LMFDB - Embedded newform 525.3.o.l.376.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(376,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("525.376");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.o (of order $6$, 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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.523596960000.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 $ x^8 - 2x^7 + 13x^6 - 2x^5 + 91x^4 - 50x^3 + 190x^2 + 100*x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.1
Root			$1.76021 - 3.04878i$ of defining polynomial
Character	$\chi$	$=$	525.376
Dual form			525.3.o.l.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76021 + 3.04878i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-4.19671 - 7.26891i) q^{4} +6.09756i q^{6} +(-0.244004 + 6.99575i) q^{7} +15.4667 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.76021 + 3.04878i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-4.19671 - 7.26891i) q^{4} +6.09756i q^{6} +(-0.244004 + 6.99575i) q^{7} +15.4667 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.29685 - 2.24621i) q^{11} +(-12.5901 - 7.26891i) q^{12} -11.5763i q^{13} +(-20.8990 - 13.0579i) q^{14} +(-10.4379 + 18.0789i) q^{16} +(-20.0957 + 11.6023i) q^{17} +(5.28064 + 9.14634i) q^{18} +(25.9538 + 14.9844i) q^{19} +(5.69249 + 10.7049i) q^{21} +9.13094 q^{22} +(-17.5542 + 30.4048i) q^{23} +(23.2000 - 13.3945i) q^{24} +(35.2936 + 20.3768i) q^{26} -5.19615i q^{27} +(51.8754 - 27.5854i) q^{28} -24.4905 q^{29} +(-32.4355 + 18.7266i) q^{31} +(-5.81233 - 10.0673i) q^{32} +(-3.89055 - 2.24621i) q^{33} -81.6898i q^{34} -25.1802 q^{36} +(12.8743 - 22.2990i) q^{37} +(-91.3685 + 52.7516i) q^{38} +(-10.0254 - 17.3645i) q^{39} +3.71113i q^{41} +(-42.6570 - 1.48783i) q^{42} -74.2225 q^{43} +(-10.8850 + 18.8534i) q^{44} +(-61.7983 - 107.038i) q^{46} +(-2.92646 - 1.68959i) q^{47} +36.1578i q^{48} +(-48.8809 - 3.41398i) q^{49} +(-20.0957 + 34.8068i) q^{51} +(-84.1471 + 48.5823i) q^{52} +(-20.0193 - 34.6744i) q^{53} +(15.8419 + 9.14634i) q^{54} +(-3.77394 + 108.201i) q^{56} +51.9076 q^{57} +(43.1085 - 74.6661i) q^{58} +(-42.7180 + 24.6632i) q^{59} +(-0.765094 - 0.441727i) q^{61} -131.852i q^{62} +(17.8095 + 11.1276i) q^{63} -42.5790 q^{64} +(13.6964 - 7.90763i) q^{66} +(-32.5272 - 56.3388i) q^{67} +(168.671 + 97.3825i) q^{68} +60.8096i q^{69} +86.0786 q^{71} +(23.2000 - 40.1836i) q^{72} +(53.3274 - 30.7886i) q^{73} +(45.3231 + 78.5019i) q^{74} -251.541i q^{76} +(16.0304 - 8.52436i) q^{77} +70.5872 q^{78} +(-13.7718 + 23.8534i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-11.3144 - 6.53239i) q^{82} +131.445i q^{83} +(53.9235 - 86.3036i) q^{84} +(130.648 - 226.288i) q^{86} +(-36.7357 + 21.2094i) q^{87} +(-20.0580 - 34.7415i) q^{88} +(-56.5108 - 32.6265i) q^{89} +(80.9849 + 2.82467i) q^{91} +294.679 q^{92} +(-32.4355 + 56.1799i) q^{93} +(10.3024 - 5.94809i) q^{94} +(-17.4370 - 10.0673i) q^{96} -42.2375i q^{97} +(96.4494 - 143.018i) q^{98} -7.78111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9	$ 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9} + 20 q^{11} - 18 q^{12} - 16 q^{14} - 2 q^{16} + 18 q^{17} + 6 q^{18} + 48 q^{21} + 16 q^{22} - 62 q^{23} + 48 q^{24} + 120 q^{26} + 120 q^{28} - 100 q^{29} - 126 q^{31} - 36 q^{32} + 60 q^{33} - 36 q^{36} + 80 q^{37} - 114 q^{38} - 12 q^{39} - 90 q^{42} - 352 q^{43} - 18 q^{44} - 82 q^{46} + 72 q^{47} + 38 q^{49} + 18 q^{51} + 48 q^{52} + 76 q^{53} + 18 q^{54} + 196 q^{56} + 40 q^{58} - 54 q^{59} - 396 q^{61} + 96 q^{63} - 4 q^{64} + 24 q^{66} - 184 q^{67} + 312 q^{68} + 164 q^{71} + 48 q^{72} - 348 q^{73} - 140 q^{74} - 152 q^{77} + 240 q^{78} - 206 q^{79} - 36 q^{81} - 204 q^{82} + 132 q^{84} + 178 q^{86} - 150 q^{87} - 124 q^{88} + 282 q^{89} - 114 q^{91} + 288 q^{92} - 126 q^{93} + 30 q^{94} - 108 q^{96} + 592 q^{98} + 120 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9 + 20 * q^11 - 18 * q^12 - 16 * q^14 - 2 * q^16 + 18 * q^17 + 6 * q^18 + 48 * q^21 + 16 * q^22 - 62 * q^23 + 48 * q^24 + 120 * q^26 + 120 * q^28 - 100 * q^29 - 126 * q^31 - 36 * q^32 + 60 * q^33 - 36 * q^36 + 80 * q^37 - 114 * q^38 - 12 * q^39 - 90 * q^42 - 352 * q^43 - 18 * q^44 - 82 * q^46 + 72 * q^47 + 38 * q^49 + 18 * q^51 + 48 * q^52 + 76 * q^53 + 18 * q^54 + 196 * q^56 + 40 * q^58 - 54 * q^59 - 396 * q^61 + 96 * q^63 - 4 * q^64 + 24 * q^66 - 184 * q^67 + 312 * q^68 + 164 * q^71 + 48 * q^72 - 348 * q^73 - 140 * q^74 - 152 * q^77 + 240 * q^78 - 206 * q^79 - 36 * q^81 - 204 * q^82 + 132 * q^84 + 178 * q^86 - 150 * q^87 - 124 * q^88 + 282 * q^89 - 114 * q^91 + 288 * q^92 - 126 * q^93 + 30 * q^94 - 108 * q^96 + 592 * q^98 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.76021	+	3.04878i	−0.880107	+	1.52439i	−0.0288858	+	0.999583i	$0.509196\pi$
$2$	−1.76021	+	3.04878i	−0.880107	+	1.52439i	−0.851221	+	0.524807i	$0.824137\pi$
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$	−4.19671	−	7.26891i	−1.04918	−	1.81723i
$5$		0			0
$5$		0			0
$6$			6.09756i			1.01626i
$7$	−0.244004	+	6.99575i	−0.0348577	+	0.999392i
$7$	−0.244004	+	6.99575i	−0.0348577	+	0.999392i
$8$	15.4667			1.93334
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.29685	−	2.24621i	−0.117896	−	0.204201i	0.801038	−	0.598614i	$-0.204281\pi$
$11$	−1.29685	−	2.24621i	−0.117896	−	0.204201i	−0.918934	+	0.394412i	$0.870948\pi$
$12$	−12.5901	−	7.26891i	−1.04918	−	0.605742i
$13$		−	11.5763i		−	0.890485i	−0.895410	−	0.445242i	$-0.853117\pi$
$13$		−	11.5763i		−	0.890485i	0.895410	−	0.445242i	$-0.146883\pi$
$14$	−20.8990	−	13.0579i	−1.49278	−	0.932709i
$15$		0			0
$16$	−10.4379	+	18.0789i	−0.652366	+	1.12993i
$17$	−20.0957	+	11.6023i	−1.18210	+	0.682486i	−0.956499	−	0.291734i	$-0.905768\pi$
$17$	−20.0957	+	11.6023i	−1.18210	+	0.682486i	−0.225600	+	0.974220i	$0.572434\pi$
$18$	5.28064	+	9.14634i	0.293369	+	0.508130i
$19$	25.9538	+	14.9844i	1.36599	+	0.788654i	0.990413	−	0.138137i	$-0.0441115\pi$
$19$	25.9538	+	14.9844i	1.36599	+	0.788654i	0.375576	+	0.926791i	$0.377445\pi$
$20$		0			0
$21$	5.69249	+	10.7049i	0.271071	+	0.509759i
$22$	9.13094			0.415043
$23$	−17.5542	+	30.4048i	−0.763226	+	1.32195i	0.177953	+	0.984039i	$0.443053\pi$
$23$	−17.5542	+	30.4048i	−0.763226	+	1.32195i	−0.941179	+	0.337908i	$0.890281\pi$
$24$	23.2000	−	13.3945i	0.966668	−	0.558106i
$25$		0			0
$26$	35.2936	+	20.3768i	1.35745	+	0.783722i
$27$		−	5.19615i		−	0.192450i
$28$	51.8754	−	27.5854i	1.85269	−	0.985194i
$29$	−24.4905			−0.844499			−0.422250	−	0.906480i	$-0.638759\pi$
$29$	−24.4905			−0.844499			−0.422250	+	0.906480i	$0.638759\pi$
$30$		0			0
$31$	−32.4355	+	18.7266i	−1.04631	+	0.604085i	−0.921613	−	0.388110i	$-0.873128\pi$
$31$	−32.4355	+	18.7266i	−1.04631	+	0.604085i	−0.124693	+	0.992195i	$0.539795\pi$
$32$	−5.81233	−	10.0673i	−0.181635	−	0.314602i
$33$	−3.89055	−	2.24621i	−0.117896	−	0.0680670i
$34$		−	81.6898i		−	2.40264i
$35$		0			0
$36$	−25.1802			−0.699451
$37$	12.8743	−	22.2990i	0.347954	−	0.602675i	−0.637932	−	0.770093i	$-0.720210\pi$
$37$	12.8743	−	22.2990i	0.347954	−	0.602675i	0.985886	+	0.167418i	$0.0535431\pi$
$38$	−91.3685	+	52.7516i	−2.40443	+	1.38820i
$39$	−10.0254	−	17.3645i	−0.257061	−	0.445242i
$40$		0			0
$41$			3.71113i			0.0905155i	0.998975	+	0.0452577i	$0.0144109\pi$
$41$			3.71113i			0.0905155i	−0.998975	+	0.0452577i	$0.985589\pi$
$42$	−42.6570	−	1.48783i	−1.01564	−	0.0354245i
$43$	−74.2225			−1.72611			−0.863053	−	0.505114i	$-0.831451\pi$
$43$	−74.2225			−1.72611			−0.863053	+	0.505114i	$0.831451\pi$
$44$	−10.8850	+	18.8534i	−0.247386	+	0.428486i
$45$		0			0
$46$	−61.7983	−	107.038i	−1.34344	−	2.32691i
$47$	−2.92646	−	1.68959i	−0.0622652	−	0.0359488i	0.468544	−	0.883440i	$-0.344779\pi$
$47$	−2.92646	−	1.68959i	−0.0622652	−	0.0359488i	−0.530809	+	0.847491i	$0.678112\pi$
$48$			36.1578i			0.753287i
$49$	−48.8809	−	3.41398i	−0.997570	−	0.0696731i
$50$		0			0
$51$	−20.0957	+	34.8068i	−0.394033	+	0.682486i
$52$	−84.1471	+	48.5823i	−1.61821	+	0.934276i
$53$	−20.0193	−	34.6744i	−0.377722	−	0.654234i	0.613008	−	0.790076i	$-0.289959\pi$
$53$	−20.0193	−	34.6744i	−0.377722	−	0.654234i	−0.990730	+	0.135843i	$0.956626\pi$
$54$	15.8419	+	9.14634i	0.293369	+	0.169377i
$55$		0			0
$56$	−3.77394	+	108.201i	−0.0673917	+	1.93216i
$57$	51.9076			0.910660
$58$	43.1085	−	74.6661i	0.743250	−	1.28735i
$59$	−42.7180	+	24.6632i	−0.724033	+	0.418021i	−0.816235	−	0.577720i	$-0.803943\pi$
$59$	−42.7180	+	24.6632i	−0.724033	+	0.418021i	0.0922022	+	0.995740i	$0.470609\pi$
$60$		0			0
$61$	−0.765094	−	0.441727i	−0.0125425	−	0.00724143i	0.493716	−	0.869623i	$-0.335638\pi$
$61$	−0.765094	−	0.441727i	−0.0125425	−	0.00724143i	−0.506258	+	0.862382i	$0.668972\pi$
$62$		−	131.852i		−	2.12664i
$63$	17.8095	+	11.1276i	0.282690	+	0.176628i
$64$	−42.5790			−0.665297
$65$		0			0
$66$	13.6964	−	7.90763i	0.207521	−	0.119813i
$67$	−32.5272	−	56.3388i	−0.485481	−	0.840877i	0.514380	−	0.857562i	$-0.328022\pi$
$67$	−32.5272	−	56.3388i	−0.485481	−	0.840877i	−0.999861	+	0.0166850i	$0.994689\pi$
$68$	168.671	+	97.3825i	2.48046	+	1.43210i
$69$			60.8096i			0.881298i
$70$		0			0
$71$	86.0786			1.21237			0.606187	−	0.795322i	$-0.292698\pi$
$71$	86.0786			1.21237			0.606187	+	0.795322i	$0.292698\pi$
$72$	23.2000	−	40.1836i	0.322223	−	0.558106i
$73$	53.3274	−	30.7886i	0.730512	−	0.421761i	−0.0880974	−	0.996112i	$-0.528079\pi$
$73$	53.3274	−	30.7886i	0.730512	−	0.421761i	0.818609	+	0.574350i	$0.194745\pi$
$74$	45.3231	+	78.5019i	0.612474	+	1.06084i
$75$		0			0
$76$		−	251.541i		−	3.30975i
$77$	16.0304	−	8.52436i	0.208187	−	0.110706i
$78$	70.5872			0.904964
$79$	−13.7718	+	23.8534i	−0.174326	+	0.301942i	−0.939928	−	0.341373i	$-0.889108\pi$
$79$	−13.7718	+	23.8534i	−0.174326	+	0.301942i	0.765602	+	0.643315i	$0.222441\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−11.3144	−	6.53239i	−0.137981	−	0.0796633i
$83$			131.445i			1.58367i	0.610732	+	0.791837i	$0.290875\pi$
$83$			131.445i			1.58367i	−0.610732	+	0.791837i	$0.709125\pi$
$84$	53.9235	−	86.3036i	0.641946	−	1.02742i
$85$		0			0
$86$	130.648	−	226.288i	1.51916	−	2.63126i
$87$	−36.7357	+	21.2094i	−0.422250	+	0.243786i
$88$	−20.0580	−	34.7415i	−0.227932	−	0.394789i
$89$	−56.5108	−	32.6265i	−0.634953	−	0.366590i	0.147715	−	0.989030i	$-0.452808\pi$
$89$	−56.5108	−	32.6265i	−0.634953	−	0.366590i	−0.782668	+	0.622440i	$0.786142\pi$
$90$		0			0
$91$	80.9849	+	2.82467i	0.889944	+	0.0310403i
$92$	294.679			3.20304
$93$	−32.4355	+	56.1799i	−0.348769	+	0.604085i
$94$	10.3024	−	5.94809i	0.109600	−	0.0632776i
$95$		0			0
$96$	−17.4370	−	10.0673i	−0.181635	−	0.104867i
$97$		−	42.2375i		−	0.435438i	−0.976011	−	0.217719i	$-0.930138\pi$
$97$		−	42.2375i		−	0.435438i	0.976011	−	0.217719i	$-0.0698616\pi$
$98$	96.4494	−	143.018i	0.984177	−	1.45937i
$99$	−7.78111			−0.0785970
$100$		0			0
$101$	−129.874	+	74.9830i	−1.28589	+	0.742406i	−0.977918	−	0.208991i	$-0.932982\pi$
$101$	−129.874	+	74.9830i	−1.28589	+	0.742406i	−0.307968	+	0.951397i	$0.599649\pi$
$102$	−70.7454	−	122.535i	−0.693583	−	1.20132i
$103$	−120.964	−	69.8388i	−1.17441	−	0.678047i	−0.219697	−	0.975568i	$-0.570507\pi$
$103$	−120.964	−	69.8388i	−1.17441	−	0.678047i	−0.954715	+	0.297521i	$0.903840\pi$
$104$		−	179.047i		−	1.72161i
$105$		0			0
$106$	140.953			1.32974
$107$	−90.6198	+	156.958i	−0.846914	+	1.46690i	0.0370350	+	0.999314i	$0.488209\pi$
$107$	−90.6198	+	156.958i	−0.846914	+	1.46690i	−0.883949	+	0.467584i	$0.845125\pi$
$108$	−37.7703	+	21.8067i	−0.349725	+	0.201914i
$109$	36.9049	+	63.9212i	0.338577	+	0.586433i	0.984165	−	0.177253i	$-0.0567211\pi$
$109$	36.9049	+	63.9212i	0.338577	+	0.586433i	−0.645588	+	0.763686i	$0.723388\pi$
$110$		0			0
$111$		−	44.5979i		−	0.401783i
$112$	−123.928	−	77.4319i	−1.10650	−	0.691356i
$113$	−7.38562			−0.0653595			−0.0326797	−	0.999466i	$-0.510404\pi$
$113$	−7.38562			−0.0653595			−0.0326797	+	0.999466i	$0.510404\pi$
$114$	−91.3685	+	158.255i	−0.801478	+	1.38820i
$115$		0			0
$116$	102.779	+	178.019i	0.886029	+	1.53465i
$117$	−30.0761	−	17.3645i	−0.257061	−	0.148414i
$118$		−	173.650i		−	1.47161i
$119$	−76.2630	−	143.415i	−0.640866	−	1.20517i
$120$		0			0
$121$	57.1364	−	98.9631i	0.472201	−	0.817877i
$122$	2.69346	−	1.55507i	0.0220775	−	0.0127465i
$123$	3.21394	+	5.56670i	0.0261296	+	0.0452577i
$124$	272.244	+	157.180i	2.19552	+	1.26758i
$125$		0			0
$126$	−65.2740	+	34.7103i	−0.518047	+	0.275478i
$127$	208.640			1.64283			0.821416	−	0.570329i	$-0.193184\pi$
$127$	208.640			1.64283			0.821416	+	0.570329i	$0.193184\pi$
$128$	98.1975	−	170.083i	0.767168	−	1.32877i
$129$	−111.334	+	64.2786i	−0.863053	+	0.498284i
$130$		0			0
$131$	94.8997	+	54.7904i	0.724425	+	0.418247i	0.816379	−	0.577516i	$-0.195978\pi$
$131$	94.8997	+	54.7904i	0.724425	+	0.418247i	−0.0919540	+	0.995763i	$0.529311\pi$
$132$			37.7068i			0.285657i
$133$	−111.160	+	177.910i	−0.835790	+	1.33767i
$134$	229.019			1.70910
$135$		0			0
$136$	−310.814	+	179.448i	−2.28540	+	1.31947i
$137$	−88.7262	−	153.678i	−0.647637	−	1.12174i	−0.983686	−	0.179895i	$-0.942424\pi$
$137$	−88.7262	−	153.678i	−0.647637	−	1.12174i	0.336049	−	0.941844i	$-0.390909\pi$
$138$	−185.395	−	107.038i	−1.34344	−	0.775636i
$139$		−	169.894i		−	1.22226i	−0.791532	−	0.611128i	$-0.790716\pi$
$139$		−	169.894i		−	1.22226i	0.791532	−	0.611128i	$-0.209284\pi$
$140$		0			0
$141$	−5.85293			−0.0415101
$142$	−151.517	+	262.435i	−1.06702	+	1.84813i
$143$	−26.0028	+	15.0127i	−0.181838	+	0.104984i
$144$	31.3136	+	54.2367i	0.217455	+	0.376644i
$145$		0			0
$146$			216.778i			1.48478i
$147$	−76.2780	+	37.2111i	−0.518898	+	0.253137i
$148$	−216.119			−1.46026
$149$	−42.6928	+	73.9461i	−0.286529	+	0.496283i	−0.972979	−	0.230894i	$-0.925835\pi$
$149$	−42.6928	+	73.9461i	−0.286529	+	0.496283i	0.686450	+	0.727177i	$0.259168\pi$
$150$		0			0
$151$	68.9977	+	119.507i	0.456938	+	0.791440i	0.998797	−	0.0490293i	$-0.0156128\pi$
$151$	68.9977	+	119.507i	0.456938	+	0.791440i	−0.541859	+	0.840469i	$0.682279\pi$
$152$	401.419	+	231.760i	2.64092	+	1.52473i
$153$			69.6135i			0.454990i
$154$	−2.22799	+	63.8777i	−0.0144675	+	0.414791i
$155$		0			0
$156$	−84.1471	+	145.747i	−0.539404	+	0.934276i
$157$	−5.94674	+	3.43335i	−0.0378773	+	0.0218685i	−0.518819	−	0.854884i	$-0.673628\pi$
$157$	−5.94674	+	3.43335i	−0.0378773	+	0.0218685i	0.480942	+	0.876753i	$0.340295\pi$
$158$	−48.4825	−	83.9742i	−0.306851	−	0.531482i
$159$	−60.0578	−	34.6744i	−0.377722	−	0.218078i
$160$		0			0
$161$	−208.421	−	130.224i	−1.29454	−	0.808843i
$162$	31.6838			0.195579
$163$	−138.363	+	239.652i	−0.848854	+	1.47026i	0.0333772	+	0.999443i	$0.489374\pi$
$163$	−138.363	+	239.652i	−0.848854	+	1.47026i	−0.882231	+	0.470816i	$0.843960\pi$
$164$	26.9759	−	15.5745i	0.164487	−	0.0949667i
$165$		0			0
$166$	−400.747	−	231.371i	−2.41414	−	1.39380i
$167$			42.3799i			0.253772i	0.991917	+	0.126886i	$0.0404982\pi$
$167$			42.3799i			0.253772i	−0.991917	+	0.126886i	$0.959502\pi$
$168$	88.0439	+	165.570i	0.524071	+	0.985535i
$169$	34.9892			0.207036
$170$		0			0
$171$	77.8614	−	44.9533i	0.455330	−	0.262885i
$172$	311.490	+	539.517i	1.81099	+	3.13673i
$173$	−25.5999	−	14.7801i	−0.147976	−	0.0854342i	0.424184	−	0.905576i	$-0.360561\pi$
$173$	−25.5999	−	14.7801i	−0.147976	−	0.0854342i	−0.572160	+	0.820142i	$0.693894\pi$
$174$		−	149.332i		−	0.858231i
$175$		0			0
$176$	54.1454			0.307644
$177$	−42.7180	+	73.9897i	−0.241344	+	0.418021i
$178$	198.942	−	114.859i	1.11765	−	0.645277i
$179$	74.3408	+	128.762i	0.415312	+	0.719341i	0.995461	−	0.0951690i	$-0.0303392\pi$
$179$	74.3408	+	128.762i	0.415312	+	0.719341i	−0.580149	+	0.814510i	$0.697006\pi$
$180$		0			0
$181$			257.302i			1.42156i	0.703414	+	0.710780i	$0.251658\pi$
$181$			257.302i			1.42156i	−0.703414	+	0.710780i	$0.748342\pi$
$182$	−151.163	+	241.933i	−0.830563	+	1.32930i
$183$	−1.53019			−0.00836168
$184$	−271.505	+	470.261i	−1.47557	+	2.55577i
$185$		0			0
$186$	−114.187	−	197.777i	−0.613908	−	1.06332i
$187$	52.1223	+	30.0928i	0.278729	+	0.160924i
$188$			28.3629i			0.150867i
$189$	36.3510	+	1.26788i	0.192333	+	0.00670837i
$190$		0			0
$191$	−60.8021	+	105.312i	−0.318336	+	0.551373i	−0.980141	−	0.198302i	$-0.936457\pi$
$191$	−60.8021	+	105.312i	−0.318336	+	0.551373i	0.661805	+	0.749676i	$0.269791\pi$
$192$	−63.8685	+	36.8745i	−0.332649	+	0.192055i
$193$	121.266	+	210.039i	0.628323	+	1.08829i	0.987888	+	0.155167i	$0.0495916\pi$
$193$	121.266	+	210.039i	0.628323	+	1.08829i	−0.359566	+	0.933120i	$0.617075\pi$
$194$	128.773	+	74.3470i	0.663777	+	0.383232i
$195$		0			0
$196$	180.323	+	369.638i	0.920015	+	1.88591i
$197$	98.9929			0.502502			0.251251	−	0.967922i	$-0.419158\pi$
$197$	98.9929			0.502502			0.251251	+	0.967922i	$0.419158\pi$
$198$	13.6964	−	23.7229i	0.0691738	−	0.119813i
$199$	68.2115	−	39.3819i	0.342772	−	0.197899i	−0.318725	−	0.947847i	$-0.603255\pi$
$199$	68.2115	−	39.3819i	0.342772	−	0.197899i	0.661497	+	0.749948i	$0.269921\pi$
$200$		0			0
$201$	−97.5816	−	56.3388i	−0.485481	−	0.280292i
$202$		−	527.945i		−	2.61359i
$203$	5.97578	−	171.329i	0.0294373	−	0.843986i
$204$	337.343			1.65364
$205$		0			0
$206$	425.846	−	245.863i	2.06722	−	1.19351i
$207$	52.6626	+	91.2143i	0.254409	+	0.440649i
$208$	209.287	+	120.832i	1.00619	+	0.580922i
$209$		−	77.7303i		−	0.371915i
$210$		0			0
$211$	−107.144			−0.507790			−0.253895	−	0.967232i	$-0.581712\pi$
$211$	−107.144			−0.507790			−0.253895	+	0.967232i	$0.581712\pi$
$212$	−168.030	+	291.036i	−0.792594	+	1.37281i
$213$	129.118	−	74.5462i	0.606187	−	0.349982i
$214$	−319.020	−	552.559i	−1.49075	−	2.58205i
$215$		0			0
$216$		−	80.3673i		−	0.372071i
$217$	−123.092	−	231.480i	−0.567246	−	1.06673i
$218$	−259.842			−1.19194
$219$	53.3274	−	92.3657i	0.243504	−	0.421761i
$220$		0			0
$221$	134.311	+	232.634i	0.607743	+	1.05264i
$222$	135.969	+	78.5019i	0.612474	+	0.353612i
$223$			8.72021i			0.0391041i	0.999809	+	0.0195520i	$0.00622400\pi$
$223$			8.72021i			0.0391041i	−0.999809	+	0.0195520i	$0.993776\pi$
$224$	71.8462	−	38.2051i	0.320742	−	0.170559i
$225$		0			0
$226$	13.0003	−	22.5171i	0.0575233	−	0.0996333i
$227$	219.123	−	126.511i	0.965299	−	0.557316i	0.0674992	−	0.997719i	$-0.478498\pi$
$227$	219.123	−	126.511i	0.965299	−	0.557316i	0.897800	+	0.440404i	$0.145165\pi$
$228$	−217.841	−	377.312i	−0.955443	−	1.65488i
$229$	125.988	+	72.7394i	0.550167	+	0.317639i	0.749189	−	0.662356i	$-0.230443\pi$
$229$	125.988	+	72.7394i	0.550167	+	0.317639i	−0.199022	+	0.979995i	$0.563777\pi$
$230$		0			0
$231$	16.6632	−	26.6692i	0.0721352	−	0.115451i
$232$	−378.787			−1.63270
$233$	128.758	−	223.015i	0.552609	−	0.957146i	−0.445477	−	0.895294i	$-0.646966\pi$
$233$	128.758	−	223.015i	0.552609	−	0.957146i	0.998085	−	0.0618526i	$-0.0197009\pi$
$234$	105.881	−	61.1303i	0.452482	−	0.261241i
$235$		0			0
$236$	358.549	+	207.009i	1.51928	+	0.877155i
$237$			47.7068i			0.201295i
$238$	571.481	+	19.9326i	2.40118	+	0.0837506i
$239$	−128.682			−0.538418			−0.269209	−	0.963082i	$-0.586762\pi$
$239$	−128.682			−0.538418			−0.269209	+	0.963082i	$0.586762\pi$
$240$		0			0
$241$	−8.02227	+	4.63166i	−0.0332874	+	0.0192185i	−0.516551	−	0.856256i	$-0.672784\pi$
$241$	−8.02227	+	4.63166i	−0.0332874	+	0.0192185i	0.483264	+	0.875475i	$0.339451\pi$
$242$	201.144	+	348.392i	0.831175	+	1.43964i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$			7.41519i			0.0303901i
$245$		0			0
$246$	−22.6289			−0.0919872
$247$	173.464	−	300.449i	0.702285	−	1.21639i
$248$	−501.670	+	289.639i	−2.02286	+	1.16790i
$249$	113.835	+	197.167i	0.457167	+	0.791837i
$250$		0			0
$251$		−	29.9212i		−	0.119208i	−0.998222	−	0.0596040i	$-0.981016\pi$
$251$		−	29.9212i		−	0.119208i	0.998222	−	0.0596040i	$-0.0189838\pi$
$252$	6.14408	−	176.155i	0.0243813	−	0.699026i
$253$	91.0608			0.359924
$254$	−367.251	+	636.097i	−1.44587	+	2.50432i
$255$		0			0
$256$	260.539	+	451.267i	1.01773	+	1.76276i
$257$	−83.7338	−	48.3438i	−0.325813	−	0.188108i	0.328168	−	0.944619i	$-0.393569\pi$
$257$	−83.7338	−	48.3438i	−0.325813	−	0.188108i	−0.653980	+	0.756511i	$0.726902\pi$
$258$		−	452.576i		−	1.75417i
$259$	152.857	+	95.5065i	0.590180	+	0.368751i
$260$		0			0
$261$	−36.7357	+	63.6281i	−0.140750	+	0.243786i
$262$	−334.088	+	192.886i	−1.27514	+	0.736204i
$263$	32.1231	+	55.6388i	0.122141	+	0.211554i	0.920612	−	0.390479i	$-0.127691\pi$
$263$	32.1231	+	55.6388i	0.122141	+	0.211554i	−0.798471	+	0.602034i	$0.794357\pi$
$264$	−60.1740	−	34.7415i	−0.227932	−	0.131596i
$265$		0			0
$266$	−346.743	−	652.062i	−1.30354	−	2.45136i
$267$	−113.022			−0.423302
$268$	−273.014	+	472.875i	−1.01871	+	1.76446i
$269$	−171.096	+	98.7823i	−0.636044	+	0.367220i	−0.783089	−	0.621910i	$-0.786357\pi$
$269$	−171.096	+	98.7823i	−0.636044	+	0.367220i	0.147045	+	0.989130i	$0.453024\pi$
$270$		0			0
$271$	−133.483	−	77.0667i	−0.492559	−	0.284379i	0.233077	−	0.972458i	$-0.425121\pi$
$271$	−133.483	−	77.0667i	−0.492559	−	0.284379i	−0.725635	+	0.688080i	$0.758454\pi$
$272$		−	484.410i		−	1.78092i
$273$	123.924	−	65.8980i	0.453932	−	0.241385i
$274$	624.708			2.27996
$275$		0			0
$276$	442.019	−	255.200i	1.60152	−	0.924637i
$277$	169.602	+	293.758i	0.612280	+	1.06050i	0.990855	+	0.134929i	$0.0430808\pi$
$277$	169.602	+	293.758i	0.612280	+	1.06050i	−0.378575	+	0.925570i	$0.623586\pi$
$278$	517.968	+	299.049i	1.86320	+	1.07572i
$279$			112.360i			0.402724i
$280$		0			0
$281$	−111.976			−0.398492			−0.199246	−	0.979949i	$-0.563849\pi$
$281$	−111.976			−0.398492			−0.199246	+	0.979949i	$0.563849\pi$
$282$	10.3024	−	17.8443i	0.0365333	−	0.0632776i
$283$	56.6453	−	32.7042i	0.200160	−	0.115563i	−0.396570	−	0.918004i	$-0.629800\pi$
$283$	56.6453	−	32.7042i	0.200160	−	0.115563i	0.596730	+	0.802442i	$0.296466\pi$
$284$	−361.246	−	625.697i	−1.27199	−	2.20316i
$285$		0			0
$286$		−	105.703i		−	0.369589i
$287$	−25.9622	−	0.905532i	−0.0904605	−	0.00315516i
$288$	−34.8740			−0.121090
$289$	124.725	−	216.029i	0.431573	−	0.747507i
$290$		0			0
$291$	−36.5787	−	63.3562i	−0.125700	−	0.217719i
$292$	−447.599	−	258.421i	−1.53287	−	0.885004i
$293$			100.992i			0.344681i	0.985037	+	0.172341i	$0.0551330\pi$
$293$			100.992i			0.344681i	−0.985037	+	0.172341i	$0.944867\pi$
$294$	20.8170	−	298.054i	0.0708060	−	1.01379i
$295$		0			0
$296$	199.123	−	344.891i	0.672713	−	1.16517i
$297$	−11.6717	+	6.73864i	−0.0392985	+	0.0226890i
$298$	−150.297	−	260.322i	−0.504352	−	0.873564i
$299$	351.975	+	203.213i	1.17717	+	0.679642i
$300$		0			0
$301$	18.1106	−	519.242i	0.0601681	−	1.72506i
$302$	−485.802			−1.60862
$303$	−129.874	+	224.949i	−0.428628	+	0.742406i
$304$	−541.804	+	312.811i	−1.78225	+	1.02898i
$305$		0			0
$306$	−212.236	−	122.535i	−0.693583	−	0.400440i
$307$		−	400.388i		−	1.30420i	−0.758135	−	0.652098i	$-0.773889\pi$
$307$		−	400.388i		−	1.30420i	0.758135	−	0.652098i	$-0.226111\pi$
$308$	−129.237	−	80.7490i	−0.419602	−	0.262172i
$309$	−241.929			−0.782941
$310$		0			0
$311$	−31.1758	+	17.9993i	−0.100244	+	0.0578757i	−0.549284	−	0.835636i	$-0.685099\pi$
$311$	−31.1758	+	17.9993i	−0.100244	+	0.0578757i	0.449040	+	0.893512i	$0.351766\pi$
$312$	−155.059	−	268.571i	−0.496985	−	0.860803i
$313$	99.1558	+	57.2476i	0.316792	+	0.182900i	0.649962	−	0.759967i	$-0.274785\pi$
$313$	99.1558	+	57.2476i	0.316792	+	0.182900i	−0.333170	+	0.942867i	$0.608118\pi$
$314$		−	24.1737i		−	0.0769864i
$315$		0			0
$316$	231.184			0.731596
$317$	2.01608	−	3.49195i	0.00635987	−	0.0110156i	−0.862828	−	0.505498i	$-0.831309\pi$
$317$	2.01608	−	3.49195i	0.00635987	−	0.0110156i	0.869188	+	0.494482i	$0.164642\pi$
$318$	211.429	−	122.069i	0.664872	−	0.383864i
$319$	31.7605	+	55.0108i	0.0995627	+	0.172448i
$320$		0			0
$321$			313.916i			0.977932i
$322$	763.888	−	406.208i	2.37232	−	1.26151i
$323$	−695.413			−2.15298
$324$	−37.7703	+	65.4202i	−0.116575	+	0.201914i
$325$		0			0
$326$	−487.098	−	843.678i	−1.49417	−	2.58797i
$327$	110.715	+	63.9212i	0.338577	+	0.195478i
$328$			57.3989i			0.174997i
$329$	12.5340	−	20.0605i	0.0380974	−	0.0609742i
$330$		0			0
$331$	−253.691	+	439.406i	−0.766439	+	1.32751i	0.173043	+	0.984914i	$0.444640\pi$
$331$	−253.691	+	439.406i	−0.766439	+	1.32751i	−0.939482	+	0.342598i	$0.888693\pi$
$332$	955.461	−	551.636i	2.87790	−	1.66155i
$333$	−38.6229	−	66.8969i	−0.115985	−	0.200892i
$334$	−129.207	−	74.5976i	−0.386847	−	0.223346i
$335$		0			0
$336$	−252.951	−	8.82265i	−0.752829	−	0.0262579i
$337$	264.279			0.784210			0.392105	−	0.919921i	$-0.371747\pi$
$337$	264.279			0.784210			0.392105	+	0.919921i	$0.371747\pi$
$338$	−61.5884	+	106.674i	−0.182214	+	0.315604i
$339$	−11.0784	+	6.39614i	−0.0326797	+	0.0188677i
$340$		0			0
$341$	84.1280	+	48.5713i	0.246710	+	0.142438i
$342$			316.510i			0.925467i
$343$	35.8105	−	341.126i	0.104404	−	0.994535i
$344$	−1147.98			−3.33714
$345$		0			0
$346$	90.1226	−	52.0323i	0.260470	−	0.150382i
$347$	−117.234	−	203.055i	−0.337849	−	0.585172i	0.646179	−	0.763186i	$-0.276366\pi$
$347$	−117.234	−	203.055i	−0.337849	−	0.585172i	−0.984028	+	0.178014i	$0.943033\pi$
$348$	308.338	+	178.019i	0.886029	+	0.511549i
$349$			54.2133i			0.155339i	0.996979	+	0.0776695i	$0.0247479\pi$
$349$			54.2133i			0.155339i	−0.996979	+	0.0776695i	$0.975252\pi$
$350$		0			0
$351$	−60.1522			−0.171374
$352$	−15.0755	+	26.1115i	−0.0428280	+	0.0741803i
$353$	451.914	−	260.913i	1.28021	−	0.739129i	0.303322	−	0.952888i	$-0.401904\pi$
$353$	451.914	−	260.913i	1.28021	−	0.739129i	0.976886	+	0.213759i	$0.0685707\pi$
$354$	−150.385	−	260.475i	−0.424818	−	0.735806i
$355$		0			0
$356$			547.696i			1.53847i
$357$	−238.596	−	149.077i	−0.668336	−	0.417584i
$358$	−523.423			−1.46208
$359$	233.973	−	405.253i	0.651735	−	1.12884i	−0.330967	−	0.943642i	$-0.607375\pi$
$359$	233.973	−	405.253i	0.651735	−	1.12884i	0.982702	−	0.185196i	$-0.0592919\pi$
$360$		0			0
$361$	268.566	+	465.171i	0.743951	+	1.28856i
$362$	−784.458	−	452.907i	−2.16701	−	1.25112i
$363$		−	197.926i		−	0.545251i
$364$	−319.337	−	600.526i	−0.877301	−	1.64980i
$365$		0			0
$366$	2.69346	−	4.66520i	0.00735917	−	0.0127465i
$367$	149.151	−	86.1123i	0.406406	−	0.234638i	−0.282839	−	0.959168i	$-0.591276\pi$
$367$	149.151	−	86.1123i	0.406406	−	0.234638i	0.689244	+	0.724529i	$0.257943\pi$
$368$	−366.456	−	634.721i	−0.995806	−	1.72479i
$369$	9.64181	+	5.56670i	0.0261296	+	0.0150859i
$370$		0			0
$371$	247.458	−	131.589i	0.667003	−	0.354687i
$372$	544.489			1.46368
$373$	−230.486	+	399.213i	−0.617924	+	1.07028i	0.371940	+	0.928257i	$0.378693\pi$
$373$	−230.486	+	399.213i	−0.617924	+	1.07028i	−0.989864	+	0.142019i	$0.954641\pi$
$374$	−183.493	+	105.940i	−0.490622	+	0.283261i
$375$		0			0
$376$	−45.2627	−	26.1324i	−0.120379	−	0.0695011i
$377$			283.509i			0.752014i
$378$	−67.8510	+	108.594i	−0.179500	+	0.287287i
$379$	444.638			1.17319			0.586594	−	0.809881i	$-0.300468\pi$
$379$	444.638			1.17319			0.586594	+	0.809881i	$0.300468\pi$
$380$		0			0
$381$	312.960	−	180.687i	0.821416	−	0.474245i
$382$	−214.049	−	370.744i	−0.560339	−	0.970535i
$383$	458.528	+	264.731i	1.19720	+	0.691205i	0.959930	−	0.280239i	$-0.0904137\pi$
$383$	458.528	+	264.731i	1.19720	+	0.691205i	0.237271	+	0.971443i	$0.423747\pi$
$384$		−	340.166i		−	0.885849i
$385$		0			0
$386$	−853.818			−2.21196
$387$	−111.334	+	192.836i	−0.287684	+	0.498284i
$388$	−307.020	+	177.258i	−0.791290	+	0.456851i
$389$	−97.7554	−	169.317i	−0.251299	−	0.435263i	0.712585	−	0.701586i	$-0.247524\pi$
$389$	−97.7554	−	169.317i	−0.251299	−	0.435263i	−0.963884	+	0.266323i	$0.914191\pi$
$390$		0			0
$391$		−	814.674i		−	2.08356i
$392$	−756.026	−	52.8030i	−1.92864	−	0.134701i
$393$	189.799			0.482950
$394$	−174.249	+	301.808i	−0.442256	+	0.766009i
$395$		0			0
$396$	32.6550	+	56.5601i	0.0824622	+	0.142829i
$397$	−25.3358	−	14.6276i	−0.0638181	−	0.0368454i	0.467751	−	0.883860i	$-0.345064\pi$
$397$	−25.3358	−	14.6276i	−0.0638181	−	0.0368454i	−0.531570	+	0.847015i	$0.678398\pi$
$398$			277.283i			0.696690i
$399$	−12.6657	+	363.132i	−0.0317435	+	0.910106i
$400$		0			0
$401$	−105.396	+	182.551i	−0.262833	+	0.455241i	−0.966994	−	0.254800i	$-0.917990\pi$
$401$	−105.396	+	182.551i	−0.262833	+	0.455241i	0.704160	+	0.710041i	$0.251324\pi$
$402$	343.529	−	198.337i	0.854550	−	0.493375i
$403$	216.785	+	375.483i	0.537929	+	0.931720i
$404$	1090.09	+	629.363i	2.69824	+	1.55783i
$405$		0			0
$406$	511.826	+	319.795i	1.26066	+	0.787672i
$407$	−66.7843			−0.164089
$408$	−310.814	+	538.345i	−0.761799	+	1.31947i
$409$	281.014	−	162.244i	0.687077	−	0.396684i	−0.115439	−	0.993315i	$-0.536828\pi$
$409$	281.014	−	162.244i	0.687077	−	0.396684i	0.802516	+	0.596631i	$0.203494\pi$
$410$		0			0
$411$	−266.179	−	153.678i	−0.647637	−	0.373913i
$412$			1172.37i			2.84556i
$413$	−162.114	−	304.862i	−0.392529	−	0.738164i
$414$	−370.790			−0.895628
$415$		0			0
$416$	−116.542	+	67.2853i	−0.280148	+	0.161744i
$417$	−147.132	−	254.841i	−0.352835	−	0.611128i
$418$	236.983	+	136.822i	0.566944	+	0.327325i
$419$		−	693.958i		−	1.65622i	−0.560563	−	0.828112i	$-0.689415\pi$
$419$		−	693.958i		−	1.65622i	0.560563	−	0.828112i	$-0.310585\pi$
$420$		0			0
$421$	−341.554			−0.811292			−0.405646	−	0.914030i	$-0.632953\pi$
$421$	−341.554			−0.811292			−0.405646	+	0.914030i	$0.632953\pi$
$422$	188.596	−	326.657i	0.446909	−	0.774070i
$423$	−8.77939	+	5.06878i	−0.0207551	+	0.0119829i
$424$	−309.632	−	536.298i	−0.730264	−	1.26485i
$425$		0			0
$426$			524.869i			1.23209i
$427$	3.27690	−	5.24462i	0.00767423	−	0.0122825i
$428$	1521.22			3.55425
$429$	−26.0028	+	45.0382i	−0.0606127	+	0.104984i
$430$		0			0
$431$	205.726	+	356.328i	0.477323	+	0.826748i	0.999662	−	0.0259902i	$-0.00827387\pi$
$431$	205.726	+	356.328i	0.477323	+	0.826748i	−0.522339	+	0.852738i	$0.674941\pi$
$432$	93.9407	+	54.2367i	0.217455	+	0.125548i
$433$			443.458i			1.02415i	0.858940	+	0.512077i	$0.171124\pi$
$433$			443.458i			1.02415i	−0.858940	+	0.512077i	$0.828876\pi$
$434$	922.400	+	32.1723i	2.12535	+	0.0741298i
$435$		0			0
$436$	309.758	−	536.517i	0.710454	−	1.23054i
$437$	−911.197	+	526.080i	−2.08512	+	1.20384i
$438$	187.735	+	325.167i	0.428619	+	0.742390i
$439$	−268.002	−	154.731i	−0.610484	−	0.352463i	0.162671	−	0.986680i	$-0.447989\pi$
$439$	−268.002	−	154.731i	−0.610484	−	0.352463i	−0.773155	+	0.634217i	$0.781322\pi$
$440$		0			0
$441$	−82.1912	+	121.875i	−0.186375	+	0.276361i
$442$	−945.666			−2.13952
$443$	409.330	−	708.981i	0.923996	−	1.60041i	0.130829	−	0.991405i	$-0.458236\pi$
$443$	409.330	−	708.981i	0.923996	−	1.60041i	0.793167	−	0.609004i	$-0.208431\pi$
$444$	−324.178	+	187.164i	−0.730131	+	0.421541i
$445$		0			0
$446$	−26.5860	−	15.3494i	−0.0596099	−	0.0344158i
$447$			147.892i			0.330855i
$448$	10.3895	−	297.872i	0.0231908	−	0.664893i
$449$	315.756			0.703243			0.351621	−	0.936142i	$-0.385630\pi$
$449$	315.756			0.703243			0.351621	+	0.936142i	$0.385630\pi$
$450$		0			0
$451$	8.33600	−	4.81279i	0.0184834	−	0.0106714i
$452$	30.9953	+	53.6854i	0.0685736	+	0.118773i
$453$	206.993	+	119.507i	0.456938	+	0.263813i
$454$			890.743i			1.96199i
$455$		0			0
$456$	802.839			1.76061
$457$	−93.6533	+	162.212i	−0.204931	+	0.354950i	−0.950111	−	0.311913i	$-0.899030\pi$
$457$	−93.6533	+	162.212i	−0.204931	+	0.354950i	0.745180	+	0.666863i	$0.232364\pi$
$458$	−443.533	+	256.074i	−0.968412	+	0.559113i
$459$	60.2871	+	104.420i	0.131344	+	0.227495i
$460$		0			0
$461$		−	8.27599i		−	0.0179523i	−0.999960	−	0.00897613i	$-0.997143\pi$
$461$		−	8.27599i		−	0.0179523i	0.999960	−	0.00897613i	$-0.00285723\pi$
$462$	51.9778	+	97.7461i	0.112506	+	0.211572i
$463$	472.925			1.02144			0.510718	−	0.859748i	$-0.329380\pi$
$463$	472.925			1.02144			0.510718	+	0.859748i	$0.329380\pi$
$464$	255.628	−	442.761i	0.550922	−	0.954226i
$465$		0			0
$466$	453.283	+	785.108i	0.972709	+	1.68478i
$467$	620.865	+	358.456i	1.32948	+	0.767573i	0.985218	−	0.171303i	$-0.0547976\pi$
$467$	620.865	+	358.456i	1.32948	+	0.767573i	0.344257	+	0.938876i	$0.388131\pi$
$468$			291.494i			0.622851i
$469$	402.069	−	213.805i	0.857289	−	0.455875i
$470$		0			0
$471$	−5.94674	+	10.3001i	−0.0126258	+	0.0218685i
$472$	−660.705	+	381.458i	−1.39980	+	0.808174i
$473$	96.2556	+	166.720i	0.203500	+	0.352473i
$474$	−145.448	−	83.9742i	−0.306851	−	0.177161i
$475$		0			0
$476$	−722.420	+	1156.22i	−1.51769	+	2.42904i
$477$	−120.116			−0.251815
$478$	226.508	−	392.323i	0.473866	−	0.820759i
$479$	178.320	−	102.953i	0.372276	−	0.214933i	−0.302177	−	0.953252i	$-0.597713\pi$
$479$	178.320	−	102.953i	0.372276	−	0.214933i	0.674452	+	0.738319i	$0.264380\pi$
$480$		0			0
$481$	−258.140	−	149.037i	−0.536673	−	0.309848i
$482$		−	32.6108i		−	0.0676573i
$483$	−425.408	−	14.8378i	−0.880762	−	0.0307201i
$484$	−959.138			−1.98169
$485$		0			0
$486$	47.5258	−	27.4390i	0.0977897	−	0.0564589i
$487$	161.439	+	279.621i	0.331498	+	0.574171i	0.982806	−	0.184643i	$-0.0591127\pi$
$487$	161.439	+	279.621i	0.331498	+	0.574171i	−0.651308	+	0.758813i	$0.725779\pi$
$488$	−11.8335	−	6.83205i	−0.0242489	−	0.0140001i
$489$			479.304i			0.980172i
$490$		0			0
$491$	272.380			0.554745			0.277372	−	0.960763i	$-0.410536\pi$
$491$	272.380			0.554745			0.277372	+	0.960763i	$0.410536\pi$
$492$	26.9759	−	46.7236i	0.0548290	−	0.0949667i
$493$	492.153	−	284.145i	0.998282	−	0.576359i
$494$	610.669	+	1057.71i	1.23617	+	2.14111i
$495$		0			0
$496$		−	781.864i		−	1.57634i
$497$	−21.0035	+	602.184i	−0.0422606	+	1.21164i
$498$	−801.494			−1.60943
$499$	−264.597	+	458.296i	−0.530255	+	0.918429i	0.469122	+	0.883134i	$0.344571\pi$
$499$	−264.597	+	458.296i	−0.530255	+	0.918429i	−0.999377	+	0.0352954i	$0.988763\pi$
$500$		0			0
$501$	36.7020	+	63.5698i	0.0732576	+	0.126886i
$502$	91.2231	+	52.6677i	0.181719	+	0.104916i
$503$			204.695i			0.406948i	0.979080	+	0.203474i	$0.0652232\pi$
$503$			204.695i			0.406948i	−0.979080	+	0.203474i	$0.934777\pi$
$504$	275.454	+	172.106i	0.546535	+	0.341481i
$505$		0			0
$506$	−160.286	+	277.624i	−0.316772	+	0.548665i
$507$	52.4837	−	30.3015i	0.103518	−	0.0597663i
$508$	−875.599	−	1516.58i	−1.72362	−	2.98540i
$509$	−473.892	−	273.602i	−0.931026	−	0.537528i	−0.0438903	−	0.999036i	$-0.513975\pi$
$509$	−473.892	−	273.602i	−0.931026	−	0.537528i	−0.887136	+	0.461508i	$0.847309\pi$
$510$		0			0
$511$	202.377	+	380.577i	0.396041	+	0.744770i
$512$	−1048.84			−2.04851
$513$	77.8614	−	134.860i	0.151777	−	0.262885i
$514$	294.779	−	170.191i	0.573500	−	0.331110i
$515$		0			0
$516$	934.470	+	539.517i	1.81099	+	1.04558i
$517$			8.76461i			0.0169528i
$518$	−560.238	+	297.914i	−1.08154	+	0.575124i
$519$	−51.1998			−0.0986509
$520$		0			0
$521$	30.1482	−	17.4061i	0.0578660	−	0.0334090i	−0.470788	−	0.882246i	$-0.656030\pi$
$521$	30.1482	−	17.4061i	0.0578660	−	0.0334090i	0.528654	+	0.848837i	$0.322697\pi$
$522$	−129.325	−	223.998i	−0.247750	−	0.429115i
$523$	−720.290	−	415.860i	−1.37723	−	0.795143i	−0.385403	−	0.922748i	$-0.625938\pi$
$523$	−720.290	−	415.860i	−1.37723	−	0.795143i	−0.991825	+	0.127606i	$0.959271\pi$
$524$		−	919.756i		−	1.75526i
$525$		0			0
$526$	−226.174			−0.429989
$527$	434.543	−	752.650i	0.824559	−	1.42818i
$528$	81.2180	−	46.8913i	0.153822	−	0.0888092i
$529$	−351.800	−	609.336i	−0.665029	−	1.15186i
$530$		0			0
$531$			147.979i			0.278680i
$532$	1759.72	+	61.3770i	3.30774	+	0.115370i
$533$	42.9612			0.0806027
$534$	198.942	−	344.578i	0.372551	−	0.645277i
$535$		0			0
$536$	−503.088	−	871.374i	−0.938597	−	1.62570i
$537$	223.022	+	128.762i	0.415312	+	0.239780i
$538$		−	695.512i		−	1.29277i
$539$	55.7228	+	114.224i	0.103382	+	0.211919i
$540$		0			0
$541$	112.177	−	194.296i	0.207351	−	0.359143i	−0.743528	−	0.668705i	$-0.766849\pi$
$541$	112.177	−	194.296i	0.207351	−	0.359143i	0.950879	+	0.309562i	$0.100182\pi$
$542$	469.919	−	271.308i	0.867008	−	0.500568i
$543$	222.830	+	385.954i	0.410369	+	0.710780i
$544$	233.606	+	134.872i	0.429422	+	0.247927i
$545$		0			0
$546$	−17.2236	+	493.810i	−0.0315450	+	0.904414i
$547$	456.739			0.834989			0.417495	−	0.908679i	$-0.362908\pi$
$547$	456.739			0.834989			0.417495	+	0.908679i	$0.362908\pi$
$548$	−744.716	+	1289.89i	−1.35897	+	2.35381i
$549$	−2.29528	+	1.32518i	−0.00418084	+	0.00241381i
$550$		0			0
$551$	−635.621	−	366.976i	−1.15358	−	0.666018i
$552$			940.522i			1.70384i
$553$	−163.512	−	102.164i	−0.295682	−	0.184745i
$554$	−1194.14			−2.15549
$555$		0			0
$556$	−1234.94	+	712.994i	−2.22112	+	1.28236i
$557$	−388.525	−	672.945i	−0.697532	−	1.20816i	−0.969320	−	0.245803i	$-0.920948\pi$
$557$	−388.525	−	672.945i	−0.697532	−	1.20816i	0.271788	−	0.962357i	$-0.412385\pi$
$558$	−342.561	−	197.777i	−0.613908	−	0.354440i
$559$			859.223i			1.53707i
$560$		0			0
$561$	104.245			0.185819
$562$	197.102	−	341.391i	0.350716	−	0.607457i
$563$	72.2428	−	41.7094i	0.128318	−	0.0740842i	−0.434467	−	0.900688i	$-0.643063\pi$
$563$	72.2428	−	41.7094i	0.128318	−	0.0740842i	0.562785	+	0.826603i	$0.309730\pi$
$564$	24.5630	+	42.5444i	0.0435514	+	0.0754333i
$565$		0			0
$566$			230.265i			0.406829i
$567$	55.6245	−	29.5790i	0.0981031	−	0.0521676i
$568$	1331.35			2.34393
$569$	111.671	−	193.421i	0.196259	−	0.339931i	−0.751053	−	0.660241i	$-0.770454\pi$
$569$	111.671	−	193.421i	0.196259	−	0.339931i	0.947313	+	0.320311i	$0.103787\pi$
$570$		0			0
$571$	−88.3631	−	153.049i	−0.154751	−	0.268037i	0.778217	−	0.627995i	$-0.216124\pi$
$571$	−88.3631	−	153.049i	−0.154751	−	0.268037i	−0.932969	+	0.359958i	$0.882791\pi$
$572$	218.252	+	126.008i	0.381560	+	0.220294i
$573$			210.625i			0.367582i
$574$	48.4597	−	77.5590i	0.0844246	−	0.135120i
$575$		0			0
$576$	−63.8685	+	110.624i	−0.110883	+	0.192055i
$577$	−780.812	+	450.802i	−1.35323	+	0.781286i	−0.988700	−	0.149907i	$-0.952103\pi$
$577$	−780.812	+	450.802i	−1.35323	+	0.781286i	−0.364527	+	0.931193i	$0.618769\pi$
$578$	439.084	+	760.516i	0.759661	+	1.31577i
$579$	363.799	+	210.039i	0.628323	+	0.362762i
$580$		0			0
$581$	−919.556	−	32.0731i	−1.58271	−	0.0552033i
$582$	257.546			0.442518
$583$	−51.9240	+	89.9351i	−0.0890635	+	0.154263i
$584$	824.798	−	476.197i	1.41233	−	0.815406i
$585$		0			0
$586$	−307.901	−	177.767i	−0.525429	−	0.303356i
$587$			163.544i			0.278610i	0.990250	+	0.139305i	$0.0444868\pi$
$587$			163.544i			0.278610i	−0.990250	+	0.139305i	$0.955513\pi$
$588$	590.601	+	398.293i	1.00442	+	0.677370i
$589$	−1122.43			−1.90566
$590$		0			0
$591$	148.489	−	85.7304i	0.251251	−	0.145060i
$592$	268.760	+	465.507i	0.453987	+	0.786329i
$593$	−1004.47	−	579.932i	−1.69388	−	0.977964i	−0.951329	−	0.308177i	$-0.900281\pi$
$593$	−1004.47	−	579.932i	−1.69388	−	0.977964i	−0.742554	−	0.669786i	$-0.766386\pi$
$594$		−	47.4458i		−	0.0798750i
$595$		0			0
$596$	716.677			1.20248
$597$	68.2115	−	118.146i	0.114257	−	0.197899i
$598$	−1239.10	+	715.396i	−2.07208	+	1.19631i
$599$	−16.3990	−	28.4039i	−0.0273773	−	0.0474188i	0.852012	−	0.523522i	$-0.175382\pi$
$599$	−16.3990	−	28.4039i	−0.0273773	−	0.0474188i	−0.879389	+	0.476103i	$0.842049\pi$
$600$		0			0
$601$		−	796.834i		−	1.32585i	−0.748687	−	0.662924i	$-0.769315\pi$
$601$		−	796.834i		−	1.32585i	0.748687	−	0.662924i	$-0.230685\pi$
$602$	1551.18	+	969.192i	2.57670	+	1.60995i
$603$	−195.163			−0.323654
$604$	579.126	−	1003.08i	0.958817	−	1.66072i
$605$		0			0
$606$	−457.214	−	791.917i	−0.754478	−	1.30679i
$607$	453.877	+	262.046i	0.747739	+	0.431707i	0.824876	−	0.565313i	$-0.191245\pi$
$607$	453.877	+	262.046i	0.747739	+	0.431707i	−0.0771375	+	0.997020i	$0.524578\pi$
$608$		−	348.378i		−	0.572990i
$609$	−139.412	−	262.169i	−0.228919	−	0.430491i
$610$		0			0
$611$	−19.5593	+	33.8776i	−0.0320119	+	0.0554462i
$612$	506.014	−	292.147i	0.826821	−	0.477365i
$613$	−126.866	−	219.738i	−0.206959	−	0.358463i	0.743796	−	0.668406i	$-0.233023\pi$
$613$	−126.866	−	219.738i	−0.206959	−	0.358463i	−0.950755	+	0.309944i	$0.899690\pi$
$614$	1220.69	+	704.769i	1.98810	+	1.14783i
$615$		0			0
$616$	247.937	−	131.844i	0.402495	−	0.214032i
$617$	−620.813			−1.00618			−0.503090	−	0.864234i	$-0.667804\pi$
$617$	−620.813			−1.00618			−0.503090	+	0.864234i	$0.667804\pi$
$618$	425.846	−	737.588i	0.689072	−	1.19351i
$619$	555.643	−	320.801i	0.897647	−	0.518257i	0.0212107	−	0.999775i	$-0.493248\pi$
$619$	555.643	−	320.801i	0.897647	−	0.518257i	0.876436	+	0.481519i	$0.159915\pi$
$620$		0			0
$621$	157.988	+	91.2143i	0.254409	+	0.146883i
$622$		−	126.731i		−	0.203747i
$623$	242.036	−	387.374i	0.388501	−	0.621789i
$624$	418.573			0.670791
$625$		0			0
$626$	−349.071	+	201.536i	−0.557621	+	0.321943i
$627$	−67.3164	−	116.595i	−0.107363	−	0.185958i
$628$	49.9134	+	28.8175i	0.0794800	+	0.0458878i
$629$			597.484i			0.949896i
$630$		0			0
$631$	−166.338			−0.263610			−0.131805	−	0.991276i	$-0.542077\pi$
$631$	−166.338			−0.263610			−0.131805	+	0.991276i	$0.542077\pi$
$632$	−213.004	+	368.933i	−0.337031	+	0.583755i
$633$	−160.715	+	92.7891i	−0.253895	+	0.146586i
$634$	7.09746	+	12.2932i	0.0111947	+	0.0193899i
$635$		0			0
$636$			582.073i			0.915209i
$637$	−39.5213	+	565.860i	−0.0620429	+	0.888321i
$638$	−223.621			−0.350503
$639$	129.118	−	223.639i	0.202062	−	0.349982i
$640$		0			0
$641$	−68.5302	−	118.698i	−0.106911	−	0.185176i	0.807606	−	0.589722i	$-0.200763\pi$
$641$	−68.5302	−	118.698i	−0.106911	−	0.185176i	−0.914518	+	0.404546i	$0.867429\pi$
$642$	−957.061	−	552.559i	−1.49075	−	0.860685i
$643$		−	812.010i		−	1.26285i	−0.775438	−	0.631423i	$-0.782471\pi$
$643$		−	812.010i		−	1.26285i	0.775438	−	0.631423i	$-0.217529\pi$
$644$	−71.9030	+	2061.50i	−0.111651	+	3.20109i
$645$		0			0
$646$	1224.08	−	2120.16i	1.89485	−	3.28198i
$647$	197.709	−	114.148i	0.305579	−	0.176426i	−0.339368	−	0.940654i	$-0.610213\pi$
$647$	197.709	−	114.148i	0.305579	−	0.176426i	0.644946	+	0.764228i	$0.276880\pi$
$648$	−69.6001	−	120.551i	−0.107408	−	0.186035i
$649$	110.798	+	63.9691i	0.170721	+	0.0985656i
$650$		0			0
$651$	−385.106	−	240.619i	−0.591561	−	0.369614i
$652$	2322.68			3.56239
$653$	−435.557	+	754.406i	−0.667009	+	1.15529i	0.311728	+	0.950171i	$0.399092\pi$
$653$	−435.557	+	754.406i	−0.667009	+	1.15529i	−0.978736	+	0.205122i	$0.934241\pi$
$654$	−389.763	+	225.030i	−0.595968	+	0.344082i
$655$		0			0
$656$	−67.0932	−	38.7363i	−0.102276	−	0.0590492i
$657$		−	184.731i		−	0.281174i
$658$	39.0975	+	73.5243i	0.0594187	+	0.111739i
$659$	−677.945			−1.02875			−0.514374	−	0.857566i	$-0.671976\pi$
$659$	−677.945			−1.02875			−0.514374	+	0.857566i	$0.671976\pi$
$660$		0			0
$661$	608.681	−	351.422i	0.920849	−	0.531652i	0.0369430	−	0.999317i	$-0.488238\pi$
$661$	608.681	−	351.422i	0.920849	−	0.531652i	0.883906	+	0.467665i	$0.154905\pi$
$662$	−893.102	−	1546.90i	−1.34910	−	2.33670i
$663$	402.934	+	232.634i	0.607743	+	0.350881i
$664$			2033.02i			3.06177i
$665$		0			0
$666$	271.939			0.408316
$667$	429.911	−	744.628i	0.644544	−	1.11638i
$668$	308.055	−	177.856i	0.461161	−	0.266251i
$669$	7.55192	+	13.0803i	0.0112884	+	0.0195520i
$670$		0			0
$671$			2.29142i			0.00341493i
$672$	74.6827	−	119.528i	0.111135	−	0.177870i
$673$	−612.283			−0.909782			−0.454891	−	0.890547i	$-0.650322\pi$
$673$	−612.283			−0.909782			−0.454891	+	0.890547i	$0.650322\pi$
$674$	−465.187	+	805.727i	−0.690188	+	1.19544i
$675$		0			0
$676$	−146.839	−	254.333i	−0.217218	−	0.376232i
$677$	5.01270	+	2.89408i	0.00740428	+	0.00427487i	0.503698	−	0.863880i	$-0.331973\pi$
$677$	5.01270	+	2.89408i	0.00740428	+	0.00427487i	−0.496293	+	0.868155i	$0.665306\pi$
$678$		−	45.0343i		−	0.0664222i
$679$	295.483	+	10.3061i	0.435173	+	0.0151784i
$680$		0			0
$681$	219.123	−	379.532i	0.321766	−	0.557316i
$682$	−296.167	+	170.992i	−0.434262	+	0.250721i
$683$	−58.3832	−	101.123i	−0.0854806	−	0.148057i	0.820115	−	0.572198i	$-0.193909\pi$
$683$	−58.3832	−	101.123i	−0.0854806	−	0.148057i	−0.905596	+	0.424142i	$0.860576\pi$
$684$	−653.523	−	377.312i	−0.955443	−	0.551625i
$685$		0			0
$686$	976.982	+	709.632i	1.42417	+	1.03445i
$687$	251.977			0.366778
$688$	774.724	−	1341.86i	1.12605	−	1.95038i
$689$	−401.401	+	231.749i	−0.582585	+	0.336356i
$690$		0			0
$691$	820.541	+	473.740i	1.18747	+	0.685585i	0.957730	−	0.287667i	$-0.0928796\pi$
$691$	820.541	+	473.740i	1.18747	+	0.685585i	0.229738	+	0.973252i	$0.426213\pi$
$692$			248.111i			0.358542i
$693$	1.89862	−	54.4346i	0.00273971	−	0.0785493i
$694$	825.425			1.18937
$695$		0			0
$696$	−568.180	+	328.039i	−0.816350	+	0.471320i
$697$	−43.0575	−	74.5778i	−0.0617755	−	0.106998i
$698$	−165.284	−	95.4270i	−0.236797	−	0.136715i
$699$		−	446.030i		−	0.638097i
$700$		0			0
$701$	1168.56			1.66700			0.833498	−	0.552523i	$-0.186335\pi$
$701$	1168.56			1.66700			0.833498	+	0.552523i	$0.186335\pi$
$702$	105.881	−	183.391i	0.150827	−	0.261241i
$703$	668.275	−	385.829i	0.950604	−	0.548832i
$704$	55.2187	+	95.6415i	0.0784356	+	0.135854i
$705$		0			0
$706$			1837.05i			2.60205i
$707$	−492.872	−	926.865i	−0.697132	−	1.31098i
$708$	717.099			1.01285
$709$	−334.781	+	579.857i	−0.472187	+	0.817852i	−0.999494	−	0.0318230i	$-0.989869\pi$
$709$	−334.781	+	579.857i	−0.472187	+	0.817852i	0.527306	+	0.849675i	$0.323202\pi$
$710$		0			0
$711$	41.3153	+	71.5602i	0.0581087	+	0.100647i
$712$	−874.035	−	504.625i	−1.22758	−	0.708742i
$713$		−	1314.93i		−	1.84422i
$714$	874.484	−	465.018i	1.22477	−	0.651286i
$715$		0			0
$716$	623.973	−	1080.75i	0.871471	−	1.50943i
$717$	−193.023	+	111.442i	−0.269209	+	0.155428i
$718$	823.685	+	1426.66i	1.14719	+	1.98700i
$719$	−805.983	−	465.334i	−1.12098	−	0.647196i	−0.179327	−	0.983790i	$-0.557392\pi$
$719$	−805.983	−	465.334i	−1.12098	−	0.647196i	−0.941650	+	0.336593i	$0.890725\pi$
$720$		0			0
$721$	518.091	−	829.195i	0.718572	−	1.15006i
$722$	−1890.94			−2.61903
$723$	−8.02227	+	13.8950i	−0.0110958	+	0.0192185i
$724$	1870.31	−	1079.82i	2.58330	−	1.49147i
$725$		0			0
$726$	603.433	+	348.392i	0.831175	+	0.479879i
$727$			290.932i			0.400182i	0.979777	+	0.200091i	$0.0641238\pi$
$727$			290.932i			0.400182i	−0.979777	+	0.200091i	$0.935876\pi$
$728$	1252.57	+	43.6882i	1.72056	+	0.0600113i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	1491.55	−	861.149i	2.04043	−	1.17804i
$732$	6.42174	+	11.1228i	0.00877288	+	0.0151951i
$733$	0.836082	+	0.482712i	0.00114063	+	0.000658543i	0.500570	−	0.865696i	$-0.333124\pi$
$733$	0.836082	+	0.482712i	0.00114063	+	0.000658543i	−0.499430	+	0.866354i	$0.666457\pi$
$734$			606.304i			0.826027i
$735$		0			0
$736$	408.124			0.554516
$737$	−84.3659	+	146.126i	−0.114472	+	0.198271i
$738$	−33.9433	+	19.5972i	−0.0459936	+	0.0265544i
$739$	49.9365	+	86.4925i	0.0675731	+	0.117040i	0.897832	−	0.440337i	$-0.145141\pi$
$739$	49.9365	+	86.4925i	0.0675731	+	0.117040i	−0.830259	+	0.557377i	$0.811808\pi$
$740$		0			0
$741$		−	600.898i		−	0.810929i
$742$	−34.3931	+	986.070i	−0.0463518	+	1.32894i
$743$	−890.635			−1.19870			−0.599351	−	0.800486i	$-0.704575\pi$
$743$	−890.635			−1.19870			−0.599351	+	0.800486i	$0.704575\pi$
$744$	−501.670	+	868.917i	−0.674287	+	1.16790i
$745$		0			0
$746$	−811.408	−	1405.40i	−1.08768	−	1.88391i
$747$	341.504	+	197.167i	0.457167	+	0.263946i
$748$		−	505.162i		−	0.675351i
$749$	−1075.93	−	672.251i	−1.43648	−	0.897532i
$750$		0			0
$751$	−310.537	+	537.867i	−0.413499	+	0.716200i	−0.995270	−	0.0971521i	$-0.969027\pi$
$751$	−310.537	+	537.867i	−0.413499	+	0.716200i	0.581771	+	0.813353i	$0.302360\pi$
$752$	61.0920	−	35.2715i	0.0812393	−	0.0469035i
$753$	−25.9125	−	44.8818i	−0.0344124	−	0.0596040i
$754$	−864.357	−	499.037i	−1.14636	−	0.661853i
$755$		0			0
$756$	−143.338	−	269.553i	−0.189601	−	0.356551i
$757$	−675.637			−0.892519			−0.446259	−	0.894904i	$-0.647244\pi$
$757$	−675.637			−0.892519			−0.446259	+	0.894904i	$0.647244\pi$
$758$	−782.658	+	1355.60i	−1.03253	+	1.78840i
$759$	136.591	−	78.8609i	0.179962	−	0.103901i
$760$		0			0
$761$	549.336	+	317.159i	0.721861	+	0.416766i	0.815437	−	0.578846i	$-0.196497\pi$
$761$	549.336	+	317.159i	0.721861	+	0.416766i	−0.0935765	+	0.995612i	$0.529830\pi$
$762$			1272.19i			1.66954i
$763$	−456.181	+	242.580i	−0.597878	+	0.317930i
$764$	1020.67			1.33596
$765$		0			0
$766$	−1614.22	+	931.967i	−2.10733	+	1.21667i
$767$	285.509	+	494.516i	0.372241	+	0.644741i
$768$	781.618	+	451.267i	1.01773	+	0.587587i
$769$			17.8434i			0.0232033i	0.999933	+	0.0116017i	$0.00369301\pi$
$769$			17.8434i			0.0232033i	−0.999933	+	0.0116017i	$0.996307\pi$
$770$		0			0
$771$	−167.468			−0.217208
$772$	1017.84	−	1762.95i	1.31844	−	2.28361i
$773$	223.935	−	129.289i	0.289697	−	0.167256i	−0.348108	−	0.937454i	$-0.613176\pi$
$773$	223.935	−	129.289i	0.289697	−	0.167256i	0.637805	+	0.770198i	$0.279843\pi$
$774$	−391.943	−	678.865i	−0.506386	−	0.877086i
$775$		0			0
$776$		−	653.274i		−	0.841848i
$777$	311.996	+	10.8821i	0.401539	+	0.0140053i
$778$	688.281			0.884680
$779$	−55.6092	+	96.3180i	−0.0713854	+	0.123643i
$780$		0			0
$781$	−111.631	−	193.351i	−0.142934	−	0.247568i
$782$	2483.76	+	1434.00i	3.17616	+	1.83376i
$783$			127.256i			0.162524i
$784$	571.933	−	848.078i	0.729506	−	1.08173i
$785$		0			0
$786$	−334.088	+	578.657i	−0.425048	+	0.736204i
$787$	−936.494	+	540.685i	−1.18995	+	0.687020i	−0.958296	−	0.285777i	$-0.907748\pi$
$787$	−936.494	+	540.685i	−1.18995	+	0.687020i	−0.231658	+	0.972797i	$0.574415\pi$
$788$	−415.444	−	719.570i	−0.527213	−	0.913160i
$789$	96.3693	+	55.6388i	0.122141	+	0.0705182i
$790$		0			0
$791$	1.80212	−	51.6679i	0.00227828	−	0.0653198i
$792$	−120.348			−0.151954
$793$	−5.11357	+	8.85696i	−0.00644838	+	0.0111689i
$794$	89.1928	−	51.4955i	0.112333	−	0.0648558i
$795$		0			0
$796$	−572.527	−	330.549i	−0.719256	−	0.415262i
$797$		−	145.723i		−	0.182839i	−0.995812	−	0.0914195i	$-0.970860\pi$
$797$		−	145.723i		−	0.182839i	0.995812	−	0.0914195i	$-0.0291404\pi$
$798$	−1084.82	−	677.805i	−1.35942	−	0.849380i
$799$	78.4124			0.0981382
$800$		0			0
$801$	−169.533	+	97.8796i	−0.211651	+	0.122197i
$802$	−371.040	−	642.659i	−0.462643	−	0.801321i
$803$	−138.315	−	79.8564i	−0.172248	−	0.0994476i
$804$			945.749i			1.17630i
$805$		0			0
$806$	−1526.35			−1.89374
$807$	−171.096	+	296.347i	−0.212015	+	0.367220i
$808$	−2008.73	+	1159.74i	−2.48605	+	1.43532i
$809$	108.425	+	187.797i	0.134023	+	0.232134i	0.925224	−	0.379422i	$-0.123877\pi$
$809$	108.425	+	187.797i	0.134023	+	0.232134i	−0.791201	+	0.611556i	$0.790544\pi$
$810$		0			0
$811$		−	8.20233i		−	0.0101139i	−0.999987	−	0.00505693i	$-0.998390\pi$
$811$		−	8.20233i		−	0.0101139i	0.999987	−	0.00505693i	$-0.00160968\pi$
$812$	−1270.45	+	675.581i	−1.56460	+	0.831996i
$813$	−266.967			−0.328372
$814$	117.555	−	203.611i	0.144416	−	0.250136i
$815$		0			0
$816$	−419.512	−	726.616i	−0.514108	−	0.890460i
$817$	−1926.36	−	1112.18i	−2.35784	−	1.36130i
$818$			1142.33i			1.39650i
$819$	128.816	−	206.168i	0.157285	−	0.251731i
$820$		0			0
$821$	−786.474	+	1362.21i	−0.957946	+	1.65921i	−0.230469	+	0.973080i	$0.574026\pi$
$821$	−786.474	+	1362.21i	−0.957946	+	1.65921i	−0.727477	+	0.686132i	$0.759307\pi$
$822$	937.063	−	541.013i	1.13998	−	0.658167i
$823$	499.339	+	864.881i	0.606731	+	1.05089i	0.991775	+	0.127991i	$0.0408527\pi$
$823$	499.339	+	864.881i	0.606731	+	1.05089i	−0.385045	+	0.922898i	$0.625814\pi$
$824$	−1870.92	−	1080.18i	−2.27053	−	1.31089i
$825$		0			0
$826$	1214.81	+	42.3714i	1.47072	+	0.0512970i
$827$	1344.24			1.62544			0.812718	−	0.582658i	$-0.197987\pi$
$827$	1344.24			1.62544			0.812718	+	0.582658i	$0.197987\pi$
$828$	442.019	−	765.599i	0.533839	−	0.924637i
$829$	−1312.22	+	757.611i	−1.58290	+	0.913885i	−0.588462	+	0.808525i	$0.700266\pi$
$829$	−1312.22	+	757.611i	−1.58290	+	0.913885i	−0.994434	+	0.105360i	$0.966400\pi$
$830$		0			0
$831$	508.805	+	293.758i	0.612280	+	0.353500i
$832$			492.908i			0.592437i
$833$	1021.91	−	498.523i	1.22678	−	0.598467i
$834$	1035.94			1.24213
$835$		0			0
$836$	−565.014	+	326.211i	−0.675855	+	0.390205i
$837$	97.3065	+	168.540i	0.116256	+	0.201362i
$838$	2115.72	+	1221.51i	2.52473	+	1.45765i
$839$			439.769i			0.524159i	0.965046	+	0.262079i	$0.0844082\pi$
$839$			439.769i			0.524159i	−0.965046	+	0.262079i	$0.915592\pi$
$840$		0			0
$841$	−241.217			−0.286821
$842$	601.208	−	1041.32i	0.714024	−	1.23673i
$843$	−167.964	+	96.9743i	−0.199246	+	0.115035i
$844$	449.650	+	778.817i	0.532761	+	0.922769i
$845$		0			0
$846$		−	35.6886i		−	0.0421851i
$847$	678.379	+	423.859i	0.800920	+	0.500424i
$848$	835.833			0.985652
$849$	56.6453	−	98.1126i	0.0667201	−	0.115563i
$850$		0			0
$851$	451.997	+	782.881i	0.531136	+	0.919955i
$852$	−1083.74	−	625.697i	−1.27199	−	0.734386i
$853$		−	222.026i		−	0.260288i	−0.991495	−	0.130144i	$-0.958456\pi$
$853$		−	222.026i		−	0.260288i	0.991495	−	0.130144i	$-0.0415439\pi$
$854$	10.2216	+	19.2222i	0.0119691	+	0.0225084i
$855$		0			0
$856$	−1401.59	+	2427.62i	−1.63737	+	2.83601i
$857$	902.699	−	521.173i	1.05332	−	0.608137i	0.129746	−	0.991547i	$-0.458584\pi$
$857$	902.699	−	521.173i	1.05332	−	0.608137i	0.923578	+	0.383410i	$0.125250\pi$
$858$	−91.5411	−	158.554i	−0.106691	−	0.184795i
$859$	132.904	+	76.7321i	0.154719	+	0.0893272i	0.575361	−	0.817900i	$-0.304862\pi$
$859$	132.904	+	76.7321i	0.154719	+	0.0893272i	−0.420642	+	0.907227i	$0.638195\pi$
$860$		0			0
$861$	−39.7274	+	21.1256i	−0.0461410	+	0.0245361i
$862$	−1448.49			−1.68038
$863$	−401.493	+	695.406i	−0.465229	+	0.805800i	−0.999212	−	0.0396949i	$-0.987361\pi$
$863$	−401.493	+	695.406i	−0.465229	+	0.805800i	0.533983	+	0.845495i	$0.320695\pi$
$864$	−52.3110	+	30.2018i	−0.0605451	+	0.0349557i
$865$		0			0
$866$	−1352.01	−	780.582i	−1.56121	−	0.901365i
$867$		−	432.059i		−	0.498338i
$868$	−1166.02	+	1866.20i	−1.34334	+	2.15000i
$869$	71.4397			0.0822091
$870$		0			0
$871$	−652.195	+	376.545i	−0.748789	+	0.432313i
$872$	570.797	+	988.649i	0.654583	+	1.13377i
$873$	−109.736	−	63.3562i	−0.125700	−	0.0725730i
$874$		−	3704.05i		−	4.23804i
$875$		0			0
$876$	−895.197			−1.02191
$877$	−672.328	+	1164.51i	−0.766622	+	1.32783i	0.172763	+	0.984963i	$0.444731\pi$
$877$	−672.328	+	1164.51i	−0.766622	+	1.32783i	−0.939385	+	0.342865i	$0.888603\pi$
$878$	943.483	−	544.720i	1.07458	−	0.620410i
$879$	87.4613	+	151.487i	0.0995009	+	0.172341i
$880$		0			0
$881$		−	1052.91i		−	1.19513i	−0.801822	−	0.597563i	$-0.796136\pi$
$881$		−	1052.91i		−	1.19513i	0.801822	−	0.597563i	$-0.203864\pi$
$882$	−226.897	−	465.110i	−0.257253	−	0.527335i
$883$	−1372.84			−1.55475			−0.777375	−	0.629037i	$-0.783449\pi$
$883$	−1372.84			−1.55475			−0.777375	+	0.629037i	$0.783449\pi$
$884$	1127.33	−	1952.59i	1.27526	−	2.20881i
$885$		0			0
$886$	1441.02	+	2495.92i	1.62643	+	2.81706i
$887$	544.825	+	314.555i	0.614233	+	0.354628i	0.774620	−	0.632427i	$-0.217941\pi$
$887$	544.825	+	314.555i	0.614233	+	0.354628i	−0.160387	+	0.987054i	$0.551274\pi$
$888$		−	689.782i		−	0.776782i
$889$	−50.9090	+	1459.59i	−0.0572654	+	1.64183i
$890$		0			0
$891$	−11.6717	+	20.2159i	−0.0130995	+	0.0226890i
$892$	63.3864	−	36.5962i	0.0710610	−	0.0410271i
$893$	−50.6352	−	87.7028i	−0.0567024	−	0.0982114i
$894$	−450.891	−	260.322i	−0.504352	−	0.291188i
$895$		0			0
$896$	1165.90	+	728.466i	1.30122	+	0.813020i
$897$	703.950			0.784783
$898$	−555.798	+	962.671i	−0.618929	+	1.07202i
$899$	794.361	−	458.624i	0.883605	−	0.510150i
$900$		0			0
$901$	804.602	+	464.537i	0.893010	+	0.515580i
$902$			33.8862i			0.0375678i
$903$	−422.511	−	794.547i	−0.467897	−	0.879897i
$904$	−114.231			−0.126362
$905$		0			0
$906$	−728.704	+	420.717i	−0.804309	+	0.464368i
$907$	−29.8954	−	51.7804i	−0.0329608	−	0.0570897i	0.849074	−	0.528273i	$-0.177160\pi$
$907$	−29.8954	−	51.7804i	−0.0329608	−	0.0570897i	−0.882035	+	0.471183i	$0.843827\pi$
$908$	−1839.19	−	1061.86i	−2.02554	−	1.16944i
$909$			449.898i			0.494938i
$910$		0			0
$911$	−850.964			−0.934099			−0.467050	−	0.884231i	$-0.654683\pi$
$911$	−850.964			−0.934099			−0.467050	+	0.884231i	$0.654683\pi$
$912$	−541.804	+	938.432i	−0.594083	+	1.02898i
$913$	295.253	−	170.465i	0.323388	−	0.186708i
$914$	−329.700	−	571.057i	−0.360722	−	0.624788i
$915$		0			0
$916$		−	1221.06i		−	1.33304i
$917$	−406.455	+	650.525i	−0.443245	+	0.709406i
$918$	−424.473			−0.462389
$919$	−330.505	+	572.452i	−0.359636	+	0.622908i	−0.987900	−	0.155093i	$-0.950432\pi$
$919$	−330.505	+	572.452i	−0.359636	+	0.622908i	0.628264	+	0.778000i	$0.283766\pi$
$920$		0			0
$921$	−346.746	−	600.582i	−0.376489	−	0.652098i
$922$	25.2317	+	14.5675i	0.0273662	+	0.0157999i
$923$		−	996.472i		−	1.07960i
$924$	−263.787	−	9.20061i	−0.285484	−	0.00995737i
$925$		0			0
$926$	−832.448	+	1441.84i	−0.898972	+	1.55707i
$927$	−362.893	+	209.517i	−0.391471	+	0.226016i
$928$	142.347	+	246.552i	0.153391	+	0.265681i
$929$	−231.638	−	133.736i	−0.249341	−	0.143957i	0.370122	−	0.928983i	$-0.379316\pi$
$929$	−231.638	−	133.736i	−0.249341	−	0.143957i	−0.619462	+	0.785026i	$0.712649\pi$
$930$		0			0
$931$	−1217.49	−	821.059i	−1.30772	−	0.881911i
$932$	−2161.43			−2.31914
$933$	−31.1758	+	53.9980i	−0.0334145	+	0.0578757i
$934$	−2185.71	+	1261.92i	−2.34016	+	1.35109i
$935$		0			0
$936$	−465.178	−	268.571i	−0.496985	−	0.286934i
$937$		−	1625.83i		−	1.73515i	−0.497309	−	0.867573i	$-0.665679\pi$
$937$		−	1625.83i		−	1.73515i	0.497309	−	0.867573i	$-0.334321\pi$
$938$	−55.8817	+	1602.16i	−0.0595754	+	1.70806i
$939$	198.312			0.211194
$940$		0			0
$941$	−257.993	+	148.952i	−0.274168	+	0.158291i	−0.630780	−	0.775961i	$-0.717265\pi$
$941$	−257.993	+	148.952i	−0.274168	+	0.158291i	0.356612	+	0.934253i	$0.383932\pi$
$942$	−20.9351	−	36.2606i	−0.0222241	−	0.0384932i
$943$	−112.836	−	65.1460i	−0.119657	−	0.0690838i
$944$		−	1029.72i		−	1.09081i
$945$		0			0
$946$	−677.722			−0.716408
$947$	−456.876	+	791.333i	−0.482446	+	0.835621i	−0.999797	−	0.0201524i	$-0.993585\pi$
$947$	−456.876	+	791.333i	−0.482446	+	0.835621i	0.517351	+	0.855773i	$0.326918\pi$
$948$	346.776	−	200.211i	0.365798	−	0.211193i
$949$	−356.418	−	617.334i	−0.375572	−	0.650510i
$950$		0			0
$951$		−	6.98391i		−	0.00734375i
$952$	−1179.54	−	2218.16i	−1.23901	−	2.33000i
$953$	1451.89			1.52349			0.761746	−	0.647875i	$-0.224342\pi$
$953$	1451.89			1.52349			0.761746	+	0.647875i	$0.224342\pi$
$954$	211.429	−	366.206i	0.221624	−	0.383864i
$955$		0			0
$956$	540.040	+	935.377i	0.564896	+	0.978428i
$957$	95.2815	+	55.0108i	0.0995627	+	0.0574826i
$958$			724.878i			0.756657i
$959$	1096.74	−	583.208i	1.14363	−	0.608142i
$960$		0			0
$961$	220.874	−	382.566i	0.229838	−	0.398091i
$962$	908.762	−	524.674i	0.944659	−	0.545399i
$963$	271.859	+	470.874i	0.282305	+	0.488966i
$964$	67.3342	+	38.8754i	0.0698487	+	0.0403272i
$965$		0			0
$966$	794.047	−	1270.86i	0.821994	−	1.31559i
$967$	−235.985			−0.244039			−0.122019	−	0.992528i	$-0.538937\pi$
$967$	−235.985			−0.244039			−0.122019	+	0.992528i	$0.538937\pi$
$968$	883.710	−	1530.63i	0.912924	−	1.58123i
$969$	−1043.12	+	602.245i	−1.07649	+	0.621512i
$970$		0			0
$971$	−555.872	−	320.933i	−0.572474	−	0.330518i	0.185663	−	0.982613i	$-0.440557\pi$
$971$	−555.872	−	320.933i	−0.572474	−	0.330518i	−0.758137	+	0.652096i	$0.773890\pi$
$972$			130.840i			0.134609i
$973$	1188.53	+	41.4548i	1.22151	+	0.0426051i
$974$	−1136.67			−1.16701
$975$		0			0
$976$	15.9719	−	9.22136i	0.0163646	−	0.00944812i
$977$	320.423	+	554.990i	0.327967	+	0.568055i	0.982108	−	0.188317i	$-0.0603033\pi$
$977$	320.423	+	554.990i	0.327967	+	0.568055i	−0.654142	+	0.756372i	$0.726970\pi$
$978$	−1461.29	−	843.678i	−1.49417	−	0.862657i
$979$			169.247i			0.172878i
$980$		0			0
$981$	221.429			0.225718
$982$	−479.446	+	830.425i	−0.488235	+	0.845647i
$983$	368.692	−	212.865i	0.375068	−	0.216546i	−0.300602	−	0.953750i	$-0.597188\pi$
$983$	368.692	−	212.865i	0.375068	−	0.216546i	0.675670	+	0.737204i	$0.263854\pi$
$984$	49.7089	+	86.0984i	0.0505172	+	0.0874984i
$985$		0			0
$986$			2000.62i			2.02903i
$987$	1.42814	−	40.9456i	0.00144695	−	0.0414849i
$988$	−2911.92			−2.94728
$989$	1302.92	−	2256.72i	1.31741	−	2.28182i
$990$		0			0
$991$	548.625	+	950.247i	0.553608	+	0.958877i	0.998010	+	0.0630498i	$0.0200827\pi$
$991$	548.625	+	950.247i	0.553608	+	0.958877i	−0.444402	+	0.895827i	$0.646584\pi$
$992$	377.052	+	217.691i	0.380093	+	0.219447i
$993$			878.813i			0.885008i
$994$	−1798.96	−	1124.01i	−1.80981	−	1.13079i
$995$		0			0
$996$	955.461	−	1654.91i	0.959299	−	1.66155i
$997$	1104.16	−	637.487i	1.10748	−	0.639405i	0.169306	−	0.985564i	$-0.445847\pi$
$997$	1104.16	−	637.487i	1.10748	−	0.639405i	0.938176	+	0.346159i	$0.112514\pi$
$998$	−931.496	−	1613.40i	−0.933362	−	1.61663i
$999$	−115.869	−	66.8969i	−0.115985	−	0.0669639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.o.l.376.1		8
5.2	odd	4		525.3.s.h.124.1		16
5.3	odd	4		525.3.s.h.124.8		16
5.4	even	2		105.3.n.a.61.4	yes	8
7.3	odd	6	inner	525.3.o.l.451.1		8
15.14	odd	2		315.3.w.a.271.1		8
35.3	even	12		525.3.s.h.199.1		16
35.9	even	6		735.3.h.a.391.1		8
35.17	even	12		525.3.s.h.199.8		16
35.19	odd	6		735.3.h.a.391.2		8
35.24	odd	6		105.3.n.a.31.4	✓	8
105.59	even	6		315.3.w.a.136.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.4	✓	8	35.24	odd	6
105.3.n.a.61.4	yes	8	5.4	even	2
315.3.w.a.136.1		8	105.59	even	6
315.3.w.a.271.1		8	15.14	odd	2
525.3.o.l.376.1		8	1.1	even	1	trivial
525.3.o.l.451.1		8	7.3	odd	6	inner
525.3.s.h.124.1		16	5.2	odd	4
525.3.s.h.124.8		16	5.3	odd	4
525.3.s.h.199.1		16	35.3	even	12
525.3.s.h.199.8		16	35.17	even	12
735.3.h.a.391.1		8	35.9	even	6
735.3.h.a.391.2		8	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76021 + 3.04878i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-4.19671 - 7.26891i) q^{4} +6.09756i q^{6} +(-0.244004 + 6.99575i) q^{7} +15.4667 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.76021 + 3.04878i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-4.19671 - 7.26891i) q^{4} +6.09756i q^{6} +(-0.244004 + 6.99575i) q^{7} +15.4667 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.29685 - 2.24621i) q^{11} +(-12.5901 - 7.26891i) q^{12} -11.5763i q^{13} +(-20.8990 - 13.0579i) q^{14} +(-10.4379 + 18.0789i) q^{16} +(-20.0957 + 11.6023i) q^{17} +(5.28064 + 9.14634i) q^{18} +(25.9538 + 14.9844i) q^{19} +(5.69249 + 10.7049i) q^{21} +9.13094 q^{22} +(-17.5542 + 30.4048i) q^{23} +(23.2000 - 13.3945i) q^{24} +(35.2936 + 20.3768i) q^{26} -5.19615i q^{27} +(51.8754 - 27.5854i) q^{28} -24.4905 q^{29} +(-32.4355 + 18.7266i) q^{31} +(-5.81233 - 10.0673i) q^{32} +(-3.89055 - 2.24621i) q^{33} -81.6898i q^{34} -25.1802 q^{36} +(12.8743 - 22.2990i) q^{37} +(-91.3685 + 52.7516i) q^{38} +(-10.0254 - 17.3645i) q^{39} +3.71113i q^{41} +(-42.6570 - 1.48783i) q^{42} -74.2225 q^{43} +(-10.8850 + 18.8534i) q^{44} +(-61.7983 - 107.038i) q^{46} +(-2.92646 - 1.68959i) q^{47} +36.1578i q^{48} +(-48.8809 - 3.41398i) q^{49} +(-20.0957 + 34.8068i) q^{51} +(-84.1471 + 48.5823i) q^{52} +(-20.0193 - 34.6744i) q^{53} +(15.8419 + 9.14634i) q^{54} +(-3.77394 + 108.201i) q^{56} +51.9076 q^{57} +(43.1085 - 74.6661i) q^{58} +(-42.7180 + 24.6632i) q^{59} +(-0.765094 - 0.441727i) q^{61} -131.852i q^{62} +(17.8095 + 11.1276i) q^{63} -42.5790 q^{64} +(13.6964 - 7.90763i) q^{66} +(-32.5272 - 56.3388i) q^{67} +(168.671 + 97.3825i) q^{68} +60.8096i q^{69} +86.0786 q^{71} +(23.2000 - 40.1836i) q^{72} +(53.3274 - 30.7886i) q^{73} +(45.3231 + 78.5019i) q^{74} -251.541i q^{76} +(16.0304 - 8.52436i) q^{77} +70.5872 q^{78} +(-13.7718 + 23.8534i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-11.3144 - 6.53239i) q^{82} +131.445i q^{83} +(53.9235 - 86.3036i) q^{84} +(130.648 - 226.288i) q^{86} +(-36.7357 + 21.2094i) q^{87} +(-20.0580 - 34.7415i) q^{88} +(-56.5108 - 32.6265i) q^{89} +(80.9849 + 2.82467i) q^{91} +294.679 q^{92} +(-32.4355 + 56.1799i) q^{93} +(10.3024 - 5.94809i) q^{94} +(-17.4370 - 10.0673i) q^{96} -42.2375i q^{97} +(96.4494 - 143.018i) q^{98} -7.78111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9	\( 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9} + 20 q^{11} - 18 q^{12} - 16 q^{14} - 2 q^{16} + 18 q^{17} + 6 q^{18} + 48 q^{21} + 16 q^{22} - 62 q^{23} + 48 q^{24} + 120 q^{26} + 120 q^{28} - 100 q^{29} - 126 q^{31} - 36 q^{32} + 60 q^{33} - 36 q^{36} + 80 q^{37} - 114 q^{38} - 12 q^{39} - 90 q^{42} - 352 q^{43} - 18 q^{44} - 82 q^{46} + 72 q^{47} + 38 q^{49} + 18 q^{51} + 48 q^{52} + 76 q^{53} + 18 q^{54} + 196 q^{56} + 40 q^{58} - 54 q^{59} - 396 q^{61} + 96 q^{63} - 4 q^{64} + 24 q^{66} - 184 q^{67} + 312 q^{68} + 164 q^{71} + 48 q^{72} - 348 q^{73} - 140 q^{74} - 152 q^{77} + 240 q^{78} - 206 q^{79} - 36 q^{81} - 204 q^{82} + 132 q^{84} + 178 q^{86} - 150 q^{87} - 124 q^{88} + 282 q^{89} - 114 q^{91} + 288 q^{92} - 126 q^{93} + 30 q^{94} - 108 q^{96} + 592 q^{98} + 120 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9 + 20 * q^11 - 18 * q^12 - 16 * q^14 - 2 * q^16 + 18 * q^17 + 6 * q^18 + 48 * q^21 + 16 * q^22 - 62 * q^23 + 48 * q^24 + 120 * q^26 + 120 * q^28 - 100 * q^29 - 126 * q^31 - 36 * q^32 + 60 * q^33 - 36 * q^36 + 80 * q^37 - 114 * q^38 - 12 * q^39 - 90 * q^42 - 352 * q^43 - 18 * q^44 - 82 * q^46 + 72 * q^47 + 38 * q^49 + 18 * q^51 + 48 * q^52 + 76 * q^53 + 18 * q^54 + 196 * q^56 + 40 * q^58 - 54 * q^59 - 396 * q^61 + 96 * q^63 - 4 * q^64 + 24 * q^66 - 184 * q^67 + 312 * q^68 + 164 * q^71 + 48 * q^72 - 348 * q^73 - 140 * q^74 - 152 * q^77 + 240 * q^78 - 206 * q^79 - 36 * q^81 - 204 * q^82 + 132 * q^84 + 178 * q^86 - 150 * q^87 - 124 * q^88 + 282 * q^89 - 114 * q^91 + 288 * q^92 - 126 * q^93 + 30 * q^94 - 108 * q^96 + 592 * q^98 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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