LMFDB - Embedded newform 1050.2.m.d.307.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(307,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1050.307");

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.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.4
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1050.307
Dual form			1050.2.m.d.643.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +1.00000i q^{6} +(2.63896 + 0.189469i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +1.00000i q^{6} +(2.63896 + 0.189469i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} -5.46410 q^{11} +(-0.707107 + 0.707107i) q^{12} +(2.63896 + 2.63896i) q^{13} +(1.73205 + 2.00000i) q^{14} -1.00000 q^{16} +(-3.53553 + 3.53553i) q^{17} +(-0.707107 + 0.707107i) q^{18} +7.46410 q^{19} +(1.73205 + 2.00000i) q^{21} +(-3.86370 - 3.86370i) q^{22} +(0.707107 - 0.707107i) q^{23} -1.00000 q^{24} +3.73205i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.189469 + 2.63896i) q^{28} +7.73205i q^{29} +7.92820i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.86370 - 3.86370i) q^{33} -5.00000 q^{34} -1.00000 q^{36} +(-4.89898 - 4.89898i) q^{37} +(5.27792 + 5.27792i) q^{38} +3.73205i q^{39} -5.73205i q^{41} +(-0.189469 + 2.63896i) q^{42} +(2.63896 - 2.63896i) q^{43} -5.46410i q^{44} +1.00000 q^{46} +(5.93426 - 5.93426i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(6.92820 + 1.00000i) q^{49} -5.00000 q^{51} +(-2.63896 + 2.63896i) q^{52} +(2.50026 - 2.50026i) q^{53} -1.00000 q^{54} +(-2.00000 + 1.73205i) q^{56} +(5.27792 + 5.27792i) q^{57} +(-5.46739 + 5.46739i) q^{58} +7.19615 q^{59} +2.46410i q^{61} +(-5.60609 + 5.60609i) q^{62} +(-0.189469 + 2.63896i) q^{63} -1.00000i q^{64} -5.46410i q^{66} +(-4.52004 - 4.52004i) q^{67} +(-3.53553 - 3.53553i) q^{68} +1.00000 q^{69} -11.4641 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-8.76268 - 8.76268i) q^{73} -6.92820i q^{74} +7.46410i q^{76} +(-14.4195 - 1.03528i) q^{77} +(-2.63896 + 2.63896i) q^{78} +12.3923i q^{79} -1.00000 q^{81} +(4.05317 - 4.05317i) q^{82} +(0.328169 + 0.328169i) q^{83} +(-2.00000 + 1.73205i) q^{84} +3.73205 q^{86} +(-5.46739 + 5.46739i) q^{87} +(3.86370 - 3.86370i) q^{88} +12.0000 q^{89} +(6.46410 + 7.46410i) q^{91} +(0.707107 + 0.707107i) q^{92} +(-5.60609 + 5.60609i) q^{93} +8.39230 q^{94} -1.00000i q^{96} +(2.17209 - 2.17209i) q^{97} +(4.19187 + 5.60609i) q^{98} -5.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 16 q^{11} - 8 q^{16} + 32 q^{19} - 8 q^{24} - 40 q^{34} - 8 q^{36} + 8 q^{46} - 40 q^{51} - 8 q^{54} - 16 q^{56} + 16 q^{59} + 8 q^{69} - 64 q^{71} - 8 q^{81} - 16 q^{84} + 16 q^{86} + 96 q^{89} + 24 q^{91} - 16 q^{94}+O(q^{100}) $ 8 * q - 16 * q^11 - 8 * q^16 + 32 * q^19 - 8 * q^24 - 40 * q^34 - 8 * q^36 + 8 * q^46 - 40 * q^51 - 8 * q^54 - 16 * q^56 + 16 * q^59 + 8 * q^69 - 64 * q^71 - 8 * q^81 - 16 * q^84 + 16 * q^86 + 96 * q^89 + 24 * q^91 - 16 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	2.63896	+	0.189469i	0.997433	+	0.0716124i
$7$	2.63896	+	0.189469i	0.997433	+	0.0716124i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−5.46410			−1.64749			−0.823744	−	0.566961i	$-0.808119\pi$
$11$	−5.46410			−1.64749			−0.823744	+	0.566961i	$0.808119\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	2.63896	+	2.63896i	0.731915	+	0.731915i	0.970999	−	0.239084i	$-0.0768470\pi$
$13$	2.63896	+	2.63896i	0.731915	+	0.731915i	−0.239084	+	0.970999i	$0.576847\pi$
$14$	1.73205	+	2.00000i	0.462910	+	0.534522i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.53553	+	3.53553i	−0.857493	+	0.857493i	−0.991042	−	0.133549i	$-0.957363\pi$
$17$	−3.53553	+	3.53553i	−0.857493	+	0.857493i	0.133549	+	0.991042i	$0.457363\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	7.46410			1.71238			0.856191	−	0.516659i	$-0.172825\pi$
$19$	7.46410			1.71238			0.856191	+	0.516659i	$0.172825\pi$
$20$		0			0
$21$	1.73205	+	2.00000i	0.377964	+	0.436436i
$22$	−3.86370	−	3.86370i	−0.823744	−	0.823744i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i	−0.629532	−	0.776974i	$-0.716753\pi$
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i	0.776974	+	0.629532i	$0.216753\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$			3.73205i			0.731915i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.189469	+	2.63896i	−0.0358062	+	0.498716i
$29$			7.73205i			1.43581i	0.696143	+	0.717903i	$0.254898\pi$
$29$			7.73205i			1.43581i	−0.696143	+	0.717903i	$0.745102\pi$
$30$		0			0
$31$			7.92820i			1.42395i	0.702206	+	0.711974i	$0.252198\pi$
$31$			7.92820i			1.42395i	−0.702206	+	0.711974i	$0.747802\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.86370	−	3.86370i	−0.672584	−	0.672584i
$34$	−5.00000			−0.857493
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−4.89898	−	4.89898i	−0.805387	−	0.805387i	0.178545	−	0.983932i	$-0.442861\pi$
$37$	−4.89898	−	4.89898i	−0.805387	−	0.805387i	−0.983932	+	0.178545i	$0.942861\pi$
$38$	5.27792	+	5.27792i	0.856191	+	0.856191i
$39$			3.73205i			0.597606i
$40$		0			0
$41$		−	5.73205i		−	0.895196i	−0.894235	−	0.447598i	$-0.852280\pi$
$41$		−	5.73205i		−	0.895196i	0.894235	−	0.447598i	$-0.147720\pi$
$42$	−0.189469	+	2.63896i	−0.0292357	+	0.407200i
$43$	2.63896	−	2.63896i	0.402437	−	0.402437i	−0.476654	−	0.879091i	$-0.658150\pi$
$43$	2.63896	−	2.63896i	0.402437	−	0.402437i	0.879091	+	0.476654i	$0.158150\pi$
$44$		−	5.46410i		−	0.823744i
$45$		0			0
$46$	1.00000			0.147442
$47$	5.93426	−	5.93426i	0.865600	−	0.865600i	−0.126382	−	0.991982i	$-0.540336\pi$
$47$	5.93426	−	5.93426i	0.865600	−	0.865600i	0.991982	+	0.126382i	$0.0403364\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	6.92820	+	1.00000i	0.989743	+	0.142857i
$50$		0			0
$51$	−5.00000			−0.700140
$52$	−2.63896	+	2.63896i	−0.365958	+	0.365958i
$53$	2.50026	−	2.50026i	0.343437	−	0.343437i	−0.514221	−	0.857658i	$-0.671919\pi$
$53$	2.50026	−	2.50026i	0.343437	−	0.343437i	0.857658	+	0.514221i	$0.171919\pi$
$54$	−1.00000			−0.136083
$55$		0			0
$56$	−2.00000	+	1.73205i	−0.267261	+	0.231455i
$57$	5.27792	+	5.27792i	0.699077	+	0.699077i
$58$	−5.46739	+	5.46739i	−0.717903	+	0.717903i
$59$	7.19615			0.936859			0.468430	−	0.883501i	$-0.344820\pi$
$59$	7.19615			0.936859			0.468430	+	0.883501i	$0.344820\pi$
$60$		0			0
$61$			2.46410i			0.315496i	0.987479	+	0.157748i	$0.0504233\pi$
$61$			2.46410i			0.315496i	−0.987479	+	0.157748i	$0.949577\pi$
$62$	−5.60609	+	5.60609i	−0.711974	+	0.711974i
$63$	−0.189469	+	2.63896i	−0.0238708	+	0.332478i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		−	5.46410i		−	0.672584i
$67$	−4.52004	−	4.52004i	−0.552211	−	0.552211i	0.374867	−	0.927078i	$-0.377688\pi$
$67$	−4.52004	−	4.52004i	−0.552211	−	0.552211i	−0.927078	+	0.374867i	$0.877688\pi$
$68$	−3.53553	−	3.53553i	−0.428746	−	0.428746i
$69$	1.00000			0.120386
$70$		0			0
$71$	−11.4641			−1.36054			−0.680269	−	0.732962i	$-0.738137\pi$
$71$	−11.4641			−1.36054			−0.680269	+	0.732962i	$0.738137\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	−8.76268	−	8.76268i	−1.02559	−	1.02559i	−0.999664	−	0.0259307i	$-0.991745\pi$
$73$	−8.76268	−	8.76268i	−1.02559	−	1.02559i	−0.0259307	−	0.999664i	$-0.508255\pi$
$74$		−	6.92820i		−	0.805387i
$75$		0			0
$76$			7.46410i			0.856191i
$77$	−14.4195	−	1.03528i	−1.64326	−	0.117981i
$78$	−2.63896	+	2.63896i	−0.298803	+	0.298803i
$79$			12.3923i			1.39424i	0.716953	+	0.697122i	$0.245536\pi$
$79$			12.3923i			1.39424i	−0.716953	+	0.697122i	$0.754464\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	4.05317	−	4.05317i	0.447598	−	0.447598i
$83$	0.328169	+	0.328169i	0.0360213	+	0.0360213i	0.724888	−	0.688867i	$-0.241891\pi$
$83$	0.328169	+	0.328169i	0.0360213	+	0.0360213i	−0.688867	+	0.724888i	$0.741891\pi$
$84$	−2.00000	+	1.73205i	−0.218218	+	0.188982i
$85$		0			0
$86$	3.73205			0.402437
$87$	−5.46739	+	5.46739i	−0.586165	+	0.586165i
$88$	3.86370	−	3.86370i	0.411872	−	0.411872i
$89$	12.0000			1.27200			0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000			1.27200			0.635999	+	0.771690i	$0.280588\pi$
$90$		0			0
$91$	6.46410	+	7.46410i	0.677622	+	0.782450i
$92$	0.707107	+	0.707107i	0.0737210	+	0.0737210i
$93$	−5.60609	+	5.60609i	−0.581324	+	0.581324i
$94$	8.39230			0.865600
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	2.17209	−	2.17209i	0.220542	−	0.220542i	−0.588185	−	0.808727i	$-0.700157\pi$
$97$	2.17209	−	2.17209i	0.220542	−	0.220542i	0.808727	+	0.588185i	$0.200157\pi$
$98$	4.19187	+	5.60609i	0.423443	+	0.566300i
$99$		−	5.46410i		−	0.549163i
$100$		0			0
$101$		−	6.53590i		−	0.650346i	−0.945655	−	0.325173i	$-0.894577\pi$
$101$		−	6.53590i		−	0.650346i	0.945655	−	0.325173i	$-0.105423\pi$
$102$	−3.53553	−	3.53553i	−0.350070	−	0.350070i
$103$	−2.91636	−	2.91636i	−0.287357	−	0.287357i	0.548677	−	0.836034i	$-0.315132\pi$
$103$	−2.91636	−	2.91636i	−0.287357	−	0.287357i	−0.836034	+	0.548677i	$0.815132\pi$
$104$	−3.73205			−0.365958
$105$		0			0
$106$	3.53590			0.343437
$107$	6.31319	+	6.31319i	0.610319	+	0.610319i	0.943029	−	0.332710i	$-0.107963\pi$
$107$	6.31319	+	6.31319i	0.610319	+	0.610319i	−0.332710	+	0.943029i	$0.607963\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	12.3923i		−	1.18697i	−0.804846	−	0.593484i	$-0.797752\pi$
$109$		−	12.3923i		−	1.18697i	0.804846	−	0.593484i	$-0.202248\pi$
$110$		0			0
$111$		−	6.92820i		−	0.657596i
$112$	−2.63896	−	0.189469i	−0.249358	−	0.0179031i
$113$	1.79315	−	1.79315i	0.168685	−	0.168685i	−0.617716	−	0.786401i	$-0.711942\pi$
$113$	1.79315	−	1.79315i	0.168685	−	0.168685i	0.786401	+	0.617716i	$0.211942\pi$
$114$			7.46410i			0.699077i
$115$		0			0
$116$	−7.73205			−0.717903
$117$	−2.63896	+	2.63896i	−0.243972	+	0.243972i
$118$	5.08845	+	5.08845i	0.468430	+	0.468430i
$119$	−10.0000	+	8.66025i	−0.916698	+	0.793884i
$120$		0			0
$121$	18.8564			1.71422
$122$	−1.74238	+	1.74238i	−0.157748	+	0.157748i
$123$	4.05317	−	4.05317i	0.365462	−	0.365462i
$124$	−7.92820			−0.711974
$125$		0			0
$126$	−2.00000	+	1.73205i	−0.178174	+	0.154303i
$127$	−5.27792	−	5.27792i	−0.468339	−	0.468339i	0.433037	−	0.901376i	$-0.357442\pi$
$127$	−5.27792	−	5.27792i	−0.468339	−	0.468339i	−0.901376	+	0.433037i	$0.857442\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	3.73205			0.328589
$130$		0			0
$131$		−	14.3923i		−	1.25746i	−0.777623	−	0.628731i	$-0.783575\pi$
$131$		−	14.3923i		−	1.25746i	0.777623	−	0.628731i	$-0.216425\pi$
$132$	3.86370	−	3.86370i	0.336292	−	0.336292i
$133$	19.6975	+	1.41421i	1.70799	+	0.122628i
$134$		−	6.39230i		−	0.552211i
$135$		0			0
$136$		−	5.00000i		−	0.428746i
$137$	5.55532	+	5.55532i	0.474623	+	0.474623i	0.903407	−	0.428784i	$-0.141058\pi$
$137$	5.55532	+	5.55532i	0.474623	+	0.474623i	−0.428784	+	0.903407i	$0.641058\pi$
$138$	0.707107	+	0.707107i	0.0601929	+	0.0601929i
$139$	−19.8564			−1.68420			−0.842099	−	0.539323i	$-0.818680\pi$
$139$	−19.8564			−1.68420			−0.842099	+	0.539323i	$0.818680\pi$
$140$		0			0
$141$	8.39230			0.706760
$142$	−8.10634	−	8.10634i	−0.680269	−	0.680269i
$143$	−14.4195	−	14.4195i	−1.20582	−	1.20582i
$144$		−	1.00000i		−	0.0833333i
$145$		0			0
$146$		−	12.3923i		−	1.02559i
$147$	4.19187	+	5.60609i	0.345740	+	0.462382i
$148$	4.89898	−	4.89898i	0.402694	−	0.402694i
$149$		−	7.73205i		−	0.633434i	−0.948520	−	0.316717i	$-0.897419\pi$
$149$		−	7.73205i		−	0.633434i	0.948520	−	0.316717i	$-0.102581\pi$
$150$		0			0
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$	−5.27792	+	5.27792i	−0.428096	+	0.428096i
$153$	−3.53553	−	3.53553i	−0.285831	−	0.285831i
$154$	−9.46410	−	10.9282i	−0.762639	−	0.880620i
$155$		0			0
$156$	−3.73205			−0.298803
$157$	5.65685	−	5.65685i	0.451466	−	0.451466i	−0.444375	−	0.895841i	$-0.646574\pi$
$157$	5.65685	−	5.65685i	0.451466	−	0.451466i	0.895841	+	0.444375i	$0.146574\pi$
$158$	−8.76268	+	8.76268i	−0.697122	+	0.697122i
$159$	3.53590			0.280415
$160$		0			0
$161$	2.00000	−	1.73205i	0.157622	−	0.136505i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−0.568406	+	0.568406i	−0.0445210	+	0.0445210i	−0.729017	−	0.684496i	$-0.760022\pi$
$163$	−0.568406	+	0.568406i	−0.0445210	+	0.0445210i	0.684496	+	0.729017i	$0.260022\pi$
$164$	5.73205			0.447598
$165$		0			0
$166$			0.464102i			0.0360213i
$167$	10.9348	−	10.9348i	0.846158	−	0.846158i	−0.143493	−	0.989651i	$-0.545834\pi$
$167$	10.9348	−	10.9348i	0.846158	−	0.846158i	0.989651	+	0.143493i	$0.0458336\pi$
$168$	−2.63896	−	0.189469i	−0.203600	−	0.0146178i
$169$			0.928203i			0.0714002i
$170$		0			0
$171$			7.46410i			0.570794i
$172$	2.63896	+	2.63896i	0.201219	+	0.201219i
$173$	−6.59059	−	6.59059i	−0.501074	−	0.501074i	0.410698	−	0.911771i	$-0.365285\pi$
$173$	−6.59059	−	6.59059i	−0.501074	−	0.501074i	−0.911771	+	0.410698i	$0.865285\pi$
$174$	−7.73205			−0.586165
$175$		0			0
$176$	5.46410			0.411872
$177$	5.08845	+	5.08845i	0.382471	+	0.382471i
$178$	8.48528	+	8.48528i	0.635999	+	0.635999i
$179$			13.8564i			1.03568i	0.855479	+	0.517838i	$0.173263\pi$
$179$			13.8564i			1.03568i	−0.855479	+	0.517838i	$0.826737\pi$
$180$		0			0
$181$			2.00000i			0.148659i	0.997234	+	0.0743294i	$0.0236816\pi$
$181$			2.00000i			0.148659i	−0.997234	+	0.0743294i	$0.976318\pi$
$182$	−0.707107	+	9.84873i	−0.0524142	+	0.730036i
$183$	−1.74238	+	1.74238i	−0.128801	+	0.128801i
$184$			1.00000i			0.0737210i
$185$		0			0
$186$	−7.92820			−0.581324
$187$	19.3185	−	19.3185i	1.41271	−	1.41271i
$188$	5.93426	+	5.93426i	0.432800	+	0.432800i
$189$	−2.00000	+	1.73205i	−0.145479	+	0.125988i
$190$		0			0
$191$	6.26795			0.453533			0.226766	−	0.973949i	$-0.427185\pi$
$191$	6.26795			0.453533			0.226766	+	0.973949i	$0.427185\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	12.6264	−	12.6264i	0.908867	−	0.908867i	−0.0873137	−	0.996181i	$-0.527828\pi$
$193$	12.6264	−	12.6264i	0.908867	−	0.908867i	0.996181	+	0.0873137i	$0.0278283\pi$
$194$	3.07180			0.220542
$195$		0			0
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$	5.22715	+	5.22715i	0.372419	+	0.372419i	0.868358	−	0.495939i	$-0.165176\pi$
$197$	5.22715	+	5.22715i	0.372419	+	0.372419i	−0.495939	+	0.868358i	$0.665176\pi$
$198$	3.86370	−	3.86370i	0.274581	−	0.274581i
$199$	16.0000			1.13421			0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000			1.13421			0.567105	+	0.823646i	$0.308063\pi$
$200$		0			0
$201$		−	6.39230i		−	0.450878i
$202$	4.62158	−	4.62158i	0.325173	−	0.325173i
$203$	−1.46498	+	20.4046i	−0.102822	+	1.43212i
$204$		−	5.00000i		−	0.350070i
$205$		0			0
$206$		−	4.12436i		−	0.287357i
$207$	0.707107	+	0.707107i	0.0491473	+	0.0491473i
$208$	−2.63896	−	2.63896i	−0.182979	−	0.182979i
$209$	−40.7846			−2.82113
$210$		0			0
$211$	−10.3205			−0.710493			−0.355247	−	0.934773i	$-0.615603\pi$
$211$	−10.3205			−0.710493			−0.355247	+	0.934773i	$0.615603\pi$
$212$	2.50026	+	2.50026i	0.171718	+	0.171718i
$213$	−8.10634	−	8.10634i	−0.555438	−	0.555438i
$214$			8.92820i			0.610319i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−1.50215	+	20.9222i	−0.101972	+	1.42029i
$218$	8.76268	−	8.76268i	0.593484	−	0.593484i
$219$		−	12.3923i		−	0.837394i
$220$		0			0
$221$	−18.6603			−1.25522
$222$	4.89898	−	4.89898i	0.328798	−	0.328798i
$223$	8.19428	+	8.19428i	0.548729	+	0.548729i	0.926073	−	0.377344i	$-0.123163\pi$
$223$	8.19428	+	8.19428i	0.548729	+	0.548729i	−0.377344	+	0.926073i	$0.623163\pi$
$224$	−1.73205	−	2.00000i	−0.115728	−	0.133631i
$225$		0			0
$226$	2.53590			0.168685
$227$	0.984508	−	0.984508i	0.0653441	−	0.0653441i	−0.673680	−	0.739024i	$-0.735287\pi$
$227$	0.984508	−	0.984508i	0.0653441	−	0.0653441i	0.739024	+	0.673680i	$0.235287\pi$
$228$	−5.27792	+	5.27792i	−0.349539	+	0.349539i
$229$	15.0718			0.995972			0.497986	−	0.867185i	$-0.334073\pi$
$229$	15.0718			0.995972			0.497986	+	0.867185i	$0.334073\pi$
$230$		0			0
$231$	−9.46410	−	10.9282i	−0.622692	−	0.719023i
$232$	−5.46739	−	5.46739i	−0.358951	−	0.358951i
$233$	7.34847	−	7.34847i	0.481414	−	0.481414i	−0.424169	−	0.905583i	$-0.639434\pi$
$233$	7.34847	−	7.34847i	0.481414	−	0.481414i	0.905583	+	0.424169i	$0.139434\pi$
$234$	−3.73205			−0.243972
$235$		0			0
$236$			7.19615i			0.468430i
$237$	−8.76268	+	8.76268i	−0.569197	+	0.569197i
$238$	−13.1948	−	0.947343i	−0.855291	−	0.0614072i
$239$		−	8.53590i		−	0.552141i	−0.961137	−	0.276071i	$-0.910968\pi$
$239$		−	8.53590i		−	0.552141i	0.961137	−	0.276071i	$-0.0890324\pi$
$240$		0			0
$241$			0.928203i			0.0597908i	0.999553	+	0.0298954i	$0.00951742\pi$
$241$			0.928203i			0.0597908i	−0.999553	+	0.0298954i	$0.990483\pi$
$242$	13.3335	+	13.3335i	0.857109	+	0.857109i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−2.46410			−0.157748
$245$		0			0
$246$	5.73205			0.365462
$247$	19.6975	+	19.6975i	1.25332	+	1.25332i
$248$	−5.60609	−	5.60609i	−0.355987	−	0.355987i
$249$			0.464102i			0.0294112i
$250$		0			0
$251$			20.2679i			1.27930i	0.768666	+	0.639651i	$0.220921\pi$
$251$			20.2679i			1.27930i	−0.768666	+	0.639651i	$0.779079\pi$
$252$	−2.63896	−	0.189469i	−0.166239	−	0.0119354i
$253$	−3.86370	+	3.86370i	−0.242909	+	0.242909i
$254$		−	7.46410i		−	0.468339i
$255$		0			0
$256$	1.00000			0.0625000
$257$	16.9198	−	16.9198i	1.05543	−	1.05543i	0.0570569	−	0.998371i	$-0.481828\pi$
$257$	16.9198	−	16.9198i	1.05543	−	1.05543i	0.998371	−	0.0570569i	$-0.0181716\pi$
$258$	2.63896	+	2.63896i	0.164294	+	0.164294i
$259$	−12.0000	−	13.8564i	−0.745644	−	0.860995i
$260$		0			0
$261$	−7.73205			−0.478602
$262$	10.1769	−	10.1769i	0.628731	−	0.628731i
$263$	−4.94975	+	4.94975i	−0.305215	+	0.305215i	−0.843050	−	0.537835i	$-0.819242\pi$
$263$	−4.94975	+	4.94975i	−0.305215	+	0.305215i	0.537835	+	0.843050i	$0.319242\pi$
$264$	5.46410			0.336292
$265$		0			0
$266$	12.9282	+	14.9282i	0.792679	+	0.915307i
$267$	8.48528	+	8.48528i	0.519291	+	0.519291i
$268$	4.52004	−	4.52004i	0.276106	−	0.276106i
$269$	−21.8564			−1.33261			−0.666304	−	0.745680i	$-0.732125\pi$
$269$	−21.8564			−1.33261			−0.666304	+	0.745680i	$0.732125\pi$
$270$		0			0
$271$		−	2.92820i		−	0.177876i	−0.996037	−	0.0889378i	$-0.971653\pi$
$271$		−	2.92820i		−	0.177876i	0.996037	−	0.0889378i	$-0.0283472\pi$
$272$	3.53553	−	3.53553i	0.214373	−	0.214373i
$273$	−0.707107	+	9.84873i	−0.0427960	+	0.596072i
$274$			7.85641i			0.474623i
$275$		0			0
$276$			1.00000i			0.0601929i
$277$	−5.93426	−	5.93426i	−0.356555	−	0.356555i	0.505987	−	0.862541i	$-0.331129\pi$
$277$	−5.93426	−	5.93426i	−0.356555	−	0.356555i	−0.862541	+	0.505987i	$0.831129\pi$
$278$	−14.0406	−	14.0406i	−0.842099	−	0.842099i
$279$	−7.92820			−0.474649
$280$		0			0
$281$	13.8564			0.826604			0.413302	−	0.910594i	$-0.364375\pi$
$281$	13.8564			0.826604			0.413302	+	0.910594i	$0.364375\pi$
$282$	5.93426	+	5.93426i	0.353380	+	0.353380i
$283$	16.1112	+	16.1112i	0.957709	+	0.957709i	0.999141	−	0.0414327i	$-0.0131922\pi$
$283$	16.1112	+	16.1112i	0.957709	+	0.957709i	−0.0414327	+	0.999141i	$0.513192\pi$
$284$		−	11.4641i		−	0.680269i
$285$		0			0
$286$		−	20.3923i		−	1.20582i
$287$	1.08604	−	15.1266i	0.0641072	−	0.892898i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$		−	8.00000i		−	0.470588i
$290$		0			0
$291$	3.07180			0.180072
$292$	8.76268	−	8.76268i	0.512797	−	0.512797i
$293$	1.31268	+	1.31268i	0.0766874	+	0.0766874i	0.744410	−	0.667723i	$-0.232731\pi$
$293$	1.31268	+	1.31268i	0.0766874	+	0.0766874i	−0.667723	+	0.744410i	$0.732731\pi$
$294$	−1.00000	+	6.92820i	−0.0583212	+	0.404061i
$295$		0			0
$296$	6.92820			0.402694
$297$	3.86370	−	3.86370i	0.224195	−	0.224195i
$298$	5.46739	−	5.46739i	0.316717	−	0.316717i
$299$	3.73205			0.215830
$300$		0			0
$301$	7.46410	−	6.46410i	0.430224	−	0.372585i
$302$	11.3137	+	11.3137i	0.651031	+	0.651031i
$303$	4.62158	−	4.62158i	0.265503	−	0.265503i
$304$	−7.46410			−0.428096
$305$		0			0
$306$		−	5.00000i		−	0.285831i
$307$	3.58630	−	3.58630i	0.204681	−	0.204681i	−0.597321	−	0.802002i	$-0.703768\pi$
$307$	3.58630	−	3.58630i	0.204681	−	0.204681i	0.802002	+	0.597321i	$0.203768\pi$
$308$	1.03528	−	14.4195i	0.0589903	−	0.821629i
$309$		−	4.12436i		−	0.234626i
$310$		0			0
$311$			25.8564i			1.46618i	0.680130	+	0.733091i	$0.261923\pi$
$311$			25.8564i			1.46618i	−0.680130	+	0.733091i	$0.738077\pi$
$312$	−2.63896	−	2.63896i	−0.149402	−	0.149402i
$313$	−21.3891	−	21.3891i	−1.20898	−	1.20898i	−0.971357	−	0.237625i	$-0.923631\pi$
$313$	−21.3891	−	21.3891i	−1.20898	−	1.20898i	−0.237625	−	0.971357i	$-0.576369\pi$
$314$	8.00000			0.451466
$315$		0			0
$316$	−12.3923			−0.697122
$317$	−19.3693	−	19.3693i	−1.08789	−	1.08789i	−0.995746	−	0.0921415i	$-0.970629\pi$
$317$	−19.3693	−	19.3693i	−1.08789	−	1.08789i	−0.0921415	−	0.995746i	$-0.529371\pi$
$318$	2.50026	+	2.50026i	0.140207	+	0.140207i
$319$		−	42.2487i		−	2.36547i
$320$		0			0
$321$			8.92820i			0.498324i
$322$	2.63896	+	0.189469i	0.147063	+	0.0105587i
$323$	−26.3896	+	26.3896i	−1.46836	+	1.46836i
$324$		−	1.00000i		−	0.0555556i
$325$		0			0
$326$	−0.803848			−0.0445210
$327$	8.76268	−	8.76268i	0.484577	−	0.484577i
$328$	4.05317	+	4.05317i	0.223799	+	0.223799i
$329$	16.7846	−	14.5359i	0.925365	−	0.801390i
$330$		0			0
$331$	−30.3205			−1.66657			−0.833283	−	0.552847i	$-0.813541\pi$
$331$	−30.3205			−1.66657			−0.833283	+	0.552847i	$0.813541\pi$
$332$	−0.328169	+	0.328169i	−0.0180106	+	0.0180106i
$333$	4.89898	−	4.89898i	0.268462	−	0.268462i
$334$	15.4641			0.846158
$335$		0			0
$336$	−1.73205	−	2.00000i	−0.0944911	−	0.109109i
$337$	−15.7458	−	15.7458i	−0.857729	−	0.857729i	0.133341	−	0.991070i	$-0.457429\pi$
$337$	−15.7458	−	15.7458i	−0.857729	−	0.857729i	−0.991070	+	0.133341i	$0.957429\pi$
$338$	−0.656339	+	0.656339i	−0.0357001	+	0.0357001i
$339$	2.53590			0.137731
$340$		0			0
$341$		−	43.3205i		−	2.34594i
$342$	−5.27792	+	5.27792i	−0.285397	+	0.285397i
$343$	18.0938	+	3.95164i	0.976972	+	0.213368i
$344$			3.73205i			0.201219i
$345$		0			0
$346$		−	9.32051i		−	0.501074i
$347$	−3.20736	−	3.20736i	−0.172180	−	0.172180i	0.615756	−	0.787937i	$-0.288851\pi$
$347$	−3.20736	−	3.20736i	−0.172180	−	0.172180i	−0.787937	+	0.615756i	$0.788851\pi$
$348$	−5.46739	−	5.46739i	−0.293083	−	0.293083i
$349$	−4.60770			−0.246644			−0.123322	−	0.992367i	$-0.539355\pi$
$349$	−4.60770			−0.246644			−0.123322	+	0.992367i	$0.539355\pi$
$350$		0			0
$351$	−3.73205			−0.199202
$352$	3.86370	+	3.86370i	0.205936	+	0.205936i
$353$	9.14162	+	9.14162i	0.486559	+	0.486559i	0.907219	−	0.420659i	$-0.138201\pi$
$353$	9.14162	+	9.14162i	0.486559	+	0.486559i	−0.420659	+	0.907219i	$0.638201\pi$
$354$			7.19615i			0.382471i
$355$		0			0
$356$			12.0000i			0.635999i
$357$	−13.1948	−	0.947343i	−0.698342	−	0.0501387i
$358$	−9.79796	+	9.79796i	−0.517838	+	0.517838i
$359$			36.1244i			1.90657i	0.302071	+	0.953285i	$0.402322\pi$
$359$			36.1244i			1.90657i	−0.302071	+	0.953285i	$0.597678\pi$
$360$		0			0
$361$	36.7128			1.93225
$362$	−1.41421	+	1.41421i	−0.0743294	+	0.0743294i
$363$	13.3335	+	13.3335i	0.699827	+	0.699827i
$364$	−7.46410	+	6.46410i	−0.391225	+	0.338811i
$365$		0			0
$366$	−2.46410			−0.128801
$367$	−7.63947	+	7.63947i	−0.398777	+	0.398777i	−0.877802	−	0.479024i	$-0.840991\pi$
$367$	−7.63947	+	7.63947i	−0.398777	+	0.398777i	0.479024	+	0.877802i	$0.340991\pi$
$368$	−0.707107	+	0.707107i	−0.0368605	+	0.0368605i
$369$	5.73205			0.298399
$370$		0			0
$371$	7.07180	−	6.12436i	0.367149	−	0.317961i
$372$	−5.60609	−	5.60609i	−0.290662	−	0.290662i
$373$	−10.8332	+	10.8332i	−0.560924	+	0.560924i	−0.929570	−	0.368646i	$-0.879821\pi$
$373$	−10.8332	+	10.8332i	−0.560924	+	0.560924i	0.368646	+	0.929570i	$0.379821\pi$
$374$	27.3205			1.41271
$375$		0			0
$376$			8.39230i			0.432800i
$377$	−20.4046	+	20.4046i	−1.05089	+	1.05089i
$378$	−2.63896	−	0.189469i	−0.135733	−	0.00974522i
$379$			19.3923i			0.996116i	0.867144	+	0.498058i	$0.165953\pi$
$379$			19.3923i			0.996116i	−0.867144	+	0.498058i	$0.834047\pi$
$380$		0			0
$381$		−	7.46410i		−	0.382398i
$382$	4.43211	+	4.43211i	0.226766	+	0.226766i
$383$	−21.0101	−	21.0101i	−1.07357	−	1.07357i	−0.997070	−	0.0764978i	$-0.975626\pi$
$383$	−21.0101	−	21.0101i	−1.07357	−	1.07357i	−0.0764978	−	0.997070i	$-0.524374\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	17.8564			0.908867
$387$	2.63896	+	2.63896i	0.134146	+	0.134146i
$388$	2.17209	+	2.17209i	0.110271	+	0.110271i
$389$			26.9282i			1.36531i	0.730739	+	0.682657i	$0.239176\pi$
$389$			26.9282i			1.36531i	−0.730739	+	0.682657i	$0.760824\pi$
$390$		0			0
$391$			5.00000i			0.252861i
$392$	−5.60609	+	4.19187i	−0.283150	+	0.211722i
$393$	10.1769	−	10.1769i	0.513357	−	0.513357i
$394$			7.39230i			0.372419i
$395$		0			0
$396$	5.46410			0.274581
$397$	−7.15900	+	7.15900i	−0.359300	+	0.359300i	−0.863555	−	0.504255i	$-0.831767\pi$
$397$	−7.15900	+	7.15900i	−0.359300	+	0.359300i	0.504255	+	0.863555i	$0.331767\pi$
$398$	11.3137	+	11.3137i	0.567105	+	0.567105i
$399$	12.9282	+	14.9282i	0.647220	+	0.747345i
$400$		0			0
$401$	−13.3205			−0.665194			−0.332597	−	0.943069i	$-0.607925\pi$
$401$	−13.3205			−0.665194			−0.332597	+	0.943069i	$0.607925\pi$
$402$	4.52004	−	4.52004i	0.225439	−	0.225439i
$403$	−20.9222	+	20.9222i	−1.04221	+	1.04221i
$404$	6.53590			0.325173
$405$		0			0
$406$	−15.4641	+	13.3923i	−0.767470	+	0.664649i
$407$	26.7685	+	26.7685i	1.32687	+	1.32687i
$408$	3.53553	−	3.53553i	0.175035	−	0.175035i
$409$	−20.3923			−1.00833			−0.504167	−	0.863606i	$-0.668201\pi$
$409$	−20.3923			−1.00833			−0.504167	+	0.863606i	$0.668201\pi$
$410$		0			0
$411$			7.85641i			0.387528i
$412$	2.91636	−	2.91636i	0.143679	−	0.143679i
$413$	18.9903	+	1.36345i	0.934454	+	0.0670908i
$414$			1.00000i			0.0491473i
$415$		0			0
$416$		−	3.73205i		−	0.182979i
$417$	−14.0406	−	14.0406i	−0.687571	−	0.687571i
$418$	−28.8391	−	28.8391i	−1.41057	−	1.41057i
$419$	−17.3397			−0.847102			−0.423551	−	0.905872i	$-0.639217\pi$
$419$	−17.3397			−0.847102			−0.423551	+	0.905872i	$0.639217\pi$
$420$		0			0
$421$	−29.3205			−1.42899			−0.714497	−	0.699638i	$-0.753344\pi$
$421$	−29.3205			−1.42899			−0.714497	+	0.699638i	$0.753344\pi$
$422$	−7.29770	−	7.29770i	−0.355247	−	0.355247i
$423$	5.93426	+	5.93426i	0.288533	+	0.288533i
$424$			3.53590i			0.171718i
$425$		0			0
$426$		−	11.4641i		−	0.555438i
$427$	−0.466870	+	6.50266i	−0.0225934	+	0.314686i
$428$	−6.31319	+	6.31319i	−0.305160	+	0.305160i
$429$		−	20.3923i		−	0.984550i
$430$		0			0
$431$	−6.80385			−0.327730			−0.163865	−	0.986483i	$-0.552396\pi$
$431$	−6.80385			−0.327730			−0.163865	+	0.986483i	$0.552396\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−0.378937	−	0.378937i	−0.0182106	−	0.0182106i	0.697943	−	0.716153i	$-0.254099\pi$
$433$	−0.378937	−	0.378937i	−0.0182106	−	0.0182106i	−0.716153	+	0.697943i	$0.754099\pi$
$434$	−15.8564	+	13.7321i	−0.761132	+	0.659160i
$435$		0			0
$436$	12.3923			0.593484
$437$	5.27792	−	5.27792i	0.252477	−	0.252477i
$438$	8.76268	−	8.76268i	0.418697	−	0.418697i
$439$	39.7846			1.89882			0.949408	−	0.314046i	$-0.101684\pi$
$439$	39.7846			1.89882			0.949408	+	0.314046i	$0.101684\pi$
$440$		0			0
$441$	−1.00000	+	6.92820i	−0.0476190	+	0.329914i
$442$	−13.1948	−	13.1948i	−0.627612	−	0.627612i
$443$	7.24693	−	7.24693i	0.344312	−	0.344312i	−0.513674	−	0.857986i	$-0.671716\pi$
$443$	7.24693	−	7.24693i	0.344312	−	0.344312i	0.857986	+	0.513674i	$0.171716\pi$
$444$	6.92820			0.328798
$445$		0			0
$446$			11.5885i			0.548729i
$447$	5.46739	−	5.46739i	0.258598	−	0.258598i
$448$	0.189469	−	2.63896i	0.00895155	−	0.124679i
$449$		−	30.7846i		−	1.45282i	−0.687264	−	0.726408i	$-0.741188\pi$
$449$		−	30.7846i		−	1.45282i	0.687264	−	0.726408i	$-0.258812\pi$
$450$		0			0
$451$			31.3205i			1.47483i
$452$	1.79315	+	1.79315i	0.0843427	+	0.0843427i
$453$	11.3137	+	11.3137i	0.531564	+	0.531564i
$454$	1.39230			0.0653441
$455$		0			0
$456$	−7.46410			−0.349539
$457$	−16.1248	−	16.1248i	−0.754284	−	0.754284i	0.220991	−	0.975276i	$-0.429071\pi$
$457$	−16.1248	−	16.1248i	−0.754284	−	0.754284i	−0.975276	+	0.220991i	$0.929071\pi$
$458$	10.6574	+	10.6574i	0.497986	+	0.497986i
$459$		−	5.00000i		−	0.233380i
$460$		0			0
$461$		−	11.6077i		−	0.540624i	−0.962773	−	0.270312i	$-0.912873\pi$
$461$		−	11.6077i		−	0.540624i	0.962773	−	0.270312i	$-0.0871269\pi$
$462$	1.03528	−	14.4195i	0.0481654	−	0.670858i
$463$	15.0759	−	15.0759i	0.700635	−	0.700635i	−0.263912	−	0.964547i	$-0.585013\pi$
$463$	15.0759	−	15.0759i	0.700635	−	0.700635i	0.964547	+	0.263912i	$0.0850127\pi$
$464$		−	7.73205i		−	0.358951i
$465$		0			0
$466$	10.3923			0.481414
$467$	−15.2282	+	15.2282i	−0.704676	+	0.704676i	−0.965411	−	0.260734i	$-0.916035\pi$
$467$	−15.2282	+	15.2282i	−0.704676	+	0.704676i	0.260734	+	0.965411i	$0.416035\pi$
$468$	−2.63896	−	2.63896i	−0.121986	−	0.121986i
$469$	−11.0718	−	12.7846i	−0.511248	−	0.590338i
$470$		0			0
$471$	8.00000			0.368621
$472$	−5.08845	+	5.08845i	−0.234215	+	0.234215i
$473$	−14.4195	+	14.4195i	−0.663011	+	0.663011i
$474$	−12.3923			−0.569197
$475$		0			0
$476$	−8.66025	−	10.0000i	−0.396942	−	0.458349i
$477$	2.50026	+	2.50026i	0.114479	+	0.114479i
$478$	6.03579	−	6.03579i	0.276071	−	0.276071i
$479$	−0.928203			−0.0424107			−0.0212053	−	0.999775i	$-0.506750\pi$
$479$	−0.928203			−0.0424107			−0.0212053	+	0.999775i	$0.506750\pi$
$480$		0			0
$481$		−	25.8564i		−	1.17895i
$482$	−0.656339	+	0.656339i	−0.0298954	+	0.0298954i
$483$	2.63896	+	0.189469i	0.120077	+	0.00862112i
$484$			18.8564i			0.857109i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	26.8701	+	26.8701i	1.21760	+	1.21760i	0.968471	+	0.249128i	$0.0801440\pi$
$487$	26.8701	+	26.8701i	1.21760	+	1.21760i	0.249128	+	0.968471i	$0.419856\pi$
$488$	−1.74238	−	1.74238i	−0.0788740	−	0.0788740i
$489$	−0.803848			−0.0363512
$490$		0			0
$491$	9.32051			0.420629			0.210314	−	0.977634i	$-0.432551\pi$
$491$	9.32051			0.420629			0.210314	+	0.977634i	$0.432551\pi$
$492$	4.05317	+	4.05317i	0.182731	+	0.182731i
$493$	−27.3369	−	27.3369i	−1.23119	−	1.23119i
$494$			27.8564i			1.25332i
$495$		0			0
$496$		−	7.92820i		−	0.355987i
$497$	−30.2533	−	2.17209i	−1.35705	−	0.0974315i
$498$	−0.328169	+	0.328169i	−0.0147056	+	0.0147056i
$499$		−	3.39230i		−	0.151860i	−0.997113	−	0.0759302i	$-0.975807\pi$
$499$		−	3.39230i		−	0.151860i	0.997113	−	0.0759302i	$-0.0241926\pi$
$500$		0			0
$501$	15.4641			0.690885
$502$	−14.3316	+	14.3316i	−0.639651	+	0.639651i
$503$	20.0764	+	20.0764i	0.895162	+	0.895162i	0.995003	−	0.0998413i	$-0.0318335\pi$
$503$	20.0764	+	20.0764i	0.895162	+	0.895162i	−0.0998413	+	0.995003i	$0.531834\pi$
$504$	−1.73205	−	2.00000i	−0.0771517	−	0.0890871i
$505$		0			0
$506$	−5.46410			−0.242909
$507$	−0.656339	+	0.656339i	−0.0291490	+	0.0291490i
$508$	5.27792	−	5.27792i	0.234170	−	0.234170i
$509$	19.8564			0.880120			0.440060	−	0.897968i	$-0.354957\pi$
$509$	19.8564			0.880120			0.440060	+	0.897968i	$0.354957\pi$
$510$		0			0
$511$	−21.4641	−	24.7846i	−0.949516	−	1.09641i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−5.27792	+	5.27792i	−0.233026	+	0.233026i
$514$	23.9282			1.05543
$515$		0			0
$516$			3.73205i			0.164294i
$517$	−32.4254	+	32.4254i	−1.42607	+	1.42607i
$518$	1.31268	−	18.2832i	0.0576757	−	0.803319i
$519$		−	9.32051i		−	0.409125i
$520$		0			0
$521$			11.5885i			0.507700i	0.967244	+	0.253850i	$0.0816969\pi$
$521$			11.5885i			0.507700i	−0.967244	+	0.253850i	$0.918303\pi$
$522$	−5.46739	−	5.46739i	−0.239301	−	0.239301i
$523$	22.9048	+	22.9048i	1.00156	+	1.00156i	0.999999	+	0.00155899i	$0.000496244\pi$
$523$	22.9048	+	22.9048i	1.00156	+	1.00156i	0.00155899	+	0.999999i	$0.499504\pi$
$524$	14.3923			0.628731
$525$		0			0
$526$	−7.00000			−0.305215
$527$	−28.0304	−	28.0304i	−1.22102	−	1.22102i
$528$	3.86370	+	3.86370i	0.168146	+	0.168146i
$529$			22.0000i			0.956522i
$530$		0			0
$531$			7.19615i			0.312286i
$532$	−1.41421	+	19.6975i	−0.0613139	+	0.853993i
$533$	15.1266	−	15.1266i	0.655208	−	0.655208i
$534$			12.0000i			0.519291i
$535$		0			0
$536$	6.39230			0.276106
$537$	−9.79796	+	9.79796i	−0.422813	+	0.422813i
$538$	−15.4548	−	15.4548i	−0.666304	−	0.666304i
$539$	−37.8564	−	5.46410i	−1.63059	−	0.235356i
$540$		0			0
$541$	5.32051			0.228747			0.114373	−	0.993438i	$-0.463514\pi$
$541$	5.32051			0.228747			0.114373	+	0.993438i	$0.463514\pi$
$542$	2.07055	−	2.07055i	0.0889378	−	0.0889378i
$543$	−1.41421	+	1.41421i	−0.0606897	+	0.0606897i
$544$	5.00000			0.214373
$545$		0			0
$546$	−7.46410	+	6.46410i	−0.319434	+	0.276638i
$547$	−28.0948	−	28.0948i	−1.20125	−	1.20125i	−0.973788	−	0.227459i	$-0.926958\pi$
$547$	−28.0948	−	28.0948i	−1.20125	−	1.20125i	−0.227459	−	0.973788i	$-0.573042\pi$
$548$	−5.55532	+	5.55532i	−0.237311	+	0.237311i
$549$	−2.46410			−0.105165
$550$		0			0
$551$			57.7128i			2.45865i
$552$	−0.707107	+	0.707107i	−0.0300965	+	0.0300965i
$553$	−2.34795	+	32.7028i	−0.0998452	+	1.39066i
$554$		−	8.39230i		−	0.356555i
$555$		0			0
$556$		−	19.8564i		−	0.842099i
$557$	−11.4152	−	11.4152i	−0.483679	−	0.483679i	0.422625	−	0.906305i	$-0.361109\pi$
$557$	−11.4152	−	11.4152i	−0.483679	−	0.483679i	−0.906305	+	0.422625i	$0.861109\pi$
$558$	−5.60609	−	5.60609i	−0.237325	−	0.237325i
$559$	13.9282			0.589100
$560$		0			0
$561$	27.3205			1.15347
$562$	9.79796	+	9.79796i	0.413302	+	0.413302i
$563$	−24.3698	−	24.3698i	−1.02706	−	1.02706i	−0.999623	−	0.0274412i	$-0.991264\pi$
$563$	−24.3698	−	24.3698i	−1.02706	−	1.02706i	−0.0274412	−	0.999623i	$-0.508736\pi$
$564$			8.39230i			0.353380i
$565$		0			0
$566$			22.7846i			0.957709i
$567$	−2.63896	−	0.189469i	−0.110826	−	0.00795694i
$568$	8.10634	−	8.10634i	0.340135	−	0.340135i
$569$			11.6077i			0.486620i	0.969949	+	0.243310i	$0.0782332\pi$
$569$			11.6077i			0.486620i	−0.969949	+	0.243310i	$0.921767\pi$
$570$		0			0
$571$	−42.4641			−1.77707			−0.888534	−	0.458811i	$-0.848275\pi$
$571$	−42.4641			−1.77707			−0.888534	+	0.458811i	$0.848275\pi$
$572$	14.4195	−	14.4195i	0.602911	−	0.602911i
$573$	4.43211	+	4.43211i	0.185154	+	0.185154i
$574$	11.4641	−	9.92820i	0.478502	−	0.414395i
$575$		0			0
$576$	1.00000			0.0416667
$577$	−16.5916	+	16.5916i	−0.690718	+	0.690718i	−0.962390	−	0.271672i	$-0.912424\pi$
$577$	−16.5916	+	16.5916i	−0.690718	+	0.690718i	0.271672	+	0.962390i	$0.412424\pi$
$578$	5.65685	−	5.65685i	0.235294	−	0.235294i
$579$	17.8564			0.742087
$580$		0			0
$581$	0.803848	+	0.928203i	0.0333492	+	0.0385084i
$582$	2.17209	+	2.17209i	0.0900360	+	0.0900360i
$583$	−13.6617	+	13.6617i	−0.565808	+	0.565808i
$584$	12.3923			0.512797
$585$		0			0
$586$			1.85641i			0.0766874i
$587$	−25.6825	+	25.6825i	−1.06003	+	1.06003i	−0.0619500	+	0.998079i	$0.519732\pi$
$587$	−25.6825	+	25.6825i	−1.06003	+	1.06003i	−0.998079	+	0.0619500i	$0.980268\pi$
$588$	−5.60609	+	4.19187i	−0.231191	+	0.172870i
$589$			59.1769i			2.43834i
$590$		0			0
$591$			7.39230i			0.304079i
$592$	4.89898	+	4.89898i	0.201347	+	0.201347i
$593$	7.07107	+	7.07107i	0.290374	+	0.290374i	0.837228	−	0.546854i	$-0.184175\pi$
$593$	7.07107	+	7.07107i	0.290374	+	0.290374i	−0.546854	+	0.837228i	$0.684175\pi$
$594$	5.46410			0.224195
$595$		0			0
$596$	7.73205			0.316717
$597$	11.3137	+	11.3137i	0.463039	+	0.463039i
$598$	2.63896	+	2.63896i	0.107915	+	0.107915i
$599$			14.5167i			0.593135i	0.955012	+	0.296567i	$0.0958419\pi$
$599$			14.5167i			0.593135i	−0.955012	+	0.296567i	$0.904158\pi$
$600$		0			0
$601$			25.3205i			1.03285i	0.856334	+	0.516423i	$0.172737\pi$
$601$			25.3205i			1.03285i	−0.856334	+	0.516423i	$0.827263\pi$
$602$	9.84873	+	0.707107i	0.401404	+	0.0288195i
$603$	4.52004	−	4.52004i	0.184070	−	0.184070i
$604$			16.0000i			0.651031i
$605$		0			0
$606$	6.53590			0.265503
$607$	−9.62209	+	9.62209i	−0.390549	+	0.390549i	−0.874883	−	0.484334i	$-0.839062\pi$
$607$	−9.62209	+	9.62209i	−0.390549	+	0.390549i	0.484334	+	0.874883i	$0.339062\pi$
$608$	−5.27792	−	5.27792i	−0.214048	−	0.214048i
$609$	−15.4641	+	13.3923i	−0.626637	+	0.542684i
$610$		0			0
$611$	31.3205			1.26709
$612$	3.53553	−	3.53553i	0.142915	−	0.142915i
$613$	−3.20736	+	3.20736i	−0.129544	+	0.129544i	−0.768906	−	0.639362i	$-0.779199\pi$
$613$	−3.20736	+	3.20736i	−0.129544	+	0.129544i	0.639362	+	0.768906i	$0.279199\pi$
$614$	5.07180			0.204681
$615$		0			0
$616$	10.9282	−	9.46410i	0.440310	−	0.381320i
$617$	−32.2223	−	32.2223i	−1.29722	−	1.29722i	−0.930221	−	0.367000i	$-0.880385\pi$
$617$	−32.2223	−	32.2223i	−1.29722	−	1.29722i	−0.367000	−	0.930221i	$-0.619615\pi$
$618$	2.91636	−	2.91636i	0.117313	−	0.117313i
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$		0			0
$621$			1.00000i			0.0401286i
$622$	−18.2832	+	18.2832i	−0.733091	+	0.733091i
$623$	31.6675	+	2.27362i	1.26873	+	0.0910908i
$624$		−	3.73205i		−	0.149402i
$625$		0			0
$626$		−	30.2487i		−	1.20898i
$627$	−28.8391	−	28.8391i	−1.15172	−	1.15172i
$628$	5.65685	+	5.65685i	0.225733	+	0.225733i
$629$	34.6410			1.38123
$630$		0			0
$631$	−2.00000			−0.0796187			−0.0398094	−	0.999207i	$-0.512675\pi$
$631$	−2.00000			−0.0796187			−0.0398094	+	0.999207i	$0.512675\pi$
$632$	−8.76268	−	8.76268i	−0.348561	−	0.348561i
$633$	−7.29770	−	7.29770i	−0.290058	−	0.290058i
$634$		−	27.3923i		−	1.08789i
$635$		0			0
$636$			3.53590i			0.140207i
$637$	15.6443	+	20.9222i	0.619849	+	0.828968i
$638$	29.8744	−	29.8744i	1.18274	−	1.18274i
$639$		−	11.4641i		−	0.453513i
$640$		0			0
$641$	−14.9282			−0.589629			−0.294814	−	0.955555i	$-0.595258\pi$
$641$	−14.9282			−0.589629			−0.294814	+	0.955555i	$0.595258\pi$
$642$	−6.31319	+	6.31319i	−0.249162	+	0.249162i
$643$	4.41851	+	4.41851i	0.174249	+	0.174249i	0.788843	−	0.614594i	$-0.210680\pi$
$643$	4.41851	+	4.41851i	0.174249	+	0.174249i	−0.614594	+	0.788843i	$0.710680\pi$
$644$	1.73205	+	2.00000i	0.0682524	+	0.0788110i
$645$		0			0
$646$	−37.3205			−1.46836
$647$	27.8038	−	27.8038i	1.09308	−	1.09308i	0.0978821	−	0.995198i	$-0.468793\pi$
$647$	27.8038	−	27.8038i	1.09308	−	1.09308i	0.995198	−	0.0978821i	$-0.0312068\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−39.3205			−1.54346
$650$		0			0
$651$	−15.8564	+	13.7321i	−0.621462	+	0.538202i
$652$	−0.568406	−	0.568406i	−0.0222605	−	0.0222605i
$653$	16.3142	−	16.3142i	0.638425	−	0.638425i	−0.311742	−	0.950167i	$-0.600912\pi$
$653$	16.3142	−	16.3142i	0.638425	−	0.638425i	0.950167	+	0.311742i	$0.100912\pi$
$654$	12.3923			0.484577
$655$		0			0
$656$			5.73205i			0.223799i
$657$	8.76268	−	8.76268i	0.341865	−	0.341865i
$658$	22.1469	+	1.59008i	0.863378	+	0.0619877i
$659$		−	7.85641i		−	0.306042i	−0.988223	−	0.153021i	$-0.951100\pi$
$659$		−	7.85641i		−	0.306042i	0.988223	−	0.153021i	$-0.0489002\pi$
$660$		0			0
$661$			4.92820i			0.191685i	0.995397	+	0.0958424i	$0.0305545\pi$
$661$			4.92820i			0.191685i	−0.995397	+	0.0958424i	$0.969446\pi$
$662$	−21.4398	−	21.4398i	−0.833283	−	0.833283i
$663$	−13.1948	−	13.1948i	−0.512443	−	0.512443i
$664$	−0.464102			−0.0180106
$665$		0			0
$666$	6.92820			0.268462
$667$	5.46739	+	5.46739i	0.211698	+	0.211698i
$668$	10.9348	+	10.9348i	0.423079	+	0.423079i
$669$			11.5885i			0.448036i
$670$		0			0
$671$		−	13.4641i		−	0.519776i
$672$	0.189469	−	2.63896i	0.00730891	−	0.101800i
$673$	−28.3722	+	28.3722i	−1.09367	+	1.09367i	−0.0985345	+	0.995134i	$0.531415\pi$
$673$	−28.3722	+	28.3722i	−1.09367	+	1.09367i	−0.995134	+	0.0985345i	$0.968585\pi$
$674$		−	22.2679i		−	0.857729i
$675$		0			0
$676$	−0.928203			−0.0357001
$677$	20.7327	−	20.7327i	0.796824	−	0.796824i	−0.185770	−	0.982593i	$-0.559478\pi$
$677$	20.7327	−	20.7327i	0.796824	−	0.796824i	0.982593	+	0.185770i	$0.0594779\pi$
$678$	1.79315	+	1.79315i	0.0688655	+	0.0688655i
$679$	6.14359	−	5.32051i	0.235769	−	0.204182i
$680$		0			0
$681$	1.39230			0.0533532
$682$	30.6322	−	30.6322i	1.17297	−	1.17297i
$683$	−24.6980	+	24.6980i	−0.945042	+	0.945042i	−0.998567	−	0.0535250i	$-0.982954\pi$
$683$	−24.6980	+	24.6980i	−0.945042	+	0.945042i	0.0535250	+	0.998567i	$0.482954\pi$
$684$	−7.46410			−0.285397
$685$		0			0
$686$	10.0000	+	15.5885i	0.381802	+	0.595170i
$687$	10.6574	+	10.6574i	0.406604	+	0.406604i
$688$	−2.63896	+	2.63896i	−0.100609	+	0.100609i
$689$	13.1962			0.502733
$690$		0			0
$691$		−	51.1769i		−	1.94686i	−0.228981	−	0.973431i	$-0.573540\pi$
$691$		−	51.1769i		−	1.94686i	0.228981	−	0.973431i	$-0.426460\pi$
$692$	6.59059	−	6.59059i	0.250537	−	0.250537i
$693$	1.03528	−	14.4195i	0.0393269	−	0.547753i
$694$		−	4.53590i		−	0.172180i
$695$		0			0
$696$		−	7.73205i		−	0.293083i
$697$	20.2659	+	20.2659i	0.767624	+	0.767624i
$698$	−3.25813	−	3.25813i	−0.123322	−	0.123322i
$699$	10.3923			0.393073
$700$		0			0
$701$	−19.9808			−0.754663			−0.377331	−	0.926078i	$-0.623158\pi$
$701$	−19.9808			−0.754663			−0.377331	+	0.926078i	$0.623158\pi$
$702$	−2.63896	−	2.63896i	−0.0996011	−	0.0996011i
$703$	−36.5665	−	36.5665i	−1.37913	−	1.37913i
$704$			5.46410i			0.205936i
$705$		0			0
$706$			12.9282i			0.486559i
$707$	1.23835	−	17.2480i	0.0465729	−	0.648676i
$708$	−5.08845	+	5.08845i	−0.191236	+	0.191236i
$709$		−	15.0718i		−	0.566033i	−0.959115	−	0.283017i	$-0.908665\pi$
$709$		−	15.0718i		−	0.566033i	0.959115	−	0.283017i	$-0.0913352\pi$
$710$		0			0
$711$	−12.3923			−0.464748
$712$	−8.48528	+	8.48528i	−0.317999	+	0.317999i
$713$	5.60609	+	5.60609i	0.209950	+	0.209950i
$714$	−8.66025	−	10.0000i	−0.324102	−	0.374241i
$715$		0			0
$716$	−13.8564			−0.517838
$717$	6.03579	−	6.03579i	0.225411	−	0.225411i
$718$	−25.5438	+	25.5438i	−0.953285	+	0.953285i
$719$	19.3205			0.720533			0.360267	−	0.932849i	$-0.382686\pi$
$719$	19.3205			0.720533			0.360267	+	0.932849i	$0.382686\pi$
$720$		0			0
$721$	−7.14359	−	8.24871i	−0.266041	−	0.307198i
$722$	25.9599	+	25.9599i	0.966127	+	0.966127i
$723$	−0.656339	+	0.656339i	−0.0244095	+	0.0244095i
$724$	−2.00000			−0.0743294
$725$		0			0
$726$			18.8564i			0.699827i
$727$	−3.49837	+	3.49837i	−0.129747	+	0.129747i	−0.768998	−	0.639251i	$-0.779245\pi$
$727$	−3.49837	+	3.49837i	−0.129747	+	0.129747i	0.639251	+	0.768998i	$0.279245\pi$
$728$	−9.84873	−	0.707107i	−0.365018	−	0.0262071i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			18.6603i			0.690174i
$732$	−1.74238	−	1.74238i	−0.0644003	−	0.0644003i
$733$	0.189469	+	0.189469i	0.00699819	+	0.00699819i	0.710597	−	0.703599i	$-0.248425\pi$
$733$	0.189469	+	0.189469i	0.00699819	+	0.00699819i	−0.703599	+	0.710597i	$0.748425\pi$
$734$	−10.8038			−0.398777
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	24.6980	+	24.6980i	0.909761	+	0.909761i
$738$	4.05317	+	4.05317i	0.149199	+	0.149199i
$739$		−	12.3205i		−	0.453217i	−0.973986	−	0.226609i	$-0.927236\pi$
$739$		−	12.3205i		−	0.453217i	0.973986	−	0.226609i	$-0.0727638\pi$
$740$		0			0
$741$			27.8564i			1.02333i
$742$	9.33109	+	0.669942i	0.342555	+	0.0245943i
$743$	−25.2020	+	25.2020i	−0.924572	+	0.924572i	−0.997348	−	0.0727764i	$-0.976814\pi$
$743$	−25.2020	+	25.2020i	−0.924572	+	0.924572i	0.0727764	+	0.997348i	$0.476814\pi$
$744$		−	7.92820i		−	0.290662i
$745$		0			0
$746$	−15.3205			−0.560924
$747$	−0.328169	+	0.328169i	−0.0120071	+	0.0120071i
$748$	19.3185	+	19.3185i	0.706355	+	0.706355i
$749$	15.4641	+	17.8564i	0.565046	+	0.652459i
$750$		0			0
$751$	−37.1769			−1.35660			−0.678302	−	0.734783i	$-0.737284\pi$
$751$	−37.1769			−1.35660			−0.678302	+	0.734783i	$0.737284\pi$
$752$	−5.93426	+	5.93426i	−0.216400	+	0.216400i
$753$	−14.3316	+	14.3316i	−0.522273	+	0.522273i
$754$	−28.8564			−1.05089
$755$		0			0
$756$	−1.73205	−	2.00000i	−0.0629941	−	0.0727393i
$757$	25.5302	+	25.5302i	0.927910	+	0.927910i	0.997571	−	0.0696608i	$-0.0221917\pi$
$757$	25.5302	+	25.5302i	0.927910	+	0.927910i	−0.0696608	+	0.997571i	$0.522192\pi$
$758$	−13.7124	+	13.7124i	−0.498058	+	0.498058i
$759$	−5.46410			−0.198334
$760$		0			0
$761$		−	13.8564i		−	0.502294i	−0.967949	−	0.251147i	$-0.919192\pi$
$761$		−	13.8564i		−	0.502294i	0.967949	−	0.251147i	$-0.0808078\pi$
$762$	5.27792	−	5.27792i	0.191199	−	0.191199i
$763$	2.34795	−	32.7028i	0.0850016	−	1.18392i
$764$			6.26795i			0.226766i
$765$		0			0
$766$		−	29.7128i		−	1.07357i
$767$	18.9903	+	18.9903i	0.685702	+	0.685702i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	15.3205			0.552472			0.276236	−	0.961090i	$-0.410913\pi$
$769$	15.3205			0.552472			0.276236	+	0.961090i	$0.410913\pi$
$770$		0			0
$771$	23.9282			0.861753
$772$	12.6264	+	12.6264i	0.454434	+	0.454434i
$773$	−5.37945	−	5.37945i	−0.193485	−	0.193485i	0.603715	−	0.797200i	$-0.293687\pi$
$773$	−5.37945	−	5.37945i	−0.193485	−	0.193485i	−0.797200	+	0.603715i	$0.793687\pi$
$774$			3.73205i			0.134146i
$775$		0			0
$776$			3.07180i			0.110271i
$777$	1.31268	−	18.2832i	0.0470920	−	0.655908i
$778$	−19.0411	+	19.0411i	−0.682657	+	0.682657i
$779$		−	42.7846i		−	1.53292i
$780$		0			0
$781$	62.6410			2.24147
$782$	−3.53553	+	3.53553i	−0.126430	+	0.126430i
$783$	−5.46739	−	5.46739i	−0.195388	−	0.195388i
$784$	−6.92820	−	1.00000i	−0.247436	−	0.0357143i
$785$		0			0
$786$	14.3923			0.513357
$787$	−13.0053	+	13.0053i	−0.463590	+	0.463590i	−0.899830	−	0.436240i	$-0.856310\pi$
$787$	−13.0053	+	13.0053i	−0.463590	+	0.463590i	0.436240	+	0.899830i	$0.356310\pi$
$788$	−5.22715	+	5.22715i	−0.186209	+	0.186209i
$789$	−7.00000			−0.249207
$790$		0			0
$791$	5.07180	−	4.39230i	0.180332	−	0.156172i
$792$	3.86370	+	3.86370i	0.137291	+	0.137291i
$793$	−6.50266	+	6.50266i	−0.230916	+	0.230916i
$794$	−10.1244			−0.359300
$795$		0			0
$796$			16.0000i			0.567105i
$797$	27.8038	−	27.8038i	0.984861	−	0.984861i	−0.0150261	−	0.999887i	$-0.504783\pi$
$797$	27.8038	−	27.8038i	0.984861	−	0.984861i	0.999887	+	0.0150261i	$0.00478312\pi$
$798$	−1.41421	+	19.6975i	−0.0500626	+	0.697282i
$799$			41.9615i			1.48449i
$800$		0			0
$801$			12.0000i			0.423999i
$802$	−9.41902	−	9.41902i	−0.332597	−	0.332597i
$803$	47.8802	+	47.8802i	1.68966	+	1.68966i
$804$	6.39230			0.225439
$805$		0			0
$806$	−29.5885			−1.04221
$807$	−15.4548	−	15.4548i	−0.544035	−	0.544035i
$808$	4.62158	+	4.62158i	0.162587	+	0.162587i
$809$			2.53590i			0.0891574i	0.999006	+	0.0445787i	$0.0141946\pi$
$809$			2.53590i			0.0891574i	−0.999006	+	0.0445787i	$0.985805\pi$
$810$		0			0
$811$			6.53590i			0.229506i	0.993394	+	0.114753i	$0.0366077\pi$
$811$			6.53590i			0.229506i	−0.993394	+	0.114753i	$0.963392\pi$
$812$	−20.4046	−	1.46498i	−0.716060	−	0.0514108i
$813$	2.07055	−	2.07055i	0.0726174	−	0.0726174i
$814$			37.8564i			1.32687i
$815$		0			0
$816$	5.00000			0.175035
$817$	19.6975	−	19.6975i	0.689127	−	0.689127i
$818$	−14.4195	−	14.4195i	−0.504167	−	0.504167i
$819$	−7.46410	+	6.46410i	−0.260817	+	0.225874i
$820$		0			0
$821$	−0.784610			−0.0273831			−0.0136915	−	0.999906i	$-0.504358\pi$
$821$	−0.784610			−0.0273831			−0.0136915	+	0.999906i	$0.504358\pi$
$822$	−5.55532	+	5.55532i	−0.193764	+	0.193764i
$823$	32.9058	−	32.9058i	1.14703	−	1.14703i	0.159891	−	0.987135i	$-0.448886\pi$
$823$	32.9058	−	32.9058i	1.14703	−	1.14703i	0.987135	−	0.159891i	$-0.0511143\pi$
$824$	4.12436			0.143679
$825$		0			0
$826$	12.4641	+	14.3923i	0.433682	+	0.500772i
$827$	7.17260	+	7.17260i	0.249416	+	0.249416i	0.820731	−	0.571315i	$-0.193567\pi$
$827$	7.17260	+	7.17260i	0.249416	+	0.249416i	−0.571315	+	0.820731i	$0.693567\pi$
$828$	−0.707107	+	0.707107i	−0.0245737	+	0.0245737i
$829$	−12.1769			−0.422922			−0.211461	−	0.977386i	$-0.567822\pi$
$829$	−12.1769			−0.422922			−0.211461	+	0.977386i	$0.567822\pi$
$830$		0			0
$831$		−	8.39230i		−	0.291126i
$832$	2.63896	−	2.63896i	0.0914894	−	0.0914894i
$833$	−28.0304	+	20.9594i	−0.971197	+	0.726199i
$834$		−	19.8564i		−	0.687571i
$835$		0			0
$836$		−	40.7846i		−	1.41057i
$837$	−5.60609	−	5.60609i	−0.193775	−	0.193775i
$838$	−12.2611	−	12.2611i	−0.423551	−	0.423551i
$839$	18.6795			0.644888			0.322444	−	0.946589i	$-0.395496\pi$
$839$	18.6795			0.644888			0.322444	+	0.946589i	$0.395496\pi$
$840$		0			0
$841$	−30.7846			−1.06154
$842$	−20.7327	−	20.7327i	−0.714497	−	0.714497i
$843$	9.79796	+	9.79796i	0.337460	+	0.337460i
$844$		−	10.3205i		−	0.355247i
$845$		0			0
$846$			8.39230i			0.288533i
$847$	49.7613	+	3.57270i	1.70982	+	0.122759i
$848$	−2.50026	+	2.50026i	−0.0858592	+	0.0858592i
$849$			22.7846i			0.781966i
$850$		0			0
$851$	−6.92820			−0.237496
$852$	8.10634	−	8.10634i	0.277719	−	0.277719i
$853$	12.2611	+	12.2611i	0.419810	+	0.419810i	0.885138	−	0.465328i	$-0.154064\pi$
$853$	12.2611	+	12.2611i	0.419810	+	0.419810i	−0.465328	+	0.885138i	$0.654064\pi$
$854$	−4.92820	+	4.26795i	−0.168640	+	0.146046i
$855$		0			0
$856$	−8.92820			−0.305160
$857$	−9.69642	+	9.69642i	−0.331224	+	0.331224i	−0.853051	−	0.521828i	$-0.825250\pi$
$857$	−9.69642	+	9.69642i	−0.331224	+	0.331224i	0.521828	+	0.853051i	$0.325250\pi$
$858$	14.4195	−	14.4195i	0.492275	−	0.492275i
$859$	46.6410			1.59137			0.795685	−	0.605710i	$-0.207111\pi$
$859$	46.6410			1.59137			0.795685	+	0.605710i	$0.207111\pi$
$860$		0			0
$861$	11.4641	−	9.92820i	0.390696	−	0.338352i
$862$	−4.81105	−	4.81105i	−0.163865	−	0.163865i
$863$	31.4644	−	31.4644i	1.07106	−	1.07106i	0.0737877	−	0.997274i	$-0.476491\pi$
$863$	31.4644	−	31.4644i	1.07106	−	1.07106i	0.997274	−	0.0737877i	$-0.0235087\pi$
$864$	1.00000			0.0340207
$865$		0			0
$866$		−	0.535898i		−	0.0182106i
$867$	5.65685	−	5.65685i	0.192117	−	0.192117i
$868$	−20.9222	−	1.50215i	−0.710146	−	0.0509862i
$869$		−	67.7128i		−	2.29700i
$870$		0			0
$871$		−	23.8564i		−	0.808343i
$872$	8.76268	+	8.76268i	0.296742	+	0.296742i
$873$	2.17209	+	2.17209i	0.0735141	+	0.0735141i
$874$	7.46410			0.252477
$875$		0			0
$876$	12.3923			0.418697
$877$	−16.9706	−	16.9706i	−0.573055	−	0.573055i	0.359926	−	0.932981i	$-0.382802\pi$
$877$	−16.9706	−	16.9706i	−0.573055	−	0.573055i	−0.932981	+	0.359926i	$0.882802\pi$
$878$	28.1320	+	28.1320i	0.949408	+	0.949408i
$879$			1.85641i			0.0626150i
$880$		0			0
$881$			6.51666i			0.219552i	0.993956	+	0.109776i	$0.0350133\pi$
$881$			6.51666i			0.219552i	−0.993956	+	0.109776i	$0.964987\pi$
$882$	−5.60609	+	4.19187i	−0.188767	+	0.141148i
$883$	−13.5737	+	13.5737i	−0.456792	+	0.456792i	−0.897601	−	0.440809i	$-0.854692\pi$
$883$	−13.5737	+	13.5737i	−0.456792	+	0.456792i	0.440809	+	0.897601i	$0.354692\pi$
$884$		−	18.6603i		−	0.627612i
$885$		0			0
$886$	10.2487			0.344312
$887$	−4.89898	+	4.89898i	−0.164492	+	0.164492i	−0.784553	−	0.620062i	$-0.787108\pi$
$887$	−4.89898	+	4.89898i	−0.164492	+	0.164492i	0.620062	+	0.784553i	$0.287108\pi$
$888$	4.89898	+	4.89898i	0.164399	+	0.164399i
$889$	−12.9282	−	14.9282i	−0.433598	−	0.500676i
$890$		0			0
$891$	5.46410			0.183054
$892$	−8.19428	+	8.19428i	−0.274365	+	0.274365i
$893$	44.2939	−	44.2939i	1.48224	−	1.48224i
$894$	7.73205			0.258598
$895$		0			0
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$	2.63896	+	2.63896i	0.0881123	+	0.0881123i
$898$	21.7680	−	21.7680i	0.726408	−	0.726408i
$899$	−61.3013			−2.04451
$900$		0			0
$901$			17.6795i			0.588989i
$902$	−22.1469	+	22.1469i	−0.737413	+	0.737413i
$903$	9.84873	+	0.707107i	0.327745	+	0.0235310i
$904$			2.53590i			0.0843427i
$905$		0			0
$906$			16.0000i			0.531564i
$907$	22.9928	+	22.9928i	0.763462	+	0.763462i	0.976946	−	0.213485i	$-0.0684813\pi$
$907$	22.9928	+	22.9928i	0.763462	+	0.763462i	−0.213485	+	0.976946i	$0.568481\pi$
$908$	0.984508	+	0.984508i	0.0326721	+	0.0326721i
$909$	6.53590			0.216782
$910$		0			0
$911$	22.5167			0.746010			0.373005	−	0.927829i	$-0.378327\pi$
$911$	22.5167			0.746010			0.373005	+	0.927829i	$0.378327\pi$
$912$	−5.27792	−	5.27792i	−0.174769	−	0.174769i
$913$	−1.79315	−	1.79315i	−0.0593446	−	0.0593446i
$914$		−	22.8038i		−	0.754284i
$915$		0			0
$916$			15.0718i			0.497986i
$917$	2.72689	−	37.9807i	0.0900499	−	1.25423i
$918$	3.53553	−	3.53553i	0.116690	−	0.116690i
$919$		−	1.60770i		−	0.0530330i	−0.999648	−	0.0265165i	$-0.991559\pi$
$919$		−	1.60770i		−	0.0530330i	0.999648	−	0.0265165i	$-0.00844145\pi$
$920$		0			0
$921$	5.07180			0.167121
$922$	8.20788	−	8.20788i	0.270312	−	0.270312i
$923$	−30.2533	−	30.2533i	−0.995799	−	0.995799i
$924$	10.9282	−	9.46410i	0.359511	−	0.311346i
$925$		0			0
$926$	21.3205			0.700635
$927$	2.91636	−	2.91636i	0.0957858	−	0.0957858i
$928$	5.46739	−	5.46739i	0.179476	−	0.179476i
$929$	−16.9090			−0.554765			−0.277383	−	0.960760i	$-0.589467\pi$
$929$	−16.9090			−0.554765			−0.277383	+	0.960760i	$0.589467\pi$
$930$		0			0
$931$	51.7128	+	7.46410i	1.69482	+	0.244626i
$932$	7.34847	+	7.34847i	0.240707	+	0.240707i
$933$	−18.2832	+	18.2832i	−0.598566	+	0.598566i
$934$	−21.5359			−0.704676
$935$		0			0
$936$		−	3.73205i		−	0.121986i
$937$	−19.7990	+	19.7990i	−0.646805	+	0.646805i	−0.952219	−	0.305415i	$-0.901205\pi$
$937$	−19.7990	+	19.7990i	−0.646805	+	0.646805i	0.305415	+	0.952219i	$0.401205\pi$
$938$	1.21114	−	16.8690i	0.0395452	−	0.550793i
$939$		−	30.2487i		−	0.987129i
$940$		0			0
$941$		−	13.0718i		−	0.426128i	−0.977038	−	0.213064i	$-0.931656\pi$
$941$		−	13.0718i		−	0.426128i	0.977038	−	0.213064i	$-0.0683443\pi$
$942$	5.65685	+	5.65685i	0.184310	+	0.184310i
$943$	−4.05317	−	4.05317i	−0.131989	−	0.131989i
$944$	−7.19615			−0.234215
$945$		0			0
$946$	−20.3923			−0.663011
$947$	42.3992	+	42.3992i	1.37779	+	1.37779i	0.848345	+	0.529444i	$0.177599\pi$
$947$	42.3992	+	42.3992i	1.37779	+	1.37779i	0.529444	+	0.848345i	$0.322401\pi$
$948$	−8.76268	−	8.76268i	−0.284599	−	0.284599i
$949$		−	46.2487i		−	1.50130i
$950$		0			0
$951$		−	27.3923i		−	0.888256i
$952$	0.947343	−	13.1948i	0.0307036	−	0.427646i
$953$	31.1127	−	31.1127i	1.00784	−	1.00784i	0.00787013	−	0.999969i	$-0.497495\pi$
$953$	31.1127	−	31.1127i	1.00784	−	1.00784i	0.999969	−	0.00787013i	$-0.00250517\pi$
$954$			3.53590i			0.114479i
$955$		0			0
$956$	8.53590			0.276071
$957$	29.8744	−	29.8744i	0.965701	−	0.965701i
$958$	−0.656339	−	0.656339i	−0.0212053	−	0.0212053i
$959$	13.6077	+	15.7128i	0.439415	+	0.507393i
$960$		0			0
$961$	−31.8564			−1.02763
$962$	18.2832	−	18.2832i	0.589475	−	0.589475i
$963$	−6.31319	+	6.31319i	−0.203440	+	0.203440i
$964$	−0.928203			−0.0298954
$965$		0			0
$966$	1.73205	+	2.00000i	0.0557278	+	0.0643489i
$967$	−10.6574	−	10.6574i	−0.342718	−	0.342718i	0.514670	−	0.857388i	$-0.327914\pi$
$967$	−10.6574	−	10.6574i	−0.342718	−	0.342718i	−0.857388	+	0.514670i	$0.827914\pi$
$968$	−13.3335	+	13.3335i	−0.428555	+	0.428555i
$969$	−37.3205			−1.19891
$970$		0			0
$971$			11.4641i			0.367901i	0.982936	+	0.183950i	$0.0588885\pi$
$971$			11.4641i			0.367901i	−0.982936	+	0.183950i	$0.941111\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−52.4002	−	3.76217i	−1.67987	−	0.120610i
$974$			38.0000i			1.21760i
$975$		0			0
$976$		−	2.46410i		−	0.0788740i
$977$	23.1822	+	23.1822i	0.741665	+	0.741665i	0.972898	−	0.231233i	$-0.0742761\pi$
$977$	23.1822	+	23.1822i	0.741665	+	0.741665i	−0.231233	+	0.972898i	$0.574276\pi$
$978$	−0.568406	−	0.568406i	−0.0181756	−	0.0181756i
$979$	−65.5692			−2.09560
$980$		0			0
$981$	12.3923			0.395656
$982$	6.59059	+	6.59059i	0.210314	+	0.210314i
$983$	5.10205	+	5.10205i	0.162730	+	0.162730i	0.783775	−	0.621045i	$-0.213292\pi$
$983$	5.10205	+	5.10205i	0.162730	+	0.162730i	−0.621045	+	0.783775i	$0.713292\pi$
$984$			5.73205i			0.182731i
$985$		0			0
$986$		−	38.6603i		−	1.23119i
$987$	22.1469	+	1.59008i	0.704945	+	0.0506128i
$988$	−19.6975	+	19.6975i	−0.626659	+	0.626659i
$989$		−	3.73205i		−	0.118672i
$990$		0			0
$991$	15.3205			0.486672			0.243336	−	0.969942i	$-0.421758\pi$
$991$	15.3205			0.486672			0.243336	+	0.969942i	$0.421758\pi$
$992$	5.60609	−	5.60609i	0.177993	−	0.177993i
$993$	−21.4398	−	21.4398i	−0.680373	−	0.680373i
$994$	−19.8564	−	22.9282i	−0.629807	−	0.727238i
$995$		0			0
$996$	−0.464102			−0.0147056
$997$	16.9706	−	16.9706i	0.537463	−	0.537463i	−0.385320	−	0.922783i	$-0.625909\pi$
$997$	16.9706	−	16.9706i	0.537463	−	0.537463i	0.922783	+	0.385320i	$0.125909\pi$
$998$	2.39872	−	2.39872i	0.0759302	−	0.0759302i
$999$	6.92820			0.219199

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.m.d.307.4	yes	8
5.2	odd	4		1050.2.m.c.643.2	yes	8
5.3	odd	4		1050.2.m.c.643.3	yes	8
5.4	even	2	inner	1050.2.m.d.307.1	yes	8
7.6	odd	2		1050.2.m.c.307.3	yes	8
35.13	even	4	inner	1050.2.m.d.643.4	yes	8
35.27	even	4	inner	1050.2.m.d.643.1	yes	8
35.34	odd	2		1050.2.m.c.307.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.m.c.307.2	✓	8	35.34	odd	2
1050.2.m.c.307.3	yes	8	7.6	odd	2
1050.2.m.c.643.2	yes	8	5.2	odd	4
1050.2.m.c.643.3	yes	8	5.3	odd	4
1050.2.m.d.307.1	yes	8	5.4	even	2	inner
1050.2.m.d.307.4	yes	8	1.1	even	1	trivial
1050.2.m.d.643.1	yes	8	35.27	even	4	inner
1050.2.m.d.643.4	yes	8	35.13	even	4	inner

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.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +1.00000i q^{6} +(2.63896 + 0.189469i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +1.00000i q^{6} +(2.63896 + 0.189469i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} -5.46410 q^{11} +(-0.707107 + 0.707107i) q^{12} +(2.63896 + 2.63896i) q^{13} +(1.73205 + 2.00000i) q^{14} -1.00000 q^{16} +(-3.53553 + 3.53553i) q^{17} +(-0.707107 + 0.707107i) q^{18} +7.46410 q^{19} +(1.73205 + 2.00000i) q^{21} +(-3.86370 - 3.86370i) q^{22} +(0.707107 - 0.707107i) q^{23} -1.00000 q^{24} +3.73205i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.189469 + 2.63896i) q^{28} +7.73205i q^{29} +7.92820i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.86370 - 3.86370i) q^{33} -5.00000 q^{34} -1.00000 q^{36} +(-4.89898 - 4.89898i) q^{37} +(5.27792 + 5.27792i) q^{38} +3.73205i q^{39} -5.73205i q^{41} +(-0.189469 + 2.63896i) q^{42} +(2.63896 - 2.63896i) q^{43} -5.46410i q^{44} +1.00000 q^{46} +(5.93426 - 5.93426i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(6.92820 + 1.00000i) q^{49} -5.00000 q^{51} +(-2.63896 + 2.63896i) q^{52} +(2.50026 - 2.50026i) q^{53} -1.00000 q^{54} +(-2.00000 + 1.73205i) q^{56} +(5.27792 + 5.27792i) q^{57} +(-5.46739 + 5.46739i) q^{58} +7.19615 q^{59} +2.46410i q^{61} +(-5.60609 + 5.60609i) q^{62} +(-0.189469 + 2.63896i) q^{63} -1.00000i q^{64} -5.46410i q^{66} +(-4.52004 - 4.52004i) q^{67} +(-3.53553 - 3.53553i) q^{68} +1.00000 q^{69} -11.4641 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-8.76268 - 8.76268i) q^{73} -6.92820i q^{74} +7.46410i q^{76} +(-14.4195 - 1.03528i) q^{77} +(-2.63896 + 2.63896i) q^{78} +12.3923i q^{79} -1.00000 q^{81} +(4.05317 - 4.05317i) q^{82} +(0.328169 + 0.328169i) q^{83} +(-2.00000 + 1.73205i) q^{84} +3.73205 q^{86} +(-5.46739 + 5.46739i) q^{87} +(3.86370 - 3.86370i) q^{88} +12.0000 q^{89} +(6.46410 + 7.46410i) q^{91} +(0.707107 + 0.707107i) q^{92} +(-5.60609 + 5.60609i) q^{93} +8.39230 q^{94} -1.00000i q^{96} +(2.17209 - 2.17209i) q^{97} +(4.19187 + 5.60609i) q^{98} -5.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 16 q^{11} - 8 q^{16} + 32 q^{19} - 8 q^{24} - 40 q^{34} - 8 q^{36} + 8 q^{46} - 40 q^{51} - 8 q^{54} - 16 q^{56} + 16 q^{59} + 8 q^{69} - 64 q^{71} - 8 q^{81} - 16 q^{84} + 16 q^{86} + 96 q^{89} + 24 q^{91} - 16 q^{94}+O(q^{100}) \) 8 * q - 16 * q^11 - 8 * q^16 + 32 * q^19 - 8 * q^24 - 40 * q^34 - 8 * q^36 + 8 * q^46 - 40 * q^51 - 8 * q^54 - 16 * q^56 + 16 * q^59 + 8 * q^69 - 64 * q^71 - 8 * q^81 - 16 * q^84 + 16 * q^86 + 96 * q^89 + 24 * q^91 - 16 * q^94

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