		−	0.0716332i
$247$		0			0
$248$	−67.5167			−0.272245
$249$	6.56029	+	24.4833i	0.0263466	+	0.0983267i
$250$	34.8275	−	60.3231i	0.139310	−	0.241292i
$251$	221.375	−	127.811i	0.881972	−	0.509207i	0.0106638	−	0.999943i	$-0.496606\pi$
$251$	221.375	−	127.811i	0.881972	−	0.509207i	0.871308	+	0.490736i	$0.163272\pi$
$252$	−132.550	+	132.550i	−0.525992	+	0.525992i
$253$	−316.277	−	84.7461i	−1.25011	−	0.334965i
$254$	−3.81604	+	14.2417i	−0.0150238	+	0.0560696i
$255$	35.6025	+	35.6025i	0.139618	+	0.139618i
$256$	−50.6051	−	87.6506i	−0.197676	−	0.342385i
$257$	−85.7731	−	49.5211i	−0.333747	−	0.192689i	0.323756	−	0.946141i	$-0.395054\pi$
$257$	−85.7731	−	49.5211i	−0.333747	−	0.192689i	−0.657504	+	0.753451i	$0.728388\pi$
$258$	−19.0192	+	5.09619i	−0.0737180	+	0.0197527i
$259$		−	186.056i		−	0.718364i
$260$		0			0
$261$	−79.4974			−0.304588
$262$	−0.399346	−	1.49038i	−0.00152422	−	0.00568848i
$263$	127.669	−	221.130i	0.485434	−	0.840797i	−0.514426	−	0.857535i	$-0.671995\pi$
$263$	127.669	−	221.130i	0.485434	−	0.840797i	0.999860	+	0.0167383i	$0.00532822\pi$
$264$	41.1384	−	23.7513i	0.155827	−	0.0899670i
$265$	38.8916	−	38.8916i	0.146761	−	0.146761i
$266$	18.7321	+	5.01924i	0.0704212	+	0.0188693i
$267$	16.9615	−	63.3013i	0.0635263	−	0.237083i
$268$	−106.622	−	106.622i	−0.397842	−	0.397842i
$269$	46.3538	+	80.2872i	0.172319	+	0.298465i	0.939230	−	0.343288i	$-0.111541\pi$
$269$	46.3538	+	80.2872i	0.172319	+	0.298465i	−0.766911	+	0.641753i	$0.778207\pi$
$270$	−21.3487	−	12.3257i	−0.0790692	−	0.0456506i
$271$	422.219	−	113.133i	1.55800	−	0.417466i	0.625973	−	0.779845i	$-0.284702\pi$
$271$	422.219	−	113.133i	1.55800	−	0.417466i	0.932031	+	0.362379i	$0.118035\pi$
$272$		−	237.382i		−	0.872728i
$273$		0			0
$274$	−50.6987			−0.185032
$275$	46.6795	+	174.210i	0.169744	+	0.633492i
$276$	−27.5885	+	47.7846i	−0.0999582	+	0.173133i
$277$	302.110	−	174.423i	1.09065	−	0.629686i	0.156899	−	0.987615i	$-0.449850\pi$
$277$	302.110	−	174.423i	1.09065	−	0.629686i	0.933749	+	0.357929i	$0.116517\pi$
$278$	11.8705	−	11.8705i	0.0426996	−	0.0426996i
$279$	−137.916	−	36.9545i	−0.494323	−	0.132453i
$280$	22.8987	−	85.4589i	0.0817809	−	0.305211i
$281$	91.9737	+	91.9737i	0.327309	+	0.327309i	0.851562	−	0.524254i	$-0.175656\pi$
$281$	91.9737	+	91.9737i	0.327309	+	0.327309i	−0.524254	+	0.851562i	$0.675656\pi$
$282$	−9.19615	−	15.9282i	−0.0326105	−	0.0564830i
$283$	30.8038	+	17.7846i	0.108848	+	0.0628431i	0.553435	−	0.832892i	$-0.313317\pi$
$283$	30.8038	+	17.7846i	0.108848	+	0.0628431i	−0.444588	+	0.895735i	$0.646650\pi$
$284$	166.772	−	44.6865i	0.587227	−	0.157347i
$285$		−	17.2154i		−	0.0604049i
$286$		0			0
$287$	275.962			0.961538
$288$	49.6506	+	185.299i	0.172398	+	0.643398i
$289$	25.9615	−	44.9667i	0.0898323	−	0.155594i
$290$	15.6840	−	9.05514i	0.0540826	−	0.0312246i
$291$	−28.3782	+	28.3782i	−0.0975197	+	0.0975197i
$292$	−98.2654	−	26.3301i	−0.336525	−	0.0901717i
$293$	−103.631	+	386.758i	−0.353691	+	1.31999i	0.528433	+	0.848975i	$0.322780\pi$
$293$	−103.631	+	386.758i	−0.353691	+	1.31999i	−0.882124	+	0.471017i	$0.843887\pi$
$294$	3.69358	+	3.69358i	0.0125632	+	0.0125632i
$295$	179.249	+	310.468i	0.607623	+	1.05243i
$296$	−108.675	−	62.7436i	−0.367145	−	0.211971i
$297$	200.210	−	53.6462i	0.674109	−	0.180627i
$298$			66.1807i			0.222083i
$299$		0			0
$300$	30.3923			0.101308
$301$	−79.8076	−	297.846i	−0.265142	−	0.989522i
$302$	−46.8494	+	81.1455i	−0.155130	+	0.268694i
$303$	−101.433	+	58.5622i	−0.334761	+	0.193275i
$304$	−57.3923	+	57.3923i	−0.188790	+	0.188790i
$305$	92.2077	+	24.7070i	0.302320	+	0.0810065i
$306$	−20.9378	+	78.1410i	−0.0684243	+	0.255363i
$307$	260.219	+	260.219i	0.847619	+	0.847619i	0.989836	−	0.142216i	$-0.0454228\pi$
$307$	260.219	+	260.219i	0.847619	+	0.847619i	−0.142216	+	0.989836i	$0.545423\pi$
$308$	179.531	+	310.956i	0.582892	+	1.00960i
$309$	−49.9385	−	28.8320i	−0.161613	−	0.0933075i
$310$	31.4186	−	8.41858i	0.101350	−	0.0271567i
$311$		−	71.4782i		−	0.229833i	−0.993375	−	0.114917i	$-0.963340\pi$
$311$		−	71.4782i		−	0.229833i	0.993375	−	0.114917i	$-0.0366601\pi$
$312$		0			0
$313$	−394.315			−1.25979			−0.629897	−	0.776679i	$-0.716903\pi$
$313$	−394.315			−1.25979			−0.629897	+	0.776679i	$0.716903\pi$
$314$	−13.0955	−	48.8731i	−0.0417054	−	0.155647i
$315$	93.5500	−	162.033i	0.296984	−	0.514391i
$316$	202.799	−	117.086i	0.641768	−	0.370525i
$317$	−206.054	+	206.054i	−0.650014	+	0.650014i	−0.952996	−	0.302982i	$-0.902018\pi$
$317$	−206.054	+	206.054i	−0.650014	+	0.650014i	0.302982	+	0.952996i	$0.402018\pi$
$318$	−5.40450	−	1.44813i	−0.0169953	−	0.00455387i
$319$	−39.4115	+	147.086i	−0.123547	+	0.461084i
$320$	104.552	+	104.552i	0.326725	+	0.326725i
$321$	−34.8949	−	60.4397i	−0.108707	−	0.188286i
$322$	53.7269	+	31.0192i	0.166854	+	0.0963330i
$323$	−112.595	+	30.1699i	−0.348593	+	0.0934052i
$324$			249.368i			0.769654i
$325$		0			0
$326$	65.5307			0.201015
$327$	13.9282	+	51.9808i	0.0425939	+	0.158963i
$328$	93.0622	−	161.188i	0.283726	−	0.491428i
$329$	249.440	−	144.014i	0.758175	−	0.437733i
$330$	−16.1821	+	16.1821i	−0.0490366	+	0.0490366i
$331$	445.597	+	119.397i	1.34622	+	0.360717i	0.858737	−	0.512417i	$-0.171250\pi$
$331$	445.597	+	119.397i	1.34622	+	0.360717i	0.487479	+	0.873135i	$0.337917\pi$
$332$	−33.4449	+	124.818i	−0.100738	+	0.375958i
$333$	−187.648	−	187.648i	−0.563508	−	0.563508i
$334$	13.5936	+	23.5448i	0.0406994	+	0.0704935i
$335$	130.338	+	75.2506i	0.389068	+	0.224629i
$336$	53.9474	−	14.4552i	0.160558	−	0.0430213i
$337$			144.779i			0.429613i	0.976657	+	0.214806i	$0.0689120\pi$
$337$			144.779i			0.429613i	−0.976657	+	0.214806i	$0.931088\pi$
$338$		0			0
$339$	105.401			0.310918
$340$	66.4352	+	247.940i	0.195398	+	0.729234i
$341$	−136.746	+	236.851i	−0.401015	+	0.694578i
$342$	23.9545	−	13.8301i	0.0700423	−	0.0404390i
$343$	−263.454	+	263.454i	−0.768087	+	0.768087i
$344$	−200.885	−	53.8269i	−0.583967	−	0.156473i
$345$	14.2539	−	53.1962i	0.0413156	−	0.154192i
$346$	−50.2384	−	50.2384i	−0.145198	−	0.145198i
$347$	−243.590	−	421.911i	−0.701989	−	1.21588i	−0.967767	−	0.251847i	$-0.918962\pi$
$347$	−243.590	−	421.911i	−0.701989	−	1.21588i	0.265778	−	0.964034i	$-0.414371\pi$
$348$	22.2224	+	12.8301i	0.0638576	+	0.0368682i
$349$	11.3468	−	3.04036i	0.0325123	−	0.00871164i	−0.242526	−	0.970145i	$-0.577976\pi$
$349$	11.3468	−	3.04036i	0.0325123	−	0.00871164i	0.275039	+	0.961433i	$0.411309\pi$
$350$		−	34.1718i		−	0.0976336i
$351$		0			0
$352$	367.454			1.04390
$353$	73.9993	+	276.169i	0.209630	+	0.782349i	0.987988	+	0.154529i	$0.0493860\pi$
$353$	73.9993	+	276.169i	0.209630	+	0.782349i	−0.778358	+	0.627820i	$0.783947\pi$
$354$	18.2346	−	31.5833i	0.0515102	−	0.0892184i
$355$	−149.242	+	86.1647i	−0.420399	+	0.242718i
$356$	236.244	−	236.244i	0.663605	−	0.663605i
$357$	77.4782	+	20.7602i	0.217026	+	0.0581519i
$358$	0.139820	−	0.521815i	0.000390559	−	0.00145758i
$359$	92.0770	+	92.0770i	0.256482	+	0.256482i	0.823622	−	0.567140i	$-0.191950\pi$
$359$	92.0770	+	92.0770i	0.256482	+	0.256482i	−0.567140	+	0.823622i	$0.691950\pi$
$360$	−63.0955	−	109.285i	−0.175265	−	0.303568i
$361$	−278.119	−	160.572i	−0.770411	−	0.444797i
$362$	11.5404	−	3.09223i	0.0318795	−	0.00854207i
$363$		−	103.842i		−	0.286067i
$364$		0			0
$365$	101.540			0.278191
$366$	−2.51339	−	9.38011i	−0.00686719	−	0.0256287i
$367$	−6.27499	+	10.8686i	−0.0170981	+	0.0296147i	−0.874448	−	0.485120i	$-0.838776\pi$
$367$	−6.27499	+	10.8686i	−0.0170981	+	0.0296147i	0.857350	+	0.514734i	$0.172109\pi$
$368$	−224.863	+	129.825i	−0.611042	+	0.352785i
$369$	278.322	−	278.322i	0.754261	−	0.754261i
$370$	58.3949	+	15.6469i	0.157824	+	0.0422888i
$371$	22.6781	−	84.6359i	0.0611270	−	0.228129i
$372$	32.5885	+	32.5885i	0.0876034	+	0.0876034i
$373$	155.638	+	269.574i	0.417261	+	0.722718i	0.995663	−	0.0930345i	$-0.0296567\pi$
$373$	155.638	+	269.574i	0.417261	+	0.722718i	−0.578402	+	0.815752i	$0.696323\pi$
$374$	134.196	+	77.4782i	0.358813	+	0.207161i
$375$	−95.1506	+	25.4955i	−0.253735	+	0.0679881i
$376$		−	194.263i		−	0.516656i
$377$		0			0
$378$	−39.2717			−0.103893
$379$	−101.783	−	379.858i	−0.268556	−	1.00226i	−0.960038	−	0.279871i	$-0.909708\pi$
$379$	−101.783	−	379.858i	−0.268556	−	1.00226i	0.691482	−	0.722394i	$-0.256958\pi$
$380$	43.8827	−	76.0070i	0.115481	−	0.200019i
$381$	18.0577	−	10.4256i	0.0473956	−	0.0273638i
$382$	107.613	−	107.613i	0.281709	−	0.281709i
$383$	−713.051	−	191.061i	−1.86175	−	0.498855i	−0.861788	−	0.507269i	$-0.830655\pi$
$383$	−713.051	−	191.061i	−1.86175	−	0.498855i	−0.999965	+	0.00841386i	$0.997322\pi$
$384$	21.0699	−	78.6340i	0.0548696	−	0.204776i
$385$	−253.415	−	253.415i	−0.658222	−	0.658222i
$386$	−85.5507	−	148.178i	−0.221634	−	0.383881i
$387$	−380.885	−	219.904i	−0.984198	−	0.568227i
$388$	−197.629	+	52.9545i	−0.509353	+	0.136481i
$389$			344.478i			0.885548i	0.896633	+	0.442774i	$0.146006\pi$
$389$			344.478i			0.885548i	−0.896633	+	0.442774i	$0.853994\pi$
$390$		0			0
$391$	−372.904			−0.953718
$392$	14.2795	+	53.2917i	0.0364272	+	0.135948i
$393$	−1.09103	+	1.88973i	−0.00277617	+	0.00480847i
$394$	39.5007	−	22.8057i	0.100256	−	0.0578826i
$395$	−165.272	+	165.272i	−0.418409	+	0.418409i
$396$	494.683	+	132.550i	1.24920	+	0.334722i
$397$	181.783	−	678.422i	0.457891	−	1.70887i	−0.221556	−	0.975148i	$-0.571114\pi$
$397$	181.783	−	678.422i	0.457891	−	1.70887i	0.679447	−	0.733725i	$-0.262220\pi$
$398$	−73.7321	−	73.7321i	−0.185256	−	0.185256i
$399$	−13.7128	−	23.7513i	−0.0343680	−	0.0595270i
$400$	123.858	+	71.5096i	0.309646	+	0.178774i
$401$	−547.989	+	146.833i	−1.36656	+	0.366168i	−0.866220	−	0.499663i	$-0.833457\pi$
$401$	−547.989	+	146.833i	−1.36656	+	0.366168i	−0.500336	+	0.865831i	$0.666790\pi$
$402$		−	15.3102i		−	0.0380851i
$403$		0			0
$404$	−597.109			−1.47799
$405$	−64.4193	−	240.416i	−0.159060	−	0.593620i
$406$	14.4256	−	24.9859i	0.0355311	−	0.0615417i
$407$	−440.214	+	254.158i	−1.08161	+	0.624466i
$408$	38.2539	−	38.2539i	0.0937595	−	0.0937595i
$409$	−98.2321	−	26.3212i	−0.240176	−	0.0643550i	0.136723	−	0.990609i	$-0.456343\pi$
$409$	−98.2321	−	26.3212i	−0.240176	−	0.0643550i	−0.376899	+	0.926254i	$0.623010\pi$
$410$	−23.2077	+	86.6122i	−0.0566040	+	0.211249i
$411$	50.6987	+	50.6987i	0.123355	+	0.123355i
$412$	−146.988	−	254.590i	−0.356767	−	0.617938i
$413$	494.603	+	285.559i	1.19758	+	0.691426i
$414$	85.4711	−	22.9019i	0.206452	−	0.0553187i
$415$		−	128.977i		−	0.310788i
$416$		0			0
$417$	−23.7410			−0.0569328
$418$	−13.7128	−	51.1769i	−0.0328058	−	0.122433i
$419$	−322.279	+	558.203i	−0.769162	+	1.33223i	0.168856	+	0.985641i	$0.445993\pi$
$419$	−322.279	+	558.203i	−0.769162	+	1.33223i	−0.938018	+	0.346587i	$0.887341\pi$
$420$	−52.3013	+	30.1962i	−0.124527	+	0.0718956i
$421$	346.619	−	346.619i	0.823322	−	0.823322i	−0.163261	−	0.986583i	$-0.552201\pi$
$421$	346.619	−	346.619i	0.823322	−	0.823322i	0.986583	+	0.163261i	$0.0522013\pi$
$422$	−36.6481	−	9.81982i	−0.0868437	−	0.0232697i
$423$	106.328	−	396.820i	0.251365	−	0.938108i
$424$	−41.7879	−	41.7879i	−0.0985563	−	0.0985563i
$425$	102.701	+	177.883i	0.241649	+	0.418547i
$426$	15.1821	+	8.76537i	0.0356387	+	0.0205760i
$427$	146.895	−	39.3604i	0.344016	−	0.0921788i
$428$		−	355.794i		−	0.831293i
$429$		0			0
$430$	100.192			0.233006
$431$	−27.2501	−	101.699i	−0.0632253	−	0.235960i	0.927081	−	0.374861i	$-0.122310\pi$
$431$	−27.2501	−	101.699i	−0.0632253	−	0.235960i	−0.990306	+	0.138901i	$0.955643\pi$
$432$	82.1821	−	142.344i	0.190236	−	0.329499i
$433$	−596.892	+	344.616i	−1.37850	+	0.795880i	−0.991979	−	0.126399i	$-0.959658\pi$
$433$	−596.892	+	344.616i	−1.37850	+	0.795880i	−0.386525	+	0.922279i	$0.626325\pi$
$434$	36.6410	−	36.6410i	0.0844263	−	0.0844263i
$435$	−24.7391	−	6.62882i	−0.0568715	−	0.0152387i
$436$	−71.0070	+	265.002i	−0.162860	+	0.607802i
$437$	90.1577	+	90.1577i	0.206310	+	0.206310i
$438$	−5.16472	−	8.94555i	−0.0117916	−	0.0204236i
$439$	−78.0577	−	45.0666i	−0.177808	−	0.102657i	0.408454	−	0.912779i	$-0.366068\pi$
$439$	−78.0577	−	45.0666i	−0.177808	−	0.102657i	−0.586262	+	0.810121i	$0.699401\pi$
$440$	−233.478	+	62.5603i	−0.530632	+	0.142182i
$441$			116.674i			0.264568i
$442$		0			0
$443$	642.277			1.44983			0.724917	−	0.688836i	$-0.241878\pi$
$443$	642.277			1.44983			0.724917	+	0.688836i	$0.241878\pi$
$444$	22.1699	+	82.7391i	0.0499321	+	0.186349i
$445$	−166.734	+	288.792i	−0.374683	+	0.648970i
$446$	−170.572	+	98.4801i	−0.382450	+	0.220807i
$447$	66.1807	−	66.1807i	0.148055	−	0.148055i
$448$	227.526	+	60.9653i	0.507870	+	0.136083i
$449$	−6.05583	+	22.6007i	−0.0134874	+	0.0503355i	−0.972342	−	0.233563i	$-0.924961\pi$
$449$	−6.05583	+	22.6007i	−0.0134874	+	0.0503355i	0.958854	+	0.283899i	$0.0916280\pi$
$450$	−34.4641	−	34.4641i	−0.0765869	−	0.0765869i
$451$	−376.970	−	652.932i	−0.835855	−	1.44774i
$452$	465.353	+	268.672i	1.02954	+	0.594407i
$453$	127.995	−	34.2961i	0.282549	−	0.0757089i
$454$			216.560i			0.477005i
$455$		0			0
$456$	−18.4974			−0.0405645
$457$	−61.2795	−	228.698i	−0.134091	−	0.500433i	−1.00000		0.000232237i	$-0.999926\pi$
$457$	−61.2795	−	228.698i	−0.134091	−	0.500433i	0.865909	−	0.500201i	$-0.166741\pi$
$458$	26.4519	−	45.8160i	0.0577553	−	0.100035i
$459$	204.431	−	118.028i	0.445383	−	0.257142i
$460$	198.531	−	198.531i	0.431589	−	0.431589i
$461$	47.0359	+	12.6032i	0.102030	+	0.0273389i	0.309473	−	0.950908i	$-0.399847\pi$
$461$	47.0359	+	12.6032i	0.102030	+	0.0273389i	−0.207443	+	0.978247i	$0.566514\pi$
$462$	−9.43594	+	35.2154i	−0.0204241	+	0.0762238i
$463$	−521.191	−	521.191i	−1.12568	−	1.12568i	−0.990871	−	0.134811i	$-0.956957\pi$
$463$	−521.191	−	521.191i	−1.12568	−	1.12568i	−0.134811	−	0.990871i	$-0.543043\pi$
$464$	60.3756	+	104.574i	0.130120	+	0.225374i
$465$	−39.8372	−	23.0000i	−0.0856713	−	0.0494624i
$466$	−128.296	+	34.3768i	−0.275314	+	0.0737700i
$467$		−	141.415i		−	0.302817i	−0.988471	−	0.151408i	$-0.951619\pi$
$467$		−	141.415i		−	0.302817i	0.988471	−	0.151408i	$-0.0483808\pi$
$468$		0			0
$469$	239.762			0.511219
$470$	24.2224	+	90.3993i	0.0515371	+	0.192339i
$471$	−35.7776	+	61.9686i	−0.0759609	+	0.131568i
$472$	333.588	−	192.597i	0.706755	−	0.408045i
$473$	−595.692	+	595.692i	−1.25939	+	1.25939i
$474$	22.9667	+	6.15390i	0.0484529	+	0.0129829i
$475$	18.1769	−	67.8372i	0.0382672	−	0.142815i
$476$	289.153	+	289.153i	0.607463	+	0.607463i
$477$	−62.4878	−	108.232i	−0.131002	−	0.226902i
$478$	24.9437	+	14.4012i	0.0521834	+	0.0301281i
$479$	−723.207	+	193.783i	−1.50983	+	0.404557i	−0.916378	−	0.400315i	$-0.868901\pi$
$479$	−723.207	+	193.783i	−1.50983	+	0.404557i	−0.593449	+	0.804872i	$0.702234\pi$
$480$			61.8038i			0.128758i
$481$		0			0
$482$	−125.053			−0.259445
$483$	−22.7077	−	84.7461i	−0.0470138	−	0.175458i
$484$	264.698	−	458.470i	0.546897	−	0.947253i
$485$	176.855	−	102.107i	0.364648	−	0.210530i
$486$	−60.0192	+	60.0192i	−0.123496	+	0.123496i
$487$	234.885	+	62.9371i	0.482309	+	0.129234i	0.491778	−	0.870721i	$-0.336347\pi$
$487$	234.885	+	62.9371i	0.482309	+	0.129234i	−0.00946847	+	0.999955i	$0.503014\pi$
$488$	26.5469	−	99.0744i	0.0543994	−	0.203021i
$489$	−65.5307	−	65.5307i	−0.134010	−	0.134010i
$490$	−13.2898	−	23.0185i	−0.0271220	−	0.0469766i
$491$	73.3191	+	42.3308i	0.149326	+	0.0862135i	0.572801	−	0.819694i	$-0.305857\pi$
$491$	73.3191	+	42.3308i	0.149326	+	0.0862135i	−0.423475	+	0.905908i	$0.639190\pi$
$492$	−122.720	+	32.8827i	−0.249431	+	0.0668347i
$493$			173.420i			0.351766i
$494$		0			0
$495$	−511.167			−1.03266
$496$	56.1314	+	209.485i	0.113168	+	0.422349i
$497$	−137.268	+	237.755i	−0.276193	+	0.478380i
$498$	−11.3628	+	6.56029i	−0.0228168	+	0.0131733i
$499$	−134.397	+	134.397i	−0.269334	+	0.269334i	−0.828832	−	0.559498i	$-0.810994\pi$
$499$	−134.397	+	134.397i	−0.269334	+	0.269334i	0.559498	+	0.828832i	$0.310994\pi$
$500$	−485.085	−	129.978i	−0.970170	−	0.259956i
$501$	9.95121	−	37.1384i	0.0198627	−	0.0741286i
$502$	93.5641	+	93.5641i	0.186383	+	0.186383i
$503$	398.200	+	689.703i	0.791650	+	1.37118i	0.924945	+	0.380102i	$0.124111\pi$
$503$	398.200	+	689.703i	0.791650	+	1.37118i	−0.133295	+	0.991076i	$0.542556\pi$
$504$	−174.100	−	100.517i	−0.345436	−	0.199438i
$505$	575.674	−	154.251i	1.13995	−	0.305448i
$506$		−	169.492i		−	0.334965i
$507$		0			0
$508$	106.301			0.209254
$509$	−21.3301	−	79.6051i	−0.0419059	−	0.156395i	0.941802	−	0.336167i	$-0.109131\pi$
$509$	−21.3301	−	79.6051i	−0.0419059	−	0.156395i	−0.983708	+	0.179772i	$0.942464\pi$
$510$	−13.0314	+	22.5711i	−0.0255518	+	0.0442571i
$511$	140.090	−	80.8808i	0.274148	−	0.158279i
$512$	351.581	−	351.581i	0.686682	−	0.686682i
$513$	−77.9615	−	20.8897i	−0.151972	−	0.0407207i
$514$	13.2691	−	49.5211i	0.0258155	−	0.0963446i
$515$	207.480	+	207.480i	0.402873	+	0.402873i
$516$	70.9808	+	122.942i	0.137560	+	0.238260i
$517$	−681.482	−	393.454i	−1.31815	−	0.761032i
$518$	93.0282	−	24.9268i	0.179591	−	0.0481213i
$519$			100.477i			0.193597i
$520$		0			0
$521$	677.011			1.29945			0.649723	−	0.760171i	$-0.274885\pi$
$521$	677.011			1.29945			0.649723	+	0.760171i	$0.274885\pi$
$522$	−10.6506	−	39.7487i	−0.0204035	−	0.0761470i
$523$	91.8269	−	159.049i	0.175577	−	0.304109i	−0.764784	−	0.644287i	$-0.777154\pi$
$523$	91.8269	−	159.049i	0.175577	−	0.304109i	0.940361	+	0.340179i	$0.110488\pi$
$524$	−9.63397	+	5.56218i	−0.0183854	+	0.0106148i
$525$	−34.1718	+	34.1718i	−0.0650891	+	0.0650891i
$526$	127.669	+	34.2089i	0.242717	+	0.0650358i
$527$	−80.6147	+	300.858i	−0.152969	+	0.570889i
$528$	−107.895	−	107.895i	−0.204346	−	0.204346i
$529$	−60.5577	−	104.889i	−0.114476	−	0.198278i
$530$	24.6563	+	14.2353i	0.0465213	+	0.0268591i
$531$	786.836	−	210.832i	1.48180	−	0.397047i
$532$		−	139.818i		−	0.262816i
$533$		0			0
$534$	33.9230			0.0635263
$535$	91.9122	+	343.021i	0.171799	+	0.641161i
$536$	80.8545	−	140.044i	0.150848	−	0.261276i
$537$	−0.661635	+	0.381995i	−0.00123210	+	0.000711351i
$538$	−33.9334	+	33.9334i	−0.0630732	+	0.0630732i
$539$	215.870	+	57.8423i	0.400502	+	0.107314i
$540$	−46.0000	+	171.674i	−0.0851852	+	0.317915i
$541$	317.629	+	317.629i	0.587114	+	0.587114i	0.936849	−	0.349735i	$-0.113728\pi$
$541$	317.629	+	317.629i	0.587114	+	0.587114i	−0.349735	+	0.936849i	$0.613728\pi$
$542$	113.133	+	195.953i	0.208733	+	0.361536i
$543$	−14.6326	−	8.44813i	−0.0269477	−	0.0155583i
$544$	404.222	−	108.311i	0.743055	−	0.199101i
$545$		−	273.832i		−	0.502444i
$546$		0			0
$547$	−724.904			−1.32524			−0.662618	−	0.748958i	$-0.730555\pi$
$547$	−724.904			−1.32524			−0.662618	+	0.748958i	$0.730555\pi$
$548$	94.6051	+	353.071i	0.172637	+	0.644290i
$549$	108.454	−	187.849i	0.197549	−	0.342165i
$550$	−80.8513	+	46.6795i	−0.147002	+	0.0848718i
$551$	41.9282	−	41.9282i	0.0760947	−	0.0760947i
$552$	−57.1577	−	15.3154i	−0.103547	−	0.0277452i
$553$	−96.3717	+	359.664i	−0.174271	+	0.650387i
$554$	127.687	+	127.687i	0.230481	+	0.230481i
$555$	−42.7480	−	74.0417i	−0.0770235	−	0.133409i
$556$	−104.818	−	60.5167i	−0.188521	−	0.108843i
$557$	115.933	−	31.0641i	0.208138	−	0.0557703i	−0.153244	−	0.988188i	$-0.548972\pi$
$557$	115.933	−	31.0641i	0.208138	−	0.0557703i	0.361381	+	0.932418i	$0.382305\pi$
$558$		−	73.9090i		−	0.132453i
$559$		0			0
$560$	−284.192			−0.507486
$561$	−56.7180	−	211.674i	−0.101102	−	0.377316i
$562$	−33.6647	+	58.3090i	−0.0599016	+	0.103753i
$563$	534.888	−	308.818i	0.950068	−	0.548522i	0.0569660	−	0.998376i	$-0.481857\pi$
$563$	534.888	−	308.818i	0.950068	−	0.548522i	0.893102	+	0.449854i	$0.148524\pi$
$564$	−93.7654	+	93.7654i	−0.166251	+	0.166251i
$565$	−518.054	−	138.812i	−0.916909	−	0.245685i
$566$	−4.76537	+	17.7846i	−0.00841938	+	0.0314216i
$567$	−280.378	−	280.378i	−0.494494	−	0.494494i
$568$	92.5814	+	160.356i	0.162995	+	0.282316i
$569$	381.315	+	220.153i	0.670150	+	0.386911i	0.796133	−	0.605121i	$-0.206875\pi$
$569$	381.315	+	220.153i	0.670150	+	0.386911i	−0.125983	+	0.992032i	$0.540209\pi$
$570$	8.60770	−	2.30642i	0.0151012	−	0.00404636i
$571$			618.249i			1.08275i	0.840782	+	0.541374i	$0.182096\pi$
$571$			618.249i			1.08275i	−0.840782	+	0.541374i	$0.817904\pi$
$572$		0			0
$573$	−215.226			−0.375612
$574$	36.9718	+	137.981i	0.0644109	+	0.240385i
$575$	112.335	−	194.569i	0.195365	−	0.338381i
$576$	290.959	−	167.985i	0.505137	−	0.291641i
$577$	−266.237	+	266.237i	−0.461415	+	0.461415i	−0.899119	−	0.437704i	$-0.855792\pi$
$577$	−266.237	+	266.237i	−0.461415	+	0.461415i	0.437704	+	0.899119i	$0.355792\pi$
$578$	25.9615	+	6.95637i	0.0449161	+	0.0120352i
$579$	−62.6274	+	233.729i	−0.108165	+	0.403677i
$580$	−92.3275	−	92.3275i	−0.159185	−	0.159185i
$581$	−102.736	−	177.944i	−0.176826	−	0.306271i
$582$	−17.9911	−	10.3872i	−0.0309125	−	0.0178473i
$583$	−231.229	+	61.9578i	−0.396620	+	0.106274i
$584$		−	109.101i		−	0.186817i
$585$		0			0
$586$	−207.263			−0.353691
$587$	−124.629	−	465.123i	−0.212316	−	0.792373i	−0.987094	−	0.160140i	$-0.948805\pi$
$587$	−124.629	−	465.123i	−0.212316	−	0.792373i	0.774779	−	0.632233i	$-0.217861\pi$
$588$	18.8301	−	32.6147i	0.0320240	−	0.0554672i
$589$	92.2295	−	53.2487i	0.156587	−	0.0904053i
$590$	−131.219	+	131.219i	−0.222405	+	0.222405i
$591$	−62.3064	−	16.6950i	−0.105425	−	0.0282487i
$592$	−104.326	+	389.351i	−0.176227	+	0.657688i
$593$	389.671	+	389.671i	0.657118	+	0.657118i	0.954697	−	0.297579i	$-0.0961792\pi$
$593$	389.671	+	389.671i	0.657118	+	0.657118i	−0.297579	+	0.954697i	$0.596179\pi$
$594$	53.6462	+	92.9179i	0.0903134	+	0.156427i
$595$	−353.469	−	204.076i	−0.594066	−	0.342984i
$596$	460.889	−	123.495i	0.773304	−	0.207206i
$597$			147.464i			0.247009i
$598$		0			0
$599$	808.596			1.34991			0.674955	−	0.737859i	$-0.264163\pi$
$599$	808.596			1.34991			0.674955	+	0.737859i	$0.264163\pi$
$600$	8.43594	+	31.4833i	0.0140599	+	0.0524722i
$601$	221.344	−	383.379i	0.368293	−	0.637903i	−0.621006	−	0.783806i	$-0.713276\pi$
$601$	221.344	−	383.379i	0.368293	−	0.637903i	0.989299	+	0.145904i	$0.0466089\pi$
$602$	138.231	−	79.8076i	0.229619	−	0.132571i
$603$	241.813	−	241.813i	0.401016	−	0.401016i
$604$	652.527	+	174.844i	1.08034	+	0.289477i
$605$	−136.759	+	510.392i	−0.226048	+	0.843623i
$606$	−42.8705	−	42.8705i	−0.0707434	−	0.0707434i
$607$	471.398	+	816.485i	0.776603	+	1.34512i	0.933889	+	0.357563i	$0.116392\pi$
$607$	471.398	+	816.485i	0.776603	+	1.34512i	−0.157286	+	0.987553i	$0.550275\pi$
$608$	−123.916	−	71.5429i	−0.203809	−	0.117669i
$609$	−39.4115	+	10.5603i	−0.0647152	+	0.0173404i
$610$			49.4139i			0.0810065i
$611$		0			0
$612$	583.252			0.953027
$613$	260.758	+	973.161i	0.425380	+	1.58754i	0.763093	+	0.646289i	$0.223680\pi$
$613$	260.758	+	973.161i	0.425380	+	1.58754i	−0.337713	+	0.941249i	$0.609653\pi$
$614$	−95.2468	+	164.972i	−0.155125	+	0.268685i
$615$	109.820	−	63.4045i	0.178569	−	0.103097i
$616$	−272.287	+	272.287i	−0.442025	+	0.442025i
$617$	268.378	+	71.9115i	0.434972	+	0.116550i	0.469659	−	0.882848i	$-0.344377\pi$
$617$	268.378	+	71.9115i	0.434972	+	0.116550i	−0.0346873	+	0.999398i	$0.511044\pi$
$618$	7.72551	−	28.8320i	0.0125008	−	0.0466537i
$619$	206.483	+	206.483i	0.333576	+	0.333576i	0.853943	−	0.520367i	$-0.174205\pi$
$619$	206.483	+	206.483i	0.333576	+	0.333576i	−0.520367	+	0.853943i	$0.674205\pi$
$620$	−117.256	−	203.093i	−0.189122	−	0.327569i
$621$	−223.608	−	129.100i	−0.360077	−	0.207890i
$622$	35.7391	−	9.57626i	0.0574583	−	0.0153959i
$623$			531.244i			0.852718i
$624$		0			0
$625$	223.140			0.357024
$626$	−52.8282	−	197.158i	−0.0843902	−	0.314948i
$627$	−37.4641	+	64.8897i	−0.0597514	+	0.103492i
$628$	−315.920	+	182.397i	−0.503058	+	0.290441i
$629$	−409.347	+	409.347i	−0.650790	+	0.650790i
$630$	93.5500	+	25.0666i	0.148492	+	0.0397883i
$631$	114.900	−	428.813i	0.182092	−	0.679577i	−0.813142	−	0.582065i	$-0.802245\pi$
$631$	114.900	−	428.813i	0.182092	−	0.679577i	0.995234	−	0.0975117i	$-0.0310883\pi$
$632$	177.580	+	177.580i	0.280980	+	0.280980i
$633$	26.8282	+	46.4679i	0.0423827	+	0.0734090i
$634$	−130.633	−	75.4212i	−0.206046	−	0.118961i
$635$	−102.485	+	27.4608i	−0.161394	+	0.0432454i
$636$			40.3397i			0.0634273i
$637$		0			0
$638$	−78.8231			−0.123547
$639$	101.347	+	378.231i	0.158602	+	0.591911i
$640$	−207.120	+	358.742i	−0.323625	+	0.560535i
$641$	471.717	−	272.346i	0.735908	−	0.424877i	−0.0846714	−	0.996409i	$-0.526984\pi$
$641$	471.717	−	272.346i	0.735908	−	0.424877i	0.820580	+	0.571532i	$0.193651\pi$
$642$	25.5448	−	25.5448i	0.0397894	−	0.0397894i
$643$	−373.478	−	100.073i	−0.580837	−	0.155635i	−0.0435749	−	0.999050i	$-0.513875\pi$
$643$	−373.478	−	100.073i	−0.580837	−	0.155635i	−0.537262	+	0.843415i	$0.680541\pi$
$644$	115.765	−	432.042i	0.179760	−	0.670873i
$645$	−100.192	−	100.192i	−0.155337	−	0.155337i
$646$	−30.1699	−	52.2558i	−0.0467026	−	0.0808913i
$647$	436.056	+	251.757i	0.673966	+	0.389114i	0.797578	−	0.603216i	$-0.206114\pi$
$647$	436.056	+	251.757i	0.673966	+	0.389114i	−0.123612	+	0.992331i	$0.539448\pi$
$648$	−258.320	+	69.2166i	−0.398642	+	0.106816i
$649$		−	1560.32i		−	2.40420i
$650$		0			0
$651$	−73.2820			−0.112568
$652$	−122.282	−	456.363i	−0.187549	−	0.699943i
$653$	−15.5692	+	26.9667i	−0.0238426	+	0.0412966i	−0.877701	−	0.479210i	$-0.840923\pi$
$653$	−15.5692	+	26.9667i	−0.0238426	+	0.0412966i	0.853858	+	0.520506i	$0.174257\pi$
$654$	−24.1244	+	13.9282i	−0.0368874	+	0.0212969i
$655$	7.85125	−	7.85125i	0.0119866	−	0.0119866i
$656$	−577.492	−	154.738i	−0.880323	−	0.235882i
$657$	59.7154	−	222.861i	0.0908910	−	0.339210i
$658$	105.426	+	105.426i	0.160221	+	0.160221i
$659$	−379.488	−	657.293i	−0.575855	−	0.997410i	−0.995948	−	0.0899292i	$-0.971336\pi$
$659$	−379.488	−	657.293i	−0.575855	−	0.997410i	0.420093	−	0.907481i	$-0.361997\pi$
$660$	142.890	+	82.4974i	0.216500	+	0.124996i
$661$	−253.064	+	67.8083i	−0.382850	+	0.102584i	−0.445111	−	0.895475i	$-0.646836\pi$
$661$	−253.064	+	67.8083i	−0.382850	+	0.102584i	0.0622605	+	0.998060i	$0.480169\pi$
$662$			238.795i			0.360717i
$663$		0			0
$664$	−138.582			−0.208708
$665$	36.1192	+	134.799i	0.0543146	+	0.202705i
$666$	68.6840	−	118.964i	0.103129	−	0.178625i
$667$	164.275	−	94.8442i	0.246289	−	0.142195i
$668$	138.603	−	138.603i	0.207489	−	0.207489i
$669$	269.053	+	72.0924i	0.402171	+	0.107761i
$670$	−20.1633	+	75.2506i	−0.0300945	+	0.112314i
$671$	−293.790	−	293.790i	−0.437839	−	0.437839i
$672$	49.2295	+	85.2679i	0.0732581	+	0.126887i
$673$	272.210	+	157.160i	0.404472	+	0.233522i	0.688412	−	0.725320i	$-0.258308\pi$
$673$	272.210	+	157.160i	0.404472	+	0.233522i	−0.283940	+	0.958842i	$0.591642\pi$
$674$	−72.3897	+	19.3968i	−0.107403	+	0.0287786i
$675$			142.221i			0.210697i
$676$		0			0
$677$	−547.384			−0.808544			−0.404272	−	0.914639i	$-0.632475\pi$
$677$	−547.384			−0.808544			−0.404272	+	0.914639i	$0.632475\pi$
$678$	14.1211	+	52.7006i	0.0208276	+	0.0777295i
$679$	162.665	−	281.745i	0.239566	−	0.414941i
$680$	−238.400	+	137.640i	−0.350588	+	0.202412i
$681$	216.560	−	216.560i	0.318003	−	0.318003i
$682$	−136.746	−	36.6410i	−0.200508	−	0.0537258i
$683$	−67.7789	+	252.954i	−0.0992371	+	0.370358i	−0.997628	−	0.0688393i	$-0.978070\pi$
$683$	−67.7789	+	252.954i	−0.0992371	+	0.370358i	0.898391	+	0.439197i	$0.144737\pi$
$684$	−141.014	−	141.014i	−0.206161	−	0.206161i
$685$	−182.418	−	315.957i	−0.266303	−	0.461251i
$686$	−167.023	−	96.4308i	−0.243474	−	0.140570i
$687$	−72.2679	+	19.3641i	−0.105194	+	0.0281865i
$688$			668.038i			0.970986i
$689$		0			0
$690$	28.5077			0.0413156
$691$	−284.764	−	1062.75i	−0.412104	−	1.53799i	−0.790566	−	0.612377i	$-0.790214\pi$
$691$	−284.764	−	1062.75i	−0.412104	−	1.53799i	0.378462	−	0.925617i	$-0.376453\pi$
$692$	−256.119	+	443.611i	−0.370114	+	0.641057i
$693$	−705.233	+	407.167i	−1.01765	+	0.587542i
$694$	178.321	−	178.321i	0.256946	−	0.256946i
$695$	116.688	+	31.2666i	0.167897	+	0.0449879i
$696$	−7.12247	+	26.5814i	−0.0102334	+	0.0381917i
$697$	−607.149	−	607.149i	−0.871089	−	0.871089i
$698$	3.04036	+	5.26606i	0.00435582	+	0.00754450i
$699$	162.673	+	93.9193i	0.232722	+	0.134362i
$700$	−237.976	+	63.7654i	−0.339965	+	0.0910934i
$701$		−	638.323i		−	0.910589i	−0.890341	−	0.455295i	$-0.849534\pi$
$701$		−	638.323i		−	0.910589i	0.890341	−	0.455295i	$-0.150466\pi$
$702$		0			0
$703$	197.937			0.281561
$704$	−166.560	−	621.611i	−0.236591	−	0.882971i
$705$	66.1769	−	114.622i	0.0938680	−	0.162584i
$706$	−128.171	+	73.9993i	−0.181545	+	0.104815i
$707$	671.363	−	671.363i	0.949594	−	0.949594i
$708$	−253.976	−	68.0526i	−0.358723	−	0.0961194i
$709$	167.518	−	625.185i	0.236273	−	0.881784i	−0.741297	−	0.671177i	$-0.765789\pi$
$709$	167.518	−	625.185i	0.236273	−	0.881784i	0.977571	−	0.210608i	$-0.0675442\pi$
$710$	−63.0770	−	63.0770i	−0.0888408	−	0.0888408i
$711$	265.545	+	459.937i	0.373481	+	0.646888i
$712$	310.298	+	179.151i	0.435812	+	0.251616i
$713$	329.081	−	88.1769i	0.461544	−	0.123670i
$714$			41.5204i			0.0581519i
$715$		0			0
$716$	−3.89488			−0.00543978
$717$	−10.5424	−	39.3449i	−0.0147035	−	0.0548743i
$718$	−33.7025	+	58.3744i	−0.0469394	+	0.0813015i
$719$	−1058.38	+	611.056i	−1.47202	+	0.849870i	−0.999505	−	0.0314543i	$-0.989986\pi$
$719$	−1058.38	+	611.056i	−1.47202	+	0.849870i	−0.472512	+	0.881324i	$0.656653\pi$
$720$	−286.624	+	286.624i	−0.398088	+	0.398088i
$721$	451.517	+	120.984i	0.626237	+	0.167800i
$722$	43.0251	−	160.572i	0.0595915	−	0.222399i
$723$	125.053	+	125.053i	0.172963	+	0.172963i
$724$	−43.0692	−	74.5981i	−0.0594879	−	0.103036i
$725$	−90.4852	−	52.2417i	−0.124807	−	0.0720575i
$726$	51.9212	−	13.9122i	0.0715168	−	0.0191629i
$727$			508.974i			0.700102i	0.936731	+	0.350051i	$0.113836\pi$
$727$			508.974i			0.700102i	−0.936731	+	0.350051i	$0.886164\pi$
$728$		0			0
$729$	−481.323			−0.660251
$730$	13.6037	+	50.7698i	0.0186353	+	0.0695477i
$731$	−479.711	+	830.885i	−0.656240	+	1.13664i
$732$	−60.6340	+	35.0070i	−0.0828333	+	0.0478238i
$733$	861.681	−	861.681i	1.17555	−	1.17555i	0.194689	−	0.980865i	$-0.437630\pi$
$733$	861.681	−	861.681i	1.17555	−	1.17555i	0.980865	−	0.194689i	$-0.0623699\pi$
$734$	−6.27499	−	1.68138i	−0.00854903	−	0.00229071i
$735$	−9.72878	+	36.3083i	−0.0132364	+	0.0493991i
$736$	−323.669	−	323.669i	−0.439768	−	0.439768i
$737$	−327.520	−	567.282i	−0.444397	−	0.769718i
$738$	176.449	+	101.873i	0.239091	+	0.138039i
$739$	−150.865	+	40.4242i	−0.204148	+	0.0547013i	−0.359444	−	0.933167i	$-0.617034\pi$
$739$	−150.865	+	40.4242i	−0.204148	+	0.0547013i	0.155296	+	0.987868i	$0.450367\pi$
$740$		−	435.865i		−	0.589007i
$741$		0			0
$742$	45.3562			0.0611270
$743$	98.9409	+	369.252i	0.133164	+	0.496975i	0.999999	−	0.00162070i	$-0.000515884\pi$
$743$	98.9409	+	369.252i	0.133164	+	0.496975i	−0.866835	+	0.498596i	$0.833849\pi$
$744$	−24.7128	+	42.8038i	−0.0332161	+	0.0575321i
$745$	−412.441	+	238.123i	−0.553613	+	0.319628i
$746$	−113.935	+	113.935i	−0.152728	+	0.152728i
$747$	−283.081	−	75.8513i	−0.378957	−	0.101541i
$748$	289.153	−	1079.13i	0.386568	−	1.44269i
$749$	400.038	+	400.038i	0.534097	+	0.534097i
$750$	−25.4955	−	44.1596i	−0.0339940	−	0.0588794i
$751$	906.415	+	523.319i	1.20694	+	0.696830i	0.962091	−	0.272730i	$-0.0879267\pi$
$751$	906.415	+	523.319i	1.20694	+	0.696830i	0.244854	+	0.969560i	$0.421260\pi$
$752$	−602.743	+	161.504i	−0.801520	+	0.214767i
$753$		−	187.128i		−	0.248510i
$754$		0			0
$755$	−674.270			−0.893073
$756$	73.2820	+	273.492i	0.0969339	+	0.361762i
$757$	188.415	−	326.345i	0.248897	−	0.431103i	−0.714323	−	0.699816i	$-0.753265\pi$
$757$	188.415	−	326.345i	0.248897	−	0.431103i	0.963220	+	0.268713i	$0.0865985\pi$
$758$	176.293	−	101.783i	0.232576	−	0.134278i
$759$	−169.492	+	169.492i	−0.223310	+	0.223310i
$760$	90.9160	+	24.3609i	0.119626	+	0.0320538i
$761$	198.830	−	742.044i	0.261275	−	0.975091i	−0.703216	−	0.710976i	$-0.748253\pi$
$761$	198.830	−	742.044i	0.261275	−	0.975091i	0.964491	−	0.264115i	$-0.0850798\pi$
$762$	7.63209	+	7.63209i	0.0100159	+	0.0100159i
$763$	−218.119	−	377.794i	−0.285871	−	0.495142i
$764$	−950.235	−	548.619i	−1.24376	−	0.718087i
$765$	−562.315	+	150.672i	−0.735052	+	0.196957i
$766$		−	382.123i		−	0.498855i
$767$		0			0
$768$	−74.0910			−0.0964727
$769$	17.6044	+	65.7006i	0.0228926	+	0.0854364i	0.976427	−	0.215848i	$-0.0692514\pi$
$769$	17.6044	+	65.7006i	0.0228926	+	0.0854364i	−0.953534	+	0.301284i	$0.902585\pi$
$770$	92.7564	−	160.659i	0.120463	−	0.208648i
$771$	−62.7903	+	36.2520i	−0.0814400	+	0.0470194i
$772$	−872.288	+	872.288i	−1.12991	+	1.12991i
$773$	890.771	+	238.681i	1.15236	+	0.308773i	0.783909	−	0.620876i	$-0.213223\pi$
$773$	890.771	+	238.681i	1.15236	+	0.308773i	0.368447	+	0.929649i	$0.379890\pi$
$774$	58.9230	−	219.904i	0.0761280	−	0.284113i
$775$	−132.694	−	132.694i	−0.171218	−	0.171218i
$776$	−109.711	−	190.025i	−0.141380	−	0.244877i
$777$	−117.955	−	68.1013i	−0.151808	−	0.0876465i
$778$	−172.239	+	46.1513i	−0.221387	+	0.0593205i
$779$			293.583i			0.376872i
$780$		0			0
$781$	750.046			0.960366
$782$	−49.9596	−	186.452i	−0.0638870	−	0.238430i
$783$	−60.0385	+	103.990i	−0.0766775	+	0.132809i
$784$	153.477	−	88.6103i	0.195762	−	0.113023i
$785$	257.461	−	257.461i	0.327976	−	0.327976i
$786$	−1.09103	−	0.292342i	−0.00138808	−	0.000371936i
$787$	−318.489	+	1188.62i	−0.404687	+	1.51031i	0.399944	+	0.916540i	$0.369030\pi$
$787$	−318.489	+	1188.62i	−0.404687	+	1.51031i	−0.804632	+	0.593774i	$0.797637\pi$
$788$	−232.531	−	232.531i	−0.295090	−	0.295090i
$789$	−93.4603	−	161.878i	−0.118454	−	0.205169i
$790$	−104.778	−	60.4936i	−0.132630	−	0.0765742i
$791$	−825.305	+	221.140i	−1.04337	+	0.279570i
$792$			549.233i			0.693476i
$793$		0			0
$794$	363.565			0.457891
$795$	−10.4210	−	38.8916i	−0.0131081	−	0.0489203i
$796$	−375.892	+	651.063i	−0.472226	+	0.817919i
$797$	22.0615	−	12.7372i	0.0276807	−	0.0159814i	−0.486096	−	0.873906i	$-0.661579\pi$
$797$	22.0615	−	12.7372i	0.0276807	−	0.0159814i	0.513776	+	0.857924i	$0.328246\pi$
$798$	10.0385	−	10.0385i	0.0125795	−	0.0125795i
$799$	−865.647	−	231.949i	−1.08341	−	0.290300i
$800$	−65.2558	+	243.538i	−0.0815697	+	0.304422i
$801$	535.788	+	535.788i	0.668899	+	0.668899i
$802$	−146.833	−	254.323i	−0.183084	−	0.317110i
$803$	−382.732	−	220.970i	−0.476628	−	0.275181i
$804$	−106.622	+	28.5692i	−0.132614	+	0.0355339i
$805$			446.438i			0.554582i
$806$		0			0
$807$	67.8667			0.0840975
$808$	−165.738	−	618.544i	−0.205122	−	0.765525i
$809$	351.463	−	608.752i	0.434442	−	0.752475i	−0.562808	−	0.826588i	$-0.690279\pi$
$809$	351.463	−	608.752i	0.434442	−	0.752475i	0.997250	+	0.0741123i	$0.0236123\pi$
$810$	111.577	−	64.4193i	0.137750	−	0.0795300i
$811$	506.292	−	506.292i	0.624282	−	0.624282i	−0.322342	−	0.946623i	$-0.604470\pi$
$811$	506.292	−	506.292i	0.624282	−	0.624282i	0.946623	+	0.322342i	$0.104470\pi$
$812$	−200.923	−	53.8372i	−0.247442	−	0.0663019i
$813$	82.8193	−	309.086i	0.101869	−	0.380179i
$814$	−186.056	−	186.056i	−0.228570	−	0.228570i
$815$	235.785	+	408.391i	0.289306	+	0.501093i
$816$	−150.494	−	86.8878i	−0.184429	−	0.106480i
$817$	316.865	−	84.9038i	0.387840	−	0.103921i
$818$		−	52.6424i		−	0.0643550i
$819$		0			0
$820$	646.482			0.788393
$821$	292.276	+	1090.79i	0.356000	+	1.32861i	0.879221	+	0.476414i	$0.158064\pi$
$821$	292.276	+	1090.79i	0.356000	+	1.32861i	−0.523220	+	0.852197i	$0.675270\pi$
$822$	−18.5570	+	32.1417i	−0.0225755	+	0.0391018i
$823$	449.858	−	259.726i	0.546607	−	0.315584i	−0.201145	−	0.979561i	$-0.564466\pi$
$823$	449.858	−	259.726i	0.546607	−	0.315584i	0.747752	+	0.663978i	$0.231133\pi$
$824$	222.931	−	222.931i	0.270547	−	0.270547i
$825$	127.531	+	34.1718i	0.154583	+	0.0414203i
$826$	−76.5153	+	285.559i	−0.0926335	+	0.345713i
$827$	−571.769	−	571.769i	−0.691377	−	0.691377i	0.271158	−	0.962535i	$-0.412594\pi$
$827$	−571.769	−	571.769i	−0.691377	−	0.691377i	−0.962535	+	0.271158i	$0.912594\pi$
$828$	−318.983	−	552.494i	−0.385245	−	0.667263i
$829$	848.094	+	489.647i	1.02303	+	0.590648i	0.914981	−	0.403497i	$-0.132205\pi$
$829$	848.094	+	489.647i	1.02303	+	0.590648i	0.108052	+	0.994145i	$0.465539\pi$
$830$	64.4885	−	17.2796i	0.0776970	−	0.0208188i
$831$		−	255.373i		−	0.307308i
$832$		0			0
$833$	254.520			0.305547
$834$	−3.18069	−	11.8705i	−0.00381377	−	0.0142332i
$835$	−97.8217	+	169.432i	−0.117152	+	0.202913i
$836$	−330.813	+	190.995i	−0.395709	+	0.228463i
$837$	−152.497	+	152.497i	−0.182195	+	0.182195i
$838$	−322.279	−	86.3543i	−0.384581	−	0.103048i
$839$	−137.661	+	513.757i	−0.164077	+	0.612344i	0.834079	+	0.551645i	$0.186000\pi$
$839$	−137.661	+	513.757i	−0.164077	+	0.612344i	−0.998156	+	0.0606993i	$0.980667\pi$
$840$	−45.7973	−	45.7973i	−0.0545206	−	0.0545206i
$841$	376.392	+	651.931i	0.447553	+	0.775185i
$842$	219.747	+	126.871i	0.260983	+	0.150678i
$843$	91.9737	−	24.6443i	0.109103	−	0.0292340i
$844$			273.545i			0.324105i
$845$		0			0
$846$	212.655			0.251365
$847$	217.869	+	813.099i	0.257224	+	0.959975i
$848$	−94.9148	+	164.397i	−0.111928	+	0.193865i
$849$	22.5500	−	13.0192i	0.0265606	−	0.0153348i
$850$	−75.1821	+	75.1821i	−0.0884495	+	0.0884495i
$851$	611.633	+	163.886i	0.718722	+	0.192581i
$852$	32.7128	−	122.086i	0.0383953	−	0.143293i
$853$	713.043	+	713.043i	0.835924	+	0.835924i	0.988320	−	0.152396i	$-0.0486989\pi$
$853$	713.043	+	713.043i	0.835924	+	0.835924i	−0.152396	+	0.988320i	$0.548699\pi$
$854$	39.3604	+	68.1742i	0.0460894	+	0.0798292i
$855$	172.380	+	99.5237i	0.201614	+	0.116402i
$856$	368.566	−	98.7569i	0.430568	−	0.115370i
$857$			311.663i			0.363667i	0.983329	+	0.181834i	$0.0582032\pi$
$857$			311.663i			0.363667i	−0.983329	+	0.181834i	$0.941797\pi$
$858$		0			0
$859$	−1475.02			−1.71714			−0.858568	−	0.512700i	$-0.828645\pi$
$859$	−1475.02			−1.71714			−0.858568	+	0.512700i	$0.828645\pi$
$860$	−186.962	−	697.750i	−0.217397	−	0.811337i
$861$	101.009	−	174.953i	0.117316	−	0.203197i
$862$	47.1985	−	27.2501i	0.0547547	−	0.0316126i
$863$	−700.396	+	700.396i	−0.811583	+	0.811583i	−0.984871	−	0.173288i	$-0.944561\pi$
$863$	−700.396	+	700.396i	−0.811583	+	0.811583i	0.173288	+	0.984871i	$0.444561\pi$
$864$	279.885	+	74.9948i	0.323940	+	0.0867996i
$865$	132.327	−	493.850i	0.152979	−	0.570925i
$866$	−252.276	−	252.276i	−0.291312	−	0.291312i
$867$	−19.0052	−	32.9179i	−0.0219206	−	0.0379676i
$868$	−323.545	−	186.799i	−0.372747	−	0.215206i
$869$	982.620	−	263.292i	1.13075	−	0.302983i
$870$		−	13.2576i		−	0.0152387i
$871$		0			0
$872$	−294.224			−0.337413
$873$	−120.098	−	448.212i	−0.137569	−	0.513416i
$874$	−33.0000	+	57.1577i	−0.0377574	+	0.0653978i
$875$	691.550	−	399.267i	0.790343	−	0.456305i
$876$	−52.6603	+	52.6603i	−0.0601144	+	0.0601144i
$877$	132.301	+	35.4498i	0.150856	+	0.0404217i	0.333457	−	0.942765i	$-0.391785\pi$
$877$	132.301	+	35.4498i	0.150856	+	0.0404217i	−0.182601	+	0.983187i	$0.558452\pi$
$878$	12.0756	−	45.0666i	0.0137535	−	0.0513287i
$879$	207.263	+	207.263i	0.235794	+	0.235794i
$880$	388.214	+	672.406i	0.441152	+	0.764098i
$881$	−383.677	−	221.516i	−0.435502	−	0.251437i	0.266186	−	0.963922i	$-0.414236\pi$
$881$	−383.677	−	221.516i	−0.435502	−	0.251437i	−0.701688	+	0.712485i	$0.747570\pi$
$882$	−58.3372	+	15.6314i	−0.0661419	+	0.0177227i
$883$		−	1305.20i		−	1.47814i	−0.673630	−	0.739069i	$-0.735266\pi$
$883$		−	1305.20i		−	1.47814i	0.673630	−	0.739069i	$-0.264734\pi$
$884$		0			0
$885$	262.438			0.296540
$886$	86.0488	+	321.138i	0.0971205	+	0.362459i
$887$	861.377	−	1491.95i	0.971113	−	1.68202i	0.278904	−	0.960319i	$-0.410029\pi$
$887$	861.377	−	1491.95i	0.971113	−	1.68202i	0.692209	−	0.721697i	$-0.256638\pi$
$888$	−79.5556	+	45.9315i	−0.0895897	+	0.0517246i
$889$	−119.520	+	119.520i	−0.134444	+	0.134444i
$890$	−166.734	−	44.6762i	−0.187342	−	0.0501980i
$891$	−280.378	+	1046.39i	−0.314678	+	1.17439i
$892$	1004.12	+	1004.12i	1.12569	+	1.12569i
$893$	153.210	+	265.368i	0.171568	+	0.297165i
$894$	41.9569	+	24.2238i	0.0469316	+	0.0270960i
$895$	3.75506	−	1.00617i	0.00419560	−	0.00112421i
$896$			659.920i			0.736518i
$897$		0			0
$898$	−12.1117			−0.0134874
$899$	−41.0070	−	153.040i	−0.0456141	−	0.170234i
$900$	−175.701	+	304.322i	−0.195223	+	0.338136i
$901$	−236.104	+	136.315i	−0.262047	+	0.151293i
$902$	275.962	−	275.962i	0.305944	−	0.305944i
$903$	−218.038	−	58.4232i	−0.241460	−	0.0646990i
$904$	−149.149	+	556.633i	−0.164988	+	0.615745i
$905$	60.7940	+	60.7940i	0.0671757	+	0.0671757i
$906$	34.2961	+	59.4026i	0.0378544	+	0.0655658i
$907$	−758.800	−	438.093i	−0.836604	−	0.483014i	0.0195043	−	0.999810i	$-0.493791\pi$
$907$	−758.800	−	438.093i	−0.836604	−	0.483014i	−0.856109	+	0.516796i	$0.827125\pi$
$908$	1508.15	−	404.107i	1.66096	−	0.445052i
$909$		−	1354.21i		−	1.48978i
$910$		0			0
$911$	−1103.35			−1.21114			−0.605569	−	0.795793i	$-0.707054\pi$
$911$	−1103.35			−1.21114			−0.605569	+	0.795793i	$0.707054\pi$
$912$	15.3782	+	57.3923i	0.0168621	+	0.0629302i
$913$	−280.679	+	486.151i	−0.307426	+	0.532477i
$914$	106.139	−	61.2795i	0.116126	−	0.0670454i
$915$	49.4139	−	49.4139i	0.0540043	−	0.0540043i
$916$	−368.428	−	98.7199i	−0.402213	−	0.107773i
$917$	4.57815	−	17.0859i	0.00499253	−	0.0186324i
$918$	86.4026	+	86.4026i	0.0941205	+	0.0941205i
$919$	328.160	+	568.389i	0.357083	+	0.618486i	0.987472	−	0.157793i	$-0.0504379\pi$
$919$	328.160	+	568.389i	0.357083	+	0.618486i	−0.630389	+	0.776279i	$0.717105\pi$
$920$	260.763	+	150.552i	0.283439	+	0.163643i
$921$	260.219	−	69.7255i	0.282540	−	0.0757063i
$922$			25.2065i			0.0273389i
$923$		0			0
$924$	262.851			0.284471
$925$	−90.2712	−	336.897i	−0.0975905	−	0.364213i
$926$	190.769	−	330.422i	0.206014	−	0.356827i
$927$	577.398	−	333.361i	0.622867	−	0.359613i
$928$	−150.524	+	150.524i	−0.162202	+	0.162202i
$929$	−819.460	−	219.574i	−0.882088	−	0.236355i	−0.210780	−	0.977533i	$-0.567601\pi$
$929$	−819.460	−	219.574i	−0.882088	−	0.236355i	−0.671308	+	0.741179i	$0.734267\pi$
$930$	6.16283	−	23.0000i	0.00662670	−	0.0247312i
$931$	−61.5359	−	61.5359i	−0.0660966	−	0.0660966i
$932$	478.808	+	829.319i	0.513742	+	0.889827i
$933$	−45.3154	−	26.1628i	−0.0485695	−	0.0280416i
$934$	70.7077	−	18.9461i	0.0757041	−	0.0202849i
$935$			1115.09i			1.19261i
$936$		0			0
$937$	842.615			0.899269			0.449635	−	0.893213i	$-0.351554\pi$
$937$	842.615			0.899269			0.449635	+	0.893213i	$0.351554\pi$
$938$	32.1220	+	119.881i	0.0342452	+	0.127805i
$939$	−144.329	+	249.986i	−0.153705	+	0.266226i
$940$	584.351	−	337.375i	0.621650	−	0.358910i
$941$	−471.659	+	471.659i	−0.501232	+	0.501232i	−0.911821	−	0.410589i	$-0.865323\pi$
$941$	−471.659	+	471.659i	−0.501232	+	0.501232i	0.410589	+	0.911821i	$0.365323\pi$
$942$	−35.7776	−	9.58657i	−0.0379804	−	0.0101768i
$943$	−243.079	+	907.183i	−0.257772	+	0.962018i
$944$	−874.911	−	874.911i	−0.926813	−	0.926813i
$945$	−141.303	−	244.743i	−0.149527	−	0.258988i
$946$	−377.654	−	218.038i	−0.399211	−	0.230485i
$947$	489.308	−	131.110i	0.516693	−	0.138447i	0.00895652	−	0.999960i	$-0.497149\pi$
$947$	489.308	−	131.110i	0.516693	−	0.138447i	0.507737	+	0.861512i	$0.330482\pi$
$948$		−	171.426i		−	0.180829i
$949$		0			0
$950$	36.3538			0.0382672
$951$	55.2121	+	206.054i	0.0580569	+	0.216671i
$952$	−219.273	+	379.792i	−0.230329	+	0.398941i
$953$	770.092	−	444.613i	0.808071	−	0.466540i	−0.0382143	−	0.999270i	$-0.512167\pi$
$953$	770.092	−	444.613i	0.808071	−	0.466540i	0.846286	+	0.532729i	$0.178834\pi$
$954$	45.7442	−	45.7442i	0.0479499	−	0.0479499i
$955$	1057.85	+	283.450i	1.10769	+	0.296806i
$956$	53.7461	−	200.583i	0.0562198	−	0.209815i
$957$	78.8231	+	78.8231i	0.0823648	+	0.0823648i
$958$	−193.783	−	335.642i	−0.202278	−	0.350356i
$959$	−503.347	−	290.608i	−0.524867	−	0.303032i
$960$	104.552	−	28.0146i	0.108908	−	0.0291819i
$961$			676.436i			0.703888i
$962$		0			0
$963$	806.922			0.837925
$964$	233.351	+	870.879i	0.242066	+	0.903401i
$965$	615.636	−	1066.31i	0.637964	−	1.10499i
$966$	39.3308	−	22.7077i	0.0407151	−	0.0235069i
$967$	−384.317	+	384.317i	−0.397432	+	0.397432i	−0.877326	−	0.479894i	$-0.840675\pi$
$967$	−384.317	+	384.317i	−0.397432	+	0.397432i	0.479894	+	0.877326i	$0.340675\pi$
$968$	548.401	+	146.943i	0.566529	+	0.151801i
$969$	−22.0859	+	82.4256i	−0.0227924	+	0.0850626i
$970$	74.7475	+	74.7475i	0.0770593	+	0.0770593i
$971$	121.863	+	211.074i	0.125503	+	0.217378i	0.921929	−	0.387358i	$-0.126612\pi$
$971$	121.863	+	211.074i	0.125503	+	0.217378i	−0.796426	+	0.604735i	$0.793279\pi$
$972$	529.977	+	305.983i	0.545244	+	0.314797i
$973$	185.895	−	49.8104i	0.191053	−	0.0511926i
$974$			125.874i			0.129234i
$975$		0			0
$976$	−329.470			−0.337572
$977$	297.426	+	1110.01i	0.304428	+	1.13614i	0.933437	+	0.358742i	$0.116794\pi$
$977$	297.426	+	1110.01i	0.304428	+	1.13614i	−0.629009	+	0.777398i	$0.716539\pi$
$978$	23.9859	−	41.5448i	0.0245255	−	0.0424794i
$979$	1256.94	−	725.692i	1.28390	−	0.741259i
$980$	−135.504	+	135.504i	−0.138270	+	0.138270i
$981$	−601.011	−	161.040i	−0.612651	−	0.164159i
$982$	−11.3425	+	42.3308i	−0.0115504	+	0.0431067i
$983$	−774.213	−	774.213i	−0.787602	−	0.787602i	0.193499	−	0.981101i	$-0.438016\pi$
$983$	−774.213	−	774.213i	−0.787602	−	0.787602i	−0.981101	+	0.193499i	$0.938016\pi$
$984$	−68.1262	−	117.998i	−0.0692340	−	0.119917i
$985$	284.253	+	164.114i	0.288582	+	0.166613i
$986$	−86.7102	+	23.2339i	−0.0879414	+	0.0235638i
$987$		−	210.851i		−	0.213628i
$988$		0			0
$989$	1049.42			1.06109
$990$	−68.4833	−	255.583i	−0.0691751	−	0.258165i
$991$	391.733	−	678.501i	0.395290	−	0.684663i	−0.597848	−	0.801609i	$-0.703977\pi$
$991$	391.733	−	678.501i	0.395290	−	0.684663i	0.993138	+	0.116947i	$0.0373107\pi$
$992$	−331.107	+	191.165i	−0.333777	+	0.192706i
$993$	238.795	−	238.795i	0.240478	−	0.240478i
$994$	−137.268	−	36.7808i	−0.138097	−	0.0370029i
$995$	194.208	−	724.795i	0.195184	−	0.728438i
$996$	66.8897	+	66.8897i	0.0671584	+	0.0671584i
$997$	−250.817	−	434.428i	−0.251572	−	0.435735i	0.712387	−	0.701787i	$-0.247614\pi$
$997$	−250.817	−	434.428i	−0.251572	−	0.435735i	−0.963959	+	0.266052i	$0.914281\pi$
$998$	−85.2046	−	49.1929i	−0.0853753	−	0.0492915i
$999$	−387.177	+	103.744i	−0.387564	+	0.103848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.3.f.c.19.1		4
13.2	odd	12		169.3.f.a.89.1		4
13.3	even	3		13.3.f.a.2.1	✓	4
13.4	even	6		169.3.d.c.70.1		4
13.5	odd	4		169.3.f.b.150.1		4
13.6	odd	12		169.3.d.c.99.1		4
13.7	odd	12		169.3.d.a.99.2		4
13.8	odd	4		13.3.f.a.7.1	yes	4
13.9	even	3		169.3.d.a.70.2		4
13.10	even	6		169.3.f.b.80.1		4
13.11	odd	12	inner	169.3.f.c.89.1		4
13.12	even	2		169.3.f.a.19.1		4
39.8	even	4		117.3.bd.b.46.1		4
39.29	odd	6		117.3.bd.b.28.1		4
52.3	odd	6		208.3.bd.d.145.1		4
52.47	even	4		208.3.bd.d.33.1		4
65.3	odd	12		325.3.w.a.249.1		4
65.8	even	4		325.3.w.b.124.1		4
65.29	even	6		325.3.t.a.301.1		4
65.34	odd	4		325.3.t.a.176.1		4
65.42	odd	12		325.3.w.b.249.1		4
65.47	even	4		325.3.w.a.124.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.f.a.2.1	✓	4	13.3	even	3
13.3.f.a.7.1	yes	4	13.8	odd	4
117.3.bd.b.28.1		4	39.29	odd	6
117.3.bd.b.46.1		4	39.8	even	4
169.3.d.a.70.2		4	13.9	even	3
169.3.d.a.99.2		4	13.7	odd	12
169.3.d.c.70.1		4	13.4	even	6
169.3.d.c.99.1		4	13.6	odd	12
169.3.f.a.19.1		4	13.12	even	2
169.3.f.a.89.1		4	13.2	odd	12
169.3.f.b.80.1		4	13.10	even	6
169.3.f.b.150.1		4	13.5	odd	4
169.3.f.c.19.1		4	1.1	even	1	trivial
169.3.f.c.89.1		4	13.11	odd	12	inner
208.3.bd.d.33.1		4	52.47	even	4
208.3.bd.d.145.1		4	52.3	odd	6
325.3.t.a.176.1		4	65.34	odd	4
325.3.t.a.301.1		4	65.29	even	6
325.3.w.a.124.1		4	65.47	even	4
325.3.w.a.249.1		4	65.3	odd	12
325.3.w.b.124.1		4	65.8	even	4
325.3.w.b.249.1		4	65.42	odd	12

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	169.f (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.133975 + 0.500000i) q^{2} +(0.366025 - 0.633975i) q^{3} +(3.23205 - 1.86603i) q^{4} +(-2.63397 + 2.63397i) q^{5} +(0.366025 + 0.0980762i) q^{6} +(-1.53590 + 5.73205i) q^{7} +(2.83013 + 2.83013i) q^{8} +(4.23205 + 7.33013i) q^{9} +(-1.66987 - 0.964102i) q^{10} +(15.6603 - 4.19615i) q^{11} -2.73205i q^{12} -3.07180 q^{14} +(0.705771 + 2.63397i) q^{15} +(6.42820 - 11.1340i) q^{16} +(15.9904 - 9.23205i) q^{17} +(-3.09808 + 3.09808i) q^{18} +(-6.09808 - 1.63397i) q^{19} +(-3.59808 + 13.4282i) q^{20} +(3.07180 + 3.07180i) q^{21} +(4.19615 + 7.26795i) q^{22} +(-17.4904 - 10.0981i) q^{23} +(2.83013 - 0.758330i) q^{24} +11.1244i q^{25} +12.7846 q^{27} +(5.73205 + 21.3923i) q^{28} +(-4.69615 + 8.13397i) q^{29} +(-1.22243 + 0.705771i) q^{30} +(-11.9282 + 11.9282i) q^{31} +(21.8923 + 5.86603i) q^{32} +(3.07180 - 11.4641i) q^{33} +(6.75833 + 6.75833i) q^{34} +(-11.0526 - 19.1436i) q^{35} +(27.3564 + 15.7942i) q^{36} +(-30.2846 + 8.11474i) q^{37} -3.26795i q^{38} -14.9090 q^{40} +(-12.0359 - 44.9186i) q^{41} +(-1.12436 + 1.94744i) q^{42} +(-45.0000 + 25.9808i) q^{43} +(42.7846 - 42.7846i) q^{44} +(-30.4545 - 8.16025i) q^{45} +(2.70577 - 10.0981i) q^{46} +(-34.3205 - 34.3205i) q^{47} +(-4.70577 - 8.15064i) q^{48} +(11.9378 + 6.89230i) q^{49} +(-5.56218 + 1.49038i) q^{50} -13.5167i q^{51} -14.7654 q^{53} +(1.71281 + 6.39230i) q^{54} +(-30.1962 + 52.3013i) q^{55} +(-20.5692 + 11.8756i) q^{56} +(-3.26795 + 3.26795i) q^{57} +(-4.69615 - 1.25833i) q^{58} +(24.9090 - 92.9615i) q^{59} +(7.19615 + 7.19615i) q^{60} +(-12.8135 - 22.1936i) q^{61} +(-7.56218 - 4.36603i) q^{62} +(-48.5167 + 13.0000i) q^{63} -39.6936i q^{64} +6.14359 q^{66} +(-10.4571 - 39.0263i) q^{67} +(34.4545 - 59.6769i) q^{68} +(-12.8038 + 7.39230i) q^{69} +(8.09103 - 8.09103i) q^{70} +(44.6865 + 11.9737i) q^{71} +(-8.76795 + 32.7224i) q^{72} +(-19.2750 - 19.2750i) q^{73} +(-8.11474 - 14.0551i) q^{74} +(7.05256 + 4.07180i) q^{75} +(-22.7583 + 6.09808i) q^{76} +96.2102i q^{77} +62.7461 q^{79} +(12.3949 + 46.2583i) q^{80} +(-33.4090 + 57.8660i) q^{81} +(20.8468 - 12.0359i) q^{82} +(-24.4833 + 24.4833i) q^{83} +(15.6603 + 4.19615i) q^{84} +(-17.8013 + 66.4352i) q^{85} +(-19.0192 - 19.0192i) q^{86} +(3.43782 + 5.95448i) q^{87} +(56.1962 + 32.4449i) q^{88} +(86.4711 - 23.1699i) q^{89} -16.3205i q^{90} -75.3731 q^{92} +(3.19615 + 11.9282i) q^{93} +(12.5622 - 21.7583i) q^{94} +(20.3660 - 11.7583i) q^{95} +(11.7321 - 11.7321i) q^{96} +(-52.9545 - 14.1891i) q^{97} +(-1.84679 + 6.89230i) q^{98} +(97.0333 + 97.0333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 2 q^{3} + 6 q^{4} - 14 q^{5} - 2 q^{6} - 20 q^{7} - 6 q^{8} + 10 q^{9} - 24 q^{10} + 28 q^{11} - 40 q^{14} + 34 q^{15} - 2 q^{16} + 12 q^{17} - 2 q^{18} - 14 q^{19} - 4 q^{20} + 40 q^{21}+ \cdots + 208 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^3 + 6 * q^4 - 14 * q^5 - 2 * q^6 - 20 * q^7 - 6 * q^8 + 10 * q^9 - 24 * q^10 + 28 * q^11 - 40 * q^14 + 34 * q^15 - 2 * q^16 + 12 * q^17 - 2 * q^18 - 14 * q^19 - 4 * q^20 + 40 * q^21 - 4 * q^22 - 18 * q^23 - 6 * q^24 - 32 * q^27 + 16 * q^28 + 2 * q^29 + 54 * q^30 - 20 * q^31 + 46 * q^32 + 40 * q^33 - 18 * q^34 + 32 * q^35 + 54 * q^36 - 38 * q^37 + 72 * q^40 - 62 * q^41 + 44 * q^42 - 180 * q^43 + 88 * q^44 - 56 * q^45 + 42 * q^46 - 68 * q^47 - 50 * q^48 + 72 * q^49 + 2 * q^50 + 128 * q^53 - 104 * q^54 - 100 * q^55 + 84 * q^56 - 20 * q^57 + 2 * q^58 - 32 * q^59 + 8 * q^60 - 124 * q^61 - 6 * q^62 - 104 * q^63 + 80 * q^66 - 170 * q^67 + 72 * q^68 - 72 * q^69 + 164 * q^70 + 106 * q^71 - 42 * q^72 + 58 * q^73 + 68 * q^74 - 48 * q^75 - 46 * q^76 - 40 * q^79 + 202 * q^80 - 2 * q^81 - 24 * q^82 - 188 * q^83 + 28 * q^84 + 102 * q^85 - 180 * q^86 + 38 * q^87 + 204 * q^88 + 190 * q^89 - 156 * q^92 - 8 * q^93 + 26 * q^94 + 78 * q^95 + 40 * q^96 - 146 * q^97 + 100 * q^98 + 208 * q^99

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