LMFDB - Embedded newform 637.2.bl.b.53.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.14
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.b.625.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.00745244 + 0.00508099i) q^{2} +(-2.32094 - 2.15352i) q^{3} +(-0.730652 - 1.86167i) q^{4} +(2.27283 - 0.701076i) q^{5} +(-0.00635467 - 0.0278416i) q^{6} +(-1.04784 + 2.42941i) q^{7} +(0.00802814 - 0.0351736i) q^{8} +(0.524933 + 7.00475i) q^{9} +O(q^{10})$	\(q+(0.00745244 + 0.00508099i) q^{2} +(-2.32094 - 2.15352i) q^{3} +(-0.730652 - 1.86167i) q^{4} +(2.27283 - 0.701076i) q^{5} +(-0.00635467 - 0.0278416i) q^{6} +(-1.04784 + 2.42941i) q^{7} +(0.00802814 - 0.0351736i) q^{8} +(0.524933 + 7.00475i) q^{9} +(0.0205003 + 0.00632351i) q^{10} +(-0.443633 + 5.91987i) q^{11} +(-2.31334 + 5.89430i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(-0.0201528 + 0.0127810i) q^{14} +(-6.78489 - 3.26743i) q^{15} +(-2.93185 + 2.72036i) q^{16} +(3.33077 - 0.502032i) q^{17} +(-0.0316790 + 0.0548697i) q^{18} +(1.92716 + 3.33794i) q^{19} +(-2.96582 - 3.71903i) q^{20} +(7.66374 - 3.38198i) q^{21} +(-0.0333849 + 0.0418634i) q^{22} +(-1.91111 - 0.288054i) q^{23} +(-0.0943797 + 0.0643470i) q^{24} +(0.543070 - 0.370259i) q^{25} +(-0.00891898 - 0.00134432i) q^{26} +(7.94435 - 9.96191i) q^{27} +(5.28837 + 0.175674i) q^{28} +(-3.47129 - 4.35286i) q^{29} +(-0.0339622 - 0.0588243i) q^{30} +(-3.31108 + 5.73497i) q^{31} +(-0.107022 + 0.0161310i) q^{32} +(13.7782 - 12.7843i) q^{33} +(0.0273732 + 0.0131822i) q^{34} +(-0.678357 + 6.25626i) q^{35} +(12.6570 - 6.09529i) q^{36} +(-0.404808 + 1.03143i) q^{37} +(-0.00259798 + 0.0346676i) q^{38} +(3.02547 + 0.933234i) q^{39} +(-0.00641274 - 0.0855720i) q^{40} +(-1.30936 + 5.73668i) q^{41} +(0.0742974 + 0.0137354i) q^{42} +(-1.13741 - 4.98332i) q^{43} +(11.3450 - 3.49947i) q^{44} +(6.10395 + 15.5526i) q^{45} +(-0.0127788 - 0.0118570i) q^{46} +(0.460375 + 0.313878i) q^{47} +12.6630 q^{48} +(-4.80408 - 5.09125i) q^{49} +0.00592848 q^{50} +(-8.81164 - 6.00767i) q^{51} +(1.46604 + 1.36029i) q^{52} +(1.57254 + 4.00677i) q^{53} +(0.109821 - 0.0338753i) q^{54} +(3.14198 + 13.7659i) q^{55} +(0.0770389 + 0.0563598i) q^{56} +(2.71548 - 11.8973i) q^{57} +(-0.00375275 - 0.0500770i) q^{58} +(-7.46401 - 2.30234i) q^{59} +(-1.12549 + 15.0186i) q^{60} +(-4.20270 + 10.7083i) q^{61} +(-0.0538150 + 0.0259159i) q^{62} +(-17.5675 - 6.06456i) q^{63} +(7.20599 + 3.47022i) q^{64} +(-1.74357 + 1.61779i) q^{65} +(0.167638 - 0.0252674i) q^{66} +(-7.65560 + 13.2599i) q^{67} +(-3.36825 - 5.83398i) q^{68} +(3.81524 + 4.78416i) q^{69} +(-0.0368434 + 0.0431777i) q^{70} +(4.91424 - 6.16226i) q^{71} +(0.250596 + 0.0377713i) q^{72} +(10.6820 - 7.28285i) q^{73} +(-0.00825751 + 0.00562988i) q^{74} +(-2.05779 - 0.310162i) q^{75} +(4.80606 - 6.02661i) q^{76} +(-13.9169 - 7.28083i) q^{77} +(0.0178054 + 0.0223272i) q^{78} +(-0.935764 - 1.62079i) q^{79} +(-4.75643 + 8.23837i) q^{80} +(-19.0537 + 2.87188i) q^{81} +(-0.0389059 + 0.0360994i) q^{82} +(9.10579 + 4.38512i) q^{83} +(-11.8957 - 11.7963i) q^{84} +(7.21831 - 3.47616i) q^{85} +(0.0168437 - 0.0429170i) q^{86} +(-1.31730 + 17.5782i) q^{87} +(0.204662 + 0.0631297i) q^{88} +(-0.516222 - 6.88850i) q^{89} +(-0.0335333 + 0.146919i) q^{90} +(-0.110013 - 2.64346i) q^{91} +(0.860096 + 3.76833i) q^{92} +(20.0352 - 6.18003i) q^{93} +(0.00183611 + 0.00467832i) q^{94} +(6.72026 + 6.23549i) q^{95} +(0.283130 + 0.193035i) q^{96} +4.27784 q^{97} +(-0.00993349 - 0.0623517i) q^{98} -41.7001 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

Coefficient data

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

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

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

$2$	0.00745244	+	0.00508099i	0.00526967	+	0.00359280i	0.565952	−	0.824438i	$-0.308509\pi$
$2$	0.00745244	+	0.00508099i	0.00526967	+	0.00359280i	−0.560682	+	0.828031i	$0.689461\pi$
$3$	−2.32094	−	2.15352i	−1.33999	−	1.24333i	−0.945978	−	0.324230i	$-0.894895\pi$
$3$	−2.32094	−	2.15352i	−1.33999	−	1.24333i	−0.394016	−	0.919103i	$-0.628915\pi$
$4$	−0.730652	−	1.86167i	−0.365326	−	0.930836i
$5$	2.27283	−	0.701076i	1.01644	−	0.313531i	0.258611	−	0.965982i	$-0.416735\pi$
$5$	2.27283	−	0.701076i	1.01644	−	0.313531i	0.757831	+	0.652451i	$0.226259\pi$
$6$	−0.00635467	−	0.0278416i	−0.00259428	−	0.0113663i
$7$	−1.04784	+	2.42941i	−0.396045	+	0.918231i
$7$	−1.04784	+	2.42941i	−0.396045	+	0.918231i
$8$	0.00802814	−	0.0351736i	0.00283838	−	0.0124357i
$9$	0.524933	+	7.00475i	0.174978	+	2.33492i
$10$	0.0205003	+	0.00632351i	0.00648277	+	0.00199967i
$11$	−0.443633	+	5.91987i	−0.133760	+	1.78491i	0.378026	+	0.925795i	$0.376603\pi$
$11$	−0.443633	+	5.91987i	−0.133760	+	1.78491i	−0.511786	+	0.859113i	$0.671016\pi$
$12$	−2.31334	+	5.89430i	−0.667804	+	1.70154i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$14$	−0.0201528	+	0.0127810i	−0.00538605	+	0.00341586i
$15$	−6.78489	−	3.26743i	−1.75185	−	0.843647i
$16$	−2.93185	+	2.72036i	−0.732962	+	0.680090i
$17$	3.33077	−	0.502032i	0.807829	−	0.121761i	0.267874	−	0.963454i	$-0.413679\pi$
$17$	3.33077	−	0.502032i	0.807829	−	0.121761i	0.539956	+	0.841693i	$0.318441\pi$
$18$	−0.0316790	+	0.0548697i	−0.00746682	+	0.0129329i
$19$	1.92716	+	3.33794i	0.442120	+	0.765775i	0.997847	−	0.0655904i	$-0.0208931\pi$
$19$	1.92716	+	3.33794i	0.442120	+	0.765775i	−0.555726	+	0.831365i	$0.687560\pi$
$20$	−2.96582	−	3.71903i	−0.663179	−	0.831600i
$21$	7.66374	−	3.38198i	1.67237	−	0.738009i
$22$	−0.0333849	+	0.0418634i	−0.00711769	+	0.00892530i
$23$	−1.91111	−	0.288054i	−0.398494	−	0.0600633i	−0.0532618	−	0.998581i	$-0.516962\pi$
$23$	−1.91111	−	0.288054i	−0.398494	−	0.0600633i	−0.345232	+	0.938517i	$0.612200\pi$
$24$	−0.0943797	+	0.0643470i	−0.0192652	+	0.0131348i
$25$	0.543070	−	0.370259i	0.108614	−	0.0740518i
$26$	−0.00891898	−	0.00134432i	−0.00174916	−	0.000263643i
$27$	7.94435	−	9.96191i	1.52889	−	1.91717i
$28$	5.28837	+	0.175674i	0.999408	+	0.0331992i
$29$	−3.47129	−	4.35286i	−0.644603	−	0.808306i	0.346968	−	0.937877i	$-0.387211\pi$
$29$	−3.47129	−	4.35286i	−0.644603	−	0.808306i	−0.991570	+	0.129571i	$0.958640\pi$
$30$	−0.0339622	−	0.0588243i	−0.00620062	−	0.0107398i
$31$	−3.31108	+	5.73497i	−0.594688	+	1.03003i	0.398903	+	0.916993i	$0.369391\pi$
$31$	−3.31108	+	5.73497i	−0.594688	+	1.03003i	−0.993591	+	0.113037i	$0.963942\pi$
$32$	−0.107022	+	0.0161310i	−0.0189190	+	0.00285158i
$33$	13.7782	−	12.7843i	2.39847	−	2.22546i
$34$	0.0273732	+	0.0131822i	0.00469446	+	0.00226073i
$35$	−0.678357	+	6.25626i	−0.114663	+	1.05750i
$36$	12.6570	−	6.09529i	2.10950	−	1.01588i
$37$	−0.404808	+	1.03143i	−0.0665500	+	0.169567i	−0.960280	−	0.279039i	$-0.909984\pi$
$37$	−0.404808	+	1.03143i	−0.0665500	+	0.169567i	0.893730	+	0.448606i	$0.148079\pi$
$38$	−0.00259798	+	0.0346676i	−0.000421448	+	0.00562383i
$39$	3.02547	+	0.933234i	0.484463	+	0.149437i
$40$	−0.00641274	−	0.0855720i	−0.00101394	−	0.0135301i
$41$	−1.30936	+	5.73668i	−0.204488	+	0.895919i	0.763676	+	0.645600i	$0.223393\pi$
$41$	−1.30936	+	5.73668i	−0.204488	+	0.895919i	−0.968163	+	0.250319i	$0.919465\pi$
$42$	0.0742974	+	0.0137354i	0.0114643	+	0.00211942i
$43$	−1.13741	−	4.98332i	−0.173453	−	0.759949i	−0.984560	−	0.175050i	$-0.943991\pi$
$43$	−1.13741	−	4.98332i	−0.173453	−	0.759949i	0.811106	−	0.584899i	$-0.198866\pi$
$44$	11.3450	−	3.49947i	1.71032	−	0.527565i
$45$	6.10395	+	15.5526i	0.909923	+	2.31845i
$46$	−0.0127788	−	0.0118570i	−0.00188414	−	0.00174822i
$47$	0.460375	+	0.313878i	0.0671526	+	0.0457839i	0.596431	−	0.802664i	$-0.296585\pi$
$47$	0.460375	+	0.313878i	0.0671526	+	0.0457839i	−0.529278	+	0.848448i	$0.677537\pi$
$48$	12.6630			1.82774
$49$	−4.80408	−	5.09125i	−0.686296	−	0.727322i
$50$	0.00592848			0.000838414
$51$	−8.81164	−	6.00767i	−1.23388	−	0.841243i
$52$	1.46604	+	1.36029i	0.203304	+	0.188638i
$53$	1.57254	+	4.00677i	0.216005	+	0.550372i	0.997271	−	0.0738260i	$-0.0235209\pi$
$53$	1.57254	+	4.00677i	0.216005	+	0.550372i	−0.781266	+	0.624198i	$0.785426\pi$
$54$	0.109821	−	0.0338753i	0.0149448	−	0.00460985i
$55$	3.14198	+	13.7659i	0.423664	+	1.85619i
$56$	0.0770389	+	0.0563598i	0.0102948	+	0.00753140i
$57$	2.71548	−	11.8973i	0.359675	−	1.57584i
$58$	−0.00375275	−	0.0500770i	−0.000492761	−	0.00657544i
$59$	−7.46401	−	2.30234i	−0.971731	−	0.299739i	−0.232055	−	0.972703i	$-0.574545\pi$
$59$	−7.46401	−	2.30234i	−0.971731	−	0.299739i	−0.739676	+	0.672963i	$0.765021\pi$
$60$	−1.12549	+	15.0186i	−0.145300	+	1.93889i
$61$	−4.20270	+	10.7083i	−0.538101	+	1.37106i	0.360692	+	0.932685i	$0.382541\pi$
$61$	−4.20270	+	10.7083i	−0.538101	+	1.37106i	−0.898793	+	0.438374i	$0.855555\pi$
$62$	−0.0538150	+	0.0259159i	−0.00683451	+	0.00329132i
$63$	−17.5675	−	6.06456i	−2.21329	−	0.764062i
$64$	7.20599	+	3.47022i	0.900749	+	0.433778i
$65$	−1.74357	+	1.61779i	−0.216263	+	0.200663i
$66$	0.167638	−	0.0252674i	0.0206348	−	0.00311020i
$67$	−7.65560	+	13.2599i	−0.935281	+	1.61995i	−0.161149	+	0.986930i	$0.551520\pi$
$67$	−7.65560	+	13.2599i	−0.935281	+	1.61995i	−0.774132	+	0.633024i	$0.781813\pi$
$68$	−3.36825	−	5.83398i	−0.408460	−	0.707474i
$69$	3.81524	+	4.78416i	0.459301	+	0.575946i
$70$	−0.0368434	+	0.0431777i	−0.00440363	+	0.00516072i
$71$	4.91424	−	6.16226i	0.583213	−	0.731326i	−0.399444	−	0.916758i	$-0.630797\pi$
$71$	4.91424	−	6.16226i	0.583213	−	0.731326i	0.982657	+	0.185432i	$0.0593683\pi$
$72$	0.250596	+	0.0377713i	0.0295331	+	0.00445139i
$73$	10.6820	−	7.28285i	1.25023	−	0.852393i	0.256759	−	0.966475i	$-0.417345\pi$
$73$	10.6820	−	7.28285i	1.25023	−	0.852393i	0.993471	+	0.114082i	$0.0363928\pi$
$74$	−0.00825751	+	0.00562988i	−0.000959916	+	0.000654460i
$75$	−2.05779	−	0.310162i	−0.237613	−	0.0358144i
$76$	4.80606	−	6.02661i	0.551293	−	0.691299i
$77$	−13.9169	−	7.28083i	−1.58598	−	0.829727i
$78$	0.0178054	+	0.0223272i	0.00201606	+	0.00252806i
$79$	−0.935764	−	1.62079i	−0.105282	−	0.182353i	0.808572	−	0.588398i	$-0.200241\pi$
$79$	−0.935764	−	1.62079i	−0.105282	−	0.182353i	−0.913853	+	0.406045i	$0.866908\pi$
$80$	−4.75643	+	8.23837i	−0.531785	+	0.921078i
$81$	−19.0537	+	2.87188i	−2.11708	+	0.319098i
$82$	−0.0389059	+	0.0360994i	−0.00429644	+	0.00398652i
$83$	9.10579	+	4.38512i	0.999490	+	0.481329i	0.860765	−	0.509002i	$-0.169985\pi$
$83$	9.10579	+	4.38512i	0.999490	+	0.481329i	0.138725	+	0.990331i	$0.455700\pi$
$84$	−11.8957	−	11.7963i	−1.29792	−	1.28708i
$85$	7.21831	−	3.47616i	0.782936	−	0.377042i
$86$	0.0168437	−	0.0429170i	0.00181630	−	0.00462786i
$87$	−1.31730	+	17.5782i	−0.141230	+	1.88458i
$88$	0.204662	+	0.0631297i	0.0218170	+	0.00672965i
$89$	−0.516222	−	6.88850i	−0.0547194	−	0.730180i	−0.955328	−	0.295548i	$-0.904498\pi$
$89$	−0.516222	−	6.88850i	−0.0547194	−	0.730180i	0.900608	−	0.434631i	$-0.143121\pi$
$90$	−0.0335333	+	0.146919i	−0.00353472	+	0.0154866i
$91$	−0.110013	−	2.64346i	−0.0115325	−	0.277110i
$92$	0.860096	+	3.76833i	0.0896712	+	0.392875i
$93$	20.0352	−	6.18003i	2.07755	−	0.640839i
$94$	0.00183611	+	0.00467832i	0.000189380	+	0.000482532i
$95$	6.72026	+	6.23549i	0.689484	+	0.639747i
$96$	0.283130	+	0.193035i	0.0288968	+	0.0197015i
$97$	4.27784			0.434349			0.217174	−	0.976133i	$-0.430316\pi$
$97$	4.27784			0.434349			0.217174	+	0.976133i	$0.430316\pi$
$98$	−0.00993349	−	0.0623517i	−0.00100343	−	0.00629848i
$99$	−41.7001			−4.19102
$100$	−1.08610	−	0.740488i	−0.108610	−	0.0740488i
$101$	2.58299	+	2.39667i	0.257017	+	0.238477i	0.798148	−	0.602461i	$-0.205813\pi$
$101$	2.58299	+	2.39667i	0.257017	+	0.238477i	−0.541131	+	0.840938i	$0.682004\pi$
$102$	−0.0351433	−	0.0895437i	−0.00347971	−	0.00886615i
$103$	−0.850421	+	0.262320i	−0.0837944	+	0.0258472i	−0.336369	−	0.941730i	$-0.609199\pi$
$103$	−0.850421	+	0.262320i	−0.0837944	+	0.0258472i	0.252575	+	0.967577i	$0.418723\pi$
$104$	0.00802814	+	0.0351736i	0.000787224	+	0.00344905i
$105$	15.0474	−	13.0595i	1.46847	−	1.27448i
$106$	−0.00863908	+	0.0378503i	−0.000839102	+	0.00367635i
$107$	0.637242	+	8.50340i	0.0616045	+	0.822054i	0.939357	+	0.342940i	$0.111423\pi$
$107$	0.637242	+	8.50340i	0.0616045	+	0.822054i	−0.877753	+	0.479114i	$0.840958\pi$
$108$	−24.3504	−	7.51109i	−2.34311	−	0.722755i
$109$	0.952103	−	12.7049i	0.0911949	−	1.21691i	−0.744464	−	0.667663i	$-0.767295\pi$
$109$	0.952103	−	12.7049i	0.0911949	−	1.21691i	0.835659	−	0.549249i	$-0.185086\pi$
$110$	−0.0465290	+	0.118554i	−0.00443636	+	0.0113037i
$111$	3.16075	−	1.52213i	0.300005	−	0.144475i
$112$	−3.53677	−	9.97316i	−0.334193	−	0.942375i
$113$	−12.8463	−	6.18644i	−1.20848	−	0.581972i	−0.282396	−	0.959298i	$-0.591129\pi$
$113$	−12.8463	−	6.18644i	−1.20848	−	0.581972i	−0.926080	+	0.377326i	$0.876844\pi$
$114$	0.0806871	−	0.0748667i	0.00755704	−	0.00701191i
$115$	−4.54558	+	0.685136i	−0.423878	+	0.0638893i
$116$	−5.56729	+	9.64283i	−0.516910	+	0.895314i
$117$	−3.51220	−	6.08330i	−0.324703	−	0.562401i
$118$	−0.0439269	−	0.0550826i	−0.00404380	−	0.00507076i
$119$	−2.27046	+	8.61785i	−0.208133	+	0.789997i
$120$	−0.169397	+	0.212417i	−0.0154638	+	0.0193910i
$121$	−23.9709	−	3.61303i	−2.17917	−	0.328458i
$122$	−0.0857292	+	0.0584492i	−0.00776156	+	0.00529174i
$123$	15.3930	−	10.4948i	1.38794	−	0.946280i
$124$	13.0959	+	1.97389i	1.17604	+	0.177260i
$125$	−6.44014	+	8.07567i	−0.576023	+	0.722310i
$126$	−0.100107	−	0.134456i	−0.00891820	−	0.0119783i
$127$	3.20384	+	4.01749i	0.284295	+	0.356494i	0.903389	−	0.428822i	$-0.141071\pi$
$127$	3.20384	+	4.01749i	0.284295	+	0.356494i	−0.619094	+	0.785317i	$0.712500\pi$
$128$	0.144301	+	0.249936i	0.0127545	+	0.0220915i
$129$	−8.09180	+	14.0154i	−0.712443	+	1.23399i
$130$	−0.0212138	+	0.00319747i	−0.00186057	+	0.000280437i
$131$	−16.5451	+	15.3517i	−1.44556	+	1.34128i	−0.609301	+	0.792939i	$0.708550\pi$
$131$	−16.5451	+	15.3517i	−1.44556	+	1.34128i	−0.836255	+	0.548341i	$0.815259\pi$
$132$	−33.8672	−	16.3096i	−2.94776	−	1.41957i
$133$	−10.1286	+	1.18425i	−0.878258	+	0.102687i
$134$	−0.124426	+	0.0599206i	−0.0107488	+	0.00517635i
$135$	11.0721	−	28.2114i	0.952938	−	2.42805i
$136$	0.00908159	−	0.121185i	0.000778740	−	0.0103916i
$137$	18.4336	+	5.68600i	1.57489	+	0.485788i	0.954425	−	0.298449i	$-0.0964694\pi$
$137$	18.4336	+	5.68600i	1.57489	+	0.485788i	0.620461	+	0.784237i	$0.286946\pi$
$138$	0.00412460	+	0.0550389i	0.000351109	+	0.00468522i
$139$	3.29491	−	14.4359i	0.279470	−	1.22444i	−0.618995	−	0.785395i	$-0.712460\pi$
$139$	3.29491	−	14.4359i	0.279470	−	1.22444i	0.898465	−	0.439045i	$-0.144683\pi$
$140$	12.1427	−	3.30827i	1.02625	−	0.279600i
$141$	−0.392560	−	1.71992i	−0.0330595	−	0.144843i
$142$	0.0679335	−	0.0209547i	0.00570085	−	0.00175848i
$143$	−2.16884	−	5.52610i	−0.181367	−	0.462116i
$144$	−20.5945	−	19.1089i	−1.71621	−	1.59241i
$145$	−10.9414	−	7.45969i	−0.908630	−	0.619493i
$146$	0.116611			0.00965078
$147$	0.185866	+	22.1621i	0.0153299	+	1.82790i
$148$	2.21597			0.182151
$149$	11.0747	+	7.55063i	0.907279	+	0.618572i	0.924459	−	0.381280i	$-0.124517\pi$
$149$	11.0747	+	7.55063i	0.907279	+	0.618572i	−0.0171809	+	0.999852i	$0.505469\pi$
$150$	−0.0137596	−	0.0127671i	−0.00112347	−	0.00104243i
$151$	−4.62766	−	11.7911i	−0.376594	−	0.959546i	−0.986009	−	0.166694i	$-0.946691\pi$
$151$	−4.62766	−	11.7911i	−0.376594	−	0.959546i	0.609415	−	0.792852i	$-0.291404\pi$
$152$	0.132879	−	0.0409876i	0.0107779	−	0.00332454i
$153$	5.26504	+	23.0677i	0.425653	+	1.86491i
$154$	−0.0667214	−	0.124972i	−0.00537656	−	0.0100705i
$155$	−3.50489	+	15.3559i	−0.281520	+	1.23342i
$156$	−0.473191	−	6.31430i	−0.0378856	−	0.505549i
$157$	21.6114	+	6.66624i	1.72478	+	0.532024i	0.989347	−	0.145574i	$-0.0465030\pi$
$157$	21.6114	+	6.66624i	1.72478	+	0.532024i	0.735432	+	0.677598i	$0.236979\pi$
$158$	0.00126149	−	0.0168335i	0.000100359	−	0.00133920i
$159$	4.97888	−	12.6860i	0.394850	−	1.00606i
$160$	−0.231934	+	0.111694i	−0.0183360	+	0.00883015i
$161$	2.70233	−	4.34104i	0.212974	−	0.342122i
$162$	−0.156588	−	0.0754090i	−0.0123028	−	0.00592469i
$163$	0.813945	−	0.755230i	0.0637531	−	0.0591542i	−0.647653	−	0.761936i	$-0.724249\pi$
$163$	0.813945	−	0.755230i	0.0637531	−	0.0591542i	0.711406	+	0.702781i	$0.248059\pi$
$164$	11.6365	−	1.75392i	0.908658	−	0.136958i
$165$	22.3528	−	38.7161i	1.74016	−	3.01404i
$166$	0.0455796	+	0.0789462i	0.00353767	+	0.00612742i
$167$	3.81624	+	4.78541i	0.295309	+	0.370306i	0.907246	−	0.420601i	$-0.138181\pi$
$167$	3.81624	+	4.78541i	0.295309	+	0.370306i	−0.611937	+	0.790907i	$0.709609\pi$
$168$	−0.0574308	−	0.296712i	−0.00443088	−	0.0228919i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	0.0714564	+	0.0107703i	0.00548045	+	0.000826046i
$171$	−22.3698	+	15.2515i	−1.71066	+	1.16631i
$172$	−8.44625	+	5.75855i	−0.644020	+	0.439086i
$173$	2.22643	+	0.335580i	0.169272	+	0.0255137i	0.233131	−	0.972445i	$-0.425103\pi$
$173$	2.22643	+	0.335580i	0.169272	+	0.0255137i	−0.0638592	+	0.997959i	$0.520341\pi$
$174$	−0.0991318	+	0.124307i	−0.00751516	+	0.00942372i
$175$	0.330462	+	1.70731i	0.0249806	+	0.129061i
$176$	−14.8035	−	18.5630i	−1.11586	−	1.39924i
$177$	12.3654	+	21.4175i	0.929439	+	1.60983i
$178$	0.0311533	−	0.0539591i	0.00233504	−	0.00404440i
$179$	−21.1462	+	3.18727i	−1.58054	+	0.238228i	−0.879854	−	0.475244i	$-0.842360\pi$
$179$	−21.1462	+	3.18727i	−1.58054	+	0.238228i	−0.700684	+	0.713472i	$0.747122\pi$
$180$	24.4940	−	22.7271i	1.82567	−	1.69398i
$181$	14.0330	+	6.75794i	1.04307	+	0.502314i	0.875334	−	0.483519i	$-0.160642\pi$
$181$	14.0330	+	6.75794i	1.04307	+	0.502314i	0.167731	+	0.985833i	$0.446356\pi$
$182$	0.0126115	−	0.0202592i	0.000934829	−	0.00150171i
$183$	32.8147	−	15.8027i	2.42574	−	1.16817i
$184$	−0.0254745	+	0.0649081i	−0.00187801	+	0.00478509i
$185$	−0.196947	+	2.62808i	−0.0144799	+	0.193220i
$186$	0.180712	+	0.0557421i	0.0132504	+	0.00408721i
$187$	1.49433	+	19.9404i	0.109276	+	1.45819i
$188$	0.247964	−	1.08640i	0.0180847	−	0.0792341i
$189$	15.8772	+	29.7386i	1.15489	+	2.16316i
$190$	0.0183999	+	0.0806152i	0.00133487	+	0.00584844i
$191$	−2.98741	+	0.921493i	−0.216161	+	0.0666769i	−0.400944	−	0.916102i	$-0.631318\pi$
$191$	−2.98741	+	0.921493i	−0.216161	+	0.0666769i	0.184783	+	0.982779i	$0.440842\pi$
$192$	−9.25148	−	23.5724i	−0.667668	−	1.70119i
$193$	−1.27942	−	1.18713i	−0.0920949	−	0.0854516i	0.632782	−	0.774330i	$-0.281913\pi$
$193$	−1.27942	−	1.18713i	−0.0920949	−	0.0854516i	−0.724877	+	0.688878i	$0.758103\pi$
$194$	0.0318803	+	0.0217356i	0.00228888	+	0.00156053i
$195$	7.53066			0.539282
$196$	−5.96813	+	12.6635i	−0.426295	+	0.904539i
$197$	−18.4986			−1.31797			−0.658984	−	0.752157i	$-0.729013\pi$
$197$	−18.4986			−1.31797			−0.658984	+	0.752157i	$0.729013\pi$
$198$	−0.310767	−	0.211878i	−0.0220853	−	0.0150575i
$199$	13.2490	+	12.2933i	0.939198	+	0.871448i	0.991882	−	0.127163i	$-0.0405871\pi$
$199$	13.2490	+	12.2933i	0.939198	+	0.871448i	−0.0526839	+	0.998611i	$0.516778\pi$
$200$	−0.00866349	−	0.0220742i	−0.000612601	−	0.00156088i
$201$	46.3236	−	14.2889i	3.26741	−	1.00786i
$202$	0.00707216	+	0.0309852i	0.000497596	+	0.00218011i
$203$	14.2122	−	3.87210i	0.997503	−	0.271768i
$204$	−4.74607	+	20.7939i	−0.332292	+	1.45586i
$205$	1.04589	+	13.9565i	0.0730484	+	0.974763i
$206$	−0.00767055	−	0.00236605i	−0.000534433	−	0.000164851i
$207$	1.01454	−	13.5381i	0.0705152	−	0.940960i
$208$	1.46119	−	3.72304i	0.101315	−	0.258146i
$209$	−20.6151	+	9.92771i	−1.42598	+	0.686714i
$210$	0.178495	−	0.0208699i	0.0123173	−	0.00144016i
$211$	−7.16004	−	3.44810i	−0.492918	−	0.237377i	0.170876	−	0.985293i	$-0.445340\pi$
$211$	−7.16004	−	3.44810i	−0.492918	−	0.237377i	−0.663793	+	0.747916i	$0.731055\pi$
$212$	6.31031	−	5.85511i	0.433394	−	0.402131i
$213$	−24.6762	+	3.71934i	−1.69078	+	0.254845i
$214$	−0.0384567	+	0.0666089i	−0.00262884	+	0.00455329i
$215$	−6.07883	−	10.5288i	−0.414573	−	0.718061i
$216$	−0.286618	−	0.359407i	−0.0195019	−	0.0244546i
$217$	−10.4631	−	14.0533i	−0.710282	−	0.954000i
$218$	0.0716491	−	0.0898451i	0.00485269	−	0.00608508i
$219$	−40.4760	−	6.10077i	−2.73511	−	0.412252i
$220$	23.3319	−	15.9074i	1.57304	−	1.07248i
$221$	−2.78309	+	1.89748i	−0.187211	+	0.127638i
$222$	0.0312892	+	0.00471609i	0.00209999	+	0.000316523i
$223$	11.1535	−	13.9860i	0.746892	−	0.936572i	−0.252628	−	0.967563i	$-0.581295\pi$
$223$	11.1535	−	13.9860i	0.746892	−	0.936572i	0.999520	+	0.0309910i	$0.00986632\pi$
$224$	0.0729528	−	0.276903i	0.00487436	−	0.0185013i
$225$	2.87865	+	3.60971i	0.191910	+	0.240647i
$226$	−0.0643029	−	0.111376i	−0.00427737	−	0.00740862i
$227$	−2.45937	+	4.25976i	−0.163234	+	0.282730i	−0.936027	−	0.351928i	$-0.885526\pi$
$227$	−2.45937	+	4.25976i	−0.163234	+	0.282730i	0.772792	+	0.634659i	$0.218859\pi$
$228$	−24.1330	+	3.63746i	−1.59824	+	0.240897i
$229$	−6.61669	+	6.13939i	−0.437243	+	0.405703i	−0.867841	−	0.496841i	$-0.834493\pi$
$229$	−6.61669	+	6.13939i	−0.437243	+	0.405703i	0.430598	+	0.902544i	$0.358303\pi$
$230$	−0.0373569	−	0.0179901i	−0.00246324	−	0.00118623i
$231$	16.6210	+	46.8687i	1.09358	+	3.08374i
$232$	−0.180974	+	0.0871524i	−0.0118815	+	0.00572183i
$233$	−2.93698	+	7.48330i	−0.192408	+	0.490248i	−0.994224	−	0.107323i	$-0.965772\pi$
$233$	−2.93698	+	7.48330i	−0.192408	+	0.490248i	0.801816	+	0.597571i	$0.203867\pi$
$234$	0.00473475	−	0.0631809i	0.000309520	−	0.00413026i
$235$	1.26641	+	0.390635i	0.0826114	+	0.0254822i
$236$	1.16739	+	15.5777i	0.0759906	+	1.01402i
$237$	−1.31855	+	5.77694i	−0.0856490	+	0.375253i
$238$	−0.0607076	+	0.0526878i	−0.00393509	+	0.00341525i
$239$	4.04351	+	17.7158i	0.261553	+	1.14594i	0.919567	+	0.392934i	$0.128540\pi$
$239$	4.04351	+	17.7158i	0.261553	+	1.14594i	−0.658014	+	0.753006i	$0.728603\pi$
$240$	28.7809	−	8.87772i	1.85780	−	0.573054i
$241$	0.140946	+	0.359124i	0.00907911	+	0.0231332i	0.935341	−	0.353746i	$-0.115092\pi$
$241$	0.140946	+	0.359124i	0.00907911	+	0.0231332i	−0.926262	+	0.376879i	$0.876997\pi$
$242$	−0.160284	−	0.148722i	−0.0103034	−	0.00956020i
$243$	18.8239	+	12.8339i	1.20755	+	0.823296i
$244$	23.0061			1.47281
$245$	−14.4882	−	8.20355i	−0.925618	−	0.524105i
$246$	0.168039			0.0107138
$247$	−3.18459	−	2.17121i	−0.202630	−	0.138151i
$248$	0.175137	+	0.162504i	0.0111212	+	0.0103190i
$249$	−11.6906	−	29.7871i	−0.740859	−	1.88768i
$250$	−0.0890272	+	0.0274612i	−0.00563057	+	0.00173680i
$251$	1.65885	+	7.26791i	0.104706	+	0.458747i	0.999914	+	0.0130986i	$0.00416954\pi$
$251$	1.65885	+	7.26791i	0.104706	+	0.458747i	−0.895208	+	0.445648i	$0.852973\pi$
$252$	1.54549	+	37.1359i	0.0973568	+	2.33934i
$253$	2.55307	−	11.1857i	0.160510	−	0.703241i
$254$	0.00346362	+	0.0462188i	0.000217327	+	0.00290002i
$255$	−24.2392	−	7.47681i	−1.51792	−	0.468216i
$256$	1.19520	−	15.9488i	0.0746997	−	0.996798i
$257$	5.82445	−	14.8405i	0.363319	−	0.925722i	−0.625982	−	0.779837i	$-0.715302\pi$
$257$	5.82445	−	14.8405i	0.363319	−	0.925722i	0.989302	−	0.145885i	$-0.0466030\pi$
$258$	−0.131516	+	0.0633346i	−0.00818781	+	0.00394304i
$259$	−2.08160	−	2.06422i	−0.129345	−	0.128264i
$260$	4.28574	+	2.06390i	0.265790	+	0.127998i
$261$	28.6685	−	26.6005i	1.77454	−	1.64653i
$262$	−0.201303	+	0.0303416i	−0.0124366	+	0.00187451i
$263$	−6.95319	+	12.0433i	−0.428752	+	0.742621i	−0.996763	−	0.0804007i	$-0.974380\pi$
$263$	−6.95319	+	12.0433i	−0.428752	+	0.742621i	0.568010	+	0.823021i	$0.307713\pi$
$264$	−0.339056	−	0.587262i	−0.0208675	−	0.0361435i
$265$	6.38318	+	8.00425i	0.392116	+	0.491697i
$266$	−0.0814997	−	0.0426376i	−0.00499707	−	0.00261428i
$267$	−13.6364	+	17.0995i	−0.834533	+	1.04647i
$268$	30.2792	+	4.56385i	1.84959	+	0.278781i
$269$	6.26942	−	4.27442i	0.382253	−	0.260616i	−0.356915	−	0.934137i	$-0.616171\pi$
$269$	6.26942	−	4.27442i	0.382253	−	0.260616i	0.739168	+	0.673521i	$0.235219\pi$
$270$	0.225856	−	0.153986i	0.0137452	−	0.00937129i
$271$	−9.02358	−	1.36009i	−0.548144	−	0.0826194i	−0.130869	−	0.991400i	$-0.541777\pi$
$271$	−9.02358	−	1.36009i	−0.548144	−	0.0826194i	−0.417275	+	0.908780i	$0.637015\pi$
$272$	−8.39960	+	10.5328i	−0.509300	+	0.638643i
$273$	−5.43741	+	6.37223i	−0.329087	+	0.385665i
$274$	0.108485	+	0.136035i	0.00655379	+	0.00821820i
$275$	1.95096	+	3.37916i	0.117647	+	0.203771i
$276$	6.11893	−	10.5983i	0.368316	−	0.637942i
$277$	−19.2204	+	2.89702i	−1.15484	+	0.174065i	−0.698414	−	0.715694i	$-0.746110\pi$
$277$	−19.2204	+	2.89702i	−1.15484	+	0.174065i	−0.456431	+	0.889759i	$0.650872\pi$
$278$	0.0979039	−	0.0908416i	0.00587189	−	0.00544831i
$279$	−41.9101	−	20.1828i	−2.50909	−	1.20832i
$280$	0.214609	+	0.0740864i	0.0128254	+	0.00442751i
$281$	16.5258	−	7.95840i	0.985846	−	0.474758i	0.129734	−	0.991549i	$-0.458588\pi$
$281$	16.5258	−	7.95840i	0.985846	−	0.474758i	0.856112	+	0.516791i	$0.172873\pi$
$282$	0.00581335	−	0.0148122i	0.000346180	−	0.000882052i
$283$	2.34906	−	31.3461i	0.139637	−	1.86333i	−0.285731	−	0.958310i	$-0.592236\pi$
$283$	2.34906	−	31.3461i	0.139637	−	1.86333i	0.425368	−	0.905020i	$-0.360145\pi$
$284$	−15.0627	−	4.64623i	−0.893807	−	0.275703i
$285$	−2.16908	−	28.9444i	−0.128485	−	1.71452i
$286$	0.0119149	−	0.0522028i	0.000704546	−	0.00308682i
$287$	−12.5648	−	9.19208i	−0.741674	−	0.542591i
$288$	−0.169173	−	0.741194i	−0.00996860	−	0.0436753i
$289$	−5.40277	+	1.66653i	−0.317810	+	0.0980314i
$290$	−0.0436372	−	0.111186i	−0.00256246	−	0.00652905i
$291$	−9.92860	−	9.21240i	−0.582025	−	0.540040i
$292$	−21.3631	−	14.5651i	−1.25018	−	0.852358i
$293$	−14.9633			−0.874166			−0.437083	−	0.899421i	$-0.643988\pi$
$293$	−14.9633			−0.874166			−0.437083	+	0.899421i	$0.643988\pi$
$294$	−0.111220	+	0.166106i	−0.00648651	+	0.00968753i
$295$	−18.5786			−1.08169
$296$	0.0330294	+	0.0225191i	0.00191979	+	0.00130889i
$297$	55.4488	+	51.4490i	3.21747	+	2.98537i
$298$	0.0441692	+	0.112541i	0.00255865	+	0.00651934i
$299$	1.84683	−	0.569672i	0.106805	−	0.0329450i
$300$	0.926110	+	4.05755i	0.0534690	+	0.234263i
$301$	13.2983	+	2.45847i	0.766504	+	0.141704i
$302$	0.0254230	−	0.111386i	0.00146293	−	0.00640952i
$303$	−0.833706	−	11.1250i	−0.0478951	−	0.639116i
$304$	−14.7305	−	4.54376i	−0.844853	−	0.260603i
$305$	−2.04470	+	27.2846i	−0.117079	+	1.56231i
$306$	−0.0779691	+	0.198662i	−0.00445720	+	0.0113567i
$307$	8.67247	−	4.17644i	0.494964	−	0.238362i	−0.169712	−	0.985494i	$-0.554284\pi$
$307$	8.67247	−	4.17644i	0.494964	−	0.238362i	0.664676	+	0.747131i	$0.268569\pi$
$308$	−3.38606	+	31.2285i	−0.192939	+	1.77941i
$309$	2.53868	+	1.22257i	0.144421	+	0.0695494i
$310$	−0.104143	+	0.0966309i	−0.00591495	+	0.00548827i
$311$	11.9847	−	1.80641i	0.679592	−	0.102432i	0.199830	−	0.979831i	$-0.435961\pi$
$311$	11.9847	−	1.80641i	0.679592	−	0.102432i	0.479762	+	0.877399i	$0.340723\pi$
$312$	0.0571141	−	0.0989245i	0.00323345	−	0.00560050i
$313$	9.70718	+	16.8133i	0.548682	+	0.950345i	0.998365	+	0.0571571i	$0.0182036\pi$
$313$	9.70718	+	16.8133i	0.548682	+	0.950345i	−0.449683	+	0.893188i	$0.648463\pi$
$314$	0.127187	+	0.159487i	0.00717757	+	0.00900038i
$315$	−44.1796	−	1.46760i	−2.48924	−	0.0826898i
$316$	−2.33366	+	2.92632i	−0.131279	+	0.164618i
$317$	−10.0457	−	1.51415i	−0.564223	−	0.0850429i	−0.139263	−	0.990255i	$-0.544473\pi$
$317$	−10.0457	−	1.51415i	−0.564223	−	0.0850429i	−0.424959	+	0.905212i	$0.639712\pi$
$318$	0.101562	−	0.0692438i	0.00569532	−	0.00388300i
$319$	27.3083	−	18.6185i	1.52897	−	1.04244i
$320$	18.8109	+	2.83529i	1.05156	+	0.158497i
$321$	16.8332	−	21.1082i	0.939538	−	1.17814i
$322$	0.0421958	−	0.0186208i	0.00235148	−	0.00103770i
$323$	8.09466	+	10.1504i	0.450399	+	0.564783i
$324$	19.2681	+	33.3734i	1.07045	+	1.85408i
$325$	−0.328640	+	0.569221i	−0.0182297	+	0.0315747i
$326$	0.00990319	−	0.00149267i	0.000548487	−	8.26711e-5i
$327$	−29.5700	+	27.4370i	−1.63523	+	1.51727i
$328$	0.191268	+	0.0921098i	0.0105610	+	0.00508591i
$329$	−1.24494	+	0.789547i	−0.0686356	+	0.0435291i
$330$	0.363299	−	0.174955i	0.0199989	−	0.00963098i
$331$	−4.30861	+	10.9782i	−0.236822	+	0.603414i	−0.999035	−	0.0439126i	$-0.986018\pi$
$331$	−4.30861	+	10.9782i	−0.236822	+	0.603414i	0.762213	+	0.647326i	$0.224113\pi$
$332$	1.51048	−	20.1560i	0.0828985	−	1.10620i
$333$	−7.43744	−	2.29415i	−0.407569	−	0.125718i
$334$	0.00412567	+	0.0550532i	0.000225747	+	0.00301238i
$335$	−8.10372	+	35.5047i	−0.442753	+	1.93983i
$336$	−13.2687	+	30.7636i	−0.723869	+	1.67829i
$337$	−3.07026	−	13.4517i	−0.167248	−	0.732759i	−0.987090	−	0.160169i	$-0.948796\pi$
$337$	−3.07026	−	13.4517i	−0.167248	−	0.732759i	0.819842	−	0.572590i	$-0.194061\pi$
$338$	0.00861900	−	0.00265861i	0.000468812	−	0.000144609i
$339$	16.4928	+	42.0230i	0.895767	+	2.28238i
$340$	−11.7455	−	10.8983i	−0.636991	−	0.591042i
$341$	−32.4813	−	22.1454i	−1.75896	−	1.19924i
$342$	−0.244202			−0.0132049
$343$	17.4026	−	6.33627i	0.939654	−	0.342126i
$344$	−0.184412			−0.00994285
$345$	12.0255	+	8.19883i	0.647430	+	0.441410i
$346$	0.0148873	+	0.0138134i	0.000800344	+	0.000742611i
$347$	−7.27550	−	18.5377i	−0.390570	−	0.995155i	−0.982014	−	0.188809i	$-0.939537\pi$
$347$	−7.27550	−	18.5377i	−0.390570	−	0.995155i	0.591444	−	0.806346i	$-0.298558\pi$
$348$	33.6873	−	10.3912i	1.80583	−	0.557025i
$349$	1.12165	+	4.91429i	0.0600408	+	0.263056i	0.996035	−	0.0889586i	$-0.0283539\pi$
$349$	1.12165	+	4.91429i	0.0600408	+	0.263056i	−0.935995	+	0.352015i	$0.885497\pi$
$350$	−0.00621208	+	0.0144027i	−0.000332050	+	0.000769857i
$351$	−2.83531	+	12.4223i	−0.151338	+	0.663053i
$352$	−0.0480147	−	0.640712i	−0.00255919	−	0.0341501i
$353$	6.36159	+	1.96229i	0.338593	+	0.104442i	0.459389	−	0.888235i	$-0.348068\pi$
$353$	6.36159	+	1.96229i	0.338593	+	0.104442i	−0.120796	+	0.992677i	$0.538545\pi$
$354$	−0.0166696	+	0.222441i	−0.000885981	+	0.0118226i
$355$	6.84903	−	17.4511i	0.363509	−	0.926206i
$356$	−12.4470	+	5.99414i	−0.659687	+	0.317689i
$357$	23.8283	−	15.1120i	1.26113	−	0.799814i
$358$	−0.173785	−	0.0836905i	−0.00918482	−	0.00442318i
$359$	−19.3908	+	17.9920i	−1.02341	+	0.949581i	−0.998743	−	0.0501148i	$-0.984041\pi$
$359$	−19.3908	+	17.9920i	−1.02341	+	0.949581i	−0.0246616	+	0.999696i	$0.507851\pi$
$360$	0.596045	−	0.0898393i	0.0314143	−	0.00473495i
$361$	2.07212	−	3.58902i	0.109059	−	0.188896i
$362$	0.0702432	+	0.121665i	0.00369190	+	0.00639456i
$363$	47.8543	+	60.0074i	2.51170	+	3.14957i
$364$	−4.84088	+	2.13626i	−0.253731	+	0.111971i
$365$	19.1725	−	24.0416i	1.00354	−	1.25839i
$366$	0.324844	+	0.0489623i	0.0169798	+	0.00255930i
$367$	26.9017	−	18.3413i	1.40426	−	0.957406i	0.405189	−	0.914233i	$-0.367206\pi$
$367$	26.9017	−	18.3413i	1.40426	−	0.957406i	0.999068	−	0.0431726i	$-0.0137465\pi$
$368$	6.38670	−	4.35438i	0.332930	−	0.226988i
$369$	−40.8713	−	6.16036i	−2.12768	−	0.320696i
$370$	−0.0148210	+	0.0185849i	−0.000770506	+	0.000966184i
$371$	−11.3819	−	0.378093i	−0.590917	−	0.0196296i
$372$	−26.1439	−	32.7835i	−1.35550	−	1.69974i
$373$	−0.818840	−	1.41827i	−0.0423979	−	0.0734354i	0.844048	−	0.536268i	$-0.180166\pi$
$373$	−0.818840	−	1.41827i	−0.0423979	−	0.0734354i	−0.886446	+	0.462833i	$0.846833\pi$
$374$	−0.0901807	+	0.156197i	−0.00466313	+	0.00807678i
$375$	32.3383	−	4.87421i	1.66994	−	0.251703i
$376$	0.0147362	−	0.0136732i	0.000759961	−	0.000705140i
$377$	5.01616	+	2.41566i	0.258345	+	0.124413i
$378$	−0.0327776	+	0.302297i	−0.00168590	+	0.0155485i
$379$	14.2647	−	6.86952i	0.732729	−	0.352864i	−0.0300278	−	0.999549i	$-0.509560\pi$
$379$	14.2647	−	6.86952i	0.732729	−	0.352864i	0.762757	+	0.646685i	$0.223845\pi$
$380$	6.69826	−	17.0669i	0.343613	−	0.875513i
$381$	1.21581	−	16.2239i	0.0622879	−	0.831174i
$382$	−0.0269456	−	0.00831161i	−0.00137866	−	0.000425259i
$383$	−0.762042	−	10.1687i	−0.0389385	−	0.519599i	−0.982236	−	0.187650i	$-0.939913\pi$
$383$	−0.762042	−	10.1687i	−0.0389385	−	0.519599i	0.943297	−	0.331949i	$-0.107706\pi$
$384$	0.203329	−	0.890841i	0.0103761	−	0.0454606i
$385$	−36.7353	−	6.79127i	−1.87220	−	0.346115i
$386$	−0.00350303	−	0.0153478i	−0.000178299	−	0.000781181i
$387$	34.3098	−	10.5832i	1.74407	−	0.537973i
$388$	−3.12561	−	7.96393i	−0.158679	−	0.404307i
$389$	10.6887	+	9.91765i	0.541938	+	0.502845i	0.902967	−	0.429710i	$-0.141384\pi$
$389$	10.6887	+	9.91765i	0.541938	+	0.502845i	−0.361029	+	0.932554i	$0.617575\pi$
$390$	0.0561218	+	0.0382632i	0.00284184	+	0.00193753i
$391$	−6.51007			−0.329229
$392$	−0.217645	+	0.128103i	−0.0109928	+	0.00647019i
$393$	71.4603			3.60470
$394$	−0.137859	−	0.0939910i	−0.00694526	−	0.00473520i
$395$	−3.26313	−	3.02775i	−0.164186	−	0.152342i
$396$	30.4683	+	77.6319i	1.53109	+	3.90115i
$397$	4.04985	−	1.24921i	0.203256	−	0.0626962i	−0.191455	−	0.981501i	$-0.561321\pi$
$397$	4.04985	−	1.24921i	0.203256	−	0.0626962i	0.394711	+	0.918805i	$0.370845\pi$
$398$	0.0362755	+	0.158933i	0.00181832	+	0.00796660i
$399$	26.0581	+	19.0635i	1.30454	+	0.954367i
$400$	−0.584963	+	2.56289i	−0.0292481	+	0.128144i
$401$	2.00410	+	26.7428i	0.100080	+	1.33547i	0.790678	+	0.612233i	$0.209728\pi$
$401$	2.00410	+	26.7428i	0.100080	+	1.33547i	−0.690598	+	0.723239i	$0.742652\pi$
$402$	0.417826	+	0.128882i	0.0208393	+	0.00642806i
$403$	0.494875	−	6.60365i	0.0246515	−	0.328951i
$404$	2.57454	−	6.55981i	0.128088	−	0.326363i
$405$	−41.2925	+	19.8854i	−2.05184	+	0.988113i
$406$	0.125590	+	0.0433556i	0.00623293	+	0.00215170i
$407$	−5.92637	−	2.85399i	−0.293759	−	0.141467i
$408$	−0.282053	+	0.261707i	−0.0139637	+	0.0129564i
$409$	−13.2785	+	2.00141i	−0.656578	+	0.0989632i	−0.468878	−	0.883263i	$-0.655341\pi$
$409$	−13.2785	+	2.00141i	−0.656578	+	0.0989632i	−0.187700	+	0.982226i	$0.560103\pi$
$410$	−0.0631182	+	0.109324i	−0.00311719	+	0.00539913i
$411$	−30.5383	−	52.8939i	−1.50634	−	2.60906i
$412$	1.10972	+	1.39154i	0.0546718	+	0.0685562i
$413$	13.4144	−	15.7207i	0.660079	−	0.773563i
$414$	0.0763475	−	0.0957368i	0.00375228	−	0.00470520i
$415$	23.7702	+	3.58279i	1.16684	+	0.175872i
$416$	0.0894245	−	0.0609686i	0.00438439	−	0.00298923i
$417$	−38.7353	+	26.4093i	−1.89688	+	1.29327i
$418$	−0.204075	−	0.0307594i	−0.00998165	−	0.00150449i
$419$	10.1493	−	12.7268i	0.495826	−	0.621746i	−0.469456	−	0.882956i	$-0.655550\pi$
$419$	10.1493	−	12.7268i	0.495826	−	0.621746i	0.965282	+	0.261210i	$0.0841215\pi$
$420$	−35.3070	−	18.4713i	−1.72280	−	0.901307i
$421$	16.2148	+	20.3327i	0.790260	+	0.990954i	0.999913	+	0.0131784i	$0.00419493\pi$
$421$	16.2148	+	20.3327i	0.790260	+	0.990954i	−0.209654	+	0.977776i	$0.567234\pi$
$422$	−0.0358401	−	0.0620768i	−0.00174467	−	0.00302185i
$423$	−1.95697	+	3.38958i	−0.0951513	+	0.164807i
$424$	0.153557	−	0.0231450i	0.00745739	−	0.00112402i
$425$	1.62296	−	1.50588i	0.0787250	−	0.0730461i
$426$	−0.202796	−	0.0976613i	−0.00982549	−	0.00473170i
$427$	−21.6111	−	21.4307i	−1.04584	−	1.03710i
$428$	15.3649	−	7.39936i	0.742692	−	0.357662i
$429$	−6.86682	+	17.4964i	−0.331533	+	0.844733i
$430$	0.00819480	−	0.109352i	0.000395188	−	0.00527342i
$431$	24.5648	+	7.57723i	1.18324	+	0.364982i	0.823090	−	0.567911i	$-0.192248\pi$
$431$	24.5648	+	7.57723i	1.18324	+	0.364982i	0.360153	+	0.932893i	$0.382724\pi$
$432$	3.80831	+	50.8183i	0.183227	+	2.44500i
$433$	0.456559	−	2.00032i	0.0219408	−	0.0961290i	−0.962772	−	0.270315i	$-0.912872\pi$
$433$	0.456559	−	2.00032i	0.0219408	−	0.0961290i	0.984713	+	0.174186i	$0.0557293\pi$
$434$	−0.00657111	−	0.157894i	−0.000315423	−	0.00757917i
$435$	9.32965	+	40.8759i	0.447322	+	1.95985i
$436$	−24.3481	+	7.51038i	−1.16606	+	0.359682i
$437$	−2.72151	−	6.93429i	−0.130187	−	0.331712i
$438$	−0.270647	−	0.251123i	−0.0129320	−	0.0119991i
$439$	−6.84553	−	4.66721i	−0.326720	−	0.222754i	0.388840	−	0.921305i	$-0.372876\pi$
$439$	−6.84553	−	4.66721i	−0.326720	−	0.222754i	−0.715560	+	0.698552i	$0.753828\pi$
$440$	0.509420			0.0242857
$441$	33.1411	−	36.3239i	1.57815	−	1.72971i
$442$	−0.0303819			−0.00144512
$443$	12.5355	+	8.54654i	0.595578	+	0.406058i	0.823249	−	0.567680i	$-0.192159\pi$
$443$	12.5355	+	8.54654i	0.595578	+	0.406058i	−0.227671	+	0.973738i	$0.573111\pi$
$444$	−5.14312	−	4.77212i	−0.244082	−	0.226475i
$445$	−6.00265	−	15.2945i	−0.284553	−	0.725029i
$446$	0.154183	−	0.0475593i	0.00730079	−	0.00225200i
$447$	−9.44339	−	41.3742i	−0.446657	−	1.95693i
$448$	−15.9813	+	13.8701i	−0.755046	+	0.655300i
$449$	−4.20638	+	18.4294i	−0.198511	+	0.869735i	0.773312	+	0.634025i	$0.218599\pi$
$449$	−4.20638	+	18.4294i	−0.198511	+	0.869735i	−0.971824	+	0.235710i	$0.924259\pi$
$450$	0.00311206	+	0.0415275i	0.000146704	+	0.00195763i
$451$	−33.3795	−	10.2962i	−1.57178	−	0.484830i
$452$	−2.13096	+	28.4357i	−0.100232	+	1.33750i
$453$	−14.6518	+	37.3322i	−0.688401	+	1.75402i
$454$	−0.0399721	+	0.0192496i	−0.00187599	+	0.000903427i
$455$	−2.10331	−	5.93102i	−0.0986048	−	0.278051i
$456$	−0.396671	−	0.191027i	−0.0185758	−	0.00894564i
$457$	22.0046	−	20.4173i	1.02933	−	0.955082i	0.0303222	−	0.999540i	$-0.490347\pi$
$457$	22.0046	−	20.4173i	1.02933	−	0.955082i	0.999011	+	0.0444583i	$0.0141562\pi$
$458$	−0.0805047	+	0.0121341i	−0.00376174	+	0.000566991i
$459$	21.4596	−	37.1691i	1.00165	−	1.73491i
$460$	4.59674	+	7.96179i	0.214324	+	0.371220i
$461$	−4.32704	−	5.42594i	−0.201530	−	0.252711i	0.670788	−	0.741649i	$-0.265956\pi$
$461$	−4.32704	−	5.42594i	−0.201530	−	0.252711i	−0.872319	+	0.488938i	$0.837385\pi$
$462$	−0.114272	+	0.433737i	−0.00531644	+	0.0201793i
$463$	3.52429	−	4.41932i	0.163788	−	0.205383i	−0.693164	−	0.720780i	$-0.743784\pi$
$463$	3.52429	−	4.41932i	0.163788	−	0.205383i	0.856952	+	0.515397i	$0.172355\pi$
$464$	22.0186	+	3.31878i	1.02219	+	0.154070i
$465$	41.2039	−	28.0924i	1.91079	−	1.30275i
$466$	−0.0599103	+	0.0408461i	−0.00277529	+	0.00189216i
$467$	−14.4035	−	2.17098i	−0.666516	−	0.100461i	−0.192935	−	0.981212i	$-0.561801\pi$
$467$	−14.4035	−	2.17098i	−0.666516	−	0.100461i	−0.473581	+	0.880750i	$0.657039\pi$
$468$	−8.75892	+	10.9833i	−0.404881	+	0.507705i
$469$	−24.1919	−	32.4928i	−1.11708	−	1.50038i
$470$	0.00745302	+	0.00934579i	0.000343782	+	0.000431089i
$471$	−35.8029	−	62.0125i	−1.64971	−	2.85739i
$472$	−0.140904	+	0.244052i	−0.00648562	+	0.0112334i
$473$	30.0052	−	4.52255i	1.37964	−	0.207947i
$474$	−0.0391790	+	0.0363528i	−0.00179955	+	0.00166974i
$475$	2.28248	+	1.09919i	0.104727	+	0.0504341i
$476$	17.7025	−	2.06980i	0.811394	−	0.0948693i
$477$	−27.2410	+	13.1186i	−1.24728	+	0.600657i
$478$	−0.0598797	+	0.152571i	−0.00273883	+	0.00697843i
$479$	1.64959	−	22.0123i	0.0753717	−	1.00577i	−0.823432	−	0.567415i	$-0.807944\pi$
$479$	1.64959	−	22.0123i	0.0753717	−	1.00577i	0.898804	−	0.438351i	$-0.144437\pi$
$480$	0.778838	+	0.240240i	0.0355489	+	0.0109654i
$481$	−0.0828030	−	1.10493i	−0.00377549	−	0.0503805i
$482$	−0.000774314		0.00339249i	−3.52690e−5		0.000154524i
$483$	−15.6205	+	4.25577i	−0.710755	+	0.193644i
$484$	10.7881	+	47.2658i	0.490369	+	2.14845i
$485$	9.72281	−	2.99909i	0.441490	−	0.136182i
$486$	0.0750750	+	0.191288i	0.00340547	+	0.00867700i
$487$	16.3953	+	15.2126i	0.742941	+	0.689348i	0.957845	−	0.287287i	$-0.0927533\pi$
$487$	16.3953	+	15.2126i	0.742941	+	0.689348i	−0.214904	+	0.976635i	$0.568944\pi$
$488$	0.342910	+	0.233792i	0.0155228	+	0.0105833i
$489$	−3.51552			−0.158977
$490$	−0.0662905	−	0.134751i	−0.00299470	−	0.00608743i
$491$	20.3048			0.916343			0.458171	−	0.888864i	$-0.348505\pi$
$491$	20.3048			0.916343			0.458171	+	0.888864i	$0.348505\pi$
$492$	−30.7847	−	20.9887i	−1.38788	−	0.946242i
$493$	−13.7473	−	12.7557i	−0.619149	−	0.574486i
$494$	−0.0127010	−	0.0323617i	−0.000571446	−	0.00145602i
$495$	−94.7774	+	29.2349i	−4.25993	+	1.31401i
$496$	−5.89356	−	25.8214i	−0.264629	−	1.15941i
$497$	9.82134	+	18.3958i	0.440548	+	0.825162i
$498$	0.0642245	−	0.281386i	0.00287797	−	0.0126092i
$499$	0.204319	+	2.72644i	0.00914655	+	0.122052i	0.999908	−	0.0135639i	$-0.00431765\pi$
$499$	0.204319	+	2.72644i	0.00914655	+	0.122052i	−0.990761	+	0.135616i	$0.956699\pi$
$500$	19.7398	+	6.08891i	0.882789	+	0.272304i
$501$	1.44821	−	19.3250i	0.0647011	−	0.863376i
$502$	−0.0245657	+	0.0625923i	−0.00109642	+	0.00279363i
$503$	−17.9468	+	8.64271i	−0.800207	+	0.385360i	−0.788858	−	0.614576i	$-0.789327\pi$
$503$	−17.9468	+	8.64271i	−0.800207	+	0.385360i	−0.0113498	+	0.999936i	$0.503613\pi$
$504$	−0.354346	+	0.569224i	−0.0157838	+	0.0253552i
$505$	7.55096	+	3.63635i	0.336013	+	0.161815i
$506$	0.0758612	−	0.0703889i	0.00337244	−	0.00312917i
$507$	−3.13077	+	0.471887i	−0.139042	+	0.0209573i
$508$	5.13835	−	8.89989i	0.227978	−	0.394869i
$509$	−4.60702	−	7.97959i	−0.204202	−	0.353689i	0.745676	−	0.666309i	$-0.232127\pi$
$509$	−4.60702	−	7.97959i	−0.204202	−	0.353689i	−0.949878	+	0.312620i	$0.898793\pi$
$510$	−0.142652	−	0.178880i	−0.00631673	−	0.00792093i
$511$	6.50006	+	33.5821i	0.287546	+	1.48559i
$512$	0.449823	−	0.564060i	0.0198796	−	0.0249282i
$513$	48.5622	+	7.31958i	2.14407	+	0.323167i
$514$	0.118811	−	0.0810037i	0.00524051	−	0.00357292i
$515$	−1.74896	+	1.19242i	−0.0770683	+	0.0525443i
$516$	32.0044	+	4.82388i	1.40891	+	0.212360i
$517$	−2.06236	+	2.58611i	−0.0907023	+	0.113737i
$518$	−0.00502476	−	0.0259601i	−0.000220775	−	0.00114062i
$519$	−4.44473	−	5.57352i	−0.195102	−	0.244650i
$520$	0.0429060	+	0.0743154i	0.00188155	+	0.00325894i
$521$	−8.21209	+	14.2238i	−0.359778	+	0.623154i	−0.987924	−	0.154942i	$-0.950481\pi$
$521$	−8.21209	+	14.2238i	−0.359778	+	0.623154i	0.628145	+	0.778096i	$0.283814\pi$
$522$	0.348807	−	0.0525742i	0.0152669	−	0.00230111i
$523$	29.7689	−	27.6215i	1.30170	−	1.20780i	0.337903	−	0.941181i	$-0.390283\pi$
$523$	29.7689	−	27.6215i	1.30170	−	1.20780i	0.963801	−	0.266623i	$-0.0859080\pi$
$524$	40.6685	+	19.5849i	1.77661	+	0.855571i
$525$	2.90974	−	4.67422i	0.126992	−	0.204000i
$526$	−0.113010	+	0.0544228i	−0.00492747	+	0.00237295i
$527$	−8.14931	+	20.7641i	−0.354989	+	0.904498i
$528$	−5.61772	+	74.9632i	−0.244480	+	3.26235i
$529$	−18.4088	−	5.67836i	−0.800383	−	0.246885i
$530$	0.00690075	+	0.0920841i	0.000299749	+	0.00399988i
$531$	12.2092	−	53.4921i	0.529835	−	2.32136i
$532$	9.60514	+	17.9908i	0.416436	+	0.780000i
$533$	−1.30936	−	5.73668i	−0.0567147	−	0.248483i
$534$	−0.188507	+	0.0581466i	−0.00815748	+	0.00251625i
$535$	7.40987	+	18.8801i	0.320357	+	0.816256i
$536$	0.404938	+	0.375727i	0.0174907	+	0.0162290i
$537$	55.9428	+	38.1411i	2.41411	+	1.64591i
$538$	0.0684407			0.00295069
$539$	32.2708	−	26.1809i	1.39000	−	1.12769i
$540$	−60.6102			−2.60825
$541$	−12.5619	−	8.56459i	−0.540080	−	0.368220i	0.262344	−	0.964974i	$-0.415504\pi$
$541$	−12.5619	−	8.56459i	−0.540080	−	0.368220i	−0.802424	+	0.596754i	$0.796457\pi$
$542$	−0.0603372	−	0.0559847i	−0.00259170	−	0.00240475i
$543$	−18.0164	−	45.9051i	−0.773159	−	1.96998i
$544$	−0.348367	+	0.107457i	−0.0149361	+	0.00460718i
$545$	−6.74315	−	29.5437i	−0.288845	−	1.26551i
$546$	−0.0728992	+	0.0198613i	−0.00311980	+	0.000849984i
$547$	3.44293	−	15.0845i	0.147209	−	0.644965i	−0.846444	−	0.532478i	$-0.821261\pi$
$547$	3.44293	−	15.0845i	0.147209	−	0.644965i	0.993653	−	0.112488i	$-0.0358819\pi$
$548$	−2.88306	−	38.4718i	−0.123158	−	1.64343i
$549$	−77.2152	−	23.8177i	−3.29546	−	1.01652i
$550$	−0.00263007	+	0.0350958i	−0.000112147	+	0.00149649i
$551$	7.83984	−	19.9756i	0.333989	−	0.850989i
$552$	0.198905	−	0.0957878i	0.00846598	−	0.00407700i
$553$	4.91810	−	0.575031i	0.209139	−	0.0244528i
$554$	−0.157959	−	0.0760690i	−0.00671103	−	0.00323186i
$555$	6.11672	−	5.67548i	0.259640	−	0.240911i
$556$	−29.2824	+	4.41361i	−1.24185	+	0.187179i
$557$	−17.0111	+	29.4641i	−0.720783	+	1.24843i	0.239904	+	0.970797i	$0.422884\pi$
$557$	−17.0111	+	29.4641i	−0.720783	+	1.24843i	−0.960687	+	0.277635i	$0.910449\pi$
$558$	−0.209784	−	0.363356i	−0.00888086	−	0.0153821i
$559$	3.18695	+	3.99631i	0.134794	+	0.169026i
$560$	−15.0304	−	20.1878i	−0.635152	−	0.853090i
$561$	39.4738	−	49.4986i	1.66658	−	2.08983i
$562$	0.163594	+	0.0246578i	0.00690079	+	0.00104013i
$563$	−18.5011	+	12.6139i	−0.779729	+	0.531610i	−0.886531	−	0.462670i	$-0.846891\pi$
$563$	−18.5011	+	12.6139i	−0.779729	+	0.531610i	0.106801	+	0.994280i	$0.465939\pi$
$564$	−2.91510	+	1.98748i	−0.122748	+	0.0836880i
$565$	−33.5346	−	5.05453i	−1.41081	−	0.212646i
$566$	0.176775	−	0.221669i	0.00743042	−	0.00931745i
$567$	12.9882	−	49.2985i	0.545452	−	2.07034i
$568$	−0.177297	−	0.222323i	−0.00743920	−	0.00932847i
$569$	−5.26935	−	9.12678i	−0.220903	−	0.382615i	0.734180	−	0.678955i	$-0.237567\pi$
$569$	−5.26935	−	9.12678i	−0.220903	−	0.382615i	−0.955082	+	0.296341i	$0.904234\pi$
$570$	0.130901	−	0.226727i	0.00548284	−	0.00949656i
$571$	5.42992	−	0.818428i	0.227235	−	0.0342502i	−0.0344377	−	0.999407i	$-0.510964\pi$
$571$	5.42992	−	0.818428i	0.227235	−	0.0342502i	0.261673	+	0.965157i	$0.415726\pi$
$572$	−8.70313	+	8.07532i	−0.363896	+	0.337646i
$573$	8.91804	+	4.29470i	0.372556	+	0.179414i
$574$	−0.0469333	−	0.132345i	−0.00195896	−	0.00552397i
$575$	−1.14452	+	0.551172i	−0.0477298	+	0.0229855i
$576$	−20.5254	+	52.2978i	−0.855224	+	2.17908i
$577$	0.517356	−	6.90364i	0.0215378	−	0.287402i	−0.976027	−	0.217651i	$-0.930160\pi$
$577$	0.517356	−	6.90364i	0.0215378	−	0.287402i	0.997564	−	0.0697510i	$-0.0222205\pi$
$578$	−0.0487315	−	0.0150317i	−0.00202696	−	0.000625235i
$579$	0.412956	+	5.51052i	0.0171619	+	0.229009i
$580$	−5.89317	+	25.8196i	−0.244700	+	1.07210i
$581$	−20.1946	+	17.5268i	−0.837815	+	0.727135i
$582$	−0.0271842	−	0.119102i	−0.00112682	−	0.00493694i
$583$	−24.4172	+	7.53171i	−1.01126	+	0.311931i
$584$	−0.170407	−	0.434191i	−0.00705151	−	0.0179670i
$585$	−12.2475	−	11.3640i	−0.506372	−	0.469844i
$586$	−0.111513	−	0.0760284i	−0.00460657	−	0.00314070i
$587$	8.49721			0.350717			0.175359	−	0.984505i	$-0.443891\pi$
$587$	8.49721			0.350717			0.175359	+	0.984505i	$0.443891\pi$
$588$	41.1228	−	16.5388i	1.69588	−	0.682050i
$589$	−25.5239			−1.05170
$590$	−0.138456	−	0.0943975i	−0.00570013	−	0.00388628i
$591$	42.9340	+	39.8369i	1.76607	+	1.63867i
$592$	−1.61903	−	4.12523i	−0.0665419	−	0.169546i
$593$	−15.2397	+	4.70081i	−0.625818	+	0.193039i	−0.591413	−	0.806369i	$-0.701430\pi$
$593$	−15.2397	+	4.70081i	−0.625818	+	0.193039i	−0.0344048	+	0.999408i	$0.510954\pi$
$594$	0.151817	+	0.665155i	0.00622914	+	0.0272917i
$595$	0.881397	+	21.1787i	0.0361337	+	0.868242i
$596$	5.96501	−	26.1344i	0.244336	−	1.07051i
$597$	−4.27635	−	57.0640i	−0.175019	−	2.33547i
$598$	0.0166579	+	0.00513829i	0.000681193	+	0.000210120i
$599$	0.110921	−	1.48014i	0.00453213	−	0.0604771i	−0.994479	−	0.104934i	$-0.966537\pi$
$599$	0.110921	−	1.48014i	0.00453213	−	0.0604771i	0.999011	+	0.0444572i	$0.0141558\pi$
$600$	−0.0274298	+	0.0698899i	−0.00111982	+	0.00285324i
$601$	−11.2704	+	5.42756i	−0.459731	+	0.221395i	−0.649390	−	0.760455i	$-0.724976\pi$
$601$	−11.2704	+	5.42756i	−0.459731	+	0.221395i	0.189660	+	0.981850i	$0.439262\pi$
$602$	0.0866137	+	0.0858903i	0.00353011	+	0.00350063i
$603$	−96.9009	−	46.6650i	−3.94611	−	1.90035i
$604$	−18.5699	+	17.2304i	−0.755600	+	0.701094i
$605$	−57.0149	+	8.59361i	−2.31799	+	0.349380i
$606$	0.0503130	−	0.0871447i	0.00204383	−	0.00354001i
$607$	11.9219	+	20.6494i	0.483896	+	0.838132i	0.999829	−	0.0184968i	$-0.00588803\pi$
$607$	11.9219	+	20.6494i	0.483896	+	0.838132i	−0.515933	+	0.856629i	$0.672555\pi$
$608$	−0.260092	−	0.326145i	−0.0105481	−	0.0132269i
$609$	−41.3244	−	21.6194i	−1.67455	−	0.876061i
$610$	−0.153871	+	0.192948i	−0.00623005	+	0.00781223i
$611$	−0.550970	−	0.0830454i	−0.0222899	−	0.00335966i
$612$	39.0975	−	26.6562i	1.58042	−	1.07751i
$613$	−19.7671	+	13.4770i	−0.798387	+	0.544331i	−0.892403	−	0.451239i	$-0.850982\pi$
$613$	−19.7671	+	13.4770i	−0.798387	+	0.544331i	0.0940156	+	0.995571i	$0.470030\pi$
$614$	0.0858516	+	0.0129400i	0.00346469	+	0.000522218i
$615$	27.6281	−	34.6445i	1.11407	−	1.39700i
$616$	−0.367820	+	0.431057i	−0.0148199	+	0.0173678i
$617$	−15.3277	−	19.2204i	−0.617072	−	0.773783i	0.370858	−	0.928690i	$-0.379064\pi$
$617$	−15.3277	−	19.2204i	−0.617072	−	0.773783i	−0.987929	+	0.154906i	$0.950492\pi$
$618$	0.0127076	+	0.0220101i	0.000511173	+	0.000885377i
$619$	−1.99818	+	3.46094i	−0.0803135	+	0.139107i	−0.903385	−	0.428831i	$-0.858925\pi$
$619$	−1.99818	+	3.46094i	−0.0803135	+	0.139107i	0.823071	+	0.567938i	$0.192259\pi$
$620$	31.1486	−	4.69489i	1.25096	−	0.188551i
$621$	−18.0521	+	16.7499i	−0.724406	+	0.672150i
$622$	0.0984939	+	0.0474322i	0.00394925	+	0.00190186i
$623$	17.2759	+	5.96391i	0.692145	+	0.238939i
$624$	−11.4090	+	5.49426i	−0.456724	+	0.219947i
$625$	−10.1763	+	25.9289i	−0.407054	+	1.03716i
$626$	−0.0130861	+	0.174622i	−0.000523027	+	0.00697931i
$627$	69.2259	+	21.3533i	2.76461	+	0.852771i
$628$	−3.38008	−	45.1041i	−0.134880	−	1.79985i
$629$	−0.830508	+	3.63869i	−0.0331145	+	0.145084i
$630$	−0.321789	−	0.235413i	−0.0128204	−	0.00937909i
$631$	9.39847	+	41.1774i	0.374147	+	1.63925i	0.714997	+	0.699127i	$0.246428\pi$
$631$	9.39847	+	41.1774i	0.374147	+	1.63925i	−0.340850	+	0.940118i	$0.610715\pi$
$632$	−0.0645215	+	0.0199022i	−0.00256653	+	0.000791669i
$633$	9.19249	+	23.4221i	0.365369	+	0.930945i
$634$	−0.0671716	−	0.0623262i	−0.00266773	−	0.00247529i
$635$	10.0984	+	6.88495i	0.400741	+	0.273221i
$636$	−27.2549			−1.08073
$637$	6.53733	+	2.50265i	0.259019	+	0.0991586i
$638$	0.298114			0.0118025
$639$	45.7448	+	31.1882i	1.80963	+	1.23379i
$640$	0.503196	+	0.466898i	0.0198906	+	0.0184558i
$641$	9.82875	+	25.0433i	0.388212	+	0.989149i	0.982726	+	0.185064i	$0.0592492\pi$
$641$	9.82875	+	25.0433i	0.388212	+	0.989149i	−0.594514	+	0.804085i	$0.702656\pi$
$642$	0.232699	−	0.0717781i	0.00918389	−	0.00283286i
$643$	−3.94546	−	17.2862i	−0.155594	−	0.681700i	−0.991200	−	0.132372i	$-0.957741\pi$
$643$	−3.94546	−	17.2862i	−0.155594	−	0.681700i	0.835607	−	0.549328i	$-0.185116\pi$
$644$	−10.0561	−	1.85907i	−0.396264	−	0.0732575i
$645$	−8.56544	+	37.5276i	−0.337264	+	1.47765i
$646$	0.00875101	+	0.116774i	0.000344304	+	0.00459441i
$647$	9.68024	+	2.98596i	0.380570	+	0.117390i	0.479137	−	0.877740i	$-0.340950\pi$
$647$	9.68024	+	2.98596i	0.380570	+	0.117390i	−0.0985673	+	0.995130i	$0.531426\pi$
$648$	−0.0519513	+	0.693242i	−0.00204084	+	0.0272331i
$649$	16.9408	−	43.1646i	0.664986	−	1.69436i
$650$	−0.00534138	+	0.00257227i	−0.000209506	+	0.000100893i
$651$	−5.97976	+	55.1493i	−0.234365	+	2.16147i
$652$	−2.00070	−	0.963487i	−0.0783535	−	0.0377331i
$653$	−26.1321	+	24.2470i	−1.02263	+	0.948859i	−0.998706	−	0.0508546i	$-0.983806\pi$
$653$	−26.1321	+	24.2470i	−1.02263	+	0.948859i	−0.0239210	+	0.999714i	$0.507615\pi$
$654$	−0.359776	+	0.0542275i	−0.0140684	+	0.00212046i
$655$	−26.8417	+	46.4912i	−1.04879	+	1.81656i
$656$	−11.7670	−	20.3810i	−0.459423	−	0.795745i
$657$	56.6219	+	71.0016i	2.20903	+	2.77003i
$658$	−0.0132895		0.000441463i	−0.000518079		1.72100e-5i
$659$	24.8564	−	31.1689i	0.968268	−	1.21417i	−0.00852102	−	0.999964i	$-0.502712\pi$
$659$	24.8564	−	31.1689i	0.968268	−	1.21417i	0.976789	−	0.214205i	$-0.0687162\pi$
$660$	−88.4088	−	13.3255i	−3.44131	−	0.518694i
$661$	−9.52798	+	6.49606i	−0.370595	+	0.252668i	−0.734269	−	0.678859i	$-0.762475\pi$
$661$	−9.52798	+	6.49606i	−0.370595	+	0.252668i	0.363673	+	0.931527i	$0.381522\pi$
$662$	−0.0878895	+	0.0599220i	−0.00341592	+	0.00232894i
$663$	10.5456	+	1.58950i	0.409559	+	0.0617311i
$664$	0.227343	−	0.285079i	0.00882261	−	0.0110632i
$665$	−22.1903	+	9.79249i	−0.860503	+	0.379737i
$666$	−0.0437705	−	0.0548865i	−0.00169607	−	0.00212681i
$667$	5.38016	+	9.31872i	0.208321	+	0.360822i
$668$	6.12052	−	10.6011i	0.236810	−	0.410167i
$669$	−56.0056	+	8.44149i	−2.16530	+	0.326367i
$670$	−0.240791	+	0.223422i	−0.00930258	+	0.00863154i
$671$	−61.5274	−	29.6300i	−2.37524	−	1.14385i
$672$	−0.765634	+	0.485569i	−0.0295350	+	0.0187312i
$673$	9.27819	−	4.46814i	0.357648	−	0.172234i	−0.246428	−	0.969161i	$-0.579257\pi$
$673$	9.27819	−	4.46814i	0.357648	−	0.172234i	0.604076	+	0.796927i	$0.293542\pi$
$674$	0.0454669	−	0.115848i	0.00175132	−	0.00446229i
$675$	0.625857	−	8.35148i	0.0240892	−	0.321449i
$676$	−1.91107	−	0.589486i	−0.0735026	−	0.0226726i
$677$	−1.40020	−	18.6844i	−0.0538141	−	0.718099i	−0.957229	−	0.289331i	$-0.906567\pi$
$677$	−1.40020	−	18.6844i	−0.0538141	−	0.718099i	0.903415	−	0.428767i	$-0.141052\pi$
$678$	−0.0906067	+	0.396974i	−0.00347973	+	0.0152457i
$679$	−4.48248	+	10.3926i	−0.172022	+	0.398832i
$680$	−0.0643193	−	0.281801i	−0.00246653	−	0.0108066i
$681$	14.8815	−	4.59034i	0.570261	−	0.175902i
$682$	−0.129545	−	0.330075i	−0.00496053	−	0.0126392i
$683$	−33.5701	−	31.1485i	−1.28452	−	1.19186i	−0.970134	−	0.242571i	$-0.922009\pi$
$683$	−33.5701	−	31.1485i	−1.28452	−	1.19186i	−0.314391	−	0.949294i	$-0.601800\pi$
$684$	44.7377	+	30.5017i	1.71059	+	1.16626i
$685$	45.8828			1.75309
$686$	0.161887	+	0.0412019i	0.00618086	+	0.00157310i
$687$	28.5782			1.09033
$688$	16.8911	+	11.5162i	0.643968	+	0.439050i
$689$	−3.15528	−	2.92768i	−0.120207	−	0.111536i
$690$	0.0479610	+	0.122203i	0.00182584	+	0.00465217i
$691$	−28.8391	+	8.89570i	−1.09709	+	0.338408i	−0.789898	−	0.613238i	$-0.789866\pi$
$691$	−28.8391	+	8.89570i	−1.09709	+	0.338408i	−0.307195	+	0.951647i	$0.599390\pi$
$692$	−1.00201	−	4.39007i	−0.0380905	−	0.166886i
$693$	43.6949	−	101.307i	1.65983	−	3.84832i
$694$	0.0399695	−	0.175118i	0.00151722	−	0.00664738i
$695$	−2.63191	−	35.1205i	−0.0998342	−	1.33219i
$696$	0.607713	+	0.187455i	0.0230353	+	0.00710545i
$697$	−1.48117	+	19.7649i	−0.0561034	+	0.748648i
$698$	−0.0166104	+	0.0423226i	−0.000628712	+	0.00160193i
$699$	22.9320	−	11.0435i	0.867367	−	0.417702i
$700$	2.93700	−	1.86266i	0.111008	−	0.0704020i
$701$	−0.915249	−	0.440761i	−0.0345685	−	0.0166473i	0.416520	−	0.909127i	$-0.363250\pi$
$701$	−0.915249	−	0.440761i	−0.0345685	−	0.0166473i	−0.451088	+	0.892479i	$0.648964\pi$
$702$	−0.0842475	+	0.0781703i	−0.00317972	+	0.00295035i
$703$	−4.22299	+	0.636513i	−0.159273	+	0.0240066i
$704$	−23.7401	+	41.1190i	−0.894738	+	1.54973i
$705$	−2.09802	−	3.63387i	−0.0790159	−	0.136860i
$706$	0.0374390	+	0.0469470i	0.00140904	+	0.00176687i
$707$	−8.52904	+	3.76383i	−0.320768	+	0.141553i
$708$	30.8375	−	38.6690i	1.15894	−	1.45327i
$709$	−37.5601	−	5.66127i	−1.41060	−	0.212613i	−0.600836	−	0.799372i	$-0.705166\pi$
$709$	−37.5601	−	5.66127i	−1.41060	−	0.212613i	−0.809762	+	0.586759i	$0.800404\pi$
$710$	0.139711	−	0.0952531i	0.00524325	−	0.00357478i
$711$	10.8620	−	7.40560i	0.407358	−	0.277732i
$712$	−0.246438	−	0.0371445i	−0.00923564	−	0.00139205i
$713$	7.97982	−	10.0064i	0.298847	−	0.374742i
$714$	0.254363	+	0.00844966i	0.00951929	+	0.000316220i
$715$	−8.80362	−	11.0394i	−0.329237	−	0.412850i
$716$	21.3841	+	37.0384i	0.799163	+	1.38419i
$717$	28.7665	−	49.8251i	1.07431	−	1.86075i
$718$	−0.235926	+	0.0355601i	−0.00880467	+	0.00132709i
$719$	−18.3402	+	17.0172i	−0.683973	+	0.634634i	−0.943605	−	0.331073i	$-0.892589\pi$
$719$	−18.3402	+	17.0172i	−0.683973	+	0.634634i	0.259632	+	0.965708i	$0.416399\pi$
$720$	−60.2046	−	28.9930i	−2.24369	−	1.08050i
$721$	0.253819	−	2.34089i	0.00945272	−	0.0871793i
$722$	0.0336782	−	0.0162186i	0.00125337	−	0.000603592i
$723$	0.446253	−	1.13703i	0.0165963	−	0.0422867i
$724$	2.32782	−	31.0626i	0.0865126	−	1.15443i
$725$	−3.49684	−	1.07863i	−0.129869	−	0.0400594i
$726$	0.0517345	+	0.690349i	0.00192005	+	0.0256212i
$727$	11.0664	−	48.4853i	0.410432	−	1.79822i	−0.171728	−	0.985144i	$-0.554935\pi$
$727$	11.0664	−	48.4853i	0.410432	−	1.79822i	0.582160	−	0.813074i	$-0.302208\pi$
$728$	−0.0938633	−	0.0173525i	−0.00347880	−	0.000643128i
$729$	−3.18786	−	13.9669i	−0.118069	−	0.517293i
$730$	0.265037	−	0.0817531i	0.00980946	−	0.00302582i
$731$	−6.29023	−	16.0272i	−0.232653	−	0.592789i
$732$	−53.3957	−	49.5440i	−1.97356	−	1.83120i
$733$	38.0095	+	25.9144i	1.40391	+	0.957172i	0.999085	+	0.0427788i	$0.0136211\pi$
$733$	38.0095	+	25.9144i	1.40391	+	0.957172i	0.404828	+	0.914393i	$0.367331\pi$
$734$	0.293675			0.0108397
$735$	15.9598	+	50.2406i	0.588686	+	1.85315i
$736$	0.209177			0.00771038
$737$	−75.1006	−	51.2027i	−2.76637	−	1.88608i
$738$	−0.273291	−	0.253577i	−0.0100600	−	0.00933428i
$739$	9.51257	+	24.2376i	0.349925	+	0.891595i	0.992147	+	0.125076i	$0.0399176\pi$
$739$	9.51257	+	24.2376i	0.349925	+	0.891595i	−0.642222	+	0.766519i	$0.721987\pi$
$740$	5.03652	−	1.55356i	0.185146	−	0.0571100i
$741$	2.71548	+	11.8973i	0.0997558	+	0.437059i
$742$	−0.0829016	−	0.0606488i	−0.00304341	−	0.00222649i
$743$	3.43015	−	15.0285i	0.125840	−	0.551340i	−0.872222	−	0.489110i	$-0.837322\pi$
$743$	3.43015	−	15.0285i	0.125840	−	0.551340i	0.998062	−	0.0622302i	$-0.0198213\pi$
$744$	−0.0565287	−	0.754323i	−0.00207244	−	0.0276548i
$745$	30.4646	+	9.39709i	1.11614	+	0.344283i
$746$	0.00110387	−	0.0147301i	4.04155e−5	−	0.000539308i
$747$	−25.9367	+	66.0857i	−0.948975	+	2.41795i
$748$	36.0307	−	17.3515i	1.31741	−	0.634432i
$749$	−21.3260	−	7.36205i	−0.779234	−	0.269004i
$750$	0.265765	+	0.127986i	0.00970436	+	0.00467337i
$751$	19.1390	−	17.7584i	0.698392	−	0.648013i	−0.248846	−	0.968543i	$-0.580051\pi$
$751$	19.1390	−	17.7584i	0.698392	−	0.648013i	0.947238	+	0.320530i	$0.103861\pi$
$752$	−2.20361	+	0.332141i	−0.0803574	+	0.0121119i
$753$	11.8015	−	20.4408i	0.430070	−	0.744902i
$754$	0.0251087	+	0.0434896i	0.000914406	+	0.00158380i
$755$	−18.7844	−	23.5548i	−0.683633	−	0.857249i
$756$	43.7627	−	51.2866i	1.59164	−	1.86528i
$757$	−27.4397	+	34.4083i	−0.997313	+	1.25059i	−0.0293321	+	0.999570i	$0.509338\pi$
$757$	−27.4397	+	34.4083i	−0.997313	+	1.25059i	−0.967981	+	0.251022i	$0.919233\pi$
$758$	0.141211	+	0.0212841i	0.00512901	+	0.000773074i
$759$	−30.0142	+	20.4633i	−1.08945	+	0.742772i
$760$	0.273276	−	0.186316i	0.00991275	−	0.00675840i
$761$	24.2964	+	3.66209i	0.880743	+	0.132751i	0.573818	−	0.818983i	$-0.305462\pi$
$761$	24.2964	+	3.66209i	0.880743	+	0.132751i	0.306925	+	0.951734i	$0.400700\pi$
$762$	0.0914941	−	0.114730i	0.00331448	−	0.00415623i
$763$	29.8678	+	15.6257i	1.08129	+	0.565690i
$764$	3.89827	+	4.88828i	0.141035	+	0.176852i
$765$	28.1387	+	48.7377i	1.01736	+	1.76212i
$766$	0.0459882	−	0.0796539i	0.00166162	−	0.00287801i
$767$	7.72379	−	1.16417i	0.278890	−	0.0420359i
$768$	−37.1199	+	34.4423i	−1.33945	+	1.24283i
$769$	17.0429	+	8.20743i	0.614583	+	0.295968i	0.715159	−	0.698962i	$-0.246354\pi$
$769$	17.0429	+	8.20743i	0.614583	+	0.295968i	−0.100576	+	0.994929i	$0.532069\pi$
$770$	−0.239261	−	0.237263i	−0.00862238	−	0.00855037i
$771$	−45.4774	+	21.9007i	−1.63783	+	0.788736i
$772$	−1.27524	+	3.24925i	−0.0458967	+	0.116943i
$773$	0.309493	−	4.12989i	0.0111317	−	0.148542i	−0.988868	−	0.148794i	$-0.952461\pi$
$773$	0.309493	−	4.12989i	0.0111317	−	0.148542i	1.00000		0.000251550i	$8.00707e-5\pi$
$774$	0.309465	+	0.0954573i	0.0111235	+	0.00343114i
$775$	0.325271	+	4.34045i	0.0116841	+	0.155913i
$776$	0.0343431	−	0.150467i	0.00123285	−	0.00540145i
$777$	0.385945	+	9.27370i	0.0138457	+	0.332692i
$778$	0.0292653	+	0.128220i	0.00104921	+	0.00459690i
$779$	−21.6720	+	6.68493i	−0.776480	+	0.239512i
$780$	−5.50229	−	14.0196i	−0.197014	−	0.501983i
$781$	34.2997	+	31.8254i	1.22734	+	1.13880i
$782$	−0.0485160	−	0.0330776i	−0.00173493	−	0.00118285i
$783$	−70.9400			−2.53519
$784$	27.9349	+	1.85798i	0.997674	+	0.0663565i
$785$	53.7927			1.91994
$786$	0.532554	+	0.363089i	0.0189956	+	0.0129510i
$787$	−17.6591	−	16.3853i	−0.629481	−	0.584073i	0.299548	−	0.954081i	$-0.403164\pi$
$787$	−17.6591	−	16.3853i	−0.629481	−	0.584073i	−0.929028	+	0.370009i	$0.879355\pi$
$788$	13.5160	+	34.4382i	0.481488	+	1.22681i
$789$	42.0734	−	12.9779i	1.49785	−	0.462026i
$790$	−0.00893437	−	0.0391440i	−0.000317871	−	0.00139268i
$791$	28.4902	−	24.7265i	1.01300	−	0.879174i
$792$	−0.334774	+	1.46674i	−0.0118957	+	0.0521184i
$793$	−0.859658	−	11.4713i	−0.0305274	−	0.407359i
$794$	0.0365285	+	0.0112675i	0.00129635	+	0.000399870i
$795$	2.42232	−	32.3237i	0.0859110	−	1.14640i
$796$	13.2056	−	33.6474i	0.468062	−	1.19260i
$797$	−3.17705	+	1.52999i	−0.112537	+	0.0541950i	−0.489305	−	0.872113i	$-0.662750\pi$
$797$	−3.17705	+	1.52999i	−0.112537	+	0.0541950i	0.376768	+	0.926308i	$0.377035\pi$
$798$	0.0973350	+	0.274470i	0.00344562	+	0.00971614i
$799$	1.69098	+	0.814332i	0.0598225	+	0.0288090i
$800$	−0.0521478	+	0.0483861i	−0.00184370	+	0.00171071i
$801$	47.9813	−	7.23201i	1.69533	−	0.255531i
$802$	−0.120944	+	0.209482i	−0.00427070	+	0.00739707i
$803$	38.3746	+	66.4668i	1.35421	+	2.34556i
$804$	−60.4478	−	75.7991i	−2.13183	−	2.67323i
$805$	3.09855	−	11.7610i	0.109210	−	0.414521i
$806$	0.0372411	−	0.0466989i	0.00131176	−	0.00164490i
$807$	−23.7560	−	3.58064i	−0.836250	−	0.126044i
$808$	0.105036	−	0.0716123i	0.00369515	−	0.00251931i
$809$	−17.1453	+	11.6894i	−0.602795	+	0.410979i	−0.825901	−	0.563815i	$-0.809333\pi$
$809$	−17.1453	+	11.6894i	−0.602795	+	0.410979i	0.223106	+	0.974794i	$0.428381\pi$
$810$	−0.408767	−	0.0616117i	−0.0143626	−	0.00216482i
$811$	−24.1345	+	30.2638i	−0.847478	+	1.06270i	0.149781	+	0.988719i	$0.452143\pi$
$811$	−24.1345	+	30.2638i	−0.847478	+	1.06270i	−0.997259	+	0.0739851i	$0.976428\pi$
$812$	−17.5928	−	23.6294i	−0.617386	−	0.829228i
$813$	18.0142	+	22.5891i	0.631786	+	0.792235i
$814$	−0.0296648	−	0.0513810i	−0.00103975	−	0.00180090i
$815$	1.32049	−	2.28715i	0.0462546	−	0.0801154i
$816$	42.1774	−	6.35723i	1.47651	−	0.222547i
$817$	14.4420	−	13.4002i	0.505262	−	0.468815i
$818$	−0.109126	−	0.0525524i	−0.00381551	−	0.00183745i
$819$	18.4590	−	2.15826i	0.645011	−	0.0754156i
$820$	25.2182	−	12.1444i	0.880658	−	0.424102i
$821$	−6.73503	+	17.1606i	−0.235054	+	0.598909i	−0.998920	−	0.0464668i	$-0.985204\pi$
$821$	−6.73503	+	17.1606i	−0.235054	+	0.598909i	0.763866	+	0.645375i	$0.223299\pi$
$822$	0.0411683	−	0.549353i	0.00143591	−	0.0191609i
$823$	23.2282	+	7.16494i	0.809683	+	0.249754i	0.671837	−	0.740699i	$-0.265506\pi$
$823$	23.2282	+	7.16494i	0.809683	+	0.249754i	0.137847	+	0.990454i	$0.455982\pi$
$824$	0.00239944	+	0.0320183i	8.35884e−5	+	0.00111541i
$825$	2.74902	−	12.0443i	0.0957087	−	0.419327i
$826$	0.179847	−	0.0489989i	0.00625766	−	0.00170489i
$827$	−7.09573	−	31.0884i	−0.246743	−	1.08105i	−0.934739	−	0.355336i	$-0.884366\pi$
$827$	−7.09573	−	31.0884i	−0.246743	−	1.08105i	0.687996	−	0.725715i	$-0.258491\pi$
$828$	−25.9447	+	8.00288i	−0.901641	+	0.278119i
$829$	15.5422	+	39.6009i	0.539803	+	1.37539i	0.897275	+	0.441471i	$0.145543\pi$
$829$	15.5422	+	39.6009i	0.539803	+	1.37539i	−0.357473	+	0.933924i	$0.616362\pi$
$830$	0.158942	+	0.147477i	0.00551697	+	0.00511900i
$831$	50.8482	+	34.6677i	1.76391	+	1.20261i
$832$	−7.99805			−0.277282
$833$	−18.5572	−	14.5460i	−0.642970	−	0.503988i
$834$	−0.422858			−0.0146424
$835$	12.0286	+	8.20097i	0.416267	+	0.283806i
$836$	33.5446	+	31.1248i	1.16016	+	1.07648i
$837$	30.8268	+	78.5453i	1.06553	+	2.71492i
$838$	0.140302	−	0.0432774i	0.00484665	−	0.00149499i
$839$	−4.58788	−	20.1008i	−0.158391	−	0.693957i	−0.990289	−	0.139028i	$-0.955602\pi$
$839$	−4.58788	−	20.1008i	−0.158391	−	0.693957i	0.831897	−	0.554930i	$-0.187255\pi$
$840$	−0.338549	−	0.634114i	−0.0116810	−	0.0218790i
$841$	−0.444432	+	1.94718i	−0.0153252	+	0.0671442i
$842$	0.0175295	+	0.233915i	0.000604107	+	0.00806125i
$843$	−55.4939	−	17.1176i	−1.91131	−	0.589561i
$844$	−1.18772	+	15.8490i	−0.0408830	+	0.545545i
$845$	0.868965	−	2.21409i	0.0298933	−	0.0761669i
$846$	−0.0318066	+	0.0153173i	−0.00109353	+	0.000526618i
$847$	33.8951	−	54.4493i	1.16465	−	1.87090i
$848$	−15.5103	−	7.46937i	−0.532626	−	0.256499i
$849$	−72.9563	+	67.6936i	−2.50385	+	2.32324i
$850$	0.0197464	−	0.00297629i	0.000677295	−	0.000102086i
$851$	1.07074	−	1.85458i	0.0367045	−	0.0635741i
$852$	24.9539	+	43.2214i	0.854906	+	1.48074i
$853$	12.6508	+	15.8637i	0.433157	+	0.543161i	0.949725	−	0.313085i	$-0.101362\pi$
$853$	12.6508	+	15.8637i	0.433157	+	0.543161i	−0.516569	+	0.856246i	$0.672791\pi$
$854$	−0.0521668	−	0.269517i	−0.00178511	−	0.00922267i
$855$	−40.1503	+	50.3469i	−1.37311	+	1.72183i
$856$	0.304211	+	0.0458524i	0.0103977	+	0.00156720i
$857$	21.8402	−	14.8904i	0.746048	−	0.508647i	−0.129618	−	0.991564i	$-0.541375\pi$
$857$	21.8402	−	14.8904i	0.746048	−	0.508647i	0.875666	+	0.482917i	$0.160423\pi$
$858$	−0.140073	+	0.0955005i	−0.00478203	+	0.00326033i
$859$	25.7038	+	3.87422i	0.877002	+	0.132187i	0.572087	−	0.820193i	$-0.306134\pi$
$859$	25.7038	+	3.87422i	0.877002	+	0.132187i	0.304915	+	0.952380i	$0.401372\pi$
$860$	−15.1597	+	19.0097i	−0.516942	+	0.648225i
$861$	9.36674	+	48.3927i	0.319218	+	1.64922i
$862$	0.144568	+	0.181282i	0.00492400	+	0.00617449i
$863$	−7.70946	−	13.3532i	−0.262433	−	0.454547i	0.704455	−	0.709749i	$-0.251192\pi$
$863$	−7.70946	−	13.3532i	−0.262433	−	0.454547i	−0.966888	+	0.255202i	$0.917858\pi$
$864$	−0.689525	+	1.19429i	−0.0234581	+	0.0406306i
$865$	5.29557	−	0.798179i	0.180055	−	0.0271389i
$866$	0.0135661	−	0.0125875i	0.000460994	−	0.000427739i
$867$	16.1284	+	7.76703i	0.547749	+	0.263782i
$868$	−18.5177	+	29.7469i	−0.628532	+	1.00968i
$869$	10.0100	−	4.82056i	0.339566	−	0.163526i
$870$	−0.138161	+	0.352029i	−0.00468410	+	0.0119349i
$871$	1.14421	−	15.2684i	0.0387700	−	0.517350i
$872$	−0.439234	−	0.135486i	−0.0148744	−	0.00458813i
$873$	2.24558	+	29.9652i	0.0760014	+	1.01417i
$874$	0.0149512	−	0.0655053i	0.000505731	−	0.00221575i
$875$	−12.8709	−	24.1077i	−0.435117	−	0.814990i
$876$	18.2162	+	79.8105i	0.615469	+	2.69655i
$877$	29.5693	−	9.12093i	0.998486	−	0.307992i	0.247915	−	0.968782i	$-0.420255\pi$
$877$	29.5693	−	9.12093i	0.998486	−	0.307992i	0.750571	+	0.660790i	$0.229779\pi$
$878$	−0.0273019	−	0.0695642i	−0.000921395	−	0.00234768i
$879$	34.7289	+	32.2237i	1.17138	+	1.08688i
$880$	−46.6600	−	31.8122i	−1.57291	−	1.07239i
$881$	27.0783			0.912292			0.456146	−	0.889905i	$-0.349230\pi$
$881$	27.0783			0.912292			0.456146	+	0.889905i	$0.349230\pi$
$882$	0.431544	−	0.102312i	0.0145308	−	0.00344503i
$883$	−24.5437			−0.825962			−0.412981	−	0.910740i	$-0.635512\pi$
$883$	−24.5437			−0.825962			−0.412981	+	0.910740i	$0.635512\pi$
$884$	5.56596	+	3.79481i	0.187203	+	0.127633i
$885$	43.1197	+	40.0092i	1.44945	+	1.34490i
$886$	0.0499950	+	0.127385i	0.00167961	+	0.00427959i
$887$	20.3563	−	6.27907i	0.683496	−	0.210831i	0.0664878	−	0.997787i	$-0.478821\pi$
$887$	20.3563	−	6.27907i	0.683496	−	0.210831i	0.617008	+	0.786957i	$0.288344\pi$
$888$	−0.0281640	−	0.123395i	−0.000945123	−	0.00414085i
$889$	−13.1172	+	3.57377i	−0.439938	+	0.119860i
$890$	0.0329768	−	0.144481i	0.00110538	−	0.00484301i
$891$	−8.54832	−	114.069i	−0.286380	−	3.82147i
$892$	−34.1867	−	10.5452i	−1.14465	−	0.353079i
$893$	−0.160490	+	2.14159i	−0.00537060	+	0.0716657i
$894$	0.139846	−	0.356321i	0.00467714	−	0.0119171i
$895$	−45.8272	+	22.0692i	−1.53183	+	0.737692i
$896$	−0.758402	+	0.0886734i	−0.0253364	+	0.00296237i
$897$	−5.51319	−	2.65501i	−0.184080	−	0.0886482i
$898$	−0.124987	+	0.115971i	−0.00417087	+	0.00387001i
$899$	36.4572	−	5.49504i	1.21592	−	0.183270i
$900$	4.61680	−	7.99654i	0.153893	−	0.266551i
$901$	7.24930	+	12.5562i	0.241509	+	0.418306i
$902$	−0.196444	−	0.246333i	−0.00654087	−	0.00820199i
$903$	−25.5703	−	34.3442i	−0.850926	−	1.14290i
$904$	−0.320731	+	0.402184i	−0.0106674	+	0.0133764i
$905$	36.6325	+	5.52146i	1.21771	+	0.183540i
$906$	−0.298876	+	0.203770i	−0.00992949	+	0.00676981i
$907$	21.1369	−	14.4109i	0.701839	−	0.478506i	−0.159068	−	0.987268i	$-0.550849\pi$
$907$	21.1369	−	14.4109i	0.701839	−	0.478506i	0.860907	+	0.508762i	$0.169897\pi$
$908$	9.72723	+	1.46614i	0.322809	+	0.0486557i
$909$	−15.4321	+	19.3513i	−0.511852	+	0.641842i
$910$	0.0144607	−	0.0548875i	0.000479366	−	0.00181950i
$911$	−14.1578	−	17.7533i	−0.469069	−	0.588194i	0.489874	−	0.871793i	$-0.337043\pi$
$911$	−14.1578	−	17.7533i	−0.469069	−	0.588194i	−0.958943	+	0.283599i	$0.908471\pi$
$912$	24.4036	+	42.2682i	0.808083	+	1.39964i
$913$	−29.9989	+	51.9597i	−0.992820	+	1.71962i
$914$	0.267728	−	0.0403536i	0.00885567	−	0.00133478i
$915$	63.5035	−	58.9227i	2.09936	−	1.94792i
$916$	16.2640	+	7.83235i	0.537379	+	0.258788i
$917$	−19.9589	−	56.2810i	−0.659099	−	1.85856i
$918$	0.348782	−	0.167965i	0.0115115	−	0.00554366i
$919$	−5.01643	+	12.7817i	−0.165477	+	0.421628i	−0.989427	−	0.145035i	$-0.953671\pi$
$919$	−5.01643	+	12.7817i	−0.165477	+	0.421628i	0.823950	+	0.566663i	$0.191766\pi$
$920$	−0.0123939	+	0.165385i	−0.000408614	+	0.00545258i
$921$	−29.1223	−	8.98305i	−0.959613	−	0.296001i
$922$	−0.00467789	−	0.0624222i	−0.000154058	−	0.00205576i
$923$	−1.75387	+	7.68422i	−0.0577294	+	0.252929i
$924$	75.1100	−	65.1876i	2.47094	−	2.14451i
$925$	0.162059	+	0.710025i	0.00532845	+	0.0233455i
$926$	0.0487191	−	0.0150278i	0.00160101	−	0.000493846i
$927$	−2.28390	−	5.81928i	−0.0750131	−	0.191130i
$928$	0.441720	+	0.409856i	0.0145002	+	0.0134542i
$929$	11.7146	+	7.98686i	0.384343	+	0.262041i	0.740043	−	0.672560i	$-0.234805\pi$
$929$	11.7146	+	7.98686i	0.384343	+	0.262041i	−0.355700	+	0.934600i	$0.615758\pi$
$930$	0.449807			0.0147497
$931$	7.73606	−	25.8473i	0.253539	−	0.847112i
$932$	16.0774			0.526632
$933$	−31.7060	−	21.6168i	−1.03801	−	0.707701i
$934$	−0.0963107	−	0.0893633i	−0.00315138	−	0.00292406i
$935$	17.3761	+	44.2736i	0.568260	+	1.44790i
$936$	−0.242168	+	0.0746989i	−0.00791551	+	0.00244161i
$937$	1.47304	+	6.45382i	0.0481222	+	0.210837i	0.993273	−	0.115798i	$-0.0369424\pi$
$937$	1.47304	+	6.45382i	0.0481222	+	0.210837i	−0.945151	+	0.326635i	$0.894085\pi$
$938$	−0.0151932	−	0.365070i	−0.000496074	−	0.0119199i
$939$	13.6780	−	59.9273i	0.446365	−	1.95565i
$940$	−0.198070	−	2.64305i	−0.00646032	−	0.0862069i
$941$	−17.3073	−	5.33859i	−0.564201	−	0.174033i	−0.000482631	−	1.00000i	$-0.500154\pi$
$941$	−17.3073	−	5.33859i	−0.564201	−	0.174033i	−0.563719	+	0.825967i	$0.690630\pi$
$942$	0.0482655	−	0.644059i	0.00157258	−	0.0209846i
$943$	4.15480	−	10.5863i	0.135299	−	0.344736i
$944$	28.1465	−	13.5547i	0.916092	−	0.441167i
$945$	56.9352	+	56.4597i	1.85210	+	1.83663i
$946$	0.246591	+	0.118752i	0.00801736	+	0.00386096i
$947$	34.6685	−	32.1677i	1.12657	−	1.04531i	0.128009	−	0.991773i	$-0.459141\pi$
$947$	34.6685	−	32.1677i	1.12657	−	1.04531i	0.998566	−	0.0535355i	$-0.0170490\pi$
$948$	11.7182	−	1.76623i	0.380588	−	0.0573645i
$949$	−6.46422	+	11.1964i	−0.209837	+	0.363449i
$950$	0.0114251	+	0.0197889i	0.000370680	+	0.000642036i
$951$	20.0547	+	25.1478i	0.650319	+	0.815474i
$952$	0.284893	+	0.149045i	0.00923344	+	0.00483059i
$953$	−32.2038	+	40.3823i	−1.04318	+	1.30811i	−0.0932567	+	0.995642i	$0.529728\pi$
$953$	−32.2038	+	40.3823i	−1.04318	+	1.30811i	−0.949928	+	0.312470i	$0.898844\pi$
$954$	−0.269667	−	0.0406457i	−0.00873079	−	0.00131595i
$955$	−6.14384	+	4.18880i	−0.198810	+	0.135546i
$956$	30.0266	−	20.4718i	0.971129	−	0.662105i
$957$	−103.476	−	15.5965i	−3.34491	−	0.504165i
$958$	0.124137	−	0.155663i	0.00401070	−	0.00502926i
$959$	−33.1290	+	38.8247i	−1.06979	+	1.25372i
$960$	−37.5531	−	47.0901i	−1.21202	−	1.51983i
$961$	−6.42655	−	11.1311i	−0.207308	−	0.359068i
$962$	0.00499705	−	0.00865515i	0.000161111	−	0.000279053i
$963$	−59.2297	+	8.92744i	−1.90865	+	0.287683i
$964$	0.565588	−	0.524789i	0.0182164	−	0.0169023i
$965$	−3.74019	−	1.80118i	−0.120401	−	0.0579820i
$966$	−0.138034	−	0.0476515i	−0.00444117	−	0.00153316i
$967$	12.6667	−	6.09995i	0.407333	−	0.196161i	−0.218986	−	0.975728i	$-0.570275\pi$
$967$	12.6667	−	6.09995i	0.407333	−	0.196161i	0.626319	+	0.779567i	$0.284561\pi$
$968$	−0.319525	+	0.814137i	−0.0102699	+	0.0261674i
$969$	3.07181	−	40.9904i	0.0986807	−	1.31680i
$970$	0.0876971	+	0.0270510i	0.00281578	+	0.000868554i
$971$	−3.15317	−	42.0762i	−0.101190	−	1.35029i	−0.784486	−	0.620147i	$-0.787073\pi$
$971$	−3.15317	−	42.0762i	−0.101190	−	1.35029i	0.683295	−	0.730142i	$-0.260546\pi$
$972$	10.1388	−	44.4210i	0.325203	−	1.42481i
$973$	31.6183	+	23.1312i	1.01364	+	0.741552i
$974$	0.0448898	+	0.196675i	0.00143836	+	0.00630188i
$975$	1.98858	−	0.613396i	0.0636855	−	0.0196444i
$976$	−16.8088	−	42.8280i	−0.538035	−	1.37089i
$977$	19.7610	+	18.3355i	0.632211	+	0.586606i	0.929790	−	0.368091i	$-0.119989\pi$
$977$	19.7610	+	18.3355i	0.632211	+	0.586606i	−0.297579	+	0.954697i	$0.596179\pi$
$978$	−0.0261992	−	0.0178623i	−0.000837758	−	0.000571173i
$979$	41.0080			1.31062
$980$	−4.68646	+	32.9663i	−0.149704	+	1.05307i
$981$	89.4946			2.85734
$982$	0.151320	+	0.103168i	0.00482883	+	0.00329224i
$983$	−6.98972	−	6.48551i	−0.222937	−	0.206856i	0.560794	−	0.827955i	$-0.310496\pi$
$983$	−6.98972	−	6.48551i	−0.222937	−	0.206856i	−0.783732	+	0.621099i	$0.786686\pi$
$984$	−0.245561	−	0.625680i	−0.00782820	−	0.0199459i
$985$	−42.0441	+	12.9689i	−1.33964	+	0.413223i
$986$	−0.0376398	−	0.164911i	−0.00119870	−	0.00525183i
$987$	4.58972	+	0.848504i	0.146093	+	0.0270082i
$988$	−1.71526	+	7.51505i	−0.0545698	+	0.239086i
$989$	0.738253	+	9.85130i	0.0234751	+	0.313253i
$990$	−0.854865	−	0.263691i	−0.0271694	−	0.00838065i
$991$	−0.670426	+	8.94621i	−0.0212968	+	0.284186i	0.976380	+	0.216060i	$0.0693208\pi$
$991$	−0.670426	+	8.94621i	−0.0212968	+	0.284186i	−0.997677	+	0.0681254i	$0.978298\pi$
$992$	0.261848	−	0.667178i	0.00831368	−	0.0211829i
$993$	33.6416	−	16.2010i	1.06759	−	0.514122i
$994$	−0.0202756	+	0.186995i	−0.000643104	+	0.00593114i
$995$	38.7313	+	18.6520i	1.22787	+	0.591309i
$996$	−46.9120	+	43.5280i	−1.48646	+	1.37924i
$997$	18.3486	−	2.76560i	0.581105	−	0.0875874i	0.148089	−	0.988974i	$-0.452688\pi$
$997$	18.3486	−	2.76560i	0.581105	−	0.0875874i	0.433015	+	0.901387i	$0.357450\pi$
$998$	−0.0123303	+	0.0213568i	−0.000390310	+	0.000676037i
$999$	7.05911	+	12.2267i	0.223340	+	0.386837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.53.14	✓	348
49.37	even	21	inner	637.2.bl.b.625.14	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.14	✓	348	1.1	even	1	trivial
637.2.bl.b.625.14	yes	348	49.37	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.00745244 + 0.00508099i) q^{2} +(-2.32094 - 2.15352i) q^{3} +(-0.730652 - 1.86167i) q^{4} +(2.27283 - 0.701076i) q^{5} +(-0.00635467 - 0.0278416i) q^{6} +(-1.04784 + 2.42941i) q^{7} +(0.00802814 - 0.0351736i) q^{8} +(0.524933 + 7.00475i) q^{9} +O(q^{10})\)	\(q+(0.00745244 + 0.00508099i) q^{2} +(-2.32094 - 2.15352i) q^{3} +(-0.730652 - 1.86167i) q^{4} +(2.27283 - 0.701076i) q^{5} +(-0.00635467 - 0.0278416i) q^{6} +(-1.04784 + 2.42941i) q^{7} +(0.00802814 - 0.0351736i) q^{8} +(0.524933 + 7.00475i) q^{9} +(0.0205003 + 0.00632351i) q^{10} +(-0.443633 + 5.91987i) q^{11} +(-2.31334 + 5.89430i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(-0.0201528 + 0.0127810i) q^{14} +(-6.78489 - 3.26743i) q^{15} +(-2.93185 + 2.72036i) q^{16} +(3.33077 - 0.502032i) q^{17} +(-0.0316790 + 0.0548697i) q^{18} +(1.92716 + 3.33794i) q^{19} +(-2.96582 - 3.71903i) q^{20} +(7.66374 - 3.38198i) q^{21} +(-0.0333849 + 0.0418634i) q^{22} +(-1.91111 - 0.288054i) q^{23} +(-0.0943797 + 0.0643470i) q^{24} +(0.543070 - 0.370259i) q^{25} +(-0.00891898 - 0.00134432i) q^{26} +(7.94435 - 9.96191i) q^{27} +(5.28837 + 0.175674i) q^{28} +(-3.47129 - 4.35286i) q^{29} +(-0.0339622 - 0.0588243i) q^{30} +(-3.31108 + 5.73497i) q^{31} +(-0.107022 + 0.0161310i) q^{32} +(13.7782 - 12.7843i) q^{33} +(0.0273732 + 0.0131822i) q^{34} +(-0.678357 + 6.25626i) q^{35} +(12.6570 - 6.09529i) q^{36} +(-0.404808 + 1.03143i) q^{37} +(-0.00259798 + 0.0346676i) q^{38} +(3.02547 + 0.933234i) q^{39} +(-0.00641274 - 0.0855720i) q^{40} +(-1.30936 + 5.73668i) q^{41} +(0.0742974 + 0.0137354i) q^{42} +(-1.13741 - 4.98332i) q^{43} +(11.3450 - 3.49947i) q^{44} +(6.10395 + 15.5526i) q^{45} +(-0.0127788 - 0.0118570i) q^{46} +(0.460375 + 0.313878i) q^{47} +12.6630 q^{48} +(-4.80408 - 5.09125i) q^{49} +0.00592848 q^{50} +(-8.81164 - 6.00767i) q^{51} +(1.46604 + 1.36029i) q^{52} +(1.57254 + 4.00677i) q^{53} +(0.109821 - 0.0338753i) q^{54} +(3.14198 + 13.7659i) q^{55} +(0.0770389 + 0.0563598i) q^{56} +(2.71548 - 11.8973i) q^{57} +(-0.00375275 - 0.0500770i) q^{58} +(-7.46401 - 2.30234i) q^{59} +(-1.12549 + 15.0186i) q^{60} +(-4.20270 + 10.7083i) q^{61} +(-0.0538150 + 0.0259159i) q^{62} +(-17.5675 - 6.06456i) q^{63} +(7.20599 + 3.47022i) q^{64} +(-1.74357 + 1.61779i) q^{65} +(0.167638 - 0.0252674i) q^{66} +(-7.65560 + 13.2599i) q^{67} +(-3.36825 - 5.83398i) q^{68} +(3.81524 + 4.78416i) q^{69} +(-0.0368434 + 0.0431777i) q^{70} +(4.91424 - 6.16226i) q^{71} +(0.250596 + 0.0377713i) q^{72} +(10.6820 - 7.28285i) q^{73} +(-0.00825751 + 0.00562988i) q^{74} +(-2.05779 - 0.310162i) q^{75} +(4.80606 - 6.02661i) q^{76} +(-13.9169 - 7.28083i) q^{77} +(0.0178054 + 0.0223272i) q^{78} +(-0.935764 - 1.62079i) q^{79} +(-4.75643 + 8.23837i) q^{80} +(-19.0537 + 2.87188i) q^{81} +(-0.0389059 + 0.0360994i) q^{82} +(9.10579 + 4.38512i) q^{83} +(-11.8957 - 11.7963i) q^{84} +(7.21831 - 3.47616i) q^{85} +(0.0168437 - 0.0429170i) q^{86} +(-1.31730 + 17.5782i) q^{87} +(0.204662 + 0.0631297i) q^{88} +(-0.516222 - 6.88850i) q^{89} +(-0.0335333 + 0.146919i) q^{90} +(-0.110013 - 2.64346i) q^{91} +(0.860096 + 3.76833i) q^{92} +(20.0352 - 6.18003i) q^{93} +(0.00183611 + 0.00467832i) q^{94} +(6.72026 + 6.23549i) q^{95} +(0.283130 + 0.193035i) q^{96} +4.27784 q^{97} +(-0.00993349 - 0.0623517i) q^{98} -41.7001 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more