LMFDB - Embedded newform 912.2.ci.g.79.3

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			79.3
Character	$\chi$	$=$	912.79
Dual form			912.2.ci.g.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{3} +(0.494739 - 2.80581i) q^{5} +(4.05139 - 2.33907i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{3} +(0.494739 - 2.80581i) q^{5} +(4.05139 - 2.33907i) q^{7} +(0.766044 - 0.642788i) q^{9} +(4.23869 + 2.44721i) q^{11} +(-0.974319 + 2.67692i) q^{13} +(0.494739 + 2.80581i) q^{15} +(-3.09819 - 2.59969i) q^{17} +(-3.35652 - 2.78097i) q^{19} +(-3.00705 + 3.58366i) q^{21} +(5.98701 - 1.05567i) q^{23} +(-2.92931 - 1.06618i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-3.64299 - 4.34155i) q^{29} +(3.14264 + 5.44322i) q^{31} +(-4.82006 - 0.849907i) q^{33} +(-4.55859 - 12.5246i) q^{35} +6.42841i q^{37} -2.84872i q^{39} +(-2.01774 - 5.54370i) q^{41} +(1.67932 + 0.296109i) q^{43} +(-1.42454 - 2.46738i) q^{45} +(-5.46079 - 6.50792i) q^{47} +(7.44249 - 12.8908i) q^{49} +(3.80049 + 1.38326i) q^{51} +(7.07029 - 1.24668i) q^{53} +(8.96344 - 10.6822i) q^{55} +(4.10524 + 1.46526i) q^{57} +(3.61390 + 3.03242i) q^{59} +(0.715468 + 4.05762i) q^{61} +(1.60002 - 4.39601i) q^{63} +(7.02888 + 4.05813i) q^{65} +(-2.79466 + 2.34500i) q^{67} +(-5.26489 + 3.03969i) q^{69} +(0.152483 - 0.864773i) q^{71} +(-9.38724 + 3.41668i) q^{73} +3.11731 q^{75} +22.8968 q^{77} +(12.2405 - 4.45516i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-4.28410 + 2.47343i) q^{83} +(-8.82701 + 7.40674i) q^{85} +(4.90819 + 2.83374i) q^{87} +(3.03768 - 8.34595i) q^{89} +(2.31416 + 13.1242i) q^{91} +(-4.81481 - 4.04010i) q^{93} +(-9.46345 + 8.04189i) q^{95} +(11.7729 - 14.0304i) q^{97} +(4.82006 - 0.849907i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$1$	$-1$

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
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$		0			0
$5$	0.494739	−	2.80581i	0.221254	−	1.25479i	−0.648464	−	0.761245i	$-0.724588\pi$
$5$	0.494739	−	2.80581i	0.221254	−	1.25479i	0.869718	−	0.493549i	$-0.164301\pi$
$6$		0			0
$7$	4.05139	−	2.33907i	1.53128	−	0.884085i	0.531978	−	0.846758i	$-0.321449\pi$
$7$	4.05139	−	2.33907i	1.53128	−	0.884085i	0.999303	−	0.0373268i	$-0.0118843\pi$
$8$		0			0
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$		0			0
$11$	4.23869	+	2.44721i	1.27801	+	0.737861i	0.976483	−	0.215595i	$-0.0691691\pi$
$11$	4.23869	+	2.44721i	1.27801	+	0.737861i	0.301531	+	0.953456i	$0.402502\pi$
$12$		0			0
$13$	−0.974319	+	2.67692i	−0.270227	+	0.742444i	0.728145	+	0.685423i	$0.240383\pi$
$13$	−0.974319	+	2.67692i	−0.270227	+	0.742444i	−0.998373	+	0.0570213i	$0.981840\pi$
$14$		0			0
$15$	0.494739	+	2.80581i	0.127741	+	0.724456i
$16$		0			0
$17$	−3.09819	−	2.59969i	−0.751421	−	0.630517i	0.184457	−	0.982840i	$-0.440947\pi$
$17$	−3.09819	−	2.59969i	−0.751421	−	0.630517i	−0.935878	+	0.352324i	$0.885392\pi$
$18$		0			0
$19$	−3.35652	−	2.78097i	−0.770038	−	0.637998i
$19$	−3.35652	−	2.78097i	−0.770038	−	0.637998i
$20$		0			0
$21$	−3.00705	+	3.58366i	−0.656192	+	0.782019i
$22$		0			0
$23$	5.98701	−	1.05567i	1.24838	−	0.220123i	0.489875	−	0.871792i	$-0.337042\pi$
$23$	5.98701	−	1.05567i	1.24838	−	0.220123i	0.758503	+	0.651670i	$0.225931\pi$
$24$		0			0
$25$	−2.92931	−	1.06618i	−0.585863	−	0.213237i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	−3.64299	−	4.34155i	−0.676487	−	0.806205i	0.313165	−	0.949699i	$-0.398611\pi$
$29$	−3.64299	−	4.34155i	−0.676487	−	0.806205i	−0.989651	+	0.143494i	$0.954166\pi$
$30$		0			0
$31$	3.14264	+	5.44322i	0.564435	+	0.977630i	0.997102	+	0.0760765i	$0.0242393\pi$
$31$	3.14264	+	5.44322i	0.564435	+	0.977630i	−0.432667	+	0.901554i	$0.642427\pi$
$32$		0			0
$33$	−4.82006	−	0.849907i	−0.839065	−	0.147950i
$34$		0			0
$35$	−4.55859	−	12.5246i	−0.770543	−	2.11705i
$36$		0			0
$37$			6.42841i			1.05682i	0.848988	+	0.528412i	$0.177212\pi$
$37$			6.42841i			1.05682i	−0.848988	+	0.528412i	$0.822788\pi$
$38$		0			0
$39$		−	2.84872i		−	0.456160i
$40$		0			0
$41$	−2.01774	−	5.54370i	−0.315118	−	0.865780i	−0.991602	−	0.129323i	$-0.958720\pi$
$41$	−2.01774	−	5.54370i	−0.315118	−	0.865780i	0.676484	−	0.736457i	$-0.263503\pi$
$42$		0			0
$43$	1.67932	+	0.296109i	0.256094	+	0.0451562i	0.300221	−	0.953870i	$-0.402940\pi$
$43$	1.67932	+	0.296109i	0.256094	+	0.0451562i	−0.0441273	+	0.999026i	$0.514051\pi$
$44$		0			0
$45$	−1.42454	−	2.46738i	−0.212359	−	0.367816i
$46$		0			0
$47$	−5.46079	−	6.50792i	−0.796538	−	0.949277i	0.203015	−	0.979176i	$-0.434926\pi$
$47$	−5.46079	−	6.50792i	−0.796538	−	0.949277i	−0.999553	+	0.0298983i	$0.990482\pi$
$48$		0			0
$49$	7.44249	−	12.8908i	1.06321	−	1.84154i
$50$		0			0
$51$	3.80049	+	1.38326i	0.532175	+	0.193696i
$52$		0			0
$53$	7.07029	−	1.24668i	0.971179	−	0.171245i	0.334519	−	0.942389i	$-0.391426\pi$
$53$	7.07029	−	1.24668i	0.971179	−	0.171245i	0.636661	+	0.771144i	$0.280315\pi$
$54$		0			0
$55$	8.96344	−	10.6822i	1.20863	−	1.44039i
$56$		0			0
$57$	4.10524	+	1.46526i	0.543753	+	0.194078i
$58$		0			0
$59$	3.61390	+	3.03242i	0.470490	+	0.394788i	0.846973	−	0.531635i	$-0.178422\pi$
$59$	3.61390	+	3.03242i	0.470490	+	0.394788i	−0.376483	+	0.926423i	$0.622867\pi$
$60$		0			0
$61$	0.715468	+	4.05762i	0.0916062	+	0.519525i	0.995735	+	0.0922638i	$0.0294103\pi$
$61$	0.715468	+	4.05762i	0.0916062	+	0.519525i	−0.904128	+	0.427261i	$0.859479\pi$
$62$		0			0
$63$	1.60002	−	4.39601i	0.201583	−	0.553846i
$64$		0			0
$65$	7.02888	+	4.05813i	0.871825	+	0.503349i
$66$		0			0
$67$	−2.79466	+	2.34500i	−0.341422	+	0.286487i	−0.797335	−	0.603537i	$-0.793757\pi$
$67$	−2.79466	+	2.34500i	−0.341422	+	0.286487i	0.455912	+	0.890025i	$0.349313\pi$
$68$		0			0
$69$	−5.26489	+	3.03969i	−0.633818	+	0.365935i
$70$		0			0
$71$	0.152483	−	0.864773i	0.0180964	−	0.102630i	−0.974422	−	0.224727i	$-0.927851\pi$
$71$	0.152483	−	0.864773i	0.0180964	−	0.102630i	0.992518	+	0.122097i	$0.0389620\pi$
$72$		0			0
$73$	−9.38724	+	3.41668i	−1.09869	+	0.399892i	−0.826835	−	0.562445i	$-0.809861\pi$
$73$	−9.38724	+	3.41668i	−1.09869	+	0.399892i	−0.271859	+	0.962337i	$0.587639\pi$
$74$		0			0
$75$	3.11731			0.359956
$76$		0			0
$77$	22.8968			2.60933
$78$		0			0
$79$	12.2405	−	4.45516i	1.37716	−	0.501245i	0.455843	−	0.890060i	$-0.349338\pi$
$79$	12.2405	−	4.45516i	1.37716	−	0.501245i	0.921316	+	0.388815i	$0.127116\pi$
$80$		0			0
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$		0			0
$83$	−4.28410	+	2.47343i	−0.470241	+	0.271494i	−0.716341	−	0.697751i	$-0.754184\pi$
$83$	−4.28410	+	2.47343i	−0.470241	+	0.271494i	0.246100	+	0.969245i	$0.420851\pi$
$84$		0			0
$85$	−8.82701	+	7.40674i	−0.957424	+	0.803374i
$86$		0			0
$87$	4.90819	+	2.83374i	0.526213	+	0.303809i
$88$		0			0
$89$	3.03768	−	8.34595i	0.321993	−	0.884669i	−0.668077	−	0.744092i	$-0.732882\pi$
$89$	3.03768	−	8.34595i	0.321993	−	0.884669i	0.990070	−	0.140576i	$-0.0448955\pi$
$90$		0			0
$91$	2.31416	+	13.1242i	0.242590	+	1.37579i
$92$		0			0
$93$	−4.81481	−	4.04010i	−0.499272	−	0.418939i
$94$		0			0
$95$	−9.46345	+	8.04189i	−0.970930	+	0.825080i
$96$		0			0
$97$	11.7729	−	14.0304i	1.19536	−	1.42457i	0.315765	−	0.948837i	$-0.397739\pi$
$97$	11.7729	−	14.0304i	1.19536	−	1.42457i	0.879590	−	0.475732i	$-0.157817\pi$
$98$		0			0
$99$	4.82006	−	0.849907i	0.484434	−	0.0854189i
$100$		0			0
$101$	−13.5739	−	4.94049i	−1.35065	−	0.491597i	−0.437501	−	0.899218i	$-0.644136\pi$
$101$	−13.5739	−	4.94049i	−1.35065	−	0.491597i	−0.913152	+	0.407620i	$0.866359\pi$
$102$		0			0
$103$	−8.37934	+	14.5134i	−0.825641	+	1.43005i	0.0757869	+	0.997124i	$0.475853\pi$
$103$	−8.37934	+	14.5134i	−0.825641	+	1.43005i	−0.901428	+	0.432929i	$0.857480\pi$
$104$		0			0
$105$	8.56735	+	10.2102i	0.836088	+	0.996411i
$106$		0			0
$107$	−1.01141	−	1.75181i	−0.0977765	−	0.169354i	0.812988	−	0.582281i	$-0.197840\pi$
$107$	−1.01141	−	1.75181i	−0.0977765	−	0.169354i	−0.910764	+	0.412927i	$0.864506\pi$
$108$		0			0
$109$	−15.7451	−	2.77628i	−1.50810	−	0.265920i	−0.642359	−	0.766404i	$-0.722044\pi$
$109$	−15.7451	−	2.77628i	−1.50810	−	0.265920i	−0.865746	+	0.500484i	$0.833155\pi$
$110$		0			0
$111$	−2.19865	−	6.04073i	−0.208686	−	0.573361i
$112$		0			0
$113$		−	1.95281i		−	0.183705i	−0.995773	−	0.0918524i	$-0.970721\pi$
$113$		−	1.95281i		−	0.183705i	0.995773	−	0.0918524i	$-0.0292788\pi$
$114$		0			0
$115$		−	17.3207i		−	1.61516i
$116$		0			0
$117$	0.974319	+	2.67692i	0.0900758	+	0.247481i
$118$		0			0
$119$	−18.6328	−	3.28547i	−1.70807	−	0.301178i
$120$		0			0
$121$	6.47767	+	11.2197i	0.588879	+	1.01997i
$122$		0			0
$123$	3.79211	+	4.51926i	0.341923	+	0.407488i
$124$		0			0
$125$	2.68198	−	4.64532i	0.239883	−	0.415490i
$126$		0			0
$127$	8.60542	+	3.13212i	0.763608	+	0.277931i	0.694320	−	0.719666i	$-0.255705\pi$
$127$	8.60542	+	3.13212i	0.763608	+	0.277931i	0.0692876	+	0.997597i	$0.477927\pi$
$128$		0			0
$129$	−1.67932	+	0.296109i	−0.147856	+	0.0260709i
$130$		0			0
$131$	5.02944	−	5.99385i	0.439424	−	0.523685i	−0.500193	−	0.865914i	$-0.666737\pi$
$131$	5.02944	−	5.99385i	0.439424	−	0.523685i	0.939617	+	0.342229i	$0.111182\pi$
$132$		0			0
$133$	−20.1034	−	3.41565i	−1.74319	−	0.296174i
$134$		0			0
$135$	2.18253	+	1.83136i	0.187842	+	0.157618i
$136$		0			0
$137$	2.05934	+	11.6791i	0.175942	+	0.997814i	0.937051	+	0.349191i	$0.113544\pi$
$137$	2.05934	+	11.6791i	0.175942	+	0.997814i	−0.761110	+	0.648623i	$0.775345\pi$
$138$		0			0
$139$	−6.25598	+	17.1882i	−0.530625	+	1.45788i	0.327704	+	0.944780i	$0.393725\pi$
$139$	−6.25598	+	17.1882i	−0.530625	+	1.45788i	−0.858329	+	0.513100i	$0.828497\pi$
$140$		0			0
$141$	7.35730	+	4.24774i	0.619597	+	0.357724i
$142$		0			0
$143$	−10.6808	+	8.96227i	−0.893175	+	0.749463i
$144$		0			0
$145$	−13.9839	+	8.07359i	−1.16130	+	0.670475i
$146$		0			0
$147$	−2.58475	+	14.6589i	−0.213187	+	1.20904i
$148$		0			0
$149$	−4.52213	+	1.64592i	−0.370467	+	0.134839i	−0.520543	−	0.853835i	$-0.674270\pi$
$149$	−4.52213	+	1.64592i	−0.370467	+	0.134839i	0.150076	+	0.988675i	$0.452048\pi$
$150$		0			0
$151$	−17.5620			−1.42918			−0.714589	−	0.699544i	$-0.753386\pi$
$151$	−17.5620			−1.42918			−0.714589	+	0.699544i	$0.753386\pi$
$152$		0			0
$153$	−4.04440			−0.326970
$154$		0			0
$155$	16.8274	−	6.12467i	1.35161	−	0.491945i
$156$		0			0
$157$	0.759551	−	4.30763i	0.0606187	−	0.343786i	−0.939381	−	0.342876i	$-0.888599\pi$
$157$	0.759551	−	4.30763i	0.0606187	−	0.343786i	1.00000		0.000910441i	$-0.000289802\pi$
$158$		0			0
$159$	−6.21751	+	3.58968i	−0.493081	+	0.284680i
$160$		0			0
$161$	21.7864	−	18.2810i	1.71701	−	1.44074i
$162$		0			0
$163$	0.0170674	+	0.00985388i	0.00133682	+	0.000771815i	0.500668	−	0.865639i	$-0.333088\pi$
$163$	0.0170674	+	0.00985388i	0.00133682	+	0.000771815i	−0.499331	+	0.866411i	$0.666421\pi$
$164$		0			0
$165$	−4.76935	+	13.1037i	−0.371293	+	1.02012i
$166$		0			0
$167$	0.384664	+	2.18154i	0.0297662	+	0.168813i	0.996067	−	0.0886029i	$-0.0282402\pi$
$167$	0.384664	+	2.18154i	0.0297662	+	0.168813i	−0.966301	+	0.257415i	$0.917129\pi$
$168$		0			0
$169$	3.74198	+	3.13989i	0.287844	+	0.241530i
$170$		0			0
$171$	−4.35881	+	0.0271842i	−0.333327	+	0.00207883i
$172$		0			0
$173$	−12.3088	+	14.6690i	−0.935817	+	1.11526i	0.0573258	+	0.998356i	$0.481743\pi$
$173$	−12.3088	+	14.6690i	−0.935817	+	1.11526i	−0.993143	+	0.116908i	$0.962702\pi$
$174$		0			0
$175$	−14.3617	+	2.53235i	−1.08564	+	0.191428i
$176$		0			0
$177$	−4.43311	−	1.61352i	−0.333213	−	0.121280i
$178$		0			0
$179$	1.83031	−	3.17018i	0.136803	−	0.236951i	−0.789481	−	0.613774i	$-0.789650\pi$
$179$	1.83031	−	3.17018i	0.136803	−	0.236951i	0.926285	+	0.376824i	$0.122984\pi$
$180$		0			0
$181$	3.11271	+	3.70959i	0.231366	+	0.275731i	0.869219	−	0.494426i	$-0.164622\pi$
$181$	3.11271	+	3.70959i	0.231366	+	0.275731i	−0.637853	+	0.770158i	$0.720177\pi$
$182$		0			0
$183$	−2.06011	−	3.56821i	−0.152287	−	0.263770i
$184$		0			0
$185$	18.0369	+	3.18039i	1.32610	+	0.233827i
$186$		0			0
$187$	−6.77028	−	18.6012i	−0.495092	−	1.36025i
$188$		0			0
$189$			4.67814i			0.340285i
$190$		0			0
$191$		−	2.75597i		−	0.199415i	−0.995017	−	0.0997076i	$-0.968209\pi$
$191$		−	2.75597i		−	0.199415i	0.995017	−	0.0997076i	$-0.0317907\pi$
$192$		0			0
$193$	4.64451	+	12.7607i	0.334319	+	0.918535i	0.986974	+	0.160879i	$0.0514330\pi$
$193$	4.64451	+	12.7607i	0.334319	+	0.918535i	−0.652655	+	0.757655i	$0.726345\pi$
$194$		0			0
$195$	−7.99295	−	1.40937i	−0.572387	−	0.100927i
$196$		0			0
$197$	7.64743	+	13.2457i	0.544857	+	0.943720i	0.998616	+	0.0525953i	$0.0167493\pi$
$197$	7.64743	+	13.2457i	0.544857	+	0.943720i	−0.453759	+	0.891124i	$0.649917\pi$
$198$		0			0
$199$	6.80642	+	8.11158i	0.482495	+	0.575015i	0.951292	−	0.308291i	$-0.0997570\pi$
$199$	6.80642	+	8.11158i	0.482495	+	0.575015i	−0.468797	+	0.883306i	$0.655313\pi$
$200$		0			0
$201$	1.82409	−	3.15941i	0.128661	−	0.222848i
$202$		0			0
$203$	−24.9144	−	9.06808i	−1.74865	−	0.636455i
$204$		0			0
$205$	−16.5528	+	2.91870i	−1.15610	+	0.203851i
$206$		0			0
$207$	3.90774	−	4.65707i	0.271607	−	0.323689i
$208$		0			0
$209$	−7.42164	−	20.0018i	−0.513365	−	1.38355i
$210$		0			0
$211$	−5.41871	−	4.54684i	−0.373039	−	0.313017i	0.436923	−	0.899499i	$-0.356068\pi$
$211$	−5.41871	−	4.54684i	−0.373039	−	0.313017i	−0.809963	+	0.586482i	$0.800513\pi$
$212$		0			0
$213$	0.152483	+	0.864773i	0.0104480	+	0.0592533i
$214$		0			0
$215$	1.66165	−	4.56534i	0.113323	−	0.311354i
$216$		0			0
$217$	25.4641	+	14.7017i	1.72862	+	0.998018i
$218$		0			0
$219$	7.65255	−	6.42125i	0.517112	−	0.433908i
$220$		0			0
$221$	9.97778	−	5.76067i	0.671178	−	0.387505i
$222$		0			0
$223$	−2.73178	+	15.4927i	−0.182933	+	1.03747i	0.745649	+	0.666339i	$0.232140\pi$
$223$	−2.73178	+	15.4927i	−0.182933	+	1.03747i	−0.928582	+	0.371127i	$0.878971\pi$
$224$		0			0
$225$	−2.92931	+	1.06618i	−0.195288	+	0.0710789i
$226$		0			0
$227$	−18.0026			−1.19488			−0.597438	−	0.801915i	$-0.703815\pi$
$227$	−18.0026			−1.19488			−0.597438	+	0.801915i	$0.703815\pi$
$228$		0			0
$229$	22.4816			1.48563			0.742813	−	0.669499i	$-0.233491\pi$
$229$	22.4816			1.48563			0.742813	+	0.669499i	$0.233491\pi$
$230$		0			0
$231$	−21.5159	+	7.83116i	−1.41564	+	0.515252i
$232$		0			0
$233$	1.95991	−	11.1152i	0.128398	−	0.728182i	−0.850833	−	0.525436i	$-0.823902\pi$
$233$	1.95991	−	11.1152i	0.128398	−	0.728182i	0.979231	−	0.202746i	$-0.0649867\pi$
$234$		0			0
$235$	−20.9616	+	12.1022i	−1.36739	+	0.789460i
$236$		0			0
$237$	−9.97851	+	8.37297i	−0.648174	+	0.543883i
$238$		0			0
$239$	17.3609	+	10.0233i	1.12299	+	0.648356i	0.942161	−	0.335159i	$-0.108790\pi$
$239$	17.3609	+	10.0233i	1.12299	+	0.648356i	0.180824	+	0.983515i	$0.442123\pi$
$240$		0			0
$241$	−4.97897	+	13.6796i	−0.320724	+	0.881181i	0.669639	+	0.742686i	$0.266449\pi$
$241$	−4.97897	+	13.6796i	−0.320724	+	0.881181i	−0.990363	+	0.138495i	$0.955774\pi$
$242$		0			0
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$		0			0
$245$	−32.4869	−	27.2598i	−2.07551	−	1.74156i
$246$		0			0
$247$	10.7147	−	6.27558i	0.681763	−	0.399306i
$248$		0			0
$249$	3.17978	−	3.78951i	0.201510	−	0.240150i
$250$		0			0
$251$	22.6495	−	3.99371i	1.42962	−	0.252081i	0.595364	−	0.803456i	$-0.297008\pi$
$251$	22.6495	−	3.99371i	1.42962	−	0.252081i	0.834257	+	0.551376i	$0.185897\pi$
$252$		0			0
$253$	27.9605	+	10.1768i	1.75786	+	0.639810i
$254$		0			0
$255$	5.76142	−	9.97908i	0.360794	−	0.624914i
$256$		0			0
$257$	7.05824	+	8.41168i	0.440281	+	0.524706i	0.939859	−	0.341562i	$-0.110956\pi$
$257$	7.05824	+	8.41168i	0.440281	+	0.524706i	−0.499578	+	0.866269i	$0.666512\pi$
$258$		0			0
$259$	15.0365	+	26.0440i	0.934323	+	1.61829i
$260$		0			0
$261$	−5.58139	−	0.984149i	−0.345479	−	0.0609173i
$262$		0			0
$263$	9.14617	+	25.1289i	0.563977	+	1.54951i	0.813754	+	0.581210i	$0.197421\pi$
$263$	9.14617	+	25.1289i	0.563977	+	1.54951i	−0.249777	+	0.968303i	$0.580357\pi$
$264$		0			0
$265$		−	20.4546i		−	1.25652i
$266$		0			0
$267$			8.88157i			0.543543i
$268$		0			0
$269$	9.03204	+	24.8153i	0.550693	+	1.51302i	0.832767	+	0.553624i	$0.186756\pi$
$269$	9.03204	+	24.8153i	0.550693	+	1.51302i	−0.282073	+	0.959393i	$0.591022\pi$
$270$		0			0
$271$	1.60301	+	0.282654i	0.0973758	+	0.0171700i	0.222124	−	0.975018i	$-0.428701\pi$
$271$	1.60301	+	0.282654i	0.0973758	+	0.0171700i	−0.124748	+	0.992188i	$0.539812\pi$
$272$		0			0
$273$	−6.66335	−	11.5413i	−0.403284	−	0.698509i
$274$		0			0
$275$	−9.80728	−	11.6879i	−0.591401	−	0.704805i
$276$		0			0
$277$	−3.46776	+	6.00633i	−0.208357	+	0.360885i	−0.951197	−	0.308584i	$-0.900145\pi$
$277$	−3.46776	+	6.00633i	−0.208357	+	0.360885i	0.742840	+	0.669469i	$0.233478\pi$
$278$		0			0
$279$	5.90623	+	2.14969i	0.353597	+	0.128699i
$280$		0			0
$281$	14.6961	−	2.59132i	0.876697	−	0.154585i	0.282851	−	0.959164i	$-0.408720\pi$
$281$	14.6961	−	2.59132i	0.876697	−	0.154585i	0.593846	+	0.804579i	$0.297609\pi$
$282$		0			0
$283$	−16.2764	+	19.3974i	−0.967530	+	1.15306i	0.0206543	+	0.999787i	$0.493425\pi$
$283$	−16.2764	+	19.3974i	−0.967530	+	1.15306i	−0.988184	+	0.153271i	$0.951019\pi$
$284$		0			0
$285$	6.14225	−	10.7936i	0.363836	−	0.639357i
$286$		0			0
$287$	−21.1418	−	17.7400i	−1.24796	−	1.04716i
$288$		0			0
$289$	−0.111631	−	0.633093i	−0.00656656	−	0.0372408i
$290$		0			0
$291$	−6.26422	+	17.2108i	−0.367215	+	1.00892i
$292$		0			0
$293$	−24.7125	−	14.2678i	−1.44372	−	0.833532i	−0.445625	−	0.895220i	$-0.647019\pi$
$293$	−24.7125	−	14.2678i	−1.44372	−	0.833532i	−0.998096	+	0.0616873i	$0.980352\pi$
$294$		0			0
$295$	10.2963	−	8.63965i	0.599475	−	0.503020i
$296$		0			0
$297$	−4.23869	+	2.44721i	−0.245954	+	0.142001i
$298$		0			0
$299$	−3.00731	+	17.0553i	−0.173917	+	0.986334i
$300$		0			0
$301$	7.49619	−	2.72839i	0.432073	−	0.157262i
$302$		0			0
$303$	14.4450			0.829846
$304$		0			0
$305$	11.7389			0.672165
$306$		0			0
$307$	23.7396	−	8.64051i	1.35489	−	0.493140i	0.440420	−	0.897792i	$-0.354829\pi$
$307$	23.7396	−	8.64051i	1.35489	−	0.493140i	0.914471	+	0.404652i	$0.132607\pi$
$308$		0			0
$309$	2.91012	−	16.5041i	0.165551	−	0.938885i
$310$		0			0
$311$	−7.51622	+	4.33949i	−0.426206	+	0.246070i	−0.697729	−	0.716362i	$-0.745806\pi$
$311$	−7.51622	+	4.33949i	−0.426206	+	0.246070i	0.271523	+	0.962432i	$0.412473\pi$
$312$		0			0
$313$	0.821120	−	0.689001i	0.0464124	−	0.0389447i	−0.619286	−	0.785165i	$-0.712578\pi$
$313$	0.821120	−	0.689001i	0.0464124	−	0.0389447i	0.665699	+	0.746221i	$0.268134\pi$
$314$		0			0
$315$	−11.5428	−	6.66422i	−0.650361	−	0.375486i
$316$		0			0
$317$	−0.652532	+	1.79282i	−0.0366498	+	0.100695i	−0.956668	−	0.291182i	$-0.905952\pi$
$317$	−0.652532	+	1.79282i	−0.0366498	+	0.100695i	0.920018	+	0.391876i	$0.128174\pi$
$318$		0			0
$319$	−4.81684	−	27.3176i	−0.269691	−	1.52949i
$320$		0			0
$321$	1.54957	+	1.30024i	0.0864884	+	0.0725723i
$322$		0			0
$323$	3.16948	+	17.3419i	0.176354	+	0.964927i
$324$		0			0
$325$	5.70817	−	6.80273i	0.316632	−	0.377348i
$326$		0			0
$327$	15.7451	−	2.77628i	0.870705	−	0.153529i
$328$		0			0
$329$	−37.3463	−	13.5929i	−2.05897	−	0.749402i
$330$		0			0
$331$	6.27220	−	10.8638i	0.344752	−	0.597127i	−0.640557	−	0.767911i	$-0.721296\pi$
$331$	6.27220	−	10.8638i	0.344752	−	0.597127i	0.985309	+	0.170783i	$0.0546298\pi$
$332$		0			0
$333$	4.13210	+	4.92445i	0.226438	+	0.269858i
$334$		0			0
$335$	5.19699	+	9.00144i	0.283942	+	0.491801i
$336$		0			0
$337$	−34.5453	−	6.09127i	−1.88180	−	0.331812i	−0.889629	−	0.456684i	$-0.849037\pi$
$337$	−34.5453	−	6.09127i	−1.88180	−	0.331812i	−0.992173	+	0.124872i	$0.960148\pi$
$338$		0			0
$339$	0.667900	+	1.83504i	0.0362753	+	0.0996657i
$340$		0			0
$341$			30.7628i			1.66590i
$342$		0			0
$343$		−	36.8871i		−	1.99172i
$344$		0			0
$345$	5.92402	+	16.2761i	0.318938	+	0.876276i
$346$		0			0
$347$	3.67240	+	0.647543i	0.197145	+	0.0347619i	0.271349	−	0.962481i	$-0.412530\pi$
$347$	3.67240	+	0.647543i	0.197145	+	0.0347619i	−0.0742038	+	0.997243i	$0.523642\pi$
$348$		0			0
$349$	5.36899	+	9.29936i	0.287395	+	0.497783i	0.973187	−	0.230015i	$-0.0738774\pi$
$349$	5.36899	+	9.29936i	0.287395	+	0.497783i	−0.685792	+	0.727798i	$0.740544\pi$
$350$		0			0
$351$	−1.83112	−	2.18224i	−0.0977380	−	0.116480i
$352$		0			0
$353$	−17.0977	+	29.6141i	−0.910019	+	1.57620i	−0.0959834	+	0.995383i	$0.530600\pi$
$353$	−17.0977	+	29.6141i	−0.910019	+	1.57620i	−0.814035	+	0.580816i	$0.802734\pi$
$354$		0			0
$355$	−2.35095	−	0.855674i	−0.124775	−	0.0454145i
$356$		0			0
$357$	18.6328	−	3.28547i	0.986153	−	0.173885i
$358$		0			0
$359$	−14.9878	+	17.8617i	−0.791024	+	0.942706i	−0.999375	−	0.0353485i	$-0.988746\pi$
$359$	−14.9878	+	17.8617i	−0.791024	+	0.942706i	0.208351	+	0.978054i	$0.433190\pi$
$360$		0			0
$361$	3.53244	+	18.6687i	0.185918	+	0.982565i
$362$		0			0
$363$	−9.92436	−	8.32753i	−0.520894	−	0.437082i
$364$		0			0
$365$	4.94229	+	28.0291i	0.258692	+	1.46711i
$366$		0			0
$367$	9.37867	−	25.7677i	0.489563	−	1.34506i	−0.411514	−	0.911403i	$-0.635000\pi$
$367$	9.37867	−	25.7677i	0.489563	−	1.34506i	0.901077	−	0.433659i	$-0.142778\pi$
$368$		0			0
$369$	−5.10910	−	2.94974i	−0.265969	−	0.153557i
$370$		0			0
$371$	25.7284	−	21.5887i	1.33575	−	1.12083i
$372$		0			0
$373$	13.6498	−	7.88074i	0.706762	−	0.408049i	−0.103099	−	0.994671i	$-0.532876\pi$
$373$	13.6498	−	7.88074i	0.706762	−	0.408049i	0.809861	+	0.586622i	$0.199542\pi$
$374$		0			0
$375$	−0.931440	+	5.28246i	−0.0480994	+	0.272785i
$376$		0			0
$377$	15.1714	−	5.52194i	0.781367	−	0.284395i
$378$		0			0
$379$	31.1656			1.60087			0.800435	−	0.599420i	$-0.204602\pi$
$379$	31.1656			1.60087			0.800435	+	0.599420i	$0.204602\pi$
$380$		0			0
$381$	−9.15770			−0.469163
$382$		0			0
$383$	−13.4728	+	4.90369i	−0.688427	+	0.250567i	−0.662462	−	0.749096i	$-0.730488\pi$
$383$	−13.4728	+	4.90369i	−0.688427	+	0.250567i	−0.0259656	+	0.999663i	$0.508266\pi$
$384$		0			0
$385$	11.3279	−	64.2439i	0.577325	−	3.27417i
$386$		0			0
$387$	1.47677	−	0.852612i	0.0750683	−	0.0433407i
$388$		0			0
$389$	9.24593	−	7.75825i	0.468787	−	0.393359i	−0.377565	−	0.925983i	$-0.623238\pi$
$389$	9.24593	−	7.75825i	0.468787	−	0.393359i	0.846352	+	0.532624i	$0.178794\pi$
$390$		0			0
$391$	−21.2933	−	12.2937i	−1.07685	−	0.621719i
$392$		0			0
$393$	−2.67611	+	7.35255i	−0.134992	+	0.370887i
$394$		0			0
$395$	−6.44448	−	36.5485i	−0.324257	−	1.83895i
$396$		0			0
$397$	−13.1135	−	11.0035i	−0.658147	−	0.552251i	0.251383	−	0.967888i	$-0.419114\pi$
$397$	−13.1135	−	11.0035i	−0.658147	−	0.552251i	−0.909531	+	0.415636i	$0.863559\pi$
$398$		0			0
$399$	20.0593	−	3.66612i	1.00422	−	0.183536i
$400$		0			0
$401$	18.4342	−	21.9690i	0.920558	−	1.09708i	−0.0744443	−	0.997225i	$-0.523718\pi$
$401$	18.4342	−	21.9690i	0.920558	−	1.09708i	0.995002	−	0.0998531i	$-0.0318373\pi$
$402$		0			0
$403$	−17.6330	+	3.10917i	−0.878362	+	0.154879i
$404$		0			0
$405$	−2.67727	−	0.974446i	−0.133035	−	0.0484206i
$406$		0			0
$407$	−15.7317	+	27.2480i	−0.779790	+	1.35064i
$408$		0			0
$409$	−0.217459	−	0.259157i	−0.0107527	−	0.0128145i	0.760641	−	0.649172i	$-0.224885\pi$
$409$	−0.217459	−	0.259157i	−0.0107527	−	0.0128145i	−0.771394	+	0.636358i	$0.780440\pi$
$410$		0			0
$411$	−5.92964	−	10.2704i	−0.292488	−	0.506604i
$412$		0			0
$413$	21.7344	+	3.83236i	1.06948	+	0.188578i
$414$		0			0
$415$	4.82044	+	13.2441i	0.236626	+	0.650125i
$416$		0			0
$417$		−	18.2913i		−	0.895726i
$418$		0			0
$419$		−	12.8576i		−	0.628135i	−0.949401	−	0.314068i	$-0.898308\pi$
$419$		−	12.8576i		−	0.628135i	0.949401	−	0.314068i	$-0.101692\pi$
$420$		0			0
$421$	−1.12274	−	3.08470i	−0.0547190	−	0.150339i	0.909322	−	0.416094i	$-0.136601\pi$
$421$	−1.12274	−	3.08470i	−0.0547190	−	0.150339i	−0.964041	+	0.265754i	$0.914379\pi$
$422$		0			0
$423$	−8.36642	−	1.47523i	−0.406789	−	0.0717279i
$424$		0			0
$425$	6.30382	+	10.9185i	0.305780	+	0.529627i
$426$		0			0
$427$	12.3897	+	14.7655i	0.599579	+	0.714550i
$428$		0			0
$429$	6.97141	−	12.0748i	0.336583	−	0.582979i
$430$		0			0
$431$	−9.71523	−	3.53605i	−0.467966	−	0.170326i	0.0972647	−	0.995259i	$-0.468991\pi$
$431$	−9.71523	−	3.53605i	−0.467966	−	0.170326i	−0.565231	+	0.824933i	$0.691213\pi$
$432$		0			0
$433$	−7.68637	+	1.35531i	−0.369383	+	0.0651323i	−0.355259	−	0.934768i	$-0.615607\pi$
$433$	−7.68637	+	1.35531i	−0.369383	+	0.0651323i	−0.0141246	+	0.999900i	$0.504496\pi$
$434$		0			0
$435$	10.3792	−	12.3695i	0.497645	−	0.593070i
$436$		0			0
$437$	−23.0313	−	13.1063i	−1.10174	−	0.626960i
$438$		0			0
$439$	3.02764	+	2.54049i	0.144501	+	0.121251i	0.712173	−	0.702004i	$-0.247711\pi$
$439$	3.02764	+	2.54049i	0.144501	+	0.121251i	−0.567672	+	0.823255i	$0.692156\pi$
$440$		0			0
$441$	−2.58475	−	14.6589i	−0.123083	−	0.698041i
$442$		0			0
$443$	6.98068	−	19.1793i	0.331662	−	0.911235i	−0.656017	−	0.754746i	$-0.727760\pi$
$443$	6.98068	−	19.1793i	0.331662	−	0.911235i	0.987680	−	0.156489i	$-0.0500175\pi$
$444$		0			0
$445$	−21.9142	−	12.6522i	−1.03883	−	0.599772i
$446$		0			0
$447$	3.68647	−	3.09332i	0.174364	−	0.146309i
$448$		0			0
$449$	−35.2788	+	20.3682i	−1.66491	+	0.961235i	−0.694588	+	0.719407i	$0.744413\pi$
$449$	−35.2788	+	20.3682i	−1.66491	+	0.961235i	−0.970319	+	0.241828i	$0.922253\pi$
$450$		0			0
$451$	5.01401	−	28.4359i	0.236101	−	1.33899i
$452$		0			0
$453$	16.5029	−	6.00657i	0.775375	−	0.282213i
$454$		0			0
$455$	37.9690			1.78001
$456$		0			0
$457$	−15.2411			−0.712950			−0.356475	−	0.934305i	$-0.616021\pi$
$457$	−15.2411			−0.712950			−0.356475	+	0.934305i	$0.616021\pi$
$458$		0			0
$459$	3.80049	−	1.38326i	0.177392	−	0.0645653i
$460$		0			0
$461$	−4.81659	+	27.3162i	−0.224331	+	1.27224i	0.639629	+	0.768684i	$0.279088\pi$
$461$	−4.81659	+	27.3162i	−0.224331	+	1.27224i	−0.863960	+	0.503560i	$0.832023\pi$
$462$		0			0
$463$	−4.60873	+	2.66085i	−0.214186	+	0.123660i	−0.603255	−	0.797548i	$-0.706130\pi$
$463$	−4.60873	+	2.66085i	−0.214186	+	0.123660i	0.389069	+	0.921208i	$0.372797\pi$
$464$		0			0
$465$	−13.7178	+	11.5106i	−0.636148	+	0.533792i
$466$		0			0
$467$	8.12931	+	4.69346i	0.376179	+	0.217187i	0.676155	−	0.736760i	$-0.263645\pi$
$467$	8.12931	+	4.69346i	0.376179	+	0.217187i	−0.299975	+	0.953947i	$0.596978\pi$
$468$		0			0
$469$	−5.83714	+	16.0374i	−0.269534	+	0.740539i
$470$		0			0
$471$	0.759551	+	4.30763i	0.0349982	+	0.198485i
$472$		0			0
$473$	6.39347	+	5.36476i	0.293972	+	0.246672i
$474$		0			0
$475$	6.86728	+	11.7250i	0.315092	+	0.537979i
$476$		0			0
$477$	4.61481	−	5.49971i	0.211297	−	0.251814i
$478$		0			0
$479$	27.2263	−	4.80073i	1.24400	−	0.219351i	0.487372	−	0.873194i	$-0.337956\pi$
$479$	27.2263	−	4.80073i	1.24400	−	0.219351i	0.756630	+	0.653843i	$0.226844\pi$
$480$		0			0
$481$	−17.2083	−	6.26332i	−0.784633	−	0.285583i
$482$		0			0
$483$	−14.2201	+	24.6299i	−0.647036	+	1.12070i
$484$		0			0
$485$	−33.5420	−	39.9738i	−1.52306	−	1.81512i
$486$		0			0
$487$	5.99966	+	10.3917i	0.271871	+	0.470894i	0.969341	−	0.245720i	$-0.0790244\pi$
$487$	5.99966	+	10.3917i	0.271871	+	0.470894i	−0.697470	+	0.716614i	$0.745691\pi$
$488$		0			0
$489$	−0.0194083	−	0.00342222i	−0.000877676	−	0.000154758i
$490$		0			0
$491$	6.28168	+	17.2588i	0.283488	+	0.778877i	0.996940	+	0.0781730i	$0.0249086\pi$
$491$	6.28168	+	17.2588i	0.283488	+	0.778877i	−0.713452	+	0.700705i	$0.752869\pi$
$492$		0			0
$493$			22.9216i			1.03234i
$494$		0			0
$495$		−	13.9446i		−	0.626765i
$496$		0			0
$497$	−1.40500	−	3.86020i	−0.0630228	−	0.173154i
$498$		0			0
$499$	16.3363	+	2.88053i	0.731313	+	0.128950i	0.526891	−	0.849933i	$-0.323357\pi$
$499$	16.3363	+	2.88053i	0.731313	+	0.128950i	0.204422	+	0.978883i	$0.434469\pi$
$500$		0			0
$501$	−1.10760	−	1.91841i	−0.0494838	−	0.0857084i
$502$		0			0
$503$	20.1798	+	24.0494i	0.899775	+	1.07231i	0.997027	+	0.0770502i	$0.0245502\pi$
$503$	20.1798	+	24.0494i	0.899775	+	1.07231i	−0.0972523	+	0.995260i	$0.531005\pi$
$504$		0			0
$505$	−20.5776	+	35.6414i	−0.915691	+	1.58602i
$506$		0			0
$507$	−4.59021	−	1.67070i	−0.203859	−	0.0741985i
$508$		0			0
$509$	−21.0772	+	3.71648i	−0.934231	+	0.164730i	−0.619987	−	0.784612i	$-0.712862\pi$
$509$	−21.0772	+	3.71648i	−0.934231	+	0.164730i	−0.314244	+	0.949342i	$0.601751\pi$
$510$		0			0
$511$	−30.0395	+	35.7997i	−1.32887	+	1.58369i
$512$		0			0
$513$	4.08665	−	1.51635i	0.180430	−	0.0669484i
$514$		0			0
$515$	36.5763	+	30.6912i	1.61175	+	1.35241i
$516$		0			0
$517$	−7.22037	−	40.9488i	−0.317552	−	1.80092i
$518$		0			0
$519$	6.54935	−	17.9942i	0.287485	−	0.789857i
$520$		0			0
$521$	−26.9656	−	15.5686i	−1.18139	−	0.682073i	−0.225051	−	0.974347i	$-0.572255\pi$
$521$	−26.9656	−	15.5686i	−1.18139	−	0.682073i	−0.956335	+	0.292274i	$0.905588\pi$
$522$		0			0
$523$	2.43227	−	2.04092i	0.106356	−	0.0892432i	−0.588059	−	0.808818i	$-0.700108\pi$
$523$	2.43227	−	2.04092i	0.106356	−	0.0892432i	0.694415	+	0.719575i	$0.255663\pi$
$524$		0			0
$525$	12.6294	−	7.29161i	0.551194	−	0.318232i
$526$		0			0
$527$	4.41417	−	25.0340i	0.192284	−	1.09050i
$528$		0			0
$529$	13.1169	−	4.77418i	0.570302	−	0.207573i
$530$		0			0
$531$	4.71761			0.204727
$532$		0			0
$533$	16.8060			0.727947
$534$		0			0
$535$	−5.41562	+	1.97112i	−0.234138	+	0.0852191i
$536$		0			0
$537$	−0.635659	+	3.60500i	−0.0274307	+	0.155567i
$538$		0			0
$539$	63.0929	−	36.4267i	2.71760	−	1.56901i
$540$		0			0
$541$	8.21236	−	6.89099i	0.353077	−	0.296267i	−0.448947	−	0.893558i	$-0.648201\pi$
$541$	8.21236	−	6.89099i	0.353077	−	0.296267i	0.802024	+	0.597292i	$0.203756\pi$
$542$		0			0
$543$	−4.19375	−	2.42126i	−0.179971	−	0.103906i
$544$		0			0
$545$	−15.5794	+	42.8041i	−0.667349	+	1.83353i
$546$		0			0
$547$	3.10634	+	17.6169i	0.132817	+	0.753245i	0.976355	+	0.216175i	$0.0693581\pi$
$547$	3.10634	+	17.6169i	0.132817	+	0.753245i	−0.843537	+	0.537071i	$0.819531\pi$
$548$		0			0
$549$	3.15627	+	2.64842i	0.134706	+	0.113032i
$550$		0			0
$551$	0.154066	+	24.7035i	0.00656343	+	1.05241i
$552$		0			0
$553$	39.1699	−	46.6809i	1.66567	−	1.98507i
$554$		0			0
$555$	−18.0369	+	3.18039i	−0.765622	+	0.135000i
$556$		0			0
$557$	8.19354	+	2.98220i	0.347171	+	0.126360i	0.509720	−	0.860341i	$-0.329749\pi$
$557$	8.19354	+	2.98220i	0.347171	+	0.126360i	−0.162548	+	0.986701i	$0.551971\pi$
$558$		0			0
$559$	−2.42885	+	4.20689i	−0.102729	+	0.177933i
$560$		0			0
$561$	12.7240	+	15.1638i	0.537206	+	0.640217i
$562$		0			0
$563$	−10.8654	−	18.8194i	−0.457923	−	0.793145i	0.540928	−	0.841069i	$-0.318073\pi$
$563$	−10.8654	−	18.8194i	−0.457923	−	0.793145i	−0.998851	+	0.0479235i	$0.984740\pi$
$564$		0			0
$565$	−5.47920	−	0.966131i	−0.230512	−	0.0406454i
$566$		0			0
$567$	−1.60002	−	4.39601i	−0.0671944	−	0.184615i
$568$		0			0
$569$		−	2.90816i		−	0.121916i	−0.998140	−	0.0609582i	$-0.980584\pi$
$569$		−	2.90816i		−	0.121916i	0.998140	−	0.0609582i	$-0.0194156\pi$
$570$		0			0
$571$		−	25.5999i		−	1.07132i	−0.844433	−	0.535661i	$-0.820062\pi$
$571$		−	25.5999i		−	1.07132i	0.844433	−	0.535661i	$-0.179938\pi$
$572$		0			0
$573$	0.942598	+	2.58977i	0.0393776	+	0.108189i
$574$		0			0
$575$	−18.6634	−	3.29086i	−0.778317	−	0.137238i
$576$		0			0
$577$	2.04834	+	3.54783i	0.0852735	+	0.147698i	0.905508	−	0.424330i	$-0.139490\pi$
$577$	2.04834	+	3.54783i	0.0852735	+	0.147698i	−0.820234	+	0.572028i	$0.806157\pi$
$578$		0			0
$579$	−8.72883	−	10.4026i	−0.362758	−	0.432318i
$580$		0			0
$581$	−11.5710	+	20.0416i	−0.480047	+	0.831466i
$582$		0			0
$583$	33.0197	+	12.0182i	1.36754	+	0.497742i
$584$		0			0
$585$	7.99295	−	1.40937i	0.330468	−	0.0582704i
$586$		0			0
$587$	−19.7796	+	23.5724i	−0.816389	+	0.972935i	−0.999949	−	0.0100735i	$-0.996793\pi$
$587$	−19.7796	+	23.5724i	−0.816389	+	0.972935i	0.183560	+	0.983009i	$0.441238\pi$
$588$		0			0
$589$	4.58907	−	27.0098i	0.189089	−	1.11292i
$590$		0			0
$591$	−11.7165	−	9.83135i	−0.481954	−	0.404408i
$592$		0			0
$593$	−1.24630	−	7.06810i	−0.0511793	−	0.290252i	0.948466	−	0.316878i	$-0.102635\pi$
$593$	−1.24630	−	7.06810i	−0.0511793	−	0.290252i	−0.999645	+	0.0266262i	$0.991524\pi$
$594$		0			0
$595$	−18.4368	+	50.6546i	−0.755834	+	2.07664i
$596$		0			0
$597$	−9.17027	−	5.29446i	−0.375314	−	0.216688i
$598$		0			0
$599$	25.0293	−	21.0021i	1.02267	−	0.858121i	0.0327087	−	0.999465i	$-0.489587\pi$
$599$	25.0293	−	21.0021i	1.02267	−	0.858121i	0.989961	+	0.141344i	$0.0451422\pi$
$600$		0			0
$601$	29.6670	−	17.1283i	1.21014	−	0.698677i	0.247353	−	0.968925i	$-0.420439\pi$
$601$	29.6670	−	17.1283i	1.21014	−	0.698677i	0.962790	+	0.270249i	$0.0871060\pi$
$602$		0			0
$603$	−0.633499	+	3.59275i	−0.0257981	+	0.146308i
$604$		0			0
$605$	34.6849	−	12.6243i	1.41014	−	0.513250i
$606$		0			0
$607$	−12.0101			−0.487474			−0.243737	−	0.969841i	$-0.578373\pi$
$607$	−12.0101			−0.487474			−0.243737	+	0.969841i	$0.578373\pi$
$608$		0			0
$609$	26.5133			1.07437
$610$		0			0
$611$	22.7417	−	8.27731i	0.920032	−	0.334864i
$612$		0			0
$613$	2.57030	−	14.5769i	0.103814	−	0.588756i	−0.887874	−	0.460087i	$-0.847818\pi$
$613$	2.57030	−	14.5769i	0.103814	−	0.588756i	0.991688	−	0.128669i	$-0.0410706\pi$
$614$		0			0
$615$	14.5563	−	8.40407i	0.586966	−	0.338885i
$616$		0			0
$617$	−1.39479	+	1.17037i	−0.0561523	+	0.0471174i	−0.670432	−	0.741971i	$-0.733891\pi$
$617$	−1.39479	+	1.17037i	−0.0561523	+	0.0471174i	0.614280	+	0.789088i	$0.289447\pi$
$618$		0			0
$619$	−22.2894	−	12.8688i	−0.895888	−	0.517241i	−0.0200241	−	0.999799i	$-0.506374\pi$
$619$	−22.2894	−	12.8688i	−0.895888	−	0.517241i	−0.875864	+	0.482558i	$0.839708\pi$
$620$		0			0
$621$	−2.07927	+	5.71274i	−0.0834381	+	0.229244i
$622$		0			0
$623$	−7.21495	−	40.9180i	−0.289061	−	1.63935i
$624$		0			0
$625$	−23.6470	−	19.8422i	−0.945879	−	0.793687i
$626$		0			0
$627$	13.8151	+	16.2572i	0.551721	+	0.649249i
$628$		0			0
$629$	16.7119	−	19.9164i	0.666345	−	0.794119i
$630$		0			0
$631$	−8.64330	+	1.52405i	−0.344084	+	0.0606714i	−0.343020	−	0.939328i	$-0.611450\pi$
$631$	−8.64330	+	1.52405i	−0.344084	+	0.0606714i	−0.00106431	+	0.999999i	$0.500339\pi$
$632$		0			0
$633$	6.64703	+	2.41932i	0.264196	+	0.0961594i
$634$		0			0
$635$	13.0456	−	22.5956i	0.517697	−	0.896678i
$636$		0			0
$637$	27.2562	+	32.4827i	1.07993	+	1.28701i
$638$		0			0
$639$	−0.439057	−	0.760469i	−0.0173688	−	0.0300837i
$640$		0			0
$641$	−29.4382	−	5.19075i	−1.16274	−	0.205022i	−0.441209	−	0.897405i	$-0.645450\pi$
$641$	−29.4382	−	5.19075i	−1.16274	−	0.205022i	−0.721531	+	0.692382i	$0.756561\pi$
$642$		0			0
$643$	−11.4284	−	31.3991i	−0.450690	−	1.23826i	−0.932239	−	0.361842i	$-0.882148\pi$
$643$	−11.4284	−	31.3991i	−0.450690	−	1.23826i	0.481549	−	0.876419i	$-0.340074\pi$
$644$		0			0
$645$			4.85834i			0.191297i
$646$		0			0
$647$			35.9167i			1.41203i	0.708197	+	0.706015i	$0.249509\pi$
$647$			35.9167i			1.41203i	−0.708197	+	0.706015i	$0.750491\pi$
$648$		0			0
$649$	7.89724	+	21.6975i	0.309994	+	0.851701i
$650$		0			0
$651$	−28.9567	−	5.10585i	−1.13490	−	0.200114i
$652$		0			0
$653$	−7.49870	−	12.9881i	−0.293447	−	0.508265i	0.681176	−	0.732120i	$-0.261469\pi$
$653$	−7.49870	−	12.9881i	−0.293447	−	0.508265i	−0.974622	+	0.223855i	$0.928136\pi$
$654$		0			0
$655$	−14.3293	−	17.0770i	−0.559893	−	0.667254i
$656$		0			0
$657$	−4.99485	+	8.65133i	−0.194868	+	0.337521i
$658$		0			0
$659$	−14.5493	−	5.29551i	−0.566760	−	0.206284i	0.0427176	−	0.999087i	$-0.486398\pi$
$659$	−14.5493	−	5.29551i	−0.566760	−	0.206284i	−0.609477	+	0.792804i	$0.708621\pi$
$660$		0			0
$661$	27.8852	−	4.91691i	1.08461	−	0.191245i	0.397355	−	0.917665i	$-0.369928\pi$
$661$	27.8852	−	4.91691i	1.08461	−	0.191245i	0.687252	+	0.726419i	$0.258817\pi$
$662$		0			0
$663$	−7.40578	+	8.82586i	−0.287617	+	0.342768i
$664$		0			0
$665$	−19.5296	+	54.7165i	−0.757325	+	2.12181i
$666$		0			0
$667$	−26.3939	−	22.1471i	−1.02198	−	0.857539i
$668$		0			0
$669$	−2.73178	−	15.4927i	−0.105617	−	0.598981i
$670$		0			0
$671$	−6.89720	+	18.9499i	−0.266263	+	0.731552i
$672$		0			0
$673$	−24.1937	−	13.9683i	−0.932600	−	0.538437i	−0.0449672	−	0.998988i	$-0.514318\pi$
$673$	−24.1937	−	13.9683i	−0.932600	−	0.538437i	−0.887633	+	0.460552i	$0.847652\pi$
$674$		0			0
$675$	2.38800	−	2.00377i	0.0919141	−	0.0771251i
$676$		0			0
$677$	20.4385	−	11.8002i	0.785516	−	0.453518i	−0.0528659	−	0.998602i	$-0.516836\pi$
$677$	20.4385	−	11.8002i	0.785516	−	0.453518i	0.838381	+	0.545084i	$0.183502\pi$
$678$		0			0
$679$	14.8785	−	84.3801i	0.570984	−	3.23821i
$680$		0			0
$681$	16.9169	−	6.15726i	0.648258	−	0.235947i
$682$		0			0
$683$	5.71809			0.218796			0.109398	−	0.993998i	$-0.465108\pi$
$683$	5.71809			0.218796			0.109398	+	0.993998i	$0.465108\pi$
$684$		0			0
$685$	33.7882			1.29098
$686$		0			0
$687$	−21.1258	+	7.68916i	−0.805999	+	0.293360i
$688$		0			0
$689$	−3.55145	+	20.1413i	−0.135299	+	0.767321i
$690$		0			0
$691$	−5.36639	+	3.09829i	−0.204147	+	0.117864i	−0.598588	−	0.801057i	$-0.704271\pi$
$691$	−5.36639	+	3.09829i	−0.204147	+	0.117864i	0.394441	+	0.918921i	$0.370938\pi$
$692$		0			0
$693$	17.5399	−	14.7178i	0.666288	−	0.559082i
$694$		0			0
$695$	45.1315	+	26.0567i	1.71194	+	0.988387i
$696$		0			0
$697$	−8.16055	+	22.4209i	−0.309103	+	0.849253i
$698$		0			0
$699$	1.95991	+	11.1152i	0.0741307	+	0.420416i
$700$		0			0
$701$	−25.0835	−	21.0475i	−0.947389	−	0.794954i	0.0314665	−	0.999505i	$-0.489982\pi$
$701$	−25.0835	−	21.0475i	−0.947389	−	0.794954i	−0.978856	+	0.204551i	$0.934427\pi$
$702$		0			0
$703$	17.8772	−	21.5771i	0.674251	−	0.813795i
$704$		0			0
$705$	15.5583	−	18.5416i	0.585959	−	0.698319i
$706$		0			0
$707$	−66.5493	+	11.7344i	−2.50284	+	0.441319i
$708$		0			0
$709$	−1.32585	−	0.482569i	−0.0497932	−	0.0181232i	0.317003	−	0.948424i	$-0.397323\pi$
$709$	−1.32585	−	0.482569i	−0.0497932	−	0.0181232i	−0.366797	+	0.930301i	$0.619546\pi$
$710$		0			0
$711$	6.51301	−	11.2809i	0.244257	−	0.423066i
$712$		0			0
$713$	24.5613	+	29.2710i	0.919827	+	1.09621i
$714$		0			0
$715$	19.8622	+	34.4023i	0.742803	+	1.28657i
$716$		0			0
$717$	−19.7421	−	3.48107i	−0.737283	−	0.130003i
$718$		0			0
$719$	7.57231	+	20.8047i	0.282399	+	0.775886i	0.997075	+	0.0764300i	$0.0243522\pi$
$719$	7.57231	+	20.8047i	0.282399	+	0.775886i	−0.714675	+	0.699456i	$0.753426\pi$
$720$		0			0
$721$			78.3995i			2.91975i
$722$		0			0
$723$		−	14.5575i		−	0.541401i
$724$		0			0
$725$	6.04258	+	16.6019i	0.224416	+	0.616577i
$726$		0			0
$727$	−12.2975	−	2.16838i	−0.456089	−	0.0804207i	−0.0591159	−	0.998251i	$-0.518828\pi$
$727$	−12.2975	−	2.16838i	−0.456089	−	0.0804207i	−0.396973	+	0.917830i	$0.629939\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	−4.43305	−	5.28310i	−0.163962	−	0.195403i
$732$		0			0
$733$	−8.44116	+	14.6205i	−0.311781	+	0.540021i	−0.978748	−	0.205066i	$-0.934259\pi$
$733$	−8.44116	+	14.6205i	−0.311781	+	0.540021i	0.666967	+	0.745088i	$0.267592\pi$
$734$		0			0
$735$	39.8511	+	14.5046i	1.46993	+	0.535011i
$736$		0			0
$737$	−17.5844	+	3.10061i	−0.647730	+	0.114212i
$738$		0			0
$739$	4.14022	−	4.93412i	0.152301	−	0.181505i	−0.684500	−	0.729013i	$-0.739979\pi$
$739$	4.14022	−	4.93412i	0.152301	−	0.181505i	0.836800	+	0.547509i	$0.184424\pi$
$740$		0			0
$741$	−7.92219	+	9.56178i	−0.291029	+	0.351261i
$742$		0			0
$743$	−22.5488	−	18.9207i	−0.827234	−	0.694132i	0.127420	−	0.991849i	$-0.459330\pi$
$743$	−22.5488	−	18.9207i	−0.827234	−	0.694132i	−0.954654	+	0.297717i	$0.903775\pi$
$744$		0			0
$745$	2.38086	+	13.5025i	0.0872279	+	0.494694i
$746$		0			0
$747$	−1.69192	+	4.64852i	−0.0619042	+	0.170080i
$748$		0			0
$749$	−8.19521	−	4.73151i	−0.299446	−	0.172885i
$750$		0			0
$751$	7.53434	−	6.32206i	0.274932	−	0.230695i	−0.494887	−	0.868957i	$-0.664791\pi$
$751$	7.53434	−	6.32206i	0.274932	−	0.230695i	0.769819	+	0.638262i	$0.220346\pi$
$752$		0			0
$753$	−19.9176	+	11.4994i	−0.725837	+	0.419062i
$754$		0			0
$755$	−8.68863	+	49.2757i	−0.316212	+	1.79332i
$756$		0			0
$757$	−23.6681	+	8.61448i	−0.860232	+	0.313099i	−0.734205	−	0.678928i	$-0.762445\pi$
$757$	−23.6681	+	8.61448i	−0.860232	+	0.313099i	−0.126027	+	0.992027i	$0.540223\pi$
$758$		0			0
$759$	−29.7550			−1.08004
$760$		0			0
$761$	37.9286			1.37491			0.687455	−	0.726227i	$-0.258728\pi$
$761$	37.9286			1.37491			0.687455	+	0.726227i	$0.258728\pi$
$762$		0			0
$763$	−70.2833	+	25.5810i	−2.54443	+	0.926096i
$764$		0			0
$765$	−2.00092	+	11.3478i	−0.0723435	+	0.410280i
$766$		0			0
$767$	−11.6386	+	6.71958i	−0.420247	+	0.242630i
$768$		0			0
$769$	18.6891	−	15.6820i	0.673945	−	0.565507i	−0.240285	−	0.970702i	$-0.577241\pi$
$769$	18.6891	−	15.6820i	0.673945	−	0.565507i	0.914230	+	0.405195i	$0.132796\pi$
$770$		0			0
$771$	−9.50954	−	5.49034i	−0.342478	−	0.197730i
$772$		0			0
$773$	−13.8058	+	37.9312i	−0.496561	+	1.36429i	0.398016	+	0.917378i	$0.369699\pi$
$773$	−13.8058	+	37.9312i	−0.496561	+	1.36429i	−0.894578	+	0.446913i	$0.852524\pi$
$774$		0			0
$775$	−3.40232	−	19.2955i	−0.122215	−	0.693115i
$776$		0			0
$777$	−23.0373	−	19.3305i	−0.826457	−	0.693480i
$778$		0			0
$779$	−8.64426	+	24.2188i	−0.309713	+	0.867729i
$780$		0			0
$781$	2.76261	−	3.29235i	0.0988539	−	0.117809i
$782$		0			0
$783$	5.58139	−	0.984149i	0.199463	−	0.0351706i
$784$		0			0
$785$	−11.7106	−	4.26230i	−0.417969	−	0.152128i
$786$		0			0
$787$	10.4259	−	18.0582i	0.371643	−	0.643705i	−0.618175	−	0.786040i	$-0.712128\pi$
$787$	10.4259	−	18.0582i	0.371643	−	0.643705i	0.989818	+	0.142336i	$0.0454612\pi$
$788$		0			0
$789$	−17.1892	−	20.4853i	−0.611951	−	0.729294i
$790$		0			0
$791$	−4.56776	−	7.91158i	−0.162411	−	0.281304i
$792$		0			0
$793$	−11.5590	−	2.03817i	−0.410472	−	0.0723774i
$794$		0			0
$795$	6.99590	+	19.2211i	0.248119	+	0.681701i
$796$		0			0
$797$			7.54992i			0.267432i	0.991020	+	0.133716i	$0.0426910\pi$
$797$			7.54992i			0.267432i	−0.991020	+	0.133716i	$0.957309\pi$
$798$		0			0
$799$			34.3591i			1.21554i
$800$		0			0
$801$	−3.03768	−	8.34595i	−0.107331	−	0.294890i
$802$		0			0
$803$	−48.1510	−	8.49031i	−1.69921	−	0.299617i
$804$		0			0
$805$	−40.5143	−	70.1728i	−1.42794	−	2.47326i
$806$		0			0
$807$	−16.9747	−	20.2296i	−0.597537	−	0.712117i
$808$		0			0
$809$	−16.9203	+	29.3068i	−0.594886	+	1.03037i	0.398677	+	0.917092i	$0.369470\pi$
$809$	−16.9203	+	29.3068i	−0.594886	+	1.03037i	−0.993563	+	0.113282i	$0.963864\pi$
$810$		0			0
$811$	25.4324	+	9.25662i	0.893051	+	0.325044i	0.747465	−	0.664302i	$-0.231271\pi$
$811$	25.4324	+	9.25662i	0.893051	+	0.325044i	0.145586	+	0.989346i	$0.453493\pi$
$812$		0			0
$813$	−1.60301	+	0.282654i	−0.0562199	+	0.00991309i
$814$		0			0
$815$	0.0360920	−	0.0430127i	0.00126425	−	0.00150667i
$816$		0			0
$817$	−4.81319	−	5.66402i	−0.168392	−	0.198159i
$818$		0			0
$819$	10.2088	+	8.56624i	0.356726	+	0.299329i
$820$		0			0
$821$	−3.04847	−	17.2888i	−0.106392	−	0.603382i	−0.990655	−	0.136392i	$-0.956449\pi$
$821$	−3.04847	−	17.2888i	−0.106392	−	0.603382i	0.884263	−	0.466990i	$-0.154662\pi$
$822$		0			0
$823$	−8.41545	+	23.1213i	−0.293344	+	0.805956i	0.702228	+	0.711952i	$0.252189\pi$
$823$	−8.41545	+	23.1213i	−0.293344	+	0.805956i	−0.995572	+	0.0940039i	$0.970033\pi$
$824$		0			0
$825$	13.2133	+	7.62871i	0.460029	+	0.265598i
$826$		0			0
$827$	−19.0960	+	16.0235i	−0.664034	+	0.557191i	−0.911293	−	0.411759i	$-0.864915\pi$
$827$	−19.0960	+	16.0235i	−0.664034	+	0.557191i	0.247259	+	0.968949i	$0.420470\pi$
$828$		0			0
$829$	28.6062	−	16.5158i	0.993534	−	0.573617i	0.0872051	−	0.996190i	$-0.472206\pi$
$829$	28.6062	−	16.5158i	0.993534	−	0.573617i	0.906329	+	0.422573i	$0.138873\pi$
$830$		0			0
$831$	1.20434	−	6.83014i	0.0417780	−	0.236935i
$832$		0			0
$833$	−56.5702	+	20.5899i	−1.96004	+	0.713397i
$834$		0			0
$835$	6.31128			0.218411
$836$		0			0
$837$	−6.28528			−0.217251
$838$		0			0
$839$	−2.64981	+	0.964450i	−0.0914815	+	0.0332965i	−0.387355	−	0.921930i	$-0.626611\pi$
$839$	−2.64981	+	0.964450i	−0.0914815	+	0.0332965i	0.295874	+	0.955227i	$0.404389\pi$
$840$		0			0
$841$	−0.541857	+	3.07303i	−0.0186847	+	0.105966i
$842$		0			0
$843$	−12.9236	+	7.46142i	−0.445111	+	0.256985i
$844$		0			0
$845$	10.6612	−	8.94583i	0.366757	−	0.307746i
$846$		0			0
$847$	52.4871	+	30.3034i	1.80348	+	1.04124i
$848$		0			0
$849$	8.66048	−	23.7945i	0.297227	−	0.816624i
$850$		0			0
$851$	6.78629	+	38.4870i	0.232631	+	1.31932i
$852$		0			0
$853$	31.6743	+	26.5779i	1.08451	+	0.910010i	0.996287	−	0.0860913i	$-0.0274377\pi$
$853$	31.6743	+	26.5779i	1.08451	+	0.910010i	0.0882201	+	0.996101i	$0.471882\pi$
$854$		0			0
$855$	−2.08020	+	12.2434i	−0.0711414	+	0.418717i
$856$		0			0
$857$	−4.36613	+	5.20335i	−0.149144	+	0.177743i	−0.835444	−	0.549576i	$-0.814789\pi$
$857$	−4.36613	+	5.20335i	−0.149144	+	0.177743i	0.686300	+	0.727319i	$0.259234\pi$
$858$		0			0
$859$	15.0100	−	2.64667i	0.512136	−	0.0903034i	0.0883926	−	0.996086i	$-0.471827\pi$
$859$	15.0100	−	2.64667i	0.512136	−	0.0903034i	0.423743	+	0.905782i	$0.360716\pi$
$860$		0			0
$861$	25.9342	+	9.43928i	0.883835	+	0.321690i
$862$		0			0
$863$	−27.9022	+	48.3280i	−0.949801	+	1.64510i	−0.203959	+	0.978979i	$0.565381\pi$
$863$	−27.9022	+	48.3280i	−0.949801	+	1.64510i	−0.745842	+	0.666123i	$0.767952\pi$
$864$		0			0
$865$	35.0687	+	41.7933i	1.19237	+	1.42101i
$866$		0			0
$867$	0.321430	+	0.556733i	0.0109163	+	0.0189076i
$868$		0			0
$869$	62.7862	+	11.0709i	2.12988	+	0.375555i
$870$		0			0
$871$	−3.55448	−	9.76587i	−0.120439	−	0.330904i
$872$		0			0
$873$		−	18.3154i		−	0.619881i
$874$		0			0
$875$		−	25.0933i		−	0.848309i
$876$		0			0
$877$	5.02720	+	13.8121i	0.169757	+	0.466402i	0.995175	−	0.0981196i	$-0.0312828\pi$
$877$	5.02720	+	13.8121i	0.169757	+	0.466402i	−0.825418	+	0.564522i	$0.809061\pi$
$878$		0			0
$879$	28.1020	+	4.95515i	0.947858	+	0.167133i
$880$		0			0
$881$	−14.1901	−	24.5780i	−0.478077	−	0.828053i	0.521607	−	0.853186i	$-0.325333\pi$
$881$	−14.1901	−	24.5780i	−0.478077	−	0.828053i	−0.999684	+	0.0251325i	$0.991999\pi$
$882$		0			0
$883$	5.51057	+	6.56724i	0.185445	+	0.221005i	0.850755	−	0.525562i	$-0.176145\pi$
$883$	5.51057	+	6.56724i	0.185445	+	0.221005i	−0.665310	+	0.746567i	$0.731701\pi$
$884$		0			0
$885$	−6.72045	+	11.6402i	−0.225906	+	0.391280i
$886$		0			0
$887$	14.7526	+	5.36951i	0.495344	+	0.180290i	0.577599	−	0.816321i	$-0.303990\pi$
$887$	14.7526	+	5.36951i	0.495344	+	0.180290i	−0.0822547	+	0.996611i	$0.526212\pi$
$888$		0			0
$889$	42.1902	−	7.43926i	1.41501	−	0.249505i
$890$		0			0
$891$	3.14607	−	3.74934i	0.105397	−	0.125608i
$892$		0			0
$893$	0.230943	+	37.0302i	0.00772820	+	1.23917i
$894$		0			0
$895$	−7.98939	−	6.70390i	−0.267056	−	0.224087i
$896$		0			0
$897$	−3.00731	−	17.0553i	−0.100411	−	0.569460i
$898$		0			0
$899$	12.1834	−	33.4735i	0.406338	−	1.11640i
$900$		0			0
$901$	−25.1461	−	14.5181i	−0.837737	−	0.483668i
$902$		0			0
$903$	−6.11095	+	5.12769i	−0.203360	+	0.170639i
$904$		0			0
$905$	11.9484	−	6.89839i	0.397177	−	0.229310i
$906$		0			0
$907$	−2.71921	+	15.4214i	−0.0902898	+	0.512059i	0.905800	+	0.423707i	$0.139271\pi$
$907$	−2.71921	+	15.4214i	−0.0902898	+	0.512059i	−0.996089	+	0.0883522i	$0.971840\pi$
$908$		0			0
$909$	−13.5739	+	4.94049i	−0.450218	+	0.163866i
$910$		0			0
$911$	−18.3009			−0.606336			−0.303168	−	0.952937i	$-0.598044\pi$
$911$	−18.3009			−0.606336			−0.303168	+	0.952937i	$0.598044\pi$
$912$		0			0
$913$	−24.2120			−0.801299
$914$		0			0
$915$	−11.0309	+	4.01493i	−0.364671	+	0.132729i
$916$		0			0
$917$	6.35617	−	36.0476i	0.209899	−	1.19040i
$918$		0			0
$919$	−3.48553	+	2.01237i	−0.114977	+	0.0663819i	−0.556386	−	0.830924i	$-0.687812\pi$
$919$	−3.48553	+	2.01237i	−0.114977	+	0.0663819i	0.441409	+	0.897306i	$0.354479\pi$
$920$		0			0
$921$	−19.3527	+	16.2389i	−0.637693	+	0.535088i
$922$		0			0
$923$	2.16636	+	1.25075i	0.0713066	+	0.0411689i
$924$		0			0
$925$	6.85386	−	18.8308i	0.225354	−	0.619154i
$926$		0			0
$927$	2.91012	+	16.5041i	0.0955807	+	0.542065i
$928$		0			0
$929$	−7.92858	−	6.65287i	−0.260128	−	0.218273i	0.503391	−	0.864059i	$-0.332086\pi$
$929$	−7.92858	−	6.65287i	−0.260128	−	0.218273i	−0.763519	+	0.645785i	$0.776530\pi$
$930$		0			0
$931$	−60.8297	+	22.5708i	−1.99361	+	0.739728i
$932$		0			0
$933$	5.57874	−	6.64849i	0.182640	−	0.217662i
$934$		0			0
$935$	−55.5408	+	9.79335i	−1.81638	+	0.320277i
$936$		0			0
$937$	3.16476	+	1.15188i	0.103388	+	0.0376303i	0.393196	−	0.919455i	$-0.371369\pi$
$937$	3.16476	+	1.15188i	0.103388	+	0.0376303i	−0.289808	+	0.957085i	$0.593591\pi$
$938$		0			0
$939$	−0.535948	+	0.928289i	−0.0174900	+	0.0302936i
$940$		0			0
$941$	19.3375	+	23.0455i	0.630384	+	0.751262i	0.982819	−	0.184574i	$-0.0590905\pi$
$941$	19.3375	+	23.0455i	0.630384	+	0.751262i	−0.352435	+	0.935836i	$0.614646\pi$
$942$		0			0
$943$	−17.9326	−	31.0601i	−0.583965	−	1.01146i
$944$		0			0
$945$	13.1259	+	2.31446i	0.426987	+	0.0752894i
$946$		0			0
$947$	−16.9107	−	46.4618i	−0.549525	−	1.50981i	−0.834354	−	0.551229i	$-0.814159\pi$
$947$	−16.9107	−	46.4618i	−0.549525	−	1.50981i	0.284829	−	0.958578i	$-0.408063\pi$
$948$		0			0
$949$		−	28.4578i		−	0.923780i
$950$		0			0
$951$		−	1.90788i		−	0.0618671i
$952$		0			0
$953$	−0.458113	−	1.25865i	−0.0148397	−	0.0407718i	0.932052	−	0.362326i	$-0.118017\pi$
$953$	−0.458113	−	1.25865i	−0.0148397	−	0.0407718i	−0.946891	+	0.321554i	$0.895795\pi$
$954$		0			0
$955$	−7.73272	−	1.36349i	−0.250225	−	0.0441214i
$956$		0			0
$957$	13.8695	+	24.0227i	0.448338	+	0.776545i
$958$		0			0
$959$	35.6615	+	42.4997i	1.15157	+	1.37239i
$960$		0			0
$961$	−4.25240	+	7.36537i	−0.137174	+	0.237592i
$962$		0			0
$963$	−1.90082	−	0.691844i	−0.0612532	−	0.0222943i
$964$		0			0
$965$	38.1018	−	6.71838i	1.22654	−	0.216272i
$966$		0			0
$967$	−26.3553	+	31.4090i	−0.847529	+	1.01005i	0.152236	+	0.988344i	$0.451353\pi$
$967$	−26.3553	+	31.4090i	−0.847529	+	1.01005i	−0.999765	+	0.0217012i	$0.993092\pi$
$968$		0			0
$969$	−8.90960	−	15.2120i	−0.286218	−	0.488680i
$970$		0			0
$971$	0.929020	+	0.779540i	0.0298137	+	0.0250166i	0.657573	−	0.753391i	$-0.271583\pi$
$971$	0.929020	+	0.779540i	0.0298137	+	0.0250166i	−0.627759	+	0.778408i	$0.716028\pi$
$972$		0			0
$973$	14.8589	+	84.2690i	0.476355	+	2.70154i
$974$		0			0
$975$	−3.03726	+	8.34479i	−0.0972700	+	0.267247i
$976$		0			0
$977$	−8.27777	−	4.77918i	−0.264829	−	0.152899i	0.361706	−	0.932292i	$-0.382194\pi$
$977$	−8.27777	−	4.77918i	−0.264829	−	0.152899i	−0.626536	+	0.779393i	$0.715528\pi$
$978$		0			0
$979$	33.3001	−	27.9421i	1.06427	−	0.893032i
$980$		0			0
$981$	−13.8460	+	7.99398i	−0.442068	+	0.255228i
$982$		0			0
$983$	1.25750	−	7.13166i	0.0401081	−	0.227465i	−0.958164	−	0.286219i	$-0.907602\pi$
$983$	1.25750	−	7.13166i	0.0401081	−	0.227465i	0.998272	+	0.0587540i	$0.0187128\pi$
$984$		0			0
$985$	40.9484	−	14.9040i	1.30473	−	0.474881i
$986$		0			0
$987$	39.7431			1.26504
$988$		0			0
$989$	10.3667			0.329642
$990$		0			0
$991$	42.9835	−	15.6447i	1.36542	−	0.496970i	0.447691	−	0.894188i	$-0.352247\pi$
$991$	42.9835	−	15.6447i	1.36542	−	0.496970i	0.917724	+	0.397218i	$0.130024\pi$
$992$		0			0
$993$	−2.17831	+	12.3538i	−0.0691267	+	0.392037i
$994$		0			0
$995$	26.1269	−	15.0844i	0.828279	−	0.478207i
$996$		0			0
$997$	2.90059	−	2.43388i	0.0918625	−	0.0770818i	−0.595700	−	0.803207i	$-0.703125\pi$
$997$	2.90059	−	2.43388i	0.0918625	−	0.0770818i	0.687562	+	0.726125i	$0.258681\pi$
$998$		0			0
$999$	−5.56717	−	3.21420i	−0.176137	−	0.101693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.g.79.3	✓	24
4.3	odd	2		912.2.ci.h.79.3	yes	24
19.13	odd	18		912.2.ci.h.127.3	yes	24
76.51	even	18	inner	912.2.ci.g.127.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.g.79.3	✓	24	1.1	even	1	trivial
912.2.ci.g.127.3	yes	24	76.51	even	18	inner
912.2.ci.h.79.3	yes	24	4.3	odd	2
912.2.ci.h.127.3	yes	24	19.13	odd	18

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)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{3} +(0.494739 - 2.80581i) q^{5} +(4.05139 - 2.33907i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{3} +(0.494739 - 2.80581i) q^{5} +(4.05139 - 2.33907i) q^{7} +(0.766044 - 0.642788i) q^{9} +(4.23869 + 2.44721i) q^{11} +(-0.974319 + 2.67692i) q^{13} +(0.494739 + 2.80581i) q^{15} +(-3.09819 - 2.59969i) q^{17} +(-3.35652 - 2.78097i) q^{19} +(-3.00705 + 3.58366i) q^{21} +(5.98701 - 1.05567i) q^{23} +(-2.92931 - 1.06618i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-3.64299 - 4.34155i) q^{29} +(3.14264 + 5.44322i) q^{31} +(-4.82006 - 0.849907i) q^{33} +(-4.55859 - 12.5246i) q^{35} +6.42841i q^{37} -2.84872i q^{39} +(-2.01774 - 5.54370i) q^{41} +(1.67932 + 0.296109i) q^{43} +(-1.42454 - 2.46738i) q^{45} +(-5.46079 - 6.50792i) q^{47} +(7.44249 - 12.8908i) q^{49} +(3.80049 + 1.38326i) q^{51} +(7.07029 - 1.24668i) q^{53} +(8.96344 - 10.6822i) q^{55} +(4.10524 + 1.46526i) q^{57} +(3.61390 + 3.03242i) q^{59} +(0.715468 + 4.05762i) q^{61} +(1.60002 - 4.39601i) q^{63} +(7.02888 + 4.05813i) q^{65} +(-2.79466 + 2.34500i) q^{67} +(-5.26489 + 3.03969i) q^{69} +(0.152483 - 0.864773i) q^{71} +(-9.38724 + 3.41668i) q^{73} +3.11731 q^{75} +22.8968 q^{77} +(12.2405 - 4.45516i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-4.28410 + 2.47343i) q^{83} +(-8.82701 + 7.40674i) q^{85} +(4.90819 + 2.83374i) q^{87} +(3.03768 - 8.34595i) q^{89} +(2.31416 + 13.1242i) q^{91} +(-4.81481 - 4.04010i) q^{93} +(-9.46345 + 8.04189i) q^{95} +(11.7729 - 14.0304i) q^{97} +(4.82006 - 0.849907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{7}+O(q^{10}) \) 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

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