LMFDB - Embedded newform 850.2.h.j.251.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [850,2,Mod(251,850)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(850, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("850.251"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.h (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,2,-4,0,-2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.1
Root			$1.65831 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	850.251
Dual form			850.2.h.j.701.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(-1.15831 - 1.15831i) q^{3} -1.00000 q^{4} +(1.15831 - 1.15831i) q^{6} +(-1.15831 + 1.15831i) q^{7} -1.00000i q^{8} -0.316625i q^{9} +(1.00000 - 1.00000i) q^{11} +(1.15831 + 1.15831i) q^{12} -1.00000 q^{13} +(-1.15831 - 1.15831i) q^{14} +1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} +0.316625 q^{18} +1.68338i q^{19} +2.68338 q^{21} +(1.00000 + 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-1.15831 + 1.15831i) q^{24} -1.00000i q^{26} +(-3.84169 + 3.84169i) q^{27} +(1.15831 - 1.15831i) q^{28} +(4.31662 + 4.31662i) q^{29} +(-0.158312 - 0.158312i) q^{31} +1.00000i q^{32} -2.31662 q^{33} +(-4.00000 - 1.00000i) q^{34} +0.316625i q^{36} +(0.316625 + 0.316625i) q^{37} -1.68338 q^{38} +(1.15831 + 1.15831i) q^{39} +(-1.31662 + 1.31662i) q^{41} +2.68338i q^{42} +6.00000i q^{43} +(-1.00000 + 1.00000i) q^{44} +(-1.00000 - 1.00000i) q^{46} -8.94987 q^{47} +(-1.15831 - 1.15831i) q^{48} +4.31662i q^{49} +(5.79156 - 3.47494i) q^{51} +1.00000 q^{52} +7.94987i q^{53} +(-3.84169 - 3.84169i) q^{54} +(1.15831 + 1.15831i) q^{56} +(1.94987 - 1.94987i) q^{57} +(-4.31662 + 4.31662i) q^{58} +8.63325i q^{59} +(-1.31662 + 1.31662i) q^{61} +(0.158312 - 0.158312i) q^{62} +(0.366750 + 0.366750i) q^{63} -1.00000 q^{64} -2.31662i q^{66} -6.63325 q^{67} +(1.00000 - 4.00000i) q^{68} +2.31662 q^{69} +(-2.84169 - 2.84169i) q^{71} -0.316625 q^{72} +(4.63325 + 4.63325i) q^{73} +(-0.316625 + 0.316625i) q^{74} -1.68338i q^{76} +2.31662i q^{77} +(-1.15831 + 1.15831i) q^{78} +(-5.47494 + 5.47494i) q^{79} +7.94987 q^{81} +(-1.31662 - 1.31662i) q^{82} +0.633250i q^{83} -2.68338 q^{84} -6.00000 q^{86} -10.0000i q^{87} +(-1.00000 - 1.00000i) q^{88} +5.36675 q^{89} +(1.15831 - 1.15831i) q^{91} +(1.00000 - 1.00000i) q^{92} +0.366750i q^{93} -8.94987i q^{94} +(1.15831 - 1.15831i) q^{96} +(-2.00000 - 2.00000i) q^{97} -4.31662 q^{98} +(-0.316625 - 0.316625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 4 q^{17} - 12 q^{18} + 24 q^{21} + 4 q^{22} - 4 q^{23} + 2 q^{24} - 22 q^{27} - 2 q^{28} + 4 q^{29} + 6 q^{31}+ \cdots + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^4 - 2 * q^6 + 2 * q^7 + 4 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 4 * q^17 - 12 * q^18 + 24 * q^21 + 4 * q^22 - 4 * q^23 + 2 * q^24 - 22 * q^27 - 2 * q^28 + 4 * q^29 + 6 * q^31 + 4 * q^33 - 16 * q^34 - 12 * q^37 - 20 * q^38 - 2 * q^39 + 8 * q^41 - 4 * q^44 - 4 * q^46 + 4 * q^47 + 2 * q^48 - 10 * q^51 + 4 * q^52 - 22 * q^54 - 2 * q^56 - 32 * q^57 - 4 * q^58 + 8 * q^61 - 6 * q^62 + 28 * q^63 - 4 * q^64 + 4 * q^68 - 4 * q^69 - 18 * q^71 + 12 * q^72 - 8 * q^73 + 12 * q^74 + 2 * q^78 - 2 * q^79 - 8 * q^81 + 8 * q^82 - 24 * q^84 - 24 * q^86 - 4 * q^88 + 48 * q^89 - 2 * q^91 + 4 * q^92 - 2 * q^96 - 8 * q^97 - 4 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.15831	−	1.15831i	−0.668752	−	0.668752i	0.288675	−	0.957427i	$-0.406785\pi$
$3$	−1.15831	−	1.15831i	−0.668752	−	0.668752i	−0.957427	+	0.288675i	$0.906785\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	1.15831	−	1.15831i	0.472879	−	0.472879i
$7$	−1.15831	+	1.15831i	−0.437801	+	0.437801i	−0.891271	−	0.453470i	$-0.850186\pi$
$7$	−1.15831	+	1.15831i	−0.437801	+	0.437801i	0.453470	+	0.891271i	$0.350186\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	0.316625i		−	0.105542i
$10$		0			0
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	−0.540094	−	0.841605i	$-0.681611\pi$
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	0.841605	+	0.540094i	$0.181611\pi$
$12$	1.15831	+	1.15831i	0.334376	+	0.334376i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	−1.15831	−	1.15831i	−0.309572	−	0.309572i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.00000	+	4.00000i	−0.242536	+	0.970143i
$17$	−1.00000	+	4.00000i	−0.242536	+	0.970143i
$18$	0.316625			0.0746292
$19$			1.68338i			0.386193i	0.981180	+	0.193096i	$0.0618530\pi$
$19$			1.68338i			0.386193i	−0.981180	+	0.193096i	$0.938147\pi$
$20$		0			0
$21$	2.68338			0.585560
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$	−1.15831	+	1.15831i	−0.236440	+	0.236440i
$25$		0			0
$26$		−	1.00000i		−	0.196116i
$27$	−3.84169	+	3.84169i	−0.739333	+	0.739333i
$28$	1.15831	−	1.15831i	0.218900	−	0.218900i
$29$	4.31662	+	4.31662i	0.801577	+	0.801577i	0.983342	−	0.181765i	$-0.0581810\pi$
$29$	4.31662	+	4.31662i	0.801577	+	0.801577i	−0.181765	+	0.983342i	$0.558181\pi$
$30$		0			0
$31$	−0.158312	−	0.158312i	−0.0284337	−	0.0284337i	0.692747	−	0.721181i	$-0.256400\pi$
$31$	−0.158312	−	0.158312i	−0.0284337	−	0.0284337i	−0.721181	+	0.692747i	$0.756400\pi$
$32$			1.00000i			0.176777i
$33$	−2.31662			−0.403273
$34$	−4.00000	−	1.00000i	−0.685994	−	0.171499i
$35$		0			0
$36$			0.316625i			0.0527708i
$37$	0.316625	+	0.316625i	0.0520528	+	0.0520528i	0.732654	−	0.680601i	$-0.238281\pi$
$37$	0.316625	+	0.316625i	0.0520528	+	0.0520528i	−0.680601	+	0.732654i	$0.738281\pi$
$38$	−1.68338			−0.273080
$39$	1.15831	+	1.15831i	0.185478	+	0.185478i
$40$		0			0
$41$	−1.31662	+	1.31662i	−0.205622	+	0.205622i	−0.802404	−	0.596782i	$-0.796446\pi$
$41$	−1.31662	+	1.31662i	−0.205622	+	0.205622i	0.596782	+	0.802404i	$0.296446\pi$
$42$			2.68338i			0.414054i
$43$			6.00000i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$			6.00000i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$	−1.00000	+	1.00000i	−0.150756	+	0.150756i
$45$		0			0
$46$	−1.00000	−	1.00000i	−0.147442	−	0.147442i
$47$	−8.94987			−1.30547			−0.652737	−	0.757585i	$-0.726379\pi$
$47$	−8.94987			−1.30547			−0.652737	+	0.757585i	$0.726379\pi$
$48$	−1.15831	−	1.15831i	−0.167188	−	0.167188i
$49$			4.31662i			0.616661i
$50$		0			0
$51$	5.79156	−	3.47494i	0.810981	−	0.486589i
$52$	1.00000			0.138675
$53$			7.94987i			1.09200i	0.837785	+	0.546000i	$0.183850\pi$
$53$			7.94987i			1.09200i	−0.837785	+	0.546000i	$0.816150\pi$
$54$	−3.84169	−	3.84169i	−0.522787	−	0.522787i
$55$		0			0
$56$	1.15831	+	1.15831i	0.154786	+	0.154786i
$57$	1.94987	−	1.94987i	0.258267	−	0.258267i
$58$	−4.31662	+	4.31662i	−0.566801	+	0.566801i
$59$			8.63325i			1.12395i	0.827153	+	0.561977i	$0.189959\pi$
$59$			8.63325i			1.12395i	−0.827153	+	0.561977i	$0.810041\pi$
$60$		0			0
$61$	−1.31662	+	1.31662i	−0.168577	+	0.168577i	−0.786353	−	0.617777i	$-0.788033\pi$
$61$	−1.31662	+	1.31662i	−0.168577	+	0.168577i	0.617777	+	0.786353i	$0.288033\pi$
$62$	0.158312	−	0.158312i	0.0201057	−	0.0201057i
$63$	0.366750	+	0.366750i	0.0462062	+	0.0462062i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		−	2.31662i		−	0.285157i
$67$	−6.63325			−0.810380			−0.405190	−	0.914232i	$-0.632795\pi$
$67$	−6.63325			−0.810380			−0.405190	+	0.914232i	$0.632795\pi$
$68$	1.00000	−	4.00000i	0.121268	−	0.485071i
$69$	2.31662			0.278889
$70$		0			0
$71$	−2.84169	−	2.84169i	−0.337246	−	0.337246i	0.518084	−	0.855330i	$-0.326646\pi$
$71$	−2.84169	−	2.84169i	−0.337246	−	0.337246i	−0.855330	+	0.518084i	$0.826646\pi$
$72$	−0.316625			−0.0373146
$73$	4.63325	+	4.63325i	0.542281	+	0.542281i	0.924197	−	0.381916i	$-0.124736\pi$
$73$	4.63325	+	4.63325i	0.542281	+	0.542281i	−0.381916	+	0.924197i	$0.624736\pi$
$74$	−0.316625	+	0.316625i	−0.0368069	+	0.0368069i
$75$		0			0
$76$		−	1.68338i		−	0.193096i
$77$			2.31662i			0.264004i
$78$	−1.15831	+	1.15831i	−0.131153	+	0.131153i
$79$	−5.47494	+	5.47494i	−0.615979	+	0.615979i	−0.944497	−	0.328519i	$-0.893451\pi$
$79$	−5.47494	+	5.47494i	−0.615979	+	0.615979i	0.328519	+	0.944497i	$0.393451\pi$
$80$		0			0
$81$	7.94987			0.883319
$82$	−1.31662	−	1.31662i	−0.145397	−	0.145397i
$83$			0.633250i			0.0695082i	0.999396	+	0.0347541i	$0.0110648\pi$
$83$			0.633250i			0.0695082i	−0.999396	+	0.0347541i	$0.988935\pi$
$84$	−2.68338			−0.292780
$85$		0			0
$86$	−6.00000			−0.646997
$87$		−	10.0000i		−	1.07211i
$88$	−1.00000	−	1.00000i	−0.106600	−	0.106600i
$89$	5.36675			0.568874			0.284437	−	0.958695i	$-0.408193\pi$
$89$	5.36675			0.568874			0.284437	+	0.958695i	$0.408193\pi$
$90$		0			0
$91$	1.15831	−	1.15831i	0.121424	−	0.121424i
$92$	1.00000	−	1.00000i	0.104257	−	0.104257i
$93$			0.366750i			0.0380302i
$94$		−	8.94987i		−	0.923109i
$95$		0			0
$96$	1.15831	−	1.15831i	0.118220	−	0.118220i
$97$	−2.00000	−	2.00000i	−0.203069	−	0.203069i	0.598244	−	0.801314i	$-0.295865\pi$
$97$	−2.00000	−	2.00000i	−0.203069	−	0.203069i	−0.801314	+	0.598244i	$0.795865\pi$
$98$	−4.31662			−0.436045
$99$	−0.316625	−	0.316625i	−0.0318220	−	0.0318220i
$100$		0			0
$101$	−7.63325			−0.759537			−0.379768	−	0.925082i	$-0.623996\pi$
$101$	−7.63325			−0.759537			−0.379768	+	0.925082i	$0.623996\pi$
$102$	3.47494	+	5.79156i	0.344070	+	0.573450i
$103$	15.5831			1.53545			0.767725	−	0.640779i	$-0.221388\pi$
$103$	15.5831			1.53545			0.767725	+	0.640779i	$0.221388\pi$
$104$			1.00000i			0.0980581i
$105$		0			0
$106$	−7.94987			−0.772160
$107$	−5.84169	−	5.84169i	−0.564737	−	0.564737i	0.365912	−	0.930649i	$-0.380757\pi$
$107$	−5.84169	−	5.84169i	−0.564737	−	0.564737i	−0.930649	+	0.365912i	$0.880757\pi$
$108$	3.84169	−	3.84169i	0.369667	−	0.369667i
$109$	−2.00000	+	2.00000i	−0.191565	+	0.191565i	−0.796372	−	0.604807i	$-0.793250\pi$
$109$	−2.00000	+	2.00000i	−0.191565	+	0.191565i	0.604807	+	0.796372i	$0.293250\pi$
$110$		0			0
$111$		−	0.733501i		−	0.0696208i
$112$	−1.15831	+	1.15831i	−0.109450	+	0.109450i
$113$	13.2665	−	13.2665i	1.24801	−	1.24801i	0.291409	−	0.956599i	$-0.405876\pi$
$113$	13.2665	−	13.2665i	1.24801	−	1.24801i	0.956599	−	0.291409i	$-0.0941239\pi$
$114$	1.94987	+	1.94987i	0.182622	+	0.182622i
$115$		0			0
$116$	−4.31662	−	4.31662i	−0.400789	−	0.400789i
$117$			0.316625i			0.0292720i
$118$	−8.63325			−0.794755
$119$	−3.47494	−	5.79156i	−0.318547	−	0.530912i
$120$		0			0
$121$			9.00000i			0.818182i
$122$	−1.31662	−	1.31662i	−0.119202	−	0.119202i
$123$	3.05013			0.275021
$124$	0.158312	+	0.158312i	0.0142169	+	0.0142169i
$125$		0			0
$126$	−0.366750	+	0.366750i	−0.0326727	+	0.0326727i
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	6.94987	−	6.94987i	0.611902	−	0.611902i
$130$		0			0
$131$	−14.7916	−	14.7916i	−1.29234	−	1.29234i	−0.933333	−	0.359012i	$-0.883114\pi$
$131$	−14.7916	−	14.7916i	−1.29234	−	1.29234i	−0.359012	−	0.933333i	$-0.616886\pi$
$132$	2.31662			0.201636
$133$	−1.94987	−	1.94987i	−0.169076	−	0.169076i
$134$		−	6.63325i		−	0.573025i
$135$		0			0
$136$	4.00000	+	1.00000i	0.342997	+	0.0857493i
$137$	19.9499			1.70443			0.852216	−	0.523189i	$-0.175258\pi$
$137$	19.9499			1.70443			0.852216	+	0.523189i	$0.175258\pi$
$138$			2.31662i			0.197204i
$139$	−13.7916	−	13.7916i	−1.16979	−	1.16979i	−0.982260	−	0.187525i	$-0.939953\pi$
$139$	−13.7916	−	13.7916i	−1.16979	−	1.16979i	−0.187525	−	0.982260i	$-0.560047\pi$
$140$		0			0
$141$	10.3668	+	10.3668i	0.873038	+	0.873038i
$142$	2.84169	−	2.84169i	0.238469	−	0.238469i
$143$	−1.00000	+	1.00000i	−0.0836242	+	0.0836242i
$144$		−	0.316625i		−	0.0263854i
$145$		0			0
$146$	−4.63325	+	4.63325i	−0.383450	+	0.383450i
$147$	5.00000	−	5.00000i	0.412393	−	0.412393i
$148$	−0.316625	−	0.316625i	−0.0260264	−	0.0260264i
$149$	21.9499			1.79820			0.899102	−	0.437739i	$-0.144221\pi$
$149$	21.9499			1.79820			0.899102	+	0.437739i	$0.144221\pi$
$150$		0			0
$151$			7.68338i			0.625264i	0.949874	+	0.312632i	$0.101211\pi$
$151$			7.68338i			0.625264i	−0.949874	+	0.312632i	$0.898789\pi$
$152$	1.68338			0.136540
$153$	1.26650	+	0.316625i	0.102390	+	0.0255976i
$154$	−2.31662			−0.186679
$155$		0			0
$156$	−1.15831	−	1.15831i	−0.0927392	−	0.0927392i
$157$	15.3166			1.22240			0.611200	−	0.791476i	$-0.290687\pi$
$157$	15.3166			1.22240			0.611200	+	0.791476i	$0.290687\pi$
$158$	−5.47494	−	5.47494i	−0.435563	−	0.435563i
$159$	9.20844	−	9.20844i	0.730277	−	0.730277i
$160$		0			0
$161$		−	2.31662i		−	0.182576i
$162$			7.94987i			0.624601i
$163$	2.84169	−	2.84169i	0.222578	−	0.222578i	−0.587005	−	0.809583i	$-0.699693\pi$
$163$	2.84169	−	2.84169i	0.222578	−	0.222578i	0.809583	+	0.587005i	$0.199693\pi$
$164$	1.31662	−	1.31662i	0.102811	−	0.102811i
$165$		0			0
$166$	−0.633250			−0.0491497
$167$	−7.00000	−	7.00000i	−0.541676	−	0.541676i	0.382344	−	0.924020i	$-0.375117\pi$
$167$	−7.00000	−	7.00000i	−0.541676	−	0.541676i	−0.924020	+	0.382344i	$0.875117\pi$
$168$		−	2.68338i		−	0.207027i
$169$	−12.0000			−0.923077
$170$		0			0
$171$	0.532998			0.0407594
$172$		−	6.00000i		−	0.457496i
$173$	−17.3166	−	17.3166i	−1.31656	−	1.31656i	−0.916481	−	0.400077i	$-0.868983\pi$
$173$	−17.3166	−	17.3166i	−1.31656	−	1.31656i	−0.400077	−	0.916481i	$-0.631017\pi$
$174$	10.0000			0.758098
$175$		0			0
$176$	1.00000	−	1.00000i	0.0753778	−	0.0753778i
$177$	10.0000	−	10.0000i	0.751646	−	0.751646i
$178$			5.36675i			0.402255i
$179$		−	8.31662i		−	0.621614i	−0.950473	−	0.310807i	$-0.899401\pi$
$179$		−	8.31662i		−	0.621614i	0.950473	−	0.310807i	$-0.100599\pi$
$180$		0			0
$181$	−4.36675	+	4.36675i	−0.324578	+	0.324578i	−0.850520	−	0.525942i	$-0.823713\pi$
$181$	−4.36675	+	4.36675i	−0.324578	+	0.324578i	0.525942	+	0.850520i	$0.323713\pi$
$182$	1.15831	+	1.15831i	0.0858598	+	0.0858598i
$183$	3.05013			0.225472
$184$	1.00000	+	1.00000i	0.0737210	+	0.0737210i
$185$		0			0
$186$	−0.366750			−0.0268914
$187$	3.00000	+	5.00000i	0.219382	+	0.365636i
$188$	8.94987			0.652737
$189$		−	8.89975i		−	0.647361i
$190$		0			0
$191$	8.94987			0.647590			0.323795	−	0.946127i	$-0.395041\pi$
$191$	8.94987			0.647590			0.323795	+	0.946127i	$0.395041\pi$
$192$	1.15831	+	1.15831i	0.0835940	+	0.0835940i
$193$	6.31662	−	6.31662i	0.454681	−	0.454681i	−0.442224	−	0.896905i	$-0.645810\pi$
$193$	6.31662	−	6.31662i	0.454681	−	0.454681i	0.896905	+	0.442224i	$0.145810\pi$
$194$	2.00000	−	2.00000i	0.143592	−	0.143592i
$195$		0			0
$196$		−	4.31662i		−	0.308330i
$197$	−7.31662	+	7.31662i	−0.521288	+	0.521288i	−0.917960	−	0.396672i	$-0.870165\pi$
$197$	−7.31662	+	7.31662i	−0.521288	+	0.521288i	0.396672	+	0.917960i	$0.370165\pi$
$198$	0.316625	−	0.316625i	0.0225015	−	0.0225015i
$199$	11.6332	+	11.6332i	0.824659	+	0.824659i	0.986772	−	0.162113i	$-0.0518309\pi$
$199$	11.6332	+	11.6332i	0.824659	+	0.824659i	−0.162113	+	0.986772i	$0.551831\pi$
$200$		0			0
$201$	7.68338	+	7.68338i	0.541944	+	0.541944i
$202$		−	7.63325i		−	0.537074i
$203$	−10.0000			−0.701862
$204$	−5.79156	+	3.47494i	−0.405490	+	0.243294i
$205$		0			0
$206$			15.5831i			1.08573i
$207$	0.316625	+	0.316625i	0.0220069	+	0.0220069i
$208$	−1.00000			−0.0693375
$209$	1.68338	+	1.68338i	0.116441	+	0.116441i
$210$		0			0
$211$	−17.1082	+	17.1082i	−1.17778	+	1.17778i	−0.197467	+	0.980310i	$0.563271\pi$
$211$	−17.1082	+	17.1082i	−1.17778	+	1.17778i	−0.980310	+	0.197467i	$0.936729\pi$
$212$		−	7.94987i		−	0.546000i
$213$			6.58312i			0.451068i
$214$	5.84169	−	5.84169i	0.399330	−	0.399330i
$215$		0			0
$216$	3.84169	+	3.84169i	0.261394	+	0.261394i
$217$	0.366750			0.0248966
$218$	−2.00000	−	2.00000i	−0.135457	−	0.135457i
$219$		−	10.7335i		−	0.725303i
$220$		0			0
$221$	1.00000	−	4.00000i	0.0672673	−	0.269069i
$222$	0.733501			0.0492294
$223$			27.5831i			1.84710i	0.383475	+	0.923551i	$0.374727\pi$
$223$			27.5831i			1.84710i	−0.383475	+	0.923551i	$0.625273\pi$
$224$	−1.15831	−	1.15831i	−0.0773930	−	0.0773930i
$225$		0			0
$226$	13.2665	+	13.2665i	0.882474	+	0.882474i
$227$	−1.15831	+	1.15831i	−0.0768799	+	0.0768799i	−0.744501	−	0.667621i	$-0.767313\pi$
$227$	−1.15831	+	1.15831i	−0.0768799	+	0.0768799i	0.667621	+	0.744501i	$0.267313\pi$
$228$	−1.94987	+	1.94987i	−0.129134	+	0.129134i
$229$			22.8997i			1.51326i	0.653844	+	0.756629i	$0.273155\pi$
$229$			22.8997i			1.51326i	−0.653844	+	0.756629i	$0.726845\pi$
$230$		0			0
$231$	2.68338	−	2.68338i	0.176553	−	0.176553i
$232$	4.31662	−	4.31662i	0.283400	−	0.283400i
$233$	−16.9499	−	16.9499i	−1.11042	−	1.11042i	−0.993093	−	0.117330i	$-0.962566\pi$
$233$	−16.9499	−	16.9499i	−1.11042	−	1.11042i	−0.117330	−	0.993093i	$-0.537434\pi$
$234$	−0.316625			−0.0206984
$235$		0			0
$236$		−	8.63325i		−	0.561977i
$237$	12.6834			0.823874
$238$	5.79156	−	3.47494i	0.375411	−	0.225247i
$239$	−4.63325			−0.299700			−0.149850	−	0.988709i	$-0.547879\pi$
$239$	−4.63325			−0.299700			−0.149850	+	0.988709i	$0.547879\pi$
$240$		0			0
$241$	13.3166	+	13.3166i	0.857799	+	0.857799i	0.991079	−	0.133279i	$-0.0425507\pi$
$241$	13.3166	+	13.3166i	0.857799	+	0.857799i	−0.133279	+	0.991079i	$0.542551\pi$
$242$	−9.00000			−0.578542
$243$	2.31662	+	2.31662i	0.148612	+	0.148612i
$244$	1.31662	−	1.31662i	0.0842883	−	0.0842883i
$245$		0			0
$246$			3.05013i			0.194469i
$247$		−	1.68338i		−	0.107111i
$248$	−0.158312	+	0.158312i	−0.0100528	+	0.0100528i
$249$	0.733501	−	0.733501i	0.0464837	−	0.0464837i
$250$		0			0
$251$	−7.26650			−0.458657			−0.229329	−	0.973349i	$-0.573653\pi$
$251$	−7.26650			−0.458657			−0.229329	+	0.973349i	$0.573653\pi$
$252$	−0.366750	−	0.366750i	−0.0231031	−	0.0231031i
$253$			2.00000i			0.125739i
$254$	2.00000			0.125491
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	9.31662i		−	0.581155i	−0.956851	−	0.290578i	$-0.906153\pi$
$257$		−	9.31662i		−	0.581155i	0.956851	−	0.290578i	$-0.0938474\pi$
$258$	6.94987	+	6.94987i	0.432680	+	0.432680i
$259$	−0.733501			−0.0455775
$260$		0			0
$261$	1.36675	−	1.36675i	0.0845997	−	0.0845997i
$262$	14.7916	−	14.7916i	0.913826	−	0.913826i
$263$		−	4.00000i		−	0.246651i	−0.992366	−	0.123325i	$-0.960644\pi$
$263$		−	4.00000i		−	0.246651i	0.992366	−	0.123325i	$-0.0393559\pi$
$264$			2.31662i			0.142578i
$265$		0			0
$266$	1.94987	−	1.94987i	0.119554	−	0.119554i
$267$	−6.21637	−	6.21637i	−0.380436	−	0.380436i
$268$	6.63325			0.405190
$269$	16.2665	+	16.2665i	0.991786	+	0.991786i	0.999967	−	0.00818058i	$-0.00260399\pi$
$269$	16.2665	+	16.2665i	0.991786	+	0.991786i	−0.00818058	+	0.999967i	$0.502604\pi$
$270$		0			0
$271$	−19.5831			−1.18959			−0.594795	−	0.803877i	$-0.702767\pi$
$271$	−19.5831			−1.18959			−0.594795	+	0.803877i	$0.702767\pi$
$272$	−1.00000	+	4.00000i	−0.0606339	+	0.242536i
$273$	−2.68338			−0.162405
$274$			19.9499i			1.20522i
$275$		0			0
$276$	−2.31662			−0.139444
$277$	0.683375	+	0.683375i	0.0410600	+	0.0410600i	0.727339	−	0.686279i	$-0.240757\pi$
$277$	0.683375	+	0.683375i	0.0410600	+	0.0410600i	−0.686279	+	0.727339i	$0.740757\pi$
$278$	13.7916	−	13.7916i	0.827163	−	0.827163i
$279$	−0.0501256	+	0.0501256i	−0.00300094	+	0.00300094i
$280$		0			0
$281$		−	5.00000i		−	0.298275i	−0.988816	−	0.149137i	$-0.952350\pi$
$281$		−	5.00000i		−	0.298275i	0.988816	−	0.149137i	$-0.0476497\pi$
$282$	−10.3668	+	10.3668i	−0.617331	+	0.617331i
$283$	6.68338	−	6.68338i	0.397285	−	0.397285i	−0.479989	−	0.877274i	$-0.659359\pi$
$283$	6.68338	−	6.68338i	0.397285	−	0.397285i	0.877274	+	0.479989i	$0.159359\pi$
$284$	2.84169	+	2.84169i	0.168623	+	0.168623i
$285$		0			0
$286$	−1.00000	−	1.00000i	−0.0591312	−	0.0591312i
$287$		−	3.05013i		−	0.180043i
$288$	0.316625			0.0186573
$289$	−15.0000	−	8.00000i	−0.882353	−	0.470588i
$290$		0			0
$291$			4.63325i			0.271606i
$292$	−4.63325	−	4.63325i	−0.271140	−	0.271140i
$293$	−19.8997			−1.16256			−0.581278	−	0.813705i	$-0.697447\pi$
$293$	−19.8997			−1.16256			−0.581278	+	0.813705i	$0.697447\pi$
$294$	5.00000	+	5.00000i	0.291606	+	0.291606i
$295$		0			0
$296$	0.316625	−	0.316625i	0.0184034	−	0.0184034i
$297$			7.68338i			0.445835i
$298$			21.9499i			1.27152i
$299$	1.00000	−	1.00000i	0.0578315	−	0.0578315i
$300$		0			0
$301$	−6.94987	−	6.94987i	−0.400584	−	0.400584i
$302$	−7.68338			−0.442129
$303$	8.84169	+	8.84169i	0.507942	+	0.507942i
$304$			1.68338i			0.0965482i
$305$		0			0
$306$	−0.316625	+	1.26650i	−0.0181002	+	0.0724009i
$307$	26.5330			1.51432			0.757159	−	0.653231i	$-0.226587\pi$
$307$	26.5330			1.51432			0.757159	+	0.653231i	$0.226587\pi$
$308$		−	2.31662i		−	0.132002i
$309$	−18.0501	−	18.0501i	−1.02684	−	1.02684i
$310$		0			0
$311$	−10.1583	−	10.1583i	−0.576025	−	0.576025i	0.357781	−	0.933806i	$-0.383534\pi$
$311$	−10.1583	−	10.1583i	−0.576025	−	0.576025i	−0.933806	+	0.357781i	$0.883534\pi$
$312$	1.15831	−	1.15831i	0.0655765	−	0.0655765i
$313$	5.94987	−	5.94987i	0.336307	−	0.336307i	−0.518669	−	0.854975i	$-0.673572\pi$
$313$	5.94987	−	5.94987i	0.336307	−	0.336307i	0.854975	+	0.518669i	$0.173572\pi$
$314$			15.3166i			0.864367i
$315$		0			0
$316$	5.47494	−	5.47494i	0.307989	−	0.307989i
$317$	−5.00000	+	5.00000i	−0.280828	+	0.280828i	−0.833439	−	0.552611i	$-0.813631\pi$
$317$	−5.00000	+	5.00000i	−0.280828	+	0.280828i	0.552611	+	0.833439i	$0.313631\pi$
$318$	9.20844	+	9.20844i	0.516384	+	0.516384i
$319$	8.63325			0.483369
$320$		0			0
$321$			13.5330i			0.755338i
$322$	2.31662			0.129100
$323$	−6.73350	−	1.68338i	−0.374662	−	0.0936655i
$324$	−7.94987			−0.441660
$325$		0			0
$326$	2.84169	+	2.84169i	0.157387	+	0.157387i
$327$	4.63325			0.256219
$328$	1.31662	+	1.31662i	0.0726984	+	0.0726984i
$329$	10.3668	−	10.3668i	0.571537	−	0.571537i
$330$		0			0
$331$		−	21.5831i		−	1.18632i	−0.805086	−	0.593158i	$-0.797881\pi$
$331$		−	21.5831i		−	1.18632i	0.805086	−	0.593158i	$-0.202119\pi$
$332$		−	0.633250i		−	0.0347541i
$333$	0.100251	−	0.100251i	0.00549374	−	0.00549374i
$334$	7.00000	−	7.00000i	0.383023	−	0.383023i
$335$		0			0
$336$	2.68338			0.146390
$337$	−4.31662	−	4.31662i	−0.235142	−	0.235142i	0.579693	−	0.814835i	$-0.303172\pi$
$337$	−4.31662	−	4.31662i	−0.235142	−	0.235142i	−0.814835	+	0.579693i	$0.803172\pi$
$338$		−	12.0000i		−	0.652714i
$339$	−30.7335			−1.66921
$340$		0			0
$341$	−0.316625			−0.0171462
$342$			0.532998i			0.0288212i
$343$	−13.1082	−	13.1082i	−0.707776	−	0.707776i
$344$	6.00000			0.323498
$345$		0			0
$346$	17.3166	−	17.3166i	0.930948	−	0.930948i
$347$	−0.791562	+	0.791562i	−0.0424933	+	0.0424933i	−0.728034	−	0.685541i	$-0.759566\pi$
$347$	−0.791562	+	0.791562i	−0.0424933	+	0.0424933i	0.685541	+	0.728034i	$0.259566\pi$
$348$			10.0000i			0.536056i
$349$			12.0501i			0.645028i	0.946565	+	0.322514i	$0.104528\pi$
$349$			12.0501i			0.645028i	−0.946565	+	0.322514i	$0.895472\pi$
$350$		0			0
$351$	3.84169	−	3.84169i	0.205054	−	0.205054i
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	−1.73350			−0.0922649			−0.0461325	−	0.998935i	$-0.514690\pi$
$353$	−1.73350			−0.0922649			−0.0461325	+	0.998935i	$0.514690\pi$
$354$	10.0000	+	10.0000i	0.531494	+	0.531494i
$355$		0			0
$356$	−5.36675			−0.284437
$357$	−2.68338	+	10.7335i	−0.142019	+	0.568077i
$358$	8.31662			0.439547
$359$			11.6834i			0.616625i	0.951285	+	0.308312i	$0.0997642\pi$
$359$			11.6834i			0.616625i	−0.951285	+	0.308312i	$0.900236\pi$
$360$		0			0
$361$	16.1662			0.850855
$362$	−4.36675	−	4.36675i	−0.229511	−	0.229511i
$363$	10.4248	−	10.4248i	0.547161	−	0.547161i
$364$	−1.15831	+	1.15831i	−0.0607121	+	0.0607121i
$365$		0			0
$366$			3.05013i			0.159433i
$367$	−26.1583	+	26.1583i	−1.36545	+	1.36545i	−0.498649	+	0.866804i	$0.666170\pi$
$367$	−26.1583	+	26.1583i	−1.36545	+	1.36545i	−0.866804	+	0.498649i	$0.833830\pi$
$368$	−1.00000	+	1.00000i	−0.0521286	+	0.0521286i
$369$	0.416876	+	0.416876i	0.0217017	+	0.0217017i
$370$		0			0
$371$	−9.20844	−	9.20844i	−0.478078	−	0.478078i
$372$		−	0.366750i		−	0.0190151i
$373$	−19.5330			−1.01138			−0.505690	−	0.862715i	$-0.668762\pi$
$373$	−19.5330			−1.01138			−0.505690	+	0.862715i	$0.668762\pi$
$374$	−5.00000	+	3.00000i	−0.258544	+	0.155126i
$375$		0			0
$376$			8.94987i			0.461555i
$377$	−4.31662	−	4.31662i	−0.222317	−	0.222317i
$378$	8.89975			0.457754
$379$	−16.4749	−	16.4749i	−0.846261	−	0.846261i	0.143404	−	0.989664i	$-0.454195\pi$
$379$	−16.4749	−	16.4749i	−0.846261	−	0.846261i	−0.989664	+	0.143404i	$0.954195\pi$
$380$		0			0
$381$	−2.31662	+	2.31662i	−0.118684	+	0.118684i
$382$			8.94987i			0.457915i
$383$			2.94987i			0.150732i	0.997156	+	0.0753658i	$0.0240124\pi$
$383$			2.94987i			0.150732i	−0.997156	+	0.0753658i	$0.975988\pi$
$384$	−1.15831	+	1.15831i	−0.0591099	+	0.0591099i
$385$		0			0
$386$	6.31662	+	6.31662i	0.321508	+	0.321508i
$387$	1.89975			0.0965697
$388$	2.00000	+	2.00000i	0.101535	+	0.101535i
$389$		−	25.2665i		−	1.28106i	−0.767932	−	0.640531i	$-0.778714\pi$
$389$		−	25.2665i		−	1.28106i	0.767932	−	0.640531i	$-0.221286\pi$
$390$		0			0
$391$	−3.00000	−	5.00000i	−0.151717	−	0.252861i
$392$	4.31662			0.218022
$393$			34.2665i			1.72852i
$394$	−7.31662	−	7.31662i	−0.368606	−	0.368606i
$395$		0			0
$396$	0.316625	+	0.316625i	0.0159110	+	0.0159110i
$397$	−23.8997	+	23.8997i	−1.19949	+	1.19949i	−0.225176	+	0.974318i	$0.572296\pi$
$397$	−23.8997	+	23.8997i	−1.19949	+	1.19949i	−0.974318	+	0.225176i	$0.927704\pi$
$398$	−11.6332	+	11.6332i	−0.583122	+	0.583122i
$399$			4.51713i			0.226139i
$400$		0			0
$401$	22.5831	−	22.5831i	1.12775	−	1.12775i	0.137205	−	0.990543i	$-0.456188\pi$
$401$	22.5831	−	22.5831i	1.12775	−	1.12775i	0.990543	−	0.137205i	$-0.0438118\pi$
$402$	−7.68338	+	7.68338i	−0.383212	+	0.383212i
$403$	0.158312	+	0.158312i	0.00788610	+	0.00788610i
$404$	7.63325			0.379768
$405$		0			0
$406$		−	10.0000i		−	0.496292i
$407$	0.633250			0.0313890
$408$	−3.47494	−	5.79156i	−0.172035	−	0.286725i
$409$	−28.8997			−1.42900			−0.714500	−	0.699635i	$-0.753346\pi$
$409$	−28.8997			−1.42900			−0.714500	+	0.699635i	$0.753346\pi$
$410$		0			0
$411$	−23.1082	−	23.1082i	−1.13984	−	1.13984i
$412$	−15.5831			−0.767725
$413$	−10.0000	−	10.0000i	−0.492068	−	0.492068i
$414$	−0.316625	+	0.316625i	−0.0155613	+	0.0155613i
$415$		0			0
$416$		−	1.00000i		−	0.0490290i
$417$			31.9499i			1.56459i
$418$	−1.68338	+	1.68338i	−0.0823366	+	0.0823366i
$419$	−7.00000	+	7.00000i	−0.341972	+	0.341972i	−0.857108	−	0.515136i	$-0.827741\pi$
$419$	−7.00000	+	7.00000i	−0.341972	+	0.341972i	0.515136	+	0.857108i	$0.327741\pi$
$420$		0			0
$421$	2.36675			0.115348			0.0576742	−	0.998335i	$-0.481632\pi$
$421$	2.36675			0.115348			0.0576742	+	0.998335i	$0.481632\pi$
$422$	−17.1082	−	17.1082i	−0.832814	−	0.832814i
$423$			2.83375i			0.137782i
$424$	7.94987			0.386080
$425$		0			0
$426$	−6.58312			−0.318953
$427$		−	3.05013i		−	0.147606i
$428$	5.84169	+	5.84169i	0.282369	+	0.282369i
$429$	2.31662			0.111848
$430$		0			0
$431$	11.4248	−	11.4248i	0.550314	−	0.550314i	−0.376218	−	0.926531i	$-0.622775\pi$
$431$	11.4248	−	11.4248i	0.550314	−	0.550314i	0.926531	+	0.376218i	$0.122775\pi$
$432$	−3.84169	+	3.84169i	−0.184833	+	0.184833i
$433$			1.36675i			0.0656818i	0.999461	+	0.0328409i	$0.0104555\pi$
$433$			1.36675i			0.0656818i	−0.999461	+	0.0328409i	$0.989545\pi$
$434$			0.366750i			0.0176046i
$435$		0			0
$436$	2.00000	−	2.00000i	0.0957826	−	0.0957826i
$437$	−1.68338	−	1.68338i	−0.0805268	−	0.0805268i
$438$	10.7335			0.512867
$439$	3.15831	+	3.15831i	0.150738	+	0.150738i	0.778448	−	0.627710i	$-0.216007\pi$
$439$	3.15831	+	3.15831i	0.150738	+	0.150738i	−0.627710	+	0.778448i	$0.716007\pi$
$440$		0			0
$441$	1.36675			0.0650834
$442$	4.00000	+	1.00000i	0.190261	+	0.0475651i
$443$	−22.9499			−1.09038			−0.545191	−	0.838312i	$-0.683543\pi$
$443$	−22.9499			−1.09038			−0.545191	+	0.838312i	$0.683543\pi$
$444$			0.733501i			0.0348104i
$445$		0			0
$446$	−27.5831			−1.30610
$447$	−25.4248	−	25.4248i	−1.20255	−	1.20255i
$448$	1.15831	−	1.15831i	0.0547251	−	0.0547251i
$449$	−14.3166	+	14.3166i	−0.675643	+	0.675643i	−0.959011	−	0.283368i	$-0.908548\pi$
$449$	−14.3166	+	14.3166i	−0.675643	+	0.675643i	0.283368	+	0.959011i	$0.408548\pi$
$450$		0			0
$451$			2.63325i			0.123995i
$452$	−13.2665	+	13.2665i	−0.624004	+	0.624004i
$453$	8.89975	−	8.89975i	0.418147	−	0.418147i
$454$	−1.15831	−	1.15831i	−0.0543623	−	0.0543623i
$455$		0			0
$456$	−1.94987	−	1.94987i	−0.0913112	−	0.0913112i
$457$			20.6834i			0.967527i	0.875199	+	0.483764i	$0.160731\pi$
$457$			20.6834i			0.967527i	−0.875199	+	0.483764i	$0.839269\pi$
$458$	−22.8997			−1.07003
$459$	−11.5251	−	19.2084i	−0.537944	−	0.896573i
$460$		0			0
$461$		−	3.89975i		−	0.181629i	−0.995868	−	0.0908147i	$-0.971053\pi$
$461$		−	3.89975i		−	0.181629i	0.995868	−	0.0908147i	$-0.0289471\pi$
$462$	2.68338	+	2.68338i	0.124842	+	0.124842i
$463$	38.6332			1.79544			0.897720	−	0.440567i	$-0.145223\pi$
$463$	38.6332			1.79544			0.897720	+	0.440567i	$0.145223\pi$
$464$	4.31662	+	4.31662i	0.200394	+	0.200394i
$465$		0			0
$466$	16.9499	−	16.9499i	0.785188	−	0.785188i
$467$			14.9499i			0.691798i	0.938272	+	0.345899i	$0.112426\pi$
$467$			14.9499i			0.691798i	−0.938272	+	0.345899i	$0.887574\pi$
$468$		−	0.316625i		−	0.0146360i
$469$	7.68338	−	7.68338i	0.354785	−	0.354785i
$470$		0			0
$471$	−17.7414	−	17.7414i	−0.817482	−	0.817482i
$472$	8.63325			0.397378
$473$	6.00000	+	6.00000i	0.275880	+	0.275880i
$474$			12.6834i			0.582567i
$475$		0			0
$476$	3.47494	+	5.79156i	0.159273	+	0.265456i
$477$	2.51713			0.115251
$478$		−	4.63325i		−	0.211920i
$479$	−10.6834	−	10.6834i	−0.488136	−	0.488136i	0.419582	−	0.907718i	$-0.362177\pi$
$479$	−10.6834	−	10.6834i	−0.488136	−	0.488136i	−0.907718	+	0.419582i	$0.862177\pi$
$480$		0			0
$481$	−0.316625	−	0.316625i	−0.0144368	−	0.0144368i
$482$	−13.3166	+	13.3166i	−0.606556	+	0.606556i
$483$	−2.68338	+	2.68338i	−0.122098	+	0.122098i
$484$		−	9.00000i		−	0.409091i
$485$		0			0
$486$	−2.31662	+	2.31662i	−0.105084	+	0.105084i
$487$	6.58312	−	6.58312i	0.298310	−	0.298310i	−0.542042	−	0.840352i	$-0.682349\pi$
$487$	6.58312	−	6.58312i	0.298310	−	0.298310i	0.840352	+	0.542042i	$0.182349\pi$
$488$	1.31662	+	1.31662i	0.0596008	+	0.0596008i
$489$	−6.58312			−0.297699
$490$		0			0
$491$			13.8997i			0.627287i	0.949541	+	0.313643i	$0.101550\pi$
$491$			13.8997i			0.627287i	−0.949541	+	0.313643i	$0.898450\pi$
$492$	−3.05013			−0.137510
$493$	−21.5831	+	12.9499i	−0.972055	+	0.583233i
$494$	1.68338			0.0757386
$495$		0			0
$496$	−0.158312	−	0.158312i	−0.00710844	−	0.00710844i
$497$	6.58312			0.295293
$498$	0.733501	+	0.733501i	0.0328690	+	0.0328690i
$499$	28.4248	−	28.4248i	1.27247	−	1.27247i	0.327681	−	0.944788i	$-0.393733\pi$
$499$	28.4248	−	28.4248i	1.27247	−	1.27247i	0.944788	−	0.327681i	$-0.106267\pi$
$500$		0			0
$501$			16.2164i			0.724494i
$502$		−	7.26650i		−	0.324320i
$503$	3.63325	−	3.63325i	0.161999	−	0.161999i	−0.621453	−	0.783452i	$-0.713457\pi$
$503$	3.63325	−	3.63325i	0.161999	−	0.161999i	0.783452	+	0.621453i	$0.213457\pi$
$504$	0.366750	−	0.366750i	0.0163364	−	0.0163364i
$505$		0			0
$506$	−2.00000			−0.0889108
$507$	13.8997	+	13.8997i	0.617310	+	0.617310i
$508$			2.00000i			0.0887357i
$509$	−31.9499			−1.41615			−0.708077	−	0.706136i	$-0.750437\pi$
$509$	−31.9499			−1.41615			−0.708077	+	0.706136i	$0.750437\pi$
$510$		0			0
$511$	−10.7335			−0.474822
$512$			1.00000i			0.0441942i
$513$	−6.46700	−	6.46700i	−0.285525	−	0.285525i
$514$	9.31662			0.410939
$515$		0			0
$516$	−6.94987	+	6.94987i	−0.305951	+	0.305951i
$517$	−8.94987	+	8.94987i	−0.393615	+	0.393615i
$518$		−	0.733501i		−	0.0322282i
$519$			40.1161i			1.76090i
$520$		0			0
$521$	13.3166	−	13.3166i	0.583412	−	0.583412i	−0.352427	−	0.935839i	$-0.614644\pi$
$521$	13.3166	−	13.3166i	0.583412	−	0.583412i	0.935839	+	0.352427i	$0.114644\pi$
$522$	1.36675	+	1.36675i	0.0598210	+	0.0598210i
$523$	9.36675			0.409579			0.204790	−	0.978806i	$-0.434349\pi$
$523$	9.36675			0.409579			0.204790	+	0.978806i	$0.434349\pi$
$524$	14.7916	+	14.7916i	0.646172	+	0.646172i
$525$		0			0
$526$	4.00000			0.174408
$527$	0.791562	−	0.474937i	0.0344810	−	0.0206886i
$528$	−2.31662			−0.100818
$529$			21.0000i			0.913043i
$530$		0			0
$531$	2.73350			0.118624
$532$	1.94987	+	1.94987i	0.0845378	+	0.0845378i
$533$	1.31662	−	1.31662i	0.0570294	−	0.0570294i
$534$	6.21637	−	6.21637i	0.269009	−	0.269009i
$535$		0			0
$536$			6.63325i			0.286513i
$537$	−9.63325	+	9.63325i	−0.415705	+	0.415705i
$538$	−16.2665	+	16.2665i	−0.701299	+	0.701299i
$539$	4.31662	+	4.31662i	0.185930	+	0.185930i
$540$		0			0
$541$	25.2665	+	25.2665i	1.08629	+	1.08629i	0.995907	+	0.0903847i	$0.0288097\pi$
$541$	25.2665	+	25.2665i	1.08629	+	1.08629i	0.0903847	+	0.995907i	$0.471190\pi$
$542$		−	19.5831i		−	0.841167i
$543$	10.1161			0.434124
$544$	−4.00000	−	1.00000i	−0.171499	−	0.0428746i
$545$		0			0
$546$		−	2.68338i		−	0.114838i
$547$	18.7916	+	18.7916i	0.803469	+	0.803469i	0.983636	−	0.180167i	$-0.0576638\pi$
$547$	18.7916	+	18.7916i	0.803469	+	0.803469i	−0.180167	+	0.983636i	$0.557664\pi$
$548$	−19.9499			−0.852216
$549$	0.416876	+	0.416876i	0.0177918	+	0.0177918i
$550$		0			0
$551$	−7.26650	+	7.26650i	−0.309563	+	0.309563i
$552$		−	2.31662i		−	0.0986021i
$553$		−	12.6834i		−	0.539352i
$554$	−0.683375	+	0.683375i	−0.0290338	+	0.0290338i
$555$		0			0
$556$	13.7916	+	13.7916i	0.584893	+	0.584893i
$557$	2.26650			0.0960347			0.0480173	−	0.998847i	$-0.484710\pi$
$557$	2.26650			0.0960347			0.0480173	+	0.998847i	$0.484710\pi$
$558$	−0.0501256	−	0.0501256i	−0.00212199	−	0.00212199i
$559$		−	6.00000i		−	0.253773i
$560$		0			0
$561$	2.31662	−	9.26650i	0.0978080	−	0.391232i
$562$	5.00000			0.210912
$563$			18.3166i			0.771954i	0.922508	+	0.385977i	$0.126136\pi$
$563$			18.3166i			0.771954i	−0.922508	+	0.385977i	$0.873864\pi$
$564$	−10.3668	−	10.3668i	−0.436519	−	0.436519i
$565$		0			0
$566$	6.68338	+	6.68338i	0.280923	+	0.280923i
$567$	−9.20844	+	9.20844i	−0.386718	+	0.386718i
$568$	−2.84169	+	2.84169i	−0.119235	+	0.119235i
$569$			37.8997i			1.58884i	0.607369	+	0.794420i	$0.292225\pi$
$569$			37.8997i			1.58884i	−0.607369	+	0.794420i	$0.707775\pi$
$570$		0			0
$571$	17.1583	−	17.1583i	0.718053	−	0.718053i	−0.250153	−	0.968206i	$-0.580481\pi$
$571$	17.1583	−	17.1583i	0.718053	−	0.718053i	0.968206	+	0.250153i	$0.0804810\pi$
$572$	1.00000	−	1.00000i	0.0418121	−	0.0418121i
$573$	−10.3668	−	10.3668i	−0.433077	−	0.433077i
$574$	3.05013			0.127310
$575$		0			0
$576$			0.316625i			0.0131927i
$577$	37.2665			1.55142			0.775712	−	0.631087i	$-0.217391\pi$
$577$	37.2665			1.55142			0.775712	+	0.631087i	$0.217391\pi$
$578$	8.00000	−	15.0000i	0.332756	−	0.623918i
$579$	−14.6332			−0.608137
$580$		0			0
$581$	−0.733501	−	0.733501i	−0.0304307	−	0.0304307i
$582$	−4.63325			−0.192054
$583$	7.94987	+	7.94987i	0.329250	+	0.329250i
$584$	4.63325	−	4.63325i	0.191725	−	0.191725i
$585$		0			0
$586$		−	19.8997i		−	0.822051i
$587$		−	20.5330i		−	0.847488i	−0.905782	−	0.423744i	$-0.860716\pi$
$587$		−	20.5330i		−	0.847488i	0.905782	−	0.423744i	$-0.139284\pi$
$588$	−5.00000	+	5.00000i	−0.206197	+	0.206197i
$589$	0.266499	−	0.266499i	0.0109809	−	0.0109809i
$590$		0			0
$591$	16.9499			0.697225
$592$	0.316625	+	0.316625i	0.0130132	+	0.0130132i
$593$		−	4.36675i		−	0.179321i	−0.995972	−	0.0896605i	$-0.971422\pi$
$593$		−	4.36675i		−	0.179321i	0.995972	−	0.0896605i	$-0.0285782\pi$
$594$	−7.68338			−0.315253
$595$		0			0
$596$	−21.9499			−0.899102
$597$		−	26.9499i		−	1.10298i
$598$	1.00000	+	1.00000i	0.0408930	+	0.0408930i
$599$	38.5330			1.57442			0.787208	−	0.616688i	$-0.211526\pi$
$599$	38.5330			1.57442			0.787208	+	0.616688i	$0.211526\pi$
$600$		0			0
$601$	−1.68338	+	1.68338i	−0.0686663	+	0.0686663i	−0.740606	−	0.671940i	$-0.765461\pi$
$601$	−1.68338	+	1.68338i	−0.0686663	+	0.0686663i	0.671940	+	0.740606i	$0.265461\pi$
$602$	6.94987	−	6.94987i	0.283256	−	0.283256i
$603$			2.10025i			0.0855288i
$604$		−	7.68338i		−	0.312632i
$605$		0			0
$606$	−8.84169	+	8.84169i	−0.359169	+	0.359169i
$607$	−5.84169	−	5.84169i	−0.237107	−	0.237107i	0.578544	−	0.815651i	$-0.303621\pi$
$607$	−5.84169	−	5.84169i	−0.237107	−	0.237107i	−0.815651	+	0.578544i	$0.803621\pi$
$608$	−1.68338			−0.0682699
$609$	11.5831	+	11.5831i	0.469372	+	0.469372i
$610$		0			0
$611$	8.94987			0.362073
$612$	−1.26650	−	0.316625i	−0.0511952	−	0.0127988i
$613$	−7.21637			−0.291467			−0.145733	−	0.989324i	$-0.546554\pi$
$613$	−7.21637			−0.291467			−0.145733	+	0.989324i	$0.546554\pi$
$614$			26.5330i			1.07078i
$615$		0			0
$616$	2.31662			0.0933395
$617$	−14.3166	−	14.3166i	−0.576366	−	0.576366i	0.357534	−	0.933900i	$-0.383617\pi$
$617$	−14.3166	−	14.3166i	−0.576366	−	0.576366i	−0.933900	+	0.357534i	$0.883617\pi$
$618$	18.0501	−	18.0501i	0.726083	−	0.726083i
$619$	−10.8997	+	10.8997i	−0.438098	+	0.438098i	−0.891371	−	0.453274i	$-0.850256\pi$
$619$	−10.8997	+	10.8997i	−0.438098	+	0.438098i	0.453274	+	0.891371i	$0.350256\pi$
$620$		0			0
$621$		−	7.68338i		−	0.308323i
$622$	10.1583	−	10.1583i	0.407311	−	0.407311i
$623$	−6.21637	+	6.21637i	−0.249054	+	0.249054i
$624$	1.15831	+	1.15831i	0.0463696	+	0.0463696i
$625$		0			0
$626$	5.94987	+	5.94987i	0.237805	+	0.237805i
$627$		−	3.89975i		−	0.155741i
$628$	−15.3166			−0.611200
$629$	−1.58312	+	0.949874i	−0.0631233	+	0.0378740i
$630$		0			0
$631$			25.3668i			1.00983i	0.863168	+	0.504917i	$0.168477\pi$
$631$			25.3668i			1.00983i	−0.863168	+	0.504917i	$0.831523\pi$
$632$	5.47494	+	5.47494i	0.217781	+	0.217781i
$633$	39.6332			1.57528
$634$	−5.00000	−	5.00000i	−0.198575	−	0.198575i
$635$		0			0
$636$	−9.20844	+	9.20844i	−0.365138	+	0.365138i
$637$		−	4.31662i		−	0.171031i
$638$			8.63325i			0.341794i
$639$	−0.899749	+	0.899749i	−0.0355935	+	0.0355935i
$640$		0			0
$641$	22.2164	+	22.2164i	0.877494	+	0.877494i	0.993275	−	0.115781i	$-0.0369370\pi$
$641$	22.2164	+	22.2164i	0.877494	+	0.877494i	−0.115781	+	0.993275i	$0.536937\pi$
$642$	−13.5330			−0.534105
$643$	7.74144	+	7.74144i	0.305292	+	0.305292i	0.843080	−	0.537788i	$-0.180740\pi$
$643$	7.74144	+	7.74144i	0.305292	+	0.305292i	−0.537788	+	0.843080i	$0.680740\pi$
$644$			2.31662i			0.0912878i
$645$		0			0
$646$	1.68338	−	6.73350i	0.0662315	−	0.264926i
$647$	31.8997			1.25411			0.627054	−	0.778976i	$-0.284260\pi$
$647$	31.8997			1.25411			0.627054	+	0.778976i	$0.284260\pi$
$648$		−	7.94987i		−	0.312301i
$649$	8.63325	+	8.63325i	0.338885	+	0.338885i
$650$		0			0
$651$	−0.424812	−	0.424812i	−0.0166497	−	0.0166497i
$652$	−2.84169	+	2.84169i	−0.111289	+	0.111289i
$653$	−6.00000	+	6.00000i	−0.234798	+	0.234798i	−0.814692	−	0.579894i	$-0.803094\pi$
$653$	−6.00000	+	6.00000i	−0.234798	+	0.234798i	0.579894	+	0.814692i	$0.303094\pi$
$654$			4.63325i			0.181174i
$655$		0			0
$656$	−1.31662	+	1.31662i	−0.0514056	+	0.0514056i
$657$	1.46700	−	1.46700i	0.0572332	−	0.0572332i
$658$	10.3668	+	10.3668i	0.404138	+	0.404138i
$659$	−6.94987			−0.270729			−0.135364	−	0.990796i	$-0.543220\pi$
$659$	−6.94987			−0.270729			−0.135364	+	0.990796i	$0.543220\pi$
$660$		0			0
$661$			13.4169i			0.521856i	0.965358	+	0.260928i	$0.0840285\pi$
$661$			13.4169i			0.521856i	−0.965358	+	0.260928i	$0.915971\pi$
$662$	21.5831			0.838852
$663$	−5.79156	+	3.47494i	−0.224926	+	0.134955i
$664$	0.633250			0.0245748
$665$		0			0
$666$	0.100251	+	0.100251i	0.00388466	+	0.00388466i
$667$	−8.63325			−0.334281
$668$	7.00000	+	7.00000i	0.270838	+	0.270838i
$669$	31.9499	−	31.9499i	1.23525	−	1.23525i
$670$		0			0
$671$			2.63325i			0.101655i
$672$			2.68338i			0.103513i
$673$	10.5831	−	10.5831i	0.407949	−	0.407949i	−0.473074	−	0.881023i	$-0.656856\pi$
$673$	10.5831	−	10.5831i	0.407949	−	0.407949i	0.881023	+	0.473074i	$0.156856\pi$
$674$	4.31662	−	4.31662i	0.166270	−	0.166270i
$675$		0			0
$676$	12.0000			0.461538
$677$	−18.2164	−	18.2164i	−0.700112	−	0.700112i	0.264322	−	0.964434i	$-0.414852\pi$
$677$	−18.2164	−	18.2164i	−0.700112	−	0.700112i	−0.964434	+	0.264322i	$0.914852\pi$
$678$		−	30.7335i		−	1.18031i
$679$	4.63325			0.177808
$680$		0			0
$681$	2.68338			0.102827
$682$		−	0.316625i		−	0.0121242i
$683$	−33.1082	−	33.1082i	−1.26685	−	1.26685i	−0.947707	−	0.319143i	$-0.896605\pi$
$683$	−33.1082	−	33.1082i	−1.26685	−	1.26685i	−0.319143	−	0.947707i	$-0.603395\pi$
$684$	−0.532998			−0.0203797
$685$		0			0
$686$	13.1082	−	13.1082i	0.500473	−	0.500473i
$687$	26.5251	−	26.5251i	1.01199	−	1.01199i
$688$			6.00000i			0.228748i
$689$		−	7.94987i		−	0.302866i
$690$		0			0
$691$	−14.0581	+	14.0581i	−0.534794	+	0.534794i	−0.921995	−	0.387201i	$-0.873442\pi$
$691$	−14.0581	+	14.0581i	−0.534794	+	0.534794i	0.387201	+	0.921995i	$0.373442\pi$
$692$	17.3166	+	17.3166i	0.658279	+	0.658279i
$693$	0.733501			0.0278634
$694$	−0.791562	−	0.791562i	−0.0300473	−	0.0300473i
$695$		0			0
$696$	−10.0000			−0.379049
$697$	−3.94987	−	6.58312i	−0.149612	−	0.249354i
$698$	−12.0501			−0.456104
$699$			39.2665i			1.48520i
$700$		0			0
$701$	22.0000			0.830929			0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000			0.830929			0.415464	+	0.909610i	$0.363619\pi$
$702$	3.84169	+	3.84169i	0.144995	+	0.144995i
$703$	−0.532998	+	0.532998i	−0.0201024	+	0.0201024i
$704$	−1.00000	+	1.00000i	−0.0376889	+	0.0376889i
$705$		0			0
$706$		−	1.73350i		−	0.0652412i
$707$	8.84169	−	8.84169i	0.332526	−	0.332526i
$708$	−10.0000	+	10.0000i	−0.375823	+	0.375823i
$709$	1.63325	+	1.63325i	0.0613380	+	0.0613380i	0.737110	−	0.675772i	$-0.236190\pi$
$709$	1.63325	+	1.63325i	0.0613380	+	0.0613380i	−0.675772	+	0.737110i	$0.736190\pi$
$710$		0			0
$711$	1.73350	+	1.73350i	0.0650114	+	0.0650114i
$712$		−	5.36675i		−	0.201127i
$713$	0.316625			0.0118577
$714$	−10.7335	−	2.68338i	−0.401691	−	0.100423i
$715$		0			0
$716$			8.31662i			0.310807i
$717$	5.36675	+	5.36675i	0.200425	+	0.200425i
$718$	−11.6834			−0.436020
$719$	25.8417	+	25.8417i	0.963732	+	0.963732i	0.999365	−	0.0356326i	$-0.0113446\pi$
$719$	25.8417	+	25.8417i	0.963732	+	0.963732i	−0.0356326	+	0.999365i	$0.511345\pi$
$720$		0			0
$721$	−18.0501	+	18.0501i	−0.672222	+	0.672222i
$722$			16.1662i			0.601645i
$723$		−	30.8496i		−	1.14731i
$724$	4.36675	−	4.36675i	0.162289	−	0.162289i
$725$		0			0
$726$	10.4248	+	10.4248i	0.386901	+	0.386901i
$727$	−25.0501			−0.929058			−0.464529	−	0.885558i	$-0.653776\pi$
$727$	−25.0501			−0.929058			−0.464529	+	0.885558i	$0.653776\pi$
$728$	−1.15831	−	1.15831i	−0.0429299	−	0.0429299i
$729$		−	29.2164i		−	1.08209i
$730$		0			0
$731$	−24.0000	−	6.00000i	−0.887672	−	0.221918i
$732$	−3.05013			−0.112736
$733$		−	15.2164i		−	0.562030i	−0.959703	−	0.281015i	$-0.909329\pi$
$733$		−	15.2164i		−	0.562030i	0.959703	−	0.281015i	$-0.0906710\pi$
$734$	−26.1583	−	26.1583i	−0.965521	−	0.965521i
$735$		0			0
$736$	−1.00000	−	1.00000i	−0.0368605	−	0.0368605i
$737$	−6.63325	+	6.63325i	−0.244339	+	0.244339i
$738$	−0.416876	+	0.416876i	−0.0153454	+	0.0153454i
$739$		−	37.5831i		−	1.38252i	−0.722607	−	0.691259i	$-0.757056\pi$
$739$		−	37.5831i		−	1.38252i	0.722607	−	0.691259i	$-0.242944\pi$
$740$		0			0
$741$	−1.94987	+	1.94987i	−0.0716304	+	0.0716304i
$742$	9.20844	−	9.20844i	0.338052	−	0.338052i
$743$	27.7414	+	27.7414i	1.01773	+	1.01773i	0.999840	+	0.0178947i	$0.00569637\pi$
$743$	27.7414	+	27.7414i	1.01773	+	1.01773i	0.0178947	+	0.999840i	$0.494304\pi$
$744$	0.366750			0.0134457
$745$		0			0
$746$		−	19.5330i		−	0.715154i
$747$	0.200503			0.00733600
$748$	−3.00000	−	5.00000i	−0.109691	−	0.182818i
$749$	13.5330			0.494485
$750$		0			0
$751$	14.8997	+	14.8997i	0.543700	+	0.543700i	0.924611	−	0.380912i	$-0.124390\pi$
$751$	14.8997	+	14.8997i	0.543700	+	0.543700i	−0.380912	+	0.924611i	$0.624390\pi$
$752$	−8.94987			−0.326368
$753$	8.41688	+	8.41688i	0.306728	+	0.306728i
$754$	4.31662	−	4.31662i	0.157202	−	0.157202i
$755$		0			0
$756$			8.89975i			0.323681i
$757$		−	16.6332i		−	0.604546i	−0.953221	−	0.302273i	$-0.902255\pi$
$757$		−	16.6332i		−	0.604546i	0.953221	−	0.302273i	$-0.0977454\pi$
$758$	16.4749	−	16.4749i	0.598397	−	0.598397i
$759$	2.31662	−	2.31662i	0.0840882	−	0.0840882i
$760$		0			0
$761$	−34.5831			−1.25364			−0.626819	−	0.779165i	$-0.715643\pi$
$761$	−34.5831			−1.25364			−0.626819	+	0.779165i	$0.715643\pi$
$762$	−2.31662	−	2.31662i	−0.0839225	−	0.0839225i
$763$		−	4.63325i		−	0.167735i
$764$	−8.94987			−0.323795
$765$		0			0
$766$	−2.94987			−0.106583
$767$		−	8.63325i		−	0.311729i
$768$	−1.15831	−	1.15831i	−0.0417970	−	0.0417970i
$769$	−16.5831			−0.598003			−0.299001	−	0.954253i	$-0.596654\pi$
$769$	−16.5831			−0.598003			−0.299001	+	0.954253i	$0.596654\pi$
$770$		0			0
$771$	−10.7916	+	10.7916i	−0.388649	+	0.388649i
$772$	−6.31662	+	6.31662i	−0.227340	+	0.227340i
$773$			24.8997i			0.895582i	0.894138	+	0.447791i	$0.147789\pi$
$773$			24.8997i			0.895582i	−0.894138	+	0.447791i	$0.852211\pi$
$774$			1.89975i			0.0682851i
$775$		0			0
$776$	−2.00000	+	2.00000i	−0.0717958	+	0.0717958i
$777$	0.849623	+	0.849623i	0.0304801	+	0.0304801i
$778$	25.2665			0.905848
$779$	−2.21637	−	2.21637i	−0.0794098	−	0.0794098i
$780$		0			0
$781$	−5.68338			−0.203367
$782$	5.00000	−	3.00000i	0.178800	−	0.107280i
$783$	−33.1662			−1.18527
$784$			4.31662i			0.154165i
$785$		0			0
$786$	−34.2665			−1.22225
$787$	11.4749	+	11.4749i	0.409037	+	0.409037i	0.881403	−	0.472365i	$-0.156600\pi$
$787$	11.4749	+	11.4749i	0.409037	+	0.409037i	−0.472365	+	0.881403i	$0.656600\pi$
$788$	7.31662	−	7.31662i	0.260644	−	0.260644i
$789$	−4.63325	+	4.63325i	−0.164948	+	0.164948i
$790$		0			0
$791$			30.7335i			1.09276i
$792$	−0.316625	+	0.316625i	−0.0112508	+	0.0112508i
$793$	1.31662	−	1.31662i	0.0467547	−	0.0467547i
$794$	−23.8997	−	23.8997i	−0.848170	−	0.848170i
$795$		0			0
$796$	−11.6332	−	11.6332i	−0.412330	−	0.412330i
$797$		−	5.41688i		−	0.191876i	−0.995387	−	0.0959378i	$-0.969415\pi$
$797$		−	5.41688i		−	0.191876i	0.995387	−	0.0959378i	$-0.0305850\pi$
$798$	−4.51713			−0.159905
$799$	8.94987	−	35.7995i	0.316624	−	1.26650i
$800$		0			0
$801$		−	1.69925i		−	0.0600399i
$802$	22.5831	+	22.5831i	0.797438	+	0.797438i
$803$	9.26650			0.327008
$804$	−7.68338	−	7.68338i	−0.270972	−	0.270972i
$805$		0			0
$806$	−0.158312	+	0.158312i	−0.00557632	+	0.00557632i
$807$		−	37.6834i		−	1.32652i
$808$			7.63325i			0.268537i
$809$	24.5831	−	24.5831i	0.864297	−	0.864297i	−0.127537	−	0.991834i	$-0.540707\pi$
$809$	24.5831	−	24.5831i	0.864297	−	0.864297i	0.991834	+	0.127537i	$0.0407072\pi$
$810$		0			0
$811$	−5.89181	−	5.89181i	−0.206890	−	0.206890i	0.596054	−	0.802944i	$-0.296734\pi$
$811$	−5.89181	−	5.89181i	−0.206890	−	0.206890i	−0.802944	+	0.596054i	$0.796734\pi$
$812$	10.0000			0.350931
$813$	22.6834	+	22.6834i	0.795541	+	0.795541i
$814$			0.633250i			0.0221954i
$815$		0			0
$816$	5.79156	−	3.47494i	0.202745	−	0.121647i
$817$	−10.1003			−0.353363
$818$		−	28.8997i		−	1.01046i
$819$	−0.366750	−	0.366750i	−0.0128153	−	0.0128153i
$820$		0			0
$821$	−33.6332	−	33.6332i	−1.17381	−	1.17381i	−0.981294	−	0.192514i	$-0.938336\pi$
$821$	−33.6332	−	33.6332i	−1.17381	−	1.17381i	−0.192514	−	0.981294i	$-0.561664\pi$
$822$	23.1082	−	23.1082i	0.805991	−	0.805991i
$823$	22.8417	−	22.8417i	0.796211	−	0.796211i	−0.186285	−	0.982496i	$-0.559645\pi$
$823$	22.8417	−	22.8417i	0.796211	−	0.796211i	0.982496	+	0.186285i	$0.0596447\pi$
$824$		−	15.5831i		−	0.542864i
$825$		0			0
$826$	10.0000	−	10.0000i	0.347945	−	0.347945i
$827$	19.6332	−	19.6332i	0.682715	−	0.682715i	−0.277896	−	0.960611i	$-0.589637\pi$
$827$	19.6332	−	19.6332i	0.682715	−	0.682715i	0.960611	+	0.277896i	$0.0896371\pi$
$828$	−0.316625	−	0.316625i	−0.0110035	−	0.0110035i
$829$	41.2164			1.43150			0.715752	−	0.698355i	$-0.246084\pi$
$829$	41.2164			1.43150			0.715752	+	0.698355i	$0.246084\pi$
$830$		0			0
$831$		−	1.58312i		−	0.0549180i
$832$	1.00000			0.0346688
$833$	−17.2665	−	4.31662i	−0.598249	−	0.149562i
$834$	−31.9499			−1.10633
$835$		0			0
$836$	−1.68338	−	1.68338i	−0.0582207	−	0.0582207i
$837$	1.21637			0.0420440
$838$	−7.00000	−	7.00000i	−0.241811	−	0.241811i
$839$	23.4248	−	23.4248i	0.808714	−	0.808714i	−0.175725	−	0.984439i	$-0.556227\pi$
$839$	23.4248	−	23.4248i	0.808714	−	0.808714i	0.984439	+	0.175725i	$0.0562269\pi$
$840$		0			0
$841$			8.26650i			0.285052i
$842$			2.36675i			0.0815636i
$843$	−5.79156	+	5.79156i	−0.199472	+	0.199472i
$844$	17.1082	−	17.1082i	0.588888	−	0.588888i
$845$		0			0
$846$	−2.83375			−0.0974264
$847$	−10.4248	−	10.4248i	−0.358201	−	0.358201i
$848$			7.94987i			0.273000i
$849$	−15.4829			−0.531371
$850$		0			0
$851$	−0.633250			−0.0217075
$852$		−	6.58312i		−	0.225534i
$853$	−15.0000	−	15.0000i	−0.513590	−	0.513590i	0.402034	−	0.915625i	$-0.368303\pi$
$853$	−15.0000	−	15.0000i	−0.513590	−	0.513590i	−0.915625	+	0.402034i	$0.868303\pi$
$854$	3.05013			0.104373
$855$		0			0
$856$	−5.84169	+	5.84169i	−0.199665	+	0.199665i
$857$	0.733501	−	0.733501i	0.0250559	−	0.0250559i	−0.694468	−	0.719524i	$-0.744360\pi$
$857$	0.733501	−	0.733501i	0.0250559	−	0.0250559i	0.719524	+	0.694468i	$0.244360\pi$
$858$			2.31662i			0.0790883i
$859$		−	18.3166i		−	0.624955i	−0.949925	−	0.312478i	$-0.898841\pi$
$859$		−	18.3166i		−	0.624955i	0.949925	−	0.312478i	$-0.101159\pi$
$860$		0			0
$861$	−3.53300	+	3.53300i	−0.120404	+	0.120404i
$862$	11.4248	+	11.4248i	0.389131	+	0.389131i
$863$	−6.00000			−0.204242			−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000			−0.204242			−0.102121	+	0.994772i	$0.532563\pi$
$864$	−3.84169	−	3.84169i	−0.130697	−	0.130697i
$865$		0			0
$866$	−1.36675			−0.0464441
$867$	8.10819	+	26.6412i	0.275368	+	0.904782i
$868$	−0.366750			−0.0124483
$869$			10.9499i			0.371449i
$870$		0			0
$871$	6.63325			0.224759
$872$	2.00000	+	2.00000i	0.0677285	+	0.0677285i
$873$	−0.633250	+	0.633250i	−0.0214323	+	0.0214323i
$874$	1.68338	−	1.68338i	0.0569410	−	0.0569410i
$875$		0			0
$876$			10.7335i			0.362651i
$877$	16.9499	−	16.9499i	0.572357	−	0.572357i	−0.360430	−	0.932786i	$-0.617370\pi$
$877$	16.9499	−	16.9499i	0.572357	−	0.572357i	0.932786	+	0.360430i	$0.117370\pi$
$878$	−3.15831	+	3.15831i	−0.106588	+	0.106588i
$879$	23.0501	+	23.0501i	0.777461	+	0.777461i
$880$		0			0
$881$	18.6834	+	18.6834i	0.629459	+	0.629459i	0.947932	−	0.318473i	$-0.103170\pi$
$881$	18.6834	+	18.6834i	0.629459	+	0.629459i	−0.318473	+	0.947932i	$0.603170\pi$
$882$			1.36675i			0.0460209i
$883$	25.5831			0.860941			0.430470	−	0.902605i	$-0.358348\pi$
$883$	25.5831			0.860941			0.430470	+	0.902605i	$0.358348\pi$
$884$	−1.00000	+	4.00000i	−0.0336336	+	0.134535i
$885$		0			0
$886$		−	22.9499i		−	0.771016i
$887$	−5.84169	−	5.84169i	−0.196145	−	0.196145i	0.602200	−	0.798345i	$-0.294291\pi$
$887$	−5.84169	−	5.84169i	−0.196145	−	0.196145i	−0.798345	+	0.602200i	$0.794291\pi$
$888$	−0.733501			−0.0246147
$889$	2.31662	+	2.31662i	0.0776971	+	0.0776971i
$890$		0			0
$891$	7.94987	−	7.94987i	0.266331	−	0.266331i
$892$		−	27.5831i		−	0.923551i
$893$		−	15.0660i		−	0.504164i
$894$	25.4248	−	25.4248i	0.850333	−	0.850333i
$895$		0			0
$896$	1.15831	+	1.15831i	0.0386965	+	0.0386965i
$897$	−2.31662			−0.0773499
$898$	−14.3166	−	14.3166i	−0.477752	−	0.477752i
$899$		−	1.36675i		−	0.0455837i
$900$		0			0
$901$	−31.7995	−	7.94987i	−1.05939	−	0.264849i
$902$	−2.63325			−0.0876776
$903$			16.1003i			0.535783i
$904$	−13.2665	−	13.2665i	−0.441237	−	0.441237i
$905$		0			0
$906$	8.89975	+	8.89975i	0.295674	+	0.295674i
$907$	−39.6332	+	39.6332i	−1.31600	+	1.31600i	−0.399088	+	0.916913i	$0.630673\pi$
$907$	−39.6332	+	39.6332i	−1.31600	+	1.31600i	−0.916913	+	0.399088i	$0.869327\pi$
$908$	1.15831	−	1.15831i	0.0384399	−	0.0384399i
$909$			2.41688i			0.0801627i
$910$		0			0
$911$	4.84169	−	4.84169i	0.160412	−	0.160412i	−0.622337	−	0.782749i	$-0.713817\pi$
$911$	4.84169	−	4.84169i	0.160412	−	0.160412i	0.782749	+	0.622337i	$0.213817\pi$
$912$	1.94987	−	1.94987i	0.0645668	−	0.0645668i
$913$	0.633250	+	0.633250i	0.0209575	+	0.0209575i
$914$	−20.6834			−0.684145
$915$		0			0
$916$		−	22.8997i		−	0.756629i
$917$	34.2665			1.13158
$918$	19.2084	−	11.5251i	0.633973	−	0.380384i
$919$	43.1662			1.42392			0.711962	−	0.702218i	$-0.247807\pi$
$919$	43.1662			1.42392			0.711962	+	0.702218i	$0.247807\pi$
$920$		0			0
$921$	−30.7335	−	30.7335i	−1.01270	−	1.01270i
$922$	3.89975			0.128431
$923$	2.84169	+	2.84169i	0.0935353	+	0.0935353i
$924$	−2.68338	+	2.68338i	−0.0882766	+	0.0882766i
$925$		0			0
$926$			38.6332i			1.26957i
$927$		−	4.93400i		−	0.162054i
$928$	−4.31662	+	4.31662i	−0.141700	+	0.141700i
$929$	21.8997	−	21.8997i	0.718507	−	0.718507i	−0.249792	−	0.968300i	$-0.580362\pi$
$929$	21.8997	−	21.8997i	0.718507	−	0.718507i	0.968300	+	0.249792i	$0.0803623\pi$
$930$		0			0
$931$	−7.26650			−0.238150
$932$	16.9499	+	16.9499i	0.555212	+	0.555212i
$933$			23.5330i			0.770436i
$934$	−14.9499			−0.489175
$935$		0			0
$936$	0.316625			0.0103492
$937$		−	50.1662i		−	1.63886i	−0.573179	−	0.819430i	$-0.694290\pi$
$937$		−	50.1662i		−	1.63886i	0.573179	−	0.819430i	$-0.305710\pi$
$938$	7.68338	+	7.68338i	0.250871	+	0.250871i
$939$	−13.7836			−0.449812
$940$		0			0
$941$	−16.6834	+	16.6834i	−0.543862	+	0.543862i	−0.924659	−	0.380796i	$-0.875650\pi$
$941$	−16.6834	+	16.6834i	−0.543862	+	0.543862i	0.380796	+	0.924659i	$0.375650\pi$
$942$	17.7414	−	17.7414i	0.578047	−	0.578047i
$943$		−	2.63325i		−	0.0857504i
$944$			8.63325i			0.280988i
$945$		0			0
$946$	−6.00000	+	6.00000i	−0.195077	+	0.195077i
$947$	2.26650	+	2.26650i	0.0736513	+	0.0736513i	0.742973	−	0.669322i	$-0.233415\pi$
$947$	2.26650	+	2.26650i	0.0736513	+	0.0736513i	−0.669322	+	0.742973i	$0.733415\pi$
$948$	−12.6834			−0.411937
$949$	−4.63325	−	4.63325i	−0.150402	−	0.150402i
$950$		0			0
$951$	11.5831			0.375609
$952$	−5.79156	+	3.47494i	−0.187706	+	0.112623i
$953$	−7.21637			−0.233761			−0.116881	−	0.993146i	$-0.537289\pi$
$953$	−7.21637			−0.233761			−0.116881	+	0.993146i	$0.537289\pi$
$954$			2.51713i			0.0814950i
$955$		0			0
$956$	4.63325			0.149850
$957$	−10.0000	−	10.0000i	−0.323254	−	0.323254i
$958$	10.6834	−	10.6834i	0.345164	−	0.345164i
$959$	−23.1082	+	23.1082i	−0.746202	+	0.746202i
$960$		0			0
$961$		−	30.9499i		−	0.998383i
$962$	0.316625	−	0.316625i	0.0102084	−	0.0102084i
$963$	−1.84962	+	1.84962i	−0.0596033	+	0.0596033i
$964$	−13.3166	−	13.3166i	−0.428900	−	0.428900i
$965$		0			0
$966$	−2.68338	−	2.68338i	−0.0863362	−	0.0863362i
$967$			23.3668i			0.751424i	0.926736	+	0.375712i	$0.122602\pi$
$967$			23.3668i			0.751424i	−0.926736	+	0.375712i	$0.877398\pi$
$968$	9.00000			0.289271
$969$	5.84962	+	9.74937i	0.187917	+	0.313195i
$970$		0			0
$971$		−	0.733501i		−	0.0235392i	−0.999931	−	0.0117696i	$-0.996254\pi$
$971$		−	0.733501i		−	0.0235392i	0.999931	−	0.0117696i	$-0.00374646\pi$
$972$	−2.31662	−	2.31662i	−0.0743058	−	0.0743058i
$973$	31.9499			1.02427
$974$	6.58312	+	6.58312i	0.210937	+	0.210937i
$975$		0			0
$976$	−1.31662	+	1.31662i	−0.0421441	+	0.0421441i
$977$		−	10.8997i		−	0.348714i	−0.984683	−	0.174357i	$-0.944215\pi$
$977$		−	10.8997i		−	0.348714i	0.984683	−	0.174357i	$-0.0557847\pi$
$978$		−	6.58312i		−	0.210505i
$979$	5.36675	−	5.36675i	0.171522	−	0.171522i
$980$		0			0
$981$	0.633250	+	0.633250i	0.0202181	+	0.0202181i
$982$	−13.8997			−0.443559
$983$	31.1583	+	31.1583i	0.993796	+	0.993796i	0.999981	−	0.00618505i	$-0.00196877\pi$
$983$	31.1583	+	31.1583i	0.993796	+	0.993796i	−0.00618505	+	0.999981i	$0.501969\pi$
$984$		−	3.05013i		−	0.0972345i
$985$		0			0
$986$	−12.9499	−	21.5831i	−0.412408	−	0.687347i
$987$	−24.0159			−0.764434
$988$			1.68338i			0.0535553i
$989$	−6.00000	−	6.00000i	−0.190789	−	0.190789i
$990$		0			0
$991$	31.4248	+	31.4248i	0.998242	+	0.998242i	0.999998	−	0.00175642i	$-0.000559086\pi$
$991$	31.4248	+	31.4248i	0.998242	+	0.998242i	−0.00175642	+	0.999998i	$0.500559\pi$
$992$	0.158312	−	0.158312i	0.00502642	−	0.00502642i
$993$	−25.0000	+	25.0000i	−0.793351	+	0.793351i
$994$			6.58312i			0.208804i
$995$		0			0
$996$	−0.733501	+	0.733501i	−0.0232419	+	0.0232419i
$997$	−21.5831	+	21.5831i	−0.683544	+	0.683544i	−0.960797	−	0.277253i	$-0.910576\pi$
$997$	−21.5831	+	21.5831i	−0.683544	+	0.683544i	0.277253	+	0.960797i	$0.410576\pi$
$998$	28.4248	+	28.4248i	0.899772	+	0.899772i
$999$	−2.43275			−0.0769687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.h.j.251.1	yes	4
5.2	odd	4		850.2.g.f.149.1		4
5.3	odd	4		850.2.g.g.149.2		4
5.4	even	2		850.2.h.i.251.2	✓	4
17.4	even	4	inner	850.2.h.j.701.1	yes	4
85.4	even	4		850.2.h.i.701.2	yes	4
85.38	odd	4		850.2.g.f.599.1		4
85.72	odd	4		850.2.g.g.599.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
850.2.g.f.149.1		4	5.2	odd	4
850.2.g.f.599.1		4	85.38	odd	4
850.2.g.g.149.2		4	5.3	odd	4
850.2.g.g.599.2		4	85.72	odd	4
850.2.h.i.251.2	✓	4	5.4	even	2
850.2.h.i.701.2	yes	4	85.4	even	4
850.2.h.j.251.1	yes	4	1.1	even	1	trivial
850.2.h.j.701.1	yes	4	17.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.15831 - 1.15831i) q^{3} -1.00000 q^{4} +(1.15831 - 1.15831i) q^{6} +(-1.15831 + 1.15831i) q^{7} -1.00000i q^{8} -0.316625i q^{9} +(1.00000 - 1.00000i) q^{11} +(1.15831 + 1.15831i) q^{12} -1.00000 q^{13} +(-1.15831 - 1.15831i) q^{14} +1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} +0.316625 q^{18} +1.68338i q^{19} +2.68338 q^{21} +(1.00000 + 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-1.15831 + 1.15831i) q^{24} -1.00000i q^{26} +(-3.84169 + 3.84169i) q^{27} +(1.15831 - 1.15831i) q^{28} +(4.31662 + 4.31662i) q^{29} +(-0.158312 - 0.158312i) q^{31} +1.00000i q^{32} -2.31662 q^{33} +(-4.00000 - 1.00000i) q^{34} +0.316625i q^{36} +(0.316625 + 0.316625i) q^{37} -1.68338 q^{38} +(1.15831 + 1.15831i) q^{39} +(-1.31662 + 1.31662i) q^{41} +2.68338i q^{42} +6.00000i q^{43} +(-1.00000 + 1.00000i) q^{44} +(-1.00000 - 1.00000i) q^{46} -8.94987 q^{47} +(-1.15831 - 1.15831i) q^{48} +4.31662i q^{49} +(5.79156 - 3.47494i) q^{51} +1.00000 q^{52} +7.94987i q^{53} +(-3.84169 - 3.84169i) q^{54} +(1.15831 + 1.15831i) q^{56} +(1.94987 - 1.94987i) q^{57} +(-4.31662 + 4.31662i) q^{58} +8.63325i q^{59} +(-1.31662 + 1.31662i) q^{61} +(0.158312 - 0.158312i) q^{62} +(0.366750 + 0.366750i) q^{63} -1.00000 q^{64} -2.31662i q^{66} -6.63325 q^{67} +(1.00000 - 4.00000i) q^{68} +2.31662 q^{69} +(-2.84169 - 2.84169i) q^{71} -0.316625 q^{72} +(4.63325 + 4.63325i) q^{73} +(-0.316625 + 0.316625i) q^{74} -1.68338i q^{76} +2.31662i q^{77} +(-1.15831 + 1.15831i) q^{78} +(-5.47494 + 5.47494i) q^{79} +7.94987 q^{81} +(-1.31662 - 1.31662i) q^{82} +0.633250i q^{83} -2.68338 q^{84} -6.00000 q^{86} -10.0000i q^{87} +(-1.00000 - 1.00000i) q^{88} +5.36675 q^{89} +(1.15831 - 1.15831i) q^{91} +(1.00000 - 1.00000i) q^{92} +0.366750i q^{93} -8.94987i q^{94} +(1.15831 - 1.15831i) q^{96} +(-2.00000 - 2.00000i) q^{97} -4.31662 q^{98} +(-0.316625 - 0.316625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 4 q^{17} - 12 q^{18} + 24 q^{21} + 4 q^{22} - 4 q^{23} + 2 q^{24} - 22 q^{27} - 2 q^{28} + 4 q^{29} + 6 q^{31}+ \cdots + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^4 - 2 * q^6 + 2 * q^7 + 4 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 4 * q^17 - 12 * q^18 + 24 * q^21 + 4 * q^22 - 4 * q^23 + 2 * q^24 - 22 * q^27 - 2 * q^28 + 4 * q^29 + 6 * q^31 + 4 * q^33 - 16 * q^34 - 12 * q^37 - 20 * q^38 - 2 * q^39 + 8 * q^41 - 4 * q^44 - 4 * q^46 + 4 * q^47 + 2 * q^48 - 10 * q^51 + 4 * q^52 - 22 * q^54 - 2 * q^56 - 32 * q^57 - 4 * q^58 + 8 * q^61 - 6 * q^62 + 28 * q^63 - 4 * q^64 + 4 * q^68 - 4 * q^69 - 18 * q^71 + 12 * q^72 - 8 * q^73 + 12 * q^74 + 2 * q^78 - 2 * q^79 - 8 * q^81 + 8 * q^82 - 24 * q^84 - 24 * q^86 - 4 * q^88 + 48 * q^89 - 2 * q^91 + 4 * q^92 - 2 * q^96 - 8 * q^97 - 4 * q^98 + 12 * q^99

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