LMFDB - Embedded newform 409.2.m.a.4.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,2,Mod(4,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(102)) chi = DirichletCharacter(H, H._module([41])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	409.m (of order $102$, degree $32$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.26588144267$
Analytic rank:	$0$
Dimension:	$1056$
Relative dimension:	$33$ over $\Q(\zeta_{102})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{102}]$

Embedding invariants

Embedding label			4.10
Character	$\chi$	$=$	409.4
Dual form			409.2.m.a.307.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36768 + 0.169355i) q^{2} +(-0.738030 + 3.36995i) q^{3} +(-0.0977346 + 0.0245812i) q^{4} +(-0.477318 + 0.958584i) q^{5} +(0.438669 - 4.73399i) q^{6} +(-3.78786 + 2.18692i) q^{7} +(2.69963 - 1.04584i) q^{8} +(-8.08647 - 3.72037i) q^{9} +(0.490476 - 1.39187i) q^{10} +(2.48798 - 0.230545i) q^{11} +(-0.0107064 - 0.347502i) q^{12} +(-2.59897 - 0.240830i) q^{13} +(4.81020 - 3.63249i) q^{14} +(-2.87810 - 2.31600i) q^{15} +(-3.33753 + 1.79221i) q^{16} +(-0.129164 + 0.832090i) q^{17} +(11.6897 + 3.71877i) q^{18} +(5.38667 + 4.06783i) q^{19} +(0.0230873 - 0.105420i) q^{20} +(-4.57426 - 14.3789i) q^{21} +(-3.36371 + 0.736664i) q^{22} +(-0.981818 + 6.32498i) q^{23} +(1.53203 + 9.86947i) q^{24} +(2.32212 + 3.07499i) q^{25} +(3.59534 - 0.110771i) q^{26} +(12.2686 - 16.2462i) q^{27} +(0.316448 - 0.306848i) q^{28} +(-3.43180 + 2.94018i) q^{29} +(4.32854 + 2.68012i) q^{30} -5.96798i q^{31} +(-0.464854 + 0.329063i) q^{32} +(-1.05928 + 8.55452i) q^{33} +(0.0357363 - 1.15991i) q^{34} +(-0.288334 - 4.67483i) q^{35} +(0.881779 + 0.164833i) q^{36} +(0.327502 - 0.0100902i) q^{37} +(-8.05614 - 4.65121i) q^{38} +(2.72970 - 8.58065i) q^{39} +(-0.286054 + 3.08702i) q^{40} +(-1.02387 - 2.90553i) q^{41} +(8.69124 + 18.8910i) q^{42} +(7.06625 - 5.33619i) q^{43} +(-0.237495 + 0.0836899i) q^{44} +(7.42610 - 5.97576i) q^{45} +(0.271643 - 8.81680i) q^{46} +(-1.86821 + 3.47905i) q^{47} +(-3.57647 - 12.5700i) q^{48} +(6.06524 - 10.5053i) q^{49} +(-3.69668 - 3.81233i) q^{50} +(-2.70877 - 1.04938i) q^{51} +(0.259929 - 0.0403485i) q^{52} +(0.459043 + 0.795086i) q^{53} +(-14.0280 + 24.2973i) q^{54} +(-0.966561 + 2.49498i) q^{55} +(-7.93863 + 9.86537i) q^{56} +(-17.6839 + 15.1506i) q^{57} +(4.19566 - 4.60242i) q^{58} +(-11.5096 - 3.27476i) q^{59} +(0.338220 + 0.155606i) q^{60} +(-7.36327 - 8.07712i) q^{61} +(1.01071 + 8.16226i) q^{62} +(38.7665 - 3.59225i) q^{63} +(6.17920 - 5.63308i) q^{64} +(1.47139 - 2.37638i) q^{65} -11.8792i q^{66} +(2.92059 + 4.12579i) q^{67} +(-0.00782999 - 0.0844991i) q^{68} +(-20.5902 - 7.97670i) q^{69} +(1.18605 + 6.34483i) q^{70} +(1.03220 + 0.0636638i) q^{71} +(-25.7214 - 1.58644i) q^{72} +(0.0581817 + 0.0564168i) q^{73} +(-0.446208 + 0.0692642i) q^{74} +(-12.0763 + 5.55600i) q^{75} +(-0.626457 - 0.265156i) q^{76} +(-8.91993 + 6.31429i) q^{77} +(-2.28017 + 12.1979i) q^{78} +(-9.99491 - 4.97687i) q^{79} +(-0.124926 - 4.05475i) q^{80} +(28.3203 + 33.0557i) q^{81} +(1.89239 + 3.80042i) q^{82} +(-2.05234 + 0.795081i) q^{83} +(0.800514 + 1.29287i) q^{84} +(-0.735976 - 0.520986i) q^{85} +(-8.76064 + 8.49489i) q^{86} +(-7.37550 - 13.7349i) q^{87} +(6.47551 - 3.22442i) q^{88} +(1.37164 + 4.82082i) q^{89} +(-9.14448 + 9.43055i) q^{90} +(10.3712 - 4.77151i) q^{91} +(-0.0595182 - 0.642304i) q^{92} +(20.1118 + 4.40455i) q^{93} +(1.96592 - 5.07461i) q^{94} +(-6.47051 + 3.22193i) q^{95} +(-0.765850 - 1.80939i) q^{96} +(0.949924 + 15.4014i) q^{97} +(-6.51616 + 15.3950i) q^{98} +(-20.9767 - 7.39190i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1056 q - 33 q^{2} - 31 q^{3} + 29 q^{4} - 22 q^{5} - 44 q^{6} - 57 q^{7} - 22 q^{8} + 2 q^{9} - 30 q^{10} + 17 q^{11} + 67 q^{12} - 34 q^{13} - 68 q^{14} - 32 q^{15} + 21 q^{16} - 27 q^{17} + 22 q^{18}+ \cdots - 229 q^{99}+O(q^{100}) $ 1056 * q - 33 * q^2 - 31 * q^3 + 29 * q^4 - 22 * q^5 - 44 * q^6 - 57 * q^7 - 22 * q^8 + 2 * q^9 - 30 * q^10 + 17 * q^11 + 67 * q^12 - 34 * q^13 - 68 * q^14 - 32 * q^15 + 21 * q^16 - 27 * q^17 + 22 * q^18 - 34 * q^19 - 51 * q^20 - 108 * q^21 - 22 * q^22 - 32 * q^23 + 87 * q^24 - 112 * q^25 - 64 * q^26 - 82 * q^27 - 75 * q^28 - 19 * q^29 - 22 * q^30 + 52 * q^32 - 43 * q^33 - 48 * q^34 - 113 * q^35 + 22 * q^36 - 10 * q^37 - 57 * q^38 + 41 * q^39 - 225 * q^40 - 288 * q^41 - 173 * q^42 + 68 * q^43 - 34 * q^44 - 42 * q^45 + 17 * q^46 - 34 * q^47 + 68 * q^48 + 369 * q^49 - 40 * q^50 + 56 * q^51 + 8 * q^52 + 104 * q^53 + 128 * q^54 + 102 * q^55 - 138 * q^56 - 55 * q^57 - 34 * q^58 - 34 * q^59 - 254 * q^60 - 68 * q^61 + 25 * q^62 - 34 * q^63 + 98 * q^64 - 34 * q^65 - 40 * q^67 - 116 * q^68 - 38 * q^69 - 17 * q^70 + 21 * q^71 - 26 * q^72 - 31 * q^73 + 203 * q^74 + 23 * q^75 - 101 * q^76 + 19 * q^77 - 102 * q^78 - 34 * q^79 + 443 * q^80 - 265 * q^81 - 50 * q^82 + 26 * q^83 - 459 * q^84 + 84 * q^85 + 136 * q^86 - 188 * q^87 + 170 * q^88 - 80 * q^89 + 613 * q^90 - 152 * q^91 + 18 * q^92 + 56 * q^93 - 34 * q^94 - 34 * q^95 + 13 * q^96 - 31 * q^97 - 293 * q^98 - 229 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{41}{102}\right)$

Coefficient data

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

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

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

$2$	−1.36768	+	0.169355i	−0.967094	+	0.119752i	−0.590861	−	0.806773i	$-0.701212\pi$
$2$	−1.36768	+	0.169355i	−0.967094	+	0.119752i	−0.376232	+	0.926525i	$0.622781\pi$
$3$	−0.738030	+	3.36995i	−0.426102	+	1.94564i	−0.124432	+	0.992228i	$0.539711\pi$
$3$	−0.738030	+	3.36995i	−0.426102	+	1.94564i	−0.301670	+	0.953413i	$0.597544\pi$
$4$	−0.0977346	+	0.0245812i	−0.0488673	+	0.0122906i
$5$	−0.477318	+	0.958584i	−0.213463	+	0.428692i	−0.975854	−	0.218426i	$-0.929908\pi$
$5$	−0.477318	+	0.958584i	−0.213463	+	0.428692i	0.762391	+	0.647117i	$0.224026\pi$
$6$	0.438669	−	4.73399i	0.179086	−	1.93264i
$7$	−3.78786	+	2.18692i	−1.43168	+	0.826578i	−0.997249	−	0.0741292i	$-0.976382\pi$
$7$	−3.78786	+	2.18692i	−1.43168	+	0.826578i	−0.434427	+	0.900707i	$0.643049\pi$
$8$	2.69963	−	1.04584i	0.954463	−	0.369761i
$9$	−8.08647	−	3.72037i	−2.69549	−	1.24012i
$10$	0.490476	−	1.39187i	0.155102	−	0.440148i
$11$	2.48798	−	0.230545i	0.750155	−	0.0695121i	0.289605	−	0.957146i	$-0.406476\pi$
$11$	2.48798	−	0.230545i	0.750155	−	0.0695121i	0.460549	+	0.887634i	$0.347652\pi$
$12$	−0.0107064	−	0.347502i	−0.00309068	−	0.100315i
$13$	−2.59897	−	0.240830i	−0.720824	−	0.0667942i	−0.274400	−	0.961616i	$-0.588479\pi$
$13$	−2.59897	−	0.240830i	−0.720824	−	0.0667942i	−0.446424	+	0.894821i	$0.647303\pi$
$14$	4.81020	−	3.63249i	1.28558	−	0.970825i
$15$	−2.87810	−	2.31600i	−0.743123	−	0.597989i
$16$	−3.33753	+	1.79221i	−0.834382	+	0.448054i
$17$	−0.129164	+	0.832090i	−0.0313270	+	0.201812i	−0.998663	−	0.0516840i	$-0.983541\pi$
$17$	−0.129164	+	0.832090i	−0.0313270	+	0.201812i	0.967337	+	0.253496i	$0.0815803\pi$
$18$	11.6897	+	3.71877i	2.75530	+	0.876523i
$19$	5.38667	+	4.06783i	1.23579	+	0.933224i	0.999262	−	0.0384016i	$-0.0122266\pi$
$19$	5.38667	+	4.06783i	1.23579	+	0.933224i	0.236526	+	0.971625i	$0.423991\pi$
$20$	0.0230873	−	0.105420i	0.00516248	−	0.0235726i
$21$	−4.57426	−	14.3789i	−0.998184	−	3.13773i
$22$	−3.36371	+	0.736664i	−0.717145	+	0.157057i
$23$	−0.981818	+	6.32498i	−0.204723	+	1.31885i	0.633594	+	0.773666i	$0.281579\pi$
$23$	−0.981818	+	6.32498i	−0.204723	+	1.31885i	−0.838317	+	0.545183i	$0.816460\pi$
$24$	1.53203	+	9.86947i	0.312723	+	2.01460i
$25$	2.32212	+	3.07499i	0.464425	+	0.614998i
$26$	3.59534	−	0.110771i	0.705103	−	0.0217240i
$27$	12.2686	−	16.2462i	2.36109	−	3.12658i
$28$	0.316448	−	0.306848i	0.0598030	−	0.0579888i
$29$	−3.43180	+	2.94018i	−0.637269	+	0.545979i	−0.909211	−	0.416335i	$-0.863314\pi$
$29$	−3.43180	+	2.94018i	−0.637269	+	0.545979i	0.271942	+	0.962314i	$0.412334\pi$
$30$	4.32854	+	2.68012i	0.790280	+	0.489321i
$31$		−	5.96798i		−	1.07188i	−0.844256	−	0.535940i	$-0.819957\pi$
$31$		−	5.96798i		−	1.07188i	0.844256	−	0.535940i	$-0.180043\pi$
$32$	−0.464854	+	0.329063i	−0.0821754	+	0.0581707i
$33$	−1.05928	+	8.55452i	−0.184397	+	1.48915i
$34$	0.0357363	−	1.15991i	0.00612873	−	0.198922i
$35$	−0.288334	−	4.67483i	−0.0487373	−	0.790191i
$36$	0.881779	+	0.164833i	0.146963	+	0.0274722i
$37$	0.327502	−	0.0100902i	0.0538409	−	0.00165882i	−0.00386342	−	0.999993i	$-0.501230\pi$
$37$	0.327502	−	0.0100902i	0.0538409	−	0.00165882i	0.0577044	+	0.998334i	$0.481622\pi$
$38$	−8.05614	−	4.65121i	−1.30688	−	0.754526i
$39$	2.72970	−	8.58065i	0.437102	−	1.37400i
$40$	−0.286054	+	3.08702i	−0.0452292	+	0.488100i
$41$	−1.02387	−	2.90553i	−0.159901	−	0.453767i	0.835508	−	0.549479i	$-0.185174\pi$
$41$	−1.02387	−	2.90553i	−0.159901	−	0.453767i	−0.995409	+	0.0957116i	$0.969487\pi$
$42$	8.69124	+	18.8910i	1.34109	+	2.91495i
$43$	7.06625	−	5.33619i	1.07759	−	0.813761i	0.0942557	−	0.995548i	$-0.469953\pi$
$43$	7.06625	−	5.33619i	1.07759	−	0.813761i	0.983338	+	0.181787i	$0.0581882\pi$
$44$	−0.237495	+	0.0836899i	−0.0358037	+	0.0126167i
$45$	7.42610	−	5.97576i	1.10702	−	0.890813i
$46$	0.271643	−	8.81680i	0.0400515	−	1.29997i
$47$	−1.86821	+	3.47905i	−0.272507	+	0.507472i	−0.979936	−	0.199312i	$-0.936129\pi$
$47$	−1.86821	+	3.47905i	−0.272507	+	0.507472i	0.707429	+	0.706784i	$0.249855\pi$
$48$	−3.57647	−	12.5700i	−0.516220	−	1.81432i
$49$	6.06524	−	10.5053i	0.866463	−	1.50076i
$50$	−3.69668	−	3.81233i	−0.522789	−	0.539144i
$51$	−2.70877	−	1.04938i	−0.379304	−	0.146943i
$52$	0.259929	−	0.0403485i	0.0360457	−	0.00559533i
$53$	0.459043	+	0.795086i	0.0630545	+	0.109214i	0.895829	−	0.444398i	$-0.146582\pi$
$53$	0.459043	+	0.795086i	0.0630545	+	0.109214i	−0.832775	+	0.553612i	$0.813249\pi$
$54$	−14.0280	+	24.2973i	−1.90898	+	3.30644i
$55$	−0.966561	+	2.49498i	−0.130331	+	0.336423i
$56$	−7.93863	+	9.86537i	−1.06084	+	1.31832i
$57$	−17.6839	+	15.1506i	−2.34229	+	2.00675i
$58$	4.19566	−	4.60242i	0.550917	−	0.604327i
$59$	−11.5096	−	3.27476i	−1.49842	−	0.426337i	−0.577597	−	0.816322i	$-0.696010\pi$
$59$	−11.5096	−	3.27476i	−1.49842	−	0.426337i	−0.920821	+	0.389985i	$0.872480\pi$
$60$	0.338220	+	0.155606i	0.0436641	+	0.0200887i
$61$	−7.36327	−	8.07712i	−0.942770	−	1.03417i	−0.999360	−	0.0357717i	$-0.988611\pi$
$61$	−7.36327	−	8.07712i	−0.942770	−	1.03417i	0.0565902	−	0.998397i	$-0.481977\pi$
$62$	1.01071	+	8.16226i	0.128360	+	1.03661i
$63$	38.7665	−	3.59225i	4.88412	−	0.452581i
$64$	6.17920	−	5.63308i	0.772400	−	0.704135i
$65$	1.47139	−	2.37638i	0.182503	−	0.294753i
$66$		−	11.8792i		−	1.46223i
$67$	2.92059	+	4.12579i	0.356806	+	0.504045i	0.954716	−	0.297518i	$-0.0961588\pi$
$67$	2.92059	+	4.12579i	0.356806	+	0.504045i	−0.597910	+	0.801563i	$0.704002\pi$
$68$	−0.00782999	−	0.0844991i	−0.000949526	−	0.0102470i
$69$	−20.5902	−	7.97670i	−2.47877	−	0.960282i
$70$	1.18605	+	6.34483i	0.141761	+	0.758352i
$71$	1.03220	+	0.0636638i	0.122499	+	0.00755550i	0.122695	−	0.992444i	$-0.460846\pi$
$71$	1.03220	+	0.0636638i	0.122499	+	0.00755550i	−0.000195187		1.00000i	$0.500062\pi$
$72$	−25.7214	−	1.58644i	−3.03129	−	0.186964i
$73$	0.0581817	+	0.0564168i	0.00680966	+	0.00660309i	0.699531	−	0.714602i	$-0.253392\pi$
$73$	0.0581817	+	0.0564168i	0.00680966	+	0.00660309i	−0.692721	+	0.721205i	$0.743588\pi$
$74$	−0.446208	+	0.0692642i	−0.0518706	+	0.00805180i
$75$	−12.0763	+	5.55600i	−1.39446	+	0.641552i
$76$	−0.626457	−	0.265156i	−0.0718595	−	0.0304155i
$77$	−8.91993	+	6.31429i	−1.01652	+	0.719580i
$78$	−2.28017	+	12.1979i	−0.258179	+	1.38113i
$79$	−9.99491	−	4.97687i	−1.12452	−	0.559942i	−0.215416	−	0.976522i	$-0.569111\pi$
$79$	−9.99491	−	4.97687i	−1.12452	−	0.559942i	−0.909099	+	0.416580i	$0.863229\pi$
$80$	−0.124926	−	4.05475i	−0.0139671	−	0.453335i
$81$	28.3203	+	33.0557i	3.14671	+	3.67285i
$82$	1.89239	+	3.80042i	0.208979	+	0.419687i
$83$	−2.05234	+	0.795081i	−0.225274	+	0.0872714i	−0.471233	−	0.882009i	$-0.656191\pi$
$83$	−2.05234	+	0.795081i	−0.225274	+	0.0872714i	0.245960	+	0.969280i	$0.420897\pi$
$84$	0.800514	+	1.29287i	0.0873433	+	0.141064i
$85$	−0.735976	−	0.520986i	−0.0798278	−	0.0565089i
$86$	−8.76064	+	8.49489i	−0.944684	+	0.916027i
$87$	−7.37550	−	13.7349i	−0.790737	−	1.47254i
$88$	6.47551	−	3.22442i	0.690292	−	0.343724i
$89$	1.37164	+	4.82082i	0.145394	+	0.511006i	0.999965	−	0.00832773i	$-0.00265083\pi$
$89$	1.37164	+	4.82082i	0.145394	+	0.511006i	−0.854572	+	0.519334i	$0.826180\pi$
$90$	−9.14448	+	9.43055i	−0.963913	+	0.994068i
$91$	10.3712	−	4.77151i	1.08720	−	0.500190i
$92$	−0.0595182	−	0.642304i	−0.00620520	−	0.0669648i
$93$	20.1118	+	4.40455i	2.08549	+	0.456730i
$94$	1.96592	−	5.07461i	0.202769	−	0.523406i
$95$	−6.47051	+	3.22193i	−0.663860	+	0.330563i
$96$	−0.765850	−	1.80939i	−0.0781643	−	0.184670i
$97$	0.949924	+	15.4014i	0.0964502	+	1.56377i	0.668599	+	0.743623i	$0.266894\pi$
$97$	0.949924	+	15.4014i	0.0964502	+	1.56377i	−0.572149	+	0.820150i	$0.693890\pi$
$98$	−6.51616	+	15.3950i	−0.658232	+	1.55513i
$99$	−20.9767	−	7.39190i	−2.10824	−	0.742914i
$100$	−0.302539	−	0.243452i	−0.0302539	−	0.0243452i
$101$	4.74552	−	5.53899i	0.472197	−	0.551150i	−0.471541	−	0.881844i	$-0.656302\pi$
$101$	4.74552	−	5.53899i	0.472197	−	0.551150i	0.943738	+	0.330694i	$0.107283\pi$
$102$	3.88245	+	0.976475i	0.384420	+	0.0966854i
$103$	1.39001	−	2.79153i	0.136962	−	0.275057i	−0.816054	−	0.577975i	$-0.803843\pi$
$103$	1.39001	−	2.79153i	0.136962	−	0.275057i	0.953017	+	0.302918i	$0.0979608\pi$
$104$	−7.26812	+	2.06796i	−0.712698	+	0.202780i
$105$	15.9667	+	2.47850i	1.55819	+	0.241877i
$106$	−0.762475	−	1.00968i	−0.0740581	−	0.0980688i
$107$	0.198714	+	0.246943i	0.0192104	+	0.0238729i	0.788594	−	0.614914i	$-0.210809\pi$
$107$	0.198714	+	0.246943i	0.0192104	+	0.0238729i	−0.769384	+	0.638787i	$0.779437\pi$
$108$	−0.799711	+	1.88939i	−0.0769522	+	0.181807i
$109$	6.55450	−	5.27438i	0.627807	−	0.505194i	−0.259881	−	0.965641i	$-0.583683\pi$
$109$	6.55450	−	5.27438i	0.627807	−	0.505194i	0.887688	+	0.460446i	$0.152311\pi$
$110$	0.899405	−	3.57602i	0.0857549	−	0.340960i
$111$	−0.207703	+	1.11111i	−0.0197143	+	0.105462i
$112$	8.72264	−	14.0876i	0.824212	−	1.33115i
$113$	−2.36006	+	0.998930i	−0.222016	+	0.0939714i	−0.497952	−	0.867205i	$-0.665914\pi$
$113$	−2.36006	+	0.998930i	−0.222016	+	0.0939714i	0.275936	+	0.961176i	$0.411012\pi$
$114$	21.6200	−	23.7160i	2.02490	−	2.22121i
$115$	−5.59438	−	3.96018i	−0.521679	−	0.369289i
$116$	0.263132	−	0.371716i	0.0244312	−	0.0345129i
$117$	20.1205	+	11.6166i	1.86014	+	1.07395i
$118$	16.2960	+	2.52960i	1.50017	+	0.232869i
$119$	−1.33046	−	3.43431i	−0.121963	−	0.314823i
$120$	−10.1920	−	3.24230i	−0.930396	−	0.295980i
$121$	−4.67581	+	0.874060i	−0.425073	+	0.0794600i
$122$	11.4385	+	9.79988i	1.03559	+	0.887240i
$123$	10.5471	−	1.30602i	0.951002	−	0.117760i
$124$	0.146700	+	0.583278i	0.0131741	+	0.0523799i
$125$	−9.31910	+	1.74204i	−0.833525	+	0.155813i
$126$	−52.4117	+	11.4783i	−4.66921	+	1.02257i
$127$	1.43383	+	0.950088i	0.127232	+	0.0843067i	0.614370	−	0.789018i	$-0.289410\pi$
$127$	1.43383	+	0.950088i	0.127232	+	0.0843067i	−0.487138	+	0.873325i	$0.661959\pi$
$128$	−6.75605	+	7.88570i	−0.597156	+	0.697004i
$129$	12.7676	+	27.7512i	1.12412	+	2.44335i
$130$	−1.60994	+	3.49930i	−0.141201	+	0.306909i
$131$	7.08091	+	8.26487i	0.618662	+	0.722105i	0.977415	−	0.211327i	$-0.0677785\pi$
$131$	7.08091	+	8.26487i	0.618662	+	0.722105i	−0.358754	+	0.933432i	$0.616798\pi$
$132$	−0.106752	−	0.862111i	−0.00929161	−	0.0750371i
$133$	−29.3000	−	3.62812i	−2.54063	−	0.314598i
$134$	−4.69314	−	5.14813i	−0.405426	−	0.444731i
$135$	9.71733	+	19.5150i	0.836335	+	1.67959i
$136$	0.521539	+	2.38142i	0.0447216	+	0.204205i
$137$	−4.74531	−	13.4662i	−0.405419	−	1.15050i	−0.950125	−	0.311869i	$-0.899045\pi$
$137$	−4.74531	−	13.4662i	−0.405419	−	1.15050i	0.544706	−	0.838627i	$-0.316641\pi$
$138$	29.5117	+	7.42249i	2.51220	+	0.631844i
$139$	−7.63966	−	11.5294i	−0.647988	−	0.977912i	−0.999135	−	0.0415914i	$-0.986757\pi$
$139$	−7.63966	−	11.5294i	−0.647988	−	0.977912i	0.351147	−	0.936320i	$-0.385792\pi$
$140$	0.143093	+	0.449805i	0.0120936	+	0.0380155i
$141$	−10.3454	−	8.86343i	−0.871243	−	0.746435i
$142$	−1.42250	+	0.0877365i	−0.119373	+	0.00736269i
$143$	−6.52171			−0.545373
$144$	33.6565	−	2.07586i	2.80471	−	0.172988i
$145$	−1.18035	−	4.69307i	−0.0980231	−	0.389738i
$146$	−0.0891283	−	0.0673066i	−0.00737631	−	0.00557033i
$147$	30.9260	+	28.1928i	2.55073	+	2.32530i
$148$	−0.0317602	+	0.00903656i	−0.00261067	+	0.000742801i
$149$	−3.38353	+	10.6359i	−0.277189	+	0.871328i	0.708928	+	0.705280i	$0.249179\pi$
$149$	−3.38353	+	10.6359i	−0.277189	+	0.871328i	−0.986118	+	0.166047i	$0.946900\pi$
$150$	15.5756	−	9.64401i	1.27174	−	0.787430i
$151$	3.65571	+	5.90417i	0.297497	+	0.480475i	0.964319	−	0.264743i	$-0.0852870\pi$
$151$	3.65571	+	5.90417i	0.297497	+	0.480475i	−0.666822	+	0.745217i	$0.732346\pi$
$152$	18.7963	+	5.34801i	1.52458	+	0.433781i
$153$	4.14016	−	6.24813i	0.334712	−	0.505132i
$154$	11.1302	−	10.1465i	0.896899	−	0.817632i
$155$	5.72080	+	2.84862i	0.459506	+	0.228807i
$156$	−0.0558633	+	0.905726i	−0.00447264	+	0.0725161i
$157$	−14.3066	+	5.04146i	−1.14179	+	0.402352i	−0.835449	−	0.549568i	$-0.814792\pi$
$157$	−14.3066	+	5.04146i	−1.14179	+	0.402352i	−0.306344	+	0.951921i	$0.599106\pi$
$158$	14.5127	+	5.11407i	1.15457	+	0.406853i
$159$	−3.01819	+	0.960155i	−0.239358	+	0.0761452i
$160$	−0.0935516	−	0.602669i	−0.00739590	−	0.0476452i
$161$	−10.1132	−	26.1053i	−0.797035	−	2.05738i
$162$	−44.3312	−	40.4133i	−3.48299	−	3.17517i
$163$	4.91285	−	1.23563i	0.384804	−	0.0967821i	−0.0466632	−	0.998911i	$-0.514859\pi$
$163$	4.91285	−	1.23563i	0.384804	−	0.0967821i	0.431467	+	0.902129i	$0.357996\pi$
$164$	0.171489	+	0.258803i	0.0133910	+	0.0202091i
$165$	−7.69461	−	5.09863i	−0.599024	−	0.396928i
$166$	2.67229	−	1.43499i	0.207410	−	0.111377i
$167$	−2.73068	+	0.868693i	−0.211307	+	0.0672215i	−0.406937	−	0.913456i	$-0.633403\pi$
$167$	−2.73068	+	0.868693i	−0.211307	+	0.0672215i	0.195630	+	0.980678i	$0.437325\pi$
$168$	−27.3868	−	34.0337i	−2.11294	−	2.62576i
$169$	−6.08201	−	1.13692i	−0.467847	−	0.0874557i
$170$	1.09481	+	0.587900i	0.0839680	+	0.0450899i
$171$	−28.4254	−	52.9348i	−2.17374	−	4.04802i
$172$	−0.559448	+	0.695228i	−0.0426575	+	0.0530106i
$173$	−6.73581	−	0.207528i	−0.512114	−	0.0157781i	−0.226289	−	0.974060i	$-0.572660\pi$
$173$	−6.73581	−	0.207528i	−0.512114	−	0.0157781i	−0.285824	+	0.958282i	$0.592267\pi$
$174$	12.4134	+	17.5359i	0.941056	+	1.32939i
$175$	−15.5206	−	6.56932i	−1.17325	−	0.496594i
$176$	−7.89052	+	5.22845i	−0.594770	+	0.394109i
$177$	19.5302	−	36.3698i	1.46798	−	2.73372i
$178$	−2.69239	−	6.36103i	−0.201803	−	0.476779i
$179$	−15.5483	−	8.34924i	−1.16213	−	0.624051i	−0.225457	−	0.974253i	$-0.572388\pi$
$179$	−15.5483	−	8.34924i	−1.16213	−	0.624051i	−0.936674	+	0.350202i	$0.886113\pi$
$180$	−0.578895	+	0.766581i	−0.0431483	+	0.0571376i
$181$	−3.09752	+	4.37574i	−0.230237	+	0.325246i	−0.914950	−	0.403566i	$-0.867770\pi$
$181$	−3.09752	+	4.37574i	−0.230237	+	0.325246i	0.684713	+	0.728812i	$0.259927\pi$
$182$	−13.3764	+	8.28230i	−0.991523	+	0.613925i
$183$	32.6538	−	18.8527i	2.41384	−	1.39363i
$184$	3.96438	+	18.1019i	0.292258	+	1.33449i
$185$	−0.146650	+	0.318754i	−0.0107819	+	0.0234353i
$186$	−28.2523	−	2.61796i	−2.07156	−	0.191958i
$187$	−0.129524	+	2.10000i	−0.00947172	+	0.153567i
$188$	0.0970696	−	0.385947i	0.00707953	−	0.0281481i
$189$	−10.9424	+	88.3686i	−0.795943	+	6.42787i
$190$	8.30392	−	5.50237i	0.602429	−	0.399184i
$191$	4.84811	−	4.99978i	0.350797	−	0.361772i	−0.519352	−	0.854561i	$-0.673827\pi$
$191$	4.84811	−	4.99978i	0.350797	−	0.361772i	0.870149	+	0.492789i	$0.164023\pi$
$192$	14.4228	+	24.9810i	1.04087	+	1.80285i
$193$	2.78719	−	9.79595i	0.200626	−	0.705128i	−0.794565	−	0.607179i	$-0.792301\pi$
$193$	2.78719	−	9.79595i	0.200626	−	0.705128i	0.995191	−	0.0979492i	$-0.0312283\pi$
$194$	−3.90749	−	20.9032i	−0.280542	−	1.50076i
$195$	6.92234	+	6.71235i	0.495719	+	0.480681i
$196$	−0.334550	+	1.17582i	−0.0238965	+	0.0839873i
$197$	−1.58321	−	1.63274i	−0.112799	−	0.116328i	0.659152	−	0.752010i	$-0.270915\pi$
$197$	−1.58321	−	1.63274i	−0.112799	−	0.116328i	−0.771952	+	0.635681i	$0.780719\pi$
$198$	29.9412	+	6.55722i	2.12783	+	0.466002i
$199$	6.56502	+	0.202266i	0.465382	+	0.0143383i	0.262640	−	0.964894i	$-0.415407\pi$
$199$	6.56502	+	0.202266i	0.465382	+	0.0143383i	0.202742	+	0.979232i	$0.435015\pi$
$200$	9.48482	+	5.87275i	0.670678	+	0.415266i
$201$	−16.0592	+	6.79727i	−1.13273	+	0.479442i
$202$	−5.55228	+	8.37923i	−0.390657	+	0.589561i
$203$	6.56921	−	18.6421i	0.461068	−	1.30842i
$204$	0.290536	+	0.0359762i	0.0203416	+	0.00251884i
$205$	3.27390	+	0.405397i	0.228659	+	0.0283141i
$206$	−1.42833	+	4.05331i	−0.0995166	+	0.282408i
$207$	31.4707	−	47.4940i	2.18736	−	3.30106i
$208$	9.10575	−	3.85413i	0.631370	−	0.267236i
$209$	14.3398	+	8.87881i	0.991902	+	0.614160i
$210$	−22.2571	−	0.685734i	−1.53589	−	0.0473201i
$211$	10.7306	+	2.35004i	0.738725	+	0.161783i	0.567413	−	0.823433i	$-0.307944\pi$
$211$	10.7306	+	2.35004i	0.738725	+	0.161783i	0.171313	+	0.985217i	$0.445199\pi$
$212$	−0.0644086	−	0.0664236i	−0.00442360	−	0.00456199i
$213$	−0.976337	+	3.43147i	−0.0668975	+	0.235120i
$214$	−0.313598	−	0.304085i	−0.0214371	−	0.0207868i
$215$	1.74233	+	9.32065i	0.118826	+	0.635663i
$216$	16.1296	−	56.6897i	1.09748	−	3.85724i
$217$	13.0515	+	22.6058i	0.885993	+	1.53458i
$218$	−8.07119	+	8.32369i	−0.546650	+	0.563752i
$219$	−0.233062	+	0.154432i	−0.0157488	+	0.0104356i
$220$	0.0331367	−	0.267605i	0.00223408	−	0.0180419i
$221$	0.536086	−	2.13147i	0.0360611	−	0.143378i
$222$	0.0958977	−	1.55482i	0.00643624	−	0.104352i
$223$	6.18196	+	0.572843i	0.413974	+	0.0383604i	0.297240	−	0.954803i	$-0.403934\pi$
$223$	6.18196	+	0.572843i	0.413974	+	0.0383604i	0.116734	+	0.993163i	$0.462757\pi$
$224$	1.04117	−	2.26304i	0.0695658	−	0.151206i
$225$	−7.33769	−	33.5049i	−0.489180	−	2.23366i
$226$	3.05863	−	1.76590i	0.203457	−	0.117466i
$227$	−22.2222	+	13.7594i	−1.47494	+	0.913245i	−0.475504	+	0.879714i	$0.657734\pi$
$227$	−22.2222	+	13.7594i	−1.47494	+	0.913245i	−0.999438	+	0.0335315i	$0.989325\pi$
$228$	1.35591	−	1.91543i	0.0897972	−	0.126853i
$229$	−7.21868	+	9.55908i	−0.477024	+	0.631682i	−0.971367	−	0.237585i	$-0.923644\pi$
$229$	−7.21868	+	9.55908i	−0.477024	+	0.631682i	0.494343	+	0.869267i	$0.335409\pi$
$230$	8.32198	+	4.46881i	0.548735	+	0.294665i
$231$	−14.6956	−	34.7198i	−0.966903	−	2.28440i
$232$	−6.18961	+	11.5265i	−0.406368	+	0.756753i
$233$	−8.43565	+	5.58966i	−0.552638	+	0.366191i	−0.797455	−	0.603378i	$-0.793821\pi$
$233$	−8.43565	+	5.58966i	−0.552638	+	0.366191i	0.244818	+	0.969569i	$0.421272\pi$
$234$	−29.4857	−	12.4802i	−1.92754	−	0.815857i
$235$	−2.44323	−	3.45145i	−0.159379	−	0.225148i
$236$	1.20538	+	0.0371374i	0.0784636	+	0.00241744i
$237$	24.1484	−	30.0093i	1.56860	−	1.94931i
$238$	2.40126	+	4.47171i	0.155650	+	0.289858i
$239$	6.25075	+	3.35658i	0.404327	+	0.217119i	0.662633	−	0.748944i	$-0.269439\pi$
$239$	6.25075	+	3.35658i	0.404327	+	0.217119i	−0.258306	+	0.966063i	$0.583164\pi$
$240$	13.7565	+	2.57154i	0.887979	+	0.165992i
$241$	−0.449040	−	0.558024i	−0.0289252	−	0.0359455i	0.764411	−	0.644730i	$-0.223030\pi$
$241$	−0.449040	−	0.558024i	−0.0289252	−	0.0359455i	−0.793336	+	0.608784i	$0.791658\pi$
$242$	6.24697	−	1.98730i	0.401570	−	0.127749i
$243$	−78.4896	+	42.1480i	−5.03511	+	2.70380i
$244$	0.918192	+	0.608416i	0.0587812	+	0.0389498i
$245$	7.17516	+	10.8284i	0.458404	+	0.691801i
$246$	−14.2039	+	3.57242i	−0.905606	+	0.227769i
$247$	−13.0201	−	11.8694i	−0.828452	−	0.755234i
$248$	−6.24156	−	16.1113i	−0.396339	−	1.02307i
$249$	−1.16469	−	7.50307i	−0.0738094	−	0.475488i
$250$	12.4505	−	3.96079i	0.787438	−	0.250502i
$251$	26.5711	+	9.36328i	1.67715	+	0.591005i	0.990687	−	0.136159i	$-0.0434757\pi$
$251$	26.5711	+	9.36328i	1.67715	+	0.591005i	0.686464	+	0.727164i	$0.259162\pi$
$252$	−3.70053	+	1.30402i	−0.233111	+	0.0821453i
$253$	−0.984551	+	15.9628i	−0.0618982	+	1.00357i
$254$	−2.12192	−	1.05659i	−0.133141	−	0.0662962i
$255$	2.29887	−	2.09570i	0.143961	−	0.131238i
$256$	−1.33255	+	2.01101i	−0.0832842	+	0.125688i
$257$	−15.2818	−	4.34804i	−0.953251	−	0.271223i	−0.238926	−	0.971038i	$-0.576795\pi$
$257$	−15.2818	−	4.34804i	−0.953251	−	0.271223i	−0.714325	+	0.699815i	$0.753266\pi$
$258$	−22.1617	−	35.7924i	−1.37973	−	2.22834i
$259$	−1.21846	+	0.754440i	−0.0757116	+	0.0468786i
$260$	−0.0853915	+	0.268423i	−0.00529575	+	0.0166469i
$261$	38.6897	−	11.0082i	2.39483	−	0.681388i
$262$	−11.0841	−	10.1045i	−0.684778	−	0.624257i
$263$	4.53404	+	3.42394i	0.279581	+	0.211129i	0.733107	−	0.680113i	$-0.238069\pi$
$263$	4.53404	+	3.42394i	0.279581	+	0.211129i	−0.453526	+	0.891243i	$0.649834\pi$
$264$	6.08701	+	24.2019i	0.374630	+	1.48952i
$265$	−0.981266	+	0.0605224i	−0.0602787	+	0.00371786i
$266$	40.6873			2.49470
$267$	−17.2582	+	1.06445i	−1.05619	+	0.0651433i
$268$	−0.386859	−	0.331441i	−0.0236312	−	0.0202460i
$269$	6.27062	+	19.7113i	0.382326	+	1.20182i	0.930762	+	0.365627i	$0.119145\pi$
$269$	6.27062	+	19.7113i	0.382326	+	1.20182i	−0.548435	+	0.836193i	$0.684776\pi$
$270$	−16.5951	−	25.0446i	−1.00995	−	1.52417i
$271$	12.9703	+	3.26216i	0.787889	+	0.198162i	0.616828	−	0.787098i	$-0.288418\pi$
$271$	12.9703	+	3.26216i	0.787889	+	0.198162i	0.171062	+	0.985260i	$0.445280\pi$
$272$	−1.06019	−	3.00861i	−0.0642838	−	0.182424i
$273$	8.42548	+	38.4719i	0.509933	+	2.32843i
$274$	8.77063	+	17.6138i	0.529853	+	1.06409i
$275$	6.48632	+	7.11516i	0.391140	+	0.429060i
$276$	2.20846	+	0.273466i	0.132933	+	0.0164607i
$277$	−2.06448	−	16.6723i	−0.124043	−	1.00174i	−0.918774	−	0.394783i	$-0.870820\pi$
$277$	−2.06448	−	16.6723i	−0.124043	−	1.00174i	0.794732	−	0.606961i	$-0.207612\pi$
$278$	12.4012	+	14.4747i	0.743772	+	0.868134i
$279$	−22.2030	+	48.2598i	−1.32926	+	2.88924i
$280$	−5.66753	−	12.3188i	−0.338700	−	0.736187i
$281$	3.88975	−	4.54013i	0.232043	−	0.270842i	−0.631211	−	0.775611i	$-0.717442\pi$
$281$	3.88975	−	4.54013i	0.232043	−	0.270842i	0.863254	+	0.504769i	$0.168422\pi$
$282$	15.6503	+	10.3703i	0.931961	+	0.617540i
$283$	25.1138	−	5.50001i	1.49286	−	0.326942i	0.608429	−	0.793608i	$-0.291800\pi$
$283$	25.1138	−	5.50001i	1.49286	−	0.326942i	0.884433	+	0.466666i	$0.154545\pi$
$284$	−0.102446	+	0.0191506i	−0.00607908	+	0.00113638i
$285$	−6.08231	−	24.1832i	−0.360285	−	1.43249i
$286$	8.91959	−	1.10448i	0.527426	−	0.0653096i
$287$	10.2324	+	8.76660i	0.604001	+	0.517476i
$288$	4.98326	−	0.931534i	0.293642	−	0.0548911i
$289$	15.5243	+	4.93864i	0.913195	+	0.290508i
$290$	2.40914	+	6.21870i	0.141469	+	0.365175i
$291$	−52.6029	−	8.16548i	−3.08364	−	0.478669i
$292$	−0.00707317	−	0.00408369i	−0.000413926	−	0.000238980i
$293$	−3.82801	+	5.40767i	−0.223635	+	0.315920i	−0.912583	−	0.408891i	$-0.865916\pi$
$293$	−3.82801	+	5.40767i	−0.223635	+	0.315920i	0.688949	+	0.724810i	$0.258073\pi$
$294$	−47.0714	−	33.3211i	−2.74526	−	1.94333i
$295$	8.63285	−	9.46979i	0.502624	−	0.551352i
$296$	0.873580	−	0.369755i	0.0507758	−	0.0214916i
$297$	26.7785	−	43.2487i	1.55384	−	2.50954i
$298$	2.82633	−	15.1195i	0.163725	−	0.875850i
$299$	4.07496	−	16.2020i	0.235661	−	0.936984i
$300$	1.04370	−	0.839865i	0.0602583	−	0.0484897i
$301$	−15.0961	+	35.6660i	−0.870127	+	2.05576i
$302$	−5.99973	−	7.45589i	−0.345246	−	0.429038i
$303$	15.1638	+	20.0801i	0.871137	+	1.15357i
$304$	−25.2686	−	3.92241i	−1.44925	−	0.224966i
$305$	11.2572	−	3.20295i	0.644586	−	0.183401i
$306$	−4.60425	+	9.24659i	−0.263208	+	0.528592i
$307$	12.3387	+	3.10331i	0.704208	+	0.177115i	0.579374	−	0.815062i	$-0.303297\pi$
$307$	12.3387	+	3.10331i	0.704208	+	0.177115i	0.124834	+	0.992178i	$0.460160\pi$
$308$	0.716573	−	0.836388i	0.0408305	−	0.0476576i
$309$	8.38143	+	6.74451i	0.476803	+	0.383682i
$310$	−8.30664	−	2.92715i	−0.471785	−	0.166251i
$311$	−11.1699	+	26.3900i	−0.633388	+	1.49644i	0.220182	+	0.975459i	$0.429335\pi$
$311$	−11.1699	+	26.3900i	−0.633388	+	1.49644i	−0.853570	+	0.520978i	$0.825567\pi$
$312$	−1.60482	−	26.0194i	−0.0908552	−	1.47306i
$313$	−0.352870	−	0.833688i	−0.0199454	−	0.0471228i	0.910631	−	0.413220i	$-0.135596\pi$
$313$	−0.352870	−	0.833688i	−0.0199454	−	0.0471228i	−0.930577	+	0.366097i	$0.880694\pi$
$314$	18.7130	−	9.31799i	1.05604	−	0.525845i
$315$	−15.0605	+	38.8756i	−0.848562	+	2.19039i
$316$	1.09919	+	0.240726i	0.0618341	+	0.0135419i
$317$	2.05692	+	22.1977i	0.115528	+	1.24675i	0.834225	+	0.551424i	$0.185915\pi$
$317$	2.05692	+	22.1977i	0.115528	+	1.24675i	−0.718697	+	0.695323i	$0.755261\pi$
$318$	3.96530	−	1.82433i	0.222363	−	0.102303i
$319$	−7.86040	+	8.10631i	−0.440098	+	0.453866i
$320$	2.45034	+	8.61205i	0.136978	+	0.481428i
$321$	−0.978843	+	0.487406i	−0.0546337	+	0.0272043i
$322$	18.2527	+	33.9908i	1.01718	+	1.89424i
$323$	−4.08057	+	3.95678i	−0.227049	+	0.220161i
$324$	−3.58043	−	2.53453i	−0.198913	−	0.140807i
$325$	−5.29458	−	8.55104i	−0.293690	−	0.474326i
$326$	−6.50993	+	2.52196i	−0.360552	+	0.139679i
$327$	12.9370	+	25.9810i	0.715417	+	1.43675i
$328$	−5.80278	−	6.77304i	−0.320405	−	0.373978i
$329$	−0.531892	−	17.2638i	−0.0293241	−	0.951784i
$330$	11.3872	+	5.67016i	0.626846	+	0.312132i
$331$	1.78831	−	9.56659i	0.0982941	−	0.525827i	−0.898013	−	0.439969i	$-0.854990\pi$
$331$	1.78831	−	9.56659i	0.0982941	−	0.525827i	0.996307	−	0.0858587i	$-0.0273634\pi$
$332$	0.181041	−	0.128156i	0.00993589	−	0.00703347i
$333$	−2.68587	−	1.13683i	−0.147185	−	0.0622980i
$334$	3.58758	−	1.65055i	0.196303	−	0.0903139i
$335$	−5.34896	+	0.830312i	−0.292245	+	0.0453648i
$336$	41.0368	+	39.7919i	2.23874	+	2.17083i
$337$	5.49284	+	0.338787i	0.299214	+	0.0184549i	0.210472	−	0.977600i	$-0.432500\pi$
$337$	5.49284	+	0.338787i	0.299214	+	0.0184549i	0.0887416	+	0.996055i	$0.471715\pi$
$338$	8.51077	+	0.524926i	0.462925	+	0.0285522i
$339$	−1.62454	−	8.69054i	−0.0882331	−	0.472005i
$340$	0.0847368	+	0.0328272i	0.00459550	+	0.00178031i
$341$	−1.37589	−	14.8482i	−0.0745086	−	0.804076i
$342$	47.8415	+	67.5837i	2.58697	+	3.65451i
$343$			22.4399i			1.21164i
$344$	13.4955	−	21.7959i	0.727626	−	1.17516i
$345$	17.4744	−	15.9300i	0.940791	−	0.857645i
$346$	9.24755	−	0.856912i	0.497151	−	0.0460679i
$347$	2.87815	+	23.2434i	0.154507	+	1.24777i	0.849048	+	0.528316i	$0.177176\pi$
$347$	2.87815	+	23.2434i	0.154507	+	1.24777i	−0.694541	+	0.719453i	$0.744392\pi$
$348$	1.05846	+	1.16108i	0.0567396	+	0.0622404i
$349$	−20.9551	−	9.64088i	−1.12170	−	0.516065i	−0.232050	−	0.972704i	$-0.574543\pi$
$349$	−20.9551	−	9.64088i	−1.12170	−	0.516065i	−0.889652	+	0.456639i	$0.849053\pi$
$350$	22.3397	+	6.35621i	1.19411	+	0.339753i
$351$	−35.7982	+	39.2687i	−1.91077	+	2.09601i
$352$	−1.08068	+	0.925874i	−0.0576007	+	0.0493492i
$353$	−5.06811	+	6.29816i	−0.269748	+	0.335217i	−0.895712	−	0.444635i	$-0.853333\pi$
$353$	−5.06811	+	6.29816i	−0.269748	+	0.335217i	0.625963	+	0.779852i	$0.284706\pi$
$354$	−20.5515	+	53.0497i	−1.09230	+	2.81956i
$355$	−0.553714	+	0.959060i	−0.0293881	+	0.0509016i
$356$	−0.252559	−	0.437444i	−0.0133856	−	0.0231845i
$357$	12.5554	−	1.94895i	0.664501	−	0.103150i
$358$	22.6790	+	8.78588i	1.19862	+	0.464348i
$359$	−1.00151	−	1.03284i	−0.0528577	−	0.0545113i	0.690966	−	0.722888i	$-0.257186\pi$
$359$	−1.00151	−	1.03284i	−0.0528577	−	0.0545113i	−0.743823	+	0.668376i	$0.766990\pi$
$360$	13.7980	−	23.8988i	0.727219	−	1.25958i
$361$	7.26944	+	25.5494i	0.382602	+	1.34471i
$362$	3.49536	−	6.50918i	0.183712	−	0.342115i
$363$	0.505350	−	16.4023i	0.0265240	−	0.860898i
$364$	−0.896336	+	0.721279i	−0.0469808	+	0.0378053i
$365$	−0.0818514	+	0.0288433i	−0.00428430	+	0.00150973i
$366$	−41.4670	+	31.3145i	−2.16752	+	1.63683i
$367$	−8.29195	−	18.0231i	−0.432836	−	0.940800i	−0.993614	−	0.112833i	$-0.964007\pi$
$367$	−8.29195	−	18.0231i	−0.432836	−	0.940800i	0.560777	−	0.827967i	$-0.310502\pi$
$368$	−8.05887	−	22.8694i	−0.420098	−	1.19215i
$369$	−2.53014	+	27.3046i	−0.131714	+	1.42142i
$370$	0.146587	−	0.460788i	0.00762071	−	0.0239552i
$371$	−3.47758	−	2.00778i	−0.180547	−	0.104239i
$372$	−2.07389	+	0.0638957i	−0.107526	+	0.00331284i
$373$	−5.90441	−	1.10372i	−0.305719	−	0.0571487i	0.0286549	−	0.999589i	$-0.490878\pi$
$373$	−5.90441	−	1.10372i	−0.305719	−	0.0571487i	−0.334373	+	0.942441i	$0.608525\pi$
$374$	−0.178500	−	2.89406i	−0.00923000	−	0.149648i
$375$	1.00719	−	32.6906i	0.0520108	−	1.68813i
$376$	−1.40494	+	11.3460i	−0.0724543	+	0.585126i
$377$	9.62722	−	6.81497i	0.495827	−	0.350989i
$378$		−	122.713i		−	6.31167i
$379$	−19.5492	−	12.1044i	−1.00417	−	0.621759i	−0.0772524	−	0.997012i	$-0.524615\pi$
$379$	−19.5492	−	12.1044i	−1.00417	−	0.621759i	−0.926923	+	0.375253i	$0.877556\pi$
$380$	0.553194	−	0.473947i	0.0283782	−	0.0243130i
$381$	−4.25996	+	4.13073i	−0.218244	+	0.211624i
$382$	−5.78391	+	7.65914i	−0.295931	+	0.391876i
$383$	−31.8124	+	0.980130i	−1.62554	+	0.0500823i	−0.830693	−	0.556730i	$-0.812056\pi$
$383$	−31.8124	+	0.980130i	−1.62554	+	0.0500823i	−0.794845	+	0.606813i	$0.792448\pi$
$384$	−21.5882	−	28.5874i	−1.10167	−	1.45885i
$385$	−1.79513	−	11.5644i	−0.0914883	−	0.589378i
$386$	−2.15298	+	13.8697i	−0.109584	+	0.705950i
$387$	−76.9936	+	16.8619i	−3.91380	+	0.857136i
$388$	−0.471425	−	1.48190i	−0.0239330	−	0.0752319i
$389$	−1.12498	+	5.13679i	−0.0570385	+	0.260446i	−0.996649	−	0.0818007i	$-0.973933\pi$
$389$	−1.12498	+	5.13679i	−0.0570385	+	0.260446i	0.939610	+	0.342247i	$0.111188\pi$
$390$	−10.6043	−	8.00799i	−0.536969	−	0.405500i
$391$	−5.13614	−	1.63392i	−0.259746	−	0.0826310i
$392$	5.38701	−	34.7037i	0.272085	−	1.75280i
$393$	−33.0781	+	17.7626i	−1.66857	+	0.896003i
$394$	2.44184	+	1.96494i	0.123018	+	0.0989923i
$395$	9.54150	−	7.20541i	0.480085	−	0.362543i
$396$	2.23185	+	0.206811i	0.112155	+	0.0103927i
$397$	0.353551	+	11.4753i	0.0177442	+	0.575930i	0.966018	+	0.258476i	$0.0832202\pi$
$397$	0.353551	+	11.4753i	0.0177442	+	0.575930i	−0.948274	+	0.317454i	$0.897172\pi$
$398$	−9.01309	+	0.835186i	−0.451785	+	0.0418641i
$399$	33.8508	−	96.0617i	1.69466	−	4.80910i
$400$	−13.2612	−	6.10111i	−0.663059	−	0.305056i
$401$	−13.1722	+	5.10294i	−0.657789	+	0.254829i	−0.666920	−	0.745130i	$-0.732388\pi$
$401$	−13.1722	+	5.10294i	−0.657789	+	0.254829i	0.00913101	+	0.999958i	$0.497093\pi$
$402$	20.8126	−	12.0162i	1.03804	−	0.599312i
$403$	−1.43727	+	15.5106i	−0.0715954	+	0.772637i
$404$	−0.327646	+	0.658002i	−0.0163010	+	0.0327368i
$405$	−45.2044	+	11.3694i	−2.24623	+	0.564948i
$406$	−5.82743	+	26.6089i	−0.289210	+	1.32058i
$407$	0.812492	−	0.100608i	0.0402737	−	0.00498697i
$408$	−8.41018			−0.416366
$409$	−15.4390	+	13.0628i	−0.763412	+	0.645912i
$409$	−15.4390	+	13.0628i	−0.763412	+	0.645912i
$410$	−4.54629			−0.224525
$411$	48.8826	−	6.05298i	2.41120	−	0.298572i
$412$	−0.0672334	+	0.306997i	−0.00331235	+	0.0151247i
$413$	50.7582	−	12.7662i	2.49765	−	0.628184i
$414$	−34.9984	+	70.2862i	−1.72008	+	3.45438i
$415$	0.217467	−	2.34685i	0.0106750	−	0.115202i
$416$	1.28739	−	0.743275i	0.0631195	−	0.0364421i
$417$	44.4918	−	17.2362i	2.17877	−	0.844062i
$418$	−21.1158	−	9.71483i	−1.03281	−	0.475168i
$419$	3.33829	−	9.47339i	0.163086	−	0.462805i	−0.832783	−	0.553599i	$-0.813254\pi$
$419$	3.33829	−	9.47339i	0.163086	−	0.462805i	0.995870	+	0.0907936i	$0.0289404\pi$
$420$	−1.62143	+	0.150247i	−0.0791176	+	0.00733133i
$421$	−0.459729	−	14.9216i	−0.0224058	−	0.727233i	−0.942242	−	0.334932i	$-0.891287\pi$
$421$	−0.459729	−	14.9216i	−0.0224058	−	0.727233i	0.919837	−	0.392302i	$-0.128321\pi$
$422$	−15.0740	−	1.39681i	−0.733791	−	0.0679957i
$423$	28.0506	−	21.1828i	1.36387	−	1.02994i
$424$	2.07078	+	1.66635i	0.100566	+	0.0809252i
$425$	−2.85860	+	1.53504i	−0.138663	+	0.0744603i
$426$	0.754177	−	4.85849i	0.0365400	−	0.235395i
$427$	45.5550	+	14.4921i	2.20456	+	0.701322i
$428$	−0.0254914	−	0.0192502i	−0.00123218	−	0.000930496i
$429$	4.81322	−	21.9778i	0.232384	−	1.06110i
$430$	−3.96145	−	12.4526i	−0.191038	−	0.600516i
$431$	−20.7110	+	4.53579i	−0.997615	+	0.218481i	−0.682748	−	0.730654i	$-0.739215\pi$
$431$	−20.7110	+	4.53579i	−0.997615	+	0.218481i	−0.314868	+	0.949136i	$0.601960\pi$
$432$	−11.8300	+	76.2100i	−0.569170	+	3.66666i
$433$	−5.86430	−	37.7784i	−0.281820	−	1.81552i	−0.531354	−	0.847150i	$-0.678317\pi$
$433$	−5.86430	−	37.7784i	−0.281820	−	1.81552i	0.249534	−	0.968366i	$-0.419723\pi$
$434$	−21.6786	−	28.7071i	−1.04061	−	1.37799i
$435$	16.6865	−	0.514107i	0.800058	−	0.0246495i
$436$	−0.510950	+	0.676608i	−0.0244701	+	0.0324036i
$437$	−31.0177	+	30.0767i	−1.48378	+	1.43877i
$438$	0.292599	−	0.250684i	0.0139809	−	0.0119781i
$439$	26.5868	+	16.4619i	1.26892	+	0.785682i	0.984898	−	0.173136i	$-0.0553899\pi$
$439$	26.5868	+	16.4619i	1.26892	+	0.785682i	0.284022	+	0.958818i	$0.408331\pi$
$440$			7.74639i			0.369295i
$441$	−88.1299	+	62.3859i	−4.19666	+	2.97076i
$442$	−0.372218	+	3.00595i	−0.0177046	+	0.142979i
$443$	−0.277464	+	9.00573i	−0.0131827	+	0.427875i	0.969770	+	0.244019i	$0.0784659\pi$
$443$	−0.277464	+	9.00573i	−0.0131827	+	0.427875i	−0.982953	+	0.183856i	$0.941142\pi$
$444$	−0.00701275	−	0.113700i	−0.000332810	−	0.00539594i
$445$	−5.27587	−	0.986230i	−0.250100	−	0.0467518i
$446$	−8.55193	+	0.263482i	−0.404946	+	0.0124762i
$447$	−33.3453	−	19.2519i	−1.57718	−	0.910585i
$448$	−11.0868	+	34.8507i	−0.523803	+	1.64654i
$449$	3.53442	−	38.1424i	0.166799	−	1.80005i	−0.342557	−	0.939497i	$-0.611293\pi$
$449$	3.53442	−	38.1424i	0.166799	−	1.80005i	0.509356	−	0.860556i	$-0.329883\pi$
$450$	15.7098	+	44.5813i	0.740568	+	2.10158i
$451$	−3.21722	−	6.99285i	−0.151493	−	0.329280i
$452$	0.206105	−	0.155643i	0.00969437	−	0.00732085i
$453$	−22.5948	+	7.96209i	−1.06160	+	0.374092i
$454$	28.0626	−	22.5819i	1.31704	−	1.05982i
$455$	−0.376469	+	12.2192i	−0.0176491	+	0.572844i
$456$	−31.8948	+	59.3956i	−1.49361	+	2.78146i
$457$	1.74018	+	6.11610i	0.0814022	+	0.286099i	0.991830	−	0.127570i	$-0.0407177\pi$
$457$	1.74018	+	6.11610i	0.0814022	+	0.286099i	−0.910427	+	0.413669i	$0.864247\pi$
$458$	8.25394	−	14.2963i	0.385682	−	0.668020i
$459$	11.9336	+	12.3070i	0.557015	+	0.574441i
$460$	0.644111	+	0.249530i	0.0300318	+	0.0116344i
$461$	20.7675	−	3.22372i	0.967240	−	0.150143i	0.349854	−	0.936804i	$-0.386231\pi$
$461$	20.7675	−	3.22372i	0.967240	−	0.150143i	0.617385	+	0.786661i	$0.288192\pi$
$462$	25.9789	+	44.9967i	1.20865	+	2.09344i
$463$	0.0373604	−	0.0647101i	0.00173629	−	0.00300733i	−0.865156	−	0.501503i	$-0.832781\pi$
$463$	0.0373604	−	0.0647101i	0.00173629	−	0.00300733i	0.866892	+	0.498496i	$0.166114\pi$
$464$	6.18428	−	15.9635i	0.287098	−	0.741085i
$465$	−13.8218	+	17.1764i	−0.640972	+	0.796538i
$466$	10.5906	−	9.07347i	0.490600	−	0.420320i
$467$	−17.6376	+	19.3475i	−0.816170	+	0.895296i	−0.996086	−	0.0883861i	$-0.971829\pi$
$467$	−17.6376	+	19.3475i	−0.816170	+	0.895296i	0.179916	+	0.983682i	$0.442417\pi$
$468$	−2.25202	−	0.640755i	−0.104100	−	0.0296189i
$469$	−20.0855	−	9.24081i	−0.927464	−	0.426701i
$470$	3.92607	+	4.30670i	0.181096	+	0.198653i
$471$	−6.43074	−	51.9333i	−0.296313	−	2.39296i
$472$	−34.4964	+	3.19657i	−1.58783	+	0.147134i
$473$	16.3505	−	14.9054i	0.751796	−	0.685352i
$474$	−27.9449	+	45.1326i	−1.28355	+	2.07301i
$475$			26.0100i			1.19342i
$476$	0.214452	+	0.302947i	0.00982937	+	0.0138855i
$477$	−0.754027	−	8.13725i	−0.0345245	−	0.372579i
$478$	−9.11746	−	3.53212i	−0.417023	−	0.161555i
$479$	2.65032	+	14.1780i	0.121096	+	0.647808i	0.988623	+	0.150417i	$0.0480615\pi$
$479$	2.65032	+	14.1780i	0.121096	+	0.647808i	−0.867526	+	0.497391i	$0.834291\pi$
$480$	2.10001	+	0.129524i	0.0958518	+	0.00591194i
$481$	−0.853597	−	0.0526480i	−0.0389207	−	0.00240054i
$482$	0.708646	+	0.687149i	0.0322779	+	0.0312988i
$483$	95.4373	−	14.8146i	4.34255	−	0.674088i
$484$	0.435503	−	0.200363i	0.0197956	−	0.00910741i
$485$	−15.2169	−	6.44077i	−0.690965	−	0.292460i
$486$	100.210	−	70.9375i	4.54564	−	3.21779i
$487$	2.31646	−	12.3920i	0.104969	−	0.561534i	−0.889538	−	0.456862i	$-0.848973\pi$
$487$	2.31646	−	12.3920i	0.104969	−	0.561534i	0.994507	−	0.104673i	$-0.0333795\pi$
$488$	−28.3255	−	14.1044i	−1.28223	−	0.638477i
$489$	0.538183	+	17.4680i	0.0243375	+	0.789930i
$490$	−11.6472	−	13.5946i	−0.526165	−	0.614142i
$491$	5.01050	+	10.0625i	0.226121	+	0.454112i	0.978949	−	0.204105i	$-0.0654285\pi$
$491$	5.01050	+	10.0625i	0.226121	+	0.454112i	−0.752828	+	0.658217i	$0.771311\pi$
$492$	−0.998715	+	0.386904i	−0.0450256	+	0.0174430i
$493$	−2.00323	−	3.23533i	−0.0902211	−	0.145712i
$494$	19.8175	+	14.0285i	0.891632	+	0.631173i
$495$	17.0983	−	16.5796i	0.768512	−	0.745199i
$496$	10.6959	+	19.9183i	0.480260	+	0.894357i
$497$	−4.04905	+	2.01619i	−0.181625	+	0.0904383i
$498$	2.86361	+	10.0645i	0.128321	+	0.451003i
$499$	21.6803	−	22.3585i	0.970542	−	1.00090i	−0.0294574	−	0.999566i	$-0.509378\pi$
$499$	21.6803	−	22.3585i	0.970542	−	1.00090i	0.999999	−	0.00133828i	$-0.000425987\pi$
$500$	0.867977	−	0.399333i	0.0388171	−	0.0178587i
$501$	−0.912124	−	9.84339i	−0.0407507	−	0.439770i
$502$	−37.9264	−	8.30600i	−1.69274	−	0.370715i
$503$	−4.65589	+	12.0182i	−0.207596	+	0.535867i	−0.996948	−	0.0780746i	$-0.975123\pi$
$503$	−4.65589	+	12.0182i	−0.207596	+	0.535867i	0.789352	+	0.613941i	$0.210417\pi$
$504$	100.898	−	50.2414i	4.49437	−	2.23793i
$505$	3.04447	+	7.19284i	0.135477	+	0.320077i
$506$	−1.35683	−	21.9987i	−0.0603185	−	0.977960i
$507$	8.32008	−	19.6570i	0.369508	−	0.872997i
$508$	−0.163489	−	0.0576113i	−0.00725365	−	0.00255609i
$509$	−8.56218	−	6.88996i	−0.379512	−	0.305392i	0.418288	−	0.908315i	$-0.362630\pi$
$509$	−8.56218	−	6.88996i	−0.379512	−	0.305392i	−0.797800	+	0.602922i	$0.794003\pi$
$510$	−2.78919	+	3.25556i	−0.123508	+	0.144159i
$511$	−0.343763	−	0.0864599i	−0.0152072	−	0.00382476i
$512$	10.7391	−	21.5669i	0.474604	−	0.953133i
$513$	132.173	−	37.6066i	5.83560	−	1.66037i
$514$	21.6369	+	3.35867i	0.954362	+	0.148144i
$515$	2.01243	+	2.66489i	0.0886783	+	0.117429i
$516$	−1.92999	−	2.39841i	−0.0849632	−	0.105584i
$517$	−3.84600	+	9.08653i	−0.169147	+	0.399625i
$518$	1.53869	−	1.23818i	0.0676064	−	0.0544026i
$519$	5.67059	−	22.5462i	0.248911	−	0.989666i
$520$	1.48689	−	7.95418i	0.0652046	−	0.348814i
$521$	−14.3150	+	23.1196i	−0.627153	+	1.01289i	0.369347	+	0.929292i	$0.379581\pi$
$521$	−14.3150	+	23.1196i	−0.627153	+	1.01289i	−0.996500	+	0.0835952i	$0.973360\pi$
$522$	−51.0507	+	21.6079i	−2.23443	+	0.945753i
$523$	−11.7007	+	12.8350i	−0.511635	+	0.561237i	−0.939475	−	0.342618i	$-0.888687\pi$
$523$	−11.7007	+	12.8350i	−0.511635	+	0.561237i	0.427840	+	0.903855i	$0.359275\pi$
$524$	−0.895211	−	0.633707i	−0.0391075	−	0.0276836i
$525$	33.5929	−	47.4553i	1.46612	−	2.07112i
$526$	−6.78096	−	3.91499i	−0.295664	−	0.170702i
$527$	4.96590	+	0.770850i	0.216318	+	0.0335787i
$528$	−11.7962	−	30.4494i	−0.513362	−	1.32514i
$529$	−17.1237	−	5.44745i	−0.744509	−	0.236845i
$530$	1.33181	−	0.248958i	0.0578499	−	0.0108140i
$531$	80.8885	+	69.3010i	3.51026	+	3.00741i
$532$	2.95280	−	0.365636i	0.128020	−	0.0158524i
$533$	1.96126	+	7.79795i	0.0849518	+	0.337767i
$534$	23.4234	−	4.37859i	1.01363	−	0.189480i
$535$	−0.331565	+	0.0726140i	−0.0143348	+	0.00313938i
$536$	12.1994	+	8.08363i	0.526935	+	0.349159i
$537$	39.6116	−	46.2348i	1.70937	−	1.99518i
$538$	−11.9144	−	25.8967i	−0.513666	−	1.11649i
$539$	12.6682	−	27.5353i	0.545660	−	1.18603i
$540$	−1.42942	−	1.66843i	−0.0615126	−	0.0717978i
$541$	3.99826	+	32.2891i	0.171899	+	1.38822i	0.795253	+	0.606278i	$0.207338\pi$
$541$	3.99826	+	32.2891i	0.171899	+	1.38822i	−0.623354	+	0.781940i	$0.714231\pi$
$542$	−18.2916	−	2.26500i	−0.785693	−	0.0972899i
$543$	−12.4600	−	13.6679i	−0.534708	−	0.586546i
$544$	−0.213768	−	0.429304i	−0.00916523	−	0.0184063i
$545$	1.92736	+	8.80059i	0.0825590	+	0.376976i
$546$	−18.0388	−	51.1903i	−0.771987	−	2.19074i
$547$	29.4656	+	7.41088i	1.25986	+	0.316867i	0.815381	−	0.578925i	$-0.196527\pi$
$547$	29.4656	+	7.41088i	1.25986	+	0.316867i	0.444475	+	0.895791i	$0.353390\pi$
$548$	0.794798	+	1.19947i	0.0339521	+	0.0512388i
$549$	29.4930	+	92.7094i	1.25873	+	3.95674i
$550$	−10.0762	−	8.63274i	−0.429650	−	0.368101i
$551$	−30.4461	+	1.87785i	−1.29705	+	0.0799993i
$552$	−63.9284			−2.72097
$553$	48.7433	−	3.00638i	2.07278	−	0.127844i
$554$	5.64709	+	22.4527i	0.239922	+	0.953926i
$555$	−0.965952	−	0.729453i	−0.0410024	−	0.0309636i
$556$	1.03007	+	0.939030i	0.0436846	+	0.0398238i
$557$	27.6836	−	7.87667i	1.17299	−	0.333745i	0.369598	−	0.929192i	$-0.379495\pi$
$557$	27.6836	−	7.87667i	1.17299	−	0.333745i	0.803395	+	0.595446i	$0.203025\pi$
$558$	22.1935	−	69.7641i	0.939528	−	2.95335i
$559$	−19.6501	+	12.1668i	−0.831110	+	0.514602i
$560$	9.34062	+	15.0856i	0.394713	+	0.637484i
$561$	−6.98131	−	1.98635i	−0.294751	−	0.0838639i
$562$	−4.55102	+	6.86818i	−0.191973	+	0.289717i
$563$	−25.1984	+	22.9714i	−1.06199	+	0.968129i	−0.999552	−	0.0299204i	$-0.990475\pi$
$563$	−25.1984	+	22.9714i	−1.06199	+	0.968129i	−0.0624343	+	0.998049i	$0.519886\pi$
$564$	1.22898	+	0.611960i	0.0517494	+	0.0257682i
$565$	0.168944	−	2.73913i	0.00710751	−	0.115236i
$566$	−33.4162	+	11.7754i	−1.40459	+	0.494957i
$567$	−179.563	−	63.2757i	−7.54096	−	2.65733i
$568$	2.85313	−	0.907647i	0.119715	−	0.0380840i
$569$	−5.77479	−	37.2018i	−0.242092	−	1.55958i	−0.728004	−	0.685573i	$-0.759552\pi$
$569$	−5.77479	−	37.2018i	−0.242092	−	1.55958i	0.485912	−	0.874007i	$-0.338487\pi$
$570$	12.4142	+	32.0447i	0.519973	+	1.34220i
$571$	21.8634	+	19.9311i	0.914953	+	0.834090i	0.986569	−	0.163342i	$-0.0522276\pi$
$571$	21.8634	+	19.9311i	0.914953	+	0.834090i	−0.0716165	+	0.997432i	$0.522816\pi$
$572$	0.637397	−	0.160312i	0.0266509	−	0.00670297i
$573$	13.2710	+	20.0279i	0.554402	+	0.836677i
$574$	−15.4793	−	10.2570i	−0.646094	−	0.428117i
$575$	−21.7291	+	11.6683i	−0.906168	+	0.486602i
$576$	−70.9250	+	22.5629i	−2.95521	+	0.940120i
$577$	−0.430028	−	0.534397i	−0.0179023	−	0.0222472i	0.770050	−	0.637984i	$-0.220231\pi$
$577$	−0.430028	−	0.534397i	−0.0179023	−	0.0222472i	−0.787952	+	0.615736i	$0.788859\pi$
$578$	−22.0686	−	4.12534i	−0.917935	−	0.171592i
$579$	30.9548	+	16.6224i	1.28644	+	0.690803i
$580$	0.230723	+	0.429661i	0.00958025	+	0.0178407i
$581$	6.03519	−	7.49995i	0.250382	−	0.311151i
$582$	73.3267	+	2.25917i	3.03949	+	0.0936456i
$583$	1.32539	+	1.87233i	0.0548922	+	0.0775440i
$584$	0.216072	+	0.0914555i	0.00894113	+	0.00378445i
$585$	−20.7393	+	13.7424i	−0.857466	+	0.568178i
$586$	4.31967	−	8.04424i	0.178444	−	0.332305i
$587$	−8.94708	−	21.1383i	−0.369285	−	0.872471i	−0.995670	−	0.0929571i	$-0.970368\pi$
$587$	−8.94708	−	21.1383i	−0.369285	−	0.872471i	0.626385	−	0.779514i	$-0.284534\pi$
$588$	−3.71555	−	1.99521i	−0.153227	−	0.0822811i
$589$	24.2767	−	32.1475i	1.00030	−	1.32462i
$590$	−10.2032	+	14.4136i	−0.420059	+	0.593400i
$591$	6.67072	−	4.13034i	0.274397	−	0.169899i
$592$	−1.07496	+	0.620629i	−0.0441806	+	0.0255077i
$593$	−0.983777	−	4.49206i	−0.0403989	−	0.184467i	0.952285	−	0.305211i	$-0.0987269\pi$
$593$	−0.983777	−	4.49206i	−0.0403989	−	0.184467i	−0.992684	+	0.120744i	$0.961472\pi$
$594$	−29.2999	+	63.6853i	−1.20219	+	2.61304i
$595$	3.92713	+	0.363902i	0.160996	+	0.0149185i
$596$	0.0692438	−	1.12267i	0.00283634	−	0.0459863i
$597$	−5.52681	+	21.9745i	−0.226197	+	0.899357i
$598$	−2.82934	+	22.8492i	−0.115700	+	0.934373i
$599$	9.73755	−	6.45234i	0.397866	−	0.263635i	−0.337473	−	0.941335i	$-0.609572\pi$
$599$	9.73755	−	6.45234i	0.397866	−	0.263635i	0.735339	+	0.677700i	$0.237023\pi$
$600$	−26.7910	+	27.6291i	−1.09374	+	1.12795i
$601$	4.09343	+	7.09003i	0.166975	+	0.289208i	0.937355	−	0.348376i	$-0.113267\pi$
$601$	4.09343	+	7.09003i	0.166975	+	0.289208i	−0.770380	+	0.637585i	$0.779934\pi$
$602$	14.6064	−	51.3362i	0.595313	−	2.09231i
$603$	−8.26778	−	44.2287i	−0.336690	−	1.80113i
$604$	−0.502421	−	0.487180i	−0.0204432	−	0.0198231i
$605$	1.39399	−	4.89935i	0.0566736	−	0.199187i
$606$	−24.1398	−	24.8950i	−0.980613	−	1.01129i
$607$	−12.1715	−	2.66559i	−0.494024	−	0.108193i	−0.0400316	−	0.999198i	$-0.512746\pi$
$607$	−12.1715	−	2.66559i	−0.494024	−	0.108193i	−0.453993	+	0.891005i	$0.650001\pi$
$608$	−3.84259	−	0.118389i	−0.155838	−	0.00480131i
$609$	57.9745	+	35.8963i	2.34925	+	1.45459i
$610$	−14.8538	+	6.28707i	−0.601413	+	0.254556i
$611$	5.69329	−	8.59203i	0.230326	−	0.347596i
$612$	−0.251050	+	0.712429i	−0.0101481	+	0.0287983i
$613$	−39.0494	−	4.83537i	−1.57719	−	0.195299i	−0.713989	−	0.700157i	$-0.753113\pi$
$613$	−39.0494	−	4.83537i	−1.57719	−	0.195299i	−0.863202	+	0.504858i	$0.831545\pi$
$614$	−17.4009	−	2.15470i	−0.702245	−	0.0869568i
$615$	−3.78240	+	10.7337i	−0.152521	+	0.432824i
$616$	−17.4768	+	26.3751i	−0.704158	+	1.06268i
$617$	14.3910	−	6.09118i	0.579359	−	0.245222i	−0.0803199	−	0.996769i	$-0.525594\pi$
$617$	14.3910	−	6.09118i	0.579359	−	0.245222i	0.659679	+	0.751547i	$0.270692\pi$
$618$	−12.6053	−	7.80487i	−0.507060	−	0.313958i
$619$	−18.1986	−	0.560693i	−0.731464	−	0.0225362i	−0.337072	−	0.941479i	$-0.609437\pi$
$619$	−18.1986	−	0.560693i	−0.731464	−	0.0225362i	−0.394391	+	0.918943i	$0.629045\pi$
$620$	−0.629143	−	0.137784i	−0.0252670	−	0.00553356i
$621$	90.7113	+	93.5492i	3.64012	+	3.75400i
$622$	10.8076	−	37.9846i	0.433344	−	1.52304i
$623$	−15.7383	−	15.2609i	−0.630543	−	0.611415i
$624$	6.26791	+	33.5304i	0.250917	+	1.34229i
$625$	−2.49423	+	8.76630i	−0.0997691	+	0.350652i
$626$	0.623801	+	1.08046i	0.0249321	+	0.0431837i
$627$	−40.5043	+	41.7714i	−1.61759	+	1.66819i
$628$	1.27433	−	0.844400i	0.0508512	−	0.0336952i
$629$	−0.0339056	+	0.273814i	−0.00135190	+	0.0109177i
$630$	14.0141	−	55.7198i	0.558335	−	2.21993i
$631$	1.34393	−	21.7895i	0.0535011	−	0.867428i	−0.872195	−	0.489159i	$-0.837304\pi$
$631$	1.34393	−	21.7895i	0.0535011	−	0.867428i	0.925696	−	0.378269i	$-0.123480\pi$
$632$	−32.1876	−	2.98262i	−1.28035	−	0.118642i
$633$	−15.8390	+	34.4272i	−0.629545	+	1.36836i
$634$	−6.57250	−	30.0109i	−0.261027	−	1.19189i
$635$	−1.59513	+	0.920949i	−0.0633008	+	0.0365467i
$636$	0.271380	−	0.168031i	0.0107609	−	0.00666287i
$637$	−18.2934	+	25.8423i	−0.724809	+	1.02391i
$638$	9.37765	−	12.4180i	0.371265	−	0.491634i
$639$	−8.10999	−	4.35497i	−0.320826	−	0.172280i
$640$	−4.33432	−	10.2402i	−0.171329	−	0.404780i
$641$	−6.75272	+	12.5752i	−0.266717	+	0.496689i	−0.978644	−	0.205564i	$-0.934097\pi$
$641$	−6.75272	+	12.5752i	−0.266717	+	0.496689i	0.711927	+	0.702253i	$0.247823\pi$
$642$	1.25620	−	0.832385i	0.0495781	−	0.0328516i
$643$	−7.90336	−	3.34521i	−0.311678	−	0.131922i	0.228325	−	0.973585i	$-0.426675\pi$
$643$	−7.90336	−	3.34521i	−0.311678	−	0.131922i	−0.540003	+	0.841663i	$0.681577\pi$
$644$	1.63011	+	2.30279i	0.0642355	+	0.0907427i
$645$	−32.6960	−	1.00735i	−1.28740	−	0.0396645i
$646$	4.91080	−	6.10266i	0.193213	−	0.240106i
$647$	−9.49619	−	17.6841i	−0.373334	−	0.695236i	0.622867	−	0.782328i	$-0.285968\pi$
$647$	−9.49619	−	17.6841i	−0.373334	−	0.695236i	−0.996200	+	0.0870924i	$0.972242\pi$
$648$	111.025	+	59.6194i	4.36149	+	2.34207i
$649$	−29.3906	−	5.49405i	−1.15368	−	0.215660i
$650$	8.68943	+	10.7984i	0.340828	+	0.423548i
$651$	−85.8129	+	27.2990i	−3.36327	+	1.06993i
$652$	−0.449782	+	0.241528i	−0.0176148	+	0.00945897i
$653$	−14.0447	−	9.30634i	−0.549610	−	0.364185i	0.246682	−	0.969096i	$-0.420660\pi$
$653$	−14.0447	−	9.30634i	−0.549610	−	0.364185i	−0.796293	+	0.604911i	$0.793209\pi$
$654$	−22.0936	−	33.3426i	−0.863929	−	1.30380i
$655$	−11.3024	+	2.84267i	−0.441622	+	0.111072i
$656$	8.62451	+	7.86228i	0.336731	+	0.306971i
$657$	−0.260594	−	0.672670i	−0.0101667	−	0.0262434i
$658$	3.65117	+	23.5212i	0.142337	+	0.916952i
$659$	26.9830	−	8.58391i	1.05111	−	0.334382i	0.272674	−	0.962107i	$-0.412092\pi$
$659$	26.9830	−	8.58391i	1.05111	−	0.334382i	0.778435	+	0.627725i	$0.216014\pi$
$660$	0.877360	+	0.309170i	0.0341512	+	0.0120344i
$661$	22.6174	−	7.97006i	0.879715	−	0.310000i	0.145859	−	0.989305i	$-0.453405\pi$
$661$	22.6174	−	7.97006i	0.879715	−	0.310000i	0.733855	+	0.679306i	$0.237719\pi$
$662$	−0.825673	+	13.3869i	−0.0320907	+	0.520295i
$663$	6.78730	+	3.37967i	0.263597	+	0.131256i
$664$	−4.70903	+	4.29284i	−0.182746	+	0.166595i
$665$	17.4633	−	26.3547i	0.677196	−	1.02199i
$666$	3.86593	+	1.09995i	0.149802	+	0.0426223i
$667$	−15.2272	−	24.5928i	−0.589600	−	0.952236i
$668$	0.245529	−	0.152025i	0.00949980	−	0.00588203i
$669$	−6.49292	+	20.4101i	−0.251031	+	0.789100i
$670$	7.17503	−	2.04147i	0.277196	−	0.0788690i
$671$	−20.1818	−	18.3982i	−0.779110	−	0.710253i
$672$	6.85793	+	5.17887i	0.264550	+	0.199779i
$673$	0.0414523	+	0.164814i	0.00159787	+	0.00635310i	0.970591	−	0.240736i	$-0.0773888\pi$
$673$	0.0414523	+	0.164814i	0.00159787	+	0.00635310i	−0.968993	+	0.247089i	$0.920526\pi$
$674$	−7.56981	+	0.466890i	−0.291578	+	0.0179839i
$675$	78.4460			3.01939
$676$	0.622370	−	0.0383865i	0.0239373	−	0.00147640i
$677$	−14.0324	−	12.0222i	−0.539307	−	0.462050i	0.338566	−	0.940942i	$-0.390058\pi$
$677$	−14.0324	−	12.0222i	−0.539307	−	0.462050i	−0.877874	+	0.478892i	$0.841038\pi$
$678$	3.69364	+	11.6107i	0.141853	+	0.445907i
$679$	−37.2798	−	56.2608i	−1.43067	−	2.15909i
$680$	−2.53173	−	0.636756i	−0.0970874	−	0.0244185i
$681$	−29.9679	−	85.0427i	−1.14837	−	3.25884i
$682$	4.39639	+	20.0745i	0.168347	+	0.768694i
$683$	8.31263	+	16.6940i	0.318074	+	0.638778i	0.995283	−	0.0970121i	$-0.0309285\pi$
$683$	8.31263	+	16.6940i	0.318074	+	0.638778i	−0.677209	+	0.735790i	$0.736811\pi$
$684$	4.07934	+	4.47483i	0.155978	+	0.171099i
$685$	15.1735	+	1.87889i	0.579750	+	0.0717886i
$686$	−3.80031	−	30.6905i	−0.145096	−	1.17177i
$687$	−26.8860	−	31.3815i	−1.02576	−	1.19728i
$688$	−14.0202	+	30.4739i	−0.534516	+	1.16181i
$689$	−1.00156	−	2.17696i	−0.0381564	−	0.0829354i
$690$	−21.2015	+	24.7465i	−0.807129	+	0.942084i
$691$	−31.5423	−	20.9007i	−1.19993	−	0.795100i	−0.216477	−	0.976288i	$-0.569457\pi$
$691$	−31.5423	−	20.9007i	−1.19993	−	0.795100i	−0.983448	+	0.181188i	$0.942006\pi$
$692$	0.663423	−	0.145292i	0.0252195	−	0.00552317i
$693$	95.6222	−	17.8749i	3.63239	−	0.679011i
$694$	−7.87276	−	31.3020i	−0.298846	−	1.18821i
$695$	14.6985	−	1.82006i	0.557544	−	0.0690389i
$696$	−34.2757	−	29.3656i	−1.29922	−	1.11310i
$697$	2.54991	−	0.476660i	0.0965847	−	0.0180548i
$698$	30.2926	+	9.63676i	1.14659	+	0.364757i
$699$	−12.6111	−	32.5530i	−0.476996	−	1.23127i
$700$	1.67838	+	0.260533i	0.0634370	+	0.00984724i
$701$	34.3810	+	19.8499i	1.29855	+	0.749721i	0.980154	−	0.198236i	$-0.0635212\pi$
$701$	34.3810	+	19.8499i	1.29855	+	0.749721i	0.318400	+	0.947957i	$0.396855\pi$
$702$	42.3100	−	59.7695i	1.59689	−	2.25586i
$703$	1.80519	+	1.27787i	0.0680840	+	0.0481957i
$704$	14.0750	−	15.4396i	0.530473	−	0.581901i
$705$	13.4344	−	5.68629i	0.505969	−	0.214158i
$706$	5.86492	−	9.47216i	0.220729	−	0.356490i
$707$	−5.86201	+	31.3590i	−0.220464	+	1.17938i
$708$	−1.01476	+	4.03466i	−0.0381370	+	0.151632i
$709$	−33.3251	+	26.8166i	−1.25155	+	1.00712i	−0.252329	+	0.967641i	$0.581197\pi$
$709$	−33.3251	+	26.8166i	−1.25155	+	1.00712i	−0.999220	+	0.0394771i	$0.987431\pi$
$710$	0.594880	−	1.40546i	0.0223254	−	0.0527459i
$711$	62.3077	+	77.4301i	2.33672	+	2.90385i
$712$	8.74473	+	11.5799i	0.327723	+	0.433975i
$713$	37.7473	+	5.85947i	1.41365	+	0.219439i
$714$	−16.8416	+	4.79186i	−0.630282	+	0.179331i
$715$	3.11293	−	6.25160i	0.116417	−	0.233797i
$716$	1.72484	+	0.433814i	0.0644602	+	0.0162124i
$717$	−15.9247	+	18.5874i	−0.594720	+	0.694161i
$718$	1.54466	+	1.24298i	0.0576461	+	0.0463877i
$719$	8.12184	+	2.86203i	0.302893	+	0.106736i	0.479489	−	0.877548i	$-0.340822\pi$
$719$	8.12184	+	2.86203i	0.302893	+	0.106736i	−0.176595	+	0.984284i	$0.556508\pi$
$720$	−14.0750	+	33.2534i	−0.524543	+	1.23928i
$721$	0.839667	+	13.6138i	0.0312708	+	0.507003i
$722$	−14.2692	−	33.7123i	−0.531044	−	1.25464i
$723$	2.21192	−	1.10140i	0.0822621	−	0.0409616i
$724$	0.195174	−	0.503802i	0.00725358	−	0.0187237i
$725$	−17.0101	−	3.72527i	−0.631739	−	0.138353i
$726$	2.08666	+	22.5186i	0.0774432	+	0.835745i
$727$	−24.8281	+	11.4227i	−0.920823	+	0.423646i	−0.820720	−	0.571331i	$-0.806427\pi$
$727$	−24.8281	+	11.4227i	−0.920823	+	0.423646i	−0.100104	+	0.994977i	$0.531917\pi$
$728$	23.0081	−	23.7279i	0.852738	−	0.879416i
$729$	−48.3727	−	170.012i	−1.79158	−	6.29676i
$730$	0.107061	−	0.0533103i	0.00396252	−	0.00197310i
$731$	3.52748	+	6.56901i	0.130469	+	0.242964i
$732$	−2.72798	+	2.64523i	−0.100829	+	0.0977705i
$733$	−29.2345	−	20.6946i	−1.07980	−	0.764374i	−0.106592	−	0.994303i	$-0.533994\pi$
$733$	−29.2345	−	20.6946i	−1.07980	−	0.764374i	−0.973207	+	0.229929i	$0.926151\pi$
$734$	14.3930	+	23.2455i	0.531256	+	0.858008i
$735$	−41.7867	+	16.1882i	−1.54132	+	0.597112i
$736$	−1.62492	−	3.26327i	−0.0598952	−	0.120286i
$737$	8.21754	+	9.59156i	0.302697	+	0.353310i
$738$	−1.16375	−	37.7724i	−0.0428384	−	1.39042i
$739$	−24.3456	−	12.1226i	−0.895566	−	0.445939i	−0.0618199	−	0.998087i	$-0.519690\pi$
$739$	−24.3456	−	12.1226i	−0.895566	−	0.445939i	−0.833746	+	0.552149i	$0.813808\pi$
$740$	0.00649742	−	0.0347581i	0.000238850	−	0.00127773i
$741$	49.6086	−	35.1172i	1.82242	−	1.29006i
$742$	5.09624	+	2.15705i	0.187089	+	0.0791879i
$743$	−8.39886	+	3.86409i	−0.308124	+	0.141760i	−0.565969	−	0.824427i	$-0.691498\pi$
$743$	−8.39886	+	3.86409i	−0.308124	+	0.141760i	0.257844	+	0.966187i	$0.416988\pi$
$744$	58.9008	−	9.14309i	2.15941	−	0.335202i
$745$	−8.58039	−	8.32010i	−0.314361	−	0.304825i
$746$	8.26224	+	0.509598i	0.302502	+	0.0186577i
$747$	19.5542	+	1.20606i	0.715450	+	0.0441274i
$748$	−0.0389617	−	0.208427i	−0.00142458	−	0.00762084i
$749$	−1.29275	−	0.500813i	−0.0472359	−	0.0182993i
$750$	4.15881	+	44.8807i	0.151858	+	1.63881i
$751$	4.26410	+	6.02371i	0.155599	+	0.219808i	0.886563	−	0.462608i	$-0.153086\pi$
$751$	4.26410	+	6.02371i	0.155599	+	0.219808i	−0.730964	+	0.682416i	$0.760929\pi$
$752$		−	14.9597i		−	0.545523i
$753$	−51.1640	+	82.6327i	−1.86452	+	3.01130i
$754$	−12.0128	+	10.9511i	−0.437480	+	0.398815i
$755$	−7.40458	+	0.686135i	−0.269480	+	0.0249710i
$756$	−1.10276	−	8.90565i	−0.0401069	−	0.323895i
$757$	−29.0285	−	31.8428i	−1.05506	−	1.15734i	−0.987173	−	0.159651i	$-0.948963\pi$
$757$	−29.0285	−	31.8428i	−1.05506	−	1.15734i	−0.0678855	−	0.997693i	$-0.521625\pi$
$758$	28.7869	+	13.2441i	1.04559	+	0.481047i
$759$	−53.0671	−	15.0989i	−1.92621	−	0.548055i
$760$	−14.0983	+	15.4651i	−0.511401	+	0.560980i
$761$	21.7592	−	18.6421i	0.788770	−	0.675777i	−0.161615	−	0.986854i	$-0.551670\pi$
$761$	21.7592	−	18.6421i	0.788770	−	0.675777i	0.950385	+	0.311077i	$0.100690\pi$
$762$	5.12668	−	6.37095i	0.185720	−	0.230795i
$763$	−13.2928	+	34.3128i	−0.481233	+	1.24221i
$764$	−0.350928	+	0.607825i	−0.0126961	+	0.0219903i
$765$	4.01318	+	6.95104i	0.145097	+	0.251315i
$766$	43.3431	−	6.72810i	1.56605	−	0.243096i
$767$	29.1244	+	11.2828i	1.05162	+	0.407400i
$768$	−5.79356	−	5.97480i	−0.209057	−	0.215597i
$769$	−10.4685	+	18.1320i	−0.377505	+	0.653858i	−0.990699	−	0.136075i	$-0.956551\pi$
$769$	−10.4685	+	18.1320i	−0.377505	+	0.653858i	0.613194	+	0.789933i	$0.289885\pi$
$770$	4.41365	+	15.5124i	0.159057	+	0.559027i
$771$	25.9311	−	48.2898i	0.933885	−	1.73911i
$772$	−0.0316081	+	1.02592i	−0.00113760	+	0.0369235i
$773$	−0.802769	+	0.645986i	−0.0288736	+	0.0232345i	−0.641253	−	0.767330i	$-0.721585\pi$
$773$	−0.802769	+	0.645986i	−0.0288736	+	0.0232345i	0.612379	+	0.790564i	$0.290213\pi$
$774$	102.447	−	36.1008i	3.68237	−	1.29762i
$775$	18.3515	−	13.8584i	0.659204	−	0.497807i
$776$	18.6718	+	40.5845i	0.670280	+	1.45690i
$777$	−1.64316	−	4.66296i	−0.0589481	−	0.167283i
$778$	0.668661	−	7.21600i	0.0239726	−	0.258706i
$779$	6.30394	−	19.8160i	0.225862	−	0.709983i
$780$	−0.841550	−	0.485869i	−0.0301323	−	0.0173969i
$781$	2.58277	−	0.0795742i	0.0924187	−	0.00284739i
$782$	7.30129	+	1.36485i	0.261094	+	0.0488069i
$783$	5.66360	+	91.8255i	0.202401	+	3.28158i
$784$	−1.41515	+	45.9319i	−0.0505410	+	1.64043i
$785$	1.99615	−	16.1205i	0.0712456	−	0.575364i
$786$	42.2320	−	29.8954i	1.50637	−	1.06633i
$787$			49.2585i			1.75588i	0.478774	+	0.877938i	$0.341081\pi$
$787$			49.2585i			1.75588i	−0.478774	+	0.877938i	$0.658919\pi$
$788$	0.194870	+	0.120658i	0.00694195	+	0.00429827i
$789$	−14.8848	+	12.7525i	−0.529912	+	0.454001i
$790$	−11.8294	+	11.4706i	−0.420872	+	0.408105i
$791$	6.75501	−	8.94507i	0.240180	−	0.318050i
$792$	−64.3600	+	1.98291i	−2.28693	+	0.0704597i
$793$	17.1917	+	22.7655i	0.610495	+	0.808426i
$794$	−2.42695	−	15.6347i	−0.0861292	−	0.554853i
$795$	0.520247	−	3.35148i	0.0184512	−	0.118865i
$796$	−0.646602	+	0.141608i	−0.0229182	+	0.00501917i
$797$	−12.6043	−	39.6210i	−0.446468	−	1.40345i	−0.867969	−	0.496618i	$-0.834575\pi$
$797$	−12.6043	−	39.6210i	−0.446468	−	1.40345i	0.421501	−	0.906828i	$-0.361504\pi$
$798$	−30.0285	+	137.114i	−1.06300	+	4.85379i
$799$	−2.65358	−	2.00389i	−0.0938770	−	0.0708926i
$800$	−2.09131	−	0.665295i	−0.0739391	−	0.0235217i
$801$	6.84348	−	44.0864i	0.241802	−	1.55772i
$802$	17.1511	−	9.20996i	0.605627	−	0.325215i
$803$	0.157762	+	0.126950i	0.00556729	+	0.00447998i
$804$	1.40245	−	1.05908i	0.0494607	−	0.0373510i
$805$	29.8513	+	2.76613i	1.05212	+	0.0974933i
$806$	−0.661079	−	21.4569i	−0.0232855	−	0.755786i
$807$	−71.0540	+	6.58412i	−2.50122	+	0.231772i
$808$	7.01823	−	19.9163i	0.246900	−	0.700652i
$809$	20.3148	+	9.34627i	0.714229	+	0.328597i	0.741428	−	0.671033i	$-0.234149\pi$
$809$	20.3148	+	9.34627i	0.714229	+	0.328597i	−0.0271990	+	0.999630i	$0.508659\pi$
$810$	59.8996	−	23.2052i	2.10466	−	0.815348i
$811$	23.2538	−	13.4256i	0.816550	−	0.471436i	−0.0326751	−	0.999466i	$-0.510403\pi$
$811$	23.2538	−	13.4256i	0.816550	−	0.471436i	0.849225	+	0.528030i	$0.177069\pi$
$812$	−0.183794	+	1.98345i	−0.00644991	+	0.0696056i
$813$	−20.5658	+	41.3017i	−0.721273	+	1.44851i
$814$	−1.09419	+	0.275199i	−0.0383512	+	0.00964573i
$815$	−1.16054	+	5.29917i	−0.0406518	+	0.185622i
$816$	10.9213	−	1.35235i	0.382323	−	0.0473419i
$817$	59.7703			2.09110
$818$	18.9034	−	20.4803i	0.660941	−	0.716078i
$819$	−101.618			−3.55082
$820$	−0.329939	+	0.0408552i	−0.0115220	+	0.00142673i
$821$	12.1692	−	55.5662i	0.424708	−	1.93927i	0.0938780	−	0.995584i	$-0.470074\pi$
$821$	12.1692	−	55.5662i	0.424708	−	1.93927i	0.330830	−	0.943690i	$-0.392671\pi$
$822$	−65.8306	+	16.5571i	−2.29610	+	0.577493i
$823$	−0.826460	+	1.65976i	−0.0288086	+	0.0578555i	−0.909100	−	0.416578i	$-0.863229\pi$
$823$	−0.826460	+	1.65976i	−0.0288086	+	0.0578555i	0.880291	+	0.474433i	$0.157347\pi$
$824$	0.833029	−	8.98982i	0.0290199	−	0.313175i
$825$	−28.7648	+	16.6074i	−1.00146	+	0.578195i
$826$	−67.2588	+	26.0562i	−2.34023	+	0.906612i
$827$	−5.50148	−	2.53108i	−0.191305	−	0.0880144i	0.319984	−	0.947423i	$-0.396322\pi$
$827$	−5.50148	−	2.53108i	−0.191305	−	0.0880144i	−0.511290	+	0.859408i	$0.670832\pi$
$828$	−1.90831	+	5.41540i	−0.0663184	+	0.188198i
$829$	−44.2886	+	4.10394i	−1.53821	+	0.142536i	−0.827706	−	0.561162i	$-0.810354\pi$
$829$	−44.2886	+	4.10394i	−1.53821	+	0.142536i	−0.710500	+	0.703698i	$0.751531\pi$
$830$	0.100025	+	3.24656i	0.00347193	+	0.112690i
$831$	57.7086	+	5.34749i	2.00189	+	0.185502i
$832$	−17.4162	+	13.1521i	−0.603797	+	0.455966i
$833$	7.95795	+	6.40374i	0.275727	+	0.221876i
$834$	−57.9314	+	31.1085i	−2.00600	+	1.07720i
$835$	0.470690	−	3.03223i	0.0162889	−	0.104935i
$836$	−1.61974	−	0.515278i	−0.0560200	−	0.0178212i
$837$	−96.9569	−	73.2185i	−3.35132	−	2.53080i
$838$	−2.96134	+	13.5219i	−0.102298	+	0.467106i
$839$	1.81736	+	5.71277i	0.0627424	+	0.197227i	0.979197	−	0.202912i	$-0.0650404\pi$
$839$	1.81736	+	5.71277i	0.0627424	+	0.197227i	−0.916455	+	0.400139i	$0.868962\pi$
$840$	45.6964	−	10.0077i	1.57668	−	0.345297i
$841$	−1.31581	+	8.47656i	−0.0453726	+	0.292295i
$842$	3.15581	+	20.3300i	0.108756	+	0.700620i
$843$	12.4293	+	16.4590i	0.428087	+	0.566878i
$844$	−1.10652	+	0.0340915i	−0.0380879	+	0.00117348i
$845$	3.99289	−	5.28744i	0.137360	−	0.181893i
$846$	−34.7767	+	33.7218i	−1.19565	+	1.15938i
$847$	15.7998	−	13.5364i	0.542887	−	0.465117i
$848$	−2.95703	−	1.83092i	−0.101545	−	0.0628740i
$849$			88.6915i			3.04388i
$850$	3.64968	−	2.58355i	0.125183	−	0.0886152i
$851$	−0.257727	+	2.08135i	−0.00883476	+	0.0713477i
$852$	0.0110722	−	0.359373i	0.000379326	−	0.0123119i
$853$	2.70379	+	43.8373i	0.0925762	+	1.50096i	0.704307	+	0.709896i	$0.251258\pi$
$853$	2.70379	+	43.8373i	0.0925762	+	1.50096i	−0.611731	+	0.791066i	$0.709526\pi$
$854$	−64.7589	−	12.1055i	−2.21600	−	0.414243i
$855$	64.3103	−	1.98138i	2.19937	−	0.0677618i
$856$	0.794718	+	0.458831i	0.0271629	+	0.0156825i
$857$	−13.0942	+	41.1609i	−0.447290	+	1.40603i	0.419682	+	0.907671i	$0.362141\pi$
$857$	−13.0942	+	41.1609i	−0.447290	+	1.40603i	−0.866972	+	0.498357i	$0.833937\pi$
$858$	−2.86087	+	30.8737i	−0.0976685	+	1.05401i
$859$	−3.26006	−	9.25139i	−0.111232	−	0.315653i	0.874239	−	0.485495i	$-0.161361\pi$
$859$	−3.26006	−	9.25139i	−0.111232	−	0.315653i	−0.985471	+	0.169842i	$0.945674\pi$
$860$	−0.399399	−	0.868122i	−0.0136194	−	0.0296027i
$861$	−37.0948	+	28.0127i	−1.26419	+	0.954671i
$862$	27.5578	−	9.71101i	0.938624	−	0.330758i
$863$	4.56685	−	3.67493i	0.155457	−	0.125096i	−0.546067	−	0.837741i	$-0.683876\pi$
$863$	4.56685	−	3.67493i	0.155457	−	0.125096i	0.701525	+	0.712645i	$0.252503\pi$
$864$	−0.357061	+	11.5892i	−0.0121475	+	0.394274i
$865$	3.41405	−	6.35778i	0.116081	−	0.216171i
$866$	14.4184	+	50.6756i	0.489958	+	1.72203i
$867$	−28.1004	+	48.6713i	−0.954339	+	1.65296i
$868$	−1.83126	−	1.88855i	−0.0621571	−	0.0641016i
$869$	−26.0145	−	10.0781i	−0.882483	−	0.341876i
$870$	−22.7347	+	3.52908i	−0.770779	+	0.119647i
$871$	−6.59690	−	11.4262i	−0.223527	−	0.387161i
$872$	12.1785	−	21.0938i	0.412417	−	0.714328i
$873$	49.6172	−	128.077i	1.67929	−	4.33474i
$874$	37.3285	−	46.3883i	1.26265	−	1.56911i
$875$	31.4897	−	26.9787i	1.06455	−	0.912047i
$876$	0.0189820	−	0.0208223i	0.000641344	−	0.000703521i
$877$	51.9639	+	14.7850i	1.75470	+	0.499254i	0.989499	−	0.144542i	$-0.0461709\pi$
$877$	51.9639	+	14.7850i	1.75470	+	0.499254i	0.765197	+	0.643796i	$0.222642\pi$
$878$	−39.1501	−	18.0119i	−1.32125	−	0.607872i
$879$	−15.3984	−	16.8912i	−0.519375	−	0.569727i
$880$	−1.24562	−	10.0594i	−0.0419898	−	0.339101i
$881$	3.77473	−	0.349781i	0.127174	−	0.0117844i	−0.0284930	−	0.999594i	$-0.509071\pi$
$881$	3.77473	−	0.349781i	0.127174	−	0.0117844i	0.155667	+	0.987810i	$0.450247\pi$
$882$	109.968	−	100.249i	3.70281	−	3.37556i
$883$	25.4401	−	41.0872i	0.856128	−	1.38269i	−0.0668183	−	0.997765i	$-0.521285\pi$
$883$	25.4401	−	41.0872i	0.856128	−	1.38269i	0.922946	−	0.384929i	$-0.125774\pi$
$884$			0.221496i			0.00744972i
$885$	25.5414	+	36.0812i	0.858564	+	1.21286i
$886$	−1.14569	−	12.3639i	−0.0384901	−	0.415374i
$887$	29.1276	+	11.2841i	0.978008	+	0.378882i	0.796587	−	0.604523i	$-0.206636\pi$
$887$	29.1276	+	11.2841i	0.978008	+	0.378882i	0.181420	+	0.983406i	$0.441931\pi$
$888$	0.601326	+	3.21681i	0.0201792	+	0.107949i
$889$	−7.50890	−	0.463133i	−0.251840	−	0.0155330i
$890$	7.38270	+	0.455350i	0.247469	+	0.0152634i
$891$	78.0813	+	75.7127i	2.61582	+	2.53647i
$892$	−0.618273	+	0.0959736i	−0.0207013	+	0.00321344i
$893$	−24.2156	+	11.1410i	−0.810346	+	0.372818i
$894$	48.8660	+	20.6832i	1.63433	+	0.691751i
$895$	15.4249	−	10.9191i	0.515598	−	0.364984i
$896$	8.34557	−	44.6448i	0.278806	−	1.49148i
$897$	51.5924	+	25.6899i	1.72262	+	0.857762i
$898$	1.62568	+	52.7651i	0.0542495	+	1.76079i
$899$	17.5469	+	20.4809i	0.585224	+	0.683076i
$900$	1.54074	+	3.09422i	0.0513580	+	0.103141i
$901$	−0.720876	+	0.279269i	−0.0240159	+	0.00930379i
$902$	5.58439	+	9.01910i	0.185940	+	0.300303i
$903$	−109.051	−	77.1958i	−3.62900	−	2.56892i
$904$	−5.32658	+	5.16499i	−0.177159	+	0.171785i
$905$	−2.71601	−	5.05785i	−0.0902832	−	0.168129i
$906$	29.5539	−	14.7161i	0.981864	−	0.488910i
$907$	8.71774	+	30.6397i	0.289468	+	1.01737i	0.961034	+	0.276429i	$0.0891512\pi$
$907$	8.71774	+	30.6397i	0.289468	+	1.01737i	−0.671567	+	0.740944i	$0.734378\pi$
$908$	1.83366	−	1.89102i	0.0608521	−	0.0627558i
$909$	−58.9816	+	27.1358i	−1.95629	+	0.900038i
$910$	−1.55449	−	16.7757i	−0.0515310	−	0.556108i
$911$	50.8282	+	11.1315i	1.68401	+	0.368804i	0.950465	−	0.310833i	$-0.100608\pi$
$911$	50.8282	+	11.1315i	1.68401	+	0.368804i	0.733548	+	0.679638i	$0.237863\pi$
$912$	31.8673	−	82.2590i	1.05523	−	2.72387i
$913$	−4.92288	+	2.45130i	−0.162924	+	0.0811263i
$914$	−3.41580	−	8.07014i	−0.112985	−	0.266937i
$915$	2.48563	+	40.3001i	0.0821722	+	1.33228i
$916$	0.470541	−	1.11170i	0.0155471	−	0.0367315i
$917$	−44.8961	−	15.8208i	−1.48260	−	0.522448i
$918$	−18.4056	−	14.8109i	−0.607476	−	0.488834i
$919$	−8.74378	+	10.2058i	−0.288431	+	0.336658i	−0.884729	−	0.466105i	$-0.845657\pi$
$919$	−8.74378	+	10.2058i	−0.288431	+	0.336658i	0.596299	+	0.802763i	$0.296637\pi$
$920$	−19.2445	−	4.84018i	−0.634471	−	0.159576i
$921$	−19.5644	+	39.2905i	−0.644667	+	1.29467i
$922$	−27.8573	+	7.92609i	−0.917431	+	0.261032i
$923$	−2.66732	−	0.414045i	−0.0877959	−	0.0136284i
$924$	2.28973	+	3.03209i	0.0753266	+	0.0997486i
$925$	0.791526	+	0.983633i	0.0260252	+	0.0323416i
$926$	−0.0401380	+	0.0948297i	−0.00131902	+	0.00311630i
$927$	−21.6258	+	17.4022i	−0.710285	+	0.571564i
$928$	0.627778	−	2.49604i	0.0206078	−	0.0819364i
$929$	−3.13318	+	16.7611i	−0.102796	+	0.549912i	0.892337	+	0.451371i	$0.149065\pi$
$929$	−3.13318	+	16.7611i	−0.102796	+	0.549912i	−0.995133	+	0.0985416i	$0.968582\pi$
$930$	15.9949	−	25.8326i	0.524493	−	0.847085i
$931$	75.4052	−	31.9163i	2.47131	−	1.04601i
$932$	0.687054	−	0.753662i	0.0225052	−	0.0246870i
$933$	−80.6891	−	57.1186i	−2.64164	−	1.86998i
$934$	20.8459	−	29.4482i	0.682099	−	0.963573i
$935$	−1.95120	−	1.12653i	−0.0638112	−	0.0368414i
$936$	66.4670	+	10.3176i	2.17254	+	0.337241i
$937$	−4.09763	−	10.5772i	−0.133864	−	0.345542i	0.849395	−	0.527758i	$-0.176967\pi$
$937$	−4.09763	−	10.5772i	−0.133864	−	0.345542i	−0.983259	+	0.182216i	$0.941673\pi$
$938$	29.0355	+	9.23686i	0.948042	+	0.301594i
$939$	3.06991	−	0.573867i	0.100183	−	0.0187274i
$940$	0.323629	+	0.277269i	0.0105556	+	0.00904351i
$941$	−32.9391	+	4.07874i	−1.07378	+	0.132963i	−0.640244	−	0.768172i	$-0.721167\pi$
$941$	−32.9391	+	4.07874i	−1.07378	+	0.132963i	−0.433539	+	0.901135i	$0.642735\pi$
$942$	17.5904	+	69.9390i	0.573125	+	2.27873i
$943$	19.3826	−	3.62324i	0.631186	−	0.117989i
$944$	44.2826	−	9.69803i	1.44127	−	0.315644i
$945$	−79.4857	−	52.6691i	−2.58567	−	1.71333i
$946$	−19.8379	+	23.1548i	−0.644984	+	0.752829i
$947$	21.3590	+	46.4253i	0.694076	+	1.50862i	0.853323	+	0.521382i	$0.174583\pi$
$947$	21.3590	+	46.4253i	0.694076	+	1.50862i	−0.159248	+	0.987239i	$0.550907\pi$
$948$	−1.62247	+	3.52654i	−0.0526952	+	0.114537i
$949$	−0.137626	−	0.160637i	−0.00446752	−	0.00521451i
$950$	−4.40492	−	35.5732i	−0.142914	−	1.15415i
$951$	−76.3232	−	9.45086i	−2.47495	−	0.306465i
$952$	−7.18349	−	7.87991i	−0.232818	−	0.255390i
$953$	10.6519	+	21.3919i	0.345049	+	0.692951i	0.997916	−	0.0645206i	$-0.0205518\pi$
$953$	10.6519	+	21.3919i	0.345049	+	0.692951i	−0.652868	+	0.757472i	$0.726434\pi$
$954$	2.40935	+	11.0014i	0.0780056	+	0.356185i
$955$	2.47862	+	7.03381i	0.0802062	+	0.227609i
$956$	−0.693423	−	0.174403i	−0.0224269	−	0.00564060i
$957$	−21.5166	−	32.4719i	−0.695534	−	1.04967i
$958$	−6.02589	−	18.9420i	−0.194688	−	0.611989i
$959$	47.4241	+	40.6305i	1.53140	+	1.31203i
$960$	−30.8306	+	1.90157i	−0.995053	+	0.0613728i
$961$	−4.61673			−0.148927
$962$	1.17636	−	0.0725554i	0.0379274	−	0.00233928i
$963$	−0.688179	−	2.73619i	−0.0221762	−	0.0881724i
$964$	0.0576037	+	0.0435003i	0.00185529	+	0.00140105i
$965$	8.05986	+	7.34754i	0.259456	+	0.236526i
$966$	−128.018	+	36.4244i	−4.11893	+	1.17194i
$967$	7.44738	−	23.4104i	0.239492	−	0.752827i	−0.755703	−	0.654914i	$-0.772705\pi$
$967$	7.44738	−	23.4104i	0.239492	−	0.752827i	0.995195	−	0.0979131i	$-0.0312167\pi$
$968$	−11.7088	+	7.24979i	−0.376335	+	0.233017i
$969$	−10.3226	−	16.6715i	−0.331609	−	0.535567i
$970$	21.9026	+	6.23183i	0.703250	+	0.200092i
$971$	−21.7171	+	32.7744i	−0.696935	+	1.05178i	0.298318	+	0.954466i	$0.403574\pi$
$971$	−21.7171	+	32.7744i	−0.696935	+	1.05178i	−0.995254	+	0.0973146i	$0.968975\pi$
$972$	6.63510	−	6.04870i	0.212821	−	0.194012i
$973$	54.1519	+	26.9644i	1.73603	+	0.864440i
$974$	−1.06953	+	17.3405i	−0.0342699	+	0.555627i
$975$	32.7241	−	11.5315i	1.04801	−	0.369305i
$976$	39.0510	+	13.7611i	1.24999	+	0.440481i
$977$	−53.1316	+	16.9024i	−1.69983	+	0.540755i	−0.987019	−	0.160600i	$-0.948657\pi$
$977$	−53.1316	+	16.9024i	−1.69983	+	0.540755i	−0.712812	+	0.701356i	$0.752578\pi$
$978$	−3.69435	−	23.7994i	−0.118132	−	0.761022i
$979$	4.52404	+	11.6779i	0.144589	+	0.373227i
$980$	−0.967438	−	0.881936i	−0.0309037	−	0.0281724i
$981$	−72.6254	+	18.2660i	−2.31875	+	0.583189i
$982$	−8.55688	−	12.9136i	−0.273061	−	0.412090i
$983$	1.68542	+	1.11680i	0.0537565	+	0.0356203i	0.578956	−	0.815359i	$-0.303460\pi$
$983$	1.68542	+	1.11680i	0.0537565	+	0.0356203i	−0.525200	+	0.850979i	$0.676009\pi$
$984$	27.1074	−	14.5564i	0.864153	−	0.464040i
$985$	2.32082	−	0.738305i	0.0739474	−	0.0235244i
$986$	3.28770	+	4.08563i	0.104702	+	0.130113i
$987$	58.5706	+	10.9487i	1.86432	+	0.348502i
$988$	1.56428	+	0.840003i	0.0497665	+	0.0267241i
$989$	26.8135	+	49.9331i	0.852619	+	1.58778i
$990$	−20.5771	+	25.5713i	−0.653984	+	0.812708i
$991$	13.8830	+	0.427731i	0.441009	+	0.0135873i	0.250541	−	0.968106i	$-0.419392\pi$
$991$	13.8830	+	0.427731i	0.441009	+	0.0135873i	0.190468	+	0.981693i	$0.438999\pi$
$992$	1.96384	+	2.77424i	0.0623521	+	0.0880821i
$993$	30.9191	+	13.0869i	0.981188	+	0.415301i
$994$	5.19634	−	3.44322i	0.164818	−	0.109212i
$995$	−3.32749	+	6.19658i	−0.105489	+	0.196445i
$996$	0.298266	+	0.704680i	0.00945091	+	0.0223287i
$997$	−25.7819	−	13.8446i	−0.816522	−	0.438463i	0.0109707	−	0.999940i	$-0.496508\pi$
$997$	−25.7819	−	13.8446i	−0.816522	−	0.438463i	−0.827492	+	0.561477i	$0.810233\pi$
$998$	−25.8651	+	34.2509i	−0.818744	+	1.08419i
$999$	3.85404	−	5.44445i	0.121937	−	0.172255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.2.m.a.4.10	✓	1056
409.307	even	102	inner	409.2.m.a.307.10	yes	1056

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.2.m.a.4.10	✓	1056	1.1	even	1	trivial
409.2.m.a.307.10	yes	1056	409.307	even	102	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	409.m (of order \(102\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36768 + 0.169355i) q^{2} +(-0.738030 + 3.36995i) q^{3} +(-0.0977346 + 0.0245812i) q^{4} +(-0.477318 + 0.958584i) q^{5} +(0.438669 - 4.73399i) q^{6} +(-3.78786 + 2.18692i) q^{7} +(2.69963 - 1.04584i) q^{8} +(-8.08647 - 3.72037i) q^{9} +(0.490476 - 1.39187i) q^{10} +(2.48798 - 0.230545i) q^{11} +(-0.0107064 - 0.347502i) q^{12} +(-2.59897 - 0.240830i) q^{13} +(4.81020 - 3.63249i) q^{14} +(-2.87810 - 2.31600i) q^{15} +(-3.33753 + 1.79221i) q^{16} +(-0.129164 + 0.832090i) q^{17} +(11.6897 + 3.71877i) q^{18} +(5.38667 + 4.06783i) q^{19} +(0.0230873 - 0.105420i) q^{20} +(-4.57426 - 14.3789i) q^{21} +(-3.36371 + 0.736664i) q^{22} +(-0.981818 + 6.32498i) q^{23} +(1.53203 + 9.86947i) q^{24} +(2.32212 + 3.07499i) q^{25} +(3.59534 - 0.110771i) q^{26} +(12.2686 - 16.2462i) q^{27} +(0.316448 - 0.306848i) q^{28} +(-3.43180 + 2.94018i) q^{29} +(4.32854 + 2.68012i) q^{30} -5.96798i q^{31} +(-0.464854 + 0.329063i) q^{32} +(-1.05928 + 8.55452i) q^{33} +(0.0357363 - 1.15991i) q^{34} +(-0.288334 - 4.67483i) q^{35} +(0.881779 + 0.164833i) q^{36} +(0.327502 - 0.0100902i) q^{37} +(-8.05614 - 4.65121i) q^{38} +(2.72970 - 8.58065i) q^{39} +(-0.286054 + 3.08702i) q^{40} +(-1.02387 - 2.90553i) q^{41} +(8.69124 + 18.8910i) q^{42} +(7.06625 - 5.33619i) q^{43} +(-0.237495 + 0.0836899i) q^{44} +(7.42610 - 5.97576i) q^{45} +(0.271643 - 8.81680i) q^{46} +(-1.86821 + 3.47905i) q^{47} +(-3.57647 - 12.5700i) q^{48} +(6.06524 - 10.5053i) q^{49} +(-3.69668 - 3.81233i) q^{50} +(-2.70877 - 1.04938i) q^{51} +(0.259929 - 0.0403485i) q^{52} +(0.459043 + 0.795086i) q^{53} +(-14.0280 + 24.2973i) q^{54} +(-0.966561 + 2.49498i) q^{55} +(-7.93863 + 9.86537i) q^{56} +(-17.6839 + 15.1506i) q^{57} +(4.19566 - 4.60242i) q^{58} +(-11.5096 - 3.27476i) q^{59} +(0.338220 + 0.155606i) q^{60} +(-7.36327 - 8.07712i) q^{61} +(1.01071 + 8.16226i) q^{62} +(38.7665 - 3.59225i) q^{63} +(6.17920 - 5.63308i) q^{64} +(1.47139 - 2.37638i) q^{65} -11.8792i q^{66} +(2.92059 + 4.12579i) q^{67} +(-0.00782999 - 0.0844991i) q^{68} +(-20.5902 - 7.97670i) q^{69} +(1.18605 + 6.34483i) q^{70} +(1.03220 + 0.0636638i) q^{71} +(-25.7214 - 1.58644i) q^{72} +(0.0581817 + 0.0564168i) q^{73} +(-0.446208 + 0.0692642i) q^{74} +(-12.0763 + 5.55600i) q^{75} +(-0.626457 - 0.265156i) q^{76} +(-8.91993 + 6.31429i) q^{77} +(-2.28017 + 12.1979i) q^{78} +(-9.99491 - 4.97687i) q^{79} +(-0.124926 - 4.05475i) q^{80} +(28.3203 + 33.0557i) q^{81} +(1.89239 + 3.80042i) q^{82} +(-2.05234 + 0.795081i) q^{83} +(0.800514 + 1.29287i) q^{84} +(-0.735976 - 0.520986i) q^{85} +(-8.76064 + 8.49489i) q^{86} +(-7.37550 - 13.7349i) q^{87} +(6.47551 - 3.22442i) q^{88} +(1.37164 + 4.82082i) q^{89} +(-9.14448 + 9.43055i) q^{90} +(10.3712 - 4.77151i) q^{91} +(-0.0595182 - 0.642304i) q^{92} +(20.1118 + 4.40455i) q^{93} +(1.96592 - 5.07461i) q^{94} +(-6.47051 + 3.22193i) q^{95} +(-0.765850 - 1.80939i) q^{96} +(0.949924 + 15.4014i) q^{97} +(-6.51616 + 15.3950i) q^{98} +(-20.9767 - 7.39190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1056 q - 33 q^{2} - 31 q^{3} + 29 q^{4} - 22 q^{5} - 44 q^{6} - 57 q^{7} - 22 q^{8} + 2 q^{9} - 30 q^{10} + 17 q^{11} + 67 q^{12} - 34 q^{13} - 68 q^{14} - 32 q^{15} + 21 q^{16} - 27 q^{17} + 22 q^{18}+ \cdots - 229 q^{99}+O(q^{100}) \) 1056 * q - 33 * q^2 - 31 * q^3 + 29 * q^4 - 22 * q^5 - 44 * q^6 - 57 * q^7 - 22 * q^8 + 2 * q^9 - 30 * q^10 + 17 * q^11 + 67 * q^12 - 34 * q^13 - 68 * q^14 - 32 * q^15 + 21 * q^16 - 27 * q^17 + 22 * q^18 - 34 * q^19 - 51 * q^20 - 108 * q^21 - 22 * q^22 - 32 * q^23 + 87 * q^24 - 112 * q^25 - 64 * q^26 - 82 * q^27 - 75 * q^28 - 19 * q^29 - 22 * q^30 + 52 * q^32 - 43 * q^33 - 48 * q^34 - 113 * q^35 + 22 * q^36 - 10 * q^37 - 57 * q^38 + 41 * q^39 - 225 * q^40 - 288 * q^41 - 173 * q^42 + 68 * q^43 - 34 * q^44 - 42 * q^45 + 17 * q^46 - 34 * q^47 + 68 * q^48 + 369 * q^49 - 40 * q^50 + 56 * q^51 + 8 * q^52 + 104 * q^53 + 128 * q^54 + 102 * q^55 - 138 * q^56 - 55 * q^57 - 34 * q^58 - 34 * q^59 - 254 * q^60 - 68 * q^61 + 25 * q^62 - 34 * q^63 + 98 * q^64 - 34 * q^65 - 40 * q^67 - 116 * q^68 - 38 * q^69 - 17 * q^70 + 21 * q^71 - 26 * q^72 - 31 * q^73 + 203 * q^74 + 23 * q^75 - 101 * q^76 + 19 * q^77 - 102 * q^78 - 34 * q^79 + 443 * q^80 - 265 * q^81 - 50 * q^82 + 26 * q^83 - 459 * q^84 + 84 * q^85 + 136 * q^86 - 188 * q^87 + 170 * q^88 - 80 * q^89 + 613 * q^90 - 152 * q^91 + 18 * q^92 + 56 * q^93 - 34 * q^94 - 34 * q^95 + 13 * q^96 - 31 * q^97 - 293 * q^98 - 229 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more