LMFDB - Embedded newform 460.2.e.b.91.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(91,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("460.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.e (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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.17
Character	$\chi$	$=$	460.91
Dual form			460.2.e.b.91.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.341935 - 1.37225i) q^{2} +2.41873i q^{3} +(-1.76616 - 0.938444i) q^{4} -1.00000i q^{5} +(3.31911 + 0.827049i) q^{6} +2.44077 q^{7} +(-1.89170 + 2.10273i) q^{8} -2.85025 q^{9} +O(q^{10})$	\(q+(0.341935 - 1.37225i) q^{2} +2.41873i q^{3} +(-1.76616 - 0.938444i) q^{4} -1.00000i q^{5} +(3.31911 + 0.827049i) q^{6} +2.44077 q^{7} +(-1.89170 + 2.10273i) q^{8} -2.85025 q^{9} +(-1.37225 - 0.341935i) q^{10} +2.59002 q^{11} +(2.26984 - 4.27186i) q^{12} -0.482508 q^{13} +(0.834584 - 3.34935i) q^{14} +2.41873 q^{15} +(2.23865 + 3.31489i) q^{16} +1.74316i q^{17} +(-0.974601 + 3.91126i) q^{18} +7.09763 q^{19} +(-0.938444 + 1.76616i) q^{20} +5.90355i q^{21} +(0.885620 - 3.55417i) q^{22} +(1.73388 + 4.47143i) q^{23} +(-5.08594 - 4.57550i) q^{24} -1.00000 q^{25} +(-0.164986 + 0.662123i) q^{26} +0.362207i q^{27} +(-4.31078 - 2.29052i) q^{28} +1.03287 q^{29} +(0.827049 - 3.31911i) q^{30} -2.87696i q^{31} +(5.31434 - 1.93851i) q^{32} +6.26456i q^{33} +(2.39206 + 0.596048i) q^{34} -2.44077i q^{35} +(5.03400 + 2.67480i) q^{36} -6.76257i q^{37} +(2.42693 - 9.73974i) q^{38} -1.16706i q^{39} +(2.10273 + 1.89170i) q^{40} +0.907172 q^{41} +(8.10117 + 2.01863i) q^{42} -1.65967 q^{43} +(-4.57439 - 2.43059i) q^{44} +2.85025i q^{45} +(6.72881 - 0.850391i) q^{46} +4.40127i q^{47} +(-8.01781 + 5.41468i) q^{48} -1.04266 q^{49} +(-0.341935 + 1.37225i) q^{50} -4.21623 q^{51} +(0.852186 + 0.452807i) q^{52} -1.89738i q^{53} +(0.497040 + 0.123851i) q^{54} -2.59002i q^{55} +(-4.61719 + 5.13228i) q^{56} +17.1672i q^{57} +(0.353174 - 1.41736i) q^{58} +3.79671i q^{59} +(-4.27186 - 2.26984i) q^{60} -8.17854i q^{61} +(-3.94792 - 0.983733i) q^{62} -6.95679 q^{63} +(-0.842973 - 7.95546i) q^{64} +0.482508i q^{65} +(8.59656 + 2.14207i) q^{66} -15.6210 q^{67} +(1.63586 - 3.07870i) q^{68} +(-10.8152 + 4.19380i) q^{69} +(-3.34935 - 0.834584i) q^{70} -11.0655i q^{71} +(5.39180 - 5.99331i) q^{72} +5.06355 q^{73} +(-9.27996 - 2.31236i) q^{74} -2.41873i q^{75} +(-12.5355 - 6.66073i) q^{76} +6.32163 q^{77} +(-1.60150 - 0.399057i) q^{78} -9.79312 q^{79} +(3.31489 - 2.23865i) q^{80} -9.42683 q^{81} +(0.310194 - 1.24487i) q^{82} -13.5571 q^{83} +(5.54015 - 10.4266i) q^{84} +1.74316 q^{85} +(-0.567501 + 2.27749i) q^{86} +2.49823i q^{87} +(-4.89953 + 5.44612i) q^{88} +2.55180i q^{89} +(3.91126 + 0.974601i) q^{90} -1.17769 q^{91} +(1.13386 - 9.52441i) q^{92} +6.95858 q^{93} +(6.03965 + 1.50495i) q^{94} -7.09763i q^{95} +(4.68874 + 12.8539i) q^{96} +1.34364i q^{97} +(-0.356523 + 1.43080i) q^{98} -7.38220 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9	$ 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48} - 12 q^{49} - 4 q^{50} + 16 q^{52} + 42 q^{54} - 10 q^{58} - 36 q^{62} - 22 q^{64} - 44 q^{69} - 42 q^{70} - 32 q^{72} - 8 q^{73} - 72 q^{77} + 122 q^{78} - 32 q^{81} + 20 q^{82} - 44 q^{85} + 64 q^{92} + 40 q^{93} - 26 q^{94} + 16 q^{96} + 62 q^{98}+O(q^{100}) $ 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9 + 24 * q^12 - 4 * q^13 + 20 * q^16 - 56 * q^18 - 6 * q^24 - 32 * q^25 + 68 * q^26 + 8 * q^29 - 16 * q^32 + 8 * q^36 + 44 * q^41 - 4 * q^46 - 4 * q^48 - 12 * q^49 - 4 * q^50 + 16 * q^52 + 42 * q^54 - 10 * q^58 - 36 * q^62 - 22 * q^64 - 44 * q^69 - 42 * q^70 - 32 * q^72 - 8 * q^73 - 72 * q^77 + 122 * q^78 - 32 * q^81 + 20 * q^82 - 44 * q^85 + 64 * q^92 + 40 * q^93 - 26 * q^94 + 16 * q^96 + 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.341935	−	1.37225i	0.241785	−	0.970330i
$2$	0.341935	−	1.37225i	0.241785	−	0.970330i
$3$			2.41873i			1.39645i	0.715877	+	0.698227i	$0.246027\pi$
$3$			2.41873i			1.39645i	−0.715877	+	0.698227i	$0.753973\pi$
$4$	−1.76616	−	0.938444i	−0.883080	−	0.469222i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	3.31911	+	0.827049i	1.35502	+	0.337641i
$7$	2.44077			0.922523			0.461261	−	0.887264i	$-0.347397\pi$
$7$	2.44077			0.922523			0.461261	+	0.887264i	$0.347397\pi$
$8$	−1.89170	+	2.10273i	−0.668816	+	0.743428i
$9$	−2.85025			−0.950083
$10$	−1.37225	−	0.341935i	−0.433945	−	0.108129i
$11$	2.59002			0.780921			0.390460	−	0.920620i	$-0.372316\pi$
$11$	2.59002			0.780921			0.390460	+	0.920620i	$0.372316\pi$
$12$	2.26984	−	4.27186i	0.655247	−	1.23318i
$13$	−0.482508			−0.133824			−0.0669118	−	0.997759i	$-0.521315\pi$
$13$	−0.482508			−0.133824			−0.0669118	+	0.997759i	$0.521315\pi$
$14$	0.834584	−	3.34935i	0.223052	−	0.895151i
$15$	2.41873			0.624513
$16$	2.23865	+	3.31489i	0.559661	+	0.828721i
$17$			1.74316i			0.422779i	0.977402	+	0.211389i	$0.0677988\pi$
$17$			1.74316i			0.422779i	−0.977402	+	0.211389i	$0.932201\pi$
$18$	−0.974601	+	3.91126i	−0.229716	+	0.921894i
$19$	7.09763			1.62831			0.814154	−	0.580650i	$-0.197201\pi$
$19$	7.09763			1.62831			0.814154	+	0.580650i	$0.197201\pi$
$20$	−0.938444	+	1.76616i	−0.209842	+	0.394925i
$21$			5.90355i			1.28826i
$22$	0.885620	−	3.55417i	0.188815	−	0.757751i
$23$	1.73388	+	4.47143i	0.361540	+	0.932357i
$23$	1.73388	+	4.47143i	0.361540	+	0.932357i
$24$	−5.08594	−	4.57550i	−1.03816	−	0.933970i
$25$	−1.00000			−0.200000
$26$	−0.164986	+	0.662123i	−0.0323565	+	0.129853i
$27$			0.362207i			0.0697068i
$28$	−4.31078	−	2.29052i	−0.814662	−	0.432868i
$29$	1.03287			0.191799			0.0958994	−	0.995391i	$-0.469427\pi$
$29$	1.03287			0.191799			0.0958994	+	0.995391i	$0.469427\pi$
$30$	0.827049	−	3.31911i	0.150998	−	0.605984i
$31$		−	2.87696i		−	0.516717i	−0.966049	−	0.258358i	$-0.916818\pi$
$31$		−	2.87696i		−	0.516717i	0.966049	−	0.258358i	$-0.0831815\pi$
$32$	5.31434	−	1.93851i	0.939451	−	0.342684i
$33$			6.26456i			1.09052i
$34$	2.39206	+	0.596048i	0.410235	+	0.102221i
$35$		−	2.44077i		−	0.412565i
$36$	5.03400	+	2.67480i	0.839000	+	0.445800i
$37$		−	6.76257i		−	1.11176i	−0.831263	−	0.555880i	$-0.812382\pi$
$37$		−	6.76257i		−	1.11176i	0.831263	−	0.555880i	$-0.187618\pi$
$38$	2.42693	−	9.73974i	0.393700	−	1.58000i
$39$		−	1.16706i		−	0.186878i
$40$	2.10273	+	1.89170i	0.332471	+	0.299103i
$41$	0.907172			0.141677			0.0708383	−	0.997488i	$-0.477433\pi$
$41$	0.907172			0.141677			0.0708383	+	0.997488i	$0.477433\pi$
$42$	8.10117	+	2.01863i	1.25004	+	0.311482i
$43$	−1.65967			−0.253098			−0.126549	−	0.991960i	$-0.540390\pi$
$43$	−1.65967			−0.253098			−0.126549	+	0.991960i	$0.540390\pi$
$44$	−4.57439	−	2.43059i	−0.689616	−	0.366425i
$45$			2.85025i			0.424890i
$46$	6.72881	−	0.850391i	0.992108	−	0.125383i
$47$			4.40127i			0.641991i	0.947081	+	0.320995i	$0.104017\pi$
$47$			4.40127i			0.641991i	−0.947081	+	0.320995i	$0.895983\pi$
$48$	−8.01781	+	5.41468i	−1.15727	+	0.781541i
$49$	−1.04266			−0.148952
$50$	−0.341935	+	1.37225i	−0.0483570	+	0.194066i
$51$	−4.21623			−0.590391
$52$	0.852186	+	0.452807i	0.118177	+	0.0627930i
$53$		−	1.89738i		−	0.260625i	−0.991473	−	0.130312i	$-0.958402\pi$
$53$		−	1.89738i		−	0.260625i	0.991473	−	0.130312i	$-0.0415980\pi$
$54$	0.497040	+	0.123851i	0.0676385	+	0.0168540i
$55$		−	2.59002i		−	0.349238i
$56$	−4.61719	+	5.13228i	−0.616997	+	0.685830i
$57$			17.1672i			2.27386i
$58$	0.353174	−	1.41736i	0.0463740	−	0.186108i
$59$			3.79671i			0.494290i	0.968978	+	0.247145i	$0.0794924\pi$
$59$			3.79671i			0.494290i	−0.968978	+	0.247145i	$0.920508\pi$
$60$	−4.27186	−	2.26984i	−0.551495	−	0.293035i
$61$		−	8.17854i		−	1.04715i	−0.851978	−	0.523577i	$-0.824597\pi$
$61$		−	8.17854i		−	1.04715i	0.851978	−	0.523577i	$-0.175403\pi$
$62$	−3.94792	−	0.983733i	−0.501386	−	0.124934i
$63$	−6.95679			−0.876473
$64$	−0.842973	−	7.95546i	−0.105372	−	0.994433i
$65$			0.482508i			0.0598477i
$66$	8.59656	+	2.14207i	1.05816	+	0.263671i
$67$	−15.6210			−1.90840			−0.954202	−	0.299163i	$-0.903292\pi$
$67$	−15.6210			−1.90840			−0.954202	+	0.299163i	$0.903292\pi$
$68$	1.63586	−	3.07870i	0.198377	−	0.373348i
$69$	−10.8152	+	4.19380i	−1.30199	+	0.504874i
$70$	−3.34935	−	0.834584i	−0.400324	−	0.0997519i
$71$		−	11.0655i		−	1.31323i	−0.754225	−	0.656616i	$-0.771987\pi$
$71$		−	11.0655i		−	1.31323i	0.754225	−	0.656616i	$-0.228013\pi$
$72$	5.39180	−	5.99331i	0.635430	−	0.706319i
$73$	5.06355			0.592644			0.296322	−	0.955088i	$-0.404240\pi$
$73$	5.06355			0.592644			0.296322	+	0.955088i	$0.404240\pi$
$74$	−9.27996	−	2.31236i	−1.07877	−	0.268806i
$75$		−	2.41873i		−	0.279291i
$76$	−12.5355	−	6.66073i	−1.43793	−	0.764038i
$77$	6.32163			0.720417
$78$	−1.60150	−	0.399057i	−0.181334	−	0.0451844i
$79$	−9.79312			−1.10181			−0.550906	−	0.834567i	$-0.685718\pi$
$79$	−9.79312			−1.10181			−0.550906	+	0.834567i	$0.685718\pi$
$80$	3.31489	−	2.23865i	0.370615	−	0.250288i
$81$	−9.42683			−1.04743
$82$	0.310194	−	1.24487i	0.0342552	−	0.137473i
$83$	−13.5571			−1.48808			−0.744041	−	0.668134i	$-0.767093\pi$
$83$	−13.5571			−1.48808			−0.744041	+	0.668134i	$0.767093\pi$
$84$	5.54015	−	10.4266i	0.604480	−	1.13764i
$85$	1.74316			0.189072
$86$	−0.567501	+	2.27749i	−0.0611952	+	0.245588i
$87$			2.49823i			0.267838i
$88$	−4.89953	+	5.44612i	−0.522292	+	0.580559i
$89$			2.55180i			0.270490i	0.990812	+	0.135245i	$0.0431822\pi$
$89$			2.55180i			0.270490i	−0.990812	+	0.135245i	$0.956818\pi$
$90$	3.91126	+	0.974601i	0.412284	+	0.102732i
$91$	−1.17769			−0.123455
$92$	1.13386	−	9.52441i	0.118214	−	0.992988i
$93$	6.95858			0.721571
$94$	6.03965	+	1.50495i	0.622943	+	0.155224i
$95$		−	7.09763i		−	0.728201i
$96$	4.68874	+	12.8539i	0.478542	+	1.31190i
$97$			1.34364i			0.136426i	0.997671	+	0.0682131i	$0.0217298\pi$
$97$			1.34364i			0.136426i	−0.997671	+	0.0682131i	$0.978270\pi$
$98$	−0.356523	+	1.43080i	−0.0360143	+	0.144532i
$99$	−7.38220			−0.741939
$100$	1.76616	+	0.938444i	0.176616	+	0.0938444i
$101$	−17.6082			−1.75208			−0.876039	−	0.482240i	$-0.839823\pi$
$101$	−17.6082			−1.75208			−0.876039	+	0.482240i	$0.839823\pi$
$102$	−1.44168	+	5.78574i	−0.142748	+	0.572874i
$103$	14.8411			1.46233			0.731167	−	0.682199i	$-0.238976\pi$
$103$	14.8411			1.46233			0.731167	+	0.682199i	$0.238976\pi$
$104$	0.912758	−	1.01459i	0.0895033	−	0.0994883i
$105$	5.90355			0.576128
$106$	−2.60368	−	0.648780i	−0.252892	−	0.0630151i
$107$	13.8673			1.34060			0.670302	−	0.742088i	$-0.266164\pi$
$107$	13.8673			1.34060			0.670302	+	0.742088i	$0.266164\pi$
$108$	0.339911	−	0.639716i	0.0327079	−	0.0615567i
$109$		−	16.3923i		−	1.57010i	−0.619434	−	0.785049i	$-0.712638\pi$
$109$		−	16.3923i		−	1.57010i	0.619434	−	0.785049i	$-0.287362\pi$
$110$	−3.55417	−	0.885620i	−0.338876	−	0.0844405i
$111$	16.3568			1.55252
$112$	5.46401	+	8.09086i	0.516300	+	0.764514i
$113$			15.5128i			1.45932i	0.683811	+	0.729660i	$0.260321\pi$
$113$			15.5128i			1.45932i	−0.683811	+	0.729660i	$0.739679\pi$
$114$	23.5578	+	5.87008i	2.20639	+	0.549784i
$115$	4.47143	−	1.73388i	0.416963	−	0.161686i
$116$	−1.82421	−	0.969289i	−0.169374	−	0.0899962i
$117$	1.37527			0.127144
$118$	5.21006	+	1.29823i	0.479625	+	0.119512i
$119$			4.25465i			0.390023i
$120$	−4.57550	+	5.08594i	−0.417684	+	0.464281i
$121$	−4.29179			−0.390163
$122$	−11.2230	−	2.79653i	−1.01609	−	0.253186i
$123$			2.19420i			0.197845i
$124$	−2.69986	+	5.08117i	−0.242455	+	0.456302i
$125$			1.00000i			0.0894427i
$126$	−2.37877	+	9.54648i	−0.211918	+	0.850468i
$127$			9.72306i			0.862782i	0.902165	+	0.431391i	$0.141977\pi$
$127$			9.72306i			0.862782i	−0.902165	+	0.431391i	$0.858023\pi$
$128$	−11.2052	−	1.56348i	−0.990405	−	0.138193i
$129$		−	4.01430i		−	0.353439i
$130$	0.662123	+	0.164986i	0.0580720	+	0.0144703i
$131$			8.55926i			0.747826i	0.927464	+	0.373913i	$0.121984\pi$
$131$			8.55926i			0.747826i	−0.927464	+	0.373913i	$0.878016\pi$
$132$	5.87894	−	11.0642i	0.511696	−	0.963016i
$133$	17.3236			1.50215
$134$	−5.34136	+	21.4359i	−0.461423	+	1.85178i
$135$	0.362207			0.0311738
$136$	−3.66540	−	3.29753i	−0.314306	−	0.282761i
$137$		−	5.34661i		−	0.456792i	−0.973568	−	0.228396i	$-0.926652\pi$
$137$		−	5.34661i		−	0.456792i	0.973568	−	0.228396i	$-0.0733480\pi$
$138$	2.05687	+	16.2752i	0.175092	+	1.38543i
$139$		−	15.1210i		−	1.28255i	−0.767312	−	0.641274i	$-0.778406\pi$
$139$		−	15.1210i		−	1.28255i	0.767312	−	0.641274i	$-0.221594\pi$
$140$	−2.29052	+	4.31078i	−0.193584	+	0.364328i
$141$	−10.6455			−0.896510
$142$	−15.1847	−	3.78368i	−1.27427	−	0.317519i
$143$	−1.24971			−0.104506
$144$	−6.38070	−	9.44825i	−0.531725	−	0.787354i
$145$		−	1.03287i		−	0.0857751i
$146$	1.73141	−	6.94848i	0.143292	−	0.575060i
$147$		−	2.52192i		−	0.208004i
$148$	−6.34629	+	11.9438i	−0.521662	+	0.981773i
$149$			14.6235i			1.19800i	0.800749	+	0.599000i	$0.204435\pi$
$149$			14.6235i			1.19800i	−0.800749	+	0.599000i	$0.795565\pi$
$150$	−3.31911	−	0.827049i	−0.271004	−	0.0675283i
$151$			6.63114i			0.539635i	0.962911	+	0.269817i	$0.0869634\pi$
$151$			6.63114i			0.539635i	−0.962911	+	0.269817i	$0.913037\pi$
$152$	−13.4266	+	14.9244i	−1.08904	+	1.21053i
$153$		−	4.96844i		−	0.401675i
$154$	2.16159	−	8.67488i	0.174186	−	0.699042i
$155$	−2.87696			−0.231083
$156$	−1.09522	+	2.06121i	−0.0876875	+	0.165029i
$157$		−	17.8150i		−	1.42180i	−0.703296	−	0.710898i	$-0.748289\pi$
$157$		−	17.8150i		−	1.42180i	0.703296	−	0.710898i	$-0.251711\pi$
$158$	−3.34861	+	13.4387i	−0.266402	+	1.06912i
$159$	4.58924			0.363951
$160$	−1.93851	−	5.31434i	−0.153253	−	0.420135i
$161$	4.23201	+	10.9137i	0.333529	+	0.860120i
$162$	−3.22337	+	12.9360i	−0.253251	+	1.01635i
$163$			4.03456i			0.316011i	0.987438	+	0.158005i	$0.0505064\pi$
$163$			4.03456i			0.316011i	−0.987438	+	0.158005i	$0.949494\pi$
$164$	−1.60221	−	0.851330i	−0.125112	−	0.0664777i
$165$	6.26456			0.487695
$166$	−4.63564	+	18.6037i	−0.359795	+	1.44393i
$167$			12.1772i			0.942301i	0.882053	+	0.471150i	$0.156161\pi$
$167$			12.1772i			0.942301i	−0.882053	+	0.471150i	$0.843839\pi$
$168$	−12.4136	−	11.1677i	−0.957729	−	0.861608i
$169$	−12.7672			−0.982091
$170$	0.596048	−	2.39206i	0.0457148	−	0.183463i
$171$	−20.2300			−1.54703
$172$	2.93125	+	1.55751i	0.223506	+	0.118759i
$173$	21.5454			1.63807			0.819035	−	0.573743i	$-0.194509\pi$
$173$	21.5454			1.63807			0.819035	+	0.573743i	$0.194509\pi$
$174$	3.42820	+	0.854233i	0.259891	+	0.0647592i
$175$	−2.44077			−0.184505
$176$	5.79814	+	8.58562i	0.437051	+	0.647166i
$177$	−9.18322			−0.690253
$178$	3.50171	+	0.872550i	0.262465	+	0.0654004i
$179$		−	25.0006i		−	1.86863i	−0.356449	−	0.934315i	$-0.616013\pi$
$179$		−	25.0006i		−	1.86863i	0.356449	−	0.934315i	$-0.383987\pi$
$180$	2.67480	−	5.03400i	0.199368	−	0.375212i
$181$		−	20.6924i		−	1.53805i	−0.639217	−	0.769026i	$-0.720742\pi$
$181$		−	20.6924i		−	1.53805i	0.639217	−	0.769026i	$-0.279258\pi$
$182$	−0.402693	+	1.61609i	−0.0298496	+	0.119792i
$183$	19.7817			1.46230
$184$	−12.6822	−	4.81268i	−0.934944	−	0.354796i
$185$	−6.76257			−0.497194
$186$	2.37938	−	9.54894i	0.174465	−	0.700162i
$187$			4.51482i			0.330157i
$188$	4.13034	−	7.77334i	0.301236	−	0.566929i
$189$			0.884062i			0.0643061i
$190$	−9.73974	−	2.42693i	−0.706595	−	0.176068i
$191$	3.12789			0.226326			0.113163	−	0.993576i	$-0.463902\pi$
$191$	3.12789			0.226326			0.113163	+	0.993576i	$0.463902\pi$
$192$	19.2421	−	2.03892i	1.38868	−	0.147147i
$193$	19.7240			1.41976			0.709882	−	0.704320i	$-0.248748\pi$
$193$	19.7240			1.41976			0.709882	+	0.704320i	$0.248748\pi$
$194$	1.84382	+	0.459439i	0.132378	+	0.0329858i
$195$	−1.16706			−0.0835746
$196$	1.84151	+	0.978481i	0.131536	+	0.0698915i
$197$	−10.6999			−0.762333			−0.381167	−	0.924506i	$-0.624478\pi$
$197$	−10.6999			−0.762333			−0.381167	+	0.924506i	$0.624478\pi$
$198$	−2.52424	+	10.1303i	−0.179390	+	0.719926i
$199$	21.1502			1.49930			0.749649	−	0.661836i	$-0.230222\pi$
$199$	21.1502			1.49930			0.749649	+	0.661836i	$0.230222\pi$
$200$	1.89170	−	2.10273i	0.133763	−	0.148686i
$201$		−	37.7829i		−	2.66500i
$202$	−6.02086	+	24.1629i	−0.423626	+	1.70009i
$203$	2.52099			0.176939
$204$	7.44655	+	3.95670i	0.521363	+	0.277024i
$205$		−	0.907172i		−	0.0633597i
$206$	5.07468	−	20.3657i	0.353570	−	1.41895i
$207$	−4.94200	−	12.7447i	−0.343493	−	0.885816i
$208$	−1.08016	−	1.59946i	−0.0748959	−	0.110902i
$209$	18.3830			1.27158
$210$	2.01863	−	8.10117i	0.139299	−	0.559034i
$211$			6.84533i			0.471252i	0.971844	+	0.235626i	$0.0757140\pi$
$211$			6.84533i			0.471252i	−0.971844	+	0.235626i	$0.924286\pi$
$212$	−1.78058	+	3.35107i	−0.122291	+	0.230153i
$213$	26.7644			1.83387
$214$	4.74173	−	19.0295i	0.324138	−	1.30083i
$215$			1.65967i			0.113189i
$216$	−0.761624	−	0.685185i	−0.0518220	−	0.0466210i
$217$		−	7.02198i		−	0.476683i
$218$	−22.4944	−	5.60510i	−1.52351	−	0.379626i
$219$			12.2474i			0.827600i
$220$	−2.43059	+	4.57439i	−0.163870	+	0.308405i
$221$		−	0.841089i		−	0.0565778i
$222$	5.59297	−	22.4457i	0.375376	−	1.50646i
$223$			9.20583i			0.616468i	0.951311	+	0.308234i	$0.0997379\pi$
$223$			9.20583i			0.616468i	−0.951311	+	0.308234i	$0.900262\pi$
$224$	12.9710	−	4.73146i	0.866665	−	0.316134i
$225$	2.85025			0.190017
$226$	21.2875	+	5.30437i	1.41602	+	0.352841i
$227$	−15.6774			−1.04055			−0.520274	−	0.853999i	$-0.674170\pi$
$227$	−15.6774			−1.04055			−0.520274	+	0.853999i	$0.674170\pi$
$228$	16.1105	−	30.3201i	1.06694	−	2.00800i
$229$		−	12.3042i		−	0.813087i	−0.913631	−	0.406543i	$-0.866734\pi$
$229$		−	12.3042i		−	0.813087i	0.913631	−	0.406543i	$-0.133266\pi$
$230$	−0.850391	−	6.72881i	−0.0560731	−	0.443684i
$231$			15.2903i			1.00603i
$232$	−1.95387	+	2.17185i	−0.128278	+	0.142589i
$233$	−7.21602			−0.472737			−0.236369	−	0.971663i	$-0.575957\pi$
$233$	−7.21602			−0.472737			−0.236369	+	0.971663i	$0.575957\pi$
$234$	0.470252	−	1.88722i	0.0307414	−	0.123371i
$235$	4.40127			0.287107
$236$	3.56300	−	6.70561i	0.231932	−	0.436498i
$237$		−	23.6869i		−	1.53863i
$238$	5.83846	+	1.45481i	0.378451	+	0.0943016i
$239$		−	0.395962i		−	0.0256126i	−0.999918	−	0.0128063i	$-0.995924\pi$
$239$		−	0.395962i		−	0.0256126i	0.999918	−	0.0128063i	$-0.00407649\pi$
$240$	5.41468	+	8.01781i	0.349516	+	0.517547i
$241$			3.11185i			0.200452i	0.994965	+	0.100226i	$0.0319565\pi$
$241$			3.11185i			0.200452i	−0.994965	+	0.100226i	$0.968043\pi$
$242$	−1.46752	+	5.88943i	−0.0943355	+	0.378587i
$243$		−	21.7143i		−	1.39297i
$244$	−7.67510	+	14.4446i	−0.491348	+	0.924722i
$245$			1.04266i			0.0666133i
$246$	3.01100	+	0.750276i	0.191975	+	0.0478358i
$247$	−3.42466			−0.217906
$248$	6.04947	+	5.44233i	0.384142	+	0.345588i
$249$		−	32.7909i		−	2.07804i
$250$	1.37225	+	0.341935i	0.0867889	+	0.0216259i
$251$	−13.7629			−0.868704			−0.434352	−	0.900743i	$-0.643023\pi$
$251$	−13.7629			−0.868704			−0.434352	+	0.900743i	$0.643023\pi$
$252$	12.2868	+	6.52856i	0.773996	+	0.411260i
$253$	4.49080	+	11.5811i	0.282334	+	0.728096i
$254$	13.3425	+	3.32466i	0.837183	+	0.208607i
$255$			4.21623i			0.264031i
$256$	−5.97693	+	14.8417i	−0.373558	+	0.927607i
$257$	−24.5390			−1.53070			−0.765351	−	0.643613i	$-0.777435\pi$
$257$	−24.5390			−1.53070			−0.765351	+	0.643613i	$0.777435\pi$
$258$	−5.50864	−	1.37263i	−0.342953	−	0.0854563i
$259$		−	16.5058i		−	1.02562i
$260$	0.452807	−	0.852186i	0.0280819	−	0.0528503i
$261$	−2.94393			−0.182225
$262$	11.7455	+	2.92671i	0.725638	+	0.180813i
$263$	−10.3038			−0.635362			−0.317681	−	0.948198i	$-0.602904\pi$
$263$	−10.3038			−0.635362			−0.317681	+	0.948198i	$0.602904\pi$
$264$	−13.1727	−	11.8506i	−0.810723	−	0.729356i
$265$	−1.89738			−0.116555
$266$	5.92357	−	23.7724i	0.363197	−	1.45758i
$267$	−6.17211			−0.377727
$268$	27.5891	+	14.6594i	1.68527	+	0.895465i
$269$	−2.31211			−0.140972			−0.0704859	−	0.997513i	$-0.522455\pi$
$269$	−2.31211			−0.140972			−0.0704859	+	0.997513i	$0.522455\pi$
$270$	0.123851	−	0.497040i	0.00753735	−	0.0302489i
$271$			21.0099i			1.27626i	0.769929	+	0.638129i	$0.220291\pi$
$271$			21.0099i			1.27626i	−0.769929	+	0.638129i	$0.779709\pi$
$272$	−5.77838	+	3.90232i	−0.350366	+	0.236613i
$273$		−	2.84851i		−	0.172400i
$274$	−7.33690	−	1.82819i	−0.443239	−	0.110445i
$275$	−2.59002			−0.156184
$276$	23.0370	+	2.74251i	1.38666	+	0.165080i
$277$	−7.45198			−0.447746			−0.223873	−	0.974618i	$-0.571870\pi$
$277$	−7.45198			−0.447746			−0.223873	+	0.974618i	$0.571870\pi$
$278$	−20.7499	−	5.17041i	−1.24449	−	0.310101i
$279$			8.20005i			0.490924i
$280$	5.13228	+	4.61719i	0.306712	+	0.275930i
$281$			14.8257i			0.884429i	0.896909	+	0.442215i	$0.145807\pi$
$281$			14.8257i			0.884429i	−0.896909	+	0.442215i	$0.854193\pi$
$282$	−3.64006	+	14.6083i	−0.216763	+	0.869911i
$283$	4.08320			0.242721			0.121360	−	0.992609i	$-0.461274\pi$
$283$	4.08320			0.242721			0.121360	+	0.992609i	$0.461274\pi$
$284$	−10.3843	+	19.5434i	−0.616197	+	1.15969i
$285$	17.1672			1.01690
$286$	−0.427318	+	1.71491i	−0.0252679	+	0.101405i
$287$	2.21419			0.130700
$288$	−15.1472	+	5.52525i	−0.892556	+	0.325578i
$289$	13.9614			0.821258
$290$	−1.41736	−	0.353174i	−0.0832301	−	0.0207391i
$291$	−3.24991			−0.190513
$292$	−8.94304	−	4.75186i	−0.523352	−	0.278082i
$293$		−	7.93619i		−	0.463637i	−0.972759	−	0.231819i	$-0.925532\pi$
$293$		−	7.93619i		−	0.463637i	0.972759	−	0.231819i	$-0.0744676\pi$
$294$	−3.46071	−	0.862333i	−0.201833	−	0.0502923i
$295$	3.79671			0.221053
$296$	14.2199	+	12.7927i	0.826514	+	0.743562i
$297$			0.938123i			0.0544354i
$298$	20.0671	+	5.00028i	1.16246	+	0.289658i
$299$	−0.836613	−	2.15750i	−0.0483826	−	0.124771i
$300$	−2.26984	+	4.27186i	−0.131049	+	0.246636i
$301$	−4.05087			−0.233488
$302$	9.09961	+	2.26742i	0.523624	+	0.130475i
$303$		−	42.5894i		−	2.44670i
$304$	15.8891	+	23.5278i	0.911301	+	1.34941i
$305$	−8.17854			−0.468302
$306$	−6.81797	−	1.69889i	−0.389757	−	0.0971189i
$307$		−	26.2313i		−	1.49710i	−0.663078	−	0.748551i	$-0.730750\pi$
$307$		−	26.2313i		−	1.49710i	0.663078	−	0.748551i	$-0.269250\pi$
$308$	−11.1650	−	5.93250i	−0.636186	−	0.338035i
$309$			35.8965i			2.04208i
$310$	−0.983733	+	3.94792i	−0.0558723	+	0.224227i
$311$		−	25.4427i		−	1.44272i	−0.692559	−	0.721361i	$-0.743517\pi$
$311$		−	25.4427i		−	1.44272i	0.692559	−	0.721361i	$-0.256483\pi$
$312$	2.45401	+	2.20771i	0.138931	+	0.124987i
$313$		−	27.2137i		−	1.53821i	−0.639123	−	0.769105i	$-0.720702\pi$
$313$		−	27.2137i		−	1.53821i	0.639123	−	0.769105i	$-0.279298\pi$
$314$	−24.4468	−	6.09159i	−1.37961	−	0.343768i
$315$			6.95679i			0.391971i
$316$	17.2962	+	9.19030i	0.972989	+	0.516995i
$317$	−19.7663			−1.11019			−0.555094	−	0.831788i	$-0.687318\pi$
$317$	−19.7663			−1.11019			−0.555094	+	0.831788i	$0.687318\pi$
$318$	1.56922	−	6.29760i	0.0879977	−	0.353152i
$319$	2.67515			0.149780
$320$	−7.95546	+	0.842973i	−0.444724	+	0.0471236i
$321$			33.5413i			1.87209i
$322$	16.4234	−	2.07561i	0.915242	−	0.115669i
$323$			12.3723i			0.688414i
$324$	16.6493	+	8.84655i	0.924961	+	0.491475i
$325$	0.482508			0.0267647
$326$	5.53644	+	1.37956i	0.306635	+	0.0764066i
$327$	39.6485			2.19257
$328$	−1.71609	+	1.90754i	−0.0947554	+	0.105326i
$329$			10.7425i			0.592251i
$330$	2.14207	−	8.59656i	0.117917	−	0.473225i
$331$			32.1515i			1.76720i	0.468238	+	0.883602i	$0.344889\pi$
$331$			32.1515i			1.76720i	−0.468238	+	0.883602i	$0.655111\pi$
$332$	23.9440	+	12.7225i	1.31410	+	0.698241i
$333$			19.2750i			1.05626i
$334$	16.7102	+	4.16382i	0.914343	+	0.227834i
$335$			15.6210i			0.853464i
$336$	−19.5696	+	13.2160i	−1.06761	+	0.720990i
$337$			25.7071i			1.40035i	0.713970	+	0.700176i	$0.246895\pi$
$337$			25.7071i			1.40035i	−0.713970	+	0.700176i	$0.753105\pi$
$338$	−4.36555	+	17.5198i	−0.237455	+	0.952953i
$339$	−37.5212			−2.03787
$340$	−3.07870	−	1.63586i	−0.166966	−	0.0887169i
$341$		−	7.45138i		−	0.403515i
$342$	−6.91735	+	27.7607i	−0.374048	+	1.50113i
$343$	−19.6303			−1.05993
$344$	3.13960	−	3.48985i	0.169276	−	0.188160i
$345$	4.19380	+	10.8152i	0.225786	+	0.582269i
$346$	7.36715	−	29.5658i	0.396060	−	1.58947i
$347$			6.50423i			0.349165i	0.984643	+	0.174583i	$0.0558576\pi$
$347$			6.50423i			0.349165i	−0.984643	+	0.174583i	$0.944142\pi$
$348$	2.34445	−	4.41227i	0.125676	−	0.236523i
$349$	13.3980			0.717177			0.358588	−	0.933496i	$-0.383258\pi$
$349$	13.3980			0.717177			0.358588	+	0.933496i	$0.383258\pi$
$350$	−0.834584	+	3.34935i	−0.0446104	+	0.179030i
$351$		−	0.174768i		−	0.00932841i
$352$	13.7642	−	5.02079i	0.733636	−	0.267609i
$353$	−35.4004			−1.88417			−0.942087	−	0.335370i	$-0.891139\pi$
$353$	−35.4004			−1.88417			−0.942087	+	0.335370i	$0.891139\pi$
$354$	−3.14007	+	12.6017i	−0.166893	+	0.669773i
$355$	−11.0655			−0.587295
$356$	2.39472	−	4.50688i	0.126920	−	0.238864i
$357$	−10.2908			−0.544649
$358$	−34.3071	−	8.54857i	−1.81319	−	0.451806i
$359$	17.3591			0.916179			0.458089	−	0.888906i	$-0.348534\pi$
$359$	17.3591			0.916179			0.458089	+	0.888906i	$0.348534\pi$
$360$	−5.99331	−	5.39180i	−0.315875	−	0.284173i
$361$	31.3763			1.65138
$362$	−28.3952	−	7.07546i	−1.49242	−	0.371878i
$363$		−	10.3807i		−	0.544845i
$364$	2.07999	+	1.10519i	0.109021	+	0.0579279i
$365$		−	5.06355i		−	0.265038i
$366$	6.76405	−	27.1455i	0.353563	−	1.41892i
$367$	15.7816			0.823792			0.411896	−	0.911231i	$-0.364867\pi$
$367$	15.7816			0.823792			0.411896	+	0.911231i	$0.364867\pi$
$368$	−10.9407	+	15.7576i	−0.570324	+	0.821420i
$369$	−2.58567			−0.134604
$370$	−2.31236	+	9.27996i	−0.120214	+	0.482442i
$371$		−	4.63105i		−	0.240432i
$372$	−12.2900	−	6.53024i	−0.637205	−	0.338577i
$373$			32.2760i			1.67119i	0.549348	+	0.835593i	$0.314876\pi$
$373$			32.2760i			1.67119i	−0.549348	+	0.835593i	$0.685124\pi$
$374$	6.19548	+	1.54378i	0.320361	+	0.0798268i
$375$	−2.41873			−0.124903
$376$	−9.25469	−	8.32586i	−0.477274	−	0.429373i
$377$	−0.498367			−0.0256672
$378$	1.21316	+	0.302292i	0.0623981	+	0.0155482i
$379$	9.04274			0.464494			0.232247	−	0.972657i	$-0.425392\pi$
$379$	9.04274			0.464494			0.232247	+	0.972657i	$0.425392\pi$
$380$	−6.66073	+	12.5355i	−0.341688	+	0.643060i
$381$	−23.5174			−1.20483
$382$	1.06954	−	4.29226i	0.0547223	−	0.219611i
$383$	5.57417			0.284827			0.142414	−	0.989807i	$-0.454514\pi$
$383$	5.57417			0.284827			0.142414	+	0.989807i	$0.454514\pi$
$384$	3.78164	−	27.1022i	0.192981	−	1.38306i
$385$		−	6.32163i		−	0.322180i
$386$	6.74433	−	27.0663i	0.343277	−	1.37764i
$387$	4.73048			0.240464
$388$	1.26093	−	2.37309i	0.0640142	−	0.120475i
$389$			4.18438i			0.212156i	0.994358	+	0.106078i	$0.0338294\pi$
$389$			4.18438i			0.212156i	−0.994358	+	0.106078i	$0.966171\pi$
$390$	−0.399057	+	1.60150i	−0.0202071	+	0.0810949i
$391$	−7.79442	+	3.02244i	−0.394181	+	0.152851i
$392$	1.97240	−	2.19244i	0.0996213	−	0.110735i
$393$	−20.7025			−1.04430
$394$	−3.65866	+	14.6829i	−0.184321	+	0.739715i
$395$			9.79312i			0.492746i
$396$	13.0382	+	6.92778i	0.655192	+	0.348134i
$397$	−10.2111			−0.512481			−0.256240	−	0.966613i	$-0.582484\pi$
$397$	−10.2111			−0.512481			−0.256240	+	0.966613i	$0.582484\pi$
$398$	7.23200	−	29.0234i	0.362507	−	1.45481i
$399$			41.9012i			2.09768i
$400$	−2.23865	−	3.31489i	−0.111932	−	0.165744i
$401$			8.28754i			0.413860i	0.978356	+	0.206930i	$0.0663473\pi$
$401$			8.28754i			0.413860i	−0.978356	+	0.206930i	$0.933653\pi$
$402$	−51.8477	−	12.9193i	−2.58593	−	0.644356i
$403$			1.38815i			0.0691489i
$404$	31.0989	+	16.5243i	1.54723	+	0.822114i
$405$			9.42683i			0.468423i
$406$	0.862015	−	3.45944i	0.0427811	−	0.171689i
$407$		−	17.5152i		−	0.868196i
$408$	7.97583	−	8.86562i	0.394863	−	0.438913i
$409$	−1.64792			−0.0814844			−0.0407422	−	0.999170i	$-0.512972\pi$
$409$	−1.64792			−0.0814844			−0.0407422	+	0.999170i	$0.512972\pi$
$410$	−1.24487	−	0.310194i	−0.0614798	−	0.0153194i
$411$	12.9320			0.637888
$412$	−26.2117	−	13.9275i	−1.29136	−	0.686159i
$413$			9.26689i			0.455994i
$414$	−19.1788	+	2.42383i	−0.942585	+	0.119125i
$415$			13.5571i			0.665490i
$416$	−2.56421	+	0.935348i	−0.125721	+	0.0458592i
$417$	36.5736			1.79102
$418$	6.28580	−	25.2261i	0.307448	−	1.23385i
$419$	27.8772			1.36189			0.680945	−	0.732334i	$-0.261569\pi$
$419$	27.8772			1.36189			0.680945	+	0.732334i	$0.261569\pi$
$420$	−10.4266	−	5.54015i	−0.508767	−	0.270332i
$421$		−	1.00728i		−	0.0490920i	−0.999699	−	0.0245460i	$-0.992186\pi$
$421$		−	1.00728i		−	0.0490920i	0.999699	−	0.0245460i	$-0.00781402\pi$
$422$	9.39353	+	2.34066i	0.457270	+	0.113942i
$423$		−	12.5447i		−	0.609944i
$424$	3.98968	+	3.58926i	0.193756	+	0.174310i
$425$		−	1.74316i		−	0.0845557i
$426$	9.15169	−	36.7276i	0.443401	−	1.77946i
$427$		−	19.9619i		−	0.966024i
$428$	−24.4919	−	13.0137i	−1.18386	−	0.629041i
$429$		−	3.02270i		−	0.145937i
$430$	2.27749	+	0.567501i	0.109830	+	0.0273673i
$431$	−32.5335			−1.56708			−0.783542	−	0.621339i	$-0.786589\pi$
$431$	−32.5335			−1.56708			−0.783542	+	0.621339i	$0.786589\pi$
$432$	−1.20067	+	0.810853i	−0.0577675	+	0.0390122i
$433$		−	25.0052i		−	1.20167i	−0.799373	−	0.600836i	$-0.794835\pi$
$433$		−	25.0052i		−	1.20167i	0.799373	−	0.600836i	$-0.205165\pi$
$434$	−9.63594	−	2.40106i	−0.462540	−	0.115255i
$435$	2.49823			0.119781
$436$	−15.3833	+	28.9514i	−0.736724	+	1.38652i
$437$	12.3065	+	31.7365i	0.588698	+	1.51816i
$438$	16.8065	+	4.18780i	0.803045	+	0.200101i
$439$		−	3.60464i		−	0.172040i	−0.996293	−	0.0860201i	$-0.972585\pi$
$439$		−	3.60464i		−	0.172040i	0.996293	−	0.0860201i	$-0.0274149\pi$
$440$	5.44612	+	4.89953i	0.259634	+	0.233576i
$441$	2.97185			0.141517
$442$	−1.15419	−	0.287598i	−0.0548991	−	0.0136796i
$443$			8.90760i			0.423213i	0.977355	+	0.211606i	$0.0678695\pi$
$443$			8.90760i			0.423213i	−0.977355	+	0.211606i	$0.932131\pi$
$444$	−28.8888	−	15.3500i	−1.37100	−	0.728477i
$445$	2.55180			0.120967
$446$	12.6327	+	3.14780i	0.598177	+	0.149053i
$447$	−35.3702			−1.67295
$448$	−2.05750	−	19.4174i	−0.0972077	−	0.917387i
$449$	24.9219			1.17614			0.588069	−	0.808811i	$-0.299888\pi$
$449$	24.9219			1.17614			0.588069	+	0.808811i	$0.299888\pi$
$450$	0.974601	−	3.91126i	0.0459431	−	0.184379i
$451$	2.34959			0.110638
$452$	14.5579	−	27.3981i	0.684745	−	1.28870i
$453$	−16.0389			−0.753575
$454$	−5.36067	+	21.5134i	−0.251589	+	1.00968i
$455$			1.17769i			0.0552109i
$456$	−36.0981	−	32.4752i	−1.69045	−	1.52079i
$457$		−	22.7410i		−	1.06378i	−0.846813	−	0.531890i	$-0.821482\pi$
$457$		−	22.7410i		−	1.06378i	0.846813	−	0.531890i	$-0.178518\pi$
$458$	−16.8845	−	4.20725i	−0.788962	−	0.196592i
$459$	−0.631385			−0.0294705
$460$	−9.52441	−	1.13386i	−0.444078	−	0.0528667i
$461$	37.7027			1.75599			0.877996	−	0.478668i	$-0.158880\pi$
$461$	37.7027			1.75599			0.877996	+	0.478668i	$0.158880\pi$
$462$	20.9822	+	5.22830i	0.976180	+	0.243242i
$463$			4.38605i			0.203837i	0.994793	+	0.101918i	$0.0324981\pi$
$463$			4.38605i			0.203837i	−0.994793	+	0.101918i	$0.967502\pi$
$464$	2.31223	+	3.42384i	0.107342	+	0.158948i
$465$		−	6.95858i		−	0.322696i
$466$	−2.46741	+	9.90221i	−0.114301	+	0.458711i
$467$	13.7395			0.635788			0.317894	−	0.948126i	$-0.397024\pi$
$467$	13.7395			0.635788			0.317894	+	0.948126i	$0.397024\pi$
$468$	−2.42894	−	1.29061i	−0.112278	−	0.0596585i
$469$	−38.1271			−1.76055
$470$	1.50495	−	6.03965i	0.0694181	−	0.278588i
$471$	43.0898			1.98547
$472$	−7.98348	−	7.18223i	−0.367469	−	0.330589i
$473$	−4.29859			−0.197649
$474$	−32.5045	−	8.09939i	−1.49298	−	0.372017i
$475$	−7.09763			−0.325661
$476$	3.99275	−	7.51439i	0.183007	−	0.344422i
$477$			5.40800i			0.247615i
$478$	−0.543360	−	0.135393i	−0.0248527	−	0.00619275i
$479$	−34.3897			−1.57130			−0.785652	−	0.618668i	$-0.787673\pi$
$479$	−34.3897			−1.57130			−0.785652	+	0.618668i	$0.787673\pi$
$480$	12.8539	−	4.68874i	0.586699	−	0.214011i
$481$			3.26299i			0.148780i
$482$	4.27025	+	1.06405i	0.194504	+	0.0484662i
$483$	−26.3973	+	10.2361i	−1.20112	+	0.465757i
$484$	7.58000	+	4.02761i	0.344545	+	0.183073i
$485$	1.34364			0.0610116
$486$	−29.7976	−	7.42489i	−1.35164	−	0.336800i
$487$			8.75208i			0.396594i	0.980142	+	0.198297i	$0.0635411\pi$
$487$			8.75208i			0.396594i	−0.980142	+	0.198297i	$0.936459\pi$
$488$	17.1973	+	15.4713i	0.778485	+	0.700353i
$489$	−9.75850			−0.441295
$490$	1.43080	+	0.356523i	0.0646369	+	0.0161061i
$491$		−	18.7020i		−	0.844009i	−0.906594	−	0.422004i	$-0.861327\pi$
$491$		−	18.7020i		−	0.844009i	0.906594	−	0.422004i	$-0.138673\pi$
$492$	2.05914	−	3.87532i	0.0928331	−	0.174713i
$493$			1.80046i			0.0810885i
$494$	−1.17101	+	4.69950i	−0.0526863	+	0.211441i
$495$			7.38220i			0.331805i
$496$	9.53678	−	6.44049i	0.428214	−	0.289186i
$497$		−	27.0083i		−	1.21149i
$498$	−44.9974	−	11.2124i	−2.01638	−	0.502438i
$499$		−	29.6215i		−	1.32604i	−0.748601	−	0.663021i	$-0.769274\pi$
$499$		−	29.6215i		−	1.32604i	0.748601	−	0.663021i	$-0.230726\pi$
$500$	0.938444	−	1.76616i	0.0419685	−	0.0789851i
$501$	−29.4534			−1.31588
$502$	−4.70601	+	18.8861i	−0.210039	+	0.842929i
$503$	18.2062			0.811774			0.405887	−	0.913923i	$-0.366963\pi$
$503$	18.2062			0.811774			0.405887	+	0.913923i	$0.366963\pi$
$504$	13.1601	−	14.6283i	0.586199	−	0.651595i
$505$			17.6082i			0.783553i
$506$	17.4277	−	2.20253i	0.774758	−	0.0979144i
$507$		−	30.8804i		−	1.37144i
$508$	9.12454	−	17.1725i	0.404836	−	0.761905i
$509$	6.43616			0.285278			0.142639	−	0.989775i	$-0.454441\pi$
$509$	6.43616			0.285278			0.142639	+	0.989775i	$0.454441\pi$
$510$	5.78574	+	1.44168i	0.256197	+	0.0638386i
$511$	12.3589			0.546727
$512$	18.3229	+	13.2768i	0.809764	+	0.586756i
$513$			2.57081i			0.113504i
$514$	−8.39076	+	33.6738i	−0.370101	+	1.48529i
$515$		−	14.8411i		−	0.653976i
$516$	−3.76720	+	7.08990i	−0.165842	+	0.312115i
$517$			11.3994i			0.501344i
$518$	−22.6502	−	5.64393i	−0.995193	−	0.247980i
$519$			52.1126i			2.28749i
$520$	−1.01459	−	0.912758i	−0.0444925	−	0.0400271i
$521$		−	16.5369i		−	0.724496i	−0.932082	−	0.362248i	$-0.882009\pi$
$521$		−	16.5369i		−	0.724496i	0.932082	−	0.362248i	$-0.117991\pi$
$522$	−1.00663	+	4.03982i	−0.0440592	+	0.176818i
$523$	−9.19096			−0.401893			−0.200946	−	0.979602i	$-0.564402\pi$
$523$	−9.19096			−0.401893			−0.200946	+	0.979602i	$0.564402\pi$
$524$	8.03238	−	15.1170i	0.350896	−	0.660390i
$525$		−	5.90355i		−	0.257652i
$526$	−3.52325	+	14.1395i	−0.153621	+	0.616511i
$527$	5.01500			0.218457
$528$	−20.7663	+	14.0241i	−0.903737	+	0.610322i
$529$	−16.9873	+	15.5059i	−0.738578	+	0.674168i
$530$	−0.648780	+	2.60368i	−0.0281812	+	0.113097i
$531$		−	10.8216i		−	0.469617i
$532$	−30.5963	−	16.2573i	−1.32652	−	0.704842i
$533$	−0.437718			−0.0189597
$534$	−2.11046	+	8.46970i	−0.0913286	+	0.366520i
$535$		−	13.8673i		−	0.599537i
$536$	29.5501	−	32.8467i	1.27637	−	1.41876i
$537$	60.4696			2.60945
$538$	−0.790592	+	3.17280i	−0.0340848	+	0.136789i
$539$	−2.70052			−0.116320
$540$	−0.639716	−	0.339911i	−0.0275290	−	0.0146274i
$541$	−30.3151			−1.30335			−0.651673	−	0.758500i	$-0.725933\pi$
$541$	−30.3151			−1.30335			−0.651673	+	0.758500i	$0.725933\pi$
$542$	28.8309	+	7.18401i	1.23839	+	0.308580i
$543$	50.0493			2.14782
$544$	3.37914	+	9.26374i	0.144879	+	0.397180i
$545$	−16.3923			−0.702169
$546$	−3.90888	−	0.974006i	−0.167284	−	0.0416836i
$547$			3.21629i			0.137519i	0.997633	+	0.0687593i	$0.0219040\pi$
$547$			3.21629i			0.137519i	−0.997633	+	0.0687593i	$0.978096\pi$
$548$	−5.01749	+	9.44297i	−0.214337	+	0.403384i
$549$			23.3109i			0.994884i
$550$	−0.885620	+	3.55417i	−0.0377629	+	0.151550i
$551$	7.33091			0.312307
$552$	11.6406	−	30.6748i	0.495456	−	1.30561i
$553$	−23.9027			−1.01645
$554$	−2.54809	+	10.2260i	−0.108258	+	0.434461i
$555$		−	16.3568i		−	0.694308i
$556$	−14.1902	+	26.7061i	−0.601800	+	1.13259i
$557$			11.5928i			0.491202i	0.969371	+	0.245601i	$0.0789854\pi$
$557$			11.5928i			0.491202i	−0.969371	+	0.245601i	$0.921015\pi$
$558$	11.2525	+	2.80389i	0.476358	+	0.118698i
$559$	0.800805			0.0338705
$560$	8.09086	−	5.46401i	0.341901	−	0.230897i
$561$	−10.9201			−0.461048
$562$	20.3447	+	5.06944i	0.858188	+	0.213841i
$563$	0.736783			0.0310517			0.0155258	−	0.999879i	$-0.495058\pi$
$563$	0.736783			0.0310517			0.0155258	+	0.999879i	$0.495058\pi$
$564$	18.8016	+	9.99018i	0.791690	+	0.420662i
$565$	15.5128			0.652627
$566$	1.39619	−	5.60318i	0.0586862	−	0.235519i
$567$	−23.0087			−0.966274
$568$	23.2678	+	20.9325i	0.976293	+	0.878309i
$569$		−	6.35339i		−	0.266348i	−0.991093	−	0.133174i	$-0.957483\pi$
$569$		−	6.35339i		−	0.266348i	0.991093	−	0.133174i	$-0.0425169\pi$
$570$	5.87008	−	23.5578i	0.245871	−	0.986728i
$571$	−19.7922			−0.828277			−0.414138	−	0.910214i	$-0.635917\pi$
$571$	−19.7922			−0.828277			−0.414138	+	0.910214i	$0.635917\pi$
$572$	2.20718	+	1.17278i	0.0922868	+	0.0490363i
$573$			7.56553i			0.316054i
$574$	0.757111	−	3.03844i	0.0316012	−	0.126822i
$575$	−1.73388	−	4.47143i	−0.0723080	−	0.186471i
$576$	2.40268	+	22.6751i	0.100112	+	0.944794i
$577$	5.69116			0.236926			0.118463	−	0.992958i	$-0.462203\pi$
$577$	5.69116			0.236926			0.118463	+	0.992958i	$0.462203\pi$
$578$	4.77389	−	19.1586i	0.198568	−	0.796891i
$579$			47.7070i			1.98264i
$580$	−0.969289	+	1.82421i	−0.0402475	+	0.0757463i
$581$	−33.0896			−1.37279
$582$	−1.11126	+	4.45969i	−0.0460631	+	0.184860i
$583$		−	4.91425i		−	0.203527i
$584$	−9.57870	+	10.6473i	−0.396369	+	0.440588i
$585$		−	1.37527i		−	0.0568603i
$586$	−10.8905	−	2.71366i	−0.449881	−	0.112100i
$587$			29.8611i			1.23250i	0.787551	+	0.616250i	$0.211349\pi$
$587$			29.8611i			1.23250i	−0.787551	+	0.616250i	$0.788651\pi$
$588$	−2.36668	+	4.45411i	−0.0976002	+	0.183685i
$589$		−	20.4196i		−	0.841374i
$590$	1.29823	−	5.21006i	0.0534473	−	0.214495i
$591$		−	25.8801i		−	1.06456i
$592$	22.4171	−	15.1390i	0.921339	−	0.622209i
$593$	−7.36795			−0.302565			−0.151283	−	0.988491i	$-0.548340\pi$
$593$	−7.36795			−0.302565			−0.151283	+	0.988491i	$0.548340\pi$
$594$	1.28734	+	0.320778i	0.0528203	+	0.0131617i
$595$	4.25465			0.174424
$596$	13.7233	−	25.8274i	0.562128	−	1.05793i
$597$			51.1566i			2.09370i
$598$	−3.24670	+	0.410320i	−0.132767	+	0.0167792i
$599$		−	18.7451i		−	0.765903i	−0.923768	−	0.382951i	$-0.874908\pi$
$599$		−	18.7451i		−	0.765903i	0.923768	−	0.382951i	$-0.125092\pi$
$600$	5.08594	+	4.57550i	0.207633	+	0.186794i
$601$	21.7119			0.885645			0.442822	−	0.896609i	$-0.353977\pi$
$601$	21.7119			0.885645			0.442822	+	0.896609i	$0.353977\pi$
$602$	−1.38514	+	5.55883i	−0.0564540	+	0.226561i
$603$	44.5236			1.81314
$604$	6.22296	−	11.7117i	0.253209	−	0.476541i
$605$			4.29179i			0.174486i
$606$	−58.4434	−	14.5628i	−2.37410	−	0.591574i
$607$		−	37.1837i		−	1.50924i	−0.656161	−	0.754621i	$-0.727821\pi$
$607$		−	37.1837i		−	1.50924i	0.656161	−	0.754621i	$-0.272179\pi$
$608$	37.7192	−	13.7588i	1.52971	−	0.557995i
$609$			6.09759i			0.247087i
$610$	−2.79653	+	11.2230i	−0.113228	+	0.454407i
$611$		−	2.12365i		−	0.0859135i
$612$	−4.66261	+	8.77507i	−0.188475	+	0.354711i
$613$		−	16.3856i		−	0.661808i	−0.943664	−	0.330904i	$-0.892646\pi$
$613$		−	16.3856i		−	0.661808i	0.943664	−	0.330904i	$-0.107354\pi$
$614$	−35.9960	−	8.96942i	−1.45268	−	0.361976i
$615$	2.19420			0.0884788
$616$	−11.9586	+	13.2927i	−0.481826	+	0.535578i
$617$			21.1275i			0.850560i	0.905062	+	0.425280i	$0.139824\pi$
$617$			21.1275i			0.850560i	−0.905062	+	0.425280i	$0.860176\pi$
$618$	49.2591	+	12.2743i	1.98149	+	0.493744i
$619$	−31.6245			−1.27110			−0.635548	−	0.772062i	$-0.719226\pi$
$619$	−31.6245			−1.27110			−0.635548	+	0.772062i	$0.719226\pi$
$620$	5.08117	+	2.69986i	0.204065	+	0.108429i
$621$	−1.61958	+	0.628025i	−0.0649916	+	0.0252018i
$622$	−34.9138	−	8.69975i	−1.39992	−	0.348828i
$623$			6.22834i			0.249533i
$624$	3.86866	−	2.61262i	0.154870	−	0.104589i
$625$	1.00000			0.0400000
$626$	−37.3441	−	9.30533i	−1.49257	−	0.371916i
$627$			44.4635i			1.77570i
$628$	−16.7184	+	31.4642i	−0.667138	+	1.25556i
$629$	11.7882			0.470028
$630$	9.54648	+	2.37877i	0.380341	+	0.0947726i
$631$	−9.34449			−0.371998			−0.185999	−	0.982550i	$-0.559552\pi$
$631$	−9.34449			−0.371998			−0.185999	+	0.982550i	$0.559552\pi$
$632$	18.5256	−	20.5923i	0.736909	−	0.819119i
$633$	−16.5570			−0.658082
$634$	−6.75880	+	27.1244i	−0.268426	+	1.07725i
$635$	9.72306			0.385848
$636$	−8.10534	−	4.30675i	−0.321398	−	0.170774i
$637$	0.503093			0.0199333
$638$	0.914728	−	3.67099i	0.0362144	−	0.145336i
$639$			31.5394i			1.24768i
$640$	−1.56348	+	11.2052i	−0.0618020	+	0.442923i
$641$			22.8441i			0.902289i	0.892451	+	0.451145i	$0.148984\pi$
$641$			22.8441i			0.902289i	−0.892451	+	0.451145i	$0.851016\pi$
$642$	46.0272	+	11.4690i	1.81655	+	0.452643i
$643$	−38.8532			−1.53222			−0.766109	−	0.642710i	$-0.777810\pi$
$643$	−38.8532			−1.53222			−0.766109	+	0.642710i	$0.777810\pi$
$644$	2.76750	−	23.2468i	0.109055	−	0.916054i
$645$	−4.01430			−0.158063
$646$	16.9779	+	4.23053i	0.667988	+	0.166448i
$647$			28.2652i			1.11122i	0.831443	+	0.555610i	$0.187515\pi$
$647$			28.2652i			1.11122i	−0.831443	+	0.555610i	$0.812485\pi$
$648$	17.8327	−	19.8221i	0.700534	−	0.778686i
$649$			9.83357i			0.386001i
$650$	0.164986	−	0.662123i	0.00647130	−	0.0259706i
$651$	16.9843			0.665666
$652$	3.78621	−	7.12568i	0.148279	−	0.279063i
$653$	41.8565			1.63797			0.818985	−	0.573815i	$-0.194537\pi$
$653$	41.8565			1.63797			0.818985	+	0.573815i	$0.194537\pi$
$654$	13.5572	−	54.4078i	0.530130	−	2.12751i
$655$	8.55926			0.334438
$656$	2.03084	+	3.00717i	0.0792909	+	0.117410i
$657$	−14.4324			−0.563061
$658$	14.7414	+	3.67323i	0.574679	+	0.143197i
$659$	−12.5653			−0.489473			−0.244737	−	0.969590i	$-0.578702\pi$
$659$	−12.5653			−0.489473			−0.244737	+	0.969590i	$0.578702\pi$
$660$	−11.0642	−	5.87894i	−0.430674	−	0.228837i
$661$			40.3545i			1.56961i	0.619743	+	0.784805i	$0.287237\pi$
$661$			40.3545i			1.56961i	−0.619743	+	0.784805i	$0.712763\pi$
$662$	44.1200	+	10.9937i	1.71477	+	0.427283i
$663$	2.03437			0.0790082
$664$	25.6459	−	28.5069i	0.995252	−	1.10628i
$665$		−	17.3236i		−	0.671782i
$666$	26.4502	+	6.59080i	1.02492	+	0.255388i
$667$	1.79087	+	4.61839i	0.0693429	+	0.178825i
$668$	11.4276	−	21.5069i	0.442148	−	0.832127i
$669$	−22.2664			−0.860869
$670$	21.4359	+	5.34136i	0.828142	+	0.206355i
$671$		−	21.1826i		−	0.817745i
$672$	11.4441	+	31.3734i	0.441466	+	1.21026i
$673$	25.6709			0.989542			0.494771	−	0.869023i	$-0.335252\pi$
$673$	25.6709			0.989542			0.494771	+	0.869023i	$0.335252\pi$
$674$	35.2766	+	8.79015i	1.35880	+	0.338584i
$675$		−	0.362207i		−	0.0139414i
$676$	22.5489	+	11.9813i	0.867265	+	0.460819i
$677$		−	31.1431i		−	1.19693i	−0.801150	−	0.598463i	$-0.795778\pi$
$677$		−	31.1431i		−	1.19693i	0.801150	−	0.598463i	$-0.204222\pi$
$678$	−12.8298	+	51.4886i	−0.492726	+	1.97741i
$679$			3.27951i			0.125856i
$680$	−3.29753	+	3.66540i	−0.126455	+	0.140562i
$681$		−	37.9195i		−	1.45308i
$682$	−10.2252	−	2.54789i	−0.391542	−	0.0975637i
$683$			42.9346i			1.64285i	0.570319	+	0.821423i	$0.306820\pi$
$683$			42.9346i			1.64285i	−0.570319	+	0.821423i	$0.693180\pi$
$684$	35.7294	+	18.9847i	1.36615	+	0.725899i
$685$	−5.34661			−0.204283
$686$	−6.71228	+	26.9377i	−0.256276	+	1.02849i
$687$	29.7606			1.13544
$688$	−3.71542	−	5.50163i	−0.141649	−	0.209748i
$689$			0.915499i			0.0348778i
$690$	16.2752	−	2.05687i	0.619585	−	0.0783035i
$691$			28.0597i			1.06744i	0.845660	+	0.533721i	$0.179207\pi$
$691$			28.0597i			1.06744i	−0.845660	+	0.533721i	$0.820793\pi$
$692$	−38.0527	−	20.2192i	−1.44655	−	0.768619i
$693$	−18.0182			−0.684456
$694$	8.92545	+	2.22402i	0.338805	+	0.0844228i
$695$	−15.1210			−0.573573
$696$	−5.25311	−	4.72589i	−0.199119	−	0.179134i
$697$			1.58135i			0.0598978i
$698$	4.58124	−	18.3854i	0.173402	−	0.695898i
$699$		−	17.4536i		−	0.660156i
$700$	4.31078	+	2.29052i	0.162932	+	0.0865736i
$701$		−	6.27098i		−	0.236852i	−0.992963	−	0.118426i	$-0.962215\pi$
$701$		−	6.27098i		−	0.236852i	0.992963	−	0.118426i	$-0.0377848\pi$
$702$	−0.239826	−	0.0597592i	−0.00905163	−	0.00225547i
$703$		−	47.9982i		−	1.81029i
$704$	−2.18332	−	20.6048i	−0.0822869	−	0.776573i
$705$			10.6455i			0.400932i
$706$	−12.1046	+	48.5783i	−0.455564	+	1.82827i
$707$	−42.9774			−1.61633
$708$	16.2190	+	8.61794i	0.609549	+	0.323882i
$709$		−	4.21638i		−	0.158349i	−0.996861	−	0.0791747i	$-0.974772\pi$
$709$		−	4.21638i		−	0.158349i	0.996861	−	0.0791747i	$-0.0252285\pi$
$710$	−3.78368	+	15.1847i	−0.141999	+	0.569870i
$711$	27.9128			1.04681
$712$	−5.36575	−	4.82722i	−0.201090	−	0.180908i
$713$	12.8641	−	4.98831i	0.481764	−	0.186814i
$714$	−3.51880	+	14.1216i	−0.131688	+	0.528489i
$715$			1.24971i			0.0467363i
$716$	−23.4616	+	44.1550i	−0.876802	+	1.65015i
$717$	0.957724			0.0357669
$718$	5.93569	−	23.8211i	0.221518	−	0.888995i
$719$		−	10.0948i		−	0.376473i	−0.982124	−	0.188237i	$-0.939723\pi$
$719$		−	10.0948i		−	0.376473i	0.982124	−	0.188237i	$-0.0602772\pi$
$720$	−9.44825	+	6.38070i	−0.352115	+	0.237795i
$721$	36.2236			1.34904
$722$	10.7287	−	43.0563i	0.399280	−	1.60239i
$723$	−7.52672			−0.279922
$724$	−19.4186	+	36.5461i	−0.721688	+	1.35822i
$725$	−1.03287			−0.0383598
$726$	−14.2449	−	3.54952i	−0.528679	−	0.131735i
$727$	35.0141			1.29860			0.649300	−	0.760532i	$-0.275062\pi$
$727$	35.0141			1.29860			0.649300	+	0.760532i	$0.275062\pi$
$728$	2.22783	−	2.47636i	0.0825688	−	0.0917802i
$729$	24.2406			0.897799
$730$	−6.94848	−	1.73141i	−0.257175	−	0.0640823i
$731$		−	2.89308i		−	0.107004i
$732$	−34.9376	−	18.5640i	−1.29133	−	0.686145i
$733$		−	10.2928i		−	0.380175i	−0.981767	−	0.190087i	$-0.939123\pi$
$733$		−	10.2928i		−	0.380175i	0.981767	−	0.190087i	$-0.0608771\pi$
$734$	5.39628	−	21.6563i	0.199180	−	0.799350i
$735$	−2.52192			−0.0930224
$736$	17.8824	+	20.4015i	0.659153	+	0.752009i
$737$	−40.4586			−1.49031
$738$	−0.884131	+	3.54819i	−0.0325453	+	0.130611i
$739$		−	23.0799i		−	0.849007i	−0.905426	−	0.424503i	$-0.860449\pi$
$739$		−	23.0799i		−	0.849007i	0.905426	−	0.424503i	$-0.139551\pi$
$740$	11.9438	+	6.34629i	0.439062	+	0.233294i
$741$		−	8.28332i		−	0.304296i
$742$	−6.35498	−	1.58352i	−0.233299	−	0.0581329i
$743$	11.9643			0.438926			0.219463	−	0.975621i	$-0.429569\pi$
$743$	11.9643			0.438926			0.219463	+	0.975621i	$0.429569\pi$
$744$	−13.1635	+	14.6320i	−0.482598	+	0.536436i
$745$	14.6235			0.535762
$746$	44.2908	+	11.0363i	1.62160	+	0.404068i
$747$	38.6410			1.41380
$748$	4.23691	−	7.97390i	0.154917	−	0.291555i
$749$	33.8469			1.23674
$750$	−0.827049	+	3.31911i	−0.0301996	+	0.121197i
$751$	−23.5856			−0.860650			−0.430325	−	0.902674i	$-0.641601\pi$
$751$	−23.5856			−0.860650			−0.430325	+	0.902674i	$0.641601\pi$
$752$	−14.5897	+	9.85287i	−0.532031	+	0.359297i
$753$		−	33.2886i		−	1.21310i
$754$	−0.170409	+	0.683886i	−0.00620594	+	0.0249057i
$755$	6.63114			0.241332
$756$	0.829643	−	1.56140i	0.0301738	−	0.0567874i
$757$		−	33.3612i		−	1.21253i	−0.795261	−	0.606267i	$-0.792666\pi$
$757$		−	33.3612i		−	1.21253i	0.795261	−	0.606267i	$-0.207334\pi$
$758$	3.09203	−	12.4089i	0.112308	−	0.450713i
$759$	−28.0115	+	10.8620i	−1.01675	+	0.394266i
$760$	14.9244	+	13.4266i	0.541365	+	0.487032i
$761$	20.9441			0.759223			0.379612	−	0.925146i	$-0.376058\pi$
$761$	20.9441			0.759223			0.379612	+	0.925146i	$0.376058\pi$
$762$	−8.04144	+	32.2719i	−0.291311	+	1.16909i
$763$		−	40.0098i		−	1.44845i
$764$	−5.52436	−	2.93535i	−0.199864	−	0.106197i
$765$	−4.96844			−0.179634
$766$	1.90601	−	7.64918i	0.0688668	−	0.276376i
$767$		−	1.83194i		−	0.0661477i
$768$	−35.8981	−	14.4566i	−1.29536	−	0.521657i
$769$		−	40.2590i		−	1.45178i	−0.687813	−	0.725888i	$-0.741429\pi$
$769$		−	40.2590i		−	1.45178i	0.687813	−	0.725888i	$-0.258571\pi$
$770$	−8.67488	−	2.16159i	−0.312621	−	0.0778983i
$771$		−	59.3533i		−	2.13756i
$772$	−34.8358	−	18.5099i	−1.25377	−	0.666185i
$773$		−	8.99653i		−	0.323583i	−0.986825	−	0.161791i	$-0.948273\pi$
$773$		−	8.99653i		−	0.323583i	0.986825	−	0.161791i	$-0.0517271\pi$
$774$	1.61752	−	6.49142i	0.0581405	−	0.233329i
$775$			2.87696i			0.103343i
$776$	−2.82532	−	2.54176i	−0.101423	−	0.0912439i
$777$	39.9232			1.43224
$778$	5.74203	+	1.43079i	0.205862	+	0.0512962i
$779$	6.43877			0.230693
$780$	2.06121	+	1.09522i	0.0738031	+	0.0392150i
$781$		−	28.6598i		−	1.02553i
$782$	1.48237	+	11.7294i	0.0530094	+	0.419442i
$783$			0.374112i			0.0133697i
$784$	−2.33415	−	3.45631i	−0.0833626	−	0.123440i
$785$	−17.8150			−0.635846
$786$	−7.07892	+	28.4091i	−0.252497	+	1.01332i
$787$	−17.3155			−0.617232			−0.308616	−	0.951187i	$-0.599866\pi$
$787$	−17.3155			−0.617232			−0.308616	+	0.951187i	$0.599866\pi$
$788$	18.8977	+	10.0412i	0.673202	+	0.357704i
$789$		−	24.9222i		−	0.887254i
$790$	13.4387	+	3.34861i	0.478126	+	0.119138i
$791$			37.8630i			1.34626i
$792$	13.9649	−	15.5228i	0.496221	−	0.551579i
$793$			3.94621i			0.140134i
$794$	−3.49154	+	14.0122i	−0.123910	+	0.497275i
$795$		−	4.58924i		−	0.162764i
$796$	−37.3547	−	19.8483i	−1.32400	−	0.703504i
$797$		−	46.3144i		−	1.64054i	−0.571976	−	0.820271i	$-0.693823\pi$
$797$		−	46.3144i		−	1.64054i	0.571976	−	0.820271i	$-0.306177\pi$
$798$	57.4991	+	14.3275i	2.03545	+	0.507188i
$799$	−7.67212			−0.271420
$800$	−5.31434	+	1.93851i	−0.187890	+	0.0685368i
$801$		−	7.27326i		−	0.256988i
$802$	11.3726	+	2.83380i	0.401581	+	0.100065i
$803$	13.1147			0.462808
$804$	−35.4571	+	66.7306i	−1.25048	+	2.35341i
$805$	10.9137	−	4.23201i	0.384657	−	0.149159i
$806$	1.90490	+	0.474659i	0.0670972	+	0.0167192i
$807$		−	5.59237i		−	0.196861i
$808$	33.3093	−	37.0253i	1.17182	−	1.30254i
$809$	16.4030			0.576698			0.288349	−	0.957525i	$-0.406894\pi$
$809$	16.4030			0.576698			0.288349	+	0.957525i	$0.406894\pi$
$810$	12.9360	+	3.22337i	0.454525	+	0.113258i
$811$		−	10.0839i		−	0.354095i	−0.984202	−	0.177048i	$-0.943345\pi$
$811$		−	10.0839i		−	0.354095i	0.984202	−	0.177048i	$-0.0566547\pi$
$812$	−4.45247	−	2.36581i	−0.156251	−	0.0830236i
$813$	−50.8172			−1.78224
$814$	−24.0353	−	5.98906i	−0.842436	−	0.209917i
$815$	4.03456			0.141324
$816$	−9.43865	−	13.9763i	−0.330419	−	0.489270i
$817$	−11.7797			−0.412121
$818$	−0.563482	+	2.26137i	−0.0197017	+	0.0790668i
$819$	3.35671			0.117293
$820$	−0.851330	+	1.60221i	−0.0297297	+	0.0559517i
$821$	29.6987			1.03649			0.518246	−	0.855232i	$-0.326585\pi$
$821$	29.6987			1.03649			0.518246	+	0.855232i	$0.326585\pi$
$822$	4.42191	−	17.7460i	0.154232	−	0.618962i
$823$			25.1840i			0.877857i	0.898522	+	0.438929i	$0.144642\pi$
$823$			25.1840i			0.877857i	−0.898522	+	0.438929i	$0.855358\pi$
$824$	−28.0748	+	31.2068i	−0.978031	+	1.08714i
$825$		−	6.26456i		−	0.218104i
$826$	12.7165	+	3.16868i	0.442464	+	0.110252i
$827$	−30.3418			−1.05509			−0.527544	−	0.849528i	$-0.676887\pi$
$827$	−30.3418			−1.05509			−0.527544	+	0.849528i	$0.676887\pi$
$828$	−3.23180	+	27.1469i	−0.112313	+	0.943421i
$829$	15.3213			0.532129			0.266065	−	0.963955i	$-0.414277\pi$
$829$	15.3213			0.532129			0.266065	+	0.963955i	$0.414277\pi$
$830$	18.6037	+	4.63564i	0.645745	+	0.160905i
$831$		−	18.0243i		−	0.625256i
$832$	0.406741	+	3.83857i	0.0141012	+	0.133079i
$833$		−	1.81753i		−	0.0629737i
$834$	12.5058	−	50.1883i	0.433041	−	1.73788i
$835$	12.1772			0.421410
$836$	−32.4673	−	17.2514i	−1.12291	−	0.596653i
$837$	1.04205			0.0360187
$838$	9.53220	−	38.2546i	0.329284	−	1.32148i
$839$	17.8938			0.617764			0.308882	−	0.951100i	$-0.400045\pi$
$839$	17.8938			0.617764			0.308882	+	0.951100i	$0.400045\pi$
$840$	−11.1677	+	12.4136i	−0.385323	+	0.428310i
$841$	−27.9332			−0.963213
$842$	−1.38225	−	0.344426i	−0.0476355	−	0.0118697i
$843$	−35.8594			−1.23506
$844$	6.42396	−	12.0900i	0.221122	−	0.416153i
$845$			12.7672i			0.439205i
$846$	−17.2145	−	4.28948i	−0.591847	−	0.147475i
$847$	−10.4753			−0.359934
$848$	6.28959	−	4.24756i	0.215985	−	0.145862i
$849$			9.87615i			0.338949i
$850$	−2.39206	−	0.596048i	−0.0820470	−	0.0204443i
$851$	30.2383	−	11.7255i	1.03656	−	0.401945i
$852$	−47.2702	−	25.1169i	−1.61945	−	0.860491i
$853$	−28.3424			−0.970425			−0.485213	−	0.874396i	$-0.661258\pi$
$853$	−28.3424			−0.970425			−0.485213	+	0.874396i	$0.661258\pi$
$854$	−27.3928	−	6.82568i	−0.937362	−	0.233570i
$855$			20.2300i			0.691852i
$856$	−26.2328	+	29.1593i	−0.896617	+	0.996643i
$857$	−0.739951			−0.0252763			−0.0126381	−	0.999920i	$-0.504023\pi$
$857$	−0.739951			−0.0252763			−0.0126381	+	0.999920i	$0.504023\pi$
$858$	−4.14791	−	1.03357i	−0.141607	−	0.0352854i
$859$			30.7839i			1.05033i	0.851000	+	0.525166i	$0.175997\pi$
$859$			30.7839i			1.05033i	−0.851000	+	0.525166i	$0.824003\pi$
$860$	1.55751	−	2.93125i	0.0531107	−	0.0999548i
$861$			5.35554i			0.182516i
$862$	−11.1244	+	44.6442i	−0.378897	+	1.52059i
$863$		−	12.5426i		−	0.426955i	−0.976948	−	0.213478i	$-0.931521\pi$
$863$		−	12.5426i		−	0.426955i	0.976948	−	0.213478i	$-0.0684790\pi$
$864$	0.702143	+	1.92489i	0.0238874	+	0.0654861i
$865$		−	21.5454i		−	0.732567i
$866$	−34.3134	−	8.55015i	−1.16602	−	0.290546i
$867$			33.7688i			1.14685i
$868$	−6.58973	+	12.4019i	−0.223670	+	0.420949i
$869$	−25.3644			−0.860428
$870$	0.854233	−	3.42820i	0.0289612	−	0.116227i
$871$	7.53723			0.255389
$872$	34.4686	+	31.0092i	1.16725	+	1.05011i
$873$		−	3.82971i		−	0.129616i
$874$	47.7586	−	6.03576i	1.61546	−	0.204163i
$875$			2.44077i			0.0825129i
$876$	11.4935	−	21.6308i	0.388328	−	0.730837i
$877$	−11.7013			−0.395126			−0.197563	−	0.980290i	$-0.563303\pi$
$877$	−11.7013			−0.395126			−0.197563	+	0.980290i	$0.563303\pi$
$878$	−4.94648	−	1.23255i	−0.166936	−	0.0415967i
$879$	19.1955			0.647448
$880$	8.58562	−	5.79814i	0.289421	−	0.195455i
$881$		−	7.76026i		−	0.261450i	−0.991419	−	0.130725i	$-0.958270\pi$
$881$		−	7.76026i		−	0.261450i	0.991419	−	0.130725i	$-0.0417305\pi$
$882$	1.01618	−	4.07813i	0.0342166	−	0.137318i
$883$			49.0477i			1.65059i	0.564704	+	0.825294i	$0.308990\pi$
$883$			49.0477i			1.65059i	−0.564704	+	0.825294i	$0.691010\pi$
$884$	−0.789315	+	1.48550i	−0.0265475	+	0.0499627i
$885$			9.18322i			0.308691i
$886$	12.2235	+	3.04582i	0.410656	+	0.102326i
$887$			1.36114i			0.0457026i	0.999739	+	0.0228513i	$0.00727443\pi$
$887$			1.36114i			0.0457026i	−0.999739	+	0.0228513i	$0.992726\pi$
$888$	−30.9421	+	34.3940i	−1.03835	+	1.15419i
$889$			23.7317i			0.795936i
$890$	0.872550	−	3.50171i	0.0292479	−	0.117378i
$891$	−24.4157			−0.817956
$892$	8.63915	−	16.2590i	0.289260	−	0.544390i
$893$			31.2385i			1.04536i
$894$	−12.0943	+	48.5369i	−0.404494	+	1.62332i
$895$	−25.0006			−0.835677
$896$	−27.3492	−	3.81609i	−0.913671	−	0.127487i
$897$	5.21840	−	2.02354i	0.174237	−	0.0675640i
$898$	8.52169	−	34.1992i	0.284372	−	1.14124i
$899$		−	2.97152i		−	0.0991057i
$900$	−5.03400	−	2.67480i	−0.167800	−	0.0891600i
$901$	3.30744			0.110187
$902$	0.803409	−	3.22424i	0.0267506	−	0.107355i
$903$		−	9.79797i		−	0.326056i
$904$	−32.6192	−	29.3455i	−1.08490	−	0.976015i
$905$	−20.6924			−0.687838
$906$	−5.48428	+	22.0095i	−0.182203	+	0.731216i
$907$	13.2300			0.439294			0.219647	−	0.975579i	$-0.429509\pi$
$907$	13.2300			0.439294			0.219647	+	0.975579i	$0.429509\pi$
$908$	27.6889	+	14.7124i	0.918888	+	0.488248i
$909$	50.1877			1.66462
$910$	1.61609	+	0.402693i	0.0535728	+	0.0133492i
$911$	12.0129			0.398004			0.199002	−	0.979999i	$-0.436230\pi$
$911$	12.0129			0.398004			0.199002	+	0.979999i	$0.436230\pi$
$912$	−56.9074	+	38.4314i	−1.88439	+	1.27259i
$913$	−35.1131			−1.16207
$914$	−31.2065	−	7.77596i	−1.03222	−	0.257206i
$915$		−	19.7817i		−	0.653962i
$916$	−11.5468	+	21.7313i	−0.381518	+	0.718021i
$917$			20.8911i			0.689886i
$918$	−0.215893	+	0.866420i	−0.00712553	+	0.0285961i
$919$	−21.1075			−0.696273			−0.348136	−	0.937444i	$-0.613185\pi$
$919$	−21.1075			−0.696273			−0.348136	+	0.937444i	$0.613185\pi$
$920$	−4.81268	+	12.6822i	−0.158669	+	0.418120i
$921$	63.4465			2.09063
$922$	12.8919	−	51.7377i	0.424572	−	1.70389i
$923$			5.33918i			0.175741i
$924$	14.3491	−	27.0052i	0.472051	−	0.888404i
$925$			6.76257i			0.222352i
$926$	6.01877	+	1.49974i	0.197789	+	0.0492847i
$927$	−42.3007			−1.38934
$928$	5.48901	−	2.00223i	0.180186	−	0.0657264i
$929$	−16.4375			−0.539295			−0.269648	−	0.962959i	$-0.586907\pi$
$929$	−16.4375			−0.539295			−0.269648	+	0.962959i	$0.586907\pi$
$930$	−9.54894	−	2.37938i	−0.313122	−	0.0780231i
$931$	−7.40043			−0.242539
$932$	12.7447	+	6.77183i	0.417465	+	0.221819i
$933$	61.5389			2.01469
$934$	4.69802	−	18.8541i	0.153724	−	0.616925i
$935$	4.51482			0.147651
$936$	−2.60159	+	2.89182i	−0.0850356	+	0.0945221i
$937$			22.1718i			0.724322i	0.932115	+	0.362161i	$0.117961\pi$
$937$			22.1718i			0.724322i	−0.932115	+	0.362161i	$0.882039\pi$
$938$	−13.0370	+	52.3201i	−0.425673	+	1.70831i
$939$	65.8226			2.14804
$940$	−7.77334	−	4.13034i	−0.253538	−	0.134717i
$941$		−	14.7090i		−	0.479500i	−0.970835	−	0.239750i	$-0.922935\pi$
$941$		−	14.7090i		−	0.479500i	0.970835	−	0.239750i	$-0.0770654\pi$
$942$	14.7339	−	59.1301i	0.480057	−	1.92656i
$943$	1.57293	+	4.05635i	0.0512217	+	0.132093i
$944$	−12.5857	+	8.49950i	−0.409629	+	0.276635i
$945$	0.884062			0.0287585
$946$	−1.46984	+	5.89875i	−0.0477886	+	0.191785i
$947$			10.0702i			0.327237i	0.986524	+	0.163619i	$0.0523166\pi$
$947$			10.0702i			0.327237i	−0.986524	+	0.163619i	$0.947683\pi$
$948$	−22.2288	+	41.8349i	−0.721959	+	1.35873i
$949$	−2.44320			−0.0793097
$950$	−2.42693	+	9.73974i	−0.0787400	+	0.315999i
$951$		−	47.8094i		−	1.55032i
$952$	−8.94639	−	8.04850i	−0.289954	−	0.260853i
$953$		−	22.9968i		−	0.744938i	−0.928045	−	0.372469i	$-0.878511\pi$
$953$		−	22.9968i		−	0.744938i	0.928045	−	0.372469i	$-0.121489\pi$
$954$	7.42115	+	1.84919i	0.240268	+	0.0598696i
$955$		−	3.12789i		−	0.101216i
$956$	−0.371588	+	0.699332i	−0.0120180	+	0.0226180i
$957$			6.47046i			0.209160i
$958$	−11.7590	+	47.1914i	−0.379918	+	1.52468i
$959$		−	13.0498i		−	0.421401i
$960$	−2.03892	−	19.2421i	−0.0658060	−	0.621036i
$961$	22.7231			0.733004
$962$	4.47765	+	1.11573i	0.144365	+	0.0359726i
$963$	−39.5253			−1.27369
$964$	2.92030	−	5.49602i	0.0940564	−	0.177015i
$965$		−	19.7240i		−	0.634938i
$966$	5.02033	+	39.7238i	0.161526	+	1.27809i
$967$		−	16.1903i		−	0.520646i	−0.965522	−	0.260323i	$-0.916171\pi$
$967$		−	16.1903i		−	0.520646i	0.965522	−	0.260323i	$-0.0838290\pi$
$968$	8.11877	−	9.02450i	0.260947	−	0.290058i
$969$	−29.9253			−0.961338
$970$	0.459439	−	1.84382i	0.0147517	−	0.0592014i
$971$	56.0221			1.79784			0.898918	−	0.438118i	$-0.144355\pi$
$971$	56.0221			1.79784			0.898918	+	0.438118i	$0.144355\pi$
$972$	−20.3777	+	38.3510i	−0.653614	+	1.23011i
$973$		−	36.9069i		−	1.18318i
$974$	12.0101	+	2.99264i	0.384827	+	0.0958905i
$975$			1.16706i			0.0373757i
$976$	27.1109	−	18.3089i	0.867800	−	0.586052i
$977$		−	27.2869i		−	0.872984i	−0.899708	−	0.436492i	$-0.856221\pi$
$977$		−	27.2869i		−	0.872984i	0.899708	−	0.436492i	$-0.143779\pi$
$978$	−3.33678	+	13.3911i	−0.106698	+	0.428201i
$979$			6.60921i			0.211231i
$980$	0.978481	−	1.84151i	0.0312564	−	0.0588249i
$981$			46.7221i			1.49172i
$982$	−25.6639	−	6.39487i	−0.818967	−	0.204069i
$983$	−49.0064			−1.56306			−0.781531	−	0.623866i	$-0.785561\pi$
$983$	−49.0064			−1.56306			−0.781531	+	0.623866i	$0.785561\pi$
$984$	−4.61382	−	4.15077i	−0.147083	−	0.132322i
$985$			10.6999i			0.340926i
$986$	2.47068	+	0.615640i	0.0786826	+	0.0196060i
$987$	−25.9831			−0.827051
$988$	6.04850	+	3.21385i	0.192428	+	0.102246i
$989$	−2.87768	−	7.42111i	−0.0915050	−	0.235977i
$990$	10.1303	+	2.52424i	0.321961	+	0.0802255i
$991$			7.65834i			0.243275i	0.992575	+	0.121638i	$0.0388146\pi$
$991$			7.65834i			0.243275i	−0.992575	+	0.121638i	$0.961185\pi$
$992$	−5.57702	−	15.2891i	−0.177071	−	0.485430i
$993$	−77.7657			−2.46782
$994$	−37.0622	−	9.23507i	−1.17554	−	0.292919i
$995$		−	21.1502i		−	0.670506i
$996$	−30.7724	+	57.9139i	−0.975061	+	1.83507i
$997$	60.3120			1.91010			0.955050	−	0.296445i	$-0.0958010\pi$
$997$	60.3120			1.91010			0.955050	+	0.296445i	$0.0958010\pi$
$998$	−40.6482	−	10.1286i	−1.28670	−	0.320617i
$999$	2.44945			0.0774971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.e.b.91.17	✓	32
4.3	odd	2	inner	460.2.e.b.91.19	yes	32
23.22	odd	2	inner	460.2.e.b.91.18	yes	32
92.91	even	2	inner	460.2.e.b.91.20	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.e.b.91.17	✓	32	1.1	even	1	trivial
460.2.e.b.91.18	yes	32	23.22	odd	2	inner
460.2.e.b.91.19	yes	32	4.3	odd	2	inner
460.2.e.b.91.20	yes	32	92.91	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.341935 - 1.37225i) q^{2} +2.41873i q^{3} +(-1.76616 - 0.938444i) q^{4} -1.00000i q^{5} +(3.31911 + 0.827049i) q^{6} +2.44077 q^{7} +(-1.89170 + 2.10273i) q^{8} -2.85025 q^{9} +O(q^{10})\)	\(q+(0.341935 - 1.37225i) q^{2} +2.41873i q^{3} +(-1.76616 - 0.938444i) q^{4} -1.00000i q^{5} +(3.31911 + 0.827049i) q^{6} +2.44077 q^{7} +(-1.89170 + 2.10273i) q^{8} -2.85025 q^{9} +(-1.37225 - 0.341935i) q^{10} +2.59002 q^{11} +(2.26984 - 4.27186i) q^{12} -0.482508 q^{13} +(0.834584 - 3.34935i) q^{14} +2.41873 q^{15} +(2.23865 + 3.31489i) q^{16} +1.74316i q^{17} +(-0.974601 + 3.91126i) q^{18} +7.09763 q^{19} +(-0.938444 + 1.76616i) q^{20} +5.90355i q^{21} +(0.885620 - 3.55417i) q^{22} +(1.73388 + 4.47143i) q^{23} +(-5.08594 - 4.57550i) q^{24} -1.00000 q^{25} +(-0.164986 + 0.662123i) q^{26} +0.362207i q^{27} +(-4.31078 - 2.29052i) q^{28} +1.03287 q^{29} +(0.827049 - 3.31911i) q^{30} -2.87696i q^{31} +(5.31434 - 1.93851i) q^{32} +6.26456i q^{33} +(2.39206 + 0.596048i) q^{34} -2.44077i q^{35} +(5.03400 + 2.67480i) q^{36} -6.76257i q^{37} +(2.42693 - 9.73974i) q^{38} -1.16706i q^{39} +(2.10273 + 1.89170i) q^{40} +0.907172 q^{41} +(8.10117 + 2.01863i) q^{42} -1.65967 q^{43} +(-4.57439 - 2.43059i) q^{44} +2.85025i q^{45} +(6.72881 - 0.850391i) q^{46} +4.40127i q^{47} +(-8.01781 + 5.41468i) q^{48} -1.04266 q^{49} +(-0.341935 + 1.37225i) q^{50} -4.21623 q^{51} +(0.852186 + 0.452807i) q^{52} -1.89738i q^{53} +(0.497040 + 0.123851i) q^{54} -2.59002i q^{55} +(-4.61719 + 5.13228i) q^{56} +17.1672i q^{57} +(0.353174 - 1.41736i) q^{58} +3.79671i q^{59} +(-4.27186 - 2.26984i) q^{60} -8.17854i q^{61} +(-3.94792 - 0.983733i) q^{62} -6.95679 q^{63} +(-0.842973 - 7.95546i) q^{64} +0.482508i q^{65} +(8.59656 + 2.14207i) q^{66} -15.6210 q^{67} +(1.63586 - 3.07870i) q^{68} +(-10.8152 + 4.19380i) q^{69} +(-3.34935 - 0.834584i) q^{70} -11.0655i q^{71} +(5.39180 - 5.99331i) q^{72} +5.06355 q^{73} +(-9.27996 - 2.31236i) q^{74} -2.41873i q^{75} +(-12.5355 - 6.66073i) q^{76} +6.32163 q^{77} +(-1.60150 - 0.399057i) q^{78} -9.79312 q^{79} +(3.31489 - 2.23865i) q^{80} -9.42683 q^{81} +(0.310194 - 1.24487i) q^{82} -13.5571 q^{83} +(5.54015 - 10.4266i) q^{84} +1.74316 q^{85} +(-0.567501 + 2.27749i) q^{86} +2.49823i q^{87} +(-4.89953 + 5.44612i) q^{88} +2.55180i q^{89} +(3.91126 + 0.974601i) q^{90} -1.17769 q^{91} +(1.13386 - 9.52441i) q^{92} +6.95858 q^{93} +(6.03965 + 1.50495i) q^{94} -7.09763i q^{95} +(4.68874 + 12.8539i) q^{96} +1.34364i q^{97} +(-0.356523 + 1.43080i) q^{98} -7.38220 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9	\( 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48} - 12 q^{49} - 4 q^{50} + 16 q^{52} + 42 q^{54} - 10 q^{58} - 36 q^{62} - 22 q^{64} - 44 q^{69} - 42 q^{70} - 32 q^{72} - 8 q^{73} - 72 q^{77} + 122 q^{78} - 32 q^{81} + 20 q^{82} - 44 q^{85} + 64 q^{92} + 40 q^{93} - 26 q^{94} + 16 q^{96} + 62 q^{98}+O(q^{100}) \) 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9 + 24 * q^12 - 4 * q^13 + 20 * q^16 - 56 * q^18 - 6 * q^24 - 32 * q^25 + 68 * q^26 + 8 * q^29 - 16 * q^32 + 8 * q^36 + 44 * q^41 - 4 * q^46 - 4 * q^48 - 12 * q^49 - 4 * q^50 + 16 * q^52 + 42 * q^54 - 10 * q^58 - 36 * q^62 - 22 * q^64 - 44 * q^69 - 42 * q^70 - 32 * q^72 - 8 * q^73 - 72 * q^77 + 122 * q^78 - 32 * q^81 + 20 * q^82 - 44 * q^85 + 64 * q^92 + 40 * q^93 - 26 * q^94 + 16 * q^96 + 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more