LMFDB - Embedded newform 912.2.ci.h.223.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			223.1
Character	$\chi$	$=$	912.223
Dual form			912.2.ci.h.319.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{3} +(-3.37195 - 2.82940i) q^{5} +(-1.97482 + 1.14016i) q^{7} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{3} +(-3.37195 - 2.82940i) q^{5} +(-1.97482 + 1.14016i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(0.618645 + 0.357175i) q^{11} +(-1.61664 + 0.285057i) q^{13} +(3.37195 - 2.82940i) q^{15} +(4.33603 - 1.57819i) q^{17} +(4.33981 + 0.407514i) q^{19} +(-0.779918 - 2.14281i) q^{21} +(4.29631 + 5.12014i) q^{23} +(2.49629 + 14.1572i) q^{25} +(0.500000 - 0.866025i) q^{27} +(0.0802763 - 0.220557i) q^{29} +(0.525925 + 0.910930i) q^{31} +(-0.459175 + 0.547224i) q^{33} +(9.88499 + 1.74299i) q^{35} +8.20022i q^{37} -1.64158i q^{39} +(3.04906 + 0.537632i) q^{41} +(3.07515 - 3.66483i) q^{43} +(2.20088 + 3.81204i) q^{45} +(2.76321 - 7.59185i) q^{47} +(-0.900053 + 1.55894i) q^{49} +(0.801266 + 4.54421i) q^{51} +(-8.01832 - 9.55587i) q^{53} +(-1.07545 - 2.95477i) q^{55} +(-1.15492 + 4.20311i) q^{57} +(8.13097 - 2.95943i) q^{59} +(1.25091 - 1.04964i) q^{61} +(2.24568 - 0.395975i) q^{63} +(6.25776 + 3.61292i) q^{65} +(-1.95216 - 0.710528i) q^{67} +(-5.78840 + 3.34193i) q^{69} +(9.45970 + 7.93763i) q^{71} +(-0.0741907 + 0.420756i) q^{73} -14.3756 q^{75} -1.62895 q^{77} +(-2.98442 + 16.9255i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-8.29456 + 4.78886i) q^{83} +(-19.0862 - 6.94681i) q^{85} +(0.203267 + 0.117356i) q^{87} +(9.14163 - 1.61192i) q^{89} +(2.86756 - 2.40617i) q^{91} +(-0.988416 + 0.359754i) q^{93} +(-13.4806 - 13.6532i) q^{95} +(-0.956771 - 2.62871i) q^{97} +(-0.459175 - 0.547224i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 9 q^{7}+O(q^{10}) $ 24 * q + 9 * q^7	$ 24 q + 9 q^{7} - 9 q^{11} - 9 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 15 q^{23} + 6 q^{25} + 12 q^{27} - 6 q^{29} - 12 q^{31} - 3 q^{33} + 30 q^{41} + 9 q^{43} + 3 q^{45} + 15 q^{47} + 27 q^{49} - 3 q^{51} + 6 q^{53} - 21 q^{55} - 9 q^{57} + 36 q^{59} - 21 q^{61} + 3 q^{63} - 9 q^{65} - 45 q^{67} + 36 q^{71} - 42 q^{75} + 108 q^{77} - 36 q^{79} + 27 q^{83} - 9 q^{85} + 9 q^{87} - 27 q^{89} + 36 q^{91} - 18 q^{93} - 30 q^{95} - 51 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 9 * q^7 - 9 * q^11 - 9 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 15 * q^23 + 6 * q^25 + 12 * q^27 - 6 * q^29 - 12 * q^31 - 3 * q^33 + 30 * q^41 + 9 * q^43 + 3 * q^45 + 15 * q^47 + 27 * q^49 - 3 * q^51 + 6 * q^53 - 21 * q^55 - 9 * q^57 + 36 * q^59 - 21 * q^61 + 3 * q^63 - 9 * q^65 - 45 * q^67 + 36 * q^71 - 42 * q^75 + 108 * q^77 - 36 * q^79 + 27 * q^83 - 9 * q^85 + 9 * q^87 - 27 * q^89 + 36 * q^91 - 18 * q^93 - 30 * q^95 - 51 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$4$		0			0
$5$	−3.37195	−	2.82940i	−1.50798	−	1.26535i	−0.867569	−	0.497317i	$-0.834319\pi$
$5$	−3.37195	−	2.82940i	−1.50798	−	1.26535i	−0.640413	−	0.768030i	$-0.721237\pi$
$6$		0			0
$7$	−1.97482	+	1.14016i	−0.746412	+	0.430941i	−0.824396	−	0.566013i	$-0.808485\pi$
$7$	−1.97482	+	1.14016i	−0.746412	+	0.430941i	0.0779837	+	0.996955i	$0.475152\pi$
$8$		0			0
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$		0			0
$11$	0.618645	+	0.357175i	0.186529	+	0.107692i	0.590356	−	0.807143i	$-0.298987\pi$
$11$	0.618645	+	0.357175i	0.186529	+	0.107692i	−0.403828	+	0.914835i	$0.632321\pi$
$12$		0			0
$13$	−1.61664	+	0.285057i	−0.448374	+	0.0790605i	−0.393276	−	0.919420i	$-0.628658\pi$
$13$	−1.61664	+	0.285057i	−0.448374	+	0.0790605i	−0.0550983	+	0.998481i	$0.517547\pi$
$14$		0			0
$15$	3.37195	−	2.82940i	0.870634	−	0.730549i
$16$		0			0
$17$	4.33603	−	1.57819i	1.05164	−	0.382766i	0.242360	−	0.970186i	$-0.422078\pi$
$17$	4.33603	−	1.57819i	1.05164	−	0.382766i	0.809282	+	0.587420i	$0.199856\pi$
$18$		0			0
$19$	4.33981	+	0.407514i	0.995620	+	0.0934900i
$19$	4.33981	+	0.407514i	0.995620	+	0.0934900i
$20$		0			0
$21$	−0.779918	−	2.14281i	−0.170192	−	0.467599i
$22$		0			0
$23$	4.29631	+	5.12014i	0.895842	+	1.06762i	0.997347	+	0.0727880i	$0.0231897\pi$
$23$	4.29631	+	5.12014i	0.895842	+	1.06762i	−0.101505	+	0.994835i	$0.532366\pi$
$24$		0			0
$25$	2.49629	+	14.1572i	0.499258	+	2.83144i
$26$		0			0
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$		0			0
$29$	0.0802763	−	0.220557i	0.0149069	−	0.0409564i	−0.932016	−	0.362417i	$-0.881952\pi$
$29$	0.0802763	−	0.220557i	0.0149069	−	0.0409564i	0.946923	+	0.321461i	$0.104174\pi$
$30$		0			0
$31$	0.525925	+	0.910930i	0.0944590	+	0.163608i	0.909383	−	0.415960i	$-0.136555\pi$
$31$	0.525925	+	0.910930i	0.0944590	+	0.163608i	−0.814924	+	0.579568i	$0.803221\pi$
$32$		0			0
$33$	−0.459175	+	0.547224i	−0.0799322	+	0.0952595i
$34$		0			0
$35$	9.88499	+	1.74299i	1.67087	+	0.294619i
$36$		0			0
$37$			8.20022i			1.34811i	0.738682	+	0.674054i	$0.235448\pi$
$37$			8.20022i			1.34811i	−0.738682	+	0.674054i	$0.764552\pi$
$38$		0			0
$39$		−	1.64158i		−	0.262862i
$40$		0			0
$41$	3.04906	+	0.537632i	0.476184	+	0.0839641i	0.406589	−	0.913611i	$-0.366718\pi$
$41$	3.04906	+	0.537632i	0.476184	+	0.0839641i	0.0695951	+	0.997575i	$0.477829\pi$
$42$		0			0
$43$	3.07515	−	3.66483i	0.468957	−	0.558881i	−0.478780	−	0.877935i	$-0.658921\pi$
$43$	3.07515	−	3.66483i	0.468957	−	0.558881i	0.947736	+	0.319054i	$0.103365\pi$
$44$		0			0
$45$	2.20088	+	3.81204i	0.328089	+	0.568266i
$46$		0			0
$47$	2.76321	−	7.59185i	0.403055	−	1.10739i	−0.557713	−	0.830034i	$-0.688321\pi$
$47$	2.76321	−	7.59185i	0.403055	−	1.10739i	0.960768	−	0.277352i	$-0.0894567\pi$
$48$		0			0
$49$	−0.900053	+	1.55894i	−0.128579	+	0.222705i
$50$		0			0
$51$	0.801266	+	4.54421i	0.112200	+	0.636316i
$52$		0			0
$53$	−8.01832	−	9.55587i	−1.10140	−	1.31260i	−0.945789	−	0.324781i	$-0.894709\pi$
$53$	−8.01832	−	9.55587i	−1.10140	−	1.31260i	−0.155612	−	0.987818i	$-0.549735\pi$
$54$		0			0
$55$	−1.07545	−	2.95477i	−0.145014	−	0.398422i
$56$		0			0
$57$	−1.15492	+	4.20311i	−0.152973	+	0.556716i
$58$		0			0
$59$	8.13097	−	2.95943i	1.05856	−	0.385285i	0.246675	−	0.969098i	$-0.420662\pi$
$59$	8.13097	−	2.95943i	1.05856	−	0.385285i	0.811888	+	0.583813i	$0.198440\pi$
$60$		0			0
$61$	1.25091	−	1.04964i	0.160163	−	0.134393i	−0.559184	−	0.829043i	$-0.688886\pi$
$61$	1.25091	−	1.04964i	0.160163	−	0.134393i	0.719347	+	0.694651i	$0.244441\pi$
$62$		0			0
$63$	2.24568	−	0.395975i	0.282930	−	0.0498881i
$64$		0			0
$65$	6.25776	+	3.61292i	0.776179	+	0.448127i
$66$		0			0
$67$	−1.95216	−	0.710528i	−0.238494	−	0.0868048i	0.220008	−	0.975498i	$-0.429392\pi$
$67$	−1.95216	−	0.710528i	−0.238494	−	0.0868048i	−0.458502	+	0.888693i	$0.651614\pi$
$68$		0			0
$69$	−5.78840	+	3.34193i	−0.696841	+	0.402322i
$70$		0			0
$71$	9.45970	+	7.93763i	1.12266	+	0.942023i	0.998736	−	0.0502683i	$-0.0160077\pi$
$71$	9.45970	+	7.93763i	1.12266	+	0.942023i	0.123924	+	0.992292i	$0.460452\pi$
$72$		0			0
$73$	−0.0741907	+	0.420756i	−0.00868337	+	0.0492458i	−0.988842	−	0.148971i	$-0.952404\pi$
$73$	−0.0741907	+	0.420756i	−0.00868337	+	0.0492458i	0.980158	+	0.198217i	$0.0635150\pi$
$74$		0			0
$75$	−14.3756			−1.65995
$76$		0			0
$77$	−1.62895			−0.185636
$78$		0			0
$79$	−2.98442	+	16.9255i	−0.335774	+	1.90427i	0.0836840	+	0.996492i	$0.473331\pi$
$79$	−2.98442	+	16.9255i	−0.335774	+	1.90427i	−0.419458	+	0.907775i	$0.637780\pi$
$80$		0			0
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$		0			0
$83$	−8.29456	+	4.78886i	−0.910446	+	0.525646i	−0.880575	−	0.473908i	$-0.842843\pi$
$83$	−8.29456	+	4.78886i	−0.910446	+	0.525646i	−0.0298712	+	0.999554i	$0.509510\pi$
$84$		0			0
$85$	−19.0862	−	6.94681i	−2.07019	−	0.753488i
$86$		0			0
$87$	0.203267	+	0.117356i	0.0217925	+	0.0125819i
$88$		0			0
$89$	9.14163	−	1.61192i	0.969011	−	0.170863i	0.333326	−	0.942812i	$-0.391829\pi$
$89$	9.14163	−	1.61192i	0.969011	−	0.170863i	0.635685	+	0.771949i	$0.280718\pi$
$90$		0			0
$91$	2.86756	−	2.40617i	0.300602	−	0.252235i
$92$		0			0
$93$	−0.988416	+	0.359754i	−0.102494	+	0.0373048i
$94$		0			0
$95$	−13.4806	−	13.6532i	−1.38308	−	1.40079i
$96$		0			0
$97$	−0.956771	−	2.62871i	−0.0971454	−	0.266905i	0.881595	−	0.472006i	$-0.156470\pi$
$97$	−0.956771	−	2.62871i	−0.0971454	−	0.266905i	−0.978741	+	0.205101i	$0.934248\pi$
$98$		0			0
$99$	−0.459175	−	0.547224i	−0.0461489	−	0.0549981i
$100$		0			0
$101$	1.92084	+	10.8936i	0.191130	+	1.08395i	0.917822	+	0.396991i	$0.129946\pi$
$101$	1.92084	+	10.8936i	0.191130	+	1.08395i	−0.726692	+	0.686964i	$0.758943\pi$
$102$		0			0
$103$	−3.52968	+	6.11358i	−0.347789	+	0.602389i	−0.985856	−	0.167592i	$-0.946401\pi$
$103$	−3.52968	+	6.11358i	−0.347789	+	0.602389i	0.638067	+	0.769981i	$0.279734\pi$
$104$		0			0
$105$	−3.43302	+	9.43214i	−0.335028	+	0.920483i
$106$		0			0
$107$	4.36525	+	7.56084i	0.422005	+	0.730934i	0.996136	−	0.0878297i	$-0.0279931\pi$
$107$	4.36525	+	7.56084i	0.422005	+	0.730934i	−0.574131	+	0.818764i	$0.694660\pi$
$108$		0			0
$109$	12.9579	−	15.4426i	1.24114	−	1.47914i	0.420912	−	0.907102i	$-0.361710\pi$
$109$	12.9579	−	15.4426i	1.24114	−	1.47914i	0.820230	−	0.572034i	$-0.193845\pi$
$110$		0			0
$111$	−8.07564	−	1.42395i	−0.766506	−	0.135156i
$112$		0			0
$113$			2.83109i			0.266326i	0.991094	+	0.133163i	$0.0425134\pi$
$113$			2.83109i			0.266326i	−0.991094	+	0.133163i	$0.957487\pi$
$114$		0			0
$115$		−	29.4208i		−	2.74351i
$116$		0			0
$117$	1.61664	+	0.285057i	0.149458	+	0.0263535i
$118$		0			0
$119$	−6.76350	+	8.06042i	−0.620009	+	0.738898i
$120$		0			0
$121$	−5.24485	−	9.08435i	−0.476805	−	0.825850i
$122$		0			0
$123$	−1.05893	+	2.90938i	−0.0954804	+	0.262330i
$124$		0			0
$125$	20.6346	−	35.7401i	1.84561	−	3.19669i
$126$		0			0
$127$	1.49758	+	8.49318i	0.132888	+	0.753648i	0.976307	+	0.216391i	$0.0694285\pi$
$127$	1.49758	+	8.49318i	0.132888	+	0.753648i	−0.843418	+	0.537257i	$0.819460\pi$
$128$		0			0
$129$	3.07515	+	3.66483i	0.270752	+	0.322670i
$130$		0			0
$131$	3.80146	+	10.4444i	0.332135	+	0.912533i	0.987556	+	0.157269i	$0.0502690\pi$
$131$	3.80146	+	10.4444i	0.332135	+	0.912533i	−0.655421	+	0.755264i	$0.727509\pi$
$132$		0			0
$133$	−9.03498	+	4.14333i	−0.783432	+	0.359272i
$134$		0			0
$135$	−4.13631	+	1.50549i	−0.355997	+	0.129572i
$136$		0			0
$137$	−12.6057	+	10.5775i	−1.07698	+	0.903695i	−0.995667	−	0.0929934i	$-0.970356\pi$
$137$	−12.6057	+	10.5775i	−1.07698	+	0.903695i	−0.0813151	+	0.996688i	$0.525912\pi$
$138$		0			0
$139$	−9.33892	+	1.64670i	−0.792116	+	0.139672i	−0.555045	−	0.831821i	$-0.687299\pi$
$139$	−9.33892	+	1.64670i	−0.792116	+	0.139672i	−0.237072	+	0.971492i	$0.576188\pi$
$140$		0			0
$141$	6.99669	+	4.03954i	0.589228	+	0.340191i
$142$		0			0
$143$	−1.10194	−	0.401073i	−0.0921489	−	0.0335394i
$144$		0			0
$145$	−0.894733	+	0.516574i	−0.0743035	+	0.0428992i
$146$		0			0
$147$	−1.37896	−	1.15709i	−0.113735	−	0.0954348i
$148$		0			0
$149$	1.81519	−	10.2944i	0.148706	−	0.843353i	−0.815611	−	0.578601i	$-0.803599\pi$
$149$	1.81519	−	10.2944i	0.148706	−	0.843353i	0.964317	−	0.264752i	$-0.0852900\pi$
$150$		0			0
$151$	11.8367			0.963254			0.481627	−	0.876376i	$-0.340046\pi$
$151$	11.8367			0.963254			0.481627	+	0.876376i	$0.340046\pi$
$152$		0			0
$153$	−4.61431			−0.373045
$154$		0			0
$155$	0.803992	−	4.55966i	0.0645782	−	0.366241i
$156$		0			0
$157$	13.1498	+	11.0340i	1.04947	+	0.880606i	0.993037	−	0.117801i	$-0.0375844\pi$
$157$	13.1498	+	11.0340i	1.04947	+	0.880606i	0.0564280	+	0.998407i	$0.482029\pi$
$158$		0			0
$159$	10.8031	−	6.23715i	0.856738	−	0.494638i
$160$		0			0
$161$	−14.3222	−	5.21287i	−1.12875	−	0.410832i
$162$		0			0
$163$	6.12534	+	3.53647i	0.479774	+	0.276997i	0.720322	−	0.693640i	$-0.243994\pi$
$163$	6.12534	+	3.53647i	0.479774	+	0.276997i	−0.240549	+	0.970637i	$0.577327\pi$
$164$		0			0
$165$	3.09663	−	0.546020i	0.241073	−	0.0425076i
$166$		0			0
$167$	6.96391	−	5.84341i	0.538883	−	0.452177i	−0.332273	−	0.943183i	$-0.607815\pi$
$167$	6.96391	−	5.84341i	0.538883	−	0.452177i	0.871156	+	0.491007i	$0.163371\pi$
$168$		0			0
$169$	−9.68375	+	3.52460i	−0.744904	+	0.271123i
$170$		0			0
$171$	−3.93871	−	1.86724i	−0.301201	−	0.142791i
$172$		0			0
$173$	3.06963	+	8.43375i	0.233380	+	0.641206i	1.00000		0.000895553i	$-0.000285063\pi$
$173$	3.06963	+	8.43375i	0.233380	+	0.641206i	−0.766620	+	0.642101i	$0.778063\pi$
$174$		0			0
$175$	−21.0712	−	25.1117i	−1.59284	−	1.89827i
$176$		0			0
$177$	1.50254	+	8.52135i	0.112938	+	0.640504i
$178$		0			0
$179$	10.8254	−	18.7502i	0.809129	−	1.40145i	−0.104339	−	0.994542i	$-0.533273\pi$
$179$	10.8254	−	18.7502i	0.809129	−	1.40145i	0.913468	−	0.406910i	$-0.133394\pi$
$180$		0			0
$181$	2.02688	−	5.56881i	0.150657	−	0.413926i	−0.841290	−	0.540585i	$-0.818203\pi$
$181$	2.02688	−	5.56881i	0.150657	−	0.413926i	0.991946	+	0.126659i	$0.0404253\pi$
$182$		0			0
$183$	0.816475	+	1.41418i	0.0603556	+	0.104539i
$184$		0			0
$185$	23.2017	−	27.6507i	1.70582	−	2.03292i
$186$		0			0
$187$	3.24616	+	0.572385i	0.237382	+	0.0418569i
$188$		0			0
$189$			2.28033i			0.165869i
$190$		0			0
$191$			11.0498i			0.799538i	0.916616	+	0.399769i	$0.130910\pi$
$191$			11.0498i			0.799538i	−0.916616	+	0.399769i	$0.869090\pi$
$192$		0			0
$193$	13.1438	+	2.31761i	0.946113	+	0.166825i	0.625359	−	0.780337i	$-0.284953\pi$
$193$	13.1438	+	2.31761i	0.946113	+	0.166825i	0.320754	+	0.947163i	$0.396064\pi$
$194$		0			0
$195$	−4.64468	+	5.53531i	−0.332612	+	0.396392i
$196$		0			0
$197$	−7.20091	−	12.4723i	−0.513044	−	0.888618i	−0.999886	−	0.0151277i	$-0.995185\pi$
$197$	−7.20091	−	12.4723i	−0.513044	−	0.888618i	0.486842	−	0.873490i	$-0.338149\pi$
$198$		0			0
$199$	6.04403	−	16.6058i	0.428450	−	1.17716i	−0.518304	−	0.855197i	$-0.673436\pi$
$199$	6.04403	−	16.6058i	0.428450	−	1.17716i	0.946754	−	0.321959i	$-0.104341\pi$
$200$		0			0
$201$	1.03872	−	1.79912i	0.0732658	−	0.126900i
$202$		0			0
$203$	0.0929401	+	0.527089i	0.00652311	+	0.0369944i
$204$		0			0
$205$	−8.76012	−	10.4399i	−0.611833	−	0.729154i
$206$		0			0
$207$	−2.28602	−	6.28078i	−0.158889	−	0.436545i
$208$		0			0
$209$	2.53925	+	1.80218i	0.175644	+	0.124659i
$210$		0			0
$211$	−18.3373	+	6.67425i	−1.26239	+	0.459474i	−0.884572	−	0.466404i	$-0.845549\pi$
$211$	−18.3373	+	6.67425i	−1.26239	+	0.459474i	−0.377823	+	0.925878i	$0.623327\pi$
$212$		0			0
$213$	−9.45970	+	7.93763i	−0.648168	+	0.543877i
$214$		0			0
$215$	−20.7385	+	3.65676i	−1.41436	+	0.249389i
$216$		0			0
$217$	−2.07722	−	1.19928i	−0.141011	−	0.0814126i
$218$		0			0
$219$	−0.401481	−	0.146127i	−0.0271296	−	0.00987436i
$220$		0			0
$221$	−6.55992	+	3.78737i	−0.441268	+	0.254766i
$222$		0			0
$223$	15.1573	+	12.7185i	1.01501	+	0.851694i	0.988992	−	0.147968i	$-0.0472732\pi$
$223$	15.1573	+	12.7185i	1.01501	+	0.851694i	0.0260169	+	0.999662i	$0.491718\pi$
$224$		0			0
$225$	2.49629	−	14.1572i	0.166419	−	0.943812i
$226$		0			0
$227$	−19.2044			−1.27464			−0.637319	−	0.770600i	$-0.719957\pi$
$227$	−19.2044			−1.27464			−0.637319	+	0.770600i	$0.719957\pi$
$228$		0			0
$229$	−0.447393			−0.0295645			−0.0147823	−	0.999891i	$-0.504706\pi$
$229$	−0.447393			−0.0295645			−0.0147823	+	0.999891i	$0.504706\pi$
$230$		0			0
$231$	0.282865	−	1.60421i	0.0186111	−	0.105549i
$232$		0			0
$233$	−9.79269	−	8.21705i	−0.641541	−	0.538317i	0.262950	−	0.964809i	$-0.415305\pi$
$233$	−9.79269	−	8.21705i	−0.641541	−	0.538317i	−0.904491	+	0.426493i	$0.859749\pi$
$234$		0			0
$235$	−30.7978	+	17.7811i	−2.00903	+	1.15991i
$236$		0			0
$237$	−16.1501	−	5.87816i	−1.04906	−	0.381828i
$238$		0			0
$239$	8.37148	+	4.83327i	0.541506	+	0.312639i	0.745689	−	0.666294i	$-0.232120\pi$
$239$	8.37148	+	4.83327i	0.541506	+	0.312639i	−0.204183	+	0.978933i	$0.565454\pi$
$240$		0			0
$241$	5.08972	−	0.897455i	0.327858	−	0.0578101i	−0.00729673	−	0.999973i	$-0.502323\pi$
$241$	5.08972	−	0.897455i	0.327858	−	0.0578101i	0.335154	+	0.942163i	$0.391212\pi$
$242$		0			0
$243$	−0.766044	+	0.642788i	−0.0491418	+	0.0412348i
$244$		0			0
$245$	7.44579	−	2.71005i	0.475694	−	0.173139i
$246$		0			0
$247$	−7.13206	+	0.578290i	−0.453802	+	0.0367957i
$248$		0			0
$249$	−3.27578	−	9.00012i	−0.207594	−	0.570359i
$250$		0			0
$251$	−0.0595679	−	0.0709902i	−0.00375989	−	0.00448086i	0.764161	−	0.645025i	$-0.223153\pi$
$251$	−0.0595679	−	0.0709902i	−0.00375989	−	0.00448086i	−0.767921	+	0.640544i	$0.778709\pi$
$252$		0			0
$253$	0.829105	+	4.70209i	0.0521254	+	0.295618i
$254$		0			0
$255$	10.1556	−	17.5900i	0.635966	−	1.10153i
$256$		0			0
$257$	3.67302	−	10.0915i	0.229117	−	0.629493i	−0.770855	−	0.637011i	$-0.780171\pi$
$257$	3.67302	−	10.0915i	0.229117	−	0.629493i	0.999972	+	0.00751767i	$0.00239297\pi$
$258$		0			0
$259$	−9.34959	−	16.1940i	−0.580956	−	1.00624i
$260$		0			0
$261$	−0.150870	+	0.179800i	−0.00933862	+	0.0111293i
$262$		0			0
$263$	−15.7726	−	2.78113i	−0.972580	−	0.171492i	−0.335289	−	0.942115i	$-0.608834\pi$
$263$	−15.7726	−	2.78113i	−0.972580	−	0.171492i	−0.637291	+	0.770623i	$0.719945\pi$
$264$		0			0
$265$			54.9090i			3.37303i
$266$		0			0
$267$			9.28265i			0.568089i
$268$		0			0
$269$	17.1529	+	3.02451i	1.04583	+	0.184408i	0.670061	−	0.742306i	$-0.266268\pi$
$269$	17.1529	+	3.02451i	1.04583	+	0.184408i	0.375768	+	0.926714i	$0.377379\pi$
$270$		0			0
$271$	−0.428648	+	0.510843i	−0.0260385	+	0.0310315i	−0.778907	−	0.627140i	$-0.784225\pi$
$271$	−0.428648	+	0.510843i	−0.0260385	+	0.0310315i	0.752868	+	0.658172i	$0.228670\pi$
$272$		0			0
$273$	1.87167	+	3.24182i	0.113278	+	0.196204i
$274$		0			0
$275$	−3.51227	+	9.64989i	−0.211798	+	0.581910i
$276$		0			0
$277$	7.32338	−	12.6845i	0.440020	−	0.762136i	−0.557671	−	0.830062i	$-0.688305\pi$
$277$	7.32338	−	12.6845i	0.440020	−	0.762136i	0.997690	+	0.0679260i	$0.0216382\pi$
$278$		0			0
$279$	−0.182652	−	1.03587i	−0.0109351	−	0.0620160i
$280$		0			0
$281$	5.24195	+	6.24712i	0.312709	+	0.372672i	0.899391	−	0.437146i	$-0.144011\pi$
$281$	5.24195	+	6.24712i	0.312709	+	0.372672i	−0.586682	+	0.809817i	$0.699566\pi$
$282$		0			0
$283$	11.3749	+	31.2523i	0.676168	+	1.85776i	0.480234	+	0.877141i	$0.340552\pi$
$283$	11.3749	+	31.2523i	0.676168	+	1.85776i	0.195935	+	0.980617i	$0.437226\pi$
$284$		0			0
$285$	15.7866	−	10.9049i	0.935120	−	0.645953i
$286$		0			0
$287$	−6.63435	+	2.41471i	−0.391613	+	0.142536i
$288$		0			0
$289$	3.28775	−	2.75875i	0.193397	−	0.162279i
$290$		0			0
$291$	2.75491	−	0.485765i	0.161496	−	0.0284761i
$292$		0			0
$293$	−19.9391	−	11.5118i	−1.16485	−	0.672529i	−0.212391	−	0.977185i	$-0.568125\pi$
$293$	−19.9391	−	11.5118i	−1.16485	−	0.672529i	−0.952462	+	0.304656i	$0.901459\pi$
$294$		0			0
$295$	−35.7907	−	13.0267i	−2.08381	−	0.758446i
$296$		0			0
$297$	0.618645	−	0.357175i	0.0358975	−	0.0207254i
$298$		0			0
$299$	−8.40510	−	7.05271i	−0.486079	−	0.407869i
$300$		0			0
$301$	−1.89438	+	10.7436i	−0.109190	+	0.619249i
$302$		0			0
$303$	−11.0617			−0.635476
$304$		0			0
$305$	−7.18787			−0.411576
$306$		0			0
$307$	−5.43411	+	30.8184i	−0.310141	+	1.75890i	0.288119	+	0.957595i	$0.406970\pi$
$307$	−5.43411	+	30.8184i	−0.310141	+	1.75890i	−0.598260	+	0.801302i	$0.704141\pi$
$308$		0			0
$309$	−5.40778	−	4.53767i	−0.307638	−	0.258139i
$310$		0			0
$311$	2.61181	−	1.50793i	0.148102	−	0.0855069i	−0.424118	−	0.905607i	$-0.639416\pi$
$311$	2.61181	−	1.50793i	0.148102	−	0.0855069i	0.572220	+	0.820100i	$0.306082\pi$
$312$		0			0
$313$	4.01587	+	1.46166i	0.226990	+	0.0826177i	0.453011	−	0.891505i	$-0.350350\pi$
$313$	4.01587	+	1.46166i	0.226990	+	0.0826177i	−0.226021	+	0.974122i	$0.572572\pi$
$314$		0			0
$315$	−8.69271	−	5.01874i	−0.489779	−	0.282774i
$316$		0			0
$317$	−25.9997	+	4.58445i	−1.46029	+	0.257488i	−0.846671	−	0.532116i	$-0.821397\pi$
$317$	−25.9997	+	4.58445i	−1.46029	+	0.257488i	−0.613616	+	0.789604i	$0.710286\pi$
$318$		0			0
$319$	0.128440	−	0.107774i	0.00719127	−	0.00603419i
$320$		0			0
$321$	−8.20399	+	2.98601i	−0.457902	+	0.166663i
$322$		0			0
$323$	19.4607	−	5.08204i	1.08282	−	0.282772i
$324$		0			0
$325$	−8.07119	−	22.1754i	−0.447709	−	1.23007i
$326$		0			0
$327$	12.9579	+	15.4426i	0.716574	+	0.853979i
$328$		0			0
$329$	3.19911	+	18.1431i	0.176373	+	1.00026i
$330$		0			0
$331$	−8.51125	+	14.7419i	−0.467821	+	0.810289i	−0.999324	−	0.0367670i	$-0.988294\pi$
$331$	−8.51125	+	14.7419i	−0.467821	+	0.810289i	0.531503	+	0.847056i	$0.321627\pi$
$332$		0			0
$333$	2.80464	−	7.70569i	0.153693	−	0.422269i
$334$		0			0
$335$	4.57222	+	7.91931i	0.249807	+	0.432678i
$336$		0			0
$337$	−2.72037	+	3.24201i	−0.148188	+	0.176604i	−0.835032	−	0.550201i	$-0.814551\pi$
$337$	−2.72037	+	3.24201i	−0.148188	+	0.176604i	0.686844	+	0.726805i	$0.258995\pi$
$338$		0			0
$339$	−2.78808	−	0.491613i	−0.151428	−	0.0267008i
$340$		0			0
$341$			0.751390i			0.0406900i
$342$		0			0
$343$		−	20.0671i		−	1.08352i
$344$		0			0
$345$	28.9739	+	5.10888i	1.55990	+	0.275053i
$346$		0			0
$347$	7.78542	−	9.27830i	0.417943	−	0.498085i	−0.515461	−	0.856913i	$-0.672379\pi$
$347$	7.78542	−	9.27830i	0.417943	−	0.498085i	0.933404	+	0.358828i	$0.116824\pi$
$348$		0			0
$349$	15.5866	+	26.9968i	0.834333	+	1.44511i	0.894573	+	0.446923i	$0.147480\pi$
$349$	15.5866	+	26.9968i	0.834333	+	1.44511i	−0.0602399	+	0.998184i	$0.519187\pi$
$350$		0			0
$351$	−0.561452	+	1.54258i	−0.0299681	+	0.0823366i
$352$		0			0
$353$	−2.84386	+	4.92571i	−0.151364	+	0.262169i	−0.931729	−	0.363154i	$-0.881700\pi$
$353$	−2.84386	+	4.92571i	−0.151364	+	0.262169i	0.780365	+	0.625324i	$0.215033\pi$
$354$		0			0
$355$	−9.43889	−	53.5306i	−0.500964	−	2.84111i
$356$		0			0
$357$	−6.76350	−	8.06042i	−0.357962	−	0.426603i
$358$		0			0
$359$	−3.93153	−	10.8018i	−0.207498	−	0.570097i	0.791667	−	0.610953i	$-0.209214\pi$
$359$	−3.93153	−	10.8018i	−0.207498	−	0.570097i	−0.999165	+	0.0408561i	$0.986991\pi$
$360$		0			0
$361$	18.6679	+	3.53706i	0.982519	+	0.186161i
$362$		0			0
$363$	9.85710	−	3.58769i	0.517363	−	0.188305i
$364$		0			0
$365$	1.44066	−	1.20885i	0.0754074	−	0.0632743i
$366$		0			0
$367$	23.7097	−	4.18066i	1.23764	−	0.218229i	0.483734	−	0.875215i	$-0.339280\pi$
$367$	23.7097	−	4.18066i	1.23764	−	0.218229i	0.753903	+	0.656986i	$0.228169\pi$
$368$		0			0
$369$	−2.68130	−	1.54805i	−0.139583	−	0.0805883i
$370$		0			0
$371$	26.7300	+	9.72893i	1.38775	+	0.505101i
$372$		0			0
$373$	−18.2818	+	10.5550i	−0.946594	+	0.546517i	−0.892021	−	0.451993i	$-0.850713\pi$
$373$	−18.2818	+	10.5550i	−0.946594	+	0.546517i	−0.0545730	+	0.998510i	$0.517380\pi$
$374$		0			0
$375$	31.6140	+	26.5273i	1.63254	+	1.36986i
$376$		0			0
$377$	−0.0669062	+	0.379444i	−0.00344585	+	0.0195424i
$378$		0			0
$379$	25.7764			1.32405			0.662023	−	0.749483i	$-0.269698\pi$
$379$	25.7764			1.32405			0.662023	+	0.749483i	$0.269698\pi$
$380$		0			0
$381$	−8.62420			−0.441831
$382$		0			0
$383$	0.942675	−	5.34617i	0.0481684	−	0.273177i	−0.951205	−	0.308558i	$-0.900154\pi$
$383$	0.942675	−	5.34617i	0.0481684	−	0.273177i	0.999374	+	0.0353815i	$0.0112646\pi$
$384$		0			0
$385$	5.49275	+	4.60896i	0.279936	+	0.234895i
$386$		0			0
$387$	−4.14314	+	2.39205i	−0.210608	+	0.121595i
$388$		0			0
$389$	−4.27479	−	1.55590i	−0.216741	−	0.0788871i	0.231368	−	0.972866i	$-0.425680\pi$
$389$	−4.27479	−	1.55590i	−0.216741	−	0.0788871i	−0.448108	+	0.893979i	$0.647902\pi$
$390$		0			0
$391$	26.7095	+	15.4207i	1.35076	+	0.779859i
$392$		0			0
$393$	−10.9459	+	1.93005i	−0.552145	+	0.0973581i
$394$		0			0
$395$	57.9524	−	48.6278i	2.91590	−	2.44673i
$396$		0			0
$397$	9.11711	−	3.31836i	0.457575	−	0.166544i	−0.102941	−	0.994687i	$-0.532825\pi$
$397$	9.11711	−	3.31836i	0.457575	−	0.166544i	0.560515	+	0.828144i	$0.310603\pi$
$398$		0			0
$399$	−2.51147	−	9.61720i	−0.125731	−	0.481462i
$400$		0			0
$401$	3.22162	+	8.85134i	0.160880	+	0.442015i	0.993774	−	0.111419i	$-0.0355395\pi$
$401$	3.22162	+	8.85134i	0.160880	+	0.442015i	−0.832893	+	0.553433i	$0.813317\pi$
$402$		0			0
$403$	−1.10990	−	1.32272i	−0.0552879	−	0.0658895i
$404$		0			0
$405$	−0.764359	−	4.33490i	−0.0379813	−	0.215403i
$406$		0			0
$407$	−2.92891	+	5.07303i	−0.145181	+	0.251461i
$408$		0			0
$409$	8.56126	−	23.5219i	0.423327	−	1.16308i	−0.526464	−	0.850197i	$-0.676483\pi$
$409$	8.56126	−	23.5219i	0.423327	−	1.16308i	0.949791	−	0.312884i	$-0.101295\pi$
$410$		0			0
$411$	−8.22782	−	14.2510i	−0.405848	−	0.702950i
$412$		0			0
$413$	−12.6830	+	15.1150i	−0.624089	+	0.743760i
$414$		0			0
$415$	41.5185	+	7.32082i	2.03806	+	0.359365i
$416$		0			0
$417$		−	9.48298i		−	0.464384i
$418$		0			0
$419$			32.6275i			1.59396i	0.604007	+	0.796979i	$0.293570\pi$
$419$			32.6275i			1.59396i	−0.604007	+	0.796979i	$0.706430\pi$
$420$		0			0
$421$	−25.7253	−	4.53606i	−1.25377	−	0.221074i	−0.492964	−	0.870050i	$-0.664086\pi$
$421$	−25.7253	−	4.53606i	−1.25377	−	0.221074i	−0.760809	+	0.648976i	$0.775198\pi$
$422$		0			0
$423$	−5.19313	+	6.18893i	−0.252499	+	0.300916i
$424$		0			0
$425$	33.1667	+	57.4464i	1.60882	+	2.78656i
$426$		0			0
$427$	−1.27357	+	3.49910i	−0.0616323	+	0.169333i
$428$		0			0
$429$	0.586330	−	1.01555i	0.0283083	−	0.0490314i
$430$		0			0
$431$	2.16637	+	12.2861i	0.104350	+	0.591800i	0.991478	+	0.130276i	$0.0415862\pi$
$431$	2.16637	+	12.2861i	0.104350	+	0.591800i	−0.887128	+	0.461524i	$0.847303\pi$
$432$		0			0
$433$	−17.4613	−	20.8095i	−0.839135	−	1.00004i	−0.999915	−	0.0130515i	$-0.995845\pi$
$433$	−17.4613	−	20.8095i	−0.839135	−	1.00004i	0.160780	−	0.986990i	$-0.448599\pi$
$434$		0			0
$435$	−0.353358	−	0.970842i	−0.0169422	−	0.0465483i
$436$		0			0
$437$	16.5586	+	23.9712i	0.792106	+	1.14670i
$438$		0			0
$439$	34.7601	−	12.6516i	1.65901	−	0.603830i	0.668803	−	0.743439i	$-0.266807\pi$
$439$	34.7601	−	12.6516i	1.65901	−	0.603830i	0.990207	+	0.139609i	$0.0445846\pi$
$440$		0			0
$441$	1.37896	−	1.15709i	0.0656648	−	0.0550993i
$442$		0			0
$443$	−11.0922	+	1.95586i	−0.527008	+	0.0929257i	−0.430821	−	0.902438i	$-0.641776\pi$
$443$	−11.0922	+	1.95586i	−0.527008	+	0.0929257i	−0.0961873	+	0.995363i	$0.530665\pi$
$444$		0			0
$445$	−35.3859	−	20.4300i	−1.67745	−	0.968477i
$446$		0			0
$447$	9.82283	+	3.57522i	0.464604	+	0.169102i
$448$		0			0
$449$	4.44572	−	2.56674i	0.209807	−	0.121132i	−0.391415	−	0.920214i	$-0.628014\pi$
$449$	4.44572	−	2.56674i	0.209807	−	0.121132i	0.601222	+	0.799082i	$0.294681\pi$
$450$		0			0
$451$	1.69426	+	1.42165i	0.0797796	+	0.0669431i
$452$		0			0
$453$	−2.05542	+	11.6568i	−0.0965719	+	0.547686i
$454$		0			0
$455$	−16.4773			−0.772467
$456$		0			0
$457$	15.6408			0.731644			0.365822	−	0.930685i	$-0.380788\pi$
$457$	15.6408			0.731644			0.365822	+	0.930685i	$0.380788\pi$
$458$		0			0
$459$	0.801266	−	4.54421i	0.0373999	−	0.212105i
$460$		0			0
$461$	9.83225	+	8.25024i	0.457934	+	0.384252i	0.842370	−	0.538900i	$-0.181160\pi$
$461$	9.83225	+	8.25024i	0.457934	+	0.384252i	−0.384436	+	0.923151i	$0.625604\pi$
$462$		0			0
$463$	0.845979	−	0.488426i	0.0393160	−	0.0226991i	−0.480213	−	0.877152i	$-0.659441\pi$
$463$	0.845979	−	0.488426i	0.0393160	−	0.0226991i	0.519529	+	0.854453i	$0.326107\pi$
$464$		0			0
$465$	4.35078	+	1.58355i	0.201763	+	0.0734356i
$466$		0			0
$467$	−3.60779	−	2.08296i	−0.166949	−	0.0963878i	0.414198	−	0.910187i	$-0.364062\pi$
$467$	−3.60779	−	2.08296i	−0.166949	−	0.0963878i	−0.581146	+	0.813799i	$0.697396\pi$
$468$		0			0
$469$	4.66529	−	0.822616i	0.215423	−	0.0379849i
$470$		0			0
$471$	−13.1498	+	11.0340i	−0.605909	+	0.508418i
$472$		0			0
$473$	3.21142	−	1.16886i	0.147661	−	0.0537442i
$474$		0			0
$475$	5.06419	+	62.4567i	0.232361	+	2.86571i
$476$		0			0
$477$	4.26646	+	11.7220i	0.195348	+	0.536714i
$478$		0			0
$479$	−25.1776	−	30.0055i	−1.15039	−	1.37099i	−0.917137	−	0.398572i	$-0.869506\pi$
$479$	−25.1776	−	30.0055i	−1.15039	−	1.37099i	−0.233258	−	0.972415i	$-0.574939\pi$
$480$		0			0
$481$	−2.33753	−	13.2568i	−0.106582	−	0.604457i
$482$		0			0
$483$	7.62071	−	13.1994i	0.346754	−	0.600596i
$484$		0			0
$485$	−4.21148	+	11.5710i	−0.191234	+	0.525410i
$486$		0			0
$487$	10.0351	+	17.3812i	0.454732	+	0.787619i	0.998673	−	0.0515048i	$-0.0164018\pi$
$487$	10.0351	+	17.3812i	0.454732	+	0.787619i	−0.543941	+	0.839124i	$0.683068\pi$
$488$		0			0
$489$	−4.54639	+	5.41818i	−0.205595	+	0.245019i
$490$		0			0
$491$	−23.0531	−	4.06488i	−1.04037	−	0.183445i	−0.372738	−	0.927936i	$-0.621581\pi$
$491$	−23.0531	−	4.06488i	−1.04037	−	0.183445i	−0.667633	+	0.744491i	$0.732692\pi$
$492$		0			0
$493$		−	1.08303i		−	0.0487774i
$494$		0			0
$495$			3.14441i			0.141331i
$496$		0			0
$497$	−27.7314	−	4.88980i	−1.24392	−	0.219337i
$498$		0			0
$499$	17.4771	−	20.8284i	0.782382	−	0.932406i	−0.216657	−	0.976248i	$-0.569515\pi$
$499$	17.4771	−	20.8284i	0.782382	−	0.932406i	0.999039	+	0.0438414i	$0.0139596\pi$
$500$		0			0
$501$	4.54537	+	7.87281i	0.203072	+	0.351731i
$502$		0			0
$503$	−10.0332	+	27.5660i	−0.447359	+	1.22911i	0.487198	+	0.873292i	$0.338019\pi$
$503$	−10.0332	+	27.5660i	−0.447359	+	1.22911i	−0.934556	+	0.355816i	$0.884203\pi$
$504$		0			0
$505$	24.3454	−	42.1675i	1.08336	−	1.87643i
$506$		0			0
$507$	−1.78948	−	10.1487i	−0.0794738	−	0.450718i
$508$		0			0
$509$	13.2753	+	15.8208i	0.588416	+	0.701247i	0.975301	−	0.220881i	$-0.0708934\pi$
$509$	13.2753	+	15.8208i	0.588416	+	0.701247i	−0.386885	+	0.922128i	$0.626449\pi$
$510$		0			0
$511$	−0.333218	−	0.915508i	−0.0147407	−	0.0404997i
$512$		0			0
$513$	2.52282	−	3.55463i	0.111385	−	0.156941i
$514$		0			0
$515$	29.1997	−	10.6278i	1.28669	−	0.468317i
$516$		0			0
$517$	4.42107	−	3.70972i	0.194438	−	0.163153i
$518$		0			0
$519$	−8.83865	+	1.55849i	−0.387974	+	0.0684103i
$520$		0			0
$521$	−12.6850	−	7.32371i	−0.555742	−	0.320858i	0.195693	−	0.980665i	$-0.437304\pi$
$521$	−12.6850	−	7.32371i	−0.555742	−	0.320858i	−0.751435	+	0.659808i	$0.770638\pi$
$522$		0			0
$523$	−9.70176	−	3.53115i	−0.424228	−	0.154406i	0.121079	−	0.992643i	$-0.461365\pi$
$523$	−9.70176	−	3.53115i	−0.424228	−	0.154406i	−0.545307	+	0.838236i	$0.683587\pi$
$524$		0			0
$525$	28.3892	−	16.3905i	1.23901	−	0.715341i
$526$		0			0
$527$	3.71805	+	3.11981i	0.161961	+	0.135901i
$528$		0			0
$529$	−3.76367	+	21.3448i	−0.163638	+	0.928036i
$530$		0			0
$531$	−8.65280			−0.375500
$532$		0			0
$533$	−5.08249			−0.220147
$534$		0			0
$535$	6.67324	−	37.8458i	0.288509	−	1.63622i
$536$		0			0
$537$	16.5855	+	13.9169i	0.715716	+	0.600557i
$538$		0			0
$539$	−1.11363	+	0.642953i	−0.0479673	+	0.0276939i
$540$		0			0
$541$	10.5757	+	3.84922i	0.454683	+	0.165491i	0.559201	−	0.829032i	$-0.311108\pi$
$541$	10.5757	+	3.84922i	0.454683	+	0.165491i	−0.104518	+	0.994523i	$0.533330\pi$
$542$		0			0
$543$	5.13224	+	2.96310i	0.220245	+	0.127159i
$544$		0			0
$545$	−87.3868	+	15.4087i	−3.74324	+	0.660034i
$546$		0			0
$547$	−17.4931	+	14.6784i	−0.747950	+	0.627604i	−0.934960	−	0.354754i	$-0.884565\pi$
$547$	−17.4931	+	14.6784i	−0.747950	+	0.627604i	0.187010	+	0.982358i	$0.440120\pi$
$548$		0			0
$549$	−1.53447	+	0.558502i	−0.0654897	+	0.0238363i
$550$		0			0
$551$	0.438264	−	0.924462i	0.0186707	−	0.0393834i
$552$		0			0
$553$	−13.4041	−	36.8276i	−0.570002	−	1.56607i
$554$		0			0
$555$	23.2017	+	27.6507i	0.984858	+	1.17371i
$556$		0			0
$557$	1.33294	+	7.55948i	0.0564785	+	0.320305i	0.999937	−	0.0111839i	$-0.00356001\pi$
$557$	1.33294	+	7.55948i	0.0564785	+	0.320305i	−0.943459	+	0.331489i	$0.892449\pi$
$558$		0			0
$559$	−3.92672	+	6.80129i	−0.166083	+	0.287664i
$560$		0			0
$561$	−1.12738	+	3.09745i	−0.0475979	+	0.130774i
$562$		0			0
$563$	9.57227	+	16.5797i	0.403423	+	0.698749i	0.994137	−	0.108132i	$-0.0344870\pi$
$563$	9.57227	+	16.5797i	0.403423	+	0.698749i	−0.590713	+	0.806881i	$0.701154\pi$
$564$		0			0
$565$	8.01029	−	9.54629i	0.336995	−	0.401615i
$566$		0			0
$567$	−2.24568	−	0.395975i	−0.0943099	−	0.0166294i
$568$		0			0
$569$		−	15.9929i		−	0.670458i	−0.942137	−	0.335229i	$-0.891186\pi$
$569$		−	15.9929i		−	0.670458i	0.942137	−	0.335229i	$-0.108814\pi$
$570$		0			0
$571$			22.6499i			0.947868i	0.880560	+	0.473934i	$0.157167\pi$
$571$			22.6499i			0.947868i	−0.880560	+	0.473934i	$0.842833\pi$
$572$		0			0
$573$	−10.8820	−	1.91878i	−0.454601	−	0.0801584i
$574$		0			0
$575$	−61.7619	+	73.6050i	−2.57565	+	3.06954i
$576$		0			0
$577$	−4.26292	−	7.38360i	−0.177468	−	0.307383i	0.763545	−	0.645755i	$-0.223457\pi$
$577$	−4.26292	−	7.38360i	−0.177468	−	0.307383i	−0.941013	+	0.338372i	$0.890124\pi$
$578$		0			0
$579$	−4.56480	+	12.5417i	−0.189707	+	0.521215i
$580$		0			0
$581$	10.9202	−	18.9143i	0.453045	−	0.784698i
$582$		0			0
$583$	−1.54738	−	8.77564i	−0.0640860	−	0.363450i
$584$		0			0
$585$	−4.64468	−	5.53531i	−0.192034	−	0.228857i
$586$		0			0
$587$	−11.6462	−	31.9977i	−0.480690	−	1.32069i	−0.908903	−	0.417008i	$-0.863079\pi$
$587$	−11.6462	−	31.9977i	−0.480690	−	1.32069i	0.428212	−	0.903678i	$-0.359144\pi$
$588$		0			0
$589$	1.91120	+	4.16758i	0.0787496	+	0.171722i
$590$		0			0
$591$	13.5333	−	4.92571i	0.556685	−	0.202617i
$592$		0			0
$593$	−19.3528	+	16.2389i	−0.794723	+	0.666852i	−0.946910	−	0.321500i	$-0.895813\pi$
$593$	−19.3528	+	16.2389i	−0.794723	+	0.666852i	0.152187	+	0.988352i	$0.451369\pi$
$594$		0			0
$595$	45.6124	−	8.04269i	1.86993	−	0.329718i
$596$		0			0
$597$	15.3040	+	8.83578i	0.626352	+	0.361624i
$598$		0			0
$599$	−24.0933	−	8.76923i	−0.984424	−	0.358301i	−0.200866	−	0.979619i	$-0.564375\pi$
$599$	−24.0933	−	8.76923i	−0.984424	−	0.358301i	−0.783559	+	0.621318i	$0.786598\pi$
$600$		0			0
$601$	36.2266	−	20.9155i	1.47772	−	0.853159i	0.478032	−	0.878342i	$-0.341350\pi$
$601$	36.2266	−	20.9155i	1.47772	−	0.853159i	0.999683	+	0.0251831i	$0.00801688\pi$
$602$		0			0
$603$	1.59142	+	1.33536i	0.0648074	+	0.0543799i
$604$		0			0
$605$	−8.01790	+	45.4718i	−0.325974	+	1.84869i
$606$		0			0
$607$	39.1422			1.58873			0.794366	−	0.607440i	$-0.207803\pi$
$607$	39.1422			1.58873			0.794366	+	0.607440i	$0.207803\pi$
$608$		0			0
$609$	−0.535221			−0.0216882
$610$		0			0
$611$	−2.30300	+	13.0609i	−0.0931692	+	0.528389i
$612$		0			0
$613$	16.0481	+	13.4659i	0.648176	+	0.543884i	0.906517	−	0.422170i	$-0.138731\pi$
$613$	16.0481	+	13.4659i	0.648176	+	0.543884i	−0.258341	+	0.966054i	$0.583176\pi$
$614$		0			0
$615$	11.8025	−	6.81416i	0.475922	−	0.274774i
$616$		0			0
$617$	0.369036	+	0.134318i	0.0148568	+	0.00540744i	0.349438	−	0.936960i	$-0.386373\pi$
$617$	0.369036	+	0.134318i	0.0148568	+	0.00540744i	−0.334581	+	0.942367i	$0.608595\pi$
$618$		0			0
$619$	−28.4234	−	16.4102i	−1.14243	−	0.659583i	−0.195400	−	0.980724i	$-0.562601\pi$
$619$	−28.4234	−	16.4102i	−1.14243	−	0.659583i	−0.947032	+	0.321140i	$0.895934\pi$
$620$		0			0
$621$	6.58233	−	1.16064i	0.264140	−	0.0465749i
$622$		0			0
$623$	−16.2152	+	13.6062i	−0.649650	+	0.545121i
$624$		0			0
$625$	−103.159	+	37.5467i	−4.12635	+	1.50187i
$626$		0			0
$627$	−2.21573	+	2.18773i	−0.0884879	+	0.0873694i
$628$		0			0
$629$	12.9415	+	35.5564i	0.516010	+	1.41773i
$630$		0			0
$631$	−8.39333	−	10.0028i	−0.334133	−	0.398204i	0.572651	−	0.819799i	$-0.305915\pi$
$631$	−8.39333	−	10.0028i	−0.334133	−	0.398204i	−0.906784	+	0.421595i	$0.861470\pi$
$632$		0			0
$633$	−3.38860	−	19.2177i	−0.134685	−	0.763836i
$634$		0			0
$635$	18.9809	−	32.8758i	0.753233	−	1.30464i
$636$		0			0
$637$	1.01067	−	2.77680i	0.0400443	−	0.110021i
$638$		0			0
$639$	−6.17438	−	10.6943i	−0.244255	−	0.423062i
$640$		0			0
$641$	13.6080	−	16.2173i	0.537482	−	0.640546i	−0.427139	−	0.904186i	$-0.640479\pi$
$641$	13.6080	−	16.2173i	0.537482	−	0.640546i	0.964621	+	0.263640i	$0.0849230\pi$
$642$		0			0
$643$	−16.9388	−	2.98677i	−0.668003	−	0.117787i	−0.170645	−	0.985333i	$-0.554585\pi$
$643$	−16.9388	−	2.98677i	−0.668003	−	0.117787i	−0.497358	+	0.867546i	$0.665696\pi$
$644$		0			0
$645$		−	21.0585i		−	0.829176i
$646$		0			0
$647$		−	14.8521i		−	0.583897i	−0.956434	−	0.291949i	$-0.905696\pi$
$647$		−	14.8521i		−	0.583897i	0.956434	−	0.291949i	$-0.0943036\pi$
$648$		0			0
$649$	6.08723	+	1.07334i	0.238945	+	0.0421324i
$650$		0			0
$651$	1.54177	−	1.83741i	0.0604266	−	0.0720137i
$652$		0			0
$653$	14.0536	+	24.3416i	0.549960	+	0.952559i	0.998277	+	0.0586837i	$0.0186904\pi$
$653$	14.0536	+	24.3416i	0.549960	+	0.952559i	−0.448317	+	0.893875i	$0.647976\pi$
$654$		0			0
$655$	16.7331	−	45.9739i	0.653818	−	1.79635i
$656$		0			0
$657$	0.213624	−	0.370007i	0.00833425	−	0.0144353i
$658$		0			0
$659$	−2.92956	−	16.6144i	−0.114119	−	0.647204i	−0.987182	−	0.159596i	$-0.948981\pi$
$659$	−2.92956	−	16.6144i	−0.114119	−	0.647204i	0.873063	−	0.487608i	$-0.162130\pi$
$660$		0			0
$661$	18.1166	+	21.5906i	0.704656	+	0.839776i	0.993045	−	0.117738i	$-0.0375641\pi$
$661$	18.1166	+	21.5906i	0.704656	+	0.839776i	−0.288389	+	0.957513i	$0.593120\pi$
$662$		0			0
$663$	−2.59071	−	7.11793i	−0.100615	−	0.276437i
$664$		0			0
$665$	42.1886	+	11.5925i	1.63601	+	0.449538i
$666$		0			0
$667$	1.47418	−	0.536556i	0.0570803	−	0.0207755i
$668$		0			0
$669$	−15.1573	+	12.7185i	−0.586016	+	0.491726i
$670$		0			0
$671$	1.14878	−	0.202560i	0.0443481	−	0.00781976i
$672$		0			0
$673$	−35.8809	−	20.7158i	−1.38311	−	0.798537i	−0.390580	−	0.920569i	$-0.627726\pi$
$673$	−35.8809	−	20.7158i	−1.38311	−	0.798537i	−0.992526	+	0.122032i	$0.961059\pi$
$674$		0			0
$675$	13.5086	+	4.91674i	0.519947	+	0.189245i
$676$		0			0
$677$	25.4959	−	14.7201i	0.979888	−	0.565739i	0.0776520	−	0.996981i	$-0.475258\pi$
$677$	25.4959	−	14.7201i	0.979888	−	0.565739i	0.902236	+	0.431242i	$0.141924\pi$
$678$		0			0
$679$	4.88661	+	4.10035i	0.187531	+	0.157357i
$680$		0			0
$681$	3.33480	−	18.9126i	0.127790	−	0.724733i
$682$		0			0
$683$	17.0766			0.653420			0.326710	−	0.945125i	$-0.394060\pi$
$683$	17.0766			0.653420			0.326710	+	0.945125i	$0.394060\pi$
$684$		0			0
$685$	72.4339			2.76756
$686$		0			0
$687$	0.0776889	−	0.440596i	0.00296402	−	0.0168098i
$688$		0			0
$689$	15.6867	+	13.1627i	0.597615	+	0.501458i
$690$		0			0
$691$	−10.4946	+	6.05906i	−0.399234	+	0.230498i	−0.686153	−	0.727457i	$-0.740702\pi$
$691$	−10.4946	+	6.05906i	−0.399234	+	0.230498i	0.286920	+	0.957955i	$0.407369\pi$
$692$		0			0
$693$	1.53071	+	0.557135i	0.0581471	+	0.0211638i
$694$		0			0
$695$	36.1496	+	20.8710i	1.37123	+	0.791680i
$696$		0			0
$697$	14.0693	−	2.48080i	0.532914	−	0.0939671i
$698$		0			0
$699$	9.79269	−	8.21705i	0.370394	−	0.310797i
$700$		0			0
$701$	−45.5798	+	16.5897i	−1.72153	+	0.626584i	−0.997970	−	0.0636811i	$-0.979716\pi$
$701$	−45.5798	+	16.5897i	−1.72153	+	0.626584i	−0.723556	+	0.690265i	$0.757494\pi$
$702$		0			0
$703$	−3.34170	+	35.5874i	−0.126035	+	1.34220i
$704$		0			0
$705$	−12.1630	−	33.4176i	−0.458085	−	1.25858i
$706$		0			0
$707$	−16.2138	−	19.3229i	−0.609783	−	0.726711i
$708$		0			0
$709$	−2.29721	−	13.0281i	−0.0862736	−	0.489282i	−0.997074	−	0.0764359i	$-0.975646\pi$
$709$	−2.29721	−	13.0281i	−0.0862736	−	0.489282i	0.910801	−	0.412846i	$-0.135465\pi$
$710$		0			0
$711$	8.59330	−	14.8840i	0.322274	−	0.558195i
$712$		0			0
$713$	−2.40455	+	6.60645i	−0.0900511	+	0.247413i
$714$		0			0
$715$	2.58089	+	4.47023i	0.0965198	+	0.167177i
$716$		0			0
$717$	−6.21354	+	7.40501i	−0.232049	+	0.276545i
$718$		0			0
$719$	−38.1557	−	6.72788i	−1.42297	−	0.250908i	−0.591422	−	0.806362i	$-0.701433\pi$
$719$	−38.1557	−	6.72788i	−1.42297	−	0.250908i	−0.831547	+	0.555455i	$0.812544\pi$
$720$		0			0
$721$		−	16.0976i		−	0.599507i
$722$		0			0
$723$			5.16824i			0.192209i
$724$		0			0
$725$	3.32286	+	0.585910i	0.123408	+	0.0217602i
$726$		0			0
$727$	−20.3114	+	24.2061i	−0.753306	+	0.897755i	−0.997405	−	0.0719949i	$-0.977063\pi$
$727$	−20.3114	+	24.2061i	−0.753306	+	0.897755i	0.244099	+	0.969750i	$0.421508\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	7.55019	−	20.7440i	0.279254	−	0.767244i
$732$		0			0
$733$	−11.4401	+	19.8149i	−0.422550	+	0.731878i	−0.996188	−	0.0872305i	$-0.972198\pi$
$733$	−11.4401	+	19.8149i	−0.422550	+	0.731878i	0.573638	+	0.819109i	$0.305532\pi$
$734$		0			0
$735$	1.37593	+	7.80327i	0.0507518	+	0.287828i
$736$		0			0
$737$	−0.953912	−	1.13683i	−0.0351378	−	0.0418756i
$738$		0			0
$739$	0.863570	+	2.37264i	0.0317669	+	0.0872789i	0.954562	−	0.298012i	$-0.0963234\pi$
$739$	0.863570	+	2.37264i	0.0317669	+	0.0872789i	−0.922795	+	0.385291i	$0.874101\pi$
$740$		0			0
$741$	0.668964	−	7.12412i	0.0245750	−	0.261711i
$742$		0			0
$743$	35.8279	−	13.0403i	1.31440	−	0.478402i	0.412739	−	0.910849i	$-0.364572\pi$
$743$	35.8279	−	13.0403i	1.31440	−	0.478402i	0.901659	+	0.432448i	$0.142350\pi$
$744$		0			0
$745$	−35.2478	+	29.5764i	−1.29138	+	1.08360i
$746$		0			0
$747$	9.43222	−	1.66316i	0.345107	−	0.0608517i
$748$		0			0
$749$	−17.2412	−	9.95421i	−0.629980	−	0.363719i
$750$		0			0
$751$	−16.3942	−	5.96700i	−0.598233	−	0.217739i	0.0251138	−	0.999685i	$-0.492005\pi$
$751$	−16.3942	−	5.96700i	−0.598233	−	0.217739i	−0.623347	+	0.781946i	$0.714227\pi$
$752$		0			0
$753$	0.0802556	−	0.0463356i	0.00292468	−	0.00168856i
$754$		0			0
$755$	−39.9127	−	33.4907i	−1.45257	−	1.21885i
$756$		0			0
$757$	0.600537	−	3.40581i	0.0218269	−	0.123786i	−0.971947	−	0.235198i	$-0.924426\pi$
$757$	0.600537	−	3.40581i	0.0218269	−	0.123786i	0.993774	+	0.111412i	$0.0355372\pi$
$758$		0			0
$759$	−4.77462			−0.173308
$760$		0			0
$761$	−21.5307			−0.780488			−0.390244	−	0.920711i	$-0.627609\pi$
$761$	−21.5307			−0.780488			−0.390244	+	0.920711i	$0.627609\pi$
$762$		0			0
$763$	−7.98242	+	45.2706i	−0.288983	+	1.63890i
$764$		0			0
$765$	15.5592	+	13.0557i	0.562545	+	0.472031i
$766$		0			0
$767$	−12.3012	+	7.10211i	−0.444171	+	0.256443i
$768$		0			0
$769$	24.6123	+	8.95814i	0.887542	+	0.323039i	0.745250	−	0.666786i	$-0.232330\pi$
$769$	24.6123	+	8.95814i	0.887542	+	0.323039i	0.142293	+	0.989825i	$0.454553\pi$
$770$		0			0
$771$	9.30041	+	5.36960i	0.334946	+	0.193381i
$772$		0			0
$773$	−17.1183	+	3.01841i	−0.615701	+	0.108565i	−0.472796	−	0.881172i	$-0.656755\pi$
$773$	−17.1183	+	3.01841i	−0.615701	+	0.108565i	−0.142905	+	0.989736i	$0.545644\pi$
$774$		0			0
$775$	−11.5833	+	9.71957i	−0.416085	+	0.349137i
$776$		0			0
$777$	17.5715	−	6.39550i	0.630374	−	0.229437i
$778$		0			0
$779$	13.0133	+	3.57576i	0.466249	+	0.128115i
$780$		0			0
$781$	3.01708	+	8.28935i	0.107959	+	0.296616i
$782$		0			0
$783$	−0.150870	−	0.179800i	−0.00539165	−	0.00642552i
$784$		0			0
$785$	−13.1208	−	74.4119i	−0.468303	−	2.65588i
$786$		0			0
$787$	13.0477	−	22.5992i	0.465099	−	0.805574i	−0.534107	−	0.845417i	$-0.679352\pi$
$787$	13.0477	−	22.5992i	0.465099	−	0.805574i	0.999206	+	0.0398423i	$0.0126856\pi$
$788$		0			0
$789$	5.47776	−	15.0500i	0.195014	−	0.535795i
$790$		0			0
$791$	−3.22790	−	5.59089i	−0.114771	−	0.198789i
$792$		0			0
$793$	−1.72306	+	2.05347i	−0.0611878	+	0.0729208i
$794$		0			0
$795$	−54.0748	−	9.53484i	−1.91784	−	0.338166i
$796$		0			0
$797$		−	2.82633i		−	0.100114i	−0.998746	−	0.0500568i	$-0.984060\pi$
$797$		−	2.82633i		−	0.100114i	0.998746	−	0.0500568i	$-0.0159402\pi$
$798$		0			0
$799$		−	37.2794i		−	1.31885i
$800$		0			0
$801$	−9.14163	−	1.61192i	−0.323004	−	0.0569542i
$802$		0			0
$803$	−0.196181	+	0.233800i	−0.00692309	+	0.00825062i
$804$		0			0
$805$	33.5446	+	58.1009i	1.18229	+	2.04779i
$806$		0			0
$807$	−5.95713	+	16.3671i	−0.209701	+	0.576148i
$808$		0			0
$809$	9.56173	−	16.5614i	0.336173	−	0.582268i	−0.647537	−	0.762034i	$-0.724201\pi$
$809$	9.56173	−	16.5614i	0.336173	−	0.582268i	0.983709	+	0.179766i	$0.0575341\pi$
$810$		0			0
$811$	−5.08573	−	28.8426i	−0.178584	−	1.01280i	−0.933925	−	0.357469i	$-0.883640\pi$
$811$	−5.08573	−	28.8426i	−0.178584	−	1.01280i	0.755341	−	0.655332i	$-0.227471\pi$
$812$		0			0
$813$	−0.428648	−	0.510843i	−0.0150334	−	0.0179161i
$814$		0			0
$815$	−10.6483	−	29.2558i	−0.372992	−	1.02479i
$816$		0			0
$817$	14.8390	−	14.6515i	0.519153	−	0.512590i
$818$		0			0
$819$	−3.51758	+	1.28029i	−0.122914	+	0.0447371i
$820$		0			0
$821$	−8.30251	+	6.96664i	−0.289760	+	0.243137i	−0.776067	−	0.630651i	$-0.782788\pi$
$821$	−8.30251	+	6.96664i	−0.289760	+	0.243137i	0.486307	+	0.873788i	$0.338344\pi$
$822$		0			0
$823$	−53.4122	+	9.41801i	−1.86183	+	0.328291i	−0.987572	−	0.157168i	$-0.949764\pi$
$823$	−53.4122	+	9.41801i	−1.86183	+	0.328291i	−0.874259	+	0.485459i	$0.838653\pi$
$824$		0			0
$825$	−8.89338	−	5.13460i	−0.309628	−	0.178764i
$826$		0			0
$827$	22.0644	+	8.03080i	0.767256	+	0.279258i	0.695848	−	0.718189i	$-0.255029\pi$
$827$	22.0644	+	8.03080i	0.767256	+	0.279258i	0.0714076	+	0.997447i	$0.477251\pi$
$828$		0			0
$829$	41.0889	−	23.7227i	1.42708	−	0.823924i	0.430189	−	0.902739i	$-0.358447\pi$
$829$	41.0889	−	23.7227i	1.42708	−	0.823924i	0.996889	+	0.0788152i	$0.0251137\pi$
$830$		0			0
$831$	11.2201	+	9.41476i	0.389220	+	0.326594i
$832$		0			0
$833$	−1.44236	+	8.18005i	−0.0499749	+	0.283422i
$834$		0			0
$835$	−40.0153			−1.38479
$836$		0			0
$837$	1.05185			0.0363573
$838$		0			0
$839$	8.17504	−	46.3629i	0.282234	−	1.60063i	−0.432769	−	0.901505i	$-0.642463\pi$
$839$	8.17504	−	46.3629i	0.282234	−	1.60063i	0.715003	−	0.699122i	$-0.246425\pi$
$840$		0			0
$841$	22.1731	+	18.6054i	0.764589	+	0.641567i
$842$		0			0
$843$	−7.06247	+	4.07752i	−0.243244	+	0.140437i
$844$		0			0
$845$	42.6256	+	15.5145i	1.46637	+	0.533714i
$846$		0			0
$847$	20.7153	+	11.9600i	0.711786	+	0.410950i
$848$		0			0
$849$	−32.7528	+	5.77520i	−1.12407	+	0.198204i
$850$		0			0
$851$	−41.9863	+	35.2307i	−1.43927	+	1.20769i
$852$		0			0
$853$	31.5399	−	11.4796i	1.07991	−	0.393054i	0.260033	−	0.965600i	$-0.416266\pi$
$853$	31.5399	−	11.4796i	1.07991	−	0.393054i	0.819873	+	0.572546i	$0.194044\pi$
$854$		0			0
$855$	7.99796	+	17.4404i	0.273524	+	0.596450i
$856$		0			0
$857$	−17.8993	−	49.1778i	−0.611427	−	1.67988i	−0.727046	−	0.686589i	$-0.759107\pi$
$857$	−17.8993	−	49.1778i	−0.611427	−	1.67988i	0.115619	−	0.993294i	$-0.463115\pi$
$858$		0			0
$859$	−11.2756	−	13.4378i	−0.384720	−	0.458491i	0.538578	−	0.842575i	$-0.318962\pi$
$859$	−11.2756	−	13.4378i	−0.384720	−	0.458491i	−0.923298	+	0.384085i	$0.874517\pi$
$860$		0			0
$861$	−1.22598	−	6.95287i	−0.0417812	−	0.236953i
$862$		0			0
$863$	−9.64785	+	16.7106i	−0.328417	+	0.568834i	−0.982198	−	0.187849i	$-0.939848\pi$
$863$	−9.64785	+	16.7106i	−0.328417	+	0.568834i	0.653781	+	0.756684i	$0.273182\pi$
$864$		0			0
$865$	13.5118	−	37.1234i	0.459415	−	1.26223i
$866$		0			0
$867$	2.14592	+	3.71685i	0.0728794	+	0.126231i
$868$		0			0
$869$	−7.89167	+	9.40492i	−0.267706	+	0.319040i
$870$		0			0
$871$	3.35847	+	0.592190i	0.113798	+	0.0200656i
$872$		0			0
$873$			2.79741i			0.0946780i
$874$		0			0
$875$			94.1071i			3.18140i
$876$		0			0
$877$	13.7911	+	2.43174i	0.465692	+	0.0821140i	0.401570	−	0.915828i	$-0.368464\pi$
$877$	13.7911	+	2.43174i	0.465692	+	0.0821140i	0.0641212	+	0.997942i	$0.479576\pi$
$878$		0			0
$879$	14.7993	−	17.6372i	0.499169	−	0.594887i
$880$		0			0
$881$	−1.35460	−	2.34624i	−0.0456376	−	0.0790467i	0.842304	−	0.539002i	$-0.181199\pi$
$881$	−1.35460	−	2.34624i	−0.0456376	−	0.0790467i	−0.887942	+	0.459956i	$0.847865\pi$
$882$		0			0
$883$	−15.0809	+	41.4345i	−0.507513	+	1.39438i	0.376282	+	0.926505i	$0.377203\pi$
$883$	−15.0809	+	41.4345i	−0.507513	+	1.39438i	−0.883795	+	0.467875i	$0.845020\pi$
$884$		0			0
$885$	19.0438	−	32.9849i	0.640151	−	1.10877i
$886$		0			0
$887$	−0.468041	−	2.65439i	−0.0157153	−	0.0891257i	0.975941	−	0.218033i	$-0.0699641\pi$
$887$	−0.468041	−	2.65439i	−0.0157153	−	0.0891257i	−0.991657	+	0.128907i	$0.958853\pi$
$888$		0			0
$889$	−12.6411	−	15.0650i	−0.423968	−	0.505265i
$890$		0			0
$891$	0.244322	+	0.671270i	0.00818510	+	0.0224884i
$892$		0			0
$893$	15.0856	−	31.8211i	0.504820	−	1.06485i
$894$		0			0
$895$	−89.5545	+	32.5952i	−2.99348	+	1.08954i
$896$		0			0
$897$	8.40510	−	7.05271i	0.280638	−	0.235483i
$898$		0			0
$899$	0.243131	−	0.0428706i	0.00810889	−	0.00142982i
$900$		0			0
$901$	−49.8486	−	28.7801i	−1.66070	−	0.958805i
$902$		0			0
$903$	−10.2514	−	3.73120i	−0.341145	−	0.124167i
$904$		0			0
$905$	−22.5909	+	13.0429i	−0.750948	+	0.433560i
$906$		0			0
$907$	−36.4084	−	30.5503i	−1.20892	−	1.01441i	−0.999329	−	0.0366174i	$-0.988342\pi$
$907$	−36.4084	−	30.5503i	−1.20892	−	1.01441i	−0.209593	−	0.977789i	$-0.567214\pi$
$908$		0			0
$909$	1.92084	−	10.8936i	0.0637102	−	0.361318i
$910$		0			0
$911$	−9.04802			−0.299774			−0.149887	−	0.988703i	$-0.547891\pi$
$911$	−9.04802			−0.299774			−0.149887	+	0.988703i	$0.547891\pi$
$912$		0			0
$913$	−6.84185			−0.226432
$914$		0			0
$915$	1.24816	−	7.07867i	0.0412629	−	0.234014i
$916$		0			0
$917$	−19.4155	−	16.2916i	−0.641158	−	0.537995i
$918$		0			0
$919$	2.30021	−	1.32803i	0.0758768	−	0.0438075i	−0.461582	−	0.887098i	$-0.652718\pi$
$919$	2.30021	−	1.32803i	0.0758768	−	0.0438075i	0.537458	+	0.843290i	$0.319385\pi$
$920$		0			0
$921$	−29.4065	−	10.7031i	−0.968979	−	0.352679i
$922$		0			0
$923$	−17.5556	−	10.1357i	−0.577849	−	0.333621i
$924$		0			0
$925$	−116.092	+	20.4701i	−3.81708	+	0.673054i
$926$		0			0
$927$	5.40778	−	4.53767i	0.177615	−	0.149036i
$928$		0			0
$929$	34.9521	−	12.7215i	1.14674	−	0.417379i	0.302397	−	0.953182i	$-0.402213\pi$
$929$	34.9521	−	12.7215i	1.14674	−	0.417379i	0.844343	+	0.535803i	$0.179991\pi$
$930$		0			0
$931$	−4.54134	+	6.39870i	−0.148837	+	0.209709i
$932$		0			0
$933$	1.03149	+	2.83398i	0.0337693	+	0.0927804i
$934$		0			0
$935$	−9.32637	−	11.1147i	−0.305005	−	0.363491i
$936$		0			0
$937$	−5.38246	−	30.5254i	−0.175837	−	0.997223i	−0.937173	−	0.348865i	$-0.886567\pi$
$937$	−5.38246	−	30.5254i	−0.175837	−	0.997223i	0.761336	−	0.648358i	$-0.224544\pi$
$938$		0			0
$939$	−2.13680	+	3.70104i	−0.0697318	+	0.120779i
$940$		0			0
$941$	2.03229	−	5.58366i	0.0662506	−	0.182022i	−0.902150	−	0.431423i	$-0.858012\pi$
$941$	2.03229	−	5.58366i	0.0662506	−	0.182022i	0.968400	+	0.249401i	$0.0802338\pi$
$942$		0			0
$943$	10.3470	+	17.9215i	0.336944	+	0.583603i
$944$		0			0
$945$	6.45197	−	7.68915i	0.209882	−	0.250128i
$946$		0			0
$947$	35.0509	+	6.18043i	1.13900	+	0.200837i	0.711169	−	0.703021i	$-0.248166\pi$
$947$	35.0509	+	6.18043i	1.13900	+	0.200837i	0.427833	+	0.903858i	$0.359277\pi$
$948$		0			0
$949$		−	0.701359i		−	0.0227671i
$950$		0			0
$951$		−	26.4008i		−	0.856104i
$952$		0			0
$953$	41.4272	+	7.30473i	1.34196	+	0.236623i	0.798085	−	0.602545i	$-0.205846\pi$
$953$	41.4272	+	7.30473i	1.34196	+	0.236623i	0.543872	+	0.839168i	$0.316958\pi$
$954$		0			0
$955$	31.2644	−	37.2595i	1.01169	−	1.20569i
$956$		0			0
$957$	0.0838333	+	0.145204i	0.00270995	+	0.00469376i
$958$		0			0
$959$	12.8340	−	35.2613i	0.414433	−	1.13865i
$960$		0			0
$961$	14.9468	−	25.8886i	0.482155	−	0.835117i
$962$		0			0
$963$	−1.51604	−	8.59787i	−0.0488536	−	0.277063i
$964$		0			0
$965$	−37.7629	−	45.0040i	−1.21563	−	1.44873i
$966$		0			0
$967$	1.76622	+	4.85264i	0.0567977	+	0.156050i	0.964847	−	0.262814i	$-0.0846505\pi$
$967$	1.76622	+	4.85264i	0.0567977	+	0.156050i	−0.908049	+	0.418864i	$0.862428\pi$
$968$		0			0
$969$	1.62552	+	20.0475i	0.0522191	+	0.644019i
$970$		0			0
$971$	31.5072	−	11.4677i	1.01111	−	0.368015i	0.217253	−	0.976115i	$-0.430290\pi$
$971$	31.5072	−	11.4677i	1.01111	−	0.368015i	0.793860	+	0.608100i	$0.208068\pi$
$972$		0			0
$973$	16.5652	−	13.8998i	0.531055	−	0.445608i
$974$		0			0
$975$	23.2401	−	4.09785i	0.744278	−	0.131236i
$976$		0			0
$977$	−12.3323	−	7.12009i	−0.394547	−	0.227792i	0.289582	−	0.957153i	$-0.406484\pi$
$977$	−12.3323	−	7.12009i	−0.394547	−	0.227792i	−0.684128	+	0.729362i	$0.739817\pi$
$978$		0			0
$979$	6.23116	+	2.26796i	0.199149	+	0.0724842i
$980$		0			0
$981$	−17.4581	+	10.0795i	−0.557395	+	0.321812i
$982$		0			0
$983$	−21.7383	−	18.2406i	−0.693344	−	0.581785i	0.226527	−	0.974005i	$-0.427263\pi$
$983$	−21.7383	−	18.2406i	−0.693344	−	0.581785i	−0.919872	+	0.392220i	$0.871707\pi$
$984$		0			0
$985$	−11.0082	+	62.4304i	−0.350749	+	1.98920i
$986$		0			0
$987$	−18.4230			−0.586409
$988$		0			0
$989$	31.9762			1.01679
$990$		0			0
$991$	−5.93168	+	33.6402i	−0.188426	+	1.06862i	0.733048	+	0.680177i	$0.238097\pi$
$991$	−5.93168	+	33.6402i	−0.188426	+	1.06862i	−0.921474	+	0.388440i	$0.873014\pi$
$992$		0			0
$993$	−13.0400	−	10.9419i	−0.413812	−	0.347229i
$994$		0			0
$995$	−67.3647	+	38.8930i	−2.13561	+	1.23299i
$996$		0			0
$997$	3.21723	+	1.17097i	0.101891	+	0.0370851i	0.392462	−	0.919768i	$-0.371623\pi$
$997$	3.21723	+	1.17097i	0.101891	+	0.0370851i	−0.290572	+	0.956853i	$0.593846\pi$
$998$		0			0
$999$	7.10160	+	4.10011i	0.224685	+	0.129722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.h.223.1	yes	24
4.3	odd	2		912.2.ci.g.223.1	✓	24
19.15	odd	18		912.2.ci.g.319.1	yes	24
76.15	even	18	inner	912.2.ci.h.319.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.g.223.1	✓	24	4.3	odd	2
912.2.ci.g.319.1	yes	24	19.15	odd	18
912.2.ci.h.223.1	yes	24	1.1	even	1	trivial
912.2.ci.h.319.1	yes	24	76.15	even	18	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{3} +(-3.37195 - 2.82940i) q^{5} +(-1.97482 + 1.14016i) q^{7} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{3} +(-3.37195 - 2.82940i) q^{5} +(-1.97482 + 1.14016i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(0.618645 + 0.357175i) q^{11} +(-1.61664 + 0.285057i) q^{13} +(3.37195 - 2.82940i) q^{15} +(4.33603 - 1.57819i) q^{17} +(4.33981 + 0.407514i) q^{19} +(-0.779918 - 2.14281i) q^{21} +(4.29631 + 5.12014i) q^{23} +(2.49629 + 14.1572i) q^{25} +(0.500000 - 0.866025i) q^{27} +(0.0802763 - 0.220557i) q^{29} +(0.525925 + 0.910930i) q^{31} +(-0.459175 + 0.547224i) q^{33} +(9.88499 + 1.74299i) q^{35} +8.20022i q^{37} -1.64158i q^{39} +(3.04906 + 0.537632i) q^{41} +(3.07515 - 3.66483i) q^{43} +(2.20088 + 3.81204i) q^{45} +(2.76321 - 7.59185i) q^{47} +(-0.900053 + 1.55894i) q^{49} +(0.801266 + 4.54421i) q^{51} +(-8.01832 - 9.55587i) q^{53} +(-1.07545 - 2.95477i) q^{55} +(-1.15492 + 4.20311i) q^{57} +(8.13097 - 2.95943i) q^{59} +(1.25091 - 1.04964i) q^{61} +(2.24568 - 0.395975i) q^{63} +(6.25776 + 3.61292i) q^{65} +(-1.95216 - 0.710528i) q^{67} +(-5.78840 + 3.34193i) q^{69} +(9.45970 + 7.93763i) q^{71} +(-0.0741907 + 0.420756i) q^{73} -14.3756 q^{75} -1.62895 q^{77} +(-2.98442 + 16.9255i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-8.29456 + 4.78886i) q^{83} +(-19.0862 - 6.94681i) q^{85} +(0.203267 + 0.117356i) q^{87} +(9.14163 - 1.61192i) q^{89} +(2.86756 - 2.40617i) q^{91} +(-0.988416 + 0.359754i) q^{93} +(-13.4806 - 13.6532i) q^{95} +(-0.956771 - 2.62871i) q^{97} +(-0.459175 - 0.547224i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 9 q^{7}+O(q^{10}) \) 24 * q + 9 * q^7	\( 24 q + 9 q^{7} - 9 q^{11} - 9 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 15 q^{23} + 6 q^{25} + 12 q^{27} - 6 q^{29} - 12 q^{31} - 3 q^{33} + 30 q^{41} + 9 q^{43} + 3 q^{45} + 15 q^{47} + 27 q^{49} - 3 q^{51} + 6 q^{53} - 21 q^{55} - 9 q^{57} + 36 q^{59} - 21 q^{61} + 3 q^{63} - 9 q^{65} - 45 q^{67} + 36 q^{71} - 42 q^{75} + 108 q^{77} - 36 q^{79} + 27 q^{83} - 9 q^{85} + 9 q^{87} - 27 q^{89} + 36 q^{91} - 18 q^{93} - 30 q^{95} - 51 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 9 * q^7 - 9 * q^11 - 9 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 15 * q^23 + 6 * q^25 + 12 * q^27 - 6 * q^29 - 12 * q^31 - 3 * q^33 + 30 * q^41 + 9 * q^43 + 3 * q^45 + 15 * q^47 + 27 * q^49 - 3 * q^51 + 6 * q^53 - 21 * q^55 - 9 * q^57 + 36 * q^59 - 21 * q^61 + 3 * q^63 - 9 * q^65 - 45 * q^67 + 36 * q^71 - 42 * q^75 + 108 * q^77 - 36 * q^79 + 27 * q^83 - 9 * q^85 + 9 * q^87 - 27 * q^89 + 36 * q^91 - 18 * q^93 - 30 * q^95 - 51 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more