LMFDB - Embedded newform 1050.2.bc.h.943.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, degree $4$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			943.4
Root			$2.69978 + 0.355433i$ of defining polynomial
Character	$\chi$	$=$	1050.943
Dual form			1050.2.bc.h.157.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(2.47207 - 0.942805i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(2.47207 - 0.942805i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.55390 + 2.69144i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(3.40812 - 3.40812i) q^{13} +(1.55050 + 2.14382i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.37891 - 5.14616i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(3.61673 - 6.26436i) q^{19} +(2.63185 - 0.270861i) q^{21} +(-2.19755 + 2.19755i) q^{22} +(-5.08638 + 1.36289i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.17408 + 2.40991i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.66947 + 2.05253i) q^{28} +4.49359i q^{29} +(-7.98911 + 4.61252i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.804359 + 3.00191i) q^{33} +5.32769 q^{34} -1.00000 q^{36} +(0.929997 + 3.47079i) q^{37} +(6.98699 + 1.87216i) q^{38} +(4.17408 - 2.40991i) q^{39} +2.51851i q^{41} +(0.942805 + 2.47207i) q^{42} +(3.86848 + 3.86848i) q^{43} +(-2.69144 - 1.55390i) q^{44} +(-2.63291 - 4.56033i) q^{46} +(3.94526 - 1.05713i) q^{47} +(0.707107 - 0.707107i) q^{48} +(5.22224 - 4.66135i) q^{49} +(2.66385 - 4.61392i) q^{51} +(-1.24746 + 4.65558i) q^{52} +(-0.890187 + 3.32222i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.41468 - 1.08135i) q^{56} +(5.11483 - 5.11483i) q^{57} +(-4.34047 + 1.16303i) q^{58} +(-0.666188 - 1.15387i) q^{59} +(10.8719 + 6.27689i) q^{61} +(-6.52308 - 6.52308i) q^{62} +(2.61228 + 0.419541i) q^{63} +1.00000i q^{64} +(-2.69144 + 1.55390i) q^{66} +(-6.43584 - 1.72448i) q^{67} +(1.37891 + 5.14616i) q^{68} -5.26581 q^{69} +9.22738 q^{71} +(-0.258819 - 0.965926i) q^{72} +(-7.95163 - 2.13063i) q^{73} +(-3.11183 + 1.79662i) q^{74} +7.23346i q^{76} +(6.37885 + 5.18839i) q^{77} +(3.40812 + 3.40812i) q^{78} +(-1.65789 - 0.957181i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-2.43270 + 0.651839i) q^{82} +(-8.97250 + 8.97250i) q^{83} +(-2.14382 + 1.55050i) q^{84} +(-2.73543 + 4.73790i) q^{86} +(-1.16303 + 4.34047i) q^{87} +(0.804359 - 3.00191i) q^{88} +(-2.03677 + 3.52779i) q^{89} +(5.21191 - 11.6383i) q^{91} +(3.72349 - 3.72349i) q^{92} +(-8.91070 + 2.38761i) q^{93} +(2.04222 + 3.53723i) q^{94} +(0.866025 + 0.500000i) q^{96} +(-2.69423 - 2.69423i) q^{97} +(5.85414 + 3.83785i) q^{98} +3.10780i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{21} - 4 q^{22} - 32 q^{23} - 8 q^{24} - 12 q^{26} + 8 q^{28} - 24 q^{31} - 8 q^{33} + 16 q^{34} - 16 q^{36} + 8 q^{37} + 28 q^{38} - 12 q^{39} + 4 q^{42} + 24 q^{43} - 4 q^{46} + 24 q^{47} + 52 q^{49} + 8 q^{51} + 8 q^{52} - 44 q^{53} - 8 q^{54} + 8 q^{56} + 8 q^{57} - 48 q^{58} + 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} - 36 q^{67} + 12 q^{68} - 8 q^{69} - 32 q^{71} + 40 q^{73} - 24 q^{74} + 44 q^{77} + 16 q^{78} + 12 q^{79} + 8 q^{81} - 12 q^{82} + 16 q^{83} + 4 q^{84} - 8 q^{86} - 12 q^{87} - 8 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 40 q^{93} + 8 q^{94} - 44 q^{97} + 8 q^{98}+O(q^{100}) $ 16 * q + 8 * q^7 + 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^21 - 4 * q^22 - 32 * q^23 - 8 * q^24 - 12 * q^26 + 8 * q^28 - 24 * q^31 - 8 * q^33 + 16 * q^34 - 16 * q^36 + 8 * q^37 + 28 * q^38 - 12 * q^39 + 4 * q^42 + 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 + 8 * q^51 + 8 * q^52 - 44 * q^53 - 8 * q^54 + 8 * q^56 + 8 * q^57 - 48 * q^58 + 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 - 36 * q^67 + 12 * q^68 - 8 * q^69 - 32 * q^71 + 40 * q^73 - 24 * q^74 + 44 * q^77 + 16 * q^78 + 12 * q^79 + 8 * q^81 - 12 * q^82 + 16 * q^83 + 4 * q^84 - 8 * q^86 - 12 * q^87 - 8 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 40 * q^93 + 8 * q^94 - 44 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	2.47207	−	0.942805i	0.934354	−	0.356347i
$7$	2.47207	−	0.942805i	0.934354	−	0.356347i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	1.55390	+	2.69144i	0.468519	+	0.811499i	0.999353	−	0.0359771i	$-0.0114543\pi$
$11$	1.55390	+	2.69144i	0.468519	+	0.811499i	−0.530833	+	0.847476i	$0.678121\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	3.40812	−	3.40812i	0.945243	−	0.945243i	−0.0533341	−	0.998577i	$-0.516985\pi$
$13$	3.40812	−	3.40812i	0.945243	−	0.945243i	0.998577	+	0.0533341i	$0.0169848\pi$
$14$	1.55050	+	2.14382i	0.414388	+	0.572960i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.37891	−	5.14616i	0.334434	−	1.24813i	−0.570047	−	0.821612i	$-0.693075\pi$
$17$	1.37891	−	5.14616i	0.334434	−	1.24813i	0.904481	−	0.426514i	$-0.140258\pi$
$18$	−0.258819	+	0.965926i	−0.0610042	+	0.227671i
$19$	3.61673	−	6.26436i	0.829735	−	1.43714i	−0.0685112	−	0.997650i	$-0.521825\pi$
$19$	3.61673	−	6.26436i	0.829735	−	1.43714i	0.898246	−	0.439493i	$-0.144842\pi$
$20$		0			0
$21$	2.63185	−	0.270861i	0.574317	−	0.0591067i
$22$	−2.19755	+	2.19755i	−0.468519	+	0.468519i
$23$	−5.08638	+	1.36289i	−1.06058	+	0.284183i	−0.746619	−	0.665252i	$-0.768324\pi$
$23$	−5.08638	+	1.36289i	−1.06058	+	0.284183i	−0.313965	+	0.949435i	$0.601657\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	4.17408	+	2.40991i	0.818604	+	0.472621i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−1.66947	+	2.05253i	−0.315500	+	0.387891i
$29$			4.49359i			0.834438i	0.908806	+	0.417219i	$0.136995\pi$
$29$			4.49359i			0.834438i	−0.908806	+	0.417219i	$0.863005\pi$
$30$		0			0
$31$	−7.98911	+	4.61252i	−1.43489	+	0.828432i	−0.997488	−	0.0708354i	$-0.977433\pi$
$31$	−7.98911	+	4.61252i	−1.43489	+	0.828432i	−0.437399	+	0.899268i	$0.644100\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	0.804359	+	3.00191i	0.140021	+	0.522565i
$34$	5.32769			0.913692
$35$		0			0
$36$	−1.00000			−0.166667
$37$	0.929997	+	3.47079i	0.152890	+	0.570595i	0.999277	+	0.0380256i	$0.0121068\pi$
$37$	0.929997	+	3.47079i	0.152890	+	0.570595i	−0.846386	+	0.532569i	$0.821227\pi$
$38$	6.98699	+	1.87216i	1.13344	+	0.303704i
$39$	4.17408	−	2.40991i	0.668387	−	0.385894i
$40$		0			0
$41$			2.51851i			0.393326i	0.980471	+	0.196663i	$0.0630104\pi$
$41$			2.51851i			0.393326i	−0.980471	+	0.196663i	$0.936990\pi$
$42$	0.942805	+	2.47207i	0.145478	+	0.381448i
$43$	3.86848	+	3.86848i	0.589938	+	0.589938i	0.937615	−	0.347677i	$-0.113029\pi$
$43$	3.86848	+	3.86848i	0.589938	+	0.589938i	−0.347677	+	0.937615i	$0.613029\pi$
$44$	−2.69144	−	1.55390i	−0.405750	−	0.234260i
$45$		0			0
$46$	−2.63291	−	4.56033i	−0.388201	−	0.672383i
$47$	3.94526	−	1.05713i	0.575476	−	0.154198i	0.0406690	−	0.999173i	$-0.487051\pi$
$47$	3.94526	−	1.05713i	0.575476	−	0.154198i	0.534807	+	0.844974i	$0.320384\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	5.22224	−	4.66135i	0.746034	−	0.665908i
$50$		0			0
$51$	2.66385	−	4.61392i	0.373013	−	0.646078i
$52$	−1.24746	+	4.65558i	−0.172991	+	0.645613i
$53$	−0.890187	+	3.32222i	−0.122277	+	0.456342i	−0.999728	−	0.0233232i	$-0.992575\pi$
$53$	−0.890187	+	3.32222i	−0.122277	+	0.456342i	0.877451	+	0.479665i	$0.159242\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	−2.41468	−	1.08135i	−0.322675	−	0.144502i
$57$	5.11483	−	5.11483i	0.677476	−	0.677476i
$58$	−4.34047	+	1.16303i	−0.569932	+	0.152713i
$59$	−0.666188	−	1.15387i	−0.0867303	−	0.150221i	0.819397	−	0.573227i	$-0.194309\pi$
$59$	−0.666188	−	1.15387i	−0.0867303	−	0.150221i	−0.906127	+	0.423005i	$0.860975\pi$
$60$		0			0
$61$	10.8719	+	6.27689i	1.39200	+	0.803673i	0.993537	−	0.113510i	$-0.0362095\pi$
$61$	10.8719	+	6.27689i	1.39200	+	0.803673i	0.398466	+	0.917183i	$0.369543\pi$
$62$	−6.52308	−	6.52308i	−0.828432	−	0.828432i
$63$	2.61228	+	0.419541i	0.329116	+	0.0528572i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−2.69144	+	1.55390i	−0.331293	+	0.191272i
$67$	−6.43584	−	1.72448i	−0.786263	−	0.210679i	−0.156719	−	0.987643i	$-0.550092\pi$
$67$	−6.43584	−	1.72448i	−0.786263	−	0.210679i	−0.629544	+	0.776965i	$0.716758\pi$
$68$	1.37891	+	5.14616i	0.167217	+	0.624063i
$69$	−5.26581			−0.633929
$70$		0			0
$71$	9.22738			1.09509			0.547544	−	0.836777i	$-0.315563\pi$
$71$	9.22738			1.09509			0.547544	+	0.836777i	$0.315563\pi$
$72$	−0.258819	−	0.965926i	−0.0305021	−	0.113835i
$73$	−7.95163	−	2.13063i	−0.930667	−	0.249372i	−0.238528	−	0.971136i	$-0.576665\pi$
$73$	−7.95163	−	2.13063i	−0.930667	−	0.249372i	−0.692139	+	0.721764i	$0.743332\pi$
$74$	−3.11183	+	1.79662i	−0.361743	+	0.208852i
$75$		0			0
$76$			7.23346i			0.829735i
$77$	6.37885	+	5.18839i	0.726938	+	0.591272i
$78$	3.40812	+	3.40812i	0.385894	+	0.385894i
$79$	−1.65789	−	0.957181i	−0.186527	−	0.107691i	0.403829	−	0.914835i	$-0.367679\pi$
$79$	−1.65789	−	0.957181i	−0.186527	−	0.107691i	−0.590356	+	0.807143i	$0.701012\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−2.43270	+	0.651839i	−0.268646	+	0.0719836i
$83$	−8.97250	+	8.97250i	−0.984860	+	0.984860i	−0.999887	−	0.0150269i	$-0.995217\pi$
$83$	−8.97250	+	8.97250i	−0.984860	+	0.984860i	0.0150269	+	0.999887i	$0.495217\pi$
$84$	−2.14382	+	1.55050i	−0.233910	+	0.169173i
$85$		0			0
$86$	−2.73543	+	4.73790i	−0.294969	+	0.510901i
$87$	−1.16303	+	4.34047i	−0.124689	+	0.465347i
$88$	0.804359	−	3.00191i	0.0857450	−	0.320005i
$89$	−2.03677	+	3.52779i	−0.215897	+	0.373945i	−0.953550	−	0.301236i	$-0.902601\pi$
$89$	−2.03677	+	3.52779i	−0.215897	+	0.373945i	0.737653	+	0.675181i	$0.235934\pi$
$90$		0			0
$91$	5.21191	−	11.6383i	0.546357	−	1.22003i
$92$	3.72349	−	3.72349i	0.388201	−	0.388201i
$93$	−8.91070	+	2.38761i	−0.923996	+	0.247584i
$94$	2.04222	+	3.53723i	0.210639	+	0.364837i
$95$		0			0
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−2.69423	−	2.69423i	−0.273558	−	0.273558i	0.556973	−	0.830531i	$-0.311963\pi$
$97$	−2.69423	−	2.69423i	−0.273558	−	0.273558i	−0.830531	+	0.556973i	$0.811963\pi$
$98$	5.85414	+	3.83785i	0.591357	+	0.387681i
$99$			3.10780i			0.312346i
$100$		0			0
$101$	−6.80907	+	3.93122i	−0.677528	+	0.391171i	−0.798923	−	0.601433i	$-0.794597\pi$
$101$	−6.80907	+	3.93122i	−0.677528	+	0.391171i	0.121395	+	0.992604i	$0.461263\pi$
$102$	5.14616	+	1.37891i	0.509545	+	0.136532i
$103$	−3.06212	−	11.4280i	−0.301720	−	1.12603i	−0.935732	−	0.352710i	$-0.885260\pi$
$103$	−3.06212	−	11.4280i	−0.301720	−	1.12603i	0.634013	−	0.773322i	$-0.281407\pi$
$104$	−4.81981			−0.472621
$105$		0			0
$106$	−3.43942			−0.334066
$107$	0.559635	+	2.08859i	0.0541020	+	0.201911i	0.987687	−	0.156446i	$-0.0500037\pi$
$107$	0.559635	+	2.08859i	0.0541020	+	0.201911i	−0.933585	+	0.358357i	$0.883337\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	−0.489782	+	0.282776i	−0.0469126	+	0.0270850i	−0.523273	−	0.852165i	$-0.675289\pi$
$109$	−0.489782	+	0.282776i	−0.0469126	+	0.0270850i	0.476360	+	0.879250i	$0.341956\pi$
$110$		0			0
$111$			3.59323i			0.341054i
$112$	0.419541	−	2.61228i	0.0396429	−	0.246837i
$113$	−9.98231	−	9.98231i	−0.939057	−	0.939057i	0.0591899	−	0.998247i	$-0.481148\pi$
$113$	−9.98231	−	9.98231i	−0.939057	−	0.939057i	−0.998247	+	0.0591899i	$0.981148\pi$
$114$	6.26436	+	3.61673i	0.586711	+	0.338738i
$115$		0			0
$116$	−2.24679	−	3.89156i	−0.208610	−	0.361322i
$117$	4.65558	−	1.24746i	0.430408	−	0.115328i
$118$	0.942132	−	0.942132i	0.0867303	−	0.0867303i
$119$	−1.44306	−	14.0217i	−0.132285	−	1.28537i
$120$		0			0
$121$	0.670774	−	1.16181i	0.0609795	−	0.105620i
$122$	−3.24916	+	12.1260i	−0.294165	+	1.09784i
$123$	−0.651839	+	2.43270i	−0.0587744	+	0.219349i
$124$	4.61252	−	7.98911i	0.414216	−	0.717443i
$125$		0			0
$126$	0.270861	+	2.63185i	0.0241302	+	0.234464i
$127$	2.14534	−	2.14534i	0.190368	−	0.190368i	−0.605487	−	0.795855i	$-0.707022\pi$
$127$	2.14534	−	2.14534i	0.190368	−	0.190368i	0.795855	+	0.605487i	$0.207022\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	2.73543	+	4.73790i	0.240841	+	0.417149i
$130$		0			0
$131$	7.59798	+	4.38669i	0.663838	+	0.383267i	0.793738	−	0.608260i	$-0.208132\pi$
$131$	7.59798	+	4.38669i	0.663838	+	0.383267i	−0.129900	+	0.991527i	$0.541466\pi$
$132$	−2.19755	−	2.19755i	−0.191272	−	0.191272i
$133$	3.03474	−	18.8958i	0.263145	−	1.63847i
$134$		−	6.66287i		−	0.575584i
$135$		0			0
$136$	−4.61392	+	2.66385i	−0.395640	+	0.228423i
$137$	−13.1416	−	3.52127i	−1.12276	−	0.300843i	−0.350760	−	0.936465i	$-0.614077\pi$
$137$	−13.1416	−	3.52127i	−1.12276	−	0.300843i	−0.772000	+	0.635622i	$0.780744\pi$
$138$	−1.36289	−	5.08638i	−0.116017	−	0.432982i
$139$	−10.9145			−0.925753			−0.462876	−	0.886423i	$-0.653183\pi$
$139$	−10.9145			−0.925753			−0.462876	+	0.886423i	$0.653183\pi$
$140$		0			0
$141$	4.08444			0.343972
$142$	2.38822	+	8.91296i	0.200415	+	0.747959i
$143$	14.4686	+	3.87686i	1.20993	+	0.324199i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$		0			0
$146$		−	8.23213i		−	0.681296i
$147$	6.25074	−	3.15091i	0.515553	−	0.259882i
$148$	−2.54080	−	2.54080i	−0.208852	−	0.208852i
$149$	−1.81017	−	1.04510i	−0.148295	−	0.0856183i	0.424016	−	0.905655i	$-0.360620\pi$
$149$	−1.81017	−	1.04510i	−0.148295	−	0.0856183i	−0.572312	+	0.820036i	$0.693953\pi$
$150$		0			0
$151$	−2.02118	−	3.50079i	−0.164481	−	0.284890i	0.771990	−	0.635635i	$-0.219262\pi$
$151$	−2.02118	−	3.50079i	−0.164481	−	0.284890i	−0.936471	+	0.350745i	$0.885928\pi$
$152$	−6.98699	+	1.87216i	−0.566720	+	0.151852i
$153$	3.76725	−	3.76725i	0.304564	−	0.304564i
$154$	−3.36063	+	7.50435i	−0.270807	+	0.604718i
$155$		0			0
$156$	−2.40991	+	4.17408i	−0.192947	+	0.334194i
$157$	−0.234379	+	0.874716i	−0.0187055	+	0.0698099i	−0.974648	−	0.223745i	$-0.928172\pi$
$157$	−0.234379	+	0.874716i	−0.0187055	+	0.0698099i	0.955942	+	0.293555i	$0.0948384\pi$
$158$	0.495474	−	1.84913i	0.0394178	−	0.147109i
$159$	−1.71971	+	2.97862i	−0.136382	+	0.236220i
$160$		0			0
$161$	−11.2889	+	8.16463i	−0.889693	+	0.643463i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−7.13062	+	1.91065i	−0.558514	+	0.149653i	−0.527023	−	0.849851i	$-0.676692\pi$
$163$	−7.13062	+	1.91065i	−0.558514	+	0.149653i	−0.0314902	+	0.999504i	$0.510025\pi$
$164$	−1.25926	−	2.18110i	−0.0983314	−	0.170315i
$165$		0			0
$166$	−10.9890	−	6.34452i	−0.852914	−	0.492430i
$167$	0.610646	+	0.610646i	0.0472532	+	0.0472532i	0.730339	−	0.683085i	$-0.239362\pi$
$167$	0.610646	+	0.610646i	0.0472532	+	0.0472532i	−0.683085	+	0.730339i	$0.739362\pi$
$168$	−2.05253	−	1.66947i	−0.158356	−	0.128803i
$169$		−	10.2306i		−	0.786967i
$170$		0			0
$171$	6.26436	−	3.61673i	0.479048	−	0.276578i
$172$	−5.28444	−	1.41596i	−0.402935	−	0.107966i
$173$	0.905215	+	3.37831i	0.0688222	+	0.256848i	0.991762	−	0.128097i	$-0.0408870\pi$
$173$	0.905215	+	3.37831i	0.0688222	+	0.256848i	−0.922939	+	0.384945i	$0.874220\pi$
$174$	−4.49359			−0.340658
$175$		0			0
$176$	3.10780			0.234260
$177$	−0.344844	−	1.28698i	−0.0259201	−	0.0967351i
$178$	−3.93474	−	1.05431i	−0.294921	−	0.0790239i
$179$	−15.6420	+	9.03091i	−1.16914	+	0.675002i	−0.953477	−	0.301467i	$-0.902524\pi$
$179$	−15.6420	+	9.03091i	−1.16914	+	0.675002i	−0.215661	+	0.976468i	$0.569190\pi$
$180$		0			0
$181$		−	21.7257i		−	1.61486i	−0.589965	−	0.807429i	$-0.700858\pi$
$181$		−	21.7257i		−	1.61486i	0.589965	−	0.807429i	$-0.299142\pi$
$182$	12.5907	+	2.02211i	0.933283	+	0.149889i
$183$	8.87686	+	8.87686i	0.656196	+	0.656196i
$184$	4.56033	+	2.63291i	0.336192	+	0.194100i
$185$		0			0
$186$	−4.61252	−	7.98911i	−0.338206	−	0.585790i
$187$	15.9932	−	4.28538i	1.16954	−	0.313378i
$188$	−2.88813	+	2.88813i	−0.210639	+	0.210639i
$189$	2.41468	+	1.08135i	0.175642	+	0.0786568i
$190$		0			0
$191$	−8.29123	+	14.3608i	−0.599932	+	1.03911i	0.392898	+	0.919582i	$0.371473\pi$
$191$	−8.29123	+	14.3608i	−0.599932	+	1.03911i	−0.992830	+	0.119531i	$0.961861\pi$
$192$	−0.258819	+	0.965926i	−0.0186787	+	0.0697097i
$193$	0.548044	−	2.04533i	0.0394491	−	0.147226i	−0.943392	−	0.331679i	$-0.892385\pi$
$193$	0.548044	−	2.04533i	0.0394491	−	0.147226i	0.982841	+	0.184453i	$0.0590515\pi$
$194$	1.90511	−	3.29975i	0.136779	−	0.236908i
$195$		0			0
$196$	−2.19191	+	6.64797i	−0.156565	+	0.474855i
$197$	1.22531	−	1.22531i	0.0872995	−	0.0872995i	−0.662108	−	0.749408i	$-0.730338\pi$
$197$	1.22531	−	1.22531i	0.0872995	−	0.0872995i	0.749408	+	0.662108i	$0.230338\pi$
$198$	−3.00191	+	0.804359i	−0.213336	+	0.0571633i
$199$	3.93901	+	6.82256i	0.279229	+	0.483638i	0.971193	−	0.238293i	$-0.0765879\pi$
$199$	3.93901	+	6.82256i	0.279229	+	0.483638i	−0.691964	+	0.721932i	$0.743255\pi$
$200$		0			0
$201$	−5.77022	−	3.33144i	−0.407000	−	0.234981i
$202$	−5.55958	−	5.55958i	−0.391171	−	0.391171i
$203$	4.23657	+	11.1085i	0.297349	+	0.779661i
$204$			5.32769i			0.373013i
$205$		0			0
$206$	10.2461	−	5.91556i	0.713876	−	0.412157i
$207$	−5.08638	−	1.36289i	−0.353528	−	0.0947276i
$208$	−1.24746	−	4.65558i	−0.0864957	−	0.322806i
$209$	22.4802			1.55499
$210$		0			0
$211$	−15.9995			−1.10145			−0.550724	−	0.834687i	$-0.685648\pi$
$211$	−15.9995			−1.10145			−0.550724	+	0.834687i	$0.685648\pi$
$212$	−0.890187	−	3.32222i	−0.0611383	−	0.228171i
$213$	8.91296	+	2.38822i	0.610706	+	0.163638i
$214$	−1.87258	+	1.08113i	−0.128007	+	0.0739047i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−15.4009	+	18.9346i	−1.04548	+	1.28537i
$218$	−0.399905	−	0.399905i	−0.0270850	−	0.0270850i
$219$	−7.12923	−	4.11606i	−0.481749	−	0.278138i
$220$		0			0
$221$	−12.8392	−	22.2382i	−0.863660	−	1.49590i
$222$	−3.47079	+	0.929997i	−0.232944	+	0.0624173i
$223$	1.20707	−	1.20707i	0.0808314	−	0.0808314i	−0.665535	−	0.746367i	$-0.731797\pi$
$223$	1.20707	−	1.20707i	0.0808314	−	0.0808314i	0.746367	+	0.665535i	$0.231797\pi$
$224$	2.63185	−	0.270861i	0.175848	−	0.0180977i
$225$		0			0
$226$	7.05856	−	12.2258i	0.469528	−	0.813247i
$227$	−1.76332	+	6.58082i	−0.117036	+	0.436784i	−0.999431	−	0.0337248i	$-0.989263\pi$
$227$	−1.76332	+	6.58082i	−0.117036	+	0.436784i	0.882395	+	0.470509i	$0.155930\pi$
$228$	−1.87216	+	6.98699i	−0.123987	+	0.462725i
$229$	9.90714	−	17.1597i	0.654682	−	1.13394i	−0.327291	−	0.944924i	$-0.606136\pi$
$229$	9.90714	−	17.1597i	0.654682	−	1.13394i	0.981973	−	0.189019i	$-0.0605309\pi$
$230$		0			0
$231$	4.81864	+	6.66257i	0.317043	+	0.438365i
$232$	3.17745	−	3.17745i	0.208610	−	0.208610i
$233$	17.3842	−	4.65807i	1.13887	−	0.305161i	0.360376	−	0.932807i	$-0.382648\pi$
$233$	17.3842	−	4.65807i	1.13887	−	0.305161i	0.778498	+	0.627647i	$0.215982\pi$
$234$	2.40991	+	4.17408i	0.157540	+	0.272868i
$235$		0			0
$236$	1.15387	+	0.666188i	0.0751107	+	0.0433652i
$237$	−1.35366	−	1.35366i	−0.0879296	−	0.0879296i
$238$	13.1704	−	5.02297i	0.853711	−	0.325591i
$239$			26.6409i			1.72325i	0.507542	+	0.861627i	$0.330554\pi$
$239$			26.6409i			1.72325i	−0.507542	+	0.861627i	$0.669446\pi$
$240$		0			0
$241$	−12.4923	+	7.21241i	−0.804697	+	0.464592i	−0.845111	−	0.534591i	$-0.820466\pi$
$241$	−12.4923	+	7.21241i	−0.804697	+	0.464592i	0.0404137	+	0.999183i	$0.487132\pi$
$242$	1.29584	+	0.347218i	0.0832995	+	0.0223200i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−12.5538			−0.803673
$245$		0			0
$246$	−2.51851			−0.160575
$247$	−9.02344	−	33.6760i	−0.574148	−	2.14275i
$248$	8.91070	+	2.38761i	0.565830	+	0.151614i
$249$	−10.9890	+	6.34452i	−0.696401	+	0.402067i
$250$		0			0
$251$		−	26.4573i		−	1.66997i	−0.550271	−	0.834986i	$-0.685476\pi$
$251$		−	26.4573i		−	1.66997i	0.550271	−	0.834986i	$-0.314524\pi$
$252$	−2.47207	+	0.942805i	−0.155726	+	0.0593911i
$253$	−11.5719	−	11.5719i	−0.727518	−	0.727518i
$254$	2.62750	+	1.51699i	0.164864	+	0.0951842i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.8329	−	2.90266i	0.675736	−	0.181063i	0.0953987	−	0.995439i	$-0.469587\pi$
$257$	10.8329	−	2.90266i	0.675736	−	0.181063i	0.580337	+	0.814376i	$0.302921\pi$
$258$	−3.86848	+	3.86848i	−0.240841	+	0.240841i
$259$	5.57130	+	7.70323i	0.346183	+	0.478656i
$260$		0			0
$261$	−2.24679	+	3.89156i	−0.139073	+	0.240882i
$262$	−2.27072	+	8.47444i	−0.140286	+	0.523553i
$263$	1.77527	−	6.62539i	0.109468	−	0.408539i	−0.889346	−	0.457235i	$-0.848840\pi$
$263$	1.77527	−	6.62539i	0.109468	−	0.408539i	0.998814	+	0.0486959i	$0.0155065\pi$
$264$	1.55390	−	2.69144i	0.0956361	−	0.165647i
$265$		0			0
$266$	19.0374	−	1.95926i	1.16726	−	0.120130i
$267$	−2.88043	+	2.88043i	−0.176279	+	0.176279i
$268$	6.43584	−	1.72448i	0.393131	−	0.105339i
$269$	4.49032	+	7.77746i	0.273780	+	0.474200i	0.969827	−	0.243796i	$-0.0783928\pi$
$269$	4.49032	+	7.77746i	0.273780	+	0.474200i	−0.696047	+	0.717996i	$0.745059\pi$
$270$		0			0
$271$	7.76980	+	4.48590i	0.471982	+	0.272499i	0.717069	−	0.697002i	$-0.245483\pi$
$271$	7.76980	+	4.48590i	0.471982	+	0.272499i	−0.245087	+	0.969501i	$0.578817\pi$
$272$	−3.76725	−	3.76725i	−0.228423	−	0.228423i
$273$	8.04653	−	9.89279i	0.486998	−	0.598739i
$274$		−	13.6052i		−	0.821918i
$275$		0			0
$276$	4.56033	−	2.63291i	0.274499	−	0.158482i
$277$	−23.8691	−	6.39571i	−1.43416	−	0.384281i	−0.543673	−	0.839297i	$-0.682967\pi$
$277$	−23.8691	−	6.39571i	−1.43416	−	0.384281i	−0.890483	+	0.455016i	$0.849633\pi$
$278$	−2.82487	−	10.5426i	−0.169424	−	0.632301i
$279$	−9.22503			−0.552288
$280$		0			0
$281$	18.4916			1.10312			0.551558	−	0.834137i	$-0.314034\pi$
$281$	18.4916			1.10312			0.551558	+	0.834137i	$0.314034\pi$
$282$	1.05713	+	3.94526i	0.0629512	+	0.234937i
$283$	−5.38190	−	1.44208i	−0.319921	−	0.0857226i	0.0952849	−	0.995450i	$-0.469624\pi$
$283$	−5.38190	−	1.44208i	−0.319921	−	0.0857226i	−0.415206	+	0.909727i	$0.636290\pi$
$284$	−7.99114	+	4.61369i	−0.474187	+	0.273772i
$285$		0			0
$286$			14.9790i			0.885729i
$287$	2.37447	+	6.22594i	0.140160	+	0.367505i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	−9.85909	−	5.69215i	−0.579947	−	0.334832i
$290$		0			0
$291$	−1.90511	−	3.29975i	−0.111679	−	0.193434i
$292$	7.95163	−	2.13063i	0.465334	−	0.124686i
$293$	17.6465	−	17.6465i	1.03092	−	1.03092i	0.0314115	−	0.999507i	$-0.490000\pi$
$293$	17.6465	−	17.6465i	1.03092	−	1.03092i	0.999507	−	0.0314115i	$-0.0100002\pi$
$294$	4.66135	+	5.22224i	0.271856	+	0.304567i
$295$		0			0
$296$	1.79662	−	3.11183i	0.104426	−	0.180871i
$297$	−0.804359	+	3.00191i	−0.0466736	+	0.174188i
$298$	0.540986	−	2.01899i	0.0313385	−	0.116957i
$299$	−12.6901	+	21.9799i	−0.733888	+	1.27113i
$300$		0			0
$301$	13.2104	+	5.91593i	0.761433	+	0.340988i
$302$	2.85838	−	2.85838i	0.164481	−	0.164481i
$303$	−7.59453	+	2.03495i	−0.436295	+	0.116905i
$304$	−3.61673	−	6.26436i	−0.207434	−	0.359286i
$305$		0			0
$306$	4.61392	+	2.66385i	0.263760	+	0.152282i
$307$	11.4807	+	11.4807i	0.655239	+	0.655239i	0.954250	−	0.299011i	$-0.0966566\pi$
$307$	11.4807	+	11.4807i	0.655239	+	0.655239i	−0.299011	+	0.954250i	$0.596657\pi$
$308$	−8.11844	−	1.30385i	−0.462591	−	0.0742939i
$309$		−	11.8311i		−	0.673049i
$310$		0			0
$311$	−11.3751	+	6.56743i	−0.645024	+	0.372405i	−0.786547	−	0.617530i	$-0.788133\pi$
$311$	−11.3751	+	6.56743i	−0.645024	+	0.372405i	0.141523	+	0.989935i	$0.454800\pi$
$312$	−4.65558	−	1.24746i	−0.263570	−	0.0706234i
$313$	6.58648	+	24.5811i	0.372290	+	1.38940i	0.857264	+	0.514877i	$0.172162\pi$
$313$	6.58648	+	24.5811i	0.372290	+	1.38940i	−0.484974	+	0.874528i	$0.661171\pi$
$314$	−0.905573			−0.0511044
$315$		0			0
$316$	1.91436			0.107691
$317$	−4.92434	−	18.3779i	−0.276578	−	1.03220i	−0.954776	−	0.297325i	$-0.903906\pi$
$317$	−4.92434	−	18.3779i	−0.276578	−	1.03220i	0.678198	−	0.734879i	$-0.262761\pi$
$318$	−3.32222	−	0.890187i	−0.186301	−	0.0499192i
$319$	−12.0942	+	6.98260i	−0.677146	+	0.390950i
$320$		0			0
$321$			2.16226i			0.120686i
$322$	−10.8082	−	8.79112i	−0.602318	−	0.489910i
$323$	−27.2502	−	27.2502i	−1.51624	−	1.51624i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$		0			0
$326$	−3.69108	−	6.39314i	−0.204430	−	0.354083i
$327$	−0.546281	+	0.146375i	−0.0302094	+	0.00809458i
$328$	1.78086	−	1.78086i	0.0983314	−	0.0983314i
$329$	8.75629	−	6.33291i	0.482750	−	0.349145i
$330$		0			0
$331$	10.4690	−	18.1329i	0.575430	−	0.996674i	−0.420565	−	0.907263i	$-0.638168\pi$
$331$	10.4690	−	18.1329i	0.575430	−	0.996674i	0.995995	−	0.0894115i	$-0.0284986\pi$
$332$	3.28416	−	12.2567i	0.180242	−	0.672672i
$333$	−0.929997	+	3.47079i	−0.0509635	+	0.190198i
$334$	−0.431792	+	0.747886i	−0.0236266	+	0.0409225i
$335$		0			0
$336$	1.08135	−	2.41468i	0.0589926	−	0.131732i
$337$	−0.272770	+	0.272770i	−0.0148587	+	0.0148587i	−0.714497	−	0.699638i	$-0.753344\pi$
$337$	−0.272770	+	0.272770i	−0.0148587	+	0.0148587i	0.699638	+	0.714497i	$0.253344\pi$
$338$	9.88197	−	2.64787i	0.537508	−	0.144025i
$339$	−7.05856	−	12.2258i	−0.383368	−	0.664013i
$340$		0			0
$341$	−24.8286	−	14.3348i	−1.34454	−	0.776273i
$342$	5.11483	+	5.11483i	0.276578	+	0.276578i
$343$	8.51498	−	16.4467i	0.459766	−	0.888040i
$344$		−	5.47086i		−	0.294969i
$345$		0			0
$346$	−3.02891	+	1.74874i	−0.162835	+	0.0940129i
$347$	−14.6116	−	3.91516i	−0.784391	−	0.210177i	−0.155671	−	0.987809i	$-0.549754\pi$
$347$	−14.6116	−	3.91516i	−0.784391	−	0.210177i	−0.628720	+	0.777632i	$0.716421\pi$
$348$	−1.16303	−	4.34047i	−0.0623447	−	0.232674i
$349$	15.2733			0.817563			0.408781	−	0.912632i	$-0.365954\pi$
$349$	15.2733			0.817563			0.408781	+	0.912632i	$0.365954\pi$
$350$		0			0
$351$	4.81981			0.257262
$352$	0.804359	+	3.00191i	0.0428725	+	0.160002i
$353$	−29.0035	−	7.77147i	−1.54370	−	0.413634i	−0.616242	−	0.787557i	$-0.711346\pi$
$353$	−29.0035	−	7.77147i	−1.54370	−	0.413634i	−0.927460	+	0.373923i	$0.878012\pi$
$354$	1.15387	−	0.666188i	0.0613276	−	0.0354075i
$355$		0			0
$356$		−	4.07354i		−	0.215897i
$357$	2.23519	−	13.9174i	0.118299	−	0.736587i
$358$	−12.7716	−	12.7716i	−0.675002	−	0.675002i
$359$	10.1537	+	5.86222i	0.535890	+	0.309396i	0.743411	−	0.668834i	$-0.233206\pi$
$359$	10.1537	+	5.86222i	0.535890	+	0.309396i	−0.207522	+	0.978230i	$0.566540\pi$
$360$		0			0
$361$	−16.6615	−	28.8585i	−0.876920	−	1.51887i
$362$	20.9854	−	5.62302i	1.10297	−	0.295540i
$363$	0.948618	−	0.948618i	0.0497895	−	0.0497895i
$364$	1.30550	+	12.6850i	0.0684267	+	0.664876i
$365$		0			0
$366$	−6.27689	+	10.8719i	−0.328098	+	0.568283i
$367$	−7.86775	+	29.3629i	−0.410693	+	1.53273i	0.382615	+	0.923908i	$0.375024\pi$
$367$	−7.86775	+	29.3629i	−0.410693	+	1.53273i	−0.793308	+	0.608821i	$0.791643\pi$
$368$	−1.36289	+	5.08638i	−0.0710457	+	0.265146i
$369$	−1.25926	+	2.18110i	−0.0655543	+	0.113543i
$370$		0			0
$371$	0.931604	+	9.05203i	0.0483665	+	0.469958i
$372$	6.52308	−	6.52308i	0.338206	−	0.338206i
$373$	29.1377	−	7.80742i	1.50869	−	0.404253i	0.592692	−	0.805429i	$-0.298065\pi$
$373$	29.1377	−	7.80742i	1.50869	−	0.404253i	0.916001	+	0.401176i	$0.131399\pi$
$374$	8.27871	+	14.3392i	0.428082	+	0.741460i
$375$		0			0
$376$	−3.53723	−	2.04222i	−0.182419	−	0.105319i
$377$	15.3147	+	15.3147i	0.788746	+	0.788746i
$378$	−0.419541	+	2.61228i	−0.0215789	+	0.134361i
$379$			4.44115i			0.228127i	0.993473	+	0.114063i	$0.0363867\pi$
$379$			4.44115i			0.228127i	−0.993473	+	0.114063i	$0.963613\pi$
$380$		0			0
$381$	2.62750	−	1.51699i	0.134611	−	0.0777176i
$382$	−16.0174	−	4.29186i	−0.819523	−	0.219590i
$383$	5.76177	+	21.5032i	0.294413	+	1.09876i	0.941683	+	0.336502i	$0.109244\pi$
$383$	5.76177	+	21.5032i	0.294413	+	1.09876i	−0.647270	+	0.762261i	$0.724089\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	2.11748			0.107777
$387$	1.41596	+	5.28444i	0.0719774	+	0.268623i
$388$	3.68039	+	0.986157i	0.186843	+	0.0500645i
$389$	10.9881	−	6.34400i	0.557120	−	0.321653i	−0.194869	−	0.980829i	$-0.562428\pi$
$389$	10.9881	−	6.34400i	0.557120	−	0.321653i	0.751989	+	0.659176i	$0.229095\pi$
$390$		0			0
$391$			28.0546i			1.41878i
$392$	−6.98876	−	0.396606i	−0.352985	−	0.0200316i
$393$	6.20372	+	6.20372i	0.312936	+	0.312936i
$394$	1.50069	+	0.866423i	0.0756036	+	0.0436498i
$395$		0			0
$396$	−1.55390	−	2.69144i	−0.0780865	−	0.135250i
$397$	−21.0326	+	5.63565i	−1.05559	+	0.282845i	−0.744561	−	0.667554i	$-0.767341\pi$
$397$	−21.0326	+	5.63565i	−1.05559	+	0.282845i	−0.311032	+	0.950399i	$0.600675\pi$
$398$	−5.57060	+	5.57060i	−0.279229	+	0.279229i
$399$	7.82192	−	17.4665i	0.391586	−	0.874418i
$400$		0			0
$401$	−13.1539	+	22.7832i	−0.656872	+	1.13774i	0.324549	+	0.945869i	$0.394788\pi$
$401$	−13.1539	+	22.7832i	−0.656872	+	1.13774i	−0.981421	+	0.191867i	$0.938546\pi$
$402$	1.72448	−	6.43584i	0.0860091	−	0.320990i
$403$	−11.5078	+	42.9479i	−0.573247	+	2.13939i
$404$	3.93122	−	6.80907i	0.195585	−	0.338764i
$405$		0			0
$406$	−9.63343	+	6.96730i	−0.478099	+	0.345781i
$407$	−7.89630	+	7.89630i	−0.391405	+	0.391405i
$408$	−5.14616	+	1.37891i	−0.254773	+	0.0682661i
$409$	−1.17325	−	2.03214i	−0.0580137	−	0.100483i	0.835560	−	0.549399i	$-0.185143\pi$
$409$	−1.17325	−	2.03214i	−0.0580137	−	0.100483i	−0.893574	+	0.448917i	$0.851810\pi$
$410$		0			0
$411$	−11.7824	−	6.80258i	−0.581184	−	0.335547i
$412$	8.36587	+	8.36587i	0.412157	+	0.412157i
$413$	−2.73474	−	2.22436i	−0.134568	−	0.109454i
$414$		−	5.26581i		−	0.258800i
$415$		0			0
$416$	4.17408	−	2.40991i	0.204651	−	0.118155i
$417$	−10.5426	−	2.82487i	−0.516271	−	0.138335i
$418$	5.81830	+	21.7142i	0.284582	+	1.06208i
$419$	−1.03087			−0.0503614			−0.0251807	−	0.999683i	$-0.508016\pi$
$419$	−1.03087			−0.0503614			−0.0251807	+	0.999683i	$0.508016\pi$
$420$		0			0
$421$	28.6945			1.39849			0.699243	−	0.714884i	$-0.253521\pi$
$421$	28.6945			1.39849			0.699243	+	0.714884i	$0.253521\pi$
$422$	−4.14097	−	15.4543i	−0.201579	−	0.752304i
$423$	3.94526	+	1.05713i	0.191825	+	0.0513994i
$424$	2.97862	−	1.71971i	0.144655	−	0.0835164i
$425$		0			0
$426$			9.22738i			0.447068i
$427$	32.7939	+	5.26683i	1.58701	+	0.254880i
$428$	−1.52895	−	1.52895i	−0.0739047	−	0.0739047i
$429$	12.9722	+	7.48952i	0.626305	+	0.361597i
$430$		0			0
$431$	12.1388	+	21.0250i	0.584704	+	1.01274i	0.994912	+	0.100745i	$0.0321227\pi$
$431$	12.1388	+	21.0250i	0.584704	+	1.01274i	−0.410208	+	0.911992i	$0.634544\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	−19.1704	+	19.1704i	−0.921271	+	0.921271i	−0.997119	−	0.0758481i	$-0.975834\pi$
$433$	−19.1704	+	19.1704i	−0.921271	+	0.921271i	0.0758481	+	0.997119i	$0.475834\pi$
$434$	−22.2755	−	9.97551i	−1.06926	−	0.478840i
$435$		0			0
$436$	0.282776	−	0.489782i	0.0135425	−	0.0234563i
$437$	−9.85843	+	36.7922i	−0.471593	+	1.76001i
$438$	2.13063	−	7.95163i	0.101806	−	0.379943i
$439$	−7.29947	+	12.6431i	−0.348385	+	0.603420i	−0.985963	−	0.166966i	$-0.946603\pi$
$439$	−7.29947	+	12.6431i	−0.348385	+	0.603420i	0.637578	+	0.770386i	$0.279936\pi$
$440$		0			0
$441$	6.85327	−	1.42573i	0.326346	−	0.0678920i
$442$	18.1574	−	18.1574i	0.863660	−	0.863660i
$443$	−21.9644	+	5.88534i	−1.04356	+	0.279621i	−0.739587	−	0.673060i	$-0.764979\pi$
$443$	−21.9644	+	5.88534i	−1.04356	+	0.279621i	−0.303971	+	0.952681i	$0.598313\pi$
$444$	−1.79662	−	3.11183i	−0.0852636	−	0.147681i
$445$		0			0
$446$	1.47835	+	0.853528i	0.0700021	+	0.0404157i
$447$	−1.47800	−	1.47800i	−0.0699071	−	0.0699071i
$448$	0.942805	+	2.47207i	0.0445433	+	0.116794i
$449$		−	41.8564i		−	1.97532i	−0.156600	−	0.987662i	$-0.550053\pi$
$449$		−	41.8564i		−	1.97532i	0.156600	−	0.987662i	$-0.449947\pi$
$450$		0			0
$451$	−6.77842	+	3.91352i	−0.319183	+	0.184281i
$452$	13.6361	+	3.65378i	0.641388	+	0.171859i
$453$	−1.04624	−	3.90462i	−0.0491566	−	0.183455i
$454$	−6.81296			−0.319748
$455$		0			0
$456$	−7.23346			−0.338738
$457$	−6.87387	−	25.6536i	−0.321546	−	1.20003i	−0.917739	−	0.397185i	$-0.869987\pi$
$457$	−6.87387	−	25.6536i	−0.321546	−	1.20003i	0.596193	−	0.802841i	$-0.296679\pi$
$458$	19.1391	+	5.12831i	0.894313	+	0.239630i
$459$	4.61392	−	2.66385i	0.215359	−	0.124338i
$460$		0			0
$461$		−	16.5608i		−	0.771313i	−0.922642	−	0.385656i	$-0.873975\pi$
$461$		−	16.5608i		−	0.771313i	0.922642	−	0.385656i	$-0.126025\pi$
$462$	−5.18839	+	6.37885i	−0.241386	+	0.296771i
$463$	19.0305	+	19.0305i	0.884424	+	0.884424i	0.993981	−	0.109557i	$-0.0349431\pi$
$463$	19.0305	+	19.0305i	0.884424	+	0.884424i	−0.109557	+	0.993981i	$0.534943\pi$
$464$	3.89156	+	2.24679i	0.180661	+	0.104305i
$465$		0			0
$466$	8.99871	+	15.5862i	0.416857	+	0.722018i
$467$	13.1429	−	3.52162i	0.608179	−	0.162961i	0.0584309	−	0.998291i	$-0.481390\pi$
$467$	13.1429	−	3.52162i	0.608179	−	0.162961i	0.549748	+	0.835330i	$0.314724\pi$
$468$	−3.40812	+	3.40812i	−0.157540	+	0.157540i
$469$	−17.5357	+	1.80471i	−0.809722	+	0.0833339i
$470$		0			0
$471$	−0.452786	+	0.784249i	−0.0208633	+	0.0361363i
$472$	−0.344844	+	1.28698i	−0.0158727	+	0.0592379i
$473$	−4.40054	+	16.4230i	−0.202337	+	0.755131i
$474$	0.957181	−	1.65789i	0.0439648	−	0.0761493i
$475$		0			0
$476$	8.26057	+	11.4216i	0.378623	+	0.523508i
$477$	−2.43203	+	2.43203i	−0.111355	+	0.111355i
$478$	−25.7331	+	6.89516i	−1.17700	+	0.315377i
$479$	−0.662643	−	1.14773i	−0.0302769	−	0.0524412i	0.850490	−	0.525991i	$-0.176306\pi$
$479$	−0.662643	−	1.14773i	−0.0302769	−	0.0524412i	−0.880767	+	0.473550i	$0.842972\pi$
$480$		0			0
$481$	14.9984	+	8.65935i	0.683869	+	0.394832i
$482$	−10.1999	−	10.1999i	−0.464592	−	0.464592i
$483$	−13.0174	+	4.96463i	−0.592314	+	0.225899i
$484$			1.34155i			0.0609795i
$485$		0			0
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	30.9501	+	8.29304i	1.40248	+	0.375794i	0.879235	−	0.476388i	$-0.158054\pi$
$487$	30.9501	+	8.29304i	1.40248	+	0.375794i	0.523246	+	0.852182i	$0.324721\pi$
$488$	−3.24916	−	12.1260i	−0.147082	−	0.548919i
$489$	−7.38217			−0.333833
$490$		0			0
$491$	−22.3460			−1.00846			−0.504231	−	0.863569i	$-0.668224\pi$
$491$	−22.3460			−1.00846			−0.504231	+	0.863569i	$0.668224\pi$
$492$	−0.651839	−	2.43270i	−0.0293872	−	0.109674i
$493$	23.1247	+	6.19624i	1.04148	+	0.279065i
$494$	30.1930	−	17.4320i	1.35845	−	0.784301i
$495$		0			0
$496$			9.22503i			0.414216i
$497$	22.8107	−	8.69961i	1.02320	−	0.390231i
$498$	−8.97250	−	8.97250i	−0.402067	−	0.402067i
$499$	−9.39838	−	5.42616i	−0.420729	−	0.242908i	0.274660	−	0.961541i	$-0.411435\pi$
$499$	−9.39838	−	5.42616i	−0.420729	−	0.242908i	−0.695389	+	0.718633i	$0.744768\pi$
$500$		0			0
$501$	0.431792	+	0.747886i	0.0192910	+	0.0334131i
$502$	25.5558	−	6.84766i	1.14061	−	0.305626i
$503$	−2.64043	+	2.64043i	−0.117731	+	0.117731i	−0.763518	−	0.645787i	$-0.776529\pi$
$503$	−2.64043	+	2.64043i	−0.117731	+	0.117731i	0.645787	+	0.763518i	$0.276529\pi$
$504$	−1.55050	−	2.14382i	−0.0690647	−	0.0954933i
$505$		0			0
$506$	8.18256	−	14.1726i	0.363759	−	0.630049i
$507$	2.64787	−	9.88197i	0.117596	−	0.438874i
$508$	−0.785250	+	2.93059i	−0.0348398	+	0.130024i
$509$	8.70464	−	15.0769i	0.385827	−	0.668271i	−0.606057	−	0.795421i	$-0.707250\pi$
$509$	8.70464	−	15.0769i	0.385827	−	0.668271i	0.991883	+	0.127150i	$0.0405830\pi$
$510$		0			0
$511$	−21.6657	+	2.22976i	−0.958435	+	0.0986389i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	6.98699	−	1.87216i	0.308483	−	0.0826578i
$514$	5.60751	+	9.71249i	0.247337	+	0.428399i
$515$		0			0
$516$	−4.73790	−	2.73543i	−0.208575	−	0.120421i
$517$	8.97575	+	8.97575i	0.394753	+	0.394753i
$518$	−5.99880	+	7.37520i	−0.263572	+	0.324048i
$519$			3.49748i			0.153522i
$520$		0			0
$521$	6.14512	−	3.54789i	0.269223	−	0.155436i	−0.359312	−	0.933218i	$-0.616989\pi$
$521$	6.14512	−	3.54789i	0.269223	−	0.155436i	0.628534	+	0.777782i	$0.283655\pi$
$522$	−4.34047	−	1.16303i	−0.189977	−	0.0509043i
$523$	−0.912232	−	3.40450i	−0.0398891	−	0.148868i	0.943109	−	0.332484i	$-0.107887\pi$
$523$	−0.912232	−	3.40450i	−0.0398891	−	0.148868i	−0.982998	+	0.183615i	$0.941220\pi$
$524$	−8.77339			−0.383267
$525$		0			0
$526$	6.85911			0.299071
$527$	12.7205	+	47.4734i	0.554112	+	2.06798i
$528$	3.00191	+	0.804359i	0.130641	+	0.0350052i
$529$	4.09523	−	2.36438i	0.178053	−	0.102799i
$530$		0			0
$531$		−	1.33238i		−	0.0578202i
$532$	6.81974	+	17.8816i	0.295673	+	0.775266i
$533$	8.58340	+	8.58340i	0.371788	+	0.371788i
$534$	−3.52779	−	2.03677i	−0.152662	−	0.0881397i
$535$		0			0
$536$	3.33144	+	5.77022i	0.143896	+	0.249235i
$537$	−17.4464	+	4.67474i	−0.752867	+	0.201730i
$538$	−6.35027	+	6.35027i	−0.273780	+	0.273780i
$539$	20.6606	+	6.81204i	0.889915	+	0.293415i
$540$		0			0
$541$	−10.1975	+	17.6627i	−0.438426	+	0.759377i	−0.997568	−	0.0696952i	$-0.977797\pi$
$541$	−10.1975	+	17.6627i	−0.438426	+	0.759377i	0.559142	+	0.829072i	$0.311131\pi$
$542$	−2.32207	+	8.66609i	−0.0997415	+	0.372240i
$543$	5.62302	−	20.9854i	0.241307	−	0.900570i
$544$	2.66385	−	4.61392i	0.114211	−	0.197820i
$545$		0			0
$546$	11.6383	+	5.21191i	0.498073	+	0.223049i
$547$	8.79499	−	8.79499i	0.376047	−	0.376047i	−0.493627	−	0.869674i	$-0.664329\pi$
$547$	8.79499	−	8.79499i	0.376047	−	0.376047i	0.869674	+	0.493627i	$0.164329\pi$
$548$	13.1416	−	3.52127i	0.561380	−	0.150421i
$549$	6.27689	+	10.8719i	0.267891	+	0.464001i
$550$		0			0
$551$	28.1495	+	16.2521i	1.19921	+	0.692363i
$552$	3.72349	+	3.72349i	0.158482	+	0.158482i
$553$	−5.00084	−	0.803154i	−0.212658	−	0.0341536i
$554$		−	24.7111i		−	1.04988i
$555$		0			0
$556$	9.45220	−	5.45723i	0.400863	−	0.231438i
$557$	−17.3515	−	4.64933i	−0.735208	−	0.196999i	−0.128261	−	0.991740i	$-0.540940\pi$
$557$	−17.3515	−	4.64933i	−0.735208	−	0.196999i	−0.606947	+	0.794742i	$0.707606\pi$
$558$	−2.38761	−	8.91070i	−0.101076	−	0.377220i
$559$	26.3685			1.11527
$560$		0			0
$561$	16.5574			0.699055
$562$	4.78598	+	17.8615i	0.201884	+	0.753442i
$563$	42.0423	+	11.2652i	1.77187	+	0.474771i	0.989063	−	0.147493i	$-0.0471203\pi$
$563$	42.0423	+	11.2652i	1.77187	+	0.474771i	0.782807	+	0.622264i	$0.213787\pi$
$564$	−3.53723	+	2.04222i	−0.148944	+	0.0859929i
$565$		0			0
$566$		−	5.57176i		−	0.234198i
$567$	2.05253	+	1.66947i	0.0861980	+	0.0701112i
$568$	−6.52474	−	6.52474i	−0.273772	−	0.273772i
$569$	−15.7466	−	9.09131i	−0.660132	−	0.381128i	0.132195	−	0.991224i	$-0.457797\pi$
$569$	−15.7466	−	9.09131i	−0.660132	−	0.381128i	−0.792327	+	0.610096i	$0.791131\pi$
$570$		0			0
$571$	13.6567	+	23.6541i	0.571516	+	0.989894i	0.996411	+	0.0846515i	$0.0269777\pi$
$571$	13.6567	+	23.6541i	0.571516	+	0.989894i	−0.424895	+	0.905243i	$0.639689\pi$
$572$	−14.4686	+	3.87686i	−0.604964	+	0.162100i
$573$	−11.7256	+	11.7256i	−0.489843	+	0.489843i
$574$	−5.39923	+	3.90495i	−0.225360	+	0.162989i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−6.40624	+	23.9084i	−0.266695	+	0.995320i	0.694509	+	0.719484i	$0.255621\pi$
$577$	−6.40624	+	23.9084i	−0.266695	+	0.995320i	−0.961205	+	0.275836i	$0.911045\pi$
$578$	2.94647	−	10.9964i	0.122557	−	0.457390i
$579$	1.05874	−	1.83379i	0.0439997	−	0.0762098i
$580$		0			0
$581$	−13.7213	+	30.6400i	−0.569256	+	1.27116i
$582$	2.69423	−	2.69423i	0.111679	−	0.111679i
$583$	−10.3248	+	2.76653i	−0.427610	+	0.114578i
$584$	4.11606	+	7.12923i	0.170324	+	0.295010i
$585$		0			0
$586$	21.6124	+	12.4779i	0.892801	+	0.515459i
$587$	−25.7187	−	25.7187i	−1.06153	−	1.06153i	−0.997979	−	0.0635463i	$-0.979759\pi$
$587$	−25.7187	−	25.7187i	−1.06153	−	1.06153i	−0.0635463	−	0.997979i	$-0.520241\pi$
$588$	−3.83785	+	5.85414i	−0.158270	+	0.241421i
$589$			66.7289i			2.74952i
$590$		0			0
$591$	1.50069	−	0.866423i	0.0617301	−	0.0356399i
$592$	3.47079	+	0.929997i	0.142649	+	0.0382226i
$593$	−7.16619	−	26.7446i	−0.294280	−	1.09827i	−0.941787	−	0.336209i	$-0.890855\pi$
$593$	−7.16619	−	26.7446i	−0.294280	−	1.09827i	0.647507	−	0.762059i	$-0.275812\pi$
$594$	−3.10780			−0.127515
$595$		0			0
$596$	2.09021			0.0856183
$597$	2.03898	+	7.60958i	0.0834499	+	0.311439i
$598$	−24.5154	−	6.56888i	−1.00251	−	0.268622i
$599$	−19.0168	+	10.9793i	−0.777004	+	0.448603i	−0.835367	−	0.549692i	$-0.814745\pi$
$599$	−19.0168	+	10.9793i	−0.777004	+	0.448603i	0.0583635	+	0.998295i	$0.481412\pi$
$600$		0			0
$601$			7.04092i			0.287205i	0.989635	+	0.143603i	$0.0458687\pi$
$601$			7.04092i			0.287205i	−0.989635	+	0.143603i	$0.954131\pi$
$602$	−2.29525	+	14.2914i	−0.0935475	+	0.582474i
$603$	−4.71136	−	4.71136i	−0.191861	−	0.191861i
$604$	3.50079	+	2.02118i	0.142445	+	0.0822407i
$605$		0			0
$606$	−3.93122	−	6.80907i	−0.159695	−	0.276600i
$607$	−22.7704	+	6.10130i	−0.924221	+	0.247644i	−0.689388	−	0.724392i	$-0.742121\pi$
$607$	−22.7704	+	6.10130i	−0.924221	+	0.247644i	−0.234832	+	0.972036i	$0.575454\pi$
$608$	5.11483	−	5.11483i	0.207434	−	0.207434i
$609$	1.21714	+	11.8264i	0.0493209	+	0.479232i
$610$		0			0
$611$	9.84311	−	17.0488i	0.398209	−	0.689719i
$612$	−1.37891	+	5.14616i	−0.0557391	+	0.208021i
$613$	3.60613	−	13.4583i	0.145650	−	0.543574i	−0.854075	−	0.520149i	$-0.825876\pi$
$613$	3.60613	−	13.4583i	0.145650	−	0.543574i	0.999726	−	0.0234247i	$-0.00745700\pi$
$614$	−8.11809	+	14.0609i	−0.327620	+	0.567454i
$615$		0			0
$616$	−0.841783	−	8.17928i	−0.0339164	−	0.329552i
$617$	−9.68360	+	9.68360i	−0.389847	+	0.389847i	−0.874633	−	0.484786i	$-0.838898\pi$
$617$	−9.68360	+	9.68360i	−0.389847	+	0.389847i	0.484786	+	0.874633i	$0.338898\pi$
$618$	11.4280	−	3.06212i	0.459701	−	0.123177i
$619$	−6.20950	−	10.7552i	−0.249581	−	0.432287i	0.713829	−	0.700320i	$-0.246960\pi$
$619$	−6.20950	−	10.7552i	−0.249581	−	0.432287i	−0.963410	+	0.268033i	$0.913626\pi$
$620$		0			0
$621$	−4.56033	−	2.63291i	−0.183000	−	0.105655i
$622$	−9.28775	−	9.28775i	−0.372405	−	0.372405i
$623$	−1.70902	+	10.6412i	−0.0684704	+	0.426331i
$624$		−	4.81981i		−	0.192947i
$625$		0			0
$626$	−22.0388	+	12.7241i	−0.880847	+	0.508557i
$627$	21.7142	+	5.81830i	0.867181	+	0.232361i
$628$	−0.234379	−	0.874716i	−0.00935276	−	0.0349050i
$629$	19.1436			0.763306
$630$		0			0
$631$	−0.546516			−0.0217565			−0.0108782	−	0.999941i	$-0.503463\pi$
$631$	−0.546516			−0.0217565			−0.0108782	+	0.999941i	$0.503463\pi$
$632$	0.495474	+	1.84913i	0.0197089	+	0.0735545i
$633$	−15.4543	−	4.14097i	−0.614253	−	0.164589i
$634$	16.4772	−	9.51309i	0.654391	−	0.377813i
$635$		0			0
$636$		−	3.43942i		−	0.136382i
$637$	1.91156	−	33.6845i	0.0757389	−	1.33463i
$638$	−9.87488	−	9.87488i	−0.390950	−	0.390950i
$639$	7.99114	+	4.61369i	0.316125	+	0.182515i
$640$		0			0
$641$	−4.37559	−	7.57874i	−0.172825	−	0.299342i	0.766581	−	0.642147i	$-0.221956\pi$
$641$	−4.37559	−	7.57874i	−0.172825	−	0.299342i	−0.939407	+	0.342805i	$0.888623\pi$
$642$	−2.08859	+	0.559635i	−0.0824300	+	0.0220870i
$643$	−10.2080	+	10.2080i	−0.402565	+	0.402565i	−0.879136	−	0.476571i	$-0.841879\pi$
$643$	−10.2080	+	10.2080i	−0.402565	+	0.402565i	0.476571	+	0.879136i	$0.341879\pi$
$644$	5.69420	−	12.7152i	0.224383	−	0.501051i
$645$		0			0
$646$	19.2688	−	33.3746i	0.758122	−	1.31311i
$647$	6.21201	−	23.1835i	0.244219	−	0.911438i	−0.729555	−	0.683922i	$-0.760273\pi$
$647$	6.21201	−	23.1835i	0.244219	−	0.911438i	0.973774	−	0.227516i	$-0.0730605\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	2.07038	−	3.58601i	0.0812696	−	0.140763i
$650$		0			0
$651$	−19.7768	+	14.3034i	−0.775114	+	0.560594i
$652$	5.21998	−	5.21998i	0.204430	−	0.204430i
$653$	−36.2525	+	9.71382i	−1.41867	+	0.380131i	−0.885011	−	0.465570i	$-0.845849\pi$
$653$	−36.2525	+	9.71382i	−1.41867	+	0.380131i	−0.533657	+	0.845701i	$0.679183\pi$
$654$	−0.282776	−	0.489782i	−0.0110574	−	0.0191520i
$655$		0			0
$656$	2.18110	+	1.25926i	0.0851575	+	0.0491657i
$657$	−5.82099	−	5.82099i	−0.227099	−	0.227099i
$658$	8.38342	+	6.81885i	0.326820	+	0.265826i
$659$		−	30.4591i		−	1.18652i	−0.805011	−	0.593259i	$-0.797841\pi$
$659$		−	30.4591i		−	1.18652i	0.805011	−	0.593259i	$-0.202159\pi$
$660$		0			0
$661$	−23.8795	+	13.7868i	−0.928805	+	0.536246i	−0.886434	−	0.462856i	$-0.846825\pi$
$661$	−23.8795	+	13.7868i	−0.928805	+	0.536246i	−0.0423719	+	0.999102i	$0.513491\pi$
$662$	20.2246	+	5.41917i	0.786052	+	0.210622i
$663$	−6.64608	−	24.8035i	−0.258112	−	0.963288i
$664$	12.6890			0.492430
$665$		0			0
$666$	−3.59323			−0.139235
$667$	−6.12427	−	22.8561i	−0.237133	−	0.884992i
$668$	−0.834158	−	0.223512i	−0.0322746	−	0.00864794i
$669$	1.47835	−	0.853528i	0.0571565	−	0.0329993i
$670$		0			0
$671$			39.0147i			1.50615i
$672$	2.61228	+	0.419541i	0.100771	+	0.0161842i
$673$	8.77420	+	8.77420i	0.338221	+	0.338221i	0.855697	−	0.517477i	$-0.173129\pi$
$673$	8.77420	+	8.77420i	0.338221	+	0.338221i	−0.517477	+	0.855697i	$0.673129\pi$
$674$	−0.334073	−	0.192877i	−0.0128680	−	0.00742935i
$675$		0			0
$676$	5.11529	+	8.85994i	0.196742	+	0.340767i
$677$	−28.6622	+	7.68002i	−1.10158	+	0.295167i	−0.763407	−	0.645917i	$-0.776475\pi$
$677$	−28.6622	+	7.68002i	−1.10158	+	0.295167i	−0.338171	+	0.941085i	$0.609808\pi$
$678$	9.98231	−	9.98231i	0.383368	−	0.383368i
$679$	−9.20045	−	4.12019i	−0.353081	−	0.158118i
$680$		0			0
$681$	−3.40648	+	5.90020i	−0.130537	+	0.226096i
$682$	7.42024	−	27.6927i	0.284136	−	1.06041i
$683$	−10.8063	+	40.3297i	−0.413492	+	1.54317i	0.374346	+	0.927289i	$0.377867\pi$
$683$	−10.8063	+	40.3297i	−0.413492	+	1.54317i	−0.787838	+	0.615882i	$0.788800\pi$
$684$	−3.61673	+	6.26436i	−0.138289	+	0.239524i
$685$		0			0
$686$	18.0902	+	3.96811i	0.690686	+	0.151503i
$687$	14.0108	−	14.0108i	0.534546	−	0.534546i
$688$	5.28444	−	1.41596i	0.201468	−	0.0539831i
$689$	8.28867	+	14.3564i	0.315773	+	0.546935i
$690$		0			0
$691$	39.0636	+	22.5534i	1.48605	+	0.857972i	0.999874	−	0.0158887i	$-0.00505775\pi$
$691$	39.0636	+	22.5534i	1.48605	+	0.857972i	0.486177	+	0.873860i	$0.338391\pi$
$692$	−2.47309	−	2.47309i	−0.0940129	−	0.0940129i
$693$	2.93005	+	7.68270i	0.111304	+	0.291842i
$694$		−	15.1270i		−	0.574214i
$695$		0			0
$696$	3.89156	−	2.24679i	0.147509	−	0.0851645i
$697$	12.9607	+	3.47280i	0.490920	+	0.131542i
$698$	3.95303	+	14.7529i	0.149624	+	0.558406i
$699$	17.9974			0.680725
$700$		0			0
$701$	−2.29359			−0.0866278			−0.0433139	−	0.999062i	$-0.513792\pi$
$701$	−2.29359			−0.0866278			−0.0433139	+	0.999062i	$0.513792\pi$
$702$	1.24746	+	4.65558i	0.0470823	+	0.175714i
$703$	25.1059	+	6.72709i	0.946885	+	0.253717i
$704$	−2.69144	+	1.55390i	−0.101437	+	0.0585649i
$705$		0			0
$706$		−	30.0267i		−	1.13007i
$707$	−13.1261	+	16.1379i	−0.493658	+	0.606927i
$708$	0.942132	+	0.942132i	0.0354075	+	0.0354075i
$709$	−41.7942	−	24.1299i	−1.56961	−	0.906217i	−0.996213	−	0.0869427i	$-0.972290\pi$
$709$	−41.7942	−	24.1299i	−1.56961	−	0.906217i	−0.573401	−	0.819275i	$-0.694376\pi$
$710$		0			0
$711$	−0.957181	−	1.65789i	−0.0358971	−	0.0621756i
$712$	3.93474	−	1.05431i	0.147461	−	0.0395119i
$713$	34.3493	−	34.3493i	1.28639	−	1.28639i
$714$	14.0217	−	1.44306i	0.524748	−	0.0540053i
$715$		0			0
$716$	9.03091	−	15.6420i	0.337501	−	0.584569i
$717$	−6.89516	+	25.7331i	−0.257505	+	0.961020i
$718$	−3.03451	+	11.3249i	−0.113247	+	0.422643i
$719$	−12.5235	+	21.6914i	−0.467048	+	0.808951i	−0.999291	−	0.0376405i	$-0.988016\pi$
$719$	−12.5235	+	21.6914i	−0.467048	+	0.808951i	0.532243	+	0.846591i	$0.321349\pi$
$720$		0			0
$721$	−18.3441	−	25.3638i	−0.683171	−	0.944596i
$722$	23.5629	−	23.5629i	0.876920	−	0.876920i
$723$	−13.9333	+	3.73342i	−0.518185	+	0.138847i
$724$	10.8628	+	18.8150i	0.403714	+	0.699254i
$725$		0			0
$726$	1.16181	+	0.670774i	0.0431190	+	0.0248948i
$727$	17.1495	+	17.1495i	0.636039	+	0.636039i	0.949576	−	0.313537i	$-0.101514\pi$
$727$	17.1495	+	17.1495i	0.636039	+	0.636039i	−0.313537	+	0.949576i	$0.601514\pi$
$728$	−11.9149	+	4.54414i	−0.441596	+	0.168417i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	25.2421	−	14.5735i	0.933612	−	0.539021i
$732$	−12.1260	−	3.24916i	−0.448190	−	0.120092i
$733$	1.92415	+	7.18102i	0.0710700	+	0.265237i	0.992313	−	0.123750i	$-0.0394920\pi$
$733$	1.92415	+	7.18102i	0.0710700	+	0.265237i	−0.921243	+	0.388986i	$0.872825\pi$
$734$	−30.3987			−1.12204
$735$		0			0
$736$	−5.26581			−0.194100
$737$	−5.35934	−	20.0013i	−0.197414	−	0.736759i
$738$	−2.43270	−	0.651839i	−0.0895488	−	0.0239945i
$739$	−7.23527	+	4.17729i	−0.266154	+	0.153664i	−0.627139	−	0.778908i	$-0.715774\pi$
$739$	−7.23527	+	4.17729i	−0.266154	+	0.153664i	0.360985	+	0.932572i	$0.382441\pi$
$740$		0			0
$741$		−	34.8639i		−	1.28076i
$742$	−8.50247	+	3.24270i	−0.312136	+	0.119043i
$743$	20.5565	+	20.5565i	0.754146	+	0.754146i	0.975250	−	0.221104i	$-0.0709661\pi$
$743$	20.5565	+	20.5565i	0.754146	+	0.754146i	−0.221104	+	0.975250i	$0.570966\pi$
$744$	7.98911	+	4.61252i	0.292895	+	0.169103i
$745$		0			0
$746$	15.0828	+	26.1241i	0.552220	+	0.956473i
$747$	−12.2567	+	3.28416i	−0.448448	+	0.120161i
$748$	−11.7079	+	11.7079i	−0.428082	+	0.428082i
$749$	3.35259	+	4.63550i	0.122501	+	0.169378i
$750$		0			0
$751$	17.3148	−	29.9902i	0.631828	−	1.09436i	−0.355350	−	0.934733i	$-0.615638\pi$
$751$	17.3148	−	29.9902i	0.631828	−	1.09436i	0.987178	−	0.159625i	$-0.0510283\pi$
$752$	1.05713	−	3.94526i	0.0385496	−	0.143869i
$753$	6.84766	−	25.5558i	0.249543	−	0.931306i
$754$	−10.8291	+	18.7566i	−0.394373	+	0.683075i
$755$		0			0
$756$	−2.63185	+	0.270861i	−0.0957195	+	0.00985112i
$757$	24.7332	−	24.7332i	0.898945	−	0.898945i	−0.0963983	−	0.995343i	$-0.530732\pi$
$757$	24.7332	−	24.7332i	0.898945	−	0.898945i	0.995343	+	0.0963983i	$0.0307323\pi$
$758$	−4.28983	+	1.14946i	−0.155813	+	0.0417501i
$759$	−8.18256	−	14.1726i	−0.297008	−	0.514433i
$760$		0			0
$761$	−32.5612	−	18.7992i	−1.18034	−	0.681471i	−0.224248	−	0.974532i	$-0.571993\pi$
$761$	−32.5612	−	18.7992i	−1.18034	−	0.681471i	−0.956094	+	0.293061i	$0.905326\pi$
$762$	2.14534	+	2.14534i	0.0777176	+	0.0777176i
$763$	−0.944172	+	1.16081i	−0.0341813	+	0.0420241i
$764$		−	16.5825i		−	0.599932i
$765$		0			0
$766$	−19.2793	+	11.1309i	−0.696588	+	0.402175i
$767$	−6.20298	−	1.66208i	−0.223977	−	0.0600144i
$768$	−0.258819	−	0.965926i	−0.00933933	−	0.0348548i
$769$	23.9494			0.863638			0.431819	−	0.901960i	$-0.357872\pi$
$769$	23.9494			0.863638			0.431819	+	0.901960i	$0.357872\pi$
$770$		0			0
$771$	11.2150			0.403899
$772$	0.548044	+	2.04533i	0.0197245	+	0.0736130i
$773$	0.0361824	+	0.00969506i	0.00130139	+	0.000348707i	0.259470	−	0.965751i	$-0.416452\pi$
$773$	0.0361824	+	0.00969506i	0.00130139	+	0.000348707i	−0.258168	+	0.966100i	$0.583119\pi$
$774$	−4.73790	+	2.73543i	−0.170300	+	0.0983230i
$775$		0			0
$776$			3.81022i			0.136779i
$777$	3.38771	+	8.88271i	0.121534	+	0.318665i
$778$	8.97176	+	8.97176i	0.321653	+	0.321653i
$779$	15.7769	+	9.10878i	0.565265	+	0.326356i
$780$		0			0
$781$	14.3384	+	24.8349i	0.513070	+	0.888663i
$782$	−27.0987	+	7.26107i	−0.969047	+	0.259655i
$783$	−3.17745	+	3.17745i	−0.113553	+	0.113553i
$784$	−1.42573	−	6.85327i	−0.0509190	−	0.244760i
$785$		0			0
$786$	−4.38669	+	7.59798i	−0.156468	+	0.271011i
$787$	6.75595	−	25.2135i	0.240824	−	0.898766i	−0.734613	−	0.678486i	$-0.762636\pi$
$787$	6.75595	−	25.2135i	0.240824	−	0.898766i	0.975437	−	0.220280i	$-0.0706970\pi$
$788$	−0.448494	+	1.67380i	−0.0159769	+	0.0596267i
$789$	3.42955	−	5.94016i	0.122095	−	0.211475i
$790$		0			0
$791$	−34.0883	−	15.2656i	−1.21204	−	0.542782i
$792$	2.19755	−	2.19755i	0.0780865	−	0.0780865i
$793$	58.4451	−	15.6603i	2.07545	−	0.556114i
$794$	−10.8872	−	18.8573i	−0.386374	−	0.669219i
$795$		0			0
$796$	−6.82256	−	3.93901i	−0.241819	−	0.139614i
$797$	0.973551	+	0.973551i	0.0344850	+	0.0344850i	0.724139	−	0.689654i	$-0.242237\pi$
$797$	0.973551	+	0.973551i	0.0344850	+	0.0344850i	−0.689654	+	0.724139i	$0.742237\pi$
$798$	18.8958	+	3.03474i	0.668904	+	0.107428i
$799$		−	21.7606i		−	0.769835i
$800$		0			0
$801$	−3.52779	+	2.03677i	−0.124648	+	0.0719657i
$802$	−25.4113	−	6.80894i	−0.897304	−	0.240432i
$803$	−6.62159	−	24.7121i	−0.233671	−	0.872071i
$804$	6.66287			0.234981
$805$		0			0
$806$	−44.4629			−1.56614
$807$	2.32436	+	8.67463i	0.0818214	+	0.305361i
$808$	7.59453	+	2.03495i	0.267175	+	0.0715893i
$809$	−34.7908	+	20.0865i	−1.22318	+	0.706203i	−0.965595	−	0.260052i	$-0.916260\pi$
$809$	−34.7908	+	20.0865i	−1.22318	+	0.706203i	−0.257585	+	0.966256i	$0.582927\pi$
$810$		0			0
$811$		−	24.5727i		−	0.862866i	−0.902145	−	0.431433i	$-0.858008\pi$
$811$		−	24.5727i		−	0.862866i	0.902145	−	0.431433i	$-0.141992\pi$
$812$	−9.22321	−	7.50191i	−0.323671	−	0.263266i
$813$	6.34402	+	6.34402i	0.222494	+	0.222494i
$814$	−9.67096	−	5.58353i	−0.338967	−	0.195703i
$815$		0			0
$816$	−2.66385	−	4.61392i	−0.0932533	−	0.161519i
$817$	38.2248	−	10.2423i	1.33732	−	0.358333i
$818$	1.65923	−	1.65923i	0.0580137	−	0.0580137i
$819$	10.3328	−	7.47310i	0.361057	−	0.261131i
$820$		0			0
$821$	24.5409	−	42.5060i	0.856482	−	1.48347i	−0.0187814	−	0.999824i	$-0.505979\pi$
$821$	24.5409	−	42.5060i	0.856482	−	1.48347i	0.875263	−	0.483647i	$-0.160688\pi$
$822$	3.52127	−	13.1416i	0.122819	−	0.458365i
$823$	−7.58153	+	28.2946i	−0.264275	+	0.986289i	0.698417	+	0.715691i	$0.253888\pi$
$823$	−7.58153	+	28.2946i	−0.264275	+	0.986289i	−0.962692	+	0.270598i	$0.912779\pi$
$824$	−5.91556	+	10.2461i	−0.206078	+	0.356938i
$825$		0			0
$826$	1.44077	−	3.21726i	0.0501307	−	0.111943i
$827$	−14.8882	+	14.8882i	−0.517712	+	0.517712i	−0.916879	−	0.399166i	$-0.869300\pi$
$827$	−14.8882	+	14.8882i	−0.517712	+	0.517712i	0.399166	+	0.916879i	$0.369300\pi$
$828$	5.08638	−	1.36289i	0.176764	−	0.0473638i
$829$	18.3844	+	31.8427i	0.638516	+	1.10594i	0.985759	+	0.168167i	$0.0537846\pi$
$829$	18.3844	+	31.8427i	0.638516	+	1.10594i	−0.347243	+	0.937775i	$0.612882\pi$
$830$		0			0
$831$	−21.4005	−	12.3556i	−0.742374	−	0.428610i
$832$	3.40812	+	3.40812i	0.118155	+	0.118155i
$833$	−16.7871	−	33.3020i	−0.581637	−	1.15385i
$834$		−	10.9145i		−	0.377937i
$835$		0			0
$836$	−19.4684	+	11.2401i	−0.673329	+	0.388747i
$837$	−8.91070	−	2.38761i	−0.307999	−	0.0825280i
$838$	−0.266809	−	0.995746i	−0.00921678	−	0.0343975i
$839$	11.6715			0.402944			0.201472	−	0.979494i	$-0.435427\pi$
$839$	11.6715			0.402944			0.201472	+	0.979494i	$0.435427\pi$
$840$		0			0
$841$	8.80767			0.303713
$842$	7.42669	+	27.7168i	0.255941	+	0.955183i
$843$	17.8615	+	4.78598i	0.615183	+	0.164838i
$844$	13.8559	−	7.99974i	0.476941	−	0.275362i
$845$		0			0
$846$			4.08444i			0.140426i
$847$	0.562835	−	3.50449i	0.0193392	−	0.120416i
$848$	2.43203	+	2.43203i	0.0835164	+	0.0835164i
$849$	−4.82528	−	2.78588i	−0.165603	−	0.0956111i
$850$		0			0
$851$	−9.46064	−	16.3863i	−0.324306	−	0.561715i
$852$	−8.91296	+	2.38822i	−0.305353	+	0.0818191i
$853$	−19.6499	+	19.6499i	−0.672801	+	0.672801i	−0.958361	−	0.285560i	$-0.907821\pi$
$853$	−19.6499	+	19.6499i	−0.672801	+	0.672801i	0.285560	+	0.958361i	$0.407821\pi$
$854$	3.40033	+	33.0397i	0.116357	+	1.13059i
$855$		0			0
$856$	1.08113	−	1.87258i	0.0369523	−	0.0640033i
$857$	14.5219	−	54.1966i	0.496059	−	1.85132i	−0.0279541	−	0.999609i	$-0.508899\pi$
$857$	14.5219	−	54.1966i	0.496059	−	1.85132i	0.524014	−	0.851710i	$-0.324434\pi$
$858$	−3.87686	+	14.4686i	−0.132354	+	0.493951i
$859$	9.51449	−	16.4796i	0.324630	−	0.562276i	−0.656807	−	0.754059i	$-0.728093\pi$
$859$	9.51449	−	16.4796i	0.324630	−	0.562276i	0.981437	+	0.191782i	$0.0614268\pi$
$860$		0			0
$861$	0.682167	+	6.62835i	0.0232482	+	0.225894i
$862$	−17.1668	+	17.1668i	−0.584704	+	0.584704i
$863$	−19.9241	+	5.33865i	−0.678224	+	0.181730i	−0.581457	−	0.813577i	$-0.697517\pi$
$863$	−19.9241	+	5.33865i	−0.678224	+	0.181730i	−0.0967676	+	0.995307i	$0.530850\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	−23.4789	−	13.5555i	−0.797844	−	0.460636i
$867$	−8.04992	−	8.04992i	−0.273389	−	0.273389i
$868$	3.87028	−	24.0983i	0.131366	−	0.817951i
$869$		−	5.94947i		−	0.201822i
$870$		0			0
$871$	−27.8113	+	16.0569i	−0.942351	+	0.544067i
$872$	0.546281	+	0.146375i	0.0184994	+	0.00495690i
$873$	−0.986157	−	3.68039i	−0.0333764	−	0.124562i
$874$	−38.0900			−1.28841
$875$		0			0
$876$	8.23213			0.278138
$877$	7.36270	+	27.4780i	0.248621	+	0.927866i	0.971529	+	0.236921i	$0.0761383\pi$
$877$	7.36270	+	27.4780i	0.248621	+	0.927866i	−0.722908	+	0.690944i	$0.757195\pi$
$878$	−14.1015	−	3.77848i	−0.475902	−	0.127518i
$879$	21.6124	−	12.4779i	0.728969	−	0.420871i
$880$		0			0
$881$			17.6227i			0.593724i	0.954920	+	0.296862i	$0.0959401\pi$
$881$			17.6227i			0.593724i	−0.954920	+	0.296862i	$0.904060\pi$
$882$	3.15091	+	6.25074i	0.106097	+	0.210473i
$883$	4.03577	+	4.03577i	0.135814	+	0.135814i	0.771746	−	0.635931i	$-0.219384\pi$
$883$	4.03577	+	4.03577i	0.135814	+	0.135814i	−0.635931	+	0.771746i	$0.719384\pi$
$884$	22.2382	+	12.8392i	0.747952	+	0.431830i
$885$		0			0
$886$	−11.3696	−	19.6927i	−0.381969	−	0.661590i
$887$	−14.4480	+	3.87133i	−0.485116	+	0.129986i	−0.493084	−	0.869982i	$-0.664130\pi$
$887$	−14.4480	+	3.87133i	−0.485116	+	0.129986i	0.00796774	+	0.999968i	$0.497464\pi$
$888$	2.54080	−	2.54080i	0.0852636	−	0.0852636i
$889$	3.28080	−	7.32608i	0.110034	−	0.245709i
$890$		0			0
$891$	−1.55390	+	2.69144i	−0.0520577	+	0.0901666i
$892$	−0.441819	+	1.64889i	−0.0147932	+	0.0552089i
$893$	7.64671	−	28.5379i	0.255887	−	0.954985i
$894$	1.04510	−	1.81017i	0.0349535	−	0.0605413i
$895$		0			0
$896$	−2.14382	+	1.55050i	−0.0716199	+	0.0517985i
$897$	−17.9465	+	17.9465i	−0.599217	+	0.599217i
$898$	40.4301	−	10.8332i	1.34917	−	0.361509i
$899$	−20.7267	−	35.8998i	−0.691276	−	1.19732i
$900$		0			0
$901$	15.8692	+	9.16208i	0.528679	+	0.305233i
$902$	−5.53456	−	5.53456i	−0.184281	−	0.184281i
$903$	11.2291	+	9.13344i	0.373681	+	0.303942i
$904$			14.1171i			0.469528i
$905$		0			0
$906$	3.50079	−	2.02118i	0.116306	−	0.0671492i
$907$	−16.8164	−	4.50593i	−0.558378	−	0.149617i	−0.0314169	−	0.999506i	$-0.510002\pi$
$907$	−16.8164	−	4.50593i	−0.558378	−	0.149617i	−0.526961	+	0.849889i	$0.676669\pi$
$908$	−1.76332	−	6.58082i	−0.0585180	−	0.218392i
$909$	−7.86244			−0.260781
$910$		0			0
$911$	9.74129			0.322743			0.161372	−	0.986894i	$-0.448408\pi$
$911$	9.74129			0.322743			0.161372	+	0.986894i	$0.448408\pi$
$912$	−1.87216	−	6.98699i	−0.0619933	−	0.231362i
$913$	−38.0913	−	10.2065i	−1.26064	−	0.337787i
$914$	23.0004	−	13.2793i	0.760786	−	0.439240i
$915$		0			0
$916$			19.8143i			0.654682i
$917$	22.9185	+	3.68080i	0.756836	+	0.121551i
$918$	3.76725	+	3.76725i	0.124338	+	0.124338i
$919$	20.0203	+	11.5587i	0.660410	+	0.381288i	0.792433	−	0.609959i	$-0.208814\pi$
$919$	20.0203	+	11.5587i	0.660410	+	0.381288i	−0.132023	+	0.991247i	$0.542147\pi$
$920$		0			0
$921$	8.11809	+	14.0609i	0.267500	+	0.463324i
$922$	15.9965	−	4.28625i	0.526816	−	0.141160i
$923$	31.4480	−	31.4480i	1.03512	−	1.03512i
$924$	−7.50435	−	3.36063i	−0.246875	−	0.110557i
$925$		0			0
$926$	−13.4566	+	23.3075i	−0.442212	+	0.765934i
$927$	3.06212	−	11.4280i	0.100573	−	0.375344i
$928$	−1.16303	+	4.34047i	−0.0381782	+	0.142483i
$929$	9.18893	−	15.9157i	0.301479	−	0.522177i	−0.674992	−	0.737825i	$-0.735853\pi$
$929$	9.18893	−	15.9157i	0.301479	−	0.522177i	0.976471	+	0.215648i	$0.0691863\pi$
$930$		0			0
$931$	−10.3130	−	49.5729i	−0.337994	−	1.62468i
$932$	−12.7261	+	12.7261i	−0.416857	+	0.416857i
$933$	−12.6873	+	3.39955i	−0.415363	+	0.111296i
$934$	6.80325	+	11.7836i	0.222609	+	0.385570i
$935$		0			0
$936$	−4.17408	−	2.40991i	−0.136434	−	0.0787702i
$937$	−12.6455	−	12.6455i	−0.413111	−	0.413111i	0.469710	−	0.882821i	$-0.344358\pi$
$937$	−12.6455	−	12.6455i	−0.413111	−	0.413111i	−0.882821	+	0.469710i	$0.844358\pi$
$938$	−6.28179	−	16.4711i	−0.205108	−	0.537799i
$939$			25.4482i			0.830471i
$940$		0			0
$941$	44.7044	−	25.8101i	1.45732	−	0.841385i	0.458442	−	0.888724i	$-0.348407\pi$
$941$	44.7044	−	25.8101i	1.45732	−	0.841385i	0.998879	+	0.0473392i	$0.0150742\pi$
$942$	−0.874716	−	0.234379i	−0.0284998	−	0.00763650i
$943$	−3.43246	−	12.8101i	−0.111776	−	0.417155i
$944$	−1.33238			−0.0433652
$945$		0			0
$946$	−17.0024			−0.552795
$947$	−13.5119	−	50.4273i	−0.439079	−	1.63867i	−0.731112	−	0.682258i	$-0.760998\pi$
$947$	−13.5119	−	50.4273i	−0.439079	−	1.63867i	0.292032	−	0.956408i	$-0.405668\pi$
$948$	1.84913	+	0.495474i	0.0600570	+	0.0160922i
$949$	−34.3616	+	19.8387i	−1.11542	+	0.643990i
$950$		0			0
$951$		−	19.0262i		−	0.616966i
$952$	−8.89443	+	10.9352i	−0.288270	+	0.354413i
$953$	−0.900242	−	0.900242i	−0.0291617	−	0.0291617i	0.692376	−	0.721537i	$-0.256564\pi$
$953$	−0.900242	−	0.900242i	−0.0291617	−	0.0291617i	−0.721537	+	0.692376i	$0.756564\pi$
$954$	−2.97862	−	1.71971i	−0.0964365	−	0.0556776i
$955$		0			0
$956$	−13.3204	−	23.0717i	−0.430814	−	0.746191i
$957$	−13.4893	+	3.61446i	−0.436048	+	0.116839i
$958$	0.937119	−	0.937119i	0.0302769	−	0.0302769i
$959$	−35.8067	+	3.68511i	−1.15626	+	0.118998i
$960$		0			0
$961$	27.0506	−	46.8530i	0.872600	−	1.51139i
$962$	−4.48241	+	16.7286i	−0.144519	+	0.539351i
$963$	−0.559635	+	2.08859i	−0.0180340	+	0.0673038i
$964$	7.21241	−	12.4923i	0.232296	−	0.402349i
$965$		0			0
$966$	−8.16463	−	11.2889i	−0.262693	−	0.363216i
$967$	−39.5119	+	39.5119i	−1.27062	+	1.27062i	−0.324852	+	0.945765i	$0.605314\pi$
$967$	−39.5119	+	39.5119i	−1.27062	+	1.27062i	−0.945765	+	0.324852i	$0.894686\pi$
$968$	−1.29584	+	0.347218i	−0.0416497	+	0.0111600i
$969$	−19.2688	−	33.3746i	−0.619004	−	1.07215i
$970$		0			0
$971$	−0.0958100	−	0.0553159i	−0.00307469	−	0.00177517i	0.498462	−	0.866912i	$-0.333898\pi$
$971$	−0.0958100	−	0.0553159i	−0.00307469	−	0.00177517i	−0.501537	+	0.865136i	$0.667232\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−26.9813	+	10.2902i	−0.864981	+	0.329889i
$974$			32.0419i			1.02669i
$975$		0			0
$976$	10.8719	−	6.27689i	0.348001	−	0.200918i
$977$	7.66383	+	2.05352i	0.245188	+	0.0656978i	0.379320	−	0.925266i	$-0.376158\pi$
$977$	7.66383	+	2.05352i	0.245188	+	0.0656978i	−0.134132	+	0.990963i	$0.542825\pi$
$978$	−1.91065	−	7.13062i	−0.0610957	−	0.228012i
$979$	−12.6598			−0.404608
$980$		0			0
$981$	−0.565551			−0.0180567
$982$	−5.78357	−	21.5846i	−0.184561	−	0.688792i
$983$	−32.1204	−	8.60664i	−1.02448	−	0.274509i	−0.292814	−	0.956170i	$-0.594592\pi$
$983$	−32.1204	−	8.60664i	−1.02448	−	0.274509i	−0.731669	+	0.681660i	$0.761258\pi$
$984$	2.18110	−	1.25926i	0.0695308	−	0.0401436i
$985$		0			0
$986$			23.9404i			0.762419i
$987$	10.0970	−	3.85083i	0.321391	−	0.122573i
$988$	24.6525	+	24.6525i	0.784301	+	0.784301i
$989$	−24.9489	−	14.4043i	−0.793329	−	0.458029i
$990$		0			0
$991$	7.16865	+	12.4165i	0.227720	+	0.394422i	0.957132	−	0.289652i	$-0.0935397\pi$
$991$	7.16865	+	12.4165i	0.227720	+	0.394422i	−0.729412	+	0.684074i	$0.760206\pi$
$992$	−8.91070	+	2.38761i	−0.282915	+	0.0758068i
$993$	14.8054	−	14.8054i	0.469837	−	0.469837i
$994$	14.3070	+	19.7818i	0.453791	+	0.627441i
$995$		0			0
$996$	6.34452	−	10.9890i	0.201034	−	0.348201i
$997$	−7.87333	+	29.3837i	−0.249351	+	0.930590i	0.721796	+	0.692106i	$0.243317\pi$
$997$	−7.87333	+	29.3837i	−0.249351	+	0.930590i	−0.971146	+	0.238484i	$0.923350\pi$
$998$	2.80879	−	10.4825i	0.0889106	−	0.331819i
$999$	−1.79662	+	3.11183i	−0.0568424	+	0.0984539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.h.943.4		16
5.2	odd	4		1050.2.bc.g.607.2		16
5.3	odd	4		210.2.u.b.187.4	yes	16
5.4	even	2		210.2.u.a.103.1	✓	16
7.3	odd	6		1050.2.bc.g.493.2		16
15.8	even	4		630.2.bv.b.397.1		16
15.14	odd	2		630.2.bv.a.523.4		16
35.3	even	12		210.2.u.a.157.1	yes	16
35.9	even	6		1470.2.m.d.1273.4		16
35.17	even	12	inner	1050.2.bc.h.157.4		16
35.19	odd	6		1470.2.m.e.1273.1		16
35.23	odd	12		1470.2.m.e.97.1		16
35.24	odd	6		210.2.u.b.73.4	yes	16
35.33	even	12		1470.2.m.d.97.4		16
105.38	odd	12		630.2.bv.a.577.4		16
105.59	even	6		630.2.bv.b.73.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.1	✓	16	5.4	even	2
210.2.u.a.157.1	yes	16	35.3	even	12
210.2.u.b.73.4	yes	16	35.24	odd	6
210.2.u.b.187.4	yes	16	5.3	odd	4
630.2.bv.a.523.4		16	15.14	odd	2
630.2.bv.a.577.4		16	105.38	odd	12
630.2.bv.b.73.1		16	105.59	even	6
630.2.bv.b.397.1		16	15.8	even	4
1050.2.bc.g.493.2		16	7.3	odd	6
1050.2.bc.g.607.2		16	5.2	odd	4
1050.2.bc.h.157.4		16	35.17	even	12	inner
1050.2.bc.h.943.4		16	1.1	even	1	trivial
1470.2.m.d.97.4		16	35.33	even	12
1470.2.m.d.1273.4		16	35.9	even	6
1470.2.m.e.97.1		16	35.23	odd	12
1470.2.m.e.1273.1		16	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(2.47207 - 0.942805i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(2.47207 - 0.942805i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.55390 + 2.69144i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(3.40812 - 3.40812i) q^{13} +(1.55050 + 2.14382i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.37891 - 5.14616i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(3.61673 - 6.26436i) q^{19} +(2.63185 - 0.270861i) q^{21} +(-2.19755 + 2.19755i) q^{22} +(-5.08638 + 1.36289i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.17408 + 2.40991i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.66947 + 2.05253i) q^{28} +4.49359i q^{29} +(-7.98911 + 4.61252i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.804359 + 3.00191i) q^{33} +5.32769 q^{34} -1.00000 q^{36} +(0.929997 + 3.47079i) q^{37} +(6.98699 + 1.87216i) q^{38} +(4.17408 - 2.40991i) q^{39} +2.51851i q^{41} +(0.942805 + 2.47207i) q^{42} +(3.86848 + 3.86848i) q^{43} +(-2.69144 - 1.55390i) q^{44} +(-2.63291 - 4.56033i) q^{46} +(3.94526 - 1.05713i) q^{47} +(0.707107 - 0.707107i) q^{48} +(5.22224 - 4.66135i) q^{49} +(2.66385 - 4.61392i) q^{51} +(-1.24746 + 4.65558i) q^{52} +(-0.890187 + 3.32222i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.41468 - 1.08135i) q^{56} +(5.11483 - 5.11483i) q^{57} +(-4.34047 + 1.16303i) q^{58} +(-0.666188 - 1.15387i) q^{59} +(10.8719 + 6.27689i) q^{61} +(-6.52308 - 6.52308i) q^{62} +(2.61228 + 0.419541i) q^{63} +1.00000i q^{64} +(-2.69144 + 1.55390i) q^{66} +(-6.43584 - 1.72448i) q^{67} +(1.37891 + 5.14616i) q^{68} -5.26581 q^{69} +9.22738 q^{71} +(-0.258819 - 0.965926i) q^{72} +(-7.95163 - 2.13063i) q^{73} +(-3.11183 + 1.79662i) q^{74} +7.23346i q^{76} +(6.37885 + 5.18839i) q^{77} +(3.40812 + 3.40812i) q^{78} +(-1.65789 - 0.957181i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-2.43270 + 0.651839i) q^{82} +(-8.97250 + 8.97250i) q^{83} +(-2.14382 + 1.55050i) q^{84} +(-2.73543 + 4.73790i) q^{86} +(-1.16303 + 4.34047i) q^{87} +(0.804359 - 3.00191i) q^{88} +(-2.03677 + 3.52779i) q^{89} +(5.21191 - 11.6383i) q^{91} +(3.72349 - 3.72349i) q^{92} +(-8.91070 + 2.38761i) q^{93} +(2.04222 + 3.53723i) q^{94} +(0.866025 + 0.500000i) q^{96} +(-2.69423 - 2.69423i) q^{97} +(5.85414 + 3.83785i) q^{98} +3.10780i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{21} - 4 q^{22} - 32 q^{23} - 8 q^{24} - 12 q^{26} + 8 q^{28} - 24 q^{31} - 8 q^{33} + 16 q^{34} - 16 q^{36} + 8 q^{37} + 28 q^{38} - 12 q^{39} + 4 q^{42} + 24 q^{43} - 4 q^{46} + 24 q^{47} + 52 q^{49} + 8 q^{51} + 8 q^{52} - 44 q^{53} - 8 q^{54} + 8 q^{56} + 8 q^{57} - 48 q^{58} + 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} - 36 q^{67} + 12 q^{68} - 8 q^{69} - 32 q^{71} + 40 q^{73} - 24 q^{74} + 44 q^{77} + 16 q^{78} + 12 q^{79} + 8 q^{81} - 12 q^{82} + 16 q^{83} + 4 q^{84} - 8 q^{86} - 12 q^{87} - 8 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 40 q^{93} + 8 q^{94} - 44 q^{97} + 8 q^{98}+O(q^{100}) \) 16 * q + 8 * q^7 + 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^21 - 4 * q^22 - 32 * q^23 - 8 * q^24 - 12 * q^26 + 8 * q^28 - 24 * q^31 - 8 * q^33 + 16 * q^34 - 16 * q^36 + 8 * q^37 + 28 * q^38 - 12 * q^39 + 4 * q^42 + 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 + 8 * q^51 + 8 * q^52 - 44 * q^53 - 8 * q^54 + 8 * q^56 + 8 * q^57 - 48 * q^58 + 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 - 36 * q^67 + 12 * q^68 - 8 * q^69 - 32 * q^71 + 40 * q^73 - 24 * q^74 + 44 * q^77 + 16 * q^78 + 12 * q^79 + 8 * q^81 - 12 * q^82 + 16 * q^83 + 4 * q^84 - 8 * q^86 - 12 * q^87 - 8 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 40 * q^93 + 8 * q^94 - 44 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more