LMFDB - Embedded newform 1148.2.i.e.165.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.3
Character	$\chi$	$=$	1148.165
Dual form			1148.2.i.e.821.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36871 + 2.37067i) q^{3} +(0.431527 + 0.747427i) q^{5} +(-2.57022 + 0.627666i) q^{7} +(-2.24672 - 3.89144i) q^{9} +O(q^{10})$	\(q+(-1.36871 + 2.37067i) q^{3} +(0.431527 + 0.747427i) q^{5} +(-2.57022 + 0.627666i) q^{7} +(-2.24672 - 3.89144i) q^{9} +(2.79534 - 4.84167i) q^{11} -1.90008 q^{13} -2.36254 q^{15} +(2.00964 - 3.48080i) q^{17} +(0.958824 + 1.66073i) q^{19} +(2.02989 - 6.95224i) q^{21} +(-4.53279 - 7.85102i) q^{23} +(2.12757 - 3.68506i) q^{25} +4.08817 q^{27} +5.61917 q^{29} +(-4.55598 + 7.89118i) q^{31} +(7.65200 + 13.2537i) q^{33} +(-1.57825 - 1.65020i) q^{35} +(-0.728052 - 1.26102i) q^{37} +(2.60065 - 4.50445i) q^{39} -1.00000 q^{41} +7.83032 q^{43} +(1.93904 - 3.35852i) q^{45} +(-5.08045 - 8.79959i) q^{47} +(6.21207 - 3.22648i) q^{49} +(5.50122 + 9.52839i) q^{51} +(0.582342 - 1.00865i) q^{53} +4.82506 q^{55} -5.24940 q^{57} +(-3.43408 + 5.94801i) q^{59} +(-2.61306 - 4.52595i) q^{61} +(8.21709 + 8.59166i) q^{63} +(-0.819934 - 1.42017i) q^{65} +(-7.32217 + 12.6824i) q^{67} +24.8162 q^{69} +3.14178 q^{71} +(2.20867 - 3.82554i) q^{73} +(5.82404 + 10.0875i) q^{75} +(-4.14569 + 14.1987i) q^{77} +(2.65104 + 4.59173i) q^{79} +(1.14465 - 1.98259i) q^{81} +6.73846 q^{83} +3.46886 q^{85} +(-7.69100 + 13.3212i) q^{87} +(1.99924 + 3.46279i) q^{89} +(4.88361 - 1.19261i) q^{91} +(-12.4716 - 21.6014i) q^{93} +(-0.827517 + 1.43330i) q^{95} +3.44705 q^{97} -25.1214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−1.36871	+	2.37067i	−0.790224	+	1.36871i	0.135604	+	0.990763i	$0.456702\pi$
$3$	−1.36871	+	2.37067i	−0.790224	+	1.36871i	−0.925828	+	0.377945i	$0.876631\pi$
$4$		0			0
$5$	0.431527	+	0.747427i	0.192985	+	0.334259i	0.946238	−	0.323471i	$-0.104850\pi$
$5$	0.431527	+	0.747427i	0.192985	+	0.334259i	−0.753253	+	0.657731i	$0.771517\pi$
$6$		0			0
$7$	−2.57022	+	0.627666i	−0.971452	+	0.237235i
$7$	−2.57022	+	0.627666i	−0.971452	+	0.237235i
$8$		0			0
$9$	−2.24672	−	3.89144i	−0.748907	−	1.29715i
$10$		0			0
$11$	2.79534	−	4.84167i	0.842826	−	1.45982i	−0.0446694	−	0.999002i	$-0.514223\pi$
$11$	2.79534	−	4.84167i	0.842826	−	1.45982i	0.887496	−	0.460816i	$-0.152443\pi$
$12$		0			0
$13$	−1.90008			−0.526986			−0.263493	−	0.964661i	$-0.584875\pi$
$13$	−1.90008			−0.526986			−0.263493	+	0.964661i	$0.584875\pi$
$14$		0			0
$15$	−2.36254			−0.610005
$16$		0			0
$17$	2.00964	−	3.48080i	0.487409	−	0.844218i	−0.512486	−	0.858696i	$-0.671275\pi$
$17$	2.00964	−	3.48080i	0.487409	−	0.844218i	0.999895	+	0.0144778i	$0.00460859\pi$
$18$		0			0
$19$	0.958824	+	1.66073i	0.219969	+	0.380998i	0.954798	−	0.297254i	$-0.0960710\pi$
$19$	0.958824	+	1.66073i	0.219969	+	0.380998i	−0.734829	+	0.678252i	$0.762738\pi$
$20$		0			0
$21$	2.02989	−	6.95224i	0.442959	−	1.51710i
$22$		0			0
$23$	−4.53279	−	7.85102i	−0.945151	−	1.63705i	−0.755448	−	0.655209i	$-0.772581\pi$
$23$	−4.53279	−	7.85102i	−0.945151	−	1.63705i	−0.189704	−	0.981841i	$-0.560753\pi$
$24$		0			0
$25$	2.12757	−	3.68506i	0.425514	−	0.737011i
$26$		0			0
$27$	4.08817			0.786769
$28$		0			0
$29$	5.61917			1.04345			0.521727	−	0.853113i	$-0.325288\pi$
$29$	5.61917			1.04345			0.521727	+	0.853113i	$0.325288\pi$
$30$		0			0
$31$	−4.55598	+	7.89118i	−0.818277	+	1.41730i	0.0886732	+	0.996061i	$0.471737\pi$
$31$	−4.55598	+	7.89118i	−0.818277	+	1.41730i	−0.906951	+	0.421237i	$0.861596\pi$
$32$		0			0
$33$	7.65200	+	13.2537i	1.33204	+	2.30717i
$34$		0			0
$35$	−1.57825	−	1.65020i	−0.266774	−	0.278934i
$36$		0			0
$37$	−0.728052	−	1.26102i	−0.119691	−	0.207311i	0.799954	−	0.600061i	$-0.204857\pi$
$37$	−0.728052	−	1.26102i	−0.119691	−	0.207311i	−0.919645	+	0.392750i	$0.871524\pi$
$38$		0			0
$39$	2.60065	−	4.50445i	0.416437	−	0.721290i
$40$		0			0
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$		0			0
$43$	7.83032			1.19411			0.597056	−	0.802199i	$-0.296337\pi$
$43$	7.83032			1.19411			0.597056	+	0.802199i	$0.296337\pi$
$44$		0			0
$45$	1.93904	−	3.35852i	0.289055	−	0.500659i
$46$		0			0
$47$	−5.08045	−	8.79959i	−0.741059	−	1.28355i	−0.952013	−	0.306056i	$-0.900990\pi$
$47$	−5.08045	−	8.79959i	−0.741059	−	1.28355i	0.210954	−	0.977496i	$-0.432343\pi$
$48$		0			0
$49$	6.21207	−	3.22648i	0.887439	−	0.460926i
$50$		0			0
$51$	5.50122	+	9.52839i	0.770325	+	1.33424i
$52$		0			0
$53$	0.582342	−	1.00865i	0.0799909	−	0.138548i	−0.823255	−	0.567672i	$-0.807844\pi$
$53$	0.582342	−	1.00865i	0.0799909	−	0.138548i	0.903246	+	0.429124i	$0.141178\pi$
$54$		0			0
$55$	4.82506			0.650611
$56$		0			0
$57$	−5.24940			−0.695300
$58$		0			0
$59$	−3.43408	+	5.94801i	−0.447080	+	0.774365i	−0.998194	−	0.0600647i	$-0.980869\pi$
$59$	−3.43408	+	5.94801i	−0.447080	+	0.774365i	0.551115	+	0.834429i	$0.314203\pi$
$60$		0			0
$61$	−2.61306	−	4.52595i	−0.334568	−	0.579488i	0.648834	−	0.760930i	$-0.275257\pi$
$61$	−2.61306	−	4.52595i	−0.334568	−	0.579488i	−0.983402	+	0.181442i	$0.941924\pi$
$62$		0			0
$63$	8.21709	+	8.59166i	1.03526	+	1.08245i
$64$		0			0
$65$	−0.819934	−	1.42017i	−0.101700	−	0.176150i
$66$		0			0
$67$	−7.32217	+	12.6824i	−0.894546	+	1.54940i	−0.0601798	+	0.998188i	$0.519167\pi$
$67$	−7.32217	+	12.6824i	−0.894546	+	1.54940i	−0.834366	+	0.551211i	$0.814166\pi$
$68$		0			0
$69$	24.8162			2.98752
$70$		0			0
$71$	3.14178			0.372860			0.186430	−	0.982468i	$-0.440308\pi$
$71$	3.14178			0.372860			0.186430	+	0.982468i	$0.440308\pi$
$72$		0			0
$73$	2.20867	−	3.82554i	0.258506	−	0.447745i	−0.707336	−	0.706877i	$-0.750103\pi$
$73$	2.20867	−	3.82554i	0.258506	−	0.447745i	0.965842	+	0.259132i	$0.0834365\pi$
$74$		0			0
$75$	5.82404	+	10.0875i	0.672502	+	1.16481i
$76$		0			0
$77$	−4.14569	+	14.1987i	−0.472445	+	1.61809i
$78$		0			0
$79$	2.65104	+	4.59173i	0.298265	+	0.516610i	0.975739	−	0.218936i	$-0.0702587\pi$
$79$	2.65104	+	4.59173i	0.298265	+	0.516610i	−0.677474	+	0.735547i	$0.736925\pi$
$80$		0			0
$81$	1.14465	−	1.98259i	0.127183	−	0.220288i
$82$		0			0
$83$	6.73846			0.739642			0.369821	−	0.929103i	$-0.379419\pi$
$83$	6.73846			0.739642			0.369821	+	0.929103i	$0.379419\pi$
$84$		0			0
$85$	3.46886			0.376250
$86$		0			0
$87$	−7.69100	+	13.3212i	−0.824562	+	1.42818i
$88$		0			0
$89$	1.99924	+	3.46279i	0.211919	+	0.367055i	0.952315	−	0.305116i	$-0.0986952\pi$
$89$	1.99924	+	3.46279i	0.211919	+	0.367055i	−0.740396	+	0.672171i	$0.765362\pi$
$90$		0			0
$91$	4.88361	−	1.19261i	0.511942	−	0.125020i
$92$		0			0
$93$	−12.4716	−	21.6014i	−1.29324	−	2.23996i
$94$		0			0
$95$	−0.827517	+	1.43330i	−0.0849015	+	0.147054i
$96$		0			0
$97$	3.44705			0.349995			0.174997	−	0.984569i	$-0.444008\pi$
$97$	3.44705			0.349995			0.174997	+	0.984569i	$0.444008\pi$
$98$		0			0
$99$	−25.1214			−2.52479
$100$		0			0
$101$	8.85405	−	15.3357i	0.881011	−	1.52596i	0.0307924	−	0.999526i	$-0.490197\pi$
$101$	8.85405	−	15.3357i	0.881011	−	1.52596i	0.850219	−	0.526430i	$-0.176470\pi$
$102$		0			0
$103$	−7.91183	−	13.7037i	−0.779576	−	1.35026i	−0.932187	−	0.361978i	$-0.882101\pi$
$103$	−7.91183	−	13.7037i	−0.779576	−	1.35026i	0.152611	−	0.988286i	$-0.451232\pi$
$104$		0			0
$105$	6.07224	−	1.48288i	0.592590	−	0.144715i
$106$		0			0
$107$	−4.57664	−	7.92697i	−0.442440	−	0.766329i	0.555430	−	0.831563i	$-0.312554\pi$
$107$	−4.57664	−	7.92697i	−0.442440	−	0.766329i	−0.997870	+	0.0652346i	$0.979220\pi$
$108$		0			0
$109$	6.94911	−	12.0362i	0.665604	−	1.15286i	−0.313517	−	0.949583i	$-0.601507\pi$
$109$	6.94911	−	12.0362i	0.665604	−	1.15286i	0.979121	−	0.203278i	$-0.0651595\pi$
$110$		0			0
$111$	3.98596			0.378331
$112$		0			0
$113$	9.44966			0.888949			0.444475	−	0.895791i	$-0.353390\pi$
$113$	9.44966			0.888949			0.444475	+	0.895791i	$0.353390\pi$
$114$		0			0
$115$	3.91204	−	6.77585i	0.364800	−	0.631852i
$116$		0			0
$117$	4.26894	+	7.39402i	0.394664	+	0.683577i
$118$		0			0
$119$	−2.98044	+	10.2078i	−0.273217	+	0.935748i
$120$		0			0
$121$	−10.1278	−	17.5419i	−0.920712	−	1.59472i
$122$		0			0
$123$	1.36871	−	2.37067i	0.123412	−	0.213756i
$124$		0			0
$125$	7.98769			0.714440
$126$		0			0
$127$	−1.14798			−0.101866			−0.0509332	−	0.998702i	$-0.516220\pi$
$127$	−1.14798			−0.101866			−0.0509332	+	0.998702i	$0.516220\pi$
$128$		0			0
$129$	−10.7174	+	18.5631i	−0.943616	+	1.63439i
$130$		0			0
$131$	−0.652793	−	1.13067i	−0.0570348	−	0.0987871i	0.836098	−	0.548580i	$-0.184831\pi$
$131$	−0.652793	−	1.13067i	−0.0570348	−	0.0987871i	−0.893133	+	0.449793i	$0.851498\pi$
$132$		0			0
$133$	−3.50677	−	3.66663i	−0.304076	−	0.317937i
$134$		0			0
$135$	1.76416	+	3.05561i	0.151834	+	0.262985i
$136$		0			0
$137$	−6.01268	+	10.4143i	−0.513698	+	0.889750i	0.486176	+	0.873861i	$0.338391\pi$
$137$	−6.01268	+	10.4143i	−0.513698	+	0.889750i	−0.999874	+	0.0158896i	$0.994942\pi$
$138$		0			0
$139$	6.79439			0.576293			0.288146	−	0.957586i	$-0.406961\pi$
$139$	6.79439			0.576293			0.288146	+	0.957586i	$0.406961\pi$
$140$		0			0
$141$	27.8146			2.34241
$142$		0			0
$143$	−5.31135	+	9.19953i	−0.444158	+	0.769304i
$144$		0			0
$145$	2.42482	+	4.19992i	0.201371	+	0.348784i
$146$		0			0
$147$	−0.853584	+	19.1429i	−0.0704024	+	1.57888i
$148$		0			0
$149$	−9.98122	−	17.2880i	−0.817694	−	1.41629i	−0.907377	−	0.420317i	$-0.861919\pi$
$149$	−9.98122	−	17.2880i	−0.817694	−	1.41629i	0.0896836	−	0.995970i	$-0.471414\pi$
$150$		0			0
$151$	3.95875	−	6.85675i	0.322158	−	0.557995i	−0.658775	−	0.752340i	$-0.728925\pi$
$151$	3.95875	−	6.85675i	0.322158	−	0.557995i	0.980933	+	0.194346i	$0.0622583\pi$
$152$		0			0
$153$	−18.0604			−1.46010
$154$		0			0
$155$	−7.86411			−0.631660
$156$		0			0
$157$	−3.92626	+	6.80049i	−0.313350	+	0.542738i	−0.979085	−	0.203450i	$-0.934785\pi$
$157$	−3.92626	+	6.80049i	−0.313350	+	0.542738i	0.665735	+	0.746188i	$0.268118\pi$
$158$		0			0
$159$	1.59411	+	2.76109i	0.126421	+	0.218968i
$160$		0			0
$161$	16.5781	+	17.3338i	1.30654	+	1.36609i
$162$		0			0
$163$	−8.93923	−	15.4832i	−0.700174	−	1.21274i	−0.968405	−	0.249383i	$-0.919772\pi$
$163$	−8.93923	−	15.4832i	−0.700174	−	1.21274i	0.268231	−	0.963355i	$-0.413561\pi$
$164$		0			0
$165$	−6.60409	+	11.4386i	−0.514128	+	0.890496i
$166$		0			0
$167$	5.60745			0.433918			0.216959	−	0.976181i	$-0.430386\pi$
$167$	5.60745			0.433918			0.216959	+	0.976181i	$0.430386\pi$
$168$		0			0
$169$	−9.38971			−0.722286
$170$		0			0
$171$	4.30842	−	7.46240i	0.329473	−	0.570664i
$172$		0			0
$173$	−3.80776	−	6.59523i	−0.289499	−	0.501426i	0.684192	−	0.729302i	$-0.260155\pi$
$173$	−3.80776	−	6.59523i	−0.289499	−	0.501426i	−0.973690	+	0.227876i	$0.926822\pi$
$174$		0			0
$175$	−3.15534	+	10.8068i	−0.238521	+	0.816918i
$176$		0			0
$177$	−9.40052	−	16.2822i	−0.706586	−	1.22384i
$178$		0			0
$179$	10.7704	−	18.6549i	0.805017	−	1.39433i	−0.111263	−	0.993791i	$-0.535490\pi$
$179$	10.7704	−	18.6549i	0.805017	−	1.39433i	0.916280	−	0.400539i	$-0.131177\pi$
$180$		0			0
$181$	4.71251			0.350278			0.175139	−	0.984544i	$-0.443962\pi$
$181$	4.71251			0.350278			0.175139	+	0.984544i	$0.443962\pi$
$182$		0			0
$183$	14.3060			1.05753
$184$		0			0
$185$	0.628348	−	1.08833i	0.0461971	−	0.0800157i
$186$		0			0
$187$	−11.2353	−	19.4600i	−0.821603	−	1.42306i
$188$		0			0
$189$	−10.5075	+	2.56601i	−0.764309	+	0.186650i
$190$		0			0
$191$	5.57040	+	9.64822i	0.403060	+	0.698120i	0.994094	−	0.108527i	$-0.0346133\pi$
$191$	5.57040	+	9.64822i	0.403060	+	0.698120i	−0.591034	+	0.806647i	$0.701280\pi$
$192$		0			0
$193$	−12.2661	+	21.2455i	−0.882933	+	1.52928i	−0.0348679	+	0.999392i	$0.511101\pi$
$193$	−12.2661	+	21.2455i	−0.882933	+	1.52928i	−0.848065	+	0.529892i	$0.822232\pi$
$194$		0			0
$195$	4.48900			0.321464
$196$		0			0
$197$	−25.7126			−1.83195			−0.915973	−	0.401241i	$-0.868579\pi$
$197$	−25.7126			−1.83195			−0.915973	+	0.401241i	$0.868579\pi$
$198$		0			0
$199$	0.486398	−	0.842466i	0.0344798	−	0.0597208i	−0.848271	−	0.529563i	$-0.822356\pi$
$199$	0.486398	−	0.842466i	0.0344798	−	0.0597208i	0.882750	+	0.469842i	$0.155689\pi$
$200$		0			0
$201$	−20.0438	−	34.7169i	−1.41378	−	2.44874i
$202$		0			0
$203$	−14.4425	+	3.52696i	−1.01367	+	0.247544i
$204$		0			0
$205$	−0.431527	−	0.747427i	−0.0301392	−	0.0522026i
$206$		0			0
$207$	−20.3678	+	35.2781i	−1.41566	+	2.45200i
$208$		0			0
$209$	10.7209			0.741584
$210$		0			0
$211$	2.56072			0.176287			0.0881436	−	0.996108i	$-0.471907\pi$
$211$	2.56072			0.176287			0.0881436	+	0.996108i	$0.471907\pi$
$212$		0			0
$213$	−4.30017	+	7.44812i	−0.294643	+	0.510337i
$214$		0			0
$215$	3.37899	+	5.85259i	0.230446	+	0.399143i
$216$		0			0
$217$	6.75684	−	23.1417i	0.458684	−	1.57096i
$218$		0			0
$219$	6.04606	+	10.4721i	0.408555	+	0.707638i
$220$		0			0
$221$	−3.81847	+	6.61378i	−0.256858	+	0.444891i
$222$		0			0
$223$	−21.6493			−1.44974			−0.724872	−	0.688884i	$-0.758101\pi$
$223$	−21.6493			−1.44974			−0.724872	+	0.688884i	$0.758101\pi$
$224$		0			0
$225$	−19.1202			−1.27468
$226$		0			0
$227$	0.322303	−	0.558244i	0.0213920	−	0.0370520i	−0.855131	−	0.518412i	$-0.826524\pi$
$227$	0.322303	−	0.558244i	0.0213920	−	0.0370520i	0.876523	+	0.481360i	$0.159857\pi$
$228$		0			0
$229$	0.659762	+	1.14274i	0.0435983	+	0.0755145i	0.887001	−	0.461767i	$-0.152784\pi$
$229$	0.659762	+	1.14274i	0.0435983	+	0.0755145i	−0.843403	+	0.537282i	$0.819451\pi$
$230$		0			0
$231$	−27.9862	−	29.2619i	−1.84136	−	1.92529i
$232$		0			0
$233$	14.1501	+	24.5087i	0.927003	+	1.60562i	0.788307	+	0.615282i	$0.210958\pi$
$233$	14.1501	+	24.5087i	0.927003	+	1.60562i	0.138696	+	0.990335i	$0.455709\pi$
$234$		0			0
$235$	4.38470	−	7.59452i	0.286026	−	0.495412i
$236$		0			0
$237$	−14.5140			−0.942785
$238$		0			0
$239$	−9.13220			−0.590713			−0.295356	−	0.955387i	$-0.595438\pi$
$239$	−9.13220			−0.590713			−0.295356	+	0.955387i	$0.595438\pi$
$240$		0			0
$241$	7.49758	−	12.9862i	0.482962	−	0.836514i	−0.516847	−	0.856078i	$-0.672894\pi$
$241$	7.49758	−	12.9862i	0.482962	−	0.836514i	0.999809	+	0.0195635i	$0.00622765\pi$
$242$		0			0
$243$	9.26564	+	16.0486i	0.594391	+	1.02952i
$244$		0			0
$245$	5.09224	+	3.25076i	0.325331	+	0.207683i
$246$		0			0
$247$	−1.82184	−	3.15551i	−0.115921	−	0.200781i
$248$		0			0
$249$	−9.22298	+	15.9747i	−0.584483	+	1.01235i
$250$		0			0
$251$	−19.0748			−1.20399			−0.601994	−	0.798500i	$-0.705627\pi$
$251$	−19.0748			−1.20399			−0.601994	+	0.798500i	$0.705627\pi$
$252$		0			0
$253$	−50.6827			−3.18639
$254$		0			0
$255$	−4.74785	+	8.22352i	−0.297322	+	0.514977i
$256$		0			0
$257$	5.88132	+	10.1868i	0.366867	+	0.635432i	0.989074	−	0.147421i	$-0.0470971\pi$
$257$	5.88132	+	10.1868i	0.366867	+	0.635432i	−0.622207	+	0.782853i	$0.713764\pi$
$258$		0			0
$259$	2.66276	+	2.78413i	0.165456	+	0.172998i
$260$		0			0
$261$	−12.6247	−	21.8666i	−0.781450	−	1.35351i
$262$		0			0
$263$	3.93624	−	6.81777i	0.242719	−	0.420402i	−0.718769	−	0.695249i	$-0.755294\pi$
$263$	3.93624	−	6.81777i	0.242719	−	0.420402i	0.961488	+	0.274848i	$0.0886274\pi$
$264$		0			0
$265$	1.00519			0.0617481
$266$		0			0
$267$	−10.9455			−0.669855
$268$		0			0
$269$	5.79086	−	10.0301i	0.353075	−	0.611543i	−0.633712	−	0.773569i	$-0.718469\pi$
$269$	5.79086	−	10.0301i	0.353075	−	0.611543i	0.986787	+	0.162026i	$0.0518028\pi$
$270$		0			0
$271$	−6.04660	−	10.4730i	−0.367305	−	0.636190i	0.621839	−	0.783145i	$-0.286386\pi$
$271$	−6.04660	−	10.4730i	−0.367305	−	0.636190i	−0.989143	+	0.146955i	$0.953053\pi$
$272$		0			0
$273$	−3.85695	+	13.2098i	−0.233433	+	0.799492i
$274$		0			0
$275$	−11.8945	−	20.6020i	−0.717268	−	1.24235i
$276$		0			0
$277$	−10.8038	+	18.7127i	−0.649135	+	1.12433i	0.334195	+	0.942504i	$0.391536\pi$
$277$	−10.8038	+	18.7127i	−0.649135	+	1.12433i	−0.983330	+	0.181830i	$0.941798\pi$
$278$		0			0
$279$	40.9440			2.45125
$280$		0			0
$281$	12.2417			0.730278			0.365139	−	0.930953i	$-0.381022\pi$
$281$	12.2417			0.730278			0.365139	+	0.930953i	$0.381022\pi$
$282$		0			0
$283$	15.2763	−	26.4593i	0.908082	−	1.57285i	0.0913573	−	0.995818i	$-0.470879\pi$
$283$	15.2763	−	26.4593i	0.908082	−	1.57285i	0.816725	−	0.577027i	$-0.195787\pi$
$284$		0			0
$285$	−2.26526	−	3.92354i	−0.134182	−	0.232411i
$286$		0			0
$287$	2.57022	−	0.627666i	0.151715	−	0.0370500i
$288$		0			0
$289$	0.422689	+	0.732118i	0.0248640	+	0.0430658i
$290$		0			0
$291$	−4.71800	+	8.17182i	−0.276574	+	0.479040i
$292$		0			0
$293$	15.2363			0.890117			0.445058	−	0.895502i	$-0.353183\pi$
$293$	15.2363			0.890117			0.445058	+	0.895502i	$0.353183\pi$
$294$		0			0
$295$	−5.92760			−0.345118
$296$		0			0
$297$	11.4278	−	19.7936i	0.663110	−	1.14854i
$298$		0			0
$299$	8.61264	+	14.9175i	0.498082	+	0.862703i
$300$		0			0
$301$	−20.1256	+	4.91482i	−1.16002	+	0.283286i
$302$		0			0
$303$	24.2372	+	41.9801i	1.39239	+	2.41169i
$304$		0			0
$305$	2.25521	−	3.90614i	0.129133	−	0.223665i
$306$		0			0
$307$	−3.85409			−0.219964			−0.109982	−	0.993934i	$-0.535079\pi$
$307$	−3.85409			−0.219964			−0.109982	+	0.993934i	$0.535079\pi$
$308$		0			0
$309$	43.3159			2.46416
$310$		0			0
$311$	−2.98817	+	5.17566i	−0.169444	+	0.293485i	−0.938224	−	0.346028i	$-0.887530\pi$
$311$	−2.98817	+	5.17566i	−0.169444	+	0.293485i	0.768781	+	0.639512i	$0.220864\pi$
$312$		0			0
$313$	−7.37342	−	12.7711i	−0.416770	−	0.721867i	0.578842	−	0.815440i	$-0.303505\pi$
$313$	−7.37342	−	12.7711i	−0.416770	−	0.721867i	−0.995612	+	0.0935724i	$0.970171\pi$
$314$		0			0
$315$	−2.87574	+	9.84921i	−0.162030	+	0.554940i
$316$		0			0
$317$	−15.1705	−	26.2761i	−0.852062	−	1.47581i	−0.879344	−	0.476186i	$-0.842019\pi$
$317$	−15.1705	−	26.2761i	−0.852062	−	1.47581i	0.0272827	−	0.999628i	$-0.491315\pi$
$318$		0			0
$319$	15.7075	−	27.2061i	0.879450	−	1.52325i
$320$		0			0
$321$	25.0563			1.39851
$322$		0			0
$323$	7.70757			0.428860
$324$		0			0
$325$	−4.04254	+	7.00188i	−0.224240	+	0.388395i
$326$		0			0
$327$	19.0226	+	32.9481i	1.05195	+	1.82204i
$328$		0			0
$329$	18.5811	+	19.4281i	1.02441	+	1.07110i
$330$		0			0
$331$	−10.1482	−	17.5771i	−0.557793	−	0.966125i	−0.997680	−	0.0680726i	$-0.978315\pi$
$331$	−10.1482	−	17.5771i	−0.557793	−	0.966125i	0.439888	−	0.898053i	$-0.355018\pi$
$332$		0			0
$333$	−3.27146	+	5.66633i	−0.179275	+	0.310513i
$334$		0			0
$335$	−12.6389			−0.690535
$336$		0			0
$337$	2.08648			0.113658			0.0568290	−	0.998384i	$-0.481901\pi$
$337$	2.08648			0.113658			0.0568290	+	0.998384i	$0.481901\pi$
$338$		0			0
$339$	−12.9338	+	22.4020i	−0.702469	+	1.21671i
$340$		0			0
$341$	25.4710	+	44.1170i	1.37933	+	2.38907i
$342$		0			0
$343$	−13.9412	+	12.1919i	−0.752756	+	0.658299i
$344$		0			0
$345$	10.7089	+	18.5483i	0.576547	+	0.998608i
$346$		0			0
$347$	−0.332371	+	0.575683i	−0.0178426	+	0.0309043i	−0.874809	−	0.484468i	$-0.839013\pi$
$347$	−0.332371	+	0.575683i	−0.0178426	+	0.0309043i	0.856966	+	0.515373i	$0.172346\pi$
$348$		0			0
$349$	−29.1533			−1.56054			−0.780272	−	0.625441i	$-0.784919\pi$
$349$	−29.1533			−1.56054			−0.780272	+	0.625441i	$0.784919\pi$
$350$		0			0
$351$	−7.76783			−0.414616
$352$		0			0
$353$	15.4099	−	26.6908i	0.820188	−	1.42061i	−0.0853535	−	0.996351i	$-0.527202\pi$
$353$	15.4099	−	26.6908i	0.820188	−	1.42061i	0.905542	−	0.424257i	$-0.139465\pi$
$354$		0			0
$355$	1.35576	+	2.34825i	0.0719564	+	0.124632i
$356$		0			0
$357$	−20.1200	−	21.0371i	−1.06486	−	1.11340i
$358$		0			0
$359$	9.46706	+	16.3974i	0.499652	+	0.865423i	1.00000		0.000401513i	$-0.000127806\pi$
$359$	9.46706	+	16.3974i	0.499652	+	0.865423i	−0.500348	+	0.865825i	$0.666794\pi$
$360$		0			0
$361$	7.66131	−	13.2698i	0.403227	−	0.698410i
$362$		0			0
$363$	55.4482			2.91027
$364$		0			0
$365$	3.81241			0.199551
$366$		0			0
$367$	−4.42852	+	7.67041i	−0.231167	+	0.400392i	−0.958152	−	0.286261i	$-0.907588\pi$
$367$	−4.42852	+	7.67041i	−0.231167	+	0.400392i	0.726985	+	0.686653i	$0.240921\pi$
$368$		0			0
$369$	2.24672	+	3.89144i	0.116960	+	0.202580i
$370$		0			0
$371$	−0.863656	+	2.95796i	−0.0448388	+	0.153570i
$372$		0			0
$373$	1.74174	+	3.01679i	0.0901840	+	0.156203i	0.907588	−	0.419861i	$-0.137921\pi$
$373$	1.74174	+	3.01679i	0.0901840	+	0.156203i	−0.817404	+	0.576064i	$0.804588\pi$
$374$		0			0
$375$	−10.9328	+	18.9362i	−0.564568	+	0.977860i
$376$		0			0
$377$	−10.6768			−0.549885
$378$		0			0
$379$	18.8253			0.966991			0.483496	−	0.875347i	$-0.339367\pi$
$379$	18.8253			0.966991			0.483496	+	0.875347i	$0.339367\pi$
$380$		0			0
$381$	1.57124	−	2.72147i	0.0804972	−	0.139425i
$382$		0			0
$383$	−0.381271	−	0.660382i	−0.0194821	−	0.0337439i	0.856120	−	0.516777i	$-0.172868\pi$
$383$	−0.381271	−	0.660382i	−0.0194821	−	0.0337439i	−0.875602	+	0.483033i	$0.839535\pi$
$384$		0			0
$385$	−12.4015	+	3.02852i	−0.632037	+	0.154348i
$386$		0			0
$387$	−17.5925	−	30.4712i	−0.894279	−	1.54894i
$388$		0			0
$389$	−3.49198	+	6.04829i	−0.177050	+	0.306660i	−0.940869	−	0.338771i	$-0.889989\pi$
$389$	−3.49198	+	6.04829i	−0.177050	+	0.306660i	0.763819	+	0.645431i	$0.223322\pi$
$390$		0			0
$391$	−36.4371			−1.84270
$392$		0			0
$393$	3.57393			0.180281
$394$		0			0
$395$	−2.28799	+	3.96292i	−0.115121	+	0.199396i
$396$		0			0
$397$	8.47240	+	14.6746i	0.425218	+	0.736499i	0.996441	−	0.0842962i	$-0.0268642\pi$
$397$	8.47240	+	14.6746i	0.425218	+	0.736499i	−0.571223	+	0.820795i	$0.693531\pi$
$398$		0			0
$399$	13.4921	−	3.29487i	0.675450	−	0.164950i
$400$		0			0
$401$	6.27930	+	10.8761i	0.313573	+	0.543125i	0.979133	−	0.203219i	$-0.0651405\pi$
$401$	6.27930	+	10.8761i	0.313573	+	0.543125i	−0.665560	+	0.746345i	$0.731807\pi$
$402$		0			0
$403$	8.65670	−	14.9938i	0.431221	−	0.746896i
$404$		0			0
$405$	1.97579			0.0981779
$406$		0			0
$407$	−8.14061			−0.403515
$408$		0			0
$409$	−9.74600	+	16.8806i	−0.481909	+	0.834690i	−0.999784	−	0.0207656i	$-0.993390\pi$
$409$	−9.74600	+	16.8806i	−0.481909	+	0.834690i	0.517876	+	0.855456i	$0.326723\pi$
$410$		0			0
$411$	−16.4592	−	28.5082i	−0.811872	−	1.40620i
$412$		0			0
$413$	5.09299	−	17.4432i	0.250610	−	0.858322i
$414$		0			0
$415$	2.90783	+	5.03651i	0.142740	+	0.247232i
$416$		0			0
$417$	−9.29954	+	16.1073i	−0.455400	+	0.788776i
$418$		0			0
$419$	34.0935			1.66558			0.832788	−	0.553593i	$-0.186744\pi$
$419$	34.0935			1.66558			0.832788	+	0.553593i	$0.186744\pi$
$420$		0			0
$421$	36.1622			1.76244			0.881219	−	0.472708i	$-0.156723\pi$
$421$	36.1622			1.76244			0.881219	+	0.472708i	$0.156723\pi$
$422$		0			0
$423$	−22.8287	+	39.5405i	−1.10997	+	1.92252i
$424$		0			0
$425$	−8.55130	−	14.8113i	−0.414799	−	0.718453i
$426$		0			0
$427$	9.55691	+	9.99256i	0.462492	+	0.483574i
$428$		0			0
$429$	−14.5394	−	25.1829i	−0.701968	−	1.21584i
$430$		0			0
$431$	−7.78774	+	13.4888i	−0.375122	+	0.649731i	−0.990345	−	0.138622i	$-0.955733\pi$
$431$	−7.78774	+	13.4888i	−0.375122	+	0.649731i	0.615223	+	0.788353i	$0.289066\pi$
$432$		0			0
$433$	8.91790			0.428567			0.214283	−	0.976772i	$-0.431258\pi$
$433$	8.91790			0.428567			0.214283	+	0.976772i	$0.431258\pi$
$434$		0			0
$435$	−13.2755			−0.636511
$436$		0			0
$437$	8.69229	−	15.0555i	0.415809	−	0.720202i
$438$		0			0
$439$	16.2277	+	28.1073i	0.774507	+	1.34149i	0.935071	+	0.354461i	$0.115336\pi$
$439$	16.2277	+	28.1073i	0.774507	+	1.34149i	−0.160563	+	0.987026i	$0.551331\pi$
$440$		0			0
$441$	−26.5124	−	16.9249i	−1.26250	−	0.805946i
$442$		0			0
$443$	−3.08759	−	5.34787i	−0.146696	−	0.254085i	0.783308	−	0.621633i	$-0.213531\pi$
$443$	−3.08759	−	5.34787i	−0.146696	−	0.254085i	−0.930004	+	0.367548i	$0.880197\pi$
$444$		0			0
$445$	−1.72546	+	2.98858i	−0.0817945	+	0.141672i
$446$		0			0
$447$	54.6455			2.58464
$448$		0			0
$449$	−33.2976			−1.57141			−0.785706	−	0.618600i	$-0.787700\pi$
$449$	−33.2976			−1.57141			−0.785706	+	0.618600i	$0.787700\pi$
$450$		0			0
$451$	−2.79534	+	4.84167i	−0.131627	+	0.227985i
$452$		0			0
$453$	10.8367	+	18.7698i	0.509154	+	0.881881i
$454$		0			0
$455$	2.99880	+	3.13550i	0.140586	+	0.146994i
$456$		0			0
$457$	−5.30011	−	9.18006i	−0.247929	−	0.429425i	0.715022	−	0.699102i	$-0.246417\pi$
$457$	−5.30011	−	9.18006i	−0.247929	−	0.429425i	−0.962951	+	0.269677i	$0.913083\pi$
$458$		0			0
$459$	8.21576	−	14.2301i	0.383479	−	0.664205i
$460$		0			0
$461$	−32.3114			−1.50489			−0.752445	−	0.658655i	$-0.771126\pi$
$461$	−32.3114			−1.50489			−0.752445	+	0.658655i	$0.771126\pi$
$462$		0			0
$463$	24.6791			1.14694			0.573469	−	0.819228i	$-0.305597\pi$
$463$	24.6791			1.14694			0.573469	+	0.819228i	$0.305597\pi$
$464$		0			0
$465$	10.7637	−	18.6432i	0.499153	−	0.864558i
$466$		0			0
$467$	1.30826	+	2.26598i	0.0605391	+	0.104857i	0.894707	−	0.446654i	$-0.147385\pi$
$467$	1.30826	+	2.26598i	0.0605391	+	0.104857i	−0.834167	+	0.551511i	$0.814051\pi$
$468$		0			0
$469$	10.8593	−	37.1924i	0.501436	−	1.71738i
$470$		0			0
$471$	−10.7478	−	18.6158i	−0.495233	−	0.857769i
$472$		0			0
$473$	21.8884	−	37.9118i	1.00643	−	1.74319i
$474$		0			0
$475$	8.15985			0.374400
$476$		0			0
$477$	−5.23344			−0.239623
$478$		0			0
$479$	10.9279	−	18.9278i	0.499311	−	0.864832i	−0.500689	−	0.865627i	$-0.666920\pi$
$479$	10.9279	−	18.9278i	0.499311	−	0.864832i	1.00000		0.000795749i	$0.000253295\pi$
$480$		0			0
$481$	1.38335	+	2.39604i	0.0630755	+	0.109250i
$482$		0			0
$483$	−63.7832	+	15.5763i	−2.90224	+	0.708747i
$484$		0			0
$485$	1.48749	+	2.57642i	0.0675436	+	0.116989i
$486$		0			0
$487$	−11.5151	+	19.9447i	−0.521799	+	0.903783i	0.477879	+	0.878425i	$0.341406\pi$
$487$	−11.5151	+	19.9447i	−0.521799	+	0.903783i	−0.999678	+	0.0253571i	$0.991928\pi$
$488$		0			0
$489$	48.9408			2.21318
$490$		0			0
$491$	19.4215			0.876480			0.438240	−	0.898858i	$-0.355602\pi$
$491$	19.4215			0.876480			0.438240	+	0.898858i	$0.355602\pi$
$492$		0			0
$493$	11.2925	−	19.5592i	0.508589	−	0.880902i
$494$		0			0
$495$	−10.8406	−	18.7764i	−0.487247	−	0.843936i
$496$		0			0
$497$	−8.07506	+	1.97199i	−0.362216	+	0.0884557i
$498$		0			0
$499$	−7.47855	−	12.9532i	−0.334786	−	0.579866i	0.648658	−	0.761080i	$-0.275331\pi$
$499$	−7.47855	−	12.9532i	−0.334786	−	0.579866i	−0.983444	+	0.181214i	$0.941997\pi$
$500$		0			0
$501$	−7.67496	+	13.2934i	−0.342892	+	0.593906i
$502$		0			0
$503$	−12.0347			−0.536602			−0.268301	−	0.963335i	$-0.586462\pi$
$503$	−12.0347			−0.536602			−0.268301	+	0.963335i	$0.586462\pi$
$504$		0			0
$505$	15.2831			0.680087
$506$		0			0
$507$	12.8518	−	22.2599i	0.570767	−	0.988598i
$508$		0			0
$509$	−3.46015	−	5.99315i	−0.153368	−	0.265642i	0.779095	−	0.626905i	$-0.215679\pi$
$509$	−3.46015	−	5.99315i	−0.153368	−	0.265642i	−0.932464	+	0.361264i	$0.882345\pi$
$510$		0			0
$511$	−3.27562	+	11.2188i	−0.144905	+	0.496290i
$512$		0			0
$513$	3.91984	+	6.78936i	0.173065	+	0.299757i
$514$		0			0
$515$	6.82834	−	11.8270i	0.300893	−	0.521161i
$516$		0			0
$517$	−56.8063			−2.49834
$518$		0			0
$519$	20.8468			0.915075
$520$		0			0
$521$	−1.39246	+	2.41181i	−0.0610047	+	0.105663i	−0.894915	−	0.446237i	$-0.852764\pi$
$521$	−1.39246	+	2.41181i	−0.0610047	+	0.105663i	0.833910	+	0.551900i	$0.186097\pi$
$522$		0			0
$523$	−7.42351	−	12.8579i	−0.324607	−	0.562236i	0.656825	−	0.754043i	$-0.271899\pi$
$523$	−7.42351	−	12.8579i	−0.324607	−	0.562236i	−0.981433	+	0.191806i	$0.938566\pi$
$524$		0			0
$525$	−21.3007	−	22.2716i	−0.929637	−	0.972014i
$526$		0			0
$527$	18.3117	+	31.7169i	0.797672	+	1.38161i
$528$		0			0
$529$	−29.5923	+	51.2554i	−1.28662	+	2.22850i
$530$		0			0
$531$	30.8617			1.33928
$532$		0			0
$533$	1.90008			0.0823014
$534$		0			0
$535$	3.94989	−	6.84140i	0.170768	−	0.295780i
$536$		0			0
$537$	29.4830	+	51.0661i	1.27229	+	2.20366i
$538$		0			0
$539$	1.74329	−	39.0959i	0.0750889	−	1.68398i
$540$		0			0
$541$	−4.11823	−	7.13299i	−0.177057	−	0.306671i	0.763814	−	0.645436i	$-0.223324\pi$
$541$	−4.11823	−	7.13299i	−0.177057	−	0.306671i	−0.940871	+	0.338765i	$0.889991\pi$
$542$		0			0
$543$	−6.45005	+	11.1718i	−0.276798	+	0.479429i
$544$		0			0
$545$	11.9949			0.513806
$546$		0			0
$547$	40.5675			1.73454			0.867270	−	0.497838i	$-0.165872\pi$
$547$	40.5675			1.73454			0.867270	+	0.497838i	$0.165872\pi$
$548$		0			0
$549$	−11.7416	+	20.3371i	−0.501120	+	0.867965i
$550$		0			0
$551$	5.38779	+	9.33193i	0.229528	+	0.397554i
$552$		0			0
$553$	−9.69583	−	10.1378i	−0.412309	−	0.431103i
$554$		0			0
$555$	1.72005	+	2.97921i	0.0730121	+	0.126461i
$556$		0			0
$557$	−11.3145	+	19.5972i	−0.479409	+	0.830360i	−0.999721	−	0.0236157i	$-0.992482\pi$
$557$	−11.3145	+	19.5972i	−0.479409	+	0.830360i	0.520312	+	0.853976i	$0.325816\pi$
$558$		0			0
$559$	−14.8782			−0.629280
$560$		0			0
$561$	61.5111			2.59700
$562$		0			0
$563$	8.67317	−	15.0224i	0.365531	−	0.633118i	−0.623331	−	0.781958i	$-0.714221\pi$
$563$	8.67317	−	15.0224i	0.365531	−	0.633118i	0.988861	+	0.148841i	$0.0475542\pi$
$564$		0			0
$565$	4.07778	+	7.06293i	0.171554	+	0.297140i
$566$		0			0
$567$	−1.69760	+	5.81416i	−0.0712925	+	0.244172i
$568$		0			0
$569$	5.29606	+	9.17305i	0.222023	+	0.384554i	0.955422	−	0.295244i	$-0.0954008\pi$
$569$	5.29606	+	9.17305i	0.222023	+	0.384554i	−0.733399	+	0.679798i	$0.762067\pi$
$570$		0			0
$571$	−5.27255	+	9.13233i	−0.220649	+	0.382176i	−0.955005	−	0.296589i	$-0.904151\pi$
$571$	−5.27255	+	9.13233i	−0.220649	+	0.382176i	0.734356	+	0.678765i	$0.237484\pi$
$572$		0			0
$573$	−30.4970			−1.27403
$574$		0			0
$575$	−38.5753			−1.60870
$576$		0			0
$577$	9.73949	−	16.8693i	0.405460	−	0.702278i	−0.588915	−	0.808195i	$-0.700445\pi$
$577$	9.73949	−	16.8693i	0.405460	−	0.702278i	0.994375	+	0.105917i	$0.0337779\pi$
$578$		0			0
$579$	−33.5774	−	58.1577i	−1.39543	−	2.41695i
$580$		0			0
$581$	−17.3193	+	4.22950i	−0.718527	+	0.175469i
$582$		0			0
$583$	−3.25569	−	5.63902i	−0.134837	−	0.233544i
$584$		0			0
$585$	−3.68433	+	6.38144i	−0.152328	+	0.263840i
$586$		0			0
$587$	16.5937			0.684896			0.342448	−	0.939537i	$-0.388744\pi$
$587$	16.5937			0.684896			0.342448	+	0.939537i	$0.388744\pi$
$588$		0			0
$589$	−17.4735			−0.719983
$590$		0			0
$591$	35.1930	−	60.9561i	1.44765	−	2.50740i
$592$		0			0
$593$	11.3275	+	19.6199i	0.465166	+	0.805691i	0.999209	−	0.0397663i	$-0.0126613\pi$
$593$	11.3275	+	19.6199i	0.465166	+	0.805691i	−0.534043	+	0.845457i	$0.679328\pi$
$594$		0			0
$595$	−8.91573	+	2.17728i	−0.365509	+	0.0892600i
$596$		0			0
$597$	1.33147	+	2.30618i	0.0544936	+	0.0943857i
$598$		0			0
$599$	9.62263	−	16.6669i	0.393170	−	0.680991i	−0.599696	−	0.800228i	$-0.704712\pi$
$599$	9.62263	−	16.6669i	0.393170	−	0.680991i	0.992866	+	0.119238i	$0.0380450\pi$
$600$		0			0
$601$	−21.9736			−0.896322			−0.448161	−	0.893953i	$-0.647921\pi$
$601$	−21.9736			−0.896322			−0.448161	+	0.893953i	$0.647921\pi$
$602$		0			0
$603$	65.8035			2.67973
$604$		0			0
$605$	8.74087	−	15.1396i	0.355367	−	0.615514i
$606$		0			0
$607$	−17.1878	−	29.7702i	−0.697633	−	1.20834i	−0.969285	−	0.245940i	$-0.920903\pi$
$607$	−17.1878	−	29.7702i	−0.697633	−	1.20834i	0.271652	−	0.962396i	$-0.412430\pi$
$608$		0			0
$609$	11.4063	−	39.0658i	0.462207	−	1.58303i
$610$		0			0
$611$	9.65323	+	16.7199i	0.390528	+	0.676414i
$612$		0			0
$613$	12.2542	−	21.2249i	0.494943	−	0.857266i	−0.505040	−	0.863096i	$-0.668522\pi$
$613$	12.2542	−	21.2249i	0.494943	−	0.857266i	0.999983	+	0.00582990i	$0.00185573\pi$
$614$		0			0
$615$	2.36254			0.0952667
$616$		0			0
$617$	−11.7986			−0.474993			−0.237496	−	0.971388i	$-0.576327\pi$
$617$	−11.7986			−0.474993			−0.237496	+	0.971388i	$0.576327\pi$
$618$		0			0
$619$	16.0799	−	27.8511i	0.646304	−	1.11943i	−0.337695	−	0.941256i	$-0.609647\pi$
$619$	16.0799	−	27.8511i	0.646304	−	1.11943i	0.983999	−	0.178176i	$-0.0570195\pi$
$620$		0			0
$621$	−18.5308	−	32.0963i	−0.743616	−	1.28798i
$622$		0			0
$623$	−7.31198	−	7.64528i	−0.292948	−	0.306302i
$624$		0			0
$625$	−7.19094	−	12.4551i	−0.287638	−	0.498203i
$626$		0			0
$627$	−14.6738	+	25.4158i	−0.586017	+	1.01501i
$628$		0			0
$629$	−5.85249			−0.233354
$630$		0			0
$631$	37.4091			1.48923			0.744617	−	0.667492i	$-0.232632\pi$
$631$	37.4091			1.48923			0.744617	+	0.667492i	$0.232632\pi$
$632$		0			0
$633$	−3.50488	+	6.07062i	−0.139306	+	0.241286i
$634$		0			0
$635$	−0.495382	−	0.858027i	−0.0196587	−	0.0340498i
$636$		0			0
$637$	−11.8034	+	6.13056i	−0.467668	+	0.242901i
$638$		0			0
$639$	−7.05870	−	12.2260i	−0.279238	−	0.483654i
$640$		0			0
$641$	−2.02939	+	3.51500i	−0.0801560	+	0.138834i	−0.903317	−	0.428974i	$-0.858875\pi$
$641$	−2.02939	+	3.51500i	−0.0801560	+	0.138834i	0.823161	+	0.567808i	$0.192209\pi$
$642$		0			0
$643$	−26.5083			−1.04539			−0.522693	−	0.852521i	$-0.675073\pi$
$643$	−26.5083			−1.04539			−0.522693	+	0.852521i	$0.675073\pi$
$644$		0			0
$645$	−18.4994			−0.728414
$646$		0			0
$647$	−4.69307	+	8.12864i	−0.184504	+	0.319570i	−0.943409	−	0.331631i	$-0.892401\pi$
$647$	−4.69307	+	8.12864i	−0.184504	+	0.319570i	0.758905	+	0.651201i	$0.225734\pi$
$648$		0			0
$649$	19.1989	+	33.2534i	0.753621	+	1.30531i
$650$		0			0
$651$	45.6132	+	47.6925i	1.78772	+	1.86922i
$652$		0			0
$653$	3.66391	+	6.34608i	0.143380	+	0.248341i	0.928767	−	0.370663i	$-0.120870\pi$
$653$	3.66391	+	6.34608i	0.143380	+	0.248341i	−0.785387	+	0.619005i	$0.787536\pi$
$654$		0			0
$655$	0.563396	−	0.975830i	0.0220137	−	0.0381288i
$656$		0			0
$657$	−19.8491			−0.774387
$658$		0			0
$659$	5.69956			0.222023			0.111012	−	0.993819i	$-0.464591\pi$
$659$	5.69956			0.222023			0.111012	+	0.993819i	$0.464591\pi$
$660$		0			0
$661$	−22.0289	+	38.1552i	−0.856824	+	1.48406i	0.0181177	+	0.999836i	$0.494233\pi$
$661$	−22.0289	+	38.1552i	−0.856824	+	1.48406i	−0.874942	+	0.484228i	$0.839101\pi$
$662$		0			0
$663$	−10.4527	−	18.1047i	−0.405951	−	0.703127i
$664$		0			0
$665$	1.22727	−	4.20331i	0.0475914	−	0.162997i
$666$		0			0
$667$	−25.4705	−	44.1162i	−0.986221	−	1.70819i
$668$		0			0
$669$	29.6315	−	51.3233i	1.14562	−	1.98428i
$670$		0			0
$671$	−29.2175			−1.12793
$672$		0			0
$673$	5.92353			0.228335			0.114168	−	0.993461i	$-0.463580\pi$
$673$	5.92353			0.228335			0.114168	+	0.993461i	$0.463580\pi$
$674$		0			0
$675$	8.69787	−	15.0651i	0.334781	−	0.579858i
$676$		0			0
$677$	10.0293	+	17.3712i	0.385457	+	0.667631i	0.991832	−	0.127548i	$-0.0407105\pi$
$677$	10.0293	+	17.3712i	0.385457	+	0.667631i	−0.606376	+	0.795178i	$0.707377\pi$
$678$		0			0
$679$	−8.85967	+	2.16359i	−0.340003	+	0.0830311i
$680$		0			0
$681$	0.882276	+	1.52815i	0.0338089	+	0.0585587i
$682$		0			0
$683$	−20.7873	+	36.0047i	−0.795404	+	1.37768i	0.127179	+	0.991880i	$0.459408\pi$
$683$	−20.7873	+	36.0047i	−0.795404	+	1.37768i	−0.922582	+	0.385800i	$0.873925\pi$
$684$		0			0
$685$	−10.3785			−0.396543
$686$		0			0
$687$	−3.61209			−0.137810
$688$		0			0
$689$	−1.10649	+	1.91650i	−0.0421541	+	0.0730130i
$690$		0			0
$691$	1.38652	+	2.40153i	0.0527459	+	0.0913586i	0.891193	−	0.453625i	$-0.149869\pi$
$691$	1.38652	+	2.40153i	0.0527459	+	0.0913586i	−0.838447	+	0.544983i	$0.816536\pi$
$692$		0			0
$693$	64.5675	−	15.7678i	2.45272	−	0.598971i
$694$		0			0
$695$	2.93196	+	5.07831i	0.111216	+	0.192631i
$696$		0			0
$697$	−2.00964	+	3.48080i	−0.0761206	+	0.131845i
$698$		0			0
$699$	−77.4693			−2.93016
$700$		0			0
$701$	32.4197			1.22448			0.612238	−	0.790674i	$-0.290269\pi$
$701$	32.4197			1.22448			0.612238	+	0.790674i	$0.290269\pi$
$702$		0			0
$703$	1.39615	−	2.41820i	0.0526567	−	0.0912040i
$704$		0			0
$705$	12.0027	+	20.7894i	0.452050	+	0.782973i
$706$		0			0
$707$	−13.1312	+	44.9734i	−0.493849	+	1.69140i
$708$		0			0
$709$	5.28526	+	9.15433i	0.198492	+	0.343798i	0.948040	−	0.318152i	$-0.103062\pi$
$709$	5.28526	+	9.15433i	0.198492	+	0.343798i	−0.749548	+	0.661950i	$0.769729\pi$
$710$		0			0
$711$	11.9123	−	20.6327i	0.446746	−	0.773786i
$712$		0			0
$713$	82.6051			3.09358
$714$		0			0
$715$	−9.16797			−0.342863
$716$		0			0
$717$	12.4993	−	21.6494i	0.466795	−	0.808513i
$718$		0			0
$719$	16.5145	+	28.6040i	0.615889	+	1.06675i	0.990228	+	0.139458i	$0.0445362\pi$
$719$	16.5145	+	28.6040i	0.615889	+	1.06675i	−0.374339	+	0.927292i	$0.622130\pi$
$720$		0			0
$721$	28.9365	+	30.2555i	1.07765	+	1.12677i
$722$		0			0
$723$	20.5240	+	35.5486i	0.763296	+	1.32207i
$724$		0			0
$725$	11.9552	−	20.7070i	0.444004	−	0.769037i
$726$		0			0
$727$	27.4483			1.01800			0.509001	−	0.860766i	$-0.330015\pi$
$727$	27.4483			1.01800			0.509001	+	0.860766i	$0.330015\pi$
$728$		0			0
$729$	−43.8599			−1.62444
$730$		0			0
$731$	15.7361	−	27.2558i	0.582022	−	1.00809i
$732$		0			0
$733$	−4.51568	−	7.82138i	−0.166790	−	0.288889i	0.770499	−	0.637441i	$-0.220007\pi$
$733$	−4.51568	−	7.82138i	−0.166790	−	0.288889i	−0.937290	+	0.348552i	$0.886674\pi$
$734$		0			0
$735$	−14.6763	+	7.62268i	−0.541342	+	0.281167i
$736$		0			0
$737$	40.9359	+	70.9031i	1.50789	+	2.61175i
$738$		0			0
$739$	−20.1127	+	34.8363i	−0.739859	+	1.28147i	0.212699	+	0.977118i	$0.431775\pi$
$739$	−20.1127	+	34.8363i	−0.739859	+	1.28147i	−0.952558	+	0.304356i	$0.901559\pi$
$740$		0			0
$741$	9.97425			0.366413
$742$		0			0
$743$	2.30265			0.0844761			0.0422380	−	0.999108i	$-0.486551\pi$
$743$	2.30265			0.0844761			0.0422380	+	0.999108i	$0.486551\pi$
$744$		0			0
$745$	8.61434	−	14.9205i	0.315605	−	0.546644i
$746$		0			0
$747$	−15.1394	−	26.2223i	−0.553923	−	0.959423i
$748$		0			0
$749$	16.7385	+	17.5015i	0.611610	+	0.639489i
$750$		0			0
$751$	−9.76857	−	16.9197i	−0.356460	−	0.617407i	0.630906	−	0.775859i	$-0.282683\pi$
$751$	−9.76857	−	16.9197i	−0.356460	−	0.617407i	−0.987367	+	0.158452i	$0.949350\pi$
$752$		0			0
$753$	26.1078	−	45.2200i	0.951421	−	1.64791i
$754$		0			0
$755$	6.83323			0.248687
$756$		0			0
$757$	8.28174			0.301005			0.150502	−	0.988610i	$-0.451911\pi$
$757$	8.28174			0.301005			0.150502	+	0.988610i	$0.451911\pi$
$758$		0			0
$759$	69.3698	−	120.152i	2.51796	−	4.36124i
$760$		0			0
$761$	−9.39601	−	16.2744i	−0.340605	−	0.589945i	0.643940	−	0.765076i	$-0.277299\pi$
$761$	−9.39601	−	16.2744i	−0.340605	−	0.589945i	−0.984545	+	0.175131i	$0.943965\pi$
$762$		0			0
$763$	−10.3060	+	35.2975i	−0.373103	+	1.27785i
$764$		0			0
$765$	−7.79356	−	13.4988i	−0.281777	−	0.488051i
$766$		0			0
$767$	6.52502	−	11.3017i	0.235605	−	0.408079i
$768$		0			0
$769$	−15.1327			−0.545700			−0.272850	−	0.962057i	$-0.587966\pi$
$769$	−15.1327			−0.545700			−0.272850	+	0.962057i	$0.587966\pi$
$770$		0			0
$771$	−32.1992			−1.15963
$772$		0			0
$773$	−13.4648	+	23.3217i	−0.484295	+	0.838824i	−0.999837	−	0.0180401i	$-0.994257\pi$
$773$	−13.4648	+	23.3217i	−0.484295	+	0.838824i	0.515542	+	0.856864i	$0.327591\pi$
$774$		0			0
$775$	19.3863	+	33.5781i	0.696376	+	1.20616i
$776$		0			0
$777$	−10.2448	+	2.50185i	−0.367530	+	0.0897534i
$778$		0			0
$779$	−0.958824	−	1.66073i	−0.0343534	−	0.0595019i
$780$		0			0
$781$	8.78233	−	15.2114i	0.314256	−	0.544308i
$782$		0			0
$783$	22.9721			0.820957
$784$		0			0
$785$	−6.77716			−0.241887
$786$		0			0
$787$	1.45946	−	2.52786i	0.0520241	−	0.0901084i	−0.838841	−	0.544377i	$-0.816766\pi$
$787$	1.45946	−	2.52786i	0.0520241	−	0.0901084i	0.890865	+	0.454269i	$0.150099\pi$
$788$		0			0
$789$	10.7751	+	18.6631i	0.383605	+	0.664423i
$790$		0			0
$791$	−24.2877	+	5.93123i	−0.863572	+	0.210890i
$792$		0			0
$793$	4.96500	+	8.59964i	0.176312	+	0.305382i
$794$		0			0
$795$	−1.37581	+	2.38297i	−0.0487948	+	0.0845151i
$796$		0			0
$797$	−16.4159			−0.581481			−0.290740	−	0.956802i	$-0.593902\pi$
$797$	−16.4159			−0.581481			−0.290740	+	0.956802i	$0.593902\pi$
$798$		0			0
$799$	−40.8395			−1.44480
$800$		0			0
$801$	8.98349	−	15.5599i	0.317416	−	0.549781i
$802$		0			0
$803$	−12.3480	−	21.3873i	−0.435751	−	0.754743i
$804$		0			0
$805$	−5.80184	+	19.8709i	−0.204488	+	0.700357i
$806$		0			0
$807$	15.8520	+	27.4564i	0.558016	+	0.966512i
$808$		0			0
$809$	−24.6839	+	42.7537i	−0.867838	+	1.50314i	−0.00363758	+	0.999993i	$0.501158\pi$
$809$	−24.6839	+	42.7537i	−0.867838	+	1.50314i	−0.864201	+	0.503147i	$0.832175\pi$
$810$		0			0
$811$	−23.4315			−0.822793			−0.411396	−	0.911457i	$-0.634959\pi$
$811$	−23.4315			−0.822793			−0.411396	+	0.911457i	$0.634959\pi$
$812$		0			0
$813$	33.1041			1.16101
$814$		0			0
$815$	7.71504	−	13.3628i	0.270246	−	0.468080i
$816$		0			0
$817$	7.50789	+	13.0041i	0.262668	+	0.454954i
$818$		0			0
$819$	−15.6131	−	16.3248i	−0.545566	−	0.570434i
$820$		0			0
$821$	2.16372	+	3.74767i	0.0755143	+	0.130795i	0.901310	−	0.433175i	$-0.142607\pi$
$821$	2.16372	+	3.74767i	0.0755143	+	0.130795i	−0.825796	+	0.563970i	$0.809273\pi$
$822$		0			0
$823$	6.54023	−	11.3280i	0.227978	−	0.394870i	−0.729231	−	0.684268i	$-0.760122\pi$
$823$	6.54023	−	11.3280i	0.227978	−	0.394870i	0.957209	+	0.289398i	$0.0934552\pi$
$824$		0			0
$825$	65.1206			2.26721
$826$		0			0
$827$	6.08156			0.211477			0.105738	−	0.994394i	$-0.466279\pi$
$827$	6.08156			0.211477			0.105738	+	0.994394i	$0.466279\pi$
$828$		0			0
$829$	−10.4973	+	18.1818i	−0.364586	+	0.631481i	−0.988710	−	0.149844i	$-0.952123\pi$
$829$	−10.4973	+	18.1818i	−0.364586	+	0.631481i	0.624124	+	0.781326i	$0.285456\pi$
$830$		0			0
$831$	−29.5744	−	51.2243i	−1.02592	−	1.77695i
$832$		0			0
$833$	1.25330	−	28.1070i	0.0434242	−	0.973851i
$834$		0			0
$835$	2.41977	+	4.19116i	0.0837395	+	0.145041i
$836$		0			0
$837$	−18.6256	+	32.2605i	−0.643795	+	1.11509i
$838$		0			0
$839$	−50.0675			−1.72852			−0.864261	−	0.503044i	$-0.832213\pi$
$839$	−50.0675			−1.72852			−0.864261	+	0.503044i	$0.832213\pi$
$840$		0			0
$841$	2.57505			0.0887948
$842$		0			0
$843$	−16.7553	+	29.0210i	−0.577083	+	0.999536i
$844$		0			0
$845$	−4.05192	−	7.01813i	−0.139390	−	0.241431i
$846$		0			0
$847$	37.0412	+	38.7297i	1.27275	+	1.33077i
$848$		0			0
$849$	41.8176	+	72.4302i	1.43518	+	2.48580i
$850$		0			0
$851$	−6.60021	+	11.4319i	−0.226252	+	0.391880i
$852$		0			0
$853$	31.8851			1.09173			0.545863	−	0.837875i	$-0.316202\pi$
$853$	31.8851			1.09173			0.545863	+	0.837875i	$0.316202\pi$
$854$		0			0
$855$	7.43680			0.254333
$856$		0			0
$857$	−25.2382	+	43.7139i	−0.862121	+	1.49324i	0.00775693	+	0.999970i	$0.497531\pi$
$857$	−25.2382	+	43.7139i	−0.862121	+	1.49324i	−0.869878	+	0.493267i	$0.835802\pi$
$858$		0			0
$859$	−27.3369	−	47.3490i	−0.932724	−	1.61553i	−0.778643	−	0.627467i	$-0.784092\pi$
$859$	−27.3369	−	47.3490i	−0.932724	−	1.61553i	−0.154081	−	0.988058i	$-0.549242\pi$
$860$		0			0
$861$	−2.02989	+	6.95224i	−0.0691785	+	0.236932i
$862$		0			0
$863$	−15.5316	−	26.9014i	−0.528700	−	0.915736i	−0.999440	−	0.0334636i	$-0.989346\pi$
$863$	−15.5316	−	26.9014i	−0.528700	−	0.915736i	0.470740	−	0.882272i	$-0.343987\pi$
$864$		0			0
$865$	3.28630	−	5.69205i	0.111738	−	0.193535i
$866$		0			0
$867$	−2.31415			−0.0785926
$868$		0			0
$869$	29.6422			1.00554
$870$		0			0
$871$	13.9127	−	24.0975i	0.471413	−	0.816511i
$872$		0			0
$873$	−7.74455	−	13.4140i	−0.262113	−	0.453994i
$874$		0			0
$875$	−20.5301	+	5.01360i	−0.694045	+	0.169491i
$876$		0			0
$877$	0.876626	+	1.51836i	0.0296016	+	0.0512714i	0.880447	−	0.474145i	$-0.157243\pi$
$877$	0.876626	+	1.51836i	0.0296016	+	0.0512714i	−0.850845	+	0.525417i	$0.823909\pi$
$878$		0			0
$879$	−20.8541	+	36.1204i	−0.703391	+	1.21831i
$880$		0			0
$881$	−7.18675			−0.242128			−0.121064	−	0.992645i	$-0.538631\pi$
$881$	−7.18675			−0.242128			−0.121064	+	0.992645i	$0.538631\pi$
$882$		0			0
$883$	−22.2021			−0.747159			−0.373579	−	0.927598i	$-0.621870\pi$
$883$	−22.2021			−0.747159			−0.373579	+	0.927598i	$0.621870\pi$
$884$		0			0
$885$	8.11316	−	14.0524i	0.272721	−	0.472366i
$886$		0			0
$887$	3.63419	+	6.29460i	0.122024	+	0.211352i	0.920566	−	0.390588i	$-0.127728\pi$
$887$	3.63419	+	6.29460i	0.122024	+	0.211352i	−0.798542	+	0.601940i	$0.794395\pi$
$888$		0			0
$889$	2.95055	−	0.720545i	0.0989583	−	0.0241663i
$890$		0			0
$891$	−6.39938	−	11.0840i	−0.214387	−	0.371329i
$892$		0			0
$893$	9.74251	−	16.8745i	0.326021	−	0.564684i
$894$		0			0
$895$	18.5909			0.621424
$896$		0			0
$897$	−47.1527			−1.57438
$898$		0			0
$899$	−25.6008	+	44.3419i	−0.853834	+	1.47888i
$900$		0			0
$901$	−2.34060	−	4.05404i	−0.0779766	−	0.135059i
$902$		0			0
$903$	15.8947	−	54.4382i	0.528942	−	1.81159i
$904$		0			0
$905$	2.03358	+	3.52226i	0.0675984	+	0.117084i
$906$		0			0
$907$	−26.6261	+	46.1178i	−0.884107	+	1.53132i	−0.0373725	+	0.999301i	$0.511899\pi$
$907$	−26.6261	+	46.1178i	−0.884107	+	1.53132i	−0.846734	+	0.532016i	$0.821435\pi$
$908$		0			0
$909$	−79.5703			−2.63918
$910$		0			0
$911$	−30.2046			−1.00072			−0.500361	−	0.865817i	$-0.666799\pi$
$911$	−30.2046			−1.00072			−0.500361	+	0.865817i	$0.666799\pi$
$912$		0			0
$913$	18.8363	−	32.6254i	0.623390	−	1.07974i
$914$		0			0
$915$	6.17344	+	10.6927i	0.204088	+	0.353490i
$916$		0			0
$917$	2.38751	+	2.49634i	0.0788424	+	0.0824363i
$918$		0			0
$919$	18.5825	+	32.1858i	0.612980	+	1.06171i	0.990735	+	0.135807i	$0.0433627\pi$
$919$	18.5825	+	32.1858i	0.612980	+	1.06171i	−0.377755	+	0.925905i	$0.623304\pi$
$920$		0			0
$921$	5.27512	−	9.13678i	0.173821	−	0.301067i
$922$		0			0
$923$	−5.96961			−0.196492
$924$		0			0
$925$	−6.19592			−0.203721
$926$		0			0
$927$	−35.5513	+	61.5767i	−1.16766	+	2.02245i
$928$		0			0
$929$	23.1261	+	40.0557i	0.758744	+	1.31418i	0.943491	+	0.331397i	$0.107520\pi$
$929$	23.1261	+	40.0557i	0.758744	+	1.31418i	−0.184747	+	0.982786i	$0.559147\pi$
$930$		0			0
$931$	11.3146	+	7.22296i	0.370821	+	0.236723i
$932$		0			0
$933$	−8.17986	−	14.1679i	−0.267797	−	0.463837i
$934$		0			0
$935$	9.69663	−	16.7951i	0.317114	−	0.549257i
$936$		0			0
$937$	29.1366			0.951850			0.475925	−	0.879486i	$-0.342113\pi$
$937$	29.1366			0.951850			0.475925	+	0.879486i	$0.342113\pi$
$938$		0			0
$939$	40.3682			1.31737
$940$		0			0
$941$	−16.3928	+	28.3932i	−0.534391	+	0.925592i	0.464802	+	0.885415i	$0.346126\pi$
$941$	−16.3928	+	28.3932i	−0.534391	+	0.925592i	−0.999193	+	0.0401772i	$0.987208\pi$
$942$		0			0
$943$	4.53279	+	7.85102i	0.147608	+	0.255664i
$944$		0			0
$945$	−6.45218	−	6.74629i	−0.209889	−	0.219457i
$946$		0			0
$947$	11.5318	+	19.9736i	0.374732	+	0.649055i	0.990287	−	0.139039i	$-0.0444013\pi$
$947$	11.5318	+	19.9736i	0.374732	+	0.649055i	−0.615555	+	0.788094i	$0.711068\pi$
$948$		0			0
$949$	−4.19665	+	7.26881i	−0.136229	+	0.235955i
$950$		0			0
$951$	83.0561			2.69328
$952$		0			0
$953$	16.8472			0.545734			0.272867	−	0.962052i	$-0.412028\pi$
$953$	16.8472			0.545734			0.272867	+	0.962052i	$0.412028\pi$
$954$		0			0
$955$	−4.80756	+	8.32693i	−0.155569	+	0.269453i
$956$		0			0
$957$	42.9979	+	74.4745i	1.38992	+	2.40742i
$958$		0			0
$959$	8.91723	−	30.5409i	0.287952	−	0.986217i
$960$		0			0
$961$	−26.0138	−	45.0573i	−0.839156	−	1.45346i
$962$		0			0
$963$	−20.5649	+	35.6194i	−0.662693	+	1.14782i
$964$		0			0
$965$	−21.1726			−0.681570
$966$		0			0
$967$	12.4420			0.400107			0.200053	−	0.979785i	$-0.435888\pi$
$967$	12.4420			0.400107			0.200053	+	0.979785i	$0.435888\pi$
$968$		0			0
$969$	−10.5494	+	18.2721i	−0.338896	+	0.586985i
$970$		0			0
$971$	5.41270	+	9.37507i	0.173702	+	0.300860i	0.939711	−	0.341969i	$-0.111094\pi$
$971$	5.41270	+	9.37507i	0.173702	+	0.300860i	−0.766009	+	0.642829i	$0.777760\pi$
$972$		0			0
$973$	−17.4631	+	4.26461i	−0.559841	+	0.136717i
$974$		0			0
$975$	−11.0661	−	19.1671i	−0.354399	−	0.613837i
$976$		0			0
$977$	13.0752	−	22.6470i	0.418314	−	0.724541i	−0.577456	−	0.816422i	$-0.695955\pi$
$977$	13.0752	−	22.6470i	0.418314	−	0.724541i	0.995770	+	0.0918808i	$0.0292879\pi$
$978$		0			0
$979$	22.3543			0.714445
$980$		0			0
$981$	−62.4509			−1.99390
$982$		0			0
$983$	−22.3856	+	38.7730i	−0.713990	+	1.23667i	0.249358	+	0.968411i	$0.419780\pi$
$983$	−22.3856	+	38.7730i	−0.713990	+	1.23667i	−0.963348	+	0.268255i	$0.913553\pi$
$984$		0			0
$985$	−11.0957	−	19.2183i	−0.353538	−	0.612345i
$986$		0			0
$987$	−71.4896	+	17.4583i	−2.27554	+	0.555703i
$988$		0			0
$989$	−35.4932	−	61.4760i	−1.12862	−	1.95482i
$990$		0			0
$991$	11.2673	−	19.5155i	0.357917	−	0.619930i	−0.629696	−	0.776842i	$-0.716820\pi$
$991$	11.2673	−	19.5155i	0.357917	−	0.619930i	0.987613	+	0.156911i	$0.0501537\pi$
$992$		0			0
$993$	55.5594			1.76312
$994$		0			0
$995$	0.839576			0.0266163
$996$		0			0
$997$	0.327788	−	0.567745i	0.0103811	−	0.0179807i	−0.860788	−	0.508963i	$-0.830029\pi$
$997$	0.327788	−	0.567745i	0.0103811	−	0.0179807i	0.871169	+	0.490983i	$0.163362\pi$
$998$		0			0
$999$	−2.97640	−	5.15528i	−0.0941692	−	0.163106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.e.165.3	✓	30
7.2	even	3	inner	1148.2.i.e.821.3	yes	30
7.3	odd	6		8036.2.a.r.1.3		15
7.4	even	3		8036.2.a.q.1.13		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.e.165.3	✓	30	1.1	even	1	trivial
1148.2.i.e.821.3	yes	30	7.2	even	3	inner
8036.2.a.q.1.13		15	7.4	even	3
8036.2.a.r.1.3		15	7.3	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36871 + 2.37067i) q^{3} +(0.431527 + 0.747427i) q^{5} +(-2.57022 + 0.627666i) q^{7} +(-2.24672 - 3.89144i) q^{9} +O(q^{10})\)	\(q+(-1.36871 + 2.37067i) q^{3} +(0.431527 + 0.747427i) q^{5} +(-2.57022 + 0.627666i) q^{7} +(-2.24672 - 3.89144i) q^{9} +(2.79534 - 4.84167i) q^{11} -1.90008 q^{13} -2.36254 q^{15} +(2.00964 - 3.48080i) q^{17} +(0.958824 + 1.66073i) q^{19} +(2.02989 - 6.95224i) q^{21} +(-4.53279 - 7.85102i) q^{23} +(2.12757 - 3.68506i) q^{25} +4.08817 q^{27} +5.61917 q^{29} +(-4.55598 + 7.89118i) q^{31} +(7.65200 + 13.2537i) q^{33} +(-1.57825 - 1.65020i) q^{35} +(-0.728052 - 1.26102i) q^{37} +(2.60065 - 4.50445i) q^{39} -1.00000 q^{41} +7.83032 q^{43} +(1.93904 - 3.35852i) q^{45} +(-5.08045 - 8.79959i) q^{47} +(6.21207 - 3.22648i) q^{49} +(5.50122 + 9.52839i) q^{51} +(0.582342 - 1.00865i) q^{53} +4.82506 q^{55} -5.24940 q^{57} +(-3.43408 + 5.94801i) q^{59} +(-2.61306 - 4.52595i) q^{61} +(8.21709 + 8.59166i) q^{63} +(-0.819934 - 1.42017i) q^{65} +(-7.32217 + 12.6824i) q^{67} +24.8162 q^{69} +3.14178 q^{71} +(2.20867 - 3.82554i) q^{73} +(5.82404 + 10.0875i) q^{75} +(-4.14569 + 14.1987i) q^{77} +(2.65104 + 4.59173i) q^{79} +(1.14465 - 1.98259i) q^{81} +6.73846 q^{83} +3.46886 q^{85} +(-7.69100 + 13.3212i) q^{87} +(1.99924 + 3.46279i) q^{89} +(4.88361 - 1.19261i) q^{91} +(-12.4716 - 21.6014i) q^{93} +(-0.827517 + 1.43330i) q^{95} +3.44705 q^{97} -25.1214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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