LMFDB - Embedded newform 6016.2.a.r.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6016,2,Mod(1,6016)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6016, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6016.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6016 = 2^{7} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6016.a (trivial)

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:	yes
Analytic conductor:	$48.0380018560$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 30 x^{12} + 56 x^{11} + 331 x^{10} - 562 x^{9} - 1630 x^{8} + 2458 x^{7} + \cdots + 128 $ x^14 - 2x^13 - 30x^12 + 56x^11 + 331x^10 - 562x^9 - 1630x^8 + 2458x^7 + 3313x^6 - 4512x^5 - 1612x^4 + 2960x^3 - 256x^2 - 512*x + 128
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.07939$ of defining polynomial
Character	$\chi$	$=$	6016.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.07939 q^{3} +2.92934 q^{5} -3.46404 q^{7} +6.48265 q^{9} +O(q^{10})$	$q-3.07939 q^{3} +2.92934 q^{5} -3.46404 q^{7} +6.48265 q^{9} +0.928404 q^{11} +4.00655 q^{13} -9.02058 q^{15} +2.61283 q^{17} +6.70844 q^{19} +10.6671 q^{21} +6.48108 q^{23} +3.58103 q^{25} -10.7244 q^{27} +7.30505 q^{29} +9.77698 q^{31} -2.85892 q^{33} -10.1474 q^{35} -7.67059 q^{37} -12.3377 q^{39} +3.13193 q^{41} -5.11675 q^{43} +18.9899 q^{45} +1.00000 q^{47} +4.99960 q^{49} -8.04594 q^{51} -11.4351 q^{53} +2.71961 q^{55} -20.6579 q^{57} +3.59319 q^{59} +1.43682 q^{61} -22.4562 q^{63} +11.7366 q^{65} -5.65998 q^{67} -19.9578 q^{69} +1.15953 q^{71} +13.4969 q^{73} -11.0274 q^{75} -3.21603 q^{77} +4.50318 q^{79} +13.5768 q^{81} +11.9242 q^{83} +7.65388 q^{85} -22.4951 q^{87} +7.93604 q^{89} -13.8789 q^{91} -30.1072 q^{93} +19.6513 q^{95} +11.8796 q^{97} +6.01851 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{3} + 6 q^{5} + 2 q^{7} + 22 q^{9}+O(q^{10}) $ 14 * q - 2 * q^3 + 6 * q^5 + 2 * q^7 + 22 * q^9	$ 14 q - 2 q^{3} + 6 q^{5} + 2 q^{7} + 22 q^{9} - 14 q^{11} + 4 q^{13} + 6 q^{15} + 8 q^{17} - 8 q^{19} + 6 q^{21} + 18 q^{23} + 22 q^{25} - 8 q^{27} + 22 q^{29} + 4 q^{31} + 2 q^{33} - 26 q^{35} + 6 q^{37} + 20 q^{39} + 16 q^{41} - 12 q^{43} + 30 q^{45} + 14 q^{47} + 34 q^{49} - 18 q^{51} + 20 q^{53} + 2 q^{55} - 4 q^{57} - 32 q^{59} + 12 q^{61} + 40 q^{65} - 16 q^{67} + 46 q^{69} + 16 q^{71} - 12 q^{73} + 16 q^{75} + 10 q^{77} + 16 q^{79} + 74 q^{81} - 14 q^{83} + 12 q^{85} + 14 q^{87} - 28 q^{91} - 16 q^{93} + 52 q^{95} + 28 q^{97} - 50 q^{99}+O(q^{100}) $ 14 * q - 2 * q^3 + 6 * q^5 + 2 * q^7 + 22 * q^9 - 14 * q^11 + 4 * q^13 + 6 * q^15 + 8 * q^17 - 8 * q^19 + 6 * q^21 + 18 * q^23 + 22 * q^25 - 8 * q^27 + 22 * q^29 + 4 * q^31 + 2 * q^33 - 26 * q^35 + 6 * q^37 + 20 * q^39 + 16 * q^41 - 12 * q^43 + 30 * q^45 + 14 * q^47 + 34 * q^49 - 18 * q^51 + 20 * q^53 + 2 * q^55 - 4 * q^57 - 32 * q^59 + 12 * q^61 + 40 * q^65 - 16 * q^67 + 46 * q^69 + 16 * q^71 - 12 * q^73 + 16 * q^75 + 10 * q^77 + 16 * q^79 + 74 * q^81 - 14 * q^83 + 12 * q^85 + 14 * q^87 - 28 * q^91 - 16 * q^93 + 52 * q^95 + 28 * q^97 - 50 * q^99

Display 100 coefficients 10 coefficients

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
$3$	−3.07939	−1.77789	−0.888944	−	0.458017i	$-0.848560\pi$
$3$	−3.07939	−1.77789	−0.888944	+	0.458017i	$0.848560\pi$
$4$	0	0
$5$	2.92934	1.31004	0.655020	−	0.755611i	$-0.272660\pi$
$5$	2.92934	1.31004	0.655020	+	0.755611i	$0.272660\pi$
$6$	0	0
$7$	−3.46404	−1.30929	−0.654643	−	0.755938i	$-0.727181\pi$
$7$	−3.46404	−1.30929	−0.654643	+	0.755938i	$0.727181\pi$
$8$	0	0
$9$	6.48265	2.16088
$10$	0	0
$11$	0.928404	0.279924	0.139962	−	0.990157i	$-0.455302\pi$
$11$	0.928404	0.279924	0.139962	+	0.990157i	$0.455302\pi$
$12$	0	0
$13$	4.00655	1.11122	0.555609	−	0.831444i	$-0.312485\pi$
$13$	4.00655	1.11122	0.555609	+	0.831444i	$0.312485\pi$
$14$	0	0
$15$	−9.02058	−2.32910
$16$	0	0
$17$	2.61283	0.633705	0.316853	−	0.948475i	$-0.397374\pi$
$17$	2.61283	0.633705	0.316853	+	0.948475i	$0.397374\pi$
$18$	0	0
$19$	6.70844	1.53902	0.769511	−	0.638634i	$-0.220500\pi$
$19$	6.70844	1.53902	0.769511	+	0.638634i	$0.220500\pi$
$20$	0	0
$21$	10.6671	2.32776
$22$	0	0
$23$	6.48108	1.35140	0.675699	−	0.737177i	$-0.263842\pi$
$23$	6.48108	1.35140	0.675699	+	0.737177i	$0.263842\pi$
$24$	0	0
$25$	3.58103	0.716206
$26$	0	0
$27$	−10.7244	−2.06392
$28$	0	0
$29$	7.30505	1.35651	0.678257	−	0.734824i	$-0.262735\pi$
$29$	7.30505	1.35651	0.678257	+	0.734824i	$0.262735\pi$
$30$	0	0
$31$	9.77698	1.75600	0.877999	−	0.478662i	$-0.158878\pi$
$31$	9.77698	1.75600	0.877999	+	0.478662i	$0.158878\pi$
$32$	0	0
$33$	−2.85892	−0.497674
$34$	0	0
$35$	−10.1474	−1.71522
$36$	0	0
$37$	−7.67059	−1.26104	−0.630519	−	0.776174i	$-0.717158\pi$
$37$	−7.67059	−1.26104	−0.630519	+	0.776174i	$0.717158\pi$
$38$	0	0
$39$	−12.3377	−1.97562
$40$	0	0
$41$	3.13193	0.489125	0.244563	−	0.969634i	$-0.421356\pi$
$41$	3.13193	0.489125	0.244563	+	0.969634i	$0.421356\pi$
$42$	0	0
$43$	−5.11675	−0.780296	−0.390148	−	0.920752i	$-0.627576\pi$
$43$	−5.11675	−0.780296	−0.390148	+	0.920752i	$0.627576\pi$
$44$	0	0
$45$	18.9899	2.83084
$46$	0	0
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	0	0
$49$	4.99960	0.714229
$50$	0	0
$51$	−8.04594	−1.12666
$52$	0	0
$53$	−11.4351	−1.57072	−0.785362	−	0.619036i	$-0.787523\pi$
$53$	−11.4351	−1.57072	−0.785362	+	0.619036i	$0.787523\pi$
$54$	0	0
$55$	2.71961	0.366712
$56$	0	0
$57$	−20.6579	−2.73621
$58$	0	0
$59$	3.59319	0.467793	0.233897	−	0.972261i	$-0.424852\pi$
$59$	3.59319	0.467793	0.233897	+	0.972261i	$0.424852\pi$
$60$	0	0
$61$	1.43682	0.183966	0.0919831	−	0.995761i	$-0.470679\pi$
$61$	1.43682	0.183966	0.0919831	+	0.995761i	$0.470679\pi$
$62$	0	0
$63$	−22.4562	−2.82921
$64$	0	0
$65$	11.7366	1.45574
$66$	0	0
$67$	−5.65998	−0.691477	−0.345739	−	0.938331i	$-0.612372\pi$
$67$	−5.65998	−0.691477	−0.345739	+	0.938331i	$0.612372\pi$
$68$	0	0
$69$	−19.9578	−2.40263
$70$	0	0
$71$	1.15953	0.137611	0.0688053	−	0.997630i	$-0.478081\pi$
$71$	1.15953	0.137611	0.0688053	+	0.997630i	$0.478081\pi$
$72$	0	0
$73$	13.4969	1.57970	0.789848	−	0.613303i	$-0.210160\pi$
$73$	13.4969	1.57970	0.789848	+	0.613303i	$0.210160\pi$
$74$	0	0
$75$	−11.0274	−1.27333
$76$	0	0
$77$	−3.21603	−0.366501
$78$	0	0
$79$	4.50318	0.506647	0.253323	−	0.967382i	$-0.418476\pi$
$79$	4.50318	0.506647	0.253323	+	0.967382i	$0.418476\pi$
$80$	0	0
$81$	13.5768	1.50853
$82$	0	0
$83$	11.9242	1.30885	0.654425	−	0.756127i	$-0.272911\pi$
$83$	11.9242	1.30885	0.654425	+	0.756127i	$0.272911\pi$
$84$	0	0
$85$	7.65388	0.830180
$86$	0	0
$87$	−22.4951	−2.41173
$88$	0	0
$89$	7.93604	0.841219	0.420609	−	0.907242i	$-0.361816\pi$
$89$	7.93604	0.841219	0.420609	+	0.907242i	$0.361816\pi$
$90$	0	0
$91$	−13.8789	−1.45490
$92$	0	0
$93$	−30.1072	−3.12197
$94$	0	0
$95$	19.6513	2.01618
$96$	0	0
$97$	11.8796	1.20619	0.603097	−	0.797668i	$-0.293933\pi$
$97$	11.8796	1.20619	0.603097	+	0.797668i	$0.293933\pi$
$98$	0	0
$99$	6.01851	0.604883
$100$	0	0
$101$	−6.69206	−0.665885	−0.332943	−	0.942947i	$-0.608042\pi$
$101$	−6.69206	−0.665885	−0.332943	+	0.942947i	$0.608042\pi$
$102$	0	0
$103$	1.99725	0.196795	0.0983975	−	0.995147i	$-0.468628\pi$
$103$	1.99725	0.196795	0.0983975	+	0.995147i	$0.468628\pi$
$104$	0	0
$105$	31.2477	3.04946
$106$	0	0
$107$	−7.85580	−0.759449	−0.379725	−	0.925100i	$-0.623981\pi$
$107$	−7.85580	−0.759449	−0.379725	+	0.925100i	$0.623981\pi$
$108$	0	0
$109$	−12.0598	−1.15512	−0.577558	−	0.816349i	$-0.695994\pi$
$109$	−12.0598	−1.15512	−0.577558	+	0.816349i	$0.695994\pi$
$110$	0	0
$111$	23.6208	2.24198
$112$	0	0
$113$	−12.8534	−1.20914	−0.604571	−	0.796551i	$-0.706656\pi$
$113$	−12.8534	−1.20914	−0.604571	+	0.796551i	$0.706656\pi$
$114$	0	0
$115$	18.9853	1.77039
$116$	0	0
$117$	25.9731	2.40121
$118$	0	0
$119$	−9.05097	−0.829701
$120$	0	0
$121$	−10.1381	−0.921642
$122$	0	0
$123$	−9.64443	−0.869609
$124$	0	0
$125$	−4.15664	−0.371781
$126$	0	0
$127$	−0.195162	−0.0173179	−0.00865893	−	0.999963i	$-0.502756\pi$
$127$	−0.195162	−0.0173179	−0.00865893	+	0.999963i	$0.502756\pi$
$128$	0	0
$129$	15.7565	1.38728
$130$	0	0
$131$	−2.16683	−0.189317	−0.0946585	−	0.995510i	$-0.530176\pi$
$131$	−2.16683	−0.189317	−0.0946585	+	0.995510i	$0.530176\pi$
$132$	0	0
$133$	−23.2383	−2.01502
$134$	0	0
$135$	−31.4155	−2.70382
$136$	0	0
$137$	−19.1209	−1.63361	−0.816806	−	0.576912i	$-0.804257\pi$
$137$	−19.1209	−1.63361	−0.816806	+	0.576912i	$0.804257\pi$
$138$	0	0
$139$	−9.47284	−0.803476	−0.401738	−	0.915755i	$-0.631594\pi$
$139$	−9.47284	−0.803476	−0.401738	+	0.915755i	$0.631594\pi$
$140$	0	0
$141$	−3.07939	−0.259331
$142$	0	0
$143$	3.71970	0.311057
$144$	0	0
$145$	21.3990	1.77709
$146$	0	0
$147$	−15.3957	−1.26982
$148$	0	0
$149$	17.7092	1.45080	0.725399	−	0.688329i	$-0.241655\pi$
$149$	17.7092	1.45080	0.725399	+	0.688329i	$0.241655\pi$
$150$	0	0
$151$	−6.54599	−0.532705	−0.266352	−	0.963876i	$-0.585818\pi$
$151$	−6.54599	−0.532705	−0.266352	+	0.963876i	$0.585818\pi$
$152$	0	0
$153$	16.9381	1.36936
$154$	0	0
$155$	28.6401	2.30043
$156$	0	0
$157$	−11.4924	−0.917194	−0.458597	−	0.888644i	$-0.651648\pi$
$157$	−11.4924	−0.917194	−0.458597	+	0.888644i	$0.651648\pi$
$158$	0	0
$159$	35.2130	2.79257
$160$	0	0
$161$	−22.4507	−1.76937
$162$	0	0
$163$	21.5089	1.68470	0.842352	−	0.538927i	$-0.181170\pi$
$163$	21.5089	1.68470	0.842352	+	0.538927i	$0.181170\pi$
$164$	0	0
$165$	−8.37474	−0.651973
$166$	0	0
$167$	4.66293	0.360829	0.180414	−	0.983591i	$-0.442256\pi$
$167$	4.66293	0.360829	0.180414	+	0.983591i	$0.442256\pi$
$168$	0	0
$169$	3.05248	0.234806
$170$	0	0
$171$	43.4885	3.32565
$172$	0	0
$173$	12.4991	0.950288	0.475144	−	0.879908i	$-0.342396\pi$
$173$	12.4991	0.950288	0.475144	+	0.879908i	$0.342396\pi$
$174$	0	0
$175$	−12.4049	−0.937719
$176$	0	0
$177$	−11.0648	−0.831684
$178$	0	0
$179$	−22.7784	−1.70254	−0.851269	−	0.524729i	$-0.824167\pi$
$179$	−22.7784	−1.70254	−0.851269	+	0.524729i	$0.824167\pi$
$180$	0	0
$181$	8.18916	0.608695	0.304348	−	0.952561i	$-0.401562\pi$
$181$	8.18916	0.608695	0.304348	+	0.952561i	$0.401562\pi$
$182$	0	0
$183$	−4.42454	−0.327071
$184$	0	0
$185$	−22.4698	−1.65201
$186$	0	0
$187$	2.42577	0.177390
$188$	0	0
$189$	37.1499	2.70226
$190$	0	0
$191$	24.4307	1.76774	0.883872	−	0.467730i	$-0.154928\pi$
$191$	24.4307	1.76774	0.883872	+	0.467730i	$0.154928\pi$
$192$	0	0
$193$	5.85344	0.421340	0.210670	−	0.977557i	$-0.432435\pi$
$193$	5.85344	0.421340	0.210670	+	0.977557i	$0.432435\pi$
$194$	0	0
$195$	−36.1415	−2.58814
$196$	0	0
$197$	−6.38225	−0.454716	−0.227358	−	0.973811i	$-0.573009\pi$
$197$	−6.38225	−0.454716	−0.227358	+	0.973811i	$0.573009\pi$
$198$	0	0
$199$	−11.3078	−0.801588	−0.400794	−	0.916168i	$-0.631266\pi$
$199$	−11.3078	−0.801588	−0.400794	+	0.916168i	$0.631266\pi$
$200$	0	0
$201$	17.4293	1.22937
$202$	0	0
$203$	−25.3050	−1.77607
$204$	0	0
$205$	9.17448	0.640774
$206$	0	0
$207$	42.0145	2.92021
$208$	0	0
$209$	6.22814	0.430810
$210$	0	0
$211$	17.2079	1.18464	0.592321	−	0.805702i	$-0.298212\pi$
$211$	17.2079	1.18464	0.592321	+	0.805702i	$0.298212\pi$
$212$	0	0
$213$	−3.57064	−0.244656
$214$	0	0
$215$	−14.9887	−1.02222
$216$	0	0
$217$	−33.8679	−2.29910
$218$	0	0
$219$	−41.5623	−2.80852
$220$	0	0
$221$	10.4685	0.704185
$222$	0	0
$223$	−23.9700	−1.60515	−0.802575	−	0.596552i	$-0.796537\pi$
$223$	−23.9700	−1.60515	−0.802575	+	0.596552i	$0.796537\pi$
$224$	0	0
$225$	23.2146	1.54764
$226$	0	0
$227$	−13.6735	−0.907540	−0.453770	−	0.891119i	$-0.649921\pi$
$227$	−13.6735	−0.907540	−0.453770	+	0.891119i	$0.649921\pi$
$228$	0	0
$229$	3.16178	0.208937	0.104468	−	0.994528i	$-0.466686\pi$
$229$	3.16178	0.208937	0.104468	+	0.994528i	$0.466686\pi$
$230$	0	0
$231$	9.90342	0.651597
$232$	0	0
$233$	6.05342	0.396573	0.198286	−	0.980144i	$-0.436462\pi$
$233$	6.05342	0.396573	0.198286	+	0.980144i	$0.436462\pi$
$234$	0	0
$235$	2.92934	0.191089
$236$	0	0
$237$	−13.8670	−0.900761
$238$	0	0
$239$	−23.5806	−1.52530	−0.762652	−	0.646809i	$-0.776103\pi$
$239$	−23.5806	−1.52530	−0.762652	+	0.646809i	$0.776103\pi$
$240$	0	0
$241$	1.08082	0.0696215	0.0348107	−	0.999394i	$-0.488917\pi$
$241$	1.08082	0.0696215	0.0348107	+	0.999394i	$0.488917\pi$
$242$	0	0
$243$	−9.63489	−0.618079
$244$	0	0
$245$	14.6455	0.935669
$246$	0	0
$247$	26.8777	1.71019
$248$	0	0
$249$	−36.7193	−2.32699
$250$	0	0
$251$	−4.33234	−0.273455	−0.136727	−	0.990609i	$-0.543658\pi$
$251$	−4.33234	−0.273455	−0.136727	+	0.990609i	$0.543658\pi$
$252$	0	0
$253$	6.01706	0.378289
$254$	0	0
$255$	−23.5693	−1.47597
$256$	0	0
$257$	2.33618	0.145727	0.0728635	−	0.997342i	$-0.476786\pi$
$257$	2.33618	0.145727	0.0728635	+	0.997342i	$0.476786\pi$
$258$	0	0
$259$	26.5713	1.65106
$260$	0	0
$261$	47.3561	2.93127
$262$	0	0
$263$	23.5896	1.45460	0.727298	−	0.686322i	$-0.240776\pi$
$263$	23.5896	1.45460	0.727298	+	0.686322i	$0.240776\pi$
$264$	0	0
$265$	−33.4971	−2.05771
$266$	0	0
$267$	−24.4382	−1.49559
$268$	0	0
$269$	−15.2973	−0.932695	−0.466348	−	0.884602i	$-0.654430\pi$
$269$	−15.2973	−0.932695	−0.466348	+	0.884602i	$0.654430\pi$
$270$	0	0
$271$	29.7348	1.80626	0.903129	−	0.429369i	$-0.141264\pi$
$271$	29.7348	1.80626	0.903129	+	0.429369i	$0.141264\pi$
$272$	0	0
$273$	42.7385	2.58665
$274$	0	0
$275$	3.32464	0.200484
$276$	0	0
$277$	−21.9588	−1.31938	−0.659689	−	0.751538i	$-0.729312\pi$
$277$	−21.9588	−1.31938	−0.659689	+	0.751538i	$0.729312\pi$
$278$	0	0
$279$	63.3807	3.79451
$280$	0	0
$281$	−0.00400181	−0.000238728 0	−0.000119364	−	1.00000i	$-0.500038\pi$
$281$	−0.00400181	−0.000238728 0	−0.000119364		1.00000i	$0.500038\pi$
$282$	0	0
$283$	−18.1807	−1.08073	−0.540364	−	0.841431i	$-0.681713\pi$
$283$	−18.1807	−1.08073	−0.540364	+	0.841431i	$0.681713\pi$
$284$	0	0
$285$	−60.5140	−3.58454
$286$	0	0
$287$	−10.8491	−0.640404
$288$	0	0
$289$	−10.1731	−0.598418
$290$	0	0
$291$	−36.5821	−2.14448
$292$	0	0
$293$	8.46786	0.494698	0.247349	−	0.968926i	$-0.420441\pi$
$293$	8.46786	0.494698	0.247349	+	0.968926i	$0.420441\pi$
$294$	0	0
$295$	10.5257	0.612828
$296$	0	0
$297$	−9.95660	−0.577741
$298$	0	0
$299$	25.9668	1.50170
$300$	0	0
$301$	17.7246	1.02163
$302$	0	0
$303$	20.6075	1.18387
$304$	0	0
$305$	4.20894	0.241003
$306$	0	0
$307$	21.9437	1.25239	0.626197	−	0.779665i	$-0.284611\pi$
$307$	21.9437	1.25239	0.626197	+	0.779665i	$0.284611\pi$
$308$	0	0
$309$	−6.15032	−0.349879
$310$	0	0
$311$	−22.3853	−1.26936	−0.634678	−	0.772776i	$-0.718867\pi$
$311$	−22.3853	−1.26936	−0.634678	+	0.772776i	$0.718867\pi$
$312$	0	0
$313$	31.7285	1.79340	0.896701	−	0.442638i	$-0.145957\pi$
$313$	31.7285	1.79340	0.896701	+	0.442638i	$0.145957\pi$
$314$	0	0
$315$	−65.7818	−3.70638
$316$	0	0
$317$	0.545887	0.0306601	0.0153300	−	0.999882i	$-0.495120\pi$
$317$	0.545887	0.0306601	0.0153300	+	0.999882i	$0.495120\pi$
$318$	0	0
$319$	6.78204	0.379721
$320$	0	0
$321$	24.1911	1.35021
$322$	0	0
$323$	17.5280	0.975286
$324$	0	0
$325$	14.3476	0.795862
$326$	0	0
$327$	37.1368	2.05367
$328$	0	0
$329$	−3.46404	−0.190979
$330$	0	0
$331$	−9.70880	−0.533644	−0.266822	−	0.963746i	$-0.585974\pi$
$331$	−9.70880	−0.533644	−0.266822	+	0.963746i	$0.585974\pi$
$332$	0	0
$333$	−49.7258	−2.72495
$334$	0	0
$335$	−16.5800	−0.905863
$336$	0	0
$337$	32.1800	1.75295	0.876477	−	0.481443i	$-0.159887\pi$
$337$	32.1800	1.75295	0.876477	+	0.481443i	$0.159887\pi$
$338$	0	0
$339$	39.5805	2.14972
$340$	0	0
$341$	9.07699	0.491547
$342$	0	0
$343$	6.92946	0.374156
$344$	0	0
$345$	−58.4631	−3.14755
$346$	0	0
$347$	−13.6545	−0.733010	−0.366505	−	0.930416i	$-0.619446\pi$
$347$	−13.6545	−0.733010	−0.366505	+	0.930416i	$0.619446\pi$
$348$	0	0
$349$	35.5581	1.90338	0.951689	−	0.307062i	$-0.0993459\pi$
$349$	35.5581	1.90338	0.951689	+	0.307062i	$0.0993459\pi$
$350$	0	0
$351$	−42.9680	−2.29346
$352$	0	0
$353$	−9.70711	−0.516657	−0.258329	−	0.966057i	$-0.583172\pi$
$353$	−9.70711	−0.516657	−0.258329	+	0.966057i	$0.583172\pi$
$354$	0	0
$355$	3.39665	0.180275
$356$	0	0
$357$	27.8715	1.47512
$358$	0	0
$359$	30.2099	1.59442	0.797209	−	0.603704i	$-0.206309\pi$
$359$	30.2099	1.59442	0.797209	+	0.603704i	$0.206309\pi$
$360$	0	0
$361$	26.0032	1.36859
$362$	0	0
$363$	31.2191	1.63858
$364$	0	0
$365$	39.5371	2.06947
$366$	0	0
$367$	13.9314	0.727215	0.363607	−	0.931552i	$-0.381545\pi$
$367$	13.9314	0.727215	0.363607	+	0.931552i	$0.381545\pi$
$368$	0	0
$369$	20.3032	1.05694
$370$	0	0
$371$	39.6115	2.05653
$372$	0	0
$373$	−11.7256	−0.607127	−0.303564	−	0.952811i	$-0.598176\pi$
$373$	−11.7256	−0.607127	−0.303564	+	0.952811i	$0.598176\pi$
$374$	0	0
$375$	12.7999	0.660985
$376$	0	0
$377$	29.2681	1.50738
$378$	0	0
$379$	−17.2650	−0.886842	−0.443421	−	0.896313i	$-0.646235\pi$
$379$	−17.2650	−0.886842	−0.443421	+	0.896313i	$0.646235\pi$
$380$	0	0
$381$	0.600981	0.0307892
$382$	0	0
$383$	4.27394	0.218388	0.109194	−	0.994020i	$-0.465173\pi$
$383$	4.27394	0.218388	0.109194	+	0.994020i	$0.465173\pi$
$384$	0	0
$385$	−9.42085	−0.480131
$386$	0	0
$387$	−33.1701	−1.68613
$388$	0	0
$389$	30.7103	1.55707	0.778537	−	0.627599i	$-0.215962\pi$
$389$	30.7103	1.55707	0.778537	+	0.627599i	$0.215962\pi$
$390$	0	0
$391$	16.9340	0.856388
$392$	0	0
$393$	6.67252	0.336584
$394$	0	0
$395$	13.1913	0.663728
$396$	0	0
$397$	−4.36597	−0.219122	−0.109561	−	0.993980i	$-0.534944\pi$
$397$	−4.36597	−0.219122	−0.109561	+	0.993980i	$0.534944\pi$
$398$	0	0
$399$	71.5599	3.58248
$400$	0	0
$401$	30.2652	1.51137	0.755686	−	0.654934i	$-0.227304\pi$
$401$	30.2652	1.51137	0.755686	+	0.654934i	$0.227304\pi$
$402$	0	0
$403$	39.1720	1.95130
$404$	0	0
$405$	39.7710	1.97624
$406$	0	0
$407$	−7.12141	−0.352995
$408$	0	0
$409$	−15.3909	−0.761030	−0.380515	−	0.924775i	$-0.624253\pi$
$409$	−15.3909	−0.761030	−0.380515	+	0.924775i	$0.624253\pi$
$410$	0	0
$411$	58.8808	2.90438
$412$	0	0
$413$	−12.4470	−0.612475
$414$	0	0
$415$	34.9300	1.71465
$416$	0	0
$417$	29.1706	1.42849
$418$	0	0
$419$	−26.5041	−1.29481	−0.647405	−	0.762146i	$-0.724146\pi$
$419$	−26.5041	−1.29481	−0.647405	+	0.762146i	$0.724146\pi$
$420$	0	0
$421$	32.3460	1.57645	0.788225	−	0.615387i	$-0.211000\pi$
$421$	32.3460	1.57645	0.788225	+	0.615387i	$0.211000\pi$
$422$	0	0
$423$	6.48265	0.315197
$424$	0	0
$425$	9.35664	0.453864
$426$	0	0
$427$	−4.97722	−0.240864
$428$	0	0
$429$	−11.4544	−0.553024
$430$	0	0
$431$	2.03867	0.0981995	0.0490997	−	0.998794i	$-0.484365\pi$
$431$	2.03867	0.0981995	0.0490997	+	0.998794i	$0.484365\pi$
$432$	0	0
$433$	−8.03954	−0.386356	−0.193178	−	0.981164i	$-0.561879\pi$
$433$	−8.03954	−0.386356	−0.193178	+	0.981164i	$0.561879\pi$
$434$	0	0
$435$	−65.8958	−3.15946
$436$	0	0
$437$	43.4779	2.07983
$438$	0	0
$439$	1.62929	0.0777616	0.0388808	−	0.999244i	$-0.487621\pi$
$439$	1.62929	0.0777616	0.0388808	+	0.999244i	$0.487621\pi$
$440$	0	0
$441$	32.4107	1.54337
$442$	0	0
$443$	−38.7692	−1.84198	−0.920990	−	0.389586i	$-0.872618\pi$
$443$	−38.7692	−1.84198	−0.920990	+	0.389586i	$0.872618\pi$
$444$	0	0
$445$	23.2474	1.10203
$446$	0	0
$447$	−54.5337	−2.57935
$448$	0	0
$449$	−30.7002	−1.44883	−0.724417	−	0.689362i	$-0.757891\pi$
$449$	−30.7002	−1.44883	−0.724417	+	0.689362i	$0.757891\pi$
$450$	0	0
$451$	2.90769	0.136918
$452$	0	0
$453$	20.1576	0.947089
$454$	0	0
$455$	−40.6560	−1.90598
$456$	0	0
$457$	−27.4669	−1.28485	−0.642424	−	0.766350i	$-0.722071\pi$
$457$	−27.4669	−1.28485	−0.642424	+	0.766350i	$0.722071\pi$
$458$	0	0
$459$	−28.0212	−1.30792
$460$	0	0
$461$	14.4790	0.674353	0.337176	−	0.941442i	$-0.390528\pi$
$461$	14.4790	0.674353	0.337176	+	0.941442i	$0.390528\pi$
$462$	0	0
$463$	10.4718	0.486667	0.243333	−	0.969943i	$-0.421759\pi$
$463$	10.4718	0.486667	0.243333	+	0.969943i	$0.421759\pi$
$464$	0	0
$465$	−88.1941	−4.08990
$466$	0	0
$467$	−41.1144	−1.90255	−0.951274	−	0.308346i	$-0.900225\pi$
$467$	−41.1144	−1.90255	−0.951274	+	0.308346i	$0.900225\pi$
$468$	0	0
$469$	19.6064	0.905341
$470$	0	0
$471$	35.3896	1.63067
$472$	0	0
$473$	−4.75041	−0.218424
$474$	0	0
$475$	24.0231	1.10226
$476$	0	0
$477$	−74.1294	−3.39415
$478$	0	0
$479$	7.27070	0.332207	0.166103	−	0.986108i	$-0.446881\pi$
$479$	7.27070	0.332207	0.166103	+	0.986108i	$0.446881\pi$
$480$	0	0
$481$	−30.7327	−1.40129
$482$	0	0
$483$	69.1346	3.14573
$484$	0	0
$485$	34.7995	1.58016
$486$	0	0
$487$	19.9072	0.902082	0.451041	−	0.892503i	$-0.351053\pi$
$487$	19.9072	0.902082	0.451041	+	0.892503i	$0.351053\pi$
$488$	0	0
$489$	−66.2342	−2.99521
$490$	0	0
$491$	−27.7321	−1.25153	−0.625767	−	0.780010i	$-0.715214\pi$
$491$	−27.7321	−1.25153	−0.625767	+	0.780010i	$0.715214\pi$
$492$	0	0
$493$	19.0869	0.859631
$494$	0	0
$495$	17.6303	0.792422
$496$	0	0
$497$	−4.01665	−0.180171
$498$	0	0
$499$	29.8268	1.33523	0.667616	−	0.744506i	$-0.267315\pi$
$499$	29.8268	1.33523	0.667616	+	0.744506i	$0.267315\pi$
$500$	0	0
$501$	−14.3590	−0.641513
$502$	0	0
$503$	−9.26107	−0.412931	−0.206465	−	0.978454i	$-0.566196\pi$
$503$	−9.26107	−0.412931	−0.206465	+	0.978454i	$0.566196\pi$
$504$	0	0
$505$	−19.6033	−0.872336
$506$	0	0
$507$	−9.39978	−0.417459
$508$	0	0
$509$	−3.66580	−0.162484	−0.0812419	−	0.996694i	$-0.525889\pi$
$509$	−3.66580	−0.162484	−0.0812419	+	0.996694i	$0.525889\pi$
$510$	0	0
$511$	−46.7539	−2.06827
$512$	0	0
$513$	−71.9442	−3.17641
$514$	0	0
$515$	5.85063	0.257809
$516$	0	0
$517$	0.928404	0.0408312
$518$	0	0
$519$	−38.4896	−1.68950
$520$	0	0
$521$	24.4337	1.07046	0.535230	−	0.844706i	$-0.320225\pi$
$521$	24.4337	1.07046	0.535230	+	0.844706i	$0.320225\pi$
$522$	0	0
$523$	25.8846	1.13185	0.565927	−	0.824455i	$-0.308518\pi$
$523$	25.8846	1.13185	0.565927	+	0.824455i	$0.308518\pi$
$524$	0	0
$525$	38.1994	1.66716
$526$	0	0
$527$	25.5456	1.11279
$528$	0	0
$529$	19.0044	0.826278
$530$	0	0
$531$	23.2934	1.01085
$532$	0	0
$533$	12.5482	0.543525
$534$	0	0
$535$	−23.0123	−0.994909
$536$	0	0
$537$	70.1436	3.02692
$538$	0	0
$539$	4.64165	0.199930
$540$	0	0
$541$	6.24180	0.268356	0.134178	−	0.990957i	$-0.457161\pi$
$541$	6.24180	0.268356	0.134178	+	0.990957i	$0.457161\pi$
$542$	0	0
$543$	−25.2176	−1.08219
$544$	0	0
$545$	−35.3272	−1.51325
$546$	0	0
$547$	22.1960	0.949033	0.474516	−	0.880247i	$-0.342623\pi$
$547$	22.1960	0.949033	0.474516	+	0.880247i	$0.342623\pi$
$548$	0	0
$549$	9.31441	0.397529
$550$	0	0
$551$	49.0055	2.08771
$552$	0	0
$553$	−15.5992	−0.663346
$554$	0	0
$555$	69.1932	2.93709
$556$	0	0
$557$	14.5135	0.614959	0.307479	−	0.951555i	$-0.400515\pi$
$557$	14.5135	0.614959	0.307479	+	0.951555i	$0.400515\pi$
$558$	0	0
$559$	−20.5005	−0.867080
$560$	0	0
$561$	−7.46988	−0.315379
$562$	0	0
$563$	15.4767	0.652266	0.326133	−	0.945324i	$-0.394254\pi$
$563$	15.4767	0.652266	0.326133	+	0.945324i	$0.394254\pi$
$564$	0	0
$565$	−37.6519	−1.58403
$566$	0	0
$567$	−47.0305	−1.97510
$568$	0	0
$569$	−21.3937	−0.896869	−0.448435	−	0.893816i	$-0.648018\pi$
$569$	−21.3937	−0.896869	−0.448435	+	0.893816i	$0.648018\pi$
$570$	0	0
$571$	−12.5760	−0.526288	−0.263144	−	0.964757i	$-0.584759\pi$
$571$	−12.5760	−0.526288	−0.263144	+	0.964757i	$0.584759\pi$
$572$	0	0
$573$	−75.2317	−3.14285
$574$	0	0
$575$	23.2089	0.967880
$576$	0	0
$577$	−27.9156	−1.16214	−0.581071	−	0.813853i	$-0.697366\pi$
$577$	−27.9156	−1.16214	−0.581071	+	0.813853i	$0.697366\pi$
$578$	0	0
$579$	−18.0250	−0.749095
$580$	0	0
$581$	−41.3060	−1.71366
$582$	0	0
$583$	−10.6163	−0.439684
$584$	0	0
$585$	76.0840	3.14569
$586$	0	0
$587$	−8.28278	−0.341867	−0.170933	−	0.985283i	$-0.554678\pi$
$587$	−8.28278	−0.341867	−0.170933	+	0.985283i	$0.554678\pi$
$588$	0	0
$589$	65.5883	2.70252
$590$	0	0
$591$	19.6534	0.808434
$592$	0	0
$593$	20.6968	0.849917	0.424958	−	0.905213i	$-0.360289\pi$
$593$	20.6968	0.849917	0.424958	+	0.905213i	$0.360289\pi$
$594$	0	0
$595$	−26.5134	−1.08694
$596$	0	0
$597$	34.8211	1.42513
$598$	0	0
$599$	1.51868	0.0620518	0.0310259	−	0.999519i	$-0.490123\pi$
$599$	1.51868	0.0620518	0.0310259	+	0.999519i	$0.490123\pi$
$600$	0	0
$601$	3.02976	0.123587	0.0617933	−	0.998089i	$-0.480318\pi$
$601$	3.02976	0.123587	0.0617933	+	0.998089i	$0.480318\pi$
$602$	0	0
$603$	−36.6917	−1.49420
$604$	0	0
$605$	−29.6978	−1.20739
$606$	0	0
$607$	−24.9384	−1.01222	−0.506109	−	0.862469i	$-0.668917\pi$
$607$	−24.9384	−1.01222	−0.506109	+	0.862469i	$0.668917\pi$
$608$	0	0
$609$	77.9241	3.15764
$610$	0	0
$611$	4.00655	0.162088
$612$	0	0
$613$	30.1002	1.21574	0.607868	−	0.794038i	$-0.292025\pi$
$613$	30.1002	1.21574	0.607868	+	0.794038i	$0.292025\pi$
$614$	0	0
$615$	−28.2518	−1.13922
$616$	0	0
$617$	17.5494	0.706511	0.353255	−	0.935527i	$-0.385075\pi$
$617$	17.5494	0.706511	0.353255	+	0.935527i	$0.385075\pi$
$618$	0	0
$619$	−7.52348	−0.302394	−0.151197	−	0.988504i	$-0.548313\pi$
$619$	−7.52348	−0.302394	−0.151197	+	0.988504i	$0.548313\pi$
$620$	0	0
$621$	−69.5059	−2.78918
$622$	0	0
$623$	−27.4908	−1.10140
$624$	0	0
$625$	−30.0814	−1.20325
$626$	0	0
$627$	−19.1789	−0.765931
$628$	0	0
$629$	−20.0420	−0.799127
$630$	0	0
$631$	17.4410	0.694314	0.347157	−	0.937807i	$-0.387147\pi$
$631$	17.4410	0.694314	0.347157	+	0.937807i	$0.387147\pi$
$632$	0	0
$633$	−52.9899	−2.10616
$634$	0	0
$635$	−0.571697	−0.0226871
$636$	0	0
$637$	20.0312	0.793665
$638$	0	0
$639$	7.51680	0.297360
$640$	0	0
$641$	−21.2387	−0.838879	−0.419439	−	0.907783i	$-0.637773\pi$
$641$	−21.2387	−0.838879	−0.419439	+	0.907783i	$0.637773\pi$
$642$	0	0
$643$	−29.7273	−1.17233	−0.586165	−	0.810192i	$-0.699363\pi$
$643$	−29.7273	−1.17233	−0.586165	+	0.810192i	$0.699363\pi$
$644$	0	0
$645$	46.1560	1.81739
$646$	0	0
$647$	30.9547	1.21696	0.608478	−	0.793571i	$-0.291780\pi$
$647$	30.9547	1.21696	0.608478	+	0.793571i	$0.291780\pi$
$648$	0	0
$649$	3.33593	0.130947
$650$	0	0
$651$	104.293	4.08755
$652$	0	0
$653$	−34.9574	−1.36799	−0.683994	−	0.729488i	$-0.739758\pi$
$653$	−34.9574	−1.36799	−0.683994	+	0.729488i	$0.739758\pi$
$654$	0	0
$655$	−6.34739	−0.248013
$656$	0	0
$657$	87.4958	3.41354
$658$	0	0
$659$	13.8982	0.541398	0.270699	−	0.962664i	$-0.412745\pi$
$659$	13.8982	0.541398	0.270699	+	0.962664i	$0.412745\pi$
$660$	0	0
$661$	−9.76793	−0.379928	−0.189964	−	0.981791i	$-0.560837\pi$
$661$	−9.76793	−0.379928	−0.189964	+	0.981791i	$0.560837\pi$
$662$	0	0
$663$	−32.2365	−1.25196
$664$	0	0
$665$	−68.0730	−2.63976
$666$	0	0
$667$	47.3446	1.83319
$668$	0	0
$669$	73.8130	2.85377
$670$	0	0
$671$	1.33395	0.0514966
$672$	0	0
$673$	36.2346	1.39674	0.698370	−	0.715737i	$-0.253909\pi$
$673$	36.2346	1.39674	0.698370	+	0.715737i	$0.253909\pi$
$674$	0	0
$675$	−38.4045	−1.47819
$676$	0	0
$677$	15.4008	0.591902	0.295951	−	0.955203i	$-0.404363\pi$
$677$	15.4008	0.591902	0.295951	+	0.955203i	$0.404363\pi$
$678$	0	0
$679$	−41.1516	−1.57925
$680$	0	0
$681$	42.1060	1.61350
$682$	0	0
$683$	−27.2287	−1.04188	−0.520938	−	0.853595i	$-0.674418\pi$
$683$	−27.2287	−1.04188	−0.520938	+	0.853595i	$0.674418\pi$
$684$	0	0
$685$	−56.0117	−2.14010
$686$	0	0
$687$	−9.73637	−0.371466
$688$	0	0
$689$	−45.8152	−1.74542
$690$	0	0
$691$	−20.1522	−0.766625	−0.383312	−	0.923619i	$-0.625217\pi$
$691$	−20.1522	−0.766625	−0.383312	+	0.923619i	$0.625217\pi$
$692$	0	0
$693$	−20.8484	−0.791965
$694$	0	0
$695$	−27.7492	−1.05259
$696$	0	0
$697$	8.18321	0.309961
$698$	0	0
$699$	−18.6409	−0.705062
$700$	0	0
$701$	−30.5985	−1.15569	−0.577844	−	0.816147i	$-0.696106\pi$
$701$	−30.5985	−1.15569	−0.577844	+	0.816147i	$0.696106\pi$
$702$	0	0
$703$	−51.4577	−1.94077
$704$	0	0
$705$	−9.02058	−0.339735
$706$	0	0
$707$	23.1816	0.871834
$708$	0	0
$709$	5.72217	0.214900	0.107450	−	0.994210i	$-0.465731\pi$
$709$	5.72217	0.214900	0.107450	+	0.994210i	$0.465731\pi$
$710$	0	0
$711$	29.1925	1.09480
$712$	0	0
$713$	63.3654	2.37305
$714$	0	0
$715$	10.8963	0.407497
$716$	0	0
$717$	72.6139	2.71182
$718$	0	0
$719$	−11.5419	−0.430441	−0.215221	−	0.976565i	$-0.569047\pi$
$719$	−11.5419	−0.430441	−0.215221	+	0.976565i	$0.569047\pi$
$720$	0	0
$721$	−6.91857	−0.257661
$722$	0	0
$723$	−3.32826	−0.123779
$724$	0	0
$725$	26.1596	0.971544
$726$	0	0
$727$	−22.1433	−0.821251	−0.410626	−	0.911804i	$-0.634690\pi$
$727$	−22.1433	−0.821251	−0.410626	+	0.911804i	$0.634690\pi$
$728$	0	0
$729$	−11.0607	−0.409656
$730$	0	0
$731$	−13.3692	−0.494478
$732$	0	0
$733$	−2.87841	−0.106316	−0.0531582	−	0.998586i	$-0.516929\pi$
$733$	−2.87841	−0.106316	−0.0531582	+	0.998586i	$0.516929\pi$
$734$	0	0
$735$	−45.0993	−1.66351
$736$	0	0
$737$	−5.25475	−0.193561
$738$	0	0
$739$	31.9327	1.17466	0.587331	−	0.809347i	$-0.300179\pi$
$739$	31.9327	1.17466	0.587331	+	0.809347i	$0.300179\pi$
$740$	0	0
$741$	−82.7671	−3.04052
$742$	0	0
$743$	−24.2641	−0.890163	−0.445082	−	0.895490i	$-0.646825\pi$
$743$	−24.2641	−0.890163	−0.445082	+	0.895490i	$0.646825\pi$
$744$	0	0
$745$	51.8764	1.90060
$746$	0	0
$747$	77.3004	2.82827
$748$	0	0
$749$	27.2128	0.994336
$750$	0	0
$751$	−27.5366	−1.00482	−0.502412	−	0.864629i	$-0.667554\pi$
$751$	−27.5366	−1.00482	−0.502412	+	0.864629i	$0.667554\pi$
$752$	0	0
$753$	13.3410	0.486172
$754$	0	0
$755$	−19.1754	−0.697865
$756$	0	0
$757$	35.8012	1.30122	0.650609	−	0.759413i	$-0.274514\pi$
$757$	35.8012	1.30122	0.650609	+	0.759413i	$0.274514\pi$
$758$	0	0
$759$	−18.5289	−0.672555
$760$	0	0
$761$	−21.7491	−0.788403	−0.394201	−	0.919024i	$-0.628979\pi$
$761$	−21.7491	−0.788403	−0.394201	+	0.919024i	$0.628979\pi$
$762$	0	0
$763$	41.7756	1.51238
$764$	0	0
$765$	49.6174	1.79392
$766$	0	0
$767$	14.3963	0.519821
$768$	0	0
$769$	−19.3900	−0.699222	−0.349611	−	0.936895i	$-0.613686\pi$
$769$	−19.3900	−0.699222	−0.349611	+	0.936895i	$0.613686\pi$
$770$	0	0
$771$	−7.19402	−0.259086
$772$	0	0
$773$	5.92834	0.213228	0.106614	−	0.994301i	$-0.465999\pi$
$773$	5.92834	0.213228	0.106614	+	0.994301i	$0.465999\pi$
$774$	0	0
$775$	35.0117	1.25766
$776$	0	0
$777$	−81.8234	−2.93540
$778$	0	0
$779$	21.0104	0.752774
$780$	0	0
$781$	1.07651	0.0385205
$782$	0	0
$783$	−78.3426	−2.79973
$784$	0	0
$785$	−33.6651	−1.20156
$786$	0	0
$787$	−45.4973	−1.62180	−0.810901	−	0.585183i	$-0.801022\pi$
$787$	−45.4973	−1.62180	−0.810901	+	0.585183i	$0.801022\pi$
$788$	0	0
$789$	−72.6415	−2.58611
$790$	0	0
$791$	44.5246	1.58311
$792$	0	0
$793$	5.75671	0.204427
$794$	0	0
$795$	103.151	3.65838
$796$	0	0
$797$	3.39291	0.120183	0.0600916	−	0.998193i	$-0.480861\pi$
$797$	3.39291	0.120183	0.0600916	+	0.998193i	$0.480861\pi$
$798$	0	0
$799$	2.61283	0.0924354
$800$	0	0
$801$	51.4466	1.81778
$802$	0	0
$803$	12.5306	0.442195
$804$	0	0
$805$	−65.7659	−2.31794
$806$	0	0
$807$	47.1065	1.65823
$808$	0	0
$809$	7.71358	0.271195	0.135598	−	0.990764i	$-0.456705\pi$
$809$	7.71358	0.271195	0.135598	+	0.990764i	$0.456705\pi$
$810$	0	0
$811$	−6.38515	−0.224213	−0.112107	−	0.993696i	$-0.535760\pi$
$811$	−6.38515	−0.224213	−0.112107	+	0.993696i	$0.535760\pi$
$812$	0	0
$813$	−91.5650	−3.21132
$814$	0	0
$815$	63.0068	2.20703
$816$	0	0
$817$	−34.3254	−1.20089
$818$	0	0
$819$	−89.9719	−3.14387
$820$	0	0
$821$	−25.4122	−0.886893	−0.443447	−	0.896301i	$-0.646244\pi$
$821$	−25.4122	−0.886893	−0.443447	+	0.896301i	$0.646244\pi$
$822$	0	0
$823$	−28.5547	−0.995356	−0.497678	−	0.867362i	$-0.665814\pi$
$823$	−28.5547	−0.995356	−0.497678	+	0.867362i	$0.665814\pi$
$824$	0	0
$825$	−10.2379	−0.356437
$826$	0	0
$827$	−45.7310	−1.59022	−0.795112	−	0.606463i	$-0.792588\pi$
$827$	−45.7310	−1.59022	−0.795112	+	0.606463i	$0.792588\pi$
$828$	0	0
$829$	−31.2130	−1.08407	−0.542036	−	0.840356i	$-0.682346\pi$
$829$	−31.2130	−1.08407	−0.542036	+	0.840356i	$0.682346\pi$
$830$	0	0
$831$	67.6199	2.34571
$832$	0	0
$833$	13.0631	0.452611
$834$	0	0
$835$	13.6593	0.472700
$836$	0	0
$837$	−104.853	−3.62424
$838$	0	0
$839$	27.3026	0.942589	0.471295	−	0.881976i	$-0.343787\pi$
$839$	27.3026	0.942589	0.471295	+	0.881976i	$0.343787\pi$
$840$	0	0
$841$	24.3638	0.840132
$842$	0	0
$843$	0.0123231	0.000424431 0
$844$	0	0
$845$	8.94175	0.307606
$846$	0	0
$847$	35.1187	1.20669
$848$	0	0
$849$	55.9854	1.92141
$850$	0	0
$851$	−49.7137	−1.70416
$852$	0	0
$853$	14.3233	0.490421	0.245211	−	0.969470i	$-0.421143\pi$
$853$	14.3233	0.490421	0.245211	+	0.969470i	$0.421143\pi$
$854$	0	0
$855$	127.392	4.35673
$856$	0	0
$857$	40.2782	1.37588	0.687939	−	0.725769i	$-0.258516\pi$
$857$	40.2782	1.37588	0.687939	+	0.725769i	$0.258516\pi$
$858$	0	0
$859$	44.6206	1.52243	0.761217	−	0.648497i	$-0.224602\pi$
$859$	44.6206	1.52243	0.761217	+	0.648497i	$0.224602\pi$
$860$	0	0
$861$	33.4087	1.13857
$862$	0	0
$863$	40.6408	1.38343	0.691715	−	0.722171i	$-0.256856\pi$
$863$	40.6408	1.38343	0.691715	+	0.722171i	$0.256856\pi$
$864$	0	0
$865$	36.6141	1.24492
$866$	0	0
$867$	31.3269	1.06392
$868$	0	0
$869$	4.18077	0.141823
$870$	0	0
$871$	−22.6770	−0.768382
$872$	0	0
$873$	77.0115	2.60644
$874$	0	0
$875$	14.3988	0.486768
$876$	0	0
$877$	−11.8316	−0.399523	−0.199762	−	0.979845i	$-0.564017\pi$
$877$	−11.8316	−0.399523	−0.199762	+	0.979845i	$0.564017\pi$
$878$	0	0
$879$	−26.0759	−0.879517
$880$	0	0
$881$	−4.41434	−0.148723	−0.0743615	−	0.997231i	$-0.523692\pi$
$881$	−4.41434	−0.148723	−0.0743615	+	0.997231i	$0.523692\pi$
$882$	0	0
$883$	23.9724	0.806734	0.403367	−	0.915038i	$-0.367840\pi$
$883$	23.9724	0.806734	0.403367	+	0.915038i	$0.367840\pi$
$884$	0	0
$885$	−32.4127	−1.08954
$886$	0	0
$887$	−44.0357	−1.47857	−0.739287	−	0.673391i	$-0.764837\pi$
$887$	−44.0357	−1.47857	−0.739287	+	0.673391i	$0.764837\pi$
$888$	0	0
$889$	0.676051	0.0226740
$890$	0	0
$891$	12.6047	0.422274
$892$	0	0
$893$	6.70844	0.224489
$894$	0	0
$895$	−66.7257	−2.23039
$896$	0	0
$897$	−79.9619	−2.66985
$898$	0	0
$899$	71.4214	2.38204
$900$	0	0
$901$	−29.8779	−0.995377
$902$	0	0
$903$	−54.5811	−1.81634
$904$	0	0
$905$	23.9888	0.797416
$906$	0	0
$907$	−45.4167	−1.50804	−0.754019	−	0.656853i	$-0.771887\pi$
$907$	−45.4167	−1.50804	−0.754019	+	0.656853i	$0.771887\pi$
$908$	0	0
$909$	−43.3823	−1.43890
$910$	0	0
$911$	−25.7835	−0.854245	−0.427122	−	0.904194i	$-0.640473\pi$
$911$	−25.7835	−0.854245	−0.427122	+	0.904194i	$0.640473\pi$
$912$	0	0
$913$	11.0705	0.366379
$914$	0	0
$915$	−12.9610	−0.428477
$916$	0	0
$917$	7.50600	0.247870
$918$	0	0
$919$	−7.83487	−0.258449	−0.129224	−	0.991615i	$-0.541249\pi$
$919$	−7.83487	−0.258449	−0.129224	+	0.991615i	$0.541249\pi$
$920$	0	0
$921$	−67.5733	−2.22662
$922$	0	0
$923$	4.64571	0.152915
$924$	0	0
$925$	−27.4686	−0.903163
$926$	0	0
$927$	12.9475	0.425251
$928$	0	0
$929$	45.9343	1.50706	0.753529	−	0.657415i	$-0.228350\pi$
$929$	45.9343	1.50706	0.753529	+	0.657415i	$0.228350\pi$
$930$	0	0
$931$	33.5396	1.09921
$932$	0	0
$933$	68.9332	2.25677
$934$	0	0
$935$	7.10589	0.232387
$936$	0	0
$937$	−47.6141	−1.55549	−0.777743	−	0.628582i	$-0.783636\pi$
$937$	−47.6141	−1.55549	−0.777743	+	0.628582i	$0.783636\pi$
$938$	0	0
$939$	−97.7045	−3.18846
$940$	0	0
$941$	−11.8541	−0.386433	−0.193216	−	0.981156i	$-0.561892\pi$
$941$	−11.8541	−0.386433	−0.193216	+	0.981156i	$0.561892\pi$
$942$	0	0
$943$	20.2983	0.661003
$944$	0	0
$945$	108.825	3.54007
$946$	0	0
$947$	13.7268	0.446060	0.223030	−	0.974812i	$-0.428405\pi$
$947$	13.7268	0.446060	0.223030	+	0.974812i	$0.428405\pi$
$948$	0	0
$949$	54.0762	1.75539
$950$	0	0
$951$	−1.68100	−0.0545101
$952$	0	0
$953$	−19.5938	−0.634705	−0.317353	−	0.948308i	$-0.602794\pi$
$953$	−19.5938	−0.634705	−0.317353	+	0.948308i	$0.602794\pi$
$954$	0	0
$955$	71.5658	2.31582
$956$	0	0
$957$	−20.8846	−0.675102
$958$	0	0
$959$	66.2358	2.13887
$960$	0	0
$961$	64.5894	2.08353
$962$	0	0
$963$	−50.9264	−1.64108
$964$	0	0
$965$	17.1467	0.551972
$966$	0	0
$967$	48.2138	1.55045	0.775226	−	0.631685i	$-0.217636\pi$
$967$	48.2138	1.55045	0.775226	+	0.631685i	$0.217636\pi$
$968$	0	0
$969$	−53.9757	−1.73395
$970$	0	0
$971$	−6.18465	−0.198475	−0.0992374	−	0.995064i	$-0.531640\pi$
$971$	−6.18465	−0.198475	−0.0992374	+	0.995064i	$0.531640\pi$
$972$	0	0
$973$	32.8143	1.05198
$974$	0	0
$975$	−44.1819	−1.41495
$976$	0	0
$977$	37.4925	1.19949	0.599746	−	0.800190i	$-0.295268\pi$
$977$	37.4925	1.19949	0.599746	+	0.800190i	$0.295268\pi$
$978$	0	0
$979$	7.36785	0.235478
$980$	0	0
$981$	−78.1793	−2.49607
$982$	0	0
$983$	−1.63142	−0.0520343	−0.0260171	−	0.999661i	$-0.508282\pi$
$983$	−1.63142	−0.0520343	−0.0260171	+	0.999661i	$0.508282\pi$
$984$	0	0
$985$	−18.6958	−0.595697
$986$	0	0
$987$	10.6671	0.339539
$988$	0	0
$989$	−33.1620	−1.05449
$990$	0	0
$991$	29.7811	0.946026	0.473013	−	0.881055i	$-0.343166\pi$
$991$	29.7811	0.946026	0.473013	+	0.881055i	$0.343166\pi$
$992$	0	0
$993$	29.8972	0.948759
$994$	0	0
$995$	−33.1244	−1.05011
$996$	0	0
$997$	42.3776	1.34211	0.671056	−	0.741406i	$-0.265841\pi$
$997$	42.3776	1.34211	0.671056	+	0.741406i	$0.265841\pi$
$998$	0	0
$999$	82.2628	2.60268

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6016.2.a.r.1.2	yes	14
4.3	odd	2		6016.2.a.t.1.13	yes	14
8.3	odd	2		6016.2.a.q.1.2	✓	14
8.5	even	2		6016.2.a.s.1.13	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6016.2.a.q.1.2	✓	14	8.3	odd	2
6016.2.a.r.1.2	yes	14	1.1	even	1	trivial
6016.2.a.s.1.13	yes	14	8.5	even	2
6016.2.a.t.1.13	yes	14	4.3	odd	2

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:	\( N \)	\(=\)	\( 6016 = 2^{7} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6016.a (trivial)

\(f(q)\)	\(=\)	\(q-3.07939 q^{3} +2.92934 q^{5} -3.46404 q^{7} +6.48265 q^{9} +O(q^{10})\)	\(q-3.07939 q^{3} +2.92934 q^{5} -3.46404 q^{7} +6.48265 q^{9} +0.928404 q^{11} +4.00655 q^{13} -9.02058 q^{15} +2.61283 q^{17} +6.70844 q^{19} +10.6671 q^{21} +6.48108 q^{23} +3.58103 q^{25} -10.7244 q^{27} +7.30505 q^{29} +9.77698 q^{31} -2.85892 q^{33} -10.1474 q^{35} -7.67059 q^{37} -12.3377 q^{39} +3.13193 q^{41} -5.11675 q^{43} +18.9899 q^{45} +1.00000 q^{47} +4.99960 q^{49} -8.04594 q^{51} -11.4351 q^{53} +2.71961 q^{55} -20.6579 q^{57} +3.59319 q^{59} +1.43682 q^{61} -22.4562 q^{63} +11.7366 q^{65} -5.65998 q^{67} -19.9578 q^{69} +1.15953 q^{71} +13.4969 q^{73} -11.0274 q^{75} -3.21603 q^{77} +4.50318 q^{79} +13.5768 q^{81} +11.9242 q^{83} +7.65388 q^{85} -22.4951 q^{87} +7.93604 q^{89} -13.8789 q^{91} -30.1072 q^{93} +19.6513 q^{95} +11.8796 q^{97} +6.01851 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} + 6 q^{5} + 2 q^{7} + 22 q^{9}+O(q^{10}) \) 14 * q - 2 * q^3 + 6 * q^5 + 2 * q^7 + 22 * q^9	\( 14 q - 2 q^{3} + 6 q^{5} + 2 q^{7} + 22 q^{9} - 14 q^{11} + 4 q^{13} + 6 q^{15} + 8 q^{17} - 8 q^{19} + 6 q^{21} + 18 q^{23} + 22 q^{25} - 8 q^{27} + 22 q^{29} + 4 q^{31} + 2 q^{33} - 26 q^{35} + 6 q^{37} + 20 q^{39} + 16 q^{41} - 12 q^{43} + 30 q^{45} + 14 q^{47} + 34 q^{49} - 18 q^{51} + 20 q^{53} + 2 q^{55} - 4 q^{57} - 32 q^{59} + 12 q^{61} + 40 q^{65} - 16 q^{67} + 46 q^{69} + 16 q^{71} - 12 q^{73} + 16 q^{75} + 10 q^{77} + 16 q^{79} + 74 q^{81} - 14 q^{83} + 12 q^{85} + 14 q^{87} - 28 q^{91} - 16 q^{93} + 52 q^{95} + 28 q^{97} - 50 q^{99}+O(q^{100}) \) 14 * q - 2 * q^3 + 6 * q^5 + 2 * q^7 + 22 * q^9 - 14 * q^11 + 4 * q^13 + 6 * q^15 + 8 * q^17 - 8 * q^19 + 6 * q^21 + 18 * q^23 + 22 * q^25 - 8 * q^27 + 22 * q^29 + 4 * q^31 + 2 * q^33 - 26 * q^35 + 6 * q^37 + 20 * q^39 + 16 * q^41 - 12 * q^43 + 30 * q^45 + 14 * q^47 + 34 * q^49 - 18 * q^51 + 20 * q^53 + 2 * q^55 - 4 * q^57 - 32 * q^59 + 12 * q^61 + 40 * q^65 - 16 * q^67 + 46 * q^69 + 16 * q^71 - 12 * q^73 + 16 * q^75 + 10 * q^77 + 16 * q^79 + 74 * q^81 - 14 * q^83 + 12 * q^85 + 14 * q^87 - 28 * q^91 - 16 * q^93 + 52 * q^95 + 28 * q^97 - 50 * q^99

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