LMFDB - Embedded newform 105.3.e.a.34.16

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			34.16
Root			$-0.366025 - 1.39311i$ of defining polynomial
Character	$\chi$	$=$	105.34
Dual form			105.3.e.a.34.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.80604i q^{2} +1.73205 q^{3} -10.4859 q^{4} +(3.71318 + 3.34847i) q^{5} +6.59225i q^{6} +(-5.08005 + 4.81592i) q^{7} -24.6856i q^{8} +3.00000 q^{9} +O(q^{10})$	\(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} +(-34.9891 + 0.871978i) 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} +(-3.31878 - 133.170i) 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	$0.400467\pi$
$2$			3.80604i			1.90302i	−0.307620	+	0.951509i	$0.599533\pi$
$3$	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	$-0.379530\pi$
$13$	9.60692			0.738994			0.369497	+	0.929232i	$0.379530\pi$
$14$	−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	$-0.177525\pi$
$17$	28.8479			1.69694			0.848468	+	0.529247i	$0.177525\pi$
$18$			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	$0.00867312\pi$
$23$			1.25323i			0.0544881i	−0.999629	+	0.0272440i	$0.991327\pi$
$24$		−	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
$35$	−34.9891	+	0.871978i	−0.999690	+	0.0249136i
$36$	−31.4578			−0.873826
$37$			23.8009i			0.643268i	0.946864	+	0.321634i	$0.104232\pi$
$37$			23.8009i			0.643268i	−0.946864	+	0.321634i	$0.895768\pi$
$38$	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	$0.162880\pi$
$43$			42.1109i			0.979323i	−0.871912	+	0.489662i	$0.837120\pi$
$44$	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	$-0.353159\pi$
$47$	41.8418			0.890250			0.445125	+	0.895468i	$0.353159\pi$
$48$	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	$-0.853673\pi$
$53$		−	47.0300i		−	0.887358i	0.896186	−	0.443679i	$-0.146327\pi$
$54$			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	$-0.641422\pi$
$67$		−	120.991i		−	1.80583i	0.429817	−	0.902916i	$-0.358578\pi$
$68$	−302.497			−4.44848
$69$			2.17065i			0.0314587i
$70$	−3.31878	−	133.170i	−0.0474111	−	1.90243i
$71$	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	$-0.639264\pi$
$73$	−61.8581			−0.847372			−0.423686	+	0.905809i	$0.639264\pi$
$74$	−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	$-0.455840\pi$
$83$	22.9558			0.276576			0.138288	+	0.990392i	$0.455840\pi$
$84$	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	$-0.469740\pi$
$97$	18.4146			0.189841			0.0949205	+	0.995485i	$0.469740\pi$
$98$	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	$-0.680932\pi$
$103$	−110.889			−1.07659			−0.538296	+	0.842756i	$0.680932\pi$
$104$		−	237.153i		−	2.28032i
$105$	−60.6030	+	1.51031i	−0.577171	+	0.0143839i
$106$	178.998			1.68866
$107$		−	203.273i		−	1.89974i	−0.312638	−	0.949872i	$-0.601213\pi$
$107$		−	203.273i		−	1.89974i	0.312638	−	0.949872i	$-0.398787\pi$
$108$	−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	$0.163378\pi$
$113$			110.972i			0.982051i	−0.871145	+	0.491026i	$0.836622\pi$
$114$	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	$0.0925354\pi$
$127$			72.8043i			0.573262i	−0.958041	+	0.286631i	$0.907465\pi$
$128$		−	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	$0.0560350\pi$
$137$			47.9860i			0.350263i	−0.984545	+	0.175131i	$0.943965\pi$
$138$	−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	$-0.00327909\pi$
$140$	366.893	−	9.14349i	2.62067	−	0.0653106i
$141$	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	$-0.174008\pi$
$157$	268.239			1.70853			0.854264	+	0.519839i	$0.174008\pi$
$158$		−	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	$0.0832119\pi$
$163$			84.2549i			0.516901i	−0.966024	+	0.258451i	$0.916788\pi$
$164$			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	$-0.511785\pi$
$167$	−12.3631			−0.0740303			−0.0370151	+	0.999315i	$0.511785\pi$
$168$	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	$-0.351957\pi$
$173$	155.182			0.897006			0.448503	+	0.893781i	$0.351957\pi$
$174$			16.6638i			0.0957689i
$175$	−132.841	−	113.922i	−0.759090	−	0.650985i
$176$	−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	$-0.869721\pi$
$193$		−	153.610i		−	0.795906i	0.917406	−	0.397953i	$-0.130279\pi$
$194$			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	$0.311352\pi$
$197$			326.808i			1.65892i	−0.558565	+	0.829461i	$0.688648\pi$
$198$		−	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
$210$	−5.74829	−	230.657i	−0.0273728	−	1.09837i
$211$	−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	$-0.492959\pi$
$223$	9.86531			0.0442391			0.0221195	+	0.999755i	$0.492959\pi$
$224$	−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	$-0.705077\pi$
$227$	−272.679			−1.20123			−0.600614	+	0.799539i	$0.705077\pi$
$228$			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	$0.00927840\pi$
$233$			13.5815i			0.0582897i	−0.999575	+	0.0291448i	$0.990722\pi$
$234$			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
$245$	173.547	−	172.935i	0.708356	−	0.705856i
$246$	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	$-0.400844\pi$
$257$	157.539			0.612991			0.306496	+	0.951872i	$0.400844\pi$
$258$	−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	$-0.979251\pi$
$263$		−	34.2625i		−	0.130276i	0.997876	−	0.0651378i	$-0.0207487\pi$
$264$			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	$-0.983668\pi$
$277$		−	28.4117i		−	0.102569i	0.998684	−	0.0512846i	$-0.0163316\pi$
$278$	10.8997			0.0392075
$279$			26.6781i			0.0956205i
$280$	21.5253	+	863.729i	0.0768762	+	3.08475i
$281$	−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	$-0.418187\pi$
$283$	143.879			0.508406			0.254203	+	0.967151i	$0.418187\pi$
$284$	−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	$-0.613444\pi$
$293$	−204.454			−0.697795			−0.348897	+	0.937161i	$0.613444\pi$
$294$	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	$-0.681339\pi$
$307$	−331.176			−1.07875			−0.539375	+	0.842066i	$0.681339\pi$
$308$	−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	$-0.223682\pi$
$313$	477.693			1.52618			0.763088	+	0.646294i	$0.223682\pi$
$314$			1020.93i			3.25136i
$315$	−104.967	+	2.61593i	−0.333230	+	0.00830455i
$316$	480.775			1.52144
$317$			243.520i			0.768201i	0.923291	+	0.384101i	$0.125488\pi$
$317$			243.520i			0.768201i	−0.923291	+	0.384101i	$0.874512\pi$
$318$	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	$0.0934149\pi$
$337$			194.973i			0.578554i	−0.957245	+	0.289277i	$0.906585\pi$
$338$		−	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	$0.146717\pi$
$347$			308.676i			0.889556i	−0.895641	+	0.444778i	$0.853283\pi$
$348$	−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	$0.711378\pi$
$350$	433.593	−	505.597i	1.23884	−	1.44456i
$351$	49.9190			0.142219
$352$		−	982.957i		−	2.79249i
$353$	−528.729			−1.49781			−0.748907	−	0.662675i	$-0.769421\pi$
$353$	−528.729			−1.49781			−0.748907	+	0.662675i	$0.769421\pi$
$354$	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	$-0.463712\pi$
$367$	83.4973			0.227513			0.113757	+	0.993509i	$0.463712\pi$
$368$			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	$-0.930494\pi$
$373$		−	161.604i		−	0.433254i	0.976254	−	0.216627i	$-0.0695055\pi$
$374$		−	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	$-0.176771\pi$
$383$	650.885			1.69944			0.849719	+	0.527235i	$0.176771\pi$
$384$		−	430.438i		−	1.12093i
$385$	346.658	−	8.63920i	0.900411	−	0.0224395i
$386$	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	$-0.644677\pi$
$397$	−348.588			−0.878056			−0.439028	+	0.898473i	$0.644677\pi$
$398$	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	$0.975269\pi$
$420$	635.478	−	15.8370i	1.51304	−	0.0377071i
$421$	−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	$-0.592346\pi$
$433$	−247.729			−0.572122			−0.286061	+	0.958211i	$0.592346\pi$
$434$	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	$-0.776967\pi$
$443$		−	571.236i		−	1.28947i	0.764405	−	0.644736i	$-0.223033\pi$
$444$		−	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
$455$	−336.138	+	8.37702i	−0.738764	+	0.0184110i
$456$	−98.1596			−0.215262
$457$		−	687.039i		−	1.50337i	−0.659524	−	0.751684i	$-0.729242\pi$
$457$		−	687.039i		−	1.50337i	0.659524	−	0.751684i	$-0.270758\pi$
$458$	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	$-0.773963\pi$
$463$		−	603.681i		−	1.30385i	0.758285	−	0.651923i	$-0.226037\pi$
$464$	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	$-0.415381\pi$
$467$	245.380			0.525438			0.262719	+	0.964872i	$0.415381\pi$
$468$	−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	$0.184517\pi$
$487$			533.512i			1.09551i	−0.836639	+	0.547754i	$0.815483\pi$
$488$	319.828			0.655386
$489$			145.934i			0.298433i
$490$	658.196	+	660.527i	1.34326	+	1.34801i
$491$	−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	$-0.527957\pi$
$503$	−88.2437			−0.175435			−0.0877174	+	0.996145i	$0.527957\pi$
$504$	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	$-0.873589\pi$
$523$	−964.595			−1.84435			−0.922175	+	0.386774i	$0.873589\pi$
$524$		−	2071.00i		−	3.95228i
$525$	−230.087	−	197.319i	−0.438261	−	0.375847i
$526$	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	$0.00819954\pi$
$547$			28.1779i			0.0515136i	−0.999668	+	0.0257568i	$0.991800\pi$
$548$		−	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	$0.0456088\pi$
$557$			159.073i			0.285589i	−0.989752	+	0.142795i	$0.954391\pi$
$558$	−101.538			−0.181968
$559$			404.556i			0.723714i
$560$	−1819.81	+	45.3523i	−3.24967	+	0.0809862i
$561$	−495.043			−0.882430
$562$		−	961.920i		−	1.71160i
$563$	−644.468			−1.14470			−0.572351	−	0.820008i	$-0.693969\pi$
$563$	−644.468			−1.14470			−0.572351	+	0.820008i	$0.693969\pi$
$564$	−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	$-0.312325\pi$
$577$	641.655			1.11205			0.556027	+	0.831165i	$0.312325\pi$
$578$			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	$-0.354365\pi$
$587$	518.592			0.883462			0.441731	+	0.897148i	$0.354365\pi$
$588$	−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	$-0.696356\pi$
$593$	−686.085			−1.15697			−0.578486	+	0.815692i	$0.696356\pi$
$594$		−	195.940i		−	0.329865i
$595$	−1009.36	+	25.1547i	−1.69641	+	0.0422769i
$596$	−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	$-0.406812\pi$
$607$	350.355			0.577191			0.288595	+	0.957451i	$0.406812\pi$
$608$	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	$0.159610\pi$
$613$			589.314i			0.961360i	−0.876896	+	0.480680i	$0.840390\pi$
$614$		−	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	$-0.833904\pi$
$617$		−	615.085i		−	0.996896i	0.866920	−	0.498448i	$-0.166096\pi$
$618$		−	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
$630$	−9.95634	−	399.510i	−0.0158037	−	0.634143i
$631$	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	$-0.517542\pi$
$643$	−70.8343			−0.110162			−0.0550811	+	0.998482i	$0.517542\pi$
$644$	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	$-0.393079\pi$
$647$	426.531			0.659243			0.329622	+	0.944113i	$0.393079\pi$
$648$		−	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	$0.0804829\pi$
$653$			326.708i			0.500318i	−0.968205	+	0.250159i	$0.919517\pi$
$654$		−	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
$665$	2.00186	+	80.3269i	0.00301031	+	0.120792i
$666$	−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	$0.0319179\pi$
$673$			134.741i			0.200210i	−0.994977	+	0.100105i	$0.968082\pi$
$674$	−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	$-0.349226\pi$
$677$	617.636			0.912313			0.456157	+	0.889900i	$0.349226\pi$
$678$	−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	$0.113345\pi$
$683$			476.196i			0.697213i	−0.937269	+	0.348606i	$0.886655\pi$
$684$			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
$700$	1392.96	+	1194.58i	1.98994	+	1.70654i
$701$	−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	$-0.463647\pi$
$727$	165.693			0.227914			0.113957	+	0.993486i	$0.463647\pi$
$728$	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	$-0.210740\pi$
$733$	1156.28			1.57746			0.788728	+	0.614742i	$0.210740\pi$
$734$			317.794i			0.432962i
$735$	300.592	−	299.532i	0.408969	−	0.407526i
$736$	−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	$0.293189\pi$
$743$			1183.23i			1.59251i	−0.604961	+	0.796255i	$0.706811\pi$
$744$	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	$0.156492\pi$
$757$			714.710i			0.944135i	−0.881562	+	0.472068i	$0.843508\pi$
$758$		−	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	$0.780773\pi$
$770$	32.8811	+	1319.39i	0.0427028	+	1.71350i
$771$	272.865			0.353911
$772$			1610.74i			2.08645i
$773$	−1145.61			−1.48203			−0.741016	−	0.671487i	$-0.765656\pi$
$773$	−1145.61			−1.48203			−0.741016	+	0.671487i	$0.765656\pi$
$774$	−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	$-0.512577\pi$
$787$	−62.1774			−0.0790056			−0.0395028	+	0.999219i	$0.512577\pi$
$788$		−	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	$-0.395032\pi$
$797$	516.172			0.647643			0.323822	+	0.946118i	$0.395032\pi$
$798$	−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
$805$	−1.09279	−	43.8493i	−0.00135750	−	0.0544712i
$806$	−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	$0.362755\pi$
$823$			1495.35i			1.81696i	−0.417933	+	0.908478i	$0.637245\pi$
$824$			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	$-0.877244\pi$
$827$		−	622.172i		−	0.752324i	0.926554	−	0.376162i	$-0.122756\pi$
$828$		−	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	$0.850956\pi$
$840$	37.2830	+	1496.02i	0.0443845	+	1.78098i
$841$	−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	$-0.592887\pi$
$853$	−490.797			−0.575377			−0.287689	+	0.957724i	$0.592887\pi$
$854$	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	$-0.293159\pi$
$857$	1037.03			1.21007			0.605035	+	0.796199i	$0.293159\pi$
$858$		−	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	$-0.959945\pi$
$863$		−	216.622i		−	0.251011i	0.992093	−	0.125505i	$-0.0400552\pi$
$864$			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
$875$	−111.796	−	867.829i	−0.127766	−	0.991804i
$876$	1123.48			1.28251
$877$			900.305i			1.02657i	0.858217	+	0.513287i	$0.171572\pi$
$877$			900.305i			1.02657i	−0.858217	+	0.513287i	$0.828428\pi$
$878$	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	$-0.856880\pi$
$883$		−	767.552i		−	0.869255i	0.900610	−	0.434627i	$-0.143120\pi$
$884$	−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	$-0.632677\pi$
$887$	−718.207			−0.809704			−0.404852	+	0.914382i	$0.632677\pi$
$888$	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	$-0.801341\pi$
$907$		−	1060.05i		−	1.16874i	0.811486	−	0.584371i	$-0.198659\pi$
$908$	2859.29			3.14899
$909$		−	226.188i		−	0.248831i
$910$	−31.8832	−	1279.35i	−0.0350365	−	1.40588i
$911$	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	$-0.651879\pi$
$937$	−860.622			−0.918486			−0.459243	+	0.888311i	$0.651879\pi$
$938$	−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
$945$	−181.809	+	4.53093i	−0.192390	+	0.00479463i
$946$	1587.95			1.67859
$947$		−	742.573i		−	0.784132i	−0.919937	−	0.392066i	$-0.871760\pi$
$947$		−	742.573i		−	0.784132i	0.919937	−	0.392066i	$-0.128240\pi$
$948$	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	$0.0841842\pi$
$953$			498.229i			0.522800i	−0.965230	+	0.261400i	$0.915816\pi$
$954$	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	$0.113143\pi$
$967$			673.056i			0.696025i	−0.937490	+	0.348012i	$0.886857\pi$
$968$			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	$0.150078\pi$
$977$			887.522i			0.908415i	−0.890896	+	0.454208i	$0.849922\pi$
$978$	−555.429			−0.567924
$979$			880.622i			0.899511i
$980$	−1819.80	+	1813.38i	−1.85694	+	1.85039i
$981$	−180.520			−0.184016
$982$		−	175.230i		−	0.178442i
$983$	571.326			0.581207			0.290603	−	0.956844i	$-0.406144\pi$
$983$	571.326			0.581207			0.290603	+	0.956844i	$0.406144\pi$
$984$	−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	$-0.759155\pi$
$997$	−1449.94			−1.45430			−0.727150	+	0.686479i	$0.759155\pi$
$998$		−	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.34.16	yes	16
3.2	odd	2		315.3.e.e.244.1		16
4.3	odd	2		1680.3.bd.c.769.8		16
5.2	odd	4		525.3.h.e.76.1		16
5.3	odd	4		525.3.h.e.76.16		16
5.4	even	2	inner	105.3.e.a.34.1	✓	16
7.6	odd	2	inner	105.3.e.a.34.15	yes	16
15.14	odd	2		315.3.e.e.244.16		16
20.19	odd	2		1680.3.bd.c.769.10		16
21.20	even	2		315.3.e.e.244.2		16
28.27	even	2		1680.3.bd.c.769.9		16
35.13	even	4		525.3.h.e.76.15		16
35.27	even	4		525.3.h.e.76.2		16
35.34	odd	2	inner	105.3.e.a.34.2	yes	16
105.104	even	2		315.3.e.e.244.15		16
140.139	even	2		1680.3.bd.c.769.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.e.a.34.1	✓	16	5.4	even	2	inner
105.3.e.a.34.2	yes	16	35.34	odd	2	inner
105.3.e.a.34.15	yes	16	7.6	odd	2	inner
105.3.e.a.34.16	yes	16	1.1	even	1	trivial
315.3.e.e.244.1		16	3.2	odd	2
315.3.e.e.244.2		16	21.20	even	2
315.3.e.e.244.15		16	105.104	even	2
315.3.e.e.244.16		16	15.14	odd	2
525.3.h.e.76.1		16	5.2	odd	4
525.3.h.e.76.2		16	35.27	even	4
525.3.h.e.76.15		16	35.13	even	4
525.3.h.e.76.16		16	5.3	odd	4
1680.3.bd.c.769.7		16	140.139	even	2
1680.3.bd.c.769.8		16	4.3	odd	2
1680.3.bd.c.769.9		16	28.27	even	2
1680.3.bd.c.769.10		16	20.19	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} +(-34.9891 + 0.871978i) 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} +(-3.31878 - 133.170i) 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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