LMFDB - Embedded newform 585.2.bu.c.316.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(316,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bu (of order $6$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.3
Root			$-1.27597 + 0.609843i$ of defining polynomial
Character	$\chi$	$=$	585.316
Dual form			585.2.bu.c.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190254 + 0.109843i) q^{2} +(-0.975869 - 1.69025i) q^{4} -1.00000i q^{5} +(-0.287734 + 0.166123i) q^{7} -0.868145i q^{8} +O(q^{10})$	\(q+(0.190254 + 0.109843i) q^{2} +(-0.975869 - 1.69025i) q^{4} -1.00000i q^{5} +(-0.287734 + 0.166123i) q^{7} -0.868145i q^{8} +(0.109843 - 0.190254i) q^{10} +(-4.65213 - 2.68591i) q^{11} +(-3.55193 + 0.619491i) q^{13} -0.0729902 q^{14} +(-1.85638 + 3.21534i) q^{16} +(2.53215 + 4.38581i) q^{17} +(-1.96410 + 1.13397i) q^{19} +(-1.69025 + 0.975869i) q^{20} +(-0.590059 - 1.02201i) q^{22} +(1.41959 - 2.45880i) q^{23} -1.00000 q^{25} +(-0.743818 - 0.272296i) q^{26} +(0.561581 + 0.324229i) q^{28} +(-1.45174 + 2.51448i) q^{29} -5.46410i q^{31} +(-2.21004 + 1.27597i) q^{32} +1.11256i q^{34} +(0.166123 + 0.287734i) q^{35} +(-5.17191 - 2.98601i) q^{37} -0.498239 q^{38} -0.868145 q^{40} +(-3.23205 - 1.86603i) q^{41} +(-2.53215 - 4.38581i) q^{43} +10.4844i q^{44} +(0.540166 - 0.311865i) q^{46} -8.34285i q^{47} +(-3.44481 + 5.96658i) q^{49} +(-0.190254 - 0.109843i) q^{50} +(4.51332 + 5.39913i) q^{52} +1.56063 q^{53} +(-2.68591 + 4.65213i) q^{55} +(0.144219 + 0.249795i) q^{56} +(-0.552399 + 0.318928i) q^{58} +(-2.34461 + 1.35366i) q^{59} +(-7.05193 - 12.2143i) q^{61} +(0.600196 - 1.03957i) q^{62} +6.86488 q^{64} +(0.619491 + 3.55193i) q^{65} +(8.94799 + 5.16612i) q^{67} +(4.94209 - 8.55995i) q^{68} +0.0729902i q^{70} +(11.0828 - 6.39866i) q^{71} -9.68922i q^{73} +(-0.655986 - 1.13620i) q^{74} +(3.83341 + 2.21322i) q^{76} +1.78477 q^{77} +4.51851 q^{79} +(3.21534 + 1.85638i) q^{80} +(-0.409941 - 0.710039i) q^{82} -4.26371i q^{83} +(4.38581 - 2.53215i) q^{85} -1.11256i q^{86} +(-2.33176 + 4.03872i) q^{88} +(2.79366 + 1.61292i) q^{89} +(0.919100 - 0.768307i) q^{91} -5.54133 q^{92} +(0.916407 - 1.58726i) q^{94} +(1.13397 + 1.96410i) q^{95} +(2.17191 - 1.25396i) q^{97} +(-1.31078 + 0.756779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) $ 8 * q + 2 * q^4 - 6 * q^7	$ 8 q + 2 q^{4} - 6 q^{7} - 2 q^{10} - 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} - 12 q^{20} - 12 q^{22} + 10 q^{23} - 8 q^{25} - 10 q^{26} - 18 q^{28} + 8 q^{29} - 6 q^{32} - 10 q^{35} + 6 q^{37} + 16 q^{38} - 12 q^{40} - 12 q^{41} - 2 q^{43} - 42 q^{46} + 12 q^{49} - 6 q^{52} + 24 q^{53} - 12 q^{56} + 36 q^{58} + 12 q^{59} - 28 q^{61} - 4 q^{62} - 8 q^{64} + 8 q^{65} + 6 q^{67} + 14 q^{68} - 10 q^{74} + 54 q^{76} + 36 q^{77} - 16 q^{79} + 4 q^{82} + 18 q^{85} - 18 q^{88} - 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 16 q^{95} - 30 q^{97} - 72 q^{98}+O(q^{100}) $ 8 * q + 2 * q^4 - 6 * q^7 - 2 * q^10 - 4 * q^14 - 2 * q^16 + 2 * q^17 + 12 * q^19 - 12 * q^20 - 12 * q^22 + 10 * q^23 - 8 * q^25 - 10 * q^26 - 18 * q^28 + 8 * q^29 - 6 * q^32 - 10 * q^35 + 6 * q^37 + 16 * q^38 - 12 * q^40 - 12 * q^41 - 2 * q^43 - 42 * q^46 + 12 * q^49 - 6 * q^52 + 24 * q^53 - 12 * q^56 + 36 * q^58 + 12 * q^59 - 28 * q^61 - 4 * q^62 - 8 * q^64 + 8 * q^65 + 6 * q^67 + 14 * q^68 - 10 * q^74 + 54 * q^76 + 36 * q^77 - 16 * q^79 + 4 * q^82 + 18 * q^85 - 18 * q^88 - 24 * q^89 + 28 * q^91 - 44 * q^92 + 32 * q^94 + 16 * q^95 - 30 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.190254	+	0.109843i	0.134530	+	0.0776710i	0.565755	−	0.824574i	$-0.308585\pi$
$2$	0.190254	+	0.109843i	0.134530	+	0.0776710i	−0.431224	+	0.902245i	$0.641918\pi$
$3$		0			0
$3$		0			0
$4$	−0.975869	−	1.69025i	−0.487934	−	0.845127i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−0.287734	+	0.166123i	−0.108753	+	0.0627887i	−0.553390	−	0.832922i	$-0.686666\pi$
$7$	−0.287734	+	0.166123i	−0.108753	+	0.0627887i	0.444637	+	0.895711i	$0.353333\pi$
$8$		−	0.868145i		−	0.306936i
$9$		0			0
$10$	0.109843	−	0.190254i	0.0347355	−	0.0601637i
$11$	−4.65213	−	2.68591i	−1.40267	−	0.809832i	−0.408004	−	0.912980i	$-0.633775\pi$
$11$	−4.65213	−	2.68591i	−1.40267	−	0.809832i	−0.994666	+	0.103149i	$0.967108\pi$
$12$		0			0
$13$	−3.55193	+	0.619491i	−0.985129	+	0.171816i
$13$	−3.55193	+	0.619491i	−0.985129	+	0.171816i
$14$	−0.0729902			−0.0195074
$15$		0			0
$16$	−1.85638	+	3.21534i	−0.464094	+	0.803835i
$17$	2.53215	+	4.38581i	0.614136	+	1.06372i	0.990535	+	0.137258i	$0.0438288\pi$
$17$	2.53215	+	4.38581i	0.614136	+	1.06372i	−0.376399	+	0.926458i	$0.622838\pi$
$18$		0			0
$19$	−1.96410	+	1.13397i	−0.450596	+	0.260152i	−0.708082	−	0.706130i	$-0.750439\pi$
$19$	−1.96410	+	1.13397i	−0.450596	+	0.260152i	0.257486	+	0.966282i	$0.417106\pi$
$20$	−1.69025	+	0.975869i	−0.377952	+	0.218211i
$21$		0			0
$22$	−0.590059	−	1.02201i	−0.125801	−	0.217894i
$23$	1.41959	−	2.45880i	0.296005	−	0.512695i	−0.679213	−	0.733941i	$-0.737679\pi$
$23$	1.41959	−	2.45880i	0.296005	−	0.512695i	0.975218	+	0.221246i	$0.0710122\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−0.743818	−	0.272296i	−0.145875	−	0.0534016i
$27$		0			0
$28$	0.561581	+	0.324229i	0.106129	+	0.0612735i
$29$	−1.45174	+	2.51448i	−0.269581	+	0.466928i	−0.968754	−	0.248025i	$-0.920219\pi$
$29$	−1.45174	+	2.51448i	−0.269581	+	0.466928i	0.699173	+	0.714953i	$0.253552\pi$
$30$		0			0
$31$		−	5.46410i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$		−	5.46410i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$	−2.21004	+	1.27597i	−0.390683	+	0.225561i
$33$		0			0
$34$			1.11256i			0.190802i
$35$	0.166123	+	0.287734i	0.0280800	+	0.0486359i
$36$		0			0
$37$	−5.17191	−	2.98601i	−0.850257	−	0.490896i	0.0104803	−	0.999945i	$-0.496664\pi$
$37$	−5.17191	−	2.98601i	−0.850257	−	0.490896i	−0.860738	+	0.509049i	$0.829997\pi$
$38$	−0.498239			−0.0808250
$39$		0			0
$40$	−0.868145			−0.137266
$41$	−3.23205	−	1.86603i	−0.504762	−	0.291424i	0.225916	−	0.974147i	$-0.427462\pi$
$41$	−3.23205	−	1.86603i	−0.504762	−	0.291424i	−0.730678	+	0.682723i	$0.760796\pi$
$42$		0			0
$43$	−2.53215	−	4.38581i	−0.386149	−	0.668830i	0.605779	−	0.795633i	$-0.292862\pi$
$43$	−2.53215	−	4.38581i	−0.386149	−	0.668830i	−0.991928	+	0.126803i	$0.959528\pi$
$44$			10.4844i			1.58058i
$45$		0			0
$46$	0.540166	−	0.311865i	0.0796432	−	0.0459820i
$47$		−	8.34285i		−	1.21693i	−0.793581	−	0.608465i	$-0.791786\pi$
$47$		−	8.34285i		−	1.21693i	0.793581	−	0.608465i	$-0.208214\pi$
$48$		0			0
$49$	−3.44481	+	5.96658i	−0.492115	+	0.852368i
$50$	−0.190254	−	0.109843i	−0.0269060	−	0.0155342i
$51$		0			0
$52$	4.51332	+	5.39913i	0.625885	+	0.748724i
$53$	1.56063			0.214369			0.107184	−	0.994239i	$-0.465817\pi$
$53$	1.56063			0.214369			0.107184	+	0.994239i	$0.465817\pi$
$54$		0			0
$55$	−2.68591	+	4.65213i	−0.362168	+	0.627293i
$56$	0.144219	+	0.249795i	0.0192721	+	0.0333802i
$57$		0			0
$58$	−0.552399	+	0.318928i	−0.0725335	+	0.0418773i
$59$	−2.34461	+	1.35366i	−0.305242	+	0.176232i	−0.644795	−	0.764355i	$-0.723057\pi$
$59$	−2.34461	+	1.35366i	−0.305242	+	0.176232i	0.339553	+	0.940587i	$0.389724\pi$
$60$		0			0
$61$	−7.05193	−	12.2143i	−0.902908	−	1.56388i	−0.823702	−	0.567023i	$-0.808095\pi$
$61$	−7.05193	−	12.2143i	−0.902908	−	1.56388i	−0.0792059	−	0.996858i	$-0.525238\pi$
$62$	0.600196	−	1.03957i	0.0762249	−	0.132025i
$63$		0			0
$64$	6.86488			0.858111
$65$	0.619491	+	3.55193i	0.0768384	+	0.440563i
$66$		0			0
$67$	8.94799	+	5.16612i	1.09317	+	0.631142i	0.934419	−	0.356176i	$-0.115920\pi$
$67$	8.94799	+	5.16612i	1.09317	+	0.631142i	0.158752	+	0.987319i	$0.449253\pi$
$68$	4.94209	−	8.55995i	0.599316	−	1.03805i
$69$		0			0
$70$			0.0729902i			0.00872400i
$71$	11.0828	−	6.39866i	1.31529	−	0.759382i	0.332321	−	0.943166i	$-0.392168\pi$
$71$	11.0828	−	6.39866i	1.31529	−	0.759382i	0.982967	+	0.183785i	$0.0588349\pi$
$72$		0			0
$73$		−	9.68922i		−	1.13404i	−0.823705	−	0.567019i	$-0.808097\pi$
$73$		−	9.68922i		−	1.13404i	0.823705	−	0.567019i	$-0.191903\pi$
$74$	−0.655986	−	1.13620i	−0.0762569	−	0.132081i
$75$		0			0
$76$	3.83341	+	2.21322i	0.439722	+	0.253874i
$77$	1.78477			0.203393
$78$		0			0
$79$	4.51851			0.508372			0.254186	−	0.967155i	$-0.418192\pi$
$79$	4.51851			0.508372			0.254186	+	0.967155i	$0.418192\pi$
$80$	3.21534	+	1.85638i	0.359486	+	0.207549i
$81$		0			0
$82$	−0.409941	−	0.710039i	−0.0452704	−	0.0784107i
$83$		−	4.26371i		−	0.468003i	−0.972236	−	0.234001i	$-0.924818\pi$
$83$		−	4.26371i		−	0.468003i	0.972236	−	0.234001i	$-0.0751821\pi$
$84$		0			0
$85$	4.38581	−	2.53215i	0.475708	−	0.274650i
$86$		−	1.11256i		−	0.119970i
$87$		0			0
$88$	−2.33176	+	4.03872i	−0.248566	+	0.430529i
$89$	2.79366	+	1.61292i	0.296127	+	0.170969i	0.640702	−	0.767790i	$-0.278644\pi$
$89$	2.79366	+	1.61292i	0.296127	+	0.170969i	−0.344575	+	0.938759i	$0.611977\pi$
$90$		0			0
$91$	0.919100	−	0.768307i	0.0963478	−	0.0805405i
$92$	−5.54133			−0.577724
$93$		0			0
$94$	0.916407	−	1.58726i	0.0945202	−	0.163714i
$95$	1.13397	+	1.96410i	0.116343	+	0.201513i
$96$		0			0
$97$	2.17191	−	1.25396i	0.220524	−	0.127320i	−0.385669	−	0.922637i	$-0.626029\pi$
$97$	2.17191	−	1.25396i	0.220524	−	0.127320i	0.606193	+	0.795318i	$0.292696\pi$
$98$	−1.31078	+	0.756779i	−0.132409	+	0.0764462i
$99$		0			0
$100$	0.975869	+	1.69025i	0.0975869	+	0.169025i
$101$	−6.22336	+	10.7792i	−0.619247	+	1.07257i	0.370376	+	0.928882i	$0.379229\pi$
$101$	−6.22336	+	10.7792i	−0.619247	+	1.07257i	−0.989623	+	0.143686i	$0.954105\pi$
$102$		0			0
$103$	15.0247			1.48043			0.740215	−	0.672370i	$-0.234724\pi$
$103$	15.0247			1.48043			0.740215	+	0.672370i	$0.234724\pi$
$104$	0.537808	+	3.08359i	0.0527364	+	0.302371i
$105$		0			0
$106$	0.296916	+	0.171425i	0.0288390	+	0.0166502i
$107$	−6.53215	+	11.3140i	−0.631487	+	1.09377i	0.355761	+	0.934577i	$0.384222\pi$
$107$	−6.53215	+	11.3140i	−0.631487	+	1.09377i	−0.987248	+	0.159190i	$0.949112\pi$
$108$		0			0
$109$			11.2325i			1.07587i	0.842985	+	0.537937i	$0.180796\pi$
$109$			11.2325i			1.07587i	−0.842985	+	0.537937i	$0.819204\pi$
$110$	−1.02201	+	0.590059i	−0.0974450	+	0.0562599i
$111$		0			0
$112$		−	1.23355i		−	0.116560i
$113$	−9.17191	−	15.8862i	−0.862821	−	1.49445i	−0.869195	−	0.494470i	$-0.835362\pi$
$113$	−9.17191	−	15.8862i	−0.862821	−	1.49445i	0.00637349	−	0.999980i	$-0.497971\pi$
$114$		0			0
$115$	−2.45880	−	1.41959i	−0.229284	−	0.132377i
$116$	5.66682			0.526151
$117$		0			0
$118$	−0.594763			−0.0547524
$119$	−1.45717	−	0.841298i	−0.133579	−	0.0771216i
$120$		0			0
$121$	8.92820	+	15.4641i	0.811655	+	1.40583i
$122$		−	3.09843i		−	0.280519i
$123$		0			0
$124$	−9.23572	+	5.33225i	−0.829392	+	0.478850i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	1.61998	−	2.80589i	0.143750	−	0.248982i	−0.785156	−	0.619298i	$-0.787417\pi$
$127$	1.61998	−	2.80589i	0.143750	−	0.248982i	0.928906	+	0.370316i	$0.120751\pi$
$128$	5.72615	+	3.30600i	0.506125	+	0.292212i
$129$		0			0
$130$	−0.272296	+	0.743818i	−0.0238819	+	0.0652372i
$131$	−0.175664			−0.0153478			−0.00767390	−	0.999971i	$-0.502443\pi$
$131$	−0.175664			−0.0153478			−0.00767390	+	0.999971i	$0.502443\pi$
$132$		0			0
$133$	0.376759	−	0.652566i	0.0326692	−	0.0565846i
$134$	1.13493	+	1.96576i	0.0980430	+	0.169815i
$135$		0			0
$136$	3.80752	−	2.19827i	0.326492	−	0.188500i
$137$	15.5736	−	8.99144i	1.33054	−	0.768190i	0.345162	−	0.938543i	$-0.387824\pi$
$137$	15.5736	−	8.99144i	1.33054	−	0.768190i	0.985383	+	0.170353i	$0.0544907\pi$
$138$		0			0
$139$	−5.99307	−	10.3803i	−0.508325	−	0.880445i	−0.999954	−	0.00964021i	$-0.996931\pi$
$139$	−5.99307	−	10.3803i	−0.508325	−	0.880445i	0.491628	−	0.870805i	$-0.336402\pi$
$140$	0.324229	−	0.561581i	0.0274024	−	0.0474623i
$141$		0			0
$142$	2.81140			0.235928
$143$	18.1879	+	6.65821i	1.52095	+	0.556788i
$144$		0			0
$145$	2.51448	+	1.45174i	0.208816	+	0.120560i
$146$	1.06430	−	1.84342i	0.0880819	−	0.152562i
$147$		0			0
$148$			11.6558i			0.958101i
$149$	−2.95350	+	1.70520i	−0.241960	+	0.139696i	−0.616077	−	0.787686i	$-0.711279\pi$
$149$	−2.95350	+	1.70520i	−0.241960	+	0.139696i	0.374117	+	0.927381i	$0.377946\pi$
$150$		0			0
$151$			7.96141i			0.647890i	0.946076	+	0.323945i	$0.105009\pi$
$151$			7.96141i			0.647890i	−0.946076	+	0.323945i	$0.894991\pi$
$152$	0.984454	+	1.70512i	0.0798498	+	0.138304i
$153$		0			0
$154$	0.339560	+	0.196045i	0.0273625	+	0.0157978i
$155$	−5.46410			−0.438887
$156$		0			0
$157$	−16.4329			−1.31148			−0.655742	−	0.754985i	$-0.727644\pi$
$157$	−16.4329			−1.31148			−0.655742	+	0.754985i	$0.727644\pi$
$158$	0.859667	+	0.496329i	0.0683914	+	0.0394858i
$159$		0			0
$160$	1.27597	+	2.21004i	0.100874	+	0.174719i
$161$			0.943307i			0.0743430i
$162$		0			0
$163$	15.4215	−	8.90361i	1.20791	−	0.697384i	0.245604	−	0.969370i	$-0.421014\pi$
$163$	15.4215	−	8.90361i	1.20791	−	0.697384i	0.962301	+	0.271986i	$0.0876804\pi$
$164$			7.28398i			0.568784i
$165$		0			0
$166$	0.468341	−	0.811190i	0.0363503	−	0.0629605i
$167$	−5.45047	−	3.14683i	−0.421770	−	0.243509i	0.274064	−	0.961711i	$-0.411632\pi$
$167$	−5.45047	−	3.14683i	−0.421770	−	0.243509i	−0.695834	+	0.718202i	$0.744965\pi$
$168$		0			0
$169$	12.2325	−	4.40078i	0.940959	−	0.338522i
$170$	1.11256			0.0853294
$171$		0			0
$172$	−4.94209	+	8.55995i	−0.376831	+	0.652690i
$173$	−7.98756	−	13.8349i	−0.607283	−	1.05184i	−0.991686	−	0.128679i	$-0.958926\pi$
$173$	−7.98756	−	13.8349i	−0.607283	−	1.05184i	0.384404	−	0.923165i	$-0.374407\pi$
$174$		0			0
$175$	0.287734	−	0.166123i	0.0217506	−	0.0125577i
$176$	17.2722	−	9.97212i	1.30194	−	0.751677i
$177$		0			0
$178$	0.354337	+	0.613729i	0.0265587	+	0.0460010i
$179$	−11.8087	+	20.4533i	−0.882625	+	1.52875i	−0.0342123	+	0.999415i	$0.510892\pi$
$179$	−11.8087	+	20.4533i	−0.882625	+	1.52875i	−0.848412	+	0.529336i	$0.822441\pi$
$180$		0			0
$181$	2.62590			0.195182			0.0975909	−	0.995227i	$-0.468886\pi$
$181$	2.62590			0.195182			0.0975909	+	0.995227i	$0.468886\pi$
$182$	0.259256	−	0.0452168i	0.0192174	−	0.00335169i
$183$		0			0
$184$	−2.13459	−	1.23241i	−0.157364	−	0.0908544i
$185$	−2.98601	+	5.17191i	−0.219536	+	0.380247i
$186$		0			0
$187$		−	27.2045i		−	1.98939i
$188$	−14.1015	+	8.14153i	−1.02846	+	0.593782i
$189$		0			0
$190$			0.498239i			0.0361460i
$191$	−1.00791	−	1.74575i	−0.0729298	−	0.126318i	0.827254	−	0.561828i	$-0.189902\pi$
$191$	−1.00791	−	1.74575i	−0.0729298	−	0.126318i	−0.900184	+	0.435509i	$0.856568\pi$
$192$		0			0
$193$	−19.7636	−	11.4105i	−1.42262	−	0.821348i	−0.426095	−	0.904678i	$-0.640111\pi$
$193$	−19.7636	−	11.4105i	−1.42262	−	0.821348i	−0.996522	+	0.0833298i	$0.973445\pi$
$194$	0.550955			0.0395563
$195$		0			0
$196$	13.4467			0.960480
$197$	0.556877	+	0.321513i	0.0396758	+	0.0229068i	0.519707	−	0.854345i	$-0.326041\pi$
$197$	0.556877	+	0.321513i	0.0396758	+	0.0229068i	−0.480031	+	0.877252i	$0.659375\pi$
$198$		0			0
$199$	1.53342	+	2.65596i	0.108701	+	0.188276i	0.915244	−	0.402899i	$-0.131997\pi$
$199$	1.53342	+	2.65596i	0.108701	+	0.188276i	−0.806543	+	0.591175i	$0.798664\pi$
$200$			0.868145i			0.0613871i
$201$		0			0
$202$	−2.36804	+	1.36719i	−0.166615	+	0.0961952i
$203$		−	0.964670i		−	0.0677065i
$204$		0			0
$205$	−1.86603	+	3.23205i	−0.130329	+	0.225736i
$206$	2.85852	+	1.65037i	0.199163	+	0.114987i
$207$		0			0
$208$	4.60185	−	12.5707i	0.319081	−	0.871620i
$209$	12.1830			0.842716
$210$		0			0
$211$	4.10020	−	7.10175i	0.282269	−	0.488904i	−0.689674	−	0.724120i	$-0.742246\pi$
$211$	4.10020	−	7.10175i	0.282269	−	0.488904i	0.971943	+	0.235215i	$0.0755796\pi$
$212$	−1.52297	−	2.63786i	−0.104598	−	0.181169i
$213$		0			0
$214$	−2.48554	+	1.43503i	−0.169908	+	0.0980964i
$215$	−4.38581	+	2.53215i	−0.299110	+	0.172691i
$216$		0			0
$217$	0.907714	+	1.57221i	0.0616197	+	0.106728i
$218$	−1.23381	+	2.13703i	−0.0835643	+	0.144738i
$219$		0			0
$220$	10.4844			0.706856
$221$	−11.7110	−	14.0095i	−0.787767	−	0.942378i
$222$		0			0
$223$	8.87174	+	5.12210i	0.594095	+	0.343001i	0.766715	−	0.641987i	$-0.221890\pi$
$223$	8.87174	+	5.12210i	0.594095	+	0.343001i	−0.172620	+	0.984989i	$0.555223\pi$
$224$	0.423935	−	0.734278i	0.0283254	−	0.0490610i
$225$		0			0
$226$		−	4.02990i		−	0.268065i
$227$	6.10012	−	3.52190i	0.404879	−	0.233757i	−0.283708	−	0.958911i	$-0.591565\pi$
$227$	6.10012	−	3.52190i	0.404879	−	0.233757i	0.688587	+	0.725154i	$0.258231\pi$
$228$		0			0
$229$			1.32899i			0.0878219i	0.999035	+	0.0439109i	$0.0139818\pi$
$229$			1.32899i			0.0878219i	−0.999035	+	0.0439109i	$0.986018\pi$
$230$	−0.311865	−	0.540166i	−0.0205638	−	0.0356175i
$231$		0			0
$232$	2.18294	+	1.26032i	0.143317	+	0.0827440i
$233$	−1.24746			−0.0817238			−0.0408619	−	0.999165i	$-0.513010\pi$
$233$	−1.24746			−0.0817238			−0.0408619	+	0.999165i	$0.513010\pi$
$234$		0			0
$235$	−8.34285			−0.544227
$236$	4.57606	+	2.64199i	0.297876	+	0.171979i
$237$		0			0
$238$	−0.184822	−	0.320121i	−0.0119802	−	0.0207504i
$239$		−	9.94207i		−	0.643099i	−0.946893	−	0.321549i	$-0.895796\pi$
$239$		−	9.94207i		−	0.643099i	0.946893	−	0.321549i	$-0.104204\pi$
$240$		0			0
$241$	−19.5608	+	11.2934i	−1.26002	+	0.727475i	−0.973079	−	0.230472i	$-0.925973\pi$
$241$	−19.5608	+	11.2934i	−1.26002	+	0.727475i	−0.286944	+	0.957947i	$0.592640\pi$
$242$			3.92282i			0.252168i
$243$		0			0
$244$	−13.7635	+	23.8391i	−0.881119	+	1.52614i
$245$	5.96658	+	3.44481i	0.381191	+	0.220081i
$246$		0			0
$247$	6.27387	−	5.24455i	0.399197	−	0.333702i
$248$	−4.74363			−0.301221
$249$		0			0
$250$	−0.109843	+	0.190254i	−0.00694711	+	0.0120327i
$251$	3.38418	+	5.86157i	0.213608	+	0.369979i	0.952841	−	0.303470i	$-0.0981453\pi$
$251$	3.38418	+	5.86157i	0.213608	+	0.369979i	−0.739233	+	0.673449i	$0.764812\pi$
$252$		0			0
$253$	−13.2082	+	7.62577i	−0.830394	+	0.479428i
$254$	0.616417	−	0.355888i	0.0386774	−	0.0223304i
$255$		0			0
$256$	−6.13860	−	10.6324i	−0.383663	−	0.664523i
$257$	5.12691	−	8.88007i	0.319808	−	0.553924i	−0.660640	−	0.750703i	$-0.729715\pi$
$257$	5.12691	−	8.88007i	0.319808	−	0.553924i	0.980448	+	0.196779i	$0.0630483\pi$
$258$		0			0
$259$	1.98418			0.123291
$260$	5.39913	−	4.51332i	0.334840	−	0.279904i
$261$		0			0
$262$	−0.0334208	−	0.0192955i	−0.00206474	−	0.00119208i
$263$	9.32850	−	16.1574i	0.575220	−	0.996310i	−0.420798	−	0.907154i	$-0.638250\pi$
$263$	9.32850	−	16.1574i	0.575220	−	0.996310i	0.996018	−	0.0891555i	$-0.0284168\pi$
$264$		0			0
$265$		−	1.56063i		−	0.0958685i
$266$	0.143360	−	0.0827690i	0.00878998	−	0.00507489i
$267$		0			0
$268$		−	20.1658i		−	1.23182i
$269$	8.97894	+	15.5520i	0.547456	+	0.948221i	0.998448	+	0.0556934i	$0.0177369\pi$
$269$	8.97894	+	15.5520i	0.547456	+	0.948221i	−0.450992	+	0.892528i	$0.648930\pi$
$270$		0			0
$271$	−26.7582	−	15.4488i	−1.62544	−	0.938450i	−0.985429	−	0.170086i	$-0.945595\pi$
$271$	−26.7582	−	15.4488i	−1.62544	−	0.938450i	−0.640014	−	0.768363i	$-0.721071\pi$
$272$	−18.8025			−1.14007
$273$		0			0
$274$	3.95060			0.238665
$275$	4.65213	+	2.68591i	0.280534	+	0.161966i
$276$		0			0
$277$	13.2522	+	22.9536i	0.796250	+	1.37915i	0.922042	+	0.387089i	$0.126519\pi$
$277$	13.2522	+	22.9536i	0.796250	+	1.37915i	−0.125792	+	0.992057i	$0.540147\pi$
$278$		−	2.63320i		−	0.157929i
$279$		0			0
$280$	0.249795	−	0.144219i	0.0149281	−	0.00861874i
$281$		−	4.97766i		−	0.296942i	−0.988917	−	0.148471i	$-0.952565\pi$
$281$		−	4.97766i		−	0.296942i	0.988917	−	0.148471i	$-0.0474352\pi$
$282$		0			0
$283$	−6.29317	+	10.9001i	−0.374090	+	0.647943i	−0.990190	−	0.139725i	$-0.955378\pi$
$283$	−6.29317	+	10.9001i	−0.374090	+	0.647943i	0.616100	+	0.787668i	$0.288712\pi$
$284$	−21.6307	−	12.4885i	−1.28355	−	0.741057i
$285$		0			0
$286$	2.72898	+	3.26458i	0.161368	+	0.193039i
$287$	1.23996			0.0731926
$288$		0			0
$289$	−4.32355	+	7.48861i	−0.254327	+	0.440507i
$290$	0.318928	+	0.552399i	0.0187281	+	0.0324380i
$291$		0			0
$292$	−16.3772	+	9.45541i	−0.958406	+	0.553336i
$293$	−14.6511	+	8.45880i	−0.855925	+	0.494168i	−0.862645	−	0.505809i	$-0.831194\pi$
$293$	−14.6511	+	8.45880i	−0.855925	+	0.494168i	0.00672072	+	0.999977i	$0.497861\pi$
$294$		0			0
$295$	1.35366	+	2.34461i	0.0788132	+	0.136508i
$296$	−2.59229	+	4.48997i	−0.150674	+	0.260974i
$297$		0			0
$298$	−0.749222			−0.0434012
$299$	−3.51908	+	9.61292i	−0.203514	+	0.555929i
$300$		0			0
$301$	1.45717	+	0.841298i	0.0839899	+	0.0484916i
$302$	−0.874509	+	1.51469i	−0.0503223	+	0.0871608i
$303$		0			0
$304$		−	8.42034i		−	0.482940i
$305$	−12.2143	+	7.05193i	−0.699389	+	0.403793i
$306$		0			0
$307$		−	4.30426i		−	0.245657i	−0.992428	−	0.122828i	$-0.960803\pi$
$307$		−	4.30426i		−	0.245657i	0.992428	−	0.122828i	$-0.0391965\pi$
$308$	−1.74170	−	3.01671i	−0.0992425	−	0.171893i
$309$		0			0
$310$	−1.03957	−	0.600196i	−0.0590436	−	0.0340888i
$311$	−2.22512			−0.126175			−0.0630875	−	0.998008i	$-0.520095\pi$
$311$	−2.22512			−0.126175			−0.0630875	+	0.998008i	$0.520095\pi$
$312$		0			0
$313$	7.20887			0.407469			0.203735	−	0.979026i	$-0.434692\pi$
$313$	7.20887			0.407469			0.203735	+	0.979026i	$0.434692\pi$
$314$	−3.12642	−	1.80504i	−0.176434	−	0.101864i
$315$		0			0
$316$	−4.40948	−	7.63744i	−0.248052	−	0.429639i
$317$		−	0.321644i		−	0.0180653i	−0.999959	−	0.00903266i	$-0.997125\pi$
$317$		−	0.321644i		−	0.0180653i	0.999959	−	0.00903266i	$-0.00287522\pi$
$318$		0			0
$319$	13.5073	−	7.79847i	0.756266	−	0.436630i
$320$		−	6.86488i		−	0.383759i
$321$		0			0
$322$	−0.103616	+	0.179468i	−0.00577430	+	0.0100014i
$323$	−9.94679	−	5.74278i	−0.553454	−	0.319537i
$324$		0			0
$325$	3.55193	−	0.619491i	0.197026	−	0.0343632i
$326$	3.91201			0.216666
$327$		0			0
$328$	−1.61998	+	2.80589i	−0.0894485	+	0.154929i
$329$	1.38594	+	2.40052i	0.0764094	+	0.132345i
$330$		0			0
$331$	−14.4037	+	8.31600i	−0.791701	+	0.457089i	−0.840561	−	0.541717i	$-0.817775\pi$
$331$	−14.4037	+	8.31600i	−0.791701	+	0.457089i	0.0488600	+	0.998806i	$0.484441\pi$
$332$	−7.20676	+	4.16082i	−0.395522	+	0.228355i
$333$		0			0
$334$	−0.691317	−	1.19740i	−0.0378272	−	0.0655186i
$335$	5.16612	−	8.94799i	0.282255	−	0.488881i
$336$		0			0
$337$	−24.2186			−1.31927			−0.659636	−	0.751586i	$-0.729289\pi$
$337$	−24.2186			−1.31927			−0.659636	+	0.751586i	$0.729289\pi$
$338$	2.81068	+	0.506387i	0.152881	+	0.0275438i
$339$		0			0
$340$	−8.55995	−	4.94209i	−0.464229	−	0.268022i
$341$	−14.6761	+	25.4197i	−0.794754	+	1.37655i
$342$		0			0
$343$		−	4.61478i		−	0.249174i
$344$	−3.80752	+	2.19827i	−0.205288	+	0.118523i
$345$		0			0
$346$		−	3.50952i		−	0.188673i
$347$	−3.13680	−	5.43309i	−0.168392	−	0.291664i	0.769463	−	0.638692i	$-0.220524\pi$
$347$	−3.13680	−	5.43309i	−0.168392	−	0.291664i	−0.937855	+	0.347028i	$0.887191\pi$
$348$		0			0
$349$	−6.12275	−	3.53497i	−0.327743	−	0.189223i	0.327095	−	0.944991i	$-0.393930\pi$
$349$	−6.12275	−	3.53497i	−0.327743	−	0.189223i	−0.654839	+	0.755769i	$0.727263\pi$
$350$	0.0729902			0.00390149
$351$		0			0
$352$	13.7085			0.730666
$353$	18.8705	+	10.8949i	1.00438	+	0.579878i	0.909541	−	0.415615i	$-0.136434\pi$
$353$	18.8705	+	10.8949i	1.00438	+	0.579878i	0.0948371	+	0.995493i	$0.469767\pi$
$354$		0			0
$355$	−6.39866	−	11.0828i	−0.339606	−	0.588214i
$356$		−	6.29598i		−	0.333687i
$357$		0			0
$358$	−4.49332	+	2.59422i	−0.237479	+	0.137109i
$359$		−	23.9737i		−	1.26528i	−0.774444	−	0.632642i	$-0.781971\pi$
$359$		−	23.9737i		−	1.26528i	0.774444	−	0.632642i	$-0.218029\pi$
$360$		0			0
$361$	−6.92820	+	12.0000i	−0.364642	+	0.631579i
$362$	0.499589	+	0.288438i	0.0262578	+	0.0151600i
$363$		0			0
$364$	−2.19556	−	0.803745i	−0.115078	−	0.0421277i
$365$	−9.68922			−0.507157
$366$		0			0
$367$	−3.19566	+	5.53505i	−0.166812	+	0.288927i	−0.937297	−	0.348531i	$-0.886681\pi$
$367$	−3.19566	+	5.53505i	−0.166812	+	0.288927i	0.770485	+	0.637458i	$0.220014\pi$
$368$	5.27059	+	9.12892i	0.274748	+	0.475878i
$369$		0			0
$370$	−1.13620	+	0.655986i	−0.0590683	+	0.0341031i
$371$	−0.449045	+	0.259256i	−0.0233133	+	0.0134599i
$372$		0			0
$373$	10.0401	+	17.3899i	0.519855	+	0.900414i	0.999734	+	0.0230798i	$0.00734719\pi$
$373$	10.0401	+	17.3899i	0.519855	+	0.900414i	−0.479879	+	0.877335i	$0.659319\pi$
$374$	2.98823	−	5.17577i	0.154518	−	0.267633i
$375$		0			0
$376$	−7.24280			−0.373519
$377$	3.59878	−	9.83062i	0.185346	−	0.506302i
$378$		0			0
$379$	−4.73007	−	2.73091i	−0.242968	−	0.140277i	0.373572	−	0.927601i	$-0.378133\pi$
$379$	−4.73007	−	2.73091i	−0.242968	−	0.140277i	−0.616540	+	0.787324i	$0.711466\pi$
$380$	2.21322	−	3.83341i	0.113536	−	0.196650i
$381$		0			0
$382$		−	0.442849i		−	0.0226581i
$383$	−4.90842	+	2.83388i	−0.250808	+	0.144804i	−0.620134	−	0.784496i	$-0.712922\pi$
$383$	−4.90842	+	2.83388i	−0.250808	+	0.144804i	0.369326	+	0.929300i	$0.379589\pi$
$384$		0			0
$385$		−	1.78477i		−	0.0909602i
$386$	−2.50675	−	4.34181i	−0.127590	−	0.220992i
$387$		0			0
$388$	−4.23901	−	2.44739i	−0.215203	−	0.124247i
$389$	10.6174			0.538325			0.269162	−	0.963095i	$-0.413253\pi$
$389$	10.6174			0.538325			0.269162	+	0.963095i	$0.413253\pi$
$390$		0			0
$391$	14.3784			0.727149
$392$	5.17986	+	2.99059i	0.261622	+	0.151048i
$393$		0			0
$394$	0.0706321	+	0.122338i	0.00355840	+	0.00616332i
$395$		−	4.51851i		−	0.227351i
$396$		0			0
$397$	24.2780	−	14.0169i	1.21848	−	0.703487i	0.253884	−	0.967235i	$-0.418292\pi$
$397$	24.2780	−	14.0169i	1.21848	−	0.703487i	0.964592	+	0.263748i	$0.0849586\pi$
$398$			0.673745i			0.0337718i
$399$		0			0
$400$	1.85638	−	3.21534i	0.0928189	−	0.160767i
$401$	−19.4979	−	11.2571i	−0.973680	−	0.562155i	−0.0733241	−	0.997308i	$-0.523361\pi$
$401$	−19.4979	−	11.2571i	−0.973680	−	0.562155i	−0.900356	+	0.435154i	$0.856694\pi$
$402$		0			0
$403$	3.38496	+	19.4081i	0.168617	+	0.966788i
$404$	24.2927			1.20861
$405$		0			0
$406$	0.105963	−	0.183533i	0.00525884	−	0.00910857i
$407$	16.0403	+	27.7826i	0.795087	+	1.37713i
$408$		0			0
$409$	−3.71328	+	2.14386i	−0.183610	+	0.106007i	−0.588988	−	0.808142i	$-0.700473\pi$
$409$	−3.71328	+	2.14386i	−0.183610	+	0.106007i	0.405378	+	0.914149i	$0.367140\pi$
$410$	−0.710039	+	0.409941i	−0.0350663	+	0.0202456i
$411$		0			0
$412$	−14.6622	−	25.3956i	−0.722353	−	1.25115i
$413$	0.449749	−	0.778989i	0.0221307	−	0.0383315i
$414$		0			0
$415$	−4.26371			−0.209297
$416$	7.05946	−	5.90125i	0.346119	−	0.289333i
$417$		0			0
$418$	2.31787	+	1.33822i	0.113371	+	0.0654546i
$419$	8.85578	−	15.3387i	0.432633	−	0.749343i	−0.564466	−	0.825456i	$-0.690918\pi$
$419$	8.85578	−	15.3387i	0.432633	−	0.749343i	0.997099	+	0.0761137i	$0.0242512\pi$
$420$		0			0
$421$		−	12.8787i		−	0.627672i	−0.949477	−	0.313836i	$-0.898386\pi$
$421$		−	12.8787i		−	0.627672i	0.949477	−	0.313836i	$-0.101614\pi$
$422$	1.56016	−	0.900759i	0.0759474	−	0.0438483i
$423$		0			0
$424$		−	1.35485i		−	0.0657973i
$425$	−2.53215	−	4.38581i	−0.122827	−	0.212743i
$426$		0			0
$427$	4.05816	+	2.34298i	0.196388	+	0.113385i
$428$	25.4981			1.23250
$429$		0			0
$430$	−1.11256			−0.0536524
$431$	−8.22590	−	4.74923i	−0.396228	−	0.228762i	0.288627	−	0.957442i	$-0.406801\pi$
$431$	−8.22590	−	4.74923i	−0.396228	−	0.228762i	−0.684855	+	0.728679i	$0.740134\pi$
$432$		0			0
$433$	−0.698141	−	1.20922i	−0.0335505	−	0.0581112i	0.848763	−	0.528774i	$-0.177348\pi$
$433$	−0.698141	−	1.20922i	−0.0335505	−	0.0581112i	−0.882313	+	0.470663i	$0.844015\pi$
$434$			0.398826i			0.0191443i
$435$		0			0
$436$	18.9857	−	10.9614i	0.909251	−	0.524956i
$437$			6.43911i			0.308024i
$438$		0			0
$439$	2.08090	−	3.60422i	0.0993159	−	0.172020i	−0.812086	−	0.583538i	$-0.801668\pi$
$439$	2.08090	−	3.60422i	0.0993159	−	0.172020i	0.911402	+	0.411518i	$0.135001\pi$
$440$	4.03872	+	2.33176i	0.192539	+	0.111162i
$441$		0			0
$442$	−0.689221	−	3.95174i	−0.0327829	−	0.187965i
$443$	−9.54563			−0.453526			−0.226763	−	0.973950i	$-0.572814\pi$
$443$	−9.54563			−0.453526			−0.226763	+	0.973950i	$0.572814\pi$
$444$		0			0
$445$	1.61292	−	2.79366i	0.0764596	−	0.132432i
$446$	1.12526	+	1.94900i	0.0532825	+	0.0922880i
$447$		0			0
$448$	−1.97526	+	1.14042i	−0.0933223	+	0.0538796i
$449$	−18.8075	+	10.8585i	−0.887582	+	0.512446i	−0.873151	−	0.487450i	$-0.837927\pi$
$449$	−18.8075	+	10.8585i	−0.887582	+	0.512446i	−0.0144310	+	0.999896i	$0.504594\pi$
$450$		0			0
$451$	10.0239	+	17.3620i	0.472009	+	0.817544i
$452$	−17.9012	+	31.0057i	−0.842000	+	1.45839i
$453$		0			0
$454$	1.54743			0.0726246
$455$	−0.768307	−	0.919100i	−0.0360188	−	0.0430881i
$456$		0			0
$457$	4.08989	+	2.36130i	0.191317	+	0.110457i	0.592599	−	0.805498i	$-0.298102\pi$
$457$	4.08989	+	2.36130i	0.191317	+	0.110457i	−0.401282	+	0.915955i	$0.631435\pi$
$458$	−0.145980	+	0.252845i	−0.00682122	+	0.0118147i
$459$		0			0
$460$			5.54133i			0.258366i
$461$	−1.54283	+	0.890753i	−0.0718568	+	0.0414865i	−0.535498	−	0.844537i	$-0.679876\pi$
$461$	−1.54283	+	0.890753i	−0.0718568	+	0.0414865i	0.463641	+	0.886023i	$0.346543\pi$
$462$		0			0
$463$			6.80200i			0.316116i	0.987430	+	0.158058i	$0.0505232\pi$
$463$			6.80200i			0.316116i	−0.987430	+	0.158058i	$0.949477\pi$
$464$	−5.38995	−	9.33566i	−0.250222	−	0.433397i
$465$		0			0
$466$	−0.237335	−	0.137025i	−0.0109943	−	0.00634758i
$467$	18.2374			0.843927			0.421963	−	0.906613i	$-0.361341\pi$
$467$	18.2374			0.843927			0.421963	+	0.906613i	$0.361341\pi$
$468$		0			0
$469$	−3.43285			−0.158514
$470$	−1.58726	−	0.916407i	−0.0732150	−	0.0422707i
$471$		0			0
$472$	1.17517	+	2.03546i	0.0540918	+	0.0936897i
$473$			27.2045i			1.25086i
$474$		0			0
$475$	1.96410	−	1.13397i	0.0901192	−	0.0520303i
$476$			3.28398i			0.150521i
$477$		0			0
$478$	1.09207	−	1.89152i	0.0499502	−	0.0865162i
$479$	−30.4674	−	17.5904i	−1.39209	−	0.803724i	−0.398544	−	0.917149i	$-0.630485\pi$
$479$	−30.4674	−	17.5904i	−1.39209	−	0.803724i	−0.993547	+	0.113425i	$0.963818\pi$
$480$		0			0
$481$	20.2201	+	7.40214i	0.921957	+	0.337508i
$482$	−4.96204			−0.226015
$483$		0			0
$484$	17.4255	−	30.1819i	0.792069	−	1.37190i
$485$	−1.25396	−	2.17191i	−0.0569392	−	0.0986215i
$486$		0			0
$487$	8.92352	−	5.15200i	0.404363	−	0.233459i	−0.284002	−	0.958824i	$-0.591662\pi$
$487$	8.92352	−	5.15200i	0.404363	−	0.233459i	0.688365	+	0.725364i	$0.258329\pi$
$488$	−10.6038	+	6.12210i	−0.480011	+	0.277134i
$489$		0			0
$490$	0.756779	+	1.31078i	0.0341878	+	0.0592150i
$491$	−4.66599	+	8.08174i	−0.210573	+	0.364724i	−0.951894	−	0.306427i	$-0.900866\pi$
$491$	−4.66599	+	8.08174i	−0.210573	+	0.364724i	0.741321	+	0.671151i	$0.234200\pi$
$492$		0			0
$493$	−14.7041			−0.662238
$494$	1.76971	−	0.308654i	0.0796230	−	0.0138870i
$495$		0			0
$496$	17.5689	+	10.1434i	0.788869	+	0.455454i
$497$	−2.12593	+	3.68222i	−0.0953611	+	0.165170i
$498$		0			0
$499$		−	23.9421i		−	1.07179i	−0.844283	−	0.535897i	$-0.819974\pi$
$499$		−	23.9421i		−	1.07179i	0.844283	−	0.535897i	$-0.180026\pi$
$500$	1.69025	−	0.975869i	0.0755905	−	0.0436422i
$501$		0			0
$502$			1.48692i			0.0663645i
$503$	21.0721	+	36.4980i	0.939560	+	1.62737i	0.766294	+	0.642490i	$0.222099\pi$
$503$	21.0721	+	36.4980i	0.939560	+	1.62737i	0.173266	+	0.984875i	$0.444568\pi$
$504$		0			0
$505$	10.7792	+	6.22336i	0.479667	+	0.276936i
$506$	−3.35056			−0.148951
$507$		0			0
$508$	−6.32355			−0.280562
$509$	29.0640	+	16.7801i	1.28824	+	0.743765i	0.978340	−	0.207005i	$-0.0663715\pi$
$509$	29.0640	+	16.7801i	1.28824	+	0.743765i	0.309899	+	0.950770i	$0.399705\pi$
$510$		0			0
$511$	1.60960	+	2.78792i	0.0712047	+	0.123330i
$512$		−	15.9211i		−	0.703621i
$513$		0			0
$514$	1.95084	−	1.12632i	0.0860477	−	0.0496796i
$515$		−	15.0247i		−	0.662069i
$516$		0			0
$517$	−22.4081	+	38.8120i	−0.985508	+	1.70695i
$518$	0.377499	+	0.217949i	0.0165864	+	0.00957614i
$519$		0			0
$520$	3.08359	−	0.537808i	0.135224	−	0.0235844i
$521$	−12.4649			−0.546098			−0.273049	−	0.962000i	$-0.588032\pi$
$521$	−12.4649			−0.546098			−0.273049	+	0.962000i	$0.588032\pi$
$522$		0			0
$523$	2.82978	−	4.90132i	0.123738	−	0.214320i	−0.797501	−	0.603317i	$-0.793845\pi$
$523$	2.82978	−	4.90132i	0.123738	−	0.214320i	0.921239	+	0.388998i	$0.127179\pi$
$524$	0.171425	+	0.296916i	0.00748872	+	0.0129708i
$525$		0			0
$526$	3.54958	−	2.04935i	0.154769	−	0.0893558i
$527$	23.9645	−	13.8359i	1.04391	−	0.602702i
$528$		0			0
$529$	7.46953	+	12.9376i	0.324762	+	0.562505i
$530$	0.171425	−	0.296916i	0.00744621	−	0.0128972i
$531$		0			0
$532$	−1.47067			−0.0637616
$533$	12.6360	+	4.62577i	0.547327	+	0.200364i
$534$		0			0
$535$	11.3140	+	6.53215i	0.489147	+	0.282409i
$536$	4.48494	−	7.76815i	0.193720	−	0.335533i
$537$		0			0
$538$			3.94511i			0.170086i
$539$	32.0514	−	18.5049i	1.38055	−	0.797061i
$540$		0			0
$541$		−	15.4750i		−	0.665321i	−0.943047	−	0.332660i	$-0.892054\pi$
$541$		−	15.4750i		−	0.665321i	0.943047	−	0.332660i	$-0.107946\pi$
$542$	−3.39391	−	5.87842i	−0.145781	−	0.252500i
$543$		0			0
$544$	−11.1923	−	6.46187i	−0.479866	−	0.277051i
$545$	11.2325			0.481146
$546$		0			0
$547$	25.1765			1.07647			0.538234	−	0.842795i	$-0.319092\pi$
$547$	25.1765			1.07647			0.538234	+	0.842795i	$0.319092\pi$
$548$	−30.3956	−	17.5489i	−1.29844	−	0.749653i
$549$		0			0
$550$	0.590059	+	1.02201i	0.0251602	+	0.0435787i
$551$		−	6.58493i		−	0.280528i
$552$		0			0
$553$	−1.30013	+	0.750630i	−0.0552871	+	0.0319200i
$554$			5.82269i			0.247382i
$555$		0			0
$556$	−11.6969	+	20.2596i	−0.496059	+	0.859199i
$557$	36.6752	+	21.1744i	1.55398	+	0.897190i	0.997812	+	0.0661194i	$0.0210618\pi$
$557$	36.6752	+	21.1744i	1.55398	+	0.897190i	0.556167	+	0.831071i	$0.312272\pi$
$558$		0			0
$559$	11.7110	+	14.0095i	0.495322	+	0.592537i
$560$	−1.23355			−0.0521270
$561$		0			0
$562$	0.546763	−	0.947022i	0.0230638	−	0.0399477i
$563$	−11.8953	−	20.6032i	−0.501326	−	0.868322i	−0.999999	−	0.00153173i	$-0.999512\pi$
$563$	−11.8953	−	20.6032i	−0.501326	−	0.868322i	0.498673	−	0.866790i	$-0.333821\pi$
$564$		0			0
$565$	−15.8862	+	9.17191i	−0.668338	+	0.385865i
$566$	−2.39461	+	1.38253i	−0.100653	+	0.0581119i
$567$		0			0
$568$	−5.55497	−	9.62148i	−0.233081	−	0.403709i
$569$	13.3710	−	23.1593i	0.560543	−	0.970889i	−0.436906	−	0.899507i	$-0.643926\pi$
$569$	13.3710	−	23.1593i	0.560543	−	0.970889i	0.997449	−	0.0713817i	$-0.0227408\pi$
$570$		0			0
$571$	16.7159			0.699539			0.349769	−	0.936836i	$-0.386260\pi$
$571$	16.7159			0.699539			0.349769	+	0.936836i	$0.386260\pi$
$572$	−6.49498	−	37.2398i	−0.271569	−	1.55707i
$573$		0			0
$574$	0.235908	+	0.136202i	0.00984661	+	0.00568494i
$575$	−1.41959	+	2.45880i	−0.0592010	+	0.102539i
$576$		0			0
$577$			20.6768i			0.860786i	0.902642	+	0.430393i	$0.141625\pi$
$577$			20.6768i			0.860786i	−0.902642	+	0.430393i	$0.858375\pi$
$578$	−1.64515	+	0.949828i	−0.0684292	+	0.0395076i
$579$		0			0
$580$		−	5.66682i		−	0.235302i
$581$	0.708301	+	1.22681i	0.0293853	+	0.0508968i
$582$		0			0
$583$	−7.26023	−	4.19170i	−0.300688	−	0.173602i
$584$	−8.41165			−0.348076
$585$		0			0
$586$	−3.71657			−0.153530
$587$	−18.0109	−	10.3986i	−0.743388	−	0.429196i	0.0799116	−	0.996802i	$-0.474536\pi$
$587$	−18.0109	−	10.3986i	−0.743388	−	0.429196i	−0.823300	+	0.567606i	$0.807870\pi$
$588$		0			0
$589$	6.19615	+	10.7321i	0.255308	+	0.442206i
$590$			0.594763i			0.0244860i
$591$		0			0
$592$	19.2021	−	11.0863i	0.789199	−	0.455644i
$593$			21.8475i			0.897169i	0.893740	+	0.448585i	$0.148072\pi$
$593$			21.8475i			0.897169i	−0.893740	+	0.448585i	$0.851928\pi$
$594$		0			0
$595$	−0.841298	+	1.45717i	−0.0344898	+	0.0597381i
$596$	5.76446	+	3.32811i	0.236121	+	0.136325i
$597$		0			0
$598$	−1.72544	+	1.44235i	−0.0705583	+	0.0589822i
$599$	3.58040			0.146291			0.0731456	−	0.997321i	$-0.476696\pi$
$599$	3.58040			0.146291			0.0731456	+	0.997321i	$0.476696\pi$
$600$		0			0
$601$	−10.6743	+	18.4885i	−0.435414	+	0.754160i	−0.997329	−	0.0730352i	$-0.976731\pi$
$601$	−10.6743	+	18.4885i	−0.435414	+	0.754160i	0.561915	+	0.827195i	$0.310065\pi$
$602$	0.184822	+	0.320121i	0.00753278	+	0.0130472i
$603$		0			0
$604$	13.4568	−	7.76929i	0.547550	−	0.316128i
$605$	15.4641	−	8.92820i	0.628705	−	0.362983i
$606$		0			0
$607$	1.64988	+	2.85767i	0.0669665	+	0.115989i	0.897565	−	0.440883i	$-0.145335\pi$
$607$	1.64988	+	2.85767i	0.0669665	+	0.115989i	−0.830598	+	0.556872i	$0.812001\pi$
$608$	2.89383	−	5.01226i	0.117360	−	0.203274i
$609$		0			0
$610$	−3.09843			−0.125452
$611$	5.16832	+	29.6332i	0.209088	+	1.19883i
$612$		0			0
$613$	8.56183	+	4.94318i	0.345809	+	0.199653i	0.662838	−	0.748763i	$-0.269352\pi$
$613$	8.56183	+	4.94318i	0.345809	+	0.199653i	−0.317029	+	0.948416i	$0.602685\pi$
$614$	0.472795	−	0.818904i	0.0190804	−	0.0330483i
$615$		0			0
$616$		−	1.54944i		−	0.0624286i
$617$	−39.5920	+	22.8584i	−1.59391	+	0.920246i	−0.601287	+	0.799033i	$0.705345\pi$
$617$	−39.5920	+	22.8584i	−1.59391	+	0.920246i	−0.992626	+	0.121213i	$0.961321\pi$
$618$		0			0
$619$			19.9143i			0.800425i	0.916422	+	0.400212i	$0.131064\pi$
$619$			19.9143i			0.800425i	−0.916422	+	0.400212i	$0.868936\pi$
$620$	5.33225	+	9.23572i	0.214148	+	0.370916i
$621$		0			0
$622$	−0.423339	−	0.244415i	−0.0169743	−	0.00980014i
$623$	−1.07177			−0.0429397
$624$		0			0
$625$	1.00000			0.0400000
$626$	1.37152	+	0.791847i	0.0548169	+	0.0316486i
$627$		0			0
$628$	16.0363	+	27.7757i	0.639918	+	1.10837i
$629$		−	30.2440i		−	1.20591i
$630$		0			0
$631$	12.6403	−	7.29790i	0.503204	−	0.290525i	−0.226832	−	0.973934i	$-0.572837\pi$
$631$	12.6403	−	7.29790i	0.503204	−	0.290525i	0.730036	+	0.683409i	$0.239503\pi$
$632$		−	3.92272i		−	0.156038i
$633$		0			0
$634$	0.0353305	−	0.0611942i	0.00140315	−	0.00243033i
$635$	−2.80589	−	1.61998i	−0.111348	−	0.0642870i
$636$		0			0
$637$	8.53948	−	23.3269i	0.338346	−	0.924246i
$638$	3.42644			0.135654
$639$		0			0
$640$	3.30600	−	5.72615i	0.130681	−	0.226346i
$641$	7.08183	+	12.2661i	0.279716	+	0.484482i	0.971314	−	0.237801i	$-0.0764265\pi$
$641$	7.08183	+	12.2661i	0.279716	+	0.484482i	−0.691598	+	0.722282i	$0.743093\pi$
$642$		0			0
$643$	−14.5246	+	8.38581i	−0.572796	+	0.330704i	−0.758265	−	0.651946i	$-0.773953\pi$
$643$	−14.5246	+	8.38581i	−0.572796	+	0.330704i	0.185469	+	0.982650i	$0.440620\pi$
$644$	1.59443	−	0.920544i	0.0628293	−	0.0362745i
$645$		0			0
$646$	−1.26161	−	2.18518i	−0.0496376	−	0.0859748i
$647$	1.49584	−	2.59087i	0.0588075	−	0.101858i	−0.835123	−	0.550063i	$-0.814604\pi$
$647$	1.49584	−	2.59087i	0.0588075	−	0.101858i	0.893930	+	0.448206i	$0.147937\pi$
$648$		0			0
$649$	14.5432			0.570872
$650$	0.743818	+	0.272296i	0.0291749	+	0.0106803i
$651$		0			0
$652$	−30.0987	−	17.3775i	−1.17876	−	0.680556i
$653$	−5.83217	+	10.1016i	−0.228230	+	0.395307i	−0.957284	−	0.289150i	$-0.906627\pi$
$653$	−5.83217	+	10.1016i	−0.228230	+	0.395307i	0.729053	+	0.684457i	$0.239961\pi$
$654$		0			0
$655$			0.175664i			0.00686374i
$656$	11.9998	−	6.92810i	0.468514	−	0.270497i
$657$		0			0
$658$			0.608946i			0.0237392i
$659$	−0.905237	−	1.56792i	−0.0352630	−	0.0610773i	0.847855	−	0.530228i	$-0.177894\pi$
$659$	−0.905237	−	1.56792i	−0.0352630	−	0.0610773i	−0.883118	+	0.469150i	$0.844560\pi$
$660$		0			0
$661$	10.6872	+	6.17028i	0.415686	+	0.239996i	0.693230	−	0.720717i	$-0.256187\pi$
$661$	10.6872	+	6.17028i	0.415686	+	0.239996i	−0.277544	+	0.960713i	$0.589520\pi$
$662$	−3.65383			−0.142010
$663$		0			0
$664$	−3.70152			−0.143647
$665$	−0.652566	−	0.376759i	−0.0253054	−	0.0146101i
$666$		0			0
$667$	4.12174	+	7.13907i	0.159594	+	0.276426i
$668$			12.2836i			0.475265i
$669$		0			0
$670$	1.96576	−	1.13493i	0.0759438	−	0.0438461i
$671$			75.7634i			2.92481i
$672$		0			0
$673$	4.63313	−	8.02481i	0.178594	−	0.309334i	−0.762805	−	0.646628i	$-0.776178\pi$
$673$	4.63313	−	8.02481i	0.178594	−	0.309334i	0.941399	+	0.337295i	$0.109512\pi$
$674$	−4.60770	−	2.66025i	−0.177482	−	0.102469i
$675$		0			0
$676$	−19.3757	−	16.3814i	−0.745220	−	0.630053i
$677$	−13.8984			−0.534158			−0.267079	−	0.963675i	$-0.586059\pi$
$677$	−13.8984			−0.534158			−0.267079	+	0.963675i	$0.586059\pi$
$678$		0			0
$679$	−0.416622	+	0.721611i	−0.0159885	+	0.0276929i
$680$	−2.19827	−	3.80752i	−0.0842999	−	0.146012i
$681$		0			0
$682$	−5.58438	+	3.22414i	−0.213837	+	0.123459i
$683$	32.6935	−	18.8756i	1.25098	−	0.722255i	0.279678	−	0.960094i	$-0.409772\pi$
$683$	32.6935	−	18.8756i	1.25098	−	0.722255i	0.971305	+	0.237838i	$0.0764388\pi$
$684$		0			0
$685$	−8.99144	−	15.5736i	−0.343545	−	0.595038i
$686$	0.506903	−	0.877981i	0.0193536	−	0.0335215i
$687$		0			0
$688$	18.8025			0.716838
$689$	−5.54324	+	0.966794i	−0.211181	+	0.0368319i
$690$		0			0
$691$	−1.43146	−	0.826456i	−0.0544554	−	0.0314399i	0.472525	−	0.881317i	$-0.343343\pi$
$691$	−1.43146	−	0.826456i	−0.0544554	−	0.0314399i	−0.526981	+	0.849877i	$0.676676\pi$
$692$	−15.5896	+	27.0020i	−0.592628	+	1.02646i
$693$		0			0
$694$		−	1.37823i		−	0.0523168i
$695$	−10.3803	+	5.99307i	−0.393747	+	0.227330i
$696$		0			0
$697$		−	18.9002i		−	0.715897i
$698$	−0.776587	−	1.34509i	−0.0293943	−	0.0509123i
$699$		0			0
$700$	−0.561581	−	0.324229i	−0.0212258	−	0.0122547i
$701$	20.4819			0.773590			0.386795	−	0.922166i	$-0.373582\pi$
$701$	20.4819			0.773590			0.386795	+	0.922166i	$0.373582\pi$
$702$		0			0
$703$	13.5442			0.510830
$704$	−31.9363	−	18.4384i	−1.20365	−	0.694925i
$705$		0			0
$706$	2.39347	+	4.14561i	0.0900794	+	0.156022i
$707$		−	4.13538i		−	0.155527i
$708$		0			0
$709$	19.0021	−	10.9709i	0.713639	−	0.412020i	−0.0987679	−	0.995110i	$-0.531490\pi$
$709$	19.0021	−	10.9709i	0.713639	−	0.412020i	0.812407	+	0.583091i	$0.198157\pi$
$710$		−	2.81140i		−	0.105510i
$711$		0			0
$712$	1.40025	−	2.42530i	0.0524764	−	0.0908919i
$713$	−13.4351	−	7.75678i	−0.503150	−	0.290494i
$714$		0			0
$715$	6.65821	−	18.1879i	0.249003	−	0.680191i
$716$	46.0950			1.72265
$717$		0			0
$718$	2.63335	−	4.56110i	0.0982759	−	0.170219i
$719$	−19.4237	−	33.6429i	−0.724384	−	1.25467i	−0.959227	−	0.282636i	$-0.908791\pi$
$719$	−19.4237	−	33.6429i	−0.724384	−	1.25467i	0.234844	−	0.972033i	$-0.424542\pi$
$720$		0			0
$721$	−4.32312	+	2.49596i	−0.161002	+	0.0929543i
$722$	−2.63624	+	1.52204i	−0.0981108	+	0.0566443i
$723$		0			0
$724$	−2.56254	−	4.43844i	−0.0952359	−	0.164953i
$725$	1.45174	−	2.51448i	0.0539162	−	0.0933856i
$726$		0			0
$727$	30.6598			1.13711			0.568555	−	0.822645i	$-0.307503\pi$
$727$	30.6598			1.13711			0.568555	+	0.822645i	$0.307503\pi$
$728$	−0.667002	−	0.797912i	−0.0247207	−	0.0295726i
$729$		0			0
$730$	−1.84342	−	1.06430i	−0.0682279	−	0.0393914i
$731$	12.8236	−	22.2110i	0.474296	−	0.821505i
$732$		0			0
$733$		−	24.3858i		−	0.900709i	−0.892850	−	0.450355i	$-0.851298\pi$
$733$		−	24.3858i		−	0.900709i	0.892850	−	0.450355i	$-0.148702\pi$
$734$	−1.21598	+	0.702045i	−0.0448826	+	0.0259130i
$735$		0			0
$736$			7.24539i			0.267069i
$737$	−27.7515	−	48.0669i	−1.02224	−	1.77057i
$738$		0			0
$739$	−33.1504	−	19.1394i	−1.21946	−	0.704054i	−0.254656	−	0.967032i	$-0.581962\pi$
$739$	−33.1504	−	19.1394i	−1.21946	−	0.704054i	−0.964802	+	0.262977i	$0.915296\pi$
$740$	11.6558			0.428476
$741$		0			0
$742$	−0.113910			−0.00418178
$743$	34.6479	+	20.0040i	1.27111	+	0.733874i	0.975196	−	0.221342i	$-0.0710437\pi$
$743$	34.6479	+	20.0040i	1.27111	+	0.733874i	0.295910	+	0.955216i	$0.404377\pi$
$744$		0			0
$745$	1.70520	+	2.95350i	0.0624738	+	0.108208i
$746$			4.41134i			0.161511i
$747$		0			0
$748$	−45.9825	+	26.5480i	−1.68129	+	0.970691i
$749$		−	4.34057i		−	0.158601i
$750$		0			0
$751$	12.8010	−	22.1720i	0.467115	−	0.809067i	−0.532179	−	0.846632i	$-0.678627\pi$
$751$	12.8010	−	22.1720i	0.467115	−	0.809067i	0.999294	+	0.0375648i	$0.0119601\pi$
$752$	26.8251	+	15.4875i	0.978211	+	0.564770i
$753$		0			0
$754$	1.76451	−	1.47502i	0.0642597	−	0.0537169i
$755$	7.96141			0.289745
$756$		0			0
$757$	0.924239	−	1.60083i	0.0335920	−	0.0581831i	−0.848741	−	0.528809i	$-0.822639\pi$
$757$	0.924239	−	1.60083i	0.0335920	−	0.0581831i	0.882333	+	0.470626i	$0.155972\pi$
$758$	−0.599945	−	1.03914i	−0.0217910	−	0.0377431i
$759$		0			0
$760$	1.70512	−	0.984454i	0.0618514	−	0.0357099i
$761$	−22.7006	+	13.1062i	−0.822896	+	0.475099i	−0.851414	−	0.524494i	$-0.824255\pi$
$761$	−22.7006	+	13.1062i	−0.822896	+	0.475099i	0.0285179	+	0.999593i	$0.490921\pi$
$762$		0			0
$763$	−1.86597	−	3.23196i	−0.0675528	−	0.117005i
$764$	−1.96718	+	3.40725i	−0.0711699	+	0.123270i
$765$		0			0
$766$	−1.24513			−0.0449884
$767$	7.48932	−	6.26058i	0.270424	−	0.226056i
$768$		0			0
$769$	−38.4078	−	22.1747i	−1.38502	−	0.799641i	−0.392271	−	0.919850i	$-0.628310\pi$
$769$	−38.4078	−	22.1747i	−1.38502	−	0.799641i	−0.992749	+	0.120208i	$0.961644\pi$
$770$	0.196045	−	0.339560i	0.00706497	−	0.0122369i
$771$		0			0
$772$			44.5408i			1.60306i
$773$	−20.1471	+	11.6319i	−0.724640	+	0.418371i	−0.816458	−	0.577405i	$-0.804065\pi$
$773$	−20.1471	+	11.6319i	−0.724640	+	0.418371i	0.0918181	+	0.995776i	$0.470732\pi$
$774$		0			0
$775$			5.46410i			0.196276i
$776$	−1.08861	−	1.88554i	−0.0390790	−	0.0676868i
$777$		0			0
$778$	2.02001	+	1.16625i	0.0724209	+	0.0418122i
$779$	8.46410			0.303258
$780$		0			0
$781$	−68.7449			−2.45989
$782$	2.73556	+	1.57938i	0.0978235	+	0.0564784i
$783$		0			0
$784$	−12.7897	−	22.1524i	−0.456776	−	0.791159i
$785$			16.4329i			0.586514i
$786$		0			0
$787$	−41.4942	+	23.9567i	−1.47911	+	0.853963i	−0.999721	−	0.0236408i	$-0.992474\pi$
$787$	−41.4942	+	23.9567i	−1.47911	+	0.853963i	−0.479387	+	0.877604i	$0.659141\pi$
$788$		−	1.25502i		−	0.0447081i
$789$		0			0
$790$	0.496329	−	0.859667i	0.0176586	−	0.0305856i
$791$	5.27814	+	3.04734i	0.187669	+	0.108351i
$792$		0			0
$793$	32.6147	+	39.0158i	1.15818	+	1.38549i
$794$	6.15865			0.218562
$795$		0			0
$796$	2.99284	−	5.18374i	0.106078	−	0.183733i
$797$	10.3476	+	17.9225i	0.366530	+	0.634849i	0.989020	−	0.147779i	$-0.0472124\pi$
$797$	10.3476	+	17.9225i	0.366530	+	0.634849i	−0.622490	+	0.782627i	$0.713879\pi$
$798$		0			0
$799$	36.5902	−	21.1253i	1.29447	−	0.747361i
$800$	2.21004	−	1.27597i	0.0781367	−	0.0451122i
$801$		0			0
$802$	−2.47305	−	4.28344i	−0.0873263	−	0.151254i
$803$	−26.0244	+	45.0755i	−0.918380	+	1.59068i
$804$		0			0
$805$	0.943307			0.0332472
$806$	−1.48785	+	4.06430i	−0.0524073	+	0.143159i
$807$		0			0
$808$	9.35788	+	5.40278i	0.329209	+	0.190069i
$809$	7.94574	−	13.7624i	0.279357	−	0.483861i	−0.691868	−	0.722024i	$-0.743212\pi$
$809$	7.94574	−	13.7624i	0.279357	−	0.483861i	0.971225	+	0.238163i	$0.0765453\pi$
$810$		0			0
$811$			23.8796i			0.838525i	0.907865	+	0.419263i	$0.137711\pi$
$811$			23.8796i			0.838525i	−0.907865	+	0.419263i	$0.862289\pi$
$812$	−1.63054	+	0.941391i	−0.0572206	+	0.0330363i
$813$		0			0
$814$			7.04768i			0.247021i
$815$	−8.90361	−	15.4215i	−0.311880	−	0.540192i
$816$		0			0
$817$	9.94679	+	5.74278i	0.347994	+	0.200915i
$818$	−0.941956			−0.0329347
$819$		0			0
$820$	7.28398			0.254368
$821$	−13.7782	−	7.95484i	−0.480862	−	0.277626i	0.239914	−	0.970794i	$-0.422881\pi$
$821$	−13.7782	−	7.95484i	−0.480862	−	0.277626i	−0.720776	+	0.693169i	$0.756214\pi$
$822$		0			0
$823$	−7.40573	−	12.8271i	−0.258147	−	0.447124i	0.707598	−	0.706615i	$-0.249779\pi$
$823$	−7.40573	−	12.8271i	−0.258147	−	0.447124i	−0.965746	+	0.259491i	$0.916445\pi$
$824$		−	13.0436i		−	0.454397i
$825$		0			0
$826$	0.171134	−	0.0988040i	0.00595450	−	0.00343783i
$827$		−	33.9498i		−	1.18055i	−0.807202	−	0.590275i	$-0.799019\pi$
$827$		−	33.9498i		−	1.18055i	0.807202	−	0.590275i	$-0.200981\pi$
$828$		0			0
$829$	11.6573	−	20.1910i	0.404875	−	0.701264i	−0.589432	−	0.807818i	$-0.700648\pi$
$829$	11.6573	−	20.1910i	0.404875	−	0.701264i	0.994307	+	0.106554i	$0.0339818\pi$
$830$	−0.811190	−	0.468341i	−0.0281568	−	0.0162563i
$831$		0			0
$832$	−24.3836	+	4.25274i	−0.845350	+	0.147437i
$833$	−34.8910			−1.20890
$834$		0			0
$835$	−3.14683	+	5.45047i	−0.108900	+	0.188621i
$836$	−11.8890	−	20.5924i	−0.411190	−	0.712202i
$837$		0			0
$838$	3.36970	−	1.94550i	0.116404	−	0.0672061i
$839$	12.8111	−	7.39649i	0.442288	−	0.255355i	−0.262280	−	0.964992i	$-0.584474\pi$
$839$	12.8111	−	7.39649i	0.442288	−	0.255355i	0.704568	+	0.709637i	$0.251141\pi$
$840$		0			0
$841$	10.2849	+	17.8140i	0.354652	+	0.614276i
$842$	1.41465	−	2.45024i	0.0487519	−	0.0844408i
$843$		0			0
$844$	−16.0050			−0.550915
$845$	−4.40078	−	12.2325i	−0.151392	−	0.420809i
$846$		0			0
$847$	−5.13789	−	2.96636i	−0.176540	−	0.101925i
$848$	−2.89711	+	5.01794i	−0.0994872	+	0.172317i
$849$		0			0
$850$		−	1.11256i		−	0.0381605i
$851$	−14.6840	+	8.47780i	−0.503360	+	0.290615i
$852$		0			0
$853$		−	16.3452i		−	0.559650i	−0.960051	−	0.279825i	$-0.909724\pi$
$853$		−	16.3452i		−	0.559650i	0.960051	−	0.279825i	$-0.0902765\pi$
$854$	0.514722	+	0.891525i	0.0176134	+	0.0305073i
$855$		0			0
$856$	9.82220	+	5.67085i	0.335716	+	0.193826i
$857$	−34.1418			−1.16626			−0.583132	−	0.812378i	$-0.698173\pi$
$857$	−34.1418			−1.16626			−0.583132	+	0.812378i	$0.698173\pi$
$858$		0			0
$859$	−45.1996			−1.54219			−0.771096	−	0.636719i	$-0.780291\pi$
$859$	−45.1996			−1.54219			−0.771096	+	0.636719i	$0.780291\pi$
$860$	8.55995	+	4.94209i	0.291892	+	0.168524i
$861$		0			0
$862$	−1.04334	−	1.80712i	−0.0355364	−	0.0615508i
$863$			4.75058i			0.161712i	0.996726	+	0.0808559i	$0.0257653\pi$
$863$			4.75058i			0.161712i	−0.996726	+	0.0808559i	$0.974235\pi$
$864$		0			0
$865$	−13.8349	+	7.98756i	−0.470399	+	0.271585i
$866$		−	0.306745i		−	0.0104236i
$867$		0			0
$868$	1.77162	−	3.06854i	0.0601327	−	0.104153i
$869$	−21.0207	−	12.1363i	−0.713079	−	0.411696i
$870$		0			0
$871$	−34.9830	−	12.8065i	−1.18535	−	0.433933i
$872$	9.75140			0.330224
$873$		0			0
$874$	−0.707294	+	1.22507i	−0.0239246	+	0.0414386i
$875$	−0.166123	−	0.287734i	−0.00561599	−	0.00972718i
$876$		0			0
$877$	−1.95294	+	1.12753i	−0.0659462	+	0.0380741i	−0.532611	−	0.846360i	$-0.678789\pi$
$877$	−1.95294	+	1.12753i	−0.0659462	+	0.0380741i	0.466664	+	0.884434i	$0.345456\pi$
$878$	0.791801	−	0.457146i	0.0267220	−	0.0154279i
$879$		0			0
$880$	−9.97212	−	17.2722i	−0.336160	−	0.582246i
$881$	1.49152	−	2.58339i	0.0502507	−	0.0870367i	−0.839806	−	0.542887i	$-0.817331\pi$
$881$	1.49152	−	2.58339i	0.0502507	−	0.0870367i	0.890057	+	0.455850i	$0.150665\pi$
$882$		0			0
$883$	−28.2874			−0.951947			−0.475973	−	0.879460i	$-0.657904\pi$
$883$	−28.2874			−0.951947			−0.475973	+	0.879460i	$0.657904\pi$
$884$	−12.2512	+	33.4660i	−0.412051	+	1.12558i
$885$		0			0
$886$	−1.81610	−	1.04852i	−0.0610130	−	0.0352259i
$887$	−13.9908	+	24.2328i	−0.469766	+	0.813658i	−0.999402	−	0.0345665i	$-0.988995\pi$
$887$	−13.9908	+	24.2328i	−0.469766	+	0.813658i	0.529637	+	0.848225i	$0.322328\pi$
$888$		0			0
$889$			1.07647i			0.0361035i
$890$	0.613729	−	0.354337i	0.0205723	−	0.0118774i
$891$		0			0
$892$		−	19.9940i		−	0.669448i
$893$	9.46058	+	16.3862i	0.316586	+	0.548343i
$894$		0			0
$895$	20.4533	+	11.8087i	0.683678	+	0.394722i
$896$	−2.19681			−0.0733903
$897$		0			0
$898$	−4.77095			−0.159209
$899$	13.7394	+	7.93244i	0.458234	+	0.264562i
$900$		0			0
$901$	3.95174	+	6.84461i	0.131651	+	0.228027i
$902$			4.40426i			0.146646i
$903$		0			0
$904$	−13.7915	+	7.96255i	−0.458700	+	0.264830i
$905$		−	2.62590i		−	0.0872879i
$906$		0			0
$907$	8.27600	−	14.3344i	0.274800	−	0.475967i	−0.695285	−	0.718734i	$-0.744722\pi$
$907$	8.27600	−	14.3344i	0.274800	−	0.475967i	0.970085	+	0.242767i	$0.0780550\pi$
$908$	−11.9058	−	6.87383i	−0.395109	−	0.228116i
$909$		0			0
$910$	−0.0452168	−	0.259256i	−0.00149892	−	0.00859426i
$911$	−7.04863			−0.233532			−0.116766	−	0.993159i	$-0.537253\pi$
$911$	−7.04863			−0.233532			−0.116766	+	0.993159i	$0.537253\pi$
$912$		0			0
$913$	−11.4519	+	19.8353i	−0.379004	+	0.656454i
$914$	0.518746	+	0.898494i	0.0171586	+	0.0297196i
$915$		0			0
$916$	2.24632	−	1.29692i	0.0742206	−	0.0428513i
$917$	0.0505443	−	0.0291818i	0.00166912	−	0.000963668i
$918$		0			0
$919$	−8.27188	−	14.3273i	−0.272864	−	0.472615i	0.696730	−	0.717334i	$-0.254638\pi$
$919$	−8.27188	−	14.3273i	−0.272864	−	0.472615i	−0.969594	+	0.244719i	$0.921304\pi$
$920$	−1.23241	+	2.13459i	−0.0406313	+	0.0703755i
$921$		0			0
$922$	−0.391374			−0.0128892
$923$	−35.4015	+	29.5933i	−1.16525	+	0.974076i
$924$		0			0
$925$	5.17191	+	2.98601i	0.170051	+	0.0981793i
$926$	−0.747155	+	1.29411i	−0.0245530	+	0.0425271i
$927$		0			0
$928$		−	7.40948i		−	0.243228i
$929$	29.3035	−	16.9184i	0.961416	−	0.555074i	0.0648073	−	0.997898i	$-0.479357\pi$
$929$	29.3035	−	16.9184i	0.961416	−	0.555074i	0.896609	+	0.442824i	$0.146023\pi$
$930$		0			0
$931$		−	15.6253i		−	0.512098i
$932$	1.21736	+	2.10853i	0.0398759	+	0.0690670i
$933$		0			0
$934$	3.46975	+	2.00326i	0.113534	+	0.0655487i
$935$	−27.2045			−0.889681
$936$		0			0
$937$	−30.4606			−0.995104			−0.497552	−	0.867434i	$-0.665768\pi$
$937$	−30.4606			−0.995104			−0.497552	+	0.867434i	$0.665768\pi$
$938$	−0.653115	−	0.377076i	−0.0213250	−	0.0123120i
$939$		0			0
$940$	8.14153	+	14.1015i	0.265547	+	0.459941i
$941$		−	38.2101i		−	1.24561i	−0.782375	−	0.622807i	$-0.785992\pi$
$941$		−	38.2101i		−	1.24561i	0.782375	−	0.622807i	$-0.214008\pi$
$942$		0			0
$943$	−9.17637	+	5.29798i	−0.298824	+	0.172526i
$944$		−	10.0516i		−	0.327153i
$945$		0			0
$946$	−2.98823	+	5.17577i	−0.0971558	+	0.168279i
$947$	45.4215	+	26.2241i	1.47600	+	0.852169i	0.999633	−	0.0270773i	$-0.00862003\pi$
$947$	45.4215	+	26.2241i	1.47600	+	0.852169i	0.476367	+	0.879247i	$0.341953\pi$
$948$		0			0
$949$	6.00239	+	34.4155i	0.194846	+	1.11717i
$950$	0.498239			0.0161650
$951$		0			0
$952$	−0.730368	+	1.26503i	−0.0236714	+	0.0410000i
$953$	−19.8750	−	34.4245i	−0.643814	−	1.11512i	−0.984574	−	0.174969i	$-0.944018\pi$
$953$	−19.8750	−	34.4245i	−0.643814	−	1.11512i	0.340760	−	0.940150i	$-0.389316\pi$
$954$		0			0
$955$	−1.74575	+	1.00791i	−0.0564912	+	0.0326152i
$956$	−16.8046	+	9.70215i	−0.543500	+	0.313790i
$957$		0			0
$958$	−3.86437	−	6.69329i	−0.124852	−	0.216250i
$959$	−2.98737	+	5.17428i	−0.0964673	+	0.167086i
$960$		0			0
$961$	1.14359			0.0368901
$962$	3.03389	+	3.62933i	0.0978164	+	0.117014i
$963$		0			0
$964$	38.1776	+	22.0418i	1.22962	+	0.709920i
$965$	−11.4105	+	19.7636i	−0.367318	+	0.636214i
$966$		0			0
$967$		−	25.7857i		−	0.829214i	−0.910001	−	0.414607i	$-0.863919\pi$
$967$		−	25.7857i		−	0.829214i	0.910001	−	0.414607i	$-0.136081\pi$
$968$	13.4251	−	7.75097i	0.431498	−	0.249126i
$969$		0			0
$970$		−	0.550955i		−	0.0176901i
$971$	−27.7626	−	48.0863i	−0.890945	−	1.54316i	−0.838744	−	0.544525i	$-0.816710\pi$
$971$	−27.7626	−	48.0863i	−0.890945	−	1.54316i	−0.0522005	−	0.998637i	$-0.516623\pi$
$972$		0			0
$973$	3.44882	+	1.99118i	0.110564	+	0.0638342i
$974$	2.26365			0.0725321
$975$		0			0
$976$	52.3642			1.67614
$977$	35.0879	+	20.2580i	1.12256	+	0.648112i	0.942054	−	0.335461i	$-0.108892\pi$
$977$	35.0879	+	20.2580i	1.12256	+	0.648112i	0.180509	+	0.983573i	$0.442226\pi$
$978$		0			0
$979$	−8.66430	−	15.0070i	−0.276912	−	0.479626i
$980$		−	13.4467i		−	0.429540i
$981$		0			0
$982$	−1.77545	+	1.02506i	−0.0566569	+	0.0327109i
$983$		−	34.8059i		−	1.11014i	−0.831805	−	0.555068i	$-0.812692\pi$
$983$		−	34.8059i		−	1.11014i	0.831805	−	0.555068i	$-0.187308\pi$
$984$		0			0
$985$	0.321513	−	0.556877i	0.0102443	−	0.0177436i
$986$	−2.79751	−	1.61514i	−0.0890910	−	0.0514367i
$987$		0			0
$988$	−14.9871	−	5.48645i	−0.476803	−	0.174547i
$989$	−14.3784			−0.457208
$990$		0			0
$991$	−21.9427	+	38.0059i	−0.697034	+	1.20730i	0.272456	+	0.962168i	$0.412164\pi$
$991$	−21.9427	+	38.0059i	−0.697034	+	1.20730i	−0.969490	+	0.245130i	$0.921169\pi$
$992$	6.97201	+	12.0759i	0.221362	+	0.383410i
$993$		0			0
$994$	−0.808936	+	0.467040i	−0.0256579	+	0.0148136i
$995$	2.65596	−	1.53342i	0.0841997	−	0.0486127i
$996$		0			0
$997$	2.74569	+	4.75567i	0.0869568	+	0.150614i	0.906223	−	0.422799i	$-0.138952\pi$
$997$	2.74569	+	4.75567i	0.0869568	+	0.150614i	−0.819267	+	0.573413i	$0.805619\pi$
$998$	2.62988	−	4.55508i	0.0832474	−	0.144189i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bu.c.316.3		8
3.2	odd	2		65.2.m.a.56.2	yes	8
12.11	even	2		1040.2.da.b.641.2		8
13.6	odd	12		7605.2.a.cj.1.2		4
13.7	odd	12		7605.2.a.cf.1.3		4
13.10	even	6	inner	585.2.bu.c.361.3		8
15.2	even	4		325.2.m.b.199.3		8
15.8	even	4		325.2.m.c.199.2		8
15.14	odd	2		325.2.n.d.251.3		8
39.2	even	12		845.2.e.n.146.2		8
39.5	even	4		845.2.e.n.191.2		8
39.8	even	4		845.2.e.m.191.3		8
39.11	even	12		845.2.e.m.146.3		8
39.17	odd	6		845.2.c.g.506.4		8
39.20	even	12		845.2.a.m.1.2		4
39.23	odd	6		65.2.m.a.36.2	✓	8
39.29	odd	6		845.2.m.g.361.3		8
39.32	even	12		845.2.a.l.1.3		4
39.35	odd	6		845.2.c.g.506.5		8
39.38	odd	2		845.2.m.g.316.3		8
156.23	even	6		1040.2.da.b.881.2		8
195.23	even	12		325.2.m.b.49.3		8
195.59	even	12		4225.2.a.bi.1.3		4
195.62	even	12		325.2.m.c.49.2		8
195.149	even	12		4225.2.a.bl.1.2		4
195.179	odd	6		325.2.n.d.101.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.2	✓	8	39.23	odd	6
65.2.m.a.56.2	yes	8	3.2	odd	2
325.2.m.b.49.3		8	195.23	even	12
325.2.m.b.199.3		8	15.2	even	4
325.2.m.c.49.2		8	195.62	even	12
325.2.m.c.199.2		8	15.8	even	4
325.2.n.d.101.3		8	195.179	odd	6
325.2.n.d.251.3		8	15.14	odd	2
585.2.bu.c.316.3		8	1.1	even	1	trivial
585.2.bu.c.361.3		8	13.10	even	6	inner
845.2.a.l.1.3		4	39.32	even	12
845.2.a.m.1.2		4	39.20	even	12
845.2.c.g.506.4		8	39.17	odd	6
845.2.c.g.506.5		8	39.35	odd	6
845.2.e.m.146.3		8	39.11	even	12
845.2.e.m.191.3		8	39.8	even	4
845.2.e.n.146.2		8	39.2	even	12
845.2.e.n.191.2		8	39.5	even	4
845.2.m.g.316.3		8	39.38	odd	2
845.2.m.g.361.3		8	39.29	odd	6
1040.2.da.b.641.2		8	12.11	even	2
1040.2.da.b.881.2		8	156.23	even	6
4225.2.a.bi.1.3		4	195.59	even	12
4225.2.a.bl.1.2		4	195.149	even	12
7605.2.a.cf.1.3		4	13.7	odd	12
7605.2.a.cj.1.2		4	13.6	odd	12

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190254 + 0.109843i) q^{2} +(-0.975869 - 1.69025i) q^{4} -1.00000i q^{5} +(-0.287734 + 0.166123i) q^{7} -0.868145i q^{8} +O(q^{10})\)	\(q+(0.190254 + 0.109843i) q^{2} +(-0.975869 - 1.69025i) q^{4} -1.00000i q^{5} +(-0.287734 + 0.166123i) q^{7} -0.868145i q^{8} +(0.109843 - 0.190254i) q^{10} +(-4.65213 - 2.68591i) q^{11} +(-3.55193 + 0.619491i) q^{13} -0.0729902 q^{14} +(-1.85638 + 3.21534i) q^{16} +(2.53215 + 4.38581i) q^{17} +(-1.96410 + 1.13397i) q^{19} +(-1.69025 + 0.975869i) q^{20} +(-0.590059 - 1.02201i) q^{22} +(1.41959 - 2.45880i) q^{23} -1.00000 q^{25} +(-0.743818 - 0.272296i) q^{26} +(0.561581 + 0.324229i) q^{28} +(-1.45174 + 2.51448i) q^{29} -5.46410i q^{31} +(-2.21004 + 1.27597i) q^{32} +1.11256i q^{34} +(0.166123 + 0.287734i) q^{35} +(-5.17191 - 2.98601i) q^{37} -0.498239 q^{38} -0.868145 q^{40} +(-3.23205 - 1.86603i) q^{41} +(-2.53215 - 4.38581i) q^{43} +10.4844i q^{44} +(0.540166 - 0.311865i) q^{46} -8.34285i q^{47} +(-3.44481 + 5.96658i) q^{49} +(-0.190254 - 0.109843i) q^{50} +(4.51332 + 5.39913i) q^{52} +1.56063 q^{53} +(-2.68591 + 4.65213i) q^{55} +(0.144219 + 0.249795i) q^{56} +(-0.552399 + 0.318928i) q^{58} +(-2.34461 + 1.35366i) q^{59} +(-7.05193 - 12.2143i) q^{61} +(0.600196 - 1.03957i) q^{62} +6.86488 q^{64} +(0.619491 + 3.55193i) q^{65} +(8.94799 + 5.16612i) q^{67} +(4.94209 - 8.55995i) q^{68} +0.0729902i q^{70} +(11.0828 - 6.39866i) q^{71} -9.68922i q^{73} +(-0.655986 - 1.13620i) q^{74} +(3.83341 + 2.21322i) q^{76} +1.78477 q^{77} +4.51851 q^{79} +(3.21534 + 1.85638i) q^{80} +(-0.409941 - 0.710039i) q^{82} -4.26371i q^{83} +(4.38581 - 2.53215i) q^{85} -1.11256i q^{86} +(-2.33176 + 4.03872i) q^{88} +(2.79366 + 1.61292i) q^{89} +(0.919100 - 0.768307i) q^{91} -5.54133 q^{92} +(0.916407 - 1.58726i) q^{94} +(1.13397 + 1.96410i) q^{95} +(2.17191 - 1.25396i) q^{97} +(-1.31078 + 0.756779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) \) 8 * q + 2 * q^4 - 6 * q^7	\( 8 q + 2 q^{4} - 6 q^{7} - 2 q^{10} - 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} - 12 q^{20} - 12 q^{22} + 10 q^{23} - 8 q^{25} - 10 q^{26} - 18 q^{28} + 8 q^{29} - 6 q^{32} - 10 q^{35} + 6 q^{37} + 16 q^{38} - 12 q^{40} - 12 q^{41} - 2 q^{43} - 42 q^{46} + 12 q^{49} - 6 q^{52} + 24 q^{53} - 12 q^{56} + 36 q^{58} + 12 q^{59} - 28 q^{61} - 4 q^{62} - 8 q^{64} + 8 q^{65} + 6 q^{67} + 14 q^{68} - 10 q^{74} + 54 q^{76} + 36 q^{77} - 16 q^{79} + 4 q^{82} + 18 q^{85} - 18 q^{88} - 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 16 q^{95} - 30 q^{97} - 72 q^{98}+O(q^{100}) \) 8 * q + 2 * q^4 - 6 * q^7 - 2 * q^10 - 4 * q^14 - 2 * q^16 + 2 * q^17 + 12 * q^19 - 12 * q^20 - 12 * q^22 + 10 * q^23 - 8 * q^25 - 10 * q^26 - 18 * q^28 + 8 * q^29 - 6 * q^32 - 10 * q^35 + 6 * q^37 + 16 * q^38 - 12 * q^40 - 12 * q^41 - 2 * q^43 - 42 * q^46 + 12 * q^49 - 6 * q^52 + 24 * q^53 - 12 * q^56 + 36 * q^58 + 12 * q^59 - 28 * q^61 - 4 * q^62 - 8 * q^64 + 8 * q^65 + 6 * q^67 + 14 * q^68 - 10 * q^74 + 54 * q^76 + 36 * q^77 - 16 * q^79 + 4 * q^82 + 18 * q^85 - 18 * q^88 - 24 * q^89 + 28 * q^91 - 44 * q^92 + 32 * q^94 + 16 * q^95 - 30 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more