LMFDB - Embedded newform 912.2.ci.h.223.3

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			223.3
Character	$\chi$	$=$	912.223
Dual form			912.2.ci.h.319.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{3} +(1.00588 + 0.844034i) q^{5} +(-3.15949 + 1.82413i) q^{7} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{3} +(1.00588 + 0.844034i) q^{5} +(-3.15949 + 1.82413i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(-2.08036 - 1.20110i) q^{11} +(-1.01858 + 0.179602i) q^{13} +(-1.00588 + 0.844034i) q^{15} +(-0.154881 + 0.0563722i) q^{17} +(-4.09960 - 1.48098i) q^{19} +(-1.24778 - 3.42825i) q^{21} +(-1.55016 - 1.84741i) q^{23} +(-0.568839 - 3.22604i) q^{25} +(0.500000 - 0.866025i) q^{27} +(-0.705807 + 1.93919i) q^{29} +(0.920238 + 1.59390i) q^{31} +(1.54410 - 1.84019i) q^{33} +(-4.71770 - 0.831857i) q^{35} -2.17328i q^{37} -1.03429i q^{39} +(-4.45654 - 0.785809i) q^{41} +(-0.789107 + 0.940421i) q^{43} +(-0.656542 - 1.13716i) q^{45} +(-0.0928046 + 0.254978i) q^{47} +(3.15491 - 5.46446i) q^{49} +(-0.0286209 - 0.162317i) q^{51} +(3.02351 + 3.60327i) q^{53} +(-1.07883 - 2.96406i) q^{55} +(2.17037 - 3.78015i) q^{57} +(-7.95309 + 2.89469i) q^{59} +(1.18712 - 0.996111i) q^{61} +(3.59284 - 0.633514i) q^{63} +(-1.17616 - 0.679054i) q^{65} +(3.43709 + 1.25100i) q^{67} +(2.08852 - 1.20581i) q^{69} +(-4.24397 - 3.56112i) q^{71} +(0.335135 - 1.90064i) q^{73} +3.27581 q^{75} +8.76385 q^{77} +(-1.63524 + 9.27388i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-15.2738 + 8.81832i) q^{83} +(-0.203372 - 0.0740214i) q^{85} +(-1.78717 - 1.03182i) q^{87} +(-16.9548 + 2.98959i) q^{89} +(2.89056 - 2.42547i) q^{91} +(-1.72948 + 0.629480i) q^{93} +(-2.87371 - 4.94989i) q^{95} +(-5.59171 - 15.3631i) q^{97} +(1.54410 + 1.84019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.00588	+	0.844034i	0.449843	+	0.377463i	0.839378	−	0.543549i	$-0.182920\pi$
$5$	1.00588	+	0.844034i	0.449843	+	0.377463i	−0.389534	+	0.921012i	$0.627364\pi$
$6$		0			0
$7$	−3.15949	+	1.82413i	−1.19417	+	0.689457i	−0.959251	−	0.282557i	$-0.908817\pi$
$7$	−3.15949	+	1.82413i	−1.19417	+	0.689457i	−0.234924	+	0.972014i	$0.575484\pi$
$8$		0			0
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$		0			0
$11$	−2.08036	−	1.20110i	−0.627254	−	0.362145i	0.152434	−	0.988314i	$-0.451289\pi$
$11$	−2.08036	−	1.20110i	−0.627254	−	0.362145i	−0.779688	+	0.626169i	$0.784622\pi$
$12$		0			0
$13$	−1.01858	+	0.179602i	−0.282502	+	0.0498127i	−0.313104	−	0.949719i	$-0.601369\pi$
$13$	−1.01858	+	0.179602i	−0.282502	+	0.0498127i	0.0306017	+	0.999532i	$0.490258\pi$
$14$		0			0
$15$	−1.00588	+	0.844034i	−0.259717	+	0.217929i
$16$		0			0
$17$	−0.154881	+	0.0563722i	−0.0375643	+	0.0136723i	−0.360734	−	0.932669i	$-0.617474\pi$
$17$	−0.154881	+	0.0563722i	−0.0375643	+	0.0136723i	0.323170	+	0.946341i	$0.395252\pi$
$18$		0			0
$19$	−4.09960	−	1.48098i	−0.940512	−	0.339759i
$19$	−4.09960	−	1.48098i	−0.940512	−	0.339759i
$20$		0			0
$21$	−1.24778	−	3.42825i	−0.272288	−	0.748104i
$22$		0			0
$23$	−1.55016	−	1.84741i	−0.323230	−	0.385211i	0.579821	−	0.814744i	$-0.303123\pi$
$23$	−1.55016	−	1.84741i	−0.323230	−	0.385211i	−0.903051	+	0.429533i	$0.858678\pi$
$24$		0			0
$25$	−0.568839	−	3.22604i	−0.113768	−	0.645209i
$26$		0			0
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$		0			0
$29$	−0.705807	+	1.93919i	−0.131065	+	0.360098i	−0.987815	−	0.155634i	$-0.950258\pi$
$29$	−0.705807	+	1.93919i	−0.131065	+	0.360098i	0.856750	+	0.515732i	$0.172480\pi$
$30$		0			0
$31$	0.920238	+	1.59390i	0.165280	+	0.286273i	0.936755	−	0.349987i	$-0.113814\pi$
$31$	0.920238	+	1.59390i	0.165280	+	0.286273i	−0.771475	+	0.636260i	$0.780481\pi$
$32$		0			0
$33$	1.54410	−	1.84019i	0.268794	−	0.320336i
$34$		0			0
$35$	−4.71770	−	0.831857i	−0.797436	−	0.140609i
$36$		0			0
$37$		−	2.17328i		−	0.357284i	−0.983914	−	0.178642i	$-0.942830\pi$
$37$		−	2.17328i		−	0.357284i	0.983914	−	0.178642i	$-0.0571704\pi$
$38$		0			0
$39$		−	1.03429i		−	0.165619i
$40$		0			0
$41$	−4.45654	−	0.785809i	−0.695995	−	0.122723i	−0.185552	−	0.982634i	$-0.559407\pi$
$41$	−4.45654	−	0.785809i	−0.695995	−	0.122723i	−0.510443	+	0.859912i	$0.670518\pi$
$42$		0			0
$43$	−0.789107	+	0.940421i	−0.120338	+	0.143413i	−0.822850	−	0.568259i	$-0.807617\pi$
$43$	−0.789107	+	0.940421i	−0.120338	+	0.143413i	0.702512	+	0.711672i	$0.252062\pi$
$44$		0			0
$45$	−0.656542	−	1.13716i	−0.0978715	−	0.169518i
$46$		0			0
$47$	−0.0928046	+	0.254978i	−0.0135369	+	0.0371924i	−0.946277	−	0.323357i	$-0.895189\pi$
$47$	−0.0928046	+	0.254978i	−0.0135369	+	0.0371924i	0.932740	+	0.360549i	$0.117411\pi$
$48$		0			0
$49$	3.15491	−	5.46446i	0.450701	−	0.780638i
$50$		0			0
$51$	−0.0286209	−	0.162317i	−0.00400773	−	0.0227290i
$52$		0			0
$53$	3.02351	+	3.60327i	0.415310	+	0.494948i	0.932625	−	0.360848i	$-0.117513\pi$
$53$	3.02351	+	3.60327i	0.415310	+	0.494948i	−0.517314	+	0.855796i	$0.673068\pi$
$54$		0			0
$55$	−1.07883	−	2.96406i	−0.145469	−	0.399674i
$56$		0			0
$57$	2.17037	−	3.78015i	0.287472	−	0.500693i
$58$		0			0
$59$	−7.95309	+	2.89469i	−1.03540	+	0.376856i	−0.803136	−	0.595796i	$-0.796837\pi$
$59$	−7.95309	+	2.89469i	−1.03540	+	0.376856i	−0.232268	+	0.972652i	$0.574615\pi$
$60$		0			0
$61$	1.18712	−	0.996111i	0.151995	−	0.127539i	−0.563619	−	0.826035i	$-0.690591\pi$
$61$	1.18712	−	0.996111i	0.151995	−	0.127539i	0.715614	+	0.698496i	$0.246147\pi$
$62$		0			0
$63$	3.59284	−	0.633514i	0.452655	−	0.0798153i
$64$		0			0
$65$	−1.17616	−	0.679054i	−0.145884	−	0.0842262i
$66$		0			0
$67$	3.43709	+	1.25100i	0.419907	+	0.152834i	0.543327	−	0.839521i	$-0.317164\pi$
$67$	3.43709	+	1.25100i	0.419907	+	0.152834i	−0.123421	+	0.992354i	$0.539386\pi$
$68$		0			0
$69$	2.08852	−	1.20581i	0.251429	−	0.145162i
$70$		0			0
$71$	−4.24397	−	3.56112i	−0.503667	−	0.422627i	0.355227	−	0.934780i	$-0.384404\pi$
$71$	−4.24397	−	3.56112i	−0.503667	−	0.422627i	−0.858894	+	0.512153i	$0.828848\pi$
$72$		0			0
$73$	0.335135	−	1.90064i	0.0392245	−	0.222453i	−0.958894	−	0.283764i	$-0.908417\pi$
$73$	0.335135	−	1.90064i	0.0392245	−	0.222453i	0.998119	+	0.0613104i	$0.0195279\pi$
$74$		0			0
$75$	3.27581			0.378258
$76$		0			0
$77$	8.76385			0.998733
$78$		0			0
$79$	−1.63524	+	9.27388i	−0.183978	+	1.04339i	0.743283	+	0.668978i	$0.233268\pi$
$79$	−1.63524	+	9.27388i	−0.183978	+	1.04339i	−0.927261	+	0.374416i	$0.877843\pi$
$80$		0			0
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$		0			0
$83$	−15.2738	+	8.81832i	−1.67651	+	0.967936i	−0.712659	+	0.701510i	$0.752509\pi$
$83$	−15.2738	+	8.81832i	−1.67651	+	0.967936i	−0.963855	+	0.266426i	$0.914157\pi$
$84$		0			0
$85$	−0.203372	−	0.0740214i	−0.0220588	−	0.00802875i
$86$		0			0
$87$	−1.78717	−	1.03182i	−0.191604	−	0.110623i
$88$		0			0
$89$	−16.9548	+	2.98959i	−1.79721	+	0.316896i	−0.969652	−	0.244488i	$-0.921380\pi$
$89$	−16.9548	+	2.98959i	−1.79721	+	0.316896i	−0.827556	+	0.561384i	$0.810269\pi$
$90$		0			0
$91$	2.89056	−	2.42547i	0.303013	−	0.254258i
$92$		0			0
$93$	−1.72948	+	0.629480i	−0.179339	+	0.0652740i
$94$		0			0
$95$	−2.87371	−	4.94989i	−0.294836	−	0.507848i
$96$		0			0
$97$	−5.59171	−	15.3631i	−0.567752	−	1.55989i	−0.808005	−	0.589176i	$-0.799452\pi$
$97$	−5.59171	−	15.3631i	−0.567752	−	1.55989i	0.240253	−	0.970710i	$-0.422770\pi$
$98$		0			0
$99$	1.54410	+	1.84019i	0.155188	+	0.184946i
$100$		0			0
$101$	2.06117	+	11.6895i	0.205094	+	1.16315i	0.897292	+	0.441438i	$0.145531\pi$
$101$	2.06117	+	11.6895i	0.205094	+	1.16315i	−0.692198	+	0.721708i	$0.743357\pi$
$102$		0			0
$103$	7.15408	−	12.3912i	0.704913	−	1.22094i	−0.261810	−	0.965119i	$-0.584320\pi$
$103$	7.15408	−	12.3912i	0.704913	−	1.22094i	0.966723	−	0.255825i	$-0.0823471\pi$
$104$		0			0
$105$	1.63844	−	4.50157i	0.159895	−	0.439309i
$106$		0			0
$107$	7.28336	+	12.6151i	0.704109	+	1.21955i	0.967012	+	0.254730i	$0.0819866\pi$
$107$	7.28336	+	12.6151i	0.704109	+	1.21955i	−0.262903	+	0.964822i	$0.584680\pi$
$108$		0			0
$109$	−4.66909	+	5.56441i	−0.447218	+	0.532974i	−0.941807	−	0.336153i	$-0.890874\pi$
$109$	−4.66909	+	5.56441i	−0.447218	+	0.532974i	0.494589	+	0.869127i	$0.335318\pi$
$110$		0			0
$111$	2.14026	+	0.377385i	0.203144	+	0.0358198i
$112$		0			0
$113$			5.66207i			0.532643i	0.963884	+	0.266321i	$0.0858082\pi$
$113$			5.66207i			0.532643i	−0.963884	+	0.266321i	$0.914192\pi$
$114$		0			0
$115$		−	3.16666i		−	0.295292i
$116$		0			0
$117$	1.01858	+	0.179602i	0.0941673	+	0.0166042i
$118$		0			0
$119$	0.386516	−	0.460631i	0.0354318	−	0.0422260i
$120$		0			0
$121$	−2.61472	−	4.52883i	−0.237702	−	0.411712i
$122$		0			0
$123$	1.54774	−	4.25238i	0.139555	−	0.383424i
$124$		0			0
$125$	5.43342	−	9.41095i	0.485980	−	0.841741i
$126$		0			0
$127$	−0.139428	−	0.790738i	−0.0123723	−	0.0701666i	0.977997	−	0.208621i	$-0.0668976\pi$
$127$	−0.139428	−	0.790738i	−0.0123723	−	0.0701666i	−0.990369	+	0.138455i	$0.955786\pi$
$128$		0			0
$129$	−0.789107	−	0.940421i	−0.0694770	−	0.0827994i
$130$		0			0
$131$	−1.20086	−	3.29934i	−0.104920	−	0.288265i	0.876113	−	0.482105i	$-0.160128\pi$
$131$	−1.20086	−	3.29934i	−0.104920	−	0.288265i	−0.981033	+	0.193841i	$0.937906\pi$
$132$		0			0
$133$	15.6541	−	2.79908i	1.35739	−	0.242711i
$134$		0			0
$135$	1.23389	−	0.449101i	0.106197	−	0.0386525i
$136$		0			0
$137$	−12.6369	+	10.6036i	−1.07964	+	0.905927i	−0.995891	−	0.0905595i	$-0.971134\pi$
$137$	−12.6369	+	10.6036i	−1.07964	+	0.905927i	−0.0837510	+	0.996487i	$0.526690\pi$
$138$		0			0
$139$	20.1214	−	3.54795i	1.70668	−	0.300933i	0.766657	−	0.642057i	$-0.221919\pi$
$139$	20.1214	−	3.54795i	1.70668	−	0.300933i	0.940018	+	0.341124i	$0.110808\pi$
$140$		0			0
$141$	−0.234989	−	0.135671i	−0.0197897	−	0.0114256i
$142$		0			0
$143$	2.33473	+	0.849772i	0.195240	+	0.0710615i
$144$		0			0
$145$	−2.34670	+	1.35487i	−0.194883	+	0.112516i
$146$		0			0
$147$	4.83360	+	4.05587i	0.398669	+	0.334523i
$148$		0			0
$149$	−4.15646	+	23.5725i	−0.340511	+	1.93113i	0.0234702	+	0.999725i	$0.492529\pi$
$149$	−4.15646	+	23.5725i	−0.340511	+	1.93113i	−0.363981	+	0.931406i	$0.618583\pi$
$150$		0			0
$151$	−6.23088			−0.507062			−0.253531	−	0.967327i	$-0.581592\pi$
$151$	−6.23088			−0.507062			−0.253531	+	0.967327i	$0.581592\pi$
$152$		0			0
$153$	0.164821			0.0133250
$154$		0			0
$155$	−0.419655	+	2.37998i	−0.0337075	+	0.191165i
$156$		0			0
$157$	5.62244	+	4.71779i	0.448720	+	0.376520i	0.838960	−	0.544192i	$-0.183164\pi$
$157$	5.62244	+	4.71779i	0.448720	+	0.376520i	−0.390241	+	0.920713i	$0.627608\pi$
$158$		0			0
$159$	−4.07356	+	2.35187i	−0.323054	+	0.186515i
$160$		0			0
$161$	8.26762	+	3.00917i	0.651580	+	0.237156i
$162$		0			0
$163$	0.512777	+	0.296052i	0.0401638	+	0.0231886i	0.519947	−	0.854198i	$-0.325952\pi$
$163$	0.512777	+	0.296052i	0.0401638	+	0.0231886i	−0.479784	+	0.877387i	$0.659285\pi$
$164$		0			0
$165$	3.10637	−	0.547736i	0.241830	−	0.0426412i
$166$		0			0
$167$	14.4260	−	12.1048i	1.11631	−	0.936698i	0.117901	−	0.993025i	$-0.462383\pi$
$167$	14.4260	−	12.1048i	1.11631	−	0.936698i	0.998412	+	0.0563269i	$0.0179389\pi$
$168$		0			0
$169$	−11.2108	+	4.08038i	−0.862367	+	0.313876i
$170$		0			0
$171$	3.34584	+	2.79381i	0.255863	+	0.213648i
$172$		0			0
$173$	6.84202	+	18.7983i	0.520189	+	1.42921i	0.870310	+	0.492504i	$0.163918\pi$
$173$	6.84202	+	18.7983i	0.520189	+	1.42921i	−0.350121	+	0.936705i	$0.613859\pi$
$174$		0			0
$175$	7.68197	+	9.15501i	0.580702	+	0.692054i
$176$		0			0
$177$	−1.46967	−	8.33492i	−0.110467	−	0.626491i
$178$		0			0
$179$	4.22246	−	7.31352i	0.315602	−	0.546638i	−0.663964	−	0.747765i	$-0.731127\pi$
$179$	4.22246	−	7.31352i	0.315602	−	0.546638i	0.979565	+	0.201127i	$0.0644604\pi$
$180$		0			0
$181$	−3.20952	+	8.81809i	−0.238562	+	0.655443i	0.761412	+	0.648268i	$0.224506\pi$
$181$	−3.20952	+	8.81809i	−0.238562	+	0.655443i	−0.999974	+	0.00717560i	$0.997716\pi$
$182$		0			0
$183$	0.774837	+	1.34206i	0.0572776	+	0.0992077i
$184$		0			0
$185$	1.83432	−	2.18605i	0.134862	−	0.160722i
$186$		0			0
$187$	0.389918	+	0.0687531i	0.0285137	+	0.00502773i
$188$		0			0
$189$			3.64826i			0.265372i
$190$		0			0
$191$		−	5.08509i		−	0.367944i	−0.982931	−	0.183972i	$-0.941104\pi$
$191$		−	5.08509i		−	0.367944i	0.982931	−	0.183972i	$-0.0588956\pi$
$192$		0			0
$193$	15.7804	+	2.78251i	1.13590	+	0.200289i	0.709810	−	0.704393i	$-0.248781\pi$
$193$	15.7804	+	2.78251i	1.13590	+	0.200289i	0.426087	+	0.904682i	$0.359892\pi$
$194$		0			0
$195$	0.872975	−	1.04037i	0.0625150	−	0.0745025i
$196$		0			0
$197$	9.07323	+	15.7153i	0.646441	+	1.11967i	0.983967	+	0.178352i	$0.0570765\pi$
$197$	9.07323	+	15.7153i	0.646441	+	1.11967i	−0.337526	+	0.941316i	$0.609590\pi$
$198$		0			0
$199$	−3.56348	+	9.79058i	−0.252608	+	0.694036i	0.746966	+	0.664862i	$0.231510\pi$
$199$	−3.56348	+	9.79058i	−0.252608	+	0.694036i	−0.999574	+	0.0291735i	$0.990712\pi$
$200$		0			0
$201$	−1.82884	+	3.16764i	−0.128996	+	0.223428i
$202$		0			0
$203$	−1.30735	−	7.41432i	−0.0917577	−	0.520384i
$204$		0			0
$205$	−3.81950	−	4.55190i	−0.266765	−	0.317919i
$206$		0			0
$207$	0.824822	+	2.26618i	0.0573291	+	0.157510i
$208$		0			0
$209$	6.74986	+	8.00500i	0.466898	+	0.553717i
$210$		0			0
$211$	10.5008	−	3.82199i	0.722908	−	0.263117i	0.0457481	−	0.998953i	$-0.485433\pi$
$211$	10.5008	−	3.82199i	0.722908	−	0.263117i	0.677160	+	0.735836i	$0.263211\pi$
$212$		0			0
$213$	4.24397	−	3.56112i	0.290792	−	0.244004i
$214$		0			0
$215$	−1.58749	+	0.279918i	−0.108266	+	0.0190902i
$216$		0			0
$217$	−5.81496	−	3.35727i	−0.394745	−	0.227906i
$218$		0			0
$219$	1.81357	+	0.660086i	0.122550	+	0.0446045i
$220$		0			0
$221$	0.147634	−	0.0852364i	0.00993092	−	0.00573362i
$222$		0			0
$223$	10.1057	+	8.47972i	0.676730	+	0.567844i	0.915049	−	0.403343i	$-0.132152\pi$
$223$	10.1057	+	8.47972i	0.676730	+	0.567844i	−0.238319	+	0.971187i	$0.576596\pi$
$224$		0			0
$225$	−0.568839	+	3.22604i	−0.0379226	+	0.215070i
$226$		0			0
$227$	11.6951			0.776230			0.388115	−	0.921611i	$-0.373126\pi$
$227$	11.6951			0.776230			0.388115	+	0.921611i	$0.373126\pi$
$228$		0			0
$229$	9.46145			0.625230			0.312615	−	0.949880i	$-0.398795\pi$
$229$	9.46145			0.625230			0.312615	+	0.949880i	$0.398795\pi$
$230$		0			0
$231$	−1.52183	+	8.63071i	−0.100129	+	0.567859i
$232$		0			0
$233$	−3.07436	−	2.57970i	−0.201408	−	0.169002i	0.536505	−	0.843897i	$-0.319744\pi$
$233$	−3.07436	−	2.57970i	−0.201408	−	0.169002i	−0.737913	+	0.674895i	$0.764189\pi$
$234$		0			0
$235$	−0.308561	+	0.178148i	−0.0201283	+	0.0116211i
$236$		0			0
$237$	−8.84904	−	3.22079i	−0.574807	−	0.209213i
$238$		0			0
$239$	13.9389	+	8.04761i	0.901630	+	0.520557i	0.877729	−	0.479158i	$-0.159058\pi$
$239$	13.9389	+	8.04761i	0.901630	+	0.520557i	0.0239016	+	0.999714i	$0.492391\pi$
$240$		0			0
$241$	−15.3833	+	2.71249i	−0.990926	+	0.174727i	−0.645534	−	0.763731i	$-0.723365\pi$
$241$	−15.3833	+	2.71249i	−0.990926	+	0.174727i	−0.345392	+	0.938458i	$0.612254\pi$
$242$		0			0
$243$	−0.766044	+	0.642788i	−0.0491418	+	0.0412348i
$244$		0			0
$245$	7.78565	−	2.83375i	0.497407	−	0.181041i
$246$		0			0
$247$	4.44174	+	0.772189i	0.282621	+	0.0491332i
$248$		0			0
$249$	−6.03209	−	16.5730i	−0.382268	−	1.05027i
$250$		0			0
$251$	−13.2218	−	15.7571i	−0.834552	−	0.994580i	−0.999965	−	0.00835568i	$-0.997340\pi$
$251$	−13.2218	−	15.7571i	−0.834552	−	0.994580i	0.165413	−	0.986224i	$-0.447104\pi$
$252$		0			0
$253$	1.00598	+	5.70518i	0.0632452	+	0.358681i
$254$		0			0
$255$	0.108212	−	0.187429i	0.00677650	−	0.0117373i
$256$		0			0
$257$	5.98891	−	16.4544i	0.373578	−	1.02640i	−0.600389	−	0.799708i	$-0.704988\pi$
$257$	5.98891	−	16.4544i	0.373578	−	1.02640i	0.973967	−	0.226689i	$-0.0727900\pi$
$258$		0			0
$259$	3.96434	+	6.86644i	0.246332	+	0.426660i
$260$		0			0
$261$	1.32648	−	1.58084i	0.0821072	−	0.0978516i
$262$		0			0
$263$	6.37287	+	1.12371i	0.392968	+	0.0692908i	0.366641	−	0.930363i	$-0.380508\pi$
$263$	6.37287	+	1.12371i	0.392968	+	0.0692908i	0.0263269	+	0.999653i	$0.491619\pi$
$264$		0			0
$265$			6.17640i			0.379413i
$266$		0			0
$267$		−	17.2164i		−	1.05363i
$268$		0			0
$269$	−23.2381	−	4.09751i	−1.41685	−	0.249829i	−0.587803	−	0.809004i	$-0.700007\pi$
$269$	−23.2381	−	4.09751i	−1.41685	−	0.249829i	−0.829050	+	0.559175i	$0.811118\pi$
$270$		0			0
$271$	−5.40943	+	6.44671i	−0.328600	+	0.391610i	−0.904897	−	0.425630i	$-0.860052\pi$
$271$	−5.40943	+	6.44671i	−0.328600	+	0.391610i	0.576298	+	0.817240i	$0.304497\pi$
$272$		0			0
$273$	1.88668	+	3.26782i	0.114187	+	0.197778i
$274$		0			0
$275$	−2.69141	+	7.39458i	−0.162298	+	0.445910i
$276$		0			0
$277$	9.76797	−	16.9186i	0.586900	−	1.01654i	−0.407735	−	0.913100i	$-0.633681\pi$
$277$	9.76797	−	16.9186i	0.586900	−	1.01654i	0.994636	−	0.103441i	$-0.0329853\pi$
$278$		0			0
$279$	−0.319595	−	1.81252i	−0.0191337	−	0.108512i
$280$		0			0
$281$	−1.92825	−	2.29800i	−0.115030	−	0.137087i	0.705457	−	0.708753i	$-0.250742\pi$
$281$	−1.92825	−	2.29800i	−0.115030	−	0.137087i	−0.820487	+	0.571666i	$0.806297\pi$
$282$		0			0
$283$	−2.10304	−	5.77805i	−0.125013	−	0.343469i	0.861360	−	0.507995i	$-0.169613\pi$
$283$	−2.10304	−	5.77805i	−0.125013	−	0.343469i	−0.986373	+	0.164525i	$0.947391\pi$
$284$		0			0
$285$	5.37370	−	1.97051i	0.318311	−	0.116723i
$286$		0			0
$287$	15.5138	−	5.64656i	0.915751	−	0.333306i
$288$		0			0
$289$	−13.0019	+	10.9099i	−0.764820	+	0.641760i
$290$		0			0
$291$	16.1007	−	2.83899i	0.943839	−	0.166424i
$292$		0			0
$293$	−17.8725	−	10.3187i	−1.04413	−	0.602826i	−0.123126	−	0.992391i	$-0.539292\pi$
$293$	−17.8725	−	10.3187i	−1.04413	−	0.602826i	−0.920999	+	0.389565i	$0.872625\pi$
$294$		0			0
$295$	−10.4431	−	3.80097i	−0.608019	−	0.221301i
$296$		0			0
$297$	−2.08036	+	1.20110i	−0.120715	+	0.0696948i
$298$		0			0
$299$	1.91075	+	1.60331i	0.110502	+	0.0927219i
$300$		0			0
$301$	0.777722	−	4.41068i	0.0448272	−	0.254227i
$302$		0			0
$303$	−11.8698			−0.681902
$304$		0			0
$305$	2.03485			0.116515
$306$		0			0
$307$	0.327674	−	1.85833i	0.0187014	−	0.106061i	−0.974028	−	0.226427i	$-0.927296\pi$
$307$	0.327674	−	1.85833i	0.0187014	−	0.106061i	0.992730	+	0.120366i	$0.0384068\pi$
$308$		0			0
$309$	10.9607	+	9.19711i	0.623532	+	0.523205i
$310$		0			0
$311$	−10.8292	+	6.25226i	−0.614069	+	0.354533i	−0.774556	−	0.632505i	$-0.782027\pi$
$311$	−10.8292	+	6.25226i	−0.614069	+	0.354533i	0.160487	+	0.987038i	$0.448693\pi$
$312$		0			0
$313$	−11.5812	−	4.21520i	−0.654607	−	0.238257i	−0.00670067	−	0.999978i	$-0.502133\pi$
$313$	−11.5812	−	4.21520i	−0.654607	−	0.238257i	−0.647906	+	0.761720i	$0.724355\pi$
$314$		0			0
$315$	4.14867	+	2.39524i	0.233751	+	0.134956i
$316$		0			0
$317$	−14.6669	+	2.58617i	−0.823776	+	0.145254i	−0.569619	−	0.821909i	$-0.692909\pi$
$317$	−14.6669	+	2.58617i	−0.823776	+	0.145254i	−0.254157	+	0.967163i	$0.581798\pi$
$318$		0			0
$319$	3.79749	−	3.18647i	0.212619	−	0.178408i
$320$		0			0
$321$	−13.6882	+	4.98211i	−0.764003	+	0.278074i
$322$		0			0
$323$	0.718438	−	0.00172766i	0.0399749	−	9.61294e-5i
$324$		0			0
$325$	1.15881	+	3.18380i	0.0642792	+	0.176606i
$326$		0			0
$327$	−4.66909	−	5.56441i	−0.258201	−	0.307713i
$328$		0			0
$329$	−0.171899	−	0.974889i	−0.00947711	−	0.0537474i
$330$		0			0
$331$	11.2965	−	19.5661i	0.620912	−	1.07545i	−0.368405	−	0.929666i	$-0.620096\pi$
$331$	11.2965	−	19.5661i	0.620912	−	1.07545i	0.989316	−	0.145785i	$-0.0465708\pi$
$332$		0			0
$333$	−0.743304	+	2.04221i	−0.0407328	+	0.111912i
$334$		0			0
$335$	2.40141	+	4.15937i	0.131203	+	0.227251i
$336$		0			0
$337$	11.4783	−	13.6793i	0.625263	−	0.745159i	−0.356703	−	0.934218i	$-0.616099\pi$
$337$	11.4783	−	13.6793i	0.625263	−	0.745159i	0.981966	+	0.189059i	$0.0605436\pi$
$338$		0			0
$339$	−5.57605	−	0.983208i	−0.302849	−	0.0534005i
$340$		0			0
$341$		−	4.42119i		−	0.239421i
$342$		0			0
$343$		−	2.51796i		−	0.135957i
$344$		0			0
$345$	3.11855	+	0.549884i	0.167897	+	0.0296048i
$346$		0			0
$347$	−15.3701	+	18.3174i	−0.825109	+	0.983327i	−0.999999	−	0.00126107i	$-0.999599\pi$
$347$	−15.3701	+	18.3174i	−0.825109	+	0.983327i	0.174890	+	0.984588i	$0.444043\pi$
$348$		0			0
$349$	12.7489	+	22.0818i	0.682434	+	1.18201i	0.974236	+	0.225532i	$0.0724120\pi$
$349$	12.7489	+	22.0818i	0.682434	+	1.18201i	−0.291801	+	0.956479i	$0.594255\pi$
$350$		0			0
$351$	−0.353748	+	0.971913i	−0.0188816	+	0.0518769i
$352$		0			0
$353$	18.1258	−	31.3948i	0.964738	−	1.67098i	0.254421	−	0.967094i	$-0.418115\pi$
$353$	18.1258	−	31.3948i	0.964738	−	1.67098i	0.710317	−	0.703882i	$-0.248552\pi$
$354$		0			0
$355$	−1.26323	−	7.16411i	−0.0670451	−	0.380232i
$356$		0			0
$357$	0.386516	+	0.460631i	0.0204566	+	0.0243792i
$358$		0			0
$359$	9.55692	+	26.2574i	0.504395	+	1.38581i	0.886944	+	0.461878i	$0.152824\pi$
$359$	9.55692	+	26.2574i	0.504395	+	1.38581i	−0.382549	+	0.923935i	$0.624954\pi$
$360$		0			0
$361$	14.6134	+	12.1428i	0.769127	+	0.639096i
$362$		0			0
$363$	4.91407	−	1.78858i	0.257922	−	0.0938758i
$364$		0			0
$365$	1.94131	−	1.62895i	0.101613	−	0.0852634i
$366$		0			0
$367$	−25.3865	+	4.47633i	−1.32517	+	0.233662i	−0.791051	−	0.611750i	$-0.790466\pi$
$367$	−25.3865	+	4.47633i	−1.32517	+	0.233662i	−0.534114	+	0.845412i	$0.679355\pi$
$368$		0			0
$369$	3.91902	+	2.26265i	0.204016	+	0.117789i
$370$		0			0
$371$	−16.1256	−	5.86923i	−0.837198	−	0.304715i
$372$		0			0
$373$	6.90246	−	3.98514i	0.357396	−	0.206343i	−0.310542	−	0.950560i	$-0.600511\pi$
$373$	6.90246	−	3.98514i	0.357396	−	0.206343i	0.667938	+	0.744217i	$0.267177\pi$
$374$		0			0
$375$	8.32448	+	6.98507i	0.429874	+	0.360707i
$376$		0			0
$377$	0.370635	−	2.10197i	0.0190887	−	0.108257i
$378$		0			0
$379$	−16.1447			−0.829298			−0.414649	−	0.909981i	$-0.636096\pi$
$379$	−16.1447			−0.829298			−0.414649	+	0.909981i	$0.636096\pi$
$380$		0			0
$381$	0.802936			0.0411357
$382$		0			0
$383$	3.24394	−	18.3973i	0.165758	−	0.940058i	−0.782522	−	0.622623i	$-0.786067\pi$
$383$	3.24394	−	18.3973i	0.165758	−	0.940058i	0.948280	−	0.317436i	$-0.102822\pi$
$384$		0			0
$385$	8.81538	+	7.39699i	0.449274	+	0.376985i
$386$		0			0
$387$	1.06316	−	0.613816i	0.0540435	−	0.0312020i
$388$		0			0
$389$	−12.7513	−	4.64109i	−0.646516	−	0.235312i	−0.00211174	−	0.999998i	$-0.500672\pi$
$389$	−12.7513	−	4.64109i	−0.646516	−	0.235312i	−0.644404	+	0.764685i	$0.722894\pi$
$390$		0			0
$391$	0.344233	+	0.198743i	0.0174086	+	0.0100509i
$392$		0			0
$393$	3.45775	−	0.609694i	0.174420	−	0.0307550i
$394$		0			0
$395$	−9.47232	+	7.94822i	−0.476604	+	0.399918i
$396$		0			0
$397$	−25.9617	+	9.44930i	−1.30298	+	0.474247i	−0.897967	−	0.440063i	$-0.854956\pi$
$397$	−25.9617	+	9.44930i	−1.30298	+	0.474247i	−0.405015	+	0.914310i	$0.632734\pi$
$398$		0			0
$399$	0.0382411	+	15.9024i	0.00191445	+	0.796114i
$400$		0			0
$401$	2.59599	+	7.13243i	0.129638	+	0.356177i	0.987482	−	0.157733i	$-0.0504187\pi$
$401$	2.59599	+	7.13243i	0.129638	+	0.356177i	−0.857844	+	0.513910i	$0.828196\pi$
$402$		0			0
$403$	−1.22360	−	1.45823i	−0.0609518	−	0.0726396i
$404$		0			0
$405$	0.228015	+	1.29313i	0.0113301	+	0.0642564i
$406$		0			0
$407$	−2.61032	+	4.52120i	−0.129389	+	0.224108i
$408$		0			0
$409$	8.81746	−	24.2258i	0.435995	−	1.19789i	−0.506080	−	0.862486i	$-0.668906\pi$
$409$	8.81746	−	24.2258i	0.435995	−	1.19789i	0.942076	−	0.335401i	$-0.108872\pi$
$410$		0			0
$411$	−8.24814	−	14.2862i	−0.406851	−	0.704686i
$412$		0			0
$413$	19.8474	−	23.6532i	0.976626	−	1.16390i
$414$		0			0
$415$	−22.8066	−	4.02141i	−1.11953	−	0.197403i
$416$		0			0
$417$			20.4318i			1.00055i
$418$		0			0
$419$			24.0811i			1.17644i	0.808701	+	0.588219i	$0.200171\pi$
$419$			24.0811i			1.17644i	−0.808701	+	0.588219i	$0.799829\pi$
$420$		0			0
$421$	23.7058	+	4.17997i	1.15535	+	0.203719i	0.718310	−	0.695723i	$-0.244916\pi$
$421$	23.7058	+	4.17997i	1.15535	+	0.203719i	0.437039	+	0.899442i	$0.356027\pi$
$422$		0			0
$423$	0.174416	−	0.207860i	0.00848037	−	0.0101065i
$424$		0			0
$425$	0.269962	+	0.467588i	0.0130951	+	0.0226813i
$426$		0			0
$427$	−1.93365	+	5.31266i	−0.0935759	+	0.257098i
$428$		0			0
$429$	−1.24228	+	2.15170i	−0.0599780	+	0.103885i
$430$		0			0
$431$	−4.28982	−	24.3288i	−0.206633	−	1.17188i	−0.894849	−	0.446370i	$-0.852717\pi$
$431$	−4.28982	−	24.3288i	−0.206633	−	1.17188i	0.688215	−	0.725506i	$-0.258394\pi$
$432$		0			0
$433$	5.14645	+	6.13330i	0.247323	+	0.294748i	0.875396	−	0.483406i	$-0.160601\pi$
$433$	5.14645	+	6.13330i	0.247323	+	0.294748i	−0.628073	+	0.778154i	$0.716156\pi$
$434$		0			0
$435$	−0.926783	−	2.54632i	−0.0444358	−	0.122086i
$436$		0			0
$437$	3.61906	+	9.86938i	0.173123	+	0.472116i
$438$		0			0
$439$	−0.551048	+	0.200565i	−0.0263001	+	0.00957245i	−0.355137	−	0.934814i	$-0.615566\pi$
$439$	−0.551048	+	0.200565i	−0.0263001	+	0.00957245i	0.328837	+	0.944387i	$0.393343\pi$
$440$		0			0
$441$	−4.83360	+	4.05587i	−0.230172	+	0.193137i
$442$		0			0
$443$	−32.4534	+	5.72241i	−1.54191	+	0.271880i	−0.879000	−	0.476822i	$-0.841789\pi$
$443$	−32.4534	+	5.72241i	−1.54191	+	0.271880i	−0.662907	+	0.748701i	$0.730678\pi$
$444$		0			0
$445$	−19.5778	−	11.3033i	−0.928079	−	0.535827i
$446$		0			0
$447$	−22.4926	−	8.18663i	−1.06386	−	0.387214i
$448$		0			0
$449$	9.20294	−	5.31332i	0.434313	−	0.250751i	−0.266869	−	0.963733i	$-0.585989\pi$
$449$	9.20294	−	5.31332i	0.434313	−	0.250751i	0.701183	+	0.712982i	$0.252656\pi$
$450$		0			0
$451$	8.32740	+	6.98752i	0.392122	+	0.329029i
$452$		0			0
$453$	1.08198	−	6.13622i	0.0508359	−	0.288305i
$454$		0			0
$455$	4.95473			0.232281
$456$		0			0
$457$	−21.2857			−0.995705			−0.497852	−	0.867262i	$-0.665878\pi$
$457$	−21.2857			−0.995705			−0.497852	+	0.867262i	$0.665878\pi$
$458$		0			0
$459$	−0.0286209	+	0.162317i	−0.00133591	+	0.00757633i
$460$		0			0
$461$	−9.22516	−	7.74083i	−0.429658	−	0.360526i	0.402164	−	0.915567i	$-0.368258\pi$
$461$	−9.22516	−	7.74083i	−0.429658	−	0.360526i	−0.831823	+	0.555041i	$0.812702\pi$
$462$		0			0
$463$	8.32899	−	4.80875i	0.387081	−	0.223481i	−0.293813	−	0.955863i	$-0.594924\pi$
$463$	8.32899	−	4.80875i	0.387081	−	0.223481i	0.680895	+	0.732381i	$0.261591\pi$
$464$		0			0
$465$	−2.27095	−	0.826560i	−0.105313	−	0.0383308i
$466$		0			0
$467$	9.11469	+	5.26237i	0.421778	+	0.243513i	0.695838	−	0.718199i	$-0.255033\pi$
$467$	9.11469	+	5.26237i	0.421778	+	0.243513i	−0.274060	+	0.961713i	$0.588367\pi$
$468$		0			0
$469$	−13.1414	+	2.31719i	−0.606814	+	0.106998i
$470$		0			0
$471$	−5.62244	+	4.71779i	−0.259068	+	0.217384i
$472$		0			0
$473$	2.77117	−	1.00862i	0.127418	−	0.0463765i
$474$		0			0
$475$	−2.44569	+	14.0679i	−0.112216	+	0.645481i
$476$		0			0
$477$	−1.60877	−	4.42007i	−0.0736607	−	0.202381i
$478$		0			0
$479$	−12.2922	−	14.6492i	−0.561643	−	0.669340i	0.408250	−	0.912870i	$-0.366139\pi$
$479$	−12.2922	−	14.6492i	−0.561643	−	0.669340i	−0.969893	+	0.243530i	$0.921695\pi$
$480$		0			0
$481$	0.390325	+	2.21364i	0.0177973	+	0.100934i
$482$		0			0
$483$	−4.39911	+	7.61948i	−0.200166	+	0.346698i
$484$		0			0
$485$	7.34238	−	20.1730i	0.333400	−	0.916010i
$486$		0			0
$487$	−19.4338	−	33.6603i	−0.880629	−	1.52529i	−0.850643	−	0.525743i	$-0.823787\pi$
$487$	−19.4338	−	33.6603i	−0.880629	−	1.52529i	−0.0299853	−	0.999550i	$-0.509546\pi$
$488$		0			0
$489$	−0.380597	+	0.453578i	−0.0172112	+	0.0205115i
$490$		0			0
$491$	2.62004	+	0.461985i	0.118241	+	0.0208491i	0.232455	−	0.972607i	$-0.425324\pi$
$491$	2.62004	+	0.461985i	0.118241	+	0.0208491i	−0.114215	+	0.993456i	$0.536435\pi$
$492$		0			0
$493$		−	0.340132i		−	0.0153188i
$494$		0			0
$495$			3.15429i			0.141775i
$496$		0			0
$497$	19.9047	+	3.50974i	0.892849	+	0.157433i
$498$		0			0
$499$	−22.0430	+	26.2698i	−0.986778	+	1.17600i	−0.00238771	+	0.999997i	$0.500760\pi$
$499$	−22.0430	+	26.2698i	−0.986778	+	1.17600i	−0.984390	+	0.175999i	$0.943684\pi$
$500$		0			0
$501$	9.41587	+	16.3088i	0.420670	+	0.728622i
$502$		0			0
$503$	8.79850	−	24.1737i	0.392306	−	1.07785i	−0.573640	−	0.819107i	$-0.694469\pi$
$503$	8.79850	−	24.1737i	0.392306	−	1.07785i	0.965946	−	0.258744i	$-0.0833085\pi$
$504$		0			0
$505$	−7.79302	+	13.4979i	−0.346785	+	0.600649i
$506$		0			0
$507$	−2.07167	−	11.7490i	−0.0920059	−	0.521791i
$508$		0			0
$509$	−23.0501	−	27.4701i	−1.02168	−	1.21759i	−0.975805	−	0.218642i	$-0.929837\pi$
$509$	−23.0501	−	27.4701i	−1.02168	−	1.21759i	−0.0458738	−	0.998947i	$-0.514607\pi$
$510$		0			0
$511$	2.40817	+	6.61639i	0.106531	+	0.292692i
$512$		0			0
$513$	−3.33236	+	2.80987i	−0.147127	+	0.124059i
$514$		0			0
$515$	17.6548	−	6.42581i	0.777962	−	0.283155i
$516$		0			0
$517$	0.499322	−	0.418981i	0.0219601	−	0.0184268i
$518$		0			0
$519$	−19.7008	+	3.47379i	−0.864770	+	0.152482i
$520$		0			0
$521$	−25.9438	−	14.9786i	−1.13662	−	0.656226i	−0.191027	−	0.981585i	$-0.561182\pi$
$521$	−25.9438	−	14.9786i	−1.13662	−	0.656226i	−0.945591	+	0.325359i	$0.894515\pi$
$522$		0			0
$523$	−19.1254	−	6.96107i	−0.836295	−	0.304386i	−0.111855	−	0.993725i	$-0.535679\pi$
$523$	−19.1254	−	6.96107i	−0.836295	−	0.304386i	−0.724440	+	0.689338i	$0.757901\pi$
$524$		0			0
$525$	−10.3499	+	5.97551i	−0.451706	+	0.260793i
$526$		0			0
$527$	−0.232379	−	0.194989i	−0.0101226	−	0.00849388i
$528$		0			0
$529$	2.98399	−	16.9230i	0.129739	−	0.735784i
$530$		0			0
$531$	8.46350			0.367285
$532$		0			0
$533$	4.68046			0.202733
$534$		0			0
$535$	−3.32142	+	18.8367i	−0.143598	+	0.814383i
$536$		0			0
$537$	6.46919	+	5.42829i	0.279166	+	0.234248i
$538$		0			0
$539$	−13.1267	+	7.57872i	−0.565408	+	0.326439i
$540$		0			0
$541$	−33.0905	−	12.0439i	−1.42267	−	0.517810i	−0.487849	−	0.872928i	$-0.662218\pi$
$541$	−33.0905	−	12.0439i	−1.42267	−	0.517810i	−0.934821	+	0.355118i	$0.884441\pi$
$542$		0			0
$543$	−8.12680	−	4.69201i	−0.348754	−	0.201353i
$544$		0			0
$545$	−9.39310	+	1.65626i	−0.402356	+	0.0709462i
$546$		0			0
$547$	6.46354	−	5.42355i	0.276361	−	0.231894i	−0.494063	−	0.869426i	$-0.664489\pi$
$547$	6.46354	−	5.42355i	0.276361	−	0.231894i	0.770424	+	0.637532i	$0.220044\pi$
$548$		0			0
$549$	−1.45622	+	0.530020i	−0.0621498	+	0.0226207i
$550$		0			0
$551$	5.76542	−	6.90461i	0.245615	−	0.294146i
$552$		0			0
$553$	−11.7503	−	32.2836i	−0.499672	−	1.37284i
$554$		0			0
$555$	1.83432	+	2.18605i	0.0778625	+	0.0927929i
$556$		0			0
$557$	0.627602	+	3.55931i	0.0265923	+	0.150813i	0.995213	−	0.0977321i	$-0.0311588\pi$
$557$	0.627602	+	3.55931i	0.0265923	+	0.150813i	−0.968620	+	0.248545i	$0.920048\pi$
$558$		0			0
$559$	0.634863	−	1.09961i	0.0268518	−	0.0465087i
$560$		0			0
$561$	−0.135417	+	0.372056i	−0.00571732	+	0.0157082i
$562$		0			0
$563$	7.79363	+	13.4990i	0.328462	+	0.568913i	0.982207	−	0.187802i	$-0.0601363\pi$
$563$	7.79363	+	13.4990i	0.328462	+	0.568913i	−0.653745	+	0.756715i	$0.726803\pi$
$564$		0			0
$565$	−4.77898	+	5.69536i	−0.201053	+	0.239606i
$566$		0			0
$567$	−3.59284	−	0.633514i	−0.150885	−	0.0266051i
$568$		0			0
$569$			10.5444i			0.442046i	0.975269	+	0.221023i	$0.0709396\pi$
$569$			10.5444i			0.442046i	−0.975269	+	0.221023i	$0.929060\pi$
$570$		0			0
$571$			9.94106i			0.416020i	0.978127	+	0.208010i	$0.0666987\pi$
$571$			9.94106i			0.416020i	−0.978127	+	0.208010i	$0.933301\pi$
$572$		0			0
$573$	5.00784	+	0.883017i	0.209205	+	0.0368886i
$574$		0			0
$575$	−5.07803	+	6.05176i	−0.211768	+	0.252376i
$576$		0			0
$577$	22.5463	+	39.0513i	0.938614	+	1.62573i	0.768059	+	0.640379i	$0.221223\pi$
$577$	22.5463	+	39.0513i	0.938614	+	1.62573i	0.170555	+	0.985348i	$0.445444\pi$
$578$		0			0
$579$	−5.48047	+	15.0575i	−0.227761	+	0.625767i
$580$		0			0
$581$	32.1715	−	55.7227i	1.33470	−	2.31177i
$582$		0			0
$583$	−1.96211	−	11.1277i	−0.0812621	−	0.460860i
$584$		0			0
$585$	0.872975	+	1.04037i	0.0360931	+	0.0430140i
$586$		0			0
$587$	0.253513	+	0.696520i	0.0104636	+	0.0287485i	0.944814	−	0.327606i	$-0.106242\pi$
$587$	0.253513	+	0.696520i	0.0104636	+	0.0287485i	−0.934351	+	0.356354i	$0.884020\pi$
$588$		0			0
$589$	−1.41208	−	7.89720i	−0.0581837	−	0.325398i
$590$		0			0
$591$	−17.0521	+	6.20645i	−0.701429	+	0.255299i
$592$		0			0
$593$	−5.60983	+	4.70721i	−0.230368	+	0.193302i	−0.750664	−	0.660684i	$-0.770266\pi$
$593$	−5.60983	+	4.70721i	−0.230368	+	0.193302i	0.520296	+	0.853986i	$0.325822\pi$
$594$		0			0
$595$	0.777577	−	0.137108i	0.0318775	−	0.00562087i
$596$		0			0
$597$	−9.02305	−	5.20946i	−0.369289	−	0.213209i
$598$		0			0
$599$	16.6609	+	6.06406i	0.680744	+	0.247771i	0.659167	−	0.751996i	$-0.270909\pi$
$599$	16.6609	+	6.06406i	0.680744	+	0.247771i	0.0215773	+	0.999767i	$0.493131\pi$
$600$		0			0
$601$	3.49433	−	2.01745i	0.142537	−	0.0822937i	−0.427036	−	0.904235i	$-0.640442\pi$
$601$	3.49433	−	2.01745i	0.142537	−	0.0822937i	0.569572	+	0.821941i	$0.307109\pi$
$602$		0			0
$603$	−2.80194	−	2.35110i	−0.114104	−	0.0957444i
$604$		0			0
$605$	1.19239	−	6.76238i	0.0484775	−	0.274930i
$606$		0			0
$607$	−43.1951			−1.75323			−0.876617	−	0.481188i	$-0.840205\pi$
$607$	−43.1951			−1.75323			−0.876617	+	0.481188i	$0.840205\pi$
$608$		0			0
$609$	7.52870			0.305078
$610$		0			0
$611$	0.0487337	−	0.276383i	0.00197156	−	0.0111812i
$612$		0			0
$613$	16.7223	+	14.0317i	0.675408	+	0.566735i	0.914661	−	0.404223i	$-0.132458\pi$
$613$	16.7223	+	14.0317i	0.675408	+	0.566735i	−0.239252	+	0.970957i	$0.576902\pi$
$614$		0			0
$615$	5.14600	−	2.97104i	0.207507	−	0.119804i
$616$		0			0
$617$	6.30652	+	2.29538i	0.253891	+	0.0924087i	0.465830	−	0.884874i	$-0.345756\pi$
$617$	6.30652	+	2.29538i	0.253891	+	0.0924087i	−0.211939	+	0.977283i	$0.567978\pi$
$618$		0			0
$619$	20.3208	+	11.7322i	0.816763	+	0.471559i	0.849299	−	0.527912i	$-0.177025\pi$
$619$	20.3208	+	11.7322i	0.816763	+	0.471559i	−0.0325357	+	0.999471i	$0.510358\pi$
$620$		0			0
$621$	−2.37498	+	0.418773i	−0.0953047	+	0.0168048i
$622$		0			0
$623$	48.1152	−	40.3734i	1.92769	−	1.61753i
$624$		0			0
$625$	−1.98275	+	0.721662i	−0.0793100	+	0.0288665i
$626$		0			0
$627$	−9.05548	+	5.25726i	−0.361641	+	0.209955i
$628$		0			0
$629$	0.122512	+	0.336600i	0.00488489	+	0.0134211i
$630$		0			0
$631$	−9.96333	−	11.8738i	−0.396634	−	0.472690i	0.530357	−	0.847775i	$-0.322058\pi$
$631$	−9.96333	−	11.8738i	−0.396634	−	0.472690i	−0.926991	+	0.375085i	$0.877614\pi$
$632$		0			0
$633$	1.94048	+	11.0050i	0.0771271	+	0.437409i
$634$		0			0
$635$	0.527161	−	0.913070i	0.0209197	−	0.0362341i
$636$		0			0
$637$	−2.23208	+	6.13260i	−0.0884383	+	0.242982i
$638$		0			0
$639$	2.77006	+	4.79788i	0.109582	+	0.189801i
$640$		0			0
$641$	25.1263	−	29.9444i	0.992429	−	1.18273i	0.00927415	−	0.999957i	$-0.497048\pi$
$641$	25.1263	−	29.9444i	0.992429	−	1.18273i	0.983155	−	0.182774i	$-0.0585077\pi$
$642$		0			0
$643$	−22.6016	−	3.98528i	−0.891322	−	0.157164i	−0.290811	−	0.956781i	$-0.593925\pi$
$643$	−22.6016	−	3.98528i	−0.891322	−	0.157164i	−0.600511	+	0.799616i	$0.705036\pi$
$644$		0			0
$645$		−	1.61198i		−	0.0634718i
$646$		0			0
$647$			35.8959i			1.41121i	0.708603	+	0.705607i	$0.249326\pi$
$647$			35.8959i			1.41121i	−0.708603	+	0.705607i	$0.750674\pi$
$648$		0			0
$649$	20.0221	+	3.53044i	0.785937	+	0.138582i
$650$		0			0
$651$	4.31602	−	5.14364i	0.169158	−	0.201595i
$652$		0			0
$653$	6.86676	+	11.8936i	0.268717	+	0.465432i	0.968531	−	0.248894i	$-0.0800670\pi$
$653$	6.86676	+	11.8936i	0.268717	+	0.465432i	−0.699814	+	0.714326i	$0.746734\pi$
$654$		0			0
$655$	1.57683	−	4.33231i	0.0616120	−	0.169277i
$656$		0			0
$657$	−0.964982	+	1.67140i	−0.0376475	+	0.0652074i
$658$		0			0
$659$	−0.461493	−	2.61726i	−0.0179772	−	0.101954i	0.974499	−	0.224392i	$-0.0720397\pi$
$659$	−0.461493	−	2.61726i	−0.0179772	−	0.101954i	−0.992476	+	0.122438i	$0.960929\pi$
$660$		0			0
$661$	−21.8143	−	25.9973i	−0.848480	−	1.01118i	−0.999743	−	0.0226850i	$-0.992779\pi$
$661$	−21.8143	−	25.9973i	−0.848480	−	1.01118i	0.151263	−	0.988494i	$-0.451666\pi$
$662$		0			0
$663$	0.0583051	+	0.160192i	0.00226438	+	0.00622134i
$664$		0			0
$665$	18.1087	+	10.3971i	0.702225	+	0.403181i
$666$		0			0
$667$	4.67658	−	1.70214i	0.181078	−	0.0659070i
$668$		0			0
$669$	−10.1057	+	8.47972i	−0.390710	+	0.327845i
$670$		0			0
$671$	−3.66607	+	0.646427i	−0.141527	+	0.0249550i
$672$		0			0
$673$	23.5010	+	13.5683i	0.905895	+	0.523019i	0.879108	−	0.476622i	$-0.158139\pi$
$673$	23.5010	+	13.5683i	0.905895	+	0.523019i	0.0267871	+	0.999641i	$0.491472\pi$
$674$		0			0
$675$	−3.07826	−	1.12039i	−0.118482	−	0.0431240i
$676$		0			0
$677$	14.5673	−	8.41044i	0.559867	−	0.323239i	−0.193225	−	0.981154i	$-0.561895\pi$
$677$	14.5673	−	8.41044i	0.559867	−	0.323239i	0.753092	+	0.657915i	$0.228561\pi$
$678$		0			0
$679$	45.6913	+	38.3395i	1.75347	+	1.47134i
$680$		0			0
$681$	−2.03083	+	11.5174i	−0.0778216	+	0.441348i
$682$		0			0
$683$	13.3232			0.509798			0.254899	−	0.966968i	$-0.417958\pi$
$683$	13.3232			0.509798			0.254899	+	0.966968i	$0.417958\pi$
$684$		0			0
$685$	−21.6610			−0.827624
$686$		0			0
$687$	−1.64296	+	9.31771i	−0.0626829	+	0.355493i
$688$		0			0
$689$	−3.72682	−	3.12718i	−0.141981	−	0.119136i
$690$		0			0
$691$	8.94276	−	5.16311i	0.340199	−	0.196414i	−0.320161	−	0.947363i	$-0.603737\pi$
$691$	8.94276	−	5.16311i	0.340199	−	0.196414i	0.660360	+	0.750949i	$0.270404\pi$
$692$		0			0
$693$	−8.23533	−	2.99741i	−0.312834	−	0.113862i
$694$		0			0
$695$	23.2343	+	13.4143i	0.881328	+	0.508835i
$696$		0			0
$697$	0.734533	−	0.129518i	0.0278224	−	0.00490585i
$698$		0			0
$699$	3.07436	−	2.57970i	0.116283	−	0.0975731i
$700$		0			0
$701$	2.66528	−	0.970082i	0.100666	−	0.0366395i	−0.291196	−	0.956663i	$-0.594053\pi$
$701$	2.66528	−	0.970082i	0.100666	−	0.0366395i	0.391862	+	0.920024i	$0.371831\pi$
$702$		0			0
$703$	−3.21857	+	8.90956i	−0.121391	+	0.336030i
$704$		0			0
$705$	−0.121860	−	0.334808i	−0.00458952	−	0.0126096i
$706$		0			0
$707$	−27.8354	−	33.1729i	−1.04686	−	1.24759i
$708$		0			0
$709$	2.14621	+	12.1718i	0.0806026	+	0.457120i	0.998219	+	0.0596533i	$0.0189995\pi$
$709$	2.14621	+	12.1718i	0.0806026	+	0.457120i	−0.917617	+	0.397467i	$0.869889\pi$
$710$		0			0
$711$	4.70847	−	8.15532i	0.176582	−	0.305848i
$712$		0			0
$713$	1.51807	−	4.17085i	0.0568520	−	0.156200i
$714$		0			0
$715$	1.63122	+	2.82536i	0.0610042	+	0.105662i
$716$		0			0
$717$	−10.3458	+	12.3297i	−0.386371	+	0.460459i
$718$		0			0
$719$	28.5488	+	5.03393i	1.06469	+	0.187734i	0.678437	−	0.734658i	$-0.262657\pi$
$719$	28.5488	+	5.03393i	1.06469	+	0.187734i	0.386255	+	0.922392i	$0.373769\pi$
$720$		0			0
$721$			52.1999i			1.94403i
$722$		0			0
$723$		−	15.6206i		−	0.580937i
$724$		0			0
$725$	6.65740	+	1.17388i	0.247250	+	0.0435968i
$726$		0			0
$727$	19.1938	−	22.8743i	0.711858	−	0.848359i	−0.281955	−	0.959428i	$-0.590983\pi$
$727$	19.1938	−	22.8743i	0.711858	−	0.848359i	0.993813	+	0.111068i	$0.0354272\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	0.0692043	−	0.190137i	0.00255961	−	0.00703248i
$732$		0			0
$733$	25.7087	−	44.5287i	0.949572	−	1.64471i	0.203244	−	0.979128i	$-0.434852\pi$
$733$	25.7087	−	44.5287i	0.949572	−	1.64471i	0.746328	−	0.665578i	$-0.231815\pi$
$734$		0			0
$735$	1.43873	+	8.15945i	0.0530684	+	0.300966i
$736$		0			0
$737$	−5.64782	−	6.73081i	−0.208040	−	0.247933i
$738$		0			0
$739$	−6.18539	−	16.9942i	−0.227533	−	0.625143i	0.772417	−	0.635116i	$-0.219048\pi$
$739$	−6.18539	−	16.9942i	−0.227533	−	0.625143i	−0.999950	+	0.00997304i	$0.996825\pi$
$740$		0			0
$741$	−1.53176	+	4.24017i	−0.0562705	+	0.155766i
$742$		0			0
$743$	37.1555	−	13.5235i	1.36310	−	0.496129i	0.446092	−	0.894987i	$-0.352816\pi$
$743$	37.1555	−	13.5235i	1.36310	−	0.496129i	0.917013	+	0.398858i	$0.130593\pi$
$744$		0			0
$745$	−24.0769	+	20.2029i	−0.882108	+	0.740176i
$746$		0			0
$747$	17.3687	−	3.06257i	0.635487	−	0.112054i
$748$		0			0
$749$	−46.0234	−	26.5716i	−1.68166	−	0.970905i
$750$		0			0
$751$	16.9226	+	6.15934i	0.617516	+	0.224757i	0.631789	−	0.775141i	$-0.282321\pi$
$751$	16.9226	+	6.15934i	0.617516	+	0.224757i	−0.0142726	+	0.999898i	$0.504543\pi$
$752$		0			0
$753$	17.8137	−	10.2847i	0.649166	−	0.374796i
$754$		0			0
$755$	−6.26752	−	5.25907i	−0.228098	−	0.191397i
$756$		0			0
$757$	−5.92298	+	33.5909i	−0.215275	+	1.22088i	0.665155	+	0.746705i	$0.268366\pi$
$757$	−5.92298	+	33.5909i	−0.215275	+	1.22088i	−0.880429	+	0.474177i	$0.842746\pi$
$758$		0			0
$759$	−5.79319			−0.210279
$760$		0			0
$761$	−42.9829			−1.55813			−0.779065	−	0.626943i	$-0.784306\pi$
$761$	−42.9829			−1.55813			−0.779065	+	0.626943i	$0.784306\pi$
$762$		0			0
$763$	4.60173	−	26.0977i	0.166594	−	0.944801i
$764$		0			0
$765$	0.165791	+	0.139115i	0.00599417	+	0.00502971i
$766$		0			0
$767$	7.58093	−	4.37685i	0.273731	−	0.158039i
$768$		0			0
$769$	−0.859039	−	0.312665i	−0.0309777	−	0.0112750i	0.326485	−	0.945202i	$-0.394136\pi$
$769$	−0.859039	−	0.312665i	−0.0309777	−	0.0112750i	−0.357463	+	0.933927i	$0.616358\pi$
$770$		0			0
$771$	15.1644	+	8.75520i	0.546134	+	0.315311i
$772$		0			0
$773$	−14.2066	+	2.50501i	−0.510976	+	0.0900989i	−0.423191	−	0.906040i	$-0.639090\pi$
$773$	−14.2066	+	2.50501i	−0.510976	+	0.0900989i	−0.0877854	+	0.996139i	$0.527979\pi$
$774$		0			0
$775$	4.61852	−	3.87540i	0.165902	−	0.139209i
$776$		0			0
$777$	−7.45052	+	2.71177i	−0.267286	+	0.0972841i
$778$		0			0
$779$	17.1063	+	9.82154i	0.612896	+	0.351893i
$780$		0			0
$781$	4.55176	+	12.5059i	0.162875	+	0.447495i
$782$		0			0
$783$	1.32648	+	1.58084i	0.0474046	+	0.0564946i
$784$		0			0
$785$	1.67353	+	9.49106i	0.0597309	+	0.338750i
$786$		0			0
$787$	1.35489	−	2.34673i	0.0482964	−	0.0836519i	−0.840867	−	0.541242i	$-0.817954\pi$
$787$	1.35489	−	2.34673i	0.0482964	−	0.0836519i	0.889163	+	0.457591i	$0.151287\pi$
$788$		0			0
$789$	−2.21327	+	6.08092i	−0.0787946	+	0.216486i
$790$		0			0
$791$	−10.3284	−	17.8892i	−0.367234	−	0.636068i
$792$		0			0
$793$	−1.03027	+	1.22782i	−0.0365858	+	0.0436013i
$794$		0			0
$795$	−6.08257	−	1.07252i	−0.215727	−	0.0380384i
$796$		0			0
$797$			25.2975i			0.896084i	0.894012	+	0.448042i	$0.147879\pi$
$797$			25.2975i			0.896084i	−0.894012	+	0.448042i	$0.852121\pi$
$798$		0			0
$799$		−	0.0447230i		−	0.00158219i
$800$		0			0
$801$	16.9548	+	2.98959i	0.599069	+	0.105632i
$802$		0			0
$803$	−2.98006	+	3.55150i	−0.105164	+	0.125330i
$804$		0			0
$805$	5.77640	+	10.0050i	0.203591	+	0.352630i
$806$		0			0
$807$	8.07051	−	22.1735i	0.284095	−	0.780546i
$808$		0			0
$809$	−0.868176	+	1.50373i	−0.0305234	+	0.0528682i	−0.880884	−	0.473333i	$-0.843051\pi$
$809$	−0.868176	+	1.50373i	−0.0305234	+	0.0528682i	0.850360	+	0.526201i	$0.176384\pi$
$810$		0			0
$811$	−6.25246	−	35.4595i	−0.219554	−	1.24515i	−0.872828	−	0.488029i	$-0.837716\pi$
$811$	−6.25246	−	35.4595i	−0.219554	−	1.24515i	0.653274	−	0.757122i	$-0.273395\pi$
$812$		0			0
$813$	−5.40943	−	6.44671i	−0.189717	−	0.226096i
$814$		0			0
$815$	0.265915	+	0.730595i	0.00931459	+	0.0255916i
$816$		0			0
$817$	4.62776	−	2.68670i	0.161905	−	0.0939957i
$818$		0			0
$819$	−3.54579	+	1.29056i	−0.123900	+	0.0450959i
$820$		0			0
$821$	12.9022	−	10.8262i	0.450290	−	0.377838i	−0.389254	−	0.921131i	$-0.627267\pi$
$821$	12.9022	−	10.8262i	0.450290	−	0.377838i	0.839543	+	0.543293i	$0.182823\pi$
$822$		0			0
$823$	−18.2409	+	3.21635i	−0.635836	+	0.112115i	−0.482269	−	0.876023i	$-0.660187\pi$
$823$	−18.2409	+	3.21635i	−0.635836	+	0.112115i	−0.153567	+	0.988138i	$0.549076\pi$
$824$		0			0
$825$	−6.81488	−	3.93457i	−0.237264	−	0.136984i
$826$		0			0
$827$	22.7960	+	8.29706i	0.792694	+	0.288517i	0.706456	−	0.707757i	$-0.250293\pi$
$827$	22.7960	+	8.29706i	0.792694	+	0.288517i	0.0862388	+	0.996274i	$0.472515\pi$
$828$		0			0
$829$	−2.90552	+	1.67750i	−0.100913	+	0.0582622i	−0.549607	−	0.835423i	$-0.685223\pi$
$829$	−2.90552	+	1.67750i	−0.100913	+	0.0582622i	0.448694	+	0.893685i	$0.351889\pi$
$830$		0			0
$831$	14.9654	+	12.5575i	0.519144	+	0.435613i
$832$		0			0
$833$	−0.180593	+	1.02419i	−0.00625717	+	0.0354862i
$834$		0			0
$835$	24.7277			0.855736
$836$		0			0
$837$	1.84048			0.0636162
$838$		0			0
$839$	−5.46470	+	30.9919i	−0.188662	+	1.06996i	0.732497	+	0.680771i	$0.238355\pi$
$839$	−5.46470	+	30.9919i	−0.188662	+	1.06996i	−0.921159	+	0.389187i	$0.872756\pi$
$840$		0			0
$841$	18.9530	+	15.9035i	0.653552	+	0.548395i
$842$		0			0
$843$	2.59793	−	1.49992i	0.0894775	−	0.0516598i
$844$		0			0
$845$	−14.7207	−	5.35789i	−0.506406	−	0.184317i
$846$		0			0
$847$	16.5224	+	9.53919i	0.567715	+	0.327771i
$848$		0			0
$849$	6.05545	−	1.06774i	0.207823	−	0.0366447i
$850$		0			0
$851$	−4.01492	+	3.36892i	−0.137630	+	0.115485i
$852$		0			0
$853$	34.0557	−	12.3953i	1.16605	−	0.424406i	0.314793	−	0.949160i	$-0.398065\pi$
$853$	34.0557	−	12.3953i	1.16605	−	0.424406i	0.851254	+	0.524754i	$0.175843\pi$
$854$		0			0
$855$	1.00744	+	5.63424i	0.0344539	+	0.192687i
$856$		0			0
$857$	−5.49699	−	15.1029i	−0.187774	−	0.515904i	0.809708	−	0.586834i	$-0.199626\pi$
$857$	−5.49699	−	15.1029i	−0.187774	−	0.515904i	−0.997481	+	0.0709294i	$0.977403\pi$
$858$		0			0
$859$	20.8374	+	24.8331i	0.710963	+	0.847293i	0.993720	−	0.111899i	$-0.0356933\pi$
$859$	20.8374	+	24.8331i	0.710963	+	0.847293i	−0.282757	+	0.959192i	$0.591249\pi$
$860$		0			0
$861$	2.86684	+	16.2586i	0.0977015	+	0.554093i
$862$		0			0
$863$	−14.8212	+	25.6711i	−0.504521	+	0.873856i	0.495466	+	0.868628i	$0.334997\pi$
$863$	−14.8212	+	25.6711i	−0.504521	+	0.873856i	−0.999986	+	0.00522805i	$0.998336\pi$
$864$		0			0
$865$	−8.98415	+	24.6837i	−0.305470	+	0.839273i
$866$		0			0
$867$	−8.48642	−	14.6989i	−0.288214	−	0.499201i
$868$		0			0
$869$	14.5407	−	17.3290i	0.493261	−	0.587845i
$870$		0			0
$871$	−3.72561	−	0.656926i	−0.126238	−	0.0222591i
$872$		0			0
$873$			16.3491i			0.553332i
$874$		0			0
$875$			39.6451i			1.34025i
$876$		0			0
$877$	−28.8134	−	5.08059i	−0.972961	−	0.171559i	−0.335499	−	0.942041i	$-0.608905\pi$
$877$	−28.8134	−	5.08059i	−0.972961	−	0.171559i	−0.637462	+	0.770481i	$0.720016\pi$
$878$		0			0
$879$	13.2655	−	15.8092i	0.447434	−	0.533231i
$880$		0			0
$881$	10.6001	+	18.3600i	0.357128	+	0.618563i	0.987480	−	0.157746i	$-0.0504228\pi$
$881$	10.6001	+	18.3600i	0.357128	+	0.618563i	−0.630352	+	0.776309i	$0.717089\pi$
$882$		0			0
$883$	4.39128	−	12.0649i	0.147778	−	0.406017i	−0.843613	−	0.536952i	$-0.819576\pi$
$883$	4.39128	−	12.0649i	0.147778	−	0.406017i	0.991391	+	0.130935i	$0.0417978\pi$
$884$		0			0
$885$	5.55664	−	9.62438i	0.186784	−	0.323520i
$886$		0			0
$887$	3.91463	+	22.2010i	0.131440	+	0.745435i	0.977273	+	0.211986i	$0.0679933\pi$
$887$	3.91463	+	22.2010i	0.131440	+	0.745435i	−0.845832	+	0.533449i	$0.820896\pi$
$888$		0			0
$889$	1.88293	+	2.24399i	0.0631515	+	0.0752610i
$890$		0			0
$891$	−0.821600	−	2.25733i	−0.0275246	−	0.0756233i
$892$		0			0
$893$	0.758079	−	0.907868i	0.0253681	−	0.0303806i
$894$		0			0
$895$	10.4201	−	3.79262i	0.348307	−	0.126773i
$896$		0			0
$897$	−1.91075	+	1.60331i	−0.0637982	+	0.0535330i
$898$		0			0
$899$	−3.74038	+	0.659530i	−0.124749	+	0.0219966i
$900$		0			0
$901$	−0.671409	−	0.387638i	−0.0223679	−	0.0129141i
$902$		0			0
$903$	4.20862	+	1.53181i	0.140054	+	0.0509756i
$904$		0			0
$905$	−10.6712	+	6.16100i	−0.354721	+	0.204799i
$906$		0			0
$907$	1.09175	+	0.916091i	0.0362511	+	0.0304183i	0.660733	−	0.750621i	$-0.270245\pi$
$907$	1.09175	+	0.916091i	0.0362511	+	0.0304183i	−0.624482	+	0.781039i	$0.714690\pi$
$908$		0			0
$909$	2.06117	−	11.6895i	0.0683646	−	0.387715i
$910$		0			0
$911$	−11.8293			−0.391923			−0.195961	−	0.980612i	$-0.562783\pi$
$911$	−11.8293			−0.391923			−0.195961	+	0.980612i	$0.562783\pi$
$912$		0			0
$913$	42.3667			1.40213
$914$		0			0
$915$	−0.353348	+	2.00394i	−0.0116813	+	0.0662481i
$916$		0			0
$917$	9.81254	+	8.23370i	0.324039	+	0.271901i
$918$		0			0
$919$	−30.0437	+	17.3457i	−0.991050	+	0.572183i	−0.905588	−	0.424158i	$-0.860570\pi$
$919$	−30.0437	+	17.3457i	−0.991050	+	0.572183i	−0.0854623	+	0.996341i	$0.527237\pi$
$920$		0			0
$921$	1.77320	+	0.645392i	0.0584289	+	0.0212664i
$922$		0			0
$923$	4.96239	+	2.86504i	0.163339	+	0.0943039i
$924$		0			0
$925$	−7.01108	+	1.23624i	−0.230523	+	0.0406474i
$926$		0			0
$927$	−10.9607	+	9.19711i	−0.359996	+	0.302073i
$928$		0			0
$929$	−43.3207	+	15.7675i	−1.42131	+	0.517314i	−0.934427	−	0.356155i	$-0.884087\pi$
$929$	−43.3207	+	15.7675i	−1.42131	+	0.517314i	−0.486880	+	0.873469i	$0.661865\pi$
$930$		0			0
$931$	−21.0266	+	17.7298i	−0.689119	+	0.581069i
$932$		0			0
$933$	−4.27680	−	11.7504i	−0.140016	−	0.384691i
$934$		0			0
$935$	0.334181	+	0.398262i	0.0109289	+	0.0130246i
$936$		0			0
$937$	4.67731	+	26.5264i	0.152801	+	0.866579i	0.960769	+	0.277351i	$0.0894566\pi$
$937$	4.67731	+	26.5264i	0.152801	+	0.866579i	−0.807967	+	0.589227i	$0.799432\pi$
$938$		0			0
$939$	6.16222	−	10.6733i	0.201096	−	0.348309i
$940$		0			0
$941$	−10.0301	+	27.5574i	−0.326971	+	0.898347i	0.661902	+	0.749590i	$0.269749\pi$
$941$	−10.0301	+	27.5574i	−0.326971	+	0.898347i	−0.988874	+	0.148757i	$0.952473\pi$
$942$		0			0
$943$	5.45664	+	9.45118i	0.177693	+	0.307773i
$944$		0			0
$945$	−3.07926	+	3.66972i	−0.100168	+	0.119376i
$946$		0			0
$947$	15.6596	+	2.76122i	0.508870	+	0.0897275i	0.422188	−	0.906508i	$-0.361262\pi$
$947$	15.6596	+	2.76122i	0.508870	+	0.0897275i	0.0866825	+	0.996236i	$0.472373\pi$
$948$		0			0
$949$			1.99614i			0.0647974i
$950$		0			0
$951$		−	14.8932i		−	0.482944i
$952$		0			0
$953$	35.8197	+	6.31597i	1.16031	+	0.204594i	0.720474	−	0.693482i	$-0.243924\pi$
$953$	35.8197	+	6.31597i	1.16031	+	0.204594i	0.439839	+	0.898077i	$0.355035\pi$
$954$		0			0
$955$	4.29199	−	5.11499i	0.138886	−	0.165517i
$956$		0			0
$957$	2.47864	+	4.29313i	0.0801230	+	0.138777i
$958$		0			0
$959$	20.5837	−	56.5533i	0.664683	−	1.82620i
$960$		0			0
$961$	13.8063	−	23.9133i	0.445365	−	0.771395i
$962$		0			0
$963$	−2.52948	−	14.3454i	−0.0815115	−	0.462275i
$964$		0			0
$965$	13.5247	+	16.1181i	0.435374	+	0.518859i
$966$		0			0
$967$	−1.44186	−	3.96146i	−0.0463669	−	0.127392i	0.914348	−	0.404930i	$-0.132704\pi$
$967$	−1.44186	−	3.96146i	−0.0463669	−	0.127392i	−0.960715	+	0.277537i	$0.910482\pi$
$968$		0			0
$969$	−0.123054	+	0.707823i	−0.00395306	+	0.0227385i
$970$		0			0
$971$	2.15280	−	0.783553i	0.0690865	−	0.0251454i	−0.307246	−	0.951630i	$-0.599407\pi$
$971$	2.15280	−	0.783553i	0.0690865	−	0.0251454i	0.376332	+	0.926485i	$0.377185\pi$
$972$		0			0
$973$	−57.1014	+	47.9138i	−1.83059	+	1.53605i
$974$		0			0
$975$	−3.33666	+	0.588343i	−0.106859	+	0.0188421i
$976$		0			0
$977$	38.2545	+	22.0862i	1.22387	+	0.706601i	0.965740	−	0.259510i	$-0.0835610\pi$
$977$	38.2545	+	22.0862i	1.22387	+	0.706601i	0.258128	+	0.966111i	$0.416894\pi$
$978$		0			0
$979$	38.8630	+	14.1450i	1.24207	+	0.452076i
$980$		0			0
$981$	6.29065	−	3.63191i	0.200845	−	0.115958i
$982$		0			0
$983$	−27.7921	−	23.3204i	−0.886431	−	0.743804i	0.0810602	−	0.996709i	$-0.474169\pi$
$983$	−27.7921	−	23.3204i	−0.886431	−	0.743804i	−0.967491	+	0.252905i	$0.918614\pi$
$984$		0			0
$985$	−4.13766	+	23.4658i	−0.131837	+	0.747683i
$986$		0			0
$987$	0.989928			0.0315098
$988$		0			0
$989$	2.96058			0.0941410
$990$		0			0
$991$	−0.945387	+	5.36155i	−0.0300312	+	0.170315i	−0.996135	−	0.0878401i	$-0.972004\pi$
$991$	−0.945387	+	5.36155i	−0.0300312	+	0.170315i	0.966103	+	0.258155i	$0.0831147\pi$
$992$		0			0
$993$	17.3072	+	14.5225i	0.549229	+	0.460858i
$994$		0			0
$995$	−11.8480	+	6.84045i	−0.375607	+	0.216857i
$996$		0			0
$997$	−20.4426	−	7.44049i	−0.647423	−	0.235643i	−0.00262601	−	0.999997i	$-0.500836\pi$
$997$	−20.4426	−	7.44049i	−0.647423	−	0.235643i	−0.644797	+	0.764354i	$0.723058\pi$
$998$		0			0
$999$	−1.88211	−	1.08664i	−0.0595474	−	0.0343797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.h.223.3	yes	24
4.3	odd	2		912.2.ci.g.223.3	✓	24
19.15	odd	18		912.2.ci.g.319.3	yes	24
76.15	even	18	inner	912.2.ci.h.319.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.g.223.3	✓	24	4.3	odd	2
912.2.ci.g.319.3	yes	24	19.15	odd	18
912.2.ci.h.223.3	yes	24	1.1	even	1	trivial
912.2.ci.h.319.3	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)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{3} +(1.00588 + 0.844034i) q^{5} +(-3.15949 + 1.82413i) q^{7} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{3} +(1.00588 + 0.844034i) q^{5} +(-3.15949 + 1.82413i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(-2.08036 - 1.20110i) q^{11} +(-1.01858 + 0.179602i) q^{13} +(-1.00588 + 0.844034i) q^{15} +(-0.154881 + 0.0563722i) q^{17} +(-4.09960 - 1.48098i) q^{19} +(-1.24778 - 3.42825i) q^{21} +(-1.55016 - 1.84741i) q^{23} +(-0.568839 - 3.22604i) q^{25} +(0.500000 - 0.866025i) q^{27} +(-0.705807 + 1.93919i) q^{29} +(0.920238 + 1.59390i) q^{31} +(1.54410 - 1.84019i) q^{33} +(-4.71770 - 0.831857i) q^{35} -2.17328i q^{37} -1.03429i q^{39} +(-4.45654 - 0.785809i) q^{41} +(-0.789107 + 0.940421i) q^{43} +(-0.656542 - 1.13716i) q^{45} +(-0.0928046 + 0.254978i) q^{47} +(3.15491 - 5.46446i) q^{49} +(-0.0286209 - 0.162317i) q^{51} +(3.02351 + 3.60327i) q^{53} +(-1.07883 - 2.96406i) q^{55} +(2.17037 - 3.78015i) q^{57} +(-7.95309 + 2.89469i) q^{59} +(1.18712 - 0.996111i) q^{61} +(3.59284 - 0.633514i) q^{63} +(-1.17616 - 0.679054i) q^{65} +(3.43709 + 1.25100i) q^{67} +(2.08852 - 1.20581i) q^{69} +(-4.24397 - 3.56112i) q^{71} +(0.335135 - 1.90064i) q^{73} +3.27581 q^{75} +8.76385 q^{77} +(-1.63524 + 9.27388i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-15.2738 + 8.81832i) q^{83} +(-0.203372 - 0.0740214i) q^{85} +(-1.78717 - 1.03182i) q^{87} +(-16.9548 + 2.98959i) q^{89} +(2.89056 - 2.42547i) q^{91} +(-1.72948 + 0.629480i) q^{93} +(-2.87371 - 4.94989i) q^{95} +(-5.59171 - 15.3631i) q^{97} +(1.54410 + 1.84019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 9 q^{7}+O(q^{10}) \) 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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