LMFDB - Embedded newform 1050.3.p.f.451.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(451,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("1050.451");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.p (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 56 x^{10} + 300 x^{9} + 1007 x^{8} + 12456 x^{7} + 209990 x^{6} - 250384 x^{5} + \cdots + 6882692292 $ x^12 - 4x^11 + 56x^10 + 300x^9 + 1007x^8 + 12456x^7 + 209990x^6 - 250384x^5 + 4799806x^4 + 51487320x^3 - 123648876x^2 + 379489320*x + 6882692292
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.6
Root			$5.18297 + 5.32390i$ of defining polynomial
Character	$\chi$	$=$	1050.451
Dual form			1050.3.p.f.901.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(6.99501 - 0.264136i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(6.99501 - 0.264136i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.03457 - 3.52398i) q^{11} +(-3.00000 + 1.73205i) q^{12} +11.1199i q^{13} +(5.26972 + 8.38034i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-2.50807 - 1.44803i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(17.9363 - 10.3556i) q^{19} +(10.7213 + 5.66166i) q^{21} +5.75463 q^{22} +(15.3199 + 26.5348i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-13.6190 + 7.86292i) q^{26} +5.19615i q^{27} +(-6.53752 + 12.3799i) q^{28} -5.75463 q^{29} +(3.32136 + 1.91759i) q^{31} +(2.82843 - 4.89898i) q^{32} +(6.10371 - 3.52398i) q^{33} -4.09566i q^{34} -6.00000 q^{36} +(4.46151 + 7.72755i) q^{37} +(25.3658 + 14.6450i) q^{38} +(-9.63007 + 16.6798i) q^{39} +56.2622i q^{41} +(0.646999 + 17.1342i) q^{42} +7.16364 q^{43} +(4.06914 + 7.04796i) q^{44} +(-21.6656 + 37.5258i) q^{46} +(41.2277 - 23.8028i) q^{47} -6.92820i q^{48} +(48.8605 - 3.69527i) q^{49} +(-2.50807 - 4.34410i) q^{51} +(-19.2601 - 11.1199i) q^{52} +(-16.6629 + 28.8610i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-19.7849 + 0.747090i) q^{56} +35.8727 q^{57} +(-4.06914 - 7.04796i) q^{58} +(-38.3489 - 22.1407i) q^{59} +(-60.3282 + 34.8305i) q^{61} +5.42375i q^{62} +(11.1788 + 17.7774i) q^{63} +8.00000 q^{64} +(8.63195 + 4.98366i) q^{66} +(46.0565 - 79.7722i) q^{67} +(5.01614 - 2.89607i) q^{68} +53.0695i q^{69} +6.64679 q^{71} +(-4.24264 - 7.34847i) q^{72} +(45.3984 + 26.2108i) q^{73} +(-6.30952 + 10.9284i) q^{74} +41.4222i q^{76} +(13.3010 - 25.1877i) q^{77} -27.2380 q^{78} +(26.7215 + 46.2830i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-68.9069 + 39.7834i) q^{82} +116.101i q^{83} +(-20.5275 + 12.9081i) q^{84} +(5.06546 + 8.77363i) q^{86} +(-8.63195 - 4.98366i) q^{87} +(-5.75463 + 9.96732i) q^{88} +(-85.6511 + 49.4507i) q^{89} +(2.93716 + 77.7835i) q^{91} -61.2794 q^{92} +(3.32136 + 5.75276i) q^{93} +(58.3047 + 33.6623i) q^{94} +(8.48528 - 4.89898i) q^{96} -132.963i q^{97} +(39.0753 + 57.2286i) q^{98} +12.2074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9}+O(q^{10}) $ 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9	$ 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9} - 4 q^{11} - 36 q^{12} + 8 q^{14} - 24 q^{16} - 24 q^{17} + 12 q^{19} + 18 q^{21} + 24 q^{22} - 60 q^{23} - 24 q^{26} + 4 q^{28} - 24 q^{29} - 198 q^{31} - 12 q^{33} - 72 q^{36} + 70 q^{37} - 60 q^{38} - 36 q^{39} + 36 q^{42} - 84 q^{43} - 8 q^{44} + 32 q^{46} - 60 q^{47} + 28 q^{49} - 24 q^{51} - 72 q^{52} + 44 q^{53} + 40 q^{56} + 24 q^{57} + 8 q^{58} - 48 q^{59} + 186 q^{61} + 30 q^{63} + 96 q^{64} + 36 q^{66} + 152 q^{67} + 48 q^{68} - 136 q^{71} + 18 q^{73} - 64 q^{74} + 132 q^{77} - 48 q^{78} - 70 q^{79} - 54 q^{81} - 84 q^{82} - 12 q^{84} - 208 q^{86} - 36 q^{87} - 24 q^{88} + 168 q^{89} + 292 q^{91} + 240 q^{92} - 198 q^{93} - 204 q^{94} + 48 q^{98} - 24 q^{99}+O(q^{100}) $ 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9 - 4 * q^11 - 36 * q^12 + 8 * q^14 - 24 * q^16 - 24 * q^17 + 12 * q^19 + 18 * q^21 + 24 * q^22 - 60 * q^23 - 24 * q^26 + 4 * q^28 - 24 * q^29 - 198 * q^31 - 12 * q^33 - 72 * q^36 + 70 * q^37 - 60 * q^38 - 36 * q^39 + 36 * q^42 - 84 * q^43 - 8 * q^44 + 32 * q^46 - 60 * q^47 + 28 * q^49 - 24 * q^51 - 72 * q^52 + 44 * q^53 + 40 * q^56 + 24 * q^57 + 8 * q^58 - 48 * q^59 + 186 * q^61 + 30 * q^63 + 96 * q^64 + 36 * q^66 + 152 * q^67 + 48 * q^68 - 136 * q^71 + 18 * q^73 - 64 * q^74 + 132 * q^77 - 48 * q^78 - 70 * q^79 - 54 * q^81 - 84 * q^82 - 12 * q^84 - 208 * q^86 - 36 * q^87 - 24 * q^88 + 168 * q^89 + 292 * q^91 + 240 * q^92 - 198 * q^93 - 204 * q^94 + 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	6.99501	−	0.264136i	0.999288	−	0.0377338i
$7$	6.99501	−	0.264136i	0.999288	−	0.0377338i
$8$	−2.82843			−0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	2.03457	−	3.52398i	0.184961	−	0.320362i	−0.758602	−	0.651554i	$-0.774117\pi$
$11$	2.03457	−	3.52398i	0.184961	−	0.320362i	0.943563	+	0.331192i	$0.107451\pi$
$12$	−3.00000	+	1.73205i	−0.250000	+	0.144338i
$13$			11.1199i			0.855373i	0.903927	+	0.427687i	$0.140671\pi$
$13$			11.1199i			0.855373i	−0.903927	+	0.427687i	$0.859329\pi$
$14$	5.26972	+	8.38034i	0.376409	+	0.598595i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−2.50807	−	1.44803i	−0.147534	−	0.0851785i	0.424416	−	0.905467i	$-0.360479\pi$
$17$	−2.50807	−	1.44803i	−0.147534	−	0.0851785i	−0.571950	+	0.820289i	$0.693813\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	17.9363	−	10.3556i	0.944018	−	0.545029i	0.0528007	−	0.998605i	$-0.483185\pi$
$19$	17.9363	−	10.3556i	0.944018	−	0.545029i	0.891218	+	0.453576i	$0.149852\pi$
$20$		0			0
$21$	10.7213	+	5.66166i	0.510537	+	0.269603i
$22$	5.75463			0.261574
$23$	15.3199	+	26.5348i	0.666081	+	1.15369i	0.978991	+	0.203903i	$0.0653628\pi$
$23$	15.3199	+	26.5348i	0.666081	+	1.15369i	−0.312910	+	0.949783i	$0.601304\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	−13.6190	+	7.86292i	−0.523807	+	0.302420i
$27$			5.19615i			0.192450i
$28$	−6.53752	+	12.3799i	−0.233483	+	0.442138i
$29$	−5.75463			−0.198436			−0.0992178	−	0.995066i	$-0.531634\pi$
$29$	−5.75463			−0.198436			−0.0992178	+	0.995066i	$0.531634\pi$
$30$		0			0
$31$	3.32136	+	1.91759i	0.107141	+	0.0618576i	0.552613	−	0.833438i	$-0.313631\pi$
$31$	3.32136	+	1.91759i	0.107141	+	0.0618576i	−0.445472	+	0.895296i	$0.646964\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	6.10371	−	3.52398i	0.184961	−	0.106787i
$34$		−	4.09566i		−	0.120461i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	4.46151	+	7.72755i	0.120581	+	0.208853i	0.919997	−	0.391925i	$-0.128191\pi$
$37$	4.46151	+	7.72755i	0.120581	+	0.208853i	−0.799416	+	0.600778i	$0.794858\pi$
$38$	25.3658	+	14.6450i	0.667522	+	0.385394i
$39$	−9.63007	+	16.6798i	−0.246925	+	0.427687i
$40$		0			0
$41$			56.2622i			1.37225i	0.727484	+	0.686125i	$0.240689\pi$
$41$			56.2622i			1.37225i	−0.727484	+	0.686125i	$0.759311\pi$
$42$	0.646999	+	17.1342i	0.0154047	+	0.407958i
$43$	7.16364			0.166596			0.0832982	−	0.996525i	$-0.473455\pi$
$43$	7.16364			0.166596			0.0832982	+	0.996525i	$0.473455\pi$
$44$	4.06914	+	7.04796i	0.0924805	+	0.160181i
$45$		0			0
$46$	−21.6656	+	37.5258i	−0.470990	+	0.815779i
$47$	41.2277	−	23.8028i	0.877184	−	0.506443i	0.00745542	−	0.999972i	$-0.497627\pi$
$47$	41.2277	−	23.8028i	0.877184	−	0.506443i	0.869729	+	0.493530i	$0.164294\pi$
$48$		−	6.92820i		−	0.144338i
$49$	48.8605	−	3.69527i	0.997152	−	0.0754138i
$50$		0			0
$51$	−2.50807	−	4.34410i	−0.0491778	−	0.0851785i
$52$	−19.2601	−	11.1199i	−0.370387	−	0.213843i
$53$	−16.6629	+	28.8610i	−0.314395	+	0.544548i	−0.979309	−	0.202372i	$-0.935135\pi$
$53$	−16.6629	+	28.8610i	−0.314395	+	0.544548i	0.664914	+	0.746920i	$0.268468\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	−19.7849	+	0.747090i	−0.353302	+	0.0133409i
$57$	35.8727			0.629346
$58$	−4.06914	−	7.04796i	−0.0701576	−	0.121517i
$59$	−38.3489	−	22.1407i	−0.649981	−	0.375267i	0.138468	−	0.990367i	$-0.455782\pi$
$59$	−38.3489	−	22.1407i	−0.649981	−	0.375267i	−0.788449	+	0.615100i	$0.789116\pi$
$60$		0			0
$61$	−60.3282	+	34.8305i	−0.988987	+	0.570992i	−0.904971	−	0.425472i	$-0.860108\pi$
$61$	−60.3282	+	34.8305i	−0.988987	+	0.570992i	−0.0840158	+	0.996464i	$0.526775\pi$
$62$			5.42375i			0.0874799i
$63$	11.1788	+	17.7774i	0.177441	+	0.282181i
$64$	8.00000			0.125000
$65$		0			0
$66$	8.63195	+	4.98366i	0.130787	+	0.0755100i
$67$	46.0565	−	79.7722i	0.687410	−	1.19063i	−0.285263	−	0.958449i	$-0.592081\pi$
$67$	46.0565	−	79.7722i	0.687410	−	1.19063i	0.972673	−	0.232180i	$-0.0745858\pi$
$68$	5.01614	−	2.89607i	0.0737668	−	0.0425893i
$69$			53.0695i			0.769124i
$70$		0			0
$71$	6.64679			0.0936168			0.0468084	−	0.998904i	$-0.485095\pi$
$71$	6.64679			0.0936168			0.0468084	+	0.998904i	$0.485095\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	45.3984	+	26.2108i	0.621896	+	0.359052i	0.777607	−	0.628751i	$-0.216434\pi$
$73$	45.3984	+	26.2108i	0.621896	+	0.359052i	−0.155711	+	0.987803i	$0.549767\pi$
$74$	−6.30952	+	10.9284i	−0.0852638	+	0.147681i
$75$		0			0
$76$			41.4222i			0.545029i
$77$	13.3010	−	25.1877i	0.172741	−	0.327113i
$78$	−27.2380			−0.349205
$79$	26.7215	+	46.2830i	0.338247	+	0.585861i	0.984103	−	0.177598i	$-0.0568328\pi$
$79$	26.7215	+	46.2830i	0.338247	+	0.585861i	−0.645856	+	0.763459i	$0.723499\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−68.9069	+	39.7834i	−0.840327	+	0.485163i
$83$			116.101i			1.39880i	0.714729	+	0.699402i	$0.246550\pi$
$83$			116.101i			1.39880i	−0.714729	+	0.699402i	$0.753450\pi$
$84$	−20.5275	+	12.9081i	−0.244376	+	0.153668i
$85$		0			0
$86$	5.06546	+	8.77363i	0.0589007	+	0.102019i
$87$	−8.63195	−	4.98366i	−0.0992178	−	0.0572834i
$88$	−5.75463	+	9.96732i	−0.0653936	+	0.113265i
$89$	−85.6511	+	49.4507i	−0.962372	+	0.555626i	−0.896902	−	0.442229i	$-0.854188\pi$
$89$	−85.6511	+	49.4507i	−0.962372	+	0.555626i	−0.0654695	+	0.997855i	$0.520855\pi$
$90$		0			0
$91$	2.93716	+	77.7835i	0.0322764	+	0.854764i
$92$	−61.2794			−0.666081
$93$	3.32136	+	5.75276i	0.0357135	+	0.0618576i
$94$	58.3047	+	33.6623i	0.620263	+	0.358109i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$		−	132.963i		−	1.37075i	−0.728189	−	0.685377i	$-0.759638\pi$
$97$		−	132.963i		−	1.37075i	0.728189	−	0.685377i	$-0.240362\pi$
$98$	39.0753	+	57.2286i	0.398728	+	0.583966i
$99$	12.2074			0.123307
$100$		0			0
$101$	−52.3294	−	30.2124i	−0.518113	−	0.299133i	0.218049	−	0.975938i	$-0.430031\pi$
$101$	−52.3294	−	30.2124i	−0.518113	−	0.299133i	−0.736162	+	0.676805i	$0.763364\pi$
$102$	3.54695	−	6.14349i	0.0347740	−	0.0602303i
$103$	27.1191	−	15.6572i	0.263293	−	0.152012i	−0.362543	−	0.931967i	$-0.618091\pi$
$103$	27.1191	−	15.6572i	0.263293	−	0.152012i	0.625836	+	0.779955i	$0.284758\pi$
$104$		−	31.4517i		−	0.302420i
$105$		0			0
$106$	−47.1299			−0.444622
$107$	−23.5200	−	40.7378i	−0.219813	−	0.380727i	0.734938	−	0.678135i	$-0.237211\pi$
$107$	−23.5200	−	40.7378i	−0.219813	−	0.380727i	−0.954751	+	0.297407i	$0.903878\pi$
$108$	−9.00000	−	5.19615i	−0.0833333	−	0.0481125i
$109$	−100.779	+	174.554i	−0.924576	+	1.60141i	−0.132335	+	0.991205i	$0.542247\pi$
$109$	−100.779	+	174.554i	−0.924576	+	1.60141i	−0.792242	+	0.610208i	$0.791086\pi$
$110$		0			0
$111$			15.4551i			0.139235i
$112$	−14.9050	−	23.7032i	−0.133081	−	0.211635i
$113$	−168.422			−1.49046			−0.745230	−	0.666807i	$-0.767661\pi$
$113$	−168.422			−1.49046			−0.745230	+	0.666807i	$0.767661\pi$
$114$	25.3658	+	43.9349i	0.222507	+	0.385394i
$115$		0			0
$116$	5.75463	−	9.96732i	0.0496089	−	0.0859252i
$117$	−28.8902	+	16.6798i	−0.246925	+	0.142562i
$118$		−	62.6234i		−	0.530707i
$119$	−17.9265	−	9.46655i	−0.150643	−	0.0795509i
$120$		0			0
$121$	52.2210	+	90.4495i	0.431579	+	0.747517i
$122$	−85.3170	−	49.2578i	−0.699320	−	0.403752i
$123$	−48.7245	+	84.3933i	−0.396134	+	0.686125i
$124$	−6.64271	+	3.83517i	−0.0535703	+	0.0309288i
$125$		0			0
$126$	−13.8682	+	26.2616i	−0.110065	+	0.208426i
$127$	29.1799			0.229763			0.114882	−	0.993379i	$-0.463351\pi$
$127$	29.1799			0.229763			0.114882	+	0.993379i	$0.463351\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	10.7455	+	6.20390i	0.0832982	+	0.0480922i
$130$		0			0
$131$	123.441	−	71.2688i	0.942299	−	0.544037i	0.0516187	−	0.998667i	$-0.483562\pi$
$131$	123.441	−	71.2688i	0.942299	−	0.544037i	0.890680	+	0.454630i	$0.150229\pi$
$132$			14.0959i			0.106787i
$133$	122.730	−	77.1749i	0.922780	−	0.580262i
$134$	130.267			0.972145
$135$		0			0
$136$	7.09389	+	4.09566i	0.0521610	+	0.0301152i
$137$	104.297	−	180.648i	0.761295	−	1.31860i	−0.180889	−	0.983504i	$-0.557897\pi$
$137$	104.297	−	180.648i	0.761295	−	1.31860i	0.942183	−	0.335098i	$-0.108769\pi$
$138$	−64.9967	+	37.5258i	−0.470990	+	0.271926i
$139$		−	152.491i		−	1.09706i	−0.836132	−	0.548528i	$-0.815188\pi$
$139$		−	152.491i		−	1.09706i	0.836132	−	0.548528i	$-0.184812\pi$
$140$		0			0
$141$	82.4553			0.584790
$142$	4.69999	+	8.14062i	0.0330985	+	0.0573283i
$143$	39.1861	+	22.6241i	0.274029	+	0.158211i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$		0			0
$146$			74.1353i			0.507776i
$147$	76.4909	+	36.7715i	0.520346	+	0.250146i
$148$	−17.8460			−0.120581
$149$	−68.2572	−	118.225i	−0.458102	−	0.793456i	0.540759	−	0.841178i	$-0.318137\pi$
$149$	−68.2572	−	118.225i	−0.458102	−	0.793456i	−0.998861	+	0.0477221i	$0.984804\pi$
$150$		0			0
$151$	−64.7993	+	112.236i	−0.429134	+	0.743282i	−0.996797	−	0.0799793i	$-0.974515\pi$
$151$	−64.7993	+	112.236i	−0.429134	+	0.743282i	0.567662	+	0.823261i	$0.307848\pi$
$152$	−50.7317	+	29.2899i	−0.333761	+	0.192697i
$153$		−	8.68821i		−	0.0567857i
$154$	40.2538	−	1.52001i	0.261388	−	0.00987018i
$155$		0			0
$156$	−19.2601	−	33.3596i	−0.123462	−	0.213843i
$157$	116.268	+	67.1273i	0.740560	+	0.427562i	0.822273	−	0.569094i	$-0.192706\pi$
$157$	116.268	+	67.1273i	0.740560	+	0.427562i	−0.0817131	+	0.996656i	$0.526039\pi$
$158$	−37.7899	+	65.4540i	−0.239177	+	0.414266i
$159$	−49.9888	+	28.8610i	−0.314395	+	0.181516i
$160$		0			0
$161$	114.171	+	181.565i	0.709139	+	1.12773i
$162$	−12.7279			−0.0785674
$163$	−80.8126	−	139.972i	−0.495783	−	0.858721i	0.504205	−	0.863584i	$-0.331786\pi$
$163$	−80.8126	−	139.972i	−0.495783	−	0.858721i	−0.999988	+	0.00486254i	$0.998452\pi$
$164$	−97.4490	−	56.2622i	−0.594201	−	0.343062i
$165$		0			0
$166$	−142.194	+	82.0956i	−0.856589	+	0.494552i
$167$		−	166.987i		−	0.999920i	−0.866049	−	0.499960i	$-0.833348\pi$
$167$		−	166.987i		−	0.999920i	0.866049	−	0.499960i	$-0.166652\pi$
$168$	−30.3243	−	16.0136i	−0.180502	−	0.0953189i
$169$	45.3489			0.268337
$170$		0			0
$171$	53.8090	+	31.0667i	0.314673	+	0.181676i
$172$	−7.16364	+	12.4078i	−0.0416491	+	0.0721383i
$173$	−10.1276	+	5.84719i	−0.0585412	+	0.0337988i	−0.528985	−	0.848631i	$-0.677427\pi$
$173$	−10.1276	+	5.84719i	−0.0585412	+	0.0337988i	0.470444	+	0.882430i	$0.344094\pi$
$174$		−	14.0959i		−	0.0810110i
$175$		0			0
$176$	−16.2766			−0.0924805
$177$	−38.3489	−	66.4222i	−0.216660	−	0.375267i
$178$	−121.129	−	69.9338i	−0.680500	−	0.392887i
$179$	−66.8799	+	115.839i	−0.373631	+	0.647147i	−0.990121	−	0.140215i	$-0.955221\pi$
$179$	−66.8799	+	115.839i	−0.373631	+	0.647147i	0.616490	+	0.787363i	$0.288554\pi$
$180$		0			0
$181$			113.035i			0.624501i	0.950000	+	0.312251i	$0.101083\pi$
$181$			113.035i			0.624501i	−0.950000	+	0.312251i	$0.898917\pi$
$182$	−93.1881	+	58.5985i	−0.512022	+	0.321970i
$183$	−120.656			−0.659325
$184$	−43.3311	−	75.0517i	−0.235495	−	0.407890i
$185$		0			0
$186$	−4.69711	+	8.13563i	−0.0252533	+	0.0437399i
$187$	−10.2057	+	5.89226i	−0.0545759	+	0.0315094i
$188$			95.2112i			0.506443i
$189$	1.37249	+	36.3472i	0.00726187	+	0.192313i
$190$		0			0
$191$	−125.518	−	217.404i	−0.657163	−	1.13824i	−0.981347	−	0.192245i	$-0.938423\pi$
$191$	−125.518	−	217.404i	−0.657163	−	1.13824i	0.324184	−	0.945994i	$-0.394910\pi$
$192$	12.0000	+	6.92820i	0.0625000	+	0.0360844i
$193$	178.495	−	309.163i	0.924846	−	1.60188i	0.133038	−	0.991111i	$-0.457527\pi$
$193$	178.495	−	309.163i	0.924846	−	1.60188i	0.791809	−	0.610769i	$-0.209140\pi$
$194$	162.846	−	94.0191i	0.839412	−	0.484635i
$195$		0			0
$196$	−42.4601	+	88.3241i	−0.216633	+	0.450633i
$197$	−35.1268			−0.178309			−0.0891543	−	0.996018i	$-0.528416\pi$
$197$	−35.1268			−0.178309			−0.0891543	+	0.996018i	$0.528416\pi$
$198$	8.63195	+	14.9510i	0.0435957	+	0.0755100i
$199$	−79.3368	−	45.8051i	−0.398677	−	0.230177i	0.287236	−	0.957860i	$-0.407264\pi$
$199$	−79.3368	−	45.8051i	−0.398677	−	0.230177i	−0.685913	+	0.727683i	$0.740597\pi$
$200$		0			0
$201$	138.169	−	79.7722i	0.687410	−	0.396876i
$202$		−	85.4536i		−	0.423038i
$203$	−40.2538	+	1.52001i	−0.198294	+	0.00748772i
$204$	10.0323			0.0491778
$205$		0			0
$206$	38.3523	+	22.1427i	0.186176	+	0.107489i
$207$	−45.9596	+	79.6043i	−0.222027	+	0.384562i
$208$	38.5203	−	22.2397i	0.185194	−	0.106922i
$209$		−	84.2764i		−	0.403237i
$210$		0			0
$211$	8.70268			0.0412449			0.0206225	−	0.999787i	$-0.493435\pi$
$211$	8.70268			0.0412449			0.0206225	+	0.999787i	$0.493435\pi$
$212$	−33.3259	−	57.7221i	−0.157197	−	0.272274i
$213$	9.97019	+	5.75629i	0.0468084	+	0.0270248i
$214$	33.2623	−	57.6120i	0.155431	−	0.269215i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	23.7394	+	12.5363i	0.109398	+	0.0577708i
$218$	−285.045			−1.30755
$219$	45.3984	+	78.6323i	0.207299	+	0.359052i
$220$		0			0
$221$	16.1019	−	27.8894i	0.0728594	−	0.126196i
$222$	−18.9286	+	10.9284i	−0.0852638	+	0.0492271i
$223$		−	158.414i		−	0.710375i	−0.934795	−	0.355187i	$-0.884417\pi$
$223$		−	158.414i		−	0.710375i	0.934795	−	0.355187i	$-0.115583\pi$
$224$	18.4909	−	35.0155i	0.0825486	−	0.156319i
$225$		0			0
$226$	−119.092	−	206.274i	−0.526957	−	0.912717i
$227$	343.311	+	198.211i	1.51239	+	0.873176i	0.999895	+	0.0144830i	$0.00461024\pi$
$227$	343.311	+	198.211i	1.51239	+	0.873176i	0.512490	+	0.858693i	$0.328723\pi$
$228$	−35.8727	+	62.1333i	−0.157336	+	0.272515i
$229$	178.548	−	103.085i	0.779685	−	0.450151i	−0.0566339	−	0.998395i	$-0.518037\pi$
$229$	178.548	−	103.085i	0.779685	−	0.450151i	0.836319	+	0.548244i	$0.184703\pi$
$230$		0			0
$231$	41.7647	−	26.2625i	0.180800	−	0.113690i
$232$	16.2766			0.0701576
$233$	55.6555	+	96.3981i	0.238865	+	0.413726i	0.960389	−	0.278664i	$-0.0898915\pi$
$233$	55.6555	+	96.3981i	0.238865	+	0.413726i	−0.721524	+	0.692389i	$0.756558\pi$
$234$	−40.8569	−	23.5888i	−0.174602	−	0.100807i
$235$		0			0
$236$	76.6977	−	44.2815i	0.324990	−	0.187633i
$237$			92.5660i			0.390574i
$238$	−1.08181	−	28.6492i	−0.00454543	−	0.120375i
$239$	−258.839			−1.08301			−0.541504	−	0.840698i	$-0.682145\pi$
$239$	−258.839			−1.08301			−0.541504	+	0.840698i	$0.682145\pi$
$240$		0			0
$241$	264.996	+	152.995i	1.09957	+	0.634835i	0.936107	−	0.351715i	$-0.114401\pi$
$241$	264.996	+	152.995i	1.09957	+	0.634835i	0.163460	+	0.986550i	$0.447735\pi$
$242$	−73.8517	+	127.915i	−0.305172	+	0.528574i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		−	139.322i		−	0.570992i
$245$		0			0
$246$	−137.814			−0.560218
$247$	115.152	+	199.450i	0.466203	+	0.807488i
$248$	−9.39422	−	5.42375i	−0.0378799	−	0.0218700i
$249$	−100.546	+	174.151i	−0.403800	+	0.699402i
$250$		0			0
$251$		−	415.878i		−	1.65688i	−0.560076	−	0.828441i	$-0.689228\pi$
$251$		−	415.878i		−	1.65688i	0.560076	−	0.828441i	$-0.310772\pi$
$252$	−41.9701	+	1.58482i	−0.166548	+	0.00628896i
$253$	124.677			0.492796
$254$	20.6333	+	35.7380i	0.0812336	+	0.140701i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−271.280	+	156.624i	−1.05556	+	0.609430i	−0.924202	−	0.381904i	$-0.875268\pi$
$257$	−271.280	+	156.624i	−1.05556	+	0.609430i	−0.131362	+	0.991334i	$0.541935\pi$
$258$			17.5473i			0.0680127i
$259$	33.2494	+	52.8759i	0.128376	+	0.204154i
$260$		0			0
$261$	−8.63195	−	14.9510i	−0.0330726	−	0.0572834i
$262$	174.572	+	100.789i	0.666306	+	0.384692i
$263$	−44.2782	+	76.6921i	−0.168358	+	0.291605i	−0.937843	−	0.347061i	$-0.887180\pi$
$263$	−44.2782	+	76.6921i	−0.168358	+	0.291605i	0.769485	+	0.638665i	$0.220513\pi$
$264$	−17.2639	+	9.96732i	−0.0653936	+	0.0377550i
$265$		0			0
$266$	181.303	+	95.7417i	0.681589	+	0.359931i
$267$	−171.302			−0.641581
$268$	92.1130	+	159.544i	0.343705	+	0.595315i
$269$	−70.7545	−	40.8501i	−0.263028	−	0.151859i	0.362687	−	0.931911i	$-0.381859\pi$
$269$	−70.7545	−	40.8501i	−0.263028	−	0.151859i	−0.625715	+	0.780052i	$0.715193\pi$
$270$		0			0
$271$	254.904	−	147.169i	0.940604	−	0.543058i	0.0504543	−	0.998726i	$-0.483933\pi$
$271$	254.904	−	147.169i	0.940604	−	0.543058i	0.890150	+	0.455668i	$0.150600\pi$
$272$			11.5843i			0.0425893i
$273$	−62.9568	+	119.219i	−0.230611	+	0.436699i
$274$	294.998			1.07663
$275$		0			0
$276$	−91.9192	−	53.0695i	−0.333040	−	0.192281i
$277$	203.122	−	351.817i	0.733292	−	1.27010i	−0.222177	−	0.975006i	$-0.571316\pi$
$277$	203.122	−	351.817i	0.733292	−	1.27010i	0.955469	−	0.295092i	$-0.0953503\pi$
$278$	186.762	−	107.827i	0.671807	−	0.387868i
$279$			11.5055i			0.0412384i
$280$		0			0
$281$	−234.304			−0.833823			−0.416912	−	0.908947i	$-0.636888\pi$
$281$	−234.304			−0.833823			−0.416912	+	0.908947i	$0.636888\pi$
$282$	58.3047	+	100.987i	0.206754	+	0.358109i
$283$	237.575	+	137.164i	0.839488	+	0.484678i	0.857090	−	0.515167i	$-0.172270\pi$
$283$	237.575	+	137.164i	0.839488	+	0.484678i	−0.0176023	+	0.999845i	$0.505603\pi$
$284$	−6.64679	+	11.5126i	−0.0234042	+	0.0405372i
$285$		0			0
$286$			63.9907i			0.223744i
$287$	14.8609	+	393.555i	0.0517801	+	1.37127i
$288$	16.9706			0.0589256
$289$	−140.306	−	243.018i	−0.485489	−	0.840892i
$290$		0			0
$291$	115.149	−	199.445i	0.395702	−	0.685377i
$292$	−90.7968	+	52.4215i	−0.310948	+	0.179526i
$293$		−	64.7274i		−	0.220913i	−0.993881	−	0.110456i	$-0.964769\pi$
$293$		−	64.7274i		−	0.220913i	0.993881	−	0.110456i	$-0.0352312\pi$
$294$	9.05154	+	119.683i	0.0307875	+	0.407086i
$295$		0			0
$296$	−12.6190	−	21.8568i	−0.0426319	−	0.0738406i
$297$	18.3111	+	10.5719i	0.0616537	+	0.0355958i
$298$	96.5302	−	167.195i	0.323927	−	0.561058i
$299$	−295.063	+	170.355i	−0.986832	+	0.569748i
$300$		0			0
$301$	50.1098	−	1.89218i	0.166478	−	0.00628631i
$302$	−183.280			−0.606887
$303$	−52.3294	−	90.6372i	−0.172704	−	0.299133i
$304$	−71.7454	−	41.4222i	−0.236005	−	0.136257i
$305$		0			0
$306$	10.6408	−	6.14349i	0.0347740	−	0.0200768i
$307$		−	164.065i		−	0.534413i	−0.963639	−	0.267207i	$-0.913899\pi$
$307$		−	164.065i		−	0.534413i	0.963639	−	0.267207i	$-0.0861006\pi$
$308$	30.3253	+	48.2258i	0.0984588	+	0.156577i
$309$	54.2383			0.175528
$310$		0			0
$311$	−197.874	−	114.243i	−0.636252	−	0.367340i	0.146918	−	0.989149i	$-0.453065\pi$
$311$	−197.874	−	114.243i	−0.636252	−	0.367340i	−0.783169	+	0.621809i	$0.786398\pi$
$312$	27.2380	−	47.1775i	0.0873012	−	0.151210i
$313$	448.148	−	258.738i	1.43178	−	0.826640i	0.434526	−	0.900659i	$-0.356916\pi$
$313$	448.148	−	258.738i	1.43178	−	0.826640i	0.997257	+	0.0740194i	$0.0235827\pi$
$314$			189.865i			0.604664i
$315$		0			0
$316$	−106.886			−0.338247
$317$	147.654	+	255.744i	0.465785	+	0.806764i	0.999237	−	0.0390670i	$-0.0124386\pi$
$317$	147.654	+	255.744i	0.465785	+	0.806764i	−0.533451	+	0.845831i	$0.679105\pi$
$318$	−70.6948	−	40.8157i	−0.222311	−	0.128351i
$319$	−11.7082	+	20.2792i	−0.0367029	+	0.0635712i
$320$		0			0
$321$		−	81.4756i		−	0.253818i
$322$	−141.639	+	268.216i	−0.439872	+	0.832970i
$323$	−59.9808			−0.185699
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	114.286	−	197.950i	0.350572	−	0.607208i
$327$	−302.336	+	174.554i	−0.924576	+	0.533804i
$328$		−	159.134i		−	0.485163i
$329$	282.101	−	177.391i	0.857450	−	0.539181i
$330$		0			0
$331$	−311.691	−	539.864i	−0.941663	−	1.63101i	−0.762298	−	0.647226i	$-0.775929\pi$
$331$	−311.691	−	539.864i	−0.941663	−	1.63101i	−0.179366	−	0.983782i	$-0.557404\pi$
$332$	−201.092	−	116.101i	−0.605700	−	0.349701i
$333$	−13.3845	+	23.1827i	−0.0401937	+	0.0696176i
$334$	204.516	−	118.077i	0.612323	−	0.353525i
$335$		0			0
$336$	−1.82999	−	48.4629i	−0.00544640	−	0.144235i
$337$	0.0404399			0.000120000			5.99998e−5	−	1.00000i	$-0.499981\pi$
$337$	0.0404399			0.000120000			5.99998e−5		1.00000i	$0.499981\pi$
$338$	32.0665	+	55.5408i	0.0948714	+	0.164322i
$339$	−252.633	−	145.858i	−0.745230	−	0.430259i
$340$		0			0
$341$	13.5151	−	7.80293i	0.0396336	−	0.0228825i
$342$			87.8698i			0.256929i
$343$	340.804	−	38.7543i	0.993597	−	0.112986i
$344$	−20.2618			−0.0589007
$345$		0			0
$346$	−14.3226	−	8.26918i	−0.0413949	−	0.0238994i
$347$	60.8256	−	105.353i	0.175290	−	0.303611i	−0.764972	−	0.644064i	$-0.777247\pi$
$347$	60.8256	−	105.353i	0.175290	−	0.303611i	0.940262	+	0.340453i	$0.110580\pi$
$348$	17.2639	−	9.96732i	0.0496089	−	0.0286417i
$349$		−	457.192i		−	1.31001i	−0.755626	−	0.655003i	$-0.772667\pi$
$349$		−	457.192i		−	1.31001i	0.755626	−	0.655003i	$-0.227333\pi$
$350$		0			0
$351$	−57.7804			−0.164617
$352$	−11.5093	−	19.9346i	−0.0326968	−	0.0566325i
$353$	23.6695	+	13.6656i	0.0670525	+	0.0387128i	0.533151	−	0.846020i	$-0.321008\pi$
$353$	23.6695	+	13.6656i	0.0670525	+	0.0387128i	−0.466099	+	0.884733i	$0.654341\pi$
$354$	54.2335	−	93.9352i	0.153202	−	0.265354i
$355$		0			0
$356$		−	197.803i		−	0.555626i
$357$	−18.6914	−	29.7246i	−0.0523569	−	0.0832622i
$358$	−189.165			−0.528394
$359$	231.018	+	400.135i	0.643504	+	1.11458i	0.984645	+	0.174569i	$0.0558532\pi$
$359$	231.018	+	400.135i	0.643504	+	1.11458i	−0.341141	+	0.940012i	$0.610813\pi$
$360$		0			0
$361$	33.9751	−	58.8466i	0.0941138	−	0.163010i
$362$	−138.439	+	79.9276i	−0.382427	+	0.220794i
$363$			180.899i			0.498344i
$364$	−137.662	−	72.6962i	−0.378193	−	0.199715i
$365$		0			0
$366$	−85.3170	−	147.773i	−0.233107	−	0.403752i
$367$	372.413	+	215.013i	1.01475	+	0.585865i	0.912578	−	0.408902i	$-0.134088\pi$
$367$	372.413	+	215.013i	1.01475	+	0.585865i	0.102170	+	0.994767i	$0.467421\pi$
$368$	61.2794	−	106.139i	0.166520	−	0.288421i
$369$	−146.174	+	84.3933i	−0.396134	+	0.228708i
$370$		0			0
$371$	−108.934	+	206.285i	−0.293623	+	0.556024i
$372$	−13.2854			−0.0357135
$373$	−334.967	−	580.179i	−0.898034	−	1.55544i	−0.830004	−	0.557757i	$-0.811662\pi$
$373$	−334.967	−	580.179i	−0.898034	−	1.55544i	−0.0680300	−	0.997683i	$-0.521671\pi$
$374$	−14.4330	−	8.33291i	−0.0385910	−	0.0222805i
$375$		0			0
$376$	−116.609	+	67.3245i	−0.310132	+	0.179055i
$377$		−	63.9907i		−	0.169737i
$378$	−43.5455	+	27.3823i	−0.115200	+	0.0724399i
$379$	704.346			1.85843			0.929216	−	0.369536i	$-0.120483\pi$
$379$	704.346			1.85843			0.929216	+	0.369536i	$0.120483\pi$
$380$		0			0
$381$	43.7699	+	25.2706i	0.114882	+	0.0663269i
$382$	177.509	−	307.455i	0.464684	−	0.804857i
$383$	25.6663	−	14.8185i	0.0670139	−	0.0386905i	−0.466119	−	0.884722i	$-0.654348\pi$
$383$	25.6663	−	14.8185i	0.0670139	−	0.0386905i	0.533133	+	0.846032i	$0.321015\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	504.861			1.30793
$387$	10.7455	+	18.6117i	0.0277661	+	0.0480922i
$388$	230.299	+	132.963i	0.593554	+	0.342688i
$389$	18.4085	−	31.8844i	0.0473225	−	0.0819650i	−0.841394	−	0.540422i	$-0.818264\pi$
$389$	18.4085	−	31.8844i	0.0473225	−	0.0819650i	0.888716	+	0.458457i	$0.151598\pi$
$390$		0			0
$391$		−	88.7348i		−	0.226943i
$392$	−138.198	+	10.4518i	−0.352547	+	0.0266628i
$393$	246.882			0.628199
$394$	−24.8384	−	43.0213i	−0.0630416	−	0.109191i
$395$		0			0
$396$	−12.2074	+	21.1439i	−0.0308268	+	0.0533936i
$397$	−79.6635	+	45.9937i	−0.200664	+	0.115853i	−0.596965	−	0.802267i	$-0.703627\pi$
$397$	−79.6635	+	45.9937i	−0.200664	+	0.115853i	0.396301	+	0.918121i	$0.370294\pi$
$398$		−	129.556i		−	0.325519i
$399$	250.930	−	9.47528i	0.628897	−	0.0237476i
$400$		0			0
$401$	−178.114	−	308.502i	−0.444174	−	0.769332i	0.553820	−	0.832636i	$-0.313170\pi$
$401$	−178.114	−	308.502i	−0.444174	−	0.769332i	−0.997994	+	0.0633041i	$0.979836\pi$
$402$	195.401	+	112.815i	0.486072	+	0.280634i
$403$	−21.3233	+	36.9330i	−0.0529113	+	0.0916451i
$404$	104.659	−	60.4248i	0.259057	−	0.149566i
$405$		0			0
$406$	−30.3253	−	48.2258i	−0.0746929	−	0.118783i
$407$	36.3090			0.0892113
$408$	7.09389	+	12.2870i	0.0173870	+	0.0301152i
$409$	−20.9491	−	12.0950i	−0.0512203	−	0.0295720i	0.474171	−	0.880433i	$-0.342748\pi$
$409$	−20.9491	−	12.0950i	−0.0512203	−	0.0295720i	−0.525391	+	0.850861i	$0.676081\pi$
$410$		0			0
$411$	312.892	−	180.648i	0.761295	−	0.439534i
$412$			62.6290i			0.152012i
$413$	−274.099	−	144.745i	−0.663678	−	0.350473i
$414$	−129.993			−0.313994
$415$		0			0
$416$	54.4759	+	31.4517i	0.130952	+	0.0756050i
$417$	132.061	−	228.736i	0.316693	−	0.548528i
$418$	103.217	−	59.5924i	0.246931	−	0.142566i
$419$			537.398i			1.28257i	0.767302	+	0.641286i	$0.221599\pi$
$419$			537.398i			1.28257i	−0.767302	+	0.641286i	$0.778401\pi$
$420$		0			0
$421$	−644.404			−1.53065			−0.765326	−	0.643643i	$-0.777422\pi$
$421$	−644.404			−1.53065			−0.765326	+	0.643643i	$0.777422\pi$
$422$	6.15372	+	10.6586i	0.0145823	+	0.0252573i
$423$	123.683	+	71.4084i	0.292395	+	0.168814i
$424$	47.1299	−	81.6314i	0.111155	−	0.192527i
$425$		0			0
$426$			16.2812i			0.0382189i
$427$	−412.797	+	259.575i	−0.966737	+	0.607904i
$428$	94.0799			0.219813
$429$	39.1861	+	67.8724i	0.0913430	+	0.158211i
$430$		0			0
$431$	233.686	−	404.756i	0.542195	−	0.939109i	−0.456583	−	0.889681i	$-0.650927\pi$
$431$	233.686	−	404.756i	0.542195	−	0.939109i	0.998778	−	0.0494278i	$-0.0157398\pi$
$432$	18.0000	−	10.3923i	0.0416667	−	0.0240563i
$433$		−	33.2022i		−	0.0766794i	−0.999265	−	0.0383397i	$-0.987793\pi$
$433$		−	33.2022i		−	0.0766794i	0.999265	−	0.0383397i	$-0.0122069\pi$
$434$	1.43261	+	37.9392i	0.00330094	+	0.0874176i
$435$		0			0
$436$	−201.558	−	349.108i	−0.462288	−	0.800706i
$437$	549.565	+	317.291i	1.25759	+	0.726067i
$438$	−64.2030	+	111.203i	−0.146582	+	0.253888i
$439$	−44.2179	+	25.5292i	−0.100724	+	0.0581531i	−0.549516	−	0.835483i	$-0.685188\pi$
$439$	−44.2179	+	25.5292i	−0.100724	+	0.0581531i	0.448792	+	0.893636i	$0.351855\pi$
$440$		0			0
$441$	82.8913	+	121.400i	0.187962	+	0.275284i
$442$	45.5431			0.103039
$443$	−396.329	−	686.462i	−0.894648	−	1.54958i	−0.834240	−	0.551401i	$-0.814093\pi$
$443$	−396.329	−	686.462i	−0.894648	−	1.54958i	−0.0604076	−	0.998174i	$-0.519240\pi$
$444$	−26.7690	−	15.4551i	−0.0602906	−	0.0348088i
$445$		0			0
$446$	194.016	−	112.015i	0.435014	−	0.251155i
$447$		−	236.450i		−	0.528970i
$448$	55.9601	−	2.11309i	0.124911	−	0.00471672i
$449$	71.7539			0.159808			0.0799041	−	0.996803i	$-0.474539\pi$
$449$	71.7539			0.159808			0.0799041	+	0.996803i	$0.474539\pi$
$450$		0			0
$451$	198.267	+	114.469i	0.439616	+	0.253812i
$452$	168.422	−	291.716i	0.372615	−	0.645388i
$453$	−194.398	+	112.236i	−0.429134	+	0.247761i
$454$			560.625i			1.23486i
$455$		0			0
$456$	−101.463			−0.222507
$457$	−314.013	−	543.886i	−0.687117	−	1.19012i	−0.972766	−	0.231787i	$-0.925543\pi$
$457$	−314.013	−	543.886i	−0.687117	−	1.19012i	0.285649	−	0.958334i	$-0.407791\pi$
$458$	252.505	+	145.784i	0.551320	+	0.318305i
$459$	7.52421	−	13.0323i	0.0163926	−	0.0283928i
$460$		0			0
$461$		−	475.402i		−	1.03124i	−0.856817	−	0.515621i	$-0.827561\pi$
$461$		−	475.402i		−	1.03124i	0.856817	−	0.515621i	$-0.172439\pi$
$462$	61.6970	+	32.5808i	0.133543	+	0.0705211i
$463$	342.588			0.739931			0.369966	−	0.929045i	$-0.379369\pi$
$463$	342.588			0.739931			0.369966	+	0.929045i	$0.379369\pi$
$464$	11.5093	+	19.9346i	0.0248045	+	0.0429626i
$465$		0			0
$466$	−78.7087	+	136.327i	−0.168903	+	0.292548i
$467$	−220.056	+	127.049i	−0.471211	+	0.272054i	−0.716747	−	0.697334i	$-0.754370\pi$
$467$	−220.056	+	127.049i	−0.471211	+	0.272054i	0.245535	+	0.969388i	$0.421036\pi$
$468$		−	66.7191i		−	0.142562i
$469$	301.095	−	570.173i	0.641994	−	1.21572i
$470$		0			0
$471$	116.268	+	201.382i	0.246853	+	0.427562i
$472$	108.467	+	62.6234i	0.229803	+	0.132677i
$473$	14.5749	−	25.2445i	0.0308138	−	0.0533711i
$474$	−113.370	+	65.4540i	−0.239177	+	0.138089i
$475$		0			0
$476$	34.3230	−	21.5830i	0.0721072	−	0.0453424i
$477$	−99.9776			−0.209597
$478$	−183.027	−	317.012i	−0.382901	−	0.663204i
$479$	−278.924	−	161.037i	−0.582305	−	0.336194i	0.179744	−	0.983713i	$-0.442473\pi$
$479$	−278.924	−	161.037i	−0.582305	−	0.336194i	−0.762049	+	0.647519i	$0.775806\pi$
$480$		0			0
$481$	−85.9293	+	49.6113i	−0.178647	+	0.103142i
$482$			432.736i			0.897793i
$483$	14.0176	+	371.222i	0.0290219	+	0.768576i
$484$	−208.884			−0.431579
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	−97.1552	+	168.278i	−0.199497	+	0.345539i	−0.948366	−	0.317180i	$-0.897264\pi$
$487$	−97.1552	+	168.278i	−0.199497	+	0.345539i	0.748868	+	0.662719i	$0.230598\pi$
$488$	170.634	−	98.5156i	0.349660	−	0.201876i
$489$		−	279.943i		−	0.572481i
$490$		0			0
$491$	−491.719			−1.00146			−0.500732	−	0.865602i	$-0.666936\pi$
$491$	−491.719			−1.00146			−0.500732	+	0.865602i	$0.666936\pi$
$492$	−97.4490	−	168.787i	−0.198067	−	0.343062i
$493$	14.4330	+	8.33291i	0.0292759	+	0.0169025i
$494$	−162.850	+	282.064i	−0.329656	+	0.570980i
$495$		0			0
$496$		−	15.3407i		−	0.0309288i
$497$	46.4944	−	1.75566i	0.0935501	−	0.00353251i
$498$	−284.388			−0.571059
$499$	−38.5757	−	66.8150i	−0.0773060	−	0.133898i	0.824781	−	0.565453i	$-0.191298\pi$
$499$	−38.5757	−	66.8150i	−0.0773060	−	0.133898i	−0.902087	+	0.431555i	$0.857965\pi$
$500$		0			0
$501$	144.615	−	250.480i	0.288652	−	0.499960i
$502$	509.344	−	294.070i	1.01463	−	0.585797i
$503$			772.176i			1.53514i	0.640965	+	0.767571i	$0.278535\pi$
$503$			772.176i			1.53514i	−0.640965	+	0.767571i	$0.721465\pi$
$504$	−31.6183	−	50.2820i	−0.0627348	−	0.0997659i
$505$		0			0
$506$	88.1602	+	152.698i	0.174230	+	0.301775i
$507$	68.0234	+	39.2733i	0.134168	+	0.0774621i
$508$	−29.1799	+	50.5411i	−0.0574408	+	0.0994904i
$509$	583.669	−	336.981i	1.14670	−	0.662046i	0.198617	−	0.980077i	$-0.436355\pi$
$509$	583.669	−	336.981i	1.14670	−	0.662046i	0.948080	+	0.318032i	$0.103022\pi$
$510$		0			0
$511$	324.486	+	171.353i	0.635001	+	0.335329i
$512$	−22.6274			−0.0441942
$513$	53.8090	+	93.2000i	0.104891	+	0.181676i
$514$	−383.648	−	221.499i	−0.746396	−	0.430932i
$515$		0			0
$516$	−21.4909	+	12.4078i	−0.0416491	+	0.0240461i
$517$		−	193.714i		−	0.374689i
$518$	−41.2486	+	78.1110i	−0.0796305	+	0.150793i
$519$	−20.2553			−0.0390275
$520$		0			0
$521$	275.030	+	158.788i	0.527888	+	0.304776i	0.740156	−	0.672435i	$-0.234752\pi$
$521$	275.030	+	158.788i	0.527888	+	0.304776i	−0.212268	+	0.977211i	$0.568085\pi$
$522$	12.2074	−	21.1439i	0.0233859	−	0.0405055i
$523$	−606.691	+	350.273i	−1.16002	+	0.669739i	−0.951309	−	0.308238i	$-0.900261\pi$
$523$	−606.691	+	350.273i	−1.16002	+	0.669739i	−0.208713	+	0.977977i	$0.566927\pi$
$524$			285.075i			0.544037i
$525$		0			0
$526$	−125.238			−0.238094
$527$	−5.55346	−	9.61888i	−0.0105379	−	0.0182521i
$528$	−24.4148	−	14.0959i	−0.0462402	−	0.0266968i
$529$	−204.896	+	354.891i	−0.387327	+	0.670871i
$530$		0			0
$531$		−	132.844i		−	0.250178i
$532$	10.9411	+	289.749i	0.0205660	+	0.544641i
$533$	−625.627			−1.17379
$534$	−121.129	−	209.801i	−0.226833	−	0.392887i
$535$		0			0
$536$	−130.267	+	225.630i	−0.243036	+	0.420951i
$537$	−200.640	+	115.839i	−0.373631	+	0.215716i
$538$		−	115.542i		−	0.214761i
$539$	86.3880	−	179.702i	0.160275	−	0.333398i
$540$		0			0
$541$	−23.3027	−	40.3614i	−0.0430733	−	0.0746052i	0.843685	−	0.536839i	$-0.180382\pi$
$541$	−23.3027	−	40.3614i	−0.0430733	−	0.0746052i	−0.886758	+	0.462233i	$0.847048\pi$
$542$	360.488	+	208.128i	0.665107	+	0.384000i
$543$	−97.8909	+	169.552i	−0.180278	+	0.312251i
$544$	−14.1878	+	8.19132i	−0.0260805	+	0.0150576i
$545$		0			0
$546$	−190.530	+	7.19454i	−0.348956	+	0.0131768i
$547$	−886.307			−1.62031			−0.810153	−	0.586219i	$-0.800616\pi$
$547$	−886.307			−1.62031			−0.810153	+	0.586219i	$0.800616\pi$
$548$	208.595	+	361.297i	0.380647	+	0.659301i
$549$	−180.985	−	104.492i	−0.329662	−	0.190331i
$550$		0			0
$551$	−103.217	+	59.5924i	−0.187327	+	0.108153i
$552$		−	150.103i		−	0.271926i
$553$	199.142	+	316.692i	0.360113	+	0.572680i
$554$	574.515			1.03703
$555$		0			0
$556$	264.122	+	152.491i	0.475039	+	0.274264i
$557$	289.104	−	500.743i	0.519038	−	0.899000i	−0.480717	−	0.876876i	$-0.659624\pi$
$557$	289.104	−	500.743i	0.519038	−	0.899000i	0.999755	−	0.0221246i	$-0.00704307\pi$
$558$	−14.0913	+	8.13563i	−0.0252533	+	0.0145800i
$559$			79.6586i			0.142502i
$560$		0			0
$561$	−20.4114			−0.0363839
$562$	−165.678	−	286.963i	−0.294801	−	0.510610i
$563$	−129.465	−	74.7467i	−0.229956	−	0.132765i	0.380596	−	0.924741i	$-0.375719\pi$
$563$	−129.465	−	74.7467i	−0.229956	−	0.132765i	−0.610552	+	0.791976i	$0.709052\pi$
$564$	−82.4553	+	142.817i	−0.146197	+	0.253221i
$565$		0			0
$566$			387.958i			0.685439i
$567$	−29.4188	+	55.7094i	−0.0518851	+	0.0982528i
$568$	−18.8000			−0.0330985
$569$	−79.3178	−	137.382i	−0.139399	−	0.241446i	0.787871	−	0.615841i	$-0.211184\pi$
$569$	−79.3178	−	137.382i	−0.139399	−	0.241446i	−0.927269	+	0.374395i	$0.877850\pi$
$570$		0			0
$571$	7.86886	−	13.6293i	0.0137808	−	0.0238691i	−0.859053	−	0.511887i	$-0.828947\pi$
$571$	7.86886	−	13.6293i	0.0137808	−	0.0238691i	0.872834	+	0.488018i	$0.162280\pi$
$572$	−78.3723	+	45.2482i	−0.137014	+	0.0791053i
$573$		−	434.807i		−	0.758826i
$574$	−471.496	+	296.486i	−0.821422	+	0.516526i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−143.510	−	82.8557i	−0.248718	−	0.143597i	0.370459	−	0.928849i	$-0.379200\pi$
$577$	−143.510	−	82.8557i	−0.248718	−	0.143597i	−0.619177	+	0.785251i	$0.712534\pi$
$578$	198.423	−	343.679i	0.343293	−	0.594600i
$579$	535.486	−	309.163i	0.924846	−	0.533960i
$580$		0			0
$581$	30.6664	+	812.126i	0.0527821	+	1.39781i
$582$	325.692			0.559608
$583$	67.8038	+	117.440i	0.116302	+	0.201440i
$584$	−128.406	−	74.1353i	−0.219873	−	0.126944i
$585$		0			0
$586$	79.2745	−	45.7692i	0.135281	−	0.0781044i
$587$			466.624i			0.794929i	0.917617	+	0.397465i	$0.130110\pi$
$587$			466.624i			0.794929i	−0.917617	+	0.397465i	$0.869890\pi$
$588$	−140.181	+	95.7146i	−0.238403	+	0.162780i
$589$	79.4307			0.134857
$590$		0			0
$591$	−52.6902	−	30.4207i	−0.0891543	−	0.0514732i
$592$	17.8460	−	30.9102i	0.0301453	−	0.0522132i
$593$	193.493	−	111.713i	0.326295	−	0.188386i	−0.327900	−	0.944712i	$-0.606341\pi$
$593$	193.493	−	111.713i	0.326295	−	0.188386i	0.654195	+	0.756326i	$0.273008\pi$
$594$			29.9020i			0.0503400i
$595$		0			0
$596$	273.029			0.458102
$597$	−79.3368	−	137.415i	−0.132892	−	0.230177i
$598$	−417.282	−	240.918i	−0.697796	−	0.402872i
$599$	−389.927	+	675.373i	−0.650963	+	1.12750i	0.331926	+	0.943305i	$0.392301\pi$
$599$	−389.927	+	675.373i	−0.650963	+	1.12750i	−0.982890	+	0.184196i	$0.941032\pi$
$600$		0			0
$601$			917.029i			1.52584i	0.646494	+	0.762919i	$0.276234\pi$
$601$			917.029i			1.52584i	−0.646494	+	0.762919i	$0.723766\pi$
$602$	37.7504	+	60.0337i	0.0627083	+	0.0997238i
$603$	276.339			0.458273
$604$	−129.599	−	224.471i	−0.214567	−	0.371641i
$605$		0			0
$606$	74.0050	−	128.180i	0.122120	−	0.211519i
$607$	−189.426	+	109.365i	−0.312070	+	0.180174i	−0.647852	−	0.761766i	$-0.724333\pi$
$607$	−189.426	+	109.365i	−0.312070	+	0.180174i	0.335783	+	0.941940i	$0.390999\pi$
$608$		−	117.160i		−	0.192697i
$609$	−61.6970	−	32.5808i	−0.101309	−	0.0534988i
$610$		0			0
$611$	264.684	+	458.446i	0.433197	+	0.750320i
$612$	15.0484	+	8.68821i	0.0245889	+	0.0141964i
$613$	448.607	−	777.010i	0.731822	−	1.26755i	−0.224282	−	0.974524i	$-0.572004\pi$
$613$	448.607	−	777.010i	0.731822	−	1.26755i	0.956104	−	0.293029i	$-0.0946631\pi$
$614$	200.938	−	116.011i	0.327260	−	0.188944i
$615$		0			0
$616$	−37.6210	+	71.2416i	−0.0610731	+	0.115652i
$617$	−1227.93			−1.99016			−0.995080	−	0.0990738i	$-0.968412\pi$
$617$	−1227.93			−1.99016			−0.995080	+	0.0990738i	$0.968412\pi$
$618$	38.3523	+	66.4281i	0.0620587	+	0.107489i
$619$	359.910	+	207.794i	0.581437	+	0.335693i	0.761704	−	0.647925i	$-0.224363\pi$
$619$	359.910	+	207.794i	0.581437	+	0.335693i	−0.180267	+	0.983618i	$0.557696\pi$
$620$		0			0
$621$	−137.879	+	79.6043i	−0.222027	+	0.128187i
$622$		−	323.127i		−	0.519497i
$623$	−586.069	+	368.532i	−0.940720	+	0.591544i
$624$	77.0406			0.123462
$625$		0			0
$626$	633.777	+	365.911i	1.01242	+	0.584523i
$627$	72.9855	−	126.415i	0.116404	−	0.201618i
$628$	−232.536	+	134.255i	−0.370280	+	0.213781i
$629$		−	25.8417i		−	0.0410837i
$630$		0			0
$631$	−67.1152			−0.106363			−0.0531816	−	0.998585i	$-0.516936\pi$
$631$	−67.1152			−0.106363			−0.0531816	+	0.998585i	$0.516936\pi$
$632$	−75.5798	−	130.908i	−0.119588	−	0.207133i
$633$	13.0540	+	7.53674i	0.0206225	+	0.0119064i
$634$	−208.814	+	361.677i	−0.329360	+	0.570468i
$635$		0			0
$636$		−	115.444i		−	0.181516i
$637$	41.0909	+	543.321i	0.0645069	+	0.852937i
$638$	−33.1158			−0.0519057
$639$	9.97019	+	17.2689i	0.0156028	+	0.0270248i
$640$		0			0
$641$	−459.366	+	795.645i	−0.716639	+	1.24126i	0.245685	+	0.969350i	$0.420987\pi$
$641$	−459.366	+	795.645i	−0.716639	+	1.24126i	−0.962324	+	0.271905i	$0.912346\pi$
$642$	99.7868	−	57.6120i	0.155431	−	0.0897383i
$643$			881.952i			1.37162i	0.727780	+	0.685810i	$0.240552\pi$
$643$			881.952i			1.37162i	−0.727780	+	0.685810i	$0.759448\pi$
$644$	−428.651	+	16.1861i	−0.665606	+	0.0251337i
$645$		0			0
$646$	−42.4129	−	73.4612i	−0.0656546	−	0.113717i
$647$	768.152	+	443.493i	1.18725	+	0.685460i	0.957681	−	0.287832i	$-0.0929344\pi$
$647$	768.152	+	443.493i	1.18725	+	0.685460i	0.229571	+	0.973292i	$0.426268\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	−156.047	+	90.0938i	−0.240442	+	0.138819i
$650$		0			0
$651$	24.7525	+	39.3633i	0.0380222	+	0.0604660i
$652$	323.251			0.495783
$653$	−500.073	−	866.151i	−0.765808	−	1.32642i	−0.939818	−	0.341675i	$-0.889006\pi$
$653$	−500.073	−	866.151i	−0.765808	−	1.32642i	0.174010	−	0.984744i	$-0.444327\pi$
$654$	−427.568	−	246.857i	−0.653774	−	0.377457i
$655$		0			0
$656$	194.898	−	112.524i	0.297101	−	0.171531i
$657$			157.265i			0.239368i
$658$	416.734	+	220.068i	0.633334	+	0.334449i
$659$	−825.607			−1.25282			−0.626409	−	0.779495i	$-0.715476\pi$
$659$	−825.607			−1.25282			−0.626409	+	0.779495i	$0.715476\pi$
$660$		0			0
$661$	923.294	+	533.064i	1.39681	+	0.806451i	0.994058	−	0.108856i	$-0.0347188\pi$
$661$	923.294	+	533.064i	1.39681	+	0.806451i	0.402757	+	0.915307i	$0.368052\pi$
$662$	440.797	−	763.483i	0.665857	−	1.15330i
$663$	48.3058	−	27.8894i	0.0728594	−	0.0420654i
$664$		−	328.382i		−	0.494552i
$665$		0			0
$666$	−37.8571			−0.0568425
$667$	−88.1602	−	152.698i	−0.132174	−	0.228932i
$668$	289.229	+	166.987i	0.432978	+	0.249980i
$669$	137.190	−	237.620i	0.205068	−	0.355187i
$670$		0			0
$671$			283.461i			0.422445i
$672$	58.0607	−	36.5097i	0.0863998	−	0.0543299i
$673$	−115.190			−0.171159			−0.0855796	−	0.996331i	$-0.527274\pi$
$673$	−115.190			−0.171159			−0.0855796	+	0.996331i	$0.527274\pi$
$674$	0.0285953	+	0.0495285i	4.24263e−5	+	7.34845e-5i
$675$		0			0
$676$	−45.3489	+	78.5466i	−0.0670842	+	0.116193i
$677$	490.897	−	283.420i	0.725107	−	0.418641i	−0.0915226	−	0.995803i	$-0.529173\pi$
$677$	490.897	−	283.420i	0.725107	−	0.418641i	0.816629	+	0.577162i	$0.195840\pi$
$678$		−	412.548i		−	0.608478i
$679$	−35.1204	−	930.079i	−0.0517237	−	1.36978i
$680$		0			0
$681$	343.311	+	594.633i	0.504128	+	0.873176i
$682$	19.1132	+	11.0350i	0.0280252	+	0.0161804i
$683$	11.8357	−	20.5001i	0.0173290	−	0.0300147i	−0.857231	−	0.514932i	$-0.827817\pi$
$683$	11.8357	−	20.5001i	0.0173290	−	0.0300147i	0.874560	+	0.484918i	$0.161150\pi$
$684$	−107.618	+	62.1333i	−0.157336	+	0.0908382i
$685$		0			0
$686$	288.449	+	389.994i	0.420479	+	0.568504i
$687$	357.096			0.519790
$688$	−14.3273	−	24.8156i	−0.0208245	−	0.0360692i
$689$	−320.931	−	185.289i	−0.465792	−	0.268925i
$690$		0			0
$691$	−922.771	+	532.762i	−1.33541	+	0.771002i	−0.986124	−	0.166013i	$-0.946911\pi$
$691$	−922.771	+	532.762i	−1.33541	+	0.771002i	−0.349290	+	0.937014i	$0.613577\pi$
$692$		−	23.3888i		−	0.0337988i
$693$	85.3911	−	3.22442i	0.123219	−	0.00465285i
$694$	172.041			0.247897
$695$		0			0
$696$	24.4148	+	14.0959i	0.0350788	+	0.0202528i
$697$	81.4696	−	141.110i	0.116886	−	0.202453i
$698$	559.944	−	323.284i	0.802212	−	0.463157i
$699$			192.796i			0.275817i
$700$		0			0
$701$	−1086.46			−1.54987			−0.774936	−	0.632040i	$-0.782218\pi$
$701$	−1086.46			−1.54987			−0.774936	+	0.632040i	$0.782218\pi$
$702$	−40.8569	−	70.7663i	−0.0582008	−	0.100807i
$703$	160.046	+	92.4027i	0.227662	+	0.131441i
$704$	16.2766	−	28.1918i	0.0231201	−	0.0400452i
$705$		0			0
$706$			38.6522i			0.0547481i
$707$	−374.025	−	197.514i	−0.529032	−	0.279369i
$708$	153.395			0.216660
$709$	299.823	+	519.309i	0.422881	+	0.732452i	0.996220	−	0.0868665i	$-0.0276854\pi$
$709$	299.823	+	519.309i	0.422881	+	0.732452i	−0.573339	+	0.819319i	$0.694352\pi$
$710$		0			0
$711$	−80.1645	+	138.849i	−0.112749	+	0.195287i
$712$	242.258	−	139.868i	0.340250	−	0.196443i
$713$			117.509i			0.164809i
$714$	23.1882	−	43.9107i	0.0324765	−	0.0614996i
$715$		0			0
$716$	−133.760	−	231.679i	−0.186815	−	0.323574i
$717$	−388.258	−	224.161i	−0.541504	−	0.312637i
$718$	−326.709	+	565.876i	−0.455026	+	0.788128i
$719$	286.589	−	165.462i	0.398594	−	0.230128i	−0.287283	−	0.957846i	$-0.592752\pi$
$719$	286.589	−	165.462i	0.398594	−	0.230128i	0.685877	+	0.727717i	$0.259419\pi$
$720$		0			0
$721$	185.563	−	116.686i	0.257369	−	0.161839i
$722$	96.0961			0.133097
$723$	264.996	+	458.986i	0.366522	+	0.634835i
$724$	−195.782	−	113.035i	−0.270417	−	0.156125i
$725$		0			0
$726$	−221.555	+	127.915i	−0.305172	+	0.176191i
$727$		−	1104.90i		−	1.51980i	−0.650039	−	0.759901i	$-0.725247\pi$
$727$		−	1104.90i		−	1.51980i	0.650039	−	0.759901i	$-0.274753\pi$
$728$	−8.30753	−	220.005i	−0.0114114	−	0.302205i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−17.9669	−	10.3732i	−0.0245785	−	0.0141904i
$732$	120.656	−	208.983i	0.164831	−	0.285496i
$733$	−869.845	+	502.205i	−1.18669	+	0.685137i	−0.957553	−	0.288257i	$-0.906924\pi$
$733$	−869.845	+	502.205i	−1.18669	+	0.685137i	−0.229138	+	0.973394i	$0.573591\pi$
$734$			608.147i			0.828539i
$735$		0			0
$736$	173.324			0.235495
$737$	−187.410	−	324.604i	−0.254288	−	0.440440i
$738$	−206.721	−	119.350i	−0.280109	−	0.161721i
$739$	−545.640	+	945.075i	−0.738348	+	1.27886i	0.214890	+	0.976638i	$0.431061\pi$
$739$	−545.640	+	945.075i	−0.738348	+	1.27886i	−0.953239	+	0.302219i	$0.902273\pi$
$740$		0			0
$741$			398.899i			0.538325i
$742$	−329.674	+	12.4487i	−0.444305	+	0.0167772i
$743$	−876.833			−1.18013			−0.590063	−	0.807358i	$-0.700897\pi$
$743$	−876.833			−1.18013			−0.590063	+	0.807358i	$0.700897\pi$
$744$	−9.39422	−	16.2713i	−0.0126266	−	0.0218700i
$745$		0			0
$746$	473.714	−	820.498i	0.635006	−	1.09986i
$747$	−301.639	+	174.151i	−0.403800	+	0.233134i
$748$		−	23.5690i		−	0.0315094i
$749$	−175.283	−	278.749i	−0.234023	−	0.372162i
$750$		0			0
$751$	56.4095	+	97.7042i	0.0751126	+	0.130099i	0.901135	−	0.433538i	$-0.142735\pi$
$751$	56.4095	+	97.7042i	0.0751126	+	0.130099i	−0.826023	+	0.563637i	$0.809402\pi$
$752$	−164.911	−	95.2112i	−0.219296	−	0.126611i
$753$	360.161	−	623.816i	0.478301	−	0.828441i
$754$	78.3723	−	45.2482i	0.103942	−	0.0600109i
$755$		0			0
$756$	−64.3276	−	33.9699i	−0.0850895	−	0.0449338i
$757$	−1279.08			−1.68966			−0.844832	−	0.535032i	$-0.820300\pi$
$757$	−1279.08			−1.68966			−0.844832	+	0.535032i	$0.820300\pi$
$758$	498.048	+	862.644i	0.657055	+	1.13805i
$759$	187.016	+	107.974i	0.246398	+	0.142258i
$760$		0			0
$761$	−794.534	+	458.724i	−1.04407	+	0.602791i	−0.920982	−	0.389605i	$-0.872612\pi$
$761$	−794.534	+	458.724i	−1.04407	+	0.602791i	−0.123083	+	0.992396i	$0.539278\pi$
$762$			71.4759i			0.0938004i
$763$	−658.843	+	1247.63i	−0.863490	+	1.63516i
$764$	502.072			0.657163
$765$		0			0
$766$	36.2977	+	20.9565i	0.0473860	+	0.0273583i
$767$	246.202	−	426.434i	0.320993	−	0.555976i
$768$	−24.0000	+	13.8564i	−0.0312500	+	0.0180422i
$769$		−	187.311i		−	0.243577i	−0.992556	−	0.121789i	$-0.961137\pi$
$769$		−	187.311i		−	0.243577i	0.992556	−	0.121789i	$-0.0388630\pi$
$770$		0			0
$771$	−542.560			−0.703709
$772$	356.991	+	618.326i	0.462423	+	0.800940i
$773$	169.320	+	97.7567i	0.219042	+	0.126464i	0.605507	−	0.795840i	$-0.292970\pi$
$773$	169.320	+	97.7567i	0.219042	+	0.126464i	−0.386464	+	0.922304i	$0.626304\pi$
$774$	−15.1964	+	26.3209i	−0.0196336	+	0.0340063i
$775$		0			0
$776$			376.076i			0.484635i
$777$	4.08226	+	108.109i	0.00525387	+	0.139136i
$778$	52.0670			0.0669241
$779$	582.626	+	1009.14i	0.747916	+	1.29543i
$780$		0			0
$781$	13.5234	−	23.4232i	0.0173154	−	0.0299912i
$782$	108.677	−	62.7450i	0.138974	−	0.0802365i
$783$		−	29.9020i		−	0.0381890i
$784$	−110.522	−	161.867i	−0.140972	−	0.206463i
$785$		0			0
$786$	174.572	+	302.368i	0.222102	+	0.384692i
$787$	426.846	+	246.440i	0.542371	+	0.313138i	0.746040	−	0.665902i	$-0.231953\pi$
$787$	426.846	+	246.440i	0.542371	+	0.313138i	−0.203668	+	0.979040i	$0.565286\pi$
$788$	35.1268	−	60.8414i	0.0445771	−	0.0772099i
$789$	−132.835	+	76.6921i	−0.168358	+	0.0972016i
$790$		0			0
$791$	−1178.11	+	44.4864i	−1.48940	+	0.0562407i
$792$	−34.5278			−0.0435957
$793$	−387.310	−	670.841i	−0.488411	−	0.845953i
$794$	−112.661	−	65.0450i	−0.141891	−	0.0819206i
$795$		0			0
$796$	158.674	−	91.6103i	0.199339	−	0.115088i
$797$		−	283.436i		−	0.355629i	−0.984064	−	0.177814i	$-0.943097\pi$
$797$		−	283.436i		−	0.355629i	0.984064	−	0.177814i	$-0.0569027\pi$
$798$	189.039	+	300.625i	0.236891	+	0.376723i
$799$	−137.869			−0.172552
$800$		0			0
$801$	−256.953	−	148.352i	−0.320791	−	0.185209i
$802$	251.891	−	436.288i	0.314079	−	0.544000i
$803$	184.732	−	106.655i	0.230053	−	0.132821i
$804$			319.089i			0.396876i
$805$		0			0
$806$	−60.3113			−0.0748279
$807$	−70.7545	−	122.550i	−0.0876759	−	0.151859i
$808$	148.010	+	85.4536i	0.183181	+	0.105759i
$809$	63.7961	−	110.498i	0.0788580	−	0.136586i	−0.823899	−	0.566736i	$-0.808206\pi$
$809$	63.7961	−	110.498i	0.0788580	−	0.136586i	0.902757	+	0.430150i	$0.141539\pi$
$810$		0			0
$811$		−	1029.60i		−	1.26955i	−0.772697	−	0.634774i	$-0.781093\pi$
$811$		−	1029.60i		−	1.26955i	0.772697	−	0.634774i	$-0.218907\pi$
$812$	37.6210	−	71.2416i	0.0463313	−	0.0877359i
$813$	509.807			0.627069
$814$	25.6743	+	44.4693i	0.0315410	+	0.0546305i
$815$		0			0
$816$	−10.0323	+	17.3764i	−0.0122945	+	0.0212946i
$817$	128.490	−	74.1835i	0.157270	−	0.0907999i
$818$		−	34.2097i		−	0.0418212i
$819$	−197.682	+	124.306i	−0.241370	+	0.151778i
$820$		0			0
$821$	357.710	+	619.572i	0.435701	+	0.754656i	0.997353	−	0.0727181i	$-0.0231673\pi$
$821$	357.710	+	619.572i	0.435701	+	0.754656i	−0.561652	+	0.827374i	$0.689834\pi$
$822$	442.496	+	255.475i	0.538317	+	0.310797i
$823$	−594.806	+	1030.23i	−0.722729	+	1.25180i	0.237173	+	0.971467i	$0.423779\pi$
$823$	−594.806	+	1030.23i	−0.722729	+	1.25180i	−0.959902	+	0.280336i	$0.909554\pi$
$824$	−76.7045	+	44.2854i	−0.0930880	+	0.0537444i
$825$		0			0
$826$	−16.5411	−	438.052i	−0.0200256	−	0.530329i
$827$	−764.411			−0.924318			−0.462159	−	0.886797i	$-0.652925\pi$
$827$	−764.411			−0.924318			−0.462159	+	0.886797i	$0.652925\pi$
$828$	−91.9192	−	159.209i	−0.111013	−	0.192281i
$829$	623.257	+	359.837i	0.751818	+	0.434062i	0.826350	−	0.563156i	$-0.190413\pi$
$829$	623.257	+	359.837i	0.751818	+	0.434062i	−0.0745327	+	0.997219i	$0.523747\pi$
$830$		0			0
$831$	609.365	−	351.817i	0.733292	−	0.423366i
$832$			88.9588i			0.106922i
$833$	−127.896	−	61.4837i	−0.153537	−	0.0738099i
$834$	373.525			0.447871
$835$		0			0
$836$	145.971	+	84.2764i	0.174607	+	0.100809i
$837$	−9.96407	+	17.2583i	−0.0119045	+	0.0206192i
$838$	−658.175	+	379.997i	−0.785412	+	0.453458i
$839$			622.729i			0.742228i	0.928587	+	0.371114i	$0.121024\pi$
$839$			622.729i			0.742228i	−0.928587	+	0.371114i	$0.878976\pi$
$840$		0			0
$841$	−807.884			−0.960623
$842$	−455.663	−	789.231i	−0.541167	−	0.937329i
$843$	−351.456	−	202.913i	−0.416912	−	0.240704i
$844$	−8.70268	+	15.0735i	−0.0103112	+	0.0178596i
$845$		0			0
$846$			201.974i			0.238739i
$847$	389.178	+	618.902i	0.459478	+	0.730699i
$848$	133.303			0.157197
$849$	237.575	+	411.492i	0.279829	+	0.484678i
$850$		0			0
$851$	−136.699	+	236.770i	−0.160634	+	0.278226i
$852$	−19.9404	+	11.5126i	−0.0234042	+	0.0135124i
$853$			748.971i			0.878044i	0.898476	+	0.439022i	$0.144675\pi$
$853$			748.971i			0.878044i	−0.898476	+	0.439022i	$0.855325\pi$
$854$	−609.804	−	322.024i	−0.714057	−	0.377077i
$855$		0			0
$856$	66.5246	+	115.224i	0.0777156	+	0.134607i
$857$	902.421	+	521.013i	1.05300	+	0.607950i	0.923488	−	0.383628i	$-0.125325\pi$
$857$	902.421	+	521.013i	1.05300	+	0.607950i	0.129512	+	0.991578i	$0.458659\pi$
$858$	−55.4176	+	95.9860i	−0.0645892	+	0.111872i
$859$	−483.193	+	278.972i	−0.562506	+	0.324763i	−0.754151	−	0.656701i	$-0.771951\pi$
$859$	−483.193	+	278.972i	−0.562506	+	0.324763i	0.191644	+	0.981464i	$0.438618\pi$
$860$		0			0
$861$	−318.537	+	603.202i	−0.369962	+	0.700584i
$862$	660.963			0.766779
$863$	729.238	+	1263.08i	0.845004	+	1.46359i	0.885618	+	0.464415i	$0.153735\pi$
$863$	729.238	+	1263.08i	0.845004	+	1.46359i	−0.0406140	+	0.999175i	$0.512931\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	40.6642	−	23.4775i	0.0469563	−	0.0271103i
$867$		−	486.036i		−	0.560595i
$868$	−45.4529	+	28.5817i	−0.0523651	+	0.0329282i
$869$	217.467			0.250250
$870$		0			0
$871$	887.055	+	512.141i	1.01843	+	0.587992i
$872$	285.045	−	493.713i	0.326887	−	0.566185i
$873$	345.448	−	199.445i	0.395702	−	0.228459i
$874$			897.435i			1.02681i
$875$		0			0
$876$	−181.594			−0.207299
$877$	347.719	+	602.267i	0.396487	+	0.686736i	0.993290	−	0.115652i	$-0.0368959\pi$
$877$	347.719	+	602.267i	0.396487	+	0.686736i	−0.596803	+	0.802388i	$0.703563\pi$
$878$	−62.5336	−	36.1038i	−0.0712228	−	0.0411205i
$879$	56.0556	−	97.0911i	0.0637720	−	0.110456i
$880$		0			0
$881$		−	795.045i		−	0.902435i	−0.892414	−	0.451218i	$-0.850990\pi$
$881$		−	795.045i		−	0.902435i	0.892414	−	0.451218i	$-0.149010\pi$
$882$	−90.0714	+	187.364i	−0.102122	+	0.212430i
$883$	1060.28			1.20077			0.600384	−	0.799712i	$-0.295014\pi$
$883$	1060.28			1.20077			0.600384	+	0.799712i	$0.295014\pi$
$884$	32.2039	+	55.7787i	0.0364297	+	0.0630981i
$885$		0			0
$886$	560.494	−	970.804i	0.632611	−	1.09572i
$887$	−1005.08	+	580.285i	−1.13313	+	0.654211i	−0.944719	−	0.327880i	$-0.893666\pi$
$887$	−1005.08	+	580.285i	−1.13313	+	0.654211i	−0.188407	+	0.982091i	$0.560333\pi$
$888$		−	43.7137i		−	0.0492271i
$889$	204.114	−	7.70748i	0.229600	−	0.00866983i
$890$		0			0
$891$	18.3111	+	31.7158i	0.0205512	+	0.0355958i
$892$	274.380	+	158.414i	0.307601	+	0.177594i
$893$	492.983	−	853.871i	0.552052	−	0.956182i
$894$	289.591	−	167.195i	0.323927	−	0.187019i
$895$		0			0
$896$	42.1578	+	67.0427i	0.0470511	+	0.0748244i
$897$	−590.125			−0.657888
$898$	50.7376	+	87.8802i	0.0565007	+	0.0978621i
$899$	−19.1132	−	11.0350i	−0.0212605	−	0.0122748i
$900$		0			0
$901$	83.5836	−	48.2570i	0.0927676	−	0.0535594i
$902$			323.768i			0.358945i
$903$	76.8034	+	40.5581i	0.0850535	+	0.0449148i
$904$	476.370			0.526957
$905$		0			0
$906$	−274.920	−	158.725i	−0.303444	−	0.175193i
$907$	724.984	−	1255.71i	0.799320	−	1.38446i	−0.120739	−	0.992684i	$-0.538526\pi$
$907$	724.984	−	1255.71i	0.799320	−	1.38446i	0.920059	−	0.391779i	$-0.128140\pi$
$908$	−686.623	+	396.422i	−0.756193	+	0.436588i
$909$		−	181.274i		−	0.199422i
$910$		0			0
$911$	803.838			0.882369			0.441185	−	0.897416i	$-0.354558\pi$
$911$	803.838			0.882369			0.441185	+	0.897416i	$0.354558\pi$
$912$	−71.7454	−	124.267i	−0.0786682	−	0.136257i
$913$	409.137	+	236.215i	0.448123	+	0.258724i
$914$	444.081	−	769.170i	0.485865	−	0.841543i
$915$		0			0
$916$			412.338i			0.450151i
$917$	844.648	−	531.131i	0.921099	−	0.579206i
$918$	21.2817			0.0231827
$919$	190.607	+	330.140i	0.207407	+	0.359239i	0.950897	−	0.309508i	$-0.100164\pi$
$919$	190.607	+	330.140i	0.207407	+	0.359239i	−0.743490	+	0.668747i	$0.766831\pi$
$920$		0			0
$921$	142.084	−	246.097i	0.154272	−	0.267207i
$922$	582.247	−	336.160i	0.631504	−	0.364599i
$923$			73.9113i			0.0800773i
$924$	3.72324	+	98.6012i	0.00402948	+	0.106711i
$925$		0			0
$926$	242.246	+	419.583i	0.261605	+	0.453114i
$927$	81.3574	+	46.9717i	0.0877642	+	0.0506707i
$928$	−16.2766	+	28.1918i	−0.0175394	+	0.0303791i
$929$	1182.30	−	682.603i	1.27266	−	0.734772i	0.297174	−	0.954823i	$-0.403956\pi$
$929$	1182.30	−	682.603i	1.27266	−	0.734772i	0.975488	+	0.220051i	$0.0706225\pi$
$930$		0			0
$931$	838.112	−	572.257i	0.900227	−	0.614669i
$932$	−222.622			−0.238865
$933$	−197.874	−	342.728i	−0.212084	−	0.367340i
$934$	−311.206	−	179.675i	−0.333197	−	0.192371i
$935$		0			0
$936$	81.7139	−	47.1775i	0.0873012	−	0.0504033i
$937$			836.234i			0.892459i	0.894918	+	0.446230i	$0.147234\pi$
$937$			836.234i			0.892459i	−0.894918	+	0.446230i	$0.852766\pi$
$938$	911.222	−	34.4083i	0.971452	−	0.0366827i
$939$	896.296			0.954522
$940$		0			0
$941$	−846.732	−	488.861i	−0.899822	−	0.519512i	−0.0226794	−	0.999743i	$-0.507220\pi$
$941$	−846.732	−	488.861i	−0.899822	−	0.519512i	−0.877142	+	0.480230i	$0.840553\pi$
$942$	−164.428	+	284.797i	−0.174552	+	0.302332i
$943$	−1492.91	+	861.929i	−1.58314	+	0.914029i
$944$			177.126i			0.187633i
$945$		0			0
$946$	41.2241			0.0435773
$947$	−477.919	−	827.780i	−0.504667	−	0.874108i	−0.999985	−	0.00539682i	$-0.998282\pi$
$947$	−477.919	−	827.780i	−0.504667	−	0.874108i	0.495319	−	0.868711i	$-0.335051\pi$
$948$	−160.329	−	92.5660i	−0.169123	−	0.0976435i
$949$	−291.460	+	504.823i	−0.307123	+	0.531953i
$950$		0			0
$951$			511.488i			0.537843i
$952$	50.7037	+	26.7755i	0.0532602	+	0.0281255i
$953$	156.597			0.164320			0.0821598	−	0.996619i	$-0.473818\pi$
$953$	156.597			0.164320			0.0821598	+	0.996619i	$0.473818\pi$
$954$	−70.6948	−	122.447i	−0.0741036	−	0.128351i
$955$		0			0
$956$	258.839	−	448.322i	0.270752	−	0.468956i
$957$	−35.1246	+	20.2792i	−0.0367029	+	0.0211904i
$958$		−	455.481i		−	0.475450i
$959$	681.846	−	1291.19i	0.710997	−	1.34639i
$960$		0			0
$961$	−473.146	−	819.512i	−0.492347	−	0.852770i
$962$	−121.522	−	70.1609i	−0.126323	−	0.0729324i
$963$	70.5600	−	122.213i	0.0732710	−	0.126909i
$964$	−529.991	+	305.991i	−0.549784	+	0.317418i
$965$		0			0
$966$	−444.741	+	279.662i	−0.460394	+	0.289505i
$967$	−1344.56			−1.39045			−0.695224	−	0.718793i	$-0.744695\pi$
$967$	−1344.56			−1.39045			−0.695224	+	0.718793i	$0.744695\pi$
$968$	−147.703	−	255.830i	−0.152586	−	0.264287i
$969$	−89.9712	−	51.9449i	−0.0928496	−	0.0536067i
$970$		0			0
$971$	−1311.13	+	756.983i	−1.35029	+	0.779591i	−0.988290	−	0.152586i	$-0.951240\pi$
$971$	−1311.13	+	756.983i	−1.35029	+	0.779591i	−0.362001	+	0.932178i	$0.617906\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−40.2784	−	1066.68i	−0.0413961	−	1.09627i
$974$	−274.796			−0.282132
$975$		0			0
$976$	241.313	+	139.322i	0.247247	+	0.142748i
$977$	16.6886	−	28.9055i	0.0170815	−	0.0295860i	−0.857358	−	0.514720i	$-0.827896\pi$
$977$	16.6886	−	28.9055i	0.0170815	−	0.0295860i	0.874440	+	0.485134i	$0.161229\pi$
$978$	342.859	−	197.950i	0.350572	−	0.202403i
$979$			402.444i			0.411076i
$980$		0			0
$981$	−604.673			−0.616384
$982$	−347.698	−	602.230i	−0.354071	−	0.613269i
$983$	1672.03	+	965.345i	1.70094	+	0.982039i	0.944809	+	0.327621i	$0.106247\pi$
$983$	1672.03	+	965.345i	1.70094	+	0.982039i	0.756133	+	0.654418i	$0.227086\pi$
$984$	137.814	−	238.700i	0.140055	−	0.242582i
$985$		0			0
$986$			23.5690i			0.0239037i
$987$	576.776	−	21.7794i	0.584373	−	0.0220663i
$988$	−460.609			−0.466203
$989$	109.746	+	190.086i	0.110967	+	0.192200i
$990$		0			0
$991$	670.602	−	1161.52i	0.676692	−	1.17206i	−0.299279	−	0.954166i	$-0.596746\pi$
$991$	670.602	−	1161.52i	0.676692	−	1.17206i	0.975971	−	0.217899i	$-0.0699205\pi$
$992$	18.7884	−	10.8475i	0.0189400	−	0.0109350i
$993$		−	1079.73i		−	1.08734i
$994$	35.0267	+	55.7023i	0.0352382	+	0.0560386i
$995$		0			0
$996$	−201.092	−	348.302i	−0.201900	−	0.349701i
$997$	−159.613	−	92.1525i	−0.160093	−	0.0924298i	0.417813	−	0.908533i	$-0.362797\pi$
$997$	−159.613	−	92.1525i	−0.160093	−	0.0924298i	−0.577906	+	0.816103i	$0.696130\pi$
$998$	54.5542	−	94.4907i	0.0546636	−	0.0946801i
$999$	−40.1536	+	23.1827i	−0.0401937	+	0.0232059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.f.451.6	yes	12
5.2	odd	4		1050.3.q.d.199.4		24
5.3	odd	4		1050.3.q.d.199.10		24
5.4	even	2		1050.3.p.e.451.1	✓	12
7.5	odd	6	inner	1050.3.p.f.901.6	yes	12
35.12	even	12		1050.3.q.d.649.10		24
35.19	odd	6		1050.3.p.e.901.1	yes	12
35.33	even	12		1050.3.q.d.649.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.e.451.1	✓	12	5.4	even	2
1050.3.p.e.901.1	yes	12	35.19	odd	6
1050.3.p.f.451.6	yes	12	1.1	even	1	trivial
1050.3.p.f.901.6	yes	12	7.5	odd	6	inner
1050.3.q.d.199.4		24	5.2	odd	4
1050.3.q.d.199.10		24	5.3	odd	4
1050.3.q.d.649.4		24	35.33	even	12
1050.3.q.d.649.10		24	35.12	even	12

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(6.99501 - 0.264136i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(6.99501 - 0.264136i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.03457 - 3.52398i) q^{11} +(-3.00000 + 1.73205i) q^{12} +11.1199i q^{13} +(5.26972 + 8.38034i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-2.50807 - 1.44803i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(17.9363 - 10.3556i) q^{19} +(10.7213 + 5.66166i) q^{21} +5.75463 q^{22} +(15.3199 + 26.5348i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-13.6190 + 7.86292i) q^{26} +5.19615i q^{27} +(-6.53752 + 12.3799i) q^{28} -5.75463 q^{29} +(3.32136 + 1.91759i) q^{31} +(2.82843 - 4.89898i) q^{32} +(6.10371 - 3.52398i) q^{33} -4.09566i q^{34} -6.00000 q^{36} +(4.46151 + 7.72755i) q^{37} +(25.3658 + 14.6450i) q^{38} +(-9.63007 + 16.6798i) q^{39} +56.2622i q^{41} +(0.646999 + 17.1342i) q^{42} +7.16364 q^{43} +(4.06914 + 7.04796i) q^{44} +(-21.6656 + 37.5258i) q^{46} +(41.2277 - 23.8028i) q^{47} -6.92820i q^{48} +(48.8605 - 3.69527i) q^{49} +(-2.50807 - 4.34410i) q^{51} +(-19.2601 - 11.1199i) q^{52} +(-16.6629 + 28.8610i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-19.7849 + 0.747090i) q^{56} +35.8727 q^{57} +(-4.06914 - 7.04796i) q^{58} +(-38.3489 - 22.1407i) q^{59} +(-60.3282 + 34.8305i) q^{61} +5.42375i q^{62} +(11.1788 + 17.7774i) q^{63} +8.00000 q^{64} +(8.63195 + 4.98366i) q^{66} +(46.0565 - 79.7722i) q^{67} +(5.01614 - 2.89607i) q^{68} +53.0695i q^{69} +6.64679 q^{71} +(-4.24264 - 7.34847i) q^{72} +(45.3984 + 26.2108i) q^{73} +(-6.30952 + 10.9284i) q^{74} +41.4222i q^{76} +(13.3010 - 25.1877i) q^{77} -27.2380 q^{78} +(26.7215 + 46.2830i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-68.9069 + 39.7834i) q^{82} +116.101i q^{83} +(-20.5275 + 12.9081i) q^{84} +(5.06546 + 8.77363i) q^{86} +(-8.63195 - 4.98366i) q^{87} +(-5.75463 + 9.96732i) q^{88} +(-85.6511 + 49.4507i) q^{89} +(2.93716 + 77.7835i) q^{91} -61.2794 q^{92} +(3.32136 + 5.75276i) q^{93} +(58.3047 + 33.6623i) q^{94} +(8.48528 - 4.89898i) q^{96} -132.963i q^{97} +(39.0753 + 57.2286i) q^{98} +12.2074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9}+O(q^{10}) \) 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9	\( 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9} - 4 q^{11} - 36 q^{12} + 8 q^{14} - 24 q^{16} - 24 q^{17} + 12 q^{19} + 18 q^{21} + 24 q^{22} - 60 q^{23} - 24 q^{26} + 4 q^{28} - 24 q^{29} - 198 q^{31} - 12 q^{33} - 72 q^{36} + 70 q^{37} - 60 q^{38} - 36 q^{39} + 36 q^{42} - 84 q^{43} - 8 q^{44} + 32 q^{46} - 60 q^{47} + 28 q^{49} - 24 q^{51} - 72 q^{52} + 44 q^{53} + 40 q^{56} + 24 q^{57} + 8 q^{58} - 48 q^{59} + 186 q^{61} + 30 q^{63} + 96 q^{64} + 36 q^{66} + 152 q^{67} + 48 q^{68} - 136 q^{71} + 18 q^{73} - 64 q^{74} + 132 q^{77} - 48 q^{78} - 70 q^{79} - 54 q^{81} - 84 q^{82} - 12 q^{84} - 208 q^{86} - 36 q^{87} - 24 q^{88} + 168 q^{89} + 292 q^{91} + 240 q^{92} - 198 q^{93} - 204 q^{94} + 48 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9 - 4 * q^11 - 36 * q^12 + 8 * q^14 - 24 * q^16 - 24 * q^17 + 12 * q^19 + 18 * q^21 + 24 * q^22 - 60 * q^23 - 24 * q^26 + 4 * q^28 - 24 * q^29 - 198 * q^31 - 12 * q^33 - 72 * q^36 + 70 * q^37 - 60 * q^38 - 36 * q^39 + 36 * q^42 - 84 * q^43 - 8 * q^44 + 32 * q^46 - 60 * q^47 + 28 * q^49 - 24 * q^51 - 72 * q^52 + 44 * q^53 + 40 * q^56 + 24 * q^57 + 8 * q^58 - 48 * q^59 + 186 * q^61 + 30 * q^63 + 96 * q^64 + 36 * q^66 + 152 * q^67 + 48 * q^68 - 136 * q^71 + 18 * q^73 - 64 * q^74 + 132 * q^77 - 48 * q^78 - 70 * q^79 - 54 * q^81 - 84 * q^82 - 12 * q^84 - 208 * q^86 - 36 * q^87 - 24 * q^88 + 168 * q^89 + 292 * q^91 + 240 * q^92 - 198 * q^93 - 204 * q^94 + 48 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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