LMFDB - Embedded newform 975.2.i.m.601.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(451,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("975.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.i (of order $3$, degree $2$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.591408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1 $ x^6 - x^5 + 4x^4 + x^3 + 10x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.3
Root			$0.155554 - 0.269427i$ of defining polynomial
Character	$\chi$	$=$	975.601
Dual form			975.2.i.m.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10716 + 1.91766i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.45161 + 2.51426i) q^{4} +(1.10716 - 1.91766i) q^{6} +(-1.91827 + 3.32254i) q^{7} -2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.10716 + 1.91766i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.45161 + 2.51426i) q^{4} +(1.10716 - 1.91766i) q^{6} +(-1.91827 + 3.32254i) q^{7} -2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.90321 - 5.02851i) q^{11} +2.90321 q^{12} +(-0.533338 + 3.56589i) q^{13} -8.49532 q^{14} +(0.688892 + 1.19320i) q^{16} +(-1.79605 + 3.11085i) q^{17} -2.21432 q^{18} +(-1.07382 + 1.85991i) q^{19} +3.83654 q^{21} +(6.42864 - 11.1347i) q^{22} +(-3.11753 - 5.39972i) q^{23} +(1.00000 + 1.73205i) q^{24} +(-7.42864 + 2.92525i) q^{26} +1.00000 q^{27} +(-5.56914 - 9.64603i) q^{28} +(-1.03334 - 1.78979i) q^{29} -5.28100 q^{31} +(-3.52543 + 6.10622i) q^{32} +(-2.90321 + 5.02851i) q^{33} -7.95407 q^{34} +(-1.45161 - 2.51426i) q^{36} +(-2.37778 - 4.11844i) q^{37} -4.75557 q^{38} +(3.35482 - 1.32106i) q^{39} +(5.55877 + 9.62806i) q^{41} +(4.24766 + 7.35716i) q^{42} +(-4.74766 + 8.22318i) q^{43} +16.8573 q^{44} +(6.90321 - 11.9567i) q^{46} -2.21432 q^{47} +(0.688892 - 1.19320i) q^{48} +(-3.85950 - 6.68485i) q^{49} +3.59210 q^{51} +(-8.19135 - 6.51721i) q^{52} +0.815792 q^{53} +(1.10716 + 1.91766i) q^{54} +(3.83654 - 6.64507i) q^{56} +2.14764 q^{57} +(2.28814 - 3.96318i) q^{58} +(4.98741 - 8.63844i) q^{59} +(-2.64050 + 4.57348i) q^{61} +(-5.84691 - 10.1271i) q^{62} +(-1.91827 - 3.32254i) q^{63} -12.8573 q^{64} -12.8573 q^{66} +(-1.77777 - 3.07919i) q^{67} +(-5.21432 - 9.03147i) q^{68} +(-3.11753 + 5.39972i) q^{69} +(-2.86987 + 4.97077i) q^{71} +(1.00000 - 1.73205i) q^{72} +2.78568 q^{73} +(5.26517 - 9.11955i) q^{74} +(-3.11753 - 5.39972i) q^{76} +22.2766 q^{77} +(6.24766 + 4.97077i) q^{78} +12.3319 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-12.3089 + 21.3196i) q^{82} -0.622216 q^{83} +(-5.56914 + 9.64603i) q^{84} -21.0257 q^{86} +(-1.03334 + 1.78979i) q^{87} +(5.80642 + 10.0570i) q^{88} +(8.08419 + 14.0022i) q^{89} +(-10.8247 - 8.61236i) q^{91} +18.1017 q^{92} +(2.64050 + 4.57348i) q^{93} +(-2.45161 - 4.24631i) q^{94} +7.05086 q^{96} +(2.12544 - 3.68137i) q^{97} +(8.54617 - 14.8024i) q^{98} +5.80642 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 2 q^{4} - 5 q^{7} - 12 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 2 * q^4 - 5 * q^7 - 12 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} - 2 q^{4} - 5 q^{7} - 12 q^{8} - 3 q^{9} - 4 q^{11} + 4 q^{12} - 3 q^{13} - 24 q^{14} + 4 q^{16} - 4 q^{17} + 10 q^{21} + 12 q^{22} + 8 q^{23} + 6 q^{24} - 18 q^{26} + 6 q^{27} - 6 q^{29} - 18 q^{31} - 8 q^{32} - 4 q^{33} - 8 q^{34} - 2 q^{36} - 14 q^{37} - 28 q^{38} + 20 q^{41} + 12 q^{42} - 15 q^{43} + 48 q^{44} + 28 q^{46} + 4 q^{48} - 30 q^{49} + 8 q^{51} - 16 q^{52} + 32 q^{53} + 10 q^{56} - 6 q^{58} - 10 q^{59} - 9 q^{61} - 2 q^{62} - 5 q^{63} - 24 q^{64} - 24 q^{66} - 11 q^{67} - 18 q^{68} + 8 q^{69} - 4 q^{71} + 6 q^{72} + 30 q^{73} - 8 q^{74} + 8 q^{76} + 24 q^{78} + 34 q^{79} - 3 q^{81} - 14 q^{82} - 4 q^{83} - 20 q^{86} - 6 q^{87} + 8 q^{88} + 22 q^{89} - 31 q^{91} + 56 q^{92} + 9 q^{93} - 8 q^{94} + 16 q^{96} - q^{97} - 2 q^{98} + 8 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 - 2 * q^4 - 5 * q^7 - 12 * q^8 - 3 * q^9 - 4 * q^11 + 4 * q^12 - 3 * q^13 - 24 * q^14 + 4 * q^16 - 4 * q^17 + 10 * q^21 + 12 * q^22 + 8 * q^23 + 6 * q^24 - 18 * q^26 + 6 * q^27 - 6 * q^29 - 18 * q^31 - 8 * q^32 - 4 * q^33 - 8 * q^34 - 2 * q^36 - 14 * q^37 - 28 * q^38 + 20 * q^41 + 12 * q^42 - 15 * q^43 + 48 * q^44 + 28 * q^46 + 4 * q^48 - 30 * q^49 + 8 * q^51 - 16 * q^52 + 32 * q^53 + 10 * q^56 - 6 * q^58 - 10 * q^59 - 9 * q^61 - 2 * q^62 - 5 * q^63 - 24 * q^64 - 24 * q^66 - 11 * q^67 - 18 * q^68 + 8 * q^69 - 4 * q^71 + 6 * q^72 + 30 * q^73 - 8 * q^74 + 8 * q^76 + 24 * q^78 + 34 * q^79 - 3 * q^81 - 14 * q^82 - 4 * q^83 - 20 * q^86 - 6 * q^87 + 8 * q^88 + 22 * q^89 - 31 * q^91 + 56 * q^92 + 9 * q^93 - 8 * q^94 + 16 * q^96 - q^97 - 2 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.10716	+	1.91766i	0.782880	+	1.35599i	0.930257	+	0.366908i	$0.119584\pi$
$2$	1.10716	+	1.91766i	0.782880	+	1.35599i	−0.147377	+	0.989080i	$0.547083\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.45161	+	2.51426i	−0.725803	+	1.25713i
$5$		0			0
$5$		0			0
$6$	1.10716	−	1.91766i	0.451996	−	0.782880i
$7$	−1.91827	+	3.32254i	−0.725037	+	1.25580i	0.233922	+	0.972255i	$0.424844\pi$
$7$	−1.91827	+	3.32254i	−0.725037	+	1.25580i	−0.958959	+	0.283546i	$0.908489\pi$
$8$	−2.00000			−0.707107
$9$	−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	$-0.506037\pi$
$12$	2.90321			0.838085
$13$	−0.533338	+	3.56589i	−0.147921	+	0.988999i
$13$	−0.533338	+	3.56589i	−0.147921	+	0.988999i
$14$	−8.49532			−2.27047
$15$		0			0
$16$	0.688892	+	1.19320i	0.172223	+	0.298299i
$17$	−1.79605	+	3.11085i	−0.435607	+	0.754493i	−0.997345	−	0.0728222i	$-0.976799\pi$
$17$	−1.79605	+	3.11085i	−0.435607	+	0.754493i	0.561738	+	0.827315i	$0.310133\pi$
$18$	−2.21432			−0.521920
$19$	−1.07382	+	1.85991i	−0.246352	+	0.426693i	−0.962511	−	0.271244i	$-0.912565\pi$
$19$	−1.07382	+	1.85991i	−0.246352	+	0.426693i	0.716159	+	0.697937i	$0.245898\pi$
$20$		0			0
$21$	3.83654			0.837201
$22$	6.42864	−	11.1347i	1.37059	−	2.37393i
$23$	−3.11753	−	5.39972i	−0.650050	−	1.12592i	−0.983110	−	0.183014i	$-0.941414\pi$
$23$	−3.11753	−	5.39972i	−0.650050	−	1.12592i	0.333060	−	0.942906i	$-0.391919\pi$
$24$	1.00000	+	1.73205i	0.204124	+	0.353553i
$25$		0			0
$26$	−7.42864	+	2.92525i	−1.45688	+	0.573688i
$27$	1.00000			0.192450
$28$	−5.56914	−	9.64603i	−1.05247	−	1.82293i
$29$	−1.03334	−	1.78979i	−0.191886	−	0.332356i	0.753989	−	0.656887i	$-0.228127\pi$
$29$	−1.03334	−	1.78979i	−0.191886	−	0.332356i	−0.945875	+	0.324530i	$0.894794\pi$
$30$		0			0
$31$	−5.28100			−0.948495			−0.474247	−	0.880392i	$-0.657280\pi$
$31$	−5.28100			−0.948495			−0.474247	+	0.880392i	$0.657280\pi$
$32$	−3.52543	+	6.10622i	−0.623213	+	1.07944i
$33$	−2.90321	+	5.02851i	−0.505384	+	0.875351i
$34$	−7.95407			−1.36411
$35$		0			0
$36$	−1.45161	−	2.51426i	−0.241934	−	0.419043i
$37$	−2.37778	−	4.11844i	−0.390905	−	0.677068i	0.601664	−	0.798749i	$-0.294505\pi$
$37$	−2.37778	−	4.11844i	−0.390905	−	0.677068i	−0.992569	+	0.121681i	$0.961171\pi$
$38$	−4.75557			−0.771455
$39$	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	$0.498653\pi$
$42$	4.24766	+	7.35716i	0.655428	+	1.13523i
$43$	−4.74766	+	8.22318i	−0.724011	+	1.25402i	0.235369	+	0.971906i	$0.424370\pi$
$43$	−4.74766	+	8.22318i	−0.724011	+	1.25402i	−0.959380	+	0.282118i	$0.908963\pi$
$44$	16.8573			2.54133
$45$		0			0
$46$	6.90321	−	11.9567i	1.01782	−	1.76292i
$47$	−2.21432			−0.322992			−0.161496	−	0.986873i	$-0.551632\pi$
$47$	−2.21432			−0.322992			−0.161496	+	0.986873i	$0.551632\pi$
$48$	0.688892	−	1.19320i	0.0994330	−	0.172223i
$49$	−3.85950	−	6.68485i	−0.551357	−	0.954979i
$50$		0			0
$51$	3.59210			0.502995
$52$	−8.19135	−	6.51721i	−1.13594	−	0.903775i
$53$	0.815792			0.112058			0.0560288	−	0.998429i	$-0.482156\pi$
$53$	0.815792			0.112058			0.0560288	+	0.998429i	$0.482156\pi$
$54$	1.10716	+	1.91766i	0.150665	+	0.260960i
$55$		0			0
$56$	3.83654	−	6.64507i	0.512679	−	0.887985i
$57$	2.14764			0.284462
$58$	2.28814	−	3.96318i	0.300448	−	0.520391i
$59$	4.98741	−	8.63844i	0.649305	−	1.12463i	−0.333984	−	0.942579i	$-0.608393\pi$
$59$	4.98741	−	8.63844i	0.649305	−	1.12463i	0.983289	−	0.182050i	$-0.0582734\pi$
$60$		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	$0.276445\pi$
$62$	−5.84691	−	10.1271i	−0.742558	−	1.28615i
$63$	−1.91827	−	3.32254i	−0.241679	−	0.418600i
$64$	−12.8573			−1.60716
$65$		0			0
$66$	−12.8573			−1.58262
$67$	−1.77777	−	3.07919i	−0.217189	−	0.376183i	0.736758	−	0.676156i	$-0.236355\pi$
$67$	−1.77777	−	3.07919i	−0.217189	−	0.376183i	−0.953948	+	0.299973i	$0.903022\pi$
$68$	−5.21432	−	9.03147i	−0.632329	−	1.09523i
$69$	−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	$0.277294\pi$
$72$	1.00000	−	1.73205i	0.117851	−	0.204124i
$73$	2.78568			0.326039			0.163020	−	0.986623i	$-0.447877\pi$
$73$	2.78568			0.326039			0.163020	+	0.986623i	$0.447877\pi$
$74$	5.26517	−	9.11955i	0.612064	−	1.06013i
$75$		0			0
$76$	−3.11753	−	5.39972i	−0.357605	−	0.619391i
$77$	22.2766			2.53865
$78$	6.24766	+	4.97077i	0.707408	+	0.562829i
$79$	12.3319			1.38744			0.693721	−	0.720244i	$-0.255970\pi$
$79$	12.3319			1.38744			0.693721	+	0.720244i	$0.255970\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−12.3089	+	21.3196i	−1.35929	+	2.35436i
$83$	−0.622216			−0.0682970			−0.0341485	−	0.999417i	$-0.510872\pi$
$83$	−0.622216			−0.0682970			−0.0341485	+	0.999417i	$0.510872\pi$
$84$	−5.56914	+	9.64603i	−0.607643	+	1.05247i
$85$		0			0
$86$	−21.0257			−2.26726
$87$	−1.03334	+	1.78979i	−0.110785	+	0.191886i
$88$	5.80642	+	10.0570i	0.618967	+	1.07208i
$89$	8.08419	+	14.0022i	0.856923	+	1.48423i	0.874850	+	0.484395i	$0.160960\pi$
$89$	8.08419	+	14.0022i	0.856923	+	1.48423i	−0.0179269	+	0.999839i	$0.505707\pi$
$90$		0			0
$91$	−10.8247	−	8.61236i	−1.13474	−	0.902821i
$92$	18.1017			1.88723
$93$	2.64050	+	4.57348i	0.273807	+	0.474247i
$94$	−2.45161	−	4.24631i	−0.252864	−	0.437973i
$95$		0			0
$96$	7.05086			0.719625
$97$	2.12544	−	3.68137i	0.215806	−	0.373787i	−0.737716	−	0.675112i	$-0.764095\pi$
$97$	2.12544	−	3.68137i	0.215806	−	0.373787i	0.953522	+	0.301325i	$0.0974288\pi$
$98$	8.54617	−	14.8024i	0.863294	−	1.49527i
$99$	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	$0.797864\pi$
$102$	3.97703	+	6.88842i	0.393785	+	0.682056i
$103$	2.44446			0.240860			0.120430	−	0.992722i	$-0.461573\pi$
$103$	2.44446			0.240860			0.120430	+	0.992722i	$0.461573\pi$
$104$	1.06668	−	7.13177i	0.104596	−	0.699328i
$105$		0			0
$106$	0.903212	+	1.56441i	0.0877277	+	0.151949i
$107$	0.826164	+	1.43096i	0.0798682	+	0.138336i	0.903193	−	0.429235i	$-0.141217\pi$
$107$	0.826164	+	1.43096i	0.0798682	+	0.138336i	−0.823325	+	0.567571i	$0.807883\pi$
$108$	−1.45161	+	2.51426i	−0.139681	+	0.241934i
$109$	−2.61285			−0.250265			−0.125133	−	0.992140i	$-0.539936\pi$
$109$	−2.61285			−0.250265			−0.125133	+	0.992140i	$0.539936\pi$
$110$		0			0
$111$	−2.37778	+	4.11844i	−0.225689	+	0.390905i
$112$	−5.28592			−0.499472
$113$	1.21432	−	2.10326i	0.114234	−	0.197858i	−0.803240	−	0.595656i	$-0.796892\pi$
$113$	1.21432	−	2.10326i	0.114234	−	0.197858i	0.917473	+	0.397798i	$0.130225\pi$
$114$	2.37778	+	4.11844i	0.222700	+	0.385728i
$115$		0			0
$116$	6.00000			0.557086
$117$	−2.82148	−	2.24483i	−0.260846	−	0.207534i
$118$	22.0874			2.03331
$119$	−6.89062	−	11.9349i	−0.631662	−	1.09407i
$120$		0			0
$121$	−11.3573	+	19.6714i	−1.03248	+	1.78831i
$122$	−11.6938			−1.05871
$123$	5.55877	−	9.62806i	0.501217	−	0.868133i
$124$	7.66593	−	13.2778i	0.688420	−	1.19238i
$125$		0			0
$126$	4.24766	−	7.35716i	0.378411	−	0.655428i
$127$	9.62790	+	16.6760i	0.854338	+	1.47976i	0.877258	+	0.480020i	$0.159371\pi$
$127$	9.62790	+	16.6760i	0.854338	+	1.47976i	−0.0229193	+	0.999737i	$0.507296\pi$
$128$	−7.18421	−	12.4434i	−0.635000	−	1.09985i
$129$	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	$0.300725\pi$
$132$	−8.42864	−	14.5988i	−0.733619	−	1.27067i
$133$	−4.11975	−	7.13562i	−0.357228	−	0.618737i
$134$	3.93655	−	6.81830i	0.340066	−	0.589012i
$135$		0			0
$136$	3.59210	−	6.22171i	0.308020	−	0.533507i
$137$	−2.36741	+	4.10048i	−0.202262	+	0.350328i	−0.949257	−	0.314502i	$-0.898162\pi$
$137$	−2.36741	+	4.10048i	−0.202262	+	0.350328i	0.746995	+	0.664830i	$0.231496\pi$
$138$	−13.8064			−1.17528
$139$	5.52074	−	9.56221i	0.468263	−	0.811056i	−0.531079	−	0.847322i	$-0.678213\pi$
$139$	5.52074	−	9.56221i	0.468263	−	0.811056i	0.999342	+	0.0362665i	$0.0115465\pi$
$140$		0			0
$141$	1.10716	+	1.91766i	0.0932397	+	0.161496i
$142$	−12.7096			−1.06657
$143$	19.4795	−	7.67063i	1.62896	−	0.641450i
$144$	−1.37778			−0.114815
$145$		0			0
$146$	3.08419	+	5.34198i	0.255250	+	0.442105i
$147$	−3.85950	+	6.68485i	−0.318326	+	0.551357i
$148$	13.8064			1.13488
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	−0.822153	−	0.569267i	$-0.807227\pi$
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	0.904076	+	0.427372i	$0.140560\pi$
$150$		0			0
$151$	8.81135			0.717057			0.358529	−	0.933519i	$-0.383279\pi$
$151$	8.81135			0.717057			0.358529	+	0.933519i	$0.383279\pi$
$152$	2.14764	−	3.71983i	0.174197	−	0.301718i
$153$	−1.79605	−	3.11085i	−0.145202	−	0.251498i
$154$	24.6637	+	42.7188i	1.98746	+	3.44238i
$155$		0			0
$156$	−1.54839	+	10.3525i	−0.123971	+	0.828865i
$157$	2.73975			0.218656			0.109328	−	0.994006i	$-0.465130\pi$
$157$	2.73975			0.218656			0.109328	+	0.994006i	$0.465130\pi$
$158$	13.6533	+	23.6483i	1.08620	+	1.88135i
$159$	−0.407896	−	0.706496i	−0.0323482	−	0.0560288i
$160$		0			0
$161$	23.9210			1.88524
$162$	1.10716	−	1.91766i	0.0869867	−	0.150665i
$163$	−12.3469	+	21.3855i	−0.967084	+	1.67504i	−0.263177	+	0.964748i	$0.584770\pi$
$163$	−12.3469	+	21.3855i	−0.967084	+	1.67504i	−0.703907	+	0.710292i	$0.748563\pi$
$164$	−32.2766			−2.52038
$165$		0			0
$166$	−0.688892	−	1.19320i	−0.0534684	−	0.0926100i
$167$	3.95407	+	6.84865i	0.305975	+	0.529964i	0.977478	−	0.211038i	$-0.0676843\pi$
$167$	3.95407	+	6.84865i	0.305975	+	0.529964i	−0.671503	+	0.741002i	$0.734351\pi$
$168$	−7.67307			−0.591990
$169$	−12.4311	−	3.80365i	−0.956239	−	0.292588i
$170$		0			0
$171$	−1.07382	−	1.85991i	−0.0821172	−	0.142231i
$172$	−13.7835	−	23.8736i	−1.05098	−	1.82035i
$173$	−1.82616	+	3.16301i	−0.138841	+	0.240479i	−0.927058	−	0.374918i	$-0.877671\pi$
$173$	−1.82616	+	3.16301i	−0.138841	+	0.240479i	0.788217	+	0.615397i	$0.211004\pi$
$174$	−4.57628			−0.346927
$175$		0			0
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$	−9.97481			−0.749753
$178$	−17.9010	+	31.0054i	−1.34174	+	2.32395i
$179$	2.92073	+	5.05885i	0.218306	+	0.378116i	0.954290	−	0.298882i	$-0.0966137\pi$
$179$	2.92073	+	5.05885i	0.218306	+	0.378116i	−0.735985	+	0.676998i	$0.763280\pi$
$180$		0			0
$181$	10.0874			0.749792			0.374896	−	0.927067i	$-0.377678\pi$
$181$	10.0874			0.749792			0.374896	+	0.927067i	$0.377678\pi$
$182$	4.53088	−	30.2933i	0.335851	−	2.24549i
$183$	5.28100			0.390382
$184$	6.23506	+	10.7994i	0.459655	+	0.796146i
$185$		0			0
$186$	−5.84691	+	10.1271i	−0.428716	+	0.742558i
$187$	20.8573			1.52524
$188$	3.21432	−	5.56737i	0.234428	−	0.406042i
$189$	−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	$0.970520\pi$
$192$	6.42864	+	11.1347i	0.463947	+	0.803580i
$193$	−1.85159	−	3.20705i	−0.133280	−	0.230849i	0.791659	−	0.610963i	$-0.209218\pi$
$193$	−1.85159	−	3.20705i	−0.133280	−	0.230849i	−0.924939	+	0.380115i	$0.875884\pi$
$194$	9.41282			0.675801
$195$		0			0
$196$	22.4099			1.60071
$197$	8.19850	+	14.2002i	0.584119	+	1.01172i	0.994985	+	0.100028i	$0.0318931\pi$
$197$	8.19850	+	14.2002i	0.584119	+	1.01172i	−0.410866	+	0.911696i	$0.634774\pi$
$198$	6.42864	+	11.1347i	0.456864	+	0.791311i
$199$	−2.64764	+	4.58585i	−0.187686	+	0.325082i	−0.944478	−	0.328573i	$-0.893432\pi$
$199$	−2.64764	+	4.58585i	−0.187686	+	0.325082i	0.756792	+	0.653656i	$0.226766\pi$
$200$		0			0
$201$	−1.77777	+	3.07919i	−0.125394	+	0.217189i
$202$	−2.47457	+	4.28609i	−0.174110	+	0.301568i
$203$	7.92888			0.556498
$204$	−5.21432	+	9.03147i	−0.365075	+	0.632329i
$205$		0			0
$206$	2.70641	+	4.68764i	0.188564	+	0.326603i
$207$	6.23506			0.433367
$208$	−4.62222	+	1.82013i	−0.320493	+	0.126204i
$209$	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	$0.922027\pi$
$212$	−1.18421	+	2.05111i	−0.0813318	+	0.140871i
$213$	5.73975			0.393281
$214$	−1.82939	+	3.16860i	−0.125055	+	0.216601i
$215$		0			0
$216$	−2.00000			−0.136083
$217$	10.1304	−	17.5463i	0.687694	−	1.19112i
$218$	−2.89284	−	5.01055i	−0.195928	−	0.339357i
$219$	−1.39284	−	2.41247i	−0.0941194	−	0.163020i
$220$		0			0
$221$	−10.1350	−	8.06366i	−0.681757	−	0.542420i
$222$	−10.5303			−0.706751
$223$	−4.68889	−	8.12140i	−0.313991	−	0.543849i	0.665231	−	0.746637i	$-0.268333\pi$
$223$	−4.68889	−	8.12140i	−0.313991	−	0.543849i	−0.979223	+	0.202788i	$0.935000\pi$
$224$	−13.5254	−	23.4267i	−0.903706	−	1.56526i
$225$		0			0
$226$	5.37778			0.357725
$227$	7.20395	−	12.4776i	0.478143	−	0.828168i	−0.521543	−	0.853225i	$-0.674643\pi$
$227$	7.20395	−	12.4776i	0.478143	−	0.828168i	0.999686	+	0.0250572i	$0.00797680\pi$
$228$	−3.11753	+	5.39972i	−0.206464	+	0.357605i
$229$	−17.9541			−1.18644			−0.593219	−	0.805041i	$-0.702143\pi$
$229$	−17.9541			−1.18644			−0.593219	+	0.805041i	$0.702143\pi$
$230$		0			0
$231$	−11.1383	−	19.2921i	−0.732845	−	1.26932i
$232$	2.06668	+	3.57959i	0.135684	+	0.235012i
$233$	−27.5210			−1.80296			−0.901480	−	0.432821i	$-0.857518\pi$
$233$	−27.5210			−1.80296			−0.901480	+	0.432821i	$0.857518\pi$
$234$	1.18098	−	7.89601i	0.0772032	−	0.516179i
$235$		0			0
$236$	14.4795	+	25.0792i	0.942535	+	1.63252i
$237$	−6.16593	−	10.6797i	−0.400520	−	0.693721i
$238$	15.2580	−	26.4277i	0.989031	−	1.71305i
$239$	−19.0321			−1.23109			−0.615543	−	0.788104i	$-0.711063\pi$
$239$	−19.0321			−1.23109			−0.615543	+	0.788104i	$0.711063\pi$
$240$		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	$0.896794\pi$
$242$	−50.2973			−3.23323
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−7.66593	−	13.2778i	−0.490761	−	0.850022i
$245$		0			0
$246$	24.6178			1.56957
$247$	−6.05953	−	4.82109i	−0.385559	−	0.306759i
$248$	10.5620			0.670687
$249$	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	$-0.152783\pi$
$252$	11.1383			0.701645
$253$	−18.1017	+	31.3531i	−1.13804	+	1.97115i
$254$	−21.3193	+	36.9260i	−1.33769	+	2.31695i
$255$		0			0
$256$	3.05086	−	5.28424i	0.190678	−	0.330265i
$257$	−5.95952	−	10.3222i	−0.371744	−	0.643880i	0.618090	−	0.786108i	$-0.287907\pi$
$257$	−5.95952	−	10.3222i	−0.371744	−	0.643880i	−0.989834	+	0.142227i	$0.954574\pi$
$258$	10.5128	+	18.2088i	0.654500	+	1.13363i
$259$	18.2449			1.13368
$260$		0			0
$261$	2.06668			0.127924
$262$	14.8501	+	25.7212i	0.917444	+	1.58906i
$263$	7.96444	+	13.7948i	0.491108	+	0.850625i	0.999948	−	0.0102370i	$-0.00325858\pi$
$263$	7.96444	+	13.7948i	0.491108	+	0.850625i	−0.508839	+	0.860862i	$0.669925\pi$
$264$	5.80642	−	10.0570i	0.357361	−	0.618967i
$265$		0			0
$266$	9.12245	−	15.8006i	0.559334	−	0.968794i
$267$	8.08419	−	14.0022i	0.494745	−	0.856923i
$268$	10.3225			0.630546
$269$	4.79383	−	8.30316i	0.292285	−	0.506252i	−0.682065	−	0.731292i	$-0.738918\pi$
$269$	4.79383	−	8.30316i	0.292285	−	0.506252i	0.974350	+	0.225039i	$0.0722511\pi$
$270$		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	$0.970194\pi$
$272$	−4.94914			−0.300086
$273$	−2.04617	+	13.6807i	−0.123840	+	0.827991i
$274$	−10.4844			−0.633387
$275$		0			0
$276$	−9.05086	−	15.6765i	−0.544797	−	0.943617i
$277$	5.90321	−	10.2247i	0.354690	−	0.614340i	−0.632375	−	0.774662i	$-0.717920\pi$
$277$	5.90321	−	10.2247i	0.354690	−	0.614340i	0.987065	+	0.160322i	$0.0512532\pi$
$278$	24.4494			1.46638
$279$	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	$0.604307\pi$
$282$	−2.45161	+	4.24631i	−0.145991	+	0.252864i
$283$	−15.5978	−	27.0162i	−0.927192	−	1.60594i	−0.787997	−	0.615680i	$-0.788882\pi$
$283$	−15.5978	−	27.0162i	−0.927192	−	1.60594i	−0.139196	−	0.990265i	$-0.544452\pi$
$284$	−8.33185	−	14.4312i	−0.494404	−	0.856334i
$285$		0			0
$286$	36.2766	+	28.8624i	2.14508	+	1.70667i
$287$	−42.6528			−2.51772
$288$	−3.52543	−	6.10622i	−0.207738	−	0.359812i
$289$	2.04839	+	3.54792i	0.120494	+	0.208701i
$290$		0			0
$291$	−4.25088			−0.249191
$292$	−4.04371	+	7.00391i	−0.236640	+	0.409873i
$293$	2.95952	−	5.12603i	0.172897	−	0.299466i	−0.766535	−	0.642203i	$-0.778021\pi$
$293$	2.95952	−	5.12603i	0.172897	−	0.299466i	0.939431	+	0.342737i	$0.111354\pi$
$294$	−17.0923			−0.996846
$295$		0			0
$296$	4.75557	+	8.23689i	0.276412	+	0.478759i
$297$	−2.90321	−	5.02851i	−0.168461	−	0.291784i
$298$	4.42864			0.256544
$299$	20.9175	−	8.23689i	1.20969	−	0.476351i
$300$		0			0
$301$	−18.2146	−	31.5485i	−1.04987	−	1.81843i
$302$	9.75557	+	16.8971i	0.561370	+	0.972321i
$303$	1.11753	−	1.93562i	0.0642005	−	0.111199i
$304$	−2.95899			−0.169710
$305$		0			0
$306$	3.97703	−	6.88842i	0.227352	−	0.393785i
$307$	−14.5877			−0.832562			−0.416281	−	0.909236i	$-0.636667\pi$
$307$	−14.5877			−0.832562			−0.416281	+	0.909236i	$0.636667\pi$
$308$	−32.3368	+	56.0089i	−1.84256	+	3.19141i
$309$	−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	$0.329783\pi$
$312$	−6.70964	+	2.64212i	−0.379858	+	0.149580i
$313$	5.79060			0.327304			0.163652	−	0.986518i	$-0.447673\pi$
$313$	5.79060			0.327304			0.163652	+	0.986518i	$0.447673\pi$
$314$	3.03334	+	5.25390i	0.171181	+	0.296495i
$315$		0			0
$316$	−17.9010	+	31.0054i	−1.00701	+	1.74419i
$317$	−4.78415			−0.268705			−0.134352	−	0.990934i	$-0.542895\pi$
$317$	−4.78415			−0.268705			−0.134352	+	0.990934i	$0.542895\pi$
$318$	0.903212	−	1.56441i	0.0506496	−	0.0877277i
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$		0			0
$321$	0.826164	−	1.43096i	0.0461120	−	0.0798682i
$322$	26.4844	+	45.8724i	1.47592	+	2.55637i
$323$	−3.85728	−	6.68100i	−0.214625	−	0.371741i
$324$	2.90321			0.161290
$325$		0			0
$326$	−54.6800			−3.02845
$327$	1.30642	+	2.26279i	0.0722454	+	0.125133i
$328$	−11.1175	−	19.2561i	−0.613863	−	1.06324i
$329$	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	$0.190072\pi$
$332$	0.903212	−	1.56441i	0.0495702	−	0.0858581i
$333$	4.75557			0.260604
$334$	−8.75557	+	15.1651i	−0.479083	+	0.829797i
$335$		0			0
$336$	2.64296	+	4.57774i	0.144185	+	0.249736i
$337$	29.0350			1.58164			0.790820	−	0.612049i	$-0.209655\pi$
$337$	29.0350			1.58164			0.790820	+	0.612049i	$0.209655\pi$
$338$	−6.46912	−	28.0498i	−0.351874	−	1.52571i
$339$	−2.42864			−0.131906
$340$		0			0
$341$	15.3319	+	26.5555i	0.830266	+	1.43806i
$342$	2.37778	−	4.11844i	0.128576	−	0.222700i
$343$	2.75848			0.148944
$344$	9.49532	−	16.4464i	0.511953	−	0.886729i
$345$		0			0
$346$	−8.08742			−0.434782
$347$	14.1541	−	24.5156i	0.759832	−	1.31607i	−0.183104	−	0.983093i	$-0.558615\pi$
$347$	14.1541	−	24.5156i	0.759832	−	1.31607i	0.942936	−	0.332974i	$-0.108052\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	16.0232	+	27.7530i	0.857702	+	1.48558i	0.874115	+	0.485719i	$0.161442\pi$
$349$	16.0232	+	27.7530i	0.857702	+	1.48558i	−0.0164125	+	0.999865i	$0.505225\pi$
$350$		0			0
$351$	−0.533338	+	3.56589i	−0.0284675	+	0.190333i
$352$	40.9403			2.18212
$353$	−7.24443	−	12.5477i	−0.385582	−	0.667848i	0.606268	−	0.795261i	$-0.292666\pi$
$353$	−7.24443	−	12.5477i	−0.385582	−	0.667848i	−0.991850	+	0.127413i	$0.959333\pi$
$354$	−11.0437	−	19.1283i	−0.586967	−	1.01666i
$355$		0			0
$356$	−46.9403			−2.48783
$357$	−6.89062	+	11.9349i	−0.364690	+	0.631662i
$358$	−6.46743	+	11.2019i	−0.341814	+	0.592039i
$359$	−24.2701			−1.28093			−0.640463	−	0.767989i	$-0.721258\pi$
$359$	−24.2701			−1.28093			−0.640463	+	0.767989i	$0.721258\pi$
$360$		0			0
$361$	7.19381	+	12.4601i	0.378622	+	0.655792i
$362$	11.1684	+	19.3442i	0.586997	+	1.01671i
$363$	22.7146			1.19221
$364$	37.3669	−	14.7143i	1.95856	−	0.771240i
$365$		0			0
$366$	5.84691	+	10.1271i	0.305623	+	0.529354i
$367$	−1.11899	−	1.93815i	−0.0584107	−	0.101170i	0.835341	−	0.549732i	$-0.185270\pi$
$367$	−1.11899	−	1.93815i	−0.0584107	−	0.101170i	−0.893752	+	0.448561i	$0.851937\pi$
$368$	4.29529	−	7.43965i	0.223907	−	0.387819i
$369$	−11.1175			−0.578756
$370$		0			0
$371$	−1.56491	+	2.71050i	−0.0812459	+	0.140722i
$372$	−15.3319			−0.794919
$373$	14.0565	−	24.3466i	0.727820	−	1.26062i	−0.229982	−	0.973195i	$-0.573867\pi$
$373$	14.0565	−	24.3466i	0.727820	−	1.26062i	0.957803	−	0.287427i	$-0.0927998\pi$
$374$	23.0923	+	39.9971i	1.19408	+	2.06820i
$375$		0			0
$376$	4.42864			0.228390
$377$	6.93332	−	2.73020i	0.357084	−	0.140613i
$378$	−8.49532			−0.436952
$379$	9.80888	+	16.9895i	0.503849	+	0.872691i	0.999990	+	0.00444967i	$0.00141638\pi$
$379$	9.80888	+	16.9895i	0.503849	+	0.872691i	−0.496142	+	0.868242i	$0.665250\pi$
$380$		0			0
$381$	9.62790	−	16.6760i	0.493252	−	0.854338i
$382$	−35.3733			−1.80986
$383$	−9.72001	+	16.8355i	−0.496669	+	0.860256i	−0.999993	−	0.00384183i	$-0.998777\pi$
$383$	−9.72001	+	16.8355i	−0.496669	+	0.860256i	0.503323	+	0.864098i	$0.332110\pi$
$384$	−7.18421	+	12.4434i	−0.366618	+	0.635000i
$385$		0			0
$386$	4.10001	−	7.10143i	0.208685	−	0.361453i
$387$	−4.74766	−	8.22318i	−0.241337	−	0.418008i
$388$	6.17061	+	10.6878i	0.313265	+	0.542591i
$389$	−2.81579			−0.142766			−0.0713832	−	0.997449i	$-0.522741\pi$
$389$	−2.81579			−0.142766			−0.0713832	+	0.997449i	$0.522741\pi$
$390$		0			0
$391$	22.3970			1.13266
$392$	7.71900	+	13.3697i	0.389869	+	0.675272i
$393$	−6.70641	−	11.6158i	−0.338294	−	0.585942i
$394$	−18.1541	+	31.4438i	−0.914590	+	1.58412i
$395$		0			0
$396$	−8.42864	+	14.5988i	−0.423555	+	0.733619i
$397$	−6.33976	+	10.9808i	−0.318184	+	0.551110i	−0.980109	−	0.198460i	$-0.936406\pi$
$397$	−6.33976	+	10.9808i	−0.318184	+	0.551110i	0.661926	+	0.749570i	$0.269739\pi$
$398$	−11.7255			−0.587744
$399$	−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	$0.840548\pi$
$402$	−7.87310			−0.392675
$403$	2.81656	−	18.8314i	0.140303	−	0.938061i
$404$	−6.48886			−0.322833
$405$		0			0
$406$	8.77854	+	15.2049i	0.435671	+	0.754605i
$407$	−13.8064	+	23.9134i	−0.684359	+	1.18534i
$408$	−7.18421			−0.355671
$409$	16.7881	−	29.0779i	0.830120	−	1.43781i	−0.0678223	−	0.997697i	$-0.521605\pi$
$409$	16.7881	−	29.0779i	0.830120	−	1.43781i	0.897942	−	0.440113i	$-0.145062\pi$
$410$		0			0
$411$	4.73483			0.233552
$412$	−3.54839	+	6.14600i	−0.174817	+	0.302792i
$413$	19.1344	+	33.1417i	0.941540	+	1.63080i
$414$	6.90321	+	11.9567i	0.339274	+	0.587640i
$415$		0			0
$416$	−19.8938	−	15.8280i	−0.975376	−	0.776029i
$417$	−11.0415			−0.540704
$418$	13.8064	+	23.9134i	0.675294	+	1.16964i
$419$	−11.4763	−	19.8775i	−0.560652	−	0.971078i	−0.997440	−	0.0715136i	$-0.977217\pi$
$419$	−11.4763	−	19.8775i	−0.560652	−	0.971078i	0.436787	−	0.899565i	$-0.356116\pi$
$420$		0			0
$421$	−31.0874			−1.51511			−0.757554	−	0.652772i	$-0.773606\pi$
$421$	−31.0874			−1.51511			−0.757554	+	0.652772i	$0.773606\pi$
$422$	8.84691	−	15.3233i	0.430661	−	0.745926i
$423$	1.10716	−	1.91766i	0.0538320	−	0.0932397i
$424$	−1.63158			−0.0792367
$425$		0			0
$426$	6.35482	+	11.0069i	0.307892	+	0.533284i
$427$	−10.1304	−	17.5463i	−0.490243	−	0.849125i
$428$	−4.79706			−0.231874
$429$	−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	$0.968033\pi$
$432$	0.688892	+	1.19320i	0.0331443	+	0.0574077i
$433$	−1.29605	+	2.24483i	−0.0622843	+	0.107880i	−0.895486	−	0.445089i	$-0.853172\pi$
$433$	−1.29605	+	2.24483i	−0.0622843	+	0.107880i	0.833202	+	0.552969i	$0.186505\pi$
$434$	44.8637			2.15353
$435$		0			0
$436$	3.79283	−	6.56937i	0.181643	−	0.314616i
$437$	13.3907			0.640564
$438$	3.08419	−	5.34198i	0.147368	−	0.255250i
$439$	6.88493	+	11.9250i	0.328600	+	0.569151i	0.982234	−	0.187659i	$-0.0600900\pi$
$439$	6.88493	+	11.9250i	0.328600	+	0.569151i	−0.653635	+	0.756810i	$0.726757\pi$
$440$		0			0
$441$	7.71900			0.367572
$442$	4.24221	−	28.3633i	0.201781	−	1.34910i
$443$	−4.71609			−0.224068			−0.112034	−	0.993704i	$-0.535737\pi$
$443$	−4.71609			−0.224068			−0.112034	+	0.993704i	$0.535737\pi$
$444$	−6.90321	−	11.9567i	−0.327612	−	0.567441i
$445$		0			0
$446$	10.3827	−	17.9834i	0.491635	−	0.851537i
$447$	−2.00000			−0.0945968
$448$	24.6637	−	42.7188i	1.16525	−	2.01827i
$449$	5.16839	−	8.95191i	0.243911	−	0.422467i	−0.717914	−	0.696132i	$-0.754903\pi$
$449$	5.16839	−	8.95191i	0.243911	−	0.422467i	0.961825	+	0.273665i	$0.0882361\pi$
$450$		0			0
$451$	32.2766	−	55.9046i	1.51984	−	2.63245i
$452$	3.52543	+	6.10622i	0.165822	+	0.287212i
$453$	−4.40567	−	7.63085i	−0.206997	−	0.358529i
$454$	31.9037			1.49731
$455$		0			0
$456$	−4.29529			−0.201145
$457$	−9.81433	−	16.9989i	−0.459095	−	0.795176i	0.539818	−	0.841782i	$-0.318493\pi$
$457$	−9.81433	−	16.9989i	−0.459095	−	0.795176i	−0.998913	+	0.0466054i	$0.985160\pi$
$458$	−19.8780	−	34.4297i	−0.928839	−	1.60880i
$459$	−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	$0.967034\pi$
$462$	24.6637	−	42.7188i	1.14746	−	1.98746i
$463$	−28.8129			−1.33905			−0.669524	−	0.742790i	$-0.733502\pi$
$463$	−28.8129			−1.33905			−0.669524	+	0.742790i	$0.733502\pi$
$464$	1.42372	−	2.46595i	0.0660944	−	0.114479i
$465$		0			0
$466$	−30.4701	−	52.7758i	−1.41150	−	2.44479i
$467$	32.3575			1.49733			0.748664	−	0.662950i	$-0.230696\pi$
$467$	32.3575			1.49733			0.748664	+	0.662950i	$0.230696\pi$
$468$	9.73975	−	3.83531i	0.450220	−	0.177287i
$469$	13.6410			0.629881
$470$		0			0
$471$	−1.36987	−	2.37269i	−0.0631204	−	0.109328i
$472$	−9.97481	+	17.2769i	−0.459128	+	0.795233i
$473$	55.1338			2.53506
$474$	13.6533	−	23.6483i	0.627118	−	1.08620i
$475$		0			0
$476$	40.0098			1.83385
$477$	−0.407896	+	0.706496i	−0.0186763	+	0.0323482i
$478$	−21.0716	−	36.4971i	−0.963792	−	1.66934i
$479$	−2.96666	−	5.13841i	−0.135550	−	0.234780i	0.790257	−	0.612775i	$-0.209947\pi$
$479$	−2.96666	−	5.13841i	−0.135550	−	0.234780i	−0.925808	+	0.377995i	$0.876614\pi$
$480$		0			0
$481$	15.9541	−	6.28239i	0.727443	−	0.286452i
$482$	−51.5526			−2.34816
$483$	−11.9605	−	20.7162i	−0.544223	−	0.942621i
$484$	−32.9726	−	57.1102i	−1.49875	−	2.59592i
$485$		0			0
$486$	−2.21432			−0.100444
$487$	−2.42149	+	4.19415i	−0.109728	+	0.190055i	−0.915660	−	0.401953i	$-0.868331\pi$
$487$	−2.42149	+	4.19415i	−0.109728	+	0.190055i	0.805932	+	0.592008i	$0.201665\pi$
$488$	5.28100	−	9.14695i	0.239059	−	0.414063i
$489$	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	$0.833883\pi$
$492$	16.1383	+	27.9523i	0.727570	+	1.26019i
$493$	7.42372			0.334347
$494$	2.53633	−	16.9578i	0.114115	−	0.762968i
$495$		0			0
$496$	−3.63804	−	6.30127i	−0.163353	−	0.282935i
$497$	−11.0104	−	19.0705i	−0.493883	−	0.855430i
$498$	−0.688892	+	1.19320i	−0.0308700	+	0.0534684i
$499$	38.0687			1.70419			0.852094	−	0.523388i	$-0.175332\pi$
$499$	38.0687			1.70419			0.852094	+	0.523388i	$0.175332\pi$
$500$		0			0
$501$	3.95407	−	6.84865i	0.176655	−	0.305975i
$502$	59.1753			2.64112
$503$	6.62714	−	11.4785i	0.295489	−	0.511803i	−0.679609	−	0.733574i	$-0.737851\pi$
$503$	6.62714	−	11.4785i	0.295489	−	0.511803i	0.975099	+	0.221772i	$0.0711839\pi$
$504$	3.83654	+	6.64507i	0.170893	+	0.295995i
$505$		0			0
$506$	−80.1659			−3.56381
$507$	2.92149	+	12.6675i	0.129748	+	0.562582i
$508$	−55.9037			−2.48033
$509$	14.2351	+	24.6559i	0.630958	+	1.09285i	0.987356	+	0.158517i	$0.0506714\pi$
$509$	14.2351	+	24.6559i	0.630958	+	1.09285i	−0.356398	+	0.934334i	$0.615995\pi$
$510$		0			0
$511$	−5.34368	+	9.25553i	−0.236391	+	0.409440i
$512$	−15.2257			−0.672887
$513$	−1.07382	+	1.85991i	−0.0474104	+	0.0821172i
$514$	13.1963	−	22.8566i	0.582063	−	1.00816i
$515$		0			0
$516$	−13.7835	+	23.8736i	−0.606783	+	1.05098i
$517$	6.42864	+	11.1347i	0.282731	+	0.489705i
$518$	20.2000	+	34.9875i	0.887538	+	1.53726i
$519$	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	$0.377654\pi$
$522$	2.28814	+	3.96318i	0.100149	+	0.173464i
$523$	0.0666765	+	0.115487i	0.00291556	+	0.00504990i	0.867480	−	0.497473i	$-0.165739\pi$
$523$	0.0666765	+	0.115487i	0.00291556	+	0.00504990i	−0.864564	+	0.502523i	$0.832405\pi$
$524$	−19.4701	+	33.7232i	−0.850556	+	1.47321i
$525$		0			0
$526$	−17.6358	+	30.5461i	−0.768958	+	1.33187i
$527$	9.48494	−	16.4284i	0.413171	−	0.715633i
$528$	−8.00000			−0.348155
$529$	−7.93801	+	13.7490i	−0.345131	+	0.597784i
$530$		0			0
$531$	4.98741	+	8.63844i	0.216435	+	0.374876i
$532$	23.9210			1.03711
$533$	−37.2973	+	14.6869i	−1.61553	+	0.636161i
$534$	35.8020			1.54930
$535$		0			0
$536$	3.55554	+	6.15837i	0.153576	+	0.266001i
$537$	2.92073	−	5.05885i	0.126039	−	0.218306i
$538$	21.2301			0.915296
$539$	−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	$0.691991\pi$
$542$	15.1946	−	26.3178i	0.652663	−	1.13045i
$543$	−5.04371	−	8.73596i	−0.216446	−	0.374896i
$544$	−12.6637	−	21.9342i	−0.542952	−	0.940420i
$545$		0			0
$546$	−28.5002	+	11.2228i	−1.21970	+	0.480292i
$547$	0.0573086			0.00245034			0.00122517	−	0.999999i	$-0.499610\pi$
$547$	0.0573086			0.00245034			0.00122517	+	0.999999i	$0.499610\pi$
$548$	−6.87310	−	11.9046i	−0.293604	−	0.508538i
$549$	−2.64050	−	4.57348i	−0.112694	−	0.195191i
$550$		0			0
$551$	4.43848			0.189086
$552$	6.23506	−	10.7994i	0.265382	−	0.459655i
$553$	−23.6558	+	40.9730i	−1.00595	+	1.74235i
$554$	26.1432			1.11072
$555$		0			0
$556$	16.0279	+	27.7611i	0.679734	+	1.17733i
$557$	20.5210	+	35.5434i	0.869502	+	1.50602i	0.862507	+	0.506046i	$0.168893\pi$
$557$	20.5210	+	35.5434i	0.869502	+	1.50602i	0.00699538	+	0.999976i	$0.497773\pi$
$558$	11.6938			0.495039
$559$	−26.7908	−	21.3154i	−1.13313	−	0.901543i
$560$		0			0
$561$	−10.4286	−	18.0629i	−0.440298	−	0.762618i
$562$	−11.9469	−	20.6927i	−0.503950	−	0.872868i
$563$	10.6128	−	18.3820i	0.447278	−	0.774709i	−0.550930	−	0.834552i	$-0.685727\pi$
$563$	10.6128	−	18.3820i	0.447278	−	0.774709i	0.998208	+	0.0598432i	$0.0190601\pi$
$564$	−6.42864			−0.270695
$565$		0			0
$566$	34.5385	−	59.8224i	1.45176	−	2.51452i
$567$	3.83654			0.161119
$568$	5.73975	−	9.94153i	0.240834	−	0.417137i
$569$	−8.18098	−	14.1699i	−0.342965	−	0.594032i	0.642017	−	0.766690i	$-0.278098\pi$
$569$	−8.18098	−	14.1699i	−0.342965	−	0.594032i	−0.984982	+	0.172658i	$0.944764\pi$
$570$		0			0
$571$	−37.7101			−1.57812			−0.789060	−	0.614317i	$-0.789432\pi$
$571$	−37.7101			−1.57812			−0.789060	+	0.614317i	$0.789432\pi$
$572$	−8.99063	+	60.1112i	−0.375917	+	2.51337i
$573$	15.9748			0.667357
$574$	−47.2235	−	81.7935i	−1.97107	−	3.41399i
$575$		0			0
$576$	6.42864	−	11.1347i	0.267860	−	0.463947i
$577$	−42.7150			−1.77825			−0.889125	−	0.457664i	$-0.848686\pi$
$577$	−42.7150			−1.77825			−0.889125	+	0.457664i	$0.848686\pi$
$578$	−4.53580	+	7.85623i	−0.188664	+	0.326776i
$579$	−1.85159	+	3.20705i	−0.0769495	+	0.133280i
$580$		0			0
$581$	1.19358	−	2.06733i	0.0495179	−	0.0857675i
$582$	−4.70641	−	8.15174i	−0.195087	−	0.337900i
$583$	−2.36842	−	4.10222i	−0.0980898	−	0.169896i
$584$	−5.57136			−0.230545
$585$		0			0
$586$	13.1066			0.541430
$587$	4.81187	+	8.33441i	0.198607	+	0.343998i	0.948077	−	0.318041i	$-0.103025\pi$
$587$	4.81187	+	8.33441i	0.198607	+	0.343998i	−0.749470	+	0.662039i	$0.769692\pi$
$588$	−11.2050	−	19.4075i	−0.462084	−	0.800354i
$589$	5.67085	−	9.82220i	0.233663	−	0.404717i
$590$		0			0
$591$	8.19850	−	14.2002i	0.337241	−	0.584119i
$592$	3.27607	−	5.67433i	0.134646	−	0.233213i
$593$	24.5018			1.00617			0.503084	−	0.864238i	$-0.332199\pi$
$593$	24.5018			1.00617			0.503084	+	0.864238i	$0.332199\pi$
$594$	6.42864	−	11.1347i	0.263770	−	0.456864i
$595$		0			0
$596$	2.90321	+	5.02851i	0.118920	+	0.205976i
$597$	5.29529			0.216722
$598$	38.9545	+	30.9930i	1.59297	+	1.26740i
$599$	−16.9654			−0.693189			−0.346595	−	0.938015i	$-0.612662\pi$
$599$	−16.9654			−0.693189			−0.346595	+	0.938015i	$0.612662\pi$
$600$		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	$0.688359\pi$
$602$	40.3329	−	69.8586i	1.64384	−	2.84722i
$603$	3.55554			0.144793
$604$	−12.7906	+	22.1540i	−0.520442	+	0.901432i
$605$		0			0
$606$	4.94914			0.201045
$607$	−9.99285	+	17.3081i	−0.405597	+	0.702515i	−0.994391	−	0.105768i	$-0.966270\pi$
$607$	−9.99285	+	17.3081i	−0.405597	+	0.702515i	0.588793	+	0.808284i	$0.299603\pi$
$608$	−7.57136	−	13.1140i	−0.307059	−	0.531842i
$609$	−3.96444	−	6.86661i	−0.160647	−	0.278249i
$610$		0			0
$611$	1.18098	−	7.89601i	0.0477774	−	0.319439i
$612$	10.4286			0.421553
$613$	5.60001	+	9.69951i	0.226182	+	0.391760i	0.956674	−	0.291163i	$-0.0940421\pi$
$613$	5.60001	+	9.69951i	0.226182	+	0.391760i	−0.730491	+	0.682922i	$0.760709\pi$
$614$	−16.1509	−	27.9741i	−0.651796	−	1.12894i
$615$		0			0
$616$	−44.5531			−1.79510
$617$	0.295286	−	0.511451i	0.0118878	−	0.0205902i	−0.860020	−	0.510260i	$-0.829549\pi$
$617$	0.295286	−	0.511451i	0.0118878	−	0.0205902i	0.871908	+	0.489670i	$0.162883\pi$
$618$	2.70641	−	4.68764i	0.108868	−	0.188564i
$619$	−12.2573			−0.492664			−0.246332	−	0.969186i	$-0.579225\pi$
$619$	−12.2573			−0.492664			−0.246332	+	0.969186i	$0.579225\pi$
$620$		0			0
$621$	−3.11753	−	5.39972i	−0.125102	−	0.216683i
$622$	19.9010	+	34.4695i	0.797957	+	1.38210i
$623$	−62.0306			−2.48520
$624$	3.88739	+	3.09289i	0.155620	+	0.123815i
$625$		0			0
$626$	6.41112	+	11.1044i	0.256240	+	0.443821i
$627$	−6.23506	−	10.7994i	−0.249004	−	0.431288i
$628$	−3.97703	+	6.88842i	−0.158701	+	0.274878i
$629$	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	$0.906509\pi$
$632$	−24.6637			−0.981069
$633$	−3.99532	+	6.92009i	−0.158800	+	0.275049i
$634$	−5.29682	−	9.17436i	−0.210364	−	0.364360i
$635$		0			0
$636$	2.36842			0.0939138
$637$	25.8959	−	10.1973i	1.02603	−	0.404030i
$638$	−26.5718			−1.05199
$639$	−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	$0.0294003\pi$
$642$	3.65878			0.144401
$643$	6.09602	−	10.5586i	0.240404	−	0.416391i	−0.720426	−	0.693532i	$-0.756054\pi$
$643$	6.09602	−	10.5586i	0.240404	−	0.416391i	0.960829	+	0.277141i	$0.0893869\pi$
$644$	−34.7239	+	60.1436i	−1.36831	+	2.36999i
$645$		0			0
$646$	8.54125	−	14.7939i	0.336051	−	0.582057i
$647$	4.73038	+	8.19326i	0.185970	+	0.322110i	0.943903	−	0.330223i	$-0.107124\pi$
$647$	4.73038	+	8.19326i	0.185970	+	0.322110i	−0.757933	+	0.652333i	$0.773790\pi$
$648$	1.00000	+	1.73205i	0.0392837	+	0.0680414i
$649$	−57.9180			−2.27348
$650$		0			0
$651$	−20.2607			−0.794081
$652$	−35.8457	−	62.0866i	−1.40383	−	2.43150i
$653$	10.1995	+	17.6661i	0.399137	+	0.691326i	0.993620	−	0.112782i	$-0.0359763\pi$
$653$	10.1995	+	17.6661i	0.399137	+	0.691326i	−0.594482	+	0.804109i	$0.702643\pi$
$654$	−2.89284	+	5.01055i	−0.113119	+	0.195928i
$655$		0			0
$656$	−7.65878	+	13.2654i	−0.299025	+	0.517927i
$657$	−1.39284	+	2.41247i	−0.0543399	+	0.0941194i
$658$	18.8113			0.733343
$659$	−17.4859	+	30.2866i	−0.681156	+	1.17980i	0.293473	+	0.955967i	$0.405189\pi$
$659$	−17.4859	+	30.2866i	−0.681156	+	1.17980i	−0.974628	+	0.223829i	$0.928144\pi$
$660$		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	$0.709788\pi$
$662$	−5.91903			−0.230050
$663$	−1.91581	+	12.8090i	−0.0744038	+	0.497462i
$664$	1.24443			0.0482933
$665$		0			0
$666$	5.26517	+	9.11955i	0.204021	+	0.353375i
$667$	−6.44293	+	11.1595i	−0.249471	+	0.432097i
$668$	−22.9590			−0.888310
$669$	−4.68889	+	8.12140i	−0.181283	+	0.313991i
$670$		0			0
$671$	30.6637			1.18376
$672$	−13.5254	+	23.4267i	−0.521755	+	0.903706i
$673$	7.13259	+	12.3540i	0.274941	+	0.476212i	0.970120	−	0.242625i	$-0.0780083\pi$
$673$	7.13259	+	12.3540i	0.274941	+	0.476212i	−0.695179	+	0.718836i	$0.744675\pi$
$674$	32.1464	+	55.6792i	1.23823	+	2.14468i
$675$		0			0
$676$	27.6084	−	25.7336i	1.06186	−	0.989752i
$677$	34.0415			1.30832			0.654160	−	0.756356i	$-0.273022\pi$
$677$	34.0415			1.30832			0.654160	+	0.756356i	$0.273022\pi$
$678$	−2.68889	−	4.65730i	−0.103266	−	0.178862i
$679$	8.15433	+	14.1237i	0.312935	+	0.542019i
$680$		0			0
$681$	−14.4079			−0.552112
$682$	−33.9496	+	58.8025i	−1.30000	+	2.25166i
$683$	14.6692	−	25.4077i	0.561300	−	0.972199i	−0.436084	−	0.899906i	$-0.643635\pi$
$683$	14.6692	−	25.4077i	0.561300	−	0.972199i	0.997383	−	0.0722933i	$-0.0230318\pi$
$684$	6.23506			0.238404
$685$		0			0
$686$	3.05408	+	5.28982i	0.116605	+	0.201966i
$687$	8.97703	+	15.5487i	0.342495	+	0.593219i
$688$	−13.0825			−0.498766
$689$	−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	$0.852654\pi$
$692$	−5.30174	−	9.18288i	−0.201542	−	0.349081i
$693$	−11.1383	+	19.2921i	−0.423108	+	0.732845i
$694$	62.6834			2.37943
$695$		0			0
$696$	2.06668	−	3.57959i	0.0783372	−	0.135684i
$697$	−39.9353			−1.51266
$698$	−35.4805	+	61.4540i	−1.34296	+	2.32607i
$699$	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	$0.485283\pi$
$702$	−7.42864	+	2.92525i	−0.280376	+	0.110406i
$703$	10.2133			0.385201
$704$	37.3274	+	64.6530i	1.40683	+	2.43670i
$705$		0			0
$706$	16.0415	−	27.7847i	0.603729	−	1.04569i
$707$	−8.57490			−0.322492
$708$	14.4795	−	25.0792i	0.544173	−	0.942535i
$709$	0.301502	−	0.522216i	0.0113231	−	0.0196122i	−0.860308	−	0.509774i	$-0.829729\pi$
$709$	0.301502	−	0.522216i	0.0113231	−	0.0196122i	0.871631	+	0.490162i	$0.163062\pi$
$710$		0			0
$711$	−6.16593	+	10.6797i	−0.231240	+	0.400520i
$712$	−16.1684	−	28.0045i	−0.605936	−	1.04951i
$713$	16.4637	+	28.5159i	0.616569	+	1.06793i
$714$	−30.5161			−1.14203
$715$		0			0
$716$	−16.9590			−0.633787
$717$	9.51606	+	16.4823i	0.355384	+	0.615543i
$718$	−26.8709	−	46.5417i	−1.00281	−	1.73692i
$719$	−21.7988	+	37.7565i	−0.812956	+	1.40808i	0.0978299	+	0.995203i	$0.468810\pi$
$719$	−21.7988	+	37.7565i	−0.812956	+	1.40808i	−0.910786	+	0.412878i	$0.864523\pi$
$720$		0			0
$721$	−4.68913	+	8.12181i	−0.174632	+	0.302472i
$722$	−15.9294	+	27.5905i	−0.592831	+	1.02681i
$723$	23.2815			0.865847
$724$	−14.6430	+	25.3623i	−0.544201	+	0.942584i
$725$		0			0
$726$	25.1486	+	43.5587i	0.933354	+	1.61662i
$727$	−32.8642			−1.21887			−0.609433	−	0.792838i	$-0.708603\pi$
$727$	−32.8642			−1.21887			−0.609433	+	0.792838i	$0.708603\pi$
$728$	21.6494	+	17.2247i	0.802381	+	0.638391i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−17.0541	−	29.5385i	−0.630768	−	1.09252i
$732$	−7.66593	+	13.2778i	−0.283341	+	0.490761i
$733$	−17.4035			−0.642811			−0.321406	−	0.946942i	$-0.604155\pi$
$733$	−17.4035			−0.642811			−0.321406	+	0.946942i	$0.604155\pi$
$734$	2.47780	−	4.29167i	0.0914572	−	0.158409i
$735$		0			0
$736$	43.9625			1.62048
$737$	−10.3225	+	17.8791i	−0.380234	+	0.658584i
$738$	−12.3089	−	21.3196i	−0.453096	−	0.784786i
$739$	−21.2924	−	36.8795i	−0.783253	−	1.35663i	−0.930037	−	0.367465i	$-0.880226\pi$
$739$	−21.2924	−	36.8795i	−0.783253	−	1.35663i	0.146785	−	0.989168i	$-0.453107\pi$
$740$		0			0
$741$	−1.14542	+	7.65825i	−0.0420781	+	0.281333i
$742$	−6.93041			−0.254423
$743$	−16.4232	−	28.4458i	−0.602508	−	1.04358i	−0.992440	−	0.122731i	$-0.960835\pi$
$743$	−16.4232	−	28.4458i	−0.602508	−	1.04358i	0.389932	−	0.920844i	$-0.372499\pi$
$744$	−5.28100	−	9.14695i	−0.193611	−	0.335344i
$745$		0			0
$746$	62.2514			2.27918
$747$	0.311108	−	0.538855i	0.0113828	−	0.0197157i
$748$	−30.2766	+	52.4405i	−1.10702	+	1.91742i
$749$	−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	$0.906422\pi$
$752$	−1.52543	−	2.64212i	−0.0556266	−	0.0963481i
$753$	−26.7239			−0.973874
$754$	12.9119	+	10.2730i	0.470223	+	0.374119i
$755$		0			0
$756$	−5.56914	−	9.64603i	−0.202548	−	0.350823i
$757$	−2.43732	−	4.22155i	−0.0885858	−	0.153435i	0.818328	−	0.574752i	$-0.194901\pi$
$757$	−2.43732	−	4.22155i	−0.0885858	−	0.153435i	−0.906914	+	0.421317i	$0.861568\pi$
$758$	−21.7200	+	37.6202i	−0.788906	+	1.36643i
$759$	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	$0.142981\pi$
$762$	42.6385			1.54463
$763$	5.01214	−	8.68128i	0.181452	−	0.314284i
$764$	−23.1891	−	40.1648i	−0.838953	−	1.45311i
$765$		0			0
$766$	−43.0464			−1.55533
$767$	28.1437	+	22.3917i	1.01621	+	0.808519i
$768$	−6.10171			−0.220177
$769$	24.0486	+	41.6535i	0.867216	+	1.50206i	0.864830	+	0.502065i	$0.167426\pi$
$769$	24.0486	+	41.6535i	0.867216	+	1.50206i	0.00238584	+	0.999997i	$0.499241\pi$
$770$		0			0
$771$	−5.95952	+	10.3222i	−0.214627	+	0.371744i
$772$	10.7511			0.386941
$773$	9.09679	−	15.7561i	0.327189	−	0.566707i	−0.654764	−	0.755833i	$-0.727232\pi$
$773$	9.09679	−	15.7561i	0.327189	−	0.566707i	0.981953	+	0.189126i	$0.0605654\pi$
$774$	10.5128	−	18.2088i	0.377876	−	0.654500i
$775$		0			0
$776$	−4.25088	+	7.36275i	−0.152598	+	0.264307i
$777$	−9.12245	−	15.8006i	−0.327266	−	0.566842i
$778$	−3.11753	−	5.39972i	−0.111769	−	0.193589i
$779$	−23.8765			−0.855464
$780$		0			0
$781$	33.3274			1.19255
$782$	24.7971	+	42.9498i	0.886741	+	1.53588i
$783$	−1.03334	−	1.78979i	−0.0369285	−	0.0639620i
$784$	5.31756	−	9.21029i	0.189913	−	0.328939i
$785$		0			0
$786$	14.8501	−	25.7212i	0.529687	−	0.917444i
$787$	−14.6486	+	25.3722i	−0.522168	+	0.904421i	0.477500	+	0.878632i	$0.341543\pi$
$787$	−14.6486	+	25.3722i	−0.522168	+	0.904421i	−0.999667	+	0.0257893i	$0.991790\pi$
$788$	−47.6040			−1.69582
$789$	7.96444	−	13.7948i	0.283542	−	0.491108i
$790$		0			0
$791$	4.65878	+	8.06924i	0.165647	+	0.286909i
$792$	−11.6128			−0.412645
$793$	−14.9002	−	11.8549i	−0.529122	−	0.420981i
$794$	−28.0765			−0.996398
$795$		0			0
$796$	−7.68667	−	13.3137i	−0.272447	−	0.471892i
$797$	13.4390	−	23.2771i	0.476034	−	0.824515i	−0.523589	−	0.851971i	$-0.675407\pi$
$797$	13.4390	−	23.2771i	0.476034	−	0.824515i	0.999623	+	0.0274557i	$0.00874051\pi$
$798$	−18.2449			−0.645863
$799$	3.97703	−	6.88842i	0.140697	−	0.243695i
$800$		0			0
$801$	−16.1684			−0.571282
$802$	1.00492	−	1.74058i	0.0354850	−	0.0614619i
$803$	−8.08742	−	14.0078i	−0.285399	−	0.494325i
$804$	−5.16124	−	8.93953i	−0.182023	−	0.315273i
$805$		0			0
$806$	39.2306	−	15.4482i	1.38184	−	0.544140i
$807$	−9.58766			−0.337502
$808$	−2.23506	−	3.87124i	−0.0786293	−	0.136190i
$809$	14.2286	+	24.6447i	0.500251	+	0.866461i	1.00000		0.000290180i	$9.23670e-5\pi$
$809$	14.2286	+	24.6447i	0.500251	+	0.866461i	−0.499749	+	0.866170i	$0.666574\pi$
$810$		0			0
$811$	−16.6316			−0.584014			−0.292007	−	0.956416i	$-0.594323\pi$
$811$	−16.6316			−0.584014			−0.292007	+	0.956416i	$0.594323\pi$
$812$	−11.5096	+	19.9352i	−0.403908	+	0.699589i
$813$	−6.86196	+	11.8853i	−0.240660	+	0.416835i
$814$	−61.1437			−2.14308
$815$		0			0
$816$	2.47457	+	4.28609i	0.0866274	+	0.150043i
$817$	−10.1963	−	17.6605i	−0.356723	−	0.617862i
$818$	74.3486			2.59954
$819$	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	$0.624418\pi$
$822$	5.24221	+	9.07977i	0.182843	+	0.316693i
$823$	9.33185	−	16.1632i	0.325288	−	0.563415i	−0.656283	−	0.754515i	$-0.727872\pi$
$823$	9.33185	−	16.1632i	0.325288	−	0.563415i	0.981571	+	0.191100i	$0.0612055\pi$
$824$	−4.88892			−0.170314
$825$		0			0
$826$	−42.3696	+	73.3863i	−1.47423	+	2.55344i
$827$	−21.2968			−0.740563			−0.370281	−	0.928920i	$-0.620739\pi$
$827$	−21.2968			−0.740563			−0.370281	+	0.928920i	$0.620739\pi$
$828$	−9.05086	+	15.6765i	−0.314539	+	0.544797i
$829$	3.59610	+	6.22862i	0.124898	+	0.216329i	0.921693	−	0.387920i	$-0.126806\pi$
$829$	3.59610	+	6.22862i	0.124898	+	0.216329i	−0.796795	+	0.604249i	$0.793473\pi$
$830$		0			0
$831$	−11.8064			−0.409560
$832$	6.85728	−	45.8476i	0.237733	−	1.58948i
$833$	27.7275			0.960700
$834$	−12.2247	−	21.1738i	−0.423306	−	0.733188i
$835$		0			0
$836$	−18.1017	+	31.3531i	−0.626061	+	1.08437i
$837$	−5.28100			−0.182538
$838$	25.4121	−	44.0151i	0.877847	−	1.52048i
$839$	0.790602	−	1.36936i	0.0272946	−	0.0472757i	−0.852055	−	0.523452i	$-0.824644\pi$
$839$	0.790602	−	1.36936i	0.0272946	−	0.0472757i	0.879350	+	0.476176i	$0.157977\pi$
$840$		0			0
$841$	12.3644	−	21.4158i	0.426359	−	0.738476i
$842$	−34.4187	−	59.6150i	−1.18615	−	2.05447i
$843$	5.39530	+	9.34494i	0.185824	+	0.321857i
$844$	23.1985			0.798525
$845$		0			0
$846$	4.90321			0.168576
$847$	−43.5726	−	75.4700i	−1.49717	−	2.59318i
$848$	0.561993	+	0.973400i	0.0192989	+	0.0334267i
$849$	−15.5978	+	27.0162i	−0.535315	+	0.927192i
$850$		0			0
$851$	−14.8256	+	25.6788i	−0.508216	+	0.880256i
$852$	−8.33185	+	14.4312i	−0.285445	+	0.494404i
$853$	23.0207			0.788215			0.394108	−	0.919064i	$-0.371054\pi$
$853$	23.0207			0.788215			0.394108	+	0.919064i	$0.371054\pi$
$854$	22.4319	−	38.8531i	0.767603	−	1.32953i
$855$		0			0
$856$	−1.65233	−	2.86191i	−0.0564754	−	0.0978182i
$857$	−47.4499			−1.62086			−0.810428	−	0.585838i	$-0.800765\pi$
$857$	−47.4499			−1.62086			−0.810428	+	0.585838i	$0.800765\pi$
$858$	6.85728	−	45.8476i	0.234104	−	1.56521i
$859$	−49.0241			−1.67268			−0.836341	−	0.548210i	$-0.815310\pi$
$859$	−49.0241			−1.67268			−0.836341	+	0.548210i	$0.815310\pi$
$860$		0			0
$861$	21.3264	+	36.9384i	0.726802	+	1.25886i
$862$	18.8780	−	32.6977i	0.642988	−	1.11369i
$863$	37.3590			1.27172			0.635858	−	0.771806i	$-0.280646\pi$
$863$	37.3590			1.27172			0.635858	+	0.771806i	$0.280646\pi$
$864$	−3.52543	+	6.10622i	−0.119937	+	0.207738i
$865$		0			0
$866$	−5.73975			−0.195045
$867$	2.04839	−	3.54792i	0.0695671	−	0.120494i
$868$	29.4106	+	50.9406i	0.998261	+	1.72904i
$869$	−35.8020	−	62.0108i	−1.21450	−	2.10357i
$870$		0			0
$871$	11.9282	−	4.69708i	0.404171	−	0.159154i
$872$	5.22570			0.176964
$873$	2.12544	+	3.68137i	0.0719353	+	0.124596i
$874$	14.8256	+	25.6788i	0.501485	+	0.868597i
$875$		0			0
$876$	8.08742			0.273249
$877$	10.3985	−	18.0108i	0.351133	−	0.608181i	−0.635315	−	0.772253i	$-0.719130\pi$
$877$	10.3985	−	18.0108i	0.351133	−	0.608181i	0.986448	+	0.164072i	$0.0524631\pi$
$878$	−15.2454	+	26.4059i	−0.514509	+	0.891155i
$879$	−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	$-0.333794\pi$
$882$	8.54617	+	14.8024i	0.287765	+	0.498423i
$883$	40.5975			1.36621			0.683107	−	0.730318i	$-0.260628\pi$
$883$	40.5975			1.36621			0.683107	+	0.730318i	$0.260628\pi$
$884$	34.9862	−	13.7768i	1.17671	−	0.463366i
$885$		0			0
$886$	−5.22146	−	9.04384i	−0.175419	−	0.303834i
$887$	24.2153	+	41.9422i	0.813071	+	1.40828i	0.910705	+	0.413058i	$0.135539\pi$
$887$	24.2153	+	41.9422i	0.813071	+	1.40828i	−0.0976338	+	0.995222i	$0.531127\pi$
$888$	4.75557	−	8.23689i	0.159586	−	0.276412i
$889$	−73.8756			−2.47771
$890$		0			0
$891$	−2.90321	+	5.02851i	−0.0972613	+	0.168461i
$892$	27.2257			0.911584
$893$	2.37778	−	4.11844i	0.0795695	−	0.137818i
$894$	−2.21432	−	3.83531i	−0.0740579	−	0.128272i
$895$		0			0
$896$	55.1249			1.84159
$897$	−17.5921	−	13.9966i	−0.587383	−	0.467334i
$898$	22.8889			0.763813
$899$	5.45706	+	9.45190i	0.182003	+	0.315238i
$900$		0			0
$901$	−1.46520	+	2.53781i	−0.0488130	+	0.0845467i
$902$	142.941			4.75942
$903$	−18.2146	+	31.5485i	−0.606143	+	1.04987i
$904$	−2.42864	+	4.20653i	−0.0807753	+	0.139907i
$905$		0			0
$906$	9.75557	−	16.8971i	0.324107	−	0.561370i
$907$	−5.14987	−	8.91983i	−0.170998	−	0.296178i	0.767771	−	0.640725i	$-0.221366\pi$
$907$	−5.14987	−	8.91983i	−0.170998	−	0.296178i	−0.938769	+	0.344547i	$0.888033\pi$
$908$	20.9146	+	36.2251i	0.694075	+	1.20217i
$909$	−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	$0.461099\pi$
$912$	1.47949	+	2.56256i	0.0489910	+	0.0848548i
$913$	1.80642	+	3.12882i	0.0597839	+	0.103549i
$914$	21.7321	−	37.6411i	0.718833	−	1.24506i
$915$		0			0
$916$	26.0622	−	45.1411i	0.861120	−	1.49150i
$917$	−25.7294	+	44.5646i	−0.849659	+	1.47165i
$918$	−7.95407			−0.262523
$919$	−0.391383	+	0.677895i	−0.0129105	+	0.0223617i	−0.872408	−	0.488777i	$-0.837443\pi$
$919$	−0.391383	+	0.677895i	−0.0129105	+	0.0223617i	0.859498	+	0.511139i	$0.170776\pi$
$920$		0			0
$921$	7.29383	+	12.6333i	0.240340	+	0.416281i
$922$	−55.8020			−1.83774
$923$	−16.1946	−	12.8847i	−0.533051	−	0.424107i
$924$	64.6735			2.12760
$925$		0			0
$926$	−31.9005	−	55.2532i	−1.04831	−	1.81573i
$927$	−1.22223	+	2.11697i	−0.0401433	+	0.0695303i
$928$	14.5718			0.478344
$929$	14.2208	−	24.6311i	0.466568	−	0.808120i	−0.532702	−	0.846303i	$-0.678823\pi$
$929$	14.2208	−	24.6311i	0.466568	−	0.808120i	0.999271	+	0.0381824i	$0.0121568\pi$
$930$		0			0
$931$	16.5777			0.543311
$932$	39.9496	−	69.1948i	1.30859	−	2.26655i
$933$	−8.98741	−	15.5666i	−0.294234	−	0.509629i
$934$	35.8249	+	62.0506i	1.17223	+	2.03036i
$935$		0			0
$936$	5.64296	+	4.48966i	0.184446	+	0.146749i
$937$	21.3747			0.698282			0.349141	−	0.937070i	$-0.386473\pi$
$937$	21.3747			0.698282			0.349141	+	0.937070i	$0.386473\pi$
$938$	15.1027	+	26.1587i	0.493121	+	0.854111i
$939$	−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	$0.714492\pi$
$942$	3.03334	−	5.25390i	0.0988315	−	0.171181i
$943$	34.6593	−	60.0316i	1.12866	−	1.95490i
$944$	13.7431			0.447301
$945$		0			0
$946$	61.0420	+	105.728i	1.98465	+	3.43751i
$947$	3.80251	+	6.58613i	0.123565	+	0.214021i	0.921171	−	0.389158i	$-0.127234\pi$
$947$	3.80251	+	6.58613i	0.123565	+	0.214021i	−0.797606	+	0.603179i	$0.793901\pi$
$948$	35.8020			1.16279
$949$	−1.48571	+	9.93342i	−0.0482282	+	0.322452i
$950$		0			0
$951$	2.39207	+	4.14319i	0.0775683	+	0.134352i
$952$	13.7812	+	23.8698i	0.446652	+	0.773625i
$953$	−16.6780	+	28.8871i	−0.540253	+	0.935746i	0.458636	+	0.888624i	$0.348338\pi$
$953$	−16.6780	+	28.8871i	−0.540253	+	0.935746i	−0.998889	+	0.0471217i	$0.984995\pi$
$954$	−1.80642			−0.0584851
$955$		0			0
$956$	27.6271	−	47.8516i	0.893525	−	1.54763i
$957$	12.0000			0.387905
$958$	6.56914	−	11.3781i	0.212239	−	0.367609i
$959$	−9.08266	−	15.7316i	−0.293294	−	0.508001i
$960$		0			0
$961$	−3.11108			−0.100357
$962$	29.7112	+	23.6388i	0.957926	+	0.762146i
$963$	−1.65233			−0.0532455
$964$	−33.7955	−	58.5356i	−1.08848	−	1.88530i
$965$		0			0
$966$	26.4844	−	45.8724i	0.852122	−	1.47592i
$967$	40.8988			1.31522			0.657608	−	0.753360i	$-0.271568\pi$
$967$	40.8988			1.31522			0.657608	+	0.753360i	$0.271568\pi$
$968$	22.7146	−	39.3428i	0.730074	−	1.26452i
$969$	−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	$0.145019\pi$
$972$	−1.45161	−	2.51426i	−0.0465603	−	0.0806448i
$973$	21.1805	+	36.6858i	0.679017	+	1.17609i
$974$	−10.7239			−0.343617
$975$		0			0
$976$	−7.27607			−0.232901
$977$	−19.3941	−	33.5915i	−0.620472	−	1.07469i	−0.989398	−	0.145230i	$-0.953608\pi$
$977$	−19.3941	−	33.5915i	−0.620472	−	1.07469i	0.368926	−	0.929459i	$-0.379725\pi$
$978$	27.3400	+	47.3543i	0.874237	+	1.51422i
$979$	46.9403	−	81.3029i	1.50022	−	2.59845i
$980$		0			0
$981$	1.30642	−	2.26279i	0.0417109	−	0.0722454i
$982$	0.0847209	−	0.146741i	0.00270355	−	0.00468269i
$983$	−21.4479			−0.684080			−0.342040	−	0.939685i	$-0.611118\pi$
$983$	−21.4479			−0.684080			−0.342040	+	0.939685i	$0.611118\pi$
$984$	−11.1175	+	19.2561i	−0.354414	+	0.613863i
$985$		0			0
$986$	8.21924	+	14.2361i	0.261754	+	0.453371i
$987$	−8.49532			−0.270409
$988$	20.9175	−	8.23689i	0.665474	−	0.262050i
$989$	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	$0.775891\pi$
$992$	18.6178	−	32.2469i	0.591115	−	1.02384i
$993$	2.67307			0.0848273
$994$	24.3805	−	42.2282i	0.773302	−	1.33940i
$995$		0			0
$996$	−1.80642			−0.0572387
$997$	−27.1123	+	46.9599i	−0.858656	+	1.48724i	0.0145557	+	0.999894i	$0.495367\pi$
$997$	−27.1123	+	46.9599i	−0.858656	+	1.48724i	−0.873212	+	0.487341i	$0.837967\pi$
$998$	42.1481	+	73.0027i	1.33418	+	2.31086i
$999$	−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.i.m.601.3		6
5.2	odd	4		975.2.bb.j.874.1		12
5.3	odd	4		975.2.bb.j.874.6		12
5.4	even	2		195.2.i.e.16.1	✓	6
13.9	even	3	inner	975.2.i.m.451.3		6
15.14	odd	2		585.2.j.g.406.3		6
65.9	even	6		195.2.i.e.61.1	yes	6
65.22	odd	12		975.2.bb.j.724.6		12
65.29	even	6		2535.2.a.y.1.3		3
65.48	odd	12		975.2.bb.j.724.1		12
65.49	even	6		2535.2.a.z.1.1		3
195.29	odd	6		7605.2.a.bu.1.1		3
195.74	odd	6		585.2.j.g.451.3		6
195.179	odd	6		7605.2.a.bt.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.e.16.1	✓	6	5.4	even	2
195.2.i.e.61.1	yes	6	65.9	even	6
585.2.j.g.406.3		6	15.14	odd	2
585.2.j.g.451.3		6	195.74	odd	6
975.2.i.m.451.3		6	13.9	even	3	inner
975.2.i.m.601.3		6	1.1	even	1	trivial
975.2.bb.j.724.1		12	65.48	odd	12
975.2.bb.j.724.6		12	65.22	odd	12
975.2.bb.j.874.1		12	5.2	odd	4
975.2.bb.j.874.6		12	5.3	odd	4
2535.2.a.y.1.3		3	65.29	even	6
2535.2.a.z.1.1		3	65.49	even	6
7605.2.a.bt.1.3		3	195.179	odd	6
7605.2.a.bu.1.1		3	195.29	odd	6

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10716 + 1.91766i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.45161 + 2.51426i) q^{4} +(1.10716 - 1.91766i) q^{6} +(-1.91827 + 3.32254i) q^{7} -2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.10716 + 1.91766i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.45161 + 2.51426i) q^{4} +(1.10716 - 1.91766i) q^{6} +(-1.91827 + 3.32254i) q^{7} -2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.90321 - 5.02851i) q^{11} +2.90321 q^{12} +(-0.533338 + 3.56589i) q^{13} -8.49532 q^{14} +(0.688892 + 1.19320i) q^{16} +(-1.79605 + 3.11085i) q^{17} -2.21432 q^{18} +(-1.07382 + 1.85991i) q^{19} +3.83654 q^{21} +(6.42864 - 11.1347i) q^{22} +(-3.11753 - 5.39972i) q^{23} +(1.00000 + 1.73205i) q^{24} +(-7.42864 + 2.92525i) q^{26} +1.00000 q^{27} +(-5.56914 - 9.64603i) q^{28} +(-1.03334 - 1.78979i) q^{29} -5.28100 q^{31} +(-3.52543 + 6.10622i) q^{32} +(-2.90321 + 5.02851i) q^{33} -7.95407 q^{34} +(-1.45161 - 2.51426i) q^{36} +(-2.37778 - 4.11844i) q^{37} -4.75557 q^{38} +(3.35482 - 1.32106i) q^{39} +(5.55877 + 9.62806i) q^{41} +(4.24766 + 7.35716i) q^{42} +(-4.74766 + 8.22318i) q^{43} +16.8573 q^{44} +(6.90321 - 11.9567i) q^{46} -2.21432 q^{47} +(0.688892 - 1.19320i) q^{48} +(-3.85950 - 6.68485i) q^{49} +3.59210 q^{51} +(-8.19135 - 6.51721i) q^{52} +0.815792 q^{53} +(1.10716 + 1.91766i) q^{54} +(3.83654 - 6.64507i) q^{56} +2.14764 q^{57} +(2.28814 - 3.96318i) q^{58} +(4.98741 - 8.63844i) q^{59} +(-2.64050 + 4.57348i) q^{61} +(-5.84691 - 10.1271i) q^{62} +(-1.91827 - 3.32254i) q^{63} -12.8573 q^{64} -12.8573 q^{66} +(-1.77777 - 3.07919i) q^{67} +(-5.21432 - 9.03147i) q^{68} +(-3.11753 + 5.39972i) q^{69} +(-2.86987 + 4.97077i) q^{71} +(1.00000 - 1.73205i) q^{72} +2.78568 q^{73} +(5.26517 - 9.11955i) q^{74} +(-3.11753 - 5.39972i) q^{76} +22.2766 q^{77} +(6.24766 + 4.97077i) q^{78} +12.3319 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-12.3089 + 21.3196i) q^{82} -0.622216 q^{83} +(-5.56914 + 9.64603i) q^{84} -21.0257 q^{86} +(-1.03334 + 1.78979i) q^{87} +(5.80642 + 10.0570i) q^{88} +(8.08419 + 14.0022i) q^{89} +(-10.8247 - 8.61236i) q^{91} +18.1017 q^{92} +(2.64050 + 4.57348i) q^{93} +(-2.45161 - 4.24631i) q^{94} +7.05086 q^{96} +(2.12544 - 3.68137i) q^{97} +(8.54617 - 14.8024i) q^{98} +5.80642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 2 q^{4} - 5 q^{7} - 12 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 2 * q^4 - 5 * q^7 - 12 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} - 2 q^{4} - 5 q^{7} - 12 q^{8} - 3 q^{9} - 4 q^{11} + 4 q^{12} - 3 q^{13} - 24 q^{14} + 4 q^{16} - 4 q^{17} + 10 q^{21} + 12 q^{22} + 8 q^{23} + 6 q^{24} - 18 q^{26} + 6 q^{27} - 6 q^{29} - 18 q^{31} - 8 q^{32} - 4 q^{33} - 8 q^{34} - 2 q^{36} - 14 q^{37} - 28 q^{38} + 20 q^{41} + 12 q^{42} - 15 q^{43} + 48 q^{44} + 28 q^{46} + 4 q^{48} - 30 q^{49} + 8 q^{51} - 16 q^{52} + 32 q^{53} + 10 q^{56} - 6 q^{58} - 10 q^{59} - 9 q^{61} - 2 q^{62} - 5 q^{63} - 24 q^{64} - 24 q^{66} - 11 q^{67} - 18 q^{68} + 8 q^{69} - 4 q^{71} + 6 q^{72} + 30 q^{73} - 8 q^{74} + 8 q^{76} + 24 q^{78} + 34 q^{79} - 3 q^{81} - 14 q^{82} - 4 q^{83} - 20 q^{86} - 6 q^{87} + 8 q^{88} + 22 q^{89} - 31 q^{91} + 56 q^{92} + 9 q^{93} - 8 q^{94} + 16 q^{96} - q^{97} - 2 q^{98} + 8 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 - 2 * q^4 - 5 * q^7 - 12 * q^8 - 3 * q^9 - 4 * q^11 + 4 * q^12 - 3 * q^13 - 24 * q^14 + 4 * q^16 - 4 * q^17 + 10 * q^21 + 12 * q^22 + 8 * q^23 + 6 * q^24 - 18 * q^26 + 6 * q^27 - 6 * q^29 - 18 * q^31 - 8 * q^32 - 4 * q^33 - 8 * q^34 - 2 * q^36 - 14 * q^37 - 28 * q^38 + 20 * q^41 + 12 * q^42 - 15 * q^43 + 48 * q^44 + 28 * q^46 + 4 * q^48 - 30 * q^49 + 8 * q^51 - 16 * q^52 + 32 * q^53 + 10 * q^56 - 6 * q^58 - 10 * q^59 - 9 * q^61 - 2 * q^62 - 5 * q^63 - 24 * q^64 - 24 * q^66 - 11 * q^67 - 18 * q^68 + 8 * q^69 - 4 * q^71 + 6 * q^72 + 30 * q^73 - 8 * q^74 + 8 * q^76 + 24 * q^78 + 34 * q^79 - 3 * q^81 - 14 * q^82 - 4 * q^83 - 20 * q^86 - 6 * q^87 + 8 * q^88 + 22 * q^89 - 31 * q^91 + 56 * q^92 + 9 * q^93 - 8 * q^94 + 16 * q^96 - q^97 - 2 * q^98 + 8 * q^99

Introduction

L-functions

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Database

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