LMFDB - Embedded newform 1150.2.e.b.1057.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(643,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("1150.643");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.e (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:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.110166016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 $ x^8 + 10x^6 + 19x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.3
Root			$0.360409i$ of defining polynomial
Character	$\chi$	$=$	1150.1057
Dual form			1150.2.e.b.643.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.254848 + 0.254848i) q^{3} +1.00000i q^{4} -0.360409 q^{6} +(-0.812668 + 0.812668i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.87011i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.254848 + 0.254848i) q^{3} +1.00000i q^{4} -0.360409 q^{6} +(-0.812668 + 0.812668i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.87011i q^{9} -3.05380i q^{11} +(-0.254848 - 0.254848i) q^{12} +(-0.697028 + 0.697028i) q^{13} -1.14929 q^{14} -1.00000 q^{16} +(-2.89444 + 2.89444i) q^{17} +(-2.02947 + 2.02947i) q^{18} -2.26493 q^{19} -0.414214i q^{21} +(2.15937 - 2.15937i) q^{22} +(-1.84214 + 4.42793i) q^{23} -0.360409i q^{24} -0.985746 q^{26} +(-1.49598 - 1.49598i) q^{27} +(-0.812668 - 0.812668i) q^{28} +6.96346i q^{29} -0.938164 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.778256 + 0.778256i) q^{33} -4.09335 q^{34} -2.87011 q^{36} +(4.39193 - 4.39193i) q^{37} +(-1.60155 - 1.60155i) q^{38} -0.355272i q^{39} -3.69853 q^{41} +(0.292893 - 0.292893i) q^{42} +(-2.58289 - 2.58289i) q^{43} +3.05380 q^{44} +(-4.43361 + 1.82843i) q^{46} +(-0.923909 - 0.923909i) q^{47} +(0.254848 - 0.254848i) q^{48} +5.67914i q^{49} -1.47528i q^{51} +(-0.697028 - 0.697028i) q^{52} +(-8.88737 - 8.88737i) q^{53} -2.11564i q^{54} -1.14929i q^{56} +(0.577212 - 0.577212i) q^{57} +(-4.92391 + 4.92391i) q^{58} +4.22248i q^{59} +10.6590i q^{61} +(-0.663382 - 0.663382i) q^{62} +(-2.33244 - 2.33244i) q^{63} -1.00000i q^{64} +1.10062i q^{66} +(2.79478 - 2.79478i) q^{67} +(-2.89444 - 2.89444i) q^{68} +(-0.658982 - 1.59791i) q^{69} +4.55438 q^{71} +(-2.02947 - 2.02947i) q^{72} +(-0.803131 + 0.803131i) q^{73} +6.21112 q^{74} -2.26493i q^{76} +(2.48173 + 2.48173i) q^{77} +(0.251215 - 0.251215i) q^{78} -16.8702 q^{79} -7.84782 q^{81} +(-2.61526 - 2.61526i) q^{82} +(8.37177 + 8.37177i) q^{83} +0.414214 q^{84} -3.65276i q^{86} +(-1.77462 - 1.77462i) q^{87} +(2.15937 + 2.15937i) q^{88} +9.61955 q^{89} -1.13290i q^{91} +(-4.42793 - 1.84214i) q^{92} +(0.239089 - 0.239089i) q^{93} -1.30661i q^{94} +0.360409 q^{96} +(-4.17254 + 4.17254i) q^{97} +(-4.01576 + 4.01576i) q^{98} +8.76474 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{6}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^6	$ 8 q + 4 q^{3} + 4 q^{6} + 4 q^{12} - 4 q^{14} - 8 q^{16} - 24 q^{17} + 8 q^{18} - 12 q^{19} + 12 q^{22} + 16 q^{23} + 12 q^{26} - 8 q^{27} - 4 q^{31} - 20 q^{33} - 4 q^{34} - 4 q^{36} - 4 q^{37} - 8 q^{38} + 12 q^{41} + 8 q^{42} + 20 q^{43} + 20 q^{44} + 16 q^{47} - 4 q^{48} - 20 q^{57} - 16 q^{58} - 4 q^{62} + 4 q^{67} - 24 q^{68} + 12 q^{69} - 44 q^{71} + 8 q^{72} - 28 q^{73} + 48 q^{74} - 4 q^{77} + 4 q^{78} + 8 q^{79} - 16 q^{81} - 8 q^{82} + 28 q^{83} - 8 q^{84} + 4 q^{87} + 12 q^{88} - 40 q^{89} - 16 q^{92} + 12 q^{93} - 4 q^{96} + 8 q^{97} - 16 q^{98} - 36 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^6 + 4 * q^12 - 4 * q^14 - 8 * q^16 - 24 * q^17 + 8 * q^18 - 12 * q^19 + 12 * q^22 + 16 * q^23 + 12 * q^26 - 8 * q^27 - 4 * q^31 - 20 * q^33 - 4 * q^34 - 4 * q^36 - 4 * q^37 - 8 * q^38 + 12 * q^41 + 8 * q^42 + 20 * q^43 + 20 * q^44 + 16 * q^47 - 4 * q^48 - 20 * q^57 - 16 * q^58 - 4 * q^62 + 4 * q^67 - 24 * q^68 + 12 * q^69 - 44 * q^71 + 8 * q^72 - 28 * q^73 + 48 * q^74 - 4 * q^77 + 4 * q^78 + 8 * q^79 - 16 * q^81 - 8 * q^82 + 28 * q^83 - 8 * q^84 + 4 * q^87 + 12 * q^88 - 40 * q^89 - 16 * q^92 + 12 * q^93 - 4 * q^96 + 8 * q^97 - 16 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.254848	+	0.254848i	−0.147136	+	0.147136i	−0.776838	−	0.629701i	$-0.783177\pi$
$3$	−0.254848	+	0.254848i	−0.147136	+	0.147136i	0.629701	+	0.776838i	$0.283177\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−0.360409			−0.147136
$7$	−0.812668	+	0.812668i	−0.307160	+	0.307160i	−0.843807	−	0.536647i	$-0.819691\pi$
$7$	−0.812668	+	0.812668i	−0.307160	+	0.307160i	0.536647	+	0.843807i	$0.319691\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			2.87011i			0.956702i
$10$		0			0
$11$		−	3.05380i		−	0.920757i	−0.887723	−	0.460378i	$-0.847714\pi$
$11$		−	3.05380i		−	0.920757i	0.887723	−	0.460378i	$-0.152286\pi$
$12$	−0.254848	−	0.254848i	−0.0735682	−	0.0735682i
$13$	−0.697028	+	0.697028i	−0.193321	+	0.193321i	−0.797129	−	0.603809i	$-0.793649\pi$
$13$	−0.697028	+	0.697028i	−0.193321	+	0.193321i	0.603809	+	0.797129i	$0.293649\pi$
$14$	−1.14929			−0.307160
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.89444	+	2.89444i	−0.702004	+	0.702004i	−0.964841	−	0.262836i	$-0.915342\pi$
$17$	−2.89444	+	2.89444i	−0.702004	+	0.702004i	0.262836	+	0.964841i	$0.415342\pi$
$18$	−2.02947	+	2.02947i	−0.478351	+	0.478351i
$19$	−2.26493			−0.519610			−0.259805	−	0.965661i	$-0.583658\pi$
$19$	−2.26493			−0.519610			−0.259805	+	0.965661i	$0.583658\pi$
$20$		0			0
$21$		−	0.414214i		−	0.0903888i
$22$	2.15937	−	2.15937i	0.460378	−	0.460378i
$23$	−1.84214	+	4.42793i	−0.384113	+	0.923286i
$23$	−1.84214	+	4.42793i	−0.384113	+	0.923286i
$24$		−	0.360409i		−	0.0735682i
$25$		0			0
$26$	−0.985746			−0.193321
$27$	−1.49598	−	1.49598i	−0.287902	−	0.287902i
$28$	−0.812668	−	0.812668i	−0.153580	−	0.153580i
$29$			6.96346i			1.29308i	0.762879	+	0.646541i	$0.223785\pi$
$29$			6.96346i			1.29308i	−0.762879	+	0.646541i	$0.776215\pi$
$30$		0			0
$31$	−0.938164			−0.168499			−0.0842496	−	0.996445i	$-0.526849\pi$
$31$	−0.938164			−0.168499			−0.0842496	+	0.996445i	$0.526849\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.778256	+	0.778256i	0.135477	+	0.135477i
$34$	−4.09335			−0.702004
$35$		0			0
$36$	−2.87011			−0.478351
$37$	4.39193	−	4.39193i	0.722028	−	0.722028i	−0.246990	−	0.969018i	$-0.579441\pi$
$37$	4.39193	−	4.39193i	0.722028	−	0.722028i	0.969018	+	0.246990i	$0.0794414\pi$
$38$	−1.60155	−	1.60155i	−0.259805	−	0.259805i
$39$		−	0.355272i		−	0.0568890i
$40$		0			0
$41$	−3.69853			−0.577614			−0.288807	−	0.957387i	$-0.593259\pi$
$41$	−3.69853			−0.577614			−0.288807	+	0.957387i	$0.593259\pi$
$42$	0.292893	−	0.292893i	0.0451944	−	0.0451944i
$43$	−2.58289	−	2.58289i	−0.393887	−	0.393887i	0.482183	−	0.876070i	$-0.339844\pi$
$43$	−2.58289	−	2.58289i	−0.393887	−	0.393887i	−0.876070	+	0.482183i	$0.839844\pi$
$44$	3.05380			0.460378
$45$		0			0
$46$	−4.43361	+	1.82843i	−0.653699	+	0.269587i
$47$	−0.923909	−	0.923909i	−0.134766	−	0.134766i	0.636506	−	0.771272i	$-0.280379\pi$
$47$	−0.923909	−	0.923909i	−0.134766	−	0.134766i	−0.771272	+	0.636506i	$0.780379\pi$
$48$	0.254848	−	0.254848i	0.0367841	−	0.0367841i
$49$			5.67914i			0.811306i
$50$		0			0
$51$		−	1.47528i		−	0.206581i
$52$	−0.697028	−	0.697028i	−0.0966603	−	0.0966603i
$53$	−8.88737	−	8.88737i	−1.22077	−	1.22077i	−0.967357	−	0.253417i	$-0.918446\pi$
$53$	−8.88737	−	8.88737i	−1.22077	−	1.22077i	−0.253417	−	0.967357i	$-0.581554\pi$
$54$		−	2.11564i		−	0.287902i
$55$		0			0
$56$		−	1.14929i		−	0.153580i
$57$	0.577212	−	0.577212i	0.0764536	−	0.0764536i
$58$	−4.92391	+	4.92391i	−0.646541	+	0.646541i
$59$			4.22248i			0.549720i	0.961484	+	0.274860i	$0.0886316\pi$
$59$			4.22248i			0.549720i	−0.961484	+	0.274860i	$0.911368\pi$
$60$		0			0
$61$			10.6590i			1.36474i	0.731006	+	0.682371i	$0.239051\pi$
$61$			10.6590i			1.36474i	−0.731006	+	0.682371i	$0.760949\pi$
$62$	−0.663382	−	0.663382i	−0.0842496	−	0.0842496i
$63$	−2.33244	−	2.33244i	−0.293860	−	0.293860i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$			1.10062i			0.135477i
$67$	2.79478	−	2.79478i	0.341437	−	0.341437i	−0.515470	−	0.856907i	$-0.672383\pi$
$67$	2.79478	−	2.79478i	0.341437	−	0.341437i	0.856907	+	0.515470i	$0.172383\pi$
$68$	−2.89444	−	2.89444i	−0.351002	−	0.351002i
$69$	−0.658982	−	1.59791i	−0.0793321	−	0.192366i
$70$		0			0
$71$	4.55438			0.540506			0.270253	−	0.962789i	$-0.412893\pi$
$71$	4.55438			0.540506			0.270253	+	0.962789i	$0.412893\pi$
$72$	−2.02947	−	2.02947i	−0.239175	−	0.239175i
$73$	−0.803131	+	0.803131i	−0.0939994	+	0.0939994i	−0.752543	−	0.658543i	$-0.771173\pi$
$73$	−0.803131	+	0.803131i	−0.0939994	+	0.0939994i	0.658543	+	0.752543i	$0.271173\pi$
$74$	6.21112			0.722028
$75$		0			0
$76$		−	2.26493i		−	0.259805i
$77$	2.48173	+	2.48173i	0.282819	+	0.282819i
$78$	0.251215	−	0.251215i	0.0284445	−	0.0284445i
$79$	−16.8702			−1.89805			−0.949024	−	0.315204i	$-0.897927\pi$
$79$	−16.8702			−1.89805			−0.949024	+	0.315204i	$0.897927\pi$
$80$		0			0
$81$	−7.84782			−0.871980
$82$	−2.61526	−	2.61526i	−0.288807	−	0.288807i
$83$	8.37177	+	8.37177i	0.918921	+	0.918921i	0.996951	−	0.0780300i	$-0.0248630\pi$
$83$	8.37177	+	8.37177i	0.918921	+	0.918921i	−0.0780300	+	0.996951i	$0.524863\pi$
$84$	0.414214			0.0451944
$85$		0			0
$86$		−	3.65276i		−	0.393887i
$87$	−1.77462	−	1.77462i	−0.190260	−	0.190260i
$88$	2.15937	+	2.15937i	0.230189	+	0.230189i
$89$	9.61955			1.01967			0.509835	−	0.860272i	$-0.329706\pi$
$89$	9.61955			1.01967			0.509835	+	0.860272i	$0.329706\pi$
$90$		0			0
$91$		−	1.13290i		−	0.118761i
$92$	−4.42793	−	1.84214i	−0.461643	−	0.192056i
$93$	0.239089	−	0.239089i	0.0247924	−	0.0247924i
$94$		−	1.30661i		−	0.134766i
$95$		0			0
$96$	0.360409			0.0367841
$97$	−4.17254	+	4.17254i	−0.423657	+	0.423657i	−0.886461	−	0.462804i	$-0.846843\pi$
$97$	−4.17254	+	4.17254i	−0.423657	+	0.423657i	0.462804	+	0.886461i	$0.346843\pi$
$98$	−4.01576	+	4.01576i	−0.405653	+	0.405653i
$99$	8.76474			0.880889
$100$		0			0
$101$	10.6002			1.05475			0.527377	−	0.849631i	$-0.323175\pi$
$101$	10.6002			1.05475			0.527377	+	0.849631i	$0.323175\pi$
$102$	1.04318	−	1.04318i	0.103290	−	0.103290i
$103$	10.4631	+	10.4631i	1.03096	+	1.03096i	0.999505	+	0.0314522i	$0.0100132\pi$
$103$	10.4631	+	10.4631i	1.03096	+	1.03096i	0.0314522	+	0.999505i	$0.489987\pi$
$104$		−	0.985746i		−	0.0966603i
$105$		0			0
$106$		−	12.5686i		−	1.22077i
$107$	7.30661	−	7.30661i	0.706356	−	0.706356i	−0.259411	−	0.965767i	$-0.583528\pi$
$107$	7.30661	−	7.30661i	0.706356	−	0.706356i	0.965767	+	0.259411i	$0.0835284\pi$
$108$	1.49598	−	1.49598i	0.143951	−	0.143951i
$109$	−3.93013			−0.376438			−0.188219	−	0.982127i	$-0.560272\pi$
$109$	−3.93013			−0.376438			−0.188219	+	0.982127i	$0.560272\pi$
$110$		0			0
$111$			2.23855i			0.212473i
$112$	0.812668	−	0.812668i	0.0767899	−	0.0767899i
$113$	2.02016	+	2.02016i	0.190041	+	0.190041i	0.795714	−	0.605673i	$-0.207096\pi$
$113$	2.02016	+	2.02016i	0.190041	+	0.190041i	−0.605673	+	0.795714i	$0.707096\pi$
$114$	0.816301			0.0764536
$115$		0			0
$116$	−6.96346			−0.646541
$117$	−2.00054	−	2.00054i	−0.184950	−	0.184950i
$118$	−2.98575	+	2.98575i	−0.274860	+	0.274860i
$119$		−	4.70444i		−	0.431255i
$120$		0			0
$121$	1.67428			0.152207
$122$	−7.53704	+	7.53704i	−0.682371	+	0.682371i
$123$	0.942563	−	0.942563i	0.0849881	−	0.0849881i
$124$		−	0.938164i		−	0.0842496i
$125$		0			0
$126$		−	3.29857i		−	0.293860i
$127$	−5.81630	−	5.81630i	−0.516113	−	0.516113i	0.400280	−	0.916393i	$-0.368913\pi$
$127$	−5.81630	−	5.81630i	−0.516113	−	0.516113i	−0.916393	+	0.400280i	$0.868913\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	1.31649			0.115910
$130$		0			0
$131$	12.5442			1.09599			0.547997	−	0.836480i	$-0.315391\pi$
$131$	12.5442			1.09599			0.547997	+	0.836480i	$0.315391\pi$
$132$	−0.778256	+	0.778256i	−0.0677385	+	0.0677385i
$133$	1.84063	−	1.84063i	0.159603	−	0.159603i
$134$	3.95242			0.341437
$135$		0			0
$136$		−	4.09335i		−	0.351002i
$137$	−8.61881	+	8.61881i	−0.736355	+	0.736355i	−0.971870	−	0.235516i	$-0.924322\pi$
$137$	−8.61881	+	8.61881i	−0.736355	+	0.736355i	0.235516	+	0.971870i	$0.424322\pi$
$138$	0.663924	−	1.59587i	0.0565170	−	0.135849i
$139$		−	19.4875i		−	1.65291i	−0.563003	−	0.826455i	$-0.690354\pi$
$139$		−	19.4875i		−	1.65291i	0.563003	−	0.826455i	$-0.309646\pi$
$140$		0			0
$141$	0.470913			0.0396580
$142$	3.22044	+	3.22044i	0.270253	+	0.270253i
$143$	2.12859	+	2.12859i	0.178001	+	0.178001i
$144$		−	2.87011i		−	0.239175i
$145$		0			0
$146$	−1.13580			−0.0939994
$147$	−1.44732	−	1.44732i	−0.119373	−	0.119373i
$148$	4.39193	+	4.39193i	0.361014	+	0.361014i
$149$	−16.8925			−1.38389			−0.691944	−	0.721951i	$-0.743246\pi$
$149$	−16.8925			−1.38389			−0.691944	+	0.721951i	$0.743246\pi$
$150$		0			0
$151$	12.0934			0.984143			0.492072	−	0.870555i	$-0.336240\pi$
$151$	12.0934			0.984143			0.492072	+	0.870555i	$0.336240\pi$
$152$	1.60155	−	1.60155i	0.129902	−	0.129902i
$153$	−8.30734	−	8.30734i	−0.671609	−	0.671609i
$154$			3.50970i			0.282819i
$155$		0			0
$156$	0.355272			0.0284445
$157$	3.53712	−	3.53712i	0.282293	−	0.282293i	−0.551730	−	0.834023i	$-0.686032\pi$
$157$	3.53712	−	3.53712i	0.282293	−	0.282293i	0.834023	+	0.551730i	$0.186032\pi$
$158$	−11.9290	−	11.9290i	−0.949024	−	0.949024i
$159$	4.52985			0.359241
$160$		0			0
$161$	−2.10139	−	5.09548i	−0.165612	−	0.401580i
$162$	−5.54925	−	5.54925i	−0.435990	−	0.435990i
$163$	7.99239	−	7.99239i	0.626012	−	0.626012i	−0.321050	−	0.947062i	$-0.604036\pi$
$163$	7.99239	−	7.99239i	0.626012	−	0.626012i	0.947062	+	0.321050i	$0.104036\pi$
$164$		−	3.69853i		−	0.288807i
$165$		0			0
$166$			11.8395i			0.918921i
$167$	13.0165	+	13.0165i	1.00725	+	1.00725i	0.999974	+	0.00727320i	$0.00231515\pi$
$167$	13.0165	+	13.0165i	1.00725	+	1.00725i	0.00727320	+	0.999974i	$0.497685\pi$
$168$	0.292893	+	0.292893i	0.0225972	+	0.0225972i
$169$			12.0283i			0.925254i
$170$		0			0
$171$		−	6.50058i		−	0.497112i
$172$	2.58289	−	2.58289i	0.196944	−	0.196944i
$173$	6.56145	−	6.56145i	0.498858	−	0.498858i	−0.412224	−	0.911082i	$-0.635248\pi$
$173$	6.56145	−	6.56145i	0.498858	−	0.498858i	0.911082	+	0.412224i	$0.135248\pi$
$174$		−	2.50970i		−	0.190260i
$175$		0			0
$176$			3.05380i			0.230189i
$177$	−1.07609	−	1.07609i	−0.0808839	−	0.0808839i
$178$	6.80205	+	6.80205i	0.509835	+	0.509835i
$179$			1.70552i			0.127477i	0.997967	+	0.0637383i	$0.0203023\pi$
$179$			1.70552i			0.127477i	−0.997967	+	0.0637383i	$0.979698\pi$
$180$		0			0
$181$			11.8225i			0.878761i	0.898301	+	0.439381i	$0.144802\pi$
$181$			11.8225i			0.878761i	−0.898301	+	0.439381i	$0.855198\pi$
$182$	0.801084	−	0.801084i	0.0593803	−	0.0593803i
$183$	−2.71642	−	2.71642i	−0.200803	−	0.200803i
$184$	−1.82843	−	4.43361i	−0.134793	−	0.326850i
$185$		0			0
$186$	0.338123			0.0247924
$187$	8.83905	+	8.83905i	0.646375	+	0.646375i
$188$	0.923909	−	0.923909i	0.0673830	−	0.0673830i
$189$	2.43148			0.176864
$190$		0			0
$191$			15.5119i			1.12240i	0.827679	+	0.561202i	$0.189661\pi$
$191$			15.5119i			1.12240i	−0.827679	+	0.561202i	$0.810339\pi$
$192$	0.254848	+	0.254848i	0.0183921	+	0.0183921i
$193$	2.93527	−	2.93527i	0.211285	−	0.211285i	−0.593528	−	0.804813i	$-0.702265\pi$
$193$	2.93527	−	2.93527i	0.211285	−	0.211285i	0.804813	+	0.593528i	$0.202265\pi$
$194$	−5.90086			−0.423657
$195$		0			0
$196$	−5.67914			−0.405653
$197$	16.1422	+	16.1422i	1.15009	+	1.15009i	0.986535	+	0.163550i	$0.0522946\pi$
$197$	16.1422	+	16.1422i	1.15009	+	1.15009i	0.163550	+	0.986535i	$0.447705\pi$
$198$	6.19761	+	6.19761i	0.440445	+	0.440445i
$199$	21.0938			1.49530			0.747649	−	0.664094i	$-0.231182\pi$
$199$	21.0938			1.49530			0.747649	+	0.664094i	$0.231182\pi$
$200$		0			0
$201$			1.42449i			0.100476i
$202$	7.49544	+	7.49544i	0.527377	+	0.527377i
$203$	−5.65898	−	5.65898i	−0.397183	−	0.397183i
$204$	1.47528			0.103290
$205$		0			0
$206$			14.7970i			1.03096i
$207$	−12.7086	−	5.28713i	−0.883310	−	0.367481i
$208$	0.697028	−	0.697028i	0.0483302	−	0.0483302i
$209$			6.91664i			0.478434i
$210$		0			0
$211$	13.8007			0.950078			0.475039	−	0.879965i	$-0.342434\pi$
$211$	13.8007			0.950078			0.475039	+	0.879965i	$0.342434\pi$
$212$	8.88737	−	8.88737i	0.610387	−	0.610387i
$213$	−1.16067	+	1.16067i	−0.0795281	+	0.0795281i
$214$	10.3331			0.706356
$215$		0			0
$216$	2.11564			0.143951
$217$	0.762416	−	0.762416i	0.0517562	−	0.0517562i
$218$	−2.77902	−	2.77902i	−0.188219	−	0.188219i
$219$		−	0.409353i		−	0.0276615i
$220$		0			0
$221$		−	4.03501i		−	0.271424i
$222$	−1.58289	+	1.58289i	−0.106237	+	0.106237i
$223$	19.2255	−	19.2255i	1.28743	−	1.28743i	0.351094	−	0.936340i	$-0.385810\pi$
$223$	19.2255	−	19.2255i	1.28743	−	1.28743i	0.936340	−	0.351094i	$-0.114190\pi$
$224$	1.14929			0.0767899
$225$		0			0
$226$			2.85694i			0.190041i
$227$	−13.2083	+	13.2083i	−0.876668	+	0.876668i	−0.993188	−	0.116520i	$-0.962826\pi$
$227$	−13.2083	+	13.2083i	−0.876668	+	0.876668i	0.116520	+	0.993188i	$0.462826\pi$
$228$	0.577212	+	0.577212i	0.0382268	+	0.0382268i
$229$	4.10182			0.271056			0.135528	−	0.990774i	$-0.456727\pi$
$229$	4.10182			0.271056			0.135528	+	0.990774i	$0.456727\pi$
$230$		0			0
$231$	−1.26493			−0.0832261
$232$	−4.92391	−	4.92391i	−0.323270	−	0.323270i
$233$	−13.7878	+	13.7878i	−0.903268	+	0.903268i	−0.995717	−	0.0924491i	$-0.970530\pi$
$233$	−13.7878	+	13.7878i	−0.903268	+	0.903268i	0.0924491	+	0.995717i	$0.470530\pi$
$234$		−	2.82919i		−	0.184950i
$235$		0			0
$236$	−4.22248			−0.274860
$237$	4.29934	−	4.29934i	0.279272	−	0.279272i
$238$	3.32654	−	3.32654i	0.215627	−	0.215627i
$239$		−	15.3810i		−	0.994914i	−0.867489	−	0.497457i	$-0.834267\pi$
$239$		−	15.3810i		−	0.994914i	0.867489	−	0.497457i	$-0.165733\pi$
$240$		0			0
$241$		−	16.7710i		−	1.08031i	−0.841565	−	0.540156i	$-0.818365\pi$
$241$		−	16.7710i		−	1.08031i	0.841565	−	0.540156i	$-0.181635\pi$
$242$	1.18389	+	1.18389i	0.0761036	+	0.0761036i
$243$	6.48795	−	6.48795i	0.416202	−	0.416202i
$244$	−10.6590			−0.682371
$245$		0			0
$246$	1.33299			0.0849881
$247$	1.57872	−	1.57872i	0.100451	−	0.100451i
$248$	0.663382	−	0.663382i	0.0421248	−	0.0421248i
$249$	−4.26706			−0.270414
$250$		0			0
$251$			21.7250i			1.37127i	0.727945	+	0.685636i	$0.240476\pi$
$251$			21.7250i			1.37127i	−0.727945	+	0.685636i	$0.759524\pi$
$252$	2.33244	−	2.33244i	0.146930	−	0.146930i
$253$	13.5220	+	5.62553i	0.850122	+	0.353674i
$254$		−	8.22549i		−	0.516113i
$255$		0			0
$256$	1.00000			0.0625000
$257$	6.92604	+	6.92604i	0.432034	+	0.432034i	0.889320	−	0.457286i	$-0.151178\pi$
$257$	6.92604	+	6.92604i	0.432034	+	0.432034i	−0.457286	+	0.889320i	$0.651178\pi$
$258$	0.930898	+	0.930898i	0.0579552	+	0.0579552i
$259$			7.13836i			0.443556i
$260$		0			0
$261$	−19.9859			−1.23709
$262$	8.87011	+	8.87011i	0.547997	+	0.547997i
$263$	20.2550	+	20.2550i	1.24897	+	1.24897i	0.956173	+	0.292801i	$0.0945874\pi$
$263$	20.2550	+	20.2550i	1.24897	+	1.24897i	0.292801	+	0.956173i	$0.405413\pi$
$264$	−1.10062			−0.0677385
$265$		0			0
$266$	2.60305			0.159603
$267$	−2.45152	+	2.45152i	−0.150031	+	0.150031i
$268$	2.79478	+	2.79478i	0.170718	+	0.170718i
$269$		−	0.742062i		−	0.0452443i	−0.999744	−	0.0226222i	$-0.992799\pi$
$269$		−	0.742062i		−	0.0452443i	0.999744	−	0.0226222i	$-0.00720147\pi$
$270$		0			0
$271$	−1.72781			−0.104957			−0.0524784	−	0.998622i	$-0.516712\pi$
$271$	−1.72781			−0.104957			−0.0524784	+	0.998622i	$0.516712\pi$
$272$	2.89444	−	2.89444i	0.175501	−	0.175501i
$273$	0.288718	+	0.288718i	0.0174740	+	0.0174740i
$274$	−12.1888			−0.736355
$275$		0			0
$276$	1.59791	−	0.658982i	0.0961830	−	0.0396661i
$277$	−8.96755	−	8.96755i	−0.538808	−	0.538808i	0.384371	−	0.923179i	$-0.374418\pi$
$277$	−8.96755	−	8.96755i	−0.538808	−	0.538808i	−0.923179	+	0.384371i	$0.874418\pi$
$278$	13.7798	−	13.7798i	0.826455	−	0.826455i
$279$		−	2.69263i		−	0.161203i
$280$		0			0
$281$		−	29.4648i		−	1.75772i	−0.477077	−	0.878861i	$-0.658304\pi$
$281$		−	29.4648i		−	1.75772i	0.477077	−	0.878861i	$-0.341696\pi$
$282$	0.332986	+	0.332986i	0.0198290	+	0.0198290i
$283$	−14.8551	−	14.8551i	−0.883043	−	0.883043i	0.110800	−	0.993843i	$-0.464659\pi$
$283$	−14.8551	−	14.8551i	−0.883043	−	0.883043i	−0.993843	+	0.110800i	$0.964659\pi$
$284$			4.55438i			0.270253i
$285$		0			0
$286$			3.01027i			0.178001i
$287$	3.00568	−	3.00568i	0.177420	−	0.177420i
$288$	2.02947	−	2.02947i	0.119588	−	0.119588i
$289$			0.244451i			0.0143795i
$290$		0			0
$291$		−	2.12672i		−	0.124671i
$292$	−0.803131	−	0.803131i	−0.0469997	−	0.0469997i
$293$	2.77872	+	2.77872i	0.162334	+	0.162334i	0.783600	−	0.621266i	$-0.213381\pi$
$293$	2.77872	+	2.77872i	0.162334	+	0.162334i	−0.621266	+	0.783600i	$0.713381\pi$
$294$		−	2.04682i		−	0.119373i
$295$		0			0
$296$			6.21112i			0.361014i
$297$	−4.56844	+	4.56844i	−0.265088	+	0.265088i
$298$	−11.9448	−	11.9448i	−0.691944	−	0.691944i
$299$	−1.80236	−	4.37041i	−0.104233	−	0.252747i
$300$		0			0
$301$	4.19807			0.241973
$302$	8.55129	+	8.55129i	0.492072	+	0.492072i
$303$	−2.70143	+	2.70143i	−0.155193	+	0.155193i
$304$	2.26493			0.129902
$305$		0			0
$306$		−	11.7484i		−	0.671609i
$307$	−9.27015	−	9.27015i	−0.529075	−	0.529075i	0.391221	−	0.920297i	$-0.372053\pi$
$307$	−9.27015	−	9.27015i	−0.529075	−	0.529075i	−0.920297	+	0.391221i	$0.872053\pi$
$308$	−2.48173	+	2.48173i	−0.141410	+	0.141410i
$309$	−5.33299			−0.303383
$310$		0			0
$311$	−13.1388			−0.745033			−0.372517	−	0.928025i	$-0.621505\pi$
$311$	−13.1388			−0.745033			−0.372517	+	0.928025i	$0.621505\pi$
$312$	0.251215	+	0.251215i	0.0142223	+	0.0142223i
$313$	3.34798	+	3.34798i	0.189239	+	0.189239i	0.795367	−	0.606128i	$-0.207278\pi$
$313$	3.34798	+	3.34798i	0.189239	+	0.189239i	−0.606128	+	0.795367i	$0.707278\pi$
$314$	5.00224			0.282293
$315$		0			0
$316$		−	16.8702i		−	0.949024i
$317$	10.6829	+	10.6829i	0.600011	+	0.600011i	0.940315	−	0.340305i	$-0.110530\pi$
$317$	10.6829	+	10.6829i	0.600011	+	0.600011i	−0.340305	+	0.940315i	$0.610530\pi$
$318$	3.20309	+	3.20309i	0.179620	+	0.179620i
$319$	21.2650			1.19061
$320$		0			0
$321$			3.72415i			0.207862i
$322$	2.11715	−	5.08895i	0.117984	−	0.283596i
$323$	6.55569	−	6.55569i	0.364768	−	0.364768i
$324$		−	7.84782i		−	0.435990i
$325$		0			0
$326$	11.3029			0.626012
$327$	1.00159	−	1.00159i	0.0553878	−	0.0553878i
$328$	2.61526	−	2.61526i	0.144403	−	0.144403i
$329$	1.50166			0.0827894
$330$		0			0
$331$	−0.952100			−0.0523322			−0.0261661	−	0.999658i	$-0.508330\pi$
$331$	−0.952100			−0.0523322			−0.0261661	+	0.999658i	$0.508330\pi$
$332$	−8.37177	+	8.37177i	−0.459460	+	0.459460i
$333$	12.6053	+	12.6053i	0.690766	+	0.690766i
$334$			18.4081i			1.00725i
$335$		0			0
$336$			0.414214i			0.0225972i
$337$	−14.5701	+	14.5701i	−0.793686	+	0.793686i	−0.982091	−	0.188405i	$-0.939668\pi$
$337$	−14.5701	+	14.5701i	−0.793686	+	0.793686i	0.188405	+	0.982091i	$0.439668\pi$
$338$	−8.50530	+	8.50530i	−0.462627	+	0.462627i
$339$	−1.02967			−0.0559238
$340$		0			0
$341$			2.86497i			0.155147i
$342$	4.59660	−	4.59660i	0.248556	−	0.248556i
$343$	−10.3039	−	10.3039i	−0.556360	−	0.556360i
$344$	3.65276			0.196944
$345$		0			0
$346$	9.27930			0.498858
$347$	0.823485	+	0.823485i	0.0442070	+	0.0442070i	0.728865	−	0.684658i	$-0.240048\pi$
$347$	0.823485	+	0.823485i	0.0442070	+	0.0442070i	−0.684658	+	0.728865i	$0.740048\pi$
$348$	1.77462	−	1.77462i	0.0951298	−	0.0951298i
$349$		−	14.2684i		−	0.763768i	−0.924210	−	0.381884i	$-0.875275\pi$
$349$		−	14.2684i		−	0.763768i	0.924210	−	0.381884i	$-0.124725\pi$
$350$		0			0
$351$	2.08548			0.111315
$352$	−2.15937	+	2.15937i	−0.115095	+	0.115095i
$353$	−17.4275	+	17.4275i	−0.927572	+	0.927572i	−0.997549	−	0.0699765i	$-0.977708\pi$
$353$	−17.4275	+	17.4275i	−0.927572	+	0.927572i	0.0699765	+	0.997549i	$0.477708\pi$
$354$		−	1.52182i		−	0.0808839i
$355$		0			0
$356$			9.61955i			0.509835i
$357$	1.19892	+	1.19892i	0.0634533	+	0.0634533i
$358$	−1.20599	+	1.20599i	−0.0637383	+	0.0637383i
$359$	−22.4365			−1.18415			−0.592075	−	0.805883i	$-0.701691\pi$
$359$	−22.4365			−1.18415			−0.592075	+	0.805883i	$0.701691\pi$
$360$		0			0
$361$	−13.8701			−0.730006
$362$	−8.35979	+	8.35979i	−0.439381	+	0.439381i
$363$	−0.426687	+	0.426687i	−0.0223952	+	0.0223952i
$364$	1.13290			0.0593803
$365$		0			0
$366$		−	3.84160i		−	0.200803i
$367$	−3.52483	+	3.52483i	−0.183995	+	0.183995i	−0.793094	−	0.609099i	$-0.791531\pi$
$367$	−3.52483	+	3.52483i	−0.183995	+	0.183995i	0.609099	+	0.793094i	$0.291531\pi$
$368$	1.84214	−	4.42793i	0.0960281	−	0.230822i
$369$		−	10.6152i		−	0.552604i
$370$		0			0
$371$	14.4450			0.749945
$372$	0.239089	+	0.239089i	0.0123962	+	0.0123962i
$373$	11.4486	+	11.4486i	0.592787	+	0.592787i	0.938383	−	0.345596i	$-0.112323\pi$
$373$	11.4486	+	11.4486i	0.592787	+	0.592787i	−0.345596	+	0.938383i	$0.612323\pi$
$374$			12.5003i			0.646375i
$375$		0			0
$376$	1.30661			0.0673830
$377$	−4.85372	−	4.85372i	−0.249979	−	0.249979i
$378$	1.71931	+	1.71931i	0.0884320	+	0.0884320i
$379$	21.0371			1.08060			0.540302	−	0.841471i	$-0.318310\pi$
$379$	21.0371			1.08060			0.540302	+	0.841471i	$0.318310\pi$
$380$		0			0
$381$	2.96454			0.151878
$382$	−10.9686	+	10.9686i	−0.561202	+	0.561202i
$383$	−16.6002	−	16.6002i	−0.848228	−	0.848228i	0.141684	−	0.989912i	$-0.454748\pi$
$383$	−16.6002	−	16.6002i	−0.848228	−	0.848228i	−0.989912	+	0.141684i	$0.954748\pi$
$384$			0.360409i			0.0183921i
$385$		0			0
$386$	4.15110			0.211285
$387$	7.41317	−	7.41317i	0.376833	−	0.376833i
$388$	−4.17254	−	4.17254i	−0.211828	−	0.211828i
$389$	−10.4680			−0.530750			−0.265375	−	0.964145i	$-0.585496\pi$
$389$	−10.4680			−0.530750			−0.265375	+	0.964145i	$0.585496\pi$
$390$		0			0
$391$	−7.48440	−	18.1483i	−0.378502	−	0.917800i
$392$	−4.01576	−	4.01576i	−0.202826	−	0.202826i
$393$	−3.19687	+	3.19687i	−0.161261	+	0.161261i
$394$			22.8285i			1.15009i
$395$		0			0
$396$			8.76474i			0.440445i
$397$	19.8627	+	19.8627i	0.996881	+	0.996881i	0.999995	−	0.00311393i	$-0.000991197\pi$
$397$	19.8627	+	19.8627i	0.996881	+	0.996881i	−0.00311393	+	0.999995i	$0.500991\pi$
$398$	14.9156	+	14.9156i	0.747649	+	0.747649i
$399$			0.938164i			0.0469669i
$400$		0			0
$401$		−	23.8437i		−	1.19070i	−0.803467	−	0.595349i	$-0.797014\pi$
$401$		−	23.8437i		−	1.19070i	0.803467	−	0.595349i	$-0.202986\pi$
$402$	−1.00727	+	1.00727i	−0.0502378	+	0.0502378i
$403$	0.653926	−	0.653926i	0.0325744	−	0.0325744i
$404$			10.6002i			0.527377i
$405$		0			0
$406$		−	8.00301i		−	0.397183i
$407$	−13.4121	−	13.4121i	−0.664812	−	0.664812i
$408$	1.04318	+	1.04318i	0.0516452	+	0.0516452i
$409$			17.1274i			0.846897i	0.905920	+	0.423449i	$0.139181\pi$
$409$			17.1274i			0.846897i	−0.905920	+	0.423449i	$0.860819\pi$
$410$		0			0
$411$		−	4.39297i		−	0.216689i
$412$	−10.4631	+	10.4631i	−0.515479	+	0.515479i
$413$	−3.43148	−	3.43148i	−0.168852	−	0.168852i
$414$	−5.24778	−	12.7249i	−0.257914	−	0.625395i
$415$		0			0
$416$	0.985746			0.0483302
$417$	4.96635	+	4.96635i	0.243203	+	0.243203i
$418$	−4.89081	+	4.89081i	−0.239217	+	0.239217i
$419$	−31.7177			−1.54951			−0.774756	−	0.632260i	$-0.782127\pi$
$419$	−31.7177			−1.54951			−0.774756	+	0.632260i	$0.782127\pi$
$420$		0			0
$421$			18.3502i			0.894334i	0.894450	+	0.447167i	$0.147567\pi$
$421$			18.3502i			0.894334i	−0.894450	+	0.447167i	$0.852433\pi$
$422$	9.75856	+	9.75856i	0.475039	+	0.475039i
$423$	2.65172	−	2.65172i	0.128931	−	0.128931i
$424$	12.5686			0.610387
$425$		0			0
$426$	−1.64144			−0.0795281
$427$	−8.66222	−	8.66222i	−0.419194	−	0.419194i
$428$	7.30661	+	7.30661i	0.353178	+	0.353178i
$429$	−1.08493			−0.0523810
$430$		0			0
$431$			24.7843i			1.19382i	0.802309	+	0.596909i	$0.203605\pi$
$431$			24.7843i			1.19382i	−0.802309	+	0.596909i	$0.796395\pi$
$432$	1.49598	+	1.49598i	0.0719756	+	0.0719756i
$433$	−4.42484	−	4.42484i	−0.212644	−	0.212644i	0.592746	−	0.805390i	$-0.298044\pi$
$433$	−4.42484	−	4.42484i	−0.212644	−	0.212644i	−0.805390	+	0.592746i	$0.798044\pi$
$434$	1.07822			0.0517562
$435$		0			0
$436$		−	3.93013i		−	0.188219i
$437$	4.17231	−	10.0289i	0.199589	−	0.479749i
$438$	0.289456	−	0.289456i	0.0138307	−	0.0138307i
$439$		−	22.0184i		−	1.05088i	−0.850830	−	0.525441i	$-0.823900\pi$
$439$		−	22.0184i		−	1.05088i	0.850830	−	0.525441i	$-0.176100\pi$
$440$		0			0
$441$	−16.2997			−0.776178
$442$	2.85318	−	2.85318i	0.135712	−	0.135712i
$443$	−27.1908	+	27.1908i	−1.29187	+	1.29187i	−0.358245	+	0.933628i	$0.616625\pi$
$443$	−27.1908	+	27.1908i	−1.29187	+	1.29187i	−0.933628	+	0.358245i	$0.883375\pi$
$444$	−2.23855			−0.106237
$445$		0			0
$446$	27.1890			1.28743
$447$	4.30502	−	4.30502i	0.203620	−	0.203620i
$448$	0.812668	+	0.812668i	0.0383950	+	0.0383950i
$449$			0.580878i			0.0274133i	0.999906	+	0.0137067i	$0.00436310\pi$
$449$			0.580878i			0.0274133i	−0.999906	+	0.0137067i	$0.995637\pi$
$450$		0			0
$451$			11.2946i			0.531842i
$452$	−2.02016	+	2.02016i	−0.0950203	+	0.0950203i
$453$	−3.08197	+	3.08197i	−0.144803	+	0.144803i
$454$	−18.6794			−0.876668
$455$		0			0
$456$			0.816301i			0.0382268i
$457$	12.9909	−	12.9909i	0.607688	−	0.607688i	−0.334653	−	0.942341i	$-0.608619\pi$
$457$	12.9909	−	12.9909i	0.607688	−	0.607688i	0.942341	+	0.334653i	$0.108619\pi$
$458$	2.90042	+	2.90042i	0.135528	+	0.135528i
$459$	8.66007			0.404217
$460$		0			0
$461$	15.6873			0.730630			0.365315	−	0.930884i	$-0.380961\pi$
$461$	15.6873			0.730630			0.365315	+	0.930884i	$0.380961\pi$
$462$	−0.894439	−	0.894439i	−0.0416130	−	0.0416130i
$463$	9.77763	−	9.77763i	0.454405	−	0.454405i	−0.442409	−	0.896814i	$-0.645876\pi$
$463$	9.77763	−	9.77763i	0.454405	−	0.454405i	0.896814	+	0.442409i	$0.145876\pi$
$464$		−	6.96346i		−	0.323270i
$465$		0			0
$466$	−19.4989			−0.903268
$467$	15.9737	−	15.9737i	0.739176	−	0.739176i	−0.233242	−	0.972419i	$-0.574934\pi$
$467$	15.9737	−	15.9737i	0.739176	−	0.739176i	0.972419	+	0.233242i	$0.0749336\pi$
$468$	2.00054	−	2.00054i	0.0924751	−	0.0924751i
$469$			4.54246i			0.209751i
$470$		0			0
$471$			1.80285i			0.0830712i
$472$	−2.98575	−	2.98575i	−0.137430	−	0.137430i
$473$	−7.88765	+	7.88765i	−0.362674	+	0.362674i
$474$	6.08018			0.279272
$475$		0			0
$476$	4.70444			0.215627
$477$	25.5077	−	25.5077i	1.16792	−	1.16792i
$478$	10.8760	−	10.8760i	0.497457	−	0.497457i
$479$	35.1636			1.60667			0.803333	−	0.595530i	$-0.203058\pi$
$479$	35.1636			1.60667			0.803333	+	0.595530i	$0.203058\pi$
$480$		0			0
$481$			6.12259i			0.279166i
$482$	11.8589	−	11.8589i	0.540156	−	0.540156i
$483$	1.83411	+	0.763039i	0.0834547	+	0.0347195i
$484$			1.67428i			0.0761036i
$485$		0			0
$486$	9.17535			0.416202
$487$	−19.6145	−	19.6145i	−0.888819	−	0.888819i	0.105591	−	0.994410i	$-0.466327\pi$
$487$	−19.6145	−	19.6145i	−0.888819	−	0.888819i	−0.994410	+	0.105591i	$0.966327\pi$
$488$	−7.53704	−	7.53704i	−0.341186	−	0.341186i
$489$			4.07369i			0.184218i
$490$		0			0
$491$	−34.8359			−1.57212			−0.786062	−	0.618148i	$-0.787883\pi$
$491$	−34.8359			−1.57212			−0.786062	+	0.618148i	$0.787883\pi$
$492$	0.942563	+	0.942563i	0.0424940	+	0.0424940i
$493$	−20.1553	−	20.1553i	−0.907749	−	0.907749i
$494$	2.23264			0.100451
$495$		0			0
$496$	0.938164			0.0421248
$497$	−3.70120	+	3.70120i	−0.166022	+	0.166022i
$498$	−3.01726	−	3.01726i	−0.135207	−	0.135207i
$499$		−	35.1206i		−	1.57221i	−0.618091	−	0.786106i	$-0.712094\pi$
$499$		−	35.1206i		−	1.57221i	0.618091	−	0.786106i	$-0.287906\pi$
$500$		0			0
$501$	−6.63445			−0.296406
$502$	−15.3619	+	15.3619i	−0.685636	+	0.685636i
$503$	−7.26752	−	7.26752i	−0.324043	−	0.324043i	0.526273	−	0.850316i	$-0.323589\pi$
$503$	−7.26752	−	7.26752i	−0.324043	−	0.324043i	−0.850316	+	0.526273i	$0.823589\pi$
$504$	3.29857			0.146930
$505$		0			0
$506$	5.58366	+	13.5394i	0.248224	+	0.601898i
$507$	−3.06539	−	3.06539i	−0.136139	−	0.136139i
$508$	5.81630	−	5.81630i	0.258057	−	0.258057i
$509$			44.5560i			1.97491i	0.157904	+	0.987454i	$0.449526\pi$
$509$			44.5560i			1.97491i	−0.157904	+	0.987454i	$0.550474\pi$
$510$		0			0
$511$		−	1.30536i		−	0.0577457i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	3.38829	+	3.38829i	0.149597	+	0.149597i
$514$			9.79490i			0.432034i
$515$		0			0
$516$			1.31649i			0.0579552i
$517$	−2.82144	+	2.82144i	−0.124087	+	0.124087i
$518$	−5.04758	+	5.04758i	−0.221778	+	0.221778i
$519$			3.34434i			0.146800i
$520$		0			0
$521$			16.2124i			0.710280i	0.934813	+	0.355140i	$0.115567\pi$
$521$			16.2124i			0.710280i	−0.934813	+	0.355140i	$0.884433\pi$
$522$	−14.1321	−	14.1321i	−0.618547	−	0.618547i
$523$	−3.90861	−	3.90861i	−0.170912	−	0.170912i	0.616468	−	0.787380i	$-0.288563\pi$
$523$	−3.90861	−	3.90861i	−0.170912	−	0.170912i	−0.787380	+	0.616468i	$0.788563\pi$
$524$			12.5442i			0.547997i
$525$		0			0
$526$			28.6448i			1.24897i
$527$	2.71546	−	2.71546i	0.118287	−	0.118287i
$528$	−0.778256	−	0.778256i	−0.0338692	−	0.0338692i
$529$	−16.2130	−	16.3137i	−0.704915	−	0.709292i
$530$		0			0
$531$	−12.1190			−0.525918
$532$	1.84063	+	1.84063i	0.0798016	+	0.0798016i
$533$	2.57798	−	2.57798i	0.111665	−	0.111665i
$534$	−3.46697			−0.150031
$535$		0			0
$536$			3.95242i			0.170718i
$537$	−0.434648	−	0.434648i	−0.0187565	−	0.0187565i
$538$	0.524717	−	0.524717i	0.0226222	−	0.0226222i
$539$	17.3430			0.747015
$540$		0			0
$541$	−19.7184			−0.847758			−0.423879	−	0.905719i	$-0.639332\pi$
$541$	−19.7184			−0.847758			−0.423879	+	0.905719i	$0.639332\pi$
$542$	−1.22174	−	1.22174i	−0.0524784	−	0.0524784i
$543$	−3.01294	−	3.01294i	−0.129298	−	0.129298i
$544$	4.09335			0.175501
$545$		0			0
$546$			0.408309i			0.0174740i
$547$	0.723090	+	0.723090i	0.0309171	+	0.0309171i	0.722396	−	0.691479i	$-0.243041\pi$
$547$	0.723090	+	0.723090i	0.0309171	+	0.0309171i	−0.691479	+	0.722396i	$0.743041\pi$
$548$	−8.61881	−	8.61881i	−0.368177	−	0.368177i
$549$	−30.5924			−1.30565
$550$		0			0
$551$		−	15.7717i		−	0.671898i
$552$	1.59587	+	0.663924i	0.0679246	+	0.0282585i
$553$	13.7099	−	13.7099i	0.583004	−	0.583004i
$554$		−	12.6820i		−	0.538808i
$555$		0			0
$556$	19.4875			0.826455
$557$	−7.40510	+	7.40510i	−0.313764	+	0.313764i	−0.846366	−	0.532602i	$-0.821214\pi$
$557$	−7.40510	+	7.40510i	−0.313764	+	0.313764i	0.532602	+	0.846366i	$0.321214\pi$
$558$	1.90398	−	1.90398i	0.0806017	−	0.0806017i
$559$	3.60069			0.152293
$560$		0			0
$561$	−4.50523			−0.190211
$562$	20.8348	−	20.8348i	0.878861	−	0.878861i
$563$	−16.0153	−	16.0153i	−0.674962	−	0.674962i	0.283893	−	0.958856i	$-0.408374\pi$
$563$	−16.0153	−	16.0153i	−0.674962	−	0.674962i	−0.958856	+	0.283893i	$0.908374\pi$
$564$			0.470913i			0.0198290i
$565$		0			0
$566$		−	21.0083i		−	0.883043i
$567$	6.37767	−	6.37767i	0.267837	−	0.267837i
$568$	−3.22044	+	3.22044i	−0.135126	+	0.135126i
$569$	0.251153			0.0105289			0.00526443	−	0.999986i	$-0.498324\pi$
$569$	0.251153			0.0105289			0.00526443	+	0.999986i	$0.498324\pi$
$570$		0			0
$571$		−	13.6282i		−	0.570324i	−0.958479	−	0.285162i	$-0.907953\pi$
$571$		−	13.6282i		−	0.570324i	0.958479	−	0.285162i	$-0.0920474\pi$
$572$	−2.12859	+	2.12859i	−0.0890006	+	0.0890006i
$573$	−3.95318	−	3.95318i	−0.165147	−	0.165147i
$574$	4.25067			0.177420
$575$		0			0
$576$	2.87011			0.119588
$577$	−29.2581	−	29.2581i	−1.21803	−	1.21803i	−0.968321	−	0.249707i	$-0.919666\pi$
$577$	−29.2581	−	29.2581i	−1.21803	−	1.21803i	−0.249707	−	0.968321i	$-0.580334\pi$
$578$	−0.172853	+	0.172853i	−0.00718973	+	0.00718973i
$579$			1.49609i			0.0621755i
$580$		0			0
$581$	−13.6069			−0.564511
$582$	1.50382	−	1.50382i	0.0623354	−	0.0623354i
$583$	−27.1403	+	27.1403i	−1.12404	+	1.12404i
$584$		−	1.13580i		−	0.0469997i
$585$		0			0
$586$			3.92970i			0.162334i
$587$	9.56129	+	9.56129i	0.394637	+	0.394637i	0.876336	−	0.481700i	$-0.159980\pi$
$587$	9.56129	+	9.56129i	0.394637	+	0.394637i	−0.481700	+	0.876336i	$0.659980\pi$
$588$	1.44732	−	1.44732i	0.0596863	−	0.0596863i
$589$	2.12487			0.0875538
$590$		0			0
$591$	−8.22762			−0.338439
$592$	−4.39193	+	4.39193i	−0.180507	+	0.180507i
$593$	−18.5159	+	18.5159i	−0.760358	+	0.760358i	−0.976387	−	0.216029i	$-0.930689\pi$
$593$	−18.5159	+	18.5159i	−0.760358	+	0.760358i	0.216029	+	0.976387i	$0.430689\pi$
$594$	−6.46075			−0.265088
$595$		0			0
$596$		−	16.8925i		−	0.691944i
$597$	−5.37571	+	5.37571i	−0.220013	+	0.220013i
$598$	1.81588	−	4.36481i	0.0742569	−	0.178490i
$599$		−	20.5744i		−	0.840646i	−0.907374	−	0.420323i	$-0.861917\pi$
$599$		−	20.5744i		−	0.840646i	0.907374	−	0.420323i	$-0.138083\pi$
$600$		0			0
$601$	12.6034			0.514102			0.257051	−	0.966398i	$-0.417249\pi$
$601$	12.6034			0.514102			0.257051	+	0.966398i	$0.417249\pi$
$602$	2.96848	+	2.96848i	0.120986	+	0.120986i
$603$	8.02132	+	8.02132i	0.326653	+	0.326653i
$604$			12.0934i			0.492072i
$605$		0			0
$606$	−3.82039			−0.155193
$607$	−20.9098	−	20.9098i	−0.848701	−	0.848701i	0.141270	−	0.989971i	$-0.454882\pi$
$607$	−20.9098	−	20.9098i	−0.848701	−	0.848701i	−0.989971	+	0.141270i	$0.954882\pi$
$608$	1.60155	+	1.60155i	0.0649512	+	0.0649512i
$609$	2.88436			0.116880
$610$		0			0
$611$	1.28798			0.0521061
$612$	8.30734	−	8.30734i	0.335804	−	0.335804i
$613$	0.241759	+	0.241759i	0.00976456	+	0.00976456i	0.711972	−	0.702208i	$-0.247802\pi$
$613$	0.241759	+	0.241759i	0.00976456	+	0.00976456i	−0.702208	+	0.711972i	$0.747802\pi$
$614$		−	13.1100i		−	0.529075i
$615$		0			0
$616$	−3.50970			−0.141410
$617$	−17.6380	+	17.6380i	−0.710078	+	0.710078i	−0.966551	−	0.256473i	$-0.917439\pi$
$617$	−17.6380	+	17.6380i	−0.710078	+	0.710078i	0.256473	+	0.966551i	$0.417439\pi$
$618$	−3.77099	−	3.77099i	−0.151691	−	0.151691i
$619$	17.5344			0.704767			0.352383	−	0.935856i	$-0.385371\pi$
$619$	17.5344			0.704767			0.352383	+	0.935856i	$0.385371\pi$
$620$		0			0
$621$	9.37992	−	3.86829i	0.376403	−	0.155229i
$622$	−9.29054	−	9.29054i	−0.372517	−	0.372517i
$623$	−7.81750	+	7.81750i	−0.313202	+	0.313202i
$624$			0.355272i			0.0142223i
$625$		0			0
$626$			4.73476i			0.189239i
$627$	−1.76269	−	1.76269i	−0.0703951	−	0.0703951i
$628$	3.53712	+	3.53712i	0.141146	+	0.141146i
$629$			25.4243i			1.01373i
$630$		0			0
$631$			20.3839i			0.811468i	0.913991	+	0.405734i	$0.132984\pi$
$631$			20.3839i			0.811468i	−0.913991	+	0.405734i	$0.867016\pi$
$632$	11.9290	−	11.9290i	0.474512	−	0.474512i
$633$	−3.51708	+	3.51708i	−0.139791	+	0.139791i
$634$			15.1079i			0.600011i
$635$		0			0
$636$			4.52985i			0.179620i
$637$	−3.95852	−	3.95852i	−0.156842	−	0.156842i
$638$	15.0367	+	15.0367i	0.595307	+	0.595307i
$639$			13.0716i			0.517103i
$640$		0			0
$641$		−	47.3067i		−	1.86850i	−0.356617	−	0.934251i	$-0.616070\pi$
$641$		−	47.3067i		−	1.86850i	0.356617	−	0.934251i	$-0.383930\pi$
$642$	−2.63337	+	2.63337i	−0.103931	+	0.103931i
$643$	25.9299	+	25.9299i	1.02258	+	1.02258i	0.999739	+	0.0228373i	$0.00726999\pi$
$643$	25.9299	+	25.9299i	1.02258	+	1.02258i	0.0228373	+	0.999739i	$0.492730\pi$
$644$	5.09548	−	2.10139i	0.200790	−	0.0828062i
$645$		0			0
$646$	9.27115			0.364768
$647$	16.6612	+	16.6612i	0.655020	+	0.655020i	0.954198	−	0.299177i	$-0.0967122\pi$
$647$	16.6612	+	16.6612i	0.655020	+	0.655020i	−0.299177	+	0.954198i	$0.596712\pi$
$648$	5.54925	−	5.54925i	0.217995	−	0.217995i
$649$	12.8946			0.506159
$650$		0			0
$651$			0.388600i			0.0152304i
$652$	7.99239	+	7.99239i	0.313006	+	0.313006i
$653$	−13.5400	+	13.5400i	−0.529861	+	0.529861i	−0.920531	−	0.390670i	$-0.872243\pi$
$653$	−13.5400	+	13.5400i	−0.529861	+	0.529861i	0.390670	+	0.920531i	$0.372243\pi$
$654$	1.41646			0.0553878
$655$		0			0
$656$	3.69853			0.144403
$657$	−2.30507	−	2.30507i	−0.0899294	−	0.0899294i
$658$	1.06184	+	1.06184i	0.0413947	+	0.0413947i
$659$	−39.6959			−1.54633			−0.773166	−	0.634204i	$-0.781328\pi$
$659$	−39.6959			−1.54633			−0.773166	+	0.634204i	$0.781328\pi$
$660$		0			0
$661$		−	12.0576i		−	0.468986i	−0.972118	−	0.234493i	$-0.924657\pi$
$661$		−	12.0576i		−	0.468986i	0.972118	−	0.234493i	$-0.0753429\pi$
$662$	−0.673236	−	0.673236i	−0.0261661	−	0.0261661i
$663$	1.02831	+	1.02831i	0.0399364	+	0.0399364i
$664$	−11.8395			−0.459460
$665$		0			0
$666$			17.8266i			0.690766i
$667$	−30.8337	−	12.8277i	−1.19388	−	0.496689i
$668$	−13.0165	+	13.0165i	−0.503623	+	0.503623i
$669$			9.79915i			0.378857i
$670$		0			0
$671$	32.5504			1.25660
$672$	−0.292893	+	0.292893i	−0.0112986	+	0.0112986i
$673$	−7.82931	+	7.82931i	−0.301798	+	0.301798i	−0.841717	−	0.539919i	$-0.818455\pi$
$673$	−7.82931	+	7.82931i	−0.301798	+	0.301798i	0.539919	+	0.841717i	$0.318455\pi$
$674$	−20.6053			−0.793686
$675$		0			0
$676$	−12.0283			−0.462627
$677$	−27.0657	+	27.0657i	−1.04022	+	1.04022i	−0.0410639	+	0.999157i	$0.513075\pi$
$677$	−27.0657	+	27.0657i	−1.04022	+	1.04022i	−0.999157	+	0.0410639i	$0.986925\pi$
$678$	−0.728084	−	0.728084i	−0.0279619	−	0.0279619i
$679$		−	6.78177i		−	0.260261i
$680$		0			0
$681$		−	6.73224i		−	0.257980i
$682$	−2.02584	+	2.02584i	−0.0775734	+	0.0775734i
$683$	6.29630	−	6.29630i	0.240921	−	0.240921i	−0.576310	−	0.817231i	$-0.695508\pi$
$683$	6.29630	−	6.29630i	0.240921	−	0.240921i	0.817231	+	0.576310i	$0.195508\pi$
$684$	6.50058			0.248556
$685$		0			0
$686$		−	14.5720i		−	0.556360i
$687$	−1.04534	+	1.04534i	−0.0398822	+	0.0398822i
$688$	2.58289	+	2.58289i	0.0984718	+	0.0984718i
$689$	12.3895			0.472002
$690$		0			0
$691$	17.7979			0.677064			0.338532	−	0.940955i	$-0.390070\pi$
$691$	17.7979			0.677064			0.338532	+	0.940955i	$0.390070\pi$
$692$	6.56145	+	6.56145i	0.249429	+	0.249429i
$693$	−7.12283	+	7.12283i	−0.270574	+	0.270574i
$694$			1.16458i			0.0442070i
$695$		0			0
$696$	2.50970			0.0951298
$697$	10.7052	−	10.7052i	0.405487	−	0.405487i
$698$	10.0893	−	10.0893i	0.381884	−	0.381884i
$699$		−	7.02758i		−	0.265807i
$700$		0			0
$701$			25.4881i			0.962673i	0.876536	+	0.481336i	$0.159848\pi$
$701$			25.4881i			0.962673i	−0.876536	+	0.481336i	$0.840152\pi$
$702$	1.47466	+	1.47466i	0.0556574	+	0.0556574i
$703$	−9.94739	+	9.94739i	−0.375173	+	0.375173i
$704$	−3.05380			−0.115095
$705$		0			0
$706$	−24.6462			−0.927572
$707$	−8.61441	+	8.61441i	−0.323978	+	0.323978i
$708$	1.07609	−	1.07609i	0.0404420	−	0.0404420i
$709$	−13.1303			−0.493118			−0.246559	−	0.969128i	$-0.579300\pi$
$709$	−13.1303			−0.493118			−0.246559	+	0.969128i	$0.579300\pi$
$710$		0			0
$711$		−	48.4193i		−	1.81587i
$712$	−6.80205	+	6.80205i	−0.254917	+	0.254917i
$713$	1.72823	−	4.15412i	0.0647226	−	0.155573i
$714$			1.69552i			0.0634533i
$715$		0			0
$716$	−1.70552			−0.0637383
$717$	3.91982	+	3.91982i	0.146388	+	0.146388i
$718$	−15.8650	−	15.8650i	−0.592075	−	0.592075i
$719$			48.8089i			1.82027i	0.414316	+	0.910133i	$0.364021\pi$
$719$			48.8089i			1.82027i	−0.414316	+	0.910133i	$0.635979\pi$
$720$		0			0
$721$	−17.0060			−0.633337
$722$	−9.80765	−	9.80765i	−0.365003	−	0.365003i
$723$	4.27404	+	4.27404i	0.158953	+	0.158953i
$724$	−11.8225			−0.439381
$725$		0			0
$726$	−0.603426			−0.0223952
$727$	27.1683	−	27.1683i	1.00762	−	1.00762i	0.00764493	−	0.999971i	$-0.497567\pi$
$727$	27.1683	−	27.1683i	1.00762	−	1.00762i	0.999971	−	0.00764493i	$-0.00243348\pi$
$728$	0.801084	+	0.801084i	0.0296902	+	0.0296902i
$729$		−	20.2366i		−	0.749503i
$730$		0			0
$731$	14.9520			0.553021
$732$	2.71642	−	2.71642i	0.100402	−	0.100402i
$733$	26.1220	+	26.1220i	0.964837	+	0.964837i	0.999402	−	0.0345652i	$-0.0110046\pi$
$733$	26.1220	+	26.1220i	0.964837	+	0.964837i	−0.0345652	+	0.999402i	$0.511005\pi$
$734$	−4.98486			−0.183995
$735$		0			0
$736$	4.43361	−	1.82843i	0.163425	−	0.0673967i
$737$	−8.53472	−	8.53472i	−0.314380	−	0.314380i
$738$	7.50606	−	7.50606i	0.276302	−	0.276302i
$739$		−	8.74415i		−	0.321659i	−0.986982	−	0.160829i	$-0.948583\pi$
$739$		−	8.74415i		−	0.321659i	0.986982	−	0.160829i	$-0.0514169\pi$
$740$		0			0
$741$			0.804665i			0.0295601i
$742$	10.2141	+	10.2141i	0.374973	+	0.374973i
$743$	3.35814	+	3.35814i	0.123198	+	0.123198i	0.766018	−	0.642820i	$-0.222235\pi$
$743$	3.35814	+	3.35814i	0.123198	+	0.123198i	−0.642820	+	0.766018i	$0.722235\pi$
$744$			0.338123i			0.0123962i
$745$		0			0
$746$			16.1908i			0.592787i
$747$	−24.0279	+	24.0279i	−0.879133	+	0.879133i
$748$	−8.83905	+	8.83905i	−0.323188	+	0.323188i
$749$			11.8757i			0.433928i
$750$		0			0
$751$		−	22.6897i		−	0.827959i	−0.910286	−	0.413979i	$-0.864139\pi$
$751$		−	22.6897i		−	0.827959i	0.910286	−	0.413979i	$-0.135861\pi$
$752$	0.923909	+	0.923909i	0.0336915	+	0.0336915i
$753$	−5.53658	−	5.53658i	−0.201764	−	0.201764i
$754$		−	6.86420i		−	0.249979i
$755$		0			0
$756$			2.43148i			0.0884320i
$757$	10.7978	−	10.7978i	0.392452	−	0.392452i	−0.483108	−	0.875561i	$-0.660492\pi$
$757$	10.7978	−	10.7978i	0.392452	−	0.392452i	0.875561	+	0.483108i	$0.160492\pi$
$758$	14.8755	+	14.8755i	0.540302	+	0.540302i
$759$	−4.87971	+	2.01240i	−0.177122	+	0.0730456i
$760$		0			0
$761$	−39.2774			−1.42381			−0.711903	−	0.702278i	$-0.752167\pi$
$761$	−39.2774			−1.42381			−0.711903	+	0.702278i	$0.752167\pi$
$762$	2.09625	+	2.09625i	0.0759391	+	0.0759391i
$763$	3.19389	−	3.19389i	0.115627	−	0.115627i
$764$	−15.5119			−0.561202
$765$		0			0
$766$		−	23.4762i		−	0.848228i
$767$	−2.94319	−	2.94319i	−0.106272	−	0.106272i
$768$	−0.254848	+	0.254848i	−0.00919603	+	0.00919603i
$769$	24.7615			0.892923			0.446462	−	0.894803i	$-0.352684\pi$
$769$	24.7615			0.892923			0.446462	+	0.894803i	$0.352684\pi$
$770$		0			0
$771$	−3.53017			−0.127136
$772$	2.93527	+	2.93527i	0.105643	+	0.105643i
$773$	−32.3049	−	32.3049i	−1.16193	−	1.16193i	−0.984053	−	0.177873i	$-0.943078\pi$
$773$	−32.3049	−	32.3049i	−1.16193	−	1.16193i	−0.177873	−	0.984053i	$-0.556922\pi$
$774$	10.4838			0.376833
$775$		0			0
$776$		−	5.90086i		−	0.211828i
$777$	−1.81920	−	1.81920i	−0.0652633	−	0.0652633i
$778$	−7.40201	−	7.40201i	−0.265375	−	0.265375i
$779$	8.37691			0.300134
$780$		0			0
$781$		−	13.9082i		−	0.497674i
$782$	7.54053	−	18.1251i	0.269649	−	0.648151i
$783$	10.4172	−	10.4172i	0.372281	−	0.372281i
$784$		−	5.67914i		−	0.202826i
$785$		0			0
$786$	−4.52106			−0.161261
$787$	−6.55956	+	6.55956i	−0.233823	+	0.233823i	−0.814286	−	0.580463i	$-0.802871\pi$
$787$	−6.55956	+	6.55956i	−0.233823	+	0.233823i	0.580463	+	0.814286i	$0.302871\pi$
$788$	−16.1422	+	16.1422i	−0.575043	+	0.575043i
$789$	−10.3239			−0.367539
$790$		0			0
$791$	−3.28344			−0.116746
$792$	−6.19761	+	6.19761i	−0.220222	+	0.220222i
$793$	−7.42960	−	7.42960i	−0.263833	−	0.263833i
$794$			28.0901i			0.996881i
$795$		0			0
$796$			21.0938i			0.747649i
$797$	−9.89605	+	9.89605i	−0.350536	+	0.350536i	−0.860309	−	0.509773i	$-0.829729\pi$
$797$	−9.89605	+	9.89605i	−0.350536	+	0.350536i	0.509773	+	0.860309i	$0.329729\pi$
$798$	−0.663382	+	0.663382i	−0.0234835	+	0.0234835i
$799$	5.34840			0.189213
$800$		0			0
$801$			27.6091i			0.975520i
$802$	16.8601	−	16.8601i	0.595349	−	0.595349i
$803$	2.45261	+	2.45261i	0.0865506	+	0.0865506i
$804$	−1.42449			−0.0502378
$805$		0			0
$806$	0.924791			0.0325744
$807$	0.189113	+	0.189113i	0.00665709	+	0.00665709i
$808$	−7.49544	+	7.49544i	−0.263689	+	0.263689i
$809$		−	30.8434i		−	1.08439i	−0.840251	−	0.542197i	$-0.817592\pi$
$809$		−	30.8434i		−	1.08439i	0.840251	−	0.542197i	$-0.182408\pi$
$810$		0			0
$811$	−32.5399			−1.14263			−0.571315	−	0.820731i	$-0.693567\pi$
$811$	−32.5399			−1.14263			−0.571315	+	0.820731i	$0.693567\pi$
$812$	5.65898	−	5.65898i	0.198591	−	0.198591i
$813$	0.440328	−	0.440328i	0.0154430	−	0.0154430i
$814$		−	18.9676i		−	0.664812i
$815$		0			0
$816$			1.47528i			0.0516452i
$817$	5.85006	+	5.85006i	0.204668	+	0.204668i
$818$	−12.1109	+	12.1109i	−0.423449	+	0.423449i
$819$	3.25155			0.113619
$820$		0			0
$821$	19.5704			0.683013			0.341506	−	0.939879i	$-0.389063\pi$
$821$	19.5704			0.683013			0.341506	+	0.939879i	$0.389063\pi$
$822$	3.10630	−	3.10630i	0.108345	−	0.108345i
$823$	−0.670676	+	0.670676i	−0.0233783	+	0.0233783i	−0.718699	−	0.695321i	$-0.755262\pi$
$823$	−0.670676	+	0.670676i	−0.0233783	+	0.0233783i	0.695321	+	0.718699i	$0.255262\pi$
$824$	−14.7970			−0.515479
$825$		0			0
$826$		−	4.85284i		−	0.168852i
$827$	31.3990	−	31.3990i	1.09185	−	1.09185i	0.0965203	−	0.995331i	$-0.469229\pi$
$827$	31.3990	−	31.3990i	1.09185	−	1.09185i	0.995331	−	0.0965203i	$-0.0307713\pi$
$828$	5.28713	−	12.7086i	0.183741	−	0.441655i
$829$		−	34.4163i		−	1.19533i	−0.801747	−	0.597664i	$-0.796096\pi$
$829$		−	34.4163i		−	1.19533i	0.801747	−	0.597664i	$-0.203904\pi$
$830$		0			0
$831$	4.57072			0.158557
$832$	0.697028	+	0.697028i	0.0241651	+	0.0241651i
$833$	−16.4379	−	16.4379i	−0.569540	−	0.569540i
$834$			7.02349i			0.243203i
$835$		0			0
$836$	−6.91664			−0.239217
$837$	1.40348	+	1.40348i	0.0485113	+	0.0485113i
$838$	−22.4278	−	22.4278i	−0.774756	−	0.774756i
$839$	16.3790			0.565465			0.282733	−	0.959199i	$-0.408759\pi$
$839$	16.3790			0.565465			0.282733	+	0.959199i	$0.408759\pi$
$840$		0			0
$841$	−19.4898			−0.672061
$842$	−12.9756	+	12.9756i	−0.447167	+	0.447167i
$843$	7.50904	+	7.50904i	0.258625	+	0.258625i
$844$			13.8007i			0.475039i
$845$		0			0
$846$	3.75009			0.128931
$847$	−1.36063	+	1.36063i	−0.0467519	+	0.0467519i
$848$	8.88737	+	8.88737i	0.305193	+	0.305193i
$849$	7.57157			0.259856
$850$		0			0
$851$	11.3566	+	27.5377i	0.389299	+	0.943979i
$852$	−1.16067	−	1.16067i	−0.0397641	−	0.0397641i
$853$	4.42162	−	4.42162i	0.151393	−	0.151393i	−0.627347	−	0.778740i	$-0.715859\pi$
$853$	4.42162	−	4.42162i	0.151393	−	0.151393i	0.778740	+	0.627347i	$0.215859\pi$
$854$		−	12.2502i		−	0.419194i
$855$		0			0
$856$			10.3331i			0.353178i
$857$	25.8582	+	25.8582i	0.883301	+	0.883301i	0.993869	−	0.110568i	$-0.0352669\pi$
$857$	25.8582	+	25.8582i	0.883301	+	0.883301i	−0.110568	+	0.993869i	$0.535267\pi$
$858$	−0.767162	−	0.767162i	−0.0261905	−	0.0261905i
$859$			51.1948i			1.74674i	0.487053	+	0.873372i	$0.338072\pi$
$859$			51.1948i			1.74674i	−0.487053	+	0.873372i	$0.661928\pi$
$860$		0			0
$861$			1.53198i			0.0522098i
$862$	−17.5251	+	17.5251i	−0.596909	+	0.596909i
$863$	19.1775	−	19.1775i	0.652809	−	0.652809i	−0.300860	−	0.953668i	$-0.597274\pi$
$863$	19.1775	−	19.1775i	0.652809	−	0.652809i	0.953668	+	0.300860i	$0.0972735\pi$
$864$			2.11564i			0.0719756i
$865$		0			0
$866$		−	6.25766i		−	0.212644i
$867$	−0.0622978	−	0.0622978i	−0.00211574	−	0.00211574i
$868$	0.762416	+	0.762416i	0.0258781	+	0.0258781i
$869$			51.5183i			1.74764i
$870$		0			0
$871$			3.89608i			0.132014i
$872$	2.77902	−	2.77902i	0.0941096	−	0.0941096i
$873$	−11.9756	−	11.9756i	−0.405313	−	0.405313i
$874$	10.0418	−	4.14125i	0.339669	−	0.140080i
$875$		0			0
$876$	0.409353			0.0138307
$877$	28.0226	+	28.0226i	0.946257	+	0.946257i	0.998628	−	0.0523705i	$-0.0166777\pi$
$877$	28.0226	+	28.0226i	0.946257	+	0.946257i	−0.0523705	+	0.998628i	$0.516678\pi$
$878$	15.5694	−	15.5694i	0.525441	−	0.525441i
$879$	−1.41630			−0.0477706
$880$		0			0
$881$			13.5604i			0.456863i	0.973560	+	0.228431i	$0.0733597\pi$
$881$			13.5604i			0.456863i	−0.973560	+	0.228431i	$0.926640\pi$
$882$	−11.5257	−	11.5257i	−0.388089	−	0.388089i
$883$	−23.1955	+	23.1955i	−0.780590	+	0.780590i	−0.979930	−	0.199340i	$-0.936120\pi$
$883$	−23.1955	+	23.1955i	−0.780590	+	0.780590i	0.199340	+	0.979930i	$0.436120\pi$
$884$	4.03501			0.135712
$885$		0			0
$886$	−38.4536			−1.29187
$887$	28.9804	+	28.9804i	0.973067	+	0.973067i	0.999647	−	0.0265799i	$-0.00846165\pi$
$887$	28.9804	+	28.9804i	0.973067	+	0.973067i	−0.0265799	+	0.999647i	$0.508462\pi$
$888$	−1.58289	−	1.58289i	−0.0531184	−	0.0531184i
$889$	9.45345			0.317058
$890$		0			0
$891$			23.9657i			0.802881i
$892$	19.2255	+	19.2255i	0.643717	+	0.643717i
$893$	2.09259	+	2.09259i	0.0700258	+	0.0700258i
$894$	6.08822			0.203620
$895$		0			0
$896$			1.14929i			0.0383950i
$897$	1.57312	+	0.654460i	0.0525249	+	0.0218518i
$898$	−0.410743	+	0.410743i	−0.0137067	+	0.0137067i
$899$		−	6.53286i		−	0.217883i
$900$		0			0
$901$	51.4479			1.71398
$902$	−7.98648	+	7.98648i	−0.265921	+	0.265921i
$903$	−1.06987	+	1.06987i	−0.0356030	+	0.0356030i
$904$	−2.85694			−0.0950203
$905$		0			0
$906$	−4.35856			−0.144803
$907$	19.1811	−	19.1811i	0.636897	−	0.636897i	−0.312892	−	0.949789i	$-0.601298\pi$
$907$	19.1811	−	19.1811i	0.636897	−	0.636897i	0.949789	+	0.312892i	$0.101298\pi$
$908$	−13.2083	−	13.2083i	−0.438334	−	0.438334i
$909$			30.4236i			1.00909i
$910$		0			0
$911$			36.9319i			1.22361i	0.791009	+	0.611805i	$0.209556\pi$
$911$			36.9319i			1.22361i	−0.791009	+	0.611805i	$0.790444\pi$
$912$	−0.577212	+	0.577212i	−0.0191134	+	0.0191134i
$913$	25.5657	−	25.5657i	0.846103	−	0.846103i
$914$	18.3719			0.607688
$915$		0			0
$916$			4.10182i			0.135528i
$917$	−10.1943	+	10.1943i	−0.336645	+	0.336645i
$918$	6.12359	+	6.12359i	0.202109	+	0.202109i
$919$	−58.3059			−1.92333			−0.961667	−	0.274219i	$-0.911581\pi$
$919$	−58.3059			−1.92333			−0.961667	+	0.274219i	$0.911581\pi$
$920$		0			0
$921$	4.72495			0.155693
$922$	11.0926	+	11.0926i	0.365315	+	0.365315i
$923$	−3.17453	+	3.17453i	−0.104491	+	0.104491i
$924$		−	1.26493i		−	0.0416130i
$925$		0			0
$926$	13.8277			0.454405
$927$	−30.0301	+	30.0301i	−0.986319	+	0.986319i
$928$	4.92391	−	4.92391i	0.161635	−	0.161635i
$929$		−	15.1024i		−	0.495494i	−0.968825	−	0.247747i	$-0.920310\pi$
$929$		−	15.1024i		−	0.495494i	0.968825	−	0.247747i	$-0.0796902\pi$
$930$		0			0
$931$		−	12.8628i		−	0.421563i
$932$	−13.7878	−	13.7878i	−0.451634	−	0.451634i
$933$	3.34840	−	3.34840i	0.109622	−	0.109622i
$934$	22.5903			0.739176
$935$		0			0
$936$	2.82919			0.0924751
$937$	9.26161	−	9.26161i	0.302564	−	0.302564i	−0.539452	−	0.842016i	$-0.681369\pi$
$937$	9.26161	−	9.26161i	0.302564	−	0.302564i	0.842016	+	0.539452i	$0.181369\pi$
$938$	−3.21200	+	3.21200i	−0.104876	+	0.104876i
$939$	−1.70645			−0.0556879
$940$		0			0
$941$			38.8905i			1.26779i	0.773418	+	0.633897i	$0.218546\pi$
$941$			38.8905i			1.26779i	−0.773418	+	0.633897i	$0.781454\pi$
$942$	−1.27481	+	1.27481i	−0.0415356	+	0.0415356i
$943$	6.81321	−	16.3768i	0.221869	−	0.533303i
$944$		−	4.22248i		−	0.137430i
$945$		0			0
$946$	−11.1548			−0.362674
$947$	13.7163	+	13.7163i	0.445720	+	0.445720i	0.893929	−	0.448209i	$-0.147938\pi$
$947$	13.7163	+	13.7163i	0.445720	+	0.445720i	−0.448209	+	0.893929i	$0.647938\pi$
$948$	4.29934	+	4.29934i	0.139636	+	0.139636i
$949$		−	1.11961i		−	0.0363441i
$950$		0			0
$951$	−5.44502			−0.176567
$952$	3.32654	+	3.32654i	0.107814	+	0.107814i
$953$	−14.8183	−	14.8183i	−0.480013	−	0.480013i	0.425122	−	0.905136i	$-0.360231\pi$
$953$	−14.8183	−	14.8183i	−0.480013	−	0.480013i	−0.905136	+	0.425122i	$0.860231\pi$
$954$	36.0733			1.16792
$955$		0			0
$956$	15.3810			0.497457
$957$	−5.41935	+	5.41935i	−0.175183	+	0.175183i
$958$	24.8644	+	24.8644i	0.803333	+	0.803333i
$959$		−	14.0085i		−	0.452357i
$960$		0			0
$961$	−30.1198			−0.971608
$962$	−4.32932	+	4.32932i	−0.139583	+	0.139583i
$963$	20.9707	+	20.9707i	0.675772	+	0.675772i
$964$	16.7710			0.540156
$965$		0			0
$966$	0.757359	+	1.83646i	0.0243676	+	0.0590871i
$967$	−16.6986	−	16.6986i	−0.536992	−	0.536992i	0.385652	−	0.922644i	$-0.373977\pi$
$967$	−16.6986	−	16.6986i	−0.536992	−	0.536992i	−0.922644	+	0.385652i	$0.873977\pi$
$968$	−1.18389	+	1.18389i	−0.0380518	+	0.0380518i
$969$			3.34141i			0.107342i
$970$		0			0
$971$			4.63581i			0.148770i	0.997230	+	0.0743852i	$0.0236994\pi$
$971$			4.63581i			0.148770i	−0.997230	+	0.0743852i	$0.976301\pi$
$972$	6.48795	+	6.48795i	0.208101	+	0.208101i
$973$	15.8369	+	15.8369i	0.507707	+	0.507707i
$974$		−	27.7391i		−	0.888819i
$975$		0			0
$976$		−	10.6590i		−	0.341186i
$977$	24.3063	−	24.3063i	0.777626	−	0.777626i	−0.201801	−	0.979427i	$-0.564679\pi$
$977$	24.3063	−	24.3063i	0.777626	−	0.777626i	0.979427	+	0.201801i	$0.0646793\pi$
$978$	−2.88053	+	2.88053i	−0.0921092	+	0.0921092i
$979$		−	29.3762i		−	0.938868i
$980$		0			0
$981$		−	11.2799i		−	0.360139i
$982$	−24.6327	−	24.6327i	−0.786062	−	0.786062i
$983$	−3.10070	−	3.10070i	−0.0988970	−	0.0988970i	0.655927	−	0.754824i	$-0.272278\pi$
$983$	−3.10070	−	3.10070i	−0.0988970	−	0.0988970i	−0.754824	+	0.655927i	$0.772278\pi$
$984$			1.33299i			0.0424940i
$985$		0			0
$986$		−	28.5039i		−	0.907749i
$987$	−0.382696	+	0.382696i	−0.0121813	+	0.0121813i
$988$	1.57872	+	1.57872i	0.0502257	+	0.0502257i
$989$	16.1949	−	6.67881i	0.514968	−	0.212374i
$990$		0			0
$991$	−1.91539			−0.0608443			−0.0304221	−	0.999537i	$-0.509685\pi$
$991$	−1.91539			−0.0608443			−0.0304221	+	0.999537i	$0.509685\pi$
$992$	0.663382	+	0.663382i	0.0210624	+	0.0210624i
$993$	0.242641	−	0.242641i	0.00769997	−	0.00769997i
$994$	−5.23429			−0.166022
$995$		0			0
$996$		−	4.26706i		−	0.135207i
$997$	36.7069	+	36.7069i	1.16252	+	1.16252i	0.983922	+	0.178597i	$0.0571559\pi$
$997$	36.7069	+	36.7069i	1.16252	+	1.16252i	0.178597	+	0.983922i	$0.442844\pi$
$998$	24.8340	−	24.8340i	0.786106	−	0.786106i
$999$	−13.1405			−0.415747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.e.b.1057.3		8
5.2	odd	4		230.2.e.a.183.2	yes	8
5.3	odd	4		1150.2.e.c.643.3		8
5.4	even	2		230.2.e.b.137.2	yes	8
23.22	odd	2		1150.2.e.c.1057.3		8
115.22	even	4		230.2.e.b.183.2	yes	8
115.68	even	4	inner	1150.2.e.b.643.3		8
115.114	odd	2		230.2.e.a.137.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.e.a.137.2	✓	8	115.114	odd	2
230.2.e.a.183.2	yes	8	5.2	odd	4
230.2.e.b.137.2	yes	8	5.4	even	2
230.2.e.b.183.2	yes	8	115.22	even	4
1150.2.e.b.643.3		8	115.68	even	4	inner
1150.2.e.b.1057.3		8	1.1	even	1	trivial
1150.2.e.c.643.3		8	5.3	odd	4
1150.2.e.c.1057.3		8	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.254848 + 0.254848i) q^{3} +1.00000i q^{4} -0.360409 q^{6} +(-0.812668 + 0.812668i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.87011i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.254848 + 0.254848i) q^{3} +1.00000i q^{4} -0.360409 q^{6} +(-0.812668 + 0.812668i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.87011i q^{9} -3.05380i q^{11} +(-0.254848 - 0.254848i) q^{12} +(-0.697028 + 0.697028i) q^{13} -1.14929 q^{14} -1.00000 q^{16} +(-2.89444 + 2.89444i) q^{17} +(-2.02947 + 2.02947i) q^{18} -2.26493 q^{19} -0.414214i q^{21} +(2.15937 - 2.15937i) q^{22} +(-1.84214 + 4.42793i) q^{23} -0.360409i q^{24} -0.985746 q^{26} +(-1.49598 - 1.49598i) q^{27} +(-0.812668 - 0.812668i) q^{28} +6.96346i q^{29} -0.938164 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.778256 + 0.778256i) q^{33} -4.09335 q^{34} -2.87011 q^{36} +(4.39193 - 4.39193i) q^{37} +(-1.60155 - 1.60155i) q^{38} -0.355272i q^{39} -3.69853 q^{41} +(0.292893 - 0.292893i) q^{42} +(-2.58289 - 2.58289i) q^{43} +3.05380 q^{44} +(-4.43361 + 1.82843i) q^{46} +(-0.923909 - 0.923909i) q^{47} +(0.254848 - 0.254848i) q^{48} +5.67914i q^{49} -1.47528i q^{51} +(-0.697028 - 0.697028i) q^{52} +(-8.88737 - 8.88737i) q^{53} -2.11564i q^{54} -1.14929i q^{56} +(0.577212 - 0.577212i) q^{57} +(-4.92391 + 4.92391i) q^{58} +4.22248i q^{59} +10.6590i q^{61} +(-0.663382 - 0.663382i) q^{62} +(-2.33244 - 2.33244i) q^{63} -1.00000i q^{64} +1.10062i q^{66} +(2.79478 - 2.79478i) q^{67} +(-2.89444 - 2.89444i) q^{68} +(-0.658982 - 1.59791i) q^{69} +4.55438 q^{71} +(-2.02947 - 2.02947i) q^{72} +(-0.803131 + 0.803131i) q^{73} +6.21112 q^{74} -2.26493i q^{76} +(2.48173 + 2.48173i) q^{77} +(0.251215 - 0.251215i) q^{78} -16.8702 q^{79} -7.84782 q^{81} +(-2.61526 - 2.61526i) q^{82} +(8.37177 + 8.37177i) q^{83} +0.414214 q^{84} -3.65276i q^{86} +(-1.77462 - 1.77462i) q^{87} +(2.15937 + 2.15937i) q^{88} +9.61955 q^{89} -1.13290i q^{91} +(-4.42793 - 1.84214i) q^{92} +(0.239089 - 0.239089i) q^{93} -1.30661i q^{94} +0.360409 q^{96} +(-4.17254 + 4.17254i) q^{97} +(-4.01576 + 4.01576i) q^{98} +8.76474 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{6}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^6	\( 8 q + 4 q^{3} + 4 q^{6} + 4 q^{12} - 4 q^{14} - 8 q^{16} - 24 q^{17} + 8 q^{18} - 12 q^{19} + 12 q^{22} + 16 q^{23} + 12 q^{26} - 8 q^{27} - 4 q^{31} - 20 q^{33} - 4 q^{34} - 4 q^{36} - 4 q^{37} - 8 q^{38} + 12 q^{41} + 8 q^{42} + 20 q^{43} + 20 q^{44} + 16 q^{47} - 4 q^{48} - 20 q^{57} - 16 q^{58} - 4 q^{62} + 4 q^{67} - 24 q^{68} + 12 q^{69} - 44 q^{71} + 8 q^{72} - 28 q^{73} + 48 q^{74} - 4 q^{77} + 4 q^{78} + 8 q^{79} - 16 q^{81} - 8 q^{82} + 28 q^{83} - 8 q^{84} + 4 q^{87} + 12 q^{88} - 40 q^{89} - 16 q^{92} + 12 q^{93} - 4 q^{96} + 8 q^{97} - 16 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^6 + 4 * q^12 - 4 * q^14 - 8 * q^16 - 24 * q^17 + 8 * q^18 - 12 * q^19 + 12 * q^22 + 16 * q^23 + 12 * q^26 - 8 * q^27 - 4 * q^31 - 20 * q^33 - 4 * q^34 - 4 * q^36 - 4 * q^37 - 8 * q^38 + 12 * q^41 + 8 * q^42 + 20 * q^43 + 20 * q^44 + 16 * q^47 - 4 * q^48 - 20 * q^57 - 16 * q^58 - 4 * q^62 + 4 * q^67 - 24 * q^68 + 12 * q^69 - 44 * q^71 + 8 * q^72 - 28 * q^73 + 48 * q^74 - 4 * q^77 + 4 * q^78 + 8 * q^79 - 16 * q^81 - 8 * q^82 + 28 * q^83 - 8 * q^84 + 4 * q^87 + 12 * q^88 - 40 * q^89 - 16 * q^92 + 12 * q^93 - 4 * q^96 + 8 * q^97 - 16 * q^98 - 36 * q^99

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