LMFDB - Embedded newform 351.2.bd.e.188.4

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			188.4
Root			$1.03270 + 1.03270i$ of defining polynomial
Character	$\chi$	$=$	351.188
Dual form			351.2.bd.e.323.4

$q$-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	0.277108	−	0.960839i	$-0.410624\pi$
$2$	1.41069	−	0.377994i	0.997511	−	0.267282i	0.720402	+	0.693556i	$0.243957\pi$
$3$		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	$-0.890246\pi$
$5$	−2.86027	−	2.86027i	−1.27915	−	1.27915i	−0.338012	−	0.941142i	$-0.609754\pi$
$6$		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	$-0.848370\pi$
$11$	−1.15529	−	4.31160i	−0.348333	−	1.29999i	0.540338	−	0.841448i	$-0.318296\pi$
$12$		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	$0.00705321\pi$
$17$	2.14016	+	3.70687i	0.519065	+	0.899048i	−0.480689	+	0.876891i	$0.659613\pi$
$18$		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	−0.676403	−	0.736532i	$-0.736462\pi$
$23$	1.43709	−	2.48911i	0.299653	−	0.519015i	0.976057	+	0.217517i	$0.0697956\pi$
$24$		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	−0.0560127	−	0.998430i	$-0.517839\pi$
$29$	−5.10882	−	2.94958i	−0.948685	−	0.547723i	−0.892672	+	0.450707i	$0.851172\pi$
$30$		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	−0.0804552	−	0.996758i	$-0.525637\pi$
$41$	2.22987	−	0.597493i	0.348248	−	0.0933127i	0.428703	+	0.903446i	$0.358971\pi$
$42$		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	−0.505650	−	0.862738i	$-0.668747\pi$
$47$	2.44807	−	2.44807i	0.357088	−	0.357088i	0.862738	+	0.505650i	$0.168747\pi$
$48$		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	$-0.884789\pi$
$53$		−	5.15572i		−	0.708193i	0.935209	−	0.354096i	$-0.115211\pi$
$54$		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	0.801532	−	0.597952i	$-0.204019\pi$
$59$	9.19205	+	2.46300i	1.19670	+	0.320656i	0.395171	+	0.918607i	$0.370685\pi$
$60$		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	−0.947381	−	0.320107i	$-0.896281\pi$
$71$	0.279146	−	1.04179i	0.0331286	−	0.123638i	0.980510	+	0.196470i	$0.0629477\pi$
$72$		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	0.979028	−	0.203726i	$-0.0653053\pi$
$83$	7.06333	+	7.06333i	0.775301	+	0.775301i	−0.203726	+	0.979028i	$0.565305\pi$
$84$		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	$0.0452531\pi$
$89$	1.91951	+	7.16369i	0.203467	+	0.759350i	−0.786444	+	0.617661i	$0.788080\pi$
$90$		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	$0.407661\pi$
$101$	−6.90247	+	11.9554i	−0.686821	+	1.18961i	−0.972861	+	0.231391i	$0.925672\pi$
$102$		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	0.661430	−	0.750007i	$-0.269950\pi$
$107$	3.54408	+	2.04617i	0.342619	+	0.197811i	−0.318811	+	0.947818i	$0.603283\pi$
$108$		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	−0.521836	−	0.853046i	$-0.674753\pi$
$113$	−0.467679	+	0.270015i	−0.0439956	+	0.0254009i	0.477841	+	0.878446i	$0.341420\pi$
$114$		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	$-0.856197\pi$
$131$		−	9.99328i		−	0.873117i	0.899676	−	0.436559i	$-0.143803\pi$
$132$		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	−0.187067	−	0.982347i	$-0.559898\pi$
$137$	−9.83483	−	2.63523i	−0.840246	−	0.225143i	−0.653179	+	0.757204i	$0.726565\pi$
$138$		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	−0.944478	−	0.328575i	$-0.893432\pi$
$149$	0.460818	−	1.71979i	0.0377516	−	0.140891i	0.982229	+	0.187684i	$0.0600982\pi$
$150$		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	$0.232465\pi$
$167$	5.60021	+	20.9003i	0.433357	+	1.61731i	−0.311611	+	0.950210i	$0.600869\pi$
$168$		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	0.970066	−	0.242843i	$-0.0780798\pi$
$173$	3.61344	+	6.25867i	0.274725	+	0.475838i	−0.695341	+	0.718680i	$0.744746\pi$
$174$		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	−0.938672	−	0.344811i	$-0.887943\pi$
$179$	−2.28409	+	3.95615i	−0.170721	+	0.295697i	0.767951	+	0.640508i	$0.221276\pi$
$180$		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	−0.292574	−	0.956243i	$-0.594512\pi$
$191$	5.37981	−	3.10604i	0.389270	−	0.224745i	0.681844	+	0.731498i	$0.261178\pi$
$192$		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	−0.743018	−	0.669272i	$-0.766606\pi$
$197$	−14.7635	+	3.95586i	−1.05185	+	0.281844i	−0.308837	+	0.951115i	$0.599940\pi$
$198$		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	−0.992066	−	0.125720i	$-0.959876\pi$
$227$	−1.05544	+	3.93894i	−0.0700517	+	0.261437i	0.922014	+	0.387156i	$0.126543\pi$
$228$		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	$-0.579580\pi$
$233$	−7.55312			−0.494822			−0.247411	+	0.968911i	$0.579580\pi$
$234$		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	0.757012	−	0.653400i	$-0.226658\pi$
$239$	1.60180	+	1.60180i	0.103612	+	0.103612i	−0.653400	+	0.757012i	$0.726658\pi$
$240$		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	$0.0530128\pi$
$251$	10.0864	+	17.4702i	0.636648	+	1.10271i	−0.349516	+	0.936931i	$0.613654\pi$
$252$		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	−0.993049	−	0.117706i	$-0.962446\pi$
$257$	−6.32573	+	10.9565i	−0.394588	+	0.683447i	0.598460	+	0.801152i	$0.295779\pi$
$258$		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	0.984919	−	0.173014i	$-0.0553507\pi$
$263$	21.5291	+	12.4299i	1.32754	+	0.766458i	0.342625	+	0.939472i	$0.388684\pi$
$264$		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	−0.368755	−	0.929526i	$-0.620216\pi$
$269$	4.13082	−	2.38493i	0.251860	−	0.145412i	0.620616	+	0.784115i	$0.286883\pi$
$270$		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	−0.764670	−	0.644422i	$-0.777098\pi$
$281$	−2.01573	+	2.01573i	−0.120249	+	0.120249i	0.644422	+	0.764670i	$0.277098\pi$
$282$		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	0.146115	−	0.989268i	$-0.453323\pi$
$293$	−3.79967	−	1.01812i	−0.221979	−	0.0594791i	−0.368094	+	0.929788i	$0.619990\pi$
$294$		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	$-0.517493\pi$
$311$	−1.93734			−0.109856			−0.0549281	+	0.998490i	$0.517493\pi$
$312$		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	0.885410	−	0.464812i	$-0.153878\pi$
$317$	7.48853	+	7.48853i	0.420598	+	0.420598i	−0.464812	+	0.885410i	$0.653878\pi$
$318$		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	0.207583	−	0.978217i	$-0.433440\pi$
$347$	21.5811	−	12.4599i	1.15854	−	0.668881i	0.950953	+	0.309337i	$0.100107\pi$
$348$		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	0.676796	−	0.736171i	$-0.263368\pi$
$353$	30.6438	−	8.21097i	1.63100	−	0.437026i	0.954208	+	0.299145i	$0.0967014\pi$
$354$		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	$-0.329284\pi$
$359$	25.9686	−	25.9686i	1.37057	−	1.37057i	0.859595	−	0.510976i	$-0.170716\pi$
$360$		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	$0.214124\pi$
$383$	−4.04634	+	15.1012i	−0.206759	+	0.771633i	−0.988906	+	0.148540i	$0.952543\pi$
$384$		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	$-0.600639\pi$
$389$	−12.2648			−0.621852			−0.310926	+	0.950434i	$0.600639\pi$
$390$		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	$0.128623\pi$
$401$	6.40341	+	23.8979i	0.319771	+	1.19340i	−0.599693	+	0.800230i	$0.704711\pi$
$402$		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	0.527974	−	0.849261i	$-0.322952\pi$
$419$	1.15611	+	0.667483i	0.0564799	+	0.0326087i	−0.471494	+	0.881869i	$0.656285\pi$
$420$		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	−0.0465468	−	0.998916i	$-0.514822\pi$
$431$	8.56581	−	2.29520i	0.412601	−	0.110556i	0.459147	+	0.888360i	$0.348155\pi$
$432$		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	$0.152433\pi$
$443$			19.3969i			0.921574i	−0.887511	+	0.460787i	$0.847567\pi$
$444$		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	0.0580812	−	0.998312i	$-0.481502\pi$
$449$	−8.28037	−	2.21872i	−0.390775	−	0.104708i	−0.448856	+	0.893604i	$0.648168\pi$
$450$		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	$-0.597085\pi$
$461$	9.37616	−	34.9923i	0.436691	−	1.62975i	0.736986	−	0.675907i	$-0.236248\pi$
$462$		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	$-0.669889\pi$
$467$	−21.9880			−1.01748			−0.508741	+	0.860919i	$0.669889\pi$
$468$		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	$0.0883084\pi$
$479$	5.81718	+	21.7100i	0.265794	+	0.991956i	−0.695969	+	0.718072i	$0.745025\pi$
$480$		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	−0.791379	−	0.611326i	$-0.790636\pi$
$491$	2.96335	−	5.13268i	0.133734	−	0.231635i	0.925113	+	0.379691i	$0.123970\pi$
$492$		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	$-0.232965\pi$
$503$	38.0063	−	21.9429i	1.69462	−	0.978387i	0.950698	−	0.310117i	$-0.100368\pi$
$504$		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	0.0483283	−	0.998832i	$-0.484611\pi$
$509$	13.3019	−	3.56424i	0.589598	−	0.157982i	0.541269	+	0.840849i	$0.317944\pi$
$510$		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	$-0.629169\pi$
$521$		−	41.9434i		−	1.83758i	0.394752	−	0.918788i	$-0.370831\pi$
$522$		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	$-0.951110\pi$
$557$	−4.93003	−	18.3991i	−0.208892	−	0.779596i	0.779336	−	0.626607i	$-0.215557\pi$
$558$		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	0.699693	−	0.714444i	$-0.253320\pi$
$563$	−6.37989	−	11.0503i	−0.268880	−	0.465714i	−0.968573	+	0.248730i	$0.919987\pi$
$564$		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	−0.939370	−	0.342906i	$-0.888589\pi$
$569$	−4.12000	+	7.13605i	−0.172719	+	0.299159i	0.766650	+	0.642065i	$0.221922\pi$
$570$		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	−0.920461	−	0.390834i	$-0.872187\pi$
$587$	−36.8797	+	9.88188i	−1.52219	+	0.407869i	−0.601725	+	0.798703i	$0.705520\pi$
$588$		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	−0.987991	−	0.154513i	$-0.950619\pi$
$593$	−20.2965	+	20.2965i	−0.833477	+	0.833477i	0.154513	+	0.987991i	$0.450619\pi$
$594$		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	$-0.999460\pi$
$599$		−	0.0830308i		−	0.00339254i	0.999999	−	0.00169627i	$-0.000539941\pi$
$600$		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	$0.205301\pi$
$617$	−4.80711	+	17.9404i	−0.193527	+	0.722253i	−0.992643	+	0.121076i	$0.961365\pi$
$618$		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	$-0.970610\pi$
$641$	−14.6267	−	25.3341i	−0.577719	−	1.00064i	0.418022	−	0.908437i	$-0.362724\pi$
$642$		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	−0.735013	−	0.678053i	$-0.762824\pi$
$647$	5.58844	−	9.67946i	0.219704	−	0.380539i	0.954717	+	0.297514i	$0.0961575\pi$
$648$		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	−0.329046	−	0.944314i	$-0.606727\pi$
$653$	−33.5105	−	19.3473i	−1.31137	−	0.757119i	−0.982323	+	0.187195i	$0.940060\pi$
$654$		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	−0.124680	−	0.992197i	$-0.539790\pi$
$659$	17.2573	−	9.96349i	0.672248	−	0.388123i	0.796928	+	0.604074i	$0.206457\pi$
$660$		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	$0.0772641\pi$
$677$			12.5077i			0.480712i	−0.970685	+	0.240356i	$0.922736\pi$
$678$		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	−0.564860	−	0.825187i	$-0.691070\pi$
$683$	−38.3295	−	10.2703i	−1.46664	−	0.392984i	−0.901776	+	0.432203i	$0.857736\pi$
$684$		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	$-0.568012\pi$
$701$	−11.2283			−0.424087			−0.212043	+	0.977260i	$0.568012\pi$
$702$		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	0.997419	−	0.0718029i	$-0.0228752\pi$
$719$	11.7051	+	20.2738i	0.436526	+	0.756086i	−0.560893	+	0.827889i	$0.689542\pi$
$720$		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	−0.930776	−	0.365591i	$-0.880867\pi$
$743$	−42.3605	+	11.3505i	−1.55406	+	0.416408i	−0.623280	+	0.781999i	$0.714200\pi$
$744$		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	0.628135	−	0.778105i	$-0.283819\pi$
$761$	21.6018	+	5.78817i	0.783063	+	0.209821i	0.154928	+	0.987926i	$0.450485\pi$
$762$		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	−0.913570	−	0.406681i	$-0.866686\pi$
$773$	2.25051	−	8.39903i	0.0809454	−	0.302092i	0.994516	+	0.104589i	$0.0333527\pi$
$774$		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	0.989241	−	0.146297i	$-0.0467356\pi$
$797$	10.3869	+	17.9906i	0.367923	+	0.637261i	−0.621318	+	0.783559i	$0.713402\pi$
$798$		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	−0.0849391	−	0.996386i	$-0.527070\pi$
$809$	−28.1672	−	16.2623i	−0.990304	−	0.571753i	−0.905365	+	0.424634i	$0.860403\pi$
$810$		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	−0.0101795	−	0.999948i	$-0.503240\pi$
$821$	13.7815	−	3.69275i	0.480979	−	0.128878i	0.491158	+	0.871070i	$0.336574\pi$
$822$		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	−0.342461	−	0.939532i	$-0.611260\pi$
$827$	17.1703	−	17.1703i	0.597071	−	0.597071i	0.939532	+	0.342461i	$0.111260\pi$
$828$		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	0.142273	−	0.989827i	$-0.454559\pi$
$839$	−6.64552	−	1.78066i	−0.229429	−	0.0614752i	−0.371702	+	0.928352i	$0.621226\pi$
$840$		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	$-0.445860\pi$
$857$	9.91039			0.338533			0.169266	+	0.985570i	$0.445860\pi$
$858$		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	0.427742	−	0.903901i	$-0.359309\pi$
$863$	−13.9880	−	13.9880i	−0.476158	−	0.476158i	−0.903901	+	0.427742i	$0.859309\pi$
$864$		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	−0.615476	−	0.788155i	$-0.711036\pi$
$881$	11.1254	−	19.2698i	0.374825	−	0.649215i	0.990301	+	0.138940i	$0.0443696\pi$
$882$		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	0.644168	−	0.764884i	$-0.277204\pi$
$887$	9.04924	+	5.22458i	0.303844	+	0.175424i	−0.340325	+	0.940308i	$0.610537\pi$
$888$		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	$0.185121\pi$
$911$			33.1613i			1.09868i	−0.835598	+	0.549342i	$0.814879\pi$
$912$		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	$-0.655149\pi$
$929$	11.5525	−	43.1147i	0.379027	−	1.41455i	0.847371	−	0.531001i	$-0.178184\pi$
$930$		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	$0.0138027\pi$
$941$	31.9766	+	31.9766i	1.04241	+	1.04241i	0.0433488	+	0.999060i	$0.486197\pi$
$942$		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	$0.0297797\pi$
$947$	5.54223	+	20.6839i	0.180098	+	0.672136i	−0.815528	+	0.578717i	$0.803554\pi$
$948$		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	0.941357	−	0.337412i	$-0.109552\pi$
$953$	5.50952	+	9.54276i	0.178471	+	0.309120i	−0.762886	+	0.646533i	$0.776218\pi$
$954$		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	−0.403832	−	0.914833i	$-0.632322\pi$
$971$	5.81217	−	3.35566i	0.186521	−	0.107688i	0.590353	+	0.807145i	$0.298989\pi$
$972$		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	−0.765936	−	0.642917i	$-0.777724\pi$
$977$	−34.6264	+	9.27812i	−1.10780	+	0.296833i	−0.341861	+	0.939750i	$0.611057\pi$
$978$		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	−0.456145	−	0.889905i	$-0.650770\pi$
$983$	13.5996	−	13.5996i	0.433760	−	0.433760i	0.889905	+	0.456145i	$0.150770\pi$
$984$		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.e.188.4	yes	20
3.2	odd	2		351.2.bd.d.188.2	✓	20
13.11	odd	12		351.2.bd.d.323.2	yes	20
39.11	even	12	inner	351.2.bd.e.323.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.bd.d.188.2	✓	20	3.2	odd	2
351.2.bd.d.323.2	yes	20	13.11	odd	12
351.2.bd.e.188.4	yes	20	1.1	even	1	trivial
351.2.bd.e.323.4	yes	20	39.11	even	12	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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
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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