LMFDB - Embedded newform 105.3.h.a.76.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(76,105)]

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, 0, 1]))

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

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

chi := DirichletCharacter("105.76");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.h (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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 21x^10 - 26x^9 + 295x^8 - 372x^7 + 1704x^6 - 1074x^5 + 5613x^4 - 5472x^3 + 4950x^2 - 1638*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.9
Root			$0.378061 - 0.654821i$ of defining polynomial
Character	$\chi$	$=$	105.76
Dual form			105.3.h.a.76.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.91758 q^{2} -1.73205i q^{3} +4.51225 q^{4} -2.23607i q^{5} -5.05339i q^{6} +(6.13981 + 3.36195i) q^{7} +1.49451 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+2.91758 q^{2} -1.73205i q^{3} +4.51225 q^{4} -2.23607i q^{5} -5.05339i q^{6} +(6.13981 + 3.36195i) q^{7} +1.49451 q^{8} -3.00000 q^{9} -6.52390i q^{10} -2.58757 q^{11} -7.81544i q^{12} -0.0498225i q^{13} +(17.9134 + 9.80876i) q^{14} -3.87298 q^{15} -13.6886 q^{16} +14.2114i q^{17} -8.75273 q^{18} +14.9314i q^{19} -10.0897i q^{20} +(5.82308 - 10.6345i) q^{21} -7.54942 q^{22} -22.2765 q^{23} -2.58857i q^{24} -5.00000 q^{25} -0.145361i q^{26} +5.19615i q^{27} +(27.7043 + 15.1700i) q^{28} +17.4169 q^{29} -11.2997 q^{30} -6.36515i q^{31} -45.9156 q^{32} +4.48180i q^{33} +41.4628i q^{34} +(7.51756 - 13.7290i) q^{35} -13.5367 q^{36} -7.14160 q^{37} +43.5635i q^{38} -0.0862951 q^{39} -3.34183i q^{40} -74.5035i q^{41} +(16.9893 - 31.0268i) q^{42} +79.2782 q^{43} -11.6757 q^{44} +6.70820i q^{45} -64.9935 q^{46} -81.3603i q^{47} +23.7094i q^{48} +(26.3945 + 41.2835i) q^{49} -14.5879 q^{50} +24.6149 q^{51} -0.224811i q^{52} -67.1978 q^{53} +15.1602i q^{54} +5.78598i q^{55} +(9.17603 + 5.02449i) q^{56} +25.8620 q^{57} +50.8151 q^{58} -4.33175i q^{59} -17.4759 q^{60} +109.670i q^{61} -18.5708i q^{62} +(-18.4194 - 10.0859i) q^{63} -79.2079 q^{64} -0.111407 q^{65} +13.0760i q^{66} -49.1800 q^{67} +64.1253i q^{68} +38.5841i q^{69} +(21.9330 - 40.0555i) q^{70} +97.3864 q^{71} -4.48354 q^{72} -116.398i q^{73} -20.8362 q^{74} +8.66025i q^{75} +67.3742i q^{76} +(-15.8872 - 8.69929i) q^{77} -0.251773 q^{78} +98.8343 q^{79} +30.6087i q^{80} +9.00000 q^{81} -217.370i q^{82} -112.111i q^{83} +(26.2752 - 47.9853i) q^{84} +31.7777 q^{85} +231.300 q^{86} -30.1669i q^{87} -3.86716 q^{88} +77.7603i q^{89} +19.5717i q^{90} +(0.167501 - 0.305901i) q^{91} -100.517 q^{92} -11.0248 q^{93} -237.375i q^{94} +33.3877 q^{95} +79.5282i q^{96} +109.997i q^{97} +(77.0080 + 120.448i) q^{98} +7.76270 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9	$ 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} + 12 q^{18} + 36 q^{21} - 88 q^{22} - 64 q^{23} - 60 q^{25} + 88 q^{28} + 104 q^{29} - 228 q^{32} + 60 q^{35} - 132 q^{36} + 32 q^{37} - 24 q^{39} - 60 q^{42} + 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 20 q^{50} + 24 q^{51} + 176 q^{53} - 368 q^{56} - 240 q^{57} - 400 q^{58} + 24 q^{63} - 20 q^{64} - 240 q^{65} + 168 q^{67} - 60 q^{70} + 32 q^{71} - 12 q^{72} + 184 q^{74} + 8 q^{77} + 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 120 q^{85} + 400 q^{86} - 536 q^{88} + 24 q^{91} + 192 q^{92} + 48 q^{93} + 884 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 + 12 * q^18 + 36 * q^21 - 88 * q^22 - 64 * q^23 - 60 * q^25 + 88 * q^28 + 104 * q^29 - 228 * q^32 + 60 * q^35 - 132 * q^36 + 32 * q^37 - 24 * q^39 - 60 * q^42 + 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 20 * q^50 + 24 * q^51 + 176 * q^53 - 368 * q^56 - 240 * q^57 - 400 * q^58 + 24 * q^63 - 20 * q^64 - 240 * q^65 + 168 * q^67 - 60 * q^70 + 32 * q^71 - 12 * q^72 + 184 * q^74 + 8 * q^77 + 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 120 * q^85 + 400 * q^86 - 536 * q^88 + 24 * q^91 + 192 * q^92 + 48 * q^93 + 884 * q^98 + 48 * 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 $

$2$	2.91758			1.45879			0.729394	−	0.684094i	$-0.239802\pi$
$2$	2.91758			1.45879			0.729394	+	0.684094i	$0.239802\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	4.51225			1.12806
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$		−	5.05339i		−	0.842231i
$7$	6.13981	+	3.36195i	0.877116	+	0.480279i
$7$	6.13981	+	3.36195i	0.877116	+	0.480279i
$8$	1.49451			0.186814
$9$	−3.00000			−0.333333
$10$		−	6.52390i		−	0.652390i
$11$	−2.58757			−0.235233			−0.117617	−	0.993059i	$-0.537525\pi$
$11$	−2.58757			−0.235233			−0.117617	+	0.993059i	$0.537525\pi$
$12$		−	7.81544i		−	0.651286i
$13$		−	0.0498225i		−	0.00383250i	−0.999998	−	0.00191625i	$-0.999390\pi$
$13$		−	0.0498225i		−	0.00383250i	0.999998	−	0.00191625i	$-0.000609962\pi$
$14$	17.9134	+	9.80876i	1.27953	+	0.700625i
$15$	−3.87298			−0.258199
$16$	−13.6886			−0.855539
$17$			14.2114i			0.835965i	0.908455	+	0.417982i	$0.137263\pi$
$17$			14.2114i			0.835965i	−0.908455	+	0.417982i	$0.862737\pi$
$18$	−8.75273			−0.486263
$19$			14.9314i			0.785864i	0.919567	+	0.392932i	$0.128539\pi$
$19$			14.9314i			0.785864i	−0.919567	+	0.392932i	$0.871461\pi$
$20$		−	10.0897i		−	0.504484i
$21$	5.82308	−	10.6345i	0.277289	−	0.506403i
$22$	−7.54942			−0.343156
$23$	−22.2765			−0.968545			−0.484273	−	0.874917i	$-0.660916\pi$
$23$	−22.2765			−0.968545			−0.484273	+	0.874917i	$0.660916\pi$
$24$		−	2.58857i		−	0.107857i
$25$	−5.00000			−0.200000
$26$		−	0.145361i		−	0.00559081i
$27$			5.19615i			0.192450i
$28$	27.7043	+	15.1700i	0.989440	+	0.541784i
$29$	17.4169			0.600583			0.300291	−	0.953848i	$-0.402916\pi$
$29$	17.4169			0.600583			0.300291	+	0.953848i	$0.402916\pi$
$30$	−11.2997			−0.376657
$31$		−	6.36515i		−	0.205327i	−0.994716	−	0.102664i	$-0.967263\pi$
$31$		−	6.36515i		−	0.205327i	0.994716	−	0.102664i	$-0.0327365\pi$
$32$	−45.9156			−1.43486
$33$			4.48180i			0.135812i
$34$			41.4628i			1.21950i
$35$	7.51756	−	13.7290i	0.214787	−	0.392258i
$36$	−13.5367			−0.376020
$37$	−7.14160			−0.193016			−0.0965081	−	0.995332i	$-0.530767\pi$
$37$	−7.14160			−0.193016			−0.0965081	+	0.995332i	$0.530767\pi$
$38$			43.5635i			1.14641i
$39$	−0.0862951			−0.00221270
$40$		−	3.34183i		−	0.0835459i
$41$		−	74.5035i		−	1.81716i	−0.417713	−	0.908579i	$-0.637168\pi$
$41$		−	74.5035i		−	1.81716i	0.417713	−	0.908579i	$-0.362832\pi$
$42$	16.9893	−	31.0268i	0.404506	−	0.738734i
$43$	79.2782			1.84368			0.921840	−	0.387570i	$-0.126686\pi$
$43$	79.2782			1.84368			0.921840	+	0.387570i	$0.126686\pi$
$44$	−11.6757			−0.265358
$45$			6.70820i			0.149071i
$46$	−64.9935			−1.41290
$47$		−	81.3603i		−	1.73107i	−0.500848	−	0.865535i	$-0.666978\pi$
$47$		−	81.3603i		−	1.73107i	0.500848	−	0.865535i	$-0.333022\pi$
$48$			23.7094i			0.493946i
$49$	26.3945	+	41.2835i	0.538664	+	0.842521i
$50$	−14.5879			−0.291758
$51$	24.6149			0.482644
$52$		−	0.224811i		−	0.00432330i
$53$	−67.1978			−1.26788			−0.633942	−	0.773381i	$-0.718564\pi$
$53$	−67.1978			−1.26788			−0.633942	+	0.773381i	$0.718564\pi$
$54$			15.1602i			0.280744i
$55$			5.78598i			0.105200i
$56$	9.17603	+	5.02449i	0.163858	+	0.0897230i
$57$	25.8620			0.453719
$58$	50.8151			0.876122
$59$		−	4.33175i		−	0.0734195i	−0.999326	−	0.0367097i	$-0.988312\pi$
$59$		−	4.33175i		−	0.0734195i	0.999326	−	0.0367097i	$-0.0116877\pi$
$60$	−17.4759			−0.291264
$61$			109.670i			1.79787i	0.438082	+	0.898935i	$0.355658\pi$
$61$			109.670i			1.79787i	−0.438082	+	0.898935i	$0.644342\pi$
$62$		−	18.5708i		−	0.299529i
$63$	−18.4194	−	10.0859i	−0.292372	−	0.160093i
$64$	−79.2079			−1.23762
$65$	−0.111407			−0.00171395
$66$			13.0760i			0.198121i
$67$	−49.1800			−0.734030			−0.367015	−	0.930215i	$-0.619620\pi$
$67$	−49.1800			−0.734030			−0.367015	+	0.930215i	$0.619620\pi$
$68$			64.1253i			0.943020i
$69$			38.5841i			0.559190i
$70$	21.9330	−	40.0555i	0.313329	−	0.572221i
$71$	97.3864			1.37164			0.685819	−	0.727772i	$-0.259444\pi$
$71$	97.3864			1.37164			0.685819	+	0.727772i	$0.259444\pi$
$72$	−4.48354			−0.0622714
$73$		−	116.398i		−	1.59450i	−0.603651	−	0.797249i	$-0.706288\pi$
$73$		−	116.398i		−	1.59450i	0.603651	−	0.797249i	$-0.293712\pi$
$74$	−20.8362			−0.281570
$75$			8.66025i			0.115470i
$76$			67.3742i			0.886503i
$77$	−15.8872	−	8.69929i	−0.206327	−	0.112978i
$78$	−0.251773			−0.00322785
$79$	98.8343			1.25107			0.625534	−	0.780197i	$-0.284881\pi$
$79$	98.8343			1.25107			0.625534	+	0.780197i	$0.284881\pi$
$80$			30.6087i			0.382609i
$81$	9.00000			0.111111
$82$		−	217.370i		−	2.65085i
$83$		−	112.111i		−	1.35073i	−0.737484	−	0.675365i	$-0.763986\pi$
$83$		−	112.111i		−	1.35073i	0.737484	−	0.675365i	$-0.236014\pi$
$84$	26.2752	−	47.9853i	0.312799	−	0.571254i
$85$	31.7777			0.373855
$86$	231.300			2.68954
$87$		−	30.1669i		−	0.346747i
$88$	−3.86716			−0.0439450
$89$			77.7603i			0.873711i	0.899532	+	0.436855i	$0.143908\pi$
$89$			77.7603i			0.873711i	−0.899532	+	0.436855i	$0.856092\pi$
$90$			19.5717i			0.217463i
$91$	0.167501	−	0.305901i	0.00184067	−	0.00336155i
$92$	−100.517			−1.09258
$93$	−11.0248			−0.118546
$94$		−	237.375i		−	2.52526i
$95$	33.3877			0.351449
$96$			79.5282i			0.828419i
$97$			109.997i			1.13399i	0.823723	+	0.566993i	$0.191893\pi$
$97$			109.997i			1.13399i	−0.823723	+	0.566993i	$0.808107\pi$
$98$	77.0080	+	120.448i	0.785796	+	1.22906i
$99$	7.76270			0.0784111
$100$	−22.5612			−0.225612
$101$			96.7400i			0.957822i	0.877864	+	0.478911i	$0.158968\pi$
$101$			96.7400i			0.957822i	−0.877864	+	0.478911i	$0.841032\pi$
$102$	71.8157			0.704076
$103$		−	106.961i		−	1.03846i	−0.854635	−	0.519230i	$-0.826219\pi$
$103$		−	106.961i		−	1.03846i	0.854635	−	0.519230i	$-0.173781\pi$
$104$		−	0.0744604i		−	0.000715966i
$105$	−23.7794	−	13.0208i	−0.226470	−	0.124008i
$106$	−196.055			−1.84957
$107$	33.0838			0.309195			0.154597	−	0.987978i	$-0.450592\pi$
$107$	33.0838			0.309195			0.154597	+	0.987978i	$0.450592\pi$
$108$			23.4463i			0.217095i
$109$	−49.8791			−0.457607			−0.228803	−	0.973473i	$-0.573481\pi$
$109$	−49.8791			−0.457607			−0.228803	+	0.973473i	$0.573481\pi$
$110$			16.8810i			0.153464i
$111$			12.3696i			0.111438i
$112$	−84.0455	−	46.0205i	−0.750407	−	0.410898i
$113$	−111.225			−0.984291			−0.492146	−	0.870513i	$-0.663787\pi$
$113$	−111.225			−0.984291			−0.492146	+	0.870513i	$0.663787\pi$
$114$	75.4543			0.661880
$115$			49.8118i			0.433146i
$116$	78.5893			0.677494
$117$			0.149468i			0.00127750i
$118$		−	12.6382i		−	0.107103i
$119$	−47.7781	+	87.2553i	−0.401497	+	0.733238i
$120$	−5.78823			−0.0482352
$121$	−114.304			−0.944665
$122$			319.971i			2.62271i
$123$	−129.044			−1.04914
$124$		−	28.7211i		−	0.231622i
$125$			11.1803i			0.0894427i
$126$	−53.7401	−	29.4263i	−0.426508	−	0.233542i
$127$	−69.4347			−0.546730			−0.273365	−	0.961910i	$-0.588137\pi$
$127$	−69.4347			−0.546730			−0.273365	+	0.961910i	$0.588137\pi$
$128$	−47.4323			−0.370565
$129$		−	137.314i		−	1.06445i
$130$	−0.325037			−0.00250028
$131$			39.7493i			0.303430i	0.988424	+	0.151715i	$0.0484796\pi$
$131$			39.7493i			0.303430i	−0.988424	+	0.151715i	$0.951520\pi$
$132$			20.2230i			0.153204i
$133$	−50.1988	+	91.6761i	−0.377434	+	0.689294i
$134$	−143.486			−1.07079
$135$	11.6190			0.0860663
$136$			21.2391i			0.156170i
$137$	−89.9621			−0.656657			−0.328329	−	0.944564i	$-0.606485\pi$
$137$	−89.9621			−0.656657			−0.328329	+	0.944564i	$0.606485\pi$
$138$			112.572i			0.815739i
$139$			126.585i			0.910684i	0.890317	+	0.455342i	$0.150483\pi$
$139$			126.585i			0.910684i	−0.890317	+	0.455342i	$0.849517\pi$
$140$	33.9211	−	61.9488i	0.242293	−	0.442491i
$141$	−140.920			−0.999434
$142$	284.132			2.00093
$143$			0.128919i			0.000901533i
$144$	41.0659			0.285180
$145$		−	38.9454i		−	0.268589i
$146$		−	339.601i		−	2.32603i
$147$	71.5052	−	45.7166i	0.486430	−	0.310998i
$148$	−32.2247			−0.217734
$149$	−91.3583			−0.613143			−0.306571	−	0.951848i	$-0.599182\pi$
$149$	−91.3583			−0.613143			−0.306571	+	0.951848i	$0.599182\pi$
$150$			25.2669i			0.168446i
$151$	21.2035			0.140421			0.0702104	−	0.997532i	$-0.477633\pi$
$151$	21.2035			0.140421			0.0702104	+	0.997532i	$0.477633\pi$
$152$			22.3152i			0.146811i
$153$		−	42.6342i		−	0.278655i
$154$	−46.3520	−	25.3808i	−0.300987	−	0.164811i
$155$	−14.2329			−0.0918252
$156$	−0.389385			−0.00249606
$157$			268.749i			1.71178i	0.517159	+	0.855890i	$0.326990\pi$
$157$			268.749i			1.71178i	−0.517159	+	0.855890i	$0.673010\pi$
$158$	288.357			1.82504
$159$			116.390i			0.732013i
$160$			102.671i			0.641691i
$161$	−136.774	−	74.8927i	−0.849526	−	0.465172i
$162$	26.2582			0.162088
$163$	−51.5630			−0.316338			−0.158169	−	0.987412i	$-0.550559\pi$
$163$	−51.5630			−0.316338			−0.158169	+	0.987412i	$0.550559\pi$
$164$		−	336.178i		−	2.04987i
$165$	10.0216			0.0607370
$166$		−	327.091i		−	1.97043i
$167$			91.2114i			0.546176i	0.961989	+	0.273088i	$0.0880450\pi$
$167$			91.2114i			0.546176i	−0.961989	+	0.273088i	$0.911955\pi$
$168$	8.70267	−	15.8933i	0.0518016	−	0.0946033i
$169$	168.998			0.999985
$170$	92.7137			0.545375
$171$		−	44.7943i		−	0.261955i
$172$	357.723			2.07978
$173$		−	120.543i		−	0.696780i	−0.937350	−	0.348390i	$-0.886729\pi$
$173$		−	120.543i		−	0.696780i	0.937350	−	0.348390i	$-0.113271\pi$
$174$		−	88.0143i		−	0.505830i
$175$	−30.6990	−	16.8098i	−0.175423	−	0.0960559i
$176$	35.4202			0.201251
$177$	−7.50281			−0.0423888
$178$			226.871i			1.27456i
$179$	−51.2128			−0.286105			−0.143053	−	0.989715i	$-0.545692\pi$
$179$	−51.2128			−0.286105			−0.143053	+	0.989715i	$0.545692\pi$
$180$			30.2691i			0.168161i
$181$		−	54.0291i		−	0.298503i	−0.988799	−	0.149252i	$-0.952314\pi$
$181$		−	54.0291i		−	0.298503i	0.988799	−	0.149252i	$-0.0476864\pi$
$182$	0.488697	−	0.892489i	0.00268515	−	0.00490378i
$183$	189.954			1.03800
$184$	−33.2926			−0.180938
$185$			15.9691i			0.0863195i
$186$	−32.1656			−0.172933
$187$		−	36.7730i		−	0.196647i
$188$		−	367.118i		−	1.95275i
$189$	−17.4692	+	31.9034i	−0.0924298	+	0.168801i
$190$	97.4110			0.512690
$191$	43.9113			0.229902			0.114951	−	0.993371i	$-0.463329\pi$
$191$	43.9113			0.229902			0.114951	+	0.993371i	$0.463329\pi$
$192$			137.192i			0.714542i
$193$	−46.6855			−0.241894			−0.120947	−	0.992659i	$-0.538593\pi$
$193$	−46.6855			−0.241894			−0.120947	+	0.992659i	$0.538593\pi$
$194$			320.923i			1.65424i
$195$			0.192962i			0.000989548i
$196$	119.099	+	186.281i	0.607646	+	0.950415i
$197$	274.811			1.39498			0.697490	−	0.716595i	$-0.254300\pi$
$197$	274.811			1.39498			0.697490	+	0.716595i	$0.254300\pi$
$198$	22.6483			0.114385
$199$		−	270.380i		−	1.35870i	−0.733816	−	0.679348i	$-0.762263\pi$
$199$		−	270.380i		−	1.35870i	0.733816	−	0.679348i	$-0.237737\pi$
$200$	−7.47257			−0.0373628
$201$			85.1822i			0.423792i
$202$			282.246i			1.39726i
$203$	106.936	+	58.5548i	0.526780	+	0.288447i
$204$	111.068			0.544453
$205$	−166.595			−0.812658
$206$		−	312.068i		−	1.51489i
$207$	66.8296			0.322848
$208$			0.682002i			0.00327885i
$209$		−	38.6361i		−	0.184862i
$210$	−69.3781	−	37.9892i	−0.330372	−	0.180901i
$211$	385.058			1.82492			0.912460	−	0.409166i	$-0.134180\pi$
$211$	385.058			1.82492			0.912460	+	0.409166i	$0.134180\pi$
$212$	−303.213			−1.43025
$213$		−	168.678i		−	0.791916i
$214$	96.5246			0.451050
$215$		−	177.272i		−	0.824519i
$216$			7.76572i			0.0359524i
$217$	21.3993	−	39.0808i	0.0986144	−	0.180096i
$218$	−145.526			−0.667551
$219$	−201.608			−0.920584
$220$			26.1078i			0.118672i
$221$	0.708048			0.00320384
$222$			36.0893i			0.162564i
$223$		−	141.356i		−	0.633883i	−0.948445	−	0.316941i	$-0.897344\pi$
$223$		−	141.356i		−	0.633883i	0.948445	−	0.316941i	$-0.102656\pi$
$224$	−281.913	−	154.366i	−1.25854	−	0.689135i
$225$	15.0000			0.0666667
$226$	−324.507			−1.43587
$227$			298.664i			1.31570i	0.753149	+	0.657850i	$0.228534\pi$
$227$			298.664i			1.31570i	−0.753149	+	0.657850i	$0.771466\pi$
$228$	116.696			0.511823
$229$		−	2.37781i		−	0.0103835i	−0.999987	−	0.00519173i	$-0.998347\pi$
$229$		−	2.37781i		−	0.0103835i	0.999987	−	0.00519173i	$-0.00165259\pi$
$230$			145.330i			0.631869i
$231$	−15.0676	+	27.5174i	−0.0652277	+	0.119123i
$232$	26.0298			0.112197
$233$	−368.120			−1.57991			−0.789956	−	0.613163i	$-0.789897\pi$
$233$	−368.120			−1.57991			−0.789956	+	0.613163i	$0.789897\pi$
$234$			0.436083i			0.00186360i
$235$	−181.927			−0.774158
$236$		−	19.5459i		−	0.0828217i
$237$		−	171.186i		−	0.722304i
$238$	−139.396	+	254.574i	−0.585698	+	1.06964i
$239$	420.588			1.75978			0.879892	−	0.475174i	$-0.157615\pi$
$239$	420.588			1.75978			0.879892	+	0.475174i	$0.157615\pi$
$240$	53.0158			0.220899
$241$			143.604i			0.595868i	0.954586	+	0.297934i	$0.0962976\pi$
$241$			143.604i			0.595868i	−0.954586	+	0.297934i	$0.903702\pi$
$242$	−333.492			−1.37807
$243$		−	15.5885i		−	0.0641500i
$244$			494.858i			2.02811i
$245$	92.3128	−	59.0199i	0.376787	−	0.240898i
$246$	−376.495			−1.53047
$247$	0.743921			0.00301183
$248$		−	9.51280i		−	0.0383581i
$249$	−194.181			−0.779844
$250$			32.6195i			0.130478i
$251$			298.338i			1.18860i	0.804245	+	0.594298i	$0.202570\pi$
$251$			298.338i			1.18860i	−0.804245	+	0.594298i	$0.797430\pi$
$252$	−83.1130	−	45.5099i	−0.329813	−	0.180595i
$253$	57.6420			0.227834
$254$	−202.581			−0.797563
$255$		−	55.0405i		−	0.215845i
$256$	178.444			0.697047
$257$			189.432i			0.737089i	0.929610	+	0.368545i	$0.120144\pi$
$257$			189.432i			0.737089i	−0.929610	+	0.368545i	$0.879856\pi$
$258$		−	400.624i		−	1.55281i
$259$	−43.8481	−	24.0097i	−0.169298	−	0.0927017i
$260$	−0.502694			−0.00193344
$261$	−52.2507			−0.200194
$262$			115.972i			0.442640i
$263$	233.105			0.886332			0.443166	−	0.896440i	$-0.353855\pi$
$263$	233.105			0.886332			0.443166	+	0.896440i	$0.353855\pi$
$264$			6.69811i			0.0253716i
$265$			150.259i			0.567015i
$266$	−146.459	+	267.472i	−0.550596	+	1.00553i
$267$	134.685			0.504437
$268$	−221.912			−0.828030
$269$		−	261.173i		−	0.970903i	−0.874264	−	0.485451i	$-0.838655\pi$
$269$		−	261.173i		−	0.970903i	0.874264	−	0.485451i	$-0.161345\pi$
$270$	33.8992			0.125552
$271$		−	172.256i		−	0.635632i	−0.948152	−	0.317816i	$-0.897050\pi$
$271$		−	172.256i		−	0.635632i	0.948152	−	0.317816i	$-0.102950\pi$
$272$		−	194.535i		−	0.715200i
$273$	−0.529836	−	0.290120i	−0.00194079	−	0.00106271i
$274$	−262.471			−0.957924
$275$	12.9378			0.0470467
$276$			174.101i			0.630800i
$277$	225.774			0.815070			0.407535	−	0.913190i	$-0.366388\pi$
$277$	225.774			0.815070			0.407535	+	0.913190i	$0.366388\pi$
$278$			369.322i			1.32849i
$279$			19.0954i			0.0684424i
$280$	11.2351	−	20.5182i	0.0401253	−	0.0732794i
$281$	156.116			0.555573			0.277787	−	0.960643i	$-0.410399\pi$
$281$	156.116			0.555573			0.277787	+	0.960643i	$0.410399\pi$
$282$	−411.145			−1.45796
$283$		−	94.6516i		−	0.334458i	−0.985918	−	0.167229i	$-0.946518\pi$
$283$		−	94.6516i		−	0.334458i	0.985918	−	0.167229i	$-0.0534819\pi$
$284$	439.431			1.54729
$285$		−	57.8291i		−	0.202909i
$286$			0.376131i			0.00131514i
$287$	250.477	−	457.437i	0.872744	−	1.59386i
$288$	137.747			0.478288
$289$	87.0361			0.301163
$290$		−	113.626i		−	0.391814i
$291$	190.520			0.654707
$292$		−	525.218i		−	1.79869i
$293$			323.853i			1.10530i	0.833413	+	0.552650i	$0.186383\pi$
$293$			323.853i			1.10530i	−0.833413	+	0.552650i	$0.813617\pi$
$294$	208.622	−	133.382i	0.709598	−	0.453679i
$295$	−9.68609			−0.0328342
$296$	−10.6732			−0.0360582
$297$		−	13.4454i		−	0.0452707i
$298$	−266.545			−0.894445
$299$			1.10987i			0.00371195i
$300$			39.0772i			0.130257i
$301$	486.753	+	266.530i	1.61712	+	0.885481i
$302$	61.8629			0.204844
$303$	167.559			0.552999
$304$		−	204.391i		−	0.672338i
$305$	245.230			0.804032
$306$		−	124.388i		−	0.406498i
$307$		−	542.844i		−	1.76822i	−0.467276	−	0.884112i	$-0.654765\pi$
$307$		−	542.844i		−	1.76822i	0.467276	−	0.884112i	$-0.345235\pi$
$308$	−71.6868	−	39.2533i	−0.232749	−	0.127446i
$309$	−185.263			−0.599555
$310$	−41.5256			−0.133953
$311$			405.345i			1.30336i	0.758494	+	0.651680i	$0.225935\pi$
$311$			405.345i			1.30336i	−0.758494	+	0.651680i	$0.774065\pi$
$312$	−0.128969			−0.000413363
$313$		−	44.1040i		−	0.140907i	−0.997515	−	0.0704536i	$-0.977555\pi$
$313$		−	44.1040i		−	0.140907i	0.997515	−	0.0704536i	$-0.0224447\pi$
$314$			784.096i			2.49712i
$315$	−22.5527	+	41.1871i	−0.0715958	+	0.130753i
$316$	445.965			1.41128
$317$	−244.609			−0.771636			−0.385818	−	0.922575i	$-0.626081\pi$
$317$	−244.609			−0.771636			−0.385818	+	0.922575i	$0.626081\pi$
$318$			339.577i			1.06785i
$319$	−45.0674			−0.141277
$320$			177.114i			0.553482i
$321$		−	57.3029i		−	0.178514i
$322$	−399.047	−	218.505i	−1.23928	−	0.678587i
$323$	−212.196			−0.656955
$324$	40.6102			0.125340
$325$			0.249113i			0.000766500i
$326$	−150.439			−0.461470
$327$			86.3932i			0.264199i
$328$		−	111.347i		−	0.339471i
$329$	273.530	−	499.537i	0.831397	−	1.51835i
$330$	29.2388			0.0886024
$331$	−516.884			−1.56158			−0.780792	−	0.624791i	$-0.785184\pi$
$331$	−516.884			−1.56158			−0.780792	+	0.624791i	$0.785184\pi$
$332$		−	505.871i		−	1.52371i
$333$	21.4248			0.0643388
$334$			266.116i			0.796755i
$335$			109.970i			0.328268i
$336$	−79.7099	+	145.571i	−0.237232	+	0.433247i
$337$	−643.730			−1.91018			−0.955089	−	0.296320i	$-0.904240\pi$
$337$	−643.730			−1.91018			−0.955089	+	0.296320i	$0.904240\pi$
$338$	493.063			1.45877
$339$			192.647i			0.568281i
$340$	143.389			0.421731
$341$			16.4702i			0.0482998i
$342$		−	130.691i		−	0.382136i
$343$	23.2640	+	342.210i	0.0678249	+	0.997697i
$344$	118.482			0.344426
$345$	86.2766			0.250077
$346$		−	351.693i		−	1.01645i
$347$	−256.423			−0.738971			−0.369485	−	0.929237i	$-0.620466\pi$
$347$	−256.423			−0.738971			−0.369485	+	0.929237i	$0.620466\pi$
$348$		−	136.121i		−	0.391151i
$349$		−	410.197i		−	1.17535i	−0.809097	−	0.587675i	$-0.800043\pi$
$349$		−	410.197i		−	1.17535i	0.809097	−	0.587675i	$-0.199957\pi$
$350$	−89.5668	−	49.0438i	−0.255905	−	0.140125i
$351$	0.258885			0.000737565
$352$	118.810			0.337528
$353$			258.233i			0.731537i	0.930706	+	0.365769i	$0.119194\pi$
$353$			258.233i			0.731537i	−0.930706	+	0.365769i	$0.880806\pi$
$354$	−21.8900			−0.0618362
$355$		−	217.763i		−	0.613416i
$356$			350.873i			0.985599i
$357$	151.131	+	82.7541i	0.423335	+	0.231804i
$358$	−149.417			−0.417366
$359$	−152.789			−0.425597			−0.212798	−	0.977096i	$-0.568258\pi$
$359$	−152.789			−0.425597			−0.212798	+	0.977096i	$0.568258\pi$
$360$			10.0255i			0.0278486i
$361$	138.053			0.382417
$362$		−	157.634i		−	0.435453i
$363$			197.981i			0.545403i
$364$	0.755806	−	1.38030i	0.00207639	−	0.00379203i
$365$	−260.275			−0.713081
$366$	554.206			1.51422
$367$		−	393.499i		−	1.07220i	−0.844153	−	0.536102i	$-0.819896\pi$
$367$		−	393.499i		−	1.07220i	0.844153	−	0.536102i	$-0.180104\pi$
$368$	304.935			0.828628
$369$			223.510i			0.605719i
$370$			46.5911i			0.125922i
$371$	−412.582	−	225.916i	−1.11208	−	0.608938i
$372$	−49.7464			−0.133727
$373$	324.962			0.871212			0.435606	−	0.900137i	$-0.356534\pi$
$373$	324.962			0.871212			0.435606	+	0.900137i	$0.356534\pi$
$374$		−	107.288i		−	0.286866i
$375$	19.3649			0.0516398
$376$		−	121.594i		−	0.323389i
$377$		−	0.867754i		−	0.00230173i
$378$	−50.9678	+	93.0805i	−0.134835	+	0.246245i
$379$	−146.945			−0.387718			−0.193859	−	0.981029i	$-0.562100\pi$
$379$	−146.945			−0.387718			−0.193859	+	0.981029i	$0.562100\pi$
$380$	150.653			0.396456
$381$			120.264i			0.315655i
$382$	128.115			0.335379
$383$		−	356.582i		−	0.931025i	−0.885041	−	0.465512i	$-0.845870\pi$
$383$		−	356.582i		−	0.931025i	0.885041	−	0.465512i	$-0.154130\pi$
$384$			82.1551i			0.213946i
$385$	−19.4522	+	35.5248i	−0.0505252	+	0.0922722i
$386$	−136.208			−0.352872
$387$	−237.835			−0.614560
$388$			496.332i			1.27921i
$389$	99.7568			0.256444			0.128222	−	0.991745i	$-0.459073\pi$
$389$	99.7568			0.256444			0.128222	+	0.991745i	$0.459073\pi$
$390$			0.562981i			0.00144354i
$391$		−	316.581i		−	0.809670i
$392$	39.4470	+	61.6988i	0.100630	+	0.157395i
$393$	68.8478			0.175185
$394$	801.782			2.03498
$395$		−	221.000i		−	0.559494i
$396$	35.0272			0.0884526
$397$			646.374i			1.62815i	0.580763	+	0.814073i	$0.302754\pi$
$397$			646.374i			1.62815i	−0.580763	+	0.814073i	$0.697246\pi$
$398$		−	788.855i		−	1.98205i
$399$	158.788	+	86.9468i	0.397964	+	0.217912i
$400$	68.4431			0.171108
$401$	219.319			0.546931			0.273465	−	0.961882i	$-0.411830\pi$
$401$	219.319			0.546931			0.273465	+	0.961882i	$0.411830\pi$
$402$			248.526i			0.618223i
$403$	−0.317128			−0.000786917
$404$			436.515i			1.08048i
$405$		−	20.1246i		−	0.0496904i
$406$	311.995	+	170.838i	0.768461	+	0.420783i
$407$	18.4794			0.0454039
$408$	36.7873			0.0901649
$409$			98.2083i			0.240118i	0.992767	+	0.120059i	$0.0383084\pi$
$409$			98.2083i			0.240118i	−0.992767	+	0.120059i	$0.961692\pi$
$410$	−486.053			−1.18550
$411$			155.819i			0.379121i
$412$		−	482.636i		−	1.17145i
$413$	14.5631	−	26.5961i	0.0352619	−	0.0643974i
$414$	194.980			0.470967
$415$	−250.687			−0.604065
$416$			2.28763i			0.00549912i
$417$	219.252			0.525784
$418$		−	112.724i		−	0.269674i
$419$			397.174i			0.947909i	0.880549	+	0.473955i	$0.157174\pi$
$419$			397.174i			0.947909i	−0.880549	+	0.473955i	$0.842826\pi$
$420$	−107.298	−	58.7530i	−0.255472	−	0.139888i
$421$	−149.418			−0.354911			−0.177456	−	0.984129i	$-0.556787\pi$
$421$	−149.418			−0.354911			−0.177456	+	0.984129i	$0.556787\pi$
$422$	1123.44			2.66217
$423$			244.081i			0.577024i
$424$	−100.428			−0.236859
$425$		−	71.0570i		−	0.167193i
$426$		−	492.131i		−	1.15524i
$427$	−368.706	+	673.354i	−0.863480	+	1.57694i
$428$	149.282			0.348791
$429$	0.223295			0.000520500
$430$		−	517.203i		−	1.20280i
$431$	−241.112			−0.559425			−0.279713	−	0.960084i	$-0.590239\pi$
$431$	−241.112			−0.559425			−0.279713	+	0.960084i	$0.590239\pi$
$432$		−	71.1282i		−	0.164649i
$433$		−	391.184i		−	0.903426i	−0.892163	−	0.451713i	$-0.850813\pi$
$433$		−	391.184i		−	0.903426i	0.892163	−	0.451713i	$-0.149187\pi$
$434$	62.4342	−	114.021i	0.143858	−	0.262721i
$435$	−67.4553			−0.155070
$436$	−225.067			−0.516208
$437$		−	332.620i		−	0.761145i
$438$	−588.206			−1.34294
$439$			111.468i			0.253914i	0.991908	+	0.126957i	$0.0405210\pi$
$439$			111.468i			0.253914i	−0.991908	+	0.126957i	$0.959479\pi$
$440$			8.64722i			0.0196528i
$441$	−79.1836	−	123.851i	−0.179555	−	0.280840i
$442$	2.06578			0.00467372
$443$	−25.3173			−0.0571497			−0.0285748	−	0.999592i	$-0.509097\pi$
$443$	−25.3173			−0.0571497			−0.0285748	+	0.999592i	$0.509097\pi$
$444$			55.8148i			0.125709i
$445$	173.877			0.390735
$446$		−	412.416i		−	0.924700i
$447$			158.237i			0.353998i
$448$	−486.321	−	266.293i	−1.08554	−	0.594405i
$449$	−486.460			−1.08343			−0.541715	−	0.840562i	$-0.682225\pi$
$449$	−486.460			−1.08343			−0.541715	+	0.840562i	$0.682225\pi$
$450$	43.7636			0.0972525
$451$			192.783i			0.427456i
$452$	−501.874			−1.11034
$453$		−	36.7256i		−	0.0810720i
$454$			871.375i			1.91933i
$455$	−0.684015	−	0.374544i	−0.00150333	−	0.000823173i
$456$	38.6511			0.0847612
$457$	352.023			0.770292			0.385146	−	0.922856i	$-0.374151\pi$
$457$	352.023			0.770292			0.385146	+	0.922856i	$0.374151\pi$
$458$		−	6.93745i		−	0.0151473i
$459$	−73.8446			−0.160881
$460$			224.763i			0.488616i
$461$		−	213.924i		−	0.464043i	−0.972711	−	0.232021i	$-0.925466\pi$
$461$		−	213.924i		−	0.464043i	0.972711	−	0.232021i	$-0.0745339\pi$
$462$	−43.9609	+	80.2841i	−0.0951534	+	0.173775i
$463$	144.676			0.312474			0.156237	−	0.987720i	$-0.450064\pi$
$463$	144.676			0.312474			0.156237	+	0.987720i	$0.450064\pi$
$464$	−238.413			−0.513822
$465$			24.6521i			0.0530153i
$466$	−1074.02			−2.30476
$467$			97.9108i			0.209659i	0.994490	+	0.104830i	$0.0334297\pi$
$467$			97.9108i			0.209659i	−0.994490	+	0.104830i	$0.966570\pi$
$468$			0.674434i			0.00144110i
$469$	−301.956	−	165.341i	−0.643829	−	0.352539i
$470$	−530.786			−1.12933
$471$	465.487			0.988296
$472$		−	6.47386i		−	0.0137158i
$473$	−205.138			−0.433695
$474$		−	499.448i		−	1.05369i
$475$		−	74.6571i		−	0.157173i
$476$	−215.586	+	393.717i	−0.452913	+	0.827137i
$477$	201.594			0.422628
$478$	1227.10			2.56715
$479$			322.314i			0.672890i	0.941703	+	0.336445i	$0.109225\pi$
$479$			322.314i			0.672890i	−0.941703	+	0.336445i	$0.890775\pi$
$480$	177.831			0.370480
$481$			0.355813i			0.000739735i
$482$			418.976i			0.869245i
$483$	−129.718	+	236.899i	−0.268567	+	0.490474i
$484$	−515.770			−1.06564
$485$	245.960			0.507134
$486$		−	45.4805i		−	0.0935813i
$487$	−349.967			−0.718617			−0.359309	−	0.933219i	$-0.616987\pi$
$487$	−349.967			−0.718617			−0.359309	+	0.933219i	$0.616987\pi$
$488$			163.903i			0.335868i
$489$			89.3098i			0.182638i
$490$	269.329	−	172.195i	0.549652	−	0.351419i
$491$	−487.352			−0.992571			−0.496286	−	0.868159i	$-0.665303\pi$
$491$	−487.352			−0.992571			−0.496286	+	0.868159i	$0.665303\pi$
$492$	−582.277			−1.18349
$493$			247.518i			0.502066i
$494$	2.17045			0.00439361
$495$		−	17.3579i		−	0.0350665i
$496$			87.1301i			0.175666i
$497$	597.934	+	327.409i	1.20309	+	0.658770i
$498$	−566.538			−1.13763
$499$	−15.0073			−0.0300748			−0.0150374	−	0.999887i	$-0.504787\pi$
$499$	−15.0073			−0.0300748			−0.0150374	+	0.999887i	$0.504787\pi$
$500$			50.4484i			0.100897i
$501$	157.983			0.315335
$502$			870.423i			1.73391i
$503$			868.775i			1.72719i	0.504189	+	0.863594i	$0.331792\pi$
$503$			868.775i			1.72719i	−0.504189	+	0.863594i	$0.668208\pi$
$504$	−27.5281	−	15.0735i	−0.0546192	−	0.0299077i
$505$	216.317			0.428351
$506$	168.175			0.332362
$507$		−	292.712i		−	0.577342i
$508$	−313.307			−0.616745
$509$		−	620.297i		−	1.21866i	−0.792917	−	0.609330i	$-0.791439\pi$
$509$		−	620.297i		−	1.21866i	0.792917	−	0.609330i	$-0.208561\pi$
$510$		−	160.585i		−	0.314872i
$511$	391.326	−	714.664i	0.765804	−	1.39856i
$512$	710.353			1.38741
$513$	−77.5859			−0.151240
$514$			552.682i			1.07526i
$515$	−239.173			−0.464413
$516$		−	619.594i		−	1.20076i
$517$			210.525i			0.407206i
$518$	−127.930	−	70.0502i	−0.246969	−	0.135232i
$519$	−208.786			−0.402286
$520$	−0.166499			−0.000320190
$521$			73.0697i			0.140249i	0.997538	+	0.0701245i	$0.0223396\pi$
$521$			73.0697i			0.140249i	−0.997538	+	0.0701245i	$0.977660\pi$
$522$	−152.445			−0.292041
$523$		−	600.742i		−	1.14865i	−0.818629	−	0.574323i	$-0.805265\pi$
$523$		−	600.742i		−	1.14865i	0.818629	−	0.574323i	$-0.194735\pi$
$524$			179.359i			0.342287i
$525$	−29.1154	+	53.1723i	−0.0554579	+	0.101281i
$526$	680.102			1.29297
$527$	90.4576			0.171646
$528$		−	61.3497i		−	0.116193i
$529$	−32.7560			−0.0619206
$530$			438.392i			0.827154i
$531$			12.9952i			0.0244732i
$532$	−226.509	+	413.665i	−0.425769	+	0.777566i
$533$	−3.71195			−0.00696426
$534$	392.953			0.735867
$535$		−	73.9777i		−	0.138276i
$536$	−73.5002			−0.137127
$537$			88.7032i			0.165183i
$538$		−	761.991i		−	1.41634i
$539$	−68.2976	−	106.824i	−0.126712	−	0.198189i
$540$	52.4276			0.0970881
$541$	−628.263			−1.16130			−0.580650	−	0.814153i	$-0.697202\pi$
$541$	−628.263			−1.16130			−0.580650	+	0.814153i	$0.697202\pi$
$542$		−	502.571i		−	0.927253i
$543$	−93.5811			−0.172341
$544$		−	652.526i		−	1.19950i
$545$			111.533i			0.204648i
$546$	−1.54584	−	0.846448i	−0.00283120	−	0.00155027i
$547$	−616.326			−1.12674			−0.563370	−	0.826205i	$-0.690495\pi$
$547$	−616.326			−1.12674			−0.563370	+	0.826205i	$0.690495\pi$
$548$	−405.931			−0.740750
$549$		−	329.010i		−	0.599290i
$550$	37.7471			0.0686311
$551$			260.059i			0.471976i
$552$			57.6645i			0.104465i
$553$	606.824	+	332.277i	1.09733	+	0.600862i
$554$	658.714			1.18901
$555$	27.6593			0.0498366
$556$			571.183i			1.02731i
$557$	444.374			0.797799			0.398900	−	0.916995i	$-0.369392\pi$
$557$	444.374			0.797799			0.398900	+	0.916995i	$0.369392\pi$
$558$			55.7124i			0.0998430i
$559$		−	3.94984i		−	0.00706591i
$560$	−102.905	+	187.932i	−0.183759	+	0.335592i
$561$	−63.6926			−0.113534
$562$	455.480			0.810464
$563$			490.184i			0.870665i	0.900270	+	0.435332i	$0.143369\pi$
$563$			490.184i			0.870665i	−0.900270	+	0.435332i	$0.856631\pi$
$564$	−635.867			−1.12742
$565$			248.706i			0.440188i
$566$		−	276.153i		−	0.487903i
$567$	55.2583	+	30.2576i	0.0974573	+	0.0533644i
$568$	145.545			0.256242
$569$	152.671			0.268315			0.134158	−	0.990960i	$-0.457167\pi$
$569$	152.671			0.268315			0.134158	+	0.990960i	$0.457167\pi$
$570$		−	168.721i		−	0.296002i
$571$	−348.236			−0.609871			−0.304936	−	0.952373i	$-0.598635\pi$
$571$	−348.236			−0.609871			−0.304936	+	0.952373i	$0.598635\pi$
$572$			0.581715i			0.00101698i
$573$		−	76.0567i		−	0.132734i
$574$	730.787	−	1334.61i	1.27315	−	2.32510i
$575$	111.383			0.193709
$576$	237.624			0.412541
$577$		−	216.610i		−	0.375407i	−0.982226	−	0.187703i	$-0.939896\pi$
$577$		−	216.610i		−	0.375407i	0.982226	−	0.187703i	$-0.0601044\pi$
$578$	253.934			0.439333
$579$			80.8617i			0.139657i
$580$		−	175.731i		−	0.302985i
$581$	376.911	−	688.338i	0.648728	−	1.18475i
$582$	555.856			0.955078
$583$	173.879			0.298249
$584$		−	173.959i		−	0.297875i
$585$	0.334220			0.000571316
$586$			944.865i			1.61240i
$587$		−	549.987i		−	0.936945i	−0.883478	−	0.468473i	$-0.844805\pi$
$587$		−	549.987i		−	0.936945i	0.883478	−	0.468473i	$-0.155195\pi$
$588$	322.649	−	206.285i	0.548722	−	0.350824i
$589$	95.0407			0.161359
$590$	−28.2599			−0.0478981
$591$		−	475.986i		−	0.805392i
$592$	97.7587			0.165133
$593$		−	496.397i		−	0.837095i	−0.908195	−	0.418547i	$-0.862539\pi$
$593$		−	496.397i		−	0.837095i	0.908195	−	0.418547i	$-0.137461\pi$
$594$		−	39.2280i		−	0.0660403i
$595$	195.109	+	106.835i	0.327914	+	0.179555i
$596$	−412.231			−0.691663
$597$	−468.313			−0.784443
$598$			3.23814i			0.00541495i
$599$	837.957			1.39893			0.699463	−	0.714669i	$-0.253422\pi$
$599$	837.957			1.39893			0.699463	+	0.714669i	$0.253422\pi$
$600$			12.9429i			0.0215714i
$601$		−	643.195i		−	1.07021i	−0.844786	−	0.535104i	$-0.820272\pi$
$601$		−	643.195i		−	1.07021i	0.844786	−	0.535104i	$-0.179728\pi$
$602$	1420.14	+	777.621i	2.35904	+	1.29173i
$603$	147.540			0.244677
$604$	95.6755			0.158403
$605$			255.593i			0.422467i
$606$	488.865			0.806707
$607$		−	137.690i		−	0.226837i	−0.993547	−	0.113419i	$-0.963820\pi$
$607$		−	137.690i		−	0.226837i	0.993547	−	0.113419i	$-0.0361801\pi$
$608$		−	685.586i		−	1.12761i
$609$	101.420	−	185.219i	0.166535	−	0.304137i
$610$	715.476			1.17291
$611$	−4.05358			−0.00663433
$612$		−	192.376i		−	0.314340i
$613$	844.662			1.37792			0.688958	−	0.724801i	$-0.258068\pi$
$613$	844.662			1.37792			0.688958	+	0.724801i	$0.258068\pi$
$614$		−	1583.79i		−	2.57946i
$615$			288.551i			0.469188i
$616$	−23.7436	−	13.0012i	−0.0385448	−	0.0211059i
$617$	−601.594			−0.975031			−0.487515	−	0.873114i	$-0.662097\pi$
$617$	−601.594			−0.975031			−0.487515	+	0.873114i	$0.662097\pi$
$618$	−540.517			−0.874623
$619$			389.067i			0.628542i	0.949333	+	0.314271i	$0.101760\pi$
$619$			389.067i			0.628542i	−0.949333	+	0.314271i	$0.898240\pi$
$620$	−64.2223			−0.103584
$621$		−	115.752i		−	0.186397i
$622$			1182.62i			1.90132i
$623$	−261.426	+	477.433i	−0.419625	+	0.766345i
$624$	1.18126			0.00189305
$625$	25.0000			0.0400000
$626$		−	128.677i		−	0.205554i
$627$	−66.9196			−0.106730
$628$			1212.66i			1.93099i
$629$		−	101.492i		−	0.161355i
$630$	−65.7991	+	120.166i	−0.104443	+	0.190740i
$631$	394.214			0.624745			0.312372	−	0.949960i	$-0.398876\pi$
$631$	394.214			0.624745			0.312372	+	0.949960i	$0.398876\pi$
$632$	147.709			0.233717
$633$		−	666.940i		−	1.05362i
$634$	−713.664			−1.12565
$635$			155.261i			0.244505i
$636$			525.180i			0.825755i
$637$	2.05685	−	1.31504i	0.00322896	−	0.00206443i
$638$	−131.488			−0.206093
$639$	−292.159			−0.457213
$640$			106.062i			0.165722i
$641$	98.0430			0.152953			0.0764766	−	0.997071i	$-0.475633\pi$
$641$	98.0430			0.152953			0.0764766	+	0.997071i	$0.475633\pi$
$642$		−	167.186i		−	0.260414i
$643$			585.514i			0.910598i	0.890339	+	0.455299i	$0.150468\pi$
$643$			585.514i			0.910598i	−0.890339	+	0.455299i	$0.849532\pi$
$644$	−617.156	−	337.934i	−0.958317	−	0.524743i
$645$	−307.043			−0.476036
$646$	−619.099			−0.958358
$647$		−	1256.79i		−	1.94248i	−0.238099	−	0.971241i	$-0.576524\pi$
$647$		−	1256.79i		−	1.94248i	0.238099	−	0.971241i	$-0.423476\pi$
$648$	13.4506			0.0207571
$649$			11.2087i			0.0172707i
$650$			0.726805i			0.00111816i
$651$	−67.6899	−	37.0647i	−0.103978	−	0.0569351i
$652$	−232.665			−0.356848
$653$	−687.810			−1.05331			−0.526654	−	0.850080i	$-0.676554\pi$
$653$	−687.810			−1.05331			−0.526654	+	0.850080i	$0.676554\pi$
$654$			252.059i			0.385411i
$655$	88.8822			0.135698
$656$			1019.85i			1.55465i
$657$			349.195i			0.531499i
$658$	798.044	−	1457.44i	1.21283	−	2.21495i
$659$	757.250			1.14909			0.574545	−	0.818473i	$-0.305179\pi$
$659$	757.250			1.14909			0.574545	+	0.818473i	$0.305179\pi$
$660$	45.2199			0.0685151
$661$			652.355i			0.986922i	0.869768	+	0.493461i	$0.164268\pi$
$661$			652.355i			0.986922i	−0.869768	+	0.493461i	$0.835732\pi$
$662$	−1508.05			−2.27802
$663$		−	1.22637i		−	0.00184974i
$664$		−	167.551i		−	0.252336i
$665$	204.994	+	112.248i	0.308262	+	0.168794i
$666$	62.5085			0.0938566
$667$	−387.988			−0.581691
$668$			411.568i			0.616120i
$669$	−244.835			−0.365972
$670$			320.845i			0.478873i
$671$		−	283.779i		−	0.422919i
$672$	−267.370	+	488.288i	−0.397873	+	0.726619i
$673$	−798.483			−1.18645			−0.593227	−	0.805035i	$-0.702146\pi$
$673$	−798.483			−1.18645			−0.593227	+	0.805035i	$0.702146\pi$
$674$	−1878.13			−2.78654
$675$		−	25.9808i		−	0.0384900i
$676$	762.558			1.12804
$677$			512.802i			0.757462i	0.925507	+	0.378731i	$0.123639\pi$
$677$			512.802i			0.757462i	−0.925507	+	0.378731i	$0.876361\pi$
$678$			562.063i			0.829001i
$679$	−369.804	+	675.358i	−0.544630	+	0.994636i
$680$	47.4922			0.0698414
$681$	517.301			0.759620
$682$			48.0532i			0.0704592i
$683$	−1332.72			−1.95127			−0.975636	−	0.219394i	$-0.929592\pi$
$683$	−1332.72			−1.95127			−0.975636	+	0.219394i	$0.929592\pi$
$684$		−	202.123i		−	0.295501i
$685$			201.161i			0.293666i
$686$	67.8743	+	998.424i	0.0989422	+	1.45543i
$687$	−4.11850			−0.00599490
$688$	−1085.21			−1.57734
$689$			3.34797i			0.00485917i
$690$	251.719			0.364810
$691$			1065.65i			1.54218i	0.636724	+	0.771092i	$0.280289\pi$
$691$			1065.65i			1.54218i	−0.636724	+	0.771092i	$0.719711\pi$
$692$		−	543.919i		−	0.786010i
$693$	47.6615	+	26.0979i	0.0687756	+	0.0376593i
$694$	−748.133			−1.07800
$695$	283.053			0.407270
$696$		−	45.0849i		−	0.0647772i
$697$	1058.80			1.51908
$698$		−	1196.78i		−	1.71459i
$699$			637.602i			0.912163i
$700$	−138.522	−	75.8498i	−0.197888	−	0.108357i
$701$	−953.569			−1.36030			−0.680149	−	0.733074i	$-0.738085\pi$
$701$	−953.569			−1.36030			−0.680149	+	0.733074i	$0.738085\pi$
$702$	0.755318			0.00107595
$703$		−	106.634i		−	0.151685i
$704$	204.956			0.291130
$705$			315.107i			0.446961i
$706$			753.413i			1.06716i
$707$	−325.235	+	593.965i	−0.460022	+	0.840120i
$708$	−33.8545			−0.0478171
$709$	68.0675			0.0960050			0.0480025	−	0.998847i	$-0.484714\pi$
$709$	68.0675			0.0960050			0.0480025	+	0.998847i	$0.484714\pi$
$710$		−	635.339i		−	0.894843i
$711$	−296.503			−0.417023
$712$			116.214i			0.163222i
$713$			141.793i			0.198869i
$714$	440.935	+	241.441i	0.617556	+	0.338153i
$715$	0.288272			0.000403178
$716$	−231.085			−0.322744
$717$		−	728.480i		−	1.01601i
$718$	−445.774			−0.620855
$719$			137.609i			0.191389i	0.995411	+	0.0956947i	$0.0305073\pi$
$719$			137.609i			0.191389i	−0.995411	+	0.0956947i	$0.969493\pi$
$720$		−	91.8261i		−	0.127536i
$721$	359.599	−	656.722i	0.498751	−	0.910849i
$722$	402.779			0.557866
$723$	248.730			0.344025
$724$		−	243.792i		−	0.336730i
$725$	−87.0845			−0.120117
$726$			577.625i			0.795627i
$727$		−	853.429i		−	1.17391i	−0.809621	−	0.586953i	$-0.800328\pi$
$727$		−	853.429i		−	1.17391i	0.809621	−	0.586953i	$-0.199672\pi$
$728$	0.250333	−	0.457173i	0.000343864	−	0.000627985i
$729$	−27.0000			−0.0370370
$730$	−759.371			−1.04023
$731$			1126.65i			1.54125i
$732$	857.120			1.17093
$733$		−	1225.71i		−	1.67219i	−0.548586	−	0.836094i	$-0.684834\pi$
$733$		−	1225.71i		−	1.67219i	0.548586	−	0.836094i	$-0.315166\pi$
$734$		−	1148.06i		−	1.56412i
$735$	−102.226	−	159.890i	−0.139082	−	0.217538i
$736$	1022.84			1.38973
$737$	127.257			0.172668
$738$			652.109i			0.883616i
$739$	−1314.44			−1.77867			−0.889334	−	0.457258i	$-0.848832\pi$
$739$	−1314.44			−1.77867			−0.889334	+	0.457258i	$0.848832\pi$
$740$			72.0565i			0.0973737i
$741$		−	1.28851i		−	0.00173888i
$742$	−1203.74	−	659.127i	−1.62229	−	0.888312i
$743$	1209.47			1.62782			0.813908	−	0.580994i	$-0.197336\pi$
$743$	1209.47			1.62782			0.813908	+	0.580994i	$0.197336\pi$
$744$	−16.4766			−0.0221460
$745$			204.283i			0.274206i
$746$	948.101			1.27091
$747$			336.332i			0.450243i
$748$		−	165.929i		−	0.221830i
$749$	203.128	+	111.226i	0.271200	+	0.148500i
$750$	56.4986			0.0753315
$751$	−173.085			−0.230473			−0.115236	−	0.993338i	$-0.536763\pi$
$751$	−173.085			−0.230473			−0.115236	+	0.993338i	$0.536763\pi$
$752$			1113.71i			1.48100i
$753$	516.736			0.686236
$754$		−	2.53174i		−	0.00335774i
$755$		−	47.4125i		−	0.0627981i
$756$	−78.8255	+	143.956i	−0.104266	+	0.190418i
$757$	723.857			0.956218			0.478109	−	0.878301i	$-0.341322\pi$
$757$	723.857			0.956218			0.478109	+	0.878301i	$0.341322\pi$
$758$	−428.723			−0.565598
$759$		−	99.8390i		−	0.131540i
$760$	49.8983			0.0656557
$761$		−	187.223i		−	0.246023i	−0.992405	−	0.123011i	$-0.960745\pi$
$761$		−	187.223i		−	0.246023i	0.992405	−	0.123011i	$-0.0392552\pi$
$762$			350.881i			0.460473i
$763$	−306.248	−	167.691i	−0.401374	−	0.219779i
$764$	198.139			0.259344
$765$	−95.3330			−0.124618
$766$		−	1040.36i		−	1.35817i
$767$	−0.215819			−0.000281380
$768$		−	309.074i		−	0.402441i
$769$		−	94.5845i		−	0.122997i	−0.998107	−	0.0614984i	$-0.980412\pi$
$769$		−	94.5845i		−	0.122997i	0.998107	−	0.0614984i	$-0.0195879\pi$
$770$	−56.7532	+	103.646i	−0.0737055	+	0.134606i
$771$	328.106			0.425559
$772$	−210.656			−0.272871
$773$		−	561.473i		−	0.726356i	−0.931720	−	0.363178i	$-0.881692\pi$
$773$		−	561.473i		−	0.726356i	0.931720	−	0.363178i	$-0.118308\pi$
$774$	−693.901			−0.896513
$775$			31.8257i			0.0410655i
$776$			164.391i			0.211845i
$777$	−41.5861	+	75.9471i	−0.0535214	+	0.0977440i
$778$	291.048			0.374098
$779$	1112.44			1.42804
$780$			0.870691i			0.00111627i
$781$	−251.994			−0.322655
$782$		−	923.648i		−	1.18114i
$783$			90.5008i			0.115582i
$784$	−361.305	−	565.115i	−0.460848	−	0.720810i
$785$	600.942			0.765531
$786$	200.869			0.255558
$787$		−	1113.97i		−	1.41547i	−0.706479	−	0.707734i	$-0.749718\pi$
$787$		−	1113.97i		−	1.41547i	0.706479	−	0.707734i	$-0.250282\pi$
$788$	1240.01			1.57362
$789$		−	403.750i		−	0.511724i
$790$		−	644.785i		−	0.816184i
$791$	−682.900	−	373.933i	−0.863337	−	0.472735i
$792$	11.6015			0.0146483
$793$	5.46404			0.00689034
$794$			1885.84i			2.37512i
$795$	260.256			0.327366
$796$		−	1220.02i		−	1.53269i
$797$			262.831i			0.329776i	0.986312	+	0.164888i	$0.0527262\pi$
$797$			262.831i			0.329776i	−0.986312	+	0.164888i	$0.947274\pi$
$798$	463.275	+	253.674i	0.580545	+	0.317887i
$799$	1156.24			1.44711
$800$	229.578			0.286973
$801$		−	233.281i		−	0.291237i
$802$	639.880			0.797855
$803$			301.189i			0.375079i
$804$			384.363i			0.478064i
$805$	−167.465	+	305.835i	−0.208031	+	0.379920i
$806$	−0.925244			−0.00114795
$807$	−452.365			−0.560551
$808$			144.579i			0.178935i
$809$	779.689			0.963769			0.481885	−	0.876235i	$-0.339952\pi$
$809$	779.689			0.963769			0.481885	+	0.876235i	$0.339952\pi$
$810$		−	58.7151i		−	0.0724877i
$811$		−	1414.43i		−	1.74406i	−0.489454	−	0.872029i	$-0.662804\pi$
$811$		−	1414.43i		−	1.74406i	0.489454	−	0.872029i	$-0.337196\pi$
$812$	482.523	+	264.214i	0.594241	+	0.325386i
$813$	−298.357			−0.366983
$814$	53.9150			0.0662346
$815$			115.298i			0.141471i
$816$	−336.944			−0.412921
$817$			1183.74i			1.44888i
$818$			286.530i			0.350281i
$819$	−0.502503	+	0.917702i	−0.000613557	+	0.00112052i
$820$	−751.717			−0.916728
$821$	301.987			0.367829			0.183914	−	0.982942i	$-0.441123\pi$
$821$	301.987			0.367829			0.183914	+	0.982942i	$0.441123\pi$
$822$			454.613i			0.553058i
$823$	411.340			0.499805			0.249903	−	0.968271i	$-0.419601\pi$
$823$	411.340			0.499805			0.249903	+	0.968271i	$0.419601\pi$
$824$		−	159.855i		−	0.193999i
$825$		−	22.4090i		−	0.0271624i
$826$	42.4891	−	77.5962i	0.0514396	−	0.0939421i
$827$	−86.0106			−0.104003			−0.0520015	−	0.998647i	$-0.516560\pi$
$827$	−86.0106			−0.104003			−0.0520015	+	0.998647i	$0.516560\pi$
$828$	301.552			0.364193
$829$			810.197i			0.977318i	0.872475	+	0.488659i	$0.162514\pi$
$829$			810.197i			0.977318i	−0.872475	+	0.488659i	$0.837486\pi$
$830$	−731.398			−0.881202
$831$		−	391.053i		−	0.470581i
$832$			3.94634i			0.00474319i
$833$	−586.697	+	375.103i	−0.704318	+	0.450304i
$834$	639.684			0.767007
$835$	203.955			0.244257
$836$		−	174.335i		−	0.208535i
$837$	33.0743			0.0395153
$838$			1158.79i			1.38280i
$839$			82.0394i			0.0977823i	0.998804	+	0.0488912i	$0.0155687\pi$
$839$			82.0394i			0.0977823i	−0.998804	+	0.0488912i	$0.984431\pi$
$840$	−35.5386	−	19.4598i	−0.0423079	−	0.0231664i
$841$	−537.652			−0.639301
$842$	−435.937			−0.517740
$843$		−	270.401i		−	0.320760i
$844$	1737.48			2.05862
$845$		−	377.890i		−	0.447207i
$846$			712.125i			0.841755i
$847$	−701.808	−	384.287i	−0.828581	−	0.453703i
$848$	919.846			1.08472
$849$	−163.941			−0.193099
$850$		−	207.314i		−	0.243899i
$851$	159.090			0.186945
$852$		−	761.117i		−	0.893330i
$853$			970.162i			1.13735i	0.822561	+	0.568677i	$0.192544\pi$
$853$			970.162i			1.13735i	−0.822561	+	0.568677i	$0.807456\pi$
$854$	−1075.73	+	1964.56i	−1.25963	+	2.30042i
$855$	−100.163			−0.117150
$856$	49.4443			0.0577620
$857$			692.118i			0.807606i	0.914846	+	0.403803i	$0.132312\pi$
$857$			692.118i			0.807606i	−0.914846	+	0.403803i	$0.867688\pi$
$858$	0.651479			0.000759299
$859$			480.223i			0.559048i	0.960139	+	0.279524i	$0.0901767\pi$
$859$			480.223i			0.559048i	−0.960139	+	0.279524i	$0.909823\pi$
$860$		−	799.893i		−	0.930108i
$861$	−792.305	−	433.840i	−0.920214	−	0.503879i
$862$	−703.463			−0.816083
$863$	929.311			1.07684			0.538419	−	0.842677i	$-0.319022\pi$
$863$	929.311			1.07684			0.538419	+	0.842677i	$0.319022\pi$
$864$		−	238.585i		−	0.276140i
$865$	−269.542			−0.311609
$866$		−	1141.31i		−	1.31791i
$867$		−	150.751i		−	0.173876i
$868$	96.5590	−	176.342i	0.111243	−	0.203159i
$869$	−255.741			−0.294293
$870$	−196.806			−0.226214
$871$			2.45027i			0.00281317i
$872$	−74.5451			−0.0854875
$873$		−	329.990i		−	0.377995i
$874$		−	970.445i		−	1.11035i
$875$	−37.5878	+	68.6452i	−0.0429575	+	0.0784516i
$876$	−909.704			−1.03847
$877$	1730.63			1.97336			0.986678	−	0.162685i	$-0.0520154\pi$
$877$	1730.63			1.97336			0.986678	+	0.162685i	$0.0520154\pi$
$878$			325.217i			0.370406i
$879$	560.930			0.638145
$880$		−	79.2021i		−	0.0900024i
$881$		−	461.033i		−	0.523307i	−0.965162	−	0.261653i	$-0.915732\pi$
$881$		−	461.033i		−	0.523307i	0.965162	−	0.261653i	$-0.0842677\pi$
$882$	−231.024	−	361.343i	−0.261932	−	0.409686i
$883$	−942.531			−1.06742			−0.533710	−	0.845668i	$-0.679202\pi$
$883$	−942.531			−1.06742			−0.533710	+	0.845668i	$0.679202\pi$
$884$	3.19489			0.00361412
$885$			16.7768i			0.0189568i
$886$	−73.8651			−0.0833692
$887$		−	178.185i		−	0.200885i	−0.994943	−	0.100443i	$-0.967974\pi$
$887$		−	178.185i		−	0.200885i	0.994943	−	0.100443i	$-0.0320259\pi$
$888$			18.4866i			0.0208182i
$889$	−426.316	−	233.436i	−0.479546	−	0.262583i
$890$	507.300			0.570000
$891$	−23.2881			−0.0261370
$892$		−	637.832i		−	0.715058i
$893$	1214.83			1.36039
$894$			461.669i			0.516408i
$895$			114.515i			0.127950i
$896$	−291.225	−	159.465i	−0.325028	−	0.177975i
$897$	1.92236			0.00214310
$898$	−1419.28			−1.58049
$899$		−	110.861i		−	0.123316i
$900$	67.6837			0.0752041
$901$		−	954.975i		−	1.05991i
$902$			562.458i			0.623568i
$903$	461.643	−	843.081i	0.511233	−	0.933645i
$904$	−166.227			−0.183880
$905$	−120.813			−0.133495
$906$		−	107.150i		−	0.118267i
$907$	617.574			0.680897			0.340449	−	0.940263i	$-0.389421\pi$
$907$	617.574			0.680897			0.340449	+	0.940263i	$0.389421\pi$
$908$			1347.64i			1.48419i
$909$		−	290.220i		−	0.319274i
$910$	−1.99567	−	1.09276i	−0.00219304	−	0.00120083i
$911$	−518.521			−0.569178			−0.284589	−	0.958650i	$-0.591857\pi$
$911$	−518.521			−0.569178			−0.284589	+	0.958650i	$0.591857\pi$
$912$	−354.015			−0.388174
$913$			290.094i			0.317737i
$914$	1027.05			1.12369
$915$		−	424.750i		−	0.464208i
$916$		−	10.7293i		−	0.0117132i
$917$	−133.635	+	244.053i	−0.145731	+	0.266143i
$918$	−215.447			−0.234692
$919$	1516.75			1.65044			0.825219	−	0.564813i	$-0.191052\pi$
$919$	1516.75			1.65044			0.825219	+	0.564813i	$0.191052\pi$
$920$			74.4445i			0.0809179i
$921$	−940.234			−1.02088
$922$		−	624.139i		−	0.676940i
$923$		−	4.85203i		−	0.00525681i
$924$	−67.9887	+	124.165i	−0.0735809	+	0.134378i
$925$	35.7080			0.0386033
$926$	422.102			0.455833
$927$			320.884i			0.346153i
$928$	−799.708			−0.861754
$929$			777.683i			0.837118i	0.908189	+	0.418559i	$0.137465\pi$
$929$			777.683i			0.837118i	−0.908189	+	0.418559i	$0.862535\pi$
$930$			71.9244i			0.0773380i
$931$	−616.422	+	394.108i	−0.662107	+	0.423316i
$932$	−1661.05			−1.78224
$933$	702.078			0.752495
$934$			285.662i			0.305848i
$935$	−82.2269			−0.0879432
$936$			0.223381i			0.000238655i
$937$		−	1118.28i		−	1.19347i	−0.802439	−	0.596734i	$-0.796465\pi$
$937$		−	1118.28i		−	1.19347i	0.802439	−	0.596734i	$-0.203535\pi$
$938$	−880.979	−	482.395i	−0.939210	−	0.514280i
$939$	−76.3903			−0.0813529
$940$	−820.900			−0.873298
$941$		−	478.740i		−	0.508757i	−0.967105	−	0.254378i	$-0.918129\pi$
$941$		−	478.740i		−	0.508757i	0.967105	−	0.254378i	$-0.0818709\pi$
$942$	1358.09			1.44171
$943$			1659.68i			1.76000i
$944$			59.2957i			0.0628132i
$945$	71.3381	+	39.0624i	0.0754901	+	0.0413359i
$946$	−598.505			−0.632669
$947$	93.2440			0.0984625			0.0492313	−	0.998787i	$-0.484323\pi$
$947$	93.2440			0.0984625			0.0492313	+	0.998787i	$0.484323\pi$
$948$		−	772.434i		−	0.814803i
$949$	−5.79926			−0.00611092
$950$		−	217.818i		−	0.229282i
$951$			423.675i			0.445504i
$952$	−71.4050	+	130.404i	−0.0750053	+	0.136979i
$953$	774.591			0.812792			0.406396	−	0.913697i	$-0.366785\pi$
$953$	774.591			0.812792			0.406396	+	0.913697i	$0.366785\pi$
$954$	588.164			0.616524
$955$		−	98.1887i		−	0.102815i
$956$	1897.80			1.98514
$957$			78.0590i			0.0815664i
$958$			940.376i			0.981603i
$959$	−552.350	−	302.448i	−0.575965	−	0.315379i
$960$	306.771			0.319553
$961$	920.485			0.957841
$962$			1.03811i			0.00107912i
$963$	−99.2515			−0.103065
$964$			647.978i			0.672176i
$965$			104.392i			0.108178i
$966$	−378.462	+	691.171i	−0.391783	+	0.715497i
$967$	1070.58			1.10711			0.553555	−	0.832813i	$-0.313271\pi$
$967$	1070.58			1.10711			0.553555	+	0.832813i	$0.313271\pi$
$968$	−170.830			−0.176477
$969$			367.535i			0.379293i
$970$	717.606			0.739800
$971$		−	807.893i		−	0.832022i	−0.909360	−	0.416011i	$-0.863428\pi$
$971$		−	807.893i		−	0.832022i	0.909360	−	0.416011i	$-0.136572\pi$
$972$		−	70.3389i		−	0.0723652i
$973$	−425.573	+	777.208i	−0.437383	+	0.798775i
$974$	−1021.05			−1.04831
$975$	0.431476			0.000442539
$976$		−	1501.23i		−	1.53815i
$977$	−1653.68			−1.69261			−0.846306	−	0.532696i	$-0.821179\pi$
$977$	−1653.68			−1.69261			−0.846306	+	0.532696i	$0.821179\pi$
$978$			260.568i			0.266430i
$979$		−	201.210i		−	0.205526i
$980$	416.538	−	266.312i	0.425039	−	0.271747i
$981$	149.637			0.152536
$982$	−1421.89			−1.44795
$983$		−	651.566i		−	0.662834i	−0.943484	−	0.331417i	$-0.892473\pi$
$983$		−	651.566i		−	0.662834i	0.943484	−	0.331417i	$-0.107527\pi$
$984$	−192.858			−0.195994
$985$		−	614.496i		−	0.623854i
$986$			722.154i			0.732407i
$987$	−865.223	−	473.767i	−0.876619	−	0.480008i
$988$	3.35675			0.00339752
$989$	−1766.04			−1.78569
$990$		−	50.6431i		−	0.0511546i
$991$	459.963			0.464140			0.232070	−	0.972699i	$-0.425450\pi$
$991$	459.963			0.464140			0.232070	+	0.972699i	$0.425450\pi$
$992$			292.260i			0.294617i
$993$			895.270i			0.901581i
$994$	1744.52	+	955.239i	1.75505	+	0.961005i
$995$	−604.589			−0.607627
$996$	−876.193			−0.879712
$997$			613.898i			0.615745i	0.951428	+	0.307872i	$0.0996170\pi$
$997$			613.898i			0.615745i	−0.951428	+	0.307872i	$0.900383\pi$
$998$	−43.7850			−0.0438727
$999$		−	37.1089i		−	0.0371460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.h.a.76.9	✓	12
3.2	odd	2		315.3.h.d.181.4		12
4.3	odd	2		1680.3.s.c.1441.7		12
5.2	odd	4		525.3.e.c.349.20		24
5.3	odd	4		525.3.e.c.349.13		24
5.4	even	2		525.3.h.d.76.4		12
7.6	odd	2	inner	105.3.h.a.76.10	yes	12
21.20	even	2		315.3.h.d.181.3		12
28.27	even	2		1680.3.s.c.1441.4		12
35.13	even	4		525.3.e.c.349.19		24
35.27	even	4		525.3.e.c.349.14		24
35.34	odd	2		525.3.h.d.76.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.9	✓	12	1.1	even	1	trivial
105.3.h.a.76.10	yes	12	7.6	odd	2	inner
315.3.h.d.181.3		12	21.20	even	2
315.3.h.d.181.4		12	3.2	odd	2
525.3.e.c.349.13		24	5.3	odd	4
525.3.e.c.349.14		24	35.27	even	4
525.3.e.c.349.19		24	35.13	even	4
525.3.e.c.349.20		24	5.2	odd	4
525.3.h.d.76.3		12	35.34	odd	2
525.3.h.d.76.4		12	5.4	even	2
1680.3.s.c.1441.4		12	28.27	even	2
1680.3.s.c.1441.7		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.91758 q^{2} -1.73205i q^{3} +4.51225 q^{4} -2.23607i q^{5} -5.05339i q^{6} +(6.13981 + 3.36195i) q^{7} +1.49451 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+2.91758 q^{2} -1.73205i q^{3} +4.51225 q^{4} -2.23607i q^{5} -5.05339i q^{6} +(6.13981 + 3.36195i) q^{7} +1.49451 q^{8} -3.00000 q^{9} -6.52390i q^{10} -2.58757 q^{11} -7.81544i q^{12} -0.0498225i q^{13} +(17.9134 + 9.80876i) q^{14} -3.87298 q^{15} -13.6886 q^{16} +14.2114i q^{17} -8.75273 q^{18} +14.9314i q^{19} -10.0897i q^{20} +(5.82308 - 10.6345i) q^{21} -7.54942 q^{22} -22.2765 q^{23} -2.58857i q^{24} -5.00000 q^{25} -0.145361i q^{26} +5.19615i q^{27} +(27.7043 + 15.1700i) q^{28} +17.4169 q^{29} -11.2997 q^{30} -6.36515i q^{31} -45.9156 q^{32} +4.48180i q^{33} +41.4628i q^{34} +(7.51756 - 13.7290i) q^{35} -13.5367 q^{36} -7.14160 q^{37} +43.5635i q^{38} -0.0862951 q^{39} -3.34183i q^{40} -74.5035i q^{41} +(16.9893 - 31.0268i) q^{42} +79.2782 q^{43} -11.6757 q^{44} +6.70820i q^{45} -64.9935 q^{46} -81.3603i q^{47} +23.7094i q^{48} +(26.3945 + 41.2835i) q^{49} -14.5879 q^{50} +24.6149 q^{51} -0.224811i q^{52} -67.1978 q^{53} +15.1602i q^{54} +5.78598i q^{55} +(9.17603 + 5.02449i) q^{56} +25.8620 q^{57} +50.8151 q^{58} -4.33175i q^{59} -17.4759 q^{60} +109.670i q^{61} -18.5708i q^{62} +(-18.4194 - 10.0859i) q^{63} -79.2079 q^{64} -0.111407 q^{65} +13.0760i q^{66} -49.1800 q^{67} +64.1253i q^{68} +38.5841i q^{69} +(21.9330 - 40.0555i) q^{70} +97.3864 q^{71} -4.48354 q^{72} -116.398i q^{73} -20.8362 q^{74} +8.66025i q^{75} +67.3742i q^{76} +(-15.8872 - 8.69929i) q^{77} -0.251773 q^{78} +98.8343 q^{79} +30.6087i q^{80} +9.00000 q^{81} -217.370i q^{82} -112.111i q^{83} +(26.2752 - 47.9853i) q^{84} +31.7777 q^{85} +231.300 q^{86} -30.1669i q^{87} -3.86716 q^{88} +77.7603i q^{89} +19.5717i q^{90} +(0.167501 - 0.305901i) q^{91} -100.517 q^{92} -11.0248 q^{93} -237.375i q^{94} +33.3877 q^{95} +79.5282i q^{96} +109.997i q^{97} +(77.0080 + 120.448i) q^{98} +7.76270 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9	\( 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} + 12 q^{18} + 36 q^{21} - 88 q^{22} - 64 q^{23} - 60 q^{25} + 88 q^{28} + 104 q^{29} - 228 q^{32} + 60 q^{35} - 132 q^{36} + 32 q^{37} - 24 q^{39} - 60 q^{42} + 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 20 q^{50} + 24 q^{51} + 176 q^{53} - 368 q^{56} - 240 q^{57} - 400 q^{58} + 24 q^{63} - 20 q^{64} - 240 q^{65} + 168 q^{67} - 60 q^{70} + 32 q^{71} - 12 q^{72} + 184 q^{74} + 8 q^{77} + 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 120 q^{85} + 400 q^{86} - 536 q^{88} + 24 q^{91} + 192 q^{92} + 48 q^{93} + 884 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 + 12 * q^18 + 36 * q^21 - 88 * q^22 - 64 * q^23 - 60 * q^25 + 88 * q^28 + 104 * q^29 - 228 * q^32 + 60 * q^35 - 132 * q^36 + 32 * q^37 - 24 * q^39 - 60 * q^42 + 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 20 * q^50 + 24 * q^51 + 176 * q^53 - 368 * q^56 - 240 * q^57 - 400 * q^58 + 24 * q^63 - 20 * q^64 - 240 * q^65 + 168 * q^67 - 60 * q^70 + 32 * q^71 - 12 * q^72 + 184 * q^74 + 8 * q^77 + 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 120 * q^85 + 400 * q^86 - 536 * q^88 + 24 * q^91 + 192 * q^92 + 48 * q^93 + 884 * q^98 + 48 * q^99

Introduction

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