LMFDB - Embedded newform 240.3.bn.a.91.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,3,Mod(91,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 0]))

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

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

chi := DirichletCharacter("240.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	240.bn (of order $4$, degree $2$, 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:	$6.53952634465$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			91.5
Character	$\chi$	$=$	240.91
Dual form			240.3.bn.a.211.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80387 - 0.863740i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(2.50791 + 3.11615i) q^{4} +(1.58114 + 1.58114i) q^{5} +(1.15142 + 3.26714i) q^{6} +0.973675 q^{7} +(-1.83240 - 7.78732i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.80387 - 0.863740i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(2.50791 + 3.11615i) q^{4} +(1.58114 + 1.58114i) q^{5} +(1.15142 + 3.26714i) q^{6} +0.973675 q^{7} +(-1.83240 - 7.78732i) q^{8} +3.00000i q^{9} +(-1.48648 - 4.21786i) q^{10} +(-0.381327 + 0.381327i) q^{11} +(0.744946 - 6.88804i) q^{12} +(-11.7061 + 11.7061i) q^{13} +(-1.75639 - 0.841002i) q^{14} -3.87298i q^{15} +(-3.42081 + 15.6300i) q^{16} -23.3777 q^{17} +(2.59122 - 5.41162i) q^{18} +(20.8333 + 20.8333i) q^{19} +(-0.961721 + 8.89242i) q^{20} +(-1.19250 - 1.19250i) q^{21} +(1.01723 - 0.358498i) q^{22} +17.5211 q^{23} +(-7.29326 + 11.7817i) q^{24} +5.00000i q^{25} +(31.2274 - 11.0053i) q^{26} +(3.67423 - 3.67423i) q^{27} +(2.44189 + 3.03412i) q^{28} +(15.4826 - 15.4826i) q^{29} +(-3.34525 + 6.98637i) q^{30} +49.9821i q^{31} +(19.6710 - 25.2399i) q^{32} +0.934057 q^{33} +(42.1703 + 20.1922i) q^{34} +(1.53952 + 1.53952i) q^{35} +(-9.34846 + 7.52372i) q^{36} +(37.4882 + 37.4882i) q^{37} +(-19.5861 - 55.5752i) q^{38} +28.6740 q^{39} +(9.41556 - 15.2101i) q^{40} +67.4644i q^{41} +(1.12111 + 3.18114i) q^{42} +(22.3988 - 22.3988i) q^{43} +(-2.14461 - 0.231941i) q^{44} +(-4.74342 + 4.74342i) q^{45} +(-31.6058 - 15.1337i) q^{46} +22.5923i q^{47} +(23.3324 - 14.9532i) q^{48} -48.0520 q^{49} +(4.31870 - 9.01936i) q^{50} +(28.6317 + 28.6317i) q^{51} +(-65.8358 - 7.12019i) q^{52} +(-30.2640 - 30.2640i) q^{53} +(-9.80143 + 3.45426i) q^{54} -1.20586 q^{55} +(-1.78416 - 7.58232i) q^{56} -51.0310i q^{57} +(-41.3015 + 14.5557i) q^{58} +(-11.5796 + 11.5796i) q^{59} +(12.0688 - 9.71308i) q^{60} +(-15.7934 + 15.7934i) q^{61} +(43.1715 - 90.1612i) q^{62} +2.92103i q^{63} +(-57.2847 + 28.5389i) q^{64} -37.0180 q^{65} +(-1.68492 - 0.806782i) q^{66} +(17.7447 + 17.7447i) q^{67} +(-58.6290 - 72.8484i) q^{68} +(-21.4589 - 21.4589i) q^{69} +(-1.44735 - 4.10683i) q^{70} -0.610274 q^{71} +(23.3620 - 5.49719i) q^{72} +30.7806i q^{73} +(-35.2438 - 100.004i) q^{74} +(6.12372 - 6.12372i) q^{75} +(-12.6718 + 117.168i) q^{76} +(-0.371289 + 0.371289i) q^{77} +(-51.7242 - 24.7669i) q^{78} -100.080i q^{79} +(-30.1220 + 19.3045i) q^{80} -9.00000 q^{81} +(58.2717 - 121.697i) q^{82} +(35.9419 + 35.9419i) q^{83} +(0.725336 - 6.70671i) q^{84} +(-36.9633 - 36.9633i) q^{85} +(-59.7513 + 21.0578i) q^{86} -37.9244 q^{87} +(3.66826 + 2.27077i) q^{88} -77.8438i q^{89} +(12.6536 - 4.45944i) q^{90} +(-11.3980 + 11.3980i) q^{91} +(43.9412 + 54.5984i) q^{92} +(61.2153 - 61.2153i) q^{93} +(19.5139 - 40.7537i) q^{94} +65.8807i q^{95} +(-55.0044 + 6.82048i) q^{96} -115.333 q^{97} +(86.6796 + 41.5044i) q^{98} +(-1.14398 - 1.14398i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 24 q^{4}+O(q^{10}) $ 64 * q - 24 * q^4	$ 64 q - 24 q^{4} + 20 q^{10} - 64 q^{11} + 72 q^{14} - 36 q^{16} - 24 q^{18} + 32 q^{19} - 80 q^{20} + 48 q^{22} + 256 q^{23} - 36 q^{24} + 240 q^{28} - 64 q^{29} - 40 q^{32} - 76 q^{34} - 12 q^{36} + 192 q^{37} - 280 q^{38} - 192 q^{43} - 280 q^{44} - 300 q^{46} + 448 q^{49} - 40 q^{50} + 96 q^{51} + 104 q^{52} + 320 q^{53} + 36 q^{54} + 112 q^{56} + 64 q^{58} + 128 q^{59} + 32 q^{61} + 48 q^{62} + 48 q^{64} - 72 q^{66} - 64 q^{67} + 280 q^{68} - 96 q^{69} + 240 q^{70} - 512 q^{71} - 120 q^{72} - 608 q^{74} - 308 q^{76} - 448 q^{77} - 360 q^{78} - 576 q^{81} - 200 q^{82} - 144 q^{84} - 160 q^{85} - 560 q^{86} - 184 q^{88} + 576 q^{91} - 56 q^{92} + 460 q^{94} + 360 q^{96} + 368 q^{98} - 192 q^{99}+O(q^{100}) $ 64 * q - 24 * q^4 + 20 * q^10 - 64 * q^11 + 72 * q^14 - 36 * q^16 - 24 * q^18 + 32 * q^19 - 80 * q^20 + 48 * q^22 + 256 * q^23 - 36 * q^24 + 240 * q^28 - 64 * q^29 - 40 * q^32 - 76 * q^34 - 12 * q^36 + 192 * q^37 - 280 * q^38 - 192 * q^43 - 280 * q^44 - 300 * q^46 + 448 * q^49 - 40 * q^50 + 96 * q^51 + 104 * q^52 + 320 * q^53 + 36 * q^54 + 112 * q^56 + 64 * q^58 + 128 * q^59 + 32 * q^61 + 48 * q^62 + 48 * q^64 - 72 * q^66 - 64 * q^67 + 280 * q^68 - 96 * q^69 + 240 * q^70 - 512 * q^71 - 120 * q^72 - 608 * q^74 - 308 * q^76 - 448 * q^77 - 360 * q^78 - 576 * q^81 - 200 * q^82 - 144 * q^84 - 160 * q^85 - 560 * q^86 - 184 * q^88 + 576 * q^91 - 56 * q^92 + 460 * q^94 + 360 * q^96 + 368 * q^98 - 192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.80387	−	0.863740i	−0.901936	−	0.431870i
$2$	−1.80387	−	0.863740i	−0.901936	−	0.431870i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$	2.50791	+	3.11615i	0.626977	+	0.779038i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$6$	1.15142	+	3.26714i	0.191904	+	0.544524i
$7$	0.973675			0.139096			0.0695482	−	0.997579i	$-0.477844\pi$
$7$	0.973675			0.139096			0.0695482	+	0.997579i	$0.477844\pi$
$8$	−1.83240	−	7.78732i	−0.229049	−	0.973415i
$9$			3.00000i			0.333333i
$10$	−1.48648	−	4.21786i	−0.148648	−	0.421786i
$11$	−0.381327	+	0.381327i	−0.0346661	+	0.0346661i	−0.724227	−	0.689561i	$-0.757803\pi$
$11$	−0.381327	+	0.381327i	−0.0346661	+	0.0346661i	0.689561	+	0.724227i	$0.257803\pi$
$12$	0.744946	−	6.88804i	0.0620789	−	0.574003i
$13$	−11.7061	+	11.7061i	−0.900470	+	0.900470i	−0.995477	−	0.0950067i	$-0.969713\pi$
$13$	−11.7061	+	11.7061i	−0.900470	+	0.900470i	0.0950067	+	0.995477i	$0.469713\pi$
$14$	−1.75639	−	0.841002i	−0.125456	−	0.0600716i
$15$		−	3.87298i		−	0.258199i
$16$	−3.42081	+	15.6300i	−0.213801	+	0.976877i
$17$	−23.3777			−1.37516			−0.687578	−	0.726110i	$-0.741326\pi$
$17$	−23.3777			−1.37516			−0.687578	+	0.726110i	$0.741326\pi$
$18$	2.59122	−	5.41162i	0.143957	−	0.300645i
$19$	20.8333	+	20.8333i	1.09649	+	1.09649i	0.994818	+	0.101672i	$0.0324192\pi$
$19$	20.8333	+	20.8333i	1.09649	+	1.09649i	0.101672	+	0.994818i	$0.467581\pi$
$20$	−0.961721	+	8.89242i	−0.0480861	+	0.444621i
$21$	−1.19250	−	1.19250i	−0.0567859	−	0.0567859i
$22$	1.01723	−	0.358498i	0.0462378	−	0.0162953i
$23$	17.5211			0.761786			0.380893	−	0.924619i	$-0.375617\pi$
$23$	17.5211			0.761786			0.380893	+	0.924619i	$0.375617\pi$
$24$	−7.29326	+	11.7817i	−0.303886	+	0.490904i
$25$			5.00000i			0.200000i
$26$	31.2274	−	11.0053i	1.20105	−	0.423280i
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	2.44189	+	3.03412i	0.0872102	+	0.108361i
$29$	15.4826	−	15.4826i	0.533882	−	0.533882i	−0.387843	−	0.921725i	$-0.626780\pi$
$29$	15.4826	−	15.4826i	0.533882	−	0.533882i	0.921725	+	0.387843i	$0.126780\pi$
$30$	−3.34525	+	6.98637i	−0.111508	+	0.232879i
$31$			49.9821i			1.61232i	0.591695	+	0.806162i	$0.298459\pi$
$31$			49.9821i			1.61232i	−0.591695	+	0.806162i	$0.701541\pi$
$32$	19.6710	−	25.2399i	0.614719	−	0.788747i
$33$	0.934057			0.0283047
$34$	42.1703	+	20.1922i	1.24030	+	0.593889i
$35$	1.53952	+	1.53952i	0.0439862	+	0.0439862i
$36$	−9.34846	+	7.52372i	−0.259679	+	0.208992i
$37$	37.4882	+	37.4882i	1.01319	+	1.01319i	0.999912	+	0.0132817i	$0.00422782\pi$
$37$	37.4882	+	37.4882i	1.01319	+	1.01319i	0.0132817	+	0.999912i	$0.495772\pi$
$38$	−19.5861	−	55.5752i	−0.515422	−	1.46250i
$39$	28.6740			0.735231
$40$	9.41556	−	15.2101i	0.235389	−	0.380253i
$41$			67.4644i			1.64547i	0.568422	+	0.822737i	$0.307554\pi$
$41$			67.4644i			1.64547i	−0.568422	+	0.822737i	$0.692446\pi$
$42$	1.12111	+	3.18114i	0.0266931	+	0.0757414i
$43$	22.3988	−	22.3988i	0.520902	−	0.520902i	−0.396942	−	0.917844i	$-0.629929\pi$
$43$	22.3988	−	22.3988i	0.520902	−	0.520902i	0.917844	+	0.396942i	$0.129929\pi$
$44$	−2.14461	−	0.231941i	−0.0487410	−	0.00527138i
$45$	−4.74342	+	4.74342i	−0.105409	+	0.105409i
$46$	−31.6058	−	15.1337i	−0.687082	−	0.328993i
$47$			22.5923i			0.480688i	0.970688	+	0.240344i	$0.0772603\pi$
$47$			22.5923i			0.480688i	−0.970688	+	0.240344i	$0.922740\pi$
$48$	23.3324	−	14.9532i	0.486092	−	0.311525i
$49$	−48.0520			−0.980652
$50$	4.31870	−	9.01936i	0.0863740	−	0.180387i
$51$	28.6317	+	28.6317i	0.561405	+	0.561405i
$52$	−65.8358	−	7.12019i	−1.26607	−	0.136927i
$53$	−30.2640	−	30.2640i	−0.571019	−	0.571019i	0.361394	−	0.932413i	$-0.382301\pi$
$53$	−30.2640	−	30.2640i	−0.571019	−	0.571019i	−0.932413	+	0.361394i	$0.882301\pi$
$54$	−9.80143	+	3.45426i	−0.181508	+	0.0639679i
$55$	−1.20586			−0.0219248
$56$	−1.78416	−	7.58232i	−0.0318600	−	0.135399i
$57$		−	51.0310i		−	0.895280i
$58$	−41.3015	+	14.5557i	−0.712095	+	0.250960i
$59$	−11.5796	+	11.5796i	−0.196265	+	0.196265i	−0.798397	−	0.602132i	$-0.794318\pi$
$59$	−11.5796	+	11.5796i	−0.196265	+	0.196265i	0.602132	+	0.798397i	$0.294318\pi$
$60$	12.0688	−	9.71308i	0.201147	−	0.161885i
$61$	−15.7934	+	15.7934i	−0.258908	+	0.258908i	−0.824610	−	0.565702i	$-0.808605\pi$
$61$	−15.7934	+	15.7934i	−0.258908	+	0.258908i	0.565702	+	0.824610i	$0.308605\pi$
$62$	43.1715	−	90.1612i	0.696315	−	1.45421i
$63$			2.92103i			0.0463655i
$64$	−57.2847	+	28.5389i	−0.895073	+	0.445920i
$65$	−37.0180			−0.569507
$66$	−1.68492	−	0.806782i	−0.0255291	−	0.0122240i
$67$	17.7447	+	17.7447i	0.264847	+	0.264847i	0.827020	−	0.562173i	$-0.190034\pi$
$67$	17.7447	+	17.7447i	0.264847	+	0.264847i	−0.562173	+	0.827020i	$0.690034\pi$
$68$	−58.6290	−	72.8484i	−0.862191	−	1.07130i
$69$	−21.4589	−	21.4589i	−0.310998	−	0.310998i
$70$	−1.44735	−	4.10683i	−0.0206764	−	0.0586690i
$71$	−0.610274			−0.00859541			−0.00429770	−	0.999991i	$-0.501368\pi$
$71$	−0.610274			−0.00859541			−0.00429770	+	0.999991i	$0.501368\pi$
$72$	23.3620	−	5.49719i	0.324472	−	0.0763498i
$73$			30.7806i			0.421652i	0.977524	+	0.210826i	$0.0676154\pi$
$73$			30.7806i			0.421652i	−0.977524	+	0.210826i	$0.932385\pi$
$74$	−35.2438	−	100.004i	−0.476268	−	1.35140i
$75$	6.12372	−	6.12372i	0.0816497	−	0.0816497i
$76$	−12.6718	+	117.168i	−0.166734	+	1.54168i
$77$	−0.371289	+	0.371289i	−0.00482193	+	0.00482193i
$78$	−51.7242	−	24.7669i	−0.663131	−	0.317524i
$79$		−	100.080i		−	1.26683i	−0.773811	−	0.633417i	$-0.781652\pi$
$79$		−	100.080i		−	1.26683i	0.773811	−	0.633417i	$-0.218348\pi$
$80$	−30.1220	+	19.3045i	−0.376525	+	0.241306i
$81$	−9.00000			−0.111111
$82$	58.2717	−	121.697i	0.710631	−	1.48411i
$83$	35.9419	+	35.9419i	0.433035	+	0.433035i	0.889659	−	0.456625i	$-0.150942\pi$
$83$	35.9419	+	35.9419i	0.433035	+	0.433035i	−0.456625	+	0.889659i	$0.650942\pi$
$84$	0.725336	−	6.70671i	0.00863495	−	0.0798418i
$85$	−36.9633	−	36.9633i	−0.434863	−	0.434863i
$86$	−59.7513	+	21.0578i	−0.694782	+	0.244858i
$87$	−37.9244			−0.435913
$88$	3.66826	+	2.27077i	0.0416847	+	0.0258042i
$89$		−	77.8438i		−	0.874649i	−0.899304	−	0.437325i	$-0.855926\pi$
$89$		−	77.8438i		−	0.874649i	0.899304	−	0.437325i	$-0.144074\pi$
$90$	12.6536	−	4.45944i	0.140595	−	0.0495493i
$91$	−11.3980	+	11.3980i	−0.125252	+	0.125252i
$92$	43.9412	+	54.5984i	0.477622	+	0.593461i
$93$	61.2153	−	61.2153i	0.658229	−	0.658229i
$94$	19.5139	−	40.7537i	0.207595	−	0.433550i
$95$			65.8807i			0.693481i
$96$	−55.0044	+	6.82048i	−0.572962	+	0.0710466i
$97$	−115.333			−1.18900			−0.594501	−	0.804095i	$-0.702650\pi$
$97$	−115.333			−1.18900			−0.594501	+	0.804095i	$0.702650\pi$
$98$	86.6796	+	41.5044i	0.884485	+	0.423514i
$99$	−1.14398	−	1.14398i	−0.0115554	−	0.0115554i
$100$	−15.5808	+	12.5395i	−0.155808	+	0.125395i
$101$	−12.6205	−	12.6205i	−0.124955	−	0.124955i	0.641864	−	0.766819i	$-0.278161\pi$
$101$	−12.6205	−	12.6205i	−0.124955	−	0.124955i	−0.766819	+	0.641864i	$0.778161\pi$
$102$	−26.9175	−	76.3782i	−0.263897	−	0.748806i
$103$	−33.2685			−0.322995			−0.161498	−	0.986873i	$-0.551632\pi$
$103$	−33.2685			−0.322995			−0.161498	+	0.986873i	$0.551632\pi$
$104$	112.609	+	69.7090i	1.08278	+	0.670279i
$105$		−	3.77103i		−	0.0359146i
$106$	28.4521	+	80.7326i	0.268416	+	0.761628i
$107$	−36.7760	+	36.7760i	−0.343701	+	0.343701i	−0.857757	−	0.514056i	$-0.828142\pi$
$107$	−36.7760	+	36.7760i	−0.343701	+	0.343701i	0.514056	+	0.857757i	$0.328142\pi$
$108$	20.6641	+	2.23484i	0.191334	+	0.0206930i
$109$	136.918	−	136.918i	1.25613	−	1.25613i	0.303205	−	0.952925i	$-0.401943\pi$
$109$	136.918	−	136.918i	1.25613	−	1.25613i	0.952925	−	0.303205i	$-0.0980569\pi$
$110$	2.17522	+	1.04155i	0.0197747	+	0.00946865i
$111$		−	91.8269i		−	0.827269i
$112$	−3.33076	+	15.2186i	−0.0297389	+	0.135880i
$113$	−135.342			−1.19772			−0.598860	−	0.800853i	$-0.704380\pi$
$113$	−135.342			−1.19772			−0.598860	+	0.800853i	$0.704380\pi$
$114$	−44.0775	+	92.0533i	−0.386645	+	0.807485i
$115$	27.7033	+	27.7033i	0.240898	+	0.240898i
$116$	87.0750	+	9.41722i	0.750646	+	0.0811829i
$117$	−35.1183	−	35.1183i	−0.300157	−	0.300157i
$118$	30.8899	−	10.8864i	0.261779	−	0.0922573i
$119$	−22.7623			−0.191279
$120$	−30.1602	+	7.09684i	−0.251335	+	0.0591403i
$121$			120.709i			0.997597i
$122$	42.1306	−	14.8478i	0.345333	−	0.121704i
$123$	82.6267	−	82.6267i	0.671762	−	0.671762i
$124$	−155.752	+	125.350i	−1.25606	+	1.01089i
$125$	−7.90569	+	7.90569i	−0.0632456	+	0.0632456i
$126$	2.52301	−	5.26916i	0.0200239	−	0.0418187i
$127$		−	122.922i		−	0.967888i	−0.875099	−	0.483944i	$-0.839204\pi$
$127$		−	122.922i		−	0.967888i	0.875099	−	0.483944i	$-0.160796\pi$
$128$	127.984	−	2.00147i	0.999878	−	0.0156365i
$129$	−54.8656			−0.425315
$130$	66.7757	+	31.9739i	0.513659	+	0.245953i
$131$	107.619	+	107.619i	0.821519	+	0.821519i	0.986326	−	0.164806i	$-0.0527000\pi$
$131$	107.619	+	107.619i	0.821519	+	0.821519i	−0.164806	+	0.986326i	$0.552700\pi$
$132$	2.34253	+	2.91066i	0.0177464	+	0.0220505i
$133$	20.2849	+	20.2849i	0.152518	+	0.152518i
$134$	−16.6824	−	47.3360i	−0.124495	−	0.353254i
$135$	11.6190			0.0860663
$136$	42.8371	+	182.049i	0.314979	+	1.33860i
$137$			187.083i			1.36557i	0.730620	+	0.682785i	$0.239231\pi$
$137$			187.083i			1.36557i	−0.730620	+	0.682785i	$0.760769\pi$
$138$	20.1742	+	57.2439i	0.146190	+	0.414811i
$139$	180.528	−	180.528i	1.29876	−	1.29876i	0.369554	−	0.929209i	$-0.379511\pi$
$139$	180.528	−	180.528i	1.29876	−	1.29876i	0.929209	−	0.369554i	$-0.120489\pi$
$140$	−0.936405	+	8.65833i	−0.00668860	+	0.0618452i
$141$	27.6699	−	27.6699i	0.196240	−	0.196240i
$142$	1.10086	+	0.527118i	0.00775251	+	0.00371210i
$143$		−	8.92771i		−	0.0624316i
$144$	−46.8901	−	10.2624i	−0.325626	−	0.0712669i
$145$	48.9602			0.337657
$146$	26.5864	−	55.5243i	0.182099	−	0.380303i
$147$	58.8514	+	58.8514i	0.400350	+	0.400350i
$148$	−22.8020	+	210.836i	−0.154068	+	1.42456i
$149$	−139.757	−	139.757i	−0.937967	−	0.937967i	0.0602184	−	0.998185i	$-0.480820\pi$
$149$	−139.757	−	139.757i	−0.937967	−	0.937967i	−0.998185	+	0.0602184i	$0.980820\pi$
$150$	−16.3357	+	5.75711i	−0.108905	+	0.0383807i
$151$	−172.895			−1.14500			−0.572499	−	0.819906i	$-0.694026\pi$
$151$	−172.895			−1.14500			−0.572499	+	0.819906i	$0.694026\pi$
$152$	124.061	−	200.410i	0.816189	−	1.31849i
$153$		−	70.1330i		−	0.458386i
$154$	0.990454	−	0.349060i	0.00643152	−	0.00226663i
$155$	−79.0286	+	79.0286i	−0.509862	+	0.509862i
$156$	71.9117	+	89.3525i	0.460972	+	0.572773i
$157$	62.7152	−	62.7152i	0.399460	−	0.399460i	−0.478583	−	0.878043i	$-0.658849\pi$
$157$	62.7152	−	62.7152i	0.399460	−	0.399460i	0.878043	+	0.478583i	$0.158849\pi$
$158$	−86.4430	+	180.531i	−0.547108	+	1.14260i
$159$			74.1314i			0.466235i
$160$	71.0103	−	8.80520i	0.443815	−	0.0550325i
$161$	17.0598			0.105962
$162$	16.2348	+	7.77366i	0.100215	+	0.0479856i
$163$	18.1480	+	18.1480i	0.111337	+	0.111337i	0.760581	−	0.649243i	$-0.224914\pi$
$163$	18.1480	+	18.1480i	0.111337	+	0.111337i	−0.649243	+	0.760581i	$0.724914\pi$
$164$	−210.229	+	169.195i	−1.28189	+	1.03167i
$165$	1.47687	+	1.47687i	0.00895075	+	0.00895075i
$166$	−33.7901	−	95.8789i	−0.203555	−	0.577584i
$167$	−2.63064			−0.0157523			−0.00787617	−	0.999969i	$-0.502507\pi$
$167$	−2.63064			−0.0157523			−0.00787617	+	0.999969i	$0.502507\pi$
$168$	−7.10127	+	11.4715i	−0.0422695	+	0.0682830i
$169$		−	105.066i		−	0.621692i
$170$	34.7504	+	98.6038i	0.204414	+	0.580022i
$171$	−62.4999	+	62.4999i	−0.365497	+	0.365497i
$172$	125.972	+	13.6240i	0.732396	+	0.0792091i
$173$	−39.9440	+	39.9440i	−0.230890	+	0.230890i	−0.813064	−	0.582174i	$-0.802202\pi$
$173$	−39.9440	+	39.9440i	−0.230890	+	0.230890i	0.582174	+	0.813064i	$0.302202\pi$
$174$	68.4108	+	32.7568i	0.393166	+	0.188258i
$175$			4.86838i			0.0278193i
$176$	−4.65571	−	7.26460i	−0.0264529	−	0.0412762i
$177$	28.3641			0.160249
$178$	−67.2368	+	140.420i	−0.377735	+	0.788877i
$179$	172.610	+	172.610i	0.964303	+	0.964303i	0.999384	−	0.0350815i	$-0.0111691\pi$
$179$	172.610	+	172.610i	0.964303	+	0.964303i	−0.0350815	+	0.999384i	$0.511169\pi$
$180$	−26.6773	−	2.88516i	−0.148207	−	0.0160287i
$181$	96.3654	+	96.3654i	0.532405	+	0.532405i	0.921287	−	0.388882i	$-0.127139\pi$
$181$	96.3654	+	96.3654i	0.532405	+	0.532405i	−0.388882	+	0.921287i	$0.627139\pi$
$182$	30.4053	−	10.7156i	0.167062	−	0.0588768i
$183$	38.6857			0.211397
$184$	−32.1056	−	136.442i	−0.174487	−	0.741534i
$185$			118.548i			0.640800i
$186$	−163.299	+	57.5504i	−0.877949	+	0.309411i
$187$	8.91454	−	8.91454i	0.0476713	−	0.0476713i
$188$	−70.4012	+	56.6595i	−0.374474	+	0.301380i
$189$	3.57751	−	3.57751i	0.0189286	−	0.0189286i
$190$	56.9038	−	118.840i	0.299494	−	0.625475i
$191$		−	296.526i		−	1.55249i	−0.630431	−	0.776246i	$-0.717122\pi$
$191$		−	296.526i		−	1.55249i	0.630431	−	0.776246i	$-0.282878\pi$
$192$	105.112	+	35.2062i	0.547458	+	0.183366i
$193$	238.952			1.23809			0.619047	−	0.785354i	$-0.287519\pi$
$193$	238.952			1.23809			0.619047	+	0.785354i	$0.287519\pi$
$194$	208.046	+	99.6179i	1.07240	+	0.513494i
$195$	45.3376	+	45.3376i	0.232500	+	0.232500i
$196$	−120.510	−	149.737i	−0.614846	−	0.763965i
$197$	−66.3504	−	66.3504i	−0.336804	−	0.336804i	0.518359	−	0.855163i	$-0.326543\pi$
$197$	−66.3504	−	66.3504i	−0.336804	−	0.336804i	−0.855163	+	0.518359i	$0.826543\pi$
$198$	1.07549	+	3.05170i	0.00543178	+	0.0154126i
$199$	53.8049			0.270376			0.135188	−	0.990820i	$-0.456836\pi$
$199$	53.8049			0.270376			0.135188	+	0.990820i	$0.456836\pi$
$200$	38.9366	−	9.16198i	0.194683	−	0.0458099i
$201$		−	43.4655i		−	0.216246i
$202$	11.8649	+	33.6665i	0.0587371	+	0.166666i
$203$	15.0750	−	15.0750i	0.0742611	−	0.0742611i
$204$	−17.4151	+	161.026i	−0.0853681	+	0.789344i
$205$	−106.671	+	106.671i	−0.520345	+	0.520345i
$206$	60.0121	+	28.7353i	0.291321	+	0.139492i
$207$			52.5633i			0.253929i
$208$	−142.923	−	223.011i	−0.687128	−	1.07217i
$209$	−15.8886			−0.0760220
$210$	−3.25719	+	6.80245i	−0.0155104	+	0.0323926i
$211$	−178.485	−	178.485i	−0.845899	−	0.845899i	0.143719	−	0.989618i	$-0.454094\pi$
$211$	−178.485	−	178.485i	−0.845899	−	0.845899i	−0.989618	+	0.143719i	$0.954094\pi$
$212$	18.4080	−	170.207i	0.0868300	−	0.802861i
$213$	0.747430	+	0.747430i	0.00350906	+	0.00350906i
$214$	98.1040	−	34.5743i	0.458430	−	0.161562i
$215$	70.8312			0.329447
$216$	−35.3451	−	21.8798i	−0.163635	−	0.101295i
$217$			48.6663i			0.224269i
$218$	−365.245	+	128.721i	−1.67543	+	0.590464i
$219$	37.6984	−	37.6984i	0.172139	−	0.172139i
$220$	−3.02419	−	3.75765i	−0.0137463	−	0.0170802i
$221$	273.661	−	273.661i	1.23829	−	1.23829i
$222$	−79.3145	+	165.644i	−0.357273	+	0.746144i
$223$		−	354.446i		−	1.58944i	−0.606975	−	0.794721i	$-0.707617\pi$
$223$		−	354.446i		−	1.58944i	0.606975	−	0.794721i	$-0.292383\pi$
$224$	19.1532	−	24.5755i	0.0855052	−	0.109712i
$225$	−15.0000			−0.0666667
$226$	244.140	+	116.901i	1.08027	+	0.517260i
$227$	−69.8665	−	69.8665i	−0.307782	−	0.307782i	0.536267	−	0.844049i	$-0.319834\pi$
$227$	−69.8665	−	69.8665i	−0.307782	−	0.307782i	−0.844049	+	0.536267i	$0.819834\pi$
$228$	159.020	−	127.981i	0.697457	−	0.561320i
$229$	30.8678	+	30.8678i	0.134794	+	0.134794i	0.771284	−	0.636491i	$-0.219615\pi$
$229$	30.8678	+	30.8678i	0.134794	+	0.134794i	−0.636491	+	0.771284i	$0.719615\pi$
$230$	−26.0447	−	73.9016i	−0.113238	−	0.321311i
$231$	0.909468			0.00393709
$232$	−148.938	−	92.1976i	−0.641974	−	0.397403i
$233$			255.294i			1.09568i	0.836583	+	0.547840i	$0.184550\pi$
$233$			255.294i			1.09568i	−0.836583	+	0.547840i	$0.815450\pi$
$234$	33.0159	+	93.6821i	0.141093	+	0.400351i
$235$	−35.7216	+	35.7216i	−0.152007	+	0.152007i
$236$	−65.1244	−	7.04325i	−0.275951	−	0.0298443i
$237$	−122.572	+	122.572i	−0.517183	+	0.517183i
$238$	41.0602	+	19.6607i	0.172522	+	0.0826079i
$239$			142.641i			0.596823i	0.954437	+	0.298412i	$0.0964568\pi$
$239$			142.641i			0.596823i	−0.954437	+	0.298412i	$0.903543\pi$
$240$	60.5349	+	13.2487i	0.252229	+	0.0552031i
$241$	−209.275			−0.868359			−0.434179	−	0.900826i	$-0.642962\pi$
$241$	−209.275			−0.868359			−0.434179	+	0.900826i	$0.642962\pi$
$242$	104.261	−	217.744i	0.430832	−	0.899768i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$	−88.8228	−	9.60625i	−0.364028	−	0.0393699i
$245$	−75.9768	−	75.9768i	−0.310109	−	0.310109i
$246$	−220.416	+	77.6800i	−0.896000	+	0.315772i
$247$	−487.754			−1.97471
$248$	389.226	−	91.5869i	1.56946	−	0.369302i
$249$		−	88.0392i		−	0.353571i
$250$	21.0893	−	7.43239i	0.0843573	−	0.0297296i
$251$	−232.177	+	232.177i	−0.925010	+	0.925010i	−0.997378	−	0.0723682i	$-0.976944\pi$
$251$	−232.177	+	232.177i	−0.925010	+	0.925010i	0.0723682	+	0.997378i	$0.476944\pi$
$252$	−9.10236	+	7.32566i	−0.0361205	+	0.0290701i
$253$	−6.68126	+	6.68126i	−0.0264082	+	0.0264082i
$254$	−106.172	+	221.735i	−0.418002	+	0.872973i
$255$			90.5413i			0.355064i
$256$	−232.596	−	106.935i	−0.908579	−	0.417714i
$257$	−305.309			−1.18797			−0.593987	−	0.804475i	$-0.702447\pi$
$257$	−305.309			−1.18797			−0.593987	+	0.804475i	$0.702447\pi$
$258$	98.9705	+	47.3896i	0.383607	+	0.183681i
$259$	36.5013	+	36.5013i	0.140932	+	0.140932i
$260$	−92.8376	−	115.354i	−0.357068	−	0.443668i
$261$	46.4477	+	46.4477i	0.177961	+	0.177961i
$262$	−101.176	−	287.086i	−0.386168	−	1.09575i
$263$	−240.463			−0.914309			−0.457155	−	0.889387i	$-0.651131\pi$
$263$	−240.463			−0.914309			−0.457155	+	0.889387i	$0.651131\pi$
$264$	−1.71156	−	7.27380i	−0.00648319	−	0.0275523i
$265$		−	95.7032i		−	0.361144i
$266$	−19.0705	−	54.1122i	−0.0716935	−	0.203429i
$267$	−95.3388	+	95.3388i	−0.357074	+	0.357074i
$268$	−10.7932	+	99.7974i	−0.0402730	+	0.372378i
$269$	200.232	−	200.232i	0.744356	−	0.744356i	−0.229057	−	0.973413i	$-0.573564\pi$
$269$	200.232	−	200.232i	0.744356	−	0.744356i	0.973413	+	0.229057i	$0.0735642\pi$
$270$	−20.9591	−	10.0358i	−0.0776263	−	0.0371695i
$271$		−	507.632i		−	1.87318i	−0.350424	−	0.936591i	$-0.613962\pi$
$271$		−	507.632i		−	1.87318i	0.350424	−	0.936591i	$-0.386038\pi$
$272$	79.9706	−	365.394i	0.294009	−	1.34336i
$273$	27.9192			0.102268
$274$	161.591	−	337.474i	0.589748	−	1.23166i
$275$	−1.90664	−	1.90664i	−0.00693322	−	0.00693322i
$276$	13.0523	−	120.686i	0.0472908	−	0.437268i
$277$	368.293	+	368.293i	1.32958	+	1.32958i	0.905737	+	0.423840i	$0.139318\pi$
$277$	368.293	+	368.293i	1.32958	+	1.32958i	0.423840	+	0.905737i	$0.360682\pi$
$278$	−481.579	+	169.720i	−1.73230	+	0.610504i
$279$	−149.946			−0.537442
$280$	9.16770	−	14.8097i	0.0327418	−	0.0528918i
$281$		−	40.6286i		−	0.144586i	−0.997383	−	0.0722929i	$-0.976968\pi$
$281$		−	40.6286i		−	0.144586i	0.997383	−	0.0722929i	$-0.0230316\pi$
$282$	−73.8124	+	26.0133i	−0.261746	+	0.0922458i
$283$	182.875	−	182.875i	0.646202	−	0.646202i	−0.305871	−	0.952073i	$-0.598948\pi$
$283$	182.875	−	182.875i	0.646202	−	0.646202i	0.952073	+	0.305871i	$0.0989475\pi$
$284$	−1.53051	−	1.90171i	−0.00538912	−	0.00669615i
$285$	80.6871	−	80.6871i	0.283112	−	0.283112i
$286$	−7.71122	+	16.1044i	−0.0269623	+	0.0563093i
$287$			65.6885i			0.228880i
$288$	75.7197	+	59.0130i	0.262916	+	0.204906i
$289$	257.515			0.891056
$290$	−88.3180	−	42.2889i	−0.304545	−	0.145824i
$291$	141.254	+	141.254i	0.485408	+	0.485408i
$292$	−95.9170	+	77.1949i	−0.328483	+	0.264366i
$293$	64.6234	+	64.6234i	0.220558	+	0.220558i	0.808733	−	0.588176i	$-0.200154\pi$
$293$	64.6234	+	64.6234i	0.220558	+	0.220558i	−0.588176	+	0.808733i	$0.700154\pi$
$294$	−55.3281	−	156.993i	−0.188191	−	0.533989i
$295$	−36.6179			−0.124129
$296$	223.239	−	360.625i	0.754186	−	1.21833i
$297$			2.80217i			0.00943492i
$298$	131.390	+	372.818i	0.440906	+	1.25107i
$299$	−205.104	+	205.104i	−0.685966	+	0.685966i
$300$	34.4402	+	3.72473i	0.114801	+	0.0124158i
$301$	21.8091	−	21.8091i	0.0724556	−	0.0724556i
$302$	311.880	+	149.336i	1.03271	+	0.494490i
$303$			30.9137i			0.102025i
$304$	−396.892	+	254.359i	−1.30557	+	0.836706i
$305$	−49.9430			−0.163748
$306$	−60.5767	+	126.511i	−0.197963	+	0.413434i
$307$	185.741	+	185.741i	0.605019	+	0.605019i	0.941640	−	0.336622i	$-0.109284\pi$
$307$	185.741	+	185.741i	0.605019	+	0.605019i	−0.336622	+	0.941640i	$0.609284\pi$
$308$	−2.08815	−	0.225835i	−0.00677971	−	0.000733230i
$309$	40.7454	+	40.7454i	0.131862	+	0.131862i
$310$	210.818	−	74.2973i	0.680057	−	0.239669i
$311$	454.743			1.46219			0.731097	−	0.682273i	$-0.239008\pi$
$311$	454.743			1.46219			0.731097	+	0.682273i	$0.239008\pi$
$312$	−52.5421	−	223.294i	−0.168404	−	0.715684i
$313$			301.051i			0.961825i	0.876769	+	0.480912i	$0.159695\pi$
$313$			301.051i			0.961825i	−0.876769	+	0.480912i	$0.840305\pi$
$314$	−167.300	+	58.9605i	−0.532802	+	0.187772i
$315$	−4.61855	+	4.61855i	−0.0146621	+	0.0146621i
$316$	311.864	−	250.991i	0.986912	−	0.794275i
$317$	91.4490	−	91.4490i	0.288483	−	0.288483i	−0.547997	−	0.836480i	$-0.684610\pi$
$317$	91.4490	−	91.4490i	0.288483	−	0.288483i	0.836480	+	0.547997i	$0.184610\pi$
$318$	64.0302	−	133.723i	0.201353	−	0.420514i
$319$			11.8079i			0.0370152i
$320$	−135.699	−	45.4510i	−0.424059	−	0.142034i
$321$	90.0824			0.280631
$322$	−30.7738	−	14.7353i	−0.0955707	−	0.0457617i
$323$	−487.034	−	487.034i	−1.50785	−	1.50785i
$324$	−22.5712	−	28.0454i	−0.0696641	−	0.0865598i
$325$	−58.5305	−	58.5305i	−0.180094	−	0.180094i
$326$	−17.0615	−	48.4117i	−0.0523358	−	0.148502i
$327$	−335.380			−1.02563
$328$	525.367	−	123.622i	1.60173	−	0.376895i
$329$			21.9976i			0.0668620i
$330$	−1.38846	−	3.93972i	−0.00420744	−	0.0119386i
$331$	−163.455	+	163.455i	−0.493821	+	0.493821i	−0.909508	−	0.415687i	$-0.863541\pi$
$331$	−163.455	+	163.455i	−0.493821	+	0.493821i	0.415687	+	0.909508i	$0.363541\pi$
$332$	−21.8615	+	202.139i	−0.0658479	+	0.608853i
$333$	−112.464	+	112.464i	−0.337731	+	0.337731i
$334$	4.74534	+	2.27219i	0.0142076	+	0.00680296i
$335$			56.1138i			0.167504i
$336$	22.7182	−	14.5596i	0.0676137	−	0.0433320i
$337$	199.528			0.592072			0.296036	−	0.955177i	$-0.404335\pi$
$337$	199.528			0.592072			0.296036	+	0.955177i	$0.404335\pi$
$338$	−90.7497	+	189.526i	−0.268490	+	0.560726i
$339$	165.760	+	165.760i	0.488968	+	0.488968i
$340$	22.4828	−	207.884i	0.0661259	−	0.611423i
$341$	−19.0595	−	19.0595i	−0.0558930	−	0.0558930i
$342$	166.726	−	58.7582i	0.487502	−	0.171807i
$343$	−94.4971			−0.275502
$344$	−215.470	−	133.383i	−0.626366	−	0.387741i
$345$		−	67.8589i		−	0.196692i
$346$	106.555	−	37.5526i	0.307963	−	0.108534i
$347$	21.9838	−	21.9838i	0.0633539	−	0.0633539i	−0.674720	−	0.738074i	$-0.735736\pi$
$347$	21.9838	−	21.9838i	0.0633539	−	0.0633539i	0.738074	+	0.674720i	$0.235736\pi$
$348$	−95.1109	−	118.178i	−0.273307	−	0.339593i
$349$	−70.9120	+	70.9120i	−0.203186	+	0.203186i	−0.801364	−	0.598177i	$-0.795892\pi$
$349$	−70.9120	+	70.9120i	−0.203186	+	0.203186i	0.598177	+	0.801364i	$0.295892\pi$
$350$	4.20501	−	8.78193i	0.0120143	−	0.0250912i
$351$			86.0220i			0.245077i
$352$	2.12357	+	17.1257i	0.00603287	+	0.0486527i
$353$	618.415			1.75188			0.875942	−	0.482416i	$-0.160241\pi$
$353$	618.415			1.75188			0.875942	+	0.482416i	$0.160241\pi$
$354$	−51.1653	−	24.4992i	−0.144535	−	0.0692069i
$355$	−0.964928	−	0.964928i	−0.00271811	−	0.00271811i
$356$	242.573	−	195.225i	0.681385	−	0.548385i
$357$	27.8780	+	27.8780i	0.0780895	+	0.0780895i
$358$	−162.276	−	460.457i	−0.453286	−	1.28619i
$359$	485.263			1.35171			0.675854	−	0.737035i	$-0.263775\pi$
$359$	485.263			1.35171			0.675854	+	0.737035i	$0.263775\pi$
$360$	45.6303	+	28.2467i	0.126751	+	0.0784630i
$361$			507.053i			1.40458i
$362$	−90.5961	−	257.065i	−0.250266	−	0.710125i
$363$	147.838	−	147.838i	0.407267	−	0.407267i
$364$	−64.1027	−	6.93276i	−0.176106	−	0.0190460i
$365$	−48.6684	+	48.6684i	−0.133338	+	0.133338i
$366$	−69.7840	−	33.4144i	−0.190667	−	0.0912961i
$367$			519.893i			1.41660i	0.705910	+	0.708302i	$0.250538\pi$
$367$			519.893i			1.41660i	−0.705910	+	0.708302i	$0.749462\pi$
$368$	−59.9363	+	273.855i	−0.162870	+	0.744172i
$369$	−202.393			−0.548491
$370$	102.395	−	213.845i	0.276742	−	0.577960i
$371$	−29.4673	−	29.4673i	−0.0794267	−	0.0794267i
$372$	344.278	+	37.2339i	0.925479	+	0.100091i
$373$	138.390	+	138.390i	0.371019	+	0.371019i	0.867848	−	0.496829i	$-0.165502\pi$
$373$	138.390	+	138.390i	0.371019	+	0.371019i	−0.496829	+	0.867848i	$0.665502\pi$
$374$	−23.7805	+	8.38084i	−0.0635843	+	0.0224087i
$375$	19.3649			0.0516398
$376$	175.934	−	41.3981i	0.467909	−	0.110101i
$377$			362.482i			0.961490i
$378$	−9.54341	+	3.36333i	−0.0252471	+	0.00889771i
$379$	−175.319	+	175.319i	−0.462583	+	0.462583i	−0.899501	−	0.436918i	$-0.856070\pi$
$379$	−175.319	+	175.319i	−0.462583	+	0.462583i	0.436918	+	0.899501i	$0.356070\pi$
$380$	−205.294	+	165.223i	−0.540248	+	0.434796i
$381$	−150.548	+	150.548i	−0.395139	+	0.395139i
$382$	−256.121	+	534.894i	−0.670474	+	1.40025i
$383$			532.343i			1.38993i	0.719043	+	0.694965i	$0.244580\pi$
$383$			532.343i			1.38993i	−0.719043	+	0.694965i	$0.755420\pi$
$384$	−159.199	−	154.297i	−0.414582	−	0.401815i
$385$	−1.17412			−0.00304966
$386$	−431.039	−	206.393i	−1.11668	−	0.534696i
$387$	67.1964	+	67.1964i	0.173634	+	0.173634i
$388$	−289.245	−	359.396i	−0.745476	−	0.926277i
$389$	−105.371	−	105.371i	−0.270876	−	0.270876i	0.558577	−	0.829453i	$-0.311348\pi$
$389$	−105.371	−	105.371i	−0.270876	−	0.270876i	−0.829453	+	0.558577i	$0.811348\pi$
$390$	−42.6233	−	120.943i	−0.109290	−	0.310110i
$391$	−409.602			−1.04758
$392$	88.0502	+	374.196i	0.224618	+	0.954581i
$393$		−	263.612i		−	0.670768i
$394$	62.3782	+	176.997i	0.158320	+	0.449232i
$395$	158.240	−	158.240i	0.400608	−	0.400608i
$396$	0.695822	−	6.43382i	0.00175713	−	0.0162470i
$397$	−120.285	+	120.285i	−0.302985	+	0.302985i	−0.842181	−	0.539196i	$-0.818728\pi$
$397$	−120.285	+	120.285i	−0.302985	+	0.302985i	0.539196	+	0.842181i	$0.318728\pi$
$398$	−97.0571	−	46.4734i	−0.243862	−	0.116767i
$399$		−	49.6876i		−	0.124530i
$400$	−78.1502	−	17.1041i	−0.195375	−	0.0427601i
$401$	667.195			1.66383			0.831914	−	0.554904i	$-0.187245\pi$
$401$	667.195			1.66383			0.831914	+	0.554904i	$0.187245\pi$
$402$	−37.5429	+	78.4062i	−0.0933903	+	0.195040i
$403$	−585.095	−	585.095i	−1.45185	−	1.45185i
$404$	7.67634	−	70.9782i	0.0190008	−	0.175689i
$405$	−14.2302	−	14.2302i	−0.0351364	−	0.0351364i
$406$	−40.2143	+	14.1725i	−0.0990499	+	0.0349076i
$407$	−28.5905			−0.0702469
$408$	170.499	−	275.429i	0.417891	−	0.675070i
$409$		−	444.554i		−	1.08693i	−0.839433	−	0.543464i	$-0.817112\pi$
$409$		−	444.554i		−	1.08693i	0.839433	−	0.543464i	$-0.182888\pi$
$410$	284.556	−	100.284i	0.694039	−	0.244596i
$411$	229.129	−	229.129i	0.557491	−	0.557491i
$412$	−83.4343	−	103.670i	−0.202510	−	0.251626i
$413$	−11.2748	+	11.2748i	−0.0272997	+	0.0272997i
$414$	45.4010	−	94.8174i	0.109664	−	0.229027i
$415$			113.658i			0.273875i
$416$	65.1901	+	525.732i	0.156707	+	1.26378i
$417$	−442.202			−1.06044
$418$	28.6610	+	13.7236i	0.0685670	+	0.0328316i
$419$	11.7447	+	11.7447i	0.0280303	+	0.0280303i	0.720983	−	0.692953i	$-0.243691\pi$
$419$	11.7447	+	11.7447i	0.0280303	+	0.0280303i	−0.692953	+	0.720983i	$0.743691\pi$
$420$	11.7511	−	9.45739i	0.0279788	−	0.0225176i
$421$	133.374	+	133.374i	0.316803	+	0.316803i	0.847538	−	0.530735i	$-0.178084\pi$
$421$	133.374	+	133.374i	0.316803	+	0.316803i	−0.530735	+	0.847538i	$0.678084\pi$
$422$	167.799	+	476.128i	0.397628	+	1.12827i
$423$	−67.7770			−0.160229
$424$	−180.220	+	291.131i	−0.425047	+	0.686630i
$425$		−	116.888i		−	0.275031i
$426$	−0.702682	−	1.99385i	−0.00164949	−	0.00468040i
$427$	−15.3776	+	15.3776i	−0.0360131	+	0.0360131i
$428$	−206.830	−	22.3688i	−0.483248	−	0.0522637i
$429$	−10.9342	+	10.9342i	−0.0254876	+	0.0254876i
$430$	−127.770	−	61.1797i	−0.297140	−	0.142278i
$431$		−	507.841i		−	1.17828i	−0.808029	−	0.589142i	$-0.799466\pi$
$431$		−	507.841i		−	1.17828i	0.808029	−	0.589142i	$-0.200534\pi$
$432$	44.8596	+	69.9973i	0.103842	+	0.162031i
$433$	619.599			1.43094			0.715472	−	0.698642i	$-0.246212\pi$
$433$	619.599			1.43094			0.715472	+	0.698642i	$0.246212\pi$
$434$	42.0350	−	87.7878i	0.0968549	−	0.202276i
$435$	−59.9638	−	59.9638i	−0.137848	−	0.137848i
$436$	770.036	+	83.2800i	1.76614	+	0.191009i
$437$	365.022	+	365.022i	0.835291	+	0.835291i
$438$	−100.565	+	35.4414i	−0.229600	+	0.0809165i
$439$	−210.219			−0.478859			−0.239430	−	0.970914i	$-0.576960\pi$
$439$	−210.219			−0.478859			−0.239430	+	0.970914i	$0.576960\pi$
$440$	2.20962	+	9.39043i	0.00502186	+	0.0213419i
$441$		−	144.156i		−	0.326884i
$442$	−730.023	+	257.278i	−1.65163	+	0.582077i
$443$	−266.878	+	266.878i	−0.602433	+	0.602433i	−0.940958	−	0.338524i	$-0.890072\pi$
$443$	−266.878	+	266.878i	−0.602433	+	0.602433i	0.338524	+	0.940958i	$0.390072\pi$
$444$	286.146	−	230.293i	0.644474	−	0.518678i
$445$	123.082	−	123.082i	0.276588	−	0.276588i
$446$	−306.149	+	639.374i	−0.686432	+	1.43358i
$447$			342.333i			0.765847i
$448$	−55.7767	+	27.7876i	−0.124501	+	0.0620260i
$449$	−721.868			−1.60772			−0.803862	−	0.594816i	$-0.797225\pi$
$449$	−721.868			−1.60772			−0.803862	+	0.594816i	$0.797225\pi$
$450$	27.0581	+	12.9561i	0.0601291	+	0.0287913i
$451$	−25.7260	−	25.7260i	−0.0570422	−	0.0570422i
$452$	−339.426	−	421.748i	−0.750943	−	0.933070i
$453$	211.752	+	211.752i	0.467443	+	0.467443i
$454$	65.6837	+	186.377i	0.144678	+	0.410521i
$455$	−36.0435			−0.0792165
$456$	−397.394	+	93.5089i	−0.871479	+	0.205063i
$457$			136.469i			0.298619i	0.988791	+	0.149310i	$0.0477051\pi$
$457$			136.469i			0.298619i	−0.988791	+	0.149310i	$0.952295\pi$
$458$	−29.0198	−	82.3433i	−0.0633620	−	0.179789i
$459$	−85.8950	+	85.8950i	−0.187135	+	0.187135i
$460$	−16.8504	+	155.805i	−0.0366313	+	0.338706i
$461$	376.809	−	376.809i	0.817372	−	0.817372i	−0.168354	−	0.985727i	$-0.553845\pi$
$461$	376.809	−	376.809i	0.817372	−	0.817372i	0.985727	+	0.168354i	$0.0538452\pi$
$462$	−1.64056	−	0.785544i	−0.00355100	−	0.00170031i
$463$			293.116i			0.633080i	0.948579	+	0.316540i	$0.102521\pi$
$463$			293.116i			0.633080i	−0.948579	+	0.316540i	$0.897479\pi$
$464$	189.030	+	294.956i	0.407393	+	0.635682i
$465$	193.580			0.416300
$466$	220.507	−	460.517i	0.473191	−	0.988233i
$467$	−56.8179	−	56.8179i	−0.121666	−	0.121666i	0.643652	−	0.765318i	$-0.277418\pi$
$467$	−56.8179	−	56.8179i	−0.121666	−	0.121666i	−0.765318	+	0.643652i	$0.777418\pi$
$468$	21.3606	−	197.508i	0.0456423	−	0.422025i
$469$	17.2776	+	17.2776i	0.0368392	+	0.0368392i
$470$	95.2915	−	33.5830i	0.202748	−	0.0714533i
$471$	−153.620			−0.326158
$472$	111.393	+	68.9557i	0.236001	+	0.146093i
$473$			17.0825i			0.0361153i
$474$	326.975	−	115.234i	0.689821	−	0.243110i
$475$	−104.167	+	104.167i	−0.219298	+	0.219298i
$476$	−57.0856	−	70.9307i	−0.119928	−	0.149014i
$477$	90.7920	−	90.7920i	0.190340	−	0.190340i
$478$	123.205	−	257.306i	0.257750	−	0.538296i
$479$			511.880i			1.06864i	0.845281	+	0.534322i	$0.179433\pi$
$479$			511.880i			1.06864i	−0.845281	+	0.534322i	$0.820567\pi$
$480$	−97.7537	−	76.1854i	−0.203653	−	0.158720i
$481$	−877.681			−1.82470
$482$	377.504	+	180.759i	0.783204	+	0.375018i
$483$	−20.8940	−	20.8940i	−0.0432587	−	0.0432587i
$484$	−376.148	+	302.727i	−0.777166	+	0.625470i
$485$	−182.358	−	182.358i	−0.375995	−	0.375995i
$486$	−10.3628	−	29.4043i	−0.0213226	−	0.0605027i
$487$	915.950			1.88080			0.940400	−	0.340069i	$-0.110451\pi$
$487$	915.950			1.88080			0.940400	+	0.340069i	$0.110451\pi$
$488$	151.928	+	94.0483i	0.311327	+	0.192722i
$489$		−	44.4533i		−	0.0909065i
$490$	71.4282	+	202.677i	0.145772	+	0.413626i
$491$	440.518	−	440.518i	0.897185	−	0.897185i	−0.0980009	−	0.995186i	$-0.531245\pi$
$491$	440.518	−	440.518i	0.897185	−	0.897185i	0.995186	+	0.0980009i	$0.0312448\pi$
$492$	464.698	+	50.2574i	0.944507	+	0.102149i
$493$	−361.947	+	361.947i	−0.734172	+	0.734172i
$494$	879.846	+	421.293i	1.78106	+	0.852819i
$495$		−	3.61759i		−	0.00730825i
$496$	−781.221	−	170.979i	−1.57504	−	0.344716i
$497$	−0.594209			−0.00119559
$498$	−76.0430	+	158.811i	−0.152697	+	0.318899i
$499$	556.559	+	556.559i	1.11535	+	1.11535i	0.992415	+	0.122933i	$0.0392301\pi$
$499$	556.559	+	556.559i	1.11535	+	1.11535i	0.122933	+	0.992415i	$0.460770\pi$
$500$	−44.4621	−	4.80861i	−0.0889242	−	0.00961721i
$501$	3.22186	+	3.22186i	0.00643086	+	0.00643086i
$502$	619.359	−	218.277i	1.23378	−	0.434816i
$503$	159.479			0.317055			0.158527	−	0.987355i	$-0.449325\pi$
$503$	159.479			0.317055			0.158527	+	0.987355i	$0.449325\pi$
$504$	22.7470	−	5.35248i	0.0451329	−	0.0106200i
$505$		−	39.9094i		−	0.0790285i
$506$	17.8230	−	6.28127i	0.0352234	−	0.0124136i
$507$	−128.679	+	128.679i	−0.253805	+	0.253805i
$508$	383.043	−	308.276i	0.754021	−	0.606843i
$509$	627.165	−	627.165i	1.23215	−	1.23215i	0.269015	−	0.963136i	$-0.413302\pi$
$509$	627.165	−	627.165i	1.23215	−	1.23215i	0.963136	−	0.269015i	$-0.0866982\pi$
$510$	78.2041	−	163.325i	0.153341	−	0.320245i
$511$			29.9703i			0.0586503i
$512$	327.210	+	393.799i	0.639081	+	0.769139i
$513$	153.093			0.298427
$514$	550.739	+	263.708i	1.07148	+	0.513050i
$515$	−52.6021	−	52.6021i	−0.102140	−	0.102140i
$516$	−137.598	−	170.970i	−0.266662	−	0.331336i
$517$	−8.61507	−	8.61507i	−0.0166636	−	0.0166636i
$518$	−34.3160	−	97.3713i	−0.0662472	−	0.187975i
$519$	97.8425			0.188521
$520$	67.8316	+	288.271i	0.130445	+	0.554367i
$521$			183.442i			0.352096i	0.984382	+	0.176048i	$0.0563314\pi$
$521$			183.442i			0.352096i	−0.984382	+	0.176048i	$0.943669\pi$
$522$	−43.6670	−	123.905i	−0.0836533	−	0.237365i
$523$	603.515	−	603.515i	1.15395	−	1.15395i	0.168195	−	0.985754i	$-0.446206\pi$
$523$	603.515	−	603.515i	1.15395	−	1.15395i	0.985754	−	0.168195i	$-0.0537937\pi$
$524$	−65.4589	+	605.256i	−0.124921	+	1.15507i
$525$	5.96252	−	5.96252i	0.0113572	−	0.0113572i
$526$	433.765	+	207.698i	0.824648	+	0.394863i
$527$		−	1168.46i		−	2.21720i
$528$	−3.19523	+	14.5993i	−0.00605158	+	0.0276503i
$529$	−222.012			−0.419682
$530$	−82.6627	+	172.636i	−0.155967	+	0.325729i
$531$	−34.7388	−	34.7388i	−0.0654215	−	0.0654215i
$532$	−12.3382	+	114.083i	−0.0231921	+	0.214442i
$533$	−789.746	−	789.746i	−1.48170	−	1.48170i
$534$	254.327	−	89.6310i	0.476267	−	0.167848i
$535$	−116.296			−0.217375
$536$	105.668	−	170.699i	0.197143	−	0.318469i
$537$		−	422.807i		−	0.787350i
$538$	−534.141	+	188.244i	−0.992826	+	0.349896i
$539$	18.3235	−	18.3235i	0.0339954	−	0.0339954i
$540$	29.1392	+	36.2064i	0.0539616	+	0.0670489i
$541$	−331.408	+	331.408i	−0.612585	+	0.612585i	−0.943619	−	0.331034i	$-0.892602\pi$
$541$	−331.408	+	331.408i	−0.612585	+	0.612585i	0.331034	+	0.943619i	$0.392602\pi$
$542$	−438.462	+	915.704i	−0.808971	+	1.68949i
$543$		−	236.046i		−	0.434707i
$544$	−459.862	+	590.050i	−0.845334	+	1.08465i
$545$	432.974			0.794447
$546$	−50.3626	−	24.1149i	−0.0922392	−	0.0441665i
$547$	−285.175	−	285.175i	−0.521344	−	0.521344i	0.396633	−	0.917977i	$-0.370179\pi$
$547$	−285.175	−	285.175i	−0.521344	−	0.521344i	−0.917977	+	0.396633i	$0.870179\pi$
$548$	−582.979	+	469.187i	−1.06383	+	0.856180i
$549$	−47.3801	−	47.3801i	−0.0863026	−	0.0863026i
$550$	1.79249	+	5.08616i	0.00325907	+	0.00924757i
$551$	645.107			1.17079
$552$	−127.786	+	206.428i	−0.231496	+	0.373964i
$553$		−	97.4453i		−	0.176212i
$554$	−346.244	−	982.462i	−0.624989	−	1.77340i
$555$	145.191	−	145.191i	0.261605	−	0.261605i
$556$	1015.30	+	109.805i	1.82608	+	0.197492i
$557$	−350.751	+	350.751i	−0.629715	+	0.629715i	−0.947996	−	0.318282i	$-0.896894\pi$
$557$	−350.751	+	350.751i	−0.629715	+	0.629715i	0.318282	+	0.947996i	$0.396894\pi$
$558$	270.484	+	129.515i	0.484738	+	0.232105i
$559$			524.405i			0.938113i
$560$	−29.3291	+	18.7963i	−0.0523734	+	0.0335648i
$561$	−21.8361			−0.0389235
$562$	−35.0926	+	73.2888i	−0.0624423	+	0.130407i
$563$	−338.656	−	338.656i	−0.601521	−	0.601521i	0.339195	−	0.940716i	$-0.389845\pi$
$563$	−338.656	−	338.656i	−0.601521	−	0.601521i	−0.940716	+	0.339195i	$0.889845\pi$
$564$	155.617	+	16.8301i	0.275917	+	0.0298406i
$565$	−213.995	−	213.995i	−0.378753	−	0.378753i
$566$	−487.840	+	171.927i	−0.861908	+	0.303758i
$567$	−8.76308			−0.0154552
$568$	1.11826	+	4.75240i	0.00196877	+	0.00836690i
$569$		−	1048.59i		−	1.84286i	−0.388549	−	0.921428i	$-0.627024\pi$
$569$		−	1048.59i		−	1.84286i	0.388549	−	0.921428i	$-0.372976\pi$
$570$	−215.242	+	75.8565i	−0.377617	+	0.133082i
$571$	−499.898	+	499.898i	−0.875479	+	0.875479i	−0.993063	−	0.117584i	$-0.962485\pi$
$571$	−499.898	+	499.898i	−0.875479	+	0.875479i	0.117584	+	0.993063i	$0.462485\pi$
$572$	27.8201	−	22.3899i	0.0486366	−	0.0391431i
$573$	−363.168	+	363.168i	−0.633802	+	0.633802i
$574$	56.7378	−	118.494i	0.0988463	−	0.206435i
$575$			87.6054i			0.152357i
$576$	−85.6167	−	171.854i	−0.148640	−	0.298358i
$577$	12.1087			0.0209856			0.0104928	−	0.999945i	$-0.496660\pi$
$577$	12.1087			0.0209856			0.0104928	+	0.999945i	$0.496660\pi$
$578$	−464.524	−	222.426i	−0.803675	−	0.384820i
$579$	−292.655	−	292.655i	−0.505450	−	0.505450i
$580$	122.788	+	152.568i	0.211703	+	0.263047i
$581$	34.9957	+	34.9957i	0.0602336	+	0.0602336i
$582$	−132.797	−	376.810i	−0.228174	−	0.647440i
$583$	23.0810			0.0395900
$584$	239.698	−	56.4022i	0.410442	−	0.0965792i
$585$		−	111.054i		−	0.189836i
$586$	−60.7545	−	172.390i	−0.103677	−	0.294181i
$587$	−127.116	+	127.116i	−0.216553	+	0.216553i	−0.807044	−	0.590491i	$-0.798934\pi$
$587$	−127.116	+	127.116i	−0.216553	+	0.216553i	0.590491	+	0.807044i	$0.298934\pi$
$588$	−35.7961	+	330.984i	−0.0608778	+	0.562897i
$589$	−1041.29	+	1041.29i	−1.76790	+	1.76790i
$590$	66.0541	+	31.6284i	0.111956	+	0.0536074i
$591$			162.525i			0.275000i
$592$	−714.181	+	457.701i	−1.20639	+	0.773144i
$593$	285.471			0.481402			0.240701	−	0.970599i	$-0.422623\pi$
$593$	285.471			0.481402			0.240701	+	0.970599i	$0.422623\pi$
$594$	2.42035	−	5.05476i	0.00407466	−	0.00850969i
$595$	−35.9903	−	35.9903i	−0.0604879	−	0.0604879i
$596$	85.0067	−	786.002i	0.142629	−	1.31880i
$597$	−65.8972	−	65.8972i	−0.110381	−	0.110381i
$598$	547.137	−	192.825i	0.914945	−	0.322449i
$599$	752.991			1.25708			0.628540	−	0.777777i	$-0.283653\pi$
$599$	752.991			1.25708			0.628540	+	0.777777i	$0.283653\pi$
$600$	−58.9085	−	36.4663i	−0.0981808	−	0.0607772i
$601$		−	987.651i		−	1.64335i	−0.569959	−	0.821673i	$-0.693041\pi$
$601$		−	987.651i		−	1.64335i	0.569959	−	0.821673i	$-0.306959\pi$
$602$	−58.1783	+	20.5035i	−0.0966418	+	0.0340589i
$603$	−53.2342	+	53.2342i	−0.0882822	+	0.0882822i
$604$	−433.603	−	538.766i	−0.717886	−	0.891996i
$605$	−190.858	+	190.858i	−0.315468	+	0.315468i
$606$	26.7014	−	55.7643i	0.0440617	−	0.0920203i
$607$		−	655.153i		−	1.07933i	−0.841880	−	0.539664i	$-0.818551\pi$
$607$		−	655.153i		−	1.07933i	0.841880	−	0.539664i	$-0.181449\pi$
$608$	935.642	−	116.019i	1.53889	−	0.190820i
$609$	−36.9261			−0.0606340
$610$	90.0908	+	43.1378i	0.147690	+	0.0707177i
$611$	−264.468	−	264.468i	−0.432845	−	0.432845i
$612$	218.545	−	175.887i	0.357100	−	0.287397i
$613$	477.400	+	477.400i	0.778793	+	0.778793i	0.979626	−	0.200832i	$-0.0643646\pi$
$613$	477.400	+	477.400i	0.778793	+	0.778793i	−0.200832	+	0.979626i	$0.564365\pi$
$614$	−174.621	−	495.484i	−0.284399	−	0.806977i
$615$	261.289			0.424860
$616$	3.57169	+	2.21100i	0.00579820	+	0.00358928i
$617$		−	406.449i		−	0.658750i	−0.944199	−	0.329375i	$-0.893162\pi$
$617$		−	406.449i		−	0.658750i	0.944199	−	0.329375i	$-0.106838\pi$
$618$	−38.3061	−	108.693i	−0.0619839	−	0.175879i
$619$	444.234	−	444.234i	0.717664	−	0.717664i	−0.250462	−	0.968126i	$-0.580583\pi$
$619$	444.234	−	444.234i	0.717664	−	0.717664i	0.968126	+	0.250462i	$0.0805825\pi$
$620$	−444.461	−	48.0688i	−0.716873	−	0.0775304i
$621$	64.3766	−	64.3766i	0.103666	−	0.103666i
$622$	−820.297	−	392.779i	−1.31881	−	0.631478i
$623$		−	75.7946i		−	0.121661i
$624$	−98.0883	+	448.176i	−0.157193	+	0.718230i
$625$	−25.0000			−0.0400000
$626$	260.030	−	543.058i	0.415383	−	0.867504i
$627$	19.4595	+	19.4595i	0.0310359	+	0.0310359i
$628$	352.714	+	38.1463i	0.561646	+	0.0607425i
$629$	−876.386	−	876.386i	−1.39330	−	1.39330i
$630$	12.3205	−	4.34204i	0.0195563	−	0.00689213i
$631$	−10.2255			−0.0162052			−0.00810258	−	0.999967i	$-0.502579\pi$
$631$	−10.2255			−0.0162052			−0.00810258	+	0.999967i	$0.502579\pi$
$632$	−779.354	+	183.386i	−1.23315	+	0.290168i
$633$			437.196i			0.690674i
$634$	−243.950	+	85.9741i	−0.384780	+	0.135606i
$635$	194.356	−	194.356i	0.306073	−	0.306073i
$636$	−231.005	+	185.914i	−0.363215	+	0.292318i
$637$	562.501	−	562.501i	0.883048	−	0.883048i
$638$	10.1989	−	21.2999i	0.0159858	−	0.0333854i
$639$		−	1.83082i		−	0.00286514i
$640$	205.526	+	199.196i	0.321134	+	0.311244i
$641$	−1029.57			−1.60620			−0.803099	−	0.595846i	$-0.796817\pi$
$641$	−1029.57			−1.60620			−0.803099	+	0.595846i	$0.796817\pi$
$642$	−162.497	−	77.8078i	−0.253111	−	0.121196i
$643$	−584.634	−	584.634i	−0.909228	−	0.909228i	0.0869820	−	0.996210i	$-0.472278\pi$
$643$	−584.634	−	584.634i	−0.909228	−	0.909228i	−0.996210	+	0.0869820i	$0.972278\pi$
$644$	42.7845	+	53.1611i	0.0664356	+	0.0825483i
$645$	−86.7501	−	86.7501i	−0.134496	−	0.134496i
$646$	457.876	+	1299.22i	0.708787	+	2.01117i
$647$	872.678			1.34881			0.674403	−	0.738363i	$-0.264401\pi$
$647$	872.678			1.34881			0.674403	+	0.738363i	$0.264401\pi$
$648$	16.4916	+	70.0859i	0.0254499	+	0.108157i
$649$		−	8.83124i		−	0.0136075i
$650$	55.0264	+	156.137i	0.0846560	+	0.240210i
$651$	59.6038	−	59.6038i	0.0915573	−	0.0915573i
$652$	−11.0384	+	102.065i	−0.0169301	+	0.156542i
$653$	−612.251	+	612.251i	−0.937597	+	0.937597i	−0.998164	−	0.0605674i	$-0.980709\pi$
$653$	−612.251	+	612.251i	−0.937597	+	0.937597i	0.0605674	+	0.998164i	$0.480709\pi$
$654$	604.982	+	289.681i	0.925049	+	0.442937i
$655$			340.321i			0.519575i
$656$	−1054.47	−	230.783i	−1.60743	−	0.351804i
$657$	−92.3418			−0.140551
$658$	19.0002	−	39.6809i	0.0288757	−	0.0603053i
$659$	−678.938	−	678.938i	−1.03025	−	1.03025i	−0.999528	−	0.0307270i	$-0.990218\pi$
$659$	−678.938	−	678.938i	−1.03025	−	1.03025i	−0.0307270	−	0.999528i	$-0.509782\pi$
$660$	−0.898302	+	8.30602i	−0.00136106	+	0.0125849i
$661$	−378.327	−	378.327i	−0.572355	−	0.572355i	0.360431	−	0.932786i	$-0.382630\pi$
$661$	−378.327	−	378.327i	−0.572355	−	0.572355i	−0.932786	+	0.360431i	$0.882630\pi$
$662$	436.034	−	153.669i	0.658662	−	0.232129i
$663$	−670.331			−1.01106
$664$	214.031	−	345.750i	0.322336	−	0.520709i
$665$			64.1464i			0.0964608i
$666$	300.012	−	105.731i	0.450468	−	0.158756i
$667$	271.272	−	271.272i	0.406704	−	0.406704i
$668$	−6.59740	−	8.19748i	−0.00987635	−	0.0122717i
$669$	−434.105	+	434.105i	−0.648887	+	0.648887i
$670$	48.4677	−	101.222i	0.0723398	−	0.151078i
$671$		−	12.0449i		−	0.0179506i
$672$	−53.5564	+	6.64093i	−0.0796970	+	0.00988234i
$673$	35.7112			0.0530627			0.0265314	−	0.999648i	$-0.491554\pi$
$673$	35.7112			0.0530627			0.0265314	+	0.999648i	$0.491554\pi$
$674$	−359.923	−	172.340i	−0.534011	−	0.255698i
$675$	18.3712	+	18.3712i	0.0272166	+	0.0272166i
$676$	327.402	−	263.496i	0.484322	−	0.389786i
$677$	−465.231	−	465.231i	−0.687195	−	0.687195i	0.274416	−	0.961611i	$-0.411515\pi$
$677$	−465.231	−	465.231i	−0.687195	−	0.687195i	−0.961611	+	0.274416i	$0.911515\pi$
$678$	−155.836	−	442.183i	−0.229847	−	0.652188i
$679$	−112.297			−0.165386
$680$	−220.114	+	355.577i	−0.323697	+	0.522907i
$681$			171.137i			0.251303i
$682$	17.9185	+	50.8434i	0.0262734	+	0.0745504i
$683$	144.241	−	144.241i	0.211188	−	0.211188i	−0.593584	−	0.804772i	$-0.702288\pi$
$683$	144.241	−	144.241i	0.211188	−	0.211188i	0.804772	+	0.593584i	$0.202288\pi$
$684$	−351.503	−	38.0153i	−0.513894	−	0.0555780i
$685$	−295.804	+	295.804i	−0.431831	+	0.431831i
$686$	170.461	+	81.6209i	0.248485	+	0.118981i
$687$		−	75.6104i		−	0.110059i
$688$	273.472	+	426.716i	0.397488	+	0.620227i
$689$	708.547			1.02837
$690$	−58.6124	+	122.409i	−0.0849455	+	0.177404i
$691$	781.092	+	781.092i	1.13038	+	1.13038i	0.990114	+	0.140265i	$0.0447955\pi$
$691$	781.092	+	781.092i	1.13038	+	1.13038i	0.140265	+	0.990114i	$0.455204\pi$
$692$	−224.648	−	24.2958i	−0.324635	−	0.0351095i
$693$	−1.11387	−	1.11387i	−0.00160731	−	0.00160731i
$694$	−58.6442	+	20.6677i	−0.0845018	+	0.0297805i
$695$	570.880			0.821410
$696$	69.4926	+	295.330i	0.0998456	+	0.424324i
$697$		−	1577.16i		−	2.26278i
$698$	189.166	−	66.6666i	0.271011	−	0.0955110i
$699$	312.669	−	312.669i	0.447310	−	0.447310i
$700$	−15.1706	+	12.2094i	−0.0216723	+	0.0174420i
$701$	16.0752	−	16.0752i	0.0229317	−	0.0229317i	−0.695548	−	0.718480i	$-0.744838\pi$
$701$	16.0752	−	16.0752i	0.0229317	−	0.0229317i	0.718480	+	0.695548i	$0.244838\pi$
$702$	74.3006	−	155.173i	0.105841	−	0.221044i
$703$			1562.00i			2.22191i
$704$	10.9615	−	32.7268i	0.0155704	−	0.0464870i
$705$	87.4998			0.124113
$706$	−1115.54	−	534.150i	−1.58009	−	0.756586i
$707$	−12.2882	−	12.2882i	−0.0173808	−	0.0173808i
$708$	71.1346	+	88.3870i	0.100473	+	0.124840i
$709$	35.3552	+	35.3552i	0.0498663	+	0.0498663i	0.731600	−	0.681734i	$-0.238774\pi$
$709$	35.3552	+	35.3552i	0.0498663	+	0.0498663i	−0.681734	+	0.731600i	$0.738774\pi$
$710$	0.907159	+	2.57405i	0.00127769	+	0.00362543i
$711$	300.240			0.422278
$712$	−606.194	+	142.641i	−0.851396	+	0.200338i
$713$			875.740i			1.22825i
$714$	−26.2090	−	74.3676i	−0.0367072	−	0.104156i
$715$	14.1160	−	14.1160i	0.0197426	−	0.0197426i
$716$	−104.989	+	970.770i	−0.146633	+	1.35582i
$717$	174.699	−	174.699i	0.243652	−	0.243652i
$718$	−875.353	−	419.141i	−1.21915	−	0.583762i
$719$			988.694i			1.37510i	0.726139	+	0.687548i	$0.241313\pi$
$719$			988.694i			1.37510i	−0.726139	+	0.687548i	$0.758687\pi$
$720$	−57.9134	−	90.3661i	−0.0804353	−	0.125508i
$721$	−32.3927			−0.0449275
$722$	437.962	−	914.659i	0.606596	−	1.26684i
$723$	256.308	+	256.308i	0.354506	+	0.354506i
$724$	−58.6138	+	541.964i	−0.0809584	+	0.748570i
$725$	77.4129	+	77.4129i	0.106776	+	0.106776i
$726$	−394.374	+	138.987i	−0.543215	+	0.191442i
$727$	535.816			0.737023			0.368511	−	0.929623i	$-0.379868\pi$
$727$	535.816			0.737023			0.368511	+	0.929623i	$0.379868\pi$
$728$	109.645	+	67.8739i	0.150611	+	0.0932334i
$729$		−	27.0000i		−	0.0370370i
$730$	129.828	−	45.7547i	0.177847	−	0.0626777i
$731$	−523.631	+	523.631i	−0.716322	+	0.716322i
$732$	97.0201	+	120.551i	0.132541	+	0.164686i
$733$	−77.4563	+	77.4563i	−0.105670	+	0.105670i	−0.757965	−	0.652295i	$-0.773806\pi$
$733$	−77.4563	+	77.4563i	−0.105670	+	0.105670i	0.652295	+	0.757965i	$0.273806\pi$
$734$	449.053	−	937.821i	0.611789	−	1.27769i
$735$			186.104i			0.253203i
$736$	344.657	−	442.230i	0.468284	−	0.600856i
$737$	−13.5331			−0.0183624
$738$	365.092	+	174.815i	0.494704	+	0.236877i
$739$	692.977	+	692.977i	0.937723	+	0.937723i	0.998171	−	0.0604485i	$-0.0192531\pi$
$739$	692.977	+	692.977i	0.937723	+	0.937723i	−0.0604485	+	0.998171i	$0.519253\pi$
$740$	−369.414	+	297.307i	−0.499207	+	0.401766i
$741$	597.374	+	597.374i	0.806173	+	0.806173i
$742$	27.7032	+	78.6073i	0.0373358	+	0.105940i
$743$	701.253			0.943813			0.471907	−	0.881648i	$-0.343566\pi$
$743$	701.253			0.943813			0.471907	+	0.881648i	$0.343566\pi$
$744$	−588.873	−	364.532i	−0.791497	−	0.489963i
$745$		−	441.951i		−	0.593222i
$746$	−130.105	−	369.171i	−0.174404	−	0.494868i
$747$	−107.826	+	107.826i	−0.144345	+	0.144345i
$748$	50.1359	+	5.42223i	0.0670266	+	0.00724897i
$749$	−35.8079	+	35.8079i	−0.0478076	+	0.0478076i
$750$	−34.9318	−	16.7263i	−0.0465758	−	0.0223017i
$751$		−	606.188i		−	0.807174i	−0.914941	−	0.403587i	$-0.867763\pi$
$751$		−	606.188i		−	0.807174i	0.914941	−	0.403587i	$-0.132237\pi$
$752$	−353.119	−	77.2842i	−0.469573	−	0.102771i
$753$	568.716			0.755267
$754$	313.090	−	653.870i	0.415239	−	0.867202i
$755$	−273.370	−	273.370i	−0.362080	−	0.362080i
$756$	20.1201	+	2.17601i	0.0266139	+	0.00287832i
$757$	−509.467	−	509.467i	−0.673008	−	0.673008i	0.285400	−	0.958408i	$-0.407873\pi$
$757$	−509.467	−	509.467i	−0.673008	−	0.673008i	−0.958408	+	0.285400i	$0.907873\pi$
$758$	467.683	−	164.823i	0.616996	−	0.217444i
$759$	16.3657			0.0215622
$760$	513.034	−	120.720i	0.675045	−	0.158841i
$761$			491.398i			0.645727i	0.946446	+	0.322864i	$0.104645\pi$
$761$			491.398i			0.645727i	−0.946446	+	0.322864i	$0.895355\pi$
$762$	401.603	−	141.535i	0.527038	−	0.185741i
$763$	133.314	−	133.314i	0.174723	−	0.174723i
$764$	924.020	−	743.659i	1.20945	−	0.973376i
$765$	110.890	−	110.890i	0.144954	−	0.144954i
$766$	459.806	−	960.279i	0.600269	−	1.25363i
$767$		−	271.104i		−	0.353461i
$768$	153.903	+	415.839i	0.200395	+	0.541457i
$769$	−122.789			−0.159674			−0.0798369	−	0.996808i	$-0.525440\pi$
$769$	−122.789			−0.159674			−0.0798369	+	0.996808i	$0.525440\pi$
$770$	2.11796	+	1.01413i	0.00275060	+	0.00131706i
$771$	373.926	+	373.926i	0.484988	+	0.484988i
$772$	599.270	+	744.611i	0.776256	+	0.964522i
$773$	679.953	+	679.953i	0.879629	+	0.879629i	0.993496	−	0.113867i	$-0.0363238\pi$
$773$	679.953	+	679.953i	0.879629	+	0.879629i	−0.113867	+	0.993496i	$0.536324\pi$
$774$	−63.1734	−	179.254i	−0.0816194	−	0.231594i
$775$	−249.910			−0.322465
$776$	211.336	+	898.136i	0.272340	+	1.15739i
$777$		−	89.4096i		−	0.115070i
$778$	99.0625	+	281.089i	0.127330	+	0.361296i
$779$	−1405.51	+	1405.51i	−1.80425	+	1.80425i
$780$	−27.5764	+	254.981i	−0.0353544	+	0.326899i
$781$	0.232714	−	0.232714i	0.000297969	−	0.000297969i
$782$	738.869	+	353.790i	0.944846	+	0.452416i
$783$		−	113.773i		−	0.145304i
$784$	164.377	−	751.054i	0.209664	−	0.957977i
$785$	198.323			0.252641
$786$	−227.692	+	475.522i	−0.289684	+	0.604990i
$787$	696.617	+	696.617i	0.885156	+	0.885156i	0.994053	−	0.108897i	$-0.0347320\pi$
$787$	696.617	+	696.617i	0.885156	+	0.885156i	−0.108897	+	0.994053i	$0.534732\pi$
$788$	40.3574	−	373.159i	0.0512150	−	0.473552i
$789$	294.506	+	294.506i	0.373265	+	0.373265i
$790$	−422.123	+	148.767i	−0.534333	+	0.188312i
$791$	−131.780			−0.166599
$792$	−6.81232	+	11.0048i	−0.00860141	+	0.0138949i
$793$		−	369.758i		−	0.466277i
$794$	320.874	−	113.084i	0.404123	−	0.142423i
$795$	−117.212	+	117.212i	−0.147436	+	0.147436i
$796$	134.938	+	167.664i	0.169520	+	0.210633i
$797$	−351.812	+	351.812i	−0.441420	+	0.441420i	−0.892489	−	0.451069i	$-0.851043\pi$
$797$	−351.812	+	351.812i	−0.441420	+	0.441420i	0.451069	+	0.892489i	$0.351043\pi$
$798$	−42.9172	+	89.6301i	−0.0537809	+	0.112318i
$799$		−	528.156i		−	0.661022i
$800$	126.199	+	98.3550i	0.157749	+	0.122944i
$801$	233.531			0.291550
$802$	−1203.53	−	576.283i	−1.50067	−	0.718558i
$803$	−11.7375	−	11.7375i	−0.0146170	−	0.0146170i
$804$	135.445	−	109.007i	0.168464	−	0.135581i
$805$	26.9740	+	26.9740i	0.0335081	+	0.0335081i
$806$	550.067	+	1560.81i	0.682465	+	1.93649i
$807$	−490.466			−0.607764
$808$	−75.1538	+	121.405i	−0.0930122	+	0.150254i
$809$			1175.61i			1.45317i	0.687077	+	0.726585i	$0.258894\pi$
$809$			1175.61i			1.45317i	−0.687077	+	0.726585i	$0.741106\pi$
$810$	13.3783	+	37.9608i	0.0165164	+	0.0468652i
$811$	−662.222	+	662.222i	−0.816549	+	0.816549i	−0.985606	−	0.169057i	$-0.945928\pi$
$811$	−662.222	+	662.222i	−0.816549	+	0.816549i	0.169057	+	0.985606i	$0.445928\pi$
$812$	84.7827	+	9.16932i	0.104412	+	0.0112923i
$813$	−621.720	+	621.720i	−0.764724	+	0.764724i
$814$	51.5736	+	24.6948i	0.0633582	+	0.0303375i
$815$			57.3889i			0.0704159i
$816$	−545.458	+	349.571i	−0.668453	+	0.428395i
$817$	933.282			1.14233
$818$	−383.979	+	801.917i	−0.469412	+	0.980339i
$819$	−34.1939	−	34.1939i	−0.0417507	−	0.0417507i
$820$	−599.922	−	64.8820i	−0.731612	−	0.0791244i
$821$	883.273	+	883.273i	1.07585	+	1.07585i	0.996877	+	0.0789729i	$0.0251641\pi$
$821$	883.273	+	883.273i	1.07585	+	1.07585i	0.0789729	+	0.996877i	$0.474836\pi$
$822$	−611.227	+	215.411i	−0.743585	+	0.262058i
$823$	1140.14			1.38534			0.692672	−	0.721253i	$-0.256433\pi$
$823$	1140.14			1.38534			0.692672	+	0.721253i	$0.256433\pi$
$824$	60.9611	+	259.072i	0.0739819	+	0.314408i
$825$			4.67028i			0.00566095i
$826$	30.0767	−	10.5998i	0.0364125	−	0.0128327i
$827$	576.851	−	576.851i	0.697523	−	0.697523i	−0.266353	−	0.963876i	$-0.585819\pi$
$827$	576.851	−	576.851i	0.697523	−	0.697523i	0.963876	+	0.266353i	$0.0858187\pi$
$828$	−163.795	+	131.824i	−0.197820	+	0.159207i
$829$	70.1100	−	70.1100i	0.0845717	−	0.0845717i	−0.663555	−	0.748127i	$-0.730953\pi$
$829$	70.1100	−	70.1100i	0.0845717	−	0.0845717i	0.748127	+	0.663555i	$0.230953\pi$
$830$	98.1711	−	205.025i	0.118278	−	0.247018i
$831$		−	902.129i		−	1.08559i
$832$	336.501	−	1004.66i	0.404448	−	1.20752i
$833$	1123.34			1.34855
$834$	797.675	+	381.947i	0.956445	+	0.457970i
$835$	−4.15941	−	4.15941i	−0.00498133	−	0.00498133i
$836$	−39.8471	−	49.5113i	−0.0476640	−	0.0592241i
$837$	183.646	+	183.646i	0.219410	+	0.219410i
$838$	−11.0416	−	31.3303i	−0.0131761	−	0.0373870i
$839$	−780.576			−0.930365			−0.465182	−	0.885215i	$-0.654011\pi$
$839$	−780.576			−0.930365			−0.465182	+	0.885215i	$0.654011\pi$
$840$	−29.3662	+	6.91002i	−0.0349598	+	0.00822621i
$841$			361.579i			0.429940i
$842$	−125.389	−	355.791i	−0.148919	−	0.422554i
$843$	−49.7597	+	49.7597i	−0.0590269	+	0.0590269i
$844$	108.563	−	1003.81i	0.128629	−	1.18935i
$845$	166.124	−	166.124i	0.196596	−	0.196596i
$846$	122.261	+	58.5417i	0.144517	+	0.0691983i
$847$			117.532i			0.138762i
$848$	576.555	−	369.500i	0.679900	−	0.435731i
$849$	−447.951			−0.527622
$850$	−100.961	+	210.852i	−0.118778	+	0.248061i
$851$	656.833	+	656.833i	0.771837	+	0.771837i
$852$	−0.454621	+	4.20359i	−0.000533593	+	0.00493379i
$853$	−1110.84	−	1110.84i	−1.30228	−	1.30228i	−0.926854	−	0.375421i	$-0.877498\pi$
$853$	−1110.84	−	1110.84i	−1.30228	−	1.30228i	−0.375421	−	0.926854i	$-0.622502\pi$
$854$	41.0215	−	14.4570i	0.0480345	−	0.0169286i
$855$	−197.642			−0.231160
$856$	353.774	+	218.998i	0.413288	+	0.255839i
$857$			1329.10i			1.55087i	0.631424	+	0.775437i	$0.282471\pi$
$857$			1329.10i			1.55087i	−0.631424	+	0.775437i	$0.717529\pi$
$858$	29.1681	−	10.2796i	0.0339955	−	0.0119808i
$859$	−321.136	+	321.136i	−0.373849	+	0.373849i	−0.868877	−	0.495028i	$-0.835158\pi$
$859$	−321.136	+	321.136i	−0.373849	+	0.373849i	0.495028	+	0.868877i	$0.335158\pi$
$860$	177.638	+	220.721i	0.206556	+	0.256652i
$861$	80.4516	−	80.4516i	0.0934397	−	0.0934397i
$862$	−438.642	+	916.079i	−0.508866	+	1.06274i
$863$			965.593i			1.11888i	0.828871	+	0.559440i	$0.188984\pi$
$863$			965.593i			1.11888i	−0.828871	+	0.559440i	$0.811016\pi$
$864$	−20.4614	−	165.013i	−0.0236822	−	0.190987i
$865$	−126.314			−0.146028
$866$	−1117.68	−	535.172i	−1.29062	−	0.617982i
$867$	−315.390	−	315.390i	−0.363772	−	0.363772i
$868$	−151.652	+	122.051i	−0.174714	+	0.140611i
$869$	38.1632	+	38.1632i	0.0439162	+	0.0439162i
$870$	56.3739	+	159.960i	0.0647975	+	0.183862i
$871$	−415.443			−0.476973
$872$	−1317.11	−	815.338i	−1.51045	−	0.935020i
$873$		−	345.999i		−	0.396334i
$874$	−343.169	−	973.737i	−0.392642	−	1.11412i
$875$	−7.69758	+	7.69758i	−0.00879723	+	0.00879723i
$876$	212.018	+	22.9299i	0.242030	+	0.0261757i
$877$	815.567	−	815.567i	0.929951	−	0.929951i	−0.0677513	−	0.997702i	$-0.521582\pi$
$877$	815.567	−	815.567i	0.929951	−	0.929951i	0.997702	+	0.0677513i	$0.0215824\pi$
$878$	379.208	+	181.575i	0.431900	+	0.206805i
$879$		−	158.294i		−	0.180085i
$880$	4.12503	−	18.8477i	0.00468753	−	0.0214178i
$881$	−610.177			−0.692596			−0.346298	−	0.938125i	$-0.612561\pi$
$881$	−610.177			−0.692596			−0.346298	+	0.938125i	$0.612561\pi$
$882$	−124.513	+	260.039i	−0.141171	+	0.294828i
$883$	−477.236	−	477.236i	−0.540471	−	0.540471i	0.383196	−	0.923667i	$-0.374823\pi$
$883$	−477.236	−	477.236i	−0.540471	−	0.540471i	−0.923667	+	0.383196i	$0.874823\pi$
$884$	1539.09	+	166.454i	1.74105	+	0.188296i
$885$	44.8476	+	44.8476i	0.0506753	+	0.0506753i
$886$	711.927	−	250.900i	0.803529	−	0.283183i
$887$	−25.0690			−0.0282627			−0.0141314	−	0.999900i	$-0.504498\pi$
$887$	−25.0690			−0.0282627			−0.0141314	+	0.999900i	$0.504498\pi$
$888$	−715.085	+	168.263i	−0.805276	+	0.189486i
$889$		−	119.686i		−	0.134630i
$890$	−328.335	+	115.713i	−0.368915	+	0.130015i
$891$	3.43194	−	3.43194i	0.00385179	−	0.00385179i
$892$	1104.51	−	888.916i	1.23824	−	0.996543i
$893$	−470.673	+	470.673i	−0.527070	+	0.527070i
$894$	295.687	−	617.526i	0.330746	−	0.690745i
$895$			545.841i			0.609879i
$896$	124.615	−	1.94878i	0.139079	−	0.00217498i
$897$	502.399			0.560089
$898$	1302.16	+	623.506i	1.45006	+	0.694328i
$899$	773.851	+	773.851i	0.860791	+	0.860791i
$900$	−37.6186	−	46.7423i	−0.0417984	−	0.0519359i
$901$	707.502	+	707.502i	0.785240	+	0.785240i
$902$	24.1858	+	68.6270i	0.0268136	+	0.0760832i
$903$	−53.4213			−0.0591598
$904$	248.001	+	1053.95i	0.274337	+	1.16588i
$905$			304.734i			0.336723i
$906$	−199.075	−	564.871i	−0.219729	−	0.623478i
$907$	461.241	−	461.241i	0.508535	−	0.508535i	−0.405541	−	0.914077i	$-0.632917\pi$
$907$	461.241	−	461.241i	0.508535	−	0.508535i	0.914077	+	0.405541i	$0.132917\pi$
$908$	42.4960	−	392.933i	0.0468018	−	0.432746i
$909$	37.8614	−	37.8614i	0.0416517	−	0.0416517i
$910$	65.0178	+	31.1322i	0.0714482	+	0.0342112i
$911$			726.455i			0.797426i	0.917076	+	0.398713i	$0.130543\pi$
$911$			726.455i			0.797426i	−0.917076	+	0.398713i	$0.869457\pi$
$912$	797.616	+	174.567i	0.874579	+	0.191412i
$913$	−27.4112			−0.0300232
$914$	117.874	−	246.172i	0.128965	−	0.269335i
$915$	61.1675	+	61.1675i	0.0668497	+	0.0668497i
$916$	−18.7752	+	173.602i	−0.0204970	+	0.189522i
$917$	104.786	+	104.786i	0.114270	+	0.114270i
$918$	229.135	−	80.7526i	0.249602	−	0.0879658i
$919$	499.929			0.543992			0.271996	−	0.962298i	$-0.412316\pi$
$919$	499.929			0.543992			0.271996	+	0.962298i	$0.412316\pi$
$920$	164.971	−	266.498i	0.179316	−	0.289671i
$921$		−	454.970i		−	0.493996i
$922$	−1005.18	+	354.250i	−1.09022	+	0.384219i
$923$	7.14393	−	7.14393i	0.00773990	−	0.00773990i
$924$	2.28086	+	2.83404i	0.00246846	+	0.00306714i
$925$	−187.441	+	187.441i	−0.202639	+	0.202639i
$926$	253.176	−	528.744i	0.273408	−	0.570998i
$927$		−	99.8055i		−	0.107665i
$928$	−86.2209	−	695.336i	−0.0929105	−	0.749285i
$929$	−382.202			−0.411412			−0.205706	−	0.978614i	$-0.565949\pi$
$929$	−382.202			−0.411412			−0.205706	+	0.978614i	$0.565949\pi$
$930$	−349.193	−	167.203i	−0.375476	−	0.179788i
$931$	−1001.08	−	1001.08i	−1.07528	−	1.07528i
$932$	−795.533	+	640.252i	−0.853577	+	0.686966i
$933$	−556.944	−	556.944i	−0.596939	−	0.596939i
$934$	53.4163	+	151.568i	0.0571909	+	0.162279i
$935$	28.1902			0.0301500
$936$	−209.127	+	337.828i	−0.223426	+	0.360928i
$937$		−	713.290i		−	0.761249i	−0.924730	−	0.380625i	$-0.875709\pi$
$937$		−	713.290i		−	0.761249i	0.924730	−	0.380625i	$-0.124291\pi$
$938$	−16.2432	−	46.0899i	−0.0173169	−	0.0491364i
$939$	368.711	−	368.711i	0.392663	−	0.392663i
$940$	−200.901	−	21.7275i	−0.213724	−	0.0231144i
$941$	−262.981	+	262.981i	−0.279470	+	0.279470i	−0.832897	−	0.553428i	$-0.813320\pi$
$941$	−262.981	+	262.981i	−0.279470	+	0.279470i	0.553428	+	0.832897i	$0.313320\pi$
$942$	277.111	+	132.688i	0.294173	+	0.140858i
$943$			1182.05i			1.25350i
$944$	−141.378	−	220.601i	−0.149765	−	0.233688i
$945$	11.3131			0.0119715
$946$	14.7549	−	30.8147i	0.0155971	−	0.0325737i
$947$	−1236.02	−	1236.02i	−1.30519	−	1.30519i	−0.924842	−	0.380351i	$-0.875803\pi$
$947$	−1236.02	−	1236.02i	−1.30519	−	1.30519i	−0.380351	−	0.924842i	$-0.624197\pi$
$948$	−689.354	−	74.5541i	−0.727167	−	0.0786436i
$949$	−360.321	−	360.321i	−0.379685	−	0.379685i
$950$	277.876	−	97.9303i	0.292501	−	0.103084i
$951$	−224.003			−0.235545
$952$	41.7095	+	177.257i	0.0438125	+	0.186194i
$953$		−	1536.45i		−	1.61222i	−0.591764	−	0.806111i	$-0.701568\pi$
$953$		−	1536.45i		−	1.61222i	0.591764	−	0.806111i	$-0.298432\pi$
$954$	−242.198	+	85.3564i	−0.253876	+	0.0894722i
$955$	468.848	−	468.848i	0.490941	−	0.490941i
$956$	−444.490	+	357.730i	−0.464948	+	0.374194i
$957$	14.4616	−	14.4616i	0.0151114	−	0.0151114i
$958$	442.132	−	923.367i	0.461515	−	0.963848i
$959$			182.158i			0.189946i
$960$	110.531	+	221.862i	0.115136	+	0.231107i
$961$	−1537.21			−1.59959
$962$	1583.22	+	758.088i	1.64576	+	0.788033i
$963$	−110.328	−	110.328i	−0.114567	−	0.114567i
$964$	−524.841	−	652.131i	−0.544441	−	0.676485i
$965$	377.817	+	377.817i	0.391520	+	0.391520i
$966$	19.6431	+	55.7370i	0.0203344	+	0.0576987i
$967$	−325.549			−0.336659			−0.168329	−	0.985731i	$-0.553837\pi$
$967$	−325.549			−0.336659			−0.168329	+	0.985731i	$0.553837\pi$
$968$	940.001	−	221.187i	0.971075	−	0.228499i
$969$			1192.98i			1.23115i
$970$	171.440	+	486.460i	0.176743	+	0.501505i
$971$	−759.314	+	759.314i	−0.781992	+	0.781992i	−0.980167	−	0.198175i	$-0.936499\pi$
$971$	−759.314	+	759.314i	−0.781992	+	0.781992i	0.198175	+	0.980167i	$0.436499\pi$
$972$	−6.70452	+	61.9923i	−0.00689765	+	0.0637781i
$973$	175.776	−	175.776i	0.180653	−	0.180653i
$974$	−1652.26	−	791.143i	−1.69636	−	0.812261i
$975$			143.370i			0.147046i
$976$	−192.825	−	300.877i	−0.197566	−	0.308276i
$977$	−641.460			−0.656561			−0.328281	−	0.944580i	$-0.606469\pi$
$977$	−641.460			−0.656561			−0.328281	+	0.944580i	$0.606469\pi$
$978$	−38.3961	+	80.1880i	−0.0392598	+	0.0819918i
$979$	29.6839	+	29.6839i	0.0303207	+	0.0303207i
$980$	46.2126	−	427.298i	0.0471557	−	0.436018i
$981$	410.755	+	410.755i	0.418710	+	0.418710i
$982$	−1175.13	+	414.145i	−1.19667	+	0.421736i
$983$	−1438.35			−1.46323			−0.731615	−	0.681718i	$-0.761233\pi$
$983$	−1438.35			−1.46323			−0.731615	+	0.681718i	$0.761233\pi$
$984$	−794.846	−	492.036i	−0.807770	−	0.500036i
$985$		−	209.819i		−	0.213014i
$986$	965.533	−	340.277i	0.979242	−	0.345109i
$987$	26.9415	−	26.9415i	0.0272963	−	0.0272963i
$988$	−1223.24	−	1519.92i	−1.23810	−	1.53838i
$989$	392.451	−	392.451i	0.396816	−	0.396816i
$990$	−3.12465	+	6.52566i	−0.00315622	+	0.00659158i
$991$			189.765i			0.191489i	0.995406	+	0.0957444i	$0.0305231\pi$
$991$			189.765i			0.191489i	−0.995406	+	0.0957444i	$0.969477\pi$
$992$	1261.54	+	983.197i	1.27172	+	0.991126i
$993$	400.381			0.403203
$994$	1.07188	+	0.513242i	0.00107835	+	0.000516340i
$995$	85.0730	+	85.0730i	0.0855005	+	0.0855005i
$996$	274.344	−	220.794i	0.275445	−	0.221681i
$997$	922.747	+	922.747i	0.925524	+	0.925524i	0.997413	−	0.0718886i	$-0.0229026\pi$
$997$	922.747	+	922.747i	0.925524	+	0.925524i	−0.0718886	+	0.997413i	$0.522903\pi$
$998$	−523.239	−	1484.68i	−0.524287	−	1.48766i
$999$	275.481			0.275756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.3.bn.a.91.5	✓	64
4.3	odd	2		960.3.bn.a.271.22		64
16.3	odd	4	inner	240.3.bn.a.211.5	yes	64
16.13	even	4		960.3.bn.a.751.22		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.3.bn.a.91.5	✓	64	1.1	even	1	trivial
240.3.bn.a.211.5	yes	64	16.3	odd	4	inner
960.3.bn.a.271.22		64	4.3	odd	2
960.3.bn.a.751.22		64	16.13	even	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.bn (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80387 - 0.863740i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(2.50791 + 3.11615i) q^{4} +(1.58114 + 1.58114i) q^{5} +(1.15142 + 3.26714i) q^{6} +0.973675 q^{7} +(-1.83240 - 7.78732i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.80387 - 0.863740i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(2.50791 + 3.11615i) q^{4} +(1.58114 + 1.58114i) q^{5} +(1.15142 + 3.26714i) q^{6} +0.973675 q^{7} +(-1.83240 - 7.78732i) q^{8} +3.00000i q^{9} +(-1.48648 - 4.21786i) q^{10} +(-0.381327 + 0.381327i) q^{11} +(0.744946 - 6.88804i) q^{12} +(-11.7061 + 11.7061i) q^{13} +(-1.75639 - 0.841002i) q^{14} -3.87298i q^{15} +(-3.42081 + 15.6300i) q^{16} -23.3777 q^{17} +(2.59122 - 5.41162i) q^{18} +(20.8333 + 20.8333i) q^{19} +(-0.961721 + 8.89242i) q^{20} +(-1.19250 - 1.19250i) q^{21} +(1.01723 - 0.358498i) q^{22} +17.5211 q^{23} +(-7.29326 + 11.7817i) q^{24} +5.00000i q^{25} +(31.2274 - 11.0053i) q^{26} +(3.67423 - 3.67423i) q^{27} +(2.44189 + 3.03412i) q^{28} +(15.4826 - 15.4826i) q^{29} +(-3.34525 + 6.98637i) q^{30} +49.9821i q^{31} +(19.6710 - 25.2399i) q^{32} +0.934057 q^{33} +(42.1703 + 20.1922i) q^{34} +(1.53952 + 1.53952i) q^{35} +(-9.34846 + 7.52372i) q^{36} +(37.4882 + 37.4882i) q^{37} +(-19.5861 - 55.5752i) q^{38} +28.6740 q^{39} +(9.41556 - 15.2101i) q^{40} +67.4644i q^{41} +(1.12111 + 3.18114i) q^{42} +(22.3988 - 22.3988i) q^{43} +(-2.14461 - 0.231941i) q^{44} +(-4.74342 + 4.74342i) q^{45} +(-31.6058 - 15.1337i) q^{46} +22.5923i q^{47} +(23.3324 - 14.9532i) q^{48} -48.0520 q^{49} +(4.31870 - 9.01936i) q^{50} +(28.6317 + 28.6317i) q^{51} +(-65.8358 - 7.12019i) q^{52} +(-30.2640 - 30.2640i) q^{53} +(-9.80143 + 3.45426i) q^{54} -1.20586 q^{55} +(-1.78416 - 7.58232i) q^{56} -51.0310i q^{57} +(-41.3015 + 14.5557i) q^{58} +(-11.5796 + 11.5796i) q^{59} +(12.0688 - 9.71308i) q^{60} +(-15.7934 + 15.7934i) q^{61} +(43.1715 - 90.1612i) q^{62} +2.92103i q^{63} +(-57.2847 + 28.5389i) q^{64} -37.0180 q^{65} +(-1.68492 - 0.806782i) q^{66} +(17.7447 + 17.7447i) q^{67} +(-58.6290 - 72.8484i) q^{68} +(-21.4589 - 21.4589i) q^{69} +(-1.44735 - 4.10683i) q^{70} -0.610274 q^{71} +(23.3620 - 5.49719i) q^{72} +30.7806i q^{73} +(-35.2438 - 100.004i) q^{74} +(6.12372 - 6.12372i) q^{75} +(-12.6718 + 117.168i) q^{76} +(-0.371289 + 0.371289i) q^{77} +(-51.7242 - 24.7669i) q^{78} -100.080i q^{79} +(-30.1220 + 19.3045i) q^{80} -9.00000 q^{81} +(58.2717 - 121.697i) q^{82} +(35.9419 + 35.9419i) q^{83} +(0.725336 - 6.70671i) q^{84} +(-36.9633 - 36.9633i) q^{85} +(-59.7513 + 21.0578i) q^{86} -37.9244 q^{87} +(3.66826 + 2.27077i) q^{88} -77.8438i q^{89} +(12.6536 - 4.45944i) q^{90} +(-11.3980 + 11.3980i) q^{91} +(43.9412 + 54.5984i) q^{92} +(61.2153 - 61.2153i) q^{93} +(19.5139 - 40.7537i) q^{94} +65.8807i q^{95} +(-55.0044 + 6.82048i) q^{96} -115.333 q^{97} +(86.6796 + 41.5044i) q^{98} +(-1.14398 - 1.14398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 24 q^{4}+O(q^{10}) \) 64 * q - 24 * q^4	\( 64 q - 24 q^{4} + 20 q^{10} - 64 q^{11} + 72 q^{14} - 36 q^{16} - 24 q^{18} + 32 q^{19} - 80 q^{20} + 48 q^{22} + 256 q^{23} - 36 q^{24} + 240 q^{28} - 64 q^{29} - 40 q^{32} - 76 q^{34} - 12 q^{36} + 192 q^{37} - 280 q^{38} - 192 q^{43} - 280 q^{44} - 300 q^{46} + 448 q^{49} - 40 q^{50} + 96 q^{51} + 104 q^{52} + 320 q^{53} + 36 q^{54} + 112 q^{56} + 64 q^{58} + 128 q^{59} + 32 q^{61} + 48 q^{62} + 48 q^{64} - 72 q^{66} - 64 q^{67} + 280 q^{68} - 96 q^{69} + 240 q^{70} - 512 q^{71} - 120 q^{72} - 608 q^{74} - 308 q^{76} - 448 q^{77} - 360 q^{78} - 576 q^{81} - 200 q^{82} - 144 q^{84} - 160 q^{85} - 560 q^{86} - 184 q^{88} + 576 q^{91} - 56 q^{92} + 460 q^{94} + 360 q^{96} + 368 q^{98} - 192 q^{99}+O(q^{100}) \) 64 * q - 24 * q^4 + 20 * q^10 - 64 * q^11 + 72 * q^14 - 36 * q^16 - 24 * q^18 + 32 * q^19 - 80 * q^20 + 48 * q^22 + 256 * q^23 - 36 * q^24 + 240 * q^28 - 64 * q^29 - 40 * q^32 - 76 * q^34 - 12 * q^36 + 192 * q^37 - 280 * q^38 - 192 * q^43 - 280 * q^44 - 300 * q^46 + 448 * q^49 - 40 * q^50 + 96 * q^51 + 104 * q^52 + 320 * q^53 + 36 * q^54 + 112 * q^56 + 64 * q^58 + 128 * q^59 + 32 * q^61 + 48 * q^62 + 48 * q^64 - 72 * q^66 - 64 * q^67 + 280 * q^68 - 96 * q^69 + 240 * q^70 - 512 * q^71 - 120 * q^72 - 608 * q^74 - 308 * q^76 - 448 * q^77 - 360 * q^78 - 576 * q^81 - 200 * q^82 - 144 * q^84 - 160 * q^85 - 560 * q^86 - 184 * q^88 + 576 * q^91 - 56 * q^92 + 460 * q^94 + 360 * q^96 + 368 * q^98 - 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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