LMFDB - Embedded newform 3234.2.e.b.2155.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(2155,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3234.2155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.e (of order $2$, degree $1$, 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:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2155.6
Root			$0.500000 - 0.921602i$ of defining polynomial
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.b.2155.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.78763i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.78763i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +1.78763 q^{10} +(-3.15519 - 1.02213i) q^{11} -1.00000i q^{12} -6.37742 q^{13} -1.78763 q^{15} +1.00000 q^{16} +0.106095 q^{17} +1.00000i q^{18} -4.15162 q^{19} -1.78763i q^{20} +(-1.02213 + 3.15519i) q^{22} +7.95866 q^{23} -1.00000 q^{24} +1.80439 q^{25} +6.37742i q^{26} -1.00000i q^{27} -7.65230i q^{29} +1.78763i q^{30} -1.27872i q^{31} -1.00000i q^{32} +(1.02213 - 3.15519i) q^{33} -0.106095i q^{34} +1.00000 q^{36} +4.52184 q^{37} +4.15162i q^{38} -6.37742i q^{39} -1.78763 q^{40} -0.0321383 q^{41} -6.87723i q^{43} +(3.15519 + 1.02213i) q^{44} -1.78763i q^{45} -7.95866i q^{46} +9.88198i q^{47} +1.00000i q^{48} -1.80439i q^{50} +0.106095i q^{51} +6.37742 q^{52} -0.627441 q^{53} -1.00000 q^{54} +(1.82718 - 5.64031i) q^{55} -4.15162i q^{57} -7.65230 q^{58} -12.4549i q^{59} +1.78763 q^{60} +9.95024 q^{61} -1.27872 q^{62} -1.00000 q^{64} -11.4004i q^{65} +(-3.15519 - 1.02213i) q^{66} +10.8722 q^{67} -0.106095 q^{68} +7.95866i q^{69} -8.42785 q^{71} -1.00000i q^{72} +0.125008 q^{73} -4.52184i q^{74} +1.80439i q^{75} +4.15162 q^{76} -6.37742 q^{78} +10.1691i q^{79} +1.78763i q^{80} +1.00000 q^{81} +0.0321383i q^{82} +12.0657 q^{83} +0.189659i q^{85} -6.87723 q^{86} +7.65230 q^{87} +(1.02213 - 3.15519i) q^{88} -5.36009i q^{89} -1.78763 q^{90} -7.95866 q^{92} +1.27872 q^{93} +9.88198 q^{94} -7.42156i q^{95} +1.00000 q^{96} +15.7498i q^{97} +(3.15519 + 1.02213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9	$ 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9} + 4 q^{10} + 8 q^{11} - 4 q^{15} + 16 q^{16} - 20 q^{19} + 2 q^{22} + 8 q^{23} - 16 q^{24} - 20 q^{25} - 2 q^{33} + 16 q^{36} - 28 q^{37} - 4 q^{40} - 32 q^{41} - 8 q^{44} - 16 q^{54} + 14 q^{55} + 4 q^{60} + 56 q^{61} + 8 q^{62} - 16 q^{64} + 8 q^{66} + 32 q^{67} - 56 q^{71} - 88 q^{73} + 20 q^{76} + 16 q^{81} - 8 q^{83} + 24 q^{86} - 2 q^{88} - 4 q^{90} - 8 q^{92} - 8 q^{93} + 28 q^{94} + 16 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9 + 4 * q^10 + 8 * q^11 - 4 * q^15 + 16 * q^16 - 20 * q^19 + 2 * q^22 + 8 * q^23 - 16 * q^24 - 20 * q^25 - 2 * q^33 + 16 * q^36 - 28 * q^37 - 4 * q^40 - 32 * q^41 - 8 * q^44 - 16 * q^54 + 14 * q^55 + 4 * q^60 + 56 * q^61 + 8 * q^62 - 16 * q^64 + 8 * q^66 + 32 * q^67 - 56 * q^71 - 88 * q^73 + 20 * q^76 + 16 * q^81 - 8 * q^83 + 24 * q^86 - 2 * q^88 - 4 * q^90 - 8 * q^92 - 8 * q^93 + 28 * q^94 + 16 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times$.

$n$	$199$	$1079$	$2059$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$			1.78763i			0.799451i	0.916635	+	0.399726i	$0.130895\pi$
$5$			1.78763i			0.799451i	−0.916635	+	0.399726i	$0.869105\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	1.78763			0.565297
$11$	−3.15519	−	1.02213i	−0.951327	−	0.308183i
$11$	−3.15519	−	1.02213i	−0.951327	−	0.308183i
$12$		−	1.00000i		−	0.288675i
$13$	−6.37742			−1.76878			−0.884389	−	0.466751i	$-0.845424\pi$
$13$	−6.37742			−1.76878			−0.884389	+	0.466751i	$0.845424\pi$
$14$		0			0
$15$	−1.78763			−0.461563
$16$	1.00000			0.250000
$17$	0.106095			0.0257319			0.0128659	−	0.999917i	$-0.495905\pi$
$17$	0.106095			0.0257319			0.0128659	+	0.999917i	$0.495905\pi$
$18$			1.00000i			0.235702i
$19$	−4.15162			−0.952448			−0.476224	−	0.879324i	$-0.657995\pi$
$19$	−4.15162			−0.952448			−0.476224	+	0.879324i	$0.657995\pi$
$20$		−	1.78763i		−	0.399726i
$21$		0			0
$22$	−1.02213	+	3.15519i	−0.217919	+	0.672690i
$23$	7.95866			1.65950			0.829748	−	0.558138i	$-0.188484\pi$
$23$	7.95866			1.65950			0.829748	+	0.558138i	$0.188484\pi$
$24$	−1.00000			−0.204124
$25$	1.80439			0.360878
$26$			6.37742i			1.25071i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		−	7.65230i		−	1.42100i	−0.703699	−	0.710498i	$-0.748470\pi$
$29$		−	7.65230i		−	1.42100i	0.703699	−	0.710498i	$-0.251530\pi$
$30$			1.78763i			0.326375i
$31$		−	1.27872i		−	0.229665i	−0.993385	−	0.114833i	$-0.963367\pi$
$31$		−	1.27872i		−	0.229665i	0.993385	−	0.114833i	$-0.0366331\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.02213	−	3.15519i	0.177930	−	0.549249i
$34$		−	0.106095i		−	0.0181952i
$35$		0			0
$36$	1.00000			0.166667
$37$	4.52184			0.743386			0.371693	−	0.928356i	$-0.378777\pi$
$37$	4.52184			0.743386			0.371693	+	0.928356i	$0.378777\pi$
$38$			4.15162i			0.673482i
$39$		−	6.37742i		−	1.02120i
$40$	−1.78763			−0.282649
$41$	−0.0321383			−0.00501915			−0.00250958	−	0.999997i	$-0.500799\pi$
$41$	−0.0321383			−0.00501915			−0.00250958	+	0.999997i	$0.500799\pi$
$42$		0			0
$43$		−	6.87723i		−	1.04877i	−0.851482	−	0.524384i	$-0.824296\pi$
$43$		−	6.87723i		−	1.04877i	0.851482	−	0.524384i	$-0.175704\pi$
$44$	3.15519	+	1.02213i	0.475663	+	0.154092i
$45$		−	1.78763i		−	0.266484i
$46$		−	7.95866i		−	1.17344i
$47$			9.88198i			1.44144i	0.693229	+	0.720718i	$0.256188\pi$
$47$			9.88198i			1.44144i	−0.693229	+	0.720718i	$0.743812\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$		−	1.80439i		−	0.255179i
$51$			0.106095i			0.0148563i
$52$	6.37742			0.884389
$53$	−0.627441			−0.0861856			−0.0430928	−	0.999071i	$-0.513721\pi$
$53$	−0.627441			−0.0861856			−0.0430928	+	0.999071i	$0.513721\pi$
$54$	−1.00000			−0.136083
$55$	1.82718	−	5.64031i	0.246378	−	0.760539i
$56$		0			0
$57$		−	4.15162i		−	0.549896i
$58$	−7.65230			−1.00480
$59$		−	12.4549i		−	1.62150i	−0.585395	−	0.810748i	$-0.699061\pi$
$59$		−	12.4549i		−	1.62150i	0.585395	−	0.810748i	$-0.300939\pi$
$60$	1.78763			0.230782
$61$	9.95024			1.27400			0.636999	−	0.770865i	$-0.280176\pi$
$61$	9.95024			1.27400			0.636999	+	0.770865i	$0.280176\pi$
$62$	−1.27872			−0.162398
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	11.4004i		−	1.41405i
$66$	−3.15519	−	1.02213i	−0.388378	−	0.125815i
$67$	10.8722			1.32825			0.664124	−	0.747623i	$-0.268805\pi$
$67$	10.8722			1.32825			0.664124	+	0.747623i	$0.268805\pi$
$68$	−0.106095			−0.0128659
$69$			7.95866i			0.958110i
$70$		0			0
$71$	−8.42785			−1.00020			−0.500101	−	0.865967i	$-0.666704\pi$
$71$	−8.42785			−1.00020			−0.500101	+	0.865967i	$0.666704\pi$
$72$		−	1.00000i		−	0.117851i
$73$	0.125008			0.0146311			0.00731556	−	0.999973i	$-0.497671\pi$
$73$	0.125008			0.0146311			0.00731556	+	0.999973i	$0.497671\pi$
$74$		−	4.52184i		−	0.525654i
$75$			1.80439i			0.208353i
$76$	4.15162			0.476224
$77$		0			0
$78$	−6.37742			−0.722100
$79$			10.1691i			1.14412i	0.820213	+	0.572059i	$0.193855\pi$
$79$			10.1691i			1.14412i	−0.820213	+	0.572059i	$0.806145\pi$
$80$			1.78763i			0.199863i
$81$	1.00000			0.111111
$82$			0.0321383i			0.00354908i
$83$	12.0657			1.32438			0.662191	−	0.749335i	$-0.269627\pi$
$83$	12.0657			1.32438			0.662191	+	0.749335i	$0.269627\pi$
$84$		0			0
$85$			0.189659i			0.0205714i
$86$	−6.87723			−0.741591
$87$	7.65230			0.820412
$88$	1.02213	−	3.15519i	0.108959	−	0.336345i
$89$		−	5.36009i		−	0.568169i	−0.958799	−	0.284084i	$-0.908310\pi$
$89$		−	5.36009i		−	0.568169i	0.958799	−	0.284084i	$-0.0916896\pi$
$90$	−1.78763			−0.188432
$91$		0			0
$92$	−7.95866			−0.829748
$93$	1.27872			0.132597
$94$	9.88198			1.01925
$95$		−	7.42156i		−	0.761436i
$96$	1.00000			0.102062
$97$			15.7498i			1.59915i	0.600569	+	0.799573i	$0.294941\pi$
$97$			15.7498i			1.59915i	−0.600569	+	0.799573i	$0.705059\pi$
$98$		0			0
$99$	3.15519	+	1.02213i	0.317109	+	0.102728i
$100$	−1.80439			−0.180439
$101$	7.57300			0.753541			0.376771	−	0.926307i	$-0.377034\pi$
$101$	7.57300			0.753541			0.376771	+	0.926307i	$0.377034\pi$
$102$	0.106095			0.0105050
$103$		−	5.23715i		−	0.516032i	−0.966141	−	0.258016i	$-0.916931\pi$
$103$		−	5.23715i		−	0.516032i	0.966141	−	0.258016i	$-0.0830687\pi$
$104$		−	6.37742i		−	0.625357i
$105$		0			0
$106$			0.627441i			0.0609424i
$107$			4.76790i			0.460930i	0.973081	+	0.230465i	$0.0740247\pi$
$107$			4.76790i			0.460930i	−0.973081	+	0.230465i	$0.925975\pi$
$108$			1.00000i			0.0962250i
$109$		−	8.50535i		−	0.814665i	−0.913280	−	0.407332i	$-0.866459\pi$
$109$		−	8.50535i		−	0.814665i	0.913280	−	0.407332i	$-0.133541\pi$
$110$	−5.64031	−	1.82718i	−0.537783	−	0.174215i
$111$			4.52184i			0.429194i
$112$		0			0
$113$	10.3003			0.968969			0.484484	−	0.874800i	$-0.339007\pi$
$113$	10.3003			0.968969			0.484484	+	0.874800i	$0.339007\pi$
$114$	−4.15162			−0.388835
$115$			14.2271i			1.32669i
$116$			7.65230i			0.710498i
$117$	6.37742			0.589593
$118$	−12.4549			−1.14657
$119$		0			0
$120$		−	1.78763i		−	0.163187i
$121$	8.91051	+	6.45003i	0.810046	+	0.586366i
$122$		−	9.95024i		−	0.900852i
$123$		−	0.0321383i		−	0.00289781i
$124$			1.27872i			0.114833i
$125$			12.1637i			1.08796i
$126$		0			0
$127$			3.18422i			0.282553i	0.989970	+	0.141277i	$0.0451207\pi$
$127$			3.18422i			0.282553i	−0.989970	+	0.141277i	$0.954879\pi$
$128$			1.00000i			0.0883883i
$129$	6.87723			0.605506
$130$	−11.4004			−0.999885
$131$	1.08620			0.0949016			0.0474508	−	0.998874i	$-0.484890\pi$
$131$	1.08620			0.0949016			0.0474508	+	0.998874i	$0.484890\pi$
$132$	−1.02213	+	3.15519i	−0.0889649	+	0.274624i
$133$		0			0
$134$		−	10.8722i		−	0.939213i
$135$	1.78763			0.153854
$136$			0.106095i			0.00909758i
$137$	−7.58196			−0.647771			−0.323885	−	0.946096i	$-0.604989\pi$
$137$	−7.58196			−0.647771			−0.323885	+	0.946096i	$0.604989\pi$
$138$	7.95866			0.677486
$139$	1.34643			0.114203			0.0571013	−	0.998368i	$-0.481814\pi$
$139$	1.34643			0.114203			0.0571013	+	0.998368i	$0.481814\pi$
$140$		0			0
$141$	−9.88198			−0.832213
$142$			8.42785i			0.707249i
$143$	20.1220	+	6.51854i	1.68269	+	0.545108i
$144$	−1.00000			−0.0833333
$145$	13.6795			1.13602
$146$		−	0.125008i		−	0.0103458i
$147$		0			0
$148$	−4.52184			−0.371693
$149$		−	0.490157i		−	0.0401552i	−0.999798	−	0.0200776i	$-0.993609\pi$
$149$		−	0.490157i		−	0.0401552i	0.999798	−	0.0200776i	$-0.00639134\pi$
$150$	1.80439			0.147328
$151$		−	3.37323i		−	0.274509i	−0.990536	−	0.137255i	$-0.956172\pi$
$151$		−	3.37323i		−	0.274509i	0.990536	−	0.137255i	$-0.0438278\pi$
$152$		−	4.15162i		−	0.336741i
$153$	−0.106095			−0.00857728
$154$		0			0
$155$	2.28588			0.183606
$156$			6.37742i			0.510602i
$157$		−	4.06299i		−	0.324262i	−0.986769	−	0.162131i	$-0.948163\pi$
$157$		−	4.06299i		−	0.324262i	0.986769	−	0.162131i	$-0.0518367\pi$
$158$	10.1691			0.809013
$159$		−	0.627441i		−	0.0497593i
$160$	1.78763			0.141324
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	20.7414			1.62459			0.812297	−	0.583244i	$-0.198217\pi$
$163$	20.7414			1.62459			0.812297	+	0.583244i	$0.198217\pi$
$164$	0.0321383			0.00250958
$165$	5.64031	+	1.82718i	0.439098	+	0.142246i
$166$		−	12.0657i		−	0.936480i
$167$	3.42870			0.265321			0.132660	−	0.991162i	$-0.457648\pi$
$167$	3.42870			0.265321			0.132660	+	0.991162i	$0.457648\pi$
$168$		0			0
$169$	27.6715			2.12857
$170$	0.189659			0.0145461
$171$	4.15162			0.317483
$172$			6.87723i			0.524384i
$173$	−21.1524			−1.60819			−0.804094	−	0.594502i	$-0.797349\pi$
$173$	−21.1524			−1.60819			−0.804094	+	0.594502i	$0.797349\pi$
$174$		−	7.65230i		−	0.580119i
$175$		0			0
$176$	−3.15519	−	1.02213i	−0.237832	−	0.0770458i
$177$	12.4549			0.936171
$178$	−5.36009			−0.401756
$179$	−14.0866			−1.05288			−0.526441	−	0.850212i	$-0.676474\pi$
$179$	−14.0866			−1.05288			−0.526441	+	0.850212i	$0.676474\pi$
$180$			1.78763i			0.133242i
$181$		−	12.4579i		−	0.925992i	−0.886360	−	0.462996i	$-0.846775\pi$
$181$		−	12.4579i		−	0.925992i	0.886360	−	0.462996i	$-0.153225\pi$
$182$		0			0
$183$			9.95024i			0.735543i
$184$			7.95866i			0.586720i
$185$			8.08337i			0.594301i
$186$		−	1.27872i		−	0.0937604i
$187$	−0.334751	−	0.108443i	−0.0244794	−	0.00793013i
$188$		−	9.88198i		−	0.720718i
$189$		0			0
$190$	−7.42156			−0.538416
$191$	−27.2293			−1.97024			−0.985122	−	0.171854i	$-0.945024\pi$
$191$	−27.2293			−1.97024			−0.985122	+	0.171854i	$0.945024\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	26.6381i		−	1.91745i	−0.284337	−	0.958724i	$-0.591773\pi$
$193$		−	26.6381i		−	1.91745i	0.284337	−	0.958724i	$-0.408227\pi$
$194$	15.7498			1.13077
$195$	11.4004			0.816403
$196$		0			0
$197$		−	11.7764i		−	0.839031i	−0.907748	−	0.419515i	$-0.862200\pi$
$197$		−	11.7764i		−	0.839031i	0.907748	−	0.419515i	$-0.137800\pi$
$198$	1.02213	−	3.15519i	0.0726395	−	0.224230i
$199$		−	21.4008i		−	1.51706i	−0.651637	−	0.758531i	$-0.725917\pi$
$199$		−	21.4008i		−	1.51706i	0.651637	−	0.758531i	$-0.274083\pi$
$200$			1.80439i			0.127590i
$201$			10.8722i			0.766864i
$202$		−	7.57300i		−	0.532834i
$203$		0			0
$204$		−	0.106095i		−	0.00742815i
$205$		−	0.0574512i		−	0.00401257i
$206$	−5.23715			−0.364889
$207$	−7.95866			−0.553165
$208$	−6.37742			−0.442194
$209$	13.0992	+	4.24349i	0.906089	+	0.293529i
$210$		0			0
$211$		−	25.2654i		−	1.73934i	−0.493630	−	0.869672i	$-0.664330\pi$
$211$		−	25.2654i		−	1.73934i	0.493630	−	0.869672i	$-0.335670\pi$
$212$	0.627441			0.0430928
$213$		−	8.42785i		−	0.577467i
$214$	4.76790			0.325927
$215$	12.2939			0.838439
$216$	1.00000			0.0680414
$217$		0			0
$218$	−8.50535			−0.576055
$219$			0.125008i			0.00844728i
$220$	−1.82718	+	5.64031i	−0.123189	+	0.380270i
$221$	−0.676613			−0.0455139
$222$	4.52184			0.303486
$223$		−	9.80133i		−	0.656346i	−0.944618	−	0.328173i	$-0.893567\pi$
$223$		−	9.80133i		−	0.656346i	0.944618	−	0.328173i	$-0.106433\pi$
$224$		0			0
$225$	−1.80439			−0.120293
$226$		−	10.3003i		−	0.685164i
$227$	−23.2907			−1.54586			−0.772931	−	0.634491i	$-0.781210\pi$
$227$	−23.2907			−1.54586			−0.772931	+	0.634491i	$0.781210\pi$
$228$			4.15162i			0.274948i
$229$		−	6.53063i		−	0.431556i	−0.976442	−	0.215778i	$-0.930771\pi$
$229$		−	6.53063i		−	0.431556i	0.976442	−	0.215778i	$-0.0692288\pi$
$230$	14.2271			0.938109
$231$		0			0
$232$	7.65230			0.502398
$233$		−	10.8677i		−	0.711964i	−0.934493	−	0.355982i	$-0.884147\pi$
$233$		−	10.8677i		−	0.711964i	0.934493	−	0.355982i	$-0.115853\pi$
$234$		−	6.37742i		−	0.416905i
$235$	−17.6653			−1.15236
$236$			12.4549i			0.810748i
$237$	−10.1691			−0.660557
$238$		0			0
$239$			7.69148i			0.497521i	0.968565	+	0.248760i	$0.0800231\pi$
$239$			7.69148i			0.497521i	−0.968565	+	0.248760i	$0.919977\pi$
$240$	−1.78763			−0.115391
$241$	22.8135			1.46955			0.734773	−	0.678313i	$-0.237289\pi$
$241$	22.8135			1.46955			0.734773	+	0.678313i	$0.237289\pi$
$242$	6.45003	−	8.91051i	0.414624	−	0.572789i
$243$			1.00000i			0.0641500i
$244$	−9.95024			−0.636999
$245$		0			0
$246$	−0.0321383			−0.00204906
$247$	26.4766			1.68467
$248$	1.27872			0.0811988
$249$			12.0657i			0.764632i
$250$	12.1637			0.769301
$251$		−	18.1111i		−	1.14317i	−0.820544	−	0.571583i	$-0.806330\pi$
$251$		−	18.1111i		−	1.14317i	0.820544	−	0.571583i	$-0.193670\pi$
$252$		0			0
$253$	−25.1111	−	8.13478i	−1.57872	−	0.511429i
$254$	3.18422			0.199795
$255$	−0.189659			−0.0118769
$256$	1.00000			0.0625000
$257$		−	3.94247i		−	0.245924i	−0.992411	−	0.122962i	$-0.960761\pi$
$257$		−	3.94247i		−	0.245924i	0.992411	−	0.122962i	$-0.0392394\pi$
$258$		−	6.87723i		−	0.428158i
$259$		0			0
$260$			11.4004i			0.707026i
$261$			7.65230i			0.473665i
$262$		−	1.08620i		−	0.0671056i
$263$		−	2.06715i		−	0.127466i	−0.997967	−	0.0637329i	$-0.979699\pi$
$263$		−	2.06715i		−	0.127466i	0.997967	−	0.0637329i	$-0.0203006\pi$
$264$	3.15519	+	1.02213i	0.194189	+	0.0629077i
$265$		−	1.12163i		−	0.0689012i
$266$		0			0
$267$	5.36009			0.328032
$268$	−10.8722			−0.664124
$269$		−	2.80480i		−	0.171011i	−0.996338	−	0.0855057i	$-0.972749\pi$
$269$		−	2.80480i		−	0.171011i	0.996338	−	0.0855057i	$-0.0272506\pi$
$270$		−	1.78763i		−	0.108792i
$271$	9.28092			0.563776			0.281888	−	0.959447i	$-0.409039\pi$
$271$	9.28092			0.563776			0.281888	+	0.959447i	$0.409039\pi$
$272$	0.106095			0.00643296
$273$		0			0
$274$			7.58196i			0.458043i
$275$	−5.69320	−	1.84432i	−0.343313	−	0.111217i
$276$		−	7.95866i		−	0.479055i
$277$			5.23096i			0.314298i	0.987575	+	0.157149i	$0.0502303\pi$
$277$			5.23096i			0.314298i	−0.987575	+	0.157149i	$0.949770\pi$
$278$		−	1.34643i		−	0.0807534i
$279$			1.27872i			0.0765550i
$280$		0			0
$281$		−	6.87281i		−	0.409998i	−0.978762	−	0.204999i	$-0.934281\pi$
$281$		−	6.87281i		−	0.409998i	0.978762	−	0.204999i	$-0.0657190\pi$
$282$			9.88198i			0.588463i
$283$	12.0108			0.713970			0.356985	−	0.934110i	$-0.383805\pi$
$283$	12.0108			0.713970			0.356985	+	0.934110i	$0.383805\pi$
$284$	8.42785			0.500101
$285$	7.42156			0.439615
$286$	6.51854	−	20.1220i	0.385449	−	1.18984i
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	−16.9887			−0.999338
$290$		−	13.6795i		−	0.803285i
$291$	−15.7498			−0.923268
$292$	−0.125008			−0.00731556
$293$	14.1147			0.824592			0.412296	−	0.911050i	$-0.364727\pi$
$293$	14.1147			0.824592			0.412296	+	0.911050i	$0.364727\pi$
$294$		0			0
$295$	22.2648			1.29631
$296$			4.52184i			0.262827i
$297$	−1.02213	+	3.15519i	−0.0593099	+	0.183083i
$298$	−0.490157			−0.0283940
$299$	−50.7557			−2.93528
$300$		−	1.80439i		−	0.104176i
$301$		0			0
$302$	−3.37323			−0.194107
$303$			7.57300i			0.435057i
$304$	−4.15162			−0.238112
$305$			17.7873i			1.01850i
$306$			0.106095i			0.00606506i
$307$	−21.0753			−1.20283			−0.601417	−	0.798936i	$-0.705397\pi$
$307$	−21.0753			−1.20283			−0.601417	+	0.798936i	$0.705397\pi$
$308$		0			0
$309$	5.23715			0.297931
$310$		−	2.28588i		−	0.129829i
$311$			13.9495i			0.791003i	0.918465	+	0.395502i	$0.129429\pi$
$311$			13.9495i			0.791003i	−0.918465	+	0.395502i	$0.870571\pi$
$312$	6.37742			0.361050
$313$			3.98407i			0.225193i	0.993641	+	0.112596i	$0.0359167\pi$
$313$			3.98407i			0.225193i	−0.993641	+	0.112596i	$0.964083\pi$
$314$	−4.06299			−0.229288
$315$		0			0
$316$		−	10.1691i		−	0.572059i
$317$	12.2985			0.690755			0.345377	−	0.938464i	$-0.387751\pi$
$317$	12.2985			0.690755			0.345377	+	0.938464i	$0.387751\pi$
$318$	−0.627441			−0.0351851
$319$	−7.82163	+	24.1445i	−0.437927	+	1.35183i
$320$		−	1.78763i		−	0.0999314i
$321$	−4.76790			−0.266118
$322$		0			0
$323$	−0.440467			−0.0245082
$324$	−1.00000			−0.0555556
$325$	−11.5073			−0.638313
$326$		−	20.7414i		−	1.14876i
$327$	8.50535			0.470347
$328$		−	0.0321383i		−	0.00177454i
$329$		0			0
$330$	1.82718	−	5.64031i	0.100583	−	0.310489i
$331$	−31.0132			−1.70464			−0.852319	−	0.523022i	$-0.824804\pi$
$331$	−31.0132			−1.70464			−0.852319	+	0.523022i	$0.824804\pi$
$332$	−12.0657			−0.662191
$333$	−4.52184			−0.247795
$334$		−	3.42870i		−	0.187610i
$335$			19.4354i			1.06187i
$336$		0			0
$337$			13.6161i			0.741718i	0.928689	+	0.370859i	$0.120937\pi$
$337$			13.6161i			0.741718i	−0.928689	+	0.370859i	$0.879063\pi$
$338$		−	27.6715i		−	1.50513i
$339$			10.3003i			0.559434i
$340$		−	0.189659i		−	0.0102857i
$341$	−1.30702	+	4.03461i	−0.0707789	+	0.218487i
$342$		−	4.15162i		−	0.224494i
$343$		0			0
$344$	6.87723			0.370795
$345$	−14.2271			−0.765963
$346$			21.1524i			1.13716i
$347$		−	27.9100i		−	1.49829i	−0.662407	−	0.749144i	$-0.730465\pi$
$347$		−	27.9100i		−	1.49829i	0.662407	−	0.749144i	$-0.269535\pi$
$348$	−7.65230			−0.410206
$349$	27.8147			1.48888			0.744442	−	0.667687i	$-0.232715\pi$
$349$	27.8147			1.48888			0.744442	+	0.667687i	$0.232715\pi$
$350$		0			0
$351$			6.37742i			0.340401i
$352$	−1.02213	+	3.15519i	−0.0544796	+	0.168172i
$353$			21.5149i			1.14512i	0.819862	+	0.572562i	$0.194050\pi$
$353$			21.5149i			1.14512i	−0.819862	+	0.572562i	$0.805950\pi$
$354$		−	12.4549i		−	0.661973i
$355$		−	15.0659i		−	0.799612i
$356$			5.36009i			0.284084i
$357$		0			0
$358$			14.0866i			0.744500i
$359$		−	20.8942i		−	1.10276i	−0.834256	−	0.551378i	$-0.814102\pi$
$359$		−	20.8942i		−	1.10276i	0.834256	−	0.551378i	$-0.185898\pi$
$360$	1.78763			0.0942162
$361$	−1.76402			−0.0928431
$362$	−12.4579			−0.654775
$363$	−6.45003	+	8.91051i	−0.338539	+	0.467680i
$364$		0			0
$365$			0.223468i			0.0116969i
$366$	9.95024			0.520107
$367$		−	5.34315i		−	0.278910i	−0.990228	−	0.139455i	$-0.955465\pi$
$367$		−	5.34315i		−	0.278910i	0.990228	−	0.139455i	$-0.0445351\pi$
$368$	7.95866			0.414874
$369$	0.0321383			0.00167305
$370$	8.08337			0.420234
$371$		0			0
$372$	−1.27872			−0.0662986
$373$		−	25.3735i		−	1.31379i	−0.753982	−	0.656895i	$-0.771869\pi$
$373$		−	25.3735i		−	1.31379i	0.753982	−	0.656895i	$-0.228131\pi$
$374$	−0.108443	+	0.334751i	−0.00560745	+	0.0173096i
$375$	−12.1637			−0.628131
$376$	−9.88198			−0.509624
$377$			48.8019i			2.51343i
$378$		0			0
$379$	22.7532			1.16875			0.584377	−	0.811483i	$-0.301339\pi$
$379$	22.7532			1.16875			0.584377	+	0.811483i	$0.301339\pi$
$380$			7.42156i			0.380718i
$381$	−3.18422			−0.163132
$382$			27.2293i			1.39317i
$383$		−	16.5480i		−	0.845565i	−0.906231	−	0.422783i	$-0.861053\pi$
$383$		−	16.5480i		−	0.845565i	0.906231	−	0.422783i	$-0.138947\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−26.6381			−1.35584
$387$			6.87723i			0.349589i
$388$		−	15.7498i		−	0.799573i
$389$	7.39812			0.375100			0.187550	−	0.982255i	$-0.439945\pi$
$389$	7.39812			0.375100			0.187550	+	0.982255i	$0.439945\pi$
$390$		−	11.4004i		−	0.577284i
$391$	0.844376			0.0427019
$392$		0			0
$393$			1.08620i			0.0547915i
$394$	−11.7764			−0.593284
$395$	−18.1786			−0.914666
$396$	−3.15519	−	1.02213i	−0.158554	−	0.0513639i
$397$			3.86738i			0.194098i	0.995280	+	0.0970492i	$0.0309404\pi$
$397$			3.86738i			0.194098i	−0.995280	+	0.0970492i	$0.969060\pi$
$398$	−21.4008			−1.07272
$399$		0			0
$400$	1.80439			0.0902194
$401$	3.13361			0.156485			0.0782426	−	0.996934i	$-0.475069\pi$
$401$	3.13361			0.156485			0.0782426	+	0.996934i	$0.475069\pi$
$402$	10.8722			0.542255
$403$			8.15494i			0.406226i
$404$	−7.57300			−0.376771
$405$			1.78763i			0.0888279i
$406$		0			0
$407$	−14.2673	−	4.62191i	−0.707204	−	0.229099i
$408$	−0.106095			−0.00525249
$409$	20.1022			0.993992			0.496996	−	0.867753i	$-0.334436\pi$
$409$	20.1022			0.993992			0.496996	+	0.867753i	$0.334436\pi$
$410$	−0.0574512			−0.00283731
$411$		−	7.58196i		−	0.373991i
$412$			5.23715i			0.258016i
$413$		0			0
$414$			7.95866i			0.391147i
$415$			21.5690i			1.05878i
$416$			6.37742i			0.312679i
$417$			1.34643i			0.0659349i
$418$	4.24349	−	13.0992i	0.207556	−	0.640702i
$419$		−	2.63035i		−	0.128501i	−0.997934	−	0.0642506i	$-0.979534\pi$
$419$		−	2.63035i		−	0.128501i	0.997934	−	0.0642506i	$-0.0204657\pi$
$420$		0			0
$421$	24.9232			1.21468			0.607341	−	0.794441i	$-0.292236\pi$
$421$	24.9232			1.21468			0.607341	+	0.794441i	$0.292236\pi$
$422$	−25.2654			−1.22990
$423$		−	9.88198i		−	0.480478i
$424$		−	0.627441i		−	0.0304712i
$425$	0.191437			0.00928605
$426$	−8.42785			−0.408331
$427$		0			0
$428$		−	4.76790i		−	0.230465i
$429$	−6.51854	+	20.1220i	−0.314718	+	0.971499i
$430$		−	12.2939i		−	0.592866i
$431$		−	13.6456i		−	0.657287i	−0.944454	−	0.328644i	$-0.893409\pi$
$431$		−	13.6456i		−	0.657287i	0.944454	−	0.328644i	$-0.106591\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	10.4001i		−	0.499795i	−0.968272	−	0.249897i	$-0.919603\pi$
$433$		−	10.4001i		−	0.499795i	0.968272	−	0.249897i	$-0.0803969\pi$
$434$		0			0
$435$			13.6795i			0.655879i
$436$			8.50535i			0.407332i
$437$	−33.0414			−1.58058
$438$	0.125008			0.00597313
$439$	23.3239			1.11319			0.556594	−	0.830785i	$-0.312108\pi$
$439$	23.3239			1.11319			0.556594	+	0.830785i	$0.312108\pi$
$440$	5.64031	+	1.82718i	0.268891	+	0.0871076i
$441$		0			0
$442$			0.676613i			0.0321832i
$443$	9.83451			0.467252			0.233626	−	0.972327i	$-0.424941\pi$
$443$	9.83451			0.467252			0.233626	+	0.972327i	$0.424941\pi$
$444$		−	4.52184i		−	0.214597i
$445$	9.58185			0.454223
$446$	−9.80133			−0.464107
$447$	0.490157			0.0231836
$448$		0			0
$449$	9.26223			0.437112			0.218556	−	0.975824i	$-0.429865\pi$
$449$	9.26223			0.437112			0.218556	+	0.975824i	$0.429865\pi$
$450$			1.80439i			0.0850597i
$451$	0.101403	+	0.0328494i	0.00477486	+	0.00154682i
$452$	−10.3003			−0.484484
$453$	3.37323			0.158488
$454$			23.2907i			1.09309i
$455$		0			0
$456$	4.15162			0.194418
$457$			2.55635i			0.119581i	0.998211	+	0.0597906i	$0.0190433\pi$
$457$			2.55635i			0.119581i	−0.998211	+	0.0597906i	$0.980957\pi$
$458$	−6.53063			−0.305156
$459$		−	0.106095i		−	0.00495210i
$460$		−	14.2271i		−	0.663343i
$461$	−29.5798			−1.37767			−0.688834	−	0.724919i	$-0.741877\pi$
$461$	−29.5798			−1.37767			−0.688834	+	0.724919i	$0.741877\pi$
$462$		0			0
$463$	−9.24447			−0.429627			−0.214813	−	0.976655i	$-0.568914\pi$
$463$	−9.24447			−0.429627			−0.214813	+	0.976655i	$0.568914\pi$
$464$		−	7.65230i		−	0.355249i
$465$			2.28588i			0.106005i
$466$	−10.8677			−0.503434
$467$		−	11.6497i		−	0.539083i	−0.962989	−	0.269541i	$-0.913128\pi$
$467$		−	11.6497i		−	0.539083i	0.962989	−	0.269541i	$-0.0868721\pi$
$468$	−6.37742			−0.294796
$469$		0			0
$470$			17.6653i			0.814840i
$471$	4.06299			0.187213
$472$	12.4549			0.573285
$473$	−7.02941	+	21.6990i	−0.323213	+	0.997721i
$474$			10.1691i			0.467084i
$475$	−7.49114			−0.343717
$476$		0			0
$477$	0.627441			0.0287285
$478$	7.69148			0.351800
$479$	−10.0552			−0.459432			−0.229716	−	0.973258i	$-0.573780\pi$
$479$	−10.0552			−0.459432			−0.229716	+	0.973258i	$0.573780\pi$
$480$			1.78763i			0.0815936i
$481$	−28.8377			−1.31489
$482$		−	22.8135i		−	1.03913i
$483$		0			0
$484$	−8.91051	−	6.45003i	−0.405023	−	0.293183i
$485$	−28.1547			−1.27844
$486$	1.00000			0.0453609
$487$	17.3146			0.784601			0.392300	−	0.919837i	$-0.371679\pi$
$487$	17.3146			0.784601			0.392300	+	0.919837i	$0.371679\pi$
$488$			9.95024i			0.450426i
$489$			20.7414i			0.937960i
$490$		0			0
$491$			8.44002i			0.380893i	0.981698	+	0.190446i	$0.0609935\pi$
$491$			8.44002i			0.380893i	−0.981698	+	0.190446i	$0.939006\pi$
$492$			0.0321383i			0.00144891i
$493$		−	0.811871i		−	0.0365648i
$494$		−	26.4766i		−	1.19124i
$495$	−1.82718	+	5.64031i	−0.0821259	+	0.253513i
$496$		−	1.27872i		−	0.0574163i
$497$		0			0
$498$	12.0657			0.540677
$499$	19.0719			0.853778			0.426889	−	0.904304i	$-0.359610\pi$
$499$	19.0719			0.853778			0.426889	+	0.904304i	$0.359610\pi$
$500$		−	12.1637i		−	0.543978i
$501$			3.42870i			0.153183i
$502$	−18.1111			−0.808340
$503$	−3.32018			−0.148039			−0.0740197	−	0.997257i	$-0.523583\pi$
$503$	−3.32018			−0.148039			−0.0740197	+	0.997257i	$0.523583\pi$
$504$		0			0
$505$			13.5377i			0.602419i
$506$	−8.13478	+	25.1111i	−0.361635	+	1.11633i
$507$			27.6715i			1.22893i
$508$		−	3.18422i		−	0.141277i
$509$			4.51879i			0.200292i	0.994973	+	0.100146i	$0.0319309\pi$
$509$			4.51879i			0.200292i	−0.994973	+	0.100146i	$0.968069\pi$
$510$			0.189659i			0.00839822i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$			4.15162i			0.183299i
$514$	−3.94247			−0.173895
$515$	9.36207			0.412542
$516$	−6.87723			−0.302753
$517$	10.1007	−	31.1796i	0.444226	−	1.37128i
$518$		0			0
$519$		−	21.1524i		−	0.928488i
$520$	11.4004			0.499943
$521$			9.36122i			0.410122i	0.978749	+	0.205061i	$0.0657393\pi$
$521$			9.36122i			0.410122i	−0.978749	+	0.205061i	$0.934261\pi$
$522$	7.65230			0.334932
$523$	17.4095			0.761266			0.380633	−	0.924726i	$-0.375706\pi$
$523$	17.4095			0.761266			0.380633	+	0.924726i	$0.375706\pi$
$524$	−1.08620			−0.0474508
$525$		0			0
$526$	−2.06715			−0.0901320
$527$		−	0.135666i		−	0.00590971i
$528$	1.02213	−	3.15519i	0.0444824	−	0.137312i
$529$	40.3403			1.75393
$530$	−1.12163			−0.0487205
$531$			12.4549i			0.540499i
$532$		0			0
$533$	0.204959			0.00887777
$534$		−	5.36009i		−	0.231954i
$535$	−8.52322			−0.368491
$536$			10.8722i			0.469606i
$537$		−	14.0866i		−	0.607881i
$538$	−2.80480			−0.120923
$539$		0			0
$540$	−1.78763			−0.0769272
$541$			39.3722i			1.69274i	0.532595	+	0.846370i	$0.321217\pi$
$541$			39.3722i			1.69274i	−0.532595	+	0.846370i	$0.678783\pi$
$542$		−	9.28092i		−	0.398650i
$543$	12.4579			0.534621
$544$		−	0.106095i		−	0.00454879i
$545$	15.2044			0.651285
$546$		0			0
$547$		−	20.3539i		−	0.870271i	−0.900365	−	0.435135i	$-0.856701\pi$
$547$		−	20.3539i		−	0.870271i	0.900365	−	0.435135i	$-0.143299\pi$
$548$	7.58196			0.323885
$549$	−9.95024			−0.424666
$550$	−1.84432	+	5.69320i	−0.0786420	+	0.242759i
$551$			31.7695i			1.35342i
$552$	−7.95866			−0.338743
$553$		0			0
$554$	5.23096			0.222242
$555$	−8.08337			−0.343120
$556$	−1.34643			−0.0571013
$557$			13.0285i			0.552035i	0.961153	+	0.276017i	$0.0890148\pi$
$557$			13.0285i			0.552035i	−0.961153	+	0.276017i	$0.910985\pi$
$558$	1.27872			0.0541326
$559$			43.8590i			1.85504i
$560$		0			0
$561$	0.108443	−	0.334751i	0.00457846	−	0.0141332i
$562$	−6.87281			−0.289912
$563$	−33.5633			−1.41452			−0.707262	−	0.706951i	$-0.750070\pi$
$563$	−33.5633			−1.41452			−0.707262	+	0.706951i	$0.750070\pi$
$564$	9.88198			0.416107
$565$			18.4131i			0.774643i
$566$		−	12.0108i		−	0.504853i
$567$		0			0
$568$		−	8.42785i		−	0.353625i
$569$		−	5.54679i		−	0.232534i	−0.993218	−	0.116267i	$-0.962907\pi$
$569$		−	5.54679i		−	0.232534i	0.993218	−	0.116267i	$-0.0370928\pi$
$570$		−	7.42156i		−	0.310855i
$571$			37.0923i			1.55226i	0.630571	+	0.776132i	$0.282821\pi$
$571$			37.0923i			1.55226i	−0.630571	+	0.776132i	$0.717179\pi$
$572$	−20.1220	−	6.51854i	−0.841343	−	0.272554i
$573$		−	27.2293i		−	1.13752i
$574$		0			0
$575$	14.3605			0.598875
$576$	1.00000			0.0416667
$577$		−	3.08219i		−	0.128313i	−0.997940	−	0.0641567i	$-0.979564\pi$
$577$		−	3.08219i		−	0.128313i	0.997940	−	0.0641567i	$-0.0204357\pi$
$578$			16.9887i			0.706639i
$579$	26.6381			1.10704
$580$	−13.6795			−0.568008
$581$		0			0
$582$			15.7498i			0.652849i
$583$	1.97970	+	0.641325i	0.0819907	+	0.0265610i
$584$			0.125008i			0.00517288i
$585$			11.4004i			0.471350i
$586$		−	14.1147i		−	0.583075i
$587$		−	46.9255i		−	1.93682i	−0.249356	−	0.968412i	$-0.580219\pi$
$587$		−	46.9255i		−	1.93682i	0.249356	−	0.968412i	$-0.419781\pi$
$588$		0			0
$589$			5.30877i			0.218744i
$590$		−	22.2648i		−	0.916627i
$591$	11.7764			0.484415
$592$	4.52184			0.185847
$593$	5.14958			0.211468			0.105734	−	0.994394i	$-0.466281\pi$
$593$	5.14958			0.211468			0.105734	+	0.994394i	$0.466281\pi$
$594$	3.15519	+	1.02213i	0.129459	+	0.0419384i
$595$		0			0
$596$			0.490157i			0.0200776i
$597$	21.4008			0.875876
$598$			50.7557i			2.07556i
$599$	−35.1462			−1.43603			−0.718017	−	0.696026i	$-0.754950\pi$
$599$	−35.1462			−1.43603			−0.718017	+	0.696026i	$0.754950\pi$
$600$	−1.80439			−0.0736639
$601$	−42.8385			−1.74742			−0.873710	−	0.486447i	$-0.838293\pi$
$601$	−42.8385			−1.74742			−0.873710	+	0.486447i	$0.838293\pi$
$602$		0			0
$603$	−10.8722			−0.442749
$604$			3.37323i			0.137255i
$605$	−11.5302	+	15.9287i	−0.468771	+	0.647592i
$606$	7.57300			0.307632
$607$	−16.6655			−0.676432			−0.338216	−	0.941069i	$-0.609823\pi$
$607$	−16.6655			−0.676432			−0.338216	+	0.941069i	$0.609823\pi$
$608$			4.15162i			0.168371i
$609$		0			0
$610$	17.7873			0.720187
$611$		−	63.0215i		−	2.54958i
$612$	0.106095			0.00428864
$613$		−	11.8955i		−	0.480456i	−0.970717	−	0.240228i	$-0.922778\pi$
$613$		−	11.8955i		−	0.480456i	0.970717	−	0.240228i	$-0.0772222\pi$
$614$			21.0753i			0.850531i
$615$	0.0574512			0.00231666
$616$		0			0
$617$	−0.0716192			−0.00288328			−0.00144164	−	0.999999i	$-0.500459\pi$
$617$	−0.0716192			−0.00288328			−0.00144164	+	0.999999i	$0.500459\pi$
$618$		−	5.23715i		−	0.210669i
$619$		−	29.2187i		−	1.17440i	−0.809442	−	0.587200i	$-0.800230\pi$
$619$		−	29.2187i		−	1.17440i	0.809442	−	0.587200i	$-0.199770\pi$
$620$	−2.28588			−0.0918030
$621$		−	7.95866i		−	0.319370i
$622$	13.9495			0.559324
$623$		0			0
$624$		−	6.37742i		−	0.255301i
$625$	−12.7222			−0.508889
$626$	3.98407			0.159235
$627$	−4.24349	+	13.0992i	−0.169469	+	0.523131i
$628$			4.06299i			0.162131i
$629$	0.479746			0.0191287
$630$		0			0
$631$	−43.3663			−1.72638			−0.863192	−	0.504876i	$-0.831538\pi$
$631$	−43.3663			−1.72638			−0.863192	+	0.504876i	$0.831538\pi$
$632$	−10.1691			−0.404507
$633$	25.2654			1.00421
$634$		−	12.2985i		−	0.488438i
$635$	−5.69219			−0.225888
$636$			0.627441i			0.0248796i
$637$		0			0
$638$	24.1445	+	7.82163i	0.955889	+	0.309661i
$639$	8.42785			0.333401
$640$	−1.78763			−0.0706622
$641$	−5.45490			−0.215456			−0.107728	−	0.994180i	$-0.534357\pi$
$641$	−5.45490			−0.215456			−0.107728	+	0.994180i	$0.534357\pi$
$642$			4.76790i			0.188174i
$643$			4.26488i			0.168190i	0.996458	+	0.0840952i	$0.0268000\pi$
$643$			4.26488i			0.168190i	−0.996458	+	0.0840952i	$0.973200\pi$
$644$		0			0
$645$			12.2939i			0.484073i
$646$			0.440467i			0.0173299i
$647$		−	23.7320i		−	0.933003i	−0.884520	−	0.466501i	$-0.845514\pi$
$647$		−	23.7320i		−	0.933003i	0.884520	−	0.466501i	$-0.154486\pi$
$648$			1.00000i			0.0392837i
$649$	−12.7306	+	39.2978i	−0.499718	+	1.54257i
$650$			11.5073i			0.451355i
$651$		0			0
$652$	−20.7414			−0.812297
$653$	33.6185			1.31559			0.657797	−	0.753195i	$-0.271489\pi$
$653$	33.6185			1.31559			0.657797	+	0.753195i	$0.271489\pi$
$654$		−	8.50535i		−	0.332586i
$655$			1.94172i			0.0758692i
$656$	−0.0321383			−0.00125479
$657$	−0.125008			−0.00487704
$658$		0			0
$659$		−	28.9405i		−	1.12736i	−0.825993	−	0.563681i	$-0.809385\pi$
$659$		−	28.9405i		−	1.12736i	0.825993	−	0.563681i	$-0.190615\pi$
$660$	−5.64031	−	1.82718i	−0.219549	−	0.0711231i
$661$			0.598886i			0.0232940i	0.999932	+	0.0116470i	$0.00370743\pi$
$661$			0.598886i			0.0232940i	−0.999932	+	0.0116470i	$0.996293\pi$
$662$			31.0132i			1.20536i
$663$		−	0.676613i		−	0.0262775i
$664$			12.0657i			0.468240i
$665$		0			0
$666$			4.52184i			0.175218i
$667$		−	60.9020i		−	2.35814i
$668$	−3.42870			−0.132660
$669$	9.80133			0.378941
$670$	19.4354			0.750855
$671$	−31.3949	−	10.1704i	−1.21199	−	0.392625i
$672$		0			0
$673$			36.3353i			1.40062i	0.713837	+	0.700312i	$0.246956\pi$
$673$			36.3353i			1.40062i	−0.713837	+	0.700312i	$0.753044\pi$
$674$	13.6161			0.524474
$675$		−	1.80439i		−	0.0694510i
$676$	−27.6715			−1.06429
$677$	19.9914			0.768332			0.384166	−	0.923264i	$-0.374489\pi$
$677$	19.9914			0.768332			0.384166	+	0.923264i	$0.374489\pi$
$678$	10.3003			0.395580
$679$		0			0
$680$	−0.189659			−0.00727307
$681$		−	23.2907i		−	0.892503i
$682$	4.03461	+	1.30702i	0.154493	+	0.0500483i
$683$	−22.0325			−0.843049			−0.421524	−	0.906817i	$-0.638505\pi$
$683$	−22.0325			−0.843049			−0.421524	+	0.906817i	$0.638505\pi$
$684$	−4.15162			−0.158741
$685$		−	13.5537i		−	0.517861i
$686$		0			0
$687$	6.53063			0.249159
$688$		−	6.87723i		−	0.262192i
$689$	4.00145			0.152443
$690$			14.2271i			0.541617i
$691$			11.4103i			0.434068i	0.976164	+	0.217034i	$0.0696383\pi$
$691$			11.4103i			0.434068i	−0.976164	+	0.217034i	$0.930362\pi$
$692$	21.1524			0.804094
$693$		0			0
$694$	−27.9100			−1.05945
$695$			2.40691i			0.0912994i
$696$			7.65230i			0.290060i
$697$	−0.00340971			−0.000129152
$698$		−	27.8147i		−	1.05280i
$699$	10.8677			0.411052
$700$		0			0
$701$		−	1.92874i		−	0.0728474i	−0.999336	−	0.0364237i	$-0.988403\pi$
$701$		−	1.92874i		−	0.0728474i	0.999336	−	0.0364237i	$-0.0115966\pi$
$702$	6.37742			0.240700
$703$	−18.7730			−0.708037
$704$	3.15519	+	1.02213i	0.118916	+	0.0385229i
$705$		−	17.6653i		−	0.665314i
$706$	21.5149			0.809725
$707$		0			0
$708$	−12.4549			−0.468086
$709$	19.0032			0.713681			0.356841	−	0.934165i	$-0.383854\pi$
$709$	19.0032			0.713681			0.356841	+	0.934165i	$0.383854\pi$
$710$	−15.0659			−0.565411
$711$		−	10.1691i		−	0.381373i
$712$	5.36009			0.200878
$713$		−	10.1769i		−	0.381128i
$714$		0			0
$715$	−11.6527	+	35.9706i	−0.435787	+	1.34523i
$716$	14.0866			0.526441
$717$	−7.69148			−0.287244
$718$	−20.8942			−0.779766
$719$			20.6690i			0.770822i	0.922745	+	0.385411i	$0.125940\pi$
$719$			20.6690i			0.770822i	−0.922745	+	0.385411i	$0.874060\pi$
$720$		−	1.78763i		−	0.0666209i
$721$		0			0
$722$			1.76402i			0.0656500i
$723$			22.8135i			0.848443i
$724$			12.4579i			0.462996i
$725$		−	13.8077i		−	0.512806i
$726$	8.91051	+	6.45003i	0.330700	+	0.239383i
$727$			1.72185i			0.0638600i	0.999490	+	0.0319300i	$0.0101654\pi$
$727$			1.72185i			0.0638600i	−0.999490	+	0.0319300i	$0.989835\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	0.223468			0.00827093
$731$		−	0.729641i		−	0.0269867i
$732$		−	9.95024i		−	0.367771i
$733$	1.19425			0.0441106			0.0220553	−	0.999757i	$-0.492979\pi$
$733$	1.19425			0.0441106			0.0220553	+	0.999757i	$0.492979\pi$
$734$	−5.34315			−0.197219
$735$		0			0
$736$		−	7.95866i		−	0.293360i
$737$	−34.3038	−	11.1128i	−1.26360	−	0.409344i
$738$		−	0.0321383i		−	0.00118303i
$739$			12.4376i			0.457525i	0.973482	+	0.228763i	$0.0734680\pi$
$739$			12.4376i			0.457525i	−0.973482	+	0.228763i	$0.926532\pi$
$740$		−	8.08337i		−	0.297151i
$741$			26.4766i			0.972644i
$742$		0			0
$743$			19.1754i			0.703479i	0.936098	+	0.351739i	$0.114410\pi$
$743$			19.1754i			0.703479i	−0.936098	+	0.351739i	$0.885590\pi$
$744$			1.27872i			0.0468802i
$745$	0.876218			0.0321022
$746$	−25.3735			−0.928990
$747$	−12.0657			−0.441461
$748$	0.334751	+	0.108443i	0.0122397	+	0.00396506i
$749$		0			0
$750$			12.1637i			0.444156i
$751$	45.9739			1.67761			0.838807	−	0.544430i	$-0.183254\pi$
$751$	45.9739			1.67761			0.838807	+	0.544430i	$0.183254\pi$
$752$			9.88198i			0.360359i
$753$	18.1111			0.660007
$754$	48.8019			1.77726
$755$	6.03007			0.219457
$756$		0			0
$757$	32.1348			1.16796			0.583979	−	0.811768i	$-0.301495\pi$
$757$	32.1348			1.16796			0.583979	+	0.811768i	$0.301495\pi$
$758$		−	22.7532i		−	0.826433i
$759$	8.13478	−	25.1111i	0.295274	−	0.911476i
$760$	7.42156			0.269208
$761$	−20.4998			−0.743116			−0.371558	−	0.928410i	$-0.621176\pi$
$761$	−20.4998			−0.743116			−0.371558	+	0.928410i	$0.621176\pi$
$762$			3.18422i			0.115352i
$763$		0			0
$764$	27.2293			0.985122
$765$		−	0.189659i		−	0.00685712i
$766$	−16.5480			−0.597905
$767$			79.4304i			2.86807i
$768$			1.00000i			0.0360844i
$769$	14.3312			0.516796			0.258398	−	0.966039i	$-0.416805\pi$
$769$	14.3312			0.516796			0.258398	+	0.966039i	$0.416805\pi$
$770$		0			0
$771$	3.94247			0.141984
$772$			26.6381i			0.958724i
$773$			29.5740i			1.06370i	0.846838	+	0.531851i	$0.178503\pi$
$773$			29.5740i			1.06370i	−0.846838	+	0.531851i	$0.821497\pi$
$774$	6.87723			0.247197
$775$		−	2.30731i		−	0.0828810i
$776$	−15.7498			−0.565384
$777$		0			0
$778$		−	7.39812i		−	0.265235i
$779$	0.133426			0.00478048
$780$	−11.4004			−0.408201
$781$	26.5915	+	8.61435i	0.951519	+	0.308246i
$782$		−	0.844376i		−	0.0301948i
$783$	−7.65230			−0.273471
$784$		0			0
$785$	7.26311			0.259232
$786$	1.08620			0.0387434
$787$	26.6975			0.951662			0.475831	−	0.879537i	$-0.342147\pi$
$787$	26.6975			0.951662			0.475831	+	0.879537i	$0.342147\pi$
$788$			11.7764i			0.419515i
$789$	2.06715			0.0735925
$790$			18.1786i			0.646767i
$791$		0			0
$792$	−1.02213	+	3.15519i	−0.0363198	+	0.112115i
$793$	−63.4568			−2.25342
$794$	3.86738			0.137248
$795$	1.12163			0.0397801
$796$			21.4008i			0.758531i
$797$			47.2556i			1.67388i	0.547294	+	0.836940i	$0.315658\pi$
$797$			47.2556i			1.67388i	−0.547294	+	0.836940i	$0.684342\pi$
$798$		0			0
$799$			1.04843i			0.0370908i
$800$		−	1.80439i		−	0.0637948i
$801$			5.36009i			0.189390i
$802$		−	3.13361i		−	0.110652i
$803$	−0.394426	−	0.127775i	−0.0139190	−	0.00450907i
$804$		−	10.8722i		−	0.383432i
$805$		0			0
$806$	8.15494			0.287245
$807$	2.80480			0.0987335
$808$			7.57300i			0.266417i
$809$		−	21.0775i		−	0.741044i	−0.928824	−	0.370522i	$-0.879179\pi$
$809$		−	21.0775i		−	0.741044i	0.928824	−	0.370522i	$-0.120821\pi$
$810$	1.78763			0.0628108
$811$	−38.7457			−1.36055			−0.680273	−	0.732959i	$-0.738139\pi$
$811$	−38.7457			−1.36055			−0.680273	+	0.732959i	$0.738139\pi$
$812$		0			0
$813$			9.28092i			0.325496i
$814$	−4.62191	+	14.2673i	−0.161998	+	0.500068i
$815$			37.0779i			1.29878i
$816$			0.106095i			0.00371407i
$817$			28.5517i			0.998897i
$818$		−	20.1022i		−	0.702858i
$819$		0			0
$820$			0.0574512i			0.00200628i
$821$			42.8317i			1.49483i	0.664355	+	0.747417i	$0.268706\pi$
$821$			42.8317i			1.49483i	−0.664355	+	0.747417i	$0.731294\pi$
$822$	−7.58196			−0.264451
$823$	33.8619			1.18035			0.590176	−	0.807275i	$-0.299059\pi$
$823$	33.8619			1.18035			0.590176	+	0.807275i	$0.299059\pi$
$824$	5.23715			0.182445
$825$	1.84432	−	5.69320i	0.0642109	−	0.198212i
$826$		0			0
$827$			15.2572i			0.530544i	0.964174	+	0.265272i	$0.0854618\pi$
$827$			15.2572i			0.530544i	−0.964174	+	0.265272i	$0.914538\pi$
$828$	7.95866			0.276583
$829$			17.2483i			0.599058i	0.954087	+	0.299529i	$0.0968295\pi$
$829$			17.2483i			0.599058i	−0.954087	+	0.299529i	$0.903171\pi$
$830$	21.5690			0.748670
$831$	−5.23096			−0.181460
$832$	6.37742			0.221097
$833$		0			0
$834$	1.34643			0.0466230
$835$			6.12924i			0.212111i
$836$	−13.0992	−	4.24349i	−0.453045	−	0.146764i
$837$	−1.27872			−0.0441991
$838$	−2.63035			−0.0908640
$839$		−	9.80607i		−	0.338543i	−0.985569	−	0.169272i	$-0.945859\pi$
$839$		−	9.80607i		−	0.338543i	0.985569	−	0.169272i	$-0.0541415\pi$
$840$		0			0
$841$	−29.5576			−1.01923
$842$		−	24.9232i		−	0.858910i
$843$	6.87281			0.236712
$844$			25.2654i			0.869672i
$845$			49.4663i			1.70169i
$846$	−9.88198			−0.339750
$847$		0			0
$848$	−0.627441			−0.0215464
$849$			12.0108i			0.412211i
$850$		−	0.191437i		−	0.00656623i
$851$	35.9878			1.23365
$852$			8.42785i			0.288733i
$853$	58.0237			1.98669			0.993346	−	0.115168i	$-0.0367407\pi$
$853$	58.0237			1.98669			0.993346	+	0.115168i	$0.0367407\pi$
$854$		0			0
$855$			7.42156i			0.253812i
$856$	−4.76790			−0.162963
$857$	41.0867			1.40350			0.701748	−	0.712426i	$-0.252403\pi$
$857$	41.0867			1.40350			0.701748	+	0.712426i	$0.252403\pi$
$858$	20.1220	+	6.51854i	0.686954	+	0.222539i
$859$		−	26.5613i		−	0.906261i	−0.891444	−	0.453130i	$-0.850307\pi$
$859$		−	26.5613i		−	0.906261i	0.891444	−	0.453130i	$-0.149693\pi$
$860$	−12.2939			−0.419219
$861$		0			0
$862$	−13.6456			−0.464772
$863$	9.08791			0.309356			0.154678	−	0.987965i	$-0.450566\pi$
$863$	9.08791			0.309356			0.154678	+	0.987965i	$0.450566\pi$
$864$	−1.00000			−0.0340207
$865$		−	37.8126i		−	1.28567i
$866$	−10.4001			−0.353408
$867$		−	16.9887i		−	0.576968i
$868$		0			0
$869$	10.3942	−	32.0856i	0.352598	−	1.08843i
$870$	13.6795			0.463777
$871$	−69.3364			−2.34937
$872$	8.50535			0.288028
$873$		−	15.7498i		−	0.533049i
$874$			33.0414i			1.11764i
$875$		0			0
$876$		−	0.125008i		−	0.00422364i
$877$		−	4.56656i		−	0.154202i	−0.997023	−	0.0771009i	$-0.975434\pi$
$877$		−	4.56656i		−	0.154202i	0.997023	−	0.0771009i	$-0.0245664\pi$
$878$		−	23.3239i		−	0.787143i
$879$			14.1147i			0.476078i
$880$	1.82718	−	5.64031i	0.0615944	−	0.190135i
$881$		−	35.4288i		−	1.19363i	−0.802380	−	0.596813i	$-0.796433\pi$
$881$		−	35.4288i		−	1.19363i	0.802380	−	0.596813i	$-0.203567\pi$
$882$		0			0
$883$	25.2987			0.851368			0.425684	−	0.904872i	$-0.360033\pi$
$883$	25.2987			0.851368			0.425684	+	0.904872i	$0.360033\pi$
$884$	0.676613			0.0227570
$885$			22.2648i			0.748423i
$886$		−	9.83451i		−	0.330397i
$887$	−44.9662			−1.50982			−0.754909	−	0.655830i	$-0.772319\pi$
$887$	−44.9662			−1.50982			−0.754909	+	0.655830i	$0.772319\pi$
$888$	−4.52184			−0.151743
$889$		0			0
$890$		−	9.58185i		−	0.321184i
$891$	−3.15519	−	1.02213i	−0.105703	−	0.0342426i
$892$			9.80133i			0.328173i
$893$		−	41.0263i		−	1.37289i
$894$		−	0.490157i		−	0.0163933i
$895$		−	25.1816i		−	0.841727i
$896$		0			0
$897$		−	50.7557i		−	1.69468i
$898$		−	9.26223i		−	0.309085i
$899$	−9.78515			−0.326353
$900$	1.80439			0.0601463
$901$	−0.0665684			−0.00221772
$902$	0.0328494	−	0.101403i	0.00109377	−	0.00337633i
$903$		0			0
$904$			10.3003i			0.342582i
$905$	22.2702			0.740285
$906$		−	3.37323i		−	0.112068i
$907$	−17.2613			−0.573151			−0.286576	−	0.958058i	$-0.592517\pi$
$907$	−17.2613			−0.573151			−0.286576	+	0.958058i	$0.592517\pi$
$908$	23.2907			0.772931
$909$	−7.57300			−0.251180
$910$		0			0
$911$	−18.9606			−0.628194			−0.314097	−	0.949391i	$-0.601702\pi$
$911$	−18.9606			−0.628194			−0.314097	+	0.949391i	$0.601702\pi$
$912$		−	4.15162i		−	0.137474i
$913$	−38.0696	−	12.3327i	−1.25992	−	0.408153i
$914$	2.55635			0.0845566
$915$	−17.7873			−0.588030
$916$			6.53063i			0.215778i
$917$		0			0
$918$	−0.106095			−0.00350166
$919$		−	35.7234i		−	1.17841i	−0.807985	−	0.589203i	$-0.799442\pi$
$919$		−	35.7234i		−	1.17841i	0.807985	−	0.589203i	$-0.200558\pi$
$920$	−14.2271			−0.469054
$921$		−	21.0753i		−	0.694456i
$922$			29.5798i			0.974158i
$923$	53.7479			1.76913
$924$		0			0
$925$	8.15916			0.268272
$926$			9.24447i			0.303792i
$927$			5.23715i			0.172011i
$928$	−7.65230			−0.251199
$929$			40.5119i			1.32915i	0.747220	+	0.664577i	$0.231388\pi$
$929$			40.5119i			1.32915i	−0.747220	+	0.664577i	$0.768612\pi$
$930$	2.28588			0.0749568
$931$		0			0
$932$			10.8677i			0.355982i
$933$	−13.9495			−0.456686
$934$	−11.6497			−0.381189
$935$	0.193855	−	0.598410i	0.00633975	−	0.0195701i
$936$			6.37742i			0.208452i
$937$	−36.2513			−1.18428			−0.592140	−	0.805835i	$-0.701717\pi$
$937$	−36.2513			−1.18428			−0.592140	+	0.805835i	$0.701717\pi$
$938$		0			0
$939$	−3.98407			−0.130015
$940$	17.6653			0.576179
$941$	−44.7796			−1.45977			−0.729887	−	0.683568i	$-0.760427\pi$
$941$	−44.7796			−1.45977			−0.729887	+	0.683568i	$0.760427\pi$
$942$		−	4.06299i		−	0.132379i
$943$	−0.255778			−0.00832927
$944$		−	12.4549i		−	0.405374i
$945$		0			0
$946$	21.6990	+	7.02941i	0.705495	+	0.228546i
$947$	−14.7070			−0.477912			−0.238956	−	0.971030i	$-0.576805\pi$
$947$	−14.7070			−0.477912			−0.238956	+	0.971030i	$0.576805\pi$
$948$	10.1691			0.330278
$949$	−0.797230			−0.0258792
$950$			7.49114i			0.243045i
$951$			12.2985i			0.398808i
$952$		0			0
$953$			23.4615i			0.759991i	0.924988	+	0.379996i	$0.124074\pi$
$953$			23.4615i			0.759991i	−0.924988	+	0.379996i	$0.875926\pi$
$954$		−	0.627441i		−	0.0203141i
$955$		−	48.6759i		−	1.57511i
$956$		−	7.69148i		−	0.248760i
$957$	−24.1445	−	7.82163i	−0.780480	−	0.252837i
$958$			10.0552i			0.324868i
$959$		0			0
$960$	1.78763			0.0576954
$961$	29.3649			0.947254
$962$			28.8377i			0.929764i
$963$		−	4.76790i		−	0.153643i
$964$	−22.8135			−0.734773
$965$	47.6189			1.53291
$966$		0			0
$967$			57.3317i			1.84366i	0.387589	+	0.921832i	$0.373308\pi$
$967$			57.3317i			1.84366i	−0.387589	+	0.921832i	$0.626692\pi$
$968$	−6.45003	+	8.91051i	−0.207312	+	0.286395i
$969$		−	0.440467i		−	0.0141498i
$970$			28.1547i			0.903993i
$971$		−	48.6951i		−	1.56270i	−0.624092	−	0.781351i	$-0.714531\pi$
$971$		−	48.6951i		−	1.56270i	0.624092	−	0.781351i	$-0.285469\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$		−	17.3146i		−	0.554797i
$975$		−	11.5073i		−	0.368530i
$976$	9.95024			0.318499
$977$	42.2556			1.35188			0.675939	−	0.736958i	$-0.263738\pi$
$977$	42.2556			1.35188			0.675939	+	0.736958i	$0.263738\pi$
$978$	20.7414			0.663238
$979$	−5.47871	+	16.9121i	−0.175100	+	0.540514i
$980$		0			0
$981$			8.50535i			0.271555i
$982$	8.44002			0.269332
$983$		−	23.6174i		−	0.753279i	−0.926360	−	0.376639i	$-0.877080\pi$
$983$		−	23.6174i		−	0.753279i	0.926360	−	0.376639i	$-0.122920\pi$
$984$	0.0321383			0.00102453
$985$	21.0517			0.670764
$986$	−0.811871			−0.0258553
$987$		0			0
$988$	−26.4766			−0.842334
$989$		−	54.7336i		−	1.74043i
$990$	5.64031	+	1.82718i	0.179261	+	0.0580718i
$991$	26.9740			0.856857			0.428429	−	0.903576i	$-0.359067\pi$
$991$	26.9740			0.856857			0.428429	+	0.903576i	$0.359067\pi$
$992$	−1.27872			−0.0405994
$993$		−	31.0132i		−	0.984173i
$994$		0			0
$995$	38.2566			1.21282
$996$		−	12.0657i		−	0.382316i
$997$	−22.3415			−0.707561			−0.353781	−	0.935328i	$-0.615104\pi$
$997$	−22.3415			−0.707561			−0.353781	+	0.935328i	$0.615104\pi$
$998$		−	19.0719i		−	0.603712i
$999$		−	4.52184i		−	0.143065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.e.b.2155.6		16
7.2	even	3		462.2.p.b.241.3	yes	16
7.3	odd	6		462.2.p.a.439.7	yes	16
7.6	odd	2		3234.2.e.a.2155.3		16
11.10	odd	2		3234.2.e.a.2155.14		16
21.2	odd	6		1386.2.bk.b.703.6		16
21.17	even	6		1386.2.bk.a.901.2		16
77.10	even	6		462.2.p.b.439.3	yes	16
77.65	odd	6		462.2.p.a.241.7	✓	16
77.76	even	2	inner	3234.2.e.b.2155.11		16
231.65	even	6		1386.2.bk.a.703.2		16
231.164	odd	6		1386.2.bk.b.901.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.7	✓	16	77.65	odd	6
462.2.p.a.439.7	yes	16	7.3	odd	6
462.2.p.b.241.3	yes	16	7.2	even	3
462.2.p.b.439.3	yes	16	77.10	even	6
1386.2.bk.a.703.2		16	231.65	even	6
1386.2.bk.a.901.2		16	21.17	even	6
1386.2.bk.b.703.6		16	21.2	odd	6
1386.2.bk.b.901.6		16	231.164	odd	6
3234.2.e.a.2155.3		16	7.6	odd	2
3234.2.e.a.2155.14		16	11.10	odd	2
3234.2.e.b.2155.6		16	1.1	even	1	trivial
3234.2.e.b.2155.11		16	77.76	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.78763i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.78763i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +1.78763 q^{10} +(-3.15519 - 1.02213i) q^{11} -1.00000i q^{12} -6.37742 q^{13} -1.78763 q^{15} +1.00000 q^{16} +0.106095 q^{17} +1.00000i q^{18} -4.15162 q^{19} -1.78763i q^{20} +(-1.02213 + 3.15519i) q^{22} +7.95866 q^{23} -1.00000 q^{24} +1.80439 q^{25} +6.37742i q^{26} -1.00000i q^{27} -7.65230i q^{29} +1.78763i q^{30} -1.27872i q^{31} -1.00000i q^{32} +(1.02213 - 3.15519i) q^{33} -0.106095i q^{34} +1.00000 q^{36} +4.52184 q^{37} +4.15162i q^{38} -6.37742i q^{39} -1.78763 q^{40} -0.0321383 q^{41} -6.87723i q^{43} +(3.15519 + 1.02213i) q^{44} -1.78763i q^{45} -7.95866i q^{46} +9.88198i q^{47} +1.00000i q^{48} -1.80439i q^{50} +0.106095i q^{51} +6.37742 q^{52} -0.627441 q^{53} -1.00000 q^{54} +(1.82718 - 5.64031i) q^{55} -4.15162i q^{57} -7.65230 q^{58} -12.4549i q^{59} +1.78763 q^{60} +9.95024 q^{61} -1.27872 q^{62} -1.00000 q^{64} -11.4004i q^{65} +(-3.15519 - 1.02213i) q^{66} +10.8722 q^{67} -0.106095 q^{68} +7.95866i q^{69} -8.42785 q^{71} -1.00000i q^{72} +0.125008 q^{73} -4.52184i q^{74} +1.80439i q^{75} +4.15162 q^{76} -6.37742 q^{78} +10.1691i q^{79} +1.78763i q^{80} +1.00000 q^{81} +0.0321383i q^{82} +12.0657 q^{83} +0.189659i q^{85} -6.87723 q^{86} +7.65230 q^{87} +(1.02213 - 3.15519i) q^{88} -5.36009i q^{89} -1.78763 q^{90} -7.95866 q^{92} +1.27872 q^{93} +9.88198 q^{94} -7.42156i q^{95} +1.00000 q^{96} +15.7498i q^{97} +(3.15519 + 1.02213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9	\( 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9} + 4 q^{10} + 8 q^{11} - 4 q^{15} + 16 q^{16} - 20 q^{19} + 2 q^{22} + 8 q^{23} - 16 q^{24} - 20 q^{25} - 2 q^{33} + 16 q^{36} - 28 q^{37} - 4 q^{40} - 32 q^{41} - 8 q^{44} - 16 q^{54} + 14 q^{55} + 4 q^{60} + 56 q^{61} + 8 q^{62} - 16 q^{64} + 8 q^{66} + 32 q^{67} - 56 q^{71} - 88 q^{73} + 20 q^{76} + 16 q^{81} - 8 q^{83} + 24 q^{86} - 2 q^{88} - 4 q^{90} - 8 q^{92} - 8 q^{93} + 28 q^{94} + 16 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9 + 4 * q^10 + 8 * q^11 - 4 * q^15 + 16 * q^16 - 20 * q^19 + 2 * q^22 + 8 * q^23 - 16 * q^24 - 20 * q^25 - 2 * q^33 + 16 * q^36 - 28 * q^37 - 4 * q^40 - 32 * q^41 - 8 * q^44 - 16 * q^54 + 14 * q^55 + 4 * q^60 + 56 * q^61 + 8 * q^62 - 16 * q^64 + 8 * q^66 + 32 * q^67 - 56 * q^71 - 88 * q^73 + 20 * q^76 + 16 * q^81 - 8 * q^83 + 24 * q^86 - 2 * q^88 - 4 * q^90 - 8 * q^92 - 8 * q^93 + 28 * q^94 + 16 * q^96 - 8 * q^99

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