LMFDB - Embedded newform 804.2.c.b.671.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.3
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40995 - 0.109793i) q^{2} +(-0.420694 - 1.68018i) q^{3} +(1.97589 + 0.309604i) q^{4} -0.933302i q^{5} +(0.408683 + 2.41516i) q^{6} +1.91511i q^{7} +(-2.75191 - 0.653464i) q^{8} +(-2.64603 + 1.41369i) q^{9} +O(q^{10})$	\(q+(-1.40995 - 0.109793i) q^{2} +(-0.420694 - 1.68018i) q^{3} +(1.97589 + 0.309604i) q^{4} -0.933302i q^{5} +(0.408683 + 2.41516i) q^{6} +1.91511i q^{7} +(-2.75191 - 0.653464i) q^{8} +(-2.64603 + 1.41369i) q^{9} +(-0.102470 + 1.31591i) q^{10} -1.29586 q^{11} +(-0.311053 - 3.45011i) q^{12} +3.83589 q^{13} +(0.210266 - 2.70021i) q^{14} +(-1.56812 + 0.392634i) q^{15} +(3.80829 + 1.22349i) q^{16} +7.71164i q^{17} +(3.88597 - 1.70270i) q^{18} +0.375504i q^{19} +(0.288954 - 1.84410i) q^{20} +(3.21774 - 0.805677i) q^{21} +(1.82709 + 0.142276i) q^{22} +1.08412 q^{23} +(0.0597709 + 4.89861i) q^{24} +4.12895 q^{25} +(-5.40840 - 0.421154i) q^{26} +(3.48842 + 3.85109i) q^{27} +(-0.592927 + 3.78406i) q^{28} -3.74170i q^{29} +(2.25407 - 0.381425i) q^{30} +8.96952i q^{31} +(-5.23515 - 2.14317i) q^{32} +(0.545160 + 2.17728i) q^{33} +(0.846683 - 10.8730i) q^{34} +1.78738 q^{35} +(-5.66596 + 1.97407i) q^{36} -7.86919 q^{37} +(0.0412277 - 0.529440i) q^{38} +(-1.61374 - 6.44500i) q^{39} +(-0.609879 + 2.56836i) q^{40} +7.73078i q^{41} +(-4.62530 + 0.782674i) q^{42} -7.24655i q^{43} +(-2.56048 - 0.401203i) q^{44} +(1.31940 + 2.46955i) q^{45} +(-1.52855 - 0.119029i) q^{46} +11.3216 q^{47} +(0.453560 - 6.91334i) q^{48} +3.33234 q^{49} +(-5.82159 - 0.453329i) q^{50} +(12.9570 - 3.24424i) q^{51} +(7.57930 + 1.18761i) q^{52} -5.24766i q^{53} +(-4.49566 - 5.81283i) q^{54} +1.20943i q^{55} +(1.25146 - 5.27021i) q^{56} +(0.630915 - 0.157972i) q^{57} +(-0.410812 + 5.27559i) q^{58} -0.895292 q^{59} +(-3.21999 + 0.290307i) q^{60} -12.6762 q^{61} +(0.984790 - 12.6465i) q^{62} +(-2.70737 - 5.06746i) q^{63} +(7.14597 + 3.59654i) q^{64} -3.58005i q^{65} +(-0.529596 - 3.12970i) q^{66} -1.00000i q^{67} +(-2.38755 + 15.2374i) q^{68} +(-0.456083 - 1.82152i) q^{69} +(-2.52011 - 0.196242i) q^{70} +12.8894 q^{71} +(8.20543 - 2.16124i) q^{72} +8.12415 q^{73} +(11.0951 + 0.863981i) q^{74} +(-1.73702 - 6.93739i) q^{75} +(-0.116258 + 0.741955i) q^{76} -2.48172i q^{77} +(1.56766 + 9.26427i) q^{78} +10.3413i q^{79} +(1.14188 - 3.55429i) q^{80} +(5.00299 - 7.48132i) q^{81} +(0.848785 - 10.9000i) q^{82} +12.4637 q^{83} +(6.60735 - 0.595703i) q^{84} +7.19729 q^{85} +(-0.795620 + 10.2172i) q^{86} +(-6.28674 + 1.57411i) q^{87} +(3.56608 + 0.846797i) q^{88} -2.29328i q^{89} +(-1.58914 - 3.62679i) q^{90} +7.34617i q^{91} +(2.14211 + 0.335649i) q^{92} +(15.0704 - 3.77342i) q^{93} +(-15.9628 - 1.24303i) q^{94} +0.350459 q^{95} +(-1.39853 + 9.69763i) q^{96} -2.62800 q^{97} +(-4.69841 - 0.365867i) q^{98} +(3.42889 - 1.83194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.40995	−	0.109793i	−0.996982	−	0.0776353i
$2$	−1.40995	−	0.109793i	−0.996982	−	0.0776353i
$3$	−0.420694	−	1.68018i	−0.242888	−	0.970054i
$3$	−0.420694	−	1.68018i	−0.242888	−	0.970054i
$4$	1.97589	+	0.309604i	0.987946	+	0.154802i
$5$		−	0.933302i		−	0.417385i	−0.977981	−	0.208693i	$-0.933079\pi$
$5$		−	0.933302i		−	0.417385i	0.977981	−	0.208693i	$-0.0669209\pi$
$6$	0.408683	+	2.41516i	0.166844	+	0.985983i
$7$			1.91511i			0.723845i	0.932208	+	0.361923i	$0.117880\pi$
$7$			1.91511i			0.723845i	−0.932208	+	0.361923i	$0.882120\pi$
$8$	−2.75191	−	0.653464i	−0.972946	−	0.231034i
$9$	−2.64603	+	1.41369i	−0.882011	+	0.471229i
$10$	−0.102470	+	1.31591i	−0.0324039	+	0.416126i
$11$	−1.29586			−0.390716			−0.195358	−	0.980732i	$-0.562587\pi$
$11$	−1.29586			−0.390716			−0.195358	+	0.980732i	$0.562587\pi$
$12$	−0.311053	−	3.45011i	−0.0897934	−	0.995960i
$13$	3.83589			1.06388			0.531942	−	0.846781i	$-0.321462\pi$
$13$	3.83589			1.06388			0.531942	+	0.846781i	$0.321462\pi$
$14$	0.210266	−	2.70021i	0.0561959	−	0.721660i
$15$	−1.56812	+	0.392634i	−0.404887	+	0.101378i
$16$	3.80829	+	1.22349i	0.952073	+	0.305872i
$17$			7.71164i			1.87035i	0.354190	+	0.935173i	$0.384756\pi$
$17$			7.71164i			1.87035i	−0.354190	+	0.935173i	$0.615244\pi$
$18$	3.88597	−	1.70270i	0.915933	−	0.401331i
$19$			0.375504i			0.0861465i	0.999072	+	0.0430732i	$0.0137149\pi$
$19$			0.375504i			0.0861465i	−0.999072	+	0.0430732i	$0.986285\pi$
$20$	0.288954	−	1.84410i	0.0646121	−	0.412354i
$21$	3.21774	−	0.805677i	0.702169	−	0.175813i
$22$	1.82709	+	0.142276i	0.389537	+	0.0303334i
$23$	1.08412			0.226055			0.113028	−	0.993592i	$-0.463945\pi$
$23$	1.08412			0.226055			0.113028	+	0.993592i	$0.463945\pi$
$24$	0.0597709	+	4.89861i	0.0122007	+	0.999926i
$25$	4.12895			0.825789
$26$	−5.40840	−	0.421154i	−1.06067	−	0.0825950i
$27$	3.48842	+	3.85109i	0.671347	+	0.741143i
$28$	−0.592927	+	3.78406i	−0.112053	+	0.715120i
$29$		−	3.74170i		−	0.694816i	−0.937714	−	0.347408i	$-0.887062\pi$
$29$		−	3.74170i		−	0.694816i	0.937714	−	0.347408i	$-0.112938\pi$
$30$	2.25407	−	0.381425i	0.411535	−	0.0696383i
$31$			8.96952i			1.61097i	0.592613	+	0.805487i	$0.298096\pi$
$31$			8.96952i			1.61097i	−0.592613	+	0.805487i	$0.701904\pi$
$32$	−5.23515	−	2.14317i	−0.925453	−	0.378863i
$33$	0.545160	+	2.17728i	0.0949002	+	0.379016i
$34$	0.846683	−	10.8730i	0.145205	−	1.86470i
$35$	1.78738			0.302122
$36$	−5.66596	+	1.97407i	−0.944326	+	0.329011i
$37$	−7.86919			−1.29369			−0.646843	−	0.762623i	$-0.723911\pi$
$37$	−7.86919			−1.29369			−0.646843	+	0.762623i	$0.723911\pi$
$38$	0.0412277	−	0.529440i	0.00668801	−	0.0858865i
$39$	−1.61374	−	6.44500i	−0.258404	−	1.03203i
$40$	−0.609879	+	2.56836i	−0.0964303	+	0.406093i
$41$			7.73078i			1.20735i	0.797232	+	0.603673i	$0.206297\pi$
$41$			7.73078i			1.20735i	−0.797232	+	0.603673i	$0.793703\pi$
$42$	−4.62530	+	0.782674i	−0.713699	+	0.120769i
$43$		−	7.24655i		−	1.10509i	−0.833483	−	0.552545i	$-0.813657\pi$
$43$		−	7.24655i		−	1.10509i	0.833483	−	0.552545i	$-0.186343\pi$
$44$	−2.56048	−	0.401203i	−0.386007	−	0.0604837i
$45$	1.31940	+	2.46955i	0.196684	+	0.368139i
$46$	−1.52855	−	0.119029i	−0.225373	−	0.0175499i
$47$	11.3216			1.65142			0.825712	−	0.564092i	$-0.190774\pi$
$47$	11.3216			1.65142			0.825712	+	0.564092i	$0.190774\pi$
$48$	0.453560	−	6.91334i	0.0654657	−	0.997855i
$49$	3.33234			0.476048
$50$	−5.82159	−	0.453329i	−0.823297	−	0.0641104i
$51$	12.9570	−	3.24424i	1.81434	−	0.454284i
$52$	7.57930	+	1.18761i	1.05106	+	0.164691i
$53$		−	5.24766i		−	0.720822i	−0.932794	−	0.360411i	$-0.882637\pi$
$53$		−	5.24766i		−	0.720822i	0.932794	−	0.360411i	$-0.117363\pi$
$54$	−4.49566	−	5.81283i	−0.611782	−	0.791027i
$55$			1.20943i			0.163079i
$56$	1.25146	−	5.27021i	0.167233	−	0.704262i
$57$	0.630915	−	0.157972i	0.0835668	−	0.0209239i
$58$	−0.410812	+	5.27559i	−0.0539423	+	0.692719i
$59$	−0.895292			−0.116557			−0.0582786	−	0.998300i	$-0.518561\pi$
$59$	−0.895292			−0.116557			−0.0582786	+	0.998300i	$0.518561\pi$
$60$	−3.21999	+	0.290307i	−0.415699	+	0.0374785i
$61$	−12.6762			−1.62302			−0.811508	−	0.584341i	$-0.801353\pi$
$61$	−12.6762			−1.62302			−0.811508	+	0.584341i	$0.801353\pi$
$62$	0.984790	−	12.6465i	0.125068	−	1.60611i
$63$	−2.70737	−	5.06746i	−0.341096	−	0.638439i
$64$	7.14597	+	3.59654i	0.893246	+	0.449568i
$65$		−	3.58005i		−	0.444050i
$66$	−0.529596	−	3.12970i	−0.0651887	−	0.385240i
$67$		−	1.00000i		−	0.122169i
$67$		−	1.00000i		−	0.122169i
$68$	−2.38755	+	15.2374i	−0.289533	+	1.84780i
$69$	−0.456083	−	1.82152i	−0.0549060	−	0.219286i
$70$	−2.52011	−	0.196242i	−0.301211	−	0.0234554i
$71$	12.8894			1.52969			0.764844	−	0.644216i	$-0.222816\pi$
$71$	12.8894			1.52969			0.764844	+	0.644216i	$0.222816\pi$
$72$	8.20543	−	2.16124i	0.967019	−	0.254705i
$73$	8.12415			0.950860			0.475430	−	0.879754i	$-0.342292\pi$
$73$	8.12415			0.950860			0.475430	+	0.879754i	$0.342292\pi$
$74$	11.0951	+	0.863981i	1.28978	+	0.100436i
$75$	−1.73702	−	6.93739i	−0.200574	−	0.801061i
$76$	−0.116258	+	0.741955i	−0.0133357	+	0.0851080i
$77$		−	2.48172i		−	0.282818i
$78$	1.56766	+	9.26427i	0.177503	+	1.04897i
$79$			10.3413i			1.16349i	0.813371	+	0.581746i	$0.197630\pi$
$79$			10.3413i			1.16349i	−0.813371	+	0.581746i	$0.802370\pi$
$80$	1.14188	−	3.55429i	0.127666	−	0.397381i
$81$	5.00299	−	7.48132i	0.555887	−	0.831258i
$82$	0.848785	−	10.9000i	0.0937326	−	1.20370i
$83$	12.4637			1.36807			0.684035	−	0.729450i	$-0.260224\pi$
$83$	12.4637			1.36807			0.684035	+	0.729450i	$0.260224\pi$
$84$	6.60735	−	0.595703i	0.720921	−	0.0649965i
$85$	7.19729			0.780656
$86$	−0.795620	+	10.2172i	−0.0857939	+	1.10175i
$87$	−6.28674	+	1.57411i	−0.674009	+	0.168762i
$88$	3.56608	+	0.846797i	0.380146	+	0.0902689i
$89$		−	2.29328i		−	0.243087i	−0.992586	−	0.121543i	$-0.961216\pi$
$89$		−	2.29328i		−	0.243087i	0.992586	−	0.121543i	$-0.0387844\pi$
$90$	−1.58914	−	3.62679i	−0.167510	−	0.382297i
$91$			7.34617i			0.770088i
$92$	2.14211	+	0.335649i	0.223330	+	0.0349938i
$93$	15.0704	−	3.77342i	1.56273	−	0.391286i
$94$	−15.9628	−	1.24303i	−1.64644	−	0.128209i
$95$	0.350459			0.0359563
$96$	−1.39853	+	9.69763i	−0.142737	+	0.989761i
$97$	−2.62800			−0.266833			−0.133417	−	0.991060i	$-0.542595\pi$
$97$	−2.62800			−0.266833			−0.133417	+	0.991060i	$0.542595\pi$
$98$	−4.69841	−	0.365867i	−0.474611	−	0.0369582i
$99$	3.42889	−	1.83194i	0.344616	−	0.184117i
$100$	8.15835	+	1.27834i	0.815835	+	0.127834i
$101$			10.6137i			1.05610i	0.849212	+	0.528052i	$0.177077\pi$
$101$			10.6137i			1.05610i	−0.849212	+	0.528052i	$0.822923\pi$
$102$	−18.6248	+	3.15161i	−1.84413	+	0.312056i
$103$			3.79342i			0.373776i	0.982381	+	0.186888i	$0.0598402\pi$
$103$			3.79342i			0.373776i	−0.982381	+	0.186888i	$0.940160\pi$
$104$	−10.5560	−	2.50661i	−1.03510	−	0.245794i
$105$	−0.751940	−	3.00313i	−0.0733818	−	0.293075i
$106$	−0.576156	+	7.39891i	−0.0559612	+	0.718646i
$107$	8.96867			0.867035			0.433517	−	0.901145i	$-0.357272\pi$
$107$	8.96867			0.867035			0.433517	+	0.901145i	$0.357272\pi$
$108$	5.70043	+	8.68937i	0.548524	+	0.836135i
$109$	9.06897			0.868649			0.434325	−	0.900756i	$-0.356987\pi$
$109$	9.06897			0.868649			0.434325	+	0.900756i	$0.356987\pi$
$110$	0.132787	−	1.70523i	0.0126607	−	0.162587i
$111$	3.31052	+	13.2217i	0.314221	+	1.25495i
$112$	−2.34312	+	7.29331i	−0.221404	+	0.689153i
$113$		−	3.41933i		−	0.321664i	−0.986982	−	0.160832i	$-0.948582\pi$
$113$		−	3.41933i		−	0.321664i	0.986982	−	0.160832i	$-0.0514177\pi$
$114$	−0.906900	+	0.153462i	−0.0849390	+	0.0143730i
$115$		−	1.01181i		−	0.0943521i
$116$	1.15845	−	7.39319i	0.107559	−	0.686440i
$117$	−10.1499	+	5.42274i	−0.938358	+	0.501333i
$118$	1.26231	+	0.0982967i	0.116205	+	0.00904895i
$119$	−14.7687			−1.35384
$120$	4.57189	−	0.0557844i	0.417354	−	0.00509239i
$121$	−9.32075			−0.847341
$122$	17.8727	+	1.39175i	1.61812	+	0.126003i
$123$	12.9891	−	3.25229i	1.17119	−	0.293249i
$124$	−2.77700	+	17.7228i	−0.249382	+	1.59155i
$125$		−	8.52007i		−	0.762058i
$126$	3.26087	+	7.44209i	0.290502	+	0.662994i
$127$		−	8.07104i		−	0.716189i	−0.933685	−	0.358095i	$-0.883427\pi$
$127$		−	8.07104i		−	0.716189i	0.933685	−	0.358095i	$-0.116573\pi$
$128$	−9.68055	−	5.85550i	−0.855648	−	0.517558i
$129$	−12.1755	+	3.04858i	−1.07200	+	0.268413i
$130$	−0.393064	+	5.04767i	−0.0344740	+	0.442710i
$131$	−19.5624			−1.70918			−0.854588	−	0.519306i	$-0.826190\pi$
$131$	−19.5624			−1.70918			−0.854588	+	0.519306i	$0.826190\pi$
$132$	0.403082	+	4.47086i	0.0350838	+	0.389138i
$133$	−0.719133			−0.0623567
$134$	−0.109793	+	1.40995i	−0.00948466	+	0.121801i
$135$	3.59423	−	3.25575i	0.309342	−	0.280210i
$136$	5.03927	−	21.2217i	0.432114	−	1.81975i
$137$		−	5.50987i		−	0.470740i	−0.971906	−	0.235370i	$-0.924370\pi$
$137$		−	5.50987i		−	0.470740i	0.971906	−	0.235370i	$-0.0756302\pi$
$138$	0.443062	+	2.61832i	0.0377160	+	0.222887i
$139$		−	0.159637i		−	0.0135402i	−0.999977	−	0.00677012i	$-0.997845\pi$
$139$		−	0.159637i		−	0.0135402i	0.999977	−	0.00677012i	$-0.00215501\pi$
$140$	3.53167	+	0.553380i	0.298481	+	0.0467692i
$141$	−4.76292	−	19.0224i	−0.401111	−	1.60197i
$142$	−18.1733	−	1.41516i	−1.52507	−	0.118758i
$143$	−4.97078			−0.415677
$144$	−11.8065	+	2.14634i	−0.983874	+	0.178861i
$145$	−3.49214			−0.290006
$146$	−11.4546	−	0.891974i	−0.947990	−	0.0738203i
$147$	−1.40189	−	5.59894i	−0.115626	−	0.461793i
$148$	−15.5487	−	2.43633i	−1.27809	−	0.200265i
$149$			2.11710i			0.173440i	0.996233	+	0.0867199i	$0.0276385\pi$
$149$			2.11710i			0.173440i	−0.996233	+	0.0867199i	$0.972361\pi$
$150$	1.68743	+	9.97205i	0.137778	+	0.814214i
$151$			11.9780i			0.974759i	0.873190	+	0.487380i	$0.162047\pi$
$151$			11.9780i			0.974759i	−0.873190	+	0.487380i	$0.837953\pi$
$152$	0.245378	−	1.03335i	0.0199028	−	0.0838159i
$153$	−10.9018	−	20.4052i	−0.881361	−	1.64967i
$154$	−0.272475	+	3.49909i	−0.0219567	+	0.281965i
$155$	8.37128			0.672397
$156$	−1.19317	−	13.2342i	−0.0955298	−	1.05959i
$157$	23.1950			1.85117			0.925583	−	0.378546i	$-0.123576\pi$
$157$	23.1950			1.85117			0.925583	+	0.378546i	$0.123576\pi$
$158$	1.13541	−	14.5807i	0.0903280	−	1.15998i
$159$	−8.81703	+	2.20766i	−0.699236	+	0.175079i
$160$	−2.00023	+	4.88598i	−0.158132	+	0.386271i
$161$			2.07622i			0.163629i
$162$	−7.87533	+	9.99896i	−0.618745	+	0.785592i
$163$			5.61801i			0.440037i	0.975496	+	0.220018i	$0.0706117\pi$
$163$			5.61801i			0.440037i	−0.975496	+	0.220018i	$0.929388\pi$
$164$	−2.39348	+	15.2752i	−0.186899	+	1.19279i
$165$	2.03206	−	0.508799i	0.158196	−	0.0396100i
$166$	−17.5731	−	1.36843i	−1.36394	−	0.106210i
$167$	12.7935			0.989992			0.494996	−	0.868895i	$-0.335169\pi$
$167$	12.7935			0.989992			0.494996	+	0.868895i	$0.335169\pi$
$168$	−9.38141	+	0.114468i	−0.723791	+	0.00883141i
$169$	1.71406			0.131850
$170$	−10.1478	−	0.790211i	−0.778299	−	0.0606064i
$171$	−0.530844	−	0.993596i	−0.0405947	−	0.0759822i
$172$	2.24356	−	14.3184i	0.171070	−	1.09177i
$173$			14.1345i			1.07463i	0.843383	+	0.537313i	$0.180561\pi$
$173$			14.1345i			1.07463i	−0.843383	+	0.537313i	$0.819439\pi$
$174$	9.03679	−	1.52917i	0.685077	−	0.115926i
$175$			7.90740i			0.597744i
$176$	−4.93501	−	1.58547i	−0.371990	−	0.119509i
$177$	0.376644	+	1.50426i	0.0283103	+	0.113067i
$178$	−0.251786	+	3.23340i	−0.0188721	+	0.242353i
$179$	−13.8602			−1.03596			−0.517979	−	0.855393i	$-0.673315\pi$
$179$	−13.8602			−1.03596			−0.517979	+	0.855393i	$0.673315\pi$
$180$	1.84240	+	5.28805i	0.137324	+	0.394148i
$181$	−13.7462			−1.02175			−0.510873	−	0.859656i	$-0.670678\pi$
$181$	−13.7462			−1.02175			−0.510873	+	0.859656i	$0.670678\pi$
$182$	0.806557	−	10.3577i	0.0597860	−	0.767763i
$183$	5.33278	+	21.2983i	0.394211	+	1.57441i
$184$	−2.98340	−	0.708434i	−0.219939	−	0.0522265i
$185$			7.34433i			0.539966i
$186$	−21.6628	+	3.66569i	−1.58839	+	0.268782i
$187$		−	9.99320i		−	0.730775i
$188$	22.3702	+	3.50521i	1.63152	+	0.255644i
$189$	−7.37528	+	6.68072i	−0.536473	+	0.485951i
$190$	−0.494127	−	0.0384779i	−0.0358478	−	0.00279148i
$191$	−6.72702			−0.486750			−0.243375	−	0.969932i	$-0.578255\pi$
$191$	−6.72702			−0.486750			−0.243375	+	0.969932i	$0.578255\pi$
$192$	3.03658	−	13.5196i	0.219146	−	0.975692i
$193$	−19.3056			−1.38965			−0.694824	−	0.719180i	$-0.744518\pi$
$193$	−19.3056			−1.38965			−0.694824	+	0.719180i	$0.744518\pi$
$194$	3.70534	+	0.288536i	0.266028	+	0.0207157i
$195$	−6.01513	+	1.50610i	−0.430753	+	0.107854i
$196$	6.58434	+	1.03171i	0.470310	+	0.0736932i
$197$			13.6055i			0.969354i	0.874693	+	0.484677i	$0.161063\pi$
$197$			13.6055i			0.969354i	−0.874693	+	0.484677i	$0.838937\pi$
$198$	−5.03568	+	2.20646i	−0.357870	+	0.156807i
$199$		−	14.8497i		−	1.05267i	−0.850278	−	0.526334i	$-0.823566\pi$
$199$		−	14.8497i		−	1.05267i	0.850278	−	0.526334i	$-0.176434\pi$
$200$	−11.3625	−	2.69812i	−0.803448	−	0.190786i
$201$	−1.68018	+	0.420694i	−0.118511	+	0.0296735i
$202$	1.16531	−	14.9647i	0.0819909	−	1.05292i
$203$	7.16578			0.502939
$204$	26.6060	−	2.39873i	1.86279	−	0.167945i
$205$	7.21516			0.503928
$206$	0.416490	−	5.34851i	0.0290183	−	0.372648i
$207$	−2.86862	+	1.53261i	−0.199383	+	0.106524i
$208$	14.6082	+	4.69316i	1.01290	+	0.325412i
$209$		−	0.486600i		−	0.0336589i
$210$	0.730472	+	4.31680i	0.0504074	+	0.297888i
$211$			19.1746i			1.32003i	0.751252	+	0.660015i	$0.229450\pi$
$211$			19.1746i			1.32003i	−0.751252	+	0.660015i	$0.770550\pi$
$212$	1.62470	−	10.3688i	0.111585	−	0.712133i
$213$	−5.42248	−	21.6565i	−0.371542	−	1.48388i
$214$	−12.6453	−	0.984697i	−0.864418	−	0.0673125i
$215$	−6.76323			−0.461248
$216$	−7.08326	−	12.8774i	−0.481955	−	0.876196i
$217$	−17.1777			−1.16610
$218$	−12.7867	−	0.995708i	−0.866028	−	0.0674379i
$219$	−3.41778	−	13.6501i	−0.230952	−	0.922386i
$220$	−0.374444	+	2.38970i	−0.0252450	+	0.161114i
$221$			29.5810i			1.98983i
$222$	−3.21600	−	19.0053i	−0.215844	−	1.27555i
$223$			9.23297i			0.618285i	0.951016	+	0.309143i	$0.100042\pi$
$223$			9.23297i			0.618285i	−0.951016	+	0.309143i	$0.899958\pi$
$224$	4.10442	−	10.0259i	0.274238	−	0.669884i
$225$	−10.9253	+	5.83703i	−0.728355	+	0.389135i
$226$	−0.375418	+	4.82107i	−0.0249725	+	0.320693i
$227$	4.98229			0.330686			0.165343	−	0.986236i	$-0.447127\pi$
$227$	4.98229			0.330686			0.165343	+	0.986236i	$0.447127\pi$
$228$	1.29553	−	0.116802i	0.0857985	−	0.00773539i
$229$	6.25758			0.413513			0.206756	−	0.978392i	$-0.433709\pi$
$229$	6.25758			0.413513			0.206756	+	0.978392i	$0.433709\pi$
$230$	−0.111090	+	1.42660i	−0.00732506	+	0.0940673i
$231$	−4.16974	+	1.04404i	−0.274349	+	0.0686931i
$232$	−2.44506	+	10.2968i	−0.160526	+	0.676018i
$233$		−	12.2211i		−	0.800632i	−0.916377	−	0.400316i	$-0.868900\pi$
$233$		−	12.2211i		−	0.800632i	0.916377	−	0.400316i	$-0.131100\pi$
$234$	14.9062	−	6.53138i	0.974447	−	0.426970i
$235$		−	10.5665i		−	0.689280i
$236$	−1.76900	−	0.277186i	−0.115152	−	0.0180433i
$237$	17.3753	−	4.35054i	1.12865	−	0.282598i
$238$	20.8230	+	1.62149i	1.34976	+	0.105106i
$239$	−8.13591			−0.526268			−0.263134	−	0.964759i	$-0.584756\pi$
$239$	−8.13591			−0.526268			−0.263134	+	0.964759i	$0.584756\pi$
$240$	−6.45224	−	0.423308i	−0.416490	−	0.0273244i
$241$	−6.85630			−0.441653			−0.220826	−	0.975313i	$-0.570875\pi$
$241$	−6.85630			−0.441653			−0.220826	+	0.975313i	$0.570875\pi$
$242$	13.1417	+	1.02335i	0.844783	+	0.0657836i
$243$	−14.6747	−	5.25859i	−0.941383	−	0.337339i
$244$	−25.0467	−	3.92459i	−1.60345	−	0.251246i
$245$		−	3.11008i		−	0.198696i
$246$	−18.6710	+	3.15944i	−1.19042	+	0.201438i
$247$			1.44039i			0.0916499i
$248$	5.86126	−	24.6833i	0.372190	−	1.56739i
$249$	−5.24340	−	20.9413i	−0.332287	−	1.32710i
$250$	−0.935443	+	12.0128i	−0.0591626	+	0.759758i
$251$	−6.28732			−0.396852			−0.198426	−	0.980116i	$-0.563583\pi$
$251$	−6.28732			−0.396852			−0.198426	+	0.980116i	$0.563583\pi$
$252$	−3.78056	−	10.8510i	−0.238153	−	0.683546i
$253$	−1.40487			−0.0883234
$254$	−0.886143	+	11.3797i	−0.0556016	+	0.714028i
$255$	−3.02785	−	12.0928i	−0.189612	−	0.757278i
$256$	13.0062	+	9.31879i	0.812885	+	0.582425i
$257$			16.1674i			1.00849i	0.863560	+	0.504246i	$0.168229\pi$
$257$			16.1674i			1.00849i	−0.863560	+	0.504246i	$0.831771\pi$
$258$	17.5016	−	2.96154i	1.08960	−	0.184378i
$259$		−	15.0704i		−	0.936429i
$260$	1.10840	−	7.07378i	0.0687398	−	0.438697i
$261$	5.28959	+	9.90066i	0.327417	+	0.612836i
$262$	27.5819	+	2.14782i	1.70402	+	0.132692i
$263$	−4.46023			−0.275030			−0.137515	−	0.990500i	$-0.543911\pi$
$263$	−4.46023			−0.275030			−0.137515	+	0.990500i	$0.543911\pi$
$264$	−0.0774548	−	6.34792i	−0.00476701	−	0.390687i
$265$	−4.89765			−0.300861
$266$	1.01394	+	0.0789557i	0.0621685	+	0.00484108i
$267$	−3.85313	+	0.964768i	−0.235808	+	0.0590428i
$268$	0.309604	−	1.97589i	0.0189121	−	0.120697i
$269$			10.2424i			0.624488i	0.950002	+	0.312244i	$0.101081\pi$
$269$			10.2424i			0.624488i	−0.950002	+	0.312244i	$0.898919\pi$
$270$	−5.42513	+	4.19581i	−0.330163	+	0.255349i
$271$		−	16.8258i		−	1.02209i	−0.859553	−	0.511046i	$-0.829258\pi$
$271$		−	16.8258i		−	1.02209i	0.859553	−	0.511046i	$-0.170742\pi$
$272$	−9.43509	+	29.3682i	−0.572086	+	1.78071i
$273$	12.3429	−	3.09049i	0.747027	−	0.187045i
$274$	−0.604945	+	7.76862i	−0.0365461	+	0.469320i
$275$	−5.35054			−0.322649
$276$	−0.337220	−	3.74034i	−0.0202983	−	0.225142i
$277$	−1.07933			−0.0648507			−0.0324253	−	0.999474i	$-0.510323\pi$
$277$	−1.07933			−0.0648507			−0.0324253	+	0.999474i	$0.510323\pi$
$278$	−0.0175270	+	0.225080i	−0.00105120	+	0.0134994i
$279$	−12.6801	−	23.7337i	−0.759137	−	1.42090i
$280$	−4.91870	−	1.16799i	−0.293949	−	0.0698006i
$281$			33.0090i			1.96915i	0.174957	+	0.984576i	$0.444021\pi$
$281$			33.0090i			1.96915i	−0.174957	+	0.984576i	$0.555979\pi$
$282$	4.62694	+	27.3434i	0.275530	+	1.62828i
$283$		−	31.1037i		−	1.84892i	−0.381278	−	0.924460i	$-0.624516\pi$
$283$		−	31.1037i		−	1.84892i	0.381278	−	0.924460i	$-0.375484\pi$
$284$	25.4680	+	3.99060i	1.51125	+	0.236799i
$285$	−0.147436	−	0.588835i	−0.00873334	−	0.0348796i
$286$	7.00852	+	0.545756i	0.414423	+	0.0322712i
$287$	−14.8053			−0.873931
$288$	16.8822	−	1.72995i	0.994791	−	0.101938i
$289$	−42.4693			−2.49820
$290$	4.92372	+	0.383412i	0.289131	+	0.0225147i
$291$	1.10558	+	4.41552i	0.0648105	+	0.258843i
$292$	16.0524	+	2.51527i	0.939398	+	0.147195i
$293$			22.9596i			1.34131i	0.741768	+	0.670656i	$0.233987\pi$
$293$			22.9596i			1.34131i	−0.741768	+	0.670656i	$0.766013\pi$
$294$	1.36187	+	8.04812i	0.0794258	+	0.469376i
$295$			0.835578i			0.0486492i
$296$	21.6553	+	5.14223i	1.25869	+	0.298886i
$297$	−4.52050	−	4.99048i	−0.262306	−	0.289577i
$298$	0.232443	−	2.98500i	0.0134651	−	0.172916i
$299$	4.15857			0.240497
$300$	−1.28432	−	14.2453i	−0.0741504	−	0.822454i
$301$	13.8780			0.799913
$302$	1.31510	−	16.8884i	0.0756757	−	0.971817i
$303$	17.8330	−	4.46512i	1.02448	−	0.256515i
$304$	−0.459424	+	1.43003i	−0.0263498	+	0.0820177i
$305$			11.8307i			0.677423i
$306$	13.1306	+	29.9672i	0.750628	+	1.71311i
$307$			24.2941i			1.38654i	0.720680	+	0.693268i	$0.243830\pi$
$307$			24.2941i			1.38654i	−0.720680	+	0.693268i	$0.756170\pi$
$308$	0.768350	−	4.90361i	0.0437808	−	0.279409i
$309$	6.37364	−	1.59587i	0.362584	−	0.0907857i
$310$	−11.8030	−	0.919107i	−0.670368	−	0.0522018i
$311$	−1.10845			−0.0628545			−0.0314272	−	0.999506i	$-0.510005\pi$
$311$	−1.10845			−0.0628545			−0.0314272	+	0.999506i	$0.510005\pi$
$312$	0.229275	+	18.7906i	0.0129801	+	1.06381i
$313$	14.0924			0.796549			0.398275	−	0.917266i	$-0.369609\pi$
$313$	14.0924			0.796549			0.398275	+	0.917266i	$0.369609\pi$
$314$	−32.7037	−	2.54665i	−1.84558	−	0.143716i
$315$	−4.72947	+	2.52679i	−0.266475	+	0.142369i
$316$	−3.20172	+	20.4334i	−0.180111	+	1.14947i
$317$		−	3.02987i		−	0.170175i	−0.996373	−	0.0850874i	$-0.972883\pi$
$317$		−	3.02987i		−	0.170175i	0.996373	−	0.0850874i	$-0.0271169\pi$
$318$	12.6739	−	2.14463i	0.710718	−	0.120265i
$319$			4.84872i			0.271476i
$320$	3.35666	−	6.66935i	0.187643	−	0.372828i
$321$	−3.77307	−	15.0690i	−0.210592	−	0.841071i
$322$	0.227954	−	2.92735i	0.0127034	−	0.163135i
$323$	−2.89575			−0.161124
$324$	12.2016	−	13.2333i	0.677867	−	0.735185i
$325$	15.8382			0.878545
$326$	0.616818	−	7.92109i	0.0341624	−	0.438709i
$327$	−3.81526	−	15.2375i	−0.210984	−	0.842637i
$328$	5.05178	−	21.2744i	0.278938	−	1.17468i
$329$			21.6821i			1.19538i
$330$	−2.92096	+	0.494273i	−0.160794	+	0.0272088i
$331$			8.71346i			0.478935i	0.970904	+	0.239467i	$0.0769728\pi$
$331$			8.71346i			0.478935i	−0.970904	+	0.239467i	$0.923027\pi$
$332$	24.6269	+	3.85881i	1.35158	+	0.211780i
$333$	20.8221	−	11.1246i	1.14105	−	0.609622i
$334$	−18.0382	−	1.40464i	−0.987004	−	0.0768584i
$335$	−0.933302			−0.0509918
$336$	13.2398	+	0.868618i	0.722292	+	0.0473870i
$337$	10.7456			0.585352			0.292676	−	0.956212i	$-0.405454\pi$
$337$	10.7456			0.585352			0.292676	+	0.956212i	$0.405454\pi$
$338$	−2.41673	−	0.188191i	−0.131453	−	0.0102363i
$339$	−5.74510	+	1.43849i	−0.312031	+	0.0781281i
$340$	14.2211	+	2.22831i	0.771245	+	0.120847i
$341$		−	11.6232i		−	0.629434i
$342$	0.639372	+	1.45920i	0.0345733	+	0.0789044i
$343$			19.7876i			1.06843i
$344$	−4.73536	+	19.9418i	−0.255313	+	1.07519i
$345$	−1.70003	+	0.425664i	−0.0915267	+	0.0229170i
$346$	1.55187	−	19.9289i	0.0834290	−	1.07138i
$347$	−13.0393			−0.699985			−0.349992	−	0.936753i	$-0.613816\pi$
$347$	−13.0393			−0.699985			−0.349992	+	0.936753i	$0.613816\pi$
$348$	−12.9093	+	1.16387i	−0.692009	+	0.0623899i
$349$	30.6809			1.64231			0.821155	−	0.570705i	$-0.193330\pi$
$349$	30.6809			1.64231			0.821155	+	0.570705i	$0.193330\pi$
$350$	0.868177	−	11.1490i	0.0464060	−	0.595940i
$351$	13.3812	+	14.7724i	0.714236	+	0.788491i
$352$	6.78402	+	2.77725i	0.361590	+	0.148028i
$353$		−	33.6065i		−	1.78869i	−0.447377	−	0.894345i	$-0.647642\pi$
$353$		−	33.6065i		−	1.78869i	0.447377	−	0.894345i	$-0.352358\pi$
$354$	−0.365891	−	2.16227i	−0.0194469	−	0.114923i
$355$		−	12.0297i		−	0.638469i
$356$	0.710008	−	4.53127i	0.0376303	−	0.240157i
$357$	6.21309	+	24.8141i	0.328831	+	1.31330i
$358$	19.5421	+	1.52175i	1.03283	+	0.0804269i
$359$	−6.51712			−0.343960			−0.171980	−	0.985100i	$-0.555017\pi$
$359$	−6.51712			−0.343960			−0.171980	+	0.985100i	$0.555017\pi$
$360$	−2.01709	−	7.65814i	−0.106310	−	0.403620i
$361$	18.8590			0.992579
$362$	19.3814	+	1.50923i	1.01866	+	0.0793236i
$363$	3.92118	+	15.6606i	0.205809	+	0.821967i
$364$	−2.27440	+	14.5152i	−0.119211	+	0.760805i
$365$		−	7.58229i		−	0.396875i
$366$	−5.18053	−	30.6149i	−0.270791	−	1.60027i
$367$		−	11.9080i		−	0.621592i	−0.950477	−	0.310796i	$-0.899404\pi$
$367$		−	11.9080i		−	0.621592i	0.950477	−	0.310796i	$-0.100596\pi$
$368$	4.12865	+	1.32641i	0.215221	+	0.0691439i
$369$	−10.9289	−	20.4559i	−0.568936	−	1.06489i
$370$	0.806356	−	10.3551i	0.0419204	−	0.538336i
$371$	10.0499			0.521763
$372$	30.9458	−	2.79000i	1.60447	−	0.144655i
$373$	−9.90047			−0.512627			−0.256313	−	0.966594i	$-0.582508\pi$
$373$	−9.90047			−0.512627			−0.256313	+	0.966594i	$0.582508\pi$
$374$	−1.09718	+	14.0899i	−0.0567340	+	0.728570i
$375$	−14.3153	+	3.58434i	−0.739238	+	0.185094i
$376$	−31.1560	−	7.39825i	−1.60675	−	0.381536i
$377$		−	14.3527i		−	0.739204i
$378$	11.1322	−	8.60970i	0.572581	−	0.442835i
$379$		−	24.3681i		−	1.25171i	−0.779941	−	0.625854i	$-0.784751\pi$
$379$		−	24.3681i		−	1.25171i	0.779941	−	0.625854i	$-0.215249\pi$
$380$	0.692468	+	0.108503i	0.0355229	+	0.00556611i
$381$	−13.5608	+	3.39544i	−0.694742	+	0.173954i
$382$	9.48472	+	0.738579i	0.485281	+	0.0377890i
$383$	27.6538			1.41304			0.706521	−	0.707692i	$-0.250263\pi$
$383$	27.6538			1.41304			0.706521	+	0.707692i	$0.250263\pi$
$384$	−5.76577	+	18.7285i	−0.294233	+	0.955734i
$385$	−2.31619			−0.118044
$386$	27.2199	+	2.11962i	1.38545	+	0.107886i
$387$	10.2443	+	19.1746i	0.520749	+	0.974701i
$388$	−5.19264	−	0.813640i	−0.263617	−	0.0413063i
$389$		−	22.3928i		−	1.13536i	−0.823250	−	0.567680i	$-0.807841\pi$
$389$		−	22.3928i		−	1.13536i	0.823250	−	0.567680i	$-0.192159\pi$
$390$	8.64637	−	1.46310i	0.437826	−	0.0740871i
$391$			8.36036i			0.422801i
$392$	−9.17028	−	2.17756i	−0.463169	−	0.109983i
$393$	8.22979	+	32.8685i	0.415138	+	1.65799i
$394$	1.49379	−	19.1831i	0.0752561	−	0.966428i
$395$	9.65160			0.485624
$396$	7.34229	−	2.55811i	0.368964	−	0.128550i
$397$	−12.6710			−0.635937			−0.317969	−	0.948101i	$-0.603001\pi$
$397$	−12.6710			−0.635937			−0.317969	+	0.948101i	$0.603001\pi$
$398$	−1.63039	+	20.9373i	−0.0817242	+	1.04949i
$399$	0.302535	+	1.20828i	0.0151457	+	0.0604894i
$400$	15.7242	+	5.05172i	0.786211	+	0.252586i
$401$		−	18.8895i		−	0.943298i	−0.881786	−	0.471649i	$-0.843659\pi$
$401$		−	18.8895i		−	0.943298i	0.881786	−	0.471649i	$-0.156341\pi$
$402$	2.41516	−	0.408683i	0.120457	−	0.0203833i
$403$			34.4061i			1.71389i
$404$	−3.28605	+	20.9715i	−0.163487	+	1.04337i
$405$	−6.98233	−	4.66930i	−0.346955	−	0.232019i
$406$	−10.1034	−	0.786752i	−0.501421	−	0.0390459i
$407$	10.1974			0.505465
$408$	−37.7763	+	0.460932i	−1.87021	+	0.0228195i
$409$	12.0394			0.595311			0.297655	−	0.954673i	$-0.403795\pi$
$409$	12.0394			0.595311			0.297655	+	0.954673i	$0.403795\pi$
$410$	−10.1730	−	0.792173i	−0.502408	−	0.0391226i
$411$	−9.25760	+	2.31797i	−0.456644	+	0.114337i
$412$	−1.17446	+	7.49538i	−0.0578614	+	0.369271i
$413$		−	1.71459i		−	0.0843693i
$414$	4.21287	−	1.84594i	0.207051	−	0.0907229i
$415$		−	11.6324i		−	0.571012i
$416$	−20.0815	−	8.22098i	−0.984575	−	0.403067i
$417$	−0.268220	+	0.0671584i	−0.0131348	+	0.00328876i
$418$	−0.0534253	+	0.686080i	−0.00261312	+	0.0335573i
$419$	−9.40533			−0.459480			−0.229740	−	0.973252i	$-0.573788\pi$
$419$	−9.40533			−0.459480			−0.229740	+	0.973252i	$0.573788\pi$
$420$	−0.555971	−	6.16666i	−0.0271286	−	0.300902i
$421$	1.84317			0.0898308			0.0449154	−	0.998991i	$-0.485698\pi$
$421$	1.84317			0.0898308			0.0449154	+	0.998991i	$0.485698\pi$
$422$	2.10523	−	27.0351i	0.102481	−	1.31605i
$423$	−29.9573	+	16.0052i	−1.45657	+	0.778198i
$424$	−3.42916	+	14.4411i	−0.166535	+	0.701320i
$425$			31.8409i			1.54451i
$426$	5.26767	+	31.1299i	0.255219	+	1.50825i
$427$		−	24.2763i		−	1.17481i
$428$	17.7211	+	2.77674i	0.856583	+	0.134219i
$429$	2.09117	+	8.35182i	0.100963	+	0.403230i
$430$	9.53578	+	0.742554i	0.459856	+	0.0358091i
$431$	−1.16679			−0.0562024			−0.0281012	−	0.999605i	$-0.508946\pi$
$431$	−1.16679			−0.0562024			−0.0281012	+	0.999605i	$0.508946\pi$
$432$	8.57316	+	18.9341i	0.412476	+	0.910968i
$433$	29.4866			1.41703			0.708517	−	0.705693i	$-0.249364\pi$
$433$	29.4866			1.41703			0.708517	+	0.705693i	$0.249364\pi$
$434$	24.2196	+	1.88599i	1.16258	+	0.0905302i
$435$	1.46912	+	5.86743i	0.0704389	+	0.281322i
$436$	17.9193	+	2.80779i	0.858178	+	0.134469i
$437$			0.407092i			0.0194739i
$438$	3.32020	+	19.6211i	0.158645	+	0.937532i
$439$			18.6446i			0.889858i	0.895566	+	0.444929i	$0.146771\pi$
$439$			18.6446i			0.889858i	−0.895566	+	0.444929i	$0.853229\pi$
$440$	0.790318	−	3.32823i	0.0376769	−	0.158667i
$441$	−8.81748	+	4.71088i	−0.419880	+	0.224328i
$442$	3.24778	−	41.7076i	0.154481	−	1.98383i
$443$	−6.97748			−0.331510			−0.165755	−	0.986167i	$-0.553006\pi$
$443$	−6.97748			−0.331510			−0.165755	+	0.986167i	$0.553006\pi$
$444$	2.44774	+	27.1495i	0.116165	+	1.28846i
$445$	−2.14032			−0.101461
$446$	1.01371	−	13.0180i	0.0480008	−	0.616419i
$447$	3.55712	−	0.890652i	0.168246	−	0.0421264i
$448$	−6.88779	+	13.6854i	−0.325417	+	0.646572i
$449$		−	10.5665i		−	0.498664i	−0.968418	−	0.249332i	$-0.919789\pi$
$449$		−	10.5665i		−	0.498664i	0.968418	−	0.249332i	$-0.0802111\pi$
$450$	16.0450	−	7.03037i	0.756368	−	0.331415i
$451$		−	10.0180i		−	0.471730i
$452$	1.05864	−	6.75623i	0.0497942	−	0.317786i
$453$	20.1253	−	5.03909i	0.945569	−	0.236757i
$454$	−7.02475	−	0.547020i	−0.329688	−	0.0256729i
$455$	6.85620			0.321423
$456$	−1.83945	+	0.0224442i	−0.0861401	+	0.00105105i
$457$	−8.54480			−0.399709			−0.199854	−	0.979826i	$-0.564047\pi$
$457$	−8.54480			−0.399709			−0.199854	+	0.979826i	$0.564047\pi$
$458$	−8.82285	−	0.687038i	−0.412265	−	0.0321032i
$459$	−29.6982	+	26.9014i	−1.38619	+	1.25565i
$460$	0.313262	−	1.99923i	0.0146059	−	0.0932147i
$461$		−	25.7095i		−	1.19741i	−0.800969	−	0.598705i	$-0.795682\pi$
$461$		−	25.7095i		−	1.19741i	0.800969	−	0.598705i	$-0.204318\pi$
$462$	5.99374	−	1.01424i	0.278854	−	0.0471865i
$463$		−	13.2973i		−	0.617976i	−0.951066	−	0.308988i	$-0.900010\pi$
$463$		−	13.2973i		−	0.617976i	0.951066	−	0.308988i	$-0.0999903\pi$
$464$	4.57792	−	14.2495i	0.212525	−	0.661515i
$465$	−3.52174	−	14.0653i	−0.163317	−	0.652262i
$466$	−1.34179	+	17.2311i	−0.0621573	+	0.798216i
$467$	−28.3214			−1.31056			−0.655279	−	0.755387i	$-0.727449\pi$
$467$	−28.3214			−1.31056			−0.655279	+	0.755387i	$0.727449\pi$
$468$	−21.7340	+	7.57230i	−1.00465	+	0.350030i
$469$	1.91511			0.0884318
$470$	−1.16012	+	14.8981i	−0.0535125	+	0.687200i
$471$	−9.75801	−	38.9719i	−0.449625	−	1.79573i
$472$	2.46376	+	0.585041i	0.113404	+	0.0269287i
$473$			9.39052i			0.431776i
$474$	−24.9759	+	4.22633i	−1.14718	+	0.194122i
$475$			1.55044i			0.0711389i
$476$	−29.1813	−	4.57244i	−1.33752	−	0.209577i
$477$	7.41854	+	13.8855i	0.339672	+	0.635773i
$478$	11.4712	+	0.893265i	0.524680	+	0.0408570i
$479$	−0.850005			−0.0388377			−0.0194189	−	0.999811i	$-0.506182\pi$
$479$	−0.850005			−0.0388377			−0.0194189	+	0.999811i	$0.506182\pi$
$480$	9.05082	+	1.30525i	0.413112	+	0.0595763i
$481$	−30.1853			−1.37633
$482$	9.66700	+	0.752773i	0.440320	+	0.0342879i
$483$	3.48843	−	0.873452i	0.158729	−	0.0397434i
$484$	−18.4168	−	2.88574i	−0.837126	−	0.131170i
$485$			2.45272i			0.111372i
$486$	20.1132	+	9.02551i	0.912353	+	0.409405i
$487$		−	6.13442i		−	0.277977i	−0.990294	−	0.138989i	$-0.955615\pi$
$487$		−	6.13442i		−	0.277977i	0.990294	−	0.138989i	$-0.0443851\pi$
$488$	34.8836	+	8.28341i	1.57911	+	0.374972i
$489$	9.43929	−	2.36346i	0.426859	−	0.106879i
$490$	−0.341465	+	4.38504i	−0.0154258	+	0.198096i
$491$	39.3299			1.77493			0.887467	−	0.460871i	$-0.152463\pi$
$491$	39.3299			1.77493			0.887467	+	0.460871i	$0.152463\pi$
$492$	26.6720	−	2.40469i	1.20247	−	0.108412i
$493$	28.8546			1.29955
$494$	0.158145	−	2.03087i	0.00711527	−	0.0913733i
$495$	−1.70975	−	3.20019i	−0.0768477	−	0.143838i
$496$	−10.9741	+	34.1586i	−0.492752	+	1.53376i
$497$			24.6846i			1.10726i
$498$	5.09370	+	30.1018i	0.228254	+	1.34889i
$499$			5.67525i			0.254059i	0.991899	+	0.127030i	$0.0405443\pi$
$499$			5.67525i			0.254059i	−0.991899	+	0.127030i	$0.959456\pi$
$500$	2.63785	−	16.8347i	0.117968	−	0.752872i
$501$	−5.38215	−	21.4955i	−0.240457	−	0.960346i
$502$	8.86478	+	0.690304i	0.395655	+	0.0308098i
$503$	−24.8415			−1.10763			−0.553815	−	0.832640i	$-0.686828\pi$
$503$	−24.8415			−1.10763			−0.553815	+	0.832640i	$0.686828\pi$
$504$	4.13903	+	15.7143i	0.184367	+	0.699972i
$505$	9.90580			0.440802
$506$	1.98079	+	0.154245i	0.0880569	+	0.00685702i
$507$	−0.721093	−	2.87993i	−0.0320249	−	0.127902i
$508$	2.49883	−	15.9475i	0.110868	−	0.707556i
$509$			27.6094i			1.22376i	0.790949	+	0.611882i	$0.209587\pi$
$509$			27.6094i			1.22376i	−0.790949	+	0.611882i	$0.790413\pi$
$510$	2.94141	+	17.3826i	0.130248	+	0.769713i
$511$			15.5587i			0.688275i
$512$	−17.3148	−	14.5670i	−0.765215	−	0.643775i
$513$	−1.44610	+	1.30992i	−0.0638469	+	0.0578342i
$514$	1.77506	−	22.7951i	0.0782946	−	1.00545i
$515$	3.54041			0.156009
$516$	−25.0014	+	2.25407i	−1.10062	+	0.0992297i
$517$	−14.6712			−0.645239
$518$	−1.65462	+	21.2484i	−0.0726999	+	0.933602i
$519$	23.7486	−	5.94630i	1.04245	−	0.261014i
$520$	−2.33943	+	9.85195i	−0.102591	+	0.432037i
$521$		−	42.9867i		−	1.88328i	−0.336621	−	0.941640i	$-0.609284\pi$
$521$		−	42.9867i		−	1.88328i	0.336621	−	0.941640i	$-0.390716\pi$
$522$	−6.37100	−	14.5401i	−0.278851	−	0.636405i
$523$		−	32.0916i		−	1.40327i	−0.712538	−	0.701634i	$-0.752454\pi$
$523$		−	32.0916i		−	1.40327i	0.712538	−	0.701634i	$-0.247546\pi$
$524$	−38.6532	−	6.05660i	−1.68857	−	0.264584i
$525$	13.2859	−	3.32660i	0.579844	−	0.145185i
$526$	6.28868	+	0.489702i	0.274199	+	0.0213520i
$527$	−69.1697			−3.01308
$528$	−0.587750	+	8.95872i	−0.0255785	+	0.389878i
$529$	−21.8247			−0.948899
$530$	6.90542	+	0.537728i	0.299952	+	0.0233574i
$531$	2.36897	−	1.26566i	0.102805	−	0.0549250i
$532$	−1.42093	−	0.222646i	−0.0616050	−	0.00965295i
$533$			29.6544i			1.28448i
$534$	5.53862	−	0.937223i	0.239680	−	0.0405576i
$535$		−	8.37049i		−	0.361888i
$536$	−0.653464	+	2.75191i	−0.0282253	+	0.118864i
$537$	5.83089	+	23.2876i	0.251621	+	1.00494i
$538$	1.12454	−	14.4412i	0.0484823	−	0.622603i
$539$	−4.31824			−0.186000
$540$	8.10981	−	5.32022i	0.348991	−	0.228946i
$541$	14.6267			0.628852			0.314426	−	0.949282i	$-0.398188\pi$
$541$	14.6267			0.628852			0.314426	+	0.949282i	$0.398188\pi$
$542$	−1.84735	+	23.7234i	−0.0793504	+	1.01901i
$543$	5.78294	+	23.0961i	0.248170	+	0.991150i
$544$	16.5274	−	40.3716i	0.708605	−	1.73092i
$545$		−	8.46409i		−	0.362562i
$546$	−17.7421	+	3.00225i	−0.759294	+	0.128485i
$547$		−	16.9243i		−	0.723631i	−0.932250	−	0.361816i	$-0.882157\pi$
$547$		−	16.9243i		−	0.723631i	0.932250	−	0.361816i	$-0.117843\pi$
$548$	1.70588	−	10.8869i	0.0728716	−	0.465066i
$549$	33.5415	−	17.9201i	1.43152	−	0.764811i
$550$	7.54396	+	0.587451i	0.321676	+	0.0250490i
$551$	1.40502			0.0598560
$552$	0.0647990	+	5.31070i	0.00275803	+	0.226038i
$553$	−19.8048			−0.842188
$554$	1.52180	+	0.118503i	0.0646549	+	0.00503470i
$555$	12.3398	−	3.08971i	0.523796	−	0.131151i
$556$	0.0494243	−	0.315426i	0.00209606	−	0.0133770i
$557$			3.01253i			0.127645i	0.997961	+	0.0638225i	$0.0203291\pi$
$557$			3.01253i			0.127645i	−0.997961	+	0.0638225i	$0.979671\pi$
$558$	15.2724	+	34.8553i	0.646534	+	1.47554i
$559$		−	27.7970i		−	1.17569i
$560$	6.80686	+	2.18684i	0.287643	+	0.0924108i
$561$	−16.7904	+	4.20408i	−0.708892	+	0.177496i
$562$	3.62415	−	46.5409i	0.152876	−	1.96321i
$563$	−20.2851			−0.854914			−0.427457	−	0.904036i	$-0.640590\pi$
$563$	−20.2851			−0.854914			−0.427457	+	0.904036i	$0.640590\pi$
$564$	−3.52162	−	39.0607i	−0.148287	−	1.64475i
$565$	−3.19127			−0.134258
$566$	−3.41496	+	43.8545i	−0.143542	+	1.84334i
$567$	14.3276	+	9.58129i	0.601702	+	0.402376i
$568$	−35.4704	−	8.42274i	−1.48830	−	0.353410i
$569$			11.9558i			0.501214i	0.968089	+	0.250607i	$0.0806302\pi$
$569$			11.9558i			0.501214i	−0.968089	+	0.250607i	$0.919370\pi$
$570$	0.143226	+	0.846412i	0.00599910	+	0.0354523i
$571$		−	16.9893i		−	0.710979i	−0.934680	−	0.355489i	$-0.884314\pi$
$571$		−	16.9893i		−	0.710979i	0.934680	−	0.355489i	$-0.115686\pi$
$572$	−9.82171	−	1.53897i	−0.410666	−	0.0643477i
$573$	2.83001	+	11.3026i	0.118226	+	0.472174i
$574$	20.8747	+	1.62552i	0.871293	+	0.0678479i
$575$	4.47628			0.186674
$576$	−23.9929	+	0.585590i	−0.999702	+	0.0243996i
$577$	10.7907			0.449221			0.224611	−	0.974449i	$-0.427889\pi$
$577$	10.7907			0.449221			0.224611	+	0.974449i	$0.427889\pi$
$578$	59.8794	+	4.66283i	2.49066	+	0.193948i
$579$	8.12175	+	32.4370i	0.337528	+	1.34803i
$580$	−6.90008	−	1.08118i	−0.286510	−	0.0448935i
$581$			23.8694i			0.990270i
$582$	−1.07402	−	6.34703i	−0.0445195	−	0.263093i
$583$			6.80023i			0.281637i
$584$	−22.3569	−	5.30884i	−0.925135	−	0.219681i
$585$	5.06106	+	9.47292i	0.209249	+	0.391657i
$586$	2.52080	−	32.3717i	0.104133	−	1.33726i
$587$	−34.3462			−1.41762			−0.708809	−	0.705401i	$-0.750767\pi$
$587$	−34.3462			−1.41762			−0.708809	+	0.705401i	$0.750767\pi$
$588$	−1.03654	−	11.4969i	−0.0427460	−	0.474125i
$589$	−3.36809			−0.138780
$590$	0.0917406	−	1.17812i	0.00377690	−	0.0485024i
$591$	22.8598	−	5.72376i	0.940326	−	0.235444i
$592$	−29.9682	−	9.62785i	−1.23168	−	0.395702i
$593$		−	38.4716i		−	1.57984i	−0.613211	−	0.789919i	$-0.710122\pi$
$593$		−	38.4716i		−	1.57984i	0.613211	−	0.789919i	$-0.289878\pi$
$594$	5.82574	+	7.53262i	0.239033	+	0.309067i
$595$			13.7836i			0.565074i
$596$	−0.655464	+	4.18316i	−0.0268488	+	0.171349i
$597$	−24.9502	+	6.24718i	−1.02114	+	0.255680i
$598$	−5.86336	−	0.456582i	−0.239771	−	0.0186710i
$599$	17.0584			0.696987			0.348493	−	0.937311i	$-0.386693\pi$
$599$	17.0584			0.696987			0.348493	+	0.937311i	$0.386693\pi$
$600$	0.246791	+	20.2261i	0.0100752	+	0.825728i
$601$	2.00283			0.0816970			0.0408485	−	0.999165i	$-0.486994\pi$
$601$	2.00283			0.0816970			0.0408485	+	0.999165i	$0.486994\pi$
$602$	−19.5672	−	1.52370i	−0.797499	−	0.0621015i
$603$	1.41369	+	2.64603i	0.0575697	+	0.107755i
$604$	−3.70845	+	23.6673i	−0.150895	+	0.963009i
$605$			8.69908i			0.353668i
$606$	−25.6338	+	4.33764i	−1.04130	+	0.176205i
$607$		−	37.4559i		−	1.52029i	−0.649754	−	0.760145i	$-0.725128\pi$
$607$		−	37.4559i		−	1.52029i	0.649754	−	0.760145i	$-0.274872\pi$
$608$	0.804770	−	1.96582i	0.0326377	−	0.0797245i
$609$	−3.01460	−	12.0398i	−0.122158	−	0.487878i
$610$	1.29893	−	16.6806i	0.0525920	−	0.675379i
$611$	43.4284			1.75692
$612$	−15.2233	−	43.6938i	−0.615365	−	1.76622i
$613$	−1.00833			−0.0407259			−0.0203629	−	0.999793i	$-0.506482\pi$
$613$	−1.00833			−0.0407259			−0.0203629	+	0.999793i	$0.506482\pi$
$614$	2.66732	−	34.2533i	0.107644	−	1.38235i
$615$	−3.03537	−	12.1228i	−0.122398	−	0.488838i
$616$	−1.62171	+	6.82946i	−0.0653407	+	0.275167i
$617$		−	24.7964i		−	0.998265i	−0.866526	−	0.499133i	$-0.833652\pi$
$617$		−	24.7964i		−	0.998265i	0.866526	−	0.499133i	$-0.166348\pi$
$618$	−9.16169	+	1.55030i	−0.368537	+	0.0623624i
$619$		−	8.24346i		−	0.331333i	−0.986182	−	0.165666i	$-0.947023\pi$
$619$		−	8.24346i		−	0.331333i	0.986182	−	0.165666i	$-0.0529775\pi$
$620$	16.5407	+	2.59178i	0.664292	+	0.104088i
$621$	3.78187	+	4.17505i	0.151761	+	0.167539i
$622$	1.56285	+	0.121700i	0.0626648	+	0.00487973i
$623$	4.39189			0.175957
$624$	1.73980	−	26.5188i	0.0696479	−	1.06160i
$625$	12.6929			0.507717
$626$	−19.8695	−	1.54725i	−0.794145	−	0.0618404i
$627$	−0.817578	+	0.204710i	−0.0326509	+	0.00817532i
$628$	45.8309	+	7.18128i	1.82885	+	0.286564i
$629$		−	60.6843i		−	2.41964i
$630$	6.94572	−	3.04338i	0.276724	−	0.121251i
$631$			16.5330i			0.658169i	0.944300	+	0.329084i	$0.106740\pi$
$631$			16.5330i			0.658169i	−0.944300	+	0.329084i	$0.893260\pi$
$632$	6.75769	−	28.4584i	0.268806	−	1.13201i
$633$	32.2168	−	8.06662i	1.28050	−	0.320619i
$634$	−0.332659	+	4.27196i	−0.0132116	+	0.169661i
$635$	−7.53272			−0.298927
$636$	−18.1050	+	1.63230i	−0.717910	+	0.0647250i
$637$	12.7825			0.506460
$638$	0.532355	−	6.83643i	0.0210761	−	0.270657i
$639$	−34.1057	+	18.2215i	−1.34920	+	0.720832i
$640$	−5.46495	+	9.03488i	−0.216021	+	0.357135i
$641$		−	20.6339i		−	0.814990i	−0.913207	−	0.407495i	$-0.866402\pi$
$641$		−	20.6339i		−	0.814990i	0.913207	−	0.407495i	$-0.133598\pi$
$642$	3.66534	+	21.6607i	0.144660	+	0.854882i
$643$		−	13.7213i		−	0.541116i	−0.962704	−	0.270558i	$-0.912792\pi$
$643$		−	13.7213i		−	0.541116i	0.962704	−	0.270558i	$-0.0872082\pi$
$644$	−0.642805	+	4.10238i	−0.0253301	+	0.161656i
$645$	2.84525	+	11.3635i	0.112031	+	0.447436i
$646$	4.08285	+	0.317933i	0.160638	+	0.0125089i
$647$	50.4334			1.98274			0.991370	−	0.131093i	$-0.0418486\pi$
$647$	50.4334			1.98274			0.991370	+	0.131093i	$0.0418486\pi$
$648$	−18.6565	+	17.3186i	−0.732897	+	0.680339i
$649$	1.16017			0.0455408
$650$	−22.3310	−	1.73892i	−0.875893	−	0.0682061i
$651$	7.22654	+	28.8616i	0.283230	+	1.13118i
$652$	−1.73936	+	11.1006i	−0.0681186	+	0.434732i
$653$		−	0.551597i		−	0.0215857i	−0.999942	−	0.0107928i	$-0.996564\pi$
$653$		−	0.551597i		−	0.0215857i	0.999942	−	0.0107928i	$-0.00343553\pi$
$654$	3.70633	+	21.9030i	0.144929	+	0.856474i
$655$			18.2577i			0.713386i
$656$	−9.45852	+	29.4411i	−0.369293	+	1.14948i
$657$	−21.4968	+	11.4850i	−0.838669	+	0.448072i
$658$	2.38055	−	30.5706i	0.0928033	−	1.19177i
$659$	4.27611			0.166574			0.0832868	−	0.996526i	$-0.473458\pi$
$659$	4.27611			0.166574			0.0832868	+	0.996526i	$0.473458\pi$
$660$	4.17266	−	0.376197i	0.162421	−	0.0146435i
$661$	−22.5131			−0.875656			−0.437828	−	0.899059i	$-0.644252\pi$
$661$	−22.5131			−0.875656			−0.437828	+	0.899059i	$0.644252\pi$
$662$	0.956676	−	12.2855i	0.0371823	−	0.477489i
$663$	49.7015	−	12.4445i	1.93025	−	0.483306i
$664$	−34.2989	−	8.14458i	−1.33106	−	0.316071i
$665$			0.671168i			0.0260268i
$666$	−30.5795	+	13.3989i	−1.18493	+	0.519197i
$667$		−	4.05646i		−	0.157067i
$668$	25.2786	+	3.96092i	0.978058	+	0.153253i
$669$	15.5131	−	3.88425i	0.599770	−	0.150174i
$670$	1.31591	+	0.102470i	0.0508379	+	0.00395876i
$671$	16.4265			0.634139
$672$	−18.5721	−	2.67834i	−0.716433	−	0.103319i
$673$	8.71009			0.335749			0.167875	−	0.985808i	$-0.446310\pi$
$673$	8.71009			0.335749			0.167875	+	0.985808i	$0.446310\pi$
$674$	−15.1507	−	1.17979i	−0.583585	−	0.0454440i
$675$	14.4035	+	15.9010i	0.554391	+	0.612028i
$676$	3.38679	+	0.530679i	0.130261	+	0.0204107i
$677$		−	3.87652i		−	0.148987i	−0.997222	−	0.0744935i	$-0.976266\pi$
$677$		−	3.87652i		−	0.148987i	0.997222	−	0.0744935i	$-0.0237340\pi$
$678$	8.25822	−	1.39742i	0.317155	−	0.0536677i
$679$		−	5.03292i		−	0.193146i
$680$	−19.8063	−	4.70317i	−0.759535	−	0.180358i
$681$	−2.09602	−	8.37116i	−0.0803196	−	0.320783i
$682$	−1.27615	+	16.3881i	−0.0488663	+	0.627534i
$683$	−16.0945			−0.615839			−0.307919	−	0.951412i	$-0.599633\pi$
$683$	−16.0945			−0.615839			−0.307919	+	0.951412i	$0.599633\pi$
$684$	−0.741269	−	2.12759i	−0.0283431	−	0.0813504i
$685$	−5.14238			−0.196480
$686$	2.17254	−	27.8994i	0.0829479	−	1.06521i
$687$	−2.63253	−	10.5139i	−0.100437	−	0.401130i
$688$	8.86607	−	27.5970i	0.338016	−	1.05213i
$689$		−	20.1295i		−	0.766871i
$690$	2.44369	−	0.413511i	0.0930296	−	0.0157421i
$691$		−	19.7417i		−	0.751011i	−0.926820	−	0.375505i	$-0.877469\pi$
$691$		−	19.7417i		−	0.751011i	0.926820	−	0.375505i	$-0.122531\pi$
$692$	−4.37610	+	27.9282i	−0.166354	+	1.06167i
$693$	3.50837	+	6.56671i	0.133272	+	0.249449i
$694$	18.3847	+	1.43162i	0.697872	+	0.0543435i
$695$	−0.148990			−0.00565150
$696$	18.3291	−	0.223645i	0.694764	−	0.00847724i
$697$	−59.6170			−2.25815
$698$	−43.2584	−	3.36854i	−1.63735	−	0.127501i
$699$	−20.5337	+	5.14135i	−0.776657	+	0.194464i
$700$	−2.44816	+	15.6242i	−0.0925319	+	0.590538i
$701$			0.697335i			0.0263380i	0.999913	+	0.0131690i	$0.00419194\pi$
$701$			0.697335i			0.0263380i	−0.999913	+	0.0131690i	$0.995808\pi$
$702$	−17.2449	−	22.2974i	−0.650865	−	0.841561i
$703$		−	2.95491i		−	0.111447i
$704$	−9.26018	−	4.66061i	−0.349006	−	0.175653i
$705$	−17.7536	+	4.44525i	−0.668640	+	0.167418i
$706$	−3.68975	+	47.3833i	−0.138866	+	1.78329i
$707$	−20.3265			−0.764455
$708$	0.278484	+	3.08885i	0.0104661	+	0.116086i
$709$	−33.9166			−1.27376			−0.636882	−	0.770962i	$-0.719776\pi$
$709$	−33.9166			−1.27376			−0.636882	+	0.770962i	$0.719776\pi$
$710$	−1.32077	+	16.9612i	−0.0495678	+	0.636542i
$711$	−14.6194	−	27.3635i	−0.548270	−	1.02621i
$712$	−1.49857	+	6.31088i	−0.0561614	+	0.236510i
$713$			9.72406i			0.364169i
$714$	−6.03570	−	35.6686i	−0.225880	−	1.33486i
$715$			4.63924i			0.173498i
$716$	−27.3862	−	4.29116i	−1.02347	−	0.160368i
$717$	3.42273	+	13.6698i	0.127824	+	0.510509i
$718$	9.18878	+	0.715534i	0.342922	+	0.0267035i
$719$	−42.9177			−1.60056			−0.800281	−	0.599625i	$-0.795316\pi$
$719$	−42.9177			−1.60056			−0.800281	+	0.599625i	$0.795316\pi$
$720$	2.00318	+	11.0190i	0.0746541	+	0.410655i
$721$	−7.26483			−0.270556
$722$	−26.5902	−	2.07058i	−0.989583	−	0.0770592i
$723$	2.88440	+	11.5198i	0.107272	+	0.428427i
$724$	−27.1610	−	4.25588i	−1.00943	−	0.158168i
$725$		−	15.4493i		−	0.573772i
$726$	−3.80923	−	22.5111i	−0.141374	−	0.835464i
$727$		−	29.4179i		−	1.09105i	−0.838095	−	0.545524i	$-0.816330\pi$
$727$		−	29.4179i		−	1.09105i	0.838095	−	0.545524i	$-0.183670\pi$
$728$	4.80045	−	20.2160i	0.177917	−	0.749253i
$729$	−2.66184	+	26.8685i	−0.0985866	+	0.995128i
$730$	−0.832482	+	10.6906i	−0.0308115	+	0.395677i
$731$	55.8828			2.06690
$732$	3.94296	+	43.7341i	0.145736	+	1.61646i
$733$	8.78246			0.324388			0.162194	−	0.986759i	$-0.448143\pi$
$733$	8.78246			0.324388			0.162194	+	0.986759i	$0.448143\pi$
$734$	−1.30741	+	16.7896i	−0.0482575	+	0.619716i
$735$	−5.22550	+	1.30839i	−0.192746	+	0.0482607i
$736$	−5.67554	−	2.32346i	−0.209203	−	0.0856439i
$737$			1.29586i			0.0477336i
$738$	13.1632	+	30.0416i	0.484545	+	1.10585i
$739$			14.6462i			0.538768i	0.963033	+	0.269384i	$0.0868201\pi$
$739$			14.6462i			0.538768i	−0.963033	+	0.269384i	$0.913180\pi$
$740$	−2.27383	+	14.5116i	−0.0835878	+	0.533457i
$741$	2.42012	−	0.605964i	0.0889054	−	0.0222606i
$742$	−14.1698	−	1.10340i	−0.520188	−	0.0405073i
$743$	29.6336			1.08715			0.543575	−	0.839360i	$-0.317070\pi$
$743$	29.6336			1.08715			0.543575	+	0.839360i	$0.317070\pi$
$744$	−43.9382	+	0.536117i	−1.61085	+	0.0196550i
$745$	1.97590			0.0723913
$746$	13.9591	+	1.08700i	0.511080	+	0.0397980i
$747$	−32.9794	+	17.6198i	−1.20665	+	0.644673i
$748$	3.09393	−	19.7455i	0.113125	−	0.721966i
$749$			17.1760i			0.627599i
$750$	20.5773	−	3.48201i	0.751376	−	0.127145i
$751$			54.3361i			1.98275i	0.131040	+	0.991377i	$0.458168\pi$
$751$			54.3361i			1.98275i	−0.131040	+	0.991377i	$0.541832\pi$
$752$	43.1159	+	13.8518i	1.57228	+	0.505124i
$753$	2.64504	+	10.5639i	0.0963905	+	0.384968i
$754$	−1.57583	+	20.2366i	−0.0573884	+	0.736973i
$755$	11.1791			0.406850
$756$	−16.6411	+	10.9170i	−0.605232	+	0.397046i
$757$	−30.0177			−1.09101			−0.545506	−	0.838107i	$-0.683662\pi$
$757$	−30.0177			−1.09101			−0.545506	+	0.838107i	$0.683662\pi$
$758$	−2.67545	+	34.3577i	−0.0971767	+	1.24793i
$759$	0.591020	+	2.36044i	0.0214527	+	0.0856785i
$760$	−0.964429	−	0.229012i	−0.0349835	−	0.00830714i
$761$		−	6.06585i		−	0.219887i	−0.993938	−	0.109943i	$-0.964933\pi$
$761$		−	6.06585i		−	0.219887i	0.993938	−	0.109943i	$-0.0350670\pi$
$762$	19.4928	−	3.29850i	0.706150	−	0.119492i
$763$			17.3681i			0.628768i
$764$	−13.2918	−	2.08271i	−0.480882	−	0.0753498i
$765$	−19.0443	+	10.1747i	−0.688547	+	0.367867i
$766$	−38.9903	−	3.03619i	−1.40878	−	0.109702i
$767$	−3.43424			−0.124003
$768$	10.1857	−	25.7731i	0.367544	−	0.930006i
$769$	14.3328			0.516855			0.258428	−	0.966031i	$-0.416796\pi$
$769$	14.3328			0.516855			0.258428	+	0.966031i	$0.416796\pi$
$770$	3.26571	+	0.254302i	0.117688	+	0.00916440i
$771$	27.1641	−	6.80151i	0.978292	−	0.244950i
$772$	−38.1458	−	5.97710i	−1.37290	−	0.215120i
$773$			8.42784i			0.303128i	0.988447	+	0.151564i	$0.0484310\pi$
$773$			8.42784i			0.303128i	−0.988447	+	0.151564i	$0.951569\pi$
$774$	−12.3387	−	28.1599i	−0.443507	−	1.01219i
$775$			37.0347i			1.33033i
$776$	7.23201	+	1.71730i	0.259614	+	0.0616476i
$777$	−25.3210	+	6.34002i	−0.908387	+	0.227447i
$778$	−2.45857	+	31.5726i	−0.0881440	+	1.13193i
$779$	−2.90294			−0.104009
$780$	−12.3515	+	1.11359i	−0.442256	+	0.0398728i
$781$	−16.7028			−0.597674
$782$	0.917908	−	11.7876i	0.0328243	−	0.421525i
$783$	14.4096	−	13.0526i	0.514958	−	0.466463i
$784$	12.6905	+	4.07707i	0.453233	+	0.145610i
$785$		−	21.6480i		−	0.772649i
$786$	−7.99483	−	47.2463i	−0.285166	−	1.68522i
$787$		−	5.72117i		−	0.203938i	−0.994788	−	0.101969i	$-0.967486\pi$
$787$		−	5.72117i		−	0.203938i	0.994788	−	0.101969i	$-0.0325142\pi$
$788$	−4.21233	+	26.8830i	−0.150058	+	0.957669i
$789$	1.87639	+	7.49400i	0.0668013	+	0.266794i
$790$	−13.6082	−	1.05968i	−0.484159	−	0.0377016i
$791$	6.54841			0.232835
$792$	−10.6331	+	2.80067i	−0.377830	+	0.0995174i
$793$	−48.6244			−1.72670
$794$	17.8654	+	1.39118i	0.634018	+	0.0493712i
$795$	2.06041	+	8.22896i	0.0730753	+	0.291851i
$796$	4.59753	−	29.3414i	0.162955	−	1.03998i
$797$			28.7502i			1.01838i	0.860653	+	0.509192i	$0.170056\pi$
$797$			28.7502i			1.01838i	−0.860653	+	0.509192i	$0.829944\pi$
$798$	−0.293897	−	1.73682i	−0.0104039	−	0.0614827i
$799$			87.3080i			3.08874i
$800$	−21.6157	−	8.84905i	−0.764229	−	0.312861i
$801$	3.24197	+	6.06809i	0.114549	+	0.214405i
$802$	−2.07394	+	26.6332i	−0.0732332	+	0.940451i
$803$	−10.5278			−0.371517
$804$	−3.45011	+	0.311053i	−0.121676	+	0.0109700i
$805$	1.93774			0.0682963
$806$	3.77755	−	48.5107i	0.133058	−	1.70872i
$807$	17.2090	−	4.30890i	0.605787	−	0.151680i
$808$	6.93567	−	29.2079i	0.243996	−	1.02753i
$809$		−	27.9282i		−	0.981905i	−0.871186	−	0.490952i	$-0.836649\pi$
$809$		−	27.9282i		−	0.981905i	0.871186	−	0.490952i	$-0.163351\pi$
$810$	9.33205	+	7.35007i	0.327895	+	0.258255i
$811$			17.3582i			0.609528i	0.952428	+	0.304764i	$0.0985777\pi$
$811$			17.3582i			0.609528i	−0.952428	+	0.304764i	$0.901422\pi$
$812$	14.1588	+	2.21855i	0.496877	+	0.0778560i
$813$	−28.2704	+	7.07849i	−0.991485	+	0.248254i
$814$	−14.3777	−	1.11960i	−0.503939	−	0.0392419i
$815$	5.24330			0.183665
$816$	53.3132	+	3.49769i	1.86633	+	0.122444i
$817$	2.72111			0.0951996
$818$	−16.9749	−	1.32184i	−0.593514	−	0.0462171i
$819$	−10.3852	−	19.4382i	−0.362887	−	0.679226i
$820$	14.2564	+	2.23384i	0.497854	+	0.0780091i
$821$		−	18.6612i		−	0.651281i	−0.945494	−	0.325640i	$-0.894420\pi$
$821$		−	18.6612i		−	0.651281i	0.945494	−	0.325640i	$-0.105580\pi$
$822$	13.3072	−	2.25179i	0.464142	−	0.0785403i
$823$		−	37.5408i		−	1.30859i	−0.756240	−	0.654294i	$-0.772966\pi$
$823$		−	37.5408i		−	1.30859i	0.756240	−	0.654294i	$-0.227034\pi$
$824$	2.47886	−	10.4391i	0.0863552	−	0.363664i
$825$	2.25094	+	8.98988i	0.0783676	+	0.312988i
$826$	−0.188249	+	2.41747i	−0.00655004	+	0.0841147i
$827$	−0.361701			−0.0125776			−0.00628878	−	0.999980i	$-0.502002\pi$
$827$	−0.361701			−0.0125776			−0.00628878	+	0.999980i	$0.502002\pi$
$828$	−6.14259	+	2.14013i	−0.213470	+	0.0743746i
$829$	13.1110			0.455364			0.227682	−	0.973736i	$-0.426885\pi$
$829$	13.1110			0.455364			0.227682	+	0.973736i	$0.426885\pi$
$830$	−1.27716	+	16.4011i	−0.0443307	+	0.569289i
$831$	0.454068	+	1.81347i	0.0157514	+	0.0629087i
$832$	27.4112	+	13.7959i	0.950311	+	0.478288i
$833$			25.6978i			0.890375i
$834$	0.385549	−	0.0652410i	0.0133505	−	0.00225911i
$835$		−	11.9402i		−	0.413208i
$836$	0.150653	−	0.961469i	0.00521046	−	0.0332531i
$837$	−34.5425	+	31.2895i	−1.19396	+	1.08152i
$838$	13.2610	+	1.03264i	0.458094	+	0.0356719i
$839$	33.0599			1.14135			0.570676	−	0.821175i	$-0.306681\pi$
$839$	33.0599			1.14135			0.570676	+	0.821175i	$0.306681\pi$
$840$	0.106833	+	8.75569i	0.00368610	+	0.302100i
$841$	14.9997			0.517231
$842$	−2.59878	−	0.202368i	−0.0895597	−	0.00697405i
$843$	55.4612	−	13.8867i	1.91018	−	0.478283i
$844$	−5.93652	+	37.8868i	−0.204343	+	1.30412i
$845$		−	1.59973i		−	0.0550325i
$846$	43.9954	−	19.2773i	1.51259	−	0.662768i
$847$		−	17.8503i		−	0.613343i
$848$	6.42045	−	19.9846i	0.220479	−	0.686275i
$849$	−52.2599	+	13.0851i	−1.79355	+	0.449080i
$850$	3.49591	−	44.8940i	0.119909	−	1.53985i
$851$	−8.53116			−0.292444
$852$	−4.00929	−	44.4697i	−0.137356	−	1.52351i
$853$	25.6227			0.877303			0.438651	−	0.898657i	$-0.355456\pi$
$853$	25.6227			0.877303			0.438651	+	0.898657i	$0.355456\pi$
$854$	−2.66537	+	34.2282i	−0.0912069	+	1.17127i
$855$	−0.927325	+	0.495438i	−0.0317139	+	0.0169436i
$856$	−24.6809	−	5.86070i	−0.843577	−	0.200315i
$857$			29.2186i			0.998087i	0.866577	+	0.499043i	$0.166315\pi$
$857$			29.2186i			0.998087i	−0.866577	+	0.499043i	$0.833685\pi$
$858$	−2.03147	−	12.0052i	−0.0693533	−	0.409851i
$859$		−	13.7455i		−	0.468990i	−0.972117	−	0.234495i	$-0.924656\pi$
$859$		−	13.7455i		−	0.468990i	0.972117	−	0.234495i	$-0.0753436\pi$
$860$	−13.3634	−	2.09392i	−0.455688	−	0.0714021i
$861$	6.22851	+	24.8757i	0.212267	+	0.847761i
$862$	1.64511	+	0.128105i	0.0560327	+	0.00436329i
$863$	−0.199200			−0.00678084			−0.00339042	−	0.999994i	$-0.501079\pi$
$863$	−0.199200			−0.00678084			−0.00339042	+	0.999994i	$0.501079\pi$
$864$	−10.0088	−	27.6373i	−0.340508	−	0.940242i
$865$	13.1918			0.448534
$866$	−41.5745	−	3.23742i	−1.41276	−	0.110012i
$867$	17.8666	+	71.3563i	0.606781	+	2.42339i
$868$	−33.9412	−	5.31827i	−1.15204	−	0.180514i
$869$		−	13.4009i		−	0.454595i
$870$	−1.42718	−	8.43405i	−0.0483858	−	0.285941i
$871$		−	3.83589i		−	0.129974i
$872$	−24.9569	−	5.92624i	−0.845149	−	0.200688i
$873$	6.95378	−	3.71517i	0.235350	−	0.125739i
$874$	0.0446958	−	0.573977i	0.00151186	−	0.0194151i
$875$	16.3169			0.551612
$876$	−2.52705	−	28.0292i	−0.0853810	−	0.947019i
$877$	44.3702			1.49828			0.749138	−	0.662414i	$-0.230468\pi$
$877$	44.3702			1.49828			0.749138	+	0.662414i	$0.230468\pi$
$878$	2.04705	−	26.2879i	0.0690844	−	0.887173i
$879$	38.5763	−	9.65895i	1.30115	−	0.325788i
$880$	−1.47972	+	4.60586i	−0.0498814	+	0.155263i
$881$		−	45.5374i		−	1.53419i	−0.641531	−	0.767097i	$-0.721700\pi$
$881$		−	45.5374i		−	1.53419i	0.641531	−	0.767097i	$-0.278300\pi$
$882$	12.9494	−	5.67398i	0.436028	−	0.191053i
$883$		−	12.9182i		−	0.434732i	−0.976090	−	0.217366i	$-0.930254\pi$
$883$		−	12.9182i		−	0.434732i	0.976090	−	0.217366i	$-0.0697465\pi$
$884$	−9.15839	+	58.4488i	−0.308030	+	1.96585i
$885$	1.40392	−	0.351523i	0.0471924	−	0.0118163i
$886$	9.83787	+	0.766078i	0.330510	+	0.0257369i
$887$	−16.8523			−0.565845			−0.282923	−	0.959143i	$-0.591304\pi$
$887$	−16.8523			−0.565845			−0.282923	+	0.959143i	$0.591304\pi$
$888$	−0.470349	−	38.5481i	−0.0157839	−	1.29359i
$889$	15.4570			0.518410
$890$	3.01774	+	0.234992i	0.101155	+	0.00787695i
$891$	−6.48317	+	9.69474i	−0.217194	+	0.324786i
$892$	−2.85856	+	18.2433i	−0.0957118	+	0.610832i
$893$			4.25130i			0.142264i
$894$	−5.11313	+	0.865224i	−0.171009	+	0.0289374i
$895$			12.9357i			0.432394i
$896$	11.2140	−	18.5394i	0.374632	−	0.619357i
$897$	−1.74949	−	6.98717i	−0.0584136	−	0.233295i
$898$	−1.16013	+	14.8982i	−0.0387140	+	0.497159i
$899$	33.5613			1.11933
$900$	−23.3944	+	8.15081i	−0.779814	+	0.271694i
$901$	40.4681			1.34819
$902$	−1.09991	+	14.1248i	−0.0366229	+	0.470306i
$903$	−5.83838	−	23.3176i	−0.194289	−	0.775959i
$904$	−2.23441	+	9.40968i	−0.0743153	+	0.312961i
$905$			12.8294i			0.426462i
$906$	−28.9288	+	4.89522i	−0.961096	+	0.162633i
$907$			42.1478i			1.39949i	0.714391	+	0.699747i	$0.246704\pi$
$907$			42.1478i			1.39949i	−0.714391	+	0.699747i	$0.753296\pi$
$908$	9.84446	+	1.54254i	0.326700	+	0.0511909i
$909$	−15.0044	−	28.0842i	−0.497666	−	0.931495i
$910$	−9.66686	−	0.752762i	−0.320453	−	0.0249538i
$911$	10.6216			0.351910			0.175955	−	0.984398i	$-0.443699\pi$
$911$	10.6216			0.351910			0.175955	+	0.984398i	$0.443699\pi$
$912$	2.59599	+	0.170313i	0.0859617	+	0.00563964i
$913$	−16.1512			−0.534527
$914$	12.0477	+	0.938159i	0.398502	+	0.0310315i
$915$	19.8777	−	4.97710i	0.657138	−	0.164538i
$916$	12.3643	+	1.93737i	0.408528	+	0.0640126i
$917$		−	37.4643i		−	1.23718i
$918$	44.8265	−	34.6689i	1.47949	−	1.14424i
$919$		−	10.9923i		−	0.362602i	−0.983428	−	0.181301i	$-0.941969\pi$
$919$		−	10.9923i		−	0.362602i	0.983428	−	0.181301i	$-0.0580308\pi$
$920$	−0.661183	+	2.78442i	−0.0217986	+	0.0917995i
$921$	40.8185	−	10.2204i	1.34502	−	0.336773i
$922$	−2.82272	+	36.2490i	−0.0929613	+	1.19380i
$923$	49.4422			1.62741
$924$	−8.56220	+	0.771948i	−0.281676	+	0.0253952i
$925$	−32.4915			−1.06831
$926$	−1.45994	+	18.7484i	−0.0479767	+	0.616111i
$927$	−5.36270	−	10.0375i	−0.176134	−	0.329675i
$928$	−8.01911	+	19.5884i	−0.263240	+	0.643019i
$929$			25.2167i			0.827334i	0.910428	+	0.413667i	$0.135752\pi$
$929$			25.2167i			0.827334i	−0.910428	+	0.413667i	$0.864248\pi$
$930$	3.42120	+	20.2179i	0.112186	+	0.662972i
$931$			1.25131i			0.0410099i
$932$	3.78371	−	24.1476i	0.123939	−	0.790981i
$933$	0.466318	+	1.86240i	0.0152666	+	0.0609723i
$934$	39.9316	+	3.10949i	1.30660	+	0.101746i
$935$	−9.32668			−0.305015
$936$	31.4751	−	8.29029i	1.02880	−	0.270977i
$937$	−48.4525			−1.58287			−0.791437	−	0.611250i	$-0.790667\pi$
$937$	−48.4525			−1.58287			−0.791437	+	0.611250i	$0.790667\pi$
$938$	−2.70021	−	0.210266i	−0.0881649	−	0.00686543i
$939$	−5.92858	−	23.6778i	−0.193472	−	0.772696i
$940$	3.27142	−	20.8782i	0.106702	−	0.680972i
$941$			16.2496i			0.529720i	0.964287	+	0.264860i	$0.0853258\pi$
$941$			16.2496i			0.529720i	−0.964287	+	0.264860i	$0.914674\pi$
$942$	9.47941	+	56.0196i	0.308856	+	1.82522i
$943$			8.38111i			0.272927i
$944$	−3.40953	−	1.09538i	−0.110971	−	0.0356515i
$945$	6.23514	+	6.88337i	0.202829	+	0.223916i
$946$	1.03101	−	13.2401i	0.0335211	−	0.430473i
$947$	−21.0889			−0.685299			−0.342649	−	0.939463i	$-0.611324\pi$
$947$	−21.0889			−0.685299			−0.342649	+	0.939463i	$0.611324\pi$
$948$	35.6787	−	3.21671i	1.15879	−	0.104474i
$949$	31.1634			1.01161
$950$	0.170227	−	2.18603i	0.00552289	−	0.0709241i
$951$	−5.09075	+	1.27465i	−0.165079	+	0.0413333i
$952$	40.6420	+	9.65078i	1.31721	+	0.312784i
$953$		−	47.8875i		−	1.55123i	−0.631208	−	0.775614i	$-0.717441\pi$
$953$		−	47.8875i		−	1.55123i	0.631208	−	0.775614i	$-0.282559\pi$
$954$	−8.93521	−	20.3923i	−0.289288	−	0.660224i
$955$			6.27834i			0.203162i
$956$	−16.0757	−	2.51891i	−0.519924	−	0.0814674i
$957$	8.14674	−	2.03983i	0.263347	−	0.0659382i
$958$	1.19846	+	0.0933246i	0.0387205	+	0.00301518i
$959$	10.5520			0.340743
$960$	−12.6179	−	2.83405i	−0.407240	−	0.0914685i
$961$	−49.4524			−1.59524
$962$	42.5597	+	3.31414i	1.37218	+	0.106852i
$963$	−23.7314	+	12.6789i	−0.764734	+	0.408571i
$964$	−13.5473	−	2.12274i	−0.436329	−	0.0683688i
$965$			18.0180i			0.580019i
$966$	−5.01439	+	0.848515i	−0.161335	+	0.0273005i
$967$			37.0686i			1.19204i	0.802968	+	0.596022i	$0.203253\pi$
$967$			37.0686i			1.19204i	−0.802968	+	0.596022i	$0.796747\pi$
$968$	25.6498	+	6.09077i	0.824416	+	0.195765i
$969$	1.21822	+	4.86539i	0.0391350	+	0.156299i
$970$	0.269291	−	3.45820i	0.00864642	−	0.111036i
$971$	6.94642			0.222921			0.111461	−	0.993769i	$-0.464447\pi$
$971$	6.94642			0.222921			0.111461	+	0.993769i	$0.464447\pi$
$972$	−27.3676	−	14.9338i	−0.877815	−	0.479000i
$973$	0.305723			0.00980104
$974$	−0.673516	+	8.64920i	−0.0215808	+	0.277138i
$975$	−6.66303	−	26.6111i	−0.213388	−	0.852236i
$976$	−48.2745	−	15.5091i	−1.54523	−	0.496435i
$977$			0.911435i			0.0291594i	0.999894	+	0.0145797i	$0.00464102\pi$
$977$			0.911435i			0.0291594i	−0.999894	+	0.0145797i	$0.995359\pi$
$978$	−13.5684	+	2.29599i	−0.433869	+	0.0734175i
$979$			2.97177i			0.0949781i
$980$	0.962893	−	6.14518i	0.0307585	−	0.196300i
$981$	−23.9968	+	12.8207i	−0.766158	+	0.409332i
$982$	−55.4530	−	4.31815i	−1.76958	−	0.137798i
$983$	−1.97235			−0.0629081			−0.0314540	−	0.999505i	$-0.510014\pi$
$983$	−1.97235			−0.0629081			−0.0314540	+	0.999505i	$0.510014\pi$
$984$	−37.8701	+	0.462076i	−1.20726	+	0.0147304i
$985$	12.6981			0.404594
$986$	−40.6834	−	3.16803i	−1.29562	−	0.100891i
$987$	36.4300	−	9.12154i	1.15958	−	0.290342i
$988$	−0.445951	+	2.84606i	−0.0141876	+	0.0905451i
$989$		−	7.85615i		−	0.249811i
$990$	2.05930	+	4.69981i	0.0654488	+	0.149370i
$991$		−	12.3674i		−	0.392862i	−0.980518	−	0.196431i	$-0.937065\pi$
$991$		−	12.3674i		−	0.392862i	0.980518	−	0.196431i	$-0.0629352\pi$
$992$	19.2232	−	46.9568i	0.610339	−	1.49088i
$993$	14.6402	−	3.66570i	0.464593	−	0.116327i
$994$	2.71020	−	34.8040i	0.0859623	−	1.10392i
$995$	−13.8593			−0.439368
$996$	−3.87688	−	43.0011i	−0.122844	−	1.36254i
$997$	36.7168			1.16283			0.581417	−	0.813606i	$-0.302499\pi$
$997$	36.7168			1.16283			0.581417	+	0.813606i	$0.302499\pi$
$998$	0.623103	−	8.00180i	0.0197240	−	0.253292i
$999$	−27.4510	−	30.3050i	−0.868512	−	0.958807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.3	✓	128
3.2	odd	2	inner	804.2.c.b.671.126	yes	128
4.3	odd	2	inner	804.2.c.b.671.125	yes	128
12.11	even	2	inner	804.2.c.b.671.4	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.3	✓	128	1.1	even	1	trivial
804.2.c.b.671.4	yes	128	12.11	even	2	inner
804.2.c.b.671.125	yes	128	4.3	odd	2	inner
804.2.c.b.671.126	yes	128	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40995 - 0.109793i) q^{2} +(-0.420694 - 1.68018i) q^{3} +(1.97589 + 0.309604i) q^{4} -0.933302i q^{5} +(0.408683 + 2.41516i) q^{6} +1.91511i q^{7} +(-2.75191 - 0.653464i) q^{8} +(-2.64603 + 1.41369i) q^{9} +O(q^{10})\)	\(q+(-1.40995 - 0.109793i) q^{2} +(-0.420694 - 1.68018i) q^{3} +(1.97589 + 0.309604i) q^{4} -0.933302i q^{5} +(0.408683 + 2.41516i) q^{6} +1.91511i q^{7} +(-2.75191 - 0.653464i) q^{8} +(-2.64603 + 1.41369i) q^{9} +(-0.102470 + 1.31591i) q^{10} -1.29586 q^{11} +(-0.311053 - 3.45011i) q^{12} +3.83589 q^{13} +(0.210266 - 2.70021i) q^{14} +(-1.56812 + 0.392634i) q^{15} +(3.80829 + 1.22349i) q^{16} +7.71164i q^{17} +(3.88597 - 1.70270i) q^{18} +0.375504i q^{19} +(0.288954 - 1.84410i) q^{20} +(3.21774 - 0.805677i) q^{21} +(1.82709 + 0.142276i) q^{22} +1.08412 q^{23} +(0.0597709 + 4.89861i) q^{24} +4.12895 q^{25} +(-5.40840 - 0.421154i) q^{26} +(3.48842 + 3.85109i) q^{27} +(-0.592927 + 3.78406i) q^{28} -3.74170i q^{29} +(2.25407 - 0.381425i) q^{30} +8.96952i q^{31} +(-5.23515 - 2.14317i) q^{32} +(0.545160 + 2.17728i) q^{33} +(0.846683 - 10.8730i) q^{34} +1.78738 q^{35} +(-5.66596 + 1.97407i) q^{36} -7.86919 q^{37} +(0.0412277 - 0.529440i) q^{38} +(-1.61374 - 6.44500i) q^{39} +(-0.609879 + 2.56836i) q^{40} +7.73078i q^{41} +(-4.62530 + 0.782674i) q^{42} -7.24655i q^{43} +(-2.56048 - 0.401203i) q^{44} +(1.31940 + 2.46955i) q^{45} +(-1.52855 - 0.119029i) q^{46} +11.3216 q^{47} +(0.453560 - 6.91334i) q^{48} +3.33234 q^{49} +(-5.82159 - 0.453329i) q^{50} +(12.9570 - 3.24424i) q^{51} +(7.57930 + 1.18761i) q^{52} -5.24766i q^{53} +(-4.49566 - 5.81283i) q^{54} +1.20943i q^{55} +(1.25146 - 5.27021i) q^{56} +(0.630915 - 0.157972i) q^{57} +(-0.410812 + 5.27559i) q^{58} -0.895292 q^{59} +(-3.21999 + 0.290307i) q^{60} -12.6762 q^{61} +(0.984790 - 12.6465i) q^{62} +(-2.70737 - 5.06746i) q^{63} +(7.14597 + 3.59654i) q^{64} -3.58005i q^{65} +(-0.529596 - 3.12970i) q^{66} -1.00000i q^{67} +(-2.38755 + 15.2374i) q^{68} +(-0.456083 - 1.82152i) q^{69} +(-2.52011 - 0.196242i) q^{70} +12.8894 q^{71} +(8.20543 - 2.16124i) q^{72} +8.12415 q^{73} +(11.0951 + 0.863981i) q^{74} +(-1.73702 - 6.93739i) q^{75} +(-0.116258 + 0.741955i) q^{76} -2.48172i q^{77} +(1.56766 + 9.26427i) q^{78} +10.3413i q^{79} +(1.14188 - 3.55429i) q^{80} +(5.00299 - 7.48132i) q^{81} +(0.848785 - 10.9000i) q^{82} +12.4637 q^{83} +(6.60735 - 0.595703i) q^{84} +7.19729 q^{85} +(-0.795620 + 10.2172i) q^{86} +(-6.28674 + 1.57411i) q^{87} +(3.56608 + 0.846797i) q^{88} -2.29328i q^{89} +(-1.58914 - 3.62679i) q^{90} +7.34617i q^{91} +(2.14211 + 0.335649i) q^{92} +(15.0704 - 3.77342i) q^{93} +(-15.9628 - 1.24303i) q^{94} +0.350459 q^{95} +(-1.39853 + 9.69763i) q^{96} -2.62800 q^{97} +(-4.69841 - 0.365867i) q^{98} +(3.42889 - 1.83194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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