LMFDB - Embedded newform 1155.2.l.f.1121.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.9
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.f.1121.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41625 q^{2} +(-1.72991 + 0.0861016i) q^{3} +0.00575714 q^{4} -1.00000i q^{5} +(2.44998 - 0.121941i) q^{6} -1.00000i q^{7} +2.82434 q^{8} +(2.98517 - 0.297896i) q^{9} +O(q^{10})$	\(q-1.41625 q^{2} +(-1.72991 + 0.0861016i) q^{3} +0.00575714 q^{4} -1.00000i q^{5} +(2.44998 - 0.121941i) q^{6} -1.00000i q^{7} +2.82434 q^{8} +(2.98517 - 0.297896i) q^{9} +1.41625i q^{10} +(-2.56458 + 2.10307i) q^{11} +(-0.00995933 + 0.000495699i) q^{12} +1.52790i q^{13} +1.41625i q^{14} +(0.0861016 + 1.72991i) q^{15} -4.01148 q^{16} -0.570654 q^{17} +(-4.22774 + 0.421894i) q^{18} +1.43623i q^{19} -0.00575714i q^{20} +(0.0861016 + 1.72991i) q^{21} +(3.63208 - 2.97847i) q^{22} -6.92922i q^{23} +(-4.88586 + 0.243180i) q^{24} -1.00000 q^{25} -2.16388i q^{26} +(-5.13843 + 0.772361i) q^{27} -0.00575714i q^{28} -7.97813 q^{29} +(-0.121941 - 2.44998i) q^{30} +1.98313 q^{31} +0.0325672 q^{32} +(4.25542 - 3.85894i) q^{33} +0.808188 q^{34} -1.00000 q^{35} +(0.0171861 - 0.00171503i) q^{36} +10.6442 q^{37} -2.03406i q^{38} +(-0.131555 - 2.64313i) q^{39} -2.82434i q^{40} -5.70731 q^{41} +(-0.121941 - 2.44998i) q^{42} +4.31362i q^{43} +(-0.0147647 + 0.0121077i) q^{44} +(-0.297896 - 2.98517i) q^{45} +9.81349i q^{46} -11.4393i q^{47} +(6.93950 - 0.345395i) q^{48} -1.00000 q^{49} +1.41625 q^{50} +(0.987180 - 0.0491342i) q^{51} +0.00879634i q^{52} +4.89812i q^{53} +(7.27729 - 1.09385i) q^{54} +(2.10307 + 2.56458i) q^{55} -2.82434i q^{56} +(-0.123662 - 2.48455i) q^{57} +11.2990 q^{58} +2.01280i q^{59} +(0.000495699 + 0.00995933i) q^{60} +13.2091i q^{61} -2.80860 q^{62} +(-0.297896 - 2.98517i) q^{63} +7.97684 q^{64} +1.52790 q^{65} +(-6.02673 + 5.46521i) q^{66} +2.03697 q^{67} -0.00328534 q^{68} +(0.596616 + 11.9869i) q^{69} +1.41625 q^{70} +5.02578i q^{71} +(8.43115 - 0.841360i) q^{72} +12.9706i q^{73} -15.0748 q^{74} +(1.72991 - 0.0861016i) q^{75} +0.00826859i q^{76} +(2.10307 + 2.56458i) q^{77} +(0.186314 + 3.74332i) q^{78} -5.30766i q^{79} +4.01148i q^{80} +(8.82252 - 1.77854i) q^{81} +8.08297 q^{82} +1.61811 q^{83} +(0.000495699 + 0.00995933i) q^{84} +0.570654i q^{85} -6.10915i q^{86} +(13.8014 - 0.686929i) q^{87} +(-7.24326 + 5.93979i) q^{88} +17.4890i q^{89} +(0.421894 + 4.22774i) q^{90} +1.52790 q^{91} -0.0398925i q^{92} +(-3.43063 + 0.170751i) q^{93} +16.2009i q^{94} +1.43623 q^{95} +(-0.0563383 + 0.00280409i) q^{96} +18.5024 q^{97} +1.41625 q^{98} +(-7.02923 + 7.04201i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.41625			−1.00144			−0.500719	−	0.865610i	$-0.666931\pi$
$2$	−1.41625			−1.00144			−0.500719	+	0.865610i	$0.666931\pi$
$3$	−1.72991	+	0.0861016i	−0.998764	+	0.0497108i
$3$	−1.72991	+	0.0861016i	−0.998764	+	0.0497108i
$4$	0.00575714			0.00287857
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	2.44998	−	0.121941i	1.00020	−	0.0497823i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.82434			0.998556
$9$	2.98517	−	0.297896i	0.995058	−	0.0992986i
$10$			1.41625i			0.447857i
$11$	−2.56458	+	2.10307i	−0.773251	+	0.634100i
$11$	−2.56458	+	2.10307i	−0.773251	+	0.634100i
$12$	−0.00995933		0.000495699i	−0.00287501		0.000143096i
$13$			1.52790i			0.423763i	0.977295	+	0.211882i	$0.0679591\pi$
$13$			1.52790i			0.423763i	−0.977295	+	0.211882i	$0.932041\pi$
$14$			1.41625i			0.378508i
$15$	0.0861016	+	1.72991i	0.0222313	+	0.446661i
$16$	−4.01148			−1.00287
$17$	−0.570654			−0.138404			−0.0692020	−	0.997603i	$-0.522045\pi$
$17$	−0.570654			−0.138404			−0.0692020	+	0.997603i	$0.522045\pi$
$18$	−4.22774	+	0.421894i	−0.996489	+	0.0994414i
$19$			1.43623i			0.329494i	0.986336	+	0.164747i	$0.0526808\pi$
$19$			1.43623i			0.329494i	−0.986336	+	0.164747i	$0.947319\pi$
$20$		−	0.00575714i		−	0.00128734i
$21$	0.0861016	+	1.72991i	0.0187889	+	0.377497i
$22$	3.63208	−	2.97847i	0.774363	−	0.635012i
$23$		−	6.92922i		−	1.44484i	−0.691454	−	0.722421i	$-0.743029\pi$
$23$		−	6.92922i		−	1.44484i	0.691454	−	0.722421i	$-0.256971\pi$
$24$	−4.88586	+	0.243180i	−0.997321	+	0.0496390i
$25$	−1.00000			−0.200000
$26$		−	2.16388i		−	0.424373i
$27$	−5.13843	+	0.772361i	−0.988891	+	0.148641i
$28$		−	0.00575714i		−	0.00108800i
$29$	−7.97813			−1.48150			−0.740751	−	0.671780i	$-0.765530\pi$
$29$	−7.97813			−1.48150			−0.740751	+	0.671780i	$0.765530\pi$
$30$	−0.121941	−	2.44998i	−0.0222633	−	0.447303i
$31$	1.98313			0.356180			0.178090	−	0.984014i	$-0.443008\pi$
$31$	1.98313			0.356180			0.178090	+	0.984014i	$0.443008\pi$
$32$	0.0325672			0.00575712
$33$	4.25542	−	3.85894i	0.740773	−	0.671755i
$34$	0.808188			0.138603
$35$	−1.00000			−0.169031
$36$	0.0171861	−	0.00171503i	0.00286434	−	0.000285838i
$37$	10.6442			1.74989			0.874945	−	0.484223i	$-0.160898\pi$
$37$	10.6442			1.74989			0.874945	+	0.484223i	$0.160898\pi$
$38$		−	2.03406i		−	0.329968i
$39$	−0.131555	−	2.64313i	−0.0210656	−	0.423239i
$40$		−	2.82434i		−	0.446568i
$41$	−5.70731			−0.891332			−0.445666	−	0.895199i	$-0.647033\pi$
$41$	−5.70731			−0.891332			−0.445666	+	0.895199i	$0.647033\pi$
$42$	−0.121941	−	2.44998i	−0.0188159	−	0.378040i
$43$			4.31362i			0.657821i	0.944361	+	0.328910i	$0.106681\pi$
$43$			4.31362i			0.657821i	−0.944361	+	0.328910i	$0.893319\pi$
$44$	−0.0147647	+	0.0121077i	−0.00222586	+	0.00182530i
$45$	−0.297896	−	2.98517i	−0.0444077	−	0.445003i
$46$			9.81349i			1.44692i
$47$		−	11.4393i		−	1.66860i	−0.551313	−	0.834298i	$-0.685873\pi$
$47$		−	11.4393i		−	1.66860i	0.551313	−	0.834298i	$-0.314127\pi$
$48$	6.93950	−	0.345395i	1.00163	−	0.0498534i
$49$	−1.00000			−0.142857
$50$	1.41625			0.200288
$51$	0.987180	−	0.0491342i	0.138233	−	0.00688017i
$52$			0.00879634i			0.00121983i
$53$			4.89812i			0.672808i	0.941718	+	0.336404i	$0.109211\pi$
$53$			4.89812i			0.672808i	−0.941718	+	0.336404i	$0.890789\pi$
$54$	7.27729	−	1.09385i	0.990314	−	0.148855i
$55$	2.10307	+	2.56458i	0.283578	+	0.345808i
$56$		−	2.82434i		−	0.377419i
$57$	−0.123662	−	2.48455i	−0.0163794	−	0.329087i
$58$	11.2990			1.48363
$59$			2.01280i			0.262044i	0.991379	+	0.131022i	$0.0418258\pi$
$59$			2.01280i			0.262044i	−0.991379	+	0.131022i	$0.958174\pi$
$60$	0.000495699		0.00995933i	6.39944e−5		0.00128574i
$61$			13.2091i			1.69125i	0.533774	+	0.845627i	$0.320773\pi$
$61$			13.2091i			1.69125i	−0.533774	+	0.845627i	$0.679227\pi$
$62$	−2.80860			−0.356693
$63$	−0.297896	−	2.98517i	−0.0375313	−	0.376096i
$64$	7.97684			0.997105
$65$	1.52790			0.189513
$66$	−6.02673	+	5.46521i	−0.741839	+	0.672721i
$67$	2.03697			0.248856			0.124428	−	0.992229i	$-0.460290\pi$
$67$	2.03697			0.248856			0.124428	+	0.992229i	$0.460290\pi$
$68$	−0.00328534			−0.000398406
$69$	0.596616	+	11.9869i	0.0718242	+	1.44306i
$70$	1.41625			0.169274
$71$			5.02578i			0.596450i	0.954496	+	0.298225i	$0.0963946\pi$
$71$			5.02578i			0.596450i	−0.954496	+	0.298225i	$0.903605\pi$
$72$	8.43115	−	0.841360i	0.993620	−	0.0991552i
$73$			12.9706i			1.51809i	0.651039	+	0.759045i	$0.274334\pi$
$73$			12.9706i			1.51809i	−0.651039	+	0.759045i	$0.725666\pi$
$74$	−15.0748			−1.75241
$75$	1.72991	−	0.0861016i	0.199753	−	0.00994215i
$76$			0.00826859i			0.000948473i
$77$	2.10307	+	2.56458i	0.239667	+	0.292261i
$78$	0.186314	+	3.74332i	0.0210959	+	0.423848i
$79$		−	5.30766i		−	0.597159i	−0.954385	−	0.298579i	$-0.903487\pi$
$79$		−	5.30766i		−	0.597159i	0.954385	−	0.298579i	$-0.0965128\pi$
$80$			4.01148i			0.448497i
$81$	8.82252	−	1.77854i	0.980280	−	0.197616i
$82$	8.08297			0.892614
$83$	1.61811			0.177610			0.0888051	−	0.996049i	$-0.471695\pi$
$83$	1.61811			0.177610			0.0888051	+	0.996049i	$0.471695\pi$
$84$	0.000495699		0.00995933i	5.40852e−5		0.00108665i
$85$			0.570654i			0.0618962i
$86$		−	6.10915i		−	0.658767i
$87$	13.8014	−	0.686929i	1.47967	−	0.0736466i
$88$	−7.24326	+	5.93979i	−0.772134	+	0.633184i
$89$			17.4890i			1.85383i	0.375267	+	0.926917i	$0.377551\pi$
$89$			17.4890i			1.85383i	−0.375267	+	0.926917i	$0.622449\pi$
$90$	0.421894	+	4.22774i	0.0444716	+	0.445643i
$91$	1.52790			0.160167
$92$		−	0.0398925i		−	0.00415908i
$93$	−3.43063	+	0.170751i	−0.355740	+	0.0177060i
$94$			16.2009i			1.67100i
$95$	1.43623			0.147354
$96$	−0.0563383	+	0.00280409i	−0.00575001	+	0.000286191i
$97$	18.5024			1.87863			0.939315	−	0.343057i	$-0.111462\pi$
$97$	18.5024			1.87863			0.939315	+	0.343057i	$0.111462\pi$
$98$	1.41625			0.143063
$99$	−7.02923	+	7.04201i	−0.706464	+	0.707749i
$100$	−0.00575714			−0.000575714
$101$	18.5798			1.84876			0.924381	−	0.381471i	$-0.124582\pi$
$101$	18.5798			1.84876			0.924381	+	0.381471i	$0.124582\pi$
$102$	−1.39809	+	0.0695862i	−0.138432	+	0.00689006i
$103$	−9.64822			−0.950667			−0.475334	−	0.879806i	$-0.657673\pi$
$103$	−9.64822			−0.950667			−0.475334	+	0.879806i	$0.657673\pi$
$104$			4.31531i			0.423151i
$105$	1.72991	−	0.0861016i	0.168822	−	0.00840265i
$106$		−	6.93695i		−	0.673776i
$107$	11.2945			1.09188			0.545940	−	0.837824i	$-0.316173\pi$
$107$	11.2945			1.09188			0.545940	+	0.837824i	$0.316173\pi$
$108$	−0.0295827	+	0.00444659i	−0.00284659	+	0.000427873i
$109$		−	7.65885i		−	0.733585i	−0.930303	−	0.366792i	$-0.880456\pi$
$109$		−	7.65885i		−	0.733585i	0.930303	−	0.366792i	$-0.119544\pi$
$110$	−2.97847	−	3.63208i	−0.283986	−	0.346306i
$111$	−18.4134	+	0.916479i	−1.74773	+	0.0869883i
$112$			4.01148i			0.379049i
$113$			5.60353i			0.527136i	0.964641	+	0.263568i	$0.0848993\pi$
$113$			5.60353i			0.527136i	−0.964641	+	0.263568i	$0.915101\pi$
$114$	0.175136	+	3.51874i	0.0164030	+	0.329560i
$115$	−6.92922			−0.646153
$116$	−0.0459312			−0.00426461
$117$	0.455155	+	4.56105i	0.0420791	+	0.421669i
$118$		−	2.85062i		−	0.262421i
$119$			0.570654i			0.0523118i
$120$	0.243180	+	4.88586i	0.0221992	+	0.446016i
$121$	2.15417	−	10.7870i	0.195834	−	0.980637i
$122$		−	18.7074i		−	1.69369i
$123$	9.87313	−	0.491408i	0.890230	−	0.0443088i
$124$	0.0114172			0.00102529
$125$			1.00000i			0.0894427i
$126$	0.421894	+	4.22774i	0.0375853	+	0.376637i
$127$		−	19.5258i		−	1.73263i	−0.499498	−	0.866315i	$-0.666482\pi$
$127$		−	19.5258i		−	1.73263i	0.499498	−	0.866315i	$-0.333518\pi$
$128$	−11.3623			−1.00430
$129$	−0.371409	−	7.46217i	−0.0327008	−	0.657007i
$130$	−2.16388			−0.189785
$131$	−7.12623			−0.622621			−0.311311	−	0.950308i	$-0.600768\pi$
$131$	−7.12623			−0.622621			−0.311311	+	0.950308i	$0.600768\pi$
$132$	0.0244990	−	0.0222165i	0.00213237	−	0.00193369i
$133$	1.43623			0.124537
$134$	−2.88486			−0.249214
$135$	0.772361	+	5.13843i	0.0664742	+	0.442246i
$136$	−1.61172			−0.138204
$137$		−	4.30662i		−	0.367939i	−0.982932	−	0.183970i	$-0.941105\pi$
$137$		−	4.30662i		−	0.367939i	0.982932	−	0.183970i	$-0.0588948\pi$
$138$	−0.844956	−	16.9764i	−0.0719275	−	1.44513i
$139$			17.3494i			1.47156i	0.677222	+	0.735778i	$0.263184\pi$
$139$			17.3494i			1.47156i	−0.677222	+	0.735778i	$0.736816\pi$
$140$	−0.00575714			−0.000486567
$141$	0.984943	+	19.7890i	0.0829472	+	1.66653i
$142$		−	7.11775i		−	0.597308i
$143$	−3.21328	−	3.91843i	−0.268708	−	0.327675i
$144$	−11.9750	+	1.19500i	−0.997914	+	0.0995836i
$145$			7.97813i			0.662547i
$146$		−	18.3695i		−	1.52027i
$147$	1.72991	−	0.0861016i	0.142681	−	0.00710154i
$148$	0.0612799			0.00503718
$149$	13.8536			1.13493			0.567466	−	0.823397i	$-0.307924\pi$
$149$	13.8536			1.13493			0.567466	+	0.823397i	$0.307924\pi$
$150$	−2.44998	+	0.121941i	−0.200040	+	0.00995645i
$151$			17.5387i			1.42728i	0.700515	+	0.713638i	$0.252954\pi$
$151$			17.5387i			1.42728i	−0.700515	+	0.713638i	$0.747046\pi$
$152$			4.05641i			0.329018i
$153$	−1.70350	+	0.169996i	−0.137720	+	0.0137433i
$154$	−2.97847	−	3.63208i	−0.240012	−	0.292682i
$155$		−	1.98313i		−	0.159289i
$156$	−0.000757378	−	0.0152169i	−6.06388e−5	−	0.00121832i
$157$	6.61607			0.528020			0.264010	−	0.964520i	$-0.414955\pi$
$157$	6.61607			0.528020			0.264010	+	0.964520i	$0.414955\pi$
$158$			7.51697i			0.598018i
$159$	−0.421736	−	8.47330i	−0.0334458	−	0.671976i
$160$		−	0.0325672i		−	0.00257466i
$161$	−6.92922			−0.546099
$162$	−12.4949	+	2.51885i	−0.981689	+	0.197900i
$163$	17.8530			1.39835			0.699177	−	0.714949i	$-0.253550\pi$
$163$	17.8530			1.39835			0.699177	+	0.714949i	$0.253550\pi$
$164$	−0.0328578			−0.00256576
$165$	−3.85894	−	4.25542i	−0.300418	−	0.331284i
$166$	−2.29164			−0.177866
$167$	16.1729			1.25149			0.625747	−	0.780026i	$-0.284794\pi$
$167$	16.1729			1.25149			0.625747	+	0.780026i	$0.284794\pi$
$168$	0.243180	+	4.88586i	0.0187618	+	0.376952i
$169$	10.6655			0.820425
$170$		−	0.808188i		−	0.0619852i
$171$	0.427848	+	4.28740i	0.0327183	+	0.327866i
$172$			0.0248341i			0.00189358i
$173$	−3.83571			−0.291623			−0.145812	−	0.989312i	$-0.546579\pi$
$173$	−3.83571			−0.291623			−0.145812	+	0.989312i	$0.546579\pi$
$174$	−19.5463	+	0.972862i	−1.48180	+	0.0737525i
$175$			1.00000i			0.0755929i
$176$	10.2878	−	8.43643i	0.775470	−	0.635920i
$177$	−0.173305	−	3.48195i	−0.0130264	−	0.261720i
$178$		−	24.7688i		−	1.85650i
$179$			15.9027i			1.18862i	0.804236	+	0.594311i	$0.202575\pi$
$179$			15.9027i			1.18862i	−0.804236	+	0.594311i	$0.797425\pi$
$180$	−0.00171503	−	0.0171861i	−0.000127831	−	0.00128097i
$181$	−7.55849			−0.561818			−0.280909	−	0.959734i	$-0.590636\pi$
$181$	−7.55849			−0.561818			−0.280909	+	0.959734i	$0.590636\pi$
$182$	−2.16388			−0.160398
$183$	−1.13733	−	22.8506i	−0.0840735	−	1.68916i
$184$		−	19.5705i		−	1.44275i
$185$		−	10.6442i		−	0.782574i
$186$	4.85863	−	0.241825i	0.356252	−	0.0177315i
$187$	1.46349	−	1.20013i	0.107021	−	0.0877620i
$188$		−	0.0658578i		−	0.00480317i
$189$	0.772361	+	5.13843i	0.0561810	+	0.373766i
$190$	−2.03406			−0.147566
$191$		−	9.99611i		−	0.723293i	−0.932315	−	0.361646i	$-0.882215\pi$
$191$		−	9.99611i		−	0.723293i	0.932315	−	0.361646i	$-0.117785\pi$
$192$	−13.7992	+	0.686818i	−0.995872	+	0.0495668i
$193$			18.0664i			1.30045i	0.759743	+	0.650224i	$0.225325\pi$
$193$			18.0664i			1.30045i	−0.759743	+	0.650224i	$0.774675\pi$
$194$	−26.2039			−1.88133
$195$	−2.64313	+	0.131555i	−0.189278	+	0.00942082i
$196$	−0.00575714			−0.000411224
$197$	3.45354			0.246055			0.123027	−	0.992403i	$-0.460740\pi$
$197$	3.45354			0.246055			0.123027	+	0.992403i	$0.460740\pi$
$198$	9.95513	−	9.97323i	0.707480	−	0.708767i
$199$	−0.0618628			−0.00438534			−0.00219267	−	0.999998i	$-0.500698\pi$
$199$	−0.0618628			−0.00438534			−0.00219267	+	0.999998i	$0.500698\pi$
$200$	−2.82434			−0.199711
$201$	−3.52378	+	0.175387i	−0.248548	+	0.0123708i
$202$	−26.3136			−1.85142
$203$			7.97813i			0.559955i
$204$	0.00568334		0.000282873i	0.000397913		1.98051e-5i
$205$			5.70731i			0.398616i
$206$	13.6643			0.952034
$207$	−2.06418	−	20.6849i	−0.143471	−	1.43770i
$208$		−	6.12914i		−	0.424980i
$209$	−3.02050	−	3.68334i	−0.208932	−	0.254782i
$210$	−2.44998	+	0.121941i	−0.169065	+	0.00841474i
$211$		−	1.95814i		−	0.134804i	−0.997726	−	0.0674019i	$-0.978529\pi$
$211$		−	1.95814i		−	0.134804i	0.997726	−	0.0674019i	$-0.0214710\pi$
$212$			0.0281992i			0.00193673i
$213$	−0.432728	−	8.69414i	−0.0296500	−	0.595713i
$214$	−15.9958			−1.09345
$215$	4.31362			0.294186
$216$	−14.5127	+	2.18141i	−0.987463	+	0.148426i
$217$		−	1.98313i		−	0.134624i
$218$			10.8468i			0.734640i
$219$	−1.11679	−	22.4379i	−0.0754654	−	1.51621i
$220$	0.0121077	+	0.0147647i	0.000816300	+	0.000995434i
$221$		−	0.871903i		−	0.0586505i
$222$	26.0780	−	1.29796i	1.75024	−	0.0871134i
$223$	−20.1052			−1.34634			−0.673171	−	0.739487i	$-0.735068\pi$
$223$	−20.1052			−1.34634			−0.673171	+	0.739487i	$0.735068\pi$
$224$		−	0.0325672i		−	0.00217599i
$225$	−2.98517	+	0.297896i	−0.199012	+	0.0198597i
$226$		−	7.93599i		−	0.527894i
$227$	−3.95003			−0.262173			−0.131086	−	0.991371i	$-0.541846\pi$
$227$	−3.95003			−0.262173			−0.131086	+	0.991371i	$0.541846\pi$
$228$	−0.000711939	−	0.0143039i	−4.71493e−5	−	0.000947300i
$229$	23.6387			1.56209			0.781043	−	0.624477i	$-0.214688\pi$
$229$	23.6387			1.56209			0.781043	+	0.624477i	$0.214688\pi$
$230$	9.81349			0.647082
$231$	−3.85894	−	4.25542i	−0.253900	−	0.279986i
$232$	−22.5330			−1.47936
$233$	12.3452			0.808764			0.404382	−	0.914590i	$-0.367487\pi$
$233$	12.3452			0.808764			0.404382	+	0.914590i	$0.367487\pi$
$234$	−0.644612	−	6.45957i	−0.0421396	−	0.422275i
$235$	−11.4393			−0.746219
$236$			0.0115880i			0.000754311i
$237$	0.456998	+	9.18178i	0.0296852	+	0.596421i
$238$		−	0.808188i		−	0.0523870i
$239$	2.41775			0.156391			0.0781957	−	0.996938i	$-0.475084\pi$
$239$	2.41775			0.156391			0.0781957	+	0.996938i	$0.475084\pi$
$240$	−0.345395	−	6.93950i	−0.0222951	−	0.447943i
$241$			4.77791i			0.307772i	0.988089	+	0.153886i	$0.0491789\pi$
$241$			4.77791i			0.307772i	−0.988089	+	0.153886i	$0.950821\pi$
$242$	−3.05084	+	15.2771i	−0.196116	+	0.982047i
$243$	−15.1090	+	3.83635i	−0.969244	+	0.246102i
$244$			0.0760467i			0.00486839i
$245$			1.00000i			0.0638877i
$246$	−13.9828	+	0.695956i	−0.891511	+	0.0443725i
$247$	−2.19442			−0.139628
$248$	5.60103			0.355666
$249$	−2.79918	+	0.139322i	−0.177391	+	0.00882914i
$250$		−	1.41625i		−	0.0895714i
$251$			9.67559i			0.610718i	0.952237	+	0.305359i	$0.0987764\pi$
$251$			9.67559i			0.610718i	−0.952237	+	0.305359i	$0.901224\pi$
$252$	−0.00171503	−	0.0171861i	−0.000108037	−	0.00108262i
$253$	14.5726	+	17.7706i	0.916174	+	1.11722i
$254$			27.6533i			1.73512i
$255$	−0.0491342	−	0.987180i	−0.00307691	−	0.0618196i
$256$	0.138170			0.00863564
$257$			18.5283i			1.15576i	0.816120	+	0.577882i	$0.196121\pi$
$257$			18.5283i			1.15576i	−0.816120	+	0.577882i	$0.803879\pi$
$258$	0.526008	+	10.5683i	0.0327478	+	0.657952i
$259$		−	10.6442i		−	0.661396i
$260$	0.00879634			0.000545526
$261$	−23.8161	+	2.37665i	−1.47418	+	0.147111i
$262$	10.0925			0.623517
$263$	3.39619			0.209418			0.104709	−	0.994503i	$-0.466609\pi$
$263$	3.39619			0.209418			0.104709	+	0.994503i	$0.466609\pi$
$264$	12.0188	−	10.8990i	0.739703	−	0.670785i
$265$	4.89812			0.300889
$266$	−2.03406			−0.124716
$267$	−1.50583	−	30.2544i	−0.0921555	−	1.85154i
$268$	0.0117271			0.000716349
$269$		−	14.6780i		−	0.894932i	−0.894301	−	0.447466i	$-0.852327\pi$
$269$		−	14.6780i		−	0.894932i	0.894301	−	0.447466i	$-0.147673\pi$
$270$	−1.09385	−	7.27729i	−0.0665698	−	0.442882i
$271$		−	19.6453i		−	1.19337i	−0.802476	−	0.596684i	$-0.796485\pi$
$271$		−	19.6453i		−	1.19337i	0.802476	−	0.596684i	$-0.203515\pi$
$272$	2.28917			0.138801
$273$	−2.64313	+	0.131555i	−0.159969	+	0.00796205i
$274$			6.09924i			0.368469i
$275$	2.56458	−	2.10307i	0.154650	−	0.126820i
$276$	0.00343480	+	0.0690104i	0.000206751	+	0.00415394i
$277$			18.6778i			1.12224i	0.827734	+	0.561121i	$0.189630\pi$
$277$			18.6778i			1.12224i	−0.827734	+	0.561121i	$0.810370\pi$
$278$		−	24.5710i		−	1.47367i
$279$	5.91998	−	0.590766i	0.354420	−	0.0353682i
$280$	−2.82434			−0.168787
$281$	−19.8827			−1.18610			−0.593050	−	0.805166i	$-0.702076\pi$
$281$	−19.8827			−1.18610			−0.593050	+	0.805166i	$0.702076\pi$
$282$	−1.39492	−	28.0261i	−0.0830665	−	1.66893i
$283$		−	3.63533i		−	0.216098i	−0.994146	−	0.108049i	$-0.965540\pi$
$283$		−	3.63533i		−	0.216098i	0.994146	−	0.108049i	$-0.0344603\pi$
$284$			0.0289341i			0.00171692i
$285$	−2.48455	+	0.123662i	−0.147172	+	0.00732510i
$286$	4.55081	+	5.54946i	0.269095	+	0.328147i
$287$			5.70731i			0.336892i
$288$	0.0972188	−	0.00970163i	0.00572867	−	0.000571674i
$289$	−16.6744			−0.980844
$290$		−	11.2990i		−	0.663500i
$291$	−32.0074	+	1.59308i	−1.87631	+	0.0933881i
$292$			0.0746734i			0.00436993i
$293$	−19.3182			−1.12858			−0.564292	−	0.825575i	$-0.690851\pi$
$293$	−19.3182			−1.12858			−0.564292	+	0.825575i	$0.690851\pi$
$294$	−2.44998	+	0.121941i	−0.142886	+	0.00711175i
$295$	2.01280			0.117190
$296$	30.0628			1.74736
$297$	11.5536	−	12.7873i	0.670408	−	0.741993i
$298$	−19.6202			−1.13657
$299$	10.5872			0.612271
$300$	0.00995933		0.000495699i	0.000575002		2.86192e-5i
$301$	4.31362			0.248633
$302$		−	24.8391i		−	1.42933i
$303$	−32.1414	+	1.59975i	−1.84648	+	0.0919033i
$304$		−	5.76142i		−	0.330440i
$305$	13.2091			0.756352
$306$	2.41258	−	0.240756i	0.137918	−	0.0137631i
$307$			12.4202i			0.708856i	0.935083	+	0.354428i	$0.115324\pi$
$307$			12.4202i			0.708856i	−0.935083	+	0.354428i	$0.884676\pi$
$308$	0.0121077	+	0.0147647i	0.000689899	+	0.000841295i
$309$	16.6905	−	0.830727i	0.949492	−	0.0472584i
$310$			2.80860i			0.159518i
$311$			24.2871i			1.37719i	0.725145	+	0.688596i	$0.241773\pi$
$311$			24.2871i			1.37719i	−0.725145	+	0.688596i	$0.758227\pi$
$312$	−0.371555	−	7.46510i	−0.0210352	−	0.422628i
$313$	−13.2033			−0.746297			−0.373148	−	0.927772i	$-0.621722\pi$
$313$	−13.2033			−0.746297			−0.373148	+	0.927772i	$0.621722\pi$
$314$	−9.36999			−0.528779
$315$	−2.98517	+	0.297896i	−0.168195	+	0.0167845i
$316$		−	0.0305570i		−	0.00171896i
$317$		−	20.0464i		−	1.12592i	−0.826484	−	0.562960i	$-0.809663\pi$
$317$		−	20.0464i		−	1.12592i	0.826484	−	0.562960i	$-0.190337\pi$
$318$	0.597282	+	12.0003i	0.0334939	+	0.672943i
$319$	20.4606	−	16.7786i	1.14557	−	0.939420i
$320$		−	7.97684i		−	0.445919i
$321$	−19.5385	+	0.972474i	−1.09053	+	0.0542782i
$322$	9.81349			0.546884
$323$		−	0.819592i		−	0.0456033i
$324$	0.0507925	−	0.0102393i	0.00282180	−	0.000568851i
$325$		−	1.52790i		−	0.0847527i
$326$	−25.2843			−1.40037
$327$	0.659439	+	13.2491i	0.0364671	+	0.732678i
$328$	−16.1194			−0.890045
$329$	−11.4393			−0.630670
$330$	5.46521	+	6.02673i	0.300850	+	0.331760i
$331$	12.1805			0.669501			0.334751	−	0.942307i	$-0.391348\pi$
$331$	12.1805			0.669501			0.334751	+	0.942307i	$0.391348\pi$
$332$	0.00931567			0.000511264
$333$	31.7747	−	3.17085i	1.74124	−	0.173762i
$334$	−22.9048			−1.25329
$335$		−	2.03697i		−	0.111292i
$336$	−0.345395	−	6.93950i	−0.0188428	−	0.378581i
$337$		−	21.3746i		−	1.16435i	−0.813064	−	0.582175i	$-0.802202\pi$
$337$		−	21.3746i		−	1.16435i	0.813064	−	0.582175i	$-0.197798\pi$
$338$	−15.1050			−0.821605
$339$	−0.482473	−	9.69360i	−0.0262043	−	0.526484i
$340$			0.00328534i			0.000178172i
$341$	−5.08590	+	4.17066i	−0.275417	+	0.225854i
$342$	−0.605938	−	6.07202i	−0.0327654	−	0.328337i
$343$			1.00000i			0.0539949i
$344$			12.1831i			0.656871i
$345$	11.9869	−	0.596616i	0.645354	−	0.0321207i
$346$	5.43231			0.292043
$347$	−3.31681			−0.178056			−0.0890278	−	0.996029i	$-0.528376\pi$
$347$	−3.31681			−0.178056			−0.0890278	+	0.996029i	$0.528376\pi$
$348$	0.0794568	−	0.00395475i	0.00425933	−	0.000211997i
$349$		−	3.23672i		−	0.173258i	−0.996241	−	0.0866289i	$-0.972391\pi$
$349$		−	3.23672i		−	0.173258i	0.996241	−	0.0866289i	$-0.0276094\pi$
$350$		−	1.41625i		−	0.0757016i
$351$	−1.18009	−	7.85101i	−0.0629886	−	0.419056i
$352$	−0.0835213	+	0.0684912i	−0.00445170	+	0.00365059i
$353$			9.96446i			0.530355i	0.964200	+	0.265177i	$0.0854305\pi$
$353$			9.96446i			0.530355i	−0.964200	+	0.265177i	$0.914569\pi$
$354$	0.245443	+	4.93131i	0.0130451	+	0.262096i
$355$	5.02578			0.266741
$356$			0.100687i			0.00533639i
$357$	−0.0491342	−	0.987180i	−0.00260046	−	0.0522471i
$358$		−	22.5221i		−	1.19033i
$359$	−5.80212			−0.306224			−0.153112	−	0.988209i	$-0.548930\pi$
$359$	−5.80212			−0.306224			−0.153112	+	0.988209i	$0.548930\pi$
$360$	−0.841360	−	8.43115i	−0.0443435	−	0.444361i
$361$	16.9372			0.891433
$362$	10.7047			0.562626
$363$	−2.79775	+	18.8460i	−0.146844	+	0.989160i
$364$	0.00879634			0.000461053
$365$	12.9706			0.678910
$366$	1.61073	+	32.3621i	0.0841944	+	1.69159i
$367$	−19.4294			−1.01421			−0.507103	−	0.861885i	$-0.669284\pi$
$367$	−19.4294			−1.01421			−0.507103	+	0.861885i	$0.669284\pi$
$368$			27.7964i			1.44899i
$369$	−17.0373	+	1.70018i	−0.886927	+	0.0885081i
$370$			15.0748i			0.783700i
$371$	4.89812			0.254298
$372$	−0.0197506		0.000983035i	−0.00102402		5.09680e-5i
$373$			36.0837i			1.86834i	0.356823	+	0.934172i	$0.383860\pi$
$373$			36.0837i			1.86834i	−0.356823	+	0.934172i	$0.616140\pi$
$374$	−2.07267	+	1.69968i	−0.107175	+	0.0878882i
$375$	−0.0861016	−	1.72991i	−0.00444627	−	0.0893321i
$376$		−	32.3086i		−	1.66619i
$377$		−	12.1898i		−	0.627806i
$378$	−1.09385	−	7.27729i	−0.0562618	−	0.374303i
$379$	24.0887			1.23735			0.618676	−	0.785646i	$-0.287669\pi$
$379$	24.0887			1.23735			0.618676	+	0.785646i	$0.287669\pi$
$380$	0.00826859			0.000424170
$381$	1.68120	+	33.7778i	0.0861304	+	1.73049i
$382$			14.1570i			0.724333i
$383$			25.6757i			1.31197i	0.754776	+	0.655983i	$0.227746\pi$
$383$			25.6757i			1.31197i	−0.754776	+	0.655983i	$0.772254\pi$
$384$	19.6558	−	0.978313i	1.00305	−	0.0499243i
$385$	2.56458	−	2.10307i	0.130703	−	0.107182i
$386$		−	25.5865i		−	1.30232i
$387$	1.28501	+	12.8769i	0.0653207	+	0.654570i
$388$	0.106521			0.00540777
$389$		−	26.6791i		−	1.35268i	−0.736589	−	0.676341i	$-0.763565\pi$
$389$		−	26.6791i		−	1.35268i	0.736589	−	0.676341i	$-0.236435\pi$
$390$	3.74332	−	0.186314i	0.189551	−	0.00943437i
$391$			3.95419i			0.199972i
$392$	−2.82434			−0.142651
$393$	12.3277	−	0.613579i	0.621851	−	0.0309510i
$394$	−4.89107			−0.246409
$395$	−5.30766			−0.267058
$396$	−0.0404683	+	0.0405419i	−0.00203361	+	0.00203731i
$397$	11.0228			0.553217			0.276609	−	0.960983i	$-0.410789\pi$
$397$	11.0228			0.553217			0.276609	+	0.960983i	$0.410789\pi$
$398$	0.0876131			0.00439165
$399$	−2.48455	+	0.123662i	−0.124383	+	0.00619084i
$400$	4.01148			0.200574
$401$			5.27990i			0.263666i	0.991272	+	0.131833i	$0.0420862\pi$
$401$			5.27990i			0.263666i	−0.991272	+	0.131833i	$0.957914\pi$
$402$	4.99054	−	0.248391i	0.248906	−	0.0123886i
$403$			3.03002i			0.150936i
$404$	0.106967			0.00532179
$405$	−1.77854	−	8.82252i	−0.0883764	−	0.438394i
$406$		−	11.2990i		−	0.560760i
$407$	−27.2978	+	22.3854i	−1.35310	+	1.10961i
$408$	2.78813	−	0.138772i	0.138033	−	0.00687023i
$409$			14.7389i			0.728792i	0.931244	+	0.364396i	$0.118725\pi$
$409$			14.7389i			0.728792i	−0.931244	+	0.364396i	$0.881275\pi$
$410$		−	8.08297i		−	0.399189i
$411$	0.370807	+	7.45006i	0.0182905	+	0.367485i
$412$	−0.0555462			−0.00273656
$413$	2.01280			0.0990432
$414$	2.92340	+	29.2950i	0.143677	+	1.43977i
$415$		−	1.61811i		−	0.0794297i
$416$			0.0497594i			0.00243966i
$417$	−1.49381	−	30.0129i	−0.0731522	−	1.46974i
$418$	4.27778	+	5.21652i	0.209233	+	0.255148i
$419$			17.9238i			0.875636i	0.899064	+	0.437818i	$0.144249\pi$
$419$			17.9238i			0.875636i	−0.899064	+	0.437818i	$0.855751\pi$
$420$	0.00995933		0.000495699i	0.000485966		2.41876e-5i
$421$	15.6397			0.762231			0.381116	−	0.924527i	$-0.375540\pi$
$421$	15.6397			0.762231			0.381116	+	0.924527i	$0.375540\pi$
$422$			2.77321i			0.134998i
$423$	−3.40773	−	34.1484i	−0.165689	−	1.66035i
$424$			13.8340i			0.671836i
$425$	0.570654			0.0276808
$426$	0.612849	+	12.3131i	0.0296926	+	0.596570i
$427$	13.2091			0.639234
$428$	0.0650240			0.00314305
$429$	5.89607	+	6.50186i	0.284665	+	0.313913i
$430$	−6.10915			−0.294609
$431$	23.9188			1.15213			0.576065	−	0.817404i	$-0.304588\pi$
$431$	23.9188			1.15213			0.576065	+	0.817404i	$0.304588\pi$
$432$	20.6127	−	3.09831i	0.991730	−	0.149068i
$433$	−14.5071			−0.697167			−0.348583	−	0.937278i	$-0.613337\pi$
$433$	−14.5071			−0.697167			−0.348583	+	0.937278i	$0.613337\pi$
$434$			2.80860i			0.134817i
$435$	−0.686929	−	13.8014i	−0.0329357	−	0.661728i
$436$		−	0.0440931i		−	0.00211168i
$437$	9.95197			0.476067
$438$	1.58164	+	31.7776i	0.0755739	+	1.51839i
$439$			15.1208i			0.721676i	0.932629	+	0.360838i	$0.117509\pi$
$439$			15.1208i			0.721676i	−0.932629	+	0.360838i	$0.882491\pi$
$440$	5.93979	+	7.24326i	0.283169	+	0.345309i
$441$	−2.98517	+	0.297896i	−0.142151	+	0.0141855i
$442$			1.23483i			0.0587349i
$443$		−	26.7414i		−	1.27052i	−0.772298	−	0.635260i	$-0.780893\pi$
$443$		−	26.7414i		−	1.27052i	0.772298	−	0.635260i	$-0.219107\pi$
$444$	−0.106009	+	0.00527630i	−0.00503095	+	0.000250402i
$445$	17.4890			0.829060
$446$	28.4739			1.34828
$447$	−23.9655	+	1.19282i	−1.13353	+	0.0564184i
$448$		−	7.97684i		−	0.376870i
$449$			20.3777i			0.961684i	0.876807	+	0.480842i	$0.159669\pi$
$449$			20.3777i			0.961684i	−0.876807	+	0.480842i	$0.840331\pi$
$450$	4.22774	−	0.421894i	0.199298	−	0.0198883i
$451$	14.6369	−	12.0029i	0.689224	−	0.565194i
$452$			0.0322603i			0.00151740i
$453$	−1.51011	−	30.3403i	−0.0709510	−	1.42551i
$454$	5.59422			0.262550
$455$		−	1.52790i		−	0.0716291i
$456$	−0.349263	−	7.01722i	−0.0163558	−	0.328612i
$457$			10.7337i			0.502102i	0.967974	+	0.251051i	$0.0807761\pi$
$457$			10.7337i			0.502102i	−0.967974	+	0.251051i	$0.919224\pi$
$458$	−33.4782			−1.56433
$459$	2.93227	−	0.440751i	0.136867	−	0.0205725i
$460$	−0.0398925			−0.00186000
$461$	3.62681			0.168917			0.0844587	−	0.996427i	$-0.473084\pi$
$461$	3.62681			0.168917			0.0844587	+	0.996427i	$0.473084\pi$
$462$	5.46521	+	6.02673i	0.254265	+	0.280389i
$463$	12.8323			0.596366			0.298183	−	0.954509i	$-0.403619\pi$
$463$	12.8323			0.596366			0.298183	+	0.954509i	$0.403619\pi$
$464$	32.0041			1.48575
$465$	0.170751	+	3.43063i	0.00791837	+	0.159092i
$466$	−17.4839			−0.809927
$467$			10.7430i			0.497127i	0.968616	+	0.248563i	$0.0799584\pi$
$467$			10.7430i			0.497127i	−0.968616	+	0.248563i	$0.920042\pi$
$468$	0.00262039	+	0.0262586i	0.000121128	+	0.00121380i
$469$		−	2.03697i		−	0.0940586i
$470$	16.2009			0.747292
$471$	−11.4452	+	0.569654i	−0.527367	+	0.0262483i
$472$			5.68482i			0.261665i
$473$	−9.07185	−	11.0626i	−0.417124	−	0.508661i
$474$	−0.647223	−	13.0037i	−0.0297279	−	0.597278i
$475$		−	1.43623i		−	0.0658989i
$476$			0.00328534i			0.000150583i
$477$	1.45913	+	14.6217i	0.0668089	+	0.669483i
$478$	−3.42414			−0.156616
$479$	−23.0269			−1.05213			−0.526063	−	0.850446i	$-0.676332\pi$
$479$	−23.0269			−1.05213			−0.526063	+	0.850446i	$0.676332\pi$
$480$	0.00280409	+	0.0563383i	0.000127989	+	0.00257148i
$481$			16.2632i			0.741539i
$482$		−	6.76670i		−	0.308215i
$483$	11.9869	−	0.596616i	0.545424	−	0.0271470i
$484$	0.0124019	−	0.0621023i	0.000563722	−	0.00282283i
$485$		−	18.5024i		−	0.840148i
$486$	21.3981	−	5.43322i	0.970638	−	0.246456i
$487$	−31.1642			−1.41218			−0.706092	−	0.708120i	$-0.749544\pi$
$487$	−31.1642			−1.41218			−0.706092	+	0.708120i	$0.749544\pi$
$488$			37.3071i			1.68881i
$489$	−30.8841	+	1.53717i	−1.39663	+	0.0695132i
$490$		−	1.41625i		−	0.0639795i
$491$	2.64388			0.119317			0.0596584	−	0.998219i	$-0.480999\pi$
$491$	2.64388			0.119317			0.0596584	+	0.998219i	$0.480999\pi$
$492$	0.0568410	−	0.00282911i	0.00256259	−	0.000127546i
$493$	4.55275			0.205046
$494$	3.10784			0.139828
$495$	7.04201	+	7.02923i	0.316515	+	0.315940i
$496$	−7.95528			−0.357203
$497$	5.02578			0.225437
$498$	3.96433	−	0.197314i	0.177646	−	0.00884184i
$499$	−24.9014			−1.11474			−0.557369	−	0.830265i	$-0.688189\pi$
$499$	−24.9014			−1.11474			−0.557369	+	0.830265i	$0.688189\pi$
$500$			0.00575714i			0.000257467i
$501$	−27.9776	+	1.39251i	−1.24995	+	0.0622127i
$502$		−	13.7030i		−	0.611596i
$503$	17.2447			0.768904			0.384452	−	0.923145i	$-0.374390\pi$
$503$	17.2447			0.768904			0.384452	+	0.923145i	$0.374390\pi$
$504$	−0.841360	−	8.43115i	−0.0374771	−	0.375553i
$505$		−	18.5798i		−	0.826791i
$506$	−20.6385	−	25.1675i	−0.917492	−	1.11883i
$507$	−18.4504	+	0.918318i	−0.819410	+	0.0407839i
$508$		−	0.112413i		−	0.00498750i
$509$		−	26.4988i		−	1.17454i	−0.809391	−	0.587270i	$-0.800203\pi$
$509$		−	26.4988i		−	1.17454i	0.809391	−	0.587270i	$-0.199797\pi$
$510$	0.0695862	+	1.39809i	0.00308133	+	0.0619085i
$511$	12.9706			0.573784
$512$	22.5289			0.995648
$513$	−1.10929	−	7.37998i	−0.0489763	−	0.325834i
$514$		−	26.2407i		−	1.15743i
$515$			9.64822i			0.425151i
$516$	−0.00213826	−	0.0429608i	−9.41315e−5	−	0.00189124i
$517$	24.0577	+	29.3371i	1.05806	+	1.29024i
$518$			15.0748i			0.662347i
$519$	6.63543	−	0.330260i	0.291263	−	0.0144968i
$520$	4.31531			0.189239
$521$			20.3017i			0.889432i	0.895672	+	0.444716i	$0.146695\pi$
$521$			20.3017i			0.889432i	−0.895672	+	0.444716i	$0.853305\pi$
$522$	33.7295	−	3.36593i	1.47630	−	0.147323i
$523$			20.7214i			0.906082i	0.891490	+	0.453041i	$0.149661\pi$
$523$			20.7214i			0.906082i	−0.891490	+	0.453041i	$0.850339\pi$
$524$	−0.0410267			−0.00179226
$525$	−0.0861016	−	1.72991i	−0.00375778	−	0.0754994i
$526$	−4.80985			−0.209719
$527$	−1.13168			−0.0492968
$528$	−17.0705	+	15.4801i	−0.742900	+	0.673683i
$529$	−25.0140			−1.08757
$530$	−6.93695			−0.301322
$531$	0.599603	+	6.00854i	0.0260206	+	0.260749i
$532$	0.00826859			0.000358489
$533$		−	8.72020i		−	0.377714i
$534$	2.13263	+	42.8478i	0.0922880	+	1.85420i
$535$		−	11.2945i		−	0.488304i
$536$	5.75311			0.248496
$537$	−1.36924	−	27.5102i	−0.0590873	−	1.18715i
$538$			20.7877i			0.896219i
$539$	2.56458	−	2.10307i	0.110464	−	0.0905857i
$540$	0.00444659	+	0.0295827i	0.000191351	+	0.00127304i
$541$		−	10.6124i		−	0.456264i	−0.973630	−	0.228132i	$-0.926738\pi$
$541$		−	10.6124i		−	0.456264i	0.973630	−	0.228132i	$-0.0732617\pi$
$542$			27.8226i			1.19508i
$543$	13.0755	−	0.650798i	0.561124	−	0.0279284i
$544$	−0.0185846			−0.000796809
$545$	−7.65885			−0.328069
$546$	3.74332	−	0.186314i	0.160200	−	0.00797350i
$547$		−	23.0855i		−	0.987064i	−0.869728	−	0.493532i	$-0.835706\pi$
$547$		−	23.0855i		−	0.987064i	0.869728	−	0.493532i	$-0.164294\pi$
$548$		−	0.0247938i		−	0.00105914i
$549$	3.93494	+	39.4315i	0.167939	+	1.68290i
$550$	−3.63208	+	2.97847i	−0.154873	+	0.127002i
$551$		−	11.4584i		−	0.488146i
$552$	1.68505	+	33.8551i	0.0717204	+	1.44097i
$553$	−5.30766			−0.225705
$554$		−	26.4524i		−	1.12386i
$555$	0.916479	+	18.4134i	0.0389024	+	0.781607i
$556$			0.0998829i			0.00423598i
$557$	24.1755			1.02435			0.512174	−	0.858882i	$-0.328840\pi$
$557$	24.1755			1.02435			0.512174	+	0.858882i	$0.328840\pi$
$558$	−8.38416	+	0.836671i	−0.354930	+	0.0354191i
$559$	−6.59078			−0.278760
$560$	4.01148			0.169516
$561$	−2.42837	+	2.20212i	−0.102526	+	0.0929736i
$562$	28.1588			1.18781
$563$	−17.7818			−0.749413			−0.374706	−	0.927144i	$-0.622256\pi$
$563$	−17.7818			−0.749413			−0.374706	+	0.927144i	$0.622256\pi$
$564$	0.00567046	+	0.113928i	0.000238769	+	0.00479723i
$565$	5.60353			0.235742
$566$			5.14853i			0.216409i
$567$	−1.77854	−	8.82252i	−0.0746917	−	0.370511i
$568$			14.1945i			0.595589i
$569$	30.6980			1.28693			0.643463	−	0.765477i	$-0.277497\pi$
$569$	30.6980			1.28693			0.643463	+	0.765477i	$0.277497\pi$
$570$	3.51874	−	0.175136i	0.147384	−	0.00733563i
$571$		−	31.0075i		−	1.29762i	−0.760949	−	0.648811i	$-0.775266\pi$
$571$		−	31.0075i		−	1.29762i	0.760949	−	0.648811i	$-0.224734\pi$
$572$	−0.0184993	−	0.0225589i	−0.000773496	−	0.000943237i
$573$	0.860680	+	17.2924i	0.0359554	+	0.722399i
$574$		−	8.08297i		−	0.337376i
$575$			6.92922i			0.288968i
$576$	23.8122	−	2.37627i	0.992177	−	0.0990111i
$577$	0.841215			0.0350202			0.0175101	−	0.999847i	$-0.494426\pi$
$577$	0.841215			0.0350202			0.0175101	+	0.999847i	$0.494426\pi$
$578$	23.6150			0.982255
$579$	−1.55554	−	31.2532i	−0.0646462	−	1.29884i
$580$			0.0459312i			0.00190719i
$581$		−	1.61811i		−	0.0671304i
$582$	45.3304	−	2.25620i	1.87901	−	0.0935224i
$583$	−10.3011	−	12.5616i	−0.426628	−	0.520249i
$584$			36.6333i			1.51590i
$585$	4.56105	−	0.455155i	0.188576	−	0.0188183i
$586$	27.3594			1.13021
$587$			7.04496i			0.290777i	0.989375	+	0.145388i	$0.0464432\pi$
$587$			7.04496i			0.290777i	−0.989375	+	0.145388i	$0.953557\pi$
$588$	0.00995933		0.000495699i	0.000410716		2.04423e-5i
$589$			2.84823i			0.117359i
$590$	−2.85062			−0.117358
$591$	−5.97432	+	0.297355i	−0.245751	+	0.0122316i
$592$	−42.6989			−1.75491
$593$	35.0909			1.44101			0.720505	−	0.693449i	$-0.243910\pi$
$593$	35.0909			1.44101			0.720505	+	0.693449i	$0.243910\pi$
$594$	−16.3628	+	18.1099i	−0.671372	+	0.743060i
$595$	0.570654			0.0233945
$596$	0.0797572			0.00326698
$597$	0.107017	−	0.00532649i	0.00437992	−	0.000217999i
$598$	−14.9940			−0.613151
$599$		−	13.2593i		−	0.541762i	−0.962613	−	0.270881i	$-0.912685\pi$
$599$		−	13.2593i		−	0.541762i	0.962613	−	0.270881i	$-0.0873150\pi$
$600$	4.88586	−	0.243180i	0.199464	−	0.00992779i
$601$		−	19.9239i		−	0.812712i	−0.913715	−	0.406356i	$-0.866799\pi$
$601$		−	19.9239i		−	0.812712i	0.913715	−	0.406356i	$-0.133201\pi$
$602$	−6.10915			−0.248990
$603$	6.08071	−	0.606806i	0.247626	−	0.0247110i
$604$			0.100973i			0.00410851i
$605$	−10.7870	−	2.15417i	−0.438554	−	0.0875796i
$606$	45.5202	−	2.26564i	1.84913	−	0.0920355i
$607$		−	13.5445i		−	0.549752i	−0.961480	−	0.274876i	$-0.911363\pi$
$607$		−	13.5445i		−	0.549752i	0.961480	−	0.274876i	$-0.0886369\pi$
$608$			0.0467741i			0.00189694i
$609$	−0.686929	−	13.8014i	−0.0278358	−	0.559263i
$610$	−18.7074			−0.757440
$611$	17.4781			0.707090
$612$	−0.00980730		0.000978688i	−0.000396437		3.95611e-5i
$613$			18.1405i			0.732687i	0.930480	+	0.366343i	$0.119390\pi$
$613$			18.1405i			0.732687i	−0.930480	+	0.366343i	$0.880610\pi$
$614$		−	17.5900i		−	0.709875i
$615$	−0.491408	−	9.87313i	−0.0198155	−	0.398123i
$616$	5.93979	+	7.24326i	0.239321	+	0.291839i
$617$		−	8.61655i		−	0.346889i	−0.984844	−	0.173445i	$-0.944510\pi$
$617$		−	8.61655i		−	0.346889i	0.984844	−	0.173445i	$-0.0554898\pi$
$618$	−23.6379	+	1.17651i	−0.950857	+	0.0473264i
$619$	15.6496			0.629012			0.314506	−	0.949256i	$-0.398161\pi$
$619$	15.6496			0.629012			0.314506	+	0.949256i	$0.398161\pi$
$620$		−	0.0114172i		−	0.000458524i
$621$	5.35186	+	35.6053i	0.214763	+	1.42879i
$622$		−	34.3965i		−	1.37917i
$623$	17.4890			0.700683
$624$	0.527729	+	10.6029i	0.0211261	+	0.424454i
$625$	1.00000			0.0400000
$626$	18.6992			0.747370
$627$	5.54233	+	6.11177i	0.221339	+	0.244081i
$628$	0.0380897			0.00151994
$629$	−6.07414			−0.242192
$630$	4.22774	−	0.421894i	0.168437	−	0.0168087i
$631$	30.5201			1.21498			0.607492	−	0.794326i	$-0.292176\pi$
$631$	30.5201			1.21498			0.607492	+	0.794326i	$0.292176\pi$
$632$		−	14.9907i		−	0.596296i
$633$	0.168599	+	3.38740i	0.00670120	+	0.134637i
$634$			28.3907i			1.12754i
$635$	−19.5258			−0.774856
$636$	−0.00242799	−	0.0487820i	−9.62761e−5	−	0.00193433i
$637$		−	1.52790i		−	0.0605376i
$638$	−28.9772	+	23.7626i	−1.14722	+	0.940771i
$639$	1.49716	+	15.0028i	0.0592267	+	0.593502i
$640$			11.3623i			0.449135i
$641$			47.4142i			1.87275i	0.351004	+	0.936374i	$0.385840\pi$
$641$			47.4142i			1.87275i	−0.351004	+	0.936374i	$0.614160\pi$
$642$	27.6713	−	1.37726i	1.09210	−	0.0543563i
$643$	−7.93634			−0.312979			−0.156489	−	0.987680i	$-0.550018\pi$
$643$	−7.93634			−0.312979			−0.156489	+	0.987680i	$0.550018\pi$
$644$	−0.0398925			−0.00157198
$645$	−7.46217	+	0.371409i	−0.293823	+	0.0146242i
$646$			1.16075i			0.0456689i
$647$			19.5310i			0.767844i	0.923366	+	0.383922i	$0.125427\pi$
$647$			19.5310i			0.767844i	−0.923366	+	0.383922i	$0.874573\pi$
$648$	24.9178	−	5.02321i	0.978864	−	0.197330i
$649$	−4.23306	−	5.16198i	−0.166162	−	0.202626i
$650$			2.16388i			0.0848746i
$651$	0.170751	+	3.43063i	0.00669224	+	0.134457i
$652$	0.102782			0.00402526
$653$		−	4.81427i		−	0.188397i	−0.995553	−	0.0941984i	$-0.969971\pi$
$653$		−	4.81427i		−	0.188397i	0.995553	−	0.0941984i	$-0.0300288\pi$
$654$	−0.933929	−	18.7640i	−0.0365195	−	0.733732i
$655$			7.12623i			0.278445i
$656$	22.8948			0.893891
$657$	3.86388	+	38.7194i	0.150744	+	1.51059i
$658$	16.2009			0.631577
$659$	21.2047			0.826018			0.413009	−	0.910727i	$-0.364478\pi$
$659$	21.2047			0.826018			0.413009	+	0.910727i	$0.364478\pi$
$660$	−0.0222165	−	0.0244990i	−0.000864774	−	0.000953624i
$661$	−16.7490			−0.651461			−0.325731	−	0.945463i	$-0.605610\pi$
$661$	−16.7490			−0.651461			−0.325731	+	0.945463i	$0.605610\pi$
$662$	−17.2506			−0.670464
$663$	0.0750722	+	1.50831i	0.00291556	+	0.0585780i
$664$	4.57009			0.177354
$665$		−	1.43623i		−	0.0556947i
$666$	−45.0008	+	4.49071i	−1.74375	+	0.174011i
$667$			55.2822i			2.14053i
$668$	0.0931094			0.00360251
$669$	34.7801	−	1.73109i	1.34468	−	0.0669277i
$670$			2.88486i			0.111452i
$671$	−27.7797	−	33.8759i	−1.07242	−	1.30776i
$672$	0.00280409	+	0.0563383i	0.000108170	+	0.00217330i
$673$		−	22.0001i		−	0.848043i	−0.905652	−	0.424022i	$-0.860618\pi$
$673$		−	22.0001i		−	0.848043i	0.905652	−	0.424022i	$-0.139382\pi$
$674$			30.2717i			1.16602i
$675$	5.13843	−	0.772361i	0.197778	−	0.0297282i
$676$	0.0614029			0.00236165
$677$	−32.2539			−1.23962			−0.619809	−	0.784752i	$-0.712790\pi$
$677$	−32.2539			−1.23962			−0.619809	+	0.784752i	$0.712790\pi$
$678$	0.683301	+	13.7285i	0.0262420	+	0.527241i
$679$		−	18.5024i		−	0.710055i
$680$			1.61172i			0.0618068i
$681$	6.83319	−	0.340104i	0.261848	−	0.0130328i
$682$	7.20289	−	5.90669i	0.275813	−	0.226179i
$683$		−	7.31299i		−	0.279824i	−0.990164	−	0.139912i	$-0.955318\pi$
$683$		−	7.31299i		−	0.279824i	0.990164	−	0.139912i	$-0.0446819\pi$
$684$	0.00246318	+	0.0246832i	9.41820e−5	+	0.000943785i
$685$	−4.30662			−0.164548
$686$		−	1.41625i		−	0.0540726i
$687$	−40.8927	+	2.03533i	−1.56016	+	0.0776525i
$688$		−	17.3040i		−	0.659709i
$689$	−7.48383			−0.285111
$690$	−16.9764	+	0.844956i	−0.646282	+	0.0321669i
$691$	−9.04002			−0.343898			−0.171949	−	0.985106i	$-0.555007\pi$
$691$	−9.04002			−0.343898			−0.171949	+	0.985106i	$0.555007\pi$
$692$	−0.0220827			−0.000839459
$693$	7.04201	+	7.02923i	0.267504	+	0.267018i
$694$	4.69742			0.178312
$695$	17.3494			0.658100
$696$	38.9800	−	1.94012i	1.47753	−	0.0735402i
$697$	3.25690			0.123364
$698$			4.58400i			0.173507i
$699$	−21.3562	+	1.06295i	−0.807764	+	0.0402043i
$700$			0.00575714i			0.000217599i
$701$	−6.27197			−0.236889			−0.118445	−	0.992961i	$-0.537791\pi$
$701$	−6.27197			−0.236889			−0.118445	+	0.992961i	$0.537791\pi$
$702$	1.67130	+	11.1190i	0.0630792	+	0.419659i
$703$			15.2875i			0.576579i
$704$	−20.4573	+	16.7759i	−0.771012	+	0.632264i
$705$	19.7890	−	0.984943i	0.745296	−	0.0370951i
$706$		−	14.1121i		−	0.531117i
$707$		−	18.5798i		−	0.698766i
$708$	−0.000997741	−	0.0200461i	−3.74974e−5	−	0.000753379i
$709$	−1.84721			−0.0693735			−0.0346868	−	0.999398i	$-0.511043\pi$
$709$	−1.84721			−0.0693735			−0.0346868	+	0.999398i	$0.511043\pi$
$710$	−7.11775			−0.267124
$711$	−1.58113	−	15.8443i	−0.0592970	−	0.594208i
$712$			49.3950i			1.85116i
$713$		−	13.7415i		−	0.514624i
$714$	0.0695862	+	1.39809i	0.00260420	+	0.0523223i
$715$	−3.91843	+	3.21328i	−0.146541	+	0.120170i
$716$			0.0915539i			0.00342153i
$717$	−4.18249	+	0.208172i	−0.156198	+	0.00777433i
$718$	8.21724			0.306665
$719$			19.9343i			0.743422i	0.928348	+	0.371711i	$0.121229\pi$
$719$			19.9343i			0.743422i	−0.928348	+	0.371711i	$0.878771\pi$
$720$	1.19500	+	11.9750i	0.0445351	+	0.446281i
$721$			9.64822i			0.359318i
$722$	−23.9873			−0.892716
$723$	−0.411386	−	8.26535i	−0.0152996	−	0.307392i
$724$	−0.0435153			−0.00161723
$725$	7.97813			0.296300
$726$	3.96230	−	26.6906i	0.147055	−	0.990582i
$727$	−10.2608			−0.380554			−0.190277	−	0.981730i	$-0.560939\pi$
$727$	−10.2608			−0.380554			−0.190277	+	0.981730i	$0.560939\pi$
$728$	4.31531			0.159936
$729$	25.8069	−	7.93744i	0.955812	−	0.293979i
$730$	−18.3695			−0.679887
$731$		−	2.46159i		−	0.0910450i
$732$	−0.00654774	−	0.131554i	−0.000242012	−	0.00486237i
$733$		−	40.5424i		−	1.49747i	−0.662872	−	0.748733i	$-0.730662\pi$
$733$		−	40.5424i		−	1.49747i	0.662872	−	0.748733i	$-0.269338\pi$
$734$	27.5168			1.01566
$735$	−0.0861016	−	1.72991i	−0.00317590	−	0.0638087i
$736$		−	0.225665i		−	0.00831813i
$737$	−5.22398	+	4.28390i	−0.192428	+	0.157799i
$738$	24.1291	−	2.40788i	0.888203	−	0.0886353i
$739$			44.0063i			1.61880i	0.587258	+	0.809400i	$0.300207\pi$
$739$			44.0063i			1.61880i	−0.587258	+	0.809400i	$0.699793\pi$
$740$		−	0.0612799i		−	0.00225270i
$741$	3.79615	−	0.188943i	0.139455	−	0.00694099i
$742$	−6.93695			−0.254663
$743$	−3.50869			−0.128721			−0.0643606	−	0.997927i	$-0.520501\pi$
$743$	−3.50869			−0.128721			−0.0643606	+	0.997927i	$0.520501\pi$
$744$	−9.68928	+	0.482258i	−0.355226	+	0.0176804i
$745$		−	13.8536i		−	0.507557i
$746$		−	51.1035i		−	1.87103i
$747$	4.83033	−	0.482027i	0.176732	−	0.0176365i
$748$	0.00842552	−	0.00690930i	0.000308068	−	0.000252629i
$749$		−	11.2945i		−	0.412692i
$750$	0.121941	+	2.44998i	0.00445266	+	0.0894606i
$751$	−33.8836			−1.23643			−0.618215	−	0.786009i	$-0.712144\pi$
$751$	−33.8836			−1.23643			−0.618215	+	0.786009i	$0.712144\pi$
$752$			45.8886i			1.67339i
$753$	−0.833083	−	16.7379i	−0.0303592	−	0.609962i
$754$			17.2638i			0.628709i
$755$	17.5387			0.638297
$756$	0.00444659	+	0.0295827i	0.000161721	+	0.00107591i
$757$	−20.9468			−0.761326			−0.380663	−	0.924714i	$-0.624304\pi$
$757$	−20.9468			−0.761326			−0.380663	+	0.924714i	$0.624304\pi$
$758$	−34.1155			−1.23913
$759$	−26.7394	−	29.4867i	−0.970580	−	1.07030i
$760$	4.05641			0.147141
$761$	−1.50451			−0.0545384			−0.0272692	−	0.999628i	$-0.508681\pi$
$761$	−1.50451			−0.0545384			−0.0272692	+	0.999628i	$0.508681\pi$
$762$	−2.38099	−	47.8377i	−0.0862543	−	1.73298i
$763$	−7.65885			−0.277269
$764$		−	0.0575490i		−	0.00208205i
$765$	0.169996	+	1.70350i	0.00614620	+	0.0615902i
$766$		−	36.3631i		−	1.31385i
$767$	−3.07535			−0.111044
$768$	−0.239022	+	0.0118967i	−0.00862496	+	0.000429284i
$769$			10.1743i			0.366893i	0.983030	+	0.183447i	$0.0587254\pi$
$769$			10.1743i			0.366893i	−0.983030	+	0.183447i	$0.941275\pi$
$770$	−3.63208	+	2.97847i	−0.130891	+	0.107337i
$771$	−1.59532	−	32.0523i	−0.0574539	−	1.15434i
$772$			0.104011i			0.00374343i
$773$			22.7521i			0.818335i	0.912459	+	0.409168i	$0.134181\pi$
$773$			22.7521i			0.818335i	−0.912459	+	0.409168i	$0.865819\pi$
$774$	−1.81989	−	18.2369i	−0.0654146	−	0.655511i
$775$	−1.98313			−0.0712361
$776$	52.2570			1.87592
$777$	0.916479	+	18.4134i	0.0328785	+	0.660578i
$778$			37.7841i			1.35463i
$779$		−	8.19703i		−	0.293689i
$780$	−0.0152169		0.000757378i	−0.000544851		2.71185e-5i
$781$	−10.5696	−	12.8890i	−0.378209	−	0.461206i
$782$		−	5.60011i		−	0.200259i
$783$	40.9950	−	6.16199i	1.46504	−	0.220212i
$784$	4.01148			0.143267
$785$		−	6.61607i		−	0.236138i
$786$	−17.4591	+	0.868980i	−0.622746	+	0.0309955i
$787$		−	20.8231i		−	0.742265i	−0.928580	−	0.371132i	$-0.878970\pi$
$787$		−	20.8231i		−	0.742265i	0.928580	−	0.371132i	$-0.121030\pi$
$788$	0.0198825			0.000708286
$789$	−5.87511	+	0.292418i	−0.209159	+	0.0104103i
$790$	7.51697			0.267442
$791$	5.60353			0.199239
$792$	−19.8529	+	19.8891i	−0.705444	+	0.706727i
$793$	−20.1822			−0.716691
$794$	−15.6110			−0.554013
$795$	−8.47330	+	0.421736i	−0.300517	+	0.0149574i
$796$	−0.000356153	0		−1.26235e−5	0
$797$			15.8113i			0.560066i	0.959990	+	0.280033i	$0.0903455\pi$
$797$			15.8113i			0.560066i	−0.959990	+	0.280033i	$0.909655\pi$
$798$	3.51874	−	0.175136i	0.124562	−	0.00619974i
$799$			6.52790i			0.230940i
$800$	−0.0325672			−0.00115142
$801$	5.20991	+	52.2078i	0.184083	+	1.84467i
$802$		−	7.47764i		−	0.264045i
$803$	−27.2780	−	33.2641i	−0.962621	−	1.17386i
$804$	−0.0202869	+	0.00100972i	−0.000715463	+	3.56103e-5i
$805$			6.92922i			0.244223i
$806$		−	4.29126i		−	0.151153i
$807$	1.26380	+	25.3916i	0.0444878	+	0.893826i
$808$	52.4758			1.84609
$809$	−46.6341			−1.63957			−0.819783	−	0.572674i	$-0.805906\pi$
$809$	−46.6341			−1.63957			−0.819783	+	0.572674i	$0.805906\pi$
$810$	2.51885	+	12.4949i	0.0885035	+	0.439025i
$811$			5.69942i			0.200134i	0.994981	+	0.100067i	$0.0319057\pi$
$811$			5.69942i			0.200134i	−0.994981	+	0.100067i	$0.968094\pi$
$812$			0.0459312i			0.00161187i
$813$	1.69149	+	33.9846i	0.0593232	+	1.19189i
$814$	38.6605	−	31.7033i	1.35505	−	1.11120i
$815$		−	17.8530i		−	0.625363i
$816$	−3.96006	+	0.197101i	−0.138630	+	0.00689992i
$817$	−6.19536			−0.216748
$818$		−	20.8739i		−	0.729840i
$819$	4.56105	−	0.455155i	0.159376	−	0.0159044i
$820$			0.0328578i			0.00114744i
$821$	−20.3894			−0.711594			−0.355797	−	0.934563i	$-0.615791\pi$
$821$	−20.3894			−0.711594			−0.355797	+	0.934563i	$0.615791\pi$
$822$	−0.525154	−	10.5511i	−0.0183169	−	0.368013i
$823$	−9.77616			−0.340775			−0.170388	−	0.985377i	$-0.554502\pi$
$823$	−9.77616			−0.340775			−0.170388	+	0.985377i	$0.554502\pi$
$824$	−27.2499			−0.949294
$825$	−4.25542	+	3.85894i	−0.148155	+	0.134351i
$826$	−2.85062			−0.0991857
$827$	−17.4819			−0.607907			−0.303953	−	0.952687i	$-0.598307\pi$
$827$	−17.4819			−0.607907			−0.303953	+	0.952687i	$0.598307\pi$
$828$	−0.0118838	−	0.119086i	−0.000412991	−	0.00413852i
$829$	41.0994			1.42744			0.713720	−	0.700431i	$-0.247009\pi$
$829$	41.0994			1.42744			0.713720	+	0.700431i	$0.247009\pi$
$830$			2.29164i			0.0795440i
$831$	−1.60819	−	32.3109i	−0.0557875	−	1.12085i
$832$			12.1878i			0.422536i
$833$	0.570654			0.0197720
$834$	2.11561	+	42.5057i	0.0732574	+	1.47185i
$835$		−	16.1729i		−	0.559685i
$836$	−0.0173895	−	0.0212055i	−0.000601427	−	0.000733407i
$837$	−10.1902	+	1.53169i	−0.352224	+	0.0529430i
$838$		−	25.3846i		−	0.876896i
$839$		−	35.9089i		−	1.23971i	−0.784716	−	0.619856i	$-0.787191\pi$
$839$		−	35.9089i		−	1.23971i	0.784716	−	0.619856i	$-0.212809\pi$
$840$	4.88586	−	0.243180i	0.168578	−	0.00839051i
$841$	34.6505			1.19485
$842$	−22.1497			−0.763327
$843$	34.3952	−	1.71193i	1.18463	−	0.0589619i
$844$		−	0.0112733i		−	0.000388043i
$845$		−	10.6655i		−	0.366905i
$846$	4.82618	+	48.3625i	0.165928	+	1.66274i
$847$	−10.7870	−	2.15417i	−0.370646	−	0.0740183i
$848$		−	19.6487i		−	0.674739i
$849$	0.313008	+	6.28879i	0.0107424	+	0.215831i
$850$	−0.808188			−0.0277206
$851$		−	73.7557i		−	2.52831i
$852$	−0.00249127	−	0.0500534i	−8.53496e−5	−	0.00171480i
$853$		−	12.1754i		−	0.416877i	−0.978036	−	0.208438i	$-0.933162\pi$
$853$		−	12.1754i		−	0.416877i	0.978036	−	0.208438i	$-0.0668381\pi$
$854$	−18.7074			−0.640153
$855$	4.28740	−	0.427848i	0.146626	−	0.0146321i
$856$	31.8995			1.09030
$857$	17.3264			0.591858			0.295929	−	0.955210i	$-0.404371\pi$
$857$	17.3264			0.591858			0.295929	+	0.955210i	$0.404371\pi$
$858$	−8.35030	−	9.20824i	−0.285075	−	0.314364i
$859$	−27.2584			−0.930044			−0.465022	−	0.885299i	$-0.653954\pi$
$859$	−27.2584			−0.930044			−0.465022	+	0.885299i	$0.653954\pi$
$860$	0.0248341			0.000846836
$861$	−0.491408	−	9.87313i	−0.0167472	−	0.336475i
$862$	−33.8750			−1.15379
$863$		−	45.5212i		−	1.54956i	−0.632232	−	0.774779i	$-0.717861\pi$
$863$		−	45.5212i		−	1.54956i	0.632232	−	0.774779i	$-0.282139\pi$
$864$	−0.167344	+	0.0251536i	−0.00569317	+	0.000855744i
$865$			3.83571i			0.130418i
$866$	20.5456			0.698169
$867$	28.8451	−	1.43569i	0.979632	−	0.0487585i
$868$		−	0.0114172i		−	0.000387523i
$869$	11.1624	+	13.6119i	0.378659	+	0.461754i
$870$	0.972862	+	19.5463i	0.0329831	+	0.662680i
$871$			3.11229i			0.105456i
$872$		−	21.6312i		−	0.732525i
$873$	55.2327	−	5.51177i	1.86934	−	0.186545i
$874$	−14.0944			−0.476752
$875$	1.00000			0.0338062
$876$	−0.00642949	−	0.129178i	−0.000217232	−	0.00436452i
$877$			20.6521i			0.697373i	0.937239	+	0.348686i	$0.113372\pi$
$877$			20.6521i			0.697373i	−0.937239	+	0.348686i	$0.886628\pi$
$878$		−	21.4148i		−	0.722714i
$879$	33.4188	−	1.66333i	1.12719	−	0.0561028i
$880$	−8.43643	−	10.2878i	−0.284392	−	0.346801i
$881$		−	44.0780i		−	1.48502i	−0.669833	−	0.742512i	$-0.733634\pi$
$881$		−	44.0780i		−	1.48502i	0.669833	−	0.742512i	$-0.266366\pi$
$882$	4.22774	−	0.421894i	0.142356	−	0.0142059i
$883$	−20.8858			−0.702862			−0.351431	−	0.936214i	$-0.614305\pi$
$883$	−20.8858			−0.702862			−0.351431	+	0.936214i	$0.614305\pi$
$884$		−	0.00501967i		−	0.000168830i
$885$	−3.48195	+	0.173305i	−0.117045	+	0.00582558i
$886$			37.8724i			1.27235i
$887$	−47.6794			−1.60092			−0.800459	−	0.599387i	$-0.795411\pi$
$887$	−47.6794			−1.60092			−0.800459	+	0.599387i	$0.795411\pi$
$888$	−52.0058	+	2.58845i	−1.74520	+	0.0868627i
$889$	−19.5258			−0.654873
$890$	−24.7688			−0.830252
$891$	−18.8857	+	23.1156i	−0.632694	+	0.774402i
$892$	−0.115748			−0.00387554
$893$	16.4295			0.549793
$894$	33.9411	−	1.68933i	1.13516	−	0.0564995i
$895$	15.9027			0.531568
$896$			11.3623i			0.379588i
$897$	−18.3148	+	0.911570i	−0.611514	+	0.0304364i
$898$		−	28.8599i		−	0.963068i
$899$	−15.8217			−0.527682
$900$	−0.0171861	+	0.00171503i	−0.000572869	+	5.71676e-5i
$901$		−	2.79513i		−	0.0931193i
$902$	−20.7294	+	16.9991i	−0.690215	+	0.566007i
$903$	−7.46217	+	0.371409i	−0.248325	+	0.0123597i
$904$			15.8263i			0.526375i
$905$			7.55849i			0.251253i
$906$	2.13868	+	42.9694i	0.0710530	+	1.42756i
$907$	6.43940			0.213817			0.106908	−	0.994269i	$-0.465905\pi$
$907$	6.43940			0.213817			0.106908	+	0.994269i	$0.465905\pi$
$908$	−0.0227409			−0.000754682
$909$	55.4640	−	5.53485i	1.83962	−	0.183579i
$910$			2.16388i			0.0717321i
$911$			4.42562i			0.146627i	0.997309	+	0.0733136i	$0.0233574\pi$
$911$			4.42562i			0.146627i	−0.997309	+	0.0733136i	$0.976643\pi$
$912$	0.496067	+	9.96673i	0.0164264	+	0.330032i
$913$	−4.14977	+	3.40300i	−0.137337	+	0.112623i
$914$		−	15.2016i		−	0.502824i
$915$	−22.8506	+	1.13733i	−0.755417	+	0.0375988i
$916$	0.136091			0.00449658
$917$			7.12623i			0.235329i
$918$	−4.15282	+	0.624213i	−0.137063	+	0.0206021i
$919$		−	8.36709i		−	0.276005i	−0.990432	−	0.138002i	$-0.955932\pi$
$919$		−	8.36709i		−	0.276005i	0.990432	−	0.138002i	$-0.0440681\pi$
$920$	−19.5705			−0.645219
$921$	−1.06940	−	21.4857i	−0.0352378	−	0.707980i
$922$	−5.13646			−0.169160
$923$	−7.67889			−0.252754
$924$	−0.0222165	−	0.0244990i	−0.000730868	−	0.000805959i
$925$	−10.6442			−0.349978
$926$	−18.1737			−0.597224
$927$	−28.8016	+	2.87416i	−0.945969	+	0.0943999i
$928$	−0.259825			−0.00852919
$929$			42.1931i			1.38431i	0.721749	+	0.692155i	$0.243339\pi$
$929$			42.1931i			1.38431i	−0.721749	+	0.692155i	$0.756661\pi$
$930$	−0.241825	−	4.85863i	−0.00792975	−	0.159321i
$931$		−	1.43623i		−	0.0470706i
$932$	0.0710733			0.00232808
$933$	−2.09115	−	42.0144i	−0.0684613	−	1.37549i
$934$		−	15.2147i		−	0.497842i
$935$	−1.20013	−	1.46349i	−0.0392484	−	0.0478613i
$936$	1.28551	+	12.8820i	0.0420183	+	0.421060i
$937$		−	6.58822i		−	0.215228i	−0.994193	−	0.107614i	$-0.965679\pi$
$937$		−	6.58822i		−	0.215228i	0.994193	−	0.107614i	$-0.0343210\pi$
$938$			2.88486i			0.0941939i
$939$	22.8406	−	1.13683i	0.745374	−	0.0370990i
$940$	−0.0658578			−0.00214804
$941$	−49.0375			−1.59858			−0.799289	−	0.600947i	$-0.794790\pi$
$941$	−49.0375			−1.59858			−0.799289	+	0.600947i	$0.794790\pi$
$942$	16.2092	−	0.806771i	0.528126	−	0.0262860i
$943$			39.5472i			1.28783i
$944$		−	8.07429i		−	0.262796i
$945$	5.13843	−	0.772361i	0.167153	−	0.0251249i
$946$	12.8480	+	15.6674i	0.417724	+	0.509392i
$947$			33.6165i			1.09239i	0.837658	+	0.546195i	$0.183924\pi$
$947$			33.6165i			1.09239i	−0.837658	+	0.546195i	$0.816076\pi$
$948$	0.00263100	+	0.0528608i	8.54510e−5	+	0.00171684i
$949$	−19.8177			−0.643310
$950$			2.03406i			0.0659936i
$951$	1.72603	+	34.6785i	0.0559703	+	1.12453i
$952$			1.61172i			0.0522362i
$953$	34.4580			1.11620			0.558102	−	0.829772i	$-0.311530\pi$
$953$	34.4580			1.11620			0.558102	+	0.829772i	$0.311530\pi$
$954$	−2.06649	−	20.7080i	−0.0669050	−	0.670446i
$955$	−9.99611			−0.323466
$956$	0.0139193			0.000450184
$957$	−33.9503	+	30.7871i	−1.09746	+	0.995206i
$958$	32.6118			1.05364
$959$	−4.30662			−0.139068
$960$	0.686818	+	13.7992i	0.0221670	+	0.445368i
$961$	−27.0672			−0.873135
$962$		−	23.0327i		−	0.742605i
$963$	33.7160	−	3.36458i	1.08648	−	0.108422i
$964$			0.0275071i			0.000885944i
$965$	18.0664			0.581578
$966$	−16.9764	+	0.844956i	−0.546208	+	0.0271860i
$967$		−	55.3583i		−	1.78020i	−0.455764	−	0.890101i	$-0.650634\pi$
$967$		−	55.3583i		−	1.78020i	0.455764	−	0.890101i	$-0.349366\pi$
$968$	6.08412	−	30.4662i	0.195551	−	0.979221i
$969$	0.0705682	+	1.41782i	0.00226698	+	0.0455470i
$970$			26.2039i			0.841357i
$971$			53.9812i			1.73234i	0.499750	+	0.866170i	$0.333425\pi$
$971$			53.9812i			1.73234i	−0.499750	+	0.866170i	$0.666575\pi$
$972$	−0.0869848	+	0.0220864i	−0.00279004	+	0.000708421i
$973$	17.3494			0.556196
$974$	44.1362			1.41422
$975$	0.131555	+	2.64313i	0.00421312	+	0.0846479i
$976$		−	52.9881i		−	1.69611i
$977$			14.8539i			0.475218i	0.971361	+	0.237609i	$0.0763637\pi$
$977$			14.8539i			0.475218i	−0.971361	+	0.237609i	$0.923636\pi$
$978$	43.7395	−	2.17701i	1.39863	−	0.0696132i
$979$	−36.7807	−	44.8521i	−1.17552	−	1.43348i
$980$			0.00575714i			0.000183905i
$981$	−2.28154	−	22.8630i	−0.0728439	−	0.729959i
$982$	−3.74439			−0.119488
$983$			19.6042i			0.625278i	0.949872	+	0.312639i	$0.101213\pi$
$983$			19.6042i			0.625278i	−0.949872	+	0.312639i	$0.898787\pi$
$984$	27.8851	−	1.38791i	0.888944	−	0.0442448i
$985$		−	3.45354i		−	0.110039i
$986$	−6.44783			−0.205341
$987$	19.7890	−	0.984943i	0.629890	−	0.0313511i
$988$	−0.0126336			−0.000401928
$989$	29.8900			0.950447
$990$	−9.97323	−	9.95513i	−0.316970	−	0.316395i
$991$	−0.999386			−0.0317466			−0.0158733	−	0.999874i	$-0.505053\pi$
$991$	−0.999386			−0.0317466			−0.0158733	+	0.999874i	$0.505053\pi$
$992$	0.0645850			0.00205058
$993$	−21.0712	+	1.04876i	−0.668674	+	0.0332814i
$994$	−7.11775			−0.225761
$995$			0.0618628i			0.00196118i
$996$	−0.0161153		0.000802094i	−0.000510632		2.54153e-5i
$997$			5.41262i			0.171419i	0.996320	+	0.0857096i	$0.0273157\pi$
$997$			5.41262i			0.171419i	−0.996320	+	0.0857096i	$0.972684\pi$
$998$	35.2665			1.11634
$999$	−54.6943	+	8.22113i	−1.73045	+	0.260105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.f.1121.9	yes	40
3.2	odd	2		1155.2.l.e.1121.32	yes	40
11.10	odd	2		1155.2.l.e.1121.31	✓	40
33.32	even	2	inner	1155.2.l.f.1121.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.31	✓	40	11.10	odd	2
1155.2.l.e.1121.32	yes	40	3.2	odd	2
1155.2.l.f.1121.9	yes	40	1.1	even	1	trivial
1155.2.l.f.1121.10	yes	40	33.32	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41625 q^{2} +(-1.72991 + 0.0861016i) q^{3} +0.00575714 q^{4} -1.00000i q^{5} +(2.44998 - 0.121941i) q^{6} -1.00000i q^{7} +2.82434 q^{8} +(2.98517 - 0.297896i) q^{9} +O(q^{10})\)	\(q-1.41625 q^{2} +(-1.72991 + 0.0861016i) q^{3} +0.00575714 q^{4} -1.00000i q^{5} +(2.44998 - 0.121941i) q^{6} -1.00000i q^{7} +2.82434 q^{8} +(2.98517 - 0.297896i) q^{9} +1.41625i q^{10} +(-2.56458 + 2.10307i) q^{11} +(-0.00995933 + 0.000495699i) q^{12} +1.52790i q^{13} +1.41625i q^{14} +(0.0861016 + 1.72991i) q^{15} -4.01148 q^{16} -0.570654 q^{17} +(-4.22774 + 0.421894i) q^{18} +1.43623i q^{19} -0.00575714i q^{20} +(0.0861016 + 1.72991i) q^{21} +(3.63208 - 2.97847i) q^{22} -6.92922i q^{23} +(-4.88586 + 0.243180i) q^{24} -1.00000 q^{25} -2.16388i q^{26} +(-5.13843 + 0.772361i) q^{27} -0.00575714i q^{28} -7.97813 q^{29} +(-0.121941 - 2.44998i) q^{30} +1.98313 q^{31} +0.0325672 q^{32} +(4.25542 - 3.85894i) q^{33} +0.808188 q^{34} -1.00000 q^{35} +(0.0171861 - 0.00171503i) q^{36} +10.6442 q^{37} -2.03406i q^{38} +(-0.131555 - 2.64313i) q^{39} -2.82434i q^{40} -5.70731 q^{41} +(-0.121941 - 2.44998i) q^{42} +4.31362i q^{43} +(-0.0147647 + 0.0121077i) q^{44} +(-0.297896 - 2.98517i) q^{45} +9.81349i q^{46} -11.4393i q^{47} +(6.93950 - 0.345395i) q^{48} -1.00000 q^{49} +1.41625 q^{50} +(0.987180 - 0.0491342i) q^{51} +0.00879634i q^{52} +4.89812i q^{53} +(7.27729 - 1.09385i) q^{54} +(2.10307 + 2.56458i) q^{55} -2.82434i q^{56} +(-0.123662 - 2.48455i) q^{57} +11.2990 q^{58} +2.01280i q^{59} +(0.000495699 + 0.00995933i) q^{60} +13.2091i q^{61} -2.80860 q^{62} +(-0.297896 - 2.98517i) q^{63} +7.97684 q^{64} +1.52790 q^{65} +(-6.02673 + 5.46521i) q^{66} +2.03697 q^{67} -0.00328534 q^{68} +(0.596616 + 11.9869i) q^{69} +1.41625 q^{70} +5.02578i q^{71} +(8.43115 - 0.841360i) q^{72} +12.9706i q^{73} -15.0748 q^{74} +(1.72991 - 0.0861016i) q^{75} +0.00826859i q^{76} +(2.10307 + 2.56458i) q^{77} +(0.186314 + 3.74332i) q^{78} -5.30766i q^{79} +4.01148i q^{80} +(8.82252 - 1.77854i) q^{81} +8.08297 q^{82} +1.61811 q^{83} +(0.000495699 + 0.00995933i) q^{84} +0.570654i q^{85} -6.10915i q^{86} +(13.8014 - 0.686929i) q^{87} +(-7.24326 + 5.93979i) q^{88} +17.4890i q^{89} +(0.421894 + 4.22774i) q^{90} +1.52790 q^{91} -0.0398925i q^{92} +(-3.43063 + 0.170751i) q^{93} +16.2009i q^{94} +1.43623 q^{95} +(-0.0563383 + 0.00280409i) q^{96} +18.5024 q^{97} +1.41625 q^{98} +(-7.02923 + 7.04201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more