LMFDB - Embedded newform 403.2.h.b.222.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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([0, 2]))

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			222.9
Character	$\chi$	$=$	403.222
Dual form			403.2.h.b.118.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.272181 q^{2} +(0.850363 - 1.47287i) q^{3} -1.92592 q^{4} +(1.58639 + 2.74770i) q^{5} +(-0.231453 + 0.400888i) q^{6} +(1.18195 - 2.04720i) q^{7} +1.06856 q^{8} +(0.0537640 + 0.0931220i) q^{9} +O(q^{10})$	\(q-0.272181 q^{2} +(0.850363 - 1.47287i) q^{3} -1.92592 q^{4} +(1.58639 + 2.74770i) q^{5} +(-0.231453 + 0.400888i) q^{6} +(1.18195 - 2.04720i) q^{7} +1.06856 q^{8} +(0.0537640 + 0.0931220i) q^{9} +(-0.431784 - 0.747872i) q^{10} +(1.18016 + 2.04409i) q^{11} +(-1.63773 + 2.83663i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-0.321705 + 0.557209i) q^{14} +5.39602 q^{15} +3.56099 q^{16} +(2.76821 - 4.79469i) q^{17} +(-0.0146335 - 0.0253460i) q^{18} +(-3.29341 + 5.70435i) q^{19} +(-3.05525 - 5.29184i) q^{20} +(-2.01018 - 3.48173i) q^{21} +(-0.321216 - 0.556362i) q^{22} +6.73494 q^{23} +(0.908664 - 1.57385i) q^{24} +(-2.53324 + 4.38770i) q^{25} +(0.136090 + 0.235716i) q^{26} +5.28506 q^{27} +(-2.27634 + 3.94274i) q^{28} +3.62955 q^{29} -1.46869 q^{30} +(-3.67362 - 4.18384i) q^{31} -3.10635 q^{32} +4.01424 q^{33} +(-0.753455 + 1.30502i) q^{34} +7.50013 q^{35} +(-0.103545 - 0.179345i) q^{36} +(2.79917 - 4.84830i) q^{37} +(0.896402 - 1.55261i) q^{38} -1.70073 q^{39} +(1.69515 + 2.93608i) q^{40} +(-3.02769 - 5.24411i) q^{41} +(0.547132 + 0.947661i) q^{42} +(0.343866 - 0.595593i) q^{43} +(-2.27288 - 3.93675i) q^{44} +(-0.170581 + 0.295455i) q^{45} -1.83312 q^{46} -9.64305 q^{47} +(3.02814 - 5.24489i) q^{48} +(0.705976 + 1.22279i) q^{49} +(0.689499 - 1.19425i) q^{50} +(-4.70798 - 8.15445i) q^{51} +(0.962959 + 1.66789i) q^{52} +(-1.25298 - 2.17023i) q^{53} -1.43849 q^{54} +(-3.74436 + 6.48543i) q^{55} +(1.26299 - 2.18756i) q^{56} +(5.60118 + 9.70154i) q^{57} -0.987894 q^{58} +(-5.82305 + 10.0858i) q^{59} -10.3923 q^{60} -5.03387 q^{61} +(0.999890 + 1.13876i) q^{62} +0.254186 q^{63} -6.27650 q^{64} +(1.58639 - 2.74770i) q^{65} -1.09260 q^{66} +(7.51547 + 13.0172i) q^{67} +(-5.33135 + 9.23417i) q^{68} +(5.72715 - 9.91971i) q^{69} -2.04139 q^{70} +(6.77864 + 11.7409i) q^{71} +(0.0574501 + 0.0995064i) q^{72} +(-7.59801 - 13.1601i) q^{73} +(-0.761879 + 1.31961i) q^{74} +(4.30835 + 7.46228i) q^{75} +(6.34283 - 10.9861i) q^{76} +5.57955 q^{77} +0.462905 q^{78} +(-8.81193 + 15.2627i) q^{79} +(5.64911 + 9.78454i) q^{80} +(4.33293 - 7.50485i) q^{81} +(0.824078 + 1.42735i) q^{82} +(0.394589 + 0.683448i) q^{83} +(3.87144 + 6.70553i) q^{84} +17.5658 q^{85} +(-0.0935937 + 0.162109i) q^{86} +(3.08644 - 5.34586i) q^{87} +(1.26107 + 2.18423i) q^{88} -12.7700 q^{89} +(0.0464289 - 0.0804172i) q^{90} -2.36391 q^{91} -12.9709 q^{92} +(-9.28617 + 1.85300i) q^{93} +2.62465 q^{94} -20.8984 q^{95} +(-2.64153 + 4.57526i) q^{96} -2.61661 q^{97} +(-0.192153 - 0.332819i) q^{98} +(-0.126900 + 0.219797i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.272181			−0.192461			−0.0962305	−	0.995359i	$-0.530679\pi$
$2$	−0.272181			−0.192461			−0.0962305	+	0.995359i	$0.530679\pi$
$3$	0.850363	−	1.47287i	0.490958	−	0.850363i	−0.508988	−	0.860773i	$-0.669980\pi$
$3$	0.850363	−	1.47287i	0.490958	−	0.850363i	0.999946	+	0.0104100i	$0.00331367\pi$
$4$	−1.92592			−0.962959
$5$	1.58639	+	2.74770i	0.709453	+	1.22881i	0.965060	+	0.262028i	$0.0843914\pi$
$5$	1.58639	+	2.74770i	0.709453	+	1.22881i	−0.255607	+	0.966781i	$0.582275\pi$
$6$	−0.231453	+	0.400888i	−0.0944901	+	0.163662i
$7$	1.18195	−	2.04720i	0.446736	−	0.773770i	−0.551435	−	0.834218i	$-0.685920\pi$
$7$	1.18195	−	2.04720i	0.446736	−	0.773770i	0.998171	+	0.0604481i	$0.0192530\pi$
$8$	1.06856			0.377793
$9$	0.0537640	+	0.0931220i	0.0179213	+	0.0310407i
$10$	−0.431784	−	0.747872i	−0.136542	−	0.236498i
$11$	1.18016	+	2.04409i	0.355830	+	0.616316i	0.987260	−	0.159117i	$-0.0508648\pi$
$11$	1.18016	+	2.04409i	0.355830	+	0.616316i	−0.631430	+	0.775433i	$0.717531\pi$
$12$	−1.63773	+	2.83663i	−0.472772	+	0.818865i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−0.321705	+	0.557209i	−0.0859792	+	0.148920i
$15$	5.39602			1.39325
$16$	3.56099			0.890248
$17$	2.76821	−	4.79469i	0.671390	−	1.16288i	−0.306120	−	0.951993i	$-0.599031\pi$
$17$	2.76821	−	4.79469i	0.671390	−	1.16288i	0.977510	−	0.210889i	$-0.0676359\pi$
$18$	−0.0146335	−	0.0253460i	−0.00344916	−	0.00597412i
$19$	−3.29341	+	5.70435i	−0.755559	+	1.30867i	0.189537	+	0.981874i	$0.439301\pi$
$19$	−3.29341	+	5.70435i	−0.755559	+	1.30867i	−0.945096	+	0.326793i	$0.894032\pi$
$20$	−3.05525	−	5.29184i	−0.683174	−	1.18329i
$21$	−2.01018	−	3.48173i	−0.438657	−	0.759776i
$22$	−0.321216	−	0.556362i	−0.0684834	−	0.118617i
$23$	6.73494			1.40433			0.702166	−	0.712013i	$-0.252216\pi$
$23$	6.73494			1.40433			0.702166	+	0.712013i	$0.252216\pi$
$24$	0.908664	−	1.57385i	0.185480	−	0.321261i
$25$	−2.53324	+	4.38770i	−0.506648	+	0.877540i
$26$	0.136090	+	0.235716i	0.0266895	+	0.0462276i
$27$	5.28506			1.01711
$28$	−2.27634	+	3.94274i	−0.430188	+	0.745108i
$29$	3.62955			0.673990			0.336995	−	0.941506i	$-0.390589\pi$
$29$	3.62955			0.673990			0.336995	+	0.941506i	$0.390589\pi$
$30$	−1.46869			−0.268145
$31$	−3.67362	−	4.18384i	−0.659802	−	0.751439i
$31$	−3.67362	−	4.18384i	−0.659802	−	0.751439i
$32$	−3.10635			−0.549131
$33$	4.01424			0.698790
$34$	−0.753455	+	1.30502i	−0.129216	+	0.223809i
$35$	7.50013			1.26775
$36$	−0.103545	−	0.179345i	−0.0172575	−	0.0298909i
$37$	2.79917	−	4.84830i	0.460180	−	0.797055i	−0.538789	−	0.842440i	$-0.681118\pi$
$37$	2.79917	−	4.84830i	0.460180	−	0.797055i	0.998970	+	0.0453851i	$0.0144515\pi$
$38$	0.896402	−	1.55261i	0.145416	−	0.251867i
$39$	−1.70073			−0.272334
$40$	1.69515	+	2.93608i	0.268026	+	0.464235i
$41$	−3.02769	−	5.24411i	−0.472845	−	0.818992i	0.526672	−	0.850069i	$-0.323440\pi$
$41$	−3.02769	−	5.24411i	−0.472845	−	0.818992i	−0.999517	+	0.0310769i	$0.990106\pi$
$42$	0.547132	+	0.947661i	0.0844243	+	0.146227i
$43$	0.343866	−	0.595593i	0.0524391	−	0.0908271i	−0.838614	−	0.544726i	$-0.816634\pi$
$43$	0.343866	−	0.595593i	0.0524391	−	0.0908271i	0.891053	+	0.453898i	$0.149967\pi$
$44$	−2.27288	−	3.93675i	−0.342650	−	0.593487i
$45$	−0.170581	+	0.295455i	−0.0254287	+	0.0440438i
$46$	−1.83312			−0.270279
$47$	−9.64305			−1.40658			−0.703292	−	0.710901i	$-0.748287\pi$
$47$	−9.64305			−1.40658			−0.703292	+	0.710901i	$0.748287\pi$
$48$	3.02814	−	5.24489i	0.437074	−	0.757035i
$49$	0.705976	+	1.22279i	0.100854	+	0.174684i
$50$	0.689499	−	1.19425i	0.0975099	−	0.168892i
$51$	−4.70798	−	8.15445i	−0.659248	−	1.14185i
$52$	0.962959	+	1.66789i	0.133538	+	0.231295i
$53$	−1.25298	−	2.17023i	−0.172110	−	0.298103i	0.767047	−	0.641591i	$-0.221725\pi$
$53$	−1.25298	−	2.17023i	−0.172110	−	0.298103i	−0.939157	+	0.343487i	$0.888392\pi$
$54$	−1.43849			−0.195754
$55$	−3.74436	+	6.48543i	−0.504890	+	0.874495i
$56$	1.26299	−	2.18756i	0.168774	−	0.292325i
$57$	5.60118	+	9.70154i	0.741895	+	1.28500i
$58$	−0.987894			−0.129717
$59$	−5.82305	+	10.0858i	−0.758096	+	1.31306i	0.185724	+	0.982602i	$0.440537\pi$
$59$	−5.82305	+	10.0858i	−0.758096	+	1.31306i	−0.943820	+	0.330459i	$0.892796\pi$
$60$	−10.3923			−1.34164
$61$	−5.03387			−0.644521			−0.322260	−	0.946651i	$-0.604443\pi$
$61$	−5.03387			−0.644521			−0.322260	+	0.946651i	$0.604443\pi$
$62$	0.999890	+	1.13876i	0.126986	+	0.144623i
$63$	0.254186			0.0320244
$64$	−6.27650			−0.784562
$65$	1.58639	−	2.74770i	0.196767	−	0.340810i
$66$	−1.09260			−0.134490
$67$	7.51547	+	13.0172i	0.918161	+	1.59030i	0.802207	+	0.597046i	$0.203659\pi$
$67$	7.51547	+	13.0172i	0.918161	+	1.59030i	0.115954	+	0.993255i	$0.463008\pi$
$68$	−5.33135	+	9.23417i	−0.646521	+	1.11981i
$69$	5.72715	−	9.91971i	0.689468	−	1.19419i
$70$	−2.04139			−0.243993
$71$	6.77864	+	11.7409i	0.804476	+	1.39339i	0.916644	+	0.399705i	$0.130887\pi$
$71$	6.77864	+	11.7409i	0.804476	+	1.39339i	−0.112168	+	0.993689i	$0.535779\pi$
$72$	0.0574501	+	0.0995064i	0.00677055	+	0.0117269i
$73$	−7.59801	−	13.1601i	−0.889280	−	1.54028i	−0.840728	−	0.541457i	$-0.817873\pi$
$73$	−7.59801	−	13.1601i	−0.889280	−	1.54028i	−0.0485514	−	0.998821i	$-0.515460\pi$
$74$	−0.761879	+	1.31961i	−0.0885667	+	0.153402i
$75$	4.30835	+	7.46228i	0.497485	+	0.861670i
$76$	6.34283	−	10.9861i	0.727572	−	1.26019i
$77$	5.57955			0.635849
$78$	0.462905			0.0524137
$79$	−8.81193	+	15.2627i	−0.991420	+	1.71719i	−0.382506	+	0.923953i	$0.624939\pi$
$79$	−8.81193	+	15.2627i	−0.991420	+	1.71719i	−0.608914	+	0.793237i	$0.708394\pi$
$80$	5.64911	+	9.78454i	0.631590	+	1.09395i
$81$	4.33293	−	7.50485i	0.481436	−	0.833872i
$82$	0.824078	+	1.42735i	0.0910042	+	0.157624i
$83$	0.394589	+	0.683448i	0.0433118	+	0.0750182i	0.886869	−	0.462022i	$-0.152876\pi$
$83$	0.394589	+	0.683448i	0.0433118	+	0.0750182i	−0.843557	+	0.537040i	$0.819542\pi$
$84$	3.87144	+	6.70553i	0.422409	+	0.731633i
$85$	17.5658			1.90528
$86$	−0.0935937	+	0.162109i	−0.0100925	+	0.0174807i
$87$	3.08644	−	5.34586i	0.330901	−	0.573137i
$88$	1.26107	+	2.18423i	0.134430	+	0.232840i
$89$	−12.7700			−1.35362			−0.676808	−	0.736160i	$-0.736637\pi$
$89$	−12.7700			−1.35362			−0.676808	+	0.736160i	$0.736637\pi$
$90$	0.0464289	−	0.0804172i	0.00489403	−	0.00847671i
$91$	−2.36391			−0.247805
$92$	−12.9709			−1.35231
$93$	−9.28617	+	1.85300i	−0.962931	+	0.192147i
$94$	2.62465			0.270712
$95$	−20.8984			−2.14414
$96$	−2.64153	+	4.57526i	−0.269600	+	0.466961i
$97$	−2.61661			−0.265677			−0.132838	−	0.991138i	$-0.542409\pi$
$97$	−2.61661			−0.265677			−0.132838	+	0.991138i	$0.542409\pi$
$98$	−0.192153	−	0.332819i	−0.0194104	−	0.0336198i
$99$	−0.126900	+	0.219797i	−0.0127539	+	0.0220904i
$100$	4.87881	−	8.45035i	0.487881	−	0.845035i
$101$	−11.2898			−1.12338			−0.561689	−	0.827349i	$-0.689848\pi$
$101$	−11.2898			−1.12338			−0.561689	+	0.827349i	$0.689848\pi$
$102$	1.28142	+	2.21949i	0.126880	+	0.219762i
$103$	−1.40770	−	2.43821i	−0.138705	−	0.240244i	0.788302	−	0.615289i	$-0.210961\pi$
$103$	−1.40770	−	2.43821i	−0.138705	−	0.240244i	−0.927007	+	0.375045i	$0.877627\pi$
$104$	−0.534280	−	0.925400i	−0.0523904	−	0.0907429i
$105$	6.37784	−	11.0467i	0.622413	−	1.07805i
$106$	0.341037	+	0.590694i	0.0331245	+	0.0573733i
$107$	−0.0859323	+	0.148839i	−0.00830739	+	0.0143888i	−0.870149	−	0.492788i	$-0.835978\pi$
$107$	−0.0859323	+	0.148839i	−0.00830739	+	0.0143888i	0.861842	+	0.507177i	$0.169311\pi$
$108$	−10.1786			−0.979435
$109$	5.19146			0.497252			0.248626	−	0.968600i	$-0.420021\pi$
$109$	5.19146			0.497252			0.248626	+	0.968600i	$0.420021\pi$
$110$	1.01914	−	1.76521i	0.0971715	−	0.168306i
$111$	−4.76062	−	8.24563i	−0.451858	−	0.782641i
$112$	4.20893	−	7.29007i	0.397706	−	0.688847i
$113$	−7.54587	−	13.0698i	−0.709855	−	1.22951i	−0.964911	−	0.262579i	$-0.915427\pi$
$113$	−7.54587	−	13.0698i	−0.709855	−	1.22951i	0.255055	−	0.966926i	$-0.417906\pi$
$114$	−1.52454	−	2.64057i	−0.142786	−	0.247312i
$115$	10.6842	+	18.5056i	0.996308	+	1.72566i
$116$	−6.99021			−0.649025
$117$	0.0537640	−	0.0931220i	0.00497049	−	0.00860913i
$118$	1.58492	−	2.74517i	0.145904	−	0.252713i
$119$	−6.54379	−	11.3342i	−0.599869	−	1.03900i
$120$	5.76597			0.526358
$121$	2.71447	−	4.70160i	0.246770	−	0.427418i
$122$	1.37012			0.124045
$123$	−10.2985			−0.928588
$124$	7.07510	+	8.05773i	0.635362	+	0.723605i
$125$	−0.210921			−0.0188653
$126$	−0.0691846			−0.00616345
$127$	10.5872	−	18.3376i	0.939464	−	1.62720i	0.172992	−	0.984923i	$-0.444657\pi$
$127$	10.5872	−	18.3376i	0.939464	−	1.62720i	0.766473	−	0.642277i	$-0.222010\pi$
$128$	7.92105			0.700128
$129$	−0.584822	−	1.01294i	−0.0514907	−	0.0891846i
$130$	−0.431784	+	0.747872i	−0.0378699	+	0.0655927i
$131$	5.14082	−	8.90417i	0.449156	−	0.777961i	−0.549175	−	0.835707i	$-0.685058\pi$
$131$	5.14082	−	8.90417i	0.449156	−	0.777961i	0.998331	+	0.0577463i	$0.0183914\pi$
$132$	−7.73110			−0.672906
$133$	7.78530	+	13.4845i	0.675071	+	1.16926i
$134$	−2.04557	−	3.54303i	−0.176710	−	0.306071i
$135$	8.38414	+	14.5218i	0.721592	+	1.24983i
$136$	2.95800	−	5.12341i	0.253647	−	0.439329i
$137$	−5.68208	−	9.84165i	−0.485453	−	0.840829i	0.514407	−	0.857546i	$-0.328012\pi$
$137$	−5.68208	−	9.84165i	−0.485453	−	0.840829i	−0.999860	+	0.0167169i	$0.994679\pi$
$138$	−1.55882	+	2.69996i	−0.132696	+	0.229836i
$139$	−11.0598			−0.938084			−0.469042	−	0.883176i	$-0.655401\pi$
$139$	−11.0598			−0.938084			−0.469042	+	0.883176i	$0.655401\pi$
$140$	−14.4446			−1.22079
$141$	−8.20010	+	14.2030i	−0.690573	+	1.19611i
$142$	−1.84502	−	3.19566i	−0.154830	−	0.268174i
$143$	1.18016	−	2.04409i	0.0986895	−	0.170935i
$144$	0.191453	+	0.331607i	0.0159544	+	0.0276339i
$145$	5.75786	+	9.97291i	0.478165	+	0.828205i
$146$	2.06803	+	3.58194i	0.171152	+	0.296443i
$147$	2.40134			0.198060
$148$	−5.39096	+	9.33742i	−0.443134	+	0.767531i
$149$	−0.517481	+	0.896304i	−0.0423937	+	0.0734281i	−0.886444	−	0.462836i	$-0.846832\pi$
$149$	−0.517481	+	0.896304i	−0.0423937	+	0.0734281i	0.844050	+	0.536265i	$0.180165\pi$
$150$	−1.17265	−	2.03109i	−0.0957465	−	0.165838i
$151$	−11.1142			−0.904460			−0.452230	−	0.891901i	$-0.649371\pi$
$151$	−11.1142			−0.904460			−0.452230	+	0.891901i	$0.649371\pi$
$152$	−3.51920	+	6.09543i	−0.285445	+	0.494405i
$153$	0.595321			0.0481289
$154$	−1.51865			−0.122376
$155$	5.66815	−	16.7312i	0.455277	−	1.34388i
$156$	3.27546			0.262247
$157$	−4.28248			−0.341779			−0.170890	−	0.985290i	$-0.554664\pi$
$157$	−4.28248			−0.341779			−0.170890	+	0.985290i	$0.554664\pi$
$158$	2.39844	−	4.15422i	0.190810	−	0.330492i
$159$	−4.26196			−0.337995
$160$	−4.92787	−	8.53533i	−0.389583	−	0.674777i
$161$	7.96038	−	13.7878i	0.627366	−	1.08663i
$162$	−1.17934	+	2.04268i	−0.0926577	+	0.160488i
$163$	0.514999			0.0403379			0.0201689	−	0.999797i	$-0.493580\pi$
$163$	0.514999			0.0403379			0.0201689	+	0.999797i	$0.493580\pi$
$164$	5.83107	+	10.0997i	0.455330	+	0.788655i
$165$	6.36814	+	11.0299i	0.495759	+	0.858680i
$166$	−0.107400	−	0.186022i	−0.00833582	−	0.0144381i
$167$	1.40979	−	2.44183i	0.109093	−	0.188955i	−0.806310	−	0.591493i	$-0.798539\pi$
$167$	1.40979	−	2.44183i	0.109093	−	0.188955i	0.915403	+	0.402538i	$0.131872\pi$
$168$	−2.14800	−	3.72044i	−0.165721	−	0.287038i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−4.78108			−0.366692
$171$	−0.708267			−0.0541625
$172$	−0.662258	+	1.14706i	−0.0504967	+	0.0874628i
$173$	0.266536	+	0.461654i	0.0202643	+	0.0350989i	0.875980	−	0.482348i	$-0.160216\pi$
$173$	0.266536	+	0.461654i	0.0202643	+	0.0350989i	−0.855715	+	0.517447i	$0.826883\pi$
$174$	−0.840069	+	1.45504i	−0.0636854	+	0.110306i
$175$	5.98834	+	10.3721i	0.452676	+	0.784057i
$176$	4.20253	+	7.27899i	0.316777	+	0.548674i
$177$	9.90341	+	17.1532i	0.744386	+	1.28931i
$178$	3.47574			0.260518
$179$	0.977311	−	1.69275i	0.0730476	−	0.126522i	−0.827188	−	0.561925i	$-0.810061\pi$
$179$	0.977311	−	1.69275i	0.0730476	−	0.126522i	0.900236	+	0.435403i	$0.143394\pi$
$180$	0.328525	−	0.569022i	0.0244868	−	0.0424124i
$181$	5.52764	+	9.57415i	0.410866	+	0.711641i	0.994985	−	0.100028i	$-0.0318931\pi$
$181$	5.52764	+	9.57415i	0.410866	+	0.711641i	−0.584119	+	0.811668i	$0.698560\pi$
$182$	0.643410			0.0476927
$183$	−4.28062	+	7.41425i	−0.316432	+	0.548077i
$184$	7.19669			0.530547
$185$	17.7622			1.30591
$186$	2.52752	−	0.504350i	0.185327	−	0.0369808i
$187$	13.0677			0.955604
$188$	18.5717			1.35448
$189$	6.24669	−	10.8196i	0.454380	−	0.787009i
$190$	5.68816			0.412662
$191$	−6.91195	−	11.9718i	−0.500131	−	0.866252i	−1.00000		0.000151274i	$-0.999952\pi$
$191$	−6.91195	−	11.9718i	−0.500131	−	0.866252i	0.499869	−	0.866101i	$-0.333381\pi$
$192$	−5.33730	+	9.24448i	−0.385187	+	0.667163i
$193$	−3.69654	+	6.40260i	−0.266083	+	0.460869i	−0.967847	−	0.251541i	$-0.919063\pi$
$193$	−3.69654	+	6.40260i	−0.266083	+	0.460869i	0.701764	+	0.712410i	$0.252396\pi$
$194$	0.712192			0.0511324
$195$	−2.69801	−	4.67309i	−0.193208	−	0.334647i
$196$	−1.35965	−	2.35499i	−0.0971180	−	0.168213i
$197$	−6.85003	−	11.8646i	−0.488045	−	0.845318i	0.511861	−	0.859068i	$-0.328956\pi$
$197$	−6.85003	−	11.8646i	−0.488045	−	0.845318i	−0.999905	+	0.0137504i	$0.995623\pi$
$198$	0.0345397	−	0.0598245i	0.00245463	−	0.00425154i
$199$	9.67207	+	16.7525i	0.685635	+	1.18755i	0.973237	+	0.229805i	$0.0738087\pi$
$199$	9.67207	+	16.7525i	0.685635	+	1.18755i	−0.287602	+	0.957750i	$0.592858\pi$
$200$	−2.70692	+	4.68852i	−0.191408	+	0.331528i
$201$	25.5635			1.80311
$202$	3.07287			0.216206
$203$	4.28995	−	7.43042i	0.301096	−	0.521513i
$204$	9.06717	+	15.7048i	0.634829	+	1.09956i
$205$	9.60616	−	16.6384i	0.670923	−	1.16207i
$206$	0.383150	+	0.663634i	0.0266953	+	0.0462376i
$207$	0.362098	+	0.627171i	0.0251675	+	0.0435914i
$208$	−1.78050	−	3.08391i	−0.123455	−	0.213831i
$209$	−15.5469			−1.07540
$210$	−1.73593	+	3.00671i	−0.119790	+	0.207483i
$211$	1.91424	−	3.31556i	0.131782	−	0.228252i	−0.792582	−	0.609766i	$-0.791264\pi$
$211$	1.91424	−	3.31556i	0.131782	−	0.228252i	0.924363	+	0.381513i	$0.124597\pi$
$212$	2.41314	+	4.17968i	0.165735	+	0.287061i
$213$	23.0572			1.57985
$214$	0.0233891	−	0.0405112i	0.00159885	−	0.00276929i
$215$	2.18202			0.148812
$216$	5.64740			0.384257
$217$	−12.9072	+	2.57555i	−0.876198	+	0.174840i
$218$	−1.41302			−0.0957016
$219$	−25.8443			−1.74639
$220$	7.21133	−	12.4904i	0.486188	−	0.842102i
$221$	−5.53643			−0.372420
$222$	1.29575	+	2.24430i	0.0869650	+	0.150628i
$223$	−0.352879	+	0.611204i	−0.0236305	+	0.0409293i	−0.877599	−	0.479396i	$-0.840856\pi$
$223$	−0.352879	+	0.611204i	−0.0236305	+	0.0409293i	0.853968	+	0.520325i	$0.174189\pi$
$224$	−3.67156	+	6.35933i	−0.245317	+	0.424901i
$225$	−0.544788			−0.0363192
$226$	2.05384	+	3.55736i	0.136619	+	0.236632i
$227$	−9.38927	−	16.2627i	−0.623188	−	1.07939i	−0.988888	−	0.148661i	$-0.952504\pi$
$227$	−9.38927	−	16.2627i	−0.623188	−	1.07939i	0.365700	−	0.930733i	$-0.380830\pi$
$228$	−10.7874	−	18.6844i	−0.714414	−	1.23740i
$229$	4.25653	−	7.37253i	0.281280	−	0.487191i	−0.690421	−	0.723408i	$-0.742574\pi$
$229$	4.25653	−	7.37253i	0.281280	−	0.487191i	0.971700	+	0.236218i	$0.0759078\pi$
$230$	−2.90804	−	5.03687i	−0.191750	−	0.332121i
$231$	4.74465	−	8.21797i	0.312175	−	0.540703i
$232$	3.87839			0.254629
$233$	8.14573			0.533644			0.266822	−	0.963746i	$-0.414026\pi$
$233$	8.14573			0.533644			0.266822	+	0.963746i	$0.414026\pi$
$234$	−0.0146335	+	0.0253460i	−0.000956624	+	0.00165692i
$235$	−15.2976	−	26.4962i	−0.997905	−	1.72842i
$236$	11.2147	−	19.4244i	0.730015	−	1.26442i
$237$	14.9867	+	25.9577i	0.973490	+	1.68613i
$238$	1.78110	+	3.08495i	0.115451	+	0.199967i
$239$	5.08527	+	8.80794i	0.328939	+	0.569738i	0.982302	−	0.187306i	$-0.0599757\pi$
$239$	5.08527	+	8.80794i	0.328939	+	0.569738i	−0.653363	+	0.757045i	$0.726642\pi$
$240$	19.2152			1.24033
$241$	−10.0893	+	17.4752i	−0.649909	+	1.12568i	0.333235	+	0.942844i	$0.391860\pi$
$241$	−10.0893	+	17.4752i	−0.649909	+	1.12568i	−0.983144	+	0.182832i	$0.941474\pi$
$242$	−0.738826	+	1.27968i	−0.0474935	+	0.0822612i
$243$	0.558460	+	0.967280i	0.0358252	+	0.0620511i
$244$	9.69482			0.620647
$245$	−2.23990	+	3.87962i	−0.143102	+	0.247860i
$246$	2.80306			0.178717
$247$	6.58681			0.419109
$248$	−3.92549	−	4.47068i	−0.249269	−	0.283888i
$249$	1.34218			0.0850570
$250$	0.0574086			0.00363084
$251$	5.59491	−	9.69067i	0.353148	−	0.611669i	−0.633652	−	0.773619i	$-0.718445\pi$
$251$	5.59491	−	9.69067i	0.353148	−	0.611669i	0.986799	+	0.161949i	$0.0517780\pi$
$252$	−0.489541			−0.0308382
$253$	7.94828	+	13.7668i	0.499704	+	0.865513i
$254$	−2.88164	+	4.99115i	−0.180810	+	0.313172i
$255$	14.9373	−	25.8722i	0.935412	−	1.62018i
$256$	10.3970			0.649815
$257$	−1.54540	−	2.67671i	−0.0963995	−	0.166969i	0.813792	−	0.581156i	$-0.197399\pi$
$257$	−1.54540	−	2.67671i	−0.0963995	−	0.166969i	−0.910192	+	0.414187i	$0.864066\pi$
$258$	0.159177	+	0.275703i	0.00990995	+	0.0171645i
$259$	−6.61696	−	11.4609i	−0.411158	−	0.712147i
$260$	−3.05525	+	5.29184i	−0.189478	+	0.328186i
$261$	0.195139	+	0.337991i	0.0120788	+	0.0209211i
$262$	−1.39923	+	2.42354i	−0.0864450	+	0.149727i
$263$	−3.32266			−0.204884			−0.102442	−	0.994739i	$-0.532666\pi$
$263$	−3.32266			−0.204884			−0.102442	+	0.994739i	$0.532666\pi$
$264$	4.28946			0.263998
$265$	3.97542	−	6.88563i	0.244208	−	0.422981i
$266$	−2.11901	−	3.67023i	−0.129925	−	0.225036i
$267$	−10.8591	+	18.8086i	−0.664568	+	1.15106i
$268$	−14.4742	−	25.0700i	−0.884151	−	1.53139i
$269$	5.60804	+	9.71341i	0.341928	+	0.592237i	0.984791	−	0.173744i	$-0.0555867\pi$
$269$	5.60804	+	9.71341i	0.341928	+	0.592237i	−0.642863	+	0.765982i	$0.722253\pi$
$270$	−2.28200	−	3.95254i	−0.138878	−	0.240544i
$271$	16.3213			0.991450			0.495725	−	0.868480i	$-0.334902\pi$
$271$	16.3213			0.991450			0.495725	+	0.868480i	$0.334902\pi$
$272$	9.85759	−	17.0738i	0.597704	−	1.03525i
$273$	−2.01018	+	3.48173i	−0.121662	+	0.210724i
$274$	1.54655	+	2.67871i	0.0934307	+	0.161827i
$275$	−11.9585			−0.721122
$276$	−11.0300	+	19.1045i	−0.663929	+	1.14996i
$277$	1.99976			0.120154			0.0600769	−	0.998194i	$-0.480865\pi$
$277$	1.99976			0.120154			0.0600769	+	0.998194i	$0.480865\pi$
$278$	3.01028			0.180544
$279$	0.192099	−	0.567035i	0.0115006	−	0.0339475i
$280$	8.01434			0.478948
$281$	−12.6356			−0.753778			−0.376889	−	0.926258i	$-0.623006\pi$
$281$	−12.6356			−0.753778			−0.376889	+	0.926258i	$0.623006\pi$
$282$	2.23191	−	3.86578i	0.132908	−	0.230204i
$283$	−8.76623			−0.521098			−0.260549	−	0.965461i	$-0.583904\pi$
$283$	−8.76623			−0.521098			−0.260549	+	0.965461i	$0.583904\pi$
$284$	−13.0551	−	22.6121i	−0.774678	−	1.34178i
$285$	−17.7713	+	30.7808i	−1.05268	+	1.82329i
$286$	−0.321216	+	0.556362i	−0.0189939	+	0.0328984i
$287$	−14.3143			−0.844948
$288$	−0.167010	−	0.289270i	−0.00984116	−	0.0170454i
$289$	−6.82601	−	11.8230i	−0.401530	−	0.695471i
$290$	−1.56718	−	2.71444i	−0.0920280	−	0.159397i
$291$	−2.22507	+	3.85394i	−0.130436	+	0.225922i
$292$	14.6331	+	25.3453i	0.856340	+	1.48322i
$293$	−10.3874	+	17.9915i	−0.606840	+	1.05108i	0.384918	+	0.922951i	$0.374230\pi$
$293$	−10.3874	+	17.9915i	−0.606840	+	1.05108i	−0.991758	+	0.128126i	$0.959104\pi$
$294$	−0.653600			−0.0381187
$295$	−36.9504			−2.15134
$296$	2.99108	−	5.18070i	0.173853	−	0.301122i
$297$	6.23719	+	10.8031i	0.361918	+	0.626861i
$298$	0.140848	−	0.243957i	0.00815913	−	0.0141320i
$299$	−3.36747	−	5.83263i	−0.194746	−	0.337310i
$300$	−8.29752	−	14.3717i	−0.479058	−	0.829752i
$301$	−0.812867	−	1.40793i	−0.0468529	−	0.0811515i
$302$	3.02507			0.174073
$303$	−9.60043	+	16.6284i	−0.551531	+	0.955279i
$304$	−11.7278	+	20.3131i	−0.672635	+	1.16504i
$305$	−7.98566	−	13.8316i	−0.457258	−	0.791993i
$306$	−0.162035			−0.00926293
$307$	1.29498	−	2.24297i	0.0739084	−	0.128013i	−0.826703	−	0.562639i	$-0.809786\pi$
$307$	1.29498	−	2.24297i	0.0739084	−	0.128013i	0.900611	+	0.434626i	$0.143119\pi$
$308$	−10.7458			−0.612296
$309$	−4.78823			−0.272393
$310$	−1.54276	+	4.55391i	−0.0876230	+	0.258645i
$311$	17.9033			1.01520			0.507602	−	0.861592i	$-0.330532\pi$
$311$	17.9033			1.01520			0.507602	+	0.861592i	$0.330532\pi$
$312$	−1.81733			−0.102886
$313$	−1.48701	+	2.57558i	−0.0840510	+	0.145581i	−0.904986	−	0.425440i	$-0.860119\pi$
$313$	−1.48701	+	2.57558i	−0.0840510	+	0.145581i	0.820935	+	0.571021i	$0.193453\pi$
$314$	1.16561			0.0657792
$315$	0.403237	+	0.698427i	0.0227198	+	0.0393519i
$316$	16.9711	−	29.3947i	0.954696	−	1.65358i
$317$	0.324446	−	0.561956i	0.0182227	−	0.0315626i	−0.856770	−	0.515698i	$-0.827533\pi$
$317$	0.324446	−	0.561956i	0.0182227	−	0.0315626i	0.874993	+	0.484136i	$0.160866\pi$
$318$	1.16002			0.0650508
$319$	4.28343	+	7.41912i	0.239826	+	0.415391i
$320$	−9.95695	−	17.2459i	−0.556610	−	0.964077i
$321$	0.146147	+	0.253135i	0.00815715	+	0.0141286i
$322$	−2.16666	+	3.75277i	−0.120743	+	0.209134i
$323$	18.2337	+	31.5817i	1.01455	+	1.75725i
$324$	−8.34486	+	14.4537i	−0.463603	+	0.802985i
$325$	5.06648			0.281038
$326$	−0.140173			−0.00776346
$327$	4.41463	−	7.64636i	0.244130	−	0.422845i
$328$	−3.23526	−	5.60364i	−0.178638	−	0.309409i
$329$	−11.3976	+	19.7413i	−0.628372	+	1.08837i
$330$	−1.73329	−	3.00214i	−0.0954142	−	0.165262i
$331$	−5.49851	−	9.52371i	−0.302226	−	0.523470i	0.674414	−	0.738353i	$-0.264396\pi$
$331$	−5.49851	−	9.52371i	−0.302226	−	0.523470i	−0.976640	+	0.214883i	$0.931063\pi$
$332$	−0.759946	−	1.31626i	−0.0417074	−	0.0722394i
$333$	0.601978			0.0329882
$334$	−0.383719	+	0.664620i	−0.0209961	+	0.0363664i
$335$	−23.8449	+	41.3005i	−1.30278	+	2.25649i
$336$	−7.15823	−	12.3984i	−0.390514	−	0.676389i
$337$	−19.8803			−1.08295			−0.541475	−	0.840717i	$-0.682134\pi$
$337$	−19.8803			−1.08295			−0.541475	+	0.840717i	$0.682134\pi$
$338$	0.136090	−	0.235716i	0.00740234	−	0.0128212i
$339$	−25.6669			−1.39404
$340$	−33.8303			−1.83471
$341$	4.21669	−	12.4468i	0.228346	−	0.674031i
$342$	0.192777			0.0104242
$343$	19.8851			1.07369
$344$	0.367441	−	0.636427i	0.0198111	−	0.0343138i
$345$	36.3419			1.95658
$346$	−0.0725460	−	0.125653i	−0.00390009	−	0.00675516i
$347$	−4.87934	+	8.45126i	−0.261937	+	0.453688i	−0.966757	−	0.255699i	$-0.917694\pi$
$347$	−4.87934	+	8.45126i	−0.261937	+	0.453688i	0.704820	+	0.709386i	$0.251028\pi$
$348$	−5.94422	+	10.2957i	−0.318644	+	0.551907i
$349$	5.07241			0.271520			0.135760	−	0.990742i	$-0.456652\pi$
$349$	5.07241			0.271520			0.135760	+	0.990742i	$0.456652\pi$
$350$	−1.62991	−	2.82309i	−0.0871224	−	0.150900i
$351$	−2.64253	−	4.57699i	−0.141048	−	0.244302i
$352$	−3.66598	−	6.34966i	−0.195397	−	0.338438i
$353$	1.58527	−	2.74577i	0.0843755	−	0.146143i	−0.820749	−	0.571288i	$-0.806444\pi$
$353$	1.58527	−	2.74577i	0.0843755	−	0.146143i	0.905125	+	0.425146i	$0.139777\pi$
$354$	−2.69552	−	4.66878i	−0.143265	−	0.248143i
$355$	−21.5071	+	37.2513i	−1.14148	+	1.97710i
$356$	24.5939			1.30348
$357$	−22.2584			−1.17804
$358$	−0.266005	+	0.460735i	−0.0140588	+	0.0243506i
$359$	−2.05744	−	3.56358i	−0.108587	−	0.188079i	0.806611	−	0.591083i	$-0.201299\pi$
$359$	−2.05744	−	3.56358i	−0.108587	−	0.188079i	−0.915198	+	0.403004i	$0.867966\pi$
$360$	−0.182276	+	0.315711i	−0.00960678	+	0.0166394i
$361$	−12.1930	−	21.1190i	−0.641739	−	1.11152i
$362$	−1.50452	−	2.60590i	−0.0790756	−	0.136963i
$363$	−4.61657	−	7.99613i	−0.242307	−	0.419688i
$364$	4.55269			0.238626
$365$	24.1067	−	41.7541i	1.26180	−	2.18551i
$366$	1.16510	−	2.01802i	0.0609009	−	0.105483i
$367$	14.6746	+	25.4172i	0.766009	+	1.32677i	0.939712	+	0.341968i	$0.111093\pi$
$367$	14.6746	+	25.4172i	0.766009	+	1.32677i	−0.173703	+	0.984798i	$0.555573\pi$
$368$	23.9831			1.25020
$369$	0.325561	−	0.563888i	0.0169480	−	0.0293549i
$370$	−4.83454			−0.251336
$371$	−5.92385			−0.307551
$372$	17.8844	−	3.56872i	0.927263	−	0.185030i
$373$	−24.6684			−1.27728			−0.638642	−	0.769504i	$-0.720503\pi$
$373$	−24.6684			−1.27728			−0.638642	+	0.769504i	$0.720503\pi$
$374$	−3.55677			−0.183916
$375$	−0.179359	+	0.310659i	−0.00926207	+	0.0160424i
$376$	−10.3042			−0.531397
$377$	−1.81477	−	3.14328i	−0.0934656	−	0.161887i
$378$	−1.70023	+	2.94488i	−0.0874503	+	0.151468i
$379$	12.2974	−	21.2996i	0.631672	−	1.09409i	−0.355537	−	0.934662i	$-0.615702\pi$
$379$	12.2974	−	21.2996i	0.631672	−	1.09409i	0.987210	−	0.159427i	$-0.0509646\pi$
$380$	40.2487			2.06471
$381$	−18.0060	−	31.1873i	−0.922474	−	1.59777i
$382$	1.88130	+	3.25851i	0.0962557	+	0.166720i
$383$	4.46963	+	7.74162i	0.228387	+	0.395578i	0.957330	−	0.288996i	$-0.0933215\pi$
$383$	4.46963	+	7.74162i	0.228387	+	0.395578i	−0.728943	+	0.684574i	$0.759988\pi$
$384$	6.73577	−	11.6667i	0.343733	−	0.595364i
$385$	8.85132	+	15.3309i	0.451105	+	0.781337i
$386$	1.00613	−	1.74266i	0.0512106	−	0.0886993i
$387$	0.0739505			0.00375911
$388$	5.03938			0.255836
$389$	−0.839534	+	1.45412i	−0.0425661	+	0.0737266i	−0.886524	−	0.462684i	$-0.846887\pi$
$389$	−0.839534	+	1.45412i	−0.0425661	+	0.0737266i	0.843957	+	0.536410i	$0.180220\pi$
$390$	0.734346	+	1.27193i	0.0371851	+	0.0644064i
$391$	18.6438	−	32.2919i	0.942855	−	1.63307i
$392$	0.754377	+	1.30662i	0.0381018	+	0.0659943i
$393$	−8.74314	−	15.1436i	−0.441033	−	0.763892i
$394$	1.86445	+	3.22932i	0.0939295	+	0.162691i
$395$	−55.9165			−2.81346
$396$	0.244398	−	0.423311i	0.0122815	−	0.0212722i
$397$	−5.32986	+	9.23159i	−0.267498	+	0.463320i	−0.968215	−	0.250119i	$-0.919530\pi$
$397$	−5.32986	+	9.23159i	−0.267498	+	0.463320i	0.700717	+	0.713439i	$0.252864\pi$
$398$	−2.63255	−	4.55972i	−0.131958	−	0.228558i
$399$	26.4813			1.32573
$400$	−9.02085	+	15.6246i	−0.451042	+	0.781228i
$401$	33.5321			1.67451			0.837257	−	0.546810i	$-0.184158\pi$
$401$	33.5321			1.67451			0.837257	+	0.546810i	$0.184158\pi$
$402$	−6.95790			−0.347028
$403$	−1.78650	+	5.27337i	−0.0889918	+	0.262685i
$404$	21.7432			1.08177
$405$	27.4948			1.36623
$406$	−1.16764	+	2.02242i	−0.0579492	+	0.100371i
$407$	13.2138			0.654984
$408$	−5.03075	−	8.71352i	−0.249059	−	0.431383i
$409$	2.69398	−	4.66611i	0.133209	−	0.230724i	−0.791703	−	0.610906i	$-0.790805\pi$
$409$	2.69398	−	4.66611i	0.133209	−	0.230724i	0.924912	+	0.380182i	$0.124139\pi$
$410$	−2.61461	+	4.52864i	−0.129126	+	0.223654i
$411$	−19.3273			−0.953347
$412$	2.71112	+	4.69579i	0.133567	+	0.231345i
$413$	13.7651	+	23.8419i	0.677338	+	1.17318i
$414$	−0.0985560	−	0.170704i	−0.00484376	−	0.00838965i
$415$	−1.25194	+	2.16842i	−0.0614554	+	0.106444i
$416$	1.55318	+	2.69018i	0.0761508	+	0.131897i
$417$	−9.40489	+	16.2897i	−0.460559	+	0.797712i
$418$	4.23157			0.206973
$419$	−31.9891			−1.56277			−0.781385	−	0.624049i	$-0.785487\pi$
$419$	−31.9891			−1.56277			−0.781385	+	0.624049i	$0.785487\pi$
$420$	−12.2832	+	21.2751i	−0.599358	+	1.03812i
$421$	17.4708	+	30.2602i	0.851473	+	1.47479i	0.879879	+	0.475198i	$0.157624\pi$
$421$	17.4708	+	30.2602i	0.851473	+	1.47479i	−0.0284061	+	0.999596i	$0.509043\pi$
$422$	−0.521019	+	0.902431i	−0.0253628	+	0.0439297i
$423$	−0.518449	−	0.897981i	−0.0252079	−	0.0436613i
$424$	−1.33888	−	2.31902i	−0.0650220	−	0.112621i
$425$	14.0251	+	24.2922i	0.680317	+	1.17834i
$426$	−6.27573			−0.304060
$427$	−5.94980	+	10.3053i	−0.287931	+	0.498711i
$428$	0.165499	−	0.286652i	0.00799967	−	0.0138558i
$429$	−2.00712	−	3.47644i	−0.0969047	−	0.167844i
$430$	−0.593903			−0.0286406
$431$	4.91708	−	8.51662i	0.236847	−	0.410231i	−0.722961	−	0.690889i	$-0.757219\pi$
$431$	4.91708	−	8.51662i	0.236847	−	0.410231i	0.959808	+	0.280658i	$0.0905526\pi$
$432$	18.8201			0.905480
$433$	−10.5628			−0.507614			−0.253807	−	0.967255i	$-0.581683\pi$
$433$	−10.5628			−0.507614			−0.253807	+	0.967255i	$0.581683\pi$
$434$	3.51309	−	0.701016i	0.168634	−	0.0336498i
$435$	19.5851			0.939034
$436$	−9.99833			−0.478833
$437$	−22.1809	+	38.4184i	−1.06106	+	1.83780i
$438$	7.03432			0.336113
$439$	1.82442	+	3.15999i	0.0870747	+	0.150818i	0.906273	−	0.422692i	$-0.138915\pi$
$439$	1.82442	+	3.15999i	0.0870747	+	0.150818i	−0.819199	+	0.573510i	$0.805581\pi$
$440$	−4.00107	+	6.93006i	−0.190744	+	0.330378i
$441$	−0.0759122	+	0.131484i	−0.00361487	+	0.00626113i
$442$	1.50691			0.0716764
$443$	−18.8392	−	32.6305i	−0.895079	−	1.55032i	−0.833707	−	0.552207i	$-0.813786\pi$
$443$	−18.8392	−	32.6305i	−0.895079	−	1.55032i	−0.0613717	−	0.998115i	$-0.519548\pi$
$444$	9.16856	+	15.8804i	0.435120	+	0.753651i
$445$	−20.2581	−	35.0881i	−0.960327	−	1.66333i
$446$	0.0960469	−	0.166358i	0.00454795	−	0.00787729i
$447$	0.880094	+	1.52437i	0.0416270	+	0.0721001i
$448$	−7.41852	+	12.8493i	−0.350492	+	0.607070i
$449$	−1.42094			−0.0670583			−0.0335292	−	0.999438i	$-0.510675\pi$
$449$	−1.42094			−0.0670583			−0.0335292	+	0.999438i	$0.510675\pi$
$450$	0.148281			0.00699003
$451$	7.14628	−	12.3777i	0.336505	−	0.582844i
$452$	14.5327	+	25.1714i	0.683561	+	1.18396i
$453$	−9.45110	+	16.3698i	−0.444051	+	0.769119i
$454$	2.55558	+	4.42640i	0.119939	+	0.207741i
$455$	−3.75007	−	6.49530i	−0.175806	−	0.304505i
$456$	5.98520	+	10.3667i	0.280283	+	0.485464i
$457$	−20.7824			−0.972161			−0.486081	−	0.873914i	$-0.661574\pi$
$457$	−20.7824			−0.972161			−0.486081	+	0.873914i	$0.661574\pi$
$458$	−1.15855	+	2.00666i	−0.0541353	+	0.0937652i
$459$	14.6302	−	25.3402i	0.682878	−	1.18278i
$460$	−20.5769	−	35.6403i	−0.959404	−	1.66174i
$461$	−9.70918			−0.452202			−0.226101	−	0.974104i	$-0.572598\pi$
$461$	−9.70918			−0.452202			−0.226101	+	0.974104i	$0.572598\pi$
$462$	−1.29140	+	2.23677i	−0.0600814	+	0.104064i
$463$	−18.3234			−0.851559			−0.425780	−	0.904827i	$-0.640000\pi$
$463$	−18.3234			−0.851559			−0.425780	+	0.904827i	$0.640000\pi$
$464$	12.9248			0.600019
$465$	−19.8229	−	22.5761i	−0.919267	−	1.04694i
$466$	−2.21711			−0.102706
$467$	5.08178			0.235157			0.117578	−	0.993064i	$-0.462487\pi$
$467$	5.08178			0.235157			0.117578	+	0.993064i	$0.462487\pi$
$468$	−0.103545	+	0.179345i	−0.00478637	+	0.00829024i
$469$	35.5317			1.64070
$470$	4.16371	+	7.21176i	0.192058	+	0.332654i
$471$	−3.64167	+	6.30755i	−0.167799	+	0.290637i
$472$	−6.22227	+	10.7773i	−0.286403	+	0.496065i
$473$	1.62326			0.0746376
$474$	−4.07909	−	7.06519i	−0.187359	−	0.324515i
$475$	−16.6860	−	28.9009i	−0.765605	−	1.32607i
$476$	12.6028	+	21.8287i	0.577649	+	1.00052i
$477$	0.134731	−	0.233360i	0.00616889	−	0.0106848i
$478$	−1.38411	−	2.39735i	−0.0633078	−	0.109652i
$479$	19.8708	−	34.4172i	0.907920	−	1.57256i	0.0909716	−	0.995853i	$-0.471003\pi$
$479$	19.8708	−	34.4172i	0.907920	−	1.57256i	0.816949	−	0.576710i	$-0.195664\pi$
$480$	−16.7619			−0.765074
$481$	−5.59833			−0.255262
$482$	2.74611	−	4.75641i	0.125082	−	0.216648i
$483$	−13.5384	−	23.4493i	−0.616020	−	1.06698i
$484$	−5.22784	+	9.05489i	−0.237629	+	0.411586i
$485$	−4.15096	−	7.18967i	−0.188485	−	0.326466i
$486$	−0.152002	−	0.263275i	−0.00689495	−	0.0119424i
$487$	2.00653	+	3.47541i	0.0909245	+	0.157486i	0.907900	−	0.419186i	$-0.137684\pi$
$487$	2.00653	+	3.47541i	0.0909245	+	0.157486i	−0.816976	+	0.576672i	$0.804351\pi$
$488$	−5.37899			−0.243495
$489$	0.437937	−	0.758528i	0.0198042	−	0.0343018i
$490$	0.609658	−	1.05596i	0.0275415	−	0.0477034i
$491$	13.9530	+	24.1673i	0.629690	+	1.09065i	0.987614	+	0.156904i	$0.0501513\pi$
$491$	13.9530	+	24.1673i	0.629690	+	1.09065i	−0.357924	+	0.933751i	$0.616515\pi$
$492$	19.8341			0.894192
$493$	10.0474	−	17.4025i	0.452511	−	0.783771i
$494$	−1.79280			−0.0806621
$495$	−0.805248			−0.0361932
$496$	−13.0817	−	14.8986i	−0.587388	−	0.668968i
$497$	32.0481			1.43755
$498$	−0.365315			−0.0163701
$499$	−5.38430	+	9.32587i	−0.241034	+	0.417483i	−0.961009	−	0.276517i	$-0.910820\pi$
$499$	−5.38430	+	9.32587i	−0.241034	+	0.417483i	0.719975	+	0.694000i	$0.244153\pi$
$500$	0.406216			0.0181665
$501$	−2.39767	−	4.15289i	−0.107120	−	0.185537i
$502$	−1.52283	+	2.63761i	−0.0679671	+	0.117722i
$503$	−10.4850	+	18.1606i	−0.467505	+	0.809742i	−0.999311	−	0.0371244i	$-0.988180\pi$
$503$	−10.4850	+	18.1606i	−0.467505	+	0.809742i	0.531806	+	0.846866i	$0.321514\pi$
$504$	0.271613			0.0120986
$505$	−17.9100	−	31.0210i	−0.796984	−	1.38042i
$506$	−2.16337	−	3.74706i	−0.0961735	−	0.166577i
$507$	0.850363	+	1.47287i	0.0377660	+	0.0654126i
$508$	−20.3901	+	35.3167i	−0.904665	+	1.56693i
$509$	8.94713	+	15.4969i	0.396574	+	0.686887i	0.993301	−	0.115558i	$-0.0368656\pi$
$509$	8.94713	+	15.4969i	0.396574	+	0.686887i	−0.596726	+	0.802445i	$0.703532\pi$
$510$	−4.06565	+	7.04192i	−0.180030	+	0.311822i
$511$	−35.9220			−1.58909
$512$	−18.6720			−0.825192
$513$	−17.4058	+	30.1478i	−0.768486	+	1.33106i
$514$	0.420629	+	0.728550i	0.0185531	+	0.0321350i
$515$	4.46632	−	7.73589i	0.196809	−	0.340884i
$516$	1.12632	+	1.95084i	0.0495834	+	0.0858810i
$517$	−11.3803	−	19.7113i	−0.500505	−	0.866900i
$518$	1.80101	+	3.11944i	0.0791319	+	0.137060i
$519$	0.906609			0.0397957
$520$	1.69515	−	2.93608i	0.0743371	−	0.128756i
$521$	19.6269	−	33.9948i	0.859869	−	1.48934i	−0.0121836	−	0.999926i	$-0.503878\pi$
$521$	19.6269	−	33.9948i	0.859869	−	1.48934i	0.872053	−	0.489412i	$-0.162788\pi$
$522$	−0.0531131	−	0.0919946i	−0.00232470	−	0.00402650i
$523$	11.4547			0.500878			0.250439	−	0.968132i	$-0.419425\pi$
$523$	11.4547			0.500878			0.250439	+	0.968132i	$0.419425\pi$
$524$	−9.90080	+	17.1487i	−0.432519	+	0.749144i
$525$	20.3691			0.888978
$526$	0.904365			0.0394322
$527$	−30.2296	+	6.03212i	−1.31682	+	0.262763i
$528$	14.2947			0.622097
$529$	22.3594			0.972150
$530$	−1.08203	+	1.87414i	−0.0470005	+	0.0814073i
$531$	−1.25228			−0.0543444
$532$	−14.9938	−	25.9701i	−0.650066	−	1.12595i
$533$	−3.02769	+	5.24411i	−0.131144	+	0.227147i
$534$	2.95565	−	5.11933i	0.127903	−	0.221535i
$535$	−0.545287			−0.0235748
$536$	8.03073	+	13.9096i	0.346874	+	0.600804i
$537$	−1.66214	−	2.87891i	−0.0717266	−	0.124234i
$538$	−1.52640	−	2.64380i	−0.0658078	−	0.113983i
$539$	−1.66632	+	2.88616i	−0.0717736	+	0.124316i
$540$	−16.1472	−	27.9677i	−0.694863	−	1.20354i
$541$	−2.11235	+	3.65870i	−0.0908171	+	0.157300i	−0.907855	−	0.419284i	$-0.862281\pi$
$541$	−2.11235	+	3.65870i	−0.0908171	+	0.157300i	0.817038	+	0.576584i	$0.195615\pi$
$542$	−4.44235			−0.190815
$543$	18.8020			0.806871
$544$	−8.59905	+	14.8940i	−0.368681	+	0.638575i
$545$	8.23566	+	14.2646i	0.352777	+	0.611028i
$546$	0.547132	−	0.947661i	0.0234151	−	0.0405561i
$547$	11.9800	+	20.7500i	0.512228	+	0.887205i	0.999899	+	0.0141778i	$0.00451308\pi$
$547$	11.9800	+	20.7500i	0.512228	+	0.887205i	−0.487671	+	0.873027i	$0.662154\pi$
$548$	10.9432	+	18.9542i	0.467471	+	0.809684i
$549$	−0.270641	−	0.468764i	−0.0115507	−	0.0200064i
$550$	3.25486			0.138788
$551$	−11.9536	+	20.7042i	−0.509239	+	0.882029i
$552$	6.11980	−	10.5998i	0.260476	−	0.451158i
$553$	20.8306	+	36.0796i	0.885806	+	1.53426i
$554$	−0.544296			−0.0231249
$555$	15.1044	−	26.1615i	0.641144	−	1.11049i
$556$	21.3003			0.903336
$557$	−9.25679			−0.392223			−0.196111	−	0.980582i	$-0.562831\pi$
$557$	−9.25679			−0.392223			−0.196111	+	0.980582i	$0.562831\pi$
$558$	−0.0522855	+	0.154336i	−0.00221342	+	0.00653357i
$559$	−0.687732			−0.0290880
$560$	26.7079			1.12862
$561$	11.1123	−	19.2470i	0.469161	−	0.812611i
$562$	3.43917			0.145073
$563$	−19.1835	−	33.2269i	−0.808490	−	1.40035i	−0.913909	−	0.405918i	$-0.866952\pi$
$563$	−19.1835	−	33.2269i	−0.808490	−	1.40035i	0.105419	−	0.994428i	$-0.466382\pi$
$564$	15.7927	−	27.3538i	0.664993	−	1.15180i
$565$	23.9413	−	41.4676i	1.00722	−	1.74455i
$566$	2.38600			0.100291
$567$	−10.2426	−	17.7408i	−0.430150	−	0.745042i
$568$	7.24338	+	12.5459i	0.303925	+	0.526414i
$569$	−7.58001	−	13.1290i	−0.317770	−	0.550394i	0.662252	−	0.749281i	$-0.269601\pi$
$569$	−7.58001	−	13.1290i	−0.317770	−	0.550394i	−0.980023	+	0.198887i	$0.936267\pi$
$570$	4.83700	−	8.37793i	0.202600	−	0.350913i
$571$	16.5657	+	28.6927i	0.693253	+	1.20075i	0.970766	+	0.240028i	$0.0771567\pi$
$571$	16.5657	+	28.6927i	0.693253	+	1.20075i	−0.277512	+	0.960722i	$0.589510\pi$
$572$	−2.27288	+	3.93675i	−0.0950340	+	0.164604i
$573$	−23.5107			−0.982172
$574$	3.89609			0.162619
$575$	−17.0612	+	29.5509i	−0.711502	+	1.23236i
$576$	−0.337450	−	0.584480i	−0.0140604	−	0.0243533i
$577$	−15.6947	+	27.1841i	−0.653380	+	1.13169i	0.328917	+	0.944359i	$0.393316\pi$
$577$	−15.6947	+	27.1841i	−0.653380	+	1.13169i	−0.982297	+	0.187329i	$0.940017\pi$
$578$	1.85791	+	3.21799i	0.0772789	+	0.133851i
$579$	6.28681	+	10.8891i	0.261271	+	0.452534i
$580$	−11.0892	−	19.2070i	−0.460453	−	0.797528i
$581$	1.86554			0.0773957
$582$	0.605622	−	1.04897i	0.0251039	−	0.0434811i
$583$	2.95742	−	5.12241i	0.122484	−	0.212148i
$584$	−8.11893	−	14.0624i	−0.335964	−	0.581906i
$585$	0.341162			0.0141053
$586$	2.82726	−	4.89695i	0.116793	−	0.202291i
$587$	−23.7961			−0.982171			−0.491085	−	0.871111i	$-0.663400\pi$
$587$	−23.7961			−0.982171			−0.491085	+	0.871111i	$0.663400\pi$
$588$	−4.62479			−0.190723
$589$	35.9648	−	7.17655i	1.48190	−	0.295704i
$590$	10.0572			0.414048
$591$	−23.3001			−0.958437
$592$	9.96781	−	17.2648i	0.409675	−	0.709577i
$593$	25.8132			1.06002			0.530010	−	0.847991i	$-0.322188\pi$
$593$	25.8132			1.06002			0.530010	+	0.847991i	$0.322188\pi$
$594$	−1.69764	−	2.94040i	−0.0696551	−	0.120646i
$595$	20.7620	−	35.9608i	0.851158	−	1.47425i
$596$	0.996626	−	1.72621i	0.0408234	−	0.0707082i
$597$	32.8991			1.34647
$598$	0.916561	+	1.58753i	0.0374810	+	0.0649189i
$599$	20.5366	+	35.5704i	0.839103	+	1.45337i	0.890646	+	0.454698i	$0.150253\pi$
$599$	20.5366	+	35.5704i	0.839103	+	1.45337i	−0.0515432	+	0.998671i	$0.516414\pi$
$600$	4.60373	+	7.97389i	0.187946	+	0.325533i
$601$	12.0024	−	20.7888i	0.489589	−	0.847994i	−0.510339	−	0.859973i	$-0.670480\pi$
$601$	12.0024	−	20.7888i	0.489589	−	0.847994i	0.999928	+	0.0119798i	$0.00381337\pi$
$602$	0.221247	+	0.383211i	0.00901734	+	0.0156185i
$603$	−0.808124	+	1.39971i	−0.0329093	+	0.0570006i
$604$	21.4050			0.870957
$605$	17.2248			0.700287
$606$	2.61305	−	4.52594i	0.106148	−	0.183854i
$607$	−9.12713	−	15.8087i	−0.370459	−	0.641654i	0.619177	−	0.785251i	$-0.287466\pi$
$607$	−9.12713	−	15.8087i	−0.370459	−	0.641654i	−0.989636	+	0.143598i	$0.954133\pi$
$608$	10.2305	−	17.7197i	0.414901	−	0.718629i
$609$	−7.29604	−	12.6371i	−0.295650	−	0.512082i
$610$	2.17354	+	3.76469i	0.0880042	+	0.152428i
$611$	4.82153	+	8.35113i	0.195058	+	0.337851i
$612$	−1.14654			−0.0463461
$613$	11.0990	−	19.2241i	0.448285	−	0.776453i	−0.549989	−	0.835172i	$-0.685368\pi$
$613$	11.0990	−	19.2241i	0.448285	−	0.776453i	0.998275	+	0.0587188i	$0.0187015\pi$
$614$	−0.352469	+	0.610494i	−0.0142245	+	0.0246375i
$615$	−16.3374	−	28.2973i	−0.658790	−	1.14106i
$616$	5.96208			0.240219
$617$	6.76084	−	11.7101i	0.272181	−	0.471432i	−0.697239	−	0.716839i	$-0.745588\pi$
$617$	6.76084	−	11.7101i	0.272181	−	0.471432i	0.969420	+	0.245407i	$0.0789217\pi$
$618$	1.30327			0.0524250
$619$	−17.3508			−0.697387			−0.348694	−	0.937237i	$-0.613375\pi$
$619$	−17.3508			−0.697387			−0.348694	+	0.937237i	$0.613375\pi$
$620$	−10.9164	+	32.2229i	−0.438413	+	1.29410i
$621$	35.5946			1.42836
$622$	−4.87294			−0.195387
$623$	−15.0935	+	26.1427i	−0.604709	+	1.04739i
$624$	−6.05628			−0.242445
$625$	12.3316	+	21.3589i	0.493264	+	0.854358i
$626$	0.404737	−	0.701024i	0.0161765	−	0.0280186i
$627$	−13.2205	+	22.8986i	−0.527977	+	0.914483i
$628$	8.24771			0.329119
$629$	−15.4974	−	26.8422i	−0.617921	−	1.07027i
$630$	−0.109753	−	0.190099i	−0.00437268	−	0.00757371i
$631$	−3.19349	−	5.53128i	−0.127131	−	0.220197i	0.795433	−	0.606041i	$-0.207243\pi$
$631$	−3.19349	−	5.53128i	−0.127131	−	0.220197i	−0.922564	+	0.385845i	$0.873910\pi$
$632$	−9.41607	+	16.3091i	−0.374551	+	0.648742i
$633$	−3.25560	−	5.63886i	−0.129398	−	0.224124i
$634$	−0.0883079	+	0.152954i	−0.00350716	+	0.00607457i
$635$	67.1817			2.66602
$636$	8.20818			0.325475
$637$	0.705976	−	1.22279i	0.0279718	−	0.0484486i
$638$	−1.16587	−	2.01934i	−0.0461571	−	0.0799465i
$639$	−0.728894	+	1.26248i	−0.0288346	+	0.0499430i
$640$	12.5658	+	21.7647i	0.496708	+	0.860324i
$641$	−1.22899	−	2.12868i	−0.0485423	−	0.0840777i	0.840733	−	0.541449i	$-0.182124\pi$
$641$	−1.22899	−	2.12868i	−0.0485423	−	0.0840777i	−0.889276	+	0.457372i	$0.848791\pi$
$642$	−0.0397785	−	0.0688984i	−0.00156993	−	0.00271920i
$643$	−21.4814			−0.847143			−0.423572	−	0.905863i	$-0.639224\pi$
$643$	−21.4814			−0.847143			−0.423572	+	0.905863i	$0.639224\pi$
$644$	−15.3310	+	26.5541i	−0.604128	+	1.04638i
$645$	1.85551	−	3.21383i	0.0730605	−	0.126545i
$646$	−4.96286	−	8.59593i	−0.195261	−	0.338202i
$647$	25.0238			0.983789			0.491894	−	0.870655i	$-0.336305\pi$
$647$	25.0238			0.983789			0.491894	+	0.870655i	$0.336305\pi$
$648$	4.62999	−	8.01938i	0.181883	−	0.315031i
$649$	−27.4884			−1.07901
$650$	−1.37900			−0.0540888
$651$	−7.18236	+	21.2008i	−0.281499	+	0.830926i
$652$	−0.991846			−0.0388437
$653$	16.4204			0.642578			0.321289	−	0.946981i	$-0.395884\pi$
$653$	16.4204			0.642578			0.321289	+	0.946981i	$0.395884\pi$
$654$	−1.20158	+	2.08119i	−0.0469854	+	0.0813811i
$655$	32.6213			1.27462
$656$	−10.7816	−	18.6742i	−0.420950	−	0.729106i
$657$	0.816999	−	1.41508i	0.0318742	−	0.0552077i
$658$	3.10222	−	5.37320i	0.120937	−	0.209469i
$659$	32.6517			1.27193			0.635964	−	0.771719i	$-0.280603\pi$
$659$	32.6517			1.27193			0.635964	+	0.771719i	$0.280603\pi$
$660$	−12.2645	−	21.2428i	−0.477395	−	0.826873i
$661$	9.52963	+	16.5058i	0.370660	+	0.642001i	0.989667	−	0.143384i	$-0.0457983\pi$
$661$	9.52963	+	16.5058i	0.370660	+	0.642001i	−0.619008	+	0.785385i	$0.712465\pi$
$662$	1.49659	+	2.59217i	0.0581666	+	0.100748i
$663$	−4.70798	+	8.15445i	−0.182843	+	0.316693i
$664$	0.421642	+	0.730305i	0.0163629	+	0.0283413i
$665$	−24.7010	+	42.7833i	−0.957863	+	1.65907i
$666$	−0.163847			−0.00634893
$667$	24.4448			0.946506
$668$	−2.71514	+	4.70277i	−0.105052	+	0.181956i
$669$	0.600151	+	1.03949i	0.0232032	+	0.0401891i
$670$	6.49011	−	11.2412i	0.250735	−	0.434286i
$671$	−5.94075	−	10.2897i	−0.229340	−	0.397229i
$672$	6.24433	+	10.8155i	0.240880	+	0.417217i
$673$	21.8199	+	37.7932i	0.841095	+	1.45682i	0.888969	+	0.457967i	$0.151422\pi$
$673$	21.8199	+	37.7932i	0.841095	+	1.45682i	−0.0478738	+	0.998853i	$0.515245\pi$
$674$	5.41104			0.208426
$675$	−13.3883	+	23.1892i	−0.515316	+	0.892554i
$676$	0.962959	−	1.66789i	0.0370369	−	0.0641498i
$677$	3.20825	+	5.55686i	0.123303	+	0.213567i	0.921068	−	0.389401i	$-0.127318\pi$
$677$	3.20825	+	5.55686i	0.123303	+	0.213567i	−0.797765	+	0.602968i	$0.793985\pi$
$678$	6.98604			0.268297
$679$	−3.09271	+	5.35674i	−0.118687	+	0.205573i
$680$	18.7701			0.719801
$681$	−31.9372			−1.22384
$682$	−1.14770	+	3.38778i	−0.0439478	+	0.129725i
$683$	23.2930			0.891283			0.445642	−	0.895211i	$-0.352976\pi$
$683$	23.2930			0.891283			0.445642	+	0.895211i	$0.352976\pi$
$684$	1.36406			0.0521563
$685$	18.0279	−	31.2253i	0.688812	−	1.19306i
$686$	−5.41233			−0.206644
$687$	−7.23920	−	12.5387i	−0.276193	−	0.478380i
$688$	1.22450	−	2.12090i	0.0466838	−	0.0808587i
$689$	−1.25298	+	2.17023i	−0.0477348	+	0.0826790i
$690$	−9.89156			−0.376565
$691$	14.0106	+	24.2671i	0.532988	+	0.923162i	0.999258	+	0.0385196i	$0.0122642\pi$
$691$	14.0106	+	24.2671i	0.532988	+	0.923162i	−0.466270	+	0.884642i	$0.654402\pi$
$692$	−0.513326	−	0.889107i	−0.0195137	−	0.0337988i
$693$	0.299979	+	0.519579i	0.0113953	+	0.0197372i
$694$	1.32806	−	2.30027i	0.0504126	−	0.0873171i
$695$	−17.5452	−	30.3891i	−0.665527	−	1.15273i
$696$	3.29804	−	5.71237i	0.125012	−	0.216527i
$697$	−33.5251			−1.26985
$698$	−1.38061			−0.0522570
$699$	6.92683	−	11.9976i	0.261997	−	0.453792i
$700$	−11.5330	−	19.9758i	−0.435908	−	0.755015i
$701$	3.75317	−	6.50068i	0.141755	−	0.245527i	−0.786402	−	0.617715i	$-0.788059\pi$
$701$	3.75317	−	6.50068i	0.141755	−	0.245527i	0.928158	+	0.372187i	$0.121392\pi$
$702$	0.719246	+	1.24577i	0.0271462	+	0.0470186i
$703$	18.4376	+	31.9348i	0.695387	+	1.20444i
$704$	−7.40724	−	12.8297i	−0.279171	−	0.483538i
$705$	−52.0341			−1.95972
$706$	−0.431481	+	0.747346i	−0.0162390	+	0.0281268i
$707$	−13.3440	+	23.1125i	−0.501853	+	0.869235i
$708$	−19.0732	−	33.0357i	−0.716813	−	1.24156i
$709$	30.2077			1.13447			0.567236	−	0.823555i	$-0.308013\pi$
$709$	30.2077			1.13447			0.567236	+	0.823555i	$0.308013\pi$
$710$	5.85381	−	10.1391i	0.219690	−	0.380514i
$711$	−1.89506			−0.0710703
$712$	−13.6455			−0.511386
$713$	−24.7416	−	28.1779i	−0.926582	−	1.05527i
$714$	6.05831			0.226727
$715$	7.48873			0.280062
$716$	−1.88222	+	3.26010i	−0.0703419	+	0.121836i
$717$	17.2973			0.645980
$718$	0.559995	+	0.969939i	0.0208988	+	0.0361978i
$719$	−13.2637	+	22.9734i	−0.494653	+	0.856764i	−0.999981	−	0.00616331i	$-0.998038\pi$
$719$	−13.2637	+	22.9734i	−0.494653	+	0.856764i	0.505328	+	0.862927i	$0.331371\pi$
$720$	−0.607438	+	1.05211i	−0.0226379	+	0.0392099i
$721$	−6.65535			−0.247858
$722$	3.31871	+	5.74818i	0.123510	+	0.213925i
$723$	17.1591	+	29.7205i	0.638155	+	1.10532i
$724$	−10.6458	−	18.4390i	−0.395647	−	0.685281i
$725$	−9.19451	+	15.9254i	−0.341476	+	0.591453i
$726$	1.25654	+	2.17639i	0.0466346	+	0.0807735i
$727$	−7.14514	+	12.3758i	−0.264999	+	0.458991i	−0.967563	−	0.252629i	$-0.918705\pi$
$727$	−7.14514	+	12.3758i	−0.264999	+	0.458991i	0.702565	+	0.711620i	$0.252038\pi$
$728$	−2.52597			−0.0936188
$729$	27.8971			1.03323
$730$	−6.56140	+	11.3647i	−0.242848	+	0.420625i
$731$	−1.90379	−	3.29746i	−0.0704142	−	0.121961i
$732$	8.24412	−	14.2792i	0.304711	−	0.527776i
$733$	4.85134	+	8.40276i	0.179188	+	0.310363i	0.941603	−	0.336726i	$-0.109320\pi$
$733$	4.85134	+	8.40276i	0.179188	+	0.310363i	−0.762414	+	0.647089i	$0.775986\pi$
$734$	−3.99415	−	6.91807i	−0.147427	−	0.255351i
$735$	3.80946	+	6.59818i	0.140514	+	0.243377i
$736$	−20.9211			−0.771162
$737$	−17.7388	+	30.7246i	−0.653418	+	1.13175i
$738$	−0.0886115	+	0.153480i	−0.00326183	+	0.00564966i
$739$	11.7931	+	20.4262i	0.433816	+	0.751391i	0.997198	−	0.0748050i	$-0.0238334\pi$
$739$	11.7931	+	20.4262i	0.433816	+	0.751391i	−0.563382	+	0.826196i	$0.690500\pi$
$740$	−34.2086			−1.25753
$741$	5.60118	−	9.70154i	0.205765	−	0.356395i
$742$	1.61236			0.0591916
$743$	27.2610			1.00011			0.500055	−	0.865994i	$-0.333313\pi$
$743$	27.2610			1.00011			0.500055	+	0.865994i	$0.333313\pi$
$744$	−9.92283	+	1.98004i	−0.363789	+	0.0725917i
$745$	−3.28370			−0.120305
$746$	6.71428			0.245827
$747$	−0.0424294	+	0.0734898i	−0.00155241	+	0.00268885i
$748$	−25.1673			−0.920207
$749$	0.203136	+	0.351842i	0.00742242	+	0.0128560i
$750$	0.0488182	−	0.0845555i	0.00178259	−	0.00308753i
$751$	−19.2721	+	33.3803i	−0.703249	+	1.21806i	0.264070	+	0.964503i	$0.414935\pi$
$751$	−19.2721	+	33.3803i	−0.703249	+	1.21806i	−0.967320	+	0.253560i	$0.918398\pi$
$752$	−34.3389			−1.25221
$753$	−9.51541	−	16.4812i	−0.346761	−	0.600608i
$754$	0.493947	+	0.855541i	0.0179885	+	0.0311570i
$755$	−17.6314	−	30.5385i	−0.641672	−	1.11141i
$756$	−12.0306	+	20.8376i	−0.437549	+	0.757857i
$757$	−25.6052	−	44.3496i	−0.930639	−	1.61191i	−0.782232	−	0.622987i	$-0.785919\pi$
$757$	−25.6052	−	44.3496i	−0.930639	−	1.61191i	−0.148406	−	0.988926i	$-0.547414\pi$
$758$	−3.34710	+	5.79735i	−0.121572	+	0.210569i
$759$	27.0357			0.981334
$760$	−22.3312			−0.810039
$761$	−5.39524	+	9.34482i	−0.195577	+	0.338750i	−0.947090	−	0.320969i	$-0.895991\pi$
$761$	−5.39524	+	9.34482i	−0.195577	+	0.338750i	0.751512	+	0.659719i	$0.229325\pi$
$762$	4.90088	+	8.48858i	0.177540	+	0.307509i
$763$	6.13606	−	10.6280i	0.222140	−	0.384759i
$764$	13.3118	+	23.0568i	0.481606	+	0.834165i
$765$	0.944409	+	1.63576i	0.0341452	+	0.0591412i
$766$	−1.21655	−	2.10712i	−0.0439556	−	0.0761333i
$767$	11.6461			0.420516
$768$	8.84126	−	15.3135i	0.319031	−	0.552579i
$769$	−20.5625	+	35.6153i	−0.741503	+	1.28432i	0.210307	+	0.977635i	$0.432554\pi$
$769$	−20.5625	+	35.6153i	−0.741503	+	1.28432i	−0.951811	+	0.306686i	$0.900780\pi$
$770$	−2.40916	−	4.17279i	−0.0868201	−	0.150377i
$771$	−5.25661			−0.189312
$772$	7.11924	−	12.3309i	0.256227	−	0.443798i
$773$	11.0581			0.397731			0.198866	−	0.980027i	$-0.436274\pi$
$773$	11.0581			0.397731			0.198866	+	0.980027i	$0.436274\pi$
$774$	−0.0201279			−0.000723483
$775$	27.6636	−	5.52009i	0.993705	−	0.198288i
$776$	−2.79601			−0.100371
$777$	−22.5073			−0.807445
$778$	0.228505	−	0.395782i	0.00819230	−	0.0141895i
$779$	39.8856			1.42905
$780$	5.19614	+	8.99998i	0.186052	+	0.322251i
$781$	−15.9997	+	27.7123i	−0.572514	+	0.991623i
$782$	−5.07447	+	8.78925i	−0.181463	+	0.314303i
$783$	19.1824			0.685522
$784$	2.51398	+	4.35433i	0.0897849	+	0.155512i
$785$	−6.79367	−	11.7670i	−0.242477	−	0.419982i
$786$	2.37971	+	4.12179i	0.0848816	+	0.147019i
$787$	3.58155	−	6.20343i	0.127668	−	0.221128i	−0.795104	−	0.606473i	$-0.792584\pi$
$787$	3.58155	−	6.20343i	0.127668	−	0.221128i	0.922773	+	0.385344i	$0.125917\pi$
$788$	13.1926	+	22.8502i	0.469967	+	0.814006i
$789$	−2.82547	+	4.89386i	−0.100589	+	0.174226i
$790$	15.2194			0.541482
$791$	−35.6754			−1.26847
$792$	−0.135600	+	0.234866i	−0.00481833	+	0.00834560i
$793$	2.51693	+	4.35946i	0.0893790	+	0.154809i
$794$	1.45069	−	2.51266i	0.0514829	−	0.0891711i
$795$	−6.76111	−	11.7106i	−0.239792	−	0.415331i
$796$	−18.6276	−	32.2640i	−0.660238	−	1.14357i
$797$	−3.58706	−	6.21297i	−0.127060	−	0.220075i	0.795476	−	0.605985i	$-0.207221\pi$
$797$	−3.58706	−	6.21297i	−0.127060	−	0.220075i	−0.922536	+	0.385910i	$0.873887\pi$
$798$	−7.20771			−0.255150
$799$	−26.6940	+	46.2354i	−0.944367	+	1.63569i
$800$	7.86914	−	13.6297i	0.278216	−	0.481884i
$801$	−0.686566	−	1.18917i	−0.0242586	−	0.0420171i
$802$	−9.12680			−0.322278
$803$	17.9337	−	31.0620i	0.632865	−	1.09615i
$804$	−49.2332			−1.73632
$805$	50.5129			1.78035
$806$	0.486250	−	1.43531i	0.0171274	−	0.0505566i
$807$	19.0755			0.671489
$808$	−12.0638			−0.424404
$809$	24.4599	−	42.3659i	0.859966	−	1.48950i	−0.0119944	−	0.999928i	$-0.503818\pi$
$809$	24.4599	−	42.3659i	0.859966	−	1.48950i	0.871960	−	0.489577i	$-0.162849\pi$
$810$	−7.48355			−0.262945
$811$	−21.2078	−	36.7331i	−0.744708	−	1.28987i	−0.950331	−	0.311241i	$-0.899255\pi$
$811$	−21.2078	−	36.7331i	−0.744708	−	1.28987i	0.205623	−	0.978631i	$-0.434078\pi$
$812$	−8.26210	+	14.3104i	−0.289943	+	0.502196i
$813$	13.8791	−	24.0392i	0.486760	−	0.843093i
$814$	−3.59654			−0.126059
$815$	0.816987	+	1.41506i	0.0286178	+	0.0495675i
$816$	−16.7651	−	29.0380i	−0.586895	−	1.01653i
$817$	2.26498	+	3.92306i	0.0792416	+	0.137251i
$818$	−0.733249	+	1.27002i	−0.0256375	+	0.0444054i
$819$	−0.127093	−	0.220132i	−0.00444099	−	0.00769202i
$820$	−18.5007	+	32.0441i	−0.646071	+	1.11903i
$821$	21.4936			0.750130			0.375065	−	0.926998i	$-0.377620\pi$
$821$	21.4936			0.750130			0.375065	+	0.926998i	$0.377620\pi$
$822$	5.26053			0.183482
$823$	20.8497	−	36.1127i	0.726774	−	1.25881i	−0.231466	−	0.972843i	$-0.574352\pi$
$823$	20.8497	−	36.1127i	0.726774	−	1.25881i	0.958240	−	0.285966i	$-0.0923146\pi$
$824$	−1.50421	−	2.60537i	−0.0524018	−	0.0907625i
$825$	−10.1690	+	17.6133i	−0.354040	+	0.613216i
$826$	−3.74661	−	6.48931i	−0.130361	−	0.225792i
$827$	−6.73947	−	11.6731i	−0.234354	−	0.405913i	0.724731	−	0.689032i	$-0.241964\pi$
$827$	−6.73947	−	11.6731i	−0.234354	−	0.405913i	−0.959085	+	0.283119i	$0.908631\pi$
$828$	−0.697370	−	1.20788i	−0.0242353	−	0.0419767i
$829$	−47.1647			−1.63810			−0.819049	−	0.573723i	$-0.805498\pi$
$829$	−47.1647			−1.63810			−0.819049	+	0.573723i	$0.805498\pi$
$830$	0.340754	−	0.590204i	0.0118278	−	0.0204863i
$831$	1.70052	−	2.94539i	0.0589904	−	0.102174i
$832$	3.13825	+	5.43561i	0.108799	+	0.188446i
$833$	7.81717			0.270849
$834$	2.55983	−	4.43376i	0.0886397	−	0.153528i
$835$	8.94590			0.309586
$836$	29.9421			1.03557
$837$	−19.4153	−	22.1118i	−0.671091	−	0.764296i
$838$	8.70683			0.300772
$839$	−21.4033			−0.738924			−0.369462	−	0.929246i	$-0.620458\pi$
$839$	−21.4033			−0.738924			−0.369462	+	0.929246i	$0.620458\pi$
$840$	6.81510	−	11.8041i	0.235143	−	0.407280i
$841$	−15.8264			−0.545737
$842$	−4.75521	−	8.23626i	−0.163875	−	0.283840i
$843$	−10.7449	+	18.6107i	−0.370073	+	0.640985i
$844$	−3.68666	+	6.38549i	−0.126900	+	0.219798i
$845$	−3.17277			−0.109147
$846$	0.141112	+	0.244413i	0.00485153	+	0.00840310i
$847$	−6.41674	−	11.1141i	−0.220482	−	0.381886i
$848$	−4.46186	−	7.72816i	−0.153221	−	0.265386i
$849$	−7.45448	+	12.9115i	−0.255837	+	0.443123i
$850$	−3.81736	−	6.61187i	−0.130934	−	0.226785i
$851$	18.8522	−	32.6530i	0.646246	−	1.11933i
$852$	−44.4063			−1.52134
$853$	46.4072			1.58895			0.794476	−	0.607296i	$-0.207746\pi$
$853$	46.4072			1.58895			0.794476	+	0.607296i	$0.207746\pi$
$854$	1.61942	−	2.80492i	0.0554154	−	0.0959823i
$855$	−1.12358	−	1.94611i	−0.0384258	−	0.0665554i
$856$	−0.0918238	+	0.159043i	−0.00313847	+	0.00543599i
$857$	−26.3248	−	45.5958i	−0.899237	−	1.55752i	−0.828472	−	0.560031i	$-0.810789\pi$
$857$	−26.3248	−	45.5958i	−0.899237	−	1.55752i	−0.0707647	−	0.997493i	$-0.522544\pi$
$858$	0.546300	+	0.946219i	0.0186504	+	0.0323034i
$859$	−17.0522	−	29.5352i	−0.581812	−	1.00773i	−0.995265	−	0.0972028i	$-0.969010\pi$
$859$	−17.0522	−	29.5352i	−0.581812	−	1.00773i	0.413452	−	0.910526i	$-0.364323\pi$
$860$	−4.20238			−0.143300
$861$	−12.1724	+	21.0832i	−0.414834	+	0.718513i
$862$	−1.33833	+	2.31806i	−0.0455838	+	0.0789535i
$863$	11.9874	+	20.7627i	0.408054	+	0.706771i	0.994672	−	0.103093i	$-0.0328740\pi$
$863$	11.9874	+	20.7627i	0.408054	+	0.706771i	−0.586617	+	0.809864i	$0.699541\pi$
$864$	−16.4173			−0.558526
$865$	−0.845657	+	1.46472i	−0.0287532	+	0.0498020i
$866$	2.87498			0.0976958
$867$	−23.2184			−0.788537
$868$	24.8582	−	4.96030i	0.843743	−	0.168364i
$869$	−41.5978			−1.41111
$870$	−5.33069			−0.180727
$871$	7.51547	−	13.0172i	0.254652	−	0.441070i
$872$	5.54739			0.187858
$873$	−0.140680	−	0.243664i	−0.00476129	−	0.00824679i
$874$	6.03722	−	10.4568i	0.204212	−	0.353705i
$875$	−0.249298	+	0.431797i	−0.00842782	+	0.0145974i
$876$	49.7740			1.68171
$877$	27.4158	+	47.4856i	0.925766	+	1.60347i	0.790325	+	0.612688i	$0.209912\pi$
$877$	27.4158	+	47.4856i	0.925766	+	1.60347i	0.135441	+	0.990785i	$0.456755\pi$
$878$	−0.496572	−	0.860088i	−0.0167585	−	0.0290265i
$879$	17.6662	+	30.5987i	0.595865	+	1.03207i
$880$	−13.3337	+	23.0946i	−0.449477	+	0.778518i
$881$	13.8695	+	24.0226i	0.467274	+	0.809343i	0.999301	−	0.0373849i	$-0.0119027\pi$
$881$	13.8695	+	24.0226i	0.467274	+	0.809343i	−0.532027	+	0.846728i	$0.678569\pi$
$882$	0.0206619	−	0.0357874i	0.000695721	−	0.00120502i
$883$	35.7790			1.20406			0.602029	−	0.798474i	$-0.294359\pi$
$883$	35.7790			1.20406			0.602029	+	0.798474i	$0.294359\pi$
$884$	10.6627			0.358625
$885$	−31.4213	+	54.4232i	−1.05621	+	1.82942i
$886$	5.12768	+	8.88140i	0.172268	+	0.298376i
$887$	−1.43864	+	2.49180i	−0.0483048	+	0.0836664i	−0.889167	−	0.457583i	$-0.848715\pi$
$887$	−1.43864	+	2.49180i	−0.0483048	+	0.0836664i	0.840862	+	0.541250i	$0.182049\pi$
$888$	−5.08700	−	8.81095i	−0.170709	−	0.295676i
$889$	−25.0272	−	43.3484i	−0.839385	−	1.45386i
$890$	5.51387	+	9.55030i	0.184825	+	0.320127i
$891$	20.4541			0.685238
$892$	0.679616	−	1.17713i	0.0227552	−	0.0394132i
$893$	31.7585	−	55.0073i	1.06276	−	1.84075i
$894$	−0.239545	−	0.414904i	−0.00801158	−	0.0138765i
$895$	6.20157			0.207296
$896$	9.36231	−	16.2160i	0.312773	−	0.541738i
$897$	−11.4543			−0.382448
$898$	0.386753			0.0129061
$899$	−13.3336	−	15.1854i	−0.444700	−	0.506463i
$900$	1.04922			0.0349739
$901$	−13.8741			−0.462212
$902$	−1.94508	+	3.36898i	−0.0647641	+	0.112175i
$903$	−2.76493			−0.0920111
$904$	−8.06321	−	13.9659i	−0.268178	−	0.464498i
$905$	−17.5379	+	30.3766i	−0.582980	+	1.00975i
$906$	2.57241	−	4.45554i	0.0854625	−	0.148025i
$907$	−22.2470			−0.738701			−0.369350	−	0.929290i	$-0.620420\pi$
$907$	−22.2470			−0.738701			−0.369350	+	0.929290i	$0.620420\pi$
$908$	18.0830	+	31.3206i	0.600104	+	1.03941i
$909$	−0.606985	−	1.05133i	−0.0201324	−	0.0348704i
$910$	1.02070	+	1.76790i	0.0338357	+	0.0586052i
$911$	−12.4224	+	21.5163i	−0.411574	+	0.712866i	−0.995062	−	0.0992550i	$-0.968354\pi$
$911$	−12.4224	+	21.5163i	−0.411574	+	0.712866i	0.583488	+	0.812121i	$0.301687\pi$
$912$	19.9458	+	34.5471i	0.660471	+	1.14397i
$913$	−0.931352	+	1.61315i	−0.0308233	+	0.0533875i
$914$	5.65658			0.187103
$915$	−27.1628			−0.897976
$916$	−8.19773	+	14.1989i	−0.270861	+	0.469144i
$917$	−12.1524	−	21.0486i	−0.401308	−	0.695086i
$918$	−3.98205	+	6.89711i	−0.131427	+	0.227639i
$919$	−25.4833	−	44.1384i	−0.840616	−	1.45599i	−0.889374	−	0.457179i	$-0.848860\pi$
$919$	−25.4833	−	44.1384i	−0.840616	−	1.45599i	0.0487582	−	0.998811i	$-0.484474\pi$
$920$	11.4167	+	19.7743i	0.376398	+	0.651941i
$921$	−2.20241	−	3.81468i	−0.0725718	−	0.125698i
$922$	2.64265			0.0870312
$923$	6.77864	−	11.7409i	0.223122	−	0.386458i
$924$	−9.13780	+	15.8271i	−0.300611	+	0.520674i
$925$	14.1819	+	24.5638i	0.466298	+	0.807653i
$926$	4.98727			0.163892
$927$	0.151367	−	0.262176i	0.00497156	−	0.00861099i
$928$	−11.2747			−0.370109
$929$	25.3599			0.832031			0.416016	−	0.909357i	$-0.363426\pi$
$929$	25.3599			0.832031			0.416016	+	0.909357i	$0.363426\pi$
$930$	5.39542	+	6.14477i	0.176923	+	0.201495i
$931$	−9.30026			−0.304804
$932$	−15.6880			−0.513877
$933$	15.2243	−	26.3693i	0.498422	−	0.863292i
$934$	−1.38316			−0.0452585
$935$	20.7304	+	35.9061i	0.677956	+	1.17425i
$936$	0.0574501	−	0.0995064i	0.00187781	−	0.00325247i
$937$	−10.3037	+	17.8466i	−0.336609	+	0.583023i	−0.983793	−	0.179311i	$-0.942613\pi$
$937$	−10.3037	+	17.8466i	−0.336609	+	0.583023i	0.647184	+	0.762334i	$0.275947\pi$
$938$	−9.67105			−0.315771
$939$	2.52900	+	4.38036i	0.0825309	+	0.142948i
$940$	29.4619	+	51.0295i	0.960942	+	1.66440i
$941$	−13.2061	−	22.8737i	−0.430507	−	0.745660i	0.566410	−	0.824124i	$-0.308332\pi$
$941$	−13.2061	−	22.8737i	−0.430507	−	0.745660i	−0.996917	+	0.0784638i	$0.974999\pi$
$942$	0.991192	−	1.71680i	0.0322948	−	0.0559362i
$943$	−20.3913	−	35.3188i	−0.664032	−	1.15014i
$944$	−20.7358	+	35.9155i	−0.674894	+	1.16895i
$945$	39.6386			1.28944
$946$	−0.441821			−0.0143648
$947$	−1.00599	+	1.74243i	−0.0326904	+	0.0566214i	−0.881908	−	0.471422i	$-0.843741\pi$
$947$	−1.00599	+	1.74243i	−0.0326904	+	0.0566214i	0.849217	+	0.528043i	$0.177074\pi$
$948$	−28.8631	−	49.9924i	−0.937431	−	1.62368i
$949$	−7.59801	+	13.1601i	−0.246642	+	0.427196i
$950$	4.54160	+	7.86628i	0.147349	+	0.255216i
$951$	−0.551794	−	0.955734i	−0.0178931	−	0.0309918i
$952$	−6.99243	−	12.1113i	−0.226626	−	0.392528i
$953$	−55.4104			−1.79492			−0.897460	−	0.441096i	$-0.854590\pi$
$953$	−55.4104			−1.79492			−0.897460	+	0.441096i	$0.854590\pi$
$954$	−0.0366711	+	0.0635162i	−0.00118727	+	0.00205641i
$955$	21.9300	−	37.9839i	0.709639	−	1.22913i
$956$	−9.79381	−	16.9634i	−0.316754	−	0.548635i
$957$	14.5699			0.470978
$958$	−5.40845	+	9.36771i	−0.174739	+	0.302657i
$959$	−26.8638			−0.867477
$960$	−33.8681			−1.09309
$961$	−4.00898	+	30.7397i	−0.129322	+	0.991603i
$962$	1.52376			0.0491280
$963$	−0.0184803			−0.000595518
$964$	19.4312	−	33.6558i	0.625835	−	1.08398i
$965$	−23.4566			−0.755094
$966$	3.68490	+	6.38244i	0.118560	+	0.205352i
$967$	−6.90872	+	11.9662i	−0.222169	+	0.384809i	−0.955466	−	0.295100i	$-0.904647\pi$
$967$	−6.90872	+	11.9662i	−0.222169	+	0.384809i	0.733297	+	0.679908i	$0.237980\pi$
$968$	2.90057	−	5.02394i	0.0932279	−	0.161475i
$969$	62.0211			1.99240
$970$	1.12981	+	1.95689i	0.0362761	+	0.0628320i
$971$	−15.2204	−	26.3625i	−0.488445	−	0.846011i	0.511467	−	0.859303i	$-0.329102\pi$
$971$	−15.2204	−	26.3625i	−0.488445	−	0.846011i	−0.999912	+	0.0132916i	$0.995769\pi$
$972$	−1.07555	−	1.86290i	−0.0344982	−	0.0597526i
$973$	−13.0722	+	22.6417i	−0.419076	+	0.725861i
$974$	−0.546139	−	0.945940i	−0.0174994	−	0.0303099i
$975$	4.30835	−	7.46228i	0.137978	−	0.238984i
$976$	−17.9256			−0.573784
$977$	−43.8979			−1.40442			−0.702210	−	0.711970i	$-0.747803\pi$
$977$	−43.8979			−1.40442			−0.702210	+	0.711970i	$0.747803\pi$
$978$	−0.119198	+	0.206457i	−0.00381153	+	0.00660176i
$979$	−15.0706	−	26.1030i	−0.481657	−	0.834255i
$980$	4.31386	−	7.47183i	0.137801	−	0.238679i
$981$	0.279114	+	0.483440i	0.00891142	+	0.0154350i
$982$	−3.79774	−	6.57787i	−0.121191	−	0.209908i
$983$	23.0379	+	39.9029i	0.734796	+	1.27270i	0.954813	+	0.297207i	$0.0960553\pi$
$983$	23.0379	+	39.9029i	0.734796	+	1.27270i	−0.220017	+	0.975496i	$0.570611\pi$
$984$	−11.0046			−0.350814
$985$	21.7336	−	37.6437i	0.692490	−	1.19943i
$986$	−2.73470	+	4.73664i	−0.0870906	+	0.150845i
$987$	19.3843	+	33.5745i	0.617008	+	1.06869i
$988$	−12.6857			−0.403585
$989$	2.31592	−	4.01129i	0.0736419	−	0.127552i
$990$	0.219173			0.00696578
$991$	−24.6163			−0.781961			−0.390981	−	0.920399i	$-0.627864\pi$
$991$	−24.6163			−0.781961			−0.390981	+	0.920399i	$0.627864\pi$
$992$	11.4116	+	12.9965i	0.362318	+	0.412639i
$993$	−18.7029			−0.593520
$994$	−8.72288			−0.276673
$995$	−30.6873	+	53.1519i	−0.972852	+	1.68503i
$996$	−2.58492			−0.0819063
$997$	6.66112	+	11.5374i	0.210960	+	0.365393i	0.952015	−	0.306051i	$-0.0990078\pi$
$997$	6.66112	+	11.5374i	0.210960	+	0.365393i	−0.741055	+	0.671444i	$0.765674\pi$
$998$	1.46550	−	2.53832i	0.0463897	−	0.0803492i
$999$	14.7938	−	25.6235i	0.468054	−	0.810693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.222.9	yes	34
31.25	even	3	inner	403.2.h.b.118.9	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.9	✓	34	31.25	even	3	inner
403.2.h.b.222.9	yes	34	1.1	even	1	trivial

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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.272181 q^{2} +(0.850363 - 1.47287i) q^{3} -1.92592 q^{4} +(1.58639 + 2.74770i) q^{5} +(-0.231453 + 0.400888i) q^{6} +(1.18195 - 2.04720i) q^{7} +1.06856 q^{8} +(0.0537640 + 0.0931220i) q^{9} +O(q^{10})\)	\(q-0.272181 q^{2} +(0.850363 - 1.47287i) q^{3} -1.92592 q^{4} +(1.58639 + 2.74770i) q^{5} +(-0.231453 + 0.400888i) q^{6} +(1.18195 - 2.04720i) q^{7} +1.06856 q^{8} +(0.0537640 + 0.0931220i) q^{9} +(-0.431784 - 0.747872i) q^{10} +(1.18016 + 2.04409i) q^{11} +(-1.63773 + 2.83663i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-0.321705 + 0.557209i) q^{14} +5.39602 q^{15} +3.56099 q^{16} +(2.76821 - 4.79469i) q^{17} +(-0.0146335 - 0.0253460i) q^{18} +(-3.29341 + 5.70435i) q^{19} +(-3.05525 - 5.29184i) q^{20} +(-2.01018 - 3.48173i) q^{21} +(-0.321216 - 0.556362i) q^{22} +6.73494 q^{23} +(0.908664 - 1.57385i) q^{24} +(-2.53324 + 4.38770i) q^{25} +(0.136090 + 0.235716i) q^{26} +5.28506 q^{27} +(-2.27634 + 3.94274i) q^{28} +3.62955 q^{29} -1.46869 q^{30} +(-3.67362 - 4.18384i) q^{31} -3.10635 q^{32} +4.01424 q^{33} +(-0.753455 + 1.30502i) q^{34} +7.50013 q^{35} +(-0.103545 - 0.179345i) q^{36} +(2.79917 - 4.84830i) q^{37} +(0.896402 - 1.55261i) q^{38} -1.70073 q^{39} +(1.69515 + 2.93608i) q^{40} +(-3.02769 - 5.24411i) q^{41} +(0.547132 + 0.947661i) q^{42} +(0.343866 - 0.595593i) q^{43} +(-2.27288 - 3.93675i) q^{44} +(-0.170581 + 0.295455i) q^{45} -1.83312 q^{46} -9.64305 q^{47} +(3.02814 - 5.24489i) q^{48} +(0.705976 + 1.22279i) q^{49} +(0.689499 - 1.19425i) q^{50} +(-4.70798 - 8.15445i) q^{51} +(0.962959 + 1.66789i) q^{52} +(-1.25298 - 2.17023i) q^{53} -1.43849 q^{54} +(-3.74436 + 6.48543i) q^{55} +(1.26299 - 2.18756i) q^{56} +(5.60118 + 9.70154i) q^{57} -0.987894 q^{58} +(-5.82305 + 10.0858i) q^{59} -10.3923 q^{60} -5.03387 q^{61} +(0.999890 + 1.13876i) q^{62} +0.254186 q^{63} -6.27650 q^{64} +(1.58639 - 2.74770i) q^{65} -1.09260 q^{66} +(7.51547 + 13.0172i) q^{67} +(-5.33135 + 9.23417i) q^{68} +(5.72715 - 9.91971i) q^{69} -2.04139 q^{70} +(6.77864 + 11.7409i) q^{71} +(0.0574501 + 0.0995064i) q^{72} +(-7.59801 - 13.1601i) q^{73} +(-0.761879 + 1.31961i) q^{74} +(4.30835 + 7.46228i) q^{75} +(6.34283 - 10.9861i) q^{76} +5.57955 q^{77} +0.462905 q^{78} +(-8.81193 + 15.2627i) q^{79} +(5.64911 + 9.78454i) q^{80} +(4.33293 - 7.50485i) q^{81} +(0.824078 + 1.42735i) q^{82} +(0.394589 + 0.683448i) q^{83} +(3.87144 + 6.70553i) q^{84} +17.5658 q^{85} +(-0.0935937 + 0.162109i) q^{86} +(3.08644 - 5.34586i) q^{87} +(1.26107 + 2.18423i) q^{88} -12.7700 q^{89} +(0.0464289 - 0.0804172i) q^{90} -2.36391 q^{91} -12.9709 q^{92} +(-9.28617 + 1.85300i) q^{93} +2.62465 q^{94} -20.8984 q^{95} +(-2.64153 + 4.57526i) q^{96} -2.61661 q^{97} +(-0.192153 - 0.332819i) q^{98} +(-0.126900 + 0.219797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more