LMFDB - Embedded newform 475.2.e.e.201.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.4
Root			$-0.245959 + 0.426014i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.e.26.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37901 - 2.38851i) q^{2} +(0.745959 - 1.29204i) q^{3} +(-2.80333 - 4.85550i) q^{4} +(-2.05737 - 3.56347i) q^{6} +2.84864 q^{7} -9.94721 q^{8} +(0.387090 + 0.670459i) q^{9} +O(q^{10})$	\(q+(1.37901 - 2.38851i) q^{2} +(0.745959 - 1.29204i) q^{3} +(-2.80333 - 4.85550i) q^{4} +(-2.05737 - 3.56347i) q^{6} +2.84864 q^{7} -9.94721 q^{8} +(0.387090 + 0.670459i) q^{9} -0.864801 q^{11} -8.36467 q^{12} +(0.321640 + 0.557098i) q^{13} +(3.92829 - 6.80401i) q^{14} +(-8.11063 + 14.0480i) q^{16} +(1.87093 - 3.24054i) q^{17} +2.13520 q^{18} +(-3.36069 + 2.77592i) q^{19} +(2.12497 - 3.68055i) q^{21} +(-1.19257 + 2.06559i) q^{22} +(0.208730 + 0.361531i) q^{23} +(-7.42021 + 12.8522i) q^{24} +1.77418 q^{26} +5.63077 q^{27} +(-7.98566 - 13.8316i) q^{28} +(4.85261 + 8.40497i) q^{29} +4.93349 q^{31} +(12.4220 + 21.5156i) q^{32} +(-0.645106 + 1.11736i) q^{33} +(-5.16005 - 8.93746i) q^{34} +(2.17028 - 3.75903i) q^{36} -6.36467 q^{37} +(1.99589 + 11.8551i) q^{38} +0.959723 q^{39} +(2.00686 - 3.47598i) q^{41} +(-5.86069 - 10.1510i) q^{42} +(-1.02915 + 1.78254i) q^{43} +(2.42432 + 4.19904i) q^{44} +1.15136 q^{46} +(-1.97698 - 3.42423i) q^{47} +(12.1004 + 20.9585i) q^{48} +1.11474 q^{49} +(-2.79127 - 4.83462i) q^{51} +(1.80333 - 3.12345i) q^{52} +(-5.49374 - 9.51544i) q^{53} +(7.76487 - 13.4492i) q^{54} -28.3360 q^{56} +(1.07966 + 6.41287i) q^{57} +26.7672 q^{58} +(-1.22980 + 2.13007i) q^{59} +(-3.16740 - 5.48609i) q^{61} +(6.80333 - 11.7837i) q^{62} +(1.10268 + 1.90989i) q^{63} +36.0778 q^{64} +(1.77921 + 3.08169i) q^{66} +(-1.26610 - 2.19295i) q^{67} -20.9793 q^{68} +0.622817 q^{69} +(0.891065 - 1.54337i) q^{71} +(-3.85046 - 6.66920i) q^{72} +(-3.56545 + 6.17554i) q^{73} +(-8.77693 + 15.2021i) q^{74} +(22.8996 + 8.53606i) q^{76} -2.46350 q^{77} +(1.32347 - 2.29231i) q^{78} +(-0.912262 + 1.58008i) q^{79} +(3.03905 - 5.26380i) q^{81} +(-5.53495 - 9.58681i) q^{82} +7.43913 q^{83} -23.8279 q^{84} +(2.83841 + 4.91626i) q^{86} +14.4794 q^{87} +8.60235 q^{88} +(-2.22294 - 3.85024i) q^{89} +(0.916237 + 1.58697i) q^{91} +(1.17028 - 2.02698i) q^{92} +(3.68018 - 6.37427i) q^{93} -10.9051 q^{94} +37.0653 q^{96} +(-5.42707 + 9.39996i) q^{97} +(1.53723 - 2.66256i) q^{98} +(-0.334755 - 0.579813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9}+O(q^{10}) $ 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9	$ 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9} - 4 q^{11} - 12 q^{12} + 7 q^{13} + q^{14} - 7 q^{16} - q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} - 23 q^{24} + 6 q^{26} - 24 q^{27} - 19 q^{28} + q^{29} + 30 q^{32} + 19 q^{33} - 15 q^{34} + 7 q^{36} + 4 q^{37} - 13 q^{38} + 30 q^{39} + 8 q^{41} - 15 q^{42} + q^{43} + 12 q^{44} + 24 q^{46} - 12 q^{47} + 23 q^{48} - 20 q^{49} - 22 q^{51} - 3 q^{52} - 5 q^{53} + 34 q^{54} - 82 q^{56} - 7 q^{57} + 54 q^{58} + 5 q^{59} + 37 q^{62} - 3 q^{63} + 112 q^{64} + 31 q^{66} + 4 q^{67} - 32 q^{68} - 18 q^{69} - 20 q^{71} + 17 q^{72} - 20 q^{73} - 25 q^{74} + 63 q^{76} - 28 q^{77} - 18 q^{78} - 17 q^{79} - 12 q^{81} + 21 q^{82} - 2 q^{83} - 40 q^{84} - 8 q^{86} + 32 q^{87} + 14 q^{88} - 11 q^{89} - 6 q^{91} - q^{92} - 8 q^{93} - 62 q^{94} + 42 q^{96} + q^{97} + 9 q^{98} - 38 q^{99}+O(q^{100}) $ 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9 - 4 * q^11 - 12 * q^12 + 7 * q^13 + q^14 - 7 * q^16 - q^17 + 20 * q^18 + 5 * q^19 + 4 * q^21 + 2 * q^22 + 2 * q^23 - 23 * q^24 + 6 * q^26 - 24 * q^27 - 19 * q^28 + q^29 + 30 * q^32 + 19 * q^33 - 15 * q^34 + 7 * q^36 + 4 * q^37 - 13 * q^38 + 30 * q^39 + 8 * q^41 - 15 * q^42 + q^43 + 12 * q^44 + 24 * q^46 - 12 * q^47 + 23 * q^48 - 20 * q^49 - 22 * q^51 - 3 * q^52 - 5 * q^53 + 34 * q^54 - 82 * q^56 - 7 * q^57 + 54 * q^58 + 5 * q^59 + 37 * q^62 - 3 * q^63 + 112 * q^64 + 31 * q^66 + 4 * q^67 - 32 * q^68 - 18 * q^69 - 20 * q^71 + 17 * q^72 - 20 * q^73 - 25 * q^74 + 63 * q^76 - 28 * q^77 - 18 * q^78 - 17 * q^79 - 12 * q^81 + 21 * q^82 - 2 * q^83 - 40 * q^84 - 8 * q^86 + 32 * q^87 + 14 * q^88 - 11 * q^89 - 6 * q^91 - q^92 - 8 * q^93 - 62 * q^94 + 42 * q^96 + q^97 + 9 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.37901	−	2.38851i	0.975106	−	1.68893i	0.295521	−	0.955336i	$-0.404507\pi$
$2$	1.37901	−	2.38851i	0.975106	−	1.68893i	0.679585	−	0.733597i	$-0.262160\pi$
$3$	0.745959	−	1.29204i	0.430680	−	0.745959i	−0.566252	−	0.824232i	$-0.691607\pi$
$3$	0.745959	−	1.29204i	0.430680	−	0.745959i	0.996932	+	0.0782728i	$0.0249405\pi$
$4$	−2.80333	−	4.85550i	−1.40166	−	2.42775i
$5$		0			0
$5$		0			0
$6$	−2.05737	−	3.56347i	−0.839917	−	1.45478i
$7$	2.84864			1.07668			0.538342	−	0.842727i	$-0.319051\pi$
$7$	2.84864			1.07668			0.538342	+	0.842727i	$0.319051\pi$
$8$	−9.94721			−3.51687
$9$	0.387090	+	0.670459i	0.129030	+	0.223486i
$10$		0			0
$11$	−0.864801			−0.260747			−0.130374	−	0.991465i	$-0.541618\pi$
$11$	−0.864801			−0.260747			−0.130374	+	0.991465i	$0.541618\pi$
$12$	−8.36467			−2.41467
$13$	0.321640	+	0.557098i	0.0892070	+	0.154511i	0.907176	−	0.420751i	$-0.138233\pi$
$13$	0.321640	+	0.557098i	0.0892070	+	0.154511i	−0.817969	+	0.575262i	$0.804900\pi$
$14$	3.92829	−	6.80401i	1.04988	−	1.81845i
$15$		0			0
$16$	−8.11063	+	14.0480i	−2.02766	+	3.51201i
$17$	1.87093	−	3.24054i	0.453766	−	0.785946i	−0.544850	−	0.838534i	$-0.683413\pi$
$17$	1.87093	−	3.24054i	0.453766	−	0.785946i	0.998616	+	0.0525872i	$0.0167467\pi$
$18$	2.13520			0.503271
$19$	−3.36069	+	2.77592i	−0.770996	+	0.636840i
$19$	−3.36069	+	2.77592i	−0.770996	+	0.636840i
$20$		0			0
$21$	2.12497	−	3.68055i	0.463706	−	0.803162i
$22$	−1.19257	+	2.06559i	−0.254256	+	0.440385i
$23$	0.208730	+	0.361531i	0.0435233	+	0.0753845i	0.886966	−	0.461834i	$-0.152808\pi$
$23$	0.208730	+	0.361531i	0.0435233	+	0.0753845i	−0.843443	+	0.537218i	$0.819475\pi$
$24$	−7.42021	+	12.8522i	−1.51464	+	2.62344i
$25$		0			0
$26$	1.77418			0.347945
$27$	5.63077			1.08364
$28$	−7.98566	−	13.8316i	−1.50915	−	2.61392i
$29$	4.85261	+	8.40497i	0.901108	+	1.56076i	0.826059	+	0.563584i	$0.190578\pi$
$29$	4.85261	+	8.40497i	0.901108	+	1.56076i	0.0750490	+	0.997180i	$0.476089\pi$
$30$		0			0
$31$	4.93349			0.886081			0.443041	−	0.896501i	$-0.353900\pi$
$31$	4.93349			0.886081			0.443041	+	0.896501i	$0.353900\pi$
$32$	12.4220	+	21.5156i	2.19593	+	3.80346i
$33$	−0.645106	+	1.11736i	−0.112299	+	0.194507i
$34$	−5.16005	−	8.93746i	−0.884941	−	1.53276i
$35$		0			0
$36$	2.17028	−	3.75903i	0.361713	−	0.626505i
$37$	−6.36467			−1.04635			−0.523173	−	0.852227i	$-0.675252\pi$
$37$	−6.36467			−1.04635			−0.523173	+	0.852227i	$0.675252\pi$
$38$	1.99589	+	11.8551i	0.323777	+	1.92315i
$39$	0.959723			0.153679
$40$		0			0
$41$	2.00686	−	3.47598i	0.313419	−	0.542857i	−0.665681	−	0.746236i	$-0.731859\pi$
$41$	2.00686	−	3.47598i	0.313419	−	0.542857i	0.979100	+	0.203379i	$0.0651924\pi$
$42$	−5.86069	−	10.1510i	−0.904325	−	1.56634i
$43$	−1.02915	+	1.78254i	−0.156944	+	0.271834i	−0.933765	−	0.357887i	$-0.883497\pi$
$43$	−1.02915	+	1.78254i	−0.156944	+	0.271834i	0.776821	+	0.629721i	$0.216831\pi$
$44$	2.42432	+	4.19904i	0.365480	+	0.633030i
$45$		0			0
$46$	1.15136			0.169759
$47$	−1.97698	−	3.42423i	−0.288372	−	0.499475i	0.685049	−	0.728497i	$-0.259781\pi$
$47$	−1.97698	−	3.42423i	−0.288372	−	0.499475i	−0.973421	+	0.229022i	$0.926447\pi$
$48$	12.1004	+	20.9585i	1.74654	+	3.02510i
$49$	1.11474			0.159248
$50$		0			0
$51$	−2.79127	−	4.83462i	−0.390856	−	0.676982i
$52$	1.80333	−	3.12345i	0.250076	−	0.433145i
$53$	−5.49374	−	9.51544i	−0.754624	−	1.30705i	−0.945561	−	0.325444i	$-0.894486\pi$
$53$	−5.49374	−	9.51544i	−0.754624	−	1.30705i	0.190937	−	0.981602i	$-0.438847\pi$
$54$	7.76487	−	13.4492i	1.05667	−	1.83020i
$55$		0			0
$56$	−28.3360			−3.78656
$57$	1.07966	+	6.41287i	0.143004	+	0.849406i
$58$	26.7672			3.51470
$59$	−1.22980	+	2.13007i	−0.160106	+	0.277311i	−0.934906	−	0.354894i	$-0.884517\pi$
$59$	−1.22980	+	2.13007i	−0.160106	+	0.277311i	0.774801	+	0.632206i	$0.217850\pi$
$60$		0			0
$61$	−3.16740	−	5.48609i	−0.405543	−	0.702422i	0.588841	−	0.808249i	$-0.299584\pi$
$61$	−3.16740	−	5.48609i	−0.405543	−	0.702422i	−0.994385	+	0.105827i	$0.966251\pi$
$62$	6.80333	−	11.7837i	0.864023	−	1.49653i
$63$	1.10268	+	1.90989i	0.138924	+	0.240624i
$64$	36.0778			4.50973
$65$		0			0
$66$	1.77921	+	3.08169i	0.219006	+	0.379329i
$67$	−1.26610	−	2.19295i	−0.154678	−	0.267911i	0.778263	−	0.627938i	$-0.216101\pi$
$67$	−1.26610	−	2.19295i	−0.154678	−	0.267911i	−0.932942	+	0.360027i	$0.882767\pi$
$68$	−20.9793			−2.54411
$69$	0.622817			0.0749783
$70$		0			0
$71$	0.891065	−	1.54337i	0.105750	−	0.183164i	−0.808294	−	0.588779i	$-0.799609\pi$
$71$	0.891065	−	1.54337i	0.105750	−	0.183164i	0.914044	+	0.405614i	$0.132942\pi$
$72$	−3.85046	−	6.66920i	−0.453781	−	0.785972i
$73$	−3.56545	+	6.17554i	−0.417304	+	0.722792i	−0.995667	−	0.0929873i	$-0.970358\pi$
$73$	−3.56545	+	6.17554i	−0.417304	+	0.722792i	0.578363	+	0.815780i	$0.303692\pi$
$74$	−8.77693	+	15.2021i	−1.02030	+	1.76721i
$75$		0			0
$76$	22.8996	+	8.53606i	2.62677	+	0.979153i
$77$	−2.46350			−0.280742
$78$	1.32347	−	2.29231i	0.149853	−	0.259553i
$79$	−0.912262	+	1.58008i	−0.102637	+	0.177773i	−0.912771	−	0.408473i	$-0.866061\pi$
$79$	−0.912262	+	1.58008i	−0.102637	+	0.177773i	0.810133	+	0.586246i	$0.199395\pi$
$80$		0			0
$81$	3.03905	−	5.26380i	0.337673	−	0.584866i
$82$	−5.53495	−	9.58681i	−0.611233	−	1.05869i
$83$	7.43913			0.816550			0.408275	−	0.912859i	$-0.366130\pi$
$83$	7.43913			0.816550			0.408275	+	0.912859i	$0.366130\pi$
$84$	−23.8279			−2.59984
$85$		0			0
$86$	2.83841	+	4.91626i	0.306073	+	0.530134i
$87$	14.4794			1.55236
$88$	8.60235			0.917014
$89$	−2.22294	−	3.85024i	−0.235631	−	0.408125i	0.723825	−	0.689984i	$-0.242382\pi$
$89$	−2.22294	−	3.85024i	−0.235631	−	0.408125i	−0.959456	+	0.281859i	$0.909049\pi$
$90$		0			0
$91$	0.916237	+	1.58697i	0.0960478	+	0.166360i
$92$	1.17028	−	2.02698i	0.122010	−	0.211327i
$93$	3.68018	−	6.37427i	0.381617	−	0.660981i
$94$	−10.9051			−1.12477
$95$		0			0
$96$	37.0653			3.78296
$97$	−5.42707	+	9.39996i	−0.551036	+	0.954422i	0.447165	+	0.894452i	$0.352434\pi$
$97$	−5.42707	+	9.39996i	−0.551036	+	0.954422i	−0.998200	+	0.0599699i	$0.980900\pi$
$98$	1.53723	−	2.66256i	0.155284	−	0.268959i
$99$	−0.334755	−	0.579813i	−0.0336442	−	0.0582734i
$100$		0			0
$101$	2.64799	+	4.58645i	0.263485	+	0.456369i	0.967166	−	0.254147i	$-0.0817948\pi$
$101$	2.64799	+	4.58645i	0.263485	+	0.456369i	−0.703681	+	0.710516i	$0.748461\pi$
$102$	−15.3967			−1.52450
$103$	0.385134			0.0379484			0.0189742	−	0.999820i	$-0.493960\pi$
$103$	0.385134			0.0379484			0.0189742	+	0.999820i	$0.493960\pi$
$104$	−3.19943	−	5.54157i	−0.313729	−	0.543395i
$105$		0			0
$106$	−30.3037			−2.94335
$107$	6.43336			0.621937			0.310968	−	0.950420i	$-0.399347\pi$
$107$	6.43336			0.621937			0.310968	+	0.950420i	$0.399347\pi$
$108$	−15.7849	−	27.3402i	−1.51890	−	2.63081i
$109$	−3.28441	+	5.68877i	−0.314590	+	0.544885i	−0.979350	−	0.202171i	$-0.935200\pi$
$109$	−3.28441	+	5.68877i	−0.314590	+	0.544885i	0.664761	+	0.747056i	$0.268534\pi$
$110$		0			0
$111$	−4.74778	+	8.22340i	−0.450640	+	0.780531i
$112$	−23.1042	+	40.0177i	−2.18315	+	3.78132i
$113$	−0.294513			−0.0277054			−0.0138527	−	0.999904i	$-0.504410\pi$
$113$	−0.294513			−0.0277054			−0.0138527	+	0.999904i	$0.504410\pi$
$114$	16.8061	+	6.26463i	1.57403	+	0.586736i
$115$		0			0
$116$	27.2069	−	47.1238i	2.52610	−	4.37533i
$117$	−0.249007	+	0.431294i	−0.0230207	+	0.0398731i
$118$	3.39180	+	5.87477i	0.312240	+	0.540816i
$119$	5.32959	−	9.23112i	0.488563	−	0.846216i
$120$		0			0
$121$	−10.2521			−0.932011
$122$	−17.4715			−1.58179
$123$	−2.99407	−	5.18588i	−0.269966	−	0.467595i
$124$	−13.8302	−	23.9546i	−1.24199	−	2.15119i
$125$		0			0
$126$	6.08241			0.541864
$127$	4.41746	+	7.65127i	0.391986	+	0.678940i	0.992711	−	0.120516i	$-0.0384548\pi$
$127$	4.41746	+	7.65127i	0.391986	+	0.678940i	−0.600725	+	0.799456i	$0.705121\pi$
$128$	24.9076	−	43.1412i	2.20154	−	3.81318i
$129$	1.53540	+	2.65940i	0.135185	+	0.234147i
$130$		0			0
$131$	−10.4564	+	18.1110i	−0.913578	+	1.58236i	−0.104609	+	0.994513i	$0.533359\pi$
$131$	−10.4564	+	18.1110i	−0.913578	+	1.58236i	−0.808969	+	0.587851i	$0.799974\pi$
$132$	7.23377			0.629619
$133$	−9.57340	+	7.90759i	−0.830119	+	0.685675i
$134$	−6.98384			−0.603312
$135$		0			0
$136$	−18.6105	+	32.2343i	−1.59584	+	2.76407i
$137$	2.60739	+	4.51613i	0.222764	+	0.385839i	0.955646	−	0.294517i	$-0.0951587\pi$
$137$	2.60739	+	4.51613i	0.222764	+	0.385839i	−0.732882	+	0.680356i	$0.761825\pi$
$138$	0.858870	−	1.48761i	0.0731118	−	0.126633i
$139$	5.36192	+	9.28711i	0.454792	+	0.787723i	0.998676	−	0.0514375i	$-0.0163803\pi$
$139$	5.36192	+	9.28711i	0.454792	+	0.787723i	−0.543884	+	0.839160i	$0.683047\pi$
$140$		0			0
$141$	−5.89898			−0.496784
$142$	−2.45757	−	4.25664i	−0.206235	−	0.357209i
$143$	−0.278155	−	0.481778i	−0.0232605	−	0.0402883i
$144$	−12.5582			−1.04651
$145$		0			0
$146$	9.83357	+	17.0322i	0.813832	+	1.40960i
$147$	0.831547	−	1.44028i	0.0685848	−	0.118792i
$148$	17.8423	+	30.9037i	1.46662	+	2.54027i
$149$	7.45578	−	12.9138i	0.610801	−	1.05794i	−0.380304	−	0.924861i	$-0.624181\pi$
$149$	7.45578	−	12.9138i	0.610801	−	1.05794i	0.991106	−	0.133078i	$-0.0424860\pi$
$150$		0			0
$151$	21.4589			1.74630			0.873152	−	0.487448i	$-0.162072\pi$
$151$	21.4589			1.74630			0.873152	+	0.487448i	$0.162072\pi$
$152$	33.4295	−	27.6127i	2.71149	−	2.23968i
$153$	2.89687			0.234198
$154$	−3.39719	+	5.88411i	−0.273753	+	0.474155i
$155$		0			0
$156$	−2.69042	−	4.65994i	−0.215406	−	0.373094i
$157$	−1.21559	+	2.10546i	−0.0970145	+	0.168034i	−0.910448	−	0.413624i	$-0.864263\pi$
$157$	−1.21559	+	2.10546i	−0.0970145	+	0.168034i	0.813433	+	0.581659i	$0.197596\pi$
$158$	2.51603	+	4.35790i	0.200165	+	0.346696i
$159$	−16.3924			−1.30000
$160$		0			0
$161$	0.594597	+	1.02987i	0.0468608	+	0.0811653i
$162$	−8.38176	−	14.5176i	−0.658533	−	1.14061i
$163$	−17.8175			−1.39558			−0.697788	−	0.716305i	$-0.745832\pi$
$163$	−17.8175			−1.39558			−0.697788	+	0.716305i	$0.745832\pi$
$164$	−22.5035			−1.75723
$165$		0			0
$166$	10.2586	−	17.7684i	0.796223	−	1.37910i
$167$	−0.202799	−	0.351258i	−0.0156931	−	0.0271812i	0.858072	−	0.513529i	$-0.171662\pi$
$167$	−0.202799	−	0.351258i	−0.0156931	−	0.0271812i	−0.873765	+	0.486348i	$0.838329\pi$
$168$	−21.1375	+	36.6112i	−1.63079	+	2.82462i
$169$	6.29309	−	10.9000i	0.484084	−	0.838458i
$170$		0			0
$171$	−3.16203	−	1.17868i	−0.241807	−	0.0901358i
$172$	11.5401			0.879928
$173$	9.01051	−	15.6067i	0.685056	−	1.18655i	−0.288363	−	0.957521i	$-0.593111\pi$
$173$	9.01051	−	15.6067i	0.685056	−	1.18655i	0.973419	−	0.229031i	$-0.0735557\pi$
$174$	19.9672	−	34.5842i	1.51371	−	2.62182i
$175$		0			0
$176$	7.01408	−	12.1487i	0.528706	−	0.915746i
$177$	1.83476	+	3.17789i	0.137909	+	0.238865i
$178$	−12.2618			−0.919061
$179$	20.1523			1.50625			0.753127	−	0.657875i	$-0.228545\pi$
$179$	20.1523			1.50625			0.753127	+	0.657875i	$0.228545\pi$
$180$		0			0
$181$	8.55541	+	14.8184i	0.635919	+	1.10144i	0.986320	+	0.164844i	$0.0527120\pi$
$181$	8.55541	+	14.8184i	0.635919	+	1.10144i	−0.350401	+	0.936600i	$0.613955\pi$
$182$	5.05399			0.374627
$183$	−9.45099			−0.698637
$184$	−2.07628	−	3.59623i	−0.153066	−	0.265117i
$185$		0			0
$186$	−10.1500	−	17.5803i	−0.744235	−	1.28905i
$187$	−1.61798	+	2.80242i	−0.118318	+	0.204933i
$188$	−11.0842	+	19.1985i	−0.808401	+	1.40019i
$189$	16.0400			1.16674
$190$		0			0
$191$	5.28080			0.382105			0.191053	−	0.981580i	$-0.438810\pi$
$191$	5.28080			0.382105			0.191053	+	0.981580i	$0.438810\pi$
$192$	26.9126	−	46.6140i	1.94225	−	3.36408i
$193$	9.00182	−	15.5916i	0.647966	−	1.12231i	−0.335642	−	0.941989i	$-0.608953\pi$
$193$	9.00182	−	15.5916i	0.647966	−	1.12231i	0.983608	−	0.180320i	$-0.0577133\pi$
$194$	14.9679	+	25.9252i	1.07464	+	1.86132i
$195$		0			0
$196$	−3.12497	−	5.41260i	−0.223212	−	0.386614i
$197$	−8.07785			−0.575523			−0.287761	−	0.957702i	$-0.592911\pi$
$197$	−8.07785			−0.575523			−0.287761	+	0.957702i	$0.592911\pi$
$198$	−1.84652			−0.131227
$199$	−0.701872	−	1.21568i	−0.0497544	−	0.0861771i	0.840076	−	0.542469i	$-0.182511\pi$
$199$	−0.701872	−	1.21568i	−0.0497544	−	0.0861771i	−0.889830	+	0.456292i	$0.849177\pi$
$200$		0			0
$201$	−3.77783			−0.266468
$202$	14.6064			1.02770
$203$	13.8233	+	23.9427i	0.970208	+	1.68045i
$204$	−15.6497	+	27.1060i	−1.09570	+	1.89780i
$205$		0			0
$206$	0.531103	−	0.919897i	0.0370037	−	0.0640923i
$207$	−0.161595	+	0.279890i	−0.0112316	+	0.0194537i
$208$	−10.4348			−0.723525
$209$	2.90633	−	2.40062i	0.201035	−	0.166054i
$210$		0			0
$211$	−9.45817	+	16.3820i	−0.651128	+	1.12779i	0.331722	+	0.943377i	$0.392370\pi$
$211$	−9.45817	+	16.3820i	−0.651128	+	1.12779i	−0.982850	+	0.184409i	$0.940963\pi$
$212$	−30.8015	+	53.3498i	−2.11546	+	3.66408i
$213$	−1.32940	−	2.30258i	−0.0910888	−	0.157770i
$214$	8.87166	−	15.3662i	0.606454	−	1.05041i
$215$		0			0
$216$	−56.0104			−3.81103
$217$	14.0537			0.954030
$218$	9.05846	+	15.6897i	0.613516	+	1.06264i
$219$	5.31936	+	9.21340i	0.359449	+	0.622584i
$220$		0			0
$221$	2.40706			0.161917
$222$	13.0945	+	22.6803i	0.878843	+	1.52220i
$223$	−8.07400	+	13.9846i	−0.540675	+	0.936477i	0.458190	+	0.888854i	$0.348498\pi$
$223$	−8.07400	+	13.9846i	−0.540675	+	0.936477i	−0.998865	+	0.0476227i	$0.984835\pi$
$224$	35.3859	+	61.2901i	2.36432	+	4.09512i
$225$		0			0
$226$	−0.406136	+	0.703448i	−0.0270157	+	0.0467926i
$227$	−26.3186			−1.74683			−0.873414	−	0.486978i	$-0.838099\pi$
$227$	−26.3186			−1.74683			−0.873414	+	0.486978i	$0.838099\pi$
$228$	28.1111	−	23.2197i	1.86170	−	1.53776i
$229$	−13.3323			−0.881026			−0.440513	−	0.897746i	$-0.645203\pi$
$229$	−13.3323			−0.881026			−0.440513	+	0.897746i	$0.645203\pi$
$230$		0			0
$231$	−1.83767	+	3.18294i	−0.120910	+	0.209422i
$232$	−48.2700	−	83.6060i	−3.16908	−	5.48900i
$233$	12.6547	−	21.9186i	0.829038	−	1.43594i	−0.0697556	−	0.997564i	$-0.522222\pi$
$233$	12.6547	−	21.9186i	0.829038	−	1.43594i	0.898794	−	0.438372i	$-0.144445\pi$
$234$	0.686767	+	1.18951i	0.0448953	+	0.0777610i
$235$		0			0
$236$	13.7901			0.897658
$237$	1.36102	+	2.35736i	0.0884077	+	0.153127i
$238$	−14.6991	−	25.4596i	−0.952801	−	1.65030i
$239$	−23.5500			−1.52332			−0.761660	−	0.647977i	$-0.775615\pi$
$239$	−23.5500			−1.52332			−0.761660	+	0.647977i	$0.775615\pi$
$240$		0			0
$241$	−4.19208	−	7.26089i	−0.270035	−	0.467715i	0.698835	−	0.715283i	$-0.253702\pi$
$241$	−4.19208	−	7.26089i	−0.270035	−	0.467715i	−0.968871	+	0.247568i	$0.920369\pi$
$242$	−14.1378	+	24.4873i	−0.908809	+	1.57410i
$243$	3.91213	+	6.77601i	0.250963	+	0.434681i
$244$	−17.7585	+	30.7586i	−1.13687	+	1.96912i
$245$		0			0
$246$	−16.5154			−1.05298
$247$	−2.62739	−	0.979387i	−0.167177	−	0.0623169i
$248$	−49.0745			−3.11623
$249$	5.54929	−	9.61165i	0.351672	−	0.609113i
$250$		0			0
$251$	−9.12391	−	15.8031i	−0.575896	−	0.997481i	−0.995944	−	0.0899792i	$-0.971320\pi$
$251$	−9.12391	−	15.8031i	−0.575896	−	0.997481i	0.420048	−	0.907502i	$-0.362013\pi$
$252$	6.18233	−	10.7081i	0.389450	−	0.674548i
$253$	−0.180510	−	0.312652i	−0.0113486	−	0.0196563i
$254$	24.3669			1.52891
$255$		0			0
$256$	−32.6176	−	56.4954i	−2.03860	−	3.53096i
$257$	7.04989	+	12.2108i	0.439760	+	0.761687i	0.997671	−	0.0682144i	$-0.0217302\pi$
$257$	7.04989	+	12.2108i	0.439760	+	0.761687i	−0.557911	+	0.829901i	$0.688397\pi$
$258$	8.46934			0.527278
$259$	−18.1306			−1.12658
$260$		0			0
$261$	−3.75679	+	6.50696i	−0.232540	+	0.402770i
$262$	28.8389	+	49.9504i	1.78167	+	3.08595i
$263$	−3.20536	+	5.55184i	−0.197651	+	0.342341i	−0.947766	−	0.318966i	$-0.896665\pi$
$263$	−3.20536	+	5.55184i	−0.197651	+	0.342341i	0.750116	+	0.661307i	$0.229998\pi$
$264$	6.41700	−	11.1146i	0.394939	−	0.684055i
$265$		0			0
$266$	5.68558	+	33.7708i	0.348605	+	2.07062i
$267$	−6.63288			−0.405926
$268$	−7.09857	+	12.2951i	−0.433614	+	0.751042i
$269$	−8.99557	+	15.5808i	−0.548469	+	0.949977i	0.449910	+	0.893074i	$0.351456\pi$
$269$	−8.99557	+	15.5808i	−0.548469	+	0.949977i	−0.998380	+	0.0569032i	$0.981877\pi$
$270$		0			0
$271$	−5.94095	+	10.2900i	−0.360887	+	0.625075i	−0.988107	−	0.153767i	$-0.950859\pi$
$271$	−5.94095	+	10.2900i	−0.360887	+	0.625075i	0.627220	+	0.778842i	$0.284193\pi$
$272$	30.3488	+	52.5656i	1.84017	+	3.18726i
$273$	2.73390			0.165463
$274$	14.3824			0.868874
$275$		0			0
$276$	−1.74596	−	3.02409i	−0.105094	−	0.182029i
$277$	−23.6240			−1.41943			−0.709715	−	0.704489i	$-0.751176\pi$
$277$	−23.6240			−1.41943			−0.709715	+	0.704489i	$0.751176\pi$
$278$	29.5765			1.77388
$279$	1.90970	+	3.30770i	0.114331	+	0.198027i
$280$		0			0
$281$	−6.90465	−	11.9592i	−0.411897	−	0.713426i	0.583200	−	0.812328i	$-0.301800\pi$
$281$	−6.90465	−	11.9592i	−0.411897	−	0.713426i	−0.995097	+	0.0989020i	$0.968467\pi$
$282$	−8.13474	+	14.0898i	−0.484417	+	0.839035i
$283$	−5.87868	+	10.1822i	−0.349451	+	0.605268i	−0.986152	−	0.165843i	$-0.946965\pi$
$283$	−5.87868	+	10.1822i	−0.349451	+	0.605268i	0.636701	+	0.771111i	$0.280299\pi$
$284$	−9.99179			−0.592904
$285$		0			0
$286$	−1.53431			−0.0907257
$287$	5.71681	−	9.90181i	0.337453	−	0.584485i
$288$	−9.61689	+	16.6569i	−0.566680	+	0.981519i
$289$	1.49927	+	2.59681i	0.0881922	+	0.152753i
$290$		0			0
$291$	8.09675	+	14.0240i	0.474640	+	0.822100i
$292$	39.9805			2.33968
$293$	27.0576			1.58072			0.790362	−	0.612640i	$-0.209892\pi$
$293$	27.0576			1.58072			0.790362	+	0.612640i	$0.209892\pi$
$294$	−2.29342	−	3.97232i	−0.133755	−	0.231670i
$295$		0			0
$296$	63.3107			3.67986
$297$	−4.86949			−0.282557
$298$	−20.5632	−	35.6165i	−1.19119	−	2.06321i
$299$	−0.134272	+	0.232566i	−0.00776516	+	0.0134497i
$300$		0			0
$301$	−2.93167	+	5.07780i	−0.168979	+	0.292679i
$302$	29.5921	−	51.2549i	1.70283	−	2.94939i
$303$	7.90117			0.453910
$304$	−11.7388	−	69.7256i	−0.673269	−	3.99904i
$305$		0			0
$306$	3.99480	−	6.91920i	0.228368	−	0.395544i
$307$	4.41912	−	7.65414i	0.252212	−	0.436845i	−0.711922	−	0.702258i	$-0.752175\pi$
$307$	4.41912	−	7.65414i	0.252212	−	0.436845i	0.964135	+	0.265414i	$0.0855085\pi$
$308$	6.90601	+	11.9616i	0.393506	+	0.681573i
$309$	0.287294	−	0.497608i	0.0163436	−	0.0283080i
$310$		0			0
$311$	−0.651493			−0.0369428			−0.0184714	−	0.999829i	$-0.505880\pi$
$311$	−0.651493			−0.0369428			−0.0184714	+	0.999829i	$0.505880\pi$
$312$	−9.54656			−0.540468
$313$	−1.48278	−	2.56825i	−0.0838116	−	0.145166i	0.821073	−	0.570824i	$-0.193376\pi$
$313$	−1.48278	−	2.56825i	−0.0838116	−	0.145166i	−0.904884	+	0.425658i	$0.860043\pi$
$314$	3.35261	+	5.80690i	0.189199	+	0.327702i
$315$		0			0
$316$	10.2295			0.575453
$317$	−5.18993	−	8.98921i	−0.291495	−	0.504885i	0.682668	−	0.730728i	$-0.260819\pi$
$317$	−5.18993	−	8.98921i	−0.291495	−	0.504885i	−0.974164	+	0.225844i	$0.927486\pi$
$318$	−22.6053	+	39.1535i	−1.26764	+	2.19562i
$319$	−4.19654	−	7.26862i	−0.234961	−	0.406965i
$320$		0			0
$321$	4.79903	−	8.31216i	0.267856	−	0.463939i
$322$	3.27981			0.182777
$323$	2.70787	+	16.0840i	0.150670	+	0.894938i
$324$	−34.0778			−1.89321
$325$		0			0
$326$	−24.5705	+	42.5574i	−1.36083	+	2.35703i
$327$	4.90007	+	8.48718i	0.270975	+	0.469342i
$328$	−19.9626	+	34.5763i	−1.10225	+	1.90916i
$329$	−5.63170	−	9.75438i	−0.310485	−	0.537776i
$330$		0			0
$331$	15.0922			0.829543			0.414772	−	0.909926i	$-0.363861\pi$
$331$	15.0922			0.829543			0.414772	+	0.909926i	$0.363861\pi$
$332$	−20.8543	−	36.1207i	−1.14453	−	1.98238i
$333$	−2.46370	−	4.26725i	−0.135010	−	0.233844i
$334$	−1.11865			−0.0612096
$335$		0			0
$336$	34.4696	+	59.7032i	1.88047	+	3.25708i
$337$	7.89872	−	13.6810i	0.430271	−	0.745251i	−0.566626	−	0.823975i	$-0.691751\pi$
$337$	7.89872	−	13.6810i	0.430271	−	0.745251i	0.996896	+	0.0787246i	$0.0250848\pi$
$338$	−17.3565	−	30.0623i	−0.944067	−	1.63517i
$339$	−0.219695	+	0.380522i	−0.0119322	+	0.0206671i
$340$		0			0
$341$	−4.26649			−0.231043
$342$	−7.17575	+	5.92714i	−0.388020	+	0.320503i
$343$	−16.7650			−0.905224
$344$	10.2371	−	17.7313i	0.551950	−	0.956005i
$345$		0			0
$346$	−24.8511	−	43.0434i	−1.33600	−	2.31403i
$347$	−10.6761	+	18.4915i	−0.573122	+	0.992676i	0.423121	+	0.906073i	$0.360935\pi$
$347$	−10.6761	+	18.4915i	−0.573122	+	0.992676i	−0.996243	+	0.0866031i	$0.972399\pi$
$348$	−40.5905	−	70.3048i	−2.17588	−	3.76873i
$349$	−32.3897			−1.73378			−0.866891	−	0.498497i	$-0.833885\pi$
$349$	−32.3897			−1.73378			−0.866891	+	0.498497i	$0.833885\pi$
$350$		0			0
$351$	1.81108	+	3.13689i	0.0966685	+	0.167435i
$352$	−10.7426	−	18.6067i	−0.572582	−	0.991741i
$353$	−0.730583			−0.0388850			−0.0194425	−	0.999811i	$-0.506189\pi$
$353$	−0.730583			−0.0388850			−0.0194425	+	0.999811i	$0.506189\pi$
$354$	10.1206			0.537902
$355$		0			0
$356$	−12.4632	+	21.5870i	−0.660551	+	1.14411i
$357$	−7.95132	−	13.7721i	−0.420828	−	0.728896i
$358$	27.7902	−	48.1340i	1.46876	−	2.54396i
$359$	13.4248	−	23.2524i	0.708533	−	1.22722i	−0.256868	−	0.966447i	$-0.582691\pi$
$359$	13.4248	−	23.2524i	0.708533	−	1.22722i	0.965401	−	0.260769i	$-0.0839761\pi$
$360$		0			0
$361$	3.58853	−	18.6580i	0.188870	−	0.982002i
$362$	47.1919			2.48035
$363$	−7.64766	+	13.2461i	−0.401398	+	0.695242i
$364$	5.13702	−	8.89759i	0.269253	−	0.466360i
$365$		0			0
$366$	−13.0330	+	22.5738i	−0.681245	+	1.17995i
$367$	−11.4822	−	19.8877i	−0.599364	−	1.03813i	−0.992915	−	0.118826i	$-0.962087\pi$
$367$	−11.4822	−	19.8877i	−0.599364	−	1.03813i	0.393551	−	0.919303i	$-0.371246\pi$
$368$	−6.77173			−0.353001
$369$	3.10734			0.161761
$370$		0			0
$371$	−15.6497	−	27.1060i	−0.812491	−	1.40728i
$372$	−41.2670			−2.13960
$373$	−29.5305			−1.52903			−0.764515	−	0.644606i	$-0.777021\pi$
$373$	−29.5305			−1.52903			−0.764515	+	0.644606i	$0.777021\pi$
$374$	4.46241	+	7.72912i	0.230746	+	0.399663i
$375$		0			0
$376$	19.6654	+	34.0615i	1.01417	+	1.75659i
$377$	−3.12159	+	5.40676i	−0.160770	+	0.278462i
$378$	22.1193	−	38.3118i	1.13769	−	1.97054i
$379$	17.5117			0.899517			0.449759	−	0.893150i	$-0.351510\pi$
$379$	17.5117			0.899517			0.449759	+	0.893150i	$0.351510\pi$
$380$		0			0
$381$	13.1810			0.675282
$382$	7.28226	−	12.6132i	0.372593	−	0.645350i
$383$	4.05326	−	7.02045i	0.207112	−	0.358728i	−0.743692	−	0.668523i	$-0.766927\pi$
$383$	4.05326	−	7.02045i	0.207112	−	0.358728i	0.950804	+	0.309794i	$0.100260\pi$
$384$	−37.1601	−	64.3631i	−1.89632	−	3.28452i
$385$		0			0
$386$	−24.8272	−	43.0019i	−1.26367	−	2.18874i
$387$	−1.59349			−0.0810016
$388$	60.8554			3.08947
$389$	−8.65392	−	14.9890i	−0.438771	−	0.759974i	0.558824	−	0.829286i	$-0.311253\pi$
$389$	−8.65392	−	14.9890i	−0.438771	−	0.759974i	−0.997595	+	0.0693125i	$0.977919\pi$
$390$		0			0
$391$	1.56208			0.0789976
$392$	−11.0885			−0.560054
$393$	15.6001	+	27.0201i	0.786920	+	1.36298i
$394$	−11.1394	+	19.2940i	−0.561196	+	0.972019i
$395$		0			0
$396$	−1.87686	+	3.25081i	−0.0943156	+	0.163359i
$397$	−5.69472	+	9.86354i	−0.285810	+	0.495037i	−0.972805	−	0.231625i	$-0.925596\pi$
$397$	−5.69472	+	9.86354i	−0.285810	+	0.495037i	0.686996	+	0.726662i	$0.258929\pi$
$398$	−3.87155			−0.194063
$399$	3.07555	+	18.2679i	0.153970	+	0.914541i
$400$		0			0
$401$	4.46930	−	7.74106i	0.223186	−	0.386570i	−0.732587	−	0.680673i	$-0.761687\pi$
$401$	4.46930	−	7.74106i	0.223186	−	0.386570i	0.955774	+	0.294103i	$0.0950208\pi$
$402$	−5.20966	+	9.02339i	−0.259834	+	0.450046i
$403$	1.58681	+	2.74844i	0.0790447	+	0.136909i
$404$	14.8464	−	25.7146i	0.738634	−	1.27935i
$405$		0			0
$406$	76.2500			3.78422
$407$	5.50417			0.272832
$408$	27.7653	+	48.0910i	1.37459	+	2.38086i
$409$	3.27235	+	5.66788i	0.161808	+	0.280259i	0.935517	−	0.353282i	$-0.114934\pi$
$409$	3.27235	+	5.66788i	0.161808	+	0.280259i	−0.773709	+	0.633541i	$0.781601\pi$
$410$		0			0
$411$	7.78001			0.383760
$412$	−1.07966	−	1.87002i	−0.0531909	−	0.0921293i
$413$	−3.50324	+	6.06780i	−0.172383	+	0.298577i
$414$	0.445681	+	0.771941i	0.0219040	+	0.0379389i
$415$		0			0
$416$	−7.99086	+	13.8406i	−0.391784	+	0.678590i
$417$	15.9991			0.783479
$418$	−1.72605	−	10.2523i	−0.0844239	−	0.501455i
$419$	21.8441			1.06715			0.533576	−	0.845752i	$-0.320848\pi$
$419$	21.8441			1.06715			0.533576	+	0.845752i	$0.320848\pi$
$420$		0			0
$421$	14.6717	−	25.4121i	0.715054	−	1.23851i	−0.247885	−	0.968789i	$-0.579736\pi$
$421$	14.6717	−	25.4121i	0.715054	−	1.23851i	0.962939	−	0.269720i	$-0.0869311\pi$
$422$	26.0858	+	45.1819i	1.26984	+	2.19942i
$423$	1.53054	−	2.65097i	0.0744172	−	0.128894i
$424$	54.6474	+	94.6521i	2.65391	+	4.59671i
$425$		0			0
$426$	−7.33299			−0.355285
$427$	−9.02276	−	15.6279i	−0.436642	−	0.756286i
$428$	−18.0348	−	31.2372i	−0.871746	−	1.50991i
$429$	−0.829969			−0.0400713
$430$		0			0
$431$	6.44336	+	11.1602i	0.310366	+	0.537570i	0.978442	−	0.206524i	$-0.0662151\pi$
$431$	6.44336	+	11.1602i	0.310366	+	0.537570i	−0.668076	+	0.744093i	$0.732882\pi$
$432$	−45.6691	+	79.1011i	−2.19725	+	3.80576i
$433$	−6.92144	−	11.9883i	−0.332623	−	0.576120i	0.650402	−	0.759590i	$-0.274600\pi$
$433$	−6.92144	−	11.9883i	−0.332623	−	0.576120i	−0.983025	+	0.183470i	$0.941267\pi$
$434$	19.3802	−	33.5675i	0.930280	−	1.61129i
$435$		0			0
$436$	36.8291			1.76379
$437$	−1.70506	−	0.635578i	−0.0815641	−	0.0304038i
$438$	29.3418			1.40200
$439$	0.0354040	−	0.0613216i	0.00168974	−	0.00292672i	−0.865179	−	0.501463i	$-0.832795\pi$
$439$	0.0354040	−	0.0613216i	0.00168974	−	0.00292672i	0.866869	+	0.498536i	$0.166129\pi$
$440$		0			0
$441$	0.431503	+	0.747384i	0.0205477	+	0.0355897i
$442$	3.31936	−	5.74930i	0.157886	−	0.273466i
$443$	−1.89457	−	3.28149i	−0.0900137	−	0.155908i	0.817503	−	0.575924i	$-0.195358\pi$
$443$	−1.89457	−	3.28149i	−0.0900137	−	0.155908i	−0.907517	+	0.420016i	$0.862024\pi$
$444$	53.2384			2.52658
$445$		0			0
$446$	22.2682	+	38.5697i	1.05443	+	1.82633i
$447$	−11.1234	−	19.2663i	−0.526120	−	0.911266i
$448$	102.773			4.85555
$449$	−26.5765			−1.25422			−0.627112	−	0.778929i	$-0.715763\pi$
$449$	−26.5765			−1.25422			−0.627112	+	0.778929i	$0.715763\pi$
$450$		0			0
$451$	−1.73553	+	3.00603i	−0.0817230	+	0.141548i
$452$	0.825616	+	1.43001i	0.0388337	+	0.0672620i
$453$	16.0075	−	27.7258i	0.752098	−	1.30267i
$454$	−36.2936	+	62.8624i	−1.70334	+	2.95028i
$455$		0			0
$456$	−10.7396	−	63.7902i	−0.502927	−	2.98725i
$457$	33.1523			1.55080			0.775400	−	0.631471i	$-0.217548\pi$
$457$	33.1523			1.55080			0.775400	+	0.631471i	$0.217548\pi$
$458$	−18.3854	+	31.8445i	−0.859094	+	1.48799i
$459$	10.5348	−	18.2467i	0.491720	−	0.851684i
$460$		0			0
$461$	9.62679	−	16.6741i	0.448364	−	0.776590i	−0.549915	−	0.835220i	$-0.685340\pi$
$461$	9.62679	−	16.6741i	0.448364	−	0.776590i	0.998280	+	0.0586304i	$0.0186734\pi$
$462$	5.06833	+	8.77861i	0.235800	+	0.408418i
$463$	−39.1713			−1.82044			−0.910222	−	0.414120i	$-0.864089\pi$
$463$	−39.1713			−1.82044			−0.910222	+	0.414120i	$0.864089\pi$
$464$	−157.431			−7.30855
$465$		0			0
$466$	−34.9019	−	60.4519i	−1.61680	−	2.80038i
$467$	39.0650			1.80771			0.903856	−	0.427836i	$-0.140724\pi$
$467$	39.0650			1.80771			0.903856	+	0.427836i	$0.140724\pi$
$468$	2.79220			0.129069
$469$	−3.60665	−	6.24691i	−0.166540	−	0.288455i
$470$		0			0
$471$	1.81356	+	3.14118i	0.0835644	+	0.144738i
$472$	12.2330	−	21.1882i	0.563071	−	0.975268i
$473$	0.890007	−	1.54154i	0.0409226	−	0.0708800i
$474$	7.50743			0.344828
$475$		0			0
$476$	−59.7623			−2.73920
$477$	4.25314	−	7.36666i	0.194738	−	0.337296i
$478$	−32.4756	+	56.2493i	−1.48540	+	2.57279i
$479$	12.3775	+	21.4385i	0.565543	+	0.979550i	0.996999	+	0.0774158i	$0.0246669\pi$
$479$	12.3775	+	21.4385i	0.565543	+	0.979550i	−0.431455	+	0.902134i	$0.642000\pi$
$480$		0			0
$481$	−2.04714	−	3.54574i	−0.0933413	−	0.161672i
$482$	−23.1236			−1.05325
$483$	1.77418			0.0807280
$484$	28.7400	+	49.7792i	1.30637	+	2.26269i
$485$		0			0
$486$	21.5794			0.978863
$487$	−21.8871			−0.991797			−0.495899	−	0.868380i	$-0.665161\pi$
$487$	−21.8871			−0.991797			−0.495899	+	0.868380i	$0.665161\pi$
$488$	31.5067	+	54.5713i	1.42624	+	2.47033i
$489$	−13.2911	+	23.0209i	−0.601046	+	1.04104i
$490$		0			0
$491$	−4.69777	+	8.13677i	−0.212007	+	0.367207i	−0.952343	−	0.305030i	$-0.901333\pi$
$491$	−4.69777	+	8.13677i	−0.212007	+	0.367207i	0.740335	+	0.672238i	$0.234667\pi$
$492$	−16.7867	+	29.0754i	−0.756803	+	1.31082i
$493$	36.3155			1.63557
$494$	−5.96247	+	4.92498i	−0.268264	+	0.221585i
$495$		0			0
$496$	−40.0137	+	69.3058i	−1.79667	+	3.11192i
$497$	2.53832	−	4.39650i	0.113859	−	0.197210i
$498$	−15.3050	−	26.5091i	−0.685834	−	1.18790i
$499$	−12.4558	+	21.5740i	−0.557596	+	0.965785i	0.440100	+	0.897949i	$0.354943\pi$
$499$	−12.4558	+	21.5740i	−0.557596	+	0.965785i	−0.997696	+	0.0678367i	$0.978390\pi$
$500$		0			0
$501$	−0.605119			−0.0270347
$502$	−50.3278			−2.24624
$503$	−15.6590	−	27.1222i	−0.698200	−	1.20932i	−0.969090	−	0.246707i	$-0.920651\pi$
$503$	−15.6590	−	27.1222i	−0.698200	−	1.20932i	0.270890	−	0.962610i	$-0.412682\pi$
$504$	−10.9686	−	18.9981i	−0.488579	−	0.846244i
$505$		0			0
$506$	−0.995699			−0.0442642
$507$	−9.38878	−	16.2619i	−0.416971	−	0.722214i
$508$	24.7672	−	42.8980i	1.09887	−	1.90329i
$509$	4.83310	+	8.37117i	0.214223	+	0.371045i	0.953032	−	0.302870i	$-0.0979447\pi$
$509$	4.83310	+	8.37117i	0.214223	+	0.371045i	−0.738809	+	0.673915i	$0.764611\pi$
$510$		0			0
$511$	−10.1567	+	17.5919i	−0.449305	+	0.778219i
$512$	−80.2896			−3.54833
$513$	−18.9233	+	15.6306i	−0.835484	+	0.690106i
$514$	38.8874			1.71525
$515$		0			0
$516$	8.60848	−	14.9103i	0.378967	−	0.656390i
$517$	1.70969	+	2.96127i	0.0751922	+	0.130237i
$518$	−25.0023	+	43.3052i	−1.09854	+	1.90272i
$519$	−13.4429	−	23.2839i	−0.590080	−	1.02205i
$520$		0			0
$521$	−0.982633			−0.0430499			−0.0215250	−	0.999768i	$-0.506852\pi$
$521$	−0.982633			−0.0430499			−0.0215250	+	0.999768i	$0.506852\pi$
$522$	10.3613	+	17.9463i	0.453502	+	0.785488i
$523$	19.8604	+	34.3993i	0.868436	+	1.50418i	0.863594	+	0.504187i	$0.168208\pi$
$523$	19.8604	+	34.3993i	0.868436	+	1.50418i	0.00484172	+	0.999988i	$0.498459\pi$
$524$	117.251			5.12212
$525$		0			0
$526$	8.84043	+	15.3121i	0.385461	+	0.667638i
$527$	9.23020	−	15.9872i	0.402074	−	0.696413i
$528$	−10.4644	−	18.1249i	−0.455406	−	0.788786i
$529$	11.4129	−	19.7677i	0.496211	−	0.859463i
$530$		0			0
$531$	−1.90417			−0.0826337
$532$	65.2327	+	24.3161i	2.82820	+	1.05424i
$533$	2.58195			0.111837
$534$	−9.14680	+	15.8427i	−0.395821	+	0.685582i
$535$		0			0
$536$	12.5941	+	21.8137i	0.543984	+	0.942208i
$537$	15.0328	−	26.0376i	0.648713	−	1.12360i
$538$	24.8099	+	42.9720i	1.06963	+	1.85266i
$539$	−0.964024			−0.0415234
$540$		0			0
$541$	−15.3887	−	26.6541i	−0.661614	−	1.14595i	−0.980191	−	0.198052i	$-0.936538\pi$
$541$	−15.3887	−	26.6541i	−0.661614	−	1.14595i	0.318577	−	0.947897i	$-0.396795\pi$
$542$	16.3852	+	28.3801i	0.703807	+	1.21903i
$543$	25.5280			1.09551
$544$	92.9629			3.98575
$545$		0			0
$546$	3.77007	−	6.52996i	0.161344	−	0.279456i
$547$	−8.93287	−	15.4722i	−0.381942	−	0.661543i	0.609398	−	0.792865i	$-0.291411\pi$
$547$	−8.93287	−	15.4722i	−0.381942	−	0.661543i	−0.991340	+	0.131322i	$0.958078\pi$
$548$	14.6187	−	25.3203i	0.624480	−	1.08163i
$549$	2.45213	−	4.24722i	0.104654	−	0.181267i
$550$		0			0
$551$	−39.6397	−	14.7761i	−1.68871	−	0.629482i
$552$	−6.19529			−0.263689
$553$	−2.59870	+	4.50109i	−0.110508	+	0.191406i
$554$	−32.5777	+	56.4263i	−1.38409	+	2.39732i
$555$		0			0
$556$	30.0624	−	52.0696i	1.27493	−	2.20824i
$557$	−5.32878	−	9.22971i	−0.225787	−	0.391075i	0.730768	−	0.682626i	$-0.239162\pi$
$557$	−5.32878	−	9.22971i	−0.225787	−	0.391075i	−0.956555	+	0.291551i	$0.905829\pi$
$558$	10.5340			0.445939
$559$	−1.32406			−0.0560019
$560$		0			0
$561$	2.41389	+	4.18098i	0.101915	+	0.176521i
$562$	−38.0863			−1.60657
$563$	−7.75961			−0.327029			−0.163514	−	0.986541i	$-0.552283\pi$
$563$	−7.75961			−0.327029			−0.163514	+	0.986541i	$0.552283\pi$
$564$	16.5368	+	28.6425i	0.696324	+	1.20607i
$565$		0			0
$566$	16.2135	+	28.0826i	0.681504	+	1.18040i
$567$	8.65716	−	14.9946i	0.363567	−	0.629716i
$568$	−8.86361	+	15.3522i	−0.371909	+	0.644165i
$569$	5.72754			0.240111			0.120056	−	0.992767i	$-0.461693\pi$
$569$	5.72754			0.240111			0.120056	+	0.992767i	$0.461693\pi$
$570$		0			0
$571$	−20.8347			−0.871903			−0.435952	−	0.899970i	$-0.643588\pi$
$571$	−20.8347			−0.871903			−0.435952	+	0.899970i	$0.643588\pi$
$572$	−1.55952	+	2.70116i	−0.0652067	+	0.112941i
$573$	3.93926	−	6.82300i	0.164565	−	0.285035i
$574$	−15.7671	−	27.3093i	−0.658104	−	1.13987i
$575$		0			0
$576$	13.9654	+	24.1887i	0.581890	+	1.00786i
$577$	5.11190			0.212811			0.106406	−	0.994323i	$-0.466066\pi$
$577$	5.11190			0.212811			0.106406	+	0.994323i	$0.466066\pi$
$578$	8.27001			0.343987
$579$	−13.4300	−	23.2614i	−0.558131	−	0.966712i
$580$		0			0
$581$	21.1914			0.879167
$582$	44.6619			1.85130
$583$	4.75099	+	8.22896i	0.196766	+	0.340809i
$584$	35.4663	−	61.4294i	1.46760	−	2.54197i
$585$		0			0
$586$	37.3127	−	64.6275i	1.54137	−	2.66974i
$587$	−5.33462	+	9.23984i	−0.220184	+	0.381369i	−0.954864	−	0.297045i	$-0.903999\pi$
$587$	−5.33462	+	9.23984i	−0.220184	+	0.381369i	0.734680	+	0.678414i	$0.237332\pi$
$588$	−9.32439			−0.384531
$589$	−16.5800	+	13.6950i	−0.683165	+	0.564292i
$590$		0			0
$591$	−6.02574	+	10.4369i	−0.247866	+	0.429316i
$592$	51.6215	−	89.4110i	2.12163	−	3.67477i
$593$	−8.50133	−	14.7247i	−0.349108	−	0.604673i	0.636983	−	0.770878i	$-0.280182\pi$
$593$	−8.50133	−	14.7247i	−0.349108	−	0.604673i	−0.986091	+	0.166205i	$0.946849\pi$
$594$	−6.71507	+	11.6308i	−0.275523	+	0.477219i
$595$		0			0
$596$	−83.6040			−3.42455
$597$	−2.09427			−0.0857128
$598$	0.370325	+	0.641421i	0.0151437	+	0.0262297i
$599$	−14.3375	−	24.8334i	−0.585816	−	1.01466i	−0.994773	−	0.102110i	$-0.967441\pi$
$599$	−14.3375	−	24.8334i	−0.585816	−	1.01466i	0.408957	−	0.912554i	$-0.365893\pi$
$600$		0			0
$601$	27.4370			1.11918			0.559590	−	0.828770i	$-0.310959\pi$
$601$	27.4370			1.11918			0.559590	+	0.828770i	$0.310959\pi$
$602$	8.08559	+	14.0046i	0.329544	+	0.570787i
$603$	0.980187	−	1.69773i	0.0399163	−	0.0691371i
$604$	−60.1564	−	104.194i	−2.44773	−	4.23959i
$605$		0			0
$606$	10.8958	−	18.8720i	0.442611	−	0.766624i
$607$	17.7547			0.720639			0.360320	−	0.932829i	$-0.382668\pi$
$607$	17.7547			0.720639			0.360320	+	0.932829i	$0.382668\pi$
$608$	−101.472	−	37.8248i	−4.11524	−	1.53400i
$609$	41.2466			1.67140
$610$		0			0
$611$	1.27175	−	2.20274i	0.0514496	−	0.0891133i
$612$	−8.12086	−	14.0657i	−0.328266	−	0.568574i
$613$	17.3196	−	29.9983i	0.699530	−	1.21162i	−0.269099	−	0.963112i	$-0.586726\pi$
$613$	17.3196	−	29.9983i	0.699530	−	1.21162i	0.968629	−	0.248509i	$-0.0799407\pi$
$614$	−12.1880	−	21.1102i	−0.491868	−	0.851940i
$615$		0			0
$616$	24.5050			0.987334
$617$	2.23284	+	3.86740i	0.0898909	+	0.155696i	0.907465	−	0.420128i	$-0.138015\pi$
$617$	2.23284	+	3.86740i	0.0898909	+	0.155696i	−0.817574	+	0.575824i	$0.804681\pi$
$618$	−0.792362	−	1.37241i	−0.0318735	−	0.0552065i
$619$	−17.9112			−0.719913			−0.359957	−	0.932969i	$-0.617209\pi$
$619$	−17.9112			−0.719913			−0.359957	+	0.932969i	$0.617209\pi$
$620$		0			0
$621$	1.17531	+	2.03570i	0.0471636	+	0.0816898i
$622$	−0.898414	+	1.55610i	−0.0360231	+	0.0623939i
$623$	−6.33234	−	10.9679i	−0.253700	−	0.439421i
$624$	−7.78396	+	13.4822i	−0.311608	+	0.539720i
$625$		0			0
$626$	−8.17906			−0.326901
$627$	−0.933688	−	5.54586i	−0.0372879	−	0.221480i
$628$	13.6308			0.543927
$629$	−11.9078	+	20.6250i	−0.474796	+	0.822371i
$630$		0			0
$631$	−2.48440	−	4.30311i	−0.0989026	−	0.171304i	0.812328	−	0.583201i	$-0.198200\pi$
$631$	−2.48440	−	4.30311i	−0.0989026	−	0.171304i	−0.911231	+	0.411896i	$0.864867\pi$
$632$	9.07446	−	15.7174i	0.360963	−	0.625205i
$633$	14.1108	+	24.4407i	0.560855	+	0.971429i
$634$	−28.6278			−1.13696
$635$		0			0
$636$	45.9534	+	79.5935i	1.82217	+	3.15609i
$637$	0.358544	+	0.621016i	0.0142060	+	0.0246056i
$638$	−23.1483			−0.916449
$639$	1.37969			0.0545796
$640$		0			0
$641$	18.9760	−	32.8675i	0.749508	−	1.29819i	−0.198550	−	0.980091i	$-0.563623\pi$
$641$	18.9760	−	32.8675i	0.749508	−	1.29819i	0.948059	−	0.318096i	$-0.103043\pi$
$642$	−13.2358	−	22.9251i	−0.522375	−	0.904780i
$643$	17.6251	−	30.5276i	0.695067	−	1.20389i	−0.275092	−	0.961418i	$-0.588708\pi$
$643$	17.6251	−	30.5276i	0.695067	−	1.20389i	0.970158	−	0.242473i	$-0.0779585\pi$
$644$	3.33370	−	5.77413i	0.131366	−	0.227533i
$645$		0			0
$646$	42.1510	+	15.7122i	1.65841	+	0.618188i
$647$	−35.5219			−1.39651			−0.698254	−	0.715850i	$-0.746040\pi$
$647$	−35.5219			−1.39651			−0.698254	+	0.715850i	$0.746040\pi$
$648$	−30.2301	+	52.3601i	−1.18755	+	2.05690i
$649$	1.06353	−	1.84209i	0.0417471	−	0.0723082i
$650$		0			0
$651$	10.4835	−	18.1580i	0.410881	−	0.711667i
$652$	49.9483	+	86.5130i	1.95613	+	3.38811i
$653$	−8.02411			−0.314008			−0.157004	−	0.987598i	$-0.550184\pi$
$653$	−8.02411			−0.314008			−0.157004	+	0.987598i	$0.550184\pi$
$654$	27.0290			1.05692
$655$		0			0
$656$	32.5538	+	56.3848i	1.27101	+	2.20146i
$657$	−5.52059			−0.215379
$658$	−31.0646			−1.21102
$659$	23.6098	+	40.8933i	0.919706	+	1.59298i	0.799861	+	0.600185i	$0.204906\pi$
$659$	23.6098	+	40.8933i	0.919706	+	1.59298i	0.119844	+	0.992793i	$0.461760\pi$
$660$		0			0
$661$	13.0580	+	22.6171i	0.507896	+	0.879702i	0.999958	+	0.00914181i	$0.00290997\pi$
$661$	13.0580	+	22.6171i	0.507896	+	0.879702i	−0.492062	+	0.870560i	$0.663757\pi$
$662$	20.8123	−	36.0479i	0.808892	−	1.40104i
$663$	1.79557	−	3.11002i	0.0697342	−	0.120783i
$664$	−73.9986			−2.87170
$665$		0			0
$666$	−13.5898			−0.526596
$667$	−2.02577	+	3.50874i	−0.0784383	+	0.135859i
$668$	−1.13702	+	1.96938i	−0.0439928	+	0.0761978i
$669$	12.0458	+	20.8639i	0.465716	+	0.806643i
$670$		0			0
$671$	2.73917	+	4.74437i	0.105744	+	0.183154i
$672$	105.586			4.07306
$673$	−15.3820			−0.592931			−0.296466	−	0.955044i	$-0.595808\pi$
$673$	−15.3820			−0.592931			−0.296466	+	0.955044i	$0.595808\pi$
$674$	−21.7848	−	37.7324i	−0.839119	−	1.45340i
$675$		0			0
$676$	−70.5664			−2.71409
$677$	−24.4763			−0.940701			−0.470350	−	0.882480i	$-0.655872\pi$
$677$	−24.4763			−0.940701			−0.470350	+	0.882480i	$0.655872\pi$
$678$	0.605921	+	1.04949i	0.0232703	+	0.0403053i
$679$	−15.4598	+	26.7771i	−0.593291	+	1.02761i
$680$		0			0
$681$	−19.6326	+	34.0047i	−0.752324	+	1.30306i
$682$	−5.88352	+	10.1906i	−0.225292	+	0.390217i
$683$	17.8502			0.683018			0.341509	−	0.939879i	$-0.389062\pi$
$683$	17.8502			0.683018			0.341509	+	0.939879i	$0.389062\pi$
$684$	3.14113	+	18.6575i	0.120104	+	0.713386i
$685$		0			0
$686$	−23.1191	+	40.0434i	−0.882689	+	1.52886i
$687$	−9.94538	+	17.2259i	−0.379440	+	0.657210i
$688$	−16.6941	−	28.9150i	−0.636455	−	1.10237i
$689$	3.53402	−	6.12110i	0.134635	−	0.233195i
$690$		0			0
$691$	−9.27242			−0.352739			−0.176370	−	0.984324i	$-0.556435\pi$
$691$	−9.27242			−0.352739			−0.176370	+	0.984324i	$0.556435\pi$
$692$	−101.038			−3.84087
$693$	−0.953597	−	1.65168i	−0.0362241	−	0.0627421i
$694$	29.4448	+	50.9999i	1.11771	+	1.93593i
$695$		0			0
$696$	−144.030			−5.45943
$697$	−7.50937	−	13.0066i	−0.284438	−	0.492660i
$698$	−44.6657	+	77.3633i	−1.69062	+	2.92824i
$699$	−18.8798	−	32.7008i	−0.714100	−	1.23686i
$700$		0			0
$701$	3.84453	−	6.65892i	0.145206	−	0.251504i	−0.784244	−	0.620453i	$-0.786949\pi$
$701$	3.84453	−	6.65892i	0.145206	−	0.251504i	0.929450	+	0.368949i	$0.120282\pi$
$702$	9.98999			0.377048
$703$	21.3897	−	17.6678i	0.806728	−	0.666354i
$704$	−31.2001			−1.17590
$705$		0			0
$706$	−1.00748	+	1.74501i	−0.0379170	+	0.0656742i
$707$	7.54316	+	13.0651i	0.283690	+	0.491365i
$708$	10.2868	−	17.8173i	0.386603	−	0.669616i
$709$	−12.2187	−	21.1635i	−0.458885	−	0.794812i	0.540018	−	0.841654i	$-0.318418\pi$
$709$	−12.2187	−	21.1635i	−0.458885	−	0.794812i	−0.998902	+	0.0468421i	$0.985084\pi$
$710$		0			0
$711$	−1.41251			−0.0529732
$712$	22.1120	+	38.2992i	0.828683	+	1.43532i
$713$	1.02977	+	1.78361i	0.0385652	+	0.0667968i
$714$	−43.8597			−1.64141
$715$		0			0
$716$	−56.4935	−	97.8496i	−2.11126	−	3.65681i
$717$	−17.5673	+	30.4275i	−0.656063	+	1.13633i
$718$	−37.0258	−	64.1305i	−1.38179	−	2.39333i
$719$	11.0563	−	19.1501i	0.412331	−	0.714178i	−0.582813	−	0.812606i	$-0.698048\pi$
$719$	11.0563	−	19.1501i	0.412331	−	0.714178i	0.995144	+	0.0984282i	$0.0313815\pi$
$720$		0			0
$721$	1.09711			0.0408584
$722$	−39.6163	−	34.3008i	−1.47437	−	1.27655i
$723$	−12.5085			−0.465195
$724$	47.9672	−	83.0817i	1.78269	−	3.08771i
$725$		0			0
$726$	21.0924	+	36.5331i	0.782812	+	1.35587i
$727$	−14.5247	+	25.1575i	−0.538692	+	0.933042i	0.460283	+	0.887772i	$0.347748\pi$
$727$	−14.5247	+	25.1575i	−0.538692	+	0.933042i	−0.998975	+	0.0452694i	$0.985585\pi$
$728$	−9.11400	−	15.7859i	−0.337787	−	0.585065i
$729$	29.9075			1.10768
$730$		0			0
$731$	3.85092	+	6.66999i	0.142431	+	0.246698i
$732$	26.4942	+	45.8893i	0.979254	+	1.69612i
$733$	−14.5428			−0.537151			−0.268576	−	0.963259i	$-0.586553\pi$
$733$	−14.5428			−0.537151			−0.268576	+	0.963259i	$0.586553\pi$
$734$	−63.3360			−2.33777
$735$		0			0
$736$	−5.18571	+	8.98191i	−0.191148	+	0.331078i
$737$	1.09492	+	1.89646i	0.0403320	+	0.0698570i
$738$	4.28504	−	7.42191i	0.157735	−	0.273204i
$739$	2.37798	−	4.11878i	0.0874754	−	0.151512i	−0.818968	−	0.573839i	$-0.805453\pi$
$739$	2.37798	−	4.11878i	0.0874754	−	0.151512i	0.906443	+	0.422327i	$0.138787\pi$
$740$		0			0
$741$	−3.22533	+	2.66411i	−0.118486	+	0.0978687i
$742$	−86.3242			−3.16906
$743$	2.93853	−	5.08968i	0.107804	−	0.186722i	−0.807076	−	0.590447i	$-0.798951\pi$
$743$	2.93853	−	5.08968i	0.107804	−	0.186722i	0.914880	+	0.403725i	$0.132285\pi$
$744$	−36.6076	+	63.4062i	−1.34210	+	2.32458i
$745$		0			0
$746$	−40.7228	+	70.5339i	−1.49097	+	2.58243i
$747$	2.87961	+	4.98763i	0.105359	+	0.182488i
$748$	18.1429			0.663370
$749$	18.3263			0.669629
$750$		0			0
$751$	−0.810481	−	1.40379i	−0.0295749	−	0.0512252i	0.850859	−	0.525394i	$-0.176082\pi$
$751$	−0.810481	−	1.40379i	−0.0295749	−	0.0512252i	−0.880434	+	0.474169i	$0.842749\pi$
$752$	64.1382			2.33888
$753$	−27.2243			−0.992107
$754$	8.60941	+	14.9119i	0.313536	+	0.543060i
$755$		0			0
$756$	−44.9654	−	77.8824i	−1.63538	−	2.83255i
$757$	−14.0567	+	24.3470i	−0.510901	+	0.884907i	0.489019	+	0.872273i	$0.337355\pi$
$757$	−14.0567	+	24.3470i	−0.510901	+	0.884907i	−0.999920	+	0.0126336i	$0.995978\pi$
$758$	24.1488	−	41.8270i	0.877125	−	1.51922i
$759$	−0.538612			−0.0195504
$760$		0			0
$761$	20.1663			0.731027			0.365514	−	0.930806i	$-0.380893\pi$
$761$	20.1663			0.731027			0.365514	+	0.930806i	$0.380893\pi$
$762$	18.1767	−	31.4829i	0.658472	−	1.14051i
$763$	−9.35610	+	16.2052i	−0.338713	+	0.586669i
$764$	−14.8038	−	25.6409i	−0.535583	−	0.927656i
$765$		0			0
$766$	−11.1790	−	19.3625i	−0.403912	−	0.699597i
$767$	−1.58221			−0.0571303
$768$	−97.3257			−3.51194
$769$	−22.6524	−	39.2350i	−0.816865	−	1.41485i	−0.907981	−	0.419011i	$-0.862377\pi$
$769$	−22.6524	−	39.2350i	−0.816865	−	1.41485i	0.0911160	−	0.995840i	$-0.470957\pi$
$770$		0			0
$771$	21.0357			0.757583
$772$	−100.940			−3.63292
$773$	−10.0881	−	17.4731i	−0.362843	−	0.628462i	0.625585	−	0.780156i	$-0.284861\pi$
$773$	−10.0881	−	17.4731i	−0.362843	−	0.628462i	−0.988428	+	0.151694i	$0.951527\pi$
$774$	−2.19744	+	3.80607i	−0.0789852	+	0.136806i
$775$		0			0
$776$	53.9842	−	93.5034i	1.93792	−	3.35658i
$777$	−13.5247	+	23.4255i	−0.485196	+	0.840385i
$778$	−47.7353			−1.71139
$779$	2.90461	+	17.2526i	0.104068	+	0.618138i
$780$		0			0
$781$	−0.770594	+	1.33471i	−0.0275740	+	0.0477596i
$782$	2.15411	−	3.73104i	0.0770310	−	0.133422i
$783$	27.3239	+	47.3264i	0.976478	+	1.69131i
$784$	−9.04120	+	15.6598i	−0.322900	+	0.559279i
$785$		0			0
$786$	86.0505			3.06932
$787$	46.1385			1.64466			0.822331	−	0.569010i	$-0.192673\pi$
$787$	46.1385			1.64466			0.822331	+	0.569010i	$0.192673\pi$
$788$	22.6448	+	39.2220i	0.806689	+	1.39723i
$789$	4.78213	+	8.28289i	0.170248	+	0.294879i
$790$		0			0
$791$	−0.838961			−0.0298300
$792$	3.32988	+	5.76753i	0.118322	+	0.204940i
$793$	2.03753	−	3.52910i	0.0723546	−	0.125322i
$794$	15.7061	+	27.2038i	0.557389	+	0.965427i
$795$		0			0
$796$	−3.93515	+	6.81588i	−0.139478	+	0.241583i
$797$	1.86497			0.0660606			0.0330303	−	0.999454i	$-0.489484\pi$
$797$	1.86497			0.0660606			0.0330303	+	0.999454i	$0.489484\pi$
$798$	47.8744	+	17.8457i	1.69474	+	0.631729i
$799$	−14.7951			−0.523414
$800$		0			0
$801$	1.72095	−	2.98078i	0.0608069	−	0.105321i
$802$	−12.3264	−	21.3500i	−0.435261	−	0.753894i
$803$	3.08340	−	5.34061i	0.108811	−	0.188466i
$804$	10.5905	+	18.3433i	0.373498	+	0.646917i
$805$		0			0
$806$	8.75290			0.308308
$807$	13.4207	+	23.2453i	0.472429	+	0.818272i
$808$	−26.3401	−	45.6224i	−0.926641	−	1.60499i
$809$	18.2267			0.640816			0.320408	−	0.947280i	$-0.396180\pi$
$809$	18.2267			0.640816			0.320408	+	0.947280i	$0.396180\pi$
$810$		0			0
$811$	10.4890	+	18.1674i	0.368317	+	0.637944i	0.989303	−	0.145878i	$-0.0466008\pi$
$811$	10.4890	+	18.1674i	0.368317	+	0.637944i	−0.620986	+	0.783822i	$0.713267\pi$
$812$	77.5027	−	134.239i	2.71981	−	4.71085i
$813$	8.86342	+	15.3519i	0.310854	+	0.538414i
$814$	7.59030	−	13.1468i	0.266040	−	0.460794i
$815$		0			0
$816$	90.5558			3.17009
$817$	−1.48953	−	8.84739i	−0.0521119	−	0.309531i
$818$	18.0504			0.631118
$819$	−0.709332	+	1.22860i	−0.0247861	+	0.0429307i
$820$		0			0
$821$	11.0433	+	19.1276i	0.385415	+	0.667558i	0.991827	−	0.127593i	$-0.0407251\pi$
$821$	11.0433	+	19.1276i	0.385415	+	0.667558i	−0.606412	+	0.795151i	$0.707392\pi$
$822$	10.7287	−	18.5827i	0.374207	−	0.648145i
$823$	7.98847	+	13.8364i	0.278461	+	0.482308i	0.971002	−	0.239070i	$-0.0768425\pi$
$823$	7.98847	+	13.8364i	0.278461	+	0.482308i	−0.692542	+	0.721378i	$0.743509\pi$
$824$	−3.83101			−0.133460
$825$		0			0
$826$	9.66200	+	16.7351i	0.336184	+	0.582288i
$827$	24.6004	+	42.6092i	0.855441	+	1.48167i	0.876235	+	0.481883i	$0.160047\pi$
$827$	24.6004	+	42.6092i	0.855441	+	1.48167i	−0.0207946	+	0.999784i	$0.506620\pi$
$828$	1.81201			0.0629717
$829$	−35.8564			−1.24534			−0.622672	−	0.782483i	$-0.713953\pi$
$829$	−35.8564			−1.24534			−0.622672	+	0.782483i	$0.713953\pi$
$830$		0			0
$831$	−17.6226	+	30.5232i	−0.611320	+	1.05884i
$832$	11.6041	+	20.0989i	0.402300	+	0.696803i
$833$	2.08559	−	3.61234i	0.0722613	−	0.125160i
$834$	22.0629	−	38.2140i	0.763975	−	1.32324i
$835$		0			0
$836$	−19.8036	−	7.38199i	−0.684922	−	0.255311i
$837$	27.7794			0.960195
$838$	30.1232	−	52.1748i	1.04059	−	1.80235i
$839$	12.7415	−	22.0689i	0.439885	−	0.761903i	−0.557795	−	0.829979i	$-0.688352\pi$
$839$	12.7415	−	22.0689i	0.439885	−	0.761903i	0.997680	+	0.0680753i	$0.0216858\pi$
$840$		0			0
$841$	−32.5957	+	56.4574i	−1.12399	+	1.94681i
$842$	−40.4647	−	70.0870i	−1.39451	−	2.41536i
$843$	−20.6024			−0.709583
$844$	106.057			3.65065
$845$		0			0
$846$	−4.22124	−	7.31141i	−0.145129	−	0.251371i
$847$	−29.2046			−1.00348
$848$	178.231			6.12047
$849$	8.77051	+	15.1910i	0.301003	+	0.521353i
$850$		0			0
$851$	−1.32850	−	2.30103i	−0.0455404	−	0.0788782i
$852$	−7.45347	+	12.9098i	−0.255352	+	0.442282i
$853$	−28.5811	+	49.5039i	−0.978598	+	1.69498i	−0.311087	+	0.950382i	$0.600693\pi$
$853$	−28.5811	+	49.5039i	−0.978598	+	1.69498i	−0.667511	+	0.744600i	$0.732640\pi$
$854$	−49.7698			−1.70309
$855$		0			0
$856$	−63.9940			−2.18727
$857$	13.0987	−	22.6876i	0.447442	−	0.774993i	−0.550776	−	0.834653i	$-0.685668\pi$
$857$	13.0987	−	22.6876i	0.447442	−	0.774993i	0.998219	+	0.0596598i	$0.0190016\pi$
$858$	−1.14453	+	1.98239i	−0.0390737	+	0.0676777i
$859$	8.87246	+	15.3675i	0.302724	+	0.524334i	0.976752	−	0.214372i	$-0.0687705\pi$
$859$	8.87246	+	15.3675i	0.302724	+	0.524334i	−0.674028	+	0.738706i	$0.735437\pi$
$860$		0			0
$861$	−8.52902	−	14.7727i	−0.290668	−	0.503452i
$862$	35.5418			1.21056
$863$	−25.0867			−0.853960			−0.426980	−	0.904261i	$-0.640422\pi$
$863$	−25.0867			−0.853960			−0.426980	+	0.904261i	$0.640422\pi$
$864$	69.9456	+	121.149i	2.37960	+	4.12158i
$865$		0			0
$866$	−38.1789			−1.29737
$867$	4.47357			0.151930
$868$	−39.3972	−	68.2380i	−1.33723	−	2.31615i
$869$	0.788924	−	1.36646i	0.0267624	−	0.0463539i
$870$		0			0
$871$	0.814457	−	1.41068i	0.0275968	−	0.0477991i
$872$	32.6707	−	56.5874i	1.10637	−	1.91629i
$873$	−8.40305			−0.284400
$874$	−3.86938	+	3.19609i	−0.130884	+	0.108109i
$875$		0			0
$876$	29.8238	−	51.6563i	1.00765	−	1.74531i
$877$	5.00784	−	8.67383i	0.169103	−	0.292895i	−0.769002	−	0.639246i	$-0.779246\pi$
$877$	5.00784	−	8.67383i	0.169103	−	0.292895i	0.938105	+	0.346352i	$0.112580\pi$
$878$	−0.0976449	−	0.169126i	−0.00329536	−	0.00570772i
$879$	20.1839	−	34.9595i	0.680786	−	1.17916i
$880$		0			0
$881$	33.3473			1.12350			0.561750	−	0.827307i	$-0.310128\pi$
$881$	33.3473			1.12350			0.561750	+	0.827307i	$0.310128\pi$
$882$	2.38018			0.0801449
$883$	−13.6785	−	23.6919i	−0.460319	−	0.797296i	0.538658	−	0.842525i	$-0.318932\pi$
$883$	−13.6785	−	23.6919i	−0.460319	−	0.797296i	−0.998977	+	0.0452288i	$0.985598\pi$
$884$	−6.74778	−	11.6875i	−0.226953	−	0.393093i
$885$		0			0
$886$	−10.4505			−0.351092
$887$	8.58172	+	14.8640i	0.288146	+	0.499084i	0.973367	−	0.229251i	$-0.0736278\pi$
$887$	8.58172	+	14.8640i	0.288146	+	0.499084i	−0.685221	+	0.728335i	$0.740294\pi$
$888$	47.2272	−	81.7999i	1.58484	−	2.74503i
$889$	12.5837	+	21.7957i	0.422045	+	0.731004i
$890$		0			0
$891$	−2.62818	+	4.55213i	−0.0880472	+	0.152502i
$892$	90.5363			3.03138
$893$	16.1494	+	6.01985i	0.540419	+	0.201447i
$894$	−61.3571			−2.05209
$895$		0			0
$896$	70.9526	−	122.894i	2.37036	−	4.10559i
$897$	0.200323	+	0.346970i	0.00668859	+	0.0115850i
$898$	−36.6492	+	63.4783i	−1.22300	+	2.11830i
$899$	23.9403	+	41.4659i	0.798455	+	1.38296i
$900$		0			0
$901$	−41.1136			−1.36969
$902$	4.78663	+	8.29068i	0.159377	+	0.276049i
$903$	4.37381	+	7.57566i	0.145551	+	0.252102i
$904$	2.92958			0.0974364
$905$		0			0
$906$	−44.1489	−	76.4682i	−1.46675	−	2.54049i
$907$	1.51053	−	2.61631i	0.0501563	−	0.0868732i	−0.839857	−	0.542807i	$-0.817361\pi$
$907$	1.51053	−	2.61631i	0.0501563	−	0.0868732i	0.890014	+	0.455934i	$0.150695\pi$
$908$	73.7797	+	127.790i	2.44847	+	4.24087i
$909$	−2.05002	+	3.55074i	−0.0679948	+	0.117770i
$910$		0			0
$911$	−19.5682			−0.648324			−0.324162	−	0.946002i	$-0.605082\pi$
$911$	−19.5682			−0.648324			−0.324162	+	0.946002i	$0.605082\pi$
$912$	−98.8449	−	36.8454i	−3.27308	−	1.22007i
$913$	−6.43336			−0.212913
$914$	45.7173	−	79.1847i	1.51219	−	2.61920i
$915$		0			0
$916$	37.3749	+	64.7353i	1.23490	+	2.13891i
$917$	−29.7864	+	51.5916i	−0.983635	+	1.70371i
$918$	−29.0550	−	50.3248i	−0.958959	−	1.66096i
$919$	−1.81420			−0.0598448			−0.0299224	−	0.999552i	$-0.509526\pi$
$919$	−1.81420			−0.0598448			−0.0299224	+	0.999552i	$0.509526\pi$
$920$		0			0
$921$	−6.59297	−	11.4194i	−0.217246	−	0.376280i
$922$	−26.5508	−	45.9874i	−0.874406	−	1.51452i
$923$	1.14641			0.0377346
$924$	20.6064			0.677901
$925$		0			0
$926$	−54.0175	+	93.5611i	−1.77513	+	3.07461i
$927$	0.149081	+	0.258217i	0.00489648	+	0.00848095i
$928$	−120.559	+	208.814i	−3.95753	+	6.85465i
$929$	11.2377	−	19.4643i	0.368698	−	0.638603i	−0.620665	−	0.784076i	$-0.713137\pi$
$929$	11.2377	−	19.4643i	0.368698	−	0.638603i	0.989362	+	0.145473i	$0.0464705\pi$
$930$		0			0
$931$	−3.74628	+	3.09442i	−0.122780	+	0.101415i
$932$	−141.901			−4.64813
$933$	−0.485987	+	0.841755i	−0.0159105	+	0.0275578i
$934$	53.8710	−	93.3072i	1.76271	−	3.05311i
$935$		0			0
$936$	2.47693	−	4.29017i	0.0809610	−	0.140229i
$937$	27.5193	+	47.6647i	0.899015	+	1.55714i	0.828756	+	0.559611i	$0.189049\pi$
$937$	27.5193	+	47.6647i	0.899015	+	1.55714i	0.0702593	+	0.997529i	$0.477617\pi$
$938$	−19.8944			−0.649576
$939$	−4.42437			−0.144384
$940$		0			0
$941$	6.09781	+	10.5617i	0.198783	+	0.344302i	0.948134	−	0.317871i	$-0.102968\pi$
$941$	6.09781	+	10.5617i	0.198783	+	0.344302i	−0.749351	+	0.662173i	$0.769635\pi$
$942$	10.0036			0.325937
$943$	1.67557			0.0545640
$944$	−19.9488	−	34.5524i	−0.649279	−	1.12458i
$945$		0			0
$946$	−2.45465	−	4.25159i	−0.0798077	−	0.138231i
$947$	15.2153	−	26.3537i	0.494432	−	0.856381i	−0.505548	−	0.862799i	$-0.668710\pi$
$947$	15.2153	−	26.3537i	0.494432	−	0.856381i	0.999979	+	0.00641783i	$0.00204287\pi$
$948$	7.63077	−	13.2169i	0.247836	−	0.429264i
$949$	−4.58717			−0.148906
$950$		0			0
$951$	−15.4859			−0.502164
$952$	−53.0146	+	91.8239i	−1.71821	+	2.97603i
$953$	7.86891	−	13.6293i	0.254899	−	0.441498i	−0.709969	−	0.704233i	$-0.751291\pi$
$953$	7.86891	−	13.6293i	0.254899	−	0.441498i	0.964868	+	0.262735i	$0.0846245\pi$
$954$	−11.7302	−	20.3174i	−0.379780	−	0.657799i
$955$		0			0
$956$	66.0182	+	114.347i	2.13518	+	3.69824i
$957$	−12.5218			−0.404772
$958$	68.2748			2.20586
$959$	7.42750	+	12.8648i	0.239846	+	0.415426i
$960$		0			0
$961$	−6.66065			−0.214860
$962$	−11.2921			−0.364071
$963$	2.49029	+	4.31331i	0.0802484	+	0.138994i
$964$	−23.5035	+	40.7093i	−0.756997	+	1.31116i
$965$		0			0
$966$	2.44661	−	4.23765i	0.0787183	−	0.136344i
$967$	15.3186	−	26.5326i	0.492614	−	0.853232i	−0.507350	−	0.861740i	$-0.669375\pi$
$967$	15.3186	−	26.5326i	0.492614	−	0.853232i	0.999964	+	0.00850791i	$0.00270819\pi$
$968$	101.980			3.27776
$969$	22.8011	+	8.49934i	0.732478	+	0.273038i
$970$		0			0
$971$	−8.23824	+	14.2690i	−0.264378	+	0.457915i	−0.967400	−	0.253252i	$-0.918500\pi$
$971$	−8.23824	+	14.2690i	−0.264378	+	0.457915i	0.703023	+	0.711167i	$0.251833\pi$
$972$	21.9340	−	37.9907i	0.703532	−	1.21855i
$973$	15.2742	+	26.4556i	0.489667	+	0.848128i
$974$	−30.1824	+	52.2775i	−0.967108	+	1.67508i
$975$		0			0
$976$	102.758			3.28921
$977$	2.77995			0.0889383			0.0444692	−	0.999011i	$-0.485840\pi$
$977$	2.77995			0.0889383			0.0444692	+	0.999011i	$0.485840\pi$
$978$	36.6572	+	63.4921i	1.17217	+	2.03025i
$979$	1.92240	+	3.32969i	0.0614401	+	0.106417i
$980$		0			0
$981$	−5.08545			−0.162366
$982$	12.9565	+	22.4413i	0.413459	+	0.716132i
$983$	−0.855856	+	1.48239i	−0.0272976	+	0.0472808i	−0.879351	−	0.476173i	$-0.842023\pi$
$983$	−0.855856	+	1.48239i	−0.0272976	+	0.0472808i	0.852054	+	0.523454i	$0.175357\pi$
$984$	29.7826	+	51.5850i	0.949436	+	1.64447i
$985$		0			0
$986$	50.0794	−	86.7401i	1.59485	−	2.76237i
$987$	−16.8041			−0.534879
$988$	2.61003	+	15.5029i	0.0830360	+	0.493212i
$989$	−0.859257			−0.0273228
$990$		0			0
$991$	4.83711	−	8.37811i	0.153656	−	0.266140i	−0.778913	−	0.627132i	$-0.784229\pi$
$991$	4.83711	−	8.37811i	0.153656	−	0.266140i	0.932569	+	0.360992i	$0.117562\pi$
$992$	61.2840	+	106.147i	1.94577	+	3.37017i
$993$	11.2582	−	19.4997i	0.357267	−	0.618805i
$994$	−7.00073	−	12.1256i	−0.222050	−	0.384601i
$995$		0			0
$996$	−62.2259			−1.97170
$997$	11.3656	+	19.6857i	0.359951	+	0.623454i	0.987952	−	0.154759i	$-0.0494600\pi$
$997$	11.3656	+	19.6857i	0.359951	+	0.623454i	−0.628001	+	0.778212i	$0.716127\pi$
$998$	34.3532	+	59.5015i	1.08743	+	1.88349i
$999$	−35.8380			−1.13386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.e.201.4		8
5.2	odd	4		475.2.j.c.49.8		16
5.3	odd	4		475.2.j.c.49.1		16
5.4	even	2		95.2.e.c.11.1	✓	8
15.14	odd	2		855.2.k.h.676.4		8
19.7	even	3	inner	475.2.e.e.26.4		8
19.8	odd	6		9025.2.a.bp.1.4		4
19.11	even	3		9025.2.a.bg.1.1		4
20.19	odd	2		1520.2.q.o.961.3		8
95.7	odd	12		475.2.j.c.349.1		16
95.49	even	6		1805.2.a.o.1.4		4
95.64	even	6		95.2.e.c.26.1	yes	8
95.83	odd	12		475.2.j.c.349.8		16
95.84	odd	6		1805.2.a.i.1.1		4
285.254	odd	6		855.2.k.h.406.4		8
380.159	odd	6		1520.2.q.o.881.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.1	✓	8	5.4	even	2
95.2.e.c.26.1	yes	8	95.64	even	6
475.2.e.e.26.4		8	19.7	even	3	inner
475.2.e.e.201.4		8	1.1	even	1	trivial
475.2.j.c.49.1		16	5.3	odd	4
475.2.j.c.49.8		16	5.2	odd	4
475.2.j.c.349.1		16	95.7	odd	12
475.2.j.c.349.8		16	95.83	odd	12
855.2.k.h.406.4		8	285.254	odd	6
855.2.k.h.676.4		8	15.14	odd	2
1520.2.q.o.881.3		8	380.159	odd	6
1520.2.q.o.961.3		8	20.19	odd	2
1805.2.a.i.1.1		4	95.84	odd	6
1805.2.a.o.1.4		4	95.49	even	6
9025.2.a.bg.1.1		4	19.11	even	3
9025.2.a.bp.1.4		4	19.8	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37901 - 2.38851i) q^{2} +(0.745959 - 1.29204i) q^{3} +(-2.80333 - 4.85550i) q^{4} +(-2.05737 - 3.56347i) q^{6} +2.84864 q^{7} -9.94721 q^{8} +(0.387090 + 0.670459i) q^{9} +O(q^{10})\)	\(q+(1.37901 - 2.38851i) q^{2} +(0.745959 - 1.29204i) q^{3} +(-2.80333 - 4.85550i) q^{4} +(-2.05737 - 3.56347i) q^{6} +2.84864 q^{7} -9.94721 q^{8} +(0.387090 + 0.670459i) q^{9} -0.864801 q^{11} -8.36467 q^{12} +(0.321640 + 0.557098i) q^{13} +(3.92829 - 6.80401i) q^{14} +(-8.11063 + 14.0480i) q^{16} +(1.87093 - 3.24054i) q^{17} +2.13520 q^{18} +(-3.36069 + 2.77592i) q^{19} +(2.12497 - 3.68055i) q^{21} +(-1.19257 + 2.06559i) q^{22} +(0.208730 + 0.361531i) q^{23} +(-7.42021 + 12.8522i) q^{24} +1.77418 q^{26} +5.63077 q^{27} +(-7.98566 - 13.8316i) q^{28} +(4.85261 + 8.40497i) q^{29} +4.93349 q^{31} +(12.4220 + 21.5156i) q^{32} +(-0.645106 + 1.11736i) q^{33} +(-5.16005 - 8.93746i) q^{34} +(2.17028 - 3.75903i) q^{36} -6.36467 q^{37} +(1.99589 + 11.8551i) q^{38} +0.959723 q^{39} +(2.00686 - 3.47598i) q^{41} +(-5.86069 - 10.1510i) q^{42} +(-1.02915 + 1.78254i) q^{43} +(2.42432 + 4.19904i) q^{44} +1.15136 q^{46} +(-1.97698 - 3.42423i) q^{47} +(12.1004 + 20.9585i) q^{48} +1.11474 q^{49} +(-2.79127 - 4.83462i) q^{51} +(1.80333 - 3.12345i) q^{52} +(-5.49374 - 9.51544i) q^{53} +(7.76487 - 13.4492i) q^{54} -28.3360 q^{56} +(1.07966 + 6.41287i) q^{57} +26.7672 q^{58} +(-1.22980 + 2.13007i) q^{59} +(-3.16740 - 5.48609i) q^{61} +(6.80333 - 11.7837i) q^{62} +(1.10268 + 1.90989i) q^{63} +36.0778 q^{64} +(1.77921 + 3.08169i) q^{66} +(-1.26610 - 2.19295i) q^{67} -20.9793 q^{68} +0.622817 q^{69} +(0.891065 - 1.54337i) q^{71} +(-3.85046 - 6.66920i) q^{72} +(-3.56545 + 6.17554i) q^{73} +(-8.77693 + 15.2021i) q^{74} +(22.8996 + 8.53606i) q^{76} -2.46350 q^{77} +(1.32347 - 2.29231i) q^{78} +(-0.912262 + 1.58008i) q^{79} +(3.03905 - 5.26380i) q^{81} +(-5.53495 - 9.58681i) q^{82} +7.43913 q^{83} -23.8279 q^{84} +(2.83841 + 4.91626i) q^{86} +14.4794 q^{87} +8.60235 q^{88} +(-2.22294 - 3.85024i) q^{89} +(0.916237 + 1.58697i) q^{91} +(1.17028 - 2.02698i) q^{92} +(3.68018 - 6.37427i) q^{93} -10.9051 q^{94} +37.0653 q^{96} +(-5.42707 + 9.39996i) q^{97} +(1.53723 - 2.66256i) q^{98} +(-0.334755 - 0.579813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9}+O(q^{10}) \) 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9	\( 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9} - 4 q^{11} - 12 q^{12} + 7 q^{13} + q^{14} - 7 q^{16} - q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} - 23 q^{24} + 6 q^{26} - 24 q^{27} - 19 q^{28} + q^{29} + 30 q^{32} + 19 q^{33} - 15 q^{34} + 7 q^{36} + 4 q^{37} - 13 q^{38} + 30 q^{39} + 8 q^{41} - 15 q^{42} + q^{43} + 12 q^{44} + 24 q^{46} - 12 q^{47} + 23 q^{48} - 20 q^{49} - 22 q^{51} - 3 q^{52} - 5 q^{53} + 34 q^{54} - 82 q^{56} - 7 q^{57} + 54 q^{58} + 5 q^{59} + 37 q^{62} - 3 q^{63} + 112 q^{64} + 31 q^{66} + 4 q^{67} - 32 q^{68} - 18 q^{69} - 20 q^{71} + 17 q^{72} - 20 q^{73} - 25 q^{74} + 63 q^{76} - 28 q^{77} - 18 q^{78} - 17 q^{79} - 12 q^{81} + 21 q^{82} - 2 q^{83} - 40 q^{84} - 8 q^{86} + 32 q^{87} + 14 q^{88} - 11 q^{89} - 6 q^{91} - q^{92} - 8 q^{93} - 62 q^{94} + 42 q^{96} + q^{97} + 9 q^{98} - 38 q^{99}+O(q^{100}) \) 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9 - 4 * q^11 - 12 * q^12 + 7 * q^13 + q^14 - 7 * q^16 - q^17 + 20 * q^18 + 5 * q^19 + 4 * q^21 + 2 * q^22 + 2 * q^23 - 23 * q^24 + 6 * q^26 - 24 * q^27 - 19 * q^28 + q^29 + 30 * q^32 + 19 * q^33 - 15 * q^34 + 7 * q^36 + 4 * q^37 - 13 * q^38 + 30 * q^39 + 8 * q^41 - 15 * q^42 + q^43 + 12 * q^44 + 24 * q^46 - 12 * q^47 + 23 * q^48 - 20 * q^49 - 22 * q^51 - 3 * q^52 - 5 * q^53 + 34 * q^54 - 82 * q^56 - 7 * q^57 + 54 * q^58 + 5 * q^59 + 37 * q^62 - 3 * q^63 + 112 * q^64 + 31 * q^66 + 4 * q^67 - 32 * q^68 - 18 * q^69 - 20 * q^71 + 17 * q^72 - 20 * q^73 - 25 * q^74 + 63 * q^76 - 28 * q^77 - 18 * q^78 - 17 * q^79 - 12 * q^81 + 21 * q^82 - 2 * q^83 - 40 * q^84 - 8 * q^86 + 32 * q^87 + 14 * q^88 - 11 * q^89 - 6 * q^91 - q^92 - 8 * q^93 - 62 * q^94 + 42 * q^96 + q^97 + 9 * q^98 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more