LMFDB - Embedded newform 912.3.be.j.145.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (of order $6$, degree $2$, not 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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 154 x^{18} - 24 x^{17} + 16374 x^{16} - 4328 x^{15} + 911836 x^{14} - 590088 x^{13} + \cdots + 338560000 $ x^20 + 154x^18 - 24x^17 + 16374x^16 - 4328x^15 + 911836x^14 - 590088x^13 + 36808708x^12 - 29040960x^11 + 727387008x^10 - 1003792064x^9 + 10261479936x^8 - 7069668864x^7 + 36940887936x^6 + 52280031232x^5 + 60574204416x^4 + 32700144640x^3 + 13448832000x^2 + 2490624000x + 338560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.10
Root			$-4.18952 + 7.25646i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.j.673.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(4.18952 + 7.25646i) q^{5} +2.67523 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(4.18952 + 7.25646i) q^{5} +2.67523 q^{7} +(1.50000 - 2.59808i) q^{9} -16.7894 q^{11} +(10.0179 + 5.78383i) q^{13} +(12.5686 + 7.25646i) q^{15} +(2.60292 + 4.50840i) q^{17} +(14.2349 + 12.5845i) q^{19} +(4.01285 - 2.31682i) q^{21} +(12.3543 - 21.3982i) q^{23} +(-22.6041 + 39.1515i) q^{25} -5.19615i q^{27} +(10.3477 + 5.97425i) q^{29} +11.2261i q^{31} +(-25.1841 + 14.5401i) q^{33} +(11.2079 + 19.4127i) q^{35} +60.7679i q^{37} +20.0358 q^{39} +(13.2346 - 7.64100i) q^{41} +(19.0534 + 33.0014i) q^{43} +25.1371 q^{45} +(14.8287 - 25.6841i) q^{47} -41.8431 q^{49} +(7.80877 + 4.50840i) q^{51} +(-36.6683 - 21.1704i) q^{53} +(-70.3397 - 121.832i) q^{55} +(32.2508 + 6.54893i) q^{57} +(-70.8038 + 40.8786i) q^{59} +(-31.8226 + 55.1183i) q^{61} +(4.01285 - 6.95046i) q^{63} +96.9259i q^{65} +(-104.474 - 60.3180i) q^{67} -42.7965i q^{69} +(68.0842 - 39.3084i) q^{71} +(47.7622 + 82.7266i) q^{73} +78.3031i q^{75} -44.9157 q^{77} +(-28.2850 + 16.3303i) q^{79} +(-4.50000 - 7.79423i) q^{81} +136.491 q^{83} +(-21.8100 + 37.7760i) q^{85} +20.6954 q^{87} +(-28.6223 - 16.5251i) q^{89} +(26.8002 + 15.4731i) q^{91} +(9.72211 + 16.8392i) q^{93} +(-31.6814 + 156.018i) q^{95} +(127.283 - 73.4869i) q^{97} +(-25.1841 + 43.6202i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	4.18952	+	7.25646i	0.837904	+	1.45129i	0.891644	+	0.452737i	$0.149552\pi$
$5$	4.18952	+	7.25646i	0.837904	+	1.45129i	−0.0537402	+	0.998555i	$0.517114\pi$
$6$		0			0
$7$	2.67523			0.382176			0.191088	−	0.981573i	$-0.438798\pi$
$7$	2.67523			0.382176			0.191088	+	0.981573i	$0.438798\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−16.7894			−1.52631			−0.763156	−	0.646214i	$-0.776351\pi$
$11$	−16.7894			−1.52631			−0.763156	+	0.646214i	$0.776351\pi$
$12$		0			0
$13$	10.0179	+	5.78383i	0.770607	+	0.444910i	0.833091	−	0.553136i	$-0.186569\pi$
$13$	10.0179	+	5.78383i	0.770607	+	0.444910i	−0.0624843	+	0.998046i	$0.519902\pi$
$14$		0			0
$15$	12.5686	+	7.25646i	0.837904	+	0.483764i
$16$		0			0
$17$	2.60292	+	4.50840i	0.153113	+	0.265200i	0.932370	−	0.361504i	$-0.117737\pi$
$17$	2.60292	+	4.50840i	0.153113	+	0.265200i	−0.779257	+	0.626704i	$0.784403\pi$
$18$		0			0
$19$	14.2349	+	12.5845i	0.749203	+	0.662340i
$19$	14.2349	+	12.5845i	0.749203	+	0.662340i
$20$		0			0
$21$	4.01285	−	2.31682i	0.191088	−	0.110325i
$22$		0			0
$23$	12.3543	−	21.3982i	0.537143	−	0.930359i	−0.461913	−	0.886925i	$-0.652837\pi$
$23$	12.3543	−	21.3982i	0.537143	−	0.930359i	0.999056	−	0.0434337i	$-0.0138297\pi$
$24$		0			0
$25$	−22.6041	+	39.1515i	−0.904166	+	1.56606i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	10.3477	+	5.97425i	0.356817	+	0.206009i	0.667684	−	0.744445i	$-0.267286\pi$
$29$	10.3477	+	5.97425i	0.356817	+	0.206009i	−0.310866	+	0.950454i	$0.600619\pi$
$30$		0			0
$31$			11.2261i			0.362133i	0.983471	+	0.181066i	$0.0579549\pi$
$31$			11.2261i			0.362133i	−0.983471	+	0.181066i	$0.942045\pi$
$32$		0			0
$33$	−25.1841	+	14.5401i	−0.763156	+	0.440608i
$34$		0			0
$35$	11.2079	+	19.4127i	0.320227	+	0.554649i
$36$		0			0
$37$			60.7679i			1.64238i	0.570658	+	0.821188i	$0.306688\pi$
$37$			60.7679i			1.64238i	−0.570658	+	0.821188i	$0.693312\pi$
$38$		0			0
$39$	20.0358			0.513738
$40$		0			0
$41$	13.2346	−	7.64100i	0.322795	−	0.186366i	−0.329843	−	0.944036i	$-0.606996\pi$
$41$	13.2346	−	7.64100i	0.322795	−	0.186366i	0.652638	+	0.757670i	$0.273662\pi$
$42$		0			0
$43$	19.0534	+	33.0014i	0.443102	+	0.767475i	0.997918	−	0.0644980i	$-0.0205446\pi$
$43$	19.0534	+	33.0014i	0.443102	+	0.767475i	−0.554816	+	0.831973i	$0.687211\pi$
$44$		0			0
$45$	25.1371			0.558603
$46$		0			0
$47$	14.8287	−	25.6841i	0.315504	−	0.546470i	−0.664040	−	0.747697i	$-0.731160\pi$
$47$	14.8287	−	25.6841i	0.315504	−	0.546470i	0.979545	+	0.201227i	$0.0644930\pi$
$48$		0			0
$49$	−41.8431			−0.853941
$50$		0			0
$51$	7.80877	+	4.50840i	0.153113	+	0.0883999i
$52$		0			0
$53$	−36.6683	−	21.1704i	−0.691854	−	0.399442i	0.112452	−	0.993657i	$-0.464130\pi$
$53$	−36.6683	−	21.1704i	−0.691854	−	0.399442i	−0.804306	+	0.594215i	$0.797463\pi$
$54$		0			0
$55$	−70.3397	−	121.832i	−1.27890	−	2.21512i
$56$		0			0
$57$	32.2508	+	6.54893i	0.565803	+	0.114894i
$58$		0			0
$59$	−70.8038	+	40.8786i	−1.20007	+	0.692858i	−0.960570	−	0.278039i	$-0.910315\pi$
$59$	−70.8038	+	40.8786i	−1.20007	+	0.692858i	−0.239496	+	0.970897i	$0.576982\pi$
$60$		0			0
$61$	−31.8226	+	55.1183i	−0.521681	+	0.903579i	0.478001	+	0.878359i	$0.341362\pi$
$61$	−31.8226	+	55.1183i	−0.521681	+	0.903579i	−0.999682	+	0.0252190i	$0.991972\pi$
$62$		0			0
$63$	4.01285	−	6.95046i	0.0636961	−	0.110325i
$64$		0			0
$65$			96.9259i			1.49117i
$66$		0			0
$67$	−104.474	−	60.3180i	−1.55931	−	0.900269i	−0.997323	−	0.0731235i	$-0.976703\pi$
$67$	−104.474	−	60.3180i	−1.55931	−	0.900269i	−0.561988	−	0.827145i	$-0.689963\pi$
$68$		0			0
$69$		−	42.7965i		−	0.620239i
$70$		0			0
$71$	68.0842	−	39.3084i	0.958933	−	0.553640i	0.0630884	−	0.998008i	$-0.479905\pi$
$71$	68.0842	−	39.3084i	0.958933	−	0.553640i	0.895844	+	0.444368i	$0.146572\pi$
$72$		0			0
$73$	47.7622	+	82.7266i	0.654277	+	1.13324i	0.982074	+	0.188493i	$0.0603604\pi$
$73$	47.7622	+	82.7266i	0.654277	+	1.13324i	−0.327797	+	0.944748i	$0.606306\pi$
$74$		0			0
$75$			78.3031i			1.04404i
$76$		0			0
$77$	−44.9157			−0.583320
$78$		0			0
$79$	−28.2850	+	16.3303i	−0.358038	+	0.206713i	−0.668220	−	0.743964i	$-0.732943\pi$
$79$	−28.2850	+	16.3303i	−0.358038	+	0.206713i	0.310182	+	0.950677i	$0.399610\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	136.491			1.64447			0.822235	−	0.569148i	$-0.192727\pi$
$83$	136.491			1.64447			0.822235	+	0.569148i	$0.192727\pi$
$84$		0			0
$85$	−21.8100	+	37.7760i	−0.256588	+	0.444424i
$86$		0			0
$87$	20.6954			0.237878
$88$		0			0
$89$	−28.6223	−	16.5251i	−0.321599	−	0.185675i	0.330506	−	0.943804i	$-0.392781\pi$
$89$	−28.6223	−	16.5251i	−0.321599	−	0.185675i	−0.652105	+	0.758129i	$0.726114\pi$
$90$		0			0
$91$	26.8002	+	15.4731i	0.294508	+	0.170034i
$92$		0			0
$93$	9.72211	+	16.8392i	0.104539	+	0.181066i
$94$		0			0
$95$	−31.6814	+	156.018i	−0.333488	+	1.64229i
$96$		0			0
$97$	127.283	−	73.4869i	1.31220	−	0.757597i	0.329737	−	0.944073i	$-0.393040\pi$
$97$	127.283	−	73.4869i	1.31220	−	0.757597i	0.982460	+	0.186475i	$0.0597065\pi$
$98$		0			0
$99$	−25.1841	+	43.6202i	−0.254385	+	0.440608i
$100$		0			0
$101$	60.8850	−	105.456i	0.602822	−	1.04412i	−0.389570	−	0.920997i	$-0.627376\pi$
$101$	60.8850	−	105.456i	0.602822	−	1.04412i	0.992392	−	0.123121i	$-0.0392903\pi$
$102$		0			0
$103$			130.299i			1.26504i	0.774543	+	0.632522i	$0.217980\pi$
$103$			130.299i			1.26504i	−0.774543	+	0.632522i	$0.782020\pi$
$104$		0			0
$105$	33.6238	+	19.4127i	0.320227	+	0.184883i
$106$		0			0
$107$			85.4806i			0.798884i	0.916758	+	0.399442i	$0.130796\pi$
$107$			85.4806i			0.798884i	−0.916758	+	0.399442i	$0.869204\pi$
$108$		0			0
$109$	−6.51725	+	3.76273i	−0.0597913	+	0.0345205i	−0.529598	−	0.848249i	$-0.677657\pi$
$109$	−6.51725	+	3.76273i	−0.0597913	+	0.0345205i	0.469806	+	0.882769i	$0.344324\pi$
$110$		0			0
$111$	52.6265	+	91.1518i	0.474113	+	0.821188i
$112$		0			0
$113$		−	50.3166i		−	0.445280i	−0.974901	−	0.222640i	$-0.928533\pi$
$113$		−	50.3166i		−	0.445280i	0.974901	−	0.222640i	$-0.0714674\pi$
$114$		0			0
$115$	207.034			1.80030
$116$		0			0
$117$	30.0537	−	17.3515i	0.256869	−	0.148303i
$118$		0			0
$119$	6.96343	+	12.0610i	0.0585162	+	0.101353i
$120$		0			0
$121$	160.885			1.32963
$122$		0			0
$123$	13.2346	−	22.9230i	0.107598	−	0.186366i
$124$		0			0
$125$	−169.326			−1.35461
$126$		0			0
$127$	−16.9736	−	9.79973i	−0.133651	−	0.0771632i	0.431684	−	0.902025i	$-0.357920\pi$
$127$	−16.9736	−	9.79973i	−0.133651	−	0.0771632i	−0.565335	+	0.824862i	$0.691253\pi$
$128$		0			0
$129$	57.1602	+	33.0014i	0.443102	+	0.255825i
$130$		0			0
$131$	12.1619	+	21.0651i	0.0928392	+	0.160802i	0.908705	−	0.417439i	$-0.137072\pi$
$131$	12.1619	+	21.0651i	0.0928392	+	0.160802i	−0.815866	+	0.578242i	$0.803739\pi$
$132$		0			0
$133$	38.0816	+	33.6664i	0.286328	+	0.253131i
$134$		0			0
$135$	37.7057	−	21.7694i	0.279301	−	0.161255i
$136$		0			0
$137$	87.9169	−	152.277i	0.641729	−	1.11151i	−0.343317	−	0.939219i	$-0.611551\pi$
$137$	87.9169	−	152.277i	0.641729	−	1.11151i	0.985047	−	0.172288i	$-0.0551160\pi$
$138$		0			0
$139$	−1.58900	+	2.75223i	−0.0114317	+	0.0198002i	−0.871685	−	0.490067i	$-0.836972\pi$
$139$	−1.58900	+	2.75223i	−0.0114317	+	0.0198002i	0.860253	+	0.509867i	$0.170306\pi$
$140$		0			0
$141$		−	51.3681i		−	0.364313i
$142$		0			0
$143$	−168.195	−	97.1072i	−1.17619	−	0.679071i
$144$		0			0
$145$			100.117i			0.690462i
$146$		0			0
$147$	−62.7647	+	36.2372i	−0.426971	+	0.246512i
$148$		0			0
$149$	−58.8295	−	101.896i	−0.394829	−	0.683864i	0.598251	−	0.801309i	$-0.295863\pi$
$149$	−58.8295	−	101.896i	−0.394829	−	0.683864i	−0.993079	+	0.117446i	$0.962529\pi$
$150$		0			0
$151$		−	40.4287i		−	0.267740i	−0.990999	−	0.133870i	$-0.957260\pi$
$151$		−	40.4287i		−	0.267740i	0.990999	−	0.133870i	$-0.0427404\pi$
$152$		0			0
$153$	15.6175			0.102075
$154$		0			0
$155$	−81.4619	+	47.0321i	−0.525561	+	0.303433i
$156$		0			0
$157$	103.387	+	179.071i	0.658513	+	1.14058i	0.981001	+	0.194004i	$0.0621475\pi$
$157$	103.387	+	179.071i	0.658513	+	1.14058i	−0.322488	+	0.946574i	$0.604519\pi$
$158$		0			0
$159$	−73.3366			−0.461236
$160$		0			0
$161$	33.0506	−	57.2453i	0.205283	−	0.355561i
$162$		0			0
$163$	213.188			1.30790			0.653952	−	0.756536i	$-0.273110\pi$
$163$	213.188			1.30790			0.653952	+	0.756536i	$0.273110\pi$
$164$		0			0
$165$	−211.019	−	121.832i	−1.27890	−	0.738375i
$166$		0			0
$167$	−109.344	−	63.1297i	−0.654754	−	0.378022i	0.135521	−	0.990774i	$-0.456729\pi$
$167$	−109.344	−	63.1297i	−0.654754	−	0.378022i	−0.790275	+	0.612752i	$0.790062\pi$
$168$		0			0
$169$	−17.5946	−	30.4748i	−0.104110	−	0.180324i
$170$		0			0
$171$	54.0477	−	18.1066i	0.316068	−	0.105886i
$172$		0			0
$173$	267.564	−	154.478i	1.54661	−	0.892936i	0.548213	−	0.836339i	$-0.315308\pi$
$173$	267.564	−	154.478i	1.54661	−	0.892936i	0.998397	−	0.0565972i	$-0.0180251\pi$
$174$		0			0
$175$	−60.4714	+	104.740i	−0.345551	+	0.598511i
$176$		0			0
$177$	−70.8038	+	122.636i	−0.400022	+	0.692858i
$178$		0			0
$179$		−	25.9904i		−	0.145198i	−0.997361	−	0.0725990i	$-0.976871\pi$
$179$		−	25.9904i		−	0.145198i	0.997361	−	0.0725990i	$-0.0231293\pi$
$180$		0			0
$181$	−13.4370	−	7.75784i	−0.0742374	−	0.0428610i	0.462422	−	0.886660i	$-0.346981\pi$
$181$	−13.4370	−	7.75784i	−0.0742374	−	0.0428610i	−0.536659	+	0.843799i	$0.680314\pi$
$182$		0			0
$183$			110.237i			0.602386i
$184$		0			0
$185$	−440.960	+	254.588i	−2.38357	+	1.37615i
$186$		0			0
$187$	−43.7016	−	75.6934i	−0.233698	−	0.404778i
$188$		0			0
$189$		−	13.9009i		−	0.0735499i
$190$		0			0
$191$	−278.674			−1.45903			−0.729513	−	0.683967i	$-0.760253\pi$
$191$	−278.674			−1.45903			−0.729513	+	0.683967i	$0.760253\pi$
$192$		0			0
$193$	285.840	−	165.030i	1.48104	−	0.855077i	0.481269	−	0.876573i	$-0.340176\pi$
$193$	285.840	−	165.030i	1.48104	−	0.855077i	0.999769	+	0.0214956i	$0.00684280\pi$
$194$		0			0
$195$	83.9403	+	145.389i	0.430463	+	0.745584i
$196$		0			0
$197$	8.44862			0.0428864			0.0214432	−	0.999770i	$-0.493174\pi$
$197$	8.44862			0.0428864			0.0214432	+	0.999770i	$0.493174\pi$
$198$		0			0
$199$	97.5691	−	168.995i	0.490297	−	0.849219i	−0.509641	−	0.860387i	$-0.670222\pi$
$199$	97.5691	−	168.995i	0.490297	−	0.849219i	0.999938	+	0.0111681i	$0.00355499\pi$
$200$		0			0
$201$	−208.948			−1.03954
$202$		0			0
$203$	27.6825	+	15.9825i	0.136367	+	0.0787316i
$204$		0			0
$205$	110.893	+	64.0243i	0.540943	+	0.312313i
$206$		0			0
$207$	−37.0629	−	64.1947i	−0.179048	−	0.310120i
$208$		0			0
$209$	−238.995	−	211.286i	−1.14352	−	1.01094i
$210$		0			0
$211$	−70.6932	+	40.8147i	−0.335039	+	0.193435i	−0.658076	−	0.752952i	$-0.728629\pi$
$211$	−70.6932	+	40.8147i	−0.335039	+	0.193435i	0.323037	+	0.946386i	$0.395296\pi$
$212$		0			0
$213$	68.0842	−	117.925i	0.319644	−	0.553640i
$214$		0			0
$215$	−159.649	+	276.520i	−0.742554	+	1.28614i
$216$		0			0
$217$			30.0325i			0.138399i
$218$		0			0
$219$	143.287	+	82.7266i	0.654277	+	0.377747i
$220$		0			0
$221$			60.2195i			0.272486i
$222$		0			0
$223$	81.2933	−	46.9347i	0.364544	−	0.210470i	−0.306528	−	0.951862i	$-0.599167\pi$
$223$	81.2933	−	46.9347i	0.364544	−	0.210470i	0.671072	+	0.741392i	$0.265834\pi$
$224$		0			0
$225$	67.8124	+	117.455i	0.301389	+	0.522020i
$226$		0			0
$227$		−	299.833i		−	1.32085i	−0.750893	−	0.660424i	$-0.770377\pi$
$227$		−	299.833i		−	1.32085i	0.750893	−	0.660424i	$-0.229623\pi$
$228$		0			0
$229$	−292.402			−1.27686			−0.638431	−	0.769679i	$-0.720416\pi$
$229$	−292.402			−1.27686			−0.638431	+	0.769679i	$0.720416\pi$
$230$		0			0
$231$	−67.3735	+	38.8981i	−0.291660	+	0.168390i
$232$		0			0
$233$	189.443	+	328.125i	0.813061	+	1.40826i	0.910712	+	0.413042i	$0.135534\pi$
$233$	189.443	+	328.125i	0.813061	+	1.40826i	−0.0976510	+	0.995221i	$0.531133\pi$
$234$		0			0
$235$	248.501			1.05745
$236$		0			0
$237$	−28.2850	+	48.9910i	−0.119346	+	0.206713i
$238$		0			0
$239$	−369.077			−1.54425			−0.772127	−	0.635468i	$-0.780807\pi$
$239$	−369.077			−1.54425			−0.772127	+	0.635468i	$0.780807\pi$
$240$		0			0
$241$	−306.901	−	177.189i	−1.27345	−	0.735225i	−0.297812	−	0.954625i	$-0.596257\pi$
$241$	−306.901	−	177.189i	−1.27345	−	0.735225i	−0.975635	+	0.219400i	$0.929590\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−175.303	−	303.633i	−0.715521	−	1.23932i
$246$		0			0
$247$	69.8169	+	208.402i	0.282660	+	0.843732i
$248$		0			0
$249$	204.736	−	118.205i	0.822235	−	0.474718i
$250$		0			0
$251$	57.5998	−	99.7658i	0.229481	−	0.397473i	−0.728173	−	0.685393i	$-0.759630\pi$
$251$	57.5998	−	99.7658i	0.229481	−	0.397473i	0.957654	+	0.287920i	$0.0929637\pi$
$252$		0			0
$253$	−207.421	+	359.264i	−0.819848	+	1.42002i
$254$		0			0
$255$			75.5521i			0.296283i
$256$		0			0
$257$	−406.631	−	234.768i	−1.58222	−	0.913496i	−0.994535	−	0.104407i	$-0.966706\pi$
$257$	−406.631	−	234.768i	−1.58222	−	0.913496i	−0.587686	−	0.809089i	$-0.699961\pi$
$258$		0			0
$259$			162.568i			0.627677i
$260$		0			0
$261$	31.0431	−	17.9228i	0.118939	−	0.0686695i
$262$		0			0
$263$	−86.2453	−	149.381i	−0.327929	−	0.567989i	0.654172	−	0.756346i	$-0.273017\pi$
$263$	−86.2453	−	149.381i	−0.327929	−	0.567989i	−0.982101	+	0.188357i	$0.939684\pi$
$264$		0			0
$265$		−	354.776i		−	1.33878i
$266$		0			0
$267$	−57.2447			−0.214399
$268$		0			0
$269$	208.174	−	120.189i	0.773882	−	0.446801i	−0.0603759	−	0.998176i	$-0.519230\pi$
$269$	208.174	−	120.189i	0.773882	−	0.446801i	0.834258	+	0.551375i	$0.185897\pi$
$270$		0			0
$271$	−64.7533	−	112.156i	−0.238942	−	0.413860i	0.721469	−	0.692447i	$-0.243467\pi$
$271$	−64.7533	−	112.156i	−0.238942	−	0.413860i	−0.960411	+	0.278587i	$0.910134\pi$
$272$		0			0
$273$	53.6004			0.196338
$274$		0			0
$275$	379.511	−	657.332i	1.38004	−	2.39030i
$276$		0			0
$277$	510.049			1.84133			0.920667	−	0.390350i	$-0.127646\pi$
$277$	510.049			1.84133			0.920667	+	0.390350i	$0.127646\pi$
$278$		0			0
$279$	29.1663	+	16.8392i	0.104539	+	0.0603555i
$280$		0			0
$281$	291.238	+	168.146i	1.03643	+	0.598385i	0.918821	−	0.394675i	$-0.129143\pi$
$281$	291.238	+	168.146i	1.03643	+	0.598385i	0.117612	+	0.993060i	$0.462476\pi$
$282$		0			0
$283$	−195.534	−	338.674i	−0.690932	−	1.19673i	−0.971533	−	0.236904i	$-0.923867\pi$
$283$	−195.534	−	338.674i	−0.690932	−	1.19673i	0.280601	−	0.959824i	$-0.409466\pi$
$284$		0			0
$285$	87.5931	+	261.463i	0.307344	+	0.917415i
$286$		0			0
$287$	35.4057	−	20.4415i	0.123365	−	0.0712246i
$288$		0			0
$289$	130.950	−	226.811i	0.453113	−	0.784814i
$290$		0			0
$291$	127.283	−	220.461i	0.437399	−	0.757597i
$292$		0			0
$293$		−	372.208i		−	1.27034i	−0.772374	−	0.635168i	$-0.780931\pi$
$293$		−	372.208i		−	1.27034i	0.772374	−	0.635168i	$-0.219069\pi$
$294$		0			0
$295$	−593.268	−	342.524i	−2.01108	−	1.16110i
$296$		0			0
$297$			87.2405i			0.293739i
$298$		0			0
$299$	247.528	−	142.910i	0.827852	−	0.477960i
$300$		0			0
$301$	50.9723	+	88.2866i	0.169343	+	0.293311i
$302$		0			0
$303$		−	210.912i		−	0.696079i
$304$		0			0
$305$	−533.285			−1.74848
$306$		0			0
$307$	176.072	−	101.655i	0.573523	−	0.331124i	−0.185032	−	0.982732i	$-0.559239\pi$
$307$	176.072	−	101.655i	0.573523	−	0.331124i	0.758555	+	0.651609i	$0.225906\pi$
$308$		0			0
$309$	112.843	+	195.449i	0.365187	+	0.632522i
$310$		0			0
$311$	−84.4687			−0.271604			−0.135802	−	0.990736i	$-0.543361\pi$
$311$	−84.4687			−0.271604			−0.135802	+	0.990736i	$0.543361\pi$
$312$		0			0
$313$	−129.424	+	224.169i	−0.413495	+	0.716195i	−0.995269	−	0.0971556i	$-0.969026\pi$
$313$	−129.424	+	224.169i	−0.413495	+	0.716195i	0.581774	+	0.813351i	$0.302359\pi$
$314$		0			0
$315$	67.2477			0.213485
$316$		0			0
$317$	88.9743	+	51.3693i	0.280676	+	0.162048i	0.633729	−	0.773555i	$-0.281523\pi$
$317$	88.9743	+	51.3693i	0.280676	+	0.162048i	−0.353053	+	0.935603i	$0.614857\pi$
$318$		0			0
$319$	−173.732	−	100.304i	−0.544615	−	0.314433i
$320$		0			0
$321$	74.0284	+	128.221i	0.230618	+	0.399442i
$322$		0			0
$323$	−19.6835	+	96.9328i	−0.0609395	+	0.300102i
$324$		0			0
$325$	−452.892	+	261.477i	−1.39351	+	0.804545i
$326$		0			0
$327$	−6.51725	+	11.2882i	−0.0199304	+	0.0345205i
$328$		0			0
$329$	39.6703	−	68.7109i	0.120578	−	0.208848i
$330$		0			0
$331$			187.032i			0.565050i	0.959260	+	0.282525i	$0.0911720\pi$
$331$			187.032i			0.565050i	−0.959260	+	0.282525i	$0.908828\pi$
$332$		0			0
$333$	157.880	+	91.1518i	0.474113	+	0.273729i
$334$		0			0
$335$		−	1010.81i		−	3.01735i
$336$		0			0
$337$	466.421	−	269.288i	1.38404	−	0.799075i	0.391404	−	0.920219i	$-0.371990\pi$
$337$	466.421	−	269.288i	1.38404	−	0.799075i	0.992635	+	0.121144i	$0.0386563\pi$
$338$		0			0
$339$	−43.5754	−	75.4749i	−0.128541	−	0.222640i
$340$		0			0
$341$		−	188.480i		−	0.552728i
$342$		0			0
$343$	−243.027			−0.708532
$344$		0			0
$345$	310.551	−	179.297i	0.900148	−	0.519701i
$346$		0			0
$347$	289.401	+	501.257i	0.834008	+	1.44454i	0.894835	+	0.446396i	$0.147293\pi$
$347$	289.401	+	501.257i	0.834008	+	1.44454i	−0.0608270	+	0.998148i	$0.519374\pi$
$348$		0			0
$349$	−328.533			−0.941356			−0.470678	−	0.882305i	$-0.655991\pi$
$349$	−328.533			−0.941356			−0.470678	+	0.882305i	$0.655991\pi$
$350$		0			0
$351$	30.0537	−	52.0545i	0.0856230	−	0.148303i
$352$		0			0
$353$	112.834			0.319643			0.159821	−	0.987146i	$-0.448908\pi$
$353$	112.834			0.319643			0.159821	+	0.987146i	$0.448908\pi$
$354$		0			0
$355$	570.480	+	329.367i	1.60699	+	0.927794i
$356$		0			0
$357$	20.8903	+	12.0610i	0.0585162	+	0.0337844i
$358$		0			0
$359$	263.085	+	455.677i	0.732828	+	1.26930i	0.955670	+	0.294441i	$0.0951335\pi$
$359$	263.085	+	455.677i	0.732828	+	1.26930i	−0.222841	+	0.974855i	$0.571533\pi$
$360$		0			0
$361$	44.2628	+	358.276i	0.122612	+	0.992455i
$362$		0			0
$363$	241.328	−	139.331i	0.664814	−	0.383831i
$364$		0			0
$365$	−400.202	+	693.170i	−1.09644	+	1.89909i
$366$		0			0
$367$	66.3917	−	114.994i	0.180904	−	0.313335i	−0.761285	−	0.648418i	$-0.775431\pi$
$367$	66.3917	−	114.994i	0.180904	−	0.313335i	0.942189	+	0.335083i	$0.108764\pi$
$368$		0			0
$369$		−	45.8460i		−	0.124244i
$370$		0			0
$371$	−98.0962	−	56.6359i	−0.264410	−	0.152657i
$372$		0			0
$373$		−	177.320i		−	0.475388i	−0.971340	−	0.237694i	$-0.923608\pi$
$373$		−	177.320i		−	0.475388i	0.971340	−	0.237694i	$-0.0763916\pi$
$374$		0			0
$375$	−253.989	+	146.641i	−0.677304	+	0.391042i
$376$		0			0
$377$	69.1081	+	119.699i	0.183311	+	0.317503i
$378$		0			0
$379$		−	245.954i		−	0.648954i	−0.945894	−	0.324477i	$-0.894812\pi$
$379$		−	245.954i		−	0.648954i	0.945894	−	0.324477i	$-0.105188\pi$
$380$		0			0
$381$	−33.9473			−0.0891004
$382$		0			0
$383$	8.52634	−	4.92269i	0.0222620	−	0.0128530i	−0.488828	−	0.872380i	$-0.662575\pi$
$383$	8.52634	−	4.92269i	0.0222620	−	0.0128530i	0.511090	+	0.859527i	$0.329242\pi$
$384$		0			0
$385$	−188.175	−	325.929i	−0.488766	−	0.846568i
$386$		0			0
$387$	114.320			0.295401
$388$		0			0
$389$	240.203	−	416.044i	0.617489	−	1.06952i	−0.372454	−	0.928051i	$-0.621483\pi$
$389$	240.203	−	416.044i	0.617489	−	1.06952i	0.989942	−	0.141471i	$-0.0451833\pi$
$390$		0			0
$391$	128.629			0.328975
$392$		0			0
$393$	36.4858	+	21.0651i	0.0928392	+	0.0536008i
$394$		0			0
$395$	−237.001	−	136.833i	−0.600002	−	0.346412i
$396$		0			0
$397$	−163.750	−	283.623i	−0.412468	−	0.714416i	0.582691	−	0.812694i	$-0.302000\pi$
$397$	−163.750	−	283.623i	−0.412468	−	0.714416i	−0.995159	+	0.0982782i	$0.968666\pi$
$398$		0			0
$399$	86.2783	+	17.5199i	0.216236	+	0.0439096i
$400$		0			0
$401$	−125.430	+	72.4171i	−0.312793	+	0.180591i	−0.648176	−	0.761491i	$-0.724468\pi$
$401$	−125.430	+	72.4171i	−0.312793	+	0.180591i	0.335383	+	0.942082i	$0.391134\pi$
$402$		0			0
$403$	−64.9300	+	112.462i	−0.161117	+	0.279062i
$404$		0			0
$405$	37.7057	−	65.3081i	0.0931004	−	0.161255i
$406$		0			0
$407$		−	1020.26i		−	2.50678i
$408$		0			0
$409$	−131.772	−	76.0788i	−0.322182	−	0.186012i	0.330183	−	0.943917i	$-0.392890\pi$
$409$	−131.772	−	76.0788i	−0.322182	−	0.186012i	−0.652365	+	0.757905i	$0.726223\pi$
$410$		0			0
$411$		−	304.553i		−	0.741005i
$412$		0			0
$413$	−189.417	+	109.360i	−0.458637	+	0.264794i
$414$		0			0
$415$	571.832	+	990.441i	1.37791	+	2.38661i
$416$		0			0
$417$			5.50446i			0.0132001i
$418$		0			0
$419$	246.940			0.589357			0.294678	−	0.955597i	$-0.404788\pi$
$419$	246.940			0.589357			0.294678	+	0.955597i	$0.404788\pi$
$420$		0			0
$421$	425.167	−	245.470i	1.00990	−	0.583065i	0.0987360	−	0.995114i	$-0.468520\pi$
$421$	425.167	−	245.470i	1.00990	−	0.583065i	0.911162	+	0.412049i	$0.135187\pi$
$422$		0			0
$423$	−44.4861	−	77.0522i	−0.105168	−	0.182157i
$424$		0			0
$425$	−235.347			−0.553759
$426$		0			0
$427$	−85.1328	+	147.454i	−0.199374	+	0.345326i
$428$		0			0
$429$	−336.389			−0.784124
$430$		0			0
$431$	−571.862	−	330.164i	−1.32683	−	0.766043i	−0.342018	−	0.939693i	$-0.611110\pi$
$431$	−571.862	−	330.164i	−1.32683	−	0.766043i	−0.984807	+	0.173651i	$0.944444\pi$
$432$		0			0
$433$	−570.369	−	329.303i	−1.31725	−	0.760514i	−0.333964	−	0.942586i	$-0.608386\pi$
$433$	−570.369	−	329.303i	−1.31725	−	0.760514i	−0.983285	+	0.182072i	$0.941720\pi$
$434$		0			0
$435$	86.7038	+	150.175i	0.199319	+	0.345231i
$436$		0			0
$437$	445.147	−	149.129i	1.01864	−	0.341257i
$438$		0			0
$439$	−264.406	+	152.655i	−0.602292	+	0.347733i	−0.769943	−	0.638113i	$-0.779715\pi$
$439$	−264.406	+	152.655i	−0.602292	+	0.347733i	0.167651	+	0.985846i	$0.446382\pi$
$440$		0			0
$441$	−62.7647	+	108.712i	−0.142324	+	0.246512i
$442$		0			0
$443$	−53.5634	+	92.7746i	−0.120911	+	0.209423i	−0.920127	−	0.391620i	$-0.871915\pi$
$443$	−53.5634	+	92.7746i	−0.120911	+	0.209423i	0.799216	+	0.601043i	$0.205248\pi$
$444$		0			0
$445$		−	276.929i		−	0.622312i
$446$		0			0
$447$	−176.488	−	101.896i	−0.394829	−	0.227955i
$448$		0			0
$449$			421.623i			0.939028i	0.882925	+	0.469514i	$0.155571\pi$
$449$			421.623i			0.939028i	−0.882925	+	0.469514i	$0.844429\pi$
$450$		0			0
$451$	−222.201	+	128.288i	−0.492686	+	0.284453i
$452$		0			0
$453$	−35.0123	−	60.6430i	−0.0772898	−	0.133870i
$454$		0			0
$455$			259.299i			0.569889i
$456$		0			0
$457$	−259.424			−0.567668			−0.283834	−	0.958873i	$-0.591606\pi$
$457$	−259.424			−0.567668			−0.283834	+	0.958873i	$0.591606\pi$
$458$		0			0
$459$	23.4263	−	13.5252i	0.0510377	−	0.0294666i
$460$		0			0
$461$	−160.763	−	278.449i	−0.348726	−	0.604010i	0.637298	−	0.770618i	$-0.280052\pi$
$461$	−160.763	−	278.449i	−0.348726	−	0.604010i	−0.986023	+	0.166607i	$0.946719\pi$
$462$		0			0
$463$	219.754			0.474630			0.237315	−	0.971433i	$-0.423733\pi$
$463$	219.754			0.474630			0.237315	+	0.971433i	$0.423733\pi$
$464$		0			0
$465$	−81.4619	+	141.096i	−0.175187	+	0.303433i
$466$		0			0
$467$	−779.164			−1.66845			−0.834223	−	0.551428i	$-0.814083\pi$
$467$	−779.164			−1.66845			−0.834223	+	0.551428i	$0.814083\pi$
$468$		0			0
$469$	−279.492	−	161.365i	−0.595932	−	0.344061i
$470$		0			0
$471$	310.160	+	179.071i	0.658513	+	0.380193i
$472$		0			0
$473$	−319.896	−	554.075i	−0.676312	−	1.17141i
$474$		0			0
$475$	−814.468	+	272.856i	−1.71467	+	0.574433i
$476$		0			0
$477$	−110.005	+	63.5113i	−0.230618	+	0.133147i
$478$		0			0
$479$	−88.6156	+	153.487i	−0.185001	+	0.320431i	−0.943577	−	0.331153i	$-0.892562\pi$
$479$	−88.6156	+	153.487i	−0.185001	+	0.320431i	0.758576	+	0.651585i	$0.225896\pi$
$480$		0			0
$481$	−351.471	+	608.766i	−0.730709	+	1.26563i
$482$		0			0
$483$		−	114.491i		−	0.237041i
$484$		0			0
$485$	1066.51	+	615.750i	2.19899	+	1.26959i
$486$		0			0
$487$		−	720.050i		−	1.47854i	−0.673408	−	0.739271i	$-0.735170\pi$
$487$		−	720.050i		−	1.47854i	0.673408	−	0.739271i	$-0.264830\pi$
$488$		0			0
$489$	319.782	−	184.626i	0.653952	−	0.377559i
$490$		0			0
$491$	−85.9476	−	148.866i	−0.175046	−	0.303188i	0.765131	−	0.643874i	$-0.222674\pi$
$491$	−85.9476	−	148.866i	−0.175046	−	0.303188i	−0.940177	+	0.340686i	$0.889341\pi$
$492$		0			0
$493$			62.2021i			0.126171i
$494$		0			0
$495$	−422.038			−0.852602
$496$		0			0
$497$	182.141	−	105.159i	0.366481	−	0.211588i
$498$		0			0
$499$	493.386	+	854.569i	0.988749	+	1.71256i	0.623916	+	0.781491i	$0.285541\pi$
$499$	493.386	+	854.569i	0.988749	+	1.71256i	0.364833	+	0.931073i	$0.381126\pi$
$500$		0			0
$501$	−218.688			−0.436503
$502$		0			0
$503$	−54.5382	+	94.4629i	−0.108426	+	0.187799i	−0.915133	−	0.403153i	$-0.867914\pi$
$503$	−54.5382	+	94.4629i	−0.108426	+	0.187799i	0.806707	+	0.590952i	$0.201248\pi$
$504$		0			0
$505$	1020.32			2.02043
$506$		0			0
$507$	−52.7839	−	30.4748i	−0.104110	−	0.0601080i
$508$		0			0
$509$	497.205	+	287.061i	0.976826	+	0.563971i	0.901311	−	0.433174i	$-0.142606\pi$
$509$	497.205	+	287.061i	0.976826	+	0.563971i	0.0755159	+	0.997145i	$0.475940\pi$
$510$		0			0
$511$	127.775	+	221.313i	0.250049	+	0.433098i
$512$		0			0
$513$	65.3908	−	73.9665i	0.127467	−	0.144184i
$514$		0			0
$515$	−945.513	+	545.892i	−1.83595	+	1.05998i
$516$		0			0
$517$	−248.966	+	431.221i	−0.481558	+	0.834083i
$518$		0			0
$519$	267.564	−	463.434i	0.515537	−	0.892936i
$520$		0			0
$521$		−	458.852i		−	0.880715i	−0.897823	−	0.440357i	$-0.854852\pi$
$521$		−	458.852i		−	0.880715i	0.897823	−	0.440357i	$-0.145148\pi$
$522$		0			0
$523$	375.837	+	216.990i	0.718618	+	0.414894i	0.814244	−	0.580523i	$-0.197152\pi$
$523$	375.837	+	216.990i	0.718618	+	0.414894i	−0.0956260	+	0.995417i	$0.530485\pi$
$524$		0			0
$525$			209.479i			0.399008i
$526$		0			0
$527$	−50.6118	+	29.2207i	−0.0960376	+	0.0554473i
$528$		0			0
$529$	−40.7567	−	70.5927i	−0.0770448	−	0.133446i
$530$		0			0
$531$			245.272i			0.461905i
$532$		0			0
$533$	176.777			0.331664
$534$		0			0
$535$	−620.286	+	358.123i	−1.15941	+	0.669388i
$536$		0			0
$537$	−22.5084	−	38.9857i	−0.0419151	−	0.0725990i
$538$		0			0
$539$	702.522			1.30338
$540$		0			0
$541$	411.165	−	712.158i	0.760009	−	1.31637i	−0.182837	−	0.983143i	$-0.558528\pi$
$541$	411.165	−	712.158i	0.760009	−	1.31637i	0.942845	−	0.333231i	$-0.108139\pi$
$542$		0			0
$543$	−26.8739			−0.0494916
$544$		0			0
$545$	−54.6083	−	31.5281i	−0.100199	−	0.0578497i
$546$		0			0
$547$	417.280	+	240.917i	0.762851	+	0.440432i	0.830319	−	0.557289i	$-0.188158\pi$
$547$	417.280	+	240.917i	0.762851	+	0.440432i	−0.0674672	+	0.997721i	$0.521492\pi$
$548$		0			0
$549$	95.4677	+	165.355i	0.173894	+	0.301193i
$550$		0			0
$551$	72.1155	+	215.263i	0.130881	+	0.390677i
$552$		0			0
$553$	−75.6689	+	43.6875i	−0.136834	+	0.0790009i
$554$		0			0
$555$	−440.960	+	763.765i	−0.794522	+	1.37615i
$556$		0			0
$557$	−288.152	+	499.094i	−0.517329	+	0.896040i	0.482469	+	0.875913i	$0.339740\pi$
$557$	−288.152	+	499.094i	−0.517329	+	0.896040i	−0.999797	+	0.0201267i	$0.993593\pi$
$558$		0			0
$559$			440.806i			0.788562i
$560$		0			0
$561$	−131.105	−	75.6934i	−0.233698	−	0.134926i
$562$		0			0
$563$			550.466i			0.977738i	0.872357	+	0.488869i	$0.162590\pi$
$563$			550.466i			0.977738i	−0.872357	+	0.488869i	$0.837410\pi$
$564$		0			0
$565$	365.120	−	210.802i	0.646231	−	0.373101i
$566$		0			0
$567$	−12.0386	−	20.8514i	−0.0212320	−	0.0367749i
$568$		0			0
$569$		−	809.154i		−	1.42206i	−0.703160	−	0.711032i	$-0.748228\pi$
$569$		−	809.154i		−	1.42206i	0.703160	−	0.711032i	$-0.251772\pi$
$570$		0			0
$571$	−306.288			−0.536406			−0.268203	−	0.963362i	$-0.586430\pi$
$571$	−306.288			−0.536406			−0.268203	+	0.963362i	$0.586430\pi$
$572$		0			0
$573$	−418.011	+	241.339i	−0.729513	+	0.421184i
$574$		0			0
$575$	558.516	+	967.378i	0.971332	+	1.68240i
$576$		0			0
$577$	350.647			0.607707			0.303853	−	0.952719i	$-0.401727\pi$
$577$	350.647			0.607707			0.303853	+	0.952719i	$0.401727\pi$
$578$		0			0
$579$	285.840	−	495.090i	0.493679	−	0.855077i
$580$		0			0
$581$	365.145			0.628477
$582$		0			0
$583$	615.640	+	355.440i	1.05599	+	0.609674i
$584$		0			0
$585$	251.821	+	145.389i	0.430463	+	0.248528i
$586$		0			0
$587$	469.865	+	813.830i	0.800451	+	1.38642i	0.919320	+	0.393512i	$0.128740\pi$
$587$	469.865	+	813.830i	0.800451	+	1.38642i	−0.118868	+	0.992910i	$0.537927\pi$
$588$		0			0
$589$	−141.275	+	159.802i	−0.239855	+	0.271311i
$590$		0			0
$591$	12.6729	−	7.31672i	0.0214432	−	0.0123802i
$592$		0			0
$593$	−430.842	+	746.241i	−0.726547	+	1.25842i	0.231787	+	0.972767i	$0.425543\pi$
$593$	−430.842	+	746.241i	−0.726547	+	1.25842i	−0.958334	+	0.285650i	$0.907791\pi$
$594$		0			0
$595$	−58.3469	+	101.060i	−0.0980619	+	0.169848i
$596$		0			0
$597$		−	337.989i		−	0.566146i
$598$		0			0
$599$	923.466	+	533.163i	1.54168	+	0.890089i	0.998733	+	0.0503214i	$0.0160246\pi$
$599$	923.466	+	533.163i	1.54168	+	0.890089i	0.542946	+	0.839767i	$0.317309\pi$
$600$		0			0
$601$			569.610i			0.947770i	0.880587	+	0.473885i	$0.157149\pi$
$601$			569.610i			0.947770i	−0.880587	+	0.473885i	$0.842851\pi$
$602$		0			0
$603$	−313.422	+	180.954i	−0.519770	+	0.300090i
$604$		0			0
$605$	674.031	+	1167.46i	1.11410	+	1.92968i
$606$		0			0
$607$		−	580.517i		−	0.956371i	−0.878259	−	0.478186i	$-0.841295\pi$
$607$		−	580.517i		−	0.956371i	0.878259	−	0.478186i	$-0.158705\pi$
$608$		0			0
$609$	55.3651			0.0909114
$610$		0			0
$611$	297.105	−	171.533i	0.486260	−	0.280742i
$612$		0			0
$613$	−552.017	−	956.121i	−0.900517	−	1.55974i	−0.826824	−	0.562460i	$-0.809855\pi$
$613$	−552.017	−	956.121i	−0.900517	−	1.55974i	−0.0736929	−	0.997281i	$-0.523478\pi$
$614$		0			0
$615$	221.787			0.360628
$616$		0			0
$617$	−268.257	+	464.636i	−0.434777	+	0.753056i	−0.997277	−	0.0737411i	$-0.976506\pi$
$617$	−268.257	+	464.636i	−0.434777	+	0.753056i	0.562500	+	0.826797i	$0.309840\pi$
$618$		0			0
$619$	279.065			0.450833			0.225416	−	0.974263i	$-0.427626\pi$
$619$	279.065			0.450833			0.225416	+	0.974263i	$0.427626\pi$
$620$		0			0
$621$	−111.189	−	64.1947i	−0.179048	−	0.103373i
$622$		0			0
$623$	−76.5714	−	44.2085i	−0.122908	−	0.0709607i
$624$		0			0
$625$	−144.291	−	249.919i	−0.230866	−	0.399871i
$626$		0			0
$627$	−541.472	−	109.953i	−0.863592	−	0.175363i
$628$		0			0
$629$	−273.966	+	158.174i	−0.435558	+	0.251469i
$630$		0			0
$631$	199.821	−	346.099i	0.316673	−	0.548493i	−0.663119	−	0.748514i	$-0.730768\pi$
$631$	199.821	−	346.099i	0.316673	−	0.548493i	0.979792	+	0.200021i	$0.0641010\pi$
$632$		0			0
$633$	−70.6932	+	122.444i	−0.111680	+	0.193435i
$634$		0			0
$635$		−	164.225i		−	0.258621i
$636$		0			0
$637$	−419.180	−	242.013i	−0.658053	−	0.379927i
$638$		0			0
$639$		−	235.851i		−	0.369093i
$640$		0			0
$641$	39.6933	−	22.9169i	0.0619240	−	0.0357518i	−0.468718	−	0.883348i	$-0.655284\pi$
$641$	39.6933	−	22.9169i	0.0619240	−	0.0357518i	0.530642	+	0.847596i	$0.321951\pi$
$642$		0			0
$643$	−149.619	−	259.147i	−0.232689	−	0.403028i	0.725910	−	0.687790i	$-0.241419\pi$
$643$	−149.619	−	259.147i	−0.232689	−	0.403028i	−0.958598	+	0.284761i	$0.908086\pi$
$644$		0			0
$645$			553.041i			0.857427i
$646$		0			0
$647$	−799.034			−1.23498			−0.617491	−	0.786578i	$-0.711851\pi$
$647$	−799.034			−1.23498			−0.617491	+	0.786578i	$0.711851\pi$
$648$		0			0
$649$	1188.76	−	686.329i	1.83167	−	1.05752i
$650$		0			0
$651$	26.0089	+	45.0488i	0.0399522	+	0.0691993i
$652$		0			0
$653$	81.4583			0.124745			0.0623723	−	0.998053i	$-0.480133\pi$
$653$	81.4583			0.124745			0.0623723	+	0.998053i	$0.480133\pi$
$654$		0			0
$655$	−101.905	+	176.505i	−0.155581	+	0.269474i
$656$		0			0
$657$	286.573			0.436185
$658$		0			0
$659$	203.456	+	117.465i	0.308734	+	0.178248i	0.646360	−	0.763033i	$-0.276290\pi$
$659$	203.456	+	117.465i	0.308734	+	0.178248i	−0.337626	+	0.941280i	$0.609624\pi$
$660$		0			0
$661$	−312.245	−	180.275i	−0.472383	−	0.272731i	0.244854	−	0.969560i	$-0.421260\pi$
$661$	−312.245	−	180.275i	−0.472383	−	0.272731i	−0.717237	+	0.696830i	$0.754593\pi$
$662$		0			0
$663$	52.1516	+	90.3292i	0.0786600	+	0.136243i
$664$		0			0
$665$	−84.7551	+	417.384i	−0.127451	+	0.627644i
$666$		0			0
$667$	255.677	−	147.615i	0.383324	−	0.221312i
$668$		0			0
$669$	81.2933	−	140.804i	0.121515	−	0.210470i
$670$		0			0
$671$	534.283	−	925.405i	0.796248	−	1.37914i
$672$		0			0
$673$			1263.61i			1.87758i	0.344487	+	0.938791i	$0.388053\pi$
$673$			1263.61i			1.87758i	−0.344487	+	0.938791i	$0.611947\pi$
$674$		0			0
$675$	203.437	+	117.455i	0.301389	+	0.174007i
$676$		0			0
$677$			46.8134i			0.0691483i	0.999402	+	0.0345741i	$0.0110075\pi$
$677$			46.8134i			0.0691483i	−0.999402	+	0.0345741i	$0.988993\pi$
$678$		0			0
$679$	340.512	−	196.595i	0.501491	−	0.289536i
$680$		0			0
$681$	−259.663	−	449.749i	−0.381296	−	0.660424i
$682$		0			0
$683$			337.323i			0.493884i	0.969030	+	0.246942i	$0.0794257\pi$
$683$			337.323i			0.493884i	−0.969030	+	0.246942i	$0.920574\pi$
$684$		0			0
$685$	1473.32			2.15083
$686$		0			0
$687$	−438.602	+	253.227i	−0.638431	+	0.368598i
$688$		0			0
$689$	−244.892	−	424.166i	−0.355432	−	0.615626i
$690$		0			0
$691$	1063.01			1.53837			0.769183	−	0.639028i	$-0.220663\pi$
$691$	1063.01			1.53837			0.769183	+	0.639028i	$0.220663\pi$
$692$		0			0
$693$	−67.3735	+	116.694i	−0.0972201	+	0.168390i
$694$		0			0
$695$	−26.6286			−0.0383145
$696$		0			0
$697$	68.8973	+	39.7779i	0.0988484	+	0.0570701i
$698$		0			0
$699$	568.330	+	328.125i	0.813061	+	0.469421i
$700$		0			0
$701$	−606.107	−	1049.81i	−0.864632	−	1.49759i	−0.867412	−	0.497591i	$-0.834218\pi$
$701$	−606.107	−	1049.81i	−0.864632	−	1.49759i	0.00277981	−	0.999996i	$-0.499115\pi$
$702$		0			0
$703$	−764.731	+	865.023i	−1.08781	+	1.23047i
$704$		0			0
$705$	372.751	−	215.208i	0.528725	−	0.305259i
$706$		0			0
$707$	162.882	−	282.119i	0.230384	−	0.399037i
$708$		0			0
$709$	−92.7019	+	160.564i	−0.130750	+	0.226466i	−0.923966	−	0.382475i	$-0.875072\pi$
$709$	−92.7019	+	160.564i	−0.130750	+	0.226466i	0.793216	+	0.608941i	$0.208405\pi$
$710$		0			0
$711$			97.9820i			0.137809i
$712$		0			0
$713$	240.219	+	138.691i	0.336914	+	0.194517i
$714$		0			0
$715$		−	1627.33i		−	2.27599i
$716$		0			0
$717$	−553.615	+	319.630i	−0.772127	+	0.445788i
$718$		0			0
$719$	171.257	+	296.626i	0.238188	+	0.412553i	0.960194	−	0.279333i	$-0.0901133\pi$
$719$	171.257	+	296.626i	0.238188	+	0.412553i	−0.722006	+	0.691886i	$0.756780\pi$
$720$		0			0
$721$			348.582i			0.483470i
$722$		0			0
$723$	−613.801			−0.848964
$724$		0			0
$725$	−467.802	+	270.086i	−0.645244	+	0.372532i
$726$		0			0
$727$	−94.5575	−	163.778i	−0.130065	−	0.225280i	0.793636	−	0.608393i	$-0.208185\pi$
$727$	−94.5575	−	163.778i	−0.130065	−	0.225280i	−0.923702	+	0.383113i	$0.874852\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−99.1890	+	171.800i	−0.135690	+	0.235021i
$732$		0			0
$733$	−186.884			−0.254957			−0.127479	−	0.991841i	$-0.540688\pi$
$733$	−186.884			−0.254957			−0.127479	+	0.991841i	$0.540688\pi$
$734$		0			0
$735$	−525.908	−	303.633i	−0.715521	−	0.413106i
$736$		0			0
$737$	1754.06	+	1012.71i	2.38000	+	1.37409i
$738$		0			0
$739$	281.612	+	487.766i	0.381072	+	0.660036i	0.991216	−	0.132255i	$-0.0422218\pi$
$739$	281.612	+	487.766i	0.381072	+	0.660036i	−0.610144	+	0.792291i	$0.708888\pi$
$740$		0			0
$741$	285.207	+	252.139i	0.384894	+	0.340269i
$742$		0			0
$743$	612.427	−	353.585i	0.824263	−	0.475888i	−0.0276216	−	0.999618i	$-0.508793\pi$
$743$	612.427	−	353.585i	0.824263	−	0.475888i	0.851884	+	0.523730i	$0.175460\pi$
$744$		0			0
$745$	492.935	−	853.788i	0.661657	−	1.14602i
$746$		0			0
$747$	204.736	−	354.614i	0.274078	−	0.474718i
$748$		0			0
$749$			228.681i			0.305315i
$750$		0			0
$751$	−1049.29	−	605.805i	−1.39718	−	0.806665i	−0.403087	−	0.915162i	$-0.632063\pi$
$751$	−1049.29	−	605.805i	−1.39718	−	0.806665i	−0.994097	+	0.108497i	$0.965396\pi$
$752$		0			0
$753$		−	199.532i		−	0.264982i
$754$		0			0
$755$	293.369	−	169.377i	0.388568	−	0.224340i
$756$		0			0
$757$	640.408	+	1109.22i	0.845982	+	1.46528i	0.884766	+	0.466036i	$0.154318\pi$
$757$	640.408	+	1109.22i	0.845982	+	1.46528i	−0.0387841	+	0.999248i	$0.512348\pi$
$758$		0			0
$759$			718.529i			0.946678i
$760$		0			0
$761$	−1125.46			−1.47893			−0.739464	−	0.673196i	$-0.764921\pi$
$761$	−1125.46			−1.47893			−0.739464	+	0.673196i	$0.764921\pi$
$762$		0			0
$763$	−17.4352	+	10.0662i	−0.0228508	+	0.0131929i
$764$		0			0
$765$	65.4300	+	113.328i	0.0855294	+	0.148141i
$766$		0			0
$767$	−945.740			−1.23304
$768$		0			0
$769$	−636.009	+	1101.60i	−0.827060	+	1.43251i	0.0732739	+	0.997312i	$0.476655\pi$
$769$	−636.009	+	1101.60i	−0.827060	+	1.43251i	−0.900334	+	0.435199i	$0.856678\pi$
$770$		0			0
$771$	−813.262			−1.05481
$772$		0			0
$773$	−537.388	−	310.261i	−0.695198	−	0.401373i	0.110358	−	0.993892i	$-0.464800\pi$
$773$	−537.388	−	310.261i	−0.695198	−	0.401373i	−0.805556	+	0.592519i	$0.798133\pi$
$774$		0			0
$775$	−439.520	−	253.757i	−0.567122	−	0.327428i
$776$		0			0
$777$	140.788	+	243.853i	0.181195	+	0.313839i
$778$		0			0
$779$	284.551	+	57.7817i	0.365277	+	0.0741742i
$780$		0			0
$781$	−1143.10	+	659.967i	−1.46363	+	0.845028i
$782$		0			0
$783$	31.0431	−	53.7683i	0.0396464	−	0.0686695i
$784$		0			0
$785$	−866.280	+	1500.44i	−1.10354	+	1.91139i
$786$		0			0
$787$		−	34.7651i		−	0.0441742i	−0.999756	−	0.0220871i	$-0.992969\pi$
$787$		−	34.7651i		−	0.0441742i	0.999756	−	0.0220871i	$-0.00703112\pi$
$788$		0			0
$789$	−258.736	−	149.381i	−0.327929	−	0.189330i
$790$		0			0
$791$		−	134.609i		−	0.170175i
$792$		0			0
$793$	−637.590	+	368.113i	−0.804022	+	0.464202i
$794$		0			0
$795$	−307.245	−	532.164i	−0.386472	−	0.669388i
$796$		0			0
$797$		−	174.387i		−	0.218805i	−0.993998	−	0.109402i	$-0.965106\pi$
$797$		−	174.387i		−	0.218805i	0.993998	−	0.109402i	$-0.0348937\pi$
$798$		0			0
$799$	154.392			0.193232
$800$		0			0
$801$	−85.8670	+	49.5753i	−0.107200	+	0.0618918i
$802$		0			0
$803$	−801.901	−	1388.93i	−0.998631	−	1.72968i
$804$		0			0
$805$	553.865			0.688031
$806$		0			0
$807$	208.174	−	360.568i	0.257961	−	0.446801i
$808$		0			0
$809$	200.471			0.247801			0.123900	−	0.992295i	$-0.460460\pi$
$809$	200.471			0.247801			0.123900	+	0.992295i	$0.460460\pi$
$810$		0			0
$811$	−657.954	−	379.870i	−0.811287	−	0.468397i	0.0361153	−	0.999348i	$-0.488502\pi$
$811$	−657.954	−	379.870i	−0.811287	−	0.468397i	−0.847403	+	0.530951i	$0.821835\pi$
$812$		0			0
$813$	−194.260	−	112.156i	−0.238942	−	0.137953i
$814$		0			0
$815$	893.156	+	1546.99i	1.09590	+	1.89815i
$816$		0			0
$817$	−144.083	+	709.548i	−0.176356	+	0.868479i
$818$		0			0
$819$	80.4006	−	46.4193i	0.0981692	−	0.0566780i
$820$		0			0
$821$	569.432	−	986.285i	0.693583	−	1.20132i	−0.277072	−	0.960849i	$-0.589364\pi$
$821$	569.432	−	986.285i	0.693583	−	1.20132i	0.970656	−	0.240473i	$-0.0773025\pi$
$822$		0			0
$823$	−163.358	+	282.945i	−0.198491	+	0.343797i	−0.948039	−	0.318153i	$-0.896937\pi$
$823$	−163.358	+	282.945i	−0.198491	+	0.343797i	0.749548	+	0.661950i	$0.230271\pi$
$824$		0			0
$825$		−	1314.66i		−	1.59353i
$826$		0			0
$827$	−736.033	−	424.949i	−0.890003	−	0.513844i	−0.0160597	−	0.999871i	$-0.505112\pi$
$827$	−736.033	−	424.949i	−0.890003	−	0.513844i	−0.873944	+	0.486027i	$0.838446\pi$
$828$		0			0
$829$		−	732.123i		−	0.883140i	−0.897227	−	0.441570i	$-0.854422\pi$
$829$		−	732.123i		−	0.883140i	0.897227	−	0.441570i	$-0.145578\pi$
$830$		0			0
$831$	765.074	−	441.716i	0.920667	−	0.531547i
$832$		0			0
$833$	−108.914	−	188.645i	−0.130750	−	0.226465i
$834$		0			0
$835$		−	1057.93i		−	1.26699i
$836$		0			0
$837$	58.3326			0.0696925
$838$		0			0
$839$	−118.162	+	68.2209i	−0.140837	+	0.0813121i	−0.568763	−	0.822502i	$-0.692578\pi$
$839$	−118.162	+	68.2209i	−0.140837	+	0.0813121i	0.427926	+	0.903814i	$0.359244\pi$
$840$		0			0
$841$	−349.117	−	604.688i	−0.415121	−	0.719010i
$842$		0			0
$843$	582.475			0.690955
$844$		0			0
$845$	147.426	−	255.349i	0.174469	−	0.302189i
$846$		0			0
$847$	430.405			0.508153
$848$		0			0
$849$	−586.601	−	338.674i	−0.690932	−	0.398910i
$850$		0			0
$851$	1300.33	+	750.744i	1.52800	+	0.882190i
$852$		0			0
$853$	−23.1342	−	40.0697i	−0.0271210	−	0.0469750i	0.852146	−	0.523304i	$-0.175301\pi$
$853$	−23.1342	−	40.0697i	−0.0271210	−	0.0469750i	−0.879267	+	0.476329i	$0.841967\pi$
$854$		0			0
$855$	357.823	+	316.337i	0.418507	+	0.369985i
$856$		0			0
$857$	810.865	−	468.153i	0.946167	−	0.546270i	0.0542790	−	0.998526i	$-0.482714\pi$
$857$	810.865	−	468.153i	0.946167	−	0.546270i	0.891888	+	0.452256i	$0.149381\pi$
$858$		0			0
$859$	158.332	−	274.239i	0.184321	−	0.319254i	−0.759026	−	0.651060i	$-0.774325\pi$
$859$	158.332	−	274.239i	0.184321	−	0.319254i	0.943348	+	0.331806i	$0.107658\pi$
$860$		0			0
$861$	35.4057	−	61.3244i	0.0411216	−	0.0712246i
$862$		0			0
$863$			1557.08i			1.80427i	0.431457	+	0.902134i	$0.358000\pi$
$863$			1557.08i			1.80427i	−0.431457	+	0.902134i	$0.642000\pi$
$864$		0			0
$865$	2241.93	+	1294.38i	2.59182	+	1.49639i
$866$		0			0
$867$		−	453.623i		−	0.523210i
$868$		0			0
$869$	474.889	−	274.177i	0.546477	−	0.315509i
$870$		0			0
$871$	−697.738	−	1208.52i	−0.801077	−	1.38751i
$872$		0			0
$873$		−	440.922i		−	0.505065i
$874$		0			0
$875$	−452.987			−0.517699
$876$		0			0
$877$	−768.785	+	443.858i	−0.876608	+	0.506110i	−0.869538	−	0.493865i	$-0.835584\pi$
$877$	−768.785	+	443.858i	−0.876608	+	0.506110i	−0.00706923	+	0.999975i	$0.502250\pi$
$878$		0			0
$879$	−322.342	−	558.313i	−0.366714	−	0.635168i
$880$		0			0
$881$	−1197.12			−1.35881			−0.679407	−	0.733762i	$-0.737763\pi$
$881$	−1197.12			−1.35881			−0.679407	+	0.733762i	$0.737763\pi$
$882$		0			0
$883$	11.1649	−	19.3382i	0.0126443	−	0.0219006i	−0.859634	−	0.510910i	$-0.829308\pi$
$883$	11.1649	−	19.3382i	0.0126443	−	0.0219006i	0.872278	+	0.489010i	$0.162642\pi$
$884$		0			0
$885$	−1186.54			−1.34072
$886$		0			0
$887$	−137.632	−	79.4619i	−0.155166	−	0.0895850i	0.420407	−	0.907336i	$-0.361887\pi$
$887$	−137.632	−	79.4619i	−0.155166	−	0.0895850i	−0.575572	+	0.817751i	$0.695221\pi$
$888$		0			0
$889$	−45.4084	−	26.2166i	−0.0510781	−	0.0294900i
$890$		0			0
$891$	75.5524	+	130.861i	0.0847951	+	0.146869i
$892$		0			0
$893$	534.305	−	178.998i	0.598326	−	0.200446i
$894$		0			0
$895$	188.599	−	108.887i	0.210725	−	0.121662i
$896$		0			0
$897$	247.528	−	428.730i	0.275951	−	0.477960i
$898$		0			0
$899$	−67.0677	+	116.165i	−0.0746025	+	0.129215i
$900$		0			0
$901$		−	220.420i		−	0.244639i
$902$		0			0
$903$	152.917	+	88.2866i	0.169343	+	0.0977703i
$904$		0			0
$905$		−	130.006i		−	0.143653i
$906$		0			0
$907$	−627.014	+	362.007i	−0.691305	+	0.399125i	−0.804101	−	0.594493i	$-0.797353\pi$
$907$	−627.014	+	362.007i	−0.691305	+	0.399125i	0.112796	+	0.993618i	$0.464019\pi$
$908$		0			0
$909$	−182.655	−	316.368i	−0.200941	−	0.348039i
$910$		0			0
$911$			741.602i			0.814052i	0.913417	+	0.407026i	$0.133434\pi$
$911$			741.602i			0.814052i	−0.913417	+	0.407026i	$0.866566\pi$
$912$		0			0
$913$	−2291.61			−2.50997
$914$		0			0
$915$	−799.927	+	461.838i	−0.874238	+	0.504741i
$916$		0			0
$917$	32.5360	+	56.3541i	0.0354810	+	0.0614548i
$918$		0			0
$919$	1006.77			1.09551			0.547754	−	0.836639i	$-0.315483\pi$
$919$	1006.77			1.09551			0.547754	+	0.836639i	$0.315483\pi$
$920$		0			0
$921$	176.072	−	304.965i	0.191174	−	0.331124i
$922$		0			0
$923$	909.413			0.985280
$924$		0			0
$925$	−2379.16	−	1373.61i	−2.57206	−	1.48498i
$926$		0			0
$927$	338.528	+	195.449i	0.365187	+	0.210841i
$928$		0			0
$929$	195.958	+	339.409i	0.210934	+	0.365349i	0.952007	−	0.306076i	$-0.0990161\pi$
$929$	195.958	+	339.409i	0.210934	+	0.365349i	−0.741073	+	0.671424i	$0.765683\pi$
$930$		0			0
$931$	−595.631	−	526.573i	−0.639776	−	0.565599i
$932$		0			0
$933$	−126.703	+	73.1521i	−0.135802	+	0.0784052i
$934$		0			0
$935$	366.178	−	634.238i	0.391634	−	0.678329i
$936$		0			0
$937$	251.292	−	435.250i	0.268188	−	0.464515i	−0.700206	−	0.713941i	$-0.746909\pi$
$937$	251.292	−	435.250i	0.268188	−	0.464515i	0.968394	+	0.249426i	$0.0802420\pi$
$938$		0			0
$939$			448.338i			0.477463i
$940$		0			0
$941$	1128.25	+	651.394i	1.19899	+	0.692236i	0.960330	−	0.278867i	$-0.0899589\pi$
$941$	1128.25	+	651.394i	1.19899	+	0.692236i	0.238659	+	0.971103i	$0.423292\pi$
$942$		0			0
$943$		−	377.596i		−	0.400420i
$944$		0			0
$945$	100.872	−	58.2382i	0.106742	−	0.0616277i
$946$		0			0
$947$	−529.593	−	917.282i	−0.559232	−	0.968619i	−0.997561	−	0.0698038i	$-0.977763\pi$
$947$	−529.593	−	917.282i	−0.559232	−	0.968619i	0.438328	−	0.898815i	$-0.355571\pi$
$948$		0			0
$949$			1104.99i			1.16438i
$950$		0			0
$951$	177.949			0.187117
$952$		0			0
$953$	930.870	−	537.438i	0.976778	−	0.563943i	0.0754824	−	0.997147i	$-0.475950\pi$
$953$	930.870	−	537.438i	0.976778	−	0.563943i	0.901296	+	0.433204i	$0.142617\pi$
$954$		0			0
$955$	−1167.51	−	2022.19i	−1.22252	−	2.11747i
$956$		0			0
$957$	−347.464			−0.363076
$958$		0			0
$959$	235.198	−	407.375i	0.245254	−	0.424792i
$960$		0			0
$961$	834.974			0.868860
$962$		0			0
$963$	222.085	+	128.221i	0.230618	+	0.133147i
$964$		0			0
$965$	2395.07	+	1382.79i	2.48193	+	1.43295i
$966$		0			0
$967$	−176.546	−	305.787i	−0.182571	−	0.316222i	0.760184	−	0.649707i	$-0.225109\pi$
$967$	−176.546	−	305.787i	−0.182571	−	0.316222i	−0.942755	+	0.333485i	$0.891775\pi$
$968$		0			0
$969$	54.4211	+	162.446i	0.0561621	+	0.167642i
$970$		0			0
$971$	−247.494	+	142.891i	−0.254885	+	0.147158i	−0.621999	−	0.783018i	$-0.713679\pi$
$971$	−247.494	+	142.891i	−0.254885	+	0.147158i	0.367114	+	0.930176i	$0.380346\pi$
$972$		0			0
$973$	−4.25095	+	7.36286i	−0.00436891	+	0.00756717i
$974$		0			0
$975$	−452.892	+	784.431i	−0.464504	+	0.804545i
$976$		0			0
$977$		−	382.454i		−	0.391458i	−0.980658	−	0.195729i	$-0.937293\pi$
$977$		−	382.454i		−	0.391458i	0.980658	−	0.195729i	$-0.0627072\pi$
$978$		0			0
$979$	480.553	+	277.447i	0.490861	+	0.283399i
$980$		0			0
$981$			22.5764i			0.0230137i
$982$		0			0
$983$	1409.22	−	813.614i	1.43359	−	0.827685i	0.436200	−	0.899850i	$-0.356324\pi$
$983$	1409.22	−	813.614i	1.43359	−	0.827685i	0.997393	+	0.0721651i	$0.0229908\pi$
$984$		0			0
$985$	35.3957	+	61.3071i	0.0359347	+	0.0622407i
$986$		0			0
$987$		−	137.422i		−	0.139232i
$988$		0			0
$989$	941.564			0.952036
$990$		0			0
$991$	−1226.18	+	707.937i	−1.23732	+	0.714366i	−0.968545	−	0.248837i	$-0.919952\pi$
$991$	−1226.18	+	707.937i	−1.23732	+	0.714366i	−0.268773	+	0.963203i	$0.586618\pi$
$992$		0			0
$993$	161.974	+	280.547i	0.163116	+	0.282525i
$994$		0			0
$995$	1635.07			1.64329
$996$		0			0
$997$	−581.911	+	1007.90i	−0.583662	+	1.01093i	0.411379	+	0.911464i	$0.365047\pi$
$997$	−581.911	+	1007.90i	−0.583662	+	1.01093i	−0.995041	+	0.0994676i	$0.968286\pi$
$998$		0			0
$999$	315.759			0.316075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.j.145.10		20
4.3	odd	2		456.3.w.a.145.10	✓	20
12.11	even	2		1368.3.bv.c.145.1		20
19.8	odd	6	inner	912.3.be.j.673.10		20
76.27	even	6		456.3.w.a.217.10	yes	20
228.179	odd	6		1368.3.bv.c.217.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.3.w.a.145.10	✓	20	4.3	odd	2
456.3.w.a.217.10	yes	20	76.27	even	6
912.3.be.j.145.10		20	1.1	even	1	trivial
912.3.be.j.673.10		20	19.8	odd	6	inner
1368.3.bv.c.145.1		20	12.11	even	2
1368.3.bv.c.217.1		20	228.179	odd	6

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(4.18952 + 7.25646i) q^{5} +2.67523 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(4.18952 + 7.25646i) q^{5} +2.67523 q^{7} +(1.50000 - 2.59808i) q^{9} -16.7894 q^{11} +(10.0179 + 5.78383i) q^{13} +(12.5686 + 7.25646i) q^{15} +(2.60292 + 4.50840i) q^{17} +(14.2349 + 12.5845i) q^{19} +(4.01285 - 2.31682i) q^{21} +(12.3543 - 21.3982i) q^{23} +(-22.6041 + 39.1515i) q^{25} -5.19615i q^{27} +(10.3477 + 5.97425i) q^{29} +11.2261i q^{31} +(-25.1841 + 14.5401i) q^{33} +(11.2079 + 19.4127i) q^{35} +60.7679i q^{37} +20.0358 q^{39} +(13.2346 - 7.64100i) q^{41} +(19.0534 + 33.0014i) q^{43} +25.1371 q^{45} +(14.8287 - 25.6841i) q^{47} -41.8431 q^{49} +(7.80877 + 4.50840i) q^{51} +(-36.6683 - 21.1704i) q^{53} +(-70.3397 - 121.832i) q^{55} +(32.2508 + 6.54893i) q^{57} +(-70.8038 + 40.8786i) q^{59} +(-31.8226 + 55.1183i) q^{61} +(4.01285 - 6.95046i) q^{63} +96.9259i q^{65} +(-104.474 - 60.3180i) q^{67} -42.7965i q^{69} +(68.0842 - 39.3084i) q^{71} +(47.7622 + 82.7266i) q^{73} +78.3031i q^{75} -44.9157 q^{77} +(-28.2850 + 16.3303i) q^{79} +(-4.50000 - 7.79423i) q^{81} +136.491 q^{83} +(-21.8100 + 37.7760i) q^{85} +20.6954 q^{87} +(-28.6223 - 16.5251i) q^{89} +(26.8002 + 15.4731i) q^{91} +(9.72211 + 16.8392i) q^{93} +(-31.6814 + 156.018i) q^{95} +(127.283 - 73.4869i) q^{97} +(-25.1841 + 43.6202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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