LMFDB - Embedded newform 325.2.e.d.126.2

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			126.2
Root			$0.904178 - 1.56608i$ of defining polynomial
Character	$\chi$	$=$	325.126
Dual form			325.2.e.d.276.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.904178 + 1.56608i) q^{2} +(-0.929015 + 1.60910i) q^{3} +(-0.635076 - 1.09998i) q^{4} +(-1.67999 - 2.90983i) q^{6} +(2.08417 + 3.60988i) q^{7} -1.31983 q^{8} +(-0.226138 - 0.391682i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.904178	+	1.56608i	−0.639350	+	1.10739i	0.346225	+	0.938151i	$0.387463\pi$
$2$	−0.904178	+	1.56608i	−0.639350	+	1.10739i	−0.985576	+	0.169236i	$0.945870\pi$
$3$	−0.929015	+	1.60910i	−0.536367	+	0.929015i	0.462729	+	0.886500i	$0.346870\pi$
$3$	−0.929015	+	1.60910i	−0.536367	+	0.929015i	−0.999096	+	0.0425151i	$0.986463\pi$
$4$	−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	0.927348	+	0.374201i	$0.122083\pi$
$7$	2.08417	+	3.60988i	0.787741	+	1.36441i	−0.139606	+	0.990207i	$0.544584\pi$
$8$	−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	0.493435	+	0.869782i	$0.335741\pi$
$11$	−1.67999	+	2.90983i	−0.506536	+	0.877346i	−0.999971	+	0.00756369i	$0.997592\pi$
$12$	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	$-0.0957598\pi$
$17$	0.910888	+	1.57770i	0.220923	+	0.382649i	−0.734166	+	0.678970i	$0.762426\pi$
$18$	0.817876			0.192775
$19$	0.364924	+	0.632067i	0.0837193	+	0.145006i	0.904845	−	0.425742i	$-0.139987\pi$
$19$	0.364924	+	0.632067i	0.0837193	+	0.145006i	−0.821125	+	0.570748i	$0.806653\pi$
$20$		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	$-0.749721\pi$
$23$	1.24531	−	2.15695i	0.259666	−	0.449755i	0.966152	+	0.257972i	$0.0830542\pi$
$24$	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	−0.419841	−	0.907597i	$-0.637914\pi$
$29$	3.10230	−	5.37333i	0.576082	−	0.997803i	0.995923	−	0.0902054i	$-0.0287524\pi$
$30$		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	0.0970080	−	0.995284i	$-0.469073\pi$
$37$	5.53802	−	9.59213i	0.910445	−	1.57694i	0.813437	−	0.581653i	$-0.197594\pi$
$38$	−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	0.171594	+	0.985168i	$0.445108\pi$
$41$	−4.91365	+	8.51069i	−0.767383	+	1.32915i	−0.938977	+	0.343979i	$0.888225\pi$
$42$	7.00276	−	12.1291i	1.08055	−	1.87157i
$43$	3.98269	+	6.89821i	0.607354	+	1.05197i	0.991675	+	0.128768i	$0.0411023\pi$
$43$	3.98269	+	6.89821i	0.607354	+	1.05197i	−0.384321	+	0.923200i	$0.625564\pi$
$44$	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	$-0.581378\pi$
$47$	−3.46732			−0.505761			−0.252880	+	0.967498i	$0.581378\pi$
$48$	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	$-0.876170\pi$
$53$	−13.4723			−1.85056			−0.925280	+	0.379286i	$0.876170\pi$
$54$	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	0.834703	−	0.550701i	$-0.185639\pi$
$59$	−0.457562	−	0.792521i	−0.0595696	−	0.103178i	−0.894272	+	0.447523i	$0.852306\pi$
$60$		0			0
$61$	1.08893	+	1.88608i	0.139423	+	0.241488i	0.927278	−	0.374373i	$-0.122142\pi$
$61$	1.08893	+	1.88608i	0.139423	+	0.241488i	−0.787855	+	0.615860i	$0.788809\pi$
$62$	−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	0.0498314	+	0.998758i	$0.484132\pi$
$67$	−6.87597	+	11.9095i	−0.840034	+	1.45498i	−0.889865	+	0.456224i	$0.849202\pi$
$68$	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	0.999591	−	0.0286096i	$-0.00910796\pi$
$71$	4.00258	+	6.93267i	0.475019	+	0.822756i	−0.524572	+	0.851366i	$0.675775\pi$
$72$	0.298463	+	0.516952i	0.0351742	+	0.0609234i
$73$	10.2944			1.20487			0.602435	−	0.798168i	$-0.294197\pi$
$73$	10.2944			1.20487			0.602435	+	0.798168i	$0.294197\pi$
$74$	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	$-0.262475\pi$
$83$	12.3694			1.35772			0.678859	+	0.734268i	$0.262475\pi$
$84$	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	−0.985810	−	0.167866i	$-0.946312\pi$
$89$	−3.27857	+	5.67866i	−0.347528	+	0.601937i	0.638282	+	0.769803i	$0.279646\pi$
$90$		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	0.987824	+	0.155573i	$0.0497223\pi$
$97$	6.19141	+	10.7238i	0.628642	+	1.08884i	−0.359182	+	0.933267i	$0.616944\pi$
$98$	−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	−0.996901	−	0.0786635i	$-0.974935\pi$
$101$	−4.32472	+	7.49064i	−0.430326	+	0.745346i	0.566575	+	0.824010i	$0.308268\pi$
$102$	3.06056	−	5.30105i	0.303041	−	0.524883i
$103$	4.85966			0.478836			0.239418	−	0.970917i	$-0.423043\pi$
$103$	4.85966			0.478836			0.239418	+	0.970917i	$0.423043\pi$
$104$	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	$-0.733121\pi$
$107$	3.20306	−	5.54787i	0.309652	−	0.536332i	0.978286	+	0.207259i	$0.0664542\pi$
$108$	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	$-0.214024\pi$
$113$	−1.57570	−	2.72919i	−0.148229	−	0.256740i	−0.930573	+	0.366106i	$0.880691\pi$
$114$	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	−0.408837	−	0.912607i	$-0.634066\pi$
$127$	6.60301	−	11.4368i	0.585923	−	1.01485i	0.994760	−	0.102240i	$-0.0326010\pi$
$128$	−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	$-0.143851\pi$
$137$	0.838239	+	1.45187i	0.0716156	+	0.124042i	−0.827994	+	0.560737i	$0.810518\pi$
$138$	−8.36846			−0.712371
$139$	−6.01595	−	10.4199i	−0.510266	−	0.883806i	−0.999929	−	0.0118949i	$-0.996214\pi$
$139$	−6.01595	−	10.4199i	−0.510266	−	0.883806i	0.489663	−	0.871912i	$-0.337120\pi$
$140$		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	0.998365	−	0.0571546i	$-0.0182028\pi$
$149$	5.48911	+	9.50742i	0.449685	+	0.778878i	−0.548680	+	0.836032i	$0.684869\pi$
$150$		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	$-0.289019\pi$
$157$	15.4203			1.23068			0.615338	+	0.788263i	$0.289019\pi$
$158$	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	$-0.133248\pi$
$163$	1.33795	+	2.31740i	0.104797	+	0.181513i	−0.808859	+	0.588003i	$0.799914\pi$
$164$	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	$-0.838006\pi$
$167$	−0.189699	+	0.328568i	−0.0146794	+	0.0254254i	0.858592	+	0.512659i	$0.171339\pi$
$168$	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	$-0.261837\pi$
$173$	−3.87421	−	6.71033i	−0.294551	−	0.510177i	−0.974880	+	0.222729i	$0.928503\pi$
$174$	−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	−0.165741	−	0.986169i	$-0.553002\pi$
$179$	10.3176	−	17.8707i	0.771177	−	1.33572i	0.936918	−	0.349548i	$-0.113665\pi$
$180$		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	0.676192	−	0.736726i	$-0.263629\pi$
$191$	−4.14508	−	7.17948i	−0.299927	−	0.519489i	−0.976119	+	0.217237i	$0.930296\pi$
$192$	1.37924	−	2.38892i	0.0995384	−	0.172406i
$193$	−0.0610966	+	0.105822i	−0.00439783	+	0.00761726i	−0.868216	−	0.496187i	$-0.834733\pi$
$193$	−0.0610966	+	0.105822i	−0.00439783	+	0.00761726i	0.863818	+	0.503804i	$0.168067\pi$
$194$	−22.3925			−1.60769
$195$		0			0
$196$	13.1779			0.941275
$197$	8.23429	−	14.2622i	0.586669	−	1.01614i	−0.407996	−	0.912984i	$-0.633772\pi$
$197$	8.23429	−	14.2622i	0.586669	−	1.01614i	0.994665	−	0.103157i	$-0.0328943\pi$
$198$	−1.37402	+	2.37988i	−0.0976476	+	0.169131i
$199$	3.43949	+	5.95736i	0.243819	+	0.422306i	0.961799	−	0.273757i	$-0.0882665\pi$
$199$	3.43949	+	5.95736i	0.243819	+	0.422306i	−0.717980	+	0.696064i	$0.754933\pi$
$200$		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	−0.897253	−	0.441517i	$-0.854441\pi$
$211$	−0.962507	+	1.66711i	−0.0662617	+	0.114769i	0.830991	+	0.556285i	$0.187774\pi$
$212$	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	$-0.956401\pi$
$223$	−5.63084	+	9.75291i	−0.377069	+	0.653103i	0.613565	+	0.789644i	$0.289735\pi$
$224$	−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	0.990491	+	0.137578i	$0.0439318\pi$
$227$	9.25674	+	16.0331i	0.614391	+	1.06416i	−0.376099	+	0.926579i	$0.622735\pi$
$228$	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	$-0.587008\pi$
$233$	−8.24132			−0.539907			−0.269953	+	0.962873i	$0.587008\pi$
$234$	−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	0.716129	−	0.697968i	$-0.245912\pi$
$241$	−3.82507	−	6.62521i	−0.246394	−	0.426767i	−0.962523	+	0.271201i	$0.912579\pi$
$242$	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	0.999382	−	0.0351416i	$-0.0111882\pi$
$251$	7.43444	+	12.8768i	0.469258	+	0.812778i	−0.530125	+	0.847920i	$0.677855\pi$
$252$	−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	$-0.872531\pi$
$257$	−1.96917	+	3.41070i	−0.122833	+	0.212754i	0.798051	+	0.602591i	$0.205865\pi$
$258$	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	$-0.769816\pi$
$263$	3.21467	−	5.56797i	0.198225	−	0.343336i	0.947953	+	0.318410i	$0.103149\pi$
$264$	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	−0.999913	−	0.0132003i	$-0.995798\pi$
$269$	−8.38739	−	14.5274i	−0.511388	−	0.885750i	0.488525	−	0.872550i	$-0.337535\pi$
$270$		0			0
$271$	3.22681	−	5.58901i	0.196015	−	0.339508i	−0.751218	−	0.660054i	$-0.770533\pi$
$271$	3.22681	−	5.58901i	0.196015	−	0.339508i	0.947233	+	0.320547i	$0.103867\pi$
$272$	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	$-0.177390\pi$
$277$	−0.560565	−	0.970927i	−0.0336811	−	0.0583373i	−0.882375	+	0.470548i	$0.844056\pi$
$278$	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	0.327675	+	0.944790i	$0.393735\pi$
$283$	−11.0083	+	19.0669i	−0.654375	+	1.13341i	−0.982050	+	0.188620i	$0.939599\pi$
$284$	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	$-0.0291881\pi$
$293$	7.16525	+	12.4106i	0.418599	+	0.725034i	−0.577200	+	0.816603i	$0.695855\pi$
$294$	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	$-0.404790\pi$
$307$	10.3261			0.589341			0.294671	+	0.955599i	$0.404790\pi$
$308$	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	$-0.620115\pi$
$313$	−13.0375			−0.736924			−0.368462	+	0.929643i	$0.620115\pi$
$314$	−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	$-0.296840\pi$
$317$	21.2154			1.19157			0.595787	+	0.803143i	$0.296840\pi$
$318$	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	0.723993	−	0.689807i	$-0.242305\pi$
$331$	−4.28262	−	7.41771i	−0.235394	−	0.407714i	−0.959387	+	0.282093i	$0.908971\pi$
$332$	−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	$-0.494081\pi$
$337$	0.682652			0.0371864			0.0185932	+	0.999827i	$0.494081\pi$
$338$	−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	$-0.318995\pi$
$347$	−8.57809	−	14.8577i	−0.460496	−	0.797603i	−0.998986	+	0.0450295i	$0.985662\pi$
$348$	7.32135	−	12.6810i	0.392466	−	0.679771i
$349$	16.5771	−	28.7125i	0.887354	−	1.53694i	0.0443633	−	0.999015i	$-0.485874\pi$
$349$	16.5771	−	28.7125i	0.887354	−	1.53694i	0.842991	−	0.537927i	$-0.180793\pi$
$350$		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	$-0.929577\pi$
$353$	−5.59464	+	9.69020i	−0.297773	+	0.515757i	0.677853	+	0.735197i	$0.262910\pi$
$354$	−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	$-0.927235\pi$
$367$	−5.56980	+	9.64718i	−0.290741	+	0.503579i	0.683244	+	0.730190i	$0.260569\pi$
$368$	−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	$-0.306598\pi$
$373$	−8.21938	−	14.2364i	−0.425583	−	0.737132i	−0.996475	+	0.0838935i	$0.973264\pi$
$374$	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	−0.782428	−	0.622741i	$-0.786019\pi$
$379$	2.88310	−	4.99368i	0.148095	−	0.256508i	0.930523	+	0.366232i	$0.119353\pi$
$380$		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	−0.863227	−	0.504815i	$-0.831561\pi$
$383$	−17.0027	−	29.4495i	−0.868797	−	1.50480i	−0.00556925	−	0.999984i	$-0.501773\pi$
$384$	−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	−0.983711	−	0.179755i	$-0.942469\pi$
$397$	−12.9019	−	22.3468i	−0.647528	−	1.12155i	0.336183	−	0.941797i	$-0.390864\pi$
$398$	−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	−0.952231	−	0.305379i	$-0.901217\pi$
$401$	−4.23827	+	7.34090i	−0.211649	+	0.366587i	0.740582	+	0.671966i	$0.234550\pi$
$402$	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	0.874802	−	0.484481i	$-0.160991\pi$
$409$	0.360554	+	0.624498i	0.0178282	+	0.0308794i	−0.856974	+	0.515360i	$0.827658\pi$
$410$		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	−0.989133	−	0.147025i	$-0.953030\pi$
$419$	−7.51719	+	13.0202i	−0.367239	+	0.636076i	0.621894	+	0.783101i	$0.286363\pi$
$420$		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	−0.551993	−	0.833849i	$-0.686132\pi$
$431$	9.26206	−	16.0424i	0.446138	−	0.772734i	0.998131	+	0.0611153i	$0.0194657\pi$
$432$	−11.6616	+	20.1985i	−0.561071	+	0.971803i
$433$	19.7894	+	34.2763i	0.951020	+	1.64721i	0.743224	+	0.669042i	$0.233295\pi$
$433$	19.7894	+	34.2763i	0.951020	+	1.64721i	0.207795	+	0.978172i	$0.433371\pi$
$434$	−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	−0.994982	−	0.100058i	$-0.968097\pi$
$439$	−8.60802	+	14.9095i	−0.410838	+	0.711593i	0.584143	+	0.811650i	$0.301431\pi$
$440$		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	$-0.357191\pi$
$443$	18.2587			0.867496			0.433748	+	0.901034i	$0.357191\pi$
$444$	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	0.641980	−	0.766722i	$-0.278113\pi$
$449$	−7.26826	−	12.5890i	−0.343010	−	0.594111i	−0.984990	+	0.172610i	$0.944780\pi$
$450$		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	$-0.824912\pi$
$457$	0.565518	−	0.979506i	0.0264538	−	0.0458194i	0.878949	+	0.476915i	$0.158245\pi$
$458$	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	−0.996959	−	0.0779332i	$-0.975168\pi$
$461$	−12.1519	−	21.0477i	−0.565971	−	0.980291i	0.430987	−	0.902358i	$-0.358165\pi$
$462$	23.5291	+	40.7537i	1.09467	+	1.89603i
$463$	−37.3049			−1.73371			−0.866854	−	0.498563i	$-0.833861\pi$
$463$	−37.3049			−1.73371			−0.866854	+	0.498563i	$0.833861\pi$
$464$	−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	$-0.740604\pi$
$467$	−29.6461			−1.37186			−0.685928	+	0.727669i	$0.740604\pi$
$468$	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	−0.971416	−	0.237382i	$-0.923711\pi$
$479$	−6.13094	+	10.6191i	−0.280130	+	0.485199i	0.691287	+	0.722581i	$0.257044\pi$
$480$		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	0.998969	+	0.0453886i	$0.0144526\pi$
$487$	11.8901	+	20.5943i	0.538792	+	0.933216i	−0.460177	+	0.887827i	$0.652214\pi$
$488$	−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	−0.587080	−	0.809529i	$-0.699723\pi$
$491$	9.03032	−	15.6410i	0.407532	−	0.705867i	0.994613	+	0.103662i	$0.0330560\pi$
$492$	−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	0.966899	+	0.255160i	$0.0821283\pi$
$503$	15.7986	+	27.3640i	0.704425	+	1.22010i	−0.262474	+	0.964939i	$0.584538\pi$
$504$	−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	−0.980427	−	0.196884i	$-0.936918\pi$
$509$	−7.21291	+	12.4931i	−0.319707	+	0.553748i	0.660720	+	0.750632i	$0.270251\pi$
$510$		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	−0.342660	−	0.939459i	$-0.611328\pi$
$523$	14.6881	−	25.4405i	0.642266	−	1.11244i	0.984926	−	0.172977i	$-0.0553387\pi$
$524$	−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	$-0.465659\pi$
$547$	5.03662			0.215350			0.107675	+	0.994186i	$0.465659\pi$
$548$	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	$-0.876953\pi$
$557$	−3.22404	+	5.58421i	−0.136607	+	0.236610i	0.789603	+	0.613618i	$0.210286\pi$
$558$	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	0.944199	+	0.329375i	$0.106838\pi$
$563$	17.9700	+	31.1250i	0.757347	+	1.31176i	−0.186853	+	0.982388i	$0.559829\pi$
$564$	−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	−0.0961179	−	0.995370i	$-0.530643\pi$
$569$	19.4159	−	33.6293i	0.813957	−	1.40981i	0.910075	−	0.414444i	$-0.136024\pi$
$570$		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	$-0.460482\pi$
$577$	5.94911			0.247665			0.123832	+	0.992303i	$0.460482\pi$
$578$	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	$-0.712196\pi$
$587$	8.99937	−	15.5874i	0.371444	−	0.643360i	0.989788	+	0.142548i	$0.0455295\pi$
$588$	−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	$-0.623605\pi$
$593$	−18.4405			−0.757260			−0.378630	+	0.925548i	$0.623605\pi$
$594$	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	−0.701746	−	0.712427i	$-0.747596\pi$
$601$	6.52369	−	11.2994i	0.266107	−	0.460911i	0.967853	+	0.251516i	$0.0809292\pi$
$602$	−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	0.993630	+	0.112691i	$0.0359469\pi$
$607$	14.6447	+	25.3653i	0.594408	+	1.02954i	−0.399222	+	0.916854i	$0.630720\pi$
$608$	−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	$-0.895241\pi$
$613$	−4.78499	+	8.28784i	−0.193264	+	0.334743i	0.753066	+	0.657945i	$0.228574\pi$
$614$	−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	−0.997328	−	0.0730486i	$-0.976727\pi$
$617$	−13.9580	−	24.1759i	−0.561926	−	0.973285i	0.435402	−	0.900236i	$-0.356606\pi$
$618$	−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	0.999994	+	0.00339834i	$0.00108173\pi$
$631$	12.6337	+	21.8822i	0.502940	+	0.871118i	−0.497054	+	0.867720i	$0.665585\pi$
$632$	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	0.940435	−	0.339973i	$-0.110418\pi$
$641$	4.45070	+	7.70884i	0.175792	+	0.304481i	−0.764643	+	0.644454i	$0.777085\pi$
$642$	−21.5244			−0.849502
$643$	−3.00256	−	5.20059i	−0.118410	−	0.205091i	0.800728	−	0.599028i	$-0.204446\pi$
$643$	−3.00256	−	5.20059i	−0.118410	−	0.205091i	−0.919138	+	0.393937i	$0.871113\pi$
$644$	−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	−0.164639	−	0.986354i	$-0.552646\pi$
$647$	19.6339	−	34.0069i	0.771888	−	1.33695i	0.936527	−	0.350596i	$-0.114021\pi$
$648$	−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	−0.0330724	−	0.999453i	$-0.510529\pi$
$653$	21.6956	−	37.5779i	0.849015	−	1.47054i	0.882088	−	0.471085i	$-0.156137\pi$
$654$	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	0.996760	−	0.0804293i	$-0.0256291\pi$
$659$	11.0058	+	19.0627i	0.428726	+	0.742576i	−0.568034	+	0.823005i	$0.692296\pi$
$660$		0			0
$661$	15.7292	−	27.2438i	0.611795	−	1.05966i	−0.379143	−	0.925338i	$-0.623781\pi$
$661$	15.7292	−	27.2438i	0.611795	−	1.05966i	0.990938	−	0.134322i	$-0.0428856\pi$
$662$	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	−0.260387	−	0.965504i	$-0.583850\pi$
$673$	18.3141	−	31.7210i	0.705958	−	1.22276i	0.966345	−	0.257251i	$-0.0828166\pi$
$674$	−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	$-0.275158\pi$
$677$	33.7766			1.29814			0.649070	+	0.760729i	$0.275158\pi$
$678$	−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	$-0.148295\pi$
$683$	1.50753	+	2.61111i	0.0576839	+	0.0999115i	−0.835741	+	0.549123i	$0.814962\pi$
$684$	−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	−0.999542	−	0.0302593i	$-0.990367\pi$
$691$	−12.4486	+	21.5615i	−0.473566	+	0.820240i	0.525976	+	0.850499i	$0.323700\pi$
$692$	−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	0.892385	−	0.451276i	$-0.149031\pi$
$709$	1.47450	+	2.55391i	0.0553761	+	0.0959142i	−0.837009	+	0.547190i	$0.815698\pi$
$710$		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	0.920663	−	0.390359i	$-0.127649\pi$
$719$	3.27857	+	5.67866i	0.122270	+	0.211778i	−0.798392	+	0.602138i	$0.794316\pi$
$720$		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	$-0.541265\pi$
$727$	−6.97127			−0.258550			−0.129275	+	0.991609i	$0.541265\pi$
$728$	−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	$-0.494586\pi$
$733$	0.920949			0.0340160			0.0170080	+	0.999855i	$0.494586\pi$
$734$	−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	−0.962419	−	0.271568i	$-0.912458\pi$
$739$	−6.68808	+	11.5841i	−0.246025	+	0.426128i	0.716394	+	0.697696i	$0.245791\pi$
$740$		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	−0.303983	−	0.952677i	$-0.598317\pi$
$743$	18.3460	−	31.7763i	0.673051	−	1.16576i	0.977034	−	0.213081i	$-0.0683499\pi$
$744$	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	−0.999991	−	0.00417160i	$-0.998672\pi$
$751$	−13.6031	+	23.5612i	−0.496383	+	0.859760i	0.503608	+	0.863932i	$0.332005\pi$
$752$	−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	$-0.992528\pi$
$757$	−13.1937	+	22.8522i	−0.479535	+	0.830579i	0.520190	+	0.854051i	$0.325861\pi$
$758$	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	0.745091	−	0.666963i	$-0.232406\pi$
$761$	−5.65688	−	9.79800i	−0.205062	−	0.355177i	−0.950152	+	0.311786i	$0.899073\pi$
$762$	−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	−0.787498	−	0.616317i	$-0.788624\pi$
$769$	3.88223	−	6.72423i	0.139997	−	0.242482i	0.927495	+	0.373835i	$0.121957\pi$
$770$		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	$-0.147108\pi$
$773$	1.70726	+	2.95706i	0.0614058	+	0.106358i	−0.833688	+	0.552235i	$0.813775\pi$
$774$	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	0.999975	+	0.00707326i	$0.00225151\pi$
$787$	14.1983	+	24.5921i	0.506113	+	0.876614i	−0.493862	+	0.869540i	$0.664415\pi$
$788$	−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	$-0.0907378\pi$
$797$	6.67052	+	11.5537i	0.236282	+	0.409252i	−0.723363	+	0.690468i	$0.757404\pi$
$798$	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	−0.346412	−	0.938083i	$-0.612600\pi$
$809$	18.1806	−	31.4898i	0.639198	−	1.10712i	0.985609	−	0.169040i	$-0.0540667\pi$
$810$		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	−0.527030	−	0.849847i	$-0.676694\pi$
$821$	13.5378	−	23.4482i	0.472474	−	0.818349i	0.999504	+	0.0314981i	$0.0100278\pi$
$822$	2.81647	−	4.87826i	0.0982356	−	0.170149i
$823$	20.6744	+	35.8091i	0.720664	+	1.24823i	0.960734	+	0.277471i	$0.0894963\pi$
$823$	20.6744	+	35.8091i	0.720664	+	1.24823i	−0.240070	+	0.970756i	$0.577170\pi$
$824$	−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	$-0.553925\pi$
$827$	−9.69711			−0.337202			−0.168601	+	0.985684i	$0.553925\pi$
$828$	0.715382	+	1.23908i	0.0248612	+	0.0430609i
$829$	−25.3041	+	43.8280i	−0.878848	+	1.52221i	−0.0262407	+	0.999656i	$0.508354\pi$
$829$	−25.3041	+	43.8280i	−0.878848	+	1.52221i	−0.852607	+	0.522553i	$0.824980\pi$
$830$		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	0.799409	−	0.600787i	$-0.205146\pi$
$839$	−3.49302	−	6.05009i	−0.120593	−	0.208872i	−0.920002	+	0.391915i	$0.871813\pi$
$840$		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	$-0.512356\pi$
$853$	−2.26681			−0.0776142			−0.0388071	+	0.999247i	$0.512356\pi$
$854$	−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	$-0.410826\pi$
$857$	16.1887			0.552994			0.276497	+	0.961015i	$0.410826\pi$
$858$	−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	$-0.668185\pi$
$863$	−29.6192			−1.00825			−0.504125	+	0.863631i	$0.668185\pi$
$864$	−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	−0.938865	−	0.344285i	$-0.888121\pi$
$877$	−22.7316	−	39.3723i	−0.767592	−	1.32951i	0.171273	−	0.985224i	$-0.445212\pi$
$878$	−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	0.460232	+	0.887799i	$0.347766\pi$
$881$	−15.9907	+	27.6967i	−0.538740	+	0.933125i	−0.998972	+	0.0453265i	$0.985567\pi$
$882$	−4.24274	+	7.34864i	−0.142861	+	0.247442i
$883$	17.0799			0.574786			0.287393	−	0.957813i	$-0.407211\pi$
$883$	17.0799			0.574786			0.287393	+	0.957813i	$0.407211\pi$
$884$	−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	$-0.789716\pi$
$887$	4.06832	−	7.04654i	0.136601	−	0.236600i	0.926208	+	0.377013i	$0.123049\pi$
$888$	−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	$-0.795526\pi$
$907$	3.56867	−	6.18111i	0.118496	−	0.205240i	0.919172	+	0.393857i	$0.128860\pi$
$908$	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	0.627505	−	0.778612i	$-0.284076\pi$
$919$	−10.9299	−	18.9312i	−0.360545	−	0.624483i	−0.988051	+	0.154129i	$0.950743\pi$
$920$		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	0.757137	+	0.653256i	$0.226597\pi$
$929$	28.7819	+	49.8518i	0.944305	+	1.63558i	0.187168	+	0.982328i	$0.440069\pi$
$930$		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	$-0.599866\pi$
$937$	−18.8937			−0.617232			−0.308616	+	0.951187i	$0.599866\pi$
$938$	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	$-0.873044\pi$
$947$	−3.82919	+	6.63235i	−0.124432	+	0.215523i	0.797079	+	0.603875i	$0.206378\pi$
$948$	−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	$-0.233319\pi$
$953$	−6.41704	−	11.1146i	−0.207868	−	0.360039i	−0.951043	+	0.309059i	$0.899986\pi$
$954$	−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	$-0.554123\pi$
$967$	−10.5239			−0.338427			−0.169214	+	0.985579i	$0.554123\pi$
$968$	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	0.641347	−	0.767251i	$-0.278376\pi$
$971$	−10.7127	−	18.5549i	−0.343785	−	0.595454i	−0.985132	+	0.171797i	$0.945043\pi$
$972$	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	$-0.679613\pi$
$977$	14.5149	−	25.1406i	0.464373	−	0.804318i	0.999173	+	0.0406611i	$0.0129464\pi$
$978$	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	$-0.575722\pi$
$983$	−14.7766			−0.471299			−0.235650	+	0.971838i	$0.575722\pi$
$984$	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	−0.934798	−	0.355180i	$-0.884419\pi$
$991$	−5.03065	+	8.71334i	−0.159804	+	0.276788i	0.774994	+	0.631969i	$0.217753\pi$
$992$	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	−0.977300	−	0.211860i	$-0.932048\pi$
$997$	−21.2226	−	36.7586i	−0.672126	−	1.16416i	0.305174	−	0.952297i	$-0.401285\pi$
$998$	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.d.126.2	yes	10
5.2	odd	4		325.2.o.c.74.3		20
5.3	odd	4		325.2.o.c.74.8		20
5.4	even	2		325.2.e.c.126.4	✓	10
13.3	even	3	inner	325.2.e.d.276.2	yes	10
13.4	even	6		4225.2.a.bm.1.2		5
13.9	even	3		4225.2.a.bn.1.4		5
65.3	odd	12		325.2.o.c.224.3		20
65.4	even	6		4225.2.a.bo.1.4		5
65.9	even	6		4225.2.a.bp.1.2		5
65.29	even	6		325.2.e.c.276.4	yes	10
65.42	odd	12		325.2.o.c.224.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.e.c.126.4	✓	10	5.4	even	2
325.2.e.c.276.4	yes	10	65.29	even	6
325.2.e.d.126.2	yes	10	1.1	even	1	trivial
325.2.e.d.276.2	yes	10	13.3	even	3	inner
325.2.o.c.74.3		20	5.2	odd	4
325.2.o.c.74.8		20	5.3	odd	4
325.2.o.c.224.3		20	65.3	odd	12
325.2.o.c.224.8		20	65.42	odd	12
4225.2.a.bm.1.2		5	13.4	even	6
4225.2.a.bn.1.4		5	13.9	even	3
4225.2.a.bo.1.4		5	65.4	even	6
4225.2.a.bp.1.2		5	65.9	even	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
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

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