LMFDB - Embedded newform 1470.2.d.g.1469.4

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			1469.4
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.g.1469.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.67905 + 0.425213i) q^{3} +1.00000 q^{4} +(-2.18793 - 0.461477i) q^{5} +(1.67905 - 0.425213i) q^{6} -1.00000 q^{8} +(2.63839 - 1.42790i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.67905 + 0.425213i) q^{3} +1.00000 q^{4} +(-2.18793 - 0.461477i) q^{5} +(1.67905 - 0.425213i) q^{6} -1.00000 q^{8} +(2.63839 - 1.42790i) q^{9} +(2.18793 + 0.461477i) q^{10} +4.08605i q^{11} +(-1.67905 + 0.425213i) q^{12} -3.50053 q^{13} +(3.86986 - 0.155494i) q^{15} +1.00000 q^{16} -0.437316i q^{17} +(-2.63839 + 1.42790i) q^{18} -7.69711i q^{19} +(-2.18793 - 0.461477i) q^{20} -4.08605i q^{22} -7.39739 q^{23} +(1.67905 - 0.425213i) q^{24} +(4.57408 + 2.01936i) q^{25} +3.50053 q^{26} +(-3.82281 + 3.51939i) q^{27} +4.95225i q^{29} +(-3.86986 + 0.155494i) q^{30} +6.81849i q^{31} -1.00000 q^{32} +(-1.73744 - 6.86067i) q^{33} +0.437316i q^{34} +(2.63839 - 1.42790i) q^{36} +4.51245i q^{37} +7.69711i q^{38} +(5.87754 - 1.48847i) q^{39} +(2.18793 + 0.461477i) q^{40} -1.34412 q^{41} -6.67867i q^{43} +4.08605i q^{44} +(-6.43155 + 1.90660i) q^{45} +7.39739 q^{46} -2.41846i q^{47} +(-1.67905 + 0.425213i) q^{48} +(-4.57408 - 2.01936i) q^{50} +(0.185952 + 0.734273i) q^{51} -3.50053 q^{52} -0.424805 q^{53} +(3.82281 - 3.51939i) q^{54} +(1.88562 - 8.94000i) q^{55} +(3.27291 + 12.9238i) q^{57} -4.95225i q^{58} -2.75261 q^{59} +(3.86986 - 0.155494i) q^{60} -5.75361i q^{61} -6.81849i q^{62} +1.00000 q^{64} +(7.65891 + 1.61541i) q^{65} +(1.73744 + 6.86067i) q^{66} -11.3926i q^{67} -0.437316i q^{68} +(12.4206 - 3.14546i) q^{69} -12.1243i q^{71} +(-2.63839 + 1.42790i) q^{72} +9.06556 q^{73} -4.51245i q^{74} +(-8.53874 - 1.44564i) q^{75} -7.69711i q^{76} +(-5.87754 + 1.48847i) q^{78} +3.37581 q^{79} +(-2.18793 - 0.461477i) q^{80} +(4.92219 - 7.53472i) q^{81} +1.34412 q^{82} +17.1321i q^{83} +(-0.201811 + 0.956816i) q^{85} +6.67867i q^{86} +(-2.10576 - 8.31505i) q^{87} -4.08605i q^{88} +4.52892 q^{89} +(6.43155 - 1.90660i) q^{90} -7.39739 q^{92} +(-2.89931 - 11.4486i) q^{93} +2.41846i q^{94} +(-3.55204 + 16.8407i) q^{95} +(1.67905 - 0.425213i) q^{96} +7.93539 q^{97} +(5.83448 + 10.7806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.67905	+	0.425213i	−0.969397	+	0.245497i
$3$	−1.67905	+	0.425213i	−0.969397	+	0.245497i
$4$	1.00000			0.500000
$5$	−2.18793	−	0.461477i	−0.978472	−	0.206379i
$5$	−2.18793	−	0.461477i	−0.978472	−	0.206379i
$6$	1.67905	−	0.425213i	0.685468	−	0.173592i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	2.63839	−	1.42790i	0.879463	−	0.475967i
$10$	2.18793	+	0.461477i	0.691884	+	0.145932i
$11$			4.08605i			1.23199i	0.787750	+	0.615996i	$0.211246\pi$
$11$			4.08605i			1.23199i	−0.787750	+	0.615996i	$0.788754\pi$
$12$	−1.67905	+	0.425213i	−0.484699	+	0.122748i
$13$	−3.50053			−0.970872			−0.485436	−	0.874272i	$-0.661339\pi$
$13$	−3.50053			−0.970872			−0.485436	+	0.874272i	$0.661339\pi$
$14$		0			0
$15$	3.86986	−	0.155494i	0.999194	−	0.0401485i
$16$	1.00000			0.250000
$17$		−	0.437316i		−	0.106065i	−0.998593	−	0.0530323i	$-0.983111\pi$
$17$		−	0.437316i		−	0.106065i	0.998593	−	0.0530323i	$-0.0168886\pi$
$18$	−2.63839	+	1.42790i	−0.621874	+	0.336560i
$19$		−	7.69711i		−	1.76584i	−0.469526	−	0.882919i	$-0.655575\pi$
$19$		−	7.69711i		−	1.76584i	0.469526	−	0.882919i	$-0.344425\pi$
$20$	−2.18793	−	0.461477i	−0.489236	−	0.103189i
$21$		0			0
$22$		−	4.08605i		−	0.871149i
$23$	−7.39739			−1.54246			−0.771231	−	0.636555i	$-0.780359\pi$
$23$	−7.39739			−1.54246			−0.771231	+	0.636555i	$0.780359\pi$
$24$	1.67905	−	0.425213i	0.342734	−	0.0867961i
$25$	4.57408	+	2.01936i	0.914816	+	0.403872i
$26$	3.50053			0.686510
$27$	−3.82281	+	3.51939i	−0.735701	+	0.677307i
$28$		0			0
$29$			4.95225i			0.919610i	0.888020	+	0.459805i	$0.152081\pi$
$29$			4.95225i			0.919610i	−0.888020	+	0.459805i	$0.847919\pi$
$30$	−3.86986	+	0.155494i	−0.706537	+	0.0283893i
$31$			6.81849i			1.22464i	0.790611	+	0.612318i	$0.209763\pi$
$31$			6.81849i			1.22464i	−0.790611	+	0.612318i	$0.790237\pi$
$32$	−1.00000			−0.176777
$33$	−1.73744	−	6.86067i	−0.302450	−	1.19429i
$34$			0.437316i			0.0749990i
$35$		0			0
$36$	2.63839	−	1.42790i	0.439731	−	0.237984i
$37$			4.51245i			0.741841i	0.928665	+	0.370921i	$0.120958\pi$
$37$			4.51245i			0.741841i	−0.928665	+	0.370921i	$0.879042\pi$
$38$			7.69711i			1.24864i
$39$	5.87754	−	1.48847i	0.941160	−	0.238346i
$40$	2.18793	+	0.461477i	0.345942	+	0.0729659i
$41$	−1.34412			−0.209916			−0.104958	−	0.994477i	$-0.533471\pi$
$41$	−1.34412			−0.209916			−0.104958	+	0.994477i	$0.533471\pi$
$42$		0			0
$43$		−	6.67867i		−	1.01849i	−0.860622	−	0.509244i	$-0.829925\pi$
$43$		−	6.67867i		−	1.01849i	0.860622	−	0.509244i	$-0.170075\pi$
$44$			4.08605i			0.615996i
$45$	−6.43155	+	1.90660i	−0.958760	+	0.284218i
$46$	7.39739			1.09069
$47$		−	2.41846i		−	0.352768i	−0.984321	−	0.176384i	$-0.943560\pi$
$47$		−	2.41846i		−	0.352768i	0.984321	−	0.176384i	$-0.0564400\pi$
$48$	−1.67905	+	0.425213i	−0.242349	+	0.0613741i
$49$		0			0
$50$	−4.57408	−	2.01936i	−0.646872	−	0.285580i
$51$	0.185952	+	0.734273i	0.0260385	+	0.102819i
$52$	−3.50053			−0.485436
$53$	−0.424805			−0.0583514			−0.0291757	−	0.999574i	$-0.509288\pi$
$53$	−0.424805			−0.0583514			−0.0291757	+	0.999574i	$0.509288\pi$
$54$	3.82281	−	3.51939i	0.520219	−	0.478928i
$55$	1.88562	−	8.94000i	0.254257	−	1.20547i
$56$		0			0
$57$	3.27291	+	12.9238i	0.433507	+	1.71180i
$58$		−	4.95225i		−	0.650262i
$59$	−2.75261			−0.358359			−0.179179	−	0.983816i	$-0.557344\pi$
$59$	−2.75261			−0.358359			−0.179179	+	0.983816i	$0.557344\pi$
$60$	3.86986	−	0.155494i	0.499597	−	0.0200742i
$61$		−	5.75361i		−	0.736674i	−0.929692	−	0.368337i	$-0.879927\pi$
$61$		−	5.75361i		−	0.736674i	0.929692	−	0.368337i	$-0.120073\pi$
$62$		−	6.81849i		−	0.865949i
$63$		0			0
$64$	1.00000			0.125000
$65$	7.65891	+	1.61541i	0.949971	+	0.200367i
$66$	1.73744	+	6.86067i	0.213864	+	0.844490i
$67$		−	11.3926i		−	1.39183i	−0.718124	−	0.695915i	$-0.754999\pi$
$67$		−	11.3926i		−	1.39183i	0.718124	−	0.695915i	$-0.245001\pi$
$68$		−	0.437316i		−	0.0530323i
$69$	12.4206	−	3.14546i	1.49526	−	0.378669i
$70$		0			0
$71$		−	12.1243i		−	1.43888i	−0.694552	−	0.719442i	$-0.744398\pi$
$71$		−	12.1243i		−	1.43888i	0.694552	−	0.719442i	$-0.255602\pi$
$72$	−2.63839	+	1.42790i	−0.310937	+	0.168280i
$73$	9.06556			1.06104			0.530522	−	0.847671i	$-0.321996\pi$
$73$	9.06556			1.06104			0.530522	+	0.847671i	$0.321996\pi$
$74$		−	4.51245i		−	0.524561i
$75$	−8.53874	−	1.44564i	−0.985969	−	0.166928i
$76$		−	7.69711i		−	0.882919i
$77$		0			0
$78$	−5.87754	+	1.48847i	−0.665501	+	0.168536i
$79$	3.37581			0.379809			0.189904	−	0.981803i	$-0.439182\pi$
$79$	3.37581			0.379809			0.189904	+	0.981803i	$0.439182\pi$
$80$	−2.18793	−	0.461477i	−0.244618	−	0.0515947i
$81$	4.92219	−	7.53472i	0.546910	−	0.837191i
$82$	1.34412			0.148433
$83$			17.1321i			1.88050i	0.340489	+	0.940249i	$0.389407\pi$
$83$			17.1321i			1.88050i	−0.340489	+	0.940249i	$0.610593\pi$
$84$		0			0
$85$	−0.201811	+	0.956816i	−0.0218895	+	0.103781i
$86$			6.67867i			0.720180i
$87$	−2.10576	−	8.31505i	−0.225761	−	0.891467i
$88$		−	4.08605i		−	0.435575i
$89$	4.52892			0.480064			0.240032	−	0.970765i	$-0.422842\pi$
$89$	4.52892			0.480064			0.240032	+	0.970765i	$0.422842\pi$
$90$	6.43155	−	1.90660i	0.677945	−	0.200973i
$91$		0			0
$92$	−7.39739			−0.771231
$93$	−2.89931	−	11.4486i	−0.300644	−	1.18716i
$94$			2.41846i			0.249445i
$95$	−3.55204	+	16.8407i	−0.364431	+	1.72782i
$96$	1.67905	−	0.425213i	0.171367	−	0.0433981i
$97$	7.93539			0.805716			0.402858	−	0.915262i	$-0.368017\pi$
$97$	7.93539			0.805716			0.402858	+	0.915262i	$0.368017\pi$
$98$		0			0
$99$	5.83448	+	10.7806i	0.586388	+	1.08349i
$100$	4.57408	+	2.01936i	0.457408	+	0.201936i
$101$	3.43427			0.341723			0.170861	−	0.985295i	$-0.445345\pi$
$101$	3.43427			0.341723			0.170861	+	0.985295i	$0.445345\pi$
$102$	−0.185952	−	0.734273i	−0.0184120	−	0.0727039i
$103$	19.8394			1.95483			0.977416	−	0.211324i	$-0.0677774\pi$
$103$	19.8394			1.95483			0.977416	+	0.211324i	$0.0677774\pi$
$104$	3.50053			0.343255
$105$		0			0
$106$	0.424805			0.0412607
$107$	10.4903			1.01414			0.507068	−	0.861906i	$-0.330729\pi$
$107$	10.4903			1.01414			0.507068	+	0.861906i	$0.330729\pi$
$108$	−3.82281	+	3.51939i	−0.367850	+	0.338653i
$109$	12.3912			1.18686			0.593429	−	0.804887i	$-0.297774\pi$
$109$	12.3912			1.18686			0.593429	+	0.804887i	$0.297774\pi$
$110$	−1.88562	+	8.94000i	−0.179787	+	0.852395i
$111$	−1.91875	−	7.57660i	−0.182120	−	0.719139i
$112$		0			0
$113$	11.9346			1.12272			0.561358	−	0.827573i	$-0.310279\pi$
$113$	11.9346			1.12272			0.561358	+	0.827573i	$0.310279\pi$
$114$	−3.27291	−	12.9238i	−0.306536	−	1.21042i
$115$	16.1850	+	3.41373i	1.50926	+	0.318332i
$116$			4.95225i			0.459805i
$117$	−9.23575	+	4.99841i	−0.853845	+	0.462103i
$118$	2.75261			0.253398
$119$		0			0
$120$	−3.86986	+	0.155494i	−0.353268	+	0.0141946i
$121$	−5.69583			−0.517803
$122$			5.75361i			0.520907i
$123$	2.25683	−	0.571535i	0.203492	−	0.0515336i
$124$			6.81849i			0.612318i
$125$	−9.07588	−	6.52905i	−0.811771	−	0.583976i
$126$		0			0
$127$		−	3.47555i		−	0.308405i	−0.988039	−	0.154203i	$-0.950719\pi$
$127$		−	3.47555i		−	0.308405i	0.988039	−	0.154203i	$-0.0492809\pi$
$128$	−1.00000			−0.0883883
$129$	2.83985	+	11.2138i	0.250035	+	0.987319i
$130$	−7.65891	−	1.61541i	−0.671731	−	0.141681i
$131$	−2.28132			−0.199320			−0.0996601	−	0.995022i	$-0.531776\pi$
$131$	−2.28132			−0.199320			−0.0996601	+	0.995022i	$0.531776\pi$
$132$	−1.73744	−	6.86067i	−0.151225	−	0.597145i
$133$		0			0
$134$			11.3926i			0.984173i
$135$	9.98817	−	5.93604i	0.859644	−	0.510893i
$136$			0.437316i			0.0374995i
$137$	22.2471			1.90070			0.950350	−	0.311183i	$-0.100725\pi$
$137$	22.2471			1.90070			0.950350	+	0.311183i	$0.100725\pi$
$138$	−12.4206	+	3.14546i	−1.05731	+	0.267760i
$139$			3.91782i			0.332305i	0.986100	+	0.166153i	$0.0531344\pi$
$139$			3.91782i			0.332305i	−0.986100	+	0.166153i	$0.946866\pi$
$140$		0			0
$141$	1.02836	+	4.06070i	0.0866033	+	0.341972i
$142$			12.1243i			1.01744i
$143$		−	14.3033i		−	1.19611i
$144$	2.63839	−	1.42790i	0.219866	−	0.118992i
$145$	2.28535	−	10.8352i	0.189788	−	0.899812i
$146$	−9.06556			−0.750271
$147$		0			0
$148$			4.51245i			0.370921i
$149$		−	20.2201i		−	1.65650i	−0.560362	−	0.828248i	$-0.689338\pi$
$149$		−	20.2201i		−	1.65650i	0.560362	−	0.828248i	$-0.310662\pi$
$150$	8.53874	+	1.44564i	0.697185	+	0.118036i
$151$	−11.1525			−0.907576			−0.453788	−	0.891110i	$-0.649928\pi$
$151$	−11.1525			−0.907576			−0.453788	+	0.891110i	$0.649928\pi$
$152$			7.69711i			0.624318i
$153$	−0.624444	−	1.15381i	−0.0504833	−	0.0932799i
$154$		0			0
$155$	3.14658	−	14.9184i	0.252739	−	1.19827i
$156$	5.87754	−	1.48847i	0.470580	−	0.119173i
$157$	−13.8740			−1.10726			−0.553632	−	0.832761i	$-0.686759\pi$
$157$	−13.8740			−1.10726			−0.553632	+	0.832761i	$0.686759\pi$
$158$	−3.37581			−0.268565
$159$	0.713267	−	0.180632i	0.0565657	−	0.0143251i
$160$	2.18793	+	0.461477i	0.172971	+	0.0364830i
$161$		0			0
$162$	−4.92219	+	7.53472i	−0.386724	+	0.591984i
$163$			11.6362i			0.911416i	0.890129	+	0.455708i	$0.150614\pi$
$163$			11.6362i			0.911416i	−0.890129	+	0.455708i	$0.849386\pi$
$164$	−1.34412			−0.104958
$165$	0.635358	+	15.8125i	0.0494626	+	1.23100i
$166$		−	17.1321i		−	1.32971i
$167$		−	3.73225i		−	0.288810i	−0.989519	−	0.144405i	$-0.953873\pi$
$167$		−	3.73225i		−	0.288810i	0.989519	−	0.144405i	$-0.0461269\pi$
$168$		0			0
$169$	−0.746310			−0.0574084
$170$	0.201811	−	0.956816i	0.0154782	−	0.0733845i
$171$	−10.9907	−	20.3080i	−0.840481	−	1.55299i
$172$		−	6.67867i		−	0.509244i
$173$		−	14.3011i		−	1.08730i	−0.839313	−	0.543648i	$-0.817043\pi$
$173$		−	14.3011i		−	1.08730i	0.839313	−	0.543648i	$-0.182957\pi$
$174$	2.10576	+	8.31505i	0.159637	+	0.630363i
$175$		0			0
$176$			4.08605i			0.307998i
$177$	4.62175	−	1.17044i	0.347392	−	0.0879759i
$178$	−4.52892			−0.339457
$179$		−	14.0130i		−	1.04738i	−0.851909	−	0.523690i	$-0.824555\pi$
$179$		−	14.0130i		−	1.04738i	0.851909	−	0.523690i	$-0.175445\pi$
$180$	−6.43155	+	1.90660i	−0.479380	+	0.142109i
$181$			13.9155i			1.03433i	0.855885	+	0.517166i	$0.173013\pi$
$181$			13.9155i			1.03433i	−0.855885	+	0.517166i	$0.826987\pi$
$182$		0			0
$183$	2.44651	+	9.66057i	0.180851	+	0.714130i
$184$	7.39739			0.545343
$185$	2.08239	−	9.87292i	0.153100	−	0.725871i
$186$	2.89931	+	11.4486i	0.212587	+	0.839449i
$187$	1.78690			0.130671
$188$		−	2.41846i		−	0.176384i
$189$		0			0
$190$	3.55204	−	16.8407i	0.257692	−	1.22175i
$191$			10.7729i			0.779496i	0.920921	+	0.389748i	$0.127438\pi$
$191$			10.7729i			0.779496i	−0.920921	+	0.389748i	$0.872562\pi$
$192$	−1.67905	+	0.425213i	−0.121175	+	0.0306871i
$193$		−	8.77793i		−	0.631849i	−0.948784	−	0.315925i	$-0.897685\pi$
$193$		−	8.77793i		−	0.631849i	0.948784	−	0.315925i	$-0.102315\pi$
$194$	−7.93539			−0.569728
$195$	−13.5466	+	0.544312i	−0.970089	+	0.0389790i
$196$		0			0
$197$	12.7615			0.909218			0.454609	−	0.890691i	$-0.349779\pi$
$197$	12.7615			0.909218			0.454609	+	0.890691i	$0.349779\pi$
$198$	−5.83448	−	10.7806i	−0.414639	−	0.766144i
$199$		−	4.18139i		−	0.296411i	−0.988957	−	0.148205i	$-0.952650\pi$
$199$		−	4.18139i		−	0.296411i	0.988957	−	0.148205i	$-0.0473497\pi$
$200$	−4.57408	−	2.01936i	−0.323436	−	0.142790i
$201$	4.84429	+	19.1287i	0.341690	+	1.34924i
$202$	−3.43427			−0.241634
$203$		0			0
$204$	0.185952	+	0.734273i	0.0130193	+	0.0514094i
$205$	2.94083	+	0.620279i	0.205397	+	0.0433221i
$206$	−19.8394			−1.38228
$207$	−19.5172	+	10.5628i	−1.35654	+	0.734162i
$208$	−3.50053			−0.242718
$209$	31.4508			2.17550
$210$		0			0
$211$	−7.19053			−0.495016			−0.247508	−	0.968886i	$-0.579612\pi$
$211$	−7.19053			−0.495016			−0.247508	+	0.968886i	$0.579612\pi$
$212$	−0.424805			−0.0291757
$213$	5.15538	+	20.3572i	0.353241	+	1.39485i
$214$	−10.4903			−0.717102
$215$	−3.08205	+	14.6125i	−0.210194	+	0.996562i
$216$	3.82281	−	3.51939i	0.260109	−	0.239464i
$217$		0			0
$218$	−12.3912			−0.839235
$219$	−15.2215	+	3.85479i	−1.02857	+	0.260483i
$220$	1.88562	−	8.94000i	0.127128	−	0.602735i
$221$			1.53084i			0.102975i
$222$	1.91875	+	7.57660i	0.128778	+	0.508508i
$223$	−0.621483			−0.0416176			−0.0208088	−	0.999783i	$-0.506624\pi$
$223$	−0.621483			−0.0416176			−0.0208088	+	0.999783i	$0.506624\pi$
$224$		0			0
$225$	14.9516	−	1.20348i	0.996776	−	0.0802322i
$226$	−11.9346			−0.793880
$227$		−	12.9728i		−	0.861034i	−0.902582	−	0.430517i	$-0.858331\pi$
$227$		−	12.9728i		−	0.861034i	0.902582	−	0.430517i	$-0.141669\pi$
$228$	3.27291	+	12.9238i	0.216753	+	0.855899i
$229$			21.2637i			1.40514i	0.711613	+	0.702572i	$0.247965\pi$
$229$			21.2637i			1.40514i	−0.711613	+	0.702572i	$0.752035\pi$
$230$	−16.1850	−	3.41373i	−1.06721	−	0.225094i
$231$		0			0
$232$		−	4.95225i		−	0.325131i
$233$	11.0664			0.724987			0.362493	−	0.931986i	$-0.381926\pi$
$233$	11.0664			0.724987			0.362493	+	0.931986i	$0.381926\pi$
$234$	9.23575	−	4.99841i	0.603760	−	0.326756i
$235$	−1.11606	+	5.29141i	−0.0728038	+	0.345174i
$236$	−2.75261			−0.179179
$237$	−5.66814	+	1.43544i	−0.368185	+	0.0932417i
$238$		0			0
$239$			0.281518i			0.0182099i	0.999959	+	0.00910495i	$0.00289824\pi$
$239$			0.281518i			0.0182099i	−0.999959	+	0.00910495i	$0.997102\pi$
$240$	3.86986	−	0.155494i	0.249798	−	0.0100371i
$241$		−	14.7273i		−	0.948668i	−0.880345	−	0.474334i	$-0.842689\pi$
$241$		−	14.7273i		−	0.948668i	0.880345	−	0.474334i	$-0.157311\pi$
$242$	5.69583			0.366142
$243$	−5.06072	+	14.7441i	−0.324645	+	0.945836i
$244$		−	5.75361i		−	0.368337i
$245$		0			0
$246$	−2.25683	+	0.571535i	−0.143890	+	0.0364397i
$247$			26.9439i			1.71440i
$248$		−	6.81849i		−	0.432974i
$249$	−7.28480	−	28.7657i	−0.461656	−	1.82295i
$250$	9.07588	+	6.52905i	0.574009	+	0.412933i
$251$	−18.5359			−1.16998			−0.584988	−	0.811042i	$-0.698901\pi$
$251$	−18.5359			−1.16998			−0.584988	+	0.811042i	$0.698901\pi$
$252$		0			0
$253$		−	30.2261i		−	1.90030i
$254$			3.47555i			0.218076i
$255$	−0.0680002	−	1.69235i	−0.00425833	−	0.105979i
$256$	1.00000			0.0625000
$257$		−	19.4528i		−	1.21344i	−0.794917	−	0.606718i	$-0.792486\pi$
$257$		−	19.4528i		−	1.21344i	0.794917	−	0.606718i	$-0.207514\pi$
$258$	−2.83985	−	11.2138i	−0.176802	−	0.698140i
$259$		0			0
$260$	7.65891	+	1.61541i	0.474985	+	0.100184i
$261$	7.07133	+	13.0660i	0.437704	+	0.808763i
$262$	2.28132			0.140941
$263$	−13.8660			−0.855011			−0.427506	−	0.904013i	$-0.640608\pi$
$263$	−13.8660			−0.855011			−0.427506	+	0.904013i	$0.640608\pi$
$264$	1.73744	+	6.86067i	0.106932	+	0.422245i
$265$	0.929443	+	0.196038i	0.0570952	+	0.0120425i
$266$		0			0
$267$	−7.60426	+	1.92575i	−0.465373	+	0.117854i
$268$		−	11.3926i		−	0.695915i
$269$	15.3624			0.936662			0.468331	−	0.883553i	$-0.344855\pi$
$269$	15.3624			0.936662			0.468331	+	0.883553i	$0.344855\pi$
$270$	−9.98817	+	5.93604i	−0.607860	+	0.361256i
$271$			16.3255i			0.991704i	0.868407	+	0.495852i	$0.165144\pi$
$271$			16.3255i			0.991704i	−0.868407	+	0.495852i	$0.834856\pi$
$272$		−	0.437316i		−	0.0265162i
$273$		0			0
$274$	−22.2471			−1.34400
$275$	−8.25121	+	18.6899i	−0.497567	+	1.12704i
$276$	12.4206	−	3.14546i	0.747630	−	0.189335i
$277$		−	3.53789i		−	0.212571i	−0.994336	−	0.106286i	$-0.966104\pi$
$277$		−	3.53789i		−	0.212571i	0.994336	−	0.106286i	$-0.0338958\pi$
$278$		−	3.91782i		−	0.234975i
$279$	9.73614	+	17.9898i	0.582887	+	1.07702i
$280$		0			0
$281$		−	12.1295i		−	0.723587i	−0.932258	−	0.361794i	$-0.882164\pi$
$281$		−	12.1295i		−	0.723587i	0.932258	−	0.361794i	$-0.117836\pi$
$282$	−1.02836	−	4.06070i	−0.0612378	−	0.241811i
$283$	−0.0695818			−0.00413621			−0.00206811	−	0.999998i	$-0.500658\pi$
$283$	−0.0695818			−0.00413621			−0.00206811	+	0.999998i	$0.500658\pi$
$284$		−	12.1243i		−	0.719442i
$285$	−1.19686	−	29.7867i	−0.0708957	−	1.76441i
$286$			14.3033i			0.845774i
$287$		0			0
$288$	−2.63839	+	1.42790i	−0.155469	+	0.0841400i
$289$	16.8088			0.988750
$290$	−2.28535	+	10.8352i	−0.134200	+	0.636264i
$291$	−13.3239	+	3.37423i	−0.781059	+	0.197801i
$292$	9.06556			0.530522
$293$			0.996528i			0.0582178i	0.999576	+	0.0291089i	$0.00926696\pi$
$293$			0.996528i			0.0582178i	−0.999576	+	0.0291089i	$0.990733\pi$
$294$		0			0
$295$	6.02251	+	1.27026i	0.350644	+	0.0739577i
$296$		−	4.51245i		−	0.262281i
$297$	−14.3804	−	15.6202i	−0.834436	−	0.906377i
$298$			20.2201i			1.17132i
$299$	25.8948			1.49753
$300$	−8.53874	−	1.44564i	−0.492985	−	0.0834641i
$301$		0			0
$302$	11.1525			0.641753
$303$	−5.76630	+	1.46029i	−0.331265	+	0.0838917i
$304$		−	7.69711i		−	0.441459i
$305$	−2.65516	+	12.5885i	−0.152034	+	0.720815i
$306$	0.624444	+	1.15381i	0.0356971	+	0.0659589i
$307$	−24.3980			−1.39247			−0.696233	−	0.717816i	$-0.745142\pi$
$307$	−24.3980			−1.39247			−0.696233	+	0.717816i	$0.745142\pi$
$308$		0			0
$309$	−33.3112	+	8.43595i	−1.89501	+	0.479905i
$310$	−3.14658	+	14.9184i	−0.178713	+	0.847307i
$311$	22.2260			1.26032			0.630162	−	0.776464i	$-0.282989\pi$
$311$	22.2260			1.26032			0.630162	+	0.776464i	$0.282989\pi$
$312$	−5.87754	+	1.48847i	−0.332750	+	0.0842679i
$313$	27.1630			1.53535			0.767673	−	0.640842i	$-0.221415\pi$
$313$	27.1630			1.53535			0.767673	+	0.640842i	$0.221415\pi$
$314$	13.8740			0.782954
$315$		0			0
$316$	3.37581			0.189904
$317$	−25.5543			−1.43527			−0.717635	−	0.696419i	$-0.754775\pi$
$317$	−25.5543			−1.43527			−0.717635	+	0.696419i	$0.754775\pi$
$318$	−0.713267	+	0.180632i	−0.0399980	+	0.0101294i
$319$	−20.2352			−1.13295
$320$	−2.18793	−	0.461477i	−0.122309	−	0.0257973i
$321$	−17.6137	+	4.46061i	−0.983100	+	0.248967i
$322$		0			0
$323$	−3.36607			−0.187293
$324$	4.92219	−	7.53472i	0.273455	−	0.418596i
$325$	−16.0117	−	7.06882i	−0.888168	−	0.392108i
$326$		−	11.6362i		−	0.644468i
$327$	−20.8053	+	5.26887i	−1.15054	+	0.291369i
$328$	1.34412			0.0742164
$329$		0			0
$330$	−0.635358	−	15.8125i	−0.0349753	−	0.870447i
$331$	−11.8460			−0.651112			−0.325556	−	0.945523i	$-0.605552\pi$
$331$	−11.8460			−0.651112			−0.325556	+	0.945523i	$0.605552\pi$
$332$			17.1321i			0.940249i
$333$	6.44333	+	11.9056i	0.353092	+	0.652422i
$334$			3.73225i			0.204220i
$335$	−5.25743	+	24.9263i	−0.287244	+	1.36187i
$336$		0			0
$337$			17.6449i			0.961179i	0.876946	+	0.480589i	$0.159577\pi$
$337$			17.6449i			0.961179i	−0.876946	+	0.480589i	$0.840423\pi$
$338$	0.746310			0.0405939
$339$	−20.0388	+	5.07476i	−1.08836	+	0.275623i
$340$	−0.201811	+	0.956816i	−0.0109447	+	0.0518907i
$341$	−27.8607			−1.50874
$342$	10.9907	+	20.3080i	0.594310	+	1.09813i
$343$		0			0
$344$			6.67867i			0.360090i
$345$	−28.6269	+	1.15025i	−1.54122	+	0.0619275i
$346$			14.3011i			0.768834i
$347$	−12.0280			−0.645699			−0.322849	−	0.946450i	$-0.604641\pi$
$347$	−12.0280			−0.645699			−0.322849	+	0.946450i	$0.604641\pi$
$348$	−2.10576	−	8.31505i	−0.112881	−	0.445734i
$349$			4.40508i			0.235798i	0.993026	+	0.117899i	$0.0376160\pi$
$349$			4.40508i			0.235798i	−0.993026	+	0.117899i	$0.962384\pi$
$350$		0			0
$351$	13.3819	−	12.3197i	0.714271	−	0.657578i
$352$		−	4.08605i		−	0.217787i
$353$			12.4014i			0.660061i	0.943970	+	0.330031i	$0.107059\pi$
$353$			12.4014i			0.660061i	−0.943970	+	0.330031i	$0.892941\pi$
$354$	−4.62175	+	1.17044i	−0.245643	+	0.0622083i
$355$	−5.59506	+	26.5270i	−0.296955	+	1.40791i
$356$	4.52892			0.240032
$357$		0			0
$358$			14.0130i			0.740610i
$359$		−	36.5002i		−	1.92641i	−0.268770	−	0.963204i	$-0.586617\pi$
$359$		−	36.5002i		−	1.92641i	0.268770	−	0.963204i	$-0.413383\pi$
$360$	6.43155	−	1.90660i	0.338973	−	0.100486i
$361$	−40.2454			−2.11818
$362$		−	13.9155i		−	0.731383i
$363$	9.56355	−	2.42194i	0.501956	−	0.127119i
$364$		0			0
$365$	−19.8348	−	4.18355i	−1.03820	−	0.218977i
$366$	−2.44651	−	9.66057i	−0.127881	−	0.504966i
$367$	5.19910			0.271391			0.135695	−	0.990751i	$-0.456673\pi$
$367$	5.19910			0.271391			0.135695	+	0.990751i	$0.456673\pi$
$368$	−7.39739			−0.385616
$369$	−3.54630	+	1.91927i	−0.184613	+	0.0999130i
$370$	−2.08239	+	9.87292i	−0.108258	+	0.513268i
$371$		0			0
$372$	−2.89931	−	11.4486i	−0.150322	−	0.593580i
$373$			23.9380i			1.23946i	0.784814	+	0.619731i	$0.212758\pi$
$373$			23.9380i			1.23946i	−0.784814	+	0.619731i	$0.787242\pi$
$374$	−1.78690			−0.0923982
$375$	18.0150	+	7.10339i	0.930293	+	0.366818i
$376$			2.41846i			0.124722i
$377$		−	17.3355i		−	0.892823i
$378$		0			0
$379$	−12.6720			−0.650914			−0.325457	−	0.945557i	$-0.605518\pi$
$379$	−12.6720			−0.650914			−0.325457	+	0.945557i	$0.605518\pi$
$380$	−3.55204	+	16.8407i	−0.182216	+	0.863911i
$381$	1.47785	+	5.83561i	0.0757125	+	0.298967i
$382$		−	10.7729i		−	0.551187i
$383$			25.8460i			1.32067i	0.750971	+	0.660335i	$0.229586\pi$
$383$			25.8460i			1.32067i	−0.750971	+	0.660335i	$0.770414\pi$
$384$	1.67905	−	0.425213i	0.0856834	−	0.0216990i
$385$		0			0
$386$			8.77793i			0.446785i
$387$	−9.53649	−	17.6209i	−0.484767	−	0.895722i
$388$	7.93539			0.402858
$389$		−	22.8632i		−	1.15921i	−0.814898	−	0.579604i	$-0.803207\pi$
$389$		−	22.8632i		−	1.15921i	0.814898	−	0.579604i	$-0.196793\pi$
$390$	13.5466	−	0.544312i	0.685956	−	0.0275623i
$391$			3.23499i			0.163601i
$392$		0			0
$393$	3.83045	−	0.970047i	0.193220	−	0.0489324i
$394$	−12.7615			−0.642914
$395$	−7.38604	−	1.55786i	−0.371632	−	0.0783844i
$396$	5.83448	+	10.7806i	0.293194	+	0.541745i
$397$	23.5983			1.18437			0.592183	−	0.805804i	$-0.298266\pi$
$397$	23.5983			1.18437			0.592183	+	0.805804i	$0.298266\pi$
$398$			4.18139i			0.209594i
$399$		0			0
$400$	4.57408	+	2.01936i	0.228704	+	0.100968i
$401$		−	31.5489i		−	1.57547i	−0.616011	−	0.787737i	$-0.711252\pi$
$401$		−	31.5489i		−	1.57547i	0.616011	−	0.787737i	$-0.288748\pi$
$402$	−4.84429	−	19.1287i	−0.241611	−	0.954054i
$403$		−	23.8683i		−	1.18896i
$404$	3.43427			0.170861
$405$	−14.2465	+	14.2140i	−0.707915	+	0.706298i
$406$		0			0
$407$	−18.4381			−0.913942
$408$	−0.185952	−	0.734273i	−0.00920600	−	0.0363519i
$409$		−	18.1161i		−	0.895782i	−0.894088	−	0.447891i	$-0.852175\pi$
$409$		−	18.1161i		−	0.895782i	0.894088	−	0.447891i	$-0.147825\pi$
$410$	−2.94083	−	0.620279i	−0.145237	−	0.0306334i
$411$	−37.3539	+	9.45976i	−1.84253	+	0.466615i
$412$	19.8394			0.977416
$413$		0			0
$414$	19.5172	−	10.5628i	0.959217	−	0.519131i
$415$	7.90609	−	37.4839i	0.388095	−	1.84001i
$416$	3.50053			0.171627
$417$	−1.66591	−	6.57820i	−0.0815798	−	0.322136i
$418$	−31.4508			−1.53831
$419$	35.2889			1.72398			0.861988	−	0.506929i	$-0.169219\pi$
$419$	35.2889			1.72398			0.861988	+	0.506929i	$0.169219\pi$
$420$		0			0
$421$	−8.88314			−0.432938			−0.216469	−	0.976290i	$-0.569454\pi$
$421$	−8.88314			−0.432938			−0.216469	+	0.976290i	$0.569454\pi$
$422$	7.19053			0.350029
$423$	−3.45332	−	6.38083i	−0.167906	−	0.310246i
$424$	0.424805			0.0206303
$425$	0.883098	−	2.00032i	0.0428365	−	0.0970296i
$426$	−5.15538	−	20.3572i	−0.249779	−	0.986308i
$427$		0			0
$428$	10.4903			0.507068
$429$	6.08196	+	24.0160i	0.293640	+	1.15950i
$430$	3.08205	−	14.6125i	0.148630	−	0.704676i
$431$			22.5439i			1.08590i	0.839765	+	0.542950i	$0.182693\pi$
$431$			22.5439i			1.08590i	−0.839765	+	0.542950i	$0.817307\pi$
$432$	−3.82281	+	3.51939i	−0.183925	+	0.169327i
$433$	25.2191			1.21195			0.605975	−	0.795484i	$-0.292783\pi$
$433$	25.2191			1.21195			0.605975	+	0.795484i	$0.292783\pi$
$434$		0			0
$435$	0.770047	+	19.1645i	0.0369209	+	0.918868i
$436$	12.3912			0.593429
$437$			56.9385i			2.72374i
$438$	15.2215	−	3.85479i	0.727311	−	0.184189i
$439$		−	12.7318i		−	0.607654i	−0.952727	−	0.303827i	$-0.901736\pi$
$439$		−	12.7318i		−	0.607654i	0.952727	−	0.303827i	$-0.0982645\pi$
$440$	−1.88562	+	8.94000i	−0.0898934	+	0.426198i
$441$		0			0
$442$		−	1.53084i		−	0.0728144i
$443$	−0.860072			−0.0408633			−0.0204316	−	0.999791i	$-0.506504\pi$
$443$	−0.860072			−0.0408633			−0.0204316	+	0.999791i	$0.506504\pi$
$444$	−1.91875	−	7.57660i	−0.0910598	−	0.359570i
$445$	−9.90896	−	2.08999i	−0.469730	−	0.0990751i
$446$	0.621483			0.0294281
$447$	8.59784	+	33.9505i	0.406664	+	1.60580i
$448$		0			0
$449$			34.0935i			1.60897i	0.593972	+	0.804486i	$0.297559\pi$
$449$			34.0935i			1.60897i	−0.593972	+	0.804486i	$0.702441\pi$
$450$	−14.9516	+	1.20348i	−0.704827	+	0.0567327i
$451$		−	5.49213i		−	0.258614i
$452$	11.9346			0.561358
$453$	18.7255	−	4.74217i	0.879802	−	0.222807i
$454$			12.9728i			0.608843i
$455$		0			0
$456$	−3.27291	−	12.9238i	−0.153268	−	0.605212i
$457$		−	33.0657i		−	1.54675i	−0.633950	−	0.773374i	$-0.718567\pi$
$457$		−	33.0657i		−	1.54675i	0.633950	−	0.773374i	$-0.281433\pi$
$458$		−	21.2637i		−	0.993587i
$459$	1.53908	+	1.67178i	0.0718383	+	0.0780318i
$460$	16.1850	+	3.41373i	0.754628	+	0.159166i
$461$	4.43329			0.206479			0.103240	−	0.994657i	$-0.467079\pi$
$461$	4.43329			0.206479			0.103240	+	0.994657i	$0.467079\pi$
$462$		0			0
$463$		−	2.89220i		−	0.134412i	−0.997739	−	0.0672060i	$-0.978592\pi$
$463$		−	2.89220i		−	0.134412i	0.997739	−	0.0672060i	$-0.0214085\pi$
$464$			4.95225i			0.229902i
$465$	1.06024	+	26.3866i	0.0491673	+	1.22365i
$466$	−11.0664			−0.512643
$467$		−	4.84781i		−	0.224330i	−0.993690	−	0.112165i	$-0.964221\pi$
$467$		−	4.84781i		−	0.224330i	0.993690	−	0.112165i	$-0.0357785\pi$
$468$	−9.23575	+	4.99841i	−0.426923	+	0.231052i
$469$		0			0
$470$	1.11606	−	5.29141i	0.0514801	−	0.244075i
$471$	23.2950	−	5.89939i	1.07338	−	0.271829i
$472$	2.75261			0.126699
$473$	27.2894			1.25477
$474$	5.66814	−	1.43544i	0.260346	−	0.0659318i
$475$	15.5432	−	35.2072i	0.713172	−	1.61542i
$476$		0			0
$477$	−1.12080	+	0.606580i	−0.0513179	+	0.0277734i
$478$		−	0.281518i		−	0.0128763i
$479$	29.7191			1.35790			0.678951	−	0.734184i	$-0.262435\pi$
$479$	29.7191			1.35790			0.678951	+	0.734184i	$0.262435\pi$
$480$	−3.86986	+	0.155494i	−0.176634	+	0.00709732i
$481$		−	15.7959i		−	0.720233i
$482$			14.7273i			0.670810i
$483$		0			0
$484$	−5.69583			−0.258901
$485$	−17.3621	−	3.66200i	−0.788371	−	0.166283i
$486$	5.06072	−	14.7441i	0.229559	−	0.668807i
$487$			28.1729i			1.27664i	0.769773	+	0.638318i	$0.220369\pi$
$487$			28.1729i			1.27664i	−0.769773	+	0.638318i	$0.779631\pi$
$488$			5.75361i			0.260454i
$489$	−4.94785	−	19.5377i	−0.223750	−	0.883524i
$490$		0			0
$491$			28.4984i			1.28611i	0.765818	+	0.643057i	$0.222334\pi$
$491$			28.4984i			1.28611i	−0.765818	+	0.643057i	$0.777666\pi$
$492$	2.25683	−	0.571535i	0.101746	−	0.0257668i
$493$	2.16570			0.0975381
$494$		−	26.9439i		−	1.21226i
$495$	−7.79045	−	26.2797i	−0.350155	−	1.18118i
$496$			6.81849i			0.306159i
$497$		0			0
$498$	7.28480	+	28.7657i	0.326440	+	1.28902i
$499$	−2.44955			−0.109657			−0.0548285	−	0.998496i	$-0.517461\pi$
$499$	−2.44955			−0.109657			−0.0548285	+	0.998496i	$0.517461\pi$
$500$	−9.07588	−	6.52905i	−0.405886	−	0.291988i
$501$	1.58700	+	6.26662i	0.0709020	+	0.279972i
$502$	18.5359			0.827298
$503$		−	16.5063i		−	0.735980i	−0.929830	−	0.367990i	$-0.880046\pi$
$503$		−	16.5063i		−	0.735980i	0.929830	−	0.367990i	$-0.119954\pi$
$504$		0			0
$505$	−7.51394	−	1.58484i	−0.334366	−	0.0705243i
$506$			30.2261i			1.34372i
$507$	1.25309	−	0.317340i	0.0556516	−	0.0140936i
$508$		−	3.47555i		−	0.154203i
$509$	−14.9398			−0.662193			−0.331097	−	0.943597i	$-0.607419\pi$
$509$	−14.9398			−0.662193			−0.331097	+	0.943597i	$0.607419\pi$
$510$	0.0680002	+	1.69235i	0.00301110	+	0.0749386i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	27.0891	+	29.4246i	1.19601	+	1.29913i
$514$			19.4528i			0.858028i
$515$	−43.4072	−	9.15542i	−1.91275	−	0.403436i
$516$	2.83985	+	11.2138i	0.125018	+	0.493660i
$517$	9.88194			0.434607
$518$		0			0
$519$	6.08102	+	24.0123i	0.266927	+	1.05402i
$520$	−7.65891	−	1.61541i	−0.335865	−	0.0708405i
$521$	−8.03385			−0.351969			−0.175985	−	0.984393i	$-0.556311\pi$
$521$	−8.03385			−0.351969			−0.175985	+	0.984393i	$0.556311\pi$
$522$	−7.07133	−	13.0660i	−0.309504	−	0.571882i
$523$	−13.6355			−0.596237			−0.298118	−	0.954529i	$-0.596359\pi$
$523$	−13.6355			−0.596237			−0.298118	+	0.954529i	$0.596359\pi$
$524$	−2.28132			−0.0996601
$525$		0			0
$526$	13.8660			0.604584
$527$	2.98183			0.129891
$528$	−1.73744	−	6.86067i	−0.0756124	−	0.298572i
$529$	31.7214			1.37919
$530$	−0.929443	−	0.196038i	−0.0403724	−	0.00851533i
$531$	−7.26245	+	3.93045i	−0.315163	+	0.170567i
$532$		0			0
$533$	4.70511			0.203801
$534$	7.60426	−	1.92575i	0.329069	−	0.0833355i
$535$	−22.9520	−	4.84103i	−0.992303	−	0.209296i
$536$			11.3926i			0.492086i
$537$	5.95850	+	23.5285i	0.257128	+	1.01533i
$538$	−15.3624			−0.662320
$539$		0			0
$540$	9.98817	−	5.93604i	0.429822	−	0.255446i
$541$	−22.5627			−0.970044			−0.485022	−	0.874502i	$-0.661188\pi$
$541$	−22.5627			−0.970044			−0.485022	+	0.874502i	$0.661188\pi$
$542$		−	16.3255i		−	0.701240i
$543$	−5.91705	−	23.3648i	−0.253925	−	1.00268i
$544$			0.437316i			0.0187498i
$545$	−27.1110	−	5.71823i	−1.16131	−	0.244942i
$546$		0			0
$547$		−	5.69200i		−	0.243372i	−0.992569	−	0.121686i	$-0.961170\pi$
$547$		−	5.69200i		−	0.243372i	0.992569	−	0.121686i	$-0.0388302\pi$
$548$	22.2471			0.950350
$549$	−8.21559	−	15.1803i	−0.350633	−	0.647878i
$550$	8.25121	−	18.6899i	0.351833	−	0.796941i
$551$	38.1180			1.62388
$552$	−12.4206	+	3.14546i	−0.528654	+	0.133880i
$553$		0			0
$554$			3.53789i			0.150311i
$555$	0.701660	+	17.4625i	0.0297838	+	0.741243i
$556$			3.91782i			0.166153i
$557$	40.4418			1.71358			0.856788	−	0.515669i	$-0.172457\pi$
$557$	40.4418			1.71358			0.856788	+	0.515669i	$0.172457\pi$
$558$	−9.73614	−	17.9898i	−0.412164	−	0.761570i
$559$			23.3789i			0.988821i
$560$		0			0
$561$	−3.00028	+	0.759810i	−0.126672	+	0.0320792i
$562$			12.1295i			0.511654i
$563$		−	28.2674i		−	1.19133i	−0.803233	−	0.595665i	$-0.796888\pi$
$563$		−	28.2674i		−	1.19133i	0.803233	−	0.595665i	$-0.203112\pi$
$564$	1.02836	+	4.06070i	0.0433017	+	0.170986i
$565$	−26.1121	−	5.50756i	−1.09855	−	0.231705i
$566$	0.0695818			0.00292474
$567$		0			0
$568$			12.1243i			0.508722i
$569$			2.40508i			0.100826i	0.998728	+	0.0504132i	$0.0160538\pi$
$569$			2.40508i			0.100826i	−0.998728	+	0.0504132i	$0.983946\pi$
$570$	1.19686	+	29.7867i	0.0501308	+	1.24763i
$571$	31.2423			1.30745			0.653724	−	0.756733i	$-0.273206\pi$
$571$	31.2423			1.30745			0.653724	+	0.756733i	$0.273206\pi$
$572$		−	14.3033i		−	0.598053i
$573$	−4.58075	−	18.0881i	−0.191364	−	0.755642i
$574$		0			0
$575$	−33.8362	−	14.9380i	−1.41107	−	0.622957i
$576$	2.63839	−	1.42790i	0.109933	−	0.0594959i
$577$	34.2061			1.42402			0.712009	−	0.702171i	$-0.247786\pi$
$577$	34.2061			1.42402			0.712009	+	0.702171i	$0.247786\pi$
$578$	−16.8088			−0.699152
$579$	3.73249	+	14.7386i	0.155117	+	0.612513i
$580$	2.28535	−	10.8352i	0.0948940	−	0.449906i
$581$		0			0
$582$	13.3239	−	3.37423i	0.552292	−	0.139866i
$583$		−	1.73577i		−	0.0718884i
$584$	−9.06556			−0.375136
$585$	22.5138	−	6.67409i	0.930832	−	0.275940i
$586$		−	0.996528i		−	0.0411662i
$587$		−	28.3288i		−	1.16926i	−0.811302	−	0.584628i	$-0.801241\pi$
$587$		−	28.3288i		−	1.16926i	0.811302	−	0.584628i	$-0.198759\pi$
$588$		0			0
$589$	52.4826			2.16251
$590$	−6.02251	−	1.27026i	−0.247943	−	0.0522960i
$591$	−21.4271	+	5.42634i	−0.881394	+	0.223210i
$592$			4.51245i			0.185460i
$593$			40.6298i			1.66846i	0.551414	+	0.834232i	$0.314089\pi$
$593$			40.6298i			1.66846i	−0.551414	+	0.834232i	$0.685911\pi$
$594$	14.3804	+	15.6202i	0.590035	+	0.640905i
$595$		0			0
$596$		−	20.2201i		−	0.828248i
$597$	1.77798	+	7.02074i	0.0727678	+	0.287340i
$598$	−25.8948			−1.05892
$599$		−	4.85564i		−	0.198396i	−0.995068	−	0.0991981i	$-0.968372\pi$
$599$		−	4.85564i		−	0.198396i	0.995068	−	0.0991981i	$-0.0316278\pi$
$600$	8.53874	+	1.44564i	0.348593	+	0.0590180i
$601$		−	2.98684i		−	0.121836i	−0.998143	−	0.0609178i	$-0.980597\pi$
$601$		−	2.98684i		−	0.121836i	0.998143	−	0.0609178i	$-0.0194027\pi$
$602$		0			0
$603$	−16.2676	−	30.0582i	−0.662466	−	1.22406i
$604$	−11.1525			−0.453788
$605$	12.4621	+	2.62849i	0.506655	+	0.106863i
$606$	5.76630	−	1.46029i	0.234240	−	0.0593204i
$607$	−36.1981			−1.46924			−0.734618	−	0.678481i	$-0.762639\pi$
$607$	−36.1981			−1.46924			−0.734618	+	0.678481i	$0.762639\pi$
$608$			7.69711i			0.312159i
$609$		0			0
$610$	2.65516	−	12.5885i	0.107504	−	0.509693i
$611$			8.46587i			0.342492i
$612$	−0.624444	−	1.15381i	−0.0252417	−	0.0466400i
$613$			29.4300i			1.18867i	0.804219	+	0.594333i	$0.202584\pi$
$613$			29.4300i			1.18867i	−0.804219	+	0.594333i	$0.797416\pi$
$614$	24.3980			0.984622
$615$	−5.20154	+	0.209002i	−0.209746	+	0.00842779i
$616$		0			0
$617$	−7.28744			−0.293381			−0.146691	−	0.989182i	$-0.546862\pi$
$617$	−7.28744			−0.293381			−0.146691	+	0.989182i	$0.546862\pi$
$618$	33.3112	−	8.43595i	1.33997	−	0.339344i
$619$			9.60843i			0.386195i	0.981180	+	0.193098i	$0.0618534\pi$
$619$			9.60843i			0.386195i	−0.981180	+	0.193098i	$0.938147\pi$
$620$	3.14658	−	14.9184i	0.126370	−	0.599136i
$621$	28.2788	−	26.0343i	1.13479	−	1.04472i
$622$	−22.2260			−0.891183
$623$		0			0
$624$	5.87754	−	1.48847i	0.235290	−	0.0595864i
$625$	16.8444	+	18.4734i	0.673775	+	0.738936i
$626$	−27.1630			−1.08565
$627$	−52.8073	+	13.3733i	−2.10892	+	0.534077i
$628$	−13.8740			−0.553632
$629$	1.97336			0.0786832
$630$		0			0
$631$	−15.4613			−0.615503			−0.307751	−	0.951467i	$-0.599576\pi$
$631$	−15.4613			−0.615503			−0.307751	+	0.951467i	$0.599576\pi$
$632$	−3.37581			−0.134283
$633$	12.0732	−	3.05750i	0.479868	−	0.121525i
$634$	25.5543			1.01489
$635$	−1.60389	+	7.60426i	−0.0636483	+	0.301766i
$636$	0.713267	−	0.180632i	0.0282829	−	0.00716254i
$637$		0			0
$638$	20.2352			0.801117
$639$	−17.3123	−	31.9885i	−0.684862	−	1.26545i
$640$	2.18793	+	0.461477i	0.0864855	+	0.0182415i
$641$			8.67553i			0.342663i	0.985213	+	0.171331i	$0.0548069\pi$
$641$			8.67553i			0.342663i	−0.985213	+	0.171331i	$0.945193\pi$
$642$	17.6137	−	4.46061i	0.695157	−	0.176046i
$643$	5.54387			0.218629			0.109314	−	0.994007i	$-0.465134\pi$
$643$	5.54387			0.218629			0.109314	+	0.994007i	$0.465134\pi$
$644$		0			0
$645$	−1.03850	−	25.8455i	−0.0408907	−	1.01767i
$646$	3.36607			0.132436
$647$			11.3977i			0.448090i	0.974579	+	0.224045i	$0.0719263\pi$
$647$			11.3977i			0.448090i	−0.974579	+	0.224045i	$0.928074\pi$
$648$	−4.92219	+	7.53472i	−0.193362	+	0.295992i
$649$		−	11.2473i		−	0.441495i
$650$	16.0117	+	7.06882i	0.628030	+	0.277262i
$651$		0			0
$652$			11.6362i			0.455708i
$653$	−10.4964			−0.410756			−0.205378	−	0.978683i	$-0.565842\pi$
$653$	−10.4964			−0.410756			−0.205378	+	0.978683i	$0.565842\pi$
$654$	20.8053	−	5.26887i	0.813552	−	0.206029i
$655$	4.99138	+	1.05278i	0.195029	+	0.0411354i
$656$	−1.34412			−0.0524789
$657$	23.9185	−	12.9447i	0.933149	−	0.505022i
$658$		0			0
$659$		−	3.10502i		−	0.120954i	−0.998170	−	0.0604772i	$-0.980738\pi$
$659$		−	3.10502i		−	0.120954i	0.998170	−	0.0604772i	$-0.0192623\pi$
$660$	0.635358	+	15.8125i	0.0247313	+	0.615499i
$661$			38.1592i			1.48422i	0.670277	+	0.742111i	$0.266175\pi$
$661$			38.1592i			1.48422i	−0.670277	+	0.742111i	$0.733825\pi$
$662$	11.8460			0.460406
$663$	−0.650931	−	2.57034i	−0.0252800	−	0.0998239i
$664$		−	17.1321i		−	0.664856i
$665$		0			0
$666$	−6.44333	−	11.9056i	−0.249674	−	0.461332i
$667$		−	36.6337i		−	1.41846i
$668$		−	3.73225i		−	0.144405i
$669$	1.04350	−	0.264263i	0.0403440	−	0.0102170i
$670$	5.25743	−	24.9263i	0.203112	−	0.962986i
$671$	23.5096			0.907576
$672$		0			0
$673$		−	5.10977i		−	0.196967i	−0.995139	−	0.0984835i	$-0.968601\pi$
$673$		−	5.10977i		−	0.196967i	0.995139	−	0.0984835i	$-0.0313992\pi$
$674$		−	17.6449i		−	0.679656i
$675$	−24.5928	+	8.37833i	−0.946576	+	0.322482i
$676$	−0.746310			−0.0287042
$677$		−	40.8152i		−	1.56866i	−0.620346	−	0.784328i	$-0.713008\pi$
$677$		−	40.8152i		−	1.56866i	0.620346	−	0.784328i	$-0.286992\pi$
$678$	20.0388	−	5.07476i	0.769585	−	0.194895i
$679$		0			0
$680$	0.201811	−	0.956816i	0.00773911	−	0.0366922i
$681$	5.51619	+	21.7819i	0.211381	+	0.834684i
$682$	27.8607			1.06684
$683$	−7.03302			−0.269111			−0.134556	−	0.990906i	$-0.542961\pi$
$683$	−7.03302			−0.269111			−0.134556	+	0.990906i	$0.542961\pi$
$684$	−10.9907	−	20.3080i	−0.420241	−	0.776494i
$685$	−48.6752	−	10.2665i	−1.85978	−	0.392264i
$686$		0			0
$687$	−9.04158	−	35.7027i	−0.344958	−	1.36214i
$688$		−	6.67867i		−	0.254622i
$689$	1.48704			0.0566517
$690$	28.6269	−	1.15025i	1.08981	−	0.0437894i
$691$		−	34.9788i		−	1.33066i	−0.746551	−	0.665328i	$-0.768292\pi$
$691$		−	34.9788i		−	1.33066i	0.746551	−	0.665328i	$-0.231708\pi$
$692$		−	14.3011i		−	0.543648i
$693$		0			0
$694$	12.0280			0.456578
$695$	1.80798	−	8.57191i	0.0685807	−	0.325151i
$696$	2.10576	+	8.31505i	0.0798186	+	0.315181i
$697$			0.587803i			0.0222646i
$698$		−	4.40508i		−	0.166735i
$699$	−18.5811	+	4.70559i	−0.702800	+	0.177982i
$700$		0			0
$701$		−	20.3459i		−	0.768455i	−0.923238	−	0.384227i	$-0.874468\pi$
$701$		−	20.3459i		−	0.768455i	0.923238	−	0.384227i	$-0.125532\pi$
$702$	−13.3819	+	12.3197i	−0.505066	+	0.464978i
$703$	34.7328			1.30997
$704$			4.08605i			0.153999i
$705$	−0.376056	−	9.35909i	−0.0141631	−	0.352484i
$706$		−	12.4014i		−	0.466734i
$707$		0			0
$708$	4.62175	−	1.17044i	0.173696	−	0.0439879i
$709$	33.0629			1.24170			0.620851	−	0.783929i	$-0.286787\pi$
$709$	33.0629			1.24170			0.620851	+	0.783929i	$0.286787\pi$
$710$	5.59506	−	26.5270i	0.209979	−	0.995541i
$711$	8.90671	−	4.82033i	0.334028	−	0.180777i
$712$	−4.52892			−0.169728
$713$		−	50.4390i		−	1.88896i
$714$		0			0
$715$	−6.60066	+	31.2947i	−0.246851	+	1.17036i
$716$		−	14.0130i		−	0.523690i
$717$	−0.119705	−	0.472682i	−0.00447047	−	0.0176526i
$718$			36.5002i			1.36218i
$719$	19.4654			0.725935			0.362968	−	0.931802i	$-0.381764\pi$
$719$	19.4654			0.725935			0.362968	+	0.931802i	$0.381764\pi$
$720$	−6.43155	+	1.90660i	−0.239690	+	0.0710546i
$721$		0			0
$722$	40.2454			1.49778
$723$	6.26223	+	24.7278i	0.232895	+	0.919636i
$724$			13.9155i			0.517166i
$725$	−10.0004	+	22.6520i	−0.371404	+	0.841273i
$726$	−9.56355	+	2.42194i	−0.354937	+	0.0898865i
$727$	−12.0495			−0.446892			−0.223446	−	0.974716i	$-0.571731\pi$
$727$	−12.0495			−0.446892			−0.223446	+	0.974716i	$0.571731\pi$
$728$		0			0
$729$	2.22780	−	26.9079i	0.0825110	−	0.996590i
$730$	19.8348	+	4.18355i	0.734120	+	0.154840i
$731$	−2.92069			−0.108026
$732$	2.44651	+	9.66057i	0.0904255	+	0.357065i
$733$	5.22478			0.192982			0.0964909	−	0.995334i	$-0.469238\pi$
$733$	5.22478			0.192982			0.0964909	+	0.995334i	$0.469238\pi$
$734$	−5.19910			−0.191902
$735$		0			0
$736$	7.39739			0.272671
$737$	46.5509			1.71472
$738$	3.54630	−	1.91927i	0.130541	−	0.0706492i
$739$	37.0678			1.36356			0.681780	−	0.731557i	$-0.261206\pi$
$739$	37.0678			1.36356			0.681780	+	0.731557i	$0.261206\pi$
$740$	2.08239	−	9.87292i	0.0765502	−	0.362936i
$741$	−11.4569	−	45.2401i	−0.420880	−	1.66194i
$742$		0			0
$743$	−14.5999			−0.535617			−0.267809	−	0.963472i	$-0.586299\pi$
$743$	−14.5999			−0.535617			−0.267809	+	0.963472i	$0.586299\pi$
$744$	2.89931	+	11.4486i	0.106294	+	0.419724i
$745$	−9.33111	+	44.2402i	−0.341865	+	1.62083i
$746$		−	23.9380i		−	0.876432i
$747$	24.4630	+	45.2013i	0.895055	+	1.65383i
$748$	1.78690			0.0653354
$749$		0			0
$750$	−18.0150	−	7.10339i	−0.657816	−	0.259379i
$751$	−17.8328			−0.650728			−0.325364	−	0.945589i	$-0.605487\pi$
$751$	−17.8328			−0.650728			−0.325364	+	0.945589i	$0.605487\pi$
$752$		−	2.41846i		−	0.0881920i
$753$	31.1227	−	7.88170i	1.13417	−	0.287225i
$754$			17.3355i			0.631321i
$755$	24.4008	+	5.14661i	0.888038	+	0.187304i
$756$		0			0
$757$		−	11.2697i		−	0.409603i	−0.978804	−	0.204801i	$-0.934345\pi$
$757$		−	11.2697i		−	0.409603i	0.978804	−	0.204801i	$-0.0656549\pi$
$758$	12.6720			0.460266
$759$	12.8525	+	50.7510i	0.466517	+	1.84215i
$760$	3.55204	−	16.8407i	0.128846	−	0.610877i
$761$	−15.3938			−0.558026			−0.279013	−	0.960287i	$-0.590007\pi$
$761$	−15.3938			−0.558026			−0.279013	+	0.960287i	$0.590007\pi$
$762$	−1.47785	−	5.83561i	−0.0535368	−	0.211402i
$763$		0			0
$764$			10.7729i			0.389748i
$765$	0.833784	+	2.81262i	0.0301455	+	0.101690i
$766$		−	25.8460i		−	0.933854i
$767$	9.63557			0.347920
$768$	−1.67905	+	0.425213i	−0.0605873	+	0.0153435i
$769$		−	25.6558i		−	0.925173i	−0.886574	−	0.462587i	$-0.846921\pi$
$769$		−	25.6558i		−	0.925173i	0.886574	−	0.462587i	$-0.153079\pi$
$770$		0			0
$771$	8.27159	+	32.6622i	0.297894	+	1.17630i
$772$		−	8.77793i		−	0.315925i
$773$			2.63678i			0.0948384i	0.998875	+	0.0474192i	$0.0150997\pi$
$773$			2.63678i			0.0948384i	−0.998875	+	0.0474192i	$0.984900\pi$
$774$	9.53649	+	17.6209i	0.342782	+	0.633371i
$775$	−13.7690	+	31.1883i	−0.494596	+	1.12032i
$776$	−7.93539			−0.284864
$777$		0			0
$778$			22.8632i			0.819684i
$779$			10.3458i			0.370677i
$780$	−13.5466	+	0.544312i	−0.485044	+	0.0194895i
$781$	49.5403			1.77269
$782$		−	3.23499i		−	0.115683i
$783$	−17.4289	−	18.9315i	−0.622858	−	0.676557i
$784$		0			0
$785$	30.3553	+	6.40252i	1.08343	+	0.228516i
$786$	−3.83045	+	0.970047i	−0.136627	+	0.0346004i
$787$	−37.9743			−1.35364			−0.676818	−	0.736150i	$-0.736642\pi$
$787$	−37.9743			−1.35364			−0.676818	+	0.736150i	$0.736642\pi$
$788$	12.7615			0.454609
$789$	23.2816	−	5.89598i	0.828846	−	0.209902i
$790$	7.38604	+	1.55786i	0.262784	+	0.0554262i
$791$		0			0
$792$	−5.83448	−	10.7806i	−0.207319	−	0.383072i
$793$			20.1407i			0.715216i
$794$	−23.5983			−0.837473
$795$	−1.64394	+	0.0660548i	−0.0583044	+	0.00234272i
$796$		−	4.18139i		−	0.148205i
$797$			4.62272i			0.163745i	0.996643	+	0.0818727i	$0.0260901\pi$
$797$			4.62272i			0.163745i	−0.996643	+	0.0818727i	$0.973910\pi$
$798$		0			0
$799$	−1.05763			−0.0374162
$800$	−4.57408	−	2.01936i	−0.161718	−	0.0713951i
$801$	11.9490	−	6.46685i	0.422199	−	0.228495i
$802$			31.5489i			1.11403i
$803$			37.0424i			1.30720i
$804$	4.84429	+	19.1287i	0.170845	+	0.674618i
$805$		0			0
$806$			23.8683i			0.840725i
$807$	−25.7942	+	6.53228i	−0.907998	+	0.229947i
$808$	−3.43427			−0.120817
$809$			45.5896i			1.60284i	0.598099	+	0.801422i	$0.295923\pi$
$809$			45.5896i			1.60284i	−0.598099	+	0.801422i	$0.704077\pi$
$810$	14.2465	−	14.2140i	0.500571	−	0.499428i
$811$		−	16.6790i		−	0.585678i	−0.956162	−	0.292839i	$-0.905400\pi$
$811$		−	16.6790i		−	0.585678i	0.956162	−	0.292839i	$-0.0945999\pi$
$812$		0			0
$813$	−6.94181	−	27.4113i	−0.243460	−	0.961355i
$814$	18.4381			0.646255
$815$	5.36983	−	25.4592i	0.188097	−	0.891795i
$816$	0.185952	+	0.734273i	0.00650963	+	0.0257047i
$817$	−51.4064			−1.79848
$818$			18.1161i			0.633414i
$819$		0			0
$820$	2.94083	+	0.620279i	0.102698	+	0.0216611i
$821$			1.62606i			0.0567500i	0.999597	+	0.0283750i	$0.00903326\pi$
$821$			1.62606i			0.0567500i	−0.999597	+	0.0283750i	$0.990967\pi$
$822$	37.3539	−	9.45976i	1.30287	−	0.329947i
$823$		−	51.2865i		−	1.78773i	−0.448332	−	0.893867i	$-0.647982\pi$
$823$		−	51.2865i		−	1.78773i	0.448332	−	0.893867i	$-0.352018\pi$
$824$	−19.8394			−0.691138
$825$	5.90696	−	34.8898i	0.205654	−	1.21471i
$826$		0			0
$827$	26.5999			0.924970			0.462485	−	0.886627i	$-0.346958\pi$
$827$	26.5999			0.924970			0.462485	+	0.886627i	$0.346958\pi$
$828$	−19.5172	+	10.5628i	−0.678269	+	0.367081i
$829$		−	4.25349i		−	0.147730i	−0.997268	−	0.0738650i	$-0.976467\pi$
$829$		−	4.25349i		−	0.147730i	0.997268	−	0.0738650i	$-0.0235334\pi$
$830$	−7.90609	+	37.4839i	−0.274424	+	1.30109i
$831$	1.50436	+	5.94028i	0.0521855	+	0.206066i
$832$	−3.50053			−0.121359
$833$		0			0
$834$	1.66591	+	6.57820i	0.0576856	+	0.227784i
$835$	−1.72235	+	8.16591i	−0.0596044	+	0.282593i
$836$	31.4508			1.08775
$837$	−23.9969	−	26.0658i	−0.829455	−	0.900966i
$838$	−35.2889			−1.21903
$839$	−2.13097			−0.0735691			−0.0367846	−	0.999323i	$-0.511712\pi$
$839$	−2.13097			−0.0735691			−0.0367846	+	0.999323i	$0.511712\pi$
$840$		0			0
$841$	4.47522			0.154318
$842$	8.88314			0.306133
$843$	5.15763	+	20.3660i	0.177638	+	0.701444i
$844$	−7.19053			−0.247508
$845$	1.63287	+	0.344405i	0.0561726	+	0.0118479i
$846$	3.45332	+	6.38083i	0.118728	+	0.219377i
$847$		0			0
$848$	−0.424805			−0.0145879
$849$	0.116831	−	0.0295871i	0.00400963	−	0.00101543i
$850$	−0.883098	+	2.00032i	−0.0302900	+	0.0686103i
$851$		−	33.3803i		−	1.14426i
$852$	5.15538	+	20.3572i	0.176621	+	0.697425i
$853$	−13.2208			−0.452671			−0.226335	−	0.974049i	$-0.572675\pi$
$853$	−13.2208			−0.452671			−0.226335	+	0.974049i	$0.572675\pi$
$854$		0			0
$855$	14.6753	+	49.5044i	0.501883	+	1.69301i
$856$	−10.4903			−0.358551
$857$			14.2759i			0.487656i	0.969818	+	0.243828i	$0.0784033\pi$
$857$			14.2759i			0.487656i	−0.969818	+	0.243828i	$0.921597\pi$
$858$	−6.08196	−	24.0160i	−0.207635	−	0.819891i
$859$		−	31.1327i		−	1.06223i	−0.847299	−	0.531116i	$-0.821773\pi$
$859$		−	31.1327i		−	1.06223i	0.847299	−	0.531116i	$-0.178227\pi$
$860$	−3.08205	+	14.6125i	−0.105097	+	0.498281i
$861$		0			0
$862$		−	22.5439i		−	0.767847i
$863$	−18.5152			−0.630264			−0.315132	−	0.949048i	$-0.602049\pi$
$863$	−18.5152			−0.630264			−0.315132	+	0.949048i	$0.602049\pi$
$864$	3.82281	−	3.51939i	0.130055	−	0.119732i
$865$	−6.59965	+	31.2899i	−0.224395	+	1.06389i
$866$	−25.2191			−0.856978
$867$	−28.2227	+	7.14729i	−0.958492	+	0.242735i
$868$		0			0
$869$			13.7937i			0.467921i
$870$	−0.770047	−	19.1645i	−0.0261070	−	0.649738i
$871$			39.8802i			1.35129i
$872$	−12.3912			−0.419617
$873$	20.9366	−	11.3310i	0.708598	−	0.383495i
$874$		−	56.9385i		−	1.92597i
$875$		0			0
$876$	−15.2215	+	3.85479i	−0.514287	+	0.130241i
$877$		−	30.9055i		−	1.04361i	−0.853066	−	0.521803i	$-0.825260\pi$
$877$		−	30.9055i		−	1.04361i	0.853066	−	0.521803i	$-0.174740\pi$
$878$			12.7318i			0.429676i
$879$	−0.423736	−	1.67322i	−0.0142923	−	0.0564362i
$880$	1.88562	−	8.94000i	0.0635642	−	0.301367i
$881$	−32.7331			−1.10281			−0.551403	−	0.834239i	$-0.685907\pi$
$881$	−32.7331			−1.10281			−0.551403	+	0.834239i	$0.685907\pi$
$882$		0			0
$883$			13.2788i			0.446867i	0.974719	+	0.223434i	$0.0717266\pi$
$883$			13.2788i			0.446867i	−0.974719	+	0.223434i	$0.928273\pi$
$884$			1.53084i			0.0514876i
$885$	−10.6522	+	0.428015i	−0.358070	+	0.0143876i
$886$	0.860072			0.0288947
$887$		−	0.0364112i		−	0.00122257i	−1.00000		0.000611285i	$-0.999805\pi$
$887$		−	0.0364112i		−	0.00122257i	1.00000		0.000611285i	$-0.000194578\pi$
$888$	1.91875	+	7.57660i	0.0643890	+	0.254254i
$889$		0			0
$890$	9.90896	+	2.08999i	0.332149	+	0.0700567i
$891$	30.7873	+	20.1123i	1.03141	+	0.673788i
$892$	−0.621483			−0.0208088
$893$	−18.6151			−0.622931
$894$	−8.59784	−	33.9505i	−0.287555	−	1.13547i
$895$	−6.46668	+	30.6595i	−0.216157	+	1.02483i
$896$		0			0
$897$	−43.4785	+	11.0108i	−1.45170	+	0.367639i
$898$		−	34.0935i		−	1.13772i
$899$	−33.7669			−1.12619
$900$	14.9516	−	1.20348i	0.498388	−	0.0401161i
$901$			0.185774i			0.00618902i
$902$			5.49213i			0.182868i
$903$		0			0
$904$	−11.9346			−0.396940
$905$	6.42168	−	30.4461i	0.213464	−	1.01206i
$906$	−18.7255	+	4.74217i	−0.622114	+	0.157548i
$907$			36.4242i			1.20945i	0.796436	+	0.604723i	$0.206716\pi$
$907$			36.4242i			1.20945i	−0.796436	+	0.604723i	$0.793284\pi$
$908$		−	12.9728i		−	0.430517i
$909$	9.06094	−	4.90380i	0.300532	−	0.162649i
$910$		0			0
$911$		−	37.1072i		−	1.22942i	−0.788754	−	0.614709i	$-0.789274\pi$
$911$		−	37.1072i		−	1.22942i	0.788754	−	0.614709i	$-0.210726\pi$
$912$	3.27291	+	12.9238i	0.108377	+	0.427949i
$913$	−70.0028			−2.31676
$914$			33.0657i			1.09372i
$915$	−0.894654	−	22.2657i	−0.0295764	−	0.736080i
$916$			21.2637i			0.702572i
$917$		0			0
$918$	−1.53908	−	1.67178i	−0.0507974	−	0.0551768i
$919$	−11.9193			−0.393181			−0.196591	−	0.980486i	$-0.562987\pi$
$919$	−11.9193			−0.393181			−0.196591	+	0.980486i	$0.562987\pi$
$920$	−16.1850	−	3.41373i	−0.533603	−	0.112547i
$921$	40.9653	−	10.3743i	1.34985	−	0.341846i
$922$	−4.43329			−0.146003
$923$			42.4413i			1.39697i
$924$		0			0
$925$	−9.11225	+	20.6403i	−0.299609	+	0.678648i
$926$			2.89220i			0.0950436i
$927$	52.3440	−	28.3287i	1.71920	−	0.930437i
$928$		−	4.95225i		−	0.162566i
$929$	−29.2936			−0.961091			−0.480545	−	0.876970i	$-0.659561\pi$
$929$	−29.2936			−0.961091			−0.480545	+	0.876970i	$0.659561\pi$
$930$	−1.06024	−	26.3866i	−0.0347665	−	0.865251i
$931$		0			0
$932$	11.0664			0.362493
$933$	−37.3186	+	9.45079i	−1.22175	+	0.309405i
$934$			4.84781i			0.158625i
$935$	−3.90960	−	0.824611i	−0.127858	−	0.0269677i
$936$	9.23575	−	4.99841i	0.301880	−	0.163378i
$937$	54.0160			1.76462			0.882312	−	0.470665i	$-0.155986\pi$
$937$	54.0160			1.76462			0.882312	+	0.470665i	$0.155986\pi$
$938$		0			0
$939$	−45.6080	+	11.5501i	−1.48836	+	0.376922i
$940$	−1.11606	+	5.29141i	−0.0364019	+	0.172587i
$941$	−19.7003			−0.642212			−0.321106	−	0.947043i	$-0.604055\pi$
$941$	−19.7003			−0.642212			−0.321106	+	0.947043i	$0.604055\pi$
$942$	−23.2950	+	5.89939i	−0.758993	+	0.192212i
$943$	9.94295			0.323787
$944$	−2.75261			−0.0895897
$945$		0			0
$946$	−27.2894			−0.887255
$947$	−7.15728			−0.232580			−0.116290	−	0.993215i	$-0.537100\pi$
$947$	−7.15728			−0.232580			−0.116290	+	0.993215i	$0.537100\pi$
$948$	−5.66814	+	1.43544i	−0.184093	+	0.0466208i
$949$	−31.7342			−1.03014
$950$	−15.5432	+	35.2072i	−0.504289	+	1.14227i
$951$	42.9068	−	10.8660i	1.39135	−	0.352354i
$952$		0			0
$953$	−22.5391			−0.730112			−0.365056	−	0.930986i	$-0.618950\pi$
$953$	−22.5391			−0.730112			−0.365056	+	0.930986i	$0.618950\pi$
$954$	1.12080	−	0.606580i	0.0362872	−	0.0196387i
$955$	4.97142	−	23.5703i	0.160872	−	0.762715i
$956$			0.281518i			0.00910495i
$957$	33.9757	−	8.60424i	1.09828	−	0.278136i
$958$	−29.7191			−0.960181
$959$		0			0
$960$	3.86986	−	0.155494i	0.124899	−	0.00501856i
$961$	−15.4918			−0.499735
$962$			15.7959i			0.509281i
$963$	27.6775	−	14.9791i	0.891895	−	0.482696i
$964$		−	14.7273i		−	0.474334i
$965$	−4.05081	+	19.2055i	−0.130400	+	0.618247i
$966$		0			0
$967$			21.5186i			0.691991i	0.938236	+	0.345995i	$0.112459\pi$
$967$			21.5186i			0.691991i	−0.938236	+	0.345995i	$0.887541\pi$
$968$	5.69583			0.183071
$969$	5.65178	−	1.43129i	0.181561	−	0.0459798i
$970$	17.3621	+	3.66200i	0.557463	+	0.117580i
$971$	35.0098			1.12352			0.561759	−	0.827301i	$-0.310125\pi$
$971$	35.0098			1.12352			0.561759	+	0.827301i	$0.310125\pi$
$972$	−5.06072	+	14.7441i	−0.162323	+	0.472918i
$973$		0			0
$974$		−	28.1729i		−	0.902718i
$975$	29.8901	+	5.06050i	0.957249	+	0.162066i
$976$		−	5.75361i		−	0.184169i
$977$	40.3000			1.28931			0.644656	−	0.764472i	$-0.277000\pi$
$977$	40.3000			1.28931			0.644656	+	0.764472i	$0.277000\pi$
$978$	4.94785	+	19.5377i	0.158215	+	0.624746i
$979$			18.5054i			0.591435i
$980$		0			0
$981$	32.6927	−	17.6934i	1.04380	−	0.564906i
$982$		−	28.4984i		−	0.909421i
$983$			12.5700i			0.400920i	0.979702	+	0.200460i	$0.0642437\pi$
$983$			12.5700i			0.400920i	−0.979702	+	0.200460i	$0.935756\pi$
$984$	−2.25683	+	0.571535i	−0.0719452	+	0.0182199i
$985$	−27.9212	−	5.88913i	−0.889645	−	0.187643i
$986$	−2.16570			−0.0689698
$987$		0			0
$988$			26.9439i			0.857200i
$989$			49.4047i			1.57098i
$990$	7.79045	+	26.2797i	0.247597	+	0.835223i
$991$	9.52668			0.302625			0.151313	−	0.988486i	$-0.451650\pi$
$991$	9.52668			0.302625			0.151313	+	0.988486i	$0.451650\pi$
$992$		−	6.81849i		−	0.216487i
$993$	19.8899	−	5.03705i	0.631187	−	0.159846i
$994$		0			0
$995$	−1.92961	+	9.14859i	−0.0611729	+	0.290030i
$996$	−7.28480	−	28.7657i	−0.230828	−	0.911475i
$997$	26.4363			0.837245			0.418622	−	0.908160i	$-0.362513\pi$
$997$	26.4363			0.837245			0.418622	+	0.908160i	$0.362513\pi$
$998$	2.44955			0.0775393
$999$	−15.8811	−	17.2502i	−0.502454	−	0.545773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.d.g.1469.4	yes	24
3.2	odd	2		1470.2.d.h.1469.3	yes	24
5.4	even	2		1470.2.d.h.1469.21	yes	24
7.6	odd	2	inner	1470.2.d.g.1469.21	yes	24
15.14	odd	2	inner	1470.2.d.g.1469.22	yes	24
21.20	even	2		1470.2.d.h.1469.22	yes	24
35.34	odd	2		1470.2.d.h.1469.4	yes	24
105.104	even	2	inner	1470.2.d.g.1469.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.d.g.1469.3	✓	24	105.104	even	2	inner
1470.2.d.g.1469.4	yes	24	1.1	even	1	trivial
1470.2.d.g.1469.21	yes	24	7.6	odd	2	inner
1470.2.d.g.1469.22	yes	24	15.14	odd	2	inner
1470.2.d.h.1469.3	yes	24	3.2	odd	2
1470.2.d.h.1469.4	yes	24	35.34	odd	2
1470.2.d.h.1469.21	yes	24	5.4	even	2
1470.2.d.h.1469.22	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.67905 + 0.425213i) q^{3} +1.00000 q^{4} +(-2.18793 - 0.461477i) q^{5} +(1.67905 - 0.425213i) q^{6} -1.00000 q^{8} +(2.63839 - 1.42790i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.67905 + 0.425213i) q^{3} +1.00000 q^{4} +(-2.18793 - 0.461477i) q^{5} +(1.67905 - 0.425213i) q^{6} -1.00000 q^{8} +(2.63839 - 1.42790i) q^{9} +(2.18793 + 0.461477i) q^{10} +4.08605i q^{11} +(-1.67905 + 0.425213i) q^{12} -3.50053 q^{13} +(3.86986 - 0.155494i) q^{15} +1.00000 q^{16} -0.437316i q^{17} +(-2.63839 + 1.42790i) q^{18} -7.69711i q^{19} +(-2.18793 - 0.461477i) q^{20} -4.08605i q^{22} -7.39739 q^{23} +(1.67905 - 0.425213i) q^{24} +(4.57408 + 2.01936i) q^{25} +3.50053 q^{26} +(-3.82281 + 3.51939i) q^{27} +4.95225i q^{29} +(-3.86986 + 0.155494i) q^{30} +6.81849i q^{31} -1.00000 q^{32} +(-1.73744 - 6.86067i) q^{33} +0.437316i q^{34} +(2.63839 - 1.42790i) q^{36} +4.51245i q^{37} +7.69711i q^{38} +(5.87754 - 1.48847i) q^{39} +(2.18793 + 0.461477i) q^{40} -1.34412 q^{41} -6.67867i q^{43} +4.08605i q^{44} +(-6.43155 + 1.90660i) q^{45} +7.39739 q^{46} -2.41846i q^{47} +(-1.67905 + 0.425213i) q^{48} +(-4.57408 - 2.01936i) q^{50} +(0.185952 + 0.734273i) q^{51} -3.50053 q^{52} -0.424805 q^{53} +(3.82281 - 3.51939i) q^{54} +(1.88562 - 8.94000i) q^{55} +(3.27291 + 12.9238i) q^{57} -4.95225i q^{58} -2.75261 q^{59} +(3.86986 - 0.155494i) q^{60} -5.75361i q^{61} -6.81849i q^{62} +1.00000 q^{64} +(7.65891 + 1.61541i) q^{65} +(1.73744 + 6.86067i) q^{66} -11.3926i q^{67} -0.437316i q^{68} +(12.4206 - 3.14546i) q^{69} -12.1243i q^{71} +(-2.63839 + 1.42790i) q^{72} +9.06556 q^{73} -4.51245i q^{74} +(-8.53874 - 1.44564i) q^{75} -7.69711i q^{76} +(-5.87754 + 1.48847i) q^{78} +3.37581 q^{79} +(-2.18793 - 0.461477i) q^{80} +(4.92219 - 7.53472i) q^{81} +1.34412 q^{82} +17.1321i q^{83} +(-0.201811 + 0.956816i) q^{85} +6.67867i q^{86} +(-2.10576 - 8.31505i) q^{87} -4.08605i q^{88} +4.52892 q^{89} +(6.43155 - 1.90660i) q^{90} -7.39739 q^{92} +(-2.89931 - 11.4486i) q^{93} +2.41846i q^{94} +(-3.55204 + 16.8407i) q^{95} +(1.67905 - 0.425213i) q^{96} +7.93539 q^{97} +(5.83448 + 10.7806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) 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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