LMFDB - Embedded newform 270.3.n.a.29.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,3,Mod(29,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1, 9]))

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

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

chi := DirichletCharacter("270.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$270 = 2 \cdot 3^{3} \cdot 5$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	270.n (of order $18$ , degree $6$ , 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:	$7.35696713773$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.13
Character	$\chi$	$=$	270.29
Dual form			270.3.n.a.149.13

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.245576 + 1.39273i) q^{2} +(2.40493 - 1.79340i) q^{3} +(-1.87939 - 0.684040i) q^{4} +(-0.604237 - 4.96336i) q^{5} +(1.90713 + 3.78983i) q^{6} +(-0.969685 - 2.66419i) q^{7} +(1.41421 - 2.44949i) q^{8} +(2.56740 - 8.62603i) q^{9} +(7.06099 + 0.377342i) q^{10} +(-3.78736 + 4.51360i) q^{11} +(-5.74656 + 1.72543i) q^{12} +(-19.1057 + 3.36884i) q^{13} +(3.94862 - 0.696248i) q^{14} +(-10.3545 - 10.8529i) q^{15} +(3.06418 + 2.57115i) q^{16} +(-9.30170 - 16.1110i) q^{17} +(11.3832 + 5.69404i) q^{18} +(12.9387 - 22.4105i) q^{19} +(-2.25954 + 9.74138i) q^{20} +(-7.10999 - 4.66815i) q^{21} +(-5.35614 - 6.38320i) q^{22} +(5.78829 + 2.10677i) q^{23} +(-0.991836 - 8.42711i) q^{24} +(-24.2698 + 5.99808i) q^{25} -27.4363i q^{26} +(-9.29553 - 25.3494i) q^{27} +5.67034i q^{28} +(42.4651 + 7.48774i) q^{29} +(17.6579 - 11.7557i) q^{30} +(-2.89434 - 1.05345i) q^{31} +(-4.33340 + 3.63616i) q^{32} +(-1.01364 + 17.6472i) q^{33} +(24.7225 - 8.99827i) q^{34} +(-12.6374 + 6.42269i) q^{35} +(-10.7257 + 14.4554i) q^{36} +(-38.1014 + 21.9979i) q^{37} +(28.0343 + 23.5236i) q^{38} +(-39.9061 + 42.3660i) q^{39} +(-13.0122 - 5.53917i) q^{40} +(25.5078 - 4.49771i) q^{41} +(8.24751 - 8.75590i) q^{42} +(27.5555 - 32.8394i) q^{43} +(10.2054 - 5.89209i) q^{44} +(-44.3654 - 7.53077i) q^{45} +(-4.35562 + 7.54415i) q^{46} +(48.0223 - 17.4787i) q^{47} +(11.9803 + 0.688135i) q^{48} +(31.3786 - 26.3298i) q^{49} +(-2.39363 - 35.2742i) q^{50} +(-51.2635 - 22.0642i) q^{51} +(38.2113 + 6.73768i) q^{52} +79.0831 q^{53} +(37.5876 - 6.72095i) q^{54} +(24.6911 + 16.0707i) q^{55} +(-7.89724 - 1.39250i) q^{56} +(-9.07436 - 77.1001i) q^{57} +(-20.8568 + 57.3035i) q^{58} +(26.8467 + 31.9947i) q^{59} +(12.0362 + 27.4796i) q^{60} +(-19.4515 + 7.07975i) q^{61} +(2.17795 - 3.77233i) q^{62} +(-25.4709 + 1.52449i) q^{63} +(-4.00000 - 6.92820i) q^{64} +(28.2651 + 92.7926i) q^{65} +(-24.3288 - 5.74544i) q^{66} +(-80.8056 + 14.2482i) q^{67} +(6.46089 + 36.6415i) q^{68} +(17.6987 - 5.31412i) q^{69} +(-5.84163 - 19.1777i) q^{70} +(63.5462 - 36.6884i) q^{71} +(-17.4985 - 18.4879i) q^{72} +(-39.5979 - 22.8619i) q^{73} +(-21.2803 - 58.4671i) q^{74} +(-47.6102 + 57.9505i) q^{75} +(-39.6465 + 33.2674i) q^{76} +(15.6976 + 5.71347i) q^{77} +(-49.2044 - 65.9824i) q^{78} +(-22.1937 + 125.867i) q^{79} +(10.9100 - 16.7622i) q^{80} +(-67.8169 - 44.2930i) q^{81} +36.6300i q^{82} +(-10.1086 + 57.3286i) q^{83} +(10.1692 + 13.6368i) q^{84} +(-74.3443 + 55.9025i) q^{85} +(38.9694 + 46.4419i) q^{86} +(115.554 - 58.1495i) q^{87} +(5.69988 + 15.6603i) q^{88} +(-58.8126 - 33.9555i) q^{89} +(21.3834 - 59.9396i) q^{90} +(27.5017 + 47.6343i) q^{91} +(-9.43732 - 7.91885i) q^{92} +(-8.84996 + 2.65724i) q^{93} +(12.5500 + 71.1743i) q^{94} +(-119.049 - 50.6782i) q^{95} +(-3.90044 + 16.5163i) q^{96} +(7.37891 - 8.79384i) q^{97} +(28.9644 + 50.1678i) q^{98} +(29.2108 + 44.2582i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$216 q - 18 q^{5} + 12 q^{6} + 12 q^{9} - 36 q^{11} + 36 q^{14} + 18 q^{15} - 72 q^{20} + 360 q^{21} + 18 q^{25} - 36 q^{29} + 144 q^{30} + 180 q^{31} + 486 q^{35} - 192 q^{36} + 348 q^{39} - 72 q^{41} + 258 q^{45}+ \cdots - 1008 q^{99}+O(q^{100})$ 216 * q - 18 * q^5 + 12 * q^6 + 12 * q^9 - 36 * q^11 + 36 * q^14 + 18 * q^15 - 72 * q^20 + 360 * q^21 + 18 * q^25 - 36 * q^29 + 144 * q^30 + 180 * q^31 + 486 * q^35 - 192 * q^36 + 348 * q^39 - 72 * q^41 + 258 * q^45 - 72 * q^49 - 288 * q^50 - 312 * q^51 - 360 * q^54 - 72 * q^56 - 612 * q^59 - 36 * q^60 - 144 * q^61 - 864 * q^64 - 234 * q^65 + 336 * q^69 + 288 * q^74 + 642 * q^75 + 72 * q^79 + 636 * q^81 - 216 * q^84 + 432 * q^86 - 1620 * q^89 - 240 * q^90 - 504 * q^94 + 108 * q^95 - 1008 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$ .

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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

)

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

$2$	−0.245576	+	1.39273i	−0.122788	+	0.696364i
$2$	−0.245576	+	1.39273i	−0.122788	+	0.696364i
$3$	2.40493	−	1.79340i	0.801644	−	0.597801i
$3$	2.40493	−	1.79340i	0.801644	−	0.597801i
$4$	−1.87939	−	0.684040i	−0.469846	−	0.171010i
$5$	−0.604237	−	4.96336i	−0.120847	−	0.992671i
$5$	−0.604237	−	4.96336i	−0.120847	−	0.992671i
$6$	1.90713	+	3.78983i	0.317855	+	0.631639i
$7$	−0.969685	−	2.66419i	−0.138526	−	0.380598i	0.850959	−	0.525232i	$-0.176022\pi$
$7$	−0.969685	−	2.66419i	−0.138526	−	0.380598i	−0.989485	+	0.144634i	$0.953799\pi$
$8$	1.41421	−	2.44949i	0.176777	−	0.306186i
$9$	2.56740	−	8.62603i	0.285267	−	0.958448i
$10$	7.06099	+	0.377342i	0.706099	+	0.0377342i
$11$	−3.78736	+	4.51360i	−0.344306	+	0.410328i	−0.910212	−	0.414142i	$-0.864082\pi$
$11$	−3.78736	+	4.51360i	−0.344306	+	0.410328i	0.565907	+	0.824469i	$0.308526\pi$
$12$	−5.74656	+	1.72543i	−0.478880	+	0.143786i
$13$	−19.1057	+	3.36884i	−1.46967	+	0.259142i	−0.850440	−	0.526072i	$-0.823664\pi$
$13$	−19.1057	+	3.36884i	−1.46967	+	0.259142i	−0.619225	+	0.785213i	$0.712553\pi$
$14$	3.94862	−	0.696248i	0.282044	−	0.0497320i
$15$	−10.3545	−	10.8529i	−0.690297	−	0.723526i
$16$	3.06418	+	2.57115i	0.191511	+	0.160697i
$17$	−9.30170	−	16.1110i	−0.547159	−	0.947707i	−0.998468	−	0.0553388i	$-0.982376\pi$
$17$	−9.30170	−	16.1110i	−0.547159	−	0.947707i	0.451309	−	0.892368i	$-0.350957\pi$
$18$	11.3832	+	5.69404i	0.632402	+	0.316336i
$19$	12.9387	−	22.4105i	0.680985	−	1.17950i	−0.293695	−	0.955899i	$-0.594885\pi$
$19$	12.9387	−	22.4105i	0.680985	−	1.17950i	0.974681	−	0.223602i	$-0.0717815\pi$
$20$	−2.25954	+	9.74138i	−0.112977	+	0.487069i
$21$	−7.10999	−	4.66815i	−0.338571	−	0.222293i
$22$	−5.35614	−	6.38320i	−0.243461	−	0.290145i
$23$	5.78829	+	2.10677i	0.251665	+	0.0915986i	0.464772	−	0.885430i	$-0.346136\pi$
$23$	5.78829	+	2.10677i	0.251665	+	0.0915986i	−0.213107	+	0.977029i	$0.568358\pi$
$24$	−0.991836	−	8.42711i	−0.0413265	−	0.351130i
$25$	−24.2698	+	5.99808i	−0.970792	+	0.239923i
$26$		−	27.4363i		−	1.05524i
$27$	−9.29553	−	25.3494i	−0.344279	−	0.938867i
$28$			5.67034i			0.202512i
$29$	42.4651	+	7.48774i	1.46431	+	0.258198i	0.848291	−	0.529531i	$-0.177632\pi$
$29$	42.4651	+	7.48774i	1.46431	+	0.258198i	0.616022	+	0.787729i	$0.288743\pi$
$30$	17.6579	−	11.7557i	0.588598	−	0.391858i
$31$	−2.89434	−	1.05345i	−0.0933658	−	0.0339824i	0.294915	−	0.955524i	$-0.404709\pi$
$31$	−2.89434	−	1.05345i	−0.0933658	−	0.0339824i	−0.388281	+	0.921541i	$0.626931\pi$
$32$	−4.33340	+	3.63616i	−0.135419	+	0.113630i
$33$	−1.01364	+	17.6472i	−0.0307163	+	0.534763i
$34$	24.7225	−	8.99827i	0.727133	−	0.264655i
$35$	−12.6374	+	6.42269i	−0.361068	+	0.183505i
$36$	−10.7257	+	14.4554i	−0.297936	+	0.401540i
$37$	−38.1014	+	21.9979i	−1.02977	+	0.594537i	−0.916918	−	0.399075i	$-0.869331\pi$
$37$	−38.1014	+	21.9979i	−1.02977	+	0.594537i	−0.112850	+	0.993612i	$0.535998\pi$
$38$	28.0343	+	23.5236i	0.737746	+	0.619042i
$39$	−39.9061	+	42.3660i	−1.02323	+	1.08631i
$40$	−13.0122	−	5.53917i	−0.325305	−	0.138479i
$41$	25.5078	−	4.49771i	0.622141	−	0.109700i	0.146313	−	0.989238i	$-0.453259\pi$
$41$	25.5078	−	4.49771i	0.622141	−	0.109700i	0.475828	+	0.879538i	$0.342148\pi$
$42$	8.24751	−	8.75590i	0.196369	−	0.208474i
$43$	27.5555	−	32.8394i	0.640826	−	0.763706i	−0.343675	−	0.939089i	$-0.611672\pi$
$43$	27.5555	−	32.8394i	0.640826	−	0.763706i	0.984500	+	0.175382i	$0.0561162\pi$
$44$	10.2054	−	5.89209i	0.231941	−	0.133911i
$45$	−44.3654	−	7.53077i	−0.985897	−	0.167351i
$46$	−4.35562	+	7.54415i	−0.0946873	+	0.164003i
$47$	48.0223	−	17.4787i	1.02175	−	0.371887i	0.223816	−	0.974631i	$-0.428148\pi$
$47$	48.0223	−	17.4787i	1.02175	−	0.371887i	0.797934	+	0.602745i	$0.205926\pi$
$48$	11.9803	+	0.688135i	0.249589	+	0.0143362i
$49$	31.3786	−	26.3298i	0.640379	−	0.537342i
$50$	−2.39363	−	35.2742i	−0.0478726	−	0.705484i
$51$	−51.2635	−	22.0642i	−1.00517	−	0.432631i
$52$	38.2113	+	6.73768i	0.734833	+	0.129571i
$53$	79.0831			1.49213			0.746067	−	0.665871i	$-0.231940\pi$
$53$	79.0831			1.49213			0.746067	+	0.665871i	$0.231940\pi$
$54$	37.5876	−	6.72095i	0.696067	−	0.124462i
$55$	24.6911	+	16.0707i	0.448929	+	0.292195i
$56$	−7.89724	−	1.39250i	−0.141022	−	0.0248660i
$57$	−9.07436	−	77.1001i	−0.159199	−	1.35263i
$58$	−20.8568	+	57.3035i	−0.359600	+	0.987992i
$59$	26.8467	+	31.9947i	0.455029	+	0.542283i	0.943969	−	0.330035i	$-0.107061\pi$
$59$	26.8467	+	31.9947i	0.455029	+	0.542283i	−0.488940	+	0.872318i	$0.662616\pi$
$60$	12.0362	+	27.4796i	0.200603	+	0.457994i
$61$	−19.4515	+	7.07975i	−0.318876	+	0.116061i	−0.496499	−	0.868037i	$-0.665381\pi$
$61$	−19.4515	+	7.07975i	−0.318876	+	0.116061i	0.177623	+	0.984099i	$0.443159\pi$
$62$	2.17795	−	3.77233i	0.0351283	−	0.0608440i
$63$	−25.4709	+	1.52449i	−0.404300	+	0.0241982i
$64$	−4.00000	−	6.92820i	−0.0625000	−	0.108253i
$65$	28.2651	+	92.7926i	0.434848	+	1.42758i
$66$	−24.3288	−	5.74544i	−0.368618	−	0.0870522i
$67$	−80.8056	+	14.2482i	−1.20605	+	0.212660i	−0.740313	−	0.672262i	$-0.765323\pi$
$67$	−80.8056	+	14.2482i	−1.20605	+	0.212660i	−0.465740	+	0.884922i	$0.654212\pi$
$68$	6.46089	+	36.6415i	0.0950131	+	0.538846i
$69$	17.6987	−	5.31412i	0.256504	−	0.0770162i
$70$	−5.84163	−	19.1777i	−0.0834518	−	0.273967i
$71$	63.5462	−	36.6884i	0.895018	−	0.516739i	0.0194371	−	0.999811i	$-0.493813\pi$
$71$	63.5462	−	36.6884i	0.895018	−	0.516739i	0.875580	+	0.483072i	$0.160479\pi$
$72$	−17.4985	−	18.4879i	−0.243035	−	0.256776i
$73$	−39.5979	−	22.8619i	−0.542437	−	0.313176i	0.203629	−	0.979048i	$-0.434726\pi$
$73$	−39.5979	−	22.8619i	−0.542437	−	0.313176i	−0.746066	+	0.665872i	$0.768060\pi$
$74$	−21.2803	−	58.4671i	−0.287571	−	0.790096i
$75$	−47.6102	+	57.9505i	−0.634803	+	0.772674i
$76$	−39.6465	+	33.2674i	−0.521665	+	0.437729i
$77$	15.6976	+	5.71347i	0.203865	+	0.0742009i
$78$	−49.2044	−	65.9824i	−0.630825	−	0.845929i
$79$	−22.1937	+	125.867i	−0.280933	+	1.59325i	0.438528	+	0.898717i	$0.355500\pi$
$79$	−22.1937	+	125.867i	−0.280933	+	1.59325i	−0.719461	+	0.694532i	$0.755611\pi$
$80$	10.9100	−	16.7622i	0.136376	−	0.209527i
$81$	−67.8169	−	44.2930i	−0.837245	−	0.546827i
$82$			36.6300i			0.446707i
$83$	−10.1086	+	57.3286i	−0.121790	+	0.690706i	0.861373	+	0.507973i	$0.169605\pi$
$83$	−10.1086	+	57.3286i	−0.121790	+	0.690706i	−0.983163	+	0.182732i	$0.941506\pi$
$84$	10.1692	+	13.6368i	0.121062	+	0.162343i
$85$	−74.3443	+	55.9025i	−0.874638	+	0.657676i
$86$	38.9694	+	46.4419i	0.453132	+	0.540022i
$87$	115.554	−	58.1495i	1.32821	−	0.668386i
$88$	5.69988	+	15.6603i	0.0647714	+	0.177958i
$89$	−58.8126	−	33.9555i	−0.660816	−	0.381522i	0.131772	−	0.991280i	$-0.457933\pi$
$89$	−58.8126	−	33.9555i	−0.660816	−	0.381522i	−0.792588	+	0.609758i	$0.791267\pi$
$90$	21.3834	−	59.9396i	0.237593	−	0.665995i
$91$	27.5017	+	47.6343i	0.302216	+	0.523454i
$92$	−9.43732	−	7.91885i	−0.102580	−	0.0860745i
$93$	−8.84996	+	2.65724i	−0.0951609	+	0.0285724i
$94$	12.5500	+	71.1743i	0.133510	+	0.757174i
$95$	−119.049	−	50.6782i	−1.25315	−	0.533455i
$96$	−3.90044	+	16.5163i	−0.0406296	+	0.172044i
$97$	7.37891	−	8.79384i	0.0760712	−	0.0906582i	−0.726667	−	0.686990i	$-0.758931\pi$
$97$	7.37891	−	8.79384i	0.0760712	−	0.0906582i	0.802738	+	0.596332i	$0.203376\pi$
$98$	28.9644	+	50.1678i	0.295555	+	0.511916i
$99$	29.2108	+	44.2582i	0.295059	+	0.447052i
$100$	49.7152	+	5.32881i	0.497152	+	0.0532881i
$101$	1.22241	+	3.35854i	0.0121030	+	0.0332528i	0.945597	−	0.325340i	$-0.105479\pi$
$101$	1.22241	+	3.35854i	0.0121030	+	0.0332528i	−0.933494	+	0.358593i	$0.883257\pi$
$102$	43.3185	−	65.9777i	0.424691	−	0.646840i
$103$	−32.5731	−	38.8192i	−0.316244	−	0.376885i	0.584383	−	0.811478i	$-0.301337\pi$
$103$	−32.5731	−	38.8192i	−0.316244	−	0.376885i	−0.900627	+	0.434593i	$0.856892\pi$
$104$	−18.7675	+	51.5634i	−0.180457	+	0.495802i
$105$	−18.8736	+	38.1101i	−0.179748	+	0.362953i
$106$	−19.4209	+	110.141i	−0.183216	+	1.03907i
$107$	−147.825			−1.38155			−0.690773	−	0.723072i	$-0.742730\pi$
$107$	−147.825			−1.38155			−0.690773	+	0.723072i	$0.742730\pi$
$108$	0.129851	+	53.9998i	0.00120232	+	0.499999i
$109$	204.770			1.87862			0.939311	−	0.343067i	$-0.111466\pi$
$109$	204.770			1.87862			0.939311	+	0.343067i	$0.111466\pi$
$110$	−28.4457	+	30.4414i	−0.258597	+	0.276740i
$111$	−52.1803	+	121.235i	−0.470093	+	1.09220i
$112$	3.87874	−	10.6567i	0.0346316	−	0.0951495i
$113$	84.4070	−	70.8259i	0.746965	−	0.626778i	−0.187734	−	0.982220i	$-0.560114\pi$
$113$	84.4070	−	70.8259i	0.746965	−	0.626778i	0.934698	+	0.355442i	$0.115670\pi$
$114$	109.608	+	6.29579i	0.961474	+	0.0552262i
$115$	6.95913	−	30.0023i	0.0605142	−	0.260890i
$116$	−74.6863	−	43.1202i	−0.643848	−	0.371726i
$117$	−19.9922	+	173.455i	−0.170873	+	1.48252i
$118$	−51.1528	+	29.5331i	−0.433498	+	0.250280i
$119$	−33.9030	+	40.4041i	−0.284899	+	0.339530i
$120$	−41.2275	+	10.0148i	−0.343562	+	0.0834567i
$121$	14.9829	+	84.9724i	0.123826	+	0.702252i
$122$	−5.08337	−	28.8292i	−0.0416669	−	0.236305i
$123$	53.2783	−	56.5625i	0.433157	−	0.459857i
$124$	4.71898	+	3.95969i	0.0380563	+	0.0319330i
$125$	44.4353	+	116.835i	0.355482	+	0.934683i
$126$	4.13184	−	35.8485i	0.0327924	−	0.284512i
$127$	20.9898	+	12.1185i	0.165274	+	0.0954211i	0.580356	−	0.814363i	$-0.302914\pi$
$127$	20.9898	+	12.1185i	0.165274	+	0.0954211i	−0.415081	+	0.909784i	$0.636247\pi$
$128$	10.6314	−	3.86952i	0.0830579	−	0.0302306i
$129$	7.37488	−	128.395i	0.0571696	−	0.995307i
$130$	−136.176	+	16.5780i	−1.04751	+	0.127523i
$131$	16.3365	−	44.8842i	0.124706	−	0.342628i	−0.861592	−	0.507602i	$-0.830532\pi$
$131$	16.3365	−	44.8842i	0.124706	−	0.342628i	0.986298	+	0.164974i	$0.0527542\pi$
$132$	13.9764	−	32.4725i	0.105882	−	0.246004i
$133$	−72.2523	−	12.7400i	−0.543250	−	0.0957896i
$134$		−	116.039i		−	0.865964i
$135$	−120.201	+	61.4541i	−0.890381	+	0.455215i
$136$	−52.6183			−0.386900
$137$	−32.7562	+	185.770i	−0.239097	+	1.35598i	0.594715	+	0.803936i	$0.297265\pi$
$137$	−32.7562	+	185.770i	−0.239097	+	1.35598i	−0.833812	+	0.552048i	$0.813846\pi$
$138$	3.05474	+	25.9546i	0.0221358	+	0.188077i
$139$	−144.890	−	52.7356i	−1.04237	−	0.379393i	−0.236594	−	0.971609i	$-0.576031\pi$
$139$	−144.890	−	52.7356i	−1.04237	−	0.379393i	−0.805780	+	0.592216i	$0.798253\pi$
$140$	28.1439	−	3.42622i	0.201028	−	0.0244730i
$141$	84.1440	−	128.158i	0.596766	−	0.908925i
$142$	35.4916	+	97.5124i	0.249941	+	0.686707i
$143$	57.1544	−	98.9944i	0.399681	−	0.692268i
$144$	30.0458	−	19.8305i	0.208651	−	0.137712i
$145$	11.5054	−	215.294i	0.0793473	−	1.48478i
$146$	41.5647	−	49.5348i	0.284689	−	0.339280i
$147$	28.2435	−	119.596i	0.192133	−	0.813577i
$148$	86.6547	−	15.2796i	0.585505	−	0.103240i
$149$	259.946	−	45.8354i	1.74460	−	0.307620i	0.791702	−	0.610907i	$-0.209195\pi$
$149$	259.946	−	45.8354i	1.74460	−	0.307620i	0.952899	+	0.303287i	$0.0980841\pi$
$150$	−69.0174	−	80.5394i	−0.460116	−	0.536929i
$151$	4.92565	+	4.13311i	0.0326202	+	0.0273716i	0.658952	−	0.752185i	$-0.271000\pi$
$151$	4.92565	+	4.13311i	0.0326202	+	0.0273716i	−0.626332	+	0.779557i	$0.715444\pi$
$152$	−36.5962	−	63.3865i	−0.240765	−	0.417017i
$153$	−162.855	+	38.8733i	−1.06441	+	0.254074i
$154$	−11.8123	+	20.4594i	−0.0767030	+	0.132854i
$155$	−3.47980	+	15.0022i	−0.0224503	+	0.0967882i
$156$	103.979	−	52.3246i	0.666532	−	0.335414i
$157$	154.374	+	183.976i	0.983273	+	1.17182i	0.985128	+	0.171821i	$0.0549650\pi$
$157$	154.374	+	183.976i	0.983273	+	1.17182i	−0.00185544	+	0.999998i	$0.500591\pi$
$158$	−169.848	−	61.8196i	−1.07499	−	0.391263i
$159$	190.190	−	141.828i	1.19616	−	0.892000i
$160$	20.6659	+	19.3111i	0.129162	+	0.120694i
$161$		−	17.4640i		−	0.108472i
$162$	78.3423	−	83.5732i	0.483595	−	0.515884i
$163$		−	148.438i		−	0.910664i	−0.890322	−	0.455332i	$-0.849521\pi$
$163$		−	148.438i		−	0.910664i	0.890322	−	0.455332i	$-0.150479\pi$
$164$	−51.0156	−	8.99542i	−0.311071	−	0.0548501i
$165$	88.2017	−	5.63202i	0.534556	−	0.0341335i
$166$	−77.3607	−	28.1570i	−0.466028	−	0.169620i
$167$	22.8506	−	19.1739i	0.136830	−	0.114814i	−0.571804	−	0.820390i	$-0.693756\pi$
$167$	22.8506	−	19.1739i	0.136830	−	0.114814i	0.708634	+	0.705576i	$0.249312\pi$
$168$	−21.4896	+	10.8141i	−0.127914	+	0.0643695i
$169$	194.869	−	70.9265i	1.15307	−	0.419683i
$170$	−59.5999	−	117.270i	−0.350587	−	0.689821i
$171$	−160.095	−	169.147i	−0.936228	−	0.989162i
$172$	−74.2509	+	42.8688i	−0.431691	+	0.249237i
$173$	−66.9511	−	56.1787i	−0.387001	−	0.324732i	0.428443	−	0.903569i	$-0.359062\pi$
$173$	−66.9511	−	56.1787i	−0.387001	−	0.324732i	−0.815443	+	0.578837i	$0.803507\pi$
$174$	52.6092	+	175.216i	0.302352	+	1.00699i
$175$	39.5141	+	58.8430i	0.225795	+	0.336246i
$176$	−23.2103	+	4.09260i	−0.131877	+	0.0232534i
$177$	121.944	+	28.7980i	0.688949	+	0.162701i
$178$	61.7337	−	73.5714i	0.346819	−	0.413322i
$179$	165.373	−	95.4783i	0.923873	−	0.533398i	0.0390041	−	0.999239i	$-0.487581\pi$
$179$	165.373	−	95.4783i	0.923873	−	0.533398i	0.884868	+	0.465841i	$0.154248\pi$
$180$	78.2283	+	44.5009i	0.434602	+	0.247227i
$181$	153.791	−	266.374i	0.849674	−	1.47168i	−0.0318253	−	0.999493i	$-0.510132\pi$
$181$	153.791	−	266.374i	0.849674	−	1.47168i	0.881499	−	0.472185i	$-0.156535\pi$
$182$	−73.0954	+	26.6045i	−0.401623	+	0.146179i
$183$	−34.0826	+	51.9106i	−0.186244	+	0.283665i
$184$	13.3464	−	11.1989i	0.0725347	−	0.0608639i
$185$	132.206	+	175.819i	0.714625	+	0.950373i
$186$	−1.52747	−	12.9781i	−0.00821222	−	0.0697750i
$187$	107.948	+	19.0341i	0.577260	+	0.101787i
$188$	−102.208			−0.543662
$189$	−58.5219	+	49.3460i	−0.309639	+	0.261090i
$190$	99.8166	−	153.358i	0.525351	−	0.807148i
$191$	−167.479	−	29.5310i	−0.876852	−	0.154613i	−0.282935	−	0.959139i	$-0.591308\pi$
$191$	−167.479	−	29.5310i	−0.876852	−	0.154613i	−0.593917	+	0.804526i	$0.702419\pi$
$192$	−22.0448	−	9.48825i	−0.114817	−	0.0494180i
$193$	−13.3424	+	36.6579i	−0.0691314	+	0.189937i	−0.969447	−	0.245300i	$-0.921113\pi$
$193$	−13.3424	+	36.6579i	−0.0691314	+	0.189937i	0.900316	+	0.435238i	$0.143336\pi$
$194$	10.4354	+	12.4364i	0.0537905	+	0.0641050i
$195$	234.390	+	172.469i	1.20200	+	0.884457i
$196$	−76.9830	+	28.0195i	−0.392771	+	0.142957i
$197$	−10.3505	+	17.9276i	−0.0525407	+	0.0910032i	−0.891100	−	0.453808i	$-0.850065\pi$
$197$	−10.3505	+	17.9276i	−0.0525407	+	0.0910032i	0.838559	+	0.544811i	$0.183399\pi$
$198$	−68.8131	+	29.8140i	−0.347541	+	0.150576i
$199$	−60.7633	−	105.245i	−0.305343	−	0.528870i	0.671995	−	0.740556i	$-0.265438\pi$
$199$	−60.7633	−	105.245i	−0.305343	−	0.528870i	−0.977338	+	0.211686i	$0.932104\pi$
$200$	−19.6304	+	67.9312i	−0.0981522	+	0.339656i
$201$	−168.779	+	179.183i	−0.839697	+	0.891458i
$202$	−4.97772	+	0.877707i	−0.0246422	+	0.00434508i
$203$	−21.2290	−	120.396i	−0.104576	−	0.593082i
$204$	81.2511	+	76.5334i	0.398290	+	0.375164i
$205$	−37.7365	−	123.887i	−0.184080	−	0.604325i
$206$	62.0637	−	35.8325i	0.301280	−	0.173944i
$207$	33.0339	−	44.5211i	0.159584	−	0.215078i
$208$	−67.2049	−	38.8008i	−0.323101	−	0.186542i
$209$	52.1486	+	143.277i	0.249515	+	0.685536i
$210$	−48.4421	−	35.6447i	−0.230677	−	0.169737i
$211$	78.7995	−	66.1207i	0.373457	−	0.313368i	−0.436670	−	0.899622i	$-0.643842\pi$
$211$	78.7995	−	66.1207i	0.373457	−	0.313368i	0.810128	+	0.586254i	$0.199398\pi$
$212$	−148.628	−	54.0960i	−0.701074	−	0.255170i
$213$	87.0273	−	202.197i	0.408579	−	0.949283i
$214$	36.3023	−	205.881i	0.169637	−	0.962059i
$215$	−179.644	−	116.925i	−0.835551	−	0.543837i
$216$	−75.2390	−	13.0802i	−0.348329	−	0.0605565i
$217$			8.73258i			0.0402423i
$218$	−50.2865	+	285.189i	−0.230672	+	1.30820i
$219$	−136.231	+	16.0338i	−0.622059	+	0.0732137i
$220$	−35.4110	−	47.0928i	−0.160959	−	0.214058i
$221$	231.990	+	276.475i	1.04973	+	1.25102i
$222$	−156.033	−	102.445i	−0.702851	−	0.461465i
$223$	−79.0828	−	217.278i	−0.354632	−	0.974342i	−0.980862	−	0.194704i	$-0.937625\pi$
$223$	−79.0828	−	217.278i	−0.354632	−	0.974342i	0.626230	−	0.779638i	$-0.284597\pi$
$224$	13.8894	+	8.01907i	0.0620064	+	0.0357994i
$225$	−10.5707	+	224.752i	−0.0469810	+	0.998896i
$226$	77.9129	+	134.949i	0.344747	+	0.597120i
$227$	−185.731	−	155.847i	−0.818199	−	0.686550i	0.134351	−	0.990934i	$-0.457105\pi$
$227$	−185.731	−	155.847i	−0.818199	−	0.686550i	−0.952550	+	0.304384i	$0.901550\pi$
$228$	−35.6854	+	151.108i	−0.156515	+	0.662755i
$229$	−39.5595	−	224.353i	−0.172749	−	0.979707i	−0.940710	−	0.339211i	$-0.889840\pi$
$229$	−39.5595	−	224.353i	−0.172749	−	0.979707i	0.767961	−	0.640496i	$-0.221271\pi$
$230$	40.0761	+	17.0600i	0.174244	+	0.0741740i
$231$	47.9983	−	14.4117i	0.207785	−	0.0623882i
$232$	78.3958	−	93.4285i	0.337913	−	0.402709i
$233$	71.5690	+	123.961i	0.307163	+	0.532022i	0.977741	−	0.209817i	$-0.0672869\pi$
$233$	71.5690	+	123.961i	0.307163	+	0.532022i	−0.670577	+	0.741840i	$0.733954\pi$
$234$	−236.666	−	70.4400i	−1.01139	−	0.301026i
$235$	−115.770	−	227.790i	−0.492637	−	0.969321i
$236$	−28.5697	−	78.4945i	−0.121058	−	0.332604i
$237$	172.356	+	342.503i	0.727239	+	1.44516i
$238$	−47.9461	−	57.1400i	−0.201454	−	0.240084i
$239$	−88.6159	+	243.470i	−0.370778	+	1.01870i	0.604284	+	0.796769i	$0.293459\pi$
$239$	−88.6159	+	243.470i	−0.370778	+	1.01870i	−0.975062	+	0.221934i	$0.928763\pi$
$240$	−3.82345	−	59.8781i	−0.0159310	−	0.249492i
$241$	−70.2254	+	398.268i	−0.291392	+	1.65256i	0.390125	+	0.920762i	$0.372432\pi$
$241$	−70.2254	+	398.268i	−0.291392	+	1.65256i	−0.681516	+	0.731803i	$0.738679\pi$
$242$	−122.023			−0.504227
$243$	−242.530	+	15.1013i	−0.998067	+	0.0621453i
$244$	41.3996			0.169671
$245$	−149.644	−	139.834i	−0.610792	−	0.570750i
$246$	65.6923	+	88.0926i	0.267042	+	0.358100i
$247$	−171.705	+	471.756i	−0.695163	+	1.90994i
$248$	−6.67364	+	5.59985i	−0.0269098	+	0.0225800i
$249$	78.5028	+	156.000i	0.315272	+	0.626506i
$250$	−173.632	+	33.1944i	−0.694529	+	0.132778i
$251$	18.7397	+	10.8194i	0.0746602	+	0.0431051i	0.536865	−	0.843668i	$-0.319608\pi$
$251$	18.7397	+	10.8194i	0.0746602	+	0.0431051i	−0.462205	+	0.886773i	$0.652942\pi$
$252$	48.9125	+	14.5580i	0.194097	+	0.0577700i
$253$	−31.4315	+	18.1470i	−0.124235	+	0.0717272i
$254$	−22.0323	+	26.2571i	−0.0867415	+	0.103374i
$255$	−78.5372	+	267.771i	−0.307989	+	1.05008i
$256$	2.77837	+	15.7569i	0.0108530	+	0.0615505i
$257$	−54.2645	−	307.749i	−0.211146	−	1.19747i	−0.887471	−	0.460864i	$-0.847540\pi$
$257$	−54.2645	−	307.749i	−0.211146	−	1.19747i	0.676325	−	0.736603i	$-0.263571\pi$
$258$	177.008	+	41.8018i	0.686077	+	0.162022i
$259$	95.5528	+	80.1783i	0.368930	+	0.309569i
$260$	10.3529	−	193.727i	0.0398187	−	0.745106i
$261$	173.615	−	347.081i	0.665190	−	1.32981i
$262$	58.4997	+	33.7748i	0.223281	+	0.128912i
$263$	155.636	−	56.6468i	0.591771	−	0.215387i	−0.0287372	−	0.999587i	$-0.509149\pi$
$263$	155.636	−	56.6468i	0.591771	−	0.215387i	0.620508	+	0.784200i	$0.286926\pi$
$264$	41.7931	+	27.4398i	0.158307	+	0.103939i
$265$	−47.7849	−	392.518i	−0.180320	−	1.48120i
$266$	35.4868	−	97.4991i	0.133409	−	0.366538i
$267$	−202.336	+	23.8141i	−0.757814	+	0.0891915i
$268$	161.611	+	28.4964i	0.603027	+	0.106330i
$269$			143.821i			0.534649i	0.963607	+	0.267324i	$0.0861395\pi$
$269$			143.821i			0.534649i	−0.963607	+	0.267324i	$0.913860\pi$
$270$	−56.0703	−	182.500i	−0.207668	−	0.675925i
$271$	−453.667			−1.67405			−0.837025	−	0.547165i	$-0.815707\pi$
$271$	−453.667			−1.67405			−0.837025	+	0.547165i	$0.815707\pi$
$272$	12.9218	−	73.2831i	0.0475066	−	0.269423i
$273$	151.567	+	65.2357i	0.555191	+	0.238959i
$274$	−250.683	−	91.2411i	−0.914901	−	0.332997i
$275$	64.8456	−	132.261i	0.235802	−	0.480950i
$276$	−36.8978	−	2.11938i	−0.133688	−	0.00767891i
$277$	45.7535	+	125.707i	0.165175	+	0.453815i	0.994473	−	0.104992i	$-0.0334816\pi$
$277$	45.7535	+	125.707i	0.165175	+	0.453815i	−0.829298	+	0.558807i	$0.811259\pi$
$278$	109.028	−	188.842i	0.392186	−	0.679287i
$279$	−16.5181	+	22.2620i	−0.0592045	+	0.0797922i
$280$	−2.13965	+	40.0382i	−0.00764162	+	0.142994i
$281$	−253.498	+	302.108i	−0.902130	+	1.07512i	0.0946963	+	0.995506i	$0.469812\pi$
$281$	−253.498	+	302.108i	−0.902130	+	1.07512i	−0.996826	+	0.0796102i	$0.974632\pi$
$282$	157.826	+	148.662i	0.559667	+	0.527171i
$283$	530.595	−	93.5581i	1.87489	−	0.330594i	0.884243	−	0.467027i	$-0.154675\pi$
$283$	530.595	−	93.5581i	1.87489	−	0.330594i	0.990649	+	0.136433i	$0.0435638\pi$
$284$	−144.524	+	25.4835i	−0.508888	+	0.0897307i
$285$	−377.192	+	91.6260i	−1.32348	+	0.321495i
$286$	123.837	+	103.911i	0.432995	+	0.363326i
$287$	−36.7172	−	63.5961i	−0.127935	−	0.221589i
$288$	20.2400	+	46.7155i	0.0702778	+	0.162207i
$289$	−28.5431	+	49.4382i	−0.0987652	+	0.171066i
$290$	297.020	+	68.8947i	1.02421	+	0.237568i
$291$	1.97487	−	34.3820i	0.00678650	−	0.118151i
$292$	58.7813	+	70.0528i	0.201306	+	0.239907i
$293$	345.134	+	125.618i	1.17793	+	0.428732i	0.855471	−	0.517851i	$-0.173268\pi$
$293$	345.134	+	125.618i	1.17793	+	0.428732i	0.322461	+	0.946583i	$0.395490\pi$
$294$	159.629	+	68.7053i	0.542954	+	0.233692i
$295$	142.579	−	152.582i	0.483319	−	0.517228i
$296$			124.439i			0.420401i
$297$	149.623	+	54.0511i	0.503780	+	0.181990i
$298$			373.290i			1.25265i
$299$	−117.687	−	20.7513i	−0.393600	−	0.0694024i
$300$	129.118	−	76.3441i	0.430395	−	0.254480i
$301$	−114.210	−	41.5692i	−0.379436	−	0.138104i
$302$	−6.96593	+	5.84511i	−0.0230660	+	0.0193547i
$303$	8.96302	+	5.88479i	0.0295809	+	0.0194217i
$304$	97.2673	−	35.4024i	0.319958	−	0.116455i
$305$	46.8926	+	92.2666i	0.153746	+	0.302514i
$306$	−14.1466	−	236.360i	−0.0462307	−	0.772417i
$307$	323.925	−	187.018i	1.05513	−	0.609179i	0.131049	−	0.991376i	$-0.458166\pi$
$307$	323.925	−	187.018i	1.05513	−	0.609179i	0.924081	+	0.382196i	$0.124832\pi$
$308$	−25.5936	−	21.4756i	−0.0830963	−	0.0697260i
$309$	−147.955	−	34.9407i	−0.478818	−	0.113077i
$310$	−20.0394	−	8.53058i	−0.0646432	−	0.0275180i
$311$	279.978	−	49.3677i	0.900251	−	0.158738i	0.295677	−	0.955288i	$-0.404455\pi$
$311$	279.978	−	49.3677i	0.900251	−	0.158738i	0.604573	+	0.796549i	$0.293344\pi$
$312$	47.3393	+	157.664i	0.151729	+	0.505334i
$313$	190.989	−	227.612i	0.610189	−	0.727194i	−0.369162	−	0.929365i	$-0.620355\pi$
$313$	190.989	−	227.612i	0.610189	−	0.727194i	0.979350	+	0.202171i	$0.0647996\pi$
$314$	−294.138	+	169.821i	−0.936747	+	0.540831i
$315$	22.9570	+	125.500i	0.0728795	+	0.398413i
$316$	127.808	−	221.371i	0.404457	−	0.700540i
$317$	−335.755	+	122.205i	−1.05917	+	0.385505i	−0.812115	−	0.583498i	$-0.801684\pi$
$317$	−335.755	+	122.205i	−1.05917	+	0.385505i	−0.247051	+	0.969003i	$0.579461\pi$
$318$	150.822	+	299.712i	0.474283	+	0.942490i
$319$	−194.627	+	163.312i	−0.610117	+	0.511949i
$320$	−31.9702	+	24.0397i	−0.0999068	+	0.0751240i
$321$	−355.510	+	265.111i	−1.10751	+	0.825890i
$322$	24.3226	+	4.28873i	0.0755360	+	0.0133190i
$323$	−481.408			−1.49043
$324$	97.1558	+	129.633i	0.299864	+	0.400102i
$325$	443.484	−	196.358i	1.36457	−	0.604180i
$326$	206.734	+	36.4528i	0.634154	+	0.111818i
$327$	492.457	−	367.235i	1.50599	−	1.12304i
$328$	25.0564	−	68.8418i	0.0763913	−	0.209884i
$329$	−93.1329	−	110.991i	−0.283079	−	0.337360i
$330$	−13.8163	+	124.224i	−0.0418676	+	0.376437i
$331$	78.3927	−	28.5326i	0.236836	−	0.0862012i	−0.220876	−	0.975302i	$-0.570891\pi$
$331$	78.3927	−	28.5326i	0.236836	−	0.0862012i	0.457711	+	0.889101i	$0.348669\pi$
$332$	58.2130	−	100.828i	0.175340	−	0.303698i
$333$	91.9326	+	385.142i	0.276074	+	1.15658i
$334$	21.0925	+	36.5333i	0.0631513	+	0.109381i
$335$	119.545	+	392.457i	0.356849	+	1.17151i
$336$	−9.78375	−	32.5849i	−0.0291183	−	0.0969789i
$337$	−79.9507	+	14.0975i	−0.237243	+	0.0418323i	−0.291005	−	0.956721i	$-0.593990\pi$
$337$	−79.9507	+	14.0975i	−0.237243	+	0.0418323i	0.0537626	+	0.998554i	$0.482879\pi$
$338$	50.9263	+	288.817i	0.150669	+	0.854489i
$339$	75.9738	−	321.707i	0.224111	−	0.948989i
$340$	177.961	−	54.2079i	0.523415	−	0.159435i
$341$	15.7168	−	9.07409i	0.0460903	−	0.0266102i
$342$	274.891	−	181.430i	0.803774	−	0.530498i
$343$	−220.886	−	127.528i	−0.643982	−	0.371803i
$344$	−41.4703	−	113.939i	−0.120553	−	0.331218i
$345$	−37.0701	−	84.6342i	−0.107450	−	0.245316i
$346$	94.6832	−	79.4486i	0.273651	−	0.229620i
$347$	−132.520	−	48.2335i	−0.381903	−	0.139001i	0.143933	−	0.989587i	$-0.454025\pi$
$347$	−132.520	−	48.2335i	−0.381903	−	0.139001i	−0.525836	+	0.850586i	$0.676247\pi$
$348$	−256.948	+	30.2416i	−0.738355	+	0.0869013i
$349$	−59.7297	+	338.744i	−0.171145	+	0.970613i	0.771354	+	0.636406i	$0.219580\pi$
$349$	−59.7297	+	338.744i	−0.171145	+	0.970613i	−0.942500	+	0.334207i	$0.891532\pi$
$350$	−91.6560	+	40.5819i	−0.261874	+	0.115948i
$351$	262.995	+	453.002i	0.749274	+	1.29060i
$352$		−	33.3307i		−	0.0946895i
$353$	93.4330	−	529.885i	0.264683	−	1.50109i	−0.505254	−	0.862971i	$-0.668601\pi$
$353$	93.4330	−	529.885i	0.264683	−	1.50109i	0.769937	−	0.638120i	$-0.220288\pi$
$354$	−70.0543	+	162.763i	−0.197893	+	0.459782i
$355$	−220.495	−	293.234i	−0.621112	−	0.826012i
$356$	87.3046	+	104.046i	0.245238	+	0.292263i
$357$	−9.07371	+	157.971i	−0.0254166	+	0.442495i
$358$	92.3637	+	253.767i	0.257999	+	0.708847i
$359$	−326.089	−	188.267i	−0.908325	−	0.524422i	−0.0284334	−	0.999596i	$-0.509052\pi$
$359$	−326.089	−	188.267i	−0.908325	−	0.524422i	−0.879892	+	0.475174i	$0.842385\pi$
$360$	−81.1887	+	98.0224i	−0.225524	+	0.272285i
$361$	−154.321	−	267.291i	−0.427481	−	0.740420i
$362$	333.219	+	279.604i	0.920495	+	0.772387i
$363$	188.423	+	177.483i	0.519071	+	0.488933i
$364$	−19.1025	−	108.335i	−0.0524793	−	0.297625i
$365$	−89.5451	+	210.353i	−0.245329	+	0.576308i
$366$	−63.9276	−	60.2158i	−0.174665	−	0.164524i
$367$	−335.333	+	399.634i	−0.913714	+	1.08892i	0.0820184	+	0.996631i	$0.473863\pi$
$367$	−335.333	+	399.634i	−0.913714	+	1.08892i	−0.995732	+	0.0922908i	$0.970581\pi$
$368$	12.3195	+	21.3381i	0.0334770	+	0.0579839i
$369$	26.6914	−	231.578i	0.0723344	−	0.627584i
$370$	−277.335	+	140.950i	−0.749553	+	0.380945i
$371$	−76.6857	−	210.692i	−0.206700	−	0.567903i
$372$	18.4501	+	1.05976i	0.0495972	+	0.00284882i
$373$	116.100	+	138.363i	0.311261	+	0.370946i	0.898883	−	0.438190i	$-0.144380\pi$
$373$	116.100	+	138.363i	0.311261	+	0.370946i	−0.587622	+	0.809136i	$0.699936\pi$
$374$	−53.0186	+	145.667i	−0.141761	+	0.389485i
$375$	316.397	+	201.291i	0.843725	+	0.536775i
$376$	25.0999	−	142.349i	0.0667551	−	0.378587i
$377$	−836.548			−2.21896
$378$	−54.3540	−	93.6232i	−0.143794	−	0.247680i
$379$	−406.413			−1.07233			−0.536165	−	0.844113i	$-0.680128\pi$
$379$	−406.413			−1.07233			−0.536165	+	0.844113i	$0.680128\pi$
$380$	189.074	+	176.678i	0.497563	+	0.464943i
$381$	72.2124	−	8.49910i	0.189534	−	0.0223073i
$382$	82.2574	−	226.000i	0.215334	−	0.591624i
$383$	−338.945	+	284.409i	−0.884974	+	0.742582i	−0.967196	−	0.254032i	$-0.918243\pi$
$383$	−338.945	+	284.409i	−0.884974	+	0.742582i	0.0822213	+	0.996614i	$0.473799\pi$
$384$	18.6282	−	28.3723i	0.0485110	−	0.0738863i
$385$	18.8729	−	81.3652i	0.0490205	−	0.211338i
$386$	−47.7779	−	27.5846i	−0.123777	−	0.0714626i
$387$	−212.527	−	322.007i	−0.549166	−	0.832059i
$388$	−19.8832	+	11.4795i	−0.0512453	+	0.0295865i
$389$	−278.359	+	331.735i	−0.715576	+	0.852790i	−0.994193	−	0.107612i	$-0.965680\pi$
$389$	−278.359	+	331.735i	−0.715576	+	0.852790i	0.278617	+	0.960402i	$0.410124\pi$
$390$	−297.763	+	284.088i	−0.763496	+	0.728430i
$391$	−19.8988	−	112.852i	−0.0508921	−	0.288623i
$392$	−20.1184	−	114.097i	−0.0513226	−	0.291065i
$393$	−41.2073	−	137.242i	−0.104853	−	0.349215i
$394$	−22.4265	−	18.8181i	−0.0569200	−	0.0477616i
$395$	638.132	+	34.1019i	1.61552	+	0.0863340i
$396$	−24.6240	−	103.159i	−0.0621818	−	0.260504i
$397$	294.157	+	169.832i	0.740950	+	0.427788i	0.822415	−	0.568888i	$-0.192626\pi$
$397$	294.157	+	169.832i	0.740950	+	0.427788i	−0.0814644	+	0.996676i	$0.525960\pi$
$398$	161.500	−	58.7811i	0.405778	−	0.147691i
$399$	−196.610	+	98.9386i	−0.492756	+	0.247966i
$400$	−89.7889	−	44.0221i	−0.224472	−	0.110055i
$401$	117.742	−	323.494i	0.293622	−	0.806719i	−0.701908	−	0.712268i	$-0.747668\pi$
$401$	117.742	−	323.494i	0.293622	−	0.806719i	0.995530	−	0.0944510i	$-0.0301096\pi$
$402$	−208.105	−	279.067i	−0.517675	−	0.694195i
$403$	58.8472	+	10.3763i	0.146023	+	0.0257478i
$404$		−	7.14816i		−	0.0176935i
$405$	−178.865	+	363.363i	−0.441641	+	0.897192i
$406$	172.892			0.425842
$407$	45.0143	−	255.289i	0.110600	−	0.627245i
$408$	−126.544	+	94.3660i	−0.310156	+	0.231289i
$409$	−215.740	−	78.5230i	−0.527482	−	0.191988i	0.0645318	−	0.997916i	$-0.479445\pi$
$409$	−215.740	−	78.5230i	−0.527482	−	0.191988i	−0.592014	+	0.805928i	$0.701667\pi$
$410$	181.807	−	22.1332i	0.443433	−	0.0539833i
$411$	254.384	+	505.509i	0.618939	+	1.22995i
$412$	34.6636	+	95.2375i	0.0841350	+	0.231159i
$413$	59.2069	−	102.549i	0.143358	−	0.248304i
$414$	53.8935	+	56.9406i	0.130177	+	0.137538i
$415$	290.650	+	15.5324i	0.700361	+	0.0374275i
$416$	70.5428	−	84.0697i	0.169574	−	0.202091i
$417$	−443.027	+	133.021i	−1.06241	+	0.318994i
$418$	−212.352	+	37.4434i	−0.508020	+	0.0895776i
$419$	156.480	−	27.5917i	0.373462	−	0.0658513i	0.0162327	−	0.999868i	$-0.494833\pi$
$419$	156.480	−	27.5917i	0.373462	−	0.0658513i	0.357229	+	0.934017i	$0.383722\pi$
$420$	61.5396	−	58.7132i	0.146523	−	0.139793i
$421$	538.245	+	451.641i	1.27849	+	1.07278i	0.993450	+	0.114267i	$0.0364520\pi$
$421$	538.245	+	451.641i	1.27849	+	1.07278i	0.285042	+	0.958515i	$0.407992\pi$
$422$	72.7369	+	125.984i	0.172362	+	0.298540i
$423$	−27.4791	−	459.116i	−0.0649623	−	1.08538i
$424$	111.840	−	193.713i	0.263775	−	0.456871i
$425$	322.385	+	335.219i	0.758554	+	0.788750i
$426$	260.234	+	170.860i	0.610878	+	0.401080i
$427$	37.7235	+	44.9572i	0.0883455	+	0.105286i
$428$	277.821	+	101.119i	0.649114	+	0.236258i
$429$	−40.0843	−	340.576i	−0.0934367	−	0.793883i
$430$	206.961	−	221.481i	0.481304	−	0.515071i
$431$			342.771i			0.795292i	0.917539	+	0.397646i	$0.130173\pi$
$431$			342.771i			0.795292i	−0.917539	+	0.397646i	$0.869827\pi$
$432$	36.6940	−	101.575i	0.0849399	−	0.235128i
$433$		−	292.446i		−	0.675395i	−0.941255	−	0.337698i	$-0.890352\pi$
$433$		−	292.446i		−	0.675395i	0.941255	−	0.337698i	$-0.109648\pi$
$434$	−12.1621	−	2.14451i	−0.0280233	−	0.00494126i
$435$	−358.439	−	538.401i	−0.823998	−	1.23770i
$436$	−384.841	−	140.071i	−0.882663	−	0.321263i
$437$	122.107	−	102.460i	0.279421	−	0.234462i
$438$	11.1242	−	193.670i	0.0253978	−	0.442169i
$439$	−481.844	+	175.377i	−1.09759	+	0.399492i	−0.826429	−	0.563041i	$-0.809631\pi$
$439$	−481.844	+	175.377i	−1.09759	+	0.399492i	−0.271165	+	0.962533i	$0.587409\pi$
$440$	74.2836	−	37.7531i	0.168826	−	0.0858025i
$441$	−146.560	−	338.272i	−0.332335	−	0.767056i
$442$	−442.026	+	255.204i	−1.00006	+	0.577385i
$443$	−355.076	−	297.944i	−0.801526	−	0.672561i	0.147043	−	0.989130i	$-0.453024\pi$
$443$	−355.076	−	297.944i	−0.801526	−	0.672561i	−0.948569	+	0.316570i	$0.897469\pi$
$444$	180.996	−	192.153i	0.407649	−	0.432778i
$445$	−132.996	+	312.425i	−0.298868	+	0.702079i
$446$	322.031	−	56.7827i	0.722042	−	0.127315i
$447$	542.950	−	576.419i	1.21465	−	1.28953i
$448$	−14.5793	+	17.3749i	−0.0325430	+	0.0387833i
$449$	505.219	−	291.688i	1.12521	−	0.649640i	0.182483	−	0.983209i	$-0.441586\pi$
$449$	505.219	−	291.688i	1.12521	−	0.649640i	0.942726	+	0.333569i	$0.108253\pi$
$450$	−310.422	−	69.9156i	−0.689827	−	0.155368i
$451$	−76.3064	+	132.166i	−0.169194	+	0.293052i
$452$	−207.081	+	75.3713i	−0.458144	+	0.166751i
$453$	19.2582	+	1.10618i	0.0425126	+	0.00244189i
$454$	262.663	−	220.401i	0.578554	−	0.485464i
$455$	219.808	−	165.283i	0.483096	−	0.363259i
$456$	−201.689	−	86.8085i	−0.442301	−	0.190370i
$457$	−38.6735	−	6.81919i	−0.0846248	−	0.0149216i	0.131175	−	0.991359i	$-0.458125\pi$
$457$	−38.6735	−	6.81919i	−0.0846248	−	0.0149216i	−0.215800	+	0.976438i	$0.569236\pi$
$458$	322.178			0.703445
$459$	−321.941	+	385.553i	−0.701396	+	0.839985i
$460$	−33.6017	+	51.6256i	−0.0730472	+	0.112230i
$461$	−397.989	−	70.1762i	−0.863316	−	0.152226i	−0.275580	−	0.961278i	$-0.588870\pi$
$461$	−397.989	−	70.1762i	−0.863316	−	0.152226i	−0.587737	+	0.809052i	$0.699981\pi$
$462$	8.28434	+	70.3878i	0.0179315	+	0.152354i
$463$	−204.796	+	562.672i	−0.442323	+	1.21527i	0.495636	+	0.868530i	$0.334935\pi$
$463$	−204.796	+	562.672i	−0.442323	+	1.21527i	−0.937960	+	0.346744i	$0.887287\pi$
$464$	110.868	+	132.128i	0.238941	+	0.284758i
$465$	18.5363	+	42.3199i	0.0398630	+	0.0910106i
$466$	−190.220	+	69.2344i	−0.408197	+	0.148572i
$467$	4.55065	−	7.88196i	0.00974444	−	0.0168779i	−0.861112	−	0.508415i	$-0.830232\pi$
$467$	4.55065	−	7.88196i	0.00974444	−	0.0168779i	0.870857	+	0.491537i	$0.163565\pi$
$468$	156.223	−	312.314i	0.333811	−	0.667337i
$469$	116.316	+	201.465i	0.248008	+	0.429562i
$470$	345.680	−	105.296i	0.735490	−	0.224034i
$471$	701.201	+	165.594i	1.48875	+	0.351580i
$472$	116.338	−	20.5135i	0.246478	−	0.0434607i
$473$	43.8612	+	248.749i	0.0927298	+	0.525897i
$474$	−519.340	+	155.934i	−1.09565	+	0.328975i
$475$	−179.600	+	621.506i	−0.378105	+	1.30843i
$476$	91.3548	−	52.7437i	0.191922	−	0.110806i
$477$	203.038	−	682.173i	0.425657	−	1.43013i
$478$	−317.326	−	183.208i	−0.663862	−	0.383281i
$479$	−232.362	−	638.408i	−0.485097	−	1.33279i	−0.905072	−	0.425258i	$-0.860183\pi$
$479$	−232.362	−	638.408i	−0.485097	−	1.33279i	0.419975	−	0.907536i	$-0.362039\pi$
$480$	84.3328	+	9.37957i	0.175693	+	0.0195408i
$481$	653.846	−	548.642i	1.35935	−	1.14063i
$482$	−537.434	−	195.610i	−1.11501	−	0.405830i
$483$	−31.3200	−	41.9997i	−0.0648447	−	0.0869560i
$484$	29.9659	−	169.945i	0.0619129	−	0.351126i
$485$	−48.1056	−	31.3106i	−0.0991868	−	0.0645579i
$486$	38.5275	−	341.487i	0.0792747	−	0.702649i
$487$		−	335.754i		−	0.689432i	−0.938707	−	0.344716i	$-0.887975\pi$
$487$		−	335.754i		−	0.689432i	0.938707	−	0.344716i	$-0.112025\pi$
$488$	−10.1667	+	57.6584i	−0.0208335	+	0.118152i
$489$	−266.210	−	356.984i	−0.544396	−	0.730029i
$490$	231.499	−	174.074i	0.472447	−	0.355253i
$491$	−369.569	−	440.435i	−0.752686	−	0.897017i	0.244676	−	0.969605i	$-0.421319\pi$
$491$	−369.569	−	440.435i	−0.752686	−	0.897017i	−0.997362	+	0.0725883i	$0.976874\pi$
$492$	−138.821	+	69.8582i	−0.282157	+	0.141988i
$493$	−274.362	−	753.804i	−0.556516	−	1.52901i
$494$	−614.861	−	354.990i	−1.24466	−	0.718604i
$495$	202.019	−	171.726i	0.408119	−	0.346921i
$496$	−6.16018	−	10.6698i	−0.0124197	−	0.0215116i
$497$	−159.365	−	133.723i	−0.320653	−	0.269060i
$498$	−236.544	+	71.0233i	−0.474988	+	0.142617i
$499$	137.519	+	779.910i	0.275590	+	1.56295i	0.737083	+	0.675802i	$0.236203\pi$
$499$	137.519	+	779.910i	0.275590	+	1.56295i	−0.461493	+	0.887144i	$0.652686\pi$
$500$	−3.59097	−	249.974i	−0.00718193	−	0.499948i
$501$	20.5675	−	87.0923i	0.0410530	−	0.173837i
$502$	−19.6705	+	23.4423i	−0.0391842	+	0.0466979i
$503$	446.862	+	773.987i	0.888393	+	1.53874i	0.841775	+	0.539829i	$0.181511\pi$
$503$	446.862	+	773.987i	0.888393	+	1.53874i	0.0466180	+	0.998913i	$0.485156\pi$
$504$	−32.2871	+	64.5467i	−0.0640617	+	0.128069i
$505$	15.9310	−	8.09660i	0.0315465	−	0.0160329i
$506$	−17.5550	−	48.2320i	−0.0346937	−	0.0953201i
$507$	341.447	−	520.052i	0.673465	−	1.02574i
$508$	−31.1584	−	37.1332i	−0.0613355	−	0.0730968i
$509$	172.117	−	472.887i	0.338147	−	0.929051i	−0.647773	−	0.761833i	$-0.724300\pi$
$509$	172.117	−	472.887i	0.338147	−	0.929051i	0.985920	−	0.167218i	$-0.0534783\pi$
$510$	−353.646	−	175.139i	−0.693423	−	0.343410i
$511$	−22.5108	+	127.665i	−0.0440524	+	0.249834i
$512$	−22.6274			−0.0441942
$513$	−688.366	−	119.671i	−1.34184	−	0.233278i
$514$	441.937			0.859799
$515$	−172.991	+	185.128i	−0.335906	+	0.359472i
$516$	−101.687	+	236.258i	−0.197069	+	0.457865i
$517$	−102.986	+	282.952i	−0.199199	+	0.547295i
$518$	−135.132	+	113.389i	−0.260873	+	0.218898i
$519$	−261.764	−	15.0355i	−0.504362	−	0.0289701i
$520$	267.267	+	61.9935i	0.513976	+	0.119218i
$521$	−390.266	−	225.320i	−0.749071	−	0.432476i	0.0762872	−	0.997086i	$-0.475693\pi$
$521$	−390.266	−	225.320i	−0.749071	−	0.432476i	−0.825358	+	0.564610i	$0.809027\pi$
$522$	440.754	+	327.033i	0.844357	+	0.626499i
$523$	−410.373	+	236.929i	−0.784652	+	0.453019i	−0.838076	−	0.545553i	$-0.816320\pi$
$523$	−410.373	+	236.929i	−0.784652	+	0.453019i	0.0534245	+	0.998572i	$0.482986\pi$
$524$	−61.4053	+	73.1799i	−0.117186	+	0.139656i
$525$	200.558	+	70.6488i	0.382015	+	0.134569i
$526$	40.6732	+	230.669i	0.0773256	+	0.438535i
$527$	9.95007	+	56.4297i	0.0188806	+	0.107077i
$528$	−48.4795	+	51.4679i	−0.0918173	+	0.0974771i
$529$	−376.172	−	315.645i	−0.711099	−	0.596683i
$530$	558.405	+	29.8413i	1.05359	+	0.0563044i
$531$	344.913	−	149.437i	0.649554	−	0.281426i
$532$	127.075	+	73.3669i	0.238863	+	0.137908i
$533$	−472.191	+	171.863i	−0.885912	+	0.322445i
$534$	16.5222	−	287.648i	0.0309405	−	0.538666i
$535$	89.3215	+	733.710i	0.166956	+	1.37142i
$536$	−79.3755	+	218.082i	−0.148089	+	0.406870i
$537$	226.480	−	526.200i	0.421751	−	0.979888i
$538$	−200.303	−	35.3188i	−0.372310	−	0.0656483i
$539$			241.351i			0.447775i
$540$	267.942	−	33.2732i	0.496189	−	0.0616170i
$541$	−120.376			−0.222507			−0.111253	−	0.993792i	$-0.535486\pi$
$541$	−120.376			−0.222507			−0.111253	+	0.993792i	$0.535486\pi$
$542$	111.410	−	631.836i	0.205553	−	1.16575i
$543$	−107.859	−	916.421i	−0.198635	−	1.68770i
$544$	98.8901	+	35.9931i	0.181783	+	0.0661637i
$545$	−123.729	−	1016.35i	−0.227026	−	1.86485i
$546$	−128.077	+	195.072i	−0.234573	+	0.357274i
$547$	291.121	+	799.847i	0.532213	+	1.46224i	0.856431	+	0.516261i	$0.172677\pi$
$547$	291.121	+	799.847i	0.532213	+	1.46224i	−0.324218	+	0.945982i	$0.605101\pi$
$548$	188.636	−	326.727i	0.344226	−	0.596216i
$549$	11.1304	+	185.965i	0.0202740	+	0.338735i
$550$	168.279	+	122.792i	0.305962	+	0.223259i
$551$	717.248	−	854.783i	1.30172	−	1.55133i
$552$	12.0129	−	50.8682i	0.0217625	−	0.0921525i
$553$	356.853	−	62.9229i	0.645304	−	0.113785i
$554$	−186.311	+	32.8517i	−0.336302	+	0.0592991i
$555$	633.260	+	185.735i	1.14101	+	0.334658i
$556$	236.231	+	198.221i	0.424875	+	0.356513i
$557$	274.453	+	475.367i	0.492735	+	0.853442i	0.999965	−	0.00836901i	$-0.00266397\pi$
$557$	274.453	+	475.367i	0.492735	+	0.853442i	−0.507230	+	0.861811i	$0.669331\pi$
$558$	−26.9485	−	28.4722i	−0.0482949	−	0.0510254i
$559$	−415.835	+	720.248i	−0.743891	+	1.28846i
$560$	−55.2369	−	12.8124i	−0.0986373	−	0.0228792i
$561$	293.743	−	147.818i	0.523605	−	0.263490i
$562$	−358.501	−	427.245i	−0.637902	−	0.760222i
$563$	413.921	+	150.655i	0.735207	+	0.267593i	0.682367	−	0.731010i	$-0.260951\pi$
$563$	413.921	+	150.655i	0.735207	+	0.267593i	0.0528396	+	0.998603i	$0.483173\pi$
$564$	−245.804	+	183.301i	−0.435824	+	0.325002i
$565$	−402.536	−	376.146i	−0.712453	−	0.665746i
$566$			761.950i			1.34620i
$567$	−52.2439	+	223.627i	−0.0921409	+	0.394404i
$568$		−	207.541i		−	0.365389i
$569$	768.229	+	135.460i	1.35014	+	0.238066i	0.801501	−	0.597993i	$-0.204035\pi$
$569$	768.229	+	135.460i	1.35014	+	0.238066i	0.548639	+	0.836060i	$0.315146\pi$
$570$	−34.9809	−	547.828i	−0.0613700	−	0.961101i
$571$	848.401	+	308.793i	1.48582	+	0.540793i	0.952344	−	0.305025i	$-0.0986649\pi$
$571$	848.401	+	308.793i	1.48582	+	0.540793i	0.533472	+	0.845818i	$0.320887\pi$
$572$	−175.131	+	146.953i	−0.306174	+	0.256910i
$573$	−455.736	+	229.337i	−0.795351	+	0.400239i
$574$	97.5890	−	35.5195i	0.170016	−	0.0618807i
$575$	−153.117	−	16.4121i	−0.266291	−	0.0285429i
$576$	−70.0325	+	16.7166i	−0.121584	+	0.0290219i
$577$	−379.825	+	219.292i	−0.658275	+	0.380055i	−0.791620	−	0.611014i	$-0.790762\pi$
$577$	−379.825	+	219.292i	−0.658275	+	0.380055i	0.133344	+	0.991070i	$0.457428\pi$
$578$	−61.8445	−	51.8937i	−0.106997	−	0.0897814i
$579$	33.6548	+	112.088i	0.0581258	+	0.193589i
$580$	−168.893	+	396.750i	−0.291194	+	0.684051i
$581$	162.536	−	28.6595i	0.279752	−	0.0493279i
$582$	47.3998	+	11.1938i	0.0814429	+	0.0192334i
$583$	−299.516	+	356.950i	−0.513750	+	0.612264i
$584$	−112.000	+	64.6631i	−0.191781	+	0.110725i
$585$	873.000	−	5.57961i	1.49231	−	0.00953780i
$586$	−259.709	+	449.829i	−0.443189	+	0.767626i
$587$	252.047	−	91.7376i	0.429382	−	0.156282i	−0.118283	−	0.992980i	$-0.537739\pi$
$587$	252.047	−	91.7376i	0.429382	−	0.156282i	0.547665	+	0.836698i	$0.315517\pi$
$588$	−134.889	+	205.447i	−0.229403	+	0.349399i
$589$	−61.0575	+	51.2333i	−0.103663	+	0.0869836i
$590$	177.492	+	236.045i	0.300833	+	0.400075i
$591$	7.25917	+	61.6774i	0.0122829	+	0.104361i
$592$	−173.309	−	30.5591i	−0.292752	−	0.0516202i
$593$	664.188			1.12005			0.560024	−	0.828476i	$-0.310792\pi$
$593$	664.188			1.12005			0.560024	+	0.828476i	$0.310792\pi$
$594$	−112.022	+	195.110i	−0.188590	+	0.328468i
$595$	221.025	+	143.859i	0.371471	+	0.241780i
$596$	−519.891	−	91.6708i	−0.872301	−	0.153810i
$597$	−334.878	−	144.134i	−0.560935	−	0.241431i
$598$	57.8019	−	158.809i	0.0966586	−	0.265567i
$599$	72.3087	+	86.1742i	0.120716	+	0.143863i	0.823018	−	0.568016i	$-0.192289\pi$
$599$	72.3087	+	86.1742i	0.120716	+	0.143863i	−0.702302	+	0.711879i	$0.747844\pi$
$600$	74.6182	+	198.575i	0.124364	+	0.330959i
$601$	−512.641	+	186.586i	−0.852980	+	0.310459i	−0.731255	−	0.682105i	$-0.761065\pi$
$601$	−512.641	+	186.586i	−0.852980	+	0.310459i	−0.121725	+	0.992564i	$0.538843\pi$
$602$	85.9418	−	148.856i	0.142761	−	0.247269i
$603$	−84.5551	+	733.612i	−0.140224	+	1.21660i
$604$	−6.42999	−	11.1371i	−0.0106457	−	0.0184388i
$605$	412.695	−	125.709i	0.682141	−	0.207784i
$606$	−10.3970	+	11.0379i	−0.0171568	+	0.0182144i
$607$	431.052	−	76.0060i	0.710134	−	0.125216i	0.193098	−	0.981179i	$-0.438146\pi$
$607$	431.052	−	76.0060i	0.710134	−	0.125216i	0.517036	+	0.855964i	$0.327035\pi$
$608$	25.4195	+	144.161i	0.0418083	+	0.237107i
$609$	−266.972	−	251.471i	−0.438378	−	0.412925i
$610$	−140.018	+	42.6502i	−0.229538	+	0.0699184i
$611$	−858.614	+	495.721i	−1.40526	+	0.811327i
$612$	332.659	+	38.3418i	0.543560	+	0.0626499i
$613$	299.456	+	172.891i	0.488509	+	0.282041i	0.723956	−	0.689846i	$-0.242322\pi$
$613$	299.456	+	172.891i	0.488509	+	0.282041i	−0.235446	+	0.971887i	$0.575655\pi$
$614$	180.917	+	497.066i	0.294654	+	0.809554i
$615$	−312.932	−	230.262i	−0.508833	−	0.374410i
$616$	36.1949	−	30.3711i	0.0587579	−	0.0493038i
$617$	545.857	+	198.676i	0.884694	+	0.322002i	0.744103	−	0.668065i	$-0.232877\pi$
$617$	545.857	+	198.676i	0.884694	+	0.322002i	0.140592	+	0.990068i	$0.455100\pi$
$618$	84.9969	−	197.480i	0.137535	−	0.319547i
$619$	−17.3232	+	98.2449i	−0.0279858	+	0.158716i	−0.995598	−	0.0937257i	$-0.970122\pi$
$619$	−17.3232	+	98.2449i	−0.0279858	+	0.158716i	0.967612	+	0.252441i	$0.0812334\pi$
$620$	16.8020	−	25.8145i	0.0271000	−	0.0416364i
$621$	−0.399927	−	166.313i	−0.000644004	−	0.267815i
$622$			402.057i			0.646393i
$623$	−33.4340	+	189.614i	−0.0536662	+	0.304356i
$624$	−231.209	+	27.2123i	−0.370527	+	0.0436095i
$625$	553.046	−	291.144i	0.884874	−	0.465831i
$626$	270.099	+	321.892i	0.431468	+	0.514204i
$627$	382.367	+	251.048i	0.609836	+	0.400396i
$628$	−164.281	−	451.359i	−0.261594	−	0.718724i
$629$	708.816	+	409.235i	1.12689	+	0.650612i
$630$	−180.425	+	1.15315i	−0.286389	+	0.00183040i
$631$	−279.779	−	484.592i	−0.443390	−	0.767974i	0.554549	−	0.832151i	$-0.312891\pi$
$631$	−279.779	−	484.592i	−0.443390	−	0.767974i	−0.997939	+	0.0641774i	$0.979558\pi$
$632$	276.923	+	232.366i	0.438169	+	0.367667i
$633$	70.9265	−	300.335i	0.112048	−	0.474463i
$634$	−87.7450	−	497.627i	−0.138399	−	0.784900i
$635$	47.4655	−	111.502i	0.0747488	−	0.175594i
$636$	−454.455	+	136.452i	−0.714553	+	0.214547i
$637$	−510.807	+	608.757i	−0.801896	+	0.955662i
$638$	−179.653	−	311.168i	−0.281588	−	0.487725i
$639$	−153.327	−	642.346i	−0.239948	−	1.00524i
$640$	−25.6297	−	50.4294i	−0.0400464	−	0.0787959i
$641$	−43.7221	−	120.126i	−0.0682092	−	0.187403i	0.900905	−	0.434017i	$-0.142904\pi$
$641$	−43.7221	−	120.126i	−0.0682092	−	0.187403i	−0.969114	+	0.246614i	$0.920682\pi$
$642$	−281.923	−	560.234i	−0.439132	−	0.872638i
$643$	108.657	+	129.492i	0.168984	+	0.201387i	0.843890	−	0.536517i	$-0.180260\pi$
$643$	108.657	+	129.492i	0.168984	+	0.201387i	−0.674906	+	0.737904i	$0.735816\pi$
$644$	−11.9461	+	32.8216i	−0.0185498	+	0.0509652i
$645$	−641.724	+	40.9766i	−0.994922	+	0.0635296i
$646$	118.222	−	670.471i	0.183006	−	1.03788i
$647$	−594.885			−0.919451			−0.459725	−	0.888061i	$-0.652052\pi$
$647$	−594.885			−0.919451			−0.459725	+	0.888061i	$0.652052\pi$
$648$	−204.403	+	103.477i	−0.315436	+	0.159687i
$649$	−246.090			−0.379183
$650$	164.565	+	665.873i	0.253177	+	1.02442i
$651$	15.6610	+	21.0013i	0.0240569	+	0.0322600i
$652$	−101.538	+	278.973i	−0.155733	+	0.427872i
$653$	183.939	−	154.343i	0.281683	−	0.236360i	−0.490989	−	0.871166i	$-0.663364\pi$
$653$	183.939	−	154.343i	0.281683	−	0.236360i	0.772672	+	0.634806i	$0.218920\pi$
$654$	390.523	+	776.044i	0.597130	+	1.18661i
$655$	−232.648	−	53.9633i	−0.355187	−	0.0823867i
$656$	89.7247	+	51.8026i	0.136775	+	0.0789673i
$657$	−298.871	+	282.877i	−0.454903	+	0.430559i
$658$	177.452	−	102.452i	0.269684	−	0.155702i
$659$	465.698	−	554.997i	0.706674	−	0.842181i	−0.286591	−	0.958053i	$-0.592522\pi$
$659$	465.698	−	554.997i	0.706674	−	0.842181i	0.993264	+	0.115872i	$0.0369664\pi$
$660$	−169.618	−	49.7488i	−0.256996	−	0.0753770i
$661$	−131.730	−	747.079i	−0.199289	−	1.13023i	−0.906177	−	0.422899i	$-0.861012\pi$
$661$	−131.730	−	747.079i	−0.199289	−	1.13023i	0.706887	−	0.707326i	$-0.250099\pi$
$662$	20.4868	+	116.187i	0.0309469	+	0.175508i
$663$	1053.75	+	248.852i	1.58937	+	0.375343i
$664$	126.130	+	105.836i	0.189955	+	0.159391i
$665$	−19.5758	+	366.312i	−0.0294373	+	0.550845i
$666$	−558.974	+	33.4558i	−0.839301	+	0.0502339i
$667$	230.025	+	132.805i	0.344866	+	0.199108i
$668$	−56.0608	+	20.4045i	−0.0839234	+	0.0305456i
$669$	−579.857	−	380.712i	−0.866751	−	0.569077i
$670$	−575.944	+	70.1151i	−0.859618	+	0.104649i
$671$	41.7145	−	114.610i	0.0621677	−	0.170804i
$672$	47.7846	−	5.62404i	0.0711080	−	0.00836911i
$673$	−721.413	−	127.205i	−1.07194	−	0.189011i	−0.390289	−	0.920692i	$-0.627625\pi$
$673$	−721.413	−	127.205i	−1.07194	−	0.189011i	−0.681647	+	0.731681i	$0.738736\pi$
$674$		−	114.812i		−	0.170344i
$675$	377.648	+	559.470i	0.559479	+	0.828844i
$676$	−414.750			−0.613536
$677$	−81.3241	+	461.212i	−0.120124	+	0.681258i	0.863961	+	0.503559i	$0.167976\pi$
$677$	−81.3241	+	461.212i	−0.120124	+	0.681258i	−0.984085	+	0.177699i	$0.943135\pi$
$678$	429.394	+	184.814i	0.633324	+	0.272587i
$679$	−30.5836	−	11.1315i	−0.0450422	−	0.0163940i
$680$	31.7939	+	261.164i	0.0467558	+	0.384064i
$681$	−726.167	−	41.7104i	−1.06633	−	0.0612488i
$682$	8.77809	+	24.1176i	0.0128711	+	0.0353630i
$683$	488.775	−	846.584i	0.715630	−	1.23951i	−0.247086	−	0.968994i	$-0.579473\pi$
$683$	488.775	−	846.584i	0.715630	−	1.23951i	0.962716	−	0.270514i	$-0.0871938\pi$
$684$	185.177	+	427.403i	0.270726	+	0.624858i
$685$	941.835	+	50.3319i	1.37494	+	0.0734773i
$686$	231.857	−	276.316i	0.337983	−	0.402793i
$687$	−497.493	−	468.608i	−0.724153	−	0.682107i
$688$	168.870	−	29.7763i	0.245451	−	0.0432795i
$689$	−1510.93	+	266.419i	−2.19294	+	0.386674i
$690$	126.976	−	30.8445i	0.184023	−	0.0447021i
$691$	−462.356	−	387.963i	−0.669112	−	0.561452i	0.243690	−	0.969853i	$-0.421642\pi$
$691$	−462.356	−	387.963i	−0.669112	−	0.561452i	−0.912802	+	0.408401i	$0.866086\pi$
$692$	87.3985	+	151.379i	0.126298	+	0.218755i
$693$	89.5867	−	120.739i	0.129274	−	0.174227i
$694$	99.7199	−	172.720i	0.143689	−	0.248876i
$695$	−174.198	+	751.005i	−0.250644	+	1.08058i
$696$	20.9816	−	365.285i	0.0301460	−	0.524834i
$697$	−309.728	−	369.120i	−0.444374	−	0.529584i
$698$	−457.110	−	166.374i	−0.654886	−	0.238359i
$699$	394.431	+	169.766i	0.564279	+	0.242870i
$700$	−34.0111	−	137.618i	−0.0485873	−	0.196597i
$701$			1073.24i			1.53101i	0.643428	+	0.765507i	$0.277512\pi$
$701$			1073.24i			1.53101i	−0.643428	+	0.765507i	$0.722488\pi$
$702$	−695.494	+	255.035i	−0.990732	+	0.363297i
$703$			1138.50i			1.61948i
$704$	46.4206	+	8.18521i	0.0659384	+	0.0116267i
$705$	−686.938	−	340.199i	−0.974381	−	0.482551i
$706$	715.041	+	260.254i	1.01281	+	0.368631i
$707$	7.76242	−	6.51344i	0.0109794	−	0.00921279i
$708$	−209.481	−	137.537i	−0.295877	−	0.194261i
$709$	677.722	−	246.671i	0.955884	−	0.347913i	0.183465	−	0.983026i	$-0.441269\pi$
$709$	677.722	−	246.671i	0.955884	−	0.347913i	0.772419	+	0.635113i	$0.219046\pi$
$710$	462.544	−	235.078i	0.651470	−	0.331096i
$711$	1028.75	+	514.594i	1.44691	+	0.723761i
$712$	−166.347	+	96.0406i	−0.233634	+	0.134888i
$713$	−14.5339	−	12.1954i	−0.0203842	−	0.0171043i
$714$	−217.782	−	51.4310i	−0.305017	−	0.0720322i
$715$	−525.879	−	223.862i	−0.735495	−	0.313093i
$716$	−376.111	+	66.3185i	−0.525295	+	0.0926236i
$717$	223.525	+	744.453i	0.311750	+	1.03829i
$718$	342.285	−	407.919i	0.476720	−	0.568133i
$719$	1126.95	−	650.647i	1.56739	−	0.904933i	0.570918	−	0.821007i	$-0.306587\pi$
$719$	1126.95	−	650.647i	1.56739	−	0.904933i	0.996472	−	0.0839261i	$-0.0267460\pi$
$720$	−116.581	−	137.146i	−0.161918	−	0.190480i
$721$	−71.8358	+	124.423i	−0.0996335	+	0.172570i
$722$	410.162	−	149.287i	0.568091	−	0.206768i
$723$	545.368	+	1083.75i	0.754313	+	1.49896i
$724$	−471.243	+	395.420i	−0.650888	+	0.546160i
$725$	−1075.53	+	72.9831i	−1.48349	+	0.100666i
$726$	−293.457	+	218.836i	−0.404211	+	0.301428i
$727$	855.820	+	150.904i	1.17719	+	0.207571i	0.727817	−	0.685771i	$-0.240535\pi$
$727$	855.820	+	150.904i	1.17719	+	0.207571i	0.449377	+	0.893342i	$0.351646\pi$
$728$	155.573			0.213699
$729$	−556.186	+	471.272i	−0.762944	+	0.646464i
$730$	−270.974	−	176.369i	−0.371197	−	0.241602i
$731$	−785.389	−	138.485i	−1.07440	−	0.189446i
$732$	99.5633	−	74.2462i	0.136015	−	0.101429i
$733$	−6.31931	+	17.3622i	−0.00862117	+	0.0236865i	−0.943929	−	0.330150i	$-0.892901\pi$
$733$	−6.31931	+	17.3622i	−0.00862117	+	0.0236865i	0.935307	+	0.353836i	$0.115123\pi$
$734$	−474.232	−	565.168i	−0.646093	−	0.769984i
$735$	−610.662	−	67.9183i	−0.830833	−	0.0924059i
$736$	−32.7435	+	11.9177i	−0.0444885	+	0.0161925i
$737$	241.729	−	418.687i	0.327991	−	0.568097i
$738$	315.971	+	94.0439i	0.428145	+	0.127431i
$739$	385.059	+	666.942i	0.521054	+	0.902493i	0.999700	+	0.0244845i	$0.00779444\pi$
$739$	385.059	+	666.942i	0.521054	+	0.902493i	−0.478646	+	0.878008i	$0.658872\pi$
$740$	−128.198	−	420.866i	−0.173240	−	0.568738i
$741$	433.110	+	1442.48i	0.584494	+	1.94666i
$742$	312.269	−	55.0615i	0.420848	−	0.0742068i
$743$	159.841	+	906.504i	0.215129	+	1.22006i	0.880682	+	0.473708i	$0.157085\pi$
$743$	159.841	+	906.504i	0.215129	+	1.22006i	−0.665553	+	0.746351i	$0.731804\pi$
$744$	−6.00686	+	25.4358i	−0.00807374	+	0.0341879i
$745$	−384.566	−	1262.51i	−0.516196	−	1.69464i
$746$	−221.213	+	127.718i	−0.296533	+	0.171203i
$747$	468.565	+	234.382i	0.627263	+	0.313765i
$748$	−189.855	−	109.613i	−0.253817	−	0.146541i
$749$	143.344	+	393.834i	0.191380	+	0.525814i
$750$	−358.043	+	391.223i	−0.477390	+	0.521631i
$751$	794.948	−	667.041i	1.05852	−	0.888203i	0.0645560	−	0.997914i	$-0.479437\pi$
$751$	794.948	−	667.041i	1.05852	−	0.888203i	0.993964	+	0.109711i	$0.0349925\pi$
$752$	192.089	+	69.9147i	0.255438	+	0.0929717i
$753$	64.4712	−	7.58800i	0.0856192	−	0.0100770i
$754$	205.436	−	1165.08i	0.272461	−	1.54520i
$755$	17.5379	−	26.9452i	0.0232290	−	0.0356889i
$756$	143.740	−	52.7088i	0.190132	−	0.0697206i
$757$			187.760i			0.248031i	0.992280	+	0.124016i	$0.0395773\pi$
$757$			187.760i			0.248031i	−0.992280	+	0.124016i	$0.960423\pi$
$758$	99.8052	−	566.023i	0.131669	−	0.746733i
$759$	−43.0457	+	100.012i	−0.0567138	+	0.131768i
$760$	−292.497	+	219.940i	−0.384864	+	0.289395i
$761$	676.066	+	805.704i	0.888391	+	1.05874i	0.997901	+	0.0647579i	$0.0206275\pi$
$761$	676.066	+	805.704i	0.888391	+	1.05874i	−0.109510	+	0.993986i	$0.534928\pi$
$762$	−5.89667	+	102.659i	−0.00773841	+	0.134724i
$763$	−198.562	−	545.545i	−0.260239	−	0.715000i
$764$	294.557	+	170.062i	0.385546	+	0.222595i
$765$	291.345	+	784.820i	0.380843	+	1.02591i
$766$	−312.868	−	541.903i	−0.408443	−	0.707445i
$767$	−620.709	−	520.837i	−0.809269	−	0.679057i
$768$	34.9403	+	32.9116i	0.0454952	+	0.0428536i
$769$	264.795	+	1501.73i	0.344337	+	1.95283i	0.300453	+	0.953797i	$0.402862\pi$
$769$	264.795	+	1501.73i	0.344337	+	1.95283i	0.0438841	+	0.999037i	$0.486027\pi$
$770$	108.685	+	46.2661i	0.141149	+	0.0600859i
$771$	−682.421	−	642.798i	−0.885111	−	0.833719i
$772$	50.1509	−	59.7675i	0.0649623	−	0.0774191i
$773$	549.095	+	951.061i	0.710343	+	1.23035i	0.964728	+	0.263247i	$0.0847936\pi$
$773$	549.095	+	951.061i	0.710343	+	1.23035i	−0.254385	+	0.967103i	$0.581873\pi$
$774$	500.659	−	216.916i	0.646847	−	0.280253i
$775$	76.5637	+	8.20662i	0.0987919	+	0.0105892i
$776$	−11.1051	−	30.5109i	−0.0143107	−	0.0393182i
$777$	373.590	+	21.4587i	0.480811	+	0.0276174i
$778$	−393.659	−	469.145i	−0.505989	−	0.603014i
$779$	229.242	−	629.837i	0.294277	−	0.808520i
$780$	−322.534	−	484.468i	−0.413505	−	0.621113i
$781$	−75.0756	+	425.775i	−0.0961275	+	0.545166i
$782$	162.059			0.207236
$783$	−204.925	−	1146.07i	−0.261718	−	1.46369i
$784$	163.847			0.208989
$785$	819.858	−	877.377i	1.04440	−	1.11768i
$786$	201.260	−	23.6874i	0.256056	−	0.0301367i
$787$	292.696	−	804.177i	0.371914	−	1.02183i	−0.602707	−	0.797963i	$-0.705911\pi$
$787$	292.696	−	804.177i	0.371914	−	1.02183i	0.974621	−	0.223863i	$-0.0718667\pi$
$788$	31.7158	−	26.6127i	0.0402485	−	0.0337725i
$789$	272.703	−	415.349i	0.345631	−	0.526425i
$790$	−204.204	+	880.369i	−0.258486	+	1.11439i
$791$	−270.542	−	156.197i	−0.342025	−	0.197468i
$792$	149.720	−	8.96106i	0.189041	−	0.0113145i
$793$	347.782	−	200.792i	0.438565	−	0.253206i
$794$	−308.767	+	367.975i	−0.388876	+	0.463444i
$795$	−818.862	−	858.281i	−1.03002	−	1.07960i
$796$	42.2057	+	239.361i	0.0530223	+	0.300704i
$797$	79.9616	+	453.485i	0.100328	+	0.568990i	0.992984	+	0.118250i	$0.0377285\pi$
$797$	79.9616	+	453.485i	0.100328	+	0.568990i	−0.892656	+	0.450739i	$0.851160\pi$
$798$	−89.5120	−	298.121i	−0.112170	−	0.373585i
$799$	−728.288	−	611.106i	−0.911499	−	0.764839i
$800$	83.3608	−	114.241i	0.104201	−	0.142801i
$801$	−443.897	+	420.142i	−0.554178	+	0.524522i
$802$	421.625	+	243.425i	0.525717	+	0.303523i
$803$	253.161	−	92.1431i	0.315269	−	0.114749i
$804$	439.769	−	221.302i	0.546977	−	0.275251i
$805$	−86.6800	+	10.5524i	−0.107677	+	0.0131085i
$806$	−28.9029	+	79.4100i	−0.0358596	+	0.0985235i
$807$	257.928	+	345.879i	0.319614	+	0.428598i
$808$	9.95545	+	1.75541i	0.0123211	+	0.00217254i
$809$			936.069i			1.15707i	0.815658	+	0.578535i	$0.196375\pi$
$809$			936.069i			1.15707i	−0.815658	+	0.578535i	$0.803625\pi$
$810$	−462.141	−	338.343i	−0.570544	−	0.417707i
$811$	−850.642			−1.04888			−0.524440	−	0.851447i	$-0.675725\pi$
$811$	−850.642			−1.04888			−0.524440	+	0.851447i	$0.675725\pi$
$812$	−42.4580	+	240.791i	−0.0522882	+	0.296541i
$813$	−1091.04	+	813.609i	−1.34199	+	1.00075i
$814$	344.494	+	125.385i	0.423211	+	0.154036i
$815$	−736.752	+	89.6918i	−0.903990	+	0.110051i
$816$	−100.350	−	199.415i	−0.122978	−	0.244381i
$817$	−379.414	−	1042.43i	−0.464400	−	1.27593i
$818$	162.342	−	281.184i	0.198462	−	0.343746i
$819$	481.503	−	114.934i	0.587916	−	0.140334i
$820$	−13.8220	+	258.644i	−0.0168561	+	0.315419i
$821$	−128.468	+	153.102i	−0.156477	+	0.186482i	−0.838587	−	0.544767i	$-0.816618\pi$
$821$	−128.468	+	153.102i	−0.156477	+	0.186482i	0.682110	+	0.731249i	$0.261062\pi$
$822$	−766.508	+	230.147i	−0.932491	+	0.279984i
$823$	251.077	−	44.2717i	0.305076	−	0.0537930i	−0.0190147	−	0.999819i	$-0.506053\pi$
$823$	251.077	−	44.2717i	0.305076	−	0.0537930i	0.324090	+	0.946026i	$0.394942\pi$
$824$	−141.152	+	24.8890i	−0.171302	+	0.0302051i
$825$	−81.2484	−	434.373i	−0.0984830	−	0.526513i
$826$	128.284	+	107.643i	0.155307	+	0.130318i
$827$	−78.6921	−	136.299i	−0.0951536	−	0.164811i	0.814519	−	0.580137i	$-0.197001\pi$
$827$	−78.6921	−	136.299i	−0.0951536	−	0.164811i	−0.909673	+	0.415326i	$0.863668\pi$
$828$	−92.5377	+	61.0757i	−0.111760	+	0.0737630i
$829$	149.179	−	258.386i	0.179951	−	0.311684i	−0.761913	−	0.647680i	$-0.775739\pi$
$829$	149.179	−	258.386i	0.179951	−	0.311684i	0.941864	+	0.335996i	$0.109073\pi$
$830$	−93.0090	+	400.982i	−0.112059	+	0.483111i
$831$	335.477	+	220.262i	0.403703	+	0.265056i
$832$	99.7626	+	118.892i	0.119907	+	0.142900i
$833$	−716.073	−	260.629i	−0.859631	−	0.312880i
$834$	−76.4649	−	649.683i	−0.0916846	−	0.778996i
$835$	−108.974	−	101.830i	−0.130508	−	0.121952i
$836$		−	304.944i		−	0.364766i
$837$	0.199977	+	83.1623i	0.000238921	+	0.0993575i
$838$			224.711i			0.268151i
$839$	1450.59	+	255.778i	1.72895	+	0.304860i	0.947653	−	0.319302i	$-0.103448\pi$
$839$	1450.59	+	255.778i	1.72895	+	0.304860i	0.781295	+	0.624162i	$0.214559\pi$
$840$	66.6589	+	100.126i	0.0793559	+	0.119198i
$841$	956.936	+	348.296i	1.13785	+	0.414145i
$842$	−761.194	+	638.717i	−0.904030	+	0.758572i
$843$	−67.8456	+	1181.17i	−0.0804811	+	1.40116i
$844$	−193.324	+	70.3641i	−0.229057	+	0.0833698i
$845$	−469.780	−	924.347i	−0.555953	−	1.09390i
$846$	646.173	+	74.4769i	0.763798	+	0.0880342i
$847$	211.854	−	122.314i	0.250122	−	0.144408i
$848$	242.325	+	203.335i	0.285760	+	0.239781i
$849$	1108.26	−	1176.57i	1.30537	−	1.38583i
$850$	−546.039	+	366.674i	−0.642398	+	0.431381i
$851$	−266.887	+	47.0593i	−0.313615	+	0.0552989i
$852$	−301.869	+	320.477i	−0.354306	+	0.376146i
$853$	2.04684	−	2.43932i	0.00239957	−	0.00285970i	−0.764843	−	0.644216i	$-0.777184\pi$
$853$	2.04684	−	2.43932i	0.00239957	−	0.00285970i	0.767243	+	0.641357i	$0.221628\pi$
$854$	−71.8771	+	41.4983i	−0.0841652	+	0.0485928i
$855$	−742.800	+	896.813i	−0.868772	+	1.04890i
$856$	−209.057	+	362.097i	−0.244225	+	0.423010i
$857$	−106.015	+	38.5864i	−0.123705	+	0.0450250i	−0.403131	−	0.915142i	$-0.632078\pi$
$857$	−106.015	+	38.5864i	−0.123705	+	0.0450250i	0.279426	+	0.960167i	$0.409856\pi$
$858$	484.173	+	27.8105i	0.564305	+	0.0324132i
$859$	154.922	−	129.995i	0.180351	−	0.151333i	−0.548143	−	0.836385i	$-0.684665\pi$
$859$	154.922	−	129.995i	0.180351	−	0.151333i	0.728494	+	0.685052i	$0.240221\pi$
$860$	257.638	+	342.631i	0.299579	+	0.398408i
$861$	−202.356	−	87.0956i	−0.235024	−	0.101156i
$862$	−477.387	−	84.1762i	−0.553813	−	0.0976522i
$863$	−808.251			−0.936560			−0.468280	−	0.883580i	$-0.655126\pi$
$863$	−808.251			−0.936560			−0.468280	+	0.883580i	$0.655126\pi$
$864$	132.456	+	76.0492i	0.153305	+	0.0880200i
$865$	−238.380	+	366.248i	−0.275584	+	0.423408i
$866$	407.298	+	71.8176i	0.470321	+	0.0829303i
$867$	20.0183	+	170.085i	0.0230891	+	0.196176i
$868$	5.97344	−	16.4119i	0.00688184	−	0.0189077i
$869$	−484.057	−	576.877i	−0.557028	−	0.663840i
$870$	837.870	−	366.990i	0.963069	−	0.421828i
$871$	1495.84	−	544.442i	1.71739	−	0.625077i
$872$	289.588	−	501.581i	0.332097	−	0.575208i
$873$	−56.9113	−	86.2281i	−0.0651905	−	0.0987721i
$874$	112.712	+	195.223i	0.128961	+	0.223368i
$875$	268.183	−	231.677i	0.306495	−	0.264774i
$876$	266.998	+	63.0537i	0.304792	+	0.0719791i
$877$	−1642.19	+	289.562i	−1.87250	+	0.330173i	−0.990105	−	0.140328i	$-0.955184\pi$
$877$	−1642.19	+	289.562i	−1.87250	+	0.330173i	−0.882399	+	0.470501i	$0.844073\pi$
$878$	−125.923	−	714.146i	−0.143420	−	0.813378i
$879$	1055.31	−	316.861i	1.20058	−	0.360478i
$880$	34.3376	+	112.728i	0.0390200	+	0.128100i
$881$	−255.400	+	147.455i	−0.289898	+	0.167373i	−0.637896	−	0.770123i	$-0.720195\pi$
$881$	−255.400	+	147.455i	−0.289898	+	0.167373i	0.347998	+	0.937495i	$0.386862\pi$
$882$	507.112	−	121.047i	0.574957	−	0.137241i
$883$	855.021	+	493.647i	0.968314	+	0.559056i	0.898722	−	0.438519i	$-0.144497\pi$
$883$	855.021	+	493.647i	0.968314	+	0.559056i	0.0695923	+	0.997576i	$0.477830\pi$
$884$	−246.879	−	678.295i	−0.279275	−	0.767302i
$885$	69.2519	−	622.652i	0.0782507	−	0.703561i
$886$	502.154	−	421.357i	0.566765	−	0.475572i
$887$	−772.902	−	281.313i	−0.871366	−	0.317151i	−0.132646	−	0.991164i	$-0.542347\pi$
$887$	−772.902	−	281.313i	−0.871366	−	0.317151i	−0.738720	+	0.674012i	$0.764569\pi$
$888$	223.169	+	299.267i	0.251316	+	0.337012i
$889$	11.9324	−	67.6719i	0.0134222	−	0.0761213i
$890$	−402.463	−	261.952i	−0.452205	−	0.294328i
$891$	456.768	−	138.345i	0.512647	−	0.155269i
$892$			462.446i			0.518437i
$893$	229.640	−	1302.36i	0.257156	−	1.45840i
$894$	669.459	+	897.737i	0.748836	+	1.00418i
$895$	−573.817	−	763.114i	−0.641136	−	0.852642i
$896$	−20.6182	−	24.5718i	−0.0230114	−	0.0274239i
$897$	−320.244	+	161.154i	−0.357016	+	0.179659i
$898$	282.173	+	775.264i	0.314224	+	0.863323i
$899$	−115.020	−	66.4071i	−0.127943	−	0.0738677i
$900$	173.606	−	415.164i	0.192895	−	0.461293i
$901$	−735.607	−	1274.11i	−0.816434	−	1.41411i
$902$	−165.333	−	138.731i	−0.183296	−	0.153804i
$903$	−349.219	+	104.854i	−0.386732	+	0.116118i
$904$	−54.1178	−	306.917i	−0.0598648	−	0.339510i
$905$	−1415.03	−	602.367i	−1.56357	−	0.665598i
$906$	−6.26995	+	26.5498i	−0.00692047	+	0.0293044i
$907$	588.143	−	700.921i	0.648449	−	0.772791i	−0.337231	−	0.941422i	$-0.609490\pi$
$907$	588.143	−	700.921i	0.648449	−	0.772791i	0.985679	+	0.168631i	$0.0539347\pi$
$908$	242.455	+	419.944i	0.267021	+	0.462493i
$909$	32.1093	−	1.92181i	0.0353237	−	0.00211420i
$910$	176.215	+	346.723i	0.193643	+	0.381014i
$911$	−522.953	−	1436.80i	−0.574043	−	1.57717i	−0.798056	−	0.602583i	$-0.794138\pi$
$911$	−522.953	−	1436.80i	−0.574043	−	1.57717i	0.224014	−	0.974586i	$-0.428084\pi$
$912$	170.431	−	259.580i	0.186876	−	0.284627i
$913$	−220.474	−	262.750i	−0.241483	−	0.287788i
$914$	18.9946	−	52.1871i	0.0207818	−	0.0570975i
$915$	278.245	+	137.798i	0.304093	+	0.150599i
$916$	−79.1190	+	448.706i	−0.0863744	+	0.489854i
$917$	−135.421			−0.147679
$918$	−457.910	−	543.058i	−0.498812	−	0.591567i
$919$	187.131			0.203624			0.101812	−	0.994804i	$-0.467536\pi$
$919$	187.131			0.203624			0.101812	+	0.994804i	$0.467536\pi$
$920$	−63.6487	−	59.4761i	−0.0691834	−	0.0646479i
$921$	443.619	−	1030.69i	0.481670	−	1.11910i
$922$	195.473	−	537.057i	0.212009	−	0.582491i
$923$	−1090.49	+	915.034i	−1.18147	+	0.991369i
$924$	−100.065	−	5.74767i	−0.108296	−	0.00622043i
$925$	792.769	−	762.420i	0.857048	−	0.824237i
$926$	−733.356	−	423.403i	−0.791961	−	0.457239i
$927$	−418.484	+	181.312i	−0.451439	+	0.195591i
$928$	−211.245	+	121.962i	−0.227635	+	0.131425i
$929$	−376.463	+	448.651i	−0.405235	+	0.482940i	−0.929609	−	0.368548i	$-0.879855\pi$
$929$	−376.463	+	448.651i	−0.405235	+	0.482940i	0.524374	+	0.851488i	$0.324299\pi$
$930$	−63.4922	+	15.4233i	−0.0682712	+	0.0165842i
$931$	−184.065	−	1043.88i	−0.197707	−	1.12125i
$932$	−49.7113	−	281.927i	−0.0533383	−	0.302497i
$933$	584.792	−	620.839i	0.626787	−	0.665423i
$934$	9.85990	+	8.27344i	0.0105566	+	0.00885807i
$935$	29.2470	−	547.283i	0.0312802	−	0.585330i
$936$	396.603	+	294.273i	0.423722	+	0.314395i
$937$	654.779	+	378.037i	0.698803	+	0.403454i	0.806902	−	0.590686i	$-0.201143\pi$
$937$	654.779	+	378.037i	0.698803	+	0.403454i	−0.108098	+	0.994140i	$0.534476\pi$
$938$	−309.150	+	112.521i	−0.329584	+	0.119959i
$939$	51.1158	−	889.912i	0.0544364	−	0.947723i
$940$	61.7581	+	507.297i	0.0657001	+	0.539678i
$941$	−34.5683	+	94.9755i	−0.0367357	+	0.100930i	−0.956704	−	0.291061i	$-0.905992\pi$
$941$	−34.5683	+	94.9755i	−0.0367357	+	0.100930i	0.919969	+	0.391992i	$0.128214\pi$
$942$	−402.826	+	935.917i	−0.427628	+	0.993542i
$943$	157.122	+	27.7049i	0.166620	+	0.0293795i
$944$			167.064i			0.176975i
$945$	280.283	+	260.648i	0.296595	+	0.275818i
$946$	−357.211			−0.377602
$947$	−194.259	+	1101.70i	−0.205131	+	1.16335i	0.692103	+	0.721798i	$0.256684\pi$
$947$	−194.259	+	1101.70i	−0.205131	+	1.16335i	−0.897234	+	0.441555i	$0.854427\pi$
$948$	−89.6364	−	761.594i	−0.0945532	−	0.803369i
$949$	833.562	+	303.392i	0.878358	+	0.319696i
$950$	−821.484	−	402.761i	−0.864720	−	0.423959i
$951$	−588.306	+	896.040i	−0.618619	+	0.942208i
$952$	51.0232	+	140.185i	0.0535958	+	0.147253i
$953$	220.249	−	381.482i	0.231111	−	0.400296i	−0.727024	−	0.686612i	$-0.759097\pi$
$953$	220.249	−	381.482i	0.231111	−	0.400296i	0.958135	+	0.286316i	$0.0924307\pi$
$954$	900.221	+	450.302i	0.943628	+	0.472015i
$955$	−45.3762	+	849.101i	−0.0475143	+	0.889111i
$956$	333.087	−	396.957i	0.348417	−	0.415227i
$957$	−175.182	+	741.799i	−0.183053	+	0.775130i
$958$	946.192	−	166.839i	0.987674	−	0.174154i
$959$	526.689	−	92.8694i	0.549206	−	0.0968399i
$960$	−33.7733	+	115.149i	−0.0351805	+	0.119947i
$961$	−728.901	−	611.621i	−0.758482	−	0.636442i
$962$	603.540	+	1045.36i	0.627381	+	1.08666i
$963$	−379.527	+	1275.15i	−0.394110	+	1.32414i
$964$	404.412	−	700.462i	0.419515	−	0.726621i
$965$	190.008	+	44.0729i	0.196899	+	0.0456714i
$966$	66.1856	−	33.3061i	0.0685152	−	0.0344784i
$967$	−277.501	−	330.713i	−0.286971	−	0.341999i	0.603230	−	0.797568i	$-0.293880\pi$
$967$	−277.501	−	330.713i	−0.286971	−	0.341999i	−0.890200	+	0.455569i	$0.849436\pi$
$968$	229.328	+	83.4686i	0.236909	+	0.0862279i
$969$	−1157.75	+	863.359i	−1.19479	+	0.890980i
$970$	55.4207	−	59.3089i	0.0571348	−	0.0611432i
$971$			1610.59i			1.65870i	0.558732	+	0.829348i	$0.311288\pi$
$971$			1610.59i			1.65870i	−0.558732	+	0.829348i	$0.688712\pi$
$972$	466.138	+	137.519i	0.479566	+	0.141481i
$973$			437.151i			0.449281i
$974$	467.614	+	82.4529i	0.480096	+	0.0846539i
$975$	714.399	−	1267.57i	0.732717	−	1.30008i
$976$	−77.8058	−	28.3190i	−0.0797191	−	0.0290154i
$977$	674.235	−	565.750i	0.690107	−	0.579069i	−0.228833	−	0.973466i	$-0.573491\pi$
$977$	674.235	−	565.750i	0.690107	−	0.579069i	0.918940	+	0.394397i	$0.129047\pi$
$978$	562.556	−	283.091i	0.575211	−	0.289459i
$979$	376.006	−	136.855i	0.384072	−	0.139791i
$980$	185.587	+	365.164i	0.189374	+	0.372616i
$981$	525.727	−	1766.35i	0.535909	−	1.80056i
$982$	704.164	−	406.549i	0.717071	−	0.414001i
$983$	230.160	+	193.127i	0.234141	+	0.196467i	0.752307	−	0.658812i	$-0.228941\pi$
$983$	230.160	+	193.127i	0.234141	+	0.196467i	−0.518167	+	0.855280i	$0.673385\pi$
$984$	−63.2023	−	210.496i	−0.0642300	−	0.213919i
$985$	95.2354	+	40.5408i	0.0966856	+	0.0411582i
$986$	1117.22	−	196.996i	1.13308	−	0.199793i
$987$	−423.031	−	99.9021i	−0.428603	−	0.101218i
$988$	645.400	−	769.158i	0.653239	−	0.778500i
$989$	228.684	−	132.031i	0.231228	−	0.133499i
$990$	189.557	+	323.529i	0.191471	+	0.326797i
$991$	−632.909	+	1096.23i	−0.638657	+	1.10619i	0.347071	+	0.937839i	$0.387176\pi$
$991$	−632.909	+	1096.23i	−0.638657	+	1.10619i	−0.985728	+	0.168347i	$0.946157\pi$
$992$	16.3729	−	5.95923i	0.0165049	−	0.00600729i
$993$	137.359	−	209.209i	0.138327	−	0.210683i
$994$	225.376	−	189.113i	0.226736	−	0.190254i
$995$	−485.653	+	365.183i	−0.488094	+	0.367018i
$996$	−40.8267	−	346.883i	−0.0409907	−	0.348277i
$997$	−220.125	−	38.8140i	−0.220788	−	0.0389308i	0.0621598	−	0.998066i	$-0.480201\pi$
$997$	−220.125	−	38.8140i	−0.220788	−	0.0389308i	−0.282948	+	0.959135i	$0.591312\pi$
$998$	−1119.97			−1.12222
$999$	911.807	+	761.368i	0.912719	+	0.762130i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.n.a.29.13	✓	216
5.4	even	2	inner	270.3.n.a.29.24	yes	216
27.14	odd	18	inner	270.3.n.a.149.24	yes	216
135.14	odd	18	inner	270.3.n.a.149.13	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.n.a.29.13	✓	216	1.1	even	1	trivial
270.3.n.a.29.24	yes	216	5.4	even	2	inner
270.3.n.a.149.13	yes	216	135.14	odd	18	inner
270.3.n.a.149.24	yes	216	27.14	odd	18	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	270.3.n.a.29.13

Level	$270$
Weight	$3$
Character	270.29
Analytic conductor	$7.357$
Analytic rank	$0$
Dimension	$216$
Inner twists	$4$