LMFDB - Embedded newform 1470.2.d.g.1469.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(1469,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1470.1469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.d (of order $2$, degree $1$, 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1469.8
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.g.1469.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.17052 + 1.27667i) q^{3} +1.00000 q^{4} +(1.07909 + 1.95846i) q^{5} +(1.17052 - 1.27667i) q^{6} -1.00000 q^{8} +(-0.259782 - 2.98873i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.17052 + 1.27667i) q^{3} +1.00000 q^{4} +(1.07909 + 1.95846i) q^{5} +(1.17052 - 1.27667i) q^{6} -1.00000 q^{8} +(-0.259782 - 2.98873i) q^{9} +(-1.07909 - 1.95846i) q^{10} -6.01614i q^{11} +(-1.17052 + 1.27667i) q^{12} -0.864346 q^{13} +(-3.76340 - 0.914769i) q^{15} +1.00000 q^{16} -2.84561i q^{17} +(0.259782 + 2.98873i) q^{18} +7.12434i q^{19} +(1.07909 + 1.95846i) q^{20} +6.01614i q^{22} +2.10323 q^{23} +(1.17052 - 1.27667i) q^{24} +(-2.67114 + 4.22670i) q^{25} +0.864346 q^{26} +(4.11971 + 3.16670i) q^{27} +9.40499i q^{29} +(3.76340 + 0.914769i) q^{30} +2.68399i q^{31} -1.00000 q^{32} +(7.68063 + 7.04199i) q^{33} +2.84561i q^{34} +(-0.259782 - 2.98873i) q^{36} +6.81763i q^{37} -7.12434i q^{38} +(1.01173 - 1.10349i) q^{39} +(-1.07909 - 1.95846i) q^{40} -5.32333 q^{41} -2.68989i q^{43} -6.01614i q^{44} +(5.57299 - 3.73388i) q^{45} -2.10323 q^{46} +3.12679i q^{47} +(-1.17052 + 1.27667i) q^{48} +(2.67114 - 4.22670i) q^{50} +(3.63291 + 3.33083i) q^{51} -0.864346 q^{52} -11.9744 q^{53} +(-4.11971 - 3.16670i) q^{54} +(11.7824 - 6.49194i) q^{55} +(-9.09545 - 8.33916i) q^{57} -9.40499i q^{58} +7.09456 q^{59} +(-3.76340 - 0.914769i) q^{60} +9.33672i q^{61} -2.68399i q^{62} +1.00000 q^{64} +(-0.932706 - 1.69279i) q^{65} +(-7.68063 - 7.04199i) q^{66} +6.56038i q^{67} -2.84561i q^{68} +(-2.46187 + 2.68514i) q^{69} -4.46562i q^{71} +(0.259782 + 2.98873i) q^{72} -12.7989 q^{73} -6.81763i q^{74} +(-2.26950 - 8.35759i) q^{75} +7.12434i q^{76} +(-1.01173 + 1.10349i) q^{78} +3.35798 q^{79} +(1.07909 + 1.95846i) q^{80} +(-8.86503 + 1.55284i) q^{81} +5.32333 q^{82} +1.28020i q^{83} +(5.57301 - 3.07066i) q^{85} +2.68989i q^{86} +(-12.0071 - 11.0087i) q^{87} +6.01614i q^{88} +3.08600 q^{89} +(-5.57299 + 3.73388i) q^{90} +2.10323 q^{92} +(-3.42657 - 3.14165i) q^{93} -3.12679i q^{94} +(-13.9527 + 7.68780i) q^{95} +(1.17052 - 1.27667i) q^{96} -1.90549 q^{97} +(-17.9806 + 1.56288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9	$ 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9} + 24 q^{16} - 8 q^{18} - 16 q^{23} + 8 q^{25} - 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} - 8 q^{50} + 16 q^{51} + 16 q^{53} + 16 q^{57} + 24 q^{64} - 48 q^{65} - 8 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} - 16 q^{92} + 64 q^{93} - 112 q^{95} - 64 q^{99}+O(q^{100}) $ 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9 + 24 * q^16 - 8 * q^18 - 16 * q^23 + 8 * q^25 - 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 - 8 * q^50 + 16 * q^51 + 16 * q^53 + 16 * q^57 + 24 * q^64 - 48 * q^65 - 8 * q^72 - 16 * q^78 - 48 * q^79 - 24 * q^81 + 16 * q^85 - 16 * q^92 + 64 * q^93 - 112 * q^95 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.17052	+	1.27667i	−0.675798	+	0.737087i
$3$	−1.17052	+	1.27667i	−0.675798	+	0.737087i
$4$	1.00000			0.500000
$5$	1.07909	+	1.95846i	0.482583	+	0.875850i
$5$	1.07909	+	1.95846i	0.482583	+	0.875850i
$6$	1.17052	−	1.27667i	0.477861	−	0.521199i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.259782	−	2.98873i	−0.0865939	−	0.996244i
$10$	−1.07909	−	1.95846i	−0.341238	−	0.619320i
$11$		−	6.01614i		−	1.81393i	−0.421202	−	0.906967i	$-0.638392\pi$
$11$		−	6.01614i		−	1.81393i	0.421202	−	0.906967i	$-0.361608\pi$
$12$	−1.17052	+	1.27667i	−0.337899	+	0.368543i
$13$	−0.864346			−0.239726			−0.119863	−	0.992790i	$-0.538246\pi$
$13$	−0.864346			−0.239726			−0.119863	+	0.992790i	$0.538246\pi$
$14$		0			0
$15$	−3.76340	−	0.914769i	−0.971706	−	0.236192i
$16$	1.00000			0.250000
$17$		−	2.84561i		−	0.690161i	−0.938573	−	0.345080i	$-0.887852\pi$
$17$		−	2.84561i		−	0.690161i	0.938573	−	0.345080i	$-0.112148\pi$
$18$	0.259782	+	2.98873i	0.0612311	+	0.704451i
$19$			7.12434i			1.63444i	0.576328	+	0.817218i	$0.304485\pi$
$19$			7.12434i			1.63444i	−0.576328	+	0.817218i	$0.695515\pi$
$20$	1.07909	+	1.95846i	0.241291	+	0.437925i
$21$		0			0
$22$			6.01614i			1.28264i
$23$	2.10323			0.438554			0.219277	−	0.975663i	$-0.429630\pi$
$23$	2.10323			0.438554			0.219277	+	0.975663i	$0.429630\pi$
$24$	1.17052	−	1.27667i	0.238931	−	0.260600i
$25$	−2.67114	+	4.22670i	−0.534227	+	0.845341i
$26$	0.864346			0.169512
$27$	4.11971	+	3.16670i	0.792838	+	0.609432i
$28$		0			0
$29$			9.40499i			1.74646i	0.487306	+	0.873231i	$0.337980\pi$
$29$			9.40499i			1.74646i	−0.487306	+	0.873231i	$0.662020\pi$
$30$	3.76340	+	0.914769i	0.687100	+	0.167013i
$31$			2.68399i			0.482058i	0.970518	+	0.241029i	$0.0774849\pi$
$31$			2.68399i			0.482058i	−0.970518	+	0.241029i	$0.922515\pi$
$32$	−1.00000			−0.176777
$33$	7.68063	+	7.04199i	1.33703	+	1.22585i
$34$			2.84561i			0.488017i
$35$		0			0
$36$	−0.259782	−	2.98873i	−0.0432970	−	0.498122i
$37$			6.81763i			1.12081i	0.828218	+	0.560406i	$0.189355\pi$
$37$			6.81763i			1.12081i	−0.828218	+	0.560406i	$0.810645\pi$
$38$		−	7.12434i		−	1.15572i
$39$	1.01173	−	1.10349i	0.162007	−	0.176699i
$40$	−1.07909	−	1.95846i	−0.170619	−	0.309660i
$41$	−5.32333			−0.831364			−0.415682	−	0.909510i	$-0.636457\pi$
$41$	−5.32333			−0.831364			−0.415682	+	0.909510i	$0.636457\pi$
$42$		0			0
$43$		−	2.68989i		−	0.410204i	−0.978741	−	0.205102i	$-0.934247\pi$
$43$		−	2.68989i		−	0.410204i	0.978741	−	0.205102i	$-0.0657526\pi$
$44$		−	6.01614i		−	0.906967i
$45$	5.57299	−	3.73388i	0.830772	−	0.556614i
$46$	−2.10323			−0.310105
$47$			3.12679i			0.456089i	0.973651	+	0.228045i	$0.0732332\pi$
$47$			3.12679i			0.456089i	−0.973651	+	0.228045i	$0.926767\pi$
$48$	−1.17052	+	1.27667i	−0.168950	+	0.184272i
$49$		0			0
$50$	2.67114	−	4.22670i	0.377756	−	0.597746i
$51$	3.63291	+	3.33083i	0.508708	+	0.466409i
$52$	−0.864346			−0.119863
$53$	−11.9744			−1.64482			−0.822408	−	0.568898i	$-0.807370\pi$
$53$	−11.9744			−1.64482			−0.822408	+	0.568898i	$0.807370\pi$
$54$	−4.11971	−	3.16670i	−0.560621	−	0.430934i
$55$	11.7824	−	6.49194i	1.58873	−	0.875373i
$56$		0			0
$57$	−9.09545	−	8.33916i	−1.20472	−	1.10455i
$58$		−	9.40499i		−	1.23494i
$59$	7.09456			0.923633			0.461817	−	0.886975i	$-0.347198\pi$
$59$	7.09456			0.923633			0.461817	+	0.886975i	$0.347198\pi$
$60$	−3.76340	−	0.914769i	−0.485853	−	0.118096i
$61$			9.33672i			1.19544i	0.801703	+	0.597722i	$0.203927\pi$
$61$			9.33672i			1.19544i	−0.801703	+	0.597722i	$0.796073\pi$
$62$		−	2.68399i		−	0.340866i
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.932706	−	1.69279i	−0.115688	−	0.209965i
$66$	−7.68063	−	7.04199i	−0.945420	−	0.866809i
$67$			6.56038i			0.801478i	0.916192	+	0.400739i	$0.131247\pi$
$67$			6.56038i			0.801478i	−0.916192	+	0.400739i	$0.868753\pi$
$68$		−	2.84561i		−	0.345080i
$69$	−2.46187	+	2.68514i	−0.296374	+	0.323252i
$70$		0			0
$71$		−	4.46562i		−	0.529971i	−0.964252	−	0.264986i	$-0.914633\pi$
$71$		−	4.46562i		−	0.529971i	0.964252	−	0.264986i	$-0.0853672\pi$
$72$	0.259782	+	2.98873i	0.0306156	+	0.352225i
$73$	−12.7989			−1.49800			−0.749000	−	0.662570i	$-0.769466\pi$
$73$	−12.7989			−1.49800			−0.749000	+	0.662570i	$0.769466\pi$
$74$		−	6.81763i		−	0.792533i
$75$	−2.26950	−	8.35759i	−0.262060	−	0.965052i
$76$			7.12434i			0.817218i
$77$		0			0
$78$	−1.01173	+	1.10349i	−0.114556	+	0.124945i
$79$	3.35798			0.377803			0.188901	−	0.981996i	$-0.439507\pi$
$79$	3.35798			0.377803			0.188901	+	0.981996i	$0.439507\pi$
$80$	1.07909	+	1.95846i	0.120646	+	0.218963i
$81$	−8.86503	+	1.55284i	−0.985003	+	0.172537i
$82$	5.32333			0.587863
$83$			1.28020i			0.140521i	0.997529	+	0.0702603i	$0.0223830\pi$
$83$			1.28020i			0.140521i	−0.997529	+	0.0702603i	$0.977617\pi$
$84$		0			0
$85$	5.57301	−	3.07066i	0.604478	−	0.333060i
$86$			2.68989i			0.290058i
$87$	−12.0071	−	11.0087i	−1.28729	−	1.18026i
$88$			6.01614i			0.641322i
$89$	3.08600			0.327116			0.163558	−	0.986534i	$-0.447703\pi$
$89$	3.08600			0.327116			0.163558	+	0.986534i	$0.447703\pi$
$90$	−5.57299	+	3.73388i	−0.587444	+	0.393585i
$91$		0			0
$92$	2.10323			0.219277
$93$	−3.42657	−	3.14165i	−0.355319	−	0.325774i
$94$		−	3.12679i		−	0.322504i
$95$	−13.9527	+	7.68780i	−1.43152	+	0.788751i
$96$	1.17052	−	1.27667i	0.119465	−	0.130300i
$97$	−1.90549			−0.193474			−0.0967368	−	0.995310i	$-0.530841\pi$
$97$	−1.90549			−0.193474			−0.0967368	+	0.995310i	$0.530841\pi$
$98$		0			0
$99$	−17.9806	+	1.56288i	−1.80712	+	0.157076i
$100$	−2.67114	+	4.22670i	−0.267114	+	0.422670i
$101$	7.02133			0.698648			0.349324	−	0.937002i	$-0.386411\pi$
$101$	7.02133			0.698648			0.349324	+	0.937002i	$0.386411\pi$
$102$	−3.63291	−	3.33083i	−0.359711	−	0.329801i
$103$	9.51562			0.937602			0.468801	−	0.883304i	$-0.344686\pi$
$103$	9.51562			0.937602			0.468801	+	0.883304i	$0.344686\pi$
$104$	0.864346			0.0847561
$105$		0			0
$106$	11.9744			1.16306
$107$	−9.23877			−0.893146			−0.446573	−	0.894747i	$-0.647356\pi$
$107$	−9.23877			−0.893146			−0.446573	+	0.894747i	$0.647356\pi$
$108$	4.11971	+	3.16670i	0.396419	+	0.304716i
$109$	4.93955			0.473123			0.236562	−	0.971616i	$-0.423979\pi$
$109$	4.93955			0.473123			0.236562	+	0.971616i	$0.423979\pi$
$110$	−11.7824	+	6.49194i	−1.12340	+	0.618982i
$111$	−8.70388	−	7.98015i	−0.826135	−	0.757442i
$112$		0			0
$113$	11.3769			1.07025			0.535126	−	0.844772i	$-0.320264\pi$
$113$	11.3769			1.07025			0.535126	+	0.844772i	$0.320264\pi$
$114$	9.09545	+	8.33916i	0.851867	+	0.781034i
$115$	2.26957	+	4.11910i	0.211639	+	0.384108i
$116$			9.40499i			0.873231i
$117$	0.224541	+	2.58330i	0.0207589	+	0.238826i
$118$	−7.09456			−0.653107
$119$		0			0
$120$	3.76340	+	0.914769i	0.343550	+	0.0835066i
$121$	−25.1939			−2.29035
$122$		−	9.33672i		−	0.845307i
$123$	6.23105	−	6.79615i	0.561835	−	0.612788i
$124$			2.68399i			0.241029i
$125$	−11.1602	−	0.670330i	−0.998201	−	0.0599562i
$126$		0			0
$127$			20.8126i			1.84682i	0.383813	+	0.923411i	$0.374611\pi$
$127$			20.8126i			1.84682i	−0.383813	+	0.923411i	$0.625389\pi$
$128$	−1.00000			−0.0883883
$129$	3.43410	+	3.14856i	0.302356	+	0.277215i
$130$	0.932706	+	1.69279i	0.0818037	+	0.148467i
$131$	−7.45191			−0.651076			−0.325538	−	0.945529i	$-0.605545\pi$
$131$	−7.45191			−0.651076			−0.325538	+	0.945529i	$0.605545\pi$
$132$	7.68063	+	7.04199i	0.668513	+	0.612926i
$133$		0			0
$134$		−	6.56038i		−	0.566731i
$135$	−1.75634	+	11.4854i	−0.151161	+	0.988509i
$136$			2.84561i			0.244009i
$137$	4.00937			0.342544			0.171272	−	0.985224i	$-0.445212\pi$
$137$	4.00937			0.342544			0.171272	+	0.985224i	$0.445212\pi$
$138$	2.46187	−	2.68514i	0.209568	−	0.228574i
$139$			15.6807i			1.33002i	0.746833	+	0.665012i	$0.231573\pi$
$139$			15.6807i			1.33002i	−0.746833	+	0.665012i	$0.768427\pi$
$140$		0			0
$141$	−3.99189	−	3.65996i	−0.336178	−	0.308224i
$142$			4.46562i			0.374746i
$143$			5.20002i			0.434848i
$144$	−0.259782	−	2.98873i	−0.0216485	−	0.249061i
$145$	−18.4193	+	10.1488i	−1.52964	+	0.842813i
$146$	12.7989			1.05925
$147$		0			0
$148$			6.81763i			0.560406i
$149$			8.37964i			0.686487i	0.939246	+	0.343243i	$0.111526\pi$
$149$			8.37964i			0.686487i	−0.939246	+	0.343243i	$0.888474\pi$
$150$	2.26950	+	8.35759i	0.185304	+	0.682395i
$151$	8.07977			0.657522			0.328761	−	0.944413i	$-0.393369\pi$
$151$	8.07977			0.657522			0.328761	+	0.944413i	$0.393369\pi$
$152$		−	7.12434i		−	0.577861i
$153$	−8.50475	+	0.739237i	−0.687568	+	0.0597637i
$154$		0			0
$155$	−5.25648	+	2.89626i	−0.422211	+	0.232633i
$156$	1.01173	−	1.10349i	0.0810033	−	0.0883496i
$157$	−4.46327			−0.356207			−0.178104	−	0.984012i	$-0.556996\pi$
$157$	−4.46327			−0.356207			−0.178104	+	0.984012i	$0.556996\pi$
$158$	−3.35798			−0.267147
$159$	14.0163	−	15.2874i	1.11156	−	1.21237i
$160$	−1.07909	−	1.95846i	−0.0853094	−	0.154830i
$161$		0			0
$162$	8.86503	−	1.55284i	0.696502	−	0.122002i
$163$		−	21.7075i		−	1.70026i	−0.526572	−	0.850131i	$-0.676523\pi$
$163$		−	21.7075i		−	1.70026i	0.526572	−	0.850131i	$-0.323477\pi$
$164$	−5.32333			−0.415682
$165$	−5.50338	+	22.6411i	−0.428437	+	1.76261i
$166$		−	1.28020i		−	0.0993631i
$167$		−	15.0916i		−	1.16783i	−0.811816	−	0.583913i	$-0.801521\pi$
$167$		−	15.0916i		−	1.16783i	0.811816	−	0.583913i	$-0.198479\pi$
$168$		0			0
$169$	−12.2529			−0.942531
$170$	−5.57301	+	3.07066i	−0.427430	+	0.235509i
$171$	21.2928	−	1.85077i	1.62830	−	0.141532i
$172$		−	2.68989i		−	0.205102i
$173$			13.9077i			1.05738i	0.848814	+	0.528692i	$0.177317\pi$
$173$			13.9077i			1.05738i	−0.848814	+	0.528692i	$0.822683\pi$
$174$	12.0071	+	11.0087i	0.910255	+	0.834567i
$175$		0			0
$176$		−	6.01614i		−	0.453483i
$177$	−8.30430	+	9.05742i	−0.624189	+	0.680798i
$178$	−3.08600			−0.231306
$179$		−	19.7081i		−	1.47305i	−0.676408	−	0.736527i	$-0.736464\pi$
$179$		−	19.7081i		−	1.47305i	0.676408	−	0.736527i	$-0.263536\pi$
$180$	5.57299	−	3.73388i	0.415386	−	0.278307i
$181$		−	6.02435i		−	0.447787i	−0.974614	−	0.223893i	$-0.928123\pi$
$181$		−	6.02435i		−	0.447787i	0.974614	−	0.223893i	$-0.0718767\pi$
$182$		0			0
$183$	−11.9199	−	10.9288i	−0.881146	−	0.807879i
$184$	−2.10323			−0.155052
$185$	−13.3521	+	7.35683i	−0.981663	+	0.540885i
$186$	3.42657	+	3.14165i	0.251248	+	0.230357i
$187$	−17.1196			−1.25191
$188$			3.12679i			0.228045i
$189$		0			0
$190$	13.9527	−	7.68780i	1.01224	−	0.557731i
$191$			1.81768i			0.131523i	0.997835	+	0.0657614i	$0.0209476\pi$
$191$			1.81768i			0.131523i	−0.997835	+	0.0657614i	$0.979052\pi$
$192$	−1.17052	+	1.27667i	−0.0844748	+	0.0921359i
$193$		−	0.613146i		−	0.0441352i	−0.999756	−	0.0220676i	$-0.992975\pi$
$193$		−	0.613146i		−	0.0441352i	0.999756	−	0.0220676i	$-0.00702491\pi$
$194$	1.90549			0.136807
$195$	3.25288	+	0.790677i	0.232944	+	0.0566216i
$196$		0			0
$197$	−12.5151			−0.891663			−0.445832	−	0.895117i	$-0.647092\pi$
$197$	−12.5151			−0.891663			−0.445832	+	0.895117i	$0.647092\pi$
$198$	17.9806	−	1.56288i	1.27783	−	0.111069i
$199$			10.7743i			0.763768i	0.924210	+	0.381884i	$0.124725\pi$
$199$			10.7743i			0.763768i	−0.924210	+	0.381884i	$0.875275\pi$
$200$	2.67114	−	4.22670i	0.188878	−	0.298873i
$201$	−8.37545	−	7.67903i	−0.590759	−	0.541637i
$202$	−7.02133			−0.494019
$203$		0			0
$204$	3.63291	+	3.33083i	0.254354	+	0.233205i
$205$	−5.74434	−	10.4255i	−0.401202	−	0.728151i
$206$	−9.51562			−0.662984
$207$	−0.546381	−	6.28599i	−0.0379761	−	0.436907i
$208$	−0.864346			−0.0599316
$209$	42.8610			2.96476
$210$		0			0
$211$	4.66797			0.321356			0.160678	−	0.987007i	$-0.448632\pi$
$211$	4.66797			0.321356			0.160678	+	0.987007i	$0.448632\pi$
$212$	−11.9744			−0.822408
$213$	5.70113	+	5.22708i	0.390635	+	0.358154i
$214$	9.23877			0.631550
$215$	5.26804	−	2.90263i	0.359277	−	0.197957i
$216$	−4.11971	−	3.16670i	−0.280311	−	0.215467i
$217$		0			0
$218$	−4.93955			−0.334549
$219$	14.9813	−	16.3400i	1.01235	−	1.10416i
$220$	11.7824	−	6.49194i	0.794367	−	0.437687i
$221$			2.45959i			0.165450i
$222$	8.70388	+	7.98015i	0.584166	+	0.535593i
$223$	0.973096			0.0651633			0.0325817	−	0.999469i	$-0.489627\pi$
$223$	0.973096			0.0651633			0.0325817	+	0.999469i	$0.489627\pi$
$224$		0			0
$225$	13.3264	+	6.88529i	0.888426	+	0.459019i
$226$	−11.3769			−0.756783
$227$			23.8398i			1.58231i	0.611618	+	0.791153i	$0.290519\pi$
$227$			23.8398i			1.58231i	−0.611618	+	0.791153i	$0.709481\pi$
$228$	−9.09545	−	8.33916i	−0.602361	−	0.552275i
$229$			19.7831i			1.30730i	0.756797	+	0.653650i	$0.226763\pi$
$229$			19.7831i			1.30730i	−0.756797	+	0.653650i	$0.773237\pi$
$230$	−2.26957	−	4.11910i	−0.149651	−	0.271605i
$231$		0			0
$232$		−	9.40499i		−	0.617468i
$233$	−1.78655			−0.117041			−0.0585205	−	0.998286i	$-0.518638\pi$
$233$	−1.78655			−0.117041			−0.0585205	+	0.998286i	$0.518638\pi$
$234$	−0.224541	−	2.58330i	−0.0146787	−	0.168875i
$235$	−6.12370	+	3.37408i	−0.399466	+	0.220101i
$236$	7.09456			0.461817
$237$	−3.93058	+	4.28704i	−0.255318	+	0.278473i
$238$		0			0
$239$			17.2961i			1.11879i	0.828900	+	0.559396i	$0.188967\pi$
$239$			17.2961i			1.11879i	−0.828900	+	0.559396i	$0.811033\pi$
$240$	−3.76340	−	0.914769i	−0.242927	−	0.0590481i
$241$			8.26145i			0.532167i	0.963950	+	0.266083i	$0.0857296\pi$
$241$			8.26145i			0.532167i	−0.963950	+	0.266083i	$0.914270\pi$
$242$	25.1939			1.61952
$243$	8.39420	−	13.1353i	0.538488	−	0.842633i
$244$			9.33672i			0.597722i
$245$		0			0
$246$	−6.23105	+	6.79615i	−0.397277	+	0.433306i
$247$		−	6.15790i		−	0.391818i
$248$		−	2.68399i		−	0.170433i
$249$	−1.63440	−	1.49850i	−0.103576	−	0.0949636i
$250$	11.1602	+	0.670330i	0.705835	+	0.0423954i
$251$	−15.8307			−0.999224			−0.499612	−	0.866249i	$-0.666524\pi$
$251$	−15.8307			−0.999224			−0.499612	+	0.866249i	$0.666524\pi$
$252$		0			0
$253$		−	12.6533i		−	0.795508i
$254$		−	20.8126i		−	1.30590i
$255$	−2.60307	+	10.7092i	−0.163011	+	0.670634i
$256$	1.00000			0.0625000
$257$		−	29.7033i		−	1.85284i	−0.376491	−	0.926420i	$-0.622869\pi$
$257$		−	29.7033i		−	1.85284i	0.376491	−	0.926420i	$-0.377131\pi$
$258$	−3.43410	−	3.14856i	−0.213798	−	0.196021i
$259$		0			0
$260$	−0.932706	−	1.69279i	−0.0578440	−	0.104982i
$261$	28.1090	−	2.44324i	1.73990	−	0.151233i
$262$	7.45191			0.460380
$263$	23.1913			1.43003			0.715017	−	0.699107i	$-0.246419\pi$
$263$	23.1913			1.43003			0.715017	+	0.699107i	$0.246419\pi$
$264$	−7.68063	−	7.04199i	−0.472710	−	0.433404i
$265$	−12.9215	−	23.4515i	−0.793760	−	1.44061i
$266$		0			0
$267$	−3.61222	+	3.93981i	−0.221064	+	0.241113i
$268$			6.56038i			0.400739i
$269$	−13.3485			−0.813873			−0.406937	−	0.913456i	$-0.633403\pi$
$269$	−13.3485			−0.813873			−0.406937	+	0.913456i	$0.633403\pi$
$270$	1.75634	−	11.4854i	0.106887	−	0.698981i
$271$		−	17.0251i		−	1.03420i	−0.855925	−	0.517099i	$-0.827012\pi$
$271$		−	17.0251i		−	1.03420i	0.855925	−	0.517099i	$-0.172988\pi$
$272$		−	2.84561i		−	0.172540i
$273$		0			0
$274$	−4.00937			−0.242215
$275$	25.4284	+	16.0699i	1.53339	+	0.969053i
$276$	−2.46187	+	2.68514i	−0.148187	+	0.161626i
$277$		−	19.4359i		−	1.16779i	−0.811830	−	0.583894i	$-0.801528\pi$
$277$		−	19.4359i		−	1.16779i	0.811830	−	0.583894i	$-0.198472\pi$
$278$		−	15.6807i		−	0.940468i
$279$	8.02171	−	0.697250i	0.480247	−	0.0417433i
$280$		0			0
$281$			10.9247i			0.651714i	0.945419	+	0.325857i	$0.105653\pi$
$281$			10.9247i			0.651714i	−0.945419	+	0.325857i	$0.894347\pi$
$282$	3.99189	+	3.65996i	0.237713	+	0.217948i
$283$	27.9118			1.65918			0.829592	−	0.558371i	$-0.188573\pi$
$283$	27.9118			1.65918			0.829592	+	0.558371i	$0.188573\pi$
$284$		−	4.46562i		−	0.264986i
$285$	6.51713	−	26.8118i	0.386042	−	1.58819i
$286$		−	5.20002i		−	0.307484i
$287$		0			0
$288$	0.259782	+	2.98873i	0.0153078	+	0.176113i
$289$	8.90252			0.523678
$290$	18.4193	−	10.1488i	1.08162	−	0.595959i
$291$	2.23041	−	2.43269i	0.130749	−	0.142607i
$292$	−12.7989			−0.749000
$293$			9.87883i			0.577127i	0.957461	+	0.288564i	$0.0931777\pi$
$293$			9.87883i			0.577127i	−0.957461	+	0.288564i	$0.906822\pi$
$294$		0			0
$295$	7.65566	+	13.8944i	0.445730	+	0.808964i
$296$		−	6.81763i		−	0.396267i
$297$	19.0513	−	24.7847i	1.10547	−	1.43816i
$298$		−	8.37964i		−	0.485420i
$299$	−1.81792			−0.105133
$300$	−2.26950	−	8.35759i	−0.131030	−	0.482526i
$301$		0			0
$302$	−8.07977			−0.464938
$303$	−8.21858	+	8.96393i	−0.472145	+	0.514964i
$304$			7.12434i			0.408609i
$305$	−18.2856	+	10.0751i	−1.04703	+	0.576901i
$306$	8.50475	−	0.739237i	0.486184	−	0.0422593i
$307$	−2.95602			−0.168709			−0.0843545	−	0.996436i	$-0.526883\pi$
$307$	−2.95602			−0.168709			−0.0843545	+	0.996436i	$0.526883\pi$
$308$		0			0
$309$	−11.1382	+	12.1483i	−0.633629	+	0.691094i
$310$	5.25648	−	2.89626i	0.298548	−	0.164496i
$311$	−8.59316			−0.487273			−0.243637	−	0.969867i	$-0.578340\pi$
$311$	−8.59316			−0.487273			−0.243637	+	0.969867i	$0.578340\pi$
$312$	−1.01173	+	1.10349i	−0.0572780	+	0.0624726i
$313$	−19.8544			−1.12224			−0.561119	−	0.827735i	$-0.689629\pi$
$313$	−19.8544			−1.12224			−0.561119	+	0.827735i	$0.689629\pi$
$314$	4.46327			0.251877
$315$		0			0
$316$	3.35798			0.188901
$317$	29.2008			1.64008			0.820041	−	0.572304i	$-0.193950\pi$
$317$	29.2008			1.64008			0.820041	+	0.572304i	$0.193950\pi$
$318$	−14.0163	+	15.2874i	−0.785994	+	0.857277i
$319$	56.5817			3.16797
$320$	1.07909	+	1.95846i	0.0603229	+	0.109481i
$321$	10.8141	−	11.7949i	0.603586	−	0.658326i
$322$		0			0
$323$	20.2731			1.12802
$324$	−8.86503	+	1.55284i	−0.492501	+	0.0862686i
$325$	2.30879	−	3.65334i	0.128068	−	0.202651i
$326$			21.7075i			1.20227i
$327$	−5.78183	+	6.30619i	−0.319736	+	0.348733i
$328$	5.32333			0.293932
$329$		0			0
$330$	5.50338	−	22.6411i	0.302951	−	1.24635i
$331$	−8.99040			−0.494157			−0.247079	−	0.968995i	$-0.579471\pi$
$331$	−8.99040			−0.494157			−0.247079	+	0.968995i	$0.579471\pi$
$332$			1.28020i			0.0702603i
$333$	20.3761	−	1.77110i	1.11660	−	0.0970555i
$334$			15.0916i			0.825777i
$335$	−12.8482	+	7.07923i	−0.701975	+	0.386780i
$336$		0			0
$337$		−	16.7043i		−	0.909939i	−0.890507	−	0.454969i	$-0.849650\pi$
$337$		−	16.7043i		−	0.909939i	0.890507	−	0.454969i	$-0.150350\pi$
$338$	12.2529			0.666470
$339$	−13.3169	+	14.5246i	−0.723274	+	0.788869i
$340$	5.57301	−	3.07066i	0.302239	−	0.166530i
$341$	16.1472			0.874421
$342$	−21.2928	+	1.85077i	−1.15138	+	0.100078i
$343$		0			0
$344$			2.68989i			0.145029i
$345$	−7.91531	−	1.92397i	−0.426146	−	0.103583i
$346$		−	13.9077i		−	0.747684i
$347$	23.5557			1.26454			0.632268	−	0.774750i	$-0.282124\pi$
$347$	23.5557			1.26454			0.632268	+	0.774750i	$0.282124\pi$
$348$	−12.0071	−	11.0087i	−0.643647	−	0.590128i
$349$			26.3071i			1.40819i	0.710108	+	0.704093i	$0.248646\pi$
$349$			26.3071i			1.40819i	−0.710108	+	0.704093i	$0.751354\pi$
$350$		0			0
$351$	−3.56085	−	2.73713i	−0.190064	−	0.146097i
$352$			6.01614i			0.320661i
$353$			8.37829i			0.445931i	0.974826	+	0.222966i	$0.0715738\pi$
$353$			8.37829i			0.445931i	−0.974826	+	0.222966i	$0.928426\pi$
$354$	8.30430	−	9.05742i	0.441369	−	0.481397i
$355$	8.74574	−	4.81880i	0.464176	−	0.255755i
$356$	3.08600			0.163558
$357$		0			0
$358$			19.7081i			1.04161i
$359$		−	26.9651i		−	1.42317i	−0.702602	−	0.711583i	$-0.747979\pi$
$359$		−	26.9651i		−	1.42317i	0.702602	−	0.711583i	$-0.252021\pi$
$360$	−5.57299	+	3.73388i	−0.293722	+	0.196793i
$361$	−31.7563			−1.67138
$362$			6.02435i			0.316633i
$363$	29.4899	−	32.1643i	1.54782	−	1.68819i
$364$		0			0
$365$	−13.8112	−	25.0662i	−0.722909	−	1.31202i
$366$	11.9199	+	10.9288i	0.623065	+	0.571257i
$367$	−24.6775			−1.28815			−0.644077	−	0.764961i	$-0.722758\pi$
$367$	−24.6775			−1.28815			−0.644077	+	0.764961i	$0.722758\pi$
$368$	2.10323			0.109639
$369$	1.38290	+	15.9100i	0.0719911	+	0.828242i
$370$	13.3521	−	7.35683i	0.694141	−	0.382463i
$371$		0			0
$372$	−3.42657	−	3.14165i	−0.177659	−	0.162887i
$373$			26.1293i			1.35293i	0.736477	+	0.676463i	$0.236488\pi$
$373$			26.1293i			1.35293i	−0.736477	+	0.676463i	$0.763512\pi$
$374$	17.1196			0.885231
$375$	13.9190	−	13.4633i	0.718775	−	0.695243i
$376$		−	3.12679i		−	0.161252i
$377$		−	8.12917i		−	0.418673i
$378$		0			0
$379$	25.5437			1.31209			0.656046	−	0.754721i	$-0.272228\pi$
$379$	25.5437			1.31209			0.656046	+	0.754721i	$0.272228\pi$
$380$	−13.9527	+	7.68780i	−0.715761	+	0.394376i
$381$	−26.5709	−	24.3615i	−1.36127	−	1.24808i
$382$		−	1.81768i		−	0.0930006i
$383$			15.2142i			0.777409i	0.921362	+	0.388705i	$0.127077\pi$
$383$			15.2142i			0.777409i	−0.921362	+	0.388705i	$0.872923\pi$
$384$	1.17052	−	1.27667i	0.0597327	−	0.0651499i
$385$		0			0
$386$			0.613146i			0.0312083i
$387$	−8.03935	+	0.698784i	−0.408663	+	0.0355212i
$388$	−1.90549			−0.0967368
$389$			15.5321i			0.787509i	0.919216	+	0.393754i	$0.128824\pi$
$389$			15.5321i			0.787509i	−0.919216	+	0.393754i	$0.871176\pi$
$390$	−3.25288	−	0.790677i	−0.164716	−	0.0400375i
$391$		−	5.98497i		−	0.302673i
$392$		0			0
$393$	8.72258	−	9.51364i	0.439996	−	0.479900i
$394$	12.5151			0.630501
$395$	3.62356	+	6.57648i	0.182321	+	0.330899i
$396$	−17.9806	+	1.56288i	−0.903560	+	0.0785378i
$397$	−9.93654			−0.498701			−0.249350	−	0.968413i	$-0.580217\pi$
$397$	−9.93654			−0.498701			−0.249350	+	0.968413i	$0.580217\pi$
$398$		−	10.7743i		−	0.540066i
$399$		0			0
$400$	−2.67114	+	4.22670i	−0.133557	+	0.211335i
$401$			14.2780i			0.713007i	0.934294	+	0.356504i	$0.116031\pi$
$401$			14.2780i			0.713007i	−0.934294	+	0.356504i	$0.883969\pi$
$402$	8.37545	+	7.67903i	0.417730	+	0.382995i
$403$		−	2.31989i		−	0.115562i
$404$	7.02133			0.349324
$405$	−12.6073	−	15.6862i	−0.626462	−	0.779452i
$406$		0			0
$407$	41.0158			2.03308
$408$	−3.63291	−	3.33083i	−0.179856	−	0.164901i
$409$		−	20.1305i		−	0.995387i	−0.867353	−	0.497694i	$-0.834180\pi$
$409$		−	20.1305i		−	0.995387i	0.867353	−	0.497694i	$-0.165820\pi$
$410$	5.74434	+	10.4255i	0.283693	+	0.514880i
$411$	−4.69304	+	5.11865i	−0.231491	+	0.252485i
$412$	9.51562			0.468801
$413$		0			0
$414$	0.546381	+	6.28599i	0.0268532	+	0.308940i
$415$	−2.50723	+	1.38145i	−0.123075	+	0.0678129i
$416$	0.864346			0.0423781
$417$	−20.0192	−	18.3546i	−0.980343	−	0.898827i
$418$	−42.8610			−2.09640
$419$	−11.8896			−0.580845			−0.290422	−	0.956899i	$-0.593796\pi$
$419$	−11.8896			−0.580845			−0.290422	+	0.956899i	$0.593796\pi$
$420$		0			0
$421$	11.6346			0.567038			0.283519	−	0.958967i	$-0.408498\pi$
$421$	11.6346			0.567038			0.283519	+	0.958967i	$0.408498\pi$
$422$	−4.66797			−0.227233
$423$	9.34514	−	0.812283i	0.454376	−	0.0394946i
$424$	11.9744			0.581530
$425$	12.0275	+	7.60100i	0.583421	+	0.368703i
$426$	−5.70113	−	5.22708i	−0.276221	−	0.253253i
$427$		0			0
$428$	−9.23877			−0.446573
$429$	−6.63872	−	6.08671i	−0.320521	−	0.293869i
$430$	−5.26804	+	2.90263i	−0.254047	+	0.139977i
$431$		−	4.34854i		−	0.209462i	−0.994501	−	0.104731i	$-0.966602\pi$
$431$		−	4.34854i		−	0.209462i	0.994501	−	0.104731i	$-0.0333981\pi$
$432$	4.11971	+	3.16670i	0.198210	+	0.152358i
$433$	−15.3505			−0.737698			−0.368849	−	0.929489i	$-0.620248\pi$
$433$	−15.3505			−0.737698			−0.368849	+	0.929489i	$0.620248\pi$
$434$		0			0
$435$	8.60340	−	35.3948i	0.412501	−	1.69705i
$436$	4.93955			0.236562
$437$			14.9841i			0.716789i
$438$	−14.9813	+	16.3400i	−0.715837	+	0.780756i
$439$			3.55667i			0.169751i	0.996392	+	0.0848753i	$0.0270492\pi$
$439$			3.55667i			0.169751i	−0.996392	+	0.0848753i	$0.972951\pi$
$440$	−11.7824	+	6.49194i	−0.561702	+	0.309491i
$441$		0			0
$442$		−	2.45959i		−	0.116991i
$443$	−9.38403			−0.445849			−0.222924	−	0.974836i	$-0.571560\pi$
$443$	−9.38403			−0.445849			−0.222924	+	0.974836i	$0.571560\pi$
$444$	−8.70388	−	7.98015i	−0.413068	−	0.378721i
$445$	3.33007	+	6.04382i	0.157860	+	0.286504i
$446$	−0.973096			−0.0460774
$447$	−10.6981	−	9.80851i	−0.506000	−	0.463927i
$448$		0			0
$449$			0.400479i			0.0188998i	0.999955	+	0.00944989i	$0.00300804\pi$
$449$			0.400479i			0.0188998i	−0.999955	+	0.00944989i	$0.996992\pi$
$450$	−13.3264	−	6.88529i	−0.628212	−	0.324576i
$451$			32.0259i			1.50804i
$452$	11.3769			0.535126
$453$	−9.45750	+	10.3152i	−0.444352	+	0.484651i
$454$		−	23.8398i		−	1.11886i
$455$		0			0
$456$	9.09545	+	8.33916i	0.425933	+	0.390517i
$457$		−	34.3815i		−	1.60830i	−0.594428	−	0.804149i	$-0.702622\pi$
$457$		−	34.3815i		−	1.60830i	0.594428	−	0.804149i	$-0.297378\pi$
$458$		−	19.7831i		−	0.924401i
$459$	9.01119	−	11.7231i	0.420606	−	0.547186i
$460$	2.26957	+	4.11910i	0.105819	+	0.192054i
$461$	−33.8119			−1.57478			−0.787389	−	0.616456i	$-0.788568\pi$
$461$	−33.8119			−1.57478			−0.787389	+	0.616456i	$0.788568\pi$
$462$		0			0
$463$			0.505232i			0.0234801i	0.999931	+	0.0117401i	$0.00373706\pi$
$463$			0.505232i			0.0234801i	−0.999931	+	0.0117401i	$0.996263\pi$
$464$			9.40499i			0.436616i
$465$	2.45523	−	10.1009i	0.113858	−	0.468419i
$466$	1.78655			0.0827604
$467$		−	24.8661i		−	1.15067i	−0.817919	−	0.575333i	$-0.804873\pi$
$467$		−	24.8661i		−	1.15067i	0.817919	−	0.575333i	$-0.195127\pi$
$468$	0.224541	+	2.58330i	0.0103794	+	0.119413i
$469$		0			0
$470$	6.12370	−	3.37408i	0.282465	−	0.155635i
$471$	5.22433	−	5.69812i	0.240724	−	0.262556i
$472$	−7.09456			−0.326554
$473$	−16.1827			−0.744083
$474$	3.93058	−	4.28704i	0.180537	−	0.196910i
$475$	−30.1125	−	19.0301i	−1.38166	−	0.873161i
$476$		0			0
$477$	3.11074	+	35.7884i	0.142431	+	1.63864i
$478$		−	17.2961i		−	0.791106i
$479$	−1.48138			−0.0676859			−0.0338430	−	0.999427i	$-0.510775\pi$
$479$	−1.48138			−0.0676859			−0.0338430	+	0.999427i	$0.510775\pi$
$480$	3.76340	+	0.914769i	0.171775	+	0.0417533i
$481$		−	5.89279i		−	0.268688i
$482$		−	8.26145i		−	0.376299i
$483$		0			0
$484$	−25.1939			−1.14518
$485$	−2.05620	−	3.73184i	−0.0933671	−	0.169454i
$486$	−8.39420	+	13.1353i	−0.380769	+	0.595832i
$487$			7.86665i			0.356472i	0.983988	+	0.178236i	$0.0570391\pi$
$487$			7.86665i			0.356472i	−0.983988	+	0.178236i	$0.942961\pi$
$488$		−	9.33672i		−	0.422653i
$489$	27.7133	+	25.4090i	1.25324	+	1.14903i
$490$		0			0
$491$		−	16.0379i		−	0.723778i	−0.932221	−	0.361889i	$-0.882132\pi$
$491$		−	16.0379i		−	0.723778i	0.932221	−	0.361889i	$-0.117868\pi$
$492$	6.23105	−	6.79615i	0.280917	−	0.306394i
$493$	26.7629			1.20534
$494$			6.15790i			0.277057i
$495$	−22.4635	−	33.5278i	−1.00966	−	1.50696i
$496$			2.68399i			0.120514i
$497$		0			0
$498$	1.63440	+	1.49850i	0.0732392	+	0.0671494i
$499$	8.37964			0.375124			0.187562	−	0.982253i	$-0.439941\pi$
$499$	8.37964			0.375124			0.187562	+	0.982253i	$0.439941\pi$
$500$	−11.1602	−	0.670330i	−0.499101	−	0.0299781i
$501$	19.2671	+	17.6650i	0.860789	+	0.789214i
$502$	15.8307			0.706558
$503$			31.5447i			1.40651i	0.710939	+	0.703254i	$0.248270\pi$
$503$			31.5447i			1.40651i	−0.710939	+	0.703254i	$0.751730\pi$
$504$		0			0
$505$	7.57663	+	13.7510i	0.337156	+	0.611911i
$506$			12.6533i			0.562509i
$507$	14.3422	−	15.6429i	0.636961	−	0.694727i
$508$			20.8126i			0.923411i
$509$	21.9316			0.972101			0.486051	−	0.873931i	$-0.338437\pi$
$509$	21.9316			0.972101			0.486051	+	0.873931i	$0.338437\pi$
$510$	2.60307	−	10.7092i	0.115266	−	0.474210i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−22.5607	+	29.3502i	−0.996079	+	1.29584i
$514$			29.7033i			1.31016i
$515$	10.2682	+	18.6360i	0.452471	+	0.821199i
$516$	3.43410	+	3.14856i	0.151178	+	0.138608i
$517$	18.8112			0.827316
$518$		0			0
$519$	−17.7556	−	16.2792i	−0.779384	−	0.714578i
$520$	0.932706	+	1.69279i	0.0409019	+	0.0742337i
$521$	−6.73422			−0.295032			−0.147516	−	0.989060i	$-0.547128\pi$
$521$	−6.73422			−0.295032			−0.147516	+	0.989060i	$0.547128\pi$
$522$	−28.1090	+	2.44324i	−1.23030	+	0.106938i
$523$	36.6831			1.60404			0.802020	−	0.597298i	$-0.203759\pi$
$523$	36.6831			1.60404			0.802020	+	0.597298i	$0.203759\pi$
$524$	−7.45191			−0.325538
$525$		0			0
$526$	−23.1913			−1.01119
$527$	7.63757			0.332698
$528$	7.68063	+	7.04199i	0.334257	+	0.306463i
$529$	−18.5764			−0.807670
$530$	12.9215	+	23.4515i	0.561273	+	1.01867i
$531$	−1.84304	−	21.2037i	−0.0799810	−	0.920164i
$532$		0			0
$533$	4.60120			0.199300
$534$	3.61222	−	3.93981i	0.156316	−	0.170492i
$535$	−9.96945	−	18.0938i	−0.431017	−	0.782262i
$536$		−	6.56038i		−	0.283365i
$537$	25.1608	+	23.0687i	1.08577	+	0.995487i
$538$	13.3485			0.575495
$539$		0			0
$540$	−1.75634	+	11.4854i	−0.0755807	+	0.494255i
$541$	6.45386			0.277473			0.138737	−	0.990329i	$-0.455696\pi$
$541$	6.45386			0.277473			0.138737	+	0.990329i	$0.455696\pi$
$542$			17.0251i			0.731289i
$543$	7.69112	+	7.05161i	0.330058	+	0.302613i
$544$			2.84561i			0.122004i
$545$	5.33021	+	9.67392i	0.228321	+	0.414385i
$546$		0			0
$547$		−	17.9484i		−	0.767418i	−0.923454	−	0.383709i	$-0.874647\pi$
$547$		−	17.9484i		−	0.767418i	0.923454	−	0.383709i	$-0.125353\pi$
$548$	4.00937			0.171272
$549$	27.9049	−	2.42551i	1.19095	−	0.103518i
$550$	−25.4284	−	16.0699i	−1.08427	−	0.685224i
$551$	−67.0044			−2.85448
$552$	2.46187	−	2.68514i	0.104784	−	0.114287i
$553$		0			0
$554$			19.4359i			0.825751i
$555$	6.23656	−	25.6575i	0.264727	−	1.08910i
$556$			15.6807i			0.665012i
$557$	11.0063			0.466354			0.233177	−	0.972434i	$-0.425088\pi$
$557$	11.0063			0.466354			0.233177	+	0.972434i	$0.425088\pi$
$558$	−8.02171	+	0.697250i	−0.339586	+	0.0295170i
$559$			2.32499i			0.0983368i
$560$		0			0
$561$	20.0387	−	21.8561i	0.846036	−	0.922763i
$562$		−	10.9247i		−	0.460831i
$563$		−	7.74278i		−	0.326319i	−0.986600	−	0.163160i	$-0.947831\pi$
$563$		−	7.74278i		−	0.326319i	0.986600	−	0.163160i	$-0.0521686\pi$
$564$	−3.99189	−	3.65996i	−0.168089	−	0.154112i
$565$	12.2767	+	22.2813i	0.516485	+	0.937381i
$566$	−27.9118			−1.17322
$567$		0			0
$568$			4.46562i			0.187373i
$569$			29.7890i			1.24882i	0.781097	+	0.624409i	$0.214660\pi$
$569$			29.7890i			1.24882i	−0.781097	+	0.624409i	$0.785340\pi$
$570$	−6.51713	+	26.8118i	−0.272973	+	1.12302i
$571$	4.12163			0.172485			0.0862424	−	0.996274i	$-0.472514\pi$
$571$	4.12163			0.172485			0.0862424	+	0.996274i	$0.472514\pi$
$572$			5.20002i			0.217424i
$573$	−2.32058	−	2.12763i	−0.0969437	−	0.0888828i
$574$		0			0
$575$	−5.61802	+	8.88974i	−0.234288	+	0.370728i
$576$	−0.259782	−	2.98873i	−0.0108242	−	0.124530i
$577$	15.2456			0.634681			0.317341	−	0.948312i	$-0.397210\pi$
$577$	15.2456			0.634681			0.317341	+	0.948312i	$0.397210\pi$
$578$	−8.90252			−0.370296
$579$	0.782786	+	0.717698i	0.0325315	+	0.0298265i
$580$	−18.4193	+	10.1488i	−0.764820	+	0.421407i
$581$		0			0
$582$	−2.23041	+	2.43269i	−0.0924536	+	0.100838i
$583$			72.0399i			2.98359i
$584$	12.7989			0.529623
$585$	−4.81699	+	3.22736i	−0.199158	+	0.133435i
$586$		−	9.87883i		−	0.408091i
$587$			3.06358i			0.126447i	0.997999	+	0.0632237i	$0.0201382\pi$
$587$			3.06358i			0.126447i	−0.997999	+	0.0632237i	$0.979862\pi$
$588$		0			0
$589$	−19.1216			−0.787893
$590$	−7.65566	−	13.8944i	−0.315178	−	0.572024i
$591$	14.6491	−	15.9777i	0.602584	−	0.657233i
$592$			6.81763i			0.280203i
$593$		−	0.944328i		−	0.0387789i	−0.999812	−	0.0193895i	$-0.993828\pi$
$593$		−	0.944328i		−	0.0387789i	0.999812	−	0.0193895i	$-0.00617224\pi$
$594$	−19.0513	+	24.7847i	−0.781685	+	1.01693i
$595$		0			0
$596$			8.37964i			0.343243i
$597$	−13.7552	−	12.6115i	−0.562963	−	0.516153i
$598$	1.81792			0.0743403
$599$		−	37.4531i		−	1.53029i	−0.643857	−	0.765146i	$-0.722667\pi$
$599$		−	37.4531i		−	1.53029i	0.643857	−	0.765146i	$-0.277333\pi$
$600$	2.26950	+	8.35759i	0.0926521	+	0.341197i
$601$			46.7301i			1.90616i	0.302716	+	0.953081i	$0.402107\pi$
$601$			46.7301i			1.90616i	−0.302716	+	0.953081i	$0.597893\pi$
$602$		0			0
$603$	19.6072	−	1.70427i	0.798467	−	0.0694031i
$604$	8.07977			0.328761
$605$	−27.1864	−	49.3413i	−1.10529	−	2.00601i
$606$	8.21858	−	8.96393i	0.333857	−	0.364135i
$607$	24.1453			0.980026			0.490013	−	0.871715i	$-0.336992\pi$
$607$	24.1453			0.980026			0.490013	+	0.871715i	$0.336992\pi$
$608$		−	7.12434i		−	0.288930i
$609$		0			0
$610$	18.2856	−	10.0751i	0.740362	−	0.407931i
$611$		−	2.70263i		−	0.109337i
$612$	−8.50475	+	0.739237i	−0.343784	+	0.0298819i
$613$		−	24.6198i		−	0.994383i	−0.867641	−	0.497191i	$-0.834365\pi$
$613$		−	24.6198i		−	0.994383i	0.867641	−	0.497191i	$-0.165635\pi$
$614$	2.95602			0.119295
$615$	20.0338	+	4.86962i	0.807842	+	0.196362i
$616$		0			0
$617$	−34.6057			−1.39317			−0.696586	−	0.717474i	$-0.745298\pi$
$617$	−34.6057			−1.39317			−0.696586	+	0.717474i	$0.745298\pi$
$618$	11.1382	−	12.1483i	0.448044	−	0.488677i
$619$		−	17.3011i		−	0.695388i	−0.937608	−	0.347694i	$-0.886965\pi$
$619$		−	17.3011i		−	0.695388i	0.937608	−	0.347694i	$-0.113035\pi$
$620$	−5.25648	+	2.89626i	−0.211105	+	0.116316i
$621$	8.66470	+	6.66031i	0.347702	+	0.267269i
$622$	8.59316			0.344554
$623$		0			0
$624$	1.01173	−	1.10349i	0.0405017	−	0.0441748i
$625$	−10.7301	−	22.5802i	−0.429202	−	0.903208i
$626$	19.8544			0.793542
$627$	−50.1695	+	54.7195i	−2.00358	+	2.18529i
$628$	−4.46327			−0.178104
$629$	19.4003			0.773540
$630$		0			0
$631$	6.04364			0.240593			0.120297	−	0.992738i	$-0.461615\pi$
$631$	6.04364			0.240593			0.120297	+	0.992738i	$0.461615\pi$
$632$	−3.35798			−0.133573
$633$	−5.46394	+	5.95947i	−0.217172	+	0.236868i
$634$	−29.2008			−1.15971
$635$	−40.7607	+	22.4587i	−1.61754	+	0.891245i
$636$	14.0163	−	15.2874i	0.555782	−	0.606186i
$637$		0			0
$638$	−56.5817			−2.24009
$639$	−13.3465	+	1.16009i	−0.527981	+	0.0458923i
$640$	−1.07909	−	1.95846i	−0.0426547	−	0.0774150i
$641$			4.78542i			0.189013i	0.995524	+	0.0945065i	$0.0301273\pi$
$641$			4.78542i			0.189013i	−0.995524	+	0.0945065i	$0.969873\pi$
$642$	−10.8141	+	11.7949i	−0.426800	+	0.465507i
$643$	40.9370			1.61440			0.807198	−	0.590280i	$-0.200983\pi$
$643$	40.9370			1.61440			0.807198	+	0.590280i	$0.200983\pi$
$644$		0			0
$645$	−2.46063	+	10.1231i	−0.0968871	+	0.398598i
$646$	−20.2731			−0.797634
$647$			24.3583i			0.957623i	0.877918	+	0.478811i	$0.158932\pi$
$647$			24.3583i			0.957623i	−0.877918	+	0.478811i	$0.841068\pi$
$648$	8.86503	−	1.55284i	0.348251	−	0.0610011i
$649$		−	42.6818i		−	1.67541i
$650$	−2.30879	+	3.65334i	−0.0905581	+	0.143296i
$651$		0			0
$652$		−	21.7075i		−	0.850131i
$653$	15.9386			0.623726			0.311863	−	0.950127i	$-0.399047\pi$
$653$	15.9386			0.623726			0.311863	+	0.950127i	$0.399047\pi$
$654$	5.78183	−	6.30619i	0.226087	−	0.246591i
$655$	−8.04127	−	14.5943i	−0.314198	−	0.570245i
$656$	−5.32333			−0.207841
$657$	3.32493	+	38.2525i	0.129718	+	1.49237i
$658$		0			0
$659$			1.76616i			0.0687997i	0.999408	+	0.0343998i	$0.0109520\pi$
$659$			1.76616i			0.0687997i	−0.999408	+	0.0343998i	$0.989048\pi$
$660$	−5.50338	+	22.6411i	−0.214219	+	0.881305i
$661$		−	30.5932i		−	1.18994i	−0.803748	−	0.594970i	$-0.797164\pi$
$661$		−	30.5932i		−	1.18994i	0.803748	−	0.594970i	$-0.202836\pi$
$662$	8.99040			0.349422
$663$	−3.14009	−	2.87899i	−0.121951	−	0.111811i
$664$		−	1.28020i		−	0.0496815i
$665$		0			0
$666$	−20.3761	+	1.77110i	−0.789556	+	0.0686286i
$667$			19.7809i			0.765918i
$668$		−	15.0916i		−	0.583913i
$669$	−1.13902	+	1.24232i	−0.0440372	+	0.0480310i
$670$	12.8482	−	7.07923i	0.496371	−	0.273494i
$671$	56.1710			2.16846
$672$		0			0
$673$			8.47471i			0.326676i	0.986570	+	0.163338i	$0.0522261\pi$
$673$			8.47471i			0.326676i	−0.986570	+	0.163338i	$0.947774\pi$
$674$			16.7043i			0.643424i
$675$	−24.3890	+	8.95409i	−0.938734	+	0.344643i
$676$	−12.2529			−0.471266
$677$			8.78118i			0.337488i	0.985660	+	0.168744i	$0.0539712\pi$
$677$			8.78118i			0.337488i	−0.985660	+	0.168744i	$0.946029\pi$
$678$	13.3169	−	14.5246i	0.511432	−	0.557814i
$679$		0			0
$680$	−5.57301	+	3.07066i	−0.213715	+	0.117754i
$681$	−30.4357	−	27.9049i	−1.16630	−	1.06932i
$682$	−16.1472			−0.618309
$683$	−19.7411			−0.755372			−0.377686	−	0.925934i	$-0.623280\pi$
$683$	−19.7411			−0.755372			−0.377686	+	0.925934i	$0.623280\pi$
$684$	21.2928	−	1.85077i	0.814149	−	0.0707661i
$685$	4.32647	+	7.85220i	0.165306	+	0.300017i
$686$		0			0
$687$	−25.2565	−	23.1564i	−0.963594	−	0.883471i
$688$		−	2.68989i		−	0.102551i
$689$	10.3501			0.394306
$690$	7.91531	+	1.92397i	0.301331	+	0.0732444i
$691$		−	31.4383i		−	1.19597i	−0.801508	−	0.597984i	$-0.795968\pi$
$691$		−	31.4383i		−	1.19597i	0.801508	−	0.597984i	$-0.204032\pi$
$692$			13.9077i			0.528692i
$693$		0			0
$694$	−23.5557			−0.894162
$695$	−30.7101	+	16.9209i	−1.16490	+	0.641847i
$696$	12.0071	+	11.0087i	0.455127	+	0.417284i
$697$			15.1481i			0.573775i
$698$		−	26.3071i		−	0.995738i
$699$	2.09119	−	2.28084i	0.0790960	−	0.0862693i
$700$		0			0
$701$		−	8.41296i		−	0.317753i	−0.987298	−	0.158877i	$-0.949213\pi$
$701$		−	8.41296i		−	0.317753i	0.987298	−	0.158877i	$-0.0507872\pi$
$702$	3.56085	+	2.73713i	0.134396	+	0.103306i
$703$	−48.5712			−1.83190
$704$		−	6.01614i		−	0.226742i
$705$	2.86029	−	11.7674i	0.107725	−	0.443185i
$706$		−	8.37829i		−	0.315321i
$707$		0			0
$708$	−8.30430	+	9.05742i	−0.312095	+	0.340399i
$709$	45.6062			1.71278			0.856388	−	0.516333i	$-0.172703\pi$
$709$	45.6062			1.71278			0.856388	+	0.516333i	$0.172703\pi$
$710$	−8.74574	+	4.81880i	−0.328222	+	0.180846i
$711$	−0.872343	−	10.0361i	−0.0327154	−	0.376384i
$712$	−3.08600			−0.115653
$713$			5.64504i			0.211409i
$714$		0			0
$715$	−10.1840	+	5.61128i	−0.380862	+	0.209850i
$716$		−	19.7081i		−	0.736527i
$717$	−22.0815	−	20.2454i	−0.824647	−	0.756078i
$718$			26.9651i			1.00633i
$719$	2.90920			0.108495			0.0542475	−	0.998528i	$-0.482724\pi$
$719$	2.90920			0.108495			0.0542475	+	0.998528i	$0.482724\pi$
$720$	5.57299	−	3.73388i	0.207693	−	0.139153i
$721$		0			0
$722$	31.7563			1.18185
$723$	−10.5472	−	9.67016i	−0.392253	−	0.359637i
$724$		−	6.02435i		−	0.223893i
$725$	−39.7521	−	25.1220i	−1.47636	−	0.933008i
$726$	−29.4899	+	32.1643i	−1.09447	+	1.19373i
$727$	−38.0076			−1.40963			−0.704813	−	0.709394i	$-0.748969\pi$
$727$	−38.0076			−1.40963			−0.704813	+	0.709394i	$0.748969\pi$
$728$		0			0
$729$	6.94398	+	26.0918i	0.257184	+	0.966362i
$730$	13.8112	+	25.0662i	0.511174	+	0.927741i
$731$	−7.65436			−0.283107
$732$	−11.9199	−	10.9288i	−0.440573	−	0.403940i
$733$	25.5691			0.944417			0.472208	−	0.881487i	$-0.343457\pi$
$733$	25.5691			0.944417			0.472208	+	0.881487i	$0.343457\pi$
$734$	24.6775			0.910862
$735$		0			0
$736$	−2.10323			−0.0775262
$737$	39.4681			1.45383
$738$	−1.38290	−	15.9100i	−0.0509054	−	0.585655i
$739$	−12.6545			−0.465503			−0.232751	−	0.972536i	$-0.574773\pi$
$739$	−12.6545			−0.465503			−0.232751	+	0.972536i	$0.574773\pi$
$740$	−13.3521	+	7.35683i	−0.490832	+	0.270442i
$741$	7.86162	+	7.20792i	0.288804	+	0.264790i
$742$		0			0
$743$	−2.67310			−0.0980667			−0.0490333	−	0.998797i	$-0.515614\pi$
$743$	−2.67310			−0.0980667			−0.0490333	+	0.998797i	$0.515614\pi$
$744$	3.42657	+	3.14165i	0.125624	+	0.115178i
$745$	−16.4112	+	9.04237i	−0.601260	+	0.331287i
$746$		−	26.1293i		−	0.956663i
$747$	3.82618	−	0.332574i	0.139993	−	0.0121682i
$748$	−17.1196			−0.625953
$749$		0			0
$750$	−13.9190	+	13.4633i	−0.508251	+	0.491611i
$751$	−23.3381			−0.851620			−0.425810	−	0.904813i	$-0.640011\pi$
$751$	−23.3381			−0.851620			−0.425810	+	0.904813i	$0.640011\pi$
$752$			3.12679i			0.114022i
$753$	18.5301	−	20.2106i	0.675274	−	0.736515i
$754$			8.12917i			0.296047i
$755$	8.71878	+	15.8239i	0.317309	+	0.575891i
$756$		0			0
$757$			27.4191i			0.996564i	0.867015	+	0.498282i	$0.166036\pi$
$757$			27.4191i			0.996564i	−0.867015	+	0.498282i	$0.833964\pi$
$758$	−25.5437			−0.927789
$759$	16.1541	+	14.8109i	0.586358	+	0.537603i
$760$	13.9527	−	7.68780i	0.506119	−	0.278866i
$761$	42.5484			1.54238			0.771188	−	0.636607i	$-0.219663\pi$
$761$	42.5484			1.54238			0.771188	+	0.636607i	$0.219663\pi$
$762$	26.5709	+	24.3615i	0.962562	+	0.882525i
$763$		0			0
$764$			1.81768i			0.0657614i
$765$	−10.6251	−	15.8585i	−0.384153	−	0.573366i
$766$		−	15.2142i		−	0.549711i
$767$	−6.13216			−0.221419
$768$	−1.17052	+	1.27667i	−0.0422374	+	0.0460679i
$769$			25.4075i			0.916219i	0.888896	+	0.458110i	$0.151473\pi$
$769$			25.4075i			0.916219i	−0.888896	+	0.458110i	$0.848527\pi$
$770$		0			0
$771$	37.9214	+	34.7682i	1.36570	+	1.25215i
$772$		−	0.613146i		−	0.0220676i
$773$		−	15.8923i		−	0.571607i	−0.958288	−	0.285804i	$-0.907739\pi$
$773$		−	15.8923i		−	0.571607i	0.958288	−	0.285804i	$-0.0922605\pi$
$774$	8.03935	−	0.698784i	0.288969	−	0.0251173i
$775$	−11.3444	−	7.16929i	−0.407503	−	0.257529i
$776$	1.90549			0.0684033
$777$		0			0
$778$		−	15.5321i		−	0.556853i
$779$		−	37.9252i		−	1.35881i
$780$	3.25288	+	0.790677i	0.116472	+	0.0283108i
$781$	−26.8658			−0.961333
$782$			5.98497i			0.214022i
$783$	−29.7828	+	38.7458i	−1.06435	+	1.38466i
$784$		0			0
$785$	−4.81626	−	8.74113i	−0.171900	−	0.311984i
$786$	−8.72258	+	9.51364i	−0.311124	+	0.339340i
$787$	26.1564			0.932375			0.466188	−	0.884686i	$-0.345627\pi$
$787$	26.1564			0.932375			0.466188	+	0.884686i	$0.345627\pi$
$788$	−12.5151			−0.445832
$789$	−27.1458	+	29.6076i	−0.966415	+	1.05406i
$790$	−3.62356	−	6.57648i	−0.128921	−	0.233981i
$791$		0			0
$792$	17.9806	−	1.56288i	0.638913	−	0.0555346i
$793$		−	8.07016i		−	0.286580i
$794$	9.93654			0.352635
$795$	45.0646	+	10.9539i	1.59828	+	0.388493i
$796$			10.7743i			0.381884i
$797$			29.9169i			1.05971i	0.848088	+	0.529856i	$0.177754\pi$
$797$			29.9169i			1.05971i	−0.848088	+	0.529856i	$0.822246\pi$
$798$		0			0
$799$	8.89762			0.314775
$800$	2.67114	−	4.22670i	0.0944390	−	0.149437i
$801$	−0.801687	−	9.22324i	−0.0283262	−	0.325887i
$802$		−	14.2780i		−	0.504172i
$803$			77.0001i			2.71727i
$804$	−8.37545	−	7.67903i	−0.295379	−	0.270819i
$805$		0			0
$806$			2.31989i			0.0817147i
$807$	15.6247	−	17.0417i	0.550014	−	0.599895i
$808$	−7.02133			−0.247009
$809$		−	21.4579i		−	0.754421i	−0.926128	−	0.377210i	$-0.876883\pi$
$809$		−	21.4579i		−	0.754421i	0.926128	−	0.377210i	$-0.123117\pi$
$810$	12.6073	+	15.6862i	0.442976	+	0.551156i
$811$			3.56272i			0.125104i	0.998042	+	0.0625520i	$0.0199239\pi$
$811$			3.56272i			0.125104i	−0.998042	+	0.0625520i	$0.980076\pi$
$812$		0			0
$813$	21.7354	+	19.9281i	0.762294	+	0.698909i
$814$	−41.0158			−1.43760
$815$	42.5133	−	23.4243i	1.48917	−	0.820517i
$816$	3.63291	+	3.33083i	0.127177	+	0.116602i
$817$	19.1637			0.670453
$818$			20.1305i			0.703845i
$819$		0			0
$820$	−5.74434	−	10.4255i	−0.200601	−	0.364075i
$821$		−	11.2180i		−	0.391512i	−0.980653	−	0.195756i	$-0.937284\pi$
$821$		−	11.2180i		−	0.391512i	0.980653	−	0.195756i	$-0.0627161\pi$
$822$	4.69304	−	5.11865i	0.163689	−	0.178534i
$823$			27.0364i			0.942429i	0.882019	+	0.471214i	$0.156184\pi$
$823$			27.0364i			0.942429i	−0.882019	+	0.471214i	$0.843816\pi$
$824$	−9.51562			−0.331492
$825$	−50.2804	+	13.6536i	−1.75054	+	0.475359i
$826$		0			0
$827$	26.8301			0.932974			0.466487	−	0.884528i	$-0.345519\pi$
$827$	26.8301			0.932974			0.466487	+	0.884528i	$0.345519\pi$
$828$	−0.546381	−	6.28599i	−0.0189881	−	0.218453i
$829$		−	6.76305i		−	0.234891i	−0.993079	−	0.117445i	$-0.962530\pi$
$829$		−	6.76305i		−	0.234891i	0.993079	−	0.117445i	$-0.0374705\pi$
$830$	2.50723	−	1.38145i	0.0870272	−	0.0479509i
$831$	24.8132	+	22.7500i	0.860761	+	0.789189i
$832$	−0.864346			−0.0299658
$833$		0			0
$834$	20.0192	+	18.3546i	0.693207	+	0.635567i
$835$	29.5564	−	16.2852i	1.02284	−	0.563573i
$836$	42.8610			1.48238
$837$	−8.49939	+	11.0572i	−0.293782	+	0.382194i
$838$	11.8896			0.410719
$839$	−52.6113			−1.81634			−0.908172	−	0.418597i	$-0.862522\pi$
$839$	−52.6113			−1.81634			−0.908172	+	0.418597i	$0.862522\pi$
$840$		0			0
$841$	−59.4538			−2.05013
$842$	−11.6346			−0.400956
$843$	−13.9473	−	12.7876i	−0.480370	−	0.440427i
$844$	4.66797			0.160678
$845$	−13.2220	−	23.9968i	−0.454849	−	0.825516i
$846$	−9.34514	+	0.812283i	−0.321293	+	0.0279269i
$847$		0			0
$848$	−11.9744			−0.411204
$849$	−32.6712	+	35.6342i	−1.12127	+	1.22296i
$850$	−12.0275	−	7.60100i	−0.412541	−	0.260712i
$851$			14.3391i			0.491537i
$852$	5.70113	+	5.22708i	0.195317	+	0.179077i
$853$	35.7772			1.22499			0.612494	−	0.790475i	$-0.290166\pi$
$853$	35.7772			1.22499			0.612494	+	0.790475i	$0.290166\pi$
$854$		0			0
$855$	26.6014	+	39.7039i	0.909750	+	1.35784i
$856$	9.23877			0.315775
$857$			26.9017i			0.918946i	0.888192	+	0.459473i	$0.151962\pi$
$857$			26.9017i			0.918946i	−0.888192	+	0.459473i	$0.848038\pi$
$858$	6.63872	+	6.08671i	0.226642	+	0.207797i
$859$		−	24.1993i		−	0.825670i	−0.910806	−	0.412835i	$-0.864539\pi$
$859$		−	24.1993i		−	0.825670i	0.910806	−	0.412835i	$-0.135461\pi$
$860$	5.26804	−	2.90263i	0.179639	−	0.0989787i
$861$		0			0
$862$			4.34854i			0.148112i
$863$	−25.2452			−0.859355			−0.429677	−	0.902982i	$-0.641373\pi$
$863$	−25.2452			−0.859355			−0.429677	+	0.902982i	$0.641373\pi$
$864$	−4.11971	−	3.16670i	−0.140155	−	0.107733i
$865$	−27.2377	+	15.0077i	−0.926110	+	0.510276i
$866$	15.3505			0.521631
$867$	−10.4206	+	11.3656i	−0.353901	+	0.385996i
$868$		0			0
$869$		−	20.2021i		−	0.685309i
$870$	−8.60340	+	35.3948i	−0.291682	+	1.19999i
$871$		−	5.67044i		−	0.192136i
$872$	−4.93955			−0.167274
$873$	0.495013	+	5.69501i	0.0167536	+	0.192747i
$874$		−	14.9841i		−	0.506846i
$875$		0			0
$876$	14.9813	−	16.3400i	0.506173	−	0.552078i
$877$		−	26.2898i		−	0.887744i	−0.896090	−	0.443872i	$-0.853604\pi$
$877$		−	26.2898i		−	0.887744i	0.896090	−	0.443872i	$-0.146396\pi$
$878$		−	3.55667i		−	0.120032i
$879$	−12.6120	−	11.5633i	−0.425393	−	0.390022i
$880$	11.7824	−	6.49194i	0.397184	−	0.218843i
$881$	31.9677			1.07702			0.538510	−	0.842619i	$-0.318988\pi$
$881$	31.9677			1.07702			0.538510	+	0.842619i	$0.318988\pi$
$882$		0			0
$883$			6.92050i			0.232893i	0.993197	+	0.116447i	$0.0371504\pi$
$883$			6.92050i			0.232893i	−0.993197	+	0.116447i	$0.962850\pi$
$884$			2.45959i			0.0827249i
$885$	−26.6997	−	6.48989i	−0.897500	−	0.218155i
$886$	9.38403			0.315263
$887$		−	37.6658i		−	1.26469i	−0.774685	−	0.632347i	$-0.782092\pi$
$887$		−	37.6658i		−	1.26469i	0.774685	−	0.632347i	$-0.217908\pi$
$888$	8.70388	+	7.98015i	0.292083	+	0.267796i
$889$		0			0
$890$	−3.33007	−	6.04382i	−0.111624	−	0.202589i
$891$	9.34207	+	53.3332i	0.312971	+	1.78673i
$892$	0.973096			0.0325817
$893$	−22.2763			−0.745449
$894$	10.6981	+	9.80851i	0.357796	+	0.328046i
$895$	38.5976	−	21.2668i	1.29017	−	0.710871i
$896$		0			0
$897$	2.12791	−	2.32089i	0.0710487	−	0.0774922i
$898$		−	0.400479i		−	0.0133642i
$899$	−25.2429			−0.841896
$900$	13.3264	+	6.88529i	0.444213	+	0.229510i
$901$			34.0746i			1.13519i
$902$		−	32.0259i		−	1.06635i
$903$		0			0
$904$	−11.3769			−0.378391
$905$	11.7985	−	6.50081i	0.392194	−	0.216094i
$906$	9.45750	−	10.3152i	0.314205	−	0.342700i
$907$			47.2413i			1.56862i	0.620367	+	0.784312i	$0.286984\pi$
$907$			47.2413i			1.56862i	−0.620367	+	0.784312i	$0.713016\pi$
$908$			23.8398i			0.791153i
$909$	−1.82401	−	20.9849i	−0.0604987	−	0.696024i
$910$		0			0
$911$		−	37.3306i		−	1.23682i	−0.785856	−	0.618409i	$-0.787777\pi$
$911$		−	37.3306i		−	1.23682i	0.785856	−	0.618409i	$-0.212223\pi$
$912$	−9.09545	−	8.33916i	−0.301180	−	0.276137i
$913$	7.70188			0.254895
$914$			34.3815i			1.13724i
$915$	8.54095	−	35.1378i	0.282355	−	1.16162i
$916$			19.7831i			0.653650i
$917$		0			0
$918$	−9.01119	+	11.7231i	−0.297414	+	0.386919i
$919$	17.6980			0.583802			0.291901	−	0.956449i	$-0.405712\pi$
$919$	17.6980			0.583802			0.291901	+	0.956449i	$0.405712\pi$
$920$	−2.26957	−	4.11910i	−0.0748256	−	0.135803i
$921$	3.46007	−	3.77387i	0.114013	−	0.124353i
$922$	33.8119			1.11354
$923$			3.85984i			0.127048i
$924$		0			0
$925$	−28.8161	−	18.2108i	−0.947468	−	0.598768i
$926$		−	0.505232i		−	0.0166030i
$927$	−2.47198	−	28.4396i	−0.0811906	−	0.934080i
$928$		−	9.40499i		−	0.308734i
$929$	−60.2744			−1.97754			−0.988770	−	0.149443i	$-0.952252\pi$
$929$	−60.2744			−1.97754			−0.988770	+	0.149443i	$0.952252\pi$
$930$	−2.45523	+	10.1009i	−0.0805101	+	0.331222i
$931$		0			0
$932$	−1.78655			−0.0585205
$933$	10.0584	−	10.9706i	0.329298	−	0.359163i
$934$			24.8661i			0.813644i
$935$	−18.4735	−	33.5280i	−0.604148	−	1.09648i
$936$	−0.224541	−	2.58330i	−0.00733936	−	0.0844377i
$937$	27.4478			0.896680			0.448340	−	0.893863i	$-0.352015\pi$
$937$	27.4478			0.896680			0.448340	+	0.893863i	$0.352015\pi$
$938$		0			0
$939$	23.2399	−	25.3476i	0.758406	−	0.827187i
$940$	−6.12370	+	3.37408i	−0.199733	+	0.110051i
$941$	−23.2585			−0.758205			−0.379103	−	0.925355i	$-0.623767\pi$
$941$	−23.2585			−0.758205			−0.379103	+	0.925355i	$0.623767\pi$
$942$	−5.22433	+	5.69812i	−0.170218	+	0.185655i
$943$	−11.1962			−0.364598
$944$	7.09456			0.230908
$945$		0			0
$946$	16.1827			0.526146
$947$	5.12103			0.166411			0.0832056	−	0.996532i	$-0.473484\pi$
$947$	5.12103			0.166411			0.0832056	+	0.996532i	$0.473484\pi$
$948$	−3.93058	+	4.28704i	−0.127659	+	0.139237i
$949$	11.0627			0.359110
$950$	30.1125	+	19.0301i	0.976978	+	0.617418i
$951$	−34.1801	+	37.2799i	−1.10836	+	1.20888i
$952$		0			0
$953$	7.47194			0.242040			0.121020	−	0.992650i	$-0.461384\pi$
$953$	7.47194			0.242040			0.121020	+	0.992650i	$0.461384\pi$
$954$	−3.11074	−	35.7884i	−0.100714	−	1.15869i
$955$	−3.55986	+	1.96144i	−0.115194	+	0.0634706i
$956$			17.2961i			0.559396i
$957$	−66.2298	+	72.2363i	−2.14091	+	2.33507i
$958$	1.48138			0.0478612
$959$		0			0
$960$	−3.76340	−	0.914769i	−0.121463	−	0.0295241i
$961$	23.7962			0.767620
$962$			5.89279i			0.189991i
$963$	2.40006	+	27.6122i	0.0773410	+	0.889791i
$964$			8.26145i			0.266083i
$965$	1.20082	−	0.661639i	0.0386558	−	0.0212989i
$966$		0			0
$967$		−	13.0565i		−	0.419869i	−0.977716	−	0.209934i	$-0.932675\pi$
$967$		−	13.0565i		−	0.419869i	0.977716	−	0.209934i	$-0.0673250\pi$
$968$	25.1939			0.809762
$969$	−23.7300	+	25.8821i	−0.762317	+	0.831452i
$970$	2.05620	+	3.73184i	0.0660205	+	0.119822i
$971$	22.5183			0.722648			0.361324	−	0.932440i	$-0.382325\pi$
$971$	22.5183			0.722648			0.361324	+	0.932440i	$0.382325\pi$
$972$	8.39420	−	13.1353i	0.269244	−	0.421317i
$973$		0			0
$974$		−	7.86665i		−	0.252064i
$975$	1.96164	+	7.22385i	0.0628226	+	0.231348i
$976$			9.33672i			0.298861i
$977$	3.50864			0.112251			0.0561257	−	0.998424i	$-0.482125\pi$
$977$	3.50864			0.112251			0.0561257	+	0.998424i	$0.482125\pi$
$978$	−27.7133	−	25.4090i	−0.886175	−	0.812489i
$979$		−	18.5658i		−	0.593366i
$980$		0			0
$981$	−1.28321	−	14.7630i	−0.0409696	−	0.471346i
$982$			16.0379i			0.511788i
$983$			32.5656i			1.03868i	0.854567	+	0.519341i	$0.173823\pi$
$983$			32.5656i			1.03868i	−0.854567	+	0.519341i	$0.826177\pi$
$984$	−6.23105	+	6.79615i	−0.198639	+	0.216653i
$985$	−13.5049	−	24.5103i	−0.430302	−	0.780964i
$986$	−26.7629			−0.852304
$987$		0			0
$988$		−	6.15790i		−	0.195909i
$989$		−	5.65746i		−	0.179897i
$990$	22.4635	+	33.5278i	0.713937	+	1.06558i
$991$	5.17862			0.164504			0.0822521	−	0.996612i	$-0.473789\pi$
$991$	5.17862			0.164504			0.0822521	+	0.996612i	$0.473789\pi$
$992$		−	2.68399i		−	0.0852166i
$993$	10.5234	−	11.4778i	0.333951	−	0.364237i
$994$		0			0
$995$	−21.1010	+	11.6264i	−0.668946	+	0.368581i
$996$	−1.63440	−	1.49850i	−0.0517879	−	0.0474818i
$997$	40.7003			1.28899			0.644496	−	0.764607i	$-0.277067\pi$
$997$	40.7003			1.28899			0.644496	+	0.764607i	$0.277067\pi$
$998$	−8.37964			−0.265253
$999$	−21.5894	+	28.0866i	−0.683059	+	0.888622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.d.g.1469.8	yes	24
3.2	odd	2		1470.2.d.h.1469.7	yes	24
5.4	even	2		1470.2.d.h.1469.17	yes	24
7.6	odd	2	inner	1470.2.d.g.1469.17	yes	24
15.14	odd	2	inner	1470.2.d.g.1469.18	yes	24
21.20	even	2		1470.2.d.h.1469.18	yes	24
35.34	odd	2		1470.2.d.h.1469.8	yes	24
105.104	even	2	inner	1470.2.d.g.1469.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.d.g.1469.7	✓	24	105.104	even	2	inner
1470.2.d.g.1469.8	yes	24	1.1	even	1	trivial
1470.2.d.g.1469.17	yes	24	7.6	odd	2	inner
1470.2.d.g.1469.18	yes	24	15.14	odd	2	inner
1470.2.d.h.1469.7	yes	24	3.2	odd	2
1470.2.d.h.1469.8	yes	24	35.34	odd	2
1470.2.d.h.1469.17	yes	24	5.4	even	2
1470.2.d.h.1469.18	yes	24	21.20	even	2

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.17052 + 1.27667i) q^{3} +1.00000 q^{4} +(1.07909 + 1.95846i) q^{5} +(1.17052 - 1.27667i) q^{6} -1.00000 q^{8} +(-0.259782 - 2.98873i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.17052 + 1.27667i) q^{3} +1.00000 q^{4} +(1.07909 + 1.95846i) q^{5} +(1.17052 - 1.27667i) q^{6} -1.00000 q^{8} +(-0.259782 - 2.98873i) q^{9} +(-1.07909 - 1.95846i) q^{10} -6.01614i q^{11} +(-1.17052 + 1.27667i) q^{12} -0.864346 q^{13} +(-3.76340 - 0.914769i) q^{15} +1.00000 q^{16} -2.84561i q^{17} +(0.259782 + 2.98873i) q^{18} +7.12434i q^{19} +(1.07909 + 1.95846i) q^{20} +6.01614i q^{22} +2.10323 q^{23} +(1.17052 - 1.27667i) q^{24} +(-2.67114 + 4.22670i) q^{25} +0.864346 q^{26} +(4.11971 + 3.16670i) q^{27} +9.40499i q^{29} +(3.76340 + 0.914769i) q^{30} +2.68399i q^{31} -1.00000 q^{32} +(7.68063 + 7.04199i) q^{33} +2.84561i q^{34} +(-0.259782 - 2.98873i) q^{36} +6.81763i q^{37} -7.12434i q^{38} +(1.01173 - 1.10349i) q^{39} +(-1.07909 - 1.95846i) q^{40} -5.32333 q^{41} -2.68989i q^{43} -6.01614i q^{44} +(5.57299 - 3.73388i) q^{45} -2.10323 q^{46} +3.12679i q^{47} +(-1.17052 + 1.27667i) q^{48} +(2.67114 - 4.22670i) q^{50} +(3.63291 + 3.33083i) q^{51} -0.864346 q^{52} -11.9744 q^{53} +(-4.11971 - 3.16670i) q^{54} +(11.7824 - 6.49194i) q^{55} +(-9.09545 - 8.33916i) q^{57} -9.40499i q^{58} +7.09456 q^{59} +(-3.76340 - 0.914769i) q^{60} +9.33672i q^{61} -2.68399i q^{62} +1.00000 q^{64} +(-0.932706 - 1.69279i) q^{65} +(-7.68063 - 7.04199i) q^{66} +6.56038i q^{67} -2.84561i q^{68} +(-2.46187 + 2.68514i) q^{69} -4.46562i q^{71} +(0.259782 + 2.98873i) q^{72} -12.7989 q^{73} -6.81763i q^{74} +(-2.26950 - 8.35759i) q^{75} +7.12434i q^{76} +(-1.01173 + 1.10349i) q^{78} +3.35798 q^{79} +(1.07909 + 1.95846i) q^{80} +(-8.86503 + 1.55284i) q^{81} +5.32333 q^{82} +1.28020i q^{83} +(5.57301 - 3.07066i) q^{85} +2.68989i q^{86} +(-12.0071 - 11.0087i) q^{87} +6.01614i q^{88} +3.08600 q^{89} +(-5.57299 + 3.73388i) q^{90} +2.10323 q^{92} +(-3.42657 - 3.14165i) q^{93} -3.12679i q^{94} +(-13.9527 + 7.68780i) q^{95} +(1.17052 - 1.27667i) q^{96} -1.90549 q^{97} +(-17.9806 + 1.56288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9	\( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9} + 24 q^{16} - 8 q^{18} - 16 q^{23} + 8 q^{25} - 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} - 8 q^{50} + 16 q^{51} + 16 q^{53} + 16 q^{57} + 24 q^{64} - 48 q^{65} - 8 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} - 16 q^{92} + 64 q^{93} - 112 q^{95} - 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9 + 24 * q^16 - 8 * q^18 - 16 * q^23 + 8 * q^25 - 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 - 8 * q^50 + 16 * q^51 + 16 * q^53 + 16 * q^57 + 24 * q^64 - 48 * q^65 - 8 * q^72 - 16 * q^78 - 48 * q^79 - 24 * q^81 + 16 * q^85 - 16 * q^92 + 64 * q^93 - 112 * q^95 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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