LMFDB - Embedded newform 115.2.g.b.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 12 x^{18} - 12 x^{17} + 56 x^{16} - 155 x^{15} + 551 x^{14} - 1189 x^{13} + \cdots + 1437601 $ x^20 - x^19 + 12x^18 - 12x^17 + 56x^16 - 155x^15 + 551x^14 - 1189x^13 + 3851x^12 - 10594x^11 + 18470x^10 - 22715x^9 + 56089x^8 + 1474x^7 - 31240x^6 + 12001x^5 + 243089x^4 + 225907x^3 + 23958x^2 + 857285x + 1437601
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			101.1
Root			$-1.14067 + 0.334930i$ of defining polynomial
Character	$\chi$	$=$	115.101
Dual form			115.2.g.b.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61435 + 0.474017i) q^{2} +(-0.778513 - 0.898452i) q^{3} +(0.698939 - 0.449181i) q^{4} +(0.142315 + 0.989821i) q^{5} +(1.68268 + 1.08139i) q^{6} +(1.06223 - 2.32595i) q^{7} +(1.28820 - 1.48666i) q^{8} +(0.225811 - 1.57055i) q^{9} +O(q^{10})$	\(q+(-1.61435 + 0.474017i) q^{2} +(-0.778513 - 0.898452i) q^{3} +(0.698939 - 0.449181i) q^{4} +(0.142315 + 0.989821i) q^{5} +(1.68268 + 1.08139i) q^{6} +(1.06223 - 2.32595i) q^{7} +(1.28820 - 1.48666i) q^{8} +(0.225811 - 1.57055i) q^{9} +(-0.698939 - 1.53046i) q^{10} +(4.12355 + 1.21078i) q^{11} +(-0.947701 - 0.278270i) q^{12} +(-2.56591 - 5.61856i) q^{13} +(-0.612269 + 4.25843i) q^{14} +(0.778513 - 0.898452i) q^{15} +(-2.06519 + 4.52213i) q^{16} +(2.45927 + 1.58048i) q^{17} +(0.379929 + 2.64246i) q^{18} +(3.55387 - 2.28394i) q^{19} +(0.544078 + 0.627899i) q^{20} +(-2.91672 + 0.856425i) q^{21} -7.23080 q^{22} +(-1.93922 + 4.38628i) q^{23} -2.33858 q^{24} +(-0.959493 + 0.281733i) q^{25} +(6.80558 + 7.85405i) q^{26} +(-4.58717 + 2.94799i) q^{27} +(-0.302341 - 2.10283i) q^{28} +(-6.89858 - 4.43345i) q^{29} +(-0.830914 + 1.81945i) q^{30} +(0.925621 - 1.06822i) q^{31} +(0.630471 - 4.38502i) q^{32} +(-2.12241 - 4.64742i) q^{33} +(-4.71931 - 1.38571i) q^{34} +(2.45345 + 0.720398i) q^{35} +(-0.547633 - 1.19915i) q^{36} +(0.434822 - 3.02425i) q^{37} +(-4.65458 + 5.37168i) q^{38} +(-3.05041 + 6.67947i) q^{39} +(1.65486 + 1.06351i) q^{40} +(0.00351200 + 0.0244265i) q^{41} +(4.30265 - 2.76515i) q^{42} +(4.65623 + 5.37358i) q^{43} +(3.42597 - 1.00596i) q^{44} +1.58670 q^{45} +(1.05142 - 8.00022i) q^{46} +11.0743 q^{47} +(5.67069 - 1.66507i) q^{48} +(0.302293 + 0.348865i) q^{49} +(1.41542 - 0.909632i) q^{50} +(-0.494592 - 3.43996i) q^{51} +(-4.31716 - 2.77447i) q^{52} +(-1.70884 + 3.74183i) q^{53} +(6.00791 - 6.93350i) q^{54} +(-0.611617 + 4.25389i) q^{55} +(-2.08955 - 4.57547i) q^{56} +(-4.81874 - 1.41491i) q^{57} +(13.2383 + 3.88711i) q^{58} +(-0.601837 - 1.31784i) q^{59} +(0.140566 - 0.977656i) q^{60} +(3.10198 - 3.57988i) q^{61} +(-0.987924 + 2.16325i) q^{62} +(-3.41316 - 2.19351i) q^{63} +(-0.354232 - 2.46373i) q^{64} +(5.19620 - 3.33940i) q^{65} +(5.62927 + 6.49653i) q^{66} +(-6.16371 + 1.80983i) q^{67} +2.42880 q^{68} +(5.45057 - 1.67247i) q^{69} -4.30222 q^{70} +(-9.02373 + 2.64961i) q^{71} +(-2.04399 - 2.35889i) q^{72} +(-7.84020 + 5.03859i) q^{73} +(0.731591 + 5.08832i) q^{74} +(1.00010 + 0.642726i) q^{75} +(1.45804 - 3.19266i) q^{76} +(7.19637 - 8.30506i) q^{77} +(1.75826 - 12.2290i) q^{78} +(0.950286 + 2.08084i) q^{79} +(-4.77001 - 1.40060i) q^{80} +(1.65252 + 0.485223i) q^{81} +(-0.0172482 - 0.0377683i) q^{82} +(-0.880246 + 6.12225i) q^{83} +(-1.65392 + 1.90872i) q^{84} +(-1.21440 + 2.65916i) q^{85} +(-10.0640 - 6.46773i) q^{86} +(1.38739 + 9.64954i) q^{87} +(7.11199 - 4.57060i) q^{88} +(9.70852 + 11.2042i) q^{89} +(-2.56150 + 0.752123i) q^{90} -15.7941 q^{91} +(0.614832 + 3.93680i) q^{92} -1.68036 q^{93} +(-17.8778 + 5.24940i) q^{94} +(2.76646 + 3.19266i) q^{95} +(-4.43056 + 2.84735i) q^{96} +(0.152308 + 1.05932i) q^{97} +(-0.653375 - 0.419899i) q^{98} +(2.83274 - 6.20283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−1.61435	+	0.474017i	−1.14152	+	0.335181i	−0.797226	−	0.603681i	$-0.793700\pi$
$2$	−1.61435	+	0.474017i	−1.14152	+	0.335181i	−0.344295	+	0.938862i	$0.611882\pi$
$3$	−0.778513	−	0.898452i	−0.449475	−	0.518722i	0.485114	−	0.874451i	$-0.338778\pi$
$3$	−0.778513	−	0.898452i	−0.449475	−	0.518722i	−0.934589	+	0.355729i	$0.884233\pi$
$4$	0.698939	−	0.449181i	0.349469	−	0.224590i
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$6$	1.68268	+	1.08139i	0.686950	+	0.441476i
$7$	1.06223	−	2.32595i	0.401484	−	0.879128i	−0.595633	−	0.803256i	$-0.703099\pi$
$7$	1.06223	−	2.32595i	0.401484	−	0.879128i	0.997118	−	0.0758714i	$-0.0241738\pi$
$8$	1.28820	−	1.48666i	0.455448	−	0.525615i
$9$	0.225811	−	1.57055i	0.0752703	−	0.523517i
$10$	−0.698939	−	1.53046i	−0.221024	−	0.483975i
$11$	4.12355	+	1.21078i	1.24330	+	0.365065i	0.836253	−	0.548344i	$-0.184741\pi$
$11$	4.12355	+	1.21078i	1.24330	+	0.365065i	0.407044	+	0.913409i	$0.366560\pi$
$12$	−0.947701	−	0.278270i	−0.273578	−	0.0803296i
$13$	−2.56591	−	5.61856i	−0.711655	−	1.55831i	−0.825242	−	0.564779i	$-0.808961\pi$
$13$	−2.56591	−	5.61856i	−0.711655	−	1.55831i	0.113587	−	0.993528i	$-0.463766\pi$
$14$	−0.612269	+	4.25843i	−0.163636	+	1.13811i
$15$	0.778513	−	0.898452i	0.201011	−	0.231979i
$16$	−2.06519	+	4.52213i	−0.516297	+	1.13053i
$17$	2.45927	+	1.58048i	0.596461	+	0.383322i	0.803758	−	0.594956i	$-0.202830\pi$
$17$	2.45927	+	1.58048i	0.596461	+	0.383322i	−0.207298	+	0.978278i	$0.566467\pi$
$18$	0.379929	+	2.64246i	0.0895500	+	0.622834i
$19$	3.55387	−	2.28394i	0.815314	−	0.523971i	−0.0652658	−	0.997868i	$-0.520790\pi$
$19$	3.55387	−	2.28394i	0.815314	−	0.523971i	0.880580	+	0.473897i	$0.157153\pi$
$20$	0.544078	+	0.627899i	0.121660	+	0.140403i
$21$	−2.91672	+	0.856425i	−0.636480	+	0.186887i
$22$	−7.23080			−1.54161
$23$	−1.93922	+	4.38628i	−0.404356	+	0.914602i
$23$	−1.93922	+	4.38628i	−0.404356	+	0.914602i
$24$	−2.33858			−0.477360
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	6.80558	+	7.85405i	1.33468	+	1.54031i
$27$	−4.58717	+	2.94799i	−0.882800	+	0.567341i
$28$	−0.302341	−	2.10283i	−0.0571372	−	0.397398i
$29$	−6.89858	−	4.43345i	−1.28103	−	0.823270i	−0.290019	−	0.957021i	$-0.593662\pi$
$29$	−6.89858	−	4.43345i	−1.28103	−	0.823270i	−0.991015	+	0.133751i	$0.957298\pi$
$30$	−0.830914	+	1.81945i	−0.151703	+	0.332184i
$31$	0.925621	−	1.06822i	0.166247	−	0.191859i	−0.666513	−	0.745493i	$-0.732214\pi$
$31$	0.925621	−	1.06822i	0.166247	−	0.191859i	0.832760	+	0.553634i	$0.186759\pi$
$32$	0.630471	−	4.38502i	0.111452	−	0.775169i
$33$	−2.12241	−	4.64742i	−0.369464	−	0.809013i
$34$	−4.71931	−	1.38571i	−0.809355	−	0.237648i
$35$	2.45345	+	0.720398i	0.414709	+	0.121769i
$36$	−0.547633	−	1.19915i	−0.0912721	−	0.199858i
$37$	0.434822	−	3.02425i	0.0714842	−	0.497184i	−0.922354	−	0.386345i	$-0.873737\pi$
$37$	0.434822	−	3.02425i	0.0714842	−	0.497184i	0.993838	−	0.110838i	$-0.0353536\pi$
$38$	−4.65458	+	5.37168i	−0.755073	+	0.871401i
$39$	−3.05041	+	6.67947i	−0.488457	+	1.06957i
$40$	1.65486	+	1.06351i	0.261656	+	0.168156i
$41$	0.00351200	+	0.0244265i	0.000548483	+	0.00381478i	0.990094	−	0.140407i	$-0.0448412\pi$
$41$	0.00351200	+	0.0244265i	0.000548483	+	0.00381478i	−0.989545	+	0.144222i	$0.953932\pi$
$42$	4.30265	−	2.76515i	0.663914	−	0.426671i
$43$	4.65623	+	5.37358i	0.710069	+	0.819463i	0.990076	−	0.140535i	$-0.0448821\pi$
$43$	4.65623	+	5.37358i	0.710069	+	0.819463i	−0.280007	+	0.959998i	$0.590337\pi$
$44$	3.42597	−	1.00596i	0.516484	−	0.151653i
$45$	1.58670			0.236531
$46$	1.05142	−	8.00022i	0.155024	−	1.17957i
$47$	11.0743			1.61535			0.807676	−	0.589627i	$-0.200725\pi$
$47$	11.0743			1.61535			0.807676	+	0.589627i	$0.200725\pi$
$48$	5.67069	−	1.66507i	0.818494	−	0.240331i
$49$	0.302293	+	0.348865i	0.0431847	+	0.0498378i
$50$	1.41542	−	0.909632i	0.200170	−	0.128641i
$51$	−0.494592	−	3.43996i	−0.0692567	−	0.481691i
$52$	−4.31716	−	2.77447i	−0.598682	−	0.384750i
$53$	−1.70884	+	3.74183i	−0.234727	+	0.513980i	−0.989938	−	0.141501i	$-0.954807\pi$
$53$	−1.70884	+	3.74183i	−0.234727	+	0.513980i	0.755211	+	0.655482i	$0.227534\pi$
$54$	6.00791	−	6.93350i	0.817573	−	0.943529i
$55$	−0.611617	+	4.25389i	−0.0824704	+	0.573594i
$56$	−2.08955	−	4.57547i	−0.279227	−	0.611423i
$57$	−4.81874	−	1.41491i	−0.638258	−	0.187410i
$58$	13.2383	+	3.88711i	1.73827	+	0.510402i
$59$	−0.601837	−	1.31784i	−0.0783526	−	0.171568i	0.866402	−	0.499348i	$-0.166427\pi$
$59$	−0.601837	−	1.31784i	−0.0783526	−	0.171568i	−0.944754	+	0.327780i	$0.893700\pi$
$60$	0.140566	−	0.977656i	0.0181470	−	0.126215i
$61$	3.10198	−	3.57988i	0.397168	−	0.458357i	−0.521579	−	0.853203i	$-0.674657\pi$
$61$	3.10198	−	3.57988i	0.397168	−	0.458357i	0.918747	+	0.394846i	$0.129202\pi$
$62$	−0.987924	+	2.16325i	−0.125466	+	0.274733i
$63$	−3.41316	−	2.19351i	−0.430018	−	0.276356i
$64$	−0.354232	−	2.46373i	−0.0442789	−	0.307967i
$65$	5.19620	−	3.33940i	0.644509	−	0.414201i
$66$	5.62927	+	6.49653i	0.692916	+	0.799667i
$67$	−6.16371	+	1.80983i	−0.753017	+	0.221106i	−0.635644	−	0.771982i	$-0.719265\pi$
$67$	−6.16371	+	1.80983i	−0.753017	+	0.221106i	−0.117373	+	0.993088i	$0.537447\pi$
$68$	2.42880			0.294535
$69$	5.45057	−	1.67247i	0.656172	−	0.201342i
$70$	−4.30222			−0.514213
$71$	−9.02373	+	2.64961i	−1.07092	+	0.314450i	−0.769241	−	0.638959i	$-0.779365\pi$
$71$	−9.02373	+	2.64961i	−1.07092	+	0.314450i	−0.301679	+	0.953410i	$0.597547\pi$
$72$	−2.04399	−	2.35889i	−0.240886	−	0.277998i
$73$	−7.84020	+	5.03859i	−0.917626	+	0.589723i	−0.911968	−	0.410261i	$-0.865437\pi$
$73$	−7.84020	+	5.03859i	−0.917626	+	0.589723i	−0.00565837	+	0.999984i	$0.501801\pi$
$74$	0.731591	+	5.08832i	0.0850457	+	0.591506i
$75$	1.00010	+	0.642726i	0.115482	+	0.0742156i
$76$	1.45804	−	3.19266i	0.167249	−	0.366223i
$77$	7.19637	−	8.30506i	0.820103	−	0.946449i
$78$	1.75826	−	12.2290i	0.199084	−	1.38466i
$79$	0.950286	+	2.08084i	0.106915	+	0.234112i	0.955527	−	0.294905i	$-0.0952880\pi$
$79$	0.950286	+	2.08084i	0.106915	+	0.234112i	−0.848611	+	0.529017i	$0.822561\pi$
$80$	−4.77001	−	1.40060i	−0.533303	−	0.156592i
$81$	1.65252	+	0.485223i	0.183613	+	0.0539136i
$82$	−0.0172482	−	0.0377683i	−0.00190475	−	0.00417081i
$83$	−0.880246	+	6.12225i	−0.0966196	+	0.672004i	0.882738	+	0.469866i	$0.155698\pi$
$83$	−0.880246	+	6.12225i	−0.0966196	+	0.672004i	−0.979357	+	0.202138i	$0.935211\pi$
$84$	−1.65392	+	1.90872i	−0.180457	+	0.208259i
$85$	−1.21440	+	2.65916i	−0.131720	+	0.288427i
$86$	−10.0640	−	6.46773i	−1.08523	−	0.697433i
$87$	1.38739	+	9.64954i	0.148744	+	1.03454i
$88$	7.11199	−	4.57060i	0.758140	−	0.487227i
$89$	9.70852	+	11.2042i	1.02910	+	1.18765i	0.982024	+	0.188754i	$0.0604449\pi$
$89$	9.70852	+	11.2042i	1.02910	+	1.18765i	0.0470762	+	0.998891i	$0.485010\pi$
$90$	−2.56150	+	0.752123i	−0.270005	+	0.0792807i
$91$	−15.7941			−1.65567
$92$	0.614832	+	3.93680i	0.0641006	+	0.410440i
$93$	−1.68036			−0.174245
$94$	−17.8778	+	5.24940i	−1.84396	+	0.541434i
$95$	2.76646	+	3.19266i	0.283833	+	0.327560i
$96$	−4.43056	+	2.84735i	−0.452192	+	0.290606i
$97$	0.152308	+	1.05932i	0.0154645	+	0.107558i	0.996092	−	0.0883256i	$-0.0281516\pi$
$97$	0.152308	+	1.05932i	0.0154645	+	0.107558i	−0.980627	+	0.195884i	$0.937243\pi$
$98$	−0.653375	−	0.419899i	−0.0660009	−	0.0424162i
$99$	2.83274	−	6.20283i	0.284701	−	0.623408i
$100$	−0.544078	+	0.627899i	−0.0544078	+	0.0627899i
$101$	1.25598	−	8.73551i	0.124974	−	0.869216i	−0.826817	−	0.562471i	$-0.809851\pi$
$101$	1.25598	−	8.73551i	0.124974	−	0.869216i	0.951792	−	0.306745i	$-0.0992400\pi$
$102$	2.42905	+	5.31887i	0.240511	+	0.526647i
$103$	5.92302	+	1.73916i	0.583612	+	0.171364i	0.560194	−	0.828362i	$-0.310727\pi$
$103$	5.92302	+	1.73916i	0.583612	+	0.171364i	0.0234188	+	0.999726i	$0.492545\pi$
$104$	−11.6583	−	3.42319i	−1.14319	−	0.335671i
$105$	−1.26280	−	2.76515i	−0.123237	−	0.269851i
$106$	0.984976	−	6.85066i	0.0956693	−	0.665395i
$107$	−1.67722	+	1.93561i	−0.162143	+	0.187122i	−0.831007	−	0.556262i	$-0.812235\pi$
$107$	−1.67722	+	1.93561i	−0.162143	+	0.187122i	0.668865	+	0.743384i	$0.266781\pi$
$108$	−1.88197	+	4.12093i	−0.181092	+	0.396537i
$109$	12.1967	+	7.83833i	1.16823	+	0.750776i	0.973186	−	0.230019i	$-0.0738787\pi$
$109$	12.1967	+	7.83833i	1.16823	+	0.750776i	0.195044	+	0.980795i	$0.437515\pi$
$110$	−1.02905	−	7.15720i	−0.0981161	−	0.682412i
$111$	−3.05566	+	1.96375i	−0.290030	+	0.186391i
$112$	8.32456	+	9.60706i	0.786597	+	0.907781i
$113$	−13.5057	+	3.96564i	−1.27051	+	0.373056i	−0.846397	−	0.532553i	$-0.821233\pi$
$113$	−13.5057	+	3.96564i	−1.27051	+	0.373056i	−0.424115	+	0.905608i	$0.639415\pi$
$114$	8.44985			0.791401
$115$	−4.61761	−	1.29525i	−0.430594	−	0.120783i
$116$	−6.81310			−0.632581
$117$	−9.40363	+	2.76116i	−0.869366	+	0.255269i
$118$	1.59626	+	1.84218i	0.146947	+	0.169586i
$119$	6.28842	−	4.04132i	0.576459	−	0.370468i
$120$	−0.332814	−	2.31477i	−0.0303816	−	0.211309i
$121$	6.28388	+	4.03840i	0.571261	+	0.367127i
$122$	−3.31078	+	7.24959i	−0.299744	+	0.656347i
$123$	0.0192119	−	0.0221717i	0.00173228	−	0.00199916i
$124$	0.167127	−	1.16239i	0.0150085	−	0.104386i
$125$	−0.415415	−	0.909632i	−0.0371558	−	0.0813600i
$126$	6.54981	+	1.92320i	0.583504	+	0.171332i
$127$	14.5978	+	4.28630i	1.29534	+	0.380347i	0.855536	−	0.517744i	$-0.173228\pi$
$127$	14.5978	+	4.28630i	1.29534	+	0.380347i	0.439809	+	0.898091i	$0.355046\pi$
$128$	5.42038	+	11.8690i	0.479098	+	1.04908i
$129$	1.20297	−	8.36681i	0.105915	−	0.736656i
$130$	−6.80558	+	7.85405i	−0.596888	+	0.688846i
$131$	−3.64105	+	7.97278i	−0.318120	+	0.696585i	−0.999371	−	0.0354645i	$-0.988709\pi$
$131$	−3.64105	+	7.97278i	−0.318120	+	0.696585i	0.681251	+	0.732050i	$0.261436\pi$
$132$	−3.57097	−	2.29492i	−0.310813	−	0.199747i
$133$	−1.53731	−	10.6922i	−0.133301	−	0.927131i
$134$	9.09251	−	5.84340i	0.785473	−	0.504793i
$135$	−3.57081	−	4.12093i	−0.307326	−	0.354673i
$136$	5.51767	−	1.62013i	0.473136	−	0.138925i
$137$	2.68759			0.229616			0.114808	−	0.993388i	$-0.463375\pi$
$137$	2.68759			0.229616			0.114808	+	0.993388i	$0.463375\pi$
$138$	−8.00637	+	5.28363i	−0.681547	+	0.449772i
$139$	6.16309			0.522747			0.261373	−	0.965238i	$-0.415825\pi$
$139$	6.16309			0.522747			0.261373	+	0.965238i	$0.415825\pi$
$140$	2.03840	−	0.598528i	0.172276	−	0.0505849i
$141$	−8.62148	−	9.94972i	−0.726060	−	0.837918i
$142$	13.3115	−	8.55480i	1.11708	−	0.717903i
$143$	−3.77780	−	26.2752i	−0.315915	−	2.19724i
$144$	6.63589	+	4.26462i	0.552990	+	0.355385i
$145$	3.40655	−	7.45930i	0.282899	−	0.619462i
$146$	10.2685	−	11.8505i	0.849826	−	0.980751i
$147$	0.0780991	−	0.543191i	0.00644151	−	0.0448017i
$148$	−1.05452	−	2.30908i	−0.0866811	−	0.189805i
$149$	−20.2368	−	5.94205i	−1.65786	−	0.486792i	−0.687044	−	0.726615i	$-0.741092\pi$
$149$	−20.2368	−	5.94205i	−1.65786	−	0.486792i	−0.970816	+	0.239824i	$0.922910\pi$
$150$	−1.91918	−	0.563522i	−0.156700	−	0.0460114i
$151$	7.95958	+	17.4290i	0.647741	+	1.41836i	0.893517	+	0.449029i	$0.148230\pi$
$151$	7.95958	+	17.4290i	0.647741	+	1.41836i	−0.245776	+	0.969327i	$0.579043\pi$
$152$	1.18266	−	8.22558i	0.0959264	−	0.667182i
$153$	3.03755	−	3.50552i	0.245571	−	0.283404i
$154$	−7.68075	+	16.8185i	−0.618933	+	1.35527i
$155$	1.18908	+	0.764176i	0.0955093	+	0.0613801i
$156$	0.868237	+	6.03872i	0.0695146	+	0.483485i
$157$	−10.3716	+	6.66540i	−0.827741	+	0.531957i	−0.884559	−	0.466427i	$-0.845541\pi$
$157$	−10.3716	+	6.66540i	−0.827741	+	0.531957i	0.0568181	+	0.998385i	$0.481905\pi$
$158$	−2.52045	−	2.90875i	−0.200516	−	0.231408i
$159$	4.69221	−	1.37776i	0.372117	−	0.109263i
$160$	4.43011			0.350231
$161$	8.14238	+	9.16977i	0.641709	+	0.722679i
$162$	−2.89775			−0.227669
$163$	2.84537	−	0.835477i	0.222867	−	0.0654396i	−0.168393	−	0.985720i	$-0.553858\pi$
$163$	2.84537	−	0.835477i	0.222867	−	0.0654396i	0.391260	+	0.920280i	$0.372039\pi$
$164$	0.0134266	+	0.0154951i	0.00104844	+	0.00120997i
$165$	4.29807	−	2.76220i	0.334604	−	0.215037i
$166$	−1.48102	−	10.3007i	−0.114950	−	0.799491i
$167$	1.46436	+	0.941089i	0.113316	+	0.0728237i	0.596071	−	0.802932i	$-0.296728\pi$
$167$	1.46436	+	0.941089i	0.113316	+	0.0728237i	−0.482755	+	0.875755i	$0.660364\pi$
$168$	−2.48410	+	5.43942i	−0.191653	+	0.419660i
$169$	−16.4711	+	19.0087i	−1.26701	+	1.46220i
$170$	0.699982	−	4.86848i	0.0536861	−	0.373395i
$171$	−2.78453	−	6.09727i	−0.212938	−	0.466270i
$172$	5.66813	+	1.66431i	0.432191	+	0.126903i
$173$	15.3746	+	4.51439i	1.16891	+	0.343223i	0.807889	−	0.589335i	$-0.200610\pi$
$173$	15.3746	+	4.51439i	1.16891	+	0.343223i	0.361021	+	0.932558i	$0.382428\pi$
$174$	−6.81379	−	14.9201i	−0.516552	−	1.13109i
$175$	−0.363903	+	2.53100i	−0.0275085	+	0.191326i
$176$	−13.9912	+	16.1467i	−1.05463	+	1.21711i
$177$	−0.715478	+	1.56668i	−0.0537786	+	0.117759i
$178$	−20.9840	−	13.4856i	−1.57282	−	1.01079i
$179$	−0.668570	−	4.65001i	−0.0499713	−	0.347558i	−0.999433	−	0.0336745i	$-0.989279\pi$
$179$	−0.668570	−	4.65001i	−0.0499713	−	0.347558i	0.949462	−	0.313883i	$-0.101630\pi$
$180$	1.10901	−	0.712715i	0.0826604	−	0.0531226i
$181$	−7.41120	−	8.55299i	−0.550870	−	0.635738i	0.410215	−	0.911989i	$-0.365454\pi$
$181$	−7.41120	−	8.55299i	−0.550870	−	0.635738i	−0.961086	+	0.276250i	$0.910908\pi$
$182$	25.4972	−	7.48666i	1.88998	−	0.554948i
$183$	−5.63129			−0.416277
$184$	4.02280	+	8.53337i	0.296565	+	0.629089i
$185$	3.05535			0.224634
$186$	2.71269	−	0.796518i	0.198904	−	0.0584035i
$187$	8.22731	+	9.49482i	0.601641	+	0.694330i
$188$	7.74025	−	4.97436i	0.564516	−	0.362792i
$189$	1.98428	+	13.8010i	0.144335	+	1.00387i
$190$	−5.97942	−	3.84274i	−0.433792	−	0.278781i
$191$	3.41196	−	7.47114i	0.246880	−	0.540593i	−0.745105	−	0.666948i	$-0.767600\pi$
$191$	3.41196	−	7.47114i	0.246880	−	0.540593i	0.991985	+	0.126355i	$0.0403278\pi$
$192$	−1.93777	+	2.23631i	−0.139847	+	0.161392i
$193$	1.90701	−	13.2635i	0.137269	−	0.954730i	−0.798469	−	0.602036i	$-0.794356\pi$
$193$	1.90701	−	13.2635i	0.137269	−	0.954730i	0.935739	−	0.352694i	$-0.114734\pi$
$194$	−0.748016	−	1.63793i	−0.0537044	−	0.117596i
$195$	−7.04560	−	2.06877i	−0.504546	−	0.148148i
$196$	0.367987	+	0.108051i	0.0262848	+	0.00771792i
$197$	−5.23571	−	11.4646i	−0.373029	−	0.816820i	−0.999307	−	0.0372201i	$-0.988150\pi$
$197$	−5.23571	−	11.4646i	−0.373029	−	0.816820i	0.626278	−	0.779600i	$-0.284578\pi$
$198$	−1.63279	+	11.3563i	−0.116038	+	0.807059i
$199$	12.5104	−	14.4378i	0.886839	−	1.02347i	−0.112716	−	0.993627i	$-0.535955\pi$
$199$	12.5104	−	14.4378i	0.886839	−	1.02347i	0.999555	−	0.0298392i	$-0.00949953\pi$
$200$	−0.817178	+	1.78937i	−0.0577832	+	0.126528i
$201$	6.42457	+	4.12882i	0.453154	+	0.291225i
$202$	2.11319	+	14.6976i	0.148684	+	1.03412i
$203$	−17.6398	+	11.3364i	−1.23807	+	0.795662i
$204$	−1.89085	−	2.18216i	−0.132386	−	0.152782i
$205$	−0.0236781	+	0.00695251i	−0.00165375	+	0.000485585i
$206$	−10.3862			−0.723643
$207$	6.45097	+	4.03612i	0.448373	+	0.280529i
$208$	30.7069			2.12914
$209$	17.4199	−	5.11495i	1.20496	−	0.353809i
$210$	3.34933	+	3.86534i	0.231126	+	0.266734i
$211$	−13.3345	+	8.56958i	−0.917987	+	0.589954i	−0.912073	−	0.410028i	$-0.865519\pi$
$211$	−13.3345	+	8.56958i	−0.917987	+	0.589954i	−0.00591408	+	0.999983i	$0.501883\pi$
$212$	0.486386	+	3.38289i	0.0334051	+	0.232338i
$213$	9.40564	+	6.04464i	0.644464	+	0.414172i
$214$	1.79011	−	3.91979i	0.122369	−	0.267951i
$215$	−4.65623	+	5.37358i	−0.317553	+	0.366475i
$216$	−1.52652	+	10.6172i	−0.103866	+	0.722407i
$217$	−1.50142	−	3.28765i	−0.101923	−	0.223180i
$218$	−23.4053	−	6.87240i	−1.58520	−	0.465458i
$219$	10.6306	+	3.12144i	0.718352	+	0.210927i
$220$	1.48328	+	3.24794i	0.100003	+	0.218976i
$221$	2.56974	−	17.8729i	0.172859	−	1.20226i
$222$	4.00206	−	4.61863i	0.268601	−	0.309982i
$223$	11.1793	−	24.4791i	0.748618	−	1.63924i	−0.0202154	−	0.999796i	$-0.506435\pi$
$223$	11.1793	−	24.4791i	0.748618	−	1.63924i	0.768833	−	0.639449i	$-0.220838\pi$
$224$	−9.52965	−	6.12433i	−0.636726	−	0.409199i
$225$	0.225811	+	1.57055i	0.0150541	+	0.104703i
$226$	19.9232	−	12.8039i	1.32527	−	0.851702i
$227$	−10.9945	−	12.6883i	−0.729729	−	0.842152i	0.262712	−	0.964874i	$-0.415383\pi$
$227$	−10.9945	−	12.6883i	−0.729729	−	0.842152i	−0.992441	+	0.122722i	$0.960837\pi$
$228$	−4.00356	+	1.17555i	−0.265142	+	0.0778527i
$229$	−18.9086			−1.24952			−0.624759	−	0.780818i	$-0.714803\pi$
$229$	−18.9086			−1.24952			−0.624759	+	0.780818i	$0.714803\pi$
$230$	8.06843	−	0.0978293i	0.532016	−	0.00645067i
$231$	−13.0642			−0.859559
$232$	−15.4778	+	4.54469i	−1.01617	+	0.298373i
$233$	13.8931	+	16.0335i	0.910169	+	1.05039i	0.998525	+	0.0543021i	$0.0172934\pi$
$233$	13.8931	+	16.0335i	0.910169	+	1.05039i	−0.0883554	+	0.996089i	$0.528161\pi$
$234$	13.8720	−	8.91496i	0.906838	−	0.582789i
$235$	1.57604	+	10.9616i	0.102809	+	0.715054i
$236$	−1.01260	−	0.650756i	−0.0659144	−	0.0423606i
$237$	1.12972	−	2.47374i	0.0733833	−	0.160687i
$238$	−8.23608	+	9.50495i	−0.533866	+	0.616114i
$239$	−3.49661	+	24.3195i	−0.226177	+	1.57310i	0.487819	+	0.872945i	$0.337793\pi$
$239$	−3.49661	+	24.3195i	−0.226177	+	1.57310i	−0.713996	+	0.700150i	$0.753116\pi$
$240$	2.45514	+	5.37601i	0.158479	+	0.347020i
$241$	25.2971	+	7.42790i	1.62953	+	0.478473i	0.963557	−	0.267503i	$-0.0861984\pi$
$241$	25.2971	+	7.42790i	1.62953	+	0.478473i	0.665973	+	0.745976i	$0.268017\pi$
$242$	−12.0587	−	3.54075i	−0.775161	−	0.227608i
$243$	5.94494	+	13.0176i	0.381368	+	0.835079i
$244$	0.560084	−	3.89547i	0.0358557	−	0.249382i
$245$	−0.302293	+	0.348865i	−0.0193128	+	0.0222881i
$246$	−0.0205051	+	0.0448998i	−0.00130735	+	0.00286271i
$247$	−21.9513	−	14.1073i	−1.39673	−	0.897624i
$248$	−0.395703	−	2.75217i	−0.0251272	−	0.174763i
$249$	6.18583	−	3.97539i	0.392011	−	0.251930i
$250$	1.10181	+	1.27155i	0.0696844	+	0.0804201i
$251$	4.09838	−	1.20339i	0.258687	−	0.0759575i	−0.149817	−	0.988714i	$-0.547869\pi$
$251$	4.09838	−	1.20339i	0.258687	−	0.0759575i	0.408505	+	0.912756i	$0.366050\pi$
$252$	−3.37087			−0.212345
$253$	−13.3073	+	15.7390i	−0.836624	+	0.989505i
$254$	−25.5978			−1.60615
$255$	3.33456	−	0.979115i	0.208818	−	0.0613146i
$256$	−11.1165	−	12.8291i	−0.694782	−	0.801821i
$257$	−0.255486	+	0.164191i	−0.0159368	+	0.0102419i	−0.548585	−	0.836095i	$-0.684833\pi$
$257$	−0.255486	+	0.164191i	−0.0159368	+	0.0102419i	0.532648	+	0.846337i	$0.321197\pi$
$258$	2.02400	+	14.0772i	0.126009	+	0.876409i
$259$	−6.57239	−	4.22382i	−0.408388	−	0.262455i
$260$	2.13183	−	4.66807i	0.132211	−	0.289501i
$261$	−8.52072	+	9.83344i	−0.527420	+	0.608675i
$262$	2.09870	−	14.5968i	0.129658	−	0.901794i
$263$	0.668046	+	1.46282i	0.0411935	+	0.0902012i	0.929110	−	0.369804i	$-0.120575\pi$
$263$	0.668046	+	1.46282i	0.0411935	+	0.0902012i	−0.887916	+	0.460005i	$0.847848\pi$
$264$	−9.64324	−	2.83151i	−0.593500	−	0.174267i
$265$	−3.94694	−	1.15893i	−0.242459	−	0.0711922i
$266$	7.55004	+	16.5323i	0.462923	+	1.01366i
$267$	2.50825	−	17.4453i	0.153503	−	1.06763i
$268$	−3.49511	+	4.03358i	−0.213498	+	0.246390i
$269$	−3.31470	+	7.25818i	−0.202101	+	0.442539i	−0.983360	−	0.181668i	$-0.941850\pi$
$269$	−3.31470	+	7.25818i	−0.202101	+	0.442539i	0.781259	+	0.624207i	$0.214578\pi$
$270$	7.71794	+	4.96002i	0.469699	+	0.301857i
$271$	−1.31832	−	9.16909i	−0.0800820	−	0.556982i	−0.989877	−	0.141925i	$-0.954671\pi$
$271$	−1.31832	−	9.16909i	−0.0800820	−	0.556982i	0.909795	−	0.415057i	$-0.136238\pi$
$272$	−12.2260	+	7.85716i	−0.741309	+	0.476410i
$273$	12.2959	+	14.1902i	0.744182	+	0.858832i
$274$	−4.33871	+	1.27396i	−0.262111	+	0.0769628i
$275$	−4.29763			−0.259157
$276$	3.05837	−	3.61725i	0.184092	−	0.217733i
$277$	−27.9622			−1.68009			−0.840044	−	0.542518i	$-0.817471\pi$
$277$	−27.9622			−1.68009			−0.840044	+	0.542518i	$0.817471\pi$
$278$	−9.94941	+	2.92141i	−0.596726	+	0.175215i
$279$	−1.46868	−	1.69495i	−0.0879278	−	0.101474i
$280$	4.23152	−	2.71943i	0.252882	−	0.162517i
$281$	−1.12487	−	7.82362i	−0.0671039	−	0.466718i	−0.995472	−	0.0950557i	$-0.969697\pi$
$281$	−1.12487	−	7.82362i	−0.0671039	−	0.466718i	0.928368	−	0.371662i	$-0.121212\pi$
$282$	18.6345	+	11.9756i	1.10967	+	0.713139i
$283$	2.20580	−	4.83003i	0.131121	−	0.287116i	−0.832672	−	0.553767i	$-0.813190\pi$
$283$	2.20580	−	4.83003i	0.131121	−	0.287116i	0.963793	+	0.266651i	$0.0859172\pi$
$284$	−5.11688	+	5.90520i	−0.303631	+	0.350409i
$285$	0.714731	−	4.97106i	0.0423370	−	0.294460i
$286$	18.5536	+	40.6267i	1.09710	+	2.40230i
$287$	0.0605455	+	0.0177778i	0.00357389	+	0.00104939i
$288$	−6.74452	−	1.98037i	−0.397425	−	0.116694i
$289$	−3.51195	−	7.69010i	−0.206585	−	0.452359i
$290$	−1.96354	+	13.6567i	−0.115303	+	0.801950i
$291$	0.833178	−	0.961539i	0.0488418	−	0.0563664i
$292$	−3.21658	+	7.04333i	−0.188236	+	0.412180i
$293$	−5.50895	−	3.54039i	−0.321836	−	0.206832i	0.369740	−	0.929135i	$-0.379447\pi$
$293$	−5.50895	−	3.54039i	−0.321836	−	0.206832i	−0.691576	+	0.722304i	$0.743083\pi$
$294$	0.131402	+	0.913923i	0.00766354	+	0.0533011i
$295$	1.21878	−	0.783260i	0.0709599	−	0.0456031i
$296$	−3.93590	−	4.54228i	−0.228770	−	0.264014i
$297$	−22.4848	+	6.60213i	−1.30470	+	0.383094i
$298$	35.4859			2.05565
$299$	29.6204	−	0.359146i	1.71299	−	0.0207700i
$300$	0.987710			0.0570254
$301$	17.4447	−	5.12222i	1.00549	−	0.295240i
$302$	−21.1112	−	24.3637i	−1.21482	−	1.40197i
$303$	−8.82624	+	5.67228i	−0.507054	+	0.325864i
$304$	2.98884	+	20.7878i	0.171422	+	1.19226i
$305$	3.98490	+	2.56094i	0.228175	+	0.146639i
$306$	−3.24200	+	7.09900i	−0.185333	+	0.405823i
$307$	3.44529	−	3.97607i	0.196633	−	0.226926i	−0.648867	−	0.760902i	$-0.724757\pi$
$307$	3.44529	−	3.97607i	0.196633	−	0.226926i	0.845500	+	0.533975i	$0.179302\pi$
$308$	1.29935	−	9.03720i	0.0740375	−	0.514942i
$309$	−3.04860	−	6.67551i	−0.173429	−	0.379756i
$310$	−2.28183	−	0.670006i	−0.129599	−	0.0380538i
$311$	−5.70257	−	1.67442i	−0.323363	−	0.0949479i	0.116022	−	0.993247i	$-0.462986\pi$
$311$	−5.70257	−	1.67442i	−0.323363	−	0.0949479i	−0.439385	+	0.898299i	$0.644804\pi$
$312$	6.00058	+	13.1394i	0.339716	+	0.743874i
$313$	0.116785	−	0.812258i	0.00660108	−	0.0459115i	−0.986255	−	0.165232i	$-0.947163\pi$
$313$	0.116785	−	0.812258i	0.00660108	−	0.0459115i	0.992856	+	0.119321i	$0.0380717\pi$
$314$	13.5839	−	15.6766i	0.766582	−	0.884683i
$315$	1.68544	−	3.69059i	0.0949636	−	0.207941i
$316$	1.59886	+	1.02753i	0.0899430	+	0.0578029i
$317$	1.22138	+	8.49491i	0.0685997	+	0.477122i	0.994943	+	0.100441i	$0.0320254\pi$
$317$	1.22138	+	8.49491i	0.0685997	+	0.477122i	−0.926343	+	0.376680i	$0.877065\pi$
$318$	−6.92181	+	4.44838i	−0.388156	+	0.249453i
$319$	−23.0787	−	26.6342i	−1.29216	−	1.49123i
$320$	2.38825	−	0.701252i	0.133507	−	0.0392012i
$321$	3.04479			0.169944
$322$	−17.4913	−	10.9436i	−0.974752	−	0.609864i
$323$	12.3496			0.687153
$324$	1.37296	−	0.403138i	0.0762756	−	0.0223965i
$325$	4.04490	+	4.66807i	0.224371	+	0.258938i
$326$	−4.19741	+	2.69751i	−0.232473	+	0.149401i
$327$	−2.45291	−	17.0604i	−0.135646	−	0.943441i
$328$	0.0408382	+	0.0262451i	0.00225491	+	0.00144914i
$329$	11.7634	−	25.7583i	0.648538	−	1.42010i
$330$	−5.62927	+	6.49653i	−0.309881	+	0.357622i
$331$	0.0938038	−	0.652420i	0.00515593	−	0.0358602i	−0.987081	−	0.160222i	$-0.948779\pi$
$331$	0.0938038	−	0.652420i	0.00515593	−	0.0358602i	0.992237	+	0.124361i	$0.0396882\pi$
$332$	2.13476	+	4.67447i	0.117160	+	0.256545i
$333$	−4.65155	−	1.36582i	−0.254903	−	0.0748464i
$334$	−2.81009	−	0.825118i	−0.153761	−	0.0451484i
$335$	−2.66859	−	5.84340i	−0.145801	−	0.319259i
$336$	2.15070	−	14.9584i	0.117330	−	0.816050i
$337$	20.4256	−	23.5723i	1.11265	−	1.28407i	0.157640	−	0.987497i	$-0.449611\pi$
$337$	20.4256	−	23.5723i	1.11265	−	1.28407i	0.955011	−	0.296571i	$-0.0958431\pi$
$338$	17.5797	−	38.4943i	0.956212	−	2.09381i
$339$	14.0773	+	9.04695i	0.764575	+	0.491363i
$340$	0.345654	+	2.40408i	0.0187457	+	0.130379i
$341$	5.11023	−	3.28415i	0.276735	−	0.177847i
$342$	7.38543	+	8.52324i	0.399358	+	0.460884i
$343$	18.3067	−	5.37533i	0.988468	−	0.290241i
$344$	13.9869			0.754121
$345$	2.43115	+	5.15707i	0.130889	+	0.277648i
$346$	−26.9600			−1.44938
$347$	11.8807	−	3.48849i	0.637790	−	0.187272i	0.0531778	−	0.998585i	$-0.483065\pi$
$347$	11.8807	−	3.48849i	0.637790	−	0.187272i	0.584612	+	0.811313i	$0.301247\pi$
$348$	5.30409	+	6.12125i	0.284329	+	0.328133i
$349$	−2.13918	+	1.37477i	−0.114508	+	0.0735897i	−0.596641	−	0.802508i	$-0.703498\pi$
$349$	−2.13918	+	1.37477i	−0.114508	+	0.0735897i	0.482133	+	0.876098i	$0.339862\pi$
$350$	−0.612269	−	4.25843i	−0.0327272	−	0.227622i
$351$	28.3337	+	18.2090i	1.51234	+	0.971923i
$352$	7.90908	−	17.3185i	0.421556	−	0.923078i
$353$	−1.58730	+	1.83184i	−0.0844836	+	0.0974993i	−0.796417	−	0.604747i	$-0.793274\pi$
$353$	−1.58730	+	1.83184i	−0.0844836	+	0.0974993i	0.711934	+	0.702247i	$0.247820\pi$
$354$	0.412402	−	2.86832i	0.0219189	−	0.152450i
$355$	−3.90685	−	8.55480i	−0.207354	−	0.454042i
$356$	11.8184	+	3.47019i	0.626373	+	0.183920i
$357$	−8.52656	−	2.50362i	−0.451273	−	0.132506i
$358$	3.28349	+	7.18984i	0.173538	+	0.379995i
$359$	−2.64132	+	18.3708i	−0.139403	+	0.969571i	0.793275	+	0.608863i	$0.208374\pi$
$359$	−2.64132	+	18.3708i	−0.139403	+	0.969571i	−0.932679	+	0.360708i	$0.882535\pi$
$360$	2.04399	−	2.35889i	0.107728	−	0.124324i
$361$	−0.479233	+	1.04937i	−0.0252228	+	0.0552302i
$362$	16.0186	+	10.2945i	0.841917	+	0.541067i
$363$	−1.26377	−	8.78971i	−0.0663307	−	0.461340i
$364$	−11.0391	+	7.09439i	−0.578606	+	0.371847i
$365$	−6.10308	−	7.04333i	−0.319450	−	0.368665i
$366$	9.09089	−	2.66933i	0.475189	−	0.139528i
$367$	18.8515			0.984042			0.492021	−	0.870583i	$-0.336258\pi$
$367$	18.8515			0.984042			0.492021	+	0.870583i	$0.336258\pi$
$368$	−15.8304	−	17.8279i	−0.825219	−	0.929343i
$369$	0.0391561			0.00203839
$370$	−4.93242	+	1.44829i	−0.256424	+	0.0752929i
$371$	6.88815	+	7.94935i	0.357615	+	0.412710i
$372$	−1.17447	+	0.754784i	−0.0608933	+	0.0391337i
$373$	−1.28430	−	8.93252i	−0.0664987	−	0.462508i	−0.995678	−	0.0928779i	$-0.970393\pi$
$373$	−1.28430	−	8.93252i	−0.0664987	−	0.462508i	0.929179	−	0.369631i	$-0.120516\pi$
$374$	−17.7825	−	11.4281i	−0.919511	−	0.590934i
$375$	−0.493855	+	1.08139i	−0.0255026	+	0.0558428i
$376$	14.2659	−	16.4637i	0.735708	−	0.849052i
$377$	−7.20845	+	50.1359i	−0.371254	+	2.58213i
$378$	−9.74522	−	21.3391i	−0.501240	−	1.09756i
$379$	−15.1456	−	4.44716i	−0.777980	−	0.228435i	−0.131449	−	0.991323i	$-0.541963\pi$
$379$	−15.1456	−	4.44716i	−0.777980	−	0.228435i	−0.646531	+	0.762888i	$0.723781\pi$
$380$	3.36767	+	0.988836i	0.172758	+	0.0507262i
$381$	−7.51354	−	16.4524i	−0.384930	−	0.842880i
$382$	−1.96666	+	13.6784i	−0.100623	+	0.699847i
$383$	−23.0208	+	26.5675i	−1.17631	+	1.35753i	−0.255841	+	0.966719i	$0.582352\pi$
$383$	−23.0208	+	26.5675i	−1.17631	+	1.35753i	−0.920469	+	0.390815i	$0.872193\pi$
$384$	6.44387	−	14.1101i	0.328837	−	0.720053i
$385$	9.24467	+	5.94119i	0.471152	+	0.302791i
$386$	3.20856	+	22.3160i	0.163311	+	1.13585i
$387$	9.49091	−	6.09943i	0.482450	−	0.310052i
$388$	0.582281	+	0.671988i	0.0295608	+	0.0341150i
$389$	12.8155	−	3.76297i	0.649772	−	0.190790i	0.0597952	−	0.998211i	$-0.480955\pi$
$389$	12.8155	−	3.76297i	0.649772	−	0.190790i	0.589976	+	0.807420i	$0.299137\pi$
$390$	12.3547			0.625606
$391$	−11.7015	+	7.72214i	−0.591770	+	0.390526i
$392$	0.908058			0.0458638
$393$	9.99777	−	2.93561i	0.504321	−	0.148082i
$394$	13.8867	+	16.0261i	0.699603	+	0.807385i
$395$	−1.92442	+	1.23675i	−0.0968279	+	0.0622275i
$396$	−0.806281	−	5.60781i	−0.0405172	−	0.281803i
$397$	−5.15385	−	3.31218i	−0.258665	−	0.166234i	0.404881	−	0.914369i	$-0.367313\pi$
$397$	−5.15385	−	3.31218i	−0.258665	−	0.166234i	−0.663546	+	0.748136i	$0.730949\pi$
$398$	−13.3525	+	29.2378i	−0.669298	+	1.46556i
$399$	−8.40962	+	9.70522i	−0.421008	+	0.485869i
$400$	0.707501	−	4.92078i	0.0353751	−	0.246039i
$401$	13.0337	+	28.5399i	0.650874	+	1.42521i	0.890787	+	0.454420i	$0.150153\pi$
$401$	13.0337	+	28.5399i	0.650874	+	1.42521i	−0.239914	+	0.970794i	$0.577119\pi$
$402$	−12.3287	−	3.62002i	−0.614898	−	0.180550i
$403$	−8.37694	−	2.45969i	−0.417285	−	0.122526i
$404$	−3.04597	−	6.66975i	−0.151543	−	0.331832i
$405$	−0.245106	+	1.70475i	−0.0121794	+	0.0847098i
$406$	23.1033	−	26.6626i	1.14660	−	1.32324i
$407$	5.45472	−	11.9442i	0.270381	−	0.592051i
$408$	−5.75120	−	3.69607i	−0.284727	−	0.182983i
$409$	4.50395	+	31.3257i	0.222706	+	1.54895i	0.727739	+	0.685854i	$0.240571\pi$
$409$	4.50395	+	31.3257i	0.222706	+	1.54895i	−0.505033	+	0.863100i	$0.668520\pi$
$410$	0.0349292	−	0.0224476i	0.00172503	−	0.00110861i
$411$	−2.09232	−	2.41467i	−0.103207	−	0.119107i
$412$	4.92102	−	1.44494i	0.242441	−	0.0711872i
$413$	−3.70452			−0.182288
$414$	−12.3273	−	3.45785i	−0.605855	−	0.169944i
$415$	−6.18520			−0.303620
$416$	−26.2552	+	7.70922i	−1.28727	+	0.377976i
$417$	−4.79805	−	5.53725i	−0.234962	−	0.271160i
$418$	−25.6973	+	16.5147i	−1.25690	+	0.807759i
$419$	−2.50887	−	17.4496i	−0.122567	−	0.852469i	−0.954631	−	0.297790i	$-0.903750\pi$
$419$	−2.50887	−	17.4496i	−0.122567	−	0.852469i	0.832065	−	0.554679i	$-0.187159\pi$
$420$	−2.12467	−	1.36544i	−0.103673	−	0.0666268i
$421$	−11.8533	+	25.9551i	−0.577695	+	1.26497i	0.364903	+	0.931045i	$0.381102\pi$
$421$	−11.8533	+	25.9551i	−0.577695	+	1.26497i	−0.942598	+	0.333930i	$0.891625\pi$
$422$	17.4645	−	20.1551i	0.850160	−	0.981136i
$423$	2.50070	−	17.3927i	0.121588	−	0.845663i
$424$	3.36152	+	7.36070i	0.163250	+	0.357467i
$425$	−2.80493	−	0.823600i	−0.136059	−	0.0399505i
$426$	−18.0493	−	5.29975i	−0.874491	−	0.256774i
$427$	−5.03162	−	11.0177i	−0.243497	−	0.533185i
$428$	−0.302832	+	2.10625i	−0.0146380	+	0.101809i
$429$	−20.6659	+	23.8497i	−0.997760	+	1.15148i
$430$	4.96964	−	10.8820i	0.239657	−	0.524776i
$431$	−33.0639	−	21.2489i	−1.59263	−	1.02352i	−0.970651	−	0.240492i	$-0.922691\pi$
$431$	−33.0639	−	21.2489i	−1.59263	−	1.02352i	−0.621982	−	0.783032i	$-0.713672\pi$
$432$	−3.85785	−	26.8319i	−0.185611	−	1.29095i
$433$	−9.85132	+	6.33106i	−0.473424	+	0.304251i	−0.755509	−	0.655138i	$-0.772610\pi$
$433$	−9.85132	+	6.33106i	−0.473424	+	0.304251i	0.282085	+	0.959389i	$0.408974\pi$
$434$	3.98222	+	4.59573i	0.191153	+	0.220602i
$435$	−9.35388	+	2.74655i	−0.448484	+	0.131687i
$436$	12.0456			0.576878
$437$	3.12622	+	20.0173i	0.149547	+	0.957559i
$438$	−18.6412			−0.890712
$439$	−9.25815	+	2.71844i	−0.441867	+	0.129744i	−0.495096	−	0.868838i	$-0.664867\pi$
$439$	−9.25815	+	2.71844i	−0.441867	+	0.129744i	0.0532284	+	0.998582i	$0.483049\pi$
$440$	5.53621	+	6.38913i	0.263929	+	0.304590i
$441$	0.616170	−	0.395989i	0.0293414	−	0.0188566i
$442$	4.32360	+	30.0713i	0.205653	+	1.43035i
$443$	−8.48657	−	5.45399i	−0.403209	−	0.259127i	0.323282	−	0.946303i	$-0.395214\pi$
$443$	−8.48657	−	5.45399i	−0.403209	−	0.259127i	−0.726491	+	0.687176i	$0.758850\pi$
$444$	−1.25364	+	2.74509i	−0.0594951	+	0.130276i
$445$	−9.70852	+	11.2042i	−0.460228	+	0.531131i
$446$	−6.44373	+	44.8172i	−0.305120	+	2.12215i
$447$	10.4159	+	22.8077i	0.492657	+	1.07877i
$448$	−6.10681	−	1.79312i	−0.288519	−	0.0847170i
$449$	−20.9433	−	6.14952i	−0.988377	−	0.290214i	−0.252699	−	0.967545i	$-0.581318\pi$
$449$	−20.9433	−	6.14952i	−0.988377	−	0.290214i	−0.735678	+	0.677331i	$0.763136\pi$
$450$	−1.10901	−	2.42838i	−0.0522791	−	0.114475i
$451$	−0.0150933	+	0.104976i	−0.000710716	+	0.00494314i
$452$	−7.65839	+	8.83825i	−0.360220	+	0.415716i
$453$	9.46253	−	20.7200i	0.444588	−	0.973513i
$454$	23.7634	+	15.2718i	1.11527	+	0.716742i
$455$	−2.24773	−	15.6333i	−0.105375	−	0.732901i
$456$	−8.31101	+	5.34116i	−0.389199	+	0.250123i
$457$	6.97941	+	8.05467i	0.326483	+	0.376781i	0.895134	−	0.445798i	$-0.147080\pi$
$457$	6.97941	+	8.05467i	0.326483	+	0.376781i	−0.568651	+	0.822579i	$0.692534\pi$
$458$	30.5252	−	8.96301i	1.42635	−	0.418814i
$459$	−15.9403			−0.744030
$460$	−3.80923	+	1.16884i	−0.177606	+	0.0544974i
$461$	40.1690			1.87086			0.935429	−	0.353516i	$-0.115014\pi$
$461$	40.1690			1.87086			0.935429	+	0.353516i	$0.115014\pi$
$462$	21.0902	−	6.19264i	0.981205	−	0.288108i
$463$	6.64251	+	7.66586i	0.308704	+	0.356263i	0.888808	−	0.458279i	$-0.151534\pi$
$463$	6.64251	+	7.66586i	0.308704	+	0.356263i	−0.580105	+	0.814542i	$0.696988\pi$
$464$	34.2955	−	22.0404i	1.59213	−	1.02320i
$465$	−0.239140	−	1.66325i	−0.0110898	−	0.0771315i
$466$	−30.0286	−	19.2982i	−1.39105	−	0.893972i
$467$	−7.03002	+	15.3936i	−0.325311	+	0.712331i	−0.999660	−	0.0260816i	$-0.991697\pi$
$467$	−7.03002	+	15.3936i	−0.325311	+	0.712331i	0.674349	+	0.738413i	$0.264424\pi$
$468$	−5.33231	+	6.15381i	−0.246486	+	0.284460i
$469$	−2.33768	+	16.2589i	−0.107944	+	0.750768i
$470$	−7.74025	−	16.9488i	−0.357031	−	0.781789i
$471$	14.0630	+	4.12926i	0.647987	+	0.190266i
$472$	−2.73447	−	0.802913i	−0.125864	−	0.0369571i
$473$	12.6940	+	27.7959i	0.583669	+	1.27806i
$474$	−0.651173	+	4.52901i	−0.0299094	+	0.208024i
$475$	−2.76646	+	3.19266i	−0.126934	+	0.146489i
$476$	2.57994	−	5.64928i	0.118251	−	0.258934i
$477$	5.49086	+	3.52876i	0.251409	+	0.161571i
$478$	−5.88307	−	40.9177i	−0.269085	−	1.87153i
$479$	−6.72193	+	4.31992i	−0.307133	+	0.197382i	−0.685123	−	0.728427i	$-0.740252\pi$
$479$	−6.72193	+	4.31992i	−0.307133	+	0.197382i	0.377990	+	0.925810i	$0.376615\pi$
$480$	−3.44890	−	3.98024i	−0.157420	−	0.181672i
$481$	−18.1076	+	5.31688i	−0.825637	+	0.242429i
$482$	−44.3594			−2.02052
$483$	1.89965	−	14.4543i	0.0864370	−	0.657694i
$484$	6.20602			0.282092
$485$	−1.02687	+	0.301515i	−0.0466275	+	0.0136911i
$486$	−15.7678	−	18.1970i	−0.715241	−	0.825433i
$487$	−7.46863	+	4.79980i	−0.338436	+	0.217500i	−0.698808	−	0.715309i	$-0.746286\pi$
$487$	−7.46863	+	4.79980i	−0.338436	+	0.217500i	0.360372	+	0.932809i	$0.382650\pi$
$488$	−1.32610	−	9.22321i	−0.0600296	−	0.417515i
$489$	−2.96580	−	1.90600i	−0.134118	−	0.0861924i
$490$	0.322640	−	0.706483i	0.0145754	−	0.0319156i
$491$	13.3407	−	15.3960i	0.602059	−	0.694813i	−0.370139	−	0.928977i	$-0.620690\pi$
$491$	13.3407	−	15.3960i	0.602059	−	0.694813i	0.972197	+	0.234164i	$0.0752352\pi$
$492$	0.00346884	−	0.0241263i	0.000156387	−	0.00108770i
$493$	−9.95851	−	21.8061i	−0.448509	−	0.982097i
$494$	42.1243	+	12.3688i	1.89526	+	0.556499i
$495$	6.54284	+	1.92115i	0.294079	+	0.0863493i
$496$	2.91906	+	6.39186i	0.131070	+	0.287003i
$497$	−3.42239	+	23.8033i	−0.153515	+	1.06772i
$498$	−8.10172	+	9.34988i	−0.363047	+	0.418978i
$499$	−1.50040	+	3.28543i	−0.0671673	+	0.147076i	−0.940238	−	0.340517i	$-0.889398\pi$
$499$	−1.50040	+	3.28543i	−0.0671673	+	0.147076i	0.873071	+	0.487593i	$0.162125\pi$
$500$	−0.698939	−	0.449181i	−0.0312575	−	0.0200880i
$501$	−0.294503	−	2.04831i	−0.0131574	−	0.0915118i
$502$	−6.04581	+	3.88540i	−0.269838	+	0.173414i
$503$	−14.4614	−	16.6893i	−0.644802	−	0.744141i	0.335414	−	0.942071i	$-0.391124\pi$
$503$	−14.4614	−	16.6893i	−0.644802	−	0.744141i	−0.980216	+	0.197930i	$0.936578\pi$
$504$	−7.65784	+	2.24855i	−0.341107	+	0.100158i
$505$	8.82534			0.392723
$506$	14.0221	−	31.7163i	0.623360	−	1.40996i
$507$	29.9013			1.32797
$508$	12.1283	−	3.56119i	0.538106	−	0.158002i
$509$	−8.57786	−	9.89938i	−0.380207	−	0.438782i	0.533101	−	0.846051i	$-0.321026\pi$
$509$	−8.57786	−	9.89938i	−0.380207	−	0.438782i	−0.913308	+	0.407269i	$0.866481\pi$
$510$	−4.91904	+	3.16128i	−0.217819	+	0.139984i
$511$	3.39145	+	23.5881i	0.150029	+	1.04348i
$512$	2.07369	+	1.33268i	0.0916449	+	0.0588966i
$513$	−9.56918	+	20.9536i	−0.422490	+	0.925123i
$514$	0.334616	−	0.386167i	0.0147593	−	0.0170331i
$515$	−0.878520	+	6.11024i	−0.0387122	+	0.269249i
$516$	−2.91741	−	6.38824i	−0.128432	−	0.281226i
$517$	45.6654	+	13.4086i	2.00836	+	0.589708i
$518$	12.6123	+	3.70331i	0.554154	+	0.162714i
$519$	−7.91337	−	17.3279i	−0.347359	−	0.760609i
$520$	1.72919	−	12.0268i	0.0758302	−	0.527410i
$521$	19.2278	−	22.1900i	0.842385	−	0.972164i	−0.157497	−	0.987519i	$-0.550343\pi$
$521$	19.2278	−	22.1900i	0.842385	−	0.972164i	0.999882	+	0.0153557i	$0.00488807\pi$
$522$	9.09424	−	19.9136i	0.398044	−	0.871595i
$523$	34.5668	+	22.2147i	1.51150	+	0.971383i	0.993230	+	0.116166i	$0.0370605\pi$
$523$	34.5668	+	22.2147i	1.51150	+	0.971383i	0.518271	+	0.855216i	$0.326576\pi$
$524$	1.03635	+	7.20798i	0.0452732	+	0.314882i
$525$	2.55729	−	1.64347i	0.111609	−	0.0717268i
$526$	−1.77186	−	2.04484i	−0.0772569	−	0.0891592i
$527$	3.96466	−	1.16413i	0.172703	−	0.0507102i
$528$	25.3994			1.10537
$529$	−15.4788	−	17.0119i	−0.672992	−	0.739649i
$530$	6.92111			0.300634
$531$	−2.20564	+	0.647633i	−0.0957164	+	0.0281049i
$532$	−5.87721	−	6.78267i	−0.254809	−	0.294066i
$533$	0.128230	−	0.0824086i	0.00555427	−	0.00356951i
$534$	4.22015	+	29.3518i	0.182624	+	1.27018i
$535$	−2.15460	−	1.38468i	−0.0931515	−	0.0598649i
$536$	−5.24949	+	11.4948i	−0.226743	+	0.496499i
$537$	−3.65732	+	4.22077i	−0.157825	+	0.182140i
$538$	1.91060	−	13.2885i	0.0823717	−	0.572908i
$539$	0.824120	+	1.80457i	0.0354974	+	0.0777284i
$540$	−4.34682	−	1.27634i	−0.187057	−	0.0549250i
$541$	−1.10909	−	0.325658i	−0.0476835	−	0.0140011i	0.257804	−	0.966197i	$-0.417001\pi$
$541$	−1.10909	−	0.325658i	−0.0476835	−	0.0140011i	−0.305487	+	0.952196i	$0.598819\pi$
$542$	6.47453	+	14.1772i	0.278105	+	0.608965i
$543$	−1.91473	+	13.3172i	−0.0821689	+	0.571497i
$544$	8.48092	−	9.78751i	0.363617	−	0.419636i
$545$	−6.02278	+	13.1880i	−0.257988	+	0.564914i
$546$	−26.5763	−	17.0796i	−1.13736	−	0.730938i
$547$	−1.18950	−	8.27316i	−0.0508594	−	0.353735i	−0.999321	−	0.0368430i	$-0.988270\pi$
$547$	−1.18950	−	8.27316i	−0.0508594	−	0.353735i	0.948462	−	0.316892i	$-0.102639\pi$
$548$	1.87846	−	1.20721i	0.0802437	−	0.0515695i
$549$	−4.92192	−	5.68020i	−0.210062	−	0.242425i
$550$	6.93790	−	2.03715i	0.295833	−	0.0868644i
$551$	−34.6424			−1.47581
$552$	4.53502	−	10.2576i	0.193023	−	0.436594i
$553$	5.84934			0.248739
$554$	45.1410	−	13.2546i	1.91786	−	0.563133i
$555$	−2.37863	−	2.74509i	−0.100967	−	0.116522i
$556$	4.30762	−	2.76834i	0.182684	−	0.117404i
$557$	−1.90880	−	13.2760i	−0.0808786	−	0.562523i	−0.989459	−	0.144813i	$-0.953742\pi$
$557$	−1.90880	−	13.2760i	−0.0808786	−	0.562523i	0.908580	−	0.417710i	$-0.137167\pi$
$558$	3.17441	+	2.04007i	0.134384	+	0.0863630i
$559$	18.2443	−	39.9494i	0.771651	−	1.68968i
$560$	−8.32456	+	9.60706i	−0.351777	+	0.405972i
$561$	2.12557	−	14.7837i	0.0897418	−	0.624168i
$562$	5.52446	+	12.0969i	0.233035	+	0.510276i
$563$	16.4757	+	4.83769i	0.694366	+	0.203884i	0.609826	−	0.792536i	$-0.291239\pi$
$563$	16.4757	+	4.83769i	0.694366	+	0.203884i	0.0845408	+	0.996420i	$0.473058\pi$
$564$	−10.4951	−	3.08164i	−0.441924	−	0.129761i
$565$	−5.84734	−	12.8039i	−0.245999	−	0.538664i
$566$	−1.27143	+	8.84297i	−0.0534421	+	0.371698i
$567$	2.88395	−	3.32826i	0.121115	−	0.139774i
$568$	−7.68530	+	16.8285i	−0.322468	+	0.706107i
$569$	5.30575	+	3.40980i	0.222429	+	0.142946i	0.647110	−	0.762397i	$-0.275977\pi$
$569$	5.30575	+	3.40980i	0.222429	+	0.142946i	−0.424681	+	0.905343i	$0.639614\pi$
$570$	1.20254	+	8.36384i	0.0503688	+	0.350323i
$571$	−14.1695	+	9.10621i	−0.592977	+	0.381083i	−0.802439	−	0.596734i	$-0.796465\pi$
$571$	−14.1695	+	9.10621i	−0.592977	+	0.381083i	0.209463	+	0.977817i	$0.432829\pi$
$572$	−14.4427	−	16.6678i	−0.603881	−	0.696916i
$573$	−9.36872	+	2.75090i	−0.391384	+	0.114921i
$574$	−0.106169			−0.00443140
$575$	0.624915	−	4.75494i	0.0260607	−	0.198295i
$576$	−3.94941			−0.164559
$577$	3.97893	−	1.16832i	0.165645	−	0.0486378i	−0.197858	−	0.980231i	$-0.563399\pi$
$577$	3.97893	−	1.16832i	0.165645	−	0.0486378i	0.363504	+	0.931593i	$0.381580\pi$
$578$	9.31477	+	10.7498i	0.387443	+	0.447133i
$579$	−13.4013	+	8.61248i	−0.556938	+	0.357923i
$580$	−0.969605	−	6.74375i	−0.0402607	−	0.280019i
$581$	13.3050	+	8.55063i	0.551986	+	0.354740i
$582$	−0.889258	+	1.94720i	−0.0368609	+	0.0807142i
$583$	−11.5770	+	13.3606i	−0.479471	+	0.553340i
$584$	−2.60907	+	18.1465i	−0.107964	+	0.750906i
$585$	−4.07133	−	8.91496i	−0.168329	−	0.368588i
$586$	10.5716	+	3.10410i	0.436709	+	0.128229i
$587$	4.97468	+	1.46070i	0.205327	+	0.0602895i	0.382779	−	0.923840i	$-0.374967\pi$
$587$	4.97468	+	1.46070i	0.205327	+	0.0602895i	−0.177452	+	0.984130i	$0.556785\pi$
$588$	−0.189405	−	0.414738i	−0.00781091	−	0.0171035i
$589$	0.849786	−	5.91039i	0.0350148	−	0.243533i
$590$	−1.59626	+	1.84218i	−0.0657169	+	0.0758413i
$591$	−6.22434	+	13.6294i	−0.256035	+	0.560638i
$592$	12.7781	+	8.21196i	0.525175	+	0.337510i
$593$	4.65659	+	32.3873i	0.191223	+	1.32999i	0.828776	+	0.559580i	$0.189037\pi$
$593$	4.65659	+	32.3873i	0.191223	+	1.32999i	−0.637553	+	0.770406i	$0.720053\pi$
$594$	33.1689	−	21.3163i	1.36094	−	0.874620i
$595$	4.89512	+	5.64928i	0.200681	+	0.231598i
$596$	−16.8133	+	4.93684i	−0.688700	+	0.202221i
$597$	−22.7112			−0.929506
$598$	−47.6476	+	14.6204i	−1.94845	+	0.597871i
$599$	−4.51653			−0.184540			−0.0922702	−	0.995734i	$-0.529412\pi$
$599$	−4.51653			−0.184540			−0.0922702	+	0.995734i	$0.529412\pi$
$600$	2.24385	−	0.658853i	0.0916047	−	0.0268976i
$601$	−29.9912	−	34.6117i	−1.22337	−	1.41184i	−0.881560	−	0.472072i	$-0.843506\pi$
$601$	−29.9912	−	34.6117i	−1.22337	−	1.41184i	−0.341808	−	0.939770i	$-0.611039\pi$
$602$	−25.7339	+	16.5381i	−1.04883	+	0.674045i
$603$	1.45059	+	10.0891i	0.0590727	+	0.410859i
$604$	13.3920	+	8.60655i	0.544915	+	0.350195i
$605$	−3.10301	+	6.79464i	−0.126155	+	0.276241i
$606$	11.5599	−	13.3408i	0.469589	−	0.541935i
$607$	−1.03630	+	7.20765i	−0.0420623	+	0.292549i	0.957922	+	0.287027i	$0.0926670\pi$
$607$	−1.03630	+	7.20765i	−0.0420623	+	0.292549i	−0.999985	+	0.00552246i	$0.998242\pi$
$608$	−7.77449	−	17.0238i	−0.315297	−	0.690404i
$609$	23.9181	+	7.02299i	0.969211	+	0.284586i
$610$	−7.64697	−	2.24535i	−0.309617	−	0.0909117i
$611$	−28.4156	−	62.2215i	−1.14957	−	2.51721i
$612$	0.548450	−	3.81455i	0.0221698	−	0.154194i
$613$	18.7818	−	21.6753i	0.758589	−	0.875459i	−0.236782	−	0.971563i	$-0.576093\pi$
$613$	18.7818	−	21.6753i	0.758589	−	0.875459i	0.995371	+	0.0961041i	$0.0306382\pi$
$614$	−3.67718	+	8.05191i	−0.148399	+	0.324949i
$615$	0.0246802	+	0.0158610i	0.000995202	+	0.000639577i
$616$	−3.07645	−	21.3972i	−0.123954	−	0.862116i
$617$	6.67383	−	4.28901i	0.268678	−	0.172669i	−0.399364	−	0.916793i	$-0.630769\pi$
$617$	6.67383	−	4.28901i	0.268678	−	0.172669i	0.668042	+	0.744123i	$0.267133\pi$
$618$	8.08582	+	9.33154i	0.325260	+	0.375370i
$619$	−14.4351	+	4.23852i	−0.580194	+	0.170360i	−0.558644	−	0.829407i	$-0.688678\pi$
$619$	−14.4351	+	4.23852i	−0.580194	+	0.170360i	−0.0215501	+	0.999768i	$0.506860\pi$
$620$	1.17435			0.0471629
$621$	−4.03517	−	25.8374i	−0.161926	−	1.03682i
$622$	9.99967			0.400950
$623$	36.3732	−	10.6801i	1.45726	−	0.427890i
$624$	−23.9057	−	27.5887i	−0.956995	−	1.10443i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	0.196492	+	1.36663i	0.00785339	+	0.0546215i
$627$	−18.1572	−	11.6689i	−0.725128	−	0.466012i
$628$	−4.25512	+	9.31742i	−0.169798	+	0.371805i
$629$	5.84911	−	6.75023i	0.233219	−	0.269149i
$630$	−0.971488	+	6.75684i	−0.0387050	+	0.269199i
$631$	−5.58787	−	12.2357i	−0.222449	−	0.487096i	0.765197	−	0.643796i	$-0.222642\pi$
$631$	−5.58787	−	12.2357i	−0.222449	−	0.487096i	−0.987646	+	0.156700i	$0.949914\pi$
$632$	4.31766	+	1.26778i	0.171747	+	0.0504295i
$633$	18.0805	+	5.30891i	0.718634	+	0.211010i
$634$	−5.99848	−	13.1348i	−0.238230	−	0.521651i
$635$	−2.16519	+	15.0592i	−0.0859228	+	0.597607i
$636$	2.66071	−	3.07062i	0.105504	−	0.121758i
$637$	1.18446	−	2.59360i	0.0469300	−	0.102762i
$638$	49.8822	+	32.0574i	1.97486	+	1.26916i
$639$	2.12368	+	14.7705i	0.0840115	+	0.584313i
$640$	−10.9768	+	7.05434i	−0.433895	+	0.278847i
$641$	−13.2653	−	15.3089i	−0.523946	−	0.604666i	0.430668	−	0.902510i	$-0.358278\pi$
$641$	−13.2653	−	15.3089i	−0.523946	−	0.604666i	−0.954615	+	0.297844i	$0.903732\pi$
$642$	−4.91537	+	1.44328i	−0.193994	+	0.0569618i
$643$	20.0230			0.789629			0.394814	−	0.918761i	$-0.370809\pi$
$643$	20.0230			0.789629			0.394814	+	0.918761i	$0.370809\pi$
$644$	9.80990	+	2.75171i	0.386564	+	0.108432i
$645$	8.45285			0.332831
$646$	−19.9367	+	5.85394i	−0.784399	+	0.230320i
$647$	−0.693050	−	0.799823i	−0.0272466	−	0.0314443i	0.741963	−	0.670441i	$-0.233895\pi$
$647$	−0.693050	−	0.799823i	−0.0272466	−	0.0314443i	−0.769209	+	0.638997i	$0.779350\pi$
$648$	2.85014	−	1.83167i	0.111964	−	0.0719548i
$649$	−0.886087	−	6.16287i	−0.0347820	−	0.241914i
$650$	−8.74264	−	5.61856i	−0.342915	−	0.220378i
$651$	−1.78492	+	3.90843i	−0.0699566	+	0.153184i
$652$	1.61346	−	1.86203i	0.0631880	−	0.0729229i
$653$	5.39143	−	37.4982i	0.210983	−	1.46742i	−0.558900	−	0.829235i	$-0.688776\pi$
$653$	5.39143	−	37.4982i	0.210983	−	1.46742i	0.769883	−	0.638185i	$-0.220314\pi$
$654$	12.0468	+	26.3788i	0.471066	+	1.03149i
$655$	−8.40981	−	2.46934i	−0.328598	−	0.0964852i
$656$	−0.117713	−	0.0345636i	−0.00459591	−	0.00134948i
$657$	6.14296	+	13.4512i	0.239660	+	0.524781i
$658$	−6.78045	+	47.1590i	−0.264329	+	1.83845i
$659$	−14.5189	+	16.7557i	−0.565575	+	0.652708i	−0.964440	−	0.264301i	$-0.914859\pi$
$659$	−14.5189	+	16.7557i	−0.565575	+	0.652708i	0.398865	+	0.917010i	$0.369404\pi$
$660$	1.76336	−	3.86122i	0.0686387	−	0.150298i
$661$	34.5483	+	22.2028i	1.34377	+	0.863591i	0.997225	−	0.0744417i	$-0.0237175\pi$
$661$	34.5483	+	22.2028i	1.34377	+	0.863591i	0.346548	+	0.938032i	$0.387354\pi$
$662$	0.157826	+	1.09770i	0.00613407	+	0.0426634i
$663$	−18.0585	+	11.6055i	−0.701336	+	0.450721i
$664$	7.96778	+	9.19531i	0.309210	+	0.356847i
$665$	10.3646	−	3.04332i	0.401922	−	0.118015i
$666$	8.15667			0.316064
$667$	32.8242	−	21.6616i	1.27096	−	0.838741i
$668$	1.44622			0.0559559
$669$	−30.6965	+	9.01332i	−1.18680	+	0.348475i
$670$	7.07793	+	8.16836i	0.273444	+	0.315571i
$671$	17.1256	−	11.0060i	0.661128	−	0.424881i
$672$	1.91654	+	13.3298i	0.0739320	+	0.514209i
$673$	−12.2585	−	7.87809i	−0.472532	−	0.303678i	0.282615	−	0.959233i	$-0.408798\pi$
$673$	−12.2585	−	7.87809i	−0.472532	−	0.303678i	−0.755147	+	0.655555i	$0.772435\pi$
$674$	−21.8004	+	47.7362i	−0.839719	+	1.83873i
$675$	3.57081	−	4.12093i	0.137440	−	0.158615i
$676$	−2.97397	+	20.6844i	−0.114383	+	0.795553i
$677$	−10.5185	−	23.0324i	−0.404260	−	0.885206i	−0.996821	−	0.0796798i	$-0.974610\pi$
$677$	−10.5185	−	23.0324i	−0.404260	−	0.885206i	0.592561	−	0.805526i	$-0.298117\pi$
$678$	−27.0142	−	7.93208i	−1.03747	−	0.304630i
$679$	2.62572	+	0.770981i	0.100766	+	0.0295876i
$680$	2.38889	+	5.23094i	0.0916098	+	0.200597i
$681$	−2.84049	+	19.7560i	−0.108848	+	0.757052i
$682$	−6.69298	+	7.72411i	−0.256288	+	0.295772i
$683$	2.34753	−	5.14038i	0.0898258	−	0.196691i	−0.859387	−	0.511326i	$-0.829155\pi$
$683$	2.34753	−	5.14038i	0.0898258	−	0.196691i	0.949213	+	0.314634i	$0.101882\pi$
$684$	−4.68499	−	3.01086i	−0.179135	−	0.115123i
$685$	0.382483	+	2.66023i	0.0146139	+	0.101642i
$686$	−27.0055	+	17.3554i	−1.03107	+	0.662631i
$687$	14.7206	+	16.9885i	0.561627	+	0.648152i
$688$	−33.9160	+	9.95864i	−1.29304	+	0.379670i
$689$	25.4084			0.967984
$690$	−6.36927	−	7.17294i	−0.242474	−	0.273069i
$691$	−7.41129			−0.281939			−0.140969	−	0.990014i	$-0.545022\pi$
$691$	−7.41129			−0.281939			−0.140969	+	0.990014i	$0.545022\pi$
$692$	12.7737	−	3.75069i	0.485583	−	0.142580i
$693$	−11.4185	−	13.1776i	−0.433752	−	0.500577i
$694$	−17.5261	+	11.2633i	−0.665280	+	0.427549i
$695$	0.877100	+	6.10036i	0.0332703	+	0.231400i
$696$	16.1329	+	10.3680i	0.611514	+	0.392996i
$697$	−0.0299686	+	0.0656221i	−0.00113514	+	0.00248561i
$698$	2.80173	−	3.23337i	0.106047	−	0.122385i
$699$	3.58937	−	24.9646i	0.135763	−	0.944249i
$700$	0.882530	+	1.93247i	0.0333565	+	0.0730406i
$701$	35.6045	+	10.4544i	1.34476	+	0.394858i	0.873367	−	0.487063i	$-0.161932\pi$
$701$	35.6045	+	10.4544i	1.34476	+	0.394858i	0.471397	+	0.881921i	$0.343750\pi$
$702$	−54.3720	−	15.9651i	−2.05214	−	0.602562i
$703$	−5.36189	−	11.7409i	−0.202228	−	0.442817i
$704$	1.52236	−	10.5882i	0.0573760	−	0.399059i
$705$	8.62148	−	9.94972i	0.324704	−	0.374728i
$706$	1.69414	−	3.70965i	0.0637599	−	0.139615i
$707$	−18.9843	−	12.2004i	−0.713977	−	0.458845i
$708$	0.203646	+	1.41639i	0.00765350	+	0.0532312i
$709$	−38.2944	+	24.6103i	−1.43818	+	0.924260i	−0.438502	+	0.898730i	$0.644491\pi$
$709$	−38.2944	+	24.6103i	−1.43818	+	0.924260i	−0.999674	+	0.0255296i	$0.991873\pi$
$710$	10.3622	+	11.9586i	0.388885	+	0.448797i
$711$	3.48264	−	1.02260i	0.130609	−	0.0383503i
$712$	29.1634			1.09295
$713$	2.89054	+	6.13156i	0.108252	+	0.229629i
$714$	14.9516			0.559551
$715$	25.4701	−	7.47869i	0.952527	−	0.279687i
$716$	−2.55598	−	2.94976i	−0.0955215	−	0.110238i
$717$	24.5720	−	15.7915i	0.917659	−	0.589744i
$718$	−4.44403	−	30.9089i	−0.165850	−	1.15351i
$719$	−15.0747	−	9.68790i	−0.562190	−	0.361298i	0.228472	−	0.973550i	$-0.426627\pi$
$719$	−15.0747	−	9.68790i	−0.562190	−	0.361298i	−0.790662	+	0.612253i	$0.790263\pi$
$720$	−3.27683	+	7.17526i	−0.122120	+	0.267406i
$721$	10.3368	−	11.9293i	0.384962	−	0.444270i
$722$	0.276231	−	1.92123i	0.0102802	−	0.0715007i
$723$	−13.0205	−	28.5110i	−0.484238	−	1.06033i
$724$	−9.02181	−	2.64904i	−0.335293	−	0.0984509i
$725$	7.86818	+	2.31031i	0.292217	+	0.0858026i
$726$	6.20665	+	13.5907i	0.230350	+	0.504397i
$727$	1.35305	−	9.41065i	0.0501818	−	0.349022i	−0.949226	−	0.314596i	$-0.898131\pi$
$727$	1.35305	−	9.41065i	0.0501818	−	0.349022i	0.999407	−	0.0344254i	$-0.0109601\pi$
$728$	−20.3459	+	23.4805i	−0.754071	+	0.870244i
$729$	9.21386	−	20.1755i	0.341254	−	0.747242i
$730$	13.1912	+	8.47747i	0.488228	+	0.313765i
$731$	2.95812	+	20.5742i	0.109410	+	0.760963i
$732$	−3.93593	+	2.52947i	−0.145476	+	0.0934918i
$733$	−3.25665	−	3.75837i	−0.120287	−	0.138819i	0.692412	−	0.721502i	$-0.256548\pi$
$733$	−3.25665	−	3.75837i	−0.120287	−	0.138819i	−0.812699	+	0.582684i	$0.802003\pi$
$734$	−30.4331	+	8.93595i	−1.12330	+	0.329832i
$735$	0.548777			0.0202420
$736$	18.0113	+	11.2689i	0.663904	+	0.415379i
$737$	−27.6077			−1.01694
$738$	−0.0632118	+	0.0185607i	−0.00232686	+	0.000683228i
$739$	7.39514	+	8.53445i	0.272035	+	0.313945i	0.875285	−	0.483607i	$-0.160674\pi$
$739$	7.39514	+	8.53445i	0.272035	+	0.313945i	−0.603251	+	0.797552i	$0.706128\pi$
$740$	2.13550	−	1.37240i	0.0785026	−	0.0504506i
$741$	4.41470	+	30.7049i	0.162178	+	1.12797i
$742$	−14.8880	−	9.56797i	−0.546557	−	0.351251i
$743$	−7.31888	+	16.0261i	−0.268504	+	0.587941i	−0.995072	−	0.0991531i	$-0.968387\pi$
$743$	−7.31888	+	16.0261i	−0.268504	+	0.587941i	0.726569	+	0.687094i	$0.241114\pi$
$744$	−2.16464	+	2.49812i	−0.0793594	+	0.0915857i
$745$	3.00158	−	20.8764i	0.109969	−	0.764853i
$746$	6.30749	+	13.8115i	0.230933	+	0.505674i
$747$	9.41653	+	2.76494i	0.344533	+	0.101164i
$748$	10.0153	+	2.94075i	0.366195	+	0.107524i
$749$	2.72055	+	5.95718i	0.0994069	+	0.217671i
$750$	0.284659	−	1.97984i	0.0103943	−	0.0722937i
$751$	−25.3701	+	29.2786i	−0.925768	+	1.06839i	0.0717110	+	0.997425i	$0.477154\pi$
$751$	−25.3701	+	29.2786i	−0.925768	+	1.06839i	−0.997479	+	0.0709674i	$0.977391\pi$
$752$	−22.8705	+	50.0794i	−0.834000	+	1.82621i
$753$	−4.27184	−	2.74534i	−0.155674	−	0.100046i
$754$	−12.1283	−	84.3539i	−0.441685	−	3.07199i
$755$	−16.1189	+	10.3590i	−0.586626	+	0.377002i
$756$	7.58602	+	8.75473i	0.275901	+	0.318407i
$757$	−16.1674	+	4.74717i	−0.587614	+	0.172539i	−0.562006	−	0.827133i	$-0.689970\pi$
$757$	−16.1674	+	4.74717i	−0.587614	+	0.172539i	−0.0256076	+	0.999672i	$0.508152\pi$
$758$	26.5585			0.964647
$759$	24.5007	−	0.297070i	0.889319	−	0.0107830i
$760$	8.31016			0.301441
$761$	5.99126	−	1.75919i	0.217183	−	0.0637706i	−0.171331	−	0.985214i	$-0.554807\pi$
$761$	5.99126	−	1.75919i	0.217183	−	0.0637706i	0.388514	+	0.921443i	$0.372989\pi$
$762$	19.9282	+	22.9984i	0.721923	+	0.833143i
$763$	31.1872	−	20.0428i	1.12905	−	0.725599i
$764$	−0.971144	−	6.75445i	−0.0351348	−	0.244368i
$765$	3.90213	+	2.50774i	0.141082	+	0.0906677i
$766$	24.5704	−	53.8016i	0.887763	−	1.94393i
$767$	−5.86010	+	6.76291i	−0.211596	+	0.244195i
$768$	−2.87202	+	19.9753i	−0.103635	+	0.720797i
$769$	−13.5186	−	29.6015i	−0.487492	−	1.06746i	−0.980335	−	0.197340i	$-0.936770\pi$
$769$	−13.5186	−	29.6015i	−0.487492	−	1.06746i	0.492843	−	0.870118i	$-0.335958\pi$
$770$	−17.7404	−	5.20905i	−0.639320	−	0.187721i
$771$	0.346417	+	0.101717i	0.0124759	+	0.00366326i
$772$	−4.62484	−	10.1270i	−0.166452	−	0.364478i
$773$	2.53291	−	17.6168i	0.0911025	−	0.633632i	−0.892198	−	0.451644i	$-0.850838\pi$
$773$	2.53291	−	17.6168i	0.0911025	−	0.633632i	0.983301	−	0.181988i	$-0.0582532\pi$
$774$	−12.4304	+	14.3455i	−0.446803	+	0.515638i
$775$	−0.587174	+	1.28573i	−0.0210919	+	0.0461848i
$776$	1.77106	+	1.13819i	0.0635773	+	0.0408587i
$777$	1.32179	+	9.19328i	0.0474191	+	0.329807i
$778$	−18.9050	+	12.1495i	−0.677778	+	0.435582i
$779$	0.0682698	+	0.0787876i	0.00244602	+	0.00282286i
$780$	−5.85370	+	1.71880i	−0.209596	+	0.0615429i
$781$	−40.4179			−1.44627
$782$	15.2299	−	18.0130i	0.544621	−	0.644143i
$783$	44.7147			1.59797
$784$	−2.20190	+	0.646536i	−0.0786393	+	0.0230906i
$785$	−8.07359	−	9.31742i	−0.288159	−	0.332553i
$786$	−14.7484	+	9.47823i	−0.526058	+	0.338077i
$787$	−1.80563	−	12.5585i	−0.0643639	−	0.447661i	−0.996364	−	0.0852020i	$-0.972846\pi$
$787$	−1.80563	−	12.5585i	−0.0643639	−	0.447661i	0.932000	−	0.362459i	$-0.118063\pi$
$788$	−8.80913	−	5.66128i	−0.313812	−	0.201675i
$789$	0.794189	−	1.73903i	0.0282739	−	0.0619111i
$790$	2.52045	−	2.90875i	0.0896735	−	0.103489i
$791$	−5.12226	+	35.6261i	−0.182127	+	1.26672i
$792$	−5.57238	−	12.2018i	−0.198006	−	0.433573i
$793$	−28.0732	−	8.24303i	−0.996908	−	0.292718i
$794$	9.89017	+	2.90402i	0.350989	+	0.103060i
$795$	2.03151	+	4.44838i	0.0720501	+	0.157768i
$796$	2.25884	−	15.7105i	0.0800623	−	0.556846i
$797$	−20.9335	+	24.1585i	−0.741502	+	0.855738i	−0.993716	−	0.111933i	$-0.964296\pi$
$797$	−20.9335	+	24.1585i	−0.741502	+	0.855738i	0.252214	+	0.967671i	$0.418841\pi$
$798$	8.97566	−	19.6540i	0.317735	−	0.695743i
$799$	27.2347	+	17.5027i	0.963494	+	0.619200i
$800$	0.630471	+	4.38502i	0.0222905	+	0.155034i
$801$	19.7891	−	12.7177i	0.699213	−	0.449357i
$802$	−34.5694	−	39.8953i	−1.22069	−	1.40875i
$803$	−38.4301	+	11.2841i	−1.35617	+	0.398207i
$804$	6.34497			0.223770
$805$	−7.91765	+	9.36449i	−0.279060	+	0.330055i
$806$	14.6893			0.517408
$807$	9.10167	−	2.67249i	0.320394	−	0.0940762i
$808$	−11.3688	−	13.1203i	−0.399953	−	0.461571i
$809$	−8.69149	+	5.58568i	−0.305576	+	0.196382i	−0.684438	−	0.729071i	$-0.739952\pi$
$809$	−8.69149	+	5.58568i	−0.305576	+	0.196382i	0.378861	+	0.925454i	$0.376316\pi$
$810$	−0.412393	−	2.86826i	−0.0144900	−	0.100780i
$811$	−20.8821	−	13.4201i	−0.733269	−	0.471243i	0.119961	−	0.992779i	$-0.461723\pi$
$811$	−20.8821	−	13.4201i	−0.733269	−	0.471243i	−0.853230	+	0.521535i	$0.825360\pi$
$812$	−7.23706	+	15.8470i	−0.253971	+	0.556119i
$813$	−7.21166	+	8.32270i	−0.252924	+	0.291890i
$814$	−3.14411	+	21.8678i	−0.110201	+	0.766464i
$815$	1.23191	+	2.69751i	0.0431520	+	0.0944897i
$816$	16.5774	+	4.86755i	0.580324	+	0.170398i
$817$	28.8206	+	8.46248i	1.00830	+	0.296065i
$818$	−22.1199	−	48.4357i	−0.773403	−	1.69352i
$819$	−3.56648	+	24.8054i	−0.124623	+	0.866770i
$820$	−0.0134266	+	0.0154951i	−0.000468877	+	0.000541113i
$821$	6.40908	−	14.0339i	0.223678	−	0.489787i	−0.764207	−	0.644971i	$-0.776870\pi$
$821$	6.40908	−	14.0339i	0.223678	−	0.489787i	0.987886	+	0.155183i	$0.0495968\pi$
$822$	4.52234	+	2.90633i	0.157735	+	0.101370i
$823$	1.35994	+	9.45860i	0.0474046	+	0.329706i	0.999699	+	0.0245259i	$0.00780763\pi$
$823$	1.35994	+	9.45860i	0.0474046	+	0.329706i	−0.952295	+	0.305180i	$0.901283\pi$
$824$	10.2156	−	6.56515i	0.355876	−	0.228708i
$825$	3.34577	+	3.86122i	0.116485	+	0.134430i
$826$	5.98041	−	1.75601i	0.208085	−	0.0610993i
$827$	19.8985			0.691938			0.345969	−	0.938246i	$-0.387550\pi$
$827$	19.8985			0.691938			0.345969	+	0.938246i	$0.387550\pi$
$828$	6.32178	−	0.0766512i	0.219697	−	0.00266381i
$829$	−9.80722			−0.340619			−0.170309	−	0.985391i	$-0.554477\pi$
$829$	−9.80722			−0.340619			−0.170309	+	0.985391i	$0.554477\pi$
$830$	9.98511	−	2.93189i	0.346588	−	0.101767i
$831$	21.7690	+	25.1227i	0.755158	+	0.871498i
$832$	−12.9337	+	8.31199i	−0.448396	+	0.288166i
$833$	0.192047	+	1.33572i	0.00665405	+	0.0462799i
$834$	10.3705	+	6.66472i	0.359101	+	0.230780i
$835$	−0.723110	+	1.58339i	−0.0250242	+	0.0547954i
$836$	9.87792	−	11.3997i	0.341635	−	0.394268i
$837$	−1.09686	+	7.62885i	−0.0379131	+	0.263691i
$838$	12.3216	+	26.9806i	0.425643	+	0.932029i
$839$	−24.5941	−	7.22148i	−0.849083	−	0.249313i	−0.171888	−	0.985117i	$-0.554987\pi$
$839$	−24.5941	−	7.22148i	−0.849083	−	0.249313i	−0.677195	+	0.735803i	$0.736805\pi$
$840$	−5.73758	−	1.68471i	−0.197965	−	0.0581279i
$841$	15.8879	+	34.7896i	0.547858	+	1.19964i
$842$	6.83226	−	47.5194i	0.235455	−	1.63763i
$843$	−6.15342	+	7.10143i	−0.211935	+	0.244586i
$844$	−5.47073	+	11.9792i	−0.188310	+	0.412342i
$845$	−21.1593	−	13.5982i	−0.727901	−	0.467793i
$846$	4.20744	+	29.2634i	0.144655	+	1.00610i
$847$	16.0680	−	10.3263i	0.552104	−	0.354816i
$848$	−13.3920	−	15.4552i	−0.459882	−	0.530733i
$849$	−6.05680	+	1.77844i	−0.207869	+	0.0610358i
$850$	4.91854			0.168705
$851$	12.4220	+	7.77195i	0.425820	+	0.266419i
$852$	9.28910			0.318239
$853$	−10.7337	+	3.15171i	−0.367516	+	0.107912i	−0.460276	−	0.887776i	$-0.652249\pi$
$853$	−10.7337	+	3.15171i	−0.367516	+	0.107912i	0.0927595	+	0.995689i	$0.470431\pi$
$854$	13.3454	+	15.4014i	0.456670	+	0.527026i
$855$	5.63893	−	3.62392i	0.192847	−	0.123935i
$856$	0.717009	+	4.98691i	0.0245069	+	0.170449i
$857$	−4.77355	−	3.06777i	−0.163061	−	0.104793i	0.456565	−	0.889690i	$-0.349080\pi$
$857$	−4.77355	−	3.06777i	−0.163061	−	0.104793i	−0.619626	+	0.784897i	$0.712716\pi$
$858$	22.0569	−	48.2979i	0.753010	−	1.64886i
$859$	34.4475	−	39.7546i	1.17533	−	1.35641i	0.254207	−	0.967150i	$-0.418186\pi$
$859$	34.4475	−	39.7546i	1.17533	−	1.35641i	0.921128	−	0.389259i	$-0.127269\pi$
$860$	−0.840714	+	5.84729i	−0.0286681	+	0.199391i
$861$	−0.0311630	−	0.0682375i	−0.00106203	−	0.00232553i
$862$	63.4492	+	18.6304i	2.16109	+	0.634553i
$863$	−45.7342	−	13.4288i	−1.55681	−	0.457121i	−0.613683	−	0.789553i	$-0.710313\pi$
$863$	−45.7342	−	13.4288i	−1.55681	−	0.457121i	−0.943127	+	0.332432i	$0.892131\pi$
$864$	10.0349	+	21.9734i	0.341395	+	0.747551i
$865$	−2.28041	+	15.8606i	−0.0775362	+	0.539276i
$866$	12.9025	−	14.8903i	0.438444	−	0.505992i
$867$	−4.17509	+	9.14216i	−0.141793	+	0.310484i
$868$	−2.52615	−	1.62346i	−0.0857431	−	0.0551037i
$869$	1.39911	+	9.73102i	0.0474615	+	0.330102i
$870$	13.7986	−	8.86779i	0.467815	−	0.300646i
$871$	25.9841	+	29.9873i	0.880438	+	1.01608i
$872$	27.3647	−	8.03501i	0.926687	−	0.272100i
$873$	1.69811			0.0574724
$874$	−14.5354	−	30.8332i	−0.491666	−	1.04295i
$875$	−2.55703			−0.0864433
$876$	8.83225	−	2.59338i	0.298414	−	0.0876223i
$877$	−35.1003	−	40.5079i	−1.18525	−	1.36785i	−0.914187	−	0.405292i	$-0.867170\pi$
$877$	−35.1003	−	40.5079i	−1.18525	−	1.36785i	−0.271064	−	0.962561i	$-0.587375\pi$
$878$	13.6573	−	8.77704i	0.460913	−	0.296211i
$879$	1.10792	+	7.70577i	0.0373693	+	0.259909i
$880$	−17.9735	−	11.5509i	−0.605888	−	0.389380i
$881$	3.52174	−	7.71153i	0.118650	−	0.259808i	−0.840983	−	0.541061i	$-0.818023\pi$
$881$	3.52174	−	7.71153i	0.118650	−	0.259808i	0.959634	+	0.281253i	$0.0907500\pi$
$882$	−0.807011	+	0.931341i	−0.0271735	+	0.0313599i
$883$	−4.54752	+	31.6287i	−0.153036	+	1.06439i	0.758056	+	0.652189i	$0.226149\pi$
$883$	−4.54752	+	31.6287i	−0.153036	+	1.06439i	−0.911093	+	0.412202i	$0.864760\pi$
$884$	−6.23208	−	13.6463i	−0.209607	−	0.458976i
$885$	−1.65255	−	0.485234i	−0.0555500	−	0.0163110i
$886$	16.2856	+	4.78189i	0.547126	+	0.160651i
$887$	−11.9148	−	26.0898i	−0.400060	−	0.876009i	−0.997264	−	0.0739199i	$-0.976449\pi$
$887$	−11.9148	−	26.0898i	−0.400060	−	0.876009i	0.597204	−	0.802089i	$-0.296278\pi$
$888$	−1.01686	+	7.07244i	−0.0341237	+	0.237336i
$889$	25.4759	−	29.4008i	0.854434	−	0.986070i
$890$	10.3620	−	22.6896i	0.347335	−	0.760557i
$891$	6.22674	+	4.00168i	0.208604	+	0.134061i
$892$	−3.18195	−	22.1309i	−0.106539	−	0.740998i
$893$	39.3566	−	25.2930i	1.31702	−	0.846397i
$894$	−27.6263	−	31.8824i	−0.923961	−	1.06631i
$895$	4.50753	−	1.32353i	0.150670	−	0.0442407i
$896$	33.3643			1.11462
$897$	−23.3826	−	26.3329i	−0.780721	−	0.879231i
$898$	36.7249			1.22553
$899$	−11.1214	+	3.26553i	−0.370919	+	0.108912i
$900$	0.863289	+	0.996288i	0.0287763	+	0.0332096i
$901$	−10.1164	+	6.50140i	−0.337025	+	0.216593i
$902$	−0.0253946	−	0.176623i	−0.000845547	−	0.00588091i
$903$	−18.1830	−	11.6855i	−0.605092	−	0.388869i
$904$	−11.5025	+	25.1870i	−0.382568	+	0.837707i
$905$	7.41120	−	8.55299i	0.246357	−	0.284311i
$906$	−5.45421	+	37.9349i	−0.181204	+	1.26030i
$907$	15.6787	+	34.3316i	0.520603	+	1.13996i	0.969211	+	0.246233i	$0.0791928\pi$
$907$	15.6787	+	34.3316i	0.520603	+	1.13996i	−0.448608	+	0.893729i	$0.648080\pi$
$908$	−13.3838	−	3.92984i	−0.444157	−	0.130416i
$909$	−13.4359	−	3.94515i	−0.445642	−	0.130852i
$910$	11.0391	+	24.1722i	0.365942	+	0.801302i
$911$	4.26966	−	29.6962i	0.141460	−	0.983877i	−0.788189	−	0.615433i	$-0.788981\pi$
$911$	4.26966	−	29.6962i	0.141460	−	0.983877i	0.929650	−	0.368445i	$-0.120110\pi$
$912$	16.3500	−	18.8689i	0.541403	−	0.624813i
$913$	−11.0425	+	24.1796i	−0.365452	+	0.800228i
$914$	−15.0853	−	9.69472i	−0.498977	−	0.320673i
$915$	−0.801416	−	5.57397i	−0.0264940	−	0.184270i
$916$	−13.2160	+	8.49339i	−0.436668	+	0.280629i
$917$	14.6767	+	16.9378i	0.484667	+	0.559336i
$918$	25.7333	−	7.55598i	0.849326	−	0.249385i
$919$	28.2831			0.932972			0.466486	−	0.884529i	$-0.345520\pi$
$919$	28.2831			0.932972			0.466486	+	0.884529i	$0.345520\pi$
$920$	−7.87401	+	5.19628i	−0.259598	+	0.171316i
$921$	−6.25451			−0.206093
$922$	−64.8470	+	19.0408i	−2.13562	+	0.627075i
$923$	38.0410	+	43.9017i	1.25214	+	1.44504i
$924$	−9.13105	+	5.86817i	−0.300390	+	0.193049i
$925$	0.434822	+	3.02425i	0.0142968	+	0.0994368i
$926$	−14.3571	−	9.22675i	−0.471804	−	0.303210i
$927$	4.06891	−	8.90968i	0.133641	−	0.292632i
$928$	−23.7901	+	27.4552i	−0.780948	+	0.901262i
$929$	5.00119	−	34.7840i	0.164084	−	1.14123i	−0.726752	−	0.686900i	$-0.758971\pi$
$929$	5.00119	−	34.7840i	0.164084	−	1.14123i	0.890835	−	0.454327i	$-0.150120\pi$
$930$	1.17447	+	2.57172i	0.0385123	+	0.0843301i
$931$	1.87109	+	0.549403i	0.0613226	+	0.0180060i
$932$	16.9124	+	4.96593i	0.553984	+	0.162664i
$933$	2.93513	+	6.42705i	0.0960920	+	0.210412i
$934$	4.05211	−	28.1831i	0.132589	−	0.922178i
$935$	−8.22731	+	9.49482i	−0.269062	+	0.310514i
$936$	−8.00886	+	17.5370i	−0.261778	+	0.573213i
$937$	−35.2338	−	22.6434i	−1.15104	−	0.739728i	−0.181193	−	0.983448i	$-0.557996\pi$
$937$	−35.2338	−	22.6434i	−1.15104	−	0.739728i	−0.969846	+	0.243720i	$0.921632\pi$
$938$	−3.93317	−	27.3558i	−0.128422	−	0.893198i
$939$	−0.820694	+	0.527428i	−0.0267823	+	0.0172120i
$940$	6.02528	+	6.95354i	0.196523	+	0.226799i
$941$	42.5299	−	12.4879i	1.38644	−	0.407094i	0.498432	−	0.866929i	$-0.333909\pi$
$941$	42.5299	−	12.4879i	1.38644	−	0.407094i	0.888005	+	0.459834i	$0.152091\pi$
$942$	−24.6599			−0.803464
$943$	−0.113952	−	0.0319639i	−0.00371079	−	0.00104089i
$944$	7.20235			0.234416
$945$	−13.3781	+	3.92817i	−0.435190	+	0.127783i
$946$	−33.6683	−	38.8553i	−1.09465	−	1.26329i
$947$	−10.0957	+	6.48812i	−0.328067	+	0.210836i	−0.694297	−	0.719689i	$-0.744285\pi$
$947$	−10.0957	+	6.48812i	−0.328067	+	0.210836i	0.366230	+	0.930524i	$0.380648\pi$
$948$	−0.321552	−	2.23644i	−0.0104435	−	0.0726363i
$949$	48.4269	+	31.1221i	1.57200	+	1.01026i
$950$	2.95266	−	6.46543i	0.0957971	−	0.209766i
$951$	6.68141	−	7.71076i	0.216659	−	0.250038i
$952$	2.09266	−	14.5548i	0.0678236	−	0.471724i
$953$	−16.2119	−	35.4991i	−0.525155	−	1.14993i	−0.967451	−	0.253059i	$-0.918563\pi$
$953$	−16.2119	−	35.4991i	−0.525155	−	1.14993i	0.442296	−	0.896869i	$-0.354164\pi$
$954$	−10.5369	−	3.09391i	−0.341144	−	0.100169i
$955$	7.88067	+	2.31397i	0.255012	+	0.0748784i
$956$	8.47991	+	18.5684i	0.274260	+	0.600546i
$957$	−5.96251	+	41.4702i	−0.192741	+	1.34054i
$958$	8.80385	−	10.1602i	0.284440	−	0.328261i
$959$	2.85483	−	6.25120i	0.0921872	−	0.201862i
$960$	−2.48932	−	1.59979i	−0.0803425	−	0.0516330i
$961$	4.12743	+	28.7069i	0.133143	+	0.926030i
$962$	26.7118	−	17.1667i	0.861224	−	0.553475i
$963$	2.66124	+	3.07123i	0.0857572	+	0.0989691i
$964$	21.0176	−	6.17132i	0.676931	−	0.198765i
$965$	13.3999			0.431359
$966$	3.78489	+	24.2349i	0.121777	+	0.779744i
$967$	−41.3620			−1.33011			−0.665056	−	0.746794i	$-0.731592\pi$
$967$	−41.3620			−1.33011			−0.665056	+	0.746794i	$0.731592\pi$
$968$	14.0986	−	4.13973i	0.453147	−	0.133056i
$969$	−9.61437	−	11.0956i	−0.308858	−	0.356441i
$970$	1.51480	−	0.973503i	0.0486373	−	0.0312573i
$971$	4.27363	+	29.7237i	0.137147	+	0.953880i	0.935911	+	0.352236i	$0.114578\pi$
$971$	4.27363	+	29.7237i	0.137147	+	0.953880i	−0.798764	+	0.601644i	$0.794512\pi$
$972$	10.0024	+	6.42815i	0.320827	+	0.206183i
$973$	6.54661	−	14.3351i	0.209875	−	0.459561i
$974$	9.78183	−	11.2888i	0.313430	−	0.361718i
$975$	1.04502	−	7.26830i	0.0334676	−	0.232772i
$976$	9.78250	+	21.4207i	0.313130	+	0.685660i
$977$	−35.0885	−	10.3029i	−1.12258	−	0.329620i	−0.332794	−	0.943000i	$-0.607991\pi$
$977$	−35.0885	−	10.3029i	−1.12258	−	0.329620i	−0.789788	+	0.613380i	$0.789810\pi$
$978$	5.69133	+	1.67112i	0.181989	+	0.0534367i
$979$	26.4677	+	57.9561i	0.845910	+	1.85228i
$980$	−0.0545810	+	0.379619i	−0.00174353	+	0.0121265i
$981$	15.0646	−	17.3855i	0.480977	−	0.555077i
$982$	−14.2387	+	31.1784i	−0.454374	+	0.994941i
$983$	−31.5679	−	20.2875i	−1.00686	−	0.647070i	−0.0702816	−	0.997527i	$-0.522390\pi$
$983$	−31.5679	−	20.2875i	−1.00686	−	0.647070i	−0.936579	+	0.350457i	$0.886026\pi$
$984$	−0.00821309	−	0.0571233i	−0.000261824	−	0.00182102i
$985$	10.6028	−	6.81401i	0.337833	−	0.217112i
$986$	26.4130	+	30.4822i	0.841162	+	0.970753i
$987$	−32.3006	+	9.48430i	−1.02814	+	0.301889i
$988$	−21.6793			−0.689712
$989$	−32.5995	+	10.0030i	−1.03660	+	0.318075i
$990$	−11.4731			−0.364639
$991$	28.8648	−	8.47548i	0.916922	−	0.269232i	0.210970	−	0.977493i	$-0.432338\pi$
$991$	28.8648	−	8.47548i	0.916922	−	0.269232i	0.705952	+	0.708260i	$0.250520\pi$
$992$	−4.10061	−	4.73235i	−0.130194	−	0.150252i
$993$	−0.659196	+	0.423639i	−0.0209189	+	0.0134438i
$994$	−5.75820	−	40.0491i	−0.182639	−	1.27028i
$995$	16.0712	+	10.3284i	0.509492	+	0.327431i
$996$	2.53785	−	5.55711i	0.0804148	−	0.176084i
$997$	−38.3256	+	44.2301i	−1.21378	+	1.40078i	−0.322973	+	0.946408i	$0.604682\pi$
$997$	−38.3256	+	44.2301i	−1.21378	+	1.40078i	−0.890811	+	0.454374i	$0.849863\pi$
$998$	0.864835	−	6.01506i	0.0273759	−	0.190403i
$999$	6.92087	+	15.1546i	0.218967	+	0.479470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.b.101.1	yes	20
5.2	odd	4		575.2.p.c.124.1		40
5.3	odd	4		575.2.p.c.124.4		40
5.4	even	2		575.2.k.c.101.2		20
23.8	even	11		2645.2.a.t.1.10		10
23.15	odd	22		2645.2.a.u.1.10		10
23.18	even	11	inner	115.2.g.b.41.1	✓	20
115.18	odd	44		575.2.p.c.524.1		40
115.64	even	22		575.2.k.c.501.2		20
115.87	odd	44		575.2.p.c.524.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.b.41.1	✓	20	23.18	even	11	inner
115.2.g.b.101.1	yes	20	1.1	even	1	trivial
575.2.k.c.101.2		20	5.4	even	2
575.2.k.c.501.2		20	115.64	even	22
575.2.p.c.124.1		40	5.2	odd	4
575.2.p.c.124.4		40	5.3	odd	4
575.2.p.c.524.1		40	115.18	odd	44
575.2.p.c.524.4		40	115.87	odd	44
2645.2.a.t.1.10		10	23.8	even	11
2645.2.a.u.1.10		10	23.15	odd	22

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61435 + 0.474017i) q^{2} +(-0.778513 - 0.898452i) q^{3} +(0.698939 - 0.449181i) q^{4} +(0.142315 + 0.989821i) q^{5} +(1.68268 + 1.08139i) q^{6} +(1.06223 - 2.32595i) q^{7} +(1.28820 - 1.48666i) q^{8} +(0.225811 - 1.57055i) q^{9} +O(q^{10})\)	\(q+(-1.61435 + 0.474017i) q^{2} +(-0.778513 - 0.898452i) q^{3} +(0.698939 - 0.449181i) q^{4} +(0.142315 + 0.989821i) q^{5} +(1.68268 + 1.08139i) q^{6} +(1.06223 - 2.32595i) q^{7} +(1.28820 - 1.48666i) q^{8} +(0.225811 - 1.57055i) q^{9} +(-0.698939 - 1.53046i) q^{10} +(4.12355 + 1.21078i) q^{11} +(-0.947701 - 0.278270i) q^{12} +(-2.56591 - 5.61856i) q^{13} +(-0.612269 + 4.25843i) q^{14} +(0.778513 - 0.898452i) q^{15} +(-2.06519 + 4.52213i) q^{16} +(2.45927 + 1.58048i) q^{17} +(0.379929 + 2.64246i) q^{18} +(3.55387 - 2.28394i) q^{19} +(0.544078 + 0.627899i) q^{20} +(-2.91672 + 0.856425i) q^{21} -7.23080 q^{22} +(-1.93922 + 4.38628i) q^{23} -2.33858 q^{24} +(-0.959493 + 0.281733i) q^{25} +(6.80558 + 7.85405i) q^{26} +(-4.58717 + 2.94799i) q^{27} +(-0.302341 - 2.10283i) q^{28} +(-6.89858 - 4.43345i) q^{29} +(-0.830914 + 1.81945i) q^{30} +(0.925621 - 1.06822i) q^{31} +(0.630471 - 4.38502i) q^{32} +(-2.12241 - 4.64742i) q^{33} +(-4.71931 - 1.38571i) q^{34} +(2.45345 + 0.720398i) q^{35} +(-0.547633 - 1.19915i) q^{36} +(0.434822 - 3.02425i) q^{37} +(-4.65458 + 5.37168i) q^{38} +(-3.05041 + 6.67947i) q^{39} +(1.65486 + 1.06351i) q^{40} +(0.00351200 + 0.0244265i) q^{41} +(4.30265 - 2.76515i) q^{42} +(4.65623 + 5.37358i) q^{43} +(3.42597 - 1.00596i) q^{44} +1.58670 q^{45} +(1.05142 - 8.00022i) q^{46} +11.0743 q^{47} +(5.67069 - 1.66507i) q^{48} +(0.302293 + 0.348865i) q^{49} +(1.41542 - 0.909632i) q^{50} +(-0.494592 - 3.43996i) q^{51} +(-4.31716 - 2.77447i) q^{52} +(-1.70884 + 3.74183i) q^{53} +(6.00791 - 6.93350i) q^{54} +(-0.611617 + 4.25389i) q^{55} +(-2.08955 - 4.57547i) q^{56} +(-4.81874 - 1.41491i) q^{57} +(13.2383 + 3.88711i) q^{58} +(-0.601837 - 1.31784i) q^{59} +(0.140566 - 0.977656i) q^{60} +(3.10198 - 3.57988i) q^{61} +(-0.987924 + 2.16325i) q^{62} +(-3.41316 - 2.19351i) q^{63} +(-0.354232 - 2.46373i) q^{64} +(5.19620 - 3.33940i) q^{65} +(5.62927 + 6.49653i) q^{66} +(-6.16371 + 1.80983i) q^{67} +2.42880 q^{68} +(5.45057 - 1.67247i) q^{69} -4.30222 q^{70} +(-9.02373 + 2.64961i) q^{71} +(-2.04399 - 2.35889i) q^{72} +(-7.84020 + 5.03859i) q^{73} +(0.731591 + 5.08832i) q^{74} +(1.00010 + 0.642726i) q^{75} +(1.45804 - 3.19266i) q^{76} +(7.19637 - 8.30506i) q^{77} +(1.75826 - 12.2290i) q^{78} +(0.950286 + 2.08084i) q^{79} +(-4.77001 - 1.40060i) q^{80} +(1.65252 + 0.485223i) q^{81} +(-0.0172482 - 0.0377683i) q^{82} +(-0.880246 + 6.12225i) q^{83} +(-1.65392 + 1.90872i) q^{84} +(-1.21440 + 2.65916i) q^{85} +(-10.0640 - 6.46773i) q^{86} +(1.38739 + 9.64954i) q^{87} +(7.11199 - 4.57060i) q^{88} +(9.70852 + 11.2042i) q^{89} +(-2.56150 + 0.752123i) q^{90} -15.7941 q^{91} +(0.614832 + 3.93680i) q^{92} -1.68036 q^{93} +(-17.8778 + 5.24940i) q^{94} +(2.76646 + 3.19266i) q^{95} +(-4.43056 + 2.84735i) q^{96} +(0.152308 + 1.05932i) q^{97} +(-0.653375 - 0.419899i) q^{98} +(2.83274 - 6.20283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more