LMFDB - Embedded newform 403.2.r.a.218.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(218,403)]

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([5, 0]))

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

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

chi := DirichletCharacter("403.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			218.6
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86490 + 1.07670i) q^{2} +(1.32944 + 2.30267i) q^{3} +(1.31857 - 2.28383i) q^{4} +3.07578i q^{5} +(-4.95857 - 2.86283i) q^{6} +(-0.437880 - 0.252810i) q^{7} +1.37202i q^{8} +(-2.03485 + 3.52446i) q^{9} +O(q^{10})$	\(q+(-1.86490 + 1.07670i) q^{2} +(1.32944 + 2.30267i) q^{3} +(1.31857 - 2.28383i) q^{4} +3.07578i q^{5} +(-4.95857 - 2.86283i) q^{6} +(-0.437880 - 0.252810i) q^{7} +1.37202i q^{8} +(-2.03485 + 3.52446i) q^{9} +(-3.31169 - 5.73602i) q^{10} +(-0.759584 + 0.438546i) q^{11} +7.01186 q^{12} +(-3.40537 - 1.18468i) q^{13} +1.08880 q^{14} +(-7.08249 + 4.08908i) q^{15} +(1.15989 + 2.00899i) q^{16} +(0.138434 - 0.239775i) q^{17} -8.76369i q^{18} +(-2.62887 - 1.51778i) q^{19} +(7.02455 + 4.05563i) q^{20} -1.34439i q^{21} +(0.944366 - 1.63569i) q^{22} +(1.42651 + 2.47079i) q^{23} +(-3.15929 + 1.82402i) q^{24} -4.46042 q^{25} +(7.62622 - 1.45724i) q^{26} -2.84420 q^{27} +(-1.15475 + 0.666695i) q^{28} +(4.79796 + 8.31031i) q^{29} +(8.80543 - 15.2515i) q^{30} +1.00000i q^{31} +(-6.70255 - 3.86972i) q^{32} +(-2.01965 - 1.16605i) q^{33} +0.596209i q^{34} +(0.777588 - 1.34682i) q^{35} +(5.36618 + 9.29449i) q^{36} +(-2.41308 + 1.39319i) q^{37} +6.53678 q^{38} +(-1.79932 - 9.41640i) q^{39} -4.22002 q^{40} +(5.01760 - 2.89691i) q^{41} +(1.44750 + 2.50715i) q^{42} +(2.04570 - 3.54326i) q^{43} +2.31301i q^{44} +(-10.8405 - 6.25874i) q^{45} +(-5.32060 - 3.07185i) q^{46} +1.26173i q^{47} +(-3.08402 + 5.34167i) q^{48} +(-3.37217 - 5.84078i) q^{49} +(8.31823 - 4.80253i) q^{50} +0.736162 q^{51} +(-7.19583 + 6.21519i) q^{52} -0.566795 q^{53} +(5.30416 - 3.06236i) q^{54} +(-1.34887 - 2.33631i) q^{55} +(0.346859 - 0.600778i) q^{56} -8.07122i q^{57} +(-17.8954 - 10.3319i) q^{58} +(-6.34573 - 3.66371i) q^{59} +21.5669i q^{60} +(4.30801 - 7.46169i) q^{61} +(-1.07670 - 1.86490i) q^{62} +(1.78204 - 1.02886i) q^{63} +12.0266 q^{64} +(3.64382 - 10.4742i) q^{65} +5.02193 q^{66} +(-9.90380 + 5.71796i) q^{67} +(-0.365070 - 0.632320i) q^{68} +(-3.79294 + 6.56956i) q^{69} +3.34892i q^{70} +(11.8567 + 6.84549i) q^{71} +(-4.83561 - 2.79184i) q^{72} +16.5818i q^{73} +(3.00011 - 5.19634i) q^{74} +(-5.92988 - 10.2708i) q^{75} +(-6.93270 + 4.00260i) q^{76} +0.443476 q^{77} +(13.4942 + 15.6233i) q^{78} +6.27460 q^{79} +(-6.17920 + 3.56756i) q^{80} +(2.32333 + 4.02413i) q^{81} +(-6.23822 + 10.8049i) q^{82} +9.50772i q^{83} +(-3.07035 - 1.77267i) q^{84} +(0.737495 + 0.425793i) q^{85} +8.81044i q^{86} +(-12.7572 + 22.0962i) q^{87} +(-0.601692 - 1.04216i) q^{88} +(1.01682 - 0.587062i) q^{89} +26.9552 q^{90} +(1.19164 + 1.37966i) q^{91} +7.52382 q^{92} +(-2.30267 + 1.32944i) q^{93} +(-1.35851 - 2.35301i) q^{94} +(4.66836 - 8.08583i) q^{95} -20.5783i q^{96} +(4.03232 + 2.32806i) q^{97} +(12.5775 + 7.26165i) q^{98} -3.56950i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) $ 68 * q + 32 * q^4 - 34 * q^9	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.86490	+	1.07670i	−1.31868	+	0.761342i	−0.983517	−	0.180816i	$-0.942126\pi$
$2$	−1.86490	+	1.07670i	−1.31868	+	0.761342i	−0.335167	+	0.942159i	$0.608793\pi$
$3$	1.32944	+	2.30267i	0.767555	+	1.32944i	0.938885	+	0.344231i	$0.111860\pi$
$3$	1.32944	+	2.30267i	0.767555	+	1.32944i	−0.171329	+	0.985214i	$0.554806\pi$
$4$	1.31857	−	2.28383i	0.659285	−	1.14191i
$5$			3.07578i			1.37553i	0.725933	+	0.687765i	$0.241408\pi$
$5$			3.07578i			1.37553i	−0.725933	+	0.687765i	$0.758592\pi$
$6$	−4.95857	−	2.86283i	−2.02433	−	1.16875i
$7$	−0.437880	−	0.252810i	−0.165503	−	0.0955532i	0.414961	−	0.909839i	$-0.363795\pi$
$7$	−0.437880	−	0.252810i	−0.165503	−	0.0955532i	−0.580464	+	0.814286i	$0.697129\pi$
$8$			1.37202i			0.485081i
$9$	−2.03485	+	3.52446i	−0.678283	+	1.17482i
$10$	−3.31169	−	5.73602i	−1.04725	−	1.81389i
$11$	−0.759584	+	0.438546i	−0.229023	+	0.132227i	−0.610121	−	0.792308i	$-0.708879\pi$
$11$	−0.759584	+	0.438546i	−0.229023	+	0.132227i	0.381098	+	0.924535i	$0.375546\pi$
$12$	7.01186			2.02415
$13$	−3.40537	−	1.18468i	−0.944479	−	0.328572i
$13$	−3.40537	−	1.18468i	−0.944479	−	0.328572i
$14$	1.08880			0.290995
$15$	−7.08249	+	4.08908i	−1.82869	+	1.05580i
$16$	1.15989	+	2.00899i	0.289972	+	0.502247i
$17$	0.138434	−	0.239775i	0.0335752	−	0.0581540i	−0.848750	−	0.528795i	$-0.822644\pi$
$17$	0.138434	−	0.239775i	0.0335752	−	0.0581540i	0.882325	+	0.470641i	$0.155977\pi$
$18$		−	8.76369i		−	2.06562i
$19$	−2.62887	−	1.51778i	−0.603105	−	0.348203i	0.167157	−	0.985930i	$-0.446541\pi$
$19$	−2.62887	−	1.51778i	−0.603105	−	0.348203i	−0.770262	+	0.637727i	$0.779875\pi$
$20$	7.02455	+	4.05563i	1.57074	+	0.906866i
$21$		−	1.34439i		−	0.293370i
$22$	0.944366	−	1.63569i	0.201340	−	0.348730i
$23$	1.42651	+	2.47079i	0.297448	+	0.515195i	0.975551	−	0.219771i	$-0.0705311\pi$
$23$	1.42651	+	2.47079i	0.297448	+	0.515195i	−0.678103	+	0.734967i	$0.737198\pi$
$24$	−3.15929	+	1.82402i	−0.644888	+	0.372326i
$25$	−4.46042			−0.892083
$26$	7.62622	−	1.45724i	1.49562	−	0.285789i
$27$	−2.84420			−0.547367
$28$	−1.15475	+	0.666695i	−0.218227	+	0.125994i
$29$	4.79796	+	8.31031i	0.890959	+	1.54319i	0.838728	+	0.544551i	$0.183300\pi$
$29$	4.79796	+	8.31031i	0.890959	+	1.54319i	0.0522306	+	0.998635i	$0.483367\pi$
$30$	8.80543	−	15.2515i	1.60764	−	2.78452i
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$	−6.70255	−	3.86972i	−1.18486	−	0.684077i
$33$	−2.01965	−	1.16605i	−0.351576	−	0.202983i
$34$			0.596209i			0.102249i
$35$	0.777588	−	1.34682i	0.131436	−	0.227654i
$36$	5.36618	+	9.29449i	0.894363	+	1.54908i
$37$	−2.41308	+	1.39319i	−0.396709	+	0.229040i	−0.685063	−	0.728484i	$-0.740225\pi$
$37$	−2.41308	+	1.39319i	−0.396709	+	0.229040i	0.288354	+	0.957524i	$0.406892\pi$
$38$	6.53678			1.06041
$39$	−1.79932	−	9.41640i	−0.288121	−	1.50783i
$40$	−4.22002			−0.667243
$41$	5.01760	−	2.89691i	0.783618	−	0.452422i	−0.0540930	−	0.998536i	$-0.517227\pi$
$41$	5.01760	−	2.89691i	0.783618	−	0.452422i	0.837711	+	0.546114i	$0.183893\pi$
$42$	1.44750	+	2.50715i	0.223355	+	0.386862i
$43$	2.04570	−	3.54326i	0.311967	−	0.540342i	−0.666821	−	0.745218i	$-0.732346\pi$
$43$	2.04570	−	3.54326i	0.311967	−	0.540342i	0.978788	+	0.204875i	$0.0656789\pi$
$44$			2.31301i			0.348700i
$45$	−10.8405	−	6.25874i	−1.61600	−	0.932998i
$46$	−5.32060	−	3.07185i	−0.784480	−	0.452920i
$47$			1.26173i			0.184043i	0.995757	+	0.0920214i	$0.0293328\pi$
$47$			1.26173i			0.184043i	−0.995757	+	0.0920214i	$0.970667\pi$
$48$	−3.08402	+	5.34167i	−0.445139	+	0.771004i
$49$	−3.37217	−	5.84078i	−0.481739	−	0.834397i
$50$	8.31823	−	4.80253i	1.17638	−	0.679181i
$51$	0.736162			0.103083
$52$	−7.19583	+	6.21519i	−0.997882	+	0.861892i
$53$	−0.566795			−0.0778552			−0.0389276	−	0.999242i	$-0.512394\pi$
$53$	−0.566795			−0.0778552			−0.0389276	+	0.999242i	$0.512394\pi$
$54$	5.30416	−	3.06236i	0.721804	−	0.416734i
$55$	−1.34887	−	2.33631i	−0.181882	−	0.315028i
$56$	0.346859	−	0.600778i	0.0463510	−	0.0802823i
$57$		−	8.07122i		−	1.06906i
$58$	−17.8954	−	10.3319i	−2.34979	−	1.35665i
$59$	−6.34573	−	3.66371i	−0.826143	−	0.476974i	0.0263870	−	0.999652i	$-0.491600\pi$
$59$	−6.34573	−	3.66371i	−0.826143	−	0.476974i	−0.852530	+	0.522678i	$0.824933\pi$
$60$			21.5669i			2.78428i
$61$	4.30801	−	7.46169i	0.551584	−	0.955371i	−0.446577	−	0.894745i	$-0.647357\pi$
$61$	4.30801	−	7.46169i	0.551584	−	0.955371i	0.998161	−	0.0606258i	$-0.0193096\pi$
$62$	−1.07670	−	1.86490i	−0.136741	−	0.236843i
$63$	1.78204	−	1.02886i	0.224516	−	0.129624i
$64$	12.0266			1.50332
$65$	3.64382	−	10.4742i	0.451961	−	1.29916i
$66$	5.02193			0.618157
$67$	−9.90380	+	5.71796i	−1.20994	+	0.698560i	−0.962747	−	0.270406i	$-0.912842\pi$
$67$	−9.90380	+	5.71796i	−1.20994	+	0.698560i	−0.247195	+	0.968966i	$0.579509\pi$
$68$	−0.365070	−	0.632320i	−0.0442712	−	0.0766800i
$69$	−3.79294	+	6.56956i	−0.456616	+	0.790882i
$70$			3.34892i			0.400272i
$71$	11.8567	+	6.84549i	1.40714	+	0.812411i	0.995111	−	0.0987618i	$-0.0314882\pi$
$71$	11.8567	+	6.84549i	1.40714	+	0.812411i	0.412025	+	0.911172i	$0.364822\pi$
$72$	−4.83561	−	2.79184i	−0.569882	−	0.329022i
$73$			16.5818i			1.94076i	0.241592	+	0.970378i	$0.422330\pi$
$73$			16.5818i			1.94076i	−0.241592	+	0.970378i	$0.577670\pi$
$74$	3.00011	−	5.19634i	0.348755	−	0.604062i
$75$	−5.92988	−	10.2708i	−0.684723	−	1.18598i
$76$	−6.93270	+	4.00260i	−0.795236	+	0.459129i
$77$	0.443476			0.0505387
$78$	13.4942	+	15.6233i	1.52792	+	1.76899i
$79$	6.27460			0.705947			0.352974	−	0.935633i	$-0.385171\pi$
$79$	6.27460			0.705947			0.352974	+	0.935633i	$0.385171\pi$
$80$	−6.17920	+	3.56756i	−0.690855	+	0.398865i
$81$	2.32333	+	4.02413i	0.258148	+	0.447125i
$82$	−6.23822	+	10.8049i	−0.688896	+	1.19320i
$83$			9.50772i			1.04361i	0.853065	+	0.521804i	$0.174741\pi$
$83$			9.50772i			1.04361i	−0.853065	+	0.521804i	$0.825259\pi$
$84$	−3.07035	−	1.77267i	−0.335003	−	0.193414i
$85$	0.737495	+	0.425793i	0.0799925	+	0.0461837i
$86$			8.81044i			0.950054i
$87$	−12.7572	+	22.0962i	−1.36772	+	2.36896i
$88$	−0.601692	−	1.04216i	−0.0641406	−	0.111095i
$89$	1.01682	−	0.587062i	0.107783	−	0.0622285i	−0.445140	−	0.895461i	$-0.646846\pi$
$89$	1.01682	−	0.587062i	0.107783	−	0.0622285i	0.552922	+	0.833233i	$0.313513\pi$
$90$	26.9552			2.84132
$91$	1.19164	+	1.37966i	0.124918	+	0.144628i
$92$	7.52382			0.784412
$93$	−2.30267	+	1.32944i	−0.238775	+	0.137857i
$94$	−1.35851	−	2.35301i	−0.140120	−	0.242694i
$95$	4.66836	−	8.08583i	0.478963	−	0.829589i
$96$		−	20.5783i		−	2.10027i
$97$	4.03232	+	2.32806i	0.409420	+	0.236379i	0.690540	−	0.723294i	$-0.257373\pi$
$97$	4.03232	+	2.32806i	0.409420	+	0.236379i	−0.281121	+	0.959672i	$0.590706\pi$
$98$	12.5775	+	7.26165i	1.27052	+	0.733537i
$99$		−	3.56950i		−	0.358748i
$100$	−5.88137	+	10.1868i	−0.588137	+	1.01868i
$101$	2.89070	+	5.00684i	0.287636	+	0.498199i	0.973245	−	0.229770i	$-0.0737975\pi$
$101$	2.89070	+	5.00684i	0.287636	+	0.498199i	−0.685609	+	0.727970i	$0.740464\pi$
$102$	−1.37287	+	0.792627i	−0.135934	+	0.0784817i
$103$	11.7984			1.16253			0.581266	−	0.813714i	$-0.302558\pi$
$103$	11.7984			1.16253			0.581266	+	0.813714i	$0.302558\pi$
$104$	1.62540	−	4.67222i	0.159384	−	0.458148i
$105$	4.13504			0.403539
$106$	1.05702	−	0.610268i	0.102666	−	0.0592745i
$107$	−6.66439	−	11.5431i	−0.644271	−	1.11591i	−0.984469	−	0.175556i	$-0.943828\pi$
$107$	−6.66439	−	11.5431i	−0.644271	−	1.11591i	0.340199	−	0.940354i	$-0.389506\pi$
$108$	−3.75028	+	6.49567i	−0.360871	+	0.625047i
$109$		−	11.3146i		−	1.08374i	−0.840461	−	0.541872i	$-0.817716\pi$
$109$		−	11.3146i		−	1.08374i	0.840461	−	0.541872i	$-0.182284\pi$
$110$	5.03102	+	2.90466i	0.479689	+	0.276949i
$111$	−6.41612	−	3.70435i	−0.608992	−	0.351601i
$112$		−	1.17293i		−	0.110831i
$113$	−8.06824	+	13.9746i	−0.758996	+	1.31462i	0.184367	+	0.982857i	$0.440976\pi$
$113$	−8.06824	+	13.9746i	−0.758996	+	1.31462i	−0.943363	+	0.331762i	$0.892357\pi$
$114$	8.69029	+	15.0520i	0.813921	+	1.40975i
$115$	−7.59961	+	4.38763i	−0.708667	+	0.409149i
$116$	25.3058			2.34958
$117$	11.1048	−	9.59143i	1.02664	−	0.886728i
$118$	15.7789			1.45256
$119$	−0.121235	+	0.0699951i	−0.0111136	+	0.00641644i
$120$	−5.61028	−	9.71729i	−0.512146	−	0.887063i
$121$	−5.11535	+	8.86005i	−0.465032	+	0.805459i
$122$			18.5537i			1.67978i
$123$	13.3413	+	7.70258i	1.20294	+	0.694518i
$124$	2.28383	+	1.31857i	0.205094	+	0.118411i
$125$			1.65964i			0.148443i
$126$	−2.21555	+	3.83744i	−0.197377	+	0.341867i
$127$	6.39285	+	11.0727i	0.567273	+	0.982546i	0.996834	+	0.0795084i	$0.0253350\pi$
$127$	6.39285	+	11.0727i	0.567273	+	0.982546i	−0.429561	+	0.903038i	$0.641332\pi$
$128$	−9.02326	+	5.20958i	−0.797551	+	0.460466i
$129$	10.8786			0.957807
$130$	4.48216	+	23.4566i	0.393112	+	2.05728i
$131$	−3.19006			−0.278717			−0.139358	−	0.990242i	$-0.544504\pi$
$131$	−3.19006			−0.278717			−0.139358	+	0.990242i	$0.544504\pi$
$132$	−5.32610	+	3.07503i	−0.463578	+	0.267647i
$133$	0.767420	+	1.32921i	0.0665438	+	0.115257i
$134$	12.3131	−	21.3269i	1.06369	−	1.84236i
$135$		−	8.74814i		−	0.752920i
$136$	0.328975	+	0.189934i	0.0282094	+	0.0162867i
$137$	−18.2647	−	10.5451i	−1.56046	−	0.900930i	−0.997210	−	0.0746417i	$-0.976219\pi$
$137$	−18.2647	−	10.5451i	−1.56046	−	0.900930i	−0.563247	−	0.826289i	$-0.690448\pi$
$138$		−	16.3354i		−	1.39056i
$139$	−0.442021	+	0.765603i	−0.0374917	+	0.0649376i	−0.884162	−	0.467180i	$-0.845270\pi$
$139$	−0.442021	+	0.765603i	−0.0374917	+	0.0649376i	0.846671	+	0.532117i	$0.178603\pi$
$140$	−2.05061	−	3.55175i	−0.173308	−	0.300178i
$141$	−2.90535	+	1.67741i	−0.244675	+	0.141263i
$142$	−29.4822			−2.47409
$143$	3.10620	−	0.593544i	0.259754	−	0.0496346i
$144$	−9.44079			−0.786732
$145$	−25.5607	+	14.7575i	−2.12270	+	1.22554i
$146$	−17.8537	−	30.9235i	−1.47758	−	2.55924i
$147$	8.96624	−	15.5300i	0.739523	−	1.28089i
$148$			7.34809i			0.604010i
$149$	16.0699	+	9.27794i	1.31649	+	0.760078i	0.983163	−	0.182732i	$-0.0584939\pi$
$149$	16.0699	+	9.27794i	1.31649	+	0.760078i	0.333331	+	0.942810i	$0.391827\pi$
$150$	22.1173	+	12.7694i	1.80587	+	1.04262i
$151$		−	17.3616i		−	1.41287i	−0.707780	−	0.706433i	$-0.750303\pi$
$151$		−	17.3616i		−	1.41287i	0.707780	−	0.706433i	$-0.249697\pi$
$152$	2.08242	−	3.60685i	0.168906	−	0.292554i
$153$	0.563385	+	0.975811i	0.0455470	+	0.0788897i
$154$	−0.827038	+	0.477490i	−0.0666446	+	0.0384773i
$155$	−3.07578			−0.247053
$156$	−23.8780	−	8.30684i	−1.91177	−	0.665079i
$157$	−22.2754			−1.77777			−0.888885	−	0.458130i	$-0.848519\pi$
$157$	−22.2754			−1.77777			−0.888885	+	0.458130i	$0.848519\pi$
$158$	−11.7015	+	6.75586i	−0.930921	+	0.537468i
$159$	−0.753522	−	1.30514i	−0.0597582	−	0.103504i
$160$	11.9024	−	20.6156i	0.940968	−	1.62980i
$161$		−	1.44255i		−	0.113689i
$162$	−8.66556	−	5.00307i	−0.680831	−	0.393078i
$163$	14.4590	+	8.34791i	1.13252	+	0.653859i	0.944567	−	0.328320i	$-0.106482\pi$
$163$	14.4590	+	8.34791i	1.13252	+	0.653859i	0.187950	+	0.982179i	$0.439816\pi$
$164$		−	15.2791i		−	1.19310i
$165$	3.58650	−	6.21200i	0.279209	−	0.483604i
$166$	−10.2370	−	17.7310i	−0.794543	−	1.37619i
$167$	3.33377	−	1.92475i	0.257975	−	0.148942i	−0.365435	−	0.930837i	$-0.619080\pi$
$167$	3.33377	−	1.92475i	0.257975	−	0.148942i	0.623410	+	0.781895i	$0.285747\pi$
$168$	1.84452			0.142308
$169$	10.1931	+	8.06856i	0.784081	+	0.620659i
$170$	−1.83381			−0.140647
$171$	10.6987	−	6.17691i	0.818151	−	0.472360i
$172$	−5.39480	−	9.34407i	−0.411350	−	0.712479i
$173$	−0.449137	+	0.777928i	−0.0341472	+	0.0591447i	−0.882594	−	0.470136i	$-0.844205\pi$
$173$	−0.449137	+	0.777928i	−0.0341472	+	0.0591447i	0.848447	+	0.529281i	$0.177538\pi$
$174$		−	54.9429i		−	4.16521i
$175$	1.95313	+	1.12764i	0.147642	+	0.0852414i
$176$	−1.76207	−	1.01733i	−0.132821	−	0.0766841i
$177$		−	19.4828i		−	1.46442i
$178$	−1.26418	+	2.18963i	−0.0947544	+	0.164119i
$179$	2.52599	+	4.37514i	0.188801	+	0.327013i	0.944851	−	0.327501i	$-0.106206\pi$
$179$	2.52599	+	4.37514i	0.188801	+	0.327013i	−0.756050	+	0.654514i	$0.772873\pi$
$180$	−28.5878	+	16.5052i	−2.13081	+	1.23022i
$181$	−9.29941			−0.691220			−0.345610	−	0.938378i	$-0.612328\pi$
$181$	−9.29941			−0.691220			−0.345610	+	0.938378i	$0.612328\pi$
$182$	−3.70777	−	1.28989i	−0.274838	−	0.0956128i
$183$	22.9090			1.69348
$184$	−3.38996	+	1.95720i	−0.249911	+	0.144286i
$185$	−4.28516	−	7.42211i	−0.315051	−	0.545685i
$186$	2.86283	−	4.95857i	0.209913	−	0.363580i
$187$			0.242839i			0.0177582i
$188$	2.88158	+	1.66368i	0.210161	+	0.121337i
$189$	1.24542	+	0.719043i	0.0905909	+	0.0523027i
$190$			20.1057i			1.45862i
$191$	5.04609	−	8.74009i	0.365122	−	0.632411i	−0.623673	−	0.781685i	$-0.714360\pi$
$191$	5.04609	−	8.74009i	0.365122	−	0.632411i	0.988796	+	0.149275i	$0.0476938\pi$
$192$	15.9887	+	27.6932i	1.15388	+	1.99858i
$193$	7.17816	−	4.14431i	0.516695	−	0.298314i	−0.218886	−	0.975750i	$-0.570242\pi$
$193$	7.17816	−	4.14431i	0.516695	−	0.298314i	0.735581	+	0.677436i	$0.236909\pi$
$194$	−10.0265			−0.719860
$195$	28.9628	−	5.53430i	2.07407	−	0.396320i
$196$	−17.7858			−1.27041
$197$	−13.2882	+	7.67195i	−0.946745	+	0.546604i	−0.892068	−	0.451901i	$-0.850746\pi$
$197$	−13.2882	+	7.67195i	−0.946745	+	0.546604i	−0.0546768	+	0.998504i	$0.517413\pi$
$198$	3.84328	+	6.65676i	0.273130	+	0.473075i
$199$	4.67264	−	8.09324i	0.331234	−	0.573715i	−0.651520	−	0.758632i	$-0.725868\pi$
$199$	4.67264	−	8.09324i	0.331234	−	0.573715i	0.982754	+	0.184917i	$0.0592016\pi$
$200$		−	6.11976i		−	0.432732i
$201$	−26.3331	−	15.2034i	−1.85739	−	1.07237i
$202$	−10.7817	−	6.22484i	−0.758601	−	0.437978i
$203$		−	4.85189i		−	0.340536i
$204$	0.970681	−	1.68127i	0.0679613	−	0.117712i
$205$	8.91027	+	15.4330i	0.622320	+	1.07789i
$206$	−22.0028	+	12.7034i	−1.53301	+	0.885084i
$207$	−11.6109			−0.807016
$208$	−1.56983	−	8.21544i	−0.108848	−	0.569638i
$209$	2.66247			0.184167
$210$	−7.71144	+	4.45220i	−0.532140	+	0.307231i
$211$	−6.09575	−	10.5582i	−0.419649	−	0.726853i	0.576255	−	0.817270i	$-0.304513\pi$
$211$	−6.09575	−	10.5582i	−0.419649	−	0.726853i	−0.995904	+	0.0904168i	$0.971180\pi$
$212$	−0.747358	+	1.29446i	−0.0513287	+	0.0889040i
$213$			36.4028i			2.49428i
$214$	24.8568	+	14.3511i	1.69918	+	0.981021i
$215$	10.8983	+	6.29213i	0.743257	+	0.429120i
$216$		−	3.90229i		−	0.265517i
$217$	0.252810	−	0.437880i	0.0171619	−	0.0297252i
$218$	12.1825	+	21.1006i	0.825100	+	1.42912i
$219$	−38.1824	+	22.0446i	−2.58013	+	1.48964i
$220$	−7.11432			−0.479647
$221$	−0.755477	+	0.652521i	−0.0508189	+	0.0438933i
$222$	15.9539			1.07076
$223$	23.4068	−	13.5139i	1.56744	−	0.904961i	0.570972	−	0.820970i	$-0.306567\pi$
$223$	23.4068	−	13.5139i	1.56744	−	0.904961i	0.996467	−	0.0839910i	$-0.0267667\pi$
$224$	1.95661	+	3.38895i	0.130731	+	0.226433i
$225$	9.07627	−	15.7206i	0.605085	−	1.04804i
$226$		−	34.7483i		−	2.31142i
$227$	3.78447	+	2.18496i	0.251184	+	0.145021i	0.620306	−	0.784360i	$-0.287008\pi$
$227$	3.78447	+	2.18496i	0.251184	+	0.145021i	−0.369122	+	0.929381i	$0.620342\pi$
$228$	−18.4333	−	10.6425i	−1.22077	−	0.704815i
$229$		−	8.87917i		−	0.586752i	−0.955997	−	0.293376i	$-0.905221\pi$
$229$		−	8.87917i		−	0.586752i	0.955997	−	0.293376i	$-0.0947788\pi$
$230$	9.44834	−	16.3650i	0.623005	−	1.07908i
$231$	0.589576	+	1.02118i	0.0387913	+	0.0671885i
$232$	−11.4019	+	6.58287i	−0.748569	+	0.432187i
$233$	−12.0255			−0.787815			−0.393907	−	0.919150i	$-0.628877\pi$
$233$	−12.0255			−0.787815			−0.393907	+	0.919150i	$0.628877\pi$
$234$	−10.3822	+	29.8436i	−0.678705	+	1.95094i
$235$	−3.88081			−0.253156
$236$	−16.7346	+	9.66170i	−1.08933	+	0.628923i
$237$	8.34173	+	14.4483i	0.541854	+	0.938518i
$238$	0.150728	−	0.261068i	0.00977021	−	0.0169225i
$239$		−	3.46463i		−	0.224108i	−0.993702	−	0.112054i	$-0.964257\pi$
$239$		−	3.46463i		−	0.224108i	0.993702	−	0.112054i	$-0.0357430\pi$
$240$	−16.4298	−	9.48575i	−1.06054	−	0.612303i
$241$	7.58394	+	4.37859i	0.488525	+	0.282050i	0.723962	−	0.689840i	$-0.242319\pi$
$241$	7.58394	+	4.37859i	0.488525	+	0.282050i	−0.235438	+	0.971889i	$0.575652\pi$
$242$		−	22.0308i		−	1.41620i
$243$	−10.4438	+	18.0892i	−0.669969	+	1.16042i
$244$	−11.3608	−	19.6775i	−0.727301	−	1.25972i
$245$	17.9649	−	10.3721i	1.14774	−	0.662647i
$246$	−33.1735			−2.11506
$247$	7.15419	+	8.28298i	0.455210	+	0.527034i
$248$	−1.37202			−0.0871230
$249$	−21.8931	+	12.6400i	−1.38742	+	0.801027i
$250$	−1.78694	−	3.09506i	−0.113016	−	0.195749i
$251$	−4.66266	+	8.07596i	−0.294304	+	0.509750i	−0.974823	−	0.222981i	$-0.928421\pi$
$251$	−4.66266	+	8.07596i	−0.294304	+	0.509750i	0.680519	+	0.732731i	$0.261755\pi$
$252$		−	5.42649i		−	0.341837i
$253$	−2.16711	−	1.25118i	−0.136245	−	0.0786612i
$254$	−23.8440	−	13.7664i	−1.49611	−	0.863779i
$255$			2.26427i			0.141794i
$256$	−0.808258	+	1.39994i	−0.0505161	+	0.0874965i
$257$	12.0995	+	20.9569i	0.754744	+	1.30726i	0.945501	+	0.325618i	$0.105572\pi$
$257$	12.0995	+	20.9569i	0.754744	+	1.30726i	−0.190757	+	0.981637i	$0.561094\pi$
$258$	−20.2875	+	11.7130i	−1.26304	+	0.729219i
$259$	1.40885			0.0875419
$260$	−19.1165	−	22.1328i	−1.18556	−	1.37262i
$261$	−39.0525			−2.41729
$262$	5.94914	−	3.43474i	0.367539	−	0.212199i
$263$	−0.639740	−	1.10806i	−0.0394481	−	0.0683260i	0.845627	−	0.533774i	$-0.179227\pi$
$263$	−0.639740	−	1.10806i	−0.0394481	−	0.0683260i	−0.885075	+	0.465448i	$0.845893\pi$
$264$	1.59983	−	2.77099i	0.0984629	−	0.170543i
$265$		−	1.74333i		−	0.107092i
$266$	−2.86232	−	1.65256i	−0.175500	−	0.101325i
$267$	2.70362	+	1.56093i	0.165459	+	0.0955276i
$268$			30.1581i			1.84220i
$269$	−3.21353	+	5.56599i	−0.195932	+	0.339365i	−0.947206	−	0.320626i	$-0.896107\pi$
$269$	−3.21353	+	5.56599i	−0.195932	+	0.339365i	0.751273	+	0.659991i	$0.229440\pi$
$270$	9.41913	+	16.3144i	0.573230	+	0.992864i
$271$	23.9906	−	13.8510i	1.45732	−	0.841385i	0.458443	−	0.888724i	$-0.348407\pi$
$271$	23.9906	−	13.8510i	1.45732	−	0.841385i	0.998879	+	0.0473381i	$0.0150738\pi$
$272$	0.642273			0.0389435
$273$	−1.59267	+	4.57813i	−0.0963930	+	0.277081i
$274$	45.4158			2.74367
$275$	3.38806	−	1.95610i	0.204308	−	0.117957i
$276$	10.0025	+	17.3248i	0.602080	+	1.04283i
$277$	−0.966281	+	1.67365i	−0.0580582	+	0.100560i	−0.893594	−	0.448877i	$-0.851824\pi$
$277$	−0.966281	+	1.67365i	−0.0580582	+	0.100560i	0.835536	+	0.549436i	$0.185158\pi$
$278$		−	1.90370i		−	0.114176i
$279$	−3.52446	−	2.03485i	−0.211004	−	0.121823i
$280$	1.84786	+	1.06686i	0.110431	+	0.0637572i
$281$		−	14.3002i		−	0.853076i	−0.904470	−	0.426538i	$-0.859733\pi$
$281$		−	14.3002i		−	0.853076i	0.904470	−	0.426538i	$-0.140267\pi$
$282$	3.61213	−	6.25639i	0.215099	−	0.372563i
$283$	−13.5466	−	23.4634i	−0.805262	−	1.39476i	−0.916114	−	0.400918i	$-0.868691\pi$
$283$	−13.5466	−	23.4634i	−0.805262	−	1.39476i	0.110851	−	0.993837i	$-0.464642\pi$
$284$	31.2679	−	18.0525i	1.85541	−	1.07122i
$285$	24.8253			1.47052
$286$	−5.15369	+	4.45135i	−0.304744	+	0.263214i
$287$	−2.92948			−0.172921
$288$	27.2774	−	15.7486i	1.60733	−	0.927995i
$289$	8.46167	+	14.6560i	0.497745	+	0.862120i
$290$	31.7787	−	55.0424i	1.86611	−	3.23220i
$291$			12.3801i			0.725734i
$292$	37.8701	+	21.8643i	2.21618	+	1.27951i
$293$	16.0335	+	9.25693i	0.936685	+	0.540796i	0.888920	−	0.458063i	$-0.151457\pi$
$293$	16.0335	+	9.25693i	0.936685	+	0.540796i	0.0477656	+	0.998859i	$0.484790\pi$
$294$			38.6158i			2.25212i
$295$	11.2688	−	19.5181i	0.656092	−	1.13639i
$296$	−1.91148	−	3.31079i	−0.111103	−	0.192436i
$297$	2.16041	−	1.24731i	0.125360	−	0.0723765i
$298$	−39.9582			−2.31472
$299$	−1.93069	−	10.1039i	−0.111655	−	0.584324i
$300$	−31.2758			−1.80571
$301$	−1.79154	+	1.03435i	−0.103263	+	0.0596189i
$302$	18.6932	+	32.3776i	1.07567	+	1.86312i
$303$	−7.68606	+	13.3126i	−0.441553	+	0.764791i
$304$		−	7.04183i		−	0.403876i
$305$	22.9505	+	13.2505i	1.31414	+	0.758720i
$306$	−2.10131	−	1.21319i	−0.120124	−	0.0693537i
$307$		−	34.6053i		−	1.97503i	−0.157536	−	0.987513i	$-0.550355\pi$
$307$		−	34.6053i		−	1.97503i	0.157536	−	0.987513i	$-0.449645\pi$
$308$	0.584753	−	1.01282i	0.0333194	−	0.0577109i
$309$	15.6853	+	27.1678i	0.892307	+	1.54552i
$310$	5.73602	−	3.31169i	0.325784	−	0.188092i
$311$	25.6016			1.45174			0.725868	−	0.687834i	$-0.241438\pi$
$311$	25.6016			1.45174			0.725868	+	0.687834i	$0.241438\pi$
$312$	12.9194	−	2.46869i	0.731419	−	0.139762i
$313$	12.1748			0.688159			0.344079	−	0.938941i	$-0.388191\pi$
$313$	12.1748			0.688159			0.344079	+	0.938941i	$0.388191\pi$
$314$	41.5414	−	23.9839i	2.34432	−	1.35349i
$315$	3.16455	+	5.48115i	0.178302	+	0.308828i
$316$	8.27349	−	14.3301i	0.465420	−	0.806132i
$317$		−	13.3234i		−	0.748318i	−0.927365	−	0.374159i	$-0.877931\pi$
$317$		−	13.3234i		−	0.748318i	0.927365	−	0.374159i	$-0.122069\pi$
$318$	2.81049	+	1.62264i	0.157604	+	0.0909929i
$319$	−7.28891	−	4.20825i	−0.408101	−	0.235617i
$320$			36.9911i			2.06786i
$321$	17.7199	−	30.6917i	0.989027	−	1.71305i
$322$	1.55319	+	2.69020i	0.0865559	+	0.149919i
$323$	−0.727852	+	0.420225i	−0.0404988	+	0.0233820i
$324$	12.2539			0.680772
$325$	15.1894	+	5.28418i	0.842554	+	0.293114i
$326$	−35.9528			−1.99124
$327$	26.0538	−	15.0422i	1.44078	−	0.831834i
$328$	3.97461	+	6.88423i	0.219461	+	0.380118i
$329$	0.318979	−	0.552488i	0.0175859	−	0.0304596i
$330$			15.4464i			0.850294i
$331$	30.4513	+	17.5811i	1.67376	+	0.966344i	0.965505	+	0.260385i	$0.0838496\pi$
$331$	30.4513	+	17.5811i	1.67376	+	0.966344i	0.708253	+	0.705959i	$0.249484\pi$
$332$	21.7140	+	12.5366i	1.19171	+	0.688035i
$333$		−	11.3398i		−	0.621415i
$334$	−4.14477	+	7.17895i	−0.226792	+	0.392815i
$335$	−17.5872	−	30.4619i	−0.960891	−	1.66431i
$336$	2.70086	−	1.55934i	0.147344	−	0.0850690i
$337$	−7.41867			−0.404121			−0.202060	−	0.979373i	$-0.564764\pi$
$337$	−7.41867			−0.404121			−0.202060	+	0.979373i	$0.564764\pi$
$338$	−27.6965	−	4.07220i	−1.50649	−	0.221499i
$339$	−42.9051			−2.33029
$340$	1.94488	−	1.12287i	0.105476	−	0.0608964i
$341$	−0.438546	−	0.759584i	−0.0237486	−	0.0411338i
$342$	−13.3014	+	23.0386i	−0.719255	+	1.24579i
$343$			6.94942i			0.375233i
$344$	4.86141	+	2.80674i	0.262110	+	0.151329i
$345$	−20.2065	−	11.6662i	−1.08788	−	0.628089i
$346$		−	1.93434i		−	0.103991i
$347$	−2.43761	+	4.22207i	−0.130858	+	0.226653i	−0.924008	−	0.382374i	$-0.875107\pi$
$347$	−2.43761	+	4.22207i	−0.130858	+	0.226653i	0.793150	+	0.609027i	$0.208440\pi$
$348$	33.6426	+	58.2707i	1.80343	+	3.12364i
$349$	0.968040	−	0.558898i	0.0518180	−	0.0299171i	−0.473867	−	0.880596i	$-0.657142\pi$
$349$	0.968040	−	0.558898i	0.0518180	−	0.0299171i	0.525685	+	0.850679i	$0.323809\pi$
$350$	−4.85651			−0.259592
$351$	9.68556	+	3.36948i	0.516977	+	0.179850i
$352$	6.78821			0.361813
$353$	−2.49331	+	1.43952i	−0.132706	+	0.0766177i	−0.564883	−	0.825171i	$-0.691079\pi$
$353$	−2.49331	+	1.43952i	−0.132706	+	0.0766177i	0.432177	+	0.901789i	$0.357745\pi$
$354$	20.9771	+	36.3335i	1.11492	+	1.93110i
$355$	−21.0552	+	36.4687i	−1.11750	+	1.93556i
$356$		−	3.09633i		−	0.164105i
$357$	−0.322351	−	0.186109i	−0.0170606	−	0.00984994i
$358$	−9.42143	−	5.43947i	−0.497938	−	0.287485i
$359$		−	10.1913i		−	0.537875i	−0.963158	−	0.268937i	$-0.913328\pi$
$359$		−	10.1913i		−	0.537875i	0.963158	−	0.268937i	$-0.0866725\pi$
$360$	8.58709	−	14.8733i	0.452579	−	0.783890i
$361$	−4.89268	−	8.47438i	−0.257510	−	0.446020i
$362$	17.3425	−	10.0127i	0.911500	−	0.526255i
$363$	−27.2023			−1.42775
$364$	4.72217	−	0.902329i	0.247509	−	0.0472949i
$365$	−51.0020			−2.66957
$366$	−42.7231	+	24.6662i	−2.23317	+	1.28932i
$367$	−16.6619	−	28.8593i	−0.869746	−	1.50644i	−0.862257	−	0.506472i	$-0.830949\pi$
$367$	−16.6619	−	28.8593i	−0.869746	−	1.50644i	−0.00748907	−	0.999972i	$-0.502384\pi$
$368$	−3.30919	+	5.73168i	−0.172503	+	0.298785i
$369$			23.5791i			1.22748i
$370$	15.9828	+	9.22767i	0.830906	+	0.479724i
$371$	0.248188	+	0.143291i	0.0128853	+	0.00743932i
$372$			7.01186i			0.363548i
$373$	−4.02525	+	6.97194i	−0.208420	+	0.360993i	−0.951217	−	0.308523i	$-0.900165\pi$
$373$	−4.02525	+	6.97194i	−0.208420	+	0.360993i	0.742797	+	0.669516i	$0.233499\pi$
$374$	−0.261465	−	0.452871i	−0.0135200	−	0.0234174i
$375$	−3.82160	+	2.20640i	−0.197347	+	0.113938i
$376$	−1.73112			−0.0892756
$377$	−6.49373	−	33.9837i	−0.334444	−	1.75025i
$378$	−3.09678			−0.159281
$379$	−3.64931	+	2.10693i	−0.187452	+	0.108226i	−0.590789	−	0.806826i	$-0.701184\pi$
$379$	−3.64931	+	2.10693i	−0.187452	+	0.108226i	0.403337	+	0.915052i	$0.367850\pi$
$380$	−12.3111	−	21.3235i	−0.631546	−	1.09387i
$381$	−16.9979	+	29.4412i	−0.870828	+	1.50832i
$382$			21.7325i			1.11193i
$383$	25.3235	+	14.6205i	1.29397	+	0.747073i	0.979355	−	0.202147i	$-0.0647919\pi$
$383$	25.3235	+	14.6205i	1.29397	+	0.747073i	0.314613	+	0.949220i	$0.398125\pi$
$384$	−23.9918	−	13.8517i	−1.22433	−	0.706866i
$385$			1.36403i			0.0695175i
$386$	−8.92437	+	15.4575i	−0.454238	+	0.786764i
$387$	8.32539	+	14.4200i	0.423203	+	0.733010i
$388$	10.6338	−	6.13941i	0.539848	−	0.311681i
$389$	7.94448			0.402801			0.201400	−	0.979509i	$-0.435451\pi$
$389$	7.94448			0.402801			0.201400	+	0.979509i	$0.435451\pi$
$390$	−48.0539	+	41.5051i	−2.43330	+	2.10169i
$391$	0.789912			0.0399476
$392$	8.01363	−	4.62667i	0.404750	−	0.233682i
$393$	−4.24101	−	7.34564i	−0.213931	−	0.370539i
$394$	16.5208	−	28.6148i	0.832305	−	1.44159i
$395$			19.2993i			0.971052i
$396$	−8.15213	−	4.70663i	−0.409660	−	0.236517i
$397$	10.1994	+	5.88865i	0.511896	+	0.295543i	0.733613	−	0.679568i	$-0.237833\pi$
$397$	10.1994	+	5.88865i	0.511896	+	0.295543i	−0.221717	+	0.975111i	$0.571166\pi$
$398$			20.1241i			1.00873i
$399$	−2.04049	+	3.53423i	−0.102152	+	0.176933i
$400$	−5.17359	−	8.96091i	−0.258679	−	0.448046i
$401$	−0.827678	+	0.477860i	−0.0413323	+	0.0238632i	−0.520524	−	0.853847i	$-0.674263\pi$
$401$	−0.827678	+	0.477860i	−0.0413323	+	0.0238632i	0.479191	+	0.877710i	$0.340930\pi$
$402$	65.4782			3.26575
$403$	1.18468	−	3.40537i	0.0590133	−	0.169633i
$404$	15.2464			0.758535
$405$	−12.3773	+	7.14605i	−0.615034	+	0.355090i
$406$	5.22403	+	9.04829i	0.259264	+	0.449059i
$407$	1.22196	−	2.11650i	0.0605703	−	0.104911i
$408$			1.01003i			0.0500037i
$409$	32.6570	+	18.8545i	1.61479	+	0.932297i	0.988240	+	0.152912i	$0.0488650\pi$
$409$	32.6570	+	18.8545i	1.61479	+	0.932297i	0.626545	+	0.779385i	$0.284468\pi$
$410$	−33.2335	−	19.1874i	−1.64129	−	0.947597i
$411$		−	56.0766i		−	2.76606i
$412$	15.5570	−	26.9455i	0.766439	−	1.32751i
$413$	1.85244	+	3.20853i	0.0911528	+	0.157881i
$414$	21.6532	−	12.5015i	1.06420	−	0.614415i
$415$	−29.2436			−1.43551
$416$	18.2403	+	21.1182i	0.894302	+	1.03541i
$417$	−2.35057			−0.115108
$418$	−4.96524	+	2.86668i	−0.242858	+	0.140214i
$419$	7.21078	+	12.4894i	0.352269	+	0.610149i	0.986647	−	0.162875i	$-0.0520767\pi$
$419$	7.21078	+	12.4894i	0.352269	+	0.610149i	−0.634377	+	0.773024i	$0.718743\pi$
$420$	5.45234	−	9.44372i	0.266047	−	0.460807i
$421$			18.6306i			0.907998i	0.891002	+	0.453999i	$0.150003\pi$
$421$			18.6306i			0.907998i	−0.891002	+	0.453999i	$0.849997\pi$
$422$	22.7359	+	13.1266i	1.10677	+	0.638993i
$423$	−4.44693	−	2.56744i	−0.216217	−	0.124833i
$424$		−	0.777651i		−	0.0377661i
$425$	−0.617474	+	1.06950i	−0.0299519	+	0.0518782i
$426$	−39.1950	−	67.8876i	−1.89900	−	3.28917i
$427$	−3.77278	+	2.17821i	−0.182578	+	0.105411i
$428$	−35.1498			−1.69903
$429$	5.49626	+	6.36346i	0.265362	+	0.307231i
$430$	−27.0990			−1.30683
$431$	−29.9366	+	17.2839i	−1.44200	+	0.832537i	−0.997983	−	0.0634840i	$-0.979779\pi$
$431$	−29.9366	+	17.2839i	−1.44200	+	0.832537i	−0.444013	+	0.896021i	$0.646445\pi$
$432$	−3.29896	−	5.71397i	−0.158721	−	0.274913i
$433$	17.2491	−	29.8763i	0.828940	−	1.43577i	−0.0699313	−	0.997552i	$-0.522278\pi$
$433$	17.2491	−	29.8763i	0.828940	−	1.43577i	0.898871	−	0.438214i	$-0.144389\pi$
$434$			1.08880i			0.0522642i
$435$	−67.9630	−	39.2385i	−3.25858	−	1.88134i
$436$	−25.8407	−	14.9191i	−1.23754	−	0.714496i
$437$		−	8.66053i		−	0.414289i
$438$	47.4709	−	82.2221i	2.26825	−	3.92872i
$439$	0.391539	+	0.678166i	0.0186871	+	0.0323671i	0.875218	−	0.483729i	$-0.160718\pi$
$439$	0.391539	+	0.678166i	0.0186871	+	0.0323671i	−0.856531	+	0.516096i	$0.827385\pi$
$440$	3.20546	−	1.85067i	0.152814	−	0.0882273i
$441$	27.4474			1.30702
$442$	0.706319	−	2.03031i	0.0335961	−	0.0965720i
$443$	−11.0785			−0.526355			−0.263177	−	0.964747i	$-0.584770\pi$
$443$	−11.0785			−0.526355			−0.263177	+	0.964747i	$0.584770\pi$
$444$	−16.9202	+	9.76889i	−0.802998	+	0.463611i
$445$	1.80567	+	3.12752i	0.0855972	+	0.148259i
$446$	−29.1010	+	50.4043i	−1.37797	+	2.38671i
$447$			49.3380i			2.33361i
$448$	−5.26619	−	3.04044i	−0.248804	−	0.143647i
$449$	−32.4390	−	18.7287i	−1.53089	−	0.883862i	−0.999321	−	0.0368485i	$-0.988268\pi$
$449$	−32.4390	−	18.7287i	−1.53089	−	0.883862i	−0.531572	−	0.847013i	$-0.678399\pi$
$450$			39.0897i			1.84271i
$451$	−2.54086	+	4.40090i	−0.119645	+	0.207230i
$452$	21.2771	+	36.8529i	1.00079	+	1.73342i
$453$	39.9779	−	23.0813i	1.87833	−	1.08445i
$454$	−9.41021			−0.441643
$455$	−4.24353	+	3.66523i	−0.198940	+	0.171828i
$456$	11.0738			0.518580
$457$	5.25467	−	3.03379i	0.245803	−	0.141914i	−0.372038	−	0.928218i	$-0.621341\pi$
$457$	5.25467	−	3.03379i	0.245803	−	0.141914i	0.617841	+	0.786303i	$0.288008\pi$
$458$	9.56021	+	16.5588i	0.446719	+	0.773740i
$459$	−0.393735	+	0.681969i	−0.0183780	+	0.0318316i
$460$			23.1416i			1.07898i
$461$	15.6254	+	9.02131i	0.727746	+	0.420164i	0.817597	−	0.575791i	$-0.195306\pi$
$461$	15.6254	+	9.02131i	0.727746	+	0.420164i	−0.0898510	+	0.995955i	$0.528639\pi$
$462$	−2.19900	−	1.26959i	−0.102307	−	0.0590669i
$463$		−	7.58105i		−	0.352321i	−0.984361	−	0.176161i	$-0.943632\pi$
$463$		−	7.58105i		−	0.352321i	0.984361	−	0.176161i	$-0.0563678\pi$
$464$	−11.1302	+	19.2781i	−0.516706	+	0.894962i
$465$	−4.08908	−	7.08249i	−0.189626	−	0.328443i
$466$	22.4263	−	12.9478i	1.03888	−	0.599797i
$467$	29.7324			1.37585			0.687926	−	0.725781i	$-0.258521\pi$
$467$	29.7324			1.37585			0.687926	+	0.725781i	$0.258521\pi$
$468$	−7.26277	−	38.0084i	−0.335722	−	1.75694i
$469$	5.78223			0.266999
$470$	7.23733	−	4.17848i	0.333833	−	0.192739i
$471$	−29.6139	−	51.2928i	−1.36454	−	2.36345i
$472$	5.02666	−	8.70643i	0.231371	−	0.400746i
$473$			3.58854i			0.165001i
$474$	−31.1130	−	17.9631i	−1.42907	−	0.825073i
$475$	11.7259	+	6.76993i	0.538020	+	0.310626i
$476$			0.369173i			0.0169210i
$477$	1.15334	−	1.99764i	0.0528078	−	0.0914659i
$478$	3.73037	+	6.46119i	0.170623	+	0.295528i
$479$	9.20847	−	5.31651i	0.420746	−	0.242918i	−0.274651	−	0.961544i	$-0.588562\pi$
$479$	9.20847	−	5.31651i	0.420746	−	0.242918i	0.695396	+	0.718627i	$0.255229\pi$
$480$	63.2944			2.88898
$481$	9.86793	−	1.88560i	0.449939	−	0.0859759i
$482$	−18.8577			−0.858946
$483$	3.32170	−	1.91779i	0.151143	−	0.0872622i
$484$	13.4899	+	23.3652i	0.613177	+	1.06205i
$485$	−7.16059	+	12.4025i	−0.325146	+	0.563169i
$486$		−	44.9793i		−	2.04030i
$487$	−4.32057	−	2.49448i	−0.195784	−	0.113036i	0.398904	−	0.916993i	$-0.369391\pi$
$487$	−4.32057	−	2.49448i	−0.195784	−	0.113036i	−0.594687	+	0.803957i	$0.702724\pi$
$488$	10.2375	+	5.91065i	0.463432	+	0.267563i
$489$			44.3923i			2.00749i
$490$	−22.3352	+	38.6857i	−1.00900	+	1.74764i
$491$	−15.7841	−	27.3388i	−0.712326	−	1.23378i	−0.963982	−	0.265968i	$-0.914309\pi$
$491$	−15.7841	−	27.3388i	−0.712326	−	1.23378i	0.251656	−	0.967817i	$-0.419025\pi$
$492$	35.1827	−	20.3128i	1.58616	−	0.915770i
$493$	2.65681			0.119657
$494$	−22.2601	−	7.74402i	−1.00153	−	0.348420i
$495$	10.9790			0.493469
$496$	−2.00899	+	1.15989i	−0.0902061	+	0.0520805i
$497$	−3.46122	−	5.99501i	−0.155257	−	0.268913i
$498$	27.2190	−	47.1447i	1.21971	−	2.11260i
$499$		−	18.3486i		−	0.821398i	−0.911771	−	0.410699i	$-0.865285\pi$
$499$		−	18.3486i		−	0.821398i	0.911771	−	0.410699i	$-0.134715\pi$
$500$	3.79034	+	2.18835i	0.169509	+	0.0978660i
$501$	8.86413	+	5.11771i	0.396020	+	0.228642i
$502$		−	20.0811i		−	0.896265i
$503$	20.6767	−	35.8132i	0.921930	−	1.59683i	0.125505	−	0.992093i	$-0.459945\pi$
$503$	20.6767	−	35.8132i	0.921930	−	1.59683i	0.796425	−	0.604737i	$-0.206722\pi$
$504$	1.41161	+	2.44498i	0.0628782	+	0.108908i
$505$	−15.3999	+	8.89116i	−0.685288	+	0.395651i
$506$	5.38860			0.239552
$507$	−5.02811	+	34.1979i	−0.223306	+	1.51878i
$508$	33.7176			1.49598
$509$	−9.13236	+	5.27257i	−0.404785	+	0.233702i	−0.688546	−	0.725192i	$-0.741751\pi$
$509$	−9.13236	+	5.27257i	−0.404785	+	0.233702i	0.283762	+	0.958895i	$0.408417\pi$
$510$	−2.43794	−	4.22264i	−0.107954	−	0.186982i
$511$	4.19205	−	7.26085i	0.185445	−	0.321201i
$512$		−	24.3193i		−	1.07477i
$513$	7.47705	+	4.31688i	0.330120	+	0.190595i
$514$	−45.1286	−	26.0550i	−1.99054	−	1.14924i
$515$			36.2893i			1.59910i
$516$	14.3442	−	24.8449i	0.631468	−	1.09373i
$517$	−0.553329	−	0.958393i	−0.0243354	−	0.0421501i
$518$	−2.62737	+	1.51691i	−0.115440	+	0.0666494i
$519$	−2.38841			−0.104840
$520$	14.3707	+	4.99938i	0.630197	+	0.219237i
$521$	16.3206			0.715020			0.357510	−	0.933909i	$-0.383626\pi$
$521$	16.3206			0.715020			0.357510	+	0.933909i	$0.383626\pi$
$522$	72.8290	−	42.0478i	3.18764	−	1.84038i
$523$	−0.677656	−	1.17373i	−0.0296318	−	0.0513238i	0.850829	−	0.525442i	$-0.176100\pi$
$523$	−0.677656	−	1.17373i	−0.0296318	−	0.0513238i	−0.880461	+	0.474119i	$0.842767\pi$
$524$	−4.20632	+	7.28555i	−0.183754	+	0.318271i
$525$			5.99653i			0.261710i
$526$	2.38610	+	1.37762i	0.104039	+	0.0600670i
$527$	0.239775	+	0.138434i	0.0104448	+	0.00603029i
$528$		−	5.40994i		−	0.235437i
$529$	7.43013	−	12.8694i	0.323049	−	0.559537i
$530$	1.87705	+	3.25115i	0.0815338	+	0.141221i
$531$	25.8252	−	14.9102i	1.12072	−	0.647046i
$532$	4.04759			0.175485
$533$	−20.5187	+	3.92079i	−0.888764	+	0.169828i
$534$	−6.72264			−0.290917
$535$	35.5039	−	20.4982i	1.53497	−	0.886214i
$536$	−7.84513	−	13.5882i	−0.338858	−	0.586919i
$537$	−6.71632	+	11.6330i	−0.289831	+	0.502002i
$538$		−	13.8400i		−	0.596686i
$539$	5.12290	+	2.95771i	0.220659	+	0.127398i
$540$	−19.9793	−	11.5350i	−0.859770	−	0.496389i
$541$			6.37899i			0.274254i	0.990553	+	0.137127i	$0.0437869\pi$
$541$			6.37899i			0.274254i	−0.990553	+	0.137127i	$0.956213\pi$
$542$	−29.8267	+	51.6613i	−1.28116	+	2.21904i
$543$	−12.3631	−	21.4134i	−0.530549	−	0.918939i
$544$	−1.85572	+	1.07140i	−0.0795635	+	0.0459360i
$545$	34.8013			1.49072
$546$	−1.95910	−	10.2526i	−0.0838418	−	0.438771i
$547$	34.0362			1.45528			0.727642	−	0.685957i	$-0.240616\pi$
$547$	34.0362			1.45528			0.727642	+	0.685957i	$0.240616\pi$
$548$	−48.1665	+	27.8089i	−2.05757	+	1.18794i
$549$	17.5323	+	30.3668i	0.748259	+	1.29602i
$550$	−4.21227	+	7.29586i	−0.179612	+	0.311096i
$551$		−	29.1290i		−	1.24094i
$552$	−9.01354	−	5.20397i	−0.383642	−	0.221496i
$553$	−2.74752	−	1.58628i	−0.116836	−	0.0674555i
$554$		−	4.16158i		−	0.176809i
$555$	11.3938	−	19.7346i	0.483638	−	0.837686i
$556$	1.16567	+	2.01900i	0.0494355	+	0.0856247i
$557$	−24.2445	+	13.9975i	−1.02727	+	0.593095i	−0.916202	−	0.400718i	$-0.868761\pi$
$557$	−24.2445	+	13.9975i	−1.02727	+	0.593095i	−0.111069	+	0.993813i	$0.535428\pi$
$558$	8.76369			0.370997
$559$	−11.1640	+	9.64260i	−0.472187	+	0.407838i
$560$	3.60766			0.152451
$561$	−0.559177	+	0.322841i	−0.0236085	+	0.0136304i
$562$	15.3970	+	26.6684i	0.649483	+	1.12494i
$563$	−7.36992	+	12.7651i	−0.310605	+	0.537983i	−0.978493	−	0.206278i	$-0.933865\pi$
$563$	−7.36992	+	12.7651i	−0.310605	+	0.537983i	0.667889	+	0.744261i	$0.267198\pi$
$564$			8.84710i			0.372530i
$565$	−42.9828	−	24.8161i	−1.80830	−	1.04402i
$566$	50.5262	+	29.1713i	2.12377	+	1.22616i
$567$		−	2.34945i		−	0.0986675i
$568$	−9.39212	+	16.2676i	−0.394085	+	0.682575i
$569$	3.95489	+	6.85007i	0.165798	+	0.287170i	0.936938	−	0.349495i	$-0.113647\pi$
$569$	3.95489	+	6.85007i	0.165798	+	0.287170i	−0.771141	+	0.636665i	$0.780313\pi$
$570$	−46.2967	+	26.7294i	−1.93916	+	1.11957i
$571$	−28.8997			−1.20942			−0.604708	−	0.796447i	$-0.706710\pi$
$571$	−28.8997			−1.20942			−0.604708	+	0.796447i	$0.706710\pi$
$572$	2.74019	−	7.87666i	0.114573	−	0.329340i
$573$	26.8340			1.12101
$574$	5.46318	−	3.15417i	0.228029	−	0.131652i
$575$	−6.36284	−	11.0208i	−0.265349	−	0.459597i
$576$	−24.4722	+	42.3872i	−1.01968	+	1.76613i
$577$		−	9.36758i		−	0.389977i	−0.980805	−	0.194989i	$-0.937533\pi$
$577$		−	9.36758i		−	0.389977i	0.980805	−	0.194989i	$-0.0624670\pi$
$578$	−31.5604	−	18.2214i	−1.31274	−	0.757909i
$579$	19.0859	+	11.0193i	0.793184	+	0.457945i
$580$			77.8349i			3.23192i
$581$	2.40365	−	4.16324i	0.0997201	−	0.172720i
$582$	−13.3297	−	23.0877i	−0.552532	−	0.957014i
$583$	0.430528	−	0.248566i	0.0178307	−	0.0102945i
$584$	−22.7505			−0.941423
$585$	29.5011	+	34.1558i	1.21972	+	1.41217i
$586$	−39.8678			−1.64692
$587$	−1.87365	+	1.08175i	−0.0773339	+	0.0446487i	−0.538168	−	0.842837i	$-0.680884\pi$
$587$	−1.87365	+	1.08175i	−0.0773339	+	0.0446487i	0.460834	+	0.887486i	$0.347550\pi$
$588$	−23.6452	−	40.9547i	−0.975112	−	1.68894i
$589$	1.51778	−	2.62887i	0.0625391	−	0.108321i
$590$			48.5323i			1.99804i
$591$	−35.3319	−	20.3989i	−1.45336	−	0.839097i
$592$	−5.59782	−	3.23190i	−0.230069	−	0.132830i
$593$			18.1557i			0.745565i	0.927919	+	0.372783i	$0.121596\pi$
$593$			18.1557i			0.745565i	−0.927919	+	0.372783i	$0.878404\pi$
$594$	−2.68597	+	4.65224i	−0.110207	+	0.190884i
$595$	−0.215289	−	0.372892i	−0.00882600	−	0.0152871i
$596$	42.3784	−	24.4672i	1.73589	−	1.00222i
$597$	24.8481			1.01696
$598$	14.4794	+	16.7640i	0.592108	+	0.685532i
$599$	−6.68979			−0.273337			−0.136669	−	0.990617i	$-0.543640\pi$
$599$	−6.68979			−0.273337			−0.136669	+	0.990617i	$0.543640\pi$
$600$	14.0918	−	8.13588i	0.575294	−	0.332146i
$601$	14.3741	+	24.8967i	0.586333	+	1.01556i	0.994708	+	0.102745i	$0.0327625\pi$
$601$	14.3741	+	24.8967i	0.586333	+	1.01556i	−0.408374	+	0.912815i	$0.633904\pi$
$602$	2.22737	−	3.85791i	0.0907807	−	0.157237i
$603$		−	46.5407i		−	1.89528i
$604$	−39.6509	−	22.8924i	−1.61337	−	0.931480i
$605$	−27.2516	−	15.7337i	−1.10793	−	0.639666i
$606$		−	33.1023i		−	1.34469i
$607$	11.8169	−	20.4675i	0.479635	−	0.830752i	−0.520092	−	0.854110i	$-0.674103\pi$
$607$	11.8169	−	20.4675i	0.479635	−	0.830752i	0.999727	+	0.0233583i	$0.00743586\pi$
$608$	11.7468	+	20.3460i	0.476395	+	0.825140i
$609$	11.1723	−	6.45032i	0.452724	−	0.261380i
$610$	−57.0672			−2.31058
$611$	1.49476	−	4.29667i	0.0604713	−	0.173825i
$612$	2.97145			0.120114
$613$	12.2045	−	7.04626i	0.492934	−	0.284596i	−0.232857	−	0.972511i	$-0.574807\pi$
$613$	12.2045	−	7.04626i	0.492934	−	0.284596i	0.725791	+	0.687915i	$0.241474\pi$
$614$	37.2595	+	64.5354i	1.50367	+	2.60444i
$615$	−23.6914	+	41.0347i	−0.955330	+	1.65468i
$616$			0.608455i			0.0245154i
$617$	−7.46721	−	4.31119i	−0.300618	−	0.173562i	0.342102	−	0.939663i	$-0.388861\pi$
$617$	−7.46721	−	4.31119i	−0.300618	−	0.173562i	−0.642721	+	0.766101i	$0.722194\pi$
$618$	−58.5032	−	33.7768i	−2.35334	−	1.35870i
$619$		−	38.8739i		−	1.56247i	−0.624234	−	0.781237i	$-0.714589\pi$
$619$		−	38.8739i		−	1.56247i	0.624234	−	0.781237i	$-0.285411\pi$
$620$	−4.05563	+	7.02455i	−0.162878	+	0.282113i
$621$	−4.05729	−	7.02743i	−0.162813	−	0.282001i
$622$	−47.7445	+	27.5653i	−1.91438	+	1.10527i
$623$	−0.593661			−0.0237845
$624$	16.8304	−	14.5368i	0.673755	−	0.581937i
$625$	−27.4068			−1.09627
$626$	−22.7047	+	13.1086i	−0.907464	+	0.523924i
$627$	3.53960	+	6.13078i	0.141358	+	0.244840i
$628$	−29.3717	+	50.8732i	−1.17206	+	2.03006i
$629$			0.771463i			0.0307602i
$630$	−11.8031	−	6.81454i	−0.470248	−	0.271498i
$631$	24.1961	+	13.9696i	0.963230	+	0.556121i	0.897166	−	0.441694i	$-0.145622\pi$
$631$	24.1961	+	13.9696i	0.963230	+	0.556121i	0.0660646	+	0.997815i	$0.478956\pi$
$632$			8.60884i			0.342441i
$633$	16.2079	−	28.0730i	0.644207	−	1.11580i
$634$	14.3453	+	24.8469i	0.569726	+	0.986795i
$635$	−34.0573	+	19.6630i	−1.35152	+	0.780302i
$636$	−3.97428			−0.157591
$637$	4.56402	+	23.8849i	0.180833	+	0.946356i
$638$	18.1241			0.717541
$639$	−48.2533	+	27.8591i	−1.90887	+	1.10209i
$640$	−16.0235	−	27.7535i	−0.633385	−	1.09705i
$641$	20.6640	−	35.7911i	0.816179	−	1.41366i	−0.0922992	−	0.995731i	$-0.529422\pi$
$641$	20.6640	−	35.7911i	0.816179	−	1.41366i	0.908478	−	0.417932i	$-0.137245\pi$
$642$			76.3160i			3.01195i
$643$	28.9230	+	16.6987i	1.14061	+	0.658533i	0.946582	−	0.322463i	$-0.104511\pi$
$643$	28.9230	+	16.6987i	1.14061	+	0.658533i	0.194030	+	0.980996i	$0.437844\pi$
$644$	−3.29453	−	1.90210i	−0.129823	−	0.0749531i
$645$			33.4602i			1.31749i
$646$	0.904914	−	1.56736i	0.0356034	−	0.0616668i
$647$	−3.85684	−	6.68024i	−0.151628	−	0.262627i	0.780198	−	0.625532i	$-0.215118\pi$
$647$	−3.85684	−	6.68024i	−0.151628	−	0.262627i	−0.931826	+	0.362905i	$0.881785\pi$
$648$	−5.52117	+	3.18765i	−0.216892	+	0.125223i
$649$	6.42682			0.252275
$650$	−34.0161	+	6.49992i	−1.33422	+	0.254948i
$651$	1.34439			0.0526907
$652$	38.1304	−	22.0146i	1.49330	−	0.862158i
$653$	−3.62874	−	6.28516i	−0.142004	−	0.245957i	0.786247	−	0.617912i	$-0.212021\pi$
$653$	−3.62874	−	6.28516i	−0.142004	−	0.245957i	−0.928251	+	0.371954i	$0.878688\pi$
$654$	−32.3918	+	56.1043i	−1.26662	+	2.19385i
$655$		−	9.81192i		−	0.383383i
$656$	11.6397	+	6.72020i	0.454455	+	0.262380i
$657$	−58.4420	−	33.7415i	−2.28004	−	1.31638i
$658$			1.37378i			0.0535555i
$659$	6.26368	−	10.8490i	0.243998	−	0.422617i	−0.717851	−	0.696197i	$-0.754874\pi$
$659$	6.26368	−	10.8490i	0.243998	−	0.422617i	0.961849	+	0.273579i	$0.0882075\pi$
$660$	−9.45810	−	16.3819i	−0.368156	−	0.637665i
$661$	−33.9367	+	19.5933i	−1.31998	+	0.762093i	−0.983726	−	0.179677i	$-0.942495\pi$
$661$	−33.9367	+	19.5933i	−1.31998	+	0.762093i	−0.336258	+	0.941770i	$0.609161\pi$
$662$	−75.7183			−2.94288
$663$	−2.50690	−	0.872119i	−0.0973601	−	0.0338703i
$664$	−13.0447			−0.506234
$665$	−4.08836	+	2.36042i	−0.158540	+	0.0915330i
$666$	12.2095	+	21.1475i	0.473110	+	0.819450i
$667$	−13.6887	+	23.7095i	−0.530028	+	0.918036i
$668$		−	10.1517i		−	0.392781i
$669$	62.2362	+	35.9321i	2.40619	+	1.38922i
$670$	65.5967	+	37.8723i	2.53422	+	1.46313i
$671$			7.55704i			0.291736i
$672$	−5.20241	+	9.01083i	−0.200687	+	0.347600i
$673$	−4.23501	−	7.33526i	−0.163248	−	0.282753i	0.772784	−	0.634669i	$-0.218864\pi$
$673$	−4.23501	−	7.33526i	−0.163248	−	0.282753i	−0.936032	+	0.351916i	$0.885530\pi$
$674$	13.8351	−	7.98769i	0.532907	−	0.307674i
$675$	12.6863			0.488297
$676$	31.8675	−	12.6402i	1.22567	−	0.486162i
$677$	−32.3259			−1.24239			−0.621193	−	0.783658i	$-0.713352\pi$
$677$	−32.3259			−1.24239			−0.621193	+	0.783658i	$0.713352\pi$
$678$	80.0138	−	46.1960i	3.07291	−	1.77415i
$679$	−1.17711	−	2.03882i	−0.0451734	−	0.0782427i
$680$	−0.584194	+	1.01185i	−0.0224028	+	0.0388028i
$681$			11.6192i			0.445247i
$682$	1.63569	+	0.944366i	0.0626338	+	0.0361617i
$683$	−23.1781	−	13.3819i	−0.886884	−	0.512043i	−0.0139621	−	0.999903i	$-0.504444\pi$
$683$	−23.1781	−	13.3819i	−0.886884	−	0.512043i	−0.872922	+	0.487860i	$0.837778\pi$
$684$		−	32.5787i		−	1.24568i
$685$	32.4345	−	56.1781i	1.23926	−	2.14646i
$686$	−7.48244	−	12.9600i	−0.285681	−	0.494814i
$687$	20.4458	−	11.8044i	0.780055	−	0.450365i
$688$	9.49115			0.361847
$689$	1.93014	+	0.671472i	0.0735326	+	0.0255810i
$690$	50.2442			1.91276
$691$	19.1059	−	11.0308i	0.726823	−	0.419631i	−0.0904358	−	0.995902i	$-0.528826\pi$
$691$	19.1059	−	11.0308i	0.726823	−	0.419631i	0.817259	+	0.576271i	$0.195493\pi$
$692$	1.18444	+	2.05150i	0.0450255	+	0.0779864i
$693$	−0.902405	+	1.56301i	−0.0342795	+	0.0593739i
$694$		−	10.4983i		−	0.398511i
$695$	−2.35483	−	1.35956i	−0.0893236	−	0.0515710i
$696$	−30.3163	−	17.5031i	−1.14914	−	0.663455i
$697$		−	1.60413i		−	0.0607607i
$698$	−1.20353	+	2.08458i	−0.0455544	+	0.0789025i
$699$	−15.9872	−	27.6906i	−0.604691	−	1.04736i
$700$	5.15066	−	2.97374i	0.194677	−	0.112397i
$701$	21.3036			0.804624			0.402312	−	0.915503i	$-0.368207\pi$
$701$	21.3036			0.804624			0.402312	+	0.915503i	$0.368207\pi$
$702$	−21.6905	+	4.14470i	−0.818656	+	0.156432i
$703$	8.45826			0.319009
$704$	−9.13520	+	5.27421i	−0.344296	+	0.198779i
$705$	−5.15933	−	8.93622i	−0.194312	−	0.336558i
$706$	3.09985	−	5.36911i	0.116665	−	0.202069i
$707$		−	2.92319i		−	0.109938i
$708$	−44.4954	−	25.6894i	−1.67224	−	0.965467i
$709$	44.8571	+	25.8983i	1.68464	+	0.972630i	0.958502	+	0.285084i	$0.0920216\pi$
$709$	44.8571	+	25.8983i	1.68464	+	0.972630i	0.726141	+	0.687545i	$0.241312\pi$
$710$		−	90.6807i		−	3.40319i
$711$	−12.7679	+	22.1146i	−0.478832	+	0.829361i
$712$	0.805459	+	1.39510i	0.0301858	+	0.0522834i
$713$	−2.47079	+	1.42651i	−0.0925318	+	0.0534233i
$714$	0.801536			0.0299967
$715$	1.82561	+	9.55399i	0.0682739	+	0.357299i
$716$	13.3228			0.497895
$717$	7.97789	−	4.60604i	0.297940	−	0.172016i
$718$	10.9730	+	19.0057i	0.409507	+	0.709287i
$719$	8.61498	−	14.9216i	0.321285	−	0.556481i	−0.659469	−	0.751732i	$-0.729219\pi$
$719$	8.61498	−	14.9216i	0.321285	−	0.556481i	0.980753	+	0.195251i	$0.0625520\pi$
$720$		−	29.0378i		−	1.08217i
$721$	−5.16628	−	2.98275i	−0.192402	−	0.111084i
$722$	18.2487	+	10.5359i	0.679148	+	0.392106i
$723$			23.2844i			0.865956i
$724$	−12.2619	+	21.2383i	−0.455711	+	0.789314i
$725$	−21.4009	−	37.0674i	−0.794809	−	1.37665i
$726$	50.7296	−	29.2888i	1.88275	−	1.08701i
$727$	15.9017			0.589760			0.294880	−	0.955534i	$-0.404720\pi$
$727$	15.9017			0.589760			0.294880	+	0.955534i	$0.404720\pi$
$728$	−1.89291	+	1.63495i	−0.0701561	+	0.0605953i
$729$	−41.5978			−1.54066
$730$	95.1137	−	54.9139i	3.52032	−	2.03246i
$731$	−0.566390	−	0.981017i	−0.0209487	−	0.0362842i
$732$	30.2071	−	52.3203i	1.11649	−	1.93381i
$733$		−	4.03659i		−	0.149095i	−0.997217	−	0.0745474i	$-0.976249\pi$
$733$		−	4.03659i		−	0.149095i	0.997217	−	0.0745474i	$-0.0237512\pi$
$734$	62.1457	+	35.8798i	2.29384	+	1.32435i
$735$	47.7668	+	27.5782i	1.76190	+	1.01724i
$736$		−	22.0808i		−	0.813909i
$737$	5.01518	−	8.68655i	0.184737	−	0.319973i
$738$	−25.3877	−	43.9727i	−0.934533	−	1.61866i
$739$	−15.6679	+	9.04586i	−0.576352	+	0.332757i	−0.759682	−	0.650294i	$-0.774646\pi$
$739$	−15.6679	+	9.04586i	−0.576352	+	0.332757i	0.183330	+	0.983051i	$0.441312\pi$
$740$	−22.6011			−0.830834
$741$	−9.56184	+	27.4855i	−0.351263	+	1.00970i
$742$	−0.617128			−0.0226555
$743$	−6.15415	+	3.55310i	−0.225774	+	0.130351i	−0.608621	−	0.793461i	$-0.708277\pi$
$743$	−6.15415	+	3.55310i	−0.225774	+	0.130351i	0.382847	+	0.923812i	$0.374944\pi$
$744$	−1.82402	−	3.15929i	−0.0668718	−	0.115825i
$745$	−28.5369	+	49.4273i	−1.04551	+	1.81088i
$746$		−	17.3360i		−	0.634715i
$747$	−33.5096	−	19.3468i	−1.22605	−	0.707861i
$748$	0.554603	+	0.320200i	0.0202783	+	0.0117077i
$749$			6.73930i			0.246249i
$750$	4.75127	−	8.22944i	0.173492	−	0.300497i
$751$	15.2058	+	26.3373i	0.554869	+	0.961061i	0.997914	+	0.0645613i	$0.0205648\pi$
$751$	15.2058	+	26.3373i	0.554869	+	0.961061i	−0.443045	+	0.896499i	$0.646102\pi$
$752$	−2.53481	+	1.46347i	−0.0924349	+	0.0533673i
$753$	−24.7950			−0.903579
$754$	48.7004	+	56.3844i	1.77357	+	2.05340i
$755$	53.4004			1.94344
$756$	3.28434	−	1.89622i	0.119450	−	0.0689647i
$757$	−1.68386	−	2.91652i	−0.0612008	−	0.106003i	0.833802	−	0.552064i	$-0.186160\pi$
$757$	−1.68386	−	2.91652i	−0.0612008	−	0.106003i	−0.895002	+	0.446061i	$0.852826\pi$
$758$	4.53706	−	7.85842i	0.164794	−	0.285431i
$759$		−	6.65351i		−	0.241507i
$760$	11.0939	+	6.40506i	0.402418	+	0.232336i
$761$	−31.3673	−	18.1099i	−1.13706	−	0.656483i	−0.191361	−	0.981520i	$-0.561290\pi$
$761$	−31.3673	−	18.1099i	−1.13706	−	0.656483i	−0.945701	+	0.325037i	$0.894623\pi$
$762$		−	73.2065i		−	2.65199i
$763$	−2.86045	+	4.95444i	−0.103555	+	0.179363i
$764$	−13.3072	−	23.0488i	−0.481439	−	0.833877i
$765$	−3.00138	+	1.73285i	−0.108515	+	0.0626512i
$766$	−62.9676			−2.27511
$767$	17.2692	+	19.9939i	0.623555	+	0.721940i
$768$	−4.29814			−0.155096
$769$	−41.7301	+	24.0929i	−1.50482	+	0.868811i	−0.504840	+	0.863213i	$0.668448\pi$
$769$	−41.7301	+	24.0929i	−1.50482	+	0.868811i	−0.999984	+	0.00559773i	$0.998218\pi$
$770$	−1.46866	−	2.54379i	−0.0529267	−	0.0916717i
$771$	−32.1712	+	55.7221i	−1.15862	+	2.00678i
$772$		−	21.8582i		−	0.786696i
$773$	12.0880	+	6.97900i	0.434775	+	0.251017i	0.701379	−	0.712789i	$-0.252568\pi$
$773$	12.0880	+	6.97900i	0.434775	+	0.251017i	−0.266604	+	0.963806i	$0.585902\pi$
$774$	−31.0520	−	17.9279i	−1.11614	−	0.644405i
$775$		−	4.46042i		−	0.160223i
$776$	−3.19413	+	5.53240i	−0.114663	+	0.198602i
$777$	1.87299	+	3.24412i	0.0671933	+	0.116382i
$778$	−14.8157	+	8.55382i	−0.531167	+	0.306669i
$779$	−17.5875			−0.630138
$780$	25.5500	−	73.4433i	0.914836	−	2.62969i
$781$	−12.0083			−0.429689
$782$	−1.47311	+	0.850499i	−0.0526782	+	0.0304138i
$783$	−13.6464	−	23.6362i	−0.487682	−	0.844689i
$784$	7.82269	−	13.5493i	0.279382	−	0.483904i
$785$		−	68.5142i		−	2.44538i
$786$	15.8181	+	9.13260i	0.564214	+	0.325749i
$787$	−1.92849	−	1.11341i	−0.0687432	−	0.0396889i	0.465234	−	0.885187i	$-0.345970\pi$
$787$	−1.92849	−	1.11341i	−0.0687432	−	0.0396889i	−0.533978	+	0.845499i	$0.679303\pi$
$788$			40.4640i			1.44147i
$789$	1.70100	−	2.94622i	0.0605571	−	0.104888i
$790$	−20.7795	−	35.9912i	−0.739303	−	1.28051i
$791$	7.06584	−	4.07946i	0.251232	−	0.145049i
$792$	4.89741			0.174022
$793$	−23.5101	+	20.3062i	−0.834868	+	0.721093i
$794$	−25.3613			−0.900038
$795$	4.01432	−	2.31767i	0.142373	−	0.0821992i
$796$	−12.3224	−	21.3430i	−0.436755	−	0.756483i
$797$	19.7497	−	34.2075i	0.699571	−	1.21169i	−0.269044	−	0.963128i	$-0.586708\pi$
$797$	19.7497	−	34.2075i	0.699571	−	1.21169i	0.968615	−	0.248565i	$-0.0799590\pi$
$798$		−	8.78797i		−	0.311091i
$799$	0.302532	+	0.174667i	0.0107028	+	0.00617928i
$800$	29.8962	+	17.2606i	1.05699	+	0.610253i
$801$			4.77833i			0.168834i
$802$	1.02902	−	1.78232i	0.0363361	−	0.0629360i
$803$	−7.27190	−	12.5953i	−0.256620	−	0.444478i
$804$	−69.4441	+	40.0936i	−2.44910	+	1.41399i
$805$	4.43695			0.156382
$806$	1.45724	+	7.62622i	0.0513293	+	0.268622i
$807$	−17.0888			−0.601556
$808$	−6.86946	+	3.96609i	−0.241667	+	0.139526i
$809$	−4.46120	−	7.72702i	−0.156847	−	0.271668i	0.776883	−	0.629645i	$-0.216800\pi$
$809$	−4.46120	−	7.72702i	−0.156847	−	0.271668i	−0.933730	+	0.357978i	$0.883466\pi$
$810$	15.3883	−	26.6534i	0.540691	−	0.936504i
$811$		−	29.3818i		−	1.03174i	−0.856668	−	0.515868i	$-0.827470\pi$
$811$		−	29.3818i		−	1.03174i	0.856668	−	0.515868i	$-0.172530\pi$
$812$	−11.0809	−	6.39755i	−0.388863	−	0.224510i
$813$	63.7882	+	36.8282i	2.23715	+	1.29162i
$814$			5.26274i			0.184459i
$815$	−25.6763	+	44.4727i	−0.899402	+	1.55781i
$816$	0.853866	+	1.47894i	0.0298913	+	0.0517733i
$817$	−10.7558	+	6.20986i	−0.376297	+	0.217255i
$818$	−81.2028			−2.83919
$819$	−7.28736	+	1.39250i	−0.254641	+	0.0486577i
$820$	46.9952			1.64114
$821$	19.2889	−	11.1365i	0.673188	−	0.388665i	−0.124095	−	0.992270i	$-0.539603\pi$
$821$	19.2889	−	11.1365i	0.673188	−	0.388665i	0.797284	+	0.603605i	$0.206270\pi$
$822$	60.3777	+	104.577i	2.10592	+	3.64755i
$823$	−11.3567	+	19.6703i	−0.395868	+	0.685664i	−0.993212	−	0.116322i	$-0.962890\pi$
$823$	−11.3567	+	19.6703i	−0.395868	+	0.685664i	0.597343	+	0.801986i	$0.296223\pi$
$824$			16.1876i			0.563921i
$825$	9.00849	+	5.20105i	0.313635	+	0.181077i
$826$	−6.90925	−	3.98906i	−0.240403	−	0.138797i
$827$			6.03594i			0.209890i	0.994478	+	0.104945i	$0.0334667\pi$
$827$			6.03594i			0.209890i	−0.994478	+	0.104945i	$0.966533\pi$
$828$	−15.3098	+	26.5174i	−0.532053	+	0.921543i
$829$	−6.93144	−	12.0056i	−0.240739	−	0.416972i	0.720186	−	0.693781i	$-0.244056\pi$
$829$	−6.93144	−	12.0056i	−0.240739	−	0.416972i	−0.960925	+	0.276809i	$0.910723\pi$
$830$	54.5365	−	31.4867i	1.89299	−	1.09292i
$831$	−5.13847			−0.178251
$832$	−40.9549	−	14.2477i	−1.41986	−	0.493950i
$833$	−1.86730			−0.0646980
$834$	4.38358	−	2.53086i	0.151791	−	0.0876366i
$835$	5.92012	+	10.2539i	0.204874	+	0.354852i
$836$	3.51065	−	6.08062i	0.121418	−	0.210303i
$837$		−	2.84420i		−	0.0983101i
$838$	−26.8948	−	15.5277i	−0.929064	−	0.536395i
$839$	22.0425	+	12.7262i	0.760990	+	0.439358i	0.829651	−	0.558282i	$-0.188539\pi$
$839$	22.0425	+	12.7262i	0.760990	+	0.439358i	−0.0686610	+	0.997640i	$0.521873\pi$
$840$			5.67334i			0.195749i
$841$	−31.5408	+	54.6303i	−1.08761	+	1.88380i
$842$	−20.0595	−	34.7441i	−0.691297	−	1.19736i
$843$	32.9285	−	19.0113i	1.13412	−	0.654783i
$844$	−32.1507			−1.10667
$845$	−24.8171	+	31.3516i	−0.853735	+	1.07853i
$846$	11.0574			0.380163
$847$	4.47982	−	2.58643i	0.153928	−	0.0888706i
$848$	−0.657419	−	1.13868i	−0.0225758	−	0.0391025i
$849$	36.0189	−	62.3866i	1.23617	−	2.14110i
$850$		−	2.65934i		−	0.0912146i
$851$	−6.88459	−	3.97482i	−0.236001	−	0.136255i
$852$	83.1378	+	47.9996i	2.84826	+	1.64444i
$853$			47.0365i			1.61050i	0.592935	+	0.805250i	$0.297969\pi$
$853$			47.0365i			1.61050i	−0.592935	+	0.805250i	$0.702031\pi$
$854$	4.69057	−	8.12431i	0.160508	−	0.278008i
$855$	18.9988	+	32.9069i	0.649745	+	1.12539i
$856$	15.8373	−	9.14364i	0.541306	−	0.312523i
$857$	6.55772			0.224007			0.112004	−	0.993708i	$-0.464273\pi$
$857$	6.55772			0.224007			0.112004	+	0.993708i	$0.464273\pi$
$858$	−17.1015	−	5.94940i	−0.583836	−	0.203109i
$859$	13.2065			0.450598			0.225299	−	0.974290i	$-0.427664\pi$
$859$	13.2065			0.450598			0.225299	+	0.974290i	$0.427664\pi$
$860$	28.7403	−	16.5932i	0.980036	−	0.565824i
$861$	−3.89458	−	6.74560i	−0.132727	−	0.229890i
$862$	37.2192	−	64.4655i	1.26769	−	2.19570i
$863$			42.1990i			1.43647i	0.695800	+	0.718235i	$0.255050\pi$
$863$			42.1990i			1.43647i	−0.695800	+	0.718235i	$0.744950\pi$
$864$	19.0634	+	11.0063i	0.648551	+	0.374441i
$865$	−2.39273	−	1.38145i	−0.0813554	−	0.0469705i
$866$			74.2885i			2.52443i
$867$	−22.4987	+	38.9688i	−0.764094	+	1.32345i
$868$	−0.666695	−	1.15475i	−0.0226291	−	0.0391948i
$869$	−4.76609	+	2.75170i	−0.161678	+	0.0933451i
$870$	168.992			5.72938
$871$	40.5000	−	7.73889i	1.37229	−	0.262222i
$872$	15.5238			0.525703
$873$	−16.4103	+	9.47449i	−0.555404	+	0.320663i
$874$	9.32480	+	16.1510i	0.315416	+	0.546316i
$875$	0.419574	−	0.726723i	0.0141842	−	0.0245677i
$876$			116.269i			3.92838i
$877$	9.60917	+	5.54786i	0.324479	+	0.187338i	0.653387	−	0.757024i	$-0.273347\pi$
$877$	9.60917	+	5.54786i	0.324479	+	0.187338i	−0.328908	+	0.944362i	$0.606681\pi$
$878$	−1.46036	−	0.843141i	−0.0492849	−	0.0284546i
$879$			49.2263i			1.66036i
$880$	3.12908	−	5.41973i	0.105481	−	0.182699i
$881$	−8.34384	−	14.4520i	−0.281111	−	0.486899i	0.690548	−	0.723287i	$-0.257370\pi$
$881$	−8.34384	−	14.4520i	−0.281111	−	0.486899i	−0.971659	+	0.236388i	$0.924036\pi$
$882$	−51.1868	+	29.5527i	−1.72355	+	0.995091i
$883$	−37.5635			−1.26411			−0.632055	−	0.774923i	$-0.717788\pi$
$883$	−37.5635			−1.26411			−0.632055	+	0.774923i	$0.717788\pi$
$884$	0.494099	+	2.58577i	0.0166183	+	0.0869690i
$885$	59.9248			2.01435
$886$	20.6603	−	11.9282i	0.694096	−	0.400736i
$887$	−2.97381	−	5.15079i	−0.0998507	−	0.172947i	0.811772	−	0.583974i	$-0.198503\pi$
$887$	−2.97381	−	5.15079i	−0.0998507	−	0.172947i	−0.911623	+	0.411028i	$0.865170\pi$
$888$	5.08243	−	8.80302i	0.170555	−	0.295410i
$889$		−	6.46470i		−	0.216819i
$890$	−6.73481	−	3.88834i	−0.225751	−	0.130338i
$891$	−3.52953	−	2.03778i	−0.118244	−	0.0682681i
$892$		−	71.2763i		−	2.38651i
$893$	1.91504	−	3.31694i	0.0640842	−	0.110997i
$894$	−53.1223	−	92.0105i	−1.77668	−	3.07729i
$895$	−13.4570	+	7.76938i	−0.449817	+	0.259702i
$896$	5.26813			0.175996
$897$	20.6992	−	17.8783i	0.691126	−	0.596940i
$898$	80.6608			2.69169
$899$	−8.31031	+	4.79796i	−0.277164	+	0.160021i
$900$	−23.9354	−	41.4573i	−0.797846	−	1.38191i
$901$	−0.0784637	+	0.135903i	−0.00261401	+	0.00452759i
$902$		−	10.9430i		−	0.364362i
$903$	−4.76352	−	2.75022i	−0.158520	−	0.0915216i
$904$	−19.1734	−	11.0697i	−0.637696	−	0.368174i
$905$		−	28.6029i		−	0.950794i
$906$	−49.7032	+	86.0885i	−1.65128	+	2.86010i
$907$	−24.7265	−	42.8276i	−0.821030	−	1.42207i	−0.904916	−	0.425591i	$-0.860066\pi$
$907$	−24.7265	−	42.8276i	−0.821030	−	1.42207i	0.0838855	−	0.996475i	$-0.473267\pi$
$908$	9.98017	−	5.76205i	0.331204	−	0.191220i
$909$	−23.5286			−0.780393
$910$	3.96741	−	11.4043i	0.131518	−	0.378049i
$911$	5.06158			0.167698			0.0838488	−	0.996478i	$-0.473279\pi$
$911$	5.06158			0.167698			0.0838488	+	0.996478i	$0.473279\pi$
$912$	16.2150	−	9.36172i	0.536932	−	0.309998i
$913$	−4.16958	−	7.22192i	−0.137993	−	0.239011i
$914$	−6.53296	+	11.3154i	−0.216091	+	0.374281i
$915$			70.4631i			2.32944i
$916$	−20.2785	−	11.7078i	−0.670021	−	0.386837i
$917$	1.39686	+	0.806479i	0.0461285	+	0.0266323i
$918$		−	1.69574i		−	0.0559677i
$919$	−22.0672	+	38.2215i	−0.727930	+	1.26081i	0.229826	+	0.973232i	$0.426184\pi$
$919$	−22.0672	+	38.2215i	−0.727930	+	1.26081i	−0.957756	+	0.287581i	$0.907149\pi$
$920$	−6.01990	−	10.4268i	−0.198470	−	0.343761i
$921$	79.6844	−	46.0058i	2.62569	−	1.51594i
$922$	−38.8530			−1.27956
$923$	−32.2668	−	37.3579i	−1.06208	−	1.22965i
$924$	3.10959			0.102298
$925$	10.7634	−	6.21423i	0.353897	−	0.204323i
$926$	8.16253	+	14.1379i	0.268237	+	0.464601i
$927$	−24.0080	+	41.5830i	−0.788525	+	1.36576i
$928$		−	74.2671i		−	2.43794i
$929$	−36.5080	−	21.0779i	−1.19779	−	0.691544i	−0.237728	−	0.971332i	$-0.576403\pi$
$929$	−36.5080	−	21.0779i	−1.19779	−	0.691544i	−0.960062	+	0.279787i	$0.909736\pi$
$930$	15.2515	+	8.80543i	0.500115	+	0.288741i
$931$			20.4729i			0.670972i
$932$	−15.8564	+	27.4641i	−0.519394	+	0.899617i
$933$	34.0360	+	58.9520i	1.11429	+	1.93000i
$934$	−55.4480	+	32.0129i	−1.81431	+	1.04749i
$935$	−0.746919			−0.0244269
$936$	13.1596	+	15.2359i	0.430135	+	0.498002i
$937$	−35.8740			−1.17195			−0.585976	−	0.810328i	$-0.699289\pi$
$937$	−35.8740			−1.17195			−0.585976	+	0.810328i	$0.699289\pi$
$938$	−10.7833	+	6.22573i	−0.352087	+	0.203277i
$939$	16.1857	+	28.0344i	0.528200	+	0.914869i
$940$	−5.11712	+	8.86312i	−0.166902	+	0.289083i
$941$		−	30.2324i		−	0.985549i	−0.870157	−	0.492774i	$-0.835983\pi$
$941$		−	30.2324i		−	0.985549i	0.870157	−	0.492774i	$-0.164017\pi$
$942$	110.454	+	63.7707i	3.59879	+	2.07776i
$943$	14.3153	+	8.26496i	0.466172	+	0.269144i
$944$		−	16.9980i		−	0.553237i
$945$	−2.21162	+	3.83063i	−0.0719439	+	0.124611i
$946$	−3.86379	−	6.69227i	−0.125623	−	0.217585i
$947$	15.9701	−	9.22037i	0.518960	−	0.299622i	−0.217549	−	0.976049i	$-0.569806\pi$
$947$	15.9701	−	9.22037i	0.518960	−	0.299622i	0.736509	+	0.676428i	$0.236473\pi$
$948$	43.9966			1.42894
$949$	19.6442	−	56.4672i	0.637678	−	1.83300i
$950$	−29.1568			−0.945971
$951$	30.6794	−	17.7128i	0.994847	−	0.574375i
$952$	−0.0960343	−	0.166336i	−0.00311249	−	0.00539099i
$953$	−19.3209	+	33.4647i	−0.625864	+	1.08403i	0.362509	+	0.931980i	$0.381920\pi$
$953$	−19.3209	+	33.4647i	−0.625864	+	1.08403i	−0.988373	+	0.152048i	$0.951413\pi$
$954$			4.96721i			0.160819i
$955$	26.8826	+	15.5207i	0.869900	+	0.502237i
$956$	−7.91262	−	4.56836i	−0.255913	−	0.147751i
$957$		−	22.3786i		−	0.723396i
$958$	−11.4486	+	19.8295i	−0.369887	+	0.640663i
$959$	5.33182	+	9.23499i	0.172174	+	0.298213i
$960$	−85.1781	+	49.1776i	−2.74911	+	1.58720i
$961$	−1.00000			−0.0322581
$962$	−16.3725	+	14.1413i	−0.527870	+	0.455933i
$963$	54.2441			1.74799
$964$	19.9999	−	11.5470i	0.644154	−	0.371902i
$965$	12.7470	+	22.0784i	0.410340	+	0.710730i
$966$	−4.12976	+	7.15296i	−0.132873	+	0.230143i
$967$		−	3.18894i		−	0.102550i	−0.998685	−	0.0512748i	$-0.983672\pi$
$967$		−	3.18894i		−	0.102550i	0.998685	−	0.0512748i	$-0.0163284\pi$
$968$	−12.1561	−	7.01834i	−0.390713	−	0.225578i
$969$	−1.93528	−	1.11733i	−0.0621701	−	0.0358939i
$970$		−	30.8393i		−	0.990189i
$971$	−20.7042	+	35.8608i	−0.664430	+	1.15083i	0.315009	+	0.949089i	$0.397992\pi$
$971$	−20.7042	+	35.8608i	−0.664430	+	1.15083i	−0.979439	+	0.201738i	$0.935341\pi$
$972$	27.5417	+	47.7037i	0.883401	+	1.53010i
$973$	0.387104	−	0.223495i	0.0124100	−	0.00716491i
$974$	10.7432			0.344236
$975$	8.02571	+	42.0010i	0.257028	+	1.34511i
$976$	19.9872			0.639776
$977$	−33.2234	+	19.1815i	−1.06291	+	0.613672i	−0.926236	−	0.376944i	$-0.876975\pi$
$977$	−33.2234	+	19.1815i	−1.06291	+	0.613672i	−0.136675	+	0.990616i	$0.543642\pi$
$978$	−47.7973	−	82.7873i	−1.52839	−	2.64725i
$979$	−0.514908	+	0.891847i	−0.0164565	+	0.0285036i
$980$		−	54.7051i		−	1.74749i
$981$	39.8779	+	23.0235i	1.27320	+	0.735085i
$982$	58.8715	+	33.9895i	1.87866	+	1.08465i
$983$			14.9366i			0.476403i	0.971216	+	0.238202i	$0.0765579\pi$
$983$			14.9366i			0.476403i	−0.971216	+	0.238202i	$0.923442\pi$
$984$	−10.5681	+	18.3044i	−0.336897	+	0.583523i
$985$	−23.5972	−	40.8716i	−0.751870	−	1.30228i
$986$	−4.95468	+	2.86058i	−0.157789	+	0.0910996i
$987$	1.69626			0.0539925
$988$	28.3502	−	5.41726i	0.901940	−	0.172346i
$989$	11.6729			0.371176
$990$	−20.4747	+	11.8211i	−0.650730	+	0.375699i
$991$	−20.4031	−	35.3393i	−0.648127	−	1.12259i	−0.983570	−	0.180528i	$-0.942219\pi$
$991$	−20.4031	−	35.3393i	−0.648127	−	1.12259i	0.335443	−	0.942061i	$-0.391114\pi$
$992$	3.86972	−	6.70255i	0.122864	−	0.212806i
$993$			93.4924i			2.96689i
$994$	12.9097	+	7.45339i	0.409469	+	0.236407i
$995$	24.8930	+	14.3720i	0.789162	+	0.455623i
$996$			66.6668i			2.11242i
$997$	−3.22342	+	5.58312i	−0.102087	+	0.176819i	−0.912544	−	0.408978i	$-0.865885\pi$
$997$	−3.22342	+	5.58312i	−0.102087	+	0.176819i	0.810458	+	0.585797i	$0.199219\pi$
$998$	19.7560	+	34.2184i	0.625365	+	1.08316i
$999$	6.86330	−	3.96253i	0.217145	−	0.125369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.6	✓	68
13.2	odd	12		5239.2.a.q.1.7		34
13.4	even	6	inner	403.2.r.a.342.6	yes	68
13.11	odd	12		5239.2.a.r.1.28		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.6	✓	68	1.1	even	1	trivial
403.2.r.a.342.6	yes	68	13.4	even	6	inner
5239.2.a.q.1.7		34	13.2	odd	12
5239.2.a.r.1.28		34	13.11	odd	12

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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86490 + 1.07670i) q^{2} +(1.32944 + 2.30267i) q^{3} +(1.31857 - 2.28383i) q^{4} +3.07578i q^{5} +(-4.95857 - 2.86283i) q^{6} +(-0.437880 - 0.252810i) q^{7} +1.37202i q^{8} +(-2.03485 + 3.52446i) q^{9} +O(q^{10})\)	\(q+(-1.86490 + 1.07670i) q^{2} +(1.32944 + 2.30267i) q^{3} +(1.31857 - 2.28383i) q^{4} +3.07578i q^{5} +(-4.95857 - 2.86283i) q^{6} +(-0.437880 - 0.252810i) q^{7} +1.37202i q^{8} +(-2.03485 + 3.52446i) q^{9} +(-3.31169 - 5.73602i) q^{10} +(-0.759584 + 0.438546i) q^{11} +7.01186 q^{12} +(-3.40537 - 1.18468i) q^{13} +1.08880 q^{14} +(-7.08249 + 4.08908i) q^{15} +(1.15989 + 2.00899i) q^{16} +(0.138434 - 0.239775i) q^{17} -8.76369i q^{18} +(-2.62887 - 1.51778i) q^{19} +(7.02455 + 4.05563i) q^{20} -1.34439i q^{21} +(0.944366 - 1.63569i) q^{22} +(1.42651 + 2.47079i) q^{23} +(-3.15929 + 1.82402i) q^{24} -4.46042 q^{25} +(7.62622 - 1.45724i) q^{26} -2.84420 q^{27} +(-1.15475 + 0.666695i) q^{28} +(4.79796 + 8.31031i) q^{29} +(8.80543 - 15.2515i) q^{30} +1.00000i q^{31} +(-6.70255 - 3.86972i) q^{32} +(-2.01965 - 1.16605i) q^{33} +0.596209i q^{34} +(0.777588 - 1.34682i) q^{35} +(5.36618 + 9.29449i) q^{36} +(-2.41308 + 1.39319i) q^{37} +6.53678 q^{38} +(-1.79932 - 9.41640i) q^{39} -4.22002 q^{40} +(5.01760 - 2.89691i) q^{41} +(1.44750 + 2.50715i) q^{42} +(2.04570 - 3.54326i) q^{43} +2.31301i q^{44} +(-10.8405 - 6.25874i) q^{45} +(-5.32060 - 3.07185i) q^{46} +1.26173i q^{47} +(-3.08402 + 5.34167i) q^{48} +(-3.37217 - 5.84078i) q^{49} +(8.31823 - 4.80253i) q^{50} +0.736162 q^{51} +(-7.19583 + 6.21519i) q^{52} -0.566795 q^{53} +(5.30416 - 3.06236i) q^{54} +(-1.34887 - 2.33631i) q^{55} +(0.346859 - 0.600778i) q^{56} -8.07122i q^{57} +(-17.8954 - 10.3319i) q^{58} +(-6.34573 - 3.66371i) q^{59} +21.5669i q^{60} +(4.30801 - 7.46169i) q^{61} +(-1.07670 - 1.86490i) q^{62} +(1.78204 - 1.02886i) q^{63} +12.0266 q^{64} +(3.64382 - 10.4742i) q^{65} +5.02193 q^{66} +(-9.90380 + 5.71796i) q^{67} +(-0.365070 - 0.632320i) q^{68} +(-3.79294 + 6.56956i) q^{69} +3.34892i q^{70} +(11.8567 + 6.84549i) q^{71} +(-4.83561 - 2.79184i) q^{72} +16.5818i q^{73} +(3.00011 - 5.19634i) q^{74} +(-5.92988 - 10.2708i) q^{75} +(-6.93270 + 4.00260i) q^{76} +0.443476 q^{77} +(13.4942 + 15.6233i) q^{78} +6.27460 q^{79} +(-6.17920 + 3.56756i) q^{80} +(2.32333 + 4.02413i) q^{81} +(-6.23822 + 10.8049i) q^{82} +9.50772i q^{83} +(-3.07035 - 1.77267i) q^{84} +(0.737495 + 0.425793i) q^{85} +8.81044i q^{86} +(-12.7572 + 22.0962i) q^{87} +(-0.601692 - 1.04216i) q^{88} +(1.01682 - 0.587062i) q^{89} +26.9552 q^{90} +(1.19164 + 1.37966i) q^{91} +7.52382 q^{92} +(-2.30267 + 1.32944i) q^{93} +(-1.35851 - 2.35301i) q^{94} +(4.66836 - 8.08583i) q^{95} -20.5783i q^{96} +(4.03232 + 2.32806i) q^{97} +(12.5775 + 7.26165i) q^{98} -3.56950i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) \) 68 * q + 32 * q^4 - 34 * q^9	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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