LMFDB - Embedded newform 1638.2.r.y.1387.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(757,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.r (of order $3$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1387.2
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	1638.1387
Dual form			1638.2.r.y.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.56155 q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.56155 q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.28078 - 2.21837i) q^{10} +(0.780776 - 1.35234i) q^{11} +(-0.500000 + 3.57071i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.06155 - 7.03482i) q^{17} +(-0.780776 - 1.35234i) q^{19} +(-1.28078 - 2.21837i) q^{20} +(-0.780776 - 1.35234i) q^{22} +(3.56155 - 6.16879i) q^{23} +1.56155 q^{25} +(2.84233 + 2.21837i) q^{26} +(-0.500000 + 0.866025i) q^{28} +(1.06155 - 1.83866i) q^{29} +(0.500000 + 0.866025i) q^{32} -8.12311 q^{34} +(-1.28078 - 2.21837i) q^{35} +(3.28078 - 5.68247i) q^{37} -1.56155 q^{38} -2.56155 q^{40} +(2.62311 - 4.54335i) q^{41} +(4.00000 + 6.92820i) q^{43} -1.56155 q^{44} +(-3.56155 - 6.16879i) q^{46} +12.6847 q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.780776 - 1.35234i) q^{50} +(3.34233 - 1.35234i) q^{52} -7.00000 q^{53} +(2.00000 - 3.46410i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-1.06155 - 1.83866i) q^{58} +(-1.56155 - 2.70469i) q^{59} +(-2.62311 - 4.54335i) q^{61} +1.00000 q^{64} +(-1.28078 + 9.14657i) q^{65} +(-0.438447 + 0.759413i) q^{67} +(-4.06155 + 7.03482i) q^{68} -2.56155 q^{70} +(6.68466 + 11.5782i) q^{71} -6.56155 q^{73} +(-3.28078 - 5.68247i) q^{74} +(-0.780776 + 1.35234i) q^{76} -1.56155 q^{77} -2.43845 q^{79} +(-1.28078 + 2.21837i) q^{80} +(-2.62311 - 4.54335i) q^{82} -3.12311 q^{83} +(-10.4039 - 18.0201i) q^{85} +8.00000 q^{86} +(-0.780776 + 1.35234i) q^{88} +(3.78078 - 6.54850i) q^{89} +(3.34233 - 1.35234i) q^{91} -7.12311 q^{92} +(6.34233 - 10.9852i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(4.56155 + 7.90084i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} - 4 q^{8} + q^{10} - q^{11} - 2 q^{13} - 4 q^{14} - 2 q^{16} - 8 q^{17} + q^{19} - q^{20} + q^{22} + 6 q^{23} - 2 q^{25} - q^{26} - 2 q^{28} - 4 q^{29} + 2 q^{32} - 16 q^{34} - q^{35} + 9 q^{37} + 2 q^{38} - 2 q^{40} - 6 q^{41} + 16 q^{43} + 2 q^{44} - 6 q^{46} + 26 q^{47} - 2 q^{49} - q^{50} + q^{52} - 28 q^{53} + 8 q^{55} + 2 q^{56} + 4 q^{58} + 2 q^{59} + 6 q^{61} + 4 q^{64} - q^{65} - 10 q^{67} - 8 q^{68} - 2 q^{70} + 2 q^{71} - 18 q^{73} - 9 q^{74} + q^{76} + 2 q^{77} - 18 q^{79} - q^{80} + 6 q^{82} + 4 q^{83} - 21 q^{85} + 32 q^{86} + q^{88} + 11 q^{89} + q^{91} - 12 q^{92} + 13 q^{94} - 8 q^{95} + 10 q^{97} + 2 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 - 4 * q^8 + q^10 - q^11 - 2 * q^13 - 4 * q^14 - 2 * q^16 - 8 * q^17 + q^19 - q^20 + q^22 + 6 * q^23 - 2 * q^25 - q^26 - 2 * q^28 - 4 * q^29 + 2 * q^32 - 16 * q^34 - q^35 + 9 * q^37 + 2 * q^38 - 2 * q^40 - 6 * q^41 + 16 * q^43 + 2 * q^44 - 6 * q^46 + 26 * q^47 - 2 * q^49 - q^50 + q^52 - 28 * q^53 + 8 * q^55 + 2 * q^56 + 4 * q^58 + 2 * q^59 + 6 * q^61 + 4 * q^64 - q^65 - 10 * q^67 - 8 * q^68 - 2 * q^70 + 2 * q^71 - 18 * q^73 - 9 * q^74 + q^76 + 2 * q^77 - 18 * q^79 - q^80 + 6 * q^82 + 4 * q^83 - 21 * q^85 + 32 * q^86 + q^88 + 11 * q^89 + q^91 - 12 * q^92 + 13 * q^94 - 8 * q^95 + 10 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.56155			1.14556			0.572781	−	0.819709i	$-0.305865\pi$
$5$	2.56155			1.14556			0.572781	+	0.819709i	$0.305865\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.28078	−	2.21837i	0.405017	−	0.701510i
$11$	0.780776	−	1.35234i	0.235413	−	0.407747i	−0.723980	−	0.689821i	$-0.757689\pi$
$11$	0.780776	−	1.35234i	0.235413	−	0.407747i	0.959393	+	0.282074i	$0.0910224\pi$
$12$		0			0
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.06155	−	7.03482i	−0.985071	−	1.70619i	−0.641619	−	0.767023i	$-0.721737\pi$
$17$	−4.06155	−	7.03482i	−0.985071	−	1.70619i	−0.343452	−	0.939170i	$-0.611596\pi$
$18$		0			0
$19$	−0.780776	−	1.35234i	−0.179122	−	0.310249i	0.762458	−	0.647038i	$-0.223992\pi$
$19$	−0.780776	−	1.35234i	−0.179122	−	0.310249i	−0.941580	+	0.336789i	$0.890659\pi$
$20$	−1.28078	−	2.21837i	−0.286390	−	0.496043i
$21$		0			0
$22$	−0.780776	−	1.35234i	−0.166462	−	0.288321i
$23$	3.56155	−	6.16879i	0.742635	−	1.28628i	−0.208656	−	0.977989i	$-0.566909\pi$
$23$	3.56155	−	6.16879i	0.742635	−	1.28628i	0.951292	−	0.308293i	$-0.0997576\pi$
$24$		0			0
$25$	1.56155			0.312311
$26$	2.84233	+	2.21837i	0.557427	+	0.435058i
$27$		0			0
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	1.06155	−	1.83866i	0.197125	−	0.341431i	−0.750470	−	0.660905i	$-0.770173\pi$
$29$	1.06155	−	1.83866i	0.197125	−	0.341431i	0.947595	+	0.319474i	$0.103506\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−8.12311			−1.39310
$35$	−1.28078	−	2.21837i	−0.216491	−	0.374973i
$36$		0			0
$37$	3.28078	−	5.68247i	0.539356	−	0.934193i	−0.459582	−	0.888135i	$-0.652001\pi$
$37$	3.28078	−	5.68247i	0.539356	−	0.934193i	0.998939	−	0.0460575i	$-0.0146657\pi$
$38$	−1.56155			−0.253317
$39$		0			0
$40$	−2.56155			−0.405017
$41$	2.62311	−	4.54335i	0.409660	−	0.709552i	−0.585191	−	0.810895i	$-0.698981\pi$
$41$	2.62311	−	4.54335i	0.409660	−	0.709552i	0.994852	+	0.101343i	$0.0323139\pi$
$42$		0			0
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−1.56155			−0.235413
$45$		0			0
$46$	−3.56155	−	6.16879i	−0.525122	−	0.909539i
$47$	12.6847			1.85025			0.925124	−	0.379666i	$-0.123961\pi$
$47$	12.6847			1.85025			0.925124	+	0.379666i	$0.123961\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.780776	−	1.35234i	0.110418	−	0.191250i
$51$		0			0
$52$	3.34233	−	1.35234i	0.463498	−	0.187536i
$53$	−7.00000			−0.961524			−0.480762	−	0.876851i	$-0.659640\pi$
$53$	−7.00000			−0.961524			−0.480762	+	0.876851i	$0.659640\pi$
$54$		0			0
$55$	2.00000	−	3.46410i	0.269680	−	0.467099i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		0			0
$58$	−1.06155	−	1.83866i	−0.139389	−	0.241428i
$59$	−1.56155	−	2.70469i	−0.203297	−	0.352120i	0.746292	−	0.665619i	$-0.231832\pi$
$59$	−1.56155	−	2.70469i	−0.203297	−	0.352120i	−0.949589	+	0.313498i	$0.898499\pi$
$60$		0			0
$61$	−2.62311	−	4.54335i	−0.335854	−	0.581717i	0.647794	−	0.761815i	$-0.275692\pi$
$61$	−2.62311	−	4.54335i	−0.335854	−	0.581717i	−0.983649	+	0.180099i	$0.942358\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.28078	+	9.14657i	−0.158861	+	1.13449i
$66$		0			0
$67$	−0.438447	+	0.759413i	−0.0535648	+	0.0927770i	−0.891565	−	0.452894i	$-0.850392\pi$
$67$	−0.438447	+	0.759413i	−0.0535648	+	0.0927770i	0.838000	+	0.545671i	$0.183725\pi$
$68$	−4.06155	+	7.03482i	−0.492536	+	0.853097i
$69$		0			0
$70$	−2.56155			−0.306164
$71$	6.68466	+	11.5782i	0.793323	+	1.37408i	0.923899	+	0.382637i	$0.124984\pi$
$71$	6.68466	+	11.5782i	0.793323	+	1.37408i	−0.130576	+	0.991438i	$0.541683\pi$
$72$		0			0
$73$	−6.56155			−0.767972			−0.383986	−	0.923339i	$-0.625449\pi$
$73$	−6.56155			−0.767972			−0.383986	+	0.923339i	$0.625449\pi$
$74$	−3.28078	−	5.68247i	−0.381383	−	0.660574i
$75$		0			0
$76$	−0.780776	+	1.35234i	−0.0895612	+	0.155125i
$77$	−1.56155			−0.177955
$78$		0			0
$79$	−2.43845			−0.274347			−0.137173	−	0.990547i	$-0.543802\pi$
$79$	−2.43845			−0.274347			−0.137173	+	0.990547i	$0.543802\pi$
$80$	−1.28078	+	2.21837i	−0.143195	+	0.248021i
$81$		0			0
$82$	−2.62311	−	4.54335i	−0.289674	−	0.501729i
$83$	−3.12311			−0.342805			−0.171403	−	0.985201i	$-0.554830\pi$
$83$	−3.12311			−0.342805			−0.171403	+	0.985201i	$0.554830\pi$
$84$		0			0
$85$	−10.4039	−	18.0201i	−1.12846	−	1.95455i
$86$	8.00000			0.862662
$87$		0			0
$88$	−0.780776	+	1.35234i	−0.0832310	+	0.144160i
$89$	3.78078	−	6.54850i	0.400761	−	0.694139i	−0.593056	−	0.805161i	$-0.702079\pi$
$89$	3.78078	−	6.54850i	0.400761	−	0.694139i	0.993818	+	0.111022i	$0.0354123\pi$
$90$		0			0
$91$	3.34233	−	1.35234i	0.350371	−	0.141764i
$92$	−7.12311			−0.742635
$93$		0			0
$94$	6.34233	−	10.9852i	0.654161	−	1.13304i
$95$	−2.00000	−	3.46410i	−0.205196	−	0.355409i
$96$		0			0
$97$	4.56155	+	7.90084i	0.463156	+	0.802209i	0.999116	−	0.0420341i	$-0.0133838\pi$
$97$	4.56155	+	7.90084i	0.463156	+	0.802209i	−0.535961	+	0.844243i	$0.680050\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$		0			0
$100$	−0.780776	−	1.35234i	−0.0780776	−	0.135234i
$101$	7.40388	−	12.8239i	0.736714	−	1.27603i	−0.217254	−	0.976115i	$-0.569710\pi$
$101$	7.40388	−	12.8239i	0.736714	−	1.27603i	0.953967	−	0.299911i	$-0.0969568\pi$
$102$		0			0
$103$	−10.2462			−1.00959			−0.504795	−	0.863239i	$-0.668432\pi$
$103$	−10.2462			−1.00959			−0.504795	+	0.863239i	$0.668432\pi$
$104$	0.500000	−	3.57071i	0.0490290	−	0.350137i
$105$		0			0
$106$	−3.50000	+	6.06218i	−0.339950	+	0.588811i
$107$	−7.46543	+	12.9305i	−0.721711	+	1.25004i	0.238603	+	0.971117i	$0.423311\pi$
$107$	−7.46543	+	12.9305i	−0.721711	+	1.25004i	−0.960314	+	0.278923i	$0.910023\pi$
$108$		0			0
$109$	4.24621			0.406713			0.203357	−	0.979105i	$-0.434815\pi$
$109$	4.24621			0.406713			0.203357	+	0.979105i	$0.434815\pi$
$110$	−2.00000	−	3.46410i	−0.190693	−	0.330289i
$111$		0			0
$112$	1.00000			0.0944911
$113$	−1.28078	−	2.21837i	−0.120485	−	0.208687i	0.799474	−	0.600701i	$-0.205112\pi$
$113$	−1.28078	−	2.21837i	−0.120485	−	0.208687i	−0.919959	+	0.392014i	$0.871778\pi$
$114$		0			0
$115$	9.12311	−	15.8017i	0.850734	−	1.47351i
$116$	−2.12311			−0.197125
$117$		0			0
$118$	−3.12311			−0.287505
$119$	−4.06155	+	7.03482i	−0.372322	+	0.644881i
$120$		0			0
$121$	4.28078	+	7.41452i	0.389161	+	0.674047i
$122$	−5.24621			−0.474970
$123$		0			0
$124$		0			0
$125$	−8.80776			−0.787790
$126$		0			0
$127$	10.2462	−	17.7470i	0.909204	−	1.57479i	0.0940321	−	0.995569i	$-0.470024\pi$
$127$	10.2462	−	17.7470i	0.909204	−	1.57479i	0.815172	−	0.579219i	$-0.196642\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	7.28078	+	5.68247i	0.638566	+	0.498386i
$131$	2.24621			0.196252			0.0981262	−	0.995174i	$-0.468715\pi$
$131$	2.24621			0.196252			0.0981262	+	0.995174i	$0.468715\pi$
$132$		0			0
$133$	−0.780776	+	1.35234i	−0.0677019	+	0.117263i
$134$	0.438447	+	0.759413i	0.0378761	+	0.0656033i
$135$		0			0
$136$	4.06155	+	7.03482i	0.348275	+	0.603230i
$137$	8.28078	+	14.3427i	0.707474	+	1.22538i	0.965791	+	0.259321i	$0.0834989\pi$
$137$	8.28078	+	14.3427i	0.707474	+	1.22538i	−0.258317	+	0.966060i	$0.583168\pi$
$138$		0			0
$139$	4.78078	+	8.28055i	0.405500	+	0.702347i	0.994380	−	0.105874i	$-0.0337640\pi$
$139$	4.78078	+	8.28055i	0.405500	+	0.702347i	−0.588879	+	0.808221i	$0.700431\pi$
$140$	−1.28078	+	2.21837i	−0.108245	+	0.187486i
$141$		0			0
$142$	13.3693			1.12193
$143$	4.43845	+	3.46410i	0.371162	+	0.289683i
$144$		0			0
$145$	2.71922	−	4.70983i	0.225819	−	0.391130i
$146$	−3.28078	+	5.68247i	−0.271519	+	0.470285i
$147$		0			0
$148$	−6.56155			−0.539356
$149$	−5.71922	−	9.90599i	−0.468537	−	0.811530i	0.530816	−	0.847487i	$-0.321885\pi$
$149$	−5.71922	−	9.90599i	−0.468537	−	0.811530i	−0.999353	+	0.0359569i	$0.988552\pi$
$150$		0			0
$151$	6.93087			0.564026			0.282013	−	0.959411i	$-0.408998\pi$
$151$	6.93087			0.564026			0.282013	+	0.959411i	$0.408998\pi$
$152$	0.780776	+	1.35234i	0.0633293	+	0.109690i
$153$		0			0
$154$	−0.780776	+	1.35234i	−0.0629168	+	0.108975i
$155$		0			0
$156$		0			0
$157$	−13.6847			−1.09215			−0.546077	−	0.837735i	$-0.683880\pi$
$157$	−13.6847			−1.09215			−0.546077	+	0.837735i	$0.683880\pi$
$158$	−1.21922	+	2.11176i	−0.0969962	+	0.168002i
$159$		0			0
$160$	1.28078	+	2.21837i	0.101254	+	0.175378i
$161$	−7.12311			−0.561379
$162$		0			0
$163$	4.24621	+	7.35465i	0.332589	+	0.576061i	0.983019	−	0.183505i	$-0.0587445\pi$
$163$	4.24621	+	7.35465i	0.332589	+	0.576061i	−0.650430	+	0.759566i	$0.725411\pi$
$164$	−5.24621			−0.409660
$165$		0			0
$166$	−1.56155	+	2.70469i	−0.121200	+	0.209925i
$167$	−10.2462	+	17.7470i	−0.792876	+	1.37330i	0.131304	+	0.991342i	$0.458084\pi$
$167$	−10.2462	+	17.7470i	−0.792876	+	1.37330i	−0.924179	+	0.381959i	$0.875250\pi$
$168$		0			0
$169$	−12.5000	−	3.57071i	−0.961538	−	0.274670i
$170$	−20.8078			−1.59588
$171$		0			0
$172$	4.00000	−	6.92820i	0.304997	−	0.528271i
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		0			0
$175$	−0.780776	−	1.35234i	−0.0590211	−	0.102228i
$176$	0.780776	+	1.35234i	0.0588532	+	0.101937i
$177$		0			0
$178$	−3.78078	−	6.54850i	−0.283381	−	0.490831i
$179$	−9.12311	+	15.8017i	−0.681893	+	1.18107i	0.292510	+	0.956263i	$0.405510\pi$
$179$	−9.12311	+	15.8017i	−0.681893	+	1.18107i	−0.974402	+	0.224811i	$0.927824\pi$
$180$		0			0
$181$	−3.24621			−0.241289			−0.120644	−	0.992696i	$-0.538496\pi$
$181$	−3.24621			−0.241289			−0.120644	+	0.992696i	$0.538496\pi$
$182$	0.500000	−	3.57071i	0.0370625	−	0.264679i
$183$		0			0
$184$	−3.56155	+	6.16879i	−0.262561	+	0.454769i
$185$	8.40388	−	14.5560i	0.617866	−	1.07017i
$186$		0			0
$187$	−12.6847			−0.927594
$188$	−6.34233	−	10.9852i	−0.462562	−	0.801181i
$189$		0			0
$190$	−4.00000			−0.290191
$191$	1.56155	+	2.70469i	0.112990	+	0.195704i	0.916974	−	0.398946i	$-0.130624\pi$
$191$	1.56155	+	2.70469i	0.112990	+	0.195704i	−0.803984	+	0.594650i	$0.797291\pi$
$192$		0			0
$193$	4.06155	−	7.03482i	0.292357	−	0.506377i	−0.682010	−	0.731343i	$-0.738894\pi$
$193$	4.06155	−	7.03482i	0.292357	−	0.506377i	0.974367	+	0.224966i	$0.0722271\pi$
$194$	9.12311			0.655001
$195$		0			0
$196$	1.00000			0.0714286
$197$	4.21922	−	7.30791i	0.300607	−	0.520667i	−0.675666	−	0.737208i	$-0.736144\pi$
$197$	4.21922	−	7.30791i	0.300607	−	0.520667i	0.976274	+	0.216541i	$0.0694773\pi$
$198$		0			0
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$	−1.56155			−0.110418
$201$		0			0
$202$	−7.40388	−	12.8239i	−0.520935	−	0.902286i
$203$	−2.12311			−0.149013
$204$		0			0
$205$	6.71922	−	11.6380i	0.469291	−	0.812836i
$206$	−5.12311	+	8.87348i	−0.356944	+	0.618245i
$207$		0			0
$208$	−2.84233	−	2.21837i	−0.197080	−	0.153816i
$209$	−2.43845			−0.168671
$210$		0			0
$211$	1.56155	−	2.70469i	0.107502	−	0.186198i	−0.807256	−	0.590202i	$-0.799048\pi$
$211$	1.56155	−	2.70469i	0.107502	−	0.186198i	0.914758	+	0.404003i	$0.132382\pi$
$212$	3.50000	+	6.06218i	0.240381	+	0.416352i
$213$		0			0
$214$	7.46543	+	12.9305i	0.510327	+	0.883912i
$215$	10.2462	+	17.7470i	0.698786	+	1.21033i
$216$		0			0
$217$		0			0
$218$	2.12311	−	3.67733i	0.143795	−	0.249060i
$219$		0			0
$220$	−4.00000			−0.269680
$221$	27.1501	−	10.9852i	1.82631	−	0.738947i
$222$		0			0
$223$	−13.1231	+	22.7299i	−0.878788	+	1.52211i	−0.0261163	+	0.999659i	$0.508314\pi$
$223$	−13.1231	+	22.7299i	−0.878788	+	1.52211i	−0.852672	+	0.522447i	$0.825019\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$	−2.56155			−0.170392
$227$	−9.56155	−	16.5611i	−0.634623	−	1.09920i	−0.986595	−	0.163188i	$-0.947822\pi$
$227$	−9.56155	−	16.5611i	−0.634623	−	1.09920i	0.351972	−	0.936010i	$-0.385511\pi$
$228$		0			0
$229$	−20.0540			−1.32520			−0.662602	−	0.748972i	$-0.730548\pi$
$229$	−20.0540			−1.32520			−0.662602	+	0.748972i	$0.730548\pi$
$230$	−9.12311	−	15.8017i	−0.601560	−	1.04193i
$231$		0			0
$232$	−1.06155	+	1.83866i	−0.0696944	+	0.120714i
$233$	23.3693			1.53097			0.765487	−	0.643451i	$-0.222498\pi$
$233$	23.3693			1.53097			0.765487	+	0.643451i	$0.222498\pi$
$234$		0			0
$235$	32.4924			2.11957
$236$	−1.56155	+	2.70469i	−0.101648	+	0.176060i
$237$		0			0
$238$	4.06155	+	7.03482i	0.263271	+	0.455999i
$239$	5.36932			0.347312			0.173656	−	0.984806i	$-0.444442\pi$
$239$	5.36932			0.347312			0.173656	+	0.984806i	$0.444442\pi$
$240$		0			0
$241$	10.4039	+	18.0201i	0.670173	+	1.16077i	0.977855	+	0.209284i	$0.0671134\pi$
$241$	10.4039	+	18.0201i	0.670173	+	1.16077i	−0.307682	+	0.951489i	$0.599553\pi$
$242$	8.56155			0.550357
$243$		0			0
$244$	−2.62311	+	4.54335i	−0.167927	+	0.290858i
$245$	−1.28078	+	2.21837i	−0.0818258	+	0.141726i
$246$		0			0
$247$	5.21922	−	2.11176i	0.332091	−	0.134368i
$248$		0			0
$249$		0			0
$250$	−4.40388	+	7.62775i	−0.278526	+	0.482421i
$251$	13.8078	+	23.9157i	0.871538	+	1.50955i	0.860405	+	0.509611i	$0.170211\pi$
$251$	13.8078	+	23.9157i	0.871538	+	1.50955i	0.0111332	+	0.999938i	$0.496456\pi$
$252$		0			0
$253$	−5.56155	−	9.63289i	−0.349652	−	0.605615i
$254$	−10.2462	−	17.7470i	−0.642904	−	1.11354i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.184658	−	0.319838i	0.0115187	−	0.0199509i	−0.860209	−	0.509942i	$-0.829667\pi$
$257$	0.184658	−	0.319838i	0.0115187	−	0.0199509i	0.871727	+	0.489991i	$0.163000\pi$
$258$		0			0
$259$	−6.56155			−0.407715
$260$	8.56155	−	3.46410i	0.530965	−	0.214834i
$261$		0			0
$262$	1.12311	−	1.94528i	0.0693857	−	0.120180i
$263$	−1.56155	+	2.70469i	−0.0962895	+	0.166778i	−0.910146	−	0.414288i	$-0.864031\pi$
$263$	−1.56155	+	2.70469i	−0.0962895	+	0.166778i	0.813857	+	0.581066i	$0.197364\pi$
$264$		0			0
$265$	−17.9309			−1.10148
$266$	0.780776	+	1.35234i	0.0478725	+	0.0829176i
$267$		0			0
$268$	0.876894			0.0535648
$269$	9.43845	+	16.3479i	0.575472	+	0.996747i	0.995990	+	0.0894630i	$0.0285151\pi$
$269$	9.43845	+	16.3479i	0.575472	+	0.996747i	−0.420518	+	0.907284i	$0.638152\pi$
$270$		0			0
$271$	−13.3693	+	23.1563i	−0.812128	+	1.40665i	0.0992436	+	0.995063i	$0.468358\pi$
$271$	−13.3693	+	23.1563i	−0.812128	+	1.40665i	−0.911372	+	0.411584i	$0.864976\pi$
$272$	8.12311			0.492536
$273$		0			0
$274$	16.5616			1.00052
$275$	1.21922	−	2.11176i	0.0735219	−	0.127344i
$276$		0			0
$277$	7.71922	+	13.3701i	0.463803	+	0.803331i	0.999147	−	0.0413038i	$-0.0131511\pi$
$277$	7.71922	+	13.3701i	0.463803	+	0.803331i	−0.535343	+	0.844634i	$0.679818\pi$
$278$	9.56155			0.573464
$279$		0			0
$280$	1.28078	+	2.21837i	0.0765410	+	0.132573i
$281$	15.9309			0.950356			0.475178	−	0.879890i	$-0.342384\pi$
$281$	15.9309			0.950356			0.475178	+	0.879890i	$0.342384\pi$
$282$		0			0
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	−0.399188	−	0.916869i	$-0.630708\pi$
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	0.993626	−	0.112728i	$-0.0359589\pi$
$284$	6.68466	−	11.5782i	0.396662	−	0.687038i
$285$		0			0
$286$	5.21922	−	2.11176i	0.308619	−	0.124871i
$287$	−5.24621			−0.309674
$288$		0			0
$289$	−24.4924	+	42.4221i	−1.44073	+	2.49542i
$290$	−2.71922	−	4.70983i	−0.159678	−	0.276571i
$291$		0			0
$292$	3.28078	+	5.68247i	0.191993	+	0.332541i
$293$	10.9654	+	18.9927i	0.640608	+	1.10956i	0.985297	+	0.170848i	$0.0546508\pi$
$293$	10.9654	+	18.9927i	0.640608	+	1.10956i	−0.344690	+	0.938717i	$0.612016\pi$
$294$		0			0
$295$	−4.00000	−	6.92820i	−0.232889	−	0.403376i
$296$	−3.28078	+	5.68247i	−0.190691	+	0.330287i
$297$		0			0
$298$	−11.4384			−0.662611
$299$	20.2462	+	15.8017i	1.17087	+	0.913835i
$300$		0			0
$301$	4.00000	−	6.92820i	0.230556	−	0.399335i
$302$	3.46543	−	6.00231i	0.199413	−	0.345394i
$303$		0			0
$304$	1.56155			0.0895612
$305$	−6.71922	−	11.6380i	−0.384742	−	0.666392i
$306$		0			0
$307$	18.9309			1.08044			0.540221	−	0.841523i	$-0.318341\pi$
$307$	18.9309			1.08044			0.540221	+	0.841523i	$0.318341\pi$
$308$	0.780776	+	1.35234i	0.0444889	+	0.0770570i
$309$		0			0
$310$		0			0
$311$	6.93087			0.393014			0.196507	−	0.980502i	$-0.437040\pi$
$311$	6.93087			0.393014			0.196507	+	0.980502i	$0.437040\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	−6.84233	+	11.8513i	−0.386135	+	0.668805i
$315$		0			0
$316$	1.21922	+	2.11176i	0.0685867	+	0.118796i
$317$	−16.5616			−0.930189			−0.465095	−	0.885261i	$-0.653980\pi$
$317$	−16.5616			−0.930189			−0.465095	+	0.885261i	$0.653980\pi$
$318$		0			0
$319$	−1.65767	−	2.87117i	−0.0928117	−	0.160755i
$320$	2.56155			0.143195
$321$		0			0
$322$	−3.56155	+	6.16879i	−0.198478	+	0.343773i
$323$	−6.34233	+	10.9852i	−0.352897	+	0.611235i
$324$		0			0
$325$	−0.780776	+	5.57586i	−0.0433097	+	0.309293i
$326$	8.49242			0.470352
$327$		0			0
$328$	−2.62311	+	4.54335i	−0.144837	+	0.250865i
$329$	−6.34233	−	10.9852i	−0.349664	−	0.605636i
$330$		0			0
$331$	2.68466	+	4.64996i	0.147562	+	0.255585i	0.930326	−	0.366734i	$-0.119524\pi$
$331$	2.68466	+	4.64996i	0.147562	+	0.255585i	−0.782764	+	0.622319i	$0.786191\pi$
$332$	1.56155	+	2.70469i	0.0857013	+	0.148439i
$333$		0			0
$334$	10.2462	+	17.7470i	0.560648	+	0.971070i
$335$	−1.12311	+	1.94528i	−0.0613618	+	0.106282i
$336$		0			0
$337$	19.4924			1.06182			0.530910	−	0.847428i	$-0.321850\pi$
$337$	19.4924			1.06182			0.530910	+	0.847428i	$0.321850\pi$
$338$	−9.34233	+	9.03996i	−0.508156	+	0.491709i
$339$		0			0
$340$	−10.4039	+	18.0201i	−0.564230	+	0.977275i
$341$		0			0
$342$		0			0
$343$	1.00000			0.0539949
$344$	−4.00000	−	6.92820i	−0.215666	−	0.373544i
$345$		0			0
$346$	−18.0000			−0.967686
$347$	−11.0270	−	19.0993i	−0.591960	−	1.02530i	−0.993968	−	0.109668i	$-0.965021\pi$
$347$	−11.0270	−	19.0993i	−0.591960	−	1.02530i	0.402009	−	0.915636i	$-0.368312\pi$
$348$		0			0
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	−0.518022	−	0.855367i	$-0.673331\pi$
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	0.999781	+	0.0209364i	$0.00666475\pi$
$350$	−1.56155			−0.0834685
$351$		0			0
$352$	1.56155			0.0832310
$353$	−6.59612	+	11.4248i	−0.351076	+	0.608081i	−0.986438	−	0.164133i	$-0.947517\pi$
$353$	−6.59612	+	11.4248i	−0.351076	+	0.608081i	0.635362	+	0.772214i	$0.280851\pi$
$354$		0			0
$355$	17.1231	+	29.6581i	0.908800	+	1.57409i
$356$	−7.56155			−0.400761
$357$		0			0
$358$	9.12311	+	15.8017i	0.482171	+	0.835145i
$359$	18.2462			0.962998			0.481499	−	0.876447i	$-0.340092\pi$
$359$	18.2462			0.962998			0.481499	+	0.876447i	$0.340092\pi$
$360$		0			0
$361$	8.28078	−	14.3427i	0.435830	−	0.754880i
$362$	−1.62311	+	2.81130i	−0.0853085	+	0.147759i
$363$		0			0
$364$	−2.84233	−	2.21837i	−0.148979	−	0.116274i
$365$	−16.8078			−0.879759
$366$		0			0
$367$	13.8078	−	23.9157i	0.720759	−	1.24839i	−0.239936	−	0.970789i	$-0.577127\pi$
$367$	13.8078	−	23.9157i	0.720759	−	1.24839i	0.960696	−	0.277603i	$-0.0895401\pi$
$368$	3.56155	+	6.16879i	0.185659	+	0.321570i
$369$		0			0
$370$	−8.40388	−	14.5560i	−0.436897	−	0.756728i
$371$	3.50000	+	6.06218i	0.181711	+	0.314733i
$372$		0			0
$373$	15.9654	+	27.6529i	0.826659	+	1.43182i	0.900645	+	0.434556i	$0.143095\pi$
$373$	15.9654	+	27.6529i	0.826659	+	1.43182i	−0.0739860	+	0.997259i	$0.523572\pi$
$374$	−6.34233	+	10.9852i	−0.327954	+	0.568033i
$375$		0			0
$376$	−12.6847			−0.654161
$377$	6.03457	+	4.70983i	0.310796	+	0.242569i
$378$		0			0
$379$	1.80776	−	3.13114i	0.0928586	−	0.160836i	−0.815854	−	0.578258i	$-0.803733\pi$
$379$	1.80776	−	3.13114i	0.0928586	−	0.160836i	0.908713	+	0.417422i	$0.137066\pi$
$380$	−2.00000	+	3.46410i	−0.102598	+	0.177705i
$381$		0			0
$382$	3.12311			0.159792
$383$	3.90388	+	6.76172i	0.199479	+	0.345508i	0.948360	−	0.317197i	$-0.102742\pi$
$383$	3.90388	+	6.76172i	0.199479	+	0.345508i	−0.748881	+	0.662705i	$0.769408\pi$
$384$		0			0
$385$	−4.00000			−0.203859
$386$	−4.06155	−	7.03482i	−0.206728	−	0.358063i
$387$		0			0
$388$	4.56155	−	7.90084i	0.231578	−	0.401104i
$389$	17.6847			0.896648			0.448324	−	0.893871i	$-0.352021\pi$
$389$	17.6847			0.896648			0.448324	+	0.893871i	$0.352021\pi$
$390$		0			0
$391$	−57.8617			−2.92619
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$		0			0
$394$	−4.21922	−	7.30791i	−0.212561	−	0.368167i
$395$	−6.24621			−0.314281
$396$		0			0
$397$	0.465435	+	0.806157i	0.0233595	+	0.0404598i	0.877469	−	0.479634i	$-0.159230\pi$
$397$	0.465435	+	0.806157i	0.0233595	+	0.0404598i	−0.854109	+	0.520093i	$0.825897\pi$
$398$	16.0000			0.802008
$399$		0			0
$400$	−0.780776	+	1.35234i	−0.0390388	+	0.0676172i
$401$	9.40388	−	16.2880i	0.469607	−	0.813384i	−0.529789	−	0.848130i	$-0.677729\pi$
$401$	9.40388	−	16.2880i	0.469607	−	0.813384i	0.999396	+	0.0347457i	$0.0110621\pi$
$402$		0			0
$403$		0			0
$404$	−14.8078			−0.736714
$405$		0			0
$406$	−1.06155	+	1.83866i	−0.0526840	+	0.0912513i
$407$	−5.12311	−	8.87348i	−0.253943	−	0.439842i
$408$		0			0
$409$	3.71922	+	6.44188i	0.183904	+	0.318531i	0.943207	−	0.332207i	$-0.107793\pi$
$409$	3.71922	+	6.44188i	0.183904	+	0.318531i	−0.759303	+	0.650737i	$0.774460\pi$
$410$	−6.71922	−	11.6380i	−0.331839	−	0.574762i
$411$		0			0
$412$	5.12311	+	8.87348i	0.252397	+	0.437165i
$413$	−1.56155	+	2.70469i	−0.0768390	+	0.133089i
$414$		0			0
$415$	−8.00000			−0.392705
$416$	−3.34233	+	1.35234i	−0.163871	+	0.0663041i
$417$		0			0
$418$	−1.21922	+	2.11176i	−0.0596342	+	0.103289i
$419$	−0.684658	+	1.18586i	−0.0334478	+	0.0579332i	−0.882265	−	0.470754i	$-0.843982\pi$
$419$	−0.684658	+	1.18586i	−0.0334478	+	0.0579332i	0.848817	+	0.528687i	$0.177315\pi$
$420$		0			0
$421$	31.3002			1.52548			0.762739	−	0.646707i	$-0.223854\pi$
$421$	31.3002			1.52548			0.762739	+	0.646707i	$0.223854\pi$
$422$	−1.56155	−	2.70469i	−0.0760152	−	0.131662i
$423$		0			0
$424$	7.00000			0.339950
$425$	−6.34233	−	10.9852i	−0.307648	−	0.532862i
$426$		0			0
$427$	−2.62311	+	4.54335i	−0.126941	+	0.219868i
$428$	14.9309			0.721711
$429$		0			0
$430$	20.4924			0.988232
$431$	−2.68466	+	4.64996i	−0.129315	+	0.223981i	−0.923412	−	0.383811i	$-0.874611\pi$
$431$	−2.68466	+	4.64996i	−0.129315	+	0.223981i	0.794096	+	0.607792i	$0.207945\pi$
$432$		0			0
$433$	16.8423	+	29.1718i	0.809391	+	1.40191i	0.913287	+	0.407318i	$0.133536\pi$
$433$	16.8423	+	29.1718i	0.809391	+	1.40191i	−0.103896	+	0.994588i	$0.533131\pi$
$434$		0			0
$435$		0			0
$436$	−2.12311	−	3.67733i	−0.101678	−	0.176112i
$437$	−11.1231			−0.532090
$438$		0			0
$439$	4.87689	−	8.44703i	0.232761	−	0.403155i	−0.725858	−	0.687844i	$-0.758557\pi$
$439$	4.87689	−	8.44703i	0.232761	−	0.403155i	0.958620	+	0.284690i	$0.0918905\pi$
$440$	−2.00000	+	3.46410i	−0.0953463	+	0.165145i
$441$		0			0
$442$	4.06155	−	29.0053i	0.193188	−	1.37964i
$443$	−10.0540			−0.477679			−0.238839	−	0.971059i	$-0.576767\pi$
$443$	−10.0540			−0.477679			−0.238839	+	0.971059i	$0.576767\pi$
$444$		0			0
$445$	9.68466	−	16.7743i	0.459097	−	0.795179i
$446$	13.1231	+	22.7299i	0.621397	+	1.07629i
$447$		0			0
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−15.6847	−	27.1666i	−0.740205	−	1.28207i	−0.952402	−	0.304845i	$-0.901395\pi$
$449$	−15.6847	−	27.1666i	−0.740205	−	1.28207i	0.212197	−	0.977227i	$-0.431938\pi$
$450$		0			0
$451$	−4.09612	−	7.09468i	−0.192879	−	0.334076i
$452$	−1.28078	+	2.21837i	−0.0602427	+	0.104343i
$453$		0			0
$454$	−19.1231			−0.897492
$455$	8.56155	−	3.46410i	0.401372	−	0.162400i
$456$		0			0
$457$	−0.0345652	+	0.0598686i	−0.00161689	+	0.00280054i	−0.866833	−	0.498599i	$-0.833848\pi$
$457$	−0.0345652	+	0.0598686i	−0.00161689	+	0.00280054i	0.865216	+	0.501400i	$0.167181\pi$
$458$	−10.0270	+	17.3673i	−0.468530	+	0.811518i
$459$		0			0
$460$	−18.2462			−0.850734
$461$	−15.5270	−	26.8935i	−0.723164	−	1.25256i	−0.959725	−	0.280940i	$-0.909354\pi$
$461$	−15.5270	−	26.8935i	−0.723164	−	1.25256i	0.236561	−	0.971617i	$-0.423980\pi$
$462$		0			0
$463$	24.6847			1.14719			0.573597	−	0.819138i	$-0.305548\pi$
$463$	24.6847			1.14719			0.573597	+	0.819138i	$0.305548\pi$
$464$	1.06155	+	1.83866i	0.0492814	+	0.0853578i
$465$		0			0
$466$	11.6847	−	20.2384i	0.541281	−	0.937527i
$467$	−28.9848			−1.34126			−0.670629	−	0.741793i	$-0.733976\pi$
$467$	−28.9848			−1.34126			−0.670629	+	0.741793i	$0.733976\pi$
$468$		0			0
$469$	0.876894			0.0404912
$470$	16.2462	−	28.1393i	0.749382	−	1.29797i
$471$		0			0
$472$	1.56155	+	2.70469i	0.0718763	+	0.124493i
$473$	12.4924			0.574402
$474$		0			0
$475$	−1.21922	−	2.11176i	−0.0559418	−	0.0968941i
$476$	8.12311			0.372322
$477$		0			0
$478$	2.68466	−	4.64996i	0.122793	−	0.212684i
$479$	13.4654	−	23.3228i	0.615251	−	1.06565i	−0.375089	−	0.926989i	$-0.622388\pi$
$479$	13.4654	−	23.3228i	0.615251	−	1.06565i	0.990340	−	0.138658i	$-0.0442788\pi$
$480$		0			0
$481$	18.6501	+	14.5560i	0.850371	+	0.663694i
$482$	20.8078			0.947768
$483$		0			0
$484$	4.28078	−	7.41452i	0.194581	−	0.337024i
$485$	11.6847	+	20.2384i	0.530573	+	0.918979i
$486$		0			0
$487$	−5.65767	−	9.79937i	−0.256374	−	0.444052i	0.708894	−	0.705315i	$-0.249194\pi$
$487$	−5.65767	−	9.79937i	−0.256374	−	0.444052i	−0.965268	+	0.261263i	$0.915861\pi$
$488$	2.62311	+	4.54335i	0.118742	+	0.205668i
$489$		0			0
$490$	1.28078	+	2.21837i	0.0578596	+	0.100216i
$491$	8.24621	−	14.2829i	0.372146	−	0.644576i	−0.617749	−	0.786375i	$-0.711955\pi$
$491$	8.24621	−	14.2829i	0.372146	−	0.644576i	0.989895	+	0.141799i	$0.0452886\pi$
$492$		0			0
$493$	−17.2462			−0.776730
$494$	0.780776	−	5.57586i	0.0351288	−	0.250870i
$495$		0			0
$496$		0			0
$497$	6.68466	−	11.5782i	0.299848	−	0.519352i
$498$		0			0
$499$	13.7538			0.615704			0.307852	−	0.951434i	$-0.400390\pi$
$499$	13.7538			0.615704			0.307852	+	0.951434i	$0.400390\pi$
$500$	4.40388	+	7.62775i	0.196948	+	0.341123i
$501$		0			0
$502$	27.6155			1.23254
$503$	2.24621	+	3.89055i	0.100154	+	0.173471i	0.911748	−	0.410750i	$-0.134733\pi$
$503$	2.24621	+	3.89055i	0.100154	+	0.173471i	−0.811594	+	0.584222i	$0.801400\pi$
$504$		0			0
$505$	18.9654	−	32.8491i	0.843951	−	1.46177i
$506$	−11.1231			−0.494482
$507$		0			0
$508$	−20.4924			−0.909204
$509$	−10.5961	+	18.3530i	−0.469665	+	0.813483i	−0.999398	−	0.0346809i	$-0.988959\pi$
$509$	−10.5961	+	18.3530i	−0.469665	+	0.813483i	0.529734	+	0.848164i	$0.322292\pi$
$510$		0			0
$511$	3.28078	+	5.68247i	0.145133	+	0.251378i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−0.184658	−	0.319838i	−0.00814493	−	0.0141074i
$515$	−26.2462			−1.15655
$516$		0			0
$517$	9.90388	−	17.1540i	0.435572	−	0.754433i
$518$	−3.28078	+	5.68247i	−0.144149	+	0.249673i
$519$		0			0
$520$	1.28078	−	9.14657i	0.0561658	−	0.401104i
$521$	−34.1231			−1.49496			−0.747480	−	0.664284i	$-0.768737\pi$
$521$	−34.1231			−1.49496			−0.747480	+	0.664284i	$0.768737\pi$
$522$		0			0
$523$	−1.90388	+	3.29762i	−0.0832509	+	0.144195i	−0.904645	−	0.426167i	$-0.859864\pi$
$523$	−1.90388	+	3.29762i	−0.0832509	+	0.144195i	0.821394	+	0.570362i	$0.193197\pi$
$524$	−1.12311	−	1.94528i	−0.0490631	−	0.0849798i
$525$		0			0
$526$	1.56155	+	2.70469i	0.0680869	+	0.117930i
$527$		0			0
$528$		0			0
$529$	−13.8693	−	24.0224i	−0.603014	−	1.04445i
$530$	−8.96543	+	15.5286i	−0.389434	+	0.674519i
$531$		0			0
$532$	1.56155			0.0677019
$533$	14.9115	+	11.6380i	0.645887	+	0.504099i
$534$		0			0
$535$	−19.1231	+	33.1222i	−0.826764	+	1.43200i
$536$	0.438447	−	0.759413i	0.0189380	−	0.0328016i
$537$		0			0
$538$	18.8769			0.813841
$539$	0.780776	+	1.35234i	0.0336304	+	0.0582496i
$540$		0			0
$541$	−26.1771			−1.12544			−0.562720	−	0.826647i	$-0.690245\pi$
$541$	−26.1771			−1.12544			−0.562720	+	0.826647i	$0.690245\pi$
$542$	13.3693	+	23.1563i	0.574261	+	0.994650i
$543$		0			0
$544$	4.06155	−	7.03482i	0.174138	−	0.301615i
$545$	10.8769			0.465915
$546$		0			0
$547$	7.61553			0.325616			0.162808	−	0.986658i	$-0.447945\pi$
$547$	7.61553			0.325616			0.162808	+	0.986658i	$0.447945\pi$
$548$	8.28078	−	14.3427i	0.353737	−	0.612691i
$549$		0			0
$550$	−1.21922	−	2.11176i	−0.0519879	−	0.0900456i
$551$	−3.31534			−0.141238
$552$		0			0
$553$	1.21922	+	2.11176i	0.0518467	+	0.0898011i
$554$	15.4384			0.655917
$555$		0			0
$556$	4.78078	−	8.28055i	0.202750	−	0.351173i
$557$	1.93845	−	3.35749i	0.0821346	−	0.142261i	−0.822032	−	0.569441i	$-0.807160\pi$
$557$	1.93845	−	3.35749i	0.0821346	−	0.142261i	0.904167	+	0.427180i	$0.140493\pi$
$558$		0			0
$559$	−26.7386	+	10.8188i	−1.13092	+	0.457585i
$560$	2.56155			0.108245
$561$		0			0
$562$	7.96543	−	13.7965i	0.336002	−	0.581972i
$563$	−11.1231	−	19.2658i	−0.468783	−	0.811956i	0.530580	−	0.847635i	$-0.321974\pi$
$563$	−11.1231	−	19.2658i	−0.468783	−	0.811956i	−0.999363	+	0.0356787i	$0.988641\pi$
$564$		0			0
$565$	−3.28078	−	5.68247i	−0.138023	−	0.239063i
$566$	−10.0000	−	17.3205i	−0.420331	−	0.728035i
$567$		0			0
$568$	−6.68466	−	11.5782i	−0.280482	−	0.485809i
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	−0.999018	−	0.0443003i	$-0.985894\pi$
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	0.537874	+	0.843025i	$0.319228\pi$
$570$		0			0
$571$	−12.8769			−0.538881			−0.269441	−	0.963017i	$-0.586839\pi$
$571$	−12.8769			−0.538881			−0.269441	+	0.963017i	$0.586839\pi$
$572$	0.780776	−	5.57586i	0.0326459	−	0.233138i
$573$		0			0
$574$	−2.62311	+	4.54335i	−0.109486	+	0.189636i
$575$	5.56155	−	9.63289i	0.231933	−	0.401719i
$576$		0			0
$577$	−31.4384			−1.30880			−0.654400	−	0.756149i	$-0.727079\pi$
$577$	−31.4384			−1.30880			−0.654400	+	0.756149i	$0.727079\pi$
$578$	24.4924	+	42.4221i	1.01875	+	1.76453i
$579$		0			0
$580$	−5.43845			−0.225819
$581$	1.56155	+	2.70469i	0.0647841	+	0.112209i
$582$		0			0
$583$	−5.46543	+	9.46641i	−0.226355	+	0.392059i
$584$	6.56155			0.271519
$585$		0			0
$586$	21.9309			0.905956
$587$	−7.12311	+	12.3376i	−0.294002	+	0.509226i	−0.974752	−	0.223289i	$-0.928321\pi$
$587$	−7.12311	+	12.3376i	−0.294002	+	0.509226i	0.680750	+	0.732516i	$0.261654\pi$
$588$		0			0
$589$		0			0
$590$	−8.00000			−0.329355
$591$		0			0
$592$	3.28078	+	5.68247i	0.134839	+	0.233548i
$593$	−31.9848			−1.31346			−0.656730	−	0.754126i	$-0.728061\pi$
$593$	−31.9848			−1.31346			−0.656730	+	0.754126i	$0.728061\pi$
$594$		0			0
$595$	−10.4039	+	18.0201i	−0.426518	+	0.738750i
$596$	−5.71922	+	9.90599i	−0.234269	+	0.405765i
$597$		0			0
$598$	23.8078	−	9.63289i	0.973572	−	0.393918i
$599$	33.8617			1.38355			0.691777	−	0.722112i	$-0.256828\pi$
$599$	33.8617			1.38355			0.691777	+	0.722112i	$0.256828\pi$
$600$		0			0
$601$	12.6501	−	21.9106i	0.516008	−	0.893752i	−0.483819	−	0.875168i	$-0.660751\pi$
$601$	12.6501	−	21.9106i	0.516008	−	0.893752i	0.999827	−	0.0185842i	$-0.00591589\pi$
$602$	−4.00000	−	6.92820i	−0.163028	−	0.282372i
$603$		0			0
$604$	−3.46543	−	6.00231i	−0.141007	−	0.244230i
$605$	10.9654	+	18.9927i	0.445808	+	0.772163i
$606$		0			0
$607$	−8.49242	−	14.7093i	−0.344697	−	0.597032i	0.640602	−	0.767873i	$-0.278685\pi$
$607$	−8.49242	−	14.7093i	−0.344697	−	0.597032i	−0.985299	+	0.170841i	$0.945352\pi$
$608$	0.780776	−	1.35234i	0.0316647	−	0.0548448i
$609$		0			0
$610$	−13.4384			−0.544107
$611$	−6.34233	+	45.2933i	−0.256583	+	1.83237i
$612$		0			0
$613$	−8.71922	+	15.1021i	−0.352166	+	0.609970i	−0.986629	−	0.162984i	$-0.947888\pi$
$613$	−8.71922	+	15.1021i	−0.352166	+	0.609970i	0.634463	+	0.772954i	$0.281221\pi$
$614$	9.46543	−	16.3946i	0.381994	−	0.661633i
$615$		0			0
$616$	1.56155			0.0629168
$617$	−11.0885	−	19.2059i	−0.446408	−	0.773201i	0.551741	−	0.834015i	$-0.313964\pi$
$617$	−11.0885	−	19.2059i	−0.446408	−	0.773201i	−0.998149	+	0.0608143i	$0.980630\pi$
$618$		0			0
$619$	30.9309			1.24322			0.621608	−	0.783328i	$-0.286480\pi$
$619$	30.9309			1.24322			0.621608	+	0.783328i	$0.286480\pi$
$620$		0			0
$621$		0			0
$622$	3.46543	−	6.00231i	0.138951	−	0.240671i
$623$	−7.56155			−0.302947
$624$		0			0
$625$	−30.3693			−1.21477
$626$	−3.00000	+	5.19615i	−0.119904	+	0.207680i
$627$		0			0
$628$	6.84233	+	11.8513i	0.273039	+	0.472917i
$629$	−53.3002			−2.12522
$630$		0			0
$631$	19.4654	+	33.7151i	0.774907	+	1.34218i	0.934847	+	0.355051i	$0.115537\pi$
$631$	19.4654	+	33.7151i	0.774907	+	1.34218i	−0.159940	+	0.987127i	$0.551130\pi$
$632$	2.43845			0.0969962
$633$		0			0
$634$	−8.28078	+	14.3427i	−0.328872	+	0.569622i
$635$	26.2462	−	45.4598i	1.04155	−	1.80402i
$636$		0			0
$637$	−2.84233	−	2.21837i	−0.112617	−	0.0878950i
$638$	−3.31534			−0.131256
$639$		0			0
$640$	1.28078	−	2.21837i	0.0506271	−	0.0876888i
$641$	6.28078	+	10.8786i	0.248076	+	0.429680i	0.962992	−	0.269530i	$-0.0868685\pi$
$641$	6.28078	+	10.8786i	0.248076	+	0.429680i	−0.714916	+	0.699210i	$0.753535\pi$
$642$		0			0
$643$	−17.6577	−	30.5840i	−0.696351	−	1.20611i	−0.969723	−	0.244206i	$-0.921473\pi$
$643$	−17.6577	−	30.5840i	−0.696351	−	1.20611i	0.273373	−	0.961908i	$-0.411861\pi$
$644$	3.56155	+	6.16879i	0.140345	+	0.243084i
$645$		0			0
$646$	6.34233	+	10.9852i	0.249536	+	0.432208i
$647$	−23.0270	+	39.8839i	−0.905284	+	1.56800i	−0.0847492	+	0.996402i	$0.527009\pi$
$647$	−23.0270	+	39.8839i	−0.905284	+	1.56800i	−0.820535	+	0.571596i	$0.806324\pi$
$648$		0			0
$649$	−4.87689			−0.191435
$650$	4.43845	+	3.46410i	0.174090	+	0.135873i
$651$		0			0
$652$	4.24621	−	7.35465i	0.166294	−	0.288030i
$653$	8.21922	−	14.2361i	0.321643	−	0.557102i	−0.659184	−	0.751982i	$-0.729098\pi$
$653$	8.21922	−	14.2361i	0.321643	−	0.557102i	0.980827	+	0.194879i	$0.0624316\pi$
$654$		0			0
$655$	5.75379			0.224819
$656$	2.62311	+	4.54335i	0.102415	+	0.177388i
$657$		0			0
$658$	−12.6847			−0.494499
$659$	15.4654	+	26.7869i	0.602448	+	1.04347i	0.992449	+	0.122656i	$0.0391412\pi$
$659$	15.4654	+	26.7869i	0.602448	+	1.04347i	−0.390001	+	0.920814i	$0.627525\pi$
$660$		0			0
$661$	−8.52699	+	14.7692i	−0.331661	+	0.574454i	−0.982838	−	0.184472i	$-0.940942\pi$
$661$	−8.52699	+	14.7692i	−0.331661	+	0.574454i	0.651176	+	0.758926i	$0.274276\pi$
$662$	5.36932			0.208684
$663$		0			0
$664$	3.12311			0.121200
$665$	−2.00000	+	3.46410i	−0.0775567	+	0.134332i
$666$		0			0
$667$	−7.56155	−	13.0970i	−0.292784	−	0.507118i
$668$	20.4924			0.792876
$669$		0			0
$670$	1.12311	+	1.94528i	0.0433894	+	0.0751526i
$671$	−8.19224			−0.316258
$672$		0			0
$673$	9.62311	−	16.6677i	0.370943	−	0.642493i	−0.618767	−	0.785574i	$-0.712368\pi$
$673$	9.62311	−	16.6677i	0.370943	−	0.642493i	0.989711	+	0.143081i	$0.0457010\pi$
$674$	9.74621	−	16.8809i	0.375410	−	0.650229i
$675$		0			0
$676$	3.15767	+	12.6107i	0.121449	+	0.485026i
$677$	−24.7386			−0.950783			−0.475391	−	0.879774i	$-0.657694\pi$
$677$	−24.7386			−0.950783			−0.475391	+	0.879774i	$0.657694\pi$
$678$		0			0
$679$	4.56155	−	7.90084i	0.175056	−	0.303206i
$680$	10.4039	+	18.0201i	0.398971	+	0.691037i
$681$		0			0
$682$		0			0
$683$	3.75379	+	6.50175i	0.143635	+	0.248783i	0.928863	−	0.370424i	$-0.120788\pi$
$683$	3.75379	+	6.50175i	0.143635	+	0.248783i	−0.785228	+	0.619207i	$0.787454\pi$
$684$		0			0
$685$	21.2116	+	36.7396i	0.810455	+	1.40375i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$		0			0
$688$	−8.00000			−0.304997
$689$	3.50000	−	24.9950i	0.133339	−	0.952234i
$690$		0			0
$691$	−16.4924	+	28.5657i	−0.627401	+	1.08669i	0.360670	+	0.932694i	$0.382548\pi$
$691$	−16.4924	+	28.5657i	−0.627401	+	1.08669i	−0.988071	+	0.153997i	$0.950785\pi$
$692$	−9.00000	+	15.5885i	−0.342129	+	0.592584i
$693$		0			0
$694$	−22.0540			−0.837157
$695$	12.2462	+	21.2111i	0.464525	+	0.804581i
$696$		0			0
$697$	−42.6155			−1.61418
$698$	−9.00000	−	15.5885i	−0.340655	−	0.590032i
$699$		0			0
$700$	−0.780776	+	1.35234i	−0.0295106	+	0.0511138i
$701$	−14.3002			−0.540111			−0.270055	−	0.962845i	$-0.587042\pi$
$701$	−14.3002			−0.540111			−0.270055	+	0.962845i	$0.587042\pi$
$702$		0			0
$703$	−10.2462			−0.386443
$704$	0.780776	−	1.35234i	0.0294266	−	0.0509684i
$705$		0			0
$706$	6.59612	+	11.4248i	0.248248	+	0.429978i
$707$	−14.8078			−0.556903
$708$		0			0
$709$	−7.65009	−	13.2504i	−0.287305	−	0.497627i	0.685860	−	0.727733i	$-0.259426\pi$
$709$	−7.65009	−	13.2504i	−0.287305	−	0.497627i	−0.973166	+	0.230106i	$0.926093\pi$
$710$	34.2462			1.28524
$711$		0			0
$712$	−3.78078	+	6.54850i	−0.141691	+	0.245415i
$713$		0			0
$714$		0			0
$715$	11.3693	+	8.87348i	0.425188	+	0.331849i
$716$	18.2462			0.681893
$717$		0			0
$718$	9.12311	−	15.8017i	0.340471	−	0.589714i
$719$	−9.90388	−	17.1540i	−0.369352	−	0.639737i	0.620112	−	0.784513i	$-0.287087\pi$
$719$	−9.90388	−	17.1540i	−0.369352	−	0.639737i	−0.989464	+	0.144776i	$0.953754\pi$
$720$		0			0
$721$	5.12311	+	8.87348i	0.190794	+	0.330466i
$722$	−8.28078	−	14.3427i	−0.308179	−	0.533781i
$723$		0			0
$724$	1.62311	+	2.81130i	0.0603222	+	0.104481i
$725$	1.65767	−	2.87117i	0.0615643	−	0.106633i
$726$		0			0
$727$	40.0000			1.48352			0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000			1.48352			0.741759	+	0.670667i	$0.233992\pi$
$728$	−3.34233	+	1.35234i	−0.123875	+	0.0501212i
$729$		0			0
$730$	−8.40388	+	14.5560i	−0.311042	+	0.538740i
$731$	32.4924	−	56.2785i	1.20178	−	2.08154i
$732$		0			0
$733$	28.8617			1.06603			0.533016	−	0.846105i	$-0.321058\pi$
$733$	28.8617			1.06603			0.533016	+	0.846105i	$0.321058\pi$
$734$	−13.8078	−	23.9157i	−0.509654	−	0.882746i
$735$		0			0
$736$	7.12311			0.262561
$737$	0.684658	+	1.18586i	0.0252197	+	0.0436818i
$738$		0			0
$739$	4.68466	−	8.11407i	0.172328	−	0.298481i	−0.766905	−	0.641760i	$-0.778204\pi$
$739$	4.68466	−	8.11407i	0.172328	−	0.298481i	0.939233	+	0.343279i	$0.111538\pi$
$740$	−16.8078			−0.617866
$741$		0			0
$742$	7.00000			0.256978
$743$	14.2462	−	24.6752i	0.522643	−	0.905244i	−0.477010	−	0.878898i	$-0.658279\pi$
$743$	14.2462	−	24.6752i	0.522643	−	0.905244i	0.999653	−	0.0263461i	$-0.00838718\pi$
$744$		0			0
$745$	−14.6501	−	25.3747i	−0.536738	−	0.929657i
$746$	31.9309			1.16907
$747$		0			0
$748$	6.34233	+	10.9852i	0.231899	+	0.401660i
$749$	14.9309			0.545562
$750$		0			0
$751$	10.0961	−	17.4870i	0.368413	−	0.638109i	−0.620905	−	0.783886i	$-0.713235\pi$
$751$	10.0961	−	17.4870i	0.368413	−	0.638109i	0.989318	+	0.145777i	$0.0465681\pi$
$752$	−6.34233	+	10.9852i	−0.231281	+	0.400590i
$753$		0			0
$754$	7.09612	−	2.87117i	0.258425	−	0.104562i
$755$	17.7538			0.646127
$756$		0			0
$757$	−1.63068	+	2.82443i	−0.0592682	+	0.102656i	−0.894137	−	0.447793i	$-0.852210\pi$
$757$	−1.63068	+	2.82443i	−0.0592682	+	0.102656i	0.834869	+	0.550449i	$0.185543\pi$
$758$	−1.80776	−	3.13114i	−0.0656609	−	0.113728i
$759$		0			0
$760$	2.00000	+	3.46410i	0.0725476	+	0.125656i
$761$	−7.49242	−	12.9773i	−0.271600	−	0.470425i	0.697672	−	0.716418i	$-0.254219\pi$
$761$	−7.49242	−	12.9773i	−0.271600	−	0.470425i	−0.969272	+	0.245993i	$0.920886\pi$
$762$		0			0
$763$	−2.12311	−	3.67733i	−0.0768616	−	0.133128i
$764$	1.56155	−	2.70469i	0.0564950	−	0.0978522i
$765$		0			0
$766$	7.80776			0.282106
$767$	10.4384	−	4.22351i	0.376910	−	0.152502i
$768$		0			0
$769$	−6.56155	+	11.3649i	−0.236616	+	0.409830i	−0.959741	−	0.280887i	$-0.909372\pi$
$769$	−6.56155	+	11.3649i	−0.236616	+	0.409830i	0.723125	+	0.690717i	$0.242705\pi$
$770$	−2.00000	+	3.46410i	−0.0720750	+	0.124838i
$771$		0			0
$772$	−8.12311			−0.292357
$773$	−14.3693	−	24.8884i	−0.516828	−	0.895173i	−0.999809	−	0.0195420i	$-0.993779\pi$
$773$	−14.3693	−	24.8884i	−0.516828	−	0.895173i	0.482981	−	0.875631i	$-0.339554\pi$
$774$		0			0
$775$		0			0
$776$	−4.56155	−	7.90084i	−0.163750	−	0.283624i
$777$		0			0
$778$	8.84233	−	15.3154i	0.317013	−	0.549082i
$779$	−8.19224			−0.293517
$780$		0			0
$781$	20.8769			0.747034
$782$	−28.9309	+	50.1097i	−1.03457	+	1.79192i
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	−35.0540			−1.25113
$786$		0			0
$787$	−22.5885	−	39.1245i	−0.805195	−	1.39464i	−0.916160	−	0.400814i	$-0.868728\pi$
$787$	−22.5885	−	39.1245i	−0.805195	−	1.39464i	0.110965	−	0.993824i	$-0.464606\pi$
$788$	−8.43845			−0.300607
$789$		0			0
$790$	−3.12311	+	5.40938i	−0.111115	+	0.192457i
$791$	−1.28078	+	2.21837i	−0.0455392	+	0.0788762i
$792$		0			0
$793$	17.5346	−	7.09468i	0.622671	−	0.251940i
$794$	0.930870			0.0330353
$795$		0			0
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	8.75379	+	15.1620i	0.310075	+	0.537066i	0.978378	−	0.206823i	$-0.0663125\pi$
$797$	8.75379	+	15.1620i	0.310075	+	0.537066i	−0.668303	+	0.743889i	$0.732979\pi$
$798$		0			0
$799$	−51.5194	−	89.2342i	−1.82263	−	3.15688i
$800$	0.780776	+	1.35234i	0.0276046	+	0.0478126i
$801$		0			0
$802$	−9.40388	−	16.2880i	−0.332063	−	0.575149i
$803$	−5.12311	+	8.87348i	−0.180790	+	0.313138i
$804$		0			0
$805$	−18.2462			−0.643094
$806$		0			0
$807$		0			0
$808$	−7.40388	+	12.8239i	−0.260468	+	0.451143i
$809$	−9.96543	+	17.2606i	−0.350366	+	0.606852i	−0.986314	−	0.164881i	$-0.947276\pi$
$809$	−9.96543	+	17.2606i	−0.350366	+	0.606852i	0.635948	+	0.771732i	$0.280609\pi$
$810$		0			0
$811$	24.0000			0.842754			0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000			0.842754			0.421377	+	0.906886i	$0.361547\pi$
$812$	1.06155	+	1.83866i	0.0372532	+	0.0645244i
$813$		0			0
$814$	−10.2462			−0.359130
$815$	10.8769	+	18.8393i	0.381001	+	0.659913i
$816$		0			0
$817$	6.24621	−	10.8188i	0.218527	−	0.378500i
$818$	7.43845			0.260079
$819$		0			0
$820$	−13.4384			−0.469291
$821$	−13.1501	+	22.7766i	−0.458941	+	0.794910i	−0.998905	−	0.0467783i	$-0.985105\pi$
$821$	−13.1501	+	22.7766i	−0.458941	+	0.794910i	0.539964	+	0.841688i	$0.318438\pi$
$822$		0			0
$823$	10.8769	+	18.8393i	0.379145	+	0.656698i	0.990938	−	0.134320i	$-0.0428849\pi$
$823$	10.8769	+	18.8393i	0.379145	+	0.656698i	−0.611793	+	0.791018i	$0.709552\pi$
$824$	10.2462			0.356944
$825$		0			0
$826$	1.56155	+	2.70469i	0.0543334	+	0.0941082i
$827$	−17.7538			−0.617360			−0.308680	−	0.951166i	$-0.599887\pi$
$827$	−17.7538			−0.617360			−0.308680	+	0.951166i	$0.599887\pi$
$828$		0			0
$829$	−12.1847	+	21.1044i	−0.423191	+	0.732988i	−0.996250	−	0.0865264i	$-0.972423\pi$
$829$	−12.1847	+	21.1044i	−0.423191	+	0.732988i	0.573059	+	0.819514i	$0.305757\pi$
$830$	−4.00000	+	6.92820i	−0.138842	+	0.240481i
$831$		0			0
$832$	−0.500000	+	3.57071i	−0.0173344	+	0.123792i
$833$	8.12311			0.281449
$834$		0			0
$835$	−26.2462	+	45.4598i	−0.908288	+	1.57320i
$836$	1.21922	+	2.11176i	0.0421677	+	0.0730367i
$837$		0			0
$838$	0.684658	+	1.18586i	0.0236511	+	0.0409650i
$839$	0.876894	+	1.51883i	0.0302738	+	0.0524357i	0.880765	−	0.473553i	$-0.157029\pi$
$839$	0.876894	+	1.51883i	0.0302738	+	0.0524357i	−0.850492	+	0.525989i	$0.823695\pi$
$840$		0			0
$841$	12.2462	+	21.2111i	0.422283	+	0.731416i
$842$	15.6501	−	27.1068i	0.539338	−	0.934161i
$843$		0			0
$844$	−3.12311			−0.107502
$845$	−32.0194	−	9.14657i	−1.10150	−	0.314652i
$846$		0			0
$847$	4.28078	−	7.41452i	0.147089	−	0.254766i
$848$	3.50000	−	6.06218i	0.120190	−	0.208176i
$849$		0			0
$850$	−12.6847			−0.435080
$851$	−23.3693	−	40.4768i	−0.801090	−	1.38753i
$852$		0			0
$853$	5.63068			0.192791			0.0963955	−	0.995343i	$-0.469269\pi$
$853$	5.63068			0.192791			0.0963955	+	0.995343i	$0.469269\pi$
$854$	2.62311	+	4.54335i	0.0897608	+	0.155470i
$855$		0			0
$856$	7.46543	−	12.9305i	0.255163	−	0.441956i
$857$	−20.5616			−0.702369			−0.351185	−	0.936306i	$-0.614221\pi$
$857$	−20.5616			−0.702369			−0.351185	+	0.936306i	$0.614221\pi$
$858$		0			0
$859$	−10.9309			−0.372956			−0.186478	−	0.982459i	$-0.559707\pi$
$859$	−10.9309			−0.372956			−0.186478	+	0.982459i	$0.559707\pi$
$860$	10.2462	−	17.7470i	0.349393	−	0.605166i
$861$		0			0
$862$	2.68466	+	4.64996i	0.0914398	+	0.158378i
$863$	−32.8769			−1.11914			−0.559571	−	0.828782i	$-0.689034\pi$
$863$	−32.8769			−1.11914			−0.559571	+	0.828782i	$0.689034\pi$
$864$		0			0
$865$	−23.0540	−	39.9307i	−0.783859	−	1.35768i
$866$	33.6847			1.14465
$867$		0			0
$868$		0			0
$869$	−1.90388	+	3.29762i	−0.0645848	+	0.111864i
$870$		0			0
$871$	−2.49242	−	1.94528i	−0.0844525	−	0.0659132i
$872$	−4.24621			−0.143795
$873$		0			0
$874$	−5.56155	+	9.63289i	−0.188122	+	0.325837i
$875$	4.40388	+	7.62775i	0.148878	+	0.257865i
$876$		0			0
$877$	−20.7732	−	35.9802i	−0.701461	−	1.21497i	−0.967954	−	0.251129i	$-0.919198\pi$
$877$	−20.7732	−	35.9802i	−0.701461	−	1.21497i	0.266492	−	0.963837i	$-0.414135\pi$
$878$	−4.87689	−	8.44703i	−0.164587	−	0.285073i
$879$		0			0
$880$	2.00000	+	3.46410i	0.0674200	+	0.116775i
$881$	28.5270	−	49.4102i	0.961099	−	1.66467i	0.241348	−	0.970439i	$-0.422410\pi$
$881$	28.5270	−	49.4102i	0.961099	−	1.66467i	0.719750	−	0.694233i	$-0.244256\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$	−23.0885	−	18.0201i	−0.776552	−	0.606080i
$885$		0			0
$886$	−5.02699	+	8.70700i	−0.168885	+	0.292517i
$887$	−23.0270	+	39.8839i	−0.773171	+	1.33917i	0.162646	+	0.986684i	$0.447997\pi$
$887$	−23.0270	+	39.8839i	−0.773171	+	1.33917i	−0.935817	+	0.352486i	$0.885336\pi$
$888$		0			0
$889$	−20.4924			−0.687294
$890$	−9.68466	−	16.7743i	−0.324630	−	0.562276i
$891$		0			0
$892$	26.2462			0.878788
$893$	−9.90388	−	17.1540i	−0.331421	−	0.574038i
$894$		0			0
$895$	−23.3693	+	40.4768i	−0.781150	+	1.35299i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−31.3693			−1.04681
$899$		0			0
$900$		0			0
$901$	28.4309	+	49.2437i	0.947170	+	1.64055i
$902$	−8.19224			−0.272772
$903$		0			0
$904$	1.28078	+	2.21837i	0.0425980	+	0.0737819i
$905$	−8.31534			−0.276411
$906$		0			0
$907$	−3.56155	+	6.16879i	−0.118259	+	0.204831i	−0.919078	−	0.394076i	$-0.871065\pi$
$907$	−3.56155	+	6.16879i	−0.118259	+	0.204831i	0.800819	+	0.598907i	$0.204398\pi$
$908$	−9.56155	+	16.5611i	−0.317311	+	0.549599i
$909$		0			0
$910$	1.28078	−	9.14657i	0.0424573	−	0.303206i
$911$	27.6155			0.914943			0.457472	−	0.889224i	$-0.348755\pi$
$911$	27.6155			0.914943			0.457472	+	0.889224i	$0.348755\pi$
$912$		0			0
$913$	−2.43845	+	4.22351i	−0.0807008	+	0.139778i
$914$	0.0345652	+	0.0598686i	0.00114331	+	0.00198028i
$915$		0			0
$916$	10.0270	+	17.3673i	0.331301	+	0.573830i
$917$	−1.12311	−	1.94528i	−0.0370882	−	0.0642387i
$918$		0			0
$919$	8.53457	+	14.7823i	0.281529	+	0.487623i	0.971762	−	0.235965i	$-0.0758250\pi$
$919$	8.53457	+	14.7823i	0.281529	+	0.487623i	−0.690232	+	0.723588i	$0.742492\pi$
$920$	−9.12311	+	15.8017i	−0.300780	+	0.520966i
$921$		0			0
$922$	−31.0540			−1.02271
$923$	−44.6847	+	18.0799i	−1.47081	+	0.595108i
$924$		0			0
$925$	5.12311	−	8.87348i	0.168447	−	0.291758i
$926$	12.3423	−	21.3775i	0.405594	−	0.702510i
$927$		0			0
$928$	2.12311			0.0696944
$929$	−9.62311	−	16.6677i	−0.315724	−	0.546850i	0.663867	−	0.747850i	$-0.268914\pi$
$929$	−9.62311	−	16.6677i	−0.315724	−	0.546850i	−0.979591	+	0.201001i	$0.935581\pi$
$930$		0			0
$931$	1.56155			0.0511778
$932$	−11.6847	−	20.2384i	−0.382744	−	0.662932i
$933$		0			0
$934$	−14.4924	+	25.1016i	−0.474207	+	0.821350i
$935$	−32.4924			−1.06262
$936$		0			0
$937$	−38.5616			−1.25975			−0.629876	−	0.776696i	$-0.716894\pi$
$937$	−38.5616			−1.25975			−0.629876	+	0.776696i	$0.716894\pi$
$938$	0.438447	−	0.759413i	0.0143158	−	0.0247957i
$939$		0			0
$940$	−16.2462	−	28.1393i	−0.529893	−	0.917802i
$941$	35.3693			1.15301			0.576503	−	0.817095i	$-0.304417\pi$
$941$	35.3693			1.15301			0.576503	+	0.817095i	$0.304417\pi$
$942$		0			0
$943$	−18.6847	−	32.3628i	−0.608456	−	1.05388i
$944$	3.12311			0.101648
$945$		0			0
$946$	6.24621	−	10.8188i	0.203082	−	0.351748i
$947$	27.2192	−	47.1451i	0.884506	−	1.53201i	0.0382270	−	0.999269i	$-0.487829\pi$
$947$	27.2192	−	47.1451i	0.884506	−	1.53201i	0.846279	−	0.532740i	$-0.178838\pi$
$948$		0			0
$949$	3.28078	−	23.4294i	0.106499	−	0.760551i
$950$	−2.43845			−0.0791137
$951$		0			0
$952$	4.06155	−	7.03482i	0.131636	−	0.228000i
$953$	10.5616	+	18.2931i	0.342122	+	0.592573i	0.984827	−	0.173541i	$-0.0555210\pi$
$953$	10.5616	+	18.2931i	0.342122	+	0.592573i	−0.642704	+	0.766114i	$0.722188\pi$
$954$		0			0
$955$	4.00000	+	6.92820i	0.129437	+	0.224191i
$956$	−2.68466	−	4.64996i	−0.0868281	−	0.150391i
$957$		0			0
$958$	−13.4654	−	23.3228i	−0.435048	−	0.753526i
$959$	8.28078	−	14.3427i	0.267400	−	0.463151i
$960$		0			0
$961$	−31.0000			−1.00000
$962$	21.9309	−	8.87348i	0.707080	−	0.286092i
$963$		0			0
$964$	10.4039	−	18.0201i	0.335086	−	0.580387i
$965$	10.4039	−	18.0201i	0.334913	−	0.580086i
$966$		0			0
$967$	4.49242			0.144467			0.0722333	−	0.997388i	$-0.476987\pi$
$967$	4.49242			0.144467			0.0722333	+	0.997388i	$0.476987\pi$
$968$	−4.28078	−	7.41452i	−0.137589	−	0.238312i
$969$		0			0
$970$	23.3693			0.750344
$971$	0.192236	+	0.332962i	0.00616914	+	0.0106853i	0.869093	−	0.494648i	$-0.164703\pi$
$971$	0.192236	+	0.332962i	0.00616914	+	0.0106853i	−0.862924	+	0.505333i	$0.831370\pi$
$972$		0			0
$973$	4.78078	−	8.28055i	0.153265	−	0.265462i
$974$	−11.3153			−0.362567
$975$		0			0
$976$	5.24621			0.167927
$977$	2.08854	−	3.61746i	0.0668183	−	0.115733i	−0.830681	−	0.556749i	$-0.812049\pi$
$977$	2.08854	−	3.61746i	0.0668183	−	0.115733i	0.897499	+	0.441016i	$0.145382\pi$
$978$		0			0
$979$	−5.90388	−	10.2258i	−0.188689	−	0.326819i
$980$	2.56155			0.0818258
$981$		0			0
$982$	−8.24621	−	14.2829i	−0.263147	−	0.455784i
$983$	30.7386			0.980410			0.490205	−	0.871607i	$-0.336922\pi$
$983$	30.7386			0.980410			0.490205	+	0.871607i	$0.336922\pi$
$984$		0			0
$985$	10.8078	−	18.7196i	0.344364	−	0.596456i
$986$	−8.62311	+	14.9357i	−0.274616	+	0.475648i
$987$		0			0
$988$	−4.43845	−	3.46410i	−0.141206	−	0.110208i
$989$	56.9848			1.81201
$990$		0			0
$991$	−24.8348	+	43.0151i	−0.788902	+	1.36642i	0.137738	+	0.990469i	$0.456017\pi$
$991$	−24.8348	+	43.0151i	−0.788902	+	1.36642i	−0.926640	+	0.375949i	$0.877317\pi$
$992$		0			0
$993$		0			0
$994$	−6.68466	−	11.5782i	−0.212024	−	0.367237i
$995$	20.4924	+	35.4939i	0.649653	+	1.12523i
$996$		0			0
$997$	−11.9924	−	20.7715i	−0.379804	−	0.657840i	0.611230	−	0.791453i	$-0.290675\pi$
$997$	−11.9924	−	20.7715i	−0.379804	−	0.657840i	−0.991033	+	0.133614i	$0.957342\pi$
$998$	6.87689	−	11.9111i	0.217684	−	0.377040i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.r.y.1387.2		4
3.2	odd	2		546.2.l.l.295.1	yes	4
13.3	even	3	inner	1638.2.r.y.757.2		4
39.17	odd	6		7098.2.a.bi.1.2		2
39.29	odd	6		546.2.l.l.211.1	✓	4
39.35	odd	6		7098.2.a.bt.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.l.211.1	✓	4	39.29	odd	6
546.2.l.l.295.1	yes	4	3.2	odd	2
1638.2.r.y.757.2		4	13.3	even	3	inner
1638.2.r.y.1387.2		4	1.1	even	1	trivial
7098.2.a.bi.1.2		2	39.17	odd	6
7098.2.a.bt.1.1		2	39.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.56155 q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.56155 q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.28078 - 2.21837i) q^{10} +(0.780776 - 1.35234i) q^{11} +(-0.500000 + 3.57071i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.06155 - 7.03482i) q^{17} +(-0.780776 - 1.35234i) q^{19} +(-1.28078 - 2.21837i) q^{20} +(-0.780776 - 1.35234i) q^{22} +(3.56155 - 6.16879i) q^{23} +1.56155 q^{25} +(2.84233 + 2.21837i) q^{26} +(-0.500000 + 0.866025i) q^{28} +(1.06155 - 1.83866i) q^{29} +(0.500000 + 0.866025i) q^{32} -8.12311 q^{34} +(-1.28078 - 2.21837i) q^{35} +(3.28078 - 5.68247i) q^{37} -1.56155 q^{38} -2.56155 q^{40} +(2.62311 - 4.54335i) q^{41} +(4.00000 + 6.92820i) q^{43} -1.56155 q^{44} +(-3.56155 - 6.16879i) q^{46} +12.6847 q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.780776 - 1.35234i) q^{50} +(3.34233 - 1.35234i) q^{52} -7.00000 q^{53} +(2.00000 - 3.46410i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-1.06155 - 1.83866i) q^{58} +(-1.56155 - 2.70469i) q^{59} +(-2.62311 - 4.54335i) q^{61} +1.00000 q^{64} +(-1.28078 + 9.14657i) q^{65} +(-0.438447 + 0.759413i) q^{67} +(-4.06155 + 7.03482i) q^{68} -2.56155 q^{70} +(6.68466 + 11.5782i) q^{71} -6.56155 q^{73} +(-3.28078 - 5.68247i) q^{74} +(-0.780776 + 1.35234i) q^{76} -1.56155 q^{77} -2.43845 q^{79} +(-1.28078 + 2.21837i) q^{80} +(-2.62311 - 4.54335i) q^{82} -3.12311 q^{83} +(-10.4039 - 18.0201i) q^{85} +8.00000 q^{86} +(-0.780776 + 1.35234i) q^{88} +(3.78078 - 6.54850i) q^{89} +(3.34233 - 1.35234i) q^{91} -7.12311 q^{92} +(6.34233 - 10.9852i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(4.56155 + 7.90084i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} - 4 q^{8} + q^{10} - q^{11} - 2 q^{13} - 4 q^{14} - 2 q^{16} - 8 q^{17} + q^{19} - q^{20} + q^{22} + 6 q^{23} - 2 q^{25} - q^{26} - 2 q^{28} - 4 q^{29} + 2 q^{32} - 16 q^{34} - q^{35} + 9 q^{37} + 2 q^{38} - 2 q^{40} - 6 q^{41} + 16 q^{43} + 2 q^{44} - 6 q^{46} + 26 q^{47} - 2 q^{49} - q^{50} + q^{52} - 28 q^{53} + 8 q^{55} + 2 q^{56} + 4 q^{58} + 2 q^{59} + 6 q^{61} + 4 q^{64} - q^{65} - 10 q^{67} - 8 q^{68} - 2 q^{70} + 2 q^{71} - 18 q^{73} - 9 q^{74} + q^{76} + 2 q^{77} - 18 q^{79} - q^{80} + 6 q^{82} + 4 q^{83} - 21 q^{85} + 32 q^{86} + q^{88} + 11 q^{89} + q^{91} - 12 q^{92} + 13 q^{94} - 8 q^{95} + 10 q^{97} + 2 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 - 4 * q^8 + q^10 - q^11 - 2 * q^13 - 4 * q^14 - 2 * q^16 - 8 * q^17 + q^19 - q^20 + q^22 + 6 * q^23 - 2 * q^25 - q^26 - 2 * q^28 - 4 * q^29 + 2 * q^32 - 16 * q^34 - q^35 + 9 * q^37 + 2 * q^38 - 2 * q^40 - 6 * q^41 + 16 * q^43 + 2 * q^44 - 6 * q^46 + 26 * q^47 - 2 * q^49 - q^50 + q^52 - 28 * q^53 + 8 * q^55 + 2 * q^56 + 4 * q^58 + 2 * q^59 + 6 * q^61 + 4 * q^64 - q^65 - 10 * q^67 - 8 * q^68 - 2 * q^70 + 2 * q^71 - 18 * q^73 - 9 * q^74 + q^76 + 2 * q^77 - 18 * q^79 - q^80 + 6 * q^82 + 4 * q^83 - 21 * q^85 + 32 * q^86 + q^88 + 11 * q^89 + q^91 - 12 * q^92 + 13 * q^94 - 8 * q^95 + 10 * q^97 + 2 * q^98

Introduction

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