LMFDB - Embedded newform 975.2.bb.j.874.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(724,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.724"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,4,0,0,0,0,6,0,-8,0,0,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			874.1
Root			$1.98293 + 0.531325i$ of defining polynomial
Character	$\chi$	$=$	975.874
Dual form			975.2.bb.j.724.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.91766 + 1.10716i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(1.45161 - 2.51426i) q^{4} +(1.10716 - 1.91766i) q^{6} +(-3.32254 - 1.91827i) q^{7} +2.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.90321 - 5.02851i) q^{11} +2.90321i q^{12} +(3.56589 + 0.533338i) q^{13} +8.49532 q^{14} +(0.688892 + 1.19320i) q^{16} +(-3.11085 - 1.79605i) q^{17} +2.21432i q^{18} +(1.07382 - 1.85991i) q^{19} +3.83654 q^{21} +(11.1347 + 6.42864i) q^{22} +(-5.39972 + 3.11753i) q^{23} +(-1.00000 - 1.73205i) q^{24} +(-7.42864 + 2.92525i) q^{26} +1.00000i q^{27} +(-9.64603 + 5.56914i) q^{28} +(1.03334 + 1.78979i) q^{29} -5.28100 q^{31} +(-6.10622 - 3.52543i) q^{32} +(5.02851 + 2.90321i) q^{33} +7.95407 q^{34} +(-1.45161 - 2.51426i) q^{36} +(4.11844 - 2.37778i) q^{37} +4.75557i q^{38} +(-3.35482 + 1.32106i) q^{39} +(5.55877 + 9.62806i) q^{41} +(-7.35716 + 4.24766i) q^{42} +(8.22318 + 4.74766i) q^{43} -16.8573 q^{44} +(6.90321 - 11.9567i) q^{46} -2.21432i q^{47} +(-1.19320 - 0.688892i) q^{48} +(3.85950 + 6.68485i) q^{49} +3.59210 q^{51} +(6.51721 - 8.19135i) q^{52} -0.815792i q^{53} +(-1.10716 - 1.91766i) q^{54} +(3.83654 - 6.64507i) q^{56} +2.14764i q^{57} +(-3.96318 - 2.28814i) q^{58} +(-4.98741 + 8.63844i) q^{59} +(-2.64050 + 4.57348i) q^{61} +(10.1271 - 5.84691i) q^{62} +(-3.32254 + 1.91827i) q^{63} +12.8573 q^{64} -12.8573 q^{66} +(3.07919 - 1.77777i) q^{67} +(-9.03147 + 5.21432i) q^{68} +(3.11753 - 5.39972i) q^{69} +(-2.86987 + 4.97077i) q^{71} +(1.73205 + 1.00000i) q^{72} -2.78568i q^{73} +(-5.26517 + 9.11955i) q^{74} +(-3.11753 - 5.39972i) q^{76} +22.2766i q^{77} +(4.97077 - 6.24766i) q^{78} -12.3319 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-21.3196 - 12.3089i) q^{82} +0.622216i q^{83} +(5.56914 - 9.64603i) q^{84} -21.0257 q^{86} +(-1.78979 - 1.03334i) q^{87} +(10.0570 - 5.80642i) q^{88} +(-8.08419 - 14.0022i) q^{89} +(-10.8247 - 8.61236i) q^{91} +18.1017i q^{92} +(4.57348 - 2.64050i) q^{93} +(2.45161 + 4.24631i) q^{94} +7.05086 q^{96} +(3.68137 + 2.12544i) q^{97} +(-14.8024 - 8.54617i) q^{98} -5.80642 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 6 q^{9} - 8 q^{11} + 48 q^{14} + 8 q^{16} + 20 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} - 36 q^{31} + 16 q^{34} - 4 q^{36} + 40 q^{41} - 96 q^{44} + 56 q^{46} + 60 q^{49} + 16 q^{51}+ \cdots - 16 q^{99}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^9 - 8 * q^11 + 48 * q^14 + 8 * q^16 + 20 * q^21 - 12 * q^24 - 36 * q^26 + 12 * q^29 - 36 * q^31 + 16 * q^34 - 4 * q^36 + 40 * q^41 - 96 * q^44 + 56 * q^46 + 60 * q^49 + 16 * q^51 + 20 * q^56 + 20 * q^59 - 18 * q^61 + 48 * q^64 - 48 * q^66 - 16 * q^69 - 8 * q^71 + 16 * q^74 + 16 * q^76 - 68 * q^79 - 6 * q^81 - 40 * q^86 - 44 * q^89 - 62 * q^91 + 16 * q^94 + 32 * q^96 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	−1.91766	+	1.10716i	−1.35599	+	0.782880i	−0.989080	−	0.147377i	$-0.952917\pi$
$2$	−1.91766	+	1.10716i	−1.35599	+	0.782880i	−0.366908	+	0.930257i	$0.619584\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	1.45161	−	2.51426i	0.725803	−	1.25713i
$5$		0			0
$5$		0			0
$6$	1.10716	−	1.91766i	0.451996	−	0.782880i
$7$	−3.32254	−	1.91827i	−1.25580	−	0.725037i	−0.283546	−	0.958959i	$-0.591511\pi$
$7$	−3.32254	−	1.91827i	−1.25580	−	0.725037i	−0.972255	+	0.233922i	$0.924844\pi$
$8$			2.00000i			0.707107i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−2.90321	−	5.02851i	−0.875351	−	1.51615i	−0.856388	−	0.516333i	$-0.827297\pi$
$11$	−2.90321	−	5.02851i	−0.875351	−	1.51615i	−0.0189633	−	0.999820i	$-0.506037\pi$
$12$			2.90321i			0.838085i
$13$	3.56589	+	0.533338i	0.988999	+	0.147921i
$13$	3.56589	+	0.533338i	0.988999	+	0.147921i
$14$	8.49532			2.27047
$15$		0			0
$16$	0.688892	+	1.19320i	0.172223	+	0.298299i
$17$	−3.11085	−	1.79605i	−0.754493	−	0.435607i	0.0728222	−	0.997345i	$-0.476799\pi$
$17$	−3.11085	−	1.79605i	−0.754493	−	0.435607i	−0.827315	+	0.561738i	$0.810133\pi$
$18$			2.21432i			0.521920i
$19$	1.07382	−	1.85991i	0.246352	−	0.426693i	−0.716159	−	0.697937i	$-0.754102\pi$
$19$	1.07382	−	1.85991i	0.246352	−	0.426693i	0.962511	+	0.271244i	$0.0874349\pi$
$20$		0			0
$21$	3.83654			0.837201
$22$	11.1347	+	6.42864i	2.37393	+	1.37059i
$23$	−5.39972	+	3.11753i	−1.12592	+	0.650050i	−0.942906	−	0.333060i	$-0.891919\pi$
$23$	−5.39972	+	3.11753i	−1.12592	+	0.650050i	−0.183014	+	0.983110i	$0.558586\pi$
$24$	−1.00000	−	1.73205i	−0.204124	−	0.353553i
$25$		0			0
$26$	−7.42864	+	2.92525i	−1.45688	+	0.573688i
$27$			1.00000i			0.192450i
$28$	−9.64603	+	5.56914i	−1.82293	+	1.05247i
$29$	1.03334	+	1.78979i	0.191886	+	0.332356i	0.945875	−	0.324530i	$-0.105206\pi$
$29$	1.03334	+	1.78979i	0.191886	+	0.332356i	−0.753989	+	0.656887i	$0.771873\pi$
$30$		0			0
$31$	−5.28100			−0.948495			−0.474247	−	0.880392i	$-0.657280\pi$
$31$	−5.28100			−0.948495			−0.474247	+	0.880392i	$0.657280\pi$
$32$	−6.10622	−	3.52543i	−1.07944	−	0.623213i
$33$	5.02851	+	2.90321i	0.875351	+	0.505384i
$34$	7.95407			1.36411
$35$		0			0
$36$	−1.45161	−	2.51426i	−0.241934	−	0.419043i
$37$	4.11844	−	2.37778i	0.677068	−	0.390905i	−0.121681	−	0.992569i	$-0.538829\pi$
$37$	4.11844	−	2.37778i	0.677068	−	0.390905i	0.798749	+	0.601664i	$0.205495\pi$
$38$			4.75557i			0.771455i
$39$	−3.35482	+	1.32106i	−0.537201	+	0.211539i
$40$		0			0
$41$	5.55877	+	9.62806i	0.868133	+	1.50365i	0.863902	+	0.503660i	$0.168014\pi$
$41$	5.55877	+	9.62806i	0.868133	+	1.50365i	0.00423144	+	0.999991i	$0.498653\pi$
$42$	−7.35716	+	4.24766i	−1.13523	+	0.655428i
$43$	8.22318	+	4.74766i	1.25402	+	0.724011i	0.971906	−	0.235369i	$-0.0756298\pi$
$43$	8.22318	+	4.74766i	1.25402	+	0.724011i	0.282118	+	0.959380i	$0.408963\pi$
$44$	−16.8573			−2.54133
$45$		0			0
$46$	6.90321	−	11.9567i	1.01782	−	1.76292i
$47$		−	2.21432i		−	0.322992i	−0.986873	−	0.161496i	$-0.948368\pi$
$47$		−	2.21432i		−	0.322992i	0.986873	−	0.161496i	$-0.0516318\pi$
$48$	−1.19320	−	0.688892i	−0.172223	−	0.0994330i
$49$	3.85950	+	6.68485i	0.551357	+	0.954979i
$50$		0			0
$51$	3.59210			0.502995
$52$	6.51721	−	8.19135i	0.903775	−	1.13594i
$53$		−	0.815792i		−	0.112058i	−0.998429	−	0.0560288i	$-0.982156\pi$
$53$		−	0.815792i		−	0.112058i	0.998429	−	0.0560288i	$-0.0178439\pi$
$54$	−1.10716	−	1.91766i	−0.150665	−	0.260960i
$55$		0			0
$56$	3.83654	−	6.64507i	0.512679	−	0.887985i
$57$			2.14764i			0.284462i
$58$	−3.96318	−	2.28814i	−0.520391	−	0.300448i
$59$	−4.98741	+	8.63844i	−0.649305	+	1.12463i	0.333984	+	0.942579i	$0.391607\pi$
$59$	−4.98741	+	8.63844i	−0.649305	+	1.12463i	−0.983289	+	0.182050i	$0.941727\pi$
$60$		0			0
$61$	−2.64050	+	4.57348i	−0.338081	+	0.585574i	−0.984072	−	0.177772i	$-0.943111\pi$
$61$	−2.64050	+	4.57348i	−0.338081	+	0.585574i	0.645991	+	0.763345i	$0.276445\pi$
$62$	10.1271	−	5.84691i	1.28615	−	0.742558i
$63$	−3.32254	+	1.91827i	−0.418600	+	0.241679i
$64$	12.8573			1.60716
$65$		0			0
$66$	−12.8573			−1.58262
$67$	3.07919	−	1.77777i	0.376183	−	0.217189i	−0.299973	−	0.953948i	$-0.596978\pi$
$67$	3.07919	−	1.77777i	0.376183	−	0.217189i	0.676156	+	0.736758i	$0.263645\pi$
$68$	−9.03147	+	5.21432i	−1.09523	+	0.632329i
$69$	3.11753	−	5.39972i	0.375307	−	0.650050i
$70$		0			0
$71$	−2.86987	+	4.97077i	−0.340591	+	0.589922i	−0.984543	−	0.175145i	$-0.943961\pi$
$71$	−2.86987	+	4.97077i	−0.340591	+	0.589922i	0.643951	+	0.765066i	$0.277294\pi$
$72$	1.73205	+	1.00000i	0.204124	+	0.117851i
$73$		−	2.78568i		−	0.326039i	−0.986623	−	0.163020i	$-0.947877\pi$
$73$		−	2.78568i		−	0.326039i	0.986623	−	0.163020i	$-0.0521234\pi$
$74$	−5.26517	+	9.11955i	−0.612064	+	1.06013i
$75$		0			0
$76$	−3.11753	−	5.39972i	−0.357605	−	0.619391i
$77$			22.2766i			2.53865i
$78$	4.97077	−	6.24766i	0.562829	−	0.707408i
$79$	−12.3319			−1.38744			−0.693721	−	0.720244i	$-0.744030\pi$
$79$	−12.3319			−1.38744			−0.693721	+	0.720244i	$0.744030\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−21.3196	−	12.3089i	−2.35436	−	1.35929i
$83$			0.622216i			0.0682970i	0.999417	+	0.0341485i	$0.0108719\pi$
$83$			0.622216i			0.0682970i	−0.999417	+	0.0341485i	$0.989128\pi$
$84$	5.56914	−	9.64603i	0.607643	−	1.05247i
$85$		0			0
$86$	−21.0257			−2.26726
$87$	−1.78979	−	1.03334i	−0.191886	−	0.110785i
$88$	10.0570	−	5.80642i	1.07208	−	0.618967i
$89$	−8.08419	−	14.0022i	−0.856923	−	1.48423i	−0.874850	−	0.484395i	$-0.839040\pi$
$89$	−8.08419	−	14.0022i	−0.856923	−	1.48423i	0.0179269	−	0.999839i	$-0.494293\pi$
$90$		0			0
$91$	−10.8247	−	8.61236i	−1.13474	−	0.902821i
$92$			18.1017i			1.88723i
$93$	4.57348	−	2.64050i	0.474247	−	0.273807i
$94$	2.45161	+	4.24631i	0.252864	+	0.437973i
$95$		0			0
$96$	7.05086			0.719625
$97$	3.68137	+	2.12544i	0.373787	+	0.215806i	0.675112	−	0.737716i	$-0.264095\pi$
$97$	3.68137	+	2.12544i	0.373787	+	0.215806i	−0.301325	+	0.953522i	$0.597429\pi$
$98$	−14.8024	−	8.54617i	−1.49527	−	0.863294i
$99$	−5.80642			−0.583568
$100$		0			0
$101$	1.11753	+	1.93562i	0.111199	+	0.192602i	0.916254	−	0.400598i	$-0.131198\pi$
$101$	1.11753	+	1.93562i	0.111199	+	0.192602i	−0.805055	+	0.593200i	$0.797864\pi$
$102$	−6.88842	+	3.97703i	−0.682056	+	0.393785i
$103$		−	2.44446i		−	0.240860i	−0.992722	−	0.120430i	$-0.961573\pi$
$103$		−	2.44446i		−	0.240860i	0.992722	−	0.120430i	$-0.0384273\pi$
$104$	−1.06668	+	7.13177i	−0.104596	+	0.699328i
$105$		0			0
$106$	0.903212	+	1.56441i	0.0877277	+	0.151949i
$107$	−1.43096	+	0.826164i	−0.138336	+	0.0798682i	−0.567571	−	0.823325i	$-0.692117\pi$
$107$	−1.43096	+	0.826164i	−0.138336	+	0.0798682i	0.429235	+	0.903193i	$0.358783\pi$
$108$	2.51426	+	1.45161i	0.241934	+	0.139681i
$109$	2.61285			0.250265			0.125133	−	0.992140i	$-0.460064\pi$
$109$	2.61285			0.250265			0.125133	+	0.992140i	$0.460064\pi$
$110$		0			0
$111$	−2.37778	+	4.11844i	−0.225689	+	0.390905i
$112$		−	5.28592i		−	0.499472i
$113$	−2.10326	−	1.21432i	−0.197858	−	0.114234i	0.397798	−	0.917473i	$-0.369775\pi$
$113$	−2.10326	−	1.21432i	−0.197858	−	0.114234i	−0.595656	+	0.803240i	$0.703108\pi$
$114$	−2.37778	−	4.11844i	−0.222700	−	0.385728i
$115$		0			0
$116$	6.00000			0.557086
$117$	2.24483	−	2.82148i	0.207534	−	0.260846i
$118$		−	22.0874i		−	2.03331i
$119$	6.89062	+	11.9349i	0.631662	+	1.09407i
$120$		0			0
$121$	−11.3573	+	19.6714i	−1.03248	+	1.78831i
$122$		−	11.6938i		−	1.05871i
$123$	−9.62806	−	5.55877i	−0.868133	−	0.501217i
$124$	−7.66593	+	13.2778i	−0.688420	+	1.19238i
$125$		0			0
$126$	4.24766	−	7.35716i	0.378411	−	0.655428i
$127$	−16.6760	+	9.62790i	−1.47976	+	0.854338i	−0.999737	−	0.0229193i	$-0.992704\pi$
$127$	−16.6760	+	9.62790i	−1.47976	+	0.854338i	−0.480020	+	0.877258i	$0.659371\pi$
$128$	−12.4434	+	7.18421i	−1.09985	+	0.635000i
$129$	−9.49532			−0.836016
$130$		0			0
$131$	13.4128			1.17188			0.585942	−	0.810353i	$-0.300725\pi$
$131$	13.4128			1.17188			0.585942	+	0.810353i	$0.300725\pi$
$132$	14.5988	−	8.42864i	1.27067	−	0.733619i
$133$	−7.13562	+	4.11975i	−0.618737	+	0.357228i
$134$	−3.93655	+	6.81830i	−0.340066	+	0.589012i
$135$		0			0
$136$	3.59210	−	6.22171i	0.308020	−	0.533507i
$137$	−4.10048	−	2.36741i	−0.350328	−	0.202262i	0.314502	−	0.949257i	$-0.398162\pi$
$137$	−4.10048	−	2.36741i	−0.350328	−	0.202262i	−0.664830	+	0.746995i	$0.731496\pi$
$138$			13.8064i			1.17528i
$139$	−5.52074	+	9.56221i	−0.468263	+	0.811056i	−0.999342	−	0.0362665i	$-0.988453\pi$
$139$	−5.52074	+	9.56221i	−0.468263	+	0.811056i	0.531079	+	0.847322i	$0.321787\pi$
$140$		0			0
$141$	1.10716	+	1.91766i	0.0932397	+	0.161496i
$142$		−	12.7096i		−	1.06657i
$143$	−7.67063	−	19.4795i	−0.641450	−	1.62896i
$144$	1.37778			0.114815
$145$		0			0
$146$	3.08419	+	5.34198i	0.255250	+	0.442105i
$147$	−6.68485	−	3.85950i	−0.551357	−	0.318326i
$148$		−	13.8064i		−	1.13488i
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	−0.904076	−	0.427372i	$-0.859440\pi$
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	0.822153	+	0.569267i	$0.192773\pi$
$150$		0			0
$151$	8.81135			0.717057			0.358529	−	0.933519i	$-0.383279\pi$
$151$	8.81135			0.717057			0.358529	+	0.933519i	$0.383279\pi$
$152$	3.71983	+	2.14764i	0.301718	+	0.174197i
$153$	−3.11085	+	1.79605i	−0.251498	+	0.145202i
$154$	−24.6637	−	42.7188i	−1.98746	−	3.44238i
$155$		0			0
$156$	−1.54839	+	10.3525i	−0.123971	+	0.828865i
$157$			2.73975i			0.218656i	0.994006	+	0.109328i	$0.0348698\pi$
$157$			2.73975i			0.218656i	−0.994006	+	0.109328i	$0.965130\pi$
$158$	23.6483	−	13.6533i	1.88135	−	1.08620i
$159$	0.407896	+	0.706496i	0.0323482	+	0.0560288i
$160$		0			0
$161$	23.9210			1.88524
$162$	1.91766	+	1.10716i	0.150665	+	0.0869867i
$163$	21.3855	+	12.3469i	1.67504	+	0.967084i	0.964748	+	0.263177i	$0.0847703\pi$
$163$	21.3855	+	12.3469i	1.67504	+	0.967084i	0.710292	+	0.703907i	$0.248563\pi$
$164$	32.2766			2.52038
$165$		0			0
$166$	−0.688892	−	1.19320i	−0.0534684	−	0.0926100i
$167$	−6.84865	+	3.95407i	−0.529964	+	0.305975i	−0.741002	−	0.671503i	$-0.765649\pi$
$167$	−6.84865	+	3.95407i	−0.529964	+	0.305975i	0.211038	+	0.977478i	$0.432316\pi$
$168$			7.67307i			0.591990i
$169$	12.4311	+	3.80365i	0.956239	+	0.292588i
$170$		0			0
$171$	−1.07382	−	1.85991i	−0.0821172	−	0.142231i
$172$	23.8736	−	13.7835i	1.82035	−	1.05098i
$173$	3.16301	+	1.82616i	0.240479	+	0.138841i	0.615397	−	0.788217i	$-0.288996\pi$
$173$	3.16301	+	1.82616i	0.240479	+	0.138841i	−0.374918	+	0.927058i	$0.622329\pi$
$174$	4.57628			0.346927
$175$		0			0
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$		−	9.97481i		−	0.749753i
$178$	31.0054	+	17.9010i	2.32395	+	1.34174i
$179$	−2.92073	−	5.05885i	−0.218306	−	0.378116i	0.735985	−	0.676998i	$-0.236720\pi$
$179$	−2.92073	−	5.05885i	−0.218306	−	0.378116i	−0.954290	+	0.298882i	$0.903386\pi$
$180$		0			0
$181$	10.0874			0.749792			0.374896	−	0.927067i	$-0.377678\pi$
$181$	10.0874			0.749792			0.374896	+	0.927067i	$0.377678\pi$
$182$	30.2933	+	4.53088i	2.24549	+	0.335851i
$183$		−	5.28100i		−	0.390382i
$184$	−6.23506	−	10.7994i	−0.459655	−	0.796146i
$185$		0			0
$186$	−5.84691	+	10.1271i	−0.428716	+	0.742558i
$187$			20.8573i			1.52524i
$188$	−5.56737	−	3.21432i	−0.406042	−	0.234428i
$189$	1.91827	−	3.32254i	0.139533	−	0.241679i
$190$		0			0
$191$	−7.98741	+	13.8346i	−0.577948	+	1.00104i	0.417766	+	0.908555i	$0.362813\pi$
$191$	−7.98741	+	13.8346i	−0.577948	+	1.00104i	−0.995714	+	0.0924813i	$0.970520\pi$
$192$	−11.1347	+	6.42864i	−0.803580	+	0.463947i
$193$	−3.20705	+	1.85159i	−0.230849	+	0.133280i	−0.610963	−	0.791659i	$-0.709218\pi$
$193$	−3.20705	+	1.85159i	−0.230849	+	0.133280i	0.380115	+	0.924939i	$0.375884\pi$
$194$	−9.41282			−0.675801
$195$		0			0
$196$	22.4099			1.60071
$197$	−14.2002	+	8.19850i	−1.01172	+	0.584119i	−0.911696	−	0.410866i	$-0.865226\pi$
$197$	−14.2002	+	8.19850i	−1.01172	+	0.584119i	−0.100028	+	0.994985i	$0.531893\pi$
$198$	11.1347	−	6.42864i	0.791311	−	0.456864i
$199$	2.64764	−	4.58585i	0.187686	−	0.325082i	−0.756792	−	0.653656i	$-0.773234\pi$
$199$	2.64764	−	4.58585i	0.187686	−	0.325082i	0.944478	+	0.328573i	$0.106568\pi$
$200$		0			0
$201$	−1.77777	+	3.07919i	−0.125394	+	0.217189i
$202$	−4.28609	−	2.47457i	−0.301568	−	0.174110i
$203$		−	7.92888i		−	0.556498i
$204$	5.21432	−	9.03147i	0.365075	−	0.632329i
$205$		0			0
$206$	2.70641	+	4.68764i	0.188564	+	0.326603i
$207$			6.23506i			0.433367i
$208$	1.82013	+	4.62222i	0.126204	+	0.320493i
$209$	−12.4701			−0.862577
$210$		0			0
$211$	−3.99532	−	6.92009i	−0.275049	−	0.476399i	0.695099	−	0.718914i	$-0.255361\pi$
$211$	−3.99532	−	6.92009i	−0.275049	−	0.476399i	−0.970147	+	0.242516i	$0.922027\pi$
$212$	−2.05111	−	1.18421i	−0.140871	−	0.0813318i
$213$		−	5.73975i		−	0.393281i
$214$	1.82939	−	3.16860i	0.125055	−	0.216601i
$215$		0			0
$216$	−2.00000			−0.136083
$217$	17.5463	+	10.1304i	1.19112	+	0.687694i
$218$	−5.01055	+	2.89284i	−0.339357	+	0.195928i
$219$	1.39284	+	2.41247i	0.0941194	+	0.163020i
$220$		0			0
$221$	−10.1350	−	8.06366i	−0.681757	−	0.542420i
$222$		−	10.5303i		−	0.706751i
$223$	−8.12140	+	4.68889i	−0.543849	+	0.313991i	−0.746637	−	0.665231i	$-0.768333\pi$
$223$	−8.12140	+	4.68889i	−0.543849	+	0.313991i	0.202788	+	0.979223i	$0.435000\pi$
$224$	13.5254	+	23.4267i	0.903706	+	1.56526i
$225$		0			0
$226$	5.37778			0.357725
$227$	12.4776	+	7.20395i	0.828168	+	0.478143i	0.853225	−	0.521543i	$-0.174643\pi$
$227$	12.4776	+	7.20395i	0.828168	+	0.478143i	−0.0250572	+	0.999686i	$0.507977\pi$
$228$	5.39972	+	3.11753i	0.357605	+	0.206464i
$229$	17.9541			1.18644			0.593219	−	0.805041i	$-0.297857\pi$
$229$	17.9541			1.18644			0.593219	+	0.805041i	$0.297857\pi$
$230$		0			0
$231$	−11.1383	−	19.2921i	−0.732845	−	1.26932i
$232$	−3.57959	+	2.06668i	−0.235012	+	0.135684i
$233$			27.5210i			1.80296i	0.432821	+	0.901480i	$0.357518\pi$
$233$			27.5210i			1.80296i	−0.432821	+	0.901480i	$0.642482\pi$
$234$	−1.18098	+	7.89601i	−0.0772032	+	0.516179i
$235$		0			0
$236$	14.4795	+	25.0792i	0.942535	+	1.63252i
$237$	10.6797	−	6.16593i	0.693721	−	0.400520i
$238$	−26.4277	−	15.2580i	−1.71305	−	0.989031i
$239$	19.0321			1.23109			0.615543	−	0.788104i	$-0.288937\pi$
$239$	19.0321			1.23109			0.615543	+	0.788104i	$0.288937\pi$
$240$		0			0
$241$	−11.6407	+	20.1623i	−0.749846	+	1.29877i	0.198051	+	0.980192i	$0.436539\pi$
$241$	−11.6407	+	20.1623i	−0.749846	+	1.29877i	−0.947896	+	0.318579i	$0.896794\pi$
$242$		−	50.2973i		−	3.23323i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	7.66593	+	13.2778i	0.490761	+	0.850022i
$245$		0			0
$246$	24.6178			1.56957
$247$	4.82109	−	6.05953i	0.306759	−	0.385559i
$248$		−	10.5620i		−	0.670687i
$249$	−0.311108	−	0.538855i	−0.0197157	−	0.0341485i
$250$		0			0
$251$	13.3620	−	23.1436i	0.843400	−	1.46081i	−0.0436042	−	0.999049i	$-0.513884\pi$
$251$	13.3620	−	23.1436i	0.843400	−	1.46081i	0.887004	−	0.461762i	$-0.152783\pi$
$252$			11.1383i			0.701645i
$253$	31.3531	+	18.1017i	1.97115	+	1.13804i
$254$	21.3193	−	36.9260i	1.33769	−	2.31695i
$255$		0			0
$256$	3.05086	−	5.28424i	0.190678	−	0.330265i
$257$	10.3222	−	5.95952i	0.643880	−	0.371744i	−0.142227	−	0.989834i	$-0.545426\pi$
$257$	10.3222	−	5.95952i	0.643880	−	0.371744i	0.786108	+	0.618090i	$0.212093\pi$
$258$	18.2088	−	10.5128i	1.13363	−	0.654500i
$259$	−18.2449			−1.13368
$260$		0			0
$261$	2.06668			0.127924
$262$	−25.7212	+	14.8501i	−1.58906	+	0.917444i
$263$	13.7948	−	7.96444i	0.850625	−	0.491108i	−0.0102370	−	0.999948i	$-0.503259\pi$
$263$	13.7948	−	7.96444i	0.850625	−	0.491108i	0.860862	+	0.508839i	$0.169925\pi$
$264$	−5.80642	+	10.0570i	−0.357361	+	0.618967i
$265$		0			0
$266$	9.12245	−	15.8006i	0.559334	−	0.968794i
$267$	14.0022	+	8.08419i	0.856923	+	0.494745i
$268$		−	10.3225i		−	0.630546i
$269$	−4.79383	+	8.30316i	−0.292285	+	0.506252i	−0.974350	−	0.225039i	$-0.927749\pi$
$269$	−4.79383	+	8.30316i	−0.292285	+	0.506252i	0.682065	+	0.731292i	$0.261082\pi$
$270$		0			0
$271$	−6.86196	−	11.8853i	−0.416835	−	0.721979i	0.578785	−	0.815481i	$-0.303527\pi$
$271$	−6.86196	−	11.8853i	−0.416835	−	0.721979i	−0.995619	+	0.0935019i	$0.970194\pi$
$272$		−	4.94914i		−	0.300086i
$273$	13.6807	+	2.04617i	0.827991	+	0.123840i
$274$	10.4844			0.633387
$275$		0			0
$276$	−9.05086	−	15.6765i	−0.544797	−	0.943617i
$277$	10.2247	+	5.90321i	0.614340	+	0.354690i	0.774662	−	0.632375i	$-0.217920\pi$
$277$	10.2247	+	5.90321i	0.614340	+	0.354690i	−0.160322	+	0.987065i	$0.551253\pi$
$278$		−	24.4494i		−	1.46638i
$279$	−2.64050	+	4.57348i	−0.158082	+	0.273807i
$280$		0			0
$281$	−10.7906			−0.643713			−0.321857	−	0.946788i	$-0.604307\pi$
$281$	−10.7906			−0.643713			−0.321857	+	0.946788i	$0.604307\pi$
$282$	−4.24631	−	2.45161i	−0.252864	−	0.145991i
$283$	−27.0162	+	15.5978i	−1.60594	+	0.927192i	−0.615680	+	0.787997i	$0.711118\pi$
$283$	−27.0162	+	15.5978i	−1.60594	+	0.927192i	−0.990265	+	0.139196i	$0.955548\pi$
$284$	8.33185	+	14.4312i	0.494404	+	0.856334i
$285$		0			0
$286$	36.2766	+	28.8624i	2.14508	+	1.70667i
$287$		−	42.6528i		−	2.51772i
$288$	−6.10622	+	3.52543i	−0.359812	+	0.207738i
$289$	−2.04839	−	3.54792i	−0.120494	−	0.208701i
$290$		0			0
$291$	−4.25088			−0.249191
$292$	−7.00391	−	4.04371i	−0.409873	−	0.236640i
$293$	−5.12603	−	2.95952i	−0.299466	−	0.172897i	0.342737	−	0.939431i	$-0.388646\pi$
$293$	−5.12603	−	2.95952i	−0.299466	−	0.172897i	−0.642203	+	0.766535i	$0.721979\pi$
$294$	17.0923			0.996846
$295$		0			0
$296$	4.75557	+	8.23689i	0.276412	+	0.478759i
$297$	5.02851	−	2.90321i	0.291784	−	0.168461i
$298$		−	4.42864i		−	0.256544i
$299$	−20.9175	+	8.23689i	−1.20969	+	0.476351i
$300$		0			0
$301$	−18.2146	−	31.5485i	−1.04987	−	1.81843i
$302$	−16.8971	+	9.75557i	−0.972321	+	0.561370i
$303$	−1.93562	−	1.11753i	−0.111199	−	0.0642005i
$304$	2.95899			0.169710
$305$		0			0
$306$	3.97703	−	6.88842i	0.227352	−	0.393785i
$307$		−	14.5877i		−	0.832562i	−0.909236	−	0.416281i	$-0.863333\pi$
$307$		−	14.5877i		−	0.832562i	0.909236	−	0.416281i	$-0.136667\pi$
$308$	56.0089	+	32.3368i	3.19141	+	1.84256i
$309$	1.22223	+	2.11697i	0.0695303	+	0.120430i
$310$		0			0
$311$	17.9748			1.01926			0.509629	−	0.860394i	$-0.329783\pi$
$311$	17.9748			1.01926			0.509629	+	0.860394i	$0.329783\pi$
$312$	−2.64212	−	6.70964i	−0.149580	−	0.379858i
$313$		−	5.79060i		−	0.327304i	−0.986518	−	0.163652i	$-0.947673\pi$
$313$		−	5.79060i		−	0.327304i	0.986518	−	0.163652i	$-0.0523275\pi$
$314$	−3.03334	−	5.25390i	−0.171181	−	0.296495i
$315$		0			0
$316$	−17.9010	+	31.0054i	−1.00701	+	1.74419i
$317$		−	4.78415i		−	0.268705i	−0.990934	−	0.134352i	$-0.957105\pi$
$317$		−	4.78415i		−	0.268705i	0.990934	−	0.134352i	$-0.0428954\pi$
$318$	−1.56441	−	0.903212i	−0.0877277	−	0.0506496i
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$	0.826164	−	1.43096i	0.0461120	−	0.0798682i
$322$	−45.8724	+	26.4844i	−2.55637	+	1.47592i
$323$	−6.68100	+	3.85728i	−0.371741	+	0.214625i
$324$	−2.90321			−0.161290
$325$		0			0
$326$	−54.6800			−3.02845
$327$	−2.26279	+	1.30642i	−0.125133	+	0.0722454i
$328$	−19.2561	+	11.1175i	−1.06324	+	0.613863i
$329$	−4.24766	+	7.35716i	−0.234181	+	0.405613i
$330$		0			0
$331$	−1.33654	+	2.31495i	−0.0734626	+	0.127241i	−0.900417	−	0.435028i	$-0.856738\pi$
$331$	−1.33654	+	2.31495i	−0.0734626	+	0.127241i	0.826954	+	0.562269i	$0.190072\pi$
$332$	1.56441	+	0.903212i	0.0858581	+	0.0495702i
$333$		−	4.75557i		−	0.260604i
$334$	8.75557	−	15.1651i	0.479083	−	0.829797i
$335$		0			0
$336$	2.64296	+	4.57774i	0.144185	+	0.249736i
$337$			29.0350i			1.58164i	0.612049	+	0.790820i	$0.290345\pi$
$337$			29.0350i			1.58164i	−0.612049	+	0.790820i	$0.709655\pi$
$338$	−28.0498	+	6.46912i	−1.52571	+	0.351874i
$339$	2.42864			0.131906
$340$		0			0
$341$	15.3319	+	26.5555i	0.830266	+	1.43806i
$342$	4.11844	+	2.37778i	0.222700	+	0.128576i
$343$		−	2.75848i		−	0.148944i
$344$	−9.49532	+	16.4464i	−0.511953	+	0.886729i
$345$		0			0
$346$	−8.08742			−0.434782
$347$	24.5156	+	14.1541i	1.31607	+	0.759832i	0.983093	−	0.183104i	$-0.0586146\pi$
$347$	24.5156	+	14.1541i	1.31607	+	0.759832i	0.332974	+	0.942936i	$0.391948\pi$
$348$	−5.19615	+	3.00000i	−0.278543	+	0.160817i
$349$	−16.0232	−	27.7530i	−0.857702	−	1.48558i	−0.874115	−	0.485719i	$-0.838558\pi$
$349$	−16.0232	−	27.7530i	−0.857702	−	1.48558i	0.0164125	−	0.999865i	$-0.494775\pi$
$350$		0			0
$351$	−0.533338	+	3.56589i	−0.0284675	+	0.190333i
$352$			40.9403i			2.18212i
$353$	−12.5477	+	7.24443i	−0.667848	+	0.385582i	−0.795261	−	0.606268i	$-0.792666\pi$
$353$	−12.5477	+	7.24443i	−0.667848	+	0.385582i	0.127413	+	0.991850i	$0.459333\pi$
$354$	11.0437	+	19.1283i	0.586967	+	1.01666i
$355$		0			0
$356$	−46.9403			−2.48783
$357$	−11.9349	−	6.89062i	−0.631662	−	0.364690i
$358$	11.2019	+	6.46743i	0.592039	+	0.341814i
$359$	24.2701			1.28093			0.640463	−	0.767989i	$-0.278742\pi$
$359$	24.2701			1.28093			0.640463	+	0.767989i	$0.278742\pi$
$360$		0			0
$361$	7.19381	+	12.4601i	0.378622	+	0.655792i
$362$	−19.3442	+	11.1684i	−1.01671	+	0.586997i
$363$		−	22.7146i		−	1.19221i
$364$	−37.3669	+	14.7143i	−1.95856	+	0.771240i
$365$		0			0
$366$	5.84691	+	10.1271i	0.305623	+	0.529354i
$367$	1.93815	−	1.11899i	0.101170	−	0.0584107i	−0.448561	−	0.893752i	$-0.648063\pi$
$367$	1.93815	−	1.11899i	0.101170	−	0.0584107i	0.549732	+	0.835341i	$0.314730\pi$
$368$	−7.43965	−	4.29529i	−0.387819	−	0.223907i
$369$	11.1175			0.578756
$370$		0			0
$371$	−1.56491	+	2.71050i	−0.0812459	+	0.140722i
$372$		−	15.3319i		−	0.794919i
$373$	−24.3466	−	14.0565i	−1.26062	−	0.727820i	−0.287427	−	0.957803i	$-0.592800\pi$
$373$	−24.3466	−	14.0565i	−1.26062	−	0.727820i	−0.973195	+	0.229982i	$0.926133\pi$
$374$	−23.0923	−	39.9971i	−1.19408	−	2.06820i
$375$		0			0
$376$	4.42864			0.228390
$377$	2.73020	+	6.93332i	0.140613	+	0.357084i
$378$			8.49532i			0.436952i
$379$	−9.80888	−	16.9895i	−0.503849	−	0.872691i	−0.999990	−	0.00444967i	$-0.998584\pi$
$379$	−9.80888	−	16.9895i	−0.503849	−	0.872691i	0.496142	−	0.868242i	$-0.334750\pi$
$380$		0			0
$381$	9.62790	−	16.6760i	0.493252	−	0.854338i
$382$		−	35.3733i		−	1.80986i
$383$	16.8355	+	9.72001i	0.860256	+	0.496669i	0.864098	−	0.503323i	$-0.167890\pi$
$383$	16.8355	+	9.72001i	0.860256	+	0.496669i	−0.00384183	+	0.999993i	$0.501223\pi$
$384$	7.18421	−	12.4434i	0.366618	−	0.635000i
$385$		0			0
$386$	4.10001	−	7.10143i	0.208685	−	0.361453i
$387$	8.22318	−	4.74766i	0.418008	−	0.241337i
$388$	10.6878	−	6.17061i	0.542591	−	0.313265i
$389$	2.81579			0.142766			0.0713832	−	0.997449i	$-0.477259\pi$
$389$	2.81579			0.142766			0.0713832	+	0.997449i	$0.477259\pi$
$390$		0			0
$391$	22.3970			1.13266
$392$	−13.3697	+	7.71900i	−0.675272	+	0.389869i
$393$	−11.6158	+	6.70641i	−0.585942	+	0.338294i
$394$	18.1541	−	31.4438i	0.914590	−	1.58412i
$395$		0			0
$396$	−8.42864	+	14.5988i	−0.423555	+	0.733619i
$397$	−10.9808	−	6.33976i	−0.551110	−	0.318184i	0.198460	−	0.980109i	$-0.436406\pi$
$397$	−10.9808	−	6.33976i	−0.551110	−	0.318184i	−0.749570	+	0.661926i	$0.769739\pi$
$398$			11.7255i			0.587744i
$399$	4.11975	−	7.13562i	0.206246	−	0.357228i
$400$		0			0
$401$	−0.453829	−	0.786055i	−0.0226631	−	0.0392537i	0.854471	−	0.519498i	$-0.173881\pi$
$401$	−0.453829	−	0.786055i	−0.0226631	−	0.0392537i	−0.877135	+	0.480245i	$0.840548\pi$
$402$		−	7.87310i		−	0.392675i
$403$	−18.8314	−	2.81656i	−0.938061	−	0.140303i
$404$	6.48886			0.322833
$405$		0			0
$406$	8.77854	+	15.2049i	0.435671	+	0.754605i
$407$	−23.9134	−	13.8064i	−1.18534	−	0.684359i
$408$			7.18421i			0.355671i
$409$	−16.7881	+	29.0779i	−0.830120	+	1.43781i	0.0678223	+	0.997697i	$0.478395\pi$
$409$	−16.7881	+	29.0779i	−0.830120	+	1.43781i	−0.897942	+	0.440113i	$0.854938\pi$
$410$		0			0
$411$	4.73483			0.233552
$412$	−6.14600	−	3.54839i	−0.302792	−	0.174817i
$413$	33.1417	−	19.1344i	1.63080	−	0.941540i
$414$	−6.90321	−	11.9567i	−0.339274	−	0.587640i
$415$		0			0
$416$	−19.8938	−	15.8280i	−0.975376	−	0.776029i
$417$		−	11.0415i		−	0.540704i
$418$	23.9134	−	13.8064i	1.16964	−	0.675294i
$419$	11.4763	+	19.8775i	0.560652	+	0.971078i	0.997440	+	0.0715136i	$0.0227829\pi$
$419$	11.4763	+	19.8775i	0.560652	+	0.971078i	−0.436787	+	0.899565i	$0.643884\pi$
$420$		0			0
$421$	−31.0874			−1.51511			−0.757554	−	0.652772i	$-0.773606\pi$
$421$	−31.0874			−1.51511			−0.757554	+	0.652772i	$0.773606\pi$
$422$	15.3233	+	8.84691i	0.745926	+	0.430661i
$423$	−1.91766	−	1.10716i	−0.0932397	−	0.0538320i
$424$	1.63158			0.0792367
$425$		0			0
$426$	6.35482	+	11.0069i	0.307892	+	0.533284i
$427$	17.5463	−	10.1304i	0.849125	−	0.490243i
$428$			4.79706i			0.231874i
$429$	16.3827	+	13.0344i	0.790965	+	0.629308i
$430$		0			0
$431$	−8.52543	−	14.7665i	−0.410655	−	0.711276i	0.584306	−	0.811533i	$-0.301367\pi$
$431$	−8.52543	−	14.7665i	−0.410655	−	0.711276i	−0.994962	+	0.100257i	$0.968033\pi$
$432$	−1.19320	+	0.688892i	−0.0574077	+	0.0331443i
$433$	2.24483	+	1.29605i	0.107880	+	0.0622843i	0.552969	−	0.833202i	$-0.313495\pi$
$433$	2.24483	+	1.29605i	0.107880	+	0.0622843i	−0.445089	+	0.895486i	$0.646828\pi$
$434$	−44.8637			−2.15353
$435$		0			0
$436$	3.79283	−	6.56937i	0.181643	−	0.314616i
$437$			13.3907i			0.640564i
$438$	−5.34198	−	3.08419i	−0.255250	−	0.147368i
$439$	−6.88493	−	11.9250i	−0.328600	−	0.569151i	0.653635	−	0.756810i	$-0.273243\pi$
$439$	−6.88493	−	11.9250i	−0.328600	−	0.569151i	−0.982234	+	0.187659i	$0.939910\pi$
$440$		0			0
$441$	7.71900			0.367572
$442$	28.3633	+	4.24221i	1.34910	+	0.201781i
$443$			4.71609i			0.224068i	0.993704	+	0.112034i	$0.0357366\pi$
$443$			4.71609i			0.224068i	−0.993704	+	0.112034i	$0.964263\pi$
$444$	6.90321	+	11.9567i	0.327612	+	0.567441i
$445$		0			0
$446$	10.3827	−	17.9834i	0.491635	−	0.851537i
$447$		−	2.00000i		−	0.0945968i
$448$	−42.7188	−	24.6637i	−2.01827	−	1.16525i
$449$	−5.16839	+	8.95191i	−0.243911	+	0.422467i	−0.961825	−	0.273665i	$-0.911764\pi$
$449$	−5.16839	+	8.95191i	−0.243911	+	0.422467i	0.717914	+	0.696132i	$0.245097\pi$
$450$		0			0
$451$	32.2766	−	55.9046i	1.51984	−	2.63245i
$452$	−6.10622	+	3.52543i	−0.287212	+	0.165822i
$453$	−7.63085	+	4.40567i	−0.358529	+	0.206997i
$454$	−31.9037			−1.49731
$455$		0			0
$456$	−4.29529			−0.201145
$457$	16.9989	−	9.81433i	0.795176	−	0.459095i	−0.0466054	−	0.998913i	$-0.514840\pi$
$457$	16.9989	−	9.81433i	0.795176	−	0.459095i	0.841782	+	0.539818i	$0.181507\pi$
$458$	−34.4297	+	19.8780i	−1.60880	+	0.928839i
$459$	1.79605	−	3.11085i	0.0838325	−	0.145202i
$460$		0			0
$461$	−12.6003	+	21.8243i	−0.586852	+	1.01646i	0.407789	+	0.913076i	$0.366300\pi$
$461$	−12.6003	+	21.8243i	−0.586852	+	1.01646i	−0.994642	+	0.103382i	$0.967034\pi$
$462$	42.7188	+	24.6637i	1.98746	+	1.14746i
$463$			28.8129i			1.33905i	0.742790	+	0.669524i	$0.233502\pi$
$463$			28.8129i			1.33905i	−0.742790	+	0.669524i	$0.766498\pi$
$464$	−1.42372	+	2.46595i	−0.0660944	+	0.114479i
$465$		0			0
$466$	−30.4701	−	52.7758i	−1.41150	−	2.44479i
$467$			32.3575i			1.49733i	0.662950	+	0.748664i	$0.269304\pi$
$467$			32.3575i			1.49733i	−0.662950	+	0.748664i	$0.730696\pi$
$468$	−3.83531	−	9.73975i	−0.177287	−	0.450220i
$469$	−13.6410			−0.629881
$470$		0			0
$471$	−1.36987	−	2.37269i	−0.0631204	−	0.109328i
$472$	−17.2769	−	9.97481i	−0.795233	−	0.459128i
$473$		−	55.1338i		−	2.53506i
$474$	−13.6533	+	23.6483i	−0.627118	+	1.08620i
$475$		0			0
$476$	40.0098			1.83385
$477$	−0.706496	−	0.407896i	−0.0323482	−	0.0186763i
$478$	−36.4971	+	21.0716i	−1.66934	+	0.963792i
$479$	2.96666	+	5.13841i	0.135550	+	0.234780i	0.925808	−	0.377995i	$-0.123386\pi$
$479$	2.96666	+	5.13841i	0.135550	+	0.234780i	−0.790257	+	0.612775i	$0.790053\pi$
$480$		0			0
$481$	15.9541	−	6.28239i	0.727443	−	0.286452i
$482$		−	51.5526i		−	2.34816i
$483$	−20.7162	+	11.9605i	−0.942621	+	0.544223i
$484$	32.9726	+	57.1102i	1.49875	+	2.59592i
$485$		0			0
$486$	−2.21432			−0.100444
$487$	−4.19415	−	2.42149i	−0.190055	−	0.109728i	0.401953	−	0.915660i	$-0.368331\pi$
$487$	−4.19415	−	2.42149i	−0.190055	−	0.109728i	−0.592008	+	0.805932i	$0.701665\pi$
$488$	−9.14695	−	5.28100i	−0.414063	−	0.239059i
$489$	−24.6938			−1.11669
$490$		0			0
$491$	−0.0382604	−	0.0662690i	−0.00172667	−	0.00299068i	0.865161	−	0.501495i	$-0.167216\pi$
$491$	−0.0382604	−	0.0662690i	−0.00172667	−	0.00299068i	−0.866887	+	0.498504i	$0.833883\pi$
$492$	−27.9523	+	16.1383i	−1.26019	+	0.727570i
$493$		−	7.42372i		−	0.334347i
$494$	−2.53633	+	16.9578i	−0.114115	+	0.762968i
$495$		0			0
$496$	−3.63804	−	6.30127i	−0.163353	−	0.282935i
$497$	19.0705	−	11.0104i	0.855430	−	0.493883i
$498$	1.19320	+	0.688892i	0.0534684	+	0.0308700i
$499$	−38.0687			−1.70419			−0.852094	−	0.523388i	$-0.824668\pi$
$499$	−38.0687			−1.70419			−0.852094	+	0.523388i	$0.824668\pi$
$500$		0			0
$501$	3.95407	−	6.84865i	0.176655	−	0.305975i
$502$			59.1753i			2.64112i
$503$	−11.4785	−	6.62714i	−0.511803	−	0.295489i	0.221772	−	0.975099i	$-0.428816\pi$
$503$	−11.4785	−	6.62714i	−0.511803	−	0.295489i	−0.733574	+	0.679609i	$0.762149\pi$
$504$	−3.83654	−	6.64507i	−0.170893	−	0.295995i
$505$		0			0
$506$	−80.1659			−3.56381
$507$	−12.6675	+	2.92149i	−0.562582	+	0.129748i
$508$			55.9037i			2.48033i
$509$	−14.2351	−	24.6559i	−0.630958	−	1.09285i	−0.987356	−	0.158517i	$-0.949329\pi$
$509$	−14.2351	−	24.6559i	−0.630958	−	1.09285i	0.356398	−	0.934334i	$-0.384005\pi$
$510$		0			0
$511$	−5.34368	+	9.25553i	−0.236391	+	0.409440i
$512$		−	15.2257i		−	0.672887i
$513$	1.85991	+	1.07382i	0.0821172	+	0.0474104i
$514$	−13.1963	+	22.8566i	−0.582063	+	1.00816i
$515$		0			0
$516$	−13.7835	+	23.8736i	−0.606783	+	1.05098i
$517$	−11.1347	+	6.42864i	−0.489705	+	0.282731i
$518$	34.9875	−	20.2000i	1.53726	−	0.887538i
$519$	−3.65233			−0.160319
$520$		0			0
$521$	17.1175			0.749933			0.374966	−	0.927038i	$-0.377654\pi$
$521$	17.1175			0.749933			0.374966	+	0.927038i	$0.377654\pi$
$522$	−3.96318	+	2.28814i	−0.173464	+	0.100149i
$523$	0.115487	−	0.0666765i	0.00504990	−	0.00291556i	−0.497473	−	0.867480i	$-0.665739\pi$
$523$	0.115487	−	0.0666765i	0.00504990	−	0.00291556i	0.502523	+	0.864564i	$0.332405\pi$
$524$	19.4701	−	33.7232i	0.850556	−	1.47321i
$525$		0			0
$526$	−17.6358	+	30.5461i	−0.768958	+	1.33187i
$527$	16.4284	+	9.48494i	0.715633	+	0.413171i
$528$			8.00000i			0.348155i
$529$	7.93801	−	13.7490i	0.345131	−	0.597784i
$530$		0			0
$531$	4.98741	+	8.63844i	0.216435	+	0.374876i
$532$			23.9210i			1.03711i
$533$	14.6869	+	37.2973i	0.636161	+	1.61553i
$534$	−35.8020			−1.54930
$535$		0			0
$536$	3.55554	+	6.15837i	0.153576	+	0.266001i
$537$	5.05885	+	2.92073i	0.218306	+	0.126039i
$538$		−	21.2301i		−	0.915296i
$539$	22.4099	−	38.8151i	0.965263	−	1.67188i
$540$		0			0
$541$	−26.3876			−1.13449			−0.567246	−	0.823548i	$-0.691991\pi$
$541$	−26.3876			−1.13449			−0.567246	+	0.823548i	$0.691991\pi$
$542$	26.3178	+	15.1946i	1.13045	+	0.652663i
$543$	−8.73596	+	5.04371i	−0.374896	+	0.216446i
$544$	12.6637	+	21.9342i	0.542952	+	0.940420i
$545$		0			0
$546$	−28.5002	+	11.2228i	−1.21970	+	0.480292i
$547$			0.0573086i			0.00245034i	0.999999	+	0.00122517i	$0.000389984\pi$
$547$			0.0573086i			0.00245034i	−0.999999	+	0.00122517i	$0.999610\pi$
$548$	−11.9046	+	6.87310i	−0.508538	+	0.293604i
$549$	2.64050	+	4.57348i	0.112694	+	0.195191i
$550$		0			0
$551$	4.43848			0.189086
$552$	10.7994	+	6.23506i	0.459655	+	0.265382i
$553$	40.9730	+	23.6558i	1.74235	+	1.00595i
$554$	−26.1432			−1.11072
$555$		0			0
$556$	16.0279	+	27.7611i	0.679734	+	1.17733i
$557$	−35.5434	+	20.5210i	−1.50602	+	0.869502i	−0.506046	+	0.862507i	$0.668893\pi$
$557$	−35.5434	+	20.5210i	−1.50602	+	0.869502i	−0.999976	+	0.00699538i	$0.997773\pi$
$558$		−	11.6938i		−	0.495039i
$559$	26.7908	+	21.3154i	1.13313	+	0.901543i
$560$		0			0
$561$	−10.4286	−	18.0629i	−0.440298	−	0.762618i
$562$	20.6927	−	11.9469i	0.872868	−	0.503950i
$563$	−18.3820	−	10.6128i	−0.774709	−	0.447278i	0.0598432	−	0.998208i	$-0.480940\pi$
$563$	−18.3820	−	10.6128i	−0.774709	−	0.447278i	−0.834552	+	0.550930i	$0.814273\pi$
$564$	6.42864			0.270695
$565$		0			0
$566$	34.5385	−	59.8224i	1.45176	−	2.51452i
$567$			3.83654i			0.161119i
$568$	−9.94153	−	5.73975i	−0.417137	−	0.240834i
$569$	8.18098	+	14.1699i	0.342965	+	0.594032i	0.984982	−	0.172658i	$-0.0552356\pi$
$569$	8.18098	+	14.1699i	0.342965	+	0.594032i	−0.642017	+	0.766690i	$0.721902\pi$
$570$		0			0
$571$	−37.7101			−1.57812			−0.789060	−	0.614317i	$-0.789432\pi$
$571$	−37.7101			−1.57812			−0.789060	+	0.614317i	$0.789432\pi$
$572$	−60.1112	−	8.99063i	−2.51337	−	0.375917i
$573$		−	15.9748i		−	0.667357i
$574$	47.2235	+	81.7935i	1.97107	+	3.41399i
$575$		0			0
$576$	6.42864	−	11.1347i	0.267860	−	0.463947i
$577$		−	42.7150i		−	1.77825i	−0.457664	−	0.889125i	$-0.651314\pi$
$577$		−	42.7150i		−	1.77825i	0.457664	−	0.889125i	$-0.348686\pi$
$578$	7.85623	+	4.53580i	0.326776	+	0.188664i
$579$	1.85159	−	3.20705i	0.0769495	−	0.133280i
$580$		0			0
$581$	1.19358	−	2.06733i	0.0495179	−	0.0857675i
$582$	8.15174	−	4.70641i	0.337900	−	0.195087i
$583$	−4.10222	+	2.36842i	−0.169896	+	0.0980898i
$584$	5.57136			0.230545
$585$		0			0
$586$	13.1066			0.541430
$587$	−8.33441	+	4.81187i	−0.343998	+	0.198607i	−0.662039	−	0.749470i	$-0.730308\pi$
$587$	−8.33441	+	4.81187i	−0.343998	+	0.198607i	0.318041	+	0.948077i	$0.396975\pi$
$588$	−19.4075	+	11.2050i	−0.800354	+	0.462084i
$589$	−5.67085	+	9.82220i	−0.233663	+	0.404717i
$590$		0			0
$591$	8.19850	−	14.2002i	0.337241	−	0.584119i
$592$	5.67433	+	3.27607i	0.233213	+	0.134646i
$593$		−	24.5018i		−	1.00617i	−0.864238	−	0.503084i	$-0.832199\pi$
$593$		−	24.5018i		−	1.00617i	0.864238	−	0.503084i	$-0.167801\pi$
$594$	−6.42864	+	11.1347i	−0.263770	+	0.456864i
$595$		0			0
$596$	2.90321	+	5.02851i	0.118920	+	0.205976i
$597$			5.29529i			0.216722i
$598$	30.9930	−	38.9545i	1.26740	−	1.59297i
$599$	16.9654			0.693189			0.346595	−	0.938015i	$-0.387338\pi$
$599$	16.9654			0.693189			0.346595	+	0.938015i	$0.387338\pi$
$600$		0			0
$601$	10.7835	+	18.6775i	0.439866	+	0.761871i	0.997679	−	0.0680961i	$-0.0216925\pi$
$601$	10.7835	+	18.6775i	0.439866	+	0.761871i	−0.557812	+	0.829967i	$0.688359\pi$
$602$	69.8586	+	40.3329i	2.84722	+	1.64384i
$603$		−	3.55554i		−	0.144793i
$604$	12.7906	−	22.1540i	0.520442	−	0.901432i
$605$		0			0
$606$	4.94914			0.201045
$607$	−17.3081	−	9.99285i	−0.702515	−	0.405597i	0.105768	−	0.994391i	$-0.466270\pi$
$607$	−17.3081	−	9.99285i	−0.702515	−	0.405597i	−0.808284	+	0.588793i	$0.799603\pi$
$608$	−13.1140	+	7.57136i	−0.531842	+	0.307059i
$609$	3.96444	+	6.86661i	0.160647	+	0.278249i
$610$		0			0
$611$	1.18098	−	7.89601i	0.0477774	−	0.319439i
$612$			10.4286i			0.421553i
$613$	9.69951	−	5.60001i	0.391760	−	0.226182i	−0.291163	−	0.956674i	$-0.594042\pi$
$613$	9.69951	−	5.60001i	0.391760	−	0.226182i	0.682922	+	0.730491i	$0.260709\pi$
$614$	16.1509	+	27.9741i	0.651796	+	1.12894i
$615$		0			0
$616$	−44.5531			−1.79510
$617$	0.511451	+	0.295286i	0.0205902	+	0.0118878i	0.510260	−	0.860020i	$-0.329549\pi$
$617$	0.511451	+	0.295286i	0.0205902	+	0.0118878i	−0.489670	+	0.871908i	$0.662883\pi$
$618$	−4.68764	−	2.70641i	−0.188564	−	0.108868i
$619$	12.2573			0.492664			0.246332	−	0.969186i	$-0.420775\pi$
$619$	12.2573			0.492664			0.246332	+	0.969186i	$0.420775\pi$
$620$		0			0
$621$	−3.11753	−	5.39972i	−0.125102	−	0.216683i
$622$	−34.4695	+	19.9010i	−1.38210	+	0.797957i
$623$			62.0306i			2.48520i
$624$	−3.88739	−	3.09289i	−0.155620	−	0.123815i
$625$		0			0
$626$	6.41112	+	11.1044i	0.256240	+	0.443821i
$627$	10.7994	−	6.23506i	0.431288	−	0.249004i
$628$	6.88842	+	3.97703i	0.274878	+	0.158701i
$629$	−17.0825			−0.681124
$630$		0			0
$631$	−18.3200	+	31.7312i	−0.729309	+	1.26320i	0.227867	+	0.973692i	$0.426825\pi$
$631$	−18.3200	+	31.7312i	−0.729309	+	1.26320i	−0.957176	+	0.289507i	$0.906509\pi$
$632$		−	24.6637i		−	0.981069i
$633$	6.92009	+	3.99532i	0.275049	+	0.158800i
$634$	5.29682	+	9.17436i	0.210364	+	0.364360i
$635$		0			0
$636$	2.36842			0.0939138
$637$	10.1973	+	25.8959i	0.404030	+	1.02603i
$638$			26.5718i			1.05199i
$639$	2.86987	+	4.97077i	0.113530	+	0.196641i
$640$		0			0
$641$	10.5827	−	18.3298i	0.417993	−	0.723985i	−0.577745	−	0.816218i	$-0.696067\pi$
$641$	10.5827	−	18.3298i	0.417993	−	0.723985i	0.995737	+	0.0922326i	$0.0294003\pi$
$642$			3.65878i			0.144401i
$643$	−10.5586	−	6.09602i	−0.416391	−	0.240404i	0.277141	−	0.960829i	$-0.410613\pi$
$643$	−10.5586	−	6.09602i	−0.416391	−	0.240404i	−0.693532	+	0.720426i	$0.743946\pi$
$644$	34.7239	−	60.1436i	1.36831	−	2.36999i
$645$		0			0
$646$	8.54125	−	14.7939i	0.336051	−	0.582057i
$647$	−8.19326	+	4.73038i	−0.322110	+	0.185970i	−0.652333	−	0.757933i	$-0.726210\pi$
$647$	−8.19326	+	4.73038i	−0.322110	+	0.185970i	0.330223	+	0.943903i	$0.392876\pi$
$648$	1.73205	−	1.00000i	0.0680414	−	0.0392837i
$649$	57.9180			2.27348
$650$		0			0
$651$	−20.2607			−0.794081
$652$	62.0866	−	35.8457i	2.43150	−	1.40383i
$653$	17.6661	−	10.1995i	0.691326	−	0.399137i	−0.112782	−	0.993620i	$-0.535976\pi$
$653$	17.6661	−	10.1995i	0.691326	−	0.399137i	0.804109	+	0.594482i	$0.202643\pi$
$654$	2.89284	−	5.01055i	0.113119	−	0.195928i
$655$		0			0
$656$	−7.65878	+	13.2654i	−0.299025	+	0.517927i
$657$	−2.41247	−	1.39284i	−0.0941194	−	0.0543399i
$658$		−	18.8113i		−	0.733343i
$659$	17.4859	−	30.2866i	0.681156	−	1.17980i	−0.293473	−	0.955967i	$-0.594811\pi$
$659$	17.4859	−	30.2866i	0.681156	−	1.17980i	0.974628	−	0.223829i	$-0.0718557\pi$
$660$		0			0
$661$	9.73014	+	16.8531i	0.378459	+	0.655510i	0.990838	−	0.135054i	$-0.0431209\pi$
$661$	9.73014	+	16.8531i	0.378459	+	0.655510i	−0.612380	+	0.790564i	$0.709788\pi$
$662$		−	5.91903i		−	0.230050i
$663$	12.8090	+	1.91581i	0.497462	+	0.0744038i
$664$	−1.24443			−0.0482933
$665$		0			0
$666$	5.26517	+	9.11955i	0.204021	+	0.353375i
$667$	−11.1595	−	6.44293i	−0.432097	−	0.249471i
$668$			22.9590i			0.888310i
$669$	4.68889	−	8.12140i	0.181283	−	0.313991i
$670$		0			0
$671$	30.6637			1.18376
$672$	−23.4267	−	13.5254i	−0.903706	−	0.521755i
$673$	12.3540	−	7.13259i	0.476212	−	0.274941i	−0.242625	−	0.970120i	$-0.578008\pi$
$673$	12.3540	−	7.13259i	0.476212	−	0.274941i	0.718836	+	0.695179i	$0.244675\pi$
$674$	−32.1464	−	55.6792i	−1.23823	−	2.14468i
$675$		0			0
$676$	27.6084	−	25.7336i	1.06186	−	0.989752i
$677$			34.0415i			1.30832i	0.756356	+	0.654160i	$0.226978\pi$
$677$			34.0415i			1.30832i	−0.756356	+	0.654160i	$0.773022\pi$
$678$	−4.65730	+	2.68889i	−0.178862	+	0.103266i
$679$	−8.15433	−	14.1237i	−0.312935	−	0.542019i
$680$		0			0
$681$	−14.4079			−0.552112
$682$	−58.8025	−	33.9496i	−2.25166	−	1.30000i
$683$	−25.4077	−	14.6692i	−0.972199	−	0.561300i	−0.0722933	−	0.997383i	$-0.523032\pi$
$683$	−25.4077	−	14.6692i	−0.972199	−	0.561300i	−0.899906	+	0.436084i	$0.856365\pi$
$684$	−6.23506			−0.238404
$685$		0			0
$686$	3.05408	+	5.28982i	0.116605	+	0.201966i
$687$	−15.5487	+	8.97703i	−0.593219	+	0.342495i
$688$			13.0825i			0.498766i
$689$	0.435093	−	2.90902i	0.0165757	−	0.110825i
$690$		0			0
$691$	−1.59457	−	2.76187i	−0.0606601	−	0.105066i	0.834101	−	0.551612i	$-0.185987\pi$
$691$	−1.59457	−	2.76187i	−0.0606601	−	0.105066i	−0.894761	+	0.446546i	$0.852654\pi$
$692$	9.18288	−	5.30174i	0.349081	−	0.201542i
$693$	19.2921	+	11.1383i	0.732845	+	0.423108i
$694$	−62.6834			−2.37943
$695$		0			0
$696$	2.06668	−	3.57959i	0.0783372	−	0.135684i
$697$		−	39.9353i		−	1.51266i
$698$	61.4540	+	35.4805i	2.32607	+	1.34296i
$699$	−13.7605	−	23.8339i	−0.520470	−	0.901480i
$700$		0			0
$701$	2.44738			0.0924361			0.0462180	−	0.998931i	$-0.485283\pi$
$701$	2.44738			0.0924361			0.0462180	+	0.998931i	$0.485283\pi$
$702$	−2.92525	−	7.42864i	−0.110406	−	0.280376i
$703$		−	10.2133i		−	0.385201i
$704$	−37.3274	−	64.6530i	−1.40683	−	2.43670i
$705$		0			0
$706$	16.0415	−	27.7847i	0.603729	−	1.04569i
$707$		−	8.57490i		−	0.322492i
$708$	−25.0792	−	14.4795i	−0.942535	−	0.544173i
$709$	−0.301502	+	0.522216i	−0.0113231	+	0.0196122i	−0.871631	−	0.490162i	$-0.836938\pi$
$709$	−0.301502	+	0.522216i	−0.0113231	+	0.0196122i	0.860308	+	0.509774i	$0.170271\pi$
$710$		0			0
$711$	−6.16593	+	10.6797i	−0.231240	+	0.400520i
$712$	28.0045	−	16.1684i	1.04951	−	0.605936i
$713$	28.5159	−	16.4637i	1.06793	−	0.616569i
$714$	30.5161			1.14203
$715$		0			0
$716$	−16.9590			−0.633787
$717$	−16.4823	+	9.51606i	−0.615543	+	0.355384i
$718$	−46.5417	+	26.8709i	−1.73692	+	1.00281i
$719$	21.7988	−	37.7565i	0.812956	−	1.40808i	−0.0978299	−	0.995203i	$-0.531190\pi$
$719$	21.7988	−	37.7565i	0.812956	−	1.40808i	0.910786	−	0.412878i	$-0.135477\pi$
$720$		0			0
$721$	−4.68913	+	8.12181i	−0.174632	+	0.302472i
$722$	−27.5905	−	15.9294i	−1.02681	−	0.592831i
$723$		−	23.2815i		−	0.865847i
$724$	14.6430	−	25.3623i	0.544201	−	0.942584i
$725$		0			0
$726$	25.1486	+	43.5587i	0.933354	+	1.61662i
$727$		−	32.8642i		−	1.21887i	−0.792838	−	0.609433i	$-0.791397\pi$
$727$		−	32.8642i		−	1.21887i	0.792838	−	0.609433i	$-0.208603\pi$
$728$	17.2247	−	21.6494i	0.638391	−	0.802381i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−17.0541	−	29.5385i	−0.630768	−	1.09252i
$732$	−13.2778	−	7.66593i	−0.490761	−	0.283341i
$733$			17.4035i			0.642811i	0.946942	+	0.321406i	$0.104155\pi$
$733$			17.4035i			0.642811i	−0.946942	+	0.321406i	$0.895845\pi$
$734$	−2.47780	+	4.29167i	−0.0914572	+	0.158409i
$735$		0			0
$736$	43.9625			1.62048
$737$	−17.8791	−	10.3225i	−0.658584	−	0.380234i
$738$	−21.3196	+	12.3089i	−0.784786	+	0.453096i
$739$	21.2924	+	36.8795i	0.783253	+	1.35663i	0.930037	+	0.367465i	$0.119774\pi$
$739$	21.2924	+	36.8795i	0.783253	+	1.35663i	−0.146785	+	0.989168i	$0.546893\pi$
$740$		0			0
$741$	−1.14542	+	7.65825i	−0.0420781	+	0.281333i
$742$		−	6.93041i		−	0.254423i
$743$	−28.4458	+	16.4232i	−1.04358	+	0.602508i	−0.920844	−	0.389932i	$-0.872499\pi$
$743$	−28.4458	+	16.4232i	−1.04358	+	0.602508i	−0.122731	+	0.992440i	$0.539165\pi$
$744$	5.28100	+	9.14695i	0.193611	+	0.335344i
$745$		0			0
$746$	62.2514			2.27918
$747$	0.538855	+	0.311108i	0.0197157	+	0.0113828i
$748$	52.4405	+	30.2766i	1.91742	+	1.10702i
$749$	6.33921			0.231630
$750$		0			0
$751$	−6.23729	−	10.8033i	−0.227602	−	0.394218i	0.729495	−	0.683986i	$-0.239755\pi$
$751$	−6.23729	−	10.8033i	−0.227602	−	0.394218i	−0.957097	+	0.289768i	$0.906422\pi$
$752$	2.64212	−	1.52543i	0.0963481	−	0.0556266i
$753$			26.7239i			0.973874i
$754$	−12.9119	−	10.2730i	−0.470223	−	0.374119i
$755$		0			0
$756$	−5.56914	−	9.64603i	−0.202548	−	0.350823i
$757$	4.22155	−	2.43732i	0.153435	−	0.0885858i	−0.421317	−	0.906914i	$-0.638432\pi$
$757$	4.22155	−	2.43732i	0.153435	−	0.0885858i	0.574752	+	0.818328i	$0.305099\pi$
$758$	37.6202	+	21.7200i	1.36643	+	0.788906i
$759$	−36.2034			−1.31410
$760$		0			0
$761$	2.05086	−	3.55219i	0.0743434	−	0.128767i	−0.826457	−	0.563000i	$-0.809647\pi$
$761$	2.05086	−	3.55219i	0.0743434	−	0.128767i	0.900801	+	0.434233i	$0.142981\pi$
$762$			42.6385i			1.54463i
$763$	−8.68128	−	5.01214i	−0.314284	−	0.181452i
$764$	23.1891	+	40.1648i	0.838953	+	1.45311i
$765$		0			0
$766$	−43.0464			−1.55533
$767$	−22.3917	+	28.1437i	−0.808519	+	1.01621i
$768$			6.10171i			0.220177i
$769$	−24.0486	−	41.6535i	−0.867216	−	1.50206i	−0.864830	−	0.502065i	$-0.832574\pi$
$769$	−24.0486	−	41.6535i	−0.867216	−	1.50206i	−0.00238584	−	0.999997i	$-0.500759\pi$
$770$		0			0
$771$	−5.95952	+	10.3222i	−0.214627	+	0.371744i
$772$			10.7511i			0.386941i
$773$	−15.7561	−	9.09679i	−0.566707	−	0.327189i	0.189126	−	0.981953i	$-0.439435\pi$
$773$	−15.7561	−	9.09679i	−0.566707	−	0.327189i	−0.755833	+	0.654764i	$0.772768\pi$
$774$	−10.5128	+	18.2088i	−0.377876	+	0.654500i
$775$		0			0
$776$	−4.25088	+	7.36275i	−0.152598	+	0.264307i
$777$	15.8006	−	9.12245i	0.566842	−	0.327266i
$778$	−5.39972	+	3.11753i	−0.193589	+	0.111769i
$779$	23.8765			0.855464
$780$		0			0
$781$	33.3274			1.19255
$782$	−42.9498	+	24.7971i	−1.53588	+	0.886741i
$783$	−1.78979	+	1.03334i	−0.0639620	+	0.0369285i
$784$	−5.31756	+	9.21029i	−0.189913	+	0.328939i
$785$		0			0
$786$	14.8501	−	25.7212i	0.529687	−	0.917444i
$787$	−25.3722	−	14.6486i	−0.904421	−	0.522168i	−0.0257893	−	0.999667i	$-0.508210\pi$
$787$	−25.3722	−	14.6486i	−0.904421	−	0.522168i	−0.878632	+	0.477500i	$0.841543\pi$
$788$			47.6040i			1.69582i
$789$	−7.96444	+	13.7948i	−0.283542	+	0.491108i
$790$		0			0
$791$	4.65878	+	8.06924i	0.165647	+	0.286909i
$792$		−	11.6128i		−	0.412645i
$793$	−11.8549	+	14.9002i	−0.420981	+	0.529122i
$794$	28.0765			0.996398
$795$		0			0
$796$	−7.68667	−	13.3137i	−0.272447	−	0.471892i
$797$	23.2771	+	13.4390i	0.824515	+	0.476034i	0.851971	−	0.523589i	$-0.175407\pi$
$797$	23.2771	+	13.4390i	0.824515	+	0.476034i	−0.0274557	+	0.999623i	$0.508741\pi$
$798$			18.2449i			0.645863i
$799$	−3.97703	+	6.88842i	−0.140697	+	0.243695i
$800$		0			0
$801$	−16.1684			−0.571282
$802$	1.74058	+	1.00492i	0.0614619	+	0.0354850i
$803$	−14.0078	+	8.08742i	−0.494325	+	0.285399i
$804$	5.16124	+	8.93953i	0.182023	+	0.315273i
$805$		0			0
$806$	39.2306	−	15.4482i	1.38184	−	0.544140i
$807$		−	9.58766i		−	0.337502i
$808$	−3.87124	+	2.23506i	−0.136190	+	0.0786293i
$809$	−14.2286	−	24.6447i	−0.500251	−	0.866461i	−1.00000		0.000290180i	$-0.999908\pi$
$809$	−14.2286	−	24.6447i	−0.500251	−	0.866461i	0.499749	−	0.866170i	$-0.333426\pi$
$810$		0			0
$811$	−16.6316			−0.584014			−0.292007	−	0.956416i	$-0.594323\pi$
$811$	−16.6316			−0.584014			−0.292007	+	0.956416i	$0.594323\pi$
$812$	−19.9352	−	11.5096i	−0.699589	−	0.403908i
$813$	11.8853	+	6.86196i	0.416835	+	0.240660i
$814$	61.1437			2.14308
$815$		0			0
$816$	2.47457	+	4.28609i	0.0866274	+	0.150043i
$817$	17.6605	−	10.1963i	0.617862	−	0.356723i
$818$		−	74.3486i		−	2.59954i
$819$	−12.8709	+	5.06829i	−0.449745	+	0.177100i
$820$		0			0
$821$	17.4844	+	30.2839i	0.610210	+	1.05692i	0.991205	+	0.132338i	$0.0422484\pi$
$821$	17.4844	+	30.2839i	0.610210	+	1.05692i	−0.380994	+	0.924577i	$0.624418\pi$
$822$	−9.07977	+	5.24221i	−0.316693	+	0.182843i
$823$	−16.1632	−	9.33185i	−0.563415	−	0.325288i	0.191100	−	0.981571i	$-0.438795\pi$
$823$	−16.1632	−	9.33185i	−0.563415	−	0.325288i	−0.754515	+	0.656283i	$0.772128\pi$
$824$	4.88892			0.170314
$825$		0			0
$826$	−42.3696	+	73.3863i	−1.47423	+	2.55344i
$827$		−	21.2968i		−	0.740563i	−0.928920	−	0.370281i	$-0.879261\pi$
$827$		−	21.2968i		−	0.740563i	0.928920	−	0.370281i	$-0.120739\pi$
$828$	15.6765	+	9.05086i	0.544797	+	0.314539i
$829$	−3.59610	−	6.22862i	−0.124898	−	0.216329i	0.796795	−	0.604249i	$-0.206527\pi$
$829$	−3.59610	−	6.22862i	−0.124898	−	0.216329i	−0.921693	+	0.387920i	$0.873194\pi$
$830$		0			0
$831$	−11.8064			−0.409560
$832$	45.8476	+	6.85728i	1.58948	+	0.237733i
$833$		−	27.7275i		−	0.960700i
$834$	12.2247	+	21.1738i	0.423306	+	0.733188i
$835$		0			0
$836$	−18.1017	+	31.3531i	−0.626061	+	1.08437i
$837$		−	5.28100i		−	0.182538i
$838$	−44.0151	−	25.4121i	−1.52048	−	0.877847i
$839$	−0.790602	+	1.36936i	−0.0272946	+	0.0472757i	−0.879350	−	0.476176i	$-0.842023\pi$
$839$	−0.790602	+	1.36936i	−0.0272946	+	0.0472757i	0.852055	+	0.523452i	$0.175356\pi$
$840$		0			0
$841$	12.3644	−	21.4158i	0.426359	−	0.738476i
$842$	59.6150	−	34.4187i	2.05447	−	1.18615i
$843$	9.34494	−	5.39530i	0.321857	−	0.185824i
$844$	−23.1985			−0.798525
$845$		0			0
$846$	4.90321			0.168576
$847$	75.4700	−	43.5726i	2.59318	−	1.49717i
$848$	0.973400	−	0.561993i	0.0334267	−	0.0192989i
$849$	15.5978	−	27.0162i	0.535315	−	0.927192i
$850$		0			0
$851$	−14.8256	+	25.6788i	−0.508216	+	0.880256i
$852$	−14.4312	−	8.33185i	−0.494404	−	0.285445i
$853$		−	23.0207i		−	0.788215i	−0.919064	−	0.394108i	$-0.871054\pi$
$853$		−	23.0207i		−	0.788215i	0.919064	−	0.394108i	$-0.128946\pi$
$854$	−22.4319	+	38.8531i	−0.767603	+	1.32953i
$855$		0			0
$856$	−1.65233	−	2.86191i	−0.0564754	−	0.0978182i
$857$		−	47.4499i		−	1.62086i	−0.585838	−	0.810428i	$-0.699235\pi$
$857$		−	47.4499i		−	1.62086i	0.585838	−	0.810428i	$-0.300765\pi$
$858$	−45.8476	−	6.85728i	−1.56521	−	0.234104i
$859$	49.0241			1.67268			0.836341	−	0.548210i	$-0.184690\pi$
$859$	49.0241			1.67268			0.836341	+	0.548210i	$0.184690\pi$
$860$		0			0
$861$	21.3264	+	36.9384i	0.726802	+	1.25886i
$862$	32.6977	+	18.8780i	1.11369	+	0.642988i
$863$		−	37.3590i		−	1.27172i	−0.771806	−	0.635858i	$-0.780646\pi$
$863$		−	37.3590i		−	1.27172i	0.771806	−	0.635858i	$-0.219354\pi$
$864$	3.52543	−	6.10622i	0.119937	−	0.207738i
$865$		0			0
$866$	−5.73975			−0.195045
$867$	3.54792	+	2.04839i	0.120494	+	0.0695671i
$868$	50.9406	−	29.4106i	1.72904	−	0.998261i
$869$	35.8020	+	62.0108i	1.21450	+	2.10357i
$870$		0			0
$871$	11.9282	−	4.69708i	0.404171	−	0.159154i
$872$			5.22570i			0.176964i
$873$	3.68137	−	2.12544i	0.124596	−	0.0719353i
$874$	−14.8256	−	25.6788i	−0.501485	−	0.868597i
$875$		0			0
$876$	8.08742			0.273249
$877$	18.0108	+	10.3985i	0.608181	+	0.351133i	0.772253	−	0.635315i	$-0.219130\pi$
$877$	18.0108	+	10.3985i	0.608181	+	0.351133i	−0.164072	+	0.986448i	$0.552463\pi$
$878$	26.4059	+	15.2454i	0.891155	+	0.514509i
$879$	5.91903			0.199644
$880$		0			0
$881$	−14.8780	−	25.7695i	−0.501253	−	0.868196i	−0.999999	−	0.00144781i	$-0.999539\pi$
$881$	−14.8780	−	25.7695i	−0.501253	−	0.868196i	0.498746	−	0.866748i	$-0.333794\pi$
$882$	−14.8024	+	8.54617i	−0.498423	+	0.287765i
$883$		−	40.5975i		−	1.36621i	−0.730318	−	0.683107i	$-0.760628\pi$
$883$		−	40.5975i		−	1.36621i	0.730318	−	0.683107i	$-0.239372\pi$
$884$	−34.9862	+	13.7768i	−1.17671	+	0.463366i
$885$		0			0
$886$	−5.22146	−	9.04384i	−0.175419	−	0.303834i
$887$	−41.9422	+	24.2153i	−1.40828	+	0.813071i	−0.995222	−	0.0976338i	$-0.968873\pi$
$887$	−41.9422	+	24.2153i	−1.40828	+	0.813071i	−0.413058	+	0.910705i	$0.635539\pi$
$888$	−8.23689	−	4.75557i	−0.276412	−	0.159586i
$889$	73.8756			2.47771
$890$		0			0
$891$	−2.90321	+	5.02851i	−0.0972613	+	0.168461i
$892$			27.2257i			0.911584i
$893$	−4.11844	−	2.37778i	−0.137818	−	0.0795695i
$894$	2.21432	+	3.83531i	0.0740579	+	0.128272i
$895$		0			0
$896$	55.1249			1.84159
$897$	13.9966	−	17.5921i	0.467334	−	0.587383i
$898$		−	22.8889i		−	0.763813i
$899$	−5.45706	−	9.45190i	−0.182003	−	0.315238i
$900$		0			0
$901$	−1.46520	+	2.53781i	−0.0488130	+	0.0845467i
$902$			142.941i			4.75942i
$903$	31.5485	+	18.2146i	1.04987	+	0.606143i
$904$	2.42864	−	4.20653i	0.0807753	−	0.139907i
$905$		0			0
$906$	9.75557	−	16.8971i	0.324107	−	0.561370i
$907$	8.91983	−	5.14987i	0.296178	−	0.170998i	−0.344547	−	0.938769i	$-0.611967\pi$
$907$	8.91983	−	5.14987i	0.296178	−	0.170998i	0.640725	+	0.767771i	$0.278634\pi$
$908$	36.2251	−	20.9146i	1.20217	−	0.694075i
$909$	2.23506			0.0741324
$910$		0			0
$911$	7.35905			0.243816			0.121908	−	0.992541i	$-0.461099\pi$
$911$	7.35905			0.243816			0.121908	+	0.992541i	$0.461099\pi$
$912$	−2.56256	+	1.47949i	−0.0848548	+	0.0489910i
$913$	3.12882	−	1.80642i	0.103549	−	0.0597839i
$914$	−21.7321	+	37.6411i	−0.718833	+	1.24506i
$915$		0			0
$916$	26.0622	−	45.1411i	0.861120	−	1.49150i
$917$	−44.5646	−	25.7294i	−1.47165	−	0.849659i
$918$			7.95407i			0.262523i
$919$	0.391383	−	0.677895i	0.0129105	−	0.0223617i	−0.859498	−	0.511139i	$-0.829224\pi$
$919$	0.391383	−	0.677895i	0.0129105	−	0.0223617i	0.872408	+	0.488777i	$0.162557\pi$
$920$		0			0
$921$	7.29383	+	12.6333i	0.240340	+	0.416281i
$922$		−	55.8020i		−	1.83774i
$923$	−12.8847	+	16.1946i	−0.424107	+	0.533051i
$924$	−64.6735			−2.12760
$925$		0			0
$926$	−31.9005	−	55.2532i	−1.04831	−	1.81573i
$927$	−2.11697	−	1.22223i	−0.0695303	−	0.0401433i
$928$		−	14.5718i		−	0.478344i
$929$	−14.2208	+	24.6311i	−0.466568	+	0.808120i	−0.999271	−	0.0381824i	$-0.987843\pi$
$929$	−14.2208	+	24.6311i	−0.466568	+	0.808120i	0.532702	+	0.846303i	$0.321177\pi$
$930$		0			0
$931$	16.5777			0.543311
$932$	69.1948	+	39.9496i	2.26655	+	1.30859i
$933$	−15.5666	+	8.98741i	−0.509629	+	0.294234i
$934$	−35.8249	−	62.0506i	−1.17223	−	2.03036i
$935$		0			0
$936$	5.64296	+	4.48966i	0.184446	+	0.146749i
$937$			21.3747i			0.698282i	0.937070	+	0.349141i	$0.113527\pi$
$937$			21.3747i			0.698282i	−0.937070	+	0.349141i	$0.886473\pi$
$938$	26.1587	−	15.1027i	0.854111	−	0.493121i
$939$	2.89530	+	5.01481i	0.0944846	+	0.163652i
$940$		0			0
$941$	−38.2830			−1.24799			−0.623995	−	0.781428i	$-0.714492\pi$
$941$	−38.2830			−1.24799			−0.623995	+	0.781428i	$0.714492\pi$
$942$	5.25390	+	3.03334i	0.171181	+	0.0988315i
$943$	−60.0316	−	34.6593i	−1.95490	−	1.12866i
$944$	−13.7431			−0.447301
$945$		0			0
$946$	61.0420	+	105.728i	1.98465	+	3.43751i
$947$	−6.58613	+	3.80251i	−0.214021	+	0.123565i	−0.603179	−	0.797606i	$-0.706099\pi$
$947$	−6.58613	+	3.80251i	−0.214021	+	0.123565i	0.389158	+	0.921171i	$0.372766\pi$
$948$		−	35.8020i		−	1.16279i
$949$	1.48571	−	9.93342i	0.0482282	−	0.322452i
$950$		0			0
$951$	2.39207	+	4.14319i	0.0775683	+	0.134352i
$952$	−23.8698	+	13.7812i	−0.773625	+	0.446652i
$953$	28.8871	+	16.6780i	0.935746	+	0.540253i	0.888624	−	0.458636i	$-0.151662\pi$
$953$	28.8871	+	16.6780i	0.935746	+	0.540253i	0.0471217	+	0.998889i	$0.484995\pi$
$954$	1.80642			0.0584851
$955$		0			0
$956$	27.6271	−	47.8516i	0.893525	−	1.54763i
$957$			12.0000i			0.387905i
$958$	−11.3781	−	6.56914i	−0.367609	−	0.212239i
$959$	9.08266	+	15.7316i	0.293294	+	0.508001i
$960$		0			0
$961$	−3.11108			−0.100357
$962$	−23.6388	+	29.7112i	−0.762146	+	0.957926i
$963$			1.65233i			0.0532455i
$964$	33.7955	+	58.5356i	1.08848	+	1.88530i
$965$		0			0
$966$	26.4844	−	45.8724i	0.852122	−	1.47592i
$967$			40.8988i			1.31522i	0.753360	+	0.657608i	$0.228432\pi$
$967$			40.8988i			1.31522i	−0.753360	+	0.657608i	$0.771568\pi$
$968$	−39.3428	−	22.7146i	−1.26452	−	0.730074i
$969$	3.85728	−	6.68100i	0.123914	−	0.214625i
$970$		0			0
$971$	2.11753	−	3.66767i	0.0679548	−	0.117701i	−0.830046	−	0.557695i	$-0.811686\pi$
$971$	2.11753	−	3.66767i	0.0679548	−	0.117701i	0.898001	+	0.439994i	$0.145019\pi$
$972$	2.51426	−	1.45161i	0.0806448	−	0.0465603i
$973$	36.6858	−	21.1805i	1.17609	−	0.679017i
$974$	10.7239			0.343617
$975$		0			0
$976$	−7.27607			−0.232901
$977$	33.5915	−	19.3941i	1.07469	−	0.620472i	0.145230	−	0.989398i	$-0.453608\pi$
$977$	33.5915	−	19.3941i	1.07469	−	0.620472i	0.929459	+	0.368926i	$0.120275\pi$
$978$	47.3543	−	27.3400i	1.51422	−	0.874237i
$979$	−46.9403	+	81.3029i	−1.50022	+	2.59845i
$980$		0			0
$981$	1.30642	−	2.26279i	0.0417109	−	0.0722454i
$982$	0.146741	+	0.0847209i	0.00468269	+	0.00270355i
$983$			21.4479i			0.684080i	0.939685	+	0.342040i	$0.111118\pi$
$983$			21.4479i			0.684080i	−0.939685	+	0.342040i	$0.888882\pi$
$984$	11.1175	−	19.2561i	0.354414	−	0.613863i
$985$		0			0
$986$	8.21924	+	14.2361i	0.261754	+	0.453371i
$987$		−	8.49532i		−	0.270409i
$988$	−8.23689	−	20.9175i	−0.262050	−	0.665474i
$989$	−59.2039			−1.88257
$990$		0			0
$991$	5.65010	+	9.78627i	0.179481	+	0.310871i	0.941703	−	0.336445i	$-0.109225\pi$
$991$	5.65010	+	9.78627i	0.179481	+	0.310871i	−0.762222	+	0.647316i	$0.775891\pi$
$992$	32.2469	+	18.6178i	1.02384	+	0.591115i
$993$		−	2.67307i		−	0.0848273i
$994$	−24.3805	+	42.2282i	−0.773302	+	1.33940i
$995$		0			0
$996$	−1.80642			−0.0572387
$997$	−46.9599	−	27.1123i	−1.48724	−	0.858656i	−0.487341	−	0.873212i	$-0.662033\pi$
$997$	−46.9599	−	27.1123i	−1.48724	−	0.858656i	−0.999894	+	0.0145557i	$0.995367\pi$
$998$	73.0027	−	42.1481i	2.31086	−	1.33418i
$999$	2.37778	+	4.11844i	0.0752298	+	0.130302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bb.j.874.1		12
5.2	odd	4		195.2.i.e.16.1	✓	6
5.3	odd	4		975.2.i.m.601.3		6
5.4	even	2	inner	975.2.bb.j.874.6		12
13.9	even	3	inner	975.2.bb.j.724.6		12
15.2	even	4		585.2.j.g.406.3		6
65.9	even	6	inner	975.2.bb.j.724.1		12
65.22	odd	12		195.2.i.e.61.1	yes	6
65.42	odd	12		2535.2.a.y.1.3		3
65.48	odd	12		975.2.i.m.451.3		6
65.62	odd	12		2535.2.a.z.1.1		3
195.62	even	12		7605.2.a.bt.1.3		3
195.107	even	12		7605.2.a.bu.1.1		3
195.152	even	12		585.2.j.g.451.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.e.16.1	✓	6	5.2	odd	4
195.2.i.e.61.1	yes	6	65.22	odd	12
585.2.j.g.406.3		6	15.2	even	4
585.2.j.g.451.3		6	195.152	even	12
975.2.i.m.451.3		6	65.48	odd	12
975.2.i.m.601.3		6	5.3	odd	4
975.2.bb.j.724.1		12	65.9	even	6	inner
975.2.bb.j.724.6		12	13.9	even	3	inner
975.2.bb.j.874.1		12	1.1	even	1	trivial
975.2.bb.j.874.6		12	5.4	even	2	inner
2535.2.a.y.1.3		3	65.42	odd	12
2535.2.a.z.1.1		3	65.62	odd	12
7605.2.a.bt.1.3		3	195.62	even	12
7605.2.a.bu.1.1		3	195.107	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.91766 + 1.10716i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(1.45161 - 2.51426i) q^{4} +(1.10716 - 1.91766i) q^{6} +(-3.32254 - 1.91827i) q^{7} +2.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.90321 - 5.02851i) q^{11} +2.90321i q^{12} +(3.56589 + 0.533338i) q^{13} +8.49532 q^{14} +(0.688892 + 1.19320i) q^{16} +(-3.11085 - 1.79605i) q^{17} +2.21432i q^{18} +(1.07382 - 1.85991i) q^{19} +3.83654 q^{21} +(11.1347 + 6.42864i) q^{22} +(-5.39972 + 3.11753i) q^{23} +(-1.00000 - 1.73205i) q^{24} +(-7.42864 + 2.92525i) q^{26} +1.00000i q^{27} +(-9.64603 + 5.56914i) q^{28} +(1.03334 + 1.78979i) q^{29} -5.28100 q^{31} +(-6.10622 - 3.52543i) q^{32} +(5.02851 + 2.90321i) q^{33} +7.95407 q^{34} +(-1.45161 - 2.51426i) q^{36} +(4.11844 - 2.37778i) q^{37} +4.75557i q^{38} +(-3.35482 + 1.32106i) q^{39} +(5.55877 + 9.62806i) q^{41} +(-7.35716 + 4.24766i) q^{42} +(8.22318 + 4.74766i) q^{43} -16.8573 q^{44} +(6.90321 - 11.9567i) q^{46} -2.21432i q^{47} +(-1.19320 - 0.688892i) q^{48} +(3.85950 + 6.68485i) q^{49} +3.59210 q^{51} +(6.51721 - 8.19135i) q^{52} -0.815792i q^{53} +(-1.10716 - 1.91766i) q^{54} +(3.83654 - 6.64507i) q^{56} +2.14764i q^{57} +(-3.96318 - 2.28814i) q^{58} +(-4.98741 + 8.63844i) q^{59} +(-2.64050 + 4.57348i) q^{61} +(10.1271 - 5.84691i) q^{62} +(-3.32254 + 1.91827i) q^{63} +12.8573 q^{64} -12.8573 q^{66} +(3.07919 - 1.77777i) q^{67} +(-9.03147 + 5.21432i) q^{68} +(3.11753 - 5.39972i) q^{69} +(-2.86987 + 4.97077i) q^{71} +(1.73205 + 1.00000i) q^{72} -2.78568i q^{73} +(-5.26517 + 9.11955i) q^{74} +(-3.11753 - 5.39972i) q^{76} +22.2766i q^{77} +(4.97077 - 6.24766i) q^{78} -12.3319 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-21.3196 - 12.3089i) q^{82} +0.622216i q^{83} +(5.56914 - 9.64603i) q^{84} -21.0257 q^{86} +(-1.78979 - 1.03334i) q^{87} +(10.0570 - 5.80642i) q^{88} +(-8.08419 - 14.0022i) q^{89} +(-10.8247 - 8.61236i) q^{91} +18.1017i q^{92} +(4.57348 - 2.64050i) q^{93} +(2.45161 + 4.24631i) q^{94} +7.05086 q^{96} +(3.68137 + 2.12544i) q^{97} +(-14.8024 - 8.54617i) q^{98} -5.80642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{9} - 8 q^{11} + 48 q^{14} + 8 q^{16} + 20 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} - 36 q^{31} + 16 q^{34} - 4 q^{36} + 40 q^{41} - 96 q^{44} + 56 q^{46} + 60 q^{49} + 16 q^{51}+ \cdots - 16 q^{99}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^9 - 8 * q^11 + 48 * q^14 + 8 * q^16 + 20 * q^21 - 12 * q^24 - 36 * q^26 + 12 * q^29 - 36 * q^31 + 16 * q^34 - 4 * q^36 + 40 * q^41 - 96 * q^44 + 56 * q^46 + 60 * q^49 + 16 * q^51 + 20 * q^56 + 20 * q^59 - 18 * q^61 + 48 * q^64 - 48 * q^66 - 16 * q^69 - 8 * q^71 + 16 * q^74 + 16 * q^76 - 68 * q^79 - 6 * q^81 - 40 * q^86 - 44 * q^89 - 62 * q^91 + 16 * q^94 + 32 * q^96 - 16 * q^99

Introduction

L-functions

Modular forms

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