LMFDB - Embedded newform 975.2.i.m.601.2

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			601.2
Root			$1.08504 - 1.87935i$ of defining polynomial
Character	$\chi$	$=$	975.601
Dual form			975.2.i.m.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.269594 - 0.466951i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.854638 - 1.48028i) q^{4} +(-0.269594 + 0.466951i) q^{6} +(-2.40049 + 4.15777i) q^{7} -2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.269594 - 0.466951i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.854638 - 1.48028i) q^{4} +(-0.269594 + 0.466951i) q^{6} +(-2.40049 + 4.15777i) q^{7} -2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.70928 + 2.96055i) q^{11} -1.70928 q^{12} +(2.25513 - 2.81325i) q^{13} +2.58864 q^{14} +(-1.17009 - 2.02665i) q^{16} +(1.43968 - 2.49360i) q^{17} +0.539189 q^{18} +(-2.48554 + 4.30507i) q^{19} +4.80098 q^{21} +(0.921622 - 1.59630i) q^{22} +(4.24846 + 7.35856i) q^{23} +(1.00000 + 1.73205i) q^{24} +(-1.92162 - 0.294598i) q^{26} +1.00000 q^{27} +(4.10310 + 7.10678i) q^{28} +(1.75513 + 3.03997i) q^{29} +3.04945 q^{31} +(-2.63090 + 4.55685i) q^{32} +(1.70928 - 2.96055i) q^{33} -1.55252 q^{34} +(0.854638 + 1.48028i) q^{36} +(1.34017 + 2.32125i) q^{37} +2.68035 q^{38} +(-3.56391 - 0.546373i) q^{39} +(1.87577 + 3.24893i) q^{41} +(-1.29432 - 2.24183i) q^{42} +(0.794319 - 1.37580i) q^{43} +5.84324 q^{44} +(2.29072 - 3.96765i) q^{46} +0.539189 q^{47} +(-1.17009 + 2.02665i) q^{48} +(-8.02472 - 13.8992i) q^{49} -2.87936 q^{51} +(-2.23707 - 5.74253i) q^{52} +13.7587 q^{53} +(-0.269594 - 0.466951i) q^{54} +(4.80098 - 8.31555i) q^{56} +4.97107 q^{57} +(0.946346 - 1.63912i) q^{58} +(-4.20261 + 7.27913i) q^{59} +(1.52472 - 2.64090i) q^{61} +(-0.822114 - 1.42394i) q^{62} +(-2.40049 - 4.15777i) q^{63} -1.84324 q^{64} -1.84324 q^{66} +(-6.42522 - 11.1288i) q^{67} +(-2.46081 - 4.26225i) q^{68} +(4.24846 - 7.35856i) q^{69} +(-1.04585 + 1.81147i) q^{71} +(1.00000 - 1.73205i) q^{72} +5.53919 q^{73} +(0.722606 - 1.25159i) q^{74} +(4.24846 + 7.35856i) q^{76} -16.4124 q^{77} +(0.705681 + 1.81147i) q^{78} +2.21235 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.01139 - 1.75178i) q^{82} -4.34017 q^{83} +(4.10310 - 7.10678i) q^{84} -0.856576 q^{86} +(1.75513 - 3.03997i) q^{87} +(-3.41855 - 5.92110i) q^{88} +(3.50667 + 6.07372i) q^{89} +(6.28345 + 16.1295i) q^{91} +14.5236 q^{92} +(-1.52472 - 2.64090i) q^{93} +(-0.145362 - 0.251775i) q^{94} +5.26180 q^{96} +(-7.13449 + 12.3573i) q^{97} +(-4.32684 + 7.49431i) q^{98} -3.41855 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 $

$2$	−0.269594	−	0.466951i	−0.190632	−	0.330184i	0.754828	−	0.655923i	$-0.227720\pi$
$2$	−0.269594	−	0.466951i	−0.190632	−	0.330184i	−0.945460	+	0.325739i	$0.894387\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.854638	−	1.48028i	0.427319	−	0.740138i
$5$		0			0
$5$		0			0
$6$	−0.269594	+	0.466951i	−0.110061	+	0.190632i
$7$	−2.40049	+	4.15777i	−0.907301	+	1.57149i	−0.0895019	+	0.995987i	$0.528528\pi$
$7$	−2.40049	+	4.15777i	−0.907301	+	1.57149i	−0.817799	+	0.575504i	$0.804806\pi$
$8$	−2.00000			−0.707107
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.70928	+	2.96055i	0.515366	+	0.892640i	0.999841	+	0.0178349i	$0.00567731\pi$
$11$	1.70928	+	2.96055i	0.515366	+	0.892640i	−0.484475	+	0.874805i	$0.660989\pi$
$12$	−1.70928			−0.493425
$13$	2.25513	−	2.81325i	0.625460	−	0.780256i
$13$	2.25513	−	2.81325i	0.625460	−	0.780256i
$14$	2.58864			0.691842
$15$		0			0
$16$	−1.17009	−	2.02665i	−0.292522	−	0.506662i
$17$	1.43968	−	2.49360i	0.349174	−	0.604787i	−0.636929	−	0.770922i	$-0.719796\pi$
$17$	1.43968	−	2.49360i	0.349174	−	0.604787i	0.986103	+	0.166135i	$0.0531289\pi$
$18$	0.539189			0.127088
$19$	−2.48554	+	4.30507i	−0.570221	+	0.987652i	0.426322	+	0.904571i	$0.359809\pi$
$19$	−2.48554	+	4.30507i	−0.570221	+	0.987652i	−0.996543	+	0.0830801i	$0.973524\pi$
$20$		0			0
$21$	4.80098			1.04766
$22$	0.921622	−	1.59630i	0.196491	−	0.340332i
$23$	4.24846	+	7.35856i	0.885866	+	1.53436i	0.844718	+	0.535212i	$0.179768\pi$
$23$	4.24846	+	7.35856i	0.885866	+	1.53436i	0.0411482	+	0.999153i	$0.486898\pi$
$24$	1.00000	+	1.73205i	0.204124	+	0.353553i
$25$		0			0
$26$	−1.92162	−	0.294598i	−0.376861	−	0.0577755i
$27$	1.00000			0.192450
$28$	4.10310	+	7.10678i	0.775413	+	1.34306i
$29$	1.75513	+	3.03997i	0.325919	+	0.564509i	0.981698	−	0.190444i	$-0.0609929\pi$
$29$	1.75513	+	3.03997i	0.325919	+	0.564509i	−0.655779	+	0.754953i	$0.727660\pi$
$30$		0			0
$31$	3.04945			0.547697			0.273849	−	0.961773i	$-0.411703\pi$
$31$	3.04945			0.547697			0.273849	+	0.961773i	$0.411703\pi$
$32$	−2.63090	+	4.55685i	−0.465081	+	0.805545i
$33$	1.70928	−	2.96055i	0.297547	−	0.515366i
$34$	−1.55252			−0.266255
$35$		0			0
$36$	0.854638	+	1.48028i	0.142440	+	0.246713i
$37$	1.34017	+	2.32125i	0.220323	+	0.381611i	0.954906	−	0.296908i	$-0.0959555\pi$
$37$	1.34017	+	2.32125i	0.220323	+	0.381611i	−0.734583	+	0.678519i	$0.762622\pi$
$38$	2.68035			0.434810
$39$	−3.56391	−	0.546373i	−0.570683	−	0.0874898i
$40$		0			0
$41$	1.87577	+	3.24893i	0.292946	+	0.507397i	0.974505	−	0.224366i	$-0.0720311\pi$
$41$	1.87577	+	3.24893i	0.292946	+	0.507397i	−0.681559	+	0.731763i	$0.738698\pi$
$42$	−1.29432	−	2.24183i	−0.199718	−	0.345921i
$43$	0.794319	−	1.37580i	0.121132	−	0.209808i	−0.799082	−	0.601222i	$-0.794681\pi$
$43$	0.794319	−	1.37580i	0.121132	−	0.209808i	0.920215	+	0.391414i	$0.128014\pi$
$44$	5.84324			0.880902
$45$		0			0
$46$	2.29072	−	3.96765i	0.337749	−	0.584998i
$47$	0.539189			0.0786488			0.0393244	−	0.999226i	$-0.487479\pi$
$47$	0.539189			0.0786488			0.0393244	+	0.999226i	$0.487479\pi$
$48$	−1.17009	+	2.02665i	−0.168887	+	0.292522i
$49$	−8.02472	−	13.8992i	−1.14639	−	1.98560i
$50$		0			0
$51$	−2.87936			−0.403191
$52$	−2.23707	−	5.74253i	−0.310226	−	0.796345i
$53$	13.7587			1.88991			0.944953	−	0.327206i	$-0.106107\pi$
$53$	13.7587			1.88991			0.944953	+	0.327206i	$0.106107\pi$
$54$	−0.269594	−	0.466951i	−0.0366872	−	0.0635440i
$55$		0			0
$56$	4.80098	−	8.31555i	0.641558	−	1.11121i
$57$	4.97107			0.658434
$58$	0.946346	−	1.63912i	0.124261	−	0.215227i
$59$	−4.20261	+	7.27913i	−0.547133	+	0.947663i	0.451336	+	0.892354i	$0.350948\pi$
$59$	−4.20261	+	7.27913i	−0.547133	+	0.947663i	−0.998469	+	0.0553085i	$0.982386\pi$
$60$		0			0
$61$	1.52472	−	2.64090i	0.195221	−	0.338133i	−0.751752	−	0.659446i	$-0.770791\pi$
$61$	1.52472	−	2.64090i	0.195221	−	0.338133i	0.946973	+	0.321313i	$0.104124\pi$
$62$	−0.822114	−	1.42394i	−0.104409	−	0.180841i
$63$	−2.40049	−	4.15777i	−0.302434	−	0.523830i
$64$	−1.84324			−0.230406
$65$		0			0
$66$	−1.84324			−0.226888
$67$	−6.42522	−	11.1288i	−0.784965	−	1.35960i	−0.929020	−	0.370030i	$-0.879347\pi$
$67$	−6.42522	−	11.1288i	−0.784965	−	1.35960i	0.144055	−	0.989570i	$-0.453986\pi$
$68$	−2.46081	−	4.26225i	−0.298417	−	0.516874i
$69$	4.24846	−	7.35856i	0.511455	−	0.885866i
$70$		0			0
$71$	−1.04585	+	1.81147i	−0.124120	+	0.214982i	−0.921389	−	0.388642i	$-0.872944\pi$
$71$	−1.04585	+	1.81147i	−0.124120	+	0.214982i	0.797269	+	0.603625i	$0.206277\pi$
$72$	1.00000	−	1.73205i	0.117851	−	0.204124i
$73$	5.53919			0.648313			0.324157	−	0.946003i	$-0.394920\pi$
$73$	5.53919			0.648313			0.324157	+	0.946003i	$0.394920\pi$
$74$	0.722606	−	1.25159i	0.0840013	−	0.145494i
$75$		0			0
$76$	4.24846	+	7.35856i	0.487332	+	0.844084i
$77$	−16.4124			−1.87037
$78$	0.705681	+	1.81147i	0.0799027	+	0.205109i
$79$	2.21235			0.248908			0.124454	−	0.992225i	$-0.460282\pi$
$79$	2.21235			0.248908			0.124454	+	0.992225i	$0.460282\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.01139	−	1.75178i	0.111690	−	0.193452i
$83$	−4.34017			−0.476396			−0.238198	−	0.971217i	$-0.576557\pi$
$83$	−4.34017			−0.476396			−0.238198	+	0.971217i	$0.576557\pi$
$84$	4.10310	−	7.10678i	0.447685	−	0.775413i
$85$		0			0
$86$	−0.856576			−0.0923669
$87$	1.75513	−	3.03997i	0.188170	−	0.325919i
$88$	−3.41855	−	5.92110i	−0.364419	−	0.631192i
$89$	3.50667	+	6.07372i	0.371706	+	0.643813i	0.989828	−	0.142269i	$-0.0454397\pi$
$89$	3.50667	+	6.07372i	0.371706	+	0.643813i	−0.618122	+	0.786082i	$0.712106\pi$
$90$		0			0
$91$	6.28345	+	16.1295i	0.658684	+	1.69083i
$92$	14.5236			1.51419
$93$	−1.52472	−	2.64090i	−0.158107	−	0.273849i
$94$	−0.145362	−	0.251775i	−0.0149930	−	0.0259686i
$95$		0			0
$96$	5.26180			0.537030
$97$	−7.13449	+	12.3573i	−0.724398	+	1.25469i	0.234824	+	0.972038i	$0.424549\pi$
$97$	−7.13449	+	12.3573i	−0.724398	+	1.25469i	−0.959221	+	0.282656i	$0.908785\pi$
$98$	−4.32684	+	7.49431i	−0.437077	+	0.757040i
$99$	−3.41855			−0.343577
$100$		0			0
$101$	−6.24846	−	10.8227i	−0.621745	−	1.07689i	−0.989161	−	0.146838i	$-0.953091\pi$
$101$	−6.24846	−	10.8227i	−0.621745	−	1.07689i	0.367415	−	0.930057i	$-0.380243\pi$
$102$	0.776260	+	1.34452i	0.0768612	+	0.133127i
$103$	−6.85043			−0.674993			−0.337497	−	0.941327i	$-0.609580\pi$
$103$	−6.85043			−0.674993			−0.337497	+	0.941327i	$0.609580\pi$
$104$	−4.51026	+	5.62651i	−0.442267	+	0.551724i
$105$		0			0
$106$	−3.70928	−	6.42465i	−0.360277	−	0.624018i
$107$	7.77985	+	13.4751i	0.752107	+	1.30269i	0.946800	+	0.321823i	$0.104296\pi$
$107$	7.77985	+	13.4751i	0.752107	+	1.30269i	−0.194693	+	0.980864i	$0.562371\pi$
$108$	0.854638	−	1.48028i	0.0822375	−	0.142440i
$109$	15.8371			1.51692			0.758460	−	0.651720i	$-0.225952\pi$
$109$	15.8371			1.51692			0.758460	+	0.651720i	$0.225952\pi$
$110$		0			0
$111$	1.34017	−	2.32125i	0.127204	−	0.220323i
$112$	11.2351			1.06162
$113$	−1.53919	+	2.66595i	−0.144795	+	0.250792i	−0.929296	−	0.369335i	$-0.879586\pi$
$113$	−1.53919	+	2.66595i	−0.144795	+	0.250792i	0.784502	+	0.620127i	$0.212919\pi$
$114$	−1.34017	−	2.32125i	−0.125519	−	0.217405i
$115$		0			0
$116$	6.00000			0.557086
$117$	1.30878	+	3.35963i	0.120997	+	0.310598i
$118$	4.53200			0.417205
$119$	6.91189	+	11.9717i	0.633611	+	1.09745i
$120$		0			0
$121$	−0.343245	+	0.594517i	−0.0312040	+	0.0540470i
$122$	−1.64423			−0.148861
$123$	1.87577	−	3.24893i	0.169132	−	0.292946i
$124$	2.60617	−	4.51402i	0.234041	−	0.405371i
$125$		0			0
$126$	−1.29432	+	2.24183i	−0.115307	+	0.199718i
$127$	−3.72733	−	6.45593i	−0.330747	−	0.572871i	0.651911	−	0.758295i	$-0.273967\pi$
$127$	−3.72733	−	6.45593i	−0.330747	−	0.572871i	−0.982659	+	0.185424i	$0.940634\pi$
$128$	5.75872	+	9.97440i	0.509004	+	0.881621i
$129$	−1.58864			−0.139872
$130$		0			0
$131$	11.6937			1.02168			0.510841	−	0.859675i	$-0.329334\pi$
$131$	11.6937			1.02168			0.510841	+	0.859675i	$0.329334\pi$
$132$	−2.92162	−	5.06040i	−0.254295	−	0.440451i
$133$	−11.9330	−	20.6686i	−1.03472	−	1.79219i
$134$	−3.46441	+	6.00053i	−0.299279	+	0.518366i
$135$		0			0
$136$	−2.87936	+	4.98720i	−0.246903	+	0.427649i
$137$	−4.63870	+	8.03446i	−0.396311	+	0.686430i	−0.993268	−	0.115843i	$-0.963043\pi$
$137$	−4.63870	+	8.03446i	−0.396311	+	0.686430i	0.596957	+	0.802273i	$0.296376\pi$
$138$	−4.58145			−0.389999
$139$	−6.45774	+	11.1851i	−0.547738	+	0.948711i	0.450691	+	0.892680i	$0.351178\pi$
$139$	−6.45774	+	11.1851i	−0.547738	+	0.948711i	−0.998429	+	0.0560304i	$0.982156\pi$
$140$		0			0
$141$	−0.269594	−	0.466951i	−0.0227039	−	0.0393244i
$142$	1.12783			0.0946451
$143$	12.1834	+	1.86781i	1.01883	+	0.156194i
$144$	2.34017			0.195014
$145$		0			0
$146$	−1.49333	−	2.58653i	−0.123589	−	0.214063i
$147$	−8.02472	+	13.8992i	−0.661868	+	1.14639i
$148$	4.58145			0.376593
$149$	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
$151$	−8.60424			−0.700203			−0.350101	−	0.936712i	$-0.613853\pi$
$151$	−8.60424			−0.700203			−0.350101	+	0.936712i	$0.613853\pi$
$152$	4.97107	−	8.61015i	0.403207	−	0.698375i
$153$	1.43968	+	2.49360i	0.116391	+	0.201596i
$154$	4.42469	+	7.66379i	0.356552	+	0.617566i
$155$		0			0
$156$	−3.85464	+	4.80862i	−0.308618	+	0.384998i
$157$	−0.908291			−0.0724895			−0.0362448	−	0.999343i	$-0.511540\pi$
$157$	−0.908291			−0.0724895			−0.0362448	+	0.999343i	$0.511540\pi$
$158$	−0.596436	−	1.03306i	−0.0474499	−	0.0821857i
$159$	−6.87936	−	11.9154i	−0.545569	−	0.944953i
$160$		0			0
$161$	−40.7936			−3.21499
$162$	−0.269594	+	0.466951i	−0.0211813	+	0.0366872i
$163$	−7.32211	+	12.6823i	−0.573512	+	0.993352i	0.422689	+	0.906275i	$0.361086\pi$
$163$	−7.32211	+	12.6823i	−0.573512	+	0.993352i	−0.996202	+	0.0870777i	$0.972247\pi$
$164$	6.41241			0.500725
$165$		0			0
$166$	1.17009	+	2.02665i	0.0908163	+	0.157298i
$167$	−2.44748	−	4.23916i	−0.189392	−	0.328036i	0.755656	−	0.654969i	$-0.227318\pi$
$167$	−2.44748	−	4.23916i	−0.189392	−	0.328036i	−0.945048	+	0.326933i	$0.893985\pi$
$168$	−9.60197			−0.740808
$169$	−2.82878	−	12.6885i	−0.217598	−	0.976038i
$170$		0			0
$171$	−2.48554	−	4.30507i	−0.190074	−	0.329217i
$172$	−1.35771	−	2.35162i	−0.103524	−	0.179309i
$173$	−8.77985	+	15.2072i	−0.667520	+	1.15618i	0.311076	+	0.950385i	$0.399311\pi$
$173$	−8.77985	+	15.2072i	−0.667520	+	1.15618i	−0.978595	+	0.205793i	$0.934023\pi$
$174$	−1.89269			−0.143485
$175$		0			0
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$	8.40522			0.631775
$178$	1.89076	−	3.27488i	0.141718	−	0.245463i
$179$	−0.692350	−	1.19919i	−0.0517487	−	0.0896314i	0.838991	−	0.544146i	$-0.183146\pi$
$179$	−0.692350	−	1.19919i	−0.0517487	−	0.0896314i	−0.890739	+	0.454514i	$0.849813\pi$
$180$		0			0
$181$	−7.46800			−0.555092			−0.277546	−	0.960712i	$-0.589521\pi$
$181$	−7.46800			−0.555092			−0.277546	+	0.960712i	$0.589521\pi$
$182$	5.83771	−	7.28249i	0.432720	−	0.539814i
$183$	−3.04945			−0.225422
$184$	−8.49693	−	14.7171i	−0.626402	−	1.08496i
$185$		0			0
$186$	−0.822114	+	1.42394i	−0.0602803	+	0.104409i
$187$	9.84324			0.719809
$188$	0.460811	−	0.798148i	0.0336081	−	0.0582109i
$189$	−2.40049	+	4.15777i	−0.174610	+	0.302434i
$190$		0			0
$191$	1.20261	−	2.08298i	0.0870178	−	0.150719i	−0.819231	−	0.573463i	$-0.805600\pi$
$191$	1.20261	−	2.08298i	0.0870178	−	0.150719i	0.906249	+	0.422744i	$0.138933\pi$
$192$	0.921622	+	1.59630i	0.0665124	+	0.115203i
$193$	−7.91075	−	13.7018i	−0.569428	−	0.986279i	−0.996623	−	0.0821189i	$-0.973831\pi$
$193$	−7.91075	−	13.7018i	−0.569428	−	0.986279i	0.427194	−	0.904160i	$-0.359502\pi$
$194$	7.69368			0.552374
$195$		0			0
$196$	−27.4329			−1.95949
$197$	9.23287	+	15.9918i	0.657814	+	1.13937i	0.981180	+	0.193094i	$0.0618522\pi$
$197$	9.23287	+	15.9918i	0.657814	+	1.13937i	−0.323366	+	0.946274i	$0.604814\pi$
$198$	0.921622	+	1.59630i	0.0654968	+	0.113444i
$199$	−5.47107	+	9.47617i	−0.387834	+	0.671748i	−0.992158	−	0.124991i	$-0.960110\pi$
$199$	−5.47107	+	9.47617i	−0.387834	+	0.671748i	0.604324	+	0.796739i	$0.293443\pi$
$200$		0			0
$201$	−6.42522	+	11.1288i	−0.453200	+	0.784965i
$202$	−3.36910	+	5.83546i	−0.237049	+	0.410581i
$203$	−16.8527			−1.18283
$204$	−2.46081	+	4.26225i	−0.172291	+	0.298417i
$205$		0			0
$206$	1.84684	+	3.19882i	0.128675	+	0.222872i
$207$	−8.49693			−0.590577
$208$	−8.34017	−	1.27861i	−0.578287	−	0.0886555i
$209$	−16.9939			−1.17549
$210$		0			0
$211$	7.08864	+	12.2779i	0.488002	+	0.845244i	0.999905	−	0.0137992i	$-0.00439257\pi$
$211$	7.08864	+	12.2779i	0.488002	+	0.845244i	−0.511903	+	0.859043i	$0.671059\pi$
$212$	11.7587	−	20.3667i	0.807592	−	1.39879i
$213$	2.09171			0.143322
$214$	4.19481	−	7.26563i	0.286751	−	0.496668i
$215$		0			0
$216$	−2.00000			−0.136083
$217$	−7.32018	+	12.6789i	−0.496926	+	0.860701i
$218$	−4.26959	−	7.39515i	−0.289173	−	0.500863i
$219$	−2.76959	−	4.79708i	−0.187152	−	0.324157i
$220$		0			0
$221$	−3.76846	−	9.67358i	−0.253494	−	0.650715i
$222$	−1.44521			−0.0969963
$223$	−2.82991	−	4.90155i	−0.189505	−	0.328232i	0.755580	−	0.655056i	$-0.227355\pi$
$223$	−2.82991	−	4.90155i	−0.189505	−	0.328232i	−0.945085	+	0.326824i	$0.894022\pi$
$224$	−12.6309	−	21.8774i	−0.843937	−	1.46174i
$225$		0			0
$226$	1.65983			0.110410
$227$	10.4397	−	18.0821i	0.692906	−	1.20015i	−0.277976	−	0.960588i	$-0.589663\pi$
$227$	10.4397	−	18.0821i	0.692906	−	1.20015i	0.970882	−	0.239560i	$-0.0770032\pi$
$228$	4.24846	−	7.35856i	0.281361	−	0.487332i
$229$	−11.5525			−0.763412			−0.381706	−	0.924284i	$-0.624663\pi$
$229$	−11.5525			−0.763412			−0.381706	+	0.924284i	$0.624663\pi$
$230$		0			0
$231$	8.20620	+	14.2136i	0.539929	+	0.935184i
$232$	−3.51026	−	6.07995i	−0.230460	−	0.399168i
$233$	3.73206			0.244495			0.122248	−	0.992500i	$-0.460990\pi$
$233$	3.73206			0.244495			0.122248	+	0.992500i	$0.460990\pi$
$234$	1.21594	−	1.51687i	0.0794885	−	0.0991612i
$235$		0			0
$236$	7.18342	+	12.4420i	0.467601	+	0.809908i
$237$	−1.10617	−	1.91595i	−0.0718537	−	0.124454i
$238$	3.72681	−	6.45503i	0.241573	−	0.418417i
$239$	27.0928			1.75248			0.876242	−	0.481871i	$-0.160043\pi$
$239$	27.0928			1.75248			0.876242	+	0.481871i	$0.160043\pi$
$240$		0			0
$241$	11.7990	−	20.4365i	0.760043	−	1.31643i	−0.182784	−	0.983153i	$-0.558511\pi$
$241$	11.7990	−	20.4365i	0.760043	−	1.31643i	0.942828	−	0.333281i	$-0.108156\pi$
$242$	0.370147			0.0237940
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.60617	−	4.51402i	−0.166843	−	0.288981i
$245$		0			0
$246$	−2.02279			−0.128968
$247$	6.50605	+	16.7009i	0.413970	+	1.06266i
$248$	−6.09890			−0.387280
$249$	2.17009	+	3.75870i	0.137524	+	0.238198i
$250$		0			0
$251$	13.4319	−	23.2647i	0.847813	−	1.46845i	−0.0353430	−	0.999375i	$-0.511252\pi$
$251$	13.4319	−	23.2647i	0.847813	−	1.46845i	0.883156	−	0.469080i	$-0.155414\pi$
$252$	−8.20620			−0.516942
$253$	−14.5236	+	25.1556i	−0.913090	+	1.58152i
$254$	−2.00974	+	3.48097i	−0.126102	+	0.218415i
$255$		0			0
$256$	1.26180	−	2.18549i	0.0788622	−	0.136593i
$257$	−1.75933	−	3.04726i	−0.109744	−	0.190083i	0.805922	−	0.592021i	$-0.201670\pi$
$257$	−1.75933	−	3.04726i	−0.109744	−	0.190083i	−0.915667	+	0.401939i	$0.868337\pi$
$258$	0.428288	+	0.741816i	0.0266640	+	0.0461835i
$259$	−12.8683			−0.799597
$260$		0			0
$261$	−3.51026			−0.217280
$262$	−3.15255	−	5.46038i	−0.194765	−	0.337343i
$263$	−4.42635	−	7.66666i	−0.272940	−	0.472747i	0.696673	−	0.717389i	$-0.254663\pi$
$263$	−4.42635	−	7.66666i	−0.272940	−	0.472747i	−0.969613	+	0.244642i	$0.921330\pi$
$264$	−3.41855	+	5.92110i	−0.210397	+	0.364419i
$265$		0			0
$266$	−6.43415	+	11.1443i	−0.394503	+	0.683299i
$267$	3.50667	−	6.07372i	0.214604	−	0.371706i
$268$	−21.9649			−1.34172
$269$	−13.6212	+	23.5925i	−0.830497	+	1.43846i	0.0671480	+	0.997743i	$0.478610\pi$
$269$	−13.6212	+	23.5925i	−0.830497	+	1.43846i	−0.897645	+	0.440720i	$0.854723\pi$
$270$		0			0
$271$	−6.93188	−	12.0064i	−0.421082	−	0.729335i	0.574964	−	0.818179i	$-0.305016\pi$
$271$	−6.93188	−	12.0064i	−0.421082	−	0.729335i	−0.996046	+	0.0888438i	$0.971683\pi$
$272$	−6.73820			−0.408564
$273$	10.8268	−	13.5064i	0.655270	−	0.817443i
$274$	5.00227			0.302198
$275$		0			0
$276$	−7.26180	−	12.5778i	−0.437109	−	0.757094i
$277$	1.29072	−	2.23560i	0.0775521	−	0.134324i	−0.824641	−	0.565656i	$-0.808623\pi$
$277$	1.29072	−	2.23560i	0.0775521	−	0.134324i	0.902193	+	0.431332i	$0.141956\pi$
$278$	6.96388			0.417666
$279$	−1.52472	+	2.64090i	−0.0912828	+	0.158107i
$280$		0			0
$281$	−5.35350			−0.319363			−0.159682	−	0.987169i	$-0.551047\pi$
$281$	−5.35350			−0.319363			−0.159682	+	0.987169i	$0.551047\pi$
$282$	−0.145362	+	0.251775i	−0.00865620	+	0.0149930i
$283$	7.94687	+	13.7644i	0.472392	+	0.818207i	0.999501	−	0.0315904i	$-0.0100572\pi$
$283$	7.94687	+	13.7644i	0.472392	+	0.818207i	−0.527109	+	0.849798i	$0.676724\pi$
$284$	1.78765	+	3.09631i	0.106078	+	0.183732i
$285$		0			0
$286$	−2.41241	−	6.19261i	−0.142649	−	0.366177i
$287$	−18.0111			−1.06316
$288$	−2.63090	−	4.55685i	−0.155027	−	0.268515i
$289$	4.35464	+	7.54245i	0.256155	+	0.443674i
$290$		0			0
$291$	14.2690			0.836463
$292$	4.73400	−	8.19953i	0.277036	−	0.479841i
$293$	−1.24067	+	2.14889i	−0.0724804	+	0.125540i	−0.899988	−	0.435915i	$-0.856425\pi$
$293$	−1.24067	+	2.14889i	−0.0724804	+	0.125540i	0.827507	+	0.561455i	$0.189758\pi$
$294$	8.65368			0.504693
$295$		0			0
$296$	−2.68035	−	4.64250i	−0.155792	−	0.269840i
$297$	1.70928	+	2.96055i	0.0991822	+	0.171789i
$298$	−1.07838			−0.0624687
$299$	30.2823	+	4.64250i	1.75127	+	0.268482i
$300$		0			0
$301$	3.81351	+	6.60519i	0.219807	+	0.380717i
$302$	2.31965	+	4.01776i	0.133481	+	0.231196i
$303$	−6.24846	+	10.8227i	−0.358965	+	0.621745i
$304$	11.6332			0.667208
$305$		0			0
$306$	0.776260	−	1.34452i	0.0443758	−	0.0768612i
$307$	22.2423			1.26944			0.634718	−	0.772744i	$-0.281116\pi$
$307$	22.2423			1.26944			0.634718	+	0.772744i	$0.281116\pi$
$308$	−14.0267	+	24.2949i	−0.799243	+	1.38433i
$309$	3.42522	+	5.93265i	0.194854	+	0.337497i
$310$		0			0
$311$	−0.405220			−0.0229779			−0.0114890	−	0.999934i	$-0.503657\pi$
$311$	−0.405220			−0.0229779			−0.0114890	+	0.999934i	$0.503657\pi$
$312$	7.12783	+	1.09275i	0.403534	+	0.0618646i
$313$	0.353504			0.0199812			0.00999061	−	0.999950i	$-0.496820\pi$
$313$	0.353504			0.0199812			0.00999061	+	0.999950i	$0.496820\pi$
$314$	0.244870	+	0.424128i	0.0138188	+	0.0239349i
$315$		0			0
$316$	1.89076	−	3.27488i	0.106363	−	0.184227i
$317$	−25.3028			−1.42115			−0.710574	−	0.703622i	$-0.751565\pi$
$317$	−25.3028			−1.42115			−0.710574	+	0.703622i	$0.751565\pi$
$318$	−3.70928	+	6.42465i	−0.208006	+	0.360277i
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$		0			0
$321$	7.77985	−	13.4751i	0.434229	−	0.752107i
$322$	10.9977	+	19.0486i	0.612880	+	1.06154i
$323$	7.15676	+	12.3959i	0.398213	+	0.689724i
$324$	−1.70928			−0.0949597
$325$		0			0
$326$	7.89601			0.437319
$327$	−7.91855	−	13.7153i	−0.437897	−	0.758460i
$328$	−3.75154	−	6.49785i	−0.207144	−	0.358784i
$329$	−1.29432	+	2.24183i	−0.0713581	+	0.123596i
$330$		0			0
$331$	−2.30098	+	3.98542i	−0.126474	+	0.219059i	−0.922308	−	0.386456i	$-0.873699\pi$
$331$	−2.30098	+	3.98542i	−0.126474	+	0.219059i	0.795834	+	0.605514i	$0.207033\pi$
$332$	−3.70928	+	6.42465i	−0.203573	+	0.352599i
$333$	−2.68035			−0.146882
$334$	−1.31965	+	2.28571i	−0.0722083	+	0.125068i
$335$		0			0
$336$	−5.61757	−	9.72991i	−0.306463	−	0.530810i
$337$	31.0338			1.69052			0.845261	−	0.534354i	$-0.179445\pi$
$337$	31.0338			1.69052			0.845261	+	0.534354i	$0.179445\pi$
$338$	−5.16229	+	4.74165i	−0.280791	+	0.257912i
$339$	3.07838			0.167195
$340$		0			0
$341$	5.21235	+	9.02805i	0.282264	+	0.488896i
$342$	−1.34017	+	2.32125i	−0.0724683	+	0.125519i
$343$	43.4463			2.34588
$344$	−1.58864	+	2.75160i	−0.0856536	+	0.148356i
$345$		0			0
$346$	9.46800			0.509003
$347$	−8.97826	+	15.5508i	−0.481978	+	0.834811i	−0.999786	−	0.0206863i	$-0.993415\pi$
$347$	−8.97826	+	15.5508i	−0.481978	+	0.834811i	0.517808	+	0.855497i	$0.326748\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	−0.0505820	−	0.0876107i	−0.00270759	−	0.00468969i	0.864668	−	0.502343i	$-0.167529\pi$
$349$	−0.0505820	−	0.0876107i	−0.00270759	−	0.00468969i	−0.867376	+	0.497653i	$0.834195\pi$
$350$		0			0
$351$	2.25513	−	2.81325i	0.120370	−	0.150160i
$352$	−17.9877			−0.958748
$353$	−14.6803	−	25.4271i	−0.781356	−	1.35335i	−0.931152	−	0.364631i	$-0.881195\pi$
$353$	−14.6803	−	25.4271i	−0.781356	−	1.35335i	0.149796	−	0.988717i	$-0.452138\pi$
$354$	−2.26600	−	3.92483i	−0.120437	−	0.208602i
$355$		0			0
$356$	11.9877			0.635348
$357$	6.91189	−	11.9717i	0.365816	−	0.633611i
$358$	−0.373308	+	0.646588i	−0.0197299	+	0.0341732i
$359$	−11.5369			−0.608895			−0.304448	−	0.952529i	$-0.598472\pi$
$359$	−11.5369			−0.608895			−0.304448	+	0.952529i	$0.598472\pi$
$360$		0			0
$361$	−2.85577	−	4.94634i	−0.150304	−	0.260334i
$362$	2.01333	+	3.48719i	0.105818	+	0.183283i
$363$	0.686489			0.0360313
$364$	29.2462	+	4.48365i	1.53292	+	0.235007i
$365$		0			0
$366$	0.822114	+	1.42394i	0.0429726	+	0.0744307i
$367$	−17.8148	−	30.8562i	−0.929927	−	1.61068i	−0.783439	−	0.621468i	$-0.786536\pi$
$367$	−17.8148	−	30.8562i	−0.929927	−	1.61068i	−0.146488	−	0.989213i	$-0.546797\pi$
$368$	9.94214	−	17.2203i	0.518270	−	0.897670i
$369$	−3.75154			−0.195297
$370$		0			0
$371$	−33.0277	+	57.2057i	−1.71471	+	2.96997i
$372$	−5.21235			−0.270248
$373$	−4.80571	+	8.32374i	−0.248830	+	0.430987i	−0.963202	−	0.268780i	$-0.913379\pi$
$373$	−4.80571	+	8.32374i	−0.248830	+	0.430987i	0.714371	+	0.699767i	$0.246713\pi$
$374$	−2.65368	−	4.59632i	−0.137219	−	0.237670i
$375$		0			0
$376$	−1.07838			−0.0556131
$377$	12.5103	+	1.91791i	0.644311	+	0.0987775i
$378$	2.58864			0.133145
$379$	−3.51139	−	6.08191i	−0.180368	−	0.312407i	0.761638	−	0.648003i	$-0.224396\pi$
$379$	−3.51139	−	6.08191i	−0.180368	−	0.312407i	−0.942006	+	0.335596i	$0.891062\pi$
$380$		0			0
$381$	−3.72733	+	6.45593i	−0.190957	+	0.330747i
$382$	−1.29687			−0.0663535
$383$	10.1067	−	17.5053i	0.516428	−	0.894480i	−0.483390	−	0.875405i	$-0.660595\pi$
$383$	10.1067	−	17.5053i	0.516428	−	0.894480i	0.999818	−	0.0190745i	$-0.00607197\pi$
$384$	5.75872	−	9.97440i	0.293874	−	0.509004i
$385$		0			0
$386$	−4.26539	+	7.38787i	−0.217103	+	0.376033i
$387$	0.794319	+	1.37580i	0.0403775	+	0.0699359i
$388$	12.1948	+	21.1220i	0.619098	+	1.07231i
$389$	−15.7587			−0.798999			−0.399500	−	0.916733i	$-0.630816\pi$
$389$	−15.7587			−0.798999			−0.399500	+	0.916733i	$0.630816\pi$
$390$		0			0
$391$	24.4657			1.23729
$392$	16.0494	+	27.7985i	0.810620	+	1.40403i
$393$	−5.84684	−	10.1270i	−0.294934	−	0.510841i
$394$	4.97826	−	8.62260i	0.250801	−	0.434400i
$395$		0			0
$396$	−2.92162	+	5.06040i	−0.146817	+	0.254295i
$397$	5.67368	−	9.82710i	0.284754	−	0.493208i	−0.687796	−	0.725904i	$-0.741421\pi$
$397$	5.67368	−	9.82710i	0.284754	−	0.493208i	0.972549	+	0.232696i	$0.0747548\pi$
$398$	5.89988			0.295734
$399$	−11.9330	+	20.6686i	−0.597398	+	1.03472i
$400$		0			0
$401$	−13.3268	−	23.0828i	−0.665511	−	1.15270i	−0.979147	−	0.203155i	$-0.934880\pi$
$401$	−13.3268	−	23.0828i	−0.665511	−	1.15270i	0.313636	−	0.949543i	$-0.398453\pi$
$402$	6.92881			0.345578
$403$	6.87690	−	8.57887i	0.342563	−	0.427344i
$404$	−21.3607			−1.06273
$405$		0			0
$406$	4.54339	+	7.86939i	0.225485	+	0.390551i
$407$	−4.58145	+	7.93530i	−0.227094	+	0.393338i
$408$	5.75872			0.285099
$409$	15.4463	−	26.7539i	0.763773	−	1.32289i	−0.177120	−	0.984189i	$-0.556678\pi$
$409$	15.4463	−	26.7539i	0.763773	−	1.32289i	0.940893	−	0.338704i	$-0.109988\pi$
$410$		0			0
$411$	9.27739			0.457620
$412$	−5.85464	+	10.1405i	−0.288437	+	0.499588i
$413$	−20.1767	−	34.9470i	−0.992829	−	1.71963i
$414$	2.29072	+	3.96765i	0.112583	+	0.194999i
$415$		0			0
$416$	6.88655	+	17.6777i	0.337641	+	0.866719i
$417$	12.9155			0.632474
$418$	4.58145	+	7.93530i	0.224086	+	0.388128i
$419$	−17.1581	−	29.7187i	−0.838227	−	1.45185i	−0.891376	−	0.453265i	$-0.850259\pi$
$419$	−17.1581	−	29.7187i	−0.838227	−	1.45185i	0.0531484	−	0.998587i	$-0.483074\pi$
$420$		0			0
$421$	−13.5320			−0.659509			−0.329755	−	0.944067i	$-0.606966\pi$
$421$	−13.5320			−0.659509			−0.329755	+	0.944067i	$0.606966\pi$
$422$	3.82211	−	6.62010i	0.186058	−	0.322261i
$423$	−0.269594	+	0.466951i	−0.0131081	+	0.0227039i
$424$	−27.5174			−1.33637
$425$		0			0
$426$	−0.563913	−	0.976726i	−0.0273217	−	0.0473225i
$427$	7.32018	+	12.6789i	0.354248	+	0.613576i
$428$	26.5958			1.28556
$429$	−4.47414	−	11.4851i	−0.216014	−	0.554504i
$430$		0			0
$431$	−7.63090	−	13.2171i	−0.367567	−	0.636645i	0.621617	−	0.783321i	$-0.286476\pi$
$431$	−7.63090	−	13.2171i	−0.367567	−	0.636645i	−0.989185	+	0.146676i	$0.953143\pi$
$432$	−1.17009	−	2.02665i	−0.0562958	−	0.0975072i
$433$	1.93968	−	3.35963i	0.0932151	−	0.161453i	−0.815647	−	0.578550i	$-0.803619\pi$
$433$	1.93968	−	3.35963i	0.0932151	−	0.161453i	0.908862	+	0.417096i	$0.136952\pi$
$434$	7.89392			0.378920
$435$		0			0
$436$	13.5350	−	23.4433i	0.648208	−	1.12273i
$437$	−42.2388			−2.02056
$438$	−1.49333	+	2.58653i	−0.0713543	+	0.123589i
$439$	10.1556	+	17.5901i	0.484701	+	0.839527i	0.999846	−	0.0175761i	$-0.00559495\pi$
$439$	10.1556	+	17.5901i	0.484701	+	0.839527i	−0.515144	+	0.857104i	$0.672262\pi$
$440$		0			0
$441$	16.0494			0.764259
$442$	−3.50113	+	4.36763i	−0.166532	+	0.207747i
$443$	35.0772			1.66657			0.833283	−	0.552847i	$-0.186458\pi$
$443$	35.0772			1.66657			0.833283	+	0.552847i	$0.186458\pi$
$444$	−2.29072	−	3.96765i	−0.108713	−	0.188296i
$445$		0			0
$446$	−1.52586	+	2.64286i	−0.0722515	+	0.125143i
$447$	−2.00000			−0.0945968
$448$	4.42469	−	7.66379i	0.209047	−	0.362080i
$449$	−3.98667	+	6.90511i	−0.188143	+	0.325872i	−0.944631	−	0.328135i	$-0.893580\pi$
$449$	−3.98667	+	6.90511i	−0.188143	+	0.325872i	0.756488	+	0.654007i	$0.226913\pi$
$450$		0			0
$451$	−6.41241	+	11.1066i	−0.301948	+	0.522990i
$452$	2.63090	+	4.55685i	0.123747	+	0.214336i
$453$	4.30212	+	7.45149i	0.202131	+	0.350101i
$454$	−11.2579			−0.528360
$455$		0			0
$456$	−9.94214			−0.465583
$457$	1.30458	+	2.25960i	0.0610256	+	0.105699i	0.894924	−	0.446218i	$-0.147230\pi$
$457$	1.30458	+	2.25960i	0.0610256	+	0.105699i	−0.833899	+	0.551918i	$0.813896\pi$
$458$	3.11450	+	5.39446i	0.145531	+	0.252067i
$459$	1.43968	−	2.49360i	0.0671986	−	0.116391i
$460$		0			0
$461$	15.0397	−	26.0495i	0.700469	−	1.21325i	−0.267833	−	0.963465i	$-0.586307\pi$
$461$	15.0397	−	26.0495i	0.700469	−	1.21325i	0.968302	−	0.249783i	$-0.0803592\pi$
$462$	4.42469	−	7.66379i	0.205855	−	0.356552i
$463$	6.36788			0.295940			0.147970	−	0.988992i	$-0.452726\pi$
$463$	6.36788			0.295940			0.147970	+	0.988992i	$0.452726\pi$
$464$	4.10731	−	7.11406i	0.190677	−	0.330262i
$465$		0			0
$466$	−1.00614	−	1.74269i	−0.0466087	−	0.0807286i
$467$	2.06892			0.0957383			0.0478692	−	0.998854i	$-0.484757\pi$
$467$	2.06892			0.0957383			0.0478692	+	0.998854i	$0.484757\pi$
$468$	6.09171	+	0.933903i	0.281589	+	0.0431697i
$469$	61.6947			2.84880
$470$		0			0
$471$	0.454146	+	0.786603i	0.0209259	+	0.0362448i
$472$	8.40522	−	14.5583i	0.386882	−	0.670099i
$473$	5.43084			0.249710
$474$	−0.596436	+	1.03306i	−0.0273952	+	0.0474499i
$475$		0			0
$476$	23.6286			1.08302
$477$	−6.87936	+	11.9154i	−0.314984	+	0.545569i
$478$	−7.30406	−	12.6510i	−0.334080	−	0.578643i
$479$	−5.75513	−	9.96818i	−0.262959	−	0.455458i	0.704068	−	0.710132i	$-0.251365\pi$
$479$	−5.75513	−	9.96818i	−0.262959	−	0.455458i	−0.967027	+	0.254675i	$0.918032\pi$
$480$		0			0
$481$	9.55252	+	1.46447i	0.435557	+	0.0667741i
$482$	−12.7238			−0.579555
$483$	20.3968	+	35.3283i	0.928087	+	1.60749i
$484$	0.586699	+	1.01619i	0.0266682	+	0.0461906i
$485$		0			0
$486$	0.539189			0.0244581
$487$	10.0742	−	17.4490i	0.456504	−	0.790689i	−0.542269	−	0.840205i	$-0.682435\pi$
$487$	10.0742	−	17.4490i	0.456504	−	0.790689i	0.998773	+	0.0495162i	$0.0157680\pi$
$488$	−3.04945	+	5.28180i	−0.138042	+	0.239096i
$489$	14.6442			0.662235
$490$		0			0
$491$	10.9408	+	18.9500i	0.493752	+	0.855204i	0.999974	−	0.00719955i	$-0.00229171\pi$
$491$	10.9408	+	18.9500i	0.493752	+	0.855204i	−0.506222	+	0.862403i	$0.668958\pi$
$492$	−3.20620	−	5.55331i	−0.144547	−	0.250362i
$493$	10.1073			0.455210
$494$	6.04453	−	7.54049i	0.271956	−	0.339263i
$495$		0			0
$496$	−3.56812	−	6.18016i	−0.160213	−	0.277497i
$497$	−5.02113	−	8.69685i	−0.225228	−	0.390107i
$498$	1.17009	−	2.02665i	0.0524328	−	0.0908163i
$499$	−23.8225			−1.06644			−0.533222	−	0.845975i	$-0.679019\pi$
$499$	−23.8225			−1.06644			−0.533222	+	0.845975i	$0.679019\pi$
$500$		0			0
$501$	−2.44748	+	4.23916i	−0.109345	+	0.189392i
$502$	−14.4846			−0.646481
$503$	2.15449	−	3.73168i	0.0960639	−	0.166388i	−0.813988	−	0.580881i	$-0.802708\pi$
$503$	2.15449	−	3.73168i	0.0960639	−	0.166388i	0.910052	+	0.414494i	$0.136041\pi$
$504$	4.80098	+	8.31555i	0.213853	+	0.370404i
$505$		0			0
$506$	15.6619			0.696257
$507$	−9.57417	+	8.79404i	−0.425204	+	0.390557i
$508$	−12.7421			−0.565338
$509$	−0.496928	−	0.860705i	−0.0220260	−	0.0381501i	0.854802	−	0.518954i	$-0.173678\pi$
$509$	−0.496928	−	0.860705i	−0.0220260	−	0.0381501i	−0.876828	+	0.480804i	$0.840345\pi$
$510$		0			0
$511$	−13.2968	+	23.0307i	−0.588215	+	1.01882i
$512$	21.6742			0.957873
$513$	−2.48554	+	4.30507i	−0.109739	+	0.190074i
$514$	−0.948614	+	1.64305i	−0.0418416	+	0.0724717i
$515$		0			0
$516$	−1.35771	+	2.35162i	−0.0597698	+	0.103524i
$517$	0.921622	+	1.59630i	0.0405329	+	0.0702050i
$518$	3.46922	+	6.00887i	0.152429	+	0.264015i
$519$	17.5597			0.770786
$520$		0			0
$521$	9.75154			0.427223			0.213611	−	0.976919i	$-0.431477\pi$
$521$	9.75154			0.427223			0.213611	+	0.976919i	$0.431477\pi$
$522$	0.946346	+	1.63912i	0.0414205	+	0.0717423i
$523$	−5.51026	−	9.54405i	−0.240947	−	0.417332i	0.720037	−	0.693935i	$-0.244125\pi$
$523$	−5.51026	−	9.54405i	−0.240947	−	0.417332i	−0.960984	+	0.276603i	$0.910791\pi$
$524$	9.99386	−	17.3099i	0.436584	−	0.756185i
$525$		0			0
$526$	−2.38664	+	4.13378i	−0.104062	+	0.180241i
$527$	4.39023	−	7.60411i	0.191242	−	0.331240i
$528$	−8.00000			−0.348155
$529$	−24.5989	+	42.6065i	−1.06952	+	1.85246i
$530$		0			0
$531$	−4.20261	−	7.27913i	−0.182378	−	0.315888i
$532$	−40.7936			−1.76863
$533$	13.3701	+	2.04974i	0.579125	+	0.0887841i
$534$	−3.78151			−0.163642
$535$		0			0
$536$	12.8504	+	22.2576i	0.555054	+	0.961382i
$537$	−0.692350	+	1.19919i	−0.0298771	+	0.0517487i
$538$	14.6888			0.633277
$539$	27.4329	−	47.5152i	1.18162	−	2.04663i
$540$		0			0
$541$	−6.28846			−0.270362			−0.135181	−	0.990821i	$-0.543162\pi$
$541$	−6.28846			−0.270362			−0.135181	+	0.990821i	$0.543162\pi$
$542$	−3.73759	+	6.47370i	−0.160543	+	0.278069i
$543$	3.73400	+	6.46748i	0.160241	+	0.277546i
$544$	7.57531	+	13.1208i	0.324789	+	0.562550i
$545$		0			0
$546$	−9.22568	−	1.41436i	−0.394823	−	0.0605291i
$547$	−27.6875			−1.18383			−0.591917	−	0.805999i	$-0.701629\pi$
$547$	−27.6875			−1.18383			−0.591917	+	0.805999i	$0.701629\pi$
$548$	7.92881	+	13.7331i	0.338702	+	0.586649i
$549$	1.52472	+	2.64090i	0.0650736	+	0.112711i
$550$		0			0
$551$	−17.4497			−0.743384
$552$	−8.49693	+	14.7171i	−0.361653	+	0.626402i
$553$	−5.31072	+	9.19844i	−0.225835	+	0.391157i
$554$	−1.39189			−0.0591357
$555$		0			0
$556$	11.0381	+	19.1185i	0.468118	+	0.810804i
$557$	−10.7321	−	18.5885i	−0.454732	−	0.787619i	0.543941	−	0.839124i	$-0.316932\pi$
$557$	−10.7321	−	18.5885i	−0.454732	−	0.787619i	−0.998673	+	0.0515046i	$0.983598\pi$
$558$	1.64423			0.0696057
$559$	−2.07918	−	5.33723i	−0.0879400	−	0.225741i
$560$		0			0
$561$	−4.92162	−	8.52450i	−0.207791	−	0.359905i
$562$	1.44327	+	2.49983i	0.0608809	+	0.105449i
$563$	−7.83710	+	13.5743i	−0.330294	+	0.572087i	−0.982570	−	0.185896i	$-0.940481\pi$
$563$	−7.83710	+	13.5743i	−0.330294	+	0.572087i	0.652275	+	0.757982i	$0.273815\pi$
$564$	−0.921622			−0.0388073
$565$		0			0
$566$	4.28486	−	7.42160i	0.180106	−	0.311953i
$567$	4.80098			0.201622
$568$	2.09171	−	3.62295i	0.0877661	−	0.152015i
$569$	−8.21594	−	14.2304i	−0.344430	−	0.596571i	0.640820	−	0.767691i	$-0.278595\pi$
$569$	−8.21594	−	14.2304i	−0.344430	−	0.596571i	−0.985250	+	0.171121i	$0.945261\pi$
$570$		0			0
$571$	14.6765			0.614191			0.307096	−	0.951679i	$-0.400643\pi$
$571$	14.6765			0.614191			0.307096	+	0.951679i	$0.400643\pi$
$572$	13.1773	−	16.4385i	0.550970	−	0.687329i
$573$	−2.40522			−0.100479
$574$	4.85568	+	8.41029i	0.202672	+	0.351039i
$575$		0			0
$576$	0.921622	−	1.59630i	0.0384009	−	0.0665124i
$577$	17.8622			0.743611			0.371806	−	0.928311i	$-0.378739\pi$
$577$	17.8622			0.743611			0.371806	+	0.928311i	$0.378739\pi$
$578$	2.34797	−	4.06681i	0.0976628	−	0.169157i
$579$	−7.91075	+	13.7018i	−0.328760	+	0.569428i
$580$		0			0
$581$	10.4186	−	18.0455i	0.432234	−	0.748652i
$582$	−3.84684	−	6.66292i	−0.159457	−	0.276187i
$583$	23.5174	+	40.7334i	0.973993	+	1.68701i
$584$	−11.0784			−0.458427
$585$		0			0
$586$	1.33791			0.0552684
$587$	−2.21174	−	3.83084i	−0.0912881	−	0.158116i	0.816765	−	0.576970i	$-0.195765\pi$
$587$	−2.21174	−	3.83084i	−0.0912881	−	0.158116i	−0.908053	+	0.418854i	$0.862432\pi$
$588$	13.7165	+	23.7576i	0.565657	+	0.979747i
$589$	−7.57951	+	13.1281i	−0.312308	+	0.540934i
$590$		0			0
$591$	9.23287	−	15.9918i	0.379789	−	0.657814i
$592$	3.13624	−	5.43212i	0.128899	−	0.223259i
$593$	−12.5380			−0.514873			−0.257436	−	0.966295i	$-0.582878\pi$
$593$	−12.5380			−0.514873			−0.257436	+	0.966295i	$0.582878\pi$
$594$	0.921622	−	1.59630i	0.0378146	−	0.0654968i
$595$		0			0
$596$	−1.70928	−	2.96055i	−0.0700146	−	0.121269i
$597$	10.9421			0.447832
$598$	−5.99612	−	15.3920i	−0.245200	−	0.629424i
$599$	23.5825			0.963555			0.481777	−	0.876294i	$-0.339991\pi$
$599$	23.5825			0.963555			0.481777	+	0.876294i	$0.339991\pi$
$600$		0			0
$601$	−1.64229	−	2.84453i	−0.0669904	−	0.116031i	0.830585	−	0.556892i	$-0.188006\pi$
$601$	−1.64229	−	2.84453i	−0.0669904	−	0.116031i	−0.897575	+	0.440861i	$0.854673\pi$
$602$	2.05620	−	3.56145i	0.0838046	−	0.145154i
$603$	12.8504			0.523310
$604$	−7.35350	+	12.7366i	−0.299210	+	0.518247i
$605$		0			0
$606$	6.73820			0.273721
$607$	−3.00421	+	5.20344i	−0.121937	+	0.211201i	−0.920531	−	0.390668i	$-0.872244\pi$
$607$	−3.00421	+	5.20344i	−0.121937	+	0.211201i	0.798595	+	0.601869i	$0.205577\pi$
$608$	−13.0784	−	22.6524i	−0.530398	−	0.918677i
$609$	8.42635	+	14.5949i	0.341453	+	0.591414i
$610$		0			0
$611$	1.21594	−	1.51687i	0.0491917	−	0.0613662i
$612$	4.92162			0.198945
$613$	−2.76539	−	4.78979i	−0.111693	−	0.193458i	0.804760	−	0.593600i	$-0.202294\pi$
$613$	−2.76539	−	4.78979i	−0.111693	−	0.193458i	−0.916453	+	0.400142i	$0.868961\pi$
$614$	−5.99641	−	10.3861i	−0.241995	−	0.419148i
$615$		0			0
$616$	32.8248			1.32255
$617$	5.94214	−	10.2921i	0.239222	−	0.414344i	−0.721270	−	0.692654i	$-0.756441\pi$
$617$	5.94214	−	10.2921i	0.239222	−	0.414344i	0.960491	+	0.278311i	$0.0897744\pi$
$618$	1.84684	−	3.19882i	0.0742907	−	0.128675i
$619$	32.2183			1.29496			0.647482	−	0.762081i	$-0.275822\pi$
$619$	32.2183			1.29496			0.647482	+	0.762081i	$0.275822\pi$
$620$		0			0
$621$	4.24846	+	7.35856i	0.170485	+	0.295289i
$622$	0.109245	+	0.189218i	0.00438032	+	0.00758695i
$623$	−33.6709			−1.34900
$624$	3.06278	+	7.86211i	0.122609	+	0.314736i
$625$		0			0
$626$	−0.0953027	−	0.165069i	−0.00380906	−	0.00659749i
$627$	8.49693	+	14.7171i	0.339335	+	0.587745i
$628$	−0.776260	+	1.34452i	−0.0309761	+	0.0536523i
$629$	7.71769			0.307724
$630$		0			0
$631$	9.87209	−	17.0990i	0.393002	−	0.680699i	−0.599842	−	0.800118i	$-0.704770\pi$
$631$	9.87209	−	17.0990i	0.393002	−	0.680699i	0.992844	+	0.119420i	$0.0381034\pi$
$632$	−4.42469			−0.176005
$633$	7.08864	−	12.2779i	0.281748	−	0.488002i
$634$	6.82150	+	11.8152i	0.270916	+	0.469241i
$635$		0			0
$636$	−23.5174			−0.932527
$637$	−57.1988	−	8.76899i	−2.26630	−	0.347440i
$638$	6.47027			0.256160
$639$	−1.04585	−	1.81147i	−0.0413734	−	0.0716608i
$640$		0			0
$641$	−18.0566	+	31.2750i	−0.713194	+	1.23529i	0.250458	+	0.968128i	$0.419419\pi$
$641$	−18.0566	+	31.2750i	−0.713194	+	1.23529i	−0.963652	+	0.267161i	$0.913914\pi$
$642$	−8.38962			−0.331112
$643$	19.5911	−	33.9328i	0.772597	−	1.33818i	−0.163537	−	0.986537i	$-0.552290\pi$
$643$	19.5911	−	33.9328i	0.772597	−	1.33818i	0.936135	−	0.351641i	$-0.114376\pi$
$644$	−34.8638	+	60.3858i	−1.37382	+	2.37953i
$645$		0			0
$646$	3.85884	−	6.68371i	0.151824	−	0.262967i
$647$	−21.0856	−	36.5213i	−0.828959	−	1.43580i	−0.898856	−	0.438245i	$-0.855600\pi$
$647$	−21.0856	−	36.5213i	−0.828959	−	1.43580i	0.0698964	−	0.997554i	$-0.477733\pi$
$648$	1.00000	+	1.73205i	0.0392837	+	0.0680414i
$649$	−28.7337			−1.12790
$650$		0			0
$651$	14.6404			0.573801
$652$	12.5155	+	21.6775i	0.490145	+	0.848956i
$653$	−16.9233	−	29.3120i	−0.662259	−	1.14707i	−0.980021	−	0.198896i	$-0.936265\pi$
$653$	−16.9233	−	29.3120i	−0.662259	−	1.14707i	0.317762	−	0.948171i	$-0.397069\pi$
$654$	−4.26959	+	7.39515i	−0.166954	+	0.289173i
$655$		0			0
$656$	4.38962	−	7.60305i	0.171386	−	0.296849i
$657$	−2.76959	+	4.79708i	−0.108052	+	0.187152i
$658$	1.39576			0.0544126
$659$	15.7659	−	27.3074i	0.614153	−	1.06374i	−0.376380	−	0.926465i	$-0.622831\pi$
$659$	15.7659	−	27.3074i	0.614153	−	1.06374i	0.990533	−	0.137278i	$-0.0438355\pi$
$660$		0			0
$661$	3.18876	+	5.52309i	0.124028	+	0.214823i	0.921353	−	0.388728i	$-0.127085\pi$
$661$	3.18876	+	5.52309i	0.124028	+	0.214823i	−0.797324	+	0.603551i	$0.793752\pi$
$662$	2.48133			0.0964396
$663$	−6.49333	+	8.10037i	−0.252180	+	0.314592i
$664$	8.68035			0.336863
$665$		0			0
$666$	0.722606	+	1.25159i	0.0280004	+	0.0484982i
$667$	−14.9132	+	25.8304i	−0.577442	+	1.00016i
$668$	−8.36683			−0.323723
$669$	−2.82991	+	4.90155i	−0.109411	+	0.189505i
$670$		0			0
$671$	10.4247			0.402441
$672$	−12.6309	+	21.8774i	−0.487247	+	0.843937i
$673$	4.86130	+	8.42002i	0.187389	+	0.324568i	0.944379	−	0.328859i	$-0.106664\pi$
$673$	4.86130	+	8.42002i	0.187389	+	0.324568i	−0.756990	+	0.653427i	$0.773331\pi$
$674$	−8.36655	−	14.4913i	−0.322268	−	0.558184i
$675$		0			0
$676$	−21.2001	−	6.65669i	−0.815387	−	0.256027i
$677$	10.0845			0.387580			0.193790	−	0.981043i	$-0.437922\pi$
$677$	10.0845			0.387580			0.193790	+	0.981043i	$0.437922\pi$
$678$	−0.829914	−	1.43745i	−0.0318726	−	0.0552050i
$679$	−34.2526	−	59.3272i	−1.31449	−	2.27677i
$680$		0			0
$681$	−20.8794			−0.800099
$682$	2.81044	−	4.86782i	0.107617	−	0.186399i
$683$	−3.36849	+	5.83440i	−0.128892	+	0.223247i	−0.923247	−	0.384206i	$-0.874475\pi$
$683$	−3.36849	+	5.83440i	−0.128892	+	0.223247i	0.794356	+	0.607453i	$0.207809\pi$
$684$	−8.49693			−0.324888
$685$		0			0
$686$	−11.7129	−	20.2873i	−0.447199	−	0.774572i
$687$	5.77626	+	10.0048i	0.220378	+	0.381706i
$688$	−3.71769			−0.141735
$689$	31.0277	−	38.7068i	1.18206	−	1.47461i
$690$		0			0
$691$	8.97220	+	15.5403i	0.341319	+	0.591181i	0.984678	−	0.174383i	$-0.0557931\pi$
$691$	8.97220	+	15.5403i	0.341319	+	0.591181i	−0.643359	+	0.765565i	$0.722460\pi$
$692$	15.0072	+	25.9932i	0.570488	+	0.988114i
$693$	8.20620	−	14.2136i	0.311728	−	0.539929i
$694$	9.68195			0.367522
$695$		0			0
$696$	−3.51026	+	6.07995i	−0.133056	+	0.230460i
$697$	10.8020			0.409156
$698$	−0.0272733	+	0.0472387i	−0.00103231	+	0.00178801i
$699$	−1.86603	−	3.23206i	−0.0705798	−	0.122248i
$700$		0			0
$701$	41.2762			1.55898			0.779490	−	0.626415i	$-0.215478\pi$
$701$	41.2762			1.55898			0.779490	+	0.626415i	$0.215478\pi$
$702$	−1.92162	−	0.294598i	−0.0725270	−	0.0111189i
$703$	−13.3242			−0.502531
$704$	−3.15061	−	5.45702i	−0.118743	−	0.205669i
$705$		0			0
$706$	−7.91548	+	13.7100i	−0.297903	+	0.515983i
$707$	59.9976			2.25644
$708$	7.18342	−	12.4420i	0.269969	−	0.467601i
$709$	−0.732866	+	1.26936i	−0.0275234	+	0.0476718i	−0.879459	−	0.475975i	$-0.842095\pi$
$709$	−0.732866	+	1.26936i	−0.0275234	+	0.0476718i	0.851936	+	0.523647i	$0.175429\pi$
$710$		0			0
$711$	−1.10617	+	1.91595i	−0.0414847	+	0.0718537i
$712$	−7.01333	−	12.1474i	−0.262836	−	0.455245i
$713$	12.9555	+	22.4395i	0.485186	+	0.840367i
$714$	−7.45362			−0.278945
$715$		0			0
$716$	−2.36683			−0.0884528
$717$	−13.5464	−	23.4630i	−0.505899	−	0.876242i
$718$	3.11029	+	5.38718i	0.116075	+	0.201048i
$719$	4.80685	−	8.32570i	0.179265	−	0.310496i	−0.762364	−	0.647149i	$-0.775961\pi$
$719$	4.80685	−	8.32570i	0.179265	−	0.310496i	0.941629	+	0.336652i	$0.109295\pi$
$720$		0			0
$721$	16.4444	−	28.4826i	0.612422	−	1.06075i
$722$	−1.53980	+	2.66701i	−0.0573054	+	0.0992559i
$723$	−23.5981			−0.877623
$724$	−6.38243	+	11.0547i	−0.237201	+	0.410845i
$725$		0			0
$726$	−0.185074	−	0.320557i	−0.00686873	−	0.0118970i
$727$	42.6547			1.58198			0.790988	−	0.611831i	$-0.209567\pi$
$727$	42.6547			1.58198			0.790988	+	0.611831i	$0.209567\pi$
$728$	−12.5669	−	32.2590i	−0.465760	−	1.19560i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.28713	−	3.96143i	−0.0845926	−	0.146519i
$732$	−2.60617	+	4.51402i	−0.0963269	+	0.166843i
$733$	6.48360			0.239477			0.119739	−	0.992805i	$-0.461794\pi$
$733$	6.48360			0.239477			0.119739	+	0.992805i	$0.461794\pi$
$734$	−9.60556	+	16.6373i	−0.354548	+	0.614095i
$735$		0			0
$736$	−44.7091			−1.64800
$737$	21.9649	−	38.0444i	0.809089	−	1.40138i
$738$	1.01139	+	1.75178i	0.0372299	+	0.0644841i
$739$	21.1845	+	36.6926i	0.779283	+	1.34976i	0.932355	+	0.361543i	$0.117750\pi$
$739$	21.1845	+	36.6926i	0.779283	+	1.34976i	−0.153072	+	0.988215i	$0.548917\pi$
$740$		0			0
$741$	11.2104	−	13.9849i	0.411825	−	0.513747i
$742$	35.6163			1.30752
$743$	−8.71481	−	15.0945i	−0.319715	−	0.553763i	0.660713	−	0.750638i	$-0.270254\pi$
$743$	−8.71481	−	15.0945i	−0.319715	−	0.553763i	−0.980429	+	0.196875i	$0.936921\pi$
$744$	3.04945	+	5.28180i	0.111798	+	0.193640i
$745$		0			0
$746$	5.18237			0.189740
$747$	2.17009	−	3.75870i	0.0793993	−	0.137524i
$748$	8.41241	−	14.5707i	0.307588	−	0.532758i
$749$	−74.7019			−2.72955
$750$		0			0
$751$	−6.68455	−	11.5780i	−0.243923	−	0.422487i	0.717905	−	0.696141i	$-0.245101\pi$
$751$	−6.68455	−	11.5780i	−0.243923	−	0.422487i	−0.961828	+	0.273654i	$0.911768\pi$
$752$	−0.630898	−	1.09275i	−0.0230065	−	0.0398484i
$753$	−26.8638			−0.978970
$754$	−2.47712	−	6.35874i	−0.0902116	−	0.231572i
$755$		0			0
$756$	4.10310	+	7.10678i	0.149228	+	0.258471i
$757$	13.8462	+	23.9824i	0.503250	+	0.871654i	0.999993	+	0.00375649i	$0.00119573\pi$
$757$	13.8462	+	23.9824i	0.503250	+	0.871654i	−0.496743	+	0.867898i	$0.665471\pi$
$758$	−1.89330	+	3.27930i	−0.0687679	+	0.119110i
$759$	29.0472			1.05435
$760$		0			0
$761$	0.261795	−	0.453443i	0.00949007	−	0.0164373i	−0.861241	−	0.508196i	$-0.830313\pi$
$761$	0.261795	−	0.453443i	0.00949007	−	0.0164373i	0.870731	+	0.491759i	$0.163646\pi$
$762$	4.01947			0.145610
$763$	−38.0168	+	65.8471i	−1.37630	+	2.38382i
$764$	−2.05559	−	3.56039i	−0.0743687	−	0.128810i
$765$		0			0
$766$	−10.8988			−0.393791
$767$	11.0006	+	28.2384i	0.397209	+	1.01963i
$768$	−2.52359			−0.0910622
$769$	7.08032	+	12.2635i	0.255323	+	0.442232i	0.964983	−	0.262312i	$-0.0844850\pi$
$769$	7.08032	+	12.2635i	0.255323	+	0.442232i	−0.709660	+	0.704544i	$0.751152\pi$
$770$		0			0
$771$	−1.75933	+	3.04726i	−0.0633609	+	0.109744i
$772$	−27.0433			−0.973310
$773$	13.7093	−	23.7452i	0.493088	−	0.854054i	−0.506880	−	0.862017i	$-0.669201\pi$
$773$	13.7093	−	23.7452i	0.493088	−	0.854054i	0.999968	+	0.00796257i	$0.00253459\pi$
$774$	0.428288	−	0.741816i	0.0153945	−	0.0266640i
$775$		0			0
$776$	14.2690	−	24.7146i	0.512227	−	0.887203i
$777$	6.43415	+	11.1443i	0.230824	+	0.399799i
$778$	4.24846	+	7.35856i	0.152315	+	0.263817i
$779$	−18.6491			−0.668175
$780$		0			0
$781$	−7.15061			−0.255869
$782$	−6.59583	−	11.4243i	−0.235866	−	0.408532i
$783$	1.75513	+	3.03997i	0.0627232	+	0.108640i
$784$	−18.7792	+	32.5266i	−0.670687	+	1.16166i
$785$		0			0
$786$	−3.15255	+	5.46038i	−0.112448	+	0.194765i
$787$	10.6851	−	18.5071i	0.380882	−	0.659707i	−0.610307	−	0.792165i	$-0.708954\pi$
$787$	10.6851	−	18.5071i	0.380882	−	0.659707i	0.991189	+	0.132459i	$0.0422872\pi$
$788$	31.5630			1.12439
$789$	−4.42635	+	7.66666i	−0.157582	+	0.272940i
$790$		0			0
$791$	−7.38962	−	12.7992i	−0.262745	−	0.455087i
$792$	6.83710			0.242946
$793$	−3.99107	−	10.2450i	−0.141727	−	0.363811i
$794$	−6.11837			−0.217133
$795$		0			0
$796$	9.35157	+	16.1974i	0.331457	+	0.574101i
$797$	1.94275	−	3.36495i	0.0688158	−	0.119193i	−0.829564	−	0.558411i	$-0.811411\pi$
$797$	1.94275	−	3.36495i	0.0688158	−	0.119193i	0.898380	+	0.439218i	$0.144745\pi$
$798$	12.8683			0.455533
$799$	0.776260	−	1.34452i	0.0274621	−	0.0475658i
$800$		0			0
$801$	−7.01333			−0.247804
$802$	−7.18568	+	12.4460i	−0.253735	+	0.439483i
$803$	9.46800	+	16.3991i	0.334118	+	0.578710i
$804$	10.9825	+	19.0222i	0.387322	+	0.670861i
$805$		0			0
$806$	−5.85989	−	0.898363i	−0.206406	−	0.0316435i
$807$	27.2423			0.958975
$808$	12.4969	+	21.6453i	0.439640	+	0.761480i
$809$	25.4524	+	44.0849i	0.894859	+	1.54994i	0.833979	+	0.551796i	$0.186057\pi$
$809$	25.4524	+	44.0849i	0.894859	+	1.54994i	0.0608794	+	0.998145i	$0.480609\pi$
$810$		0			0
$811$	−42.5174			−1.49299			−0.746495	−	0.665391i	$-0.768265\pi$
$811$	−42.5174			−1.49299			−0.746495	+	0.665391i	$0.768265\pi$
$812$	−14.4030	+	24.9466i	−0.505445	+	0.875456i
$813$	−6.93188	+	12.0064i	−0.243112	+	0.421082i
$814$	4.94053			0.173166
$815$		0			0
$816$	3.36910	+	5.83546i	0.117942	+	0.204282i
$817$	3.94861	+	6.83920i	0.138145	+	0.239273i
$818$	−16.6570			−0.582398
$819$	−17.1103	−	2.62313i	−0.597882	−	0.0916596i
$820$		0			0
$821$	1.99773	+	3.46017i	0.0697213	+	0.120761i	0.898779	−	0.438403i	$-0.144456\pi$
$821$	1.99773	+	3.46017i	0.0697213	+	0.120761i	−0.829057	+	0.559164i	$0.811122\pi$
$822$	−2.50113	−	4.33209i	−0.0872371	−	0.151099i
$823$	−0.787653	+	1.36426i	−0.0274559	+	0.0475549i	−0.879427	−	0.476034i	$-0.842074\pi$
$823$	−0.787653	+	1.36426i	−0.0274559	+	0.0475549i	0.851971	+	0.523589i	$0.175407\pi$
$824$	13.7009			0.477292
$825$		0			0
$826$	−10.8790	+	18.8430i	−0.378530	+	0.655633i
$827$	−9.17850			−0.319168			−0.159584	−	0.987184i	$-0.551015\pi$
$827$	−9.17850			−0.319168			−0.159584	+	0.987184i	$0.551015\pi$
$828$	−7.26180	+	12.5778i	−0.252365	+	0.437109i
$829$	−24.7358	−	42.8437i	−0.859112	−	1.48802i	−0.872778	−	0.488118i	$-0.837683\pi$
$829$	−24.7358	−	42.8437i	−0.859112	−	1.48802i	0.0136660	−	0.999907i	$-0.495650\pi$
$830$		0			0
$831$	−2.58145			−0.0895495
$832$	−4.15676	+	5.18551i	−0.144110	+	0.179775i
$833$	−46.2122			−1.60116
$834$	−3.48194	−	6.03090i	−0.120570	−	0.208833i
$835$		0			0
$836$	−14.5236	+	25.1556i	−0.502309	+	0.870024i
$837$	3.04945			0.105404
$838$	−9.25145	+	16.0240i	−0.319586	+	0.553539i
$839$	−4.64650	+	8.04797i	−0.160415	+	0.277847i	−0.935018	−	0.354601i	$-0.884617\pi$
$839$	−4.64650	+	8.04797i	−0.160415	+	0.277847i	0.774603	+	0.632448i	$0.217950\pi$
$840$		0			0
$841$	8.33904	−	14.4436i	0.287553	−	0.498057i
$842$	3.64815	+	6.31878i	0.125724	+	0.217760i
$843$	2.67675	+	4.63627i	0.0921922	+	0.159682i
$844$	24.2329			0.834130
$845$		0			0
$846$	0.290725			0.00999532
$847$	−1.64791	−	2.85427i	−0.0566229	−	0.0980738i
$848$	−16.0989	−	27.8841i	−0.552838	−	0.957544i
$849$	7.94687	−	13.7644i	0.272736	−	0.472392i
$850$		0			0
$851$	−11.3874	+	19.7235i	−0.390353	+	0.676112i
$852$	1.78765	−	3.09631i	0.0612440	−	0.106078i
$853$	11.0423			0.378080			0.189040	−	0.981969i	$-0.439462\pi$
$853$	11.0423			0.378080			0.189040	+	0.981969i	$0.439462\pi$
$854$	3.94696	−	6.83633i	0.135062	−	0.233934i
$855$		0			0
$856$	−15.5597	−	26.9502i	−0.531820	−	0.921139i
$857$	8.58476			0.293250			0.146625	−	0.989192i	$-0.453159\pi$
$857$	8.58476			0.293250			0.146625	+	0.989192i	$0.453159\pi$
$858$	−4.15676	+	5.18551i	−0.141909	+	0.177030i
$859$	−46.6202			−1.59066			−0.795331	−	0.606176i	$-0.792703\pi$
$859$	−46.6202			−1.59066			−0.795331	+	0.606176i	$0.792703\pi$
$860$		0			0
$861$	9.00553	+	15.5980i	0.306908	+	0.531580i
$862$	−4.11450	+	7.12651i	−0.140140	+	0.242730i
$863$	−10.6947			−0.364053			−0.182026	−	0.983294i	$-0.558266\pi$
$863$	−10.6947			−0.364053			−0.182026	+	0.983294i	$0.558266\pi$
$864$	−2.63090	+	4.55685i	−0.0895050	+	0.155027i
$865$		0			0
$866$	−2.09171			−0.0710792
$867$	4.35464	−	7.54245i	0.147891	−	0.256155i
$868$	12.5122	+	21.6718i	0.424692	+	0.735588i
$869$	3.78151	+	6.54977i	0.128279	+	0.222186i
$870$		0			0
$871$	−45.7978	−	7.02113i	−1.55180	−	0.237902i
$872$	−31.6742			−1.07262
$873$	−7.13449	−	12.3573i	−0.241466	−	0.418231i
$874$	11.3874	+	19.7235i	0.385183	+	0.667157i
$875$		0			0
$876$	−9.46800			−0.319894
$877$	−5.29791	+	9.17625i	−0.178898	+	0.309860i	−0.941503	−	0.337004i	$-0.890586\pi$
$877$	−5.29791	+	9.17625i	−0.178898	+	0.309860i	0.762605	+	0.646864i	$0.223920\pi$
$878$	5.47580	−	9.48436i	0.184799	−	0.320082i
$879$	2.48133			0.0836932
$880$		0			0
$881$	8.11450	+	14.0547i	0.273384	+	0.473515i	0.969726	−	0.244195i	$-0.0785236\pi$
$881$	8.11450	+	14.0547i	0.273384	+	0.473515i	−0.696342	+	0.717710i	$0.745190\pi$
$882$	−4.32684	−	7.49431i	−0.145692	−	0.252347i
$883$	−12.6137			−0.424484			−0.212242	−	0.977217i	$-0.568077\pi$
$883$	−12.6137			−0.424484			−0.212242	+	0.977217i	$0.568077\pi$
$884$	−17.5402	−	2.68904i	−0.589942	−	0.0904423i
$885$		0			0
$886$	−9.45661	−	16.3793i	−0.317701	−	0.550274i
$887$	−6.69533	−	11.5967i	−0.224807	−	0.389378i	0.731454	−	0.681890i	$-0.238842\pi$
$887$	−6.69533	−	11.5967i	−0.224807	−	0.389378i	−0.956262	+	0.292513i	$0.905509\pi$
$888$	−2.68035	+	4.64250i	−0.0899465	+	0.155792i
$889$	35.7897			1.20035
$890$		0			0
$891$	1.70928	−	2.96055i	0.0572629	−	0.0991822i
$892$	−9.67420			−0.323916
$893$	−1.34017	+	2.32125i	−0.0448472	+	0.0776776i
$894$	0.539189	+	0.933903i	0.0180332	+	0.0312344i
$895$		0			0
$896$	−55.2951			−1.84728
$897$	−11.1206	−	28.5465i	−0.371307	−	0.953140i
$898$	4.29914			0.143464
$899$	5.35218	+	9.27024i	0.178505	+	0.309180i
$900$		0			0
$901$	19.8082	−	34.3088i	0.659906	−	1.14299i
$902$	6.91500			0.230244
$903$	3.81351	−	6.60519i	0.126906	−	0.219807i
$904$	3.07838	−	5.33191i	0.102385	−	0.177337i
$905$		0			0
$906$	2.31965	−	4.01776i	0.0770653	−	0.133481i
$907$	−23.1526	−	40.1014i	−0.768768	−	1.33154i	−0.938231	−	0.346008i	$-0.887537\pi$
$907$	−23.1526	−	40.1014i	−0.768768	−	1.33154i	0.169464	−	0.985536i	$-0.445796\pi$
$908$	−17.8443	−	30.9072i	−0.592184	−	1.02569i
$909$	12.4969			0.414497
$910$		0			0
$911$	−40.6947			−1.34828			−0.674138	−	0.738605i	$-0.735485\pi$
$911$	−40.6947			−1.34828			−0.674138	+	0.738605i	$0.735485\pi$
$912$	−5.81658	−	10.0746i	−0.192606	−	0.333604i
$913$	−7.41855	−	12.8493i	−0.245518	−	0.425250i
$914$	0.703414	−	1.21835i	0.0232669	−	0.0402994i
$915$		0			0
$916$	−9.87322	+	17.1009i	−0.326220	+	0.565030i
$917$	−28.0706	+	48.6197i	−0.926972	+	1.60556i
$918$	−1.55252			−0.0512408
$919$	22.2937	−	38.6138i	0.735402	−	1.27375i	−0.219145	−	0.975692i	$-0.570327\pi$
$919$	22.2937	−	38.6138i	0.735402	−	1.27375i	0.954547	−	0.298061i	$-0.0963398\pi$
$920$		0			0
$921$	−11.1212	−	19.2624i	−0.366455	−	0.634718i
$922$	−16.2185			−0.534128
$923$	2.73759	+	7.02736i	0.0901090	+	0.231308i
$924$	28.0533			0.922887
$925$		0			0
$926$	−1.71674	−	2.97349i	−0.0564157	−	0.0977149i
$927$	3.42522	−	5.93265i	0.112499	−	0.194854i
$928$	−18.4703			−0.606316
$929$	−14.4885	+	25.0948i	−0.475353	+	0.823335i	−0.999601	−	0.0282300i	$-0.991013\pi$
$929$	−14.4885	+	25.0948i	−0.475353	+	0.823335i	0.524249	+	0.851565i	$0.324346\pi$
$930$		0			0
$931$	79.7829			2.61478
$932$	3.18956	−	5.52448i	0.104478	−	0.180960i
$933$	0.202610	+	0.350931i	0.00663315	+	0.0114890i
$934$	−0.557770	−	0.966086i	−0.0182508	−	0.0316113i
$935$		0			0
$936$	−2.61757	−	6.71925i	−0.0855578	−	0.219626i
$937$	53.1871			1.73755			0.868774	−	0.495209i	$-0.164909\pi$
$937$	53.1871			1.73755			0.868774	+	0.495209i	$0.164909\pi$
$938$	−16.6326	−	28.8084i	−0.543072	−	0.940629i
$939$	−0.176752	−	0.306143i	−0.00576808	−	0.00999061i
$940$		0			0
$941$	26.3617			0.859368			0.429684	−	0.902979i	$-0.358625\pi$
$941$	26.3617			0.859368			0.429684	+	0.902979i	$0.358625\pi$
$942$	0.244870	−	0.424128i	0.00797830	−	0.0138188i
$943$	−15.9383	+	27.6059i	−0.519021	+	0.898971i
$944$	19.6697			0.640193
$945$		0			0
$946$	−1.46412	−	2.53594i	−0.0476028	−	0.0824504i
$947$	−25.3890	−	43.9751i	−0.825032	−	1.42900i	−0.901895	−	0.431956i	$-0.857824\pi$
$947$	−25.3890	−	43.9751i	−0.825032	−	1.42900i	0.0768629	−	0.997042i	$-0.475510\pi$
$948$	−3.78151			−0.122818
$949$	12.4916	−	15.5831i	0.405494	−	0.505850i
$950$		0			0
$951$	12.6514	+	21.9129i	0.410250	+	0.710574i
$952$	−13.8238	−	23.9435i	−0.448031	−	0.776012i
$953$	−10.4163	+	18.0415i	−0.337417	+	0.584423i	−0.983946	−	0.178466i	$-0.942886\pi$
$953$	−10.4163	+	18.0415i	−0.337417	+	0.584423i	0.646529	+	0.762889i	$0.276220\pi$
$954$	7.41855			0.240184
$955$		0			0
$956$	23.1545	−	40.1047i	0.748870	−	1.29708i
$957$	12.0000			0.387905
$958$	−3.10310	+	5.37473i	−0.100257	+	0.173650i
$959$	−22.2703	−	38.5733i	−0.719146	−	1.24560i
$960$		0			0
$961$	−21.7009			−0.700028
$962$	−1.89147	−	4.85537i	−0.0609834	−	0.156544i
$963$	−15.5597			−0.501405
$964$	−20.1678	−	34.9317i	−0.649562	−	1.12507i
$965$		0			0
$966$	10.9977	−	19.0486i	0.353846	−	0.612880i
$967$	5.92777			0.190624			0.0953120	−	0.995447i	$-0.469615\pi$
$967$	5.92777			0.190624			0.0953120	+	0.995447i	$0.469615\pi$
$968$	0.686489	−	1.18903i	0.0220646	−	0.0382170i
$969$	7.15676	−	12.3959i	0.229908	−	0.398213i
$970$		0			0
$971$	−5.24846	+	9.09061i	−0.168431	+	0.291731i	−0.937868	−	0.346991i	$-0.887203\pi$
$971$	−5.24846	+	9.09061i	−0.168431	+	0.291731i	0.769437	+	0.638722i	$0.220537\pi$
$972$	0.854638	+	1.48028i	0.0274125	+	0.0474799i
$973$	−31.0035	−	53.6996i	−0.993927	−	1.72153i
$974$	−10.8638			−0.348097
$975$		0			0
$976$	−7.13624			−0.228425
$977$	26.6609	+	46.1780i	0.852957	+	1.47736i	0.878528	+	0.477692i	$0.158526\pi$
$977$	26.6609	+	46.1780i	0.852957	+	1.47736i	−0.0255707	+	0.999673i	$0.508140\pi$
$978$	−3.94800	−	6.83814i	−0.126243	−	0.218660i
$979$	−11.9877	+	20.7633i	−0.383129	+	0.663599i
$980$		0			0
$981$	−7.91855	+	13.7153i	−0.252820	+	0.437897i
$982$	5.89917	−	10.2177i	0.188250	−	0.326058i
$983$	−21.7275			−0.693000			−0.346500	−	0.938050i	$-0.612630\pi$
$983$	−21.7275			−0.693000			−0.346500	+	0.938050i	$0.612630\pi$
$984$	−3.75154	+	6.49785i	−0.119595	+	0.207144i
$985$		0			0
$986$	−2.72487	−	4.71962i	−0.0867777	−	0.150303i
$987$	2.58864			0.0823972
$988$	30.2823	+	4.64250i	0.963409	+	0.147697i
$989$	13.4985			0.429228
$990$		0			0
$991$	4.37823	+	7.58331i	0.139079	+	0.240892i	0.927148	−	0.374695i	$-0.122252\pi$
$991$	4.37823	+	7.58331i	0.139079	+	0.240892i	−0.788069	+	0.615587i	$0.788919\pi$
$992$	−8.02279	+	13.8959i	−0.254724	+	0.441194i
$993$	4.60197			0.146039
$994$	−2.70734	+	4.68925i	−0.0858715	+	0.148734i
$995$		0			0
$996$	7.41855			0.235066
$997$	1.72960	−	2.99576i	0.0547770	−	0.0948766i	−0.837337	−	0.546688i	$-0.815889\pi$
$997$	1.72960	−	2.99576i	0.0547770	−	0.0948766i	0.892114	+	0.451811i	$0.149222\pi$
$998$	6.42243	+	11.1240i	0.203298	+	0.352123i
$999$	1.34017	+	2.32125i	0.0424012	+	0.0734410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.i.m.601.2		6
5.2	odd	4		975.2.bb.j.874.4		12
5.3	odd	4		975.2.bb.j.874.3		12
5.4	even	2		195.2.i.e.16.2	✓	6
13.9	even	3	inner	975.2.i.m.451.2		6
15.14	odd	2		585.2.j.g.406.2		6
65.9	even	6		195.2.i.e.61.2	yes	6
65.22	odd	12		975.2.bb.j.724.3		12
65.29	even	6		2535.2.a.y.1.2		3
65.48	odd	12		975.2.bb.j.724.4		12
65.49	even	6		2535.2.a.z.1.2		3
195.29	odd	6		7605.2.a.bu.1.2		3
195.74	odd	6		585.2.j.g.451.2		6
195.179	odd	6		7605.2.a.bt.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.e.16.2	✓	6	5.4	even	2
195.2.i.e.61.2	yes	6	65.9	even	6
585.2.j.g.406.2		6	15.14	odd	2
585.2.j.g.451.2		6	195.74	odd	6
975.2.i.m.451.2		6	13.9	even	3	inner
975.2.i.m.601.2		6	1.1	even	1	trivial
975.2.bb.j.724.3		12	65.22	odd	12
975.2.bb.j.724.4		12	65.48	odd	12
975.2.bb.j.874.3		12	5.3	odd	4
975.2.bb.j.874.4		12	5.2	odd	4
2535.2.a.y.1.2		3	65.29	even	6
2535.2.a.z.1.2		3	65.49	even	6
7605.2.a.bt.1.2		3	195.179	odd	6
7605.2.a.bu.1.2		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)

\(f(q)\)	\(=\)	\(q+(-0.269594 - 0.466951i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.854638 - 1.48028i) q^{4} +(-0.269594 + 0.466951i) q^{6} +(-2.40049 + 4.15777i) q^{7} -2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.269594 - 0.466951i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.854638 - 1.48028i) q^{4} +(-0.269594 + 0.466951i) q^{6} +(-2.40049 + 4.15777i) q^{7} -2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.70928 + 2.96055i) q^{11} -1.70928 q^{12} +(2.25513 - 2.81325i) q^{13} +2.58864 q^{14} +(-1.17009 - 2.02665i) q^{16} +(1.43968 - 2.49360i) q^{17} +0.539189 q^{18} +(-2.48554 + 4.30507i) q^{19} +4.80098 q^{21} +(0.921622 - 1.59630i) q^{22} +(4.24846 + 7.35856i) q^{23} +(1.00000 + 1.73205i) q^{24} +(-1.92162 - 0.294598i) q^{26} +1.00000 q^{27} +(4.10310 + 7.10678i) q^{28} +(1.75513 + 3.03997i) q^{29} +3.04945 q^{31} +(-2.63090 + 4.55685i) q^{32} +(1.70928 - 2.96055i) q^{33} -1.55252 q^{34} +(0.854638 + 1.48028i) q^{36} +(1.34017 + 2.32125i) q^{37} +2.68035 q^{38} +(-3.56391 - 0.546373i) q^{39} +(1.87577 + 3.24893i) q^{41} +(-1.29432 - 2.24183i) q^{42} +(0.794319 - 1.37580i) q^{43} +5.84324 q^{44} +(2.29072 - 3.96765i) q^{46} +0.539189 q^{47} +(-1.17009 + 2.02665i) q^{48} +(-8.02472 - 13.8992i) q^{49} -2.87936 q^{51} +(-2.23707 - 5.74253i) q^{52} +13.7587 q^{53} +(-0.269594 - 0.466951i) q^{54} +(4.80098 - 8.31555i) q^{56} +4.97107 q^{57} +(0.946346 - 1.63912i) q^{58} +(-4.20261 + 7.27913i) q^{59} +(1.52472 - 2.64090i) q^{61} +(-0.822114 - 1.42394i) q^{62} +(-2.40049 - 4.15777i) q^{63} -1.84324 q^{64} -1.84324 q^{66} +(-6.42522 - 11.1288i) q^{67} +(-2.46081 - 4.26225i) q^{68} +(4.24846 - 7.35856i) q^{69} +(-1.04585 + 1.81147i) q^{71} +(1.00000 - 1.73205i) q^{72} +5.53919 q^{73} +(0.722606 - 1.25159i) q^{74} +(4.24846 + 7.35856i) q^{76} -16.4124 q^{77} +(0.705681 + 1.81147i) q^{78} +2.21235 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.01139 - 1.75178i) q^{82} -4.34017 q^{83} +(4.10310 - 7.10678i) q^{84} -0.856576 q^{86} +(1.75513 - 3.03997i) q^{87} +(-3.41855 - 5.92110i) q^{88} +(3.50667 + 6.07372i) q^{89} +(6.28345 + 16.1295i) q^{91} +14.5236 q^{92} +(-1.52472 - 2.64090i) q^{93} +(-0.145362 - 0.251775i) q^{94} +5.26180 q^{96} +(-7.13449 + 12.3573i) q^{97} +(-4.32684 + 7.49431i) q^{98} -3.41855 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

Modular forms

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Representations

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Database

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