LMFDB - Embedded newform 325.2.e.c.276.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(126,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, 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("325.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 8x^{8} - 2x^{7} + 52x^{6} - 5x^{5} + 97x^{4} + 60x^{3} + 141x^{2} + 36x + 9 $ x^10 + 8x^8 - 2x^7 + 52x^6 - 5x^5 + 97x^4 + 60x^3 + 141x^2 + 36x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			276.4
Root			$0.904178 + 1.56608i$ of defining polynomial
Character	$\chi$	$=$	325.276
Dual form			325.2.e.c.126.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.904178 + 1.56608i) q^{2} +(0.929015 + 1.60910i) q^{3} +(-0.635076 + 1.09998i) q^{4} +(-1.67999 + 2.90983i) q^{6} +(-2.08417 + 3.60988i) q^{7} +1.31983 q^{8} +(-0.226138 + 0.391682i) q^{9} +O(q^{10})$	\(q+(0.904178 + 1.56608i) q^{2} +(0.929015 + 1.60910i) q^{3} +(-0.635076 + 1.09998i) q^{4} +(-1.67999 + 2.90983i) q^{6} +(-2.08417 + 3.60988i) q^{7} +1.31983 q^{8} +(-0.226138 + 0.391682i) q^{9} +(-1.67999 - 2.90983i) q^{11} -2.35998 q^{12} +(1.76539 - 3.14379i) q^{13} -7.53784 q^{14} +(2.46351 + 4.26692i) q^{16} +(-0.910888 + 1.57770i) q^{17} -0.817876 q^{18} +(0.364924 - 0.632067i) q^{19} -7.74489 q^{21} +(3.03802 - 5.26201i) q^{22} +(-1.24531 - 2.15695i) q^{23} +(1.22614 + 2.12373i) q^{24} +(6.51966 - 0.0777936i) q^{26} +4.73375 q^{27} +(-2.64721 - 4.58510i) q^{28} +(3.10230 + 5.37333i) q^{29} +3.17786 q^{31} +(-3.13508 + 5.43011i) q^{32} +(3.12147 - 5.40655i) q^{33} -3.29442 q^{34} +(-0.287229 - 0.497496i) q^{36} +(-5.53802 - 9.59213i) q^{37} +1.31983 q^{38} +(6.69875 - 0.0799306i) q^{39} +(-4.91365 - 8.51069i) q^{41} +(-7.00276 - 12.1291i) q^{42} +(-3.98269 + 6.89821i) q^{43} +4.26768 q^{44} +(2.25197 - 3.90053i) q^{46} +3.46732 q^{47} +(-4.57727 + 7.92807i) q^{48} +(-5.18751 - 8.98504i) q^{49} -3.38491 q^{51} +(2.33696 + 3.93844i) q^{52} +13.4723 q^{53} +(4.28015 + 7.41344i) q^{54} +(-2.75074 + 4.76442i) q^{56} +1.35608 q^{57} +(-5.61005 + 9.71690i) q^{58} +(-0.457562 + 0.792521i) q^{59} +(1.08893 - 1.88608i) q^{61} +(2.87335 + 4.97678i) q^{62} +(-0.942619 - 1.63266i) q^{63} -1.48463 q^{64} +11.2895 q^{66} +(6.87597 + 11.9095i) q^{67} +(-1.15697 - 2.00392i) q^{68} +(2.31383 - 4.00767i) q^{69} +(4.00258 - 6.93267i) q^{71} +(-0.298463 + 0.516952i) q^{72} -10.2944 q^{73} +(10.0147 - 17.3460i) q^{74} +(0.463509 + 0.802821i) q^{76} +14.0055 q^{77} +(6.18204 + 10.4185i) q^{78} -3.21448 q^{79} +(5.07614 + 8.79213i) q^{81} +(8.88563 - 15.3904i) q^{82} -12.3694 q^{83} +(4.91859 - 8.51926i) q^{84} -14.4042 q^{86} +(-5.76416 + 9.98381i) q^{87} +(-2.21729 - 3.84047i) q^{88} +(-3.27857 - 5.67866i) q^{89} +(7.66933 + 12.9250i) q^{91} +3.16348 q^{92} +(2.95228 + 5.11349i) q^{93} +(3.13508 + 5.43011i) q^{94} -11.6501 q^{96} +(-6.19141 + 10.7238i) q^{97} +(9.38087 - 16.2481i) q^{98} +1.51964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 10 * q - 3 * q^3 - 6 * q^4 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 4 * q^9	$ 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9} - 3 q^{11} + 4 q^{12} + 10 q^{13} - 16 q^{14} - 4 q^{16} - 4 q^{17} - 4 q^{18} + 4 q^{19} - 16 q^{21} - 8 q^{22} - 15 q^{23} + 14 q^{24} - 9 q^{26} + 42 q^{27} + 17 q^{28} + q^{29} - 31 q^{32} + 2 q^{33} + 54 q^{34} + 13 q^{36} - 17 q^{37} + 6 q^{38} - 10 q^{39} - 6 q^{41} - 32 q^{42} - 12 q^{43} - 16 q^{44} + 7 q^{46} - 24 q^{47} + 2 q^{48} - 7 q^{49} + 23 q^{52} + 16 q^{53} - 19 q^{54} + 17 q^{56} - 8 q^{57} - 38 q^{58} + 12 q^{59} - 5 q^{61} - 13 q^{62} - 26 q^{63} - 10 q^{64} + 86 q^{66} + 16 q^{67} - 25 q^{68} - 20 q^{69} - 19 q^{71} + 45 q^{72} - 16 q^{73} - 2 q^{74} - 24 q^{76} + 64 q^{77} + 42 q^{78} - 28 q^{79} - 29 q^{81} + 23 q^{82} - 14 q^{83} + 34 q^{84} - 84 q^{86} - 21 q^{87} - 2 q^{88} + 10 q^{89} + 17 q^{91} + 142 q^{92} + 33 q^{93} + 31 q^{94} + 34 q^{96} - 37 q^{97} + 21 q^{98} + 56 q^{99}+O(q^{100}) $ 10 * q - 3 * q^3 - 6 * q^4 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 4 * q^9 - 3 * q^11 + 4 * q^12 + 10 * q^13 - 16 * q^14 - 4 * q^16 - 4 * q^17 - 4 * q^18 + 4 * q^19 - 16 * q^21 - 8 * q^22 - 15 * q^23 + 14 * q^24 - 9 * q^26 + 42 * q^27 + 17 * q^28 + q^29 - 31 * q^32 + 2 * q^33 + 54 * q^34 + 13 * q^36 - 17 * q^37 + 6 * q^38 - 10 * q^39 - 6 * q^41 - 32 * q^42 - 12 * q^43 - 16 * q^44 + 7 * q^46 - 24 * q^47 + 2 * q^48 - 7 * q^49 + 23 * q^52 + 16 * q^53 - 19 * q^54 + 17 * q^56 - 8 * q^57 - 38 * q^58 + 12 * q^59 - 5 * q^61 - 13 * q^62 - 26 * q^63 - 10 * q^64 + 86 * q^66 + 16 * q^67 - 25 * q^68 - 20 * q^69 - 19 * q^71 + 45 * q^72 - 16 * q^73 - 2 * q^74 - 24 * q^76 + 64 * q^77 + 42 * q^78 - 28 * q^79 - 29 * q^81 + 23 * q^82 - 14 * q^83 + 34 * q^84 - 84 * q^86 - 21 * q^87 - 2 * q^88 + 10 * q^89 + 17 * q^91 + 142 * q^92 + 33 * q^93 + 31 * q^94 + 34 * q^96 - 37 * q^97 + 21 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.904178	+	1.56608i	0.639350	+	1.10739i	0.985576	+	0.169236i	$0.0541300\pi$
$2$	0.904178	+	1.56608i	0.639350	+	1.10739i	−0.346225	+	0.938151i	$0.612537\pi$
$3$	0.929015	+	1.60910i	0.536367	+	0.929015i	0.999096	+	0.0425151i	$0.0135371\pi$
$3$	0.929015	+	1.60910i	0.536367	+	0.929015i	−0.462729	+	0.886500i	$0.653130\pi$
$4$	−0.635076	+	1.09998i	−0.317538	+	0.549992i
$5$		0			0
$5$		0			0
$6$	−1.67999	+	2.90983i	−0.685853	+	1.18793i
$7$	−2.08417	+	3.60988i	−0.787741	+	1.36441i	0.139606	+	0.990207i	$0.455416\pi$
$7$	−2.08417	+	3.60988i	−0.787741	+	1.36441i	−0.927348	+	0.374201i	$0.877917\pi$
$8$	1.31983			0.466629
$9$	−0.226138	+	0.391682i	−0.0753793	+	0.130561i
$10$		0			0
$11$	−1.67999	−	2.90983i	−0.506536	−	0.877346i	−0.999971	−	0.00756369i	$-0.997592\pi$
$11$	−1.67999	−	2.90983i	−0.506536	−	0.877346i	0.493435	−	0.869782i	$-0.335741\pi$
$12$	−2.35998			−0.681268
$13$	1.76539	−	3.14379i	0.489632	−	0.871929i
$13$	1.76539	−	3.14379i	0.489632	−	0.871929i
$14$	−7.53784			−2.01457
$15$		0			0
$16$	2.46351	+	4.26692i	0.615877	+	1.06673i
$17$	−0.910888	+	1.57770i	−0.220923	+	0.382649i	−0.955088	−	0.296321i	$-0.904240\pi$
$17$	−0.910888	+	1.57770i	−0.220923	+	0.382649i	0.734166	+	0.678970i	$0.237574\pi$
$18$	−0.817876			−0.192775
$19$	0.364924	−	0.632067i	0.0837193	−	0.145006i	−0.821125	−	0.570748i	$-0.806653\pi$
$19$	0.364924	−	0.632067i	0.0837193	−	0.145006i	0.904845	+	0.425742i	$0.139987\pi$
$20$		0			0
$21$	−7.74489			−1.69007
$22$	3.03802	−	5.26201i	0.647708	−	1.12186i
$23$	−1.24531	−	2.15695i	−0.259666	−	0.449755i	0.706486	−	0.707727i	$-0.250279\pi$
$23$	−1.24531	−	2.15695i	−0.259666	−	0.449755i	−0.966152	+	0.257972i	$0.916946\pi$
$24$	1.22614	+	2.12373i	0.250284	+	0.433505i
$25$		0			0
$26$	6.51966	−	0.0777936i	1.27861	−	0.0152566i
$27$	4.73375			0.911010
$28$	−2.64721	−	4.58510i	−0.500276	−	0.866503i
$29$	3.10230	+	5.37333i	0.576082	+	0.997803i	0.995923	+	0.0902054i	$0.0287524\pi$
$29$	3.10230	+	5.37333i	0.576082	+	0.997803i	−0.419841	+	0.907597i	$0.637914\pi$
$30$		0			0
$31$	3.17786			0.570760			0.285380	−	0.958414i	$-0.407880\pi$
$31$	3.17786			0.570760			0.285380	+	0.958414i	$0.407880\pi$
$32$	−3.13508	+	5.43011i	−0.554208	+	0.959917i
$33$	3.12147	−	5.40655i	0.543379	−	0.941159i
$34$	−3.29442			−0.564988
$35$		0			0
$36$	−0.287229	−	0.497496i	−0.0478716	−	0.0829160i
$37$	−5.53802	−	9.59213i	−0.910445	−	1.57694i	−0.813437	−	0.581653i	$-0.802406\pi$
$37$	−5.53802	−	9.59213i	−0.910445	−	1.57694i	−0.0970080	−	0.995284i	$-0.530927\pi$
$38$	1.31983			0.214104
$39$	6.69875	−	0.0799306i	1.07266	−	0.0127991i
$40$		0			0
$41$	−4.91365	−	8.51069i	−0.767383	−	1.32915i	−0.938977	−	0.343979i	$-0.888225\pi$
$41$	−4.91365	−	8.51069i	−0.767383	−	1.32915i	0.171594	−	0.985168i	$-0.445108\pi$
$42$	−7.00276	−	12.1291i	−1.08055	−	1.87157i
$43$	−3.98269	+	6.89821i	−0.607354	+	1.05197i	0.384321	+	0.923200i	$0.374436\pi$
$43$	−3.98269	+	6.89821i	−0.607354	+	1.05197i	−0.991675	+	0.128768i	$0.958898\pi$
$44$	4.26768			0.643378
$45$		0			0
$46$	2.25197	−	3.90053i	0.332035	−	0.575102i
$47$	3.46732			0.505761			0.252880	−	0.967498i	$-0.418622\pi$
$47$	3.46732			0.505761			0.252880	+	0.967498i	$0.418622\pi$
$48$	−4.57727	+	7.92807i	−0.660673	+	1.14432i
$49$	−5.18751	−	8.98504i	−0.741073	−	1.28358i
$50$		0			0
$51$	−3.38491			−0.473983
$52$	2.33696	+	3.93844i	0.324077	+	0.546164i
$53$	13.4723			1.85056			0.925280	−	0.379286i	$-0.123830\pi$
$53$	13.4723			1.85056			0.925280	+	0.379286i	$0.123830\pi$
$54$	4.28015	+	7.41344i	0.582455	+	1.00884i
$55$		0			0
$56$	−2.75074	+	4.76442i	−0.367583	+	0.636672i
$57$	1.35608			0.179617
$58$	−5.61005	+	9.71690i	−0.736636	+	1.27589i
$59$	−0.457562	+	0.792521i	−0.0595696	+	0.103178i	−0.894272	−	0.447523i	$-0.852306\pi$
$59$	−0.457562	+	0.792521i	−0.0595696	+	0.103178i	0.834703	+	0.550701i	$0.185639\pi$
$60$		0			0
$61$	1.08893	−	1.88608i	0.139423	−	0.241488i	−0.787855	−	0.615860i	$-0.788809\pi$
$61$	1.08893	−	1.88608i	0.139423	−	0.241488i	0.927278	+	0.374373i	$0.122142\pi$
$62$	2.87335	+	4.97678i	0.364915	+	0.632052i
$63$	−0.942619	−	1.63266i	−0.118759	−	0.205696i
$64$	−1.48463			−0.185579
$65$		0			0
$66$	11.2895			1.38964
$67$	6.87597	+	11.9095i	0.840034	+	1.45498i	0.889865	+	0.456224i	$0.150798\pi$
$67$	6.87597	+	11.9095i	0.840034	+	1.45498i	−0.0498314	+	0.998758i	$0.515868\pi$
$68$	−1.15697	−	2.00392i	−0.140303	−	0.243011i
$69$	2.31383	−	4.00767i	0.278553	−	0.482467i
$70$		0			0
$71$	4.00258	−	6.93267i	0.475019	−	0.822756i	−0.524572	−	0.851366i	$-0.675775\pi$
$71$	4.00258	−	6.93267i	0.475019	−	0.822756i	0.999591	+	0.0286096i	$0.00910796\pi$
$72$	−0.298463	+	0.516952i	−0.0351742	+	0.0609234i
$73$	−10.2944			−1.20487			−0.602435	−	0.798168i	$-0.705803\pi$
$73$	−10.2944			−1.20487			−0.602435	+	0.798168i	$0.705803\pi$
$74$	10.0147	−	17.3460i	1.16419	−	2.01643i
$75$		0			0
$76$	0.463509	+	0.802821i	0.0531681	+	0.0920899i
$77$	14.0055			1.59608
$78$	6.18204	+	10.4185i	0.699978	+	1.17966i
$79$	−3.21448			−0.361657			−0.180829	−	0.983515i	$-0.557878\pi$
$79$	−3.21448			−0.361657			−0.180829	+	0.983515i	$0.557878\pi$
$80$		0			0
$81$	5.07614	+	8.79213i	0.564015	+	0.976903i
$82$	8.88563	−	15.3904i	0.981254	−	1.69958i
$83$	−12.3694			−1.35772			−0.678859	−	0.734268i	$-0.737525\pi$
$83$	−12.3694			−1.35772			−0.678859	+	0.734268i	$0.737525\pi$
$84$	4.91859	−	8.51926i	0.536663	−	0.929527i
$85$		0			0
$86$	−14.4042			−1.55325
$87$	−5.76416	+	9.98381i	−0.617983	+	1.07038i
$88$	−2.21729	−	3.84047i	−0.236364	−	0.409395i
$89$	−3.27857	−	5.67866i	−0.347528	−	0.601937i	0.638282	−	0.769803i	$-0.279646\pi$
$89$	−3.27857	−	5.67866i	−0.347528	−	0.601937i	−0.985810	+	0.167866i	$0.946312\pi$
$90$		0			0
$91$	7.66933	+	12.9250i	0.803965	+	1.35491i
$92$	3.16348			0.329815
$93$	2.95228	+	5.11349i	0.306137	+	0.530244i
$94$	3.13508	+	5.43011i	0.323358	+	0.560073i
$95$		0			0
$96$	−11.6501			−1.18904
$97$	−6.19141	+	10.7238i	−0.628642	+	1.08884i	0.359182	+	0.933267i	$0.383056\pi$
$97$	−6.19141	+	10.7238i	−0.628642	+	1.08884i	−0.987824	+	0.155573i	$0.950278\pi$
$98$	9.38087	−	16.2481i	0.947611	−	1.64131i
$99$	1.51964			0.152729
$100$		0			0
$101$	−4.32472	−	7.49064i	−0.430326	−	0.745346i	0.566575	−	0.824010i	$-0.308268\pi$
$101$	−4.32472	−	7.49064i	−0.430326	−	0.745346i	−0.996901	+	0.0786635i	$0.974935\pi$
$102$	−3.06056	−	5.30105i	−0.303041	−	0.524883i
$103$	−4.85966			−0.478836			−0.239418	−	0.970917i	$-0.576957\pi$
$103$	−4.85966			−0.478836			−0.239418	+	0.970917i	$0.576957\pi$
$104$	2.33001	−	4.14925i	0.228476	−	0.406867i
$105$		0			0
$106$	12.1813	+	21.0987i	1.18316	+	2.04929i
$107$	−3.20306	−	5.54787i	−0.309652	−	0.536332i	0.668635	−	0.743591i	$-0.266879\pi$
$107$	−3.20306	−	5.54787i	−0.309652	−	0.536332i	−0.978286	+	0.207259i	$0.933546\pi$
$108$	−3.00629	+	5.20705i	−0.289280	+	0.501048i
$109$	−1.78552			−0.171022			−0.0855110	−	0.996337i	$-0.527252\pi$
$109$	−1.78552			−0.171022			−0.0855110	+	0.996337i	$0.527252\pi$
$110$		0			0
$111$	10.2898	−	17.8225i	0.976665	−	1.69163i
$112$	−20.5375			−1.94061
$113$	1.57570	−	2.72919i	0.148229	−	0.256740i	−0.782344	−	0.622847i	$-0.785976\pi$
$113$	1.57570	−	2.72919i	0.148229	−	0.256740i	0.930573	+	0.366106i	$0.119309\pi$
$114$	1.22614	+	2.12373i	0.114838	+	0.198906i
$115$		0			0
$116$	−7.88077			−0.731711
$117$	0.832144	+	1.40240i	0.0769317	+	0.129652i
$118$	−1.65487			−0.152343
$119$	−3.79689	−	6.57640i	−0.348060	−	0.602858i
$120$		0			0
$121$	−0.144733	+	0.250685i	−0.0131575	+	0.0227895i
$122$	3.93834			0.356560
$123$	9.12971	−	15.8131i	0.823198	−	1.42582i
$124$	−2.01818	+	3.49559i	−0.181238	+	0.313913i
$125$		0			0
$126$	1.70459	−	2.95244i	0.151857	−	0.263024i
$127$	−6.60301	−	11.4368i	−0.585923	−	1.01485i	−0.994760	−	0.102240i	$-0.967399\pi$
$127$	−6.60301	−	11.4368i	−0.585923	−	1.01485i	0.408837	−	0.912607i	$-0.365934\pi$
$128$	4.92778	+	8.53517i	0.435558	+	0.754409i
$129$	−14.7999			−1.30306
$130$		0			0
$131$	6.39233			0.558501			0.279250	−	0.960218i	$-0.409914\pi$
$131$	6.39233			0.558501			0.279250	+	0.960218i	$0.409914\pi$
$132$	3.96474	+	6.86714i	0.345087	+	0.597707i
$133$	1.52113	+	2.63467i	0.131898	+	0.228455i
$134$	−12.4342	+	21.5367i	−1.07415	+	1.86049i
$135$		0			0
$136$	−1.20221	+	2.08229i	−0.103089	+	0.178555i
$137$	−0.838239	+	1.45187i	−0.0716156	+	0.124042i	−0.899610	−	0.436695i	$-0.856149\pi$
$137$	−0.838239	+	1.45187i	−0.0716156	+	0.124042i	0.827994	+	0.560737i	$0.189482\pi$
$138$	8.36846			0.712371
$139$	−6.01595	+	10.4199i	−0.510266	+	0.883806i	0.489663	+	0.871912i	$0.337120\pi$
$139$	−6.01595	+	10.4199i	−0.510266	+	0.883806i	−0.999929	+	0.0118949i	$0.996214\pi$
$140$		0			0
$141$	3.22119	+	5.57927i	0.271273	+	0.469859i
$142$	14.4762			1.21481
$143$	−12.1137	+	0.144543i	−1.01300	+	0.0120873i
$144$	−2.22837			−0.185698
$145$		0			0
$146$	−9.30799	−	16.1219i	−0.770335	−	1.33426i
$147$	9.63855	−	16.6945i	0.794975	−	1.37694i
$148$	14.0683			1.15640
$149$	5.48911	−	9.50742i	0.449685	−	0.778878i	−0.548680	−	0.836032i	$-0.684869\pi$
$149$	5.48911	−	9.50742i	0.449685	−	0.778878i	0.998365	+	0.0571546i	$0.0182028\pi$
$150$		0			0
$151$	−14.8646			−1.20966			−0.604832	−	0.796353i	$-0.706760\pi$
$151$	−14.8646			−1.20966			−0.604832	+	0.796353i	$0.706760\pi$
$152$	0.481636	−	0.834219i	0.0390659	−	0.0676641i
$153$	−0.411973	−	0.713557i	−0.0333060	−	0.0576877i
$154$	12.6635	+	21.9338i	1.02045	+	1.76748i
$155$		0			0
$156$	−4.16629	+	7.41927i	−0.333570	+	0.594017i
$157$	−15.4203			−1.23068			−0.615338	−	0.788263i	$-0.710981\pi$
$157$	−15.4203			−1.23068			−0.615338	+	0.788263i	$0.710981\pi$
$158$	−2.90646	−	5.03414i	−0.231226	−	0.400495i
$159$	12.5159	+	21.6783i	0.992579	+	1.71920i
$160$		0			0
$161$	10.3818			0.818199
$162$	−9.17946	+	15.8993i	−0.721207	+	1.24917i
$163$	−1.33795	+	2.31740i	−0.104797	+	0.181513i	−0.913655	−	0.406490i	$-0.866752\pi$
$163$	−1.33795	+	2.31740i	−0.104797	+	0.181513i	0.808859	+	0.588003i	$0.200086\pi$
$164$	12.4822			0.974693
$165$		0			0
$166$	−11.1841	−	19.3715i	−0.868058	−	1.50352i
$167$	0.189699	+	0.328568i	0.0146794	+	0.0254254i	0.873272	−	0.487233i	$-0.161994\pi$
$167$	0.189699	+	0.328568i	0.0146794	+	0.0254254i	−0.858592	+	0.512659i	$0.828661\pi$
$168$	−10.2219			−0.788637
$169$	−6.76678	−	11.1000i	−0.520522	−	0.853848i
$170$		0			0
$171$	0.165046	+	0.285869i	0.0126214	+	0.0218609i
$172$	−5.05861	−	8.76178i	−0.385716	−	0.668079i
$173$	3.87421	−	6.71033i	0.294551	−	0.510177i	−0.680329	−	0.732906i	$-0.738163\pi$
$173$	3.87421	−	6.71033i	0.294551	−	0.510177i	0.974880	+	0.222729i	$0.0714966\pi$
$174$	−20.8473			−1.58043
$175$		0			0
$176$	8.27734	−	14.3368i	0.623928	−	1.08068i
$177$	−1.70033			−0.127805
$178$	5.92883	−	10.2690i	0.444385	−	0.769697i
$179$	10.3176	+	17.8707i	0.771177	+	1.33572i	0.936918	+	0.349548i	$0.113665\pi$
$179$	10.3176	+	17.8707i	0.771177	+	1.33572i	−0.165741	+	0.986169i	$0.553002\pi$
$180$		0			0
$181$	−13.4357			−0.998664			−0.499332	−	0.866411i	$-0.666421\pi$
$181$	−13.4357			−0.998664			−0.499332	+	0.866411i	$0.666421\pi$
$182$	−13.3072	+	23.6973i	−0.986398	+	1.75656i
$183$	4.04652			0.299127
$184$	−1.64360	−	2.84680i	−0.121168	−	0.209869i
$185$		0			0
$186$	−5.33877	+	9.24701i	−0.391457	+	0.678024i
$187$	6.12113			0.447621
$188$	−2.20201	+	3.81400i	−0.160598	+	0.278164i
$189$	−9.86593	+	17.0883i	−0.717641	+	1.24299i
$190$		0			0
$191$	−4.14508	+	7.17948i	−0.299927	+	0.519489i	−0.976119	−	0.217237i	$-0.930296\pi$
$191$	−4.14508	+	7.17948i	−0.299927	+	0.519489i	0.676192	+	0.736726i	$0.263629\pi$
$192$	−1.37924	−	2.38892i	−0.0995384	−	0.172406i
$193$	0.0610966	+	0.105822i	0.00439783	+	0.00761726i	0.868216	−	0.496187i	$-0.165267\pi$
$193$	0.0610966	+	0.105822i	0.00439783	+	0.00761726i	−0.863818	+	0.503804i	$0.831933\pi$
$194$	−22.3925			−1.60769
$195$		0			0
$196$	13.1779			0.941275
$197$	−8.23429	−	14.2622i	−0.586669	−	1.01614i	−0.994665	−	0.103157i	$-0.967106\pi$
$197$	−8.23429	−	14.2622i	−0.586669	−	1.01614i	0.407996	−	0.912984i	$-0.366228\pi$
$198$	1.37402	+	2.37988i	0.0976476	+	0.169131i
$199$	3.43949	−	5.95736i	0.243819	−	0.422306i	−0.717980	−	0.696064i	$-0.754933\pi$
$199$	3.43949	−	5.95736i	0.243819	−	0.422306i	0.961799	+	0.273757i	$0.0882665\pi$
$200$		0			0
$201$	−12.7758	+	22.1283i	−0.901133	+	1.56081i
$202$	7.82064	−	13.5457i	0.550258	−	0.953075i
$203$	−25.8628			−1.81521
$204$	2.14968	−	3.72335i	0.150507	−	0.260687i
$205$		0			0
$206$	−4.39399	−	7.61062i	−0.306144	−	0.530257i
$207$	1.12645			0.0782938
$208$	17.7634	−	0.211955i	1.23167	−	0.0146965i
$209$	−2.45228			−0.169627
$210$		0			0
$211$	−0.962507	−	1.66711i	−0.0662617	−	0.114769i	0.830991	−	0.556285i	$-0.187774\pi$
$211$	−0.962507	−	1.66711i	−0.0662617	−	0.114769i	−0.897253	+	0.441517i	$0.854441\pi$
$212$	−8.55592	+	14.8193i	−0.587623	+	1.01779i
$213$	14.8738			1.01914
$214$	5.79228	−	10.0325i	0.395952	−	0.685809i
$215$		0			0
$216$	6.24772			0.425104
$217$	−6.62319	+	11.4717i	−0.449611	+	0.778749i
$218$	−1.61443	−	2.79627i	−0.109343	−	0.189387i
$219$	−9.56367	−	16.5648i	−0.646253	−	1.11934i
$220$		0			0
$221$	3.35189	+	5.64890i	0.225473	+	0.379986i
$222$	37.2153			2.49773
$223$	5.63084	+	9.75291i	0.377069	+	0.653103i	0.990634	−	0.136541i	$-0.0435986\pi$
$223$	5.63084	+	9.75291i	0.377069	+	0.653103i	−0.613565	+	0.789644i	$0.710265\pi$
$224$	−13.0680	−	22.6345i	−0.873146	−	1.51233i
$225$		0			0
$226$	5.69885			0.379082
$227$	−9.25674	+	16.0331i	−0.614391	+	1.06416i	0.376099	+	0.926579i	$0.377265\pi$
$227$	−9.25674	+	16.0331i	−0.614391	+	1.06416i	−0.990491	+	0.137578i	$0.956068\pi$
$228$	−0.861214	+	1.49167i	−0.0570353	+	0.0987880i
$229$	−12.3645			−0.817066			−0.408533	−	0.912744i	$-0.633960\pi$
$229$	−12.3645			−0.817066			−0.408533	+	0.912744i	$0.633960\pi$
$230$		0			0
$231$	13.0113	+	22.5363i	0.856084	+	1.48278i
$232$	4.09449	+	7.09186i	0.268816	+	0.465604i
$233$	8.24132			0.539907			0.269953	−	0.962873i	$-0.412992\pi$
$233$	8.24132			0.539907			0.269953	+	0.962873i	$0.412992\pi$
$234$	−1.44387	+	2.57123i	−0.0943888	+	0.168086i
$235$		0			0
$236$	−0.581174	−	1.00662i	−0.0378312	−	0.0655255i
$237$	−2.98630	−	5.17242i	−0.193981	−	0.335985i
$238$	6.86612	−	11.8925i	0.445065	−	0.770875i
$239$	20.8980			1.35178			0.675890	−	0.737002i	$-0.263759\pi$
$239$	20.8980			1.35178			0.675890	+	0.737002i	$0.263759\pi$
$240$		0			0
$241$	−3.82507	+	6.62521i	−0.246394	+	0.426767i	−0.962523	−	0.271201i	$-0.912579\pi$
$241$	−3.82507	+	6.62521i	−0.246394	+	0.426767i	0.716129	+	0.697968i	$0.245912\pi$
$242$	−0.523457			−0.0336491
$243$	−2.33099	+	4.03740i	−0.149533	+	0.258999i
$244$	1.38310	+	2.39561i	0.0885441	+	0.153363i
$245$		0			0
$246$	33.0195			2.10525
$247$	−1.34285	−	2.26309i	−0.0854435	−	0.143997i
$248$	4.19422			0.266333
$249$	−11.4914	−	19.9036i	−0.728236	−	1.26134i
$250$		0			0
$251$	7.43444	−	12.8768i	0.469258	−	0.812778i	−0.530125	−	0.847920i	$-0.677855\pi$
$251$	7.43444	−	12.8768i	0.469258	−	0.812778i	0.999382	+	0.0351416i	$0.0111882\pi$
$252$	2.39454			0.150842
$253$	−4.18423	+	7.24730i	−0.263060	+	0.455634i
$254$	11.9406	−	20.6817i	0.749220	−	1.29769i
$255$		0			0
$256$	−10.3958	+	18.0061i	−0.649738	+	1.12538i
$257$	1.96917	+	3.41070i	0.122833	+	0.212754i	0.920884	−	0.389837i	$-0.127469\pi$
$257$	1.96917	+	3.41070i	0.122833	+	0.212754i	−0.798051	+	0.602591i	$0.794135\pi$
$258$	−13.3817	−	23.1779i	−0.833111	−	1.44299i
$259$	46.1687			2.86878
$260$		0			0
$261$	−2.80619			−0.173699
$262$	5.77981	+	10.0109i	0.357078	+	0.618477i
$263$	−3.21467	−	5.56797i	−0.198225	−	0.343336i	0.749728	−	0.661746i	$-0.230184\pi$
$263$	−3.21467	−	5.56797i	−0.198225	−	0.343336i	−0.947953	+	0.318410i	$0.896851\pi$
$264$	4.11980	−	7.13570i	0.253556	−	0.439172i
$265$		0			0
$266$	−2.75074	+	4.76442i	−0.168659	+	0.292125i
$267$	6.09169	−	10.5511i	0.372805	−	0.645718i
$268$	−17.4671			−1.06697
$269$	−8.38739	+	14.5274i	−0.511388	+	0.885750i	0.488525	+	0.872550i	$0.337535\pi$
$269$	−8.38739	+	14.5274i	−0.511388	+	0.885750i	−0.999913	+	0.0132003i	$0.995798\pi$
$270$		0			0
$271$	3.22681	+	5.58901i	0.196015	+	0.339508i	0.947233	−	0.320547i	$-0.103867\pi$
$271$	3.22681	+	5.58901i	0.196015	+	0.339508i	−0.751218	+	0.660054i	$0.770533\pi$
$272$	−8.97592			−0.544245
$273$	−13.6728	+	24.3483i	−0.827514	+	1.47363i
$274$	−3.03167			−0.183150
$275$		0			0
$276$	2.93892	+	5.09035i	0.176902	+	0.306403i
$277$	0.560565	−	0.970927i	0.0336811	−	0.0583373i	−0.848694	−	0.528885i	$-0.822610\pi$
$277$	0.560565	−	0.970927i	0.0336811	−	0.0583373i	0.882375	+	0.470548i	$0.155944\pi$
$278$	−21.7579			−1.30495
$279$	−0.718634	+	1.24471i	−0.0430235	+	0.0745188i
$280$		0			0
$281$	15.5423			0.927176			0.463588	−	0.886051i	$-0.346562\pi$
$281$	15.5423			0.927176			0.463588	+	0.886051i	$0.346562\pi$
$282$	−5.82507	+	10.0893i	−0.346878	+	0.600810i
$283$	11.0083	+	19.0669i	0.654375	+	1.13341i	0.982050	+	0.188620i	$0.0604015\pi$
$283$	11.0083	+	19.0669i	0.654375	+	1.13341i	−0.327675	+	0.944790i	$0.606265\pi$
$284$	5.08388	+	8.80554i	0.301673	+	0.522513i
$285$		0			0
$286$	−11.1793	−	18.8404i	−0.661047	−	1.11406i
$287$	40.9635			2.41800
$288$	−1.41792	−	2.45591i	−0.0835517	−	0.144716i
$289$	6.84057	+	11.8482i	0.402386	+	0.696953i
$290$		0			0
$291$	−23.0076			−1.34873
$292$	6.53774	−	11.3237i	0.382592	−	0.662669i
$293$	−7.16525	+	12.4106i	−0.418599	+	0.725034i	−0.995799	−	0.0915686i	$-0.970812\pi$
$293$	−7.16525	+	12.4106i	−0.418599	+	0.725034i	0.577200	+	0.816603i	$0.304145\pi$
$294$	34.8599			2.03307
$295$		0			0
$296$	−7.30922	−	12.6599i	−0.424840	−	0.735844i
$297$	−7.95265	−	13.7744i	−0.461460	−	0.799271i
$298$	19.8525			1.15003
$299$	−8.97945	+	0.107144i	−0.519295	+	0.00619632i
$300$		0			0
$301$	−16.6012	−	28.7541i	−0.956876	−	1.65736i
$302$	−13.4403	−	23.2792i	−0.773400	−	1.33957i
$303$	8.03547	−	13.9178i	0.461625	−	0.799559i
$304$	3.59598			0.206243
$305$		0			0
$306$	0.744993	−	1.29037i	0.0425884	−	0.0737653i
$307$	−10.3261			−0.589341			−0.294671	−	0.955599i	$-0.595210\pi$
$307$	−10.3261			−0.589341			−0.294671	+	0.955599i	$0.595210\pi$
$308$	−8.89457	+	15.4058i	−0.506815	+	0.877830i
$309$	−4.51469	−	7.81968i	−0.256832	−	0.444846i
$310$		0			0
$311$	23.8742			1.35378			0.676892	−	0.736082i	$-0.263326\pi$
$311$	23.8742			1.35378			0.676892	+	0.736082i	$0.263326\pi$
$312$	8.84118	−	0.105494i	0.500533	−	0.00597244i
$313$	13.0375			0.736924			0.368462	−	0.929643i	$-0.379885\pi$
$313$	13.0375			0.736924			0.368462	+	0.929643i	$0.379885\pi$
$314$	−13.9427	−	24.1495i	−0.786834	−	1.36284i
$315$		0			0
$316$	2.04144	−	3.53587i	0.114840	−	0.198908i
$317$	−21.2154			−1.19157			−0.595787	−	0.803143i	$-0.703160\pi$
$317$	−21.2154			−1.19157			−0.595787	+	0.803143i	$0.703160\pi$
$318$	−22.6333	+	39.2020i	−1.26921	+	2.19834i
$319$	10.4237	−	18.0543i	0.583612	−	1.01085i
$320$		0			0
$321$	5.95138	−	10.3081i	0.332174	−	0.575342i
$322$	9.38698	+	16.2587i	0.523116	+	0.906063i
$323$	0.664810	+	1.15148i	0.0369910	+	0.0640703i
$324$	−12.8949			−0.716385
$325$		0			0
$326$	−4.83899			−0.268007
$327$	−1.65878	−	2.87308i	−0.0917305	−	0.158882i
$328$	−6.48516	−	11.2326i	−0.358083	−	0.620218i
$329$	−7.22648	+	12.5166i	−0.398409	+	0.690064i
$330$		0			0
$331$	−4.28262	+	7.41771i	−0.235394	+	0.407714i	−0.959387	−	0.282093i	$-0.908971\pi$
$331$	−4.28262	+	7.41771i	−0.235394	+	0.407714i	0.723993	+	0.689807i	$0.242305\pi$
$332$	7.85551	−	13.6061i	0.431127	−	0.746734i
$333$	5.00943			0.274515
$334$	−0.343044	+	0.594169i	−0.0187705	+	0.0325115i
$335$		0			0
$336$	−19.0796	−	33.0469i	−1.04088	−	1.80285i
$337$	−0.682652			−0.0371864			−0.0185932	−	0.999827i	$-0.505919\pi$
$337$	−0.682652			−0.0371864			−0.0185932	+	0.999827i	$0.505919\pi$
$338$	11.2652	−	20.6337i	0.612745	−	1.12233i
$339$	5.85539			0.318021
$340$		0			0
$341$	−5.33877	−	9.24701i	−0.289110	−	0.500754i
$342$	−0.298463	+	0.516952i	−0.0161390	+	0.0279536i
$343$	14.0682			0.759614
$344$	−5.25645	+	9.10444i	−0.283409	+	0.490879i
$345$		0			0
$346$	14.0119			0.753285
$347$	8.57809	−	14.8577i	0.460496	−	0.797603i	−0.538490	−	0.842632i	$-0.681005\pi$
$347$	8.57809	−	14.8577i	0.460496	−	0.797603i	0.998986	+	0.0450295i	$0.0143382\pi$
$348$	−7.32135	−	12.6810i	−0.392466	−	0.679771i
$349$	16.5771	+	28.7125i	0.887354	+	1.53694i	0.842991	+	0.537927i	$0.180793\pi$
$349$	16.5771	+	28.7125i	0.887354	+	1.53694i	0.0443633	+	0.999015i	$0.485874\pi$
$350$		0			0
$351$	8.35692	−	14.8819i	0.446059	−	0.794337i
$352$	21.0676			1.12291
$353$	5.59464	+	9.69020i	0.297773	+	0.515757i	0.975626	−	0.219440i	$-0.0704230\pi$
$353$	5.59464	+	9.69020i	0.297773	+	0.515757i	−0.677853	+	0.735197i	$0.737090\pi$
$354$	−1.53740	−	2.66286i	−0.0817119	−	0.141529i
$355$		0			0
$356$	8.32857			0.441414
$357$	7.05473	−	12.2191i	0.373376	−	0.646706i
$358$	−18.6580	+	32.3166i	−0.986105	+	1.70798i
$359$	−2.18281			−0.115204			−0.0576021	−	0.998340i	$-0.518345\pi$
$359$	−2.18281			−0.115204			−0.0576021	+	0.998340i	$0.518345\pi$
$360$		0			0
$361$	9.23366	+	15.9932i	0.485982	+	0.841746i
$362$	−12.1482	−	21.0413i	−0.638496	−	1.10591i
$363$	−0.537836			−0.0282291
$364$	−19.0879	+	0.227760i	−1.00048	+	0.0119379i
$365$		0			0
$366$	3.65878	+	6.33719i	0.191247	+	0.331250i
$367$	5.56980	+	9.64718i	0.290741	+	0.503579i	0.973985	−	0.226612i	$-0.0727648\pi$
$367$	5.56980	+	9.64718i	0.290741	+	0.503579i	−0.683244	+	0.730190i	$0.739431\pi$
$368$	6.13569	−	10.6273i	0.319845	−	0.553987i
$369$	4.44465			0.231379
$370$		0			0
$371$	−28.0785	+	48.6334i	−1.45776	+	2.52492i
$372$	−7.49968			−0.388840
$373$	8.21938	−	14.2364i	0.425583	−	0.737132i	−0.570891	−	0.821026i	$-0.693402\pi$
$373$	8.21938	−	14.2364i	0.425583	−	0.737132i	0.996475	+	0.0838935i	$0.0267356\pi$
$374$	5.53459	+	9.58619i	0.286187	+	0.495690i
$375$		0			0
$376$	4.57626			0.236003
$377$	22.3694	−	0.266915i	1.15208	−	0.0137468i
$378$	−35.6822			−1.83530
$379$	2.88310	+	4.99368i	0.148095	+	0.256508i	0.930523	−	0.366232i	$-0.119353\pi$
$379$	2.88310	+	4.99368i	0.148095	+	0.256508i	−0.782428	+	0.622741i	$0.786019\pi$
$380$		0			0
$381$	12.2686	−	21.2498i	0.628539	−	1.08866i
$382$	−14.9915			−0.767034
$383$	17.0027	−	29.4495i	0.868797	−	1.50480i	0.00556925	−	0.999984i	$-0.498227\pi$
$383$	17.0027	−	29.4495i	0.868797	−	1.50480i	0.863227	−	0.504815i	$-0.168439\pi$
$384$	−9.15597	+	15.8586i	−0.467238	+	0.809281i
$385$		0			0
$386$	−0.110484	+	0.191365i	−0.00562351	+	0.00974020i
$387$	−1.80127	−	3.11990i	−0.0915638	−	0.158593i
$388$	−7.86403	−	13.6209i	−0.399235	−	0.691496i
$389$	29.7804			1.50993			0.754963	−	0.655768i	$-0.227655\pi$
$389$	29.7804			1.50993			0.754963	+	0.655768i	$0.227655\pi$
$390$		0			0
$391$	4.53737			0.229465
$392$	−6.84661	−	11.8587i	−0.345806	−	0.598954i
$393$	5.93858	+	10.2859i	0.299561	+	0.518856i
$394$	14.8905	−	25.7911i	0.750174	−	1.29934i
$395$		0			0
$396$	−0.965085	+	1.67158i	−0.0484974	+	0.0839999i
$397$	12.9019	−	22.3468i	0.647528	−	1.12155i	−0.336183	−	0.941797i	$-0.609136\pi$
$397$	12.9019	−	22.3468i	0.647528	−	1.12155i	0.983711	−	0.179755i	$-0.0575306\pi$
$398$	12.4396			0.623542
$399$	−2.82630	+	4.89529i	−0.141492	+	0.245071i
$400$		0			0
$401$	−4.23827	−	7.34090i	−0.211649	−	0.366587i	0.740582	−	0.671966i	$-0.234550\pi$
$401$	−4.23827	−	7.34090i	−0.211649	−	0.366587i	−0.952231	+	0.305379i	$0.901217\pi$
$402$	−46.2063			−2.30456
$403$	5.61016	−	9.99050i	0.279462	−	0.497662i
$404$	10.9861			0.546579
$405$		0			0
$406$	−23.3846	−	40.5033i	−1.16056	−	2.01015i
$407$	−18.6076	+	32.2294i	−0.922346	+	1.59755i
$408$	−4.46750			−0.221174
$409$	0.360554	−	0.624498i	0.0178282	−	0.0308794i	−0.856974	−	0.515360i	$-0.827658\pi$
$409$	0.360554	−	0.624498i	0.0178282	−	0.0308794i	0.874802	+	0.484481i	$0.160991\pi$
$410$		0			0
$411$	−3.11495			−0.153649
$412$	3.08625	−	5.34554i	0.152049	−	0.263356i
$413$	−1.90727	−	3.30350i	−0.0938508	−	0.162554i
$414$	1.01851	+	1.76412i	0.0500572	+	0.0867016i
$415$		0			0
$416$	11.5365	+	19.4423i	0.565622	+	0.953236i
$417$	−22.3556			−1.09476
$418$	−2.21729	−	3.84047i	−0.108451	−	0.187843i
$419$	−7.51719	−	13.0202i	−0.367239	−	0.636076i	0.621894	−	0.783101i	$-0.286363\pi$
$419$	−7.51719	−	13.0202i	−0.367239	−	0.636076i	−0.989133	+	0.147025i	$0.953030\pi$
$420$		0			0
$421$	16.9722			0.827172			0.413586	−	0.910465i	$-0.364276\pi$
$421$	16.9722			0.827172			0.413586	+	0.910465i	$0.364276\pi$
$422$	1.74055	−	3.01473i	0.0847289	−	0.146755i
$423$	−0.784093	+	1.35809i	−0.0381239	+	0.0660325i
$424$	17.7811			0.863524
$425$		0			0
$426$	13.4486	+	23.2936i	0.651586	+	1.12858i
$427$	4.53902	+	7.86181i	0.219658	+	0.380460i
$428$	8.13675			0.393305
$429$	−11.4864	−	19.3579i	−0.554569	−	0.934609i
$430$		0			0
$431$	9.26206	+	16.0424i	0.446138	+	0.772734i	0.998131	−	0.0611153i	$-0.0194657\pi$
$431$	9.26206	+	16.0424i	0.446138	+	0.772734i	−0.551993	+	0.833849i	$0.686132\pi$
$432$	11.6616	+	20.1985i	0.561071	+	0.971803i
$433$	−19.7894	+	34.2763i	−0.951020	+	1.64721i	−0.207795	+	0.978172i	$0.566629\pi$
$433$	−19.7894	+	34.2763i	−0.951020	+	1.64721i	−0.743224	+	0.669042i	$0.766705\pi$
$434$	−23.9542			−1.14984
$435$		0			0
$436$	1.13394	−	1.96404i	0.0543059	−	0.0940606i
$437$	−1.81778			−0.0869563
$438$	17.2945	−	29.9550i	0.826364	−	1.43130i
$439$	−8.60802	−	14.9095i	−0.410838	−	0.711593i	0.584143	−	0.811650i	$-0.301431\pi$
$439$	−8.60802	−	14.9095i	−0.410838	−	0.711593i	−0.994982	+	0.100058i	$0.968097\pi$
$440$		0			0
$441$	4.69237			0.223446
$442$	−5.81594	+	10.3569i	−0.276636	+	0.492630i
$443$	−18.2587			−0.867496			−0.433748	−	0.901034i	$-0.642809\pi$
$443$	−18.2587			−0.867496			−0.433748	+	0.901034i	$0.642809\pi$
$444$	13.0696	+	22.6372i	0.620257	+	1.07432i
$445$		0			0
$446$	−10.1826	+	17.6367i	−0.482159	+	0.835123i
$447$	20.3979			0.964786
$448$	3.09422	−	5.35935i	0.146188	−	0.253205i
$449$	−7.26826	+	12.5890i	−0.343010	+	0.594111i	−0.984990	−	0.172610i	$-0.944780\pi$
$449$	−7.26826	+	12.5890i	−0.343010	+	0.594111i	0.641980	+	0.766722i	$0.278113\pi$
$450$		0			0
$451$	−16.5098	+	28.5958i	−0.777415	+	1.34652i
$452$	2.00138	+	3.46648i	0.0941368	+	0.163050i
$453$	−13.8094	−	23.9187i	−0.648824	−	1.12380i
$454$	−33.4790			−1.57125
$455$		0			0
$456$	1.78979			0.0838146
$457$	−0.565518	−	0.979506i	−0.0264538	−	0.0458194i	0.852495	−	0.522735i	$-0.175088\pi$
$457$	−0.565518	−	0.979506i	−0.0264538	−	0.0458194i	−0.878949	+	0.476915i	$0.841755\pi$
$458$	−11.1797	−	19.3637i	−0.522391	−	0.904809i
$459$	−4.31191	+	7.46845i	−0.201263	+	0.348598i
$460$		0			0
$461$	−12.1519	+	21.0477i	−0.565971	+	0.980291i	0.430987	+	0.902358i	$0.358165\pi$
$461$	−12.1519	+	21.0477i	−0.565971	+	0.980291i	−0.996959	+	0.0779332i	$0.975168\pi$
$462$	−23.5291	+	40.7537i	−1.09467	+	1.89603i
$463$	37.3049			1.73371			0.866854	−	0.498563i	$-0.166139\pi$
$463$	37.3049			1.73371			0.866854	+	0.498563i	$0.166139\pi$
$464$	−15.2851	+	26.4745i	−0.709591	+	1.22905i
$465$		0			0
$466$	7.45162	+	12.9066i	0.345190	+	0.597886i
$467$	29.6461			1.37186			0.685928	−	0.727669i	$-0.259396\pi$
$467$	29.6461			1.37186			0.685928	+	0.727669i	$0.259396\pi$
$468$	−2.07109	+	0.0247126i	−0.0957363	+	0.00114234i
$469$	−57.3227			−2.64692
$470$		0			0
$471$	−14.3257	−	24.8129i	−0.660095	−	1.14332i
$472$	−0.603903	+	1.04599i	−0.0277969	+	0.0481456i
$473$	26.7635			1.23059
$474$	5.40029	−	9.35358i	0.248044	−	0.429624i
$475$		0			0
$476$	9.64524			0.442089
$477$	−3.04659	+	5.27685i	−0.139494	+	0.241610i
$478$	18.8955	+	32.7280i	0.864261	+	1.49694i
$479$	−6.13094	−	10.6191i	−0.280130	−	0.485199i	0.691287	−	0.722581i	$-0.257044\pi$
$479$	−6.13094	−	10.6191i	−0.280130	−	0.485199i	−0.971416	+	0.237382i	$0.923711\pi$
$480$		0			0
$481$	−39.9324	+	0.476480i	−1.82076	+	0.0217256i
$482$	−13.8342			−0.630129
$483$	9.64483	+	16.7053i	0.438855	+	0.760119i
$484$	−0.183833	−	0.318407i	−0.00835603	−	0.0144731i
$485$		0			0
$486$	−8.43053			−0.382417
$487$	−11.8901	+	20.5943i	−0.538792	+	0.933216i	0.460177	+	0.887827i	$0.347786\pi$
$487$	−11.8901	+	20.5943i	−0.538792	+	0.933216i	−0.998969	+	0.0453886i	$0.985547\pi$
$488$	1.43720	−	2.48929i	0.0650588	−	0.112685i
$489$	−4.97191			−0.224838
$490$		0			0
$491$	9.03032	+	15.6410i	0.407532	+	0.705867i	0.994613	−	0.103662i	$-0.0330560\pi$
$491$	9.03032	+	15.6410i	0.407532	+	0.705867i	−0.587080	+	0.809529i	$0.699723\pi$
$492$	11.5961	+	20.0851i	0.522793	+	0.905505i
$493$	−11.3034			−0.509078
$494$	2.33001	−	4.14925i	0.104832	−	0.186684i
$495$		0			0
$496$	7.82868	+	13.5597i	0.351518	+	0.608847i
$497$	16.6841	+	28.8977i	0.748384	+	1.29624i
$498$	20.7805	−	35.9928i	0.931195	−	1.61288i
$499$	−5.64603			−0.252751			−0.126375	−	0.991982i	$-0.540334\pi$
$499$	−5.64603			−0.252751			−0.126375	+	0.991982i	$0.540334\pi$
$500$		0			0
$501$	−0.352467	+	0.610490i	−0.0157470	+	0.0272747i
$502$	26.8882			1.20008
$503$	−15.7986	+	27.3640i	−0.704425	+	1.22010i	0.262474	+	0.964939i	$0.415462\pi$
$503$	−15.7986	+	27.3640i	−0.704425	+	1.22010i	−0.966899	+	0.255160i	$0.917872\pi$
$504$	−1.24409	−	2.15483i	−0.0554163	−	0.0959838i
$505$		0			0
$506$	−15.1332			−0.672751
$507$	11.5746	−	21.2005i	0.514047	−	0.941549i
$508$	16.7737			0.744210
$509$	−7.21291	−	12.4931i	−0.319707	−	0.553748i	0.660720	−	0.750632i	$-0.270251\pi$
$509$	−7.21291	−	12.4931i	−0.319707	−	0.553748i	−0.980427	+	0.196884i	$0.936918\pi$
$510$		0			0
$511$	21.4553	−	37.1617i	0.949127	−	1.64394i
$512$	−17.8875			−0.790525
$513$	1.72746	−	2.99205i	0.0762692	−	0.132102i
$514$	−3.56096	+	6.16776i	−0.157067	+	0.272048i
$515$		0			0
$516$	9.39906	−	16.2796i	0.413770	−	0.716672i
$517$	−5.82507	−	10.0893i	−0.256186	−	0.443727i
$518$	41.7447	+	72.3039i	1.83416	+	3.17685i
$519$	14.3968			0.631950
$520$		0			0
$521$	1.72016			0.0753617			0.0376809	−	0.999290i	$-0.488003\pi$
$521$	1.72016			0.0753617			0.0376809	+	0.999290i	$0.488003\pi$
$522$	−2.53729	−	4.39472i	−0.111054	−	0.192352i
$523$	−14.6881	−	25.4405i	−0.642266	−	1.11244i	−0.984926	−	0.172977i	$-0.944661\pi$
$523$	−14.6881	−	25.4405i	−0.642266	−	1.11244i	0.342660	−	0.939459i	$-0.388672\pi$
$524$	−4.05962	+	7.03146i	−0.177345	+	0.307171i
$525$		0			0
$526$	5.81326	−	10.0689i	0.253470	−	0.439024i
$527$	−2.89467	+	5.01372i	−0.126094	+	0.218401i
$528$	30.7591			1.33862
$529$	8.39838	−	14.5464i	0.365147	−	0.632453i
$530$		0			0
$531$	−0.206944	−	0.358438i	−0.00898062	−	0.0155549i
$532$	−3.86412			−0.167531
$533$	−35.4303	+	0.422760i	−1.53466	+	0.0183118i
$534$	22.0319			0.953413
$535$		0			0
$536$	9.07509	+	15.7185i	0.391984	+	0.678936i
$537$	−19.1705	+	33.2043i	−0.827268	+	1.43287i
$538$	−30.3348			−1.30783
$539$	−17.4299	+	30.1895i	−0.750761	+	1.30036i
$540$		0			0
$541$	10.0416			0.431721			0.215861	−	0.976424i	$-0.430744\pi$
$541$	10.0416			0.431721			0.215861	+	0.976424i	$0.430744\pi$
$542$	−5.83523	+	10.1069i	−0.250645	+	0.434129i
$543$	−12.4819	−	21.6193i	−0.535651	−	0.927774i
$544$	−5.71140	−	9.89244i	−0.244874	−	0.424135i
$545$		0			0
$546$	−50.4940	+	0.602503i	−2.16095	+	0.0257848i
$547$	−5.03662			−0.215350			−0.107675	−	0.994186i	$-0.534341\pi$
$547$	−5.03662			−0.215350			−0.107675	+	0.994186i	$0.534341\pi$
$548$	−1.06469	−	1.84410i	−0.0454813	−	0.0787760i
$549$	0.492496	+	0.853028i	0.0210192	+	0.0364063i
$550$		0			0
$551$	4.52841			0.192917
$552$	3.05386	−	5.28943i	0.129981	−	0.225133i
$553$	6.69951	−	11.6039i	0.284892	−	0.493448i
$554$	2.02740			0.0861360
$555$		0			0
$556$	−7.64116	−	13.2349i	−0.324058	−	0.561284i
$557$	3.22404	+	5.58421i	0.136607	+	0.236610i	0.926210	−	0.377007i	$-0.123047\pi$
$557$	3.22404	+	5.58421i	0.136607	+	0.236610i	−0.789603	+	0.613618i	$0.789714\pi$
$558$	−2.59909			−0.110028
$559$	14.6555	+	24.6988i	0.619862	+	1.04465i
$560$		0			0
$561$	5.68662	+	9.84952i	0.240089	+	0.415847i
$562$	14.0530	+	24.3405i	0.592791	+	1.02674i
$563$	−17.9700	+	31.1250i	−0.757347	+	1.31176i	0.186853	+	0.982388i	$0.440171\pi$
$563$	−17.9700	+	31.1250i	−0.757347	+	1.31176i	−0.944199	+	0.329375i	$0.893162\pi$
$564$	−8.18281			−0.344558
$565$		0			0
$566$	−19.9069	+	34.4798i	−0.836750	+	1.44929i
$567$	−42.3181			−1.77719
$568$	5.28271	−	9.14992i	0.221657	−	0.383922i
$569$	19.4159	+	33.6293i	0.813957	+	1.40981i	0.910075	+	0.414444i	$0.136024\pi$
$569$	19.4159	+	33.6293i	0.813957	+	1.40981i	−0.0961179	+	0.995370i	$0.530643\pi$
$570$		0			0
$571$	−10.3932			−0.434941			−0.217471	−	0.976067i	$-0.569781\pi$
$571$	−10.3932			−0.434941			−0.217471	+	0.976067i	$0.569781\pi$
$572$	7.53413	−	13.4167i	0.315018	−	0.560980i
$573$	−15.4033			−0.643484
$574$	37.0383	+	64.1522i	1.54595	+	2.67766i
$575$		0			0
$576$	0.335731	−	0.581504i	0.0139888	−	0.0242293i
$577$	−5.94911			−0.247665			−0.123832	−	0.992303i	$-0.539518\pi$
$577$	−5.94911			−0.247665			−0.123832	+	0.992303i	$0.539518\pi$
$578$	−12.3702	+	21.4258i	−0.514532	+	0.891195i
$579$	−0.113519	+	0.196621i	−0.00471770	+	0.00817130i
$580$		0			0
$581$	25.7799	−	44.6521i	1.06953	−	1.85248i
$582$	−20.8030	−	36.0319i	−0.862312	−	1.49357i
$583$	−22.6333	−	39.2020i	−0.937375	−	1.62358i
$584$	−13.5868			−0.562227
$585$		0			0
$586$	−25.9147			−1.07052
$587$	−8.99937	−	15.5874i	−0.371444	−	0.643360i	0.618344	−	0.785908i	$-0.287804\pi$
$587$	−8.99937	−	15.5874i	−0.371444	−	0.643360i	−0.989788	+	0.142548i	$0.954471\pi$
$588$	12.2424	+	21.2045i	0.504869	+	0.874459i
$589$	1.15968	−	2.00862i	0.0477836	−	0.0827637i
$590$		0			0
$591$	15.2996	−	26.4996i	0.629340	−	1.09005i
$592$	27.2859	−	47.2606i	1.12144	−	1.94240i
$593$	18.4405			0.757260			0.378630	−	0.925548i	$-0.376395\pi$
$593$	18.4405			0.757260			0.378630	+	0.925548i	$0.376395\pi$
$594$	14.3812	−	24.9090i	0.590069	−	1.02203i
$595$		0			0
$596$	6.97200	+	12.0759i	0.285584	+	0.494647i
$597$	12.7813			0.523105
$598$	−8.28682	−	13.9657i	−0.338873	−	0.571099i
$599$	35.5522			1.45262			0.726312	−	0.687365i	$-0.241233\pi$
$599$	35.5522			1.45262			0.726312	+	0.687365i	$0.241233\pi$
$600$		0			0
$601$	6.52369	+	11.2994i	0.266107	+	0.460911i	0.967853	−	0.251516i	$-0.0809292\pi$
$601$	6.52369	+	11.2994i	0.266107	+	0.460911i	−0.701746	+	0.712427i	$0.747596\pi$
$602$	30.0208	−	51.9976i	1.22356	−	2.11926i
$603$	−6.21967			−0.253285
$604$	9.44015	−	16.3508i	0.384114	−	0.665306i
$605$		0			0
$606$	29.0620			1.18056
$607$	−14.6447	+	25.3653i	−0.594408	+	1.02954i	0.399222	+	0.916854i	$0.369280\pi$
$607$	−14.6447	+	25.3653i	−0.594408	+	1.02954i	−0.993630	+	0.112691i	$0.964053\pi$
$608$	2.28813	+	3.96316i	0.0927959	+	0.160727i
$609$	−24.0269	−	41.6159i	−0.973621	−	1.68636i
$610$		0			0
$611$	6.12118	−	10.9005i	0.247636	−	0.440988i
$612$	1.04654			0.0423037
$613$	4.78499	+	8.28784i	0.193264	+	0.334743i	0.946330	−	0.323202i	$-0.104759\pi$
$613$	4.78499	+	8.28784i	0.193264	+	0.334743i	−0.753066	+	0.657945i	$0.771426\pi$
$614$	−9.33662	−	16.1715i	−0.376795	−	0.652629i
$615$		0			0
$616$	18.4849			0.744776
$617$	13.9580	−	24.1759i	0.561926	−	0.973285i	−0.435402	−	0.900236i	$-0.643394\pi$
$617$	13.9580	−	24.1759i	0.561926	−	0.973285i	0.997328	−	0.0730486i	$-0.0232728\pi$
$618$	8.16417	−	14.1408i	0.328411	−	0.568825i
$619$	−35.0236			−1.40772			−0.703859	−	0.710339i	$-0.748542\pi$
$619$	−35.0236			−1.40772			−0.703859	+	0.710339i	$0.748542\pi$
$620$		0			0
$621$	−5.89501	−	10.2104i	−0.236558	−	0.409731i
$622$	21.5866	+	37.3890i	0.865542	+	1.49916i
$623$	27.3324			1.09505
$624$	16.8435	+	28.3861i	0.674279	+	1.13635i
$625$		0			0
$626$	11.7882	+	20.4178i	0.471153	+	0.816060i
$627$	−2.27820	−	3.94596i	−0.0909826	−	0.157586i
$628$	9.79308	−	16.9621i	0.390787	−	0.676862i
$629$	20.1781			0.804552
$630$		0			0
$631$	12.6337	−	21.8822i	0.502940	−	0.871118i	−0.497054	−	0.867720i	$-0.665585\pi$
$631$	12.6337	−	21.8822i	0.502940	−	0.871118i	0.999994	−	0.00339834i	$-0.00108173\pi$
$632$	−4.24255			−0.168760
$633$	1.78837	−	3.09754i	0.0710812	−	0.123116i
$634$	−19.1825	−	33.2250i	−0.761833	−	1.31953i
$635$		0			0
$636$	−31.7943			−1.26073
$637$	−37.4050	+	0.446323i	−1.48204	+	0.0176840i
$638$	37.6993			1.49253
$639$	1.81027	+	3.13548i	0.0716132	+	0.124038i
$640$		0			0
$641$	4.45070	−	7.70884i	0.175792	−	0.304481i	−0.764643	−	0.644454i	$-0.777085\pi$
$641$	4.45070	−	7.70884i	0.175792	−	0.304481i	0.940435	+	0.339973i	$0.110418\pi$
$642$	21.5244			0.849502
$643$	3.00256	−	5.20059i	0.118410	−	0.205091i	−0.800728	−	0.599028i	$-0.795554\pi$
$643$	3.00256	−	5.20059i	0.118410	−	0.205091i	0.919138	+	0.393937i	$0.128887\pi$
$644$	−6.59322	+	11.4198i	−0.259809	+	0.450003i
$645$		0			0
$646$	−1.20221	+	2.08229i	−0.0473004	+	0.0819268i
$647$	−19.6339	−	34.0069i	−0.771888	−	1.33695i	−0.936527	−	0.350596i	$-0.885979\pi$
$647$	−19.6339	−	34.0069i	−0.771888	−	1.33695i	0.164639	−	0.986354i	$-0.447354\pi$
$648$	6.69962	+	11.6041i	0.263186	+	0.455851i
$649$	3.07480			0.120697
$650$		0			0
$651$	−24.6122			−0.964626
$652$	−1.69940	−	2.94345i	−0.0665538	−	0.115274i
$653$	−21.6956	−	37.5779i	−0.849015	−	1.47054i	−0.882088	−	0.471085i	$-0.843863\pi$
$653$	−21.6956	−	37.5779i	−0.849015	−	1.47054i	0.0330724	−	0.999453i	$-0.489471\pi$
$654$	2.99966	−	5.19556i	0.117296	−	0.203162i
$655$		0			0
$656$	24.2096	−	41.9323i	0.945228	−	1.63718i
$657$	2.32796	−	4.03214i	0.0908223	−	0.157309i
$658$	−26.1361			−1.01889
$659$	11.0058	−	19.0627i	0.428726	−	0.742576i	−0.568034	−	0.823005i	$-0.692296\pi$
$659$	11.0058	−	19.0627i	0.428726	−	0.742576i	0.996760	+	0.0804293i	$0.0256291\pi$
$660$		0			0
$661$	15.7292	+	27.2438i	0.611795	+	1.05966i	0.990938	+	0.134322i	$0.0428856\pi$
$661$	15.7292	+	27.2438i	0.611795	+	1.05966i	−0.379143	+	0.925338i	$0.623781\pi$
$662$	−15.4890			−0.601997
$663$	−5.97570	+	10.6414i	−0.232077	+	0.413280i
$664$	−16.3255			−0.633551
$665$		0			0
$666$	4.52941	+	7.84517i	0.175511	+	0.303994i
$667$	7.72667	−	13.3830i	0.299178	−	0.518191i
$668$	−0.481893			−0.0186450
$669$	−10.4623	+	18.1212i	−0.404495	+	0.700606i
$670$		0			0
$671$	−7.31755			−0.282491
$672$	24.2808	−	42.0556i	0.936653	−	1.62233i
$673$	−18.3141	−	31.7210i	−0.705958	−	1.22276i	−0.966345	−	0.257251i	$-0.917183\pi$
$673$	−18.3141	−	31.7210i	−0.705958	−	1.22276i	0.260387	−	0.965504i	$-0.416150\pi$
$674$	−0.617239	−	1.06909i	−0.0237752	−	0.0411798i
$675$		0			0
$676$	16.5073	−	0.393991i	0.634895	−	0.0151535i
$677$	−33.7766			−1.29814			−0.649070	−	0.760729i	$-0.724842\pi$
$677$	−33.7766			−1.29814			−0.649070	+	0.760729i	$0.724842\pi$
$678$	5.29431	+	9.17002i	0.203327	+	0.352172i
$679$	−25.8079	−	44.7005i	−0.990415	−	1.71545i
$680$		0			0
$681$	−34.3986			−1.31816
$682$	9.65439	−	16.7219i	0.369686	−	0.640314i
$683$	−1.50753	+	2.61111i	−0.0576839	+	0.0999115i	−0.893425	−	0.449212i	$-0.851705\pi$
$683$	−1.50753	+	2.61111i	−0.0576839	+	0.0999115i	0.835741	+	0.549123i	$0.185038\pi$
$684$	−0.419268			−0.0160311
$685$		0			0
$686$	12.7202	+	22.0320i	0.485659	+	0.841187i
$687$	−11.4868	−	19.8957i	−0.438247	−	0.759067i
$688$	−39.2455			−1.49622
$689$	23.7838	−	42.3540i	0.906092	−	1.61356i
$690$		0			0
$691$	−12.4486	−	21.5615i	−0.473566	−	0.820240i	0.525976	−	0.850499i	$-0.323700\pi$
$691$	−12.4486	−	21.5615i	−0.473566	−	0.820240i	−0.999542	+	0.0302593i	$0.990367\pi$
$692$	4.92084	+	8.52314i	0.187062	+	0.324001i
$693$	−3.16718	+	5.48572i	−0.120311	+	0.208385i
$694$	31.0245			1.17767
$695$		0			0
$696$	−7.60768	+	13.1769i	−0.288369	+	0.499469i
$697$	17.9031			0.678130
$698$	−29.9774	+	51.9224i	−1.13466	+	1.96529i
$699$	7.65631	+	13.2611i	0.289588	+	0.501581i
$700$		0			0
$701$	4.54811			0.171780			0.0858899	−	0.996305i	$-0.472627\pi$
$701$	4.54811			0.171780			0.0858899	+	0.996305i	$0.472627\pi$
$702$	30.8624	−	0.368255i	1.16483	−	0.0138989i
$703$	−8.08383			−0.304887
$704$	2.49416	+	4.32002i	0.0940024	+	0.162817i
$705$		0			0
$706$	−10.1171	+	17.5233i	−0.380762	+	0.659499i
$707$	36.0538			1.35594
$708$	1.07984	−	1.87033i	0.0405828	−	0.0702915i
$709$	1.47450	−	2.55391i	0.0553761	−	0.0959142i	−0.837009	−	0.547190i	$-0.815698\pi$
$709$	1.47450	−	2.55391i	0.0553761	−	0.0959142i	0.892385	+	0.451276i	$0.149031\pi$
$710$		0			0
$711$	0.726916	−	1.25905i	0.0272615	−	0.0472182i
$712$	−4.32715	−	7.49484i	−0.162167	−	0.280881i
$713$	−3.95743	−	6.85447i	−0.148207	−	0.256702i
$714$	25.5149			0.954872
$715$		0			0
$716$	−26.2099			−0.979512
$717$	19.4146	+	33.6270i	0.725051	+	1.25582i
$718$	−1.97365	−	3.41846i	−0.0736559	−	0.127576i
$719$	3.27857	−	5.67866i	0.122270	−	0.211778i	−0.798392	−	0.602138i	$-0.794316\pi$
$719$	3.27857	−	5.67866i	0.122270	−	0.211778i	0.920663	+	0.390359i	$0.127649\pi$
$720$		0			0
$721$	10.1283	−	17.5428i	0.377199	−	0.653328i
$722$	−16.6977	+	28.9213i	−0.621426	+	1.07634i
$723$	−14.2142			−0.528631
$724$	8.53266	−	14.7790i	0.317114	−	0.549257i
$725$		0			0
$726$	−0.486299	−	0.842295i	−0.0180483	−	0.0312605i
$727$	6.97127			0.258550			0.129275	−	0.991609i	$-0.458735\pi$
$727$	6.97127			0.258550			0.129275	+	0.991609i	$0.458735\pi$
$728$	10.1222	+	17.0588i	0.375153	+	0.632241i
$729$	21.7947			0.807212
$730$		0			0
$731$	−7.25556	−	12.5670i	−0.268357	−	0.464807i
$732$	−2.56985	+	4.45111i	−0.0949843	+	0.164518i
$733$	−0.920949			−0.0340160			−0.0170080	−	0.999855i	$-0.505414\pi$
$733$	−0.920949			−0.0340160			−0.0170080	+	0.999855i	$0.505414\pi$
$734$	−10.0722	+	17.4455i	−0.371771	+	0.643926i
$735$		0			0
$736$	15.6166			0.575636
$737$	23.1031	−	40.0158i	0.851015	−	1.47400i
$738$	4.01876	+	6.96069i	0.147932	+	0.256227i
$739$	−6.68808	−	11.5841i	−0.246025	−	0.426128i	0.716394	−	0.697696i	$-0.245791\pi$
$739$	−6.68808	−	11.5841i	−0.246025	−	0.426128i	−0.962419	+	0.271568i	$0.912458\pi$
$740$		0			0
$741$	2.39401	−	4.26323i	0.0879463	−	0.156614i
$742$	−101.552			−3.72808
$743$	−18.3460	−	31.7763i	−0.673051	−	1.16576i	−0.977034	−	0.213081i	$-0.931650\pi$
$743$	−18.3460	−	31.7763i	−0.673051	−	1.16576i	0.303983	−	0.952677i	$-0.401683\pi$
$744$	3.89649	+	6.74892i	0.142852	+	0.247427i
$745$		0			0
$746$	29.7271			1.08839
$747$	2.79719	−	4.84488i	0.102344	−	0.177265i
$748$	−3.88738	+	6.73314i	−0.142137	+	0.246188i
$749$	26.7029			0.975702
$750$		0			0
$751$	−13.6031	−	23.5612i	−0.496383	−	0.859760i	0.503608	−	0.863932i	$-0.332005\pi$
$751$	−13.6031	−	23.5612i	−0.496383	−	0.859760i	−0.999991	+	0.00417160i	$0.998672\pi$
$752$	8.54178	+	14.7948i	0.311487	+	0.539511i
$753$	27.6268			1.00678
$754$	20.6439	+	34.7909i	0.751807	+	1.26701i
$755$		0			0
$756$	−12.5312	−	21.7047i	−0.455756	−	0.789393i
$757$	13.1937	+	22.8522i	0.479535	+	0.830579i	0.999724	−	0.0234720i	$-0.00747206\pi$
$757$	13.1937	+	22.8522i	0.479535	+	0.830579i	−0.520190	+	0.854051i	$0.674139\pi$
$758$	−5.21368	+	9.03035i	−0.189369	+	0.327997i
$759$	−15.5489			−0.564388
$760$		0			0
$761$	−5.65688	+	9.79800i	−0.205062	+	0.355177i	−0.950152	−	0.311786i	$-0.899073\pi$
$761$	−5.65688	+	9.79800i	−0.205062	+	0.355177i	0.745091	+	0.666963i	$0.232406\pi$
$762$	44.3720			1.60743
$763$	3.72133	−	6.44553i	0.134721	−	0.233344i
$764$	−5.26487	−	9.11903i	−0.190476	−	0.329915i
$765$		0			0
$766$	61.4938			2.22186
$767$	1.68374	+	2.83759i	0.0607964	+	0.102459i
$768$	−38.6315			−1.39399
$769$	3.88223	+	6.72423i	0.139997	+	0.242482i	0.927495	−	0.373835i	$-0.121957\pi$
$769$	3.88223	+	6.72423i	0.139997	+	0.242482i	−0.787498	+	0.616317i	$0.788624\pi$
$770$		0			0
$771$	−3.65878	+	6.33719i	−0.131768	+	0.228228i
$772$	−0.155204			−0.00558591
$773$	−1.70726	+	2.95706i	−0.0614058	+	0.106358i	−0.895094	−	0.445878i	$-0.852892\pi$
$773$	−1.70726	+	2.95706i	−0.0614058	+	0.106358i	0.833688	+	0.552235i	$0.186225\pi$
$774$	3.25734	−	5.64188i	0.117083	−	0.202793i
$775$		0			0
$776$	−8.17158	+	14.1536i	−0.293343	+	0.508084i
$777$	42.8914	+	74.2900i	1.53872	+	2.66514i
$778$	26.9268	+	46.6385i	0.965372	+	1.67207i
$779$	−7.17244			−0.256979
$780$		0			0
$781$	−26.8972			−0.962456
$782$	4.10259	+	7.10589i	0.146708	+	0.254106i
$783$	14.6855	+	25.4360i	0.524816	+	0.909009i
$784$	25.5590	−	44.2694i	0.912820	−	1.58105i
$785$		0			0
$786$	−10.7391	+	18.6006i	−0.383050	+	0.663461i
$787$	−14.1983	+	24.5921i	−0.506113	+	0.876614i	0.493862	+	0.869540i	$0.335585\pi$
$787$	−14.1983	+	24.5921i	−0.506113	+	0.876614i	−0.999975	+	0.00707326i	$0.997748\pi$
$788$	20.9176			0.745158
$789$	5.97295	−	10.3455i	0.212643	−	0.368308i
$790$		0			0
$791$	6.56804	+	11.3762i	0.233533	+	0.404490i
$792$	2.00566			0.0712679
$793$	−4.00704	−	6.75302i	−0.142294	−	0.239807i
$794$	46.6625			1.65599
$795$		0			0
$796$	4.36867	+	7.56675i	0.154843	+	0.268196i
$797$	−6.67052	+	11.5537i	−0.236282	+	0.409252i	−0.959644	−	0.281216i	$-0.909262\pi$
$797$	−6.67052	+	11.5537i	−0.236282	+	0.409252i	0.723363	+	0.690468i	$0.242596\pi$
$798$	−10.2219			−0.361852
$799$	−3.15834	+	5.47041i	−0.111734	+	0.193529i
$800$		0			0
$801$	2.96564			0.104786
$802$	7.66430	−	13.2750i	0.270636	−	0.468755i
$803$	17.2945	+	29.9550i	0.610310	+	1.05709i
$804$	−16.2272	−	28.1063i	−0.572288	−	0.991231i
$805$		0			0
$806$	20.7185	−	0.247217i	0.729779	−	0.00870785i
$807$	−31.1680			−1.09717
$808$	−5.70788	−	9.88634i	−0.200803	−	0.347800i
$809$	18.1806	+	31.4898i	0.639198	+	1.10712i	0.985609	+	0.169040i	$0.0540667\pi$
$809$	18.1806	+	31.4898i	0.639198	+	1.10712i	−0.346412	+	0.938083i	$0.612600\pi$
$810$		0			0
$811$	8.37262			0.294002			0.147001	−	0.989136i	$-0.453038\pi$
$811$	8.37262			0.294002			0.147001	+	0.989136i	$0.453038\pi$
$812$	16.4249	−	28.4487i	0.576399	−	0.998353i
$813$	−5.99552	+	10.3845i	−0.210272	+	0.364202i
$814$	−67.2985			−2.35881
$815$		0			0
$816$	−8.33877	−	14.4432i	−0.291915	−	0.505612i
$817$	2.90676	+	5.03465i	0.101695	+	0.176140i
$818$	1.30402			0.0455940
$819$	−6.79684	+	0.0811010i	−0.237501	+	0.00283390i
$820$		0			0
$821$	13.5378	+	23.4482i	0.472474	+	0.818349i	0.999504	−	0.0314981i	$-0.0100278\pi$
$821$	13.5378	+	23.4482i	0.472474	+	0.818349i	−0.527030	+	0.849847i	$0.676694\pi$
$822$	−2.81647	−	4.87826i	−0.0982356	−	0.170149i
$823$	−20.6744	+	35.8091i	−0.720664	+	1.24823i	0.240070	+	0.970756i	$0.422830\pi$
$823$	−20.6744	+	35.8091i	−0.720664	+	1.24823i	−0.960734	+	0.277471i	$0.910504\pi$
$824$	−6.41390			−0.223439
$825$		0			0
$826$	3.44903	−	5.97390i	0.120007	−	0.207858i
$827$	9.69711			0.337202			0.168601	−	0.985684i	$-0.446075\pi$
$827$	9.69711			0.337202			0.168601	+	0.985684i	$0.446075\pi$
$828$	−0.715382	+	1.23908i	−0.0248612	+	0.0430609i
$829$	−25.3041	−	43.8280i	−0.878848	−	1.52221i	−0.852607	−	0.522553i	$-0.824980\pi$
$829$	−25.3041	−	43.8280i	−0.878848	−	1.52221i	−0.0262407	−	0.999656i	$-0.508354\pi$
$830$		0			0
$831$	2.08309			0.0722617
$832$	−2.62095	+	4.66736i	−0.0908653	+	0.161812i
$833$	18.9010			0.654880
$834$	−20.2135	−	35.0107i	−0.699935	−	1.21232i
$835$		0			0
$836$	1.55738	−	2.69746i	0.0538632	−	0.0932937i
$837$	15.0432			0.519968
$838$	13.5938	−	23.5451i	0.469588	−	0.813351i
$839$	−3.49302	+	6.05009i	−0.120593	+	0.208872i	−0.920002	−	0.391915i	$-0.871813\pi$
$839$	−3.49302	+	6.05009i	−0.120593	+	0.208872i	0.799409	+	0.600787i	$0.205146\pi$
$840$		0			0
$841$	−4.74847	+	8.22459i	−0.163740	+	0.283607i
$842$	15.3458	+	26.5798i	0.528853	+	0.916000i
$843$	14.4390	+	25.0091i	0.497307	+	0.861361i
$844$	2.44506			0.0841624
$845$		0			0
$846$	−2.83584			−0.0974981
$847$	−0.603295	−	1.04494i	−0.0207295	−	0.0359045i
$848$	33.1891	+	57.4852i	1.13972	+	1.97405i
$849$	−20.4537	+	35.4269i	−0.701970	+	1.21585i
$850$		0			0
$851$	−13.7932	+	23.8904i	−0.472823	+	0.818954i
$852$	−9.44601	+	16.3610i	−0.323615	+	0.560517i
$853$	2.26681			0.0776142			0.0388071	−	0.999247i	$-0.487644\pi$
$853$	2.26681			0.0776142			0.0388071	+	0.999247i	$0.487644\pi$
$854$	−8.20816	+	14.2169i	−0.280877	+	0.486494i
$855$		0			0
$856$	−4.22748	−	7.32221i	−0.144492	−	0.250268i
$857$	−16.1887			−0.552994			−0.276497	−	0.961015i	$-0.589174\pi$
$857$	−16.1887			−0.552994			−0.276497	+	0.961015i	$0.589174\pi$
$858$	19.9303	−	35.4917i	0.680410	−	1.21167i
$859$	−40.9076			−1.39575			−0.697875	−	0.716219i	$-0.745871\pi$
$859$	−40.9076			−1.39575			−0.697875	+	0.716219i	$0.745871\pi$
$860$		0			0
$861$	38.0557	+	65.9144i	1.29693	+	2.24636i
$862$	−16.7491	+	29.0103i	−0.570477	+	0.988095i
$863$	29.6192			1.00825			0.504125	−	0.863631i	$-0.331815\pi$
$863$	29.6192			1.00825			0.504125	+	0.863631i	$0.331815\pi$
$864$	−14.8407	+	25.7048i	−0.504889	+	0.874494i
$865$		0			0
$866$	−71.5727			−2.43214
$867$	−12.7100	+	22.0143i	−0.431654	+	0.747646i
$868$	−8.41245	−	14.5708i	−0.285537	−	0.494565i
$869$	5.40029	+	9.35358i	0.183192	+	0.317298i
$870$		0			0
$871$	49.5798	−	0.591595i	1.67995	−	0.0200454i
$872$	−2.35658			−0.0798038
$873$	−2.80022	−	4.85013i	−0.0947732	−	0.164152i
$874$	−1.64360	−	2.84680i	−0.0555955	−	0.0962943i
$875$		0			0
$876$	24.2946			0.820839
$877$	22.7316	−	39.3723i	0.767592	−	1.32951i	−0.171273	−	0.985224i	$-0.554788\pi$
$877$	22.7316	−	39.3723i	0.767592	−	1.32951i	0.938865	−	0.344285i	$-0.111879\pi$
$878$	15.5664	−	26.9617i	0.525339	−	0.909914i
$879$	−26.6265			−0.898090
$880$		0			0
$881$	−15.9907	−	27.6967i	−0.538740	−	0.933125i	−0.998972	−	0.0453265i	$-0.985567\pi$
$881$	−15.9907	−	27.6967i	−0.538740	−	0.933125i	0.460232	−	0.887799i	$-0.347766\pi$
$882$	4.24274	+	7.34864i	0.142861	+	0.247442i
$883$	−17.0799			−0.574786			−0.287393	−	0.957813i	$-0.592789\pi$
$883$	−17.0799			−0.574786			−0.287393	+	0.957813i	$0.592789\pi$
$884$	−8.34240	+	0.0995430i	−0.280585	+	0.00334799i
$885$		0			0
$886$	−16.5091	−	28.5946i	−0.554634	−	0.960654i
$887$	−4.06832	−	7.04654i	−0.136601	−	0.236600i	0.789607	−	0.613613i	$-0.210284\pi$
$887$	−4.06832	−	7.04654i	−0.136601	−	0.236600i	−0.926208	+	0.377013i	$0.876951\pi$
$888$	13.5808	−	23.5226i	0.455740	−	0.789365i
$889$	55.0471			1.84622
$890$		0			0
$891$	17.0557	−	29.5414i	0.571388	−	0.989673i
$892$	−14.3040			−0.478935
$893$	1.26531	−	2.19158i	0.0423420	−	0.0733384i
$894$	18.4433	+	31.9447i	0.616836	+	1.06839i
$895$		0			0
$896$	−41.0813			−1.37243
$897$	−8.51445	−	14.3493i	−0.284289	−	0.479109i
$898$	−26.2872			−0.877215
$899$	9.85865	+	17.0757i	0.328804	+	0.569506i
$900$		0			0
$901$	−12.2717	+	21.2553i	−0.408831	+	0.708115i
$902$	−59.7111			−1.98816
$903$	30.8455	−	53.4259i	1.02647	−	1.77790i
$904$	2.07965	−	3.60205i	0.0691680	−	0.119803i
$905$		0			0
$906$	24.9724	−	43.2535i	0.829652	−	1.43700i
$907$	−3.56867	−	6.18111i	−0.118496	−	0.205240i	0.800676	−	0.599098i	$-0.204474\pi$
$907$	−3.56867	−	6.18111i	−0.118496	−	0.205240i	−0.919172	+	0.393857i	$0.871140\pi$
$908$	−11.7575	−	20.3645i	−0.390185	−	0.675821i
$909$	3.91194			0.129751
$910$		0			0
$911$	−11.6780			−0.386909			−0.193454	−	0.981109i	$-0.561969\pi$
$911$	−11.6780			−0.386909			−0.193454	+	0.981109i	$0.561969\pi$
$912$	3.34072	+	5.78629i	0.110622	+	0.191603i
$913$	20.7805	+	35.9928i	0.687733	+	1.19119i
$914$	1.02266	−	1.77130i	0.0338265	−	0.0585893i
$915$		0			0
$916$	7.85236	−	13.6007i	0.259449	−	0.449380i
$917$	−13.3227	+	23.0756i	−0.439954	+	0.762023i
$918$	−15.5949			−0.514710
$919$	−10.9299	+	18.9312i	−0.360545	+	0.624483i	−0.988051	−	0.154129i	$-0.950743\pi$
$919$	−10.9299	+	18.9312i	−0.360545	+	0.624483i	0.627505	+	0.778612i	$0.284076\pi$
$920$		0			0
$921$	−9.59309	−	16.6157i	−0.316103	−	0.547507i
$922$	−43.9500			−1.44742
$923$	−14.7287	−	24.8221i	−0.484801	−	0.817030i
$924$	−33.0528			−1.08736
$925$		0			0
$926$	33.7303	+	58.4226i	1.10845	+	1.91989i
$927$	1.09895	−	1.90344i	0.0360943	−	0.0625172i
$928$	−38.9037			−1.27708
$929$	28.7819	−	49.8518i	0.944305	−	1.63558i	0.187168	−	0.982328i	$-0.440069\pi$
$929$	28.7819	−	49.8518i	0.944305	−	1.63558i	0.757137	−	0.653256i	$-0.226597\pi$
$930$		0			0
$931$	−7.57220			−0.248169
$932$	−5.23386	+	9.06531i	−0.171441	+	0.296944i
$933$	22.1795	+	38.4161i	0.726125	+	1.25769i
$934$	26.8053	+	46.4282i	0.877097	+	1.51918i
$935$		0			0
$936$	1.09828	+	1.85093i	0.0358986	+	0.0604994i
$937$	18.8937			0.617232			0.308616	−	0.951187i	$-0.400134\pi$
$937$	18.8937			0.617232			0.308616	+	0.951187i	$0.400134\pi$
$938$	−51.8300	−	89.7721i	−1.69231	−	2.93116i
$939$	12.1120	+	20.9787i	0.395262	+	0.684613i
$940$		0			0
$941$	−47.4723			−1.54755			−0.773777	−	0.633459i	$-0.781635\pi$
$941$	−47.4723			−1.54755			−0.773777	+	0.633459i	$0.781635\pi$
$942$	25.9060	−	44.8705i	0.844063	−	1.46196i
$943$	−12.2381	+	21.1970i	−0.398527	+	0.690269i
$944$	−4.50884			−0.146750
$945$		0			0
$946$	24.1990	+	41.9138i	0.786776	+	1.36274i
$947$	3.82919	+	6.63235i	0.124432	+	0.215523i	0.921511	−	0.388353i	$-0.126956\pi$
$947$	3.82919	+	6.63235i	0.124432	+	0.215523i	−0.797079	+	0.603875i	$0.793622\pi$
$948$	7.58611			0.246385
$949$	−18.1737	+	32.3635i	−0.589943	+	1.05056i
$950$		0			0
$951$	−19.7094	−	34.1377i	−0.639121	−	1.10699i
$952$	−5.01123	−	8.67970i	−0.162415	−	0.281311i
$953$	6.41704	−	11.1146i	0.207868	−	0.360039i	−0.743174	−	0.669098i	$-0.766681\pi$
$953$	6.41704	−	11.1146i	0.207868	−	0.360039i	0.951043	+	0.309059i	$0.100014\pi$
$954$	−11.0186			−0.356742
$955$		0			0
$956$	−13.2718	+	22.9875i	−0.429242	+	0.743468i
$957$	38.7349			1.25212
$958$	11.0869	−	19.2031i	0.358202	−	0.620424i
$959$	−3.49406	−	6.05189i	−0.112829	−	0.195426i
$960$		0			0
$961$	−20.9012			−0.674233
$962$	−36.8522	−	62.1066i	−1.18816	−	2.00240i
$963$	2.89733			0.0933653
$964$	−4.85841	−	8.41502i	−0.156479	−	0.271029i
$965$		0			0
$966$	−17.4413	+	30.2092i	−0.561164	+	0.971965i
$967$	10.5239			0.338427			0.169214	−	0.985579i	$-0.445877\pi$
$967$	10.5239			0.338427			0.169214	+	0.985579i	$0.445877\pi$
$968$	−0.191022	+	0.330860i	−0.00613968	+	0.0106342i
$969$	−1.23524	+	2.13949i	−0.0396815	+	0.0687304i
$970$		0			0
$971$	−10.7127	+	18.5549i	−0.343785	+	0.595454i	−0.985132	−	0.171797i	$-0.945043\pi$
$971$	−10.7127	+	18.5549i	−0.343785	+	0.595454i	0.641347	+	0.767251i	$0.278376\pi$
$972$	−2.96071	−	5.12811i	−0.0949650	−	0.164484i
$973$	−25.0765	−	43.4337i	−0.803915	−	1.39242i
$974$	−43.0031			−1.37791
$975$		0			0
$976$	10.7303			0.343470
$977$	−14.5149	−	25.1406i	−0.464373	−	0.804318i	0.534800	−	0.844979i	$-0.320387\pi$
$977$	−14.5149	−	25.1406i	−0.464373	−	0.804318i	−0.999173	+	0.0406611i	$0.987054\pi$
$978$	−4.49550	−	7.78643i	−0.143750	−	0.248982i
$979$	−11.0159	+	19.0802i	−0.352071	+	0.609805i
$980$		0			0
$981$	0.403774	−	0.699357i	0.0128915	−	0.0223288i
$982$	−16.3300	+	28.2844i	−0.521112	+	0.902593i
$983$	14.7766			0.471299			0.235650	−	0.971838i	$-0.424278\pi$
$983$	14.7766			0.471299			0.235650	+	0.971838i	$0.424278\pi$
$984$	12.0496	−	20.8706i	0.384128	−	0.665329i
$985$		0			0
$986$	−10.2203	−	17.7020i	−0.325479	−	0.563747i
$987$	−26.8540			−0.854773
$988$	3.34217	−	0.0398794i	0.106329	−	0.00126873i
$989$	19.8388			0.630837
$990$		0			0
$991$	−5.03065	−	8.71334i	−0.159804	−	0.276788i	0.774994	−	0.631969i	$-0.217753\pi$
$991$	−5.03065	−	8.71334i	−0.159804	−	0.276788i	−0.934798	+	0.355180i	$0.884419\pi$
$992$	−9.96282	+	17.2561i	−0.316320	+	0.547882i
$993$	−15.9145			−0.505030
$994$	−30.1708	+	52.2573i	−0.956959	+	1.65750i
$995$		0			0
$996$	29.1915			0.924970
$997$	21.2226	−	36.7586i	0.672126	−	1.16416i	−0.305174	−	0.952297i	$-0.598715\pi$
$997$	21.2226	−	36.7586i	0.672126	−	1.16416i	0.977300	−	0.211860i	$-0.0679520\pi$
$998$	−5.10502	−	8.84215i	−0.161596	−	0.279893i
$999$	−26.2156	−	45.4067i	−0.829425	−	1.43661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.e.c.276.4	yes	10
5.2	odd	4		325.2.o.c.224.3		20
5.3	odd	4		325.2.o.c.224.8		20
5.4	even	2		325.2.e.d.276.2	yes	10
13.3	even	3		4225.2.a.bp.1.2		5
13.9	even	3	inner	325.2.e.c.126.4	✓	10
13.10	even	6		4225.2.a.bo.1.4		5
65.9	even	6		325.2.e.d.126.2	yes	10
65.22	odd	12		325.2.o.c.74.8		20
65.29	even	6		4225.2.a.bn.1.4		5
65.48	odd	12		325.2.o.c.74.3		20
65.49	even	6		4225.2.a.bm.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.e.c.126.4	✓	10	13.9	even	3	inner
325.2.e.c.276.4	yes	10	1.1	even	1	trivial
325.2.e.d.126.2	yes	10	65.9	even	6
325.2.e.d.276.2	yes	10	5.4	even	2
325.2.o.c.74.3		20	65.48	odd	12
325.2.o.c.74.8		20	65.22	odd	12
325.2.o.c.224.3		20	5.2	odd	4
325.2.o.c.224.8		20	5.3	odd	4
4225.2.a.bm.1.2		5	65.49	even	6
4225.2.a.bn.1.4		5	65.29	even	6
4225.2.a.bo.1.4		5	13.10	even	6
4225.2.a.bp.1.2		5	13.3	even	3

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.904178 + 1.56608i) q^{2} +(0.929015 + 1.60910i) q^{3} +(-0.635076 + 1.09998i) q^{4} +(-1.67999 + 2.90983i) q^{6} +(-2.08417 + 3.60988i) q^{7} +1.31983 q^{8} +(-0.226138 + 0.391682i) q^{9} +O(q^{10})\)	\(q+(0.904178 + 1.56608i) q^{2} +(0.929015 + 1.60910i) q^{3} +(-0.635076 + 1.09998i) q^{4} +(-1.67999 + 2.90983i) q^{6} +(-2.08417 + 3.60988i) q^{7} +1.31983 q^{8} +(-0.226138 + 0.391682i) q^{9} +(-1.67999 - 2.90983i) q^{11} -2.35998 q^{12} +(1.76539 - 3.14379i) q^{13} -7.53784 q^{14} +(2.46351 + 4.26692i) q^{16} +(-0.910888 + 1.57770i) q^{17} -0.817876 q^{18} +(0.364924 - 0.632067i) q^{19} -7.74489 q^{21} +(3.03802 - 5.26201i) q^{22} +(-1.24531 - 2.15695i) q^{23} +(1.22614 + 2.12373i) q^{24} +(6.51966 - 0.0777936i) q^{26} +4.73375 q^{27} +(-2.64721 - 4.58510i) q^{28} +(3.10230 + 5.37333i) q^{29} +3.17786 q^{31} +(-3.13508 + 5.43011i) q^{32} +(3.12147 - 5.40655i) q^{33} -3.29442 q^{34} +(-0.287229 - 0.497496i) q^{36} +(-5.53802 - 9.59213i) q^{37} +1.31983 q^{38} +(6.69875 - 0.0799306i) q^{39} +(-4.91365 - 8.51069i) q^{41} +(-7.00276 - 12.1291i) q^{42} +(-3.98269 + 6.89821i) q^{43} +4.26768 q^{44} +(2.25197 - 3.90053i) q^{46} +3.46732 q^{47} +(-4.57727 + 7.92807i) q^{48} +(-5.18751 - 8.98504i) q^{49} -3.38491 q^{51} +(2.33696 + 3.93844i) q^{52} +13.4723 q^{53} +(4.28015 + 7.41344i) q^{54} +(-2.75074 + 4.76442i) q^{56} +1.35608 q^{57} +(-5.61005 + 9.71690i) q^{58} +(-0.457562 + 0.792521i) q^{59} +(1.08893 - 1.88608i) q^{61} +(2.87335 + 4.97678i) q^{62} +(-0.942619 - 1.63266i) q^{63} -1.48463 q^{64} +11.2895 q^{66} +(6.87597 + 11.9095i) q^{67} +(-1.15697 - 2.00392i) q^{68} +(2.31383 - 4.00767i) q^{69} +(4.00258 - 6.93267i) q^{71} +(-0.298463 + 0.516952i) q^{72} -10.2944 q^{73} +(10.0147 - 17.3460i) q^{74} +(0.463509 + 0.802821i) q^{76} +14.0055 q^{77} +(6.18204 + 10.4185i) q^{78} -3.21448 q^{79} +(5.07614 + 8.79213i) q^{81} +(8.88563 - 15.3904i) q^{82} -12.3694 q^{83} +(4.91859 - 8.51926i) q^{84} -14.4042 q^{86} +(-5.76416 + 9.98381i) q^{87} +(-2.21729 - 3.84047i) q^{88} +(-3.27857 - 5.67866i) q^{89} +(7.66933 + 12.9250i) q^{91} +3.16348 q^{92} +(2.95228 + 5.11349i) q^{93} +(3.13508 + 5.43011i) q^{94} -11.6501 q^{96} +(-6.19141 + 10.7238i) q^{97} +(9.38087 - 16.2481i) q^{98} +1.51964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 10 * q - 3 * q^3 - 6 * q^4 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 4 * q^9	\( 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9} - 3 q^{11} + 4 q^{12} + 10 q^{13} - 16 q^{14} - 4 q^{16} - 4 q^{17} - 4 q^{18} + 4 q^{19} - 16 q^{21} - 8 q^{22} - 15 q^{23} + 14 q^{24} - 9 q^{26} + 42 q^{27} + 17 q^{28} + q^{29} - 31 q^{32} + 2 q^{33} + 54 q^{34} + 13 q^{36} - 17 q^{37} + 6 q^{38} - 10 q^{39} - 6 q^{41} - 32 q^{42} - 12 q^{43} - 16 q^{44} + 7 q^{46} - 24 q^{47} + 2 q^{48} - 7 q^{49} + 23 q^{52} + 16 q^{53} - 19 q^{54} + 17 q^{56} - 8 q^{57} - 38 q^{58} + 12 q^{59} - 5 q^{61} - 13 q^{62} - 26 q^{63} - 10 q^{64} + 86 q^{66} + 16 q^{67} - 25 q^{68} - 20 q^{69} - 19 q^{71} + 45 q^{72} - 16 q^{73} - 2 q^{74} - 24 q^{76} + 64 q^{77} + 42 q^{78} - 28 q^{79} - 29 q^{81} + 23 q^{82} - 14 q^{83} + 34 q^{84} - 84 q^{86} - 21 q^{87} - 2 q^{88} + 10 q^{89} + 17 q^{91} + 142 q^{92} + 33 q^{93} + 31 q^{94} + 34 q^{96} - 37 q^{97} + 21 q^{98} + 56 q^{99}+O(q^{100}) \) 10 * q - 3 * q^3 - 6 * q^4 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 4 * q^9 - 3 * q^11 + 4 * q^12 + 10 * q^13 - 16 * q^14 - 4 * q^16 - 4 * q^17 - 4 * q^18 + 4 * q^19 - 16 * q^21 - 8 * q^22 - 15 * q^23 + 14 * q^24 - 9 * q^26 + 42 * q^27 + 17 * q^28 + q^29 - 31 * q^32 + 2 * q^33 + 54 * q^34 + 13 * q^36 - 17 * q^37 + 6 * q^38 - 10 * q^39 - 6 * q^41 - 32 * q^42 - 12 * q^43 - 16 * q^44 + 7 * q^46 - 24 * q^47 + 2 * q^48 - 7 * q^49 + 23 * q^52 + 16 * q^53 - 19 * q^54 + 17 * q^56 - 8 * q^57 - 38 * q^58 + 12 * q^59 - 5 * q^61 - 13 * q^62 - 26 * q^63 - 10 * q^64 + 86 * q^66 + 16 * q^67 - 25 * q^68 - 20 * q^69 - 19 * q^71 + 45 * q^72 - 16 * q^73 - 2 * q^74 - 24 * q^76 + 64 * q^77 + 42 * q^78 - 28 * q^79 - 29 * q^81 + 23 * q^82 - 14 * q^83 + 34 * q^84 - 84 * q^86 - 21 * q^87 - 2 * q^88 + 10 * q^89 + 17 * q^91 + 142 * q^92 + 33 * q^93 + 31 * q^94 + 34 * q^96 - 37 * q^97 + 21 * q^98 + 56 * q^99

Introduction

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