LMFDB - Embedded newform 403.2.f.c.94.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.18
Character	$\chi$	$=$	403.94
Dual form			403.2.f.c.373.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20670 + 2.09007i) q^{2} +(-0.882453 - 1.52845i) q^{3} +(-1.91225 + 3.31212i) q^{4} +3.22507 q^{5} +(2.12971 - 3.68877i) q^{6} +(-1.47346 + 2.55211i) q^{7} -4.40325 q^{8} +(-0.0574470 + 0.0995011i) q^{9} +O(q^{10})$	\(q+(1.20670 + 2.09007i) q^{2} +(-0.882453 - 1.52845i) q^{3} +(-1.91225 + 3.31212i) q^{4} +3.22507 q^{5} +(2.12971 - 3.68877i) q^{6} +(-1.47346 + 2.55211i) q^{7} -4.40325 q^{8} +(-0.0574470 + 0.0995011i) q^{9} +(3.89169 + 6.74061i) q^{10} +(0.649128 + 1.12432i) q^{11} +6.74989 q^{12} +(3.25938 - 1.54158i) q^{13} -7.11212 q^{14} +(-2.84597 - 4.92937i) q^{15} +(-1.48891 - 2.57886i) q^{16} +(-1.01729 + 1.76200i) q^{17} -0.277285 q^{18} +(-1.39262 + 2.41208i) q^{19} +(-6.16714 + 10.6818i) q^{20} +5.20105 q^{21} +(-1.56661 + 2.71344i) q^{22} +(1.45821 + 2.52569i) q^{23} +(3.88567 + 6.73017i) q^{24} +5.40108 q^{25} +(7.15509 + 4.95209i) q^{26} -5.09194 q^{27} +(-5.63527 - 9.76057i) q^{28} +(-1.65563 - 2.86763i) q^{29} +(6.86847 - 11.8965i) q^{30} +1.00000 q^{31} +(-0.809927 + 1.40284i) q^{32} +(1.14565 - 1.98432i) q^{33} -4.91025 q^{34} +(-4.75203 + 8.23075i) q^{35} +(-0.219706 - 0.380542i) q^{36} +(-4.16706 - 7.21756i) q^{37} -6.72189 q^{38} +(-5.23248 - 3.62144i) q^{39} -14.2008 q^{40} +(-3.79107 - 6.56632i) q^{41} +(6.27611 + 10.8705i) q^{42} +(5.82687 - 10.0924i) q^{43} -4.96518 q^{44} +(-0.185270 + 0.320898i) q^{45} +(-3.51924 + 6.09551i) q^{46} -1.30142 q^{47} +(-2.62778 + 4.55145i) q^{48} +(-0.842194 - 1.45872i) q^{49} +(6.51748 + 11.2886i) q^{50} +3.59084 q^{51} +(-1.12686 + 13.7433i) q^{52} +11.6438 q^{53} +(-6.14445 - 10.6425i) q^{54} +(2.09348 + 3.62602i) q^{55} +(6.48804 - 11.2376i) q^{56} +4.91568 q^{57} +(3.99569 - 6.92073i) q^{58} +(-2.23576 + 3.87245i) q^{59} +21.7689 q^{60} +(4.15886 - 7.20336i) q^{61} +(1.20670 + 2.09007i) q^{62} +(-0.169292 - 0.293222i) q^{63} -9.86498 q^{64} +(10.5117 - 4.97170i) q^{65} +5.52982 q^{66} +(-4.67226 - 8.09260i) q^{67} +(-3.89063 - 6.73876i) q^{68} +(2.57360 - 4.45761i) q^{69} -22.9371 q^{70} +(2.66595 - 4.61757i) q^{71} +(0.252954 - 0.438128i) q^{72} -13.9024 q^{73} +(10.0568 - 17.4189i) q^{74} +(-4.76620 - 8.25530i) q^{75} +(-5.32607 - 9.22502i) q^{76} -3.82587 q^{77} +(1.25501 - 15.3062i) q^{78} +8.52556 q^{79} +(-4.80183 - 8.31701i) q^{80} +(4.66574 + 8.08130i) q^{81} +(9.14937 - 15.8472i) q^{82} -3.50086 q^{83} +(-9.94572 + 17.2265i) q^{84} +(-3.28083 + 5.68256i) q^{85} +28.1251 q^{86} +(-2.92202 + 5.06109i) q^{87} +(-2.85828 - 4.95068i) q^{88} +(1.52054 + 2.63366i) q^{89} -0.894264 q^{90} +(-0.868290 + 10.5898i) q^{91} -11.1539 q^{92} +(-0.882453 - 1.52845i) q^{93} +(-1.57043 - 2.72006i) q^{94} +(-4.49129 + 7.77914i) q^{95} +2.85889 q^{96} +(-9.01176 + 15.6088i) q^{97} +(2.03255 - 3.52048i) q^{98} -0.149162 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.20670	+	2.09007i	0.853266	+	1.47790i	0.878244	+	0.478212i	$0.158715\pi$
$2$	1.20670	+	2.09007i	0.853266	+	1.47790i	−0.0249785	+	0.999688i	$0.507952\pi$
$3$	−0.882453	−	1.52845i	−0.509485	−	0.882453i	−0.999940	−	0.0109866i	$-0.996503\pi$
$3$	−0.882453	−	1.52845i	−0.509485	−	0.882453i	0.490455	−	0.871466i	$-0.336831\pi$
$4$	−1.91225	+	3.31212i	−0.956126	+	1.65606i
$5$	3.22507			1.44230			0.721148	−	0.692781i	$-0.243615\pi$
$5$	3.22507			1.44230			0.721148	+	0.692781i	$0.243615\pi$
$6$	2.12971	−	3.68877i	0.869452	−	1.50593i
$7$	−1.47346	+	2.55211i	−0.556917	+	0.964609i	0.440834	+	0.897588i	$0.354683\pi$
$7$	−1.47346	+	2.55211i	−0.556917	+	0.964609i	−0.997752	+	0.0670204i	$0.978651\pi$
$8$	−4.40325			−1.55679
$9$	−0.0574470	+	0.0995011i	−0.0191490	+	0.0331670i
$10$	3.89169	+	6.74061i	1.23066	+	2.13157i
$11$	0.649128	+	1.12432i	0.195719	+	0.338996i	0.947136	−	0.320832i	$-0.103962\pi$
$11$	0.649128	+	1.12432i	0.195719	+	0.338996i	−0.751417	+	0.659828i	$0.770629\pi$
$12$	6.74989			1.94852
$13$	3.25938	−	1.54158i	0.903988	−	0.427557i
$13$	3.25938	−	1.54158i	0.903988	−	0.427557i
$14$	−7.11212			−1.90079
$15$	−2.84597	−	4.92937i	−0.734827	−	1.27276i
$16$	−1.48891	−	2.57886i	−0.372227	−	0.644715i
$17$	−1.01729	+	1.76200i	−0.246729	+	0.427347i	−0.962616	−	0.270869i	$-0.912689\pi$
$17$	−1.01729	+	1.76200i	−0.246729	+	0.427347i	0.715887	+	0.698216i	$0.246022\pi$
$18$	−0.277285			−0.0653567
$19$	−1.39262	+	2.41208i	−0.319488	+	0.553370i	−0.980381	−	0.197110i	$-0.936844\pi$
$19$	−1.39262	+	2.41208i	−0.319488	+	0.553370i	0.660893	+	0.750480i	$0.270178\pi$
$20$	−6.16714	+	10.6818i	−1.37902	+	2.38852i
$21$	5.20105			1.13496
$22$	−1.56661	+	2.71344i	−0.334001	+	0.578507i
$23$	1.45821	+	2.52569i	0.304058	+	0.526644i	0.977051	−	0.213005i	$-0.0683251\pi$
$23$	1.45821	+	2.52569i	0.304058	+	0.526644i	−0.672993	+	0.739649i	$0.734992\pi$
$24$	3.88567	+	6.73017i	0.793158	+	1.37379i
$25$	5.40108			1.08022
$26$	7.15509	+	4.95209i	1.40323	+	0.971185i
$27$	−5.09194			−0.979945
$28$	−5.63527	−	9.76057i	−1.06497	−	1.84457i
$29$	−1.65563	−	2.86763i	−0.307442	−	0.532505i	0.670360	−	0.742036i	$-0.266140\pi$
$29$	−1.65563	−	2.86763i	−0.307442	−	0.532505i	−0.977802	+	0.209531i	$0.932806\pi$
$30$	6.86847	−	11.8965i	1.25401	−	2.17200i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.809927	+	1.40284i	−0.143176	+	0.247989i
$33$	1.14565	−	1.98432i	0.199432	−	0.345426i
$34$	−4.91025			−0.842102
$35$	−4.75203	+	8.23075i	−0.803239	+	1.39125i
$36$	−0.219706	−	0.380542i	−0.0366177	−	0.0634237i
$37$	−4.16706	−	7.21756i	−0.685060	−	1.18656i	−0.973418	−	0.229036i	$-0.926443\pi$
$37$	−4.16706	−	7.21756i	−0.685060	−	1.18656i	0.288358	−	0.957523i	$-0.406891\pi$
$38$	−6.72189			−1.09043
$39$	−5.23248	−	3.62144i	−0.837867	−	0.579894i
$40$	−14.2008			−2.24534
$41$	−3.79107	−	6.56632i	−0.592065	−	1.02549i	−0.993954	−	0.109799i	$-0.964979\pi$
$41$	−3.79107	−	6.56632i	−0.592065	−	1.02549i	0.401889	−	0.915689i	$-0.368354\pi$
$42$	6.27611	+	10.8705i	0.968425	+	1.67736i
$43$	5.82687	−	10.0924i	0.888589	−	1.53908i	0.0470441	−	0.998893i	$-0.485020\pi$
$43$	5.82687	−	10.0924i	0.888589	−	1.53908i	0.841545	−	0.540188i	$-0.181647\pi$
$44$	−4.96518			−0.748529
$45$	−0.185270	+	0.320898i	−0.0276185	+	0.0478366i
$46$	−3.51924	+	6.09551i	−0.518884	+	0.898734i
$47$	−1.30142			−0.189832			−0.0949160	−	0.995485i	$-0.530258\pi$
$47$	−1.30142			−0.189832			−0.0949160	+	0.995485i	$0.530258\pi$
$48$	−2.62778	+	4.55145i	−0.379287	+	0.656945i
$49$	−0.842194	−	1.45872i	−0.120313	−	0.208389i
$50$	6.51748	+	11.2886i	0.921711	+	1.59645i
$51$	3.59084			0.502818
$52$	−1.12686	+	13.7433i	−0.156267	+	1.90586i
$53$	11.6438			1.59940			0.799702	−	0.600397i	$-0.204991\pi$
$53$	11.6438			1.59940			0.799702	+	0.600397i	$0.204991\pi$
$54$	−6.14445	−	10.6425i	−0.836153	−	1.44826i
$55$	2.09348	+	3.62602i	0.282285	+	0.488932i
$56$	6.48804	−	11.2376i	0.867001	−	1.50169i
$57$	4.91568			0.651098
$58$	3.99569	−	6.92073i	0.524659	−	0.908737i
$59$	−2.23576	+	3.87245i	−0.291071	+	0.504150i	−0.974063	−	0.226276i	$-0.927345\pi$
$59$	−2.23576	+	3.87245i	−0.291071	+	0.504150i	0.682992	+	0.730426i	$0.260678\pi$
$60$	21.7689			2.81035
$61$	4.15886	−	7.20336i	0.532488	−	0.922296i	−0.466793	−	0.884367i	$-0.654591\pi$
$61$	4.15886	−	7.20336i	0.532488	−	0.922296i	0.999280	−	0.0379292i	$-0.0120761\pi$
$62$	1.20670	+	2.09007i	0.153251	+	0.265439i
$63$	−0.169292	−	0.293222i	−0.0213288	−	0.0369426i
$64$	−9.86498			−1.23312
$65$	10.5117	−	4.97170i	1.30382	−	0.616663i
$66$	5.52982			0.680674
$67$	−4.67226	−	8.09260i	−0.570808	−	0.988668i	−0.996483	−	0.0837925i	$-0.973297\pi$
$67$	−4.67226	−	8.09260i	−0.570808	−	0.988668i	0.425675	−	0.904876i	$-0.360037\pi$
$68$	−3.89063	−	6.73876i	−0.471808	−	0.817195i
$69$	2.57360	−	4.45761i	0.309825	−	0.536633i
$70$	−22.9371			−2.74151
$71$	2.66595	−	4.61757i	0.316390	−	0.548004i	−0.663342	−	0.748317i	$-0.730862\pi$
$71$	2.66595	−	4.61757i	0.316390	−	0.548004i	0.979732	+	0.200312i	$0.0641957\pi$
$72$	0.252954	−	0.438128i	0.0298109	−	0.0516339i
$73$	−13.9024			−1.62716			−0.813579	−	0.581455i	$-0.802484\pi$
$73$	−13.9024			−1.62716			−0.813579	+	0.581455i	$0.802484\pi$
$74$	10.0568	−	17.4189i	1.16908	−	2.02490i
$75$	−4.76620	−	8.25530i	−0.550353	−	0.953240i
$76$	−5.32607	−	9.22502i	−0.610942	−	1.05818i
$77$	−3.82587			−0.435998
$78$	1.25501	−	15.3062i	0.142102	−	1.73309i
$79$	8.52556			0.959200			0.479600	−	0.877487i	$-0.340782\pi$
$79$	8.52556			0.959200			0.479600	+	0.877487i	$0.340782\pi$
$80$	−4.80183	−	8.31701i	−0.536861	−	0.929870i
$81$	4.66574	+	8.08130i	0.518416	+	0.897922i
$82$	9.14937	−	15.8472i	1.01038	−	1.75003i
$83$	−3.50086			−0.384269			−0.192135	−	0.981369i	$-0.561541\pi$
$83$	−3.50086			−0.384269			−0.192135	+	0.981369i	$0.561541\pi$
$84$	−9.94572	+	17.2265i	−1.08517	+	1.87956i
$85$	−3.28083	+	5.68256i	−0.355856	+	0.616361i
$86$	28.1251			3.03281
$87$	−2.92202	+	5.06109i	−0.313274	+	0.542606i
$88$	−2.85828	−	4.95068i	−0.304693	−	0.527744i
$89$	1.52054	+	2.63366i	0.161177	+	0.279167i	0.935291	−	0.353879i	$-0.115138\pi$
$89$	1.52054	+	2.63366i	0.161177	+	0.279167i	−0.774114	+	0.633046i	$0.781804\pi$
$90$	−0.894264			−0.0942637
$91$	−0.868290	+	10.5898i	−0.0910216	+	1.11011i
$92$	−11.1539			−1.16287
$93$	−0.882453	−	1.52845i	−0.0915061	−	0.158493i
$94$	−1.57043	−	2.72006i	−0.161977	−	0.280553i
$95$	−4.49129	+	7.77914i	−0.460797	+	0.798123i
$96$	2.85889			0.291784
$97$	−9.01176	+	15.6088i	−0.915005	+	1.58484i	−0.108111	+	0.994139i	$0.534480\pi$
$97$	−9.01176	+	15.6088i	−0.915005	+	1.58484i	−0.806894	+	0.590697i	$0.798853\pi$
$98$	2.03255	−	3.52048i	0.205319	−	0.355622i
$99$	−0.149162			−0.0149913
$100$	−10.3282	+	17.8890i	−1.03282	+	1.78890i
$101$	−6.27536	−	10.8692i	−0.624421	−	1.08153i	−0.988652	−	0.150221i	$-0.952002\pi$
$101$	−6.27536	−	10.8692i	−0.624421	−	1.08153i	0.364231	−	0.931309i	$-0.381332\pi$
$102$	4.33307	+	7.50510i	0.429038	+	0.743115i
$103$	−7.11343			−0.700908			−0.350454	−	0.936580i	$-0.613973\pi$
$103$	−7.11343			−0.700908			−0.350454	+	0.936580i	$0.613973\pi$
$104$	−14.3519	+	6.78796i	−1.40732	+	0.665614i
$105$	16.7738			1.63695
$106$	14.0506	+	24.3364i	1.36472	+	2.36376i
$107$	−6.31749	−	10.9422i	−0.610735	−	1.05782i	−0.991117	−	0.132994i	$-0.957541\pi$
$107$	−6.31749	−	10.9422i	−0.610735	−	1.05782i	0.380382	−	0.924829i	$-0.375792\pi$
$108$	9.73707	−	16.8651i	0.936950	−	1.62285i
$109$	11.6220			1.11319			0.556593	−	0.830786i	$-0.312108\pi$
$109$	11.6220			1.11319			0.556593	+	0.830786i	$0.312108\pi$
$110$	−5.05241	+	8.75104i	−0.481729	+	0.834378i
$111$	−7.35447	+	12.7383i	−0.698055	+	1.20907i
$112$	8.77540			0.829197
$113$	−4.53921	+	7.86215i	−0.427013	+	0.739608i	−0.996606	−	0.0823185i	$-0.973768\pi$
$113$	−4.53921	+	7.86215i	−0.427013	+	0.739608i	0.569593	+	0.821927i	$0.307101\pi$
$114$	5.93175	+	10.2741i	0.555559	+	0.962257i
$115$	4.70283	+	8.14554i	0.438541	+	0.759576i
$116$	12.6639			1.17581
$117$	−0.0338526	+	0.412870i	−0.00312968	+	0.0381699i
$118$	−10.7916			−0.993444
$119$	−2.99788	−	5.19248i	−0.274815	−	0.475994i
$120$	12.5315	+	21.7053i	1.14397	+	1.98141i
$121$	4.65727	−	8.06662i	0.423388	−	0.733329i
$122$	20.0740			1.81741
$123$	−6.69088	+	11.5889i	−0.603296	+	1.04494i
$124$	−1.91225	+	3.31212i	−0.171725	+	0.297437i
$125$	1.29350			0.115695
$126$	0.408570	−	0.707663i	0.0363983	−	0.0630437i
$127$	3.82750	+	6.62943i	0.339636	+	0.588267i	0.984364	−	0.176145i	$-0.0563628\pi$
$127$	3.82750	+	6.62943i	0.339636	+	0.588267i	−0.644728	+	0.764412i	$0.723029\pi$
$128$	−10.2842	−	17.8128i	−0.909006	−	1.57444i
$129$	−20.5677			−1.81089
$130$	23.0757	+	15.9708i	2.02387	+	1.40074i
$131$	11.8720			1.03726			0.518629	−	0.854999i	$-0.326443\pi$
$131$	11.8720			1.03726			0.518629	+	0.854999i	$0.326443\pi$
$132$	4.38154	+	7.58905i	0.381364	+	0.660542i
$133$	−4.10394	−	7.10824i	−0.355857	−	0.616363i
$134$	11.2760	−	19.5307i	0.974102	−	1.68719i
$135$	−16.4219			−1.41337
$136$	4.47938	−	7.75852i	0.384104	−	0.665288i
$137$	−0.00670178	+	0.0116078i	−0.000572572	+	0.000991723i	−0.866312	−	0.499504i	$-0.833516\pi$
$137$	−0.00670178	+	0.0116078i	−0.000572572	+	0.000991723i	0.865739	+	0.500496i	$0.166849\pi$
$138$	12.4223			1.05745
$139$	−2.78758	+	4.82823i	−0.236440	+	0.409525i	−0.959690	−	0.281060i	$-0.909314\pi$
$139$	−2.78758	+	4.82823i	−0.236440	+	0.409525i	0.723251	+	0.690586i	$0.242647\pi$
$140$	−18.1741	−	31.4785i	−1.53599	−	2.66042i
$141$	1.14844	+	1.98916i	0.0967164	+	0.167518i
$142$	12.8680			1.07986
$143$	3.84898	+	2.66391i	0.321868	+	0.222767i
$144$	0.342133			0.0285110
$145$	−5.33951	−	9.24830i	−0.443422	−	0.768030i
$146$	−16.7761	−	29.0570i	−1.38840	−	2.40478i
$147$	−1.48639	+	2.57451i	−0.122596	+	0.212342i
$148$	31.8739			2.62001
$149$	−7.25215	+	12.5611i	−0.594119	+	1.02904i	0.399551	+	0.916711i	$0.369166\pi$
$149$	−7.25215	+	12.5611i	−0.594119	+	1.02904i	−0.993671	+	0.112334i	$0.964167\pi$
$150$	11.5027	−	19.9233i	0.939195	−	1.62673i
$151$	−17.9192			−1.45825			−0.729123	−	0.684383i	$-0.760072\pi$
$151$	−17.9192			−1.45825			−0.729123	+	0.684383i	$0.760072\pi$
$152$	6.13205	−	10.6210i	0.497375	−	0.861479i
$153$	−0.116880	−	0.202443i	−0.00944922	−	0.0163665i
$154$	−4.61667	−	7.99631i	−0.372022	−	0.644361i
$155$	3.22507			0.259044
$156$	22.0004	−	10.4055i	1.76144	−	0.833105i
$157$	15.4981			1.23689			0.618443	−	0.785830i	$-0.287764\pi$
$157$	15.4981			1.23689			0.618443	+	0.785830i	$0.287764\pi$
$158$	10.2878	+	17.8190i	0.818453	+	1.41760i
$159$	−10.2751	−	17.7971i	−0.814871	−	1.41140i
$160$	−2.61207	+	4.52424i	−0.206502	+	0.357673i
$161$	−8.59448			−0.677340
$162$	−11.2603	+	19.5034i	−0.884693	+	1.53233i
$163$	−6.17735	+	10.6995i	−0.483847	+	0.838048i	−0.999828	−	0.0185525i	$-0.994094\pi$
$163$	−6.17735	+	10.6995i	−0.483847	+	0.838048i	0.515981	+	0.856600i	$0.327428\pi$
$164$	28.9979			2.26436
$165$	3.69480	−	6.39958i	0.287640	−	0.498207i
$166$	−4.22449	−	7.31703i	−0.327884	−	0.567912i
$167$	−0.837290	−	1.45023i	−0.0647915	−	0.112222i	0.831810	−	0.555060i	$-0.187305\pi$
$167$	−0.837290	−	1.45023i	−0.0647915	−	0.112222i	−0.896601	+	0.442838i	$0.853972\pi$
$168$	−22.9016			−1.76689
$169$	8.24707	−	10.0492i	0.634390	−	0.773013i
$170$	−15.8359			−1.21456
$171$	−0.160003	−	0.277134i	−0.0122358	−	0.0211930i
$172$	22.2849	+	38.5985i	1.69920	+	2.94311i
$173$	−3.53795	+	6.12792i	−0.268986	+	0.465897i	−0.968600	−	0.248624i	$-0.920022\pi$
$173$	−3.53795	+	6.12792i	−0.268986	+	0.465897i	0.699615	+	0.714520i	$0.253355\pi$
$174$	−14.1040			−1.06922
$175$	−7.95830	+	13.7842i	−0.601591	+	1.04199i
$176$	1.93298	−	3.34802i	0.145704	−	0.252367i
$177$	7.89181			0.593185
$178$	−3.66968	+	6.35608i	−0.275054	+	0.476408i
$179$	3.26407	+	5.65354i	0.243968	+	0.422566i	0.961841	−	0.273609i	$-0.0882174\pi$
$179$	3.26407	+	5.65354i	0.243968	+	0.422566i	−0.717873	+	0.696174i	$0.754884\pi$
$180$	−0.708567	−	1.22727i	−0.0528135	−	0.0914757i
$181$	12.6349			0.939144			0.469572	−	0.882894i	$-0.344408\pi$
$181$	12.6349			0.939144			0.469572	+	0.882894i	$0.344408\pi$
$182$	−23.1811	+	10.9639i	−1.71830	+	0.812697i
$183$	−14.6800			−1.08518
$184$	−6.42087	−	11.1213i	−0.473353	−	0.819871i
$185$	−13.4391	−	23.2771i	−0.988059	−	1.71137i
$186$	2.12971	−	3.68877i	0.156158	−	0.270474i
$187$	−2.64140			−0.193159
$188$	2.48865	−	4.31046i	0.181503	−	0.314373i
$189$	7.50279	−	12.9952i	0.545748	−	0.945263i
$190$	−21.6786			−1.57273
$191$	1.73356	−	3.00261i	0.125436	−	0.217261i	−0.796467	−	0.604681i	$-0.793300\pi$
$191$	1.73356	−	3.00261i	0.125436	−	0.217261i	0.921903	+	0.387420i	$0.126634\pi$
$192$	8.70539	+	15.0782i	0.628257	+	1.08817i
$193$	3.56973	+	6.18296i	0.256955	+	0.445059i	0.965425	−	0.260682i	$-0.0839474\pi$
$193$	3.56973	+	6.18296i	0.256955	+	0.445059i	−0.708470	+	0.705741i	$0.750614\pi$
$194$	−43.4980			−3.12297
$195$	−16.8751	−	11.6794i	−1.20845	−	0.836378i
$196$	6.44194			0.460139
$197$	−9.57939	−	16.5920i	−0.682503	−	1.18213i	−0.974215	−	0.225624i	$-0.927558\pi$
$197$	−9.57939	−	16.5920i	−0.682503	−	1.18213i	0.291711	−	0.956506i	$-0.405775\pi$
$198$	−0.179993	−	0.311758i	−0.0127916	−	0.0221557i
$199$	−8.49590	+	14.7153i	−0.602259	+	1.04314i	0.390220	+	0.920722i	$0.372399\pi$
$199$	−8.49590	+	14.7153i	−0.602259	+	1.04314i	−0.992478	+	0.122421i	$0.960934\pi$
$200$	−23.7823			−1.68166
$201$	−8.24611	+	14.2827i	−0.581636	+	1.00742i
$202$	15.1449	−	26.2318i	1.06559	−	1.84566i
$203$	9.75802			0.684879
$204$	−6.86659	+	11.8933i	−0.480757	+	0.832696i
$205$	−12.2265	−	21.1769i	−0.853933	−	1.47906i
$206$	−8.58378	−	14.8675i	−0.598061	−	1.03587i
$207$	−0.335079			−0.0232896
$208$	−8.82842	−	6.11021i	−0.612141	−	0.423667i
$209$	−3.61595			−0.250120
$210$	20.2409	+	35.0583i	1.39675	+	2.41925i
$211$	9.75835	+	16.9020i	0.671792	+	1.16358i	0.977395	+	0.211420i	$0.0678086\pi$
$211$	9.75835	+	16.9020i	0.671792	+	1.16358i	−0.305603	+	0.952159i	$0.598858\pi$
$212$	−22.2659	+	38.5657i	−1.52923	+	2.64871i
$213$	−9.41031			−0.644784
$214$	15.2466	−	26.4079i	1.04224	−	1.80521i
$215$	18.7920	−	32.5488i	1.28161	−	2.21981i
$216$	22.4211			1.52556
$217$	−1.47346	+	2.55211i	−0.100025	+	0.173249i
$218$	14.0243	+	24.2907i	0.949843	+	1.64518i
$219$	12.2683	+	21.2492i	0.829012	+	1.43589i
$220$	−16.0131			−1.07960
$221$	−0.599473	+	7.31124i	−0.0403249	+	0.491807i
$222$	−35.4986			−2.38251
$223$	5.31379	+	9.20375i	0.355837	+	0.616329i	0.987261	−	0.159110i	$-0.0508623\pi$
$223$	5.31379	+	9.20375i	0.355837	+	0.616329i	−0.631423	+	0.775438i	$0.717529\pi$
$224$	−2.38680	−	4.13406i	−0.159475	−	0.276218i
$225$	−0.310276	+	0.537413i	−0.0206850	+	0.0358275i
$226$	−21.9099			−1.45742
$227$	12.5937	−	21.8130i	0.835876	−	1.44778i	−0.0574399	−	0.998349i	$-0.518294\pi$
$227$	12.5937	−	21.8130i	0.835876	−	1.44778i	0.893316	−	0.449430i	$-0.148373\pi$
$228$	−9.40001	+	16.2813i	−0.622531	+	1.07826i
$229$	−19.4999			−1.28859			−0.644294	−	0.764778i	$-0.722849\pi$
$229$	−19.4999			−1.28859			−0.644294	+	0.764778i	$0.722849\pi$
$230$	−11.3498	+	19.6585i	−0.748384	+	1.29624i
$231$	3.37615	+	5.84766i	0.222134	+	0.384748i
$232$	7.29014	+	12.6269i	0.478621	+	0.828996i
$233$	−7.02545			−0.460252			−0.230126	−	0.973161i	$-0.573914\pi$
$233$	−7.02545			−0.460252			−0.230126	+	0.973161i	$0.573914\pi$
$234$	−0.903776	+	0.427457i	−0.0590817	+	0.0279437i
$235$	−4.19718			−0.273794
$236$	−8.55066	−	14.8102i	−0.556601	−	0.964061i
$237$	−7.52340	−	13.0309i	−0.488698	−	0.846449i
$238$	7.23508	−	12.5315i	0.468981	−	0.812299i
$239$	−17.8702			−1.15593			−0.577963	−	0.816063i	$-0.696152\pi$
$239$	−17.8702			−1.15593			−0.577963	+	0.816063i	$0.696152\pi$
$240$	−8.47477	+	14.6787i	−0.547044	+	0.947509i
$241$	−4.90945	+	8.50341i	−0.316245	+	0.547753i	−0.979701	−	0.200462i	$-0.935756\pi$
$241$	−4.90945	+	8.50341i	−0.316245	+	0.547753i	0.663456	+	0.748215i	$0.269089\pi$
$242$	22.4797			1.44505
$243$	0.596682	−	1.03348i	0.0382772	−	0.0662980i
$244$	15.9056	+	27.5493i	1.01825	+	1.76366i
$245$	−2.71613	−	4.70448i	−0.173527	−	0.300558i
$246$	−32.2955			−2.05909
$247$	−0.820649	+	10.0087i	−0.0522166	+	0.636840i
$248$	−4.40325			−0.279607
$249$	3.08935	+	5.35090i	0.195779	+	0.339100i
$250$	1.56087	+	2.70351i	0.0987183	+	0.170985i
$251$	9.08819	−	15.7412i	0.573641	−	0.993576i	−0.422547	−	0.906341i	$-0.638864\pi$
$251$	9.08819	−	15.7412i	0.573641	−	0.993576i	0.996188	−	0.0872346i	$-0.0278030\pi$
$252$	1.29492			0.0815720
$253$	−1.89313	+	3.27900i	−0.119020	+	0.206149i
$254$	−9.23730	+	15.9995i	−0.579600	+	1.00390i
$255$	11.5807			0.725212
$256$	14.9550	−	25.9028i	0.934685	−	1.61892i
$257$	11.6018	+	20.0950i	0.723702	+	1.25349i	0.959506	+	0.281688i	$0.0908943\pi$
$257$	11.6018	+	20.0950i	0.723702	+	1.25349i	−0.235804	+	0.971801i	$0.575772\pi$
$258$	−24.8191	−	42.9879i	−1.54517	−	2.67631i
$259$	24.5600			1.52609
$260$	−3.63421	+	44.3232i	−0.225384	+	2.74881i
$261$	0.380443			0.0235488
$262$	14.3259	+	24.8132i	0.885057	+	1.53296i
$263$	4.45847	+	7.72229i	0.274921	+	0.476177i	0.970115	−	0.242645i	$-0.0780150\pi$
$263$	4.45847	+	7.72229i	0.274921	+	0.476177i	−0.695194	+	0.718822i	$0.744682\pi$
$264$	−5.04459	+	8.73748i	−0.310473	+	0.537755i
$265$	37.5522			2.30681
$266$	9.90446	−	17.1550i	0.607282	−	1.05184i
$267$	2.68362	−	4.64816i	0.164235	−	0.284463i
$268$	35.7382			2.18306
$269$	10.0168	−	17.3497i	0.610737	−	1.05783i	−0.380379	−	0.924831i	$-0.624206\pi$
$269$	10.0168	−	17.3497i	0.610737	−	1.05783i	0.991116	−	0.132997i	$-0.0424602\pi$
$270$	−19.8163	−	34.3228i	−1.20598	−	2.08882i
$271$	−3.87614	−	6.71367i	−0.235459	−	0.407826i	0.723947	−	0.689855i	$-0.242326\pi$
$271$	−3.87614	−	6.71367i	−0.235459	−	0.407826i	−0.959406	+	0.282029i	$0.908993\pi$
$272$	6.05859			0.367356
$273$	16.9522	−	8.01783i	1.02599	−	0.485261i
$274$	−0.0323482			−0.00195422
$275$	3.50599	+	6.07255i	0.211419	+	0.366189i
$276$	9.84275	+	17.0481i	0.592464	+	1.02618i
$277$	−9.63011	+	16.6798i	−0.578617	+	1.00219i	0.417021	+	0.908897i	$0.363074\pi$
$277$	−9.63011	+	16.6798i	−0.578617	+	1.00219i	−0.995638	+	0.0932979i	$0.970259\pi$
$278$	−13.4551			−0.806983
$279$	−0.0574470	+	0.0995011i	−0.00343926	+	0.00595697i
$280$	20.9244	−	36.2421i	1.25047	−	2.16588i
$281$	31.4761			1.87771			0.938853	−	0.344317i	$-0.111890\pi$
$281$	31.4761			1.87771			0.938853	+	0.344317i	$0.111890\pi$
$282$	−2.77166	+	4.80065i	−0.165050	+	0.285874i
$283$	−3.83832	−	6.64817i	−0.228165	−	0.395193i	0.729100	−	0.684408i	$-0.239939\pi$
$283$	−3.83832	−	6.64817i	−0.228165	−	0.395193i	−0.957264	+	0.289215i	$0.906606\pi$
$284$	10.1959	+	17.6599i	0.605018	+	1.04792i
$285$	15.8534			0.939075
$286$	−0.923177	+	11.2592i	−0.0545886	+	0.665769i
$287$	22.3440			1.31893
$288$	−0.0930557	−	0.161177i	−0.00548336	−	0.00949746i
$289$	6.43024	+	11.1375i	0.378250	+	0.655148i
$290$	12.8864	−	22.3199i	0.756714	−	1.31067i
$291$	31.8098			1.86472
$292$	26.5850	−	46.0465i	1.55577	−	2.69467i
$293$	−10.0118	+	17.3410i	−0.584898	+	1.01307i	0.409990	+	0.912090i	$0.365532\pi$
$293$	−10.0118	+	17.3410i	−0.584898	+	1.01307i	−0.994888	+	0.100983i	$0.967801\pi$
$294$	−7.17452			−0.418427
$295$	−7.21048	+	12.4889i	−0.419810	+	0.727133i
$296$	18.3486	+	31.7807i	1.06649	+	1.84722i
$297$	−3.30532	−	5.72498i	−0.191794	−	0.332197i
$298$	−35.0047			−2.02777
$299$	8.64641	+	5.98424i	0.500035	+	0.346078i
$300$	36.4567			2.10483
$301$	17.1714	+	29.7417i	0.989740	+	1.71428i
$302$	−21.6231	−	37.4524i	−1.24427	−	2.15514i
$303$	−11.0754	+	19.1832i	−0.636266	+	1.10204i
$304$	8.29391			0.475688
$305$	13.4126	−	23.2313i	0.768005	−	1.33022i
$306$	0.282079	−	0.488575i	0.0161254	−	0.0279300i
$307$	−11.5486			−0.659113			−0.329557	−	0.944136i	$-0.606899\pi$
$307$	−11.5486			−0.659113			−0.329557	+	0.944136i	$0.606899\pi$
$308$	7.31602	−	12.6717i	0.416869	−	0.722038i
$309$	6.27727	+	10.8726i	0.357102	+	0.618518i
$310$	3.89169	+	6.74061i	0.221033	+	0.382841i
$311$	−5.18801			−0.294185			−0.147093	−	0.989123i	$-0.546992\pi$
$311$	−5.18801			−0.294185			−0.147093	+	0.989123i	$0.546992\pi$
$312$	23.0399	+	15.9461i	1.30438	+	0.902770i
$313$	−22.5723			−1.27586			−0.637931	−	0.770093i	$-0.720210\pi$
$313$	−22.5723			−1.27586			−0.637931	+	0.770093i	$0.720210\pi$
$314$	18.7016	+	32.3921i	1.05539	+	1.82799i
$315$	−0.545979	−	0.945663i	−0.0307624	−	0.0532821i
$316$	−16.3030	+	28.2376i	−0.917116	+	1.58849i
$317$	24.0810			1.35252			0.676262	−	0.736662i	$-0.263599\pi$
$317$	24.0810			1.35252			0.676262	+	0.736662i	$0.263599\pi$
$318$	24.7980	−	42.9514i	1.39060	−	2.40860i
$319$	2.14943	−	3.72291i	0.120345	−	0.208443i
$320$	−31.8153			−1.77853
$321$	−11.1498	+	19.3120i	−0.622320	+	1.07789i
$322$	−10.3710	−	17.9630i	−0.577951	−	1.00104i
$323$	−2.83339	−	4.90758i	−0.157654	−	0.273065i
$324$	−35.6883			−1.98268
$325$	17.6041	−	8.32618i	0.976502	−	0.461854i
$326$	−29.8168			−1.65140
$327$	−10.2559	−	17.7637i	−0.567151	−	0.982334i
$328$	16.6930	+	28.9132i	0.921719	+	1.59646i
$329$	1.91760	−	3.32138i	0.105721	−	0.183114i
$330$	17.8341			0.981733
$331$	8.76955	−	15.1893i	0.482018	−	0.834880i	−0.517769	−	0.855521i	$-0.673237\pi$
$331$	8.76955	−	15.1893i	0.482018	−	0.834880i	0.999787	+	0.0206406i	$0.00657058\pi$
$332$	6.69453	−	11.5953i	0.367410	−	0.636372i
$333$	0.957539			0.0524728
$334$	2.02072	−	3.49998i	0.110569	−	0.191511i
$335$	−15.0684	−	26.0992i	−0.823274	−	1.42595i
$336$	−7.74388	−	13.4128i	−0.422463	−	0.731728i
$337$	−9.81800			−0.534821			−0.267410	−	0.963583i	$-0.586168\pi$
$337$	−9.81800			−0.534821			−0.267410	+	0.963583i	$0.586168\pi$
$338$	30.9552	+	5.11060i	1.68374	+	0.277980i
$339$	16.0226			0.870226
$340$	−12.5475	−	21.7330i	−0.680486	−	1.17864i
$341$	0.649128	+	1.12432i	0.0351522	+	0.0608855i
$342$	0.386152	−	0.668835i	0.0208807	−	0.0361665i
$343$	−15.6647			−0.845816
$344$	−25.6572	+	44.4395i	−1.38334	+	2.39602i
$345$	8.30005	−	14.3761i	0.446860	−	0.773984i
$346$	−17.0770			−0.918065
$347$	−13.3781	+	23.1716i	−0.718176	+	1.24392i	0.243545	+	0.969890i	$0.421690\pi$
$347$	−13.3781	+	23.1716i	−0.718176	+	1.24392i	−0.961722	+	0.274028i	$0.911644\pi$
$348$	−11.1753	−	19.3562i	−0.599058	−	1.03760i
$349$	17.6841	+	30.6298i	0.946608	+	1.63957i	0.752498	+	0.658594i	$0.228849\pi$
$349$	17.6841	+	30.6298i	0.946608	+	1.63957i	0.194110	+	0.980980i	$0.437818\pi$
$350$	−38.4131			−2.05327
$351$	−16.5966	+	7.84963i	−0.885859	+	0.418982i
$352$	−2.10299			−0.112090
$353$	2.96636	+	5.13789i	0.157883	+	0.273462i	0.934105	−	0.356998i	$-0.116200\pi$
$353$	2.96636	+	5.13789i	0.157883	+	0.273462i	−0.776222	+	0.630460i	$0.782866\pi$
$354$	9.52305	+	16.4944i	0.506144	+	0.876668i
$355$	8.59788	−	14.8920i	0.456328	−	0.790384i
$356$	−11.6306			−0.616423
$357$	−5.29098	+	9.16424i	−0.280028	+	0.485023i
$358$	−7.87752	+	13.6443i	−0.416340	+	0.721122i
$359$	24.2390			1.27929			0.639643	−	0.768672i	$-0.279082\pi$
$359$	24.2390			1.27929			0.639643	+	0.768672i	$0.279082\pi$
$360$	0.815793	−	1.41300i	0.0429961	−	0.0744714i
$361$	5.62123	+	9.73626i	0.295854	+	0.512435i
$362$	15.2465	+	26.4078i	0.801340	+	1.38796i
$363$	−16.4393			−0.862838
$364$	−33.4141	−	23.1262i	−1.75138	−	1.21214i
$365$	−44.8363			−2.34684
$366$	−17.7144	−	30.6822i	−0.925945	−	1.60378i
$367$	0.666657	+	1.15468i	0.0347992	+	0.0602740i	0.882900	−	0.469560i	$-0.155588\pi$
$367$	0.666657	+	1.15468i	0.0347992	+	0.0602740i	−0.848101	+	0.529834i	$0.822254\pi$
$368$	4.34228	−	7.52104i	0.226357	−	0.392061i
$369$	0.871141			0.0453498
$370$	32.4338	−	56.1770i	1.68615	−	2.92051i
$371$	−17.1568	+	29.7164i	−0.890735	+	1.54280i
$372$	6.74989			0.349965
$373$	−7.54999	+	13.0770i	−0.390924	+	0.677100i	−0.992572	−	0.121662i	$-0.961178\pi$
$373$	−7.54999	+	13.0770i	−0.390924	+	0.677100i	0.601648	+	0.798761i	$0.294511\pi$
$374$	−3.18738	−	5.52071i	−0.164816	−	0.285469i
$375$	−1.14146	−	1.97706i	−0.0589446	−	0.102095i
$376$	5.73049			0.295528
$377$	−9.81698	−	6.79440i	−0.505600	−	0.349930i
$378$	36.2145			1.86267
$379$	−17.1338	−	29.6767i	−0.880106	−	1.52439i	−0.851222	−	0.524806i	$-0.824138\pi$
$379$	−17.1338	−	29.6767i	−0.880106	−	1.52439i	−0.0288844	−	0.999583i	$-0.509195\pi$
$380$	−17.1769	−	29.7513i	−0.881159	−	1.52621i
$381$	6.75518	−	11.7003i	0.346079	−	0.599426i
$382$	8.36754			0.428121
$383$	16.6253	−	28.7959i	0.849516	−	1.47140i	−0.0321257	−	0.999484i	$-0.510228\pi$
$383$	16.6253	−	28.7959i	0.849516	−	1.47140i	0.881641	−	0.471920i	$-0.156439\pi$
$384$	−18.1507	+	31.4379i	−0.926248	+	1.60431i
$385$	−12.3387			−0.628838
$386$	−8.61520	+	14.9220i	−0.438502	+	0.759508i
$387$	0.669471	+	1.15956i	0.0340311	+	0.0589437i
$388$	−34.4655	−	59.6960i	−1.74972	−	3.03060i
$389$	17.4450			0.884499			0.442249	−	0.896892i	$-0.354181\pi$
$389$	17.4450			0.884499			0.442249	+	0.896892i	$0.354181\pi$
$390$	4.04749	−	49.3636i	0.204953	−	2.49962i
$391$	−5.93369			−0.300079
$392$	3.70839	+	6.42313i	0.187302	+	0.324417i
$393$	−10.4765	−	18.1457i	−0.528467	−	0.915332i
$394$	23.1189	−	40.0431i	1.16471	−	2.01734i
$395$	27.4955			1.38345
$396$	0.285235	−	0.494041i	0.0143336	−	0.0248265i
$397$	−3.52867	+	6.11184i	−0.177099	+	0.306745i	−0.940886	−	0.338724i	$-0.890005\pi$
$397$	−3.52867	+	6.11184i	−0.177099	+	0.306745i	0.763787	+	0.645469i	$0.223338\pi$
$398$	−41.0080			−2.05555
$399$	−7.24308	+	12.5454i	−0.362607	+	0.628054i
$400$	−8.04170	−	13.9286i	−0.402085	−	0.696432i
$401$	8.88224	+	15.3845i	0.443558	+	0.768265i	0.997951	−	0.0639903i	$-0.0203827\pi$
$401$	8.88224	+	15.3845i	0.443558	+	0.768265i	−0.554392	+	0.832255i	$0.687049\pi$
$402$	−39.8023			−1.98516
$403$	3.25938	−	1.54158i	0.162361	−	0.0767915i
$404$	48.0002			2.38810
$405$	15.0473	+	26.0628i	0.747708	+	1.29507i
$406$	11.7750	+	20.3949i	0.584384	+	1.01218i
$407$	5.40991	−	9.37024i	0.268159	−	0.464465i
$408$	−15.8114			−0.782780
$409$	1.24515	−	2.15666i	0.0615686	−	0.106640i	−0.833598	−	0.552371i	$-0.813723\pi$
$409$	1.24515	−	2.15666i	0.0615686	−	0.106640i	0.895167	+	0.445731i	$0.147056\pi$
$410$	29.5073	−	51.1082i	1.45726	−	2.52406i
$411$	0.0236560			0.00116687
$412$	13.6027	−	23.5605i	0.670156	−	1.16074i
$413$	−6.58862	−	11.4118i	−0.324205	−	0.561539i
$414$	−0.404340	−	0.700337i	−0.0198722	−	0.0344197i
$415$	−11.2905			−0.554230
$416$	−0.477278	+	5.82094i	−0.0234005	+	0.285395i
$417$	9.83964			0.481849
$418$	−4.36336	−	7.55757i	−0.213419	−	0.369653i
$419$	18.0240	+	31.2185i	0.880532	+	1.52513i	0.850751	+	0.525570i	$0.176148\pi$
$419$	18.0240	+	31.2185i	0.880532	+	1.52513i	0.0297812	+	0.999556i	$0.490519\pi$
$420$	−32.0756	+	55.5566i	−1.56513	+	2.71089i
$421$	−24.3202			−1.18529			−0.592647	−	0.805463i	$-0.701917\pi$
$421$	−24.3202			−1.18529			−0.592647	+	0.805463i	$0.701917\pi$
$422$	−23.5508	+	40.7912i	−1.14644	+	1.98568i
$423$	0.0747627	−	0.129493i	0.00363509	−	0.00629616i
$424$	−51.2708			−2.48993
$425$	−5.49446	+	9.51668i	−0.266520	+	0.461627i
$426$	−11.3554	−	19.6682i	−0.550172	−	0.952926i
$427$	12.2559	+	21.2278i	0.593103	+	1.02728i
$428$	48.3225			2.33576
$429$	0.675114	−	8.23377i	0.0325948	−	0.397530i
$430$	90.7055			4.37421
$431$	−14.0849	−	24.3958i	−0.678448	−	1.17511i	−0.975448	−	0.220229i	$-0.929320\pi$
$431$	−14.0849	−	24.3958i	−0.678448	−	1.17511i	0.297000	−	0.954877i	$-0.404014\pi$
$432$	7.58142	+	13.1314i	0.364761	+	0.631785i
$433$	13.1518	−	22.7796i	0.632036	−	1.09472i	−0.355099	−	0.934829i	$-0.615553\pi$
$433$	13.1518	−	22.7796i	0.632036	−	1.09472i	0.987135	−	0.159890i	$-0.0511139\pi$
$434$	−7.11212			−0.341393
$435$	−9.42373	+	16.3224i	−0.451833	+	0.782598i
$436$	−22.2242	+	38.4934i	−1.06434	+	1.84350i
$437$	−8.12292			−0.388572
$438$	−29.6082	+	51.2829i	−1.41473	+	2.45039i
$439$	4.19154	+	7.25996i	0.200051	+	0.346499i	0.948545	−	0.316643i	$-0.102556\pi$
$439$	4.19154	+	7.25996i	0.200051	+	0.346499i	−0.748493	+	0.663142i	$0.769222\pi$
$440$	−9.21814	−	15.9663i	−0.439457	−	0.761163i
$441$	0.193526			0.00921552
$442$	−16.0044	+	7.56954i	−0.761250	+	0.360046i
$443$	17.5144			0.832132			0.416066	−	0.909334i	$-0.363409\pi$
$443$	17.5144			0.832132			0.416066	+	0.909334i	$0.363409\pi$
$444$	−28.1272	−	48.7177i	−1.33486	−	2.31204i
$445$	4.90386	+	8.49374i	0.232465	+	0.402642i
$446$	−12.8243	+	22.2123i	−0.607248	+	1.05178i
$447$	25.5987			1.21078
$448$	14.5357	−	25.1766i	0.686747	−	1.18948i
$449$	16.1689	−	28.0053i	0.763056	−	1.32165i	−0.178213	−	0.983992i	$-0.557032\pi$
$449$	16.1689	−	28.0053i	0.763056	−	1.32165i	0.941268	−	0.337659i	$-0.109635\pi$
$450$	−1.49764			−0.0705993
$451$	4.92178	−	8.52476i	0.231757	−	0.401416i
$452$	−17.3602	−	30.0688i	−0.816556	−	1.41432i
$453$	15.8129	+	27.3887i	0.742954	+	1.28683i
$454$	60.7875			2.85290
$455$	−2.80030	+	34.1527i	−0.131280	+	1.60110i
$456$	−21.6450			−1.01362
$457$	9.76941	+	16.9211i	0.456994	+	0.791536i	0.998800	−	0.0489668i	$-0.0155928\pi$
$457$	9.76941	+	16.9211i	0.456994	+	0.791536i	−0.541807	+	0.840503i	$0.682260\pi$
$458$	−23.5305	−	40.7560i	−1.09951	−	1.90440i
$459$	5.17998	−	8.97199i	0.241781	−	0.418776i
$460$	−35.9720			−1.67720
$461$	3.30324	−	5.72139i	0.153847	−	0.266472i	−0.778791	−	0.627283i	$-0.784167\pi$
$461$	3.30324	−	5.72139i	0.153847	−	0.266472i	0.932639	+	0.360812i	$0.117500\pi$
$462$	−8.14800	+	14.1127i	−0.379079	+	0.656584i
$463$	−19.5253			−0.907419			−0.453709	−	0.891150i	$-0.649900\pi$
$463$	−19.5253			−0.907419			−0.453709	+	0.891150i	$0.649900\pi$
$464$	−4.93014	+	8.53926i	−0.228876	+	0.396425i
$465$	−2.84597	−	4.92937i	−0.131979	−	0.228594i
$466$	−8.47761	−	14.6837i	−0.392718	−	0.680207i
$467$	−18.2144			−0.842864			−0.421432	−	0.906860i	$-0.638472\pi$
$467$	−18.2144			−0.842864			−0.421432	+	0.906860i	$0.638472\pi$
$468$	−1.30274	−	0.901636i	−0.0602192	−	0.0416781i
$469$	27.5377			1.27157
$470$	−5.06474	−	8.77238i	−0.233619	−	0.404640i
$471$	−13.6764	−	23.6882i	−0.630174	−	1.09149i
$472$	9.84462	−	17.0514i	0.453135	−	0.784853i
$473$	15.1295			0.695656
$474$	18.1570	−	31.4488i	0.833978	−	1.44449i
$475$	−7.52164	+	13.0279i	−0.345116	+	0.597759i
$476$	22.9308			1.05103
$477$	−0.668903	+	1.15857i	−0.0306270	+	0.0530474i
$478$	−21.5640	−	37.3499i	−0.986312	−	1.70834i
$479$	−12.0438	−	20.8604i	−0.550293	−	0.953136i	−0.998253	−	0.0590822i	$-0.981183\pi$
$479$	−12.0438	−	20.8604i	−0.550293	−	0.953136i	0.447960	−	0.894054i	$-0.352151\pi$
$480$	9.22013			0.420839
$481$	−24.7084	−	17.1009i	−1.12661	−	0.779734i
$482$	−23.6969			−1.07937
$483$	7.58423	+	13.1363i	0.345094	+	0.597721i
$484$	17.8117	+	30.8508i	0.809624	+	1.40231i
$485$	−29.0635	+	50.3395i	−1.31971	+	2.28580i
$486$	2.88007			0.130642
$487$	16.5193	−	28.6123i	0.748563	−	1.29655i	−0.199949	−	0.979806i	$-0.564078\pi$
$487$	16.5193	−	28.6123i	0.748563	−	1.29655i	0.948512	−	0.316743i	$-0.102589\pi$
$488$	−18.3125	+	31.7182i	−0.828969	+	1.43582i
$489$	21.8049			0.986050
$490$	6.55512	−	11.3538i	0.296130	−	0.512912i
$491$	−15.8726	−	27.4922i	−0.716321	−	1.24070i	−0.962448	−	0.271467i	$-0.912491\pi$
$491$	−15.8726	−	27.4922i	−0.716321	−	1.24070i	0.246127	−	0.969238i	$-0.420842\pi$
$492$	−25.5893	−	44.3219i	−1.15365	−	1.99819i
$493$	6.73700			0.303419
$494$	−21.9092	+	10.3623i	−0.985740	+	0.466223i
$495$	−0.481057			−0.0216219
$496$	−1.48891	−	2.57886i	−0.0668539	−	0.115794i
$497$	7.85637	+	13.6076i	0.352406	+	0.610386i
$498$	−7.45583	+	12.9139i	−0.334104	+	0.578685i
$499$	22.4073			1.00309			0.501544	−	0.865132i	$-0.332766\pi$
$499$	22.4073			1.00309			0.501544	+	0.865132i	$0.332766\pi$
$500$	−2.47351	+	4.28424i	−0.110619	+	0.191597i
$501$	−1.47774	+	2.55952i	−0.0660205	+	0.114351i
$502$	43.8669			1.95787
$503$	7.78542	−	13.4847i	0.347135	−	0.601255i	−0.638605	−	0.769535i	$-0.720488\pi$
$503$	7.78542	−	13.4847i	0.347135	−	0.601255i	0.985739	+	0.168280i	$0.0538214\pi$
$504$	0.745436	+	1.29113i	0.0332044	+	0.0575116i
$505$	−20.2385	−	35.0540i	−0.900600	−	1.55988i
$506$	−9.13776			−0.406223
$507$	−22.6373	−	3.73735i	−1.00536	−	0.165982i
$508$	−29.2766			−1.29894
$509$	5.26854	+	9.12538i	0.233524	+	0.404475i	0.958843	−	0.283938i	$-0.0916409\pi$
$509$	5.26854	+	9.12538i	0.233524	+	0.404475i	−0.725319	+	0.688413i	$0.758308\pi$
$510$	13.9745	+	24.2045i	0.618799	+	1.07179i
$511$	20.4847	−	35.4806i	0.906192	−	1.56957i
$512$	31.0478			1.37213
$513$	7.09113	−	12.2822i	0.313081	−	0.542272i
$514$	−27.9999	+	48.4972i	−1.23502	+	2.13912i
$515$	−22.9413			−1.01092
$516$	39.3307	−	68.1227i	1.73144	−	2.99894i
$517$	−0.844789	−	1.46322i	−0.0371538	−	0.0643523i
$518$	29.6366	+	51.3321i	1.30216	+	2.25540i
$519$	12.4883			0.548176
$520$	−46.2858	+	21.8917i	−2.02977	+	0.960012i
$521$	9.96144			0.436418			0.218209	−	0.975902i	$-0.429978\pi$
$521$	9.96144			0.436418			0.218209	+	0.975902i	$0.429978\pi$
$522$	0.459080	+	0.795150i	0.0200934	+	0.0348028i
$523$	−0.298094	−	0.516314i	−0.0130347	−	0.0225768i	0.859434	−	0.511246i	$-0.170816\pi$
$523$	−0.298094	−	0.516314i	−0.0130347	−	0.0225768i	−0.872469	+	0.488669i	$0.837483\pi$
$524$	−22.7022	+	39.3213i	−0.991749	+	1.71776i
$525$	28.0913			1.22600
$526$	−10.7601	+	18.6370i	−0.469161	+	0.812611i
$527$	−1.01729	+	1.76200i	−0.0443138	+	0.0767538i
$528$	−6.82306			−0.296936
$529$	7.24725	−	12.5526i	0.315098	−	0.545765i
$530$	45.3142	+	78.4865i	1.96832	+	3.40924i
$531$	−0.256875	−	0.444921i	−0.0111474	−	0.0193079i
$532$	31.3911			1.36098
$533$	−22.4790	−	15.5579i	−0.973674	−	0.673887i
$534$	12.9533			0.560544
$535$	−20.3743	−	35.2894i	−0.880860	−	1.52569i
$536$	20.5732	+	35.6338i	0.888626	+	1.53914i
$537$	5.76079	−	9.97797i	0.248596	−	0.430581i
$538$	48.3493			2.08449
$539$	1.09338	−	1.89379i	0.0470953	−	0.0815715i
$540$	31.4027	−	54.3911i	1.35136	−	2.34062i
$541$	8.23712			0.354142			0.177071	−	0.984198i	$-0.443338\pi$
$541$	8.23712			0.354142			0.177071	+	0.984198i	$0.443338\pi$
$542$	9.35467	−	16.2028i	0.401817	−	0.695968i
$543$	−11.1497	−	19.3119i	−0.478480	−	0.828751i
$544$	−1.64786	−	2.85418i	−0.0706515	−	0.122372i
$545$	37.4817			1.60554
$546$	37.2140	+	25.7561i	1.59261	+	1.10226i
$547$	−18.2950			−0.782237			−0.391118	−	0.920340i	$-0.627912\pi$
$547$	−18.2950			−0.782237			−0.391118	+	0.920340i	$0.627912\pi$
$548$	−0.0256310	−	0.0443942i	−0.00109490	−	0.00189642i
$549$	0.477828	+	0.827622i	0.0203932	+	0.0353221i
$550$	−8.46136	+	14.6555i	−0.360794	+	0.624913i
$551$	9.22261			0.392897
$552$	−11.3322	+	19.6280i	−0.482332	+	0.835423i
$553$	−12.5621	+	21.7582i	−0.534195	+	0.925253i
$554$	−46.4826			−1.97486
$555$	−23.7187	+	41.0820i	−1.00680	+	1.74383i
$556$	−10.6611	−	18.4656i	−0.452132	−	0.783115i
$557$	−10.0670	−	17.4366i	−0.426553	−	0.738811i	0.570011	−	0.821637i	$-0.306939\pi$
$557$	−10.0670	−	17.4366i	−0.426553	−	0.738811i	−0.996564	+	0.0828259i	$0.973605\pi$
$558$	−0.277285			−0.0117384
$559$	3.43368	−	41.8776i	0.145229	−	1.77123i
$560$	28.3013			1.19595
$561$	2.33091	+	4.03726i	0.0984113	+	0.170453i
$562$	37.9822	+	65.7871i	1.60218	+	2.77506i
$563$	−2.29600	+	3.97680i	−0.0967651	+	0.167602i	−0.910344	−	0.413853i	$-0.864183\pi$
$563$	−2.29600	+	3.97680i	−0.0967651	+	0.167602i	0.813579	+	0.581455i	$0.197516\pi$
$564$	−8.78445			−0.369892
$565$	−14.6393	+	25.3560i	−0.615879	+	1.06673i
$566$	9.26341	−	16.0447i	0.389370	−	0.674409i
$567$	−27.4992			−1.15486
$568$	−11.7389	+	20.3323i	−0.492552	+	0.853125i
$569$	4.78343	+	8.28514i	0.200532	+	0.347331i	0.948700	−	0.316178i	$-0.102400\pi$
$569$	4.78343	+	8.28514i	0.200532	+	0.347331i	−0.748168	+	0.663509i	$0.769066\pi$
$570$	19.1303	+	33.1347i	0.801281	+	1.38786i
$571$	17.2537			0.722043			0.361021	−	0.932558i	$-0.382428\pi$
$571$	17.2537			0.722043			0.361021	+	0.932558i	$0.382428\pi$
$572$	−16.1834	+	7.65422i	−0.676662	+	0.320039i
$573$	−6.11913			−0.255630
$574$	26.9625	+	46.7005i	1.12539	+	1.94924i
$575$	7.87591	+	13.6415i	0.328448	+	0.568889i
$576$	0.566713	−	0.981576i	0.0236131	−	0.0408990i
$577$	−1.91043			−0.0795323			−0.0397661	−	0.999209i	$-0.512661\pi$
$577$	−1.91043			−0.0795323			−0.0397661	+	0.999209i	$0.512661\pi$
$578$	−15.5188	+	26.8793i	−0.645495	+	1.11803i
$579$	6.30025	−	10.9123i	0.261829	−	0.453502i
$580$	40.8419			1.69587
$581$	5.15839	−	8.93460i	0.214006	−	0.370670i
$582$	38.3849	+	66.4846i	1.59111	+	2.75588i
$583$	7.55834	+	13.0914i	0.313034	+	0.542191i
$584$	61.2160			2.53314
$585$	−0.109177	+	1.33154i	−0.00451392	+	0.0550522i
$586$	−48.3252			−1.99629
$587$	12.1590	+	21.0601i	0.501857	+	0.869242i	0.999998	+	0.00214594i	$0.000683073\pi$
$587$	12.1590	+	21.0601i	0.501857	+	0.869242i	−0.498140	+	0.867096i	$0.665984\pi$
$588$	−5.68471	−	9.84621i	−0.234434	−	0.406051i
$589$	−1.39262	+	2.41208i	−0.0573818	+	0.0993882i
$590$	−34.8035			−1.43284
$591$	−16.9067	+	29.2833i	−0.695450	+	1.20455i
$592$	−12.4087	+	21.4925i	−0.509995	+	0.883338i
$593$	−10.1680			−0.417550			−0.208775	−	0.977964i	$-0.566948\pi$
$593$	−10.1680			−0.417550			−0.208775	+	0.977964i	$0.566948\pi$
$594$	7.97706	−	13.8167i	0.327303	−	0.566905i
$595$	−9.66837	−	16.7461i	−0.396365	−	0.686524i
$596$	−27.7359	−	48.0399i	−1.13611	−	1.96779i
$597$	29.9889			1.22737
$598$	−2.07384	+	25.2928i	−0.0848055	+	1.03430i
$599$	11.5189			0.470648			0.235324	−	0.971917i	$-0.424385\pi$
$599$	11.5189			0.470648			0.235324	+	0.971917i	$0.424385\pi$
$600$	20.9868	+	36.3502i	0.856782	+	1.48399i
$601$	3.53851	+	6.12889i	0.144339	+	0.250002i	0.929126	−	0.369763i	$-0.120561\pi$
$601$	3.53851	+	6.12889i	0.144339	+	0.250002i	−0.784787	+	0.619765i	$0.787228\pi$
$602$	−41.4414	+	71.7785i	−1.68902	+	2.92547i
$603$	1.07363			0.0437216
$604$	34.2661	−	59.3506i	1.39427	−	2.41494i
$605$	15.0200	−	26.0154i	0.610650	−	1.05768i
$606$	−53.4588			−2.17162
$607$	−4.70975	+	8.15753i	−0.191163	+	0.331104i	−0.945636	−	0.325227i	$-0.894559\pi$
$607$	−4.70975	+	8.15753i	−0.191163	+	0.331104i	0.754473	+	0.656331i	$0.227893\pi$
$608$	−2.25584	−	3.90723i	−0.0914863	−	0.158459i
$609$	−8.61100	−	14.9147i	−0.348935	−	0.604373i
$610$	64.7401			2.62125
$611$	−4.24182	+	2.00624i	−0.171606	+	0.0811639i
$612$	0.894019			0.0361386
$613$	8.84000	+	15.3113i	0.357044	+	0.618419i	0.987466	−	0.157834i	$-0.0504512\pi$
$613$	8.84000	+	15.3113i	0.357044	+	0.618419i	−0.630421	+	0.776253i	$0.717118\pi$
$614$	−13.9357	−	24.1373i	−0.562399	−	0.974103i
$615$	−21.5786	+	37.3752i	−0.870131	+	1.50711i
$616$	16.8463			0.678755
$617$	−21.6489	+	37.4969i	−0.871550	+	1.50957i	−0.0111568	+	0.999938i	$0.503551\pi$
$617$	−21.6489	+	37.4969i	−0.871550	+	1.50957i	−0.860393	+	0.509631i	$0.829782\pi$
$618$	−15.1496	+	26.2398i	−0.609405	+	1.05552i
$619$	−44.4185			−1.78533			−0.892666	−	0.450719i	$-0.851168\pi$
$619$	−44.4185			−1.78533			−0.892666	+	0.450719i	$0.851168\pi$
$620$	−6.16714	+	10.6818i	−0.247678	+	0.428992i
$621$	−7.42512	−	12.8607i	−0.297960	−	0.516082i
$622$	−6.26037	−	10.8433i	−0.251018	−	0.434776i
$623$	−8.96187			−0.359050
$624$	−1.54851	+	18.8858i	−0.0619901	+	0.756038i
$625$	−22.8337			−0.913350
$626$	−27.2380	−	47.1776i	−1.08865	−	1.88560i
$627$	3.19090	+	5.52681i	0.127432	+	0.220719i
$628$	−29.6363	+	51.3316i	−1.18262	+	2.04835i
$629$	16.9564			0.676097
$630$	1.31767	−	2.28226i	0.0524971	−	0.0909276i
$631$	−13.3655	+	23.1497i	−0.532072	+	0.921575i	0.467227	+	0.884137i	$0.345253\pi$
$631$	−13.3655	+	23.1497i	−0.532072	+	0.921575i	−0.999299	+	0.0374381i	$0.988080\pi$
$632$	−37.5402			−1.49327
$633$	17.2226	−	29.8304i	0.684536	−	1.18565i
$634$	29.0585	+	50.3309i	1.15406	+	1.99889i
$635$	12.3440	+	21.3804i	0.489855	+	0.848454i
$636$	78.5946			3.11648
$637$	−4.99376	−	3.45622i	−0.197860	−	0.136940i
$638$	10.3748			0.410744
$639$	0.306302	+	0.530530i	0.0121171	+	0.0209875i
$640$	−33.1673	−	57.4475i	−1.31105	−	2.27081i
$641$	1.62343	−	2.81187i	0.0641217	−	0.111062i	−0.832182	−	0.554502i	$-0.812909\pi$
$641$	1.62343	−	2.81187i	0.0641217	−	0.111062i	0.896304	+	0.443440i	$0.146242\pi$
$642$	−53.8177			−2.12402
$643$	−24.8678	+	43.0723i	−0.980690	+	1.69860i	−0.320977	+	0.947087i	$0.604011\pi$
$643$	−24.8678	+	43.0723i	−0.980690	+	1.69860i	−0.659713	+	0.751518i	$0.729322\pi$
$644$	16.4348	−	28.4659i	0.647622	−	1.12171i
$645$	−66.3324			−2.61184
$646$	6.83811	−	11.8439i	0.269042	−	0.465994i
$647$	−16.0579	−	27.8130i	−0.631299	−	1.09344i	−0.987286	−	0.158951i	$-0.949189\pi$
$647$	−16.0579	−	27.8130i	−0.631299	−	1.09344i	0.355987	−	0.934491i	$-0.384145\pi$
$648$	−20.5444	−	35.5840i	−0.807062	−	1.39787i
$649$	−5.80517			−0.227873
$650$	38.6452	+	26.7466i	1.51579	+	1.04909i
$651$	5.20105			0.203845
$652$	−23.6253	−	40.9202i	−0.925237	−	1.60256i
$653$	13.3336	+	23.0944i	0.521783	+	0.903755i	0.999679	+	0.0253382i	$0.00806625\pi$
$653$	13.3336	+	23.0944i	0.521783	+	0.903755i	−0.477896	+	0.878416i	$0.658600\pi$
$654$	24.7515	−	42.8709i	0.967861	−	1.67638i
$655$	38.2879			1.49603
$656$	−11.2891	+	19.5533i	−0.440765	+	0.763427i
$657$	0.798653	−	1.38331i	0.0311584	−	0.0539680i
$658$	9.25587			0.360831
$659$	10.6695	−	18.4802i	0.415626	−	0.719886i	−0.579868	−	0.814711i	$-0.696896\pi$
$659$	10.6695	−	18.4802i	0.415626	−	0.719886i	0.995494	+	0.0948248i	$0.0302291\pi$
$660$	14.1308	+	24.4752i	0.550040	+	0.952697i
$661$	5.03274	+	8.71697i	0.195751	+	0.339051i	0.947146	−	0.320801i	$-0.103952\pi$
$661$	5.03274	+	8.71697i	0.195751	+	0.339051i	−0.751395	+	0.659852i	$0.770619\pi$
$662$	42.3289			1.64516
$663$	11.7039	−	5.53556i	0.454542	−	0.214983i
$664$	15.4152			0.598225
$665$	−13.2355	−	22.9246i	−0.513251	−	0.888977i
$666$	1.15546	+	2.00132i	0.0447733	+	0.0775496i
$667$	4.82850	−	8.36321i	0.186960	−	0.323825i
$668$	6.40444			0.247795
$669$	9.37833	−	16.2438i	0.362587	−	0.628020i
$670$	36.3660	−	62.9878i	1.40494	−	2.43343i
$671$	10.7985			0.416873
$672$	−4.21247	+	7.29622i	−0.162500	+	0.281458i
$673$	−10.6469	−	18.4410i	−0.410408	−	0.710848i	0.584526	−	0.811375i	$-0.301280\pi$
$673$	−10.6469	−	18.4410i	−0.410408	−	0.710848i	−0.994934	+	0.100527i	$0.967947\pi$
$674$	−11.8474	−	20.5203i	−0.456344	−	0.790411i
$675$	−27.5020			−1.05855
$676$	17.5135	+	46.5318i	0.673598	+	1.78968i
$677$	−37.7026			−1.44903			−0.724513	−	0.689261i	$-0.757935\pi$
$677$	−37.7026			−1.44903			−0.724513	+	0.689261i	$0.757935\pi$
$678$	19.3344	+	33.4882i	0.742535	+	1.28611i
$679$	−26.5570	−	45.9981i	−1.01916	−	1.76524i
$680$	14.4463	−	25.0218i	0.553991	−	0.959541i
$681$	−44.4535			−1.70346
$682$	−1.56661	+	2.71344i	−0.0599884	+	0.103903i
$683$	−7.15245	+	12.3884i	−0.273681	+	0.474029i	−0.969801	−	0.243896i	$-0.921575\pi$
$683$	−7.15245	+	12.3884i	−0.273681	+	0.474029i	0.696121	+	0.717925i	$0.254908\pi$
$684$	1.22387			0.0467957
$685$	−0.0216137	+	0.0374361i	−0.000825818	+	0.00143036i
$686$	−18.9026	−	32.7403i	−0.721706	−	1.25003i
$687$	17.2077	+	29.8047i	0.656516	+	1.13712i
$688$	−34.7026			−1.32303
$689$	37.9516	−	17.9499i	1.44584	−	0.683836i
$690$	40.0627			1.52516
$691$	−2.58097	−	4.47037i	−0.0981848	−	0.170061i	0.812749	−	0.582615i	$-0.197970\pi$
$691$	−2.58097	−	4.47037i	−0.0981848	−	0.170061i	−0.910933	+	0.412554i	$0.864637\pi$
$692$	−13.5309	−	23.4362i	−0.514368	−	0.890912i
$693$	0.219784	−	0.380678i	0.00834892	−	0.0144608i
$694$	−64.5736			−2.45118
$695$	−8.99014	+	15.5714i	−0.341016	+	0.590656i
$696$	12.8664	−	22.2853i	0.487700	−	0.844722i
$697$	15.4265			0.584319
$698$	−42.6788	+	73.9219i	−1.61542	+	2.79799i
$699$	6.19963	+	10.7381i	0.234492	+	0.406151i
$700$	−30.4365	−	52.7176i	−1.15039	−	1.99254i
$701$	−13.4781			−0.509062			−0.254531	−	0.967065i	$-0.581921\pi$
$701$	−13.4781			−0.509062			−0.254531	+	0.967065i	$0.581921\pi$
$702$	−36.4333	−	25.2158i	−1.37509	−	0.951707i
$703$	23.2125			0.875475
$704$	−6.40364	−	11.0914i	−0.241346	−	0.418024i
$705$	3.70381	+	6.41519i	0.139494	+	0.241610i
$706$	−7.15902	+	12.3998i	−0.269433	+	0.466672i
$707$	36.9860			1.39100
$708$	−15.0911	+	26.1386i	−0.567159	+	0.982348i
$709$	−16.0855	+	27.8609i	−0.604103	+	1.04634i	0.388090	+	0.921622i	$0.373135\pi$
$709$	−16.0855	+	27.8609i	−0.604103	+	1.04634i	−0.992193	+	0.124715i	$0.960198\pi$
$710$	41.5003			1.55748
$711$	−0.489767	+	0.848302i	−0.0183677	+	0.0318138i
$712$	−6.69534	−	11.5967i	−0.250919	−	0.434604i
$713$	1.45821	+	2.52569i	0.0546104	+	0.0945880i
$714$	−25.5385			−0.955754
$715$	12.4132	+	8.59129i	0.464229	+	0.321296i
$716$	−24.9669			−0.933058
$717$	15.7696	+	27.3137i	0.588926	+	1.02005i
$718$	29.2492	+	50.6611i	1.09157	+	1.89066i
$719$	−12.4869	+	21.6280i	−0.465685	+	0.806589i	−0.999232	−	0.0391807i	$-0.987525\pi$
$719$	−12.4869	+	21.6280i	−0.465685	+	0.806589i	0.533548	+	0.845770i	$0.320859\pi$
$720$	1.10340			0.0411213
$721$	10.4814	−	18.1543i	0.390347	−	0.676102i
$722$	−13.5663	+	23.4975i	−0.504885	+	0.874486i
$723$	17.3294			0.644489
$724$	−24.1611	+	41.8482i	−0.897940	+	1.55528i
$725$	−8.94216	−	15.4883i	−0.332104	−	0.575220i
$726$	−19.8373	−	34.3592i	−0.736230	−	1.27519i
$727$	−46.0065			−1.70629			−0.853143	−	0.521678i	$-0.825306\pi$
$727$	−46.0065			−1.70629			−0.853143	+	0.521678i	$0.825306\pi$
$728$	3.82330	−	46.6294i	0.141701	−	1.72820i
$729$	25.8883			0.958825
$730$	−54.1040	−	93.7109i	−2.00248	−	3.46840i
$731$	11.8552	+	20.5338i	0.438481	+	0.759471i
$732$	28.0719	−	48.6219i	1.03757	−	1.79712i
$733$	26.4220			0.975917			0.487959	−	0.872867i	$-0.337742\pi$
$733$	26.4220			0.975917			0.487959	+	0.872867i	$0.337742\pi$
$734$	−1.60891	+	2.78671i	−0.0593859	+	0.102859i
$735$	−4.79372	+	8.30297i	−0.176819	+	0.306260i
$736$	−4.72418			−0.174135
$737$	6.06579	−	10.5063i	0.223436	−	0.387003i
$738$	1.05121	+	1.82074i	0.0386954	+	0.0670225i
$739$	−4.55398	−	7.88773i	−0.167521	−	0.290155i	0.770027	−	0.638012i	$-0.220243\pi$
$739$	−4.55398	−	7.88773i	−0.167521	−	0.290155i	−0.937548	+	0.347857i	$0.886910\pi$
$740$	102.795			3.77883
$741$	16.0221	−	7.57790i	0.588585	−	0.278381i
$742$	−82.8123			−3.04014
$743$	−9.65618	−	16.7250i	−0.354251	−	0.613581i	0.632738	−	0.774366i	$-0.281931\pi$
$743$	−9.65618	−	16.7250i	−0.354251	−	0.613581i	−0.986989	+	0.160785i	$0.948597\pi$
$744$	3.88567	+	6.73017i	0.142455	+	0.246740i
$745$	−23.3887	+	40.5104i	−0.856895	+	1.48419i
$746$	−36.4423			−1.33425
$747$	0.201114	−	0.348339i	0.00735837	−	0.0127451i
$748$	5.05103	−	8.74864i	0.184684	−	0.319882i
$749$	37.2344			1.36051
$750$	2.75479	−	4.77144i	0.100591	−	0.174228i
$751$	24.9263	+	43.1737i	0.909575	+	1.57543i	0.814656	+	0.579945i	$0.196926\pi$
$751$	24.9263	+	43.1737i	0.909575	+	1.57543i	0.0949187	+	0.995485i	$0.469741\pi$
$752$	1.93770	+	3.35619i	0.0706605	+	0.122388i
$753$	−32.0796			−1.16905
$754$	2.35460	−	28.7169i	0.0857494	−	1.04581i
$755$	−57.7908			−2.10322
$756$	28.6945	+	49.7002i	1.04361	+	1.80758i
$757$	−3.96481	−	6.86726i	−0.144104	−	0.249595i	0.784935	−	0.619579i	$-0.212697\pi$
$757$	−3.96481	−	6.86726i	−0.144104	−	0.249595i	−0.929038	+	0.369984i	$0.879363\pi$
$758$	41.3508	−	71.6217i	1.50193	−	2.60142i
$759$	6.68239			0.242555
$760$	19.7763	−	34.2535i	0.717362	−	1.24251i
$761$	−4.82278	+	8.35331i	−0.174826	+	0.302807i	−0.940101	−	0.340896i	$-0.889270\pi$
$761$	−4.82278	+	8.35331i	−0.174826	+	0.302807i	0.765275	+	0.643703i	$0.222603\pi$
$762$	32.6059			1.18119
$763$	−17.1246	+	29.6607i	−0.619952	+	1.07379i
$764$	6.63000	+	11.4835i	0.239865	+	0.415458i
$765$	−0.376947	−	0.652892i	−0.0136286	−	0.0236054i
$766$	80.2472			2.89945
$767$	−1.31750	+	16.0684i	−0.0475721	+	0.580195i
$768$	−52.7882			−1.90483
$769$	4.55829	+	7.89519i	0.164376	+	0.284708i	0.936434	−	0.350845i	$-0.114106\pi$
$769$	4.55829	+	7.89519i	0.164376	+	0.284708i	−0.772057	+	0.635553i	$0.780772\pi$
$770$	−14.8891	−	25.7887i	−0.536566	−	0.929359i
$771$	20.4761	−	35.4657i	0.737430	−	1.27727i
$772$	−27.3049			−0.982725
$773$	−6.26590	+	10.8529i	−0.225369	+	0.390350i	−0.956430	−	0.291962i	$-0.905692\pi$
$773$	−6.26590	+	10.8529i	−0.225369	+	0.390350i	0.731061	+	0.682312i	$0.239025\pi$
$774$	−1.61570	+	2.79848i	−0.0580752	+	0.100589i
$775$	5.40108			0.194012
$776$	39.6811	−	68.7296i	1.42447	−	2.46725i
$777$	−21.6731	−	37.5389i	−0.777518	−	1.34670i
$778$	21.0509	+	36.4613i	0.754713	+	1.30720i
$779$	21.1180			0.756632
$780$	70.9529	−	33.5584i	2.54052	−	1.20158i
$781$	6.92218			0.247695
$782$	−7.16018	−	12.4018i	−0.256048	−	0.443487i
$783$	8.43035	+	14.6018i	0.301276	+	0.521825i
$784$	−2.50790	+	4.34380i	−0.0895677	+	0.155136i
$785$	49.9825			1.78395
$786$	25.2839	−	43.7930i	0.901846	−	1.56204i
$787$	4.49854	−	7.79170i	0.160356	−	0.277744i	−0.774641	−	0.632402i	$-0.782069\pi$
$787$	4.49854	−	7.79170i	0.160356	−	0.277744i	0.934996	+	0.354658i	$0.115403\pi$
$788$	73.2728			2.61023
$789$	7.86878	−	13.6291i	0.280136	−	0.485210i
$790$	33.1789	+	57.4675i	1.18045	+	2.04460i
$791$	−13.3767	−	23.1692i	−0.475622	−	0.823801i
$792$	0.656797			0.0233383
$793$	2.45076	−	29.8897i	0.0870289	−	1.06141i
$794$	−17.0322			−0.604451
$795$	−33.1380	−	57.3968i	−1.17529	−	2.03565i
$796$	−32.4926	−	56.2788i	−1.15167	−	1.99475i
$797$	5.21192	−	9.02731i	0.184616	−	0.319764i	−0.758831	−	0.651287i	$-0.774229\pi$
$797$	5.21192	−	9.02731i	0.184616	−	0.319764i	0.943447	+	0.331524i	$0.107563\pi$
$798$	−34.9609			−1.23760
$799$	1.32392	−	2.29310i	0.0468370	−	0.0811241i
$800$	−4.37448	+	7.57682i	−0.154661	+	0.267881i
$801$	−0.349403			−0.0123455
$802$	−21.4364	+	37.1290i	−0.756946	+	1.31107i
$803$	−9.02446	−	15.6308i	−0.318466	−	0.551600i
$804$	−31.5373	−	54.6241i	−1.11223	−	1.92644i
$805$	−27.7178			−0.976924
$806$	7.15509	+	4.95209i	0.252027	+	0.174430i
$807$	−35.3576			−1.24464
$808$	27.6320	+	47.8600i	0.972090	+	1.68371i
$809$	−8.53755	−	14.7875i	−0.300164	−	0.519900i	0.676009	−	0.736894i	$-0.263708\pi$
$809$	−8.53755	−	14.7875i	−0.300164	−	0.519900i	−0.976173	+	0.216994i	$0.930375\pi$
$810$	−36.3153	+	62.8999i	−1.27599	+	2.21008i
$811$	14.0114			0.492006			0.246003	−	0.969269i	$-0.420883\pi$
$811$	14.0114			0.492006			0.246003	+	0.969269i	$0.420883\pi$
$812$	−18.6598	+	32.3197i	−0.654830	+	1.13420i
$813$	−6.84102	+	11.8490i	−0.239925	+	0.415562i
$814$	26.1125			0.915244
$815$	−19.9224	+	34.5066i	−0.697850	+	1.20871i
$816$	−5.34643	−	9.26028i	−0.187162	−	0.324175i
$817$	16.2292	+	28.1098i	0.567788	+	0.983437i
$818$	6.01008			0.210137
$819$	−1.00381	−	0.694746i	−0.0350760	−	0.0242764i
$820$	93.5202			3.26587
$821$	−5.40884	−	9.36839i	−0.188770	−	0.326959i	0.756071	−	0.654490i	$-0.227117\pi$
$821$	−5.40884	−	9.36839i	−0.188770	−	0.326959i	−0.944840	+	0.327531i	$0.893783\pi$
$822$	0.0285457	+	0.0494427i	0.000995647	+	0.00172451i
$823$	−5.59244	+	9.68638i	−0.194940	+	0.337646i	−0.946881	−	0.321585i	$-0.895785\pi$
$823$	−5.59244	+	9.68638i	−0.194940	+	0.337646i	0.751941	+	0.659231i	$0.229118\pi$
$824$	31.3223			1.09116
$825$	6.18774	−	10.7175i	0.215430	−	0.373135i
$826$	15.9010	−	27.5413i	0.553266	−	0.958285i
$827$	−18.8095			−0.654071			−0.327035	−	0.945012i	$-0.606050\pi$
$827$	−18.8095			−0.654071			−0.327035	+	0.945012i	$0.606050\pi$
$828$	0.640755	−	1.10982i	0.0222678	−	0.0385689i
$829$	14.7895	+	25.6162i	0.513661	+	0.889687i	0.999874	+	0.0158471i	$0.00504450\pi$
$829$	14.7895	+	25.6162i	0.513661	+	0.889687i	−0.486213	+	0.873840i	$0.661622\pi$
$830$	−13.6243	−	23.5979i	−0.472906	−	0.819096i
$831$	33.9925			1.17919
$832$	−32.1537	+	15.2076i	−1.11473	+	0.527230i
$833$	3.42702			0.118739
$834$	11.8735	+	20.5655i	0.411145	+	0.712125i
$835$	−2.70032	−	4.67709i	−0.0934484	−	0.161857i
$836$	6.91460	−	11.9764i	0.239146	−	0.414214i
$837$	−5.09194			−0.176003
$838$	−43.4992	+	75.3429i	−1.50266	+	2.60268i
$839$	5.09276	−	8.82092i	0.175822	−	0.304532i	−0.764624	−	0.644477i	$-0.777075\pi$
$839$	5.09276	−	8.82092i	0.175822	−	0.304532i	0.940445	+	0.339945i	$0.110408\pi$
$840$	−73.8591			−2.54838
$841$	9.01781	−	15.6193i	0.310959	−	0.538597i
$842$	−29.3472	−	50.8308i	−1.01137	−	1.75174i
$843$	−27.7762	−	48.1098i	−0.956663	−	1.65699i
$844$	−74.6416			−2.56927
$845$	26.5974	−	32.4093i	0.914978	−	1.11491i
$846$	0.360865			0.0124068
$847$	13.7246	+	23.7718i	0.471584	+	0.816807i
$848$	−17.3366	−	30.0278i	−0.595341	−	1.03116i
$849$	−6.77428	+	11.7334i	−0.232493	+	0.402689i
$850$	−26.5207			−0.909651
$851$	12.1529	−	21.0494i	0.416596	−	0.721565i
$852$	17.9949	−	31.1680i	0.616494	−	1.06780i
$853$	−42.4027			−1.45184			−0.725920	−	0.687780i	$-0.758586\pi$
$853$	−42.4027			−1.45184			−0.725920	+	0.687780i	$0.758586\pi$
$854$	−29.5783	+	51.2312i	−1.01215	+	1.75309i
$855$	−0.516022	−	0.893776i	−0.0176476	−	0.0305665i
$856$	27.8175	+	48.1813i	0.950783	+	1.64680i
$857$	−30.2080			−1.03188			−0.515942	−	0.856623i	$-0.672558\pi$
$857$	−30.2080			−1.03188			−0.515942	+	0.856623i	$0.672558\pi$
$858$	18.0238	−	8.52465i	0.615322	−	0.291027i
$859$	−9.54255			−0.325588			−0.162794	−	0.986660i	$-0.552051\pi$
$859$	−9.54255			−0.325588			−0.162794	+	0.986660i	$0.552051\pi$
$860$	71.8702	+	124.483i	2.45075	+	4.24483i
$861$	−19.7175	−	34.1518i	−0.671972	−	1.16389i
$862$	33.9926	−	58.8769i	1.15779	−	2.00536i
$863$	52.9173			1.80133			0.900664	−	0.434517i	$-0.143081\pi$
$863$	52.9173			1.80133			0.900664	+	0.434517i	$0.143081\pi$
$864$	4.12410	−	7.14316i	0.140305	−	0.243015i
$865$	−11.4101	+	19.7630i	−0.387957	+	0.671961i
$866$	63.4812			2.15718
$867$	11.3488	−	19.6567i	0.385425	−	0.667575i
$868$	−5.63527	−	9.76057i	−0.191273	−	0.331295i
$869$	5.53418	+	9.58547i	0.187734	+	0.325165i
$870$	−45.4865			−1.54214
$871$	−27.7040	−	19.1742i	−0.938716	−	0.649692i
$872$	−51.1746			−1.73299
$873$	−1.03540	−	1.79336i	−0.0350428	−	0.0606960i
$874$	−9.80192	−	16.9774i	−0.331555	−	0.574270i
$875$	−1.90593	+	3.30117i	−0.0644323	+	0.111600i
$876$	−93.8399			−3.17056
$877$	−19.8498	+	34.3809i	−0.670281	+	1.16096i	0.307543	+	0.951534i	$0.400493\pi$
$877$	−19.8498	+	34.3809i	−0.670281	+	1.16096i	−0.977824	+	0.209427i	$0.932840\pi$
$878$	−10.1159	+	17.5212i	−0.341394	+	0.591312i
$879$	35.3399			1.19199
$880$	6.23400	−	10.7976i	0.210148	−	0.363987i
$881$	−14.1925	−	24.5821i	−0.478156	−	0.828191i	0.521530	−	0.853233i	$-0.325361\pi$
$881$	−14.1925	−	24.5821i	−0.478156	−	0.828191i	−0.999686	+	0.0250420i	$0.992028\pi$
$882$	0.233528	+	0.404482i	0.00786329	+	0.0136196i
$883$	−38.6766			−1.30157			−0.650785	−	0.759262i	$-0.725560\pi$
$883$	−38.6766			−1.30157			−0.650785	+	0.759262i	$0.725560\pi$
$884$	−23.0693	−	15.9665i	−0.775906	−	0.537010i
$885$	25.4516			0.855547
$886$	21.1346	+	36.6062i	0.710030	+	1.22981i
$887$	−0.0355456	−	0.0615667i	−0.00119350	−	0.00206721i	0.865428	−	0.501033i	$-0.167047\pi$
$887$	−0.0355456	−	0.0615667i	−0.00119350	−	0.00206721i	−0.866622	+	0.498966i	$0.833713\pi$
$888$	32.3836	−	56.0900i	1.08672	−	1.88226i
$889$	−22.5588			−0.756596
$890$	−11.8350	+	20.4988i	−0.396709	+	0.687121i
$891$	−6.05732	+	10.4916i	−0.202928	+	0.351482i
$892$	−40.6452			−1.36090
$893$	1.81238	−	3.13914i	0.0606491	−	0.105047i
$894$	30.8900	+	53.5030i	1.03312	+	1.78941i
$895$	10.5269	+	18.2331i	0.351874	+	0.609464i
$896$	60.6137			2.02496
$897$	1.51659	−	18.4965i	0.0506373	−	0.617578i
$898$	78.0439			2.60436
$899$	−1.65563	−	2.86763i	−0.0552182	−	0.0956407i
$900$	−1.18665	−	2.05534i	−0.0395550	−	0.0685112i
$901$	−11.8452	+	20.5164i	−0.394619	+	0.683500i
$902$	23.7564			0.791003
$903$	30.3058	−	52.4912i	1.00851	−	1.74680i
$904$	19.9873	−	34.6190i	0.664768	−	1.15141i
$905$	40.7484			1.35452
$906$	−38.1628	+	66.0999i	−1.26787	+	2.19602i
$907$	3.10984	+	5.38641i	0.103261	+	0.178853i	0.913026	−	0.407901i	$-0.133739\pi$
$907$	3.10984	+	5.38641i	0.103261	+	0.178853i	−0.809766	+	0.586753i	$0.800406\pi$
$908$	48.1648	+	83.4238i	1.59840	+	2.76852i
$909$	1.44200			0.0478281
$910$	−74.7606	+	35.3593i	−2.47829	+	1.17215i
$911$	−0.700769			−0.0232175			−0.0116088	−	0.999933i	$-0.503695\pi$
$911$	−0.700769			−0.0232175			−0.0116088	+	0.999933i	$0.503695\pi$
$912$	−7.31899	−	12.6769i	−0.242356	−	0.419773i
$913$	−2.27251	−	3.93610i	−0.0752090	−	0.130266i
$914$	−23.5775	+	40.8374i	−0.779874	+	1.35078i
$915$	−47.3440			−1.56515
$916$	37.2887	−	64.5858i	1.23205	−	2.13398i
$917$	−17.4929	+	30.2986i	−0.577667	+	1.00055i
$918$	25.0027			0.825213
$919$	−25.2162	+	43.6757i	−0.831805	+	1.44073i	0.0648011	+	0.997898i	$0.479359\pi$
$919$	−25.2162	+	43.6757i	−0.831805	+	1.44073i	−0.896606	+	0.442830i	$0.853975\pi$
$920$	−20.7078	−	35.8669i	−0.682714	−	1.18250i
$921$	10.1911	+	17.6515i	0.335808	+	0.581637i
$922$	15.9441			0.525091
$923$	1.57101	−	19.1602i	0.0517103	−	0.630664i
$924$	−25.8242			−0.849553
$925$	−22.5066	−	38.9826i	−0.740013	−	1.28174i
$926$	−23.5612	−	40.8092i	−0.774269	−	1.34107i
$927$	0.408645	−	0.707794i	0.0134217	−	0.0232470i
$928$	5.36375			0.176074
$929$	−3.20880	+	5.55780i	−0.105277	+	0.182346i	−0.913851	−	0.406049i	$-0.866906\pi$
$929$	−3.20880	+	5.55780i	−0.105277	+	0.182346i	0.808574	+	0.588394i	$0.200240\pi$
$930$	6.86847	−	11.8965i	0.225226	−	0.390103i
$931$	4.69142			0.153755
$932$	13.4344	−	23.2691i	0.440059	−	0.762205i
$933$	4.57817	+	7.92963i	0.149883	+	0.259604i
$934$	−21.9794	−	38.0694i	−0.719187	−	1.24567i
$935$	−8.51871			−0.278592
$936$	0.149062	−	1.81797i	0.00487224	−	0.0594223i
$937$	−58.5275			−1.91201			−0.956005	−	0.293352i	$-0.905229\pi$
$937$	−58.5275			−1.91201			−0.956005	+	0.293352i	$0.905229\pi$
$938$	33.2297	+	57.5555i	1.08499	+	1.87925i
$939$	19.9190	+	34.5007i	0.650032	+	1.12589i
$940$	8.02606	−	13.9015i	0.261781	−	0.453418i
$941$	−38.6382			−1.25957			−0.629785	−	0.776770i	$-0.716857\pi$
$941$	−38.6382			−1.25957			−0.629785	+	0.776770i	$0.716857\pi$
$942$	33.0066	−	57.1690i	1.07541	−	1.86267i
$943$	11.0563	−	19.1502i	0.360044	−	0.623615i
$944$	13.3153			0.433377
$945$	24.1970	−	41.9105i	0.787130	−	1.36335i
$946$	18.2568	+	31.6217i	0.593580	+	1.02811i
$947$	−6.44083	−	11.1558i	−0.209299	−	0.362516i	0.742195	−	0.670184i	$-0.233785\pi$
$947$	−6.44083	−	11.1558i	−0.209299	−	0.362516i	−0.951494	+	0.307668i	$0.900451\pi$
$948$	57.5466			1.86903
$949$	−45.3133	+	21.4317i	−1.47093	+	0.695702i
$950$	−36.3054			−1.17790
$951$	−21.2503	−	36.8067i	−0.689090	−	1.19354i
$952$	13.2004	+	22.8638i	0.427828	+	0.741020i
$953$	−14.8680	+	25.7522i	−0.481622	+	0.834195i	−0.999778	−	0.0210921i	$-0.993286\pi$
$953$	−14.8680	+	25.7522i	−0.481622	+	0.834195i	0.518155	+	0.855287i	$0.326619\pi$
$954$	−3.22866			−0.104532
$955$	5.59085	−	9.68363i	0.180916	−	0.313355i
$956$	34.1723	−	59.1881i	1.10521	−	1.91428i
$957$	−7.58707			−0.245255
$958$	29.0664	−	50.3445i	0.939093	−	1.62656i
$959$	−0.0197497	−	0.0342074i	−0.000637750	−	0.00110462i
$960$	28.0755	+	48.6282i	0.906132	+	1.56947i
$961$	1.00000			0.0322581
$962$	5.92631	−	72.2779i	0.191072	−	2.33033i
$963$	1.45168			0.0467798
$964$	−18.7762	−	32.5213i	−0.604741	−	1.04744i
$965$	11.5126	+	19.9405i	0.370605	+	0.641907i
$966$	−18.3038	+	31.7031i	−0.588914	+	1.02003i
$967$	11.5931			0.372811			0.186405	−	0.982473i	$-0.440316\pi$
$967$	11.5931			0.372811			0.186405	+	0.982473i	$0.440316\pi$
$968$	−20.5071	+	35.5194i	−0.659124	+	1.14164i
$969$	−5.00067	+	8.66141i	−0.160645	+	0.278245i
$970$	−140.284			−4.50425
$971$	20.5155	−	35.5338i	0.658373	−	1.14034i	−0.322664	−	0.946514i	$-0.604578\pi$
$971$	20.5155	−	35.5338i	0.658373	−	1.14034i	0.981037	−	0.193822i	$-0.0620883\pi$
$972$	2.28201	+	3.95256i	0.0731956	+	0.126778i
$973$	−8.21480	−	14.2285i	−0.263354	−	0.456143i
$974$	79.7356			2.55489
$975$	−28.2610	−	19.5597i	−0.905077	−	0.626410i
$976$	−24.7686			−0.792824
$977$	15.6101	+	27.0375i	0.499411	+	0.865005i	1.00000		0.000680043i	$-0.000216464\pi$
$977$	15.6101	+	27.0375i	0.499411	+	0.865005i	−0.500589	+	0.865685i	$0.666883\pi$
$978$	26.3119	+	45.5736i	0.841363	+	1.45728i
$979$	−1.97405	+	3.41916i	−0.0630911	+	0.109277i
$980$	20.7757			0.663656
$981$	−0.667648	+	1.15640i	−0.0213164	+	0.0369210i
$982$	38.3070	−	66.3496i	1.22242	−	2.11730i
$983$	23.4606			0.748275			0.374138	−	0.927373i	$-0.377939\pi$
$983$	23.4606			0.748275			0.374138	+	0.927373i	$0.377939\pi$
$984$	29.4616	−	51.0291i	0.939203	−	1.62675i
$985$	−30.8942	−	53.5103i	−0.984371	−	1.70498i
$986$	8.12954	+	14.0808i	0.258897	+	0.448423i
$987$	−6.76876			−0.215452
$988$	−31.5808	−	21.8573i	−1.00472	−	0.695372i
$989$	33.9872			1.08073
$990$	−0.580491	−	1.00544i	−0.0184492	−	0.0319550i
$991$	10.8605	+	18.8109i	0.344995	+	0.597549i	0.985353	−	0.170528i	$-0.0545473\pi$
$991$	10.8605	+	18.8109i	0.344995	+	0.597549i	−0.640358	+	0.768077i	$0.721214\pi$
$992$	−0.809927	+	1.40284i	−0.0257152	+	0.0445401i
$993$	−30.9549			−0.982323
$994$	−18.9606	+	32.8407i	−0.601393	+	1.04164i
$995$	−27.3999	+	47.4580i	−0.868635	+	1.50452i
$996$	−23.6304			−0.748758
$997$	2.06819	−	3.58222i	0.0655004	−	0.113450i	−0.831415	−	0.555651i	$-0.812469\pi$
$997$	2.06819	−	3.58222i	0.0655004	−	0.113450i	0.896916	+	0.442201i	$0.145802\pi$
$998$	27.0389	+	46.8327i	0.855900	+	1.48246i
$999$	21.2184	+	36.7514i	0.671321	+	1.16276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.94.18	✓	36
13.3	even	3		5239.2.a.p.1.1		18
13.9	even	3	inner	403.2.f.c.373.18	yes	36
13.10	even	6		5239.2.a.o.1.18		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.18	✓	36	1.1	even	1	trivial
403.2.f.c.373.18	yes	36	13.9	even	3	inner
5239.2.a.o.1.18		18	13.10	even	6
5239.2.a.p.1.1		18	13.3	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20670 + 2.09007i) q^{2} +(-0.882453 - 1.52845i) q^{3} +(-1.91225 + 3.31212i) q^{4} +3.22507 q^{5} +(2.12971 - 3.68877i) q^{6} +(-1.47346 + 2.55211i) q^{7} -4.40325 q^{8} +(-0.0574470 + 0.0995011i) q^{9} +O(q^{10})\)	\(q+(1.20670 + 2.09007i) q^{2} +(-0.882453 - 1.52845i) q^{3} +(-1.91225 + 3.31212i) q^{4} +3.22507 q^{5} +(2.12971 - 3.68877i) q^{6} +(-1.47346 + 2.55211i) q^{7} -4.40325 q^{8} +(-0.0574470 + 0.0995011i) q^{9} +(3.89169 + 6.74061i) q^{10} +(0.649128 + 1.12432i) q^{11} +6.74989 q^{12} +(3.25938 - 1.54158i) q^{13} -7.11212 q^{14} +(-2.84597 - 4.92937i) q^{15} +(-1.48891 - 2.57886i) q^{16} +(-1.01729 + 1.76200i) q^{17} -0.277285 q^{18} +(-1.39262 + 2.41208i) q^{19} +(-6.16714 + 10.6818i) q^{20} +5.20105 q^{21} +(-1.56661 + 2.71344i) q^{22} +(1.45821 + 2.52569i) q^{23} +(3.88567 + 6.73017i) q^{24} +5.40108 q^{25} +(7.15509 + 4.95209i) q^{26} -5.09194 q^{27} +(-5.63527 - 9.76057i) q^{28} +(-1.65563 - 2.86763i) q^{29} +(6.86847 - 11.8965i) q^{30} +1.00000 q^{31} +(-0.809927 + 1.40284i) q^{32} +(1.14565 - 1.98432i) q^{33} -4.91025 q^{34} +(-4.75203 + 8.23075i) q^{35} +(-0.219706 - 0.380542i) q^{36} +(-4.16706 - 7.21756i) q^{37} -6.72189 q^{38} +(-5.23248 - 3.62144i) q^{39} -14.2008 q^{40} +(-3.79107 - 6.56632i) q^{41} +(6.27611 + 10.8705i) q^{42} +(5.82687 - 10.0924i) q^{43} -4.96518 q^{44} +(-0.185270 + 0.320898i) q^{45} +(-3.51924 + 6.09551i) q^{46} -1.30142 q^{47} +(-2.62778 + 4.55145i) q^{48} +(-0.842194 - 1.45872i) q^{49} +(6.51748 + 11.2886i) q^{50} +3.59084 q^{51} +(-1.12686 + 13.7433i) q^{52} +11.6438 q^{53} +(-6.14445 - 10.6425i) q^{54} +(2.09348 + 3.62602i) q^{55} +(6.48804 - 11.2376i) q^{56} +4.91568 q^{57} +(3.99569 - 6.92073i) q^{58} +(-2.23576 + 3.87245i) q^{59} +21.7689 q^{60} +(4.15886 - 7.20336i) q^{61} +(1.20670 + 2.09007i) q^{62} +(-0.169292 - 0.293222i) q^{63} -9.86498 q^{64} +(10.5117 - 4.97170i) q^{65} +5.52982 q^{66} +(-4.67226 - 8.09260i) q^{67} +(-3.89063 - 6.73876i) q^{68} +(2.57360 - 4.45761i) q^{69} -22.9371 q^{70} +(2.66595 - 4.61757i) q^{71} +(0.252954 - 0.438128i) q^{72} -13.9024 q^{73} +(10.0568 - 17.4189i) q^{74} +(-4.76620 - 8.25530i) q^{75} +(-5.32607 - 9.22502i) q^{76} -3.82587 q^{77} +(1.25501 - 15.3062i) q^{78} +8.52556 q^{79} +(-4.80183 - 8.31701i) q^{80} +(4.66574 + 8.08130i) q^{81} +(9.14937 - 15.8472i) q^{82} -3.50086 q^{83} +(-9.94572 + 17.2265i) q^{84} +(-3.28083 + 5.68256i) q^{85} +28.1251 q^{86} +(-2.92202 + 5.06109i) q^{87} +(-2.85828 - 4.95068i) q^{88} +(1.52054 + 2.63366i) q^{89} -0.894264 q^{90} +(-0.868290 + 10.5898i) q^{91} -11.1539 q^{92} +(-0.882453 - 1.52845i) q^{93} +(-1.57043 - 2.72006i) q^{94} +(-4.49129 + 7.77914i) q^{95} +2.85889 q^{96} +(-9.01176 + 15.6088i) q^{97} +(2.03255 - 3.52048i) q^{98} -0.149162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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