LMFDB - Embedded newform 1160.2.bl.c.737.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1160,2,Mod(713,1160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1160, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3, 3]))

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

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

chi := DirichletCharacter("1160.713");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1160 = 2^{3} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1160.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.26264663447$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.12
Character	$\chi$	$=$	1160.737
Dual form			1160.2.bl.c.713.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.111611 q^{3} +(-0.657451 + 2.13723i) q^{5} +(3.03882 + 3.03882i) q^{7} -2.98754 q^{9} +(0.789225 + 0.789225i) q^{11} +(0.986968 + 0.986968i) q^{13} +(-0.0733790 + 0.238539i) q^{15} -1.36500i q^{17} +(-4.08789 + 4.08789i) q^{19} +(0.339167 + 0.339167i) q^{21} +(2.20484 - 2.20484i) q^{23} +(-4.13552 - 2.81025i) q^{25} -0.668278 q^{27} +(1.16225 + 5.25825i) q^{29} +(-3.93858 - 3.93858i) q^{31} +(0.0880865 + 0.0880865i) q^{33} +(-8.49254 + 4.49679i) q^{35} -0.535366 q^{37} +(0.110157 + 0.110157i) q^{39} +(-0.232411 + 0.232411i) q^{41} -2.82349 q^{43} +(1.96416 - 6.38507i) q^{45} -3.66266 q^{47} +11.4689i q^{49} -0.152350i q^{51} +(2.30615 - 2.30615i) q^{53} +(-2.20563 + 1.16788i) q^{55} +(-0.456255 + 0.456255i) q^{57} -6.73589i q^{59} +(5.50192 + 5.50192i) q^{61} +(-9.07861 - 9.07861i) q^{63} +(-2.75826 + 1.46050i) q^{65} +(-10.1501 + 10.1501i) q^{67} +(0.246085 - 0.246085i) q^{69} +2.23409i q^{71} +12.1214i q^{73} +(-0.461571 - 0.313656i) q^{75} +4.79663i q^{77} +(-2.04222 + 2.04222i) q^{79} +8.88804 q^{81} +(12.0434 - 12.0434i) q^{83} +(2.91733 + 0.897423i) q^{85} +(0.129721 + 0.586880i) q^{87} +(-5.02522 + 5.02522i) q^{89} +5.99844i q^{91} +(-0.439590 - 0.439590i) q^{93} +(-6.04918 - 11.4244i) q^{95} +3.69354 q^{97} +(-2.35784 - 2.35784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 8 q^{3} - 2 q^{5} + 4 q^{7} + 34 q^{9} + 2 q^{11} + 4 q^{13} - 4 q^{15} + 8 q^{19} + 4 q^{21} - 20 q^{23} + 4 q^{25} - 8 q^{27} + 20 q^{29} + 2 q^{31} - 10 q^{33} + 16 q^{35} - 12 q^{37} + 10 q^{39}+ \cdots + 60 q^{99}+O(q^{100}) $ 42 * q - 8 * q^3 - 2 * q^5 + 4 * q^7 + 34 * q^9 + 2 * q^11 + 4 * q^13 - 4 * q^15 + 8 * q^19 + 4 * q^21 - 20 * q^23 + 4 * q^25 - 8 * q^27 + 20 * q^29 + 2 * q^31 - 10 * q^33 + 16 * q^35 - 12 * q^37 + 10 * q^39 - 30 * q^41 + 4 * q^43 - 32 * q^45 - 4 * q^47 + 16 * q^53 + 2 * q^55 + 40 * q^57 + 26 * q^61 + 80 * q^63 + 8 * q^65 + 44 * q^67 + 12 * q^69 + 4 * q^75 - 42 * q^79 + 114 * q^81 - 68 * q^83 + 30 * q^85 - 32 * q^87 + 18 * q^89 + 6 * q^93 - 26 * q^95 - 24 * q^97 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1160\mathbb{Z}\right)^\times$.

$n$	$321$	$581$	$697$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	0.111611			0.0644389			0.0322194	−	0.999481i	$-0.489742\pi$
$3$	0.111611			0.0644389			0.0322194	+	0.999481i	$0.489742\pi$
$4$		0			0
$5$	−0.657451	+	2.13723i	−0.294021	+	0.955799i
$5$	−0.657451	+	2.13723i	−0.294021	+	0.955799i
$6$		0			0
$7$	3.03882	+	3.03882i	1.14857	+	1.14857i	0.986835	+	0.161732i	$0.0517079\pi$
$7$	3.03882	+	3.03882i	1.14857	+	1.14857i	0.161732	+	0.986835i	$0.448292\pi$
$8$		0			0
$9$	−2.98754			−0.995848
$10$		0			0
$11$	0.789225	+	0.789225i	0.237960	+	0.237960i	0.816005	−	0.578045i	$-0.196184\pi$
$11$	0.789225	+	0.789225i	0.237960	+	0.237960i	−0.578045	+	0.816005i	$0.696184\pi$
$12$		0			0
$13$	0.986968	+	0.986968i	0.273736	+	0.273736i	0.830602	−	0.556866i	$-0.187996\pi$
$13$	0.986968	+	0.986968i	0.273736	+	0.273736i	−0.556866	+	0.830602i	$0.687996\pi$
$14$		0			0
$15$	−0.0733790	+	0.238539i	−0.0189464	+	0.0615906i
$16$		0			0
$17$		−	1.36500i		−	0.331062i	−0.986205	−	0.165531i	$-0.947066\pi$
$17$		−	1.36500i		−	0.331062i	0.986205	−	0.165531i	$-0.0529338\pi$
$18$		0			0
$19$	−4.08789	+	4.08789i	−0.937827	+	0.937827i	−0.998177	−	0.0603505i	$-0.980778\pi$
$19$	−4.08789	+	4.08789i	−0.937827	+	0.937827i	0.0603505	+	0.998177i	$0.480778\pi$
$20$		0			0
$21$	0.339167	+	0.339167i	0.0740123	+	0.0740123i
$22$		0			0
$23$	2.20484	−	2.20484i	0.459741	−	0.459741i	−0.438829	−	0.898570i	$-0.644607\pi$
$23$	2.20484	−	2.20484i	0.459741	−	0.459741i	0.898570	+	0.438829i	$0.144607\pi$
$24$		0			0
$25$	−4.13552	−	2.81025i	−0.827103	−	0.562050i
$26$		0			0
$27$	−0.668278			−0.128610
$28$		0			0
$29$	1.16225	+	5.25825i	0.215825	+	0.976432i
$29$	1.16225	+	5.25825i	0.215825	+	0.976432i
$30$		0			0
$31$	−3.93858	−	3.93858i	−0.707390	−	0.707390i	0.258596	−	0.965986i	$-0.416740\pi$
$31$	−3.93858	−	3.93858i	−0.707390	−	0.707390i	−0.965986	+	0.258596i	$0.916740\pi$
$32$		0			0
$33$	0.0880865	+	0.0880865i	0.0153339	+	0.0153339i
$34$		0			0
$35$	−8.49254	+	4.49679i	−1.43550	+	0.760096i
$36$		0			0
$37$	−0.535366			−0.0880136			−0.0440068	−	0.999031i	$-0.514012\pi$
$37$	−0.535366			−0.0880136			−0.0440068	+	0.999031i	$0.514012\pi$
$38$		0			0
$39$	0.110157	+	0.110157i	0.0176392	+	0.0176392i
$40$		0			0
$41$	−0.232411	+	0.232411i	−0.0362965	+	0.0362965i	−0.725022	−	0.688726i	$-0.758170\pi$
$41$	−0.232411	+	0.232411i	−0.0362965	+	0.0362965i	0.688726	+	0.725022i	$0.258170\pi$
$42$		0			0
$43$	−2.82349			−0.430579			−0.215289	−	0.976550i	$-0.569069\pi$
$43$	−2.82349			−0.430579			−0.215289	+	0.976550i	$0.569069\pi$
$44$		0			0
$45$	1.96416	−	6.38507i	0.292800	−	0.951830i
$46$		0			0
$47$	−3.66266			−0.534254			−0.267127	−	0.963661i	$-0.586074\pi$
$47$	−3.66266			−0.534254			−0.267127	+	0.963661i	$0.586074\pi$
$48$		0			0
$49$			11.4689i			1.63841i
$50$		0			0
$51$		−	0.152350i		−	0.0213333i
$52$		0			0
$53$	2.30615	−	2.30615i	0.316774	−	0.316774i	−0.530753	−	0.847527i	$-0.678091\pi$
$53$	2.30615	−	2.30615i	0.316774	−	0.316774i	0.847527	+	0.530753i	$0.178091\pi$
$54$		0			0
$55$	−2.20563	+	1.16788i	−0.297408	+	0.157477i
$56$		0			0
$57$	−0.456255	+	0.456255i	−0.0604325	+	0.0604325i
$58$		0			0
$59$		−	6.73589i		−	0.876938i	−0.898746	−	0.438469i	$-0.855521\pi$
$59$		−	6.73589i		−	0.876938i	0.898746	−	0.438469i	$-0.144479\pi$
$60$		0			0
$61$	5.50192	+	5.50192i	0.704449	+	0.704449i	0.965362	−	0.260913i	$-0.0840237\pi$
$61$	5.50192	+	5.50192i	0.704449	+	0.704449i	−0.260913	+	0.965362i	$0.584024\pi$
$62$		0			0
$63$	−9.07861	−	9.07861i	−1.14380	−	1.14380i
$64$		0			0
$65$	−2.75826	+	1.46050i	−0.342120	+	0.181152i
$66$		0			0
$67$	−10.1501	+	10.1501i	−1.24004	+	1.24004i	−0.280052	+	0.959985i	$0.590352\pi$
$67$	−10.1501	+	10.1501i	−1.24004	+	1.24004i	−0.959985	+	0.280052i	$0.909648\pi$
$68$		0			0
$69$	0.246085	−	0.246085i	0.0296252	−	0.0296252i
$70$		0			0
$71$			2.23409i			0.265138i	0.991174	+	0.132569i	$0.0423226\pi$
$71$			2.23409i			0.265138i	−0.991174	+	0.132569i	$0.957677\pi$
$72$		0			0
$73$			12.1214i			1.41870i	0.704858	+	0.709349i	$0.251011\pi$
$73$			12.1214i			1.41870i	−0.704858	+	0.709349i	$0.748989\pi$
$74$		0			0
$75$	−0.461571	−	0.313656i	−0.0532976	−	0.0362179i
$76$		0			0
$77$			4.79663i			0.546627i
$78$		0			0
$79$	−2.04222	+	2.04222i	−0.229767	+	0.229767i	−0.812595	−	0.582828i	$-0.801946\pi$
$79$	−2.04222	+	2.04222i	−0.229767	+	0.229767i	0.582828	+	0.812595i	$0.301946\pi$
$80$		0			0
$81$	8.88804			0.987560
$82$		0			0
$83$	12.0434	−	12.0434i	1.32193	−	1.32193i	0.409726	−	0.912208i	$-0.365624\pi$
$83$	12.0434	−	12.0434i	1.32193	−	1.32193i	0.912208	−	0.409726i	$-0.134376\pi$
$84$		0			0
$85$	2.91733	+	0.897423i	0.316429	+	0.0973392i
$86$		0			0
$87$	0.129721	+	0.586880i	0.0139075	+	0.0629202i
$88$		0			0
$89$	−5.02522	+	5.02522i	−0.532672	+	0.532672i	−0.921367	−	0.388695i	$-0.872926\pi$
$89$	−5.02522	+	5.02522i	−0.532672	+	0.532672i	0.388695	+	0.921367i	$0.372926\pi$
$90$		0			0
$91$			5.99844i			0.628807i
$92$		0			0
$93$	−0.439590	−	0.439590i	−0.0455834	−	0.0455834i
$94$		0			0
$95$	−6.04918	−	11.4244i	−0.620633	−	1.17211i
$96$		0			0
$97$	3.69354			0.375022			0.187511	−	0.982262i	$-0.439958\pi$
$97$	3.69354			0.375022			0.187511	+	0.982262i	$0.439958\pi$
$98$		0			0
$99$	−2.35784	−	2.35784i	−0.236972	−	0.236972i
$100$		0			0
$101$	7.90096	+	7.90096i	0.786175	+	0.786175i	0.980865	−	0.194690i	$-0.0623700\pi$
$101$	7.90096	+	7.90096i	0.786175	+	0.786175i	−0.194690	+	0.980865i	$0.562370\pi$
$102$		0			0
$103$	−9.73930	+	9.73930i	−0.959642	+	0.959642i	−0.999217	−	0.0395748i	$-0.987400\pi$
$103$	−9.73930	+	9.73930i	−0.959642	+	0.959642i	0.0395748	+	0.999217i	$0.487400\pi$
$104$		0			0
$105$	−0.947864	+	0.501893i	−0.0925021	+	0.0489797i
$106$		0			0
$107$	3.78439	+	3.78439i	0.365851	+	0.365851i	0.865962	−	0.500110i	$-0.166707\pi$
$107$	3.78439	+	3.78439i	0.365851	+	0.365851i	−0.500110	+	0.865962i	$0.666707\pi$
$108$		0			0
$109$	10.4421			1.00017			0.500086	−	0.865976i	$-0.333302\pi$
$109$	10.4421			1.00017			0.500086	+	0.865976i	$0.333302\pi$
$110$		0			0
$111$	−0.0597529			−0.00567150
$112$		0			0
$113$			17.2444i			1.62221i	0.584899	+	0.811106i	$0.301134\pi$
$113$			17.2444i			1.62221i	−0.584899	+	0.811106i	$0.698866\pi$
$114$		0			0
$115$	3.26268	+	6.16183i	0.304247	+	0.574594i
$116$		0			0
$117$	−2.94861	−	2.94861i	−0.272599	−	0.272599i
$118$		0			0
$119$	4.14800	−	4.14800i	0.380247	−	0.380247i
$120$		0			0
$121$		−	9.75425i		−	0.886750i
$122$		0			0
$123$	−0.0259397	+	0.0259397i	−0.00233890	+	0.00233890i
$124$		0			0
$125$	8.72506	−	6.99095i	0.780393	−	0.625290i
$126$		0			0
$127$			1.60556i			0.142470i	0.997460	+	0.0712352i	$0.0226941\pi$
$127$			1.60556i			0.142470i	−0.997460	+	0.0712352i	$0.977306\pi$
$128$		0			0
$129$	−0.315134			−0.0277460
$130$		0			0
$131$	3.54857	−	3.54857i	0.310040	−	0.310040i	−0.534885	−	0.844925i	$-0.679645\pi$
$131$	3.54857	−	3.54857i	0.310040	−	0.310040i	0.844925	+	0.534885i	$0.179645\pi$
$132$		0			0
$133$	−24.8447			−2.15431
$134$		0			0
$135$	0.439360	−	1.42826i	0.0378141	−	0.122925i
$136$		0			0
$137$		−	11.8965i		−	1.01638i	−0.861244	−	0.508192i	$-0.830314\pi$
$137$		−	11.8965i		−	1.01638i	0.861244	−	0.508192i	$-0.169686\pi$
$138$		0			0
$139$			9.23244i			0.783085i	0.920160	+	0.391543i	$0.128058\pi$
$139$			9.23244i			0.783085i	−0.920160	+	0.391543i	$0.871942\pi$
$140$		0			0
$141$	−0.408794			−0.0344267
$142$		0			0
$143$			1.55788i			0.130276i
$144$		0			0
$145$	−12.0022	−	0.973035i	−0.996730	−	0.0808062i
$146$		0			0
$147$			1.28006i			0.105577i
$148$		0			0
$149$	8.31396			0.681106			0.340553	−	0.940225i	$-0.389386\pi$
$149$	8.31396			0.681106			0.340553	+	0.940225i	$0.389386\pi$
$150$		0			0
$151$		−	18.3229i		−	1.49110i	−0.666451	−	0.745549i	$-0.732187\pi$
$151$		−	18.3229i		−	1.49110i	0.666451	−	0.745549i	$-0.267813\pi$
$152$		0			0
$153$			4.07801i			0.329687i
$154$		0			0
$155$	11.0071	−	5.82823i	0.884110	−	0.468135i
$156$		0			0
$157$	−14.6007			−1.16527			−0.582633	−	0.812735i	$-0.697978\pi$
$157$	−14.6007			−1.16527			−0.582633	+	0.812735i	$0.697978\pi$
$158$		0			0
$159$	0.257393	−	0.257393i	0.0204126	−	0.0204126i
$160$		0			0
$161$	13.4002			1.05609
$162$		0			0
$163$			11.6798i			0.914836i	0.889252	+	0.457418i	$0.151226\pi$
$163$			11.6798i			0.914836i	−0.889252	+	0.457418i	$0.848774\pi$
$164$		0			0
$165$	−0.246174	+	0.130349i	−0.0191646	+	0.0101476i
$166$		0			0
$167$	10.3572	−	10.3572i	0.801465	−	0.801465i	−0.181860	−	0.983324i	$-0.558212\pi$
$167$	10.3572	−	10.3572i	0.801465	−	0.801465i	0.983324	+	0.181860i	$0.0582117\pi$
$168$		0			0
$169$		−	11.0518i		−	0.850138i
$170$		0			0
$171$	12.2128	−	12.2128i	0.933933	−	0.933933i
$172$		0			0
$173$	9.63530	+	9.63530i	0.732559	+	0.732559i	0.971126	−	0.238567i	$-0.0766778\pi$
$173$	9.63530	+	9.63530i	0.732559	+	0.732559i	−0.238567	+	0.971126i	$0.576678\pi$
$174$		0			0
$175$	−4.02724	−	21.1069i	−0.304431	−	1.59553i
$176$		0			0
$177$		−	0.751802i		−	0.0565089i
$178$		0			0
$179$	1.61089			0.120404			0.0602018	−	0.998186i	$-0.480826\pi$
$179$	1.61089			0.120404			0.0602018	+	0.998186i	$0.480826\pi$
$180$		0			0
$181$	7.71318			0.573316			0.286658	−	0.958033i	$-0.407456\pi$
$181$	7.71318			0.573316			0.286658	+	0.958033i	$0.407456\pi$
$182$		0			0
$183$	0.614077	+	0.614077i	0.0453939	+	0.0453939i
$184$		0			0
$185$	0.351977	−	1.14420i	0.0258779	−	0.0841233i
$186$		0			0
$187$	1.07730	−	1.07730i	0.0787796	−	0.0787796i
$188$		0			0
$189$	−2.03078	−	2.03078i	−0.147717	−	0.147717i
$190$		0			0
$191$	−3.65341	−	3.65341i	−0.264351	−	0.264351i	0.562468	−	0.826819i	$-0.309852\pi$
$191$	−3.65341	−	3.65341i	−0.264351	−	0.264351i	−0.826819	+	0.562468i	$0.809852\pi$
$192$		0			0
$193$	12.8621			0.925833			0.462917	−	0.886402i	$-0.346803\pi$
$193$	12.8621			0.925833			0.462917	+	0.886402i	$0.346803\pi$
$194$		0			0
$195$	−0.307853	+	0.163008i	−0.0220458	+	0.0116732i
$196$		0			0
$197$	−11.2813	−	11.2813i	−0.803759	−	0.803759i	0.179922	−	0.983681i	$-0.442415\pi$
$197$	−11.2813	−	11.2813i	−0.803759	−	0.803759i	−0.983681	+	0.179922i	$0.942415\pi$
$198$		0			0
$199$		−	25.6822i		−	1.82056i	−0.413989	−	0.910282i	$-0.635865\pi$
$199$		−	25.6822i		−	1.82056i	0.413989	−	0.910282i	$-0.364135\pi$
$200$		0			0
$201$	−1.13287	+	1.13287i	−0.0799066	+	0.0799066i
$202$		0			0
$203$	−12.4470	+	19.5108i	−0.873608	+	1.36939i
$204$		0			0
$205$	−0.343917	−	0.649515i	−0.0240202	−	0.0453641i
$206$		0			0
$207$	−6.58706	+	6.58706i	−0.457832	+	0.457832i
$208$		0			0
$209$	−6.45253			−0.446331
$210$		0			0
$211$	5.37571	−	5.37571i	0.370079	−	0.370079i	−0.497427	−	0.867506i	$-0.665722\pi$
$211$	5.37571	−	5.37571i	0.370079	−	0.370079i	0.867506	+	0.497427i	$0.165722\pi$
$212$		0			0
$213$			0.249350i			0.0170852i
$214$		0			0
$215$	1.85631	−	6.03446i	0.126599	−	0.411547i
$216$		0			0
$217$		−	23.9373i		−	1.62497i
$218$		0			0
$219$			1.35288i			0.0914193i
$220$		0			0
$221$	1.34721	−	1.34721i	0.0906235	−	0.0906235i
$222$		0			0
$223$	−13.3770	+	13.3770i	−0.895790	+	0.895790i	−0.995060	−	0.0992705i	$-0.968349\pi$
$223$	−13.3770	+	13.3770i	−0.895790	+	0.895790i	0.0992705	+	0.995060i	$0.468349\pi$
$224$		0			0
$225$	12.3550	+	8.39574i	0.823669	+	0.559716i
$226$		0			0
$227$	−6.98475	−	6.98475i	−0.463594	−	0.463594i	0.436237	−	0.899832i	$-0.356311\pi$
$227$	−6.98475	−	6.98475i	−0.463594	−	0.463594i	−0.899832	+	0.436237i	$0.856311\pi$
$228$		0			0
$229$	20.9513	+	20.9513i	1.38450	+	1.38450i	0.836437	+	0.548062i	$0.184634\pi$
$229$	20.9513	+	20.9513i	1.38450	+	1.38450i	0.548062	+	0.836437i	$0.315366\pi$
$230$		0			0
$231$			0.535358i			0.0352240i
$232$		0			0
$233$	14.3795	−	14.3795i	0.942032	−	0.942032i	−0.0563779	−	0.998409i	$-0.517955\pi$
$233$	14.3795	−	14.3795i	0.942032	−	0.942032i	0.998409	+	0.0563779i	$0.0179552\pi$
$234$		0			0
$235$	2.40802	−	7.82795i	0.157082	−	0.510639i
$236$		0			0
$237$	−0.227935	+	0.227935i	−0.0148059	+	0.0148059i
$238$		0			0
$239$			8.90857i			0.576248i	0.957593	+	0.288124i	$0.0930315\pi$
$239$			8.90857i			0.576248i	−0.957593	+	0.288124i	$0.906969\pi$
$240$		0			0
$241$			6.25420i			0.402869i	0.979502	+	0.201434i	$0.0645603\pi$
$241$			6.25420i			0.402869i	−0.979502	+	0.201434i	$0.935440\pi$
$242$		0			0
$243$	2.99684			0.192247
$244$		0			0
$245$	−24.5116	−	7.54022i	−1.56599	−	0.481727i
$246$		0			0
$247$	−8.06924			−0.513433
$248$		0			0
$249$	1.34418	−	1.34418i	0.0851840	−	0.0851840i
$250$		0			0
$251$	14.4661	+	14.4661i	0.913094	+	0.913094i	0.996514	−	0.0834205i	$-0.0265845\pi$
$251$	14.4661	+	14.4661i	0.913094	+	0.913094i	−0.0834205	+	0.996514i	$0.526584\pi$
$252$		0			0
$253$	3.48023			0.218800
$254$		0			0
$255$	0.325607	+	0.100163i	0.0203903	+	0.00627243i
$256$		0			0
$257$	−5.38550	−	5.38550i	−0.335938	−	0.335938i	0.518898	−	0.854836i	$-0.326342\pi$
$257$	−5.38550	−	5.38550i	−0.335938	−	0.335938i	−0.854836	+	0.518898i	$0.826342\pi$
$258$		0			0
$259$	−1.62688	−	1.62688i	−0.101090	−	0.101090i
$260$		0			0
$261$	−3.47228	−	15.7092i	−0.214929	−	0.972378i
$262$		0			0
$263$	−18.9364			−1.16767			−0.583835	−	0.811873i	$-0.698448\pi$
$263$	−18.9364			−1.16767			−0.583835	+	0.811873i	$0.698448\pi$
$264$		0			0
$265$	3.41260	+	6.44496i	0.209634	+	0.395911i
$266$		0			0
$267$	−0.560872	+	0.560872i	−0.0343248	+	0.0343248i
$268$		0			0
$269$	8.94862	+	8.94862i	0.545607	+	0.545607i	0.925167	−	0.379560i	$-0.123925\pi$
$269$	8.94862	+	8.94862i	0.545607	+	0.545607i	−0.379560	+	0.925167i	$0.623925\pi$
$270$		0			0
$271$	−9.68347	+	9.68347i	−0.588229	+	0.588229i	−0.937152	−	0.348922i	$-0.886548\pi$
$271$	−9.68347	+	9.68347i	−0.588229	+	0.588229i	0.348922	+	0.937152i	$0.386548\pi$
$272$		0			0
$273$			0.669494i			0.0405196i
$274$		0			0
$275$	−1.04593	−	5.48177i	−0.0630721	−	0.330563i
$276$		0			0
$277$	−11.5961	−	11.5961i	−0.696743	−	0.696743i	0.266964	−	0.963707i	$-0.413980\pi$
$277$	−11.5961	−	11.5961i	−0.696743	−	0.696743i	−0.963707	+	0.266964i	$0.913980\pi$
$278$		0			0
$279$	11.7667	+	11.7667i	0.704453	+	0.704453i
$280$		0			0
$281$	20.4708			1.22119			0.610593	−	0.791945i	$-0.290931\pi$
$281$	20.4708			1.22119			0.610593	+	0.791945i	$0.290931\pi$
$282$		0			0
$283$	13.4703	+	13.4703i	0.800729	+	0.800729i	0.983209	−	0.182481i	$-0.0584127\pi$
$283$	13.4703	+	13.4703i	0.800729	+	0.800729i	−0.182481	+	0.983209i	$0.558413\pi$
$284$		0			0
$285$	−0.675157	−	1.27509i	−0.0399929	−	0.0755297i
$286$		0			0
$287$	−1.41251			−0.0833778
$288$		0			0
$289$	15.1368			0.890398
$290$		0			0
$291$	0.412241			0.0241660
$292$		0			0
$293$	1.19347			0.0697233			0.0348617	−	0.999392i	$-0.488901\pi$
$293$	1.19347			0.0697233			0.0348617	+	0.999392i	$0.488901\pi$
$294$		0			0
$295$	14.3962	+	4.42852i	0.838176	+	0.257838i
$296$		0			0
$297$	−0.527422	−	0.527422i	−0.0306041	−	0.0306041i
$298$		0			0
$299$	4.35222			0.251695
$300$		0			0
$301$	−8.58009	−	8.58009i	−0.494548	−	0.494548i
$302$		0			0
$303$	0.881837	+	0.881837i	0.0506602	+	0.0506602i
$304$		0			0
$305$	−15.3761	+	8.14164i	−0.880434	+	0.466189i
$306$		0			0
$307$			17.0802i			0.974817i	0.873174	+	0.487408i	$0.162058\pi$
$307$			17.0802i			0.974817i	−0.873174	+	0.487408i	$0.837942\pi$
$308$		0			0
$309$	−1.08702	+	1.08702i	−0.0618382	+	0.0618382i
$310$		0			0
$311$	−13.2601	−	13.2601i	−0.751910	−	0.751910i	0.222925	−	0.974836i	$-0.428439\pi$
$311$	−13.2601	−	13.2601i	−0.751910	−	0.751910i	−0.974836	+	0.222925i	$0.928439\pi$
$312$		0			0
$313$	4.86551	−	4.86551i	0.275015	−	0.275015i	−0.556100	−	0.831115i	$-0.687703\pi$
$313$	4.86551	−	4.86551i	0.275015	−	0.275015i	0.831115	+	0.556100i	$0.187703\pi$
$314$		0			0
$315$	25.3718	−	13.4343i	1.42954	−	0.756940i
$316$		0			0
$317$	27.3719			1.53736			0.768680	−	0.639633i	$-0.220914\pi$
$317$	27.3719			1.53736			0.768680	+	0.639633i	$0.220914\pi$
$318$		0			0
$319$	−3.23266	+	5.06722i	−0.180994	+	0.283710i
$320$		0			0
$321$	0.422381	+	0.422381i	0.0235750	+	0.0235750i
$322$		0			0
$323$	5.57999	+	5.57999i	0.310479	+	0.310479i
$324$		0			0
$325$	−1.30799	−	6.85525i	−0.0725545	−	0.380261i
$326$		0			0
$327$	1.16546			0.0644499
$328$		0			0
$329$	−11.1302	−	11.1302i	−0.613626	−	0.613626i
$330$		0			0
$331$	18.5465	−	18.5465i	1.01941	−	1.01941i	0.0195998	−	0.999808i	$-0.493761\pi$
$331$	18.5465	−	18.5465i	1.01941	−	1.01941i	0.999808	−	0.0195998i	$-0.00623921\pi$
$332$		0			0
$333$	1.59943			0.0876482
$334$		0			0
$335$	−15.0200	−	28.3664i	−0.820629	−	1.54982i
$336$		0			0
$337$	33.7679			1.83945			0.919726	−	0.392561i	$-0.128411\pi$
$337$	33.7679			1.83945			0.919726	+	0.392561i	$0.128411\pi$
$338$		0			0
$339$			1.92467i			0.104534i
$340$		0			0
$341$		−	6.21685i		−	0.336662i
$342$		0			0
$343$	−13.5801	+	13.5801i	−0.733257	+	0.733257i
$344$		0			0
$345$	0.364152	+	0.687731i	0.0196053	+	0.0370262i
$346$		0			0
$347$	17.6588	−	17.6588i	0.947974	−	0.947974i	−0.0507381	−	0.998712i	$-0.516157\pi$
$347$	17.6588	−	17.6588i	0.947974	−	0.947974i	0.998712	+	0.0507381i	$0.0161574\pi$
$348$		0			0
$349$			8.48972i			0.454444i	0.973843	+	0.227222i	$0.0729643\pi$
$349$			8.48972i			0.454444i	−0.973843	+	0.227222i	$0.927036\pi$
$350$		0			0
$351$	−0.659569	−	0.659569i	−0.0352052	−	0.0352052i
$352$		0			0
$353$	−15.0796	−	15.0796i	−0.802606	−	0.802606i	0.180896	−	0.983502i	$-0.442100\pi$
$353$	−15.0796	−	15.0796i	−0.802606	−	0.802606i	−0.983502	+	0.180896i	$0.942100\pi$
$354$		0			0
$355$	−4.77477	−	1.46881i	−0.253418	−	0.0779561i
$356$		0			0
$357$	0.462964	−	0.462964i	0.0245027	−	0.0245027i
$358$		0			0
$359$	1.29845	−	1.29845i	0.0685296	−	0.0685296i	−0.672011	−	0.740541i	$-0.734569\pi$
$359$	1.29845	−	1.29845i	0.0685296	−	0.0685296i	0.740541	+	0.672011i	$0.234569\pi$
$360$		0			0
$361$		−	14.4217i		−	0.759038i
$362$		0			0
$363$		−	1.08868i		−	0.0571411i
$364$		0			0
$365$	−25.9061	−	7.96920i	−1.35599	−	0.417127i
$366$		0			0
$367$		−	18.1775i		−	0.948858i	−0.880294	−	0.474429i	$-0.842654\pi$
$367$		−	18.1775i		−	0.948858i	0.880294	−	0.474429i	$-0.157346\pi$
$368$		0			0
$369$	0.694337	−	0.694337i	0.0361458	−	0.0361458i
$370$		0			0
$371$	14.0160			0.727672
$372$		0			0
$373$	4.72419	−	4.72419i	0.244609	−	0.244609i	−0.574145	−	0.818754i	$-0.694665\pi$
$373$	4.72419	−	4.72419i	0.244609	−	0.244609i	0.818754	+	0.574145i	$0.194665\pi$
$374$		0			0
$375$	0.973815	−	0.780270i	0.0502876	−	0.0402930i
$376$		0			0
$377$	−4.04261	+	6.33683i	−0.208205	+	0.326363i
$378$		0			0
$379$	−12.4809	+	12.4809i	−0.641102	+	0.641102i	−0.950826	−	0.309725i	$-0.899763\pi$
$379$	−12.4809	+	12.4809i	−0.641102	+	0.641102i	0.309725	+	0.950826i	$0.399763\pi$
$380$		0			0
$381$			0.179199i			0.00918063i
$382$		0			0
$383$	−3.91433	−	3.91433i	−0.200013	−	0.200013i	0.599993	−	0.800005i	$-0.295170\pi$
$383$	−3.91433	−	3.91433i	−0.200013	−	0.200013i	−0.800005	+	0.599993i	$0.795170\pi$
$384$		0			0
$385$	−10.2515	−	3.15355i	−0.522465	−	0.160720i
$386$		0			0
$387$	8.43531			0.428791
$388$		0			0
$389$	12.2041	+	12.2041i	0.618773	+	0.618773i	0.945217	−	0.326444i	$-0.105850\pi$
$389$	12.2041	+	12.2041i	0.618773	+	0.618773i	−0.326444	+	0.945217i	$0.605850\pi$
$390$		0			0
$391$	−3.00962	−	3.00962i	−0.152203	−	0.152203i
$392$		0			0
$393$	0.396060	−	0.396060i	0.0199786	−	0.0199786i
$394$		0			0
$395$	−3.02203	−	5.70735i	−0.152055	−	0.287168i
$396$		0			0
$397$	−25.7991	−	25.7991i	−1.29482	−	1.29482i	−0.931771	−	0.363047i	$-0.881736\pi$
$397$	−25.7991	−	25.7991i	−1.29482	−	1.29482i	−0.363047	−	0.931771i	$-0.618264\pi$
$398$		0			0
$399$	−2.77296			−0.138821
$400$		0			0
$401$	16.1462			0.806303			0.403151	−	0.915133i	$-0.367915\pi$
$401$	16.1462			0.806303			0.403151	+	0.915133i	$0.367915\pi$
$402$		0			0
$403$		−	7.77451i		−	0.387276i
$404$		0			0
$405$	−5.84345	+	18.9958i	−0.290364	+	0.943909i
$406$		0			0
$407$	−0.422524	−	0.422524i	−0.0209438	−	0.0209438i
$408$		0			0
$409$	−7.21711	+	7.21711i	−0.356863	+	0.356863i	−0.862655	−	0.505792i	$-0.831200\pi$
$409$	−7.21711	+	7.21711i	−0.356863	+	0.356863i	0.505792	+	0.862655i	$0.331200\pi$
$410$		0			0
$411$		−	1.32778i		−	0.0654946i
$412$		0			0
$413$	20.4692	−	20.4692i	1.00722	−	1.00722i
$414$		0			0
$415$	17.8216	+	33.6575i	0.874827	+	1.65218i
$416$		0			0
$417$			1.03045i			0.0504611i
$418$		0			0
$419$	15.3722			0.750980			0.375490	−	0.926826i	$-0.377474\pi$
$419$	15.3722			0.750980			0.375490	+	0.926826i	$0.377474\pi$
$420$		0			0
$421$	−28.8223	+	28.8223i	−1.40471	+	1.40471i	−0.620526	+	0.784186i	$0.713081\pi$
$421$	−28.8223	+	28.8223i	−1.40471	+	1.40471i	−0.784186	+	0.620526i	$0.786919\pi$
$422$		0			0
$423$	10.9423			0.532035
$424$		0			0
$425$	−3.83600	+	5.64499i	−0.186073	+	0.273822i
$426$		0			0
$427$			33.4387i			1.61821i
$428$		0			0
$429$			0.173877i			0.00839487i
$430$		0			0
$431$	17.3717			0.836767			0.418383	−	0.908271i	$-0.362597\pi$
$431$	17.3717			0.836767			0.418383	+	0.908271i	$0.362597\pi$
$432$		0			0
$433$			4.72720i			0.227175i	0.993528	+	0.113587i	$0.0362342\pi$
$433$			4.72720i			0.227175i	−0.993528	+	0.113587i	$0.963766\pi$
$434$		0			0
$435$	−1.33958	−	0.108602i	−0.0642281	−	0.00520706i
$436$		0			0
$437$			18.0263i			0.862315i
$438$		0			0
$439$	39.0732			1.86486			0.932431	−	0.361348i	$-0.117683\pi$
$439$	39.0732			1.86486			0.932431	+	0.361348i	$0.117683\pi$
$440$		0			0
$441$		−	34.2637i		−	1.63161i
$442$		0			0
$443$			6.63361i			0.315173i	0.987505	+	0.157586i	$0.0503712\pi$
$443$			6.63361i			0.315173i	−0.987505	+	0.157586i	$0.949629\pi$
$444$		0			0
$445$	−7.43622	−	14.0439i	−0.352511	−	0.665744i
$446$		0			0
$447$	0.927933			0.0438897
$448$		0			0
$449$	−18.3025	+	18.3025i	−0.863746	+	0.863746i	−0.991771	−	0.128025i	$-0.959136\pi$
$449$	−18.3025	+	18.3025i	−0.863746	+	0.863746i	0.128025	+	0.991771i	$0.459136\pi$
$450$		0			0
$451$	−0.366849			−0.0172742
$452$		0			0
$453$		−	2.04505i		−	0.0960847i
$454$		0			0
$455$	−12.8201	−	3.94368i	−0.601013	−	0.184883i
$456$		0			0
$457$	−16.5907	+	16.5907i	−0.776082	+	0.776082i	−0.979162	−	0.203080i	$-0.934905\pi$
$457$	−16.5907	+	16.5907i	−0.776082	+	0.776082i	0.203080	+	0.979162i	$0.434905\pi$
$458$		0			0
$459$			0.912202i			0.0425779i
$460$		0			0
$461$	0.452012	−	0.452012i	0.0210523	−	0.0210523i	−0.696502	−	0.717555i	$-0.745261\pi$
$461$	0.452012	−	0.452012i	0.0210523	−	0.0210523i	0.717555	+	0.696502i	$0.245261\pi$
$462$		0			0
$463$	−5.03929	−	5.03929i	−0.234196	−	0.234196i	0.580246	−	0.814442i	$-0.302957\pi$
$463$	−5.03929	−	5.03929i	−0.234196	−	0.234196i	−0.814442	+	0.580246i	$0.802957\pi$
$464$		0			0
$465$	1.22852	−	0.650497i	0.0569711	−	0.0301661i
$466$		0			0
$467$			12.5928i			0.582726i	0.956613	+	0.291363i	$0.0941087\pi$
$467$			12.5928i			0.582726i	−0.956613	+	0.291363i	$0.905891\pi$
$468$		0			0
$469$	−61.6889			−2.84853
$470$		0			0
$471$	−1.62961			−0.0750884
$472$		0			0
$473$	−2.22837	−	2.22837i	−0.102461	−	0.102461i
$474$		0			0
$475$	28.3935	−	5.41754i	1.30279	−	0.248574i
$476$		0			0
$477$	−6.88972	+	6.88972i	−0.315459	+	0.315459i
$478$		0			0
$479$	21.8299	+	21.8299i	0.997435	+	0.997435i	0.999997	−	0.00256128i	$-0.000815281\pi$
$479$	21.8299	+	21.8299i	0.997435	+	0.997435i	−0.00256128	+	0.999997i	$0.500815\pi$
$480$		0			0
$481$	−0.528389	−	0.528389i	−0.0240925	−	0.0240925i
$482$		0			0
$483$	1.49562			0.0680530
$484$		0			0
$485$	−2.42832	+	7.89395i	−0.110264	+	0.358446i
$486$		0			0
$487$	−11.3194	−	11.3194i	−0.512931	−	0.512931i	0.402492	−	0.915423i	$-0.368144\pi$
$487$	−11.3194	−	11.3194i	−0.512931	−	0.512931i	−0.915423	+	0.402492i	$0.868144\pi$
$488$		0			0
$489$			1.30360i			0.0589510i
$490$		0			0
$491$	−7.37068	+	7.37068i	−0.332634	+	0.332634i	−0.853586	−	0.520952i	$-0.825577\pi$
$491$	−7.37068	+	7.37068i	−0.332634	+	0.332634i	0.520952	+	0.853586i	$0.325577\pi$
$492$		0			0
$493$	7.17753	−	1.58648i	0.323260	−	0.0714515i
$494$		0			0
$495$	6.58943	−	3.48909i	0.296173	−	0.156823i
$496$		0			0
$497$	−6.78900	+	6.78900i	−0.304528	+	0.304528i
$498$		0			0
$499$	−18.4883			−0.827650			−0.413825	−	0.910356i	$-0.635808\pi$
$499$	−18.4883			−0.827650			−0.413825	+	0.910356i	$0.635808\pi$
$500$		0			0
$501$	1.15598	−	1.15598i	0.0516455	−	0.0516455i
$502$		0			0
$503$			5.45289i			0.243132i	0.992583	+	0.121566i	$0.0387917\pi$
$503$			5.45289i			0.243132i	−0.992583	+	0.121566i	$0.961208\pi$
$504$		0			0
$505$	−22.0807	+	11.6917i	−0.982577	+	0.520273i
$506$		0			0
$507$		−	1.23351i		−	0.0547819i
$508$		0			0
$509$		−	17.5561i		−	0.778163i	−0.921203	−	0.389081i	$-0.872793\pi$
$509$		−	17.5561i		−	0.778163i	0.921203	−	0.389081i	$-0.127207\pi$
$510$		0			0
$511$	−36.8346	+	36.8346i	−1.62947	+	1.62947i
$512$		0			0
$513$	2.73185	−	2.73185i	0.120614	−	0.120614i
$514$		0			0
$515$	−14.4120	−	27.2183i	−0.635070	−	1.19938i
$516$		0			0
$517$	−2.89066	−	2.89066i	−0.127131	−	0.127131i
$518$		0			0
$519$	1.07541	+	1.07541i	0.0472052	+	0.0472052i
$520$		0			0
$521$			36.6983i			1.60778i	0.594775	+	0.803892i	$0.297241\pi$
$521$			36.6983i			1.60778i	−0.594775	+	0.803892i	$0.702759\pi$
$522$		0			0
$523$	−23.6594	+	23.6594i	−1.03456	+	1.03456i	−0.0351742	+	0.999381i	$0.511199\pi$
$523$	−23.6594	+	23.6594i	−1.03456	+	1.03456i	−0.999381	+	0.0351742i	$0.988801\pi$
$524$		0			0
$525$	−0.449486	−	2.35577i	−0.0196172	−	0.102814i
$526$		0			0
$527$	−5.37618	+	5.37618i	−0.234190	+	0.234190i
$528$		0			0
$529$			13.2773i			0.577276i
$530$		0			0
$531$			20.1238i			0.873297i
$532$		0			0
$533$	−0.458764			−0.0198713
$534$		0			0
$535$	−10.5762	+	5.60007i	−0.457248	+	0.242112i
$536$		0			0
$537$	0.179794			0.00775868
$538$		0			0
$539$	−9.05152	+	9.05152i	−0.389877	+	0.389877i
$540$		0			0
$541$	19.6123	+	19.6123i	0.843198	+	0.843198i	0.989273	−	0.146076i	$-0.0466643\pi$
$541$	19.6123	+	19.6123i	0.843198	+	0.843198i	−0.146076	+	0.989273i	$0.546664\pi$
$542$		0			0
$543$	0.860878			0.0369438
$544$		0			0
$545$	−6.86517	+	22.3172i	−0.294072	+	0.955963i
$546$		0			0
$547$	18.7111	+	18.7111i	0.800031	+	0.800031i	0.983100	−	0.183069i	$-0.0586032\pi$
$547$	18.7111	+	18.7111i	0.800031	+	0.800031i	−0.183069	+	0.983100i	$0.558603\pi$
$548$		0			0
$549$	−16.4372	−	16.4372i	−0.701524	−	0.701524i
$550$		0			0
$551$	−26.2463	−	16.7440i	−1.11813	−	0.713317i
$552$		0			0
$553$	−12.4119			−0.527806
$554$		0			0
$555$	0.0392846	−	0.127706i	0.00166754	−	0.00542081i
$556$		0			0
$557$	−8.06718	+	8.06718i	−0.341817	+	0.341817i	−0.857050	−	0.515233i	$-0.827705\pi$
$557$	−8.06718	+	8.06718i	−0.341817	+	0.341817i	0.515233	+	0.857050i	$0.327705\pi$
$558$		0			0
$559$	−2.78670	−	2.78670i	−0.117865	−	0.117865i
$560$		0			0
$561$	0.120238	−	0.120238i	0.00507647	−	0.00507647i
$562$		0			0
$563$		−	12.9679i		−	0.546533i	−0.961938	−	0.273267i	$-0.911896\pi$
$563$		−	12.9679i		−	0.546533i	0.961938	−	0.273267i	$-0.0881041\pi$
$564$		0			0
$565$	−36.8552	−	11.3373i	−1.55051	−	0.476965i
$566$		0			0
$567$	27.0092	+	27.0092i	1.13428	+	1.13428i
$568$		0			0
$569$	−29.1001	−	29.1001i	−1.21994	−	1.21994i	−0.967653	−	0.252285i	$-0.918818\pi$
$569$	−29.1001	−	29.1001i	−1.21994	−	1.21994i	−0.252285	−	0.967653i	$-0.581182\pi$
$570$		0			0
$571$	22.0919			0.924516			0.462258	−	0.886745i	$-0.347039\pi$
$571$	22.0919			0.924516			0.462258	+	0.886745i	$0.347039\pi$
$572$		0			0
$573$	−0.407762	−	0.407762i	−0.0170345	−	0.0170345i
$574$		0			0
$575$	−15.3143	+	2.92200i	−0.638651	+	0.121856i
$576$		0			0
$577$	−22.1361			−0.921536			−0.460768	−	0.887521i	$-0.652426\pi$
$577$	−22.1361			−0.921536			−0.460768	+	0.887521i	$0.652426\pi$
$578$		0			0
$579$	1.43555			0.0596596
$580$		0			0
$581$	73.1955			3.03666
$582$		0			0
$583$	3.64014			0.150759
$584$		0			0
$585$	8.24043	−	4.36329i	0.340700	−	0.180400i
$586$		0			0
$587$	−13.6093	−	13.6093i	−0.561717	−	0.561717i	0.368078	−	0.929795i	$-0.380016\pi$
$587$	−13.6093	−	13.6093i	−0.561717	−	0.561717i	−0.929795	+	0.368078i	$0.880016\pi$
$588$		0			0
$589$	32.2010			1.32682
$590$		0			0
$591$	−1.25912	−	1.25912i	−0.0517933	−	0.0517933i
$592$		0			0
$593$	6.75484	+	6.75484i	0.277388	+	0.277388i	0.832065	−	0.554677i	$-0.187158\pi$
$593$	6.75484	+	6.75484i	0.277388	+	0.277388i	−0.554677	+	0.832065i	$0.687158\pi$
$594$		0			0
$595$	6.13813	+	11.5923i	0.251639	+	0.475240i
$596$		0			0
$597$		−	2.86643i		−	0.117315i
$598$		0			0
$599$	−5.64758	+	5.64758i	−0.230754	+	0.230754i	−0.813007	−	0.582254i	$-0.802171\pi$
$599$	−5.64758	+	5.64758i	−0.230754	+	0.230754i	0.582254	+	0.813007i	$0.302171\pi$
$600$		0			0
$601$	−1.68284	−	1.68284i	−0.0686447	−	0.0686447i	0.671951	−	0.740596i	$-0.265457\pi$
$601$	−1.68284	−	1.68284i	−0.0686447	−	0.0686447i	−0.740596	+	0.671951i	$0.765457\pi$
$602$		0			0
$603$	30.3240	−	30.3240i	1.23489	−	1.23489i
$604$		0			0
$605$	20.8471	+	6.41294i	0.847554	+	0.260723i
$606$		0			0
$607$	15.3508			0.623070			0.311535	−	0.950235i	$-0.399157\pi$
$607$	15.3508			0.623070			0.311535	+	0.950235i	$0.399157\pi$
$608$		0			0
$609$	−1.38923	+	2.17762i	−0.0562943	+	0.0882417i
$610$		0			0
$611$	−3.61493	−	3.61493i	−0.146244	−	0.146244i
$612$		0			0
$613$	−24.2570	−	24.2570i	−0.979732	−	0.979732i	0.0200669	−	0.999799i	$-0.493612\pi$
$613$	−24.2570	−	24.2570i	−0.979732	−	0.979732i	−0.999799	+	0.0200669i	$0.993612\pi$
$614$		0			0
$615$	−0.0383850	−	0.0724932i	−0.00154783	−	0.00292321i
$616$		0			0
$617$	−14.8311			−0.597079			−0.298540	−	0.954397i	$-0.596499\pi$
$617$	−14.8311			−0.597079			−0.298540	+	0.954397i	$0.596499\pi$
$618$		0			0
$619$	5.28755	+	5.28755i	0.212525	+	0.212525i	0.805339	−	0.592814i	$-0.201983\pi$
$619$	5.28755	+	5.28755i	0.212525	+	0.212525i	−0.592814	+	0.805339i	$0.701983\pi$
$620$		0			0
$621$	−1.47345	+	1.47345i	−0.0591274	+	0.0591274i
$622$		0			0
$623$	−30.5415			−1.22362
$624$		0			0
$625$	9.20498	+	23.2437i	0.368199	+	0.929747i
$626$		0			0
$627$	−0.720176			−0.0287611
$628$		0			0
$629$			0.730777i			0.0291380i
$630$		0			0
$631$		−	7.66638i		−	0.305194i	−0.988289	−	0.152597i	$-0.951236\pi$
$631$		−	7.66638i		−	0.305194i	0.988289	−	0.152597i	$-0.0487636\pi$
$632$		0			0
$633$	0.599991	−	0.599991i	0.0238475	−	0.0238475i
$634$		0			0
$635$	−3.43145	−	1.05558i	−0.136173	−	0.0418893i
$636$		0			0
$637$	−11.3194	+	11.3194i	−0.448491	+	0.448491i
$638$		0			0
$639$		−	6.67444i		−	0.264037i
$640$		0			0
$641$	−12.2711	−	12.2711i	−0.484680	−	0.484680i	0.421943	−	0.906622i	$-0.361348\pi$
$641$	−12.2711	−	12.2711i	−0.484680	−	0.484680i	−0.906622	+	0.421943i	$0.861348\pi$
$642$		0			0
$643$	−5.79768	−	5.79768i	−0.228638	−	0.228638i	0.583486	−	0.812124i	$-0.301688\pi$
$643$	−5.79768	−	5.79768i	−0.228638	−	0.228638i	−0.812124	+	0.583486i	$0.801688\pi$
$644$		0			0
$645$	0.207185	−	0.673514i	0.00815791	−	0.0265196i
$646$		0			0
$647$	−10.5241	+	10.5241i	−0.413745	+	0.413745i	−0.883041	−	0.469296i	$-0.844508\pi$
$647$	−10.5241	+	10.5241i	−0.413745	+	0.413745i	0.469296	+	0.883041i	$0.344508\pi$
$648$		0			0
$649$	5.31613	−	5.31613i	0.208676	−	0.208676i
$650$		0			0
$651$		−	2.67167i		−	0.104711i
$652$		0			0
$653$			23.2875i			0.911309i	0.890157	+	0.455655i	$0.150595\pi$
$653$			23.2875i			0.911309i	−0.890157	+	0.455655i	$0.849405\pi$
$654$		0			0
$655$	5.25110	+	9.91712i	0.205177	+	0.387494i
$656$		0			0
$657$		−	36.2131i		−	1.41281i
$658$		0			0
$659$	24.8937	−	24.8937i	0.969721	−	0.969721i	−0.0298340	−	0.999555i	$-0.509498\pi$
$659$	24.8937	−	24.8937i	0.969721	−	0.969721i	0.999555	+	0.0298340i	$0.00949785\pi$
$660$		0			0
$661$	17.2394			0.670535			0.335268	−	0.942123i	$-0.391173\pi$
$661$	17.2394			0.670535			0.335268	+	0.942123i	$0.391173\pi$
$662$		0			0
$663$	0.150365	−	0.150365i	0.00583967	−	0.00583967i
$664$		0			0
$665$	16.3342	−	53.0990i	0.633414	−	2.05909i
$666$		0			0
$667$	14.1562	+	9.03102i	0.548130	+	0.349682i
$668$		0			0
$669$	−1.49303	+	1.49303i	−0.0577237	+	0.0577237i
$670$		0			0
$671$			8.68451i			0.335262i
$672$		0			0
$673$	−6.49859	−	6.49859i	−0.250502	−	0.250502i	0.570674	−	0.821177i	$-0.306682\pi$
$673$	−6.49859	−	6.49859i	−0.250502	−	0.250502i	−0.821177	+	0.570674i	$0.806682\pi$
$674$		0			0
$675$	2.76367	+	1.87803i	0.106374	+	0.0722853i
$676$		0			0
$677$	10.9356			0.420289			0.210144	−	0.977670i	$-0.432607\pi$
$677$	10.9356			0.420289			0.210144	+	0.977670i	$0.432607\pi$
$678$		0			0
$679$	11.2240	+	11.2240i	0.430738	+	0.430738i
$680$		0			0
$681$	−0.779578	−	0.779578i	−0.0298735	−	0.0298735i
$682$		0			0
$683$	−27.1259	+	27.1259i	−1.03794	+	1.03794i	−0.0386909	+	0.999251i	$0.512319\pi$
$683$	−27.1259	+	27.1259i	−1.03794	+	1.03794i	−0.999251	+	0.0386909i	$0.987681\pi$
$684$		0			0
$685$	25.4255	+	7.82134i	0.971458	+	0.298838i
$686$		0			0
$687$	2.33840	+	2.33840i	0.0892156	+	0.0892156i
$688$		0			0
$689$	4.55219			0.173425
$690$		0			0
$691$	−12.9533			−0.492767			−0.246383	−	0.969172i	$-0.579242\pi$
$691$	−12.9533			−0.492767			−0.246383	+	0.969172i	$0.579242\pi$
$692$		0			0
$693$		−	14.3301i		−	0.544357i
$694$		0			0
$695$	−19.7319	−	6.06988i	−0.748472	−	0.230244i
$696$		0			0
$697$	0.317242	+	0.317242i	0.0120164	+	0.0120164i
$698$		0			0
$699$	1.60491	−	1.60491i	0.0607034	−	0.0607034i
$700$		0			0
$701$			19.4640i			0.735144i	0.929995	+	0.367572i	$0.119811\pi$
$701$			19.4640i			0.735144i	−0.929995	+	0.367572i	$0.880189\pi$
$702$		0			0
$703$	2.18852	−	2.18852i	0.0825416	−	0.0825416i
$704$		0			0
$705$	0.268762	−	0.873688i	0.0101222	−	0.0329050i
$706$		0			0
$707$			48.0192i			1.80595i
$708$		0			0
$709$	−1.36436			−0.0512397			−0.0256199	−	0.999672i	$-0.508156\pi$
$709$	−1.36436			−0.0512397			−0.0256199	+	0.999672i	$0.508156\pi$
$710$		0			0
$711$	6.10121	−	6.10121i	0.228813	−	0.228813i
$712$		0			0
$713$	−17.3679			−0.650433
$714$		0			0
$715$	−3.32955	−	1.02423i	−0.124518	−	0.0383040i
$716$		0			0
$717$			0.994298i			0.0371327i
$718$		0			0
$719$		−	11.2828i		−	0.420777i	−0.977618	−	0.210389i	$-0.932527\pi$
$719$		−	11.2828i		−	0.420777i	0.977618	−	0.210389i	$-0.0674729\pi$
$720$		0			0
$721$	−59.1920			−2.20442
$722$		0			0
$723$			0.698040i			0.0259604i
$724$		0			0
$725$	9.97047	−	25.0118i	0.370294	−	0.928915i
$726$		0			0
$727$		−	4.76329i		−	0.176661i	−0.996091	−	0.0883304i	$-0.971847\pi$
$727$		−	4.76329i		−	0.176661i	0.996091	−	0.0883304i	$-0.0281531\pi$
$728$		0			0
$729$	−26.3296			−0.975172
$730$		0			0
$731$			3.85408i			0.142548i
$732$		0			0
$733$			41.7313i			1.54138i	0.637209	+	0.770691i	$0.280089\pi$
$733$			41.7313i			1.54138i	−0.637209	+	0.770691i	$0.719911\pi$
$734$		0			0
$735$	−2.73578	−	0.841575i	−0.100911	−	0.0310419i
$736$		0			0
$737$	−16.0215			−0.590159
$738$		0			0
$739$	−22.2962	+	22.2962i	−0.820178	+	0.820178i	−0.986133	−	0.165955i	$-0.946929\pi$
$739$	−22.2962	+	22.2962i	−0.820178	+	0.820178i	0.165955	+	0.986133i	$0.446929\pi$
$740$		0			0
$741$	−0.900619			−0.0330851
$742$		0			0
$743$		−	21.2063i		−	0.777984i	−0.921241	−	0.388992i	$-0.872823\pi$
$743$		−	21.2063i		−	0.777984i	0.921241	−	0.388992i	$-0.127177\pi$
$744$		0			0
$745$	−5.46602	+	17.7689i	−0.200260	+	0.651001i
$746$		0			0
$747$	−35.9802	+	35.9802i	−1.31645	+	1.31645i
$748$		0			0
$749$			23.0002i			0.840409i
$750$		0			0
$751$	23.1872	−	23.1872i	0.846114	−	0.846114i	−0.143532	−	0.989646i	$-0.545846\pi$
$751$	23.1872	−	23.1872i	0.846114	−	0.846114i	0.989646	+	0.143532i	$0.0458460\pi$
$752$		0			0
$753$	1.61458	+	1.61458i	0.0588387	+	0.0588387i
$754$		0			0
$755$	39.1603	+	12.0464i	1.42519	+	0.438414i
$756$		0			0
$757$		−	8.45983i		−	0.307478i	−0.988112	−	0.153739i	$-0.950869\pi$
$757$		−	8.45983i		−	0.307478i	0.988112	−	0.153739i	$-0.0491315\pi$
$758$		0			0
$759$	0.388434			0.0140992
$760$		0			0
$761$	43.1756			1.56511			0.782557	−	0.622580i	$-0.213915\pi$
$761$	43.1756			1.56511			0.782557	+	0.622580i	$0.213915\pi$
$762$		0			0
$763$	31.7317	+	31.7317i	1.14876	+	1.14876i
$764$		0			0
$765$	−8.71564	−	2.68109i	−0.315115	−	0.0969350i
$766$		0			0
$767$	6.64811	−	6.64811i	0.240049	−	0.240049i
$768$		0			0
$769$	36.0717	+	36.0717i	1.30078	+	1.30078i	0.927867	+	0.372911i	$0.121640\pi$
$769$	36.0717	+	36.0717i	1.30078	+	1.30078i	0.372911	+	0.927867i	$0.378360\pi$
$770$		0			0
$771$	−0.601083	−	0.601083i	−0.0216475	−	0.0216475i
$772$		0			0
$773$	39.7356			1.42919			0.714595	−	0.699538i	$-0.246611\pi$
$773$	39.7356			1.42919			0.714595	+	0.699538i	$0.246611\pi$
$774$		0			0
$775$	5.21966	+	27.3565i	0.187496	+	0.982673i
$776$		0			0
$777$	−0.181579	−	0.181579i	−0.00651409	−	0.00651409i
$778$		0			0
$779$		−	1.90014i		−	0.0680796i
$780$		0			0
$781$	−1.76320	+	1.76320i	−0.0630923	+	0.0630923i
$782$		0			0
$783$	−0.776709	−	3.51397i	−0.0277573	−	0.125579i
$784$		0			0
$785$	9.59928	−	31.2052i	0.342613	−	1.11376i
$786$		0			0
$787$	−5.90443	+	5.90443i	−0.210470	+	0.210470i	−0.804467	−	0.593997i	$-0.797549\pi$
$787$	−5.90443	+	5.90443i	−0.210470	+	0.210470i	0.593997	+	0.804467i	$0.297549\pi$
$788$		0			0
$789$	−2.11352			−0.0752433
$790$		0			0
$791$	−52.4025	+	52.4025i	−1.86322	+	1.86322i
$792$		0			0
$793$			10.8604i			0.385666i
$794$		0			0
$795$	0.380884	+	0.719331i	0.0135086	+	0.0255120i
$796$		0			0
$797$		−	40.6134i		−	1.43860i	−0.694699	−	0.719300i	$-0.744462\pi$
$797$		−	40.6134i		−	1.43860i	0.694699	−	0.719300i	$-0.255538\pi$
$798$		0			0
$799$			4.99954i			0.176871i
$800$		0			0
$801$	15.0131	−	15.0131i	0.530460	−	0.530460i
$802$		0			0
$803$	−9.56648	+	9.56648i	−0.337594	+	0.337594i
$804$		0			0
$805$	−8.81000	+	28.6394i	−0.310512	+	1.00941i
$806$		0			0
$807$	0.998768	+	0.998768i	0.0351583	+	0.0351583i
$808$		0			0
$809$	−35.4359	−	35.4359i	−1.24586	−	1.24586i	−0.957532	−	0.288327i	$-0.906901\pi$
$809$	−35.4359	−	35.4359i	−1.24586	−	1.24586i	−0.288327	−	0.957532i	$-0.593099\pi$
$810$		0			0
$811$			0.622276i			0.0218511i	0.999940	+	0.0109255i	$0.00347778\pi$
$811$			0.622276i			0.0218511i	−0.999940	+	0.0109255i	$0.996522\pi$
$812$		0			0
$813$	−1.08079	+	1.08079i	−0.0379048	+	0.0379048i
$814$		0			0
$815$	−24.9625	−	7.67893i	−0.874399	−	0.268981i
$816$		0			0
$817$	11.5421	−	11.5421i	0.403808	−	0.403808i
$818$		0			0
$819$		−	17.9206i		−	0.626196i
$820$		0			0
$821$		−	7.77929i		−	0.271499i	−0.990743	−	0.135750i	$-0.956656\pi$
$821$		−	7.77929i		−	0.271499i	0.990743	−	0.135750i	$-0.0433443\pi$
$822$		0			0
$823$	0.222068			0.00774079			0.00387040	−	0.999993i	$-0.498768\pi$
$823$	0.222068			0.00774079			0.00387040	+	0.999993i	$0.498768\pi$
$824$		0			0
$825$	−0.116738	−	0.611828i	−0.00406429	−	0.0213011i
$826$		0			0
$827$	−32.1988			−1.11966			−0.559831	−	0.828607i	$-0.689134\pi$
$827$	−32.1988			−1.11966			−0.559831	+	0.828607i	$0.689134\pi$
$828$		0			0
$829$	13.8953	−	13.8953i	0.482604	−	0.482604i	−0.423359	−	0.905962i	$-0.639149\pi$
$829$	13.8953	−	13.8953i	0.482604	−	0.482604i	0.905962	+	0.423359i	$0.139149\pi$
$830$		0			0
$831$	−1.29426	−	1.29426i	−0.0448973	−	0.0448973i
$832$		0			0
$833$	15.6550			0.542415
$834$		0			0
$835$	15.3264	+	28.9451i	0.530392	+	1.00169i
$836$		0			0
$837$	2.63207	+	2.63207i	0.0909775	+	0.0909775i
$838$		0			0
$839$	−35.8380	−	35.8380i	−1.23726	−	1.23726i	−0.961115	−	0.276150i	$-0.910941\pi$
$839$	−35.8380	−	35.8380i	−1.23726	−	1.23726i	−0.276150	−	0.961115i	$-0.589059\pi$
$840$		0			0
$841$	−26.2983	+	12.2228i	−0.906839	+	0.421477i
$842$		0			0
$843$	2.28477			0.0786918
$844$		0			0
$845$	23.6202	+	7.26601i	0.812561	+	0.249958i
$846$		0			0
$847$	29.6414	−	29.6414i	1.01849	−	1.01849i
$848$		0			0
$849$	1.50344	+	1.50344i	0.0515980	+	0.0515980i
$850$		0			0
$851$	−1.18040	+	1.18040i	−0.0404635	+	0.0404635i
$852$		0			0
$853$			5.84769i			0.200221i	0.994976	+	0.100111i	$0.0319196\pi$
$853$			5.84769i			0.200221i	−0.994976	+	0.100111i	$0.968080\pi$
$854$		0			0
$855$	18.0722	+	34.1308i	0.618056	+	1.16725i
$856$		0			0
$857$	22.7796	+	22.7796i	0.778135	+	0.778135i	0.979513	−	0.201379i	$-0.0645421\pi$
$857$	22.7796	+	22.7796i	0.778135	+	0.778135i	−0.201379	+	0.979513i	$0.564542\pi$
$858$		0			0
$859$	−34.6757	−	34.6757i	−1.18312	−	1.18312i	−0.978931	−	0.204189i	$-0.934544\pi$
$859$	−34.6757	−	34.6757i	−1.18312	−	1.18312i	−0.204189	−	0.978931i	$-0.565456\pi$
$860$		0			0
$861$	−0.157652			−0.00537277
$862$		0			0
$863$	−26.8224	−	26.8224i	−0.913045	−	0.913045i	0.0834656	−	0.996511i	$-0.473401\pi$
$863$	−26.8224	−	26.8224i	−0.913045	−	0.913045i	−0.996511	+	0.0834656i	$0.973401\pi$
$864$		0			0
$865$	−26.9276	+	14.2581i	−0.915567	+	0.484791i
$866$		0			0
$867$	1.68944			0.0573762
$868$		0			0
$869$	−3.22354			−0.109351
$870$		0			0
$871$	−20.0357			−0.678885
$872$		0			0
$873$	−11.0346			−0.373465
$874$		0			0
$875$	47.7581	+	5.26963i	1.61452	+	0.178146i
$876$		0			0
$877$	−10.8215	−	10.8215i	−0.365417	−	0.365417i	0.500386	−	0.865803i	$-0.333192\pi$
$877$	−10.8215	−	10.8215i	−0.365417	−	0.365417i	−0.865803	+	0.500386i	$0.833192\pi$
$878$		0			0
$879$	0.133205			0.00449289
$880$		0			0
$881$	32.9479	+	32.9479i	1.11004	+	1.11004i	0.993144	+	0.116898i	$0.0372950\pi$
$881$	32.9479	+	32.9479i	1.11004	+	1.11004i	0.116898	+	0.993144i	$0.462705\pi$
$882$		0			0
$883$	24.9085	+	24.9085i	0.838236	+	0.838236i	0.988627	−	0.150390i	$-0.0480530\pi$
$883$	24.9085	+	24.9085i	0.838236	+	0.838236i	−0.150390	+	0.988627i	$0.548053\pi$
$884$		0			0
$885$	1.60677	+	0.494273i	0.0540111	+	0.0166148i
$886$		0			0
$887$		−	16.3631i		−	0.549420i	−0.961527	−	0.274710i	$-0.911418\pi$
$887$		−	16.3631i		−	0.549420i	0.961527	−	0.274710i	$-0.0885819\pi$
$888$		0			0
$889$	−4.87901	+	4.87901i	−0.163637	+	0.163637i
$890$		0			0
$891$	7.01467	+	7.01467i	0.235000	+	0.235000i
$892$		0			0
$893$	14.9726	−	14.9726i	0.501037	−	0.501037i
$894$		0			0
$895$	−1.05908	+	3.44285i	−0.0354012	+	0.115082i
$896$		0			0
$897$	0.485757			0.0162189
$898$		0			0
$899$	16.1324	−	25.2877i	0.538046	−	0.843391i
$900$		0			0
$901$	−3.14790	−	3.14790i	−0.104872	−	0.104872i
$902$		0			0
$903$	−0.957636	−	0.957636i	−0.0318681	−	0.0318681i
$904$		0			0
$905$	−5.07104	+	16.4848i	−0.168567	+	0.547975i
$906$		0			0
$907$	14.9938			0.497863			0.248931	−	0.968521i	$-0.419921\pi$
$907$	14.9938			0.497863			0.248931	+	0.968521i	$0.419921\pi$
$908$		0			0
$909$	−23.6045	−	23.6045i	−0.782910	−	0.782910i
$910$		0			0
$911$	15.6146	−	15.6146i	0.517333	−	0.517333i	−0.399430	−	0.916764i	$-0.630792\pi$
$911$	15.6146	−	15.6146i	0.517333	−	0.517333i	0.916764	+	0.399430i	$0.130792\pi$
$912$		0			0
$913$	19.0099			0.629136
$914$		0			0
$915$	−1.71615	+	0.908699i	−0.0567342	+	0.0300407i
$916$		0			0
$917$	21.5669			0.712202
$918$		0			0
$919$		−	39.8562i		−	1.31473i	−0.753571	−	0.657367i	$-0.771670\pi$
$919$		−	39.8562i		−	1.31473i	0.753571	−	0.657367i	$-0.228330\pi$
$920$		0			0
$921$			1.90634i			0.0628161i
$922$		0			0
$923$	−2.20498	+	2.20498i	−0.0725777	+	0.0725777i
$924$		0			0
$925$	2.21402	+	1.50451i	0.0727964	+	0.0494681i
$926$		0			0
$927$	29.0966	−	29.0966i	0.955657	−	0.955657i
$928$		0			0
$929$			18.6598i			0.612208i	0.951998	+	0.306104i	$0.0990256\pi$
$929$			18.6598i			0.612208i	−0.951998	+	0.306104i	$0.900974\pi$
$930$		0			0
$931$	−46.8835	−	46.8835i	−1.53654	−	1.53654i
$932$		0			0
$933$	−1.47998	−	1.47998i	−0.0484522	−	0.0484522i
$934$		0			0
$935$	1.59416	+	3.01070i	0.0521346	+	0.0984603i
$936$		0			0
$937$	−32.7695	+	32.7695i	−1.07053	+	1.07053i	−0.0732176	+	0.997316i	$0.523327\pi$
$937$	−32.7695	+	32.7695i	−1.07053	+	1.07053i	−0.997316	+	0.0732176i	$0.976673\pi$
$938$		0			0
$939$	0.543046	−	0.543046i	0.0177216	−	0.0177216i
$940$		0			0
$941$		−	8.46235i		−	0.275865i	−0.990442	−	0.137932i	$-0.955954\pi$
$941$		−	8.46235i		−	0.275865i	0.990442	−	0.137932i	$-0.0440457\pi$
$942$		0			0
$943$			1.02486i			0.0333740i
$944$		0			0
$945$	5.67538	−	3.00510i	0.184620	−	0.0977560i
$946$		0			0
$947$		−	35.3099i		−	1.14742i	−0.819059	−	0.573709i	$-0.805504\pi$
$947$		−	35.3099i		−	1.14742i	0.819059	−	0.573709i	$-0.194496\pi$
$948$		0			0
$949$	−11.9634	+	11.9634i	−0.388348	+	0.388348i
$950$		0			0
$951$	3.05502			0.0990658
$952$		0			0
$953$	−7.65407	+	7.65407i	−0.247940	+	0.247940i	−0.820125	−	0.572185i	$-0.806096\pi$
$953$	−7.65407	+	7.65407i	−0.247940	+	0.247940i	0.572185	+	0.820125i	$0.306096\pi$
$954$		0			0
$955$	10.2101	−	5.40624i	0.330392	−	0.174942i
$956$		0			0
$957$	−0.360802	+	0.565559i	−0.0116631	+	0.0182819i
$958$		0			0
$959$	36.1512	−	36.1512i	1.16738	−	1.16738i
$960$		0			0
$961$			0.0248400i			0.000801291i
$962$		0			0
$963$	−11.3060	−	11.3060i	−0.364332	−	0.364332i
$964$		0			0
$965$	−8.45619	+	27.4892i	−0.272214	+	0.884910i
$966$		0			0
$967$	14.4266			0.463929			0.231965	−	0.972724i	$-0.425485\pi$
$967$	14.4266			0.463929			0.231965	+	0.972724i	$0.425485\pi$
$968$		0			0
$969$	0.622790	+	0.622790i	0.0200069	+	0.0200069i
$970$		0			0
$971$	−41.2960	−	41.2960i	−1.32525	−	1.32525i	−0.909460	−	0.415791i	$-0.863505\pi$
$971$	−41.2960	−	41.2960i	−1.32525	−	1.32525i	−0.415791	−	0.909460i	$-0.636495\pi$
$972$		0			0
$973$	−28.0557	+	28.0557i	−0.899425	+	0.899425i
$974$		0			0
$975$	−0.145987	−	0.765124i	−0.00467533	−	0.0245036i
$976$		0			0
$977$	−6.07552	−	6.07552i	−0.194373	−	0.194373i	0.603210	−	0.797583i	$-0.293888\pi$
$977$	−6.07552	−	6.07552i	−0.194373	−	0.194373i	−0.797583	+	0.603210i	$0.793888\pi$
$978$		0			0
$979$	−7.93206			−0.253510
$980$		0			0
$981$	−31.1962			−0.996018
$982$		0			0
$983$		−	42.2826i		−	1.34861i	−0.738455	−	0.674303i	$-0.764444\pi$
$983$		−	42.2826i		−	1.34861i	0.738455	−	0.674303i	$-0.235556\pi$
$984$		0			0
$985$	31.5276	−	16.6938i	1.00455	−	0.531910i
$986$		0			0
$987$	−1.24225	−	1.24225i	−0.0395413	−	0.0395413i
$988$		0			0
$989$	−6.22536	+	6.22536i	−0.197955	+	0.197955i
$990$		0			0
$991$		−	51.6864i		−	1.64187i	−0.571020	−	0.820936i	$-0.693452\pi$
$991$		−	51.6864i		−	1.64187i	0.571020	−	0.820936i	$-0.306548\pi$
$992$		0			0
$993$	2.07000	−	2.07000i	0.0656895	−	0.0656895i
$994$		0			0
$995$	54.8888	+	16.8848i	1.74009	+	0.535284i
$996$		0			0
$997$		−	0.835424i		−	0.0264581i	−0.999912	−	0.0132291i	$-0.995789\pi$
$997$		−	0.835424i		−	0.0264581i	0.999912	−	0.0132291i	$-0.00421107\pi$
$998$		0			0
$999$	0.357773			0.0113194

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1160.2.bl.c.737.12	yes	42
5.3	odd	4		1160.2.s.d.273.12	yes	42
29.17	odd	4		1160.2.s.d.17.10	✓	42
145.133	even	4	inner	1160.2.bl.c.713.12	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1160.2.s.d.17.10	✓	42	29.17	odd	4
1160.2.s.d.273.12	yes	42	5.3	odd	4
1160.2.bl.c.713.12	yes	42	145.133	even	4	inner
1160.2.bl.c.737.12	yes	42	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1160 = 2^{3} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1160.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.111611 q^{3} +(-0.657451 + 2.13723i) q^{5} +(3.03882 + 3.03882i) q^{7} -2.98754 q^{9} +(0.789225 + 0.789225i) q^{11} +(0.986968 + 0.986968i) q^{13} +(-0.0733790 + 0.238539i) q^{15} -1.36500i q^{17} +(-4.08789 + 4.08789i) q^{19} +(0.339167 + 0.339167i) q^{21} +(2.20484 - 2.20484i) q^{23} +(-4.13552 - 2.81025i) q^{25} -0.668278 q^{27} +(1.16225 + 5.25825i) q^{29} +(-3.93858 - 3.93858i) q^{31} +(0.0880865 + 0.0880865i) q^{33} +(-8.49254 + 4.49679i) q^{35} -0.535366 q^{37} +(0.110157 + 0.110157i) q^{39} +(-0.232411 + 0.232411i) q^{41} -2.82349 q^{43} +(1.96416 - 6.38507i) q^{45} -3.66266 q^{47} +11.4689i q^{49} -0.152350i q^{51} +(2.30615 - 2.30615i) q^{53} +(-2.20563 + 1.16788i) q^{55} +(-0.456255 + 0.456255i) q^{57} -6.73589i q^{59} +(5.50192 + 5.50192i) q^{61} +(-9.07861 - 9.07861i) q^{63} +(-2.75826 + 1.46050i) q^{65} +(-10.1501 + 10.1501i) q^{67} +(0.246085 - 0.246085i) q^{69} +2.23409i q^{71} +12.1214i q^{73} +(-0.461571 - 0.313656i) q^{75} +4.79663i q^{77} +(-2.04222 + 2.04222i) q^{79} +8.88804 q^{81} +(12.0434 - 12.0434i) q^{83} +(2.91733 + 0.897423i) q^{85} +(0.129721 + 0.586880i) q^{87} +(-5.02522 + 5.02522i) q^{89} +5.99844i q^{91} +(-0.439590 - 0.439590i) q^{93} +(-6.04918 - 11.4244i) q^{95} +3.69354 q^{97} +(-2.35784 - 2.35784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 8 q^{3} - 2 q^{5} + 4 q^{7} + 34 q^{9} + 2 q^{11} + 4 q^{13} - 4 q^{15} + 8 q^{19} + 4 q^{21} - 20 q^{23} + 4 q^{25} - 8 q^{27} + 20 q^{29} + 2 q^{31} - 10 q^{33} + 16 q^{35} - 12 q^{37} + 10 q^{39}+ \cdots + 60 q^{99}+O(q^{100}) \) 42 * q - 8 * q^3 - 2 * q^5 + 4 * q^7 + 34 * q^9 + 2 * q^11 + 4 * q^13 - 4 * q^15 + 8 * q^19 + 4 * q^21 - 20 * q^23 + 4 * q^25 - 8 * q^27 + 20 * q^29 + 2 * q^31 - 10 * q^33 + 16 * q^35 - 12 * q^37 + 10 * q^39 - 30 * q^41 + 4 * q^43 - 32 * q^45 - 4 * q^47 + 16 * q^53 + 2 * q^55 + 40 * q^57 + 26 * q^61 + 80 * q^63 + 8 * q^65 + 44 * q^67 + 12 * q^69 + 4 * q^75 - 42 * q^79 + 114 * q^81 - 68 * q^83 + 30 * q^85 - 32 * q^87 + 18 * q^89 + 6 * q^93 - 26 * q^95 - 24 * q^97 + 60 * q^99

Introduction

L-functions

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