LMFDB - Embedded newform 351.2.bd.d.188.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(80,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("351.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.bd (of order $12$, degree $4$, 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 88 x^{16} - 6 x^{15} + 48 x^{13} + 1980 x^{12} - 204 x^{11} + 18 x^{10} + 2076 x^{9} + \cdots + 81 $ x^20 + 88x^16 - 6x^15 + 48x^13 + 1980x^12 - 204x^11 + 18x^10 + 2076x^9 + 8020x^8 + 2220x^7 + 792x^6 + 4350x^5 + 10936x^4 + 6648x^3 + 1800x^2 - 540*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.2
Root			$1.03270 + 1.03270i$ of defining polynomial
Character	$\chi$	$=$	351.188
Dual form			351.2.bd.d.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41069 + 0.377994i) q^{2} +(0.115125 - 0.0664674i) q^{4} +(2.86027 + 2.86027i) q^{5} +(0.575104 - 2.14632i) q^{7} +(1.92812 - 1.92812i) q^{8} +O(q^{10})$	\(q+(-1.41069 + 0.377994i) q^{2} +(0.115125 - 0.0664674i) q^{4} +(2.86027 + 2.86027i) q^{5} +(0.575104 - 2.14632i) q^{7} +(1.92812 - 1.92812i) q^{8} +(-5.11614 - 2.95380i) q^{10} +(1.15529 + 4.31160i) q^{11} +(1.47083 - 3.29191i) q^{13} +3.24518i q^{14} +(-2.12410 + 3.67905i) q^{16} +(-2.14016 - 3.70687i) q^{17} +(3.53117 + 0.946174i) q^{19} +(0.519404 + 0.139174i) q^{20} +(-3.25952 - 5.64565i) q^{22} +(-1.43709 + 2.48911i) q^{23} +11.3623i q^{25} +(-0.830565 + 5.19984i) q^{26} +(-0.0764513 - 0.285320i) q^{28} +(5.10882 + 2.94958i) q^{29} +(-4.00290 + 4.00290i) q^{31} +(0.194314 - 0.725192i) q^{32} +(4.42029 + 4.42029i) q^{34} +(7.78401 - 4.49410i) q^{35} +(8.91557 - 2.38892i) q^{37} -5.33905 q^{38} +11.0299 q^{40} +(-2.22987 + 0.597493i) q^{41} +(-2.75162 + 1.58865i) q^{43} +(0.419583 + 0.419583i) q^{44} +(1.08642 - 4.05458i) q^{46} +(-2.44807 + 2.44807i) q^{47} +(1.78625 + 1.03129i) q^{49} +(-4.29490 - 16.0288i) q^{50} +(-0.0494757 - 0.476743i) q^{52} +5.15572i q^{53} +(-9.02790 + 15.6368i) q^{55} +(-3.02948 - 5.24721i) q^{56} +(-8.32191 - 2.22985i) q^{58} +(-9.19205 - 2.46300i) q^{59} +(-4.13769 - 7.16668i) q^{61} +(4.13380 - 7.15994i) q^{62} -7.39992i q^{64} +(13.6227 - 5.20879i) q^{65} +(-1.13626 - 4.24057i) q^{67} +(-0.492772 - 0.284502i) q^{68} +(-9.28210 + 9.28210i) q^{70} +(-0.279146 + 1.04179i) q^{71} +(-7.70808 - 7.70808i) q^{73} +(-11.6741 + 6.74007i) q^{74} +(0.469415 - 0.125779i) q^{76} +9.91846 q^{77} +6.13223 q^{79} +(-16.5986 + 4.44758i) q^{80} +(2.91982 - 1.68576i) q^{82} +(-7.06333 - 7.06333i) q^{83} +(4.48121 - 16.7241i) q^{85} +(3.28119 - 3.28119i) q^{86} +(10.5408 + 6.08573i) q^{88} +(-1.91951 - 7.16369i) q^{89} +(-6.21960 - 5.05005i) q^{91} +0.382078i q^{92} +(2.52812 - 4.37884i) q^{94} +(7.39380 + 12.8064i) q^{95} +(8.40243 + 2.25142i) q^{97} +(-2.90967 - 0.779645i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{5}+O(q^{10}) $ 20 * q - 6 * q^5	$ 20 q - 6 q^{5} - 12 q^{10} - 8 q^{13} + 24 q^{16} + 12 q^{17} - 12 q^{19} - 36 q^{20} + 8 q^{22} + 42 q^{26} + 2 q^{28} + 6 q^{29} - 22 q^{31} + 36 q^{32} - 6 q^{34} + 36 q^{35} + 8 q^{37} - 72 q^{38} - 36 q^{40} - 30 q^{41} - 30 q^{43} - 36 q^{44} - 48 q^{46} - 6 q^{47} + 30 q^{49} - 54 q^{50} + 4 q^{52} - 28 q^{55} + 60 q^{56} + 44 q^{58} - 30 q^{59} - 16 q^{61} + 30 q^{62} + 78 q^{65} + 18 q^{67} - 6 q^{68} + 38 q^{70} + 60 q^{71} + 72 q^{74} - 8 q^{76} + 12 q^{77} - 16 q^{79} - 126 q^{80} + 78 q^{82} - 12 q^{83} + 12 q^{85} - 18 q^{86} - 84 q^{89} + 30 q^{91} - 22 q^{94} + 66 q^{95} + 26 q^{97} - 42 q^{98}+O(q^{100}) $ 20 * q - 6 * q^5 - 12 * q^10 - 8 * q^13 + 24 * q^16 + 12 * q^17 - 12 * q^19 - 36 * q^20 + 8 * q^22 + 42 * q^26 + 2 * q^28 + 6 * q^29 - 22 * q^31 + 36 * q^32 - 6 * q^34 + 36 * q^35 + 8 * q^37 - 72 * q^38 - 36 * q^40 - 30 * q^41 - 30 * q^43 - 36 * q^44 - 48 * q^46 - 6 * q^47 + 30 * q^49 - 54 * q^50 + 4 * q^52 - 28 * q^55 + 60 * q^56 + 44 * q^58 - 30 * q^59 - 16 * q^61 + 30 * q^62 + 78 * q^65 + 18 * q^67 - 6 * q^68 + 38 * q^70 + 60 * q^71 + 72 * q^74 - 8 * q^76 + 12 * q^77 - 16 * q^79 - 126 * q^80 + 78 * q^82 - 12 * q^83 + 12 * q^85 - 18 * q^86 - 84 * q^89 + 30 * q^91 - 22 * q^94 + 66 * q^95 + 26 * q^97 - 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$

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 $

$2$	−1.41069	+	0.377994i	−0.997511	+	0.267282i	−0.720402	−	0.693556i	$-0.756043\pi$
$2$	−1.41069	+	0.377994i	−0.997511	+	0.267282i	−0.277108	+	0.960839i	$0.589376\pi$
$3$		0			0
$3$		0			0
$4$	0.115125	−	0.0664674i	0.0575625	−	0.0332337i
$5$	2.86027	+	2.86027i	1.27915	+	1.27915i	0.941142	+	0.338012i	$0.109754\pi$
$5$	2.86027	+	2.86027i	1.27915	+	1.27915i	0.338012	+	0.941142i	$0.390246\pi$
$6$		0			0
$7$	0.575104	−	2.14632i	0.217369	−	0.811231i	−0.767951	−	0.640509i	$-0.778723\pi$
$7$	0.575104	−	2.14632i	0.217369	−	0.811231i	0.985319	−	0.170722i	$-0.0546100\pi$
$8$	1.92812	−	1.92812i	0.681692	−	0.681692i
$9$		0			0
$10$	−5.11614	−	2.95380i	−1.61786	−	0.934074i
$11$	1.15529	+	4.31160i	0.348333	+	1.29999i	0.888670	+	0.458547i	$0.151630\pi$
$11$	1.15529	+	4.31160i	0.348333	+	1.29999i	−0.540338	+	0.841448i	$0.681704\pi$
$12$		0			0
$13$	1.47083	−	3.29191i	0.407934	−	0.913011i
$13$	1.47083	−	3.29191i	0.407934	−	0.913011i
$14$			3.24518i			0.867311i
$15$		0			0
$16$	−2.12410	+	3.67905i	−0.531025	+	0.919762i
$17$	−2.14016	−	3.70687i	−0.519065	−	0.899048i	−0.999755	−	0.0221565i	$-0.992947\pi$
$17$	−2.14016	−	3.70687i	−0.519065	−	0.899048i	0.480689	−	0.876891i	$-0.340387\pi$
$18$		0			0
$19$	3.53117	+	0.946174i	0.810106	+	0.217067i	0.640016	−	0.768361i	$-0.278928\pi$
$19$	3.53117	+	0.946174i	0.810106	+	0.217067i	0.170090	+	0.985429i	$0.445594\pi$
$20$	0.519404	+	0.139174i	0.116142	+	0.0311202i
$21$		0			0
$22$	−3.25952	−	5.64565i	−0.694931	−	1.20366i
$23$	−1.43709	+	2.48911i	−0.299653	+	0.519015i	−0.976057	−	0.217517i	$-0.930204\pi$
$23$	−1.43709	+	2.48911i	−0.299653	+	0.519015i	0.676403	+	0.736532i	$0.263538\pi$
$24$		0			0
$25$			11.3623i			2.27247i
$26$	−0.830565	+	5.19984i	−0.162887	+	1.01977i
$27$		0			0
$28$	−0.0764513	−	0.285320i	−0.0144479	−	0.0539204i
$29$	5.10882	+	2.94958i	0.948685	+	0.547723i	0.892672	−	0.450707i	$-0.148828\pi$
$29$	5.10882	+	2.94958i	0.948685	+	0.547723i	0.0560127	+	0.998430i	$0.482161\pi$
$30$		0			0
$31$	−4.00290	+	4.00290i	−0.718943	+	0.718943i	−0.968389	−	0.249446i	$-0.919752\pi$
$31$	−4.00290	+	4.00290i	−0.718943	+	0.718943i	0.249446	+	0.968389i	$0.419752\pi$
$32$	0.194314	−	0.725192i	0.0343503	−	0.128197i
$33$		0			0
$34$	4.42029	+	4.42029i	0.758073	+	0.758073i
$35$	7.78401	−	4.49410i	1.31574	−	0.759641i
$36$		0			0
$37$	8.91557	−	2.38892i	1.46571	−	0.392736i	0.564253	−	0.825602i	$-0.309164\pi$
$37$	8.91557	−	2.38892i	1.46571	−	0.392736i	0.901458	+	0.432866i	$0.142498\pi$
$38$	−5.33905			−0.866107
$39$		0			0
$40$	11.0299			1.74398
$41$	−2.22987	+	0.597493i	−0.348248	+	0.0933127i	−0.428703	−	0.903446i	$-0.641029\pi$
$41$	−2.22987	+	0.597493i	−0.348248	+	0.0933127i	0.0804552	+	0.996758i	$0.474363\pi$
$42$		0			0
$43$	−2.75162	+	1.58865i	−0.419618	+	0.242266i	−0.694914	−	0.719093i	$-0.744557\pi$
$43$	−2.75162	+	1.58865i	−0.419618	+	0.242266i	0.275296	+	0.961360i	$0.411224\pi$
$44$	0.419583	+	0.419583i	0.0632545	+	0.0632545i
$45$		0			0
$46$	1.08642	−	4.05458i	0.160184	−	0.597815i
$47$	−2.44807	+	2.44807i	−0.357088	+	0.357088i	−0.862738	−	0.505650i	$-0.831253\pi$
$47$	−2.44807	+	2.44807i	−0.357088	+	0.357088i	0.505650	+	0.862738i	$0.331253\pi$
$48$		0			0
$49$	1.78625	+	1.03129i	0.255179	+	0.147327i
$50$	−4.29490	−	16.0288i	−0.607390	−	2.26681i
$51$		0			0
$52$	−0.0494757	−	0.476743i	−0.00686104	−	0.0661123i
$53$			5.15572i			0.708193i	0.935209	+	0.354096i	$0.115211\pi$
$53$			5.15572i			0.708193i	−0.935209	+	0.354096i	$0.884789\pi$
$54$		0			0
$55$	−9.02790	+	15.6368i	−1.21732	+	2.10846i
$56$	−3.02948	−	5.24721i	−0.404831	−	0.701188i
$57$		0			0
$58$	−8.32191	−	2.22985i	−1.09272	−	0.292793i
$59$	−9.19205	−	2.46300i	−1.19670	−	0.320656i	−0.395171	−	0.918607i	$-0.629315\pi$
$59$	−9.19205	−	2.46300i	−1.19670	−	0.320656i	−0.801532	+	0.597952i	$0.795981\pi$
$60$		0			0
$61$	−4.13769	−	7.16668i	−0.529777	−	0.917600i	−0.999397	−	0.0347314i	$-0.988942\pi$
$61$	−4.13769	−	7.16668i	−0.529777	−	0.917600i	0.469620	−	0.882869i	$-0.344391\pi$
$62$	4.13380	−	7.15994i	0.524993	−	0.909314i
$63$		0			0
$64$		−	7.39992i		−	0.924990i
$65$	13.6227	−	5.20879i	1.68969	−	0.646071i
$66$		0			0
$67$	−1.13626	−	4.24057i	−0.138816	−	0.518068i	−0.999953	−	0.00969513i	$-0.996914\pi$
$67$	−1.13626	−	4.24057i	−0.138816	−	0.518068i	0.861137	−	0.508373i	$-0.169753\pi$
$68$	−0.492772	−	0.284502i	−0.0597574	−	0.0345009i
$69$		0			0
$70$	−9.28210	+	9.28210i	−1.10942	+	1.10942i
$71$	−0.279146	+	1.04179i	−0.0331286	+	0.123638i	−0.980510	−	0.196470i	$-0.937052\pi$
$71$	−0.279146	+	1.04179i	−0.0331286	+	0.123638i	0.947381	+	0.320107i	$0.103719\pi$
$72$		0			0
$73$	−7.70808	−	7.70808i	−0.902162	−	0.902162i	0.0934609	−	0.995623i	$-0.470207\pi$
$73$	−7.70808	−	7.70808i	−0.902162	−	0.902162i	−0.995623	+	0.0934609i	$0.970207\pi$
$74$	−11.6741	+	6.74007i	−1.35709	+	0.783517i
$75$		0			0
$76$	0.469415	−	0.125779i	0.0538456	−	0.0144279i
$77$	9.91846			1.13031
$78$		0			0
$79$	6.13223			0.689929			0.344965	−	0.938616i	$-0.387891\pi$
$79$	6.13223			0.689929			0.344965	+	0.938616i	$0.387891\pi$
$80$	−16.5986	+	4.44758i	−1.85578	+	0.497254i
$81$		0			0
$82$	2.91982	−	1.68576i	0.322440	−	0.186161i
$83$	−7.06333	−	7.06333i	−0.775301	−	0.775301i	0.203726	−	0.979028i	$-0.434695\pi$
$83$	−7.06333	−	7.06333i	−0.775301	−	0.775301i	−0.979028	+	0.203726i	$0.934695\pi$
$84$		0			0
$85$	4.48121	−	16.7241i	0.486056	−	1.81398i
$86$	3.28119	−	3.28119i	0.353820	−	0.353820i
$87$		0			0
$88$	10.5408	+	6.08573i	1.12365	+	0.648741i
$89$	−1.91951	−	7.16369i	−0.203467	−	0.759350i	−0.989911	−	0.141688i	$-0.954747\pi$
$89$	−1.91951	−	7.16369i	−0.203467	−	0.759350i	0.786444	−	0.617661i	$-0.211920\pi$
$90$		0			0
$91$	−6.21960	−	5.05005i	−0.651991	−	0.529389i
$92$			0.382078i			0.0398344i
$93$		0			0
$94$	2.52812	−	4.37884i	0.260756	−	0.451642i
$95$	7.39380	+	12.8064i	0.758588	+	1.31391i
$96$		0			0
$97$	8.40243	+	2.25142i	0.853137	+	0.228597i	0.658782	−	0.752334i	$-0.271072\pi$
$97$	8.40243	+	2.25142i	0.853137	+	0.228597i	0.194355	+	0.980931i	$0.437739\pi$
$98$	−2.90967	−	0.779645i	−0.293921	−	0.0787560i
$99$		0			0
$100$	0.755225	+	1.30809i	0.0755225	+	0.130809i
$101$	6.90247	−	11.9554i	0.686821	−	1.18961i	−0.286039	−	0.958218i	$-0.592339\pi$
$101$	6.90247	−	11.9554i	0.686821	−	1.18961i	0.972861	−	0.231391i	$-0.0743278\pi$
$102$		0			0
$103$			0.612148i			0.0603168i	0.999545	+	0.0301584i	$0.00960117\pi$
$103$			0.612148i			0.0603168i	−0.999545	+	0.0301584i	$0.990399\pi$
$104$	−3.51126	−	9.18311i	−0.344307	−	0.900478i
$105$		0			0
$106$	−1.94883	−	7.27314i	−0.189287	−	0.706430i
$107$	−3.54408	−	2.04617i	−0.342619	−	0.197811i	0.318811	−	0.947818i	$-0.396717\pi$
$107$	−3.54408	−	2.04617i	−0.342619	−	0.197811i	−0.661430	+	0.750007i	$0.730050\pi$
$108$		0			0
$109$	5.22391	−	5.22391i	0.500360	−	0.500360i	−0.411190	−	0.911550i	$-0.634887\pi$
$109$	5.22391	−	5.22391i	0.500360	−	0.500360i	0.911550	+	0.411190i	$0.134887\pi$
$110$	6.82499	−	25.4712i	0.650737	−	2.42858i
$111$		0			0
$112$	6.67482	+	6.67482i	0.630711	+	0.630711i
$113$	0.467679	−	0.270015i	0.0439956	−	0.0254009i	−0.477841	−	0.878446i	$-0.658580\pi$
$113$	0.467679	−	0.270015i	0.0439956	−	0.0254009i	0.521836	+	0.853046i	$0.325247\pi$
$114$		0			0
$115$	−11.2300	+	3.00907i	−1.04720	+	0.280597i
$116$	0.784204			0.0728115
$117$		0			0
$118$	13.8982			1.27943
$119$	−9.18692	+	2.46163i	−0.842164	+	0.225657i
$120$		0			0
$121$	−7.72889	+	4.46227i	−0.702626	+	0.405661i
$122$	8.54597	+	8.54597i	0.773716	+	0.773716i
$123$		0			0
$124$	−0.194771	+	0.726897i	−0.0174910	+	0.0652772i
$125$	−18.1980	+	18.1980i	−1.62768	+	1.62768i
$126$		0			0
$127$	7.11785	+	4.10949i	0.631607	+	0.364659i	0.781374	−	0.624063i	$-0.214519\pi$
$127$	7.11785	+	4.10949i	0.631607	+	0.364659i	−0.149767	+	0.988721i	$0.547852\pi$
$128$	3.18576	+	11.8894i	0.281584	+	1.05088i
$129$		0			0
$130$	−17.2486	+	12.4973i	−1.51280	+	1.09609i
$131$			9.99328i			0.873117i	0.899676	+	0.436559i	$0.143803\pi$
$131$			9.99328i			0.873117i	−0.899676	+	0.436559i	$0.856197\pi$
$132$		0			0
$133$	4.06158	−	7.03486i	0.352183	−	0.609999i
$134$	3.20582	+	5.55264i	0.276941	+	0.479675i
$135$		0			0
$136$	−11.2738	−	3.02079i	−0.966716	−	0.259031i
$137$	9.83483	+	2.63523i	0.840246	+	0.225143i	0.653179	−	0.757204i	$-0.273435\pi$
$137$	9.83483	+	2.63523i	0.840246	+	0.225143i	0.187067	+	0.982347i	$0.440102\pi$
$138$		0			0
$139$	1.53975	+	2.66692i	0.130600	+	0.226205i	0.923908	−	0.382615i	$-0.124976\pi$
$139$	1.53975	+	2.66692i	0.130600	+	0.226205i	−0.793308	+	0.608820i	$0.791643\pi$
$140$	0.597422	−	1.03477i	0.0504914	−	0.0874536i
$141$		0			0
$142$		−	1.57516i		−	0.132184i
$143$	15.8926	+	2.53851i	1.32901	+	0.212281i
$144$		0			0
$145$	6.17603	+	23.0493i	0.512891	+	1.91414i
$146$	13.7873	+	7.96012i	1.14105	+	0.658784i
$147$		0			0
$148$	0.867619	−	0.867619i	0.0713179	−	0.0713179i
$149$	−0.460818	+	1.71979i	−0.0377516	+	0.140891i	−0.982229	−	0.187684i	$-0.939902\pi$
$149$	−0.460818	+	1.71979i	−0.0377516	+	0.140891i	0.944478	+	0.328575i	$0.106568\pi$
$150$		0			0
$151$	−13.8313	−	13.8313i	−1.12558	−	1.12558i	−0.990888	−	0.134689i	$-0.956997\pi$
$151$	−13.8313	−	13.8313i	−1.12558	−	1.12558i	−0.134689	−	0.990888i	$-0.543003\pi$
$152$	8.63284	−	4.98417i	0.700216	−	0.404270i
$153$		0			0
$154$	−13.9919	+	3.74912i	−1.12750	+	0.302113i
$155$	−22.8988			−1.83928
$156$		0			0
$157$	−7.12683			−0.568783			−0.284392	−	0.958708i	$-0.591792\pi$
$157$	−7.12683			−0.568783			−0.284392	+	0.958708i	$0.591792\pi$
$158$	−8.65069	+	2.31795i	−0.688212	+	0.184406i
$159$		0			0
$160$	2.63004	−	1.51845i	0.207923	−	0.120044i
$161$	4.51594	+	4.51594i	0.355906	+	0.355906i
$162$		0			0
$163$	2.25091	−	8.40050i	0.176305	−	0.657978i	−0.820021	−	0.572333i	$-0.806038\pi$
$163$	2.25091	−	8.40050i	0.176305	−	0.657978i	0.996326	−	0.0856444i	$-0.0272949\pi$
$164$	−0.217000	+	0.217000i	−0.0169449	+	0.0169449i
$165$		0			0
$166$	12.6341	+	7.29430i	0.980596	+	0.566147i
$167$	−5.60021	−	20.9003i	−0.433357	−	1.61731i	−0.744968	−	0.667100i	$-0.767535\pi$
$167$	−5.60021	−	20.9003i	−0.433357	−	1.61731i	0.311611	−	0.950210i	$-0.399131\pi$
$168$		0			0
$169$	−8.67333	−	9.68366i	−0.667179	−	0.744897i
$170$			25.2865i			1.93938i
$171$		0			0
$172$	−0.211187	+	0.365786i	−0.0161028	+	0.0278909i
$173$	−3.61344	−	6.25867i	−0.274725	−	0.475838i	0.695341	−	0.718680i	$-0.255254\pi$
$173$	−3.61344	−	6.25867i	−0.274725	−	0.475838i	−0.970066	+	0.242843i	$0.921920\pi$
$174$		0			0
$175$	24.3872	+	6.53452i	1.84350	+	0.493963i
$176$	−18.3165	−	4.90789i	−1.38066	−	0.369946i
$177$		0			0
$178$	5.41567	+	9.38021i	0.405921	+	0.703076i
$179$	2.28409	−	3.95615i	0.170721	−	0.295697i	−0.767951	−	0.640508i	$-0.778724\pi$
$179$	2.28409	−	3.95615i	0.170721	−	0.295697i	0.938672	+	0.344811i	$0.112057\pi$
$180$		0			0
$181$			24.4811i			1.81967i	0.414974	+	0.909833i	$0.363791\pi$
$181$			24.4811i			1.81967i	−0.414974	+	0.909833i	$0.636209\pi$
$182$	10.6828	+	4.77310i	0.791864	+	0.353806i
$183$		0			0
$184$	2.02842	+	7.57016i	0.149537	+	0.558080i
$185$	32.3340	+	18.6680i	2.37724	+	1.37250i
$186$		0			0
$187$	13.5100	−	13.5100i	0.987950	−	0.987950i
$188$	−0.119117	+	0.444551i	−0.00868751	+	0.0324222i
$189$		0			0
$190$	−15.2711	−	15.2711i	−1.10788	−	1.10788i
$191$	−5.37981	+	3.10604i	−0.389270	+	0.224745i	−0.681844	−	0.731498i	$-0.738822\pi$
$191$	−5.37981	+	3.10604i	−0.389270	+	0.224745i	0.292574	+	0.956243i	$0.405488\pi$
$192$		0			0
$193$	−11.7367	+	3.14483i	−0.844824	+	0.226370i	−0.655170	−	0.755481i	$-0.727403\pi$
$193$	−11.7367	+	3.14483i	−0.844824	+	0.226370i	−0.189654	+	0.981851i	$0.560737\pi$
$194$	−12.7043			−0.912114
$195$		0			0
$196$	0.274189			0.0195849
$197$	14.7635	−	3.95586i	1.05185	−	0.281844i	0.308837	−	0.951115i	$-0.400060\pi$
$197$	14.7635	−	3.95586i	1.05185	−	0.281844i	0.743018	+	0.669272i	$0.233394\pi$
$198$		0			0
$199$	19.6220	−	11.3288i	1.39096	−	0.803074i	0.397543	−	0.917584i	$-0.369863\pi$
$199$	19.6220	−	11.3288i	1.39096	−	0.803074i	0.993422	+	0.114510i	$0.0365297\pi$
$200$	21.9079	+	21.9079i	1.54912	+	1.54912i
$201$		0			0
$202$	−5.21818	+	19.4745i	−0.367150	+	1.37022i
$203$	9.26884	−	9.26884i	0.650545	−	0.650545i
$204$		0			0
$205$	−8.08704	−	4.66906i	−0.564823	−	0.326101i
$206$	−0.231388	−	0.863553i	−0.0161216	−	0.0601666i
$207$		0			0
$208$	8.98690	+	12.4036i	0.623130	+	0.860034i
$209$			16.3181i			1.12875i
$210$		0			0
$211$	0.217991	−	0.377571i	0.0150071	−	0.0259931i	−0.858424	−	0.512940i	$-0.828556\pi$
$211$	0.217991	−	0.377571i	0.0150071	−	0.0259931i	0.873431	+	0.486947i	$0.161890\pi$
$212$	0.342687	+	0.593552i	0.0235359	+	0.0407653i
$213$		0			0
$214$	5.77305	+	1.54688i	0.394638	+	0.105743i
$215$	−12.4144	−	3.32642i	−0.846652	−	0.226860i
$216$		0			0
$217$	6.28941	+	10.8936i	0.426953	+	0.739505i
$218$	−5.39473	+	9.34395i	−0.365377	+	0.632852i
$219$		0			0
$220$			2.40025i			0.161824i
$221$	−15.3505	+	1.59305i	−1.03259	+	0.107160i
$222$		0			0
$223$	1.18517	+	4.42310i	0.0793646	+	0.296193i	0.994187	−	0.107663i	$-0.0343366\pi$
$223$	1.18517	+	4.42310i	0.0793646	+	0.296193i	−0.914823	+	0.403855i	$0.867670\pi$
$224$	−1.44474	−	0.834121i	−0.0965307	−	0.0557320i
$225$		0			0
$226$	−0.557688	+	0.557688i	−0.0370969	+	0.0370969i
$227$	1.05544	−	3.93894i	0.0700517	−	0.261437i	−0.922014	−	0.387156i	$-0.873457\pi$
$227$	1.05544	−	3.93894i	0.0700517	−	0.261437i	0.992066	+	0.125720i	$0.0401240\pi$
$228$		0			0
$229$	−18.1451	−	18.1451i	−1.19906	−	1.19906i	−0.974447	−	0.224615i	$-0.927887\pi$
$229$	−18.1451	−	18.1451i	−1.19906	−	1.19906i	−0.224615	−	0.974447i	$-0.572113\pi$
$230$	14.7047	−	8.48974i	0.969597	−	0.559797i
$231$		0			0
$232$	15.5375	−	4.16327i	1.02009	−	0.273332i
$233$	7.55312			0.494822			0.247411	−	0.968911i	$-0.420420\pi$
$233$	7.55312			0.494822			0.247411	+	0.968911i	$0.420420\pi$
$234$		0			0
$235$	−14.0043			−0.913541
$236$	−1.22194	+	0.327419i	−0.0795418	+	0.0213132i
$237$		0			0
$238$	12.0295	−	6.94521i	0.779753	−	0.450191i
$239$	−1.60180	−	1.60180i	−0.103612	−	0.103612i	0.653400	−	0.757012i	$-0.273342\pi$
$239$	−1.60180	−	1.60180i	−0.103612	−	0.103612i	−0.757012	+	0.653400i	$0.773342\pi$
$240$		0			0
$241$	−1.45284	+	5.42207i	−0.0935856	+	0.349266i	−0.996801	−	0.0799209i	$-0.974533\pi$
$241$	−1.45284	+	5.42207i	−0.0935856	+	0.349266i	0.903216	+	0.429187i	$0.141200\pi$
$242$	9.21637	−	9.21637i	0.592451	−	0.592451i
$243$		0			0
$244$	−0.952702	−	0.550043i	−0.0609905	−	0.0352129i
$245$	2.15939	+	8.05894i	0.137958	+	0.514867i
$246$		0			0
$247$	8.30846	−	10.2326i	0.528655	−	0.651087i
$248$			15.4361i			0.980195i
$249$		0			0
$250$	18.7931	−	32.5506i	1.18858	−	2.05868i
$251$	−10.0864	−	17.4702i	−0.636648	−	1.10271i	−0.986163	−	0.165776i	$-0.946987\pi$
$251$	−10.0864	−	17.4702i	−0.636648	−	1.10271i	0.349516	−	0.936931i	$-0.386346\pi$
$252$		0			0
$253$	−12.3923	−	3.32050i	−0.779096	−	0.208758i
$254$	−11.5945	−	3.10673i	−0.727502	−	0.194934i
$255$		0			0
$256$	−1.58833	−	2.75106i	−0.0992704	−	0.171941i
$257$	6.32573	−	10.9565i	0.394588	−	0.683447i	−0.598460	−	0.801152i	$-0.704221\pi$
$257$	6.32573	−	10.9565i	0.394588	−	0.683447i	0.993049	+	0.117706i	$0.0375539\pi$
$258$		0			0
$259$		−	20.5095i		−	1.27440i
$260$	1.22210	−	1.50513i	0.0757915	−	0.0933442i
$261$		0			0
$262$	−3.77740	−	14.0975i	−0.233369	−	0.870944i
$263$	−21.5291	−	12.4299i	−1.32754	−	0.766458i	−0.342625	−	0.939472i	$-0.611316\pi$
$263$	−21.5291	−	12.4299i	−1.32754	−	0.766458i	−0.984919	+	0.173014i	$0.944649\pi$
$264$		0			0
$265$	−14.7468	+	14.7468i	−0.905887	+	0.905887i
$266$	−3.07050	+	11.4593i	−0.188265	+	0.702613i
$267$		0			0
$268$	−0.412671	−	0.412671i	−0.0252079	−	0.0252079i
$269$	−4.13082	+	2.38493i	−0.251860	+	0.145412i	−0.620616	−	0.784115i	$-0.713117\pi$
$269$	−4.13082	+	2.38493i	−0.251860	+	0.145412i	0.368755	+	0.929526i	$0.379784\pi$
$270$		0			0
$271$	−29.0155	+	7.77469i	−1.76257	+	0.472279i	−0.987234	−	0.159274i	$-0.949085\pi$
$271$	−29.0155	+	7.77469i	−1.76257	+	0.472279i	−0.775333	+	0.631552i	$0.782418\pi$
$272$	18.1837			1.10255
$273$		0			0
$274$	−14.8700			−0.898331
$275$	−48.9898	+	13.1268i	−2.95420	+	0.791575i
$276$		0			0
$277$	−2.95845	+	1.70806i	−0.177756	+	0.102628i	−0.586238	−	0.810139i	$-0.699392\pi$
$277$	−2.95845	+	1.70806i	−0.177756	+	0.102628i	0.408482	+	0.912766i	$0.366058\pi$
$278$	−3.18019	−	3.18019i	−0.190735	−	0.190735i
$279$		0			0
$280$	6.34333	−	23.6736i	0.379086	−	1.41477i
$281$	2.01573	−	2.01573i	0.120249	−	0.120249i	−0.644422	−	0.764670i	$-0.722902\pi$
$281$	2.01573	−	2.01573i	0.120249	−	0.120249i	0.764670	+	0.644422i	$0.222902\pi$
$282$		0			0
$283$	4.93733	+	2.85057i	0.293494	+	0.169449i	0.639516	−	0.768777i	$-0.279135\pi$
$283$	4.93733	+	2.85057i	0.293494	+	0.169449i	−0.346023	+	0.938226i	$0.612468\pi$
$284$	0.0371083	+	0.138490i	0.00220197	+	0.00821787i
$285$		0			0
$286$	−23.3791	+	2.42625i	−1.38244	+	0.143467i
$287$			5.12963i			0.302793i
$288$		0			0
$289$	−0.660581	+	1.14416i	−0.0388577	+	0.0673035i
$290$	−17.4250	−	30.1809i	−1.02323	−	1.77228i
$291$		0			0
$292$	−1.39973	−	0.375056i	−0.0819128	−	0.0219485i
$293$	3.79967	+	1.01812i	0.221979	+	0.0594791i	0.368094	−	0.929788i	$-0.380010\pi$
$293$	3.79967	+	1.01812i	0.221979	+	0.0594791i	−0.146115	+	0.989268i	$0.546677\pi$
$294$		0			0
$295$	−19.2469	−	33.3367i	−1.12060	−	1.94094i
$296$	12.5841	−	21.7964i	0.731439	−	1.26689i
$297$		0			0
$298$		−	2.60029i		−	0.150631i
$299$	6.08021	+	8.39181i	0.351628	+	0.485311i
$300$		0			0
$301$	1.82727	+	6.81948i	0.105322	+	0.393068i
$302$	24.7399	+	14.2836i	1.42362	+	0.821928i
$303$		0			0
$304$	−10.9816	+	10.9816i	−0.629836	+	0.629836i
$305$	8.66376	−	32.3336i	0.496086	−	1.85142i
$306$		0			0
$307$	18.8281	+	18.8281i	1.07458	+	1.07458i	0.996985	+	0.0775908i	$0.0247228\pi$
$307$	18.8281	+	18.8281i	1.07458	+	1.07458i	0.0775908	+	0.996985i	$0.475277\pi$
$308$	1.14186	−	0.659254i	0.0650636	−	0.0375645i
$309$		0			0
$310$	32.3032	−	8.65562i	1.83470	−	0.491606i
$311$	1.93734			0.109856			0.0549281	−	0.998490i	$-0.482507\pi$
$311$	1.93734			0.109856			0.0549281	+	0.998490i	$0.482507\pi$
$312$		0			0
$313$	−18.7914			−1.06215			−0.531076	−	0.847324i	$-0.678212\pi$
$313$	−18.7914			−1.06215			−0.531076	+	0.847324i	$0.678212\pi$
$314$	10.0538	−	2.69390i	0.567367	−	0.152026i
$315$		0			0
$316$	0.705972	−	0.407593i	0.0397140	−	0.0229289i
$317$	−7.48853	−	7.48853i	−0.420598	−	0.420598i	0.464812	−	0.885410i	$-0.346122\pi$
$317$	−7.48853	−	7.48853i	−0.420598	−	0.420598i	−0.885410	+	0.464812i	$0.846122\pi$
$318$		0			0
$319$	−6.81523	+	25.4348i	−0.381580	+	1.42408i
$320$	21.1658	−	21.1658i	1.18320	−	1.18320i
$321$		0			0
$322$	−8.07760	−	4.66360i	−0.450147	−	0.259893i
$323$	−4.04993	−	15.1145i	−0.225344	−	0.840996i
$324$		0			0
$325$	37.4038	+	16.7120i	2.07479	+	0.927018i
$326$			12.7014i			0.703463i
$327$		0			0
$328$	−3.14742	+	5.45149i	−0.173787	+	0.301008i
$329$	3.84644	+	6.66223i	0.212061	+	0.367301i
$330$		0			0
$331$	30.9421	+	8.29091i	1.70073	+	0.455710i	0.973124	−	0.230283i	$-0.0739652\pi$
$331$	30.9421	+	8.29091i	1.70073	+	0.455710i	0.727608	+	0.685993i	$0.240632\pi$
$332$	−1.28265	−	0.343684i	−0.0703944	−	0.0188621i
$333$		0			0
$334$	15.8003	+	27.3670i	0.864556	+	1.49746i
$335$	8.87918	−	15.3792i	0.485122	−	0.840255i
$336$		0			0
$337$		−	1.28855i		−	0.0701916i	−0.999384	−	0.0350958i	$-0.988826\pi$
$337$		−	1.28855i		−	0.0701916i	0.999384	−	0.0350958i	$-0.0111736\pi$
$338$	15.8958	+	10.3822i	0.864616	+	0.564718i
$339$		0			0
$340$	−0.595709	−	2.22322i	−0.0323069	−	0.120571i
$341$	−21.8834	−	12.6344i	−1.18505	−	0.684191i
$342$		0			0
$343$	14.2392	−	14.2392i	0.768847	−	0.768847i
$344$	−2.24234	+	8.36854i	−0.120899	+	0.451201i
$345$		0			0
$346$	7.46320	+	7.46320i	0.401224	+	0.401224i
$347$	−21.5811	+	12.4599i	−1.15854	+	0.668881i	−0.950953	−	0.309337i	$-0.899893\pi$
$347$	−21.5811	+	12.4599i	−1.15854	+	0.668881i	−0.207583	+	0.978217i	$0.566560\pi$
$348$		0			0
$349$	29.5349	−	7.91385i	1.58097	−	0.423618i	0.641741	−	0.766922i	$-0.278212\pi$
$349$	29.5349	−	7.91385i	1.58097	−	0.423618i	0.939225	+	0.343303i	$0.111546\pi$
$350$	−36.8728			−1.97094
$351$		0			0
$352$	3.35122			0.178621
$353$	−30.6438	+	8.21097i	−1.63100	+	0.437026i	−0.954208	−	0.299145i	$-0.903299\pi$
$353$	−30.6438	+	8.21097i	−1.63100	+	0.437026i	−0.676796	+	0.736171i	$0.736632\pi$
$354$		0			0
$355$	−3.77824	+	2.18137i	−0.200528	+	0.115775i
$356$	−0.697135	−	0.697135i	−0.0369481	−	0.0369481i
$357$		0			0
$358$	−1.72674	+	6.44429i	−0.0912611	+	0.340591i
$359$	−25.9686	+	25.9686i	−1.37057	+	1.37057i	−0.510976	+	0.859595i	$0.670716\pi$
$359$	−25.9686	+	25.9686i	−1.37057	+	1.37057i	−0.859595	+	0.510976i	$0.829284\pi$
$360$		0			0
$361$	−4.88057	−	2.81780i	−0.256872	−	0.148305i
$362$	−9.25371	−	34.5353i	−0.486364	−	1.81514i
$363$		0			0
$364$	−1.05169	−	0.167986i	−0.0551238	−	0.00880486i
$365$		−	44.0944i		−	2.30801i
$366$		0			0
$367$	−7.20126	+	12.4729i	−0.375903	+	0.651082i	−0.990462	−	0.137788i	$-0.956001\pi$
$367$	−7.20126	+	12.4729i	−0.375903	+	0.651082i	0.614559	+	0.788871i	$0.289334\pi$
$368$	−6.10503	−	10.5742i	−0.318247	−	0.551219i
$369$		0			0
$370$	−52.6697	−	14.1128i	−2.73817	−	0.733689i
$371$	11.0658	+	2.96507i	0.574508	+	0.153939i
$372$		0			0
$373$	3.83661	+	6.64521i	0.198652	+	0.344076i	0.948092	−	0.317997i	$-0.103010\pi$
$373$	3.83661	+	6.64521i	0.198652	+	0.344076i	−0.749439	+	0.662073i	$0.769677\pi$
$374$	−13.9518	+	24.1652i	−0.721429	+	1.24955i
$375$		0			0
$376$			9.44034i			0.486848i
$377$	17.2240	−	12.4795i	0.887079	−	0.642725i
$378$		0			0
$379$	3.21024	+	11.9808i	0.164899	+	0.615411i	0.998053	+	0.0623705i	$0.0198660\pi$
$379$	3.21024	+	11.9808i	0.164899	+	0.615411i	−0.833154	+	0.553041i	$0.813467\pi$
$380$	1.70242	+	0.982893i	0.0873323	+	0.0504213i
$381$		0			0
$382$	6.41520	−	6.41520i	0.328230	−	0.328230i
$383$	4.04634	−	15.1012i	0.206759	−	0.771633i	−0.782148	−	0.623093i	$-0.785876\pi$
$383$	4.04634	−	15.1012i	0.206759	−	0.771633i	0.988906	−	0.148540i	$-0.0474575\pi$
$384$		0			0
$385$	28.3695	+	28.3695i	1.44584	+	1.44584i
$386$	15.3681	−	8.87279i	0.782216	−	0.451613i
$387$		0			0
$388$	1.11698	−	0.299293i	0.0567058	−	0.0151943i
$389$	12.2648			0.621852			0.310926	−	0.950434i	$-0.399361\pi$
$389$	12.2648			0.621852			0.310926	+	0.950434i	$0.399361\pi$
$390$		0			0
$391$	12.3024			0.622159
$392$	5.43255	−	1.45565i	0.274385	−	0.0735213i
$393$		0			0
$394$	−19.3315	+	11.1610i	−0.973904	+	0.562284i
$395$	17.5399	+	17.5399i	0.882526	+	0.882526i
$396$		0			0
$397$	2.37885	−	8.87800i	0.119391	−	0.445574i	−0.880187	−	0.474628i	$-0.842583\pi$
$397$	2.37885	−	8.87800i	0.119391	−	0.445574i	0.999578	+	0.0290536i	$0.00924934\pi$
$398$	−23.3984	+	23.3984i	−1.17286	+	1.17286i
$399$		0			0
$400$	−41.8026	−	24.1347i	−2.09013	−	1.20674i
$401$	−6.40341	−	23.8979i	−0.319771	−	1.19340i	−0.919465	−	0.393173i	$-0.871377\pi$
$401$	−6.40341	−	23.8979i	−0.319771	−	1.19340i	0.599693	−	0.800230i	$-0.295289\pi$
$402$		0			0
$403$	7.28961	+	19.0648i	0.363121	+	0.949684i
$404$		−	1.83516i		−	0.0913024i
$405$		0			0
$406$	−9.57192	+	16.5790i	−0.475046	+	0.822804i
$407$	20.6001	+	35.6804i	1.02111	+	1.76861i
$408$		0			0
$409$	3.11794	+	0.835449i	0.154172	+	0.0413103i	0.335080	−	0.942190i	$-0.391237\pi$
$409$	3.11794	+	0.835449i	0.154172	+	0.0413103i	−0.180907	+	0.983500i	$0.557903\pi$
$410$	13.1732	+	3.52975i	0.650578	+	0.174322i
$411$		0			0
$412$	0.0406879	+	0.0704735i	0.00200455	+	0.00347198i
$413$	−10.5728	+	18.3126i	−0.520252	+	0.901103i
$414$		0			0
$415$		−	40.4061i		−	1.98346i
$416$	−2.10146	−	1.70630i	−0.103033	−	0.0836581i
$417$		0			0
$418$	−6.16814	−	23.0198i	−0.301693	−	1.12594i
$419$	−1.15611	−	0.667483i	−0.0564799	−	0.0326087i	0.471494	−	0.881869i	$-0.343715\pi$
$419$	−1.15611	−	0.667483i	−0.0564799	−	0.0326087i	−0.527974	+	0.849261i	$0.677048\pi$
$420$		0			0
$421$	−11.5788	+	11.5788i	−0.564318	+	0.564318i	−0.930531	−	0.366213i	$-0.880654\pi$
$421$	−11.5788	+	11.5788i	−0.564318	+	0.564318i	0.366213	+	0.930531i	$0.380654\pi$
$422$	−0.164799	+	0.615037i	−0.00802227	+	0.0299395i
$423$		0			0
$424$	9.94083	+	9.94083i	0.482769	+	0.482769i
$425$	42.1187	−	24.3172i	2.04306	−	1.17956i
$426$		0			0
$427$	−17.7616	+	4.75920i	−0.859543	+	0.230314i
$428$	−0.544016			−0.0262960
$429$		0			0
$430$	18.7702			0.905180
$431$	−8.56581	+	2.29520i	−0.412601	+	0.110556i	−0.459147	−	0.888360i	$-0.651845\pi$
$431$	−8.56581	+	2.29520i	−0.412601	+	0.110556i	0.0465468	+	0.998916i	$0.485178\pi$
$432$		0			0
$433$	−26.2040	+	15.1289i	−1.25928	+	0.727047i	−0.972935	−	0.231079i	$-0.925774\pi$
$433$	−26.2040	+	15.1289i	−1.25928	+	0.727047i	−0.286347	+	0.958126i	$0.592441\pi$
$434$	−12.9901	−	12.9901i	−0.623547	−	0.623547i
$435$		0			0
$436$	0.254183	−	0.948622i	0.0121731	−	0.0454308i
$437$	−7.42973	+	7.42973i	−0.355412	+	0.355412i
$438$		0			0
$439$	6.48134	+	3.74201i	0.309338	+	0.178596i	0.646630	−	0.762804i	$-0.276178\pi$
$439$	6.48134	+	3.74201i	0.309338	+	0.178596i	−0.337292	+	0.941400i	$0.609511\pi$
$440$	12.7427	+	47.5564i	0.607484	+	2.26716i
$441$		0			0
$442$	21.0527	−	8.04970i	1.00137	−	0.382885i
$443$		−	19.3969i		−	0.921574i	−0.887511	−	0.460787i	$-0.847567\pi$
$443$		−	19.3969i		−	0.921574i	0.887511	−	0.460787i	$-0.152433\pi$
$444$		0			0
$445$	14.9998	−	25.9804i	0.711059	−	1.23159i
$446$	−3.34381	−	5.79165i	−0.158334	−	0.274243i
$447$		0			0
$448$	−15.8826	−	4.25572i	−0.750381	−	0.201064i
$449$	8.28037	+	2.21872i	0.390775	+	0.104708i	0.448856	−	0.893604i	$-0.351832\pi$
$449$	8.28037	+	2.21872i	0.390775	+	0.104708i	−0.0580812	+	0.998312i	$0.518498\pi$
$450$		0			0
$451$	−5.15229	−	8.92403i	−0.242612	−	0.420216i
$452$	0.0358944	−	0.0621709i	0.00168833	−	0.00292427i
$453$		0			0
$454$			5.95558i			0.279509i
$455$	−3.34523	−	32.2343i	−0.156827	−	1.51117i
$456$		0			0
$457$	−4.78836	−	17.8704i	−0.223990	−	0.835943i	−0.982807	−	0.184638i	$-0.940889\pi$
$457$	−4.78836	−	17.8704i	−0.223990	−	0.835943i	0.758816	−	0.651305i	$-0.225778\pi$
$458$	32.4559	+	18.7384i	1.51657	+	0.875590i
$459$		0			0
$460$	−1.09285	+	1.09285i	−0.0509543	+	0.0509543i
$461$	−9.37616	+	34.9923i	−0.436691	+	1.62975i	0.300295	+	0.953846i	$0.402915\pi$
$461$	−9.37616	+	34.9923i	−0.436691	+	1.62975i	−0.736986	+	0.675907i	$0.763752\pi$
$462$		0			0
$463$	29.5934	+	29.5934i	1.37532	+	1.37532i	0.852352	+	0.522968i	$0.175175\pi$
$463$	29.5934	+	29.5934i	1.37532	+	1.37532i	0.522968	+	0.852352i	$0.324825\pi$
$464$	−21.7033	+	12.5304i	−1.00755	+	0.581709i
$465$		0			0
$466$	−10.6551	+	2.85504i	−0.493590	+	0.132257i
$467$	21.9880			1.01748			0.508741	−	0.860919i	$-0.330111\pi$
$467$	21.9880			1.01748			0.508741	+	0.860919i	$0.330111\pi$
$468$		0			0
$469$	−9.75506			−0.450447
$470$	19.7558	−	5.29355i	0.911267	−	0.244173i
$471$		0			0
$472$	−22.4723	+	12.9744i	−1.03437	+	0.597195i
$473$	−10.0285	−	10.0285i	−0.461112	−	0.461112i
$474$		0			0
$475$	−10.7508	+	40.1223i	−0.493278	+	1.84094i
$476$	−0.894026	+	0.894026i	−0.0409776	+	0.0409776i
$477$		0			0
$478$	2.86512	+	1.65418i	0.131048	+	0.0756604i
$479$	−5.81718	−	21.7100i	−0.265794	−	0.991956i	−0.961763	−	0.273884i	$-0.911692\pi$
$479$	−5.81718	−	21.7100i	−0.265794	−	0.991956i	0.695969	−	0.718072i	$-0.254975\pi$
$480$		0			0
$481$	5.24917	−	32.8629i	0.239341	−	1.49842i
$482$		−	8.19804i		−	0.373411i
$483$		0			0
$484$	−0.593191	+	1.02744i	−0.0269632	+	0.0467017i
$485$	17.5936	+	30.4729i	0.798883	+	1.38371i
$486$		0			0
$487$	−27.6154	−	7.39953i	−1.25137	−	0.335305i	−0.428507	−	0.903539i	$-0.640960\pi$
$487$	−27.6154	−	7.39953i	−1.25137	−	0.335305i	−0.822867	+	0.568234i	$0.807627\pi$
$488$	−21.7961	−	5.84026i	−0.986665	−	0.264376i
$489$		0			0
$490$	−6.09247	−	10.5525i	−0.275230	−	0.476712i
$491$	−2.96335	+	5.13268i	−0.133734	+	0.231635i	−0.925113	−	0.379691i	$-0.876030\pi$
$491$	−2.96335	+	5.13268i	−0.133734	+	0.231635i	0.791379	+	0.611326i	$0.209364\pi$
$492$		0			0
$493$		−	25.2503i		−	1.13722i
$494$	−7.85282	+	17.5757i	−0.353315	+	0.790766i
$495$		0			0
$496$	−6.22431	−	23.2294i	−0.279480	−	1.04303i
$497$	2.07547	+	1.19827i	0.0930975	+	0.0537499i
$498$		0			0
$499$	26.0680	−	26.0680i	1.16696	−	1.16696i	0.184045	−	0.982918i	$-0.441081\pi$
$499$	26.0680	−	26.0680i	1.16696	−	1.16696i	0.982918	−	0.184045i	$-0.0589193\pi$
$500$	−0.885471	+	3.30462i	−0.0395995	+	0.147787i
$501$		0			0
$502$	20.8324	+	20.8324i	0.929797	+	0.929797i
$503$	−38.0063	+	21.9429i	−1.69462	+	0.978387i	−0.743918	+	0.668270i	$0.767035\pi$
$503$	−38.0063	+	21.9429i	−1.69462	+	0.978387i	−0.950698	+	0.310117i	$0.899632\pi$
$504$		0			0
$505$	53.9387	−	14.4528i	2.40024	−	0.643143i
$506$	18.7368			0.832954
$507$		0			0
$508$	1.09259			0.0484758
$509$	−13.3019	+	3.56424i	−0.589598	+	0.157982i	−0.541269	−	0.840849i	$-0.682056\pi$
$509$	−13.3019	+	3.56424i	−0.589598	+	0.157982i	−0.0483283	+	0.998832i	$0.515389\pi$
$510$		0			0
$511$	−20.9769	+	12.1110i	−0.927964	+	0.535760i
$512$	−14.1268	−	14.1268i	−0.624321	−	0.624321i
$513$		0			0
$514$	−4.78218	+	17.8473i	−0.210933	+	0.787212i
$515$	−1.75091	+	1.75091i	−0.0771544	+	0.0771544i
$516$		0			0
$517$	−13.3833	−	7.72687i	−0.588598	−	0.339827i
$518$	7.75247	+	28.9326i	0.340624	+	1.27123i
$519$		0			0
$520$	16.2231	−	36.3094i	0.711428	−	1.59227i
$521$			41.9434i			1.83758i	0.394752	+	0.918788i	$0.370831\pi$
$521$			41.9434i			1.83758i	−0.394752	+	0.918788i	$0.629169\pi$
$522$		0			0
$523$	−16.7016	+	28.9280i	−0.730308	+	1.26493i	0.226443	+	0.974024i	$0.427290\pi$
$523$	−16.7016	+	28.9280i	−0.730308	+	1.26493i	−0.956751	+	0.290907i	$0.906043\pi$
$524$	0.664228	+	1.15048i	0.0290169	+	0.0502588i
$525$		0			0
$526$	35.0694	+	9.39683i	1.52910	+	0.409721i
$527$	23.4051	+	6.27138i	1.01954	+	0.273186i
$528$		0			0
$529$	7.36956	+	12.7645i	0.320416	+	0.554976i
$530$	15.2290	−	26.3774i	0.661505	−	1.14576i
$531$		0			0
$532$		−	1.07985i		−	0.0468174i
$533$	−1.31287	+	8.21935i	−0.0568666	+	0.356019i
$534$		0			0
$535$	−4.28442	−	15.9897i	−0.185231	−	0.691293i
$536$	−10.3671	−	5.98547i	−0.447792	−	0.258533i
$537$		0			0
$538$	4.92582	−	4.92582i	0.212367	−	0.212367i
$539$	−2.38288	+	8.89303i	−0.102638	+	0.383050i
$540$		0			0
$541$	−18.6243	−	18.6243i	−0.800721	−	0.800721i	0.182487	−	0.983208i	$-0.441585\pi$
$541$	−18.6243	−	18.6243i	−0.800721	−	0.800721i	−0.983208	+	0.182487i	$0.941585\pi$
$542$	37.9932	−	21.9354i	1.63195	−	0.942206i
$543$		0			0
$544$	−3.10405	+	0.831729i	−0.133085	+	0.0356601i
$545$	29.8836			1.28007
$546$		0			0
$547$	−18.8322			−0.805209			−0.402604	−	0.915374i	$-0.631895\pi$
$547$	−18.8322			−0.805209			−0.402604	+	0.915374i	$0.631895\pi$
$548$	1.30739	−	0.350314i	0.0558490	−	0.0149647i
$549$		0			0
$550$	64.1477	−	37.0357i	2.73527	−	1.57921i
$551$	15.2493	+	15.2493i	0.649642	+	0.649642i
$552$		0			0
$553$	3.52667	−	13.1617i	0.149969	−	0.559692i
$554$	3.52783	−	3.52783i	0.149883	−	0.149883i
$555$		0			0
$556$	0.354527	+	0.204686i	0.0150353	+	0.00868062i
$557$	4.93003	+	18.3991i	0.208892	+	0.779596i	0.988228	+	0.152989i	$0.0488900\pi$
$557$	4.93003	+	18.3991i	0.208892	+	0.779596i	−0.779336	+	0.626607i	$0.784443\pi$
$558$		0			0
$559$	1.18253	+	11.3947i	0.0500155	+	0.481945i
$560$			38.1836i			1.61355i
$561$		0			0
$562$	−2.08165	+	3.60552i	−0.0878090	+	0.152090i
$563$	6.37989	+	11.0503i	0.268880	+	0.465714i	0.968573	−	0.248730i	$-0.0800130\pi$
$563$	6.37989	+	11.0503i	0.268880	+	0.465714i	−0.699693	+	0.714444i	$0.746680\pi$
$564$		0			0
$565$	2.11001	+	0.565375i	0.0887687	+	0.0237855i
$566$	−8.04256	−	2.15500i	−0.338054	−	0.0905813i
$567$		0			0
$568$	1.47046	+	2.54692i	0.0616993	+	0.106866i
$569$	4.12000	−	7.13605i	0.172719	−	0.299159i	−0.766650	−	0.642065i	$-0.778078\pi$
$569$	4.12000	−	7.13605i	0.172719	−	0.299159i	0.939370	+	0.342906i	$0.111411\pi$
$570$		0			0
$571$			4.04220i			0.169161i	0.996417	+	0.0845804i	$0.0269550\pi$
$571$			4.04220i			0.169161i	−0.996417	+	0.0845804i	$0.973045\pi$
$572$	1.99836	−	0.764095i	0.0835558	−	0.0319484i
$573$		0			0
$574$	−1.93897	−	7.23634i	−0.0809311	−	0.302039i
$575$	−28.2821	−	16.3287i	−1.17944	−	0.680953i
$576$		0			0
$577$	15.7434	−	15.7434i	0.655405	−	0.655405i	−0.298885	−	0.954289i	$-0.596615\pi$
$577$	15.7434	−	15.7434i	0.655405	−	0.655405i	0.954289	+	0.298885i	$0.0966146\pi$
$578$	0.499391	−	1.86375i	0.0207719	−	0.0775219i
$579$		0			0
$580$	2.24304	+	2.24304i	0.0931371	+	0.0931371i
$581$	−19.2223	+	11.0980i	−0.797475	+	0.460422i
$582$		0			0
$583$	−22.2294	+	5.95634i	−0.920647	+	0.246687i
$584$	−29.7241			−1.22999
$585$		0			0
$586$	−5.74501			−0.237324
$587$	36.8797	−	9.88188i	1.52219	−	0.407869i	0.601725	−	0.798703i	$-0.294480\pi$
$587$	36.8797	−	9.88188i	1.52219	−	0.407869i	0.920461	+	0.390834i	$0.127813\pi$
$588$		0			0
$589$	−17.9224	+	10.3475i	−0.738479	+	0.426361i
$590$	39.7526	+	39.7526i	1.63659	+	1.63659i
$591$		0			0
$592$	−10.1486	+	37.8751i	−0.417105	+	1.55666i
$593$	20.2965	−	20.2965i	0.833477	−	0.833477i	−0.154513	−	0.987991i	$-0.549381\pi$
$593$	20.2965	−	20.2965i	0.833477	−	0.833477i	0.987991	+	0.154513i	$0.0493810\pi$
$594$		0			0
$595$	−33.3181	−	19.2362i	−1.36591	−	0.788607i
$596$	0.0612587	+	0.228621i	0.00250925	+	0.00936466i
$597$		0			0
$598$	−11.7494	−	9.53999i	−0.480467	−	0.390119i
$599$			0.0830308i			0.00339254i	0.999999	+	0.00169627i	$0.000539941\pi$
$599$			0.0830308i			0.00339254i	−0.999999	+	0.00169627i	$0.999460\pi$
$600$		0			0
$601$	1.71462	−	2.96981i	0.0699408	−	0.121141i	−0.828934	−	0.559346i	$-0.811052\pi$
$601$	1.71462	−	2.96981i	0.0699408	−	0.121141i	0.898875	+	0.438205i	$0.144386\pi$
$602$	−5.15545	−	8.92949i	−0.210120	−	0.363939i
$603$		0			0
$604$	−2.51166	−	0.672998i	−0.102198	−	0.0273839i
$605$	−34.8701	−	9.34340i	−1.41767	−	0.379863i
$606$		0			0
$607$	−11.8585	−	20.5396i	−0.481323	−	0.833675i	0.518448	−	0.855109i	$-0.326510\pi$
$607$	−11.8585	−	20.5396i	−0.481323	−	0.833675i	−0.999770	+	0.0214340i	$0.993177\pi$
$608$	1.37231	−	2.37692i	0.0556547	−	0.0963968i
$609$		0			0
$610$			48.8876i			1.97940i
$611$	4.45814	+	11.6595i	0.180357	+	0.471694i
$612$		0			0
$613$	6.90062	+	25.7535i	0.278713	+	1.04017i	0.953312	+	0.301988i	$0.0976502\pi$
$613$	6.90062	+	25.7535i	0.278713	+	1.04017i	−0.674598	+	0.738185i	$0.735683\pi$
$614$	−33.6776	−	19.4438i	−1.35912	−	0.784686i
$615$		0			0
$616$	19.1239	−	19.1239i	0.770526	−	0.770526i
$617$	4.80711	−	17.9404i	0.193527	−	0.722253i	−0.799116	−	0.601177i	$-0.794699\pi$
$617$	4.80711	−	17.9404i	0.193527	−	0.722253i	0.992643	−	0.121076i	$-0.0386345\pi$
$618$		0			0
$619$	7.33810	+	7.33810i	0.294943	+	0.294943i	0.839029	−	0.544086i	$-0.183124\pi$
$619$	7.33810	+	7.33810i	0.294943	+	0.294943i	−0.544086	+	0.839029i	$0.683124\pi$
$620$	−2.63622	+	1.52202i	−0.105873	+	0.0611260i
$621$		0			0
$622$	−2.73299	+	0.732302i	−0.109583	+	0.0293626i
$623$	−16.4795			−0.660236
$624$		0			0
$625$	−47.2911			−1.89164
$626$	26.5089	−	7.10304i	1.05951	−	0.283895i
$627$		0			0
$628$	−0.820476	+	0.473702i	−0.0327406	+	0.0189028i
$629$	−27.9362	−	27.9362i	−1.11389	−	1.11389i
$630$		0			0
$631$	3.21713	−	12.0065i	0.128072	−	0.477970i	−0.871859	−	0.489757i	$-0.837085\pi$
$631$	3.21713	−	12.0065i	0.128072	−	0.477970i	0.999931	+	0.0117870i	$0.00375200\pi$
$632$	11.8236	−	11.8236i	0.470319	−	0.470319i
$633$		0			0
$634$	13.3946	+	7.73340i	0.531969	+	0.307133i
$635$	8.60473	+	32.1133i	0.341468	+	1.27438i
$636$		0			0
$637$	6.02219	−	4.36332i	0.238608	−	0.172881i
$638$		−	38.4568i		−	1.52252i
$639$		0			0
$640$	−24.8948	+	43.1191i	−0.984054	+	1.70443i
$641$	14.6267	+	25.3341i	0.577719	+	1.00064i	0.995740	+	0.0922009i	$0.0293902\pi$
$641$	14.6267	+	25.3341i	0.577719	+	1.00064i	−0.418022	+	0.908437i	$0.637276\pi$
$642$		0			0
$643$	−31.1676	−	8.35133i	−1.22913	−	0.329344i	−0.414889	−	0.909872i	$-0.636180\pi$
$643$	−31.1676	−	8.35133i	−1.22913	−	0.329344i	−0.814240	+	0.580528i	$0.802846\pi$
$644$	0.820060	+	0.219734i	0.0323149	+	0.00865874i
$645$		0			0
$646$	11.4264	+	19.7911i	0.449566	+	0.778672i
$647$	−5.58844	+	9.67946i	−0.219704	+	0.380539i	−0.954717	−	0.297514i	$-0.903843\pi$
$647$	−5.58844	+	9.67946i	−0.219704	+	0.380539i	0.735013	+	0.678053i	$0.237176\pi$
$648$		0			0
$649$		−	42.4779i		−	1.66740i
$650$	−59.0823	−	9.43716i	−2.31740	−	0.370156i
$651$		0			0
$652$	−0.299224	−	1.11672i	−0.0117185	−	0.0437341i
$653$	33.5105	+	19.3473i	1.31137	+	0.757119i	0.982323	−	0.187195i	$-0.0599396\pi$
$653$	33.5105	+	19.3473i	1.31137	+	0.757119i	0.329046	+	0.944314i	$0.393273\pi$
$654$		0			0
$655$	−28.5835	+	28.5835i	−1.11685	+	1.11685i
$656$	2.53827	−	9.47294i	0.0991027	−	0.369856i
$657$		0			0
$658$	−7.94443	−	7.94443i	−0.309706	−	0.309706i
$659$	−17.2573	+	9.96349i	−0.672248	+	0.388123i	−0.796928	−	0.604074i	$-0.793543\pi$
$659$	−17.2573	+	9.96349i	−0.672248	+	0.388123i	0.124680	+	0.992197i	$0.460210\pi$
$660$		0			0
$661$	12.1562	−	3.25724i	0.472820	−	0.126692i	−0.0145373	−	0.999894i	$-0.504628\pi$
$661$	12.1562	−	3.25724i	0.472820	−	0.126692i	0.487357	+	0.873203i	$0.337961\pi$
$662$	−46.7837			−1.81830
$663$		0			0
$664$	−27.2379			−1.05703
$665$	31.7388	−	8.50440i	1.23078	−	0.329786i
$666$		0			0
$667$	−14.6837	+	8.47761i	−0.568553	+	0.328254i
$668$	−2.03391	−	2.03391i	−0.0786943	−	0.0786943i
$669$		0			0
$670$	−6.71256	+	25.0516i	−0.259329	+	0.967828i
$671$	26.1196	−	26.1196i	1.00834	−	1.00834i
$672$		0			0
$673$	38.5206	+	22.2399i	1.48486	+	0.857284i	0.999852	−	0.0172265i	$-0.00548363\pi$
$673$	38.5206	+	22.2399i	1.48486	+	0.857284i	0.485007	+	0.874510i	$0.338817\pi$
$674$	0.487063	+	1.81774i	0.0187610	+	0.0700168i
$675$		0			0
$676$	−1.64216	−	0.538337i	−0.0631602	−	0.0207053i
$677$		−	12.5077i		−	0.480712i	−0.970685	−	0.240356i	$-0.922736\pi$
$677$		−	12.5077i		−	0.480712i	0.970685	−	0.240356i	$-0.0772641\pi$
$678$		0			0
$679$	9.66453	−	16.7395i	0.370891	−	0.642402i
$680$	−23.6057	−	40.8863i	−0.905239	−	1.56792i
$681$		0			0
$682$	35.6465	+	9.55145i	1.36498	+	0.365744i
$683$	38.3295	+	10.2703i	1.46664	+	0.392984i	0.901776	−	0.432203i	$-0.142264\pi$
$683$	38.3295	+	10.2703i	1.46664	+	0.392984i	0.564860	+	0.825187i	$0.308930\pi$
$684$		0			0
$685$	20.5928	+	35.6678i	0.786811	+	1.36280i
$686$	−14.7049	+	25.4696i	−0.561434	+	0.972432i
$687$		0			0
$688$		−	13.4978i		−	0.514598i
$689$	16.9722	+	7.58318i	0.646588	+	0.288896i
$690$		0			0
$691$	−3.99167	−	14.8971i	−0.151850	−	0.566713i	−0.999355	−	0.0359243i	$-0.988562\pi$
$691$	−3.99167	−	14.8971i	−0.151850	−	0.566713i	0.847504	−	0.530789i	$-0.178104\pi$
$692$	−0.831995	−	0.480352i	−0.0316277	−	0.0182603i
$693$		0			0
$694$	25.7346	−	25.7346i	0.976872	−	0.976872i
$695$	−3.22403	+	12.0322i	−0.122294	+	0.456409i
$696$		0			0
$697$	6.98711	+	6.98711i	0.264656	+	0.264656i
$698$	−38.6733	+	22.3280i	−1.46380	+	0.845128i
$699$		0			0
$700$	3.24190	−	0.868665i	0.122532	−	0.0328325i
$701$	11.2283			0.424087			0.212043	−	0.977260i	$-0.431988\pi$
$701$	11.2283			0.424087			0.212043	+	0.977260i	$0.431988\pi$
$702$		0			0
$703$	33.7427			1.27263
$704$	31.9055	−	8.54905i	1.20248	−	0.322204i
$705$		0			0
$706$	40.1253	−	23.1663i	1.51013	−	0.871876i
$707$	−21.6905	−	21.6905i	−0.815755	−	0.815755i
$708$		0			0
$709$	4.91587	−	18.3463i	0.184619	−	0.689009i	−0.810092	−	0.586302i	$-0.800583\pi$
$709$	4.91587	−	18.3463i	0.184619	−	0.689009i	0.994712	−	0.102707i	$-0.0327503\pi$
$710$	4.50539	−	4.50539i	0.169084	−	0.169084i
$711$		0			0
$712$	−17.5135	−	10.1114i	−0.656345	−	0.378941i
$713$	−4.21114	−	15.7162i	−0.157708	−	0.588576i
$714$		0			0
$715$	38.1964	+	52.7181i	1.42846	+	1.97154i
$716$		−	0.607269i		−	0.0226947i
$717$		0			0
$718$	26.8178	−	46.4497i	1.00083	−	1.73349i
$719$	−11.7051	−	20.2738i	−0.436526	−	0.756086i	0.560893	−	0.827889i	$-0.310458\pi$
$719$	−11.7051	−	20.2738i	−0.436526	−	0.756086i	−0.997419	+	0.0718029i	$0.977125\pi$
$720$		0			0
$721$	1.31386	+	0.352049i	0.0489308	+	0.0131110i
$722$	7.95010	+	2.13022i	0.295872	+	0.0792787i
$723$		0			0
$724$	1.62720	+	2.81839i	0.0604742	+	0.104744i
$725$	−33.5141	+	58.0482i	−1.24468	+	2.15586i
$726$		0			0
$727$			8.84565i			0.328067i	0.986455	+	0.164033i	$0.0524505\pi$
$727$			8.84565i			0.328067i	−0.986455	+	0.164033i	$0.947550\pi$
$728$	−21.7292	+	2.25502i	−0.805338	+	0.0835767i
$729$		0			0
$730$	16.6674	+	62.2037i	0.616889	+	2.30226i
$731$	11.7778	+	6.79992i	0.435618	+	0.251504i
$732$		0			0
$733$	−24.1754	+	24.1754i	−0.892939	+	0.892939i	−0.994799	−	0.101860i	$-0.967521\pi$
$733$	−24.1754	+	24.1754i	−0.892939	+	0.892939i	0.101860	+	0.994799i	$0.467521\pi$
$734$	5.44407	−	20.3175i	0.200944	−	0.749934i
$735$		0			0
$736$	1.52583	+	1.52583i	0.0562430	+	0.0562430i
$737$	16.9709	−	9.79816i	0.625132	−	0.360920i
$738$		0			0
$739$	−18.1089	+	4.85226i	−0.666146	+	0.178493i	−0.576018	−	0.817437i	$-0.695394\pi$
$739$	−18.1089	+	4.85226i	−0.666146	+	0.178493i	−0.0901281	+	0.995930i	$0.528728\pi$
$740$	4.96326			0.182453
$741$		0			0
$742$	−16.7312			−0.614223
$743$	42.3605	−	11.3505i	1.55406	−	0.416408i	0.623280	−	0.781999i	$-0.285800\pi$
$743$	42.3605	−	11.3505i	1.55406	−	0.416408i	0.930776	+	0.365591i	$0.119133\pi$
$744$		0			0
$745$	−6.23715	+	3.60102i	−0.228511	+	0.131931i
$746$	−7.92414	−	7.92414i	−0.290123	−	0.290123i
$747$		0			0
$748$	0.657364	−	2.45331i	0.0240356	−	0.0897021i
$749$	−6.42995	+	6.42995i	−0.234945	+	0.234945i
$750$		0			0
$751$	42.5665	+	24.5758i	1.55328	+	0.896784i	0.997872	+	0.0652026i	$0.0207694\pi$
$751$	42.5665	+	24.5758i	1.55328	+	0.896784i	0.555403	+	0.831581i	$0.312564\pi$
$752$	−3.80663	−	14.2065i	−0.138813	−	0.518058i
$753$		0			0
$754$	−19.5806	+	24.1152i	−0.713082	+	0.878225i
$755$		−	79.1227i		−	2.87957i
$756$		0			0
$757$	2.66206	−	4.61083i	0.0967543	−	0.167583i	−0.813585	−	0.581446i	$-0.802487\pi$
$757$	2.66206	−	4.61083i	0.0967543	−	0.167583i	0.910339	+	0.413862i	$0.135821\pi$
$758$	−9.05733	−	15.6878i	−0.328977	−	0.569805i
$759$		0			0
$760$	38.9484	+	10.4362i	1.41281	+	0.378560i
$761$	−21.6018	−	5.78817i	−0.783063	−	0.209821i	−0.154928	−	0.987926i	$-0.549515\pi$
$761$	−21.6018	−	5.78817i	−0.783063	−	0.209821i	−0.628135	+	0.778105i	$0.716181\pi$
$762$		0			0
$763$	−8.20788	−	14.2165i	−0.297145	−	0.514670i
$764$	−0.412900	+	0.715164i	−0.0149382	+	0.0258737i
$765$		0			0
$766$			22.8326i			0.824975i
$767$	−21.6279	+	26.6368i	−0.780939	+	0.961797i
$768$		0			0
$769$	−7.42819	−	27.7224i	−0.267867	−	0.999694i	−0.960472	−	0.278377i	$-0.910204\pi$
$769$	−7.42819	−	27.7224i	−0.267867	−	0.999694i	0.692605	−	0.721317i	$-0.256463\pi$
$770$	−50.7442	−	29.2972i	−1.82869	−	1.05580i
$771$		0			0
$772$	−1.14215	+	1.14215i	−0.0411070	+	0.0411070i
$773$	−2.25051	+	8.39903i	−0.0809454	+	0.302092i	−0.994516	−	0.104589i	$-0.966647\pi$
$773$	−2.25051	+	8.39903i	−0.0809454	+	0.302092i	0.913570	+	0.406681i	$0.133314\pi$
$774$		0			0
$775$	−45.4824	−	45.4824i	−1.63377	−	1.63377i
$776$	20.5419	−	11.8599i	0.737410	−	0.425744i
$777$		0			0
$778$	−17.3019	+	4.63604i	−0.620304	+	0.166210i
$779$	−8.43939			−0.302373
$780$		0			0
$781$	−4.81427			−0.172268
$782$	−17.3549	+	4.65023i	−0.620610	+	0.166292i
$783$		0			0
$784$	−7.58834	+	4.38113i	−0.271012	+	0.156469i
$785$	−20.3847	−	20.3847i	−0.727561	−	0.727561i
$786$		0			0
$787$	−1.33848	+	4.99526i	−0.0477115	+	0.178062i	−0.985670	−	0.168686i	$-0.946047\pi$
$787$	−1.33848	+	4.99526i	−0.0477115	+	0.178062i	0.937958	+	0.346748i	$0.112714\pi$
$788$	1.43671	−	1.43671i	0.0511806	−	0.0511806i
$789$		0			0
$790$	−31.3733	−	18.1134i	−1.11621	−	0.644445i
$791$	−0.310573	−	1.15907i	−0.0110427	−	0.0412119i
$792$		0			0
$793$	−29.6779	+	3.07993i	−1.05389	+	0.109371i
$794$			13.4233i			0.476376i
$795$		0			0
$796$	1.50599	−	2.60844i	0.0533782	−	0.0924538i
$797$	−10.3869	−	17.9906i	−0.367923	−	0.637261i	0.621318	−	0.783559i	$-0.286598\pi$
$797$	−10.3869	−	17.9906i	−0.367923	−	0.637261i	−0.989241	+	0.146297i	$0.953264\pi$
$798$		0			0
$799$	14.3139	+	3.83541i	0.506391	+	0.135687i
$800$	8.23987	+	2.20787i	0.291323	+	0.0780599i
$801$		0			0
$802$	18.0665	+	31.2921i	0.637950	+	1.10496i
$803$	24.3291	−	42.1392i	0.858554	−	1.48706i
$804$		0			0
$805$			25.8336i			0.910516i
$806$	−17.4898	−	24.1391i	−0.616051	−	0.850265i
$807$		0			0
$808$	−9.74269	−	36.3602i	−0.342747	−	1.27915i
$809$	28.1672	+	16.2623i	0.990304	+	0.571753i	0.905365	−	0.424634i	$-0.139597\pi$
$809$	28.1672	+	16.2623i	0.990304	+	0.571753i	0.0849391	+	0.996386i	$0.472930\pi$
$810$		0			0
$811$	14.1138	−	14.1138i	0.495604	−	0.495604i	−0.414462	−	0.910066i	$-0.636030\pi$
$811$	14.1138	−	14.1138i	0.495604	−	0.495604i	0.910066	+	0.414462i	$0.136030\pi$
$812$	0.450999	−	1.68315i	0.0158269	−	0.0590670i
$813$		0			0
$814$	−42.5474	−	42.5474i	−1.49129	−	1.49129i
$815$	30.4659	−	17.5895i	1.06717	−	0.616134i
$816$		0			0
$817$	−11.2196	+	3.00627i	−0.392523	+	0.105176i
$818$	−4.71425			−0.164830
$819$		0			0
$820$	−1.24136			−0.0433502
$821$	−13.7815	+	3.69275i	−0.480979	+	0.128878i	−0.491158	−	0.871070i	$-0.663426\pi$
$821$	−13.7815	+	3.69275i	−0.480979	+	0.128878i	0.0101795	+	0.999948i	$0.496760\pi$
$822$		0			0
$823$	2.88216	−	1.66402i	0.100466	−	0.0580040i	−0.448925	−	0.893569i	$-0.648193\pi$
$823$	2.88216	−	1.66402i	0.100466	−	0.0580040i	0.549391	+	0.835565i	$0.314860\pi$
$824$	1.18029	+	1.18029i	0.0411175	+	0.0411175i
$825$		0			0
$826$	7.99289	−	29.8299i	0.278108	−	1.03791i
$827$	−17.1703	+	17.1703i	−0.597071	+	0.597071i	−0.939532	−	0.342461i	$-0.888740\pi$
$827$	−17.1703	+	17.1703i	−0.597071	+	0.597071i	0.342461	+	0.939532i	$0.388740\pi$
$828$		0			0
$829$	−12.0223	−	6.94108i	−0.417552	−	0.241074i	0.276478	−	0.961020i	$-0.410833\pi$
$829$	−12.0223	−	6.94108i	−0.417552	−	0.241074i	−0.694029	+	0.719947i	$0.744166\pi$
$830$	15.2733	+	57.0007i	0.530143	+	1.97852i
$831$		0			0
$832$	−24.3599	−	10.8840i	−0.844527	−	0.377335i
$833$		−	8.82852i		−	0.305890i
$834$		0			0
$835$	43.7623	−	75.7986i	1.51446	−	2.62312i
$836$	1.08462	+	1.87862i	0.0375124	+	0.0649733i
$837$		0			0
$838$	1.88323	+	0.504609i	0.0650550	+	0.0174314i
$839$	6.64552	+	1.78066i	0.229429	+	0.0614752i	0.371702	−	0.928352i	$-0.378774\pi$
$839$	6.64552	+	1.78066i	0.229429	+	0.0614752i	−0.142273	+	0.989827i	$0.545441\pi$
$840$		0			0
$841$	2.90006	+	5.02305i	0.100002	+	0.173209i
$842$	11.9575	−	20.7109i	0.412081	−	0.713745i
$843$		0			0
$844$		−	0.0579572i		−	0.00199497i
$845$	2.88984	−	52.5060i	0.0994134	−	1.80626i
$846$		0			0
$847$	5.13254	+	19.1549i	0.176356	+	0.658170i
$848$	−18.9681	−	10.9513i	−0.651369	−	0.376068i
$849$		0			0
$850$	−50.2248	+	50.2248i	−1.72270	+	1.72270i
$851$	−6.86617	+	25.6249i	−0.235369	+	0.878411i
$852$		0			0
$853$	6.95752	+	6.95752i	0.238221	+	0.238221i	0.816113	−	0.577892i	$-0.196125\pi$
$853$	6.95752	+	6.95752i	0.238221	+	0.238221i	−0.577892	+	0.816113i	$0.696125\pi$
$854$	23.2572	−	13.4275i	0.795844	−	0.459481i
$855$		0			0
$856$	−10.7787	+	2.88813i	−0.368407	+	0.0987144i
$857$	−9.91039			−0.338533			−0.169266	−	0.985570i	$-0.554140\pi$
$857$	−9.91039			−0.338533			−0.169266	+	0.985570i	$0.554140\pi$
$858$		0			0
$859$	24.5641			0.838116			0.419058	−	0.907959i	$-0.362360\pi$
$859$	24.5641			0.838116			0.419058	+	0.907959i	$0.362360\pi$
$860$	−1.65030	+	0.442196i	−0.0562747	+	0.0150788i
$861$		0			0
$862$	11.2162	−	6.47565i	0.382024	−	0.220562i
$863$	13.9880	+	13.9880i	0.476158	+	0.476158i	0.903901	−	0.427742i	$-0.140691\pi$
$863$	13.9880	+	13.9880i	0.476158	+	0.476158i	−0.427742	+	0.903901i	$0.640691\pi$
$864$		0			0
$865$	7.56607	−	28.2370i	0.257254	−	0.960085i
$866$	31.2471	−	31.2471i	1.06182	−	1.06182i
$867$		0			0
$868$	1.44814	+	0.836082i	0.0491529	+	0.0283785i
$869$	7.08449	+	26.4397i	0.240325	+	0.896905i
$870$		0			0
$871$	−15.6308	−	2.49669i	−0.529630	−	0.0845972i
$872$		−	20.1446i		−	0.682183i
$873$		0			0
$874$	7.67267	−	13.2895i	0.259532	−	0.449523i
$875$	28.5930	+	49.5245i	0.966619	+	1.67423i
$876$		0			0
$877$	−50.3184	−	13.4828i	−1.69913	−	0.455281i	−0.726411	−	0.687260i	$-0.758813\pi$
$877$	−50.3184	−	13.4828i	−1.69913	−	0.455281i	−0.972721	+	0.231979i	$0.925480\pi$
$878$	−10.5576	−	2.82891i	−0.356303	−	0.0954712i
$879$		0			0
$880$	−38.3523	−	66.4282i	−1.29286	−	2.23929i
$881$	−11.1254	+	19.2698i	−0.374825	+	0.649215i	−0.990301	−	0.138940i	$-0.955630\pi$
$881$	−11.1254	+	19.2698i	−0.374825	+	0.649215i	0.615476	+	0.788155i	$0.288964\pi$
$882$		0			0
$883$		−	56.9678i		−	1.91712i	−0.284891	−	0.958560i	$-0.591958\pi$
$883$		−	56.9678i		−	1.91712i	0.284891	−	0.958560i	$-0.408042\pi$
$884$	−1.66134	+	1.20371i	−0.0558768	+	0.0404850i
$885$		0			0
$886$	7.33191	+	27.3631i	0.246320	+	0.919280i
$887$	−9.04924	−	5.22458i	−0.303844	−	0.175424i	0.340325	−	0.940308i	$-0.389463\pi$
$887$	−9.04924	−	5.22458i	−0.303844	−	0.175424i	−0.644168	+	0.764884i	$0.722796\pi$
$888$		0			0
$889$	12.9138	−	12.9138i	0.433114	−	0.433114i
$890$	−11.3397	+	42.3203i	−0.380107	+	1.41858i
$891$		0			0
$892$	0.430434	+	0.430434i	0.0144120	+	0.0144120i
$893$	−10.9609	+	6.32826i	−0.366791	+	0.211767i
$894$		0			0
$895$	17.8488	−	4.78257i	0.596619	−	0.159864i
$896$	27.3506			0.913718
$897$		0			0
$898$	−12.5197			−0.417789
$899$	−32.2570	+	8.64325i	−1.07583	+	0.288268i
$900$		0			0
$901$	19.1116	−	11.0341i	0.636699	−	0.367598i
$902$	10.6415	+	10.6415i	0.354324	+	0.354324i
$903$		0			0
$904$	0.381120	−	1.42236i	0.0126759	−	0.0473070i
$905$	−70.0227	+	70.0227i	−2.32763	+	2.32763i
$906$		0			0
$907$	1.72283	+	0.994679i	0.0572058	+	0.0330278i	0.528330	−	0.849039i	$-0.322818\pi$
$907$	1.72283	+	0.994679i	0.0572058	+	0.0330278i	−0.471124	+	0.882067i	$0.656152\pi$
$908$	−0.140304	−	0.523622i	−0.00465615	−	0.0173770i
$909$		0			0
$910$	16.9035	+	44.2082i	0.560344	+	1.46549i
$911$		−	33.1613i		−	1.09868i	−0.835598	−	0.549342i	$-0.814879\pi$
$911$		−	33.1613i		−	1.09868i	0.835598	−	0.549342i	$-0.185121\pi$
$912$		0			0
$913$	22.2940	−	38.6144i	0.737825	−	1.27795i
$914$	13.5098	+	23.3997i	0.446865	+	0.773993i
$915$		0			0
$916$	−3.29501	−	0.882896i	−0.108870	−	0.0291717i
$917$	21.4487	+	5.74717i	0.708300	+	0.189788i
$918$		0			0
$919$	1.40003	+	2.42492i	0.0461826	+	0.0799906i	0.888193	−	0.459471i	$-0.151961\pi$
$919$	1.40003	+	2.42492i	0.0461826	+	0.0799906i	−0.842010	+	0.539462i	$0.818628\pi$
$920$	−15.8509	+	27.4546i	−0.522589	+	0.905150i
$921$		0			0
$922$		−	52.9075i		−	1.74242i
$923$	3.01890	+	2.45122i	0.0993682	+	0.0806828i
$924$		0			0
$925$	27.1437	+	101.302i	0.892480	+	3.33078i
$926$	−52.9333	−	30.5610i	−1.73950	−	1.00430i
$927$		0			0
$928$	3.13173	−	3.13173i	0.102804	−	0.102804i
$929$	−11.5525	+	43.1147i	−0.379027	+	1.41455i	0.468345	+	0.883546i	$0.344851\pi$
$929$	−11.5525	+	43.1147i	−0.379027	+	1.41455i	−0.847371	+	0.531001i	$0.821816\pi$
$930$		0			0
$931$	5.33177	+	5.33177i	0.174742	+	0.174742i
$932$	0.869553	−	0.502036i	0.0284831	−	0.0164448i
$933$		0			0
$934$	−31.0183	+	8.31133i	−1.01495	+	0.271955i
$935$	77.2847			2.52748
$936$		0			0
$937$	18.3615			0.599843			0.299922	−	0.953964i	$-0.403039\pi$
$937$	18.3615			0.599843			0.299922	+	0.953964i	$0.403039\pi$
$938$	13.7614	−	3.68736i	0.449326	−	0.120396i
$939$		0			0
$940$	−1.61225	+	0.930830i	−0.0525857	+	0.0303603i
$941$	−31.9766	−	31.9766i	−1.04241	−	1.04241i	−0.999060	−	0.0433488i	$-0.986197\pi$
$941$	−31.9766	−	31.9766i	−1.04241	−	1.04241i	−0.0433488	−	0.999060i	$-0.513803\pi$
$942$		0			0
$943$	1.71730	−	6.40904i	0.0559229	−	0.208707i
$944$	28.5863	−	28.5863i	0.930406	−	0.930406i
$945$		0			0
$946$	17.9379	+	10.3564i	0.583211	+	0.336717i
$947$	−5.54223	−	20.6839i	−0.180098	−	0.672136i	−0.995627	−	0.0934194i	$-0.970220\pi$
$947$	−5.54223	−	20.6839i	−0.180098	−	0.672136i	0.815528	−	0.578717i	$-0.196446\pi$
$948$		0			0
$949$	−36.7115	+	14.0370i	−1.19171	+	0.455661i
$950$		−	60.6640i		−	1.96820i
$951$		0			0
$952$	−12.9672	+	22.4598i	−0.420268	+	0.727925i
$953$	−5.50952	−	9.54276i	−0.178471	−	0.309120i	0.762886	−	0.646533i	$-0.223782\pi$
$953$	−5.50952	−	9.54276i	−0.178471	−	0.309120i	−0.941357	+	0.337412i	$0.890448\pi$
$954$		0			0
$955$	−24.2719	−	6.50362i	−0.785419	−	0.210452i
$956$	−0.290875	−	0.0779397i	−0.00940757	−	0.00252075i
$957$		0			0
$958$	16.4125	+	28.4273i	0.530264	+	0.918444i
$959$	11.3121	−	19.5931i	0.365286	−	0.632695i
$960$		0			0
$961$		−	1.04649i		−	0.0337578i
$962$	5.01704	+	48.3437i	0.161756	+	1.55866i
$963$		0			0
$964$	0.193133	+	0.720782i	0.00622039	+	0.0232148i
$965$	−42.5652	−	24.5750i	−1.37022	−	0.791098i
$966$		0			0
$967$	−22.2238	+	22.2238i	−0.714668	+	0.714668i	−0.967508	−	0.252840i	$-0.918635\pi$
$967$	−22.2238	+	22.2238i	−0.714668	+	0.714668i	0.252840	+	0.967508i	$0.418635\pi$
$968$	−6.29841	+	23.5060i	−0.202438	+	0.755511i
$969$		0			0
$970$	−36.3377	−	36.3377i	−1.16673	−	1.16673i
$971$	−5.81217	+	3.35566i	−0.186521	+	0.107688i	−0.590353	−	0.807145i	$-0.701011\pi$
$971$	−5.81217	+	3.35566i	−0.186521	+	0.107688i	0.403832	+	0.914833i	$0.367678\pi$
$972$		0			0
$973$	6.60957	−	1.77103i	0.211893	−	0.0567766i
$974$	41.7539			1.33788
$975$		0			0
$976$	35.1554			1.12530
$977$	34.6264	−	9.27812i	1.10780	−	0.296833i	0.341861	−	0.939750i	$-0.388943\pi$
$977$	34.6264	−	9.27812i	1.10780	−	0.296833i	0.765936	+	0.642917i	$0.222276\pi$
$978$		0			0
$979$	28.6694	−	16.5523i	0.916277	−	0.529013i
$980$	0.784256	+	0.784256i	0.0250521	+	0.0250521i
$981$		0			0
$982$	2.24026	−	8.36077i	0.0714896	−	0.266803i
$983$	−13.5996	+	13.5996i	−0.433760	+	0.433760i	−0.889905	−	0.456145i	$-0.849230\pi$
$983$	−13.5996	+	13.5996i	−0.433760	+	0.433760i	0.456145	+	0.889905i	$0.349230\pi$
$984$		0			0
$985$	53.5425	+	30.9128i	1.70600	+	0.984962i
$986$	9.54447	+	35.6205i	0.303958	+	1.13439i
$987$		0			0
$988$	0.276375	−	1.73027i	0.00879265	−	0.0550473i
$989$		−	9.13210i		−	0.290384i
$990$		0			0
$991$	−18.3366	+	31.7599i	−0.582481	+	1.00889i	0.412704	+	0.910865i	$0.364585\pi$
$991$	−18.3366	+	31.7599i	−0.582481	+	1.00889i	−0.995184	+	0.0980209i	$0.968749\pi$
$992$	2.12505	+	3.68069i	0.0674704	+	0.116862i
$993$		0			0
$994$	−3.38079	−	0.905880i	−0.107232	−	0.0287328i
$995$	88.5276	+	23.7209i	2.80651	+	0.752003i
$996$		0			0
$997$	4.27729	+	7.40849i	0.135463	+	0.234629i	0.925774	−	0.378077i	$-0.123414\pi$
$997$	4.27729	+	7.40849i	0.135463	+	0.234629i	−0.790311	+	0.612706i	$0.790081\pi$
$998$	−26.9204	+	46.6275i	−0.852150	+	1.47597i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.bd.d.188.2	✓	20
3.2	odd	2		351.2.bd.e.188.4	yes	20
13.11	odd	12		351.2.bd.e.323.4	yes	20
39.11	even	12	inner	351.2.bd.d.323.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.bd.d.188.2	✓	20	1.1	even	1	trivial
351.2.bd.d.323.2	yes	20	39.11	even	12	inner
351.2.bd.e.188.4	yes	20	3.2	odd	2
351.2.bd.e.323.4	yes	20	13.11	odd	12

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41069 + 0.377994i) q^{2} +(0.115125 - 0.0664674i) q^{4} +(2.86027 + 2.86027i) q^{5} +(0.575104 - 2.14632i) q^{7} +(1.92812 - 1.92812i) q^{8} +O(q^{10})\)	\(q+(-1.41069 + 0.377994i) q^{2} +(0.115125 - 0.0664674i) q^{4} +(2.86027 + 2.86027i) q^{5} +(0.575104 - 2.14632i) q^{7} +(1.92812 - 1.92812i) q^{8} +(-5.11614 - 2.95380i) q^{10} +(1.15529 + 4.31160i) q^{11} +(1.47083 - 3.29191i) q^{13} +3.24518i q^{14} +(-2.12410 + 3.67905i) q^{16} +(-2.14016 - 3.70687i) q^{17} +(3.53117 + 0.946174i) q^{19} +(0.519404 + 0.139174i) q^{20} +(-3.25952 - 5.64565i) q^{22} +(-1.43709 + 2.48911i) q^{23} +11.3623i q^{25} +(-0.830565 + 5.19984i) q^{26} +(-0.0764513 - 0.285320i) q^{28} +(5.10882 + 2.94958i) q^{29} +(-4.00290 + 4.00290i) q^{31} +(0.194314 - 0.725192i) q^{32} +(4.42029 + 4.42029i) q^{34} +(7.78401 - 4.49410i) q^{35} +(8.91557 - 2.38892i) q^{37} -5.33905 q^{38} +11.0299 q^{40} +(-2.22987 + 0.597493i) q^{41} +(-2.75162 + 1.58865i) q^{43} +(0.419583 + 0.419583i) q^{44} +(1.08642 - 4.05458i) q^{46} +(-2.44807 + 2.44807i) q^{47} +(1.78625 + 1.03129i) q^{49} +(-4.29490 - 16.0288i) q^{50} +(-0.0494757 - 0.476743i) q^{52} +5.15572i q^{53} +(-9.02790 + 15.6368i) q^{55} +(-3.02948 - 5.24721i) q^{56} +(-8.32191 - 2.22985i) q^{58} +(-9.19205 - 2.46300i) q^{59} +(-4.13769 - 7.16668i) q^{61} +(4.13380 - 7.15994i) q^{62} -7.39992i q^{64} +(13.6227 - 5.20879i) q^{65} +(-1.13626 - 4.24057i) q^{67} +(-0.492772 - 0.284502i) q^{68} +(-9.28210 + 9.28210i) q^{70} +(-0.279146 + 1.04179i) q^{71} +(-7.70808 - 7.70808i) q^{73} +(-11.6741 + 6.74007i) q^{74} +(0.469415 - 0.125779i) q^{76} +9.91846 q^{77} +6.13223 q^{79} +(-16.5986 + 4.44758i) q^{80} +(2.91982 - 1.68576i) q^{82} +(-7.06333 - 7.06333i) q^{83} +(4.48121 - 16.7241i) q^{85} +(3.28119 - 3.28119i) q^{86} +(10.5408 + 6.08573i) q^{88} +(-1.91951 - 7.16369i) q^{89} +(-6.21960 - 5.05005i) q^{91} +0.382078i q^{92} +(2.52812 - 4.37884i) q^{94} +(7.39380 + 12.8064i) q^{95} +(8.40243 + 2.25142i) q^{97} +(-2.90967 - 0.779645i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{5}+O(q^{10}) \) 20 * q - 6 * q^5	\( 20 q - 6 q^{5} - 12 q^{10} - 8 q^{13} + 24 q^{16} + 12 q^{17} - 12 q^{19} - 36 q^{20} + 8 q^{22} + 42 q^{26} + 2 q^{28} + 6 q^{29} - 22 q^{31} + 36 q^{32} - 6 q^{34} + 36 q^{35} + 8 q^{37} - 72 q^{38} - 36 q^{40} - 30 q^{41} - 30 q^{43} - 36 q^{44} - 48 q^{46} - 6 q^{47} + 30 q^{49} - 54 q^{50} + 4 q^{52} - 28 q^{55} + 60 q^{56} + 44 q^{58} - 30 q^{59} - 16 q^{61} + 30 q^{62} + 78 q^{65} + 18 q^{67} - 6 q^{68} + 38 q^{70} + 60 q^{71} + 72 q^{74} - 8 q^{76} + 12 q^{77} - 16 q^{79} - 126 q^{80} + 78 q^{82} - 12 q^{83} + 12 q^{85} - 18 q^{86} - 84 q^{89} + 30 q^{91} - 22 q^{94} + 66 q^{95} + 26 q^{97} - 42 q^{98}+O(q^{100}) \) 20 * q - 6 * q^5 - 12 * q^10 - 8 * q^13 + 24 * q^16 + 12 * q^17 - 12 * q^19 - 36 * q^20 + 8 * q^22 + 42 * q^26 + 2 * q^28 + 6 * q^29 - 22 * q^31 + 36 * q^32 - 6 * q^34 + 36 * q^35 + 8 * q^37 - 72 * q^38 - 36 * q^40 - 30 * q^41 - 30 * q^43 - 36 * q^44 - 48 * q^46 - 6 * q^47 + 30 * q^49 - 54 * q^50 + 4 * q^52 - 28 * q^55 + 60 * q^56 + 44 * q^58 - 30 * q^59 - 16 * q^61 + 30 * q^62 + 78 * q^65 + 18 * q^67 - 6 * q^68 + 38 * q^70 + 60 * q^71 + 72 * q^74 - 8 * q^76 + 12 * q^77 - 16 * q^79 - 126 * q^80 + 78 * q^82 - 12 * q^83 + 12 * q^85 - 18 * q^86 - 84 * q^89 + 30 * q^91 - 22 * q^94 + 66 * q^95 + 26 * q^97 - 42 * q^98

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