LMFDB - Embedded newform 1638.2.y.c.827.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1638,2,Mod(827,1638)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1638, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1638.827"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.y (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} + 20 x^{14} - 12 x^{13} + 40 x^{12} + 40 x^{11} + 82 x^{10} + 104 x^{9} + 537 x^{8} + \cdots + 16 $ x^16 - 8x^15 + 20x^14 - 12x^13 + 40x^12 + 40x^11 + 82x^10 + 104x^9 + 537x^8 - 2528x^7 + 5494x^6 - 7284x^5 + 6002x^4 - 2984x^3 + 1000x^2 - 192*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			827.4
Root			$0.457766 - 1.10514i$ of defining polynomial
Character	$\chi$	$=$	1638.827
Dual form			1638.2.y.c.1331.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.34991 - 2.34991i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.32328i q^{10} +(-0.324149 - 0.324149i) q^{11} +(-0.665596 - 3.54358i) q^{13} +1.00000i q^{14} -1.00000 q^{16} +1.62982 q^{17} +(5.77706 + 5.77706i) q^{19} +(-2.34991 - 2.34991i) q^{20} +0.458415 q^{22} -0.0634972 q^{23} -6.04418i q^{25} +(2.97634 + 2.03504i) q^{26} +(-0.707107 - 0.707107i) q^{28} -4.93529i q^{29} +(6.43095 + 6.43095i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.15245 + 1.15245i) q^{34} -3.32328i q^{35} +(1.02017 - 1.02017i) q^{37} -8.17000 q^{38} +3.32328 q^{40} +(1.70138 - 1.70138i) q^{41} +2.64926i q^{43} +(-0.324149 + 0.324149i) q^{44} +(0.0448993 - 0.0448993i) q^{46} +(-7.39872 - 7.39872i) q^{47} -1.00000i q^{49} +(4.27388 + 4.27388i) q^{50} +(-3.54358 + 0.665596i) q^{52} -5.78862i q^{53} -1.52344 q^{55} +1.00000 q^{56} +(3.48978 + 3.48978i) q^{58} +(-3.10768 - 3.10768i) q^{59} +6.02310 q^{61} -9.09474 q^{62} +1.00000i q^{64} +(-9.89120 - 6.76302i) q^{65} +(-5.17274 - 5.17274i) q^{67} -1.62982i q^{68} +(2.34991 + 2.34991i) q^{70} +(2.44819 - 2.44819i) q^{71} +(-6.66296 + 6.66296i) q^{73} +1.44274i q^{74} +(5.77706 - 5.77706i) q^{76} -0.458415 q^{77} +0.341405 q^{79} +(-2.34991 + 2.34991i) q^{80} +2.40611i q^{82} +(1.32362 - 1.32362i) q^{83} +(3.82992 - 3.82992i) q^{85} +(-1.87331 - 1.87331i) q^{86} -0.458415i q^{88} +(-8.87914 - 8.87914i) q^{89} +(-2.97634 - 2.03504i) q^{91} +0.0634972i q^{92} +10.4634 q^{94} +27.1512 q^{95} +(-1.56229 - 1.56229i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{5} + 8 q^{11} + 4 q^{13} - 16 q^{16} + 8 q^{17} + 16 q^{19} + 4 q^{20} - 8 q^{22} - 24 q^{23} - 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} - 16 q^{38} + 16 q^{41} + 8 q^{44} - 4 q^{47} + 16 q^{50}+ \cdots - 28 q^{97}+O(q^{100}) $ 16 * q - 4 * q^5 + 8 * q^11 + 4 * q^13 - 16 * q^16 + 8 * q^17 + 16 * q^19 + 4 * q^20 - 8 * q^22 - 24 * q^23 - 8 * q^26 - 8 * q^31 + 4 * q^34 - 4 * q^37 - 16 * q^38 + 16 * q^41 + 8 * q^44 - 4 * q^47 + 16 * q^50 - 16 * q^55 + 16 * q^56 + 4 * q^58 + 8 * q^59 - 40 * q^61 - 24 * q^62 - 56 * q^65 - 4 * q^67 - 4 * q^70 + 24 * q^71 - 12 * q^73 + 16 * q^76 + 8 * q^77 + 16 * q^79 + 4 * q^80 + 8 * q^85 - 24 * q^86 - 16 * q^89 + 8 * q^91 - 8 * q^94 + 40 * q^95 - 28 * q^97

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	2.34991	−	2.34991i	1.05091	−	1.05091i	0.0522805	−	0.998632i	$-0.483351\pi$
$5$	2.34991	−	2.34991i	1.05091	−	1.05091i	0.998632	−	0.0522805i	$-0.0166490\pi$
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$			3.32328i			1.05091i
$11$	−0.324149	−	0.324149i	−0.0977345	−	0.0977345i	0.656549	−	0.754283i	$-0.272016\pi$
$11$	−0.324149	−	0.324149i	−0.0977345	−	0.0977345i	−0.754283	+	0.656549i	$0.772016\pi$
$12$		0			0
$13$	−0.665596	−	3.54358i	−0.184603	−	0.982813i
$13$	−0.665596	−	3.54358i	−0.184603	−	0.982813i
$14$			1.00000i			0.267261i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.62982			0.395288			0.197644	−	0.980274i	$-0.436671\pi$
$17$	1.62982			0.395288			0.197644	+	0.980274i	$0.436671\pi$
$18$		0			0
$19$	5.77706	+	5.77706i	1.32535	+	1.32535i	0.909378	+	0.415971i	$0.136558\pi$
$19$	5.77706	+	5.77706i	1.32535	+	1.32535i	0.415971	+	0.909378i	$0.363442\pi$
$20$	−2.34991	−	2.34991i	−0.525456	−	0.525456i
$21$		0			0
$22$	0.458415			0.0977345
$23$	−0.0634972			−0.0132401			−0.00662004	−	0.999978i	$-0.502107\pi$
$23$	−0.0634972			−0.0132401			−0.00662004	+	0.999978i	$0.502107\pi$
$24$		0			0
$25$		−	6.04418i		−	1.20884i
$26$	2.97634	+	2.03504i	0.583708	+	0.399105i
$27$		0			0
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$		−	4.93529i		−	0.916460i	−0.888834	−	0.458230i	$-0.848484\pi$
$29$		−	4.93529i		−	0.916460i	0.888834	−	0.458230i	$-0.151516\pi$
$30$		0			0
$31$	6.43095	+	6.43095i	1.15503	+	1.15503i	0.985529	+	0.169504i	$0.0542166\pi$
$31$	6.43095	+	6.43095i	1.15503	+	1.15503i	0.169504	+	0.985529i	$0.445783\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−1.15245	+	1.15245i	−0.197644	+	0.197644i
$35$		−	3.32328i		−	0.561737i
$36$		0			0
$37$	1.02017	−	1.02017i	0.167715	−	0.167715i	−0.618259	−	0.785974i	$-0.712162\pi$
$37$	1.02017	−	1.02017i	0.167715	−	0.167715i	0.785974	+	0.618259i	$0.212162\pi$
$38$	−8.17000			−1.32535
$39$		0			0
$40$	3.32328			0.525456
$41$	1.70138	−	1.70138i	0.265710	−	0.265710i	−0.561659	−	0.827369i	$-0.689837\pi$
$41$	1.70138	−	1.70138i	0.265710	−	0.265710i	0.827369	+	0.561659i	$0.189837\pi$
$42$		0			0
$43$			2.64926i			0.404009i	0.979385	+	0.202004i	$0.0647455\pi$
$43$			2.64926i			0.404009i	−0.979385	+	0.202004i	$0.935255\pi$
$44$	−0.324149	+	0.324149i	−0.0488672	+	0.0488672i
$45$		0			0
$46$	0.0448993	−	0.0448993i	0.00662004	−	0.00662004i
$47$	−7.39872	−	7.39872i	−1.07921	−	1.07921i	−0.996580	−	0.0826350i	$-0.973666\pi$
$47$	−7.39872	−	7.39872i	−1.07921	−	1.07921i	−0.0826350	−	0.996580i	$-0.526334\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	4.27388	+	4.27388i	0.604418	+	0.604418i
$51$		0			0
$52$	−3.54358	+	0.665596i	−0.491407	+	0.0923016i
$53$		−	5.78862i		−	0.795128i	−0.917574	−	0.397564i	$-0.869856\pi$
$53$		−	5.78862i		−	0.795128i	0.917574	−	0.397564i	$-0.130144\pi$
$54$		0			0
$55$	−1.52344			−0.205421
$56$	1.00000			0.133631
$57$		0			0
$58$	3.48978	+	3.48978i	0.458230	+	0.458230i
$59$	−3.10768	−	3.10768i	−0.404585	−	0.404585i	0.475260	−	0.879845i	$-0.342354\pi$
$59$	−3.10768	−	3.10768i	−0.404585	−	0.404585i	−0.879845	+	0.475260i	$0.842354\pi$
$60$		0			0
$61$	6.02310			0.771179			0.385590	−	0.922670i	$-0.373998\pi$
$61$	6.02310			0.771179			0.385590	+	0.922670i	$0.373998\pi$
$62$	−9.09474			−1.15503
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−9.89120	−	6.76302i	−1.22685	−	0.838849i
$66$		0			0
$67$	−5.17274	−	5.17274i	−0.631951	−	0.631951i	0.316606	−	0.948557i	$-0.397457\pi$
$67$	−5.17274	−	5.17274i	−0.631951	−	0.631951i	−0.948557	+	0.316606i	$0.897457\pi$
$68$		−	1.62982i		−	0.197644i
$69$		0			0
$70$	2.34991	+	2.34991i	0.280868	+	0.280868i
$71$	2.44819	−	2.44819i	0.290546	−	0.290546i	−0.546750	−	0.837296i	$-0.684135\pi$
$71$	2.44819	−	2.44819i	0.290546	−	0.290546i	0.837296	+	0.546750i	$0.184135\pi$
$72$		0			0
$73$	−6.66296	+	6.66296i	−0.779841	+	0.779841i	−0.979804	−	0.199963i	$-0.935918\pi$
$73$	−6.66296	+	6.66296i	−0.779841	+	0.779841i	0.199963	+	0.979804i	$0.435918\pi$
$74$			1.44274i			0.167715i
$75$		0			0
$76$	5.77706	−	5.77706i	0.662674	−	0.662674i
$77$	−0.458415			−0.0522413
$78$		0			0
$79$	0.341405			0.0384111			0.0192056	−	0.999816i	$-0.493886\pi$
$79$	0.341405			0.0384111			0.0192056	+	0.999816i	$0.493886\pi$
$80$	−2.34991	+	2.34991i	−0.262728	+	0.262728i
$81$		0			0
$82$			2.40611i			0.265710i
$83$	1.32362	−	1.32362i	0.145286	−	0.145286i	−0.630723	−	0.776008i	$-0.717241\pi$
$83$	1.32362	−	1.32362i	0.145286	−	0.145286i	0.776008	+	0.630723i	$0.217241\pi$
$84$		0			0
$85$	3.82992	−	3.82992i	0.415414	−	0.415414i
$86$	−1.87331	−	1.87331i	−0.202004	−	0.202004i
$87$		0			0
$88$		−	0.458415i		−	0.0488672i
$89$	−8.87914	−	8.87914i	−0.941187	−	0.941187i	0.0571769	−	0.998364i	$-0.481790\pi$
$89$	−8.87914	−	8.87914i	−0.941187	−	0.941187i	−0.998364	+	0.0571769i	$0.981790\pi$
$90$		0			0
$91$	−2.97634	−	2.03504i	−0.312005	−	0.213331i
$92$			0.0634972i			0.00662004i
$93$		0			0
$94$	10.4634			1.07921
$95$	27.1512			2.78565
$96$		0			0
$97$	−1.56229	−	1.56229i	−0.158626	−	0.158626i	0.623332	−	0.781958i	$-0.285779\pi$
$97$	−1.56229	−	1.56229i	−0.158626	−	0.158626i	−0.781958	+	0.623332i	$0.785779\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$	−6.04418			−0.604418
$101$	−15.8373			−1.57587			−0.787933	−	0.615761i	$-0.788849\pi$
$101$	−15.8373			−1.57587			−0.787933	+	0.615761i	$0.788849\pi$
$102$		0			0
$103$		−	8.93993i		−	0.880878i	−0.897783	−	0.440439i	$-0.854823\pi$
$103$		−	8.93993i		−	0.880878i	0.897783	−	0.440439i	$-0.145177\pi$
$104$	2.03504	−	2.97634i	0.199552	−	0.291854i
$105$		0			0
$106$	4.09317	+	4.09317i	0.397564	+	0.397564i
$107$		−	6.39853i		−	0.618570i	−0.950969	−	0.309285i	$-0.899910\pi$
$107$		−	6.39853i		−	0.618570i	0.950969	−	0.309285i	$-0.100090\pi$
$108$		0			0
$109$	4.12784	+	4.12784i	0.395376	+	0.395376i	0.876598	−	0.481223i	$-0.159807\pi$
$109$	4.12784	+	4.12784i	0.395376	+	0.395376i	−0.481223	+	0.876598i	$0.659807\pi$
$110$	1.07724	−	1.07724i	0.102710	−	0.102710i
$111$		0			0
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$			7.68101i			0.722568i	0.932456	+	0.361284i	$0.117662\pi$
$113$			7.68101i			0.722568i	−0.932456	+	0.361284i	$0.882338\pi$
$114$		0			0
$115$	−0.149213	+	0.149213i	−0.0139142	+	0.0139142i
$116$	−4.93529			−0.458230
$117$		0			0
$118$	4.39492			0.404585
$119$	1.15245	−	1.15245i	0.105645	−	0.105645i
$120$		0			0
$121$		−	10.7899i		−	0.980896i
$122$	−4.25898	+	4.25898i	−0.385590	+	0.385590i
$123$		0			0
$124$	6.43095	−	6.43095i	0.577517	−	0.577517i
$125$	−2.45373	−	2.45373i	−0.219468	−	0.219468i
$126$		0			0
$127$		−	0.345230i		−	0.0306342i	−0.999883	−	0.0153171i	$-0.995124\pi$
$127$		−	0.345230i		−	0.0306342i	0.999883	−	0.0153171i	$-0.00487577\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	11.7763	−	2.21196i	1.03285	−	0.194002i
$131$		−	5.61993i		−	0.491016i	−0.969395	−	0.245508i	$-0.921045\pi$
$131$		−	5.61993i		−	0.491016i	0.969395	−	0.245508i	$-0.0789548\pi$
$132$		0			0
$133$	8.17000			0.708429
$134$	7.31536			0.631951
$135$		0			0
$136$	1.15245	+	1.15245i	0.0988221	+	0.0988221i
$137$	10.4753	+	10.4753i	0.894961	+	0.894961i	0.994985	−	0.100024i	$-0.0318920\pi$
$137$	10.4753	+	10.4753i	0.894961	+	0.894961i	−0.100024	+	0.994985i	$0.531892\pi$
$138$		0			0
$139$	15.6420			1.32674			0.663370	−	0.748292i	$-0.269126\pi$
$139$	15.6420			1.32674			0.663370	+	0.748292i	$0.269126\pi$
$140$	−3.32328			−0.280868
$141$		0			0
$142$			3.46226i			0.290546i
$143$	−0.932895	+	1.36440i	−0.0780126	+	0.114097i
$144$		0			0
$145$	−11.5975	−	11.5975i	−0.963120	−	0.963120i
$146$		−	9.42285i		−	0.779841i
$147$		0			0
$148$	−1.02017	−	1.02017i	−0.0838573	−	0.0838573i
$149$	−7.62823	+	7.62823i	−0.624929	+	0.624929i	−0.946788	−	0.321859i	$-0.895692\pi$
$149$	−7.62823	+	7.62823i	−0.624929	+	0.624929i	0.321859	+	0.946788i	$0.395692\pi$
$150$		0			0
$151$	2.40058	−	2.40058i	0.195357	−	0.195357i	−0.602649	−	0.798006i	$-0.705888\pi$
$151$	2.40058	−	2.40058i	0.195357	−	0.195357i	0.798006	+	0.602649i	$0.205888\pi$
$152$			8.17000i			0.662674i
$153$		0			0
$154$	0.324149	−	0.324149i	0.0261206	−	0.0261206i
$155$	30.2244			2.42768
$156$		0			0
$157$	−6.14017			−0.490039			−0.245019	−	0.969518i	$-0.578794\pi$
$157$	−6.14017			−0.490039			−0.245019	+	0.969518i	$0.578794\pi$
$158$	−0.241410	+	0.241410i	−0.0192056	+	0.0192056i
$159$		0			0
$160$		−	3.32328i		−	0.262728i
$161$	−0.0448993	+	0.0448993i	−0.00353856	+	0.00353856i
$162$		0			0
$163$	8.31791	−	8.31791i	0.651509	−	0.651509i	−0.301847	−	0.953356i	$-0.597603\pi$
$163$	8.31791	−	8.31791i	0.651509	−	0.651509i	0.953356	+	0.301847i	$0.0976032\pi$
$164$	−1.70138	−	1.70138i	−0.132855	−	0.132855i
$165$		0			0
$166$			1.87187i			0.145286i
$167$	16.1126	+	16.1126i	1.24683	+	1.24683i	0.957110	+	0.289723i	$0.0935632\pi$
$167$	16.1126	+	16.1126i	1.24683	+	1.24683i	0.289723	+	0.957110i	$0.406437\pi$
$168$		0			0
$169$	−12.1140	+	4.71719i	−0.931843	+	0.362861i
$170$			5.41633i			0.415414i
$171$		0			0
$172$	2.64926			0.202004
$173$	22.3436			1.69876			0.849378	−	0.527785i	$-0.176977\pi$
$173$	22.3436			1.69876			0.849378	+	0.527785i	$0.176977\pi$
$174$		0			0
$175$	−4.27388	−	4.27388i	−0.323075	−	0.323075i
$176$	0.324149	+	0.324149i	0.0244336	+	0.0244336i
$177$		0			0
$178$	12.5570			0.941187
$179$	18.6770			1.39598			0.697992	−	0.716106i	$-0.254077\pi$
$179$	18.6770			1.39598			0.697992	+	0.716106i	$0.254077\pi$
$180$		0			0
$181$			22.6676i			1.68487i	0.538796	+	0.842436i	$0.318879\pi$
$181$			22.6676i			1.68487i	−0.538796	+	0.842436i	$0.681121\pi$
$182$	3.54358	−	0.665596i	0.262668	−	0.0493373i
$183$		0			0
$184$	−0.0448993	−	0.0448993i	−0.00331002	−	0.00331002i
$185$		−	4.79461i		−	0.352507i
$186$		0			0
$187$	−0.528302	−	0.528302i	−0.0386333	−	0.0386333i
$188$	−7.39872	+	7.39872i	−0.539607	+	0.539607i
$189$		0			0
$190$	−19.1988	+	19.1988i	−1.39283	+	1.39283i
$191$			17.1930i			1.24404i	0.783000	+	0.622022i	$0.213689\pi$
$191$			17.1930i			1.24404i	−0.783000	+	0.622022i	$0.786311\pi$
$192$		0			0
$193$	2.65661	−	2.65661i	0.191227	−	0.191227i	−0.604999	−	0.796226i	$-0.706827\pi$
$193$	2.65661	−	2.65661i	0.191227	−	0.191227i	0.796226	+	0.604999i	$0.206827\pi$
$194$	2.20941			0.158626
$195$		0			0
$196$	−1.00000			−0.0714286
$197$	−4.66485	+	4.66485i	−0.332357	+	0.332357i	−0.853481	−	0.521124i	$-0.825513\pi$
$197$	−4.66485	+	4.66485i	−0.332357	+	0.332357i	0.521124	+	0.853481i	$0.325513\pi$
$198$		0			0
$199$			22.2752i			1.57905i	0.613719	+	0.789525i	$0.289673\pi$
$199$			22.2752i			1.57905i	−0.613719	+	0.789525i	$0.710327\pi$
$200$	4.27388	−	4.27388i	0.302209	−	0.302209i
$201$		0			0
$202$	11.1986	−	11.1986i	0.787933	−	0.787933i
$203$	−3.48978	−	3.48978i	−0.244934	−	0.244934i
$204$		0			0
$205$		−	7.99618i		−	0.558477i
$206$	6.32149	+	6.32149i	0.440439	+	0.440439i
$207$		0			0
$208$	0.665596	+	3.54358i	0.0461508	+	0.245703i
$209$		−	3.74525i		−	0.259065i
$210$		0			0
$211$	−15.1062			−1.03995			−0.519977	−	0.854180i	$-0.674060\pi$
$211$	−15.1062			−1.03995			−0.519977	+	0.854180i	$0.674060\pi$
$212$	−5.78862			−0.397564
$213$		0			0
$214$	4.52445	+	4.52445i	0.309285	+	0.309285i
$215$	6.22553	+	6.22553i	0.424578	+	0.424578i
$216$		0			0
$217$	9.09474			0.617391
$218$	−5.83765			−0.395376
$219$		0			0
$220$			1.52344i			0.102710i
$221$	−1.08480	−	5.77539i	−0.0729715	−	0.388495i
$222$		0			0
$223$	−6.75687	−	6.75687i	−0.452473	−	0.452473i	0.443701	−	0.896175i	$-0.353665\pi$
$223$	−6.75687	−	6.75687i	−0.452473	−	0.452473i	−0.896175	+	0.443701i	$0.853665\pi$
$224$		−	1.00000i		−	0.0668153i
$225$		0			0
$226$	−5.43129	−	5.43129i	−0.361284	−	0.361284i
$227$	−3.91662	+	3.91662i	−0.259955	+	0.259955i	−0.825036	−	0.565081i	$-0.808845\pi$
$227$	−3.91662	+	3.91662i	−0.259955	+	0.259955i	0.565081	+	0.825036i	$0.308845\pi$
$228$		0			0
$229$	10.3547	−	10.3547i	0.684256	−	0.684256i	−0.276700	−	0.960956i	$-0.589241\pi$
$229$	10.3547	−	10.3547i	0.684256	−	0.684256i	0.960956	+	0.276700i	$0.0892409\pi$
$230$		−	0.211019i		−	0.0139142i
$231$		0			0
$232$	3.48978	−	3.48978i	0.229115	−	0.229115i
$233$	9.21159			0.603471			0.301736	−	0.953392i	$-0.402434\pi$
$233$	9.21159			0.603471			0.301736	+	0.953392i	$0.402434\pi$
$234$		0			0
$235$	−34.7727			−2.26832
$236$	−3.10768	+	3.10768i	−0.202293	+	0.202293i
$237$		0			0
$238$			1.62982i			0.105645i
$239$	−12.5343	+	12.5343i	−0.810780	+	0.810780i	−0.984751	−	0.173971i	$-0.944340\pi$
$239$	−12.5343	+	12.5343i	−0.810780	+	0.810780i	0.173971	+	0.984751i	$0.444340\pi$
$240$		0			0
$241$	−4.38083	+	4.38083i	−0.282194	+	0.282194i	−0.833984	−	0.551789i	$-0.813945\pi$
$241$	−4.38083	+	4.38083i	−0.282194	+	0.282194i	0.551789	+	0.833984i	$0.313945\pi$
$242$	7.62958	+	7.62958i	0.490448	+	0.490448i
$243$		0			0
$244$		−	6.02310i		−	0.385590i
$245$	−2.34991	−	2.34991i	−0.150130	−	0.150130i
$246$		0			0
$247$	16.6263	−	24.3167i	1.05791	−	1.54723i
$248$			9.09474i			0.577517i
$249$		0			0
$250$	3.47010			0.219468
$251$	−16.7074			−1.05456			−0.527282	−	0.849691i	$-0.676789\pi$
$251$	−16.7074			−1.05456			−0.527282	+	0.849691i	$0.676789\pi$
$252$		0			0
$253$	0.0205825	+	0.0205825i	0.00129401	+	0.00129401i
$254$	0.244114	+	0.244114i	0.0153171	+	0.0153171i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−23.7154			−1.47932			−0.739662	−	0.672978i	$-0.765015\pi$
$257$	−23.7154			−1.47932			−0.739662	+	0.672978i	$0.765015\pi$
$258$		0			0
$259$		−	1.44274i		−	0.0896472i
$260$	−6.76302	+	9.89120i	−0.419425	+	0.613426i
$261$		0			0
$262$	3.97389	+	3.97389i	0.245508	+	0.245508i
$263$		−	24.5094i		−	1.51132i	−0.654966	−	0.755659i	$-0.727317\pi$
$263$		−	24.5094i		−	1.51132i	0.654966	−	0.755659i	$-0.272683\pi$
$264$		0			0
$265$	−13.6028	−	13.6028i	−0.835611	−	0.835611i
$266$	−5.77706	+	5.77706i	−0.354214	+	0.354214i
$267$		0			0
$268$	−5.17274	+	5.17274i	−0.315976	+	0.315976i
$269$		−	2.64650i		−	0.161360i	−0.996740	−	0.0806800i	$-0.974291\pi$
$269$		−	2.64650i		−	0.161360i	0.996740	−	0.0806800i	$-0.0257092\pi$
$270$		0			0
$271$	17.8317	−	17.8317i	1.08320	−	1.08320i	0.0869918	−	0.996209i	$-0.472275\pi$
$271$	17.8317	−	17.8317i	1.08320	−	1.08320i	0.996209	−	0.0869918i	$-0.0277254\pi$
$272$	−1.62982			−0.0988221
$273$		0			0
$274$	−14.8142			−0.894961
$275$	−1.95921	+	1.95921i	−0.118145	+	0.118145i
$276$		0			0
$277$		−	2.21059i		−	0.132821i	−0.997792	−	0.0664106i	$-0.978845\pi$
$277$		−	2.21059i		−	0.132821i	0.997792	−	0.0664106i	$-0.0211547\pi$
$278$	−11.0606	+	11.0606i	−0.663370	+	0.663370i
$279$		0			0
$280$	2.34991	−	2.34991i	0.140434	−	0.140434i
$281$	−8.10646	−	8.10646i	−0.483591	−	0.483591i	0.422685	−	0.906276i	$-0.361088\pi$
$281$	−8.10646	−	8.10646i	−0.483591	−	0.483591i	−0.906276	+	0.422685i	$0.861088\pi$
$282$		0			0
$283$			24.6870i			1.46749i	0.679425	+	0.733745i	$0.262229\pi$
$283$			24.6870i			1.46749i	−0.679425	+	0.733745i	$0.737771\pi$
$284$	−2.44819	−	2.44819i	−0.145273	−	0.145273i
$285$		0			0
$286$	−0.305120	−	1.62443i	−0.0180421	−	0.0960547i
$287$		−	2.40611i		−	0.142028i
$288$		0			0
$289$	−14.3437			−0.843747
$290$	16.4013			0.963120
$291$		0			0
$292$	6.66296	+	6.66296i	0.389920	+	0.389920i
$293$	−13.8944	−	13.8944i	−0.811718	−	0.811718i	0.173174	−	0.984891i	$-0.444598\pi$
$293$	−13.8944	−	13.8944i	−0.811718	−	0.811718i	−0.984891	+	0.173174i	$0.944598\pi$
$294$		0			0
$295$	−14.6055			−0.850367
$296$	1.44274			0.0838573
$297$		0			0
$298$		−	10.7879i		−	0.624929i
$299$	0.0422635	+	0.225008i	0.00244416	+	0.0130125i
$300$		0			0
$301$	1.87331	+	1.87331i	0.107976	+	0.107976i
$302$			3.39494i			0.195357i
$303$		0			0
$304$	−5.77706	−	5.77706i	−0.331337	−	0.331337i
$305$	14.1538	−	14.1538i	0.810442	−	0.810442i
$306$		0			0
$307$	−12.2425	+	12.2425i	−0.698718	+	0.698718i	−0.964134	−	0.265416i	$-0.914491\pi$
$307$	−12.2425	+	12.2425i	−0.698718	+	0.698718i	0.265416	+	0.964134i	$0.414491\pi$
$308$			0.458415i			0.0261206i
$309$		0			0
$310$	−21.3719	+	21.3719i	−1.21384	+	1.21384i
$311$	27.4849			1.55852			0.779262	−	0.626698i	$-0.215594\pi$
$311$	27.4849			1.55852			0.779262	+	0.626698i	$0.215594\pi$
$312$		0			0
$313$	−34.7566			−1.96456			−0.982279	−	0.187424i	$-0.939986\pi$
$313$	−34.7566			−1.96456			−0.982279	+	0.187424i	$0.939986\pi$
$314$	4.34175	−	4.34175i	0.245019	−	0.245019i
$315$		0			0
$316$		−	0.341405i		−	0.0192056i
$317$	7.91647	−	7.91647i	0.444633	−	0.444633i	−0.448932	−	0.893566i	$-0.648196\pi$
$317$	7.91647	−	7.91647i	0.444633	−	0.444633i	0.893566	+	0.448932i	$0.148196\pi$
$318$		0			0
$319$	−1.59977	+	1.59977i	−0.0895697	+	0.0895697i
$320$	2.34991	+	2.34991i	0.131364	+	0.131364i
$321$		0			0
$322$		−	0.0634972i		−	0.00353856i
$323$	9.41554	+	9.41554i	0.523895	+	0.523895i
$324$		0			0
$325$	−21.4181	+	4.02298i	−1.18806	+	0.223155i
$326$			11.7633i			0.651509i
$327$		0			0
$328$	2.40611			0.132855
$329$	−10.4634			−0.576865
$330$		0			0
$331$	22.0478	+	22.0478i	1.21186	+	1.21186i	0.970416	+	0.241440i	$0.0776196\pi$
$331$	22.0478	+	22.0478i	1.21186	+	1.21186i	0.241440	+	0.970416i	$0.422380\pi$
$332$	−1.32362	−	1.32362i	−0.0726428	−	0.0726428i
$333$		0			0
$334$	−22.7867			−1.24683
$335$	−24.3110			−1.32825
$336$		0			0
$337$			35.9438i			1.95798i	0.203905	+	0.978991i	$0.434637\pi$
$337$			35.9438i			1.95798i	−0.203905	+	0.978991i	$0.565363\pi$
$338$	5.23031	−	11.9014i	0.284491	−	0.647352i
$339$		0			0
$340$	−3.82992	−	3.82992i	−0.207707	−	0.207707i
$341$		−	4.16917i		−	0.225773i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−1.87331	+	1.87331i	−0.101002	+	0.101002i
$345$		0			0
$346$	−15.7993	+	15.7993i	−0.849378	+	0.849378i
$347$			23.3475i			1.25336i	0.779277	+	0.626680i	$0.215587\pi$
$347$			23.3475i			1.25336i	−0.779277	+	0.626680i	$0.784413\pi$
$348$		0			0
$349$	3.71738	−	3.71738i	0.198987	−	0.198987i	−0.600579	−	0.799566i	$-0.705063\pi$
$349$	3.71738	−	3.71738i	0.198987	−	0.198987i	0.799566	+	0.600579i	$0.205063\pi$
$350$	6.04418			0.323075
$351$		0			0
$352$	−0.458415			−0.0244336
$353$	13.5947	−	13.5947i	0.723574	−	0.723574i	−0.245757	−	0.969331i	$-0.579037\pi$
$353$	13.5947	−	13.5947i	0.723574	−	0.723574i	0.969331	+	0.245757i	$0.0790367\pi$
$354$		0			0
$355$		−	11.5061i		−	0.610678i
$356$	−8.87914	+	8.87914i	−0.470594	+	0.470594i
$357$		0			0
$358$	−13.2066	+	13.2066i	−0.697992	+	0.697992i
$359$	0.510808	+	0.510808i	0.0269594	+	0.0269594i	0.720458	−	0.693499i	$-0.243932\pi$
$359$	0.510808	+	0.510808i	0.0269594	+	0.0269594i	−0.693499	+	0.720458i	$0.743932\pi$
$360$		0			0
$361$			47.7489i			2.51310i
$362$	−16.0284	−	16.0284i	−0.842436	−	0.842436i
$363$		0			0
$364$	−2.03504	+	2.97634i	−0.106665	+	0.156003i
$365$			31.3148i			1.63909i
$366$		0			0
$367$	−2.08236			−0.108698			−0.0543491	−	0.998522i	$-0.517308\pi$
$367$	−2.08236			−0.108698			−0.0543491	+	0.998522i	$0.517308\pi$
$368$	0.0634972			0.00331002
$369$		0			0
$370$	3.39030	+	3.39030i	0.176253	+	0.176253i
$371$	−4.09317	−	4.09317i	−0.212507	−	0.212507i
$372$		0			0
$373$	16.2677			0.842311			0.421155	−	0.906988i	$-0.361625\pi$
$373$	16.2677			0.842311			0.421155	+	0.906988i	$0.361625\pi$
$374$	0.747132			0.0386333
$375$		0			0
$376$		−	10.4634i		−	0.539607i
$377$	−17.4886	+	3.28491i	−0.900709	+	0.169181i
$378$		0			0
$379$	−9.60317	−	9.60317i	−0.493282	−	0.493282i	0.416057	−	0.909339i	$-0.363412\pi$
$379$	−9.60317	−	9.60317i	−0.493282	−	0.493282i	−0.909339	+	0.416057i	$0.863412\pi$
$380$		−	27.1512i		−	1.39283i
$381$		0			0
$382$	−12.1573	−	12.1573i	−0.622022	−	0.622022i
$383$	7.31052	−	7.31052i	0.373550	−	0.373550i	−0.495218	−	0.868769i	$-0.664912\pi$
$383$	7.31052	−	7.31052i	0.373550	−	0.373550i	0.868769	+	0.495218i	$0.164912\pi$
$384$		0			0
$385$	−1.07724	+	1.07724i	−0.0549010	+	0.0549010i
$386$			3.75701i			0.191227i
$387$		0			0
$388$	−1.56229	+	1.56229i	−0.0793130	+	0.0793130i
$389$	−20.7184			−1.05046			−0.525231	−	0.850960i	$-0.676021\pi$
$389$	−20.7184			−1.05046			−0.525231	+	0.850960i	$0.676021\pi$
$390$		0			0
$391$	−0.103489			−0.00523365
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$		−	6.59709i		−	0.332357i
$395$	0.802273	−	0.802273i	0.0403667	−	0.0403667i
$396$		0			0
$397$	27.2204	−	27.2204i	1.36615	−	1.36615i	0.500297	−	0.865854i	$-0.333224\pi$
$397$	27.2204	−	27.2204i	1.36615	−	1.36615i	0.865854	−	0.500297i	$-0.166776\pi$
$398$	−15.7510	−	15.7510i	−0.789525	−	0.789525i
$399$		0			0
$400$			6.04418i			0.302209i
$401$	14.9967	+	14.9967i	0.748899	+	0.748899i	0.974272	−	0.225373i	$-0.0723602\pi$
$401$	14.9967	+	14.9967i	0.748899	+	0.748899i	−0.225373	+	0.974272i	$0.572360\pi$
$402$		0			0
$403$	18.5082	−	27.0690i	0.921959	−	1.34841i
$404$			15.8373i			0.787933i
$405$		0			0
$406$	4.93529			0.244934
$407$	−0.661372			−0.0327830
$408$		0			0
$409$	−28.0059	−	28.0059i	−1.38480	−	1.38480i	−0.835864	−	0.548937i	$-0.815033\pi$
$409$	−28.0059	−	28.0059i	−1.38480	−	1.38480i	−0.548937	−	0.835864i	$-0.684967\pi$
$410$	5.65415	+	5.65415i	0.279239	+	0.279239i
$411$		0			0
$412$	−8.93993			−0.440439
$413$	−4.39492			−0.216260
$414$		0			0
$415$		−	6.22076i		−	0.305365i
$416$	−2.97634	−	2.03504i	−0.145927	−	0.0997762i
$417$		0			0
$418$	2.64829	+	2.64829i	0.129532	+	0.129532i
$419$			37.3499i			1.82466i	0.409455	+	0.912330i	$0.365719\pi$
$419$			37.3499i			1.82466i	−0.409455	+	0.912330i	$0.634281\pi$
$420$		0			0
$421$	20.5126	+	20.5126i	0.999723	+	0.999723i	1.00000		0.000277066i	$-8.81929e-5\pi$
$421$	20.5126	+	20.5126i	0.999723	+	0.999723i	−0.000277066		1.00000i	$0.500088\pi$
$422$	10.6817	−	10.6817i	0.519977	−	0.519977i
$423$		0			0
$424$	4.09317	−	4.09317i	0.198782	−	0.198782i
$425$		−	9.85090i		−	0.477839i
$426$		0			0
$427$	4.25898	−	4.25898i	0.206106	−	0.206106i
$428$	−6.39853			−0.309285
$429$		0			0
$430$	−8.80423			−0.424578
$431$	−27.8444	+	27.8444i	−1.34122	+	1.34122i	−0.446372	+	0.894847i	$0.647284\pi$
$431$	−27.8444	+	27.8444i	−1.34122	+	1.34122i	−0.894847	+	0.446372i	$0.852716\pi$
$432$		0			0
$433$			23.6705i			1.13753i	0.822499	+	0.568767i	$0.192579\pi$
$433$			23.6705i			1.13753i	−0.822499	+	0.568767i	$0.807421\pi$
$434$	−6.43095	+	6.43095i	−0.308696	+	0.308696i
$435$		0			0
$436$	4.12784	−	4.12784i	0.197688	−	0.197688i
$437$	−0.366827	−	0.366827i	−0.0175477	−	0.0175477i
$438$		0			0
$439$			2.80498i			0.133874i	0.997757	+	0.0669371i	$0.0213227\pi$
$439$			2.80498i			0.133874i	−0.997757	+	0.0669371i	$0.978677\pi$
$440$	−1.07724	−	1.07724i	−0.0513552	−	0.0513552i
$441$		0			0
$442$	4.85088	+	3.31675i	0.230733	+	0.157762i
$443$		−	5.39588i		−	0.256366i	−0.991751	−	0.128183i	$-0.959086\pi$
$443$		−	5.39588i		−	0.256366i	0.991751	−	0.128183i	$-0.0409145\pi$
$444$		0			0
$445$	−41.7304			−1.97821
$446$	9.55565			0.452473
$447$		0			0
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	−0.0774135	−	0.0774135i	−0.00365337	−	0.00365337i	0.705278	−	0.708931i	$-0.250822\pi$
$449$	−0.0774135	−	0.0774135i	−0.00365337	−	0.00365337i	−0.708931	+	0.705278i	$0.750822\pi$
$450$		0			0
$451$	−1.10300			−0.0519381
$452$	7.68101			0.361284
$453$		0			0
$454$		−	5.53894i		−	0.259955i
$455$	−11.7763	+	2.21196i	−0.552082	+	0.103698i
$456$		0			0
$457$	−1.07515	−	1.07515i	−0.0502932	−	0.0502932i	0.681513	−	0.731806i	$-0.261322\pi$
$457$	−1.07515	−	1.07515i	−0.0502932	−	0.0502932i	−0.731806	+	0.681513i	$0.761322\pi$
$458$			14.6437i			0.684256i
$459$		0			0
$460$	0.149213	+	0.149213i	0.00695708	+	0.00695708i
$461$	8.12530	−	8.12530i	0.378433	−	0.378433i	−0.492104	−	0.870537i	$-0.663772\pi$
$461$	8.12530	−	8.12530i	0.378433	−	0.378433i	0.870537	+	0.492104i	$0.163772\pi$
$462$		0			0
$463$	−7.26506	+	7.26506i	−0.337636	+	0.337636i	−0.855477	−	0.517841i	$-0.826736\pi$
$463$	−7.26506	+	7.26506i	−0.337636	+	0.337636i	0.517841	+	0.855477i	$0.326736\pi$
$464$			4.93529i			0.229115i
$465$		0			0
$466$	−6.51357	+	6.51357i	−0.301736	+	0.301736i
$467$	−16.6533			−0.770623			−0.385311	−	0.922787i	$-0.625906\pi$
$467$	−16.6533			−0.770623			−0.385311	+	0.922787i	$0.625906\pi$
$468$		0			0
$469$	−7.31536			−0.337792
$470$	24.5880	−	24.5880i	1.13416	−	1.13416i
$471$		0			0
$472$		−	4.39492i		−	0.202293i
$473$	0.858754	−	0.858754i	0.0394856	−	0.0394856i
$474$		0			0
$475$	34.9176	−	34.9176i	1.60213	−	1.60213i
$476$	−1.15245	−	1.15245i	−0.0528226	−	0.0528226i
$477$		0			0
$478$		−	17.7262i		−	0.810780i
$479$	15.1218	+	15.1218i	0.690932	+	0.690932i	0.962437	−	0.271505i	$-0.0875215\pi$
$479$	15.1218	+	15.1218i	0.690932	+	0.690932i	−0.271505	+	0.962437i	$0.587521\pi$
$480$		0			0
$481$	−4.29407	−	2.93603i	−0.195793	−	0.133871i
$482$		−	6.19543i		−	0.282194i
$483$		0			0
$484$	−10.7899			−0.490448
$485$	−7.34247			−0.333404
$486$		0			0
$487$	6.57561	+	6.57561i	0.297969	+	0.297969i	0.840218	−	0.542249i	$-0.182427\pi$
$487$	6.57561	+	6.57561i	0.297969	+	0.297969i	−0.542249	+	0.840218i	$0.682427\pi$
$488$	4.25898	+	4.25898i	0.192795	+	0.192795i
$489$		0			0
$490$	3.32328			0.150130
$491$	10.5855			0.477715			0.238857	−	0.971055i	$-0.423227\pi$
$491$	10.5855			0.477715			0.238857	+	0.971055i	$0.423227\pi$
$492$		0			0
$493$		−	8.04361i		−	0.362266i
$494$	5.43792	+	28.9511i	0.244664	+	1.30257i
$495$		0			0
$496$	−6.43095	−	6.43095i	−0.288758	−	0.288758i
$497$		−	3.46226i		−	0.155304i
$498$		0			0
$499$	−6.72637	−	6.72637i	−0.301114	−	0.301114i	0.540336	−	0.841450i	$-0.318297\pi$
$499$	−6.72637	−	6.72637i	−0.301114	−	0.301114i	−0.841450	+	0.540336i	$0.818297\pi$
$500$	−2.45373	+	2.45373i	−0.109734	+	0.109734i
$501$		0			0
$502$	11.8139	−	11.8139i	0.527282	−	0.527282i
$503$			0.511519i			0.0228075i	0.999935	+	0.0114037i	$0.00363000\pi$
$503$			0.511519i			0.0228075i	−0.999935	+	0.0114037i	$0.996370\pi$
$504$		0			0
$505$	−37.2162	+	37.2162i	−1.65610	+	1.65610i
$506$	−0.0291081			−0.00129401
$507$		0			0
$508$	−0.345230			−0.0153171
$509$	−0.247912	+	0.247912i	−0.0109885	+	0.0109885i	−0.712580	−	0.701591i	$-0.752473\pi$
$509$	−0.247912	+	0.247912i	−0.0109885	+	0.0109885i	0.701591	+	0.712580i	$0.252473\pi$
$510$		0			0
$511$			9.42285i			0.416842i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	16.7693	−	16.7693i	0.739662	−	0.739662i
$515$	−21.0081	−	21.0081i	−0.925726	−	0.925726i
$516$		0			0
$517$			4.79657i			0.210953i
$518$	1.02017	+	1.02017i	0.0448236	+	0.0448236i
$519$		0			0
$520$	−2.21196	−	11.7763i	−0.0970009	−	0.516426i
$521$			36.1949i			1.58573i	0.609399	+	0.792864i	$0.291411\pi$
$521$			36.1949i			1.58573i	−0.609399	+	0.792864i	$0.708589\pi$
$522$		0			0
$523$	−16.7958			−0.734429			−0.367214	−	0.930136i	$-0.619688\pi$
$523$	−16.7958			−0.734429			−0.367214	+	0.930136i	$0.619688\pi$
$524$	−5.61993			−0.245508
$525$		0			0
$526$	17.3308	+	17.3308i	0.755659	+	0.755659i
$527$	10.4813	+	10.4813i	0.456571	+	0.456571i
$528$		0			0
$529$	−22.9960			−0.999825
$530$	19.2372			0.835611
$531$		0			0
$532$		−	8.17000i		−	0.354214i
$533$	−7.16140	−	4.89654i	−0.310195	−	0.212093i
$534$		0			0
$535$	−15.0360	−	15.0360i	−0.650063	−	0.650063i
$536$		−	7.31536i		−	0.315976i
$537$		0			0
$538$	1.87136	+	1.87136i	0.0806800	+	0.0806800i
$539$	−0.324149	+	0.324149i	−0.0139621	+	0.0139621i
$540$		0			0
$541$	13.8904	−	13.8904i	0.597197	−	0.597197i	−0.342369	−	0.939566i	$-0.611229\pi$
$541$	13.8904	−	13.8904i	0.597197	−	0.597197i	0.939566	+	0.342369i	$0.111229\pi$
$542$			25.2179i			1.08320i
$543$		0			0
$544$	1.15245	−	1.15245i	0.0494110	−	0.0494110i
$545$	19.4001			0.831011
$546$		0			0
$547$	−4.42168			−0.189057			−0.0945286	−	0.995522i	$-0.530134\pi$
$547$	−4.42168			−0.189057			−0.0945286	+	0.995522i	$0.530134\pi$
$548$	10.4753	−	10.4753i	0.447481	−	0.447481i
$549$		0			0
$550$		−	2.77074i		−	0.118145i
$551$	28.5115	−	28.5115i	1.21463	−	1.21463i
$552$		0			0
$553$	0.241410	−	0.241410i	0.0102658	−	0.0102658i
$554$	1.56312	+	1.56312i	0.0664106	+	0.0664106i
$555$		0			0
$556$		−	15.6420i		−	0.663370i
$557$	−5.48894	−	5.48894i	−0.232574	−	0.232574i	0.581192	−	0.813766i	$-0.302586\pi$
$557$	−5.48894	−	5.48894i	−0.232574	−	0.232574i	−0.813766	+	0.581192i	$0.802586\pi$
$558$		0			0
$559$	9.38788	−	1.76334i	0.397065	−	0.0745813i
$560$			3.32328i			0.140434i
$561$		0			0
$562$	11.4643			0.483591
$563$	17.7500			0.748074			0.374037	−	0.927414i	$-0.377973\pi$
$563$	17.7500			0.748074			0.374037	+	0.927414i	$0.377973\pi$
$564$		0			0
$565$	18.0497	+	18.0497i	0.759356	+	0.759356i
$566$	−17.4564	−	17.4564i	−0.733745	−	0.733745i
$567$		0			0
$568$	3.46226			0.145273
$569$	−31.3344			−1.31361			−0.656803	−	0.754063i	$-0.728091\pi$
$569$	−31.3344			−1.31361			−0.656803	+	0.754063i	$0.728091\pi$
$570$		0			0
$571$		−	0.467596i		−	0.0195683i	−0.999952	−	0.00978413i	$-0.996886\pi$
$571$		−	0.467596i		−	0.0195683i	0.999952	−	0.00978413i	$-0.00311444\pi$
$572$	1.36440	+	0.932895i	0.0570484	+	0.0390063i
$573$		0			0
$574$	1.70138	+	1.70138i	0.0710141	+	0.0710141i
$575$			0.383788i			0.0160051i
$576$		0			0
$577$	−21.0902	−	21.0902i	−0.877996	−	0.877996i	0.115331	−	0.993327i	$-0.463207\pi$
$577$	−21.0902	−	21.0902i	−0.877996	−	0.877996i	−0.993327	+	0.115331i	$0.963207\pi$
$578$	10.1425	−	10.1425i	0.421874	−	0.421874i
$579$		0			0
$580$	−11.5975	+	11.5975i	−0.481560	+	0.481560i
$581$		−	1.87187i		−	0.0776585i
$582$		0			0
$583$	−1.87637	+	1.87637i	−0.0777115	+	0.0777115i
$584$	−9.42285			−0.389920
$585$		0			0
$586$	19.6496			0.811718
$587$	−10.8388	+	10.8388i	−0.447365	+	0.447365i	−0.894478	−	0.447112i	$-0.852452\pi$
$587$	−10.8388	+	10.8388i	−0.447365	+	0.447365i	0.447112	+	0.894478i	$0.352452\pi$
$588$		0			0
$589$			74.3040i			3.06164i
$590$	10.3277	−	10.3277i	0.425184	−	0.425184i
$591$		0			0
$592$	−1.02017	+	1.02017i	−0.0419286	+	0.0419286i
$593$	−3.31352	−	3.31352i	−0.136070	−	0.136070i	0.635791	−	0.771861i	$-0.280674\pi$
$593$	−3.31352	−	3.31352i	−0.136070	−	0.136070i	−0.771861	+	0.635791i	$0.780674\pi$
$594$		0			0
$595$		−	5.41633i		−	0.222048i
$596$	7.62823	+	7.62823i	0.312464	+	0.312464i
$597$		0			0
$598$	−0.188989	−	0.129220i	−0.00772834	−	0.00528418i
$599$			35.4039i			1.44657i	0.690552	+	0.723283i	$0.257368\pi$
$599$			35.4039i			1.44657i	−0.690552	+	0.723283i	$0.742632\pi$
$600$		0			0
$601$	38.1203			1.55496			0.777480	−	0.628908i	$-0.216498\pi$
$601$	38.1203			1.55496			0.777480	+	0.628908i	$0.216498\pi$
$602$	−2.64926			−0.107976
$603$		0			0
$604$	−2.40058	−	2.40058i	−0.0976783	−	0.0976783i
$605$	−25.3552	−	25.3552i	−1.03084	−	1.03084i
$606$		0			0
$607$	−1.19850			−0.0486457			−0.0243229	−	0.999704i	$-0.507743\pi$
$607$	−1.19850			−0.0486457			−0.0243229	+	0.999704i	$0.507743\pi$
$608$	8.17000			0.331337
$609$		0			0
$610$			20.0165i			0.810442i
$611$	−21.2934	+	31.1426i	−0.861440	+	1.25989i
$612$		0			0
$613$	31.8712	+	31.8712i	1.28726	+	1.28726i	0.936442	+	0.350823i	$0.114098\pi$
$613$	31.8712	+	31.8712i	1.28726	+	1.28726i	0.350823	+	0.936442i	$0.385902\pi$
$614$		−	17.3136i		−	0.698718i
$615$		0			0
$616$	−0.324149	−	0.324149i	−0.0130603	−	0.0130603i
$617$	1.01263	−	1.01263i	0.0407670	−	0.0407670i	−0.686429	−	0.727196i	$-0.740823\pi$
$617$	1.01263	−	1.01263i	0.0407670	−	0.0407670i	0.727196	+	0.686429i	$0.240823\pi$
$618$		0			0
$619$	26.8814	−	26.8814i	1.08046	−	1.08046i	0.0839891	−	0.996467i	$-0.473234\pi$
$619$	26.8814	−	26.8814i	1.08046	−	1.08046i	0.996467	−	0.0839891i	$-0.0267661\pi$
$620$		−	30.2244i		−	1.21384i
$621$		0			0
$622$	−19.4347	+	19.4347i	−0.779262	+	0.779262i
$623$	−12.5570			−0.503086
$624$		0			0
$625$	18.6888			0.747552
$626$	24.5766	−	24.5766i	0.982279	−	0.982279i
$627$		0			0
$628$			6.14017i			0.245019i
$629$	1.66269	−	1.66269i	0.0662956	−	0.0662956i
$630$		0			0
$631$	1.03671	−	1.03671i	0.0412709	−	0.0412709i	−0.686170	−	0.727441i	$-0.740709\pi$
$631$	1.03671	−	1.03671i	0.0412709	−	0.0412709i	0.727441	+	0.686170i	$0.240709\pi$
$632$	0.241410	+	0.241410i	0.00960278	+	0.00960278i
$633$		0			0
$634$			11.1956i			0.444633i
$635$	−0.811260	−	0.811260i	−0.0321939	−	0.0321939i
$636$		0			0
$637$	−3.54358	+	0.665596i	−0.140402	+	0.0263719i
$638$		−	2.26241i		−	0.0895697i
$639$		0			0
$640$	−3.32328			−0.131364
$641$	37.0824			1.46467			0.732333	−	0.680946i	$-0.238431\pi$
$641$	37.0824			1.46467			0.732333	+	0.680946i	$0.238431\pi$
$642$		0			0
$643$	−3.90601	−	3.90601i	−0.154038	−	0.154038i	0.625881	−	0.779919i	$-0.284740\pi$
$643$	−3.90601	−	3.90601i	−0.154038	−	0.154038i	−0.779919	+	0.625881i	$0.784740\pi$
$644$	0.0448993	+	0.0448993i	0.00176928	+	0.00176928i
$645$		0			0
$646$	−13.3156			−0.523895
$647$	21.6049			0.849377			0.424689	−	0.905339i	$-0.360384\pi$
$647$	21.6049			0.849377			0.424689	+	0.905339i	$0.360384\pi$
$648$		0			0
$649$			2.01470i			0.0790838i
$650$	12.3002	−	17.9895i	0.482452	−	0.705607i
$651$		0			0
$652$	−8.31791	−	8.31791i	−0.325755	−	0.325755i
$653$			2.85031i			0.111541i	0.998444	+	0.0557705i	$0.0177615\pi$
$653$			2.85031i			0.111541i	−0.998444	+	0.0557705i	$0.982238\pi$
$654$		0			0
$655$	−13.2064	−	13.2064i	−0.516015	−	0.516015i
$656$	−1.70138	+	1.70138i	−0.0664276	+	0.0664276i
$657$		0			0
$658$	7.39872	−	7.39872i	0.288432	−	0.288432i
$659$			32.7638i			1.27629i	0.769914	+	0.638147i	$0.220299\pi$
$659$			32.7638i			1.27629i	−0.769914	+	0.638147i	$0.779701\pi$
$660$		0			0
$661$	−27.0495	+	27.0495i	−1.05211	+	1.05211i	−0.0535393	+	0.998566i	$0.517050\pi$
$661$	−27.0495	+	27.0495i	−1.05211	+	1.05211i	−0.998566	+	0.0535393i	$0.982950\pi$
$662$	−31.1803			−1.21186
$663$		0			0
$664$	1.87187			0.0726428
$665$	19.1988	−	19.1988i	0.744497	−	0.744497i
$666$		0			0
$667$			0.313377i			0.0121340i
$668$	16.1126	−	16.1126i	0.623417	−	0.623417i
$669$		0			0
$670$	17.1905	−	17.1905i	0.664126	−	0.664126i
$671$	−1.95238	−	1.95238i	−0.0753708	−	0.0753708i
$672$		0			0
$673$		−	4.59738i		−	0.177216i	−0.996067	−	0.0886080i	$-0.971758\pi$
$673$		−	4.59738i		−	0.177216i	0.996067	−	0.0886080i	$-0.0282418\pi$
$674$	−25.4161	−	25.4161i	−0.978991	−	0.978991i
$675$		0			0
$676$	4.71719	+	12.1140i	0.181430	+	0.465922i
$677$		−	3.00267i		−	0.115402i	−0.998334	−	0.0577010i	$-0.981623\pi$
$677$		−	3.00267i		−	0.115402i	0.998334	−	0.0577010i	$-0.0183770\pi$
$678$		0			0
$679$	−2.20941			−0.0847892
$680$	5.41633			0.207707
$681$		0			0
$682$	2.94805	+	2.94805i	0.112887	+	0.112887i
$683$	22.8496	+	22.8496i	0.874314	+	0.874314i	0.992939	−	0.118625i	$-0.0378486\pi$
$683$	22.8496	+	22.8496i	0.874314	+	0.874314i	−0.118625	+	0.992939i	$0.537849\pi$
$684$		0			0
$685$	49.2318			1.88105
$686$	1.00000			0.0381802
$687$		0			0
$688$		−	2.64926i		−	0.101002i
$689$	−20.5125	+	3.85289i	−0.781463	+	0.146783i
$690$		0			0
$691$	30.2769	+	30.2769i	1.15179	+	1.15179i	0.986194	+	0.165594i	$0.0529541\pi$
$691$	30.2769	+	30.2769i	1.15179	+	1.15179i	0.165594	+	0.986194i	$0.447046\pi$
$692$		−	22.3436i		−	0.849378i
$693$		0			0
$694$	−16.5092	−	16.5092i	−0.626680	−	0.626680i
$695$	36.7574	−	36.7574i	1.39429	−	1.39429i
$696$		0			0
$697$	2.77293	−	2.77293i	0.105032	−	0.105032i
$698$			5.25717i			0.198987i
$699$		0			0
$700$	−4.27388	+	4.27388i	−0.161537	+	0.161537i
$701$	44.8135			1.69258			0.846291	−	0.532721i	$-0.178831\pi$
$701$	44.8135			1.69258			0.846291	+	0.532721i	$0.178831\pi$
$702$		0			0
$703$	11.7871			0.444561
$704$	0.324149	−	0.324149i	0.0122168	−	0.0122168i
$705$		0			0
$706$			19.2258i			0.723574i
$707$	−11.1986	+	11.1986i	−0.421168	+	0.421168i
$708$		0			0
$709$	0.247922	−	0.247922i	0.00931089	−	0.00931089i	−0.702436	−	0.711747i	$-0.747904\pi$
$709$	0.247922	−	0.247922i	0.00931089	−	0.00931089i	0.711747	+	0.702436i	$0.247904\pi$
$710$	8.13601	+	8.13601i	0.305339	+	0.305339i
$711$		0			0
$712$		−	12.5570i		−	0.470594i
$713$	−0.408348	−	0.408348i	−0.0152927	−	0.0152927i
$714$		0			0
$715$	1.01400	+	5.39844i	0.0379213	+	0.201890i
$716$		−	18.6770i		−	0.697992i
$717$		0			0
$718$	−0.722392			−0.0269594
$719$	−35.7000			−1.33139			−0.665693	−	0.746225i	$-0.731864\pi$
$719$	−35.7000			−1.33139			−0.665693	+	0.746225i	$0.731864\pi$
$720$		0			0
$721$	−6.32149	−	6.32149i	−0.235425	−	0.235425i
$722$	−33.7636	−	33.7636i	−1.25655	−	1.25655i
$723$		0			0
$724$	22.6676			0.842436
$725$	−29.8298			−1.10785
$726$		0			0
$727$		−	27.3342i		−	1.01377i	−0.862014	−	0.506885i	$-0.830797\pi$
$727$		−	27.3342i		−	1.01377i	0.862014	−	0.506885i	$-0.169203\pi$
$728$	−0.665596	−	3.54358i	−0.0246686	−	0.131334i
$729$		0			0
$730$	−22.1429	−	22.1429i	−0.819545	−	0.819545i
$731$			4.31781i			0.159700i
$732$		0			0
$733$	−17.2102	−	17.2102i	−0.635675	−	0.635675i	0.313811	−	0.949485i	$-0.398394\pi$
$733$	−17.2102	−	17.2102i	−0.635675	−	0.635675i	−0.949485	+	0.313811i	$0.898394\pi$
$734$	1.47245	−	1.47245i	0.0543491	−	0.0543491i
$735$		0			0
$736$	−0.0448993	+	0.0448993i	−0.00165501	+	0.00165501i
$737$			3.35348i			0.123527i
$738$		0			0
$739$	−6.32632	+	6.32632i	−0.232718	+	0.232718i	−0.813826	−	0.581108i	$-0.802619\pi$
$739$	−6.32632	+	6.32632i	−0.232718	+	0.232718i	0.581108	+	0.813826i	$0.302619\pi$
$740$	−4.79461			−0.176253
$741$		0			0
$742$	5.78862			0.212507
$743$	−7.15604	+	7.15604i	−0.262530	+	0.262530i	−0.826081	−	0.563551i	$-0.809435\pi$
$743$	−7.15604	+	7.15604i	−0.262530	+	0.262530i	0.563551	+	0.826081i	$0.309435\pi$
$744$		0			0
$745$			35.8513i			1.31349i
$746$	−11.5030	+	11.5030i	−0.421155	+	0.421155i
$747$		0			0
$748$	−0.528302	+	0.528302i	−0.0193166	+	0.0193166i
$749$	−4.52445	−	4.52445i	−0.165320	−	0.165320i
$750$		0			0
$751$			22.5613i			0.823273i	0.911348	+	0.411637i	$0.135043\pi$
$751$			22.5613i			0.823273i	−0.911348	+	0.411637i	$0.864957\pi$
$752$	7.39872	+	7.39872i	0.269804	+	0.269804i
$753$		0			0
$754$	10.0435	−	14.6891i	0.365764	−	0.534945i
$755$		−	11.2823i		−	0.410606i
$756$		0			0
$757$	49.8330			1.81121			0.905605	−	0.424123i	$-0.139417\pi$
$757$	49.8330			1.81121			0.905605	+	0.424123i	$0.139417\pi$
$758$	13.5809			0.493282
$759$		0			0
$760$	19.1988	+	19.1988i	0.696413	+	0.696413i
$761$	−32.0627	−	32.0627i	−1.16227	−	1.16227i	−0.983977	−	0.178294i	$-0.942942\pi$
$761$	−32.0627	−	32.0627i	−1.16227	−	1.16227i	−0.178294	−	0.983977i	$-0.557058\pi$
$762$		0			0
$763$	5.83765			0.211337
$764$	17.1930			0.622022
$765$		0			0
$766$			10.3386i			0.373550i
$767$	−8.94385	+	13.0808i	−0.322944	+	0.472319i
$768$		0			0
$769$	−33.8870	−	33.8870i	−1.22200	−	1.22200i	−0.966921	−	0.255076i	$-0.917900\pi$
$769$	−33.8870	−	33.8870i	−1.22200	−	1.22200i	−0.255076	−	0.966921i	$-0.582100\pi$
$770$		−	1.52344i		−	0.0549010i
$771$		0			0
$772$	−2.65661	−	2.65661i	−0.0956135	−	0.0956135i
$773$	−3.31434	+	3.31434i	−0.119209	+	0.119209i	−0.764194	−	0.644986i	$-0.776863\pi$
$773$	−3.31434	+	3.31434i	−0.119209	+	0.119209i	0.644986	+	0.764194i	$0.276863\pi$
$774$		0			0
$775$	38.8698	−	38.8698i	1.39625	−	1.39625i
$776$		−	2.20941i		−	0.0793130i
$777$		0			0
$778$	14.6501	−	14.6501i	0.525231	−	0.525231i
$779$	19.6579			0.704318
$780$		0			0
$781$	−1.58715			−0.0567928
$782$	0.0731776	−	0.0731776i	0.00261682	−	0.00261682i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	−14.4289	+	14.4289i	−0.514988	+	0.514988i
$786$		0			0
$787$	16.1443	−	16.1443i	0.575481	−	0.575481i	−0.358174	−	0.933655i	$-0.616601\pi$
$787$	16.1443	−	16.1443i	0.575481	−	0.575481i	0.933655	+	0.358174i	$0.116601\pi$
$788$	4.66485	+	4.66485i	0.166178	+	0.166178i
$789$		0			0
$790$			1.13458i			0.0403667i
$791$	5.43129	+	5.43129i	0.193115	+	0.193115i
$792$		0			0
$793$	−4.00896	−	21.3434i	−0.142362	−	0.757925i
$794$			38.4954i			1.36615i
$795$		0			0
$796$	22.2752			0.789525
$797$	−53.0289			−1.87838			−0.939190	−	0.343398i	$-0.888422\pi$
$797$	−53.0289			−1.87838			−0.939190	+	0.343398i	$0.888422\pi$
$798$		0			0
$799$	−12.0586	−	12.0586i	−0.426601	−	0.426601i
$800$	−4.27388	−	4.27388i	−0.151104	−	0.151104i
$801$		0			0
$802$	−21.2085			−0.748899
$803$	4.31958			0.152435
$804$		0			0
$805$			0.211019i			0.00743744i
$806$	6.05343	+	32.2280i	0.213223	+	1.13518i
$807$		0			0
$808$	−11.1986	−	11.1986i	−0.393966	−	0.393966i
$809$		−	32.1044i		−	1.12873i	−0.825525	−	0.564365i	$-0.809121\pi$
$809$		−	32.1044i		−	1.12873i	0.825525	−	0.564365i	$-0.190879\pi$
$810$		0			0
$811$	18.4043	+	18.4043i	0.646262	+	0.646262i	0.952087	−	0.305826i	$-0.0989325\pi$
$811$	18.4043	+	18.4043i	0.646262	+	0.646262i	−0.305826	+	0.952087i	$0.598933\pi$
$812$	−3.48978	+	3.48978i	−0.122467	+	0.122467i
$813$		0			0
$814$	0.467661	−	0.467661i	0.0163915	−	0.0163915i
$815$		−	39.0927i		−	1.36936i
$816$		0			0
$817$	−15.3049	+	15.3049i	−0.535452	+	0.535452i
$818$	39.6063			1.38480
$819$		0			0
$820$	−7.99618			−0.279239
$821$	−28.0434	+	28.0434i	−0.978721	+	0.978721i	−0.999778	−	0.0210570i	$-0.993297\pi$
$821$	−28.0434	+	28.0434i	−0.978721	+	0.978721i	0.0210570	+	0.999778i	$0.493297\pi$
$822$		0			0
$823$			20.4780i			0.713818i	0.934139	+	0.356909i	$0.116169\pi$
$823$			20.4780i			0.713818i	−0.934139	+	0.356909i	$0.883831\pi$
$824$	6.32149	−	6.32149i	0.220219	−	0.220219i
$825$		0			0
$826$	3.10768	−	3.10768i	0.108130	−	0.108130i
$827$	11.5479	+	11.5479i	0.401561	+	0.401561i	0.878783	−	0.477222i	$-0.158356\pi$
$827$	11.5479	+	11.5479i	0.401561	+	0.401561i	−0.477222	+	0.878783i	$0.658356\pi$
$828$		0			0
$829$			30.8426i			1.07121i	0.844470	+	0.535603i	$0.179916\pi$
$829$			30.8426i			1.07121i	−0.844470	+	0.535603i	$0.820084\pi$
$830$	4.39874	+	4.39874i	0.152683	+	0.152683i
$831$		0			0
$832$	3.54358	−	0.665596i	0.122852	−	0.0230754i
$833$		−	1.62982i		−	0.0564698i
$834$		0			0
$835$	75.7266			2.62063
$836$	−3.74525			−0.129532
$837$		0			0
$838$	−26.4104	−	26.4104i	−0.912330	−	0.912330i
$839$	−17.9743	−	17.9743i	−0.620540	−	0.620540i	0.325129	−	0.945670i	$-0.394592\pi$
$839$	−17.9743	−	17.9743i	−0.620540	−	0.620540i	−0.945670	+	0.325129i	$0.894592\pi$
$840$		0			0
$841$	4.64293			0.160101
$842$	−29.0092			−0.999723
$843$		0			0
$844$			15.1062i			0.519977i
$845$	−17.3818	+	39.5517i	−0.597951	+	1.36062i
$846$		0			0
$847$	−7.62958	−	7.62958i	−0.262155	−	0.262155i
$848$			5.78862i			0.198782i
$849$		0			0
$850$	6.96564	+	6.96564i	0.238919	+	0.238919i
$851$	−0.0647778	+	0.0647778i	−0.00222055	+	0.00222055i
$852$		0			0
$853$	9.15287	−	9.15287i	0.313388	−	0.313388i	−0.532833	−	0.846221i	$-0.678872\pi$
$853$	9.15287	−	9.15287i	0.313388	−	0.313388i	0.846221	+	0.532833i	$0.178872\pi$
$854$			6.02310i			0.206106i
$855$		0			0
$856$	4.52445	−	4.52445i	0.154642	−	0.154642i
$857$	29.6346			1.01230			0.506149	−	0.862446i	$-0.331069\pi$
$857$	29.6346			1.01230			0.506149	+	0.862446i	$0.331069\pi$
$858$		0			0
$859$	−49.5643			−1.69111			−0.845556	−	0.533887i	$-0.820731\pi$
$859$	−49.5643			−1.69111			−0.845556	+	0.533887i	$0.820731\pi$
$860$	6.22553	−	6.22553i	0.212289	−	0.212289i
$861$		0			0
$862$		−	39.3780i		−	1.34122i
$863$	−20.7245	+	20.7245i	−0.705472	+	0.705472i	−0.965580	−	0.260108i	$-0.916242\pi$
$863$	−20.7245	+	20.7245i	−0.705472	+	0.705472i	0.260108	+	0.965580i	$0.416242\pi$
$864$		0			0
$865$	52.5056	−	52.5056i	1.78524	−	1.78524i
$866$	−16.7376	−	16.7376i	−0.568767	−	0.568767i
$867$		0			0
$868$		−	9.09474i		−	0.308696i
$869$	−0.110666	−	0.110666i	−0.00375409	−	0.00375409i
$870$		0			0
$871$	−14.8871	+	21.7730i	−0.504430	+	0.737750i
$872$			5.83765i			0.197688i
$873$		0			0
$874$	0.518772			0.0175477
$875$	−3.47010			−0.117311
$876$		0			0
$877$	7.26081	+	7.26081i	0.245180	+	0.245180i	0.818989	−	0.573809i	$-0.194535\pi$
$877$	7.26081	+	7.26081i	0.245180	+	0.245180i	−0.573809	+	0.818989i	$0.694535\pi$
$878$	−1.98342	−	1.98342i	−0.0669371	−	0.0669371i
$879$		0			0
$880$	1.52344			0.0513552
$881$	44.7712			1.50838			0.754191	−	0.656656i	$-0.228029\pi$
$881$	44.7712			1.50838			0.754191	+	0.656656i	$0.228029\pi$
$882$		0			0
$883$		−	34.4466i		−	1.15922i	−0.814894	−	0.579609i	$-0.803205\pi$
$883$		−	34.4466i		−	1.15922i	0.814894	−	0.579609i	$-0.196795\pi$
$884$	−5.77539	+	1.08480i	−0.194247	+	0.0364857i
$885$		0			0
$886$	3.81546	+	3.81546i	0.128183	+	0.128183i
$887$		−	35.4251i		−	1.18946i	−0.803926	−	0.594729i	$-0.797259\pi$
$887$		−	35.4251i		−	1.18946i	0.803926	−	0.594729i	$-0.202741\pi$
$888$		0			0
$889$	−0.244114	−	0.244114i	−0.00818733	−	0.00818733i
$890$	29.5079	−	29.5079i	0.989106	−	0.989106i
$891$		0			0
$892$	−6.75687	+	6.75687i	−0.226237	+	0.226237i
$893$		−	85.4858i		−	2.86067i
$894$		0			0
$895$	43.8893	−	43.8893i	1.46706	−	1.46706i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	0.109479			0.00365337
$899$	31.7386	−	31.7386i	1.05854	−	1.05854i
$900$		0			0
$901$		−	9.43439i		−	0.314305i
$902$	0.779937	−	0.779937i	0.0259691	−	0.0259691i
$903$		0			0
$904$	−5.43129	+	5.43129i	−0.180642	+	0.180642i
$905$	53.2670	+	53.2670i	1.77065	+	1.77065i
$906$		0			0
$907$		−	33.1702i		−	1.10140i	−0.834703	−	0.550700i	$-0.814361\pi$
$907$		−	33.1702i		−	1.10140i	0.834703	−	0.550700i	$-0.185639\pi$
$908$	3.91662	+	3.91662i	0.129978	+	0.129978i
$909$		0			0
$910$	6.76302	−	9.89120i	0.224192	−	0.327890i
$911$			11.7245i			0.388450i	0.980957	+	0.194225i	$0.0622192\pi$
$911$			11.7245i			0.388450i	−0.980957	+	0.194225i	$0.937781\pi$
$912$		0			0
$913$	−0.858096			−0.0283988
$914$	1.52049			0.0502932
$915$		0			0
$916$	−10.3547	−	10.3547i	−0.342128	−	0.342128i
$917$	−3.97389	−	3.97389i	−0.131230	−	0.131230i
$918$		0			0
$919$	38.9310			1.28421			0.642107	−	0.766615i	$-0.278061\pi$
$919$	38.9310			1.28421			0.642107	+	0.766615i	$0.278061\pi$
$920$	−0.211019			−0.00695708
$921$		0			0
$922$			11.4909i			0.378433i
$923$	−10.3049	−	7.04585i	−0.339189	−	0.231917i
$924$		0			0
$925$	−6.16608	−	6.16608i	−0.202739	−	0.202739i
$926$		−	10.2744i		−	0.337636i
$927$		0			0
$928$	−3.48978	−	3.48978i	−0.114557	−	0.114557i
$929$	12.1389	−	12.1389i	0.398264	−	0.398264i	−0.479356	−	0.877620i	$-0.659130\pi$
$929$	12.1389	−	12.1389i	0.398264	−	0.398264i	0.877620	+	0.479356i	$0.159130\pi$
$930$		0			0
$931$	5.77706	−	5.77706i	0.189336	−	0.189336i
$932$		−	9.21159i		−	0.301736i
$933$		0			0
$934$	11.7757	−	11.7757i	0.385311	−	0.385311i
$935$	−2.48293			−0.0812005
$936$		0			0
$937$	38.5000			1.25774			0.628870	−	0.777511i	$-0.283518\pi$
$937$	38.5000			1.25774			0.628870	+	0.777511i	$0.283518\pi$
$938$	5.17274	−	5.17274i	0.168896	−	0.168896i
$939$		0			0
$940$			34.7727i			1.13416i
$941$	−18.3074	+	18.3074i	−0.596803	+	0.596803i	−0.939460	−	0.342657i	$-0.888673\pi$
$941$	−18.3074	+	18.3074i	−0.596803	+	0.596803i	0.342657	+	0.939460i	$0.388673\pi$
$942$		0			0
$943$	−0.108033	+	0.108033i	−0.00351803	+	0.00351803i
$944$	3.10768	+	3.10768i	0.101146	+	0.101146i
$945$		0			0
$946$			1.21446i			0.0394856i
$947$	−34.2562	−	34.2562i	−1.11318	−	1.11318i	−0.992718	−	0.120459i	$-0.961563\pi$
$947$	−34.2562	−	34.2562i	−1.11318	−	1.11318i	−0.120459	−	0.992718i	$-0.538437\pi$
$948$		0			0
$949$	28.0456	+	19.1759i	0.910399	+	0.622477i
$950$			49.3809i			1.60213i
$951$		0			0
$952$	1.62982			0.0528226
$953$	−21.6617			−0.701692			−0.350846	−	0.936433i	$-0.614106\pi$
$953$	−21.6617			−0.701692			−0.350846	+	0.936433i	$0.614106\pi$
$954$		0			0
$955$	40.4021	+	40.4021i	1.30738	+	1.30738i
$956$	12.5343	+	12.5343i	0.405390	+	0.405390i
$957$		0			0
$958$	−21.3854			−0.690932
$959$	14.8142			0.478377
$960$		0			0
$961$			51.7144i			1.66821i
$962$	5.11245	−	0.960279i	0.164832	−	0.0309606i
$963$		0			0
$964$	4.38083	+	4.38083i	0.141097	+	0.141097i
$965$		−	12.4856i		−	0.401926i
$966$		0			0
$967$	−6.41773	−	6.41773i	−0.206380	−	0.206380i	0.596347	−	0.802727i	$-0.296618\pi$
$967$	−6.41773	−	6.41773i	−0.206380	−	0.206380i	−0.802727	+	0.596347i	$0.796618\pi$
$968$	7.62958	−	7.62958i	0.245224	−	0.245224i
$969$		0			0
$970$	5.19191	−	5.19191i	0.166702	−	0.166702i
$971$			14.3098i			0.459225i	0.973282	+	0.229612i	$0.0737458\pi$
$971$			14.3098i			0.459225i	−0.973282	+	0.229612i	$0.926254\pi$
$972$		0			0
$973$	11.0606	−	11.0606i	0.354586	−	0.354586i
$974$	−9.29932			−0.297969
$975$		0			0
$976$	−6.02310			−0.192795
$977$	−38.7117	+	38.7117i	−1.23850	+	1.23850i	−0.277880	+	0.960616i	$0.589632\pi$
$977$	−38.7117	+	38.7117i	−1.23850	+	1.23850i	−0.960616	+	0.277880i	$0.910368\pi$
$978$		0			0
$979$			5.75632i			0.183973i
$980$	−2.34991	+	2.34991i	−0.0750652	+	0.0750652i
$981$		0			0
$982$	−7.48504	+	7.48504i	−0.238857	+	0.238857i
$983$	8.82770	+	8.82770i	0.281560	+	0.281560i	0.833731	−	0.552171i	$-0.186200\pi$
$983$	8.82770	+	8.82770i	0.281560	+	0.281560i	−0.552171	+	0.833731i	$0.686200\pi$
$984$		0			0
$985$			21.9240i			0.698556i
$986$	5.68769	+	5.68769i	0.181133	+	0.181133i
$987$		0			0
$988$	−24.3167	−	16.6263i	−0.773617	−	0.528953i
$989$		−	0.168221i		−	0.00534910i
$990$		0			0
$991$	−21.6781			−0.688629			−0.344314	−	0.938854i	$-0.611889\pi$
$991$	−21.6781			−0.688629			−0.344314	+	0.938854i	$0.611889\pi$
$992$	9.09474			0.288758
$993$		0			0
$994$	2.44819	+	2.44819i	0.0776518	+	0.0776518i
$995$	52.3448	+	52.3448i	1.65944	+	1.65944i
$996$		0			0
$997$	4.75475			0.150584			0.0752922	−	0.997162i	$-0.476011\pi$
$997$	4.75475			0.150584			0.0752922	+	0.997162i	$0.476011\pi$
$998$	9.51253			0.301114
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.y.c.827.4	✓	16
3.2	odd	2		1638.2.y.d.827.5	yes	16
13.5	odd	4		1638.2.y.d.1331.5	yes	16
39.5	even	4	inner	1638.2.y.c.1331.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.y.c.827.4	✓	16	1.1	even	1	trivial
1638.2.y.c.1331.4	yes	16	39.5	even	4	inner
1638.2.y.d.827.5	yes	16	3.2	odd	2
1638.2.y.d.1331.5	yes	16	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.34991 - 2.34991i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.32328i q^{10} +(-0.324149 - 0.324149i) q^{11} +(-0.665596 - 3.54358i) q^{13} +1.00000i q^{14} -1.00000 q^{16} +1.62982 q^{17} +(5.77706 + 5.77706i) q^{19} +(-2.34991 - 2.34991i) q^{20} +0.458415 q^{22} -0.0634972 q^{23} -6.04418i q^{25} +(2.97634 + 2.03504i) q^{26} +(-0.707107 - 0.707107i) q^{28} -4.93529i q^{29} +(6.43095 + 6.43095i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.15245 + 1.15245i) q^{34} -3.32328i q^{35} +(1.02017 - 1.02017i) q^{37} -8.17000 q^{38} +3.32328 q^{40} +(1.70138 - 1.70138i) q^{41} +2.64926i q^{43} +(-0.324149 + 0.324149i) q^{44} +(0.0448993 - 0.0448993i) q^{46} +(-7.39872 - 7.39872i) q^{47} -1.00000i q^{49} +(4.27388 + 4.27388i) q^{50} +(-3.54358 + 0.665596i) q^{52} -5.78862i q^{53} -1.52344 q^{55} +1.00000 q^{56} +(3.48978 + 3.48978i) q^{58} +(-3.10768 - 3.10768i) q^{59} +6.02310 q^{61} -9.09474 q^{62} +1.00000i q^{64} +(-9.89120 - 6.76302i) q^{65} +(-5.17274 - 5.17274i) q^{67} -1.62982i q^{68} +(2.34991 + 2.34991i) q^{70} +(2.44819 - 2.44819i) q^{71} +(-6.66296 + 6.66296i) q^{73} +1.44274i q^{74} +(5.77706 - 5.77706i) q^{76} -0.458415 q^{77} +0.341405 q^{79} +(-2.34991 + 2.34991i) q^{80} +2.40611i q^{82} +(1.32362 - 1.32362i) q^{83} +(3.82992 - 3.82992i) q^{85} +(-1.87331 - 1.87331i) q^{86} -0.458415i q^{88} +(-8.87914 - 8.87914i) q^{89} +(-2.97634 - 2.03504i) q^{91} +0.0634972i q^{92} +10.4634 q^{94} +27.1512 q^{95} +(-1.56229 - 1.56229i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{5} + 8 q^{11} + 4 q^{13} - 16 q^{16} + 8 q^{17} + 16 q^{19} + 4 q^{20} - 8 q^{22} - 24 q^{23} - 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} - 16 q^{38} + 16 q^{41} + 8 q^{44} - 4 q^{47} + 16 q^{50}+ \cdots - 28 q^{97}+O(q^{100}) \) 16 * q - 4 * q^5 + 8 * q^11 + 4 * q^13 - 16 * q^16 + 8 * q^17 + 16 * q^19 + 4 * q^20 - 8 * q^22 - 24 * q^23 - 8 * q^26 - 8 * q^31 + 4 * q^34 - 4 * q^37 - 16 * q^38 + 16 * q^41 + 8 * q^44 - 4 * q^47 + 16 * q^50 - 16 * q^55 + 16 * q^56 + 4 * q^58 + 8 * q^59 - 40 * q^61 - 24 * q^62 - 56 * q^65 - 4 * q^67 - 4 * q^70 + 24 * q^71 - 12 * q^73 + 16 * q^76 + 8 * q^77 + 16 * q^79 + 4 * q^80 + 8 * q^85 - 24 * q^86 - 16 * q^89 + 8 * q^91 - 8 * q^94 + 40 * q^95 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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