LMFDB - Embedded newform 525.2.n.d.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (of order $5$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			211.1
Character	$\chi$	$=$	525.211
Dual form			525.2.n.d.316.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.01265 + 1.46227i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.29447 - 3.98396i) q^{4} +(-1.44782 + 1.70406i) q^{5} +(0.768762 + 2.36601i) q^{6} -1.00000 q^{7} +(1.68281 + 5.17916i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-2.01265 + 1.46227i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.29447 - 3.98396i) q^{4} +(-1.44782 + 1.70406i) q^{5} +(0.768762 + 2.36601i) q^{6} -1.00000 q^{7} +(1.68281 + 5.17916i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.422145 - 5.54678i) q^{10} +(-0.214637 + 0.155943i) q^{11} +(-3.38896 - 2.46222i) q^{12} +(1.25901 + 0.914723i) q^{13} +(2.01265 - 1.46227i) q^{14} +(1.17326 + 1.90354i) q^{15} +(-4.18232 - 3.03864i) q^{16} +(0.612083 + 1.88380i) q^{17} +2.48777 q^{18} +(-1.44527 - 4.44809i) q^{19} +(4.91476 + 7.97391i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(0.203957 - 0.627717i) q^{22} +(-3.31980 + 2.41198i) q^{23} +5.44569 q^{24} +(-0.807642 - 4.93434i) q^{25} -3.87151 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.29447 + 3.98396i) q^{28} +(2.89950 - 8.92374i) q^{29} +(-5.14485 - 2.11553i) q^{30} +(-0.569538 - 1.75286i) q^{31} +1.96947 q^{32} +(0.0819841 + 0.252321i) q^{33} +(-3.98653 - 2.89639i) q^{34} +(1.44782 - 1.70406i) q^{35} +(-3.38896 + 2.46222i) q^{36} +(-8.66441 - 6.29506i) q^{37} +(9.41315 + 6.83905i) q^{38} +(1.25901 - 0.914723i) q^{39} +(-11.2620 - 4.63087i) q^{40} +(-8.64316 - 6.27962i) q^{41} +(-0.768762 - 2.36601i) q^{42} +0.340414 q^{43} +(0.343430 + 1.05697i) q^{44} +(2.17293 - 0.527607i) q^{45} +(3.15462 - 9.70891i) q^{46} +(0.0625691 - 0.192568i) q^{47} +(-4.18232 + 3.03864i) q^{48} +1.00000 q^{49} +(8.84085 + 8.75009i) q^{50} +1.98074 q^{51} +(5.27397 - 3.83176i) q^{52} +(2.55637 - 7.86769i) q^{53} +(0.768762 - 2.36601i) q^{54} +(0.0450194 - 0.591532i) q^{55} +(-1.68281 - 5.17916i) q^{56} -4.67700 q^{57} +(7.21328 + 22.2002i) q^{58} +(1.85859 + 1.35035i) q^{59} +(9.10238 - 2.21014i) q^{60} +(7.35885 - 5.34652i) q^{61} +(3.70944 + 2.69506i) q^{62} +(0.809017 + 0.587785i) q^{63} +(4.40079 - 3.19736i) q^{64} +(-3.38156 + 0.821073i) q^{65} +(-0.533968 - 0.387950i) q^{66} +(2.88757 + 8.88701i) q^{67} +8.29730 q^{68} +(1.26805 + 3.90266i) q^{69} +(-0.422145 + 5.54678i) q^{70} +(3.11812 - 9.59658i) q^{71} +(1.68281 - 5.17916i) q^{72} +(1.04996 - 0.762843i) q^{73} +26.6435 q^{74} +(-4.94241 - 0.756681i) q^{75} -19.5919 q^{76} +(0.214637 - 0.155943i) q^{77} +(-1.19636 + 3.68203i) q^{78} +(-2.18567 + 6.72681i) q^{79} +(11.2333 - 2.72754i) q^{80} +(0.309017 + 0.951057i) q^{81} +26.5781 q^{82} +(-1.57735 - 4.85459i) q^{83} +(3.38896 + 2.46222i) q^{84} +(-4.09629 - 1.68437i) q^{85} +(-0.685132 + 0.497778i) q^{86} +(-7.59099 - 5.51518i) q^{87} +(-1.16885 - 0.849218i) q^{88} +(-2.89584 + 2.10395i) q^{89} +(-3.60184 + 4.23931i) q^{90} +(-1.25901 - 0.914723i) q^{91} +(5.31185 + 16.3482i) q^{92} -1.84306 q^{93} +(0.155657 + 0.479065i) q^{94} +(9.67231 + 3.97720i) q^{95} +(0.608601 - 1.87308i) q^{96} +(-1.37639 + 4.23608i) q^{97} +(-2.01265 + 1.46227i) q^{98} +0.265306 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) $ 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−2.01265	+	1.46227i	−1.42316	+	1.03398i	−0.431915	+	0.901914i	$0.642162\pi$
$2$	−2.01265	+	1.46227i	−1.42316	+	1.03398i	−0.991241	+	0.132069i	$0.957838\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	1.29447	−	3.98396i	0.647234	−	1.99198i
$5$	−1.44782	+	1.70406i	−0.647484	+	0.762079i
$5$	−1.44782	+	1.70406i	−0.647484	+	0.762079i
$6$	0.768762	+	2.36601i	0.313846	+	0.965918i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	1.68281	+	5.17916i	0.594963	+	1.83111i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	0.422145	−	5.54678i	0.133494	−	1.75404i
$11$	−0.214637	+	0.155943i	−0.0647156	+	0.0470186i	−0.619673	−	0.784860i	$-0.712735\pi$
$11$	−0.214637	+	0.155943i	−0.0647156	+	0.0470186i	0.554957	+	0.831879i	$0.312735\pi$
$12$	−3.38896	−	2.46222i	−0.978309	−	0.710783i
$13$	1.25901	+	0.914723i	0.349186	+	0.253698i	0.748527	−	0.663104i	$-0.230761\pi$
$13$	1.25901	+	0.914723i	0.349186	+	0.253698i	−0.399342	+	0.916802i	$0.630761\pi$
$14$	2.01265	−	1.46227i	0.537902	−	0.390809i
$15$	1.17326	+	1.90354i	0.302934	+	0.491492i
$16$	−4.18232	−	3.03864i	−1.04558	−	0.759659i
$17$	0.612083	+	1.88380i	0.148452	+	0.456888i	0.997439	−	0.0715260i	$-0.0227869\pi$
$17$	0.612083	+	1.88380i	0.148452	+	0.456888i	−0.848987	+	0.528414i	$0.822787\pi$
$18$	2.48777			0.586372
$19$	−1.44527	−	4.44809i	−0.331568	−	1.02046i	−0.968388	−	0.249449i	$-0.919750\pi$
$19$	−1.44527	−	4.44809i	−0.331568	−	1.02046i	0.636820	−	0.771013i	$-0.280250\pi$
$20$	4.91476	+	7.97391i	1.09897	+	1.78302i
$21$	−0.309017	+	0.951057i	−0.0674330	+	0.207538i
$22$	0.203957	−	0.627717i	0.0434839	−	0.133830i
$23$	−3.31980	+	2.41198i	−0.692226	+	0.502932i	−0.877391	−	0.479776i	$-0.840718\pi$
$23$	−3.31980	+	2.41198i	−0.692226	+	0.502932i	0.185165	+	0.982707i	$0.440718\pi$
$24$	5.44569			1.11160
$25$	−0.807642	−	4.93434i	−0.161528	−	0.986868i
$26$	−3.87151			−0.759266
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−1.29447	+	3.98396i	−0.244631	+	0.752898i
$29$	2.89950	−	8.92374i	0.538424	−	1.65710i	−0.197710	−	0.980261i	$-0.563350\pi$
$29$	2.89950	−	8.92374i	0.538424	−	1.65710i	0.736133	−	0.676837i	$-0.236650\pi$
$30$	−5.14485	−	2.11553i	−0.939316	−	0.386242i
$31$	−0.569538	−	1.75286i	−0.102292	−	0.314823i	0.886793	−	0.462166i	$-0.152928\pi$
$31$	−0.569538	−	1.75286i	−0.102292	−	0.314823i	−0.989085	+	0.147344i	$0.952928\pi$
$32$	1.96947			0.348157
$33$	0.0819841	+	0.252321i	0.0142716	+	0.0439235i
$34$	−3.98653	−	2.89639i	−0.683685	−	0.496726i
$35$	1.44782	−	1.70406i	0.244726	−	0.288039i
$36$	−3.38896	+	2.46222i	−0.564827	+	0.410371i
$37$	−8.66441	−	6.29506i	−1.42442	−	1.03490i	−0.991022	−	0.133700i	$-0.957314\pi$
$37$	−8.66441	−	6.29506i	−1.42442	−	1.03490i	−0.433399	−	0.901202i	$-0.642686\pi$
$38$	9.41315	+	6.83905i	1.52701	+	1.10944i
$39$	1.25901	−	0.914723i	0.201603	−	0.146473i
$40$	−11.2620	−	4.63087i	−1.78068	−	0.732205i
$41$	−8.64316	−	6.27962i	−1.34983	−	0.980712i	−0.999020	−	0.0442671i	$-0.985905\pi$
$41$	−8.64316	−	6.27962i	−1.34983	−	0.980712i	−0.350815	−	0.936445i	$-0.614095\pi$
$42$	−0.768762	−	2.36601i	−0.118623	−	0.365083i
$43$	0.340414			0.0519126			0.0259563	−	0.999663i	$-0.491737\pi$
$43$	0.340414			0.0519126			0.0259563	+	0.999663i	$0.491737\pi$
$44$	0.343430	+	1.05697i	0.0517741	+	0.159344i
$45$	2.17293	−	0.527607i	0.323921	−	0.0786510i
$46$	3.15462	−	9.70891i	0.465123	−	1.43150i
$47$	0.0625691	−	0.192568i	0.00912665	−	0.0280889i	−0.946389	−	0.323028i	$-0.895299\pi$
$47$	0.0625691	−	0.192568i	0.00912665	−	0.0280889i	0.955516	+	0.294939i	$0.0952993\pi$
$48$	−4.18232	+	3.03864i	−0.603667	+	0.438589i
$49$	1.00000			0.142857
$50$	8.84085	+	8.75009i	1.25029	+	1.23745i
$51$	1.98074			0.277359
$52$	5.27397	−	3.83176i	0.731368	−	0.531370i
$53$	2.55637	−	7.86769i	0.351144	−	1.08071i	−0.607068	−	0.794650i	$-0.707654\pi$
$53$	2.55637	−	7.86769i	0.351144	−	1.08071i	0.958212	−	0.286060i	$-0.0923457\pi$
$54$	0.768762	−	2.36601i	0.104615	−	0.321973i
$55$	0.0450194	−	0.591532i	0.00607041	−	0.0797622i
$56$	−1.68281	−	5.17916i	−0.224875	−	0.692094i
$57$	−4.67700			−0.619484
$58$	7.21328	+	22.2002i	0.947150	+	2.91503i
$59$	1.85859	+	1.35035i	0.241968	+	0.175800i	0.702160	−	0.712019i	$-0.252219\pi$
$59$	1.85859	+	1.35035i	0.241968	+	0.175800i	−0.460191	+	0.887820i	$0.652219\pi$
$60$	9.10238	−	2.21014i	1.17511	−	0.285328i
$61$	7.35885	−	5.34652i	0.942205	−	0.684552i	−0.00674566	−	0.999977i	$-0.502147\pi$
$61$	7.35885	−	5.34652i	0.942205	−	0.684552i	0.948950	+	0.315425i	$0.102147\pi$
$62$	3.70944	+	2.69506i	0.471099	+	0.342273i
$63$	0.809017	+	0.587785i	0.101927	+	0.0740540i
$64$	4.40079	−	3.19736i	0.550099	−	0.399670i
$65$	−3.38156	+	0.821073i	−0.419431	+	0.101842i
$66$	−0.533968	−	0.387950i	−0.0657269	−	0.0477534i
$67$	2.88757	+	8.88701i	0.352772	+	1.08572i	0.957290	+	0.289130i	$0.0933659\pi$
$67$	2.88757	+	8.88701i	0.352772	+	1.08572i	−0.604518	+	0.796592i	$0.706634\pi$
$68$	8.29730			1.00620
$69$	1.26805	+	3.90266i	0.152655	+	0.469825i
$70$	−0.422145	+	5.54678i	−0.0504560	+	0.662967i
$71$	3.11812	−	9.59658i	0.370053	−	1.13890i	−0.576704	−	0.816953i	$-0.695661\pi$
$71$	3.11812	−	9.59658i	0.370053	−	1.13890i	0.946756	−	0.321951i	$-0.104339\pi$
$72$	1.68281	−	5.17916i	0.198321	−	0.610370i
$73$	1.04996	−	0.762843i	0.122889	−	0.0892841i	−0.524643	−	0.851322i	$-0.675801\pi$
$73$	1.04996	−	0.762843i	0.122889	−	0.0892841i	0.647532	+	0.762038i	$0.275801\pi$
$74$	26.6435			3.09724
$75$	−4.94241	−	0.756681i	−0.570701	−	0.0873740i
$76$	−19.5919			−2.24734
$77$	0.214637	−	0.155943i	0.0244602	−	0.0177714i
$78$	−1.19636	+	3.68203i	−0.135461	+	0.416907i
$79$	−2.18567	+	6.72681i	−0.245907	+	0.756825i	0.749579	+	0.661915i	$0.230256\pi$
$79$	−2.18567	+	6.72681i	−0.245907	+	0.756825i	−0.995486	+	0.0949095i	$0.969744\pi$
$80$	11.2333	−	2.72754i	1.25592	−	0.304948i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	26.5781			2.93506
$83$	−1.57735	−	4.85459i	−0.173137	−	0.532861i	0.826406	−	0.563074i	$-0.190381\pi$
$83$	−1.57735	−	4.85459i	−0.173137	−	0.532861i	−0.999543	+	0.0302131i	$0.990381\pi$
$84$	3.38896	+	2.46222i	0.369766	+	0.268651i
$85$	−4.09629	−	1.68437i	−0.444305	−	0.182696i
$86$	−0.685132	+	0.497778i	−0.0738797	+	0.0536768i
$87$	−7.59099	−	5.51518i	−0.813839	−	0.591289i
$88$	−1.16885	−	0.849218i	−0.124600	−	0.0905269i
$89$	−2.89584	+	2.10395i	−0.306959	+	0.223019i	−0.730590	−	0.682816i	$-0.760755\pi$
$89$	−2.89584	+	2.10395i	−0.306959	+	0.223019i	0.423632	+	0.905834i	$0.360755\pi$
$90$	−3.60184	+	4.23931i	−0.379667	+	0.446862i
$91$	−1.25901	−	0.914723i	−0.131980	−	0.0958890i
$92$	5.31185	+	16.3482i	0.553798	+	1.70442i
$93$	−1.84306			−0.191117
$94$	0.155657	+	0.479065i	0.0160548	+	0.0494117i
$95$	9.67231	+	3.97720i	0.992358	+	0.408052i
$96$	0.608601	−	1.87308i	0.0621151	−	0.191171i
$97$	−1.37639	+	4.23608i	−0.139751	+	0.430109i	−0.996299	−	0.0859587i	$-0.972605\pi$
$97$	−1.37639	+	4.23608i	−0.139751	+	0.430109i	0.856548	+	0.516068i	$0.172605\pi$
$98$	−2.01265	+	1.46227i	−0.203308	+	0.147712i
$99$	0.265306			0.0266643
$100$	−20.7037	−	3.16973i	−2.07037	−	0.316973i
$101$	−10.7501			−1.06968			−0.534838	−	0.844955i	$-0.679627\pi$
$101$	−10.7501			−1.06968			−0.534838	+	0.844955i	$0.679627\pi$
$102$	−3.98653	+	2.89639i	−0.394726	+	0.286785i
$103$	3.67326	−	11.3051i	0.361937	−	1.11393i	−0.589939	−	0.807447i	$-0.700848\pi$
$103$	3.67326	−	11.3051i	0.361937	−	1.11393i	0.951877	−	0.306481i	$-0.0991516\pi$
$104$	−2.61882	+	8.05991i	−0.256797	+	0.790339i
$105$	−1.17326	−	1.90354i	−0.114498	−	0.185767i
$106$	6.35965	+	19.5730i	0.617704	+	1.90110i
$107$	−13.5746			−1.31231			−0.656154	−	0.754627i	$-0.727818\pi$
$107$	−13.5746			−1.31231			−0.656154	+	0.754627i	$0.727818\pi$
$108$	1.29447	+	3.98396i	0.124560	+	0.383357i
$109$	−3.90051	−	2.83389i	−0.373601	−	0.271437i	0.385101	−	0.922874i	$-0.374166\pi$
$109$	−3.90051	−	2.83389i	−0.373601	−	0.271437i	−0.758703	+	0.651437i	$0.774166\pi$
$110$	0.774373	+	1.25638i	0.0738336	+	0.119791i
$111$	−8.66441	+	6.29506i	−0.822390	+	0.597501i
$112$	4.18232	+	3.03864i	0.395193	+	0.287124i
$113$	−15.9835	−	11.6127i	−1.50360	−	1.09243i	−0.968921	−	0.247370i	$-0.920434\pi$
$113$	−15.9835	−	11.6127i	−1.50360	−	1.09243i	−0.534676	−	0.845057i	$-0.679566\pi$
$114$	9.41315	−	6.83905i	0.881622	−	0.640536i
$115$	0.696316	−	9.14924i	0.0649318	−	0.853171i
$116$	−31.7986	−	23.1030i	−2.95242	−	2.14506i
$117$	−0.480898	−	1.48005i	−0.0444591	−	0.136831i
$118$	−5.71527			−0.526133
$119$	−0.612083	−	1.88380i	−0.0561095	−	0.172687i
$120$	−7.88437	+	9.27978i	−0.719741	+	0.847125i
$121$	−3.37744	+	10.3947i	−0.307040	+	0.944971i
$122$	−6.99270	+	21.5213i	−0.633089	+	1.94845i
$123$	−8.64316	+	6.27962i	−0.779327	+	0.566214i
$124$	−7.72057			−0.693328
$125$	9.57773	+	5.76776i	0.856658	+	0.515884i
$126$	−2.48777			−0.221628
$127$	8.44490	−	6.13558i	0.749363	−	0.544444i	−0.146266	−	0.989245i	$-0.546726\pi$
$127$	8.44490	−	6.13558i	0.749363	−	0.544444i	0.895629	+	0.444801i	$0.146726\pi$
$128$	−5.39902	+	16.6165i	−0.477211	+	1.46870i
$129$	0.105194	−	0.323753i	0.00926178	−	0.0285048i
$130$	5.60525	−	6.59729i	0.491613	−	0.578620i
$131$	6.32689	+	19.4722i	0.552783	+	1.70129i	0.701727	+	0.712446i	$0.252413\pi$
$131$	6.32689	+	19.4722i	0.552783	+	1.70129i	−0.148944	+	0.988846i	$0.547587\pi$
$132$	1.11136			0.0967318
$133$	1.44527	+	4.44809i	0.125321	+	0.385698i
$134$	−18.8069	−	13.6640i	−1.62467	−	1.18039i
$135$	0.169688	−	2.22962i	0.0146045	−	0.191895i
$136$	−8.72647	+	6.34015i	−0.748288	+	0.543663i
$137$	−3.06296	−	2.22537i	−0.261686	−	0.190126i	0.449204	−	0.893429i	$-0.351708\pi$
$137$	−3.06296	−	2.22537i	−0.261686	−	0.190126i	−0.710890	+	0.703303i	$0.751708\pi$
$138$	−8.25889	−	6.00043i	−0.703043	−	0.510791i
$139$	−5.96443	+	4.33341i	−0.505897	+	0.367555i	−0.811265	−	0.584679i	$-0.801220\pi$
$139$	−5.96443	+	4.33341i	−0.505897	+	0.367555i	0.305368	+	0.952234i	$0.401220\pi$
$140$	−4.91476	−	7.97391i	−0.415373	−	0.673918i
$141$	−0.163808	−	0.119014i	−0.0137951	−	0.0100228i
$142$	7.75715	+	23.8741i	0.650966	+	2.00347i
$143$	−0.412875			−0.0345263
$144$	1.59751	+	4.91662i	0.133125	+	0.409718i
$145$	11.0086	+	17.8609i	0.914218	+	1.48327i
$146$	−0.997720	+	3.07067i	−0.0825719	+	0.254130i
$147$	0.309017	−	0.951057i	0.0254873	−	0.0784418i
$148$	−36.2951	+	26.3699i	−2.98344	+	2.16760i
$149$	8.18680			0.670689			0.335345	−	0.942096i	$-0.391147\pi$
$149$	8.18680			0.670689			0.335345	+	0.942096i	$0.391147\pi$
$150$	11.0538	−	5.70422i	0.902539	−	0.465748i
$151$	−2.21986			−0.180649			−0.0903246	−	0.995912i	$-0.528790\pi$
$151$	−2.21986			−0.180649			−0.0903246	+	0.995912i	$0.528790\pi$
$152$	20.6053	−	14.9706i	1.67131	−	1.21428i
$153$	0.612083	−	1.88380i	0.0494840	−	0.152296i
$154$	−0.203957	+	0.627717i	−0.0164354	+	0.0505828i
$155$	3.81156	+	1.56729i	0.306152	+	0.125888i
$156$	−2.01448	−	6.19992i	−0.161287	−	0.496391i
$157$	2.86518			0.228666			0.114333	−	0.993442i	$-0.463527\pi$
$157$	2.86518			0.228666			0.114333	+	0.993442i	$0.463527\pi$
$158$	−5.43744	−	16.7347i	−0.432580	−	1.33134i
$159$	−6.69266	−	4.86250i	−0.530762	−	0.385621i
$160$	−2.85144	+	3.35610i	−0.225426	+	0.265323i
$161$	3.31980	−	2.41198i	0.261637	−	0.190090i
$162$	−2.01265	−	1.46227i	−0.158128	−	0.114887i
$163$	8.34779	+	6.06502i	0.653849	+	0.475049i	0.864580	−	0.502495i	$-0.167584\pi$
$163$	8.34779	+	6.06502i	0.653849	+	0.475049i	−0.210731	+	0.977544i	$0.567584\pi$
$164$	−36.2061	+	26.3053i	−2.82722	+	2.05410i
$165$	−0.548669	−	0.225609i	−0.0427138	−	0.0175637i
$166$	10.2734	+	7.46406i	0.797370	+	0.579323i
$167$	6.72959	+	20.7116i	0.520752	+	1.60271i	0.772567	+	0.634933i	$0.218972\pi$
$167$	6.72959	+	20.7116i	0.520752	+	1.60271i	−0.251815	+	0.967775i	$0.581028\pi$
$168$	−5.44569			−0.420144
$169$	−3.26884	−	10.0604i	−0.251449	−	0.773881i
$170$	10.7074	−	2.59985i	0.821219	−	0.199399i
$171$	−1.44527	+	4.44809i	−0.110523	+	0.340154i
$172$	0.440655	−	1.35620i	0.0335996	−	0.103409i
$173$	15.5004	−	11.2617i	1.17847	−	0.856211i	0.186475	−	0.982460i	$-0.440294\pi$
$173$	15.5004	−	11.2617i	1.17847	−	0.856211i	0.991999	+	0.126249i	$0.0402938\pi$
$174$	23.3427			1.76960
$175$	0.807642	+	4.93434i	0.0610520	+	0.373001i
$176$	1.37154			0.103383
$177$	1.85859	−	1.35035i	0.139701	−	0.101498i
$178$	2.75175	−	8.46902i	0.206253	−	0.634780i
$179$	−2.02361	+	6.22804i	−0.151252	+	0.465506i	−0.997762	−	0.0668672i	$-0.978700\pi$
$179$	−2.02361	+	6.22804i	−0.151252	+	0.465506i	0.846510	+	0.532373i	$0.178700\pi$
$180$	0.710823	−	9.33985i	0.0529816	−	0.696151i
$181$	0.567237	+	1.74578i	0.0421624	+	0.129763i	0.969922	−	0.243416i	$-0.0782680\pi$
$181$	0.567237	+	1.74578i	0.0421624	+	0.129763i	−0.927760	+	0.373178i	$0.878268\pi$
$182$	3.87151			0.286976
$183$	−2.81083	−	8.65085i	−0.207783	−	0.639489i
$184$	−18.0786	−	13.1349i	−1.33277	−	0.968316i
$185$	23.2717	−	5.65057i	1.71097	−	0.415438i
$186$	3.70944	−	2.69506i	0.271989	−	0.197612i
$187$	−0.425141	−	0.308883i	−0.0310894	−	0.0225878i
$188$	−0.686190	−	0.498546i	−0.0500456	−	0.0363602i
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	−25.2827	+	6.13886i	−1.83420	+	0.445360i
$191$	−14.1900	−	10.3097i	−1.02676	−	0.745981i	−0.0590986	−	0.998252i	$-0.518823\pi$
$191$	−14.1900	−	10.3097i	−1.02676	−	0.745981i	−0.967657	+	0.252271i	$0.918823\pi$
$192$	−1.68095	−	5.17344i	−0.121312	−	0.373361i
$193$	−25.7200			−1.85136			−0.925682	−	0.378302i	$-0.876508\pi$
$193$	−25.7200			−1.85136			−0.925682	+	0.378302i	$0.876508\pi$
$194$	−3.42413	−	10.5384i	−0.245838	−	0.756612i
$195$	−0.264072	+	3.46978i	−0.0189106	+	0.248476i
$196$	1.29447	−	3.98396i	0.0924620	−	0.284569i
$197$	0.498765	−	1.53504i	0.0355355	−	0.109367i	−0.931715	−	0.363189i	$-0.881688\pi$
$197$	0.498765	−	1.53504i	0.0355355	−	0.109367i	0.967251	+	0.253822i	$0.0816878\pi$
$198$	−0.533968	+	0.387950i	−0.0379474	+	0.0275704i
$199$	17.6785			1.25320			0.626599	−	0.779342i	$-0.284447\pi$
$199$	17.6785			1.25320			0.626599	+	0.779342i	$0.284447\pi$
$200$	24.1966	−	12.4865i	1.71096	−	0.882927i
$201$	9.34436			0.659100
$202$	21.6362	−	15.7196i	1.52232	−	1.10603i
$203$	−2.89950	+	8.92374i	−0.203505	+	0.626324i
$204$	2.56401	−	7.89120i	0.179516	−	0.552495i
$205$	23.2146	−	5.63671i	1.62138	−	0.393685i
$206$	9.13822	+	28.1246i	0.636690	+	1.95953i
$207$	4.10350			0.285213
$208$	−2.48607	−	7.65133i	−0.172378	−	0.530525i
$209$	1.00386	+	0.729346i	0.0694383	+	0.0504499i
$210$	5.14485	+	2.11553i	0.355028	+	0.145986i
$211$	−18.7756	+	13.6413i	−1.29257	+	0.939104i	−0.999854	−	0.0170967i	$-0.994558\pi$
$211$	−18.7756	+	13.6413i	−1.29257	+	0.939104i	−0.292712	+	0.956201i	$0.594558\pi$
$212$	−28.0354	−	20.3689i	−1.92548	−	1.39894i
$213$	−8.16334	−	5.93101i	−0.559343	−	0.406386i
$214$	27.3209	−	19.8498i	1.86762	−	1.35691i
$215$	−0.492857	+	0.580086i	−0.0336126	+	0.0395615i
$216$	−4.40566	−	3.20090i	−0.299767	−	0.217793i
$217$	0.569538	+	1.75286i	0.0386628	+	0.118992i
$218$	11.9943			0.812355
$219$	−0.401050	−	1.23431i	−0.0271005	−	0.0834067i
$220$	−2.29837	−	0.945075i	−0.154956	−	0.0637169i
$221$	−0.952535	+	2.93160i	−0.0640744	+	0.197201i
$222$	8.23329	−	25.3395i	0.552582	−	1.70067i
$223$	12.0571	−	8.76000i	0.807404	−	0.586613i	−0.105673	−	0.994401i	$-0.533700\pi$
$223$	12.0571	−	8.76000i	0.807404	−	0.586613i	0.913077	+	0.407788i	$0.133700\pi$
$224$	−1.96947			−0.131591
$225$	−2.24694	+	4.46669i	−0.149796	+	0.297779i
$226$	49.1499			3.26940
$227$	−20.9487	+	15.2201i	−1.39041	+	1.01019i	−0.394593	+	0.918856i	$0.629114\pi$
$227$	−20.9487	+	15.2201i	−1.39041	+	1.01019i	−0.995820	+	0.0913382i	$0.970886\pi$
$228$	−6.05423	+	18.6330i	−0.400951	+	1.23400i
$229$	−5.55333	+	17.0914i	−0.366975	+	1.12943i	0.581761	+	0.813360i	$0.302364\pi$
$229$	−5.55333	+	17.0914i	−0.366975	+	1.12943i	−0.948735	+	0.316072i	$0.897636\pi$
$230$	11.9773	+	19.4324i	0.789757	+	1.28133i
$231$	−0.0819841	−	0.252321i	−0.00539416	−	0.0166015i
$232$	51.0968			3.35467
$233$	−7.04138	−	21.6711i	−0.461296	−	1.41972i	−0.863581	−	0.504210i	$-0.831784\pi$
$233$	−7.04138	−	21.6711i	−0.461296	−	1.41972i	0.402285	−	0.915515i	$-0.368216\pi$
$234$	3.13212	+	2.27562i	0.204753	+	0.148762i
$235$	0.237559	+	0.385425i	0.0154966	+	0.0251424i
$236$	7.78563	−	5.65659i	0.506801	−	0.368213i
$237$	5.72216	+	4.15739i	0.371694	+	0.270052i
$238$	3.98653	+	2.89639i	0.258409	+	0.187745i
$239$	−12.9135	+	9.38217i	−0.835302	+	0.606882i	−0.921054	−	0.389434i	$-0.872671\pi$
$239$	−12.9135	+	9.38217i	−0.835302	+	0.606882i	0.0857524	+	0.996316i	$0.472671\pi$
$240$	0.877228	−	11.5263i	0.0566248	−	0.744021i
$241$	18.0397	+	13.1066i	1.16204	+	0.844270i	0.990034	−	0.140826i	$-0.0449759\pi$
$241$	18.0397	+	13.1066i	1.16204	+	0.844270i	0.172004	+	0.985096i	$0.444976\pi$
$242$	−8.40228	−	25.8595i	−0.540119	−	1.66231i
$243$	1.00000			0.0641500
$244$	−11.7745	−	36.2383i	−0.753788	−	2.31992i
$245$	−1.44782	+	1.70406i	−0.0924977	+	0.108868i
$246$	8.21310	−	25.2773i	0.523648	−	1.61162i
$247$	2.24916	−	6.92220i	0.143111	−	0.440449i
$248$	8.11991	−	5.89946i	0.515615	−	0.374616i
$249$	−5.10442			−0.323480
$250$	−27.7106	+	2.39680i	−1.75257	+	0.151587i
$251$	25.8119			1.62923			0.814617	−	0.580000i	$-0.196947\pi$
$251$	25.8119			1.62923			0.814617	+	0.580000i	$0.196947\pi$
$252$	3.38896	−	2.46222i	0.213485	−	0.155106i
$253$	0.336422	−	1.03540i	0.0211507	−	0.0650950i
$254$	−8.02470	+	24.6975i	−0.503514	+	1.54966i
$255$	−2.86775	+	3.37530i	−0.179586	+	0.211370i
$256$	−10.0696	−	30.9911i	−0.629350	−	1.93694i
$257$	18.9059			1.17932			0.589659	−	0.807652i	$-0.299262\pi$
$257$	18.9059			1.17932			0.589659	+	0.807652i	$0.299262\pi$
$258$	0.261697	+	0.805422i	0.0162926	+	0.0501434i
$259$	8.66441	+	6.29506i	0.538380	+	0.391156i
$260$	−1.10620	+	14.5349i	−0.0686033	+	0.901413i
$261$	−7.59099	+	5.51518i	−0.469870	+	0.341381i
$262$	−41.2074	−	29.9390i	−2.54580	−	1.84963i
$263$	7.29198	+	5.29794i	0.449643	+	0.326685i	0.789455	−	0.613809i	$-0.210363\pi$
$263$	7.29198	+	5.29794i	0.449643	+	0.326685i	−0.339812	+	0.940493i	$0.610363\pi$
$264$	−1.16885	+	0.849218i	−0.0719376	+	0.0522657i
$265$	9.70586	+	15.7472i	0.596226	+	0.967342i
$266$	−9.41315	−	6.83905i	−0.577157	−	0.419329i
$267$	1.10611	+	3.40427i	0.0676930	+	0.208338i
$268$	39.1434			2.39106
$269$	−4.53751	−	13.9650i	−0.276657	−	0.851462i	−0.988776	−	0.149404i	$-0.952265\pi$
$269$	−4.53751	−	13.9650i	−0.276657	−	0.851462i	0.712120	−	0.702058i	$-0.247735\pi$
$270$	2.91879	+	4.73557i	0.177632	+	0.288197i
$271$	−4.70960	+	14.4947i	−0.286088	+	0.880488i	0.699983	+	0.714160i	$0.253191\pi$
$271$	−4.70960	+	14.4947i	−0.286088	+	0.880488i	−0.986071	+	0.166328i	$0.946809\pi$
$272$	3.16425	−	9.73855i	0.191861	−	0.590486i
$273$	−1.25901	+	0.914723i	−0.0761986	+	0.0553615i
$274$	9.41875			0.569007
$275$	0.942826	+	0.933147i	0.0568546	+	0.0562709i
$276$	17.1895			1.03469
$277$	2.58289	−	1.87658i	0.155191	−	0.112753i	−0.507480	−	0.861664i	$-0.669423\pi$
$277$	2.58289	−	1.87658i	0.155191	−	0.112753i	0.662671	+	0.748911i	$0.269423\pi$
$278$	5.66766	−	17.4433i	0.339923	−	1.04618i
$279$	−0.569538	+	1.75286i	−0.0340974	+	0.104941i
$280$	11.2620	+	4.63087i	0.673033	+	0.276748i
$281$	−5.92526	−	18.2361i	−0.353472	−	1.08787i	−0.956890	−	0.290449i	$-0.906195\pi$
$281$	−5.92526	−	18.2361i	−0.353472	−	1.08787i	0.603419	−	0.797425i	$-0.293805\pi$
$282$	0.503718			0.0299960
$283$	−2.80803	−	8.64223i	−0.166920	−	0.513727i	0.832252	−	0.554397i	$-0.187051\pi$
$283$	−2.80803	−	8.64223i	−0.166920	−	0.513727i	−0.999173	+	0.0406693i	$0.987051\pi$
$284$	−34.1961	−	24.8449i	−2.02917	−	1.47428i
$285$	6.77145	−	7.96989i	0.401106	−	0.472096i
$286$	0.830971	−	0.603735i	0.0491363	−	0.0356996i
$287$	8.64316	+	6.27962i	0.510189	+	0.370674i
$288$	−1.59334	−	1.15763i	−0.0938884	−	0.0682139i
$289$	10.5792	−	7.68627i	0.622308	−	0.452133i
$290$	−48.2740	−	19.8500i	−2.83475	−	1.16563i
$291$	3.60343	+	2.61804i	0.211237	+	0.153472i
$292$	−1.68000	−	5.17049i	−0.0983143	−	0.302580i
$293$	−20.5582			−1.20103			−0.600513	−	0.799615i	$-0.705037\pi$
$293$	−20.5582			−1.20103			−0.600513	+	0.799615i	$0.705037\pi$
$294$	0.768762	+	2.36601i	0.0448351	+	0.137988i
$295$	−4.99198	+	1.21210i	−0.290644	+	0.0705711i
$296$	18.0226	−	55.4678i	1.04754	−	3.22400i
$297$	0.0819841	−	0.252321i	0.00475720	−	0.0146412i
$298$	−16.4771	+	11.9713i	−0.954495	+	0.693481i
$299$	−6.38594			−0.369309
$300$	−9.41239	+	18.7109i	−0.543424	+	1.08027i
$301$	−0.340414			−0.0196211
$302$	4.46778	−	3.24603i	0.257092	−	0.186788i
$303$	−3.32197	+	10.2240i	−0.190842	+	0.587351i
$304$	−7.47153	+	22.9950i	−0.428522	+	1.31885i
$305$	−1.54349	+	20.2807i	−0.0883802	+	1.16127i
$306$	1.52272	+	4.68645i	0.0870481	+	0.267906i
$307$	−25.7370			−1.46889			−0.734443	−	0.678670i	$-0.762557\pi$
$307$	−25.7370			−1.46889			−0.734443	+	0.678670i	$0.762557\pi$
$308$	−0.343430	−	1.05697i	−0.0195688	−	0.0602265i
$309$	−9.61673	−	6.98696i	−0.547076	−	0.397474i
$310$	−9.96314	+	2.41914i	−0.565868	+	0.137398i
$311$	8.21045	−	5.96524i	0.465572	−	0.338258i	−0.330141	−	0.943932i	$-0.607096\pi$
$311$	8.21045	−	5.96524i	0.465572	−	0.338258i	0.795713	+	0.605674i	$0.207096\pi$
$312$	6.85617	+	4.98130i	0.388154	+	0.282010i
$313$	−2.85865	−	2.07693i	−0.161580	−	0.117395i	0.504057	−	0.863670i	$-0.331840\pi$
$313$	−2.85865	−	2.07693i	−0.161580	−	0.117395i	−0.665637	+	0.746276i	$0.731840\pi$
$314$	−5.76658	+	4.18967i	−0.325427	+	0.236437i
$315$	−2.17293	+	0.527607i	−0.122431	+	0.0297273i
$316$	23.9701	+	17.4153i	1.34842	+	0.979686i
$317$	1.06209	+	3.26878i	0.0596529	+	0.183593i	0.976442	−	0.215778i	$-0.0692287\pi$
$317$	1.06209	+	3.26878i	0.0596529	+	0.183593i	−0.916790	+	0.399371i	$0.869229\pi$
$318$	20.5802			1.15408
$319$	0.769255	+	2.36752i	0.0430700	+	0.132556i
$320$	−0.923050	+	12.1284i	−0.0516001	+	0.677999i
$321$	−4.19479	+	12.9102i	−0.234130	+	0.720579i
$322$	−3.15462	+	9.70891i	−0.175800	+	0.541056i
$323$	7.49468	−	5.44520i	0.417015	−	0.302979i
$324$	4.18899			0.232721
$325$	3.49672	−	6.95114i	0.193963	−	0.385580i
$326$	−25.6699			−1.42172
$327$	−3.90051	+	2.83389i	−0.215699	+	0.156714i
$328$	17.9784	−	55.3317i	0.992689	−	3.05518i
$329$	−0.0625691	+	0.192568i	−0.00344955	+	0.0106166i
$330$	1.43418	−	0.348231i	0.0789489	−	0.0191695i
$331$	1.32114	+	4.06605i	0.0726164	+	0.223490i	0.980777	−	0.195131i	$-0.0625133\pi$
$331$	1.32114	+	4.06605i	0.0726164	+	0.223490i	−0.908161	+	0.418622i	$0.862513\pi$
$332$	−21.3824			−1.17351
$333$	3.30951	+	10.1856i	0.181360	+	0.558169i
$334$	−43.8302	−	31.8445i	−2.39828	−	1.74246i
$335$	−19.3247	−	7.94620i	−1.05582	−	0.434147i
$336$	4.18232	−	3.03864i	0.228165	−	0.165771i
$337$	8.21403	+	5.96784i	0.447447	+	0.325089i	0.788587	−	0.614923i	$-0.210813\pi$
$337$	8.21403	+	5.96784i	0.447447	+	0.325089i	−0.341140	+	0.940012i	$0.610813\pi$
$338$	21.2901	+	15.4682i	1.15803	+	0.841359i
$339$	−15.9835	+	11.6127i	−0.868102	+	0.630713i
$340$	−12.0130	+	14.1391i	−0.651496	+	0.766800i
$341$	0.395590	+	0.287413i	0.0214224	+	0.0155643i
$342$	−3.59550	−	11.0658i	−0.194422	−	0.598371i
$343$	−1.00000			−0.0539949
$344$	0.572852	+	1.76306i	0.0308861	+	0.0950577i
$345$	−8.48627	−	3.48951i	−0.456886	−	0.187869i
$346$	−14.7291	+	45.3316i	−0.791843	+	2.43704i
$347$	3.59873	−	11.0758i	0.193190	−	0.594578i	−0.806803	−	0.590821i	$-0.798804\pi$
$347$	3.59873	−	11.0758i	0.193190	−	0.594578i	0.999993	−	0.00375706i	$-0.00119591\pi$
$348$	−31.7986	+	23.1030i	−1.70458	+	1.23845i
$349$	11.6475			0.623478			0.311739	−	0.950168i	$-0.399089\pi$
$349$	11.6475			0.623478			0.311739	+	0.950168i	$0.399089\pi$
$350$	−8.84085	−	8.75009i	−0.472563	−	0.467712i
$351$	−1.55622			−0.0830648
$352$	−0.422723	+	0.307126i	−0.0225312	+	0.0163699i
$353$	−0.859063	+	2.64393i	−0.0457233	+	0.140722i	−0.971312	−	0.237809i	$-0.923571\pi$
$353$	−0.859063	+	2.64393i	−0.0457233	+	0.140722i	0.925589	+	0.378531i	$0.123571\pi$
$354$	−1.76612	+	5.43555i	−0.0938680	+	0.288896i
$355$	11.8387	+	19.2076i	0.628332	+	1.01943i
$356$	4.63349	+	14.2604i	0.245575	+	0.755801i
$357$	−1.98074			−0.104832
$358$	−5.03428	−	15.4939i	−0.266070	−	0.818879i
$359$	4.08888	+	2.97074i	0.215803	+	0.156790i	0.690435	−	0.723394i	$-0.257419\pi$
$359$	4.08888	+	2.97074i	0.215803	+	0.156790i	−0.474633	+	0.880184i	$0.657419\pi$
$360$	6.38919	+	10.3661i	0.336740	+	0.546341i
$361$	−2.32538	+	1.68949i	−0.122388	+	0.0889204i
$362$	−3.69445	−	2.68417i	−0.194176	−	0.141077i
$363$	8.84224	+	6.42427i	0.464097	+	0.337186i
$364$	−5.27397	+	3.83176i	−0.276431	+	0.200839i
$365$	−0.220226	+	2.89366i	−0.0115272	+	0.151461i
$366$	18.3071	+	13.3009i	0.956928	+	0.695249i
$367$	−9.09810	−	28.0011i	−0.474917	−	1.46164i	−0.846070	−	0.533072i	$-0.821038\pi$
$367$	−9.09810	−	28.0011i	−0.474917	−	1.46164i	0.371153	−	0.928572i	$-0.378962\pi$
$368$	21.2136			1.10584
$369$	3.30139	+	10.1606i	0.171864	+	0.528942i
$370$	−38.5750	+	45.4021i	−2.00542	+	2.36034i
$371$	−2.55637	+	7.86769i	−0.132720	+	0.408470i
$372$	−2.38579	+	7.34270i	−0.123697	+	0.380701i
$373$	12.2475	−	8.89836i	0.634153	−	0.460739i	−0.223683	−	0.974662i	$-0.571808\pi$
$373$	12.2475	−	8.89836i	0.634153	−	0.460739i	0.857837	+	0.513923i	$0.171808\pi$
$374$	1.30733			0.0676004
$375$	8.44515	−	7.32663i	0.436105	−	0.378346i
$376$	1.10263			0.0568639
$377$	11.8132	−	8.58282i	0.608413	−	0.442038i
$378$	−0.768762	+	2.36601i	−0.0395409	+	0.121694i
$379$	3.45309	−	10.6275i	0.177373	−	0.545899i	−0.822361	−	0.568967i	$-0.807343\pi$
$379$	3.45309	−	10.6275i	0.177373	−	0.545899i	0.999734	+	0.0230679i	$0.00734339\pi$
$380$	28.3655	−	33.3858i	1.45512	−	1.71265i
$381$	−3.22566	−	9.92757i	−0.165256	−	0.508605i
$382$	43.6351			2.23256
$383$	−5.41100	−	16.6533i	−0.276489	−	0.850946i	−0.988822	−	0.149104i	$-0.952361\pi$
$383$	−5.41100	−	16.6533i	−0.276489	−	0.850946i	0.712333	−	0.701842i	$-0.247639\pi$
$384$	14.1348	+	10.2696i	0.721315	+	0.524066i
$385$	−0.0450194	+	0.591532i	−0.00229440	+	0.0301473i
$386$	51.7652	−	37.6096i	2.63478	−	1.91428i
$387$	−0.275401	−	0.200090i	−0.0139994	−	0.0101712i
$388$	15.0947	+	10.9669i	0.766317	+	0.556762i
$389$	27.9710	−	20.3222i	1.41819	−	1.03037i	0.426121	−	0.904666i	$-0.359880\pi$
$389$	27.9710	−	20.3222i	1.41819	−	1.03037i	0.992067	−	0.125708i	$-0.0401202\pi$
$390$	−4.54228	−	7.36958i	−0.230007	−	0.373173i
$391$	−6.57567	−	4.77750i	−0.332546	−	0.241609i
$392$	1.68281	+	5.17916i	0.0849948	+	0.261587i
$393$	20.4743			1.03279
$394$	1.24081	+	3.81882i	0.0625112	+	0.192390i
$395$	−8.29843	−	13.4637i	−0.417539	−	0.677433i
$396$	0.343430	−	1.05697i	0.0172580	−	0.0531148i
$397$	−6.14329	+	18.9071i	−0.308323	+	0.948921i	0.670093	+	0.742277i	$0.266254\pi$
$397$	−6.14329	+	18.9071i	−0.308323	+	0.948921i	−0.978416	+	0.206644i	$0.933746\pi$
$398$	−35.5806	+	25.8508i	−1.78349	+	1.29578i
$399$	4.67700			0.234143
$400$	−11.6158	+	23.0911i	−0.580792	+	1.15456i
$401$	28.3827			1.41736			0.708682	−	0.705528i	$-0.249290\pi$
$401$	28.3827			1.41736			0.708682	+	0.705528i	$0.249290\pi$
$402$	−18.8069	+	13.6640i	−0.938002	+	0.681499i
$403$	0.886326	−	2.72783i	0.0441511	−	0.135883i
$404$	−13.9157	+	42.8280i	−0.692331	+	2.13078i
$405$	−2.06806	−	0.850374i	−0.102763	−	0.0422554i
$406$	−7.21328	−	22.2002i	−0.357989	−	1.10178i
$407$	2.84138			0.140842
$408$	3.33321	+	10.2586i	0.165019	+	0.507875i
$409$	12.7972	+	9.29774i	0.632783	+	0.459743i	0.857363	−	0.514712i	$-0.172101\pi$
$409$	12.7972	+	9.29774i	0.632783	+	0.459743i	−0.224580	+	0.974456i	$0.572101\pi$
$410$	−38.4803	+	45.2907i	−1.90041	+	2.23675i
$411$	−3.06296	+	2.22537i	−0.151085	+	0.109769i
$412$	−40.2843	−	29.2683i	−1.98467	−	1.44194i
$413$	−1.85859	−	1.35035i	−0.0914555	−	0.0664463i
$414$	−8.25889	+	6.00043i	−0.405902	+	0.294905i
$415$	10.5562	+	4.34067i	0.518186	+	0.213075i
$416$	2.47958	+	1.80152i	0.121572	+	0.0883269i
$417$	2.27821	+	7.01161i	0.111564	+	0.343360i
$418$	−3.08691			−0.150986
$419$	−0.690509	−	2.12517i	−0.0337336	−	0.103821i	0.932772	−	0.360467i	$-0.117383\pi$
$419$	−0.690509	−	2.12517i	−0.0337336	−	0.103821i	−0.966506	+	0.256646i	$0.917383\pi$
$420$	−9.10238	+	2.21014i	−0.444151	+	0.107844i
$421$	−7.94896	+	24.4644i	−0.387409	+	1.19232i	0.547309	+	0.836930i	$0.315652\pi$
$421$	−7.94896	+	24.4644i	−0.387409	+	1.19232i	−0.934718	+	0.355391i	$0.884348\pi$
$422$	17.8414	−	54.9101i	0.868505	−	2.67298i
$423$	−0.163808	+	0.119014i	−0.00796463	+	0.00578664i
$424$	45.0499			2.18782
$425$	8.80095	−	4.54166i	0.426909	−	0.220303i
$426$	25.1027			1.21623
$427$	−7.35885	+	5.34652i	−0.356120	+	0.258736i
$428$	−17.5719	+	54.0808i	−0.849371	+	2.61409i
$429$	−0.127585	+	0.392667i	−0.00615988	+	0.0189581i
$430$	0.143704	−	1.88820i	0.00693003	−	0.0910570i
$431$	−1.22942	−	3.78377i	−0.0592191	−	0.182258i	0.917071	−	0.398724i	$-0.130547\pi$
$431$	−1.22942	−	3.78377i	−0.0592191	−	0.182258i	−0.976290	+	0.216466i	$0.930547\pi$
$432$	5.16964			0.248724
$433$	−7.67118	−	23.6095i	−0.368654	−	1.13460i	−0.947661	−	0.319277i	$-0.896560\pi$
$433$	−7.67118	−	23.6095i	−0.368654	−	1.13460i	0.579008	−	0.815322i	$-0.303440\pi$
$434$	−3.70944	−	2.69506i	−0.178059	−	0.129367i
$435$	20.3886	−	4.95053i	0.977557	−	0.237360i
$436$	−16.3392	+	11.8711i	−0.782506	+	0.568524i
$437$	15.5267	+	11.2808i	0.742743	+	0.539634i
$438$	2.61207	+	1.89778i	0.124809	+	0.0906793i
$439$	−25.0253	+	18.1820i	−1.19439	+	0.867777i	−0.993722	−	0.111882i	$-0.964312\pi$
$439$	−25.0253	+	18.1820i	−1.19439	+	0.867777i	−0.200671	+	0.979659i	$0.564312\pi$
$440$	3.13940	−	0.762274i	0.149665	−	0.0363400i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	−2.36969	−	7.29314i	−0.112714	−	0.346899i
$443$	−33.2526			−1.57988			−0.789939	−	0.613186i	$-0.789888\pi$
$443$	−33.2526			−1.57988			−0.789939	+	0.613186i	$0.789888\pi$
$444$	13.8635	+	42.6675i	0.657932	+	2.02491i
$445$	0.607392	−	7.98083i	0.0287932	−	0.378328i
$446$	−11.4572	+	35.2616i	−0.542513	+	1.66968i
$447$	2.52986	−	7.78611i	0.119658	−	0.368271i
$448$	−4.40079	+	3.19736i	−0.207918	+	0.151061i
$449$	12.5413			0.591859			0.295929	−	0.955210i	$-0.404371\pi$
$449$	12.5413			0.591859			0.295929	+	0.955210i	$0.404371\pi$
$450$	−2.00923	−	12.2755i	−0.0947159	−	0.578672i
$451$	2.83441			0.133467
$452$	−66.9545	+	48.6453i	−3.14927	+	2.28808i
$453$	−0.685973	+	2.11121i	−0.0322298	+	0.0991932i
$454$	19.9063	−	61.2654i	0.934250	−	2.87533i
$455$	3.38156	−	0.821073i	0.158530	−	0.0384925i
$456$	−7.87051	−	24.2229i	−0.368570	−	1.13434i
$457$	−20.0613			−0.938428			−0.469214	−	0.883085i	$-0.655463\pi$
$457$	−20.0613			−0.938428			−0.469214	+	0.883085i	$0.655463\pi$
$458$	−13.8154	−	42.5194i	−0.645551	−	1.98680i
$459$	−1.60245	−	1.16425i	−0.0747961	−	0.0543426i
$460$	−35.5489	−	14.6175i	−1.65748	−	0.681544i
$461$	13.8412	−	10.0562i	0.644649	−	0.468365i	−0.216795	−	0.976217i	$-0.569560\pi$
$461$	13.8412	−	10.0562i	0.644649	−	0.468365i	0.861444	+	0.507852i	$0.169560\pi$
$462$	0.533968	+	0.387950i	0.0248424	+	0.0180491i
$463$	−27.5180	−	19.9930i	−1.27887	−	0.929153i	−0.279351	−	0.960189i	$-0.590119\pi$
$463$	−27.5180	−	19.9930i	−1.27887	−	0.929153i	−0.999518	+	0.0310363i	$0.990119\pi$
$464$	−39.2427	+	28.5115i	−1.82179	+	1.32361i
$465$	2.66842	−	3.14069i	0.123745	−	0.145646i
$466$	45.8609	+	33.3199i	2.12447	+	1.54352i
$467$	12.1228	+	37.3101i	0.560975	+	1.72650i	0.679616	+	0.733568i	$0.262146\pi$
$467$	12.1228	+	37.3101i	0.560975	+	1.72650i	−0.118641	+	0.992937i	$0.537854\pi$
$468$	−6.51898			−0.301340
$469$	−2.88757	−	8.88701i	−0.133335	−	0.410364i
$470$	−1.04172	−	0.428349i	−0.0480509	−	0.0197583i
$471$	0.885388	−	2.72494i	0.0407965	−	0.125559i
$472$	−3.86600	+	11.8983i	−0.177947	+	0.547665i
$473$	−0.0730655	+	0.0530852i	−0.00335955	+	0.00244086i
$474$	−17.5959			−0.808208
$475$	−20.7811	+	10.7239i	−0.953504	+	0.492048i
$476$	−8.29730			−0.380306
$477$	−6.69266	+	4.86250i	−0.306436	+	0.222639i
$478$	12.2709	−	37.7660i	0.561259	−	1.72738i
$479$	1.22122	−	3.75853i	0.0557990	−	0.171732i	−0.919273	−	0.393621i	$-0.871222\pi$
$479$	1.22122	−	3.75853i	0.0557990	−	0.171732i	0.975072	+	0.221889i	$0.0712223\pi$
$480$	2.31070	+	3.74898i	0.105469	+	0.171117i
$481$	−5.15032	−	15.8511i	−0.234835	−	0.722746i
$482$	−55.4729			−2.52672
$483$	−1.26805	−	3.90266i	−0.0576983	−	0.177577i
$484$	37.0400	+	26.9112i	1.68364	+	1.22323i
$485$	−5.22578	−	8.47852i	−0.237290	−	0.384990i
$486$	−2.01265	+	1.46227i	−0.0912955	+	0.0663301i
$487$	−31.0579	−	22.5649i	−1.40737	−	1.02251i	−0.993699	−	0.112085i	$-0.964247\pi$
$487$	−31.0579	−	22.5649i	−1.40737	−	1.02251i	−0.413669	−	0.910427i	$-0.635753\pi$
$488$	40.0740	+	29.1155i	1.81407	+	1.31800i
$489$	8.34779	−	6.06502i	0.377500	−	0.274270i
$490$	0.422145	−	5.54678i	0.0190706	−	0.250578i
$491$	−19.8753	−	14.4402i	−0.896958	−	0.651678i	0.0407252	−	0.999170i	$-0.487033\pi$
$491$	−19.8753	−	14.4402i	−0.896958	−	0.651678i	−0.937683	+	0.347493i	$0.887033\pi$
$492$	13.8295	+	42.5628i	0.623482	+	1.91888i
$493$	18.5853			0.837038
$494$	5.59539	+	17.2208i	0.251748	+	0.774802i
$495$	−0.384115	+	0.452098i	−0.0172647	+	0.0203203i
$496$	−2.94431	+	9.06164i	−0.132203	+	0.406880i
$497$	−3.11812	+	9.59658i	−0.139867	+	0.430465i
$498$	10.2734	−	7.46406i	0.460362	−	0.334472i
$499$	−20.4169			−0.913987			−0.456993	−	0.889470i	$-0.651074\pi$
$499$	−20.4169			−0.913987			−0.456993	+	0.889470i	$0.651074\pi$
$500$	35.3766	−	30.6912i	1.58209	−	1.37255i
$501$	21.7774			0.972944
$502$	−51.9502	+	37.7441i	−2.31865	+	1.68460i
$503$	−2.61594	+	8.05103i	−0.116639	+	0.358978i	−0.992285	−	0.123975i	$-0.960436\pi$
$503$	−2.61594	+	8.05103i	−0.116639	+	0.358978i	0.875646	+	0.482953i	$0.160436\pi$
$504$	−1.68281	+	5.17916i	−0.0749584	+	0.230698i
$505$	15.5642	−	18.3188i	0.692598	−	0.815178i
$506$	0.836939	+	2.57583i	0.0372065	+	0.114510i
$507$	−10.5782			−0.469794
$508$	−13.5123	−	41.5865i	−0.599510	−	1.84510i
$509$	3.90385	+	2.83632i	0.173035	+	0.125717i	0.670932	−	0.741519i	$-0.265894\pi$
$509$	3.90385	+	2.83632i	0.173035	+	0.125717i	−0.497897	+	0.867236i	$0.665894\pi$
$510$	0.836161	−	10.9867i	0.0370258	−	0.486501i
$511$	−1.04996	+	0.762843i	−0.0464477	+	0.0337462i
$512$	37.3143	+	27.1104i	1.64907	+	1.19812i
$513$	3.78377	+	2.74907i	0.167058	+	0.121374i
$514$	−38.0509	+	27.6456i	−1.67835	+	1.21939i
$515$	13.9464	+	22.6273i	0.614553	+	0.997076i
$516$	−1.15365	−	0.838175i	−0.0507866	−	0.0368986i
$517$	0.0166000	+	0.0510895i	0.000730067	+	0.00224691i
$518$	−26.6435			−1.17065
$519$	−5.92062	−	18.2218i	−0.259887	−	0.799849i
$520$	−9.94299	−	16.1319i	−0.436029	−	0.707431i
$521$	1.37180	−	4.22198i	0.0600998	−	0.184968i	−0.916499	−	0.400037i	$-0.868997\pi$
$521$	1.37180	−	4.22198i	0.0600998	−	0.184968i	0.976599	+	0.215068i	$0.0689974\pi$
$522$	7.21328	−	22.2002i	0.315717	−	0.971676i
$523$	29.2550	−	21.2550i	1.27923	−	0.929416i	0.279702	−	0.960087i	$-0.409764\pi$
$523$	29.2550	−	21.2550i	1.27923	−	0.929416i	0.999530	+	0.0306711i	$0.00976443\pi$
$524$	85.7664			3.74672
$525$	4.94241	+	0.756681i	0.215705	+	0.0330243i
$526$	−22.4232			−0.977699
$527$	2.95343	−	2.14579i	0.128653	−	0.0934721i
$528$	0.423828	−	1.30441i	0.0184448	−	0.0567671i
$529$	−1.90395	+	5.85975i	−0.0827803	+	0.254772i
$530$	−42.5612	−	17.5009i	−1.84874	−	0.760191i
$531$	−0.709920	−	2.18491i	−0.0308079	−	0.0948170i
$532$	19.5919			0.849416
$533$	−5.13769	−	15.8122i	−0.222538	−	0.684902i
$534$	−7.20418	−	5.23414i	−0.311755	−	0.226504i
$535$	19.6536	−	23.1320i	0.849699	−	1.00008i
$536$	−41.1680	+	29.9103i	−1.77819	+	1.29193i
$537$	5.29789	+	3.84914i	0.228621	+	0.166103i
$538$	29.5531	+	21.4716i	1.27412	+	0.925704i
$539$	−0.214637	+	0.155943i	−0.00924508	+	0.00671694i
$540$	−8.66307	−	3.56220i	−0.372799	−	0.153293i
$541$	−8.07477	−	5.86666i	−0.347161	−	0.252227i	0.400516	−	0.916290i	$-0.368831\pi$
$541$	−8.07477	−	5.86666i	−0.347161	−	0.252227i	−0.747677	+	0.664062i	$0.768831\pi$
$542$	−11.7164	−	36.0593i	−0.503262	−	1.54888i
$543$	1.83562			0.0787739
$544$	1.20548	+	3.71009i	0.0516846	+	0.159069i
$545$	10.4764	−	2.54375i	0.448758	−	0.108962i
$546$	1.19636	−	3.68203i	0.0511996	−	0.157576i
$547$	3.98130	−	12.2532i	0.170228	−	0.523908i	−0.829156	−	0.559018i	$-0.811178\pi$
$547$	3.98130	−	12.2532i	0.170228	−	0.523908i	0.999383	+	0.0351104i	$0.0111783\pi$
$548$	−12.8307	+	9.32204i	−0.548100	+	0.398218i
$549$	−9.09604			−0.388210
$550$	−3.26209	−	0.499425i	−0.139096	−	0.0212956i
$551$	−43.8842			−1.86953
$552$	−18.0786	+	13.1349i	−0.769476	+	0.559057i
$553$	2.18567	−	6.72681i	0.0929442	−	0.286053i
$554$	−2.45437	+	7.55378i	−0.104276	+	0.320929i
$555$	1.81733	−	23.8788i	0.0771413	−	1.01360i
$556$	9.54339	+	29.3715i	0.404730	+	1.24563i
$557$	42.9169			1.81845			0.909224	−	0.416308i	$-0.136676\pi$
$557$	42.9169			1.81845			0.909224	+	0.416308i	$0.136676\pi$
$558$	−1.41688	−	4.36070i	−0.0599813	−	0.184603i
$559$	0.428584	+	0.311384i	0.0181272	+	0.0131701i
$560$	−11.2333	+	2.72754i	−0.474692	+	0.115260i
$561$	−0.425141	+	0.308883i	−0.0179495	+	0.0130410i
$562$	38.5916	+	28.0384i	1.62789	+	1.18273i
$563$	25.9940	+	18.8858i	1.09552	+	0.795940i	0.980322	−	0.197403i	$-0.0632507\pi$
$563$	25.9940	+	18.8858i	1.09552	+	0.795940i	0.115195	+	0.993343i	$0.463251\pi$
$564$	−0.686190	+	0.498546i	−0.0288938	+	0.0209926i
$565$	42.9298	−	10.4237i	1.80607	−	0.438530i
$566$	18.2889	+	13.2876i	0.768739	+	0.558522i
$567$	−0.309017	−	0.951057i	−0.0129775	−	0.0399406i
$568$	54.9494			2.30563
$569$	2.11070	+	6.49607i	0.0884852	+	0.272330i	0.985501	−	0.169669i	$-0.0542698\pi$
$569$	2.11070	+	6.49607i	0.0884852	+	0.272330i	−0.897016	+	0.441998i	$0.854270\pi$
$570$	−1.97437	+	25.9423i	−0.0826974	+	1.08660i
$571$	−9.43191	+	29.0284i	−0.394713	+	1.21480i	0.534472	+	0.845186i	$0.320511\pi$
$571$	−9.43191	+	29.0284i	−0.394713	+	1.21480i	−0.929185	+	0.369616i	$0.879489\pi$
$572$	−0.534453	+	1.64488i	−0.0223466	+	0.0687758i
$573$	−14.1900	+	10.3097i	−0.592797	+	0.430693i
$574$	−26.5781			−1.10935
$575$	14.5827	+	14.4330i	0.608141	+	0.601898i
$576$	−5.43968			−0.226653
$577$	8.89810	−	6.46485i	0.370433	−	0.269135i	−0.386958	−	0.922098i	$-0.626474\pi$
$577$	8.89810	−	6.46485i	0.370433	−	0.269135i	0.757390	+	0.652962i	$0.226474\pi$
$578$	−10.0528	+	30.9395i	−0.418143	+	1.28691i
$579$	−7.94791	+	24.4612i	−0.330304	+	1.01657i
$580$	85.4074	−	20.7377i	3.54635	−	0.861086i
$581$	1.57735	+	4.85459i	0.0654396	+	0.201403i
$582$	−11.0807			−0.459310
$583$	0.678220	+	2.08735i	0.0280890	+	0.0864491i
$584$	5.71778	+	4.15421i	0.236603	+	0.171902i
$585$	3.21835	+	1.32337i	0.133062	+	0.0547145i
$586$	41.3765	−	30.0618i	1.70925	−	1.24184i
$587$	19.3825	+	14.0822i	0.800000	+	0.581234i	0.910914	−	0.412596i	$-0.135378\pi$
$587$	19.3825	+	14.0822i	0.800000	+	0.581234i	−0.110914	+	0.993830i	$0.535378\pi$
$588$	−3.38896	−	2.46222i	−0.139758	−	0.101540i
$589$	−6.97374	+	5.06672i	−0.287348	+	0.208770i
$590$	8.27467	−	9.73916i	0.340663	−	0.400955i
$591$	−1.30578	−	0.948707i	−0.0537128	−	0.0390246i
$592$	17.1090	+	52.6560i	0.703174	+	2.16415i
$593$	−24.7528			−1.01648			−0.508238	−	0.861217i	$-0.669703\pi$
$593$	−24.7528			−1.01648			−0.508238	+	0.861217i	$0.669703\pi$
$594$	0.203957	+	0.627717i	0.00836848	+	0.0257555i
$595$	4.09629	+	1.68437i	0.167931	+	0.0690525i
$596$	10.5976	−	32.6159i	0.434093	−	1.33600i
$597$	5.46296	−	16.8133i	0.223584	−	0.688122i
$598$	12.8526	−	9.33799i	0.525584	−	0.381859i
$599$	27.6193			1.12850			0.564248	−	0.825605i	$-0.309166\pi$
$599$	27.6193			1.12850			0.564248	+	0.825605i	$0.309166\pi$
$600$	−4.39817	−	26.8709i	−0.179555	−	1.09700i
$601$	−42.8771			−1.74899			−0.874497	−	0.485032i	$-0.838808\pi$
$601$	−42.8771			−1.74899			−0.874497	+	0.485032i	$0.838808\pi$
$602$	0.685132	−	0.497778i	0.0279239	−	0.0202879i
$603$	2.88757	−	8.88701i	0.117591	−	0.361907i
$604$	−2.87353	+	8.84382i	−0.116922	+	0.359850i
$605$	−12.8232	−	20.8050i	−0.521339	−	0.845842i
$606$	−8.26428	−	25.4348i	−0.335713	−	1.03322i
$607$	0.238068			0.00966288			0.00483144	−	0.999988i	$-0.498462\pi$
$607$	0.238068			0.00966288			0.00483144	+	0.999988i	$0.498462\pi$
$608$	−2.84643	−	8.76040i	−0.115438	−	0.355281i
$609$	7.59099	+	5.51518i	0.307602	+	0.223486i
$610$	−26.5494	−	43.0749i	−1.07496	−	1.74405i
$611$	0.254921	−	0.185211i	0.0103130	−	0.00749284i
$612$	−6.71266	−	4.87703i	−0.271343	−	0.197142i
$613$	−5.22461	−	3.79590i	−0.211020	−	0.153315i	0.477255	−	0.878765i	$-0.341632\pi$
$613$	−5.22461	−	3.79590i	−0.211020	−	0.153315i	−0.688275	+	0.725450i	$0.741632\pi$
$614$	51.7994	−	37.6345i	2.09045	−	1.51880i
$615$	1.81287	−	23.8202i	0.0731020	−	0.960524i
$616$	1.16885	+	0.849218i	0.0470942	+	0.0342160i
$617$	10.9258	+	33.6261i	0.439856	+	1.35374i	0.888028	+	0.459790i	$0.152075\pi$
$617$	10.9258	+	33.6261i	0.439856	+	1.35374i	−0.448172	+	0.893947i	$0.647925\pi$
$618$	29.5719			1.18956
$619$	14.3386	+	44.1298i	0.576318	+	1.77373i	0.631645	+	0.775258i	$0.282380\pi$
$619$	14.3386	+	44.1298i	0.576318	+	1.77373i	−0.0553268	+	0.998468i	$0.517620\pi$
$620$	11.1780	−	13.1563i	0.448919	−	0.528371i
$621$	1.26805	−	3.90266i	0.0508851	−	0.156608i
$622$	−7.80192	+	24.0118i	−0.312829	+	0.962787i
$623$	2.89584	−	2.10395i	0.116019	−	0.0842931i
$624$	−8.04509			−0.322061
$625$	−23.6954	+	7.97037i	−0.947817	+	0.318815i
$626$	8.79048			0.351338
$627$	1.00386	−	0.729346i	0.0400902	−	0.0291273i
$628$	3.70888	−	11.4148i	0.148000	−	0.455498i
$629$	6.55529	−	20.1751i	0.261376	−	0.804434i
$630$	3.60184	−	4.23931i	0.143501	−	0.168898i
$631$	−8.69925	−	26.7735i	−0.346312	−	1.06584i	−0.960878	−	0.276972i	$-0.910669\pi$
$631$	−8.69925	−	26.7735i	−0.346312	−	1.06584i	0.614566	−	0.788865i	$-0.289331\pi$
$632$	−38.5173			−1.53213
$633$	7.17164	+	22.0720i	0.285047	+	0.877285i
$634$	−6.91746	−	5.02583i	−0.274727	−	0.199601i
$635$	−1.77129	+	23.2738i	−0.0702914	+	0.923593i
$636$	−28.0354	+	20.3689i	−1.11168	+	0.807681i
$637$	1.25901	+	0.914723i	0.0498837	+	0.0362426i
$638$	−5.01021	−	3.64013i	−0.198356	−	0.144114i
$639$	−8.16334	+	5.93101i	−0.322937	+	0.234627i
$640$	−20.4987	−	33.2579i	−0.810282	−	1.31463i
$641$	−9.91464	−	7.20340i	−0.391605	−	0.284517i	0.374508	−	0.927224i	$-0.377812\pi$
$641$	−9.91464	−	7.20340i	−0.391605	−	0.284517i	−0.766113	+	0.642706i	$0.777812\pi$
$642$	−10.4357	−	32.1177i	−0.411863	−	1.26758i
$643$	22.3423			0.881096			0.440548	−	0.897729i	$-0.354784\pi$
$643$	22.3423			0.881096			0.440548	+	0.897729i	$0.354784\pi$
$644$	−5.31185	−	16.3482i	−0.209316	−	0.644209i
$645$	0.399393	+	0.647992i	0.0157261	+	0.0255146i
$646$	−7.12176	+	21.9185i	−0.280202	+	0.862373i
$647$	7.95322	−	24.4775i	0.312673	−	0.962309i	−0.664028	−	0.747707i	$-0.731155\pi$
$647$	7.95322	−	24.4775i	0.312673	−	0.962309i	0.976702	−	0.214602i	$-0.0688454\pi$
$648$	−4.40566	+	3.20090i	−0.173071	+	0.125743i
$649$	−0.609501			−0.0239250
$650$	3.12680	+	19.1034i	0.122643	+	0.749295i
$651$	1.84306			0.0722354
$652$	34.9688	−	25.4063i	1.36948	−	0.994988i
$653$	−1.31006	+	4.03195i	−0.0512666	+	0.157782i	−0.973412	−	0.229061i	$-0.926435\pi$
$653$	−1.31006	+	4.03195i	−0.0512666	+	0.157782i	0.922146	+	0.386843i	$0.126435\pi$
$654$	3.70643	−	11.4072i	0.144933	−	0.446058i
$655$	−42.3419	−	17.4108i	−1.65444	−	0.680295i
$656$	17.0670	+	52.5268i	0.666354	+	2.05083i
$657$	−1.29783			−0.0506330
$658$	−0.155657	−	0.479065i	−0.00606816	−	0.0186759i
$659$	1.59069	+	1.15571i	0.0619646	+	0.0450199i	0.618336	−	0.785914i	$-0.287807\pi$
$659$	1.59069	+	1.15571i	0.0619646	+	0.0450199i	−0.556372	+	0.830933i	$0.687807\pi$
$660$	−1.60905	+	1.89383i	−0.0626323	+	0.0737173i
$661$	−2.85512	+	2.07437i	−0.111051	+	0.0806836i	−0.641925	−	0.766767i	$-0.721864\pi$
$661$	−2.85512	+	2.07437i	−0.111051	+	0.0806836i	0.530874	+	0.847451i	$0.321864\pi$
$662$	−8.60466	−	6.25165i	−0.334430	−	0.242977i
$663$	2.49377	+	1.81183i	0.0968500	+	0.0703656i
$664$	22.4883	−	16.3387i	0.872716	−	0.634066i
$665$	−9.67231	−	3.97720i	−0.375076	−	0.154229i
$666$	−21.5550	−	15.6607i	−0.835241	−	0.606838i
$667$	11.8981	+	36.6186i	0.460696	+	1.41788i
$668$	91.2253			3.52961
$669$	−4.60541	−	14.1740i	−0.178055	−	0.547998i
$670$	50.5133	−	12.2651i	1.95150	−	0.473841i
$671$	−0.745731	+	2.29512i	−0.0287886	+	0.0886023i
$672$	−0.608601	+	1.87308i	−0.0234773	+	0.0722557i
$673$	−16.0139	+	11.6348i	−0.617290	+	0.448487i	−0.851974	−	0.523585i	$-0.824594\pi$
$673$	−16.0139	+	11.6348i	−0.617290	+	0.448487i	0.234684	+	0.972072i	$0.424594\pi$
$674$	−25.2586			−0.972923
$675$	3.55373	+	3.51724i	0.136783	+	0.135379i
$676$	−44.3119			−1.70430
$677$	−21.3791	+	15.5328i	−0.821666	+	0.596975i	−0.917189	−	0.398452i	$-0.869548\pi$
$677$	−21.3791	+	15.5328i	−0.821666	+	0.596975i	0.0955233	+	0.995427i	$0.469548\pi$
$678$	15.1882	−	46.7444i	0.583298	−	1.79521i
$679$	1.37639	−	4.23608i	0.0528209	−	0.162566i
$680$	1.83035	−	24.0498i	0.0701905	−	0.922268i
$681$	8.00169	+	24.6267i	0.306625	+	0.943696i
$682$	−1.21646			−0.0465807
$683$	−6.84086	−	21.0540i	−0.261758	−	0.805609i	−0.992422	−	0.122872i	$-0.960789\pi$
$683$	−6.84086	−	21.0540i	−0.261758	−	0.805609i	0.730664	−	0.682737i	$-0.239211\pi$
$684$	15.8502	+	11.5158i	0.606047	+	0.440319i
$685$	8.22677	−	1.99753i	0.314329	−	0.0763218i
$686$	2.01265	−	1.46227i	0.0768432	−	0.0558298i
$687$	14.5388	+	10.5631i	0.554691	+	0.403006i
$688$	−1.42372	−	1.03439i	−0.0542788	−	0.0394359i
$689$	10.4152	−	7.56711i	0.396789	−	0.288284i
$690$	22.1825	−	5.38610i	0.844472	−	0.205045i
$691$	−33.1958	−	24.1182i	−1.26283	−	0.917498i	−0.263935	−	0.964541i	$-0.585020\pi$
$691$	−33.1958	−	24.1182i	−1.26283	−	0.917498i	−0.998893	+	0.0470426i	$0.985020\pi$
$692$	−24.8014	−	76.3309i	−0.942808	−	2.90167i
$693$	−0.265306			−0.0100782
$694$	8.95281	+	27.5539i	0.339844	+	1.04593i
$695$	1.25102	−	16.4377i	0.0474538	−	0.623519i
$696$	15.7898	−	48.5959i	0.598510	−	1.84202i
$697$	6.53921	−	20.1256i	0.247690	−	0.762312i
$698$	−23.4424	+	17.0319i	−0.887306	+	0.644666i
$699$	−22.7864			−0.861861
$700$	20.7037	+	3.16973i	0.782526	+	0.119804i
$701$	−41.2940			−1.55965			−0.779826	−	0.625996i	$-0.784693\pi$
$701$	−41.2940			−1.55965			−0.779826	+	0.625996i	$0.784693\pi$
$702$	3.13212	−	2.27562i	0.118214	−	0.0858876i
$703$	−15.4786	+	47.6382i	−0.583786	+	1.79671i
$704$	−0.445967	+	1.37255i	−0.0168080	+	0.0517298i
$705$	0.439971	−	0.106829i	0.0165703	−	0.00402341i
$706$	−2.13715	−	6.57747i	−0.0804327	−	0.247546i
$707$	10.7501			0.404300
$708$	−2.97385	−	9.15255i	−0.111764	−	0.343974i
$709$	−3.39017	−	2.46310i	−0.127321	−	0.0925038i	0.522302	−	0.852760i	$-0.325073\pi$
$709$	−3.39017	−	2.46310i	−0.127321	−	0.0925038i	−0.649623	+	0.760257i	$0.725073\pi$
$710$	−51.9138	−	21.3467i	−1.94829	−	0.801126i
$711$	5.72216	−	4.15739i	0.214598	−	0.155914i
$712$	−15.7699	−	11.4575i	−0.591000	−	0.429387i
$713$	6.11861	+	4.44543i	0.229144	+	0.166483i
$714$	3.98653	−	2.89639i	0.149192	−	0.108394i
$715$	0.597768	−	0.703563i	0.0223552	−	0.0263118i
$716$	22.1928	+	16.1240i	0.829384	+	0.602583i
$717$	4.93250	+	15.1807i	0.184208	+	0.566933i
$718$	−12.5735			−0.469239
$719$	6.44749	+	19.8433i	0.240451	+	0.740032i	0.996351	+	0.0853453i	$0.0271993\pi$
$719$	6.44749	+	19.8433i	0.240451	+	0.740032i	−0.755901	+	0.654686i	$0.772801\pi$
$720$	−10.6911	−	4.39612i	−0.398434	−	0.163834i
$721$	−3.67326	+	11.3051i	−0.136799	+	0.421025i
$722$	2.20968	−	6.80068i	0.0822356	−	0.253095i
$723$	18.0397	−	13.1066i	0.670903	−	0.487440i
$724$	7.68938			0.285774
$725$	−46.3745	−	7.09992i	−1.72231	−	0.263685i
$726$	−27.1903			−1.00913
$727$	−24.8104	+	18.0258i	−0.920168	+	0.668542i	−0.943566	−	0.331185i	$-0.892552\pi$
$727$	−24.8104	+	18.0258i	−0.920168	+	0.668542i	0.0233975	+	0.999726i	$0.492552\pi$
$728$	2.61882	−	8.05991i	0.0970600	−	0.298720i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−3.78808	−	6.14595i	−0.140203	−	0.227472i
$731$	0.208361	+	0.641271i	0.00770653	+	0.0237182i
$732$	−38.1032			−1.40834
$733$	10.0357	+	30.8866i	0.370676	+	1.14082i	0.946350	+	0.323144i	$0.104740\pi$
$733$	10.0357	+	30.8866i	0.370676	+	1.14082i	−0.575674	+	0.817679i	$0.695260\pi$
$734$	59.2564	+	43.0523i	2.18720	+	1.58909i
$735$	1.17326	+	1.90354i	0.0432762	+	0.0702132i
$736$	−6.53826	+	4.75033i	−0.241004	+	0.175099i
$737$	−2.00565	−	1.45719i	−0.0738790	−	0.0536762i
$738$	−21.5022	−	15.6222i	−0.791506	−	0.575063i
$739$	−3.14004	+	2.28137i	−0.115508	+	0.0839216i	−0.644040	−	0.764992i	$-0.722743\pi$
$739$	−3.14004	+	2.28137i	−0.115508	+	0.0839216i	0.528531	+	0.848914i	$0.322743\pi$
$740$	7.61277	−	100.028i	0.279851	−	3.67710i
$741$	−5.88838	−	4.27816i	−0.216315	−	0.157162i
$742$	−6.35965	−	19.5730i	−0.233470	−	0.718547i
$743$	36.3679			1.33421			0.667105	−	0.744964i	$-0.267533\pi$
$743$	36.3679			1.33421			0.667105	+	0.744964i	$0.267533\pi$
$744$	−3.10153	−	9.54552i	−0.113708	−	0.349956i
$745$	−11.8530	+	13.9508i	−0.434261	+	0.511118i
$746$	−11.6381	+	35.8185i	−0.426102	+	1.31141i
$747$	−1.57735	+	4.85459i	−0.0577123	+	0.177620i
$748$	−1.78091	+	1.29391i	−0.0651165	+	0.0473099i
$749$	13.5746			0.496006
$750$	−6.28356	+	27.0950i	−0.229443	+	0.989370i
$751$	−1.09247			−0.0398647			−0.0199324	−	0.999801i	$-0.506345\pi$
$751$	−1.09247			−0.0398647			−0.0199324	+	0.999801i	$0.506345\pi$
$752$	−0.846829	+	0.615257i	−0.0308807	+	0.0224361i
$753$	7.97632	−	24.5486i	0.290673	−	0.894600i
$754$	−11.2254	+	34.5484i	−0.408807	+	1.25818i
$755$	3.21395	−	3.78277i	0.116968	−	0.137669i
$756$	−1.29447	−	3.98396i	−0.0470794	−	0.144895i
$757$	−4.89617			−0.177954			−0.0889771	−	0.996034i	$-0.528360\pi$
$757$	−4.89617			−0.177954			−0.0889771	+	0.996034i	$0.528360\pi$
$758$	8.59048	+	26.4388i	0.312020	+	0.960300i
$759$	−0.880764	−	0.639912i	−0.0319697	−	0.0232273i
$760$	−4.32188	+	56.7873i	−0.156771	+	2.05989i
$761$	40.2854	−	29.2690i	1.46034	−	1.06100i	0.477070	−	0.878865i	$-0.341699\pi$
$761$	40.2854	−	29.2690i	1.46034	−	1.06100i	0.983273	−	0.182137i	$-0.0583014\pi$
$762$	21.0089	+	15.2639i	0.761073	+	0.552952i
$763$	3.90051	+	2.83389i	0.141208	+	0.102594i
$764$	−59.4419	+	43.1871i	−2.15053	+	1.56245i
$765$	2.32392	+	3.77042i	0.0840215	+	0.136320i
$766$	35.2422	+	25.6049i	1.27335	+	0.925143i
$767$	1.10479	+	3.40020i	0.0398917	+	0.122774i
$768$	−32.5859			−1.17584
$769$	−6.30997	−	19.4201i	−0.227543	−	0.700307i	−0.998023	−	0.0628426i	$-0.979983\pi$
$769$	−6.30997	−	19.4201i	−0.227543	−	0.700307i	0.770480	−	0.637464i	$-0.220017\pi$
$770$	−0.774373	−	1.25638i	−0.0279065	−	0.0452766i
$771$	5.84225	−	17.9806i	0.210403	−	0.647555i
$772$	−33.2937	+	102.467i	−1.19827	+	3.68788i
$773$	2.11944	−	1.53987i	0.0762311	−	0.0553851i	−0.549017	−	0.835811i	$-0.684998\pi$
$773$	2.11944	−	1.53987i	0.0762311	−	0.0553851i	0.625248	+	0.780426i	$0.284998\pi$
$774$	0.846870			0.0304401
$775$	−8.18922	+	4.22598i	−0.294165	+	0.151802i
$776$	−24.2555			−0.870723
$777$	8.66441	−	6.29506i	0.310834	−	0.225834i
$778$	−26.5793	+	81.8026i	−0.952913	+	2.93277i
$779$	−15.4406	+	47.5213i	−0.553217	+	1.70263i
$780$	13.4816	+	5.54357i	0.482720	+	0.198492i
$781$	0.827256	+	2.54603i	0.0296015	+	0.0911042i
$782$	20.2205			0.723084
$783$	2.89950	+	8.92374i	0.103620	+	0.318909i
$784$	−4.18232	−	3.03864i	−0.149369	−	0.108523i
$785$	−4.14825	+	4.88243i	−0.148058	+	0.174261i
$786$	−41.2074	+	29.9390i	−1.46982	+	1.06789i
$787$	7.40945	+	5.38328i	0.264118	+	0.191893i	0.711961	−	0.702219i	$-0.247807\pi$
$787$	7.40945	+	5.38328i	0.264118	+	0.191893i	−0.447842	+	0.894113i	$0.647807\pi$
$788$	−5.46991	−	3.97412i	−0.194858	−	0.141572i
$789$	7.29198	−	5.29794i	0.259602	−	0.188612i
$790$	36.3894	+	14.9631i	1.29468	+	0.532364i
$791$	15.9835	+	11.6127i	0.568306	+	0.412899i
$792$	0.446460	+	1.37406i	0.0158643	+	0.0488252i
$793$	14.1554			0.502674
$794$	−15.2831	−	47.0365i	−0.542376	−	1.66926i
$795$	17.9757	−	4.36467i	0.637534	−	0.154799i
$796$	22.8843	−	70.4306i	0.811112	−	2.49635i
$797$	1.26653	−	3.89797i	0.0448627	−	0.138073i	−0.926116	−	0.377238i	$-0.876874\pi$
$797$	1.26653	−	3.89797i	0.0448627	−	0.138073i	0.970979	+	0.239165i	$0.0768737\pi$
$798$	−9.41315	+	6.83905i	−0.333222	+	0.242100i
$799$	0.401057			0.0141884
$800$	−1.59063	−	9.71806i	−0.0562373	−	0.343585i
$801$	3.57946			0.126474
$802$	−57.1244	+	41.5033i	−2.01713	+	1.46553i
$803$	−0.106401	+	0.327469i	−0.00375482	+	0.0115561i
$804$	12.0960	−	37.2276i	0.426592	−	1.31292i
$805$	−0.696316	+	9.14924i	−0.0245419	+	0.322468i
$806$	2.20497	+	6.78621i	0.0776669	+	0.239034i
$807$	−14.6837			−0.516890
$808$	−18.0904	−	55.6765i	−0.636418	−	1.95869i
$809$	−31.7234	−	23.0484i	−1.11534	−	0.810339i	−0.131840	−	0.991271i	$-0.542089\pi$
$809$	−31.7234	−	23.0484i	−1.11534	−	0.810339i	−0.983496	+	0.180932i	$0.942089\pi$
$810$	5.40575	−	1.31256i	0.189939	−	0.0461188i
$811$	−19.4376	+	14.1223i	−0.682547	+	0.495900i	−0.874202	−	0.485563i	$-0.838615\pi$
$811$	−19.4376	+	14.1223i	−0.682547	+	0.495900i	0.191654	+	0.981462i	$0.438615\pi$
$812$	31.7986	+	23.1030i	1.11591	+	0.810756i
$813$	12.3299	+	8.95819i	0.432428	+	0.314177i
$814$	−5.71869	+	4.15487i	−0.200440	+	0.145628i
$815$	−22.4213	+	5.44408i	−0.785382	+	0.190698i
$816$	−8.28410	−	6.01875i	−0.290002	−	0.210699i
$817$	−0.491991	−	1.51419i	−0.0172126	−	0.0529749i
$818$	−39.3521			−1.37592
$819$	0.480898	+	1.48005i	0.0168039	+	0.0517172i
$820$	7.59409	−	99.7826i	0.265197	−	3.48456i
$821$	5.11447	−	15.7407i	0.178496	−	0.549355i	−0.821280	−	0.570526i	$-0.806739\pi$
$821$	5.11447	−	15.7407i	0.178496	−	0.549355i	0.999776	+	0.0211709i	$0.00673942\pi$
$822$	2.91055	−	8.95776i	0.101517	−	0.312438i
$823$	7.02235	−	5.10204i	0.244784	−	0.177846i	−0.458628	−	0.888628i	$-0.651659\pi$
$823$	7.02235	−	5.10204i	0.244784	−	0.177846i	0.703412	+	0.710782i	$0.251659\pi$
$824$	64.7325			2.25506
$825$	1.17882	−	0.608323i	0.0410414	−	0.0211791i
$826$	5.71527			0.198860
$827$	−2.57150	+	1.86831i	−0.0894199	+	0.0649673i	−0.631597	−	0.775297i	$-0.717600\pi$
$827$	−2.57150	+	1.86831i	−0.0894199	+	0.0649673i	0.542177	+	0.840264i	$0.317600\pi$
$828$	5.31185	−	16.3482i	0.184599	−	0.568139i
$829$	−1.11727	+	3.43861i	−0.0388044	+	0.119428i	−0.968582	−	0.248693i	$-0.919999\pi$
$829$	−1.11727	+	3.43861i	−0.0388044	+	0.119428i	0.929778	+	0.368121i	$0.119999\pi$
$830$	−27.5932	+	6.69988i	−0.957775	+	0.232556i
$831$	−0.986576	−	3.03637i	−0.0342239	−	0.105330i
$832$	8.46533			0.293483
$833$	0.612083	+	1.88380i	0.0212074	+	0.0652697i
$834$	−14.8381	−	10.7805i	−0.513802	−	0.373299i
$835$	−45.0370	−	18.5189i	−1.55857	−	0.640875i
$836$	4.20515	−	3.05522i	0.145438	−	0.105667i
$837$	1.49107	+	1.08333i	0.0515389	+	0.0374452i
$838$	4.49732	+	3.26750i	0.155358	+	0.112874i
$839$	3.35916	−	2.44058i	0.115971	−	0.0842580i	−0.528288	−	0.849065i	$-0.677166\pi$
$839$	3.35916	−	2.44058i	0.115971	−	0.0842580i	0.644259	+	0.764807i	$0.277166\pi$
$840$	7.88437	−	9.27978i	0.272037	−	0.320183i
$841$	−47.7646	−	34.7030i	−1.64705	−	1.19666i
$842$	−19.7752	−	60.8617i	−0.681497	−	2.09743i
$843$	−19.1746			−0.660407
$844$	30.0419	+	92.4595i	1.03409	+	3.18259i
$845$	21.8763	+	8.99541i	0.752567	+	0.309451i
$846$	0.155657	−	0.479065i	0.00535161	−	0.0164706i
$847$	3.37744	−	10.3947i	0.116050	−	0.357165i
$848$	−34.5986	+	25.1374i	−1.18812	+	0.863220i
$849$	−9.08698			−0.311864
$850$	−11.0721	+	22.0102i	−0.379768	+	0.754942i
$851$	43.9477			1.50651
$852$	−34.1961	+	24.8449i	−1.17154	+	0.851173i
$853$	−2.60564	+	8.01934i	−0.0892155	+	0.274577i	−0.985703	−	0.168492i	$-0.946110\pi$
$853$	−2.60564	+	8.01934i	−0.0892155	+	0.274577i	0.896488	+	0.443069i	$0.146110\pi$
$854$	6.99270	−	21.5213i	0.239285	−	0.736444i
$855$	−5.48732	−	8.90286i	−0.187662	−	0.304471i
$856$	−22.8435	−	70.3052i	−0.780776	−	2.40298i
$857$	−33.7778			−1.15383			−0.576914	−	0.816805i	$-0.695743\pi$
$857$	−33.7778			−1.15383			−0.576914	+	0.816805i	$0.695743\pi$
$858$	−0.317403	−	0.976864i	−0.0108359	−	0.0333496i
$859$	−12.5937	−	9.14986i	−0.429692	−	0.312189i	0.351834	−	0.936062i	$-0.385558\pi$
$859$	−12.5937	−	9.14986i	−0.429692	−	0.312189i	−0.781526	+	0.623873i	$0.785558\pi$
$860$	1.67305	+	2.71443i	0.0570506	+	0.0925612i
$861$	8.64316	−	6.27962i	0.294558	−	0.214009i
$862$	8.00729	+	5.81764i	0.272729	+	0.198149i
$863$	−16.0437	−	11.6565i	−0.546135	−	0.396790i	0.280223	−	0.959935i	$-0.409591\pi$
$863$	−16.0437	−	11.6565i	−0.546135	−	0.396790i	−0.826359	+	0.563144i	$0.809591\pi$
$864$	−1.59334	+	1.15763i	−0.0542065	+	0.0393833i
$865$	−3.25115	+	42.7185i	−0.110542	+	1.45247i
$866$	49.9629	+	36.3001i	1.69781	+	1.23353i
$867$	−4.04091	−	12.4366i	−0.137237	−	0.422371i
$868$	7.72057			0.262053
$869$	−0.579872	−	1.78466i	−0.0196708	−	0.0605406i
$870$	−33.7959	+	39.7773i	−1.14579	+	1.34858i
$871$	−4.49369	+	13.8301i	−0.152263	+	0.468616i
$872$	8.11333	−	24.9703i	0.274752	−	0.845600i
$873$	3.60343	−	2.61804i	0.121957	−	0.0886073i
$874$	−47.7454			−1.61501
$875$	−9.57773	−	5.76776i	−0.323786	−	0.194986i
$876$	−5.43658			−0.183685
$877$	16.9374	−	12.3057i	0.571934	−	0.415535i	−0.263873	−	0.964557i	$-0.585000\pi$
$877$	16.9374	−	12.3057i	0.571934	−	0.415535i	0.835807	+	0.549023i	$0.185000\pi$
$878$	23.7801	−	73.1877i	0.802540	−	2.46996i
$879$	−6.35285	+	19.5520i	−0.214276	+	0.659474i
$880$	−1.98574	+	2.33718i	−0.0669392	+	0.0787864i
$881$	−1.60711	−	4.94618i	−0.0541450	−	0.166641i	0.920327	−	0.391149i	$-0.127922\pi$
$881$	−1.60711	−	4.94618i	−0.0541450	−	0.166641i	−0.974472	+	0.224508i	$0.927922\pi$
$882$	2.48777			0.0837675
$883$	2.98080	+	9.17395i	0.100312	+	0.308728i	0.988602	−	0.150555i	$-0.0481062\pi$
$883$	2.98080	+	9.17395i	0.100312	+	0.308728i	−0.888290	+	0.459283i	$0.848106\pi$
$884$	10.4464	+	7.58973i	0.351349	+	0.255270i
$885$	−0.389834	+	5.12222i	−0.0131041	+	0.172181i
$886$	66.9257	−	48.6244i	2.24841	−	1.63357i
$887$	−10.5831	−	7.68906i	−0.355345	−	0.258173i	0.395763	−	0.918353i	$-0.370480\pi$
$887$	−10.5831	−	7.68906i	−0.355345	−	0.258173i	−0.751108	+	0.660179i	$0.770480\pi$
$888$	−47.1837	−	34.2810i	−1.58338	−	1.15039i
$889$	−8.44490	+	6.13558i	−0.283233	+	0.205781i
$890$	10.4477	+	16.9508i	0.350207	+	0.568191i
$891$	−0.214637	−	0.155943i	−0.00719062	−	0.00522429i
$892$	−19.2920	−	59.3746i	−0.645944	−	1.98801i
$893$	−0.946990			−0.0316898
$894$	6.29371	+	19.3700i	0.210493	+	0.647831i
$895$	−7.68314	−	12.4654i	−0.256819	−	0.416674i
$896$	5.39902	−	16.6165i	0.180369	−	0.555118i
$897$	−1.97336	+	6.07339i	−0.0658887	+	0.202785i
$898$	−25.2411	+	18.3387i	−0.842307	+	0.611972i
$899$	−17.2934			−0.576768
$900$	14.8865	+	14.7337i	0.496217	+	0.491123i
$901$	16.3858			0.545891
$902$	−5.70466	+	4.14468i	−0.189944	+	0.138003i
$903$	−0.105194	+	0.323753i	−0.00350063	+	0.0107738i
$904$	33.2467	−	102.323i	1.10577	−	3.40320i
$905$	−3.79616	−	1.56096i	−0.126189	−	0.0518881i
$906$	−1.70654	−	5.25219i	−0.0566960	−	0.174492i
$907$	34.5045			1.14570			0.572851	−	0.819660i	$-0.305837\pi$
$907$	34.5045			1.14570			0.572851	+	0.819660i	$0.305837\pi$
$908$	33.5190	+	103.161i	1.11237	+	3.42351i
$909$	8.69702	+	6.31876i	0.288462	+	0.209580i
$910$	−5.60525	+	6.59729i	−0.185812	+	0.218698i
$911$	19.2708	−	14.0011i	0.638470	−	0.463876i	−0.220854	−	0.975307i	$-0.570884\pi$
$911$	19.2708	−	14.0011i	0.638470	−	0.463876i	0.859324	+	0.511431i	$0.170884\pi$
$912$	19.5607	+	14.2117i	0.647721	+	0.470597i
$913$	1.09560	+	0.795999i	0.0362590	+	0.0263437i
$914$	40.3763	−	29.3351i	1.33553	−	0.970319i
$915$	18.8111	+	7.73504i	0.621877	+	0.255712i
$916$	60.9029	+	44.2486i	2.01229	+	1.46201i
$917$	−6.32689	−	19.4722i	−0.208932	−	0.643028i
$918$	4.92762			0.162636
$919$	−7.53537	−	23.1915i	−0.248569	−	0.765016i	−0.995029	−	0.0995861i	$-0.968248\pi$
$919$	−7.53537	−	23.1915i	−0.248569	−	0.765016i	0.746460	−	0.665430i	$-0.231752\pi$
$920$	48.5572	−	11.7901i	1.60088	−	0.388708i
$921$	−7.95316	+	24.4773i	−0.262066	+	0.806555i
$922$	−13.1525	+	40.4792i	−0.433154	+	1.33311i
$923$	12.7039	−	9.22996i	0.418155	−	0.303808i
$924$	−1.11136			−0.0365612
$925$	−24.0642	+	47.8373i	−0.791227	+	1.57288i
$926$	84.6192			2.78076
$927$	−9.61673	+	6.98696i	−0.315855	+	0.229482i
$928$	5.71049	−	17.5751i	0.187456	−	0.576930i
$929$	6.83586	−	21.0386i	0.224277	−	0.690255i	−0.774087	−	0.633079i	$-0.781791\pi$
$929$	6.83586	−	21.0386i	0.224277	−	0.690255i	0.998364	−	0.0571752i	$-0.0182094\pi$
$930$	−0.778041	+	10.2231i	−0.0255130	+	0.335228i
$931$	−1.44527	−	4.44809i	−0.0473669	−	0.145780i
$932$	−95.4519			−3.12663
$933$	−3.13611	−	9.65196i	−0.102672	−	0.315991i
$934$	−78.9564	−	57.3652i	−2.58353	−	1.87705i
$935$	1.14188	−	0.277259i	0.0373435	−	0.00906735i
$936$	6.85617	−	4.98130i	0.224101	−	0.162819i
$937$	33.3514	+	24.2312i	1.08954	+	0.791599i	0.979322	−	0.202308i	$-0.0648441\pi$
$937$	33.3514	+	24.2312i	1.08954	+	0.791599i	0.110221	+	0.993907i	$0.464844\pi$
$938$	18.8069	+	13.6640i	0.614067	+	0.446146i
$939$	−2.85865	+	2.07693i	−0.0932884	+	0.0677780i
$940$	1.84303	−	0.447505i	0.0601131	−	0.0145960i
$941$	−25.8493	−	18.7806i	−0.842662	−	0.612230i	0.0804507	−	0.996759i	$-0.474364\pi$
$941$	−25.8493	−	18.7806i	−0.842662	−	0.612230i	−0.923113	+	0.384529i	$0.874364\pi$
$942$	2.20264	+	6.77903i	0.0717659	+	0.220873i
$943$	43.8398			1.42762
$944$	−3.67003	−	11.2952i	−0.119449	−	0.367627i
$945$	−0.169688	+	2.22962i	−0.00551996	+	0.0725295i
$946$	0.0694299	−	0.213683i	0.00225736	−	0.00694744i
$947$	4.61287	−	14.1970i	0.149898	−	0.461339i	−0.847710	−	0.530460i	$-0.822019\pi$
$947$	4.61287	−	14.1970i	0.149898	−	0.461339i	0.997608	+	0.0691206i	$0.0220193\pi$
$948$	23.9701	−	17.4153i	0.778512	−	0.565622i
$949$	2.01970			0.0655623
$950$	26.1437	−	51.9712i	0.848215	−	1.68617i
$951$	3.43700			0.111452
$952$	8.72647	−	6.34015i	0.282826	−	0.205485i
$953$	−14.6440	+	45.0697i	−0.474367	+	1.45995i	0.372443	+	0.928055i	$0.378520\pi$
$953$	−14.6440	+	45.0697i	−0.474367	+	1.45995i	−0.846810	+	0.531896i	$0.821480\pi$
$954$	6.35965	−	19.5730i	0.205901	−	0.633699i
$955$	38.1129	−	9.25415i	1.23330	−	0.299457i
$956$	20.6622	+	63.5917i	0.668263	+	2.05670i
$957$	2.48936			0.0804697
$958$	3.03811	+	9.35035i	0.0981569	+	0.302096i
$959$	3.06296	+	2.22537i	0.0989080	+	0.0718609i
$960$	11.2496	+	4.62576i	0.363078	+	0.149296i
$961$	22.3314	−	16.2247i	0.720367	−	0.523378i
$962$	33.5444	+	24.3714i	1.08151	+	0.785766i
$963$	10.9821	+	7.97897i	0.353893	+	0.257119i
$964$	75.5680	−	54.9034i	2.43388	−	1.76832i
$965$	37.2379	−	43.8284i	1.19873	−	1.41089i
$966$	8.25889	+	6.00043i	0.265725	+	0.193061i
$967$	−4.91565	−	15.1288i	−0.158077	−	0.486510i	0.840383	−	0.541993i	$-0.182330\pi$
$967$	−4.91565	−	15.1288i	−0.158077	−	0.486510i	−0.998460	+	0.0554831i	$0.982330\pi$
$968$	−59.5193			−1.91302
$969$	−2.86271	−	8.81052i	−0.0919635	−	0.283035i
$970$	22.9156	+	9.42275i	0.735774	+	0.302546i
$971$	2.19776	−	6.76400i	0.0705293	−	0.217067i	−0.909579	−	0.415532i	$-0.863596\pi$
$971$	2.19776	−	6.76400i	0.0705293	−	0.217067i	0.980108	+	0.198465i	$0.0635955\pi$
$972$	1.29447	−	3.98396i	0.0415201	−	0.127786i
$973$	5.96443	−	4.33341i	0.191211	−	0.138923i
$974$	95.5046			3.06016
$975$	−5.53038	−	5.47360i	−0.177114	−	0.175296i
$976$	−47.0232			−1.50518
$977$	14.6169	−	10.6198i	0.467636	−	0.339757i	−0.328883	−	0.944371i	$-0.606672\pi$
$977$	14.6169	−	10.6198i	0.467636	−	0.339757i	0.796519	+	0.604613i	$0.206672\pi$
$978$	−7.93242	+	24.4135i	−0.253651	+	0.780657i
$979$	0.293459	−	0.903173i	0.00937898	−	0.0288655i
$980$	4.91476	+	7.97391i	0.156996	+	0.254717i
$981$	1.48986	+	4.58533i	0.0475677	+	0.146398i
$982$	61.1174			1.95033
$983$	−5.84860	−	18.0002i	−0.186542	−	0.574116i	0.813430	−	0.581663i	$-0.197598\pi$
$983$	−5.84860	−	18.0002i	−0.186542	−	0.574116i	−0.999972	+	0.00754707i	$0.997598\pi$
$984$	−47.0680	−	34.1969i	−1.50047	−	1.09016i
$985$	1.89368	+	3.07239i	0.0603377	+	0.0978944i
$986$	−37.4055	+	27.1767i	−1.19124	+	0.865483i
$987$	0.163808	+	0.119014i	0.00521407	+	0.00378824i
$988$	−24.6663	−	17.9211i	−0.784741	−	0.570148i
$989$	−1.13011	+	0.821070i	−0.0359353	+	0.0261085i
$990$	0.111998	−	1.47159i	0.00355952	−	0.0467703i
$991$	27.4032	+	19.9096i	0.870490	+	0.632448i	0.930719	−	0.365736i	$-0.119183\pi$
$991$	27.4032	+	19.9096i	0.870490	+	0.632448i	−0.0602281	+	0.998185i	$0.519183\pi$
$992$	−1.12169	−	3.45221i	−0.0356137	−	0.109608i
$993$	4.27530			0.135672
$994$	−7.75715	−	23.8741i	−0.246042	−	0.757239i
$995$	−25.5953	+	30.1253i	−0.811425	+	0.955035i
$996$	−6.60751	+	20.3358i	−0.209367	+	0.644365i
$997$	−2.52741	+	7.77856i	−0.0800438	+	0.246350i	−0.983068	−	0.183240i	$-0.941342\pi$
$997$	−2.52741	+	7.77856i	−0.0800438	+	0.246350i	0.903024	+	0.429589i	$0.141342\pi$
$998$	41.0920	−	29.8551i	1.30075	−	0.945047i
$999$	10.7098			0.338843

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.d.211.1	✓	32
25.16	even	5	inner	525.2.n.d.316.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.d.211.1	✓	32	1.1	even	1	trivial
525.2.n.d.316.1	yes	32	25.16	even	5	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.01265 + 1.46227i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.29447 - 3.98396i) q^{4} +(-1.44782 + 1.70406i) q^{5} +(0.768762 + 2.36601i) q^{6} -1.00000 q^{7} +(1.68281 + 5.17916i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-2.01265 + 1.46227i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.29447 - 3.98396i) q^{4} +(-1.44782 + 1.70406i) q^{5} +(0.768762 + 2.36601i) q^{6} -1.00000 q^{7} +(1.68281 + 5.17916i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.422145 - 5.54678i) q^{10} +(-0.214637 + 0.155943i) q^{11} +(-3.38896 - 2.46222i) q^{12} +(1.25901 + 0.914723i) q^{13} +(2.01265 - 1.46227i) q^{14} +(1.17326 + 1.90354i) q^{15} +(-4.18232 - 3.03864i) q^{16} +(0.612083 + 1.88380i) q^{17} +2.48777 q^{18} +(-1.44527 - 4.44809i) q^{19} +(4.91476 + 7.97391i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(0.203957 - 0.627717i) q^{22} +(-3.31980 + 2.41198i) q^{23} +5.44569 q^{24} +(-0.807642 - 4.93434i) q^{25} -3.87151 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.29447 + 3.98396i) q^{28} +(2.89950 - 8.92374i) q^{29} +(-5.14485 - 2.11553i) q^{30} +(-0.569538 - 1.75286i) q^{31} +1.96947 q^{32} +(0.0819841 + 0.252321i) q^{33} +(-3.98653 - 2.89639i) q^{34} +(1.44782 - 1.70406i) q^{35} +(-3.38896 + 2.46222i) q^{36} +(-8.66441 - 6.29506i) q^{37} +(9.41315 + 6.83905i) q^{38} +(1.25901 - 0.914723i) q^{39} +(-11.2620 - 4.63087i) q^{40} +(-8.64316 - 6.27962i) q^{41} +(-0.768762 - 2.36601i) q^{42} +0.340414 q^{43} +(0.343430 + 1.05697i) q^{44} +(2.17293 - 0.527607i) q^{45} +(3.15462 - 9.70891i) q^{46} +(0.0625691 - 0.192568i) q^{47} +(-4.18232 + 3.03864i) q^{48} +1.00000 q^{49} +(8.84085 + 8.75009i) q^{50} +1.98074 q^{51} +(5.27397 - 3.83176i) q^{52} +(2.55637 - 7.86769i) q^{53} +(0.768762 - 2.36601i) q^{54} +(0.0450194 - 0.591532i) q^{55} +(-1.68281 - 5.17916i) q^{56} -4.67700 q^{57} +(7.21328 + 22.2002i) q^{58} +(1.85859 + 1.35035i) q^{59} +(9.10238 - 2.21014i) q^{60} +(7.35885 - 5.34652i) q^{61} +(3.70944 + 2.69506i) q^{62} +(0.809017 + 0.587785i) q^{63} +(4.40079 - 3.19736i) q^{64} +(-3.38156 + 0.821073i) q^{65} +(-0.533968 - 0.387950i) q^{66} +(2.88757 + 8.88701i) q^{67} +8.29730 q^{68} +(1.26805 + 3.90266i) q^{69} +(-0.422145 + 5.54678i) q^{70} +(3.11812 - 9.59658i) q^{71} +(1.68281 - 5.17916i) q^{72} +(1.04996 - 0.762843i) q^{73} +26.6435 q^{74} +(-4.94241 - 0.756681i) q^{75} -19.5919 q^{76} +(0.214637 - 0.155943i) q^{77} +(-1.19636 + 3.68203i) q^{78} +(-2.18567 + 6.72681i) q^{79} +(11.2333 - 2.72754i) q^{80} +(0.309017 + 0.951057i) q^{81} +26.5781 q^{82} +(-1.57735 - 4.85459i) q^{83} +(3.38896 + 2.46222i) q^{84} +(-4.09629 - 1.68437i) q^{85} +(-0.685132 + 0.497778i) q^{86} +(-7.59099 - 5.51518i) q^{87} +(-1.16885 - 0.849218i) q^{88} +(-2.89584 + 2.10395i) q^{89} +(-3.60184 + 4.23931i) q^{90} +(-1.25901 - 0.914723i) q^{91} +(5.31185 + 16.3482i) q^{92} -1.84306 q^{93} +(0.155657 + 0.479065i) q^{94} +(9.67231 + 3.97720i) q^{95} +(0.608601 - 1.87308i) q^{96} +(-1.37639 + 4.23608i) q^{97} +(-2.01265 + 1.46227i) q^{98} +0.265306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more