LMFDB - Embedded newform 35.3.i.a.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(19,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("35.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.i (of order $6$, 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:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 180x^{8} - 669x^{6} + 1980x^{4} - 135x^{2} + 9 $ x^12 - 15x^10 + 180x^8 - 669x^6 + 1980x^4 - 135*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Root			$2.85853 + 1.65037i$ of defining polynomial
Character	$\chi$	$=$	35.19
Dual form			35.3.i.a.24.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.85853 + 1.65037i) q^{2} +(-2.20085 - 3.81198i) q^{3} +(3.44745 + 5.97116i) q^{4} +(-1.72321 + 4.69367i) q^{5} -14.5289i q^{6} +(-5.32175 - 4.54742i) q^{7} +9.55533i q^{8} +(-5.18747 + 8.98496i) q^{9} +O(q^{10})$	\(q+(2.85853 + 1.65037i) q^{2} +(-2.20085 - 3.81198i) q^{3} +(3.44745 + 5.97116i) q^{4} +(-1.72321 + 4.69367i) q^{5} -14.5289i q^{6} +(-5.32175 - 4.54742i) q^{7} +9.55533i q^{8} +(-5.18747 + 8.98496i) q^{9} +(-12.6721 + 10.5731i) q^{10} +(-0.240016 - 0.415720i) q^{11} +(15.1746 - 26.2832i) q^{12} +11.0991 q^{13} +(-7.70744 - 21.7818i) q^{14} +(21.6847 - 3.76124i) q^{15} +(-1.98003 + 3.42952i) q^{16} +(9.10382 + 15.7683i) q^{17} +(-29.6570 + 17.1225i) q^{18} +(-5.12231 - 2.95736i) q^{19} +(-33.9673 + 5.89167i) q^{20} +(-5.62231 + 30.2946i) q^{21} -1.58446i q^{22} +(8.07841 + 4.66407i) q^{23} +(36.4247 - 21.0298i) q^{24} +(-19.0611 - 16.1763i) q^{25} +(31.7271 + 18.3177i) q^{26} +6.05204 q^{27} +(8.80689 - 47.4540i) q^{28} -10.3350 q^{29} +(68.1937 + 25.0362i) q^{30} +(-1.63768 + 0.945514i) q^{31} +(21.7807 - 12.5751i) q^{32} +(-1.05648 + 1.82987i) q^{33} +60.0987i q^{34} +(30.5145 - 17.1424i) q^{35} -71.5341 q^{36} +(-42.5933 - 24.5912i) q^{37} +(-9.76150 - 16.9074i) q^{38} +(-24.4275 - 42.3096i) q^{39} +(-44.8496 - 16.4658i) q^{40} -11.9884i q^{41} +(-66.0688 + 77.3190i) q^{42} +62.7080i q^{43} +(1.65489 - 2.86635i) q^{44} +(-33.2334 - 39.8312i) q^{45} +(15.3949 + 26.6648i) q^{46} +(23.8333 - 41.2805i) q^{47} +17.4310 q^{48} +(7.64201 + 48.4004i) q^{49} +(-27.7898 - 77.6984i) q^{50} +(40.0723 - 69.4072i) q^{51} +(38.2637 + 66.2746i) q^{52} +(43.0379 - 24.8479i) q^{53} +(17.2999 + 9.98811i) q^{54} +(2.36485 - 0.410186i) q^{55} +(43.4520 - 50.8510i) q^{56} +26.0348i q^{57} +(-29.5429 - 17.0566i) q^{58} +(-48.0612 + 27.7482i) q^{59} +(97.2159 + 116.516i) q^{60} +(-52.5096 - 30.3164i) q^{61} -6.24180 q^{62} +(68.4647 - 24.2261i) q^{63} +98.8544 q^{64} +(-19.1261 + 52.0956i) q^{65} +(-6.03994 + 3.48716i) q^{66} +(-71.3332 + 41.1843i) q^{67} +(-62.7699 + 108.721i) q^{68} -41.0597i q^{69} +(115.518 + 1.35829i) q^{70} +92.6337 q^{71} +(-85.8542 - 49.5679i) q^{72} +(-24.5977 - 42.6044i) q^{73} +(-81.1693 - 140.589i) q^{74} +(-19.7132 + 108.262i) q^{75} -40.7815i q^{76} +(-0.613147 + 3.30381i) q^{77} -161.258i q^{78} +(1.72254 - 2.98353i) q^{79} +(-12.6850 - 15.2034i) q^{80} +(33.3676 + 57.7943i) q^{81} +(19.7854 - 34.2693i) q^{82} +30.5486 q^{83} +(-200.276 + 70.8674i) q^{84} +(-89.6989 + 15.5584i) q^{85} +(-103.491 + 179.252i) q^{86} +(22.7458 + 39.3968i) q^{87} +(3.97234 - 2.29343i) q^{88} +(121.079 + 69.9048i) q^{89} +(-29.2622 - 168.706i) q^{90} +(-59.0667 - 50.4723i) q^{91} +64.3166i q^{92} +(7.20857 + 4.16187i) q^{93} +(136.256 - 78.6676i) q^{94} +(22.7077 - 18.9463i) q^{95} +(-95.8719 - 55.3517i) q^{96} +130.732 q^{97} +(-58.0338 + 150.966i) q^{98} +4.98030 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 18 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 - 18 * q^9	$ 12 q + 6 q^{4} - 18 q^{9} - 54 q^{10} + 6 q^{11} - 66 q^{14} + 48 q^{15} - 6 q^{16} + 18 q^{19} + 12 q^{21} + 216 q^{24} + 18 q^{25} + 18 q^{26} + 48 q^{30} - 108 q^{31} + 222 q^{35} - 204 q^{36} - 240 q^{39} - 162 q^{40} - 42 q^{44} - 216 q^{45} + 114 q^{46} - 324 q^{49} - 192 q^{50} + 180 q^{51} + 252 q^{54} + 336 q^{56} + 396 q^{59} + 384 q^{60} - 108 q^{61} + 372 q^{64} - 54 q^{65} - 108 q^{66} + 300 q^{70} + 192 q^{71} - 594 q^{74} - 216 q^{75} - 192 q^{79} - 504 q^{80} + 294 q^{81} - 1200 q^{84} - 192 q^{85} - 384 q^{86} + 684 q^{89} - 72 q^{91} + 990 q^{94} + 288 q^{95} - 540 q^{96} + 396 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 - 18 * q^9 - 54 * q^10 + 6 * q^11 - 66 * q^14 + 48 * q^15 - 6 * q^16 + 18 * q^19 + 12 * q^21 + 216 * q^24 + 18 * q^25 + 18 * q^26 + 48 * q^30 - 108 * q^31 + 222 * q^35 - 204 * q^36 - 240 * q^39 - 162 * q^40 - 42 * q^44 - 216 * q^45 + 114 * q^46 - 324 * q^49 - 192 * q^50 + 180 * q^51 + 252 * q^54 + 336 * q^56 + 396 * q^59 + 384 * q^60 - 108 * q^61 + 372 * q^64 - 54 * q^65 - 108 * q^66 + 300 * q^70 + 192 * q^71 - 594 * q^74 - 216 * q^75 - 192 * q^79 - 504 * q^80 + 294 * q^81 - 1200 * q^84 - 192 * q^85 - 384 * q^86 + 684 * q^89 - 72 * q^91 + 990 * q^94 + 288 * q^95 - 540 * q^96 + 396 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.85853	+	1.65037i	1.42926	+	0.825186i	0.997063	−	0.0765917i	$-0.0244038\pi$
$2$	2.85853	+	1.65037i	1.42926	+	0.825186i	0.432201	+	0.901777i	$0.357737\pi$
$3$	−2.20085	−	3.81198i	−0.733616	−	1.27066i	−0.955328	−	0.295548i	$-0.904498\pi$
$3$	−2.20085	−	3.81198i	−0.733616	−	1.27066i	0.221712	−	0.975112i	$-0.428836\pi$
$4$	3.44745	+	5.97116i	0.861863	+	1.49279i
$5$	−1.72321	+	4.69367i	−0.344641	+	0.938735i
$5$	−1.72321	+	4.69367i	−0.344641	+	0.938735i
$6$		−	14.5289i		−	2.42148i
$7$	−5.32175	−	4.54742i	−0.760250	−	0.649631i
$7$	−5.32175	−	4.54742i	−0.760250	−	0.649631i
$8$			9.55533i			1.19442i
$9$	−5.18747	+	8.98496i	−0.576385	+	0.998328i
$10$	−12.6721	+	10.5731i	−1.26721	+	1.05731i
$11$	−0.240016	−	0.415720i	−0.0218196	−	0.0377927i	0.854909	−	0.518777i	$-0.173613\pi$
$11$	−0.240016	−	0.415720i	−0.0218196	−	0.0377927i	−0.876729	+	0.480985i	$0.840279\pi$
$12$	15.1746	−	26.2832i	1.26455	−	2.19027i
$13$	11.0991			0.853779			0.426889	−	0.904304i	$-0.359609\pi$
$13$	11.0991			0.853779			0.426889	+	0.904304i	$0.359609\pi$
$14$	−7.70744	−	21.7818i	−0.550531	−	1.55584i
$15$	21.6847	−	3.76124i	1.44565	−	0.250749i
$16$	−1.98003	+	3.42952i	−0.123752	+	0.214345i
$17$	9.10382	+	15.7683i	0.535519	+	0.927546i	0.999138	+	0.0415112i	$0.0132172\pi$
$17$	9.10382	+	15.7683i	0.535519	+	0.927546i	−0.463619	+	0.886035i	$0.653449\pi$
$18$	−29.6570	+	17.1225i	−1.64761	+	0.951250i
$19$	−5.12231	−	2.95736i	−0.269595	−	0.155651i	0.359109	−	0.933296i	$-0.383081\pi$
$19$	−5.12231	−	2.95736i	−0.269595	−	0.155651i	−0.628704	+	0.777645i	$0.716414\pi$
$20$	−33.9673	+	5.89167i	−1.69837	+	0.294584i
$21$	−5.62231	+	30.2946i	−0.267729	+	1.44260i
$22$		−	1.58446i		−	0.0720210i
$23$	8.07841	+	4.66407i	0.351235	+	0.202786i	0.665229	−	0.746639i	$-0.268334\pi$
$23$	8.07841	+	4.66407i	0.351235	+	0.202786i	−0.313994	+	0.949425i	$0.601667\pi$
$24$	36.4247	−	21.0298i	1.51770	−	0.876243i
$25$	−19.0611	−	16.1763i	−0.762445	−	0.647053i
$26$	31.7271	+	18.3177i	1.22027	+	0.704526i
$27$	6.05204			0.224150
$28$	8.80689	−	47.4540i	0.314532	−	1.69479i
$29$	−10.3350			−0.356379			−0.178190	−	0.983996i	$-0.557024\pi$
$29$	−10.3350			−0.356379			−0.178190	+	0.983996i	$0.557024\pi$
$30$	68.1937	+	25.0362i	2.27312	+	0.834541i
$31$	−1.63768	+	0.945514i	−0.0528284	+	0.0305005i	−0.526182	−	0.850372i	$-0.676377\pi$
$31$	−1.63768	+	0.945514i	−0.0528284	+	0.0305005i	0.473353	+	0.880873i	$0.343043\pi$
$32$	21.7807	−	12.5751i	0.680646	−	0.392971i
$33$	−1.05648	+	1.82987i	−0.0320145	+	0.0554507i
$34$			60.0987i			1.76761i
$35$	30.5145	−	17.1424i	0.871844	−	0.489783i
$36$	−71.5341			−1.98706
$37$	−42.5933	−	24.5912i	−1.15117	−	0.664628i	−0.201997	−	0.979386i	$-0.564743\pi$
$37$	−42.5933	−	24.5912i	−1.15117	−	0.664628i	−0.949172	+	0.314758i	$0.898077\pi$
$38$	−9.76150	−	16.9074i	−0.256882	−	0.444932i
$39$	−24.4275	−	42.3096i	−0.626346	−	1.08486i
$40$	−44.8496	−	16.4658i	−1.12124	−	0.411645i
$41$		−	11.9884i		−	0.292401i	−0.989255	−	0.146200i	$-0.953296\pi$
$41$		−	11.9884i		−	0.292401i	0.989255	−	0.146200i	$-0.0467044\pi$
$42$	−66.0688	+	77.3190i	−1.57307	+	1.84093i
$43$			62.7080i			1.45833i	0.684341	+	0.729163i	$0.260090\pi$
$43$			62.7080i			1.45833i	−0.684341	+	0.729163i	$0.739910\pi$
$44$	1.65489	−	2.86635i	0.0376110	−	0.0651442i
$45$	−33.2334	−	39.8312i	−0.738519	−	0.885138i
$46$	15.3949	+	26.6648i	0.334672	+	0.579669i
$47$	23.8333	−	41.2805i	0.507092	−	0.878308i	−0.492875	−	0.870100i	$-0.664054\pi$
$47$	23.8333	−	41.2805i	0.507092	−	0.878308i	0.999966	−	0.00820814i	$-0.00261276\pi$
$48$	17.4310			0.363146
$49$	7.64201	+	48.4004i	0.155959	+	0.987763i
$50$	−27.7898	−	77.6984i	−0.555796	−	1.55397i
$51$	40.0723	−	69.4072i	0.785730	−	1.36093i
$52$	38.2637	+	66.2746i	0.735840	+	1.27451i
$53$	43.0379	−	24.8479i	0.812036	−	0.468829i	−0.0356265	−	0.999365i	$-0.511343\pi$
$53$	43.0379	−	24.8479i	0.812036	−	0.468829i	0.847662	+	0.530536i	$0.178009\pi$
$54$	17.2999	+	9.98811i	0.320369	+	0.184965i
$55$	2.36485	−	0.410186i	0.0429973	−	0.00745792i
$56$	43.4520	−	50.8510i	0.775929	−	0.908054i
$57$			26.0348i			0.456752i
$58$	−29.5429	−	17.0566i	−0.509360	−	0.294079i
$59$	−48.0612	+	27.7482i	−0.814597	+	0.470308i	−0.848550	−	0.529116i	$-0.822524\pi$
$59$	−48.0612	+	27.7482i	−0.814597	+	0.470308i	0.0339529	+	0.999423i	$0.489190\pi$
$60$	97.2159	+	116.516i	1.62026	+	1.94194i
$61$	−52.5096	−	30.3164i	−0.860813	−	0.496991i	0.00347154	−	0.999994i	$-0.498895\pi$
$61$	−52.5096	−	30.3164i	−0.860813	−	0.496991i	−0.864284	+	0.503003i	$0.832228\pi$
$62$	−6.24180			−0.100674
$63$	68.4647	−	24.2261i	1.08674	−	0.384541i
$64$	98.8544			1.54460
$65$	−19.1261	+	52.0956i	−0.294247	+	0.801471i
$66$	−6.03994	+	3.48716i	−0.0915142	+	0.0528357i
$67$	−71.3332	+	41.1843i	−1.06468	+	0.614690i	−0.926722	−	0.375748i	$-0.877386\pi$
$67$	−71.3332	+	41.1843i	−1.06468	+	0.614690i	−0.137953	+	0.990439i	$0.544052\pi$
$68$	−62.7699	+	108.721i	−0.923087	+	1.59883i
$69$		−	41.0597i		−	0.595068i
$70$	115.518	+	1.35829i	1.65026	+	0.0194042i
$71$	92.6337			1.30470			0.652350	−	0.757918i	$-0.273783\pi$
$71$	92.6337			1.30470			0.652350	+	0.757918i	$0.273783\pi$
$72$	−85.8542	−	49.5679i	−1.19242	−	0.688444i
$73$	−24.5977	−	42.6044i	−0.336954	−	0.583622i	0.646904	−	0.762571i	$-0.276063\pi$
$73$	−24.5977	−	42.6044i	−0.336954	−	0.583622i	−0.983858	+	0.178950i	$0.942730\pi$
$74$	−81.1693	−	140.589i	−1.09688	−	1.89986i
$75$	−19.7132	+	108.262i	−0.262843	+	1.44350i
$76$		−	40.7815i		−	0.536598i
$77$	−0.613147	+	3.30381i	−0.00796294	+	0.0429066i
$78$		−	161.258i		−	2.06741i
$79$	1.72254	−	2.98353i	0.0218043	−	0.0377662i	−0.854917	−	0.518764i	$-0.826392\pi$
$79$	1.72254	−	2.98353i	0.0218043	−	0.0377662i	0.876722	+	0.480998i	$0.159726\pi$
$80$	−12.6850	−	15.2034i	−0.158563	−	0.190042i
$81$	33.3676	+	57.7943i	0.411945	+	0.713510i
$82$	19.7854	−	34.2693i	0.241285	−	0.417918i
$83$	30.5486			0.368056			0.184028	−	0.982921i	$-0.441086\pi$
$83$	30.5486			0.368056			0.184028	+	0.982921i	$0.441086\pi$
$84$	−200.276	+	70.8674i	−2.38424	+	0.843659i
$85$	−89.6989	+	15.5584i	−1.05528	+	0.183040i
$86$	−103.491	+	179.252i	−1.20339	+	2.08433i
$87$	22.7458	+	39.3968i	0.261446	+	0.452837i
$88$	3.97234	−	2.29343i	0.0451402	−	0.0260617i
$89$	121.079	+	69.9048i	1.36043	+	0.785447i	0.989682	−	0.143284i	$-0.0457663\pi$
$89$	121.079	+	69.9048i	1.36043	+	0.785447i	0.370753	+	0.928732i	$0.379100\pi$
$90$	−29.2622	−	168.706i	−0.325136	−	1.87451i
$91$	−59.0667	−	50.4723i	−0.649085	−	0.554641i
$92$			64.3166i			0.699094i
$93$	7.20857	+	4.16187i	0.0775115	+	0.0447513i
$94$	136.256	−	78.6676i	1.44954	−	0.836889i
$95$	22.7077	−	18.9463i	0.239028	−	0.199434i
$96$	−95.8719	−	55.3517i	−0.998666	−	0.576580i
$97$	130.732			1.34775			0.673877	−	0.738843i	$-0.264628\pi$
$97$	130.732			1.34775			0.673877	+	0.738843i	$0.264628\pi$
$98$	−58.0338	+	150.966i	−0.592181	+	1.54047i
$99$	4.98030			0.0503060
$100$	30.8791	−	169.584i	0.308791	−	1.69584i
$101$	−63.7022	+	36.7785i	−0.630715	+	0.364143i	−0.781029	−	0.624495i	$-0.785305\pi$
$101$	−63.7022	+	36.7785i	−0.630715	+	0.364143i	0.150314	+	0.988638i	$0.451971\pi$
$102$	229.095	−	132.268i	2.24603	−	1.29675i
$103$	29.6605	−	51.3735i	0.287966	−	0.498772i	−0.685358	−	0.728206i	$-0.740354\pi$
$103$	29.6605	−	51.3735i	0.287966	−	0.498772i	0.973324	+	0.229434i	$0.0736876\pi$
$104$			106.056i			1.01977i
$105$	−132.504	−	78.5930i	−1.26195	−	0.748505i
$106$	164.033			1.54748
$107$	−111.300	−	64.2591i	−1.04019	−	0.600553i	−0.120301	−	0.992737i	$-0.538386\pi$
$107$	−111.300	−	64.2591i	−1.04019	−	0.600553i	−0.919886	+	0.392185i	$0.871719\pi$
$108$	20.8641	+	36.1377i	0.193186	+	0.334608i
$109$	20.2090	+	35.0030i	0.185404	+	0.321129i	0.943712	−	0.330767i	$-0.107307\pi$
$109$	20.2090	+	35.0030i	0.185404	+	0.321129i	−0.758309	+	0.651896i	$0.773974\pi$
$110$	7.43694	+	2.73035i	0.0676086	+	0.0248214i
$111$			216.486i			1.95033i
$112$	26.1327	−	9.24699i	0.233327	−	0.0825624i
$113$			120.513i			1.06649i	0.845962	+	0.533243i	$0.179027\pi$
$113$			120.513i			1.06649i	−0.845962	+	0.533243i	$0.820973\pi$
$114$	−42.9672	+	74.4213i	−0.376905	+	0.652818i
$115$	−35.8124	+	29.8803i	−0.311412	+	0.259828i
$116$	−35.6294	−	61.7119i	−0.307150	−	0.531999i
$117$	−57.5763	+	99.7251i	−0.492105	+	0.852351i
$118$	−183.179			−1.55236
$119$	23.2567	−	125.314i	0.195434	−	1.05306i
$120$	35.9398	+	207.204i	0.299499	+	1.72670i
$121$	60.3848	−	104.590i	0.499048	−	0.864376i
$122$	−100.067	−	173.321i	−0.820219	−	1.42066i
$123$	−45.6997	+	26.3847i	−0.371542	+	0.214510i
$124$	−11.2916	−	6.51923i	−0.0910616	−	0.0525744i
$125$	108.773	−	61.5916i	0.870181	−	0.492732i
$126$	235.690	+	43.7413i	1.87056	+	0.347153i
$127$		−	214.900i		−	1.69212i	−0.533086	−	0.846061i	$-0.678968\pi$
$127$		−	214.900i		−	1.69212i	0.533086	−	0.846061i	$-0.321032\pi$
$128$	195.455	+	112.846i	1.52700	+	0.881611i
$129$	239.042	−	138.011i	1.85304	−	1.06985i
$130$	−140.650	+	117.352i	−1.08192	+	0.902705i
$131$	−13.7292	−	7.92658i	−0.104803	−	0.0605082i	0.446682	−	0.894693i	$-0.352605\pi$
$131$	−13.7292	−	7.92658i	−0.104803	−	0.0605082i	−0.551486	+	0.834184i	$0.685939\pi$
$132$	−14.5686			−0.110368
$133$	13.8113	+	39.0316i	0.103844	+	0.293471i
$134$	−271.877			−2.02893
$135$	−10.4289	+	28.4063i	−0.0772512	+	0.210417i
$136$	−150.671	+	86.9900i	−1.10788	+	0.639632i
$137$	−90.6856	+	52.3574i	−0.661939	+	0.382170i	−0.793015	−	0.609202i	$-0.791490\pi$
$137$	−90.6856	+	52.3574i	−0.661939	+	0.382170i	0.131077	+	0.991372i	$0.458157\pi$
$138$	67.7637	−	117.370i	0.491041	−	0.850508i
$139$			107.341i			0.772238i	0.922449	+	0.386119i	$0.126185\pi$
$139$			107.341i			0.772238i	−0.922449	+	0.386119i	$0.873815\pi$
$140$	207.557	+	123.110i	1.48255	+	0.879355i
$141$	−209.814			−1.48804
$142$	264.796	+	152.880i	1.86476	+	1.07662i
$143$	−2.66397	−	4.61412i	−0.0186291	−	0.0322666i
$144$	−20.5427	−	35.5810i	−0.142658	−	0.247090i
$145$	17.8093	−	48.5091i	0.122823	−	0.334545i
$146$		−	162.381i		−	1.11220i
$147$	167.683	−	135.653i	1.14070	−	0.922811i
$148$		−	339.108i		−	2.29127i
$149$	−0.730827	+	1.26583i	−0.00490488	+	0.00849551i	−0.868467	−	0.495746i	$-0.834895\pi$
$149$	−0.730827	+	1.26583i	−0.00490488	+	0.00849551i	0.863563	+	0.504242i	$0.168228\pi$
$150$	−235.024	+	276.937i	−1.56682	+	1.84624i
$151$	−2.08277	−	3.60746i	−0.0137931	−	0.0238904i	0.859046	−	0.511898i	$-0.171057\pi$
$151$	−2.08277	−	3.60746i	−0.0137931	−	0.0238904i	−0.872840	+	0.488007i	$0.837724\pi$
$152$	28.2586	−	48.9453i	0.185912	−	0.322009i
$153$	−188.903			−1.23466
$154$	−7.20521	+	8.43210i	−0.0467870	+	0.0547539i
$155$	−1.61588	−	9.31605i	−0.0104250	−	0.0601035i
$156$	168.425	−	291.721i	1.07965	−	1.87001i
$157$	62.4948	+	108.244i	0.398056	+	0.689453i	0.993486	−	0.113954i	$-0.0363517\pi$
$157$	62.4948	+	108.244i	0.398056	+	0.689453i	−0.595430	+	0.803407i	$0.703018\pi$
$158$	9.84787	−	5.68567i	0.0623283	−	0.0359853i
$159$	−189.440	−	109.373i	−1.19145	−	0.687881i
$160$	21.4907	+	123.901i	0.134317	+	0.774380i
$161$	−21.7818	−	61.5569i	−0.135291	−	0.382341i
$162$			220.276i			1.35973i
$163$	−77.3771	−	44.6737i	−0.474706	−	0.274072i	0.243502	−	0.969901i	$-0.421704\pi$
$163$	−77.3771	−	44.6737i	−0.474706	−	0.274072i	−0.718208	+	0.695829i	$0.755037\pi$
$164$	71.5849	−	41.3295i	0.436493	−	0.252009i
$165$	−6.76829	−	8.11200i	−0.0410200	−	0.0491637i
$166$	87.3241	+	50.4166i	0.526049	+	0.303714i
$167$	−119.740			−0.717004			−0.358502	−	0.933529i	$-0.616712\pi$
$167$	−119.740			−0.717004			−0.358502	+	0.933529i	$0.616712\pi$
$168$	−289.475	−	53.7230i	−1.72306	−	0.319779i
$169$	−45.8095			−0.271062
$170$	−282.084	−	103.562i	−1.65932	−	0.609191i
$171$	53.1436	−	30.6825i	0.310781	−	0.179430i
$172$	−374.439	+	216.183i	−2.17697	+	1.25688i
$173$	55.2221	−	95.6475i	0.319203	−	0.552876i	−0.661119	−	0.750281i	$-0.729918\pi$
$173$	55.2221	−	95.6475i	0.319203	−	0.552876i	0.980322	+	0.197405i	$0.0632515\pi$
$174$			150.156i			0.862964i
$175$	27.8780	+	172.765i	0.159303	+	0.987230i
$176$	1.90096			0.0108009
$177$	211.551	+	122.139i	1.19520	+	0.690051i
$178$	230.738	+	399.650i	1.29628	+	2.24522i
$179$	33.9066	+	58.7279i	0.189422	+	0.328089i	0.945058	−	0.326903i	$-0.106005\pi$
$179$	33.9066	+	58.7279i	0.189422	+	0.328089i	−0.755636	+	0.654992i	$0.772672\pi$
$180$	123.268	−	335.758i	0.684822	−	1.86532i
$181$		−	244.918i		−	1.35314i	−0.736380	−	0.676568i	$-0.763466\pi$
$181$		−	244.918i		−	1.35314i	0.736380	−	0.676568i	$-0.236534\pi$
$182$	−85.5458	−	241.759i	−0.470032	−	1.32834i
$183$			266.887i			1.45840i
$184$	−44.5667	+	77.1918i	−0.242210	+	0.419521i
$185$	188.820	−	157.543i	1.02065	−	0.851584i
$186$	13.7373	+	23.7936i	0.0738562	+	0.127923i
$187$	4.37012	−	7.56927i	0.0233696	−	0.0404774i
$188$	328.657			1.74817
$189$	−32.2074	−	27.5211i	−0.170410	−	0.145615i
$190$	96.1789	−	16.6823i	0.506205	−	0.0878018i
$191$	−120.803	+	209.238i	−0.632479	+	1.09549i	0.354565	+	0.935032i	$0.384629\pi$
$191$	−120.803	+	209.238i	−0.632479	+	1.09549i	−0.987043	+	0.160454i	$0.948704\pi$
$192$	−217.564	−	376.831i	−1.13314	−	1.96266i
$193$	264.818	−	152.893i	1.37212	−	0.792191i	0.380921	−	0.924607i	$-0.375607\pi$
$193$	264.818	−	152.893i	1.37212	−	0.792191i	0.991194	+	0.132416i	$0.0422735\pi$
$194$	373.701	+	215.757i	1.92630	+	1.11215i
$195$	240.681	−	41.7464i	1.23426	−	0.214084i
$196$	−262.661	+	212.490i	−1.34011	+	1.08413i
$197$			82.4745i			0.418653i	0.977846	+	0.209326i	$0.0671271\pi$
$197$			82.4745i			0.418653i	−0.977846	+	0.209326i	$0.932873\pi$
$198$	14.2363	+	8.21934i	0.0719006	+	0.0415118i
$199$	−88.4551	+	51.0696i	−0.444498	+	0.256631i	−0.705504	−	0.708706i	$-0.749279\pi$
$199$	−88.4551	+	51.0696i	−0.444498	+	0.256631i	0.261006	+	0.965337i	$0.415946\pi$
$200$	154.570	−	182.135i	0.772850	−	0.910676i
$201$	313.987	+	181.281i	1.56213	+	0.901894i
$202$	−242.793			−1.20194
$203$	55.0003	+	46.9975i	0.270937	+	0.231515i
$204$	552.588			2.70877
$205$	56.2698	+	20.6585i	0.274487	+	0.100773i
$206$	169.571	−	97.9017i	0.823159	−	0.475251i
$207$	−83.8130	+	48.3894i	−0.404894	+	0.233765i
$208$	−21.9766	+	38.0646i	−0.105657	+	0.183003i
$209$			2.83926i			0.0135850i
$210$	−249.060	−	443.342i	−1.18600	−	2.11115i
$211$	−177.792			−0.842617			−0.421308	−	0.906917i	$-0.638429\pi$
$211$	−177.792			−0.842617			−0.421308	+	0.906917i	$0.638429\pi$
$212$	296.742	+	171.324i	1.39973	+	0.808133i
$213$	−203.873	−	353.118i	−0.957149	−	1.65783i
$214$	−212.103	−	367.373i	−0.991135	−	1.71670i
$215$	−294.331	−	108.059i	−1.36898	−	0.502599i
$216$			57.8292i			0.267728i
$217$	13.0150	+	2.41542i	0.0599768	+	0.0111310i
$218$			133.409i			0.611970i
$219$	−108.271	+	187.532i	−0.494390	+	0.856309i
$220$	10.6020	+	12.7068i	0.0481908	+	0.0577582i
$221$	101.044	+	175.014i	0.457214	+	0.791919i
$222$	−357.283	+	618.832i	−1.60938	+	2.78753i
$223$	−344.072			−1.54292			−0.771462	−	0.636276i	$-0.780474\pi$
$223$	−344.072			−1.54292			−0.771462	+	0.636276i	$0.780474\pi$
$224$	−173.095	−	32.1244i	−0.772747	−	0.143412i
$225$	244.223	−	87.3492i	1.08543	−	0.388219i
$226$	−198.891	+	344.489i	−0.880048	+	1.52429i
$227$	44.8937	+	77.7581i	0.197769	+	0.342547i	0.947805	−	0.318851i	$-0.103297\pi$
$227$	44.8937	+	77.7581i	0.197769	+	0.342547i	−0.750035	+	0.661398i	$0.769964\pi$
$228$	−155.458	+	89.7538i	−0.681834	+	0.393657i
$229$	−261.003	−	150.690i	−1.13975	−	0.658035i	−0.193381	−	0.981124i	$-0.561945\pi$
$229$	−261.003	−	150.690i	−1.13975	−	0.658035i	−0.946369	+	0.323089i	$0.895279\pi$
$230$	−151.684	+	26.3098i	−0.659497	+	0.114390i
$231$	13.9435	−	4.93388i	0.0603615	−	0.0213588i
$232$		−	98.7543i		−	0.425665i
$233$	−218.293	−	126.032i	−0.936881	−	0.540908i	−0.0478997	−	0.998852i	$-0.515253\pi$
$233$	−218.293	−	126.032i	−0.936881	−	0.540908i	−0.888981	+	0.457944i	$0.848586\pi$
$234$	−329.167	+	190.045i	−1.40670	+	0.812157i
$235$	152.687	+	183.001i	0.649734	+	0.778726i
$236$	−331.377	−	191.321i	−1.40414	−	0.810681i
$237$	−15.1642			−0.0639841
$238$	273.294	−	319.830i	1.14829	−	1.34382i
$239$	266.473			1.11495			0.557475	−	0.830194i	$-0.311770\pi$
$239$	266.473			1.11495			0.557475	+	0.830194i	$0.311770\pi$
$240$	−30.0372	+	81.8154i	−0.125155	+	0.340898i
$241$	28.0587	−	16.1997i	0.116426	−	0.0672187i	−0.440656	−	0.897676i	$-0.645254\pi$
$241$	28.0587	−	16.1997i	0.116426	−	0.0672187i	0.557082	+	0.830457i	$0.311921\pi$
$242$	345.223	−	199.315i	1.42654	−	0.823614i
$243$	174.108	−	301.564i	0.716494	−	1.24100i
$244$		−	418.058i		−	1.71335i
$245$	−240.344	−	47.5348i	−0.980998	−	0.194019i
$246$	−174.178			−0.708042
$247$	−56.8531	−	32.8241i	−0.230174	−	0.132891i
$248$	−9.03470	−	15.6486i	−0.0364302	−	0.0630990i
$249$	−67.2329	−	116.451i	−0.270012	−	0.467674i
$250$	412.578	+	3.45405i	1.65031	+	0.0138162i
$251$		−	240.863i		−	0.959613i	−0.877374	−	0.479807i	$-0.840707\pi$
$251$		−	240.863i		−	0.959613i	0.877374	−	0.479807i	$-0.159293\pi$
$252$	380.687	+	325.296i	1.51066	+	1.29086i
$253$		−	4.47781i		−	0.0176988i
$254$	354.664	−	614.296i	1.39632	−	2.41849i
$255$	256.722	+	307.689i	1.00675	+	1.20662i
$256$	174.767	+	302.706i	0.682685	+	1.18245i
$257$	−88.4523	+	153.204i	−0.344172	+	0.596124i	−0.985203	−	0.171391i	$-0.945174\pi$
$257$	−88.4523	+	153.204i	−0.344172	+	0.596124i	0.641031	+	0.767515i	$0.278507\pi$
$258$	911.076			3.53130
$259$	114.844	+	324.558i	0.443413	+	1.25312i
$260$	−377.008	+	65.3924i	−1.45003	+	0.251509i
$261$	53.6125	−	92.8595i	0.205412	−	0.355784i
$262$	−26.1636	−	45.3167i	−0.0998610	−	0.172964i
$263$	−358.407	+	206.926i	−1.36276	+	0.786792i	−0.989991	−	0.141130i	$-0.954926\pi$
$263$	−358.407	+	206.926i	−1.36276	+	0.786792i	−0.372773	+	0.927923i	$0.621593\pi$
$264$	−17.4850	−	10.0950i	−0.0662311	−	0.0382386i
$265$	42.4650	+	244.824i	0.160245	+	0.923864i
$266$	−24.9368	+	134.367i	−0.0937474	+	0.505138i
$267$		−	615.400i		−	2.30487i
$268$	−491.836	−	283.961i	−1.83521	−	1.05956i
$269$	−354.850	+	204.873i	−1.31915	+	0.761609i	−0.983591	−	0.180412i	$-0.942257\pi$
$269$	−354.850	+	204.873i	−1.31915	+	0.761609i	−0.335554	+	0.942021i	$0.608924\pi$
$270$	−76.6923	+	63.9886i	−0.284045	+	0.236995i
$271$	322.701	+	186.311i	1.19078	+	0.687496i	0.958483	−	0.285149i	$-0.0920431\pi$
$271$	322.701	+	186.311i	1.19078	+	0.687496i	0.232295	+	0.972645i	$0.425376\pi$
$272$	−72.1034			−0.265086
$273$	−62.4026	+	336.243i	−0.228581	+	1.23166i
$274$	−345.636			−1.26145
$275$	−2.14984	+	11.8067i	−0.00781761	+	0.0429333i
$276$	245.174	−	141.551i	0.888311	−	0.512867i
$277$	79.7252	−	46.0294i	0.287817	−	0.166171i	−0.349140	−	0.937071i	$-0.613526\pi$
$277$	79.7252	−	46.0294i	0.287817	−	0.166171i	0.636957	+	0.770899i	$0.280193\pi$
$278$	−177.153	+	306.837i	−0.637239	+	1.10373i
$279$		−	19.6193i		−	0.0703201i
$280$	163.801	+	291.576i	0.585005	+	1.04134i
$281$	221.139			0.786971			0.393486	−	0.919331i	$-0.371269\pi$
$281$	221.139			0.786971			0.393486	+	0.919331i	$0.371269\pi$
$282$	−599.759	−	346.271i	−2.12680	−	1.22791i
$283$	169.467	+	293.526i	0.598825	+	1.03719i	0.992995	+	0.118157i	$0.0376988\pi$
$283$	169.467	+	293.526i	0.598825	+	1.03719i	−0.394170	+	0.919038i	$0.628968\pi$
$284$	319.350	+	553.131i	1.12447	+	1.94764i
$285$	−122.199	−	44.8634i	−0.428768	−	0.157415i
$286$		−	17.5861i		−	0.0614900i
$287$	−54.5164	+	63.7994i	−0.189953	+	0.222298i
$288$			260.931i			0.906011i
$289$	−21.2591	+	36.8218i	−0.0735607	+	0.127411i
$290$	130.966	−	109.273i	0.451608	−	0.376802i
$291$	−287.722	−	498.349i	−0.988734	−	1.71254i
$292$	169.598	−	293.753i	0.580816	−	1.00600i
$293$	−9.00667			−0.0307395			−0.0153697	−	0.999882i	$-0.504893\pi$
$293$	−9.00667			−0.0307395			−0.0153697	+	0.999882i	$0.504893\pi$
$294$	703.203	−	111.030i	2.39185	−	0.377652i
$295$	−47.4214	−	273.399i	−0.160751	−	0.926777i
$296$	234.977	−	406.993i	0.793842	−	1.37497i
$297$	−1.45259	−	2.51595i	−0.00489086	−	0.00847122i
$298$	−4.17818	+	2.41227i	−0.0140207	+	0.00809488i
$299$	89.6633	+	51.7671i	0.299877	+	0.173134i
$300$	−714.412	+	255.518i	−2.38137	+	0.851728i
$301$	285.159	−	333.716i	0.947373	−	1.10869i
$302$		−	13.7493i		−	0.0455276i
$303$	280.398	+	161.888i	0.925405	+	0.534283i
$304$	20.2847	−	11.7114i	0.0667258	−	0.0385242i
$305$	232.780	−	194.221i	0.763214	−	0.636791i
$306$	−539.984	−	311.760i	−1.76466	−	1.01882i
$307$	162.784			0.530240			0.265120	−	0.964215i	$-0.414588\pi$
$307$	162.784			0.530240			0.265120	+	0.964215i	$0.414588\pi$
$308$	−21.8414	+	7.72852i	−0.0709135	+	0.0250926i
$309$	−261.113			−0.845027
$310$	10.7559	−	29.2970i	0.0346965	−	0.0945063i
$311$	−286.756	+	165.559i	−0.922045	+	0.532343i	−0.884287	−	0.466944i	$-0.845355\pi$
$311$	−286.756	+	165.559i	−0.922045	+	0.532343i	−0.0377579	+	0.999287i	$0.512022\pi$
$312$	404.282	−	233.413i	1.29578	−	0.748117i
$313$	−255.584	+	442.685i	−0.816564	+	1.41433i	0.0916356	+	0.995793i	$0.470790\pi$
$313$	−255.584	+	442.685i	−0.816564	+	1.41433i	−0.908200	+	0.418538i	$0.862543\pi$
$314$			412.558i			1.31388i
$315$	−4.26939	+	363.098i	−0.0135536	+	1.15269i
$316$	23.7535			0.0751694
$317$	516.529	+	298.218i	1.62943	+	0.940752i	0.984263	+	0.176711i	$0.0565458\pi$
$317$	516.529	+	298.218i	1.62943	+	0.940752i	0.645168	+	0.764041i	$0.276788\pi$
$318$	−361.013	−	625.292i	−1.13526	−	1.96633i
$319$	2.48056	+	4.29646i	0.00777606	+	0.0134685i
$320$	−170.346	+	463.990i	−0.532333	+	1.44997i
$321$			565.698i			1.76230i
$322$	39.3279	−	211.910i	0.122136	−	0.658106i
$323$		−	107.693i		−	0.333416i
$324$	−230.066	+	398.486i	−0.710081	+	1.22990i
$325$	−211.562	−	179.543i	−0.650959	−	0.552440i
$326$	−147.456	−	255.402i	−0.452320	−	0.783442i
$327$	88.9539	−	154.073i	0.272030	−	0.471170i
$328$	114.553			0.349248
$329$	−314.554	+	111.304i	−0.956093	+	0.338311i
$330$	−5.95953	−	34.3586i	−0.0180592	−	0.104117i
$331$	209.897	−	363.552i	0.634130	−	1.09834i	−0.352569	−	0.935786i	$-0.614692\pi$
$331$	209.897	−	363.552i	0.634130	−	1.09834i	0.986699	−	0.162559i	$-0.0519747\pi$
$332$	105.315	+	182.411i	0.317214	+	0.549430i
$333$	441.902	−	255.132i	1.32703	−	0.766163i
$334$	−342.279	−	197.615i	−1.02479	−	0.591662i
$335$	−70.3836	−	405.784i	−0.210100	−	1.21129i
$336$	−92.7634	−	79.2660i	−0.276081	−	0.235911i
$337$			358.442i			1.06362i	0.846862	+	0.531812i	$0.178489\pi$
$337$			358.442i			1.06362i	−0.846862	+	0.531812i	$0.821511\pi$
$338$	−130.948	−	75.6027i	−0.387419	−	0.223677i
$339$	459.393	−	265.231i	1.35514	−	0.782391i
$340$	−402.134	−	481.970i	−1.18275	−	1.41756i
$341$	0.786138	+	0.453877i	0.00230539	+	0.00133102i
$342$	202.550			0.592251
$343$	179.428	−	292.326i	0.523114	−	0.852263i
$344$	−599.195			−1.74185
$345$	192.721	+	70.7542i	0.558610	+	0.205085i
$346$	315.708	−	182.274i	0.912450	−	0.526803i
$347$	−22.5297	+	13.0075i	−0.0649270	+	0.0374856i	−0.532112	−	0.846674i	$-0.678602\pi$
$347$	−22.5297	+	13.0075i	−0.0649270	+	0.0374856i	0.467185	+	0.884160i	$0.345268\pi$
$348$	−156.830	+	271.637i	−0.450660	+	0.780567i
$349$		−	203.134i		−	0.582046i	−0.956716	−	0.291023i	$-0.906004\pi$
$349$		−	203.134i		−	0.582046i	0.956716	−	0.291023i	$-0.0939956\pi$
$350$	−205.437	+	539.863i	−0.586962	+	1.54247i
$351$	67.1723			0.191374
$352$	−10.4554	−	6.03644i	−0.0297029	−	0.0171490i
$353$	−152.451	−	264.053i	−0.431872	−	0.748024i	0.565162	−	0.824980i	$-0.308813\pi$
$353$	−152.451	−	264.053i	−0.431872	−	0.748024i	−0.997035	+	0.0769552i	$0.975480\pi$
$354$	403.149	+	698.275i	1.13884	+	1.97253i
$355$	−159.627	+	434.792i	−0.449653	+	1.22477i
$356$			963.974i			2.70779i
$357$	−528.878	+	187.142i	−1.48145	+	0.524208i
$358$			223.834i			0.625234i
$359$	238.769	−	413.561i	0.665095	−	1.15198i	−0.314164	−	0.949369i	$-0.601724\pi$
$359$	238.769	−	413.561i	0.665095	−	1.15198i	0.979259	−	0.202610i	$-0.0649425\pi$
$360$	380.600	−	317.556i	1.05722	−	0.882099i
$361$	−163.008	−	282.338i	−0.451546	−	0.782100i
$362$	404.205	−	700.104i	1.11659	−	1.93399i
$363$	−531.591			−1.46444
$364$	97.7487	−	526.698i	0.268540	−	1.44697i
$365$	242.358	−	42.0372i	0.663994	−	0.115170i
$366$	−440.463	+	762.905i	−1.20345	+	2.08444i
$367$	−81.0555	−	140.392i	−0.220860	−	0.382540i	0.734210	−	0.678923i	$-0.237553\pi$
$367$	−81.0555	−	140.392i	−0.220860	−	0.382540i	−0.955069	+	0.296383i	$0.904220\pi$
$368$	−31.9910	+	18.4700i	−0.0869321	+	0.0501903i
$369$	107.716	+	62.1896i	0.291912	+	0.168536i
$370$	799.752	−	138.718i	2.16149	−	0.374913i
$371$	−342.031	−	63.4768i	−0.921916	−	0.171096i
$372$			57.3913i			0.154278i
$373$	−183.255	−	105.802i	−0.491300	−	0.283652i	0.233814	−	0.972281i	$-0.424879\pi$
$373$	−183.255	−	105.802i	−0.491300	−	0.283652i	−0.725114	+	0.688629i	$0.758213\pi$
$374$	24.9842	−	14.4246i	0.0668027	−	0.0385686i
$375$	−474.178	−	279.085i	−1.26447	−	0.744228i
$376$	394.449	+	227.735i	1.04907	+	0.605678i
$377$	−114.709			−0.304269
$378$	−46.6457	−	131.824i	−0.123401	−	0.348741i
$379$	185.327			0.488988			0.244494	−	0.969651i	$-0.421378\pi$
$379$	185.327			0.488988			0.244494	+	0.969651i	$0.421378\pi$
$380$	191.415	+	70.2748i	0.503723	+	0.184934i
$381$	−819.193	+	472.961i	−2.15011	+	1.24137i
$382$	−690.640	+	398.741i	−1.80796	+	1.04382i
$383$	326.332	−	565.223i	0.852041	−	1.47578i	−0.0273218	−	0.999627i	$-0.508698\pi$
$383$	326.332	−	565.223i	0.852041	−	1.47578i	0.879363	−	0.476152i	$-0.157969\pi$
$384$		−	993.430i		−	2.58706i
$385$	−14.4504	−	8.57105i	−0.0375335	−	0.0222625i
$386$	1009.32			2.61482
$387$	−563.428	−	325.296i	−1.45589	−	0.840557i
$388$	450.693	+	780.623i	1.16158	+	2.01191i
$389$	99.4966	+	172.333i	0.255775	+	0.443016i	0.965106	−	0.261860i	$-0.0843359\pi$
$389$	99.4966	+	172.333i	0.255775	+	0.443016i	−0.709330	+	0.704876i	$0.751003\pi$
$390$	756.891	+	277.880i	1.94075	+	0.712513i
$391$			169.843i			0.434382i
$392$	−462.482	+	73.0219i	−1.17980	+	0.186280i
$393$			69.7808i			0.177559i
$394$	−136.114	+	235.756i	−0.345466	+	0.598365i
$395$	11.0354	+	13.2263i	0.0279378	+	0.0334843i
$396$	17.1693	+	29.7382i	0.0433569	+	0.0750963i
$397$	159.071	−	275.519i	0.400682	−	0.694002i	−0.593126	−	0.805110i	$-0.702106\pi$
$397$	159.071	−	275.519i	0.400682	−	0.694002i	0.993808	+	0.111107i	$0.0354397\pi$
$398$	−337.135			−0.847073
$399$	118.391	−	138.551i	0.296720	−	0.347245i
$400$	93.2186	−	33.3408i	0.233046	−	0.0833520i
$401$	−118.055	+	204.477i	−0.294401	+	0.509917i	−0.974845	−	0.222883i	$-0.928453\pi$
$401$	−118.055	+	204.477i	−0.294401	+	0.509917i	0.680445	+	0.732799i	$0.261787\pi$
$402$	598.361	+	1036.39i	1.48846	+	2.57809i
$403$	−18.1768	+	10.4944i	−0.0451037	+	0.0260406i
$404$	−439.220	−	253.584i	−1.08718	−	0.627683i
$405$	−328.767	+	57.0250i	−0.811770	+	0.140802i
$406$	79.6563	+	225.115i	0.196198	+	0.554469i
$407$			23.6091i			0.0580077i
$408$	663.208	+	382.903i	1.62551	+	0.938489i
$409$	124.390	−	71.8168i	0.304133	−	0.175591i	−0.340165	−	0.940366i	$-0.610483\pi$
$409$	124.390	−	71.8168i	0.304133	−	0.175591i	0.644298	+	0.764775i	$0.277150\pi$
$410$	126.754	+	151.919i	0.309157	+	0.370534i
$411$	399.171	+	230.461i	0.971218	+	0.560733i
$412$	409.013			0.992749
$413$	381.952	+	70.8857i	0.924823	+	0.171636i
$414$	−319.442			−0.771599
$415$	−52.6416	+	143.385i	−0.126847	+	0.345507i
$416$	241.746	−	139.572i	0.581121	−	0.335510i
$417$	409.182	−	236.241i	0.981252	−	0.566526i
$418$	−4.68583	+	8.11609i	−0.0112101	+	0.0194165i
$419$		−	609.050i		−	1.45358i	−0.686859	−	0.726790i	$-0.741011\pi$
$419$		−	609.050i		−	1.45358i	0.686859	−	0.726790i	$-0.258989\pi$
$420$	12.4890	−	1062.15i	0.0297358	−	2.52893i
$421$	117.056			0.278043			0.139021	−	0.990289i	$-0.455604\pi$
$421$	117.056			0.278043			0.139021	+	0.990289i	$0.455604\pi$
$422$	−508.224	−	293.423i	−1.20432	−	0.695315i
$423$	247.269	+	428.282i	0.584560	+	1.01249i
$424$	237.430	+	411.241i	0.559977	+	0.969908i
$425$	81.5437	−	447.827i	0.191868	−	1.05371i
$426$		−	1345.86i		−	3.15930i
$427$	141.581	+	400.119i	0.331572	+	0.937048i
$428$		−	886.121i		−	2.07038i
$429$	−11.7260	+	20.3100i	−0.0273333	+	0.0473426i
$430$	−663.015	−	794.644i	−1.54190	−	1.84801i
$431$	295.934	+	512.573i	0.686622	+	1.18926i	0.972924	+	0.231125i	$0.0742407\pi$
$431$	295.934	+	512.573i	0.686622	+	1.18926i	−0.286302	+	0.958140i	$0.592426\pi$
$432$	−11.9832	+	20.7556i	−0.0277390	+	0.0480453i
$433$	47.7887			0.110367			0.0551833	−	0.998476i	$-0.482426\pi$
$433$	47.7887			0.110367			0.0551833	+	0.998476i	$0.482426\pi$
$434$	33.2173	+	28.3841i	0.0765375	+	0.0654011i
$435$	−224.111	+	38.8724i	−0.515199	+	0.0893617i
$436$	−139.339	+	241.342i	−0.319585	+	0.553538i
$437$	−27.5867	−	47.7816i	−0.0631275	−	0.109340i
$438$	−618.993	+	357.376i	−1.41323	+	0.815927i
$439$	435.435	+	251.398i	0.991878	+	0.572661i	0.905835	−	0.423630i	$-0.139244\pi$
$439$	435.435	+	251.398i	0.991878	+	0.572661i	0.0860430	+	0.996291i	$0.472578\pi$
$440$	3.91946	+	22.5969i	0.00890786	+	0.0513566i
$441$	−474.518	−	182.412i	−1.07601	−	0.413634i
$442$			667.043i			1.50915i
$443$	661.691	+	382.028i	1.49366	+	0.862365i	0.999974	−	0.00727504i	$-0.00231574\pi$
$443$	661.691	+	382.028i	1.49366	+	0.862365i	0.493686	+	0.869640i	$0.335649\pi$
$444$	−1292.67	+	746.326i	−2.91143	+	1.68091i
$445$	−536.754	+	447.843i	−1.20619	+	1.00639i
$446$	−983.539	−	567.847i	−2.20524	−	1.27320i
$447$	6.43376			0.0143932
$448$	−526.078	−	449.532i	−1.17428	−	1.00342i
$449$	282.557			0.629303			0.314651	−	0.949207i	$-0.398112\pi$
$449$	282.557			0.629303			0.314651	+	0.949207i	$0.398112\pi$
$450$	842.275	+	153.368i	1.87172	+	0.340817i
$451$	−4.98383	+	2.87741i	−0.0110506	+	0.00638008i
$452$	−719.602	+	415.462i	−1.59204	+	0.919164i
$453$	−9.16770	+	15.8789i	−0.0202378	+	0.0350528i
$454$			296.365i			0.652786i
$455$	338.685	−	190.266i	0.744362	−	0.418166i
$456$	−248.771			−0.545551
$457$	−191.874	−	110.779i	−0.419856	−	0.242404i	0.275159	−	0.961399i	$-0.411269\pi$
$457$	−191.874	−	110.779i	−0.419856	−	0.242404i	−0.695016	+	0.718994i	$0.744603\pi$
$458$	−497.389	−	861.502i	−1.08600	−	1.88101i
$459$	55.0967	+	95.4303i	0.120036	+	0.207909i
$460$	−301.881	−	110.831i	−0.656264	−	0.240936i
$461$			256.792i			0.557032i	0.960432	+	0.278516i	$0.0898426\pi$
$461$			256.792i			0.557032i	−0.960432	+	0.278516i	$0.910157\pi$
$462$	48.0006	+	8.90832i	0.103897	+	0.0192821i
$463$		−	68.2120i		−	0.147326i	−0.997283	−	0.0736631i	$-0.976531\pi$
$463$		−	68.2120i		−	0.147326i	0.997283	−	0.0736631i	$-0.0234689\pi$
$464$	20.4636	−	35.4440i	0.0441026	−	0.0763880i
$465$	−31.9563	+	26.6629i	−0.0687232	+	0.0573396i
$466$	−415.998	−	720.530i	−0.892700	−	1.54620i
$467$	−280.428	+	485.716i	−0.600489	+	1.04008i	0.392258	+	0.919855i	$0.371694\pi$
$467$	−280.428	+	485.716i	−0.600489	+	1.04008i	−0.992747	+	0.120222i	$0.961639\pi$
$468$	−793.966			−1.69651
$469$	566.899	+	105.210i	1.20874	+	0.224328i
$470$	134.442	+	775.103i	0.286048	+	1.64916i
$471$	275.083	−	476.458i	0.584040	−	1.01159i
$472$	−265.143	−	459.240i	−0.561743	−	0.972967i
$473$	26.0689	−	15.0509i	0.0551140	−	0.0318201i
$474$	−43.3473	−	25.0266i	−0.0914501	−	0.0527987i
$475$	49.7976	+	139.231i	0.104837	+	0.293117i
$476$	828.444	−	293.143i	1.74043	−	0.615847i
$477$			515.592i			1.08090i
$478$	761.720	+	439.779i	1.59356	+	0.920040i
$479$	−414.055	+	239.055i	−0.864416	+	0.499071i	−0.865489	−	0.500928i	$-0.832992\pi$
$479$	−414.055	+	239.055i	−0.864416	+	0.499071i	0.00107240	+	0.999999i	$0.499659\pi$
$480$	425.010	−	354.609i	0.885437	−	0.738769i
$481$	−472.748	−	272.941i	−0.982844	−	0.567445i
$482$	106.942			0.221872
$483$	−186.715	+	218.509i	−0.386574	+	0.452400i
$484$	832.694			1.72044
$485$	−225.278	+	613.614i	−0.464492	+	1.26518i
$486$	995.386	−	574.686i	2.04812	−	1.18248i
$487$	388.954	−	224.563i	0.798674	−	0.461115i	−0.0443330	−	0.999017i	$-0.514116\pi$
$487$	388.954	−	224.563i	0.798674	−	0.461115i	0.843007	+	0.537902i	$0.180783\pi$
$488$	289.683	−	501.746i	0.593613	−	1.02817i
$489$			393.280i			0.804254i
$490$	−608.581	−	532.537i	−1.24200	−	1.08681i
$491$	−541.454			−1.10276			−0.551379	−	0.834255i	$-0.685898\pi$
$491$	−541.454			−1.10276			−0.551379	+	0.834255i	$0.685898\pi$
$492$	−315.095	−	181.920i	−0.640437	−	0.369756i
$493$	−94.0879	−	162.965i	−0.190848	−	0.330558i
$494$	−108.344	−	187.657i	−0.219320	−	0.379873i
$495$	−8.58208	+	23.3759i	−0.0173375	+	0.0472240i
$496$		−	7.48859i		−	0.0150980i
$497$	−492.973	−	421.244i	−0.991898	−	0.847574i
$498$		−	443.837i		−	0.891239i
$499$	−145.854	+	252.626i	−0.292292	+	0.506264i	−0.974351	−	0.225032i	$-0.927751\pi$
$499$	−145.854	+	252.626i	−0.292292	+	0.506264i	0.682059	+	0.731297i	$0.261085\pi$
$500$	742.761	+	437.165i	1.48552	+	0.874330i
$501$	263.529	+	456.446i	0.526006	+	0.911069i
$502$	397.513	−	688.513i	0.791859	−	1.37154i
$503$	690.684			1.37313			0.686565	−	0.727069i	$-0.259118\pi$
$503$	690.684			1.37313			0.686565	+	0.727069i	$0.259118\pi$
$504$	231.488	+	654.203i	0.459302	+	1.29802i
$505$	−62.8542	−	362.374i	−0.124464	−	0.717572i
$506$	7.39004	−	12.7999i	0.0146048	−	0.0252963i
$507$	100.820	+	174.625i	0.198856	+	0.344428i
$508$	1283.20	−	740.856i	2.52598	−	1.45838i
$509$	−173.093	−	99.9350i	−0.340064	−	0.196336i	0.320236	−	0.947338i	$-0.396238\pi$
$509$	−173.093	−	99.9350i	−0.340064	−	0.196336i	−0.660300	+	0.751002i	$0.729571\pi$
$510$	226.045	+	1303.22i	0.443226	+	2.55534i
$511$	−62.8374	+	338.586i	−0.122969	+	0.662594i
$512$			250.955i			0.490146i
$513$	−31.0004	−	17.8981i	−0.0604296	−	0.0348891i
$514$	−505.687	+	291.958i	−0.983826	+	0.568012i
$515$	190.019	+	227.744i	0.368970	+	0.442221i
$516$	1648.17	+	951.571i	3.19413	+	1.84413i
$517$	−22.8815			−0.0442582
$518$	−207.356	+	1117.29i	−0.400301	+	2.15693i
$519$	−486.142			−0.936689
$520$	−497.791	−	182.756i	−0.957290	−	0.351453i
$521$	782.209	−	451.609i	1.50136	−	0.866811i	0.501362	−	0.865238i	$-0.332833\pi$
$521$	782.209	−	451.609i	1.50136	−	0.866811i	0.999999	−	0.00157328i	$-0.000500790\pi$
$522$	306.505	−	176.961i	0.587175	−	0.339006i
$523$	−197.343	+	341.808i	−0.377329	+	0.653552i	−0.990673	−	0.136264i	$-0.956491\pi$
$523$	−197.343	+	341.808i	−0.377329	+	0.653552i	0.613344	+	0.789816i	$0.289824\pi$
$524$		−	109.306i		−	0.208599i
$525$	597.222	−	486.501i	1.13757	−	0.926668i
$526$	−1366.02			−2.59700
$527$	−29.8183	−	17.2156i	−0.0565812	−	0.0326671i
$528$	−4.18372	−	7.24641i	−0.00792371	−	0.0137243i
$529$	−220.993	−	382.771i	−0.417756	−	0.723574i
$530$	−282.663	+	769.919i	−0.533327	+	1.45268i
$531$		−	575.770i		−	1.08431i
$532$	−185.450	+	217.029i	−0.348591	+	0.407949i
$533$		−	133.061i		−	0.249646i
$534$	1015.64	−	1759.14i	1.90194	−	3.29426i
$535$	493.404	−	411.674i	0.922251	−	0.769485i
$536$	−393.529	−	681.612i	−0.734196	−	1.27166i
$537$	149.247	−	258.503i	0.277926	−	0.481383i
$538$	−1352.46			−2.51387
$539$	18.2868	−	14.7938i	0.0339273	−	0.0274468i
$540$	−205.572	+	35.6566i	−0.380688	+	0.0660308i
$541$	311.501	−	539.536i	0.575788	−	0.997294i	−0.420167	−	0.907447i	$-0.638029\pi$
$541$	311.501	−	539.536i	0.575788	−	0.997294i	0.995956	−	0.0898478i	$-0.0286381\pi$
$542$	614.966	+	1065.15i	1.13462	+	1.96523i
$543$	−933.622	+	539.027i	−1.71938	+	0.992683i
$544$	396.575	+	228.962i	0.728997	+	0.420887i
$545$	−199.117	+	34.5371i	−0.365352	+	0.0633707i
$546$	−733.306	+	858.173i	−1.34305	+	1.57174i
$547$		−	141.361i		−	0.258429i	−0.991617	−	0.129215i	$-0.958754\pi$
$547$		−	141.361i		−	0.258429i	0.991617	−	0.129215i	$-0.0412456\pi$
$548$	−625.268	−	360.999i	−1.14100	−	0.658757i
$549$	544.783	−	314.531i	0.992320	−	0.572916i
$550$	−25.6308	+	30.2016i	−0.0466014	+	0.0549120i
$551$	52.9390	+	30.5644i	0.0960781	+	0.0554707i
$552$	392.338			0.710758
$553$	−22.7343	+	8.04449i	−0.0411109	+	0.0145470i
$554$	303.862			0.548488
$555$	−1016.12	−	373.050i	−1.83084	−	0.672163i
$556$	−640.951	+	370.053i	−1.15279	+	0.665563i
$557$	−264.986	+	152.990i	−0.475738	+	0.274667i	−0.718639	−	0.695384i	$-0.755234\pi$
$557$	−264.986	+	152.990i	−0.475738	+	0.274667i	0.242901	+	0.970051i	$0.421901\pi$
$558$	32.3791	−	56.0823i	0.0580271	−	0.100506i
$559$			696.003i			1.24509i
$560$	−1.62961	+	138.593i	−0.00291001	+	0.247487i
$561$	−38.4719			−0.0685774
$562$	632.132	+	364.961i	1.12479	+	0.649398i
$563$	57.4413	+	99.4912i	0.102027	+	0.176716i	0.912520	−	0.409033i	$-0.134134\pi$
$563$	57.4413	+	99.4912i	0.102027	+	0.176716i	−0.810493	+	0.585749i	$0.800800\pi$
$564$	−723.323	−	1252.83i	−1.28249	−	2.22133i
$565$	−565.648	−	207.668i	−1.00115	−	0.367555i
$566$			1118.74i			1.97657i
$567$	85.2411	−	459.303i	0.150337	−	0.810059i
$568$			885.145i			1.55835i
$569$	−414.014	+	717.093i	−0.727617	+	1.26027i	0.230271	+	0.973127i	$0.426039\pi$
$569$	−414.014	+	717.093i	−0.727617	+	1.26027i	−0.957888	+	0.287143i	$0.907295\pi$
$570$	−275.268	−	329.917i	−0.482926	−	0.578802i
$571$	461.015	+	798.502i	0.807383	+	1.39843i	0.914671	+	0.404200i	$0.132450\pi$
$571$	461.015	+	798.502i	0.807383	+	1.39843i	−0.107288	+	0.994228i	$0.534217\pi$
$572$	18.3678	−	31.8139i	0.0321115	−	0.0556188i
$573$	1063.48			1.85599
$574$	−261.129	+	92.4001i	−0.454929	+	0.160976i
$575$	−78.5361	−	219.581i	−0.136584	−	0.381881i
$576$	−512.804	+	888.203i	−0.890285	+	1.54202i
$577$	−344.274	−	596.300i	−0.596662	−	1.03345i	−0.993310	−	0.115478i	$-0.963160\pi$
$577$	−344.274	−	596.300i	−0.596662	−	1.03345i	0.396648	−	0.917971i	$-0.370173\pi$
$578$	−121.539	+	70.1707i	−0.210275	+	0.121403i
$579$	−1165.65	−	672.988i	−2.01321	−	1.16233i
$580$	351.052	−	60.8904i	0.605263	−	0.104983i
$581$	−162.572	−	138.917i	−0.279814	−	0.239100i
$582$		−	1899.39i		−	3.26356i
$583$	−20.6596	−	11.9278i	−0.0354366	−	0.0204594i
$584$	407.099	−	235.039i	0.697087	−	0.402463i
$585$	−368.861	−	442.091i	−0.630532	−	0.755712i
$586$	−25.7458	−	14.8643i	−0.0439348	−	0.0253658i
$587$	0.215255			0.000366703			0.000183352	−	1.00000i	$-0.499942\pi$
$587$	0.215255			0.000366703			0.000183352		1.00000i	$0.499942\pi$
$588$	1388.08	+	533.602i	2.36069	+	0.907486i
$589$	11.1849			0.0189897
$590$	315.655	−	859.782i	0.535009	−	1.45726i
$591$	314.391	−	181.514i	0.531965	−	0.307130i
$592$	168.672	−	97.3828i	0.284919	−	0.164498i
$593$	−326.245	+	565.072i	−0.550159	+	0.952904i	0.448103	+	0.893982i	$0.352100\pi$
$593$	−326.245	+	565.072i	−0.550159	+	0.952904i	−0.998263	+	0.0589222i	$0.981234\pi$
$594$		−	9.58922i		−	0.0161435i
$595$	548.105	+	325.100i	0.921185	+	0.546387i
$596$	−10.0780			−0.0169093
$597$	389.352	+	224.793i	0.652182	+	0.376537i
$598$	170.870	+	295.955i	0.285736	+	0.494909i
$599$	−262.354	−	454.410i	−0.437986	−	0.758614i	0.559548	−	0.828798i	$-0.310975\pi$
$599$	−262.354	−	454.410i	−0.437986	−	0.758614i	−0.997534	+	0.0701839i	$0.977641\pi$
$600$	−1034.48	−	188.366i	−1.72414	−	0.313943i
$601$			248.076i			0.412772i	0.978471	+	0.206386i	$0.0661703\pi$
$601$			248.076i			0.412772i	−0.978471	+	0.206386i	$0.933830\pi$
$602$	1365.89	−	483.318i	2.26892	−	0.802853i
$603$		−	854.568i		−	1.41719i
$604$	14.3605	−	24.8731i	0.0237756	−	0.0411806i
$605$	386.854	+	463.656i	0.639427	+	0.766373i
$606$	534.350	+	925.521i	0.881765	+	1.52726i
$607$	−23.7361	+	41.1121i	−0.0391039	+	0.0677300i	−0.884915	−	0.465753i	$-0.845784\pi$
$607$	−23.7361	+	41.1121i	−0.0391039	+	0.0677300i	0.845811	+	0.533483i	$0.179117\pi$
$608$	−148.756			−0.244665
$609$	58.1065	−	313.094i	0.0954130	−	0.514112i
$610$	985.946	−	171.013i	1.61630	−	0.280350i
$611$	264.529	−	458.177i	0.432944	−	0.749881i
$612$	−651.234	−	1127.97i	−1.06411	−	1.84309i
$613$	851.761	−	491.765i	1.38950	−	0.802226i	0.396238	−	0.918148i	$-0.370315\pi$
$613$	851.761	−	491.765i	1.38950	−	0.802226i	0.993258	+	0.115922i	$0.0369821\pi$
$614$	465.322	+	268.654i	0.757853	+	0.437547i
$615$	−45.0913	−	259.966i	−0.0733192	−	0.422708i
$616$	−31.5690	−	5.85881i	−0.0512483	−	0.00951106i
$617$			467.447i			0.757613i	0.925476	+	0.378807i	$0.123665\pi$
$617$			467.447i			0.757613i	−0.925476	+	0.378807i	$0.876335\pi$
$618$	−746.399	−	430.934i	−1.20777	−	0.697304i
$619$	−336.116	+	194.056i	−0.542998	+	0.313500i	−0.746293	−	0.665618i	$-0.768168\pi$
$619$	−336.116	+	194.056i	−0.542998	+	0.313500i	0.203295	+	0.979117i	$0.434835\pi$
$620$	50.0569	−	41.7653i	0.0807370	−	0.0673633i
$621$	48.8909	+	28.2272i	0.0787292	+	0.0454544i
$622$	−1092.93			−1.75713
$623$	−326.464	−	922.611i	−0.524019	−	1.48092i
$624$	193.469			0.310046
$625$	101.653	+	616.678i	0.162645	+	0.986685i
$626$	−1461.19	+	843.619i	−2.33417	+	1.34763i
$627$	10.8232	−	6.24878i	0.0172619	−	0.00996615i
$628$	−430.895	+	746.333i	−0.686139	+	1.18843i
$629$		−	895.497i		−	1.42368i
$630$	−611.450	+	1030.88i	−0.970556	+	1.63631i
$631$	−366.713			−0.581162			−0.290581	−	0.956850i	$-0.593849\pi$
$631$	−366.713			−0.581162			−0.290581	+	0.956850i	$0.593849\pi$
$632$	28.5086	+	16.4595i	0.0451086	+	0.0260435i
$633$	391.294	+	677.740i	0.618157	+	1.07068i
$634$	984.342	+	1704.93i	1.55259	+	2.68917i
$635$	1008.67	+	370.316i	1.58845	+	0.583175i
$636$		−	1508.23i		−	2.37144i
$637$	84.8196	+	537.202i	0.133155	+	0.843331i
$638$			16.3754i			0.0256668i
$639$	−480.534	+	832.310i	−0.752010	+	1.30252i
$640$	−866.473	+	722.946i	−1.35386	+	1.12960i
$641$	−334.103	−	578.684i	−0.521222	−	0.902783i	−0.999695	−	0.0246813i	$-0.992143\pi$
$641$	−334.103	−	578.684i	−0.521222	−	0.902783i	0.478473	−	0.878102i	$-0.341190\pi$
$642$	−933.612	+	1617.06i	−1.45422	+	2.51879i
$643$	−106.816			−0.166121			−0.0830605	−	0.996545i	$-0.526469\pi$
$643$	−106.816			−0.166121			−0.0830605	+	0.996545i	$0.526469\pi$
$644$	292.475	−	342.277i	0.454153	−	0.531486i
$645$	235.859	+	1359.80i	0.365674	+	2.10822i
$646$	177.734	−	307.844i	0.275130	−	0.476539i
$647$	−208.211	−	360.632i	−0.321810	−	0.557391i	0.659052	−	0.752098i	$-0.270958\pi$
$647$	−208.211	−	360.632i	−0.321810	−	0.557391i	−0.980862	+	0.194707i	$0.937625\pi$
$648$	−552.244	+	318.838i	−0.852228	+	0.492034i
$649$	23.0709	+	13.3200i	0.0355484	+	0.0205239i
$650$	−308.442	−	862.384i	−0.474527	−	1.32674i
$651$	−19.4364	−	54.9288i	−0.0298563	−	0.0843760i
$652$		−	616.041i		−	0.944849i
$653$	−934.744	−	539.675i	−1.43146	−	0.826455i	−0.434229	−	0.900802i	$-0.642979\pi$
$653$	−934.744	−	539.675i	−1.43146	−	0.826455i	−0.997232	+	0.0743477i	$0.976313\pi$
$654$	508.554	−	293.614i	0.777606	−	0.448951i
$655$	60.8631	−	50.7814i	0.0929207	−	0.0775289i
$656$	41.1145	+	23.7375i	0.0626746	+	0.0361852i
$657$	510.398			0.776862
$658$	−1082.86	−	200.965i	−1.64568	−	0.305418i
$659$	129.177			0.196020			0.0980099	−	0.995185i	$-0.468752\pi$
$659$	129.177			0.196020			0.0980099	+	0.995185i	$0.468752\pi$
$660$	25.1047	−	68.3803i	0.0380374	−	0.103607i
$661$	492.050	−	284.085i	0.744402	−	0.429781i	−0.0792659	−	0.996854i	$-0.525258\pi$
$661$	492.050	−	284.085i	0.744402	−	0.429781i	0.823668	+	0.567073i	$0.191924\pi$
$662$	1199.99	−	692.816i	1.81268	−	1.04655i
$663$	444.767	−	770.359i	0.670840	−	1.16193i
$664$			291.902i			0.439612i
$665$	−207.001	−	2.43397i	−0.311280	−	0.00366011i
$666$	1684.25			2.52891
$667$	−83.4903	−	48.2032i	−0.125173	−	0.0722686i
$668$	−412.797	−	714.985i	−0.617959	−	1.07034i
$669$	757.250	+	1311.60i	1.13191	+	1.96053i
$670$	468.500	−	1276.10i	0.699254	−	1.90463i
$671$			29.1057i			0.0433766i
$672$	258.499	+	730.537i	0.384671	+	1.08711i
$673$			336.775i			0.500408i	0.968193	+	0.250204i	$0.0804978\pi$
$673$			336.775i			0.500408i	−0.968193	+	0.250204i	$0.919502\pi$
$674$	−591.562	+	1024.61i	−0.877688	+	1.52020i
$675$	−115.359	−	97.8998i	−0.170902	−	0.145037i
$676$	−157.926	−	273.536i	−0.233618	−	0.404639i
$677$	−101.559	+	175.906i	−0.150014	+	0.259831i	−0.931232	−	0.364426i	$-0.881265\pi$
$677$	−101.559	+	175.906i	−0.150014	+	0.259831i	0.781219	+	0.624258i	$0.214598\pi$
$678$	1750.92			2.58247
$679$	−695.724	−	594.494i	−1.02463	−	0.875543i
$680$	−148.665	−	857.102i	−0.218625	−	1.26044i
$681$	197.608	−	342.268i	0.290174	−	0.502596i
$682$	1.49813	+	2.59484i	0.00219667	+	0.00380475i
$683$	−232.168	+	134.042i	−0.339924	+	0.196255i	−0.660238	−	0.751056i	$-0.729545\pi$
$683$	−232.168	+	134.042i	−0.339924	+	0.196255i	0.320315	+	0.947311i	$0.396211\pi$
$684$	366.420	+	211.553i	0.535701	+	0.309287i
$685$	−89.4784	−	515.871i	−0.130625	−	0.753096i
$686$	995.346	−	539.499i	1.45094	−	0.786442i
$687$			1326.58i			1.93098i
$688$	−215.058	−	124.164i	−0.312584	−	0.180471i
$689$	477.683	−	275.790i	0.693299	−	0.400276i
$690$	434.126	+	520.313i	0.629169	+	0.754077i
$691$	−236.062	−	136.290i	−0.341623	−	0.197236i	0.319366	−	0.947631i	$-0.396530\pi$
$691$	−236.062	−	136.290i	−0.341623	−	0.197236i	−0.660990	+	0.750395i	$0.729863\pi$
$692$	761.502			1.10044
$693$	−26.5039	−	22.6475i	−0.0382452	−	0.0326804i
$694$	−85.8689			−0.123730
$695$	−503.824	−	184.971i	−0.724926	−	0.266145i
$696$	−376.449	+	217.343i	−0.540876	+	0.312275i
$697$	189.037	−	109.141i	0.271215	−	0.156586i
$698$	335.247	−	580.664i	0.480296	−	0.831897i
$699$			1109.51i			1.58728i
$700$	−935.501	+	762.064i	−1.33643	+	1.08866i
$701$	522.602			0.745509			0.372755	−	0.927930i	$-0.378413\pi$
$701$	522.602			0.745509			0.372755	+	0.927930i	$0.378413\pi$
$702$	192.014	+	110.859i	0.273524	+	0.157919i
$703$	145.450	+	251.928i	0.206900	+	0.358361i
$704$	−23.7266	−	41.0957i	−0.0337026	−	0.0583746i
$705$	361.553	−	984.798i	0.512840	−	1.39688i
$706$		−	1006.40i		−	1.42550i
$707$	506.254	+	93.9546i	0.716059	+	0.132892i
$708$			1684.27i			2.37892i
$709$	392.368	−	679.602i	0.553411	−	0.958535i	−0.444615	−	0.895722i	$-0.646659\pi$
$709$	392.368	−	679.602i	0.553411	−	0.958535i	0.998025	−	0.0628135i	$-0.0200073\pi$
$710$	−1173.87	+	979.422i	−1.65333	+	1.37947i
$711$	17.8713	+	30.9540i	0.0251354	+	0.0435358i
$712$	−667.963	+	1156.95i	−0.938151	+	1.62492i
$713$	−17.6398			−0.0247402
$714$	−1820.67	−	337.893i	−2.54995	−	0.473240i
$715$	26.2477	−	4.55270i	0.0367101	−	0.00636741i
$716$	−233.783	+	404.923i	−0.326512	+	0.565535i
$717$	−586.466	−	1015.79i	−0.817945	−	1.41672i
$718$	1365.06	−	788.116i	1.90119	−	1.09765i
$719$	−30.5028	−	17.6108i	−0.0424240	−	0.0244935i	0.478638	−	0.878012i	$-0.341131\pi$
$719$	−30.5028	−	17.6108i	−0.0424240	−	0.0244935i	−0.521062	+	0.853519i	$0.674464\pi$
$720$	202.405	−	35.1073i	0.281118	−	0.0487602i
$721$	−391.463	+	138.518i	−0.542944	+	0.192120i
$722$		−	1076.09i		−	1.49044i
$723$	−123.506	−	71.3062i	−0.170824	−	0.0986254i
$724$	1462.44	−	844.342i	2.01995	−	1.16622i
$725$	196.997	+	167.182i	0.271720	+	0.230596i
$726$	−1519.57	−	877.323i	−2.09307	−	1.20843i
$727$	62.1195			0.0854464			0.0427232	−	0.999087i	$-0.486397\pi$
$727$	62.1195			0.0854464			0.0427232	+	0.999087i	$0.486397\pi$
$728$	482.280	−	564.402i	0.662472	−	0.775277i
$729$	−932.126			−1.27864
$730$	762.163	+	279.816i	1.04406	+	0.383309i
$731$	−988.797	+	570.882i	−1.35266	+	0.780960i
$732$	−1593.63	+	920.081i	−2.17709	+	1.25694i
$733$	−523.215	+	906.236i	−0.713800	+	1.23634i	0.249621	+	0.968344i	$0.419694\pi$
$733$	−523.215	+	906.236i	−0.713800	+	1.23634i	−0.963421	+	0.267994i	$0.913639\pi$
$734$		−	535.087i		−	0.729001i
$735$	347.760	+	1020.81i	0.473143	+	1.38885i
$736$	234.604			0.318756
$737$	34.2422	+	19.7698i	0.0464616	+	0.0268246i
$738$	205.272	+	355.541i	0.278146	+	0.481763i
$739$	−440.521	−	763.005i	−0.596105	−	1.03248i	−0.993390	−	0.114788i	$-0.963381\pi$
$739$	−440.521	−	763.005i	−0.596105	−	1.03248i	0.397285	−	0.917695i	$-0.369952\pi$
$740$	1591.66	+	584.353i	2.15090	+	0.789666i
$741$			288.964i			0.389965i
$742$	−872.944	−	745.928i	−1.17647	−	1.00529i
$743$			661.842i			0.890770i	0.895339	+	0.445385i	$0.146933\pi$
$743$			661.842i			0.890770i	−0.895339	+	0.445385i	$0.853067\pi$
$744$	−39.7680	+	68.8802i	−0.0534516	+	0.0925809i
$745$	−4.68203	−	5.61155i	−0.00628460	−	0.00753228i
$746$	−349.226	−	604.877i	−0.468131	−	0.810827i
$747$	−158.470	+	274.478i	−0.212142	+	0.367441i
$748$	60.2631			0.0805657
$749$	300.098	+	848.099i	0.400665	+	1.13231i
$750$	−894.856	−	1580.34i	−1.19314	−	2.10712i
$751$	−326.637	+	565.752i	−0.434936	+	0.753332i	−0.997290	−	0.0735648i	$-0.976562\pi$
$751$	−326.637	+	565.752i	−0.434936	+	0.753332i	0.562354	+	0.826896i	$0.309896\pi$
$752$	94.3814	+	163.473i	0.125507	+	0.217385i
$753$	−918.165	+	530.103i	−1.21934	+	0.703988i
$754$	−327.900	−	189.313i	−0.434880	−	0.251078i
$755$	20.5212	−	3.55943i	0.0271805	−	0.00471448i
$756$	53.2996	−	287.194i	0.0705022	−	0.379886i
$757$		−	994.601i		−	1.31387i	−0.753946	−	0.656936i	$-0.771852\pi$
$757$		−	994.601i		−	1.31387i	0.753946	−	0.656936i	$-0.228148\pi$
$758$	529.761	+	305.858i	0.698893	+	0.403506i
$759$	−17.0693	+	9.85497i	−0.0224892	+	0.0129842i
$760$	181.038	+	216.979i	0.238208	+	0.285499i
$761$	579.912	+	334.812i	0.762039	+	0.439964i	0.830027	−	0.557722i	$-0.188325\pi$
$761$	579.912	+	334.812i	0.762039	+	0.439964i	−0.0679881	+	0.997686i	$0.521658\pi$
$762$	−3122.25			−4.09744
$763$	51.6261	−	278.176i	0.0676620	−	0.364582i
$764$	−1665.86			−2.18044
$765$	325.519	−	886.649i	0.425515	−	1.15902i
$766$	1865.66	−	1077.14i	2.43558	−	1.40618i
$767$	−533.437	+	307.980i	−0.695485	+	0.401539i
$768$	769.273	−	1332.42i	1.00166	−	1.73492i
$769$		−	685.995i		−	0.892061i	−0.895018	−	0.446031i	$-0.852837\pi$
$769$		−	685.995i		−	0.892061i	0.895018	−	0.446031i	$-0.147163\pi$
$770$	−27.1615	−	48.3491i	−0.0352747	−	0.0627911i
$771$	778.680			1.00996
$772$	1825.90	+	1054.18i	2.36515	+	1.36552i
$773$	−43.7398	−	75.7595i	−0.0565844	−	0.0980071i	0.836346	−	0.548202i	$-0.184688\pi$
$773$	−43.7398	−	75.7595i	−0.0565844	−	0.0980071i	−0.892930	+	0.450195i	$0.851354\pi$
$774$	−1073.72	−	1859.73i	−1.38723	−	2.40275i
$775$	46.5110	+	8.46906i	0.0600141	+	0.0109278i
$776$			1249.19i			1.60978i
$777$	984.453	−	1152.09i	1.26699	−	1.48274i
$778$			656.825i			0.844249i
$779$	−35.4542	+	61.4084i	−0.0455124	+	0.0788298i
$780$	1079.01	+	1293.23i	1.38335	+	1.65798i
$781$	−22.2336	−	38.5097i	−0.0284681	−	0.0493081i
$782$	−280.305	+	485.502i	−0.358446	+	0.620847i
$783$	−62.5478			−0.0798823
$784$	−181.121	−	69.6260i	−0.231022	−	0.0888086i
$785$	−615.754	+	106.803i	−0.784400	+	0.136055i
$786$	−115.164	+	199.470i	−0.146519	+	0.253779i
$787$	122.263	+	211.765i	0.155353	+	0.269079i	0.933187	−	0.359390i	$-0.117015\pi$
$787$	122.263	+	211.765i	0.155353	+	0.269079i	−0.777835	+	0.628469i	$0.783682\pi$
$788$	−492.469	+	284.327i	−0.624960	+	0.360821i
$789$	1577.60	+	910.827i	1.99949	+	1.15441i
$790$	9.71678	+	56.0203i	0.0122997	+	0.0709117i
$791$	548.022	−	641.339i	0.692822	−	0.810795i
$792$			47.5884i			0.0600863i
$793$	−582.810	−	336.486i	−0.734944	−	0.424320i
$794$	909.417	−	525.052i	1.14536	−	0.661275i
$795$	839.805	−	700.696i	1.05636	−	0.881379i
$796$	−609.889	−	352.120i	−0.766192	−	0.442361i
$797$	−1257.39			−1.57765			−0.788824	−	0.614619i	$-0.789310\pi$
$797$	−1257.39			−1.57765			−0.788824	+	0.614619i	$0.789310\pi$
$798$	567.085	−	200.662i	0.710633	−	0.251456i
$799$	867.896			1.08623
$800$	−618.583	−	112.636i	−0.773228	−	0.140795i
$801$	−1256.18	+	725.258i	−1.56827	+	0.905440i
$802$	−674.925	+	389.668i	−0.841552	+	0.485870i
$803$	−11.8077	+	20.4515i	−0.0147044	+	0.0254688i
$804$			2499.82i			3.10923i
$805$	326.462	+	3.83863i	0.405543	+	0.00476848i
$806$	−69.2785			−0.0859535
$807$	1561.94	+	901.788i	1.93549	+	1.11746i
$808$	−351.430	−	608.695i	−0.434938	−	0.753335i
$809$	−260.666	−	451.486i	−0.322207	−	0.558080i	0.658736	−	0.752374i	$-0.271092\pi$
$809$	−260.666	−	451.486i	−0.322207	−	0.558080i	−0.980943	+	0.194295i	$0.937758\pi$
$810$	−1033.90	−	379.580i	−1.27642	−	0.468617i
$811$			1454.61i			1.79360i	0.442435	+	0.896801i	$0.354115\pi$
$811$			1454.61i			1.79360i	−0.442435	+	0.896801i	$0.645885\pi$
$812$	−91.0191	+	490.437i	−0.112093	+	0.603986i
$813$		−	1640.17i		−	2.01743i
$814$	−38.9639	+	67.4874i	−0.0478671	+	0.0829083i
$815$	343.020	−	286.201i	0.420884	−	0.351167i
$816$	158.689	+	274.857i	0.194471	+	0.336834i
$817$	185.450	−	321.209i	0.226989	−	0.393157i
$818$	474.097			0.579581
$819$	759.898	−	268.888i	0.927837	−	0.328313i
$820$	70.6319	+	407.215i	0.0861365	+	0.496604i
$821$	−131.810	+	228.302i	−0.160548	+	0.278078i	−0.935066	−	0.354475i	$-0.884660\pi$
$821$	−131.810	+	228.302i	−0.160548	+	0.278078i	0.774517	+	0.632553i	$0.217993\pi$
$822$	760.693	+	1317.56i	0.925417	+	1.60287i
$823$	−521.969	+	301.359i	−0.634227	+	0.366171i	−0.782387	−	0.622792i	$-0.785998\pi$
$823$	−521.969	+	301.359i	−0.634227	+	0.366171i	0.148160	+	0.988963i	$0.452665\pi$
$824$	490.891	+	283.416i	0.595741	+	0.343951i
$825$	49.7382	−	17.7895i	0.0602888	−	0.0215630i
$826$	974.833	+	832.991i	1.18018	+	1.00846i
$827$			738.163i			0.892579i	0.894889	+	0.446290i	$0.147255\pi$
$827$			738.163i			0.892579i	−0.894889	+	0.446290i	$0.852745\pi$
$828$	−577.882	−	333.640i	−0.697925	−	0.402947i
$829$	−414.886	+	239.534i	−0.500465	+	0.288944i	−0.728906	−	0.684614i	$-0.759971\pi$
$829$	−414.886	+	239.534i	−0.500465	+	0.288944i	0.228440	+	0.973558i	$0.426637\pi$
$830$	−387.116	+	322.993i	−0.466405	+	0.389148i
$831$	−350.926	−	202.607i	−0.422294	−	0.243812i
$832$	1097.20			1.31875
$833$	−693.620	+	561.130i	−0.832677	+	0.673625i
$834$	1559.54			1.86996
$835$	206.336	−	562.019i	0.247109	−	0.673077i
$836$	−16.9537	+	9.78820i	−0.0202795	+	0.0117084i
$837$	−9.91130	+	5.72229i	−0.0118415	+	0.00683667i
$838$	1005.16	−	1740.99i	1.19947	−	2.07755i
$839$			374.411i			0.446259i	0.974789	+	0.223129i	$0.0716273\pi$
$839$			374.411i			0.446259i	−0.974789	+	0.223129i	$0.928373\pi$
$840$	750.982	−	1266.12i	0.894026	−	1.50729i
$841$	−734.188			−0.872994
$842$	334.608	+	193.186i	0.397396	+	0.229437i
$843$	−486.693	−	842.978i	−0.577335	−	0.999973i
$844$	−612.930	−	1061.63i	−0.726220	−	1.25785i
$845$	78.9392	−	215.015i	0.0934192	−	0.254455i
$846$			1632.34i			1.92948i
$847$	−796.965	+	282.004i	−0.940926	+	0.332945i
$848$			196.799i			0.232074i
$849$	745.944	−	1292.01i	0.878615	−	1.52181i
$850$	972.177	−	1145.55i	1.14374	−	1.34771i
$851$	−229.391	−	397.316i	−0.269554	−	0.466881i
$852$	1405.68	−	2434.71i	1.64986	−	2.85765i
$853$	1554.52			1.82242			0.911210	−	0.411941i	$-0.135149\pi$
$853$	1554.52			1.82242			0.911210	+	0.411941i	$0.135149\pi$
$854$	−255.631	+	1377.41i	−0.299334	+	1.61290i
$855$	52.4361	+	302.311i	0.0613288	+	0.353580i
$856$	614.017	−	1063.51i	0.717309	−	1.24242i
$857$	261.957	+	453.722i	0.305667	+	0.529431i	0.977410	−	0.211354i	$-0.0677872\pi$
$857$	261.957	+	453.722i	0.305667	+	0.529431i	−0.671743	+	0.740785i	$0.734454\pi$
$858$	−67.0380	+	38.7044i	−0.0781329	+	0.0451100i
$859$	−472.025	−	272.524i	−0.549505	−	0.317257i	0.199417	−	0.979915i	$-0.436095\pi$
$859$	−472.025	−	272.524i	−0.549505	−	0.317257i	−0.748922	+	0.662658i	$0.769428\pi$
$860$	−369.455	−	2130.02i	−0.429599	−	2.47677i
$861$	363.185	+	67.4026i	0.421817	+	0.0782841i
$862$			1953.61i			2.26636i
$863$	495.559	+	286.111i	0.574228	+	0.331531i	0.758836	−	0.651282i	$-0.225768\pi$
$863$	495.559	+	286.111i	0.574228	+	0.331531i	−0.184608	+	0.982812i	$0.559102\pi$
$864$	131.818	−	76.1049i	0.152567	−	0.0880843i
$865$	353.779	+	424.015i	0.408993	+	0.490190i
$866$	136.605	+	78.8691i	0.157743	+	0.0910729i
$867$	187.152			0.215861
$868$	30.4456	+	86.0415i	0.0350756	+	0.0991261i
$869$	−1.65375			−0.00190305
$870$	−704.782	−	258.749i	−0.810094	−	0.297413i
$871$	−791.736	+	457.109i	−0.908997	+	0.524810i
$872$	−334.465	+	193.104i	−0.383561	+	0.221449i
$873$	−678.169	+	1174.62i	−0.776826	+	1.34550i
$874$		−	182.113i		−	0.208368i
$875$	−858.943	−	166.860i	−0.981649	−	0.190697i
$876$	−1493.04			−1.70439
$877$	−1144.70	−	660.896i	−1.30525	−	0.753587i	−0.323951	−	0.946074i	$-0.605011\pi$
$877$	−1144.70	−	660.896i	−1.30525	−	0.753587i	−0.981300	+	0.192487i	$0.938345\pi$
$878$	829.801	+	1437.26i	0.945103	+	1.63697i
$879$	19.8223	+	34.3333i	0.0225510	+	0.0390594i
$880$	−3.27574	+	8.92247i	−0.00372243	+	0.0101392i
$881$		−	270.973i		−	0.307575i	−0.988104	−	0.153787i	$-0.950853\pi$
$881$		−	270.973i		−	0.307575i	0.988104	−	0.153787i	$-0.0491471\pi$
$882$	−1055.37	−	1304.56i	−1.19657	−	1.47910i
$883$		−	98.7644i		−	0.111851i	−0.998435	−	0.0559255i	$-0.982189\pi$
$883$		−	98.7644i		−	0.111851i	0.998435	−	0.0559255i	$-0.0178109\pi$
$884$	−696.691	+	1206.70i	−0.788112	+	1.36505i
$885$	−937.826	+	782.480i	−1.05969	+	0.884158i
$886$	1260.98	+	2184.07i	1.42322	+	2.46509i
$887$	12.8841	−	22.3159i	0.0145255	−	0.0251589i	−0.858671	−	0.512527i	$-0.828710\pi$
$887$	12.8841	−	22.3159i	0.0145255	−	0.0251589i	0.873197	+	0.487368i	$0.162043\pi$
$888$	−2068.60			−2.32950
$889$	−977.238	+	1143.64i	−1.09926	+	1.28644i
$890$	−2273.43	+	394.329i	−2.55442	+	0.443067i
$891$	16.0175	−	27.7431i	0.0179770	−	0.0311371i
$892$	−1186.17	−	2054.51i	−1.32979	−	2.30326i
$893$	−244.163	+	140.968i	−0.273419	+	0.157858i
$894$	18.3911	+	10.6181i	0.0205717	+	0.0118771i
$895$	−334.078	+	57.9461i	−0.373271	+	0.0647443i
$896$	−527.006	−	1489.36i	−0.588176	−	1.66223i
$897$		−	455.726i		−	0.508056i
$898$	807.697	+	466.324i	0.899439	+	0.519292i
$899$	16.9254	−	9.77189i	0.0188269	−	0.0108697i
$900$	1363.52	+	1157.16i	1.51502	+	1.28573i
$901$	783.619	+	452.422i	0.869721	+	0.502134i
$902$	−18.9952			−0.0210590
$903$	−1899.71	−	352.563i	−2.10378	−	0.390436i
$904$	−1151.54			−1.27383
$905$	1149.56	+	422.043i	1.27024	+	0.466346i
$906$	−52.4122	+	30.2602i	−0.0578502	+	0.0333998i
$907$	1008.71	−	582.379i	1.11214	−	0.642094i	0.172757	−	0.984965i	$-0.444733\pi$
$907$	1008.71	−	582.379i	1.11214	−	0.642094i	0.939383	+	0.342870i	$0.111399\pi$
$908$	−309.537	+	536.134i	−0.340900	+	0.590456i
$909$		−	763.148i		−	0.839547i
$910$	1282.15	+	15.0758i	1.40895	+	0.0165668i
$911$	−247.959			−0.272183			−0.136092	−	0.990696i	$-0.543454\pi$
$911$	−247.959			−0.272183			−0.136092	+	0.990696i	$0.543454\pi$
$912$	−89.2869	−	51.5498i	−0.0979023	−	0.0565239i
$913$	−7.33216	−	12.6997i	−0.00803084	−	0.0139098i
$914$	−365.652	−	633.328i	−0.400057	−	0.692919i
$915$	−1252.68	−	459.902i	−1.36905	−	0.502625i
$916$		−	2077.98i		−	2.26854i
$917$	37.0181	+	104.616i	0.0403687	+	0.114085i
$918$			363.720i			0.396209i
$919$	748.132	−	1295.80i	0.814071	−	1.41001i	−0.0959215	−	0.995389i	$-0.530580\pi$
$919$	748.132	−	1295.80i	0.814071	−	1.41001i	0.909993	−	0.414624i	$-0.136087\pi$
$920$	−285.516	−	342.199i	−0.310343	−	0.371955i
$921$	−358.262	−	620.529i	−0.388993	−	0.673755i
$922$	−423.802	+	734.047i	−0.459655	+	0.796146i
$923$	1028.15			1.11393
$924$	77.5305	+	66.2495i	0.0839074	+	0.0716986i
$925$	414.080	+	1157.74i	0.447654	+	1.25161i
$926$	112.575	−	194.986i	0.121571	−	0.210568i
$927$	307.726	+	532.997i	0.331959	+	0.574970i
$928$	−225.103	+	129.963i	−0.242568	+	0.140047i
$929$	185.735	+	107.234i	0.199931	+	0.115430i	0.596623	−	0.802522i	$-0.296509\pi$
$929$	185.735	+	107.234i	0.199931	+	0.115430i	−0.396693	+	0.917952i	$0.629842\pi$
$930$	−135.352	+	23.4769i	−0.145539	+	0.0252440i
$931$	103.993	−	270.522i	0.111700	−	0.290571i
$932$		−	1737.95i		−	1.86476i
$933$	1262.21	+	728.739i	1.35285	+	0.781070i
$934$	−1603.22	+	925.621i	−1.71651	+	0.991029i
$935$	27.9971	+	33.5553i	0.0299434	+	0.0358881i
$936$	−952.906	−	550.161i	−1.01806	−	0.587778i
$937$	945.464			1.00903			0.504517	−	0.863402i	$-0.331671\pi$
$937$	945.464			1.00903			0.504517	+	0.863402i	$0.331671\pi$
$938$	1446.86	+	1236.34i	1.54250	+	1.31806i
$939$	2250.01			2.39618
$940$	−566.343	+	1542.61i	−0.602492	+	1.64107i
$941$	335.526	−	193.716i	0.356564	−	0.205862i	−0.311009	−	0.950407i	$-0.600667\pi$
$941$	335.526	−	193.716i	0.356564	−	0.205862i	0.667572	+	0.744545i	$0.267333\pi$
$942$	1572.66	−	907.978i	1.66950	−	0.963883i
$943$	55.9149	−	96.8475i	0.0592947	−	0.102701i
$944$		−	219.769i		−	0.232806i
$945$	184.675	−	103.747i	0.195424	−	0.109785i
$946$	99.3584			0.105030
$947$	−619.745	−	357.810i	−0.654430	−	0.377835i	0.135722	−	0.990747i	$-0.456665\pi$
$947$	−619.745	−	357.810i	−0.654430	−	0.377835i	−0.790151	+	0.612912i	$0.789998\pi$
$948$	−52.2779	−	90.5480i	−0.0551455	−	0.0955148i
$949$	−273.012	−	472.871i	−0.287684	−	0.498284i
$950$	−87.4346	+	480.179i	−0.0920364	+	0.505452i
$951$		−	2625.33i		−	2.76060i
$952$	1197.41	+	222.225i	1.25779	+	0.233430i
$953$		−	828.542i		−	0.869404i	−0.900574	−	0.434702i	$-0.856854\pi$
$953$		−	828.542i		−	0.869404i	0.900574	−	0.434702i	$-0.143146\pi$
$954$	−850.918	+	1473.83i	−0.891947	+	1.54490i
$955$	−773.924	−	927.571i	−0.810392	−	0.971279i
$956$	918.652	+	1591.15i	0.960933	+	1.66439i
$957$	10.9187	−	18.9117i	0.0114093	−	0.0197615i
$958$	−1578.12			−1.64730
$959$	720.697	+	133.753i	0.751509	+	0.139471i
$960$	2143.63	−	371.815i	2.23295	−	0.387307i
$961$	−478.712	+	829.154i	−0.498139	+	0.862803i
$962$	−900.908	−	1560.42i	−0.936495	−	1.62206i
$963$	1154.73	−	666.684i	1.19910	−	0.692299i
$964$	193.462	+	111.695i	0.200687	+	0.115867i
$965$	261.293	+	1506.44i	0.270770	+	1.56107i
$966$	−894.352	+	316.465i	−0.925830	+	0.327603i
$967$		−	50.9850i		−	0.0527249i	−0.999652	−	0.0263624i	$-0.991608\pi$
$967$		−	50.9850i		−	0.0527249i	0.999652	−	0.0263624i	$-0.00839240\pi$
$968$	999.387	+	576.996i	1.03242	+	0.596071i
$969$	−410.525	+	237.016i	−0.423658	+	0.244599i
$970$	−1656.66	+	1382.24i	−1.70789	+	1.42499i
$971$	798.161	+	460.818i	0.821999	+	0.474581i	0.851105	−	0.524995i	$-0.175933\pi$
$971$	798.161	+	460.818i	0.821999	+	0.474581i	−0.0291063	+	0.999576i	$0.509266\pi$
$972$	2400.92			2.47008
$973$	488.124	−	571.242i	0.501669	−	0.587093i
$974$	1482.45			1.52202
$975$	−218.799	+	1201.62i	−0.224409	+	1.23243i
$976$	207.941	−	120.055i	0.213055	−	0.123007i
$977$	−140.663	+	81.2120i	−0.143975	+	0.0831238i	−0.570257	−	0.821466i	$-0.693156\pi$
$977$	−140.663	+	81.2120i	−0.143975	+	0.0831238i	0.426282	+	0.904590i	$0.359823\pi$
$978$	−649.058	+	1124.20i	−0.663659	+	1.14949i
$979$		−	67.1131i		−	0.0685527i
$980$	−544.738	−	1599.01i	−0.555855	−	1.63164i
$981$	−419.334			−0.427456
$982$	−1547.76	−	893.600i	−1.57613	−	0.909980i
$983$	−48.5988	−	84.1755i	−0.0494392	−	0.0856313i	0.840247	−	0.542204i	$-0.182410\pi$
$983$	−48.5988	−	84.1755i	−0.0494392	−	0.0856313i	−0.889686	+	0.456573i	$0.849077\pi$
$984$	−252.115	−	436.675i	−0.256214	−	0.443776i
$985$	−387.109	−	142.121i	−0.393004	−	0.144285i
$986$		−	621.120i		−	0.629939i
$987$	1116.58	+	954.111i	1.13128	+	0.966678i
$988$		−	452.638i		−	0.458136i
$989$	−292.475	+	506.581i	−0.295728	+	0.512215i
$990$	−63.1110	+	52.6570i	−0.0637485	+	0.0531889i
$991$	−415.186	−	719.123i	−0.418957	−	0.725654i	0.576878	−	0.816830i	$-0.304271\pi$
$991$	−415.186	−	719.123i	−0.418957	−	0.725654i	−0.995835	+	0.0911762i	$0.970937\pi$
$992$	−23.7798	+	41.1879i	−0.0239716	+	0.0415200i
$993$	−1847.80			−1.86083
$994$	−713.968	−	2017.73i	−0.718278	−	2.02991i
$995$	−87.2775	−	503.182i	−0.0877161	−	0.505711i
$996$	463.564	−	802.917i	0.465426	−	0.806141i
$997$	892.933	+	1546.60i	0.895620	+	1.55126i	0.833036	+	0.553219i	$0.186601\pi$
$997$	892.933	+	1546.60i	0.895620	+	1.55126i	0.0625836	+	0.998040i	$0.480066\pi$
$998$	−833.853	+	481.425i	−0.835524	+	0.482390i
$999$	−257.776	−	148.827i	−0.258034	−	0.148976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.i.a.19.6	yes	12
3.2	odd	2		315.3.bi.c.19.1		12
4.3	odd	2		560.3.br.a.369.6		12
5.2	odd	4		175.3.i.c.26.1		12
5.3	odd	4		175.3.i.c.26.6		12
5.4	even	2	inner	35.3.i.a.19.1	✓	12
7.2	even	3		245.3.c.a.244.2		12
7.3	odd	6	inner	35.3.i.a.24.1	yes	12
7.4	even	3		245.3.i.d.129.1		12
7.5	odd	6		245.3.c.a.244.1		12
7.6	odd	2		245.3.i.d.19.6		12
15.14	odd	2		315.3.bi.c.19.6		12
20.19	odd	2		560.3.br.a.369.1		12
21.17	even	6		315.3.bi.c.199.6		12
28.3	even	6		560.3.br.a.129.1		12
35.3	even	12		175.3.i.c.101.6		12
35.4	even	6		245.3.i.d.129.6		12
35.9	even	6		245.3.c.a.244.11		12
35.17	even	12		175.3.i.c.101.1		12
35.19	odd	6		245.3.c.a.244.12		12
35.24	odd	6	inner	35.3.i.a.24.6	yes	12
35.34	odd	2		245.3.i.d.19.1		12
105.59	even	6		315.3.bi.c.199.1		12
140.59	even	6		560.3.br.a.129.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.i.a.19.1	✓	12	5.4	even	2	inner
35.3.i.a.19.6	yes	12	1.1	even	1	trivial
35.3.i.a.24.1	yes	12	7.3	odd	6	inner
35.3.i.a.24.6	yes	12	35.24	odd	6	inner
175.3.i.c.26.1		12	5.2	odd	4
175.3.i.c.26.6		12	5.3	odd	4
175.3.i.c.101.1		12	35.17	even	12
175.3.i.c.101.6		12	35.3	even	12
245.3.c.a.244.1		12	7.5	odd	6
245.3.c.a.244.2		12	7.2	even	3
245.3.c.a.244.11		12	35.9	even	6
245.3.c.a.244.12		12	35.19	odd	6
245.3.i.d.19.1		12	35.34	odd	2
245.3.i.d.19.6		12	7.6	odd	2
245.3.i.d.129.1		12	7.4	even	3
245.3.i.d.129.6		12	35.4	even	6
315.3.bi.c.19.1		12	3.2	odd	2
315.3.bi.c.19.6		12	15.14	odd	2
315.3.bi.c.199.1		12	105.59	even	6
315.3.bi.c.199.6		12	21.17	even	6
560.3.br.a.129.1		12	28.3	even	6
560.3.br.a.129.6		12	140.59	even	6
560.3.br.a.369.1		12	20.19	odd	2
560.3.br.a.369.6		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.85853 + 1.65037i) q^{2} +(-2.20085 - 3.81198i) q^{3} +(3.44745 + 5.97116i) q^{4} +(-1.72321 + 4.69367i) q^{5} -14.5289i q^{6} +(-5.32175 - 4.54742i) q^{7} +9.55533i q^{8} +(-5.18747 + 8.98496i) q^{9} +O(q^{10})\)	\(q+(2.85853 + 1.65037i) q^{2} +(-2.20085 - 3.81198i) q^{3} +(3.44745 + 5.97116i) q^{4} +(-1.72321 + 4.69367i) q^{5} -14.5289i q^{6} +(-5.32175 - 4.54742i) q^{7} +9.55533i q^{8} +(-5.18747 + 8.98496i) q^{9} +(-12.6721 + 10.5731i) q^{10} +(-0.240016 - 0.415720i) q^{11} +(15.1746 - 26.2832i) q^{12} +11.0991 q^{13} +(-7.70744 - 21.7818i) q^{14} +(21.6847 - 3.76124i) q^{15} +(-1.98003 + 3.42952i) q^{16} +(9.10382 + 15.7683i) q^{17} +(-29.6570 + 17.1225i) q^{18} +(-5.12231 - 2.95736i) q^{19} +(-33.9673 + 5.89167i) q^{20} +(-5.62231 + 30.2946i) q^{21} -1.58446i q^{22} +(8.07841 + 4.66407i) q^{23} +(36.4247 - 21.0298i) q^{24} +(-19.0611 - 16.1763i) q^{25} +(31.7271 + 18.3177i) q^{26} +6.05204 q^{27} +(8.80689 - 47.4540i) q^{28} -10.3350 q^{29} +(68.1937 + 25.0362i) q^{30} +(-1.63768 + 0.945514i) q^{31} +(21.7807 - 12.5751i) q^{32} +(-1.05648 + 1.82987i) q^{33} +60.0987i q^{34} +(30.5145 - 17.1424i) q^{35} -71.5341 q^{36} +(-42.5933 - 24.5912i) q^{37} +(-9.76150 - 16.9074i) q^{38} +(-24.4275 - 42.3096i) q^{39} +(-44.8496 - 16.4658i) q^{40} -11.9884i q^{41} +(-66.0688 + 77.3190i) q^{42} +62.7080i q^{43} +(1.65489 - 2.86635i) q^{44} +(-33.2334 - 39.8312i) q^{45} +(15.3949 + 26.6648i) q^{46} +(23.8333 - 41.2805i) q^{47} +17.4310 q^{48} +(7.64201 + 48.4004i) q^{49} +(-27.7898 - 77.6984i) q^{50} +(40.0723 - 69.4072i) q^{51} +(38.2637 + 66.2746i) q^{52} +(43.0379 - 24.8479i) q^{53} +(17.2999 + 9.98811i) q^{54} +(2.36485 - 0.410186i) q^{55} +(43.4520 - 50.8510i) q^{56} +26.0348i q^{57} +(-29.5429 - 17.0566i) q^{58} +(-48.0612 + 27.7482i) q^{59} +(97.2159 + 116.516i) q^{60} +(-52.5096 - 30.3164i) q^{61} -6.24180 q^{62} +(68.4647 - 24.2261i) q^{63} +98.8544 q^{64} +(-19.1261 + 52.0956i) q^{65} +(-6.03994 + 3.48716i) q^{66} +(-71.3332 + 41.1843i) q^{67} +(-62.7699 + 108.721i) q^{68} -41.0597i q^{69} +(115.518 + 1.35829i) q^{70} +92.6337 q^{71} +(-85.8542 - 49.5679i) q^{72} +(-24.5977 - 42.6044i) q^{73} +(-81.1693 - 140.589i) q^{74} +(-19.7132 + 108.262i) q^{75} -40.7815i q^{76} +(-0.613147 + 3.30381i) q^{77} -161.258i q^{78} +(1.72254 - 2.98353i) q^{79} +(-12.6850 - 15.2034i) q^{80} +(33.3676 + 57.7943i) q^{81} +(19.7854 - 34.2693i) q^{82} +30.5486 q^{83} +(-200.276 + 70.8674i) q^{84} +(-89.6989 + 15.5584i) q^{85} +(-103.491 + 179.252i) q^{86} +(22.7458 + 39.3968i) q^{87} +(3.97234 - 2.29343i) q^{88} +(121.079 + 69.9048i) q^{89} +(-29.2622 - 168.706i) q^{90} +(-59.0667 - 50.4723i) q^{91} +64.3166i q^{92} +(7.20857 + 4.16187i) q^{93} +(136.256 - 78.6676i) q^{94} +(22.7077 - 18.9463i) q^{95} +(-95.8719 - 55.3517i) q^{96} +130.732 q^{97} +(-58.0338 + 150.966i) q^{98} +4.98030 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 18 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 - 18 * q^9	\( 12 q + 6 q^{4} - 18 q^{9} - 54 q^{10} + 6 q^{11} - 66 q^{14} + 48 q^{15} - 6 q^{16} + 18 q^{19} + 12 q^{21} + 216 q^{24} + 18 q^{25} + 18 q^{26} + 48 q^{30} - 108 q^{31} + 222 q^{35} - 204 q^{36} - 240 q^{39} - 162 q^{40} - 42 q^{44} - 216 q^{45} + 114 q^{46} - 324 q^{49} - 192 q^{50} + 180 q^{51} + 252 q^{54} + 336 q^{56} + 396 q^{59} + 384 q^{60} - 108 q^{61} + 372 q^{64} - 54 q^{65} - 108 q^{66} + 300 q^{70} + 192 q^{71} - 594 q^{74} - 216 q^{75} - 192 q^{79} - 504 q^{80} + 294 q^{81} - 1200 q^{84} - 192 q^{85} - 384 q^{86} + 684 q^{89} - 72 q^{91} + 990 q^{94} + 288 q^{95} - 540 q^{96} + 396 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 - 18 * q^9 - 54 * q^10 + 6 * q^11 - 66 * q^14 + 48 * q^15 - 6 * q^16 + 18 * q^19 + 12 * q^21 + 216 * q^24 + 18 * q^25 + 18 * q^26 + 48 * q^30 - 108 * q^31 + 222 * q^35 - 204 * q^36 - 240 * q^39 - 162 * q^40 - 42 * q^44 - 216 * q^45 + 114 * q^46 - 324 * q^49 - 192 * q^50 + 180 * q^51 + 252 * q^54 + 336 * q^56 + 396 * q^59 + 384 * q^60 - 108 * q^61 + 372 * q^64 - 54 * q^65 - 108 * q^66 + 300 * q^70 + 192 * q^71 - 594 * q^74 - 216 * q^75 - 192 * q^79 - 504 * q^80 + 294 * q^81 - 1200 * q^84 - 192 * q^85 - 384 * q^86 + 684 * q^89 - 72 * q^91 + 990 * q^94 + 288 * q^95 - 540 * q^96 + 396 * q^99

Introduction

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