LMFDB - Embedded newform 775.2.e.g.676.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(501,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("775.501");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.e (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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 23x^{4} + x^{3} + 16x^{2} + 3x + 9 $ x^8 - x^7 + 6x^6 + 3x^5 + 23x^4 + x^3 + 16x^2 + 3*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			676.2
Root			$-0.392238 + 0.679376i$ of defining polynomial
Character	$\chi$	$=$	775.676
Dual form			775.2.e.g.501.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.784476 q^{2} +(-0.892238 - 1.54540i) q^{3} -1.38460 q^{4} +(0.699939 + 1.21233i) q^{6} +(-2.44756 - 4.23929i) q^{7} +2.65514 q^{8} +(-0.0921773 + 0.159656i) q^{9} +O(q^{10})$	\(q-0.784476 q^{2} +(-0.892238 - 1.54540i) q^{3} -1.38460 q^{4} +(0.699939 + 1.21233i) q^{6} +(-2.44756 - 4.23929i) q^{7} +2.65514 q^{8} +(-0.0921773 + 0.159656i) q^{9} +(2.31993 - 4.01823i) q^{11} +(1.23539 + 2.13976i) q^{12} +(2.21217 - 3.83158i) q^{13} +(1.92005 + 3.32562i) q^{14} +0.686305 q^{16} +(2.83551 + 4.91125i) q^{17} +(0.0723109 - 0.125246i) q^{18} +(-2.64749 - 4.58560i) q^{19} +(-4.36760 + 7.56491i) q^{21} +(-1.81993 + 3.15221i) q^{22} +1.98472 q^{23} +(-2.36901 - 4.10325i) q^{24} +(-1.73539 + 3.00578i) q^{26} -5.02445 q^{27} +(3.38888 + 5.86971i) q^{28} -0.0152811 q^{29} +(0.587896 - 5.53664i) q^{31} -5.84866 q^{32} -8.27971 q^{33} +(-2.22439 - 3.85276i) q^{34} +(0.127628 - 0.221059i) q^{36} +(-2.48442 - 4.30313i) q^{37} +(2.07690 + 3.59729i) q^{38} -7.89511 q^{39} +(-1.36473 + 2.36378i) q^{41} +(3.42628 - 5.93449i) q^{42} +(0.811983 + 1.40640i) q^{43} +(-3.21217 + 5.56363i) q^{44} -1.55696 q^{46} +5.40905 q^{47} +(-0.612347 - 1.06062i) q^{48} +(-8.48106 + 14.6896i) q^{49} +(5.05990 - 8.76401i) q^{51} +(-3.06296 + 5.30520i) q^{52} +(1.04737 - 1.81410i) q^{53} +3.94156 q^{54} +(-6.49859 - 11.2559i) q^{56} +(-4.72439 + 8.18289i) q^{57} +0.0119877 q^{58} +(3.59077 + 6.21939i) q^{59} -2.59280 q^{61} +(-0.461190 + 4.34336i) q^{62} +0.902436 q^{63} +3.21552 q^{64} +6.49523 q^{66} +(6.13221 - 10.6213i) q^{67} +(-3.92604 - 6.80010i) q^{68} +(-1.77084 - 3.06719i) q^{69} +(-2.37524 + 4.11404i) q^{71} +(-0.244743 + 0.423908i) q^{72} +(-5.03973 + 8.72907i) q^{73} +(1.94896 + 3.37570i) q^{74} +(3.66571 + 6.34920i) q^{76} -22.7126 q^{77} +6.19353 q^{78} +(3.55960 + 6.16541i) q^{79} +(4.75954 + 8.24376i) q^{81} +(1.07060 - 1.85433i) q^{82} +(-5.10471 + 8.84161i) q^{83} +(6.04737 - 10.4744i) q^{84} +(-0.636981 - 1.10328i) q^{86} +(0.0136344 + 0.0236155i) q^{87} +(6.15972 - 10.6689i) q^{88} -0.934844 q^{89} -21.6576 q^{91} -2.74804 q^{92} +(-9.08087 + 4.03147i) q^{93} -4.24327 q^{94} +(5.21840 + 9.03853i) q^{96} +15.9831 q^{97} +(6.65319 - 11.5237i) q^{98} +(0.427689 + 0.740779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9	$ 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9} + 4 q^{11} + 8 q^{12} - q^{13} - 8 q^{14} + 10 q^{16} + 12 q^{17} + 11 q^{18} - 5 q^{19} + 9 q^{21} - 10 q^{23} + 2 q^{24} - 12 q^{26} + 6 q^{27} - 4 q^{28} - 26 q^{29} + 19 q^{31} + 28 q^{32} - 8 q^{33} + 24 q^{34} - 5 q^{36} - 16 q^{37} - 9 q^{38} - 22 q^{39} - 4 q^{41} - 6 q^{42} + q^{43} - 7 q^{44} - 22 q^{46} - 20 q^{47} + 27 q^{48} - 37 q^{49} - 12 q^{51} - 21 q^{52} + q^{53} + 24 q^{54} - 29 q^{56} + 4 q^{57} - 26 q^{58} + 6 q^{59} - 2 q^{61} + 17 q^{62} - 24 q^{63} + 34 q^{64} + 2 q^{66} + 7 q^{67} + 5 q^{68} - 6 q^{69} + 12 q^{71} - 14 q^{72} - 20 q^{73} + 18 q^{74} - 23 q^{76} - 58 q^{77} - 22 q^{78} - 2 q^{79} + 12 q^{81} + 18 q^{82} + 4 q^{83} + 41 q^{84} - 13 q^{86} + 10 q^{88} + 54 q^{89} - 44 q^{91} - 86 q^{92} - 55 q^{93} - 48 q^{94} + 13 q^{96} + 18 q^{97} + 46 q^{98} - 7 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9 + 4 * q^11 + 8 * q^12 - q^13 - 8 * q^14 + 10 * q^16 + 12 * q^17 + 11 * q^18 - 5 * q^19 + 9 * q^21 - 10 * q^23 + 2 * q^24 - 12 * q^26 + 6 * q^27 - 4 * q^28 - 26 * q^29 + 19 * q^31 + 28 * q^32 - 8 * q^33 + 24 * q^34 - 5 * q^36 - 16 * q^37 - 9 * q^38 - 22 * q^39 - 4 * q^41 - 6 * q^42 + q^43 - 7 * q^44 - 22 * q^46 - 20 * q^47 + 27 * q^48 - 37 * q^49 - 12 * q^51 - 21 * q^52 + q^53 + 24 * q^54 - 29 * q^56 + 4 * q^57 - 26 * q^58 + 6 * q^59 - 2 * q^61 + 17 * q^62 - 24 * q^63 + 34 * q^64 + 2 * q^66 + 7 * q^67 + 5 * q^68 - 6 * q^69 + 12 * q^71 - 14 * q^72 - 20 * q^73 + 18 * q^74 - 23 * q^76 - 58 * q^77 - 22 * q^78 - 2 * q^79 + 12 * q^81 + 18 * q^82 + 4 * q^83 + 41 * q^84 - 13 * q^86 + 10 * q^88 + 54 * q^89 - 44 * q^91 - 86 * q^92 - 55 * q^93 - 48 * q^94 + 13 * q^96 + 18 * q^97 + 46 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.784476			−0.554708			−0.277354	−	0.960768i	$-0.589458\pi$
$2$	−0.784476			−0.554708			−0.277354	+	0.960768i	$0.589458\pi$
$3$	−0.892238	−	1.54540i	−0.515134	−	0.892238i	−0.999846	−	0.0175641i	$-0.994409\pi$
$3$	−0.892238	−	1.54540i	−0.515134	−	0.892238i	0.484712	−	0.874674i	$-0.338924\pi$
$4$	−1.38460			−0.692299
$5$		0			0
$5$		0			0
$6$	0.699939	+	1.21233i	0.285749	+	0.494932i
$7$	−2.44756	−	4.23929i	−0.925089	−	1.60230i	−0.791418	−	0.611275i	$-0.790657\pi$
$7$	−2.44756	−	4.23929i	−0.925089	−	1.60230i	−0.133671	−	0.991026i	$-0.542677\pi$
$8$	2.65514			0.938732
$9$	−0.0921773	+	0.159656i	−0.0307258	+	0.0532186i
$10$		0			0
$11$	2.31993	−	4.01823i	0.699484	−	1.21154i	−0.269161	−	0.963095i	$-0.586746\pi$
$11$	2.31993	−	4.01823i	0.699484	−	1.21154i	0.968645	−	0.248447i	$-0.0799203\pi$
$12$	1.23539	+	2.13976i	0.356626	+	0.617695i
$13$	2.21217	−	3.83158i	0.613544	−	1.06269i	−0.377094	−	0.926175i	$-0.623077\pi$
$13$	2.21217	−	3.83158i	0.613544	−	1.06269i	0.990638	−	0.136515i	$-0.0435901\pi$
$14$	1.92005	+	3.32562i	0.513155	+	0.888810i
$15$		0			0
$16$	0.686305			0.171576
$17$	2.83551	+	4.91125i	0.687713	+	1.19115i	0.972576	+	0.232585i	$0.0747184\pi$
$17$	2.83551	+	4.91125i	0.687713	+	1.19115i	−0.284863	+	0.958568i	$0.591948\pi$
$18$	0.0723109	−	0.125246i	0.0170438	−	0.0295208i
$19$	−2.64749	−	4.58560i	−0.607377	−	1.05201i	−0.991671	−	0.128797i	$-0.958888\pi$
$19$	−2.64749	−	4.58560i	−0.607377	−	1.05201i	0.384294	−	0.923211i	$-0.374445\pi$
$20$		0			0
$21$	−4.36760	+	7.56491i	−0.953089	+	1.65080i
$22$	−1.81993	+	3.15221i	−0.388010	+	0.672053i
$23$	1.98472			0.413842			0.206921	−	0.978358i	$-0.433656\pi$
$23$	1.98472			0.413842			0.206921	+	0.978358i	$0.433656\pi$
$24$	−2.36901	−	4.10325i	−0.483573	−	0.837572i
$25$		0			0
$26$	−1.73539	+	3.00578i	−0.340338	+	0.589483i
$27$	−5.02445			−0.966956
$28$	3.38888	+	5.86971i	0.640438	+	1.10927i
$29$	−0.0152811			−0.00283764			−0.00141882	−	0.999999i	$-0.500452\pi$
$29$	−0.0152811			−0.00283764			−0.00141882	+	0.999999i	$0.500452\pi$
$30$		0			0
$31$	0.587896	−	5.53664i	0.105589	−	0.994410i
$31$	0.587896	−	5.53664i	0.105589	−	0.994410i
$32$	−5.84866			−1.03391
$33$	−8.27971			−1.44131
$34$	−2.22439	−	3.85276i	−0.381480	−	0.660743i
$35$		0			0
$36$	0.127628	−	0.221059i	0.0212714	−	0.0368432i
$37$	−2.48442	−	4.30313i	−0.408435	−	0.707431i	0.586279	−	0.810109i	$-0.300592\pi$
$37$	−2.48442	−	4.30313i	−0.408435	−	0.707431i	−0.994715	+	0.102678i	$0.967259\pi$
$38$	2.07690	+	3.59729i	0.336917	+	0.583557i
$39$	−7.89511			−1.26423
$40$		0			0
$41$	−1.36473	+	2.36378i	−0.213135	+	0.369161i	−0.952694	−	0.303931i	$-0.901701\pi$
$41$	−1.36473	+	2.36378i	−0.213135	+	0.369161i	0.739559	+	0.673092i	$0.235034\pi$
$42$	3.42628	−	5.93449i	0.528687	−	0.915712i
$43$	0.811983	+	1.40640i	0.123826	+	0.214473i	0.921274	−	0.388915i	$-0.127150\pi$
$43$	0.811983	+	1.40640i	0.123826	+	0.214473i	−0.797447	+	0.603389i	$0.793817\pi$
$44$	−3.21217	+	5.56363i	−0.484252	+	0.838749i
$45$		0			0
$46$	−1.55696			−0.229562
$47$	5.40905			0.788991			0.394495	−	0.918898i	$-0.370919\pi$
$47$	5.40905			0.788991			0.394495	+	0.918898i	$0.370919\pi$
$48$	−0.612347	−	1.06062i	−0.0883847	−	0.153087i
$49$	−8.48106	+	14.6896i	−1.21158	+	2.09852i
$50$		0			0
$51$	5.05990	−	8.76401i	0.708528	−	1.22721i
$52$	−3.06296	+	5.30520i	−0.424756	+	0.735699i
$53$	1.04737	−	1.81410i	0.143868	−	0.249186i	−0.785082	−	0.619392i	$-0.787379\pi$
$53$	1.04737	−	1.81410i	0.143868	−	0.249186i	0.928950	+	0.370205i	$0.120713\pi$
$54$	3.94156			0.536379
$55$		0			0
$56$	−6.49859	−	11.2559i	−0.868411	−	1.50413i
$57$	−4.72439	+	8.18289i	−0.625761	+	1.08385i
$58$	0.0119877			0.00157406
$59$	3.59077	+	6.21939i	0.467478	+	0.809696i	0.999310	−	0.0371542i	$-0.0118293\pi$
$59$	3.59077	+	6.21939i	0.467478	+	0.809696i	−0.531831	+	0.846850i	$0.678496\pi$
$60$		0			0
$61$	−2.59280			−0.331974			−0.165987	−	0.986128i	$-0.553081\pi$
$61$	−2.59280			−0.331974			−0.165987	+	0.986128i	$0.553081\pi$
$62$	−0.461190	+	4.34336i	−0.0585712	+	0.551607i
$63$	0.902436			0.113696
$64$	3.21552			0.401941
$65$		0			0
$66$	6.49523			0.799508
$67$	6.13221	−	10.6213i	0.749169	−	1.29760i	−0.199052	−	0.979989i	$-0.563786\pi$
$67$	6.13221	−	10.6213i	0.749169	−	1.29760i	0.948221	−	0.317610i	$-0.102880\pi$
$68$	−3.92604	−	6.80010i	−0.476103	−	0.824634i
$69$	−1.77084	−	3.06719i	−0.213184	−	0.369246i
$70$		0			0
$71$	−2.37524	+	4.11404i	−0.281890	+	0.488247i	−0.971850	−	0.235600i	$-0.924295\pi$
$71$	−2.37524	+	4.11404i	−0.281890	+	0.488247i	0.689960	+	0.723847i	$0.257628\pi$
$72$	−0.244743	+	0.423908i	−0.0288433	+	0.0499580i
$73$	−5.03973	+	8.72907i	−0.589856	+	1.02166i	0.404395	+	0.914585i	$0.367482\pi$
$73$	−5.03973	+	8.72907i	−0.589856	+	1.02166i	−0.994251	+	0.107076i	$0.965851\pi$
$74$	1.94896	+	3.37570i	0.226562	+	0.392418i
$75$		0			0
$76$	3.66571	+	6.34920i	0.420486	+	0.728304i
$77$	−22.7126			−2.58834
$78$	6.19353			0.701279
$79$	3.55960	+	6.16541i	0.400486	+	0.693662i	0.993785	−	0.111320i	$-0.0355079\pi$
$79$	3.55960	+	6.16541i	0.400486	+	0.693662i	−0.593298	+	0.804983i	$0.702175\pi$
$80$		0			0
$81$	4.75954	+	8.24376i	0.528838	+	0.915974i
$82$	1.07060	−	1.85433i	0.118228	−	0.204777i
$83$	−5.10471	+	8.84161i	−0.560314	+	0.970493i	0.437154	+	0.899386i	$0.355986\pi$
$83$	−5.10471	+	8.84161i	−0.560314	+	0.970493i	−0.997469	+	0.0711064i	$0.977347\pi$
$84$	6.04737	−	10.4744i	0.659823	−	1.14285i
$85$		0			0
$86$	−0.636981	−	1.10328i	−0.0686874	−	0.118970i
$87$	0.0136344	+	0.0236155i	0.00146176	+	0.00253185i
$88$	6.15972	−	10.6689i	0.656628	−	1.13731i
$89$	−0.934844			−0.0990933			−0.0495466	−	0.998772i	$-0.515778\pi$
$89$	−0.934844			−0.0990933			−0.0495466	+	0.998772i	$0.515778\pi$
$90$		0			0
$91$	−21.6576			−2.27033
$92$	−2.74804			−0.286503
$93$	−9.08087	+	4.03147i	−0.941643	+	0.418044i
$94$	−4.24327			−0.437660
$95$		0			0
$96$	5.21840	+	9.03853i	0.532600	+	0.922491i
$97$	15.9831			1.62284			0.811421	−	0.584462i	$-0.198694\pi$
$97$	15.9831			1.62284			0.811421	+	0.584462i	$0.198694\pi$
$98$	6.65319	−	11.5237i	0.672073	−	1.16406i
$99$	0.427689	+	0.740779i	0.0429844	+	0.0744511i
$100$		0			0
$101$	14.0693			1.39995			0.699975	−	0.714167i	$-0.253194\pi$
$101$	14.0693			1.39995			0.699975	+	0.714167i	$0.253194\pi$
$102$	−3.96937	+	6.87515i	−0.393026	+	0.680742i
$103$	−0.496641	+	0.860208i	−0.0489355	+	0.0847588i	−0.889456	−	0.457022i	$-0.848916\pi$
$103$	−0.496641	+	0.860208i	−0.0489355	+	0.0847588i	0.840520	+	0.541780i	$0.182250\pi$
$104$	5.87360	−	10.1734i	0.575954	−	0.997581i
$105$		0			0
$106$	−0.821639	+	1.42312i	−0.0798047	+	0.138226i
$107$	−1.23252	−	2.13478i	−0.119152	−	0.206377i	0.800280	−	0.599627i	$-0.204684\pi$
$107$	−1.23252	−	2.13478i	−0.119152	−	0.206377i	−0.919432	+	0.393249i	$0.871351\pi$
$108$	6.95684			0.669423
$109$	3.69548			0.353962			0.176981	−	0.984214i	$-0.443367\pi$
$109$	3.69548			0.353962			0.176981	+	0.984214i	$0.443367\pi$
$110$		0			0
$111$	−4.43338	+	7.67884i	−0.420798	+	0.728843i
$112$	−1.67977	−	2.90945i	−0.158723	−	0.274917i
$113$	3.40641	−	5.90008i	0.320448	−	0.555033i	−0.660132	−	0.751150i	$-0.729500\pi$
$113$	3.40641	−	5.90008i	0.320448	−	0.555033i	0.980581	+	0.196116i	$0.0628331\pi$
$114$	3.70617	−	6.41928i	0.347115	−	0.601220i
$115$		0			0
$116$	0.0211582			0.00196449
$117$	0.407823	+	0.706370i	0.0377032	+	0.0653039i
$118$	−2.81687	−	4.87897i	−0.259314	−	0.449145i
$119$	13.8801	−	24.0411i	1.27239	−	2.20385i
$120$		0			0
$121$	−5.26412	−	9.11773i	−0.478557	−	0.828885i
$122$	2.03399			0.184148
$123$	4.87066			0.439173
$124$	−0.813999	+	7.66602i	−0.0730992	+	0.688429i
$125$		0			0
$126$	−0.707939			−0.0630683
$127$	1.88717	+	3.26867i	0.167459	+	0.290047i	0.937526	−	0.347916i	$-0.113110\pi$
$127$	1.88717	+	3.26867i	0.167459	+	0.290047i	−0.770067	+	0.637963i	$0.779777\pi$
$128$	9.17482			0.810947
$129$	1.44896	−	2.50968i	0.127574	−	0.220965i
$130$		0			0
$131$	−5.37158	−	9.30385i	−0.469317	−	0.812881i	0.530067	−	0.847956i	$-0.322167\pi$
$131$	−5.37158	−	9.30385i	−0.469317	−	0.812881i	−0.999385	+	0.0350741i	$0.988833\pi$
$132$	11.4641			0.997819
$133$	−12.9598	+	22.4470i	−1.12376	+	1.94640i
$134$	−4.81057	+	8.33216i	−0.415570	+	0.719789i
$135$		0			0
$136$	7.52867	+	13.0400i	0.645578	+	1.11817i
$137$	1.68466	−	2.91791i	0.143930	−	0.249294i	−0.785043	−	0.619441i	$-0.787359\pi$
$137$	1.68466	−	2.91791i	0.143930	−	0.249294i	0.928973	+	0.370147i	$0.120693\pi$
$138$	1.38918	+	2.40614i	0.118255	+	0.204824i
$139$	−8.44975			−0.716699			−0.358349	−	0.933588i	$-0.616660\pi$
$139$	−8.44975			−0.716699			−0.358349	+	0.933588i	$0.616660\pi$
$140$		0			0
$141$	−4.82616	−	8.35915i	−0.406436	−	0.703968i
$142$	1.86332	−	3.22737i	0.156367	−	0.270835i
$143$	−10.2641	−	17.7780i	−0.858329	−	1.48667i
$144$	−0.0632617	+	0.109573i	−0.00527181	+	0.00913104i
$145$		0			0
$146$	3.95355	−	6.84775i	0.327198	−	0.566724i
$147$	30.2685			2.49650
$148$	3.43991	+	5.95811i	0.282759	+	0.489753i
$149$	−0.417479	−	0.723095i	−0.0342012	−	0.0592382i	0.848418	−	0.529327i	$-0.177555\pi$
$149$	−0.417479	−	0.723095i	−0.0342012	−	0.0592382i	−0.882619	+	0.470088i	$0.844222\pi$
$150$		0			0
$151$	2.63129			0.214131			0.107066	−	0.994252i	$-0.465854\pi$
$151$	2.63129			0.214131			0.107066	+	0.994252i	$0.465854\pi$
$152$	−7.02946	−	12.1754i	−0.570164	−	0.987553i
$153$	−1.04548			−0.0845220
$154$	17.8175			1.43577
$155$		0			0
$156$	10.9316			0.875224
$157$	0.383990			0.0306458			0.0153229	−	0.999883i	$-0.495122\pi$
$157$	0.383990			0.0306458			0.0153229	+	0.999883i	$0.495122\pi$
$158$	−2.79242	−	4.83661i	−0.222153	−	0.384780i
$159$	−3.73803			−0.296445
$160$		0			0
$161$	−4.85771	−	8.41380i	−0.382841	−	0.663100i
$162$	−3.73374	−	6.46703i	−0.293351	−	0.508098i
$163$	−13.8884			−1.08782			−0.543911	−	0.839143i	$-0.683057\pi$
$163$	−13.8884			−1.08782			−0.543911	+	0.839143i	$0.683057\pi$
$164$	1.88960	−	3.27289i	0.147553	−	0.255570i
$165$		0			0
$166$	4.00452	−	6.93603i	0.310811	−	0.538340i
$167$	11.4564	+	19.8431i	0.886525	+	1.53551i	0.843956	+	0.536412i	$0.180221\pi$
$167$	11.4564	+	19.8431i	0.886525	+	1.53551i	0.0425684	+	0.999094i	$0.486446\pi$
$168$	−11.5966	+	20.0859i	−0.894696	+	1.54966i
$169$	−3.28735	−	5.69386i	−0.252873	−	0.437989i
$170$		0			0
$171$	0.976155			0.0746485
$172$	−1.12427	−	1.94729i	−0.0857247	−	0.148480i
$173$	11.1056	−	19.2355i	0.844345	−	1.46245i	−0.0418431	−	0.999124i	$-0.513323\pi$
$173$	11.1056	−	19.2355i	0.844345	−	1.46245i	0.886188	−	0.463325i	$-0.153344\pi$
$174$	−0.0106959	−	0.0185258i	−0.000810852	−	0.00140444i
$175$		0			0
$176$	1.59218	−	2.75773i	0.120015	−	0.207872i
$177$	6.40764	−	11.0984i	0.481628	−	0.834204i
$178$	0.733363			0.0549679
$179$	−3.04309	−	5.27079i	−0.227451	−	0.393957i	0.729601	−	0.683873i	$-0.239706\pi$
$179$	−3.04309	−	5.27079i	−0.227451	−	0.393957i	−0.957052	+	0.289916i	$0.906373\pi$
$180$		0			0
$181$	−10.0160	+	17.3483i	−0.744485	+	1.28949i	0.205950	+	0.978563i	$0.433972\pi$
$181$	−10.0160	+	17.3483i	−0.744485	+	1.28949i	−0.950435	+	0.310923i	$0.899362\pi$
$182$	16.9899			1.25937
$183$	2.31339	+	4.00691i	0.171011	+	0.296199i
$184$	5.26970			0.388487
$185$		0			0
$186$	7.12373	−	3.16259i	0.522337	−	0.231892i
$187$	26.3127			1.92418
$188$	−7.48936			−0.546217
$189$	12.2976	+	21.3001i	0.894521	+	1.54936i
$190$		0			0
$191$	−1.71124	+	2.96396i	−0.123821	+	0.214465i	−0.921272	−	0.388920i	$-0.872848\pi$
$191$	−1.71124	+	2.96396i	−0.123821	+	0.214465i	0.797450	+	0.603385i	$0.206182\pi$
$192$	−2.86901	−	4.96928i	−0.207053	−	0.358627i
$193$	0.745047	+	1.29046i	0.0536296	+	0.0928893i	0.891594	−	0.452836i	$-0.149588\pi$
$193$	0.745047	+	1.29046i	0.0536296	+	0.0928893i	−0.837964	+	0.545725i	$0.816254\pi$
$194$	−12.5384			−0.900204
$195$		0			0
$196$	11.7428	−	20.3392i	0.838775	−	1.45280i
$197$	0.447556	−	0.775189i	0.0318870	−	0.0552299i	−0.849642	−	0.527361i	$-0.823182\pi$
$197$	0.447556	−	0.775189i	0.0318870	−	0.0552299i	0.881529	+	0.472131i	$0.156515\pi$
$198$	−0.335512	−	0.581124i	−0.0238438	−	0.0412987i
$199$	12.1799	−	21.0962i	0.863410	−	1.49547i	−0.00520820	−	0.999986i	$-0.501658\pi$
$199$	12.1799	−	21.0962i	0.863410	−	1.49547i	0.868618	−	0.495483i	$-0.165009\pi$
$200$		0			0
$201$	−21.8856			−1.54369
$202$	−11.0370			−0.776564
$203$	0.0374015	+	0.0647812i	0.00262507	+	0.00454675i
$204$	−7.00593	+	12.1346i	−0.490513	+	0.849594i
$205$		0			0
$206$	0.389603	−	0.674812i	0.0271449	−	0.0470164i
$207$	−0.182946	+	0.316872i	−0.0127156	+	0.0220241i
$208$	1.51822	−	2.62963i	0.105270	−	0.182332i
$209$	−24.5680			−1.69940
$210$		0			0
$211$	5.07518	+	8.79048i	0.349390	+	0.605161i	0.986141	−	0.165908i	$-0.0530555\pi$
$211$	5.07518	+	8.79048i	0.349390	+	0.605161i	−0.636751	+	0.771069i	$0.719722\pi$
$212$	−1.45019	+	2.51180i	−0.0995995	+	0.172511i
$213$	8.47713			0.580844
$214$	0.966880	+	1.67469i	0.0660946	+	0.114479i
$215$		0			0
$216$	−13.3406			−0.907713
$217$	−24.9103	+	11.0590i	−1.69102	+	0.750732i
$218$	−2.89901			−0.196346
$219$	17.9866			1.21542
$220$		0			0
$221$	25.0905			1.68777
$222$	3.47788	−	6.02386i	0.233420	−	0.404295i
$223$	6.34915	+	10.9970i	0.425170	+	0.736417i	0.996436	−	0.0843484i	$-0.0268809\pi$
$223$	6.34915	+	10.9970i	0.425170	+	0.736417i	−0.571266	+	0.820765i	$0.693548\pi$
$224$	14.3149	+	24.7942i	0.956456	+	1.65663i
$225$		0			0
$226$	−2.67225	+	4.62847i	−0.177755	+	0.307881i
$227$	0.692299	−	1.19910i	0.0459495	−	0.0795868i	−0.842136	−	0.539265i	$-0.818702\pi$
$227$	0.692299	−	1.19910i	0.0459495	−	0.0795868i	0.888085	+	0.459678i	$0.152035\pi$
$228$	6.54138	−	11.3300i	0.433213	−	0.750348i
$229$	5.48777	+	9.50510i	0.362642	+	0.628115i	0.988395	−	0.151907i	$-0.0485413\pi$
$229$	5.48777	+	9.50510i	0.362642	+	0.628115i	−0.625753	+	0.780022i	$0.715208\pi$
$230$		0			0
$231$	20.2650	+	35.1001i	1.33334	+	2.30942i
$232$	−0.0405735			−0.00266378
$233$	−19.6020			−1.28417			−0.642084	−	0.766634i	$-0.721930\pi$
$233$	−19.6020			−1.28417			−0.642084	+	0.766634i	$0.721930\pi$
$234$	−0.319927	−	0.554130i	−0.0209143	−	0.0362246i
$235$		0			0
$236$	−4.97177	−	8.61136i	−0.323635	−	0.560552i
$237$	6.35202	−	11.0020i	0.412608	−	0.714658i
$238$	−10.8886	+	18.8597i	−0.705806	+	1.22249i
$239$	11.1892	−	19.3803i	0.723772	−	1.25361i	−0.235705	−	0.971825i	$-0.575740\pi$
$239$	11.1892	−	19.3803i	0.723772	−	1.25361i	0.959477	−	0.281785i	$-0.0909266\pi$
$240$		0			0
$241$	−1.41639	−	2.45325i	−0.0912374	−	0.158028i	0.816795	−	0.576929i	$-0.195749\pi$
$241$	−1.41639	−	2.45325i	−0.0912374	−	0.158028i	−0.908032	+	0.418901i	$0.862416\pi$
$242$	4.12958	+	7.15264i	0.265459	+	0.459789i
$243$	0.956605	−	1.65689i	0.0613662	−	0.106289i
$244$	3.58998			0.229825
$245$		0			0
$246$	−3.82092			−0.243613
$247$	−23.4268			−1.49061
$248$	1.56094	−	14.7005i	0.0991199	−	0.933484i
$249$	18.2185			1.15455
$250$		0			0
$251$	6.55960	+	11.3616i	0.414038	+	0.717135i	0.995327	−	0.0965621i	$-0.0307846\pi$
$251$	6.55960	+	11.3616i	0.414038	+	0.717135i	−0.581289	+	0.813697i	$0.697451\pi$
$252$	−1.24951			−0.0787118
$253$	4.60440	−	7.97506i	0.289476	−	0.501388i
$254$	−1.48044	−	2.56419i	−0.0928909	−	0.160892i
$255$		0			0
$256$	−13.6285			−0.851780
$257$	2.57690	−	4.46332i	0.160742	−	0.278414i	−0.774393	−	0.632705i	$-0.781945\pi$
$257$	2.57690	−	4.46332i	0.160742	−	0.278414i	0.935135	+	0.354291i	$0.115278\pi$
$258$	−1.13668	+	1.96878i	−0.0707665	+	0.122571i
$259$	−12.1615	+	21.0643i	−0.755678	+	1.30887i
$260$		0			0
$261$	0.00140857	−	0.00243972i	8.71886e−5	−	0.000151015i
$262$	4.21388	+	7.29865i	0.260334	+	0.450912i
$263$	−15.3127			−0.944223			−0.472111	−	0.881539i	$-0.656508\pi$
$263$	−15.3127			−0.944223			−0.472111	+	0.881539i	$0.656508\pi$
$264$	−21.9837			−1.35301
$265$		0			0
$266$	10.1666	−	17.6091i	0.623357	−	1.07969i
$267$	0.834103	+	1.44471i	0.0510463	+	0.0884148i
$268$	−8.49065	+	14.7062i	−0.518649	+	0.898326i
$269$	−2.25954	+	3.91364i	−0.137766	+	0.238619i	−0.926651	−	0.375923i	$-0.877326\pi$
$269$	−2.25954	+	3.91364i	−0.137766	+	0.238619i	0.788884	+	0.614542i	$0.210659\pi$
$270$		0			0
$271$	7.52764			0.457272			0.228636	−	0.973512i	$-0.426574\pi$
$271$	7.52764			0.457272			0.228636	+	0.973512i	$0.426574\pi$
$272$	1.94603	+	3.37062i	0.117995	+	0.204374i
$273$	19.3237	+	33.4697i	1.16952	+	2.02568i
$274$	−1.32157	+	2.28903i	−0.0798392	+	0.138286i
$275$		0			0
$276$	2.45190	+	4.24682i	0.147587	+	0.255629i
$277$	3.22346			0.193679			0.0968394	−	0.995300i	$-0.469127\pi$
$277$	3.22346			0.193679			0.0968394	+	0.995300i	$0.469127\pi$
$278$	6.62863			0.397559
$279$	0.829766	+	0.604213i	0.0496768	+	0.0361733i
$280$		0			0
$281$	18.9844			1.13251			0.566256	−	0.824230i	$-0.308391\pi$
$281$	18.9844			1.13251			0.566256	+	0.824230i	$0.308391\pi$
$282$	3.78601	+	6.55755i	0.225453	+	0.390497i
$283$	−10.5124			−0.624895			−0.312447	−	0.949935i	$-0.601149\pi$
$283$	−10.5124			−0.624895			−0.312447	+	0.949935i	$0.601149\pi$
$284$	3.28876	−	5.69630i	0.195152	−	0.338013i
$285$		0			0
$286$	8.05196	+	13.9464i	0.476122	+	0.824668i
$287$	13.3610			0.788676
$288$	0.539114	−	0.933772i	0.0317676	−	0.0550231i
$289$	−7.58026	+	13.1294i	−0.445897	+	0.772317i
$290$		0			0
$291$	−14.2608	−	24.7004i	−0.835981	−	1.44796i
$292$	6.97800	−	12.0863i	0.408357	−	0.707294i
$293$	−0.595840	−	1.03202i	−0.0348093	−	0.0602915i	0.848096	−	0.529843i	$-0.177749\pi$
$293$	−0.595840	−	1.03202i	−0.0348093	−	0.0602915i	−0.882905	+	0.469551i	$0.844416\pi$
$294$	−23.7449			−1.38483
$295$		0			0
$296$	−6.59646	−	11.4254i	−0.383411	−	0.664088i
$297$	−11.6564	+	20.1894i	−0.676371	+	1.17151i
$298$	0.327502	+	0.567251i	0.0189717	+	0.0328599i
$299$	4.39053	−	7.60461i	0.253911	−	0.439786i
$300$		0			0
$301$	3.97475	−	6.88446i	0.229101	−	0.396814i
$302$	−2.06418			−0.118780
$303$	−12.5532	−	21.7428i	−0.721162	−	1.24909i
$304$	−1.81699	−	3.14712i	−0.104211	−	0.180500i
$305$		0			0
$306$	0.820153			0.0468850
$307$	−6.38991	−	11.0676i	−0.364691	−	0.631664i	0.624035	−	0.781396i	$-0.285492\pi$
$307$	−6.38991	−	11.0676i	−0.364691	−	0.631664i	−0.988727	+	0.149732i	$0.952159\pi$
$308$	31.4478			1.79191
$309$	1.77249			0.100833
$310$		0			0
$311$	−33.5839			−1.90437			−0.952183	−	0.305528i	$-0.901167\pi$
$311$	−33.5839			−1.90437			−0.952183	+	0.305528i	$0.901167\pi$
$312$	−20.9626			−1.18677
$313$	−3.78191	−	6.55045i	−0.213766	−	0.370254i	0.739124	−	0.673569i	$-0.235240\pi$
$313$	−3.78191	−	6.55045i	−0.213766	−	0.370254i	−0.952890	+	0.303316i	$0.901906\pi$
$314$	−0.301231			−0.0169995
$315$		0			0
$316$	−4.92861	−	8.53661i	−0.277256	−	0.480222i
$317$	−2.85630	−	4.94726i	−0.160426	−	0.277866i	0.774596	−	0.632457i	$-0.217953\pi$
$317$	−2.85630	−	4.94726i	−0.160426	−	0.277866i	−0.935021	+	0.354591i	$0.884620\pi$
$318$	2.93239			0.164440
$319$	−0.0354511	+	0.0614032i	−0.00198488	+	0.00343792i
$320$		0			0
$321$	−2.19940	+	3.80947i	−0.122758	+	0.212624i
$322$	3.81076	+	6.60042i	0.212365	+	0.367827i
$323$	15.0140	−	26.0050i	0.835402	−	1.44696i
$324$	−6.59004	−	11.4143i	−0.366114	−	0.634127i
$325$		0			0
$326$	10.8951			0.603424
$327$	−3.29724	−	5.71099i	−0.182338	−	0.315819i
$328$	−3.62355	+	6.27617i	−0.200077	+	0.346543i
$329$	−13.2389	−	22.9305i	−0.729887	−	1.26420i
$330$		0			0
$331$	13.0922	−	22.6763i	0.719611	−	1.24640i	−0.241543	−	0.970390i	$-0.577653\pi$
$331$	13.0922	−	22.6763i	0.719611	−	1.24640i	0.961154	−	0.276013i	$-0.0890133\pi$
$332$	7.06796	−	12.2421i	0.387905	−	0.671871i
$333$	0.916027			0.0501979
$334$	−8.98729	−	15.5664i	−0.491763	−	0.851758i
$335$		0			0
$336$	−2.99751	+	5.19184i	−0.163527	+	0.283238i
$337$	−14.3140			−0.779731			−0.389866	−	0.920872i	$-0.627479\pi$
$337$	−14.3140			−0.779731			−0.389866	+	0.920872i	$0.627479\pi$
$338$	2.57885	+	4.46669i	0.140271	+	0.242956i
$339$	−12.1573			−0.660295
$340$		0			0
$341$	−20.8836	−	15.2069i	−1.13091	−	0.823500i
$342$	−0.765771			−0.0414081
$343$	48.7656			2.63310
$344$	2.15592	+	3.73417i	0.116240	+	0.201333i
$345$		0			0
$346$	−8.71210	+	15.0898i	−0.468365	+	0.811233i
$347$	0.745047	+	1.29046i	0.0399962	+	0.0692755i	0.885331	−	0.464962i	$-0.153932\pi$
$347$	0.745047	+	1.29046i	0.0399962	+	0.0692755i	−0.845334	+	0.534238i	$0.820599\pi$
$348$	−0.0188782	−	0.0326980i	−0.00101198	−	0.00175280i
$349$	−8.37055			−0.448066			−0.224033	−	0.974582i	$-0.571922\pi$
$349$	−8.37055			−0.448066			−0.224033	+	0.974582i	$0.571922\pi$
$350$		0			0
$351$	−11.1149	+	19.2516i	−0.593270	+	1.02757i
$352$	−13.5685	+	23.5013i	−0.723202	+	1.25262i
$353$	0.775123	+	1.34255i	0.0412556	+	0.0714569i	0.885916	−	0.463846i	$-0.153531\pi$
$353$	0.775123	+	1.34255i	0.0412556	+	0.0714569i	−0.844660	+	0.535303i	$0.820198\pi$
$354$	−5.02664	+	8.70640i	−0.267163	+	0.462740i
$355$		0			0
$356$	1.29438			0.0686021
$357$	−49.5376			−2.62181
$358$	2.38723	+	4.13481i	0.126169	+	0.218531i
$359$	4.99780	−	8.65645i	0.263774	−	0.456870i	−0.703468	−	0.710727i	$-0.748366\pi$
$359$	4.99780	−	8.65645i	0.263774	−	0.456870i	0.967242	+	0.253857i	$0.0816994\pi$
$360$		0			0
$361$	−4.51846	+	7.82620i	−0.237814	+	0.411905i
$362$	7.85733	−	13.6093i	0.412972	−	0.715289i
$363$	−9.39370	+	16.2704i	−0.493042	+	0.853973i
$364$	29.9870			1.57175
$365$		0			0
$366$	−1.81480	−	3.14333i	−0.0948611	−	0.164304i
$367$	−1.86015	+	3.22187i	−0.0970988	+	0.168180i	−0.910483	−	0.413547i	$-0.864290\pi$
$367$	−1.86015	+	3.22187i	−0.0970988	+	0.168180i	0.813384	+	0.581727i	$0.197623\pi$
$368$	1.36212			0.0710055
$369$	−0.251594	−	0.435774i	−0.0130975	−	0.0226855i
$370$		0			0
$371$	−10.2540			−0.532362
$372$	12.5734	−	5.58196i	0.651898	−	0.289411i
$373$	2.66652			0.138067			0.0690335	−	0.997614i	$-0.478008\pi$
$373$	2.66652			0.138067			0.0690335	+	0.997614i	$0.478008\pi$
$374$	−20.6417			−1.06736
$375$		0			0
$376$	14.3618			0.740651
$377$	−0.0338044	+	0.0585510i	−0.00174102	+	0.00301553i
$378$	−9.64719	−	16.7094i	−0.496198	−	0.859440i
$379$	19.3850	+	33.5759i	0.995742	+	1.72468i	0.577702	+	0.816248i	$0.303950\pi$
$379$	19.3850	+	33.5759i	0.995742	+	1.72468i	0.418041	+	0.908428i	$0.362717\pi$
$380$		0			0
$381$	3.36760	−	5.83286i	0.172528	−	0.298827i
$382$	1.34243	−	2.32515i	0.0686846	−	0.118965i
$383$	3.00692	−	5.20813i	0.153646	−	0.266123i	−0.778919	−	0.627125i	$-0.784232\pi$
$383$	3.00692	−	5.20813i	0.153646	−	0.266123i	0.932565	+	0.361001i	$0.117565\pi$
$384$	−8.18612	−	14.1788i	−0.417746	−	0.723558i
$385$		0			0
$386$	−0.584471	−	1.01233i	−0.0297488	−	0.0515264i
$387$	−0.299386			−0.0152186
$388$	−22.1302			−1.12349
$389$	3.99694	+	6.92291i	0.202653	+	0.351006i	0.949382	−	0.314123i	$-0.101710\pi$
$389$	3.99694	+	6.92291i	0.202653	+	0.351006i	−0.746729	+	0.665128i	$0.768377\pi$
$390$		0			0
$391$	5.62769	+	9.74745i	0.284605	+	0.492950i
$392$	−22.5184	+	39.0029i	−1.13735	+	1.96995i
$393$	−9.58546	+	16.6025i	−0.483522	+	0.837485i
$394$	−0.351097	+	0.608117i	−0.0176880	+	0.0306365i
$395$		0			0
$396$	−0.592177	−	1.02568i	−0.0297580	−	0.0515424i
$397$	−2.54652	−	4.41070i	−0.127806	−	0.221366i	0.795020	−	0.606583i	$-0.207460\pi$
$397$	−2.54652	−	4.41070i	−0.127806	−	0.221366i	−0.922826	+	0.385216i	$0.874127\pi$
$398$	−9.55483	+	16.5495i	−0.478940	+	0.829549i
$399$	46.2528			2.31554
$400$		0			0
$401$	−11.5498			−0.576768			−0.288384	−	0.957515i	$-0.593118\pi$
$401$	−11.5498			−0.576768			−0.288384	+	0.957515i	$0.593118\pi$
$402$	17.1687			0.856297
$403$	−19.9136	−	14.5005i	−0.991966	−	0.722323i
$404$	−19.4803			−0.969184
$405$		0			0
$406$	−0.0293405	−	0.0508193i	−0.00145615	−	0.00252212i
$407$	−23.0546			−1.14278
$408$	13.4347	−	23.2696i	0.665118	−	1.15202i
$409$	−5.29732	−	9.17523i	−0.261936	−	0.453686i	0.704821	−	0.709386i	$-0.251027\pi$
$409$	−5.29732	−	9.17523i	−0.261936	−	0.453686i	−0.966756	+	0.255700i	$0.917694\pi$
$410$		0			0
$411$	−6.01246			−0.296573
$412$	0.687648	−	1.19104i	0.0338780	−	0.0586784i
$413$	17.5772	−	30.4446i	0.864918	−	1.49808i
$414$	0.143517	−	0.248578i	0.00705346	−	0.0122170i
$415$		0			0
$416$	−12.9382	+	22.4096i	−0.634348	+	1.09872i
$417$	7.53919	+	13.0583i	0.369196	+	0.639466i
$418$	19.2730			0.942673
$419$	−20.7227			−1.01237			−0.506186	−	0.862424i	$-0.668945\pi$
$419$	−20.7227			−1.01237			−0.506186	+	0.862424i	$0.668945\pi$
$420$		0			0
$421$	−9.26217	+	16.0426i	−0.451411	+	0.781866i	−0.998474	−	0.0552250i	$-0.982412\pi$
$421$	−9.26217	+	16.0426i	−0.451411	+	0.781866i	0.547063	+	0.837091i	$0.315746\pi$
$422$	−3.98136	−	6.89592i	−0.193810	−	0.335688i
$423$	−0.498591	+	0.863586i	−0.0242423	+	0.0419890i
$424$	2.78092	−	4.81669i	0.135053	−	0.233919i
$425$		0			0
$426$	−6.65011			−0.322199
$427$	6.34601	+	10.9916i	0.307105	+	0.531922i
$428$	1.70654	+	2.95581i	0.0824887	+	0.142875i
$429$	−18.3161	+	31.7244i	−0.884309	+	1.53167i
$430$		0			0
$431$	8.36291	+	14.4850i	0.402827	+	0.697718i	0.994066	−	0.108779i	$-0.0346942\pi$
$431$	8.36291	+	14.4850i	0.402827	+	0.697718i	−0.591239	+	0.806497i	$0.701361\pi$
$432$	−3.44831			−0.165907
$433$	20.9899			1.00871			0.504354	−	0.863497i	$-0.331731\pi$
$433$	20.9899			1.00871			0.504354	+	0.863497i	$0.331731\pi$
$434$	19.5416	−	8.67550i	0.938025	−	0.416437i
$435$		0			0
$436$	−5.11675			−0.245048
$437$	−5.25453	−	9.10112i	−0.251358	−	0.435366i
$438$	−14.1100			−0.674203
$439$	18.0602	−	31.2812i	0.861967	−	1.49297i	−0.00806128	−	0.999968i	$-0.502566\pi$
$439$	18.0602	−	31.2812i	0.861967	−	1.49297i	0.870028	−	0.493002i	$-0.164101\pi$
$440$		0			0
$441$	−1.56352	−	2.70810i	−0.0744534	−	0.128957i
$442$	−19.6829			−0.936219
$443$	−1.83894	+	3.18513i	−0.0873705	+	0.151330i	−0.906399	−	0.422423i	$-0.861180\pi$
$443$	−1.83894	+	3.18513i	−0.0873705	+	0.151330i	0.819028	+	0.573753i	$0.194513\pi$
$444$	6.13845	−	10.6321i	0.291318	−	0.504577i
$445$		0			0
$446$	−4.98075	−	8.62692i	−0.235845	−	0.408496i
$447$	−0.744981	+	1.29035i	−0.0352364	+	0.0610312i
$448$	−7.87017	−	13.6315i	−0.371831	−	0.644030i
$449$	−39.2798			−1.85373			−0.926865	−	0.375396i	$-0.877507\pi$
$449$	−39.2798			−1.85373			−0.926865	+	0.375396i	$0.877507\pi$
$450$		0			0
$451$	6.33215	+	10.9676i	0.298169	+	0.516445i
$452$	−4.71651	+	8.16924i	−0.221846	+	0.384249i
$453$	−2.34774	−	4.06640i	−0.110306	−	0.191056i
$454$	−0.543092	+	0.940662i	−0.0254886	+	0.0441475i
$455$		0			0
$456$	−12.5439	+	21.7267i	−0.587422	+	1.01744i
$457$	20.8924			0.977306			0.488653	−	0.872478i	$-0.337488\pi$
$457$	20.8924			0.977306			0.488653	+	0.872478i	$0.337488\pi$
$458$	−4.30503	−	7.45653i	−0.201161	−	0.348421i
$459$	−14.2469	−	24.6763i	−0.664988	−	1.15179i
$460$		0			0
$461$	28.7830			1.34056			0.670280	−	0.742109i	$-0.266174\pi$
$461$	28.7830			1.34056			0.670280	+	0.742109i	$0.266174\pi$
$462$	−15.8974	−	27.5352i	−0.739616	−	1.28105i
$463$	−30.2834			−1.40739			−0.703694	−	0.710503i	$-0.748467\pi$
$463$	−30.2834			−1.40739			−0.703694	+	0.710503i	$0.748467\pi$
$464$	−0.0104875			−0.000486871
$465$		0			0
$466$	15.3773			0.712338
$467$	−33.1760			−1.53520			−0.767602	−	0.640927i	$-0.778550\pi$
$467$	−33.1760			−1.53520			−0.767602	+	0.640927i	$0.778550\pi$
$468$	−0.564670	−	0.978038i	−0.0261019	−	0.0452098i
$469$	−60.0357			−2.77219
$470$		0			0
$471$	−0.342611	−	0.593419i	−0.0157867	−	0.0273433i
$472$	9.53398	+	16.5133i	0.438837	+	0.760088i
$473$	7.53497			0.346458
$474$	−4.98301	+	8.63082i	−0.228877	+	0.396427i
$475$		0			0
$476$	−19.2184	+	33.2873i	−0.880875	+	1.52572i
$477$	0.193088	+	0.334438i	0.00884089	+	0.0153129i
$478$	−8.77769	+	15.2034i	−0.401482	+	0.695388i
$479$	17.7474	+	30.7395i	0.810901	+	1.40452i	0.912234	+	0.409669i	$0.134356\pi$
$479$	17.7474	+	30.7395i	0.810901	+	1.40452i	−0.101333	+	0.994853i	$0.532311\pi$
$480$		0			0
$481$	−21.9837			−1.00237
$482$	1.11112	+	1.92452i	0.0506102	+	0.0876594i
$483$	−8.66847	+	15.0142i	−0.394429	+	0.683171i
$484$	7.28869	+	12.6244i	0.331304	+	0.573836i
$485$		0			0
$486$	−0.750433	+	1.29979i	−0.0340404	+	0.0589596i
$487$	−10.6853	+	18.5075i	−0.484199	+	0.838657i	−0.999835	−	0.0181507i	$-0.994222\pi$
$487$	−10.6853	+	18.5075i	−0.484199	+	0.838657i	0.515637	+	0.856807i	$0.327555\pi$
$488$	−6.88423			−0.311634
$489$	12.3918	+	21.4631i	0.560374	+	0.970597i
$490$		0			0
$491$	11.5615	−	20.0252i	0.521765	−	0.903724i	−0.477914	−	0.878407i	$-0.658607\pi$
$491$	11.5615	−	20.0252i	0.521765	−	0.903724i	0.999679	−	0.0253176i	$-0.00805971\pi$
$492$	−6.74390			−0.304039
$493$	−0.0433299	−	0.0750495i	−0.00195148	−	0.00338006i
$494$	18.3777			0.826854
$495$		0			0
$496$	0.403476	−	3.79982i	0.0181166	−	0.170617i
$497$	23.2542			1.04309
$498$	−14.2919			−0.640437
$499$	1.94530	+	3.36936i	0.0870837	+	0.150833i	0.906277	−	0.422684i	$-0.138912\pi$
$499$	1.94530	+	3.36936i	0.0870837	+	0.150833i	−0.819194	+	0.573517i	$0.805579\pi$
$500$		0			0
$501$	20.4437	−	35.4095i	0.913358	−	1.58198i
$502$	−5.14585	−	8.91287i	−0.229670	−	0.397801i
$503$	16.7719	+	29.0498i	0.747822	+	1.29527i	0.948865	+	0.315683i	$0.102234\pi$
$503$	16.7719	+	29.0498i	0.747822	+	1.29527i	−0.201043	+	0.979582i	$0.564433\pi$
$504$	2.39609			0.106730
$505$		0			0
$506$	−3.61204	+	6.25624i	−0.160575	+	0.278124i
$507$	−5.86620	+	10.1605i	−0.260527	+	0.451246i
$508$	−2.61297	−	4.52579i	−0.115932	−	0.200799i
$509$	17.9774	−	31.1379i	0.796836	−	1.38016i	−0.124830	−	0.992178i	$-0.539839\pi$
$509$	17.9774	−	31.1379i	0.796836	−	1.38016i	0.921666	−	0.387983i	$-0.126828\pi$
$510$		0			0
$511$	49.3401			2.18268
$512$	−7.65843			−0.338458
$513$	13.3022	+	23.0401i	0.587307	+	1.01725i
$514$	−2.02151	+	3.50136i	−0.0891651	+	0.154439i
$515$		0			0
$516$	−2.00623	+	3.47490i	−0.0883194	+	0.152974i
$517$	12.5486	−	21.7348i	0.551887	−	0.955896i
$518$	9.54040	−	16.5245i	0.419181	−	0.726043i
$519$	−39.6355			−1.73980
$520$		0			0
$521$	−7.26107	−	12.5765i	−0.318113	−	0.550988i	0.661981	−	0.749520i	$-0.269716\pi$
$521$	−7.26107	−	12.5765i	−0.318113	−	0.550988i	−0.980094	+	0.198532i	$0.936383\pi$
$522$	−0.00110499	+	0.00191390i	−4.83642e−5	+	8.37693e-5i
$523$	10.0623			0.439995			0.219998	−	0.975500i	$-0.429395\pi$
$523$	10.0623			0.439995			0.219998	+	0.975500i	$0.429395\pi$
$524$	7.43748	+	12.8821i	0.324908	+	0.562757i
$525$		0			0
$526$	12.0125			0.523768
$527$	28.8588	−	12.8119i	1.25711	−	0.558095i
$528$	−5.68240			−0.247295
$529$	−19.0609			−0.828734
$530$		0			0
$531$	−1.32395			−0.0574545
$532$	17.9441	−	31.0801i	0.777975	−	1.34749i
$533$	6.03802	+	10.4582i	0.261536	+	0.452993i
$534$	−0.654334	−	1.13334i	−0.0283158	−	0.0490444i
$535$		0			0
$536$	16.2819	−	28.2010i	0.703269	−	1.21810i
$537$	−5.43032	+	9.40560i	−0.234336	+	0.405881i
$538$	1.77255	−	3.07015i	0.0764202	−	0.132364i
$539$	39.3509	+	68.1577i	1.69496	+	2.93576i
$540$		0			0
$541$	−10.3092	−	17.8561i	−0.443228	−	0.767694i	0.554698	−	0.832051i	$-0.312834\pi$
$541$	−10.3092	−	17.8561i	−0.443228	−	0.767694i	−0.997927	+	0.0643572i	$0.979500\pi$
$542$	−5.90525			−0.253652
$543$	35.7467			1.53404
$544$	−16.5839	−	28.7242i	−0.711031	−	1.23154i
$545$		0			0
$546$	−15.1590	−	26.2562i	−0.648745	−	1.12366i
$547$	7.65178	−	13.2533i	0.327166	−	0.566669i	−0.654782	−	0.755818i	$-0.727240\pi$
$547$	7.65178	−	13.2533i	0.327166	−	0.566669i	0.981948	+	0.189149i	$0.0605729\pi$
$548$	−2.33257	+	4.04014i	−0.0996426	+	0.172586i
$549$	0.238997	−	0.413955i	0.0102001	−	0.0176672i
$550$		0			0
$551$	0.0404568	+	0.0700732i	0.00172352	+	0.00298522i
$552$	−4.70182	−	8.14380i	−0.200123	−	0.346623i
$553$	17.4246	−	30.1804i	0.740971	−	1.28340i
$554$	−2.52872			−0.107435
$555$		0			0
$556$	11.6995			0.496170
$557$	8.89777			0.377011			0.188505	−	0.982072i	$-0.439636\pi$
$557$	8.89777			0.377011			0.188505	+	0.982072i	$0.439636\pi$
$558$	−0.650931	−	0.473991i	−0.0275561	−	0.0200656i
$559$	7.18496			0.303892
$560$		0			0
$561$	−23.4772	−	40.6637i	−0.991209	−	1.71682i
$562$	−14.8928			−0.628214
$563$	−19.0351	+	32.9698i	−0.802234	+	1.38951i	0.115909	+	0.993260i	$0.463022\pi$
$563$	−19.0351	+	32.9698i	−0.802234	+	1.38951i	−0.918143	+	0.396250i	$0.870311\pi$
$564$	6.68229	+	11.5741i	0.281375	+	0.487356i
$565$		0			0
$566$	8.24669			0.346634
$567$	23.2985	−	40.3541i	0.978444	−	1.69471i
$568$	−6.30660	+	10.9233i	−0.264619	+	0.458333i
$569$	14.1077	−	24.4353i	0.591426	−	1.02438i	−0.402614	−	0.915370i	$-0.631898\pi$
$569$	14.1077	−	24.4353i	0.591426	−	1.02438i	0.994041	−	0.109010i	$-0.0347682\pi$
$570$		0			0
$571$	7.57886	−	13.1270i	0.317165	−	0.549347i	−0.662730	−	0.748858i	$-0.730602\pi$
$571$	7.57886	−	13.1270i	0.317165	−	0.549347i	0.979895	+	0.199512i	$0.0639356\pi$
$572$	14.2117	+	24.6154i	0.594220	+	1.02922i
$573$	6.10734			0.255138
$574$	−10.4814			−0.437485
$575$		0			0
$576$	−0.296398	+	0.513377i	−0.0123499	+	0.0213907i
$577$	−16.2321	−	28.1148i	−0.675751	−	1.17043i	−0.976249	−	0.216652i	$-0.930486\pi$
$577$	−16.2321	−	28.1148i	−0.675751	−	1.17043i	0.300498	−	0.953782i	$-0.402847\pi$
$578$	5.94653	−	10.2997i	0.247343	−	0.428411i
$579$	1.32952	−	2.30279i	0.0552529	−	0.0957008i
$580$		0			0
$581$	49.9762			2.07336
$582$	11.1872	+	19.3768i	0.463726	+	0.803196i
$583$	−4.85966	−	8.41718i	−0.201267	−	0.348604i
$584$	−13.3812	+	23.1769i	−0.553717	+	0.959066i
$585$		0			0
$586$	0.467422	+	0.809599i	0.0193090	+	0.0334442i
$587$	4.01652			0.165780			0.0828898	−	0.996559i	$-0.473585\pi$
$587$	4.01652			0.165780			0.0828898	+	0.996559i	$0.473585\pi$
$588$	−41.9097			−1.72833
$589$	−26.9452	+	11.9624i	−1.11026	+	0.492901i
$590$		0			0
$591$	−1.59730			−0.0657043
$592$	−1.70507	−	2.95326i	−0.0700778	−	0.121378i
$593$	24.9844			1.02598			0.512992	−	0.858393i	$-0.328537\pi$
$593$	24.9844			1.02598			0.512992	+	0.858393i	$0.328537\pi$
$594$	9.14414	−	15.8381i	0.375188	−	0.649845i
$595$		0			0
$596$	0.578040	+	1.00120i	0.0236775	+	0.0410106i
$597$	−43.4694			−1.77909
$598$	−3.44426	+	5.96564i	−0.140846	+	0.243953i
$599$	3.59340	−	6.22396i	0.146822	−	0.254304i	−0.783229	−	0.621733i	$-0.786429\pi$
$599$	3.59340	−	6.22396i	0.146822	−	0.254304i	0.930051	+	0.367429i	$0.119762\pi$
$600$		0			0
$601$	14.2079	+	24.6088i	0.579552	+	1.00381i	0.995531	+	0.0944387i	$0.0301056\pi$
$601$	14.2079	+	24.6088i	0.579552	+	1.00381i	−0.415979	+	0.909374i	$0.636561\pi$
$602$	−3.11809	+	5.40070i	−0.127084	+	0.220116i
$603$	1.13050	+	1.95809i	0.0460376	+	0.0797394i
$604$	−3.64328			−0.148243
$605$		0			0
$606$	9.84767	+	17.0567i	0.400034	+	0.692880i
$607$	11.5851	−	20.0659i	0.470224	−	0.814452i	−0.529196	−	0.848499i	$-0.677507\pi$
$607$	11.5851	−	20.0659i	0.470224	−	0.814452i	0.999420	+	0.0340478i	$0.0108399\pi$
$608$	15.4843	+	26.8196i	0.627971	+	1.08768i
$609$	0.0667420	−	0.115601i	0.00270452	−	0.00468437i
$610$		0			0
$611$	11.9657	−	20.7252i	0.484081	−	0.838453i
$612$	1.44757			0.0585145
$613$	−6.41313	−	11.1079i	−0.259024	−	0.448643i	0.706957	−	0.707257i	$-0.250068\pi$
$613$	−6.41313	−	11.1079i	−0.259024	−	0.448643i	−0.965981	+	0.258614i	$0.916734\pi$
$614$	5.01273	+	8.68230i	0.202297	+	0.350389i
$615$		0			0
$616$	−60.3050			−2.42976
$617$	16.7861	+	29.0743i	0.675782	+	1.17049i	0.976240	+	0.216693i	$0.0695272\pi$
$617$	16.7861	+	29.0743i	0.675782	+	1.17049i	−0.300458	+	0.953795i	$0.597139\pi$
$618$	−1.39047			−0.0559331
$619$	20.1245			0.808871			0.404435	−	0.914567i	$-0.367468\pi$
$619$	20.1245			0.808871			0.404435	+	0.914567i	$0.367468\pi$
$620$		0			0
$621$	−9.97212			−0.400168
$622$	26.3457			1.05637
$623$	2.28808	+	3.96308i	0.0916701	+	0.158777i
$624$	−5.41845			−0.216912
$625$		0			0
$626$	2.96681	+	5.13867i	0.118578	+	0.205383i
$627$	21.9205	+	37.9674i	0.875420	+	1.51627i
$628$	−0.531672			−0.0212160
$629$	14.0892	−	24.4032i	0.561772	−	0.973018i
$630$		0			0
$631$	−20.2901	+	35.1434i	−0.807734	+	1.39904i	0.106695	+	0.994292i	$0.465973\pi$
$631$	−20.2901	+	35.1434i	−0.807734	+	1.39904i	−0.914430	+	0.404745i	$0.867360\pi$
$632$	9.45122	+	16.3700i	0.375949	+	0.651163i
$633$	9.05654	−	15.6864i	0.359965	−	0.623478i
$634$	2.24070	+	3.88101i	0.0889896	+	0.154134i
$635$		0			0
$636$	5.17566			0.205228
$637$	37.5230	+	64.9917i	1.48672	+	2.57507i
$638$	0.0278106	−	0.0481693i	0.00110103	−	0.00190704i
$639$	−0.437887	−	0.758443i	−0.0173225	−	0.0300035i
$640$		0			0
$641$	14.0487	−	24.3331i	0.554892	−	0.961100i	−0.443020	−	0.896512i	$-0.646093\pi$
$641$	14.0487	−	24.3331i	0.554892	−	0.961100i	0.997912	−	0.0645889i	$-0.0205736\pi$
$642$	1.72537	−	2.98844i	0.0680951	−	0.117944i
$643$	11.5583			0.455816			0.227908	−	0.973683i	$-0.426811\pi$
$643$	11.5583			0.455816			0.227908	+	0.973683i	$0.426811\pi$
$644$	6.72597	+	11.6497i	0.265040	+	0.459064i
$645$		0			0
$646$	−11.7781	+	20.4003i	−0.463404	+	0.802640i
$647$	23.6826			0.931061			0.465530	−	0.885032i	$-0.345864\pi$
$647$	23.6826			0.931061			0.465530	+	0.885032i	$0.345864\pi$
$648$	12.6372	+	21.8883i	0.496437	+	0.859854i
$649$	33.3213			1.30797
$650$		0			0
$651$	39.3165	+	28.6292i	1.54094	+	1.12207i
$652$	19.2298			0.753098
$653$	−16.9308			−0.662553			−0.331276	−	0.943534i	$-0.607479\pi$
$653$	−16.9308			−0.662553			−0.331276	+	0.943534i	$0.607479\pi$
$654$	2.58661	+	4.48014i	0.101144	+	0.175187i
$655$		0			0
$656$	−0.936622	+	1.62228i	−0.0365689	+	0.0633392i
$657$	−0.929098	−	1.60924i	−0.0362476	−	0.0627826i
$658$	10.3856	+	17.9885i	0.404874	+	0.701263i
$659$	−11.5916			−0.451543			−0.225771	−	0.974180i	$-0.572490\pi$
$659$	−11.5916			−0.451543			−0.225771	+	0.974180i	$0.572490\pi$
$660$		0			0
$661$	−18.7895	+	32.5443i	−0.730826	+	1.26583i	0.225704	+	0.974196i	$0.427532\pi$
$661$	−18.7895	+	32.5443i	−0.730826	+	1.26583i	−0.956530	+	0.291632i	$0.905802\pi$
$662$	−10.2705	+	17.7890i	−0.399174	+	0.691390i
$663$	−22.3867	−	38.7749i	−0.869427	−	1.50589i
$664$	−13.5537	+	23.4757i	−0.525985	+	0.911033i
$665$		0			0
$666$	−0.718601			−0.0278452
$667$	−0.0303288			−0.00117433
$668$	−15.8625	−	27.4747i	−0.613740	−	1.06303i
$669$	11.3299	−	19.6240i	0.438039	−	0.758706i
$670$		0			0
$671$	−6.01510	+	10.4185i	−0.232210	+	0.402200i
$672$	25.5446	−	44.2446i	0.985406	−	1.70677i
$673$	−6.80263	+	11.7825i	−0.262222	+	0.454182i	−0.966832	−	0.255413i	$-0.917789\pi$
$673$	−6.80263	+	11.7825i	−0.262222	+	0.454182i	0.704610	+	0.709595i	$0.251122\pi$
$674$	11.2290			0.432523
$675$		0			0
$676$	4.55166	+	7.88370i	0.175064	+	0.303219i
$677$	−17.4751	+	30.2678i	−0.671624	+	1.16329i	0.305820	+	0.952089i	$0.401069\pi$
$677$	−17.4751	+	30.2678i	−0.671624	+	1.16329i	−0.977444	+	0.211197i	$0.932264\pi$
$678$	9.53713			0.366271
$679$	−39.1196	−	67.7572i	−1.50127	−	2.60028i
$680$		0			0
$681$	−2.47078			−0.0946805
$682$	16.3827	+	11.9294i	0.627326	+	0.456802i
$683$	1.22886			0.0470211			0.0235106	−	0.999724i	$-0.492516\pi$
$683$	1.22886			0.0470211			0.0235106	+	0.999724i	$0.492516\pi$
$684$	−1.35158			−0.0516790
$685$		0			0
$686$	−38.2555			−1.46060
$687$	9.79280	−	16.9616i	0.373619	−	0.647127i
$688$	0.557268	+	0.965216i	0.0212456	+	0.0367985i
$689$	−4.63393	−	8.02620i	−0.176539	−	0.305774i
$690$		0			0
$691$	23.9608	−	41.5014i	0.911513	−	1.57879i	0.0995857	−	0.995029i	$-0.468248\pi$
$691$	23.9608	−	41.5014i	0.911513	−	1.57879i	0.811928	−	0.583758i	$-0.198418\pi$
$692$	−15.3768	+	26.6334i	−0.584539	+	1.01245i
$693$	2.09359	−	3.62620i	0.0795288	−	0.137748i
$694$	−0.584471	−	1.01233i	−0.0221862	−	0.0384277i
$695$		0			0
$696$	0.0362012	+	0.0627024i	0.00137220	+	0.00237673i
$697$	−15.4788			−0.586303
$698$	6.56650			0.248546
$699$	17.4896	+	30.2929i	0.661518	+	1.14578i
$700$		0			0
$701$	−8.11235	−	14.0510i	−0.306399	−	0.530699i	0.671173	−	0.741301i	$-0.265791\pi$
$701$	−8.11235	−	14.0510i	−0.306399	−	0.530699i	−0.977572	+	0.210602i	$0.932458\pi$
$702$	8.71939	−	15.1024i	0.329092	−	0.570004i
$703$	−13.1550	+	22.7850i	−0.496148	+	0.859354i
$704$	7.45978	−	12.9207i	0.281151	−	0.486968i
$705$		0			0
$706$	−0.608066	−	1.05320i	−0.0228849	−	0.0396377i
$707$	−34.4355	−	59.6440i	−1.29508	−	2.24314i
$708$	−8.87200	+	15.3668i	−0.333430	+	0.577518i
$709$	2.16907			0.0814613			0.0407306	−	0.999170i	$-0.487031\pi$
$709$	2.16907			0.0814613			0.0407306	+	0.999170i	$0.487031\pi$
$710$		0			0
$711$	−1.31246			−0.0492210
$712$	−2.48214			−0.0930220
$713$	1.16681	−	10.9887i	0.0436973	−	0.411529i
$714$	38.8610			1.45434
$715$		0			0
$716$	4.21346	+	7.29792i	0.157464	+	0.272736i
$717$	−39.9339			−1.49136
$718$	−3.92066	+	6.79077i	−0.146318	+	0.253429i
$719$	7.68369	+	13.3085i	0.286553	+	0.496325i	0.972985	−	0.230870i	$-0.0741572\pi$
$719$	7.68369	+	13.3085i	0.286553	+	0.496325i	−0.686431	+	0.727194i	$0.740824\pi$
$720$		0			0
$721$	4.86223			0.181079
$722$	3.54462	−	6.13946i	0.131917	−	0.228487i
$723$	−2.52751	+	4.37777i	−0.0939990	+	0.162811i
$724$	13.8682	−	24.0204i	0.515406	−	0.892709i
$725$		0			0
$726$	7.36913	−	12.7637i	0.273494	−	0.473706i
$727$	16.7369	+	28.9892i	0.620738	+	1.07515i	0.989348	+	0.145566i	$0.0465005\pi$
$727$	16.7369	+	28.9892i	0.620738	+	1.07515i	−0.368610	+	0.929584i	$0.620166\pi$
$728$	−57.5038			−2.13123
$729$	25.1432			0.931228
$730$		0			0
$731$	−4.60477	+	7.97570i	−0.170314	+	0.294992i
$732$	−3.20312	−	5.54796i	−0.118391	−	0.205058i
$733$	11.4194	−	19.7791i	0.421787	−	0.730556i	−0.574328	−	0.818626i	$-0.694736\pi$
$733$	11.4194	−	19.7791i	0.421787	−	0.730556i	0.996114	+	0.0880696i	$0.0280698\pi$
$734$	1.45924	−	2.52748i	0.0538615	−	0.0932909i
$735$		0			0
$736$	−11.6079			−0.427875
$737$	−28.4526	−	49.2813i	−1.04806	−	1.81530i
$738$	0.197370	+	0.341854i	0.00726528	+	0.0125838i
$739$	24.0703	−	41.6910i	0.885440	−	1.53363i	0.0402321	−	0.999190i	$-0.487190\pi$
$739$	24.0703	−	41.6910i	0.885440	−	1.53363i	0.845208	−	0.534437i	$-0.179476\pi$
$740$		0			0
$741$	20.9023	+	36.2038i	0.767864	+	1.32998i
$742$	8.04403			0.295306
$743$	−6.88842			−0.252712			−0.126356	−	0.991985i	$-0.540328\pi$
$743$	−6.88842			−0.252712			−0.126356	+	0.991985i	$0.540328\pi$
$744$	−24.1110	+	10.7041i	−0.883950	+	0.392431i
$745$		0			0
$746$	−2.09182			−0.0765869
$747$	−0.941076	−	1.62999i	−0.0344322	−	0.0596383i
$748$	−36.4325			−1.33211
$749$	−6.03331	+	10.4500i	−0.220452	+	0.381835i
$750$		0			0
$751$	−20.7530	−	35.9453i	−0.757289	−	1.31166i	−0.944228	−	0.329292i	$-0.893190\pi$
$751$	−20.7530	−	35.9453i	−0.757289	−	1.31166i	0.186939	−	0.982372i	$-0.440143\pi$
$752$	3.71226			0.135372
$753$	11.7054	−	20.2744i	0.426570	−	0.738841i
$754$	0.0265188	−	0.0459318i	0.000965756	−	0.00167274i
$755$		0			0
$756$	−17.0273	−	29.4921i	−0.619275	−	1.07262i
$757$	16.4507	−	28.4935i	0.597912	−	1.03561i	−0.395216	−	0.918588i	$-0.629330\pi$
$757$	16.4507	−	28.4935i	0.597912	−	1.03561i	0.993129	−	0.117027i	$-0.0373363\pi$
$758$	−15.2071	−	26.3395i	−0.552347	−	0.956692i
$759$	−16.4329			−0.596476
$760$		0			0
$761$	16.4347	+	28.4657i	0.595756	+	1.03188i	0.993440	+	0.114357i	$0.0364808\pi$
$761$	16.4347	+	28.4657i	0.595756	+	1.03188i	−0.397684	+	0.917523i	$0.630186\pi$
$762$	−2.64180	+	4.57574i	−0.0957025	+	0.165762i
$763$	−9.04488	−	15.6662i	−0.327447	−	0.567154i
$764$	2.36938	−	4.10389i	0.0857212	−	0.148474i
$765$		0			0
$766$	−2.35885	+	4.08565i	−0.0852289	+	0.147621i
$767$	31.7735			1.14727
$768$	12.1598	+	21.0615i	0.438781	+	0.759990i
$769$	−12.6487	−	21.9082i	−0.456125	−	0.790032i	0.542627	−	0.839974i	$-0.317430\pi$
$769$	−12.6487	−	21.9082i	−0.456125	−	0.790032i	−0.998752	+	0.0499420i	$0.984096\pi$
$770$		0			0
$771$	−9.19682			−0.331215
$772$	−1.03159	−	1.78677i	−0.0371277	−	0.0643071i
$773$	34.6120			1.24491			0.622454	−	0.782657i	$-0.286136\pi$
$773$	34.6120			1.24491			0.622454	+	0.782657i	$0.286136\pi$
$774$	0.234861			0.00844190
$775$		0			0
$776$	42.4374			1.52341
$777$	43.4038			1.55710
$778$	−3.13551	−	5.43086i	−0.112413	−	0.194706i
$779$	14.4525			0.517814
$780$		0			0
$781$	11.0208	+	19.0886i	0.394355	+	0.683043i
$782$	−4.41479	−	7.64664i	−0.157873	−	0.273443i
$783$	0.0767794			0.00274387
$784$	−5.82059	+	10.0816i	−0.207878	+	0.360056i
$785$		0			0
$786$	7.51956	−	13.0243i	0.268214	−	0.464560i
$787$	−15.8838	−	27.5116i	−0.566197	−	0.980681i	−0.996937	−	0.0782055i	$-0.975081\pi$
$787$	−15.8838	−	27.5116i	−0.566197	−	0.980681i	0.430741	−	0.902476i	$-0.358252\pi$
$788$	−0.619684	+	1.07332i	−0.0220753	+	0.0382356i
$789$	13.6626	+	23.6643i	0.486401	+	0.842472i
$790$		0			0
$791$	−33.3496			−1.18577
$792$	1.13557	+	1.96687i	0.0403508	+	0.0698897i
$793$	−5.73569	+	9.93451i	−0.203680	+	0.352785i
$794$	1.99768	+	3.46008i	0.0708950	+	0.122794i
$795$		0			0
$796$	−16.8642	+	29.2097i	−0.597737	+	1.03531i
$797$	20.2693	−	35.1075i	0.717976	−	1.24357i	−0.243824	−	0.969819i	$-0.578402\pi$
$797$	20.2693	−	35.1075i	0.717976	−	1.24357i	0.961800	−	0.273752i	$-0.0882646\pi$
$798$	−36.2842			−1.28445
$799$	15.3374	+	26.5652i	0.542599	+	0.939809i
$800$		0			0
$801$	0.0861714	−	0.149253i	0.00304472	−	0.00527360i
$802$	9.06052			0.319938
$803$	23.3836	+	40.5016i	0.825190	+	1.42927i
$804$	30.3027			1.06869
$805$		0			0
$806$	15.6217	+	11.3753i	0.550252	+	0.400679i
$807$	8.06418			0.283873
$808$	37.3560			1.31418
$809$	−20.0350	−	34.7016i	−0.704392	−	1.22004i	−0.966911	−	0.255116i	$-0.917886\pi$
$809$	−20.0350	−	34.7016i	−0.704392	−	1.22004i	0.262519	−	0.964927i	$-0.415447\pi$
$810$		0			0
$811$	−12.6529	+	21.9155i	−0.444305	+	0.769558i	−0.998003	−	0.0631587i	$-0.979883\pi$
$811$	−12.6529	+	21.9155i	−0.444305	+	0.769558i	0.553699	+	0.832717i	$0.313216\pi$
$812$	−0.0517860	−	0.0896959i	−0.00181733	−	0.00314771i
$813$	−6.71645	−	11.6332i	−0.235556	−	0.407995i
$814$	18.0858			0.633908
$815$		0			0
$816$	3.47264	−	6.01478i	0.121567	−	0.210559i
$817$	4.29944	−	7.44685i	0.150418	−	0.260532i
$818$	4.15562	+	7.19775i	0.145298	+	0.251663i
$819$	1.99634	−	3.45776i	0.0697577	−	0.120824i
$820$		0			0
$821$	14.2890			0.498691			0.249345	−	0.968415i	$-0.419785\pi$
$821$	14.2890			0.498691			0.249345	+	0.968415i	$0.419785\pi$
$822$	4.71663			0.164511
$823$	−24.6255	−	42.6526i	−0.858391	−	1.48678i	−0.873463	−	0.486890i	$-0.838131\pi$
$823$	−24.6255	−	42.6526i	−0.858391	−	1.48678i	0.0150724	−	0.999886i	$-0.495202\pi$
$824$	−1.31865	+	2.28397i	−0.0459373	+	0.0795658i
$825$		0			0
$826$	−13.7889	+	23.8831i	−0.479777	+	0.830999i
$827$	24.5858	−	42.5839i	0.854933	−	1.48079i	−0.0217741	−	0.999763i	$-0.506931\pi$
$827$	24.5858	−	42.5839i	0.854933	−	1.48079i	0.876707	−	0.481025i	$-0.159735\pi$
$828$	0.253307	−	0.438740i	0.00880301	−	0.0152473i
$829$	41.2594			1.43300			0.716499	−	0.697588i	$-0.245743\pi$
$829$	41.2594			1.43300			0.716499	+	0.697588i	$0.245743\pi$
$830$		0			0
$831$	−2.87609	−	4.98153i	−0.0997705	−	0.172808i
$832$	7.11327	−	12.3205i	0.246608	−	0.427138i
$833$	−96.1925			−3.33287
$834$	−5.91431	−	10.2439i	−0.204796	−	0.354717i
$835$		0			0
$836$	34.0168			1.17649
$837$	−2.95385	+	27.8186i	−0.102100	+	0.961551i
$838$	16.2565			0.561571
$839$	−5.19276			−0.179274			−0.0896370	−	0.995974i	$-0.528571\pi$
$839$	−5.19276			−0.179274			−0.0896370	+	0.995974i	$0.528571\pi$
$840$		0			0
$841$	−28.9998			−0.999992
$842$	7.26595	−	12.5850i	0.250401	−	0.433708i
$843$	−16.9386	−	29.3385i	−0.583395	−	1.01047i
$844$	−7.02709	−	12.1713i	−0.241882	−	0.418952i
$845$		0			0
$846$	0.391133	−	0.677462i	0.0134474	−	0.0232916i
$847$	−25.7685	+	44.6323i	−0.885415	+	1.53358i
$848$	0.718817	−	1.24503i	0.0246843	−	0.0427544i
$849$	9.37953	+	16.2458i	0.321905	+	0.557555i
$850$		0			0
$851$	−4.93087	−	8.54051i	−0.169028	−	0.292765i
$852$	−11.7374			−0.402117
$853$	24.8051			0.849312			0.424656	−	0.905355i	$-0.360395\pi$
$853$	24.8051			0.849312			0.424656	+	0.905355i	$0.360395\pi$
$854$	−4.97830	−	8.62266i	−0.170354	−	0.295061i
$855$		0			0
$856$	−3.27250	−	5.66814i	−0.111852	−	0.193733i
$857$	−27.5952	+	47.7964i	−0.942635	+	1.63269i	−0.182218	+	0.983258i	$0.558328\pi$
$857$	−27.5952	+	47.7964i	−0.942635	+	1.63269i	−0.760418	+	0.649434i	$0.775006\pi$
$858$	14.3685	−	24.8870i	0.490533	−	0.849629i
$859$	−4.27922	+	7.41183i	−0.146005	+	0.252888i	−0.929748	−	0.368198i	$-0.879975\pi$
$859$	−4.27922	+	7.41183i	−0.146005	+	0.252888i	0.783742	+	0.621086i	$0.213308\pi$
$860$		0			0
$861$	−11.9212	−	20.6481i	−0.406274	−	0.703687i
$862$	−6.56051	−	11.3631i	−0.223452	−	0.387030i
$863$	16.0305	−	27.7656i	0.545685	−	0.945153i	−0.452879	−	0.891572i	$-0.649603\pi$
$863$	16.0305	−	27.7656i	0.545685	−	0.945153i	0.998563	−	0.0535814i	$-0.0170637\pi$
$864$	29.3863			0.999743
$865$		0			0
$866$	−16.4660			−0.559539
$867$	27.0536			0.918787
$868$	34.4908	−	15.3122i	1.17069	−	0.519731i
$869$	33.0320			1.12054
$870$		0			0
$871$	−27.1309	−	46.9922i	−0.919297	−	1.59227i
$872$	9.81199			0.332276
$873$	−1.47328	+	2.55180i	−0.0498631	+	0.0863653i
$874$	4.12205	+	7.13961i	0.139431	+	0.241501i
$875$		0			0
$876$	−24.9042			−0.841433
$877$	−7.45122	+	12.9059i	−0.251610	+	0.435801i	−0.963969	−	0.266014i	$-0.914293\pi$
$877$	−7.45122	+	12.9059i	−0.251610	+	0.435801i	0.712359	+	0.701815i	$0.247627\pi$
$878$	−14.1678	+	24.5393i	−0.478140	+	0.828163i
$879$	−1.06326	+	1.84162i	−0.0358629	+	0.0621164i
$880$		0			0
$881$	4.59614	−	7.96075i	0.154848	−	0.268205i	−0.778156	−	0.628071i	$-0.783845\pi$
$881$	4.59614	−	7.96075i	0.154848	−	0.268205i	0.933004	+	0.359867i	$0.117178\pi$
$882$	1.22654	+	2.12444i	0.0412999	+	0.0715336i
$883$	46.9198			1.57898			0.789489	−	0.613765i	$-0.210346\pi$
$883$	46.9198			1.57898			0.789489	+	0.613765i	$0.210346\pi$
$884$	−34.7402			−1.16844
$885$		0			0
$886$	1.44260	−	2.49866i	0.0484651	−	0.0839441i
$887$	23.1689	+	40.1297i	0.777936	+	1.34742i	0.933130	+	0.359540i	$0.117066\pi$
$887$	23.1689	+	40.1297i	0.777936	+	1.34742i	−0.155194	+	0.987884i	$0.549600\pi$
$888$	−11.7712	+	20.3884i	−0.395016	+	0.684188i
$889$	9.23789	−	16.0005i	0.309829	−	0.536639i
$890$		0			0
$891$	44.1671			1.47965
$892$	−8.79101	−	15.2265i	−0.294345	−	0.509820i
$893$	−14.3204	−	24.8037i	−0.479215	−	0.830025i
$894$	0.584420	−	1.01225i	0.0195459	−	0.0338545i
$895$		0			0
$896$	−22.4559	−	38.8947i	−0.750198	−	1.29938i
$897$	−15.6696			−0.523192
$898$	30.8141			1.02828
$899$	−0.00898372	+	0.0846062i	−0.000299624	+	0.00282177i
$900$		0			0
$901$	11.8794			0.395759
$902$	−4.96742	−	8.60383i	−0.165397	−	0.286476i
$903$	−14.1857			−0.472070
$904$	9.04449	−	15.6655i	0.300815	−	0.521027i
$905$		0			0
$906$	1.84174	+	3.18999i	0.0611878	+	0.105980i
$907$	−39.0882			−1.29790			−0.648951	−	0.760831i	$-0.724792\pi$
$907$	−39.0882			−1.29790			−0.648951	+	0.760831i	$0.724792\pi$
$908$	−0.958555	+	1.66027i	−0.0318108	+	0.0550979i
$909$	−1.29687	+	2.24625i	−0.0430145	+	0.0745033i
$910$		0			0
$911$	−12.5957	−	21.8164i	−0.417315	−	0.722811i	0.578353	−	0.815786i	$-0.303695\pi$
$911$	−12.5957	−	21.8164i	−0.417315	−	0.722811i	−0.995668	+	0.0929756i	$0.970362\pi$
$912$	−3.24237	+	5.61595i	−0.107366	+	0.185963i
$913$	23.6851	+	41.0238i	0.783862	+	1.35769i
$914$	−16.3896			−0.542120
$915$		0			0
$916$	−7.59836	−	13.1607i	−0.251057	−	0.434843i
$917$	−26.2945	+	45.5434i	−0.868321	+	1.50398i
$918$	11.1763	+	19.3580i	0.368874	+	0.638909i
$919$	−27.5322	+	47.6872i	−0.908204	+	1.57306i	−0.0916461	+	0.995792i	$0.529213\pi$
$919$	−27.5322	+	47.6872i	−0.908204	+	1.57306i	−0.816558	+	0.577264i	$0.804120\pi$
$920$		0			0
$921$	−11.4026	+	19.7499i	−0.375730	+	0.650783i
$922$	−22.5796			−0.743619
$923$	10.5089	+	18.2019i	0.345904	+	0.599123i
$924$	−28.0589	−	48.5995i	−0.923071	−	1.59881i
$925$		0			0
$926$	23.7566			0.780690
$927$	−0.0915581	−	0.158583i	−0.00300716	−	0.00520856i
$928$	0.0893742			0.00293385
$929$	−45.4497			−1.49115			−0.745577	−	0.666419i	$-0.767826\pi$
$929$	−45.4497			−1.49115			−0.745577	+	0.666419i	$0.767826\pi$
$930$		0			0
$931$	89.8142			2.94354
$932$	27.1408			0.889028
$933$	29.9648	+	51.9006i	0.981004	+	1.69915i
$934$	26.0258			0.851590
$935$		0			0
$936$	1.08282	+	1.87551i	0.0353932	+	0.0613029i
$937$	8.48062	+	14.6889i	0.277050	+	0.479864i	0.970650	−	0.240496i	$-0.0773100\pi$
$937$	8.48062	+	14.6889i	0.277050	+	0.479864i	−0.693600	+	0.720360i	$0.743977\pi$
$938$	47.0966			1.53776
$939$	−6.74872	+	11.6891i	−0.220236	+	0.381460i
$940$		0			0
$941$	−17.2001	+	29.7914i	−0.560706	+	0.971172i	0.436729	+	0.899593i	$0.356137\pi$
$941$	−17.2001	+	29.7914i	−0.560706	+	0.971172i	−0.997435	+	0.0715786i	$0.977196\pi$
$942$	0.268770	+	0.465523i	0.00875700	+	0.0151676i
$943$	−2.70861	+	4.69145i	−0.0882044	+	0.152774i
$944$	2.46436	+	4.26840i	0.0802082	+	0.138925i
$945$		0			0
$946$	−5.91100			−0.192183
$947$	−4.66229	−	8.07532i	−0.151504	−	0.262413i	0.780277	−	0.625435i	$-0.215078\pi$
$947$	−4.66229	−	8.07532i	−0.151504	−	0.262413i	−0.931781	+	0.363022i	$0.881745\pi$
$948$	−8.79499	+	15.2334i	−0.285648	+	0.494757i
$949$	22.2974	+	38.6203i	0.723806	+	1.25367i
$950$		0			0
$951$	−5.09700	+	8.82826i	−0.165282	+	0.286276i
$952$	36.8537	−	63.8324i	1.19443	−	2.06882i
$953$	−28.8189			−0.933534			−0.466767	−	0.884380i	$-0.654581\pi$
$953$	−28.8189			−0.933534			−0.466767	+	0.884380i	$0.654581\pi$
$954$	−0.151473	−	0.262359i	−0.00490412	−	0.00849418i
$955$		0			0
$956$	−15.4926	+	26.8340i	−0.501066	+	0.867872i
$957$	0.126523			0.00408992
$958$	−13.9224	−	24.1144i	−0.449813	−	0.779100i
$959$	−16.4932			−0.532592
$960$		0			0
$961$	−30.3088	−	6.50993i	−0.977702	−	0.209998i
$962$	17.2457			0.556024
$963$	0.454440			0.0146441
$964$	1.96112	+	3.39677i	0.0631636	+	0.109403i
$965$		0			0
$966$	6.80020	−	11.7783i	0.218793	−	0.378961i
$967$	−0.777693	−	1.34700i	−0.0250089	−	0.0433167i	0.853250	−	0.521502i	$-0.174628\pi$
$967$	−0.777693	−	1.34700i	−0.0250089	−	0.0433167i	−0.878259	+	0.478185i	$0.841295\pi$
$968$	−13.9770	−	24.2088i	−0.449237	−	0.778101i
$969$	−53.5843			−1.72137
$970$		0			0
$971$	1.24505	−	2.15648i	0.0399555	−	0.0692049i	−0.845356	−	0.534203i	$-0.820612\pi$
$971$	1.24505	−	2.15648i	0.0399555	−	0.0692049i	0.885312	+	0.464998i	$0.153945\pi$
$972$	−1.32451	+	2.29412i	−0.0424838	+	0.0735840i
$973$	20.6812	+	35.8210i	0.663010	+	1.14837i
$974$	8.38239	−	14.5187i	0.268589	−	0.465210i
$975$		0			0
$976$	−1.77945			−0.0569588
$977$	−36.5350			−1.16886			−0.584429	−	0.811445i	$-0.698681\pi$
$977$	−36.5350			−1.16886			−0.584429	+	0.811445i	$0.698681\pi$
$978$	−9.72103	−	16.8373i	−0.310844	−	0.538398i
$979$	−2.16877	+	3.75642i	−0.0693142	+	0.120056i
$980$		0			0
$981$	−0.340639	+	0.590004i	−0.0108758	+	0.0188374i
$982$	−9.06976	+	15.7093i	−0.289428	+	0.501303i
$983$	−23.6515	+	40.9656i	−0.754365	+	1.30660i	0.191324	+	0.981527i	$0.438722\pi$
$983$	−23.6515	+	40.9656i	−0.754365	+	1.30660i	−0.945689	+	0.325072i	$0.894611\pi$
$984$	12.9323			0.412265
$985$		0			0
$986$	0.0339912	+	0.0588746i	0.00108250	+	0.00187495i
$987$	−23.6246	+	40.9190i	−0.751979	+	1.30247i
$988$	32.4367			1.03195
$989$	1.61156	+	2.79130i	0.0512446	+	0.0887582i
$990$		0			0
$991$	8.87030			0.281774			0.140887	−	0.990026i	$-0.455005\pi$
$991$	8.87030			0.281774			0.140887	+	0.990026i	$0.455005\pi$
$992$	−3.43840	+	32.3819i	−0.109169	+	1.02813i
$993$	−46.7254			−1.48278
$994$	−18.2423			−0.578612
$995$		0			0
$996$	−25.2252			−0.799292
$997$	−18.2458	+	31.6027i	−0.577850	+	1.00087i	0.417875	+	0.908504i	$0.362775\pi$
$997$	−18.2458	+	31.6027i	−0.577850	+	1.00087i	−0.995726	+	0.0923616i	$0.970558\pi$
$998$	−1.52604	−	2.64318i	−0.0483060	−	0.0836685i
$999$	12.4828	+	21.6209i	0.394939	+	0.684055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.e.g.676.2		8
5.2	odd	4		775.2.o.e.149.4		16
5.3	odd	4		775.2.o.e.149.5		16
5.4	even	2		155.2.e.c.56.3	yes	8
31.5	even	3	inner	775.2.e.g.501.2		8
155.67	odd	12		775.2.o.e.749.4		16
155.98	odd	12		775.2.o.e.749.5		16
155.99	odd	6		4805.2.a.k.1.3		4
155.129	even	6		155.2.e.c.36.3	✓	8
155.149	even	6		4805.2.a.i.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.e.c.36.3	✓	8	155.129	even	6
155.2.e.c.56.3	yes	8	5.4	even	2
775.2.e.g.501.2		8	31.5	even	3	inner
775.2.e.g.676.2		8	1.1	even	1	trivial
775.2.o.e.149.4		16	5.2	odd	4
775.2.o.e.149.5		16	5.3	odd	4
775.2.o.e.749.4		16	155.67	odd	12
775.2.o.e.749.5		16	155.98	odd	12
4805.2.a.i.1.3		4	155.149	even	6
4805.2.a.k.1.3		4	155.99	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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.784476 q^{2} +(-0.892238 - 1.54540i) q^{3} -1.38460 q^{4} +(0.699939 + 1.21233i) q^{6} +(-2.44756 - 4.23929i) q^{7} +2.65514 q^{8} +(-0.0921773 + 0.159656i) q^{9} +O(q^{10})\)	\(q-0.784476 q^{2} +(-0.892238 - 1.54540i) q^{3} -1.38460 q^{4} +(0.699939 + 1.21233i) q^{6} +(-2.44756 - 4.23929i) q^{7} +2.65514 q^{8} +(-0.0921773 + 0.159656i) q^{9} +(2.31993 - 4.01823i) q^{11} +(1.23539 + 2.13976i) q^{12} +(2.21217 - 3.83158i) q^{13} +(1.92005 + 3.32562i) q^{14} +0.686305 q^{16} +(2.83551 + 4.91125i) q^{17} +(0.0723109 - 0.125246i) q^{18} +(-2.64749 - 4.58560i) q^{19} +(-4.36760 + 7.56491i) q^{21} +(-1.81993 + 3.15221i) q^{22} +1.98472 q^{23} +(-2.36901 - 4.10325i) q^{24} +(-1.73539 + 3.00578i) q^{26} -5.02445 q^{27} +(3.38888 + 5.86971i) q^{28} -0.0152811 q^{29} +(0.587896 - 5.53664i) q^{31} -5.84866 q^{32} -8.27971 q^{33} +(-2.22439 - 3.85276i) q^{34} +(0.127628 - 0.221059i) q^{36} +(-2.48442 - 4.30313i) q^{37} +(2.07690 + 3.59729i) q^{38} -7.89511 q^{39} +(-1.36473 + 2.36378i) q^{41} +(3.42628 - 5.93449i) q^{42} +(0.811983 + 1.40640i) q^{43} +(-3.21217 + 5.56363i) q^{44} -1.55696 q^{46} +5.40905 q^{47} +(-0.612347 - 1.06062i) q^{48} +(-8.48106 + 14.6896i) q^{49} +(5.05990 - 8.76401i) q^{51} +(-3.06296 + 5.30520i) q^{52} +(1.04737 - 1.81410i) q^{53} +3.94156 q^{54} +(-6.49859 - 11.2559i) q^{56} +(-4.72439 + 8.18289i) q^{57} +0.0119877 q^{58} +(3.59077 + 6.21939i) q^{59} -2.59280 q^{61} +(-0.461190 + 4.34336i) q^{62} +0.902436 q^{63} +3.21552 q^{64} +6.49523 q^{66} +(6.13221 - 10.6213i) q^{67} +(-3.92604 - 6.80010i) q^{68} +(-1.77084 - 3.06719i) q^{69} +(-2.37524 + 4.11404i) q^{71} +(-0.244743 + 0.423908i) q^{72} +(-5.03973 + 8.72907i) q^{73} +(1.94896 + 3.37570i) q^{74} +(3.66571 + 6.34920i) q^{76} -22.7126 q^{77} +6.19353 q^{78} +(3.55960 + 6.16541i) q^{79} +(4.75954 + 8.24376i) q^{81} +(1.07060 - 1.85433i) q^{82} +(-5.10471 + 8.84161i) q^{83} +(6.04737 - 10.4744i) q^{84} +(-0.636981 - 1.10328i) q^{86} +(0.0136344 + 0.0236155i) q^{87} +(6.15972 - 10.6689i) q^{88} -0.934844 q^{89} -21.6576 q^{91} -2.74804 q^{92} +(-9.08087 + 4.03147i) q^{93} -4.24327 q^{94} +(5.21840 + 9.03853i) q^{96} +15.9831 q^{97} +(6.65319 - 11.5237i) q^{98} +(0.427689 + 0.740779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9	\( 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9} + 4 q^{11} + 8 q^{12} - q^{13} - 8 q^{14} + 10 q^{16} + 12 q^{17} + 11 q^{18} - 5 q^{19} + 9 q^{21} - 10 q^{23} + 2 q^{24} - 12 q^{26} + 6 q^{27} - 4 q^{28} - 26 q^{29} + 19 q^{31} + 28 q^{32} - 8 q^{33} + 24 q^{34} - 5 q^{36} - 16 q^{37} - 9 q^{38} - 22 q^{39} - 4 q^{41} - 6 q^{42} + q^{43} - 7 q^{44} - 22 q^{46} - 20 q^{47} + 27 q^{48} - 37 q^{49} - 12 q^{51} - 21 q^{52} + q^{53} + 24 q^{54} - 29 q^{56} + 4 q^{57} - 26 q^{58} + 6 q^{59} - 2 q^{61} + 17 q^{62} - 24 q^{63} + 34 q^{64} + 2 q^{66} + 7 q^{67} + 5 q^{68} - 6 q^{69} + 12 q^{71} - 14 q^{72} - 20 q^{73} + 18 q^{74} - 23 q^{76} - 58 q^{77} - 22 q^{78} - 2 q^{79} + 12 q^{81} + 18 q^{82} + 4 q^{83} + 41 q^{84} - 13 q^{86} + 10 q^{88} + 54 q^{89} - 44 q^{91} - 86 q^{92} - 55 q^{93} - 48 q^{94} + 13 q^{96} + 18 q^{97} + 46 q^{98} - 7 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9 + 4 * q^11 + 8 * q^12 - q^13 - 8 * q^14 + 10 * q^16 + 12 * q^17 + 11 * q^18 - 5 * q^19 + 9 * q^21 - 10 * q^23 + 2 * q^24 - 12 * q^26 + 6 * q^27 - 4 * q^28 - 26 * q^29 + 19 * q^31 + 28 * q^32 - 8 * q^33 + 24 * q^34 - 5 * q^36 - 16 * q^37 - 9 * q^38 - 22 * q^39 - 4 * q^41 - 6 * q^42 + q^43 - 7 * q^44 - 22 * q^46 - 20 * q^47 + 27 * q^48 - 37 * q^49 - 12 * q^51 - 21 * q^52 + q^53 + 24 * q^54 - 29 * q^56 + 4 * q^57 - 26 * q^58 + 6 * q^59 - 2 * q^61 + 17 * q^62 - 24 * q^63 + 34 * q^64 + 2 * q^66 + 7 * q^67 + 5 * q^68 - 6 * q^69 + 12 * q^71 - 14 * q^72 - 20 * q^73 + 18 * q^74 - 23 * q^76 - 58 * q^77 - 22 * q^78 - 2 * q^79 + 12 * q^81 + 18 * q^82 + 4 * q^83 + 41 * q^84 - 13 * q^86 + 10 * q^88 + 54 * q^89 - 44 * q^91 - 86 * q^92 - 55 * q^93 - 48 * q^94 + 13 * q^96 + 18 * q^97 + 46 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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