LMFDB - Embedded newform 396.2.r.b.271.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(19,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("396.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.r (of order $10$, 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:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			271.10
Character	$\chi$	$=$	396.271
Dual form			396.2.r.b.19.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12117 + 0.861957i) q^{2} +(0.514062 + 1.93281i) q^{4} +(1.53251 - 1.11343i) q^{5} +(1.07196 + 3.29914i) q^{7} +(-1.08964 + 2.61011i) q^{8} +O(q^{10})$	\(q+(1.12117 + 0.861957i) q^{2} +(0.514062 + 1.93281i) q^{4} +(1.53251 - 1.11343i) q^{5} +(1.07196 + 3.29914i) q^{7} +(-1.08964 + 2.61011i) q^{8} +(2.67794 + 0.0726042i) q^{10} +(-0.210969 - 3.30991i) q^{11} +(1.06787 - 1.46980i) q^{13} +(-1.64187 + 4.62289i) q^{14} +(-3.47148 + 1.98716i) q^{16} +(-1.74921 - 2.40759i) q^{17} +(-1.34636 + 4.14366i) q^{19} +(2.93986 + 2.38967i) q^{20} +(2.61646 - 3.89283i) q^{22} +3.82341i q^{23} +(-0.436233 + 1.34259i) q^{25} +(2.46418 - 0.727444i) q^{26} +(-5.82555 + 3.76785i) q^{28} +(8.48417 - 2.75668i) q^{29} +(1.65449 - 2.27721i) q^{31} +(-5.60498 - 0.764309i) q^{32} +(0.114062 - 4.20707i) q^{34} +(5.31616 + 3.86242i) q^{35} +(-3.51620 - 10.8218i) q^{37} +(-5.08115 + 3.48526i) q^{38} +(1.23630 + 5.21327i) q^{40} +(-7.37845 - 2.39740i) q^{41} +2.35165 q^{43} +(6.28896 - 2.10926i) q^{44} +(-3.29561 + 4.28671i) q^{46} +(-2.66757 - 0.866745i) q^{47} +(-4.07214 + 2.95858i) q^{49} +(-1.64634 + 1.12926i) q^{50} +(3.38980 + 1.30843i) q^{52} +(-5.05557 - 3.67309i) q^{53} +(-4.00867 - 4.83757i) q^{55} +(-9.77918 - 0.796961i) q^{56} +(11.8884 + 4.22228i) q^{58} +(-7.68642 + 2.49747i) q^{59} +(4.57345 + 6.29481i) q^{61} +(3.81783 - 1.12705i) q^{62} +(-5.62536 - 5.68818i) q^{64} -3.44150i q^{65} -15.0787i q^{67} +(3.75420 - 4.61854i) q^{68} +(2.63111 + 8.91274i) q^{70} +(-3.24129 - 4.46126i) q^{71} +(11.1487 - 3.62244i) q^{73} +(5.38561 - 15.1639i) q^{74} +(-8.70100 - 0.472149i) q^{76} +(10.6937 - 4.24410i) q^{77} +(-4.34223 - 3.15482i) q^{79} +(-3.10750 + 6.91061i) q^{80} +(-6.20607 - 9.04781i) q^{82} +(6.10662 - 4.43672i) q^{83} +(-5.36138 - 1.74202i) q^{85} +(2.63661 + 2.02702i) q^{86} +(8.86911 + 3.05596i) q^{88} +5.20905 q^{89} +(5.99381 + 1.94751i) q^{91} +(-7.38991 + 1.96547i) q^{92} +(-2.24371 - 3.27110i) q^{94} +(2.55038 + 7.84928i) q^{95} +(6.72491 + 4.88593i) q^{97} +(-7.11574 - 0.192922i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} + 14 q^{14} - 24 q^{16} + 22 q^{20} - 26 q^{22} - 20 q^{25} + 38 q^{26} - 10 q^{28} - 48 q^{37} - 58 q^{38} + 70 q^{40} + 40 q^{41} - 34 q^{44} + 70 q^{46} - 28 q^{49} - 70 q^{50} + 30 q^{52} + 64 q^{53} - 60 q^{56} - 54 q^{58} - 40 q^{64} + 4 q^{70} + 20 q^{73} - 50 q^{74} + 8 q^{77} - 58 q^{80} + 62 q^{82} + 40 q^{85} - 8 q^{86} + 8 q^{88} - 48 q^{89} - 42 q^{92} - 10 q^{94} + 48 q^{97}+O(q^{100}) $ 48 * q - 4 * q^4 + 14 * q^14 - 24 * q^16 + 22 * q^20 - 26 * q^22 - 20 * q^25 + 38 * q^26 - 10 * q^28 - 48 * q^37 - 58 * q^38 + 70 * q^40 + 40 * q^41 - 34 * q^44 + 70 * q^46 - 28 * q^49 - 70 * q^50 + 30 * q^52 + 64 * q^53 - 60 * q^56 - 54 * q^58 - 40 * q^64 + 4 * q^70 + 20 * q^73 - 50 * q^74 + 8 * q^77 - 58 * q^80 + 62 * q^82 + 40 * q^85 - 8 * q^86 + 8 * q^88 - 48 * q^89 - 42 * q^92 - 10 * q^94 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.12117	+	0.861957i	0.792790	+	0.609495i
$2$	1.12117	+	0.861957i	0.792790	+	0.609495i
$3$		0			0
$3$		0			0
$4$	0.514062	+	1.93281i	0.257031	+	0.966403i
$5$	1.53251	−	1.11343i	0.685359	−	0.497943i	−0.189772	−	0.981828i	$-0.560775\pi$
$5$	1.53251	−	1.11343i	0.685359	−	0.497943i	0.875131	+	0.483886i	$0.160775\pi$
$6$		0			0
$7$	1.07196	+	3.29914i	0.405162	+	1.24696i	0.920760	+	0.390129i	$0.127570\pi$
$7$	1.07196	+	3.29914i	0.405162	+	1.24696i	−0.515599	+	0.856830i	$0.672430\pi$
$8$	−1.08964	+	2.61011i	−0.385247	+	0.922814i
$9$		0			0
$10$	2.67794	+	0.0726042i	0.846839	+	0.0229595i
$11$	−0.210969	−	3.30991i	−0.0636096	−	0.997975i
$11$	−0.210969	−	3.30991i	−0.0636096	−	0.997975i
$12$		0			0
$13$	1.06787	−	1.46980i	0.296175	−	0.407650i	−0.634833	−	0.772650i	$-0.718931\pi$
$13$	1.06787	−	1.46980i	0.296175	−	0.407650i	0.931008	+	0.365000i	$0.118931\pi$
$14$	−1.64187	+	4.62289i	−0.438808	+	1.23552i
$15$		0			0
$16$	−3.47148	+	1.98716i	−0.867870	+	0.496791i
$17$	−1.74921	−	2.40759i	−0.424247	−	0.583926i	0.542374	−	0.840137i	$-0.317526\pi$
$17$	−1.74921	−	2.40759i	−0.424247	−	0.583926i	−0.966621	+	0.256212i	$0.917526\pi$
$18$		0			0
$19$	−1.34636	+	4.14366i	−0.308875	+	0.950621i	0.669327	+	0.742968i	$0.266582\pi$
$19$	−1.34636	+	4.14366i	−0.308875	+	0.950621i	−0.978203	+	0.207653i	$0.933418\pi$
$20$	2.93986	+	2.38967i	0.657372	+	0.534347i
$21$		0			0
$22$	2.61646	−	3.89283i	0.557832	−	0.829954i
$23$			3.82341i			0.797236i	0.917117	+	0.398618i	$0.130510\pi$
$23$			3.82341i			0.797236i	−0.917117	+	0.398618i	$0.869490\pi$
$24$		0			0
$25$	−0.436233	+	1.34259i	−0.0872466	+	0.268517i
$26$	2.46418	−	0.727444i	0.483265	−	0.142663i
$27$		0			0
$28$	−5.82555	+	3.76785i	−1.10093	+	0.712056i
$29$	8.48417	−	2.75668i	1.57547	−	0.511902i	0.614587	−	0.788849i	$-0.289323\pi$
$29$	8.48417	−	2.75668i	1.57547	−	0.511902i	0.960885	+	0.276948i	$0.0893228\pi$
$30$		0			0
$31$	1.65449	−	2.27721i	0.297155	−	0.408999i	−0.634167	−	0.773196i	$-0.718657\pi$
$31$	1.65449	−	2.27721i	0.297155	−	0.408999i	0.931322	+	0.364197i	$0.118657\pi$
$32$	−5.60498	−	0.764309i	−0.990830	−	0.135112i
$33$		0			0
$34$	0.114062	−	4.20707i	0.0195615	−	0.721507i
$35$	5.31616	+	3.86242i	0.898595	+	0.652868i
$36$		0			0
$37$	−3.51620	−	10.8218i	−0.578060	−	1.77909i	−0.625513	−	0.780213i	$-0.715110\pi$
$37$	−3.51620	−	10.8218i	−0.578060	−	1.77909i	0.0474530	−	0.998873i	$-0.484890\pi$
$38$	−5.08115	+	3.48526i	−0.824272	+	0.565384i
$39$		0			0
$40$	1.23630	+	5.21327i	0.195476	+	0.824290i
$41$	−7.37845	−	2.39740i	−1.15232	−	0.374412i	−0.330304	−	0.943875i	$-0.607151\pi$
$41$	−7.37845	−	2.39740i	−1.15232	−	0.374412i	−0.822017	+	0.569463i	$0.807151\pi$
$42$		0			0
$43$	2.35165			0.358623			0.179312	−	0.983792i	$-0.442613\pi$
$43$	2.35165			0.358623			0.179312	+	0.983792i	$0.442613\pi$
$44$	6.28896	−	2.10926i	0.948096	−	0.317983i
$45$		0			0
$46$	−3.29561	+	4.28671i	−0.485912	+	0.632041i
$47$	−2.66757	−	0.866745i	−0.389104	−	0.126428i	0.107930	−	0.994158i	$-0.465578\pi$
$47$	−2.66757	−	0.866745i	−0.389104	−	0.126428i	−0.497034	+	0.867731i	$0.665578\pi$
$48$		0			0
$49$	−4.07214	+	2.95858i	−0.581734	+	0.422654i
$50$	−1.64634	+	1.12926i	−0.232828	+	0.159701i
$51$		0			0
$52$	3.38980	+	1.30843i	0.470081	+	0.181446i
$53$	−5.05557	−	3.67309i	−0.694437	−	0.504538i	0.183679	−	0.982986i	$-0.441199\pi$
$53$	−5.05557	−	3.67309i	−0.694437	−	0.504538i	−0.878116	+	0.478449i	$0.841199\pi$
$54$		0			0
$55$	−4.00867	−	4.83757i	−0.540530	−	0.652297i
$56$	−9.77918	−	0.796961i	−1.30680	−	0.106498i
$57$		0			0
$58$	11.8884	+	4.22228i	1.56102	+	0.554412i
$59$	−7.68642	+	2.49747i	−1.00069	+	0.325143i	−0.763140	−	0.646233i	$-0.776343\pi$
$59$	−7.68642	+	2.49747i	−1.00069	+	0.325143i	−0.237547	+	0.971376i	$0.576343\pi$
$60$		0			0
$61$	4.57345	+	6.29481i	0.585570	+	0.805968i	0.994292	−	0.106691i	$-0.0340255\pi$
$61$	4.57345	+	6.29481i	0.585570	+	0.805968i	−0.408722	+	0.912659i	$0.634025\pi$
$62$	3.81783	−	1.12705i	0.484864	−	0.143135i
$63$		0			0
$64$	−5.62536	−	5.68818i	−0.703170	−	0.711022i
$65$		−	3.44150i		−	0.426865i
$66$		0			0
$67$		−	15.0787i		−	1.84216i	−0.389377	−	0.921079i	$-0.627310\pi$
$67$		−	15.0787i		−	1.84216i	0.389377	−	0.921079i	$-0.372690\pi$
$68$	3.75420	−	4.61854i	0.455263	−	0.560081i
$69$		0			0
$70$	2.63111	+	8.91274i	0.314477	+	1.06528i
$71$	−3.24129	−	4.46126i	−0.384671	−	0.529454i	0.572144	−	0.820153i	$-0.306112\pi$
$71$	−3.24129	−	4.46126i	−0.384671	−	0.529454i	−0.956814	+	0.290700i	$0.906112\pi$
$72$		0			0
$73$	11.1487	−	3.62244i	1.30486	−	0.423974i	0.427589	−	0.903973i	$-0.359363\pi$
$73$	11.1487	−	3.62244i	1.30486	−	0.423974i	0.877269	+	0.479999i	$0.159363\pi$
$74$	5.38561	−	15.1639i	0.626065	−	1.76277i
$75$		0			0
$76$	−8.70100	−	0.472149i	−0.998073	−	0.0541593i
$77$	10.6937	−	4.24410i	1.21866	−	0.483660i
$78$		0			0
$79$	−4.34223	−	3.15482i	−0.488539	−	0.354945i	0.316083	−	0.948732i	$-0.397632\pi$
$79$	−4.34223	−	3.15482i	−0.488539	−	0.354945i	−0.804622	+	0.593787i	$0.797632\pi$
$80$	−3.10750	+	6.91061i	−0.347429	+	0.772630i
$81$		0			0
$82$	−6.20607	−	9.04781i	−0.685346	−	0.999164i
$83$	6.10662	−	4.43672i	0.670288	−	0.486993i	−0.199833	−	0.979830i	$-0.564040\pi$
$83$	6.10662	−	4.43672i	0.670288	−	0.486993i	0.870122	+	0.492837i	$0.164040\pi$
$84$		0			0
$85$	−5.36138	−	1.74202i	−0.581523	−	0.188948i
$86$	2.63661	+	2.02702i	0.284313	+	0.218579i
$87$		0			0
$88$	8.86911	+	3.05596i	0.945450	+	0.325767i
$89$	5.20905			0.552158			0.276079	−	0.961135i	$-0.410965\pi$
$89$	5.20905			0.552158			0.276079	+	0.961135i	$0.410965\pi$
$90$		0			0
$91$	5.99381	+	1.94751i	0.628322	+	0.204154i
$92$	−7.38991	+	1.96547i	−0.770452	+	0.204914i
$93$		0			0
$94$	−2.24371	−	3.27110i	−0.231421	−	0.337388i
$95$	2.55038	+	7.84928i	0.261664	+	0.805319i
$96$		0			0
$97$	6.72491	+	4.88593i	0.682811	+	0.496091i	0.874289	−	0.485406i	$-0.161328\pi$
$97$	6.72491	+	4.88593i	0.682811	+	0.496091i	−0.191478	+	0.981497i	$0.561328\pi$
$98$	−7.11574	−	0.192922i	−0.718799	−	0.0194880i
$99$		0			0
$100$	−2.81921	−	0.152981i	−0.281921	−	0.0152981i
$101$	−7.18085	+	9.88359i	−0.714521	+	0.983454i	0.285167	+	0.958478i	$0.407951\pi$
$101$	−7.18085	+	9.88359i	−0.714521	+	0.983454i	−0.999688	+	0.0249764i	$0.992049\pi$
$102$		0			0
$103$	−13.0192	+	4.23019i	−1.28282	+	0.416813i	−0.869572	−	0.493806i	$-0.835605\pi$
$103$	−13.0192	+	4.23019i	−1.28282	+	0.416813i	−0.413246	+	0.910619i	$0.635605\pi$
$104$	2.67275	+	4.38883i	0.262085	+	0.430360i
$105$		0			0
$106$	−2.50213	−	8.47586i	−0.243029	−	0.823248i
$107$	1.16180	−	3.57564i	0.112315	−	0.345670i	−0.879062	−	0.476707i	$-0.841830\pi$
$107$	1.16180	−	3.57564i	0.112315	−	0.345670i	0.991378	+	0.131036i	$0.0418304\pi$
$108$		0			0
$109$			1.43350i			0.137305i	0.997641	+	0.0686524i	$0.0218699\pi$
$109$			1.43350i			0.137305i	−0.997641	+	0.0686524i	$0.978130\pi$
$110$	−0.324650	−	8.87906i	−0.0309541	−	0.846585i
$111$		0			0
$112$	−10.2772	−	9.32276i	−0.971106	−	0.880918i
$113$	−3.77854	+	11.6292i	−0.355455	+	1.09398i	0.600290	+	0.799783i	$0.295052\pi$
$113$	−3.77854	+	11.6292i	−0.355455	+	1.09398i	−0.955745	+	0.294196i	$0.904948\pi$
$114$		0			0
$115$	4.25711	+	5.85941i	0.396978	+	0.546393i
$116$	9.68951	+	14.9812i	0.899648	+	1.39097i
$117$		0			0
$118$	−10.7705	−	3.82526i	−0.991507	−	0.352144i
$119$	6.06789	−	8.35174i	0.556243	−	0.765603i
$120$		0			0
$121$	−10.9110	+	1.39658i	−0.991908	+	0.126962i
$122$	−0.298223	+	10.9997i	−0.0269999	+	0.995866i
$123$		0			0
$124$	5.25191	+	2.02718i	0.471636	+	0.182046i
$125$	3.75318	+	11.5511i	0.335695	+	1.03316i
$126$		0			0
$127$	4.15959	−	3.02212i	0.369104	−	0.268170i	−0.387735	−	0.921771i	$-0.626742\pi$
$127$	4.15959	−	3.02212i	0.369104	−	0.268170i	0.756839	+	0.653601i	$0.226742\pi$
$128$	−1.40405	−	11.2262i	−0.124101	−	0.992270i
$129$		0			0
$130$	2.96642	−	3.85851i	0.260172	−	0.338414i
$131$	−3.48536			−0.304517			−0.152259	−	0.988341i	$-0.548655\pi$
$131$	−3.48536			−0.304517			−0.152259	+	0.988341i	$0.548655\pi$
$132$		0			0
$133$	−15.1138			−1.31053
$134$	12.9972	−	16.9059i	1.12279	−	1.46044i
$135$		0			0
$136$	8.19009	−	1.94224i	0.702294	−	0.166545i
$137$	2.73135	−	1.98444i	0.233355	−	0.169542i	−0.464963	−	0.885330i	$-0.653932\pi$
$137$	2.73135	−	1.98444i	0.233355	−	0.169542i	0.698318	+	0.715788i	$0.253932\pi$
$138$		0			0
$139$	7.02174	+	21.6107i	0.595577	+	1.83300i	0.551835	+	0.833953i	$0.313928\pi$
$139$	7.02174	+	21.6107i	0.595577	+	1.83300i	0.0437412	+	0.999043i	$0.486072\pi$
$140$	−4.73247	+	12.2606i	−0.399967	+	1.03621i
$141$		0			0
$142$	0.211357	−	7.79570i	0.0177367	−	0.654201i
$143$	−5.09020	−	3.22448i	−0.425664	−	0.269645i
$144$		0			0
$145$	9.93271	−	13.6712i	0.824866	−	1.13533i
$146$	15.6220	+	5.54833i	1.29289	+	0.459183i
$147$		0			0
$148$	19.1088	−	12.3592i	1.57074	−	1.01592i
$149$	8.22015	+	11.3141i	0.673421	+	0.926884i	0.999832	−	0.0183440i	$-0.00583941\pi$
$149$	8.22015	+	11.3141i	0.673421	+	0.926884i	−0.326411	+	0.945228i	$0.605839\pi$
$150$		0			0
$151$	2.51556	−	7.74210i	0.204713	−	0.630043i	−0.795012	−	0.606594i	$-0.792535\pi$
$151$	2.51556	−	7.74210i	0.204713	−	0.630043i	0.999725	−	0.0234490i	$-0.00746473\pi$
$152$	−9.34836	−	8.02925i	−0.758252	−	0.651258i
$153$		0			0
$154$	15.6477	+	4.45915i	1.26093	+	0.359328i
$155$		−	5.33201i		−	0.428277i
$156$		0			0
$157$	−5.73392	+	17.6472i	−0.457617	+	1.40840i	0.410419	+	0.911897i	$0.365382\pi$
$157$	−5.73392	+	17.6472i	−0.457617	+	1.40840i	−0.868036	+	0.496502i	$0.834618\pi$
$158$	−2.14908	−	7.27991i	−0.170972	−	0.579159i
$159$		0			0
$160$	−9.44070	+	5.06946i	−0.746353	+	0.400776i
$161$	−12.6140	+	4.09853i	−0.994121	+	0.323009i
$162$		0			0
$163$	−0.374651	+	0.515663i	−0.0293450	+	0.0403899i	−0.823437	−	0.567407i	$-0.807947\pi$
$163$	−0.374651	+	0.515663i	−0.0293450	+	0.0403899i	0.794092	+	0.607797i	$0.207947\pi$
$164$	0.840738	−	15.4935i	0.0656506	−	1.20984i
$165$		0			0
$166$	10.6708	+	0.289307i	0.828218	+	0.0224546i
$167$	−7.36364	−	5.35000i	−0.569816	−	0.413995i	0.265223	−	0.964187i	$-0.414555\pi$
$167$	−7.36364	−	5.35000i	−0.569816	−	0.413995i	−0.835038	+	0.550192i	$0.814555\pi$
$168$		0			0
$169$	2.99726	+	9.22460i	0.230558	+	0.709585i
$170$	−4.50949	−	6.57438i	−0.345862	−	0.504232i
$171$		0			0
$172$	1.20889	+	4.54528i	0.0921772	+	0.346574i
$173$	−15.6017	−	5.06931i	−1.18618	−	0.385412i	−0.351519	−	0.936181i	$-0.614335\pi$
$173$	−15.6017	−	5.06931i	−1.18618	−	0.385412i	−0.834658	+	0.550769i	$0.814335\pi$
$174$		0			0
$175$	−4.89701			−0.370179
$176$	7.30971	+	11.0711i	0.550990	+	0.834512i
$177$		0			0
$178$	5.84025	+	4.48997i	0.437745	+	0.336538i
$179$	0.513988	+	0.167005i	0.0384172	+	0.0124825i	0.328163	−	0.944621i	$-0.393571\pi$
$179$	0.513988	+	0.167005i	0.0384172	+	0.0124825i	−0.289745	+	0.957104i	$0.593571\pi$
$180$		0			0
$181$	4.07479	−	2.96051i	0.302877	−	0.220053i	−0.425957	−	0.904743i	$-0.640063\pi$
$181$	4.07479	−	2.96051i	0.302877	−	0.220053i	0.728834	+	0.684690i	$0.240063\pi$
$182$	5.04143	+	7.34989i	0.373696	+	0.544810i
$183$		0			0
$184$	−9.97953	−	4.16615i	−0.735700	−	0.307133i
$185$	−17.4379	−	12.6694i	−1.28206	−	0.931473i
$186$		0			0
$187$	−7.59986	+	6.29767i	−0.555757	+	0.460531i
$188$	0.303956	−	5.60145i	0.0221683	−	0.408528i
$189$		0			0
$190$	−3.90631	+	10.9987i	−0.283394	+	0.797931i
$191$	−2.78876	+	0.906124i	−0.201788	+	0.0655648i	−0.408167	−	0.912907i	$-0.633832\pi$
$191$	−2.78876	+	0.906124i	−0.201788	+	0.0655648i	0.206379	+	0.978472i	$0.433832\pi$
$192$		0			0
$193$	6.51760	+	8.97070i	0.469147	+	0.645725i	0.976374	−	0.216087i	$-0.0693295\pi$
$193$	6.51760	+	8.97070i	0.469147	+	0.645725i	−0.507227	+	0.861812i	$0.669329\pi$
$194$	3.32833	+	11.2746i	0.238960	+	0.809466i
$195$		0			0
$196$	−7.81169	−	6.34976i	−0.557978	−	0.453554i
$197$			5.97699i			0.425843i	0.977069	+	0.212921i	$0.0682978\pi$
$197$			5.97699i			0.425843i	−0.977069	+	0.212921i	$0.931702\pi$
$198$		0			0
$199$		−	2.73310i		−	0.193745i	−0.995297	−	0.0968723i	$-0.969116\pi$
$199$		−	2.73310i		−	0.193745i	0.995297	−	0.0968723i	$-0.0308838\pi$
$200$	−3.02896	−	2.60156i	−0.214180	−	0.183958i
$201$		0			0
$202$	−16.5702	+	4.89165i	−1.16588	+	0.344175i
$203$	18.1893	+	25.0355i	1.27664	+	1.75715i
$204$		0			0
$205$	−13.9769	+	4.54137i	−0.976189	+	0.317183i
$206$	−18.2430	−	6.47919i	−1.27105	−	0.451427i
$207$		0			0
$208$	−0.786366	+	7.22444i	−0.0545247	+	0.500925i
$209$	13.9992	+	3.58213i	0.968343	+	0.247781i
$210$		0			0
$211$	20.5281	+	14.9146i	1.41321	+	1.02676i	0.992845	+	0.119408i	$0.0380996\pi$
$211$	20.5281	+	14.9146i	1.41321	+	1.02676i	0.420370	+	0.907353i	$0.361900\pi$
$212$	4.50049	−	11.6596i	0.309095	−	0.800788i
$213$		0			0
$214$	4.38462	−	3.00750i	0.299727	−	0.205588i
$215$	3.60392	−	2.61840i	0.245786	−	0.178574i
$216$		0			0
$217$	9.28638	+	3.01733i	0.630401	+	0.204830i
$218$	−1.23562	+	1.60721i	−0.0836866	+	0.108854i
$219$		0			0
$220$	7.28937	−	10.2348i	0.491449	−	0.690030i
$221$	−5.40662			−0.363689
$222$		0			0
$223$	−19.2234	−	6.24606i	−1.28729	−	0.418267i	−0.416150	−	0.909296i	$-0.636621\pi$
$223$	−19.2234	−	6.24606i	−1.28729	−	0.418267i	−0.871143	+	0.491029i	$0.836621\pi$
$224$	−3.48673	−	19.3109i	−0.232967	−	1.29027i
$225$		0			0
$226$	−14.2602	+	9.78137i	−0.948576	+	0.650647i
$227$	1.06125	+	3.26618i	0.0704373	+	0.216784i	0.980078	−	0.198612i	$-0.0636432\pi$
$227$	1.06125	+	3.26618i	0.0704373	+	0.216784i	−0.909641	+	0.415395i	$0.863643\pi$
$228$		0			0
$229$	−4.73582	−	3.44077i	−0.312952	−	0.227373i	0.420210	−	0.907427i	$-0.361956\pi$
$229$	−4.73582	−	3.44077i	−0.312952	−	0.227373i	−0.733162	+	0.680054i	$0.761956\pi$
$230$	−0.277596	+	10.2389i	−0.0183041	+	0.675131i
$231$		0			0
$232$	−2.04949	+	25.1484i	−0.134555	+	1.65108i
$233$	5.80493	−	7.98980i	0.380294	−	0.523429i	−0.575369	−	0.817894i	$-0.695141\pi$
$233$	5.80493	−	7.98980i	0.380294	−	0.523429i	0.955662	+	0.294465i	$0.0951414\pi$
$234$		0			0
$235$	−5.05313	+	1.64186i	−0.329630	+	0.107103i
$236$	−8.77842	−	13.5725i	−0.571427	−	0.883495i
$237$		0			0
$238$	14.0020	−	4.13349i	0.907615	−	0.267934i
$239$	−6.05813	+	18.6450i	−0.391868	+	1.20605i	0.539506	+	0.841982i	$0.318611\pi$
$239$	−6.05813	+	18.6450i	−0.391868	+	1.20605i	−0.931374	+	0.364064i	$0.881389\pi$
$240$		0			0
$241$		−	12.1924i		−	0.785384i	−0.919670	−	0.392692i	$-0.871544\pi$
$241$		−	12.1924i		−	0.785384i	0.919670	−	0.392692i	$-0.128456\pi$
$242$	−13.4369	−	7.83899i	−0.863757	−	0.503909i
$243$		0			0
$244$	−9.81562	+	12.0755i	−0.628381	+	0.773056i
$245$	−2.94641	+	9.06811i	−0.188239	+	0.579340i
$246$		0			0
$247$	4.65262	+	6.40379i	0.296039	+	0.407463i
$248$	4.14097	+	6.79975i	0.262952	+	0.431784i
$249$		0			0
$250$	−5.74858	+	16.1859i	−0.363572	+	1.02369i
$251$	−13.7792	+	18.9654i	−0.869733	+	1.19708i	0.109427	+	0.993995i	$0.465098\pi$
$251$	−13.7792	+	18.9654i	−0.869733	+	1.19708i	−0.979160	+	0.203090i	$0.934902\pi$
$252$		0			0
$253$	12.6551	−	0.806622i	0.795622	−	0.0507119i
$254$	7.26857	+	0.197065i	0.456070	+	0.0123650i
$255$		0			0
$256$	8.10236	−	13.7968i	0.506397	−	0.862300i
$257$	4.56819	+	14.0594i	0.284956	+	0.877004i	0.986412	+	0.164291i	$0.0525336\pi$
$257$	4.56819	+	14.0594i	0.284956	+	0.877004i	−0.701456	+	0.712713i	$0.747466\pi$
$258$		0			0
$259$	31.9333	−	23.2009i	1.98424	−	1.44164i
$260$	6.65174	−	1.76914i	0.412524	−	0.109717i
$261$		0			0
$262$	−3.90769	−	3.00423i	−0.241418	−	0.185602i
$263$	10.3241			0.636611			0.318306	−	0.947988i	$-0.396886\pi$
$263$	10.3241			0.636611			0.318306	+	0.947988i	$0.396886\pi$
$264$		0			0
$265$	−11.8375			−0.727169
$266$	−16.9452	−	13.0274i	−1.03897	−	0.798762i
$267$		0			0
$268$	29.1442	−	7.75139i	1.78027	−	0.473491i
$269$	4.14874	−	3.01423i	0.252953	−	0.183781i	−0.454082	−	0.890960i	$-0.650033\pi$
$269$	4.14874	−	3.01423i	0.252953	−	0.183781i	0.707034	+	0.707179i	$0.250033\pi$
$270$		0			0
$271$	−3.21618	−	9.89839i	−0.195369	−	0.601284i	−0.999972	−	0.00747111i	$-0.997622\pi$
$271$	−3.21618	−	9.89839i	−0.195369	−	0.601284i	0.804603	−	0.593813i	$-0.202378\pi$
$272$	10.8566	+	4.88192i	0.658280	+	0.296010i
$273$		0			0
$274$	4.77282	+	0.129401i	0.288337	+	0.00781737i
$275$	4.53587	+	1.16065i	0.273523	+	0.0699896i
$276$		0			0
$277$	10.9032	−	15.0070i	0.655110	−	0.901681i	−0.344197	−	0.938897i	$-0.611849\pi$
$277$	10.9032	−	15.0070i	0.655110	−	0.901681i	0.999307	+	0.0372160i	$0.0118490\pi$
$278$	−10.7549	+	30.2818i	−0.645036	+	1.81618i
$279$		0			0
$280$	−15.8741	+	9.66712i	−0.948656	+	0.577721i
$281$	7.89816	+	10.8709i	0.471165	+	0.648503i	0.976777	−	0.214258i	$-0.0687334\pi$
$281$	7.89816	+	10.8709i	0.471165	+	0.648503i	−0.505612	+	0.862761i	$0.668733\pi$
$282$		0			0
$283$	0.130142	−	0.400534i	0.00773611	−	0.0238093i	−0.947114	−	0.320897i	$-0.896016\pi$
$283$	0.130142	−	0.400534i	0.00773611	−	0.0238093i	0.954850	+	0.297088i	$0.0960155\pi$
$284$	6.95652	−	8.55815i	0.412794	−	0.507833i
$285$		0			0
$286$	−2.92764	−	8.00274i	−0.173115	−	0.473212i
$287$		−	26.9125i		−	1.58859i
$288$		0			0
$289$	2.51656	−	7.74519i	0.148033	−	0.455599i
$290$	22.9203	−	6.76623i	1.34592	−	0.397327i
$291$		0			0
$292$	12.7326	+	19.6862i	0.745119	+	1.15205i
$293$	17.0553	−	5.54161i	0.996382	−	0.323744i	0.234963	−	0.972004i	$-0.424503\pi$
$293$	17.0553	−	5.54161i	0.996382	−	0.323744i	0.761419	+	0.648260i	$0.224503\pi$
$294$		0			0
$295$	−8.99875	+	12.3857i	−0.523928	+	0.721124i
$296$	32.0774	+	2.61417i	1.86446	+	0.151945i
$297$		0			0
$298$	−0.536015	+	19.7704i	−0.0310505	+	1.14527i
$299$	5.61966	+	4.08292i	0.324993	+	0.236122i
$300$		0			0
$301$	2.52087	+	7.75843i	0.145300	+	0.447188i
$302$	9.49374	−	6.51194i	0.546303	−	0.374720i
$303$		0			0
$304$	−3.56028	−	17.0601i	−0.204196	−	0.978462i
$305$	14.0177	+	4.55463i	0.802652	+	0.260797i
$306$		0			0
$307$	−9.77664			−0.557983			−0.278991	−	0.960294i	$-0.590000\pi$
$307$	−9.77664			−0.557983			−0.278991	+	0.960294i	$0.590000\pi$
$308$	13.7002	+	18.4871i	0.780644	+	1.05340i
$309$		0			0
$310$	4.59596	−	5.97811i	0.261033	−	0.339534i
$311$	−10.8311	−	3.51925i	−0.614178	−	0.199558i	−0.0146241	−	0.999893i	$-0.504655\pi$
$311$	−10.8311	−	3.51925i	−0.614178	−	0.199558i	−0.599554	+	0.800335i	$0.704655\pi$
$312$		0			0
$313$	−10.8009	+	7.84731i	−0.610503	+	0.443556i	−0.849591	−	0.527442i	$-0.823151\pi$
$313$	−10.8009	+	7.84731i	−0.610503	+	0.443556i	0.239089	+	0.970998i	$0.423151\pi$
$314$	−21.6398	+	14.8432i	−1.22121	+	0.837649i
$315$		0			0
$316$	3.86547	−	10.0145i	0.217450	−	0.563358i
$317$	−9.51230	−	6.91109i	−0.534264	−	0.388165i	0.287686	−	0.957725i	$-0.407114\pi$
$317$	−9.51230	−	6.91109i	−0.534264	−	0.388165i	−0.821950	+	0.569559i	$0.807114\pi$
$318$		0			0
$319$	−10.9142	−	27.5003i	−0.611080	−	1.53972i
$320$	−14.9543	−	2.45372i	−0.835972	−	0.137167i
$321$		0			0
$322$	−17.6752	−	6.27754i	−0.985002	−	0.349833i
$323$	12.3313	−	4.00668i	0.686131	−	0.222938i
$324$		0			0
$325$	1.50750	+	2.07489i	0.0836209	+	0.115094i
$326$	−0.864529	+	0.255215i	−0.0478818	+	0.0141351i
$327$		0			0
$328$	14.2974	−	16.6463i	0.789440	−	0.919136i
$329$		−	9.72980i		−	0.536421i
$330$		0			0
$331$			0.109341i			0.00600991i	0.999995	+	0.00300496i	$0.000956508\pi$
$331$			0.109341i			0.00600991i	−0.999995	+	0.00300496i	$0.999043\pi$
$332$	11.7145	+	9.52216i	0.642916	+	0.522596i
$333$		0			0
$334$	−3.64446	−	12.3454i	−0.199416	−	0.675511i
$335$	−16.7891	−	23.1083i	−0.917288	−	1.26254i
$336$		0			0
$337$	−19.3456	+	6.28577i	−1.05382	+	0.342408i	−0.784167	−	0.620549i	$-0.786910\pi$
$337$	−19.3456	+	6.28577i	−1.05382	+	0.342408i	−0.269655	+	0.962957i	$0.586910\pi$
$338$	−4.59076	+	12.9259i	−0.249705	+	0.703076i
$339$		0			0
$340$	0.610902	−	11.2580i	0.0331308	−	0.610551i
$341$	−7.88640	−	4.99579i	−0.427073	−	0.270537i
$342$		0			0
$343$	5.51899	+	4.00978i	0.297998	+	0.216508i
$344$	−2.56246	+	6.13806i	−0.138158	+	0.330942i
$345$		0			0
$346$	−13.1227	−	19.1316i	−0.705482	−	1.02852i
$347$	−0.0735503	+	0.0534374i	−0.00394839	+	0.00286867i	−0.589758	−	0.807580i	$-0.700777\pi$
$347$	−0.0735503	+	0.0534374i	−0.00394839	+	0.00286867i	0.585809	+	0.810449i	$0.300777\pi$
$348$		0			0
$349$	3.99941	+	1.29949i	0.214083	+	0.0695599i	0.414095	−	0.910234i	$-0.364098\pi$
$349$	3.99941	+	1.29949i	0.214083	+	0.0695599i	−0.200012	+	0.979793i	$0.564098\pi$
$350$	−5.49040	−	4.22101i	−0.293474	−	0.225622i
$351$		0			0
$352$	−1.34732	+	18.7132i	−0.0718122	+	0.997418i
$353$	−22.5015			−1.19764			−0.598818	−	0.800885i	$-0.704363\pi$
$353$	−22.5015			−1.19764			−0.598818	+	0.800885i	$0.704363\pi$
$354$		0			0
$355$	−9.93463	−	3.22796i	−0.527275	−	0.171322i
$356$	2.67777	+	10.0681i	0.141922	+	0.533607i
$357$		0			0
$358$	0.432319	+	0.630276i	0.0228488	+	0.0333111i
$359$	0.804066	+	2.47466i	0.0424370	+	0.130608i	0.970030	−	0.242984i	$-0.0781262\pi$
$359$	0.804066	+	2.47466i	0.0424370	+	0.130608i	−0.927593	+	0.373591i	$0.878126\pi$
$360$		0			0
$361$	0.0140835	+	0.0102322i	0.000741236	+	0.000538539i
$362$	7.12038	+	0.193047i	0.374239	+	0.0101463i
$363$		0			0
$364$	−0.682965	+	12.5860i	−0.0357971	+	0.659686i
$365$	13.0522	−	17.9648i	0.683182	−	0.940319i
$366$		0			0
$367$	−14.6886	+	4.77262i	−0.766739	+	0.249129i	−0.666169	−	0.745801i	$-0.732067\pi$
$367$	−14.6886	+	4.77262i	−0.766739	+	0.249129i	−0.100571	+	0.994930i	$0.532067\pi$
$368$	−7.59774	−	13.2729i	−0.396060	−	0.691898i
$369$		0			0
$370$	−8.63048	−	29.2353i	−0.448677	−	1.51987i
$371$	6.69869	−	20.6165i	0.347779	−	1.07035i
$372$		0			0
$373$		−	5.55960i		−	0.287865i	−0.989587	−	0.143933i	$-0.954025\pi$
$373$		−	5.55960i		−	0.287865i	0.989587	−	0.143933i	$-0.0459749\pi$
$374$	−13.9491	+	0.510028i	−0.721290	+	0.0263729i
$375$		0			0
$376$	5.16899	−	6.01820i	0.266570	−	0.310365i
$377$	5.00826	−	15.4139i	0.257939	−	0.793854i
$378$		0			0
$379$	15.1814	+	20.8954i	0.779818	+	1.07333i	0.995302	+	0.0968197i	$0.0308670\pi$
$379$	15.1814	+	20.8954i	0.779818	+	1.07333i	−0.215484	+	0.976507i	$0.569133\pi$
$380$	−13.8601	+	8.96441i	−0.711007	+	0.459865i
$381$		0			0
$382$	−3.90773	−	1.38787i	−0.199937	−	0.0710096i
$383$	−0.0646313	+	0.0889574i	−0.00330251	+	0.00454551i	−0.810665	−	0.585510i	$-0.800894\pi$
$383$	−0.0646313	+	0.0889574i	−0.00330251	+	0.00454551i	0.807363	+	0.590056i	$0.200894\pi$
$384$		0			0
$385$	11.6627	−	18.4109i	0.594386	−	0.938304i
$386$	−0.424996	+	15.6756i	−0.0216317	+	0.797867i
$387$		0			0
$388$	−5.98654	+	15.5096i	−0.303921	+	0.787382i
$389$	−6.06738	−	18.6735i	−0.307628	−	0.946782i	−0.978683	−	0.205375i	$-0.934159\pi$
$389$	−6.06738	−	18.6735i	−0.307628	−	0.946782i	0.671055	−	0.741407i	$-0.265841\pi$
$390$		0			0
$391$	9.20520	−	6.68797i	0.465527	−	0.338225i
$392$	−3.28505	−	13.8525i	−0.165920	−	0.699658i
$393$		0			0
$394$	−5.15190	+	6.70124i	−0.259549	+	0.337604i
$395$	−10.1672			−0.511567
$396$		0			0
$397$	30.2146			1.51643			0.758215	−	0.652005i	$-0.226072\pi$
$397$	30.2146			1.51643			0.758215	+	0.652005i	$0.226072\pi$
$398$	2.35582	−	3.06428i	0.118086	−	0.153599i
$399$		0			0
$400$	−1.15357	−	5.52763i	−0.0576783	−	0.276382i
$401$	0.155811	−	0.113203i	0.00778083	−	0.00565310i	−0.583888	−	0.811834i	$-0.698469\pi$
$401$	0.155811	−	0.113203i	0.00778083	−	0.00565310i	0.591669	+	0.806181i	$0.298469\pi$
$402$		0			0
$403$	−1.58026	−	4.86355i	−0.0787185	−	0.242271i
$404$	−22.7945	−	8.79842i	−1.13407	−	0.437738i
$405$		0			0
$406$	−1.18608	+	43.7475i	−0.0588642	+	2.17115i
$407$	−35.0772	+	13.9214i	−1.73871	+	0.690057i
$408$		0			0
$409$	−18.2103	+	25.0644i	−0.900443	+	1.23935i	0.0698831	+	0.997555i	$0.477737\pi$
$409$	−18.2103	+	25.0644i	−0.900443	+	1.23935i	−0.970326	+	0.241799i	$0.922263\pi$
$410$	−19.5850	−	6.95582i	−0.967234	−	0.343523i
$411$		0			0
$412$	−14.8688	−	22.9890i	−0.732533	−	1.13259i
$413$	−16.4790	−	22.6814i	−0.810880	−	1.11608i
$414$		0			0
$415$	4.41846	−	13.5986i	0.216894	−	0.667530i
$416$	−7.10880	+	7.42204i	−0.348538	+	0.363895i
$417$		0			0
$418$	12.6079	+	16.0829i	0.616671	+	0.786639i
$419$		−	28.8010i		−	1.40702i	−0.710686	−	0.703510i	$-0.751615\pi$
$419$		−	28.8010i		−	1.40702i	0.710686	−	0.703510i	$-0.248385\pi$
$420$		0			0
$421$	−0.977355	+	3.00799i	−0.0476334	+	0.146601i	−0.972044	−	0.234798i	$-0.924557\pi$
$421$	−0.977355	+	3.00799i	−0.0476334	+	0.146601i	0.924411	+	0.381398i	$0.124557\pi$
$422$	10.1599	+	34.4162i	0.494576	+	1.67535i
$423$		0			0
$424$	15.0959	−	9.19326i	0.733124	−	0.446464i
$425$	3.99546	−	1.29820i	0.193808	−	0.0629721i
$426$		0			0
$427$	−15.8650	+	21.8362i	−0.767759	+	1.05673i
$428$	7.50826	+	0.407427i	0.362925	+	0.0196937i
$429$		0			0
$430$	6.29758	+	0.170740i	0.303696	+	0.00823379i
$431$	2.16293	+	1.57146i	0.104185	+	0.0756947i	0.638658	−	0.769491i	$-0.279490\pi$
$431$	2.16293	+	1.57146i	0.104185	+	0.0756947i	−0.534473	+	0.845185i	$0.679490\pi$
$432$		0			0
$433$	−6.48467	−	19.9578i	−0.311634	−	0.959110i	−0.977118	−	0.212698i	$-0.931775\pi$
$433$	−6.48467	−	19.9578i	−0.311634	−	0.959110i	0.665484	−	0.746412i	$-0.268225\pi$
$434$	7.81084	+	11.3874i	0.374932	+	0.546613i
$435$		0			0
$436$	−2.77069	+	0.736910i	−0.132692	+	0.0352916i
$437$	−15.8429	−	5.14767i	−0.757869	−	0.246247i
$438$		0			0
$439$	9.75312			0.465491			0.232746	−	0.972538i	$-0.425229\pi$
$439$	9.75312			0.465491			0.232746	+	0.972538i	$0.425229\pi$
$440$	16.9946	−	5.19187i	0.810186	−	0.247513i
$441$		0			0
$442$	−6.06176	−	4.66027i	−0.288329	−	0.221667i
$443$	19.6000	+	6.36841i	0.931222	+	0.302572i	0.735062	−	0.678000i	$-0.237153\pi$
$443$	19.6000	+	6.36841i	0.931222	+	0.302572i	0.196160	+	0.980572i	$0.437153\pi$
$444$		0			0
$445$	7.98292	−	5.79993i	0.378427	−	0.274943i
$446$	−16.1689	−	23.5726i	−0.765621	−	1.11620i
$447$		0			0
$448$	12.7360	−	24.6563i	0.601718	−	1.16490i
$449$	32.3068	+	23.4722i	1.52465	+	1.10772i	0.959121	+	0.282995i	$0.0913281\pi$
$449$	32.3068	+	23.4722i	1.52465	+	1.10772i	0.565529	+	0.824728i	$0.308672\pi$
$450$		0			0
$451$	−6.37856	+	24.9278i	−0.300355	+	1.17380i
$452$	−24.4193	−	1.32508i	−1.14859	−	0.0623267i
$453$		0			0
$454$	−1.62546	+	4.57670i	−0.0762867	+	0.214795i
$455$	11.3540	−	3.68913i	0.532283	−	0.172949i
$456$		0			0
$457$	−19.8109	−	27.2674i	−0.926716	−	1.27552i	−0.961127	−	0.276107i	$-0.910955\pi$
$457$	−19.8109	−	27.2674i	−0.926716	−	1.27552i	0.0344108	−	0.999408i	$-0.489045\pi$
$458$	−2.34388	−	7.93978i	−0.109522	−	0.371001i
$459$		0			0
$460$	−9.13669	+	11.2403i	−0.426001	+	0.524081i
$461$		−	18.4692i		−	0.860196i	−0.902782	−	0.430098i	$-0.858479\pi$
$461$		−	18.4692i		−	0.860196i	0.902782	−	0.430098i	$-0.141521\pi$
$462$		0			0
$463$		−	21.9821i		−	1.02159i	−0.859701	−	0.510797i	$-0.829350\pi$
$463$		−	21.9821i		−	1.02159i	0.859701	−	0.510797i	$-0.170650\pi$
$464$	−23.9747	+	26.4292i	−1.11300	+	1.22694i
$465$		0			0
$466$	13.3952	−	3.95436i	0.620520	−	0.183182i
$467$	21.5485	+	29.6590i	0.997147	+	1.37245i	0.927060	+	0.374914i	$0.122328\pi$
$467$	21.5485	+	29.6590i	0.997147	+	1.37245i	0.0700868	+	0.997541i	$0.477672\pi$
$468$		0			0
$469$	49.7468	−	16.1637i	2.29709	−	0.746371i
$470$	−7.08066	−	2.51477i	−0.326606	−	0.115998i
$471$		0			0
$472$	1.85678	−	22.7838i	0.0854651	−	1.04871i
$473$	−0.496125	−	7.78374i	−0.0228119	−	0.357897i
$474$		0			0
$475$	−4.97590	−	3.61520i	−0.228310	−	0.165877i
$476$	19.2616	+	7.43475i	0.882853	+	0.340771i
$477$		0			0
$478$	−22.8634	+	15.6825i	−1.04575	+	0.717299i
$479$	19.1217	−	13.8928i	0.873695	−	0.634776i	−0.0578810	−	0.998323i	$-0.518434\pi$
$479$	19.1217	−	13.8928i	0.873695	−	0.634776i	0.931576	+	0.363547i	$0.118434\pi$
$480$		0			0
$481$	−19.6607	−	6.38816i	−0.896452	−	0.291275i
$482$	10.5093	−	13.6698i	0.478688	−	0.622644i
$483$		0			0
$484$	−8.30823	−	20.3709i	−0.377647	−	0.925950i
$485$	15.7462			0.714996
$486$		0			0
$487$	−35.0909	−	11.4017i	−1.59012	−	0.516661i	−0.625482	−	0.780238i	$-0.715098\pi$
$487$	−35.0909	−	11.4017i	−1.59012	−	0.516661i	−0.964638	+	0.263577i	$0.915098\pi$
$488$	−21.4136	+	5.07812i	−0.969347	+	0.229875i
$489$		0			0
$490$	−11.1198	+	7.62725i	−0.502339	+	0.344564i
$491$	−5.75631	−	17.7161i	−0.259779	−	0.799517i	−0.992850	−	0.119365i	$-0.961914\pi$
$491$	−5.75631	−	17.7161i	−0.259779	−	0.799517i	0.733072	−	0.680151i	$-0.238086\pi$
$492$		0			0
$493$	−21.4776	−	15.6044i	−0.967302	−	0.702786i
$494$	−0.303386	+	11.1901i	−0.0136500	+	0.503467i
$495$		0			0
$496$	−1.21834	+	11.1930i	−0.0547051	+	0.502582i
$497$	11.2438	−	15.4758i	0.504353	−	0.694183i
$498$		0			0
$499$	32.6136	−	10.5968i	1.45998	−	0.474377i	0.531919	−	0.846795i	$-0.321471\pi$
$499$	32.6136	−	10.5968i	1.45998	−	0.474377i	0.928065	+	0.372418i	$0.121471\pi$
$500$	−20.3967	+	13.1922i	−0.912168	+	0.589971i
$501$		0			0
$502$	−31.7962	+	9.38646i	−1.41913	+	0.418938i
$503$	1.01615	−	3.12740i	0.0453080	−	0.139444i	−0.925843	−	0.377907i	$-0.876644\pi$
$503$	1.01615	−	3.12740i	0.0453080	−	0.139444i	0.971151	+	0.238464i	$0.0766438\pi$
$504$		0			0
$505$			23.1421i			1.02981i
$506$	14.8839	+	10.0038i	0.661669	+	0.444724i
$507$		0			0
$508$	7.97946	+	6.48613i	0.354031	+	0.287776i
$509$	−10.4865	+	32.2741i	−0.464806	+	1.43052i	0.394421	+	0.918930i	$0.370945\pi$
$509$	−10.4865	+	32.2741i	−0.464806	+	1.43052i	−0.859227	+	0.511595i	$0.829055\pi$
$510$		0			0
$511$	23.9019	+	32.8981i	1.05736	+	1.45533i
$512$	20.9764	−	8.48473i	0.927035	−	0.374976i
$513$		0			0
$514$	−6.99689	+	19.7007i	−0.308620	+	0.868959i
$515$	−15.2420	+	20.9788i	−0.671642	+	0.924436i
$516$		0			0
$517$	−2.30607	+	9.01225i	−0.101421	+	0.396358i
$518$	55.8010	+	1.51287i	2.45176	+	0.0664719i
$519$		0			0
$520$	8.98268	+	3.75000i	0.393917	+	0.164448i
$521$	−6.93119	−	21.3320i	−0.303661	−	0.934572i	−0.980174	−	0.198141i	$-0.936510\pi$
$521$	−6.93119	−	21.3320i	−0.303661	−	0.934572i	0.676513	−	0.736431i	$-0.263490\pi$
$522$		0			0
$523$	21.7656	−	15.8137i	0.951744	−	0.691483i	0.000525638	−	1.00000i	$-0.499833\pi$
$523$	21.7656	−	15.8137i	0.951744	−	0.691483i	0.951219	+	0.308517i	$0.0998327\pi$
$524$	−1.79169	−	6.73653i	−0.0782704	−	0.294286i
$525$		0			0
$526$	11.5751	+	8.89893i	0.504699	+	0.388012i
$527$	−8.37664			−0.364892
$528$		0			0
$529$	8.38153			0.364414
$530$	−13.2719	−	10.2034i	−0.576492	−	0.443206i
$531$		0			0
$532$	−7.76941	−	29.2120i	−0.336847	−	1.26650i
$533$	−11.4030	+	8.28475i	−0.493918	+	0.358852i
$534$		0			0
$535$	−2.20078	−	6.77329i	−0.0951478	−	0.292835i
$536$	39.3571	+	16.4304i	1.69997	+	0.709685i
$537$		0			0
$538$	7.24959	+	0.196551i	0.312552	+	0.00847390i
$539$	10.6517	+	12.8542i	0.458802	+	0.553671i
$540$		0			0
$541$	−8.91106	+	12.2650i	−0.383116	+	0.527315i	−0.956407	−	0.292038i	$-0.905667\pi$
$541$	−8.91106	+	12.2650i	−0.383116	+	0.527315i	0.573290	+	0.819352i	$0.305667\pi$
$542$	4.92608	−	13.8700i	0.211593	−	0.595768i
$543$		0			0
$544$	7.96418	+	14.8314i	0.341461	+	0.635892i
$545$	1.59611	+	2.19686i	0.0683699	+	0.0941031i
$546$		0			0
$547$	−2.14142	+	6.59062i	−0.0915606	+	0.281795i	−0.986342	−	0.164710i	$-0.947331\pi$
$547$	−2.14142	+	6.59062i	−0.0915606	+	0.281795i	0.894781	+	0.446504i	$0.147331\pi$
$548$	5.23963	+	4.25905i	0.223826	+	0.181937i
$549$		0			0
$550$	4.08507	+	5.21101i	0.174188	+	0.222198i
$551$			38.8670i			1.65579i
$552$		0			0
$553$	5.75351	−	17.7075i	0.244664	−	0.752998i
$554$	25.1597	−	7.42734i	1.06893	−	0.315557i
$555$		0			0
$556$	−38.1597	+	24.6809i	−1.61833	+	1.04670i
$557$	0.278322	−	0.0904324i	0.0117929	−	0.00383174i	−0.303115	−	0.952954i	$-0.598027\pi$
$557$	0.278322	−	0.0904324i	0.0117929	−	0.00383174i	0.314908	+	0.949122i	$0.398027\pi$
$558$		0			0
$559$	2.51127	−	3.45646i	0.106215	−	0.146193i
$560$	−26.1302	−	2.84422i	−1.10420	−	0.120190i
$561$		0			0
$562$	−0.515019	+	18.9960i	−0.0217248	+	0.801299i
$563$	−15.4345	−	11.2138i	−0.650486	−	0.472606i	0.212951	−	0.977063i	$-0.431693\pi$
$563$	−15.4345	−	11.2138i	−0.650486	−	0.472606i	−0.863437	+	0.504457i	$0.831693\pi$
$564$		0			0
$565$	7.15764	+	22.0290i	0.301124	+	0.926765i
$566$	0.491154	−	0.336892i	0.0206448	−	0.0141606i
$567$		0			0
$568$	15.1762	−	3.59896i	0.636780	−	0.151009i
$569$	29.4110	+	9.55621i	1.23297	+	0.400617i	0.851791	−	0.523882i	$-0.175517\pi$
$569$	29.4110	+	9.55621i	1.23297	+	0.400617i	0.381183	+	0.924500i	$0.375517\pi$
$570$		0			0
$571$	−14.7169			−0.615883			−0.307942	−	0.951405i	$-0.599640\pi$
$571$	−14.7169			−0.615883			−0.307942	+	0.951405i	$0.599640\pi$
$572$	3.61562	−	11.4960i	0.151177	−	0.480670i
$573$		0			0
$574$	23.1974	−	30.1736i	0.968241	−	1.25942i
$575$	−5.13326	−	1.66790i	−0.214072	−	0.0695561i
$576$		0			0
$577$	5.09251	−	3.69993i	0.212004	−	0.154030i	−0.476716	−	0.879057i	$-0.658173\pi$
$577$	5.09251	−	3.69993i	0.212004	−	0.154030i	0.688720	+	0.725027i	$0.258173\pi$
$578$	9.49752	−	6.51453i	0.395045	−	0.270969i
$579$		0			0
$580$	31.5298	+	12.1702i	1.30920	+	0.505338i
$581$	21.1834	+	15.3906i	0.878835	+	0.638511i
$582$		0			0
$583$	−11.0910	+	17.5084i	−0.459343	+	0.725124i
$584$	−2.69315	+	33.0465i	−0.111443	+	1.36748i
$585$		0			0
$586$	23.8986	+	8.48783i	0.987242	+	0.350629i
$587$	−40.0307	+	13.0068i	−1.65224	+	0.536847i	−0.979225	−	0.202778i	$-0.935003\pi$
$587$	−40.0307	+	13.0068i	−1.65224	+	0.536847i	−0.673020	+	0.739624i	$0.735003\pi$
$588$		0			0
$589$	7.20845	+	9.92158i	0.297019	+	0.408811i
$590$	−20.7651	+	6.13001i	−0.854886	+	0.252369i
$591$		0			0
$592$	33.7111	+	30.5803i	1.38552	+	1.25684i
$593$			19.2298i			0.789675i	0.918751	+	0.394837i	$0.129199\pi$
$593$			19.2298i			0.789675i	−0.918751	+	0.394837i	$0.870801\pi$
$594$		0			0
$595$		−	19.5553i		−	0.801690i
$596$	−17.6422	+	21.7041i	−0.722654	+	0.889034i
$597$		0			0
$598$	2.78132	+	9.42157i	0.113736	+	0.385277i
$599$	9.14751	+	12.5905i	0.373757	+	0.514433i	0.953917	−	0.300070i	$-0.0970100\pi$
$599$	9.14751	+	12.5905i	0.373757	+	0.514433i	−0.580160	+	0.814502i	$0.697010\pi$
$600$		0			0
$601$	−4.94174	+	1.60567i	−0.201578	+	0.0654966i	−0.408066	−	0.912953i	$-0.633797\pi$
$601$	−4.94174	+	1.60567i	−0.201578	+	0.0654966i	0.206488	+	0.978449i	$0.433797\pi$
$602$	−3.86110	+	10.8714i	−0.157367	+	0.443086i
$603$		0			0
$604$	16.2571	+	0.882174i	0.661494	+	0.0358951i
$605$	−15.1662	+	14.2889i	−0.616593	+	0.580927i
$606$		0			0
$607$	4.32559	+	3.14273i	0.175570	+	0.127559i	0.672100	−	0.740460i	$-0.265393\pi$
$607$	4.32559	+	3.14273i	0.175570	+	0.127559i	−0.496529	+	0.868020i	$0.665393\pi$
$608$	10.7133	−	22.1961i	0.434483	−	0.900171i
$609$		0			0
$610$	11.7904	+	17.1892i	0.477379	+	0.695970i
$611$	−4.12257	+	2.99522i	−0.166781	+	0.121174i
$612$		0			0
$613$	−20.2178	−	6.56916i	−0.816590	−	0.265326i	−0.129203	−	0.991618i	$-0.541242\pi$
$613$	−20.2178	−	6.56916i	−0.816590	−	0.265326i	−0.687386	+	0.726292i	$0.741242\pi$
$614$	−10.9613	−	8.42704i	−0.442363	−	0.340088i
$615$		0			0
$616$	−0.574762	+	32.5363i	−0.0231578	+	1.31093i
$617$	−5.45994			−0.219809			−0.109905	−	0.993942i	$-0.535055\pi$
$617$	−5.45994			−0.219809			−0.109905	+	0.993942i	$0.535055\pi$
$618$		0			0
$619$	6.31236	+	2.05101i	0.253715	+	0.0824371i	0.433113	−	0.901339i	$-0.357415\pi$
$619$	6.31236	+	2.05101i	0.253715	+	0.0824371i	−0.179398	+	0.983777i	$0.557415\pi$
$620$	10.3057	−	2.74098i	0.413889	−	0.110081i
$621$		0			0
$622$	−9.11015	−	13.2817i	−0.365284	−	0.532546i
$623$	5.58387	+	17.1854i	0.223713	+	0.688519i
$624$		0			0
$625$	12.9028	+	9.37445i	0.516113	+	0.374978i
$626$	−18.8737	−	0.511704i	−0.754346	−	0.0204518i
$627$		0			0
$628$	−37.0562	−	2.01081i	−1.47870	−	0.0802400i
$629$	−19.9037	+	27.3952i	−0.793614	+	1.09232i
$630$		0			0
$631$	−19.5656	+	6.35725i	−0.778894	+	0.253078i	−0.671368	−	0.741124i	$-0.734293\pi$
$631$	−19.5656	+	6.35725i	−0.778894	+	0.253078i	−0.107526	+	0.994202i	$0.534293\pi$
$632$	12.9659	−	7.89609i	0.515756	−	0.314089i
$633$		0			0
$634$	−4.70788	−	15.9477i	−0.186974	−	0.633365i
$635$	3.00969	−	9.26286i	0.119436	−	0.367585i
$636$		0			0
$637$			9.14464i			0.362324i
$638$	11.4673	−	40.2402i	0.453994	−	1.59312i
$639$		0			0
$640$	−14.6514	−	15.6410i	−0.579147	−	0.618266i
$641$	6.24661	−	19.2251i	0.246726	−	0.759346i	−0.748621	−	0.662998i	$-0.769284\pi$
$641$	6.24661	−	19.2251i	0.246726	−	0.759346i	0.995348	−	0.0963480i	$-0.0307162\pi$
$642$		0			0
$643$	−12.0086	−	16.5284i	−0.473573	−	0.651817i	0.503681	−	0.863890i	$-0.331979\pi$
$643$	−12.0086	−	16.5284i	−0.473573	−	0.651817i	−0.977254	+	0.212072i	$0.931979\pi$
$644$	−14.4060	−	22.2735i	−0.567677	−	0.877698i
$645$		0			0
$646$	17.2791	+	6.13685i	0.679837	+	0.241451i
$647$	8.24593	−	11.3496i	0.324181	−	0.446197i	−0.615557	−	0.788092i	$-0.711069\pi$
$647$	8.24593	−	11.3496i	0.324181	−	0.446197i	0.939738	+	0.341896i	$0.111069\pi$
$648$		0			0
$649$	9.88799	+	24.9145i	0.388138	+	0.977978i
$650$	−0.0983001	+	3.62571i	−0.00385565	+	0.142212i
$651$		0			0
$652$	−1.18927	−	0.459046i	−0.0465755	−	0.0179776i
$653$	−13.1470	−	40.4622i	−0.514480	−	1.58341i	−0.784226	−	0.620476i	$-0.786940\pi$
$653$	−13.1470	−	40.4622i	−0.514480	−	1.58341i	0.269745	−	0.962932i	$-0.413060\pi$
$654$		0			0
$655$	−5.34135	+	3.88072i	−0.208704	+	0.151632i
$656$	30.3782	−	6.33965i	1.18607	−	0.247522i
$657$		0			0
$658$	8.38666	−	10.9088i	0.326946	−	0.425269i
$659$	35.3651			1.37763			0.688815	−	0.724937i	$-0.258131\pi$
$659$	35.3651			1.37763			0.688815	+	0.724937i	$0.258131\pi$
$660$		0			0
$661$	−6.75994			−0.262931			−0.131466	−	0.991321i	$-0.541968\pi$
$661$	−6.75994			−0.262931			−0.131466	+	0.991321i	$0.541968\pi$
$662$	−0.0942470	+	0.122590i	−0.00366301	+	0.00476460i
$663$		0			0
$664$	4.92629	+	20.7734i	0.191177	+	0.806164i
$665$	−23.1620	+	16.8282i	−0.898183	+	0.652569i
$666$		0			0
$667$	10.5399	+	32.4385i	0.408107	+	1.25602i
$668$	6.55514	−	16.9827i	0.253626	−	0.657081i
$669$		0			0
$670$	1.09478	−	40.3799i	0.0422950	−	1.56001i
$671$	19.8704	−	16.4657i	0.767088	−	0.635652i
$672$		0			0
$673$	−21.9062	+	30.1512i	−0.844420	+	1.16224i	0.140645	+	0.990060i	$0.455083\pi$
$673$	−21.9062	+	30.1512i	−0.844420	+	1.16224i	−0.985065	+	0.172184i	$0.944917\pi$
$674$	−27.1079	−	9.62764i	−1.04416	−	0.370843i
$675$		0			0
$676$	−16.2886	+	10.5351i	−0.626485	+	0.405197i
$677$	20.6777	+	28.4604i	0.794709	+	1.09382i	0.993506	+	0.113782i	$0.0362967\pi$
$677$	20.6777	+	28.4604i	0.794709	+	1.09382i	−0.198797	+	0.980041i	$0.563703\pi$
$678$		0			0
$679$	−8.91058	+	27.4240i	−0.341957	+	1.05243i
$680$	10.3888	−	12.0956i	0.398394	−	0.463846i
$681$		0			0
$682$	−4.53587	−	12.3989i	−0.173688	−	0.474778i
$683$			6.86049i			0.262509i	0.991349	+	0.131255i	$0.0419005\pi$
$683$			6.86049i			0.262509i	−0.991349	+	0.131255i	$0.958099\pi$
$684$		0			0
$685$	1.97628	−	6.08235i	0.0755096	−	0.232395i
$686$	2.73149	+	9.25280i	0.104289	+	0.353274i
$687$		0			0
$688$	−8.16370	+	4.67311i	−0.311238	+	0.178161i
$689$	−10.7974	+	3.50830i	−0.411350	+	0.133656i
$690$		0			0
$691$	17.7244	−	24.3956i	0.674270	−	0.928053i	−0.325578	−	0.945515i	$-0.605559\pi$
$691$	17.7244	−	24.3956i	0.674270	−	0.928053i	0.999848	+	0.0174625i	$0.00555878\pi$
$692$	1.77774	−	32.7610i	0.0675795	−	1.24539i
$693$		0			0
$694$	−0.128523	−	0.00348452i	−0.00487868	−	0.000132271i
$695$	34.8230	+	25.3004i	1.32091	+	0.959698i
$696$		0			0
$697$	7.13454	+	21.9578i	0.270240	+	0.831713i
$698$	3.36393	+	4.90427i	0.127327	+	0.185629i
$699$		0			0
$700$	−2.51737	−	9.46497i	−0.0951475	−	0.357742i
$701$	−2.65130	−	0.861459i	−0.100138	−	0.0325369i	0.258519	−	0.966006i	$-0.416765\pi$
$701$	−2.65130	−	0.861459i	−0.100138	−	0.0325369i	−0.358658	+	0.933469i	$0.616765\pi$
$702$		0			0
$703$	49.5758			1.86979
$704$	−17.6406	+	19.8195i	−0.664854	+	0.746974i
$705$		0			0
$706$	−25.2281	−	19.3953i	−0.949473	−	0.729953i
$707$	−40.3050	−	13.0959i	−1.51582	−	0.492521i
$708$		0			0
$709$	19.9662	−	14.5063i	0.749846	−	0.544795i	−0.145933	−	0.989294i	$-0.546618\pi$
$709$	19.9662	−	14.5063i	0.749846	−	0.544795i	0.895779	+	0.444499i	$0.146618\pi$
$710$	−8.35609	−	12.1823i	−0.313598	−	0.457194i
$711$		0			0
$712$	−5.67600	+	13.5962i	−0.212717	+	0.509539i
$713$	8.70671	+	6.32579i	0.326069	+	0.236903i
$714$		0			0
$715$	−11.3910	+	0.726049i	−0.426001	+	0.0271527i
$716$	−0.0585663	+	1.07929i	−0.00218873	+	0.0403349i
$717$		0			0
$718$	−1.23155	+	3.46760i	−0.0459611	+	0.129410i
$719$	−17.1274	+	5.56504i	−0.638745	+	0.207541i	−0.610445	−	0.792059i	$-0.709009\pi$
$719$	−17.1274	+	5.56504i	−0.638745	+	0.207541i	−0.0283002	+	0.999599i	$0.509009\pi$
$720$		0			0
$721$	−27.9120	−	38.4176i	−1.03950	−	1.43075i
$722$	0.00697028	+	0.0236115i	0.000259407	+	0.000878728i
$723$		0			0
$724$	7.81678	+	6.35390i	0.290508	+	0.236141i
$725$			12.5933i			0.467703i
$726$		0			0
$727$		−	3.09840i		−	0.114913i	−0.998348	−	0.0574566i	$-0.981701\pi$
$727$		−	3.09840i		−	0.114913i	0.998348	−	0.0574566i	$-0.0182991\pi$
$728$	−11.6143	+	13.5224i	−0.430455	+	0.501174i
$729$		0			0
$730$	30.1186	−	8.89123i	1.11474	−	0.329079i
$731$	−4.11354	−	5.66180i	−0.152145	−	0.209409i
$732$		0			0
$733$	−5.56847	+	1.80931i	−0.205676	+	0.0668283i	−0.410043	−	0.912066i	$-0.634486\pi$
$733$	−5.56847	+	1.80931i	−0.205676	+	0.0668283i	0.204367	+	0.978894i	$0.434486\pi$
$734$	−20.5823	−	7.31001i	−0.759706	−	0.269817i
$735$		0			0
$736$	2.92227	−	21.4301i	0.107716	−	0.789926i
$737$	−49.9091	+	3.18114i	−1.83843	+	0.117179i
$738$		0			0
$739$	−3.46213	−	2.51539i	−0.127357	−	0.0925300i	0.522283	−	0.852772i	$-0.325080\pi$
$739$	−3.46213	−	2.51539i	−0.127357	−	0.0925300i	−0.649640	+	0.760242i	$0.725080\pi$
$740$	15.5233	−	40.2170i	0.570649	−	1.47841i
$741$		0			0
$742$	25.2809	−	17.3407i	0.928091	−	0.636595i
$743$	34.1318	−	24.7982i	1.25217	−	0.909757i	0.253827	−	0.967250i	$-0.418310\pi$
$743$	34.1318	−	24.7982i	1.25217	−	0.909757i	0.998346	+	0.0574923i	$0.0183105\pi$
$744$		0			0
$745$	25.1949	+	8.18632i	0.923070	+	0.299924i
$746$	4.79214	−	6.23328i	0.175453	−	0.228217i
$747$		0			0
$748$	−16.0790	−	11.4517i	−0.587905	−	0.418715i
$749$	13.0420			0.476543
$750$		0			0
$751$	10.4683	+	3.40134i	0.381992	+	0.124117i	0.493718	−	0.869622i	$-0.335638\pi$
$751$	10.4683	+	3.40134i	0.381992	+	0.124117i	−0.111725	+	0.993739i	$0.535638\pi$
$752$	10.9828	−	2.29200i	0.400500	−	0.0835808i
$753$		0			0
$754$	18.9012	−	12.9647i	0.688341	−	0.472147i
$755$	−4.76519	−	14.6658i	−0.173423	−	0.533742i
$756$		0			0
$757$	−17.6019	−	12.7886i	−0.639753	−	0.464808i	0.220012	−	0.975497i	$-0.429390\pi$
$757$	−17.6019	−	12.7886i	−0.639753	−	0.464808i	−0.859765	+	0.510689i	$0.829390\pi$
$758$	−0.989943	+	36.5132i	−0.0359564	+	1.32622i
$759$		0			0
$760$	−23.2665	−	1.89612i	−0.843964	−	0.0687794i
$761$	−4.47259	+	6.15599i	−0.162131	+	0.223154i	−0.882351	−	0.470591i	$-0.844041\pi$
$761$	−4.47259	+	6.15599i	−0.162131	+	0.223154i	0.720220	+	0.693745i	$0.244041\pi$
$762$		0			0
$763$	−4.72934	+	1.53665i	−0.171213	+	0.0556306i
$764$	−3.18496	−	4.92433i	−0.115228	−	0.178156i
$765$		0			0
$766$	−0.149140	+	0.0440273i	−0.00538866	+	0.00159077i
$767$	−4.53735	+	13.9645i	−0.163834	+	0.504229i
$768$		0			0
$769$		−	12.9034i		−	0.465307i	−0.972560	−	0.232653i	$-0.925259\pi$
$769$		−	12.9034i		−	0.465307i	0.972560	−	0.232653i	$-0.0747408\pi$
$770$	28.9453	−	10.5890i	1.04312	−	0.381602i
$771$		0			0
$772$	−13.9882	+	17.2088i	−0.503446	+	0.619357i
$773$	7.73840	−	23.8163i	0.278331	−	0.856614i	−0.709988	−	0.704214i	$-0.751300\pi$
$773$	7.73840	−	23.8163i	0.278331	−	0.856614i	0.988319	−	0.152401i	$-0.0487004\pi$
$774$		0			0
$775$	2.33561	+	3.21469i	0.0838976	+	0.115475i
$776$	−20.0806	+	12.2288i	−0.720851	+	0.438990i
$777$		0			0
$778$	9.29313	−	26.1660i	0.333175	−	0.938097i
$779$	19.8681	−	27.3460i	0.711847	−	0.979773i
$780$		0			0
$781$	−14.0825	+	11.6696i	−0.503913	+	0.417570i
$782$	16.0854	+	0.436106i	0.575211	+	0.0155951i
$783$		0			0
$784$	8.25716	−	18.3627i	0.294899	−	0.655809i
$785$	10.8617	+	33.4288i	0.387670	+	1.19313i
$786$		0			0
$787$	−3.63457	+	2.64067i	−0.129558	+	0.0941296i	−0.650677	−	0.759355i	$-0.725515\pi$
$787$	−3.63457	+	2.64067i	−0.129558	+	0.0941296i	0.521119	+	0.853484i	$0.325515\pi$
$788$	−11.5524	+	3.07254i	−0.411536	+	0.109455i
$789$		0			0
$790$	−11.3992	−	8.76368i	−0.405565	−	0.311798i
$791$	−42.4167			−1.50816
$792$		0			0
$793$	14.1360			0.501984
$794$	33.8759	+	26.0437i	1.20221	+	0.924256i
$795$		0			0
$796$	5.28256	−	1.40498i	0.187235	−	0.0497983i
$797$	−3.79132	+	2.75456i	−0.134296	+	0.0975714i	−0.652905	−	0.757440i	$-0.726450\pi$
$797$	−3.79132	+	2.75456i	−0.134296	+	0.0975714i	0.518609	+	0.855011i	$0.326450\pi$
$798$		0			0
$799$	2.57938	+	7.93852i	0.0912520	+	0.280845i
$800$	3.47123	−	7.19176i	0.122727	−	0.254267i
$801$		0			0
$802$	0.272268	+	0.00738171i	0.00961410	+	0.000260657i
$803$	−14.3420	−	36.1370i	−0.506117	−	1.27525i
$804$		0			0
$805$	−14.7676	+	20.3259i	−0.520490	+	0.716393i
$806$	2.42042	−	6.81500i	0.0852556	−	0.240048i
$807$		0			0
$808$	−17.9727	−	29.5124i	−0.632278	−	1.03824i
$809$	−5.40400	−	7.43797i	−0.189995	−	0.261505i	0.703384	−	0.710810i	$-0.251672\pi$
$809$	−5.40400	−	7.43797i	−0.189995	−	0.261505i	−0.893378	+	0.449305i	$0.851672\pi$
$810$		0			0
$811$	0.540273	−	1.66279i	0.0189716	−	0.0583884i	−0.941123	−	0.338066i	$-0.890227\pi$
$811$	0.540273	−	1.66279i	0.0189716	−	0.0583884i	0.960094	+	0.279677i	$0.0902274\pi$
$812$	−39.0383	+	48.0262i	−1.36997	+	1.68539i
$813$		0			0
$814$	−51.3273	−	14.6268i	−1.79902	−	0.512668i
$815$			1.20741i			0.0422937i
$816$		0			0
$817$	−3.16616	+	9.74443i	−0.110770	+	0.340914i
$818$	−42.0214	+	12.4050i	−1.46924	+	0.433731i
$819$		0			0
$820$	−15.9626	−	24.6801i	−0.557438	−	0.861866i
$821$	−21.3086	+	6.92358i	−0.743675	+	0.241635i	−0.656258	−	0.754537i	$-0.727862\pi$
$821$	−21.3086	+	6.92358i	−0.743675	+	0.241635i	−0.0874178	+	0.996172i	$0.527862\pi$
$822$		0			0
$823$	−16.2633	+	22.3844i	−0.566901	+	0.780273i	−0.992183	−	0.124788i	$-0.960175\pi$
$823$	−16.2633	+	22.3844i	−0.566901	+	0.780273i	0.425282	+	0.905061i	$0.360175\pi$
$824$	3.14499	−	38.5909i	0.109561	−	1.34438i
$825$		0			0
$826$	1.07456	−	39.6340i	0.0373886	−	1.37904i
$827$	5.02913	+	3.65387i	0.174880	+	0.127058i	0.671782	−	0.740749i	$-0.265529\pi$
$827$	5.02913	+	3.65387i	0.174880	+	0.127058i	−0.496902	+	0.867807i	$0.665529\pi$
$828$		0			0
$829$	−5.92631	−	18.2393i	−0.205829	−	0.633477i	−0.999678	−	0.0253622i	$-0.991926\pi$
$829$	−5.92631	−	18.2393i	−0.205829	−	0.633477i	0.793849	−	0.608115i	$-0.208074\pi$
$830$	16.6753	−	11.4379i	0.578808	−	0.397015i
$831$		0			0
$832$	−14.3677	+	2.19391i	−0.498110	+	0.0760603i
$833$	14.2461	+	4.62883i	0.493598	+	0.160380i
$834$		0			0
$835$	−17.2417			−0.596674
$836$	0.272871	+	28.8991i	0.00943746	+	0.999497i
$837$		0			0
$838$	24.8252	−	32.2909i	0.857572	−	1.11547i
$839$	−39.6524	−	12.8838i	−1.36895	−	0.444800i	−0.469931	−	0.882703i	$-0.655721\pi$
$839$	−39.6524	−	12.8838i	−1.36895	−	0.444800i	−0.899022	+	0.437904i	$0.855721\pi$
$840$		0			0
$841$	40.9205	−	29.7305i	1.41105	−	1.02519i
$842$	−3.68854	+	2.53004i	−0.127116	+	0.0871910i
$843$		0			0
$844$	−18.2742	+	47.3439i	−0.629025	+	1.62964i
$845$	14.8643	+	10.7996i	0.511348	+	0.371516i
$846$		0			0
$847$	−16.3036	−	34.4998i	−0.560199	−	1.18543i
$848$	24.8494	+	2.70481i	0.853331	+	0.0928834i
$849$		0			0
$850$	5.59860	+	1.98840i	0.192030	+	0.0682016i
$851$	41.3760	−	13.4439i	1.41835	−	0.460851i
$852$		0			0
$853$	14.8390	+	20.4241i	0.508078	+	0.699309i	0.983594	−	0.180398i	$-0.0577385\pi$
$853$	14.8390	+	20.4241i	0.508078	+	0.699309i	−0.475516	+	0.879707i	$0.657738\pi$
$854$	−36.6093	+	10.8073i	−1.25274	+	0.369819i
$855$		0			0
$856$	8.06688	+	6.92859i	0.275720	+	0.236814i
$857$			20.1558i			0.688510i	0.938876	+	0.344255i	$0.111868\pi$
$857$			20.1558i			0.688510i	−0.938876	+	0.344255i	$0.888132\pi$
$858$		0			0
$859$			2.64305i			0.0901798i	0.998983	+	0.0450899i	$0.0143574\pi$
$859$			2.64305i			0.0901798i	−0.998983	+	0.0450899i	$0.985643\pi$
$860$	6.91351	+	5.61967i	0.235749	+	0.191629i
$861$		0			0
$862$	1.07049	+	3.62624i	0.0364611	+	0.123510i
$863$	−18.9266	−	26.0502i	−0.644267	−	0.886758i	0.354567	−	0.935031i	$-0.384628\pi$
$863$	−18.9266	−	26.0502i	−0.644267	−	0.886758i	−0.998834	+	0.0482726i	$0.984628\pi$
$864$		0			0
$865$	−29.5541	+	9.60272i	−1.00487	+	0.326502i
$866$	9.93229	−	27.9656i	0.337513	−	0.950311i
$867$		0			0
$868$	−1.05814	+	19.4999i	−0.0359155	+	0.661869i
$869$	−9.52608	+	15.0380i	−0.323150	+	0.510128i
$870$		0			0
$871$	−22.1627	−	16.1022i	−0.750955	−	0.545601i
$872$	−3.74160	−	1.56201i	−0.126707	−	0.0528962i
$873$		0			0
$874$	−13.3256	−	19.4273i	−0.450745	−	0.657140i
$875$	−34.0855	+	24.7646i	−1.15230	+	0.837196i
$876$		0			0
$877$	−32.3463	−	10.5100i	−1.09226	−	0.354896i	−0.293139	−	0.956070i	$-0.594700\pi$
$877$	−32.3463	−	10.5100i	−1.09226	−	0.354896i	−0.799118	+	0.601174i	$0.794700\pi$
$878$	10.9349	+	8.40677i	0.369037	+	0.283715i
$879$		0			0
$880$	23.5291	+	8.82763i	0.793165	+	0.297579i
$881$	4.53963			0.152944			0.0764719	−	0.997072i	$-0.475634\pi$
$881$	4.53963			0.152944			0.0764719	+	0.997072i	$0.475634\pi$
$882$		0			0
$883$	−2.08769	−	0.678332i	−0.0702564	−	0.0228277i	0.273678	−	0.961821i	$-0.411760\pi$
$883$	−2.08769	−	0.678332i	−0.0702564	−	0.0228277i	−0.343934	+	0.938994i	$0.611760\pi$
$884$	−2.77934	−	10.4500i	−0.0934793	−	0.351470i
$885$		0			0
$886$	16.4857	+	24.0344i	0.553847	+	0.807452i
$887$	6.21007	+	19.1126i	0.208514	+	0.641739i	0.999551	+	0.0299709i	$0.00954145\pi$
$887$	6.21007	+	19.1126i	0.208514	+	0.641739i	−0.791037	+	0.611768i	$0.790459\pi$
$888$		0			0
$889$	14.4293	+	10.4835i	0.483944	+	0.351606i
$890$	13.9495	+	0.378199i	0.467589	+	0.0126773i
$891$		0			0
$892$	2.19041	−	40.3659i	0.0733403	−	1.35155i
$893$	7.18299	−	9.88654i	0.240370	−	0.330840i
$894$		0			0
$895$	0.973640	−	0.316355i	0.0325452	−	0.0105746i
$896$	35.5319	−	16.6662i	1.18704	−	0.556779i
$897$		0			0
$898$	15.9895	+	54.1635i	0.533575	+	1.80746i
$899$	7.75945	−	23.8811i	0.258792	−	0.796480i
$900$		0			0
$901$			18.5968i			0.619548i
$902$	−28.6381	+	22.4503i	−0.953546	+	0.747514i
$903$		0			0
$904$	−26.2361	−	22.5340i	−0.872601	−	0.749471i
$905$	2.94833	−	9.07401i	0.0980057	−	0.301630i
$906$		0			0
$907$	−25.2363	−	34.7347i	−0.837957	−	1.15335i	−0.986389	−	0.164426i	$-0.947423\pi$
$907$	−25.2363	−	34.7347i	−0.837957	−	1.15335i	0.148433	−	0.988922i	$-0.452577\pi$
$908$	−5.76734	+	3.73020i	−0.191396	+	0.123791i
$909$		0			0
$910$	15.9097	+	5.65048i	0.527400	+	0.187312i
$911$	13.7521	−	18.9282i	0.455628	−	0.627118i	−0.517967	−	0.855401i	$-0.673311\pi$
$911$	13.7521	−	18.9282i	0.455628	−	0.627118i	0.973595	+	0.228283i	$0.0733111\pi$
$912$		0			0
$913$	−15.9734	−	19.2763i	−0.528643	−	0.637953i
$914$	1.29182	−	47.6477i	0.0427296	−	1.57604i
$915$		0			0
$916$	4.21585	−	10.9222i	0.139296	−	0.360879i
$917$	−3.73615	−	11.4987i	−0.123379	−	0.379721i
$918$		0			0
$919$	−13.0131	+	9.45455i	−0.429261	+	0.311877i	−0.781354	−	0.624089i	$-0.785470\pi$
$919$	−13.0131	+	9.45455i	−0.429261	+	0.311877i	0.352092	+	0.935965i	$0.385470\pi$
$920$	−19.9325	+	4.72687i	−0.657153	+	0.155840i
$921$		0			0
$922$	15.9196	−	20.7072i	0.524286	−	0.681955i
$923$	−10.0185			−0.329762
$924$		0			0
$925$	16.0630			0.528150
$926$	18.9476	−	24.6457i	0.622657	−	0.809909i
$927$		0			0
$928$	−49.6606	+	8.96658i	−1.63019	+	0.294343i
$929$	5.33225	−	3.87411i	0.174945	−	0.127105i	−0.496867	−	0.867827i	$-0.665516\pi$
$929$	5.33225	−	3.87411i	0.174945	−	0.127105i	0.671812	+	0.740722i	$0.265516\pi$
$930$		0			0
$931$	−6.77680	−	20.8569i	−0.222101	−	0.683556i
$932$	18.4268	+	7.11255i	0.603591	+	0.232979i
$933$		0			0
$934$	−1.40513	+	51.8268i	−0.0459771	+	1.69582i
$935$	−4.63483	+	18.1132i	−0.151575	+	0.592364i
$936$		0			0
$937$	6.99890	−	9.63316i	0.228644	−	0.314702i	−0.679245	−	0.733911i	$-0.737693\pi$
$937$	6.99890	−	9.63316i	0.228644	−	0.314702i	0.907889	+	0.419210i	$0.137693\pi$
$938$	69.7073	+	24.7573i	2.27602	+	0.808353i
$939$		0			0
$940$	−5.77103	−	8.92271i	−0.188230	−	0.291027i
$941$	6.88516	+	9.47660i	0.224450	+	0.308928i	0.906359	−	0.422508i	$-0.138850\pi$
$941$	6.88516	+	9.47660i	0.224450	+	0.308928i	−0.681909	+	0.731437i	$0.738850\pi$
$942$		0			0
$943$	9.16626	−	28.2109i	0.298495	−	0.918672i
$944$	21.7204	−	23.9441i	0.706938	−	0.779314i
$945$		0			0
$946$	6.15300	−	9.15456i	0.200051	−	0.297641i
$947$			34.4025i			1.11793i	0.829191	+	0.558966i	$0.188802\pi$
$947$			34.4025i			1.11793i	−0.829191	+	0.558966i	$0.811198\pi$
$948$		0			0
$949$	6.58116	−	20.2547i	0.213634	−	0.657496i
$950$	−2.46270	−	8.34228i	−0.0799006	−	0.270659i
$951$		0			0
$952$	15.1871	+	24.9383i	0.492218	+	0.808255i
$953$	−19.7117	+	6.40471i	−0.638523	+	0.207469i	−0.610347	−	0.792134i	$-0.708970\pi$
$953$	−19.7117	+	6.40471i	−0.638523	+	0.207469i	−0.0281762	+	0.999603i	$0.508970\pi$
$954$		0			0
$955$	−3.26490	+	4.49375i	−0.105650	+	0.145414i
$956$	−39.1514	−	2.12451i	−1.26625	−	0.0687114i
$957$		0			0
$958$	33.4138	+	0.905912i	1.07955	+	0.0292687i
$959$	9.47485	+	6.88388i	0.305959	+	0.222292i
$960$		0			0
$961$	7.13118	+	21.9475i	0.230038	+	0.707984i
$962$	−16.5368	−	24.1089i	−0.533167	−	0.777303i
$963$		0			0
$964$	23.5656	−	6.26766i	0.758997	−	0.201868i
$965$	19.9766	+	6.49078i	0.643068	+	0.208946i
$966$		0			0
$967$	55.9913			1.80056			0.900280	−	0.435312i	$-0.143362\pi$
$967$	55.9913			1.80056			0.900280	+	0.435312i	$0.143362\pi$
$968$	8.24385	−	30.0006i	0.264967	−	0.964257i
$969$		0			0
$970$	17.6542	+	13.5725i	0.566841	+	0.435787i
$971$	48.0716	+	15.6194i	1.54269	+	0.501251i	0.952118	−	0.305732i	$-0.0989010\pi$
$971$	48.0716	+	15.6194i	1.54269	+	0.501251i	0.590575	+	0.806983i	$0.298901\pi$
$972$		0			0
$973$	−63.7698	+	46.3315i	−2.04437	+	1.48532i
$974$	−29.5152	−	43.0301i	−0.945728	−	1.37877i
$975$		0			0
$976$	−28.3855	−	12.7641i	−0.908597	−	0.408570i
$977$	−17.4903	−	12.7074i	−0.559563	−	0.406546i	0.271736	−	0.962372i	$-0.412402\pi$
$977$	−17.4903	−	12.7074i	−0.559563	−	0.406546i	−0.831299	+	0.555826i	$0.812402\pi$
$978$		0			0
$979$	−1.09895	−	17.2415i	−0.0351225	−	0.551040i
$980$	−19.0415	−	1.03327i	−0.608260	−	0.0330065i
$981$		0			0
$982$	8.81669	−	24.8245i	0.281352	−	0.792183i
$983$	−1.27749	+	0.415082i	−0.0407456	+	0.0132391i	−0.329319	−	0.944219i	$-0.606819\pi$
$983$	−1.27749	+	0.415082i	−0.0407456	+	0.0132391i	0.288573	+	0.957458i	$0.406819\pi$
$984$		0			0
$985$	6.65498	+	9.15979i	0.212045	+	0.291855i
$986$	−10.6298	−	36.0080i	−0.338522	−	1.14673i
$987$		0			0
$988$	−9.98555	+	12.2846i	−0.317683	+	0.390824i
$989$			8.99132i			0.285907i
$990$		0			0
$991$		−	18.7949i		−	0.597039i	−0.954404	−	0.298520i	$-0.903507\pi$
$991$		−	18.7949i		−	0.597039i	0.954404	−	0.298520i	$-0.0964928\pi$
$992$	−11.0139	+	11.4992i	−0.349691	+	0.365099i
$993$		0			0
$994$	25.9457	−	7.65936i	0.822948	−	0.242940i
$995$	−3.04313	−	4.18851i	−0.0964737	−	0.132785i
$996$		0			0
$997$	−14.1935	+	4.61173i	−0.449511	+	0.146055i	−0.525020	−	0.851090i	$-0.675942\pi$
$997$	−14.1935	+	4.61173i	−0.449511	+	0.146055i	0.0755083	+	0.997145i	$0.475942\pi$
$998$	45.6995	+	16.2306i	1.44659	+	0.513772i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.r.b.271.10		48
3.2	odd	2		132.2.j.a.7.3	✓	48
4.3	odd	2	inner	396.2.r.b.271.2		48
11.8	odd	10	inner	396.2.r.b.19.2		48
12.11	even	2		132.2.j.a.7.11	yes	48
33.8	even	10		132.2.j.a.19.11	yes	48
44.19	even	10	inner	396.2.r.b.19.10		48
132.107	odd	10		132.2.j.a.19.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.3	✓	48	3.2	odd	2
132.2.j.a.7.11	yes	48	12.11	even	2
132.2.j.a.19.3	yes	48	132.107	odd	10
132.2.j.a.19.11	yes	48	33.8	even	10
396.2.r.b.19.2		48	11.8	odd	10	inner
396.2.r.b.19.10		48	44.19	even	10	inner
396.2.r.b.271.2		48	4.3	odd	2	inner
396.2.r.b.271.10		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12117 + 0.861957i) q^{2} +(0.514062 + 1.93281i) q^{4} +(1.53251 - 1.11343i) q^{5} +(1.07196 + 3.29914i) q^{7} +(-1.08964 + 2.61011i) q^{8} +O(q^{10})\)	\(q+(1.12117 + 0.861957i) q^{2} +(0.514062 + 1.93281i) q^{4} +(1.53251 - 1.11343i) q^{5} +(1.07196 + 3.29914i) q^{7} +(-1.08964 + 2.61011i) q^{8} +(2.67794 + 0.0726042i) q^{10} +(-0.210969 - 3.30991i) q^{11} +(1.06787 - 1.46980i) q^{13} +(-1.64187 + 4.62289i) q^{14} +(-3.47148 + 1.98716i) q^{16} +(-1.74921 - 2.40759i) q^{17} +(-1.34636 + 4.14366i) q^{19} +(2.93986 + 2.38967i) q^{20} +(2.61646 - 3.89283i) q^{22} +3.82341i q^{23} +(-0.436233 + 1.34259i) q^{25} +(2.46418 - 0.727444i) q^{26} +(-5.82555 + 3.76785i) q^{28} +(8.48417 - 2.75668i) q^{29} +(1.65449 - 2.27721i) q^{31} +(-5.60498 - 0.764309i) q^{32} +(0.114062 - 4.20707i) q^{34} +(5.31616 + 3.86242i) q^{35} +(-3.51620 - 10.8218i) q^{37} +(-5.08115 + 3.48526i) q^{38} +(1.23630 + 5.21327i) q^{40} +(-7.37845 - 2.39740i) q^{41} +2.35165 q^{43} +(6.28896 - 2.10926i) q^{44} +(-3.29561 + 4.28671i) q^{46} +(-2.66757 - 0.866745i) q^{47} +(-4.07214 + 2.95858i) q^{49} +(-1.64634 + 1.12926i) q^{50} +(3.38980 + 1.30843i) q^{52} +(-5.05557 - 3.67309i) q^{53} +(-4.00867 - 4.83757i) q^{55} +(-9.77918 - 0.796961i) q^{56} +(11.8884 + 4.22228i) q^{58} +(-7.68642 + 2.49747i) q^{59} +(4.57345 + 6.29481i) q^{61} +(3.81783 - 1.12705i) q^{62} +(-5.62536 - 5.68818i) q^{64} -3.44150i q^{65} -15.0787i q^{67} +(3.75420 - 4.61854i) q^{68} +(2.63111 + 8.91274i) q^{70} +(-3.24129 - 4.46126i) q^{71} +(11.1487 - 3.62244i) q^{73} +(5.38561 - 15.1639i) q^{74} +(-8.70100 - 0.472149i) q^{76} +(10.6937 - 4.24410i) q^{77} +(-4.34223 - 3.15482i) q^{79} +(-3.10750 + 6.91061i) q^{80} +(-6.20607 - 9.04781i) q^{82} +(6.10662 - 4.43672i) q^{83} +(-5.36138 - 1.74202i) q^{85} +(2.63661 + 2.02702i) q^{86} +(8.86911 + 3.05596i) q^{88} +5.20905 q^{89} +(5.99381 + 1.94751i) q^{91} +(-7.38991 + 1.96547i) q^{92} +(-2.24371 - 3.27110i) q^{94} +(2.55038 + 7.84928i) q^{95} +(6.72491 + 4.88593i) q^{97} +(-7.11574 - 0.192922i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} + 14 q^{14} - 24 q^{16} + 22 q^{20} - 26 q^{22} - 20 q^{25} + 38 q^{26} - 10 q^{28} - 48 q^{37} - 58 q^{38} + 70 q^{40} + 40 q^{41} - 34 q^{44} + 70 q^{46} - 28 q^{49} - 70 q^{50} + 30 q^{52} + 64 q^{53} - 60 q^{56} - 54 q^{58} - 40 q^{64} + 4 q^{70} + 20 q^{73} - 50 q^{74} + 8 q^{77} - 58 q^{80} + 62 q^{82} + 40 q^{85} - 8 q^{86} + 8 q^{88} - 48 q^{89} - 42 q^{92} - 10 q^{94} + 48 q^{97}+O(q^{100}) \) 48 * q - 4 * q^4 + 14 * q^14 - 24 * q^16 + 22 * q^20 - 26 * q^22 - 20 * q^25 + 38 * q^26 - 10 * q^28 - 48 * q^37 - 58 * q^38 + 70 * q^40 + 40 * q^41 - 34 * q^44 + 70 * q^46 - 28 * q^49 - 70 * q^50 + 30 * q^52 + 64 * q^53 - 60 * q^56 - 54 * q^58 - 40 * q^64 + 4 * q^70 + 20 * q^73 - 50 * q^74 + 8 * q^77 - 58 * q^80 + 62 * q^82 + 40 * q^85 - 8 * q^86 + 8 * q^88 - 48 * q^89 - 42 * q^92 - 10 * q^94 + 48 * q^97

Introduction

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