LMFDB - Embedded newform 169.3.f.g.80.5

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:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.5
Character	$\chi$	$=$	169.80
Dual form			169.3.f.g.150.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60455 - 0.429937i) q^{2} +(-0.677024 - 1.17264i) q^{3} +(-1.07438 - 0.620291i) q^{4} +(1.57408 - 1.57408i) q^{5} +(0.582156 + 2.17264i) q^{6} +(-12.1635 + 3.25921i) q^{7} +(6.15564 + 6.15564i) q^{8} +(3.58328 - 6.20642i) q^{9} +(-3.20245 + 1.84893i) q^{10} +(-1.97950 + 7.38758i) q^{11} +1.67981i q^{12} +20.9182 q^{14} +(-2.91152 - 0.780141i) q^{15} +(-4.74931 - 8.22605i) q^{16} +(12.9801 + 7.49406i) q^{17} +(-8.41790 + 8.41790i) q^{18} +(5.75221 + 21.4675i) q^{19} +(-2.66754 + 0.714766i) q^{20} +(12.0569 + 12.0569i) q^{21} +(6.35239 - 11.0027i) q^{22} +(-21.0979 + 12.1809i) q^{23} +(3.05084 - 11.3859i) q^{24} +20.0445i q^{25} -21.8903 q^{27} +(15.0899 + 4.04332i) q^{28} +(16.0668 + 27.8285i) q^{29} +(4.33627 + 2.50354i) q^{30} +(-1.13095 + 1.13095i) q^{31} +(-4.92867 - 18.3941i) q^{32} +(10.0031 - 2.68033i) q^{33} +(-17.6052 - 17.6052i) q^{34} +(-14.0161 + 24.2767i) q^{35} +(-7.69957 + 4.44535i) q^{36} +(-0.295912 + 1.10436i) q^{37} -36.9188i q^{38} +19.3790 q^{40} +(-25.8863 - 6.93622i) q^{41} +(-14.1622 - 24.5296i) q^{42} +(-2.53837 - 1.46553i) q^{43} +(6.70917 - 6.70917i) q^{44} +(-4.12904 - 15.4098i) q^{45} +(39.0895 - 10.4740i) q^{46} +(-28.5191 - 28.5191i) q^{47} +(-6.43080 + 11.1385i) q^{48} +(94.8941 - 54.7871i) q^{49} +(8.61789 - 32.1624i) q^{50} -20.2946i q^{51} -80.4313 q^{53} +(35.1240 + 9.41145i) q^{54} +(8.51276 + 14.7445i) q^{55} +(-94.9370 - 54.8119i) q^{56} +(21.2793 - 21.2793i) q^{57} +(-13.8154 - 51.5599i) q^{58} +(-16.2551 + 4.35554i) q^{59} +(2.64416 + 2.64416i) q^{60} +(-10.8503 + 18.7932i) q^{61} +(2.30090 - 1.32843i) q^{62} +(-23.3573 + 87.1707i) q^{63} +69.6277i q^{64} -17.2029 q^{66} +(-13.8651 - 3.71513i) q^{67} +(-9.29699 - 16.1029i) q^{68} +(28.5676 + 16.4935i) q^{69} +(32.9270 - 32.9270i) q^{70} +(1.12218 + 4.18802i) q^{71} +(60.2618 - 16.1471i) q^{72} +(-26.0918 - 26.0918i) q^{73} +(0.949610 - 1.64477i) q^{74} +(23.5050 - 13.5706i) q^{75} +(7.13609 - 26.6323i) q^{76} -96.3107i q^{77} +36.3029 q^{79} +(-20.4243 - 5.47267i) q^{80} +(-17.4292 - 30.1883i) q^{81} +(38.5537 + 22.2590i) q^{82} +(-56.7270 + 56.7270i) q^{83} +(-5.47485 - 20.4324i) q^{84} +(32.2280 - 8.63546i) q^{85} +(3.44285 + 3.44285i) q^{86} +(21.7553 - 37.6812i) q^{87} +(-57.6603 + 33.2902i) q^{88} +(25.7887 - 96.2446i) q^{89} +26.5009i q^{90} +30.2227 q^{92} +(2.09188 + 0.560517i) q^{93} +(33.4989 + 58.0217i) q^{94} +(42.8461 + 24.7372i) q^{95} +(-18.2328 + 18.2328i) q^{96} +(41.3528 + 154.331i) q^{97} +(-175.817 + 47.1101i) q^{98} +(38.7573 + 38.7573i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{3} - 84 q^{9} + 376 q^{14} - 188 q^{16} + 136 q^{22} + 120 q^{27} - 84 q^{29} - 176 q^{35} - 1048 q^{40} + 368 q^{42} + 368 q^{48} - 88 q^{53} + 704 q^{55} + 8 q^{61} - 1480 q^{66} + 168 q^{68}+ \cdots - 1132 q^{94}+O(q^{100}) $ 48 * q - 12 * q^3 - 84 * q^9 + 376 * q^14 - 188 * q^16 + 136 * q^22 + 120 * q^27 - 84 * q^29 - 176 * q^35 - 1048 * q^40 + 368 * q^42 + 368 * q^48 - 88 * q^53 + 704 * q^55 + 8 * q^61 - 1480 * q^66 + 168 * q^68 - 744 * q^74 - 600 * q^79 - 240 * q^81 + 952 * q^87 + 3472 * q^92 - 1132 * q^94

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

Coefficient data

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

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

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

$2$	−1.60455	−	0.429937i	−0.802274	−	0.214969i	−0.165692	−	0.986178i	$-0.552986\pi$
$2$	−1.60455	−	0.429937i	−0.802274	−	0.214969i	−0.636582	+	0.771209i	$0.719652\pi$
$3$	−0.677024	−	1.17264i	−0.225675	−	0.390880i	0.730847	−	0.682541i	$-0.239125\pi$
$3$	−0.677024	−	1.17264i	−0.225675	−	0.390880i	−0.956522	+	0.291661i	$0.905792\pi$
$4$	−1.07438	−	0.620291i	−0.268594	−	0.155073i
$5$	1.57408	−	1.57408i	0.314816	−	0.314816i	−0.531956	−	0.846772i	$-0.678543\pi$
$5$	1.57408	−	1.57408i	0.314816	−	0.314816i	0.846772	+	0.531956i	$0.178543\pi$
$6$	0.582156	+	2.17264i	0.0970260	+	0.362106i
$7$	−12.1635	+	3.25921i	−1.73765	+	0.465602i	−0.981922	−	0.189285i	$-0.939383\pi$
$7$	−12.1635	+	3.25921i	−1.73765	+	0.465602i	−0.755727	+	0.654887i	$0.772716\pi$
$8$	6.15564	+	6.15564i	0.769455	+	0.769455i
$9$	3.58328	−	6.20642i	0.398142	−	0.689602i
$10$	−3.20245	+	1.84893i	−0.320245	+	0.184893i
$11$	−1.97950	+	7.38758i	−0.179954	+	0.671598i	0.815700	+	0.578474i	$0.196352\pi$
$11$	−1.97950	+	7.38758i	−0.179954	+	0.671598i	−0.995655	+	0.0931234i	$0.970315\pi$
$12$			1.67981i			0.139984i
$13$		0			0
$13$		0			0
$14$	20.9182			1.49416
$15$	−2.91152	−	0.780141i	−0.194102	−	0.0520094i
$16$	−4.74931	−	8.22605i	−0.296832	−	0.514128i
$17$	12.9801	+	7.49406i	0.763535	+	0.440827i	0.830563	−	0.556924i	$-0.188019\pi$
$17$	12.9801	+	7.49406i	0.763535	+	0.440827i	−0.0670287	+	0.997751i	$0.521352\pi$
$18$	−8.41790	+	8.41790i	−0.467661	+	0.467661i
$19$	5.75221	+	21.4675i	0.302748	+	1.12987i	0.934867	+	0.354999i	$0.115519\pi$
$19$	5.75221	+	21.4675i	0.302748	+	1.12987i	−0.632119	+	0.774872i	$0.717814\pi$
$20$	−2.66754	+	0.714766i	−0.133377	+	0.0357383i
$21$	12.0569	+	12.0569i	0.574138	+	0.574138i
$22$	6.35239	−	11.0027i	0.288745	−	0.500121i
$23$	−21.0979	+	12.1809i	−0.917299	+	0.529603i	−0.882772	−	0.469801i	$-0.844326\pi$
$23$	−21.0979	+	12.1809i	−0.917299	+	0.529603i	−0.0345267	+	0.999404i	$0.510992\pi$
$24$	3.05084	−	11.3859i	0.127118	−	0.474411i
$25$			20.0445i			0.801781i
$26$		0			0
$27$	−21.8903			−0.810752
$28$	15.0899	+	4.04332i	0.538924	+	0.144404i
$29$	16.0668	+	27.8285i	0.554028	+	0.959605i	0.997978	+	0.0635536i	$0.0202434\pi$
$29$	16.0668	+	27.8285i	0.554028	+	0.959605i	−0.443950	+	0.896051i	$0.646423\pi$
$30$	4.33627	+	2.50354i	0.144542	+	0.0834515i
$31$	−1.13095	+	1.13095i	−0.0364823	+	0.0364823i	−0.725113	−	0.688630i	$-0.758212\pi$
$31$	−1.13095	+	1.13095i	−0.0364823	+	0.0364823i	0.688630	+	0.725113i	$0.258212\pi$
$32$	−4.92867	−	18.3941i	−0.154021	−	0.574814i
$33$	10.0031	−	2.68033i	0.303125	−	0.0812222i
$34$	−17.6052	−	17.6052i	−0.517800	−	0.517800i
$35$	−14.0161	+	24.2767i	−0.400461	+	0.693620i
$36$	−7.69957	+	4.44535i	−0.213877	+	0.123482i
$37$	−0.295912	+	1.10436i	−0.00799762	+	0.0298475i	−0.969809	−	0.243864i	$-0.921585\pi$
$37$	−0.295912	+	1.10436i	−0.00799762	+	0.0298475i	0.961812	+	0.273712i	$0.0882515\pi$
$38$		−	36.9188i		−	0.971547i
$39$		0			0
$40$	19.3790			0.484474
$41$	−25.8863	−	6.93622i	−0.631374	−	0.169176i	−0.0710809	−	0.997471i	$-0.522645\pi$
$41$	−25.8863	−	6.93622i	−0.631374	−	0.169176i	−0.560293	+	0.828294i	$0.689312\pi$
$42$	−14.1622	−	24.5296i	−0.337194	−	0.584038i
$43$	−2.53837	−	1.46553i	−0.0590319	−	0.0340821i	0.470194	−	0.882563i	$-0.344184\pi$
$43$	−2.53837	−	1.46553i	−0.0590319	−	0.0340821i	−0.529225	+	0.848481i	$0.677517\pi$
$44$	6.70917	−	6.70917i	0.152481	−	0.152481i
$45$	−4.12904	−	15.4098i	−0.0917564	−	0.342439i
$46$	39.0895	−	10.4740i	0.849773	−	0.227696i
$47$	−28.5191	−	28.5191i	−0.606790	−	0.606790i	0.335316	−	0.942106i	$-0.391157\pi$
$47$	−28.5191	−	28.5191i	−0.606790	−	0.606790i	−0.942106	+	0.335316i	$0.891157\pi$
$48$	−6.43080	+	11.1385i	−0.133975	+	0.232052i
$49$	94.8941	−	54.7871i	1.93661	−	1.11810i
$50$	8.61789	−	32.1624i	0.172358	−	0.643248i
$51$		−	20.2946i		−	0.397934i
$52$		0			0
$53$	−80.4313			−1.51757			−0.758786	−	0.651340i	$-0.774207\pi$
$53$	−80.4313			−1.51757			−0.758786	+	0.651340i	$0.774207\pi$
$54$	35.1240	+	9.41145i	0.650445	+	0.174286i
$55$	8.51276	+	14.7445i	0.154778	+	0.268083i
$56$	−94.9370	−	54.8119i	−1.69530	−	0.978783i
$57$	21.2793	−	21.2793i	0.373322	−	0.373322i
$58$	−13.8154	−	51.5599i	−0.238197	−	0.888964i
$59$	−16.2551	+	4.35554i	−0.275510	+	0.0738228i	−0.393929	−	0.919141i	$-0.628884\pi$
$59$	−16.2551	+	4.35554i	−0.275510	+	0.0738228i	0.118418	+	0.992964i	$0.462218\pi$
$60$	2.64416	+	2.64416i	0.0440693	+	0.0440693i
$61$	−10.8503	+	18.7932i	−0.177873	+	0.308086i	−0.941152	−	0.337984i	$-0.890255\pi$
$61$	−10.8503	+	18.7932i	−0.177873	+	0.308086i	0.763279	+	0.646069i	$0.223588\pi$
$62$	2.30090	−	1.32843i	0.0371113	−	0.0214262i
$63$	−23.3573	+	87.1707i	−0.370751	+	1.38366i
$64$			69.6277i			1.08793i
$65$		0			0
$66$	−17.2029			−0.260650
$67$	−13.8651	−	3.71513i	−0.206941	−	0.0554498i	0.153859	−	0.988093i	$-0.450830\pi$
$67$	−13.8651	−	3.71513i	−0.206941	−	0.0554498i	−0.360800	+	0.932643i	$0.617496\pi$
$68$	−9.29699	−	16.1029i	−0.136721	−	0.236807i
$69$	28.5676	+	16.4935i	0.414023	+	0.239036i
$70$	32.9270	−	32.9270i	0.470386	−	0.470386i
$71$	1.12218	+	4.18802i	0.0158053	+	0.0589862i	0.973378	−	0.229205i	$-0.0736127\pi$
$71$	1.12218	+	4.18802i	0.0158053	+	0.0589862i	−0.957573	+	0.288191i	$0.906946\pi$
$72$	60.2618	−	16.1471i	0.836970	−	0.224265i
$73$	−26.0918	−	26.0918i	−0.357422	−	0.357422i	0.505440	−	0.862862i	$-0.331330\pi$
$73$	−26.0918	−	26.0918i	−0.357422	−	0.357422i	−0.862862	+	0.505440i	$0.831330\pi$
$74$	0.949610	−	1.64477i	0.0128326	−	0.0222267i
$75$	23.5050	−	13.5706i	0.313400	−	0.180942i
$76$	7.13609	−	26.6323i	0.0938959	−	0.350424i
$77$		−	96.3107i		−	1.25079i
$78$		0			0
$79$	36.3029			0.459530			0.229765	−	0.973246i	$-0.426204\pi$
$79$	36.3029			0.459530			0.229765	+	0.973246i	$0.426204\pi$
$80$	−20.4243	−	5.47267i	−0.255304	−	0.0684084i
$81$	−17.4292	−	30.1883i	−0.215176	−	0.372695i
$82$	38.5537	+	22.2590i	0.470167	+	0.271451i
$83$	−56.7270	+	56.7270i	−0.683457	+	0.683457i	−0.960778	−	0.277320i	$-0.910554\pi$
$83$	−56.7270	+	56.7270i	−0.683457	+	0.683457i	0.277320	+	0.960778i	$0.410554\pi$
$84$	−5.47485	−	20.4324i	−0.0651768	−	0.243243i
$85$	32.2280	−	8.63546i	0.379153	−	0.101594i
$86$	3.44285	+	3.44285i	0.0400332	+	0.0400332i
$87$	21.7553	−	37.6812i	0.250060	−	0.433117i
$88$	−57.6603	+	33.2902i	−0.655231	+	0.378298i
$89$	25.7887	−	96.2446i	0.289760	−	1.08140i	−0.655530	−	0.755169i	$-0.727555\pi$
$89$	25.7887	−	96.2446i	0.289760	−	1.08140i	0.945290	−	0.326231i	$-0.105779\pi$
$90$			26.5009i			0.294455i
$91$		0			0
$92$	30.2227			0.328508
$93$	2.09188	+	0.560517i	0.0224933	+	0.00602707i
$94$	33.4989	+	58.0217i	0.356371	+	0.617252i
$95$	42.8461	+	24.7372i	0.451012	+	0.260392i
$96$	−18.2328	+	18.2328i	−0.189925	+	0.189925i
$97$	41.3528	+	154.331i	0.426318	+	1.59104i	0.761029	+	0.648718i	$0.224695\pi$
$97$	41.3528	+	154.331i	0.426318	+	1.59104i	−0.334711	+	0.942321i	$0.608639\pi$
$98$	−175.817	+	47.1101i	−1.79405	+	0.480715i
$99$	38.7573	+	38.7573i	0.391488	+	0.391488i
$100$	12.4334	−	21.5354i	0.124334	−	0.215354i
$101$	−129.158	+	74.5696i	−1.27879	+	0.738312i	−0.976627	−	0.214942i	$-0.931044\pi$
$101$	−129.158	+	74.5696i	−1.27879	+	0.738312i	−0.302168	+	0.953255i	$0.597710\pi$
$102$	−8.72542	+	32.5637i	−0.0855433	+	0.319252i
$103$			105.545i			1.02471i	0.858774	+	0.512354i	$0.171227\pi$
$103$			105.545i			1.02471i	−0.858774	+	0.512354i	$0.828773\pi$
$104$		0			0
$105$	37.9571			0.361496
$106$	129.056	+	34.5804i	1.21751	+	0.326230i
$107$	46.2189	+	80.0535i	0.431952	+	0.748164i	0.997041	−	0.0768664i	$-0.0244915\pi$
$107$	46.2189	+	80.0535i	0.431952	+	0.748164i	−0.565089	+	0.825030i	$0.691158\pi$
$108$	23.5184	+	13.5784i	0.217763	+	0.125726i
$109$	−30.2071	+	30.2071i	−0.277129	+	0.277129i	−0.831962	−	0.554833i	$-0.812782\pi$
$109$	−30.2071	+	30.2071i	−0.277129	+	0.277129i	0.554833	+	0.831962i	$0.312782\pi$
$110$	−7.31991	−	27.3183i	−0.0665446	−	0.248348i
$111$	1.49536	−	0.400679i	0.0134717	−	0.00360972i
$112$	84.5789	+	84.5789i	0.755169	+	0.755169i
$113$	−55.5647	+	96.2408i	−0.491723	+	0.851689i	−0.999955	−	0.00953164i	$-0.996966\pi$
$113$	−55.5647	+	96.2408i	−0.491723	+	0.851689i	0.508232	+	0.861220i	$0.330299\pi$
$114$	−43.2925	+	24.9949i	−0.379758	+	0.219254i
$115$	−14.0361	+	52.3835i	−0.122053	+	0.455508i
$116$		−	39.8644i		−	0.343659i
$117$		0			0
$118$	27.9547			0.236904
$119$	−182.309	−	48.8494i	−1.53201	−	0.410500i
$120$	−13.1200	−	22.7246i	−0.109334	−	0.189371i
$121$	54.1312	+	31.2527i	0.447365	+	0.258286i
$122$	25.4897	−	25.4897i	0.208932	−	0.208932i
$123$	9.39198	+	35.0514i	0.0763576	+	0.284970i
$124$	1.91658	−	0.513547i	0.0154563	−	0.00414151i
$125$	70.9038	+	70.9038i	0.567230	+	0.567230i
$126$	74.9558	−	129.827i	0.594887	−	1.03038i
$127$	0.501697	−	0.289655i	0.00395037	−	0.00228075i	−0.498024	−	0.867164i	$-0.665941\pi$
$127$	0.501697	−	0.289655i	0.00395037	−	0.00228075i	0.501974	+	0.864883i	$0.332607\pi$
$128$	10.2208	−	38.1447i	0.0798502	−	0.298005i
$129$			3.96880i			0.0307659i
$130$		0			0
$131$	190.994			1.45797			0.728983	−	0.684532i	$-0.239993\pi$
$131$	190.994			1.45797			0.728983	+	0.684532i	$0.239993\pi$
$132$	−12.4097	−	3.32517i	−0.0940130	−	0.0251907i
$133$	−139.935	−	242.374i	−1.05214	−	1.82236i
$134$	20.6499	+	11.9222i	0.154104	+	0.0889717i
$135$	−34.4571	+	34.4571i	−0.255238	+	0.255238i
$136$	33.7700	+	126.031i	0.248309	+	0.926702i
$137$	−100.047	+	26.8075i	−0.730270	+	0.195675i	−0.604750	−	0.796416i	$-0.706727\pi$
$137$	−100.047	+	26.8075i	−0.730270	+	0.195675i	−0.125521	+	0.992091i	$0.540060\pi$
$138$	−38.7468	−	38.7468i	−0.280774	−	0.280774i
$139$	115.864	−	200.682i	0.833554	−	1.44376i	−0.0616482	−	0.998098i	$-0.519636\pi$
$139$	115.864	−	200.682i	0.833554	−	1.44376i	0.895202	−	0.445660i	$-0.147031\pi$
$140$	30.1172	−	17.3882i	0.215123	−	0.124201i
$141$	−14.1345	+	52.7508i	−0.100245	+	0.374119i
$142$		−	7.20235i		−	0.0507207i
$143$		0			0
$144$	−68.0724			−0.472725
$145$	69.0949	+	18.5139i	0.476517	+	0.127682i
$146$	30.6477	+	53.0834i	0.209916	+	0.363585i
$147$	−128.491	−	74.1845i	−0.874090	−	0.504656i
$148$	1.00294	−	1.00294i	0.00677665	−	0.00677665i
$149$	−42.2214	−	157.572i	−0.283365	−	1.05753i	−0.950026	−	0.312171i	$-0.898944\pi$
$149$	−42.2214	−	157.572i	−0.283365	−	1.05753i	0.666661	−	0.745361i	$-0.267723\pi$
$150$	−43.5495	+	11.6690i	−0.290330	+	0.0777936i
$151$	−67.8221	−	67.8221i	−0.449153	−	0.449153i	0.445920	−	0.895073i	$-0.352877\pi$
$151$	−67.8221	−	67.8221i	−0.449153	−	0.449153i	−0.895073	+	0.445920i	$0.852877\pi$
$152$	−96.7380	+	167.555i	−0.636434	+	1.10234i
$153$	93.0225	−	53.7066i	0.607990	−	0.351023i
$154$	−41.4076	+	154.535i	−0.268880	+	1.00347i
$155$			3.56042i			0.0229704i
$156$		0			0
$157$	−124.176			−0.790928			−0.395464	−	0.918482i	$-0.629416\pi$
$157$	−124.176			−0.790928			−0.395464	+	0.918482i	$0.629416\pi$
$158$	−58.2497	−	15.6079i	−0.368669	−	0.0987845i
$159$	54.4540	+	94.3170i	0.342478	+	0.593189i
$160$	−36.7119	−	21.1956i	−0.229449	−	0.132473i
$161$	216.925	−	216.925i	1.34736	−	1.34736i
$162$	14.9869	+	55.9320i	0.0925120	+	0.345259i
$163$	−5.68411	+	1.52305i	−0.0348718	+	0.00934388i	−0.276213	−	0.961097i	$-0.589079\pi$
$163$	−5.68411	+	1.52305i	−0.0348718	+	0.00934388i	0.241341	+	0.970440i	$0.422413\pi$
$164$	23.5092	+	23.5092i	0.143349	+	0.143349i
$165$	11.5267	−	19.9648i	0.0698588	−	0.120999i
$166$	115.410	−	66.6321i	0.695242	−	0.401398i
$167$	26.8945	−	100.372i	0.161045	−	0.601028i	−0.837467	−	0.546488i	$-0.815964\pi$
$167$	26.8945	−	100.372i	0.161045	−	0.601028i	0.998512	−	0.0545395i	$-0.0173691\pi$
$168$			148.436i			0.883547i
$169$		0			0
$170$	−55.4240			−0.326024
$171$	153.848	+	41.2235i	0.899698	+	0.241073i
$172$	1.81811	+	3.14906i	0.0105704	+	0.0183085i
$173$	5.10185	+	2.94555i	0.0294904	+	0.0170263i	0.514673	−	0.857387i	$-0.327913\pi$
$173$	5.10185	+	2.94555i	0.0294904	+	0.0170263i	−0.485182	+	0.874413i	$0.661247\pi$
$174$	−51.1079	+	51.1079i	−0.293723	+	0.293723i
$175$	−65.3294	−	243.813i	−0.373311	−	1.39321i
$176$	70.1718	−	18.8025i	0.398704	−	0.106832i
$177$	16.1126	+	16.1126i	0.0910316	+	0.0910316i
$178$	−82.7582	+	143.341i	−0.464934	+	0.805289i
$179$	−41.2206	+	23.7987i	−0.230283	+	0.132954i	−0.610702	−	0.791860i	$-0.709113\pi$
$179$	−41.2206	+	23.7987i	−0.230283	+	0.132954i	0.380420	+	0.924814i	$0.375780\pi$
$180$	−5.12241	+	19.1171i	−0.0284578	+	0.106206i
$181$		−	201.671i		−	1.11420i	−0.830444	−	0.557102i	$-0.811913\pi$
$181$		−	201.671i		−	1.11420i	0.830444	−	0.557102i	$-0.188087\pi$
$182$		0			0
$183$	29.3836			0.160566
$184$	−204.852	−	54.8899i	−1.11333	−	0.298315i
$185$	1.27256	+	2.20414i	0.00687871	+	0.0119143i
$186$	−3.11553	−	1.79875i	−0.0167502	−	0.00967072i
$187$	−81.0569	+	81.0569i	−0.433460	+	0.433460i
$188$	12.9501	+	48.3304i	0.0688835	+	0.257077i
$189$	266.264	−	71.3451i	1.40880	−	0.377487i
$190$	−58.1132	−	58.1132i	−0.305859	−	0.305859i
$191$	−82.2122	+	142.396i	−0.430430	+	0.745527i	−0.996910	−	0.0785485i	$-0.974971\pi$
$191$	−82.2122	+	142.396i	−0.430430	+	0.745527i	0.566480	+	0.824075i	$0.308305\pi$
$192$	81.6482	−	47.1396i	0.425251	−	0.245519i
$193$	50.9404	−	190.112i	0.263940	−	0.985038i	−0.698956	−	0.715165i	$-0.746352\pi$
$193$	50.9404	−	190.112i	0.263940	−	0.985038i	0.962896	−	0.269873i	$-0.0869818\pi$
$194$		−	265.410i		−	1.36809i
$195$		0			0
$196$	−135.936			−0.693551
$197$	115.484	+	30.9438i	0.586213	+	0.157075i	0.539722	−	0.841843i	$-0.318529\pi$
$197$	115.484	+	30.9438i	0.586213	+	0.157075i	0.0464911	+	0.998919i	$0.485196\pi$
$198$	−45.5247	−	78.8511i	−0.229923	−	0.398238i
$199$	−179.903	−	103.867i	−0.904035	−	0.521945i	−0.0255280	−	0.999674i	$-0.508127\pi$
$199$	−179.903	−	103.867i	−0.904035	−	0.521945i	−0.878507	+	0.477729i	$0.841460\pi$
$200$	−123.387	+	123.387i	−0.616935	+	0.616935i
$201$	5.03047	+	18.7740i	0.0250272	+	0.0934029i
$202$	239.301	−	64.1204i	1.18466	−	0.317428i
$203$	−286.129	−	286.129i	−1.40950	−	1.40950i
$204$	−12.5886	+	21.8041i	−0.0617087	+	0.106883i
$205$	−51.6654	+	29.8290i	−0.252026	+	0.145507i
$206$	45.3777	−	169.352i	0.220280	−	0.822097i
$207$			174.590i			0.843428i
$208$		0			0
$209$	−169.980			−0.813300
$210$	−60.9040	−	16.3192i	−0.290019	−	0.0777103i
$211$	109.944	+	190.428i	0.521060	+	0.902503i	0.999700	+	0.0244913i	$0.00779661\pi$
$211$	109.944	+	190.428i	0.521060	+	0.902503i	−0.478640	+	0.878011i	$0.658870\pi$
$212$	86.4135	+	49.8908i	0.407611	+	0.235334i
$213$	4.15130	−	4.15130i	0.0194897	−	0.0194897i
$214$	−39.7425	−	148.321i	−0.185712	−	0.693088i
$215$	−6.30247	+	1.68874i	−0.0293138	+	0.00785461i
$216$	−134.749	−	134.749i	−0.623837	−	0.623837i
$217$	10.0704	−	17.4424i	0.0464072	−	0.0803796i
$218$	61.4558	−	35.4815i	0.281908	−	0.162759i
$219$	−12.9315	+	48.2611i	−0.0590480	+	0.220370i
$220$		−	21.1216i		−	0.0960071i
$221$		0			0
$222$	−2.57164			−0.0115839
$223$	258.058	+	69.1464i	1.15721	+	0.310074i	0.785851	−	0.618415i	$-0.212225\pi$
$223$	258.058	+	69.1464i	1.15721	+	0.310074i	0.371360	+	0.928489i	$0.378892\pi$
$224$	119.900	+	207.673i	0.535269	+	0.927113i
$225$	124.405	+	71.8251i	0.552910	+	0.319223i
$226$	130.534	−	130.534i	0.577582	−	0.577582i
$227$	4.37307	+	16.3205i	0.0192646	+	0.0718966i	0.974889	−	0.222691i	$-0.0714842\pi$
$227$	4.37307	+	16.3205i	0.0192646	+	0.0718966i	−0.955624	+	0.294588i	$0.904818\pi$
$228$	−36.0614	+	9.66262i	−0.158164	+	0.0423799i
$229$	305.425	+	305.425i	1.33373	+	1.33373i	0.902001	+	0.431733i	$0.142098\pi$
$229$	305.425	+	305.425i	1.33373	+	1.33373i	0.431733	+	0.902001i	$0.357902\pi$
$230$	45.0432	−	78.0171i	0.195840	−	0.339205i
$231$	−112.938	+	65.2047i	−0.488908	+	0.282271i
$232$	−72.4010	+	270.204i	−0.312073	+	1.16467i
$233$			247.342i			1.06156i	0.847511	+	0.530778i	$0.178100\pi$
$233$			247.342i			1.06156i	−0.847511	+	0.530778i	$0.821900\pi$
$234$		0			0
$235$	−89.7829			−0.382055
$236$	20.1658	+	5.40341i	0.0854483	+	0.0228958i
$237$	−24.5779	−	42.5702i	−0.103704	−	0.179621i
$238$	271.521	+	156.762i	1.14084	+	0.658666i
$239$	26.3028	−	26.3028i	0.110053	−	0.110053i	−0.649936	−	0.759989i	$-0.725204\pi$
$239$	26.3028	−	26.3028i	0.110053	−	0.110053i	0.759989	+	0.649936i	$0.225204\pi$
$240$	7.41026	+	27.6555i	0.0308761	+	0.115231i
$241$	74.8033	−	20.0435i	0.310387	−	0.0831680i	−0.100263	−	0.994961i	$-0.531968\pi$
$241$	74.8033	−	20.0435i	0.310387	−	0.0831680i	0.410650	+	0.911793i	$0.365302\pi$
$242$	−73.4194	−	73.4194i	−0.303386	−	0.303386i
$243$	−122.106	+	211.494i	−0.502495	+	0.870347i
$244$	23.3145	−	13.4606i	0.0955513	−	0.0551666i
$245$	63.1317	−	235.611i	0.257680	−	0.961676i
$246$		−	60.2795i		−	0.245039i
$247$		0			0
$248$	−13.9234			−0.0561429
$249$	104.926	+	28.1148i	0.421389	+	0.112911i
$250$	−83.2843	−	144.253i	−0.333137	−	0.577011i
$251$	−369.027	−	213.058i	−1.47023	−	0.848837i	−0.470786	−	0.882247i	$-0.656030\pi$
$251$	−369.027	−	213.058i	−1.47023	−	0.848837i	−0.999442	+	0.0334107i	$0.989363\pi$
$252$	79.1657	−	79.1657i	0.314150	−	0.314150i
$253$	−48.2239	−	179.974i	−0.190608	−	0.711360i
$254$	−0.929530	+	0.249067i	−0.00365957	+	0.000980578i
$255$	−31.9454	−	31.9454i	−0.125276	−	0.125276i
$256$	106.456	−	184.387i	0.415843	−	0.720260i
$257$	29.3689	−	16.9562i	0.114276	−	0.0659773i	−0.441773	−	0.897127i	$-0.645650\pi$
$257$	29.3689	−	16.9562i	0.114276	−	0.0659773i	0.556049	+	0.831150i	$0.312317\pi$
$258$	1.70633	−	6.36812i	0.00661369	−	0.0246826i
$259$		−	14.3974i		−	0.0555882i
$260$		0			0
$261$	230.287			0.882327
$262$	−306.458	−	82.1152i	−1.16969	−	0.313417i
$263$	−155.488	−	269.313i	−0.591208	−	1.02400i	−0.994070	−	0.108741i	$-0.965318\pi$
$263$	−155.488	−	269.313i	−0.591208	−	1.02400i	0.402862	−	0.915261i	$-0.368015\pi$
$264$	78.0749	+	45.0766i	0.295738	+	0.170745i
$265$	−126.606	+	126.606i	−0.477757	+	0.477757i
$266$	120.326	+	449.063i	0.452354	+	1.68821i
$267$	−130.320	+	34.9191i	−0.488089	+	0.130783i
$268$	12.5918	+	12.5918i	0.0469844	+	0.0469844i
$269$	143.628	−	248.770i	0.533932	−	0.924797i	−0.465283	−	0.885162i	$-0.654047\pi$
$269$	143.628	−	248.770i	0.533932	−	0.924797i	0.999214	−	0.0396345i	$-0.0126194\pi$
$270$	70.1025	−	40.4737i	0.259639	−	0.149903i
$271$	−106.680	+	398.135i	−0.393653	+	1.46913i	0.430411	+	0.902633i	$0.358369\pi$
$271$	−106.680	+	398.135i	−0.393653	+	1.46913i	−0.824063	+	0.566498i	$0.808298\pi$
$272$		−	142.367i		−	0.523406i
$273$		0			0
$274$	172.056			0.627941
$275$	−148.081	−	39.6781i	−0.538475	−	0.144284i
$276$	−20.4615	−	35.4404i	−0.0741360	−	0.128407i
$277$	−72.5025	−	41.8594i	−0.261742	−	0.151117i	0.363387	−	0.931638i	$-0.381620\pi$
$277$	−72.5025	−	41.8594i	−0.261742	−	0.151117i	−0.625129	+	0.780521i	$0.714954\pi$
$278$	−272.190	+	272.190i	−0.979101	+	0.979101i
$279$	2.96664	+	11.0717i	0.0106331	+	0.0396834i
$280$	−235.717	+	63.1602i	−0.841846	+	0.225572i
$281$	315.207	+	315.207i	1.12173	+	1.12173i	0.991481	+	0.130253i	$0.0415791\pi$
$281$	315.207	+	315.207i	1.12173	+	1.12173i	0.130253	+	0.991481i	$0.458421\pi$
$282$	45.3591	−	78.5642i	0.160848	−	0.278597i
$283$	−151.579	+	87.5140i	−0.535614	+	0.309237i	−0.743299	−	0.668959i	$-0.766740\pi$
$283$	−151.579	+	87.5140i	−0.535614	+	0.309237i	0.207686	+	0.978196i	$0.433407\pi$
$284$	1.39215	−	5.19559i	0.00490195	−	0.0182943i
$285$		−	66.9908i		−	0.235056i
$286$		0			0
$287$	337.476			1.17588
$288$	−131.822	−	35.3216i	−0.457715	−	0.122644i
$289$	−32.1782	−	55.7343i	−0.111343	−	0.192852i
$290$	−102.906	−	59.4129i	−0.354849	−	0.204872i
$291$	152.978	−	152.978i	0.525697	−	0.525697i
$292$	11.8479	+	44.2169i	0.0405749	+	0.151428i
$293$	−489.465	+	131.152i	−1.67053	+	0.447617i	−0.965254	−	0.261315i	$-0.915844\pi$
$293$	−489.465	+	131.152i	−1.67053	+	0.447617i	−0.705277	+	0.708932i	$0.749177\pi$
$294$	174.276	+	174.276i	0.592774	+	0.592774i
$295$	−18.7309	+	32.4429i	−0.0634946	+	0.109976i
$296$	−8.61956	+	4.97651i	−0.0291201	+	0.0168125i
$297$	43.3317	−	161.716i	0.145898	−	0.544499i
$298$			270.985i			0.909345i
$299$		0			0
$300$	−33.6710			−0.112237
$301$	35.6521	+	9.55294i	0.118445	+	0.0317373i
$302$	79.6645	+	137.983i	0.263790	+	0.456897i
$303$	174.887	+	100.971i	0.577183	+	0.333237i
$304$	149.274	−	149.274i	0.491033	−	0.491033i
$305$	12.5029	+	46.6613i	0.0409930	+	0.152988i
$306$	−172.349	+	46.1809i	−0.563233	+	0.150918i
$307$	−38.2585	−	38.2585i	−0.124621	−	0.124621i	0.642046	−	0.766666i	$-0.278086\pi$
$307$	−38.2585	−	38.2585i	−0.124621	−	0.124621i	−0.766666	+	0.642046i	$0.778086\pi$
$308$	−59.7407	+	103.474i	−0.193963	+	0.335954i
$309$	123.766	−	71.4566i	0.400538	−	0.231251i
$310$	1.53076	−	5.71286i	0.00493792	−	0.0184286i
$311$			64.9628i			0.208884i	0.994531	+	0.104442i	$0.0333056\pi$
$311$			64.9628i			0.208884i	−0.994531	+	0.104442i	$0.966694\pi$
$312$		0			0
$313$	8.09749			0.0258706			0.0129353	−	0.999916i	$-0.495882\pi$
$313$	8.09749			0.0258706			0.0129353	+	0.999916i	$0.495882\pi$
$314$	199.246	+	53.3877i	0.634540	+	0.170025i
$315$	100.447	+	173.980i	0.318881	+	0.552318i
$316$	−39.0029	−	22.5183i	−0.123427	−	0.0712606i
$317$	335.718	−	335.718i	1.05905	−	1.05905i	0.0609026	−	0.998144i	$-0.480602\pi$
$317$	335.718	−	335.718i	1.05905	−	1.05905i	0.998144	−	0.0609026i	$-0.0193979\pi$
$318$	−46.8236	−	174.748i	−0.147244	−	0.549522i
$319$	−237.390	+	63.6084i	−0.744168	+	0.199399i
$320$	109.600	+	109.600i	0.342499	+	0.342499i
$321$	62.5827	−	108.396i	0.194962	−	0.337683i
$322$	−441.330	+	254.802i	−1.37059	+	0.791311i
$323$	−86.2148	+	321.758i	−0.266919	+	0.996155i
$324$			43.2448i			0.133471i
$325$		0			0
$326$	9.77524			0.0299854
$327$	55.8730	+	14.9711i	0.170865	+	0.0457832i
$328$	−116.650	−	202.044i	−0.355641	−	0.615988i
$329$	439.844	+	253.944i	1.33691	+	0.771866i
$330$	−27.0787	+	27.0787i	−0.0820568	+	0.0820568i
$331$	82.8635	+	309.251i	0.250343	+	0.934293i	0.970622	+	0.240609i	$0.0773470\pi$
$331$	82.8635	+	309.251i	0.250343	+	0.934293i	−0.720279	+	0.693684i	$0.755986\pi$
$332$	96.1333	−	25.7588i	0.289558	−	0.0775869i
$333$	5.79378	+	5.79378i	0.0173987	+	0.0173987i
$334$	−86.3070	+	149.488i	−0.258404	+	0.447569i
$335$	−27.6727	+	15.9768i	−0.0826050	+	0.0476920i
$336$	41.9187	−	156.443i	0.124758	−	0.465603i
$337$		−	373.214i		−	1.10746i	−0.832696	−	0.553730i	$-0.813204\pi$
$337$		−	373.214i		−	1.10746i	0.832696	−	0.553730i	$-0.186796\pi$
$338$		0			0
$339$	150.475			0.443878
$340$	−39.9815	−	10.7130i	−0.117593	−	0.0315088i
$341$	−6.11627	−	10.5937i	−0.0179363	−	0.0310665i
$342$	−229.133	−	132.290i	−0.669981	−	0.386813i
$343$	−539.374	+	539.374i	−1.57252	+	1.57252i
$344$	−6.60403	−	24.6466i	−0.0191978	−	0.0716470i
$345$	70.9298	−	19.0056i	0.205594	−	0.0550886i
$346$	−6.91975	−	6.91975i	−0.0199993	−	0.0199993i
$347$	269.696	−	467.127i	0.777222	−	1.34619i	−0.156316	−	0.987707i	$-0.549962\pi$
$347$	269.696	−	467.127i	0.777222	−	1.34619i	0.933537	−	0.358480i	$-0.116705\pi$
$348$	−46.7466	+	26.9892i	−0.134329	+	0.0775551i
$349$	125.254	−	467.455i	0.358895	−	1.33941i	−0.516617	−	0.856217i	$-0.672809\pi$
$349$	125.254	−	467.455i	0.358895	−	1.33941i	0.875512	−	0.483197i	$-0.160524\pi$
$350$			419.296i			1.19799i
$351$		0			0
$352$	145.644			0.413761
$353$	−280.940	−	75.2776i	−0.795863	−	0.213251i	−0.162096	−	0.986775i	$-0.551825\pi$
$353$	−280.940	−	75.2776i	−0.795863	−	0.213251i	−0.633767	+	0.773524i	$0.718492\pi$
$354$	−18.9260	−	32.7808i	−0.0534633	−	0.0926012i
$355$	8.35869	+	4.82589i	0.0235456	+	0.0135941i
$356$	−87.4064	+	87.4064i	−0.245523	+	0.245523i
$357$	66.1445	+	246.855i	0.185279	+	0.691470i
$358$	76.3723	−	20.4639i	0.213331	−	0.0571618i
$359$	−276.533	−	276.533i	−0.770287	−	0.770287i	0.207870	−	0.978156i	$-0.433347\pi$
$359$	−276.533	−	276.533i	−0.770287	−	0.770287i	−0.978156	+	0.207870i	$0.933347\pi$
$360$	69.4402	−	120.274i	0.192889	−	0.334094i
$361$	−115.132	+	66.4718i	−0.318927	+	0.184132i
$362$	−86.7058	+	323.590i	−0.239519	+	0.893896i
$363$		−	84.6352i		−	0.233155i
$364$		0			0
$365$	−82.1412			−0.225045
$366$	−47.1474	−	12.6331i	−0.128818	−	0.0345167i
$367$	143.103	+	247.862i	0.389928	+	0.675375i	0.992439	−	0.122735i	$-0.0391667\pi$
$367$	143.103	+	247.862i	0.389928	+	0.675375i	−0.602512	+	0.798110i	$0.705833\pi$
$368$	200.401	+	115.702i	0.544568	+	0.314406i
$369$	−135.807	+	135.807i	−0.368041	+	0.368041i
$370$	−1.09424	−	4.08377i	−0.00295741	−	0.0110372i
$371$	978.330	−	262.143i	2.63701	−	0.706584i
$372$	−1.89978	−	1.89978i	−0.00510694	−	0.00510694i
$373$	−179.456	+	310.827i	−0.481116	+	0.833317i	−0.999765	−	0.0216699i	$-0.993102\pi$
$373$	−179.456	+	310.827i	−0.481116	+	0.833317i	0.518649	+	0.854987i	$0.326435\pi$
$374$	164.909	−	95.2103i	0.440933	−	0.254573i
$375$	35.1411	−	131.148i	0.0937095	−	0.349729i
$376$		−	351.107i		−	0.933795i
$377$		0			0
$378$	−457.907			−1.21139
$379$	−29.0239	−	7.77694i	−0.0765803	−	0.0205196i	0.220325	−	0.975426i	$-0.429288\pi$
$379$	−29.0239	−	7.77694i	−0.0765803	−	0.0205196i	−0.296906	+	0.954907i	$0.595955\pi$
$380$	−30.6886	−	53.1541i	−0.0807594	−	0.139879i
$381$	−0.679322	−	0.392207i	−0.00178300	−	0.00102941i
$382$	193.134	−	193.134i	0.505588	−	0.505588i
$383$	−154.761	−	577.577i	−0.404076	−	1.50803i	−0.805753	−	0.592252i	$-0.798239\pi$
$383$	−154.761	−	577.577i	−0.404076	−	1.50803i	0.401677	−	0.915781i	$-0.368428\pi$
$384$	−51.6497	+	13.8395i	−0.134504	+	0.0360404i
$385$	−151.601	−	151.601i	−0.393769	−	0.393769i
$386$	−163.473	+	283.143i	−0.423504	+	0.733531i
$387$	−18.1914	+	10.5028i	−0.0470061	+	0.0271390i
$388$	51.3016	−	191.460i	0.132221	−	0.493454i
$389$			430.894i			1.10770i	0.832618	+	0.553848i	$0.186841\pi$
$389$			430.894i			1.10770i	−0.832618	+	0.553848i	$0.813159\pi$
$390$		0			0
$391$	−365.136			−0.933853
$392$	921.384	+	246.884i	2.35047	+	0.629806i
$393$	−129.307	−	223.967i	−0.329026	−	0.569890i
$394$	−171.996	−	99.3017i	−0.436537	−	0.252035i
$395$	57.1437	−	57.1437i	0.144668	−	0.144668i
$396$	−17.5991	−	65.6807i	−0.0444421	−	0.165860i
$397$	141.940	−	38.0326i	0.357531	−	0.0958001i	−0.0755826	−	0.997140i	$-0.524082\pi$
$397$	141.940	−	38.0326i	0.357531	−	0.0958001i	0.433113	+	0.901339i	$0.357415\pi$
$398$	244.007	+	244.007i	0.613082	+	0.613082i
$399$	−189.478	+	328.186i	−0.474883	+	0.822521i
$400$	164.887	−	95.1978i	0.412218	−	0.237994i
$401$	−138.078	+	515.314i	−0.344334	+	1.28507i	0.549054	+	0.835787i	$0.314988\pi$
$401$	−138.078	+	515.314i	−0.344334	+	1.28507i	−0.893388	+	0.449285i	$0.851679\pi$
$402$		−	32.2865i		−	0.0803147i
$403$		0			0
$404$	185.019			0.457969
$405$	−74.9539	−	20.0838i	−0.185071	−	0.0495897i
$406$	336.090	+	582.124i	0.827807	+	1.43380i
$407$	−7.57278	−	4.37215i	−0.0186063	−	0.0107424i
$408$	124.927	−	124.927i	0.306192	−	0.306192i
$409$	86.2913	+	322.044i	0.210981	+	0.787393i	0.987543	+	0.157351i	$0.0502954\pi$
$409$	86.2913	+	322.044i	0.210981	+	0.787393i	−0.776562	+	0.630041i	$0.783038\pi$
$410$	95.7242	−	25.6492i	0.233474	−	0.0625591i
$411$	99.1698	+	99.1698i	0.241289	+	0.241289i
$412$	65.4686	−	113.395i	0.158904	−	0.275231i
$413$	183.524	−	105.958i	0.444368	−	0.256556i
$414$	75.0626	−	280.137i	0.181311	−	0.676660i
$415$			178.586i			0.430327i
$416$		0			0
$417$	−313.771			−0.752449
$418$	272.740	+	73.0806i	0.652489	+	0.174834i
$419$	−39.7623	−	68.8704i	−0.0948982	−	0.164368i	0.814668	−	0.579928i	$-0.196919\pi$
$419$	−39.7623	−	68.8704i	−0.0948982	−	0.164368i	−0.909566	+	0.415559i	$0.863586\pi$
$420$	−40.7802	−	23.5445i	−0.0970957	−	0.0560582i
$421$	186.173	−	186.173i	0.442215	−	0.442215i	−0.450541	−	0.892756i	$-0.648769\pi$
$421$	186.173	−	186.173i	0.442215	−	0.442215i	0.892756	+	0.450541i	$0.148769\pi$
$422$	−94.5377	−	352.820i	−0.224023	−	0.836066i
$423$	−279.193	+	74.8097i	−0.660032	+	0.176855i
$424$	−495.106	−	495.106i	−1.16770	−	1.16770i
$425$	−150.215	+	260.180i	−0.353447	+	0.612188i
$426$	−8.44576	+	4.87616i	−0.0198257	+	0.0114464i
$427$	70.7267	−	263.955i	0.165636	−	0.618163i
$428$		−	114.677i		−	0.267936i
$429$		0			0
$430$	10.8387			0.0252062
$431$	−615.768	−	164.994i	−1.42869	−	0.382818i	−0.540135	−	0.841578i	$-0.681627\pi$
$431$	−615.768	−	164.994i	−1.42869	−	0.382818i	−0.888560	+	0.458761i	$0.848294\pi$
$432$	103.964	+	180.071i	0.240657	+	0.416830i
$433$	−150.078	−	86.6473i	−0.346600	−	0.200109i	0.316587	−	0.948563i	$-0.397463\pi$
$433$	−150.078	−	86.6473i	−0.346600	−	0.200109i	−0.663187	+	0.748454i	$0.730796\pi$
$434$	−23.6575	+	23.6575i	−0.0545103	+	0.0545103i
$435$	−25.0688	−	93.5579i	−0.0576293	−	0.215076i
$436$	51.1909	−	13.7166i	0.117410	−	0.0314600i
$437$	−382.853	−	382.853i	−0.876093	−	0.876093i
$438$	41.4985	−	71.8774i	0.0947453	−	0.164104i
$439$	729.932	−	421.426i	1.66271	−	0.959968i	0.691303	−	0.722565i	$-0.257037\pi$
$439$	729.932	−	421.426i	1.66271	−	0.959968i	0.971411	−	0.237404i	$-0.0762964\pi$
$440$	−38.3606	+	143.164i	−0.0871831	+	0.325372i
$441$		−	785.270i		−	1.78066i
$442$		0			0
$443$	−424.878			−0.959094			−0.479547	−	0.877516i	$-0.659199\pi$
$443$	−424.878			−0.959094			−0.479547	+	0.877516i	$0.659199\pi$
$444$	−1.85511	−	0.497076i	−0.00417818	−	0.00111954i
$445$	−110.903	−	192.090i	−0.249221	−	0.431664i
$446$	−384.338	−	221.897i	−0.861744	−	0.497528i
$447$	−156.191	+	156.191i	−0.349420	+	0.349420i
$448$	−226.931	−	846.919i	−0.506543	−	1.89044i
$449$	361.853	−	96.9583i	0.805909	−	0.215943i	0.167732	−	0.985833i	$-0.446356\pi$
$449$	361.853	−	96.9583i	0.805909	−	0.215943i	0.638177	+	0.769890i	$0.279689\pi$
$450$	−168.733	−	168.733i	−0.374962	−	0.374962i
$451$	102.484	−	177.507i	0.227237	−	0.393586i
$452$	119.395	−	68.9325i	0.264147	−	0.152506i
$453$	−33.6137	+	125.448i	−0.0742025	+	0.276927i
$454$		−	28.0672i		−	0.0618220i
$455$		0			0
$456$	261.976			0.574508
$457$	−400.057	−	107.195i	−0.875397	−	0.234562i	−0.206977	−	0.978346i	$-0.566363\pi$
$457$	−400.057	−	107.195i	−0.875397	−	0.234562i	−0.668420	+	0.743784i	$0.733029\pi$
$458$	−358.756	−	621.383i	−0.783309	−	1.35673i
$459$	−284.138	−	164.047i	−0.619037	−	0.357401i
$460$	47.5731	−	47.5731i	0.103420	−	0.103420i
$461$	116.647	+	435.334i	0.253031	+	0.944326i	0.969175	+	0.246373i	$0.0792388\pi$
$461$	116.647	+	435.334i	0.253031	+	0.944326i	−0.716144	+	0.697953i	$0.754095\pi$
$462$	209.248	−	56.0678i	0.452918	−	0.121359i
$463$	21.3332	+	21.3332i	0.0460761	+	0.0460761i	0.729769	−	0.683693i	$-0.239627\pi$
$463$	21.3332	+	21.3332i	0.0460761	+	0.0460761i	−0.683693	+	0.729769i	$0.739627\pi$
$464$	152.613	−	264.333i	0.328907	−	0.569683i
$465$	4.17509	−	2.41049i	0.00897869	−	0.00518385i
$466$	106.342	−	396.872i	0.228201	−	0.851658i
$467$		−	281.867i		−	0.603570i	−0.953376	−	0.301785i	$-0.902418\pi$
$467$		−	281.867i		−	0.603570i	0.953376	−	0.301785i	$-0.0975825\pi$
$468$		0			0
$469$	180.757			0.385409
$470$	144.061	+	38.6010i	0.306513	+	0.0821298i
$471$	84.0699	+	145.613i	0.178492	+	0.309158i
$472$	−126.872	−	73.2495i	−0.268796	−	0.155190i
$473$	15.8514	−	15.8514i	0.0335125	−	0.0335125i
$474$	21.1339	+	78.8729i	0.0445863	+	0.166398i
$475$	−430.307	+	115.300i	−0.905909	+	0.242738i
$476$	165.567	+	165.567i	0.347830	+	0.347830i
$477$	−288.208	+	499.190i	−0.604209	+	1.04652i
$478$	−53.5126	+	30.8955i	−0.111951	+	0.0646350i
$479$	−94.1457	+	351.357i	−0.196546	+	0.733521i	0.795315	+	0.606197i	$0.207306\pi$
$479$	−94.1457	+	351.357i	−0.196546	+	0.733521i	−0.991861	+	0.127324i	$0.959361\pi$
$480$			57.3998i			0.119583i
$481$		0			0
$482$	−128.643			−0.266894
$483$	−401.239	−	107.512i	−0.830722	−	0.222591i
$484$	−38.7715	−	67.1542i	−0.0801064	−	0.138748i
$485$	308.022	+	177.837i	0.635097	+	0.366673i
$486$	286.855	−	286.855i	0.590236	−	0.590236i
$487$	27.6734	+	103.278i	0.0568241	+	0.212071i	0.988500	−	0.151220i	$-0.0483200\pi$
$487$	27.6734	+	103.278i	0.0568241	+	0.212071i	−0.931676	+	0.363290i	$0.881653\pi$
$488$	−182.475	+	48.8939i	−0.373923	+	0.100192i
$489$	5.63428	+	5.63428i	0.0115220	+	0.0115220i
$490$	−202.595	+	350.906i	−0.413460	+	0.716134i
$491$	0.981954	−	0.566932i	0.00199991	−	0.00115465i	−0.499000	−	0.866602i	$-0.666299\pi$
$491$	0.981954	−	0.566932i	0.00199991	−	0.00115465i	0.501000	+	0.865448i	$0.332966\pi$
$492$	11.6515	−	43.4841i	0.0236820	−	0.0883823i
$493$			481.623i			0.976922i
$494$		0			0
$495$	122.014			0.246494
$496$	14.6745	+	3.93202i	0.0295857	+	0.00792746i
$497$	−27.2993	−	47.2838i	−0.0549282	−	0.0951384i
$498$	−156.271	−	90.2231i	−0.313797	−	0.181171i
$499$	616.689	−	616.689i	1.23585	−	1.23585i	0.274169	−	0.961682i	$-0.411597\pi$
$499$	616.689	−	616.689i	1.23585	−	1.23585i	0.961682	−	0.274169i	$-0.0884026\pi$
$500$	−32.1963	−	120.158i	−0.0643926	−	0.240317i
$501$	−135.908	+	36.4165i	−0.271274	+	0.0726876i
$502$	500.520	+	500.520i	0.997052	+	0.997052i
$503$	253.315	−	438.754i	0.503608	−	0.872275i	−0.496383	−	0.868104i	$-0.665339\pi$
$503$	253.315	−	438.754i	0.503608	−	0.872275i	0.999991	−	0.00417148i	$-0.00132783\pi$
$504$	−680.371	+	392.812i	−1.34994	+	0.779389i
$505$	−85.9271	+	320.684i	−0.170153	+	0.635018i
$506$			309.510i			0.611680i
$507$		0			0
$508$	−0.718681			−0.00141473
$509$	820.945	+	219.972i	1.61286	+	0.432164i	0.948893	−	0.315598i	$-0.102205\pi$
$509$	820.945	+	219.972i	1.61286	+	0.432164i	0.663966	+	0.747763i	$0.268872\pi$
$510$	37.5234	+	64.9925i	0.0735753	+	0.127436i
$511$	402.407	+	232.330i	0.787490	+	0.454658i
$512$	−361.783	+	361.783i	−0.706608	+	0.706608i
$513$	−125.918	−	469.931i	−0.245453	−	0.916045i
$514$	−54.4139	+	14.5802i	−0.105864	+	0.0283661i
$515$	166.137	+	166.137i	0.322595	+	0.322595i
$516$	2.46181	−	4.26398i	0.00477095	−	0.00826352i
$517$	267.141	−	154.234i	0.516713	−	0.298325i
$518$	−6.18996	+	23.1012i	−0.0119497	+	0.0445970i
$519$		−	7.97684i		−	0.0153696i
$520$		0			0
$521$	−499.516			−0.958764			−0.479382	−	0.877606i	$-0.659139\pi$
$521$	−499.516			−0.958764			−0.479382	+	0.877606i	$0.659139\pi$
$522$	−369.507	−	99.0091i	−0.707868	−	0.189673i
$523$	355.627	+	615.964i	0.679976	+	1.17775i	0.974988	+	0.222259i	$0.0713430\pi$
$523$	355.627	+	615.964i	0.679976	+	1.17775i	−0.295012	+	0.955494i	$0.595324\pi$
$524$	−205.199	−	118.472i	−0.391601	−	0.226091i
$525$	−241.675	+	241.675i	−0.460333	+	0.460333i
$526$	133.700	+	498.975i	0.254182	+	0.948621i
$527$	−23.1552	+	6.20443i	−0.0439378	+	0.0117731i
$528$	−69.5566	−	69.5566i	−0.131736	−	0.131736i
$529$	32.2470	−	55.8534i	0.0609584	−	0.105583i
$530$	257.577	−	148.712i	0.485994	−	0.280589i
$531$	−31.2142	+	116.493i	−0.0587839	+	0.219384i
$532$			347.201i			0.652633i
$533$		0			0
$534$	224.117			0.419695
$535$	198.763	+	53.2584i	0.371520	+	0.0995484i
$536$	−62.4793	−	108.217i	−0.116566	−	0.201898i
$537$	55.8147	+	32.2246i	0.103938	+	0.0600086i
$538$	−337.413	+	337.413i	−0.627161	+	0.627161i
$539$	216.902	+	809.488i	0.402415	+	1.50183i
$540$	58.3933	−	15.6464i	0.108136	−	0.0289749i
$541$	−126.688	−	126.688i	−0.234173	−	0.234173i	0.580259	−	0.814432i	$-0.302951\pi$
$541$	−126.688	−	126.688i	−0.234173	−	0.234173i	−0.814432	+	0.580259i	$0.802951\pi$
$542$	342.346	−	592.960i	0.631634	−	1.09402i
$543$	−236.487	+	136.536i	−0.435520	+	0.251448i
$544$	73.8715	−	275.692i	0.135793	−	0.506787i
$545$			95.0968i			0.174490i
$546$		0			0
$547$	909.695			1.66306			0.831531	−	0.555478i	$-0.187465\pi$
$547$	909.695			1.66306			0.831531	+	0.555478i	$0.187465\pi$
$548$	124.117	+	33.2569i	0.226490	+	0.0606878i
$549$	77.7590	+	134.683i	0.141638	+	0.245323i
$550$	220.543	+	127.331i	0.400987	+	0.231510i
$551$	−504.991	+	504.991i	−0.916499	+	0.916499i
$552$	74.3236	+	277.380i	0.134644	+	0.502499i
$553$	−441.571	+	118.319i	−0.798502	+	0.213958i
$554$	98.3369	+	98.3369i	0.177503	+	0.177503i
$555$	1.72311	−	2.98451i	0.00310470	−	0.00537750i
$556$	−248.963	+	143.739i	−0.447775	+	0.258523i
$557$	13.8904	−	51.8399i	0.0249380	−	0.0930698i	−0.952335	−	0.305053i	$-0.901326\pi$
$557$	13.8904	−	51.8399i	0.0249380	−	0.0930698i	0.977273	+	0.211984i	$0.0679924\pi$
$558$		−	19.0405i		−	0.0341227i
$559$		0			0
$560$	266.268			0.475479
$561$	149.928	+	40.1731i	0.267252	+	0.0716099i
$562$	−370.246	−	641.284i	−0.658800	−	1.14108i
$563$	795.077	+	459.038i	1.41222	+	0.815343i	0.995597	−	0.0937388i	$-0.0298819\pi$
$563$	795.077	+	459.038i	1.41222	+	0.815343i	0.416618	+	0.909082i	$0.363215\pi$
$564$	47.9067	−	47.9067i	0.0849409	−	0.0849409i
$565$	64.0276	+	238.954i	0.113323	+	0.422928i
$566$	280.841	−	75.2510i	0.496185	−	0.132952i
$567$	310.391	+	310.391i	0.547427	+	0.547427i
$568$	−18.8722	+	32.6877i	−0.0332258	+	0.0575487i
$569$	−918.009	+	530.013i	−1.61337	+	0.931482i	−0.624792	+	0.780791i	$0.714816\pi$
$569$	−918.009	+	530.013i	−1.61337	+	0.931482i	−0.988581	+	0.150691i	$0.951850\pi$
$570$	−28.8018	+	107.490i	−0.0505295	+	0.188579i
$571$		−	478.156i		−	0.837400i	−0.908125	−	0.418700i	$-0.862486\pi$
$571$		−	478.156i		−	0.837400i	0.908125	−	0.418700i	$-0.137514\pi$
$572$		0			0
$573$	222.639			0.388549
$574$	−541.497	−	145.094i	−0.943374	−	0.252776i
$575$	−244.160	−	422.897i	−0.424626	−	0.735473i
$576$	432.138	+	249.495i	0.750240	+	0.433151i
$577$	−147.501	+	147.501i	−0.255634	+	0.255634i	−0.823276	−	0.567642i	$-0.807856\pi$
$577$	−147.501	+	147.501i	−0.255634	+	0.255634i	0.567642	+	0.823276i	$0.307856\pi$
$578$	27.6692	+	103.263i	0.0478706	+	0.178655i
$579$	−257.421	+	68.9759i	−0.444597	+	0.119129i
$580$	−62.7499	−	62.7499i	−0.108189	−	0.108189i
$581$	505.116	−	874.886i	0.869390	−	1.50583i
$582$	−311.231	+	179.689i	−0.534761	+	0.308744i
$583$	159.213	−	594.193i	0.273093	−	1.01920i
$584$		−	321.223i		−	0.550040i
$585$		0			0
$586$	841.757			1.43645
$587$	225.214	+	60.3460i	0.383670	+	0.102804i	0.445499	−	0.895283i	$-0.353026\pi$
$587$	225.214	+	60.3460i	0.383670	+	0.102804i	−0.0618283	+	0.998087i	$0.519693\pi$
$588$	92.0319	+	159.404i	0.156517	+	0.271095i
$589$	−30.7842	−	17.7733i	−0.0522652	−	0.0301753i
$590$	44.0030	−	44.0030i	0.0745813	−	0.0745813i
$591$	−41.8995	−	156.371i	−0.0708959	−	0.264587i
$592$	10.4899	−	2.81076i	0.0177194	−	0.00474790i
$593$	451.487	+	451.487i	0.761361	+	0.761361i	0.976568	−	0.215207i	$-0.0690428\pi$
$593$	451.487	+	451.487i	0.761361	+	0.761361i	−0.215207	+	0.976568i	$0.569043\pi$
$594$	−139.056	+	240.851i	−0.234100	+	0.405474i
$595$	−363.862	+	210.076i	−0.611532	+	0.353068i
$596$	−52.3791	+	195.481i	−0.0878844	+	0.327989i
$597$			281.282i			0.471159i
$598$		0			0
$599$	−759.661			−1.26822			−0.634108	−	0.773245i	$-0.718632\pi$
$599$	−759.661			−1.26822			−0.634108	+	0.773245i	$0.718632\pi$
$600$	228.225	+	61.1526i	0.380374	+	0.101921i
$601$	369.738	+	640.405i	0.615205	+	1.06557i	0.990349	+	0.138599i	$0.0442600\pi$
$601$	369.738	+	640.405i	0.615205	+	1.06557i	−0.375144	+	0.926967i	$0.622407\pi$
$602$	−53.0983	−	30.6563i	−0.0882031	−	0.0509241i
$603$	−72.7400	+	72.7400i	−0.120630	+	0.120630i
$604$	30.7970	+	114.936i	0.0509883	+	0.190291i
$605$	134.401	−	36.0127i	0.222151	−	0.0595251i
$606$	−237.203	−	237.203i	−0.391424	−	0.391424i
$607$	−528.810	+	915.925i	−0.871186	+	1.50894i	−0.0104143	+	0.999946i	$0.503315\pi$
$607$	−528.810	+	915.925i	−0.871186	+	1.50894i	−0.860771	+	0.508992i	$0.830018\pi$
$608$	366.524	−	211.613i	0.602836	−	0.348048i
$609$	−141.810	+	529.242i	−0.232857	+	0.869035i
$610$		−	80.2457i		−	0.131550i
$611$		0			0
$612$	−133.255			−0.217737
$613$	−416.368	−	111.565i	−0.679230	−	0.181999i	−0.0973207	−	0.995253i	$-0.531027\pi$
$613$	−416.368	−	111.565i	−0.679230	−	0.181999i	−0.581909	+	0.813254i	$0.697694\pi$
$614$	44.9389	+	77.8364i	0.0731904	+	0.126769i
$615$	69.9575	+	40.3900i	0.113752	+	0.0656747i
$616$	592.854	−	592.854i	0.962426	−	0.962426i
$617$	−61.8106	−	230.680i	−0.100179	−	0.373874i	0.897575	−	0.440863i	$-0.145327\pi$
$617$	−61.8106	−	230.680i	−0.100179	−	0.373874i	−0.997754	+	0.0669889i	$0.978661\pi$
$618$	−229.311	+	61.4437i	−0.371053	+	0.0994234i
$619$	324.998	+	324.998i	0.525037	+	0.525037i	0.919088	−	0.394051i	$-0.128927\pi$
$619$	324.998	+	324.998i	0.525037	+	0.525037i	−0.394051	+	0.919088i	$0.628927\pi$
$620$	2.20849	−	3.82523i	0.00356209	−	0.00616972i
$621$	461.839	−	266.643i	0.743702	−	0.429376i
$622$	27.9299	−	104.236i	0.0449034	−	0.167582i
$623$			1254.73i			2.01401i
$624$		0			0
$625$	−277.897			−0.444635
$626$	−12.9928	−	3.48141i	−0.0207553	−	0.00556136i
$627$	115.080	+	199.325i	0.183541	+	0.317903i
$628$	133.411	+	77.0250i	0.212438	+	0.122651i
$629$	−12.1171	+	12.1171i	−0.0192641	+	0.0192641i
$630$	−86.3722	−	322.345i	−0.137099	−	0.511659i
$631$	−688.010	+	184.352i	−1.09035	+	0.292158i	−0.758829	−	0.651290i	$-0.774228\pi$
$631$	−688.010	+	184.352i	−1.09035	+	0.292158i	−0.331520	+	0.943448i	$0.607561\pi$
$632$	223.467	+	223.467i	0.353588	+	0.353588i
$633$	148.869	−	257.849i	0.235180	−	0.407344i
$634$	−683.012	+	394.337i	−1.07731	+	0.621983i
$635$	0.333772	−	1.24565i	0.000525625	−	0.00196166i
$636$		−	135.109i		−	0.212436i
$637$		0			0
$638$	408.251			0.639891
$639$	30.0137	+	8.04214i	0.0469698	+	0.0125855i
$640$	−43.9544	−	76.1312i	−0.0686787	−	0.118955i
$641$	−801.516	−	462.756i	−1.25042	−	0.721928i	−0.279224	−	0.960226i	$-0.590077\pi$
$641$	−801.516	−	462.756i	−1.25042	−	0.721928i	−0.971192	+	0.238298i	$0.923410\pi$
$642$	−147.020	+	147.020i	−0.229004	+	0.229004i
$643$	127.199	+	474.714i	0.197822	+	0.738280i	0.991518	+	0.129967i	$0.0414870\pi$
$643$	127.199	+	474.714i	0.197822	+	0.738280i	−0.793697	+	0.608314i	$0.791846\pi$
$644$	−367.616	+	98.5023i	−0.570832	+	0.152954i
$645$	6.24721	+	6.24721i	0.00968560	+	0.00968560i
$646$	276.672	−	479.209i	0.428284	−	0.741810i
$647$	−140.376	+	81.0463i	−0.216965	+	0.125265i	−0.604544	−	0.796572i	$-0.706645\pi$
$647$	−140.376	+	81.0463i	−0.216965	+	0.125265i	0.387579	+	0.921836i	$0.373311\pi$
$648$	78.5403	−	293.116i	0.121204	−	0.452340i
$649$		−	128.708i		−	0.198317i
$650$		0			0
$651$	−27.2715			−0.0418917
$652$	7.05161	+	1.88947i	0.0108153	+	0.00289796i
$653$	190.039	+	329.157i	0.291024	+	0.504069i	0.974052	−	0.226324i	$-0.0726707\pi$
$653$	190.039	+	329.157i	0.291024	+	0.504069i	−0.683028	+	0.730392i	$0.739337\pi$
$654$	−83.2142	−	48.0437i	−0.127239	−	0.0734614i
$655$	300.640	−	300.640i	0.458992	−	0.458992i
$656$	65.8846	+	245.885i	0.100434	+	0.374824i
$657$	−255.431	+	68.4424i	−0.388783	+	0.104174i
$658$	−596.570	−	596.570i	−0.906641	−	0.906641i
$659$	−204.007	+	353.351i	−0.309571	+	0.536192i	−0.978268	−	0.207342i	$-0.933519\pi$
$659$	−204.007	+	353.351i	−0.309571	+	0.536192i	0.668698	+	0.743534i	$0.266852\pi$
$660$	−24.7680	+	14.2998i	−0.0375273	+	0.0216664i
$661$	44.8596	−	167.418i	0.0678663	−	0.253280i	−0.923655	−	0.383225i	$-0.874813\pi$
$661$	44.8596	−	167.418i	0.0678663	−	0.253280i	0.991521	+	0.129945i	$0.0414800\pi$
$662$		−	531.834i		−	0.803374i
$663$		0			0
$664$	−698.382			−1.05178
$665$	−601.785	−	161.248i	−0.904939	−	0.242478i
$666$	−6.80543	−	11.7873i	−0.0102184	−	0.0176987i
$667$	−677.952	−	391.416i	−1.01642	−	0.586830i
$668$	−91.1544	+	91.1544i	−0.136459	+	0.136459i
$669$	−93.6277	−	349.423i	−0.139952	−	0.522307i
$670$	51.2711	−	13.7381i	0.0765241	−	0.0205046i
$671$	−117.358	−	117.358i	−0.174901	−	0.174901i
$672$	162.351	−	281.200i	0.241593	−	0.418452i
$673$	909.212	−	524.934i	1.35098	−	0.779991i	0.362596	−	0.931946i	$-0.381890\pi$
$673$	909.212	−	524.934i	1.35098	−	0.779991i	0.988387	+	0.151955i	$0.0485570\pi$
$674$	−160.458	+	598.839i	−0.238069	+	0.888485i
$675$		−	438.781i		−	0.650046i
$676$		0			0
$677$	539.705			0.797201			0.398601	−	0.917125i	$-0.369496\pi$
$677$	539.705			0.797201			0.398601	+	0.917125i	$0.369496\pi$
$678$	−241.443	−	64.6946i	−0.356111	−	0.0954197i
$679$	−1005.99	−	1742.43i	−1.48158	−	2.56617i
$680$	251.541	+	145.227i	0.369913	+	0.213569i
$681$	16.1774	−	16.1774i	0.0237554	−	0.0237554i
$682$	5.25922	+	19.6277i	0.00771147	+	0.0287796i
$683$	944.242	−	253.009i	1.38249	−	0.370438i	0.510466	−	0.859898i	$-0.329473\pi$
$683$	944.242	−	253.009i	1.38249	−	0.370438i	0.872026	+	0.489460i	$0.162806\pi$
$684$	−139.720	−	139.720i	−0.204269	−	0.204269i
$685$	−115.285	+	199.679i	−0.168299	+	0.291503i
$686$	1097.35	−	633.554i	1.59963	−	0.923548i
$687$	151.374	−	564.934i	0.220340	−	0.822321i
$688$			27.8410i			0.0404666i
$689$		0			0
$690$	−121.981			−0.176785
$691$	1028.23	+	275.514i	1.48804	+	0.398718i	0.909073	−	0.416637i	$-0.136791\pi$
$691$	1028.23	+	275.514i	1.48804	+	0.398718i	0.578962	+	0.815355i	$0.303458\pi$
$692$	−3.65420	−	6.32926i	−0.00528064	−	0.00914633i
$693$	−597.744	−	345.108i	−0.862546	−	0.497991i
$694$	−633.575	+	633.575i	−0.912933	+	0.912933i
$695$	−133.511	−	498.270i	−0.192102	−	0.716935i
$696$	365.870	−	98.0344i	0.525675	−	0.140854i
$697$	−284.027	−	284.027i	−0.407499	−	0.407499i
$698$	−401.953	+	696.203i	−0.575864	+	0.997425i
$699$	290.044	−	167.457i	0.414941	−	0.239566i
$700$	−81.0465	+	302.470i	−0.115781	+	0.432099i
$701$		−	179.431i		−	0.255964i	−0.991777	−	0.127982i	$-0.959150\pi$
$701$		−	179.431i		−	0.255964i	0.991777	−	0.127982i	$-0.0408499\pi$
$702$		0			0
$703$	−25.4100			−0.0361451
$704$	−514.380	−	137.828i	−0.730653	−	0.195778i
$705$	60.7852	+	105.283i	0.0862202	+	0.149338i
$706$	418.416	+	241.573i	0.592658	+	0.342171i
$707$	1327.98	−	1327.98i	1.87834	−	1.87834i
$708$	−7.31648	−	27.3055i	−0.0103340	−	0.0385671i
$709$	764.925	−	204.961i	1.07888	−	0.289084i	0.324742	−	0.945803i	$-0.394723\pi$
$709$	764.925	−	204.961i	1.07888	−	0.289084i	0.754136	+	0.656718i	$0.228056\pi$
$710$	−11.3371	−	11.3371i	−0.0159677	−	0.0159677i
$711$	130.083	−	225.311i	0.182958	−	0.316893i
$712$	751.193	−	433.701i	1.05505	−	0.609131i
$713$	10.0847	−	37.6366i	0.0141440	−	0.0527863i
$714$		−	424.528i		−	0.594577i
$715$		0			0
$716$	59.0485			0.0824700
$717$	−48.6513	−	13.0361i	−0.0678540	−	0.0181814i
$718$	324.818	+	562.602i	0.452393	+	0.783568i
$719$	99.3951	+	57.3858i	0.138241	+	0.0798134i	0.567525	−	0.823356i	$-0.307901\pi$
$719$	99.3951	+	57.3858i	0.138241	+	0.0798134i	−0.429285	+	0.903169i	$0.641234\pi$
$720$	−107.152	+	107.152i	−0.148822	+	0.148822i
$721$	−343.994	−	1283.80i	−0.477106	−	1.78058i
$722$	213.314	−	57.1574i	0.295449	−	0.0791653i
$723$	−74.1475	−	74.1475i	−0.102555	−	0.102555i
$724$	−125.095	+	216.670i	−0.172783	+	0.299268i
$725$	−557.810	+	322.052i	−0.769393	+	0.444209i
$726$	−36.3878	+	135.801i	−0.0501210	+	0.187054i
$727$		−	191.685i		−	0.263666i	−0.991272	−	0.131833i	$-0.957914\pi$
$727$		−	191.685i		−	0.263666i	0.991272	−	0.131833i	$-0.0420862\pi$
$728$		0			0
$729$	16.9500			0.0232510
$730$	131.800	+	35.3156i	0.180547	+	0.0483775i
$731$	−21.9655	−	38.0454i	−0.0300486	−	0.0520457i
$732$	−31.5690	−	18.2264i	−0.0431271	−	0.0248994i
$733$	−417.210	+	417.210i	−0.569181	+	0.569181i	−0.931899	−	0.362718i	$-0.881849\pi$
$733$	−417.210	+	417.210i	−0.569181	+	0.569181i	0.362718	+	0.931899i	$0.381849\pi$
$734$	−123.051	−	459.233i	−0.167644	−	0.625657i
$735$	−319.028	+	85.4833i	−0.434052	+	0.116304i
$736$	328.040	+	328.040i	0.445706	+	0.445706i
$737$	54.8917	−	95.0752i	0.0744799	−	0.129003i
$738$	276.297	−	159.520i	0.374386	−	0.216152i
$739$	−216.456	+	807.824i	−0.292904	+	1.09313i	0.649964	+	0.759965i	$0.274784\pi$
$739$	−216.456	+	807.824i	−0.292904	+	1.09313i	−0.942868	+	0.333167i	$0.891883\pi$
$740$		−	3.15743i		−	0.00426680i
$741$		0			0
$742$	−1682.48			−2.26750
$743$	643.721	+	172.485i	0.866381	+	0.232146i	0.664522	−	0.747269i	$-0.268635\pi$
$743$	643.721	+	172.485i	0.866381	+	0.232146i	0.201859	+	0.979415i	$0.435302\pi$
$744$	9.42651	+	16.3272i	0.0126700	+	0.0219452i
$745$	−314.492	−	181.572i	−0.422136	−	0.243721i
$746$	421.582	−	421.582i	0.565124	−	0.565124i
$747$	148.803	+	555.339i	0.199200	+	0.743426i
$748$	137.365	−	36.8067i	0.183642	−	0.0492068i
$749$	−823.097	−	823.097i	−1.09893	−	1.09893i
$750$	−112.771	+	195.325i	−0.150361	+	0.260433i
$751$	−439.023	+	253.470i	−0.584585	+	0.337510i	−0.762953	−	0.646454i	$-0.776251\pi$
$751$	−439.023	+	253.470i	−0.584585	+	0.337510i	0.178369	+	0.983964i	$0.442918\pi$
$752$	−99.1536	+	370.046i	−0.131853	+	0.492083i
$753$			576.982i			0.766244i
$754$		0			0
$755$	−213.515			−0.282801
$756$	−330.322	−	88.5095i	−0.436934	−	0.117076i
$757$	571.272	+	989.472i	0.754652	+	1.30710i	0.945547	+	0.325485i	$0.105528\pi$
$757$	571.272	+	989.472i	0.754652	+	1.30710i	−0.190895	+	0.981610i	$0.561139\pi$
$758$	43.2267	+	24.9569i	0.0570273	+	0.0329247i
$759$	−178.396	+	178.396i	−0.235041	+	0.235041i
$760$	111.472	+	416.019i	0.146674	+	0.547393i
$761$	49.7913	−	13.3415i	0.0654288	−	0.0175316i	−0.225956	−	0.974137i	$-0.572551\pi$
$761$	49.7913	−	13.3415i	0.0654288	−	0.0175316i	0.291385	+	0.956606i	$0.405884\pi$
$762$	0.921380	+	0.921380i	0.00120916	+	0.00120916i
$763$	268.974	−	465.876i	0.352522	−	0.610585i
$764$	176.653	−	101.991i	0.231222	−	0.133496i
$765$	61.8865	−	230.964i	0.0808974	−	0.301913i
$766$			993.287i			1.29672i
$767$		0			0
$768$	−288.292			−0.375381
$769$	751.552	+	201.378i	0.977310	+	0.261870i	0.711911	−	0.702269i	$-0.247830\pi$
$769$	751.552	+	201.378i	0.977310	+	0.261870i	0.265399	+	0.964139i	$0.414496\pi$
$770$	178.072	+	308.430i	0.231262	+	0.400558i
$771$	−39.7669	−	22.9595i	−0.0515784	−	0.0297788i
$772$	−172.654	+	172.654i	−0.223645	+	0.223645i
$773$	−131.820	−	491.961i	−0.170531	−	0.636430i	−0.997270	−	0.0738443i	$-0.976473\pi$
$773$	−131.820	−	491.961i	−0.170531	−	0.636430i	0.826739	−	0.562586i	$-0.190193\pi$
$774$	33.7045	−	9.03108i	0.0435458	−	0.0116681i
$775$	−22.6694	−	22.6694i	−0.0292508	−	0.0292508i
$776$	−695.452	+	1204.56i	−0.896201	+	1.55227i
$777$	−16.8829	+	9.74736i	−0.0217283	+	0.0125449i
$778$	185.257	−	691.389i	0.238120	−	0.888675i
$779$		−	595.615i		−	0.764589i
$780$		0			0
$781$	−33.1607			−0.0424593
$782$	585.879	+	156.986i	0.749206	+	0.200749i
$783$	−351.707	−	609.175i	−0.449179	−	0.778002i
$784$	−901.364	−	520.403i	−1.14970	−	0.663779i
$785$	−195.463	+	195.463i	−0.248997	+	0.248997i
$786$	111.188	+	414.959i	0.141461	+	0.527938i
$787$	1174.55	−	314.720i	1.49244	−	0.399898i	0.581880	−	0.813275i	$-0.302317\pi$
$787$	1174.55	−	314.720i	1.49244	−	0.399898i	0.910560	+	0.413377i	$0.135651\pi$
$788$	−104.879	−	104.879i	−0.133095	−	0.133095i
$789$	−210.538	+	364.662i	−0.266841	+	0.462183i
$790$	−116.258	+	67.1215i	−0.147162	+	0.0849640i
$791$	362.194	−	1351.73i	0.457894	−	1.70888i
$792$			477.152i			0.602465i
$793$		0			0
$794$	−244.101			−0.307432
$795$	234.178	+	62.7477i	0.294563	+	0.0789280i
$796$	128.856	+	223.184i	0.161879	+	0.280382i
$797$	353.791	+	204.261i	0.443904	+	0.256288i	0.705252	−	0.708957i	$-0.250834\pi$
$797$	353.791	+	204.261i	0.443904	+	0.256288i	−0.261348	+	0.965245i	$0.584167\pi$
$798$	445.126	−	445.126i	0.557802	−	0.557802i
$799$	−156.457	−	583.905i	−0.195816	−	0.730795i
$800$	368.700	−	98.7929i	0.460875	−	0.123491i
$801$	−504.926	−	504.926i	−0.630370	−	0.630370i
$802$	443.105	−	767.481i	0.552500	−	0.956958i
$803$	244.404	−	141.107i	0.304363	−	0.175724i
$804$	6.24071	−	23.2907i	0.00776208	−	0.0289685i
$805$		−	682.915i		−	0.848342i
$806$		0			0
$807$	−388.958			−0.481980
$808$	−1254.08	−	336.028i	−1.55207	−	0.415877i
$809$	−45.0218	−	77.9801i	−0.0556512	−	0.0963907i	0.836858	−	0.547420i	$-0.184390\pi$
$809$	−45.0218	−	77.9801i	−0.0556512	−	0.0963907i	−0.892509	+	0.451030i	$0.851057\pi$
$810$	111.632	+	64.4509i	0.137818	+	0.0795690i
$811$	−419.295	+	419.295i	−0.517010	+	0.517010i	−0.916665	−	0.399656i	$-0.869130\pi$
$811$	−419.295	+	419.295i	−0.517010	+	0.517010i	0.399656	+	0.916665i	$0.369130\pi$
$812$	129.927	+	484.893i	0.160008	+	0.597158i
$813$	539.094	−	144.450i	0.663092	−	0.177675i
$814$	10.2711	+	10.2711i	0.0126181	+	0.0126181i
$815$	−6.54985	+	11.3447i	−0.00803662	+	0.0139198i
$816$	−166.945	+	96.3856i	−0.204589	+	0.118120i
$817$	16.8601	−	62.9226i	0.0206366	−	0.0770167i
$818$		−	553.834i		−	0.677059i
$819$		0			0
$820$	74.0107			0.0902570
$821$	−891.824	−	238.964i	−1.08627	−	0.291064i	−0.329106	−	0.944293i	$-0.606747\pi$
$821$	−891.824	−	238.964i	−1.08627	−	0.291064i	−0.757160	+	0.653229i	$0.773414\pi$
$822$	−116.486	−	201.760i	−0.141710	−	0.245450i
$823$	1172.63	+	677.017i	1.42482	+	0.822621i	0.996706	−	0.0811034i	$-0.0258444\pi$
$823$	1172.63	+	677.017i	1.42482	+	0.822621i	0.428115	+	0.903724i	$0.359178\pi$
$824$	−649.697	+	649.697i	−0.788468	+	0.788468i
$825$	53.7260	+	200.508i	0.0651224	+	0.243040i
$826$	−340.028	+	91.1103i	−0.411657	+	0.110303i
$827$	55.7922	+	55.7922i	0.0674633	+	0.0674633i	0.740033	−	0.672570i	$-0.234810\pi$
$827$	55.7922	+	55.7922i	0.0674633	+	0.0674633i	−0.672570	+	0.740033i	$0.734810\pi$
$828$	108.296	−	187.575i	0.130793	−	0.226540i
$829$	−1059.57	+	611.745i	−1.27813	+	0.737931i	−0.976505	−	0.215495i	$-0.930864\pi$
$829$	−1059.57	+	611.745i	−1.27813	+	0.737931i	−0.301628	+	0.953426i	$0.597530\pi$
$830$	76.7807	−	286.549i	0.0925068	−	0.345240i
$831$			113.359i			0.136413i
$832$		0			0
$833$	1642.31			1.97156
$834$	503.460	+	134.902i	0.603670	+	0.161753i
$835$	−115.659	−	200.327i	−0.138514	−	0.239913i
$836$	182.622	+	105.437i	0.218447	+	0.126121i
$837$	24.7568	−	24.7568i	0.0295781	−	0.0295781i
$838$	34.1906	+	127.601i	0.0408003	+	0.152269i
$839$	−602.958	+	161.562i	−0.718662	+	0.192565i	−0.599575	−	0.800319i	$-0.704664\pi$
$839$	−602.958	+	161.562i	−0.718662	+	0.192565i	−0.119088	+	0.992884i	$0.537997\pi$
$840$	233.650	+	233.650i	0.278155	+	0.278155i
$841$	−95.7853	+	165.905i	−0.113895	+	0.197271i
$842$	−378.765	+	218.680i	−0.449840	+	0.259715i
$843$	156.222	−	583.028i	0.185317	−	0.691611i
$844$		−	272.788i		−	0.323209i
$845$		0			0
$846$	480.143			0.567544
$847$	−760.286	−	203.718i	−0.897622	−	0.240517i
$848$	381.994	+	661.632i	0.450464	+	0.780227i
$849$	205.245	+	118.498i	0.241749	+	0.139574i
$850$	352.888	−	352.888i	0.415162	−	0.415162i
$851$	−7.20893	−	26.9041i	−0.00847113	−	0.0316147i
$852$	−7.03508	+	1.88504i	−0.00825713	+	0.00221249i
$853$	415.508	+	415.508i	0.487114	+	0.487114i	0.907394	−	0.420281i	$-0.138068\pi$
$853$	415.508	+	415.508i	0.487114	+	0.487114i	−0.420281	+	0.907394i	$0.638068\pi$
$854$	−226.969	+	393.121i	−0.265771	+	0.460329i
$855$	307.059	−	177.281i	0.359133	−	0.207346i
$856$	−208.274	+	777.288i	−0.243310	+	0.908046i
$857$			697.279i			0.813628i	0.913511	+	0.406814i	$0.133360\pi$
$857$			697.279i			0.813628i	−0.913511	+	0.406814i	$0.866640\pi$
$858$		0			0
$859$	719.036			0.837062			0.418531	−	0.908203i	$-0.362545\pi$
$859$	719.036			0.837062			0.418531	+	0.908203i	$0.362545\pi$
$860$	7.81873	+	2.09502i	0.00909154	+	0.00243607i
$861$	−228.480	−	395.738i	−0.265365	−	0.459626i
$862$	917.091	+	529.483i	1.06391	+	0.614249i
$863$	30.6850	−	30.6850i	0.0355563	−	0.0355563i	−0.689105	−	0.724661i	$-0.741996\pi$
$863$	30.6850	−	30.6850i	0.0355563	−	0.0355563i	0.724661	+	0.689105i	$0.241996\pi$
$864$	107.890	+	402.651i	0.124873	+	0.466032i
$865$	12.6673	−	3.39418i	0.0146442	−	0.00392391i
$866$	203.554	+	203.554i	0.235050	+	0.235050i
$867$	−43.5708	+	75.4669i	−0.0502547	+	0.0870437i
$868$	−21.6387	+	12.4931i	−0.0249294	+	0.0143930i
$869$	−71.8613	+	268.190i	−0.0826943	+	0.308619i
$870$			160.896i			0.184938i
$871$		0			0
$872$	−371.888			−0.426477
$873$	1106.02	+	296.357i	1.26692	+	0.339470i
$874$	449.703	+	778.908i	0.514534	+	0.891199i
$875$	−1093.53	−	631.351i	−1.24975	−	0.721544i
$876$	43.8292	−	43.8292i	0.0500334	−	0.0500334i
$877$	−71.7955	−	267.945i	−0.0818649	−	0.305524i	0.912837	−	0.408324i	$-0.133887\pi$
$877$	−71.7955	−	267.945i	−0.0818649	−	0.305524i	−0.994702	+	0.102800i	$0.967220\pi$
$878$	−1352.40	+	362.374i	−1.54031	+	0.412726i
$879$	485.174	+	485.174i	0.551961	+	0.551961i
$880$	80.8596	−	140.053i	0.0918859	−	0.159151i
$881$	−469.562	+	271.102i	−0.532988	+	0.307721i	−0.742232	−	0.670143i	$-0.766233\pi$
$881$	−469.562	+	271.102i	−0.532988	+	0.307721i	0.209245	+	0.977863i	$0.432900\pi$
$882$	−337.617	+	1260.00i	−0.382785	+	1.42857i
$883$		−	849.149i		−	0.961664i	−0.876813	−	0.480832i	$-0.840335\pi$
$883$		−	849.149i		−	0.961664i	0.876813	−	0.480832i	$-0.159665\pi$
$884$		0			0
$885$	50.7251			0.0573165
$886$	681.738	+	182.671i	0.769456	+	0.206175i
$887$	−62.1261	−	107.606i	−0.0700407	−	0.121314i	0.828878	−	0.559429i	$-0.188980\pi$
$887$	−62.1261	−	107.606i	−0.0700407	−	0.121314i	−0.898919	+	0.438115i	$0.855646\pi$
$888$	11.6713	+	6.73843i	0.0131434	+	0.00758833i
$889$	−5.15837	+	5.15837i	−0.00580244	+	0.00580244i
$890$	95.3630	+	355.899i	0.107149	+	0.399887i
$891$	257.519	−	69.0021i	0.289023	−	0.0774434i
$892$	−234.360	−	234.360i	−0.262736	−	0.262736i
$893$	448.188	−	776.284i	0.501890	−	0.869299i
$894$	317.768	−	183.463i	0.355445	−	0.205216i
$895$	−27.4235	+	102.346i	−0.0306407	+	0.114353i
$896$			497.286i			0.555007i
$897$		0			0
$898$	−622.296			−0.692980
$899$	−49.6435	−	13.3019i	−0.0552208	−	0.0147964i
$900$	−89.1049	−	154.334i	−0.0990055	−	0.171483i
$901$	−1044.01	−	602.757i	−1.15872	−	0.668987i
$902$	−240.757	+	240.757i	−0.266915	+	0.266915i
$903$	−12.9351	−	48.2746i	−0.0143246	−	0.0534603i
$904$	−934.460	+	250.388i	−1.03369	+	0.276978i
$905$	−317.446	−	317.446i	−0.350769	−	0.350769i
$906$	107.870	−	186.836i	0.119061	−	0.206220i
$907$	−241.263	+	139.293i	−0.266001	+	0.153576i	−0.627069	−	0.778964i	$-0.715746\pi$
$907$	−241.263	+	139.293i	−0.266001	+	0.153576i	0.361068	+	0.932540i	$0.382412\pi$
$908$	5.42516	−	20.2470i	0.00597484	−	0.0222984i
$909$			1068.81i			1.17581i
$910$		0			0
$911$	−702.767			−0.771423			−0.385712	−	0.922619i	$-0.626044\pi$
$911$	−702.767			−0.771423			−0.385712	+	0.922619i	$0.626044\pi$
$912$	−276.107	−	73.9827i	−0.302749	−	0.0811214i
$913$	−306.784	−	531.365i	−0.336018	−	0.581999i
$914$	595.823	+	343.998i	0.651885	+	0.376366i
$915$	46.2522	−	46.2522i	0.0505488	−	0.0505488i
$916$	−138.689	−	517.594i	−0.151407	−	0.565059i
$917$	−2323.16	+	622.489i	−2.53343	+	0.678832i
$918$	385.383	+	385.383i	0.419807	+	0.419807i
$919$	394.084	−	682.574i	0.428818	−	0.742735i	−0.567950	−	0.823063i	$-0.692263\pi$
$919$	394.084	−	682.574i	0.428818	−	0.742735i	0.996768	+	0.0803278i	$0.0255967\pi$
$920$	−408.855	+	236.053i	−0.444408	+	0.256579i
$921$	−18.9616	+	70.7655i	−0.0205880	+	0.0768355i
$922$		−	748.665i		−	0.812002i
$923$		0			0
$924$	161.784			0.175090
$925$	−22.1364	−	5.93142i	−0.0239312	−	0.00641234i
$926$	−25.0582	−	43.4021i	−0.0270607	−	0.0468705i
$927$	655.056	+	378.197i	0.706641	+	0.407979i
$928$	432.692	−	432.692i	0.466263	−	0.466263i
$929$	469.295	+	1751.43i	0.505161	+	1.88529i	0.463379	+	0.886160i	$0.346637\pi$
$929$	469.295	+	1751.43i	0.505161	+	1.88529i	0.0417820	+	0.999127i	$0.486697\pi$
$930$	−7.73549	+	2.07272i	−0.00831773	+	0.00222873i
$931$	1722.00	+	1722.00i	1.84962	+	1.84962i
$932$	153.424	−	265.739i	0.164618	−	0.285127i
$933$	76.1781	−	43.9814i	0.0816485	−	0.0471398i
$934$	−121.185	+	452.269i	−0.129749	+	0.484228i
$935$			255.181i			0.272920i
$936$		0			0
$937$	1827.40			1.95026			0.975132	−	0.221626i	$-0.0711363\pi$
$937$	1827.40			1.95026			0.975132	+	0.221626i	$0.0711363\pi$
$938$	−290.033	−	77.7140i	−0.309203	−	0.0828508i
$939$	−5.48220	−	9.49545i	−0.00583834	−	0.0101123i
$940$	96.4606	+	55.6915i	0.102618	+	0.0592463i
$941$	−473.343	+	473.343i	−0.503022	+	0.503022i	−0.912376	−	0.409354i	$-0.865754\pi$
$941$	−473.343	+	473.343i	−0.503022	+	0.503022i	0.409354	+	0.912376i	$0.365754\pi$
$942$	−72.2896	−	269.788i	−0.0767405	−	0.286400i
$943$	630.636	−	168.978i	0.668755	−	0.179192i
$944$	113.030	+	113.030i	0.119735	+	0.119735i
$945$	306.818	−	531.424i	0.324675	−	0.562353i
$946$	−32.2494	+	18.6192i	−0.0340903	+	0.0196820i
$947$	396.736	−	1480.64i	0.418940	−	1.56351i	−0.357870	−	0.933772i	$-0.616497\pi$
$947$	396.736	−	1480.64i	0.418940	−	1.56351i	0.776810	−	0.629735i	$-0.216837\pi$
$948$			60.9819i			0.0643269i
$949$		0			0
$950$	740.020			0.778968
$951$	−620.965	−	166.387i	−0.652960	−	0.174960i
$952$	−821.527	−	1422.93i	−0.862948	−	1.49467i
$953$	−1241.21	−	716.612i	−1.30242	−	0.751954i	−0.321603	−	0.946875i	$-0.604222\pi$
$953$	−1241.21	−	716.612i	−1.30242	−	0.751954i	−0.980819	+	0.194921i	$0.937555\pi$
$954$	677.063	−	677.063i	0.709710	−	0.709710i
$955$	94.7337	+	353.551i	0.0991976	+	0.370211i
$956$	−44.5744	+	11.9437i	−0.0466260	+	0.0124934i
$957$	235.308	+	235.308i	0.245881	+	0.245881i
$958$	302.123	−	523.292i	0.315368	−	0.546233i
$959$	1129.55	−	652.149i	1.17785	−	0.680030i
$960$	54.3194	−	202.723i	0.0565827	−	0.211169i
$961$			958.442i			0.997338i
$962$		0			0
$963$	662.460			0.687913
$964$	−92.7996	−	24.8656i	−0.0962652	−	0.0257942i
$965$	−219.068	−	379.437i	−0.227013	−	0.393199i
$966$	597.583	+	345.015i	0.618616	+	0.357158i
$967$	−261.931	+	261.931i	−0.270870	+	0.270870i	−0.829450	−	0.558581i	$-0.811346\pi$
$967$	−261.931	+	261.931i	−0.270870	+	0.270870i	0.558581	+	0.829450i	$0.311346\pi$
$968$	140.832	+	525.592i	0.145488	+	0.542967i
$969$	435.676	−	116.739i	0.449614	−	0.120474i
$970$	−417.777	−	417.777i	−0.430698	−	0.430698i
$971$	−120.377	+	208.498i	−0.123972	+	0.214725i	−0.921331	−	0.388780i	$-0.872897\pi$
$971$	−120.377	+	208.498i	−0.123972	+	0.214725i	0.797359	+	0.603506i	$0.206230\pi$
$972$	262.376	−	151.483i	0.269934	−	0.155847i
$973$	−755.251	+	2818.63i	−0.776208	+	2.89685i
$974$		−	177.613i		−	0.182354i
$975$		0			0
$976$	206.125			0.211194
$977$	−1055.59	−	282.844i	−1.08044	−	0.289502i	−0.325662	−	0.945486i	$-0.605587\pi$
$977$	−1055.59	−	282.844i	−1.08044	−	0.289502i	−0.754775	+	0.655984i	$0.772254\pi$
$978$	−6.61808	−	11.4628i	−0.00676695	−	0.0117207i
$979$	659.966	+	381.031i	0.674122	+	0.389205i
$980$	−213.974	+	213.974i	−0.218341	+	0.218341i
$981$	79.2374	+	295.718i	0.0807721	+	0.301446i
$982$	−1.81934	+	0.487490i	−0.00185269	+	0.000496426i
$983$	107.710	+	107.710i	0.109572	+	0.109572i	0.759767	−	0.650195i	$-0.225313\pi$
$983$	107.710	+	107.710i	0.109572	+	0.109572i	−0.650195	+	0.759767i	$0.725313\pi$
$984$	−157.950	+	273.577i	−0.160518	+	0.278026i
$985$	230.489	−	133.073i	0.233999	−	0.135100i
$986$	207.067	−	772.786i	0.210008	−	0.783759i
$987$		−	687.705i		−	0.696763i
$988$		0			0
$989$	71.4057			0.0721999
$990$	−195.778	−	52.4585i	−0.197755	−	0.0529884i
$991$	−316.936	−	548.949i	−0.319814	−	0.553935i	0.660635	−	0.750708i	$-0.270287\pi$
$991$	−316.936	−	548.949i	−0.319814	−	0.553935i	−0.980449	+	0.196773i	$0.936954\pi$
$992$	26.3768	+	15.2287i	0.0265896	+	0.0153515i
$993$	306.540	−	306.540i	0.308700	−	0.308700i
$994$	23.4740	+	87.6061i	0.0236157	+	0.0881349i
$995$	−446.677	+	119.687i	−0.448922	+	0.120288i
$996$	−95.2904	−	95.2904i	−0.0956731	−	0.0956731i
$997$	−472.579	+	818.531i	−0.474001	+	0.820994i	−0.999557	−	0.0297650i	$-0.990524\pi$
$997$	−472.579	+	818.531i	−0.474001	+	0.820994i	0.525556	+	0.850759i	$0.323857\pi$
$998$	−1254.64	+	724.369i	−1.25716	+	0.725821i
$999$	6.47760	−	24.1747i	0.00648409	−	0.0241989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.3.f.g.80.5		48
13.2	odd	12		169.3.d.e.99.5	yes	24
13.3	even	3		169.3.d.e.70.8	yes	24
13.4	even	6	inner	169.3.f.g.19.5		48
13.5	odd	4	inner	169.3.f.g.89.5		48
13.6	odd	12	inner	169.3.f.g.150.8		48
13.7	odd	12	inner	169.3.f.g.150.5		48
13.8	odd	4	inner	169.3.f.g.89.8		48
13.9	even	3	inner	169.3.f.g.19.8		48
13.10	even	6		169.3.d.e.70.5	✓	24
13.11	odd	12		169.3.d.e.99.8	yes	24
13.12	even	2	inner	169.3.f.g.80.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.3.d.e.70.5	✓	24	13.10	even	6
169.3.d.e.70.8	yes	24	13.3	even	3
169.3.d.e.99.5	yes	24	13.2	odd	12
169.3.d.e.99.8	yes	24	13.11	odd	12
169.3.f.g.19.5		48	13.4	even	6	inner
169.3.f.g.19.8		48	13.9	even	3	inner
169.3.f.g.80.5		48	1.1	even	1	trivial
169.3.f.g.80.8		48	13.12	even	2	inner
169.3.f.g.89.5		48	13.5	odd	4	inner
169.3.f.g.89.8		48	13.8	odd	4	inner
169.3.f.g.150.5		48	13.7	odd	12	inner
169.3.f.g.150.8		48	13.6	odd	12	inner

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+(-1.60455 - 0.429937i) q^{2} +(-0.677024 - 1.17264i) q^{3} +(-1.07438 - 0.620291i) q^{4} +(1.57408 - 1.57408i) q^{5} +(0.582156 + 2.17264i) q^{6} +(-12.1635 + 3.25921i) q^{7} +(6.15564 + 6.15564i) q^{8} +(3.58328 - 6.20642i) q^{9} +(-3.20245 + 1.84893i) q^{10} +(-1.97950 + 7.38758i) q^{11} +1.67981i q^{12} +20.9182 q^{14} +(-2.91152 - 0.780141i) q^{15} +(-4.74931 - 8.22605i) q^{16} +(12.9801 + 7.49406i) q^{17} +(-8.41790 + 8.41790i) q^{18} +(5.75221 + 21.4675i) q^{19} +(-2.66754 + 0.714766i) q^{20} +(12.0569 + 12.0569i) q^{21} +(6.35239 - 11.0027i) q^{22} +(-21.0979 + 12.1809i) q^{23} +(3.05084 - 11.3859i) q^{24} +20.0445i q^{25} -21.8903 q^{27} +(15.0899 + 4.04332i) q^{28} +(16.0668 + 27.8285i) q^{29} +(4.33627 + 2.50354i) q^{30} +(-1.13095 + 1.13095i) q^{31} +(-4.92867 - 18.3941i) q^{32} +(10.0031 - 2.68033i) q^{33} +(-17.6052 - 17.6052i) q^{34} +(-14.0161 + 24.2767i) q^{35} +(-7.69957 + 4.44535i) q^{36} +(-0.295912 + 1.10436i) q^{37} -36.9188i q^{38} +19.3790 q^{40} +(-25.8863 - 6.93622i) q^{41} +(-14.1622 - 24.5296i) q^{42} +(-2.53837 - 1.46553i) q^{43} +(6.70917 - 6.70917i) q^{44} +(-4.12904 - 15.4098i) q^{45} +(39.0895 - 10.4740i) q^{46} +(-28.5191 - 28.5191i) q^{47} +(-6.43080 + 11.1385i) q^{48} +(94.8941 - 54.7871i) q^{49} +(8.61789 - 32.1624i) q^{50} -20.2946i q^{51} -80.4313 q^{53} +(35.1240 + 9.41145i) q^{54} +(8.51276 + 14.7445i) q^{55} +(-94.9370 - 54.8119i) q^{56} +(21.2793 - 21.2793i) q^{57} +(-13.8154 - 51.5599i) q^{58} +(-16.2551 + 4.35554i) q^{59} +(2.64416 + 2.64416i) q^{60} +(-10.8503 + 18.7932i) q^{61} +(2.30090 - 1.32843i) q^{62} +(-23.3573 + 87.1707i) q^{63} +69.6277i q^{64} -17.2029 q^{66} +(-13.8651 - 3.71513i) q^{67} +(-9.29699 - 16.1029i) q^{68} +(28.5676 + 16.4935i) q^{69} +(32.9270 - 32.9270i) q^{70} +(1.12218 + 4.18802i) q^{71} +(60.2618 - 16.1471i) q^{72} +(-26.0918 - 26.0918i) q^{73} +(0.949610 - 1.64477i) q^{74} +(23.5050 - 13.5706i) q^{75} +(7.13609 - 26.6323i) q^{76} -96.3107i q^{77} +36.3029 q^{79} +(-20.4243 - 5.47267i) q^{80} +(-17.4292 - 30.1883i) q^{81} +(38.5537 + 22.2590i) q^{82} +(-56.7270 + 56.7270i) q^{83} +(-5.47485 - 20.4324i) q^{84} +(32.2280 - 8.63546i) q^{85} +(3.44285 + 3.44285i) q^{86} +(21.7553 - 37.6812i) q^{87} +(-57.6603 + 33.2902i) q^{88} +(25.7887 - 96.2446i) q^{89} +26.5009i q^{90} +30.2227 q^{92} +(2.09188 + 0.560517i) q^{93} +(33.4989 + 58.0217i) q^{94} +(42.8461 + 24.7372i) q^{95} +(-18.2328 + 18.2328i) q^{96} +(41.3528 + 154.331i) q^{97} +(-175.817 + 47.1101i) q^{98} +(38.7573 + 38.7573i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{3} - 84 q^{9} + 376 q^{14} - 188 q^{16} + 136 q^{22} + 120 q^{27} - 84 q^{29} - 176 q^{35} - 1048 q^{40} + 368 q^{42} + 368 q^{48} - 88 q^{53} + 704 q^{55} + 8 q^{61} - 1480 q^{66} + 168 q^{68}+ \cdots - 1132 q^{94}+O(q^{100}) \) 48 * q - 12 * q^3 - 84 * q^9 + 376 * q^14 - 188 * q^16 + 136 * q^22 + 120 * q^27 - 84 * q^29 - 176 * q^35 - 1048 * q^40 + 368 * q^42 + 368 * q^48 - 88 * q^53 + 704 * q^55 + 8 * q^61 - 1480 * q^66 + 168 * q^68 - 744 * q^74 - 600 * q^79 - 240 * q^81 + 952 * q^87 + 3472 * q^92 - 1132 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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