LMFDB - Embedded newform 69.3.f.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,3,Mod(7,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, degree $10$, 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:	$1.88011382409$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	69.7
Dual form			69.3.f.a.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14901 + 2.48009i) q^{2} +(-1.45709 + 0.936417i) q^{3} +(-0.963341 - 6.70018i) q^{4} +(-3.83816 + 1.75283i) q^{5} +(0.808910 - 5.62609i) q^{6} +(-1.29720 - 4.41787i) q^{7} +(7.64456 + 4.91286i) q^{8} +(1.24625 - 2.72890i) q^{9} +O(q^{10})$	\(q+(-2.14901 + 2.48009i) q^{2} +(-1.45709 + 0.936417i) q^{3} +(-0.963341 - 6.70018i) q^{4} +(-3.83816 + 1.75283i) q^{5} +(0.808910 - 5.62609i) q^{6} +(-1.29720 - 4.41787i) q^{7} +(7.64456 + 4.91286i) q^{8} +(1.24625 - 2.72890i) q^{9} +(3.90107 - 13.2858i) q^{10} +(3.90366 - 3.38254i) q^{11} +(7.67785 + 8.86071i) q^{12} +(-3.70048 - 1.08656i) q^{13} +(13.7444 + 6.27686i) q^{14} +(3.95118 - 6.14816i) q^{15} +(-2.63301 + 0.773120i) q^{16} +(-30.2251 - 4.34571i) q^{17} +(4.08971 + 8.95522i) q^{18} +(-29.1083 + 4.18514i) q^{19} +(15.4417 + 24.0278i) q^{20} +(6.02711 + 5.22252i) q^{21} +16.9505i q^{22} +(-3.89009 + 22.6686i) q^{23} -15.7393 q^{24} +(-4.71246 + 5.43847i) q^{25} +(10.6471 - 6.84250i) q^{26} +(0.739490 + 5.14326i) q^{27} +(-28.3509 + 12.9474i) q^{28} +(5.94808 - 41.3698i) q^{29} +(6.75685 + 23.0117i) q^{30} +(5.87274 + 3.77418i) q^{31} +(-11.3587 + 24.8722i) q^{32} +(-2.52053 + 8.58414i) q^{33} +(75.7318 - 65.6219i) q^{34} +(12.7226 + 14.6827i) q^{35} +(-19.4847 - 5.72121i) q^{36} +(17.6648 + 8.06725i) q^{37} +(52.1745 - 81.1851i) q^{38} +(6.40942 - 1.88198i) q^{39} +(-37.9524 - 5.45674i) q^{40} +(-10.5832 - 23.1741i) q^{41} +(-25.9046 + 3.72453i) q^{42} +(33.3409 + 51.8795i) q^{43} +(-26.4242 - 22.8967i) q^{44} +12.6584i q^{45} +(-47.8604 - 58.3629i) q^{46} -74.2173 q^{47} +(3.11257 - 3.59210i) q^{48} +(23.3866 - 15.0297i) q^{49} +(-3.36077 - 23.3746i) q^{50} +(48.1102 - 21.9712i) q^{51} +(-3.71532 + 25.8406i) q^{52} +(1.17447 + 3.99987i) q^{53} +(-14.3449 - 9.21892i) q^{54} +(-9.05386 + 19.8252i) q^{55} +(11.7878 - 40.1456i) q^{56} +(38.4945 - 33.3557i) q^{57} +(89.8183 + 103.656i) q^{58} +(67.4746 + 19.8123i) q^{59} +(-45.0001 - 20.5509i) q^{60} +(-38.4763 + 59.8703i) q^{61} +(-21.9809 + 6.45417i) q^{62} +(-13.6725 - 1.96581i) q^{63} +(-41.8350 - 91.6059i) q^{64} +(16.1076 - 2.31592i) q^{65} +(-15.8728 - 24.6985i) q^{66} +(-15.6728 - 13.5806i) q^{67} +206.700i q^{68} +(-15.5591 - 36.6731i) q^{69} -63.7555 q^{70} +(-42.1926 + 48.6929i) q^{71} +(22.9337 - 14.7386i) q^{72} +(-17.6682 - 122.885i) q^{73} +(-57.9693 + 26.4737i) q^{74} +(1.77382 - 12.3372i) q^{75} +(56.0825 + 190.999i) q^{76} +(-20.0075 - 12.8580i) q^{77} +(-9.10644 + 19.9403i) q^{78} +(-14.9340 + 50.8606i) q^{79} +(8.75075 - 7.58257i) q^{80} +(-5.89375 - 6.80175i) q^{81} +(80.2173 + 23.5539i) q^{82} +(80.7154 + 36.8615i) q^{83} +(29.1857 - 45.4138i) q^{84} +(123.626 - 36.2999i) q^{85} +(-200.316 - 28.8011i) q^{86} +(30.0725 + 65.8496i) q^{87} +(46.4597 - 6.67990i) q^{88} +(-36.9688 - 57.5246i) q^{89} +(-31.3939 - 27.2030i) q^{90} +17.7577i q^{91} +(155.632 + 4.22670i) q^{92} -12.0913 q^{93} +(159.494 - 184.065i) q^{94} +(104.387 - 67.0851i) q^{95} +(-6.73998 - 46.8776i) q^{96} +(-61.1812 + 27.9405i) q^{97} +(-12.9831 + 90.2998i) q^{98} +(-4.36569 - 14.8682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} - 12 q^{6} - 4 q^{8} - 24 q^{9}+O(q^{10}) $ 80 * q + 4 * q^2 - 12 * q^6 - 4 * q^8 - 24 * q^9	$ 80 q + 4 q^{2} - 12 q^{6} - 4 q^{8} - 24 q^{9} + 8 q^{13} - 208 q^{16} - 110 q^{17} + 12 q^{18} - 66 q^{19} - 176 q^{20} - 8 q^{23} - 12 q^{24} + 244 q^{25} + 328 q^{26} + 528 q^{28} + 50 q^{29} + 182 q^{31} + 428 q^{32} - 242 q^{34} - 536 q^{35} - 198 q^{36} - 352 q^{37} - 770 q^{38} - 216 q^{39} - 110 q^{40} - 208 q^{41} - 330 q^{42} - 88 q^{43} - 154 q^{44} - 72 q^{46} + 24 q^{47} + 360 q^{48} + 256 q^{49} + 726 q^{50} + 264 q^{51} + 506 q^{52} + 352 q^{53} + 162 q^{54} - 38 q^{55} + 1210 q^{56} + 528 q^{57} - 306 q^{58} + 776 q^{59} + 330 q^{60} - 308 q^{61} + 392 q^{62} - 288 q^{64} - 22 q^{67} - 108 q^{69} + 344 q^{70} - 80 q^{71} - 12 q^{72} + 46 q^{73} - 374 q^{74} + 72 q^{75} - 946 q^{76} - 728 q^{77} - 144 q^{78} - 572 q^{79} - 2178 q^{80} - 72 q^{81} - 820 q^{82} - 704 q^{83} - 922 q^{85} - 1100 q^{86} + 192 q^{87} - 528 q^{88} - 264 q^{89} + 330 q^{92} + 24 q^{93} + 874 q^{94} + 622 q^{95} - 468 q^{96} + 792 q^{97} - 724 q^{98} - 330 q^{99}+O(q^{100}) $ 80 * q + 4 * q^2 - 12 * q^6 - 4 * q^8 - 24 * q^9 + 8 * q^13 - 208 * q^16 - 110 * q^17 + 12 * q^18 - 66 * q^19 - 176 * q^20 - 8 * q^23 - 12 * q^24 + 244 * q^25 + 328 * q^26 + 528 * q^28 + 50 * q^29 + 182 * q^31 + 428 * q^32 - 242 * q^34 - 536 * q^35 - 198 * q^36 - 352 * q^37 - 770 * q^38 - 216 * q^39 - 110 * q^40 - 208 * q^41 - 330 * q^42 - 88 * q^43 - 154 * q^44 - 72 * q^46 + 24 * q^47 + 360 * q^48 + 256 * q^49 + 726 * q^50 + 264 * q^51 + 506 * q^52 + 352 * q^53 + 162 * q^54 - 38 * q^55 + 1210 * q^56 + 528 * q^57 - 306 * q^58 + 776 * q^59 + 330 * q^60 - 308 * q^61 + 392 * q^62 - 288 * q^64 - 22 * q^67 - 108 * q^69 + 344 * q^70 - 80 * q^71 - 12 * q^72 + 46 * q^73 - 374 * q^74 + 72 * q^75 - 946 * q^76 - 728 * q^77 - 144 * q^78 - 572 * q^79 - 2178 * q^80 - 72 * q^81 - 820 * q^82 - 704 * q^83 - 922 * q^85 - 1100 * q^86 + 192 * q^87 - 528 * q^88 - 264 * q^89 + 330 * q^92 + 24 * q^93 + 874 * q^94 + 622 * q^95 - 468 * q^96 + 792 * q^97 - 724 * q^98 - 330 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{19}{22}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.14901	+	2.48009i	−1.07450	+	1.24004i	−0.105130	+	0.994458i	$0.533526\pi$
$2$	−2.14901	+	2.48009i	−1.07450	+	1.24004i	−0.969375	+	0.245586i	$0.921020\pi$
$3$	−1.45709	+	0.936417i	−0.485698	+	0.312139i
$3$	−1.45709	+	0.936417i	−0.485698	+	0.312139i
$4$	−0.963341	−	6.70018i	−0.240835	−	1.67505i
$5$	−3.83816	+	1.75283i	−0.767632	+	0.350566i	−0.760440	−	0.649408i	$-0.775017\pi$
$5$	−3.83816	+	1.75283i	−0.767632	+	0.350566i	−0.00719206	+	0.999974i	$0.502289\pi$
$6$	0.808910	−	5.62609i	0.134818	−	0.937682i
$7$	−1.29720	−	4.41787i	−0.185315	−	0.631124i	−0.998774	−	0.0495020i	$-0.984237\pi$
$7$	−1.29720	−	4.41787i	−0.185315	−	0.631124i	0.813459	−	0.581622i	$-0.197582\pi$
$8$	7.64456	+	4.91286i	0.955570	+	0.614107i
$9$	1.24625	−	2.72890i	0.138472	−	0.303211i
$10$	3.90107	−	13.2858i	0.390107	−	1.32858i
$11$	3.90366	−	3.38254i	0.354878	−	0.307504i	−0.459116	−	0.888376i	$-0.651834\pi$
$11$	3.90366	−	3.38254i	0.354878	−	0.307504i	0.813995	+	0.580872i	$0.197288\pi$
$12$	7.67785	+	8.86071i	0.639821	+	0.738392i
$13$	−3.70048	−	1.08656i	−0.284653	−	0.0835815i	0.136290	−	0.990669i	$-0.456482\pi$
$13$	−3.70048	−	1.08656i	−0.284653	−	0.0835815i	−0.420942	+	0.907088i	$0.638300\pi$
$14$	13.7444	+	6.27686i	0.981743	+	0.448347i
$15$	3.95118	−	6.14816i	0.263412	−	0.409877i
$16$	−2.63301	+	0.773120i	−0.164563	+	0.0483200i
$17$	−30.2251	−	4.34571i	−1.77795	−	0.255630i	−0.826389	−	0.563100i	$-0.809609\pi$
$17$	−30.2251	−	4.34571i	−1.77795	−	0.255630i	−0.951558	+	0.307470i	$0.900518\pi$
$18$	4.08971	+	8.95522i	0.227206	+	0.497512i
$19$	−29.1083	+	4.18514i	−1.53202	+	0.220271i	−0.856140	−	0.516744i	$-0.827144\pi$
$19$	−29.1083	+	4.18514i	−1.53202	+	0.220271i	−0.675877	+	0.737015i	$0.736235\pi$
$20$	15.4417	+	24.0278i	0.772087	+	1.20139i
$21$	6.02711	+	5.22252i	0.287005	+	0.248692i
$22$			16.9505i			0.770479i
$23$	−3.89009	+	22.6686i	−0.169134	+	0.985593i
$23$	−3.89009	+	22.6686i	−0.169134	+	0.985593i
$24$	−15.7393			−0.655805
$25$	−4.71246	+	5.43847i	−0.188498	+	0.217539i
$26$	10.6471	−	6.84250i	0.409505	−	0.263173i
$27$	0.739490	+	5.14326i	0.0273885	+	0.190491i
$28$	−28.3509	+	12.9474i	−1.01253	+	0.462407i
$29$	5.94808	−	41.3698i	0.205106	−	1.42655i	−0.583733	−	0.811946i	$-0.698409\pi$
$29$	5.94808	−	41.3698i	0.205106	−	1.42655i	0.788839	−	0.614600i	$-0.210682\pi$
$30$	6.75685	+	23.0117i	0.225228	+	0.767057i
$31$	5.87274	+	3.77418i	0.189443	+	0.121748i	0.631924	−	0.775030i	$-0.282265\pi$
$31$	5.87274	+	3.77418i	0.189443	+	0.121748i	−0.442481	+	0.896778i	$0.645902\pi$
$32$	−11.3587	+	24.8722i	−0.354960	+	0.777255i
$33$	−2.52053	+	8.58414i	−0.0763797	+	0.260125i
$34$	75.7318	−	65.6219i	2.22740	−	1.93006i
$35$	12.7226	+	14.6827i	0.363504	+	0.419506i
$36$	−19.4847	−	5.72121i	−0.541241	−	0.158923i
$37$	17.6648	+	8.06725i	0.477427	+	0.218034i	0.639569	−	0.768734i	$-0.279113\pi$
$37$	17.6648	+	8.06725i	0.477427	+	0.218034i	−0.162142	+	0.986768i	$0.551840\pi$
$38$	52.1745	−	81.1851i	1.37301	−	2.13645i
$39$	6.40942	−	1.88198i	0.164344	−	0.0482558i
$40$	−37.9524	−	5.45674i	−0.948811	−	0.136418i
$41$	−10.5832	−	23.1741i	−0.258128	−	0.565222i	0.735552	−	0.677468i	$-0.236923\pi$
$41$	−10.5832	−	23.1741i	−0.258128	−	0.565222i	−0.993680	+	0.112246i	$0.964195\pi$
$42$	−25.9046	+	3.72453i	−0.616777	+	0.0886792i
$43$	33.3409	+	51.8795i	0.775371	+	1.20650i	0.974027	+	0.226431i	$0.0727059\pi$
$43$	33.3409	+	51.8795i	0.775371	+	1.20650i	−0.198656	+	0.980069i	$0.563658\pi$
$44$	−26.4242	−	22.8967i	−0.600550	−	0.520380i
$45$			12.6584i			0.281298i
$46$	−47.8604	−	58.3629i	−1.04044	−	1.26876i
$47$	−74.2173			−1.57909			−0.789546	−	0.613692i	$-0.789684\pi$
$47$	−74.2173			−1.57909			−0.789546	+	0.613692i	$0.789684\pi$
$48$	3.11257	−	3.59210i	0.0648453	−	0.0748354i
$49$	23.3866	−	15.0297i	0.477278	−	0.306728i
$50$	−3.36077	−	23.3746i	−0.0672153	−	0.467493i
$51$	48.1102	−	21.9712i	0.943337	−	0.430808i
$52$	−3.71532	+	25.8406i	−0.0714485	+	0.496936i
$53$	1.17447	+	3.99987i	0.0221598	+	0.0754692i	0.969831	−	0.243780i	$-0.0783875\pi$
$53$	1.17447	+	3.99987i	0.0221598	+	0.0754692i	−0.947671	+	0.319249i	$0.896569\pi$
$54$	−14.3449	−	9.21892i	−0.265647	−	0.170721i
$55$	−9.05386	+	19.8252i	−0.164616	+	0.360458i
$56$	11.7878	−	40.1456i	0.210497	−	0.716886i
$57$	38.4945	−	33.3557i	0.675342	−	0.585187i
$58$	89.8183	+	103.656i	1.54859	+	1.78717i
$59$	67.4746	+	19.8123i	1.14364	+	0.335802i	0.798054	−	0.602586i	$-0.205863\pi$
$59$	67.4746	+	19.8123i	1.14364	+	0.335802i	0.345583	+	0.938388i	$0.387681\pi$
$60$	−45.0001	−	20.5509i	−0.750002	−	0.342514i
$61$	−38.4763	+	59.8703i	−0.630759	+	0.981480i	0.367908	+	0.929862i	$0.380074\pi$
$61$	−38.4763	+	59.8703i	−0.630759	+	0.981480i	−0.998667	+	0.0516177i	$0.983562\pi$
$62$	−21.9809	+	6.45417i	−0.354530	+	0.104099i
$63$	−13.6725	−	1.96581i	−0.217024	−	0.0312034i
$64$	−41.8350	−	91.6059i	−0.653672	−	1.43134i
$65$	16.1076	−	2.31592i	0.247809	−	0.0356296i
$66$	−15.8728	−	24.6985i	−0.240497	−	0.374220i
$67$	−15.6728	−	13.5806i	−0.233922	−	0.202695i	0.530010	−	0.847992i	$-0.322188\pi$
$67$	−15.6728	−	13.5806i	−0.233922	−	0.202695i	−0.763932	+	0.645297i	$0.776734\pi$
$68$			206.700i			3.03971i
$69$	−15.5591	−	36.6731i	−0.225494	−	0.531494i
$70$	−63.7555			−0.910792
$71$	−42.1926	+	48.6929i	−0.594262	+	0.685815i	−0.970609	−	0.240664i	$-0.922635\pi$
$71$	−42.1926	+	48.6929i	−0.594262	+	0.685815i	0.376346	+	0.926479i	$0.377180\pi$
$72$	22.9337	−	14.7386i	0.318523	−	0.204702i
$73$	−17.6682	−	122.885i	−0.242030	−	1.68335i	−0.641906	−	0.766784i	$-0.721856\pi$
$73$	−17.6682	−	122.885i	−0.242030	−	1.68335i	0.399876	−	0.916569i	$-0.369053\pi$
$74$	−57.9693	+	26.4737i	−0.783370	+	0.357753i
$75$	1.77382	−	12.3372i	0.0236509	−	0.164496i
$76$	56.0825	+	190.999i	0.737927	+	2.51315i
$77$	−20.0075	−	12.8580i	−0.259837	−	0.166987i
$78$	−9.10644	+	19.9403i	−0.116749	+	0.255645i
$79$	−14.9340	+	50.8606i	−0.189038	+	0.643806i	0.809364	+	0.587307i	$0.199812\pi$
$79$	−14.9340	+	50.8606i	−0.189038	+	0.643806i	−0.998403	+	0.0564986i	$0.982006\pi$
$80$	8.75075	−	7.58257i	0.109384	−	0.0947821i
$81$	−5.89375	−	6.80175i	−0.0727623	−	0.0839722i
$82$	80.2173	+	23.5539i	0.978260	+	0.287243i
$83$	80.7154	+	36.8615i	0.972475	+	0.444114i	0.837322	−	0.546710i	$-0.184120\pi$
$83$	80.7154	+	36.8615i	0.972475	+	0.444114i	0.135153	+	0.990825i	$0.456847\pi$
$84$	29.1857	−	45.4138i	0.347449	−	0.540641i
$85$	123.626	−	36.2999i	1.45442	−	0.427057i
$86$	−200.316	−	28.8011i	−2.32925	−	0.334896i
$87$	30.0725	+	65.8496i	0.345661	+	0.756892i
$88$	46.4597	−	6.67990i	0.527952	−	0.0759080i
$89$	−36.9688	−	57.5246i	−0.415380	−	0.646343i	0.569013	−	0.822328i	$-0.307325\pi$
$89$	−36.9688	−	57.5246i	−0.415380	−	0.646343i	−0.984393	+	0.175985i	$0.943689\pi$
$90$	−31.3939	−	27.2030i	−0.348822	−	0.302256i
$91$			17.7577i			0.195140i
$92$	155.632	+	4.22670i	1.69165	+	0.0459424i
$93$	−12.0913			−0.130014
$94$	159.494	−	184.065i	1.69674	−	1.95814i
$95$	104.387	−	67.0851i	1.09881	−	0.706159i
$96$	−6.73998	−	46.8776i	−0.0702081	−	0.488308i
$97$	−61.1812	+	27.9405i	−0.630734	+	0.288046i	−0.705017	−	0.709191i	$-0.749061\pi$
$97$	−61.1812	+	27.9405i	−0.630734	+	0.288046i	0.0742829	+	0.997237i	$0.476333\pi$
$98$	−12.9831	+	90.2998i	−0.132481	+	0.921426i
$99$	−4.36569	−	14.8682i	−0.0440979	−	0.150184i
$100$	40.9784	+	26.3352i	0.409784	+	0.263352i
$101$	32.5981	−	71.3799i	0.322754	−	0.706732i	−0.676813	−	0.736155i	$-0.736640\pi$
$101$	32.5981	−	71.3799i	0.322754	−	0.706732i	0.999567	+	0.0294227i	$0.00936690\pi$
$102$	−48.8988	+	166.534i	−0.479400	+	1.63269i
$103$	−65.8348	+	57.0462i	−0.639173	+	0.553846i	−0.913014	−	0.407929i	$-0.866251\pi$
$103$	−65.8348	+	57.0462i	−0.639173	+	0.553846i	0.273841	+	0.961775i	$0.411706\pi$
$104$	−22.9504	−	26.4862i	−0.220677	−	0.254675i
$105$	−32.2872	−	9.48038i	−0.307497	−	0.0902893i
$106$	−12.4440	−	5.68297i	−0.117396	−	0.0536129i
$107$	33.6503	−	52.3609i	0.314489	−	0.489354i	−0.647641	−	0.761946i	$-0.724244\pi$
$107$	33.6503	−	52.3609i	0.314489	−	0.489354i	0.962130	+	0.272591i	$0.0878807\pi$
$108$	33.7484	−	9.90943i	0.312485	−	0.0917540i
$109$	−138.525	−	19.9169i	−1.27087	−	0.182724i	−0.526320	−	0.850287i	$-0.676428\pi$
$109$	−138.525	−	19.9169i	−1.27087	−	0.182724i	−0.744553	+	0.667563i	$0.767338\pi$
$110$	−29.7114	−	65.0589i	−0.270104	−	0.591445i
$111$	−33.2936	+	4.78690i	−0.299942	+	0.0431252i
$112$	6.83108	+	10.6294i	0.0609918	+	0.0949051i
$113$	11.4520	+	9.92325i	0.101346	+	0.0878164i	0.704060	−	0.710141i	$-0.251369\pi$
$113$	11.4520	+	9.92325i	0.101346	+	0.0878164i	−0.602714	+	0.797957i	$0.705914\pi$
$114$			167.151i			1.46624i
$115$	−24.8034	−	93.8245i	−0.215682	−	0.815865i
$116$	−282.915			−2.43893
$117$	−7.57682	+	8.74411i	−0.0647591	+	0.0747360i
$118$	−194.140	+	124.766i	−1.64525	+	1.05734i
$119$	20.0093	+	139.168i	0.168145	+	1.16948i
$120$	60.4100	−	27.5883i	0.503417	−	0.229903i
$121$	−13.4231	+	93.3598i	−0.110935	+	0.771568i
$122$	−65.7977	−	224.086i	−0.539325	−	1.83677i
$123$	37.1214	+	23.8565i	0.301800	+	0.193955i
$124$	19.6303	−	42.9843i	0.158308	−	0.346647i
$125$	38.2735	−	130.347i	0.306188	−	1.04278i
$126$	34.2578	−	29.6845i	0.271887	−	0.235592i
$127$	−124.799	−	144.026i	−0.982669	−	1.13406i	−0.990968	−	0.134095i	$-0.957187\pi$
$127$	−124.799	−	144.026i	−0.982669	−	1.13406i	0.00829901	−	0.999966i	$-0.497358\pi$
$128$	212.153	+	62.2936i	1.65744	+	0.486669i
$129$	−97.1618	−	44.3723i	−0.753192	−	0.343971i
$130$	−28.8717	+	44.9252i	−0.222090	+	0.345579i
$131$	155.664	−	45.7070i	1.18827	−	0.348908i	0.372914	−	0.927866i	$-0.378359\pi$
$131$	155.664	−	45.7070i	1.18827	−	0.348908i	0.815357	+	0.578958i	$0.196540\pi$
$132$	59.9435	+	8.61857i	0.454117	+	0.0652922i
$133$	56.2488	+	123.168i	0.422923	+	0.926073i
$134$	67.3620	−	9.68519i	0.502701	−	0.0722775i
$135$	−11.8535	−	18.4445i	−0.0878040	−	0.136626i
$136$	−209.708	−	181.713i	−1.54197	−	1.33612i
$137$		−	1.22960i		−	0.00897515i	−0.999990	−	0.00448758i	$-0.998572\pi$
$137$		−	1.22960i		−	0.00897515i	0.999990	−	0.00448758i	$-0.00142844\pi$
$138$	124.389	+	40.2229i	0.901370	+	0.291470i
$139$	2.69796			0.0194098			0.00970491	−	0.999953i	$-0.496911\pi$
$139$	2.69796			0.0194098			0.00970491	+	0.999953i	$0.496911\pi$
$140$	86.1206	−	99.3884i	0.615147	−	0.709917i
$141$	108.142	−	69.4984i	0.766961	−	0.492896i
$142$	−30.0903	−	209.283i	−0.211904	−	1.47382i
$143$	−18.1208	+	8.27548i	−0.126719	+	0.0578705i
$144$	−1.17161	+	8.14869i	−0.00813615	+	0.0565882i
$145$	49.6845	+	169.210i	0.342652	+	1.16696i
$146$	342.734	+	220.262i	2.34749	+	1.50864i
$147$	−20.0025	+	43.7993i	−0.136071	+	0.297954i
$148$	37.0348	−	126.129i	0.250235	−	0.852223i
$149$	−113.252	+	98.1331i	−0.760078	+	0.658611i	−0.946078	−	0.323938i	$-0.894993\pi$
$149$	−113.252	+	98.1331i	−0.760078	+	0.658611i	0.186000	+	0.982550i	$0.440447\pi$
$150$	26.7854	+	30.9120i	0.178569	+	0.206080i
$151$	138.126	+	40.5574i	0.914742	+	0.268592i	0.705035	−	0.709172i	$-0.250931\pi$
$151$	138.126	+	40.5574i	0.914742	+	0.268592i	0.209706	+	0.977764i	$0.432749\pi$
$152$	−243.081	−	111.011i	−1.59922	−	0.730339i
$153$	−49.5269	+	77.0653i	−0.323705	+	0.503695i
$154$	74.8853	−	21.9883i	0.486268	−	0.142781i
$155$	−29.1560	−	4.19200i	−0.188103	−	0.0270452i
$156$	−18.7841	−	41.1313i	−0.120411	−	0.263662i
$157$	108.344	−	15.5775i	0.690090	−	0.0992199i	0.211657	−	0.977344i	$-0.432114\pi$
$157$	108.344	−	15.5775i	0.690090	−	0.0992199i	0.478433	+	0.878124i	$0.341205\pi$
$158$	−94.0455	−	146.338i	−0.595225	−	0.926188i
$159$	−5.45685	−	4.72839i	−0.0343198	−	0.0297383i
$160$		−	115.373i		−	0.721083i
$161$	105.193	−	12.2199i	0.653374	−	0.0759001i
$162$	29.5347			0.182313
$163$	46.3888	−	53.5355i	0.284594	−	0.328439i	−0.595395	−	0.803433i	$-0.703004\pi$
$163$	46.3888	−	53.5355i	0.284594	−	0.328439i	0.879989	+	0.474994i	$0.157550\pi$
$164$	−145.075	+	93.2343i	−0.884606	+	0.568502i
$165$	−5.37233	−	37.3654i	−0.0325596	−	0.226457i
$166$	−264.878	+	120.966i	−1.59565	+	0.728709i
$167$	−6.25329	+	43.4926i	−0.0374448	+	0.260434i	−0.999941	−	0.0108607i	$-0.996543\pi$
$167$	−6.25329	+	43.4926i	−0.0374448	+	0.260434i	0.962496	+	0.271295i	$0.0874520\pi$
$168$	20.4171	+	69.5342i	0.121530	+	0.413894i
$169$	−129.659	−	83.3267i	−0.767212	−	0.493057i
$170$	−175.647	+	384.612i	−1.03322	+	2.26243i
$171$	−24.8553	+	84.6493i	−0.145352	+	0.495025i
$172$	315.484	−	273.368i	1.83421	−	1.58935i
$173$	96.1257	+	110.935i	0.555640	+	0.641243i	0.962188	−	0.272387i	$-0.0878130\pi$
$173$	96.1257	+	110.935i	0.555640	+	0.641243i	−0.406548	+	0.913629i	$0.633268\pi$
$174$	−227.939	−	66.9289i	−1.30999	−	0.384649i
$175$	30.1394	+	13.7642i	0.172225	+	0.0786527i
$176$	−7.66325	+	11.9243i	−0.0435412	+	0.0677514i
$177$	−116.869	+	34.3160i	−0.660279	+	0.193875i
$178$	222.112	+	31.9349i	1.24782	+	0.179410i
$179$	122.103	+	267.369i	0.682141	+	1.49368i	0.860359	+	0.509689i	$0.170239\pi$
$179$	122.103	+	267.369i	0.682141	+	1.49368i	−0.178218	+	0.983991i	$0.557033\pi$
$180$	84.8136	−	12.1943i	0.471186	−	0.0677464i
$181$	−3.05113	−	4.74766i	−0.0168571	−	0.0262301i	0.832723	−	0.553690i	$-0.186781\pi$
$181$	−3.05113	−	4.74766i	−0.0168571	−	0.0262301i	−0.849580	+	0.527460i	$0.823144\pi$
$182$	−44.0408	−	38.1615i	−0.241982	−	0.209679i
$183$		−	123.266i		−	0.673587i
$184$	−141.106	+	154.180i	−0.766880	+	0.837936i
$185$	−81.9409			−0.442924
$186$	25.9844	−	29.9876i	0.139701	−	0.161224i
$187$	−132.688	+	85.2735i	−0.709562	+	0.456008i
$188$	71.4966	+	497.270i	0.380301	+	2.64505i
$189$	21.7630	−	9.93882i	0.115148	−	0.0525864i
$190$	−57.9505	+	403.055i	−0.305003	+	2.12134i
$191$	0.687457	+	2.34126i	0.00359925	+	0.0122579i	0.961273	−	0.275598i	$-0.0888758\pi$
$191$	0.687457	+	2.34126i	0.00359925	+	0.0122579i	−0.957674	+	0.287856i	$0.907058\pi$
$192$	146.739	+	94.3033i	0.764265	+	0.491163i
$193$	86.7198	−	189.890i	0.449326	−	0.983886i	−0.540466	−	0.841366i	$-0.681752\pi$
$193$	86.7198	−	189.890i	0.449326	−	0.983886i	0.989792	−	0.142520i	$-0.0455205\pi$
$194$	62.1840	−	211.779i	0.320536	−	1.09165i
$195$	−21.3016	+	18.4580i	−0.109239	+	0.0946562i
$196$	−123.231	−	142.216i	−0.628729	−	0.725592i
$197$	−140.094	−	41.1354i	−0.711138	−	0.208809i	−0.0938958	−	0.995582i	$-0.529932\pi$
$197$	−140.094	−	41.1354i	−0.711138	−	0.208809i	−0.617242	+	0.786773i	$0.711750\pi$
$198$	46.2563	+	21.1245i	0.233618	+	0.106690i
$199$	−59.9935	+	93.3517i	−0.301475	+	0.469104i	−0.958632	−	0.284650i	$-0.908123\pi$
$199$	−59.9935	+	93.3517i	−0.301475	+	0.469104i	0.657157	+	0.753754i	$0.271759\pi$
$200$	−62.7431	+	18.4230i	−0.313715	+	0.0921152i
$201$	35.5538	+	5.11186i	0.176885	+	0.0254322i
$202$	106.975	+	234.242i	0.529579	+	1.15962i
$203$	−190.482	+	27.3872i	−0.938336	+	0.134912i
$204$	−193.558	−	301.181i	−0.948812	−	1.47638i
$205$	81.2404	+	70.3952i	0.396295	+	0.343391i
$206$		−	285.869i		−	1.38771i
$207$	57.0124	+	38.8663i	0.275422	+	0.187760i
$208$	10.5834			0.0508819
$209$	−99.4726	+	114.798i	−0.475946	+	0.549270i
$210$	92.8977	−	59.7017i	0.442370	−	0.284294i
$211$	−46.8139	−	325.598i	−0.221867	−	1.54312i	−0.730969	−	0.682411i	$-0.760931\pi$
$211$	−46.8139	−	325.598i	−0.221867	−	1.54312i	0.509102	−	0.860706i	$-0.329978\pi$
$212$	25.6684	−	11.7224i	0.121078	−	0.0552943i
$213$	15.8817	−	110.460i	0.0745622	−	0.518591i
$214$	57.5449	+	195.980i	0.268901	+	0.915794i
$215$	−218.904	−	140.681i	−1.01816	−	0.654330i
$216$	−19.6151	+	42.9510i	−0.0908105	+	0.198847i
$217$	9.05569	−	30.8408i	0.0417313	−	0.142124i
$218$	347.088	−	300.753i	1.59214	−	1.37960i
$219$	140.816	+	162.510i	0.642994	+	0.742054i
$220$	141.554	+	41.5641i	0.643429	+	0.188928i
$221$	107.126	+	48.9226i	0.484731	+	0.221369i
$222$	59.6763	−	92.8582i	0.268812	−	0.418280i
$223$	−327.858	+	96.2677i	−1.47021	+	0.431694i	−0.916169	−	0.400793i	$-0.868735\pi$
$223$	−327.858	+	96.2677i	−1.47021	+	0.431694i	−0.554045	+	0.832486i	$0.686917\pi$
$224$	124.616	+	17.9171i	0.556323	+	0.0799872i
$225$	8.96813	+	19.6375i	0.0398584	+	0.0872777i
$226$	−49.2211	+	7.07693i	−0.217793	+	0.0313138i
$227$	−174.088	−	270.887i	−0.766910	−	1.19333i	−0.976494	−	0.215544i	$-0.930847\pi$
$227$	−174.088	−	270.887i	−0.766910	−	1.19333i	0.209584	−	0.977791i	$-0.432789\pi$
$228$	−260.573	−	225.787i	−1.14286	−	0.990296i
$229$		−	264.101i		−	1.15328i	−0.816999	−	0.576639i	$-0.804364\pi$
$229$		−	264.101i		−	1.15328i	0.816999	−	0.576639i	$-0.195636\pi$
$230$	285.996	+	140.115i	1.24346	+	0.609196i
$231$	41.1932			0.178326
$232$	248.715	−	287.032i	1.07205	−	1.23721i
$233$	125.980	−	80.9622i	0.540685	−	0.347477i	−0.241622	−	0.970371i	$-0.577679\pi$
$233$	125.980	−	80.9622i	0.540685	−	0.347477i	0.782307	+	0.622893i	$0.214043\pi$
$234$	−5.40353	−	37.5824i	−0.0230920	−	0.160608i
$235$	284.858	−	130.090i	1.21216	−	0.553575i
$236$	67.7452	−	471.178i	0.287056	−	1.99652i
$237$	−25.8665	−	88.0932i	−0.109141	−	0.371701i
$238$	−388.148	−	249.448i	−1.63088	−	1.04810i
$239$	−50.6739	+	110.960i	−0.212024	+	0.464269i	−0.985526	−	0.169526i	$-0.945776\pi$
$239$	−50.6739	+	110.960i	−0.212024	+	0.464269i	0.773501	+	0.633795i	$0.218504\pi$
$240$	−5.65021	+	19.2429i	−0.0235426	+	0.0801786i
$241$	−168.603	+	146.096i	−0.699598	+	0.606205i	−0.930291	−	0.366821i	$-0.880446\pi$
$241$	−168.603	+	146.096i	−0.699598	+	0.606205i	0.230693	+	0.973027i	$0.425901\pi$
$242$	−202.694	−	233.922i	−0.837579	−	0.966618i
$243$	14.9570	+	4.39178i	0.0615515	+	0.0180732i
$244$	438.208	+	200.123i	1.79593	+	0.820175i
$245$	−63.4171	+	98.6790i	−0.258845	+	0.402771i
$246$	−138.940	+	40.7966i	−0.564798	+	0.165840i
$247$	112.262	+	16.1409i	0.454503	+	0.0653477i
$248$	26.3525	+	57.7039i	0.106260	+	0.232677i
$249$	−152.128	+	21.8727i	−0.610954	+	0.0878420i
$250$	241.023	+	375.040i	0.964093	+	1.50016i
$251$	−133.912	−	116.035i	−0.533514	−	0.462292i	0.345953	−	0.938252i	$-0.387555\pi$
$251$	−133.912	−	116.035i	−0.533514	−	0.462292i	−0.879467	+	0.475959i	$0.842101\pi$
$252$			93.5022i			0.371041i
$253$	61.4920	+	101.649i	0.243052	+	0.401775i
$254$	625.391			2.46217
$255$	−146.143	+	168.658i	−0.573109	+	0.661403i
$256$	−271.533	+	174.503i	−1.06067	+	0.681654i
$257$	−29.1668	−	202.859i	−0.113489	−	0.789336i	−0.964480	−	0.264156i	$-0.914907\pi$
$257$	−29.1668	−	202.859i	−0.113489	−	0.789336i	0.850991	−	0.525181i	$-0.176002\pi$
$258$	318.849	−	145.613i	1.23585	−	0.564393i
$259$	12.7252	−	88.5056i	0.0491320	−	0.341721i
$260$	−31.0342	−	105.693i	−0.119362	−	0.406511i
$261$	−105.481	−	67.7886i	−0.404142	−	0.259727i
$262$	−221.165	+	484.284i	−0.844142	+	1.84841i
$263$	25.8435	−	88.0148i	0.0982641	−	0.334657i	−0.895658	−	0.444744i	$-0.853295\pi$
$263$	25.8435	−	88.0148i	0.0982641	−	0.334657i	0.993922	+	0.110087i	$0.0351129\pi$
$264$	−61.4410	+	53.2389i	−0.232731	+	0.201663i
$265$	−11.5189	−	13.2935i	−0.0434674	−	0.0501641i
$266$	−426.346	−	125.186i	−1.60280	−	0.470626i
$267$	107.734	+	49.2005i	0.403498	+	0.184271i
$268$	−75.8940	+	118.093i	−0.283186	+	0.440647i
$269$	−298.432	+	87.6275i	−1.10941	+	0.325753i	−0.784585	−	0.620021i	$-0.787124\pi$
$269$	−298.432	+	87.6275i	−1.10941	+	0.325753i	−0.324826	+	0.945774i	$0.605306\pi$
$270$	71.2173	+	10.2395i	0.263768	+	0.0379241i
$271$	79.9315	+	175.026i	0.294950	+	0.645851i	0.997857	−	0.0654310i	$-0.0208422\pi$
$271$	79.9315	+	175.026i	0.294950	+	0.645851i	−0.702907	+	0.711282i	$0.748115\pi$
$272$	82.9426	−	11.9253i	0.304936	−	0.0438432i
$273$	−16.6286	−	25.8747i	−0.0609108	−	0.0947790i
$274$	3.04951	+	2.64241i	0.0111296	+	0.00964384i
$275$			37.1700i			0.135164i
$276$	−230.728	+	139.577i	−0.835970	+	0.505715i
$277$	234.469			0.846458			0.423229	−	0.906023i	$-0.360896\pi$
$277$	234.469			0.846458			0.423229	+	0.906023i	$0.360896\pi$
$278$	−5.79795	+	6.69119i	−0.0208559	+	0.0240690i
$279$	17.6182	−	11.3225i	0.0631477	−	0.0405826i
$280$	25.1249	+	174.747i	0.0897317	+	0.624097i
$281$	139.559	−	63.7345i	0.496651	−	0.226813i	−0.151310	−	0.988486i	$-0.548349\pi$
$281$	139.559	−	63.7345i	0.496651	−	0.226813i	0.647961	+	0.761673i	$0.275622\pi$
$282$	−60.0351	+	417.553i	−0.212890	+	1.48069i
$283$	−30.1283	−	102.607i	−0.106460	−	0.362570i	0.888981	−	0.457943i	$-0.151414\pi$
$283$	−30.1283	−	102.607i	−0.106460	−	0.362570i	−0.995442	+	0.0953731i	$0.969596\pi$
$284$	366.897	+	235.790i	1.29189	+	0.830248i
$285$	−89.2813	+	195.499i	−0.313268	+	0.685960i
$286$	18.4178	−	62.7252i	0.0643979	−	0.219319i
$287$	−88.6514	+	76.8169i	−0.308890	+	0.267655i
$288$	53.7178	+	61.9936i	0.186520	+	0.215256i
$289$	617.378	+	181.278i	2.13625	+	0.627261i
$290$	−526.428	−	240.412i	−1.81527	−	0.829006i
$291$	62.9827	−	98.0031i	0.216436	−	0.336780i
$292$	−806.330	+	236.760i	−2.76140	+	0.810821i
$293$	−503.446	−	72.3846i	−1.71825	−	0.247046i	−0.788444	−	0.615107i	$-0.789113\pi$
$293$	−503.446	−	72.3846i	−1.71825	−	0.247046i	−0.929802	+	0.368061i	$0.880022\pi$
$294$	−65.6406	−	143.733i	−0.223267	−	0.488887i
$295$	−293.706	+	42.2285i	−0.995613	+	0.143148i
$296$	95.4064	+	148.455i	0.322319	+	0.501538i
$297$	20.2840	+	17.5762i	0.0682964	+	0.0591792i
$298$		−	491.763i		−	1.65021i
$299$	39.0261	−	79.6581i	0.130522	−	0.266415i
$300$	−84.3702			−0.281234
$301$	185.947	−	214.594i	0.617764	−	0.712937i
$302$	−397.420	+	255.406i	−1.31596	+	0.845717i
$303$	19.3429	+	134.533i	0.0638379	+	0.444002i
$304$	73.4067	−	33.5237i	0.241470	−	0.110275i
$305$	42.7358	−	297.234i	0.140117	−	0.974538i
$306$	−84.6951	−	288.445i	−0.276781	−	0.942631i
$307$	15.2565	+	9.80477i	0.0496955	+	0.0319374i	0.565253	−	0.824918i	$-0.308779\pi$
$307$	15.2565	+	9.80477i	0.0496955	+	0.0319374i	−0.515557	+	0.856855i	$0.672415\pi$
$308$	−66.8771	+	146.440i	−0.217133	+	0.475456i
$309$	42.5084	−	144.770i	0.137568	−	0.468513i
$310$	73.0530	−	63.3008i	0.235655	−	0.204196i
$311$	257.083	+	296.689i	0.826632	+	0.953984i	0.999521	−	0.0309570i	$-0.00985549\pi$
$311$	257.083	+	296.689i	0.826632	+	0.953984i	−0.172889	+	0.984941i	$0.555310\pi$
$312$	58.2431	+	17.1017i	0.186677	+	0.0548132i
$313$	486.627	+	222.235i	1.55472	+	0.710017i	0.993088	−	0.117371i	$-0.0374467\pi$
$313$	486.627	+	222.235i	1.55472	+	0.710017i	0.561631	+	0.827388i	$0.310174\pi$
$314$	−194.199	+	302.179i	−0.618467	+	0.962354i
$315$	55.9231	−	16.4205i	0.177534	−	0.0521286i
$316$	355.162	+	51.0646i	1.12393	+	0.161597i
$317$	70.0719	+	153.436i	0.221047	+	0.484026i	0.987370	−	0.158430i	$-0.0506431\pi$
$317$	70.0719	+	153.436i	0.221047	+	0.484026i	−0.766323	+	0.642455i	$0.777916\pi$
$318$	23.4537	−	3.37213i	0.0737537	−	0.0106042i
$319$	−116.716	−	181.613i	−0.365880	−	0.569321i
$320$	321.139	+	278.268i	1.00356	+	0.869589i
$321$			107.805i			0.335843i
$322$	−195.755	+	287.149i	−0.607934	+	0.891768i
$323$	897.989			2.78015
$324$	−39.8953	+	46.0416i	−0.123134	+	0.142104i
$325$	23.3476	−	15.0046i	0.0718388	−	0.0461680i
$326$	33.0829	+	230.097i	0.101481	+	0.705818i
$327$	220.495	−	100.697i	0.674296	−	0.307941i
$328$	32.9467	−	229.150i	0.100447	−	0.698627i
$329$	96.2749	+	327.882i	0.292629	+	0.996602i
$330$	104.215	+	66.9747i	0.315802	+	0.202954i
$331$	214.531	−	469.758i	0.648130	−	1.41921i	−0.245051	−	0.969510i	$-0.578805\pi$
$331$	214.531	−	469.758i	0.648130	−	1.41921i	0.893181	−	0.449697i	$-0.148468\pi$
$332$	169.222	−	576.318i	0.509706	−	1.73590i
$333$	44.0294	−	38.1517i	0.132220	−	0.114570i
$334$	−94.4270	−	108.975i	−0.282716	−	0.326271i
$335$	83.9591	+	24.6526i	0.250624	+	0.0735899i
$336$	−19.9071	−	9.09125i	−0.0592472	−	0.0270573i
$337$	−167.787	+	261.082i	−0.497885	+	0.774724i	−0.995708	−	0.0925549i	$-0.970497\pi$
$337$	−167.787	+	261.082i	−0.497885	+	0.774724i	0.497823	+	0.867279i	$0.334133\pi$
$338$	485.296	−	142.496i	1.43579	−	0.421585i
$339$	−25.9790	−	3.73522i	−0.0766343	−	0.0110183i
$340$	−362.310	−	793.348i	−1.06562	−	2.33338i
$341$	35.6915	−	5.13167i	0.104667	−	0.0150489i
$342$	−156.524	−	243.555i	−0.457671	−	0.712150i
$343$	−267.244	−	231.568i	−0.779138	−	0.675127i
$344$			560.396i			1.62906i
$345$	124.000	+	113.485i	0.359420	+	0.328941i
$346$	−481.704			−1.39221
$347$	−162.218	+	187.209i	−0.467486	+	0.539507i	−0.939711	−	0.341971i	$-0.888906\pi$
$347$	−162.218	+	187.209i	−0.467486	+	0.539507i	0.472225	+	0.881478i	$0.343451\pi$
$348$	412.234	−	264.927i	1.18458	−	0.761284i
$349$	78.3571	+	544.985i	0.224519	+	1.56156i	0.720640	+	0.693309i	$0.243848\pi$
$349$	78.3571	+	544.985i	0.224519	+	1.56156i	−0.496121	+	0.868253i	$0.665243\pi$
$350$	−98.9064	+	45.1691i	−0.282590	+	0.129054i
$351$	2.85199	−	19.8361i	0.00812534	−	0.0565130i
$352$	39.7905	+	135.514i	0.113041	+	0.384983i
$353$	−322.825	−	207.467i	−0.914519	−	0.587726i	−0.00345683	−	0.999994i	$-0.501100\pi$
$353$	−322.825	−	207.467i	−0.914519	−	0.587726i	−0.911063	+	0.412268i	$0.864737\pi$
$354$	166.047	−	363.592i	0.469059	−	1.02710i
$355$	76.5917	−	260.847i	0.215751	−	0.734782i
$356$	−349.812	+	303.113i	−0.982617	+	0.851442i
$357$	−159.474	−	184.043i	−0.446707	−	0.515528i
$358$	−925.499	−	271.751i	−2.58519	−	0.759081i
$359$	−592.825	−	270.734i	−1.65132	−	0.754135i	−0.651335	−	0.758790i	$-0.725791\pi$
$359$	−592.825	−	270.734i	−1.65132	−	0.754135i	−0.999989	+	0.00465566i	$0.998518\pi$
$360$	−62.1889	+	96.7678i	−0.172747	+	0.268800i
$361$	483.402	−	141.940i	1.33906	−	0.393184i
$362$	18.3315	+	2.63568i	0.0506396	+	0.00728087i
$363$	−67.8650	−	148.604i	−0.186956	−	0.409376i
$364$	118.980	−	17.1067i	0.326868	−	0.0469966i
$365$	283.209	+	440.682i	0.775915	+	1.20735i
$366$	305.712	+	264.901i	0.835278	+	0.723773i
$367$		−	203.478i		−	0.554437i	−0.960807	−	0.277218i	$-0.910587\pi$
$367$		−	203.478i		−	0.554437i	0.960807	−	0.277218i	$-0.0894125\pi$
$368$	−7.28295	−	62.6942i	−0.0197906	−	0.170365i
$369$	−76.4290			−0.207125
$370$	176.092	−	203.221i	0.475924	−	0.549245i
$371$	16.1474	−	10.3773i	0.0435239	−	0.0279711i
$372$	11.6481	+	81.0142i	0.0313121	+	0.217780i
$373$	−224.665	+	102.601i	−0.602319	+	0.275070i	−0.693147	−	0.720797i	$-0.743776\pi$
$373$	−224.665	+	102.601i	−0.602319	+	0.275070i	0.0908273	+	0.995867i	$0.471049\pi$
$374$	73.6622	−	512.332i	0.196958	−	1.36987i
$375$	66.2916	+	225.768i	0.176778	+	0.602049i
$376$	−567.358	−	364.619i	−1.50893	−	0.969732i
$377$	−66.9616	+	146.625i	−0.177617	+	0.388927i
$378$	−22.1197	+	75.3328i	−0.0585177	+	0.199293i
$379$	−474.894	+	411.498i	−1.25302	+	1.08575i	−0.260269	+	0.965536i	$0.583811\pi$
$379$	−474.894	+	411.498i	−1.25302	+	1.08575i	−0.992748	+	0.120210i	$0.961643\pi$
$380$	−550.043	−	634.783i	−1.44748	−	1.67048i
$381$	316.712	+	92.9951i	0.831265	+	0.244082i
$382$	−7.28389	−	3.32644i	−0.0190678	−	0.00870796i
$383$	66.3368	−	103.222i	0.173203	−	0.269509i	−0.743789	−	0.668414i	$-0.766973\pi$
$383$	66.3368	−	103.222i	0.173203	−	0.269509i	0.916992	+	0.398905i	$0.130610\pi$
$384$	−367.459	+	107.896i	−0.956924	+	0.280978i
$385$	99.3297	+	14.2815i	0.257999	+	0.0370947i
$386$	284.582	+	623.148i	0.737260	+	1.61437i
$387$	183.125	−	26.3294i	0.473191	−	0.0680346i
$388$	246.145	+	383.009i	0.634394	+	0.987137i
$389$	369.106	+	319.832i	0.948859	+	0.822191i	0.984178	−	0.177185i	$-0.0566991\pi$
$389$	369.106	+	319.832i	0.948859	+	0.822191i	−0.0353185	+	0.999376i	$0.511245\pi$
$390$		−	92.4962i		−	0.237170i
$391$	216.090	−	668.257i	0.552659	−	1.70910i
$392$	252.619			0.644436
$393$	−184.016	+	212.365i	−0.468233	+	0.540370i
$394$	403.083	−	259.046i	1.02305	−	0.657477i
$395$	−31.8308	−	221.388i	−0.0805843	−	0.560476i
$396$	−95.4138	+	43.5740i	−0.240944	+	0.110035i
$397$	−65.0291	+	452.287i	−0.163801	+	1.13926i	0.727585	+	0.686018i	$0.240643\pi$
$397$	−65.0291	+	452.287i	−0.163801	+	1.13926i	−0.891386	+	0.453245i	$0.850266\pi$
$398$	−102.594	−	349.403i	−0.257774	−	0.877897i
$399$	−197.296	−	126.795i	−0.494477	−	0.317781i
$400$	8.20334	−	17.9628i	0.0205084	−	0.0449070i
$401$	−199.938	+	680.928i	−0.498600	+	1.69807i	0.197648	+	0.980273i	$0.436670\pi$
$401$	−199.938	+	680.928i	−0.498600	+	1.69807i	−0.696248	+	0.717802i	$0.745148\pi$
$402$	−89.0833	+	77.1911i	−0.221600	+	0.192018i
$403$	−17.6311	−	20.3474i	−0.0437496	−	0.0504898i
$404$	−509.662	−	149.650i	−1.26154	−	0.370421i
$405$	34.5434	+	15.7755i	0.0852924	+	0.0389517i
$406$	341.425	−	531.268i	0.840949	−	1.30854i
$407$	96.2453	−	28.2602i	0.236475	−	0.0694353i
$408$	475.723	+	68.3986i	1.16599	+	0.167644i
$409$	−79.6292	−	174.364i	−0.194693	−	0.426317i	0.786958	−	0.617007i	$-0.211655\pi$
$409$	−79.6292	−	174.364i	−0.194693	−	0.426317i	−0.981650	+	0.190690i	$0.938928\pi$
$410$	−349.173	+	50.2035i	−0.851641	+	0.122447i
$411$	1.15141	+	1.79164i	0.00280150	+	0.00435921i
$412$	445.641	+	386.150i	1.08165	+	0.937258i
$413$		−	323.794i		−	0.784006i
$414$	−218.912	+	57.8716i	−0.528773	+	0.139786i
$415$	−374.410			−0.902194
$416$	69.0579	−	79.6970i	0.166005	−	0.191579i
$417$	−3.93119	+	2.52642i	−0.00942731	+	0.00605856i
$418$	−70.9405	−	493.402i	−0.169714	−	1.18039i
$419$	135.140	−	61.7164i	0.322530	−	0.147295i	−0.247570	−	0.968870i	$-0.579632\pi$
$419$	135.140	−	61.7164i	0.322530	−	0.147295i	0.570100	+	0.821576i	$0.306905\pi$
$420$	−32.4167	+	225.463i	−0.0771826	+	0.536817i
$421$	−67.7654	−	230.788i	−0.160963	−	0.548189i	−0.999992	−	0.00410201i	$-0.998694\pi$
$421$	−67.7654	−	230.788i	−0.160963	−	0.548189i	0.839029	−	0.544087i	$-0.183124\pi$
$422$	908.115	+	583.610i	2.15193	+	1.38296i
$423$	−92.4929	+	202.531i	−0.218659	+	0.478797i
$424$	−10.6725	+	36.3472i	−0.0251710	+	0.0857246i
$425$	166.069	−	143.899i	0.390749	−	0.338586i
$426$	239.821	+	276.768i	0.562959	+	0.649689i
$427$	314.410	+	92.3192i	0.736324	+	0.216204i
$428$	−383.244	−	175.022i	−0.895431	−	0.408930i
$429$	18.6544	−	29.0268i	0.0434834	−	0.0676614i
$430$	819.328	−	240.576i	1.90541	−	0.559480i
$431$	−131.441	−	18.8984i	−0.304968	−	0.0438477i	−0.0118678	−	0.999930i	$-0.503778\pi$
$431$	−131.441	−	18.8984i	−0.304968	−	0.0438477i	−0.293100	+	0.956082i	$0.594687\pi$
$432$	−5.92344	−	12.9705i	−0.0137117	−	0.0300244i
$433$	−239.029	+	34.3671i	−0.552029	+	0.0793698i	−0.412684	−	0.910874i	$-0.635409\pi$
$433$	−239.029	+	34.3671i	−0.552029	+	0.0793698i	−0.139345	+	0.990244i	$0.544500\pi$
$434$	57.0273	+	88.7362i	0.131399	+	0.204461i
$435$	−230.846	−	200.029i	−0.530681	−	0.459837i
$436$			947.331i			2.17278i
$437$	18.3625	−	676.127i	0.0420194	−	1.54720i
$438$	−705.653			−1.61108
$439$	−380.592	+	439.226i	−0.866951	+	1.00052i	0.133004	+	0.991115i	$0.457538\pi$
$439$	−380.592	+	439.226i	−0.866951	+	1.00052i	−0.999956	+	0.00939989i	$0.997008\pi$
$440$	−166.611	+	107.074i	−0.378662	+	0.243351i
$441$	−11.8689	−	82.5503i	−0.0269137	−	0.187189i
$442$	−351.546	+	160.546i	−0.795354	+	0.363226i
$443$	18.2632	−	127.023i	0.0412261	−	0.286734i	−0.958771	−	0.284181i	$-0.908278\pi$
$443$	18.2632	−	127.023i	0.0412261	−	0.286734i	0.999997	−	0.00255281i	$-0.000812585\pi$
$444$	64.1462	+	218.462i	0.144473	+	0.492031i
$445$	242.723	+	155.988i	0.545444	+	0.350536i
$446$	465.817	−	1020.00i	1.04443	−	2.28699i
$447$	73.1247	−	249.040i	0.163590	−	0.557136i
$448$	−350.434	+	303.653i	−0.782219	+	0.677797i
$449$	−199.737	−	230.509i	−0.444850	−	0.513384i	0.488396	−	0.872622i	$-0.337582\pi$
$449$	−199.737	−	230.509i	−0.444850	−	0.513384i	−0.933246	+	0.359238i	$0.883037\pi$
$450$	−67.9753	−	19.9593i	−0.151056	−	0.0443541i
$451$	−119.701	−	54.6655i	−0.265412	−	0.121210i
$452$	55.4554	−	86.2903i	0.122689	−	0.190908i
$453$	−239.241	+	70.2476i	−0.528126	+	0.155072i
$454$	1045.94	+	150.384i	2.30384	+	0.331242i
$455$	−31.1263	−	68.1570i	−0.0684094	−	0.149796i
$456$	458.145	−	65.8714i	1.00470	−	0.144455i
$457$	−335.136	−	521.481i	−0.733338	−	1.14110i	−0.984878	−	0.173250i	$-0.944573\pi$
$457$	−335.136	−	521.481i	−0.733338	−	1.14110i	0.251540	−	0.967847i	$-0.419063\pi$
$458$	654.994	+	567.555i	1.43012	+	1.23920i
$459$		−	158.669i		−	0.345685i
$460$	−604.747	+	256.573i	−1.31467	+	0.557767i
$461$	−620.443			−1.34586			−0.672931	−	0.739705i	$-0.734965\pi$
$461$	−620.443			−1.34586			−0.672931	+	0.739705i	$0.734965\pi$
$462$	−88.5246	+	102.163i	−0.191612	+	0.221132i
$463$	228.443	−	146.812i	0.493398	−	0.317088i	−0.270173	−	0.962812i	$-0.587081\pi$
$463$	228.443	−	146.812i	0.493398	−	0.317088i	0.763571	+	0.645724i	$0.223444\pi$
$464$	16.3225	+	113.526i	0.0351778	+	0.244667i
$465$	46.4085	−	21.1940i	0.0998032	−	0.0455786i
$466$	−69.9380	+	486.429i	−0.150081	+	1.04384i
$467$	−13.9151	−	47.3905i	−0.0297968	−	0.101479i	0.943252	−	0.332078i	$-0.107750\pi$
$467$	−13.9151	−	47.3905i	−0.0297968	−	0.101479i	−0.973049	+	0.230599i	$0.925931\pi$
$468$	65.8862	+	42.3425i	0.140783	+	0.0904755i
$469$	−39.6663	+	86.8570i	−0.0845763	+	0.185196i
$470$	−289.527	+	986.038i	−0.616014	+	2.09795i
$471$	−143.280	+	124.153i	−0.304205	+	0.263595i
$472$	418.478	+	482.950i	0.886607	+	1.02320i
$473$	305.637	+	89.7430i	0.646166	+	0.189731i
$474$	274.066	+	125.162i	0.578199	+	0.264055i
$475$	114.411	−	178.027i	0.240865	−	0.374794i
$476$	913.173	−	268.132i	1.91843	−	0.563302i
$477$	12.3789	+	1.77982i	0.0259516	+	0.00373127i
$478$	−166.293	−	364.130i	−0.347893	−	0.761779i
$479$	−14.6692	+	2.10911i	−0.0306247	+	0.00440316i	−0.157610	−	0.987501i	$-0.550379\pi$
$479$	−14.6692	+	2.10911i	−0.0306247	+	0.00440316i	0.126985	+	0.991905i	$0.459470\pi$
$480$	108.037	+	168.110i	0.225078	+	0.350228i
$481$	−56.6028	−	49.0466i	−0.117677	−	0.101968i
$482$		−	732.112i		−	1.51890i
$483$	−141.834	+	116.310i	−0.293651	+	0.240808i
$484$	638.459			1.31913
$485$	185.848	−	214.480i	0.383192	−	0.442227i
$486$	−43.0348	+	27.6568i	−0.0885489	+	0.0569069i
$487$	−19.2780	−	134.082i	−0.0395853	−	0.275322i	0.960409	−	0.278593i	$-0.0898679\pi$
$487$	−19.2780	−	134.082i	−0.0395853	−	0.275322i	−0.999995	+	0.00327091i	$0.998959\pi$
$488$	−588.268	+	268.653i	−1.20547	+	0.550519i
$489$	−17.4612	+	121.446i	−0.0357080	+	0.248355i
$490$	−108.449	−	369.342i	−0.221324	−	0.753760i
$491$	92.6139	+	59.5194i	0.188623	+	0.121221i	0.631544	−	0.775340i	$-0.282421\pi$
$491$	92.6139	+	59.5194i	0.188623	+	0.121221i	−0.442921	+	0.896561i	$0.646058\pi$
$492$	124.082	−	271.702i	0.252200	−	0.552240i
$493$	−359.563	+	1224.56i	−0.729336	+	2.48389i
$494$	−281.283	+	243.733i	−0.569400	+	0.493388i
$495$	42.8176	+	49.4141i	0.0865001	+	0.0998264i
$496$	−18.3808	−	5.39710i	−0.0370582	−	0.0108813i
$497$	269.851	+	123.237i	0.542960	+	0.247961i
$498$	272.678	−	424.295i	0.547545	−	0.851997i
$499$	−342.364	+	100.527i	−0.686101	+	0.201457i	−0.606161	−	0.795342i	$-0.707291\pi$
$499$	−342.364	+	100.527i	−0.686101	+	0.201457i	−0.0799403	+	0.996800i	$0.525473\pi$
$500$	−910.223	−	130.870i	−1.82045	−	0.261741i
$501$	−31.6156	−	69.2284i	−0.0631049	−	0.138180i
$502$	575.556	−	82.7525i	1.14653	−	0.164846i
$503$	185.506	+	288.653i	0.368799	+	0.573863i	0.975208	−	0.221290i	$-0.0710268\pi$
$503$	185.506	+	288.653i	0.368799	+	0.573863i	−0.606409	+	0.795153i	$0.707390\pi$
$504$	−94.8627	−	82.1990i	−0.188220	−	0.163093i
$505$			331.106i			0.655656i
$506$	−384.246	−	65.9392i	−0.759379	−	0.130315i
$507$	266.954			0.526536
$508$	−844.775	+	974.922i	−1.66294	+	1.91914i
$509$	260.312	−	167.292i	0.511417	−	0.328668i	−0.259351	−	0.965783i	$-0.583509\pi$
$509$	260.312	−	167.292i	0.511417	−	0.328668i	0.770769	+	0.637115i	$0.219872\pi$
$510$	−104.224	−	724.895i	−0.204361	−	1.42136i
$511$	−519.969	+	237.462i	−1.01755	+	0.464701i
$512$	24.8738	−	173.001i	0.0485816	−	0.337892i
$513$	−43.0506	−	146.617i	−0.0839193	−	0.285803i
$514$	565.789	+	363.611i	1.10076	+	0.707414i
$515$	152.692	−	334.349i	0.296490	−	0.649222i
$516$	−203.703	+	693.748i	−0.394773	+	1.34447i
$517$	−289.719	+	251.043i	−0.560385	+	0.485577i
$518$	192.155	+	221.759i	0.370956	+	0.428106i
$519$	−243.946	−	71.6289i	−0.470030	−	0.138013i
$520$	134.513	+	61.4302i	0.258679	+	0.118135i
$521$	−265.836	+	413.650i	−0.510243	+	0.793953i	−0.996820	−	0.0796843i	$-0.974609\pi$
$521$	−265.836	+	413.650i	−0.510243	+	0.793953i	0.486577	+	0.873637i	$0.338245\pi$
$522$	394.802	−	115.924i	0.756325	−	0.222077i
$523$	−512.936	−	73.7491i	−0.980757	−	0.141012i	−0.366756	−	0.930317i	$-0.619532\pi$
$523$	−512.936	−	73.7491i	−0.980757	−	0.141012i	−0.614001	+	0.789305i	$0.710441\pi$
$524$	−456.202	−	998.943i	−0.870615	−	1.90638i
$525$	−56.8050	+	8.16733i	−0.108200	+	0.0155568i
$526$	162.747	+	253.239i	0.309404	+	0.481442i
$527$	−161.103	−	139.596i	−0.305697	−	0.264888i
$528$		−	24.5508i		−	0.0464976i
$529$	−498.734	−	176.366i	−0.942787	−	0.333395i
$530$	57.7232			0.108912
$531$	138.156	−	159.440i	0.260180	−	0.300264i
$532$	771.059	−	495.530i	1.44936	−	0.931447i
$533$	13.9831	+	97.2546i	0.0262347	+	0.182466i
$534$	−353.543	+	161.458i	−0.662065	+	0.302355i
$535$	−37.3756	+	259.953i	−0.0698609	+	0.485893i
$536$	−53.0922	−	180.816i	−0.0990527	−	0.337343i
$537$	−428.284	−	275.242i	−0.797550	−	0.512554i
$538$	424.009	−	928.450i	0.788120	−	1.72574i
$539$	40.4550	−	137.777i	0.0750556	−	0.255616i
$540$	−112.162	+	97.1892i	−0.207708	+	0.179980i
$541$	−143.036	−	165.073i	−0.264393	−	0.305125i	0.607994	−	0.793941i	$-0.291974\pi$
$541$	−143.036	−	165.073i	−0.264393	−	0.305125i	−0.872387	+	0.488816i	$0.837429\pi$
$542$	−605.853	−	177.894i	−1.11781	−	0.328218i
$543$	8.89158	+	4.06065i	0.0163749	+	0.00747817i
$544$	451.406	−	702.401i	0.829790	−	1.29118i
$545$	566.593	−	166.367i	1.03962	−	0.305260i
$546$	99.9066	+	14.3644i	0.182979	+	0.0263084i
$547$	49.5111	+	108.414i	0.0905139	+	0.198198i	0.949475	−	0.313844i	$-0.101617\pi$
$547$	49.5111	+	108.414i	0.0905139	+	0.198198i	−0.858961	+	0.512041i	$0.828889\pi$
$548$	−8.23852	+	1.18452i	−0.0150338	+	0.00216153i
$549$	115.429	+	179.611i	0.210253	+	0.327160i
$550$	−92.1850	−	79.8788i	−0.167609	−	0.145234i
$551$			1229.10i			2.23067i
$552$	61.2274	−	356.789i	0.110919	−	0.646357i
$553$	244.068			0.441353
$554$	−503.876	+	581.504i	−0.909524	+	1.04965i
$555$	119.396	−	76.7309i	0.215127	−	0.138254i
$556$	−2.59906	−	18.0769i	−0.00467457	−	0.0325123i
$557$	234.588	−	107.133i	0.421163	−	0.192339i	−0.193549	−	0.981091i	$-0.562000\pi$
$557$	234.588	−	107.133i	0.421163	−	0.192339i	0.614711	+	0.788752i	$0.289272\pi$
$558$	−9.78080	+	68.0270i	−0.0175283	+	0.121912i
$559$	−67.0074	−	228.206i	−0.119870	−	0.408240i
$560$	−44.8503	−	28.8235i	−0.0800897	−	0.0514705i
$561$	113.487	−	248.503i	0.202295	−	0.442964i
$562$	−141.847	+	483.085i	−0.252396	+	0.859582i
$563$	278.867	−	241.640i	0.495324	−	0.429200i	−0.371038	−	0.928618i	$-0.620998\pi$
$563$	278.867	−	241.640i	0.495324	−	0.429200i	0.866362	+	0.499417i	$0.166453\pi$
$564$	−569.829	−	657.618i	−1.01034	−	1.16599i
$565$	−61.3485	−	18.0136i	−0.108581	−	0.0318824i
$566$	319.221	+	145.784i	0.563995	+	0.257568i
$567$	−22.4038	+	34.8610i	−0.0395129	+	0.0614833i
$568$	−561.765	+	164.949i	−0.989023	+	0.290403i
$569$	−196.447	−	28.2449i	−0.345250	−	0.0496395i	−0.0324912	−	0.999472i	$-0.510344\pi$
$569$	−196.447	−	28.2449i	−0.345250	−	0.0496395i	−0.312759	+	0.949833i	$0.601253\pi$
$570$	−292.988	−	641.554i	−0.514014	−	1.12553i
$571$	995.240	−	143.094i	1.74298	−	0.250602i	0.804012	−	0.594613i	$-0.202695\pi$
$571$	995.240	−	143.094i	1.74298	−	0.250602i	0.938966	+	0.344011i	$0.111786\pi$
$572$	72.9037	+	113.440i	0.127454	+	0.198322i
$573$	−3.19409	−	2.76769i	−0.00557433	−	0.00483018i
$574$		−	384.943i		−	0.670633i
$575$	−104.951	−	127.981i	−0.182523	−	0.222576i
$576$	−302.120			−0.524513
$577$	471.671	−	544.338i	0.817454	−	0.943393i	−0.181747	−	0.983345i	$-0.558175\pi$
$577$	471.671	−	544.338i	0.817454	−	0.943393i	0.999202	+	0.0399526i	$0.0127207\pi$
$578$	−1776.34	+	1141.58i	−3.07325	+	1.97506i
$579$	51.4573	+	357.893i	0.0888727	+	0.618123i
$580$	1085.87	−	495.902i	1.87220	−	0.855004i
$581$	58.1449	−	404.407i	0.100077	−	0.696053i
$582$	107.706	+	366.812i	0.185062	+	0.630262i
$583$	18.1144	+	11.6414i	0.0310711	+	0.0199682i
$584$	468.650	−	1026.20i	0.802483	−	1.75719i
$585$	13.7541	−	46.8422i	0.0235113	−	0.0800721i
$586$	1261.43	−	1093.04i	2.15261	−	1.86525i
$587$	472.319	+	545.085i	0.804632	+	0.928595i	0.998626	−	0.0524080i	$-0.0166896\pi$
$587$	472.319	+	545.085i	0.804632	+	0.928595i	−0.193994	+	0.981003i	$0.562144\pi$
$588$	312.732	+	91.8265i	0.531858	+	0.156168i
$589$	−186.741	−	85.2818i	−0.317048	−	0.144791i
$590$	526.446	−	819.166i	0.892282	−	1.38842i
$591$	242.650	−	71.2486i	0.410576	−	0.120556i
$592$	−52.7485	−	7.58409i	−0.0891022	−	0.0128110i
$593$	−78.7145	−	172.361i	−0.132740	−	0.290659i	0.831578	−	0.555408i	$-0.187438\pi$
$593$	−78.7145	−	172.361i	−0.132740	−	0.290659i	−0.964317	+	0.264749i	$0.914711\pi$
$594$	−87.1811	+	12.5348i	−0.146770	+	0.0211023i
$595$	−320.736	−	499.075i	−0.539052	−	0.838781i
$596$	766.610	+	664.271i	1.28626	+	1.11455i
$597$		−	192.201i		−	0.321945i
$598$	113.692	+	267.974i	0.190120	+	0.448117i
$599$	−209.738			−0.350148			−0.175074	−	0.984555i	$-0.556016\pi$
$599$	−209.738			−0.350148			−0.175074	+	0.984555i	$0.556016\pi$
$600$	74.1709	−	85.5978i	0.123618	−	0.142663i
$601$	434.471	−	279.218i	0.722914	−	0.464588i	−0.126736	−	0.991937i	$-0.540450\pi$
$601$	434.471	−	279.218i	0.722914	−	0.464588i	0.849649	+	0.527348i	$0.176814\pi$
$602$	132.611	+	922.330i	0.220284	+	1.53211i
$603$	−56.5921	+	25.8447i	−0.0938509	+	0.0428602i
$604$	138.680	−	964.540i	0.229603	−	1.59692i
$605$	−112.124	−	381.858i	−0.185328	−	0.631170i
$606$	−375.221	−	241.140i	−0.619177	−	0.397921i
$607$	10.7697	−	23.5823i	0.0177425	−	0.0388506i	−0.900553	−	0.434746i	$-0.856838\pi$
$607$	10.7697	−	23.5823i	0.0177425	−	0.0388506i	0.918296	+	0.395895i	$0.129566\pi$
$608$	226.540	−	771.525i	0.372599	−	1.26895i
$609$	251.905	−	218.277i	0.413636	−	0.358418i
$610$	645.327	+	744.747i	1.05791	+	1.22090i
$611$	274.640	+	80.6415i	0.449492	+	0.131983i
$612$	564.063	+	257.599i	0.921672	+	0.420913i
$613$	−284.182	+	442.196i	−0.463593	+	0.721364i	−0.991807	−	0.127747i	$-0.959225\pi$
$613$	−284.182	+	442.196i	−0.463593	+	0.721364i	0.528214	+	0.849111i	$0.322862\pi$
$614$	−57.1031	+	16.7670i	−0.0930018	+	0.0273078i
$615$	−184.294	−	26.4975i	−0.299665	−	0.0430854i
$616$	−89.7786	−	196.588i	−0.145744	−	0.319136i
$617$	−316.575	+	45.5167i	−0.513088	+	0.0737709i	−0.393996	−	0.919112i	$-0.628908\pi$
$617$	−316.575	+	45.5167i	−0.513088	+	0.0737709i	−0.119092	+	0.992883i	$0.537998\pi$
$618$	267.693	+	416.538i	0.433159	+	0.674009i
$619$	470.021	+	407.276i	0.759323	+	0.657957i	0.945891	−	0.324485i	$-0.105191\pi$
$619$	470.021	+	407.276i	0.759323	+	0.657957i	−0.186568	+	0.982442i	$0.559736\pi$
$620$			199.389i			0.321595i
$621$	−119.467	−	3.24454i	−0.192379	−	0.00522470i
$622$	−1288.29			−2.07120
$623$	−206.180	+	237.944i	−0.330947	+	0.381933i
$624$	−15.4211	+	9.91051i	−0.0247132	+	0.0158822i
$625$	55.9742	+	389.309i	0.0895588	+	0.622895i
$626$	−1596.93	+	729.293i	−2.55101	+	1.16501i
$627$	37.4426	−	260.419i	0.0597170	−	0.415341i
$628$	−208.745	−	710.919i	−0.332396	−	1.13204i
$629$	−498.863	−	320.600i	−0.793104	−	0.509697i
$630$	−79.4549	+	173.982i	−0.126119	+	0.276162i
$631$	−173.375	+	590.460i	−0.274762	+	0.935753i	0.700305	+	0.713843i	$0.253047\pi$
$631$	−173.375	+	590.460i	−0.274762	+	0.935753i	−0.975067	+	0.221910i	$0.928771\pi$
$632$	−364.035	+	315.438i	−0.576005	+	0.499111i
$633$	373.108	+	430.589i	0.589428	+	0.680236i
$634$	−531.120	−	155.951i	−0.837729	−	0.245980i
$635$	731.451	+	334.042i	1.15189	+	0.526051i
$636$	−26.4243	+	41.1170i	−0.0415476	+	0.0646493i
$637$	−102.872	+	30.2061i	−0.161495	+	0.0474192i
$638$	701.241	+	100.823i	1.09912	+	0.158030i
$639$	80.2955	+	175.823i	0.125658	+	0.275153i
$640$	−923.465	+	132.774i	−1.44291	+	0.207460i
$641$	469.723	+	730.903i	0.732797	+	1.14025i	0.984996	+	0.172579i	$0.0552099\pi$
$641$	469.723	+	730.903i	0.732797	+	1.14025i	−0.252199	+	0.967675i	$0.581154\pi$
$642$	−267.367	−	231.675i	−0.416460	−	0.360865i
$643$			733.530i			1.14079i	0.821369	+	0.570397i	$0.193210\pi$
$643$			733.530i			1.14079i	−0.821369	+	0.570397i	$0.806790\pi$
$644$	−183.213	−	693.042i	−0.284492	−	1.07615i
$645$	450.699			0.698759
$646$	−1929.79	+	2227.09i	−2.98729	+	3.44751i
$647$	−4.85154	+	3.11790i	−0.00749852	+	0.00481901i	−0.544385	−	0.838836i	$-0.683237\pi$
$647$	−4.85154	+	3.11790i	−0.00749852	+	0.00481901i	0.536886	+	0.843655i	$0.319600\pi$
$648$	−11.6391	−	80.9515i	−0.0179615	−	0.124925i
$649$	330.414	−	150.895i	0.509113	−	0.232504i
$650$	−12.9615	+	90.1491i	−0.0199407	+	0.138691i
$651$	15.6849	+	53.4179i	0.0240936	+	0.0820552i
$652$	−403.386	−	259.240i	−0.618690	−	0.397608i
$653$	−1.51126	+	3.30919i	−0.00231433	+	0.00506767i	−0.910786	−	0.412880i	$-0.864523\pi$
$653$	−1.51126	+	3.30919i	−0.00231433	+	0.00506767i	0.908471	+	0.417947i	$0.137250\pi$
$654$	−224.109	+	763.244i	−0.342674	+	1.16704i
$655$	−517.345	+	448.282i	−0.789840	+	0.684400i
$656$	45.7821	+	52.8354i	0.0697898	+	0.0805417i
$657$	−357.359	−	104.930i	−0.543925	−	0.159711i
$658$	−1020.07	−	465.851i	−1.55026	−	0.707981i
$659$	−69.3850	+	107.965i	−0.105288	+	0.163832i	−0.889900	−	0.456156i	$-0.849226\pi$
$659$	−69.3850	+	107.965i	−0.105288	+	0.163832i	0.784612	+	0.619988i	$0.212862\pi$
$660$	−245.179	+	71.9912i	−0.371484	+	0.109078i
$661$	−820.638	−	117.990i	−1.24151	−	0.178502i	−0.509904	−	0.860231i	$-0.670319\pi$
$661$	−820.638	−	117.990i	−1.24151	−	0.178502i	−0.731605	+	0.681729i	$0.761228\pi$
$662$	704.011	+	1541.57i	1.06346	+	2.32866i
$663$	−201.904	+	29.0294i	−0.304531	+	0.0437849i
$664$	435.938	+	678.333i	0.656534	+	1.02159i
$665$	−431.784	−	374.143i	−0.649299	−	0.562621i
$666$			191.185i			0.287065i
$667$	914.659	+	295.767i	1.37130	+	0.443429i
$668$	297.432			0.445258
$669$	387.573	−	447.283i	0.579332	−	0.668584i
$670$	−241.570	+	155.247i	−0.360551	+	0.231712i
$671$	52.3153	+	363.861i	0.0779662	+	0.542267i
$672$	−198.356	+	90.5860i	−0.295172	+	0.134801i
$673$	174.309	−	1212.35i	0.259003	−	1.80141i	−0.280962	−	0.959719i	$-0.590654\pi$
$673$	174.309	−	1212.35i	0.259003	−	1.80141i	0.539965	−	0.841687i	$-0.318437\pi$
$674$	−286.930	−	977.195i	−0.425713	−	1.44984i
$675$	−31.4563	−	20.2157i	−0.0466019	−	0.0299492i
$676$	−433.399	+	949.010i	−0.641122	+	1.40386i
$677$	343.682	−	1170.47i	0.507655	−	1.72891i	−0.162516	−	0.986706i	$-0.551961\pi$
$677$	343.682	−	1170.47i	0.507655	−	1.72891i	0.670171	−	0.742207i	$-0.266221\pi$
$678$	65.0928	−	56.4032i	0.0960071	−	0.0831906i
$679$	202.802	+	234.046i	0.298677	+	0.344692i
$680$	1123.40	+	329.861i	1.65206	+	0.485089i
$681$	507.327	+	231.688i	0.744973	+	0.340218i
$682$	−63.9744	+	99.5461i	−0.0938041	+	0.145962i
$683$	−334.819	+	98.3118i	−0.490219	+	0.143941i	−0.517494	−	0.855687i	$-0.673135\pi$
$683$	−334.819	+	98.3118i	−0.490219	+	0.143941i	0.0272754	+	0.999628i	$0.491317\pi$
$684$	591.110	+	84.9888i	0.864196	+	0.124253i
$685$	2.15527	+	4.71939i	0.00314638	+	0.00688961i
$686$	1148.62	−	165.147i	1.67437	−	0.240739i
$687$	247.309	+	384.820i	0.359983	+	0.560145i
$688$	−127.896	−	110.823i	−0.185895	−	0.161079i
$689$		−	16.0776i		−	0.0233346i
$690$	−547.929	+	63.6509i	−0.794100	+	0.0922477i
$691$	329.151			0.476340			0.238170	−	0.971224i	$-0.423452\pi$
$691$	329.151			0.476340			0.238170	+	0.971224i	$0.423452\pi$
$692$	650.683	−	750.928i	0.940293	−	1.08516i
$693$	−60.0224	+	38.5741i	−0.0866124	+	0.0556624i
$694$	−115.688	−	804.628i	−0.166697	−	1.15941i
$695$	−10.3552	+	4.72907i	−0.0148996	+	0.00680442i
$696$	−93.6188	+	651.133i	−0.134510	+	0.935536i
$697$	219.172	+	746.431i	0.314450	+	1.07092i
$698$	−1520.00	−	976.846i	−2.17765	−	1.39949i
$699$	−107.750	+	235.939i	−0.154148	+	0.337538i
$700$	63.1883	−	215.199i	0.0902689	−	0.307428i
$701$	369.096	−	319.824i	0.526528	−	0.456239i	−0.350580	−	0.936533i	$-0.614015\pi$
$701$	369.096	−	319.824i	0.526528	−	0.456239i	0.877108	+	0.480294i	$0.159470\pi$
$702$	43.0662	+	49.7011i	0.0613479	+	0.0707993i
$703$	−547.956	−	160.894i	−0.779453	−	0.228868i
$704$	−473.171	−	216.090i	−0.672117	−	0.306946i
$705$	−293.246	+	456.299i	−0.415951	+	0.647233i
$706$	1208.29	−	354.787i	1.71146	−	0.502531i
$707$	−357.633	−	51.4199i	−0.505846	−	0.0727297i
$708$	342.508	+	749.989i	0.483769	+	1.05931i
$709$	954.934	−	137.299i	1.34687	−	0.193651i	0.569138	−	0.822242i	$-0.307277\pi$
$709$	954.934	−	137.299i	1.34687	−	0.193651i	0.777736	+	0.628591i	$0.216368\pi$
$710$	482.329	+	750.518i	0.679336	+	1.05707i
$711$	120.182	+	104.138i	0.169032	+	0.146467i
$712$		−	621.372i		−	0.872714i
$713$	−108.401	+	118.445i	−0.152035	+	0.166122i
$714$	799.156			1.11927
$715$	55.0449	−	63.5252i	0.0769859	−	0.0888465i
$716$	1673.79	−	1075.68i	2.33770	−	1.50235i
$717$	−30.0686	−	209.131i	−0.0419366	−	0.291676i
$718$	1945.43	−	888.449i	2.70952	−	1.23739i
$719$	93.6874	−	651.610i	0.130302	−	0.906273i	−0.814857	−	0.579662i	$-0.803184\pi$
$719$	93.6874	−	651.610i	0.130302	−	0.906273i	0.945159	−	0.326610i	$-0.105906\pi$
$720$	−9.78646	−	33.3296i	−0.0135923	−	0.0462911i
$721$	337.423	+	216.849i	0.467994	+	0.300761i
$722$	−686.812	+	1503.91i	−0.951263	+	2.08298i
$723$	108.864	−	370.758i	0.150573	−	0.512805i
$724$	−28.8709	+	25.0168i	−0.0398769	+	0.0345535i
$725$	196.958	+	227.302i	0.271667	+	0.313520i
$726$	514.393	+	151.039i	0.708530	+	0.208043i
$727$	−838.537	−	382.947i	−1.15342	−	0.526750i	−0.255457	−	0.966820i	$-0.582226\pi$
$727$	−838.537	−	382.947i	−1.15342	−	0.526750i	−0.897963	+	0.440071i	$0.854953\pi$
$728$	−87.2412	+	135.750i	−0.119837	+	0.186470i
$729$	−25.9063	+	7.60678i	−0.0355368	+	0.0104345i
$730$	−1701.55	−	244.646i	−2.33089	−	0.335131i
$731$	−782.280	−	1712.95i	−1.07015	−	2.34330i
$732$	−825.908	+	118.748i	−1.12829	+	0.162224i
$733$	−295.774	−	460.234i	−0.403512	−	0.627877i	0.578725	−	0.815523i	$-0.303551\pi$
$733$	−295.774	−	460.234i	−0.403512	−	0.627877i	−0.982237	+	0.187646i	$0.939914\pi$
$734$	504.644	+	437.277i	0.687526	+	0.595745i
$735$		−	203.169i		−	0.276421i
$736$	−519.631	−	354.242i	−0.706021	−	0.481307i
$737$	−107.118			−0.145343
$738$	164.247	−	189.551i	0.222556	−	0.256844i
$739$	124.675	−	80.1240i	0.168708	−	0.108422i	−0.453562	−	0.891225i	$-0.649847\pi$
$739$	124.675	−	80.1240i	0.168708	−	0.108422i	0.622270	+	0.782803i	$0.286211\pi$
$740$	78.9370	+	549.019i	0.106672	+	0.741918i
$741$	−178.691	+	81.6056i	−0.241149	+	0.110129i
$742$	−8.96425	+	62.3478i	−0.0120812	+	0.0840266i
$743$	−45.5986	−	155.294i	−0.0613709	−	0.209010i	0.923099	−	0.384562i	$-0.125647\pi$
$743$	−45.5986	−	155.294i	−0.0613709	−	0.209010i	−0.984470	+	0.175551i	$0.943829\pi$
$744$	−92.4329	−	59.4030i	−0.124238	−	0.0798428i
$745$	262.667	−	575.161i	0.352574	−	0.772028i
$746$	228.348	−	777.680i	0.306096	−	1.04247i
$747$	201.182	−	174.325i	0.269320	−	0.233367i
$748$	699.172	+	806.887i	0.934722	+	1.07873i
$749$	−274.975	−	80.7399i	−0.367123	−	0.107797i
$750$	−702.387	−	320.770i	−0.936516	−	0.427693i
$751$	−18.4195	+	28.6613i	−0.0245266	+	0.0381642i	−0.853300	−	0.521420i	$-0.825403\pi$
$751$	−18.4195	+	28.6613i	−0.0245266	+	0.0381642i	0.828774	+	0.559584i	$0.189039\pi$
$752$	195.414	−	57.3789i	0.259860	−	0.0763017i
$753$	303.780	+	43.6769i	0.403426	+	0.0580039i
$754$	−219.743	−	481.170i	−0.291436	−	0.638156i
$755$	−601.240	+	86.4452i	−0.796344	+	0.114497i
$756$	−87.5571	−	136.242i	−0.115816	−	0.180214i
$757$	−882.392	−	764.597i	−1.16564	−	1.01004i	−0.999714	−	0.0238984i	$-0.992392\pi$
$757$	−882.392	−	764.597i	−1.16564	−	1.01004i	−0.165929	−	0.986138i	$-0.553062\pi$
$758$		−	2062.09i		−	2.72044i
$759$	−184.786	−	90.5301i	−0.243459	−	0.119275i
$760$	1127.57			1.48364
$761$	−634.985	+	732.812i	−0.834409	+	0.962959i	−0.999729	−	0.0232809i	$-0.992589\pi$
$761$	−634.985	+	732.812i	−0.834409	+	0.962959i	0.165320	+	0.986240i	$0.447134\pi$
$762$	−911.253	+	585.627i	−1.19587	+	0.768539i
$763$	91.7049	+	637.822i	0.120190	+	0.835940i
$764$	15.0246	−	6.86152i	0.0196658	−	0.00898105i
$765$	55.0097	−	382.601i	0.0719081	−	0.500132i
$766$	113.441	+	386.346i	0.148096	+	0.504368i
$767$	−228.161	−	146.630i	−0.297472	−	0.191174i
$768$	232.240	−	508.536i	0.302396	−	0.662156i
$769$	216.732	−	738.122i	0.281837	−	0.959847i	−0.689925	−	0.723881i	$-0.742356\pi$
$769$	216.732	−	738.122i	0.281837	−	0.959847i	0.971761	−	0.235966i	$-0.0758254\pi$
$770$	−248.880	+	215.656i	−0.323221	+	0.280072i
$771$	232.460	+	268.273i	0.301504	+	0.347955i
$772$	−1355.84	−	398.110i	−1.75627	−	0.515687i
$773$	912.978	+	416.943i	1.18108	+	0.539383i	0.906511	−	0.422183i	$-0.138736\pi$
$773$	912.978	+	416.943i	1.18108	+	0.539383i	0.274574	+	0.961566i	$0.411463\pi$
$774$	−328.238	+	510.748i	−0.424080	+	0.659881i
$775$	−48.2008	+	14.1530i	−0.0621946	+	0.0182620i
$776$	−604.971	−	86.9817i	−0.779602	−	0.112090i
$777$	64.3364	+	140.877i	0.0828011	+	0.181309i
$778$	−1586.43	+	228.094i	−2.03911	+	0.293179i
$779$	405.047	+	630.266i	0.519958	+	0.809071i
$780$	144.192	+	124.943i	0.184862	+	0.160184i
$781$			332.799i			0.426119i
$782$	1192.96	+	1972.01i	1.52552	+	2.52175i
$783$	217.174			0.277362
$784$	−49.9573	+	57.6538i	−0.0637211	+	0.0735381i
$785$	−388.537	+	249.698i	−0.494952	+	0.318086i
$786$	−131.234	−	912.750i	−0.166964	−	1.16126i
$787$	946.737	−	432.360i	1.20297	−	0.549378i	0.289851	−	0.957072i	$-0.406394\pi$
$787$	946.737	−	432.360i	1.20297	−	0.549378i	0.913118	+	0.407694i	$0.133667\pi$
$788$	−140.656	+	978.285i	−0.178498	+	1.24148i
$789$	44.7622	+	152.446i	0.0567328	+	0.193214i
$790$	617.467	+	396.822i	0.781603	+	0.502306i
$791$	28.9840	−	63.4661i	0.0366422	−	0.0802352i
$792$	39.6715	−	135.109i	0.0500902	−	0.170592i
$793$	207.433	−	179.742i	0.261581	−	0.226661i
$794$	−981.964	−	1133.25i	−1.23673	−	1.42726i
$795$	29.2323	+	8.58339i	0.0367702	+	0.0107967i
$796$	683.268	+	312.038i	0.858377	+	0.392008i
$797$	−420.911	+	654.951i	−0.528119	+	0.821770i	−0.998145	−	0.0608830i	$-0.980608\pi$
$797$	−420.911	+	654.951i	−0.528119	+	0.821770i	0.470026	+	0.882653i	$0.344245\pi$
$798$	738.453	−	216.829i	0.925380	−	0.271716i
$799$	2243.22	+	322.527i	2.80754	+	0.403663i
$800$	−81.7388	−	178.983i	−0.102174	−	0.223729i
$801$	−203.051	+	29.1943i	−0.253496	+	0.0364473i
$802$	−1259.09	−	1959.19i	−1.56994	−	2.44288i
$803$	−484.633	−	419.937i	−0.603529	−	0.522961i
$804$		−	243.141i		−	0.302415i
$805$	−382.329	+	231.288i	−0.474943	+	0.287314i
$806$	88.3527			0.109619
$807$	352.787	−	407.138i	0.437159	−	0.504508i
$808$	599.878	−	385.518i	0.742423	−	0.477126i
$809$	−34.2728	−	238.372i	−0.0423644	−	0.294651i	−0.999978	−	0.00659565i	$-0.997901\pi$
$809$	−34.2728	−	238.372i	−0.0423644	−	0.294651i	0.957614	−	0.288055i	$-0.0930086\pi$
$810$	−113.359	+	51.7692i	−0.139949	+	0.0639126i
$811$	−100.457	+	698.695i	−0.123868	+	0.861523i	0.829240	+	0.558893i	$0.188774\pi$
$811$	−100.457	+	698.695i	−0.123868	+	0.861523i	−0.953108	+	0.302630i	$0.902135\pi$
$812$	366.999	+	1249.88i	0.451969	+	1.53926i
$813$	−280.365	−	180.179i	−0.344852	−	0.221623i
$814$	−136.744	+	299.428i	−0.167991	+	0.367848i
$815$	−84.2090	+	286.789i	−0.103324	+	0.351889i
$816$	−109.688	+	95.0452i	−0.134422	+	0.116477i
$817$	−1187.62	−	1370.59i	−1.45364	−	1.67759i
$818$	603.562	+	177.222i	0.737850	+	0.216652i
$819$	48.4590	+	22.1305i	0.0591685	+	0.0270213i
$820$	393.399	−	612.140i	0.479754	−	0.746512i
$821$	−618.781	+	181.691i	−0.753692	+	0.221304i	−0.635939	−	0.771739i	$-0.719387\pi$
$821$	−618.781	+	181.691i	−0.753692	+	0.221304i	−0.117753	+	0.993043i	$0.537569\pi$
$822$	−6.91782	−	0.994632i	−0.00841584	−	0.00121002i
$823$	435.683	+	954.014i	0.529384	+	1.15919i	0.965763	+	0.259427i	$0.0835337\pi$
$823$	435.683	+	954.014i	0.529384	+	1.15919i	−0.436378	+	0.899763i	$0.643739\pi$
$824$	−783.538	+	112.656i	−0.950895	+	0.136718i
$825$	−34.8067	−	54.1602i	−0.0421899	−	0.0656488i
$826$	803.039	+	695.837i	0.972202	+	0.842418i
$827$			301.454i			0.364515i	0.983251	+	0.182257i	$0.0583404\pi$
$827$			301.454i			0.364515i	−0.983251	+	0.182257i	$0.941660\pi$
$828$	205.489	−	419.435i	0.248175	−	0.506564i
$829$	−201.015			−0.242479			−0.121239	−	0.992623i	$-0.538687\pi$
$829$	−201.015			−0.242479			−0.121239	+	0.992623i	$0.538687\pi$
$830$	804.612	−	928.571i	0.969412	−	1.11876i
$831$	−341.643	+	219.561i	−0.411123	+	0.264213i
$832$	55.2745	+	384.442i	0.0664356	+	0.462070i
$833$	−772.177	+	352.642i	−0.926983	+	0.423339i
$834$	2.18241	−	15.1790i	0.00261680	−	0.0182002i
$835$	−52.2339	−	177.892i	−0.0625556	−	0.213045i
$836$	864.991	+	555.896i	1.03468	+	0.664947i
$837$	−15.0688	+	32.9960i	−0.0180033	+	0.0394218i
$838$	−137.355	+	467.789i	−0.163908	+	0.558220i
$839$	−31.0414	+	26.8975i	−0.0369981	+	0.0320590i	−0.673164	−	0.739494i	$-0.735065\pi$
$839$	−31.0414	+	26.8975i	−0.0369981	+	0.0320590i	0.636165	+	0.771553i	$0.280520\pi$
$840$	−200.246	−	231.096i	−0.238388	−	0.275114i
$841$	−869.148	−	255.205i	−1.03347	−	0.303454i
$842$	718.002	+	327.901i	0.852734	+	0.389431i
$843$	−143.669	+	223.553i	−0.170425	+	0.265187i
$844$	−2136.47	+	627.323i	−2.53136	+	0.743274i
$845$	643.709	+	92.5514i	0.761786	+	0.109528i
$846$	−303.527	−	664.632i	−0.358779	−	0.785617i
$847$	429.864	−	61.8050i	0.507513	−	0.0729694i
$848$	−6.18476	−	9.62367i	−0.00729334	−	0.0113487i
$849$	139.983	+	121.296i	0.164880	+	0.142869i
$850$			721.105i			0.848359i
$851$	−251.591	+	369.055i	−0.295642	+	0.433672i
$852$	−755.402			−0.886622
$853$	63.4712	−	73.2497i	0.0744094	−	0.0858731i	−0.717324	−	0.696740i	$-0.754633\pi$
$853$	63.4712	−	73.2497i	0.0744094	−	0.0858731i	0.791734	+	0.610866i	$0.209179\pi$
$854$	−904.631	+	581.371i	−1.05929	+	0.680762i
$855$	−52.9772	−	368.464i	−0.0619616	−	0.430953i
$856$	514.484	−	234.957i	0.601032	−	0.274482i
$857$	−73.0856	+	508.322i	−0.0852808	+	0.593141i	0.901707	+	0.432347i	$0.142315\pi$
$857$	−73.0856	+	508.322i	−0.0852808	+	0.593141i	−0.986988	+	0.160794i	$0.948595\pi$
$858$	31.9005	+	108.643i	0.0371801	+	0.126624i
$859$	264.914	+	170.250i	0.308398	+	0.198195i	0.685680	−	0.727903i	$-0.259505\pi$
$859$	264.914	+	170.250i	0.308398	+	0.198195i	−0.377282	+	0.926098i	$0.623141\pi$
$860$	−731.709	+	1602.22i	−0.850825	+	1.86305i
$861$	57.2407	−	194.944i	0.0664817	−	0.226416i
$862$	329.338	−	285.373i	0.382062	−	0.331059i
$863$	−348.751	−	402.481i	−0.404115	−	0.466374i	0.516817	−	0.856096i	$-0.327117\pi$
$863$	−348.751	−	402.481i	−0.404115	−	0.466374i	−0.920933	+	0.389722i	$0.872571\pi$
$864$	−136.324	−	40.0282i	−0.157782	−	0.0463290i
$865$	−563.396	−	257.294i	−0.651325	−	0.297450i
$866$	428.441	−	666.667i	0.494736	−	0.769824i
$867$	−1069.33	+	313.983i	−1.23337	+	0.362149i
$868$	−215.363	−	30.9645i	−0.248114	−	0.0356734i
$869$	113.741	+	249.058i	0.130887	+	0.286603i
$870$	992.181	−	142.654i	1.14044	−	0.163970i
$871$	43.2408	+	67.2840i	0.0496450	+	0.0772492i
$872$	−961.115	−	832.811i	−1.10220	−	0.955058i
$873$			201.778i			0.231132i
$874$	1637.39	+	1498.54i	1.87345	+	1.71458i
$875$	−625.506			−0.714864
$876$	953.193	−	1100.04i	1.08812	−	1.25576i
$877$	247.461	−	159.034i	0.282168	−	0.181338i	−0.391900	−	0.920008i	$-0.628182\pi$
$877$	247.461	−	159.034i	0.282168	−	0.181338i	0.674068	+	0.738670i	$0.264546\pi$
$878$	−271.425	−	1887.80i	−0.309140	−	2.15012i
$879$	801.350	−	365.964i	0.911661	−	0.416342i
$880$	8.51161	−	59.1996i	0.00967229	−	0.0672722i
$881$	−193.170	−	657.877i	−0.219262	−	0.746739i	−0.993499	−	0.113843i	$-0.963684\pi$
$881$	−193.170	−	657.877i	−0.219262	−	0.746739i	0.774236	−	0.632896i	$-0.218134\pi$
$882$	230.239	+	147.965i	0.261041	+	0.167761i
$883$	−35.6843	+	78.1377i	−0.0404126	+	0.0884912i	−0.928762	−	0.370678i	$-0.879125\pi$
$883$	−35.6843	+	78.1377i	−0.0404126	+	0.0884912i	0.888349	+	0.459169i	$0.151853\pi$
$884$	224.592	−	764.890i	0.254063	−	0.865260i
$885$	388.413	−	336.562i	0.438885	−	0.380296i
$886$	275.781	+	318.268i	0.311265	+	0.359219i
$887$	1493.82	+	438.624i	1.68412	+	0.494503i	0.977117	−	0.212704i	$-0.0682271\pi$
$887$	1493.82	+	438.624i	1.68412	+	0.494503i	0.707006	+	0.707207i	$0.250045\pi$
$888$	−278.032	−	126.973i	−0.313099	−	0.142988i
$889$	−474.397	+	738.176i	−0.533630	+	0.830344i
$890$	−908.479	+	266.753i	−1.02076	+	0.299723i
$891$	−46.0144	−	6.61587i	−0.0516435	−	0.00742522i
$892$	960.850	+	2103.97i	1.07719	+	2.35871i
$893$	2160.34	−	310.610i	2.41919	−	0.347828i
$894$	460.495	+	716.545i	0.515096	+	0.801504i
$895$	−937.303	−	812.178i	−1.04727	−	0.907461i
$896$		−	1018.07i		−	1.13624i
$897$	17.7286	+	152.614i	0.0197643	+	0.170138i
$898$	1000.92			1.11461
$899$	191.069	−	220.505i	0.212535	−	0.245278i
$900$	122.935	−	79.0057i	0.136595	−	0.0877842i
$901$	−18.1161	−	126.000i	−0.0201067	−	0.139845i
$902$	392.813	−	179.392i	0.435492	−	0.198882i
$903$	−69.9924	+	486.808i	−0.0775109	+	0.539100i
$904$	38.7943	+	132.121i	0.0429140	+	0.146152i
$905$	20.0326	+	12.8741i	0.0221354	+	0.0142256i
$906$	339.911	−	744.302i	0.375178	−	0.821526i
$907$	−129.780	+	441.989i	−0.143087	+	0.487309i	−0.999584	−	0.0288429i	$-0.990818\pi$
$907$	−129.780	+	441.989i	−0.143087	+	0.487309i	0.856497	+	0.516152i	$0.172636\pi$
$908$	−1647.29	+	1427.38i	−1.81419	+	1.57201i
$909$	−154.163	−	177.914i	−0.169596	−	0.195725i
$910$	235.926	+	69.2741i	0.259259	+	0.0761254i
$911$	−1033.97	−	472.200i	−1.13499	−	0.518332i	−0.242836	−	0.970067i	$-0.578078\pi$
$911$	−1033.97	−	472.200i	−1.13499	−	0.518332i	−0.892152	+	0.451736i	$0.850805\pi$
$912$	−75.5683	+	117.587i	−0.0828600	+	0.128933i
$913$	439.771	−	129.128i	0.481677	−	0.141433i
$914$	2013.53	+	289.502i	2.20299	+	0.316742i
$915$	216.065	+	473.116i	0.236137	+	0.517067i
$916$	−1769.52	+	254.419i	−1.93180	+	0.277750i
$917$	−403.854	−	628.410i	−0.440408	−	0.685289i
$918$	393.514	+	340.982i	0.428664	+	0.371440i
$919$			967.326i			1.05259i	0.850303	+	0.526293i	$0.176418\pi$
$919$			967.326i			1.05259i	−0.850303	+	0.526293i	$0.823582\pi$
$920$	271.335	−	839.103i	0.294930	−	0.912068i
$921$	−31.4115			−0.0341059
$922$	1333.34	−	1538.75i	1.44614	−	1.66893i
$923$	209.041	−	134.342i	0.226480	−	0.145550i
$924$	−39.6831	−	276.002i	−0.0429471	−	0.298704i
$925$	−127.118	+	58.0529i	−0.137425	+	0.0627599i
$926$	−126.821	+	882.060i	−0.136956	+	0.952548i
$927$	73.6268	+	250.750i	0.0794248	+	0.270496i
$928$	961.394	+	617.850i	1.03598	+	0.665787i
$929$	−90.9921	+	199.245i	−0.0979463	+	0.214473i	−0.952262	−	0.305282i	$-0.901249\pi$
$929$	−90.9921	+	199.245i	−0.0979463	+	0.214473i	0.854316	+	0.519754i	$0.173977\pi$
$930$	−47.1692	+	160.643i	−0.0507195	+	0.172735i
$931$	−617.844	+	535.365i	−0.663634	+	0.575043i
$932$	−663.823	−	766.093i	−0.712256	−	0.821988i
$933$	−652.418	−	191.567i	−0.699269	−	0.205324i
$934$	147.436	+	67.3319i	0.157855	+	0.0720899i
$935$	359.808	−	559.873i	0.384822	−	0.598794i
$936$	−100.880	+	29.6211i	−0.107778	+	0.0316464i
$937$	1605.41	+	230.823i	1.71335	+	0.246342i	0.927965	−	0.372667i	$-0.121557\pi$
$937$	1605.41	+	230.823i	1.71335	+	0.246342i	0.785383	+	0.619010i	$0.212466\pi$
$938$	−130.170	−	285.033i	−0.138774	−	0.303873i
$939$	−917.166	+	131.869i	−0.976748	+	0.140435i
$940$	−1146.04	−	1783.28i	−1.21920	−	1.89710i
$941$	317.280	+	274.925i	0.337174	+	0.292163i	0.806946	−	0.590625i	$-0.201119\pi$
$941$	317.280	+	274.925i	0.337174	+	0.292163i	−0.469773	+	0.882787i	$0.655664\pi$
$942$		−	622.154i		−	0.660461i
$943$	566.495	−	149.759i	0.600737	−	0.158811i
$944$	−192.978			−0.204426
$945$	−66.1087	+	76.2936i	−0.0699563	+	0.0807339i
$946$	−879.386	+	565.147i	−0.929584	+	0.597407i
$947$	198.062	+	1377.55i	0.209147	+	1.45465i	0.775951	+	0.630794i	$0.217271\pi$
$947$	198.062	+	1377.55i	0.209147	+	1.45465i	−0.566804	+	0.823853i	$0.691820\pi$
$948$	−565.322	+	258.174i	−0.596332	+	0.272336i
$949$	−68.1409	+	473.930i	−0.0718029	+	0.499400i
$950$	195.652	+	666.331i	0.205950	+	0.701401i
$951$	−245.782	−	157.954i	−0.258445	−	0.166093i
$952$	−530.749	+	1162.18i	−0.557510	+	1.22078i
$953$	154.287	−	525.453i	0.161896	−	0.551367i	−0.838087	−	0.545536i	$-0.816326\pi$
$953$	154.287	−	525.453i	0.161896	−	0.551367i	0.999983	−	0.00583040i	$-0.00185589\pi$
$954$	−31.0165	+	26.8759i	−0.0325120	+	0.0281718i
$955$	−6.74240	−	7.78115i	−0.00706011	−	0.00814780i
$956$	792.270	+	232.632i	0.828735	+	0.243338i
$957$	340.132	+	155.333i	0.355415	+	0.162312i
$958$	26.2935	−	40.9135i	0.0274462	−	0.0427072i
$959$	−5.43219	+	1.59504i	−0.00566443	+	0.00166323i
$960$	−728.505	−	104.743i	−0.758859	−	0.109107i
$961$	−378.969	−	829.827i	−0.394349	−	0.863503i
$962$	243.280	−	34.9784i	0.252890	−	0.0363600i
$963$	−100.951	−	157.083i	−0.104830	−	0.163118i
$964$	1141.29	+	988.933i	1.18391	+	1.02586i
$965$			880.833i			0.912780i
$966$	16.3415	−	601.712i	0.0169167	−	0.622890i
$967$	511.536			0.528993			0.264496	−	0.964387i	$-0.414794\pi$
$967$	511.536			0.528993			0.264496	+	0.964387i	$0.414794\pi$
$968$	−561.277	+	647.748i	−0.579832	+	0.669162i
$969$	−1308.45	+	840.893i	−1.35031	+	0.867794i
$970$	132.541	+	921.840i	0.136640	+	0.950351i
$971$	−228.413	+	104.313i	−0.235234	+	0.107428i	−0.529545	−	0.848282i	$-0.677637\pi$
$971$	−228.413	+	104.313i	−0.235234	+	0.107428i	0.294311	+	0.955710i	$0.404910\pi$
$972$	15.0170	−	104.446i	0.0154496	−	0.107454i
$973$	−3.49981	−	11.9192i	−0.00359692	−	0.0122500i
$974$	373.963	+	240.332i	0.383946	+	0.246747i
$975$	−19.9691	+	43.7262i	−0.0204811	+	0.0448474i
$976$	55.0214	−	187.386i	0.0563743	−	0.191993i
$977$	−214.707	+	186.045i	−0.219762	+	0.190425i	−0.757783	−	0.652507i	$-0.773717\pi$
$977$	−214.707	+	186.045i	−0.219762	+	0.190425i	0.538021	+	0.842931i	$0.319172\pi$
$978$	−263.671	−	304.293i	−0.269603	−	0.311138i
$979$	−338.893	−	99.5079i	−0.346162	−	0.101642i
$980$	722.260	+	329.845i	0.737000	+	0.336576i
$981$	−226.987	+	353.199i	−0.231384	+	0.360040i
$982$	−346.642	+	101.783i	−0.352995	+	0.103649i
$983$	178.154	+	25.6146i	0.181235	+	0.0260576i	0.232334	−	0.972636i	$-0.425364\pi$
$983$	178.154	+	25.6146i	0.181235	+	0.0260576i	−0.0510999	+	0.998694i	$0.516273\pi$
$984$	166.573	+	364.744i	0.169282	+	0.370675i
$985$	609.807	−	87.6771i	0.619094	−	0.0890122i
$986$	−2264.31	−	3523.33i	−2.29646	−	3.57336i
$987$	−447.316	−	387.601i	−0.453208	−	0.392707i
$988$		−	767.727i		−	0.777052i
$989$	−1305.74	+	553.978i	−1.32026	+	0.560139i
$990$	−214.567			−0.216734
$991$	1176.92	−	1358.24i	1.18761	−	1.37058i	0.275158	−	0.961399i	$-0.411270\pi$
$991$	1176.92	−	1358.24i	1.18761	−	1.37058i	0.912454	−	0.409178i	$-0.134185\pi$
$992$	−160.579	+	103.198i	−0.161874	+	0.104030i
$993$	127.297	+	885.372i	0.128195	+	0.891613i
$994$	−885.551	+	404.417i	−0.890896	+	0.406859i
$995$	66.6351	−	463.457i	0.0669699	−	0.465786i
$996$	293.102	+	998.213i	0.294279	+	1.00222i
$997$	273.717	+	175.907i	0.274540	+	0.176436i	0.670665	−	0.741760i	$-0.266009\pi$
$997$	273.717	+	175.907i	0.274540	+	0.176436i	−0.396125	+	0.918197i	$0.629645\pi$
$998$	486.428	−	1065.13i	0.487402	−	1.06726i
$999$	−28.4290	+	96.8204i	−0.0284575	+	0.0969173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.3.f.a.7.2	✓	80
3.2	odd	2		207.3.j.b.145.7		80
23.10	odd	22	inner	69.3.f.a.10.2	yes	80
69.56	even	22		207.3.j.b.10.7		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.3.f.a.7.2	✓	80	1.1	even	1	trivial
69.3.f.a.10.2	yes	80	23.10	odd	22	inner
207.3.j.b.10.7		80	69.56	even	22
207.3.j.b.145.7		80	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14901 + 2.48009i) q^{2} +(-1.45709 + 0.936417i) q^{3} +(-0.963341 - 6.70018i) q^{4} +(-3.83816 + 1.75283i) q^{5} +(0.808910 - 5.62609i) q^{6} +(-1.29720 - 4.41787i) q^{7} +(7.64456 + 4.91286i) q^{8} +(1.24625 - 2.72890i) q^{9} +O(q^{10})\)	\(q+(-2.14901 + 2.48009i) q^{2} +(-1.45709 + 0.936417i) q^{3} +(-0.963341 - 6.70018i) q^{4} +(-3.83816 + 1.75283i) q^{5} +(0.808910 - 5.62609i) q^{6} +(-1.29720 - 4.41787i) q^{7} +(7.64456 + 4.91286i) q^{8} +(1.24625 - 2.72890i) q^{9} +(3.90107 - 13.2858i) q^{10} +(3.90366 - 3.38254i) q^{11} +(7.67785 + 8.86071i) q^{12} +(-3.70048 - 1.08656i) q^{13} +(13.7444 + 6.27686i) q^{14} +(3.95118 - 6.14816i) q^{15} +(-2.63301 + 0.773120i) q^{16} +(-30.2251 - 4.34571i) q^{17} +(4.08971 + 8.95522i) q^{18} +(-29.1083 + 4.18514i) q^{19} +(15.4417 + 24.0278i) q^{20} +(6.02711 + 5.22252i) q^{21} +16.9505i q^{22} +(-3.89009 + 22.6686i) q^{23} -15.7393 q^{24} +(-4.71246 + 5.43847i) q^{25} +(10.6471 - 6.84250i) q^{26} +(0.739490 + 5.14326i) q^{27} +(-28.3509 + 12.9474i) q^{28} +(5.94808 - 41.3698i) q^{29} +(6.75685 + 23.0117i) q^{30} +(5.87274 + 3.77418i) q^{31} +(-11.3587 + 24.8722i) q^{32} +(-2.52053 + 8.58414i) q^{33} +(75.7318 - 65.6219i) q^{34} +(12.7226 + 14.6827i) q^{35} +(-19.4847 - 5.72121i) q^{36} +(17.6648 + 8.06725i) q^{37} +(52.1745 - 81.1851i) q^{38} +(6.40942 - 1.88198i) q^{39} +(-37.9524 - 5.45674i) q^{40} +(-10.5832 - 23.1741i) q^{41} +(-25.9046 + 3.72453i) q^{42} +(33.3409 + 51.8795i) q^{43} +(-26.4242 - 22.8967i) q^{44} +12.6584i q^{45} +(-47.8604 - 58.3629i) q^{46} -74.2173 q^{47} +(3.11257 - 3.59210i) q^{48} +(23.3866 - 15.0297i) q^{49} +(-3.36077 - 23.3746i) q^{50} +(48.1102 - 21.9712i) q^{51} +(-3.71532 + 25.8406i) q^{52} +(1.17447 + 3.99987i) q^{53} +(-14.3449 - 9.21892i) q^{54} +(-9.05386 + 19.8252i) q^{55} +(11.7878 - 40.1456i) q^{56} +(38.4945 - 33.3557i) q^{57} +(89.8183 + 103.656i) q^{58} +(67.4746 + 19.8123i) q^{59} +(-45.0001 - 20.5509i) q^{60} +(-38.4763 + 59.8703i) q^{61} +(-21.9809 + 6.45417i) q^{62} +(-13.6725 - 1.96581i) q^{63} +(-41.8350 - 91.6059i) q^{64} +(16.1076 - 2.31592i) q^{65} +(-15.8728 - 24.6985i) q^{66} +(-15.6728 - 13.5806i) q^{67} +206.700i q^{68} +(-15.5591 - 36.6731i) q^{69} -63.7555 q^{70} +(-42.1926 + 48.6929i) q^{71} +(22.9337 - 14.7386i) q^{72} +(-17.6682 - 122.885i) q^{73} +(-57.9693 + 26.4737i) q^{74} +(1.77382 - 12.3372i) q^{75} +(56.0825 + 190.999i) q^{76} +(-20.0075 - 12.8580i) q^{77} +(-9.10644 + 19.9403i) q^{78} +(-14.9340 + 50.8606i) q^{79} +(8.75075 - 7.58257i) q^{80} +(-5.89375 - 6.80175i) q^{81} +(80.2173 + 23.5539i) q^{82} +(80.7154 + 36.8615i) q^{83} +(29.1857 - 45.4138i) q^{84} +(123.626 - 36.2999i) q^{85} +(-200.316 - 28.8011i) q^{86} +(30.0725 + 65.8496i) q^{87} +(46.4597 - 6.67990i) q^{88} +(-36.9688 - 57.5246i) q^{89} +(-31.3939 - 27.2030i) q^{90} +17.7577i q^{91} +(155.632 + 4.22670i) q^{92} -12.0913 q^{93} +(159.494 - 184.065i) q^{94} +(104.387 - 67.0851i) q^{95} +(-6.73998 - 46.8776i) q^{96} +(-61.1812 + 27.9405i) q^{97} +(-12.9831 + 90.2998i) q^{98} +(-4.36569 - 14.8682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} - 12 q^{6} - 4 q^{8} - 24 q^{9}+O(q^{10}) \) 80 * q + 4 * q^2 - 12 * q^6 - 4 * q^8 - 24 * q^9	\( 80 q + 4 q^{2} - 12 q^{6} - 4 q^{8} - 24 q^{9} + 8 q^{13} - 208 q^{16} - 110 q^{17} + 12 q^{18} - 66 q^{19} - 176 q^{20} - 8 q^{23} - 12 q^{24} + 244 q^{25} + 328 q^{26} + 528 q^{28} + 50 q^{29} + 182 q^{31} + 428 q^{32} - 242 q^{34} - 536 q^{35} - 198 q^{36} - 352 q^{37} - 770 q^{38} - 216 q^{39} - 110 q^{40} - 208 q^{41} - 330 q^{42} - 88 q^{43} - 154 q^{44} - 72 q^{46} + 24 q^{47} + 360 q^{48} + 256 q^{49} + 726 q^{50} + 264 q^{51} + 506 q^{52} + 352 q^{53} + 162 q^{54} - 38 q^{55} + 1210 q^{56} + 528 q^{57} - 306 q^{58} + 776 q^{59} + 330 q^{60} - 308 q^{61} + 392 q^{62} - 288 q^{64} - 22 q^{67} - 108 q^{69} + 344 q^{70} - 80 q^{71} - 12 q^{72} + 46 q^{73} - 374 q^{74} + 72 q^{75} - 946 q^{76} - 728 q^{77} - 144 q^{78} - 572 q^{79} - 2178 q^{80} - 72 q^{81} - 820 q^{82} - 704 q^{83} - 922 q^{85} - 1100 q^{86} + 192 q^{87} - 528 q^{88} - 264 q^{89} + 330 q^{92} + 24 q^{93} + 874 q^{94} + 622 q^{95} - 468 q^{96} + 792 q^{97} - 724 q^{98} - 330 q^{99}+O(q^{100}) \) 80 * q + 4 * q^2 - 12 * q^6 - 4 * q^8 - 24 * q^9 + 8 * q^13 - 208 * q^16 - 110 * q^17 + 12 * q^18 - 66 * q^19 - 176 * q^20 - 8 * q^23 - 12 * q^24 + 244 * q^25 + 328 * q^26 + 528 * q^28 + 50 * q^29 + 182 * q^31 + 428 * q^32 - 242 * q^34 - 536 * q^35 - 198 * q^36 - 352 * q^37 - 770 * q^38 - 216 * q^39 - 110 * q^40 - 208 * q^41 - 330 * q^42 - 88 * q^43 - 154 * q^44 - 72 * q^46 + 24 * q^47 + 360 * q^48 + 256 * q^49 + 726 * q^50 + 264 * q^51 + 506 * q^52 + 352 * q^53 + 162 * q^54 - 38 * q^55 + 1210 * q^56 + 528 * q^57 - 306 * q^58 + 776 * q^59 + 330 * q^60 - 308 * q^61 + 392 * q^62 - 288 * q^64 - 22 * q^67 - 108 * q^69 + 344 * q^70 - 80 * q^71 - 12 * q^72 + 46 * q^73 - 374 * q^74 + 72 * q^75 - 946 * q^76 - 728 * q^77 - 144 * q^78 - 572 * q^79 - 2178 * q^80 - 72 * q^81 - 820 * q^82 - 704 * q^83 - 922 * q^85 - 1100 * q^86 + 192 * q^87 - 528 * q^88 - 264 * q^89 + 330 * q^92 + 24 * q^93 + 874 * q^94 + 622 * q^95 - 468 * q^96 + 792 * q^97 - 724 * q^98 - 330 * q^99

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