LMFDB - Embedded newform 1638.2.y.d.827.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(827,1638)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$16$
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			827.8
Root			$-0.777611 - 1.87732i$ of defining polynomial
Character	$\chi$	$=$	1638.827
Dual form			1638.2.y.d.1331.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(3.00337 - 3.00337i) q^{5} +(0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(3.00337 - 3.00337i) q^{5} +(0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} -4.24741i q^{10} +(-2.53473 - 2.53473i) q^{11} +(2.84530 + 2.21455i) q^{13} -1.00000i q^{14} -1.00000 q^{16} +7.16415 q^{17} +(4.75928 + 4.75928i) q^{19} +(-3.00337 - 3.00337i) q^{20} -3.58464 q^{22} -5.70954 q^{23} -13.0405i q^{25} +(3.57786 - 0.446008i) q^{26} +(-0.707107 - 0.707107i) q^{28} -3.76120i q^{29} +(0.0835445 + 0.0835445i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.06582 - 5.06582i) q^{34} -4.24741i q^{35} +(-1.86236 + 1.86236i) q^{37} +6.73064 q^{38} -4.24741 q^{40} +(-3.47354 + 3.47354i) q^{41} +7.91560i q^{43} +(-2.53473 + 2.53473i) q^{44} +(-4.03725 + 4.03725i) q^{46} +(-1.55421 - 1.55421i) q^{47} -1.00000i q^{49} +(-9.22102 - 9.22102i) q^{50} +(2.21455 - 2.84530i) q^{52} -5.22095i q^{53} -15.2255 q^{55} -1.00000 q^{56} +(-2.65957 - 2.65957i) q^{58} +(4.33095 + 4.33095i) q^{59} -12.2542 q^{61} +0.118150 q^{62} +1.00000i q^{64} +(15.1966 - 1.89438i) q^{65} +(0.568664 + 0.568664i) q^{67} -7.16415i q^{68} +(-3.00337 - 3.00337i) q^{70} +(-8.61297 + 8.61297i) q^{71} +(-3.94683 + 3.94683i) q^{73} +2.63378i q^{74} +(4.75928 - 4.75928i) q^{76} -3.58464 q^{77} -9.08222 q^{79} +(-3.00337 + 3.00337i) q^{80} +4.91233i q^{82} +(8.23786 - 8.23786i) q^{83} +(21.5166 - 21.5166i) q^{85} +(5.59717 + 5.59717i) q^{86} +3.58464i q^{88} +(8.69652 + 8.69652i) q^{89} +(3.57786 - 0.446008i) q^{91} +5.70954i q^{92} -2.19799 q^{94} +28.5878 q^{95} +(-9.42542 - 9.42542i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^5	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	3.00337	−	3.00337i	1.34315	−	1.34315i	0.450243	−	0.892906i	$-0.351337\pi$
$5$	3.00337	−	3.00337i	1.34315	−	1.34315i	0.892906	−	0.450243i	$-0.148663\pi$
$6$		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
$10$		−	4.24741i		−	1.34315i
$11$	−2.53473	−	2.53473i	−0.764249	−	0.764249i	0.212839	−	0.977087i	$-0.431729\pi$
$11$	−2.53473	−	2.53473i	−0.764249	−	0.764249i	−0.977087	+	0.212839i	$0.931729\pi$
$12$		0			0
$13$	2.84530	+	2.21455i	0.789145	+	0.614207i
$13$	2.84530	+	2.21455i	0.789145	+	0.614207i
$14$		−	1.00000i		−	0.267261i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	7.16415			1.73756			0.868781	−	0.495196i	$-0.164904\pi$
$17$	7.16415			1.73756			0.868781	+	0.495196i	$0.164904\pi$
$18$		0			0
$19$	4.75928	+	4.75928i	1.09185	+	1.09185i	0.995331	+	0.0965227i	$0.0307720\pi$
$19$	4.75928	+	4.75928i	1.09185	+	1.09185i	0.0965227	+	0.995331i	$0.469228\pi$
$20$	−3.00337	−	3.00337i	−0.671575	−	0.671575i
$21$		0			0
$22$	−3.58464			−0.764249
$23$	−5.70954			−1.19052			−0.595261	−	0.803533i	$-0.702951\pi$
$23$	−5.70954			−1.19052			−0.595261	+	0.803533i	$0.702951\pi$
$24$		0			0
$25$		−	13.0405i		−	2.60810i
$26$	3.57786	−	0.446008i	0.701676	−	0.0874694i
$27$		0			0
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$		−	3.76120i		−	0.698438i	−0.937041	−	0.349219i	$-0.886447\pi$
$29$		−	3.76120i		−	0.698438i	0.937041	−	0.349219i	$-0.113553\pi$
$30$		0			0
$31$	0.0835445	+	0.0835445i	0.0150050	+	0.0150050i	0.714569	−	0.699564i	$-0.246623\pi$
$31$	0.0835445	+	0.0835445i	0.0150050	+	0.0150050i	−0.699564	+	0.714569i	$0.746623\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	5.06582	−	5.06582i	0.868781	−	0.868781i
$35$		−	4.24741i		−	0.717943i
$36$		0			0
$37$	−1.86236	+	1.86236i	−0.306171	+	0.306171i	−0.843422	−	0.537251i	$-0.819463\pi$
$37$	−1.86236	+	1.86236i	−0.306171	+	0.306171i	0.537251	+	0.843422i	$0.319463\pi$
$38$	6.73064			1.09185
$39$		0			0
$40$	−4.24741			−0.671575
$41$	−3.47354	+	3.47354i	−0.542476	+	0.542476i	−0.924254	−	0.381778i	$-0.875312\pi$
$41$	−3.47354	+	3.47354i	−0.542476	+	0.542476i	0.381778	+	0.924254i	$0.375312\pi$
$42$		0			0
$43$			7.91560i			1.20712i	0.797318	+	0.603559i	$0.206251\pi$
$43$			7.91560i			1.20712i	−0.797318	+	0.603559i	$0.793749\pi$
$44$	−2.53473	+	2.53473i	−0.382124	+	0.382124i
$45$		0			0
$46$	−4.03725	+	4.03725i	−0.595261	+	0.595261i
$47$	−1.55421	−	1.55421i	−0.226705	−	0.226705i	0.584610	−	0.811315i	$-0.301248\pi$
$47$	−1.55421	−	1.55421i	−0.226705	−	0.226705i	−0.811315	+	0.584610i	$0.801248\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	−9.22102	−	9.22102i	−1.30405	−	1.30405i
$51$		0			0
$52$	2.21455	−	2.84530i	0.307103	−	0.394573i
$53$		−	5.22095i		−	0.717153i	−0.933500	−	0.358576i	$-0.883262\pi$
$53$		−	5.22095i		−	0.717153i	0.933500	−	0.358576i	$-0.116738\pi$
$54$		0			0
$55$	−15.2255			−2.05300
$56$	−1.00000			−0.133631
$57$		0			0
$58$	−2.65957	−	2.65957i	−0.349219	−	0.349219i
$59$	4.33095	+	4.33095i	0.563842	+	0.563842i	0.930397	−	0.366554i	$-0.119463\pi$
$59$	4.33095	+	4.33095i	0.563842	+	0.563842i	−0.366554	+	0.930397i	$0.619463\pi$
$60$		0			0
$61$	−12.2542			−1.56898			−0.784492	−	0.620139i	$-0.787076\pi$
$61$	−12.2542			−1.56898			−0.784492	+	0.620139i	$0.787076\pi$
$62$	0.118150			0.0150050
$63$		0			0
$64$			1.00000i			0.125000i
$65$	15.1966	−	1.89438i	1.88491	−	0.234969i
$66$		0			0
$67$	0.568664	+	0.568664i	0.0694734	+	0.0694734i	0.740990	−	0.671516i	$-0.234357\pi$
$67$	0.568664	+	0.568664i	0.0694734	+	0.0694734i	−0.671516	+	0.740990i	$0.734357\pi$
$68$		−	7.16415i		−	0.868781i
$69$		0			0
$70$	−3.00337	−	3.00337i	−0.358972	−	0.358972i
$71$	−8.61297	+	8.61297i	−1.02217	+	1.02217i	−0.0224230	+	0.999749i	$0.507138\pi$
$71$	−8.61297	+	8.61297i	−1.02217	+	1.02217i	−0.999749	+	0.0224230i	$0.992862\pi$
$72$		0			0
$73$	−3.94683	+	3.94683i	−0.461942	+	0.461942i	−0.899292	−	0.437350i	$-0.855917\pi$
$73$	−3.94683	+	3.94683i	−0.461942	+	0.461942i	0.437350	+	0.899292i	$0.355917\pi$
$74$			2.63378i			0.306171i
$75$		0			0
$76$	4.75928	−	4.75928i	0.545927	−	0.545927i
$77$	−3.58464			−0.408508
$78$		0			0
$79$	−9.08222			−1.02183			−0.510915	−	0.859631i	$-0.670693\pi$
$79$	−9.08222			−1.02183			−0.510915	+	0.859631i	$0.670693\pi$
$80$	−3.00337	+	3.00337i	−0.335787	+	0.335787i
$81$		0			0
$82$			4.91233i			0.542476i
$83$	8.23786	−	8.23786i	0.904223	−	0.904223i	−0.0915751	−	0.995798i	$-0.529190\pi$
$83$	8.23786	−	8.23786i	0.904223	−	0.904223i	0.995798	+	0.0915751i	$0.0291902\pi$
$84$		0			0
$85$	21.5166	−	21.5166i	2.33380	−	2.33380i
$86$	5.59717	+	5.59717i	0.603559	+	0.603559i
$87$		0			0
$88$			3.58464i			0.382124i
$89$	8.69652	+	8.69652i	0.921829	+	0.921829i	0.997159	−	0.0753299i	$-0.0240010\pi$
$89$	8.69652	+	8.69652i	0.921829	+	0.921829i	−0.0753299	+	0.997159i	$0.524001\pi$
$90$		0			0
$91$	3.57786	−	0.446008i	0.375062	−	0.0467544i
$92$			5.70954i			0.595261i
$93$		0			0
$94$	−2.19799			−0.226705
$95$	28.5878			2.93304
$96$		0			0
$97$	−9.42542	−	9.42542i	−0.957006	−	0.957006i	0.0421070	−	0.999113i	$-0.486593\pi$
$97$	−9.42542	−	9.42542i	−0.957006	−	0.957006i	−0.999113	+	0.0421070i	$0.986593\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$		0			0
$100$	−13.0405			−1.30405
$101$	8.94096			0.889658			0.444829	−	0.895615i	$-0.353264\pi$
$101$	8.94096			0.889658			0.444829	+	0.895615i	$0.353264\pi$
$102$		0			0
$103$			17.4234i			1.71678i	0.512995	+	0.858392i	$0.328536\pi$
$103$			17.4234i			1.71678i	−0.512995	+	0.858392i	$0.671464\pi$
$104$	−0.446008	−	3.57786i	−0.0437347	−	0.350838i
$105$		0			0
$106$	−3.69177	−	3.69177i	−0.358576	−	0.358576i
$107$			6.36508i			0.615335i	0.951494	+	0.307668i	$0.0995485\pi$
$107$			6.36508i			0.615335i	−0.951494	+	0.307668i	$0.900452\pi$
$108$		0			0
$109$	2.46859	+	2.46859i	0.236448	+	0.236448i	0.815378	−	0.578930i	$-0.196529\pi$
$109$	2.46859	+	2.46859i	0.236448	+	0.236448i	−0.578930	+	0.815378i	$0.696529\pi$
$110$	−10.7660	+	10.7660i	−1.02650	+	1.02650i
$111$		0			0
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$			4.11099i			0.386729i	0.981127	+	0.193365i	$0.0619401\pi$
$113$			4.11099i			0.386729i	−0.981127	+	0.193365i	$0.938060\pi$
$114$		0			0
$115$	−17.1479	+	17.1479i	−1.59905	+	1.59905i
$116$	−3.76120			−0.349219
$117$		0			0
$118$	6.12490			0.563842
$119$	5.06582	−	5.06582i	0.464383	−	0.464383i
$120$		0			0
$121$			1.84968i			0.168153i
$122$	−8.66500	+	8.66500i	−0.784492	+	0.784492i
$123$		0			0
$124$	0.0835445	−	0.0835445i	0.00750252	−	0.00750252i
$125$	−24.1486	−	24.1486i	−2.15992	−	2.15992i
$126$		0			0
$127$		−	19.7825i		−	1.75541i	−0.479201	−	0.877705i	$-0.659073\pi$
$127$		−	19.7825i		−	1.75541i	0.479201	−	0.877705i	$-0.340927\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	9.40612	−	12.0852i	0.824971	−	1.05994i
$131$		−	12.9454i		−	1.13104i	−0.824733	−	0.565522i	$-0.808675\pi$
$131$		−	12.9454i		−	1.13104i	0.824733	−	0.565522i	$-0.191325\pi$
$132$		0			0
$133$	6.73064			0.583620
$134$	0.804213			0.0694734
$135$		0			0
$136$	−5.06582	−	5.06582i	−0.434391	−	0.434391i
$137$	−6.35706	−	6.35706i	−0.543120	−	0.543120i	0.381322	−	0.924442i	$-0.375469\pi$
$137$	−6.35706	−	6.35706i	−0.543120	−	0.543120i	−0.924442	+	0.381322i	$0.875469\pi$
$138$		0			0
$139$	−1.45054			−0.123033			−0.0615165	−	0.998106i	$-0.519594\pi$
$139$	−1.45054			−0.123033			−0.0615165	+	0.998106i	$0.519594\pi$
$140$	−4.24741			−0.358972
$141$		0			0
$142$			12.1806i			1.02217i
$143$	−1.59878	−	12.8254i	−0.133697	−	1.07251i
$144$		0			0
$145$	−11.2963	−	11.2963i	−0.938106	−	0.938106i
$146$			5.58166i			0.461942i
$147$		0			0
$148$	1.86236	+	1.86236i	0.153085	+	0.153085i
$149$	5.20091	−	5.20091i	0.426075	−	0.426075i	−0.461214	−	0.887289i	$-0.652586\pi$
$149$	5.20091	−	5.20091i	0.426075	−	0.426075i	0.887289	+	0.461214i	$0.152586\pi$
$150$		0			0
$151$	−7.76020	+	7.76020i	−0.631516	+	0.631516i	−0.948448	−	0.316932i	$-0.897347\pi$
$151$	−7.76020	+	7.76020i	−0.631516	+	0.631516i	0.316932	+	0.948448i	$0.397347\pi$
$152$		−	6.73064i		−	0.545927i
$153$		0			0
$154$	−2.53473	+	2.53473i	−0.204254	+	0.204254i
$155$	0.501831			0.0403080
$156$		0			0
$157$	11.7086			0.934446			0.467223	−	0.884139i	$-0.345254\pi$
$157$	11.7086			0.934446			0.467223	+	0.884139i	$0.345254\pi$
$158$	−6.42210	+	6.42210i	−0.510915	+	0.510915i
$159$		0			0
$160$			4.24741i			0.335787i
$161$	−4.03725	+	4.03725i	−0.318180	+	0.318180i
$162$		0			0
$163$	2.18476	−	2.18476i	0.171124	−	0.171124i	−0.616349	−	0.787473i	$-0.711389\pi$
$163$	2.18476	−	2.18476i	0.171124	−	0.171124i	0.787473	+	0.616349i	$0.211389\pi$
$164$	3.47354	+	3.47354i	0.271238	+	0.271238i
$165$		0			0
$166$		−	11.6501i		−	0.904223i
$167$	−2.11815	−	2.11815i	−0.163908	−	0.163908i	0.620388	−	0.784295i	$-0.286975\pi$
$167$	−2.11815	−	2.11815i	−0.163908	−	0.163908i	−0.784295	+	0.620388i	$0.786975\pi$
$168$		0			0
$169$	3.19151	+	12.6022i	0.245501	+	0.969396i
$170$		−	30.4291i		−	2.33380i
$171$		0			0
$172$	7.91560			0.603559
$173$	5.06663			0.385209			0.192604	−	0.981276i	$-0.438307\pi$
$173$	5.06663			0.385209			0.192604	+	0.981276i	$0.438307\pi$
$174$		0			0
$175$	−9.22102	−	9.22102i	−0.697044	−	0.697044i
$176$	2.53473	+	2.53473i	0.191062	+	0.191062i
$177$		0			0
$178$	12.2987			0.921829
$179$	0.961445			0.0718618			0.0359309	−	0.999354i	$-0.488560\pi$
$179$	0.961445			0.0718618			0.0359309	+	0.999354i	$0.488560\pi$
$180$		0			0
$181$			14.9714i			1.11282i	0.830909	+	0.556408i	$0.187821\pi$
$181$			14.9714i			1.11282i	−0.830909	+	0.556408i	$0.812179\pi$
$182$	2.21455	−	2.84530i	0.164154	−	0.210908i
$183$		0			0
$184$	4.03725	+	4.03725i	0.297630	+	0.297630i
$185$			11.1868i			0.822466i
$186$		0			0
$187$	−18.1592	−	18.1592i	−1.32793	−	1.32793i
$188$	−1.55421	+	1.55421i	−0.113353	+	0.113353i
$189$		0			0
$190$	20.2146	−	20.2146i	1.46652	−	1.46652i
$191$			19.5793i			1.41671i	0.705856	+	0.708356i	$0.250563\pi$
$191$			19.5793i			1.41671i	−0.705856	+	0.708356i	$0.749437\pi$
$192$		0			0
$193$	−4.06219	+	4.06219i	−0.292403	+	0.292403i	−0.838029	−	0.545626i	$-0.816292\pi$
$193$	−4.06219	+	4.06219i	−0.292403	+	0.292403i	0.545626	+	0.838029i	$0.316292\pi$
$194$	−13.3296			−0.957006
$195$		0			0
$196$	−1.00000			−0.0714286
$197$	−4.34520	+	4.34520i	−0.309583	+	0.309583i	−0.844748	−	0.535165i	$-0.820249\pi$
$197$	−4.34520	+	4.34520i	−0.309583	+	0.309583i	0.535165	+	0.844748i	$0.320249\pi$
$198$		0			0
$199$			0.564211i			0.0399959i	0.999800	+	0.0199979i	$0.00636596\pi$
$199$			0.564211i			0.0399959i	−0.999800	+	0.0199979i	$0.993634\pi$
$200$	−9.22102	+	9.22102i	−0.652025	+	0.652025i
$201$		0			0
$202$	6.32221	−	6.32221i	0.444829	−	0.444829i
$203$	−2.65957	−	2.65957i	−0.186665	−	0.186665i
$204$		0			0
$205$			20.8647i			1.45725i
$206$	12.3202	+	12.3202i	0.858392	+	0.858392i
$207$		0			0
$208$	−2.84530	−	2.21455i	−0.197286	−	0.153552i
$209$		−	24.1269i		−	1.66890i
$210$		0			0
$211$	13.3542			0.919342			0.459671	−	0.888089i	$-0.347967\pi$
$211$	13.3542			0.919342			0.459671	+	0.888089i	$0.347967\pi$
$212$	−5.22095			−0.358576
$213$		0			0
$214$	4.50079	+	4.50079i	0.307668	+	0.307668i
$215$	23.7735	+	23.7735i	1.62134	+	1.62134i
$216$		0			0
$217$	0.118150			0.00802053
$218$	3.49111			0.236448
$219$		0			0
$220$			15.2255i			1.02650i
$221$	20.3842	+	15.8654i	1.37119	+	1.06722i
$222$		0			0
$223$	3.80927	+	3.80927i	0.255087	+	0.255087i	0.823053	−	0.567965i	$-0.192269\pi$
$223$	3.80927	+	3.80927i	0.255087	+	0.255087i	−0.567965	+	0.823053i	$0.692269\pi$
$224$			1.00000i			0.0668153i
$225$		0			0
$226$	2.90691	+	2.90691i	0.193365	+	0.193365i
$227$	9.92499	−	9.92499i	0.658744	−	0.658744i	−0.296339	−	0.955083i	$-0.595766\pi$
$227$	9.92499	−	9.92499i	0.658744	−	0.658744i	0.955083	+	0.296339i	$0.0957657\pi$
$228$		0			0
$229$	6.50911	−	6.50911i	0.430134	−	0.430134i	−0.458540	−	0.888674i	$-0.651627\pi$
$229$	6.50911	−	6.50911i	0.430134	−	0.430134i	0.888674	+	0.458540i	$0.151627\pi$
$230$			24.2508i			1.59905i
$231$		0			0
$232$	−2.65957	+	2.65957i	−0.174609	+	0.174609i
$233$	17.0947			1.11991			0.559955	−	0.828523i	$-0.310819\pi$
$233$	17.0947			1.11991			0.559955	+	0.828523i	$0.310819\pi$
$234$		0			0
$235$	−9.33576			−0.608998
$236$	4.33095	−	4.33095i	0.281921	−	0.281921i
$237$		0			0
$238$		−	7.16415i		−	0.464383i
$239$	−5.78149	+	5.78149i	−0.373974	+	0.373974i	−0.868922	−	0.494949i	$-0.835187\pi$
$239$	−5.78149	+	5.78149i	−0.373974	+	0.373974i	0.494949	+	0.868922i	$0.335187\pi$
$240$		0			0
$241$	14.4471	−	14.4471i	0.930622	−	0.930622i	−0.0671225	−	0.997745i	$-0.521382\pi$
$241$	14.4471	−	14.4471i	0.930622	−	0.930622i	0.997745	+	0.0671225i	$0.0213818\pi$
$242$	1.30792	+	1.30792i	0.0840763	+	0.0840763i
$243$		0			0
$244$			12.2542i			0.784492i
$245$	−3.00337	−	3.00337i	−0.191878	−	0.191878i
$246$		0			0
$247$	3.00192	+	24.0813i	0.191008	+	1.53225i
$248$		−	0.118150i		−	0.00750252i
$249$		0			0
$250$	−34.1513			−2.15992
$251$	−17.0939			−1.07896			−0.539479	−	0.841999i	$-0.681379\pi$
$251$	−17.0939			−1.07896			−0.539479	+	0.841999i	$0.681379\pi$
$252$		0			0
$253$	14.4721	+	14.4721i	0.909855	+	0.909855i
$254$	−13.9883	−	13.9883i	−0.877705	−	0.877705i
$255$		0			0
$256$	1.00000			0.0625000
$257$	25.8713			1.61381			0.806903	−	0.590684i	$-0.201142\pi$
$257$	25.8713			1.61381			0.806903	+	0.590684i	$0.201142\pi$
$258$		0			0
$259$			2.63378i			0.163655i
$260$	−1.89438	−	15.1966i	−0.117484	−	0.942455i
$261$		0			0
$262$	−9.15378	−	9.15378i	−0.565522	−	0.565522i
$263$		−	4.09575i		−	0.252555i	−0.991995	−	0.126277i	$-0.959697\pi$
$263$		−	4.09575i		−	0.252555i	0.991995	−	0.126277i	$-0.0403029\pi$
$264$		0			0
$265$	−15.6805	−	15.6805i	−0.963243	−	0.963243i
$266$	4.75928	−	4.75928i	0.291810	−	0.291810i
$267$		0			0
$268$	0.568664	−	0.568664i	0.0347367	−	0.0347367i
$269$			22.4500i			1.36880i	0.729106	+	0.684400i	$0.239936\pi$
$269$			22.4500i			1.36880i	−0.729106	+	0.684400i	$0.760064\pi$
$270$		0			0
$271$	15.1392	−	15.1392i	0.919643	−	0.919643i	−0.0773603	−	0.997003i	$-0.524649\pi$
$271$	15.1392	−	15.1392i	0.919643	−	0.919643i	0.997003	+	0.0773603i	$0.0246492\pi$
$272$	−7.16415			−0.434391
$273$		0			0
$274$	−8.99023			−0.543120
$275$	−33.0541	+	33.0541i	−1.99324	+	1.99324i
$276$		0			0
$277$			24.5278i			1.47373i	0.676037	+	0.736867i	$0.263696\pi$
$277$			24.5278i			1.47373i	−0.676037	+	0.736867i	$0.736304\pi$
$278$	−1.02569	+	1.02569i	−0.0615165	+	0.0615165i
$279$		0			0
$280$	−3.00337	+	3.00337i	−0.179486	+	0.179486i
$281$	−5.13979	−	5.13979i	−0.306614	−	0.306614i	0.536981	−	0.843595i	$-0.319565\pi$
$281$	−5.13979	−	5.13979i	−0.306614	−	0.306614i	−0.843595	+	0.536981i	$0.819565\pi$
$282$		0			0
$283$		−	2.58173i		−	0.153468i	−0.997052	−	0.0767340i	$-0.975551\pi$
$283$		−	2.58173i		−	0.153468i	0.997052	−	0.0767340i	$-0.0244492\pi$
$284$	8.61297	+	8.61297i	0.511086	+	0.511086i
$285$		0			0
$286$	−10.1994	−	7.93839i	−0.603103	−	0.469407i
$287$			4.91233i			0.289966i
$288$		0			0
$289$	34.3251			2.01912
$290$	−15.9754			−0.938106
$291$		0			0
$292$	3.94683	+	3.94683i	0.230971	+	0.230971i
$293$	3.60392	+	3.60392i	0.210543	+	0.210543i	0.804498	−	0.593955i	$-0.202434\pi$
$293$	3.60392	+	3.60392i	0.210543	+	0.210543i	−0.593955	+	0.804498i	$0.702434\pi$
$294$		0			0
$295$	26.0149			1.51465
$296$	2.63378			0.153085
$297$		0			0
$298$		−	7.35520i		−	0.426075i
$299$	−16.2454	−	12.6441i	−0.939494	−	0.731226i
$300$		0			0
$301$	5.59717	+	5.59717i	0.322616	+	0.322616i
$302$			10.9746i			0.631516i
$303$		0			0
$304$	−4.75928	−	4.75928i	−0.272963	−	0.272963i
$305$	−36.8038	+	36.8038i	−2.10738	+	2.10738i
$306$		0			0
$307$	−14.0322	+	14.0322i	−0.800858	+	0.800858i	−0.983230	−	0.182371i	$-0.941623\pi$
$307$	−14.0322	+	14.0322i	−0.800858	+	0.800858i	0.182371	+	0.983230i	$0.441623\pi$
$308$			3.58464i			0.204254i
$309$		0			0
$310$	0.354848	−	0.354848i	0.0201540	−	0.0201540i
$311$	−22.4477			−1.27289			−0.636445	−	0.771322i	$-0.719596\pi$
$311$	−22.4477			−1.27289			−0.636445	+	0.771322i	$0.719596\pi$
$312$		0			0
$313$	23.3587			1.32031			0.660156	−	0.751128i	$-0.270490\pi$
$313$	23.3587			1.32031			0.660156	+	0.751128i	$0.270490\pi$
$314$	8.27922	−	8.27922i	0.467223	−	0.467223i
$315$		0			0
$316$			9.08222i			0.510915i
$317$	1.86545	−	1.86545i	0.104774	−	0.104774i	−0.652777	−	0.757551i	$-0.726396\pi$
$317$	1.86545	−	1.86545i	0.104774	−	0.104774i	0.757551	+	0.652777i	$0.226396\pi$
$318$		0			0
$319$	−9.53362	+	9.53362i	−0.533780	+	0.533780i
$320$	3.00337	+	3.00337i	0.167894	+	0.167894i
$321$		0			0
$322$			5.70954i			0.318180i
$323$	34.0962	+	34.0962i	1.89716	+	1.89716i
$324$		0			0
$325$	28.8789	−	37.1042i	1.60191	−	2.05817i
$326$		−	3.08972i		−	0.171124i
$327$		0			0
$328$	4.91233			0.271238
$329$	−2.19799			−0.121179
$330$		0			0
$331$	−15.6984	−	15.6984i	−0.862862	−	0.862862i	0.128808	−	0.991670i	$-0.458885\pi$
$331$	−15.6984	−	15.6984i	−0.862862	−	0.862862i	−0.991670	+	0.128808i	$0.958885\pi$
$332$	−8.23786	−	8.23786i	−0.452112	−	0.452112i
$333$		0			0
$334$	−2.99552			−0.163908
$335$	3.41582			0.186626
$336$		0			0
$337$			5.07534i			0.276471i	0.990399	+	0.138236i	$0.0441431\pi$
$337$			5.07534i			0.276471i	−0.990399	+	0.138236i	$0.955857\pi$
$338$	11.1678	+	6.65433i	0.607449	+	0.361948i
$339$		0			0
$340$	−21.5166	−	21.5166i	−1.16690	−	1.16690i
$341$		−	0.423525i		−	0.0229352i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	5.59717	−	5.59717i	0.301779	−	0.301779i
$345$		0			0
$346$	3.58265	−	3.58265i	0.192604	−	0.192604i
$347$		−	14.2741i		−	0.766276i	−0.923691	−	0.383138i	$-0.874843\pi$
$347$		−	14.2741i		−	0.766276i	0.923691	−	0.383138i	$-0.125157\pi$
$348$		0			0
$349$	−6.17873	+	6.17873i	−0.330740	+	0.330740i	−0.852867	−	0.522127i	$-0.825139\pi$
$349$	−6.17873	+	6.17873i	−0.330740	+	0.330740i	0.522127	+	0.852867i	$0.325139\pi$
$350$	−13.0405			−0.697044
$351$		0			0
$352$	3.58464			0.191062
$353$	18.3126	−	18.3126i	0.974679	−	0.974679i	−0.0250078	−	0.999687i	$-0.507961\pi$
$353$	18.3126	−	18.3126i	0.974679	−	0.974679i	0.999687	+	0.0250078i	$0.00796107\pi$
$354$		0			0
$355$			51.7359i			2.74586i
$356$	8.69652	−	8.69652i	0.460914	−	0.460914i
$357$		0			0
$358$	0.679845	−	0.679845i	0.0359309	−	0.0359309i
$359$	0.831801	+	0.831801i	0.0439008	+	0.0439008i	0.728716	−	0.684816i	$-0.240117\pi$
$359$	0.831801	+	0.831801i	0.0439008	+	0.0439008i	−0.684816	+	0.728716i	$0.740117\pi$
$360$		0			0
$361$			26.3015i			1.38429i
$362$	10.5864	+	10.5864i	0.556408	+	0.556408i
$363$		0			0
$364$	−0.446008	−	3.57786i	−0.0233772	−	0.187531i
$365$			23.7076i			1.24091i
$366$		0			0
$367$	33.1794			1.73195			0.865975	−	0.500088i	$-0.166699\pi$
$367$	33.1794			1.73195			0.865975	+	0.500088i	$0.166699\pi$
$368$	5.70954			0.297630
$369$		0			0
$370$	7.91023	+	7.91023i	0.411233	+	0.411233i
$371$	−3.69177	−	3.69177i	−0.191667	−	0.191667i
$372$		0			0
$373$	−30.4259			−1.57539			−0.787697	−	0.616063i	$-0.788727\pi$
$373$	−30.4259			−1.57539			−0.787697	+	0.616063i	$0.788727\pi$
$374$	−25.6809			−1.32793
$375$		0			0
$376$			2.19799i			0.113353i
$377$	8.32938	−	10.7018i	0.428985	−	0.551169i
$378$		0			0
$379$	12.1657	+	12.1657i	0.624911	+	0.624911i	0.946783	−	0.321873i	$-0.104312\pi$
$379$	12.1657	+	12.1657i	0.624911	+	0.624911i	−0.321873	+	0.946783i	$0.604312\pi$
$380$		−	28.5878i		−	1.46652i
$381$		0			0
$382$	13.8447	+	13.8447i	0.708356	+	0.708356i
$383$	−26.5124	+	26.5124i	−1.35472	+	1.35472i	−0.474425	+	0.880296i	$0.657344\pi$
$383$	−26.5124	+	26.5124i	−1.35472	+	1.35472i	−0.880296	+	0.474425i	$0.842656\pi$
$384$		0			0
$385$	−10.7660	+	10.7660i	−0.548687	+	0.548687i
$386$			5.74480i			0.292403i
$387$		0			0
$388$	−9.42542	+	9.42542i	−0.478503	+	0.478503i
$389$	−3.73757			−0.189502			−0.0947512	−	0.995501i	$-0.530206\pi$
$389$	−3.73757			−0.189502			−0.0947512	+	0.995501i	$0.530206\pi$
$390$		0			0
$391$	−40.9040			−2.06860
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$		0			0
$394$			6.14504i			0.309583i
$395$	−27.2773	+	27.2773i	−1.37247	+	1.37247i
$396$		0			0
$397$	−22.9598	+	22.9598i	−1.15232	+	1.15232i	−0.166231	+	0.986087i	$0.553160\pi$
$397$	−22.9598	+	22.9598i	−1.15232	+	1.15232i	−0.986087	+	0.166231i	$0.946840\pi$
$398$	0.398958	+	0.398958i	0.0199979	+	0.0199979i
$399$		0			0
$400$			13.0405i			0.652025i
$401$	−15.6263	−	15.6263i	−0.780341	−	0.780341i	0.199547	−	0.979888i	$-0.436053\pi$
$401$	−15.6263	−	15.6263i	−0.780341	−	0.780341i	−0.979888	+	0.199547i	$0.936053\pi$
$402$		0			0
$403$	0.0526958	+	0.422723i	0.00262496	+	0.0210573i
$404$		−	8.94096i		−	0.444829i
$405$		0			0
$406$	−3.76120			−0.186665
$407$	9.44117			0.467982
$408$		0			0
$409$	19.4055	+	19.4055i	0.959539	+	0.959539i	0.999213	−	0.0396740i	$-0.0126319\pi$
$409$	19.4055	+	19.4055i	0.959539	+	0.959539i	−0.0396740	+	0.999213i	$0.512632\pi$
$410$	14.7536	+	14.7536i	0.728627	+	0.728627i
$411$		0			0
$412$	17.4234			0.858392
$413$	6.12490			0.301386
$414$		0			0
$415$		−	49.4828i		−	2.42901i
$416$	−3.57786	+	0.446008i	−0.175419	+	0.0218673i
$417$		0			0
$418$	−17.0603	−	17.0603i	−0.834448	−	0.834448i
$419$			8.84076i			0.431899i	0.976404	+	0.215950i	$0.0692847\pi$
$419$			8.84076i			0.431899i	−0.976404	+	0.215950i	$0.930715\pi$
$420$		0			0
$421$	7.59479	+	7.59479i	0.370147	+	0.370147i	0.867531	−	0.497383i	$-0.165706\pi$
$421$	7.59479	+	7.59479i	0.370147	+	0.370147i	−0.497383	+	0.867531i	$0.665706\pi$
$422$	9.44285	−	9.44285i	0.459671	−	0.459671i
$423$		0			0
$424$	−3.69177	+	3.69177i	−0.179288	+	0.179288i
$425$		−	93.4241i		−	4.53173i
$426$		0			0
$427$	−8.66500	+	8.66500i	−0.419329	+	0.419329i
$428$	6.36508			0.307668
$429$		0			0
$430$	33.6208			1.62134
$431$	2.99857	−	2.99857i	0.144436	−	0.144436i	−0.631191	−	0.775627i	$-0.717434\pi$
$431$	2.99857	−	2.99857i	0.144436	−	0.144436i	0.775627	+	0.631191i	$0.217434\pi$
$432$		0			0
$433$			10.4330i			0.501380i	0.968067	+	0.250690i	$0.0806574\pi$
$433$			10.4330i			0.501380i	−0.968067	+	0.250690i	$0.919343\pi$
$434$	0.0835445	−	0.0835445i	0.00401026	−	0.00401026i
$435$		0			0
$436$	2.46859	−	2.46859i	0.118224	−	0.118224i
$437$	−27.1733	−	27.1733i	−1.29987	−	1.29987i
$438$		0			0
$439$			11.5804i			0.552703i	0.961057	+	0.276352i	$0.0891255\pi$
$439$			11.5804i			0.552703i	−0.961057	+	0.276352i	$0.910875\pi$
$440$	10.7660	+	10.7660i	0.513250	+	0.513250i
$441$		0			0
$442$	25.6323	−	3.19527i	1.21921	−	0.151983i
$443$		−	11.7229i		−	0.556971i	−0.960440	−	0.278486i	$-0.910168\pi$
$443$		−	11.7229i		−	0.556971i	0.960440	−	0.278486i	$-0.0898325\pi$
$444$		0			0
$445$	52.2378			2.47631
$446$	5.38712			0.255087
$447$		0			0
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	−19.0283	−	19.0283i	−0.898000	−	0.898000i	0.0972590	−	0.995259i	$-0.468992\pi$
$449$	−19.0283	−	19.0283i	−0.898000	−	0.898000i	−0.995259	+	0.0972590i	$0.968992\pi$
$450$		0			0
$451$	17.6090			0.829174
$452$	4.11099			0.193365
$453$		0			0
$454$		−	14.0360i		−	0.658744i
$455$	9.40612	−	12.0852i	0.440966	−	0.566562i
$456$		0			0
$457$	−25.1280	−	25.1280i	−1.17544	−	1.17544i	−0.980894	−	0.194544i	$-0.937677\pi$
$457$	−25.1280	−	25.1280i	−1.17544	−	1.17544i	−0.194544	−	0.980894i	$-0.562323\pi$
$458$		−	9.20528i		−	0.430134i
$459$		0			0
$460$	17.1479	+	17.1479i	0.799524	+	0.799524i
$461$	−21.5174	+	21.5174i	−1.00216	+	1.00216i	−0.00216692	+	0.999998i	$0.500690\pi$
$461$	−21.5174	+	21.5174i	−1.00216	+	1.00216i	−0.999998	+	0.00216692i	$0.999310\pi$
$462$		0			0
$463$	12.6794	−	12.6794i	0.589263	−	0.589263i	−0.348169	−	0.937432i	$-0.613196\pi$
$463$	12.6794	−	12.6794i	0.589263	−	0.589263i	0.937432	+	0.348169i	$0.113196\pi$
$464$			3.76120i			0.174609i
$465$		0			0
$466$	12.0878	−	12.0878i	0.559955	−	0.559955i
$467$	−12.6572			−0.585706			−0.292853	−	0.956157i	$-0.594605\pi$
$467$	−12.6572			−0.585706			−0.292853	+	0.956157i	$0.594605\pi$
$468$		0			0
$469$	0.804213			0.0371351
$470$	−6.60138	+	6.60138i	−0.304499	+	0.304499i
$471$		0			0
$472$		−	6.12490i		−	0.281921i
$473$	20.0639	−	20.0639i	0.922538	−	0.922538i
$474$		0			0
$475$	62.0634	−	62.0634i	2.84766	−	2.84766i
$476$	−5.06582	−	5.06582i	−0.232191	−	0.232191i
$477$		0			0
$478$			8.17627i			0.373974i
$479$	−6.81265	−	6.81265i	−0.311278	−	0.311278i	0.534127	−	0.845405i	$-0.320641\pi$
$479$	−6.81265	−	6.81265i	−0.311278	−	0.311278i	−0.845405	+	0.534127i	$0.820641\pi$
$480$		0			0
$481$	−9.42330	+	1.17469i	−0.429665	+	0.0535612i
$482$		−	20.4313i		−	0.930622i
$483$		0			0
$484$	1.84968			0.0840763
$485$	−56.6161			−2.57080
$486$		0			0
$487$	20.4577	+	20.4577i	0.927026	+	0.927026i	0.997513	−	0.0704871i	$-0.0224554\pi$
$487$	20.4577	+	20.4577i	0.927026	+	0.927026i	−0.0704871	+	0.997513i	$0.522455\pi$
$488$	8.66500	+	8.66500i	0.392246	+	0.392246i
$489$		0			0
$490$	−4.24741			−0.191878
$491$	40.9998			1.85030			0.925148	−	0.379606i	$-0.123941\pi$
$491$	40.9998			1.85030			0.925148	+	0.379606i	$0.123941\pi$
$492$		0			0
$493$		−	26.9458i		−	1.21358i
$494$	19.1507	+	14.9054i	0.861631	+	0.670624i
$495$		0			0
$496$	−0.0835445	−	0.0835445i	−0.00375126	−	0.00375126i
$497$			12.1806i			0.546374i
$498$		0			0
$499$	3.12135	+	3.12135i	0.139731	+	0.139731i	0.773512	−	0.633781i	$-0.218498\pi$
$499$	3.12135	+	3.12135i	0.139731	+	0.139731i	−0.633781	+	0.773512i	$0.718498\pi$
$500$	−24.1486	+	24.1486i	−1.07996	+	1.07996i
$501$		0			0
$502$	−12.0872	+	12.0872i	−0.539479	+	0.539479i
$503$			0.981307i			0.0437543i	0.999761	+	0.0218771i	$0.00696427\pi$
$503$			0.981307i			0.0437543i	−0.999761	+	0.0218771i	$0.993036\pi$
$504$		0			0
$505$	26.8530	−	26.8530i	1.19494	−	1.19494i
$506$	20.4667			0.909855
$507$		0			0
$508$	−19.7825			−0.877705
$509$	−16.9483	+	16.9483i	−0.751219	+	0.751219i	−0.974707	−	0.223488i	$-0.928256\pi$
$509$	−16.9483	+	16.9483i	−0.751219	+	0.751219i	0.223488	+	0.974707i	$0.428256\pi$
$510$		0			0
$511$			5.58166i			0.246918i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	18.2938	−	18.2938i	0.806903	−	0.806903i
$515$	52.3291	+	52.3291i	2.30590	+	2.30590i
$516$		0			0
$517$			7.87901i			0.346518i
$518$	1.86236	+	1.86236i	0.0818276	+	0.0818276i
$519$		0			0
$520$	−12.0852	−	9.40612i	−0.529970	−	0.412485i
$521$		−	44.4621i		−	1.94792i	−0.226723	−	0.973959i	$-0.572801\pi$
$521$		−	44.4621i		−	1.94792i	0.226723	−	0.973959i	$-0.427199\pi$
$522$		0			0
$523$	1.28397			0.0561441			0.0280720	−	0.999606i	$-0.491063\pi$
$523$	1.28397			0.0561441			0.0280720	+	0.999606i	$0.491063\pi$
$524$	−12.9454			−0.565522
$525$		0			0
$526$	−2.89613	−	2.89613i	−0.126277	−	0.126277i
$527$	0.598526	+	0.598526i	0.0260722	+	0.0260722i
$528$		0			0
$529$	9.59885			0.417341
$530$	−22.1755			−0.963243
$531$		0			0
$532$		−	6.73064i		−	0.291810i
$533$	−17.5756	+	2.19094i	−0.761285	+	0.0949002i
$534$		0			0
$535$	19.1167	+	19.1167i	0.826487	+	0.826487i
$536$		−	0.804213i		−	0.0347367i
$537$		0			0
$538$	15.8745	+	15.8745i	0.684400	+	0.684400i
$539$	−2.53473	+	2.53473i	−0.109178	+	0.109178i
$540$		0			0
$541$	24.2007	−	24.2007i	1.04047	−	1.04047i	0.0413221	−	0.999146i	$-0.486843\pi$
$541$	24.2007	−	24.2007i	1.04047	−	1.04047i	0.999146	−	0.0413221i	$-0.0131570\pi$
$542$		−	21.4101i		−	0.919643i
$543$		0			0
$544$	−5.06582	+	5.06582i	−0.217195	+	0.217195i
$545$	14.8282			0.635170
$546$		0			0
$547$	−23.8487			−1.01970			−0.509849	−	0.860264i	$-0.670299\pi$
$547$	−23.8487			−1.01970			−0.509849	+	0.860264i	$0.670299\pi$
$548$	−6.35706	+	6.35706i	−0.271560	+	0.271560i
$549$		0			0
$550$			46.7455i			1.99324i
$551$	17.9006	−	17.9006i	0.762592	−	0.762592i
$552$		0			0
$553$	−6.42210	+	6.42210i	−0.273095	+	0.273095i
$554$	17.3438	+	17.3438i	0.736867	+	0.736867i
$555$		0			0
$556$			1.45054i			0.0615165i
$557$	−26.4867	−	26.4867i	−1.12228	−	1.12228i	−0.991398	−	0.130881i	$-0.958220\pi$
$557$	−26.4867	−	26.4867i	−1.12228	−	1.12228i	−0.130881	−	0.991398i	$-0.541780\pi$
$558$		0			0
$559$	−17.5295	+	22.5223i	−0.741420	+	0.952591i
$560$			4.24741i			0.179486i
$561$		0			0
$562$	−7.26876			−0.306614
$563$	−19.0628			−0.803401			−0.401701	−	0.915771i	$-0.631581\pi$
$563$	−19.0628			−0.803401			−0.401701	+	0.915771i	$0.631581\pi$
$564$		0			0
$565$	12.3468	+	12.3468i	0.519435	+	0.519435i
$566$	−1.82556	−	1.82556i	−0.0767340	−	0.0767340i
$567$		0			0
$568$	12.1806			0.511086
$569$	6.65003			0.278784			0.139392	−	0.990237i	$-0.455485\pi$
$569$	6.65003			0.278784			0.139392	+	0.990237i	$0.455485\pi$
$570$		0			0
$571$		−	29.8722i		−	1.25011i	−0.780579	−	0.625057i	$-0.785076\pi$
$571$		−	29.8722i		−	1.25011i	0.780579	−	0.625057i	$-0.214924\pi$
$572$	−12.8254	+	1.59878i	−0.536255	+	0.0668484i
$573$		0			0
$574$	3.47354	+	3.47354i	0.144983	+	0.144983i
$575$			74.4552i			3.10500i
$576$		0			0
$577$	−8.74494	−	8.74494i	−0.364057	−	0.364057i	0.501247	−	0.865304i	$-0.332875\pi$
$577$	−8.74494	−	8.74494i	−0.364057	−	0.364057i	−0.865304	+	0.501247i	$0.832875\pi$
$578$	24.2715	−	24.2715i	1.00956	−	1.00956i
$579$		0			0
$580$	−11.2963	+	11.2963i	−0.469053	+	0.469053i
$581$		−	11.6501i		−	0.483328i
$582$		0			0
$583$	−13.2337	+	13.2337i	−0.548083	+	0.548083i
$584$	5.58166			0.230971
$585$		0			0
$586$	5.09672			0.210543
$587$	24.7147	−	24.7147i	1.02009	−	1.02009i	0.0202912	−	0.999794i	$-0.493541\pi$
$587$	24.7147	−	24.7147i	1.02009	−	1.02009i	0.999794	−	0.0202912i	$-0.00645934\pi$
$588$		0			0
$589$			0.795223i			0.0327666i
$590$	18.3953	−	18.3953i	0.757324	−	0.757324i
$591$		0			0
$592$	1.86236	−	1.86236i	0.0765427	−	0.0765427i
$593$	−17.5245	−	17.5245i	−0.719645	−	0.719645i	0.248888	−	0.968532i	$-0.419935\pi$
$593$	−17.5245	−	17.5245i	−0.719645	−	0.719645i	−0.968532	+	0.248888i	$0.919935\pi$
$594$		0			0
$595$		−	30.4291i		−	1.24747i
$596$	−5.20091	−	5.20091i	−0.213038	−	0.213038i
$597$		0			0
$598$	−20.4279	+	2.54650i	−0.835360	+	0.104134i
$599$			12.1383i			0.495958i	0.968765	+	0.247979i	$0.0797664\pi$
$599$			12.1383i			0.495958i	−0.968765	+	0.247979i	$0.920234\pi$
$600$		0			0
$601$	−37.5161			−1.53031			−0.765156	−	0.643845i	$-0.777338\pi$
$601$	−37.5161			−1.53031			−0.765156	+	0.643845i	$0.777338\pi$
$602$	7.91560			0.322616
$603$		0			0
$604$	7.76020	+	7.76020i	0.315758	+	0.315758i
$605$	5.55527	+	5.55527i	0.225854	+	0.225854i
$606$		0			0
$607$	−11.2703			−0.457448			−0.228724	−	0.973491i	$-0.573455\pi$
$607$	−11.2703			−0.457448			−0.228724	+	0.973491i	$0.573455\pi$
$608$	−6.73064			−0.272963
$609$		0			0
$610$			52.0484i			2.10738i
$611$	−0.980320	−	7.86409i	−0.0396595	−	0.318147i
$612$		0			0
$613$	−15.9175	−	15.9175i	−0.642902	−	0.642902i	0.308366	−	0.951268i	$-0.400218\pi$
$613$	−15.9175	−	15.9175i	−0.642902	−	0.642902i	−0.951268	+	0.308366i	$0.900218\pi$
$614$			19.8445i			0.800858i
$615$		0			0
$616$	2.53473	+	2.53473i	0.102127	+	0.102127i
$617$	−24.0948	+	24.0948i	−0.970021	+	0.970021i	−0.999564	−	0.0295423i	$-0.990595\pi$
$617$	−24.0948	+	24.0948i	−0.970021	+	0.970021i	0.0295423	+	0.999564i	$0.490595\pi$
$618$		0			0
$619$	−31.9301	+	31.9301i	−1.28338	+	1.28338i	−0.344648	+	0.938732i	$0.612002\pi$
$619$	−31.9301	+	31.9301i	−1.28338	+	1.28338i	−0.938732	+	0.344648i	$0.887998\pi$
$620$		−	0.501831i		−	0.0201540i
$621$		0			0
$622$	−15.8729	+	15.8729i	−0.636445	+	0.636445i
$623$	12.2987			0.492738
$624$		0			0
$625$	−79.8520			−3.19408
$626$	16.5171	−	16.5171i	0.660156	−	0.660156i
$627$		0			0
$628$		−	11.7086i		−	0.467223i
$629$	−13.3423	+	13.3423i	−0.531991	+	0.531991i
$630$		0			0
$631$	32.0392	−	32.0392i	1.27546	−	1.27546i	0.332277	−	0.943182i	$-0.392183\pi$
$631$	32.0392	−	32.0392i	1.27546	−	1.27546i	0.943182	−	0.332277i	$-0.107817\pi$
$632$	6.42210	+	6.42210i	0.255457	+	0.255457i
$633$		0			0
$634$		−	2.63814i		−	0.104774i
$635$	−59.4141	−	59.4141i	−2.35778	−	2.35778i
$636$		0			0
$637$	2.21455	−	2.84530i	0.0877438	−	0.112735i
$638$			13.4826i			0.533780i
$639$		0			0
$640$	4.24741			0.167894
$641$	45.8530			1.81108			0.905542	−	0.424256i	$-0.139464\pi$
$641$	45.8530			1.81108			0.905542	+	0.424256i	$0.139464\pi$
$642$		0			0
$643$	−23.0966	−	23.0966i	−0.910841	−	0.910841i	0.0854970	−	0.996338i	$-0.472752\pi$
$643$	−23.0966	−	23.0966i	−0.910841	−	0.910841i	−0.996338	+	0.0854970i	$0.972752\pi$
$644$	4.03725	+	4.03725i	0.159090	+	0.159090i
$645$		0			0
$646$	48.2193			1.89716
$647$	22.8866			0.899765			0.449882	−	0.893088i	$-0.351466\pi$
$647$	22.8866			0.899765			0.449882	+	0.893088i	$0.351466\pi$
$648$		0			0
$649$		−	21.9556i		−	0.861832i
$650$	−5.81617	−	46.6571i	−0.228129	−	1.83004i
$651$		0			0
$652$	−2.18476	−	2.18476i	−0.0855618	−	0.0855618i
$653$			6.65079i			0.260266i	0.991497	+	0.130133i	$0.0415404\pi$
$653$			6.65079i			0.260266i	−0.991497	+	0.130133i	$0.958460\pi$
$654$		0			0
$655$	−38.8799	−	38.8799i	−1.51916	−	1.51916i
$656$	3.47354	−	3.47354i	0.135619	−	0.135619i
$657$		0			0
$658$	−1.55421	+	1.55421i	−0.0605895	+	0.0605895i
$659$			26.9997i			1.05176i	0.850559	+	0.525880i	$0.176264\pi$
$659$			26.9997i			1.05176i	−0.850559	+	0.525880i	$0.823736\pi$
$660$		0			0
$661$	23.4722	−	23.4722i	0.912962	−	0.912962i	−0.0835420	−	0.996504i	$-0.526623\pi$
$661$	23.4722	−	23.4722i	0.912962	−	0.912962i	0.996504	+	0.0835420i	$0.0266233\pi$
$662$	−22.2009			−0.862862
$663$		0			0
$664$	−11.6501			−0.452112
$665$	20.2146	−	20.2146i	0.783889	−	0.783889i
$666$		0			0
$667$			21.4747i			0.831505i
$668$	−2.11815	+	2.11815i	−0.0819538	+	0.0819538i
$669$		0			0
$670$	2.41535	−	2.41535i	0.0933132	−	0.0933132i
$671$	31.0609	+	31.0609i	1.19909	+	1.19909i
$672$		0			0
$673$			23.1428i			0.892090i	0.895011	+	0.446045i	$0.147168\pi$
$673$			23.1428i			0.892090i	−0.895011	+	0.446045i	$0.852832\pi$
$674$	3.58880	+	3.58880i	0.138236	+	0.138236i
$675$		0			0
$676$	12.6022	−	3.19151i	0.484698	−	0.122750i
$677$			30.5270i			1.17325i	0.809859	+	0.586625i	$0.199544\pi$
$677$			30.5270i			1.17325i	−0.809859	+	0.586625i	$0.800456\pi$
$678$		0			0
$679$	−13.3296			−0.511541
$680$	−30.4291			−1.16690
$681$		0			0
$682$	−0.299477	−	0.299477i	−0.0114676	−	0.0114676i
$683$	28.1274	+	28.1274i	1.07627	+	1.07627i	0.996841	+	0.0794250i	$0.0253084\pi$
$683$	28.1274	+	28.1274i	1.07627	+	1.07627i	0.0794250	+	0.996841i	$0.474692\pi$
$684$		0			0
$685$	−38.1852			−1.45898
$686$	−1.00000			−0.0381802
$687$		0			0
$688$		−	7.91560i		−	0.301779i
$689$	11.5621	−	14.8552i	0.440480	−	0.565938i
$690$		0			0
$691$	−33.4816	−	33.4816i	−1.27370	−	1.27370i	−0.944132	−	0.329569i	$-0.893097\pi$
$691$	−33.4816	−	33.4816i	−1.27370	−	1.27370i	−0.329569	−	0.944132i	$-0.606903\pi$
$692$		−	5.06663i		−	0.192604i
$693$		0			0
$694$	−10.0933	−	10.0933i	−0.383138	−	0.383138i
$695$	−4.35651	+	4.35651i	−0.165252	+	0.165252i
$696$		0			0
$697$	−24.8850	+	24.8850i	−0.942586	+	0.942586i
$698$			8.73805i			0.330740i
$699$		0			0
$700$	−9.22102	+	9.22102i	−0.348522	+	0.348522i
$701$	−10.1952			−0.385067			−0.192534	−	0.981290i	$-0.561670\pi$
$701$	−10.1952			−0.385067			−0.192534	+	0.981290i	$0.561670\pi$
$702$		0			0
$703$	−17.7270			−0.668588
$704$	2.53473	−	2.53473i	0.0955311	−	0.0955311i
$705$		0			0
$706$		−	25.8979i		−	0.974679i
$707$	6.32221	−	6.32221i	0.237771	−	0.237771i
$708$		0			0
$709$	2.94732	−	2.94732i	0.110689	−	0.110689i	−0.649593	−	0.760282i	$-0.725061\pi$
$709$	2.94732	−	2.94732i	0.110689	−	0.110689i	0.760282	+	0.649593i	$0.225061\pi$
$710$	36.5828	+	36.5828i	1.37293	+	1.37293i
$711$		0			0
$712$		−	12.2987i		−	0.460914i
$713$	−0.477001	−	0.477001i	−0.0178638	−	0.0178638i
$714$		0			0
$715$	−43.3211	−	33.7176i	−1.62012	−	1.26097i
$716$		−	0.961445i		−	0.0359309i
$717$		0			0
$718$	1.17634			0.0439008
$719$	9.34789			0.348618			0.174309	−	0.984691i	$-0.444231\pi$
$719$	9.34789			0.348618			0.174309	+	0.984691i	$0.444231\pi$
$720$		0			0
$721$	12.3202	+	12.3202i	0.458830	+	0.458830i
$722$	18.5980	+	18.5980i	0.692144	+	0.692144i
$723$		0			0
$724$	14.9714			0.556408
$725$	−49.0479			−1.82159
$726$		0			0
$727$			8.92965i			0.331182i	0.986194	+	0.165591i	$0.0529532\pi$
$727$			8.92965i			0.331182i	−0.986194	+	0.165591i	$0.947047\pi$
$728$	−2.84530	−	2.21455i	−0.105454	−	0.0820768i
$729$		0			0
$730$	16.7638	+	16.7638i	0.620457	+	0.620457i
$731$			56.7086i			2.09744i
$732$		0			0
$733$	20.3409	+	20.3409i	0.751309	+	0.751309i	0.974724	−	0.223414i	$-0.0717202\pi$
$733$	20.3409	+	20.3409i	0.751309	+	0.751309i	−0.223414	+	0.974724i	$0.571720\pi$
$734$	23.4614	−	23.4614i	0.865975	−	0.865975i
$735$		0			0
$736$	4.03725	−	4.03725i	0.148815	−	0.148815i
$737$		−	2.88282i		−	0.106190i
$738$		0			0
$739$	12.0731	−	12.0731i	0.444118	−	0.444118i	−0.449276	−	0.893393i	$-0.648318\pi$
$739$	12.0731	−	12.0731i	0.444118	−	0.444118i	0.893393	+	0.449276i	$0.148318\pi$
$740$	11.1868			0.411233
$741$		0			0
$742$	−5.22095			−0.191667
$743$	8.18690	−	8.18690i	0.300348	−	0.300348i	−0.540802	−	0.841150i	$-0.681879\pi$
$743$	8.18690	−	8.18690i	0.300348	−	0.300348i	0.841150	+	0.540802i	$0.181879\pi$
$744$		0			0
$745$		−	31.2406i		−	1.14457i
$746$	−21.5144	+	21.5144i	−0.787697	+	0.787697i
$747$		0			0
$748$	−18.1592	+	18.1592i	−0.663965	+	0.663965i
$749$	4.50079	+	4.50079i	0.164455	+	0.164455i
$750$		0			0
$751$		−	10.8054i		−	0.394294i	−0.980374	−	0.197147i	$-0.936832\pi$
$751$		−	10.8054i		−	0.394294i	0.980374	−	0.197147i	$-0.0631676\pi$
$752$	1.55421	+	1.55421i	0.0566763	+	0.0566763i
$753$		0			0
$754$	−1.67753	−	13.4571i	−0.0610919	−	0.490077i
$755$			46.6135i			1.69644i
$756$		0			0
$757$	−11.4815			−0.417304			−0.208652	−	0.977990i	$-0.566908\pi$
$757$	−11.4815			−0.417304			−0.208652	+	0.977990i	$0.566908\pi$
$758$	17.2049			0.624911
$759$		0			0
$760$	−20.2146	−	20.2146i	−0.733261	−	0.733261i
$761$	−10.1139	−	10.1139i	−0.366629	−	0.366629i	0.499617	−	0.866246i	$-0.333474\pi$
$761$	−10.1139	−	10.1139i	−0.366629	−	0.366629i	−0.866246	+	0.499617i	$0.833474\pi$
$762$		0			0
$763$	3.49111			0.126387
$764$	19.5793			0.708356
$765$		0			0
$766$			37.4942i			1.35472i
$767$	2.73175	+	21.9140i	0.0986379	+	0.791269i
$768$		0			0
$769$	20.2565	+	20.2565i	0.730468	+	0.730468i	0.970712	−	0.240245i	$-0.0772276\pi$
$769$	20.2565	+	20.2565i	0.730468	+	0.730468i	−0.240245	+	0.970712i	$0.577228\pi$
$770$			15.2255i			0.548687i
$771$		0			0
$772$	4.06219	+	4.06219i	0.146201	+	0.146201i
$773$	24.7776	−	24.7776i	0.891189	−	0.891189i	−0.103446	−	0.994635i	$-0.532987\pi$
$773$	24.7776	−	24.7776i	0.891189	−	0.891189i	0.994635	+	0.103446i	$0.0329869\pi$
$774$		0			0
$775$	1.08946	−	1.08946i	0.0391346	−	0.0391346i
$776$			13.3296i			0.478503i
$777$		0			0
$778$	−2.64286	+	2.64286i	−0.0947512	+	0.0947512i
$779$	−33.0631			−1.18461
$780$		0			0
$781$	43.6631			1.56239
$782$	−28.9235	+	28.9235i	−1.03430	+	1.03430i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	35.1652	−	35.1652i	1.25510	−	1.25510i
$786$		0			0
$787$	9.17773	−	9.17773i	0.327151	−	0.327151i	−0.524351	−	0.851502i	$-0.675692\pi$
$787$	9.17773	−	9.17773i	0.327151	−	0.327151i	0.851502	+	0.524351i	$0.175692\pi$
$788$	4.34520	+	4.34520i	0.154791	+	0.154791i
$789$		0			0
$790$			38.5759i			1.37247i
$791$	2.90691	+	2.90691i	0.103358	+	0.103358i
$792$		0			0
$793$	−34.8668	−	27.1375i	−1.23816	−	0.963680i
$794$			32.4700i			1.15232i
$795$		0			0
$796$	0.564211			0.0199979
$797$	−46.2995			−1.64001			−0.820006	−	0.572355i	$-0.806030\pi$
$797$	−46.2995			−1.64001			−0.820006	+	0.572355i	$0.806030\pi$
$798$		0			0
$799$	−11.1346	−	11.1346i	−0.393914	−	0.393914i
$800$	9.22102	+	9.22102i	0.326012	+	0.326012i
$801$		0			0
$802$	−22.0989			−0.780341
$803$	20.0083			0.706077
$804$		0			0
$805$			24.2508i			0.854727i
$806$	0.336172	+	0.261649i	0.0118412	+	0.00921619i
$807$		0			0
$808$	−6.32221	−	6.32221i	−0.222415	−	0.222415i
$809$		−	45.9996i		−	1.61726i	−0.588317	−	0.808630i	$-0.700209\pi$
$809$		−	45.9996i		−	1.61726i	0.588317	−	0.808630i	$-0.299791\pi$
$810$		0			0
$811$	−2.08788	−	2.08788i	−0.0733153	−	0.0733153i	0.669498	−	0.742814i	$-0.266509\pi$
$811$	−2.08788	−	2.08788i	−0.0733153	−	0.0733153i	−0.742814	+	0.669498i	$0.766509\pi$
$812$	−2.65957	+	2.65957i	−0.0933327	+	0.0933327i
$813$		0			0
$814$	6.67592	−	6.67592i	0.233991	−	0.233991i
$815$		−	13.1233i		−	0.459689i
$816$		0			0
$817$	−37.6725	+	37.6725i	−1.31800	+	1.31800i
$818$	27.4435			0.959539
$819$		0			0
$820$	20.8647			0.728627
$821$	2.68463	−	2.68463i	0.0936941	−	0.0936941i	−0.658706	−	0.752400i	$-0.728896\pi$
$821$	2.68463	−	2.68463i	0.0936941	−	0.0936941i	0.752400	+	0.658706i	$0.228896\pi$
$822$		0			0
$823$			3.92051i			0.136660i	0.997663	+	0.0683301i	$0.0217671\pi$
$823$			3.92051i			0.136660i	−0.997663	+	0.0683301i	$0.978233\pi$
$824$	12.3202	−	12.3202i	0.429196	−	0.429196i
$825$		0			0
$826$	4.33095	−	4.33095i	0.150693	−	0.150693i
$827$	−14.9222	−	14.9222i	−0.518896	−	0.518896i	0.398341	−	0.917237i	$-0.369586\pi$
$827$	−14.9222	−	14.9222i	−0.518896	−	0.518896i	−0.917237	+	0.398341i	$0.869586\pi$
$828$		0			0
$829$			14.0509i			0.488007i	0.969774	+	0.244003i	$0.0784608\pi$
$829$			14.0509i			0.488007i	−0.969774	+	0.244003i	$0.921539\pi$
$830$	−34.9896	−	34.9896i	−1.21451	−	1.21451i
$831$		0			0
$832$	−2.21455	+	2.84530i	−0.0767758	+	0.0986432i
$833$		−	7.16415i		−	0.248223i
$834$		0			0
$835$	−12.7232			−0.440304
$836$	−24.1269			−0.834448
$837$		0			0
$838$	6.25136	+	6.25136i	0.215950	+	0.215950i
$839$	−23.9852	−	23.9852i	−0.828061	−	0.828061i	0.159187	−	0.987248i	$-0.449113\pi$
$839$	−23.9852	−	23.9852i	−0.828061	−	0.828061i	−0.987248	+	0.159187i	$0.949113\pi$
$840$		0			0
$841$	14.8534			0.512185
$842$	10.7407			0.370147
$843$		0			0
$844$		−	13.3542i		−	0.459671i
$845$	47.4343	+	28.2637i	1.63179	+	0.972300i
$846$		0			0
$847$	1.30792	+	1.30792i	0.0449407	+	0.0449407i
$848$			5.22095i			0.179288i
$849$		0			0
$850$	−66.0608	−	66.0608i	−2.26587	−	2.26587i
$851$	10.6332	−	10.6332i	0.364503	−	0.364503i
$852$		0			0
$853$	22.4555	−	22.4555i	0.768860	−	0.768860i	−0.209046	−	0.977906i	$-0.567036\pi$
$853$	22.4555	−	22.4555i	0.768860	−	0.768860i	0.977906	+	0.209046i	$0.0670357\pi$
$854$			12.2542i			0.419329i
$855$		0			0
$856$	4.50079	−	4.50079i	0.153834	−	0.153834i
$857$	−22.3940			−0.764966			−0.382483	−	0.923963i	$-0.624931\pi$
$857$	−22.3940			−0.764966			−0.382483	+	0.923963i	$0.624931\pi$
$858$		0			0
$859$	−49.2514			−1.68044			−0.840219	−	0.542247i	$-0.817574\pi$
$859$	−49.2514			−1.68044			−0.840219	+	0.542247i	$0.817574\pi$
$860$	23.7735	−	23.7735i	0.810669	−	0.810669i
$861$		0			0
$862$		−	4.24061i		−	0.144436i
$863$	25.4860	−	25.4860i	0.867552	−	0.867552i	−0.124649	−	0.992201i	$-0.539780\pi$
$863$	25.4860	−	25.4860i	0.867552	−	0.867552i	0.992201	+	0.124649i	$0.0397804\pi$
$864$		0			0
$865$	15.2170	−	15.2170i	0.517393	−	0.517393i
$866$	7.37727	+	7.37727i	0.250690	+	0.250690i
$867$		0			0
$868$		−	0.118150i		−	0.00401026i
$869$	23.0209	+	23.0209i	0.780932	+	0.780932i
$870$		0			0
$871$	0.358686	+	2.87736i	0.0121536	+	0.0974956i
$872$		−	3.49111i		−	0.118224i
$873$		0			0
$874$	−38.4288			−1.29987
$875$	−34.1513			−1.15452
$876$		0			0
$877$	5.47083	+	5.47083i	0.184737	+	0.184737i	0.793416	−	0.608679i	$-0.208300\pi$
$877$	5.47083	+	5.47083i	0.184737	+	0.184737i	−0.608679	+	0.793416i	$0.708300\pi$
$878$	8.18860	+	8.18860i	0.276352	+	0.276352i
$879$		0			0
$880$	15.2255			0.513250
$881$	5.90254			0.198862			0.0994308	−	0.995044i	$-0.468298\pi$
$881$	5.90254			0.198862			0.0994308	+	0.995044i	$0.468298\pi$
$882$		0			0
$883$			9.29205i			0.312702i	0.987702	+	0.156351i	$0.0499732\pi$
$883$			9.29205i			0.312702i	−0.987702	+	0.156351i	$0.950027\pi$
$884$	15.8654	−	20.3842i	0.533611	−	0.685594i
$885$		0			0
$886$	−8.28934	−	8.28934i	−0.278486	−	0.278486i
$887$			32.2058i			1.08137i	0.841226	+	0.540683i	$0.181834\pi$
$887$			32.2058i			1.08137i	−0.841226	+	0.540683i	$0.818166\pi$
$888$		0			0
$889$	−13.9883	−	13.9883i	−0.469153	−	0.469153i
$890$	36.9377	−	36.9377i	1.23815	−	1.23815i
$891$		0			0
$892$	3.80927	−	3.80927i	0.127544	−	0.127544i
$893$		−	14.7939i		−	0.495058i
$894$		0			0
$895$	2.88758	−	2.88758i	0.0965211	−	0.0965211i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−26.9101			−0.898000
$899$	0.314228	−	0.314228i	0.0104801	−	0.0104801i
$900$		0			0
$901$		−	37.4037i		−	1.24610i
$902$	12.4514	−	12.4514i	0.414587	−	0.414587i
$903$		0			0
$904$	2.90691	−	2.90691i	0.0966824	−	0.0966824i
$905$	44.9647	+	44.9647i	1.49468	+	1.49468i
$906$		0			0
$907$		−	9.25441i		−	0.307288i	−0.988126	−	0.153644i	$-0.950899\pi$
$907$		−	9.25441i		−	0.307288i	0.988126	−	0.153644i	$-0.0491009\pi$
$908$	−9.92499	−	9.92499i	−0.329372	−	0.329372i
$909$		0			0
$910$	−1.89438	−	15.1966i	−0.0627981	−	0.503764i
$911$		−	43.8510i		−	1.45285i	−0.687246	−	0.726425i	$-0.741181\pi$
$911$		−	43.8510i		−	1.45285i	0.687246	−	0.726425i	$-0.258819\pi$
$912$		0			0
$913$	−41.7615			−1.38210
$914$	−35.5363			−1.17544
$915$		0			0
$916$	−6.50911	−	6.50911i	−0.215067	−	0.215067i
$917$	−9.15378	−	9.15378i	−0.302284	−	0.302284i
$918$		0			0
$919$	20.2837			0.669099			0.334549	−	0.942378i	$-0.391416\pi$
$919$	20.2837			0.669099			0.334549	+	0.942378i	$0.391416\pi$
$920$	24.2508			0.799524
$921$		0			0
$922$			30.4302i			1.00216i
$923$	−43.5804	+	5.43264i	−1.43447	+	0.178817i
$924$		0			0
$925$	24.2862	+	24.2862i	0.798524	+	0.798524i
$926$		−	17.9314i		−	0.589263i
$927$		0			0
$928$	2.65957	+	2.65957i	0.0873047	+	0.0873047i
$929$	25.3806	−	25.3806i	0.832712	−	0.832712i	−0.155175	−	0.987887i	$-0.549594\pi$
$929$	25.3806	−	25.3806i	0.832712	−	0.832712i	0.987887	+	0.155175i	$0.0495942\pi$
$930$		0			0
$931$	4.75928	−	4.75928i	0.155979	−	0.155979i
$932$		−	17.0947i		−	0.559955i
$933$		0			0
$934$	−8.95001	+	8.95001i	−0.292853	+	0.292853i
$935$	−109.077			−3.56722
$936$		0			0
$937$	−23.5723			−0.770072			−0.385036	−	0.922901i	$-0.625811\pi$
$937$	−23.5723			−0.770072			−0.385036	+	0.922901i	$0.625811\pi$
$938$	0.568664	−	0.568664i	0.0185676	−	0.0185676i
$939$		0			0
$940$			9.33576i			0.304499i
$941$	−10.3997	+	10.3997i	−0.339020	+	0.339020i	−0.855998	−	0.516979i	$-0.827057\pi$
$941$	−10.3997	+	10.3997i	−0.339020	+	0.339020i	0.516979	+	0.855998i	$0.327057\pi$
$942$		0			0
$943$	19.8323	−	19.8323i	0.645830	−	0.645830i
$944$	−4.33095	−	4.33095i	−0.140961	−	0.140961i
$945$		0			0
$946$		−	28.3746i		−	0.922538i
$947$	−8.62956	−	8.62956i	−0.280423	−	0.280423i	0.552855	−	0.833278i	$-0.313538\pi$
$947$	−8.62956	−	8.62956i	−0.280423	−	0.280423i	−0.833278	+	0.552855i	$0.813538\pi$
$948$		0			0
$949$	−19.9704	+	2.48947i	−0.648267	+	0.0808115i
$950$		−	87.7708i		−	2.84766i
$951$		0			0
$952$	−7.16415			−0.232191
$953$	−25.6873			−0.832094			−0.416047	−	0.909343i	$-0.636585\pi$
$953$	−25.6873			−0.832094			−0.416047	+	0.909343i	$0.636585\pi$
$954$		0			0
$955$	58.8041	+	58.8041i	1.90285	+	1.90285i
$956$	5.78149	+	5.78149i	0.186987	+	0.186987i
$957$		0			0
$958$	−9.63454			−0.311278
$959$	−8.99023			−0.290310
$960$		0			0
$961$		−	30.9860i		−	0.999550i
$962$	−5.83265	+	7.49391i	−0.188052	+	0.241613i
$963$		0			0
$964$	−14.4471	−	14.4471i	−0.465311	−	0.465311i
$965$			24.4005i			0.785481i
$966$		0			0
$967$	7.91958	+	7.91958i	0.254677	+	0.254677i	0.822885	−	0.568208i	$-0.192363\pi$
$967$	7.91958	+	7.91958i	0.254677	+	0.254677i	−0.568208	+	0.822885i	$0.692363\pi$
$968$	1.30792	−	1.30792i	0.0420382	−	0.0420382i
$969$		0			0
$970$	−40.0336	+	40.0336i	−1.28540	+	1.28540i
$971$		−	15.3284i		−	0.491912i	−0.969281	−	0.245956i	$-0.920898\pi$
$971$		−	15.3284i		−	0.491912i	0.969281	−	0.245956i	$-0.0791019\pi$
$972$		0			0
$973$	−1.02569	+	1.02569i	−0.0328820	+	0.0328820i
$974$	28.9315			0.927026
$975$		0			0
$976$	12.2542			0.392246
$977$	−29.0548	+	29.0548i	−0.929546	+	0.929546i	−0.997676	−	0.0681300i	$-0.978297\pi$
$977$	−29.0548	+	29.0548i	−0.929546	+	0.929546i	0.0681300	+	0.997676i	$0.478297\pi$
$978$		0			0
$979$		−	44.0866i		−	1.40901i
$980$	−3.00337	+	3.00337i	−0.0959392	+	0.0959392i
$981$		0			0
$982$	28.9913	−	28.9913i	0.925148	−	0.925148i
$983$	−36.0946	−	36.0946i	−1.15124	−	1.15124i	−0.986305	−	0.164934i	$-0.947259\pi$
$983$	−36.0946	−	36.0946i	−1.15124	−	1.15124i	−0.164934	−	0.986305i	$-0.552741\pi$
$984$		0			0
$985$			26.1005i			0.831632i
$986$	−19.0536	−	19.0536i	−0.606790	−	0.606790i
$987$		0			0
$988$	24.0813	−	3.00192i	0.766127	−	0.0955038i
$989$		−	45.1944i		−	1.43710i
$990$		0			0
$991$	−25.4375			−0.808047			−0.404024	−	0.914748i	$-0.632389\pi$
$991$	−25.4375			−0.808047			−0.404024	+	0.914748i	$0.632389\pi$
$992$	−0.118150			−0.00375126
$993$		0			0
$994$	8.61297	+	8.61297i	0.273187	+	0.273187i
$995$	1.69454	+	1.69454i	0.0537204	+	0.0537204i
$996$		0			0
$997$	−9.63659			−0.305194			−0.152597	−	0.988289i	$-0.548764\pi$
$997$	−9.63659			−0.305194			−0.152597	+	0.988289i	$0.548764\pi$
$998$	4.41426			0.139731
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.y.d.827.8	yes	16
3.2	odd	2		1638.2.y.c.827.1	✓	16
13.5	odd	4		1638.2.y.c.1331.1	yes	16
39.5	even	4	inner	1638.2.y.d.1331.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.y.c.827.1	✓	16	3.2	odd	2
1638.2.y.c.1331.1	yes	16	13.5	odd	4
1638.2.y.d.827.8	yes	16	1.1	even	1	trivial
1638.2.y.d.1331.8	yes	16	39.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(3.00337 - 3.00337i) q^{5} +(0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(3.00337 - 3.00337i) q^{5} +(0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} -4.24741i q^{10} +(-2.53473 - 2.53473i) q^{11} +(2.84530 + 2.21455i) q^{13} -1.00000i q^{14} -1.00000 q^{16} +7.16415 q^{17} +(4.75928 + 4.75928i) q^{19} +(-3.00337 - 3.00337i) q^{20} -3.58464 q^{22} -5.70954 q^{23} -13.0405i q^{25} +(3.57786 - 0.446008i) q^{26} +(-0.707107 - 0.707107i) q^{28} -3.76120i q^{29} +(0.0835445 + 0.0835445i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.06582 - 5.06582i) q^{34} -4.24741i q^{35} +(-1.86236 + 1.86236i) q^{37} +6.73064 q^{38} -4.24741 q^{40} +(-3.47354 + 3.47354i) q^{41} +7.91560i q^{43} +(-2.53473 + 2.53473i) q^{44} +(-4.03725 + 4.03725i) q^{46} +(-1.55421 - 1.55421i) q^{47} -1.00000i q^{49} +(-9.22102 - 9.22102i) q^{50} +(2.21455 - 2.84530i) q^{52} -5.22095i q^{53} -15.2255 q^{55} -1.00000 q^{56} +(-2.65957 - 2.65957i) q^{58} +(4.33095 + 4.33095i) q^{59} -12.2542 q^{61} +0.118150 q^{62} +1.00000i q^{64} +(15.1966 - 1.89438i) q^{65} +(0.568664 + 0.568664i) q^{67} -7.16415i q^{68} +(-3.00337 - 3.00337i) q^{70} +(-8.61297 + 8.61297i) q^{71} +(-3.94683 + 3.94683i) q^{73} +2.63378i q^{74} +(4.75928 - 4.75928i) q^{76} -3.58464 q^{77} -9.08222 q^{79} +(-3.00337 + 3.00337i) q^{80} +4.91233i q^{82} +(8.23786 - 8.23786i) q^{83} +(21.5166 - 21.5166i) q^{85} +(5.59717 + 5.59717i) q^{86} +3.58464i q^{88} +(8.69652 + 8.69652i) q^{89} +(3.57786 - 0.446008i) q^{91} +5.70954i q^{92} -2.19799 q^{94} +28.5878 q^{95} +(-9.42542 - 9.42542i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^5	\( 16 q + 4 q^{5} - 8 q^{11} + 4 q^{13} - 16 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{20} - 8 q^{22} + 24 q^{23} + 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 8 q^{44} + 4 q^{47} - 16 q^{50} - 16 q^{55} - 16 q^{56} + 4 q^{58} - 8 q^{59} - 40 q^{61} + 24 q^{62} + 56 q^{65} - 4 q^{67} - 4 q^{70} - 24 q^{71} - 12 q^{73} + 16 q^{76} - 8 q^{77} + 16 q^{79} - 4 q^{80} + 8 q^{85} + 24 q^{86} + 16 q^{89} + 8 q^{91} - 8 q^{94} - 40 q^{95} - 28 q^{97}+O(q^{100}) \) 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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