LMFDB - Embedded newform 105.3.e.a.34.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(34,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.34");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.e (of order $2$, degree $1$, 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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 72 x^{14} - 292 x^{13} + 1148 x^{12} - 2304 x^{11} + 4996 x^{10} - 4490 x^{9} + \cdots + 1849 $ x^16 - 8x^15 + 72x^14 - 292x^13 + 1148x^12 - 2304x^11 + 4996x^10 - 4490x^9 + 9786x^8 - 5744x^7 + 8608x^6 + 4740x^5 + 22841x^4 + 22790x^3 + 18930x^2 + 8170*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.1
Root			$1.36603 - 5.19914i$ of defining polynomial
Character	$\chi$	$=$	105.34
Dual form			105.3.e.a.34.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.80604i q^{2} -1.73205 q^{3} -10.4859 q^{4} +(-3.71318 + 3.34847i) q^{5} +6.59225i q^{6} +(5.08005 - 4.81592i) q^{7} +24.6856i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.80604i q^{2} -1.73205 q^{3} -10.4859 q^{4} +(-3.71318 + 3.34847i) q^{5} +6.59225i q^{6} +(5.08005 - 4.81592i) q^{7} +24.6856i q^{8} +3.00000 q^{9} +(12.7444 + 14.1325i) q^{10} -9.90760 q^{11} +18.1621 q^{12} -9.60692 q^{13} +(-18.3296 - 19.3349i) q^{14} +(6.43142 - 5.79973i) q^{15} +52.0108 q^{16} -28.8479 q^{17} -11.4181i q^{18} -2.29577i q^{19} +(38.9361 - 35.1118i) q^{20} +(-8.79890 + 8.34142i) q^{21} +37.7087i q^{22} -1.25323i q^{23} -42.7568i q^{24} +(2.57543 - 24.8670i) q^{25} +36.5643i q^{26} -5.19615 q^{27} +(-53.2690 + 50.4994i) q^{28} +2.52779 q^{29} +(-22.0740 - 24.4782i) q^{30} +8.89270i q^{31} -99.2125i q^{32} +17.1605 q^{33} +109.796i q^{34} +(-2.73715 + 34.8928i) q^{35} -31.4578 q^{36} -23.8009i q^{37} -8.73778 q^{38} +16.6397 q^{39} +(-82.6593 - 91.6623i) q^{40} -59.7286i q^{41} +(31.7478 + 33.4889i) q^{42} -42.1109i q^{43} +103.890 q^{44} +(-11.1395 + 10.0454i) q^{45} -4.76982 q^{46} -41.8418 q^{47} -90.0853 q^{48} +(2.61379 - 48.9302i) q^{49} +(-94.6447 - 9.80219i) q^{50} +49.9660 q^{51} +100.737 q^{52} +47.0300i q^{53} +19.7767i q^{54} +(36.7887 - 33.1753i) q^{55} +(118.884 + 125.404i) q^{56} +3.97639i q^{57} -9.62085i q^{58} -19.2974i q^{59} +(-67.4393 + 60.8155i) q^{60} +12.9561i q^{61} +33.8460 q^{62} +(15.2401 - 14.4478i) q^{63} -169.563 q^{64} +(35.6722 - 32.1685i) q^{65} -65.3133i q^{66} +120.991i q^{67} +302.497 q^{68} +2.17065i q^{69} +(132.803 + 10.4177i) q^{70} +36.1349 q^{71} +74.0569i q^{72} +61.8581 q^{73} -90.5871 q^{74} +(-4.46078 + 43.0709i) q^{75} +24.0732i q^{76} +(-50.3311 + 47.7142i) q^{77} -63.3312i q^{78} -45.8496 q^{79} +(-193.126 + 174.157i) q^{80} +9.00000 q^{81} -227.329 q^{82} -22.9558 q^{83} +(92.2646 - 87.4675i) q^{84} +(107.118 - 96.5965i) q^{85} -160.276 q^{86} -4.37825 q^{87} -244.575i q^{88} -88.8835i q^{89} +(38.2333 + 42.3975i) q^{90} +(-48.8036 + 46.2662i) q^{91} +13.1412i q^{92} -15.4026i q^{93} +159.251i q^{94} +(7.68732 + 8.52460i) q^{95} +171.841i q^{96} -18.4146 q^{97} +(-186.230 - 9.94818i) q^{98} -29.7228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) $ 16 * q - 32 * q^4 + 48 * q^9	$ 16 q - 32 q^{4} + 48 q^{9} - 56 q^{11} - 84 q^{14} + 24 q^{15} + 112 q^{16} - 12 q^{21} + 16 q^{25} - 32 q^{29} - 72 q^{30} - 4 q^{35} - 96 q^{36} + 72 q^{39} + 568 q^{44} - 96 q^{46} - 152 q^{49} - 96 q^{50} + 24 q^{51} + 444 q^{56} - 288 q^{60} - 992 q^{64} - 296 q^{65} + 504 q^{70} - 56 q^{71} - 48 q^{74} + 464 q^{79} + 144 q^{81} + 228 q^{84} + 608 q^{85} - 456 q^{86} - 88 q^{91} - 24 q^{95} - 168 q^{99}+O(q^{100}) $ 16 * q - 32 * q^4 + 48 * q^9 - 56 * q^11 - 84 * q^14 + 24 * q^15 + 112 * q^16 - 12 * q^21 + 16 * q^25 - 32 * q^29 - 72 * q^30 - 4 * q^35 - 96 * q^36 + 72 * q^39 + 568 * q^44 - 96 * q^46 - 152 * q^49 - 96 * q^50 + 24 * q^51 + 444 * q^56 - 288 * q^60 - 992 * q^64 - 296 * q^65 + 504 * q^70 - 56 * q^71 - 48 * q^74 + 464 * q^79 + 144 * q^81 + 228 * q^84 + 608 * q^85 - 456 * q^86 - 88 * q^91 - 24 * q^95 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	3.80604i		−	1.90302i	−0.307620	−	0.951509i	$-0.599533\pi$
$2$		−	3.80604i		−	1.90302i	0.307620	−	0.951509i	$-0.400467\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−10.4859			−2.62148
$5$	−3.71318	+	3.34847i	−0.742636	+	0.669695i
$5$	−3.71318	+	3.34847i	−0.742636	+	0.669695i
$6$			6.59225i			1.09871i
$7$	5.08005	−	4.81592i	0.725721	−	0.687989i
$7$	5.08005	−	4.81592i	0.725721	−	0.687989i
$8$			24.6856i			3.08571i
$9$	3.00000			0.333333
$10$	12.7444	+	14.1325i	1.27444	+	1.41325i
$11$	−9.90760			−0.900690			−0.450345	−	0.892854i	$-0.648699\pi$
$11$	−9.90760			−0.900690			−0.450345	+	0.892854i	$0.648699\pi$
$12$	18.1621			1.51351
$13$	−9.60692			−0.738994			−0.369497	−	0.929232i	$-0.620470\pi$
$13$	−9.60692			−0.738994			−0.369497	+	0.929232i	$0.620470\pi$
$14$	−18.3296	−	19.3349i	−1.30926	−	1.38106i
$15$	6.43142	−	5.79973i	0.428761	−	0.386649i
$16$	52.0108			3.25068
$17$	−28.8479			−1.69694			−0.848468	−	0.529247i	$-0.822475\pi$
$17$	−28.8479			−1.69694			−0.848468	+	0.529247i	$0.822475\pi$
$18$		−	11.4181i		−	0.634340i
$19$		−	2.29577i		−	0.120830i	−0.998173	−	0.0604149i	$-0.980758\pi$
$19$		−	2.29577i		−	0.120830i	0.998173	−	0.0604149i	$-0.0192424\pi$
$20$	38.9361	−	35.1118i	1.94681	−	1.75559i
$21$	−8.79890	+	8.34142i	−0.418995	+	0.397211i
$22$			37.7087i			1.71403i
$23$		−	1.25323i		−	0.0544881i	−0.999629	−	0.0272440i	$-0.991327\pi$
$23$		−	1.25323i		−	0.0544881i	0.999629	−	0.0272440i	$-0.00867312\pi$
$24$		−	42.7568i		−	1.78153i
$25$	2.57543	−	24.8670i	0.103017	−	0.994680i
$26$			36.5643i			1.40632i
$27$	−5.19615			−0.192450
$28$	−53.2690	+	50.4994i	−1.90246	+	1.80355i
$29$	2.52779			0.0871650			0.0435825	−	0.999050i	$-0.486123\pi$
$29$	2.52779			0.0871650			0.0435825	+	0.999050i	$0.486123\pi$
$30$	−22.0740	−	24.4782i	−0.735799	−	0.815941i
$31$			8.89270i			0.286861i	0.989660	+	0.143431i	$0.0458134\pi$
$31$			8.89270i			0.286861i	−0.989660	+	0.143431i	$0.954187\pi$
$32$		−	99.2125i		−	3.10039i
$33$	17.1605			0.520014
$34$			109.796i			3.22930i
$35$	−2.73715	+	34.8928i	−0.0782042	+	0.996937i
$36$	−31.4578			−0.873826
$37$		−	23.8009i		−	0.643268i	−0.946864	−	0.321634i	$-0.895768\pi$
$37$		−	23.8009i		−	0.643268i	0.946864	−	0.321634i	$-0.104232\pi$
$38$	−8.73778			−0.229941
$39$	16.6397			0.426658
$40$	−82.6593	−	91.6623i	−2.06648	−	2.29156i
$41$		−	59.7286i		−	1.45680i	−0.685154	−	0.728398i	$-0.740265\pi$
$41$		−	59.7286i		−	1.45680i	0.685154	−	0.728398i	$-0.259735\pi$
$42$	31.7478	+	33.4889i	0.755899	+	0.797356i
$43$		−	42.1109i		−	0.979323i	−0.871912	−	0.489662i	$-0.837120\pi$
$43$		−	42.1109i		−	0.979323i	0.871912	−	0.489662i	$-0.162880\pi$
$44$	103.890			2.36114
$45$	−11.1395	+	10.0454i	−0.247545	+	0.223232i
$46$	−4.76982			−0.103692
$47$	−41.8418			−0.890250			−0.445125	−	0.895468i	$-0.646841\pi$
$47$	−41.8418			−0.890250			−0.445125	+	0.895468i	$0.646841\pi$
$48$	−90.0853			−1.87678
$49$	2.61379	−	48.9302i	0.0533426	−	0.998576i
$50$	−94.6447	−	9.80219i	−1.89289	−	0.196044i
$51$	49.9660			0.979726
$52$	100.737			1.93726
$53$			47.0300i			0.887358i	0.896186	+	0.443679i	$0.146327\pi$
$53$			47.0300i			0.887358i	−0.896186	+	0.443679i	$0.853673\pi$
$54$			19.7767i			0.366236i
$55$	36.7887	−	33.1753i	0.668885	−	0.603188i
$56$	118.884	+	125.404i	2.12293	+	2.23936i
$57$			3.97639i			0.0697612i
$58$		−	9.62085i		−	0.165877i
$59$		−	19.2974i		−	0.327075i	−0.986537	−	0.163537i	$-0.947710\pi$
$59$		−	19.2974i		−	0.327075i	0.986537	−	0.163537i	$-0.0522904\pi$
$60$	−67.4393	+	60.8155i	−1.12399	+	1.01359i
$61$			12.9561i			0.212394i	0.994345	+	0.106197i	$0.0338675\pi$
$61$			12.9561i			0.212394i	−0.994345	+	0.106197i	$0.966133\pi$
$62$	33.8460			0.545903
$63$	15.2401	−	14.4478i	0.241907	−	0.229330i
$64$	−169.563			−2.64942
$65$	35.6722	−	32.1685i	0.548804	−	0.494900i
$66$		−	65.3133i		−	0.989596i
$67$			120.991i			1.80583i	0.429817	+	0.902916i	$0.358578\pi$
$67$			120.991i			1.80583i	−0.429817	+	0.902916i	$0.641422\pi$
$68$	302.497			4.44848
$69$			2.17065i			0.0314587i
$70$	132.803	+	10.4177i	1.89719	+	0.148824i
$71$	36.1349			0.508942			0.254471	−	0.967080i	$-0.418099\pi$
$71$	36.1349			0.508942			0.254471	+	0.967080i	$0.418099\pi$
$72$			74.0569i			1.02857i
$73$	61.8581			0.847372			0.423686	−	0.905809i	$-0.360736\pi$
$73$	61.8581			0.847372			0.423686	+	0.905809i	$0.360736\pi$
$74$	−90.5871			−1.22415
$75$	−4.46078	+	43.0709i	−0.0594771	+	0.574279i
$76$			24.0732i			0.316753i
$77$	−50.3311	+	47.7142i	−0.653650	+	0.619665i
$78$		−	63.3312i		−	0.811939i
$79$	−45.8496			−0.580375			−0.290187	−	0.956970i	$-0.593718\pi$
$79$	−45.8496			−0.580375			−0.290187	+	0.956970i	$0.593718\pi$
$80$	−193.126	+	174.157i	−2.41407	+	2.17696i
$81$	9.00000			0.111111
$82$	−227.329			−2.77231
$83$	−22.9558			−0.276576			−0.138288	−	0.990392i	$-0.544160\pi$
$83$	−22.9558			−0.276576			−0.138288	+	0.990392i	$0.544160\pi$
$84$	92.2646	−	87.4675i	1.09839	−	1.04128i
$85$	107.118	−	96.5965i	1.26021	−	1.13643i
$86$	−160.276			−1.86367
$87$	−4.37825			−0.0503248
$88$		−	244.575i		−	2.77927i
$89$		−	88.8835i		−	0.998691i	−0.866403	−	0.499345i	$-0.833574\pi$
$89$		−	88.8835i		−	0.998691i	0.866403	−	0.499345i	$-0.166426\pi$
$90$	38.2333	+	42.3975i	0.424814	+	0.471084i
$91$	−48.8036	+	46.2662i	−0.536304	+	0.508420i
$92$			13.1412i			0.142839i
$93$		−	15.4026i		−	0.165620i
$94$			159.251i			1.69416i
$95$	7.68732	+	8.52460i	0.0809192	+	0.0897326i
$96$			171.841i			1.79001i
$97$	−18.4146			−0.189841			−0.0949205	−	0.995485i	$-0.530260\pi$
$97$	−18.4146			−0.189841			−0.0949205	+	0.995485i	$0.530260\pi$
$98$	−186.230	−	9.94818i	−1.90031	−	0.101512i
$99$	−29.7228			−0.300230
$100$	−27.0058	+	260.753i	−0.270058	+	2.60753i
$101$		−	75.3959i		−	0.746494i	−0.927732	−	0.373247i	$-0.878244\pi$
$101$		−	75.3959i		−	0.746494i	0.927732	−	0.373247i	$-0.121756\pi$
$102$		−	190.173i		−	1.86444i
$103$	110.889			1.07659			0.538296	−	0.842756i	$-0.319068\pi$
$103$	110.889			1.07659			0.538296	+	0.842756i	$0.319068\pi$
$104$		−	237.153i		−	2.28032i
$105$	4.74088	−	60.4361i	0.0451512	−	0.575582i
$106$	178.998			1.68866
$107$			203.273i			1.89974i	0.312638	+	0.949872i	$0.398787\pi$
$107$			203.273i			1.89974i	−0.312638	+	0.949872i	$0.601213\pi$
$108$	54.4864			0.504504
$109$	−60.1732			−0.552048			−0.276024	−	0.961151i	$-0.589017\pi$
$109$	−60.1732			−0.552048			−0.276024	+	0.961151i	$0.589017\pi$
$110$	−126.267	−	140.019i	−1.14788	−	1.27290i
$111$			41.2244i			0.371391i
$112$	264.217	−	250.480i	2.35908	−	2.23643i
$113$		−	110.972i		−	0.982051i	−0.871145	−	0.491026i	$-0.836622\pi$
$113$		−	110.972i		−	0.982051i	0.871145	−	0.491026i	$-0.163378\pi$
$114$	15.1343			0.132757
$115$	4.19640	+	4.65346i	0.0364904	+	0.0404648i
$116$	−26.5062			−0.228501
$117$	−28.8208			−0.246331
$118$	−73.4466			−0.622429
$119$	−146.549	+	138.929i	−1.23150	+	1.16747i
$120$	143.170	+	158.764i	1.19308	+	1.32303i
$121$	−22.8396			−0.188757
$122$	49.3112			0.404190
$123$			103.453i			0.841081i
$124$		−	93.2482i		−	0.752001i
$125$	73.7034	+	100.959i	0.589627	+	0.807675i
$126$	−54.9887	−	58.0046i	−0.436419	−	0.460354i
$127$		−	72.8043i		−	0.573262i	−0.958041	−	0.286631i	$-0.907465\pi$
$127$		−	72.8043i		−	0.573262i	0.958041	−	0.286631i	$-0.0925354\pi$
$128$			248.514i			1.94151i
$129$			72.9382i			0.565413i
$130$	−122.435	−	135.770i	−0.941805	−	1.04438i
$131$			197.503i			1.50765i	0.657074	+	0.753826i	$0.271794\pi$
$131$			197.503i			1.50765i	−0.657074	+	0.753826i	$0.728206\pi$
$132$	−179.943			−1.36321
$133$	−11.0562	−	11.6626i	−0.0831296	−	0.0876888i
$134$	460.495			3.43653
$135$	19.2943	−	17.3992i	0.142920	−	0.128883i
$136$		−	712.129i		−	5.23624i
$137$		−	47.9860i		−	0.350263i	−0.984545	−	0.175131i	$-0.943965\pi$
$137$		−	47.9860i		−	0.350263i	0.984545	−	0.175131i	$-0.0560350\pi$
$138$	8.26158			0.0598665
$139$		−	2.86379i		−	0.0206028i	−0.999947	−	0.0103014i	$-0.996721\pi$
$139$		−	2.86379i		−	0.0206028i	0.999947	−	0.0103014i	$-0.00327909\pi$
$140$	28.7015	−	365.883i	0.205011	−	2.61345i
$141$	72.4721			0.513986
$142$		−	137.531i		−	0.968526i
$143$	95.1815			0.665605
$144$	156.032			1.08356
$145$	−9.38613	+	8.46423i	−0.0647319	+	0.0583740i
$146$		−	235.434i		−	1.61256i
$147$	−4.52721	+	84.7497i	−0.0307974	+	0.576528i
$148$			249.574i			1.68631i
$149$	64.0297			0.429729			0.214865	−	0.976644i	$-0.431069\pi$
$149$	64.0297			0.429729			0.214865	+	0.976644i	$0.431069\pi$
$150$	163.929	+	16.9779i	1.09286	+	0.113186i
$151$	−165.776			−1.09785			−0.548927	−	0.835870i	$-0.684963\pi$
$151$	−165.776			−1.09785			−0.548927	+	0.835870i	$0.684963\pi$
$152$	56.6725			0.372845
$153$	−86.5437			−0.565645
$154$	181.602	+	191.562i	1.17923	+	1.24391i
$155$	−29.7770	−	33.0202i	−0.192110	−	0.213034i
$156$	−174.482			−1.11848
$157$	−268.239			−1.70853			−0.854264	−	0.519839i	$-0.825992\pi$
$157$	−268.239			−1.70853			−0.854264	+	0.519839i	$0.825992\pi$
$158$			174.505i			1.10446i
$159$		−	81.4583i		−	0.512316i
$160$	332.210	+	368.394i	2.07632	+	2.30246i
$161$	−6.03544	−	6.36645i	−0.0374872	−	0.0395432i
$162$		−	34.2543i		−	0.211447i
$163$		−	84.2549i		−	0.516901i	−0.966024	−	0.258451i	$-0.916788\pi$
$163$		−	84.2549i		−	0.516901i	0.966024	−	0.258451i	$-0.0832119\pi$
$164$			626.309i			3.81896i
$165$	−63.7199	+	57.4614i	−0.386181	+	0.348251i
$166$			87.3708i			0.526330i
$167$	12.3631			0.0740303			0.0370151	−	0.999315i	$-0.488215\pi$
$167$	12.3631			0.0740303			0.0370151	+	0.999315i	$0.488215\pi$
$168$	−205.913	−	217.207i	−1.22567	−	1.29290i
$169$	−76.7071			−0.453888
$170$	−367.650	−	407.693i	−2.16265	−	2.39820i
$171$		−	6.88730i		−	0.0402766i
$172$			441.572i			2.56728i
$173$	−155.182			−0.897006			−0.448503	−	0.893781i	$-0.648043\pi$
$173$	−155.182			−0.897006			−0.448503	+	0.893781i	$0.648043\pi$
$174$			16.6638i			0.0957689i
$175$	−106.674	−	138.729i	−0.609567	−	0.792735i
$176$	−515.302			−2.92785
$177$			33.4241i			0.188837i
$178$	−338.294			−1.90053
$179$	−227.175			−1.26913			−0.634567	−	0.772868i	$-0.718822\pi$
$179$	−227.175			−1.26913			−0.634567	+	0.772868i	$0.718822\pi$
$180$	116.808	−	105.335i	0.648935	−	0.585197i
$181$			164.157i			0.906946i	0.891270	+	0.453473i	$0.149815\pi$
$181$			164.157i			0.906946i	−0.891270	+	0.453473i	$0.850185\pi$
$182$	176.091	+	185.748i	0.967532	+	1.02060i
$183$		−	22.4405i		−	0.122626i
$184$	30.9367			0.168134
$185$	79.6967	+	88.3771i	0.430793	+	0.477714i
$186$	−58.6229			−0.315177
$187$	285.813			1.52841
$188$	438.749			2.33377
$189$	−26.3967	+	25.0243i	−0.139665	+	0.132404i
$190$	32.4449	−	29.2582i	0.170763	−	0.153991i
$191$	321.674			1.68416			0.842079	−	0.539354i	$-0.181332\pi$
$191$	321.674			1.68416			0.842079	+	0.539354i	$0.181332\pi$
$192$	293.692			1.52965
$193$			153.610i			0.795906i	0.917406	+	0.397953i	$0.130279\pi$
$193$			153.610i			0.795906i	−0.917406	+	0.397953i	$0.869721\pi$
$194$			70.0866i			0.361271i
$195$	−61.7861	+	55.7175i	−0.316852	+	0.285731i
$196$	−27.4080	+	513.078i	−0.139837	+	2.61775i
$197$		−	326.808i		−	1.65892i	−0.558565	−	0.829461i	$-0.688648\pi$
$197$		−	326.808i		−	1.65892i	0.558565	−	0.829461i	$-0.311352\pi$
$198$			113.126i			0.571344i
$199$		−	271.322i		−	1.36343i	−0.731619	−	0.681714i	$-0.761235\pi$
$199$		−	271.322i		−	1.36343i	0.731619	−	0.681714i	$-0.238765\pi$
$200$	613.858	+	63.5762i	3.06929	+	0.317881i
$201$		−	209.562i		−	1.04260i
$202$	−286.960			−1.42059
$203$	12.8413	−	12.1736i	0.0632575	−	0.0599686i
$204$	−523.940			−2.56833
$205$	200.000	+	221.783i	0.975609	+	1.08187i
$206$		−	422.048i		−	2.04878i
$207$		−	3.75968i		−	0.0181627i
$208$	−499.664			−2.40223
$209$			22.7455i			0.108830i
$210$	−230.022	−	18.0440i	−1.09534	−	0.0859237i
$211$	−150.284			−0.712248			−0.356124	−	0.934439i	$-0.615902\pi$
$211$	−150.284			−0.712248			−0.356124	+	0.934439i	$0.615902\pi$
$212$		−	493.153i		−	2.32619i
$213$	−62.5874			−0.293838
$214$	773.663			3.61525
$215$	141.007	+	156.365i	0.655848	+	0.727281i
$216$		−	128.270i		−	0.593844i
$217$	42.8266	+	45.1754i	0.197357	+	0.208181i
$218$			229.022i			1.05056i
$219$	−107.141			−0.489230
$220$	−385.763	+	347.874i	−1.75347	+	1.58124i
$221$	277.140			1.25403
$222$	156.902			0.706764
$223$	−9.86531			−0.0442391			−0.0221195	−	0.999755i	$-0.507041\pi$
$223$	−9.86531			−0.0442391			−0.0221195	+	0.999755i	$0.507041\pi$
$224$	−477.799	−	504.004i	−2.13303	−	2.25002i
$225$	7.72630	−	74.6010i	0.0343391	−	0.331560i
$226$	−422.363			−1.86886
$227$	272.679			1.20123			0.600614	−	0.799539i	$-0.294923\pi$
$227$	272.679			1.20123			0.600614	+	0.799539i	$0.294923\pi$
$228$		−	41.6961i		−	0.182877i
$229$		−	360.741i		−	1.57529i	−0.616132	−	0.787643i	$-0.711301\pi$
$229$		−	360.741i		−	1.57529i	0.616132	−	0.787643i	$-0.288699\pi$
$230$	17.7112	−	15.9716i	0.0770053	−	0.0694419i
$231$	87.1760	−	82.6434i	0.377385	−	0.357764i
$232$			62.4000i			0.268966i
$233$		−	13.5815i		−	0.0582897i	−0.999575	−	0.0291448i	$-0.990722\pi$
$233$		−	13.5815i		−	0.0582897i	0.999575	−	0.0291448i	$-0.00927840\pi$
$234$			109.693i			0.468773i
$235$	155.366	−	140.106i	0.661132	−	0.596196i
$236$			202.351i			0.857419i
$237$	79.4138			0.335079
$238$	528.770	+	557.770i	2.22172	+	2.34357i
$239$	267.331			1.11854			0.559269	−	0.828986i	$-0.311082\pi$
$239$	267.331			1.11854			0.559269	+	0.828986i	$0.311082\pi$
$240$	334.503	−	301.649i	1.39376	−	1.25687i
$241$			207.223i			0.859848i	0.902865	+	0.429924i	$0.141460\pi$
$241$			207.223i			0.859848i	−0.902865	+	0.429924i	$0.858540\pi$
$242$			86.9282i			0.359207i
$243$	−15.5885			−0.0641500
$244$		−	135.856i		−	0.556787i
$245$	154.136	+	190.439i	0.629127	+	0.777302i
$246$	393.746			1.60059
$247$			22.0553i			0.0892925i
$248$	−219.522			−0.885170
$249$	39.7607			0.159681
$250$	384.255	−	280.518i	1.53702	−	1.12207i
$251$		−	67.7515i		−	0.269926i	−0.990851	−	0.134963i	$-0.956908\pi$
$251$		−	67.7515i		−	0.269926i	0.990851	−	0.134963i	$-0.0430916\pi$
$252$	−159.807	+	151.498i	−0.634154	+	0.601183i
$253$			12.4165i			0.0490769i
$254$	−277.096			−1.09093
$255$	−185.533	+	167.310i	−0.727580	+	0.656118i
$256$	267.599			1.04531
$257$	−157.539			−0.612991			−0.306496	−	0.951872i	$-0.599156\pi$
$257$	−157.539			−0.612991			−0.306496	+	0.951872i	$0.599156\pi$
$258$	277.606			1.07599
$259$	−114.623	−	120.910i	−0.442561	−	0.466833i
$260$	−374.056	+	337.317i	−1.43868	+	1.29737i
$261$	7.58336			0.0290550
$262$	751.702			2.86909
$263$			34.2625i			0.130276i	0.997876	+	0.0651378i	$0.0207487\pi$
$263$			34.2625i			0.130276i	−0.997876	+	0.0651378i	$0.979251\pi$
$264$			423.617i			1.60461i
$265$	−157.479	−	174.631i	−0.594259	−	0.658984i
$266$	−44.3883	+	42.0805i	−0.166873	+	0.158197i
$267$			153.951i			0.576594i
$268$		−	1268.70i		−	4.73395i
$269$		−	360.350i		−	1.33959i	−0.742545	−	0.669796i	$-0.766382\pi$
$269$		−	360.350i		−	1.33959i	0.742545	−	0.669796i	$-0.233618\pi$
$270$	−66.2219	−	73.4347i	−0.245266	−	0.271980i
$271$			389.497i			1.43726i	0.695393	+	0.718629i	$0.255230\pi$
$271$			389.497i			1.43726i	−0.695393	+	0.718629i	$0.744770\pi$
$272$	−1500.40			−5.51619
$273$	84.5303	−	80.1354i	0.309635	−	0.293536i
$274$	−182.636			−0.666556
$275$	−25.5163	+	246.372i	−0.0927867	+	0.895898i
$276$		−	22.7613i		−	0.0824684i
$277$			28.4117i			0.102569i	0.998684	+	0.0512846i	$0.0163316\pi$
$277$			28.4117i			0.102569i	−0.998684	+	0.0512846i	$0.983668\pi$
$278$	−10.8997			−0.0392075
$279$			26.6781i			0.0956205i
$280$	−861.351	−	67.5683i	−3.07625	−	0.241315i
$281$	−252.735			−0.899414			−0.449707	−	0.893176i	$-0.648472\pi$
$281$	−252.735			−0.899414			−0.449707	+	0.893176i	$0.648472\pi$
$282$		−	275.831i		−	0.978125i
$283$	−143.879			−0.508406			−0.254203	−	0.967151i	$-0.581813\pi$
$283$	−143.879			−0.508406			−0.254203	+	0.967151i	$0.581813\pi$
$284$	−378.907			−1.33418
$285$	−13.3148	−	14.7650i	−0.0467187	−	0.0518072i
$286$		−	362.264i		−	1.26666i
$287$	−287.648	−	303.424i	−1.00226	−	1.05723i
$288$		−	297.637i		−	1.03346i
$289$	543.202			1.87959
$290$	32.2152	+	35.7240i	0.111087	+	0.123186i
$291$	31.8950			0.109605
$292$	−648.639			−2.22137
$293$	204.454			0.697795			0.348897	−	0.937161i	$-0.386556\pi$
$293$	204.454			0.697795			0.348897	+	0.937161i	$0.386556\pi$
$294$	322.560	+	17.2307i	1.09714	+	0.0586080i
$295$	64.6168	+	71.6547i	0.219040	+	0.242897i
$296$	587.541			1.98493
$297$	51.4814			0.173338
$298$		−	243.699i		−	0.817783i
$299$			12.0396i			0.0402664i
$300$	46.7754	−	451.638i	0.155918	−	1.50546i
$301$	−202.803	−	213.925i	−0.673764	−	0.710716i
$302$			630.949i			2.08924i
$303$			130.590i			0.430989i
$304$		−	119.405i		−	0.392779i
$305$	−43.3830	−	48.1082i	−0.142239	−	0.157732i
$306$			329.389i			1.07643i
$307$	331.176			1.07875			0.539375	−	0.842066i	$-0.318661\pi$
$307$	331.176			1.07875			0.539375	+	0.842066i	$0.318661\pi$
$308$	527.767	−	500.327i	1.71353	−	1.62444i
$309$	−192.065			−0.621571
$310$	−125.676	+	113.332i	−0.405407	+	0.365588i
$311$		−	261.410i		−	0.840546i	−0.907398	−	0.420273i	$-0.861934\pi$
$311$		−	261.410i		−	0.840546i	0.907398	−	0.420273i	$-0.138066\pi$
$312$			410.761i			1.31654i
$313$	−477.693			−1.52618			−0.763088	−	0.646294i	$-0.776318\pi$
$313$	−477.693			−1.52618			−0.763088	+	0.646294i	$0.776318\pi$
$314$			1020.93i			3.25136i
$315$	−8.21145	+	104.678i	−0.0260681	+	0.332312i
$316$	480.775			1.52144
$317$		−	243.520i		−	0.768201i	−0.923291	−	0.384101i	$-0.874512\pi$
$317$		−	243.520i		−	0.768201i	0.923291	−	0.384101i	$-0.125488\pi$
$318$	−310.033			−0.974948
$319$	−25.0443			−0.0785087
$320$	629.619	−	567.778i	1.96756	−	1.77431i
$321$		−	352.079i		−	1.09682i
$322$	−24.2309	+	22.9711i	−0.0752514	+	0.0713388i
$323$			66.2281i			0.205041i
$324$	−94.3733			−0.291275
$325$	−24.7420	+	238.895i	−0.0761292	+	0.735062i
$326$	−320.677			−0.983673
$327$	104.223			0.318725
$328$	1474.44			4.49524
$329$	−212.558	+	201.507i	−0.646074	+	0.612482i
$330$	218.700	+	242.520i	0.662728	+	0.734910i
$331$	83.1438			0.251190			0.125595	−	0.992082i	$-0.459916\pi$
$331$	83.1438			0.251190			0.125595	+	0.992082i	$0.459916\pi$
$332$	240.713			0.725039
$333$		−	71.4027i		−	0.214423i
$334$		−	47.0542i		−	0.140881i
$335$	−405.134	−	449.260i	−1.20936	−	1.34108i
$336$	−457.638	+	433.844i	−1.36202	+	1.29120i
$337$		−	194.973i		−	0.578554i	−0.957245	−	0.289277i	$-0.906585\pi$
$337$		−	194.973i		−	0.578554i	0.957245	−	0.289277i	$-0.0934149\pi$
$338$			291.950i			0.863758i
$339$			192.209i			0.566987i
$340$	−1123.23	+	1012.90i	−3.30360	+	2.97913i
$341$		−	88.1053i		−	0.258373i
$342$	−26.2133			−0.0766472
$343$	−222.366	−	261.156i	−0.648297	−	0.761387i
$344$	1039.53			3.02190
$345$	−7.26837	−	8.06002i	−0.0210677	−	0.0233624i
$346$			590.628i			1.70702i
$347$		−	308.676i		−	0.889556i	−0.895641	−	0.444778i	$-0.853283\pi$
$347$		−	308.676i		−	0.889556i	0.895641	−	0.444778i	$-0.146717\pi$
$348$	45.9100			0.131925
$349$			549.671i			1.57499i	0.616321	+	0.787495i	$0.288622\pi$
$349$			549.671i			1.57499i	−0.616321	+	0.787495i	$0.711378\pi$
$350$	−528.006	+	406.006i	−1.50859	+	1.16002i
$351$	49.9190			0.142219
$352$			982.957i			2.79249i
$353$	528.729			1.49781			0.748907	−	0.662675i	$-0.230579\pi$
$353$	528.729			1.49781			0.748907	+	0.662675i	$0.230579\pi$
$354$	127.213			0.359359
$355$	−134.175	+	120.997i	−0.377959	+	0.340836i
$356$			932.025i			2.61805i
$357$	253.830	−	240.633i	0.711008	−	0.674041i
$358$			864.637i			2.41519i
$359$	−17.0239			−0.0474204			−0.0237102	−	0.999719i	$-0.507548\pi$
$359$	−17.0239			−0.0474204			−0.0237102	+	0.999719i	$0.507548\pi$
$360$	−247.978	−	274.987i	−0.688827	−	0.763852i
$361$	355.729			0.985400
$362$	624.788			1.72593
$363$	39.5593			0.108979
$364$	511.751	−	485.143i	1.40591	−	1.33281i
$365$	−229.690	+	207.130i	−0.629289	+	0.567481i
$366$	−85.4095			−0.233359
$367$	−83.4973			−0.227513			−0.113757	−	0.993509i	$-0.536288\pi$
$367$	−83.4973			−0.227513			−0.113757	+	0.993509i	$0.536288\pi$
$368$		−	65.1813i		−	0.177123i
$369$		−	179.186i		−	0.485599i
$370$	336.366	−	303.329i	0.909099	−	0.819807i
$371$	226.493	+	238.915i	0.610493	+	0.643975i
$372$			161.511i			0.434168i
$373$			161.604i			0.433254i	0.976254	+	0.216627i	$0.0695055\pi$
$373$			161.604i			0.433254i	−0.976254	+	0.216627i	$0.930494\pi$
$374$		−	1087.82i		−	2.90860i
$375$	−127.658	−	174.867i	−0.340422	−	0.466312i
$376$		−	1032.89i		−	2.74705i
$377$	−24.2842			−0.0644144
$378$	95.2433	+	100.467i	0.251966	+	0.265785i
$379$	−135.824			−0.358374			−0.179187	−	0.983815i	$-0.557347\pi$
$379$	−135.824			−0.358374			−0.179187	+	0.983815i	$0.557347\pi$
$380$	−80.6086	−	89.3883i	−0.212128	−	0.235232i
$381$			126.101i			0.330973i
$382$		−	1224.30i		−	3.20498i
$383$	−650.885			−1.69944			−0.849719	−	0.527235i	$-0.823229\pi$
$383$	−650.885			−1.69944			−0.849719	+	0.527235i	$0.823229\pi$
$384$		−	430.438i		−	1.12093i
$385$	27.1186	−	345.704i	0.0704378	−	0.897932i
$386$	584.645			1.51462
$387$		−	126.333i		−	0.326441i
$388$	193.094			0.497664
$389$	−85.8607			−0.220722			−0.110361	−	0.993892i	$-0.535201\pi$
$389$	−85.8607			−0.220722			−0.110361	+	0.993892i	$0.535201\pi$
$390$	212.063	+	235.160i	0.543751	+	0.602975i
$391$			36.1529i			0.0924628i
$392$	1207.87	+	64.5231i	3.08131	+	0.164600i
$393$		−	342.084i		−	0.870444i
$394$	−1243.84			−3.15696
$395$	170.248	−	153.526i	0.431007	−	0.388674i
$396$	311.671			0.787047
$397$	348.588			0.878056			0.439028	−	0.898473i	$-0.355323\pi$
$397$	348.588			0.878056			0.439028	+	0.898473i	$0.355323\pi$
$398$	−1032.66			−2.59463
$399$	19.1500	+	20.2002i	0.0479949	+	0.0506272i
$400$	133.950	−	1293.35i	0.334876	−	3.23338i
$401$	−735.817			−1.83495			−0.917477	−	0.397788i	$-0.869778\pi$
$401$	−735.817			−1.83495			−0.917477	+	0.397788i	$0.869778\pi$
$402$	−797.601			−1.98408
$403$		−	85.4315i		−	0.211989i
$404$			790.596i			1.95692i
$405$	−33.4186	+	30.1363i	−0.0825151	+	0.0744106i
$406$	−46.3333	−	48.8744i	−0.114121	−	0.120380i
$407$			235.810i			0.579385i
$408$			1233.44i			3.02315i
$409$			504.416i			1.23329i	0.787241	+	0.616646i	$0.211509\pi$
$409$			504.416i			1.23329i	−0.787241	+	0.616646i	$0.788491\pi$
$410$	844.115	−	761.207i	2.05882	−	1.85660i
$411$			83.1142i			0.202224i
$412$	−1162.77			−2.82227
$413$	−92.9348	−	98.0317i	−0.225024	−	0.237365i
$414$	−14.3095			−0.0345639
$415$	85.2392	−	76.8671i	0.205396	−	0.185222i
$416$			953.126i			2.29117i
$417$			4.96022i			0.0118950i
$418$	86.5704			0.207106
$419$			65.0428i			0.155233i	0.996983	+	0.0776167i	$0.0247310\pi$
$419$			65.0428i			0.155233i	−0.996983	+	0.0776167i	$0.975269\pi$
$420$	−49.7125	+	633.728i	−0.118363	+	1.50888i
$421$	−703.846			−1.67184			−0.835921	−	0.548849i	$-0.815066\pi$
$421$	−703.846			−1.67184			−0.835921	+	0.548849i	$0.815066\pi$
$422$			571.988i			1.35542i
$423$	−125.525			−0.296750
$424$	−1160.97			−2.73813
$425$	−74.2959	+	717.361i	−0.174814	+	1.68791i
$426$			238.210i			0.559179i
$427$	62.3953	+	65.8174i	0.146125	+	0.154139i
$428$		−	2131.50i		−	4.98014i
$429$	−164.859			−0.384287
$430$	595.133	−	536.679i	1.38403	−	1.24809i
$431$	323.448			0.750459			0.375229	−	0.926932i	$-0.377564\pi$
$431$	323.448			0.750459			0.375229	+	0.926932i	$0.377564\pi$
$432$	−270.256			−0.625593
$433$	247.729			0.572122			0.286061	−	0.958211i	$-0.407654\pi$
$433$	247.729			0.572122			0.286061	+	0.958211i	$0.407654\pi$
$434$	171.939	−	162.999i	0.396173	−	0.375575i
$435$	16.2573	−	14.6605i	0.0373730	−	0.0337022i
$436$	630.971			1.44718
$437$	−2.87712			−0.00658379
$438$			407.784i			0.931014i
$439$		−	811.956i		−	1.84956i	−0.380506	−	0.924779i	$-0.624250\pi$
$439$		−	811.956i		−	1.84956i	0.380506	−	0.924779i	$-0.375750\pi$
$440$	818.954	+	908.153i	1.86126	+	2.06398i
$441$	7.84137	−	146.791i	0.0177809	−	0.332859i
$442$		−	1054.80i		−	2.38643i
$443$			571.236i			1.28947i	0.764405	+	0.644736i	$0.223033\pi$
$443$			571.236i			1.28947i	−0.764405	+	0.644736i	$0.776967\pi$
$444$		−	432.275i		−	0.973593i
$445$	297.624	+	330.041i	0.668818	+	0.741664i
$446$			37.5477i			0.0841877i
$447$	−110.903			−0.248104
$448$	−861.389	+	816.603i	−1.92274	+	1.82277i
$449$	−638.152			−1.42127			−0.710637	−	0.703559i	$-0.751593\pi$
$449$	−638.152			−1.42127			−0.710637	+	0.703559i	$0.751593\pi$
$450$	−283.934	−	29.4066i	−0.630965	−	0.0653480i
$451$			591.767i			1.31212i
$452$			1163.64i			2.57443i
$453$	287.132			0.633846
$454$		−	1037.83i		−	2.28596i
$455$	26.2956	−	335.212i	0.0577925	−	0.736731i
$456$	−98.1596			−0.215262
$457$			687.039i			1.50337i	0.659524	+	0.751684i	$0.270758\pi$
$457$			687.039i			1.50337i	−0.659524	+	0.751684i	$0.729242\pi$
$458$	−1372.99			−2.99780
$459$	149.898			0.326575
$460$	−44.0031	−	48.7957i	−0.0956588	−	0.106078i
$461$		−	396.503i		−	0.860094i	−0.902807	−	0.430047i	$-0.858497\pi$
$461$		−	396.503i		−	0.860094i	0.902807	−	0.430047i	$-0.141503\pi$
$462$	−314.544	−	331.795i	−0.680831	−	0.718171i
$463$			603.681i			1.30385i	0.758285	+	0.651923i	$0.226037\pi$
$463$			603.681i			1.30385i	−0.758285	+	0.651923i	$0.773963\pi$
$464$	131.472			0.283345
$465$	51.5753	+	57.1927i	0.110915	+	0.122995i
$466$	−51.6917			−0.110926
$467$	−245.380			−0.525438			−0.262719	−	0.964872i	$-0.584619\pi$
$467$	−245.380			−0.525438			−0.262719	+	0.964872i	$0.584619\pi$
$468$	302.212			0.645752
$469$	582.682	+	614.639i	1.24239	+	1.31053i
$470$	−533.249	−	591.329i	−1.13457	−	1.25815i
$471$	464.604			0.986420
$472$	476.369			1.00926
$473$			417.218i			0.882067i
$474$		−	302.252i		−	0.637662i
$475$	−57.0888	−	5.91260i	−0.120187	−	0.0124476i
$476$	1536.70	−	1456.80i	3.22836	−	3.06051i
$477$			141.090i			0.295786i
$478$		−	1017.47i		−	2.12860i
$479$		−	28.8550i		−	0.0602401i	−0.999546	−	0.0301201i	$-0.990411\pi$
$479$		−	28.8550i		−	0.0602401i	0.999546	−	0.0301201i	$-0.00958897\pi$
$480$	−575.405	−	638.077i	−1.19876	−	1.32933i
$481$			228.653i			0.475371i
$482$	788.700			1.63631
$483$	10.4537	+	11.0270i	0.0216432	+	0.0228303i
$484$	239.494			0.494822
$485$	68.3767	−	61.6607i	0.140983	−	0.127136i
$486$			59.3302i			0.122079i
$487$		−	533.512i		−	1.09551i	−0.836639	−	0.547754i	$-0.815483\pi$
$487$		−	533.512i		−	1.09551i	0.836639	−	0.547754i	$-0.184517\pi$
$488$	−319.828			−0.655386
$489$			145.934i			0.298433i
$490$	724.818	−	586.648i	1.47922	−	1.19724i
$491$	−46.0401			−0.0937681			−0.0468841	−	0.998900i	$-0.514929\pi$
$491$	−46.0401			−0.0937681			−0.0468841	+	0.998900i	$0.514929\pi$
$492$		−	1084.80i		−	2.20488i
$493$	−72.9213			−0.147913
$494$	83.9431			0.169925
$495$	110.366	−	99.5260i	0.222962	−	0.201063i
$496$			462.517i			0.932493i
$497$	183.567	−	174.023i	0.369350	−	0.350146i
$498$		−	151.331i		−	0.303877i
$499$	−326.860			−0.655029			−0.327515	−	0.944846i	$-0.606211\pi$
$499$	−326.860			−0.655029			−0.327515	+	0.944846i	$0.606211\pi$
$500$	−772.848	−	1058.65i	−1.54570	−	2.11730i
$501$	−21.4134			−0.0427414
$502$	−257.865			−0.513675
$503$	88.2437			0.175435			0.0877174	−	0.996145i	$-0.472043\pi$
$503$	88.2437			0.175435			0.0877174	+	0.996145i	$0.472043\pi$
$504$	356.652	+	376.213i	0.707644	+	0.746454i
$505$	252.461	+	279.959i	0.499924	+	0.554374i
$506$	47.2575			0.0933942
$507$	132.861			0.262052
$508$			763.420i			1.50279i
$509$		−	463.905i		−	0.911405i	−0.890132	−	0.455703i	$-0.849388\pi$
$509$		−	463.905i		−	0.911405i	0.890132	−	0.455703i	$-0.150612\pi$
$510$	636.788	+	706.145i	1.24860	+	1.38460i
$511$	314.242	−	297.904i	0.614956	−	0.582982i
$512$		−	24.4392i		−	0.0477328i
$513$			11.9292i			0.0232537i
$514$			599.598i			1.16653i
$515$	−411.751	+	371.309i	−0.799517	+	0.720989i
$516$		−	764.824i		−	1.48222i
$517$	414.551			0.801840
$518$	−460.187	+	436.261i	−0.888392	+	0.842202i
$519$	268.783			0.517887
$520$	794.101	+	880.592i	1.52712	+	1.69345i
$521$		−	548.290i		−	1.05238i	−0.850367	−	0.526190i	$-0.823620\pi$
$521$		−	548.290i		−	1.05238i	0.850367	−	0.526190i	$-0.176380\pi$
$522$		−	28.8625i		−	0.0552922i
$523$	964.595			1.84435			0.922175	−	0.386774i	$-0.126411\pi$
$523$	964.595			1.84435			0.922175	+	0.386774i	$0.126411\pi$
$524$		−	2071.00i		−	3.95228i
$525$	184.765	+	240.285i	0.351933	+	0.457686i
$526$	130.404			0.247917
$527$		−	256.536i		−	0.486785i
$528$	892.529			1.69040
$529$	527.429			0.997031
$530$	−664.652	+	599.370i	−1.25406	+	1.13089i
$531$		−	57.8922i		−	0.109025i
$532$	115.935	+	122.293i	0.217923	+	0.229874i
$533$			573.808i			1.07656i
$534$	585.942			1.09727
$535$	−680.653	−	754.788i	−1.27225	−	1.41082i
$536$	−2986.73			−5.57226
$537$	393.479			0.732735
$538$	−1371.51			−2.54927
$539$	−25.8964	+	484.781i	−0.0480452	+	0.899408i
$540$	−202.318	+	182.446i	−0.374663	+	0.337864i
$541$	−431.085			−0.796831			−0.398415	−	0.917205i	$-0.630440\pi$
$541$	−431.085			−0.796831			−0.398415	+	0.917205i	$0.630440\pi$
$542$	1482.44			2.73513
$543$		−	284.329i		−	0.523625i
$544$			2862.07i			5.26116i
$545$	223.434	−	201.489i	0.409971	−	0.369704i
$546$	−304.998	−	321.726i	−0.558605	−	0.589241i
$547$		−	28.1779i		−	0.0515136i	−0.999668	−	0.0257568i	$-0.991800\pi$
$547$		−	28.1779i		−	0.0515136i	0.999668	−	0.0257568i	$-0.00819954\pi$
$548$			503.177i			0.918207i
$549$			38.8682i			0.0707981i
$550$	937.701	+	97.1162i	1.70491	+	0.176575i
$551$		−	5.80321i		−	0.0105321i
$552$	−53.5839			−0.0970723
$553$	−232.918	+	220.808i	−0.421190	+	0.399291i
$554$	108.136			0.195191
$555$	−138.039	−	153.074i	−0.248719	−	0.275808i
$556$			30.0294i			0.0540097i
$557$		−	159.073i		−	0.285589i	−0.989752	−	0.142795i	$-0.954391\pi$
$557$		−	159.073i		−	0.285589i	0.989752	−	0.142795i	$-0.0456088\pi$
$558$	101.538			0.181968
$559$			404.556i			0.723714i
$560$	−142.361	+	1814.80i	−0.254217	+	3.24072i
$561$	−495.043			−0.882430
$562$			961.920i			1.71160i
$563$	644.468			1.14470			0.572351	−	0.820008i	$-0.306031\pi$
$563$	644.468			1.14470			0.572351	+	0.820008i	$0.306031\pi$
$564$	−759.936			−1.34740
$565$	371.586	+	412.058i	0.657675	+	0.729307i
$566$			547.609i			0.967506i
$567$	45.7204	−	43.3433i	0.0806357	−	0.0764432i
$568$			892.012i			1.57044i
$569$	522.250			0.917839			0.458919	−	0.888478i	$-0.348237\pi$
$569$	522.250			0.917839			0.458919	+	0.888478i	$0.348237\pi$
$570$	−56.1963	+	50.6767i	−0.0985900	+	0.0889065i
$571$	−86.9380			−0.152256			−0.0761278	−	0.997098i	$-0.524256\pi$
$571$	−86.9380			−0.152256			−0.0761278	+	0.997098i	$0.524256\pi$
$572$	−998.065			−1.74487
$573$	−557.156			−0.972349
$574$	−1154.84	+	1094.80i	−2.01192	+	1.90732i
$575$	−31.1640	−	3.22760i	−0.0541982	−	0.00561322i
$576$	−508.689			−0.883141
$577$	−641.655			−1.11205			−0.556027	−	0.831165i	$-0.687675\pi$
$577$	−641.655			−1.11205			−0.556027	+	0.831165i	$0.687675\pi$
$578$		−	2067.45i		−	3.57690i
$579$		−	266.060i		−	0.459517i
$580$	98.4222	−	88.7552i	0.169693	−	0.153026i
$581$	−116.617	+	110.554i	−0.200717	+	0.190282i
$582$		−	121.393i		−	0.208580i
$583$		−	465.954i		−	0.799235i
$584$			1527.01i			2.61474i
$585$	107.017	−	96.5056i	0.182935	−	0.164967i
$586$		−	778.159i		−	1.32792i
$587$	−518.592			−0.883462			−0.441731	−	0.897148i	$-0.645635\pi$
$587$	−518.592			−0.883462			−0.441731	+	0.897148i	$0.645635\pi$
$588$	47.4720	−	888.678i	0.0807347	−	1.51136i
$589$	20.4156			0.0346614
$590$	272.721	−	245.934i	0.462238	−	0.416837i
$591$			566.047i			0.957779i
$592$		−	1237.90i		−	2.09105i
$593$	686.085			1.15697			0.578486	−	0.815692i	$-0.303644\pi$
$593$	686.085			1.15697			0.578486	+	0.815692i	$0.303644\pi$
$594$		−	195.940i		−	0.329865i
$595$	78.9610	−	1006.58i	0.132708	−	1.69174i
$596$	−671.410			−1.12653
$597$			469.944i			0.787176i
$598$	45.8233			0.0766276
$599$	879.387			1.46809			0.734046	−	0.679100i	$-0.237630\pi$
$599$	879.387			1.46809			0.734046	+	0.679100i	$0.237630\pi$
$600$	−1063.23	−	110.117i	−1.77205	−	0.183529i
$601$			414.796i			0.690176i	0.938570	+	0.345088i	$0.112151\pi$
$601$			414.796i			0.690176i	−0.938570	+	0.345088i	$0.887849\pi$
$602$	−814.208	+	771.875i	−1.35251	+	1.28218i
$603$			362.972i			0.601944i
$604$	1738.31			2.87800
$605$	84.8074	−	76.4777i	0.140178	−	0.126409i
$606$	497.029			0.820180
$607$	−350.355			−0.577191			−0.288595	−	0.957451i	$-0.593188\pi$
$607$	−350.355			−0.577191			−0.288595	+	0.957451i	$0.593188\pi$
$608$	−227.769			−0.374620
$609$	−22.2417	+	21.0853i	−0.0365217	+	0.0346229i
$610$	−183.101	+	165.117i	−0.300166	+	0.270684i
$611$	401.970			0.657890
$612$	907.490			1.48283
$613$		−	589.314i		−	0.961360i	−0.876896	−	0.480680i	$-0.840390\pi$
$613$		−	589.314i		−	0.961360i	0.876896	−	0.480680i	$-0.159610\pi$
$614$		−	1260.47i		−	2.05288i
$615$	−346.410	−	384.140i	−0.563268	−	0.624618i
$616$	−1177.86	−	1242.45i	−1.91210	−	2.01697i
$617$			615.085i			0.996896i	0.866920	+	0.498448i	$0.166096\pi$
$617$			615.085i			0.996896i	−0.866920	+	0.498448i	$0.833904\pi$
$618$			731.008i			1.18286i
$619$		−	597.351i		−	0.965026i	−0.875889	−	0.482513i	$-0.839724\pi$
$619$		−	597.351i		−	0.965026i	0.875889	−	0.482513i	$-0.160276\pi$
$620$	312.239	+	346.247i	0.503611	+	0.558463i
$621$			6.51195i			0.0104862i
$622$	−994.935			−1.59957
$623$	−428.056	−	451.532i	−0.687088	−	0.724771i
$624$	865.443			1.38693
$625$	−611.734	−	128.087i	−0.978775	−	0.204938i
$626$			1818.12i			2.90434i
$627$		−	39.3964i		−	0.0628332i
$628$	2812.73			4.47887
$629$			686.606i			1.09158i
$630$	398.410	+	31.2531i	0.632397	+	0.0496080i
$631$	779.812			1.23584			0.617918	−	0.786243i	$-0.287977\pi$
$631$	779.812			1.23584			0.617918	+	0.786243i	$0.287977\pi$
$632$		−	1131.83i		−	1.79087i
$633$	260.300			0.411217
$634$	−926.845			−1.46190
$635$	243.783	+	270.335i	0.383911	+	0.425725i
$636$			854.165i			1.34303i
$637$	−25.1105	+	470.069i	−0.0394199	+	0.737942i
$638$			95.3195i			0.149404i
$639$	108.405			0.169647
$640$	−832.141	−	922.776i	−1.30022	−	1.44184i
$641$	−33.0462			−0.0515541			−0.0257770	−	0.999668i	$-0.508206\pi$
$641$	−33.0462			−0.0515541			−0.0257770	+	0.999668i	$0.508206\pi$
$642$	−1340.02			−2.08727
$643$	70.8343			0.110162			0.0550811	−	0.998482i	$-0.482458\pi$
$643$	70.8343			0.110162			0.0550811	+	0.998482i	$0.482458\pi$
$644$	63.2871	+	66.7581i	0.0982719	+	0.103662i
$645$	−244.232	−	270.833i	−0.378654	−	0.419896i
$646$	252.067			0.390196
$647$	−426.531			−0.659243			−0.329622	−	0.944113i	$-0.606921\pi$
$647$	−426.531			−0.659243			−0.329622	+	0.944113i	$0.606921\pi$
$648$			222.171i			0.342856i
$649$			191.191i			0.294593i
$650$	909.244	+	94.1689i	1.39884	+	0.144875i
$651$	−74.1778	−	78.2460i	−0.113944	−	0.120194i
$652$			883.490i			1.35505i
$653$		−	326.708i		−	0.500318i	−0.968205	−	0.250159i	$-0.919517\pi$
$653$		−	326.708i		−	0.500318i	0.968205	−	0.250159i	$-0.0804829\pi$
$654$		−	396.677i		−	0.606540i
$655$	−661.332	−	733.363i	−1.00967	−	1.11964i
$656$		−	3106.53i		−	4.73557i
$657$	185.574			0.282457
$658$	766.942	+	809.004i	1.16557	+	1.22949i
$659$	−19.8979			−0.0301941			−0.0150971	−	0.999886i	$-0.504806\pi$
$659$	−19.8979			−0.0301941			−0.0150971	+	0.999886i	$0.504806\pi$
$660$	668.162	−	602.535i	1.01237	−	0.912932i
$661$		−	804.972i		−	1.21781i	−0.793243	−	0.608905i	$-0.791609\pi$
$661$		−	804.972i		−	1.21781i	0.793243	−	0.608905i	$-0.208391\pi$
$662$		−	316.448i		−	0.478019i
$663$	−480.020			−0.724012
$664$		−	566.680i		−	0.853433i
$665$	80.1058	+	6.28386i	0.120460	+	0.00944941i
$666$	−271.761			−0.408050
$667$		−	3.16789i		−	0.00474946i
$668$	−129.638			−0.194069
$669$	17.0872			0.0255414
$670$	−1709.90	+	1541.96i	−2.55209	+	2.30143i
$671$		−	128.363i		−	0.191302i
$672$	827.573	+	872.961i	1.23151	+	1.29905i
$673$		−	134.741i		−	0.200210i	−0.994977	−	0.100105i	$-0.968082\pi$
$673$		−	134.741i		−	0.200210i	0.994977	−	0.100105i	$-0.0319179\pi$
$674$	−742.074			−1.10100
$675$	−13.3823	+	129.213i	−0.0198257	+	0.191426i
$676$	804.344			1.18986
$677$	−617.636			−0.912313			−0.456157	−	0.889900i	$-0.650774\pi$
$677$	−617.636			−0.912313			−0.456157	+	0.889900i	$0.650774\pi$
$678$	731.554			1.07899
$679$	−93.5469	+	88.6832i	−0.137772	+	0.130608i
$680$	2384.55	+	2644.26i	3.50669	+	3.88862i
$681$	−472.293			−0.693529
$682$	−335.332			−0.491689
$683$		−	476.196i		−	0.697213i	−0.937269	−	0.348606i	$-0.886655\pi$
$683$		−	476.196i		−	0.697213i	0.937269	−	0.348606i	$-0.113345\pi$
$684$			72.2197i			0.105584i
$685$	160.680	+	178.181i	0.234569	+	0.260118i
$686$	−993.969	+	846.333i	−1.44893	+	1.23372i
$687$			624.821i			0.909492i
$688$		−	2190.22i		−	3.18346i
$689$		−	451.813i		−	0.655752i
$690$	−30.6767	+	27.6637i	−0.0444590	+	0.0400923i
$691$		−	135.493i		−	0.196082i	−0.995182	−	0.0980411i	$-0.968742\pi$
$691$		−	135.493i		−	0.196082i	0.995182	−	0.0980411i	$-0.0312577\pi$
$692$	1627.23			2.35148
$693$	−150.993	+	143.143i	−0.217883	+	0.206555i
$694$	−1174.83			−1.69284
$695$	9.58931	+	10.6338i	0.0137976	+	0.0153004i
$696$		−	108.080i		−	0.155287i
$697$			1723.05i			2.47209i
$698$	2092.07			2.99723
$699$			23.5238i			0.0336536i
$700$	1118.58	+	1454.70i	1.59797	+	2.07814i
$701$	−252.981			−0.360886			−0.180443	−	0.983585i	$-0.557753\pi$
$701$	−252.981			−0.360886			−0.180443	+	0.983585i	$0.557753\pi$
$702$		−	189.994i		−	0.270646i
$703$	−54.6414			−0.0777260
$704$	1679.96			2.38631
$705$	−269.102	+	242.671i	−0.381705	+	0.344214i
$706$		−	2012.36i		−	2.85037i
$707$	−363.101	−	383.015i	−0.513580	−	0.541747i
$708$		−	350.482i		−	0.495031i
$709$	−522.023			−0.736280			−0.368140	−	0.929770i	$-0.620005\pi$
$709$	−522.023			−0.736280			−0.368140	+	0.929770i	$0.620005\pi$
$710$	460.518	+	510.676i	0.648617	+	0.719262i
$711$	−137.549			−0.193458
$712$	2194.15			3.08167
$713$	11.1446			0.0156305
$714$	−915.856	−	966.086i	−1.28271	−	1.35306i
$715$	−353.426	+	318.713i	−0.494302	+	0.445752i
$716$	2382.14			3.32701
$717$	−463.031			−0.645789
$718$			64.7937i			0.0902419i
$719$		−	412.956i		−	0.574348i	−0.957878	−	0.287174i	$-0.907284\pi$
$719$		−	412.956i		−	0.574348i	0.957878	−	0.287174i	$-0.0927158\pi$
$720$	−579.377	+	522.471i	−0.804690	+	0.725654i
$721$	563.322	−	534.033i	0.781306	−	0.740684i
$722$		−	1353.92i		−	1.87523i
$723$		−	358.922i		−	0.496434i
$724$		−	1721.34i		−	2.37754i
$725$	6.51014	−	62.8584i	0.00897951	−	0.0867013i
$726$		−	150.564i		−	0.207388i
$727$	−165.693			−0.227914			−0.113957	−	0.993486i	$-0.536353\pi$
$727$	−165.693			−0.227914			−0.113957	+	0.993486i	$0.536353\pi$
$728$	−1142.11	−	1204.75i	−1.56883	−	1.65487i
$729$	27.0000			0.0370370
$730$	788.346	+	874.210i	1.07993	+	1.19755i
$731$			1214.81i			1.66185i
$732$			235.310i			0.321461i
$733$	−1156.28			−1.57746			−0.788728	−	0.614742i	$-0.789260\pi$
$733$	−1156.28			−1.57746			−0.788728	+	0.614742i	$0.789260\pi$
$734$			317.794i			0.432962i
$735$	−266.972	−	329.850i	−0.363227	−	0.448776i
$736$	−124.336			−0.168934
$737$		−	1198.73i		−	1.62650i
$738$	−681.988			−0.924103
$739$	−735.714			−0.995553			−0.497777	−	0.867305i	$-0.665850\pi$
$739$	−735.714			−0.995553			−0.497777	+	0.867305i	$0.665850\pi$
$740$	−835.693	−	926.715i	−1.12932	−	1.25232i
$741$		−	38.2008i		−	0.0515531i
$742$	909.318	−	862.040i	1.22550	−	1.16178i
$743$		−	1183.23i		−	1.59251i	−0.604961	−	0.796255i	$-0.706811\pi$
$743$		−	1183.23i		−	1.59251i	0.604961	−	0.796255i	$-0.293189\pi$
$744$	380.223			0.511053
$745$	−237.754	+	214.402i	−0.319133	+	0.287788i
$746$	615.070			0.824490
$747$	−68.8675			−0.0921921
$748$	−2997.02			−4.00671
$749$	978.945	+	1032.64i	1.30700	+	1.37868i
$750$	−665.550	+	485.871i	−0.887400	+	0.647829i
$751$	154.633			0.205902			0.102951	−	0.994686i	$-0.467171\pi$
$751$	154.633			0.205902			0.102951	+	0.994686i	$0.467171\pi$
$752$	−2176.22			−2.89391
$753$			117.349i			0.155842i
$754$			92.4267i			0.122582i
$755$	615.556	−	555.096i	0.815306	−	0.735227i
$756$	276.794	−	262.402i	0.366129	−	0.347093i
$757$		−	714.710i		−	0.944135i	−0.881562	−	0.472068i	$-0.843508\pi$
$757$		−	714.710i		−	0.944135i	0.881562	−	0.472068i	$-0.156492\pi$
$758$			516.950i			0.681992i
$759$		−	21.5059i		−	0.0283346i
$760$	−210.435	+	189.766i	−0.276889	+	0.249693i
$761$			812.891i			1.06819i	0.845425	+	0.534094i	$0.179347\pi$
$761$			812.891i			1.06819i	−0.845425	+	0.534094i	$0.820653\pi$
$762$	479.944			0.629848
$763$	−305.683	+	289.790i	−0.400633	+	0.379803i
$764$	−3373.05			−4.41499
$765$	321.353	−	289.789i	0.420069	−	0.378810i
$766$			2477.29i			3.23406i
$767$			185.389i			0.241706i
$768$	−463.496			−0.603510
$769$			977.478i			1.27110i	0.772059	+	0.635551i	$0.219227\pi$
$769$			977.478i			1.27110i	−0.772059	+	0.635551i	$0.780773\pi$
$770$	−1315.76	−	103.214i	−1.70878	−	0.134044i
$771$	272.865			0.353911
$772$		−	1610.74i		−	2.08645i
$773$	1145.61			1.48203			0.741016	−	0.671487i	$-0.234344\pi$
$773$	1145.61			1.48203			0.741016	+	0.671487i	$0.234344\pi$
$774$	−480.827			−0.621224
$775$	221.135	+	22.9026i	0.285335	+	0.0295517i
$776$		−	454.576i		−	0.585793i
$777$	198.533	+	209.422i	0.255513	+	0.269526i
$778$			326.789i			0.420037i
$779$	−137.123			−0.176024
$780$	647.884	−	584.249i	0.830621	−	0.749038i
$781$	−358.010			−0.458399
$782$	137.599			0.175958
$783$	−13.1348			−0.0167749
$784$	135.945	−	2544.90i	0.173400	−	3.24605i
$785$	996.020	−	898.192i	1.26882	−	1.14419i
$786$	−1301.99			−1.65647
$787$	62.1774			0.0790056			0.0395028	−	0.999219i	$-0.487423\pi$
$787$	62.1774			0.0790056			0.0395028	+	0.999219i	$0.487423\pi$
$788$			3426.88i			4.34883i
$789$		−	59.3443i		−	0.0752146i
$790$	−584.326	−	647.970i	−0.739654	−	0.820215i
$791$	−534.431	−	563.742i	−0.675640	−	0.712695i
$792$		−	733.726i		−	0.926422i
$793$		−	124.468i		−	0.156958i
$794$		−	1326.74i		−	1.67096i
$795$	272.761	+	302.470i	0.343096	+	0.380465i
$796$			2845.06i			3.57420i
$797$	−516.172			−0.647643			−0.323822	−	0.946118i	$-0.604968\pi$
$797$	−516.172			−0.647643			−0.323822	+	0.946118i	$0.604968\pi$
$798$	76.8828	−	72.8855i	0.0963444	−	0.0913352i
$799$	1207.05			1.51070
$800$	−2467.12	−	255.515i	−3.08389	−	0.319394i
$801$		−	266.650i		−	0.332897i
$802$			2800.55i			3.49195i
$803$	−612.865			−0.763220
$804$			2197.45i			2.73315i
$805$	43.7286	+	3.43027i	0.0543212	+	0.00426120i
$806$	−325.155			−0.403419
$807$			624.145i			0.773414i
$808$	1861.20			2.30346
$809$	319.779			0.395277			0.197639	−	0.980275i	$-0.436673\pi$
$809$	319.779			0.395277			0.197639	+	0.980275i	$0.436673\pi$
$810$	114.700	+	127.193i	0.141605	+	0.157028i
$811$		−	99.9660i		−	0.123263i	−0.998099	−	0.0616313i	$-0.980370\pi$
$811$		−	99.9660i		−	0.123263i	0.998099	−	0.0616313i	$-0.0196303\pi$
$812$	−134.653	+	127.652i	−0.165828	+	0.157206i
$813$		−	674.629i		−	0.829802i
$814$	897.501			1.10258
$815$	282.125	+	312.854i	0.346166	+	0.383870i
$816$	2598.77			3.18477
$817$	−96.6769			−0.118332
$818$	1919.83			2.34698
$819$	−146.411	+	138.799i	−0.178768	+	0.169473i
$820$	−2097.18	−	2325.60i	−2.55754	−	2.83610i
$821$	−377.056			−0.459264			−0.229632	−	0.973278i	$-0.573752\pi$
$821$	−377.056			−0.459264			−0.229632	+	0.973278i	$0.573752\pi$
$822$	316.336			0.384837
$823$		−	1495.35i		−	1.81696i	−0.417933	−	0.908478i	$-0.637245\pi$
$823$		−	1495.35i		−	1.81696i	0.417933	−	0.908478i	$-0.362755\pi$
$824$			2737.37i			3.32205i
$825$	44.1956	−	426.729i	0.0535704	−	0.517247i
$826$	−373.112	+	353.713i	−0.451710	+	0.428224i
$827$			622.172i			0.752324i	0.926554	+	0.376162i	$0.122756\pi$
$827$			622.172i			0.752324i	−0.926554	+	0.376162i	$0.877244\pi$
$828$			39.4237i			0.0476131i
$829$		−	704.939i		−	0.850348i	−0.905112	−	0.425174i	$-0.860213\pi$
$829$		−	704.939i		−	0.850348i	0.905112	−	0.425174i	$-0.139787\pi$
$830$	−292.559	−	324.424i	−0.352481	−	0.390872i
$831$		−	49.2105i		−	0.0592184i
$832$	1628.98			1.95791
$833$	−75.4023	+	1411.53i	−0.0905190	+	1.69452i
$834$	18.8788			0.0226364
$835$	−45.9063	+	41.3974i	−0.0549776	+	0.0495777i
$836$		−	238.508i		−	0.285296i
$837$		−	46.2078i		−	0.0552065i
$838$	247.555			0.295412
$839$			757.300i			0.902622i	0.892367	+	0.451311i	$0.149044\pi$
$839$			757.300i			0.902622i	−0.892367	+	0.451311i	$0.850956\pi$
$840$	1491.90	+	117.032i	1.77608	+	0.139323i
$841$	−834.610			−0.992402
$842$			2678.86i			3.18155i
$843$	437.750			0.519277
$844$	1575.87			1.86714
$845$	284.827	−	256.852i	0.337074	−	0.303967i
$846$			477.754i			0.564721i
$847$	−116.026	+	109.994i	−0.136985	+	0.129862i
$848$			2446.07i			2.88451i
$849$	249.206			0.293528
$850$	2730.30	+	282.773i	3.21212	+	0.332674i
$851$	−29.8279			−0.0350504
$852$	656.287			0.770289
$853$	490.797			0.575377			0.287689	−	0.957724i	$-0.407113\pi$
$853$	490.797			0.575377			0.287689	+	0.957724i	$0.407113\pi$
$854$	250.503	−	237.479i	0.293329	−	0.278078i
$855$	23.0620	+	25.5738i	0.0269731	+	0.0299109i
$856$	−5017.92			−5.86205
$857$	−1037.03			−1.21007			−0.605035	−	0.796199i	$-0.706841\pi$
$857$	−1037.03			−1.21007			−0.605035	+	0.796199i	$0.706841\pi$
$858$			627.460i			0.731305i
$859$		−	282.365i		−	0.328714i	−0.986401	−	0.164357i	$-0.947445\pi$
$859$		−	282.365i		−	0.328714i	0.986401	−	0.164357i	$-0.0525549\pi$
$860$	−1478.59	−	1639.64i	−1.71929	−	1.90655i
$861$	498.222	+	525.546i	0.578655	+	0.610391i
$862$		−	1231.05i		−	1.42814i
$863$			216.622i			0.251011i	0.992093	+	0.125505i	$0.0400552\pi$
$863$			216.622i			0.251011i	−0.992093	+	0.125505i	$0.959945\pi$
$864$			515.523i			0.596670i
$865$	576.219	−	519.623i	0.666149	−	0.600720i
$866$		−	942.866i		−	1.08876i
$867$	−940.853			−1.08518
$868$	−449.076	−	473.705i	−0.517368	−	0.545743i
$869$	454.259			0.522738
$870$	−55.7983	−	61.8757i	−0.0641360	−	0.0711215i
$871$		−	1162.35i		−	1.33450i
$872$		−	1485.41i		−	1.70346i
$873$	−55.2437			−0.0632803
$874$			10.9504i			0.0125291i
$875$	860.630	+	157.929i	0.983577	+	0.180490i
$876$	1123.48			1.28251
$877$		−	900.305i		−	1.02657i	−0.858217	−	0.513287i	$-0.828428\pi$
$877$		−	900.305i		−	1.02657i	0.858217	−	0.513287i	$-0.171572\pi$
$878$	−3090.33			−3.51974
$879$	−354.125			−0.402872
$880$	1913.41	−	1725.48i	2.17433	−	1.96077i
$881$		−	1476.40i		−	1.67583i	−0.545802	−	0.837914i	$-0.683775\pi$
$881$		−	1476.40i		−	1.67583i	0.545802	−	0.837914i	$-0.316225\pi$
$882$	−558.691	−	29.8445i	−0.633436	−	0.0338373i
$883$			767.552i			0.869255i	0.900610	+	0.434627i	$0.143120\pi$
$883$			767.552i			0.869255i	−0.900610	+	0.434627i	$0.856880\pi$
$884$	−2906.06			−3.28740
$885$	−111.920	−	124.110i	−0.126463	−	0.140237i
$886$	2174.15			2.45389
$887$	718.207			0.809704			0.404852	−	0.914382i	$-0.367323\pi$
$887$	718.207			0.809704			0.404852	+	0.914382i	$0.367323\pi$
$888$	−1017.65			−1.14600
$889$	−350.620	−	369.849i	−0.394398	−	0.416028i
$890$	1256.15	−	1132.77i	1.41140	−	1.27277i
$891$	−89.1684			−0.100077
$892$	103.447			0.115972
$893$			96.0590i			0.107569i
$894$			422.100i			0.472147i
$895$	843.542	−	760.690i	0.942505	−	0.849933i
$896$	1196.82	+	1262.46i	1.33574	+	1.40900i
$897$		−	20.8533i		−	0.0232478i
$898$			2428.83i			2.70471i
$899$			22.4789i			0.0250043i
$900$	−81.0173	+	782.260i	−0.0900193	+	0.869177i
$901$		−	1356.72i		−	1.50579i
$902$	2252.29			2.49699
$903$	351.265	+	370.530i	0.388998	+	0.410332i
$904$	2739.41			3.03032
$905$	−549.676	−	609.545i	−0.607377	−	0.673531i
$906$		−	1092.84i		−	1.20622i
$907$			1060.05i			1.16874i	0.811486	+	0.584371i	$0.198659\pi$
$907$			1060.05i			1.16874i	−0.811486	+	0.584371i	$0.801341\pi$
$908$	−2859.29			−3.14899
$909$		−	226.188i		−	0.248831i
$910$	−1275.83	−	100.082i	−1.40201	−	0.109980i
$911$	1388.19			1.52380			0.761902	−	0.647692i	$-0.224266\pi$
$911$	1388.19			1.52380			0.761902	+	0.647692i	$0.224266\pi$
$912$			206.815i			0.226771i
$913$	227.437			0.249110
$914$	2614.90			2.86094
$915$	75.1416	+	83.3258i	0.0821219	+	0.0910664i
$916$			3782.70i			4.12958i
$917$	951.157	+	1003.32i	1.03725	+	1.09414i
$918$		−	570.518i		−	0.621479i
$919$	177.865			0.193542			0.0967708	−	0.995307i	$-0.469149\pi$
$919$	177.865			0.193542			0.0967708	+	0.995307i	$0.469149\pi$
$920$	−114.874	+	103.591i	−0.124863	+	0.112599i
$921$	−573.614			−0.622817
$922$	−1509.11			−1.63677
$923$	−347.145			−0.376105
$924$	−914.120	+	866.592i	−0.989307	+	0.937870i
$925$	−591.857	−	61.2976i	−0.639845	−	0.0662677i
$926$	2297.63			2.48124
$927$	332.667			0.358864
$928$		−	250.788i		−	0.270246i
$929$			272.252i			0.293059i	0.989206	+	0.146529i	$0.0468103\pi$
$929$			272.252i			0.293059i	−0.989206	+	0.146529i	$0.953190\pi$
$930$	217.678	−	196.297i	0.234062	−	0.211072i
$931$	−112.332	−	6.00065i	−0.120658	−	0.00644538i
$932$			142.414i			0.152805i
$933$			452.775i			0.485289i
$934$			933.924i			0.999918i
$935$	−1061.28	+	957.039i	−1.13506	+	1.02357i
$936$		−	711.459i		−	0.760106i
$937$	860.622			0.918486			0.459243	−	0.888311i	$-0.348121\pi$
$937$	860.622			0.918486			0.459243	+	0.888311i	$0.348121\pi$
$938$	2339.34	−	2217.71i	2.49396	−	2.36430i
$939$	827.389			0.881139
$940$	−1629.16	+	1469.14i	−1.73314	+	1.56292i
$941$			566.773i			0.602309i	0.953575	+	0.301155i	$0.0973720\pi$
$941$			566.773i			0.602309i	−0.953575	+	0.301155i	$0.902628\pi$
$942$		−	1768.30i		−	1.87717i
$943$	−74.8535			−0.0793780
$944$		−	1003.67i		−	1.06321i
$945$	14.2226	−	181.308i	0.0150504	−	0.191861i
$946$	1587.95			1.67859
$947$			742.573i			0.784132i	0.919937	+	0.392066i	$0.128240\pi$
$947$			742.573i			0.784132i	−0.919937	+	0.392066i	$0.871760\pi$
$948$	−832.727			−0.878404
$949$	−594.266			−0.626202
$950$	−22.5036	+	217.282i	−0.0236880	+	0.228718i
$951$			421.789i			0.443521i
$952$	−3429.56	−	3617.65i	−3.60248	−	3.80005i
$953$		−	498.229i		−	0.522800i	−0.965230	−	0.261400i	$-0.915816\pi$
$953$		−	498.229i		−	0.522800i	0.965230	−	0.261400i	$-0.0841842\pi$
$954$	536.994			0.562886
$955$	−1194.43	+	1077.12i	−1.25072	+	1.12787i
$956$	−2803.21			−2.93223
$957$	43.3780			0.0453270
$958$	−109.823			−0.114638
$959$	−231.097	−	243.771i	−0.240977	−	0.254193i
$960$	−1090.53	+	983.420i	−1.13597	+	1.02440i
$961$	881.920			0.917711
$962$	870.263			0.904640
$963$			609.818i			0.633248i
$964$		−	2172.93i		−	2.25407i
$965$	−514.359	−	570.382i	−0.533014	−	0.591069i
$966$	41.9692	−	39.7871i	0.0434464	−	0.0411875i
$967$		−	673.056i		−	0.696025i	−0.937490	−	0.348012i	$-0.886857\pi$
$967$		−	673.056i		−	0.696025i	0.937490	−	0.348012i	$-0.113143\pi$
$968$		−	563.809i		−	0.582447i
$969$		−	114.710i		−	0.118380i
$970$	−234.683	−	260.244i	−0.241941	−	0.268293i
$971$			1554.04i			1.60046i	0.599695	+	0.800229i	$0.295289\pi$
$971$			1554.04i			1.60046i	−0.599695	+	0.800229i	$0.704711\pi$
$972$	163.459			0.168168
$973$	−13.7918	−	14.5482i	−0.0141745	−	0.0149519i
$974$	−2030.57			−2.08477
$975$	42.8544	−	413.779i	0.0439532	−	0.424388i
$976$			673.855i			0.690425i
$977$		−	887.522i		−	0.908415i	−0.890896	−	0.454208i	$-0.849922\pi$
$977$		−	887.522i		−	0.908415i	0.890896	−	0.454208i	$-0.150078\pi$
$978$	555.429			0.567924
$979$			880.622i			0.899511i
$980$	−1616.26	−	1996.93i	−1.64924	−	2.03768i
$981$	−180.520			−0.184016
$982$			175.230i			0.178442i
$983$	−571.326			−0.581207			−0.290603	−	0.956844i	$-0.593856\pi$
$983$	−571.326			−0.581207			−0.290603	+	0.956844i	$0.593856\pi$
$984$	−2553.80			−2.59533
$985$	1094.31	+	1213.50i	1.11097	+	1.23198i
$986$			277.541i			0.281482i
$987$	368.162	−	349.020i	0.373011	−	0.353617i
$988$		−	231.270i		−	0.234079i
$989$	−52.7745			−0.0533615
$990$	−378.800	−	420.057i	−0.382626	−	0.424300i
$991$	−321.931			−0.324854			−0.162427	−	0.986721i	$-0.551932\pi$
$991$	−321.931			−0.324854			−0.162427	+	0.986721i	$0.551932\pi$
$992$	882.267			0.889382
$993$	−144.009			−0.145024
$994$	−662.337	−	698.662i	−0.666335	−	0.702880i
$995$	908.516	+	1007.47i	0.913081	+	1.01253i
$996$	−416.927			−0.418602
$997$	1449.94			1.45430			0.727150	−	0.686479i	$-0.240845\pi$
$997$	1449.94			1.45430			0.727150	+	0.686479i	$0.240845\pi$
$998$			1244.04i			1.24653i
$999$			123.673i			0.123797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.e.a.34.1	✓	16
3.2	odd	2		315.3.e.e.244.16		16
4.3	odd	2		1680.3.bd.c.769.10		16
5.2	odd	4		525.3.h.e.76.16		16
5.3	odd	4		525.3.h.e.76.1		16
5.4	even	2	inner	105.3.e.a.34.16	yes	16
7.6	odd	2	inner	105.3.e.a.34.2	yes	16
15.14	odd	2		315.3.e.e.244.1		16
20.19	odd	2		1680.3.bd.c.769.8		16
21.20	even	2		315.3.e.e.244.15		16
28.27	even	2		1680.3.bd.c.769.7		16
35.13	even	4		525.3.h.e.76.2		16
35.27	even	4		525.3.h.e.76.15		16
35.34	odd	2	inner	105.3.e.a.34.15	yes	16
105.104	even	2		315.3.e.e.244.2		16
140.139	even	2		1680.3.bd.c.769.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.e.a.34.1	✓	16	1.1	even	1	trivial
105.3.e.a.34.2	yes	16	7.6	odd	2	inner
105.3.e.a.34.15	yes	16	35.34	odd	2	inner
105.3.e.a.34.16	yes	16	5.4	even	2	inner
315.3.e.e.244.1		16	15.14	odd	2
315.3.e.e.244.2		16	105.104	even	2
315.3.e.e.244.15		16	21.20	even	2
315.3.e.e.244.16		16	3.2	odd	2
525.3.h.e.76.1		16	5.3	odd	4
525.3.h.e.76.2		16	35.13	even	4
525.3.h.e.76.15		16	35.27	even	4
525.3.h.e.76.16		16	5.2	odd	4
1680.3.bd.c.769.7		16	28.27	even	2
1680.3.bd.c.769.8		16	20.19	odd	2
1680.3.bd.c.769.9		16	140.139	even	2
1680.3.bd.c.769.10		16	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.80604i q^{2} -1.73205 q^{3} -10.4859 q^{4} +(-3.71318 + 3.34847i) q^{5} +6.59225i q^{6} +(5.08005 - 4.81592i) q^{7} +24.6856i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.80604i q^{2} -1.73205 q^{3} -10.4859 q^{4} +(-3.71318 + 3.34847i) q^{5} +6.59225i q^{6} +(5.08005 - 4.81592i) q^{7} +24.6856i q^{8} +3.00000 q^{9} +(12.7444 + 14.1325i) q^{10} -9.90760 q^{11} +18.1621 q^{12} -9.60692 q^{13} +(-18.3296 - 19.3349i) q^{14} +(6.43142 - 5.79973i) q^{15} +52.0108 q^{16} -28.8479 q^{17} -11.4181i q^{18} -2.29577i q^{19} +(38.9361 - 35.1118i) q^{20} +(-8.79890 + 8.34142i) q^{21} +37.7087i q^{22} -1.25323i q^{23} -42.7568i q^{24} +(2.57543 - 24.8670i) q^{25} +36.5643i q^{26} -5.19615 q^{27} +(-53.2690 + 50.4994i) q^{28} +2.52779 q^{29} +(-22.0740 - 24.4782i) q^{30} +8.89270i q^{31} -99.2125i q^{32} +17.1605 q^{33} +109.796i q^{34} +(-2.73715 + 34.8928i) q^{35} -31.4578 q^{36} -23.8009i q^{37} -8.73778 q^{38} +16.6397 q^{39} +(-82.6593 - 91.6623i) q^{40} -59.7286i q^{41} +(31.7478 + 33.4889i) q^{42} -42.1109i q^{43} +103.890 q^{44} +(-11.1395 + 10.0454i) q^{45} -4.76982 q^{46} -41.8418 q^{47} -90.0853 q^{48} +(2.61379 - 48.9302i) q^{49} +(-94.6447 - 9.80219i) q^{50} +49.9660 q^{51} +100.737 q^{52} +47.0300i q^{53} +19.7767i q^{54} +(36.7887 - 33.1753i) q^{55} +(118.884 + 125.404i) q^{56} +3.97639i q^{57} -9.62085i q^{58} -19.2974i q^{59} +(-67.4393 + 60.8155i) q^{60} +12.9561i q^{61} +33.8460 q^{62} +(15.2401 - 14.4478i) q^{63} -169.563 q^{64} +(35.6722 - 32.1685i) q^{65} -65.3133i q^{66} +120.991i q^{67} +302.497 q^{68} +2.17065i q^{69} +(132.803 + 10.4177i) q^{70} +36.1349 q^{71} +74.0569i q^{72} +61.8581 q^{73} -90.5871 q^{74} +(-4.46078 + 43.0709i) q^{75} +24.0732i q^{76} +(-50.3311 + 47.7142i) q^{77} -63.3312i q^{78} -45.8496 q^{79} +(-193.126 + 174.157i) q^{80} +9.00000 q^{81} -227.329 q^{82} -22.9558 q^{83} +(92.2646 - 87.4675i) q^{84} +(107.118 - 96.5965i) q^{85} -160.276 q^{86} -4.37825 q^{87} -244.575i q^{88} -88.8835i q^{89} +(38.2333 + 42.3975i) q^{90} +(-48.8036 + 46.2662i) q^{91} +13.1412i q^{92} -15.4026i q^{93} +159.251i q^{94} +(7.68732 + 8.52460i) q^{95} +171.841i q^{96} -18.4146 q^{97} +(-186.230 - 9.94818i) q^{98} -29.7228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) \) 16 * q - 32 * q^4 + 48 * q^9	\( 16 q - 32 q^{4} + 48 q^{9} - 56 q^{11} - 84 q^{14} + 24 q^{15} + 112 q^{16} - 12 q^{21} + 16 q^{25} - 32 q^{29} - 72 q^{30} - 4 q^{35} - 96 q^{36} + 72 q^{39} + 568 q^{44} - 96 q^{46} - 152 q^{49} - 96 q^{50} + 24 q^{51} + 444 q^{56} - 288 q^{60} - 992 q^{64} - 296 q^{65} + 504 q^{70} - 56 q^{71} - 48 q^{74} + 464 q^{79} + 144 q^{81} + 228 q^{84} + 608 q^{85} - 456 q^{86} - 88 q^{91} - 24 q^{95} - 168 q^{99}+O(q^{100}) \) 16 * q - 32 * q^4 + 48 * q^9 - 56 * q^11 - 84 * q^14 + 24 * q^15 + 112 * q^16 - 12 * q^21 + 16 * q^25 - 32 * q^29 - 72 * q^30 - 4 * q^35 - 96 * q^36 + 72 * q^39 + 568 * q^44 - 96 * q^46 - 152 * q^49 - 96 * q^50 + 24 * q^51 + 444 * q^56 - 288 * q^60 - 992 * q^64 - 296 * q^65 + 504 * q^70 - 56 * q^71 - 48 * q^74 + 464 * q^79 + 144 * q^81 + 228 * q^84 + 608 * q^85 - 456 * q^86 - 88 * q^91 - 24 * q^95 - 168 * q^99

Introduction

L-functions

Modular forms

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Database

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